LMFDB - Embedded newform 175.4.x.a.3.55

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.55
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.55

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.78061 - 4.28176i) q^{2} +(2.17796 - 5.67379i) q^{3} +(-7.34780 - 16.5034i) q^{4} +(11.0343 + 1.80104i) q^{5} +(-18.2377 - 25.1021i) q^{6} +(-13.3513 + 12.8352i) q^{7} +(-50.7546 - 8.03874i) q^{8} +(-7.38346 - 6.64810i) q^{9} +(38.3938 - 42.2383i) q^{10} +(-14.9911 - 16.6493i) q^{11} +(-109.640 + 5.74600i) q^{12} +(-33.3392 - 16.9872i) q^{13} +(17.8326 + 92.8568i) q^{14} +(34.2511 - 58.6838i) q^{15} +(-78.8444 + 87.5656i) q^{16} +(51.2162 - 63.2467i) q^{17} +(-48.9961 + 13.1285i) q^{18} +(28.9974 + 12.9105i) q^{19} +(-51.3546 - 195.338i) q^{20} +(43.7457 + 103.707i) q^{21} +(-112.973 + 17.8932i) q^{22} +(104.969 + 68.1680i) q^{23} +(-156.152 + 270.463i) q^{24} +(118.512 + 39.7466i) q^{25} +(-165.438 + 95.5158i) q^{26} +(92.4055 - 47.0830i) q^{27} +(309.928 + 126.031i) q^{28} +(-55.2822 + 76.0894i) q^{29} +(-156.031 - 309.832i) q^{30} +(98.5579 - 10.3589i) q^{31} +(49.2996 + 183.988i) q^{32} +(-127.115 + 48.7949i) q^{33} +(-128.395 - 395.160i) q^{34} +(-170.439 + 117.582i) q^{35} +(-55.4642 + 170.701i) q^{36} +(-17.0667 - 325.653i) q^{37} +(135.910 - 88.2610i) q^{38} +(-168.993 + 152.162i) q^{39} +(-545.564 - 180.113i) q^{40} +(32.4428 - 10.5413i) q^{41} +(565.689 + 101.060i) q^{42} +(359.144 + 359.144i) q^{43} +(-164.619 + 369.741i) q^{44} +(-69.4979 - 86.6552i) q^{45} +(583.758 - 259.906i) q^{46} +(-310.823 + 251.699i) q^{47} +(325.109 + 638.062i) q^{48} +(13.5141 - 342.734i) q^{49} +(499.722 - 396.922i) q^{50} +(-247.302 - 428.339i) q^{51} +(-35.3768 + 675.029i) q^{52} +(197.600 + 75.8516i) q^{53} +(55.3455 - 526.578i) q^{54} +(-135.431 - 210.714i) q^{55} +(780.818 - 544.119i) q^{56} +(136.407 - 136.407i) q^{57} +(172.078 + 448.280i) q^{58} +(-247.333 - 52.5722i) q^{59} +(-1220.15 - 134.064i) q^{60} +(176.398 + 829.886i) q^{61} +(229.697 - 450.805i) q^{62} +(183.909 - 6.00765i) q^{63} +(28.3642 + 9.21610i) q^{64} +(-337.281 - 247.487i) q^{65} +(-144.529 + 679.956i) q^{66} +(-249.643 - 202.157i) q^{67} +(-1420.11 - 380.518i) q^{68} +(615.390 - 447.107i) q^{69} +(29.5319 + 1056.73i) q^{70} +(-541.294 - 393.273i) q^{71} +(321.302 + 396.775i) q^{72} +(-296.558 - 15.5419i) q^{73} +(-1441.82 - 832.436i) q^{74} +(483.630 - 585.848i) q^{75} -573.420i q^{76} +(413.849 + 29.8757i) q^{77} +(181.618 + 1146.69i) q^{78} +(907.955 + 95.4299i) q^{79} +(-1027.70 + 824.225i) q^{80} +(-93.9234 - 893.621i) q^{81} +(45.0753 - 168.223i) q^{82} +(-224.817 + 1419.44i) q^{83} +(1390.09 - 1483.97i) q^{84} +(679.046 - 605.642i) q^{85} +(2536.41 - 539.130i) q^{86} +(311.313 + 479.379i) q^{87} +(627.029 + 965.540i) q^{88} +(-549.439 + 116.787i) q^{89} +(-564.283 + 56.6195i) q^{90} +(663.156 - 201.115i) q^{91} +(353.710 - 2233.24i) q^{92} +(155.882 - 581.758i) q^{93} +(213.440 + 2030.75i) q^{94} +(296.715 + 194.684i) q^{95} +(1151.28 + 121.005i) q^{96} +(-4.41746 - 27.8907i) q^{97} +(-1429.93 - 1010.87i) q^{98} +222.592i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	2.78061	−	4.28176i	0.983093	−	1.51383i	0.130372	−	0.991465i	$-0.458383\pi$
$2$	2.78061	−	4.28176i	0.983093	−	1.51383i	0.852722	−	0.522366i	$-0.174950\pi$
$3$	2.17796	−	5.67379i	0.419149	−	1.09192i	−0.547723	−	0.836660i	$-0.684505\pi$
$3$	2.17796	−	5.67379i	0.419149	−	1.09192i	0.966872	−	0.255262i	$-0.0821616\pi$
$4$	−7.34780	−	16.5034i	−0.918475	−	2.06293i
$5$	11.0343	+	1.80104i	0.986940	+	0.161090i
$5$	11.0343	+	1.80104i	0.986940	+	0.161090i
$6$	−18.2377	−	25.1021i	−1.24092	−	1.70798i
$7$	−13.3513	+	12.8352i	−0.720902	+	0.693037i
$7$	−13.3513	+	12.8352i	−0.720902	+	0.693037i
$8$	−50.7546	−	8.03874i	−2.24306	−	0.355265i
$9$	−7.38346	−	6.64810i	−0.273461	−	0.246226i
$10$	38.3938	−	42.2383i	1.21412	−	1.33569i
$11$	−14.9911	−	16.6493i	−0.410909	−	0.456361i	0.501792	−	0.864988i	$-0.332674\pi$
$11$	−14.9911	−	16.6493i	−0.410909	−	0.456361i	−0.912701	+	0.408628i	$0.866008\pi$
$12$	−109.640	+	5.74600i	−2.63753	+	0.138227i
$13$	−33.3392	−	16.9872i	−0.711279	−	0.362415i	0.0606190	−	0.998161i	$-0.480693\pi$
$13$	−33.3392	−	16.9872i	−0.711279	−	0.362415i	−0.771898	+	0.635746i	$0.780693\pi$
$14$	17.8326	+	92.8568i	0.340427	+	1.77264i
$15$	34.2511	−	58.6838i	0.589573	−	1.01014i
$16$	−78.8444	+	87.5656i	−1.23194	+	1.36821i
$17$	51.2162	−	63.2467i	0.730691	−	0.902329i	−0.267431	−	0.963577i	$-0.586175\pi$
$17$	51.2162	−	63.2467i	0.730691	−	0.902329i	0.998123	+	0.0612484i	$0.0195082\pi$
$18$	−48.9961	+	13.1285i	−0.641582	+	0.171911i
$19$	28.9974	+	12.9105i	0.350130	+	0.155888i	0.574263	−	0.818671i	$-0.305289\pi$
$19$	28.9974	+	12.9105i	0.350130	+	0.155888i	−0.224134	+	0.974558i	$0.571955\pi$
$20$	−51.3546	−	195.338i	−0.574162	−	2.18394i
$21$	43.7457	+	103.707i	0.454576	+	1.07765i
$22$	−112.973	+	17.8932i	−1.09481	+	0.173402i
$23$	104.969	+	68.1680i	0.951637	+	0.618000i	0.924317	−	0.381627i	$-0.124636\pi$
$23$	104.969	+	68.1680i	0.951637	+	0.618000i	0.0273201	+	0.999627i	$0.491303\pi$
$24$	−156.152	+	270.463i	−1.32810	+	2.30033i
$25$	118.512	+	39.7466i	0.948100	+	0.317973i
$26$	−165.438	+	95.5158i	−1.24789	+	0.720469i
$27$	92.4055	−	47.0830i	0.658646	−	0.335597i
$28$	309.928	+	126.031i	2.09182	+	0.850632i
$29$	−55.2822	+	76.0894i	−0.353988	+	0.487222i	−0.948461	−	0.316893i	$-0.897360\pi$
$29$	−55.2822	+	76.0894i	−0.353988	+	0.487222i	0.594474	+	0.804115i	$0.297360\pi$
$30$	−156.031	−	309.832i	−0.949575	−	1.88558i
$31$	98.5579	−	10.3589i	0.571017	−	0.0600163i	0.185380	−	0.982667i	$-0.440648\pi$
$31$	98.5579	−	10.3589i	0.571017	−	0.0600163i	0.385637	+	0.922651i	$0.373982\pi$
$32$	49.2996	+	183.988i	0.272344	+	1.01640i
$33$	−127.115	+	48.7949i	−0.670542	+	0.257397i
$34$	−128.395	−	395.160i	−0.647635	−	1.99322i
$35$	−170.439	+	117.582i	−0.823128	+	0.567855i
$36$	−55.4642	+	170.701i	−0.256779	+	0.790283i
$37$	−17.0667	−	325.653i	−0.0758312	−	1.44694i	−0.726282	−	0.687397i	$-0.758753\pi$
$37$	−17.0667	−	325.653i	−0.0758312	−	1.44694i	0.650451	−	0.759548i	$-0.274580\pi$
$38$	135.910	−	88.2610i	0.580198	−	0.376785i
$39$	−168.993	+	152.162i	−0.693861	+	0.624755i
$40$	−545.564	−	180.113i	−2.15653	−	0.711960i
$41$	32.4428	−	10.5413i	0.123578	−	0.0401530i	−0.246575	−	0.969124i	$-0.579305\pi$
$41$	32.4428	−	10.5413i	0.123578	−	0.0401530i	0.370153	+	0.928971i	$0.379305\pi$
$42$	565.689	+	101.060i	2.07828	+	0.371283i
$43$	359.144	+	359.144i	1.27370	+	1.27370i	0.944133	+	0.329564i	$0.106902\pi$
$43$	359.144	+	359.144i	1.27370	+	1.27370i	0.329564	+	0.944133i	$0.393098\pi$
$44$	−164.619	+	369.741i	−0.564030	+	1.26683i
$45$	−69.4979	−	86.6552i	−0.230225	−	0.287062i
$46$	583.758	−	259.906i	1.87109	−	0.833065i
$47$	−310.823	+	251.699i	−0.964642	+	0.781152i	−0.975773	−	0.218786i	$-0.929790\pi$
$47$	−310.823	+	251.699i	−0.964642	+	0.781152i	0.0111305	+	0.999938i	$0.496457\pi$
$48$	325.109	+	638.062i	0.977612	+	1.91867i
$49$	13.5141	−	342.734i	0.0393997	−	0.999224i
$50$	499.722	−	396.922i	1.41343	−	1.12267i
$51$	−247.302	−	428.339i	−0.679003	−	1.17607i
$52$	−35.3768	+	675.029i	−0.0943438	+	1.80019i
$53$	197.600	+	75.8516i	0.512122	+	0.196585i	0.600686	−	0.799485i	$-0.294894\pi$
$53$	197.600	+	75.8516i	0.512122	+	0.196585i	−0.0885637	+	0.996071i	$0.528228\pi$
$54$	55.3455	−	526.578i	0.139474	−	1.32700i
$55$	−135.431	−	210.714i	−0.332027	−	0.516594i
$56$	780.818	−	544.119i	1.86324	−	1.29841i
$57$	136.407	−	136.407i	0.316974	−	0.316974i
$58$	172.078	+	448.280i	0.389569	+	1.01486i
$59$	−247.333	−	52.5722i	−0.545763	−	0.116005i	−0.0732242	−	0.997316i	$-0.523329\pi$
$59$	−247.333	−	52.5722i	−0.545763	−	0.116005i	−0.472538	+	0.881310i	$0.656662\pi$
$60$	−1220.15	−	134.064i	−2.62535	−	0.288459i
$61$	176.398	+	829.886i	0.370253	+	1.74190i	0.630342	+	0.776317i	$0.282915\pi$
$61$	176.398	+	829.886i	0.370253	+	1.74190i	−0.260090	+	0.965584i	$0.583752\pi$
$62$	229.697	−	450.805i	0.470508	−	0.923424i
$63$	183.909	−	6.00765i	0.367783	−	0.0120142i
$64$	28.3642	+	9.21610i	0.0553989	+	0.0180002i
$65$	−337.281	−	247.487i	−0.643608	−	0.472262i
$66$	−144.529	+	679.956i	−0.269550	+	1.26813i
$67$	−249.643	−	202.157i	−0.455205	−	0.368618i	0.374124	−	0.927379i	$-0.377944\pi$
$67$	−249.643	−	202.157i	−0.455205	−	0.368618i	−0.829329	+	0.558761i	$0.811277\pi$
$68$	−1420.11	−	380.518i	−2.53256	−	0.678597i
$69$	615.390	−	447.107i	1.07369	−	0.780078i
$70$	29.5319	+	1056.73i	0.0504249	+	1.80433i
$71$	−541.294	−	393.273i	−0.904785	−	0.657365i	0.0349053	−	0.999391i	$-0.488887\pi$
$71$	−541.294	−	393.273i	−0.904785	−	0.657365i	−0.939691	+	0.342026i	$0.888887\pi$
$72$	321.302	+	396.775i	0.525914	+	0.649450i
$73$	−296.558	−	15.5419i	−0.475472	−	0.0249184i	−0.186905	−	0.982378i	$-0.559846\pi$
$73$	−296.558	−	15.5419i	−0.475472	−	0.0249184i	−0.288567	+	0.957460i	$0.593179\pi$
$74$	−1441.82	−	832.436i	−2.26498	−	1.30769i
$75$	483.630	−	585.848i	0.744597	−	0.901972i
$76$		−	573.420i		−	0.865471i
$77$	413.849	+	29.8757i	0.612500	+	0.0442163i
$78$	181.618	+	1146.69i	0.263644	+	1.66458i
$79$	907.955	+	95.4299i	1.29307	+	0.135908i	0.725963	−	0.687733i	$-0.241394\pi$
$79$	907.955	+	95.4299i	1.29307	+	0.135908i	0.567112	+	0.823641i	$0.308061\pi$
$80$	−1027.70	+	824.225i	−1.43626	+	1.15189i
$81$	−93.9234	−	893.621i	−0.128839	−	1.22582i
$82$	45.0753	−	168.223i	0.0607041	−	0.226551i
$83$	−224.817	+	1419.44i	−0.297312	+	1.87715i	0.158921	+	0.987291i	$0.449199\pi$
$83$	−224.817	+	1419.44i	−0.297312	+	1.87715i	−0.456232	+	0.889861i	$0.650801\pi$
$84$	1390.09	−	1483.97i	1.80561	−	1.92756i
$85$	679.046	−	605.642i	0.866505	−	0.772837i
$86$	2536.41	−	539.130i	3.18032	−	0.675999i
$87$	311.313	+	479.379i	0.383635	+	0.590745i
$88$	627.029	+	965.540i	0.759563	+	1.16962i
$89$	−549.439	+	116.787i	−0.654387	+	0.139094i	−0.523128	−	0.852254i	$-0.675235\pi$
$89$	−549.439	+	116.787i	−0.654387	+	0.139094i	−0.131259	+	0.991348i	$0.541902\pi$
$90$	−564.283	+	56.6195i	−0.660896	+	0.0663136i
$91$	663.156	−	201.115i	0.763930	−	0.231677i
$92$	353.710	−	2233.24i	0.400835	−	2.53078i
$93$	155.882	−	581.758i	0.173808	−	0.648661i
$94$	213.440	+	2030.75i	0.234199	+	2.22825i
$95$	296.715	+	194.684i	0.320445	+	0.210254i
$96$	1151.28	+	121.005i	1.22398	+	0.128646i
$97$	−4.41746	−	27.8907i	−0.00462397	−	0.0291946i	0.985268	−	0.171015i	$-0.0547046\pi$
$97$	−4.41746	−	27.8907i	−0.00462397	−	0.0291946i	−0.989892	+	0.141820i	$0.954705\pi$
$98$	−1429.93	−	1010.87i	−1.47392	−	1.04197i
$99$			222.592i			0.225973i
$100$	−214.851	−	2247.91i	−0.214851	−	2.24791i
$101$	−1678.37	−	969.007i	−1.65350	−	0.954651i	−0.975616	−	0.219486i	$-0.929562\pi$
$101$	−1678.37	−	969.007i	−1.65350	−	0.954651i	−0.677889	−	0.735165i	$-0.737105\pi$
$102$	−2521.69	−	132.156i	−2.44789	−	0.128289i
$103$	901.636	+	1113.43i	0.862532	+	1.06514i	0.997239	+	0.0742534i	$0.0236574\pi$
$103$	901.636	+	1113.43i	0.862532	+	1.06514i	−0.134707	+	0.990885i	$0.543009\pi$
$104$	1555.56	+	1130.18i	1.46669	+	1.06561i
$105$	295.923	+	1223.13i	0.275040	+	1.13681i
$106$	874.226	−	635.163i	0.801060	−	0.582004i
$107$	1508.46	+	404.191i	1.36288	+	0.365184i	0.864875	−	0.501988i	$-0.167398\pi$
$107$	1508.46	+	404.191i	1.36288	+	0.365184i	0.498010	+	0.867171i	$0.334064\pi$
$108$	−1456.01	−	1179.05i	−1.29726	−	1.05050i
$109$	−161.852	+	761.455i	−0.142226	+	0.669121i	0.848040	+	0.529933i	$0.177783\pi$
$109$	−161.852	+	761.455i	−0.142226	+	0.669121i	−0.990266	+	0.139189i	$0.955551\pi$
$110$	−1278.81	−	6.03042i	−1.10845	−	0.00522707i
$111$	−1884.86	−	612.427i	−1.61173	−	0.523684i
$112$	−71.2490	−	2181.10i	−0.0601107	−	1.84013i
$113$	−208.518	+	409.239i	−0.173590	+	0.340690i	−0.961367	−	0.275271i	$-0.911232\pi$
$113$	−208.518	+	409.239i	−0.173590	+	0.340690i	0.787776	+	0.615961i	$0.211232\pi$
$114$	−204.767	−	963.354i	−0.168230	−	0.791460i
$115$	1035.49	+	941.242i	0.839654	+	0.763228i
$116$	1661.94	+	353.256i	1.33023	+	0.282750i
$117$	133.226	+	347.066i	0.105272	+	0.274242i
$118$	−912.837	+	912.837i	−0.712148	+	0.712148i
$119$	127.983	+	1501.80i	0.0985901	+	1.15689i
$120$	−2210.14	+	2703.14i	−1.68131	+	2.05635i
$121$	86.6609	−	824.523i	0.0651096	−	0.619477i
$122$	4043.87	+	1552.29i	3.00094	+	1.15195i
$123$	10.8501	−	207.032i	0.00795382	−	0.151768i
$124$	−895.140	−	1550.43i	−0.648274	−	1.12284i
$125$	1236.12	+	652.023i	0.884495	+	0.466550i
$126$	485.654	−	804.157i	0.343377	−	0.568572i
$127$	−75.1667	−	147.523i	−0.0525194	−	0.103075i	0.863255	−	0.504768i	$-0.168422\pi$
$127$	−75.1667	−	147.523i	−0.0525194	−	0.103075i	−0.915774	+	0.401693i	$0.868422\pi$
$128$	−1065.91	+	863.155i	−0.736046	+	0.596038i
$129$	2819.91	−	1255.51i	1.92465	−	0.856908i
$130$	−1997.53	+	755.990i	−1.34765	+	0.510037i
$131$	−277.104	+	622.385i	−0.184814	+	0.415099i	−0.982063	−	0.188551i	$-0.939621\pi$
$131$	−277.104	+	622.385i	−0.184814	+	0.415099i	0.797249	+	0.603650i	$0.206288\pi$
$132$	1739.30	+	1739.30i	1.14687	+	1.14687i
$133$	−552.862	+	199.817i	−0.360445	+	0.130273i
$134$	−1559.75	+	506.792i	−1.00553	+	0.326718i
$135$	1104.43	−	353.102i	0.704106	−	0.225113i
$136$	−3107.88	+	2798.35i	−1.95955	+	1.76439i
$137$	1803.54	−	1171.23i	1.12472	−	0.730401i	0.158305	−	0.987390i	$-0.449397\pi$
$137$	1803.54	−	1171.23i	1.12472	−	0.730401i	0.966414	+	0.256989i	$0.0827305\pi$
$138$	−203.247	−	3878.18i	−0.125373	−	2.39227i
$139$	49.5608	−	152.532i	0.0302424	−	0.0930765i	−0.934796	−	0.355185i	$-0.884418\pi$
$139$	49.5608	−	152.532i	0.0302424	−	0.0930765i	0.965038	+	0.262109i	$0.0844178\pi$
$140$	3192.85	+	1948.86i	1.92747	+	1.17649i
$141$	751.129	+	2311.74i	0.448627	+	1.38073i
$142$	−3189.03	+	1224.15i	−1.88463	+	0.723441i
$143$	216.967	+	809.733i	0.126879	+	0.473519i
$144$	1164.29	−	122.372i	0.673779	−	0.0708170i
$145$	−747.041	+	740.029i	−0.427851	+	0.423835i
$146$	−891.158	+	1226.57i	−0.505156	+	0.695287i
$147$	−1915.17	−	823.138i	−1.07456	−	0.461845i
$148$	−5248.98	+	2674.49i	−2.91529	+	1.48542i
$149$	−1233.02	+	711.882i	−0.677937	+	0.391407i	−0.799077	−	0.601228i	$-0.794678\pi$
$149$	−1233.02	+	711.882i	−0.677937	+	0.391407i	0.121141	+	0.992635i	$0.461345\pi$
$150$	−1163.68	−	3699.80i	−0.633426	−	2.01392i
$151$	−1427.89	+	2473.18i	−0.769536	+	1.33288i	0.168278	+	0.985740i	$0.446179\pi$
$151$	−1427.89	+	2473.18i	−0.769536	+	1.33288i	−0.937815	+	0.347136i	$0.887154\pi$
$152$	−1367.97	−	888.369i	−0.729979	−	0.474054i
$153$	−798.623	+	126.489i	−0.421992	+	0.0668370i
$154$	1278.67	−	1688.93i	0.669080	−	0.883752i
$155$	1106.18	+	63.2042i	0.573227	+	0.0327528i
$156$	3752.93	+	1670.91i	1.92612	+	0.857563i
$157$	−3499.06	+	937.570i	−1.77870	+	0.476600i	−0.990345	−	0.138625i	$-0.955732\pi$
$157$	−3499.06	+	937.570i	−1.77870	+	0.476600i	−0.788351	+	0.615225i	$0.789065\pi$
$158$	2933.27	−	3622.29i	1.47695	−	1.82389i
$159$	860.732	−	955.939i	0.429311	−	0.476798i
$160$	212.616	+	2118.98i	0.105055	+	1.04700i
$161$	−2276.43	+	437.176i	−1.11433	+	0.214002i
$162$	−4087.44	−	2082.65i	−1.98234	−	1.01005i
$163$	1178.11	−	61.7419i	0.566113	−	0.0296687i	0.232867	−	0.972509i	$-0.425189\pi$
$163$	1178.11	−	61.7419i	0.566113	−	0.0296687i	0.333246	+	0.942840i	$0.391856\pi$
$164$	−412.351	−	457.962i	−0.196336	−	0.218054i
$165$	−1490.51	+	309.479i	−0.703249	+	0.146017i
$166$	5452.57	+	4909.51i	2.54941	+	2.29549i
$167$	−460.380	−	72.9170i	−0.213325	−	0.0337873i	0.0488572	−	0.998806i	$-0.484442\pi$
$167$	−460.380	−	72.9170i	−0.213325	−	0.0337873i	−0.262182	+	0.965018i	$0.584442\pi$
$168$	−1386.62	−	5615.27i	−0.636787	−	2.57874i
$169$	−468.426	−	644.733i	−0.213212	−	0.293461i
$170$	−705.054	−	4591.57i	−0.318089	−	2.07151i
$171$	−128.271	−	288.102i	−0.0573634	−	0.128840i
$172$	3288.19	−	8566.03i	1.45769	−	3.79740i
$173$	954.616	−	1469.98i	0.419527	−	0.646014i	−0.564210	−	0.825631i	$-0.690819\pi$
$173$	954.616	−	1469.98i	0.419527	−	0.646014i	0.983737	+	0.179617i	$0.0574858\pi$
$174$	2918.23			1.27144
$175$	−2092.45	+	990.466i	−0.903854	+	0.427841i
$176$	2639.88			1.13062
$177$	−836.966	+	1288.81i	−0.355425	+	0.547306i
$178$	−1027.72	+	2677.31i	−0.432758	+	1.12737i
$179$	424.886	+	954.310i	0.177416	+	0.398483i	0.980262	−	0.197704i	$-0.0633484\pi$
$179$	424.886	+	954.310i	0.177416	+	0.398483i	−0.802846	+	0.596187i	$0.796682\pi$
$180$	−919.450	+	1783.68i	−0.380732	+	0.738598i
$181$	−140.906	−	193.941i	−0.0578645	−	0.0796436i	0.779104	−	0.626895i	$-0.215674\pi$
$181$	−140.906	−	193.941i	−0.0578645	−	0.0796436i	−0.836969	+	0.547251i	$0.815674\pi$
$182$	982.848	−	3398.70i	0.400294	−	1.38422i
$183$	5092.79	+	806.618i	2.05721	+	0.325830i
$184$	−4779.70	−	4303.66i	−1.91502	−	1.72429i
$185$	398.195	−	3624.09i	0.158248	−	1.44026i
$186$	−2057.50	−	2285.09i	−0.811094	−	0.900811i
$187$	−1820.81	+	95.4244i	−0.712035	+	0.0373162i
$188$	6437.77	+	3280.21i	2.49746	+	1.27252i
$189$	−629.413	+	1814.66i	−0.242238	+	0.698399i
$190$	1658.64	−	729.120i	0.633317	−	0.278400i
$191$	289.375	−	321.384i	0.109625	−	0.121751i	−0.685835	−	0.727758i	$-0.740563\pi$
$191$	289.375	−	321.384i	0.109625	−	0.121751i	0.795460	+	0.606006i	$0.207229\pi$
$192$	114.067	−	140.860i	0.0428752	−	0.0529465i
$193$	−1608.14	+	430.900i	−0.599774	+	0.160709i	−0.545916	−	0.837840i	$-0.683818\pi$
$193$	−1608.14	+	430.900i	−0.599774	+	0.160709i	−0.0538577	+	0.998549i	$0.517152\pi$
$194$	−131.705	−	58.6387i	−0.0487414	−	0.0217011i
$195$	−2138.78	+	1374.64i	−0.785441	+	0.504821i
$196$	−5755.58	+	2295.31i	−2.09751	+	0.836483i
$197$	274.000	−	43.3973i	0.0990947	−	0.0156951i	−0.106690	−	0.994292i	$-0.534025\pi$
$197$	274.000	−	43.3973i	0.0990947	−	0.0156951i	0.205785	+	0.978597i	$0.434025\pi$
$198$	953.087	+	618.942i	0.342085	+	0.222153i
$199$	−1060.26	+	1836.42i	−0.377686	+	0.654172i	−0.990725	−	0.135881i	$-0.956614\pi$
$199$	−1060.26	+	1836.42i	−0.377686	+	0.654172i	0.613039	+	0.790053i	$0.289947\pi$
$200$	−5695.54	−	2970.01i	−2.01368	−	1.05006i
$201$	−1690.71	+	976.131i	−0.593300	+	0.342542i
$202$	−8815.94	+	4491.94i	−3.07073	+	1.56461i
$203$	−238.536	−	1725.45i	−0.0824725	−	0.596566i
$204$	−5251.94	+	7228.67i	−1.80250	+	2.48092i
$205$	376.970	−	57.8852i	0.128433	−	0.0197214i
$206$	7274.53	−	764.584i	2.46039	−	0.258597i
$207$	−321.850	−	1201.16i	−0.108068	−	0.403317i
$208$	4116.10	−	1580.02i	1.37212	−	0.526706i
$209$	−219.753	−	676.331i	−0.0727304	−	0.223841i
$210$	6059.98	+	2133.96i	1.99132	+	0.701225i
$211$	1763.31	−	5426.93i	0.575316	−	1.77064i	−0.0597862	−	0.998211i	$-0.519042\pi$
$211$	1763.31	−	5426.93i	0.575316	−	1.77064i	0.635102	−	0.772428i	$-0.280958\pi$
$212$	−200.115	−	3818.42i	−0.0648299	−	1.23703i
$213$	−3410.27	+	2214.65i	−1.09703	+	0.712420i
$214$	5925.09	−	5334.98i	1.89267	−	1.70417i
$215$	3316.08	+	4609.75i	1.05188	+	1.46224i
$216$	−5068.49	+	1646.85i	−1.59661	+	0.518769i
$217$	−1182.92	+	1403.32i	−0.370054	+	0.439002i
$218$	2810.32	+	2810.32i	0.873115	+	0.873115i
$219$	−734.074	+	1648.76i	−0.226503	+	0.508734i
$220$	−2482.38	+	3783.36i	−0.760737	+	1.15943i
$221$	−2781.89	+	1238.58i	−0.846743	+	0.376994i
$222$	−7863.31	+	6367.58i	−2.37725	+	1.92506i
$223$	1517.04	+	2977.36i	0.455555	+	0.894076i	0.998523	+	0.0543234i	$0.0173002\pi$
$223$	1517.04	+	2977.36i	0.455555	+	0.894076i	−0.542969	+	0.839753i	$0.682700\pi$
$224$	−3019.75	−	1823.71i	−0.900738	−	0.543982i
$225$	−610.793	−	1081.35i	−0.180976	−	0.320400i
$226$	1172.46	+	2030.76i	0.345092	+	0.597717i
$227$	58.8850	−	1123.59i	0.0172173	−	0.328526i	−0.976419	−	0.215886i	$-0.930736\pi$
$227$	58.8850	−	1123.59i	0.0172173	−	0.328526i	0.993636	−	0.112640i	$-0.0359307\pi$
$228$	−3253.47	−	1248.89i	−0.945027	−	0.362762i
$229$	380.194	−	3617.30i	0.109711	−	1.04384i	−0.791711	−	0.610895i	$-0.790810\pi$
$229$	380.194	−	3617.30i	0.109711	−	1.04384i	0.901423	−	0.432940i	$-0.142524\pi$
$230$	6909.47	−	1816.51i	1.98086	−	0.520770i
$231$	1070.86	−	2283.02i	0.305010	−	0.650268i
$232$	3417.49	−	3417.49i	0.967107	−	0.967107i
$233$	1489.86	+	3881.22i	0.418901	+	1.09127i	0.966981	+	0.254848i	$0.0820256\pi$
$233$	1489.86	+	3881.22i	0.418901	+	1.09127i	−0.548080	+	0.836426i	$0.684641\pi$
$234$	1856.50	+	394.612i	0.518647	+	0.110242i
$235$	−3883.04	+	2217.53i	−1.07788	+	0.615555i
$236$	949.730	+	4468.13i	0.261958	+	1.23242i
$237$	2518.94	−	4943.70i	0.690392	−	1.35497i
$238$	6786.21	+	3627.91i	1.84825	+	0.988079i
$239$	4989.00	+	1621.02i	1.35026	+	0.438725i	0.892779	−	0.450496i	$-0.148753\pi$
$239$	4989.00	+	1621.02i	1.35026	+	0.438725i	0.457478	+	0.889221i	$0.348753\pi$
$240$	2438.18	+	7626.11i	0.655765	+	2.05110i
$241$	−9.27682	+	43.6440i	−0.00247955	+	0.0116654i	−0.979370	−	0.202075i	$-0.935231\pi$
$241$	−9.27682	+	43.6440i	−0.00247955	+	0.0116654i	0.976890	+	0.213741i	$0.0685648\pi$
$242$	−3289.44	−	2663.74i	−0.873774	−	0.707568i
$243$	−2570.05	−	688.642i	−0.678472	−	0.181796i
$244$	12399.8	−	9009.00i	3.25335	−	2.36370i
$245$	766.397	−	3757.49i	0.199850	−	0.979826i
$246$	−856.292	−	622.133i	−0.221932	−	0.161243i
$247$	−747.438	−	923.009i	−0.192544	−	0.237772i
$248$	−5085.54	−	266.522i	−1.30214	−	0.0682425i
$249$	7563.95	+	4367.05i	1.92508	+	1.11145i
$250$	6228.97	−	3479.75i	1.57582	−	0.880314i
$251$		−	7466.35i		−	1.87758i	−0.344494	−	0.938789i	$-0.611949\pi$
$251$		−	7466.35i		−	1.87758i	0.344494	−	0.938789i	$-0.388051\pi$
$252$	−1450.47	−	2990.98i	−0.362583	−	0.747674i
$253$	−438.660	−	2769.59i	−0.109005	−	0.688231i
$254$	−840.667	−	88.3576i	−0.207670	−	0.0218270i
$255$	−1957.35	−	5171.83i	−0.480682	−	1.27009i
$256$	756.892	+	7201.34i	0.184788	+	1.75814i
$257$	−1231.25	+	4595.08i	−0.298845	+	1.11530i	0.639271	+	0.768982i	$0.279236\pi$
$257$	−1231.25	+	4595.08i	−0.298845	+	1.11530i	−0.938116	+	0.346322i	$0.887430\pi$
$258$	2465.29	−	15565.3i	0.594893	−	3.75601i
$259$	4407.69	+	4128.83i	1.05745	+	0.990552i
$260$	−1606.12	+	7384.77i	−0.383104	+	1.76148i
$261$	914.023	−	194.282i	0.216769	−	0.0460756i
$262$	1894.39	+	2917.10i	0.446701	+	0.687859i
$263$	455.538	+	701.467i	0.106805	+	0.164465i	0.888032	−	0.459782i	$-0.152072\pi$
$263$	455.538	+	701.467i	0.106805	+	0.164465i	−0.781227	+	0.624247i	$0.785406\pi$
$264$	6843.92	−	1454.72i	1.59551	−	0.339136i
$265$	2043.77	+	1192.86i	0.473765	+	0.276516i
$266$	−681.725	+	2922.83i	−0.157140	+	0.673724i
$267$	−534.034	+	3371.76i	−0.122406	+	0.772840i
$268$	−1501.95	+	5605.37i	−0.342337	+	1.27762i
$269$	−553.895	−	5269.96i	−0.125545	−	1.19448i	−0.857995	−	0.513658i	$-0.828290\pi$
$269$	−553.895	−	5269.96i	−0.125545	−	1.19448i	0.732450	−	0.680821i	$-0.238377\pi$
$270$	1559.09	−	5710.75i	0.351419	−	1.28720i
$271$	2103.93	+	221.132i	0.471605	+	0.0495676i	0.337350	−	0.941379i	$-0.390469\pi$
$271$	2103.93	+	221.132i	0.471605	+	0.0495676i	0.134254	+	0.990947i	$0.457136\pi$
$272$	1500.13	+	9471.43i	0.334407	+	2.11136i
$273$	303.243	−	4200.63i	0.0672274	−	0.931258i
$274$		−	10979.0i		−	2.42069i
$275$	−1114.88	−	2569.00i	−0.244472	−	0.563333i
$276$	−11900.6	−	6870.79i	−2.59540	−	1.49845i
$277$	2732.64	+	143.211i	0.592737	+	0.0310641i	0.346347	−	0.938107i	$-0.387422\pi$
$277$	2732.64	+	143.211i	0.592737	+	0.0310641i	0.246391	+	0.969171i	$0.420755\pi$
$278$	−515.298	−	636.340i	−0.111171	−	0.137285i
$279$	−796.565	−	578.738i	−0.170929	−	0.124187i
$280$	9595.78	−	4597.69i	2.04806	−	0.981303i
$281$	6925.51	−	5031.68i	1.47025	−	1.06820i	0.489713	−	0.871884i	$-0.337101\pi$
$281$	6925.51	−	5031.68i	1.47025	−	1.06820i	0.980540	−	0.196318i	$-0.0628985\pi$
$282$	11986.9	+	3211.88i	2.53124	+	0.678243i
$283$	−3999.71	−	3238.90i	−0.840134	−	0.680327i	0.109398	−	0.993998i	$-0.465108\pi$
$283$	−3999.71	−	3238.90i	−0.840134	−	0.680327i	−0.949532	+	0.313671i	$0.898441\pi$
$284$	−2513.03	+	11822.9i	−0.525074	+	2.47028i
$285$	1750.83	−	1259.48i	0.363896	−	0.261773i
$286$	4070.38	+	1322.55i	0.841562	+	0.273440i
$287$	−297.853	+	557.151i	−0.0612604	+	0.114591i
$288$	859.172	−	1686.22i	0.175789	−	0.345005i
$289$	−355.580	−	1672.87i	−0.0723754	−	0.340500i
$290$	1091.40	+	5256.38i	0.220997	+	1.06436i
$291$	−167.867	−	35.6813i	−0.0338163	−	0.00718788i
$292$	1922.55	+	5008.42i	0.385304	+	1.00375i
$293$	2670.15	−	2670.15i	0.532395	−	0.532395i	−0.388890	−	0.921284i	$-0.627141\pi$
$293$	2670.15	−	2670.15i	0.532395	−	0.532395i	0.921284	+	0.388890i	$0.127141\pi$
$294$	−8849.80	+	5911.46i	−1.75555	+	1.17266i
$295$	−2634.46	−	1025.56i	−0.519947	−	0.202407i
$296$	−1751.62	+	16665.6i	−0.343956	+	3.27252i
$297$	−2169.16	−	832.664i	−0.423797	−	0.162680i
$298$	−380.425	+	7258.94i	−0.0739511	+	1.41107i
$299$	−2341.62	−	4055.80i	−0.452907	−	0.784458i
$300$	−13222.1	−	3676.85i	−2.54460	−	0.707611i
$301$	−9404.74	−	185.344i	−1.80093	−	0.0354918i
$302$	6619.15	+	12990.8i	1.26122	+	2.47529i
$303$	−9153.37	+	7412.25i	−1.73547	+	1.40536i
$304$	−3416.80	+	1521.26i	−0.644628	+	0.287007i
$305$	451.768	+	9474.93i	0.0848136	+	1.77880i
$306$	−1679.06	+	3771.23i	−0.313678	+	0.704532i
$307$	−2166.51	−	2166.51i	−0.402766	−	0.402766i	0.476441	−	0.879207i	$-0.341927\pi$
$307$	−2166.51	−	2166.51i	−0.402766	−	0.402766i	−0.879207	+	0.476441i	$0.841927\pi$
$308$	−2547.83	−	7049.45i	−0.471351	−	1.30415i
$309$	8281.09	−	2690.69i	1.52458	−	0.495365i
$310$	3346.47	−	4560.64i	0.613118	−	0.835570i
$311$	−6315.90	+	5686.86i	−1.15158	+	1.03689i	−0.152765	+	0.988263i	$0.548818\pi$
$311$	−6315.90	+	5686.86i	−1.15158	+	1.03689i	−0.998817	+	0.0486261i	$0.984516\pi$
$312$	9800.37	−	6364.44i	1.77832	−	1.15486i
$313$	−30.6013	−	583.909i	−0.00552617	−	0.105446i	−1.00000		0.000459816i	$-0.999854\pi$
$313$	−30.6013	−	583.909i	−0.00552617	−	0.105446i	0.994474	−	0.104986i	$-0.0334797\pi$
$314$	−5715.06	+	17589.1i	−1.02713	+	3.16119i
$315$	2040.13	+	264.937i	0.364915	+	0.0473889i
$316$	−5096.55	−	15685.6i	−0.907289	−	2.79235i
$317$	−5974.10	+	2293.24i	−1.05848	+	0.406313i	−0.824461	−	0.565918i	$-0.808522\pi$
$317$	−5974.10	+	2293.24i	−1.05848	+	0.406313i	−0.234021	+	0.972232i	$0.575188\pi$
$318$	−1699.75	−	6343.54i	−0.299739	−	1.11864i
$319$	2095.58	−	220.254i	0.367806	−	0.0386579i
$320$	296.382	+	152.779i	0.0517757	+	0.0266893i
$321$	5578.68	−	7678.39i	0.970004	−	1.33510i
$322$	−4457.97	+	10962.7i	−0.771531	+	1.89730i
$323$	2301.68	−	1172.77i	0.396499	−	0.202026i
$324$	−14057.7	+	8116.21i	−2.41044	+	1.39167i
$325$	−3275.93	−	3338.31i	−0.559126	−	0.569773i
$326$	3011.49	−	5216.05i	0.511628	−	0.886166i
$327$	3967.83	+	2576.74i	0.671014	+	0.435761i
$328$	−1731.36	+	274.220i	−0.291458	+	0.0461625i
$329$	919.270	−	7350.00i	0.154046	−	1.23167i
$330$	−2819.41	+	7242.55i	−0.470313	+	1.20815i
$331$	−5872.47	−	2614.59i	−0.975167	−	0.434172i	−0.143624	−	0.989632i	$-0.545876\pi$
$331$	−5872.47	−	2614.59i	−0.975167	−	0.434172i	−0.831543	+	0.555460i	$0.812542\pi$
$332$	25077.5	−	6719.50i	4.14550	−	1.11078i
$333$	−2038.96	+	2517.90i	−0.335538	+	0.414355i
$334$	−1592.35	+	1768.48i	−0.260866	+	0.289722i
$335$	−2390.55	−	2680.28i	−0.389879	−	0.437132i
$336$	−12530.3	−	4346.11i	−2.03447	−	0.705653i
$337$	2341.94	+	1193.28i	0.378556	+	0.192884i	0.632907	−	0.774228i	$-0.281862\pi$
$337$	2341.94	+	1193.28i	0.378556	+	0.192884i	−0.254350	+	0.967112i	$0.581862\pi$
$338$	−4063.10	+	212.938i	−0.653857	+	0.0342672i
$339$	1867.79	+	2074.39i	0.299247	+	0.332347i
$340$	−14984.7	−	6756.45i	−2.39017	−	1.07771i
$341$	−1649.96	−	1485.63i	−0.262025	−	0.235928i
$342$	−1590.25	−	251.872i	−0.251436	−	0.0398235i
$343$	4218.63	+	4749.39i	0.664095	+	0.747648i
$344$	−15341.1	−	21115.3i	−2.40447	−	3.30948i
$345$	7595.67	−	3825.18i	1.18533	−	0.596930i
$346$	−3639.69	−	8174.87i	−0.565523	−	1.27018i
$347$	1047.91	−	2729.89i	0.162117	−	0.422329i	−0.828327	−	0.560245i	$-0.810707\pi$
$347$	1047.91	−	2729.89i	0.162117	−	0.422329i	0.990444	+	0.137916i	$0.0440404\pi$
$348$	5623.94	−	8660.11i	0.866307	−	1.33400i
$349$	−3195.24			−0.490078			−0.245039	−	0.969513i	$-0.578801\pi$
$349$	−3195.24			−0.490078			−0.245039	+	0.969513i	$0.578801\pi$
$350$	−1577.35	+	11713.5i	−0.240894	+	1.78889i
$351$	−3880.53			−0.590107
$352$	2324.23	−	3579.00i	0.351937	−	0.541936i
$353$	2894.60	−	7540.70i	0.436442	−	1.13697i	−0.522317	−	0.852751i	$-0.674932\pi$
$353$	2894.60	−	7540.70i	0.436442	−	1.13697i	0.958759	−	0.284220i	$-0.0917345\pi$
$354$	3191.12	+	7167.37i	0.479113	+	1.07611i
$355$	−5264.51	−	5314.39i	−0.787073	−	0.794532i
$356$	5964.55	+	8209.50i	0.887979	+	1.22220i
$357$	8799.62	+	2544.71i	1.30455	+	0.377256i
$358$	5267.57	+	834.301i	0.777653	+	0.123168i
$359$	−4730.32	−	4259.20i	−0.695423	−	0.626161i	0.243657	−	0.969862i	$-0.421653\pi$
$359$	−4730.32	−	4259.20i	−0.695423	−	0.626161i	−0.939079	+	0.343700i	$0.888320\pi$
$360$	2830.74	+	4956.82i	0.414425	+	0.725687i
$361$	−3915.40	−	4348.49i	−0.570841	−	0.633983i
$362$	−1222.21	+	64.0534i	−0.177453	+	0.00929992i
$363$	−4489.43	−	2287.48i	−0.649129	−	0.330748i
$364$	−8191.82	−	9466.58i	−1.17958	−	1.36314i
$365$	−3244.32	−	705.608i	−0.465248	−	0.101187i
$366$	17614.8	−	19563.2i	2.51568	−	2.79395i
$367$	2125.65	−	2624.96i	0.302338	−	0.373357i	−0.603223	−	0.797573i	$-0.706117\pi$
$367$	2125.65	−	2624.96i	0.302338	−	0.373357i	0.905561	+	0.424216i	$0.139450\pi$
$368$	−14245.4	+	3817.05i	−2.01792	+	0.540700i
$369$	−309.620	−	137.852i	−0.0436806	−	0.0194479i
$370$	−14410.3	−	11782.2i	−2.02474	−	1.65547i
$371$	−3611.79	+	1523.52i	−0.505430	+	0.213201i
$372$	−10746.4	+	1702.06i	−1.49778	+	0.237225i
$373$	3191.18	+	2072.38i	0.442984	+	0.287677i	0.746794	−	0.665055i	$-0.231592\pi$
$373$	3191.18	+	2072.38i	0.442984	+	0.287677i	−0.303810	+	0.952733i	$0.598259\pi$
$374$	−4654.36	+	8061.59i	−0.643506	+	1.11459i
$375$	6391.66	−	5593.40i	0.880171	−	0.770245i
$376$	17799.0	−	10276.3i	2.44126	−	1.40946i
$377$	3135.61	−	1597.67i	0.428361	−	0.218261i
$378$	6019.81	+	7740.86i	0.819115	+	1.05330i
$379$	−3478.91	+	4788.30i	−0.471502	+	0.648967i	−0.976844	−	0.213952i	$-0.931366\pi$
$379$	−3478.91	+	4788.30i	−0.471502	+	0.648967i	0.505342	+	0.862919i	$0.331366\pi$
$380$	1032.76	−	6327.30i	0.139419	−	0.854168i
$381$	−1000.72	+	105.180i	−0.134563	+	0.0141432i
$382$	−571.449	−	2132.68i	−0.0765390	−	0.285647i
$383$	−13325.9	+	5115.35i	−1.77787	+	0.682460i	−0.779437	+	0.626481i	$0.784495\pi$
$383$	−13325.9	+	5115.35i	−1.77787	+	0.682460i	−0.998432	+	0.0559792i	$0.982172\pi$
$384$	2575.85	+	7927.66i	0.342314	+	1.05353i
$385$	4512.74	+	1075.02i	0.597378	+	0.142307i
$386$	−2626.60	+	8083.83i	−0.346348	+	1.06595i
$387$	−264.101	−	5039.35i	−0.0346900	−	0.661924i
$388$	−427.834	+	277.838i	−0.0559793	+	0.0363534i
$389$	2367.31	−	2131.54i	0.308554	−	0.277823i	−0.500276	−	0.865866i	$-0.666768\pi$
$389$	2367.31	−	2131.54i	0.308554	−	0.277823i	0.808830	+	0.588043i	$0.200101\pi$
$390$	−61.2096	+	12980.1i	−0.00794735	+	1.68531i
$391$	9687.54	−	3147.67i	1.25299	−	0.407122i
$392$	−3441.05	+	17286.7i	−0.443365	+	2.22732i
$393$	2927.76	+	2927.76i	0.375791	+	0.375791i
$394$	576.068	−	1293.87i	0.0736597	−	0.165442i
$395$	9846.79	+	2688.27i	1.25429	+	0.342434i
$396$	3673.53	−	1635.56i	0.466167	−	0.207551i
$397$	−491.545	+	398.045i	−0.0621409	+	0.0503207i	−0.659888	−	0.751364i	$-0.729396\pi$
$397$	−491.545	+	398.045i	−0.0621409	+	0.0503207i	0.597747	+	0.801685i	$0.296063\pi$
$398$	4914.94	+	9646.12i	0.619005	+	1.21486i
$399$	−70.3956	+	3572.02i	−0.00883255	+	0.448182i
$400$	−12824.5	+	7243.82i	−1.60306	+	0.905478i
$401$	−1090.79	−	1889.31i	−0.135839	−	0.235281i	0.790078	−	0.613006i	$-0.210040\pi$
$401$	−1090.79	−	1889.31i	−0.135839	−	0.235281i	−0.925918	+	0.377725i	$0.876706\pi$
$402$	−521.638	+	9953.44i	−0.0647187	+	1.23491i
$403$	−3461.81	−	1328.86i	−0.427903	−	0.164257i
$404$	−3659.61	+	34818.9i	−0.450675	+	4.28788i
$405$	573.071	−	10029.7i	0.0703114	−	1.23056i
$406$	−8051.24	−	3776.45i	−0.984178	−	0.461630i
$407$	−5166.05	+	5166.05i	−0.629169	+	0.629169i
$408$	9108.39	+	23728.2i	1.10523	+	2.87921i
$409$	−8086.38	−	1718.81i	−0.977618	−	0.207799i	−0.308720	−	0.951153i	$-0.599900\pi$
$409$	−8086.38	−	1718.81i	−0.977618	−	0.207799i	−0.668898	+	0.743354i	$0.733234\pi$
$410$	800.354	−	1775.05i	0.0964065	−	0.213813i
$411$	−2717.28	−	12783.8i	−0.326115	−	1.53425i
$412$	11750.3	−	23061.3i	1.40509	−	2.75765i
$413$	3976.99	−	2472.66i	0.473837	−	0.294605i
$414$	−6038.03	−	1961.87i	−0.716794	−	0.232901i
$415$	−5037.17	+	15257.6i	−0.595820	+	1.80474i
$416$	1481.84	−	6971.49i	0.174647	−	0.821647i
$417$	−757.496	−	613.408i	−0.0889562	−	0.0720353i
$418$	−3506.93	−	939.680i	−0.410358	−	0.109955i
$419$	−1032.19	+	749.933i	−0.120348	+	0.0874383i	−0.646331	−	0.763057i	$-0.723698\pi$
$419$	−1032.19	+	749.933i	−0.120348	+	0.0874383i	0.525983	+	0.850495i	$0.323698\pi$
$420$	18011.4	−	13871.0i	2.09254	−	1.61152i
$421$	4211.71	+	3059.99i	0.487569	+	0.354239i	0.804249	−	0.594293i	$-0.202568\pi$
$421$	4211.71	+	3059.99i	0.487569	+	0.354239i	−0.316680	+	0.948532i	$0.602568\pi$
$422$	−18333.7	−	22640.2i	−2.11486	−	2.61163i
$423$	3968.27	+	207.968i	0.456132	+	0.0239049i
$424$	−9419.36	−	5438.27i	−1.07888	−	0.622891i
$425$	8583.60	−	5459.86i	0.979684	−	0.623158i
$426$			20760.0i			2.36110i
$427$	−13006.9	−	8815.95i	−1.47412	−	0.999142i
$428$	−4413.34	−	27864.7i	−0.498427	−	3.14694i
$429$	5066.80	+	532.542i	0.570227	+	0.0599333i
$430$	28958.5	−	1380.75i	3.24769	−	0.154851i
$431$	242.035	+	2302.81i	0.0270497	+	0.257361i	0.999687	+	0.0250307i	$0.00796836\pi$
$431$	242.035	+	2302.81i	0.0270497	+	0.257361i	−0.972637	+	0.232330i	$0.925365\pi$
$432$	−3162.81	+	11803.8i	−0.352247	+	1.31461i
$433$	−1825.33	+	11524.7i	−0.202586	+	1.27907i	0.651383	+	0.758750i	$0.274189\pi$
$433$	−1825.33	+	11524.7i	−0.202586	+	1.27907i	−0.853968	+	0.520325i	$0.825811\pi$
$434$	2719.44	+	8967.04i	0.300777	+	0.991778i
$435$	2571.74	+	5850.31i	0.283461	+	0.644830i
$436$	13755.9	−	2923.90i	1.51098	−	0.321169i
$437$	2163.76	+	3331.90i	0.236858	+	0.364729i
$438$	5018.41	+	7727.67i	0.547463	+	0.843019i
$439$	1463.38	−	311.050i	0.159096	−	0.0338169i	−0.127675	−	0.991816i	$-0.540751\pi$
$439$	1463.38	−	311.050i	0.159096	−	0.0338169i	0.286771	+	0.957999i	$0.407418\pi$
$440$	5179.86	+	11783.4i	0.561228	+	1.27671i
$441$	−2378.31	+	2440.72i	−0.256809	+	0.263548i
$442$	−2432.05	+	15355.4i	−0.261722	+	1.65245i
$443$	−2724.60	+	10168.3i	−0.292211	+	1.09055i	0.651196	+	0.758910i	$0.274268\pi$
$443$	−2724.60	+	10168.3i	−0.292211	+	1.09055i	−0.943407	+	0.331637i	$0.892399\pi$
$444$	3742.40	+	35606.5i	0.400014	+	3.80588i
$445$	−6273.03	+	299.100i	−0.668247	+	0.0318622i
$446$	16966.7	+	1783.27i	1.80133	+	0.189328i
$447$	1353.60	+	8546.32i	0.143229	+	0.904311i
$448$	−496.990	+	241.015i	−0.0524120	+	0.0254171i
$449$		−	11541.2i		−	1.21305i	−0.795063	−	0.606527i	$-0.792562\pi$
$449$		−	11541.2i		−	1.21305i	0.795063	−	0.606527i	$-0.207438\pi$
$450$	−6328.46	−	391.541i	−0.662947	−	0.0410165i
$451$	−661.860	−	382.125i	−0.0691037	−	0.0398971i
$452$	8285.99	+	434.251i	0.862258	+	0.0451890i
$453$	10922.4	+	13488.0i	1.13285	+	1.39895i
$454$	−4647.22	−	3376.40i	−0.480407	−	0.349036i
$455$	7679.69	−	1024.80i	0.791273	−	0.105590i
$456$	−8019.80	+	5826.73i	−0.823600	+	0.598381i
$457$	500.708	+	134.164i	0.0512519	+	0.0137329i	0.284354	−	0.958719i	$-0.408221\pi$
$457$	500.708	+	134.164i	0.0512519	+	0.0137329i	−0.233102	+	0.972452i	$0.574888\pi$
$458$	−14431.3	−	11686.2i	−1.47233	−	1.19227i
$459$	1754.82	−	8255.76i	0.178448	−	0.839533i
$460$	7925.12	−	24005.2i	0.803284	−	2.43315i
$461$	−4554.06	−	1479.70i	−0.460095	−	0.149494i	0.0697930	−	0.997561i	$-0.477766\pi$
$461$	−4554.06	−	1479.70i	−0.460095	−	0.149494i	−0.529888	+	0.848068i	$0.677766\pi$
$462$	−6797.73	−	10933.3i	−0.684544	−	1.10101i
$463$	−5926.11	+	11630.6i	−0.594837	+	1.16743i	0.375758	+	0.926718i	$0.377382\pi$
$463$	−5926.11	+	11630.6i	−0.594837	+	1.16743i	−0.970596	+	0.240716i	$0.922618\pi$
$464$	−2304.12	−	10840.0i	−0.230531	−	1.08456i
$465$	2767.82	−	6138.56i	0.276031	−	0.612191i
$466$	20761.2	+	4412.92i	2.06382	+	0.438679i
$467$	346.132	+	901.704i	0.0342978	+	0.0893488i	0.949660	−	0.313283i	$-0.101429\pi$
$467$	346.132	+	901.704i	0.0342978	+	0.0893488i	−0.915362	+	0.402632i	$0.868096\pi$
$468$	4748.86	−	4748.86i	0.469052	−	0.469052i
$469$	5927.78	−	505.167i	0.583624	−	0.0497365i
$470$	−1302.30	+	22792.3i	−0.127810	+	2.23688i
$471$	−2301.25	+	21894.9i	−0.225129	+	2.14196i
$472$	12130.7	+	4656.52i	1.18296	+	0.454097i
$473$	595.536	−	11363.5i	0.0578917	−	1.10464i
$474$	−14163.6	−	24532.0i	−1.37248	−	2.37720i
$475$	2923.41	+	2682.60i	0.282390	+	0.259129i
$476$	23844.4	−	13147.1i	2.29602	−	1.26596i
$477$	−954.704	−	1873.71i	−0.0916412	−	0.179856i
$478$	20813.3	−	16854.3i	1.99158	−	1.61275i
$479$	−2096.56	+	933.448i	−0.199988	+	0.0890403i	−0.504287	−	0.863536i	$-0.668245\pi$
$479$	−2096.56	+	933.448i	−0.199988	+	0.0890403i	0.304299	+	0.952577i	$0.401578\pi$
$480$	12485.7	+	3408.72i	1.18727	+	0.324138i
$481$	−4962.92	+	11146.9i	−0.470457	+	1.05666i
$482$	161.078	+	161.078i	0.0152218	+	0.0152218i
$483$	−2477.54	+	13868.1i	−0.233399	+	1.30646i
$484$	−14244.2	+	4628.23i	−1.33774	+	0.434657i
$485$	1.48879	−	315.711i	0.000139386	−	0.0295582i
$486$	−10094.9	+	9089.49i	−0.942210	+	0.848369i
$487$	−11172.3	+	7255.36i	−1.03956	+	0.675096i	−0.947204	−	0.320630i	$-0.896105\pi$
$487$	−11172.3	+	7255.36i	−1.03956	+	0.675096i	−0.0923526	+	0.995726i	$0.529439\pi$
$488$	−2281.76	−	43538.5i	−0.211660	−	4.03872i
$489$	2215.56	−	6818.80i	0.204890	−	0.630586i
$490$	−13957.6	−	13729.6i	−1.28682	−	1.26580i
$491$	852.556	+	2623.90i	0.0783612	+	0.241171i	0.982562	−	0.185938i	$-0.0595322\pi$
$491$	852.556	+	2623.90i	0.0783612	+	0.241171i	−0.904200	+	0.427108i	$0.859532\pi$
$492$	−3496.46	+	1342.17i	−0.320392	+	0.122987i
$493$	1981.06	+	7393.42i	0.180979	+	0.675422i
$494$	−6030.44	+	633.824i	−0.549235	+	0.0577269i
$495$	−400.899	+	2456.15i	−0.0364021	+	0.223022i
$496$	−6863.66	+	9447.02i	−0.621346	+	0.855209i
$497$	12274.7	−	1696.92i	1.10784	−	0.153154i
$498$	39731.0	−	20244.0i	3.57508	−	1.82160i
$499$	−11604.5	+	6699.87i	−1.04106	+	0.601057i	−0.920134	−	0.391604i	$-0.871920\pi$
$499$	−11604.5	+	6699.87i	−1.04106	+	0.601057i	−0.120927	+	0.992661i	$0.538587\pi$
$500$	1677.86	−	25191.1i	0.150072	−	2.25316i
$501$	−1416.41	+	2453.29i	−0.126308	+	0.218772i
$502$	−31969.1	−	20761.0i	−2.84233	−	1.84583i
$503$	−6986.20	+	1106.50i	−0.619283	+	0.0980847i	−0.458190	−	0.888854i	$-0.651502\pi$
$503$	−6986.20	+	1106.50i	−0.619283	+	0.0980847i	−0.161093	+	0.986939i	$0.551502\pi$
$504$	−9382.50	−	1173.48i	−0.829225	−	0.103712i
$505$	−16774.4	−	13715.1i	−1.47812	−	1.20855i
$506$	−13078.4	−	5822.90i	−1.14903	−	0.511580i
$507$	−4678.29	+	1253.55i	−0.409803	+	0.109807i
$508$	−1882.32	+	2324.48i	−0.164399	+	0.203016i
$509$	−7693.97	+	8545.02i	−0.669999	+	0.744109i	−0.978303	−	0.207179i	$-0.933572\pi$
$509$	−7693.97	+	8545.02i	−0.669999	+	0.744109i	0.308304	+	0.951288i	$0.400238\pi$
$510$	−27587.2	−	5999.94i	−2.39525	−	0.520945i
$511$	4158.91	−	3598.88i	0.360038	−	0.311556i
$512$	23162.4	+	11801.8i	1.99931	+	1.01870i
$513$	3287.39	−	172.285i	0.282927	−	0.0148276i
$514$	16251.4	+	18049.0i	1.39459	+	1.54885i
$515$	7943.61	+	13909.8i	0.679684	+	1.19017i
$516$	−41440.3	−	37313.0i	−3.53548	−	3.18336i
$517$	8850.22	+	1401.74i	0.752867	+	0.119242i
$518$	29934.7	−	7392.00i	2.53910	−	0.627000i
$519$	−6261.24	−	8617.85i	−0.529553	−	0.728867i
$520$	15129.1	+	15272.4i	1.27587	+	1.28796i
$521$	2529.29	+	5680.88i	0.212688	+	0.477704i	0.988112	−	0.153736i	$-0.0491306\pi$
$521$	2529.29	+	5680.88i	0.212688	+	0.477704i	−0.775424	+	0.631441i	$0.782464\pi$
$522$	1709.67	−	4453.85i	0.143353	−	0.373448i
$523$	2068.26	−	3184.84i	0.172923	−	0.266278i	−0.741574	−	0.670871i	$-0.765920\pi$
$523$	2068.26	−	3184.84i	0.172923	−	0.266278i	0.914497	+	0.404593i	$0.132587\pi$
$524$	12307.6			1.02607
$525$	1062.41	+	14029.3i	0.0883188	+	1.16627i
$526$	4270.19			0.353971
$527$	4392.60	−	6764.01i	0.363083	−	0.559098i
$528$	5749.56	−	14978.1i	0.473897	−	1.23454i
$529$	1422.95	+	3196.00i	0.116952	+	0.262677i
$530$	10790.5	−	5434.07i	0.884353	−	0.445360i
$531$	1476.67	+	2032.46i	0.120681	+	0.166104i
$532$	7359.98	+	7655.90i	0.599804	+	0.623920i
$533$	−1260.68	−	199.673i	−0.102451	−	0.0162266i
$534$	12952.1	+	11662.1i	1.04961	+	0.945076i
$535$	15916.9	+	7176.79i	1.28626	+	0.579962i
$536$	11045.4	+	12267.2i	0.890093	+	0.988549i
$537$	6339.94	−	332.262i	0.509476	−	0.0267005i
$538$	−24104.8	−	12282.0i	−1.93166	−	0.984231i
$539$	−5908.88	+	4912.97i	−0.472196	+	0.392609i
$540$	−13942.5	−	15632.4i	−1.11109	−	1.24576i
$541$	894.258	−	993.174i	0.0710668	−	0.0789277i	−0.706563	−	0.707650i	$-0.749755\pi$
$541$	894.258	−	993.174i	0.0710668	−	0.0789277i	0.777630	+	0.628723i	$0.216422\pi$
$542$	6797.05	−	8393.65i	0.538668	−	0.665200i
$543$	−1407.27	+	377.076i	−0.111218	+	0.0298009i
$544$	14161.6	+	6305.15i	1.11613	+	0.496932i
$545$	−3157.35	+	8110.64i	−0.248157	+	0.637471i
$546$	−17142.9	−	12978.7i	−1.34368	−	1.01728i
$547$	19881.3	−	3148.89i	1.55405	−	0.246137i	0.680453	−	0.732792i	$-0.261783\pi$
$547$	19881.3	−	3148.89i	1.55405	−	0.246137i	0.873594	+	0.486655i	$0.161783\pi$
$548$	−32581.3	−	21158.6i	−2.53979	−	1.64936i
$549$	4214.74	−	7300.14i	0.327651	−	0.567509i
$550$	−14099.9	−	2369.73i	−1.09313	−	0.183719i
$551$	−2585.39	+	1492.68i	−0.199894	+	0.115409i
$552$	−34828.1	+	17745.8i	−2.68547	+	1.36832i
$553$	−13347.2	+	10379.7i	−1.02637	+	0.798173i
$554$	8211.59	−	11302.3i	0.629742	−	0.866765i
$555$	−19695.1	−	10152.4i	−1.50632	−	0.776480i
$556$	−2881.47	+	302.855i	−0.219787	+	0.0231005i
$557$	−2082.28	−	7771.16i	−0.158400	−	0.591158i	−0.998790	−	0.0491754i	$-0.984341\pi$
$557$	−2082.28	−	7771.16i	−0.158400	−	0.591158i	0.840390	−	0.541982i	$-0.182326\pi$
$558$	−4692.95	+	1801.46i	−0.356037	+	0.136670i
$559$	−5872.74	−	18074.4i	−0.444348	−	1.36756i
$560$	3142.07	−	24195.3i	0.237102	−	1.82578i
$561$	−3424.23	+	10538.7i	−0.257703	+	0.793127i
$562$	−2287.31	−	43644.5i	−0.171680	−	3.27586i
$563$	−9654.53	+	6269.72i	−0.722717	+	0.469338i	−0.852848	−	0.522159i	$-0.825127\pi$
$563$	−9654.53	+	6269.72i	−0.722717	+	0.469338i	0.130131	+	0.991497i	$0.458460\pi$
$564$	32632.4	−	29382.4i	2.43630	−	2.19365i
$565$	−3037.91	+	4140.13i	−0.226205	+	0.308277i
$566$	−24989.8	+	8119.68i	−1.85583	+	0.602995i
$567$	12723.8	+	10725.5i	0.942417	+	0.794405i
$568$	24311.7	+	24311.7i	1.79595	+	1.79595i
$569$	7357.41	−	16525.0i	0.542071	−	1.21751i	−0.410126	−	0.912029i	$-0.634515\pi$
$569$	7357.41	−	16525.0i	0.542071	−	1.21751i	0.952197	−	0.305483i	$-0.0988180\pi$
$570$	−524.424	−	10998.8i	−0.0385364	−	0.808223i
$571$	−20782.7	+	9253.07i	−1.52317	+	0.678160i	−0.986218	−	0.165452i	$-0.947092\pi$
$571$	−20782.7	+	9253.07i	−1.52317	+	0.678160i	−0.536953	+	0.843612i	$0.680425\pi$
$572$	11769.1	−	9530.46i	0.860301	−	0.696658i
$573$	−1193.22	−	2341.82i	−0.0869935	−	0.170734i
$574$	1557.37	+	2824.55i	0.113246	+	0.205391i
$575$	9730.74	+	12250.9i	0.705739	+	0.888520i
$576$	−148.157	−	256.615i	−0.0107174	−	0.0185630i
$577$	−700.895	+	13373.9i	−0.0505696	+	0.964925i	0.849067	+	0.528285i	$0.177165\pi$
$577$	−700.895	+	13373.9i	−0.0505696	+	0.964925i	−0.899637	+	0.436640i	$0.856168\pi$
$578$	−8151.58	−	3129.10i	−0.586611	−	0.225179i
$579$	−1057.64	+	10062.7i	−0.0759133	+	0.722267i
$580$	17702.1	+	6891.16i	1.26731	+	0.493344i
$581$	−15217.2	−	21836.9i	−1.08660	−	1.55929i
$582$	−619.551	+	619.551i	−0.0441258	+	0.0441258i
$583$	−1699.37	−	4427.01i	−0.120722	−	0.314491i
$584$	14926.7	+	3172.77i	1.05766	+	0.224812i
$585$	844.980	+	4069.59i	0.0597190	+	0.287618i
$586$	−4008.30	−	18857.6i	−0.282562	−	1.32935i
$587$	6661.96	−	13074.8i	0.468430	−	0.919346i	−0.529063	−	0.848582i	$-0.677457\pi$
$587$	6661.96	−	13074.8i	0.468430	−	0.919346i	0.997493	−	0.0707631i	$-0.0225434\pi$
$588$	487.659	+	37655.0i	0.0342019	+	2.64093i
$589$	2991.66	+	972.050i	0.209286	+	0.0680011i
$590$	−11716.6	+	8428.48i	−0.817567	+	0.588127i
$591$	350.534	−	1649.13i	0.0243977	−	0.114782i
$592$	29861.6	+	24181.4i	2.07315	+	1.67880i
$593$	−8962.26	−	2401.43i	−0.620634	−	0.166298i	−0.0652180	−	0.997871i	$-0.520774\pi$
$593$	−8962.26	−	2401.43i	−0.620634	−	0.166298i	−0.555416	+	0.831573i	$0.687441\pi$
$594$	−9596.86	+	6972.53i	−0.662902	+	0.481627i
$595$	−1292.59	+	16801.8i	−0.0890607	+	1.15766i
$596$	20808.4	+	15118.2i	1.43011	+	1.03904i
$597$	8110.25	+	10015.3i	0.555997	+	0.686599i
$598$	−23877.1	−	1251.34i	−1.63279	−	0.0855707i
$599$	11187.6	+	6459.16i	0.763127	+	0.440591i	0.830417	−	0.557142i	$-0.188102\pi$
$599$	11187.6	+	6459.16i	0.763127	+	0.440591i	−0.0672905	+	0.997733i	$0.521435\pi$
$600$	−29255.9	+	25846.7i	−1.99061	+	1.75865i
$601$			5979.24i			0.405821i	0.979197	+	0.202910i	$0.0650400\pi$
$601$			5979.24i			0.405821i	−0.979197	+	0.202910i	$0.934960\pi$
$602$	−26944.5	+	39753.5i	−1.82421	+	2.69141i
$603$	499.270	+	3152.27i	0.0337178	+	0.212886i
$604$	51307.7	+	5392.66i	3.45643	+	0.363285i
$605$	2441.25	−	8941.98i	0.164051	−	0.600898i
$606$	6285.56	+	59803.1i	0.421342	+	4.00880i
$607$	−2008.20	+	7494.70i	−0.134284	+	0.501154i	0.865716	+	0.500536i	$0.166864\pi$
$607$	−2008.20	+	7494.70i	−0.134284	+	0.501154i	−1.00000		0.000618591i	$0.999803\pi$
$608$	−945.820	+	5971.67i	−0.0630889	+	0.398328i
$609$	−10309.4	−	2404.57i	−0.685971	−	0.159997i
$610$	41825.6	+	24411.7i	2.77618	+	1.62033i
$611$	14638.3	−	3111.46i	0.969231	−	0.206016i
$612$	7955.63	+	12250.6i	0.525469	+	0.809152i
$613$	−2307.62	−	3553.42i	−0.152046	−	0.234130i	0.754437	−	0.656372i	$-0.227910\pi$
$613$	−2307.62	−	3553.42i	−0.152046	−	0.234130i	−0.906483	+	0.422242i	$0.861243\pi$
$614$	−15300.7	+	3252.26i	−1.00568	+	0.213763i
$615$	492.598	−	2264.92i	0.0322983	−	0.148505i
$616$	−20764.6	−	4843.15i	−1.35816	−	0.316780i
$617$	3111.60	−	19645.9i	0.203028	−	1.28187i	−0.649972	−	0.759958i	$-0.725219\pi$
$617$	3111.60	−	19645.9i	0.203028	−	1.28187i	0.853000	−	0.521911i	$-0.174781\pi$
$618$	11505.6	−	42939.4i	0.748903	−	2.79494i
$619$	−461.136	−	4387.41i	−0.0299428	−	0.284887i	−0.999239	−	0.0389927i	$-0.987585\pi$
$619$	−461.136	−	4387.41i	−0.0299428	−	0.284887i	0.969297	−	0.245894i	$-0.0790816\pi$
$620$	−7084.87	−	18720.1i	−0.458928	−	1.21261i
$621$	12909.3	+	1356.82i	0.834191	+	0.0876770i
$622$	6787.74	+	42856.1i	0.437562	+	2.76266i
$623$	5836.74	−	8611.43i	0.375351	−	0.553788i
$624$		−	26795.1i		−	1.71901i
$625$	12465.4	+	9420.94i	0.797787	+	0.602940i
$626$	−2585.25	−	1492.59i	−0.165059	−	0.0952971i
$627$	−4315.97	−	226.191i	−0.274902	−	0.0144070i
$628$	41183.5	+	50857.4i	2.61688	+	3.23158i
$629$	−21470.6	−	15599.3i	−1.36103	−	0.988845i
$630$	6807.19	−	7998.64i	0.430484	−	0.505831i
$631$	11843.6	−	8604.88i	0.747205	−	0.542876i	−0.147754	−	0.989024i	$-0.547204\pi$
$631$	11843.6	−	8604.88i	0.747205	−	0.542876i	0.894959	+	0.446148i	$0.147204\pi$
$632$	−45315.7	−	12142.3i	−2.85216	−	0.764233i
$633$	−26950.8	−	21824.3i	−1.69226	−	1.37036i
$634$	−6792.51	+	31956.3i	−0.425497	+	2.00181i
$635$	−563.718	−	1763.19i	−0.0352291	−	0.110189i
$636$	−22100.8	−	7180.97i	−1.37791	−	0.447711i
$637$	−6272.62	+	11196.9i	−0.390158	+	0.696448i
$638$	4883.91	−	9585.21i	0.303066	−	0.594800i
$639$	1382.10	+	6502.29i	0.0855637	+	0.402546i
$640$	−13316.2	+	7604.58i	−0.822449	+	0.469684i
$641$	27917.9	+	5934.13i	1.72027	+	0.365654i	0.959136	−	0.282945i	$-0.0913112\pi$
$641$	27917.9	+	5934.13i	1.72027	+	0.365654i	0.761131	+	0.648599i	$0.224645\pi$
$642$	−17364.9	−	45237.1i	−1.06751	−	2.78095i
$643$	515.604	−	515.604i	0.0316227	−	0.0316227i	−0.691119	−	0.722741i	$-0.742882\pi$
$643$	515.604	−	515.604i	0.0316227	−	0.0316227i	0.722741	+	0.691119i	$0.242882\pi$
$644$	23941.6	+	34356.6i	1.46496	+	2.10223i
$645$	33377.0	−	8774.87i	2.03755	−	0.535675i
$646$	1378.57	−	13116.3i	0.0839617	−	0.798843i
$647$	−19736.3	−	7576.05i	−1.19925	−	0.460348i	−0.324946	−	0.945732i	$-0.605346\pi$
$647$	−19736.3	−	7576.05i	−1.19925	−	0.460348i	−0.874301	+	0.485385i	$0.838680\pi$
$648$	−2416.54	+	46110.4i	−0.146498	+	2.79535i
$649$	2832.51	+	4906.05i	0.171318	+	0.296732i
$650$	−23402.9	+	4744.21i	−1.41221	+	0.286282i
$651$	5385.77	+	9768.00i	0.324247	+	0.588077i
$652$	−9675.43	−	18989.1i	−0.581165	−	1.14060i
$653$	19206.2	−	15552.9i	1.15099	−	0.932053i	0.152573	−	0.988292i	$-0.451244\pi$
$653$	19206.2	−	15552.9i	1.15099	−	0.932053i	0.998417	+	0.0562388i	$0.0179108\pi$
$654$	22066.0	−	9824.40i	1.31934	−	0.587407i
$655$	−4178.59	+	6368.52i	−0.249269	+	0.379906i
$656$	−1634.88	+	3672.00i	−0.0973038	+	0.218548i
$657$	2086.30	+	2086.30i	0.123888	+	0.123888i
$658$	−28914.8	−	24373.5i	−1.71309	−	1.44404i
$659$	−6769.68	+	2199.60i	−0.400166	+	0.130022i	−0.502184	−	0.864761i	$-0.667470\pi$
$659$	−6769.68	+	2199.60i	−0.400166	+	0.130022i	0.102018	+	0.994783i	$0.467470\pi$
$660$	16059.4	+	22324.5i	0.947140	+	1.31664i
$661$	−7366.85	+	6633.14i	−0.433490	+	0.390317i	−0.856783	−	0.515676i	$-0.827541\pi$
$661$	−7366.85	+	6633.14i	−0.433490	+	0.390317i	0.423293	+	0.905993i	$0.360874\pi$
$662$	−27524.1	+	17874.4i	−1.61594	+	1.04941i
$663$	968.571	+	18481.4i	0.0567363	+	1.08259i
$664$	22821.0	−	70235.8i	1.33377	−	4.10493i
$665$	−6460.34	+	1209.11i	−0.376723	+	0.0705073i
$666$	5111.52	+	15731.6i	0.297398	+	0.915298i
$667$	−10989.8	+	4218.59i	−0.637971	+	0.244894i
$668$	2179.40	+	8133.62i	0.126233	+	0.471107i
$669$	20197.0	−	2122.79i	1.16721	−	0.122678i
$670$	−18123.5	+	2782.94i	−1.04503	+	0.160469i
$671$	11172.7	−	15377.8i	0.642795	−	0.884732i
$672$	−16924.3	+	13161.4i	−0.971529	+	0.755525i
$673$	1565.82	−	797.825i	0.0896849	−	0.0456967i	−0.408573	−	0.912726i	$-0.633973\pi$
$673$	1565.82	−	797.825i	0.0896849	−	0.0456967i	0.498258	+	0.867029i	$0.333973\pi$
$674$	11621.3	−	6709.58i	0.664150	−	0.383447i
$675$	12822.6	−	1907.11i	0.731173	−	0.108748i
$676$	−7198.40	+	12468.0i	−0.409559	+	0.709376i
$677$	19323.9	+	12549.1i	1.09701	+	0.712410i	0.960514	−	0.278230i	$-0.0897478\pi$
$677$	19323.9	+	12549.1i	1.09701	+	0.712410i	0.136500	+	0.990640i	$0.456414\pi$
$678$	14075.7	−	2229.37i	0.797304	−	0.126281i
$679$	416.962	+	315.678i	0.0235663	+	0.0178418i
$680$	−39333.3	+	25280.4i	−2.21818	+	1.42568i
$681$	−6246.78	−	2781.25i	−0.351508	−	0.156502i
$682$	−10949.0	+	2933.78i	−0.614751	+	0.164722i
$683$	8225.56	−	10157.7i	0.460823	−	0.569069i	−0.492773	−	0.870158i	$-0.664017\pi$
$683$	8225.56	−	10157.7i	0.460823	−	0.569069i	0.953596	+	0.301089i	$0.0973500\pi$
$684$	−3812.15	+	4233.83i	−0.213101	+	0.236673i
$685$	22010.2	−	9675.48i	1.22769	−	0.539681i
$686$	32066.1	−	4856.97i	1.78468	−	0.270321i
$687$	−19695.8	−	10035.5i	−1.09380	−	0.557319i
$688$	−59765.2	+	3132.16i	−3.31181	+	0.173565i
$689$	−5299.32	−	5885.50i	−0.293016	−	0.325428i
$690$	4742.09	−	43159.2i	0.261635	−	2.38122i
$691$	−16188.5	−	14576.2i	−0.891229	−	0.802466i	0.0898739	−	0.995953i	$-0.471354\pi$
$691$	−16188.5	−	14576.2i	−0.891229	−	0.802466i	−0.981103	+	0.193487i	$0.938020\pi$
$692$	−31274.0	−	4953.32i	−1.71801	−	0.272105i
$693$	−2857.02	−	2971.90i	−0.156608	−	0.162905i
$694$	−8774.92	−	12077.6i	−0.479959	−	0.660606i
$695$	821.588	−	1593.83i	0.0448411	−	0.0869892i
$696$	−11946.9	−	26833.3i	−0.650643	−	1.46137i
$697$	994.893	−	2591.79i	0.0540664	−	0.140848i
$698$	−8884.71	+	13681.3i	−0.481793	+	0.741895i
$699$	25266.1			1.36717
$700$	31721.0	+	27254.9i	1.71277	+	1.47162i
$701$	−8415.79			−0.453438			−0.226719	−	0.973960i	$-0.572800\pi$
$701$	−8415.79			−0.453438			−0.226719	+	0.973960i	$0.572800\pi$
$702$	−10790.2	+	16615.5i	−0.580130	+	0.893322i
$703$	3709.44	−	9663.42i	0.199010	−	0.518440i
$704$	−271.770	−	610.406i	−0.0145493	−	0.0326783i
$705$	4124.66	+	26861.3i	0.220345	+	1.43497i
$706$	−24238.7	−	33361.7i	−1.29212	−	1.77845i
$707$	34845.8	−	8604.74i	1.85362	−	0.457729i
$708$	27419.7	+	4342.85i	1.45550	+	0.230529i
$709$	−7508.68	−	6760.85i	−0.397735	−	0.358123i	0.445859	−	0.895103i	$-0.352898\pi$
$709$	−7508.68	−	6760.85i	−0.397735	−	0.358123i	−0.843595	+	0.536980i	$0.819565\pi$
$710$	−37393.5	+	7764.12i	−1.97655	+	0.410397i
$711$	−6069.42	−	6740.78i	−0.320142	−	0.355554i
$712$	28825.4	−	1510.67i	1.51724	−	0.0795153i
$713$	11051.7	+	5631.13i	0.580491	+	0.295775i
$714$	35364.1	−	30602.0i	1.85360	−	1.60400i
$715$	935.722	+	9325.62i	0.0489427	+	0.487774i
$716$	12627.4	−	14024.2i	0.659090	−	0.731993i
$717$	20063.2	−	24776.0i	1.04501	−	1.29048i
$718$	−31390.0	+	8410.93i	−1.63157	+	0.437177i
$719$	−6924.36	−	3082.92i	−0.359158	−	0.159908i	0.219222	−	0.975675i	$-0.429648\pi$
$719$	−6924.36	−	3082.92i	−0.359158	−	0.159908i	−0.578380	+	0.815767i	$0.696315\pi$
$720$	13067.5	+	746.647i	0.676387	+	0.0386471i
$721$	−26329.1	−	3293.00i	−1.35998	−	0.170094i
$722$	−29506.4	+	4673.35i	−1.52093	+	0.240892i
$723$	227.422	+	147.690i	0.0116984	+	0.00759701i
$724$	−2165.33	+	3750.47i	−0.111152	+	0.192521i
$725$	−9575.92	+	6820.26i	−0.490539	+	0.349377i
$726$	−22277.8	+	12862.1i	−1.13885	+	0.657516i
$727$	22878.0	−	11656.9i	1.16712	−	0.594678i	0.240491	−	0.970651i	$-0.422691\pi$
$727$	22878.0	−	11656.9i	1.16712	−	0.594678i	0.926631	+	0.375973i	$0.122691\pi$
$728$	−35274.9	+	4876.59i	−1.79584	+	0.248267i
$729$	4755.39	−	6545.23i	0.241599	−	0.332532i
$730$	−12042.4	+	11929.4i	−0.610562	+	0.604831i
$731$	41108.7	−	4320.70i	2.07997	−	0.218614i
$732$	−24108.8	−	89975.3i	−1.21733	−	4.54315i
$733$	19177.4	−	7361.50i	0.966346	−	0.370946i	0.176534	−	0.984295i	$-0.443511\pi$
$733$	19177.4	−	7361.50i	0.966346	−	0.370946i	0.789812	+	0.613349i	$0.210178\pi$
$734$	−5328.85	−	16400.5i	−0.267972	−	0.824733i
$735$	−19650.0	−	12532.1i	−0.986126	−	0.628915i
$736$	−7367.17	+	22673.8i	−0.368964	+	1.13555i
$737$	376.652	+	7186.95i	0.0188252	+	0.359206i
$738$	−1451.18	+	942.406i	−0.0723829	+	0.0470060i
$739$	21798.6	−	19627.6i	1.08508	−	0.977011i	0.0852680	−	0.996358i	$-0.472825\pi$
$739$	21798.6	−	19627.6i	1.08508	−	0.977011i	0.999813	+	0.0193469i	$0.00615869\pi$
$740$	−62735.8	+	20057.5i	−3.11651	+	0.996391i
$741$	−6864.86	+	2230.53i	−0.340333	+	0.110581i
$742$	−3519.60	+	19701.1i	−0.174136	+	0.974732i
$743$	−14418.5	−	14418.5i	−0.711927	−	0.711927i	0.255011	−	0.966938i	$-0.417921\pi$
$743$	−14418.5	−	14418.5i	−0.711927	−	0.711927i	−0.966938	+	0.255011i	$0.917921\pi$
$744$	−12588.3	+	28273.8i	−0.620309	+	1.39324i
$745$	−14887.6	+	5634.42i	−0.732134	+	0.277086i
$746$	17746.8	−	7901.40i	0.870989	−	0.387789i
$747$	11096.5	−	8985.76i	0.543507	−	0.440123i
$748$	14953.7	+	29348.4i	0.730966	+	1.43460i
$749$	−25327.8	+	13965.0i	−1.23559	+	0.681267i
$750$	−6176.88	−	42920.6i	−0.300731	−	2.08965i
$751$	2767.87	+	4794.10i	0.134489	+	0.232941i	0.925402	−	0.378987i	$-0.123727\pi$
$751$	2767.87	+	4794.10i	0.134489	+	0.232941i	−0.790913	+	0.611928i	$0.790394\pi$
$752$	2466.44	−	47062.5i	0.119604	−	2.28217i
$753$	−42362.5	−	16261.4i	−2.05017	−	0.786985i
$754$	1878.05	−	17868.4i	0.0907087	−	0.863036i
$755$	−20210.1	+	24718.1i	−0.974199	+	1.19150i
$756$	34573.0	−	2946.32i	1.66324	−	0.141741i
$757$	−18917.0	+	18917.0i	−0.908254	+	0.908254i	−0.996131	−	0.0878771i	$-0.971992\pi$
$757$	−18917.0	+	18917.0i	−0.908254	+	0.908254i	0.0878771	+	0.996131i	$0.471992\pi$
$758$	10828.9	+	28210.2i	0.518896	+	1.35177i
$759$	−16669.4	−	3543.20i	−0.797184	−	0.169447i
$760$	−13494.6	−	12266.3i	−0.644080	−	0.585455i
$761$	3536.83	+	16639.5i	0.168476	+	0.792616i	0.978504	+	0.206226i	$0.0661181\pi$
$761$	3536.83	+	16639.5i	0.168476	+	0.792616i	−0.810029	+	0.586390i	$0.800549\pi$
$762$	−2332.26	+	4577.33i	−0.110878	+	0.217610i
$763$	−7612.51	−	12243.8i	−0.361195	−	0.580939i
$764$	−7430.21	−	2414.22i	−0.351853	−	0.114324i
$765$	−9040.08	−	42.6299i	−0.427248	−	0.00201476i
$766$	−15151.5	+	71282.3i	−0.714682	+	3.36231i
$767$	7352.82	+	5954.20i	0.346147	+	0.280305i
$768$	42507.4	+	11389.8i	1.99720	+	0.535149i
$769$	−23104.9	+	16786.7i	−1.08347	+	0.787184i	−0.978284	−	0.207269i	$-0.933543\pi$
$769$	−23104.9	+	16786.7i	−1.08347	+	0.787184i	−0.105182	+	0.994453i	$0.533543\pi$
$770$	17151.1	−	16333.3i	0.802706	−	0.764428i
$771$	23389.9	+	16993.8i	1.09256	+	0.793794i
$772$	18927.6	+	23373.6i	0.882408	+	1.08968i
$773$	23647.6	+	1239.32i	1.10032	+	0.0576651i	0.593836	−	0.804586i	$-0.297613\pi$
$773$	23647.6	+	1239.32i	1.10032	+	0.0576651i	0.506480	+	0.862252i	$0.330946\pi$
$774$	−22311.7	−	12881.6i	−1.03614	−	0.598218i
$775$	12092.1	+	2689.69i	0.560465	+	0.124666i
$776$			1451.09i			0.0671278i
$777$	33025.9	−	16015.8i	1.52484	−	0.739466i
$778$	−2544.17	−	16063.2i	−0.117240	−	0.740225i
$779$	1076.85	+	113.182i	0.0495278	+	0.00520559i
$780$	38401.6	+	25196.5i	1.76282	+	1.15664i
$781$	1566.87	+	14907.8i	0.0717889	+	0.683026i
$782$	13459.7	−	50232.1i	0.615494	−	2.29706i
$783$	−1525.86	+	9633.93i	−0.0696423	+	0.439704i
$784$	28946.2	+	28206.0i	1.31861	+	1.28489i
$785$	−40298.3	+	4043.49i	−1.83224	+	0.183845i
$786$	20676.9	−	4395.01i	0.938322	−	0.199446i
$787$	13518.3	+	20816.3i	0.612292	+	0.942847i	0.999780	+	0.0209721i	$0.00667613\pi$
$787$	13518.3	+	20816.3i	0.612292	+	0.942847i	−0.387488	+	0.921875i	$0.626657\pi$
$788$	−2729.50	−	4203.06i	−0.123394	−	0.190010i
$789$	4972.12	−	1056.86i	0.224350	−	0.0476871i
$790$	38890.6	−	34686.6i	1.75148	−	1.56214i
$791$	−2468.69	−	8140.25i	−0.110969	−	0.365909i
$792$	1789.36	−	11297.6i	0.0802805	−	0.506871i
$793$	8216.46	−	30664.2i	0.367938	−	1.37316i
$794$	337.541	+	3211.48i	0.0150867	+	0.143541i
$795$	11219.3	−	8997.93i	0.500512	−	0.401413i
$796$	38097.7	+	4004.23i	1.69640	+	0.178299i
$797$	3485.86	+	22008.9i	0.154926	+	0.978161i	0.935559	+	0.353172i	$0.114897\pi$
$797$	3485.86	+	22008.9i	0.154926	+	0.978161i	−0.780633	+	0.624990i	$0.785103\pi$
$798$	15098.8	+	10233.8i	0.669788	+	0.453975i
$799$			32549.6i			1.44121i
$800$	−1470.30	+	23764.4i	−0.0649788	+	1.05025i
$801$	4833.17	+	2790.43i	0.213198	+	0.123090i
$802$	−11122.6	−	582.913i	−0.489718	−	0.0256650i
$803$	4186.98	+	5170.48i	0.184004	+	0.227226i
$804$	28532.5	+	20730.1i	1.25157	+	0.909319i
$805$	−25906.2	+	723.990i	−1.13425	+	0.0316985i
$806$	−15315.8	+	11127.6i	−0.669326	+	0.486293i
$807$	−31107.0	−	8335.09i	−1.35690	−	0.363580i
$808$	77395.3	+	62673.5i	3.36975	+	2.72877i
$809$	1342.01	−	6313.65i	0.0583220	−	0.274383i	−0.939318	−	0.343048i	$-0.888541\pi$
$809$	1342.01	−	6313.65i	0.0583220	−	0.274383i	0.997640	+	0.0686648i	$0.0218739\pi$
$810$	−41351.1	−	30342.3i	−1.79374	−	1.31620i
$811$	−3018.34	−	980.717i	−0.130688	−	0.0424632i	0.242943	−	0.970041i	$-0.421887\pi$
$811$	−3018.34	−	980.717i	−0.130688	−	0.0424632i	−0.373631	+	0.927577i	$0.621887\pi$
$812$	−26723.1	+	16614.9i	−1.15492	+	0.718066i
$813$	5836.95	−	11455.7i	0.251797	−	0.494179i
$814$	7755.03	+	36484.6i	0.333924	+	1.57099i
$815$	13110.8	+	1440.54i	0.563498	+	0.0619140i
$816$	57006.1	+	12117.0i	2.44561	+	0.519829i
$817$	5777.53	+	15051.0i	0.247405	+	0.644513i
$818$	−29844.6	+	29844.6i	−1.27566	+	1.27566i
$819$	−6233.42	−	2923.80i	−0.265950	−	0.124744i
$820$	−3725.20	−	5795.96i	−0.158646	−	0.246834i
$821$	−2876.23	+	27365.5i	−0.122267	+	1.16329i	0.745564	+	0.666434i	$0.232180\pi$
$821$	−2876.23	+	27365.5i	−0.122267	+	1.16329i	−0.867831	+	0.496859i	$0.834487\pi$
$822$	−62292.8	−	23912.0i	−2.64320	−	1.01463i
$823$	265.282	−	5061.88i	0.0112359	−	0.214394i	−0.987241	−	0.159230i	$-0.949099\pi$
$823$	265.282	−	5061.88i	0.0112359	−	0.214394i	0.998477	−	0.0551632i	$-0.0175679\pi$
$824$	−36811.6	−	63759.6i	−1.55630	−	2.69559i
$825$	−17004.2	+	730.414i	−0.717586	+	0.0308239i
$826$	471.089	−	23904.0i	0.0198442	−	1.00693i
$827$	−15065.7	−	29568.1i	−0.633477	−	1.24327i	−0.955067	−	0.296390i	$-0.904217\pi$
$827$	−15065.7	−	29568.1i	−0.633477	−	1.24327i	0.321590	−	0.946879i	$-0.395783\pi$
$828$	−17458.4	+	14137.5i	−0.732755	+	0.593373i
$829$	10317.3	−	4593.55i	0.432248	−	0.192449i	−0.179066	−	0.983837i	$-0.557308\pi$
$829$	10317.3	−	4593.55i	0.432248	−	0.192449i	0.611315	+	0.791388i	$0.290641\pi$
$830$	51323.1	+	63993.5i	2.14633	+	2.67620i
$831$	6764.14	−	15192.5i	0.282365	−	0.634202i
$832$	−789.086	−	789.086i	−0.0328806	−	0.0328806i
$833$	−20984.6	−	18408.2i	−0.872839	−	0.765675i
$834$	−4732.76	+	1537.77i	−0.196501	+	0.0638472i
$835$	−4948.65	−	1633.75i	−0.205096	−	0.0677106i
$836$	−9547.07	+	8596.22i	−0.394967	+	0.355630i
$837$	8619.57	−	5597.61i	0.355957	−	0.231161i
$838$	340.906	+	6504.88i	0.0140530	+	0.268147i
$839$	5646.20	−	17377.2i	0.232334	−	0.715051i	−0.765130	−	0.643876i	$-0.777325\pi$
$839$	5646.20	−	17377.2i	0.232334	−	0.715051i	0.997464	−	0.0711749i	$-0.0226748\pi$
$840$	−5187.08	−	64458.1i	−0.213061	−	2.64764i
$841$	4803.14	+	14782.5i	0.196939	+	0.606115i
$842$	24813.3	−	9524.92i	1.01558	−	0.389846i
$843$	−13465.2	−	50252.7i	−0.550137	−	2.05314i
$844$	−102519.	+	10775.2i	−4.18111	+	0.439453i
$845$	−4007.57	−	7957.85i	−0.163153	−	0.323974i
$846$	11924.7	−	16412.9i	0.484608	−	0.667006i
$847$	9425.91	+	12120.8i	0.382383	+	0.491705i
$848$	−22221.7	+	11322.5i	−0.899876	+	0.458510i
$849$	−27088.0	+	15639.3i	−1.09500	+	0.632201i
$850$	489.823	−	51934.6i	0.0197656	−	2.09570i
$851$	20407.6	−	35347.0i	0.822048	−	1.42383i
$852$	61607.3	+	40008.3i	2.47727	+	1.60876i
$853$	24823.9	−	3931.72i	0.996430	−	0.157819i	0.363141	−	0.931734i	$-0.381704\pi$
$853$	24823.9	−	3931.72i	0.996430	−	0.157819i	0.633289	+	0.773915i	$0.281704\pi$
$854$	−73914.9	+	31178.8i	−2.96173	+	1.24932i
$855$	−896.501	−	3410.03i	−0.0358593	−	0.136398i
$856$	−73312.2	−	32640.7i	−2.92729	−	1.30331i
$857$	−24271.2	+	6503.44i	−0.967430	+	0.259222i	−0.707742	−	0.706471i	$-0.750286\pi$
$857$	−24271.2	+	6503.44i	−0.967430	+	0.259222i	−0.259688	+	0.965693i	$0.583620\pi$
$858$	16369.0	−	20214.0i	0.651315	−	0.804307i
$859$	−259.372	+	288.062i	−0.0103023	+	0.0114419i	−0.748274	−	0.663390i	$-0.769117\pi$
$859$	−259.372	+	288.062i	−0.0103023	+	0.0114419i	0.737972	+	0.674832i	$0.235784\pi$
$860$	51710.7	−	88598.1i	2.05037	−	3.51299i
$861$	2512.44	+	2903.41i	0.0994469	+	0.114922i
$862$	10533.1	+	5366.88i	0.416193	+	0.212061i
$863$	34212.4	−	1793.00i	1.34948	−	0.0707235i	0.636160	−	0.771557i	$-0.280522\pi$
$863$	34212.4	−	1793.00i	1.34948	−	0.0707235i	0.713325	+	0.700834i	$0.247189\pi$
$864$	13218.3	+	14680.4i	0.520480	+	0.578052i
$865$	13181.0	−	14500.9i	0.518114	−	0.569996i
$866$	44270.3	+	39861.1i	1.73714	+	1.56413i
$867$	−10266.0	−	1625.97i	−0.402135	−	0.0636919i
$868$	31851.4	+	9210.90i	1.24551	+	0.360182i
$869$	−12022.4	−	16547.5i	−0.469313	−	0.645954i
$870$	32200.6	+	5255.85i	1.25483	+	0.204816i
$871$	4888.82	+	10980.5i	0.190185	+	0.427163i
$872$	14335.9	−	37346.3i	0.556737	−	1.45035i
$873$	−152.804	+	235.298i	−0.00592398	+	0.00912213i
$874$	20283.0			0.784991
$875$	−24872.7	+	7160.52i	−0.960970	+	0.276651i
$876$	32604.0			1.25752
$877$	18926.3	−	29144.0i	0.728731	−	1.12215i	−0.258984	−	0.965882i	$-0.583388\pi$
$877$	18926.3	−	29144.0i	0.728731	−	1.12215i	0.987715	−	0.156266i	$-0.0499457\pi$
$878$	2737.23	−	7130.74i	0.105213	−	0.274090i
$879$	−9334.37	−	20965.3i	−0.358180	−	0.804486i
$880$	29129.3	+	4754.54i	1.11585	+	0.182131i
$881$	−10310.1	−	14190.6i	−0.394274	−	0.542671i	0.565022	−	0.825076i	$-0.308868\pi$
$881$	−10310.1	−	14190.6i	−0.394274	−	0.542671i	−0.959295	+	0.282405i	$0.908868\pi$
$882$	3837.43	+	16970.0i	0.146500	+	0.647857i
$883$	−45375.1	−	7186.71i	−1.72932	−	0.273898i	−0.789053	−	0.614325i	$-0.789428\pi$
$883$	−45375.1	−	7186.71i	−1.72932	−	0.273898i	−0.940271	+	0.340427i	$0.889428\pi$
$884$	40881.5	+	36809.9i	1.55542	+	1.40051i
$885$	−11556.6	+	12713.8i	−0.438949	+	0.482903i
$886$	35962.3	+	39940.2i	1.36363	+	1.51447i
$887$	33902.1	−	1776.73i	1.28334	−	0.0672568i	0.601566	−	0.798823i	$-0.294544\pi$
$887$	33902.1	−	1776.73i	1.28334	−	0.0672568i	0.681771	+	0.731566i	$0.261210\pi$
$888$	90741.9	+	46235.3i	3.42917	+	1.74725i
$889$	2897.06	+	1004.84i	0.109296	+	0.0379092i
$890$	−16162.1	+	27691.3i	−0.608715	+	1.04294i
$891$	−13470.2	+	14960.2i	−0.506474	+	0.562497i
$892$	37989.8	−	46913.5i	1.42600	−	1.76096i
$893$	−12262.6	+	3285.76i	−0.459522	+	0.123129i
$894$	40357.1	+	17968.2i	1.50978	+	0.672198i
$895$	2969.58	+	11295.4i	0.110907	+	0.421859i
$896$	3152.46	−	25205.4i	0.117541	−	0.939792i
$897$	−28111.7	+	4452.46i	−1.04640	+	0.165734i
$898$	−49416.5	−	32091.4i	−1.83636	−	1.19254i
$899$	−4660.30	+	8071.87i	−0.172892	+	0.299457i
$900$	−13358.0	+	18025.7i	−0.494740	+	0.667619i
$901$	14917.7	−	8612.73i	0.551587	−	0.318459i
$902$	−3476.54	+	1771.39i	−0.128333	+	0.0653888i
$903$	−21534.8	+	52956.8i	−0.793613	+	1.95160i
$904$	13873.0	−	19094.5i	0.510408	−	0.702517i
$905$	−1205.51	−	2393.78i	−0.0442789	−	0.0879248i
$906$	88123.4	−	9262.14i	3.23146	−	0.339640i
$907$	2811.85	+	10494.0i	0.102939	+	0.384174i	0.998103	−	0.0615625i	$-0.0196084\pi$
$907$	2811.85	+	10494.0i	0.102939	+	0.384174i	−0.895164	+	0.445737i	$0.852942\pi$
$908$	−18975.8	+	7284.13i	−0.693540	+	0.266225i
$909$	5950.12	+	18312.6i	0.217110	+	0.668196i
$910$	16966.3	−	35732.1i	0.618051	−	1.30166i
$911$	2394.36	−	7369.10i	0.0870788	−	0.268001i	−0.898030	−	0.439935i	$-0.855002\pi$
$911$	2394.36	−	7369.10i	0.0870788	−	0.268001i	0.985109	+	0.171934i	$0.0550015\pi$
$912$	1189.63	+	22699.5i	0.0431935	+	0.824182i
$913$	27003.0	−	17535.9i	0.978826	−	0.635657i
$914$	1966.73	−	1770.85i	0.0711747	−	0.0640860i
$915$	54742.7	+	18072.8i	1.97786	+	0.652972i
$916$	−62491.5	+	20304.7i	−2.25412	+	0.732409i
$917$	−4288.76	−	11866.3i	−0.154446	−	0.427329i
$918$	−30469.7	−	30469.7i	−1.09548	−	1.09548i
$919$	−9297.59	+	20882.7i	−0.333731	+	0.749573i	0.666261	+	0.745718i	$0.267894\pi$
$919$	−9297.59	+	20882.7i	−0.333731	+	0.749573i	−0.999993	+	0.00385433i	$0.998773\pi$
$920$	−44989.6	−	56096.4i	−1.61224	−	2.01026i
$921$	−17010.9	+	7573.73i	−0.608608	+	0.270970i
$922$	−18998.8	+	15384.9i	−0.678625	+	0.549540i
$923$	11365.7	+	22306.5i	0.405316	+	0.795478i
$924$	−45546.2	−	897.602i	−1.62160	−	0.0319577i
$925$	10921.0	−	39272.2i	0.388193	−	1.39596i
$926$	33321.4	+	57714.4i	1.18252	+	2.04818i
$927$	744.982	−	14215.1i	0.0263953	−	0.503652i
$928$	−16724.9	−	6420.11i	−0.591620	−	0.227102i
$929$	−907.565	+	8634.91i	−0.0320519	+	0.304954i	0.966738	+	0.255770i	$0.0823288\pi$
$929$	−907.565	+	8634.91i	−0.0320519	+	0.304954i	−0.998790	+	0.0491843i	$0.984338\pi$
$930$	−18587.6	−	28920.1i	−0.655389	−	1.01971i
$931$	4816.73	−	9763.92i	0.169562	−	0.343716i
$932$	53106.2	−	53106.2i	1.86647	−	1.86647i
$933$	18510.3	+	48220.9i	0.649516	+	1.69205i
$934$	4823.34	+	1025.23i	0.168977	+	0.0359171i
$935$	−20263.2	−	2226.41i	−0.708747	−	0.0778731i
$936$	−3971.87	−	18686.2i	−0.138702	−	0.652539i
$937$	−12938.4	+	25393.0i	−0.451097	+	0.885328i	0.547718	+	0.836663i	$0.315497\pi$
$937$	−12938.4	+	25393.0i	−0.451097	+	0.885328i	−0.998815	+	0.0486650i	$0.984503\pi$
$938$	14319.8	−	26786.0i	0.498464	−	0.932403i
$939$	−3379.62	−	1098.11i	−0.117455	−	0.0381633i
$940$	65128.6	+	47789.6i	2.25985	+	1.65822i
$941$	844.896	−	3974.92i	0.0292697	−	0.137703i	−0.961087	−	0.276248i	$-0.910909\pi$
$941$	844.896	−	3974.92i	0.0292697	−	0.137703i	0.990356	+	0.138544i	$0.0442424\pi$
$942$	87349.9	+	70734.6i	3.02125	+	2.44656i
$943$	4124.08	+	1105.04i	0.142416	+	0.0381603i
$944$	24104.3	−	17512.8i	0.831069	−	0.603807i
$945$	−10213.4	+	18890.0i	−0.351580	+	0.650255i
$946$	−46999.8	−	34147.4i	−1.61532	−	1.17360i
$947$	−13127.7	−	16211.3i	−0.450467	−	0.556280i	0.500434	−	0.865774i	$-0.333174\pi$
$947$	−13127.7	−	16211.3i	−0.450467	−	0.556280i	−0.950901	+	0.309494i	$0.899840\pi$
$948$	−100097.	−	5245.85i	−3.42931	−	0.179723i
$949$	9622.99	+	5555.83i	0.329163	+	0.190042i
$950$	19615.1	−	5058.07i	0.669893	−	0.172743i
$951$			38890.4i			1.32609i
$952$	5576.80	−	77251.9i	0.189858	−	2.62999i
$953$	6055.52	+	38233.1i	0.205832	+	1.29957i	0.846762	+	0.531972i	$0.178549\pi$
$953$	6055.52	+	38233.1i	0.205832	+	1.29957i	−0.640931	+	0.767599i	$0.721451\pi$
$954$	−10677.4	−	1122.24i	−0.362364	−	0.0380859i
$955$	3771.89	−	3025.08i	0.127807	−	0.102502i
$956$	−9905.70	−	94246.5i	−0.335119	−	3.18844i
$957$	3314.42	−	12369.6i	0.111954	−	0.417818i
$958$	−1832.91	+	11572.5i	−0.0618147	+	0.390283i
$959$	−9046.54	+	38786.2i	−0.304617	+	1.30602i
$960$	1512.34	−	1348.86i	0.0508444	−	0.0453482i
$961$	−19533.6	+	4152.00i	−0.655689	+	0.139371i
$962$	33928.5	+	52245.2i	1.13711	+	1.75099i
$963$	−8450.57	−	13012.7i	−0.282779	−	0.435441i
$964$	788.439	−	167.588i	0.0263422	−	0.00559922i
$965$	−18520.8	+	1858.36i	−0.617830	+	0.0619923i
$966$	52491.0	+	49170.0i	1.74831	+	1.63770i
$967$	−1097.57	+	6929.81i	−0.0365001	+	0.230453i	−0.999194	−	0.0401399i	$-0.987220\pi$
$967$	−1097.57	+	6929.81i	−0.0365001	+	0.230453i	0.962694	+	0.270593i	$0.0872196\pi$
$968$	−11026.6	+	41151.7i	−0.366123	+	1.36639i
$969$	−1641.05	−	15613.5i	−0.0544045	−	0.517625i
$970$	−1347.66	−	884.243i	−0.0446090	−	0.0292694i
$971$	−16249.2	−	1707.86i	−0.537034	−	0.0564446i	−0.167871	−	0.985809i	$-0.553689\pi$
$971$	−16249.2	−	1707.86i	−0.537034	−	0.0564446i	−0.369164	+	0.929364i	$0.620356\pi$
$972$	7519.24	+	47474.6i	0.248127	+	1.56661i
$973$	1296.09	+	2672.63i	0.0427037	+	0.0880582i
$974$			68011.3i			2.23740i
$975$	−26075.7	+	11316.2i	−0.856504	+	0.371701i
$976$	−86577.5	−	49985.5i	−2.83942	−	1.63934i
$977$	−17416.1	−	912.737i	−0.570306	−	0.0298885i	−0.234996	−	0.971996i	$-0.575508\pi$
$977$	−17416.1	−	912.737i	−0.570306	−	0.0298885i	−0.335310	+	0.942108i	$0.608841\pi$
$978$	−23035.8	−	28446.9i	−0.753175	−	0.930094i
$979$	10181.1	+	7397.03i	0.332371	+	0.241481i
$980$	−67642.8	+	14961.1i	−2.20487	+	0.487669i
$981$	6257.26	−	4546.16i	0.203648	−	0.147959i
$982$	13605.5	+	3645.59i	0.442128	+	0.118468i
$983$	7185.81	+	5818.95i	0.233155	+	0.188806i	0.738777	−	0.673950i	$-0.235404\pi$
$983$	7185.81	+	5818.95i	0.233155	+	0.188806i	−0.505622	+	0.862755i	$0.668737\pi$
$984$	−2214.97	+	10420.6i	−0.0717588	+	0.337599i
$985$	3101.56	+	14.6259i	0.100329	+	0.000473117i
$986$	37165.4	+	12075.8i	1.20039	+	0.390032i
$987$	−39700.2	−	21223.8i	−1.28032	−	0.684458i
$988$	−9740.79	+	19117.4i	−0.313660	+	0.615592i
$989$	13217.0	+	62181.3i	0.424952	+	1.99924i
$990$	9401.92	+	8546.15i	0.301831	+	0.274358i
$991$	−7155.06	−	1520.86i	−0.229352	−	0.0487503i	0.0918018	−	0.995777i	$-0.470737\pi$
$991$	−7155.06	−	1520.86i	−0.229352	−	0.0487503i	−0.321154	+	0.947027i	$0.604071\pi$
$992$	6764.77	+	17622.8i	0.216514	+	0.564038i
$993$	−27624.7	+	27624.7i	−0.882823	+	0.882823i
$994$	26865.4	−	57275.9i	0.857261	−	1.82765i
$995$	−15006.7	+	18354.1i	−0.478134	+	0.584787i
$996$	16492.9	−	156919.i	0.524696	−	4.99215i
$997$	44671.1	+	17147.6i	1.41901	+	0.544705i	0.942423	−	0.334425i	$-0.108542\pi$
$997$	44671.1	+	17147.6i	1.41901	+	0.544705i	0.476583	+	0.879130i	$0.341875\pi$
$998$	−3580.37	+	68317.5i	−0.113562	+	2.16689i
$999$	−16909.7	−	29288.5i	−0.535536	−	0.927576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.3.55	✓	928
7.5	odd	6	inner	175.4.x.a.103.4	yes	928
25.17	odd	20	inner	175.4.x.a.17.4	yes	928
175.117	even	60	inner	175.4.x.a.117.55	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.55	✓	928	1.1	even	1	trivial
175.4.x.a.17.4	yes	928	25.17	odd	20	inner
175.4.x.a.103.4	yes	928	7.5	odd	6	inner
175.4.x.a.117.55	yes	928	175.117	even	60	inner

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.78061 - 4.28176i) q^{2} +(2.17796 - 5.67379i) q^{3} +(-7.34780 - 16.5034i) q^{4} +(11.0343 + 1.80104i) q^{5} +(-18.2377 - 25.1021i) q^{6} +(-13.3513 + 12.8352i) q^{7} +(-50.7546 - 8.03874i) q^{8} +(-7.38346 - 6.64810i) q^{9} +(38.3938 - 42.2383i) q^{10} +(-14.9911 - 16.6493i) q^{11} +(-109.640 + 5.74600i) q^{12} +(-33.3392 - 16.9872i) q^{13} +(17.8326 + 92.8568i) q^{14} +(34.2511 - 58.6838i) q^{15} +(-78.8444 + 87.5656i) q^{16} +(51.2162 - 63.2467i) q^{17} +(-48.9961 + 13.1285i) q^{18} +(28.9974 + 12.9105i) q^{19} +(-51.3546 - 195.338i) q^{20} +(43.7457 + 103.707i) q^{21} +(-112.973 + 17.8932i) q^{22} +(104.969 + 68.1680i) q^{23} +(-156.152 + 270.463i) q^{24} +(118.512 + 39.7466i) q^{25} +(-165.438 + 95.5158i) q^{26} +(92.4055 - 47.0830i) q^{27} +(309.928 + 126.031i) q^{28} +(-55.2822 + 76.0894i) q^{29} +(-156.031 - 309.832i) q^{30} +(98.5579 - 10.3589i) q^{31} +(49.2996 + 183.988i) q^{32} +(-127.115 + 48.7949i) q^{33} +(-128.395 - 395.160i) q^{34} +(-170.439 + 117.582i) q^{35} +(-55.4642 + 170.701i) q^{36} +(-17.0667 - 325.653i) q^{37} +(135.910 - 88.2610i) q^{38} +(-168.993 + 152.162i) q^{39} +(-545.564 - 180.113i) q^{40} +(32.4428 - 10.5413i) q^{41} +(565.689 + 101.060i) q^{42} +(359.144 + 359.144i) q^{43} +(-164.619 + 369.741i) q^{44} +(-69.4979 - 86.6552i) q^{45} +(583.758 - 259.906i) q^{46} +(-310.823 + 251.699i) q^{47} +(325.109 + 638.062i) q^{48} +(13.5141 - 342.734i) q^{49} +(499.722 - 396.922i) q^{50} +(-247.302 - 428.339i) q^{51} +(-35.3768 + 675.029i) q^{52} +(197.600 + 75.8516i) q^{53} +(55.3455 - 526.578i) q^{54} +(-135.431 - 210.714i) q^{55} +(780.818 - 544.119i) q^{56} +(136.407 - 136.407i) q^{57} +(172.078 + 448.280i) q^{58} +(-247.333 - 52.5722i) q^{59} +(-1220.15 - 134.064i) q^{60} +(176.398 + 829.886i) q^{61} +(229.697 - 450.805i) q^{62} +(183.909 - 6.00765i) q^{63} +(28.3642 + 9.21610i) q^{64} +(-337.281 - 247.487i) q^{65} +(-144.529 + 679.956i) q^{66} +(-249.643 - 202.157i) q^{67} +(-1420.11 - 380.518i) q^{68} +(615.390 - 447.107i) q^{69} +(29.5319 + 1056.73i) q^{70} +(-541.294 - 393.273i) q^{71} +(321.302 + 396.775i) q^{72} +(-296.558 - 15.5419i) q^{73} +(-1441.82 - 832.436i) q^{74} +(483.630 - 585.848i) q^{75} -573.420i q^{76} +(413.849 + 29.8757i) q^{77} +(181.618 + 1146.69i) q^{78} +(907.955 + 95.4299i) q^{79} +(-1027.70 + 824.225i) q^{80} +(-93.9234 - 893.621i) q^{81} +(45.0753 - 168.223i) q^{82} +(-224.817 + 1419.44i) q^{83} +(1390.09 - 1483.97i) q^{84} +(679.046 - 605.642i) q^{85} +(2536.41 - 539.130i) q^{86} +(311.313 + 479.379i) q^{87} +(627.029 + 965.540i) q^{88} +(-549.439 + 116.787i) q^{89} +(-564.283 + 56.6195i) q^{90} +(663.156 - 201.115i) q^{91} +(353.710 - 2233.24i) q^{92} +(155.882 - 581.758i) q^{93} +(213.440 + 2030.75i) q^{94} +(296.715 + 194.684i) q^{95} +(1151.28 + 121.005i) q^{96} +(-4.41746 - 27.8907i) q^{97} +(-1429.93 - 1010.87i) q^{98} +222.592i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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