LMFDB - Embedded newform 23.4.c.a.16.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,4,Mod(2,23)] 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("23.2"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	23.c (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.35704393013$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			16.5
Character	$\chi$	$=$	23.16
Dual form			23.4.c.a.13.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.50231 - 4.04189i) q^{2} +(-4.18746 + 2.69112i) q^{3} +(-2.93212 - 20.3933i) q^{4} +(6.92690 + 15.1678i) q^{5} +(-3.78861 + 26.3504i) q^{6} +(7.38228 - 2.16763i) q^{7} +(-56.7033 - 36.4410i) q^{8} +(-0.923481 + 2.02214i) q^{9} +(85.5667 + 25.1246i) q^{10} +(-12.2093 - 14.0903i) q^{11} +(67.1590 + 77.5057i) q^{12} +(-28.3722 - 8.33084i) q^{13} +(17.0937 - 37.4301i) q^{14} +(-69.8245 - 44.8735i) q^{15} +(-187.736 + 55.1241i) q^{16} +(-6.29713 + 43.7975i) q^{17} +(4.93894 + 10.8148i) q^{18} +(-8.21881 - 57.1631i) q^{19} +(289.011 - 185.736i) q^{20} +(-25.0797 + 28.9435i) q^{21} -99.7120 q^{22} +(104.797 - 34.4177i) q^{23} +335.510 q^{24} +(-100.222 + 115.663i) q^{25} +(-133.041 + 85.5001i) q^{26} +(-20.7014 - 143.981i) q^{27} +(-65.8510 - 144.194i) q^{28} +(18.6280 - 129.561i) q^{29} +(-425.921 + 125.062i) q^{30} +(128.180 + 82.3762i) q^{31} +(-210.700 + 461.369i) q^{32} +(89.0446 + 26.1458i) q^{33} +(154.970 + 178.845i) q^{34} +(84.0146 + 96.9580i) q^{35} +(43.9460 + 12.9037i) q^{36} +(-35.6666 + 78.0990i) q^{37} +(-259.831 - 166.984i) q^{38} +(141.227 - 41.4680i) q^{39} +(159.952 - 1112.49i) q^{40} +(138.850 + 304.039i) q^{41} +(29.1494 + 202.738i) q^{42} +(-168.181 + 108.084i) q^{43} +(-251.549 + 290.303i) q^{44} -37.0683 q^{45} +(227.920 - 544.119i) q^{46} +126.827 q^{47} +(637.790 - 736.049i) q^{48} +(-238.750 + 153.436i) q^{49} +(116.486 + 810.176i) q^{50} +(-91.4953 - 200.347i) q^{51} +(-86.7029 + 603.032i) q^{52} +(728.372 - 213.869i) q^{53} +(-654.459 - 420.595i) q^{54} +(129.146 - 282.790i) q^{55} +(-497.591 - 146.106i) q^{56} +(188.249 + 217.250i) q^{57} +(-458.429 - 529.055i) q^{58} +(-711.630 - 208.953i) q^{59} +(-710.386 + 1555.53i) q^{60} +(-221.221 - 142.170i) q^{61} +(781.881 - 229.581i) q^{62} +(-2.43414 + 16.9298i) q^{63} +(476.619 + 1043.65i) q^{64} +(-70.1712 - 488.051i) q^{65} +(417.541 - 268.337i) q^{66} +(66.9323 - 77.2440i) q^{67} +911.641 q^{68} +(-346.212 + 426.144i) q^{69} +686.139 q^{70} +(-180.423 + 208.219i) q^{71} +(126.053 - 81.0095i) q^{72} +(86.8834 + 604.287i) q^{73} +(190.752 + 417.688i) q^{74} +(108.415 - 754.045i) q^{75} +(-1141.65 + 335.218i) q^{76} +(-120.675 - 77.5531i) q^{77} +(327.012 - 716.057i) q^{78} +(-954.614 - 280.300i) q^{79} +(-2136.54 - 2465.69i) q^{80} +(434.851 + 501.845i) q^{81} +(1715.19 + 503.625i) q^{82} +(154.027 - 337.272i) q^{83} +(663.791 + 426.593i) q^{84} +(-707.931 + 207.867i) q^{85} +(-152.162 + 1058.31i) q^{86} +(270.659 + 592.661i) q^{87} +(178.844 + 1243.88i) q^{88} +(630.092 - 404.935i) q^{89} +(-129.825 + 149.826i) q^{90} -227.510 q^{91} +(-1009.17 - 2036.24i) q^{92} -758.432 q^{93} +(444.189 - 512.621i) q^{94} +(810.107 - 520.624i) q^{95} +(-359.300 - 2498.99i) q^{96} +(-153.971 - 337.150i) q^{97} +(-216.010 + 1502.38i) q^{98} +(39.7676 - 11.6768i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9} + 47 q^{10} - 53 q^{11} + 36 q^{12} - 65 q^{13} + 117 q^{14} - 425 q^{15} - 499 q^{16} - 117 q^{17} + 24 q^{18}+ \cdots - 755 q^{99}+O(q^{100}) $ 50 * q - 11 * q^2 - 13 * q^3 - 27 * q^4 - 19 * q^5 - 4 * q^6 - 19 * q^7 + 28 * q^8 + 24 * q^9 + 47 * q^10 - 53 * q^11 + 36 * q^12 - 65 * q^13 + 117 * q^14 - 425 * q^15 - 499 * q^16 - 117 * q^17 + 24 * q^18 + 73 * q^19 + 529 * q^20 + 429 * q^21 + 310 * q^22 + 542 * q^23 + 1606 * q^24 + 246 * q^25 + 324 * q^26 + 65 * q^27 - 677 * q^28 - 497 * q^29 - 1041 * q^30 - 471 * q^31 - 915 * q^32 - 391 * q^33 - 2751 * q^34 - 737 * q^35 - 1865 * q^36 - 1071 * q^37 - 1504 * q^38 + 127 * q^39 + 1479 * q^40 + 569 * q^41 + 3059 * q^42 + 1615 * q^43 + 2518 * q^44 + 2768 * q^45 + 4041 * q^46 + 2904 * q^47 + 2702 * q^48 + 1226 * q^49 + 1322 * q^50 + 589 * q^51 - 2156 * q^52 + 391 * q^53 - 5862 * q^54 - 3323 * q^55 - 7028 * q^56 - 7623 * q^57 - 5639 * q^58 - 2445 * q^59 - 3157 * q^60 - 1059 * q^61 + 1468 * q^62 + 3155 * q^63 + 4570 * q^64 + 2641 * q^65 + 5206 * q^66 + 27 * q^67 + 8350 * q^68 + 4005 * q^69 + 9702 * q^70 + 3465 * q^71 + 5629 * q^72 + 435 * q^73 - 994 * q^74 - 7819 * q^75 - 3598 * q^76 - 5931 * q^77 - 8996 * q^78 - 2559 * q^79 - 14052 * q^80 - 4788 * q^81 - 3822 * q^82 - 3967 * q^83 - 8427 * q^84 + 299 * q^85 + 721 * q^86 + 8363 * q^87 + 5825 * q^88 + 3717 * q^89 + 16742 * q^90 + 7238 * q^91 + 9550 * q^92 + 12750 * q^93 + 6035 * q^94 + 4551 * q^95 + 2493 * q^96 - 2419 * q^97 - 5687 * q^98 - 755 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	3.50231	−	4.04189i	1.23826	−	1.42902i	0.372894	−	0.927874i	$-0.378366\pi$
$2$	3.50231	−	4.04189i	1.23826	−	1.42902i	0.865361	−	0.501148i	$-0.167089\pi$
$3$	−4.18746	+	2.69112i	−0.805878	+	0.517906i	−0.877529	−	0.479524i	$-0.840809\pi$
$3$	−4.18746	+	2.69112i	−0.805878	+	0.517906i	0.0716513	+	0.997430i	$0.477173\pi$
$4$	−2.93212	−	20.3933i	−0.366515	−	2.54917i
$5$	6.92690	+	15.1678i	0.619561	+	1.35665i	0.915838	+	0.401547i	$0.131527\pi$
$5$	6.92690	+	15.1678i	0.619561	+	1.35665i	−0.296278	+	0.955102i	$0.595745\pi$
$6$	−3.78861	+	26.3504i	−0.257783	+	1.79292i
$7$	7.38228	−	2.16763i	0.398606	−	0.117041i	−0.0762847	−	0.997086i	$-0.524306\pi$
$7$	7.38228	−	2.16763i	0.398606	−	0.117041i	0.474891	+	0.880045i	$0.342488\pi$
$8$	−56.7033	−	36.4410i	−2.50596	−	1.61048i
$9$	−0.923481	+	2.02214i	−0.0342030	+	0.0748941i
$10$	85.5667	+	25.1246i	2.70586	+	0.794511i
$11$	−12.2093	−	14.0903i	−0.334658	−	0.386216i	0.563333	−	0.826230i	$-0.309519\pi$
$11$	−12.2093	−	14.0903i	−0.334658	−	0.386216i	−0.897991	+	0.440014i	$0.854973\pi$
$12$	67.1590	+	77.5057i	1.61560	+	1.86450i
$13$	−28.3722	−	8.33084i	−0.605311	−	0.177735i	−0.0353059	−	0.999377i	$-0.511241\pi$
$13$	−28.3722	−	8.33084i	−0.605311	−	0.177735i	−0.570005	+	0.821641i	$0.693059\pi$
$14$	17.0937	−	37.4301i	0.326321	−	0.714544i
$15$	−69.8245	−	44.8735i	−1.20191	−	0.772419i
$16$	−187.736	+	55.1241i	−2.93337	+	0.861314i
$17$	−6.29713	+	43.7975i	−0.0898399	+	0.624850i	0.894302	+	0.447465i	$0.147673\pi$
$17$	−6.29713	+	43.7975i	−0.0898399	+	0.624850i	−0.984141	+	0.177385i	$0.943236\pi$
$18$	4.93894	+	10.8148i	0.0646733	+	0.141615i
$19$	−8.21881	−	57.1631i	−0.0992381	−	0.690216i	−0.977330	−	0.211723i	$-0.932092\pi$
$19$	−8.21881	−	57.1631i	−0.0992381	−	0.690216i	0.878092	−	0.478493i	$-0.158817\pi$
$20$	289.011	−	185.736i	3.23125	−	2.07660i
$21$	−25.0797	+	28.9435i	−0.260611	+	0.300761i
$22$	−99.7120			−0.966304
$23$	104.797	−	34.4177i	0.950074	−	0.312026i
$23$	104.797	−	34.4177i	0.950074	−	0.312026i
$24$	335.510			2.85357
$25$	−100.222	+	115.663i	−0.801780	+	0.925303i
$26$	−133.041	+	85.5001i	−1.00352	+	0.644921i
$27$	−20.7014	−	143.981i	−0.147555	−	1.02627i
$28$	−65.8510	−	144.194i	−0.444453	−	0.973216i
$29$	18.6280	−	129.561i	0.119281	−	0.829615i	−0.839071	−	0.544023i	$-0.816901\pi$
$29$	18.6280	−	129.561i	0.119281	−	0.829615i	0.958351	−	0.285592i	$-0.0921904\pi$
$30$	−425.921	+	125.062i	−2.59207	+	0.761101i
$31$	128.180	+	82.3762i	0.742638	+	0.477264i	0.856445	−	0.516238i	$-0.172668\pi$
$31$	128.180	+	82.3762i	0.742638	+	0.477264i	−0.113807	+	0.993503i	$0.536305\pi$
$32$	−210.700	+	461.369i	−1.16397	+	2.54873i
$33$	89.0446	+	26.1458i	0.469717	+	0.137921i
$34$	154.970	+	178.845i	0.781680	+	0.902107i
$35$	84.0146	+	96.9580i	0.405744	+	0.468254i
$36$	43.9460	+	12.9037i	0.203453	+	0.0597393i
$37$	−35.6666	+	78.0990i	−0.158475	+	0.347011i	−0.972169	−	0.234283i	$-0.924726\pi$
$37$	−35.6666	+	78.0990i	−0.158475	+	0.347011i	0.813694	+	0.581293i	$0.197453\pi$
$38$	−259.831	−	166.984i	−1.10922	−	0.712850i
$39$	141.227	−	41.4680i	0.579857	−	0.170261i
$40$	159.952	−	1112.49i	0.632264	−	4.39749i
$41$	138.850	+	304.039i	0.528896	+	1.15812i	0.965960	+	0.258690i	$0.0832909\pi$
$41$	138.850	+	304.039i	0.528896	+	1.15812i	−0.437064	+	0.899430i	$0.643982\pi$
$42$	29.1494	+	202.738i	0.107092	+	0.744839i
$43$	−168.181	+	108.084i	−0.596452	+	0.383316i	−0.803755	−	0.594961i	$-0.797168\pi$
$43$	−168.181	+	108.084i	−0.596452	+	0.383316i	0.207303	+	0.978277i	$0.433531\pi$
$44$	−251.549	+	290.303i	−0.861872	+	0.994654i
$45$	−37.0683			−0.122796
$46$	227.920	−	544.119i	0.730542	−	1.74404i
$47$	126.827			0.393610			0.196805	−	0.980443i	$-0.436943\pi$
$47$	126.827			0.393610			0.196805	+	0.980443i	$0.436943\pi$
$48$	637.790	−	736.049i	1.91786	−	2.21332i
$49$	−238.750	+	153.436i	−0.696066	+	0.447334i
$50$	116.486	+	810.176i	0.329471	+	2.29152i
$51$	−91.4953	−	200.347i	−0.251214	−	0.550082i
$52$	−86.7029	+	603.032i	−0.231222	+	1.60818i
$53$	728.372	−	213.869i	1.88773	−	0.554287i	0.893221	−	0.449617i	$-0.148440\pi$
$53$	728.372	−	213.869i	1.88773	−	0.554287i	0.994507	−	0.104670i	$-0.0333785\pi$
$54$	−654.459	−	420.595i	−1.64927	−	1.05992i
$55$	129.146	−	282.790i	0.316619	−	0.693298i
$56$	−497.591	−	146.106i	−1.18738	−	0.348647i
$57$	188.249	+	217.250i	0.437441	+	0.504834i
$58$	−458.429	−	529.055i	−1.03784	−	1.19773i
$59$	−711.630	−	208.953i	−1.57028	−	0.461075i	−0.623194	−	0.782067i	$-0.714165\pi$
$59$	−711.630	−	208.953i	−1.57028	−	0.461075i	−0.947082	+	0.320993i	$0.895984\pi$
$60$	−710.386	+	1555.53i	−1.52851	+	3.34696i
$61$	−221.221	−	142.170i	−0.464335	−	0.298410i	0.287477	−	0.957787i	$-0.407183\pi$
$61$	−221.221	−	142.170i	−0.464335	−	0.298410i	−0.751812	+	0.659378i	$0.770820\pi$
$62$	781.881	−	229.581i	1.60160	−	0.470271i
$63$	−2.43414	+	16.9298i	−0.00486781	+	0.0338564i
$64$	476.619	+	1043.65i	0.930896	+	2.03838i
$65$	−70.1712	−	488.051i	−0.133902	−	0.931312i
$66$	417.541	−	268.337i	0.778722	−	0.500455i
$67$	66.9323	−	77.2440i	0.122046	−	0.140849i	−0.691438	−	0.722436i	$-0.743023\pi$
$67$	66.9323	−	77.2440i	0.122046	−	0.140849i	0.813484	+	0.581587i	$0.197568\pi$
$68$	911.641			1.62578
$69$	−346.212	+	426.144i	−0.604043	+	0.743504i
$70$	686.139			1.17156
$71$	−180.423	+	208.219i	−0.301582	+	0.348044i	−0.886232	−	0.463242i	$-0.846686\pi$
$71$	−180.423	+	208.219i	−0.301582	+	0.348044i	0.584650	+	0.811285i	$0.301232\pi$
$72$	126.053	−	81.0095i	0.206327	−	0.132598i
$73$	86.8834	+	604.287i	0.139300	+	0.968856i	0.932828	+	0.360322i	$0.117333\pi$
$73$	86.8834	+	604.287i	0.139300	+	0.968856i	−0.793528	+	0.608534i	$0.791758\pi$
$74$	190.752	+	417.688i	0.299654	+	0.656152i
$75$	108.415	−	754.045i	0.166916	−	1.16093i
$76$	−1141.65	+	335.218i	−1.72310	+	0.505949i
$77$	−120.675	−	77.5531i	−0.178600	−	0.114779i
$78$	327.012	−	716.057i	0.474703	−	1.03946i
$79$	−954.614	−	280.300i	−1.35953	−	0.399193i	−0.480930	−	0.876759i	$-0.659701\pi$
$79$	−954.614	−	280.300i	−1.35953	−	0.399193i	−0.878596	+	0.477567i	$0.841519\pi$
$80$	−2136.54	−	2465.69i	−2.98590	−	3.44591i
$81$	434.851	+	501.845i	0.596504	+	0.688402i
$82$	1715.19	+	503.625i	2.30989	+	0.678244i
$83$	154.027	−	337.272i	0.203695	−	0.446029i	−0.780023	−	0.625751i	$-0.784793\pi$
$83$	154.027	−	337.272i	0.203695	−	0.446029i	0.983717	+	0.179722i	$0.0575199\pi$
$84$	663.791	+	426.593i	0.862209	+	0.554108i
$85$	−707.931	+	207.867i	−0.903364	+	0.265252i
$86$	−152.162	+	1058.31i	−0.190792	+	1.32699i
$87$	270.659	+	592.661i	0.333537	+	0.730344i
$88$	178.844	+	1243.88i	0.216645	+	1.50680i
$89$	630.092	−	404.935i	0.750445	−	0.482282i	−0.108661	−	0.994079i	$-0.534656\pi$
$89$	630.092	−	404.935i	0.750445	−	0.482282i	0.859106	+	0.511797i	$0.171020\pi$
$90$	−129.825	+	149.826i	−0.152053	+	0.175478i
$91$	−227.510			−0.262083
$92$	−1009.17	−	2036.24i	−1.14362	−	2.30753i
$93$	−758.432			−0.845653
$94$	444.189	−	512.621i	0.487389	−	0.562477i
$95$	810.107	−	520.624i	0.874897	−	0.562262i
$96$	−359.300	−	2498.99i	−0.381989	−	2.65679i
$97$	−153.971	−	337.150i	−0.161169	−	0.352911i	0.811769	−	0.583979i	$-0.198505\pi$
$97$	−153.971	−	337.150i	−0.161169	−	0.352911i	−0.972937	+	0.231069i	$0.925778\pi$
$98$	−216.010	+	1502.38i	−0.222656	+	1.54861i
$99$	39.7676	−	11.6768i	0.0403716	−	0.0118542i
$100$	2652.62	+	1704.73i	2.65262	+	1.70473i
$101$	−246.426	+	539.598i	−0.242775	+	0.531604i	−0.991319	−	0.131482i	$-0.958026\pi$
$101$	−246.426	+	539.598i	−0.242775	+	0.531604i	0.748543	+	0.663086i	$0.230754\pi$
$102$	−1130.22	−	331.864i	−1.09715	−	0.322151i
$103$	735.259	+	848.534i	0.703371	+	0.811733i	0.989204	−	0.146546i	$-0.0468158\pi$
$103$	735.259	+	848.534i	0.703371	+	0.811733i	−0.285833	+	0.958279i	$0.592270\pi$
$104$	1305.22	+	1506.30i	1.23064	+	1.42024i
$105$	−612.733	−	179.915i	−0.569492	−	0.167218i
$106$	1686.55	−	3693.03i	1.54540	−	3.38395i
$107$	894.964	+	575.159i	0.808593	+	0.519651i	0.878410	−	0.477909i	$-0.158605\pi$
$107$	894.964	+	575.159i	0.808593	+	0.519651i	−0.0698164	+	0.997560i	$0.522241\pi$
$108$	−2875.56	+	844.341i	−2.56205	+	0.752285i
$109$	−179.917	+	1251.35i	−0.158100	+	1.09961i	0.744031	+	0.668145i	$0.232912\pi$
$109$	−179.917	+	1251.35i	−0.158100	+	1.09961i	−0.902131	+	0.431463i	$0.857998\pi$
$110$	−690.695	−	1512.41i	−0.598684	−	1.31093i
$111$	−60.8211	−	423.020i	−0.0520080	−	0.361723i
$112$	−1266.43	+	813.884i	−1.06845	+	0.686650i
$113$	491.714	−	567.468i	0.409350	−	0.472415i	−0.513213	−	0.858261i	$-0.671545\pi$
$113$	491.714	−	567.468i	0.409350	−	0.472415i	0.922563	+	0.385846i	$0.126090\pi$
$114$	1537.41			1.26308
$115$	1247.96	+	1351.13i	1.01194	+	1.09560i
$116$	−2696.80			−2.15855
$117$	43.0473	−	49.6793i	0.0340148	−	0.0392551i
$118$	−3336.92	+	2144.51i	−2.60329	+	1.67303i
$119$	48.4498	+	336.976i	0.0373225	+	0.259584i
$120$	2324.05	+	5088.95i	1.76796	+	3.87130i
$121$	139.952	−	973.388i	0.105148	−	0.731321i
$122$	−1349.42	+	396.225i	−1.00140	+	0.294037i
$123$	−1399.64	−	899.491i	−1.02602	−	0.659385i
$124$	1304.09	−	2855.55i	0.944439	−	2.06803i
$125$	−448.681	−	131.745i	−0.321050	−	0.0942688i
$126$	59.9032	+	69.1319i	0.0423539	+	0.0488791i
$127$	−231.234	−	266.859i	−0.161565	−	0.186456i	0.669195	−	0.743087i	$-0.266639\pi$
$127$	−231.234	−	266.859i	−0.161565	−	0.186456i	−0.830760	+	0.556631i	$0.812094\pi$
$128$	1994.31	+	585.582i	1.37714	+	0.404364i
$129$	413.387	−	905.192i	0.282145	−	0.617812i
$130$	−2218.41	−	1425.68i	−1.49667	−	0.961852i
$131$	−804.282	+	236.159i	−0.536416	+	0.157506i	−0.538710	−	0.842491i	$-0.681088\pi$
$131$	−804.282	+	236.159i	−0.536416	+	0.157506i	0.00229387	+	0.999997i	$0.499270\pi$
$132$	272.112	−	1892.58i	0.179426	−	1.24794i
$133$	−184.582	−	404.179i	−0.120341	−	0.263509i
$134$	−77.7935	−	541.065i	−0.0501517	−	0.348813i
$135$	2040.48	−	1311.34i	1.30087	−	0.836015i
$136$	1953.09	−	2253.99i	1.23144	−	1.42116i
$137$	1875.91			1.16985			0.584926	−	0.811087i	$-0.301124\pi$
$137$	1875.91			1.16985			0.584926	+	0.811087i	$0.301124\pi$
$138$	509.885	+	2891.84i	0.314524	+	1.78384i
$139$	−1414.19			−0.862950			−0.431475	−	0.902125i	$-0.642007\pi$
$139$	−1414.19			−0.862950			−0.431475	+	0.902125i	$0.642007\pi$
$140$	1730.96	−	1997.63i	1.04495	−	1.20593i
$141$	−531.085	+	341.307i	−0.317201	+	0.203853i
$142$	209.701	+	1458.50i	0.123927	+	0.861933i
$143$	229.021	+	501.486i	0.133928	+	0.293261i
$144$	61.9014	−	430.534i	0.0358226	−	0.249151i
$145$	2094.19	−	614.909i	1.19940	−	0.352175i
$146$	2746.75	+	1765.23i	1.55701	+	1.00063i
$147$	586.845	−	1285.01i	0.329267	−	0.720993i
$148$	1697.28	+	498.366i	0.942672	+	0.276794i
$149$	−1706.52	−	1969.43i	−0.938278	−	1.08283i	−0.996422	−	0.0845218i	$-0.973064\pi$
$149$	−1706.52	−	1969.43i	−0.938278	−	1.08283i	0.0581441	−	0.998308i	$-0.481482\pi$
$150$	−2668.06	−	3079.10i	−1.45231	−	1.67605i
$151$	−910.266	−	267.278i	−0.490572	−	0.144045i	0.0270851	−	0.999633i	$-0.491377\pi$
$151$	−910.266	−	267.278i	−0.490572	−	0.144045i	−0.517657	+	0.855588i	$0.673196\pi$
$152$	−1617.05	+	3540.84i	−0.862893	+	1.88947i
$153$	−82.7494	−	53.1798i	−0.0437248	−	0.0281002i
$154$	−736.103	+	216.139i	−0.385174	+	0.113097i
$155$	−361.576	+	2514.82i	−0.187371	+	1.30319i
$156$	−1259.76	−	2758.50i	−0.646551	−	1.41575i
$157$	287.913	+	2002.48i	0.146356	+	1.01793i	0.922119	+	0.386906i	$0.126456\pi$
$157$	287.913	+	2002.48i	0.146356	+	1.01793i	−0.775763	+	0.631024i	$0.782635\pi$
$158$	−4476.30	+	2876.74i	−2.25389	+	1.44849i
$159$	−2474.48	+	2855.71i	−1.23421	+	1.42435i
$160$	−8457.46			−4.17888
$161$	699.036	−	481.243i	0.342185	−	0.235573i
$162$	3551.39			1.72237
$163$	−182.467	+	210.578i	−0.0876806	+	0.101189i	−0.797894	−	0.602797i	$-0.794053\pi$
$163$	−182.467	+	210.578i	−0.0876806	+	0.101189i	0.710214	+	0.703986i	$0.248598\pi$
$164$	5793.25	−	3723.10i	2.75839	−	1.77271i
$165$	220.228	+	1531.72i	0.103907	+	0.722692i
$166$	−823.764	−	1803.79i	−0.385160	−	0.843382i
$167$	91.5971	−	637.072i	0.0424431	−	0.295198i	−0.957533	−	0.288323i	$-0.906902\pi$
$167$	91.5971	−	637.072i	0.0424431	−	0.295198i	0.999976	−	0.00687540i	$-0.00218852\pi$
$168$	2476.83	−	727.263i	1.13745	−	0.333986i
$169$	−1112.65	−	715.059i	−0.506442	−	0.325471i
$170$	−1639.22	+	3589.39i	−0.739544	+	1.61938i
$171$	123.182	+	36.1694i	0.0550874	+	0.0161751i
$172$	2697.31	+	3112.87i	1.19575	+	1.37996i
$173$	−1336.86	−	1542.82i	−0.587511	−	0.678024i	0.381691	−	0.924290i	$-0.375342\pi$
$173$	−1336.86	−	1542.82i	−0.587511	−	0.678024i	−0.969202	+	0.246266i	$0.920796\pi$
$174$	3343.40	+	981.712i	1.45668	+	0.427721i
$175$	−489.156	+	1071.10i	−0.211296	+	0.462673i
$176$	3068.83	+	1972.22i	1.31433	+	0.844668i
$177$	3542.24	−	1040.10i	1.50424	−	0.441686i
$178$	570.077	−	3964.97i	0.240051	−	1.66959i
$179$	1671.82	+	3660.78i	0.698089	+	1.52860i	0.842273	+	0.539051i	$0.181217\pi$
$179$	1671.82	+	3660.78i	0.698089	+	1.52860i	−0.144184	+	0.989551i	$0.546056\pi$
$180$	108.689	+	755.946i	0.0450065	+	0.313027i
$181$	3301.18	−	2121.54i	1.35566	−	0.871230i	0.357624	−	0.933866i	$-0.383587\pi$
$181$	3301.18	−	2121.54i	1.35566	−	0.871230i	0.998036	+	0.0626356i	$0.0199506\pi$
$182$	−796.812	+	919.570i	−0.324525	+	0.374522i
$183$	1308.95			0.528745
$184$	−7196.56	−	1867.31i	−2.88336	−	0.748152i
$185$	−1431.65			−0.568957
$186$	−2656.27	+	3065.50i	−1.04713	+	1.20846i
$187$	694.002	−	446.008i	0.271393	−	0.174414i
$188$	−371.873	−	2586.43i	−0.144264	−	1.00338i
$189$	−464.922	−	1018.04i	−0.178932	−	0.391806i
$190$	732.946	−	5097.75i	0.279860	−	1.94647i
$191$	−4287.65	+	1258.97i	−1.62431	+	0.476940i	−0.962172	−	0.272442i	$-0.912169\pi$
$191$	−4287.65	+	1258.97i	−1.62431	+	0.476940i	−0.662138	+	0.749382i	$0.730351\pi$
$192$	−4804.41	−	3087.61i	−1.80588	−	1.16057i
$193$	1250.31	−	2737.80i	0.466318	−	1.02109i	−0.519683	−	0.854359i	$-0.673950\pi$
$193$	1250.31	−	2737.80i	0.466318	−	1.02109i	0.986002	−	0.166736i	$-0.0533227\pi$
$194$	−1901.97	−	558.470i	−0.703886	−	0.206680i
$195$	1607.24	+	1854.86i	0.590241	+	0.681175i
$196$	3829.11	+	4419.03i	1.39545	+	1.61043i
$197$	−4791.02	−	1406.77i	−1.73272	−	0.508773i	−0.745278	−	0.666754i	$-0.767683\pi$
$197$	−4791.02	−	1406.77i	−1.73272	−	0.508773i	−0.987442	+	0.157981i	$0.949502\pi$
$198$	92.0822	−	201.632i	0.0330505	−	0.0723704i
$199$	1262.75	+	811.522i	0.449820	+	0.289082i	0.745871	−	0.666090i	$-0.232034\pi$
$199$	1262.75	+	811.522i	0.449820	+	0.289082i	−0.296051	+	0.955172i	$0.595670\pi$
$200$	9897.82	−	2906.26i	3.49941	−	1.02752i
$201$	−72.4038	+	503.579i	−0.0254078	+	0.176715i
$202$	1317.93	+	2885.87i	0.459056	+	1.00519i
$203$	−143.323	−	996.834i	−0.0495532	−	0.344650i
$204$	−3817.46	+	2453.34i	−1.31018	+	0.841999i
$205$	−3649.80	+	4212.10i	−1.24348	+	1.43505i
$206$	6004.78			2.03094
$207$	−27.1805	+	243.698i	−0.00912647	+	0.0818271i
$208$	5785.71			1.92869
$209$	−705.097	+	813.726i	−0.233362	+	0.269314i
$210$	−2873.18	+	1846.48i	−0.944135	+	0.606758i
$211$	−64.9877	−	451.999i	−0.0212035	−	0.147473i	0.976469	−	0.215656i	$-0.0691890\pi$
$211$	−64.9877	−	451.999i	−0.0212035	−	0.147473i	−0.997673	+	0.0681827i	$0.978280\pi$
$212$	−6497.18	−	14226.8i	−2.10485	−	4.60898i
$213$	195.172	−	1357.45i	0.0627839	−	0.436671i
$214$	5459.17	−	1602.96i	1.74384	−	0.512037i
$215$	−2804.37	−	1802.26i	−0.889563	−	0.571688i
$216$	−4072.99	+	8918.60i	−1.28302	+	2.80942i
$217$	1124.82	+	330.277i	0.351879	+	0.103321i
$218$	4427.68	+	5109.81i	1.37560	+	1.58752i
$219$	−1990.03	−	2296.62i	−0.614036	−	0.708635i
$220$	−6145.70	−	1804.54i	−1.88338	−	0.553010i
$221$	543.534	−	1190.17i	0.165439	−	0.362261i
$222$	−1922.81	−	1235.72i	−0.581310	−	0.373585i
$223$	−477.247	+	140.132i	−0.143313	+	0.0420806i	−0.352602	−	0.935773i	$-0.614703\pi$
$223$	−477.247	+	140.132i	−0.143313	+	0.0420806i	0.209289	+	0.977854i	$0.432885\pi$
$224$	−555.370	+	3862.68i	−0.165657	+	1.15217i
$225$	−141.333	−	309.476i	−0.0418765	−	0.0916967i
$226$	−571.505	−	3974.90i	−0.168212	−	1.16994i
$227$	2765.31	−	1777.16i	0.808547	−	0.519622i	−0.0698477	−	0.997558i	$-0.522251\pi$
$227$	2765.31	−	1777.16i	0.808547	−	0.519622i	0.878395	+	0.477936i	$0.158615\pi$
$228$	3878.49	−	4476.02i	1.12658	−	1.30014i
$229$	−3859.28			−1.11366			−0.556830	−	0.830626i	$-0.687983\pi$
$229$	−3859.28			−1.11366			−0.556830	+	0.830626i	$0.687983\pi$
$230$	9831.87	−	312.023i	2.81867	−	0.0894529i
$231$	714.027			0.203375
$232$	−5777.60	+	6667.71i	−1.63499	+	1.88688i
$233$	621.238	−	399.246i	0.174672	−	0.112255i	−0.450383	−	0.892835i	$-0.648713\pi$
$233$	621.238	−	399.246i	0.174672	−	0.112255i	0.625056	+	0.780580i	$0.285076\pi$
$234$	−50.0327	−	347.985i	−0.0139775	−	0.0972157i
$235$	878.520	+	1923.69i	0.243865	+	0.533990i
$236$	−2174.67	+	15125.2i	−0.599827	+	4.17189i
$237$	4751.73	−	1395.23i	1.30236	−	0.382406i
$238$	1531.70	+	984.366i	0.417166	+	0.268096i
$239$	769.191	−	1684.29i	0.208179	−	0.455849i	−0.776524	−	0.630087i	$-0.783019\pi$
$239$	769.191	−	1684.29i	0.208179	−	0.455849i	0.984703	+	0.174238i	$0.0557463\pi$
$240$	15582.1	+	4575.33i	4.19093	+	1.23057i
$241$	−2238.07	−	2582.87i	−0.598203	−	0.690363i	0.373213	−	0.927746i	$-0.378256\pi$
$241$	−2238.07	−	2582.87i	−0.598203	−	0.690363i	−0.971416	+	0.237382i	$0.923711\pi$
$242$	−3444.17	−	3974.78i	−0.914874	−	1.05582i
$243$	596.933	+	175.275i	0.157586	+	0.0462713i
$244$	−2250.67	+	4928.29i	−0.590511	+	1.29304i
$245$	−3981.08	−	2558.49i	−1.03813	−	0.667166i
$246$	−8537.60	+	2506.87i	−2.21275	+	0.649723i
$247$	−243.030	+	1690.31i	−0.0626059	+	0.435434i
$248$	−4266.35	−	9342.01i	−1.09239	−	2.39201i
$249$	262.657	+	1826.82i	0.0668482	+	0.464939i
$250$	−2103.92	+	1352.11i	−0.532254	+	0.342059i
$251$	3607.25	−	4162.99i	0.907122	−	1.04687i	−0.0915726	−	0.995798i	$-0.529189\pi$
$251$	3607.25	−	4162.99i	0.907122	−	1.04687i	0.998695	−	0.0510764i	$-0.0162652\pi$
$252$	352.392			0.0880897
$253$	−1764.45	−	1056.40i	−0.438459	−	0.262512i
$254$	−1888.47			−0.466508
$255$	2405.04	−	2775.56i	0.590625	−	0.681618i
$256$	1629.98	−	1047.53i	0.397945	−	0.255743i
$257$	903.219	+	6282.02i	0.219227	+	1.52475i	0.740904	+	0.671611i	$0.234397\pi$
$257$	903.219	+	6282.02i	0.219227	+	1.52475i	−0.521677	+	0.853143i	$0.674693\pi$
$258$	−2210.87	−	4841.13i	−0.533499	−	1.16820i
$259$	−94.0111	+	653.862i	−0.0225543	+	0.156869i
$260$	−9747.24	+	2862.05i	−2.32499	+	0.682680i
$261$	244.788	+	157.315i	0.0580535	+	0.0373087i
$262$	−1862.32	+	4077.92i	−0.439140	+	0.961583i
$263$	757.739	+	222.492i	0.177659	+	0.0521652i	0.369352	−	0.929290i	$-0.379580\pi$
$263$	757.739	+	222.492i	0.177659	+	0.0521652i	−0.191693	+	0.981455i	$0.561398\pi$
$264$	−4096.34	−	4727.43i	−0.954971	−	1.10210i
$265$	8289.29	+	9566.35i	1.92154	+	2.21757i
$266$	−2280.11	−	669.500i	−0.525573	−	0.154322i
$267$	−1548.76	+	3391.30i	−0.354990	+	0.777320i
$268$	−1771.52	−	1138.48i	−0.403778	−	0.259493i
$269$	−2031.56	+	596.520i	−0.460470	+	0.135206i	−0.503736	−	0.863857i	$-0.668042\pi$
$269$	−2031.56	+	596.520i	−0.460470	+	0.135206i	0.0432667	+	0.999064i	$0.486223\pi$
$270$	1846.13	−	12840.1i	0.416118	−	2.89417i
$271$	−1057.17	−	2314.88i	−0.236968	−	0.518888i	0.753364	−	0.657604i	$-0.228430\pi$
$271$	−1057.17	−	2314.88i	−0.236968	−	0.518888i	−0.990332	+	0.138716i	$0.955703\pi$
$272$	−1232.10	−	8569.47i	−0.274659	−	1.91030i
$273$	952.690	−	612.257i	0.211207	−	0.135734i
$274$	6570.02	−	7582.21i	1.44857	−	1.67174i
$275$	2853.37			0.625689
$276$	9705.64	+	5810.90i	2.11671	+	1.26730i
$277$	6965.82			1.51096			0.755479	−	0.655172i	$-0.227404\pi$
$277$	6965.82			1.51096			0.755479	+	0.655172i	$0.227404\pi$
$278$	−4952.94	+	5716.00i	−1.06855	+	1.23318i
$279$	−284.948	+	183.125i	−0.0611447	+	0.0392953i
$280$	−1230.66	−	8559.42i	−0.262664	−	1.82687i
$281$	2720.87	+	5957.88i	0.577628	+	1.26483i	0.942635	+	0.333825i	$0.108339\pi$
$281$	2720.87	+	5957.88i	0.577628	+	1.26483i	−0.365007	+	0.931005i	$0.618933\pi$
$282$	−480.500	+	3341.95i	−0.101466	+	0.705710i
$283$	−2469.67	+	725.159i	−0.518750	+	0.152319i	−0.530619	−	0.847611i	$-0.678040\pi$
$283$	−2469.67	+	725.159i	−0.518750	+	0.152319i	0.0118682	+	0.999930i	$0.496222\pi$
$284$	4775.31	+	3068.91i	0.997755	+	0.641218i
$285$	−1991.23	+	4360.19i	−0.413861	+	0.906229i
$286$	2829.05	+	830.685i	0.584914	+	0.171746i
$287$	1684.08	+	1943.53i	0.346369	+	0.399731i
$288$	−738.376	−	852.131i	−0.151074	−	0.174348i
$289$	2835.42	+	832.555i	0.577126	+	0.169460i
$290$	4849.11	−	10618.1i	0.981895	−	2.15005i
$291$	1552.06	+	997.447i	0.312657	+	0.200933i
$292$	12068.7	−	3543.69i	2.41872	−	0.710200i
$293$	−676.150	+	4702.72i	−0.134816	+	0.937666i	0.804339	+	0.594171i	$0.202520\pi$
$293$	−676.150	+	4702.72i	−0.134816	+	0.937666i	−0.939155	+	0.343495i	$0.888389\pi$
$294$	−3138.56	−	6872.48i	−0.622600	−	1.36330i
$295$	−1760.03	−	12241.3i	−0.347365	−	2.41598i
$296$	4868.43	−	3128.75i	0.955985	−	0.614374i
$297$	−1775.99	+	2049.60i	−0.346981	+	0.400437i
$298$	−13937.0			−2.70922
$299$	−3260.05	+	103.461i	−0.630548	+	0.0200110i
$300$	−15695.4			−3.02058
$301$	−1007.28	+	1162.46i	−0.192885	+	0.222602i
$302$	−4268.34	+	2743.10i	−0.813297	+	0.522674i
$303$	−420.222	−	2922.71i	−0.0796736	−	0.554142i
$304$	4694.03	+	10278.5i	0.885595	+	1.93918i
$305$	624.030	−	4340.23i	0.117154	−	0.814822i
$306$	−504.761	+	148.211i	−0.0942983	+	0.0276885i
$307$	−4767.22	−	3063.71i	−0.886253	−	0.569560i	0.0164308	−	0.999865i	$-0.494770\pi$
$307$	−4767.22	−	3063.71i	−0.886253	−	0.569560i	−0.902684	+	0.430305i	$0.858406\pi$
$308$	−1227.73	+	2688.36i	−0.227132	+	0.497349i
$309$	−5362.37	−	1574.53i	−0.987232	−	0.289878i
$310$	8898.25	+	10269.1i	1.63028	+	1.88144i
$311$	2243.64	+	2589.30i	0.409084	+	0.472108i	0.922481	−	0.386043i	$-0.126158\pi$
$311$	2243.64	+	2589.30i	0.409084	+	0.472108i	−0.513397	+	0.858151i	$0.671613\pi$
$312$	−9519.18	−	2795.08i	−1.72730	−	0.507181i
$313$	2840.01	−	6218.76i	0.512866	−	1.12302i	−0.459204	−	0.888331i	$-0.651865\pi$
$313$	2840.01	−	6218.76i	0.512866	−	1.12302i	0.972070	−	0.234689i	$-0.0754073\pi$
$314$	9102.14	+	5849.59i	1.63587	+	1.05131i
$315$	−273.649	+	80.3505i	−0.0489471	+	0.0143722i
$316$	−2917.21	+	20289.6i	−0.519322	+	3.61197i
$317$	529.017	+	1158.39i	0.0937304	+	0.205241i	0.950690	−	0.310142i	$-0.100377\pi$
$317$	529.017	+	1158.39i	0.0937304	+	0.205241i	−0.856960	+	0.515383i	$0.827649\pi$
$318$	2876.02	+	20003.2i	0.507167	+	3.52743i
$319$	−2052.98	+	1319.37i	−0.360329	+	0.231569i
$320$	−12528.4	+	14458.5i	−2.18862	+	2.52580i
$321$	−5295.45			−0.920758
$322$	503.115	−	4510.89i	0.0870731	−	0.780690i
$323$	2555.35			0.440197
$324$	8959.26	−	10339.5i	1.53622	−	1.77290i
$325$	3807.10	−	2446.68i	0.649785	−	0.417592i
$326$	212.076	+	1475.02i	0.0360301	+	0.250595i
$327$	−2614.13	−	5724.15i	−0.442085	−	0.968031i
$328$	3206.24	−	22299.9i	0.539740	−	3.75398i
$329$	936.275	−	274.915i	0.156895	−	0.0460686i
$330$	6962.34	+	4474.43i	1.16141	+	0.746391i
$331$	1815.45	−	3975.29i	0.301469	−	0.660125i	−0.696903	−	0.717166i	$-0.745439\pi$
$331$	1815.45	−	3975.29i	0.301469	−	0.660125i	0.998372	+	0.0570403i	$0.0181664\pi$
$332$	−7329.73	−	2152.20i	−1.21166	−	0.355775i
$333$	−124.990	−	144.246i	−0.0205688	−	0.0237376i
$334$	−2254.17	−	2601.45i	−0.369289	−	0.426183i
$335$	1635.25	+	480.154i	0.266697	+	0.0783093i
$336$	3112.86	−	6816.22i	0.505418	−	1.10671i
$337$	−4742.62	−	3047.90i	−0.766609	−	0.492669i	0.0979563	−	0.995191i	$-0.468769\pi$
$337$	−4742.62	−	3047.90i	−0.766609	−	0.492669i	−0.864565	+	0.502521i	$0.832406\pi$
$338$	−6787.05	+	1992.86i	−1.09221	+	0.320702i
$339$	−531.910	+	3699.51i	−0.0852194	+	0.592714i
$340$	6314.85	+	13827.6i	1.00727	+	2.20561i
$341$	−404.282	−	2811.84i	−0.0642026	−	0.446539i
$342$	577.614	−	371.210i	0.0913268	−	0.0586922i
$343$	−3158.12	+	3644.67i	−0.497151	+	0.573742i
$344$	13475.1			2.11201
$345$	−8861.84	−	2299.41i	−1.38291	−	0.358829i
$346$	−10918.0			−1.69640
$347$	2598.96	−	2999.35i	0.402073	−	0.464017i	−0.518220	−	0.855247i	$-0.673405\pi$
$347$	2598.96	−	2999.35i	0.402073	−	0.464017i	0.920293	+	0.391231i	$0.127951\pi$
$348$	11292.7	−	7257.40i	1.73952	−	1.11792i
$349$	−31.5962	−	219.757i	−0.00484615	−	0.0337057i	0.987255	−	0.159147i	$-0.0508744\pi$
$349$	−31.5962	−	219.757i	−0.00484615	−	0.0337057i	−0.992101	+	0.125441i	$0.959965\pi$
$350$	2616.09	+	5728.45i	0.399532	+	0.874853i
$351$	−612.141	+	4257.53i	−0.0930873	+	0.647437i
$352$	9073.32	−	2664.17i	1.37389	−	0.403411i
$353$	1870.62	+	1202.18i	0.282048	+	0.181262i	0.674014	−	0.738718i	$-0.264569\pi$
$353$	1870.62	+	1202.18i	0.282048	+	0.181262i	−0.391966	+	0.919980i	$0.628205\pi$
$354$	8202.09	−	17960.1i	1.23146	−	2.69652i
$355$	−4408.00	−	1294.31i	−0.659021	−	0.193506i
$356$	−10105.5	−	11662.4i	−1.50447	−	1.73625i
$357$	−1109.72	−	1280.69i	−0.164518	−	0.189863i
$358$	20651.7	+	6063.89i	3.04882	+	0.895214i
$359$	−1864.30	+	4082.25i	−0.274078	+	0.600148i	−0.995751	−	0.0920867i	$-0.970646\pi$
$359$	−1864.30	+	4082.25i	−0.274078	+	0.600148i	0.721673	+	0.692234i	$0.243374\pi$
$360$	2101.89	+	1350.81i	0.307721	+	0.197760i
$361$	3381.09	−	992.779i	0.492943	−	0.144741i
$362$	2986.75	−	20773.3i	0.433646	−	3.01607i
$363$	2033.46	+	4452.65i	0.294019	+	0.643812i
$364$	667.087	+	4639.69i	0.0960573	+	0.668093i
$365$	−8563.88	+	5503.67i	−1.22809	+	0.789247i
$366$	4584.35	−	5290.63i	0.654721	−	0.755589i
$367$	−3655.81			−0.519978			−0.259989	−	0.965612i	$-0.583719\pi$
$367$	−3655.81			−0.519978			−0.259989	+	0.965612i	$0.583719\pi$
$368$	−17776.9	+	12238.3i	−2.51816	+	1.73360i
$369$	−743.035			−0.104826
$370$	−5014.09	+	5786.56i	−0.704513	+	0.813052i
$371$	4913.46	−	3157.69i	0.687585	−	0.441884i
$372$	2223.81	+	15467.0i	0.309945	+	2.15571i
$373$	1763.52	+	3861.57i	0.244803	+	0.536044i	0.991651	−	0.128951i	$-0.0411610\pi$
$373$	1763.52	+	3861.57i	0.244803	+	0.536044i	−0.746848	+	0.664995i	$0.768434\pi$
$374$	627.900	−	4367.14i	0.0868126	−	0.603795i
$375$	2233.38	−	655.778i	0.307549	−	0.0903047i
$376$	−7191.53	−	4621.72i	−0.986369	−	0.633901i
$377$	−1607.87	+	3520.74i	−0.219654	+	0.480975i
$378$	−5743.10	−	1686.33i	−0.781463	−	0.229458i
$379$	−4615.18	−	5326.21i	−0.625504	−	0.721870i	0.351238	−	0.936286i	$-0.385761\pi$
$379$	−4615.18	−	5326.21i	−0.625504	−	0.721870i	−0.976742	+	0.214416i	$0.931215\pi$
$380$	−12992.6	−	14994.3i	−1.75396	−	2.02418i
$381$	1686.43	+	495.182i	0.226768	+	0.0665851i
$382$	−9928.08	+	21739.5i	−1.32975	+	2.91175i
$383$	7778.20	+	4998.75i	1.03772	+	0.666904i	0.944422	−	0.328734i	$-0.106622\pi$
$383$	7778.20	+	4998.75i	1.03772	+	0.666904i	0.0932999	+	0.995638i	$0.470258\pi$
$384$	−9926.97	+	2914.82i	−1.31923	+	0.387360i
$385$	340.406	−	2367.58i	0.0450616	−	0.313410i
$386$	−6686.90	−	14642.3i	−0.881746	−	1.93076i
$387$	−63.2480	−	439.899i	−0.00830769	−	0.0577813i
$388$	−6424.14	+	4128.55i	−0.840558	+	0.540194i
$389$	2747.62	−	3170.93i	0.358123	−	0.413297i	−0.547887	−	0.836553i	$-0.684567\pi$
$389$	2747.62	−	3170.93i	0.358123	−	0.413297i	0.906010	+	0.423256i	$0.139113\pi$
$390$	13126.2			1.70428
$391$	847.490	+	4806.58i	0.109615	+	0.621686i
$392$	19129.3			2.46473
$393$	2732.37	−	3153.32i	0.350712	−	0.404743i
$394$	−22465.7	+	14437.8i	−2.87260	+	1.84611i
$395$	−2360.98	−	16421.0i	−0.300744	−	2.09172i
$396$	−354.732	−	776.755i	−0.0450151	−	0.0985693i
$397$	−1105.29	+	7687.47i	−0.139730	+	0.971846i	0.792472	+	0.609908i	$0.208794\pi$
$397$	−1105.29	+	7687.47i	−0.139730	+	0.971846i	−0.932202	+	0.361938i	$0.882115\pi$
$398$	7702.64	−	2261.70i	0.970096	−	0.284846i
$399$	1860.62	+	1195.75i	0.233453	+	0.150031i
$400$	12439.5	−	27238.7i	1.55494	−	3.40484i
$401$	14932.6	+	4384.62i	1.85960	+	0.546028i	0.999346	+	0.0361637i	$0.0115138\pi$
$401$	14932.6	+	4384.62i	1.85960	+	0.546028i	0.860255	+	0.509864i	$0.170304\pi$
$402$	1781.83	+	2056.34i	0.221069	+	0.255127i
$403$	−2950.49	−	3405.04i	−0.364700	−	0.420886i
$404$	11726.7	+	3443.28i	1.44413	+	0.424034i
$405$	−4599.71	+	10072.0i	−0.564350	+	1.23575i
$406$	−4531.05	−	2911.93i	−0.553872	−	0.355952i
$407$	1535.90	−	450.981i	0.187056	−	0.0549246i
$408$	−2112.75	+	14694.5i	−0.256365	+	1.78306i
$409$	236.009	+	516.789i	0.0285328	+	0.0624781i	0.923362	−	0.383931i	$-0.125430\pi$
$409$	236.009	+	516.789i	0.0285328	+	0.0624781i	−0.894829	+	0.446409i	$0.852703\pi$
$410$	4242.06	+	29504.2i	0.510977	+	3.55392i
$411$	−7855.30	+	5048.29i	−0.942757	+	0.605873i
$412$	15148.6	−	17482.4i	1.81145	−	2.09052i
$413$	−5706.39			−0.679886
$414$	889.807	+	963.369i	0.105632	+	0.114365i
$415$	6182.60			0.731306
$416$	9821.63	−	11334.8i	1.15756	−	1.33590i
$417$	5921.87	−	3805.76i	0.695432	−	0.446927i
$418$	819.514	+	5699.85i	0.0958941	+	0.666958i
$419$	5407.74	+	11841.3i	0.630514	+	1.38063i	0.907620	+	0.419793i	$0.137897\pi$
$419$	5407.74	+	11841.3i	0.630514	+	1.38063i	−0.277106	+	0.960839i	$0.589375\pi$
$420$	−1872.46	+	13023.2i	−0.217539	+	1.51302i
$421$	8004.75	−	2350.41i	0.926669	−	0.272095i	0.216628	−	0.976254i	$-0.430494\pi$
$421$	8004.75	−	2350.41i	0.926669	−	0.272095i	0.710042	+	0.704160i	$0.248676\pi$
$422$	−2054.54	−	1320.37i	−0.236998	−	0.152310i
$423$	−117.123	+	256.463i	−0.0134626	+	0.0294791i
$424$	−49094.7	−	14415.5i	−5.62323	−	1.65113i
$425$	−4434.63	−	5117.84i	−0.506144	−	0.584122i
$426$	−4803.11	−	5543.08i	−0.546271	−	0.630430i
$427$	−1941.29	−	570.013i	−0.220013	−	0.0646016i
$428$	9105.26	−	19937.7i	1.02832	−	2.25170i
$429$	−2308.58	−	1483.63i	−0.259811	−	0.166971i
$430$	−17106.3	+	5022.86i	−1.91846	+	0.563311i
$431$	664.082	−	4618.79i	0.0742174	−	0.516193i	−0.918471	−	0.395488i	$-0.870575\pi$
$431$	664.082	−	4618.79i	0.0742174	−	0.516193i	0.992688	−	0.120705i	$-0.0385155\pi$
$432$	11823.2	+	25889.3i	1.31677	+	2.88333i
$433$	104.624	+	727.675i	0.0116118	+	0.0807617i	0.994803	−	0.101816i	$-0.0324651\pi$
$433$	104.624	+	727.675i	0.0116118	+	0.0807617i	−0.983192	+	0.182577i	$0.941556\pi$
$434$	5274.42	−	3389.66i	0.583365	−	0.374906i
$435$	−7114.54	+	8210.61i	−0.784174	+	0.904986i
$436$	26046.7			2.86103
$437$	−2828.73	−	5707.65i	−0.309649	−	0.624791i
$438$	−16252.4			−1.77299
$439$	−2979.87	+	3438.95i	−0.323966	+	0.373877i	−0.894248	−	0.447572i	$-0.852289\pi$
$439$	−2979.87	+	3438.95i	−0.323966	+	0.373877i	0.570281	+	0.821449i	$0.306834\pi$
$440$	−17628.2	+	11328.9i	−1.90998	+	1.22747i
$441$	−89.7869	−	624.482i	−0.00969517	−	0.0674314i
$442$	−2906.92	−	6365.26i	−0.312823	−	0.684988i
$443$	950.942	−	6613.94i	0.101988	−	0.709341i	−0.873103	−	0.487536i	$-0.837896\pi$
$443$	950.942	−	6613.94i	0.101988	−	0.709341i	0.975091	−	0.221805i	$-0.0711949\pi$
$444$	−8448.46	+	2480.69i	−0.903031	+	0.265154i
$445$	10506.6	+	6752.16i	1.11923	+	0.719287i
$446$	−1105.07	+	2419.77i	−0.117324	+	0.256904i
$447$	12445.9	+	3654.46i	1.31694	+	0.386689i
$448$	5780.79	+	6671.38i	0.609635	+	0.703556i
$449$	−8.64256	−	9.97405i	−0.000908392	−	0.00104834i	0.755295	−	0.655385i	$-0.227493\pi$
$449$	−8.64256	−	9.97405i	−0.000908392	−	0.00104834i	−0.756204	+	0.654336i	$0.772948\pi$
$450$	−1745.86	−	512.631i	−0.182890	−	0.0537015i
$451$	2588.73	−	5668.54i	0.270285	−	0.591843i
$452$	−13014.3	−	8363.80i	−1.35430	−	0.870355i
$453$	4530.98	−	1330.42i	0.469943	−	0.137988i
$454$	2501.92	−	17401.2i	0.258636	−	1.79886i
$455$	−1575.94	−	3450.83i	−0.162376	−	0.355554i
$456$	−2757.49	−	19178.8i	−0.283183	−	1.96958i
$457$	−3911.77	+	2513.94i	−0.400405	+	0.257324i	−0.725310	−	0.688422i	$-0.758304\pi$
$457$	−3911.77	+	2513.94i	−0.400405	+	0.257324i	0.324906	+	0.945746i	$0.394667\pi$
$458$	−13516.4	+	15598.8i	−1.37900	+	1.59145i
$459$	6436.38			0.654520
$460$	23894.9	−	29411.7i	2.42197	−	2.98115i
$461$	−7703.46			−0.778277			−0.389139	−	0.921179i	$-0.627227\pi$
$461$	−7703.46			−0.778277			−0.389139	+	0.921179i	$0.627227\pi$
$462$	2500.75	−	2886.02i	0.251830	−	0.290627i
$463$	2545.01	−	1635.58i	0.255457	−	0.164172i	−0.406644	−	0.913587i	$-0.633301\pi$
$463$	2545.01	−	1635.58i	0.255457	−	0.164172i	0.662101	+	0.749414i	$0.269665\pi$
$464$	3644.78	+	25350.0i	0.364665	+	2.53630i
$465$	−5253.58	−	11503.7i	−0.523934	−	1.14725i
$466$	562.066	−	3909.26i	0.0558739	−	0.388611i
$467$	−17818.5	+	5231.97i	−1.76561	+	0.518430i	−0.993172	−	0.116660i	$-0.962781\pi$
$467$	−17818.5	+	5231.97i	−1.76561	+	0.518430i	−0.772438	+	0.635090i	$0.780963\pi$
$468$	−1139.35	−	732.213i	−0.112535	−	0.0723217i
$469$	326.677	−	715.322i	0.0321632	−	0.0704275i
$470$	10852.2	+	3186.49i	1.06505	+	0.312727i
$471$	−6594.53	−	7610.49i	−0.645137	−	0.744528i
$472$	32737.3	+	37780.9i	3.19249	+	3.68433i
$473$	3576.30	+	1050.10i	0.347650	+	0.102079i
$474$	11002.7	−	24092.5i	1.06618	−	2.33461i
$475$	7435.36	+	4778.41i	0.718226	+	0.461576i
$476$	6729.99	−	1976.10i	0.648044	−	0.190283i
$477$	−240.164	+	1670.37i	−0.0230531	+	0.160338i
$478$	−4113.77	−	9007.91i	−0.393639	−	0.861950i
$479$	1824.07	+	12686.7i	0.173995	+	1.21016i	0.870338	+	0.492454i	$0.163900\pi$
$479$	1824.07	+	12686.7i	0.173995	+	1.21016i	−0.696343	+	0.717709i	$0.745191\pi$
$480$	35415.3	−	22760.0i	3.36766	−	2.16427i
$481$	1662.57	−	1918.71i	0.157602	−	0.181883i
$482$	−18278.1			−1.72727
$483$	−1632.11	+	3896.38i	−0.153755	+	0.367063i
$484$	−20261.0			−1.90280
$485$	4047.27	−	4670.80i	0.378922	−	0.437299i
$486$	2799.09	−	1798.87i	0.261254	−	0.167898i
$487$	−2756.22	−	19169.9i	−0.256460	−	1.78372i	−0.557568	−	0.830131i	$-0.688265\pi$
$487$	−2756.22	−	19169.9i	−0.256460	−	1.78372i	0.301107	−	0.953590i	$-0.402644\pi$
$488$	7363.14	+	16123.0i	0.683019	+	1.49560i
$489$	197.383	−	1372.83i	0.0182535	−	0.126956i
$490$	−24284.1	+	7130.46i	−2.23887	+	0.657390i
$491$	−3368.84	−	2165.02i	−0.309641	−	0.198994i	0.376586	−	0.926382i	$-0.377098\pi$
$491$	−3368.84	−	2165.02i	−0.309641	−	0.198994i	−0.686227	+	0.727387i	$0.740734\pi$
$492$	−14239.7	+	31180.6i	−1.30483	+	2.85718i
$493$	5557.14	+	1631.72i	0.507669	+	0.149065i
$494$	5980.89	+	6902.31i	0.544722	+	0.628643i
$495$	452.577	+	522.302i	0.0410946	+	0.0474257i
$496$	−28604.8	−	8399.13i	−2.58950	−	0.760347i
$497$	−880.591	+	1928.23i	−0.0794767	+	0.174030i
$498$	8303.70	+	5336.46i	0.747184	+	0.480186i
$499$	−1491.48	+	437.937i	−0.133803	+	0.0392881i	−0.347948	−	0.937514i	$-0.613122\pi$
$499$	−1491.48	+	437.937i	−0.133803	+	0.0392881i	0.214145	+	0.976802i	$0.431303\pi$
$500$	−1371.13	+	9536.40i	−0.122637	+	0.852961i
$501$	1330.88	+	2914.21i	0.118681	+	0.259875i
$502$	−4192.60	−	29160.2i	−0.372759	−	2.59260i
$503$	13314.3	−	8556.55i	1.18023	−	0.758485i	0.204798	−	0.978804i	$-0.434346\pi$
$503$	13314.3	−	8556.55i	1.18023	−	0.758485i	0.975428	+	0.220319i	$0.0707100\pi$
$504$	754.962	−	871.273i	0.0667236	−	0.0770031i
$505$	−9891.47			−0.871613
$506$	−10449.5	+	3431.86i	−0.918060	+	0.301512i
$507$	6583.50			0.576694
$508$	−4764.13	+	5498.10i	−0.416091	+	0.480195i
$509$	4895.34	−	3146.04i	0.426291	−	0.273960i	−0.309855	−	0.950784i	$-0.600280\pi$
$509$	4895.34	−	3146.04i	0.426291	−	0.273960i	0.736145	+	0.676824i	$0.236644\pi$
$510$	−2795.31	−	19441.8i	−0.242703	−	1.68803i
$511$	1951.27	+	4272.69i	0.168922	+	0.369888i
$512$	−891.687	+	6201.82i	−0.0769676	+	0.535321i
$513$	−8060.27	+	2366.71i	−0.693703	+	0.203690i
$514$	28554.6	+	18350.9i	2.45037	+	1.57476i
$515$	−7777.32	+	17030.0i	−0.665456	+	1.45714i
$516$	−19672.0	−	5776.22i	−1.67832	−	0.492798i
$517$	−1548.47	−	1787.03i	−0.131725	−	0.152018i
$518$	2313.58	+	2670.01i	0.196241	+	0.226474i
$519$	9749.95	+	2862.84i	0.824615	+	0.242129i
$520$	−13806.1	+	30231.2i	−1.16431	+	2.54948i
$521$	502.790	+	323.123i	0.0422795	+	0.0271714i	0.561610	−	0.827402i	$-0.310182\pi$
$521$	502.790	+	323.123i	0.0422795	+	0.0271714i	−0.519330	+	0.854574i	$0.673819\pi$
$522$	1493.17	−	438.435i	0.125200	−	0.0367621i
$523$	657.703	−	4574.42i	0.0549891	−	0.382458i	−0.943679	−	0.330863i	$-0.892660\pi$
$523$	657.703	−	4574.42i	0.0549891	−	0.382458i	0.998668	−	0.0515953i	$-0.0164306\pi$
$524$	7174.31	+	15709.6i	0.598113	+	1.30969i
$525$	−834.141	−	5801.58i	−0.0693427	−	0.482289i
$526$	3553.13	−	2283.46i	0.294532	−	0.189284i
$527$	−4415.04	+	5095.22i	−0.364937	+	0.421160i
$528$	−18158.1			−1.49665
$529$	9797.84	−	7213.75i	0.805280	−	0.592895i
$530$	67697.8			5.54831
$531$	1079.71	−	1246.05i	0.0882399	−	0.101834i
$532$	−7701.33	+	4949.35i	−0.627623	+	0.403349i
$533$	−1406.58	−	9783.01i	−0.114308	−	0.795027i
$534$	8283.03	+	18137.3i	0.671239	+	1.46981i
$535$	−2524.56	+	17558.7i	−0.204012	+	1.41893i
$536$	−6610.14	+	1940.91i	−0.532676	+	0.156408i
$537$	−16852.3	−	10830.3i	−1.35425	−	0.870322i
$538$	−4704.09	+	10300.5i	−0.376966	+	0.825441i
$539$	5076.92	+	1490.72i	0.405712	+	0.119128i
$540$	−32725.5	−	37767.3i	−2.60793	−	3.00971i
$541$	1343.74	+	1550.76i	0.106787	+	0.123239i	0.806627	−	0.591061i	$-0.201291\pi$
$541$	1343.74	+	1550.76i	0.106787	+	0.123239i	−0.699840	+	0.714300i	$0.746745\pi$
$542$	−13059.0	−	3834.47i	−1.03493	−	0.303883i
$543$	−8114.25	+	17767.7i	−0.641281	+	1.40421i
$544$	−18880.0	−	12133.5i	−1.48800	−	0.956282i
$545$	−20226.4	+	5939.02i	−1.58973	+	0.466788i
$546$	861.948	−	5994.98i	0.0675604	−	0.469893i
$547$	−6168.40	−	13506.9i	−0.482161	−	1.05578i	−0.981864	−	0.189588i	$-0.939285\pi$
$547$	−6168.40	−	13506.9i	−0.482161	−	1.05578i	0.499703	−	0.866197i	$-0.333442\pi$
$548$	−5500.39	−	38256.0i	−0.428768	−	2.98215i
$549$	491.781	−	316.048i	0.0382308	−	0.0245694i
$550$	9993.39	−	11533.0i	0.774763	−	0.894124i
$551$	−7559.19			−0.584451
$552$	35160.5	−	11547.5i	2.71110	−	0.890388i
$553$	−7654.82			−0.588637
$554$	24396.5	−	28155.1i	1.87095	−	2.15919i
$555$	5994.98	−	3852.74i	0.458509	−	0.294666i
$556$	4146.58	+	28840.1i	0.316284	+	2.19980i
$557$	−1656.33	−	3626.86i	−0.125998	−	0.275897i	0.836112	−	0.548559i	$-0.184823\pi$
$557$	−1656.33	−	3626.86i	−0.125998	−	0.275897i	−0.962110	+	0.272661i	$0.912096\pi$
$558$	−257.807	+	1793.09i	−0.0195589	+	0.136035i
$559$	5672.11	−	1665.48i	0.429167	−	0.126015i
$560$	−21117.2	−	13571.2i	−1.59351	−	1.02409i
$561$	−1705.85	+	3735.29i	−0.128380	+	0.281112i
$562$	33610.4	+	9868.91i	2.52272	+	0.740738i
$563$	1001.42	+	1155.70i	0.0749638	+	0.0865129i	0.791993	−	0.610531i	$-0.209044\pi$
$563$	1001.42	+	1155.70i	0.0749638	+	0.0865129i	−0.717029	+	0.697044i	$0.754498\pi$
$564$	8517.60	+	9829.83i	0.635914	+	0.733884i
$565$	12013.3	+	3527.42i	0.894519	+	0.262654i
$566$	−5718.53	+	12521.8i	−0.424678	+	0.929916i
$567$	4298.01	+	2762.16i	0.318341	+	0.204586i
$568$	17818.3	−	5231.93i	1.31627	−	0.386491i
$569$	−213.858	+	1487.41i	−0.0157564	+	0.109588i	−0.996182	−	0.0873026i	$-0.972175\pi$
$569$	−213.858	+	1487.41i	−0.0157564	+	0.109588i	0.980425	+	0.196891i	$0.0630844\pi$
$570$	10649.5	+	23319.1i	0.782556	+	1.71356i
$571$	2624.14	+	18251.3i	0.192324	+	1.33764i	0.825837	+	0.563909i	$0.190703\pi$
$571$	2624.14	+	18251.3i	0.192324	+	1.33764i	−0.633514	+	0.773732i	$0.718388\pi$
$572$	9555.46	−	6140.92i	0.698486	−	0.448890i
$573$	14566.3	−	16810.4i	1.06198	−	1.22560i
$574$	13753.7			1.00012
$575$	−6522.16	+	15570.6i	−0.473031	+	1.12928i
$576$	−2550.55			−0.184502
$577$	−4614.99	+	5325.98i	−0.332971	+	0.384270i	−0.897404	−	0.441210i	$-0.854550\pi$
$577$	−4614.99	+	5325.98i	−0.332971	+	0.384270i	0.564433	+	0.825479i	$0.309095\pi$
$578$	13295.6	−	8544.58i	0.956791	−	0.614892i
$579$	2132.11	+	14829.2i	0.153036	+	1.06439i
$580$	−18680.4	−	40904.5i	−1.33735	−	2.92839i
$581$	405.988	−	2823.71i	0.0289901	−	0.201630i
$582$	9467.36	−	2779.87i	0.674286	−	0.197988i
$583$	−11906.4	−	7651.77i	−0.845818	−	0.543574i
$584$	17094.3	−	37431.2i	1.21124	−	2.65225i
$585$	1051.71	+	308.810i	0.0743297	+	0.0218252i
$586$	16639.8	+	19203.3i	1.17301	+	1.35372i
$587$	−290.556	−	335.320i	−0.0204302	−	0.0235777i	0.745443	−	0.666570i	$-0.232238\pi$
$587$	−290.556	−	335.320i	−0.0204302	−	0.0235777i	−0.765873	+	0.642992i	$0.777693\pi$
$588$	−27926.4	−	8199.93i	−1.95861	−	0.575101i
$589$	3655.39	−	8004.19i	0.255718	−	0.559944i
$590$	−55641.9	−	35758.9i	−3.88261	−	2.49520i
$591$	23848.0	−	7002.40i	1.65986	−	0.487378i
$592$	2390.75	−	16628.1i	0.165979	−	1.15441i
$593$	−1494.63	−	3272.78i	−0.103503	−	0.226639i	0.850795	−	0.525498i	$-0.176121\pi$
$593$	−1494.63	−	3272.78i	−0.103503	−	0.226639i	−0.954297	+	0.298859i	$0.903394\pi$
$594$	2064.18	+	14356.7i	0.142583	+	0.991686i
$595$	−4775.57	+	3069.07i	−0.329041	+	0.211462i
$596$	−35159.5	+	40576.2i	−2.41642	+	2.78870i
$597$	−7471.63			−0.512217
$598$	−10999.6	+	13539.1i	−0.752183	+	0.925846i
$599$	−18693.3			−1.27510			−0.637552	−	0.770407i	$-0.720053\pi$
$599$	−18693.3			−1.27510			−0.637552	+	0.770407i	$0.720053\pi$
$600$	−33625.7	+	38806.1i	−2.28794	+	2.64042i
$601$	−1146.18	+	736.608i	−0.0777934	+	0.0499948i	−0.578959	−	0.815356i	$-0.696541\pi$
$601$	−1146.18	+	736.608i	−0.0777934	+	0.0499948i	0.501166	+	0.865351i	$0.332905\pi$
$602$	1170.73	+	8142.60i	0.0792614	+	0.551275i
$603$	94.3875	+	206.680i	0.00637439	+	0.0139580i
$604$	−2781.69	+	19347.0i	−0.187393	+	1.30334i
$605$	15733.6	−	4619.80i	1.05729	−	0.310449i
$606$	−13285.0	−	8537.75i	−0.890538	−	0.572314i
$607$	−10047.5	+	22000.9i	−0.671852	+	1.47115i	0.199199	+	0.979959i	$0.436166\pi$
$607$	−10047.5	+	22000.9i	−0.671852	+	1.47115i	−0.871051	+	0.491192i	$0.836561\pi$
$608$	28105.0	+	8252.37i	1.87468	+	0.550457i
$609$	3282.76	+	3788.50i	0.218430	+	0.252082i
$610$	−15357.2	−	17723.1i	−1.01933	−	1.17637i
$611$	−3598.37	−	1056.58i	−0.238256	−	0.0699584i
$612$	−841.883	+	1843.47i	−0.0556064	+	0.121761i
$613$	3848.79	+	2473.47i	0.253591	+	0.162973i	0.661260	−	0.750157i	$-0.270022\pi$
$613$	3848.79	+	2473.47i	0.253591	+	0.162973i	−0.407669	+	0.913130i	$0.633658\pi$
$614$	−29079.5	+	8538.50i	−1.91132	+	0.561215i
$615$	3948.16	−	27460.1i	0.258870	−	1.80048i
$616$	4016.56	+	8795.04i	0.262714	+	0.575263i
$617$	73.1420	+	508.714i	0.00477243	+	0.0331930i	0.992069	−	0.125698i	$-0.0401171\pi$
$617$	73.1420	+	508.714i	0.00477243	+	0.0331930i	−0.987296	+	0.158891i	$0.949208\pi$
$618$	−25144.8	+	16159.6i	−1.63669	+	1.05183i
$619$	14141.6	−	16320.3i	0.918253	−	1.05972i	−0.0797669	−	0.996814i	$-0.525418\pi$
$619$	14141.6	−	16320.3i	0.918253	−	1.05972i	0.998019	−	0.0629064i	$-0.0200369\pi$
$620$	52345.7			3.39073
$621$	−7124.96	−	14376.3i	−0.460410	−	0.928989i
$622$	18323.6			1.18120
$623$	3773.76	−	4355.16i	0.242685	−	0.280073i
$624$	−24227.4	+	15570.0i	−1.55428	+	0.998878i
$625$	1612.86	+	11217.7i	0.103223	+	0.717932i
$626$	−15188.9	−	33259.1i	−0.969762	−	2.12348i
$627$	762.736	−	5304.95i	0.0485817	−	0.337893i
$628$	39993.0	−	11743.0i	2.54123	−	0.746173i
$629$	−3195.95	−	2053.91i	−0.202593	−	0.130198i
$630$	−633.636	+	1387.47i	−0.0400709	+	0.0877430i
$631$	−27232.6	−	7996.20i	−1.71808	−	0.504475i	−0.733546	−	0.679640i	$-0.762136\pi$
$631$	−27232.6	−	7996.20i	−1.71808	−	0.504475i	−0.984539	+	0.175165i	$0.943954\pi$
$632$	43915.4	+	50681.1i	2.76402	+	3.18985i
$633$	1488.52	+	1717.84i	0.0934648	+	0.107864i
$634$	6534.84	+	1918.80i	0.409356	+	0.120198i
$635$	2445.92	−	5355.82i	0.152856	−	0.334707i
$636$	65492.9	+	42089.7i	4.08327	+	2.62416i
$637$	8052.13	−	2364.32i	0.500843	−	0.147061i
$638$	−1857.44	+	12918.8i	−0.115261	+	0.801660i
$639$	−254.432	−	557.128i	−0.0157514	−	0.0344908i
$640$	4932.39	+	34305.6i	0.304641	+	2.11882i
$641$	−4008.32	+	2575.99i	−0.246988	+	0.158730i	−0.658278	−	0.752775i	$-0.728715\pi$
$641$	−4008.32	+	2575.99i	−0.246988	+	0.158730i	0.411290	+	0.911505i	$0.365078\pi$
$642$	−18546.3	+	21403.6i	−1.14013	+	1.31578i
$643$	−19.9338			−0.00122257			−0.000611284	−	1.00000i	$-0.500195\pi$
$643$	−19.9338			−0.00122257			−0.000611284		1.00000i	$0.500195\pi$
$644$	−11863.8	−	12844.6i	−0.725931	−	0.785946i
$645$	16593.3			1.01296
$646$	8949.65	−	10328.5i	0.545077	−	0.629052i
$647$	−21203.2	+	13626.5i	−1.28839	+	0.827995i	−0.991897	−	0.127042i	$-0.959452\pi$
$647$	−21203.2	+	13626.5i	−1.28839	+	0.827995i	−0.296488	+	0.955037i	$0.595815\pi$
$648$	−6369.77	−	44302.7i	−0.386155	−	2.68576i
$649$	5744.28	+	12578.2i	0.347431	+	0.760768i
$650$	3444.48	−	23956.9i	0.207852	−	1.44564i
$651$	−5598.96	+	1644.00i	−0.337082	+	0.0989763i
$652$	4829.41	+	3103.68i	0.290083	+	0.186425i
$653$	11421.9	−	25010.5i	0.684492	−	1.49883i	−0.173320	−	0.984866i	$-0.555449\pi$
$653$	11421.9	−	25010.5i	0.684492	−	1.49883i	0.857812	−	0.513963i	$-0.171823\pi$
$654$	−32291.9	−	9481.74i	−1.93075	−	0.566920i
$655$	−9153.19	−	10563.3i	−0.546022	−	0.630143i
$656$	−42827.0	−	49425.0i	−2.54895	−	2.94165i
$657$	−1302.19	−	382.357i	−0.0773261	−	0.0227050i
$658$	2167.95	−	4747.16i	0.128443	−	0.281251i
$659$	15675.5	+	10074.1i	0.926604	+	0.595492i	0.914567	−	0.404435i	$-0.132532\pi$
$659$	15675.5	+	10074.1i	0.926604	+	0.595492i	0.0120376	+	0.999928i	$0.496168\pi$
$660$	30591.1	−	8982.37i	1.80418	−	0.529755i
$661$	431.526	−	3001.33i	0.0253925	−	0.176609i	−0.973178	−	0.230052i	$-0.926110\pi$
$661$	431.526	−	3001.33i	0.0253925	−	0.176609i	0.998571	+	0.0534431i	$0.0170196\pi$
$662$	−9709.37	−	21260.6i	−0.570038	−	1.24821i
$663$	926.869	+	6446.52i	0.0542935	+	0.377620i
$664$	−21024.4	+	13511.5i	−1.22877	+	0.789683i
$665$	4851.92	−	5599.41i	0.282931	−	0.326520i
$666$	−1020.78			−0.0593910
$667$	−2507.03	−	14218.7i	−0.145536	−	0.825414i
$668$	−13260.6			−0.768066
$669$	1621.34	−	1871.13i	0.0936991	−	0.108135i
$670$	7667.90	−	4927.86i	0.442145	−	0.284149i
$671$	697.735	+	4852.85i	0.0401427	+	0.279199i
$672$	−8069.34	−	17669.4i	−0.463217	−	1.01430i
$673$	−873.673	+	6076.53i	−0.0500410	+	0.348043i	0.949383	+	0.314120i	$0.101709\pi$
$673$	−873.673	+	6076.53i	−0.0500410	+	0.348043i	−0.999424	+	0.0339234i	$0.989200\pi$
$674$	−28929.4	+	8494.44i	−1.65329	+	0.485451i
$675$	18728.0	+	12035.8i	1.06792	+	0.686307i
$676$	−11320.0	+	24787.3i	−0.644060	+	1.41030i
$677$	−7602.39	−	2232.26i	−0.431586	−	0.126725i	0.0587221	−	0.998274i	$-0.481297\pi$
$677$	−7602.39	−	2232.26i	−0.431586	−	0.126725i	−0.490308	+	0.871549i	$0.663116\pi$
$678$	13090.1	+	15106.8i	0.741478	+	0.855711i
$679$	−1867.47	−	2155.18i	−0.105548	−	0.121809i
$680$	47717.0	+	14011.0i	2.69097	+	0.790141i
$681$	−6797.10	+	14883.6i	−0.382475	+	0.837503i
$682$	−12781.1	−	8213.90i	−0.717614	−	0.461182i
$683$	2763.27	−	811.369i	0.154808	−	0.0454556i	−0.203411	−	0.979094i	$-0.565203\pi$
$683$	2763.27	−	811.369i	0.154808	−	0.0454556i	0.358218	+	0.933638i	$0.383384\pi$
$684$	376.431	−	2618.14i	0.0210427	−	0.146355i
$685$	12994.2	+	28453.4i	0.724794	+	1.58708i
$686$	3670.60	+	25529.6i	0.204292	+	1.42088i
$687$	16160.6	−	10385.8i	0.897474	−	0.576771i
$688$	25615.6	−	29562.0i	1.41946	−	1.63814i
$689$	−22447.3			−1.24118
$690$	−40330.9	+	27765.3i	−2.22518	+	1.53189i
$691$	3629.33			0.199807			0.0999033	−	0.994997i	$-0.468147\pi$
$691$	3629.33			0.199807			0.0999033	+	0.994997i	$0.468147\pi$
$692$	−27543.4	+	31786.7i	−1.51307	+	1.74617i
$693$	268.264	−	172.403i	0.0147049	−	0.00945029i
$694$	−3020.69	−	21009.4i	−0.165222	−	1.14914i
$695$	−9795.96	−	21450.2i	−0.534650	−	1.17072i
$696$	6249.90	−	43469.0i	0.340376	−	2.36737i
$697$	−14190.5	+	4166.71i	−0.771168	+	0.226435i
$698$	−998.891	−	641.949i	−0.0541670	−	0.0348110i
$699$	−1526.99	+	3343.65i	−0.0826270	+	0.180928i
$700$	23277.6	+	6834.92i	1.25687	+	0.369051i
$701$	19117.4	+	22062.6i	1.03003	+	1.18872i	0.981806	+	0.189885i	$0.0608116\pi$
$701$	19117.4	+	22062.6i	1.03003	+	1.18872i	0.0482269	+	0.998836i	$0.484643\pi$
$702$	15064.6	+	17385.4i	0.809936	+	0.934716i
$703$	4757.52	+	1396.93i	0.255239	+	0.0749450i
$704$	8886.13	−	19457.9i	0.475723	−	1.04169i
$705$	−8855.65	−	5691.18i	−0.473082	−	0.304032i
$706$	11410.6	−	3350.44i	0.608275	−	0.178606i
$707$	−649.536	+	4517.62i	−0.0345521	+	0.240315i
$708$	−31597.3	−	69188.4i	−1.67726	−	3.67268i
$709$	331.416	+	2305.05i	0.0175551	+	0.122099i	0.996715	−	0.0809946i	$-0.0258097\pi$
$709$	331.416	+	2305.05i	0.0175551	+	0.122099i	−0.979159	+	0.203093i	$0.934901\pi$
$710$	−20669.6	+	13283.6i	−1.09256	+	0.702146i
$711$	1448.37	−	1671.51i	0.0763970	−	0.0881668i
$712$	−50484.6			−2.65729
$713$	16268.1	+	4221.12i	0.854480	+	0.221714i
$714$	−9062.99			−0.475034
$715$	−6020.03	+	6947.49i	−0.314876	+	0.363387i
$716$	69753.6	−	44827.9i	3.64080	−	2.33980i
$717$	1311.68	+	9122.90i	0.0683200	+	0.475176i
$718$	9970.63	+	21832.6i	0.518246	+	1.13480i
$719$	889.218	−	6184.65i	0.0461227	−	0.320791i	−0.953678	−	0.300829i	$-0.902737\pi$
$719$	889.218	−	6184.65i	0.0461227	−	0.320791i	0.999801	−	0.0199614i	$-0.00635433\pi$
$720$	6959.03	−	2043.36i	0.360205	−	0.105766i
$721$	7267.20	+	4670.34i	0.375374	+	0.241238i
$722$	7828.96	−	17143.0i	0.403551	−	0.883653i
$723$	16322.7	+	4792.77i	0.839622	+	0.246535i
$724$	−52944.7	−	61101.4i	−2.71778	−	3.13649i
$725$	13118.4	+	15139.5i	0.672009	+	0.775539i
$726$	25118.9	+	7375.58i	1.28409	+	0.377043i
$727$	10625.9	−	23267.5i	0.542081	−	1.18699i	−0.418302	−	0.908308i	$-0.637375\pi$
$727$	10625.9	−	23267.5i	0.542081	−	1.18699i	0.960383	−	0.278683i	$-0.0898980\pi$
$728$	12900.6	+	8290.70i	0.656768	+	0.422079i
$729$	−20174.1	+	5923.64i	−1.02495	+	0.300952i
$730$	−7748.18	+	53889.8i	−0.392840	+	2.73226i
$731$	−3674.73	−	8046.54i	−0.185930	−	0.407130i
$732$	−3838.00	−	26693.9i	−0.193793	−	1.34786i
$733$	−16451.2	+	10572.6i	−0.828977	+	0.532751i	−0.884953	−	0.465681i	$-0.845810\pi$
$733$	−16451.2	+	10572.6i	−0.828977	+	0.532751i	0.0559754	+	0.998432i	$0.482173\pi$
$734$	−12803.8	+	14776.4i	−0.643865	+	0.743060i
$735$	23555.8			1.18214
$736$	−6201.48	+	55602.0i	−0.310584	+	2.78467i
$737$	−1905.58			−0.0952417
$738$	−2602.34	+	3003.26i	−0.129802	+	0.149799i
$739$	1487.23	−	955.786i	0.0740307	−	0.0475767i	−0.503102	−	0.864227i	$-0.667808\pi$
$739$	1487.23	−	955.786i	0.0740307	−	0.0475767i	0.577133	+	0.816650i	$0.304172\pi$
$740$	4197.77	+	29196.1i	0.208531	+	1.45037i
$741$	−3531.15	−	7732.15i	−0.175061	−	0.383330i
$742$	4445.46	−	30918.9i	0.219943	−	1.52974i
$743$	23137.2	−	6793.70i	1.14242	−	0.335446i	0.344845	−	0.938660i	$-0.387931\pi$
$743$	23137.2	−	6793.70i	1.14242	−	0.335446i	0.797580	+	0.603213i	$0.206113\pi$
$744$	43005.6	+	27638.0i	2.11917	+	1.36191i
$745$	18051.0	−	39526.1i	0.887700	−	1.94379i
$746$	21784.4	+	6396.48i	1.06915	+	0.313930i
$747$	539.770	+	622.928i	0.0264380	+	0.0305110i
$748$	−11130.5	−	12845.3i	−0.544079	−	0.627901i
$749$	7853.62	+	2306.03i	0.383131	+	0.112497i
$750$	5171.40	−	11323.8i	0.251777	−	0.551315i
$751$	−6865.78	−	4412.37i	−0.333603	−	0.214394i	0.363105	−	0.931748i	$-0.381717\pi$
$751$	−6865.78	−	4412.37i	−0.333603	−	0.214394i	−0.696708	+	0.717354i	$0.745353\pi$
$752$	−23810.0	+	6991.24i	−1.15460	+	0.339022i
$753$	−3902.13	+	27139.9i	−0.188847	+	1.31346i
$754$	8599.18	+	18829.6i	0.415336	+	0.909460i
$755$	−2251.30	−	15658.1i	−0.108521	−	0.754778i
$756$	−19398.0	+	12466.3i	−0.933198	+	0.599730i
$757$	−14604.0	+	16854.0i	−0.701180	+	0.809204i	−0.988911	−	0.148507i	$-0.952553\pi$
$757$	−14604.0	+	16854.0i	−0.701180	+	0.809204i	0.287732	+	0.957711i	$0.407099\pi$
$758$	−37691.7			−1.80610
$759$	10231.5	−	324.705i	0.489301	−	0.0155284i
$760$	−64907.8			−3.09797
$761$	−10216.8	+	11790.9i	−0.486676	+	0.561654i	−0.944974	−	0.327145i	$-0.893914\pi$
$761$	−10216.8	+	11790.9i	−0.486676	+	0.561654i	0.458299	+	0.888798i	$0.348459\pi$
$762$	7907.89	−	5082.09i	0.375948	−	0.241607i
$763$	1384.27	+	9627.79i	0.0656800	+	0.456815i
$764$	38246.4	+	83748.0i	1.81113	+	3.96583i
$765$	233.424	−	1623.50i	0.0110320	−	0.0767290i
$766$	47446.1	−	13931.4i	2.23799	−	0.657132i
$767$	18449.8	+	11856.9i	0.868556	+	0.558187i
$768$	−4006.47	+	8772.95i	−0.188244	+	0.412196i
$769$	−17508.4	−	5140.92i	−0.821024	−	0.241074i	−0.155867	−	0.987778i	$-0.549817\pi$
$769$	−17508.4	−	5140.92i	−0.821024	−	0.241074i	−0.665157	+	0.746704i	$0.731635\pi$
$770$	−8377.27	−	9667.88i	−0.392072	−	0.452476i
$771$	−20687.9	−	23875.1i	−0.966349	−	1.11523i
$772$	−59499.0	−	17470.5i	−2.77385	−	0.814477i
$773$	−6420.56	+	14059.1i	−0.298747	+	0.654165i	−0.998165	−	0.0605475i	$-0.980715\pi$
$773$	−6420.56	+	14059.1i	−0.298747	+	0.654165i	0.699418	+	0.714713i	$0.253443\pi$
$774$	−1999.54	−	1285.03i	−0.0928578	−	0.0596761i
$775$	−22374.4	+	6569.71i	−1.03705	+	0.304504i
$776$	−3555.40	+	24728.4i	−0.164474	+	1.14394i
$777$	−1365.95	−	2991.02i	−0.0630672	−	0.138098i
$778$	−3193.48	−	22211.2i	−0.147162	−	1.02353i
$779$	16238.6	−	10435.9i	0.746867	−	0.479982i
$780$	33114.1	−	38215.7i	1.52010	−	1.75428i
$781$	5136.71			0.235347
$782$	22395.8	+	13408.7i	1.02413	+	0.613164i
$783$	−19040.0			−0.869007
$784$	36363.9	−	41966.2i	1.65652	−	1.91173i
$785$	−28378.8	+	18238.0i	−1.29030	+	0.829224i
$786$	−3175.76	−	22087.9i	−0.144116	−	1.00235i
$787$	17346.3	+	37983.0i	0.785677	+	1.72039i	0.688631	+	0.725112i	$0.258212\pi$
$787$	17346.3	+	37983.0i	0.785677	+	1.72039i	0.0970460	+	0.995280i	$0.469061\pi$
$788$	−14640.9	+	101830.i	−0.661879	+	4.60347i
$789$	−3771.76	+	1107.49i	−0.170188	+	0.0499716i
$790$	−74640.7	−	47968.7i	−3.36152	−	2.16032i
$791$	2399.91	−	5255.07i	0.107877	−	0.236218i
$792$	−2680.47	−	787.056i	−0.120260	−	0.0353117i
$793$	5092.13	+	5876.63i	0.228029	+	0.263159i
$794$	27200.8	+	31391.4i	1.21577	+	1.40307i
$795$	−60455.3	−	17751.3i	−2.69702	−	0.791915i
$796$	12847.1	−	28131.2i	0.572052	−	1.25262i
$797$	−29840.2	−	19177.1i	−1.32621	−	0.852306i	−0.330412	−	0.943837i	$-0.607188\pi$
$797$	−29840.2	−	19177.1i	−1.32621	−	0.852306i	−0.995802	+	0.0915305i	$0.970824\pi$
$798$	11349.6	−	3332.54i	0.503472	−	0.147833i
$799$	−798.648	+	5554.72i	−0.0353619	+	0.245947i
$800$	−32246.4	−	70609.8i	−1.42510	−	3.12054i
$801$	236.959	+	1648.08i	0.0104526	+	0.0726994i
$802$	70020.9	−	44999.7i	3.08295	−	1.98129i
$803$	7453.79	−	8602.13i	0.327570	−	0.378036i
$804$	10482.0			0.459789
$805$	12141.6	+	7269.32i	0.531594	+	0.318273i
$806$	−24096.3			−1.05305
$807$	6901.77	−	7965.07i	0.301058	−	0.347440i
$808$	33636.7	−	21617.0i	1.46452	−	0.941191i
$809$	−5523.62	−	38417.6i	−0.240050	−	1.66958i	−0.651880	−	0.758322i	$-0.726020\pi$
$809$	−5523.62	−	38417.6i	−0.240050	−	1.66958i	0.411831	−	0.911260i	$-0.364889\pi$
$810$	24600.1	+	53866.7i	1.06711	+	2.33665i
$811$	3226.21	−	22438.8i	0.139689	−	0.971556i	−0.792575	−	0.609775i	$-0.791260\pi$
$811$	3226.21	−	22438.8i	0.139689	−	0.971556i	0.932263	−	0.361781i	$-0.117831\pi$
$812$	−19908.5	+	5845.67i	−0.860409	+	0.252639i
$813$	10656.5	+	6848.49i	0.459703	+	0.295433i
$814$	3556.39	−	7787.42i	0.153135	−	0.335318i
$815$	−4457.94	−	1308.97i	−0.191601	−	0.0562592i
$816$	28220.9	+	32568.6i	1.21070	+	1.39722i
$817$	7560.64	+	8725.44i	0.323762	+	0.373641i
$818$	2915.38	+	856.033i	0.124614	+	0.0365898i
$819$	210.101	−	460.057i	0.00896402	−	0.0196285i
$820$	96600.4	+	62081.3i	4.11394	+	2.64387i
$821$	20087.7	−	5898.29i	0.853917	−	0.250733i	0.174656	−	0.984629i	$-0.444119\pi$
$821$	20087.7	−	5898.29i	0.853917	−	0.250733i	0.679261	+	0.733897i	$0.262300\pi$
$822$	−7107.09	+	49430.9i	−0.301567	+	2.09745i
$823$	−5898.72	−	12916.4i	−0.249838	−	0.547068i	0.742612	−	0.669722i	$-0.233587\pi$
$823$	−5898.72	−	12916.4i	−0.249838	−	0.547068i	−0.992449	+	0.122654i	$0.960859\pi$
$824$	−10770.2	−	74908.3i	−0.455336	−	3.16693i
$825$	−11948.4	+	7678.75i	−0.504229	+	0.324048i
$826$	−19985.6	+	23064.6i	−0.841872	+	0.971572i
$827$	44936.9			1.88949			0.944746	−	0.327803i	$-0.106308\pi$
$827$	44936.9			1.88949			0.944746	+	0.327803i	$0.106308\pi$
$828$	5049.52	−	160.251i	0.211936	−	0.00672597i
$829$	−9240.93			−0.387154			−0.193577	−	0.981085i	$-0.562009\pi$
$829$	−9240.93			−0.387154			−0.193577	+	0.981085i	$0.562009\pi$
$830$	21653.4	−	24989.4i	0.905543	−	1.04505i
$831$	−29169.1	+	18745.9i	−1.21765	+	0.782535i
$832$	−4828.26	−	33581.3i	−0.201190	−	1.39931i
$833$	−5216.65	−	11422.9i	−0.216982	−	0.475125i
$834$	5357.82	−	37264.5i	0.222454	−	1.54720i
$835$	10297.5	−	3023.61i	0.426776	−	0.125313i
$836$	18662.0	+	11993.3i	0.772057	+	0.496171i
$837$	9207.13	−	20160.8i	0.380221	−	0.832568i
$838$	66800.8	+	19614.5i	2.75369	+	0.808557i
$839$	−21410.5	−	24709.1i	−0.881017	−	1.01675i	−0.999716	−	0.0238180i	$-0.992418\pi$
$839$	−21410.5	−	24709.1i	−0.881017	−	1.01675i	0.118699	−	0.992930i	$-0.462128\pi$
$840$	28187.8	+	32530.4i	1.15782	+	1.33620i
$841$	6962.07	+	2044.25i	0.285460	+	0.0838185i
$842$	18535.1	−	40586.2i	0.758624	−	1.66115i
$843$	−27426.9	−	17626.2i	−1.12056	−	0.720141i
$844$	−9027.22	+	2650.63i	−0.368163	+	0.108102i
$845$	3138.63	−	21829.6i	0.127778	−	0.888713i
$846$	626.393	+	1371.61i	0.0254561	+	0.0557410i
$847$	−1076.78	−	7489.19i	−0.0436821	−	0.303815i
$848$	−124952.	+	80301.7i	−5.05999	+	3.25186i
$849$	8390.14	−	9682.74i	0.339162	−	0.391414i
$850$	−36217.2			−1.46146
$851$	−1049.77	+	9412.11i	−0.0422862	+	0.379134i
$852$	−28255.2			−1.13616
$853$	−28689.4	+	33109.3i	−1.15159	+	1.32900i	−0.215803	+	0.976437i	$0.569237\pi$
$853$	−28689.4	+	33109.3i	−1.15159	+	1.32900i	−0.935786	+	0.352568i	$0.885309\pi$
$854$	−9102.92	+	5850.09i	−0.364749	+	0.234410i
$855$	304.657	+	2118.94i	0.0121860	+	0.0847557i
$856$	−29788.1	−	65226.8i	−1.18941	−	2.60445i
$857$	−655.392	+	4558.35i	−0.0261234	+	0.181692i	−0.998705	−	0.0508680i	$-0.983801\pi$
$857$	−655.392	+	4558.35i	−0.0261234	+	0.181692i	0.972582	+	0.232560i	$0.0747103\pi$
$858$	−14082.0	+	4134.86i	−0.560318	+	0.164524i
$859$	−14270.6	−	9171.16i	−0.566830	−	0.364279i	0.225621	−	0.974215i	$-0.427559\pi$
$859$	−14270.6	−	9171.16i	−0.566830	−	0.364279i	−0.792451	+	0.609936i	$0.791195\pi$
$860$	−28531.3	+	62474.8i	−1.13129	+	2.47718i
$861$	−12282.3	−	3606.40i	−0.486154	−	0.142748i
$862$	−16342.8	−	18860.6i	−0.645752	−	0.745238i
$863$	5942.70	+	6858.24i	0.234405	+	0.270518i	0.860750	−	0.509028i	$-0.169995\pi$
$863$	5942.70	+	6858.24i	0.234405	+	0.270518i	−0.626344	+	0.779546i	$0.715450\pi$
$864$	70790.4	+	20785.9i	2.78743	+	0.818462i
$865$	14140.8	−	30964.1i	0.555842	−	1.21712i
$866$	3307.60	+	2125.67i	0.129789	+	0.0834101i
$867$	−14113.7	+	4144.16i	−0.552857	+	0.162334i
$868$	3437.35	−	23907.3i	0.134414	−	0.934868i
$869$	7705.66	+	16873.0i	0.300802	+	0.658664i
$870$	8269.02	+	57512.3i	0.322237	+	2.24121i
$871$	−2542.53	+	1633.98i	−0.0989096	+	0.0635653i
$872$	55802.2	−	64399.2i	2.16709	−	2.50095i
$873$	823.953			0.0319434
$874$	−32976.8	−	8556.57i	−1.27627	−	0.331156i
$875$	−3597.87			−0.139006
$876$	−41000.7	+	47317.3i	−1.58138	+	1.82500i
$877$	13533.7	−	8697.61i	0.521097	−	0.334889i	−0.253509	−	0.967333i	$-0.581585\pi$
$877$	13533.7	−	8697.61i	0.521097	−	0.334889i	0.774606	+	0.632444i	$0.217948\pi$
$878$	3463.41	+	24088.6i	0.133126	+	0.925910i
$879$	−9824.24	−	21512.1i	−0.376978	−	0.825466i
$880$	−8656.71	+	60208.8i	−0.331611	+	2.30641i
$881$	−10952.6	+	3215.98i	−0.418845	+	0.122984i	−0.484363	−	0.874867i	$-0.660948\pi$
$881$	−10952.6	+	3215.98i	−0.418845	+	0.122984i	0.0655172	+	0.997851i	$0.479130\pi$
$882$	−2838.55	−	1824.22i	−0.108366	−	0.0696426i
$883$	−15603.9	+	34167.8i	−0.594693	+	1.30220i	0.337872	+	0.941192i	$0.390293\pi$
$883$	−15603.9	+	34167.8i	−0.594693	+	1.30220i	−0.932565	+	0.361003i	$0.882434\pi$
$884$	−25865.3	−	7594.74i	−0.984100	−	0.288958i
$885$	40312.7	+	46523.3i	1.53118	+	1.76708i
$886$	−23402.3	−	27007.7i	−0.887377	−	1.02409i
$887$	29621.4	+	8697.61i	1.12129	+	0.329242i	0.789280	−	0.614033i	$-0.210454\pi$
$887$	29621.4	+	8697.61i	1.12129	+	0.329242i	0.332014	+	0.943275i	$0.392272\pi$
$888$	−11966.5	+	26203.0i	−0.452219	+	0.990221i
$889$	−2285.49	−	1468.80i	−0.0862237	−	0.0554126i
$890$	64088.7	−	18818.1i	2.41377	−	0.708748i
$891$	1761.91	−	12254.3i	0.0662471	−	0.460759i
$892$	4257.12	+	9321.78i	0.159797	+	0.349906i
$893$	−1042.37	−	7249.84i	−0.0390611	−	0.271676i
$894$	58360.5	−	37506.0i	2.18330	−	1.40312i
$895$	−43945.5	+	50715.8i	−1.64127	+	1.89412i
$896$	15991.9			0.596263
$897$	13372.9	−	9206.43i	0.497781	−	0.342691i
$898$	−70.5829			−0.00262292
$899$	13060.5	−	15072.6i	0.484528	−	0.559175i
$900$	−5896.85	+	3789.68i	−0.218402	+	0.140358i
$901$	4780.29	+	33247.6i	0.176753	+	1.22934i
$902$	−13845.0	−	30316.4i	−0.511074	−	1.11910i
$903$	1089.62	−	7578.46i	0.0401553	−	0.279286i
$904$	−48560.9	+	14258.8i	−1.78663	+	0.524602i
$905$	55046.0	+	35375.9i	2.02187	+	1.29938i
$906$	10491.5	−	22973.2i	0.384722	−	0.842423i
$907$	14858.7	+	4362.91i	0.543963	+	0.159722i	0.542158	−	0.840276i	$-0.317607\pi$
$907$	14858.7	+	4362.91i	0.543963	+	0.159722i	0.00180498	+	0.999998i	$0.499425\pi$
$908$	−44350.4	−	51183.1i	−1.62095	−	1.87067i
$909$	−863.573	−	996.616i	−0.0315103	−	0.0363649i
$910$	−19467.3	−	5716.11i	−0.709158	−	0.208228i
$911$	2955.14	−	6470.86i	0.107473	−	0.235334i	−0.848253	−	0.529592i	$-0.822345\pi$
$911$	2955.14	−	6470.86i	0.107473	−	0.235334i	0.955726	+	0.294258i	$0.0950724\pi$
$912$	−47316.7	−	30408.6i	−1.71800	−	1.10409i
$913$	−6632.81	+	1947.57i	−0.240432	+	0.0705971i
$914$	−3539.18	+	24615.5i	−0.128081	+	0.890820i
$915$	9066.96	+	19853.9i	0.327590	+	0.717321i
$916$	11315.9	+	78703.5i	0.408173	+	2.83891i
$917$	−5425.53	+	3486.78i	−0.195384	+	0.125566i
$918$	22542.2	−	26015.1i	0.810463	−	0.935324i
$919$	28732.6			1.03134			0.515669	−	0.856788i	$-0.327543\pi$
$919$	28732.6			1.03134			0.515669	+	0.856788i	$0.327543\pi$
$920$	−21526.9	−	122091.i	−0.771434	−	4.37523i
$921$	28207.4			1.00919
$922$	−26979.9	+	31136.5i	−0.963706	+	1.11218i
$923$	6853.65	−	4404.57i	0.244410	−	0.157073i
$924$	−2093.61	−	14561.4i	−0.0745398	−	0.518436i
$925$	−5458.56	−	11952.6i	−0.194029	−	0.424863i
$926$	2302.60	−	16014.9i	0.0817151	−	0.568341i
$927$	−2394.85	+	703.192i	−0.0848514	+	0.0249146i
$928$	55850.5	+	35892.9i	1.97563	+	1.26966i
$929$	4801.42	−	10513.7i	0.169569	−	0.371304i	−0.805701	−	0.592323i	$-0.798211\pi$
$929$	4801.42	−	10513.7i	0.169569	−	0.371304i	0.975270	+	0.221019i	$0.0709382\pi$
$930$	−64896.5	−	19055.3i	−2.28822	−	0.671881i
$931$	10733.1	+	12386.7i	0.377833	+	0.436043i
$932$	−9963.49	−	11498.5i	−0.350177	−	0.404126i
$933$	−16363.3	−	4804.69i	−0.574179	−	0.168594i
$934$	−41258.8	+	90344.2i	−1.44543	+	3.16505i
$935$	11572.2	+	7437.03i	0.404762	+	0.260125i
$936$	−4251.29	+	1248.29i	−0.148459	+	0.0435916i
$937$	−1372.55	+	9546.29i	−0.0478540	+	0.332832i	0.951805	+	0.306705i	$0.0992265\pi$
$937$	−1372.55	+	9546.29i	−0.0478540	+	0.332832i	−0.999659	+	0.0261269i	$0.991683\pi$
$938$	−1747.13	−	3825.67i	−0.0608163	−	0.133169i
$939$	4842.98	+	33683.7i	0.168312	+	1.17063i
$940$	36654.5	−	23556.4i	1.27185	−	0.817369i
$941$	9454.27	−	10910.8i	0.327524	−	0.377983i	−0.567975	−	0.823046i	$-0.692273\pi$
$941$	9454.27	−	10910.8i	0.327524	−	0.377983i	0.895500	+	0.445062i	$0.146819\pi$
$942$	−53856.8			−1.86279
$943$	25015.4	+	27083.5i	0.863854	+	0.935271i
$944$	145117.			5.00333
$945$	12220.9	−	14103.7i	0.420684	−	0.485496i
$946$	16769.7	−	10777.2i	0.576353	−	0.370400i
$947$	6382.72	+	44392.8i	0.219018	+	1.52331i	0.741673	+	0.670762i	$0.234033\pi$
$947$	6382.72	+	44392.8i	0.219018	+	1.52331i	−0.522654	+	0.852545i	$0.675058\pi$
$948$	−42386.1	−	92812.7i	−1.45215	−	3.17976i
$949$	2569.15	−	17868.8i	0.0878799	−	0.611218i
$950$	45354.8	−	13317.4i	1.54895	−	0.454813i
$951$	−5332.59	−	3427.05i	−0.181831	−	0.116856i
$952$	9532.47	−	20873.2i	0.324526	−	0.710614i
$953$	−54025.8	−	15863.4i	−1.83638	−	0.539209i	−0.836417	−	0.548094i	$-0.815353\pi$
$953$	−54025.8	−	15863.4i	−1.83638	−	0.539209i	−0.999961	+	0.00888538i	$0.997172\pi$
$954$	5910.34	+	6820.89i	0.200581	+	0.231483i
$955$	−48795.8	−	56313.4i	−1.65340	−	1.90812i
$956$	−36603.7	−	10747.8i	−1.23834	−	0.363608i
$957$	5046.20	−	11049.6i	0.170450	−	0.373233i
$958$	57666.5	+	37060.0i	1.94480	+	1.24985i
$959$	13848.5	−	4066.28i	0.466310	−	0.136921i
$960$	13552.5	−	94259.8i	0.455631	−	3.16898i
$961$	−2731.40	−	5980.92i	−0.0916853	−	0.200763i
$962$	−1932.36	−	13439.9i	−0.0647628	−	0.450435i
$963$	−1989.53	+	1278.60i	−0.0665751	+	0.0427852i
$964$	−46111.1	+	53215.1i	−1.54060	+	1.77795i
$965$	50187.2			1.67418
$966$	10032.6	+	20243.1i	0.334154	+	0.674236i
$967$	30681.6			1.02033			0.510163	−	0.860078i	$-0.329585\pi$
$967$	30681.6			1.02033			0.510163	+	0.860078i	$0.329585\pi$
$968$	−43407.0	+	50094.3i	−1.44127	+	1.66332i
$969$	−10700.5	+	6876.76i	−0.354745	+	0.227981i
$970$	−4704.03	−	32717.2i	−0.155708	−	1.08298i
$971$	−13423.5	−	29393.4i	−0.443647	−	0.971450i	−0.990915	−	0.134493i	$-0.957059\pi$
$971$	−13423.5	−	29393.4i	−0.443647	−	0.971450i	0.547268	−	0.836957i	$-0.315668\pi$
$972$	1824.17	−	12687.4i	0.0601958	−	0.418671i
$973$	−10440.0	+	3065.45i	−0.343977	+	0.101001i
$974$	−87135.8	−	55998.8i	−2.86654	−	1.84221i
$975$	−9357.81	+	20490.7i	−0.307374	+	0.673055i
$976$	49368.0	+	14495.7i	1.61909	+	0.475407i
$977$	22272.7	+	25704.1i	0.729342	+	0.841706i	0.992397	−	0.123075i	$-0.0392755\pi$
$977$	22272.7	+	25704.1i	0.729342	+	0.841706i	−0.263055	+	0.964781i	$0.584730\pi$
$978$	−4857.53	−	5605.88i	−0.158821	−	0.183289i
$979$	−13398.6	−	3934.19i	−0.437407	−	0.128434i
$980$	−40503.0	+	88689.3i	−1.32023	+	2.89089i
$981$	−2364.25	−	1519.41i	−0.0769467	−	0.0494506i
$982$	−20549.5	+	6033.89i	−0.667782	+	0.196078i
$983$	−2761.82	+	19208.9i	−0.0896118	+	0.623264i	0.894679	+	0.446709i	$0.147404\pi$
$983$	−2761.82	+	19208.9i	−0.0896118	+	0.623264i	−0.984291	+	0.176554i	$0.943505\pi$
$984$	46585.6	+	102008.i	1.50924	+	3.30478i
$985$	−11849.3	−	82413.7i	−0.383300	−	2.66591i
$986$	26058.1	−	16746.5i	0.841641	−	0.540890i
$987$	−3180.79	+	3670.83i	−0.102579	+	0.118383i
$988$	35183.7			1.13294
$989$	−13904.9	+	17115.3i	−0.447068	+	0.550287i
$990$	3696.15			0.118658
$991$	9881.56	−	11403.9i	0.316749	−	0.365548i	−0.574941	−	0.818195i	$-0.694975\pi$
$991$	9881.56	−	11403.9i	0.316749	−	0.365548i	0.891690	+	0.452647i	$0.149520\pi$
$992$	−65013.4	+	41781.6i	−2.08082	+	1.33726i
$993$	3095.83	+	21532.0i	0.0989357	+	0.688113i
$994$	4709.56	+	10312.5i	0.150280	+	0.329067i
$995$	−3562.04	+	24774.5i	−0.113492	+	0.789351i
$996$	36484.8	−	10712.9i	1.16071	−	0.340814i
$997$	−45081.2	−	28971.9i	−1.43203	−	0.920311i	−0.999828	−	0.0185350i	$-0.994100\pi$
$997$	−45081.2	−	28971.9i	−1.43203	−	0.920311i	−0.432204	−	0.901776i	$-0.642264\pi$
$998$	−3453.53	+	7562.17i	−0.109539	+	0.239856i
$999$	11983.2	+	3518.57i	0.379510	+	0.111434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.4.c.a.16.5	yes	50
3.2	odd	2		207.4.i.a.154.1		50
23.6	even	11		529.4.a.n.1.1		25
23.13	even	11	inner	23.4.c.a.13.5	✓	50
23.17	odd	22		529.4.a.m.1.1		25
69.59	odd	22		207.4.i.a.82.1		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.13.5	✓	50	23.13	even	11	inner
23.4.c.a.16.5	yes	50	1.1	even	1	trivial
207.4.i.a.82.1		50	69.59	odd	22
207.4.i.a.154.1		50	3.2	odd	2
529.4.a.m.1.1		25	23.17	odd	22
529.4.a.n.1.1		25	23.6	even	11

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(3.50231 - 4.04189i) q^{2} +(-4.18746 + 2.69112i) q^{3} +(-2.93212 - 20.3933i) q^{4} +(6.92690 + 15.1678i) q^{5} +(-3.78861 + 26.3504i) q^{6} +(7.38228 - 2.16763i) q^{7} +(-56.7033 - 36.4410i) q^{8} +(-0.923481 + 2.02214i) q^{9} +(85.5667 + 25.1246i) q^{10} +(-12.2093 - 14.0903i) q^{11} +(67.1590 + 77.5057i) q^{12} +(-28.3722 - 8.33084i) q^{13} +(17.0937 - 37.4301i) q^{14} +(-69.8245 - 44.8735i) q^{15} +(-187.736 + 55.1241i) q^{16} +(-6.29713 + 43.7975i) q^{17} +(4.93894 + 10.8148i) q^{18} +(-8.21881 - 57.1631i) q^{19} +(289.011 - 185.736i) q^{20} +(-25.0797 + 28.9435i) q^{21} -99.7120 q^{22} +(104.797 - 34.4177i) q^{23} +335.510 q^{24} +(-100.222 + 115.663i) q^{25} +(-133.041 + 85.5001i) q^{26} +(-20.7014 - 143.981i) q^{27} +(-65.8510 - 144.194i) q^{28} +(18.6280 - 129.561i) q^{29} +(-425.921 + 125.062i) q^{30} +(128.180 + 82.3762i) q^{31} +(-210.700 + 461.369i) q^{32} +(89.0446 + 26.1458i) q^{33} +(154.970 + 178.845i) q^{34} +(84.0146 + 96.9580i) q^{35} +(43.9460 + 12.9037i) q^{36} +(-35.6666 + 78.0990i) q^{37} +(-259.831 - 166.984i) q^{38} +(141.227 - 41.4680i) q^{39} +(159.952 - 1112.49i) q^{40} +(138.850 + 304.039i) q^{41} +(29.1494 + 202.738i) q^{42} +(-168.181 + 108.084i) q^{43} +(-251.549 + 290.303i) q^{44} -37.0683 q^{45} +(227.920 - 544.119i) q^{46} +126.827 q^{47} +(637.790 - 736.049i) q^{48} +(-238.750 + 153.436i) q^{49} +(116.486 + 810.176i) q^{50} +(-91.4953 - 200.347i) q^{51} +(-86.7029 + 603.032i) q^{52} +(728.372 - 213.869i) q^{53} +(-654.459 - 420.595i) q^{54} +(129.146 - 282.790i) q^{55} +(-497.591 - 146.106i) q^{56} +(188.249 + 217.250i) q^{57} +(-458.429 - 529.055i) q^{58} +(-711.630 - 208.953i) q^{59} +(-710.386 + 1555.53i) q^{60} +(-221.221 - 142.170i) q^{61} +(781.881 - 229.581i) q^{62} +(-2.43414 + 16.9298i) q^{63} +(476.619 + 1043.65i) q^{64} +(-70.1712 - 488.051i) q^{65} +(417.541 - 268.337i) q^{66} +(66.9323 - 77.2440i) q^{67} +911.641 q^{68} +(-346.212 + 426.144i) q^{69} +686.139 q^{70} +(-180.423 + 208.219i) q^{71} +(126.053 - 81.0095i) q^{72} +(86.8834 + 604.287i) q^{73} +(190.752 + 417.688i) q^{74} +(108.415 - 754.045i) q^{75} +(-1141.65 + 335.218i) q^{76} +(-120.675 - 77.5531i) q^{77} +(327.012 - 716.057i) q^{78} +(-954.614 - 280.300i) q^{79} +(-2136.54 - 2465.69i) q^{80} +(434.851 + 501.845i) q^{81} +(1715.19 + 503.625i) q^{82} +(154.027 - 337.272i) q^{83} +(663.791 + 426.593i) q^{84} +(-707.931 + 207.867i) q^{85} +(-152.162 + 1058.31i) q^{86} +(270.659 + 592.661i) q^{87} +(178.844 + 1243.88i) q^{88} +(630.092 - 404.935i) q^{89} +(-129.825 + 149.826i) q^{90} -227.510 q^{91} +(-1009.17 - 2036.24i) q^{92} -758.432 q^{93} +(444.189 - 512.621i) q^{94} +(810.107 - 520.624i) q^{95} +(-359.300 - 2498.99i) q^{96} +(-153.971 - 337.150i) q^{97} +(-216.010 + 1502.38i) q^{98} +(39.7676 - 11.6768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - 11 q^{2} - 13 q^{3} - 27 q^{4} - 19 q^{5} - 4 q^{6} - 19 q^{7} + 28 q^{8} + 24 q^{9} + 47 q^{10} - 53 q^{11} + 36 q^{12} - 65 q^{13} + 117 q^{14} - 425 q^{15} - 499 q^{16} - 117 q^{17} + 24 q^{18}+ \cdots - 755 q^{99}+O(q^{100}) \) 50 * q - 11 * q^2 - 13 * q^3 - 27 * q^4 - 19 * q^5 - 4 * q^6 - 19 * q^7 + 28 * q^8 + 24 * q^9 + 47 * q^10 - 53 * q^11 + 36 * q^12 - 65 * q^13 + 117 * q^14 - 425 * q^15 - 499 * q^16 - 117 * q^17 + 24 * q^18 + 73 * q^19 + 529 * q^20 + 429 * q^21 + 310 * q^22 + 542 * q^23 + 1606 * q^24 + 246 * q^25 + 324 * q^26 + 65 * q^27 - 677 * q^28 - 497 * q^29 - 1041 * q^30 - 471 * q^31 - 915 * q^32 - 391 * q^33 - 2751 * q^34 - 737 * q^35 - 1865 * q^36 - 1071 * q^37 - 1504 * q^38 + 127 * q^39 + 1479 * q^40 + 569 * q^41 + 3059 * q^42 + 1615 * q^43 + 2518 * q^44 + 2768 * q^45 + 4041 * q^46 + 2904 * q^47 + 2702 * q^48 + 1226 * q^49 + 1322 * q^50 + 589 * q^51 - 2156 * q^52 + 391 * q^53 - 5862 * q^54 - 3323 * q^55 - 7028 * q^56 - 7623 * q^57 - 5639 * q^58 - 2445 * q^59 - 3157 * q^60 - 1059 * q^61 + 1468 * q^62 + 3155 * q^63 + 4570 * q^64 + 2641 * q^65 + 5206 * q^66 + 27 * q^67 + 8350 * q^68 + 4005 * q^69 + 9702 * q^70 + 3465 * q^71 + 5629 * q^72 + 435 * q^73 - 994 * q^74 - 7819 * q^75 - 3598 * q^76 - 5931 * q^77 - 8996 * q^78 - 2559 * q^79 - 14052 * q^80 - 4788 * q^81 - 3822 * q^82 - 3967 * q^83 - 8427 * q^84 + 299 * q^85 + 721 * q^86 + 8363 * q^87 + 5825 * q^88 + 3717 * q^89 + 16742 * q^90 + 7238 * q^91 + 9550 * q^92 + 12750 * q^93 + 6035 * q^94 + 4551 * q^95 + 2493 * q^96 - 2419 * q^97 - 5687 * q^98 - 755 * q^99

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