LMFDB - Embedded newform 77.4.f.a.64.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,4,Mod(15,77)] 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("77.15"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	77.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.54314707044$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.1
Character	$\chi$	$=$	77.64
Dual form			77.4.f.a.71.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.68700 + 5.19206i) q^{2} +(7.39468 - 5.37255i) q^{3} +(-17.6394 - 12.8158i) q^{4} +(-3.09523 - 9.52615i) q^{5} +(15.4198 + 47.4572i) q^{6} +(-5.66312 - 4.11450i) q^{7} +(60.9649 - 44.2936i) q^{8} +(17.4736 - 53.7781i) q^{9} +54.6820 q^{10} +(34.9237 - 10.5515i) q^{11} -199.291 q^{12} +(-2.42072 + 7.45022i) q^{13} +(30.9164 - 22.4621i) q^{14} +(-74.0680 - 53.8136i) q^{15} +(73.2258 + 225.366i) q^{16} +(-0.0243718 - 0.0750087i) q^{17} +(249.741 + 181.448i) q^{18} +(0.608726 - 0.442265i) q^{19} +(-67.4869 + 207.703i) q^{20} -63.9823 q^{21} +(-4.13263 + 199.126i) q^{22} -124.351 q^{23} +(212.846 - 655.074i) q^{24} +(19.9600 - 14.5018i) q^{25} +(-34.5982 - 25.1371i) q^{26} +(-83.4523 - 256.840i) q^{27} +(47.1635 + 145.154i) q^{28} +(23.3625 + 16.9738i) q^{29} +(404.356 - 293.782i) q^{30} +(-5.84157 + 17.9785i) q^{31} -690.792 q^{32} +(201.562 - 265.654i) q^{33} +0.430565 q^{34} +(-21.6666 + 66.6831i) q^{35} +(-997.431 + 724.676i) q^{36} +(233.025 + 169.303i) q^{37} +(1.26935 + 3.90664i) q^{38} +(22.1262 + 68.0975i) q^{39} +(-610.648 - 443.662i) q^{40} +(-121.938 + 88.5929i) q^{41} +(107.938 - 332.200i) q^{42} +351.919 q^{43} +(-751.258 - 261.453i) q^{44} -566.383 q^{45} +(209.781 - 645.639i) q^{46} +(202.590 - 147.190i) q^{47} +(1752.27 + 1273.10i) q^{48} +(15.1418 + 46.6018i) q^{49} +(41.6216 + 128.098i) q^{50} +(-0.583210 - 0.423727i) q^{51} +(138.180 - 100.394i) q^{52} +(-79.5600 + 244.860i) q^{53} +1474.31 q^{54} +(-208.612 - 300.030i) q^{55} -527.497 q^{56} +(2.12524 - 6.54082i) q^{57} +(-127.542 + 92.6646i) q^{58} +(-333.901 - 242.593i) q^{59} +(616.852 + 1898.48i) q^{60} +(290.995 + 895.589i) q^{61} +(-83.4908 - 60.6596i) q^{62} +(-320.225 + 232.657i) q^{63} +(579.562 - 1783.71i) q^{64} +78.4647 q^{65} +(1039.26 + 1494.68i) q^{66} +778.370 q^{67} +(-0.531390 + 1.63545i) q^{68} +(-919.538 + 668.084i) q^{69} +(-309.671 - 224.989i) q^{70} +(-86.4845 - 266.172i) q^{71} +(-1316.75 - 4052.54i) q^{72} +(-784.479 - 569.957i) q^{73} +(-1272.14 + 924.267i) q^{74} +(69.6864 - 214.473i) q^{75} -16.4055 q^{76} +(-241.191 - 83.9394i) q^{77} -390.893 q^{78} +(-292.710 + 900.868i) q^{79} +(1920.22 - 1395.12i) q^{80} +(-761.835 - 553.506i) q^{81} +(-254.271 - 782.564i) q^{82} +(214.079 + 658.867i) q^{83} +(1128.61 + 819.982i) q^{84} +(-0.639108 + 0.464339i) q^{85} +(-593.689 + 1827.19i) q^{86} +263.951 q^{87} +(1661.76 - 2190.16i) q^{88} +340.214 q^{89} +(955.491 - 2940.70i) q^{90} +(44.3628 - 32.2314i) q^{91} +(2193.48 + 1593.66i) q^{92} +(53.3939 + 164.330i) q^{93} +(422.451 + 1300.17i) q^{94} +(-6.09723 - 4.42990i) q^{95} +(-5108.19 + 3711.32i) q^{96} +(-182.437 + 561.484i) q^{97} -267.504 q^{98} +(42.8048 - 2062.50i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} + 18 q^{3} - 48 q^{4} + 16 q^{5} + 30 q^{6} - 56 q^{7} + 62 q^{8} - 46 q^{9} - 72 q^{10} - 94 q^{11} - 544 q^{12} + 72 q^{13} + 56 q^{14} + 140 q^{15} + 296 q^{16} + 8 q^{17} + 422 q^{18}+ \cdots + 10027 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 + 18 * q^3 - 48 * q^4 + 16 * q^5 + 30 * q^6 - 56 * q^7 + 62 * q^8 - 46 * q^9 - 72 * q^10 - 94 * q^11 - 544 * q^12 + 72 * q^13 + 56 * q^14 + 140 * q^15 + 296 * q^16 + 8 * q^17 + 422 * q^18 + 51 * q^19 - 149 * q^20 - 294 * q^21 - 66 * q^22 - 830 * q^23 + 868 * q^24 - 256 * q^25 + 775 * q^26 + 27 * q^27 + 14 * q^28 + 236 * q^29 + 1008 * q^30 + 554 * q^31 - 1836 * q^32 + 895 * q^33 - 234 * q^34 + 112 * q^35 - 2322 * q^36 + 1439 * q^37 - 267 * q^38 - 18 * q^39 - 1232 * q^40 - 42 * q^41 + 210 * q^42 - 404 * q^43 + 591 * q^44 - 3020 * q^45 + 2169 * q^46 - 714 * q^47 + 4500 * q^48 - 392 * q^49 - 1035 * q^50 + 745 * q^51 + 725 * q^52 + 1351 * q^53 + 648 * q^54 + 1708 * q^55 - 966 * q^56 + 1561 * q^57 - 2529 * q^58 + 543 * q^59 - 316 * q^60 - 1542 * q^61 - 4231 * q^62 - 567 * q^63 + 1172 * q^64 - 4084 * q^65 + 5058 * q^66 - 1744 * q^67 + 2522 * q^68 - 1584 * q^69 + 126 * q^70 - 561 * q^71 - 4810 * q^72 - 144 * q^73 + 575 * q^74 + 1623 * q^75 - 3278 * q^76 + 567 * q^77 - 6582 * q^78 + 5785 * q^79 + 3199 * q^80 + 2403 * q^81 + 1998 * q^82 - 4177 * q^83 + 1652 * q^84 - 4090 * q^85 - 184 * q^86 - 940 * q^87 + 5446 * q^88 - 11554 * q^89 + 11896 * q^90 - 826 * q^91 + 12958 * q^92 - 578 * q^93 - 2042 * q^94 - 1390 * q^95 - 10074 * q^96 - q^97 - 588 * q^98 + 10027 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−1.68700	+	5.19206i	−0.596446	+	1.83567i	−0.0490507	+	0.998796i	$0.515620\pi$
$2$	−1.68700	+	5.19206i	−0.596446	+	1.83567i	−0.547395	+	0.836874i	$0.684380\pi$
$3$	7.39468	−	5.37255i	1.42311	−	1.03395i	0.431859	−	0.901941i	$-0.357858\pi$
$3$	7.39468	−	5.37255i	1.42311	−	1.03395i	0.991249	−	0.132007i	$-0.0421421\pi$
$4$	−17.6394	−	12.8158i	−2.20492	−	1.60197i
$5$	−3.09523	−	9.52615i	−0.276846	−	0.852045i	−0.988725	−	0.149743i	$-0.952155\pi$
$5$	−3.09523	−	9.52615i	−0.276846	−	0.852045i	0.711879	−	0.702302i	$-0.247845\pi$
$6$	15.4198	+	47.4572i	1.04918	+	3.22905i
$7$	−5.66312	−	4.11450i	−0.305780	−	0.222162i
$7$	−5.66312	−	4.11450i	−0.305780	−	0.222162i
$8$	60.9649	−	44.2936i	2.69429	−	1.95752i
$9$	17.4736	−	53.7781i	0.647169	−	1.99178i
$10$	54.6820			1.72920
$11$	34.9237	−	10.5515i	0.957264	−	0.289217i
$11$	34.9237	−	10.5515i	0.957264	−	0.289217i
$12$	−199.291			−4.79420
$13$	−2.42072	+	7.45022i	−0.0516452	+	0.158948i	−0.973553	−	0.228462i	$-0.926630\pi$
$13$	−2.42072	+	7.45022i	−0.0516452	+	0.158948i	0.921908	+	0.387410i	$0.126630\pi$
$14$	30.9164	−	22.4621i	0.590197	−	0.428803i
$15$	−74.0680	−	53.8136i	−1.27495	−	0.926307i
$16$	73.2258	+	225.366i	1.14415	+	3.52134i
$17$	−0.0243718	−	0.0750087i	−0.000347708	−	0.00107013i	0.950883	−	0.309552i	$-0.100179\pi$
$17$	−0.0243718	−	0.0750087i	−0.000347708	−	0.00107013i	−0.951230	+	0.308482i	$0.900179\pi$
$18$	249.741	+	181.448i	3.27026	+	2.37598i
$19$	0.608726	−	0.442265i	0.00735007	−	0.00534014i	−0.584104	−	0.811679i	$-0.698554\pi$
$19$	0.608726	−	0.442265i	0.00735007	−	0.00534014i	0.591454	+	0.806339i	$0.298554\pi$
$20$	−67.4869	+	207.703i	−0.754526	+	2.32219i
$21$	−63.9823			−0.664861
$22$	−4.13263	+	199.126i	−0.0400491	+	1.92972i
$23$	−124.351			−1.12735			−0.563675	−	0.825997i	$-0.690613\pi$
$23$	−124.351			−1.12735			−0.563675	+	0.825997i	$0.690613\pi$
$24$	212.846	−	655.074i	1.81030	−	5.57152i
$25$	19.9600	−	14.5018i	0.159680	−	0.116014i
$26$	−34.5982	−	25.1371i	−0.260972	−	0.189607i
$27$	−83.4523	−	256.840i	−0.594830	−	1.83070i
$28$	47.1635	+	145.154i	0.318324	+	0.979700i
$29$	23.3625	+	16.9738i	0.149597	+	0.108688i	0.660066	−	0.751208i	$-0.270528\pi$
$29$	23.3625	+	16.9738i	0.149597	+	0.108688i	−0.510469	+	0.859896i	$0.670528\pi$
$30$	404.356	−	293.782i	2.46083	−	1.78790i
$31$	−5.84157	+	17.9785i	−0.0338444	+	0.104162i	−0.966552	−	0.256472i	$-0.917440\pi$
$31$	−5.84157	+	17.9785i	−0.0338444	+	0.104162i	0.932707	+	0.360635i	$0.117440\pi$
$32$	−690.792			−3.81612
$33$	201.562	−	265.654i	1.06325	−	1.40135i
$34$	0.430565			0.00217180
$35$	−21.6666	+	66.6831i	−0.104638	+	0.322043i
$36$	−997.431	+	724.676i	−4.61773	+	3.35498i
$37$	233.025	+	169.303i	1.03538	+	0.752248i	0.969379	−	0.245571i	$-0.0789755\pi$
$37$	233.025	+	169.303i	1.03538	+	0.752248i	0.0660024	+	0.997819i	$0.478975\pi$
$38$	1.26935	+	3.90664i	0.00541882	+	0.0166774i
$39$	22.1262	+	68.0975i	0.0908470	+	0.279598i
$40$	−610.648	−	443.662i	−2.41380	−	1.75373i
$41$	−121.938	+	88.5929i	−0.464475	+	0.337461i	−0.795284	−	0.606237i	$-0.792678\pi$
$41$	−121.938	+	88.5929i	−0.464475	+	0.337461i	0.330809	+	0.943698i	$0.392678\pi$
$42$	107.938	−	332.200i	0.396554	−	1.22047i
$43$	351.919			1.24807			0.624037	−	0.781395i	$-0.285491\pi$
$43$	351.919			1.24807			0.624037	+	0.781395i	$0.285491\pi$
$44$	−751.258	−	261.453i	−2.57401	−	0.895807i
$45$	−566.383			−1.87625
$46$	209.781	−	645.639i	0.672402	−	2.06944i
$47$	202.590	−	147.190i	0.628740	−	0.456806i	−0.227223	−	0.973843i	$-0.572965\pi$
$47$	202.590	−	147.190i	0.628740	−	0.456806i	0.855964	+	0.517036i	$0.172965\pi$
$48$	1752.27	+	1273.10i	5.26914	+	3.82825i
$49$	15.1418	+	46.6018i	0.0441453	+	0.135865i
$50$	41.6216	+	128.098i	0.117724	+	0.362317i
$51$	−0.583210	−	0.423727i	−0.00160129	−	0.00116340i
$52$	138.180	−	100.394i	0.368503	−	0.267733i
$53$	−79.5600	+	244.860i	−0.206196	+	0.634607i	0.793466	+	0.608615i	$0.208274\pi$
$53$	−79.5600	+	244.860i	−0.206196	+	0.634607i	−0.999662	+	0.0259920i	$0.991726\pi$
$54$	1474.31			3.71534
$55$	−208.612	−	300.030i	−0.511440	−	0.735563i
$56$	−527.497			−1.25875
$57$	2.12524	−	6.54082i	0.00493851	−	0.0151992i
$58$	−127.542	+	92.6646i	−0.288742	+	0.209784i
$59$	−333.901	−	242.593i	−0.736782	−	0.535304i	0.154920	−	0.987927i	$-0.450488\pi$
$59$	−333.901	−	242.593i	−0.736782	−	0.535304i	−0.891702	+	0.452624i	$0.850488\pi$
$60$	616.852	+	1898.48i	1.32726	+	4.08487i
$61$	290.995	+	895.589i	0.610787	+	1.87981i	0.450607	+	0.892722i	$0.351208\pi$
$61$	290.995	+	895.589i	0.610787	+	1.87981i	0.160180	+	0.987088i	$0.448792\pi$
$62$	−83.4908	−	60.6596i	−0.171022	−	0.124255i
$63$	−320.225	+	232.657i	−0.640390	+	0.465270i
$64$	579.562	−	1783.71i	1.13196	−	3.48380i
$65$	78.4647			0.149728
$66$	1039.26	+	1494.68i	1.93824	+	2.78761i
$67$	778.370			1.41930			0.709650	−	0.704555i	$-0.248853\pi$
$67$	778.370			1.41930			0.709650	+	0.704555i	$0.248853\pi$
$68$	−0.531390	+	1.63545i	−0.000947654	+	0.00291658i
$69$	−919.538	+	668.084i	−1.60434	+	1.16562i
$70$	−309.671	−	224.989i	−0.528754	−	0.384162i
$71$	−86.4845	−	266.172i	−0.144561	−	0.444912i	0.852393	−	0.522901i	$-0.175150\pi$
$71$	−86.4845	−	266.172i	−0.144561	−	0.444912i	−0.996954	+	0.0779885i	$0.975150\pi$
$72$	−1316.75	−	4052.54i	−2.15529	−	6.63329i
$73$	−784.479	−	569.957i	−1.25776	−	0.913814i	−0.259112	−	0.965847i	$-0.583430\pi$
$73$	−784.479	−	569.957i	−1.25776	−	0.913814i	−0.998645	+	0.0520327i	$0.983430\pi$
$74$	−1272.14	+	924.267i	−1.99843	+	1.45194i
$75$	69.6864	−	214.473i	0.107289	−	0.330202i
$76$	−16.4055			−0.0247611
$77$	−241.191	−	83.9394i	−0.356965	−	0.124231i
$78$	−390.893			−0.567435
$79$	−292.710	+	900.868i	−0.416866	+	1.28298i	0.493705	+	0.869630i	$0.335642\pi$
$79$	−292.710	+	900.868i	−0.416866	+	1.28298i	−0.910571	+	0.413353i	$0.864358\pi$
$80$	1920.22	−	1395.12i	2.68359	−	1.94974i
$81$	−761.835	−	553.506i	−1.04504	−	0.759267i
$82$	−254.271	−	782.564i	−0.342433	−	1.05390i
$83$	214.079	+	658.867i	0.283111	+	0.871326i	0.986959	+	0.160975i	$0.0514638\pi$
$83$	214.079	+	658.867i	0.283111	+	0.871326i	−0.703848	+	0.710351i	$0.748536\pi$
$84$	1128.61	+	819.982i	1.46597	+	1.06509i
$85$	−0.639108	+	0.464339i	−0.000815541	+	0.000592525i
$86$	−593.689	+	1827.19i	−0.744408	+	2.29105i
$87$	263.951			0.325270
$88$	1661.76	−	2190.16i	2.01300	−	2.65309i
$89$	340.214			0.405198			0.202599	−	0.979262i	$-0.435061\pi$
$89$	340.214			0.405198			0.202599	+	0.979262i	$0.435061\pi$
$90$	955.491	−	2940.70i	1.11908	−	3.44419i
$91$	44.3628	−	32.2314i	0.0511042	−	0.0371294i
$92$	2193.48	+	1593.66i	2.48572	+	1.80598i
$93$	53.3939	+	164.330i	0.0595343	+	0.183228i
$94$	422.451	+	1300.17i	0.463537	+	1.42662i
$95$	−6.09723	−	4.42990i	−0.00658487	−	0.00478419i
$96$	−5108.19	+	3711.32i	−5.43075	+	3.94567i
$97$	−182.437	+	561.484i	−0.190966	+	0.587733i	−1.00000		2.88374e-5i	$-0.999991\pi$
$97$	−182.437	+	561.484i	−0.190966	+	0.587733i	0.809034	+	0.587762i	$0.199991\pi$
$98$	−267.504			−0.275734
$99$	42.8048	−	2062.50i	0.0434550	−	2.09383i
$100$	−537.934			−0.537934
$101$	259.440	−	798.474i	0.255596	−	0.786645i	−0.738115	−	0.674675i	$-0.764284\pi$
$101$	259.440	−	798.474i	0.255596	−	0.786645i	0.993712	−	0.111970i	$-0.0357161\pi$
$102$	3.18389	−	2.31323i	0.00309071	−	0.00224553i
$103$	−774.623	−	562.797i	−0.741028	−	0.538389i	0.152005	−	0.988380i	$-0.451427\pi$
$103$	−774.623	−	562.797i	−0.741028	−	0.538389i	−0.893033	+	0.449991i	$0.851427\pi$
$104$	182.418	+	561.424i	0.171996	+	0.529348i
$105$	198.040	+	609.505i	0.184064	+	0.566492i
$106$	−1137.11	−	826.160i	−1.04194	−	0.757017i
$107$	169.811	−	123.375i	0.153423	−	0.111468i	−0.508425	−	0.861106i	$-0.669772\pi$
$107$	169.811	−	123.375i	0.153423	−	0.111468i	0.661848	+	0.749638i	$0.269772\pi$
$108$	−1819.55	+	5600.00i	−1.62117	+	4.98945i
$109$	304.746			0.267792			0.133896	−	0.990995i	$-0.457251\pi$
$109$	304.746			0.267792			0.133896	+	0.990995i	$0.457251\pi$
$110$	1909.70	−	576.975i	1.65530	−	0.500113i
$111$	2632.73			2.25124
$112$	512.581	−	1577.56i	0.432449	−	1.33094i
$113$	1053.43	−	765.359i	0.876974	−	0.637159i	−0.0554753	−	0.998460i	$-0.517667\pi$
$113$	1053.43	−	765.359i	0.876974	−	0.637159i	0.932449	+	0.361301i	$0.117667\pi$
$114$	30.3751	+	22.0688i	0.0249551	+	0.0181310i
$115$	384.896	+	1184.59i	0.312102	+	0.960552i
$116$	−194.567	−	598.816i	−0.155734	−	0.479299i
$117$	358.360	+	260.364i	0.283166	+	0.205732i
$118$	1822.85	−	1324.38i	1.42209	−	1.03321i
$119$	−0.170603	+	0.525061i	−0.000131421	+	0.000404473i
$120$	−6899.14			−5.24836
$121$	1108.33	−	736.992i	0.832707	−	0.553713i
$122$	−5140.86			−3.81501
$123$	−425.721	+	1310.23i	−0.312081	+	0.960486i
$124$	333.450	−	242.266i	0.241490	−	0.175452i
$125$	−1212.86	−	881.191i	−0.867849	−	0.630529i
$126$	−667.749	−	2055.12i	−0.472125	−	1.45305i
$127$	278.940	+	858.489i	0.194897	+	0.599831i	0.999978	+	0.00666598i	$0.00212186\pi$
$127$	278.940	+	858.489i	0.194897	+	0.599831i	−0.805081	+	0.593165i	$0.797878\pi$
$128$	3812.49	+	2769.94i	2.63266	+	1.91274i
$129$	2602.33	−	1890.70i	1.77614	−	1.29044i
$130$	−132.370	+	407.393i	−0.0893048	+	0.274852i
$131$	−300.470			−0.200398			−0.100199	−	0.994967i	$-0.531948\pi$
$131$	−300.470			−0.200398			−0.100199	+	0.994967i	$0.531948\pi$
$132$	−6959.99	+	2102.81i	−4.58931	+	1.38656i
$133$	−5.26699			−0.00343388
$134$	−1313.11	+	4041.34i	−0.846535	+	2.60537i
$135$	−2188.39	+	1589.96i	−1.39516	+	1.01364i
$136$	−4.80823	−	3.49338i	−0.00303163	−	0.00220261i
$137$	−230.093	−	708.153i	−0.143490	−	0.441617i	0.853324	−	0.521382i	$-0.174583\pi$
$137$	−230.093	−	708.153i	−0.143490	−	0.441617i	−0.996814	+	0.0797643i	$0.974583\pi$
$138$	−1917.47	−	5901.36i	−1.18279	−	3.64027i
$139$	1815.75	+	1319.22i	1.10798	+	0.804997i	0.982345	−	0.187079i	$-0.0599020\pi$
$139$	1815.75	+	1319.22i	1.10798	+	0.804997i	0.125639	+	0.992076i	$0.459902\pi$
$140$	1236.78	−	898.574i	0.746622	−	0.542452i
$141$	707.302	−	2176.85i	0.422451	−	1.30017i
$142$	1527.88			0.902935
$143$	−5.93001	+	285.732i	−0.00346778	+	0.167092i
$144$	13399.3			7.75421
$145$	89.3830	−	275.093i	0.0511921	−	0.157553i
$146$	4282.67	−	3111.54i	2.42765	−	1.76379i
$147$	362.340	+	263.255i	0.203301	+	0.147707i
$148$	−1940.68	−	5972.79i	−1.07786	−	3.31730i
$149$	−306.878	−	944.474i	−0.168728	−	0.519291i	0.830564	−	0.556923i	$-0.188018\pi$
$149$	−306.878	−	944.474i	−0.168728	−	0.519291i	−0.999292	+	0.0376327i	$0.988018\pi$
$150$	995.994	+	723.632i	0.542150	+	0.393895i
$151$	−1485.40	+	1079.21i	−0.800530	+	0.581619i	−0.911070	−	0.412252i	$-0.864742\pi$
$151$	−1485.40	+	1079.21i	−0.800530	+	0.581619i	0.110539	+	0.993872i	$0.464742\pi$
$152$	17.5214	−	53.9253i	0.00934981	−	0.0287758i
$153$	−4.45969			−0.00235650
$154$	842.709	−	1110.67i	0.440957	−	0.581173i
$155$	189.347			0.0981208
$156$	482.429	−	1484.76i	0.247597	−	0.762027i
$157$	−3055.95	+	2220.28i	−1.55345	+	1.12865i	−0.612315	+	0.790614i	$0.709762\pi$
$157$	−3055.95	+	2220.28i	−1.55345	+	1.12865i	−0.941134	+	0.338033i	$0.890238\pi$
$158$	−4183.56	−	3039.54i	−2.10650	−	1.53046i
$159$	727.204	+	2238.11i	0.362711	+	1.11631i
$160$	2138.16	+	6580.59i	1.05648	+	3.25151i
$161$	704.216	+	511.643i	0.344721	+	0.250454i
$162$	4159.05	−	3021.73i	2.01707	−	1.46549i
$163$	−358.809	+	1104.30i	−0.172418	+	0.530647i	−0.999506	−	0.0314246i	$-0.989996\pi$
$163$	−358.809	+	1104.30i	−0.172418	+	0.530647i	0.827088	+	0.562072i	$0.189996\pi$
$164$	3286.29			1.56473
$165$	−3154.54	−	1097.85i	−1.48837	−	0.517983i
$166$	−3782.03			−1.76833
$167$	152.466	−	469.243i	0.0706478	−	0.217432i	−0.909498	−	0.415707i	$-0.863534\pi$
$167$	152.466	−	469.243i	0.0706478	−	0.217432i	0.980146	+	0.198276i	$0.0635341\pi$
$168$	−3900.67	+	2834.00i	−1.79133	+	1.30148i
$169$	1727.76	+	1255.29i	0.786420	+	0.571367i
$170$	−1.33270	−	4.10163i	−0.000601255	−	0.00185047i
$171$	−13.1476	−	40.4641i	−0.00587965	−	0.0180957i
$172$	−6207.64	−	4510.11i	−2.75191	−	1.99938i
$173$	2534.07	−	1841.11i	1.11365	−	0.809115i	0.130416	−	0.991459i	$-0.458369\pi$
$173$	2534.07	−	1841.11i	1.11365	−	0.809115i	0.983235	+	0.182344i	$0.0583686\pi$
$174$	−445.286	+	1370.45i	−0.194006	+	0.597089i
$175$	−172.704			−0.0746010
$176$	4935.26	+	7097.98i	2.11369	+	3.03994i
$177$	−3772.43			−1.60200
$178$	−573.942	+	1766.41i	−0.241678	+	0.743809i
$179$	−1858.40	+	1350.21i	−0.775997	+	0.563795i	−0.903775	−	0.428008i	$-0.859215\pi$
$179$	−1858.40	+	1350.21i	−0.775997	+	0.563795i	0.127778	+	0.991803i	$0.459215\pi$
$180$	9990.65	+	7258.64i	4.13700	+	3.00570i
$181$	−974.611	−	2999.54i	−0.400233	−	1.23179i	−0.924810	−	0.380429i	$-0.875776\pi$
$181$	−974.611	−	2999.54i	−0.400233	−	1.23179i	0.524577	−	0.851363i	$-0.324224\pi$
$182$	92.5075	+	284.709i	0.0376764	+	0.115956i
$183$	6963.41	+	5059.21i	2.81284	+	2.04365i
$184$	−7581.06	+	5507.96i	−3.03741	+	2.20681i
$185$	891.536	−	2743.86i	0.354308	−	1.09045i
$186$	−943.285			−0.371855
$187$	−1.64261	−	2.36243i	−0.000642349	−	0.000923838i
$188$	−5459.92			−2.11811
$189$	−584.166	+	1797.88i	−0.224824	+	0.691939i
$190$	33.2864	−	24.1840i	0.0127097	−	0.00923415i
$191$	−198.813	−	144.446i	−0.0753172	−	0.0547211i	0.549490	−	0.835501i	$-0.314822\pi$
$191$	−198.813	−	144.446i	−0.0753172	−	0.0547211i	−0.624807	+	0.780779i	$0.714822\pi$
$192$	−5297.39	−	16303.7i	−1.99118	−	6.12821i
$193$	−121.220	−	373.077i	−0.0452104	−	0.139143i	0.925903	−	0.377761i	$-0.123306\pi$
$193$	−121.220	−	373.077i	−0.0452104	−	0.139143i	−0.971114	+	0.238617i	$0.923306\pi$
$194$	−2607.49	−	1894.45i	−0.964984	−	0.701102i
$195$	580.221	−	421.556i	0.213080	−	0.154811i
$196$	330.145	−	1016.08i	0.120315	−	0.370292i
$197$	−2149.95			−0.777550			−0.388775	−	0.921333i	$-0.627102\pi$
$197$	−2149.95			−0.777550			−0.388775	+	0.921333i	$0.627102\pi$
$198$	10636.4	+	3701.70i	3.81767	+	1.32863i
$199$	4298.82			1.53133			0.765666	−	0.643238i	$-0.222410\pi$
$199$	4298.82			1.53133			0.765666	+	0.643238i	$0.222410\pi$
$200$	574.523	−	1768.20i	0.203125	−	0.625154i
$201$	5755.80	−	4181.83i	2.01982	−	1.46748i
$202$	3708.05	+	2694.06i	1.29157	+	0.938382i
$203$	−62.4657	−	192.250i	−0.0215972	−	0.0664694i
$204$	4.85708	+	14.9486i	0.00166698	+	0.00513043i
$205$	1221.38	+	887.381i	0.416120	+	0.302329i
$206$	4228.87	−	3072.45i	1.43029	−	1.03916i
$207$	−2172.86	+	6687.38i	−0.729586	+	2.24543i
$208$	−1856.29			−0.618799
$209$	16.5924	−	21.8685i	0.00549150	−	0.00723768i
$210$	−3498.68			−1.14968
$211$	769.816	−	2369.25i	0.251167	−	0.773014i	−0.743393	−	0.668855i	$-0.766785\pi$
$211$	769.816	−	2369.25i	0.251167	−	0.773014i	0.994561	−	0.104159i	$-0.0332151\pi$
$212$	4541.46	−	3299.56i	1.47127	−	1.06894i
$213$	−2069.55	−	1503.61i	−0.665742	−	0.483690i
$214$	354.099	+	1089.80i	0.113111	+	0.348119i
$215$	−1089.27	−	3352.44i	−0.345525	−	1.06342i
$216$	−16464.0	−	11961.8i	−5.18627	−	3.76804i
$217$	107.054	−	77.7793i	0.0334899	−	0.0243318i
$218$	−514.107	+	1582.26i	−0.159723	+	0.491578i
$219$	−8863.10			−2.73476
$220$	−165.322	+	7965.86i	−0.0506636	+	2.44117i
$221$	0.617829			0.000188053
$222$	−4441.43	+	13669.3i	−1.34274	+	4.13254i
$223$	3304.97	−	2401.20i	0.992452	−	0.721059i	0.0319955	−	0.999488i	$-0.489814\pi$
$223$	3304.97	−	2401.20i	0.992452	−	0.721059i	0.960457	+	0.278429i	$0.0898138\pi$
$224$	3912.04	+	2842.26i	1.16689	+	0.847797i
$225$	−431.107	−	1326.81i	−0.127735	−	0.393129i
$226$	2196.66	+	6760.62i	0.646547	+	1.98987i
$227$	−2254.60	−	1638.07i	−0.659222	−	0.478953i	0.207178	−	0.978303i	$-0.433572\pi$
$227$	−2254.60	−	1638.07i	−0.659222	−	0.478953i	−0.866400	+	0.499351i	$0.833572\pi$
$228$	−121.314	+	88.1395i	−0.0352377	+	0.0256017i
$229$	894.578	−	2753.23i	0.258146	−	0.794491i	−0.735048	−	0.678015i	$-0.762840\pi$
$229$	894.578	−	2753.23i	0.258146	−	0.794491i	0.993194	−	0.116475i	$-0.0371596\pi$
$230$	−6799.78			−1.94941
$231$	−2234.50	+	675.107i	−0.636448	+	0.192289i
$232$	2176.12			0.615817
$233$	969.975	−	2985.28i	0.272726	−	0.839365i	−0.717086	−	0.696985i	$-0.754525\pi$
$233$	969.975	−	2985.28i	0.272726	−	0.839365i	0.989812	−	0.142380i	$-0.0454755\pi$
$234$	−1956.38	+	1421.39i	−0.546550	+	0.397092i
$235$	−2029.22	−	1474.31i	−0.563284	−	0.409250i
$236$	2780.79	+	8558.38i	0.767007	+	2.36061i
$237$	2675.47	+	8234.24i	0.733292	+	2.25684i
$238$	−2.43834	−	1.77156i	−0.000664093	−	0.000482492i
$239$	−5365.42	+	3898.21i	−1.45213	+	1.05504i	−0.466808	+	0.884359i	$0.654596\pi$
$239$	−5365.42	+	3898.21i	−1.45213	+	1.05504i	−0.985327	+	0.170679i	$0.945404\pi$
$240$	6704.05	−	20633.0i	1.80310	−	5.54938i
$241$	−5814.93			−1.55424			−0.777122	−	0.629351i	$-0.783321\pi$
$241$	−5814.93			−1.55424			−0.777122	+	0.629351i	$0.783321\pi$
$242$	1956.75	+	6997.84i	0.519771	+	1.85884i
$243$	−1315.72			−0.347340
$244$	6344.69	−	19527.0i	1.66466	−	5.12330i
$245$	397.068	−	288.487i	0.103542	−	0.0752275i
$246$	−6084.62	−	4420.73i	−1.57700	−	1.14575i
$247$	1.82142	+	5.60575i	0.000469206	+	0.00144407i
$248$	440.202	+	1354.80i	0.112713	+	0.346895i
$249$	5122.84	+	3721.96i	1.30380	+	0.947268i
$250$	6621.29	−	4810.65i	1.67507	−	1.21701i
$251$	−1623.72	+	4997.30i	−0.408320	+	1.25668i	0.509770	+	0.860311i	$0.329730\pi$
$251$	−1623.72	+	4997.30i	−0.408320	+	1.25668i	−0.918091	+	0.396370i	$0.870270\pi$
$252$	8630.25			2.15736
$253$	−4342.81	+	1312.09i	−1.07917	+	0.326048i
$254$	−4927.90			−1.21734
$255$	−2.23131	+	6.86728i	−0.000547962	+	0.00168645i
$256$	−8674.89	+	6302.67i	−2.11789	+	1.53874i
$257$	−3708.58	−	2694.44i	−0.900136	−	0.653987i	0.0383650	−	0.999264i	$-0.487785\pi$
$257$	−3708.58	−	2694.44i	−0.900136	−	0.653987i	−0.938501	+	0.345277i	$0.887785\pi$
$258$	5426.51	+	16701.1i	1.30946	+	4.03009i
$259$	−623.054	−	1917.56i	−0.149478	−	0.460045i
$260$	−1384.07	−	1005.58i	−0.330139	−	0.239860i
$261$	1321.05	−	959.797i	0.313298	−	0.227624i
$262$	506.893	−	1560.06i	0.119527	−	0.367865i
$263$	2566.00			0.601620			0.300810	−	0.953684i	$-0.402743\pi$
$263$	2566.00			0.601620			0.300810	+	0.953684i	$0.402743\pi$
$264$	521.407	−	25123.5i	0.121554	−	5.85698i
$265$	2578.83			0.597798
$266$	8.88542	−	27.3465i	0.00204812	−	0.00630347i
$267$	2515.77	−	1827.82i	0.576640	−	0.418953i
$268$	−13730.0	−	9975.40i	−3.12944	−	2.27367i
$269$	1717.26	+	5285.17i	0.389230	+	1.19793i	0.933365	+	0.358930i	$0.116858\pi$
$269$	1717.26	+	5285.17i	0.389230	+	1.19793i	−0.544134	+	0.838998i	$0.683142\pi$
$270$	−4563.34	−	14044.5i	−1.02858	−	3.16564i
$271$	1674.00	+	1216.23i	0.375233	+	0.272623i	0.759377	−	0.650650i	$-0.225504\pi$
$271$	1674.00	+	1216.23i	0.375233	+	0.272623i	−0.384145	+	0.923273i	$0.625504\pi$
$272$	15.1198	−	10.9851i	0.00337048	−	0.00244880i
$273$	154.884	−	476.683i	0.0343369	−	0.105678i
$274$	4064.94			0.896248
$275$	544.063	−	717.065i	0.119303	−	0.157239i
$276$	24782.1			5.40473
$277$	−286.206	+	880.852i	−0.0620811	+	0.191066i	−0.977287	−	0.211921i	$-0.932028\pi$
$277$	−286.206	+	880.852i	−0.0620811	+	0.191066i	0.915206	+	0.402987i	$0.132028\pi$
$278$	−9912.63	+	7201.95i	−2.13856	+	1.55376i
$279$	864.778	+	628.298i	0.185566	+	0.134822i
$280$	1632.73	+	5025.02i	0.348479	+	1.07251i
$281$	13.3321	+	41.0319i	0.00283034	+	0.00871088i	0.952462	−	0.304658i	$-0.0985423\pi$
$281$	13.3321	+	41.0319i	0.00283034	+	0.00871088i	−0.949631	+	0.313369i	$0.898542\pi$
$282$	10109.1	+	7344.71i	2.13471	+	1.55096i
$283$	515.914	−	374.833i	0.108367	−	0.0787333i	−0.532282	−	0.846567i	$-0.678665\pi$
$283$	515.914	−	374.833i	0.108367	−	0.0787333i	0.640649	+	0.767834i	$0.278665\pi$
$284$	−1885.66	+	5803.47i	−0.393991	+	1.21258i
$285$	−68.8870			−0.0143176
$286$	−1473.53	−	512.819i	−0.304657	−	0.106027i
$287$	1055.06			0.216998
$288$	−12070.6	+	37149.5i	−2.46968	+	7.60089i
$289$	3974.70	−	2887.79i	0.809016	−	0.587785i
$290$	1277.51	+	928.164i	0.258682	+	0.187944i
$291$	1667.54	+	5132.15i	0.335920	+	1.03386i
$292$	6533.29	+	20107.4i	1.30936	+	4.02978i
$293$	−5218.12	−	3791.19i	−1.04043	−	0.755917i	−0.0700606	−	0.997543i	$-0.522319\pi$
$293$	−5218.12	−	3791.19i	−1.04043	−	0.755917i	−0.970369	+	0.241626i	$0.922319\pi$
$294$	−1978.10	+	1437.18i	−0.392399	+	0.285095i
$295$	−1277.48	+	3931.67i	−0.252127	+	0.775968i
$296$	21705.4			4.26216
$297$	−5624.50	−	8089.26i	−1.09888	−	1.58043i
$298$	5421.47			1.05388
$299$	301.020	−	926.445i	0.0582222	−	0.179190i
$300$	−3977.85	+	2890.08i	−0.765538	+	0.556196i
$301$	−1992.96	−	1447.97i	−0.381636	−	0.277275i
$302$	−3097.43	−	9532.91i	−0.590189	−	1.81641i
$303$	−2371.37	−	7298.32i	−0.449609	−	1.38375i
$304$	144.246	+	104.801i	0.0272141	+	0.0197722i
$305$	7630.82	−	5544.12i	1.43259	−	1.04084i
$306$	7.52351	−	23.1550i	0.00140552	−	0.00432576i
$307$	−4768.51			−0.886493			−0.443247	−	0.896400i	$-0.646173\pi$
$307$	−4768.51			−0.886493			−0.443247	+	0.896400i	$0.646173\pi$
$308$	3178.72	+	4571.69i	0.588065	+	0.845767i
$309$	−8751.75			−1.61123
$310$	−319.429	+	983.102i	−0.0585237	+	0.180118i
$311$	−1256.47	+	912.882i	−0.229094	+	0.166446i	−0.696411	−	0.717644i	$-0.745221\pi$
$311$	−1256.47	+	912.882i	−0.229094	+	0.166446i	0.467317	+	0.884090i	$0.345221\pi$
$312$	4365.20	+	3171.51i	0.792086	+	0.575484i
$313$	222.777	+	685.636i	0.0402303	+	0.123816i	0.969155	−	0.246454i	$-0.0792653\pi$
$313$	222.777	+	685.636i	0.0402303	+	0.123816i	−0.928924	+	0.370270i	$0.879265\pi$
$314$	−6372.42	−	19612.3i	−1.14528	−	3.52480i
$315$	3207.50	+	2330.38i	0.573721	+	0.416832i
$316$	16708.5	−	12139.5i	2.97446	−	2.16107i
$317$	−614.702	+	1891.86i	−0.108912	+	0.335197i	−0.990629	−	0.136583i	$-0.956388\pi$
$317$	−614.702	+	1891.86i	−0.108912	+	0.335197i	0.881717	+	0.471779i	$0.156388\pi$
$318$	−12847.2			−2.26551
$319$	995.004	+	346.282i	0.174638	+	0.0607776i
$320$	−18785.7			−3.28173
$321$	592.861	−	1824.64i	0.103085	−	0.317263i
$322$	−3844.50	+	2793.19i	−0.665358	+	0.483411i
$323$	−0.0480095	−	0.0348809i	−8.27034e−6	−	6.00875e-6i
$324$	6344.71	+	19527.0i	1.08791	+	3.34825i
$325$	59.7240	+	183.812i	0.0101935	+	0.0313724i
$326$	−5128.28	−	3725.92i	−0.871256	−	0.633004i
$327$	2253.50	−	1637.26i	0.381097	−	0.276883i
$328$	−3509.82	+	10802.1i	−0.590845	+	1.81843i
$329$	−1752.90			−0.293741
$330$	11021.8	−	14526.5i	1.83858	−	2.42321i
$331$	8148.20			1.35307			0.676534	−	0.736411i	$-0.263481\pi$
$331$	8148.20			1.35307			0.676534	+	0.736411i	$0.263481\pi$
$332$	4667.66	−	14365.6i	0.771600	−	2.37474i
$333$	13176.6	−	9573.33i	2.16838	−	1.57542i
$334$	2179.13	+	1583.23i	0.356995	+	0.259372i
$335$	−2409.24	−	7414.87i	−0.392928	−	1.20931i
$336$	−4685.16	−	14419.4i	−0.760703	−	2.34120i
$337$	1100.30	+	799.413i	0.177855	+	0.129219i	0.673151	−	0.739505i	$-0.264940\pi$
$337$	1100.30	+	799.413i	0.177855	+	0.129219i	−0.495296	+	0.868724i	$0.664940\pi$
$338$	−9432.31	+	6852.97i	−1.51790	+	1.10282i
$339$	3677.82	−	11319.2i	0.589239	−	1.81349i
$340$	17.2243			0.00274741
$341$	−14.3100	+	689.514i	−0.00227253	+	0.109499i
$342$	232.272			0.0367247
$343$	105.993	−	326.212i	0.0166853	−	0.0513522i
$344$	21454.7	−	15587.8i	3.36267	−	2.44313i
$345$	9210.45	+	6691.79i	1.43732	+	1.04427i
$346$	5284.17	+	16263.0i	0.821036	+	2.52689i
$347$	761.974	+	2345.11i	0.117882	+	0.362802i	0.992537	−	0.121943i	$-0.0389125\pi$
$347$	761.974	+	2345.11i	0.117882	+	0.362802i	−0.874656	+	0.484745i	$0.838912\pi$
$348$	−4655.93	−	3382.73i	−0.717196	−	0.521074i
$349$	−8313.27	+	6039.94i	−1.27507	+	0.926392i	−0.999392	−	0.0348584i	$-0.988902\pi$
$349$	−8313.27	+	6039.94i	−1.27507	+	0.926392i	−0.275677	+	0.961250i	$0.588902\pi$
$350$	291.352	−	896.688i	0.0444954	−	0.136943i
$351$	2115.53			0.321705
$352$	−24125.0	+	7288.86i	−3.65304	+	1.10369i
$353$	−11267.0			−1.69881			−0.849406	−	0.527740i	$-0.823039\pi$
$353$	−11267.0			−1.69881			−0.849406	+	0.527740i	$0.823039\pi$
$354$	6364.10	−	19586.7i	0.955504	−	2.94074i
$355$	−2267.90	+	1647.73i	−0.339064	+	0.246345i
$356$	−6001.16	−	4360.10i	−0.893430	−	0.649115i
$357$	1.55936	+	4.79923i	0.000231177	+	0.000711491i
$358$	−3875.23	−	11926.7i	−0.572101	−	1.76075i
$359$	7262.15	+	5276.26i	1.06764	+	0.775684i	0.975486	−	0.220061i	$-0.0706257\pi$
$359$	7262.15	+	5276.26i	1.06764	+	0.775684i	0.0921511	+	0.995745i	$0.470626\pi$
$360$	−34529.5	+	25087.1i	−5.05518	+	3.67280i
$361$	−2119.37	+	6522.76i	−0.308991	+	0.950978i
$362$	17218.0			2.49988
$363$	4236.25	−	11404.4i	0.612521	−	1.64897i
$364$	−1195.60			−0.172161
$365$	−3001.35	+	9237.22i	−0.430406	+	1.32465i
$366$	−38015.0	+	27619.5i	−5.42918	+	3.94453i
$367$	−3001.10	−	2180.43i	−0.426856	−	0.310129i	0.353535	−	0.935421i	$-0.384980\pi$
$367$	−3001.10	−	2180.43i	−0.426856	−	0.310129i	−0.780390	+	0.625293i	$0.784980\pi$
$368$	−9105.72	−	28024.5i	−1.28986	−	3.96978i
$369$	2633.67	+	8105.62i	0.371554	+	1.14353i
$370$	12742.3	+	9257.81i	1.79038	+	1.30079i
$371$	1458.03	−	1059.32i	0.204036	−	0.148241i
$372$	1164.17	−	3582.96i	0.162257	−	0.499375i
$373$	−9795.50			−1.35976			−0.679882	−	0.733322i	$-0.737969\pi$
$373$	−9795.50			−1.35976			−0.679882	+	0.733322i	$0.737969\pi$
$374$	15.0369	−	4.54309i	0.00207899	−	0.000628122i
$375$	−13702.9			−1.88698
$376$	5831.29	−	17946.9i	0.799803	−	2.46154i
$377$	−183.013	+	132.967i	−0.0250017	+	0.0181648i
$378$	−8349.20	−	6066.05i	−1.13608	−	0.825407i
$379$	2386.38	+	7344.53i	0.323431	+	0.995417i	0.972144	+	0.234384i	$0.0753073\pi$
$379$	2386.38	+	7344.53i	0.323431	+	0.995417i	−0.648714	+	0.761033i	$0.724693\pi$
$380$	50.7789	+	156.281i	0.00685501	+	0.0210975i
$381$	6674.95	+	4849.63i	0.897554	+	0.652111i
$382$	1085.37	−	788.567i	0.145373	−	0.105619i
$383$	327.343	−	1007.46i	0.0436722	−	0.134409i	−0.926843	−	0.375449i	$-0.877488\pi$
$383$	327.343	−	1007.46i	0.0436722	−	0.134409i	0.970515	+	0.241040i	$0.0774885\pi$
$384$	43073.8			5.72422
$385$	−53.0765	+	2557.44i	−0.00702605	+	0.338543i
$386$	2141.54			0.282387
$387$	6149.29	−	18925.6i	0.807715	−	2.48589i
$388$	10413.9	−	7566.17i	1.36260	−	0.989984i
$389$	−5057.38	−	3674.40i	−0.659175	−	0.478919i	0.207209	−	0.978297i	$-0.433562\pi$
$389$	−5057.38	−	3674.40i	−0.659175	−	0.478919i	−0.866384	+	0.499378i	$0.833562\pi$
$390$	1209.91	+	3723.71i	0.157092	+	0.483481i
$391$	3.03066	+	9.32743i	0.000391988	+	0.00120641i
$392$	2987.28	+	2170.38i	0.384899	+	0.279645i
$393$	−2221.88	+	1614.29i	−0.285188	+	0.207201i
$394$	3626.97	−	11162.7i	0.463766	−	1.42733i
$395$	9487.82			1.20857
$396$	−27187.6	+	35832.7i	−3.45007	+	4.54713i
$397$	−8470.75			−1.07087			−0.535434	−	0.844577i	$-0.679852\pi$
$397$	−8470.75			−1.07087			−0.535434	+	0.844577i	$0.679852\pi$
$398$	−7252.12	+	22319.7i	−0.913356	+	2.81102i
$399$	−38.9477	+	28.2972i	−0.00488678	+	0.00355045i
$400$	4729.80	+	3436.40i	0.591225	+	0.429550i
$401$	−4514.68	−	13894.8i	−0.562225	−	1.73035i	−0.676055	−	0.736851i	$-0.736312\pi$
$401$	−4514.68	−	13894.8i	−0.562225	−	1.73035i	0.113829	−	0.993500i	$-0.463688\pi$
$402$	12002.3	+	36939.2i	1.48910	+	4.58299i
$403$	−119.803	−	87.0421i	−0.0148085	−	0.0107590i
$404$	−14809.4	+	10759.7i	−1.82375	+	1.32503i
$405$	−2914.72	+	8970.59i	−0.357614	+	1.10062i
$406$	1103.55			0.134898
$407$	9924.50	+	3453.93i	1.20870	+	0.420651i
$408$	−54.3237			−0.00659172
$409$	−3563.71	+	10968.0i	−0.430841	+	1.32599i	0.466448	+	0.884549i	$0.345534\pi$
$409$	−3563.71	+	10968.0i	−0.430841	+	1.32599i	−0.897289	+	0.441444i	$0.854466\pi$
$410$	−6667.80	+	4844.44i	−0.803169	+	0.583536i
$411$	−5506.05	−	4000.38i	−0.660812	−	0.480108i
$412$	6451.21	+	19854.8i	0.771428	+	2.37421i
$413$	892.771	+	2747.67i	0.106369	+	0.327370i
$414$	−31055.7	−	22563.3i	−3.68672	−	2.67856i
$415$	5613.84	−	4078.69i	0.664030	−	0.482446i
$416$	1672.22	−	5146.55i	0.197085	−	0.606564i
$417$	20514.4			2.40910
$418$	85.5511	+	123.041i	0.0100106	+	0.0143975i
$419$	9171.83			1.06939			0.534693	−	0.845046i	$-0.320427\pi$
$419$	9171.83			1.06939			0.534693	+	0.845046i	$0.320427\pi$
$420$	4317.97	−	13289.3i	0.501655	−	1.54394i
$421$	−4187.22	+	3042.20i	−0.484733	+	0.352179i	−0.803155	−	0.595770i	$-0.796847\pi$
$421$	−4187.22	+	3042.20i	−0.484733	+	0.352179i	0.318422	+	0.947949i	$0.396847\pi$
$422$	11002.6	+	7993.86i	1.26919	+	0.922121i
$423$	−4375.64	−	13466.9i	−0.502958	−	1.54794i
$424$	5995.38	+	18451.9i	0.686701	+	2.11345i
$425$	−1.57422	−	1.14374i	−0.000179673	−	0.000130540i
$426$	11298.2	−	8208.61i	1.28497	−	0.933588i
$427$	2036.96	−	6269.12i	0.230856	−	0.710501i
$428$	−4576.51			−0.516855
$429$	1491.26	+	2144.76i	0.167829	+	0.241375i
$430$	19243.7			2.15817
$431$	−3238.65	+	9967.55i	−0.361950	+	1.11397i	0.589919	+	0.807462i	$0.299160\pi$
$431$	−3238.65	+	9967.55i	−0.361950	+	1.11397i	−0.951869	+	0.306505i	$0.900840\pi$
$432$	51772.1	−	37614.6i	5.76594	−	4.18920i
$433$	9285.65	+	6746.42i	1.03058	+	0.748758i	0.968424	−	0.249309i	$-0.0802035\pi$
$433$	9285.65	+	6746.42i	1.03058	+	0.748758i	0.0621525	+	0.998067i	$0.480203\pi$
$434$	223.235	+	687.045i	0.0246903	+	0.0759890i
$435$	−816.991	−	2514.44i	−0.0900499	−	0.277145i
$436$	−5375.52	−	3905.55i	−0.590461	−	0.428995i
$437$	−75.6958	+	54.9962i	−0.00828609	+	0.00602020i
$438$	14952.1	−	46017.8i	1.63114	−	5.02012i
$439$	−1183.53			−0.128672			−0.0643359	−	0.997928i	$-0.520493\pi$
$439$	−1183.53			−0.128672			−0.0643359	+	0.997928i	$0.520493\pi$
$440$	−26007.4	−	9051.09i	−2.81785	−	0.980668i
$441$	2770.74			0.299183
$442$	−1.04228	+	3.20781i	−0.000112163	+	0.000345203i
$443$	−4873.05	+	3540.48i	−0.522631	+	0.379714i	−0.817594	−	0.575795i	$-0.804693\pi$
$443$	−4873.05	+	3540.48i	−0.522631	+	0.379714i	0.294963	+	0.955509i	$0.404693\pi$
$444$	−46439.8	−	33740.5i	−4.96382	−	3.60643i
$445$	−1053.04	−	3240.93i	−0.112177	−	0.345247i
$446$	6891.68	+	21210.4i	0.731683	+	2.25189i
$447$	−7343.50	−	5335.37i	−0.777037	−	0.564551i
$448$	−10621.2	+	7716.74i	−1.12010	+	0.813799i
$449$	−4339.53	+	13355.7i	−0.456114	+	1.40377i	0.413709	+	0.910409i	$0.364233\pi$
$449$	−4339.53	+	13355.7i	−0.456114	+	1.40377i	−0.869823	+	0.493364i	$0.835767\pi$
$450$	7616.16			0.797843
$451$	−3323.73	+	4380.61i	−0.347026	+	0.457373i
$452$	−28390.5			−2.95437
$453$	−5185.97	+	15960.8i	−0.537876	+	1.65541i
$454$	12308.5	−	8942.62i	1.27239	−	0.924445i
$455$	−444.355	−	322.843i	−0.0457839	−	0.0332639i
$456$	−160.151	−	492.895i	−0.0164469	−	0.0506182i
$457$	−3066.23	−	9436.87i	−0.313855	−	0.965948i	−0.976223	−	0.216769i	$-0.930448\pi$
$457$	−3066.23	−	9436.87i	−0.313855	−	0.965948i	0.662367	−	0.749179i	$-0.269552\pi$
$458$	12785.8	+	9289.40i	1.30445	+	0.947741i
$459$	−17.2313	+	12.5193i	−0.00175226	+	0.00127310i
$460$	8392.08	−	25828.2i	0.850614	−	2.61792i
$461$	10702.4			1.08126			0.540632	−	0.841259i	$-0.318185\pi$
$461$	10702.4			1.08126			0.540632	+	0.841259i	$0.318185\pi$
$462$	264.415	−	12740.6i	0.0266271	−	1.28300i
$463$	−5022.54			−0.504141			−0.252070	−	0.967709i	$-0.581111\pi$
$463$	−5022.54			−0.504141			−0.252070	+	0.967709i	$0.581111\pi$
$464$	−2114.59	+	6508.03i	−0.211567	+	0.651138i
$465$	1400.16	−	1017.28i	0.139637	−	0.101452i
$466$	13863.4	+	10072.3i	1.37813	+	1.00127i
$467$	−3297.70	−	10149.3i	−0.326766	−	1.00568i	−0.970637	−	0.240548i	$-0.922673\pi$
$467$	−3297.70	−	10149.3i	−0.326766	−	1.00568i	0.643872	−	0.765133i	$-0.277327\pi$
$468$	−2984.49	−	9185.32i	−0.294782	−	0.907247i
$469$	−4408.00	−	3202.60i	−0.433993	−	0.315314i
$470$	11078.0	−	8048.66i	1.08722	−	0.789909i
$471$	−10669.2	+	32836.5i	−1.04376	+	3.21237i
$472$	−31101.5			−3.03297
$473$	12290.3	−	3713.26i	1.19474	−	0.360964i
$474$	−47266.2			−4.58018
$475$	5.73654	−	17.6552i	0.000554127	−	0.00170543i
$476$	9.73838	−	7.07535i	0.000937727	−	0.000681298i
$477$	11777.9	+	8557.17i	1.13055	+	0.821396i
$478$	−11188.2	−	34433.9i	−1.07058	−	3.29491i
$479$	−326.001	−	1003.33i	−0.0310968	−	0.0957062i	0.934303	−	0.356479i	$-0.116023\pi$
$479$	−326.001	−	1003.33i	−0.0310968	−	0.0957062i	−0.965400	+	0.260772i	$0.916023\pi$
$480$	51165.6	+	37174.0i	4.86537	+	3.53490i
$481$	−1825.43	+	1326.25i	−0.173041	+	0.125721i
$482$	9809.80	−	30191.5i	0.927021	−	2.85308i
$483$	7956.28			0.749531
$484$	−28995.4	−	1204.05i	−2.72309	−	0.113077i
$485$	5913.47			0.553643
$486$	2219.63	−	6831.31i	0.207169	−	0.637602i
$487$	−15531.4	+	11284.2i	−1.44516	+	1.04997i	−0.458228	+	0.888835i	$0.651516\pi$
$487$	−15531.4	+	11284.2i	−1.44516	+	1.04997i	−0.986932	+	0.161136i	$0.948484\pi$
$488$	57409.3	+	41710.3i	5.32540	+	3.86913i
$489$	3279.63	+	10093.7i	0.303293	+	0.933439i
$490$	827.986	+	2548.28i	0.0763359	+	0.234938i
$491$	10339.2	+	7511.87i	0.950309	+	0.690440i	0.950880	−	0.309560i	$-0.100182\pi$
$491$	10339.2	+	7511.87i	0.950309	+	0.690440i	−0.000570737		1.00000i	$0.500182\pi$
$492$	24301.1	−	17655.8i	2.22678	−	1.61785i
$493$	0.703800	−	2.16607i	6.42952e−5	−	0.000197880i
$494$	−32.1781			−0.00293069
$495$	−19780.2	+	5976.17i	−1.79607	+	0.542644i
$496$	−4479.50			−0.405515
$497$	−605.391	+	1863.20i	−0.0546389	+	0.168161i
$498$	−27966.9	+	20319.1i	−2.51652	+	1.82836i
$499$	11787.6	+	8564.19i	1.05749	+	0.768309i	0.973622	−	0.228169i	$-0.0732737\pi$
$499$	11787.6	+	8564.19i	1.05749	+	0.768309i	0.0838644	+	0.996477i	$0.473274\pi$
$500$	10100.9	+	31087.3i	0.903451	+	2.78054i
$501$	−1393.59	−	4289.03i	−0.124274	−	0.382475i
$502$	−23207.1	−	16860.9i	−2.06331	−	1.49908i
$503$	430.206	−	312.563i	0.0381351	−	0.0277068i	−0.568554	−	0.822646i	$-0.692497\pi$
$503$	430.206	−	312.563i	0.0381351	−	0.0277068i	0.606690	+	0.794939i	$0.292497\pi$
$504$	−9217.26	+	28367.8i	−0.814622	+	2.50715i
$505$	−8409.41			−0.741018
$506$	513.898	−	24761.6i	0.0451493	−	2.17547i
$507$	19520.4			1.70992
$508$	6081.86	−	18718.0i	0.531179	−	1.63480i
$509$	10167.0	−	7386.73i	0.885349	−	0.643244i	−0.0493124	−	0.998783i	$-0.515703\pi$
$509$	10167.0	−	7386.73i	0.885349	−	0.643244i	0.934661	+	0.355540i	$0.115703\pi$
$510$	−31.8911	−	23.1702i	−0.00276894	−	0.00201176i
$511$	2097.51	+	6455.47i	0.181582	+	0.558852i
$512$	−6439.36	−	19818.3i	−0.555825	−	1.71065i
$513$	−164.391	−	119.437i	−0.0141482	−	0.0102793i
$514$	20246.1	−	14709.6i	1.73739	−	1.26229i
$515$	−2963.65	+	9121.17i	−0.253580	+	0.780440i
$516$	−70134.3			−5.98351
$517$	5522.13	−	7278.05i	0.469754	−	0.619126i
$518$	11007.2			0.933645
$519$	8847.18	−	27228.8i	0.748263	−	2.30292i
$520$	4783.59	−	3475.48i	0.403412	−	0.293096i
$521$	−8849.62	−	6429.63i	−0.744163	−	0.540666i	0.149849	−	0.988709i	$-0.452121\pi$
$521$	−8849.62	−	6429.63i	−0.744163	−	0.540666i	−0.894012	+	0.448043i	$0.852121\pi$
$522$	2754.72	+	8478.14i	0.230978	+	0.710878i
$523$	−1892.09	−	5823.25i	−0.158194	−	0.486870i	0.840277	−	0.542158i	$-0.182392\pi$
$523$	−1892.09	−	5823.25i	−0.158194	−	0.486870i	−0.998470	+	0.0552876i	$0.982392\pi$
$524$	5300.10	+	3850.75i	0.441862	+	0.321032i
$525$	−1277.09	+	927.859i	−0.106165	+	0.0771335i
$526$	−4328.84	+	13322.8i	−0.358834	+	1.10438i
$527$	1.49091			0.000123236
$528$	74628.9	+	25972.4i	6.15115	+	2.14073i
$529$	3296.24			0.270916
$530$	−4350.50	+	13389.5i	−0.356554	+	1.09736i
$531$	−18880.6	+	13717.6i	−1.54303	+	1.12108i
$532$	92.9064	+	67.5004i	0.00757143	+	0.00550097i
$533$	−364.859	−	1122.92i	−0.0296507	−	0.0912554i
$534$	5246.02	+	16145.6i	0.425126	+	1.30840i
$535$	−1700.89	−	1235.77i	−0.137451	−	0.0998637i
$536$	47453.2	−	34476.8i	3.82401	−	2.77830i
$537$	−6488.23	+	19968.7i	−0.521392	+	1.60468i
$538$	−30338.0			−2.43116
$539$	1020.53	+	1467.74i	0.0815532	+	0.117291i
$540$	58978.4			4.70005
$541$	819.953	−	2523.56i	0.0651618	−	0.200547i	−0.913175	−	0.407568i	$-0.866377\pi$
$541$	819.953	−	2523.56i	0.0651618	−	0.200547i	0.978337	+	0.207021i	$0.0663768\pi$
$542$	−9138.78	+	6639.71i	−0.724251	+	0.526199i
$543$	−23322.1	−	16944.5i	−1.84318	−	1.33915i
$544$	16.8358	+	51.8154i	0.00132690	+	0.00408376i
$545$	−943.259	−	2903.05i	−0.0741372	−	0.228171i
$546$	2213.68	+	1608.33i	0.173510	+	0.126063i
$547$	−3648.80	+	2651.01i	−0.285213	+	0.207219i	−0.721188	−	0.692740i	$-0.756404\pi$
$547$	−3648.80	+	2651.01i	−0.285213	+	0.207219i	0.435975	+	0.899959i	$0.356404\pi$
$548$	−5016.82	+	15440.2i	−0.391073	+	1.20360i
$549$	53247.8			4.13946
$550$	2805.21	+	4034.50i	0.217481	+	0.312785i
$551$	21.7283			0.00167996
$552$	−26467.7	+	81459.3i	−2.04083	+	6.28104i
$553$	5364.27	−	3897.37i	0.412499	−	0.299698i
$554$	−4090.60	−	2972.00i	−0.313706	−	0.227921i
$555$	−8148.93	−	25079.8i	−0.623248	−	1.91816i
$556$	−15121.9	−	46540.4i	−1.15344	−	3.54991i
$557$	−11614.1	−	8438.12i	−0.883491	−	0.641894i	0.0506820	−	0.998715i	$-0.483860\pi$
$557$	−11614.1	−	8438.12i	−0.883491	−	0.641894i	−0.934173	+	0.356821i	$0.883860\pi$
$558$	−4721.04	+	3430.04i	−0.358168	+	0.260224i
$559$	−851.899	+	2621.88i	−0.0644571	+	0.198378i
$560$	−16614.6			−1.25374
$561$	−24.8388	−	8.64441i	−0.00186933	−	0.000650565i
$562$	−235.531			−0.0176785
$563$	128.396	−	395.163i	0.00961146	−	0.0295810i	−0.946136	−	0.323770i	$-0.895050\pi$
$563$	128.396	−	395.163i	0.00961146	−	0.0295810i	0.955747	+	0.294189i	$0.0950495\pi$
$564$	−40374.4	+	29333.7i	−3.01430	+	2.19002i
$565$	−10551.5	−	7666.14i	−0.785675	−	0.570826i
$566$	1075.81	+	3311.00i	0.0798933	+	0.245886i
$567$	2036.97	+	6269.14i	0.150872	+	0.464337i
$568$	−17062.2	−	12396.4i	−1.26041	−	0.915743i
$569$	−8312.58	+	6039.45i	−0.612446	+	0.444968i	−0.850275	−	0.526339i	$-0.823564\pi$
$569$	−8312.58	+	6039.45i	−0.612446	+	0.444968i	0.237829	+	0.971307i	$0.423564\pi$
$570$	116.213	−	357.665i	0.00853966	−	0.0262824i
$571$	−1774.66			−0.130066			−0.0650328	−	0.997883i	$-0.520715\pi$
$571$	−1774.66			−0.130066			−0.0650328	+	0.997883i	$0.520715\pi$
$572$	3766.47	−	4964.13i	0.275322	−	0.362869i
$573$	−2246.20			−0.163763
$574$	−1779.89	+	5477.95i	−0.129427	+	0.398337i
$575$	−2482.05	+	1803.32i	−0.180015	+	0.130789i
$576$	−85797.4	−	62335.5i	−6.20641	−	4.50922i
$577$	−6339.29	−	19510.3i	−0.457379	−	1.40767i	−0.868319	−	0.496006i	$-0.834799\pi$
$577$	−6339.29	−	19510.3i	−0.457379	−	1.40767i	0.410939	−	0.911663i	$-0.365201\pi$
$578$	8288.23	+	25508.6i	0.596445	+	1.83567i
$579$	−2900.76	−	2107.52i	−0.208206	−	0.151271i
$580$	−5102.18	+	3706.95i	−0.365270	+	0.265384i
$581$	1498.55	−	4612.07i	0.107006	−	0.329330i
$582$	−29459.6			−2.09818
$583$	−194.897	+	9390.91i	−0.0138453	+	0.667121i
$584$	−73071.1			−5.17757
$585$	1371.06	−	4219.68i	0.0968996	−	0.298226i
$586$	28487.1	−	20697.1i	2.00817	−	1.45902i
$587$	−641.922	−	466.384i	−0.0451362	−	0.0327934i	0.564988	−	0.825099i	$-0.308881\pi$
$587$	−641.922	−	466.384i	−0.0451362	−	0.0327934i	−0.610125	+	0.792305i	$0.708881\pi$
$588$	−3017.63	−	9287.31i	−0.211641	−	0.651365i
$589$	4.39536	+	13.5275i	0.000307483	+	0.000946335i
$590$	−18258.4	−	13265.5i	−1.27404	−	0.925646i
$591$	−15898.2	+	11550.7i	−1.10654	+	0.803947i
$592$	−21091.6	+	64913.2i	−1.46429	+	4.50662i
$593$	9695.74			0.671427			0.335714	−	0.941964i	$-0.391023\pi$
$593$	9695.74			0.671427			0.335714	+	0.941964i	$0.391023\pi$
$594$	51488.5	−	15556.1i	3.55656	−	1.07454i
$595$	5.52986			0.000381012
$596$	−6691.01	+	20592.8i	−0.459856	+	1.41529i
$597$	31788.4	−	23095.6i	2.17925	−	1.58332i
$598$	4302.34	+	3125.83i	0.294207	+	0.213754i
$599$	−801.745	−	2467.52i	−0.0546885	−	0.168314i	0.919982	−	0.391962i	$-0.128203\pi$
$599$	−801.745	−	2467.52i	−0.0546885	−	0.168314i	−0.974670	+	0.223648i	$0.928203\pi$
$600$	−5251.33	−	16161.9i	−0.357308	−	1.09968i
$601$	−4564.65	−	3316.41i	−0.309810	−	0.225090i	0.422005	−	0.906594i	$-0.361327\pi$
$601$	−4564.65	−	3316.41i	−0.309810	−	0.225090i	−0.731815	+	0.681503i	$0.761327\pi$
$602$	10880.1	−	7904.84i	0.736610	−	0.535178i
$603$	13600.9	−	41859.3i	0.918527	−	2.82694i
$604$	40032.4			2.69684
$605$	−10451.3	−	8276.99i	−0.702320	−	0.556211i
$606$	41893.8			2.80828
$607$	−3446.90	+	10608.5i	−0.230486	+	0.709364i	0.767202	+	0.641406i	$0.221648\pi$
$607$	−3446.90	+	10608.5i	−0.230486	+	0.709364i	−0.997688	+	0.0679581i	$0.978352\pi$
$608$	−420.503	+	305.513i	−0.0280488	+	0.0203786i
$609$	−1494.79	−	1086.03i	−0.0994611	−	0.0722627i
$610$	15912.2	+	48972.6i	1.05617	+	3.25056i
$611$	606.186	+	1865.65i	0.0401369	+	0.123529i
$612$	78.6662	+	57.1543i	0.00519590	+	0.00377504i
$613$	12844.1	−	9331.77i	0.846277	−	0.614856i	−0.0778403	−	0.996966i	$-0.524802\pi$
$613$	12844.1	−	9331.77i	0.846277	−	0.614856i	0.924117	+	0.382110i	$0.124802\pi$
$614$	8044.49	−	24758.4i	0.528745	−	1.62731i
$615$	13799.2			0.904775
$616$	−18422.2	+	5565.86i	−1.20495	+	0.364050i
$617$	17224.4			1.12387			0.561935	−	0.827181i	$-0.310057\pi$
$617$	17224.4			1.12387			0.561935	+	0.827181i	$0.310057\pi$
$618$	14764.2	−	45439.6i	0.961010	−	2.95769i
$619$	18825.9	−	13677.8i	1.22242	−	0.888141i	0.226122	−	0.974099i	$-0.427395\pi$
$619$	18825.9	−	13677.8i	1.22242	−	0.888141i	0.996299	+	0.0859582i	$0.0273951\pi$
$620$	−3339.97	−	2426.63i	−0.216349	−	0.157187i
$621$	10377.4	+	31938.3i	0.670581	+	2.06384i
$622$	−2620.06	−	8063.72i	−0.168899	−	0.519816i
$623$	−1926.67	−	1399.81i	−0.123901	−	0.0900195i
$624$	−13726.6	+	9972.99i	−0.880618	+	0.639806i
$625$	−3687.28	+	11348.3i	−0.235986	+	0.726291i
$626$	−3935.69			−0.251281
$627$	5.20618	−	250.854i	0.000331602	−	0.0159779i
$628$	82359.7			5.23329
$629$	7.01993	−	21.6051i	0.000444997	−	0.00136956i
$630$	−17510.5	+	12722.2i	−1.10736	+	0.804544i
$631$	−2248.92	−	1633.94i	−0.141883	−	0.103084i	0.514580	−	0.857443i	$-0.327948\pi$
$631$	−2248.92	−	1633.94i	−0.141883	−	0.103084i	−0.656463	+	0.754359i	$0.727948\pi$
$632$	22057.7	+	67886.5i	1.38830	+	4.27275i
$633$	−7036.37	−	21655.7i	−0.441818	−	1.35978i
$634$	−8785.64	−	6383.14i	−0.550351	−	0.399853i
$635$	7314.71	−	5314.45i	0.457127	−	0.332122i
$636$	15855.6	−	48798.5i	0.988545	−	3.04243i
$637$	−383.848			−0.0238754
$638$	−3476.49	+	4581.94i	−0.215730	+	0.284327i
$639$	−15825.4			−0.979724
$640$	14586.3	−	44892.0i	0.900897	−	2.77268i
$641$	4122.70	−	2995.31i	0.254035	−	0.184568i	−0.453478	−	0.891268i	$-0.649817\pi$
$641$	4122.70	−	2995.31i	0.254035	−	0.184568i	0.707513	+	0.706700i	$0.249817\pi$
$642$	8473.48	+	6156.34i	0.520906	+	0.378460i
$643$	−8100.03	−	24929.3i	−0.496787	−	1.52895i	−0.814153	−	0.580651i	$-0.802798\pi$
$643$	−8100.03	−	24929.3i	−0.496787	−	1.52895i	0.317366	−	0.948303i	$-0.397202\pi$
$644$	−5864.84	−	18050.1i	−0.358862	−	1.10446i
$645$	−26066.0	−	18938.0i	−1.59123	−	1.15610i
$646$	0.262096	−	0.190424i	1.59629e−5	−	1.15977e-5i
$647$	379.749	−	1168.75i	0.0230749	−	0.0710173i	−0.938856	−	0.344310i	$-0.888113\pi$
$647$	379.749	−	1168.75i	0.0230749	−	0.0710173i	0.961931	+	0.273293i	$0.0881128\pi$
$648$	−70961.9			−4.30192
$649$	−14220.8	−	4949.11i	−0.860114	−	0.299337i
$650$	−1055.12			−0.0636693
$651$	373.758	−	1150.31i	0.0225019	−	0.0692536i
$652$	20481.6	−	14880.8i	1.23025	−	0.893828i
$653$	4434.05	+	3221.53i	0.265724	+	0.193060i	0.712667	−	0.701503i	$-0.247487\pi$
$653$	4434.05	+	3221.53i	0.265724	+	0.193060i	−0.446943	+	0.894563i	$0.647487\pi$
$654$	4699.11	+	14462.4i	0.280963	+	0.864714i
$655$	930.024	+	2862.32i	0.0554795	+	0.170748i
$656$	−28894.8	−	20993.3i	−1.71975	−	1.24947i
$657$	−44358.9	+	32228.6i	−2.63410	+	1.91379i
$658$	2957.16	−	9101.19i	0.175201	−	0.539212i
$659$	−22775.7			−1.34630			−0.673152	−	0.739504i	$-0.735060\pi$
$659$	−22775.7			−1.34630			−0.673152	+	0.739504i	$0.735060\pi$
$660$	41574.5	+	59793.2i	2.45195	+	3.52643i
$661$	−1287.77			−0.0757770			−0.0378885	−	0.999282i	$-0.512063\pi$
$661$	−1287.77			−0.0757770			−0.0378885	+	0.999282i	$0.512063\pi$
$662$	−13746.0	+	42306.0i	−0.807032	+	2.48379i
$663$	4.56865	−	3.31932i	0.000267619	−	0.000194437i
$664$	42234.8	+	30685.4i	2.46842	+	1.79341i
$665$	16.3026	+	50.1741i	0.000950656	+	0.00292582i
$666$	27476.4	+	84563.8i	1.59863	+	4.92009i
$667$	−2905.16	−	2110.72i	−0.168648	−	0.122530i
$668$	−8703.11	+	6323.18i	−0.504092	+	0.366244i
$669$	11538.6	−	35512.2i	0.666829	−	2.05229i
$670$	42562.9			2.45425
$671$	19612.4	+	28206.9i	1.12836	+	1.62282i
$672$	44198.5			2.53719
$673$	−9016.79	+	27750.8i	−0.516452	+	1.58947i	0.264174	+	0.964475i	$0.414901\pi$
$673$	−9016.79	+	27750.8i	−0.516452	+	1.58947i	−0.780625	+	0.624999i	$0.785099\pi$
$674$	−6006.81	+	4364.20i	−0.343284	+	0.249411i
$675$	−5390.35	−	3916.32i	−0.307370	−	0.223317i
$676$	−14389.1	−	44285.2i	−0.818681	−	2.51964i
$677$	1382.43	+	4254.68i	0.0784802	+	0.241537i	0.982598	−	0.185747i	$-0.0594704\pi$
$677$	1382.43	+	4254.68i	0.0784802	+	0.241537i	−0.904117	+	0.427284i	$0.859470\pi$
$678$	52565.4	+	38191.0i	2.97752	+	2.16330i
$679$	3343.39	−	2429.12i	0.188965	−	0.137291i
$680$	−18.3959	+	56.6167i	−0.00103743	+	0.00319287i
$681$	−25472.7			−1.43336
$682$	−3555.86	−	1237.51i	−0.199649	−	0.0694820i
$683$	10500.7			0.588286			0.294143	−	0.955761i	$-0.404966\pi$
$683$	10500.7			0.588286			0.294143	+	0.955761i	$0.404966\pi$
$684$	−286.663	+	882.258i	−0.0160246	+	0.0493187i
$685$	−6033.78	+	4383.80i	−0.336553	+	0.244520i
$686$	1514.90	+	1100.64i	0.0843139	+	0.0612576i
$687$	−8176.74	−	25165.4i	−0.454093	−	1.39756i
$688$	25769.6	+	79310.6i	1.42799	+	4.39490i
$689$	−1631.67	−	1185.48i	−0.0902202	−	0.0655488i
$690$	−50282.2	+	36532.2i	−2.77422	+	2.01559i
$691$	−2995.74	+	9219.95i	−0.164925	+	0.507588i	−0.999031	−	0.0440169i	$-0.985984\pi$
$691$	−2995.74	+	9219.95i	−0.164925	+	0.507588i	0.834105	+	0.551605i	$0.185984\pi$
$692$	−68294.6			−3.75169
$693$	−8728.58	+	11504.1i	−0.478458	+	0.630598i
$694$	−13461.4			−0.736295
$695$	6946.91	−	21380.4i	0.379153	−	1.16691i
$696$	16091.7	−	11691.3i	0.876373	−	0.636723i
$697$	9.61708	+	6.98722i	0.000522630	+	0.000379713i
$698$	−17335.2	−	53352.4i	−0.940041	−	2.89315i
$699$	−8865.90	−	27286.4i	−0.479741	−	1.47649i
$700$	3046.39	+	2213.33i	0.164489	+	0.119509i
$701$	396.744	−	288.251i	0.0213763	−	0.0155308i	−0.577046	−	0.816712i	$-0.695795\pi$
$701$	396.744	−	288.251i	0.0213763	−	0.0155308i	0.598422	+	0.801181i	$0.295795\pi$
$702$	−3568.90	+	10984.0i	−0.191880	+	0.590545i
$703$	216.725			0.0116272
$704$	1419.74	−	68408.9i	0.0760066	−	3.66230i
$705$	−22926.3			−1.22476
$706$	19007.4	−	58498.8i	1.01325	−	3.11846i
$707$	−4754.56	+	3454.39i	−0.252919	+	0.183756i
$708$	66543.4	+	48346.6i	3.53228	+	2.56635i
$709$	1501.21	+	4620.24i	0.0795190	+	0.244734i	0.982911	−	0.184081i	$-0.0589310\pi$
$709$	1501.21	+	4620.24i	0.0795190	+	0.244734i	−0.903392	+	0.428816i	$0.858931\pi$
$710$	−4729.15	−	14554.8i	−0.249974	−	0.769342i
$711$	43332.3	+	31482.8i	2.28564	+	1.66061i
$712$	20741.1	−	15069.3i	1.09172	−	0.793181i
$713$	726.407	−	2235.65i	0.0381545	−	0.117428i
$714$	−27.5486			−0.00144395
$715$	2740.28	−	827.916i	0.143330	−	0.0433039i
$716$	50085.0			2.61419
$717$	−18732.3	+	57652.0i	−0.975690	+	3.00286i
$718$	−39645.9	+	28804.5i	−2.06069	+	1.49718i
$719$	7316.92	+	5316.05i	0.379520	+	0.275738i	0.761148	−	0.648579i	$-0.224636\pi$
$719$	7316.92	+	5316.05i	0.379520	+	0.275738i	−0.381627	+	0.924316i	$0.624636\pi$
$720$	−41473.9	−	127644.i	−2.14672	−	6.60694i
$721$	2071.16	+	6374.37i	0.106982	+	0.329257i
$722$	−30291.2	−	22007.8i	−1.56139	−	1.13441i
$723$	−42999.6	+	31241.0i	−2.21186	+	1.60701i
$724$	−21249.9	+	65400.5i	−1.09081	+	3.35717i
$725$	712.467			0.0364971
$726$	52065.8	+	41234.1i	2.66163	+	2.10791i
$727$	26154.5			1.33427			0.667136	−	0.744936i	$-0.267520\pi$
$727$	26154.5			1.33427			0.667136	+	0.744936i	$0.267520\pi$
$728$	1276.92	−	3929.97i	0.0650082	−	0.200075i
$729$	10840.2	−	7875.87i	0.550739	−	0.400136i
$730$	−42896.9	−	31166.4i	−2.17491	−	1.58017i
$731$	−8.57691	−	26.3970i	−0.000433965	−	0.00133561i
$732$	−57992.6	−	178483.i	−2.92823	−	9.01218i
$733$	−5478.39	−	3980.28i	−0.276056	−	0.200566i	0.441139	−	0.897439i	$-0.354574\pi$
$733$	−5478.39	−	3980.28i	−0.276056	−	0.200566i	−0.717195	+	0.696872i	$0.754574\pi$
$734$	16383.8	−	11903.5i	0.823891	−	0.598592i
$735$	1386.28	−	4266.54i	0.0695698	−	0.214114i
$736$	85900.9			4.30210
$737$	27183.6	−	8212.94i	1.35864	−	0.410485i
$738$	−46527.9			−2.32075
$739$	396.405	−	1220.01i	0.0197321	−	0.0607291i	−0.940706	−	0.339224i	$-0.889836\pi$
$739$	396.405	−	1220.01i	0.0197321	−	0.0607291i	0.960438	+	0.278495i	$0.0898355\pi$
$740$	−50890.8	+	36974.4i	−2.52809	+	1.83676i
$741$	43.5860	+	31.6671i	0.00216082	+	0.00156993i
$742$	3040.37	+	9357.29i	0.150425	+	0.462961i
$743$	1865.49	+	5741.39i	0.0921107	+	0.283488i	0.986490	−	0.163822i	$-0.0523822\pi$
$743$	1865.49	+	5741.39i	0.0921107	+	0.283488i	−0.894379	+	0.447310i	$0.852382\pi$
$744$	10533.9	+	7653.32i	0.519075	+	0.377130i
$745$	−8047.34	+	5846.74i	−0.395747	+	0.287527i
$746$	16525.0	−	50858.8i	0.811025	−	2.49608i
$747$	39173.3			1.91871
$748$	−1.30174	+	62.7230i	−6.36314e−5	+	0.00306601i
$749$	−1469.29			−0.0716777
$750$	23116.9	−	71146.5i	1.12548	−	3.46387i
$751$	−3918.85	+	2847.21i	−0.190414	+	0.138344i	−0.678908	−	0.734224i	$-0.737546\pi$
$751$	−3918.85	+	2847.21i	−0.190414	+	0.138344i	0.488494	+	0.872567i	$0.337546\pi$
$752$	48006.5	+	34878.7i	2.32795	+	1.69135i
$753$	14841.4	+	45677.0i	0.718259	+	2.21057i
$754$	−381.628	−	1174.53i	−0.0184325	−	0.0567293i
$755$	14878.3	+	10809.7i	0.717189	+	0.521069i
$756$	33345.5	−	24226.9i	1.60419	−	1.16551i
$757$	4022.96	−	12381.4i	0.193153	−	0.594464i	−0.806840	−	0.590770i	$-0.798824\pi$
$757$	4022.96	−	12381.4i	0.193153	−	0.594464i	0.999993	−	0.00369432i	$-0.00117594\pi$
$758$	−42159.1			−2.02017
$759$	−25064.5	+	33034.4i	−1.19866	+	1.57981i
$760$	−567.933			−0.0271067
$761$	−2521.94	+	7761.73i	−0.120132	+	0.369727i	−0.992983	−	0.118259i	$-0.962269\pi$
$761$	−2521.94	+	7761.73i	−0.120132	+	0.369727i	0.872851	+	0.487987i	$0.162269\pi$
$762$	−36440.2	+	26475.4i	−1.73240	+	1.25866i
$763$	−1725.81	−	1253.87i	−0.0818854	−	0.0594932i
$764$	1655.75	+	5095.87i	0.0784069	+	0.241312i
$765$	13.8038	+	42.4837i	0.000652388	+	0.00200784i
$766$	4678.55	+	3399.17i	0.220683	+	0.160335i
$767$	2615.65	−	1900.38i	0.123137	−	0.0894639i
$768$	−30286.6	+	93212.6i	−1.42301	+	4.37958i
$769$	−31005.1			−1.45393			−0.726966	−	0.686673i	$-0.759070\pi$
$769$	−31005.1			−1.45393			−0.726966	+	0.686673i	$0.759070\pi$
$770$	−13188.8	−	4589.98i	−0.617263	−	0.214820i
$771$	−41899.8			−1.95718
$772$	−2643.02	+	8134.37i	−0.123218	+	0.379226i
$773$	8451.01	−	6140.02i	0.393223	−	0.285693i	−0.373552	−	0.927609i	$-0.621860\pi$
$773$	8451.01	−	6140.02i	0.393223	−	0.285693i	0.766775	+	0.641916i	$0.221860\pi$
$774$	87888.8	+	63854.9i	4.08152	+	2.96540i
$775$	144.123	+	443.565i	0.00668007	+	0.0205591i
$776$	13747.9	+	42311.6i	0.635979	+	1.95734i
$777$	−14909.5	−	10832.4i	−0.688385	−	0.500141i
$778$	27609.5	−	20059.5i	1.27230	−	0.924380i
$779$	−35.0451	+	107.858i	−0.00161183	+	0.00496072i
$780$	−15637.3			−0.717827
$781$	−5828.86	−	8383.18i	−0.267059	−	0.384089i
$782$	−53.5413			−0.00244838
$783$	2409.90	−	7416.92i	0.109991	−	0.338517i
$784$	−9393.68	+	6824.91i	−0.427919	+	0.310901i
$785$	30609.6	+	22239.2i	1.39172	+	1.01115i
$786$	−4633.17	−	14259.4i	−0.210254	−	0.647096i
$787$	891.513	+	2743.80i	0.0403799	+	0.124277i	0.969214	−	0.246218i	$-0.0791880\pi$
$787$	891.513	+	2743.80i	0.0403799	+	0.124277i	−0.928834	+	0.370495i	$0.879188\pi$
$788$	37923.7	+	27553.2i	1.71444	+	1.24561i
$789$	18974.7	−	13785.9i	0.856170	−	0.622044i
$790$	−16006.0	+	49261.3i	−0.720844	+	2.21853i
$791$	−9114.75			−0.409713
$792$	−88746.1	−	127636.i	−3.98163	−	5.72646i
$793$	−7376.76			−0.330336
$794$	14290.2	−	43980.6i	0.638714	−	1.96576i
$795$	19069.7	−	13854.9i	0.850731	−	0.618092i
$796$	−75828.5	−	55092.6i	−3.37647	−	2.45315i
$797$	7267.20	+	22366.2i	0.322983	+	0.994040i	0.972343	+	0.233558i	$0.0750370\pi$
$797$	7267.20	+	22366.2i	0.322983	+	0.994040i	−0.649360	+	0.760481i	$0.724963\pi$
$798$	−81.2157	−	249.956i	−0.00360276	−	0.0110882i
$799$	−15.9780	−	11.6087i	−0.000707462	−	0.000514001i
$800$	−13788.2	+	10017.7i	−0.609359	+	0.442725i
$801$	5944.75	−	18296.1i	0.262232	−	0.807066i
$802$	79758.7			3.51169
$803$	−33410.8	−	11627.6i	−1.46830	−	0.510997i
$804$	−155122.			−6.80440
$805$	2694.27	−	8292.12i	0.117964	−	0.363055i
$806$	654.036	−	475.185i	0.0285824	−	0.0207663i
$807$	41093.4	+	29856.1i	1.79251	+	1.30234i
$808$	−19550.5	−	60170.4i	−0.851220	−	2.61978i
$809$	6277.14	+	19319.1i	0.272797	+	0.839582i	0.989794	+	0.142506i	$0.0455160\pi$
$809$	6277.14	+	19319.1i	0.272797	+	0.839582i	−0.716997	+	0.697076i	$0.754484\pi$
$810$	−41658.7	−	30266.8i	−1.80708	−	1.31292i
$811$	−11306.7	+	8214.78i	−0.489557	+	0.355684i	−0.805014	−	0.593256i	$-0.797842\pi$
$811$	−11306.7	+	8214.78i	−0.489557	+	0.355684i	0.315457	+	0.948940i	$0.397842\pi$
$812$	−1361.97	+	4191.71i	−0.0588618	+	0.181158i
$813$	18912.9			0.815874
$814$	−34675.6	+	45701.8i	−1.49310	+	1.96787i
$815$	11630.3			0.499869
$816$	52.7876	−	162.463i	0.00226462	−	0.00696980i
$817$	214.222	−	155.642i	0.00917343	−	0.00666489i
$818$	−50934.3	−	37006.0i	−2.17711	−	1.58176i
$819$	−958.170	−	2948.95i	−0.0408806	−	0.125817i
$820$	−10171.8	−	31305.7i	−0.433190	−	1.33322i
$821$	14830.9	+	10775.3i	0.630453	+	0.458051i	0.856557	−	0.516052i	$-0.172599\pi$
$821$	14830.9	+	10775.3i	0.630453	+	0.458051i	−0.226104	+	0.974103i	$0.572599\pi$
$822$	30059.0	−	21839.1i	1.27546	−	0.926674i
$823$	5100.57	−	15697.9i	0.216033	−	0.664880i	−0.783046	−	0.621964i	$-0.786335\pi$
$823$	5100.57	−	15697.9i	0.216033	−	0.664880i	0.999079	−	0.0429162i	$-0.0136649\pi$
$824$	−72153.1			−3.05045
$825$	170.710	−	8225.47i	0.00720406	−	0.347120i
$826$	−15772.2			−0.664387
$827$	2689.56	−	8277.62i	0.113090	−	0.348055i	−0.878454	−	0.477827i	$-0.841425\pi$
$827$	2689.56	−	8277.62i	0.113090	−	0.348055i	0.991544	+	0.129772i	$0.0414246\pi$
$828$	124032.	−	90114.4i	5.20580	−	3.78224i
$829$	21953.3	+	15950.0i	0.919747	+	0.668235i	0.943461	−	0.331484i	$-0.107549\pi$
$829$	21953.3	+	15950.0i	0.919747	+	0.668235i	−0.0237141	+	0.999719i	$0.507549\pi$
$830$	11706.3	+	36028.2i	0.489555	+	1.50669i
$831$	2616.02	+	8051.28i	0.109204	+	0.336096i
$832$	11886.1	+	8635.73i	0.495282	+	0.359844i
$833$	3.12650	−	2.27154i	0.000130044	−	9.44828e-5i
$834$	−34607.9	+	106512.i	−1.43690	+	4.42232i
$835$	−4941.99			−0.204820
$836$	−572.942	+	173.102i	−0.0237029	+	0.00716132i
$837$	5105.09			0.210822
$838$	−15472.9	+	47620.7i	−0.637831	+	1.96304i
$839$	14242.8	−	10348.0i	0.586074	−	0.425808i	−0.254835	−	0.966985i	$-0.582021\pi$
$839$	14242.8	−	10348.0i	0.586074	−	0.425808i	0.840909	+	0.541177i	$0.182021\pi$
$840$	39070.7	+	28386.5i	1.60484	+	1.16598i
$841$	−7278.92	−	22402.2i	−0.298451	−	0.918538i
$842$	−8731.41	−	26872.5i	−0.357368	−	1.09987i
$843$	319.033	+	231.791i	0.0130345	+	0.00947010i
$844$	−43942.8	+	31926.3i	−1.79215	+	1.30207i
$845$	6610.29	−	20344.4i	0.269113	−	0.828246i
$846$	77302.4			3.14150
$847$	−9308.98	−	386.560i	−0.377639	−	0.0156816i
$848$	−61009.0			−2.47059
$849$	1801.21	−	5543.55i	0.0728119	−	0.224092i
$850$	8.59409	−	6.24397i	0.000346794	−	0.000251961i
$851$	−28977.0	−	21053.0i	−1.16724	−	0.848047i
$852$	17235.6	+	53045.7i	0.693053	+	2.13300i
$853$	−7978.19	−	24554.4i	−0.320244	−	0.985610i	−0.973542	−	0.228509i	$-0.926615\pi$
$853$	−7978.19	−	24554.4i	−0.320244	−	0.985610i	0.653298	−	0.757101i	$-0.273385\pi$
$854$	29113.3	+	21152.1i	1.16655	+	0.847551i
$855$	−344.772	+	250.492i	−0.0137906	+	0.0100195i
$856$	4887.79	−	15043.1i	0.195165	−	0.600657i
$857$	−18103.2			−0.721580			−0.360790	−	0.932647i	$-0.617493\pi$
$857$	−18103.2			−0.721580			−0.360790	+	0.932647i	$0.617493\pi$
$858$	−13651.5	+	4124.49i	−0.543185	+	0.164112i
$859$	45507.6			1.80757			0.903784	−	0.427990i	$-0.140778\pi$
$859$	45507.6			1.80757			0.903784	+	0.427990i	$0.140778\pi$
$860$	−23749.9	+	73094.8i	−0.941704	+	2.89827i
$861$	7801.86	−	5668.38i	0.308811	−	0.224365i
$862$	−46288.5	−	33630.6i	−1.82899	−	1.32884i
$863$	2470.52	+	7603.49i	0.0974480	+	0.299914i	0.987884	−	0.155195i	$-0.0496004\pi$
$863$	2470.52	+	7603.49i	0.0974480	+	0.299914i	−0.890436	+	0.455109i	$0.849600\pi$
$864$	57648.2	+	177423.i	2.26994	+	6.98617i
$865$	−25382.2	−	18441.3i	−0.997712	−	0.724880i
$866$	−50692.7	+	36830.4i	−1.98916	+	1.44521i
$867$	13876.8	−	42708.5i	0.543578	−	1.67296i
$868$	−2885.17			−0.112821
$869$	−717.047	+	34550.2i	−0.0279910	+	1.34872i
$870$	14433.4			0.562457
$871$	−1884.22	+	5799.03i	−0.0733000	+	0.225594i
$872$	18578.8	−	13498.3i	0.721510	−	0.524208i
$873$	27007.8	+	19622.3i	1.04705	+	0.760726i
$874$	−157.845	−	485.796i	−0.00610890	−	0.0188013i
$875$	3242.89	+	9980.58i	0.125291	+	0.385606i
$876$	156340.	+	113587.i	6.02994	+	4.38101i
$877$	28123.9	−	20433.2i	1.08287	−	0.786751i	0.104689	−	0.994505i	$-0.466615\pi$
$877$	28123.9	−	20433.2i	1.08287	−	0.786751i	0.978181	+	0.207754i	$0.0666152\pi$
$878$	1996.62	−	6144.97i	0.0767457	−	0.236199i
$879$	−58954.7			−2.26222
$880$	52340.6	−	68983.9i	2.00500	−	2.64255i
$881$	−5998.98			−0.229411			−0.114705	−	0.993400i	$-0.536592\pi$
$881$	−5998.98			−0.229411			−0.114705	+	0.993400i	$0.536592\pi$
$882$	−4674.24	+	14385.8i	−0.178447	+	0.549202i
$883$	2385.39	−	1733.09i	0.0909114	−	0.0660510i	−0.541401	−	0.840765i	$-0.682106\pi$
$883$	2385.39	−	1733.09i	0.0909114	−	0.0660510i	0.632312	+	0.774713i	$0.282106\pi$
$884$	−10.8981	−	7.91795i	−0.000414642	−	0.000301255i
$885$	11676.6	+	35936.8i	0.443507	+	1.36497i
$886$	−10161.5	−	31274.0i	−0.385308	−	1.18586i
$887$	3040.80	+	2209.27i	0.115107	+	0.0836301i	0.643850	−	0.765152i	$-0.277336\pi$
$887$	3040.80	+	2209.27i	0.115107	+	0.0836301i	−0.528743	+	0.848782i	$0.677336\pi$
$888$	160504.	−	116613.i	6.06551	−	4.40685i
$889$	1952.58	−	6009.42i	0.0736641	−	0.226715i
$890$	18603.6			0.700667
$891$	−32446.4	−	11292.0i	−1.21997	−	0.424575i
$892$	−89070.7			−3.34340
$893$	58.2246	−	179.197i	0.00218187	−	0.00671512i
$894$	40090.1	−	29127.1i	1.49979	−	1.08966i
$895$	18614.5	+	13524.2i	0.695210	+	0.505100i
$896$	−10193.7	−	31373.0i	−0.380076	−	1.16975i
$897$	−2751.42	−	8468.01i	−0.102416	−	0.315205i
$898$	−62022.8	−	45062.2i	−2.30482	−	1.67455i
$899$	−441.638	+	320.869i	−0.0163843	+	0.0119039i
$900$	−9399.63	+	28929.1i	−0.348135	+	1.07145i
$901$	20.3057			0.000750810
$902$	−17137.3	−	24647.1i	−0.632604	−	0.909823i
$903$	−22516.6			−0.829796
$904$	30321.5	−	93320.0i	1.11557	−	3.43338i
$905$	−25557.5	+	18568.6i	−0.938739	+	0.682034i
$906$	−74120.5	−	53851.7i	−2.71798	−	1.97473i
$907$	−830.117	−	2554.84i	−0.0303899	−	0.0935304i	0.934711	−	0.355408i	$-0.115658\pi$
$907$	−830.117	−	2554.84i	−0.0303899	−	0.0935304i	−0.965101	+	0.261878i	$0.915658\pi$
$908$	18776.8	+	57788.9i	0.686265	+	2.11211i
$909$	−38407.1	−	27904.4i	−1.40141	−	1.01818i
$910$	2425.85	−	1762.48i	0.0883693	−	0.0642040i
$911$	−1333.59	+	4104.38i	−0.0485005	+	0.149269i	−0.972374	−	0.233429i	$-0.925005\pi$
$911$	−1333.59	+	4104.38i	−0.0485005	+	0.149269i	0.923873	+	0.382699i	$0.125005\pi$
$912$	1629.70			0.0591719
$913$	14428.4	+	20751.2i	0.523014	+	0.752208i
$914$	54169.5			1.96036
$915$	26641.5	−	81994.0i	0.962557	−	2.96244i
$916$	−51064.5	+	37100.5i	−1.84194	+	1.33825i
$917$	1701.60	+	1236.28i	0.0612777	+	0.0445208i
$918$	−35.9316	−	110.586i	−0.00129185	−	0.00397591i
$919$	11856.8	+	36491.6i	0.425594	+	1.30984i	0.902424	+	0.430849i	$0.141786\pi$
$919$	11856.8	+	36491.6i	0.425594	+	1.30984i	−0.476830	+	0.878995i	$0.658214\pi$
$920$	75934.8	+	55169.9i	2.72119	+	1.97706i
$921$	−35261.6	+	25619.1i	−1.26158	+	0.916588i
$922$	−18055.1	+	55567.7i	−0.644915	+	1.98484i
$923$	2192.39			0.0781837
$924$	48067.2	+	16728.4i	1.71136	+	0.595588i
$925$	7106.38			0.252602
$926$	8473.04	−	26077.3i	0.300693	−	0.925437i
$927$	−43801.6	+	31823.7i	−1.55192	+	1.12754i
$928$	−16138.6	−	11725.4i	−0.570880	−	0.414768i
$929$	−8963.64	−	27587.2i	−0.316563	−	0.974282i	−0.975106	−	0.221739i	$-0.928827\pi$
$929$	−8963.64	−	27587.2i	−0.316563	−	0.974282i	0.658543	−	0.752543i	$-0.271173\pi$
$930$	2919.69	+	8985.88i	0.102947	+	0.316837i
$931$	29.8276	+	21.6710i	0.00105001	+	0.000762877i
$932$	−55368.4	+	40227.5i	−1.94598	+	1.41384i
$933$	−4386.72	+	13500.9i	−0.153928	+	0.473742i
$934$	58259.0			2.04100
$935$	−17.4206	+	22.9600i	−0.000609319	+	0.000803071i
$936$	33379.8			1.16566
$937$	4540.45	−	13974.1i	0.158303	−	0.487207i	−0.840178	−	0.542311i	$-0.817549\pi$
$937$	4540.45	−	13974.1i	0.158303	−	0.487207i	0.998481	+	0.0551047i	$0.0175493\pi$
$938$	24064.4	−	17483.8i	0.837666	−	0.608600i
$939$	5330.98	+	3873.18i	0.185271	+	0.134608i
$940$	16899.7	+	52012.0i	0.586392	+	1.80473i
$941$	−7311.25	−	22501.7i	−0.253284	−	0.779527i	−0.994163	−	0.107889i	$-0.965591\pi$
$941$	−7311.25	−	22501.7i	−0.253284	−	0.779527i	0.740879	−	0.671638i	$-0.234409\pi$
$942$	−152490.	−	110791.i	−5.27431	−	3.83201i
$943$	15163.1	−	11016.6i	0.523625	−	0.380436i
$944$	30222.0	−	93013.9i	1.04200	−	3.20693i
$945$	18935.0			0.651805
$946$	−1454.35	+	70076.4i	−0.0499842	+	2.40844i
$947$	16661.7			0.571735			0.285867	−	0.958269i	$-0.407718\pi$
$947$	16661.7			0.571735			0.285867	+	0.958269i	$0.407718\pi$
$948$	58334.4	−	179535.i	1.99854	−	6.15087i
$949$	6145.32	−	4464.83i	0.210206	−	0.152724i
$950$	81.9896	+	59.5689i	0.00280010	+	0.00203439i
$951$	5618.58	+	17292.2i	0.191583	+	0.589631i
$952$	12.8561	+	39.5669i	0.000437675	+	0.00134703i
$953$	5512.22	+	4004.86i	0.187364	+	0.136128i	0.677513	−	0.735511i	$-0.263058\pi$
$953$	5512.22	+	4004.86i	0.187364	+	0.136128i	−0.490149	+	0.871639i	$0.663058\pi$
$954$	−64298.8	+	46715.8i	−2.18213	+	1.58541i
$955$	−760.641	+	2341.01i	−0.0257736	+	0.0793229i
$956$	144601.			4.89198
$957$	9218.16	−	2785.07i	0.311370	−	0.0940736i
$958$	5759.31			0.194233
$959$	−1610.65	+	4957.07i	−0.0542342	+	0.166916i
$960$	−138915.	+	100927.i	−4.67026	+	3.39314i
$961$	23812.3	+	17300.7i	0.799313	+	0.580735i
$962$	−3806.48	−	11715.2i	−0.127574	−	0.392632i
$963$	−3667.67	−	11287.9i	−0.122730	−	0.377724i
$964$	102572.	+	74522.8i	3.42699	+	2.48985i
$965$	−3178.78	+	2309.52i	−0.106040	+	0.0770426i
$966$	−13422.3	+	41309.5i	−0.447054	+	1.37589i
$967$	54467.5			1.81133			0.905665	−	0.423993i	$-0.139372\pi$
$967$	54467.5			1.81133			0.905665	+	0.423993i	$0.139372\pi$
$968$	34925.4	−	94022.7i	1.15965	−	3.12190i
$969$	−0.542415			−1.79823e−5
$970$	−9976.05	+	30703.1i	−0.330218	+	1.01631i
$971$	9518.32	−	6915.47i	0.314580	−	0.228556i	−0.419279	−	0.907857i	$-0.637717\pi$
$971$	9518.32	−	6915.47i	0.314580	−	0.228556i	0.733859	+	0.679301i	$0.237717\pi$
$972$	23208.5	+	16862.0i	0.765858	+	0.556428i
$973$	−4854.88	−	14941.8i	−0.159959	−	0.492304i
$974$	−32386.8	−	99676.2i	−1.06544	−	3.27909i
$975$	1429.18	+	1038.36i	0.0469439	+	0.0341067i
$976$	−180527.	+	131160.i	−5.92062	+	4.30158i
$977$	−17580.3	+	54106.6i	−0.575684	+	1.77177i	0.0581529	+	0.998308i	$0.481479\pi$
$977$	−17580.3	+	54106.6i	−0.575684	+	1.77177i	−0.633837	+	0.773466i	$0.718521\pi$
$978$	−57939.7			−1.89438
$979$	11881.5	−	3589.75i	0.387881	−	0.117190i
$980$	−10701.2			−0.348814
$981$	5325.00	−	16388.7i	0.173307	−	0.533384i
$982$	−56444.4	+	41009.2i	−1.83423	+	1.33264i
$983$	−9798.07	−	7118.72i	−0.317915	−	0.230978i	0.417371	−	0.908736i	$-0.362952\pi$
$983$	−9798.07	−	7118.72i	−0.317915	−	0.230978i	−0.735285	+	0.677758i	$0.762952\pi$
$984$	32080.9	+	98734.9i	1.03933	+	3.19873i
$985$	6654.59	+	20480.7i	0.215262	+	0.662508i
$986$	10.0591	+	7.30834i	0.000324895	+	0.000236050i
$987$	−12962.2	+	9417.57i	−0.418025	+	0.303713i
$988$	39.7132	−	122.225i	0.00127879	−	0.00393572i
$989$	−43761.6			−1.40702
$990$	2340.65	−	112782.i	0.0751422	−	3.62065i
$991$	13279.8			0.425679			0.212840	−	0.977087i	$-0.431729\pi$
$991$	13279.8			0.425679			0.212840	+	0.977087i	$0.431729\pi$
$992$	4035.31	−	12419.4i	0.129155	−	0.397497i
$993$	60253.4	−	43776.7i	1.92556	−	1.39900i
$994$	−8652.57	−	6286.46i	−0.276099	−	0.200598i
$995$	−13305.8	−	40951.2i	−0.423943	−	1.30476i
$996$	−42664.0	−	131306.i	−1.35729	−	4.17731i
$997$	881.973	+	640.791i	0.0280164	+	0.0203551i	0.601705	−	0.798718i	$-0.294488\pi$
$997$	881.973	+	640.791i	0.0280164	+	0.0203551i	−0.573689	+	0.819073i	$0.694488\pi$
$998$	−64351.5	+	46754.1i	−2.04109	+	1.48294i
$999$	24037.2	−	73978.8i	0.761264	−	2.34293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.4.f.a.64.1	✓	32
11.4	even	5		847.4.a.o.1.1		16
11.5	even	5	inner	77.4.f.a.71.1	yes	32
11.7	odd	10		847.4.a.p.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.f.a.64.1	✓	32	1.1	even	1	trivial
77.4.f.a.71.1	yes	32	11.5	even	5	inner
847.4.a.o.1.1		16	11.4	even	5
847.4.a.p.1.16		16	11.7	odd	10

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	77.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68700 + 5.19206i) q^{2} +(7.39468 - 5.37255i) q^{3} +(-17.6394 - 12.8158i) q^{4} +(-3.09523 - 9.52615i) q^{5} +(15.4198 + 47.4572i) q^{6} +(-5.66312 - 4.11450i) q^{7} +(60.9649 - 44.2936i) q^{8} +(17.4736 - 53.7781i) q^{9} +54.6820 q^{10} +(34.9237 - 10.5515i) q^{11} -199.291 q^{12} +(-2.42072 + 7.45022i) q^{13} +(30.9164 - 22.4621i) q^{14} +(-74.0680 - 53.8136i) q^{15} +(73.2258 + 225.366i) q^{16} +(-0.0243718 - 0.0750087i) q^{17} +(249.741 + 181.448i) q^{18} +(0.608726 - 0.442265i) q^{19} +(-67.4869 + 207.703i) q^{20} -63.9823 q^{21} +(-4.13263 + 199.126i) q^{22} -124.351 q^{23} +(212.846 - 655.074i) q^{24} +(19.9600 - 14.5018i) q^{25} +(-34.5982 - 25.1371i) q^{26} +(-83.4523 - 256.840i) q^{27} +(47.1635 + 145.154i) q^{28} +(23.3625 + 16.9738i) q^{29} +(404.356 - 293.782i) q^{30} +(-5.84157 + 17.9785i) q^{31} -690.792 q^{32} +(201.562 - 265.654i) q^{33} +0.430565 q^{34} +(-21.6666 + 66.6831i) q^{35} +(-997.431 + 724.676i) q^{36} +(233.025 + 169.303i) q^{37} +(1.26935 + 3.90664i) q^{38} +(22.1262 + 68.0975i) q^{39} +(-610.648 - 443.662i) q^{40} +(-121.938 + 88.5929i) q^{41} +(107.938 - 332.200i) q^{42} +351.919 q^{43} +(-751.258 - 261.453i) q^{44} -566.383 q^{45} +(209.781 - 645.639i) q^{46} +(202.590 - 147.190i) q^{47} +(1752.27 + 1273.10i) q^{48} +(15.1418 + 46.6018i) q^{49} +(41.6216 + 128.098i) q^{50} +(-0.583210 - 0.423727i) q^{51} +(138.180 - 100.394i) q^{52} +(-79.5600 + 244.860i) q^{53} +1474.31 q^{54} +(-208.612 - 300.030i) q^{55} -527.497 q^{56} +(2.12524 - 6.54082i) q^{57} +(-127.542 + 92.6646i) q^{58} +(-333.901 - 242.593i) q^{59} +(616.852 + 1898.48i) q^{60} +(290.995 + 895.589i) q^{61} +(-83.4908 - 60.6596i) q^{62} +(-320.225 + 232.657i) q^{63} +(579.562 - 1783.71i) q^{64} +78.4647 q^{65} +(1039.26 + 1494.68i) q^{66} +778.370 q^{67} +(-0.531390 + 1.63545i) q^{68} +(-919.538 + 668.084i) q^{69} +(-309.671 - 224.989i) q^{70} +(-86.4845 - 266.172i) q^{71} +(-1316.75 - 4052.54i) q^{72} +(-784.479 - 569.957i) q^{73} +(-1272.14 + 924.267i) q^{74} +(69.6864 - 214.473i) q^{75} -16.4055 q^{76} +(-241.191 - 83.9394i) q^{77} -390.893 q^{78} +(-292.710 + 900.868i) q^{79} +(1920.22 - 1395.12i) q^{80} +(-761.835 - 553.506i) q^{81} +(-254.271 - 782.564i) q^{82} +(214.079 + 658.867i) q^{83} +(1128.61 + 819.982i) q^{84} +(-0.639108 + 0.464339i) q^{85} +(-593.689 + 1827.19i) q^{86} +263.951 q^{87} +(1661.76 - 2190.16i) q^{88} +340.214 q^{89} +(955.491 - 2940.70i) q^{90} +(44.3628 - 32.2314i) q^{91} +(2193.48 + 1593.66i) q^{92} +(53.3939 + 164.330i) q^{93} +(422.451 + 1300.17i) q^{94} +(-6.09723 - 4.42990i) q^{95} +(-5108.19 + 3711.32i) q^{96} +(-182.437 + 561.484i) q^{97} -267.504 q^{98} +(42.8048 - 2062.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} + 18 q^{3} - 48 q^{4} + 16 q^{5} + 30 q^{6} - 56 q^{7} + 62 q^{8} - 46 q^{9} - 72 q^{10} - 94 q^{11} - 544 q^{12} + 72 q^{13} + 56 q^{14} + 140 q^{15} + 296 q^{16} + 8 q^{17} + 422 q^{18}+ \cdots + 10027 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 + 18 * q^3 - 48 * q^4 + 16 * q^5 + 30 * q^6 - 56 * q^7 + 62 * q^8 - 46 * q^9 - 72 * q^10 - 94 * q^11 - 544 * q^12 + 72 * q^13 + 56 * q^14 + 140 * q^15 + 296 * q^16 + 8 * q^17 + 422 * q^18 + 51 * q^19 - 149 * q^20 - 294 * q^21 - 66 * q^22 - 830 * q^23 + 868 * q^24 - 256 * q^25 + 775 * q^26 + 27 * q^27 + 14 * q^28 + 236 * q^29 + 1008 * q^30 + 554 * q^31 - 1836 * q^32 + 895 * q^33 - 234 * q^34 + 112 * q^35 - 2322 * q^36 + 1439 * q^37 - 267 * q^38 - 18 * q^39 - 1232 * q^40 - 42 * q^41 + 210 * q^42 - 404 * q^43 + 591 * q^44 - 3020 * q^45 + 2169 * q^46 - 714 * q^47 + 4500 * q^48 - 392 * q^49 - 1035 * q^50 + 745 * q^51 + 725 * q^52 + 1351 * q^53 + 648 * q^54 + 1708 * q^55 - 966 * q^56 + 1561 * q^57 - 2529 * q^58 + 543 * q^59 - 316 * q^60 - 1542 * q^61 - 4231 * q^62 - 567 * q^63 + 1172 * q^64 - 4084 * q^65 + 5058 * q^66 - 1744 * q^67 + 2522 * q^68 - 1584 * q^69 + 126 * q^70 - 561 * q^71 - 4810 * q^72 - 144 * q^73 + 575 * q^74 + 1623 * q^75 - 3278 * q^76 + 567 * q^77 - 6582 * q^78 + 5785 * q^79 + 3199 * q^80 + 2403 * q^81 + 1998 * q^82 - 4177 * q^83 + 1652 * q^84 - 4090 * q^85 - 184 * q^86 - 940 * q^87 + 5446 * q^88 - 11554 * q^89 + 11896 * q^90 - 826 * q^91 + 12958 * q^92 - 578 * q^93 - 2042 * q^94 - 1390 * q^95 - 10074 * q^96 - q^97 - 588 * q^98 + 10027 * q^99

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