LMFDB - Embedded newform 63.4.s.a.47.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(47,63)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("63.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			47.12
Character	$\chi$	$=$	63.47
Dual form			63.4.s.a.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.647627 - 0.373907i) q^{2} +(4.16400 - 3.10824i) q^{3} +(-3.72039 + 6.44390i) q^{4} +8.70220 q^{5} +(1.53452 - 3.56993i) q^{6} +(18.2993 + 2.85258i) q^{7} +11.5468i q^{8} +(7.67775 - 25.8854i) q^{9} +O(q^{10})$	\(q+(0.647627 - 0.373907i) q^{2} +(4.16400 - 3.10824i) q^{3} +(-3.72039 + 6.44390i) q^{4} +8.70220 q^{5} +(1.53452 - 3.56993i) q^{6} +(18.2993 + 2.85258i) q^{7} +11.5468i q^{8} +(7.67775 - 25.8854i) q^{9} +(5.63577 - 3.25382i) q^{10} -41.5070i q^{11} +(4.53747 + 38.3962i) q^{12} +(-33.0053 + 19.0556i) q^{13} +(12.9177 - 4.99482i) q^{14} +(36.2359 - 27.0485i) q^{15} +(-25.4456 - 44.0731i) q^{16} +(39.9685 + 69.2274i) q^{17} +(-4.70642 - 19.6348i) q^{18} +(-49.4113 - 28.5276i) q^{19} +(-32.3755 + 56.0761i) q^{20} +(85.0645 - 45.0003i) q^{21} +(-15.5198 - 26.8811i) q^{22} +177.014i q^{23} +(35.8903 + 48.0810i) q^{24} -49.2718 q^{25} +(-14.2501 + 24.6818i) q^{26} +(-48.4877 - 131.651i) q^{27} +(-86.4620 + 107.306i) q^{28} +(-60.1430 - 34.7236i) q^{29} +(13.3537 - 31.0662i) q^{30} +(-225.864 - 130.403i) q^{31} +(-112.957 - 65.2160i) q^{32} +(-129.014 - 172.835i) q^{33} +(51.7693 + 29.8890i) q^{34} +(159.244 + 24.8237i) q^{35} +(138.238 + 145.778i) q^{36} +(-74.9359 + 129.793i) q^{37} -42.6668 q^{38} +(-78.2046 + 181.936i) q^{39} +100.483i q^{40} +(-54.7122 - 94.7643i) q^{41} +(38.2641 - 60.9496i) q^{42} +(124.193 - 215.108i) q^{43} +(267.467 + 154.422i) q^{44} +(66.8133 - 225.260i) q^{45} +(66.1867 + 114.639i) q^{46} +(147.528 + 255.526i) q^{47} +(-242.945 - 104.429i) q^{48} +(326.726 + 104.400i) q^{49} +(-31.9097 + 18.4231i) q^{50} +(381.604 + 164.031i) q^{51} -283.577i q^{52} +(263.613 - 152.197i) q^{53} +(-80.6271 - 67.1307i) q^{54} -361.202i q^{55} +(-32.9382 + 211.299i) q^{56} +(-294.419 + 34.7930i) q^{57} -51.9336 q^{58} +(360.346 - 624.138i) q^{59} +(39.4860 + 334.131i) q^{60} +(-561.494 + 324.179i) q^{61} -195.034 q^{62} +(214.337 - 451.782i) q^{63} +309.591 q^{64} +(-287.218 + 165.826i) q^{65} +(-148.177 - 63.6935i) q^{66} +(97.4263 - 168.747i) q^{67} -594.793 q^{68} +(550.200 + 737.084i) q^{69} +(112.412 - 43.4659i) q^{70} -98.7349i q^{71} +(298.894 + 88.6537i) q^{72} +(226.289 - 130.648i) q^{73} +112.076i q^{74} +(-205.168 + 153.148i) q^{75} +(367.658 - 212.268i) q^{76} +(118.402 - 759.548i) q^{77} +(17.3797 + 147.068i) q^{78} +(577.124 + 999.608i) q^{79} +(-221.433 - 383.533i) q^{80} +(-611.104 - 397.483i) q^{81} +(-70.8661 - 40.9146i) q^{82} +(-285.406 + 494.337i) q^{83} +(-26.4957 + 715.566i) q^{84} +(347.813 + 602.431i) q^{85} -185.746i q^{86} +(-358.365 + 42.3497i) q^{87} +479.275 q^{88} +(89.5115 - 155.038i) q^{89} +(-40.9561 - 170.866i) q^{90} +(-658.330 + 254.553i) q^{91} +(-1140.66 - 658.559i) q^{92} +(-1345.82 + 159.042i) q^{93} +(191.086 + 110.324i) q^{94} +(-429.987 - 248.253i) q^{95} +(-673.061 + 79.5390i) q^{96} +(-956.569 - 552.275i) q^{97} +(250.632 - 54.5529i) q^{98} +(-1074.42 - 318.681i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) $ 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.647627	−	0.373907i	0.228971	−	0.132196i	−0.381126	−	0.924523i	$-0.624464\pi$
$2$	0.647627	−	0.373907i	0.228971	−	0.132196i	0.610097	+	0.792327i	$0.291130\pi$
$3$	4.16400	−	3.10824i	0.801362	−	0.598180i
$3$	4.16400	−	3.10824i	0.801362	−	0.598180i
$4$	−3.72039	+	6.44390i	−0.465048	+	0.805487i
$5$	8.70220			0.778348			0.389174	−	0.921164i	$-0.372760\pi$
$5$	8.70220			0.778348			0.389174	+	0.921164i	$0.372760\pi$
$6$	1.53452	−	3.56993i	0.104411	−	0.242903i
$7$	18.2993	+	2.85258i	0.988067	+	0.154025i
$7$	18.2993	+	2.85258i	0.988067	+	0.154025i
$8$			11.5468i			0.510303i
$9$	7.67775	−	25.8854i	0.284361	−	0.958717i
$10$	5.63577	−	3.25382i	0.178219	−	0.102895i
$11$		−	41.5070i		−	1.13771i	−0.822437	−	0.568856i	$-0.807386\pi$
$11$		−	41.5070i		−	1.13771i	0.822437	−	0.568856i	$-0.192614\pi$
$12$	4.53747	+	38.3962i	0.109155	+	0.923669i
$13$	−33.0053	+	19.0556i	−0.704155	+	0.406544i	−0.808893	−	0.587956i	$-0.799933\pi$
$13$	−33.0053	+	19.0556i	−0.704155	+	0.406544i	0.104738	+	0.994500i	$0.466600\pi$
$14$	12.9177	−	4.99482i	0.246600	−	0.0953516i
$15$	36.2359	−	27.0485i	0.623738	−	0.465592i
$16$	−25.4456	−	44.0731i	−0.397588	−	0.688643i
$17$	39.9685	+	69.2274i	0.570222	+	0.987654i	0.996543	+	0.0830818i	$0.0264763\pi$
$17$	39.9685	+	69.2274i	0.570222	+	0.987654i	−0.426320	+	0.904572i	$0.640190\pi$
$18$	−4.70642	−	19.6348i	−0.0616285	−	0.257110i
$19$	−49.4113	−	28.5276i	−0.596617	−	0.344457i	0.171092	−	0.985255i	$-0.445270\pi$
$19$	−49.4113	−	28.5276i	−0.596617	−	0.344457i	−0.767710	+	0.640798i	$0.778604\pi$
$20$	−32.3755	+	56.0761i	−0.361969	+	0.626949i
$21$	85.0645	−	45.0003i	0.883933	−	0.467613i
$22$	−15.5198	−	26.8811i	−0.150401	−	0.260503i
$23$			177.014i			1.60478i	0.596802	+	0.802389i	$0.296438\pi$
$23$			177.014i			1.60478i	−0.596802	+	0.802389i	$0.703562\pi$
$24$	35.8903	+	48.0810i	0.305253	+	0.408937i
$25$	−49.2718			−0.394174
$26$	−14.2501	+	24.6818i	−0.107487	+	0.186173i
$27$	−48.4877	−	131.651i	−0.345610	−	0.938378i
$28$	−86.4620	+	107.306i	−0.583564	+	0.724247i
$29$	−60.1430	−	34.7236i	−0.385113	−	0.222345i	0.294927	−	0.955520i	$-0.404705\pi$
$29$	−60.1430	−	34.7236i	−0.385113	−	0.222345i	−0.680041	+	0.733174i	$0.738038\pi$
$30$	13.3537	−	31.0662i	0.0812682	−	0.189063i
$31$	−225.864	−	130.403i	−1.30859	−	0.755517i	−0.326732	−	0.945117i	$-0.605947\pi$
$31$	−225.864	−	130.403i	−1.30859	−	0.755517i	−0.981861	+	0.189601i	$0.939281\pi$
$32$	−112.957	−	65.2160i	−0.624007	−	0.360271i
$33$	−129.014	−	172.835i	−0.680557	−	0.911720i
$34$	51.7693	+	29.8890i	0.261128	+	0.150762i
$35$	159.244	+	24.8237i	0.769060	+	0.119885i
$36$	138.238	+	145.778i	0.639993	+	0.674899i
$37$	−74.9359	+	129.793i	−0.332957	+	0.576698i	−0.983090	−	0.183122i	$-0.941380\pi$
$37$	−74.9359	+	129.793i	−0.332957	+	0.576698i	0.650134	+	0.759820i	$0.274713\pi$
$38$	−42.6668			−0.182144
$39$	−78.2046	+	181.936i	−0.321096	+	0.747000i
$40$			100.483i			0.397193i
$41$	−54.7122	−	94.7643i	−0.208405	−	0.360968i	0.742807	−	0.669505i	$-0.233494\pi$
$41$	−54.7122	−	94.7643i	−0.208405	−	0.360968i	−0.951212	+	0.308537i	$0.900161\pi$
$42$	38.2641	−	60.9496i	0.140578	−	0.223922i
$43$	124.193	−	215.108i	0.440446	−	0.762875i	−0.557276	−	0.830327i	$-0.688154\pi$
$43$	124.193	−	215.108i	0.440446	−	0.762875i	0.997723	+	0.0674517i	$0.0214869\pi$
$44$	267.467	+	154.422i	0.916413	+	0.529092i
$45$	66.8133	−	225.260i	0.221332	−	0.746216i
$46$	66.1867	+	114.639i	0.212146	+	0.367447i
$47$	147.528	+	255.526i	0.457855	+	0.793029i	0.998847	−	0.0479988i	$-0.0152844\pi$
$47$	147.528	+	255.526i	0.457855	+	0.793029i	−0.540992	+	0.841028i	$0.681951\pi$
$48$	−242.945	−	104.429i	−0.730544	−	0.314023i
$49$	326.726	+	104.400i	0.952553	+	0.304373i
$50$	−31.9097	+	18.4231i	−0.0902543	+	0.0521084i
$51$	381.604	+	164.031i	1.04775	+	0.450372i
$52$		−	283.577i		−	0.756251i
$53$	263.613	−	152.197i	0.683208	−	0.394450i	−0.117855	−	0.993031i	$-0.537602\pi$
$53$	263.613	−	152.197i	0.683208	−	0.394450i	0.801062	+	0.598581i	$0.204268\pi$
$54$	−80.6271	−	67.1307i	−0.203185	−	0.169173i
$55$		−	361.202i		−	0.885537i
$56$	−32.9382	+	211.299i	−0.0785992	+	0.504214i
$57$	−294.419	+	34.7930i	−0.684154	+	0.0808499i
$58$	−51.9336			−0.117573
$59$	360.346	−	624.138i	0.795137	−	1.37722i	−0.127615	−	0.991824i	$-0.540732\pi$
$59$	360.346	−	624.138i	0.795137	−	1.37722i	0.922752	−	0.385394i	$-0.125935\pi$
$60$	39.4860	+	334.131i	0.0849603	+	0.718936i
$61$	−561.494	+	324.179i	−1.17856	+	0.680440i	−0.955680	−	0.294407i	$-0.904878\pi$
$61$	−561.494	+	324.179i	−1.17856	+	0.680440i	−0.222876	+	0.974847i	$0.571544\pi$
$62$	−195.034			−0.399506
$63$	214.337	−	451.782i	0.428634	−	0.903478i
$64$	309.591			0.604671
$65$	−287.218	+	165.826i	−0.548078	+	0.316433i
$66$	−148.177	−	63.6935i	−0.276353	−	0.118790i
$67$	97.4263	−	168.747i	0.177649	−	0.307698i	−0.763426	−	0.645896i	$-0.776484\pi$
$67$	97.4263	−	168.747i	0.177649	−	0.307698i	0.941075	+	0.338198i	$0.109817\pi$
$68$	−594.793			−1.06072
$69$	550.200	+	737.084i	0.959946	+	1.28601i
$70$	112.412	−	43.4659i	0.191940	−	0.0742168i
$71$		−	98.7349i		−	0.165038i	−0.996590	−	0.0825188i	$-0.973704\pi$
$71$		−	98.7349i		−	0.165038i	0.996590	−	0.0825188i	$-0.0262965\pi$
$72$	298.894	+	88.6537i	0.489236	+	0.145110i
$73$	226.289	−	130.648i	0.362809	−	0.209468i	−0.307503	−	0.951547i	$-0.599493\pi$
$73$	226.289	−	130.648i	0.362809	−	0.209468i	0.670312	+	0.742079i	$0.266160\pi$
$74$			112.076i			0.176062i
$75$	−205.168	+	153.148i	−0.315876	+	0.235787i
$76$	367.658	−	212.268i	0.554912	−	0.320379i
$77$	118.402	−	759.548i	0.175236	−	1.12414i
$78$	17.3797	+	147.068i	0.0252290	+	0.213489i
$79$	577.124	+	999.608i	0.821918	+	1.42360i	0.904252	+	0.426999i	$0.140429\pi$
$79$	577.124	+	999.608i	0.821918	+	1.42360i	−0.0823344	+	0.996605i	$0.526238\pi$
$80$	−221.433	−	383.533i	−0.309462	−	0.536004i
$81$	−611.104	−	397.483i	−0.838278	−	0.545244i
$82$	−70.8661	−	40.9146i	−0.0954372	−	0.0551007i
$83$	−285.406	+	494.337i	−0.377438	+	0.653741i	−0.990689	−	0.136147i	$-0.956528\pi$
$83$	−285.406	+	494.337i	−0.377438	+	0.653741i	0.613251	+	0.789888i	$0.289861\pi$
$84$	−26.4957	+	715.566i	−0.0344157	+	0.929460i
$85$	347.813	+	602.431i	0.443831	+	0.768739i
$86$		−	185.746i		−	0.232901i
$87$	−358.365	+	42.3497i	−0.441617	+	0.0521881i
$88$	479.275			0.580578
$89$	89.5115	−	155.038i	0.106609	−	0.184652i	−0.807785	−	0.589477i	$-0.799334\pi$
$89$	89.5115	−	155.038i	0.106609	−	0.184652i	0.914394	+	0.404824i	$0.132667\pi$
$90$	−40.9561	−	170.866i	−0.0479684	−	0.200121i
$91$	−658.330	+	254.553i	−0.758370	+	0.293236i
$92$	−1140.66	−	658.559i	−1.29263	−	0.746299i
$93$	−1345.82	+	159.042i	−1.50059	+	0.177332i
$94$	191.086	+	110.324i	0.209671	+	0.121054i
$95$	−429.987	−	248.253i	−0.464376	−	0.268108i
$96$	−673.061	+	79.5390i	−0.715562	+	0.0845616i
$97$	−956.569	−	552.275i	−1.00129	−	0.578093i	−0.0926581	−	0.995698i	$-0.529536\pi$
$97$	−956.569	−	552.275i	−1.00129	−	0.578093i	−0.908629	+	0.417605i	$0.862870\pi$
$98$	250.632	−	54.5529i	0.258344	−	0.0562314i
$99$	−1074.42	−	318.681i	−1.09075	−	0.323521i
$100$	183.310	−	317.502i	0.183310	−	0.317502i
$101$	−0.750795			−0.000739672			−0.000369836	−	1.00000i	$-0.500118\pi$
$101$	−0.750795			−0.000739672			−0.000369836		1.00000i	$0.500118\pi$
$102$	308.469	−	36.4534i	0.299441	−	0.0353865i
$103$			753.027i			0.720369i	0.932881	+	0.360184i	$0.117286\pi$
$103$			753.027i			0.720369i	−0.932881	+	0.360184i	$0.882714\pi$
$104$	−220.032	−	381.107i	−0.207461	−	0.359332i
$105$	740.248	−	391.601i	0.688008	−	0.363965i
$106$	113.815	−	197.134i	0.104290	−	0.180635i
$107$	1089.54	+	629.045i	0.984388	+	0.568337i	0.903592	−	0.428394i	$-0.140920\pi$
$107$	1089.54	+	629.045i	0.984388	+	0.568337i	0.0807962	+	0.996731i	$0.474254\pi$
$108$	1028.74	+	177.342i	0.916577	+	0.158007i
$109$	−110.812	−	191.932i	−0.0973748	−	0.168658i	0.813222	−	0.581953i	$-0.197711\pi$
$109$	−110.812	−	191.932i	−0.0973748	−	0.168658i	−0.910597	+	0.413295i	$0.864378\pi$
$110$	−135.056	−	233.924i	−0.117065	−	0.202762i
$111$	91.3937	+	773.376i	0.0781505	+	0.661311i
$112$	−339.914	−	879.091i	−0.286776	−	0.741664i
$113$	1345.36	−	776.746i	1.12001	−	0.646638i	0.178607	−	0.983921i	$-0.442841\pi$
$113$	1345.36	−	776.746i	1.12001	−	0.646638i	0.941404	+	0.337282i	$0.109508\pi$
$114$	−177.664	+	132.618i	−0.145963	+	0.108955i
$115$			1540.41i			1.24908i
$116$	447.511	−	258.370i	0.358192	−	0.206803i
$117$	239.855	+	1000.66i	0.189527	+	0.790691i
$118$		−	538.945i		−	0.420457i
$119$	533.917	+	1380.82i	0.411295	+	1.06370i
$120$	312.324	+	418.410i	0.237593	+	0.318296i
$121$	−391.834			−0.294391
$122$	−242.426	+	419.893i	−0.179903	+	0.311601i
$123$	−522.371	−	224.540i	−0.382932	−	0.164602i
$124$	1680.60	−	970.297i	1.21712	−	0.702703i
$125$	−1516.55			−1.08515
$126$	−30.1141	−	372.728i	−0.0212919	−	0.263534i
$127$	2425.06			1.69440			0.847202	−	0.531271i	$-0.178285\pi$
$127$	2425.06			1.69440			0.847202	+	0.531271i	$0.178285\pi$
$128$	1104.16	−	637.486i	0.762459	−	0.440206i
$129$	−151.468	−	1281.73i	−0.103380	−	0.874805i
$130$	−124.007	+	214.786i	−0.0836624	+	0.144908i
$131$	−48.8347			−0.0325703			−0.0162851	−	0.999867i	$-0.505184\pi$
$131$	−48.8347			−0.0325703			−0.0162851	+	0.999867i	$0.505184\pi$
$132$	1593.71	−	188.337i	1.05087	−	0.124187i
$133$	−822.813	−	662.984i	−0.536443	−	0.432241i
$134$		−	145.714i		−	0.0939384i
$135$	−421.949	−	1145.65i	−0.269005	−	0.730385i
$136$	−799.358	+	461.510i	−0.504003	+	0.290986i
$137$			1532.32i			0.955583i	0.878473	+	0.477792i	$0.158563\pi$
$137$			1532.32i			0.955583i	−0.878473	+	0.477792i	$0.841437\pi$
$138$	631.925	+	271.631i	0.389805	+	0.167557i
$139$	638.674	−	368.739i	0.389724	−	0.225007i	−0.292317	−	0.956322i	$-0.594426\pi$
$139$	638.674	−	368.739i	0.389724	−	0.225007i	0.682040	+	0.731314i	$0.261093\pi$
$140$	−752.409	+	933.797i	−0.454216	+	0.563716i
$141$	1408.54	+	605.459i	0.841282	+	0.361623i
$142$	−36.9177	−	63.9433i	−0.0218174	−	0.0377888i
$143$	790.942	+	1369.95i	0.462531	+	0.801126i
$144$	−1336.21	+	320.287i	−0.773272	+	0.185351i
$145$	−523.376	−	302.172i	−0.299752	−	0.173062i
$146$	97.7003	−	169.222i	0.0553817	−	0.0959240i
$147$	1684.98	−	580.819i	0.945409	−	0.325885i
$148$	−557.581	−	965.759i	−0.309682	−	0.536385i
$149$		−	1475.76i		−	0.811400i	−0.914006	−	0.405700i	$-0.867028\pi$
$149$		−	1475.76i		−	0.811400i	0.914006	−	0.405700i	$-0.132972\pi$
$150$	−75.6087	+	175.897i	−0.0411562	+	0.0957460i
$151$	−1274.88			−0.687073			−0.343536	−	0.939139i	$-0.611625\pi$
$151$	−1274.88			−0.687073			−0.343536	+	0.939139i	$0.611625\pi$
$152$	329.404	−	570.544i	0.175778	−	0.304456i
$153$	2098.85	−	503.088i	1.10903	−	0.265832i
$154$	−207.320	−	536.175i	−0.108483	−	0.280560i
$155$	−1965.51	−	1134.79i	−1.01854	−	0.588055i
$156$	−881.423	−	1180.81i	−0.452374	−	0.606030i
$157$	−1718.19	−	991.999i	−0.873418	−	0.504268i	−0.00493568	−	0.999988i	$-0.501571\pi$
$157$	−1718.19	−	991.999i	−0.873418	−	0.504268i	−0.868483	+	0.495719i	$0.834904\pi$
$158$	747.522	+	431.582i	0.376390	+	0.217309i
$159$	624.619	−	1453.12i	0.311544	−	0.724778i
$160$	−982.977	−	567.522i	−0.485695	−	0.280416i
$161$	−504.945	+	3239.22i	−0.247175	+	1.58563i
$162$	−544.389	−	28.9239i	−0.264020	−	0.0140276i
$163$	−1836.59	+	3181.06i	−0.882532	+	1.52859i	−0.0340145	+	0.999421i	$0.510829\pi$
$163$	−1836.59	+	3181.06i	−0.882532	+	1.52859i	−0.848517	+	0.529168i	$0.822504\pi$
$164$	814.202			0.387674
$165$	−1122.70	−	1504.05i	−0.529710	−	0.709635i
$166$			426.861i			0.199583i
$167$	2007.55	+	3477.17i	0.930231	+	1.61121i	0.782925	+	0.622116i	$0.213727\pi$
$167$	2007.55	+	3477.17i	0.930231	+	1.61121i	0.147306	+	0.989091i	$0.452940\pi$
$168$	519.611	+	982.226i	0.238624	+	0.451074i
$169$	−372.268	+	644.787i	−0.169444	+	0.293485i
$170$	450.507	+	260.100i	0.203249	+	0.117346i
$171$	−1117.82	+	1060.00i	−0.499892	+	0.474037i
$172$	924.089	+	1600.57i	0.409658	+	0.709548i
$173$	−1046.75	−	1813.03i	−0.460019	−	0.796776i	0.538943	−	0.842342i	$-0.318824\pi$
$173$	−1046.75	−	1813.03i	−0.460019	−	0.796776i	−0.998961	+	0.0455667i	$0.985491\pi$
$174$	−216.252	+	161.422i	−0.0942183	+	0.0703297i
$175$	−901.637	−	140.552i	−0.389471	−	0.0607125i
$176$	−1829.35	+	1056.17i	−0.783478	+	0.452341i
$177$	−439.487	−	3718.95i	−0.186632	−	1.57929i
$178$		−	133.876i		−	0.0563732i
$179$	3194.00	−	1844.06i	1.33369	−	0.770008i	0.347829	−	0.937558i	$-0.386919\pi$
$179$	3194.00	−	1844.06i	1.33369	−	0.770008i	0.985863	+	0.167551i	$0.0535857\pi$
$180$	1202.98	+	1268.59i	0.498137	+	0.525306i
$181$		−	1648.55i		−	0.676995i	−0.940967	−	0.338497i	$-0.890081\pi$
$181$		−	1648.55i		−	0.676995i	0.940967	−	0.338497i	$-0.109919\pi$
$182$	−331.172	+	411.010i	−0.134880	+	0.167396i
$183$	−1330.44	+	3095.13i	−0.537424	+	1.25027i
$184$	−2043.95			−0.818923
$185$	−652.107	+	1129.48i	−0.259156	+	0.448871i
$186$	−812.122	+	606.212i	−0.320149	+	0.238976i
$187$	2873.43	−	1658.97i	1.12367	−	0.648749i
$188$	−2195.45			−0.851700
$189$	−511.745	−	2547.43i	−0.196952	−	0.980413i
$190$	−371.295			−0.141771
$191$	3175.89	−	1833.60i	1.20314	−	0.694631i	0.241885	−	0.970305i	$-0.422234\pi$
$191$	3175.89	−	1833.60i	1.20314	−	0.694631i	0.961251	+	0.275674i	$0.0889010\pi$
$192$	1289.14	−	962.283i	0.484560	−	0.361702i
$193$	171.063	−	296.289i	0.0637998	−	0.110504i	−0.832361	−	0.554234i	$-0.813011\pi$
$193$	171.063	−	296.289i	0.0637998	−	0.110504i	0.896161	+	0.443729i	$0.146345\pi$
$194$	−825.999			−0.305687
$195$	−680.551	+	1583.24i	−0.249925	+	0.581426i
$196$	−1888.29	+	1716.98i	−0.688152	+	0.625721i
$197$		−	468.339i		−	0.169380i	−0.996407	−	0.0846898i	$-0.973010\pi$
$197$		−	468.339i		−	0.169380i	0.996407	−	0.0846898i	$-0.0269899\pi$
$198$	−814.983	+	195.349i	−0.292517	+	0.0701155i
$199$	−1359.11	+	784.682i	−0.484144	+	0.279521i	−0.722142	−	0.691745i	$-0.756842\pi$
$199$	−1359.11	+	784.682i	−0.484144	+	0.279521i	0.237998	+	0.971266i	$0.423509\pi$
$200$		−	568.933i		−	0.201148i
$201$	−118.823	−	1005.49i	−0.0416973	−	0.352844i
$202$	−0.486235	+	0.280728i	−0.000169363	+	9.77818e-5i
$203$	−1001.52	−	806.979i	−0.346271	−	0.279009i
$204$	−2476.72	+	1848.76i	−0.850023	+	0.634504i
$205$	−476.116	−	824.657i	−0.162212	−	0.280959i
$206$	281.563	+	487.681i	0.0952300	+	0.164943i
$207$	4582.06	+	1359.07i	1.53853	+	0.456336i
$208$	1679.68	+	969.764i	0.559927	+	0.323274i
$209$	−1184.10	+	2050.92i	−0.391893	+	0.678779i
$210$	332.982	−	530.396i	0.109419	−	0.174289i
$211$	1244.68	+	2155.85i	0.406101	+	0.703387i	0.994449	−	0.105221i	$-0.0335549\pi$
$211$	1244.68	+	2155.85i	0.406101	+	0.703387i	−0.588348	+	0.808608i	$0.700222\pi$
$212$			2264.93i			0.733753i
$213$	−306.891	−	411.132i	−0.0987222	−	0.132255i
$214$	940.818			0.300528
$215$	1080.75	−	1871.91i	0.342821	−	0.593783i
$216$	1520.15	−	559.879i	0.478857	−	0.176366i
$217$	−3761.16	−	3030.57i	−1.17661	−	0.948057i
$218$	−143.530	−	82.8668i	−0.0445920	−	0.0257452i
$219$	536.181	−	1247.37i	0.165442	−	0.384885i
$220$	2327.55	+	1343.81i	0.713289	+	0.411817i
$221$	−2638.34	−	1523.25i	−0.803050	−	0.463641i
$222$	348.360	+	466.686i	0.105317	+	0.141090i
$223$	858.894	+	495.883i	0.257918	+	0.148909i	0.623385	−	0.781915i	$-0.285757\pi$
$223$	858.894	+	495.883i	0.257918	+	0.148909i	−0.365466	+	0.930825i	$0.619090\pi$
$224$	−1881.00	−	1515.62i	−0.561071	−	0.452084i
$225$	−378.296	+	1275.42i	−0.112088	+	0.377902i
$226$	580.862	−	1006.08i	0.170966	−	0.296122i
$227$	603.465			0.176447			0.0882233	−	0.996101i	$-0.471881\pi$
$227$	603.465			0.176447			0.0882233	+	0.996101i	$0.471881\pi$
$228$	871.151	−	2026.65i	0.253041	−	0.588676i
$229$		−	1295.25i		−	0.373765i	−0.982382	−	0.186883i	$-0.940162\pi$
$229$		−	1295.25i		−	0.373765i	0.982382	−	0.186883i	$-0.0598384\pi$
$230$	575.969	+	997.608i	0.165123	+	0.286002i
$231$	−1867.83	−	3530.78i	−0.532009	−	1.00566i
$232$	400.948	−	694.462i	0.113463	−	0.196524i
$233$	−3699.70	−	2136.02i	−1.04024	−	0.600581i	−0.120336	−	0.992733i	$-0.538397\pi$
$233$	−3699.70	−	2136.02i	−1.04024	−	0.600581i	−0.919900	+	0.392152i	$0.871731\pi$
$234$	529.490	+	558.369i	0.147922	+	0.155990i
$235$	1283.82	+	2223.64i	0.356371	+	0.617253i
$236$	2681.26	+	4644.07i	0.739555	+	1.28095i
$237$	5510.16	+	2368.53i	1.51022	+	0.649166i
$238$	862.079	+	694.623i	0.234791	+	0.189184i
$239$	2074.66	−	1197.80i	0.561500	−	0.324182i	−0.192247	−	0.981346i	$-0.561578\pi$
$239$	2074.66	−	1197.80i	0.561500	−	0.324182i	0.753747	+	0.657164i	$0.228244\pi$
$240$	−2114.16	−	908.765i	−0.568618	−	0.244419i
$241$		−	818.126i		−	0.218673i	−0.994005	−	0.109336i	$-0.965127\pi$
$241$		−	818.126i		−	0.218673i	0.994005	−	0.109336i	$-0.0348726\pi$
$242$	−253.762	+	146.510i	−0.0674068	+	0.0389174i
$243$	−3780.11	+	244.339i	−0.997917	+	0.0645036i
$244$		−	4824.28i		−	1.26575i
$245$	2843.23	+	908.509i	0.741418	+	0.236908i
$246$	−422.258	+	49.9004i	−0.109440	+	0.0129331i
$247$	2174.44			0.560148
$248$	1505.74	−	2608.02i	0.385542	−	0.667779i
$249$	348.087	+	2945.53i	0.0885910	+	0.749659i
$250$	−982.156	+	567.048i	−0.248468	+	0.143453i
$251$	−7516.24			−1.89012			−0.945062	−	0.326891i	$-0.893999\pi$
$251$	−7516.24			−1.89012			−0.945062	+	0.326891i	$0.893999\pi$
$252$	2113.82	+	3061.97i	0.528405	+	0.765420i
$253$	7347.31			1.82578
$254$	1570.53	−	906.748i	0.387969	−	0.223994i
$255$	3320.79	+	1427.43i	0.815514	+	0.350546i
$256$	−761.644	+	1319.21i	−0.185948	+	0.322072i
$257$	5548.61			1.34674			0.673372	−	0.739304i	$-0.264845\pi$
$257$	5548.61			1.34674			0.673372	+	0.739304i	$0.264845\pi$
$258$	−577.343	−	773.446i	−0.139317	−	0.186638i
$259$	−1741.52	+	2161.35i	−0.417809	+	0.518532i
$260$		−	2467.74i		−	0.588626i
$261$	−1360.60	+	1290.23i	−0.322677	+	0.305988i
$262$	−31.6267	+	18.2597i	−0.00745764	+	0.00430567i
$263$		−	6373.65i		−	1.49436i	−0.664623	−	0.747179i	$-0.731408\pi$
$263$		−	6373.65i		−	1.49436i	0.664623	−	0.747179i	$-0.268592\pi$
$264$	1995.70	−	1489.70i	0.465253	−	0.347290i
$265$	2294.01	−	1324.45i	0.531773	−	0.307019i
$266$	−780.770	−	121.710i	−0.179970	−	0.0280546i
$267$	−109.170	−	923.802i	−0.0250229	−	0.211745i
$268$	724.927	+	1255.61i	0.165231	+	0.286189i
$269$	2137.07	+	3701.52i	0.484385	+	0.838979i	0.999839	−	0.0179379i	$-0.00571013\pi$
$269$	2137.07	+	3701.52i	0.484385	+	0.838979i	−0.515454	+	0.856917i	$0.672377\pi$
$270$	−701.633	−	584.184i	−0.158148	−	0.131675i
$271$	−1818.38	−	1049.84i	−0.407597	−	0.235326i	0.282160	−	0.959367i	$-0.408949\pi$
$271$	−1818.38	−	1049.84i	−0.407597	−	0.235326i	−0.689757	+	0.724041i	$0.742283\pi$
$272$	2034.05	−	3523.07i	0.453427	−	0.785359i
$273$	−1950.07	+	3106.20i	−0.432321	+	0.688630i
$274$	572.946	+	992.371i	0.126325	+	0.218800i
$275$			2045.13i			0.448457i
$276$	−6796.65	+	803.194i	−1.48228	+	0.175169i
$277$	4410.66			0.956718			0.478359	−	0.878164i	$-0.341232\pi$
$277$	4410.66			0.956718			0.478359	+	0.878164i	$0.341232\pi$
$278$	275.748	−	477.610i	0.0594902	−	0.103040i
$279$	−5109.65	+	4845.38i	−1.09644	+	1.03973i
$280$	−286.635	+	1838.76i	−0.0611775	+	0.392454i
$281$	−4392.19	−	2535.83i	−0.932443	−	0.538346i	−0.0448593	−	0.998993i	$-0.514284\pi$
$281$	−4392.19	−	2535.83i	−0.932443	−	0.538346i	−0.887583	+	0.460647i	$0.847617\pi$
$282$	1138.60	−	134.554i	0.240434	−	0.0284133i
$283$	478.561	+	276.297i	0.100521	+	0.0580360i	0.549418	−	0.835548i	$-0.314850\pi$
$283$	478.561	+	276.297i	0.100521	+	0.0580360i	−0.448897	+	0.893584i	$0.648183\pi$
$284$	636.238	+	367.332i	0.132936	+	0.0767505i
$285$	−2562.09	+	302.775i	−0.532510	+	0.0629293i
$286$	1024.47	+	591.478i	0.211812	+	0.122290i
$287$	−730.870	−	1890.19i	−0.150320	−	0.388760i
$288$	−2555.40	+	2423.23i	−0.522841	+	0.495800i
$289$	−738.458	+	1279.05i	−0.150307	+	0.260339i
$290$	−451.937			−0.0915125
$291$	−5699.75	+	673.568i	−1.14820	+	0.135688i
$292$			1944.24i			0.389651i
$293$	496.106	+	859.280i	0.0989174	+	0.171330i	0.911237	−	0.411883i	$-0.135129\pi$
$293$	496.106	+	859.280i	0.0989174	+	0.171330i	−0.812319	+	0.583213i	$0.801795\pi$
$294$	874.068	−	1006.18i	0.173390	−	0.199598i
$295$	3135.80	−	5431.37i	0.618894	−	1.07196i
$296$	−1498.70	−	865.273i	−0.294291	−	0.169909i
$297$	−5464.44	+	2012.58i	−1.06761	+	0.393204i
$298$	−551.796	−	955.739i	−0.107264	−	0.185787i
$299$	−3373.10	−	5842.38i	−0.652413	−	1.13001i
$300$	−223.569	−	1891.85i	−0.0430259	−	0.364087i
$301$	2886.24	−	3582.05i	0.552692	−	0.685933i
$302$	−825.644	+	476.686i	−0.157319	+	0.0908284i
$303$	−3.12631	+	2.33365i	−0.000592745	+	0.000442457i
$304$			2903.62i			0.547808i
$305$	−4886.23	+	2821.07i	−0.917327	+	0.529619i
$306$	1171.16	−	1110.59i	0.218793	−	0.207477i
$307$		−	256.830i		−	0.0477462i	−0.999715	−	0.0238731i	$-0.992400\pi$
$307$		−	256.830i		−	0.0477462i	0.999715	−	0.0238731i	$-0.00759977\pi$
$308$	4453.95	+	3588.78i	0.823985	+	0.663928i
$309$	2340.59	+	3135.60i	0.430910	+	0.577276i
$310$	−1697.22			−0.310955
$311$	−361.742	+	626.556i	−0.0659566	+	0.114240i	−0.897118	−	0.441791i	$-0.854343\pi$
$311$	−361.742	+	626.556i	−0.0659566	+	0.114240i	0.831161	+	0.556031i	$0.187677\pi$
$312$	−2100.78	−	903.016i	−0.381197	−	0.163856i
$313$	−5961.98	+	3442.15i	−1.07665	+	0.621604i	−0.929991	−	0.367584i	$-0.880185\pi$
$313$	−5961.98	+	3442.15i	−1.07665	+	0.621604i	−0.146659	+	0.989187i	$0.546852\pi$
$314$	−1483.66			−0.266649
$315$	1865.20	−	3931.49i	0.333626	−	0.703221i
$316$	−8588.50			−1.52893
$317$	−318.148	+	183.683i	−0.0563690	+	0.0325447i	−0.527920	−	0.849294i	$-0.677028\pi$
$317$	−318.148	+	183.683i	−0.0563690	+	0.0325447i	0.471551	+	0.881839i	$0.343694\pi$
$318$	−138.812	−	1174.63i	−0.0244785	−	0.207138i
$319$	−1441.27	+	2496.36i	−0.252965	+	0.438148i
$320$	2694.12			0.470644
$321$	6492.05	−	767.198i	1.12882	−	0.133398i
$322$	884.152	+	2286.61i	0.153018	+	0.395738i
$323$		−	4560.82i		−	0.785669i
$324$	4834.88	−	2459.11i	0.829026	−	0.421657i
$325$	1626.23	−	938.904i	0.277560	−	0.160249i
$326$			2746.85i			0.466669i
$327$	−1057.99	−	454.774i	−0.178920	−	0.0769085i
$328$	1094.23	−	631.753i	0.184203	−	0.106350i
$329$	1970.75	+	5096.78i	0.330246	+	0.854087i
$330$	−1289.47	−	554.273i	−0.215099	−	0.0924599i
$331$	−1912.88	−	3313.20i	−0.317647	−	0.550182i	0.662349	−	0.749195i	$-0.269560\pi$
$331$	−1912.88	−	3313.20i	−0.317647	−	0.550182i	−0.979997	+	0.199014i	$0.936226\pi$
$332$	−2123.64	−	3678.25i	−0.351054	−	0.608043i
$333$	2784.40	+	2936.26i	0.458210	+	0.483202i
$334$	2600.28	+	1501.27i	0.425991	+	0.245946i
$335$	847.823	−	1468.47i	0.138273	−	0.239496i
$336$	−4147.83	−	2604.00i	−0.673460	−	0.422797i
$337$	−477.374	−	826.836i	−0.0771639	−	0.133652i	0.824861	−	0.565335i	$-0.191253\pi$
$337$	−477.374	−	826.836i	−0.0771639	−	0.133652i	−0.902025	+	0.431683i	$0.857920\pi$
$338$			556.775i			0.0895993i
$339$	3187.78	−	7416.08i	0.510727	−	1.18816i
$340$	−5176.00			−0.825612
$341$	−5412.63	+	9374.95i	−0.859561	+	1.48880i
$342$	−327.585	+	1104.44i	−0.0517946	+	0.174624i
$343$	5681.03	+	2842.45i	0.894305	+	0.447458i
$344$	2483.82	+	1434.03i	0.389298	+	0.224761i
$345$	4787.95	+	6414.25i	0.747172	+	1.00096i
$346$	−1355.81	−	782.778i	−0.210662	−	0.121625i
$347$	−4912.79	−	2836.40i	−0.760036	−	0.438807i	0.0692728	−	0.997598i	$-0.477932\pi$
$347$	−4912.79	−	2836.40i	−0.760036	−	0.438807i	−0.829309	+	0.558791i	$0.811265\pi$
$348$	1060.36	−	2466.82i	0.163337	−	0.379987i
$349$	−163.883	−	94.6178i	−0.0251360	−	0.0145123i	0.487379	−	0.873190i	$-0.337953\pi$
$349$	−163.883	−	94.6178i	−0.0251360	−	0.0145123i	−0.512515	+	0.858678i	$0.671286\pi$
$350$	−636.478	+	246.104i	−0.0972033	+	0.0375852i
$351$	4109.04	+	3421.21i	0.624855	+	0.520258i
$352$	−2706.92	+	4688.53i	−0.409885	+	0.709941i
$353$	−10440.7			−1.57422			−0.787110	−	0.616812i	$-0.788424\pi$
$353$	−10440.7			−1.57422			−0.787110	+	0.616812i	$0.788424\pi$
$354$	−1675.17	−	2244.16i	−0.251509	−	0.336938i
$355$		−	859.210i		−	0.128457i
$356$	666.035	+	1153.61i	0.0991566	+	0.171744i
$357$	6515.15	+	4090.21i	0.965878	+	0.606377i
$358$	1379.01	−	2388.52i	0.203584	−	0.352618i
$359$	9191.43	+	5306.67i	1.35127	+	0.780155i	0.988427	−	0.151697i	$-0.0484737\pi$
$359$	9191.43	+	5306.67i	1.35127	+	0.780155i	0.362840	+	0.931851i	$0.381807\pi$
$360$	2601.04	+	771.482i	0.380796	+	0.112946i
$361$	−1801.85	−	3120.89i	−0.262698	−	0.455007i
$362$	−616.407	−	1067.65i	−0.0894962	−	0.155012i
$363$	−1631.60	+	1217.91i	−0.235914	+	0.176099i
$364$	808.924	−	5189.25i	0.116481	−	0.747226i
$365$	1969.21	−	1136.92i	0.282392	−	0.163039i
$366$	295.668	+	2501.95i	0.0422263	+	0.357320i
$367$		−	882.734i		−	0.125554i	−0.998028	−	0.0627770i	$-0.980004\pi$
$367$		−	882.734i		−	0.125554i	0.998028	−	0.0627770i	$-0.0199957\pi$
$368$	7801.55	−	4504.22i	1.10512	−	0.638041i
$369$	−2873.07	+	688.668i	−0.405329	+	0.0971562i
$370$			975.311i			0.137038i
$371$	5258.07	−	2033.11i	0.735810	−	0.284512i
$372$	3982.12	−	9264.02i	0.555009	−	1.29118i
$373$	2616.16			0.363162			0.181581	−	0.983376i	$-0.441879\pi$
$373$	2616.16			0.363162			0.181581	+	0.983376i	$0.441879\pi$
$374$	1240.60	−	2148.79i	0.171524	−	0.297089i
$375$	−6314.90	+	4713.79i	−0.869600	+	0.649117i
$376$	−2950.52	+	1703.48i	−0.404685	+	0.233645i
$377$	2646.72			0.361573
$378$	−1283.92	−	1458.44i	−0.174703	−	0.198449i
$379$	636.672			0.0862892			0.0431446	−	0.999069i	$-0.486262\pi$
$379$	636.672			0.0862892			0.0431446	+	0.999069i	$0.486262\pi$
$380$	3199.43	−	1847.19i	0.431915	−	0.249366i
$381$	10097.9	−	7537.66i	1.35783	−	1.01356i
$382$	1371.19	−	2374.97i	0.183655	−	0.318100i
$383$	−7569.77			−1.00991			−0.504957	−	0.863145i	$-0.668492\pi$
$383$	−7569.77			−1.00991			−0.504957	+	0.863145i	$0.668492\pi$
$384$	2616.26	−	6086.48i	0.347683	−	0.808852i
$385$	1030.36	−	6609.73i	0.136394	−	0.874970i
$386$		−	255.846i		−	0.0337364i
$387$	−4614.63	−	4866.32i	−0.606136	−	0.639196i
$388$	7117.61	−	4109.35i	0.931294	−	0.537683i
$389$			11135.5i			1.45139i	0.688015	+	0.725697i	$0.258482\pi$
$389$			11135.5i			1.45139i	−0.688015	+	0.725697i	$0.741518\pi$
$390$	151.242	+	1279.81i	0.0196370	+	0.166169i
$391$	−12254.2	+	7074.96i	−1.58496	+	0.915080i
$392$	−1205.49	+	3772.65i	−0.155323	+	0.486091i
$393$	−203.348	+	151.790i	−0.0261006	+	0.0194829i
$394$	−175.115	−	303.309i	−0.0223913	−	0.0387829i
$395$	5022.24	+	8698.78i	0.639738	+	1.10806i
$396$	6050.82	−	5737.87i	0.767841	−	0.728128i
$397$	−777.013	−	448.609i	−0.0982297	−	0.0567129i	0.450080	−	0.892988i	$-0.351395\pi$
$397$	−777.013	−	448.609i	−0.0982297	−	0.0567129i	−0.548310	+	0.836275i	$0.684729\pi$
$398$	−586.797	+	1016.36i	−0.0739032	+	0.128004i
$399$	−5486.90	−	203.167i	−0.688443	−	0.0254914i
$400$	1253.75	+	2171.56i	0.156719	+	0.271445i
$401$			4026.51i			0.501432i	0.968061	+	0.250716i	$0.0806660\pi$
$401$			4026.51i			0.501432i	−0.968061	+	0.250716i	$0.919334\pi$
$402$	−452.912	−	606.751i	−0.0561921	−	0.0752786i
$403$	9939.61			1.22860
$404$	2.79325	−	4.83804i	0.000343983	−	0.000595796i
$405$	−5317.95	−	3458.97i	−0.652472	−	0.424389i
$406$	−950.347	−	148.145i	−0.116170	−	0.0181091i
$407$	5387.32	+	3110.37i	0.656116	+	0.378809i
$408$	−1894.04	+	4406.32i	−0.229826	+	0.534670i
$409$	−9468.68	−	5466.74i	−1.14473	−	0.660912i	−0.197135	−	0.980376i	$-0.563164\pi$
$409$	−9468.68	−	5466.74i	−1.14473	−	0.660912i	−0.947598	+	0.319464i	$0.896497\pi$
$410$	−616.691	−	356.047i	−0.0742834	−	0.0428875i
$411$	4762.81	+	6380.58i	0.571611	+	0.765768i
$412$	−4852.43	−	2801.55i	−0.580248	−	0.335006i
$413$	8374.47	−	10393.4i	0.997774	−	1.23831i
$414$	3475.63	−	833.099i	0.412604	−	0.0989000i
$415$	−2483.66	+	4301.82i	−0.293778	+	0.508838i
$416$	4970.92			0.585864
$417$	1513.31	−	3520.58i	0.177715	−	0.413437i
$418$			1770.97i			0.207227i
$419$	−2433.63	−	4215.18i	−0.283749	−	0.491467i	0.688556	−	0.725183i	$-0.258245\pi$
$419$	−2433.63	−	4215.18i	−0.283749	−	0.491467i	−0.972305	+	0.233716i	$0.924912\pi$
$420$	−230.571	+	6226.99i	−0.0267874	+	0.723443i
$421$	−5868.66	+	10164.8i	−0.679385	+	1.17673i	0.295781	+	0.955256i	$0.404420\pi$
$421$	−5868.66	+	10164.8i	−0.679385	+	1.17673i	−0.975166	+	0.221474i	$0.928913\pi$
$422$	1612.17	+	930.789i	0.185970	+	0.107370i
$423$	7747.08	−	1856.96i	0.890487	−	0.213447i
$424$	1757.39	+	3043.89i	0.201289	+	0.348643i
$425$	−1969.32	−	3410.96i	−0.224767	−	0.389308i
$426$	−352.476	−	151.511i	−0.0400881	−	0.0172318i
$427$	−11199.7	+	4330.52i	−1.26930	+	0.490793i
$428$	−8107.00	+	4680.58i	−0.915576	+	0.528608i
$429$	7551.61	+	3246.04i	0.849872	+	0.365315i
$430$		−	1616.40i		−	0.181278i
$431$	8093.99	−	4673.07i	0.904580	−	0.522260i	0.0258967	−	0.999665i	$-0.491756\pi$
$431$	8093.99	−	4673.07i	0.904580	−	0.522260i	0.878683	+	0.477405i	$0.158423\pi$
$432$	−4568.47	+	5486.95i	−0.508797	+	0.611090i
$433$		−	582.680i		−	0.0646693i	−0.999477	−	0.0323346i	$-0.989706\pi$
$433$		−	582.680i		−	0.0646693i	0.999477	−	0.0323346i	$-0.0102942\pi$
$434$	−3568.98	−	556.350i	−0.394738	−	0.0615337i
$435$	−3118.56	+	368.536i	−0.343732	+	0.0406205i
$436$	1649.05			0.181136
$437$	5049.78	−	8746.47i	0.552777	−	0.957438i
$438$	−119.158	−	1008.32i	−0.0129990	−	0.109998i
$439$	5577.42	−	3220.13i	0.606369	−	0.350087i	−0.165174	−	0.986264i	$-0.552819\pi$
$439$	5577.42	−	3220.13i	0.606369	−	0.350087i	0.771543	+	0.636177i	$0.219485\pi$
$440$	4170.75			0.451892
$441$	5210.95	−	7655.86i	0.562677	−	0.826677i
$442$	−2278.21			−0.245166
$443$	−10151.6	+	5861.05i	−1.08876	+	0.628593i	−0.933245	−	0.359241i	$-0.883036\pi$
$443$	−10151.6	+	5861.05i	−1.08876	+	0.628593i	−0.155511	+	0.987834i	$0.549702\pi$
$444$	−5323.57	−	2288.32i	−0.569022	−	0.244593i
$445$	778.946	−	1349.17i	0.0829789	−	0.143724i
$446$	741.657			0.0787409
$447$	−4587.00	−	6145.04i	−0.485364	−	0.650225i
$448$	5665.29	+	883.133i	0.597455	+	0.0931341i
$449$			10126.0i			1.06431i	0.846648	+	0.532153i	$0.178617\pi$
$449$			10126.0i			1.06431i	−0.846648	+	0.532153i	$0.821383\pi$
$450$	231.894	+	967.443i	0.0242924	+	0.101346i
$451$	−3933.38	+	2270.94i	−0.410678	+	0.237105i
$452$			11559.2i			1.20287i
$453$	−5308.58	+	3962.61i	−0.550594	+	0.410993i
$454$	390.820	−	225.640i	0.0404011	−	0.0233256i
$455$	−5728.91	+	2215.17i	−0.590276	+	0.228239i
$456$	−401.749	−	3399.61i	−0.0412579	−	0.349126i
$457$	3527.39	+	6109.61i	0.361059	+	0.625373i	0.988135	−	0.153585i	$-0.0490818\pi$
$457$	3527.39	+	6109.61i	0.361059	+	0.625373i	−0.627076	+	0.778958i	$0.715748\pi$
$458$	−484.302	−	838.835i	−0.0494104	−	0.0855812i
$459$	7175.87	−	8618.56i	0.729719	−	0.876427i
$460$	−9926.22	−	5730.91i	−1.00611	−	0.580880i
$461$	1300.85	−	2253.14i	0.131425	−	0.227634i	−0.792801	−	0.609480i	$-0.791378\pi$
$461$	1300.85	−	2253.14i	0.131425	−	0.227634i	0.924226	+	0.381846i	$0.124712\pi$
$462$	−2529.84	−	1588.23i	−0.254759	−	0.159938i
$463$	−4858.94	−	8415.93i	−0.487719	−	0.844755i	0.512181	−	0.858878i	$-0.328838\pi$
$463$	−4858.94	−	8415.93i	−0.487719	−	0.844755i	−0.999900	+	0.0141228i	$0.995504\pi$
$464$			3534.26i			0.353607i
$465$	−11711.6	+	1384.02i	−1.16798	+	0.138026i
$466$	−3194.70			−0.317578
$467$	−4239.34	+	7342.76i	−0.420072	+	0.727585i	−0.995946	−	0.0899527i	$-0.971328\pi$
$467$	−4239.34	+	7342.76i	−0.420072	+	0.727585i	0.575874	+	0.817538i	$0.304662\pi$
$468$	−7340.49	−	2177.23i	−0.725031	−	0.215048i
$469$	2264.19	−	2810.03i	0.222923	−	0.276664i
$470$	1662.87	+	960.059i	0.163197	+	0.0942218i
$471$	−10237.9	+	1209.87i	−1.00157	+	0.118360i
$472$	7206.82	+	4160.86i	0.702799	+	0.405761i
$473$	−8928.49	−	5154.87i	−0.867933	−	0.501102i
$474$	4454.14	−	526.367i	0.431614	−	0.0510060i
$475$	2434.58	+	1405.61i	0.235171	+	0.135776i
$476$	−10884.3	−	1696.69i	−1.04807	−	0.163378i
$477$	−1915.72	−	7992.24i	−0.183888	−	0.767169i
$478$	895.736	−	1551.46i	0.0857113	−	0.148456i
$479$	−19701.4			−1.87929			−0.939645	−	0.342150i	$-0.888845\pi$
$479$	−19701.4			−1.87929			−0.939645	+	0.342150i	$0.888845\pi$
$480$	−5857.11	+	692.164i	−0.556957	+	0.0658183i
$481$		−	5711.80i		−	0.541446i
$482$	−305.903	−	529.840i	−0.0289077	−	0.0500696i
$483$	7965.66	+	15057.6i	0.750414	+	1.41852i
$484$	1457.77	−	2524.94i	0.136906	−	0.237128i
$485$	−8324.25	−	4806.01i	−0.779350	−	0.449958i
$486$	−2356.74	+	1571.65i	−0.219967	+	0.146690i
$487$	−7141.08	−	12368.7i	−0.664463	−	1.15088i	−0.979431	−	0.201781i	$-0.935327\pi$
$487$	−7141.08	−	12368.7i	−0.664463	−	1.15088i	0.314968	−	0.949102i	$-0.398006\pi$
$488$	−3743.24	−	6483.48i	−0.347230	−	0.601421i
$489$	2239.95	+	18954.5i	0.207145	+	1.75287i
$490$	2181.05	−	474.730i	0.201081	−	0.0437676i
$491$	9090.51	−	5248.41i	0.835537	−	0.482398i	−0.0202074	−	0.999796i	$-0.506433\pi$
$491$	9090.51	−	5248.41i	0.835537	−	0.482398i	0.855745	+	0.517398i	$0.173099\pi$
$492$	3390.33	−	2530.73i	0.310667	−	0.231899i
$493$		−	5551.40i		−	0.507145i
$494$	1408.23	−	813.041i	0.128257	−	0.0740495i
$495$	−9349.86	−	2773.22i	−0.848979	−	0.251812i
$496$			13272.7i			1.20154i
$497$	281.649	−	1806.77i	0.0254199	−	0.163068i
$498$	1326.78	+	1777.45i	0.119387	+	0.159938i
$499$	16828.4			1.50970			0.754850	−	0.655897i	$-0.227710\pi$
$499$	16828.4			1.50970			0.754850	+	0.655897i	$0.227710\pi$
$500$	5642.14	−	9772.48i	0.504649	−	0.874077i
$501$	19167.3	+	8239.01i	1.70924	+	0.734714i
$502$	−4867.72	+	2810.38i	−0.432783	+	0.249867i
$503$	12335.3			1.09344			0.546722	−	0.837314i	$-0.315875\pi$
$503$	12335.3			1.09344			0.546722	+	0.837314i	$0.315875\pi$
$504$	5216.65	+	2474.92i	0.461048	+	0.218733i
$505$	−6.53356			−0.000575722
$506$	4758.31	−	2747.21i	0.418049	−	0.241361i
$507$	454.027	+	3841.99i	0.0397713	+	0.336546i
$508$	−9022.16	+	15626.8i	−0.787980	+	1.36482i
$509$	14453.1			1.25859			0.629295	−	0.777166i	$-0.283344\pi$
$509$	14453.1			1.25859			0.629295	+	0.777166i	$0.283344\pi$
$510$	2684.36	−	317.224i	0.233070	−	0.0275430i
$511$	4513.59	−	1745.25i	0.390743	−	0.151087i
$512$			11338.9i			0.978739i
$513$	−1359.85	+	7888.28i	−0.117035	+	0.678901i
$514$	3593.43	−	2074.67i	0.308365	−	0.178034i
$515$			6552.99i			0.560698i
$516$	8822.85	+	3792.48i	0.752721	+	0.323555i
$517$	10606.1	−	6123.46i	0.902239	−	0.520908i
$518$	−319.706	+	2050.91i	−0.0271179	+	0.173961i
$519$	−9994.01	−	4295.90i	−0.845257	−	0.363332i
$520$	−1914.76	−	3316.46i	−0.161477	−	0.279686i
$521$	3797.90	+	6578.16i	0.319365	+	0.553156i	0.980356	−	0.197238i	$-0.0631971\pi$
$521$	3797.90	+	6578.16i	0.319365	+	0.553156i	−0.660991	+	0.750394i	$0.729864\pi$
$522$	−398.733	+	1344.32i	−0.0334331	+	0.112719i
$523$	15947.4	+	9207.24i	1.33333	+	0.769799i	0.985809	−	0.167873i	$-0.0536900\pi$
$523$	15947.4	+	9207.24i	1.33333	+	0.769799i	0.347522	+	0.937672i	$0.387023\pi$
$524$	181.684	−	314.686i	0.0151468	−	0.0262350i
$525$	−4191.28	+	2217.24i	−0.348424	+	0.184321i
$526$	−2383.15	−	4127.74i	−0.197548	−	0.342164i
$527$		−	20848.0i		−	1.72325i
$528$	−4334.56	+	10083.9i	−0.357268	+	0.831150i
$529$	−19166.8			−1.57531
$530$	990.441	−	1715.49i	0.0811736	−	0.140597i
$531$	−13389.4	−	14119.7i	−1.09426	−	1.15394i
$532$	7333.38	−	2835.57i	0.597636	−	0.231085i
$533$	3611.58	+	2085.15i	0.293499	+	0.169452i
$534$	−416.118	−	557.459i	−0.0337213	−	0.0451753i
$535$	9481.37	+	5474.07i	0.766197	+	0.442364i
$536$	1948.50	+	1124.97i	0.157019	+	0.0906551i
$537$	7568.05	−	17606.4i	0.608167	−	1.41484i
$538$	2768.05	+	1598.13i	0.221820	+	0.128068i
$539$	4333.34	−	13561.4i	0.346289	−	1.08373i
$540$	8952.28	+	1543.27i	0.713416	+	0.122985i
$541$	10525.6	−	18230.9i	0.836474	−	1.44882i	−0.0563503	−	0.998411i	$-0.517946\pi$
$541$	10525.6	−	18230.9i	0.836474	−	1.44882i	0.892825	−	0.450405i	$-0.148720\pi$
$542$	−1570.18			−0.124437
$543$	−5124.09	−	6864.58i	−0.404965	−	0.542518i
$544$		−	10426.3i		−	0.821738i
$545$	−964.307	−	1670.23i	−0.0757915	−	0.131275i
$546$	−101.486	+	2740.81i	−0.00795455	+	0.214827i
$547$	−8242.69	+	14276.8i	−0.644300	+	1.11596i	0.340163	+	0.940367i	$0.389518\pi$
$547$	−8242.69	+	14276.8i	−0.644300	+	1.11596i	−0.984463	+	0.175594i	$0.943815\pi$
$548$	−9874.11	−	5700.82i	−0.769710	−	0.444392i
$549$	4080.47	+	17023.4i	0.317214	+	1.32339i
$550$	764.688	+	1324.48i	0.0592844	+	0.102684i
$551$	1981.16	+	3431.48i	0.153177	+	0.265310i
$552$	−8510.99	+	6353.07i	−0.656253	+	0.489863i
$553$	7709.48	+	19938.4i	0.592840	+	1.53321i
$554$	2856.46	−	1649.18i	0.219060	−	0.126474i
$555$	795.325	+	6730.07i	0.0608283	+	0.514730i
$556$			5487.40i			0.418557i
$557$	−5731.63	+	3309.16i	−0.436009	+	0.251730i	−0.701903	−	0.712272i	$-0.747666\pi$
$557$	−5731.63	+	3309.16i	−0.436009	+	0.251730i	0.265894	+	0.964002i	$0.414333\pi$
$558$	−1497.42	+	5048.53i	−0.113604	+	0.383013i
$559$			9466.26i			0.716243i
$560$	−2958.00	−	7650.03i	−0.223211	−	0.577272i
$561$	6808.46	−	15839.2i	0.512395	−	1.19204i
$562$	−3792.67			−0.284669
$563$	8503.32	−	14728.2i	0.636540	−	1.10252i	−0.349647	−	0.936882i	$-0.613698\pi$
$563$	8503.32	−	14728.2i	0.636540	−	1.10252i	0.986187	−	0.165638i	$-0.0529683\pi$
$564$	−9141.84	+	6823.97i	−0.682520	+	0.509470i
$565$	11707.6	−	6759.40i	0.871758	−	0.503310i
$566$	413.239			0.0306885
$567$	−10048.9	−	9016.86i	−0.744293	−	0.667853i
$568$	1140.08			0.0842192
$569$	−9769.80	+	5640.60i	−0.719809	+	0.415582i	−0.814682	−	0.579907i	$-0.803089\pi$
$569$	−9769.80	+	5640.60i	−0.719809	+	0.415582i	0.0948734	+	0.995489i	$0.469755\pi$
$570$	−1546.07	+	1154.07i	−0.113610	+	0.0848047i
$571$	12233.2	−	21188.5i	0.896571	−	1.55291i	0.0647233	−	0.997903i	$-0.479384\pi$
$571$	12233.2	−	21188.5i	0.896571	−	1.55291i	0.831848	−	0.555004i	$-0.187283\pi$
$572$	−11770.4			−0.860396
$573$	7525.13	−	17506.5i	0.548633	−	1.27634i
$574$	−1180.09	−	950.857i	−0.0858115	−	0.0691429i
$575$		−	8721.78i		−	0.632562i
$576$	2376.96	−	8013.89i	0.171945	−	0.579708i
$577$	−14445.8	+	8340.28i	−1.04226	+	0.601751i	−0.920474	−	0.390805i	$-0.872197\pi$
$577$	−14445.8	+	8340.28i	−1.04226	+	0.601751i	−0.121790	+	0.992556i	$0.538863\pi$
$578$			1104.46i			0.0794801i
$579$	−208.632	−	1765.45i	−0.0149749	−	0.126718i
$580$	3894.33	−	2248.39i	0.278798	−	0.160964i
$581$	−6632.84	+	8231.86i	−0.473626	+	0.587806i
$582$	−3439.46	+	2567.40i	−0.244966	+	0.182856i
$583$	−6317.24	−	10941.8i	−0.448771	−	0.777294i
$584$	1508.57	+	2612.92i	0.106892	+	0.185143i
$585$	2087.27	+	8707.92i	0.147518	+	0.615433i
$586$	642.582	+	370.995i	0.0452984	+	0.0261530i
$587$	7866.86	−	13625.8i	0.553152	−	0.958087i	−0.444893	−	0.895584i	$-0.646758\pi$
$587$	7866.86	−	13625.8i	0.553152	−	0.958087i	0.998045	−	0.0625029i	$-0.0199083\pi$
$588$	−2526.06	+	13018.7i	−0.177165	+	0.913068i
$589$	7440.16	+	12886.7i	0.520486	+	0.901509i
$590$		−	4690.00i		−	0.327262i
$591$	−1455.71	−	1950.16i	−0.101319	−	0.135734i
$592$	7627.17			0.529518
$593$	2335.26	−	4044.79i	0.161716	−	0.280101i	−0.773768	−	0.633469i	$-0.781630\pi$
$593$	2335.26	−	4044.79i	0.161716	−	0.280101i	0.935484	+	0.353368i	$0.114964\pi$
$594$	−2786.40	+	3346.59i	−0.192470	+	0.231166i
$595$	4646.25	+	12016.2i	0.320131	+	0.827926i
$596$	9509.62	+	5490.38i	0.653573	+	0.377340i
$597$	−3220.35	+	7491.85i	−0.220771	+	0.513603i
$598$	−4369.02	−	2522.45i	−0.298767	−	0.172493i
$599$	−11047.3	−	6378.15i	−0.753556	−	0.435066i	0.0734215	−	0.997301i	$-0.476608\pi$
$599$	−11047.3	−	6378.15i	−0.753556	−	0.435066i	−0.826977	+	0.562235i	$0.809941\pi$
$600$	−1768.38	−	2369.04i	−0.120323	−	0.161193i
$601$	17937.2	+	10356.0i	1.21743	+	0.702882i	0.964367	−	0.264569i	$-0.0852297\pi$
$601$	17937.2	+	10356.0i	1.21743	+	0.702882i	0.253060	+	0.967451i	$0.418563\pi$
$602$	529.855	−	3399.02i	0.0358725	−	0.230122i
$603$	−3620.07	−	3817.51i	−0.244479	−	0.257813i
$604$	4743.03	−	8215.17i	0.319522	−	0.553428i
$605$	−3409.82			−0.229139
$606$	−1.15211	+	2.68028i	−7.72299e−5	+	0.000179668i
$607$			24485.0i			1.63726i	0.574325	+	0.818628i	$0.305265\pi$
$607$			24485.0i			1.63726i	−0.574325	+	0.818628i	$0.694735\pi$
$608$	3720.91	+	6444.81i	0.248196	+	0.429888i
$609$	−6678.61	−	247.293i	−0.444386	−	0.0164546i
$610$	−2109.63	+	3653.99i	−0.140027	+	0.242534i
$611$	−9738.42	−	5622.48i	−0.644803	−	0.372277i
$612$	−4566.67	+	15396.4i	−0.301629	+	1.01693i
$613$	−2415.65	−	4184.03i	−0.159164	−	0.275679i	0.775404	−	0.631466i	$-0.217546\pi$
$613$	−2415.65	−	4184.03i	−0.159164	−	0.275679i	−0.934567	+	0.355786i	$0.884213\pi$
$614$	−96.0308	−	166.330i	−0.00631187	−	0.0109325i
$615$	−4545.77	−	1953.99i	−0.298054	−	0.128118i
$616$	8770.38	+	1367.17i	0.573650	+	0.0894233i
$617$	−5042.06	+	2911.04i	−0.328988	+	0.189942i	−0.655392	−	0.755289i	$-0.727497\pi$
$617$	−5042.06	+	2911.04i	−0.328988	+	0.189942i	0.326404	+	0.945231i	$0.394163\pi$
$618$	2688.25	+	1155.54i	0.174980	+	0.0752145i
$619$		−	1448.25i		−	0.0940388i	−0.998894	−	0.0470194i	$-0.985028\pi$
$619$		−	1448.25i		−	0.0940388i	0.998894	−	0.0470194i	$-0.0149723\pi$
$620$	14624.9	−	8443.71i	0.947341	−	0.546948i
$621$	23304.0	−	8582.98i	1.50589	−	0.554626i
$622$			541.032i			0.0348769i
$623$	2080.25	−	2581.75i	0.133778	−	0.166028i
$624$	10008.4	−	1182.75i	0.642081	−	0.0758779i
$625$	−7038.32			−0.450452
$626$	−2574.09	+	4458.46i	−0.164347	+	0.284658i
$627$	1444.15	+	12220.5i	0.0919839	+	0.778371i
$628$	12784.7	−	7381.24i	0.812363	−	0.469018i
$629$	−11980.3			−0.759437
$630$	−262.059	−	3243.55i	−0.0165725	−	0.205121i
$631$	−22632.9			−1.42790			−0.713948	−	0.700199i	$-0.753095\pi$
$631$	−22632.9			−1.42790			−0.713948	+	0.700199i	$0.753095\pi$
$632$	−11542.3	+	6663.96i	−0.726469	+	0.419427i
$633$	11883.7	+	5108.19i	0.746185	+	0.320746i
$634$	−137.361	+	237.916i	−0.00860456	+	0.0149035i
$635$	21103.4			1.31884
$636$	7039.92	+	9431.14i	0.438917	+	0.588002i
$637$	−12773.1	+	2780.20i	−0.794486	+	0.172929i
$638$			2155.61i			0.133764i
$639$	−2555.79	−	758.062i	−0.158224	−	0.0469303i
$640$	9608.61	−	5547.53i	0.593459	−	0.342633i
$641$			15231.9i			0.938571i	0.883046	+	0.469286i	$0.155489\pi$
$641$			15231.9i			0.938571i	−0.883046	+	0.469286i	$0.844511\pi$
$642$	3917.56	−	2924.28i	0.240832	−	0.179770i
$643$	−12428.6	+	7175.65i	−0.762264	+	0.440093i	−0.830108	−	0.557603i	$-0.811721\pi$
$643$	−12428.6	+	7175.65i	−0.762264	+	0.440093i	0.0678441	+	0.997696i	$0.478388\pi$
$644$	−18994.6	−	15305.0i	−1.16225	−	0.936490i
$645$	−1318.11	−	11153.9i	−0.0804657	−	0.680903i
$646$	−1705.33	−	2953.71i	−0.103862	−	0.179895i
$647$	14009.3	+	24264.9i	0.851258	+	1.47442i	0.880073	+	0.474838i	$0.157493\pi$
$647$	14009.3	+	24264.9i	0.851258	+	1.47442i	−0.0288151	+	0.999585i	$0.509173\pi$
$648$	4589.67	−	7056.32i	0.278239	−	0.427776i
$649$	−25906.1	−	14956.9i	−1.56688	−	0.904638i
$650$	702.126	−	1216.12i	0.0423687	−	0.0733847i
$651$	−25081.2	−	928.698i	−1.51000	−	0.0559117i
$652$	−13665.6	−	23669.6i	−0.820840	−	1.42174i
$653$			12216.5i			0.732113i	0.930593	+	0.366057i	$0.119292\pi$
$653$			12216.5i			0.732113i	−0.930593	+	0.366057i	$0.880708\pi$
$654$	−855.226	+	101.066i	−0.0511345	+	0.00604282i
$655$	−424.969			−0.0253510
$656$	−2784.37	+	4822.67i	−0.165719	+	0.287033i
$657$	−1644.48	−	6860.64i	−0.0976517	−	0.407396i
$658$	3182.03	+	2563.93i	0.188524	+	0.151903i
$659$	5703.43	+	3292.88i	0.337138	+	0.194647i	0.659006	−	0.752138i	$-0.270977\pi$
$659$	5703.43	+	3292.88i	0.337138	+	0.194647i	−0.321868	+	0.946785i	$0.604311\pi$
$660$	13868.8	−	1638.95i	0.817943	−	0.0966604i
$661$	−6336.72	−	3658.51i	−0.372874	−	0.215279i	0.301839	−	0.953359i	$-0.402399\pi$
$661$	−6336.72	−	3658.51i	−0.372874	−	0.215279i	−0.674713	+	0.738080i	$0.735733\pi$
$662$	−2477.66	−	1430.48i	−0.145464	−	0.0839836i
$663$	−15720.7	+	1857.79i	−0.920874	+	0.108824i
$664$	−5708.03	−	3295.53i	−0.333606	−	0.192608i
$665$	−7160.28	−	5769.42i	−0.417539	−	0.336434i
$666$	2901.14	+	860.494i	0.168794	+	0.0500653i
$667$	6146.55	−	10646.1i	0.356815	−	0.618021i
$668$	−29875.4			−1.73041
$669$	5117.75	−	604.790i	0.295760	−	0.0349515i
$670$		−	1268.03i		−	0.0731167i
$671$	13455.7	+	23305.9i	0.774145	+	1.34086i
$672$	−12543.4	−	464.453i	−0.720048	−	0.0266617i
$673$	1486.23	−	2574.23i	0.0851263	−	0.147443i	−0.820319	−	0.571907i	$-0.806204\pi$
$673$	1486.23	−	2574.23i	0.0851263	−	0.147443i	0.905445	+	0.424464i	$0.139537\pi$
$674$	−618.320	−	356.987i	−0.0353365	−	0.0204015i
$675$	2389.07	+	6486.67i	0.136230	+	0.369885i
$676$	−2769.96	−	4797.71i	−0.157599	−	0.272970i
$677$	8554.38	+	14816.6i	0.485630	+	0.841136i	0.999864	−	0.0165140i	$-0.00525681\pi$
$677$	8554.38	+	14816.6i	0.485630	+	0.841136i	−0.514233	+	0.857650i	$0.671923\pi$
$678$	−708.433	−	5994.78i	−0.0401286	−	0.339570i
$679$	−15929.1	−	12834.9i	−0.900298	−	0.725418i
$680$	−6956.17	+	4016.15i	−0.392290	+	0.226488i
$681$	2512.83	−	1875.71i	0.141397	−	0.105547i
$682$			8095.29i			0.454523i
$683$	4555.42	−	2630.07i	0.255210	−	0.147346i	−0.366938	−	0.930246i	$-0.619594\pi$
$683$	4555.42	−	2630.07i	0.255210	−	0.147346i	0.622147	+	0.782900i	$0.286260\pi$
$684$	−2671.84	−	11146.7i	−0.149357	−	0.623107i
$685$			13334.5i			0.743776i
$686$	4742.00	−	283.330i	0.263922	−	0.0157691i
$687$	−4025.93	−	5393.40i	−0.223579	−	0.299521i
$688$	−12640.6			−0.700465
$689$	−5800.41	+	10046.6i	−0.320723	+	0.555508i
$690$	5499.14	+	2363.79i	0.303404	+	0.130417i
$691$	−16770.2	+	9682.26i	−0.923252	+	0.533040i	−0.884671	−	0.466216i	$-0.845617\pi$
$691$	−16770.2	+	9682.26i	−0.923252	+	0.533040i	−0.0385810	+	0.999255i	$0.512284\pi$
$692$	15577.3			0.855724
$693$	−18752.1	−	8896.50i	−1.02790	−	0.487662i
$694$	−4242.21			−0.232034
$695$	5557.87	−	3208.84i	0.303341	−	0.175134i
$696$	−489.005	−	4137.98i	−0.0266318	−	0.225359i
$697$	4373.52	−	7575.17i	0.237674	−	0.411664i
$698$	−141.513			−0.00767386
$699$	−22044.8	+	2605.14i	−1.19286	+	0.140966i
$700$	4260.14	−	5287.15i	0.230026	−	0.285479i
$701$			23797.7i			1.28221i	0.767455	+	0.641103i	$0.221523\pi$
$701$			23797.7i			1.28221i	−0.767455	+	0.641103i	$0.778477\pi$
$702$	3940.34	+	679.268i	0.211850	+	0.0365204i
$703$	7405.36	−	4275.49i	0.397295	−	0.229379i
$704$		−	12850.2i		−	0.687942i
$705$	12257.4	+	5268.82i	0.654810	+	0.281469i
$706$	−6761.64	+	3903.84i	−0.360450	+	0.208106i
$707$	−13.7390	−	2.14170i	−0.000730845	−	0.000113928i
$708$	25599.6	+	11003.9i	1.35889	+	0.584114i
$709$	−7213.51	−	12494.2i	−0.382100	−	0.661817i	0.609262	−	0.792969i	$-0.291466\pi$
$709$	−7213.51	−	12494.2i	−0.382100	−	0.661817i	−0.991362	+	0.131152i	$0.958132\pi$
$710$	−321.265	−	556.447i	−0.0169815	−	0.0294128i
$711$	30306.2	−	7264.33i	1.59855	−	0.383169i
$712$	1790.20	+	1033.57i	0.0942285	+	0.0544029i
$713$	23083.0	−	39981.0i	1.21244	−	2.10000i
$714$	5748.75	+	212.863i	0.301318	+	0.0111571i
$715$	6882.93	+	11921.6i	0.360010	+	0.623555i
$716$			27442.4i			1.43236i
$717$	4915.81	−	11436.2i	0.256045	−	0.595665i
$718$	7936.82			0.412534
$719$	2139.85	−	3706.33i	0.110992	−	0.192243i	−0.805179	−	0.593032i	$-0.797931\pi$
$719$	2139.85	−	3706.33i	0.110992	−	0.192243i	0.916170	+	0.400789i	$0.131264\pi$
$720$	−11628.0	+	2787.20i	−0.601875	+	0.144268i
$721$	−2148.07	+	13779.8i	−0.110955	+	0.711773i
$722$	−2333.85	−	1347.45i	−0.120300	−	0.0694555i
$723$	−2542.93	−	3406.68i	−0.130806	−	0.175236i
$724$	10623.1	+	6133.26i	0.545311	+	0.314835i
$725$	2963.36	+	1710.89i	0.151802	+	0.0876428i
$726$	−601.279	+	1398.82i	−0.0307377	+	0.0715083i
$727$	8438.47	+	4871.95i	0.430489	+	0.248543i	0.699555	−	0.714579i	$-0.253382\pi$
$727$	8438.47	+	4871.95i	0.430489	+	0.248543i	−0.269066	+	0.963122i	$0.586715\pi$
$728$	−2939.29	−	7601.62i	−0.149639	−	0.386999i
$729$	−14980.9	+	12766.9i	−0.761108	+	0.648625i
$730$	850.207	−	1472.60i	0.0431063	−	0.0746623i
$731$	19855.2			1.00461
$732$	−14995.0	−	20088.3i	−0.757146	−	1.01432i
$733$		−	4535.45i		−	0.228541i	−0.993450	−	0.114271i	$-0.963547\pi$
$733$		−	4535.45i		−	0.228541i	0.993450	−	0.114271i	$-0.0364531\pi$
$734$	−330.061	−	571.682i	−0.0165978	−	0.0287482i
$735$	14663.1	−	5054.40i	0.735858	−	0.253652i
$736$	11544.1	−	19995.0i	0.578154	−	1.00139i
$737$	−7004.20	−	4043.88i	−0.350072	−	0.202114i
$738$	−1603.18	+	1520.26i	−0.0799646	+	0.0758288i
$739$	15942.1	+	27612.6i	0.793561	+	1.37449i	0.923749	+	0.382998i	$0.125108\pi$
$739$	15942.1	+	27612.6i	0.793561	+	1.37449i	−0.130189	+	0.991489i	$0.541558\pi$
$740$	−4852.18	−	8404.22i	−0.241040	−	0.417494i
$741$	9054.38	−	6758.69i	0.448881	−	0.335070i
$742$	2645.07	−	3282.73i	0.130867	−	0.162416i
$743$	−10135.3	+	5851.64i	−0.500444	+	0.288931i	−0.728897	−	0.684624i	$-0.759967\pi$
$743$	−10135.3	+	5851.64i	−0.500444	+	0.288931i	0.228453	+	0.973555i	$0.426633\pi$
$744$	−1836.43	−	15540.0i	−0.0904932	−	0.765756i
$745$		−	12842.3i		−	0.631552i
$746$	1694.29	−	978.200i	0.0831534	−	0.0480086i
$747$	10604.8	+	11183.2i	0.519425	+	0.547755i
$748$			24688.1i			1.20680i
$749$	18143.3	+	14619.0i	0.885104	+	0.713175i
$750$	−2327.18	+	5413.96i	−0.113302	+	0.263586i
$751$	−16580.5			−0.805635			−0.402817	−	0.915280i	$-0.631969\pi$
$751$	−16580.5			−0.805635			−0.402817	+	0.915280i	$0.631969\pi$
$752$	7507.90	−	13004.1i	0.364076	−	0.630598i
$753$	−31297.6	+	23362.3i	−1.51467	+	1.13063i
$754$	1714.08	−	989.627i	0.0827895	−	0.0477985i
$755$	−11094.2			−0.534782
$756$	18319.3	+	6179.78i	0.881303	+	0.297297i
$757$	−16410.7			−0.787923			−0.393962	−	0.919127i	$-0.628896\pi$
$757$	−16410.7			−0.787923			−0.393962	+	0.919127i	$0.628896\pi$
$758$	412.325	−	238.056i	0.0197577	−	0.0114071i
$759$	30594.2	−	22837.2i	1.46311	−	1.09214i
$760$	2866.54	−	4964.99i	0.136816	−	0.236972i
$761$	21191.0			1.00943			0.504713	−	0.863287i	$-0.331598\pi$
$761$	21191.0			1.00943			0.504713	+	0.863287i	$0.331598\pi$
$762$	3721.31	−	8657.29i	0.176915	−	0.411575i
$763$	−1480.28	−	3828.31i	−0.0702354	−	0.181644i
$764$			27286.8i			1.29215i
$765$	18264.6	−	4377.97i	0.863211	−	0.206910i
$766$	−4902.38	+	2830.39i	−0.231241	+	0.133507i
$767$			27466.5i			1.29303i
$768$	928.919	+	7860.54i	0.0436451	+	0.369326i
$769$	−4457.86	+	2573.75i	−0.209044	+	0.120691i	−0.600867	−	0.799349i	$-0.705178\pi$
$769$	−4457.86	+	2573.75i	−0.209044	+	0.120691i	0.391823	+	0.920041i	$0.371844\pi$
$770$	−1804.14	−	4665.90i	−0.0844374	−	0.218373i
$771$	23104.4	−	17246.4i	1.07923	−	0.805595i
$772$	1272.84	+	2204.62i	0.0593400	+	0.102780i
$773$	−13537.8	−	23448.2i	−0.629912	−	1.09104i	−0.987569	−	0.157187i	$-0.949758\pi$
$773$	−13537.8	−	23448.2i	−0.629912	−	1.09104i	0.357657	−	0.933853i	$-0.383576\pi$
$774$	−4808.11	−	1426.11i	−0.223287	−	0.0662281i
$775$	11128.7	+	6425.17i	0.515814	+	0.297805i
$776$	6377.03	−	11045.3i	0.295003	−	0.510960i
$777$	−533.676	+	14412.9i	−0.0246403	+	0.665457i
$778$	4163.64	+	7211.64i	0.191869	+	0.332326i
$779$			6243.23i			0.287146i
$780$	−7670.32	−	10275.7i	−0.352104	−	0.471702i
$781$	−4098.19			−0.187765
$782$	−5290.76	+	9163.87i	−0.241940	+	0.419053i
$783$	−1655.19	+	9601.55i	−0.0755451	+	0.438227i
$784$	−3712.51	−	17056.4i	−0.169119	−	0.776984i
$785$	−14952.0	−	8632.57i	−0.679823	−	0.392496i
$786$	−74.9380	+	174.336i	−0.00340070	+	0.00791141i
$787$	−9407.72	−	5431.55i	−0.426110	−	0.246015i	0.271578	−	0.962416i	$-0.412455\pi$
$787$	−9407.72	−	5431.55i	−0.426110	−	0.246015i	−0.697688	+	0.716401i	$0.745788\pi$
$788$	3017.93	+	1742.40i	0.136433	+	0.0787697i
$789$	−19810.8	−	26539.8i	−0.893895	−	1.19752i
$790$	6505.08	+	3755.71i	0.292962	+	0.169142i
$791$	26834.9	−	10376.1i	1.20624	−	0.466413i
$792$	3679.75	−	12406.2i	0.165094	−	0.556610i
$793$	12354.8	−	21399.2i	0.553257	−	0.958270i
$794$	−670.953			−0.0299889
$795$	5435.56	−	12645.3i	0.242490	−	0.564130i
$796$		−	11677.3i		−	0.519963i
$797$	3869.66	+	6702.44i	0.171983	+	0.297883i	0.939113	−	0.343608i	$-0.111649\pi$
$797$	3869.66	+	6702.44i	0.171983	+	0.297883i	−0.767130	+	0.641491i	$0.778316\pi$
$798$	−3629.43	+	1920.02i	−0.161003	+	0.0851727i
$799$	−11793.0	+	20426.0i	−0.522159	+	0.904406i
$800$	5565.61	+	3213.31i	0.245968	+	0.142010i
$801$	−3325.98	−	3507.38i	−0.146714	−	0.154716i
$802$	1505.54	+	2607.67i	0.0662874	+	0.114813i
$803$	−5422.80	−	9392.57i	−0.238314	−	0.412773i
$804$	6921.33	+	2975.11i	0.303602	+	0.130503i
$805$	−4394.13	+	28188.3i	−0.192388	+	1.23417i
$806$	6437.15	−	3716.49i	0.281314	−	0.162417i
$807$	20403.9	+	8770.58i	0.890028	+	0.382576i
$808$		−	8.66930i		−	0.000377457i
$809$	−18111.7	+	10456.8i	−0.787114	+	0.454440i	−0.838945	−	0.544215i	$-0.816827\pi$
$809$	−18111.7	+	10456.8i	−0.787114	+	0.454440i	0.0518317	+	0.998656i	$0.483494\pi$
$810$	−4737.38	−	251.702i	−0.205499	−	0.0109184i
$811$		−	31359.1i		−	1.35779i	−0.734235	−	0.678895i	$-0.762459\pi$
$811$		−	31359.1i		−	1.35779i	0.734235	−	0.678895i	$-0.237541\pi$
$812$	8926.13	−	3451.43i	0.385771	−	0.149164i
$813$	−10834.9	+	1280.41i	−0.467400	+	0.0552350i
$814$	4651.96			0.200308
$815$	−15982.3	+	27682.2i	−0.686917	+	1.18977i
$816$	−2480.77	−	20992.4i	−0.106427	−	0.900588i
$817$	−12273.0	+	7085.84i	−0.525556	+	0.303430i
$818$	−8176.22			−0.349480
$819$	1534.72	+	18995.5i	0.0654791	+	0.810447i
$820$	7085.34			0.301745
$821$	16357.5	−	9444.03i	0.695349	−	0.401460i	−0.110264	−	0.993902i	$-0.535169\pi$
$821$	16357.5	−	9444.03i	0.695349	−	0.401460i	0.805613	+	0.592442i	$0.201836\pi$
$822$	5470.27	+	2351.38i	0.232114	+	0.0997735i
$823$	6742.64	−	11678.6i	0.285582	−	0.494642i	−0.687168	−	0.726498i	$-0.741147\pi$
$823$	6742.64	−	11678.6i	0.285582	−	0.494642i	0.972750	+	0.231856i	$0.0744799\pi$
$824$	−8695.09			−0.367606
$825$	6356.73	+	8515.90i	0.268258	+	0.359376i
$826$	1537.38	−	9862.29i	0.0647607	−	0.415439i
$827$		−	17296.9i		−	0.727292i	−0.931537	−	0.363646i	$-0.881532\pi$
$827$		−	17296.9i		−	0.727292i	0.931537	−	0.363646i	$-0.118468\pi$
$828$	−25804.7	+	24470.1i	−1.08306	+	1.02705i
$829$	−4067.89	+	2348.59i	−0.170426	+	0.0983957i	−0.582787	−	0.812625i	$-0.698038\pi$
$829$	−4067.89	+	2348.59i	−0.170426	+	0.0983957i	0.412360	+	0.911021i	$0.364704\pi$
$830$			3714.63i			0.155345i
$831$	18366.0	−	13709.4i	0.766677	−	0.572290i
$832$	−10218.1	+	5899.45i	−0.425782	+	0.245825i
$833$	5831.38	+	26791.1i	0.242551	+	1.11435i
$834$	−336.309	−	2845.86i	−0.0139633	−	0.118158i
$835$	17470.1	+	30259.0i	0.724043	+	1.25408i
$836$	−8810.60	−	15260.4i	−0.364499	−	0.631330i
$837$	−6216.00	+	36058.1i	−0.256698	+	1.48907i
$838$	−3152.17	−	1819.91i	−0.129940	−	0.0750210i
$839$	1606.27	−	2782.14i	0.0660960	−	0.114482i	−0.831084	−	0.556147i	$-0.812279\pi$
$839$	1606.27	−	2782.14i	0.0660960	−	0.114482i	0.897180	+	0.441666i	$0.145612\pi$
$840$	4521.76	+	8547.53i	0.185733	+	0.351092i
$841$	−9783.04	−	16944.7i	−0.401125	−	0.694769i
$842$			8777.35i			0.359249i
$843$	−26171.1	+	3092.76i	−1.06925	+	0.126359i
$844$	−18522.7			−0.755425
$845$	−3239.55	+	5611.06i	−0.131886	+	0.228434i
$846$	4322.89	−	4099.30i	0.175678	−	0.166592i
$847$	−7170.28	−	1117.74i	−0.290878	−	0.0453434i
$848$	−13415.6	−	7745.50i	−0.543270	−	0.313657i
$849$	2851.52	−	336.979i	0.115270	−	0.0136220i
$850$	−2550.77	−	1472.69i	−0.102930	−	0.0594267i
$851$	−22975.1	−	13264.7i	−0.925471	−	0.534321i
$852$	3791.05	−	448.007i	0.152440	−	0.0180146i
$853$	−34142.7	−	19712.3i	−1.37048	−	0.791249i	−0.379495	−	0.925194i	$-0.623902\pi$
$853$	−34142.7	−	19712.3i	−1.37048	−	0.791249i	−0.990989	+	0.133945i	$0.957235\pi$
$854$	−5633.99	+	6992.20i	−0.225751	+	0.280173i
$855$	−9727.45	+	9224.34i	−0.389090	+	0.368966i
$856$	−7263.48	+	12580.7i	−0.290024	+	0.502336i
$857$	−1759.78			−0.0701435			−0.0350718	−	0.999385i	$-0.511166\pi$
$857$	−1759.78			−0.0701435			−0.0350718	+	0.999385i	$0.511166\pi$
$858$	6104.34	−	721.380i	0.242889	−	0.0287034i
$859$			5140.46i			0.204179i	0.994775	+	0.102090i	$0.0325529\pi$
$859$			5140.46i			0.204179i	−0.994775	+	0.102090i	$0.967447\pi$
$860$	8041.60	+	13928.5i	0.318856	+	0.552275i
$861$	−8918.48	−	5599.01i	−0.353009	−	0.221619i
$862$	3494.59	−	6052.81i	0.138081	−	0.239164i
$863$	−30321.8	−	17506.3i	−1.19602	−	0.690523i	−0.236355	−	0.971667i	$-0.575953\pi$
$863$	−30321.8	−	17506.3i	−1.19602	−	0.690523i	−0.959666	+	0.281144i	$0.909286\pi$
$864$	−3108.70	+	18033.1i	−0.122407	+	0.710068i
$865$	−9109.06	−	15777.4i	−0.358055	−	0.620169i
$866$	−217.868	−	377.359i	−0.00854903	−	0.0148074i
$867$	900.641	+	7621.25i	0.0352796	+	0.298537i
$868$	33521.6	−	12961.7i	1.31083	−	0.506852i
$869$	41490.8	−	23954.7i	1.61965	−	0.935107i
$870$	−1881.86	+	1404.73i	−0.0733346	+	0.0547410i
$871$			7426.07i			0.288889i
$872$	2216.21	−	1279.53i	0.0860668	−	0.0496907i
$873$	−21640.1	+	20520.9i	−0.838955	+	0.795564i
$874$		−	7552.60i		−	0.292300i
$875$	−27751.7	−	4326.07i	−1.07220	−	0.167140i
$876$	6043.16	+	8095.81i	0.233081	+	0.312251i
$877$	17341.8			0.667721			0.333860	−	0.942623i	$-0.391649\pi$
$877$	17341.8			0.667721			0.333860	+	0.942623i	$0.391649\pi$
$878$	2408.06	−	4170.88i	0.0925604	−	0.160319i
$879$	4736.63	+	2036.03i	0.181755	+	0.0781268i
$880$	−15919.3	+	9191.03i	−0.609819	+	0.352079i
$881$	−38797.9			−1.48369			−0.741846	−	0.670570i	$-0.766050\pi$
$881$	−38797.9			−1.48369			−0.741846	+	0.670570i	$0.766050\pi$
$882$	512.169	−	6906.55i	0.0195529	−	0.263668i
$883$	27338.7			1.04193			0.520963	−	0.853579i	$-0.325573\pi$
$883$	27338.7			1.04193			0.520963	+	0.853579i	$0.325573\pi$
$884$	19631.3	−	11334.1i	0.746914	−	0.431231i
$885$	−3824.50	−	32363.0i	−0.145265	−	1.22923i
$886$	−4382.98	+	7591.54i	−0.166195	+	0.287859i
$887$	−43410.3			−1.64326			−0.821631	−	0.570019i	$-0.806936\pi$
$887$	−43410.3			−1.64326			−0.821631	+	0.570019i	$0.806936\pi$
$888$	−8930.04	+	1055.31i	−0.337469	+	0.0398804i
$889$	44376.8	+	6917.67i	1.67418	+	0.260980i
$890$		−	1165.02i		−	0.0438780i
$891$	−16498.3	+	25365.1i	−0.620331	+	0.953719i
$892$	−6390.83	+	3689.75i	−0.239889	+	0.138500i
$893$		−	16834.5i		−	0.630847i
$894$	−5268.34	−	2264.58i	−0.197091	−	0.0847192i
$895$	27794.8	−	16047.4i	1.03808	−	0.599334i
$896$	22023.8	−	8515.83i	0.821163	−	0.317516i
$897$	−32205.1	−	13843.3i	−1.19877	−	0.515288i
$898$	3786.17	+	6557.84i	0.140697	+	0.243695i
$899$	9056.10	+	15685.6i	0.335971	+	0.581919i
$900$	−6811.26	−	7182.75i	−0.252269	−	0.266028i
$901$	21072.4	+	12166.2i	0.779160	+	0.449848i
$902$	−1698.24	+	2941.44i	−0.0626888	+	0.108580i
$903$	884.471	−	23886.8i	0.0325951	−	0.880289i
$904$	8968.96	+	15534.7i	0.329981	+	0.571545i
$905$		−	14346.0i		−	0.526938i
$906$	−1956.33	+	4551.21i	−0.0717380	+	0.166892i
$907$	−5130.22			−0.187813			−0.0939064	−	0.995581i	$-0.529935\pi$
$907$	−5130.22			−0.187813			−0.0939064	+	0.995581i	$0.529935\pi$
$908$	−2245.12	+	3888.67i	−0.0820562	+	0.142125i
$909$	−5.76441	+	19.4346i	−0.000210334	+	0.000709136i
$910$	−2881.93	+	3576.69i	−0.104983	+	0.130292i
$911$	20476.8	+	11822.3i	0.744707	+	0.429957i	0.823778	−	0.566912i	$-0.191862\pi$
$911$	20476.8	+	11822.3i	0.744707	+	0.429957i	−0.0790715	+	0.996869i	$0.525196\pi$
$912$	9025.12	+	12090.6i	0.327688	+	0.438993i
$913$	20518.5	+	11846.3i	0.743770	+	0.429416i
$914$	4568.86	+	2637.83i	0.165344	+	0.0954614i
$915$	−11577.7	+	26934.5i	−0.418303	+	0.973143i
$916$	8346.43	+	4818.81i	0.301063	+	0.173819i
$917$	−893.639	−	139.305i	−0.0321816	−	0.00501663i
$918$	1424.74	−	8264.72i	0.0512238	−	0.297142i
$919$	−22890.0	+	39646.7i	−0.821623	+	1.42309i	0.0828494	+	0.996562i	$0.473598\pi$
$919$	−22890.0	+	39646.7i	−0.821623	+	1.42309i	−0.904473	+	0.426531i	$0.859735\pi$
$920$	−17786.8			−0.637407
$921$	−798.290	−	1069.44i	−0.0285608	−	0.0382620i
$922$		−	1945.59i		−	0.0694953i
$923$	1881.45	+	3258.77i	0.0670951	+	0.116212i
$924$	29701.0	+	1099.76i	1.05746	+	0.0391552i
$925$	3692.23	−	6395.13i	0.131243	−	0.227319i
$926$	−6293.56	−	3633.59i	−0.223347	−	0.128949i
$927$	19492.4	+	5781.55i	0.690630	+	0.204845i
$928$	4529.07	+	7844.57i	0.160209	+	0.277490i
$929$	−14332.6	−	24824.8i	−0.506176	−	0.876723i	−0.999974	−	0.00714671i	$-0.997725\pi$
$929$	−14332.6	−	24824.8i	−0.506176	−	0.876723i	0.493798	−	0.869577i	$-0.335608\pi$
$930$	−7067.24	+	5275.37i	−0.249187	+	0.186007i
$931$	−13165.7	−	14479.2i	−0.463466	−	0.509708i
$932$	27528.6	−	15893.6i	0.967521	−	0.558598i
$933$	441.189	+	3733.36i	0.0154811	+	0.131002i
$934$			6340.49i			0.222128i
$935$	25005.1	−	14436.7i	0.874604	−	0.504953i
$936$	−11554.4	+	2769.57i	−0.403492	+	0.0967160i
$937$		−	20013.0i		−	0.697754i	−0.937168	−	0.348877i	$-0.886563\pi$
$937$		−	20013.0i		−	0.697754i	0.937168	−	0.348877i	$-0.113437\pi$
$938$	415.659	−	2666.45i	0.0144688	−	0.0928174i
$939$	−14126.7	+	32864.4i	−0.490954	+	1.14216i
$940$	−19105.2			−0.662919
$941$	11943.4	−	20686.6i	0.413757	−	0.716647i	−0.581540	−	0.813517i	$-0.697550\pi$
$941$	11943.4	−	20686.6i	0.413757	−	0.716647i	0.995297	+	0.0968701i	$0.0308831\pi$
$942$	−6177.97	+	4611.57i	−0.213683	+	0.159504i
$943$	16774.6	−	9684.80i	0.579273	−	0.334444i
$944$	−36677.0			−1.26455
$945$	−4453.30	−	22168.2i	−0.153297	−	0.763103i
$946$	−7709.77			−0.264975
$947$	8161.37	−	4711.97i	0.280052	−	0.161688i	−0.353395	−	0.935474i	$-0.614973\pi$
$947$	8161.37	−	4711.97i	0.280052	−	0.161688i	0.633447	+	0.773786i	$0.281640\pi$
$948$	−35762.5	+	26695.1i	−1.22522	+	0.914573i
$949$	−4979.14	+	8624.13i	−0.170316	+	0.294996i
$950$	2102.27			0.0717964
$951$	−753.838	+	1753.73i	−0.0257044	+	0.0597988i
$952$	−15944.1	+	6165.05i	−0.542808	+	0.209885i
$953$		−	42523.4i		−	1.44540i	−0.691161	−	0.722701i	$-0.742900\pi$
$953$		−	42523.4i		−	1.44540i	0.691161	−	0.722701i	$-0.257100\pi$
$954$	−4229.03	−	4459.69i	−0.143522	−	0.151350i
$955$	27637.2	−	15956.3i	0.936459	−	0.540665i
$956$			17825.2i			0.603041i
$957$	1757.81	+	14874.7i	0.0593751	+	0.502434i
$958$	−12759.2	+	7366.50i	−0.430302	+	0.248435i
$959$	−4371.06	+	28040.3i	−0.147183	+	0.944180i
$960$	11218.3	−	8373.97i	0.377156	−	0.281530i
$961$	19114.2	+	33106.8i	0.641611	+	1.11130i
$962$	−2135.68	−	3699.11i	−0.0715771	−	0.123975i
$963$	24648.2	−	23373.4i	0.824796	−	0.782137i
$964$	5271.92	+	3043.75i	0.176138	+	0.101693i
$965$	1488.62	−	2578.37i	0.0496584	−	0.0860109i
$966$	10788.9	+	6773.27i	0.359345	+	0.225597i
$967$	−2110.16	−	3654.91i	−0.0701739	−	0.121545i	0.828803	−	0.559540i	$-0.189022\pi$
$967$	−2110.16	−	3654.91i	−0.0701739	−	0.121545i	−0.898977	+	0.437995i	$0.855689\pi$
$968$		−	4524.45i		−	0.150229i
$969$	−14176.1	−	18991.3i	−0.469971	−	0.629605i
$970$	−7188.01			−0.237931
$971$	5026.42	−	8706.01i	0.166123	−	0.287733i	−0.770931	−	0.636919i	$-0.780208\pi$
$971$	5026.42	−	8706.01i	0.166123	−	0.287733i	0.937054	+	0.349186i	$0.113542\pi$
$972$	12489.0	−	25267.7i	0.412123	−	0.833807i
$973$	12739.1	−	4925.78i	0.419730	−	0.162295i
$974$	−9249.51	−	5340.21i	−0.304285	−	0.175679i
$975$	3853.28	−	8964.29i	0.126568	−	0.294448i
$976$	28575.1	+	16497.9i	0.937160	+	0.541070i
$977$	−18918.6	−	10922.7i	−0.619509	−	0.357674i	0.157169	−	0.987572i	$-0.449763\pi$
$977$	−18918.6	−	10922.7i	−0.619509	−	0.357674i	−0.776678	+	0.629898i	$0.783097\pi$
$978$	8537.87	+	11437.9i	0.279152	+	0.373971i
$979$	−6435.19	−	3715.36i	−0.210081	−	0.121290i
$980$	−16432.3	+	14941.5i	−0.535622	+	0.487029i
$981$	−5819.01	+	1394.80i	−0.189385	+	0.0453951i
$982$	3924.84	−	6798.02i	0.127542	−	0.220910i
$983$	44724.2			1.45115			0.725575	−	0.688143i	$-0.241574\pi$
$983$	44724.2			1.45115			0.725575	+	0.688143i	$0.241574\pi$
$984$	2592.73	−	6031.73i	0.0839970	−	0.195411i
$985$		−	4075.58i		−	0.131836i
$986$	−2075.71	−	3595.23i	−0.0670426	−	0.116121i
$987$	24048.2	+	15097.4i	0.775544	+	0.486886i
$988$	−8089.78	+	14011.9i	−0.260496	+	0.451192i
$989$	38077.0	+	21983.8i	1.22425	+	0.706818i
$990$	−7092.14	+	1699.97i	−0.227680	+	0.0545743i
$991$	−8670.77	−	15018.2i	−0.277937	−	0.481402i	0.692935	−	0.721000i	$-0.256317\pi$
$991$	−8670.77	−	15018.2i	−0.277937	−	0.481402i	−0.970872	+	0.239599i	$0.922984\pi$
$992$	17008.7	+	29459.9i	0.544381	+	0.942896i
$993$	−18263.4	−	7850.49i	−0.583658	−	0.250884i
$994$	−493.163	−	1275.43i	−0.0157366	−	0.0406982i
$995$	−11827.2	+	6828.46i	−0.376833	+	0.217565i
$996$	−20275.7	−	8715.45i	−0.645040	−	0.277269i
$997$		−	56296.2i		−	1.78828i	−0.447783	−	0.894142i	$-0.647786\pi$
$997$		−	56296.2i		−	1.78828i	0.447783	−	0.894142i	$-0.352214\pi$
$998$	10898.5	−	6292.25i	0.345677	−	0.199577i
$999$	20720.8	+	3572.03i	0.656234	+	0.113127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.s.a.47.12	yes	44
3.2	odd	2		189.4.s.a.89.11		44
7.3	odd	6		63.4.i.a.38.12	yes	44
9.4	even	3		189.4.i.a.152.12		44
9.5	odd	6		63.4.i.a.5.11	✓	44
21.17	even	6		189.4.i.a.143.11		44
63.31	odd	6		189.4.s.a.17.11		44
63.59	even	6	inner	63.4.s.a.59.12	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.i.a.5.11	✓	44	9.5	odd	6
63.4.i.a.38.12	yes	44	7.3	odd	6
63.4.s.a.47.12	yes	44	1.1	even	1	trivial
63.4.s.a.59.12	yes	44	63.59	even	6	inner
189.4.i.a.143.11		44	21.17	even	6
189.4.i.a.152.12		44	9.4	even	3
189.4.s.a.17.11		44	63.31	odd	6
189.4.s.a.89.11		44	3.2	odd	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647627 - 0.373907i) q^{2} +(4.16400 - 3.10824i) q^{3} +(-3.72039 + 6.44390i) q^{4} +8.70220 q^{5} +(1.53452 - 3.56993i) q^{6} +(18.2993 + 2.85258i) q^{7} +11.5468i q^{8} +(7.67775 - 25.8854i) q^{9} +O(q^{10})\)	\(q+(0.647627 - 0.373907i) q^{2} +(4.16400 - 3.10824i) q^{3} +(-3.72039 + 6.44390i) q^{4} +8.70220 q^{5} +(1.53452 - 3.56993i) q^{6} +(18.2993 + 2.85258i) q^{7} +11.5468i q^{8} +(7.67775 - 25.8854i) q^{9} +(5.63577 - 3.25382i) q^{10} -41.5070i q^{11} +(4.53747 + 38.3962i) q^{12} +(-33.0053 + 19.0556i) q^{13} +(12.9177 - 4.99482i) q^{14} +(36.2359 - 27.0485i) q^{15} +(-25.4456 - 44.0731i) q^{16} +(39.9685 + 69.2274i) q^{17} +(-4.70642 - 19.6348i) q^{18} +(-49.4113 - 28.5276i) q^{19} +(-32.3755 + 56.0761i) q^{20} +(85.0645 - 45.0003i) q^{21} +(-15.5198 - 26.8811i) q^{22} +177.014i q^{23} +(35.8903 + 48.0810i) q^{24} -49.2718 q^{25} +(-14.2501 + 24.6818i) q^{26} +(-48.4877 - 131.651i) q^{27} +(-86.4620 + 107.306i) q^{28} +(-60.1430 - 34.7236i) q^{29} +(13.3537 - 31.0662i) q^{30} +(-225.864 - 130.403i) q^{31} +(-112.957 - 65.2160i) q^{32} +(-129.014 - 172.835i) q^{33} +(51.7693 + 29.8890i) q^{34} +(159.244 + 24.8237i) q^{35} +(138.238 + 145.778i) q^{36} +(-74.9359 + 129.793i) q^{37} -42.6668 q^{38} +(-78.2046 + 181.936i) q^{39} +100.483i q^{40} +(-54.7122 - 94.7643i) q^{41} +(38.2641 - 60.9496i) q^{42} +(124.193 - 215.108i) q^{43} +(267.467 + 154.422i) q^{44} +(66.8133 - 225.260i) q^{45} +(66.1867 + 114.639i) q^{46} +(147.528 + 255.526i) q^{47} +(-242.945 - 104.429i) q^{48} +(326.726 + 104.400i) q^{49} +(-31.9097 + 18.4231i) q^{50} +(381.604 + 164.031i) q^{51} -283.577i q^{52} +(263.613 - 152.197i) q^{53} +(-80.6271 - 67.1307i) q^{54} -361.202i q^{55} +(-32.9382 + 211.299i) q^{56} +(-294.419 + 34.7930i) q^{57} -51.9336 q^{58} +(360.346 - 624.138i) q^{59} +(39.4860 + 334.131i) q^{60} +(-561.494 + 324.179i) q^{61} -195.034 q^{62} +(214.337 - 451.782i) q^{63} +309.591 q^{64} +(-287.218 + 165.826i) q^{65} +(-148.177 - 63.6935i) q^{66} +(97.4263 - 168.747i) q^{67} -594.793 q^{68} +(550.200 + 737.084i) q^{69} +(112.412 - 43.4659i) q^{70} -98.7349i q^{71} +(298.894 + 88.6537i) q^{72} +(226.289 - 130.648i) q^{73} +112.076i q^{74} +(-205.168 + 153.148i) q^{75} +(367.658 - 212.268i) q^{76} +(118.402 - 759.548i) q^{77} +(17.3797 + 147.068i) q^{78} +(577.124 + 999.608i) q^{79} +(-221.433 - 383.533i) q^{80} +(-611.104 - 397.483i) q^{81} +(-70.8661 - 40.9146i) q^{82} +(-285.406 + 494.337i) q^{83} +(-26.4957 + 715.566i) q^{84} +(347.813 + 602.431i) q^{85} -185.746i q^{86} +(-358.365 + 42.3497i) q^{87} +479.275 q^{88} +(89.5115 - 155.038i) q^{89} +(-40.9561 - 170.866i) q^{90} +(-658.330 + 254.553i) q^{91} +(-1140.66 - 658.559i) q^{92} +(-1345.82 + 159.042i) q^{93} +(191.086 + 110.324i) q^{94} +(-429.987 - 248.253i) q^{95} +(-673.061 + 79.5390i) q^{96} +(-956.569 - 552.275i) q^{97} +(250.632 - 54.5529i) q^{98} +(-1074.42 - 318.681i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9}+O(q^{10}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9	\( 44 q - 3 q^{2} - 3 q^{3} + 81 q^{4} - 6 q^{5} - 24 q^{6} + 5 q^{7} - 3 q^{9} - 6 q^{10} - 3 q^{12} + 36 q^{13} + 129 q^{14} - 141 q^{15} - 263 q^{16} + 72 q^{17} - 15 q^{18} - 6 q^{19} - 24 q^{20} - 306 q^{21} + 14 q^{22} - 66 q^{24} + 698 q^{25} + 96 q^{26} - 432 q^{27} - 156 q^{28} - 132 q^{29} + 852 q^{30} + 177 q^{31} - 501 q^{32} + 849 q^{33} - 24 q^{34} - 765 q^{35} + 1122 q^{36} + 82 q^{37} - 1746 q^{38} - 645 q^{39} - 618 q^{41} - 963 q^{42} + 82 q^{43} - 603 q^{44} + 303 q^{45} + 266 q^{46} - 201 q^{47} + 1569 q^{48} + 515 q^{49} - 1845 q^{50} + 417 q^{51} - 564 q^{53} - 684 q^{54} + 3600 q^{56} + 1170 q^{57} - 538 q^{58} + 747 q^{59} - 516 q^{60} - 1209 q^{61} + 2904 q^{62} + 1557 q^{63} - 1144 q^{64} - 831 q^{65} + 1029 q^{66} + 295 q^{67} + 7008 q^{68} + 1005 q^{69} - 390 q^{70} - 1119 q^{72} - 6 q^{73} - 1788 q^{75} + 144 q^{76} - 1203 q^{77} - 5985 q^{78} - 551 q^{79} + 4239 q^{80} + 3741 q^{81} + 18 q^{82} - 1830 q^{83} - 7725 q^{84} - 237 q^{85} - 2130 q^{87} + 1246 q^{88} - 4266 q^{89} - 9993 q^{90} - 1140 q^{91} + 7896 q^{92} - 1479 q^{93} - 3 q^{94} - 1053 q^{95} + 5034 q^{96} + 792 q^{97} - 5667 q^{98} + 4335 q^{99}+O(q^{100}) \) 44 * q - 3 * q^2 - 3 * q^3 + 81 * q^4 - 6 * q^5 - 24 * q^6 + 5 * q^7 - 3 * q^9 - 6 * q^10 - 3 * q^12 + 36 * q^13 + 129 * q^14 - 141 * q^15 - 263 * q^16 + 72 * q^17 - 15 * q^18 - 6 * q^19 - 24 * q^20 - 306 * q^21 + 14 * q^22 - 66 * q^24 + 698 * q^25 + 96 * q^26 - 432 * q^27 - 156 * q^28 - 132 * q^29 + 852 * q^30 + 177 * q^31 - 501 * q^32 + 849 * q^33 - 24 * q^34 - 765 * q^35 + 1122 * q^36 + 82 * q^37 - 1746 * q^38 - 645 * q^39 - 618 * q^41 - 963 * q^42 + 82 * q^43 - 603 * q^44 + 303 * q^45 + 266 * q^46 - 201 * q^47 + 1569 * q^48 + 515 * q^49 - 1845 * q^50 + 417 * q^51 - 564 * q^53 - 684 * q^54 + 3600 * q^56 + 1170 * q^57 - 538 * q^58 + 747 * q^59 - 516 * q^60 - 1209 * q^61 + 2904 * q^62 + 1557 * q^63 - 1144 * q^64 - 831 * q^65 + 1029 * q^66 + 295 * q^67 + 7008 * q^68 + 1005 * q^69 - 390 * q^70 - 1119 * q^72 - 6 * q^73 - 1788 * q^75 + 144 * q^76 - 1203 * q^77 - 5985 * q^78 - 551 * q^79 + 4239 * q^80 + 3741 * q^81 + 18 * q^82 - 1830 * q^83 - 7725 * q^84 - 237 * q^85 - 2130 * q^87 + 1246 * q^88 - 4266 * q^89 - 9993 * q^90 - 1140 * q^91 + 7896 * q^92 - 1479 * q^93 - 3 * q^94 - 1053 * q^95 + 5034 * q^96 + 792 * q^97 - 5667 * q^98 + 4335 * q^99

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