LMFDB - Embedded newform 161.4.e.a.93.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(93,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("161.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.3
Character	$\chi$	$=$	161.93
Dual form			161.4.e.a.116.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.44746 + 4.23912i) q^{2} +(3.42021 + 5.92398i) q^{3} +(-7.98009 - 13.8219i) q^{4} +(-9.57184 + 16.5789i) q^{5} -33.4833 q^{6} +(-17.5280 + 5.98075i) q^{7} +38.9644 q^{8} +(-9.89567 + 17.1398i) q^{9} +(-46.8533 - 81.1523i) q^{10} +(27.4254 + 47.5022i) q^{11} +(54.5872 - 94.5477i) q^{12} +53.1504 q^{13} +(17.5459 - 88.9409i) q^{14} -130.951 q^{15} +(-31.5229 + 54.5993i) q^{16} +(-13.7268 - 23.7755i) q^{17} +(-48.4384 - 83.8978i) q^{18} +(-43.6641 + 75.6284i) q^{19} +305.536 q^{20} +(-95.3793 - 83.3800i) q^{21} -268.490 q^{22} +(11.5000 - 19.9186i) q^{23} +(133.266 + 230.824i) q^{24} +(-120.740 - 209.128i) q^{25} +(-130.083 + 225.311i) q^{26} +49.3103 q^{27} +(222.540 + 194.544i) q^{28} +285.853 q^{29} +(320.496 - 555.116i) q^{30} +(28.1479 + 48.7536i) q^{31} +(1.55559 + 2.69436i) q^{32} +(-187.601 + 324.935i) q^{33} +134.383 q^{34} +(68.6208 - 347.842i) q^{35} +315.873 q^{36} +(-8.63998 + 14.9649i) q^{37} +(-213.732 - 370.194i) q^{38} +(181.785 + 314.862i) q^{39} +(-372.961 + 645.987i) q^{40} -11.3634 q^{41} +(586.894 - 200.255i) q^{42} -155.388 q^{43} +(437.714 - 758.143i) q^{44} +(-189.440 - 328.119i) q^{45} +(56.2915 + 97.4997i) q^{46} +(-67.9947 + 117.770i) q^{47} -431.260 q^{48} +(271.461 - 209.661i) q^{49} +1182.03 q^{50} +(93.8970 - 162.634i) q^{51} +(-424.145 - 734.640i) q^{52} +(-150.725 - 261.063i) q^{53} +(-120.685 + 209.032i) q^{54} -1050.05 q^{55} +(-682.967 + 233.036i) q^{56} -597.361 q^{57} +(-699.613 + 1211.77i) q^{58} +(85.7195 + 148.470i) q^{59} +(1045.00 + 1809.99i) q^{60} +(-245.124 + 424.567i) q^{61} -275.563 q^{62} +(70.9423 - 359.610i) q^{63} -519.595 q^{64} +(-508.747 + 881.175i) q^{65} +(-918.292 - 1590.53i) q^{66} +(-510.862 - 884.840i) q^{67} +(-219.082 + 379.461i) q^{68} +157.330 q^{69} +(1306.60 + 1142.22i) q^{70} -32.0266 q^{71} +(-385.579 + 667.842i) q^{72} +(359.436 + 622.562i) q^{73} +(-42.2920 - 73.2518i) q^{74} +(825.913 - 1430.52i) q^{75} +1393.77 q^{76} +(-764.811 - 668.593i) q^{77} -1779.65 q^{78} +(549.715 - 952.135i) q^{79} +(-603.464 - 1045.23i) q^{80} +(435.835 + 754.888i) q^{81} +(27.8114 - 48.1708i) q^{82} -433.857 q^{83} +(-391.337 + 1983.70i) q^{84} +525.563 q^{85} +(380.307 - 658.710i) q^{86} +(977.678 + 1693.39i) q^{87} +(1068.61 + 1850.89i) q^{88} +(-3.26655 + 5.65783i) q^{89} +1854.58 q^{90} +(-931.620 + 317.879i) q^{91} -367.084 q^{92} +(-192.543 + 333.495i) q^{93} +(-332.828 - 576.475i) q^{94} +(-835.891 - 1447.81i) q^{95} +(-10.6409 + 18.4305i) q^{96} +700.729 q^{97} +(224.389 + 1663.89i) q^{98} -1085.57 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) $ 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.44746	+	4.23912i	−0.865307	+	1.49875i	0.00143583	+	0.999999i	$0.499543\pi$
$2$	−2.44746	+	4.23912i	−0.865307	+	1.49875i	−0.866742	+	0.498756i	$0.833790\pi$
$3$	3.42021	+	5.92398i	0.658220	+	1.14007i	0.981076	+	0.193622i	$0.0620235\pi$
$3$	3.42021	+	5.92398i	0.658220	+	1.14007i	−0.322857	+	0.946448i	$0.604643\pi$
$4$	−7.98009	−	13.8219i	−0.997511	−	1.72774i
$5$	−9.57184	+	16.5789i	−0.856131	+	1.48286i	0.0194603	+	0.999811i	$0.493805\pi$
$5$	−9.57184	+	16.5789i	−0.856131	+	1.48286i	−0.875592	+	0.483052i	$0.839528\pi$
$6$	−33.4833			−2.27825
$7$	−17.5280	+	5.98075i	−0.946423	+	0.322930i
$7$	−17.5280	+	5.98075i	−0.946423	+	0.322930i
$8$	38.9644			1.72200
$9$	−9.89567	+	17.1398i	−0.366506	+	0.634808i
$10$	−46.8533	−	81.1523i	−1.48163	−	2.56626i
$11$	27.4254	+	47.5022i	0.751733	+	1.30204i	0.946982	+	0.321287i	$0.104115\pi$
$11$	27.4254	+	47.5022i	0.751733	+	1.30204i	−0.195249	+	0.980754i	$0.562551\pi$
$12$	54.5872	−	94.5477i	1.31316	−	2.27446i
$13$	53.1504			1.13394			0.566972	−	0.823737i	$-0.308115\pi$
$13$	53.1504			1.13394			0.566972	+	0.823737i	$0.308115\pi$
$14$	17.5459	−	88.9409i	0.334952	−	1.69789i
$15$	−130.951			−2.25409
$16$	−31.5229	+	54.5993i	−0.492545	+	0.853114i
$17$	−13.7268	−	23.7755i	−0.195837	−	0.339200i	0.751337	−	0.659918i	$-0.229409\pi$
$17$	−13.7268	−	23.7755i	−0.195837	−	0.339200i	−0.947175	+	0.320718i	$0.896076\pi$
$18$	−48.4384	−	83.8978i	−0.634281	−	1.09861i
$19$	−43.6641	+	75.6284i	−0.527222	+	0.913176i	0.472274	+	0.881452i	$0.343433\pi$
$19$	−43.6641	+	75.6284i	−0.527222	+	0.913176i	−0.999497	+	0.0317243i	$0.989900\pi$
$20$	305.536			3.41600
$21$	−95.3793	−	83.3800i	−0.991117	−	0.866429i
$22$	−268.490			−2.60192
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$	133.266	+	230.824i	1.13345	+	1.96320i
$25$	−120.740	−	209.128i	−0.965921	−	1.67303i
$26$	−130.083	+	225.311i	−0.981209	+	1.69950i
$27$	49.3103			0.351473
$28$	222.540	+	194.544i	1.50201	+	1.31305i
$29$	285.853			1.83040			0.915200	−	0.403000i	$-0.132033\pi$
$29$	285.853			1.83040			0.915200	+	0.403000i	$0.132033\pi$
$30$	320.496	−	555.116i	1.95048	−	3.37833i
$31$	28.1479	+	48.7536i	0.163081	+	0.282464i	0.935972	−	0.352074i	$-0.114524\pi$
$31$	28.1479	+	48.7536i	0.163081	+	0.282464i	−0.772891	+	0.634539i	$0.781190\pi$
$32$	1.55559	+	2.69436i	0.00859349	+	0.0148844i
$33$	−187.601	+	324.935i	−0.989611	+	1.71406i
$34$	134.383			0.677838
$35$	68.6208	−	347.842i	0.331401	−	1.67989i
$36$	315.873			1.46238
$37$	−8.63998	+	14.9649i	−0.0383893	+	0.0664922i	−0.884582	−	0.466385i	$-0.845556\pi$
$37$	−8.63998	+	14.9649i	−0.0383893	+	0.0664922i	0.846192	+	0.532878i	$0.178889\pi$
$38$	−213.732	−	370.194i	−0.912418	−	1.58035i
$39$	181.785	+	314.862i	0.746384	+	1.29277i
$40$	−372.961	+	645.987i	−1.47426	+	2.55349i
$41$	−11.3634			−0.0432845			−0.0216422	−	0.999766i	$-0.506889\pi$
$41$	−11.3634			−0.0432845			−0.0216422	+	0.999766i	$0.506889\pi$
$42$	586.894	−	200.255i	2.15619	−	0.735715i
$43$	−155.388			−0.551082			−0.275541	−	0.961289i	$-0.588857\pi$
$43$	−155.388			−0.551082			−0.275541	+	0.961289i	$0.588857\pi$
$44$	437.714	−	758.143i	1.49972	−	2.59760i
$45$	−189.440	−	328.119i	−0.627555	−	1.08696i
$46$	56.2915	+	97.4997i	0.180429	+	0.312512i
$47$	−67.9947	+	117.770i	−0.211022	+	0.365501i	−0.952035	−	0.305990i	$-0.901013\pi$
$47$	−67.9947	+	117.770i	−0.211022	+	0.365501i	0.741013	+	0.671491i	$0.234346\pi$
$48$	−431.260			−1.29681
$49$	271.461	−	209.661i	0.791432	−	0.611257i
$50$	1182.03			3.34327
$51$	93.8970	−	162.634i	0.257808	−	0.446537i
$52$	−424.145	−	734.640i	−1.13112	−	1.95916i
$53$	−150.725	−	261.063i	−0.390634	−	0.676599i	0.601899	−	0.798572i	$-0.294411\pi$
$53$	−150.725	−	261.063i	−0.390634	−	0.676599i	−0.992533	+	0.121974i	$0.961078\pi$
$54$	−120.685	+	209.032i	−0.304132	+	0.526772i
$55$	−1050.05			−2.57433
$56$	−682.967	+	233.036i	−1.62974	+	0.556085i
$57$	−597.361			−1.38811
$58$	−699.613	+	1211.77i	−1.58386	+	2.74332i
$59$	85.7195	+	148.470i	0.189148	+	0.327614i	0.944966	−	0.327167i	$-0.106094\pi$
$59$	85.7195	+	148.470i	0.189148	+	0.327614i	−0.755819	+	0.654781i	$0.772761\pi$
$60$	1045.00	+	1809.99i	2.24848	+	3.89448i
$61$	−245.124	+	424.567i	−0.514506	+	0.891150i	0.485352	+	0.874319i	$0.338691\pi$
$61$	−245.124	+	424.567i	−0.514506	+	0.891150i	−0.999858	+	0.0168318i	$0.994642\pi$
$62$	−275.563			−0.564460
$63$	70.9423	−	359.610i	0.141871	−	0.719152i
$64$	−519.595			−1.01483
$65$	−508.747	+	881.175i	−0.970804	+	1.68148i
$66$	−918.292	−	1590.53i	−1.71263	−	2.96637i
$67$	−510.862	−	884.840i	−0.931519	−	1.61344i	−0.780726	−	0.624873i	$-0.785151\pi$
$67$	−510.862	−	884.840i	−0.931519	−	1.61344i	−0.150793	−	0.988565i	$-0.548183\pi$
$68$	−219.082	+	379.461i	−0.390700	+	0.676712i
$69$	157.330			0.274497
$70$	1306.60	+	1142.22i	2.23097	+	1.95030i
$71$	−32.0266			−0.0535332			−0.0267666	−	0.999642i	$-0.508521\pi$
$71$	−32.0266			−0.0535332			−0.0267666	+	0.999642i	$0.508521\pi$
$72$	−385.579	+	667.842i	−0.631123	+	1.09314i
$73$	359.436	+	622.562i	0.576285	+	0.998155i	0.995901	+	0.0904532i	$0.0288316\pi$
$73$	359.436	+	622.562i	0.576285	+	0.998155i	−0.419616	+	0.907702i	$0.637835\pi$
$74$	−42.2920	−	73.2518i	−0.0664370	−	0.115072i
$75$	825.913	−	1430.52i	1.27158	−	2.20244i
$76$	1393.77			2.10364
$77$	−764.811	−	668.593i	−1.13193	−	0.989523i
$78$	−1779.65			−2.58340
$79$	549.715	−	952.135i	0.782884	−	1.35599i	−0.147372	−	0.989081i	$-0.547081\pi$
$79$	549.715	−	952.135i	0.782884	−	1.35599i	0.930255	−	0.366913i	$-0.119585\pi$
$80$	−603.464	−	1045.23i	−0.843367	−	1.46075i
$81$	435.835	+	754.888i	0.597853	+	1.03551i
$82$	27.8114	−	48.1708i	0.0374543	−	0.0648728i
$83$	−433.857			−0.573760			−0.286880	−	0.957967i	$-0.592618\pi$
$83$	−433.857			−0.573760			−0.286880	+	0.957967i	$0.592618\pi$
$84$	−391.337	+	1983.70i	−0.508314	+	2.57667i
$85$	525.563			0.670650
$86$	380.307	−	658.710i	0.476855	−	0.825937i
$87$	977.678	+	1693.39i	1.20481	+	2.08678i
$88$	1068.61	+	1850.89i	1.29448	+	2.24211i
$89$	−3.26655	+	5.65783i	−0.00389049	+	0.00673853i	−0.867964	−	0.496627i	$-0.834572\pi$
$89$	−3.26655	+	5.65783i	−0.00389049	+	0.00673853i	0.864074	+	0.503365i	$0.167905\pi$
$90$	1854.58			2.17211
$91$	−931.620	+	317.879i	−1.07319	+	0.366185i
$92$	−367.084			−0.415991
$93$	−192.543	+	333.495i	−0.214686	+	0.371847i
$94$	−332.828	−	576.475i	−0.365198	−	0.632541i
$95$	−835.891	−	1447.81i	−0.902743	−	1.56360i
$96$	−10.6409	+	18.4305i	−0.0113128	+	0.0195944i
$97$	700.729			0.733487			0.366744	−	0.930322i	$-0.380473\pi$
$97$	700.729			0.733487			0.366744	+	0.930322i	$0.380473\pi$
$98$	224.389	+	1663.89i	0.231293	+	1.71509i
$99$	−1085.57			−1.10206
$100$	−1927.03	+	3337.72i	−1.92703	+	3.33772i
$101$	−921.952	−	1596.87i	−0.908294	−	1.57321i	−0.816434	−	0.577439i	$-0.804052\pi$
$101$	−921.952	−	1596.87i	−0.908294	−	1.57321i	−0.0918601	−	0.995772i	$-0.529281\pi$
$102$	459.618	+	796.081i	0.446166	+	0.772782i
$103$	−304.450	+	527.322i	−0.291246	+	0.504453i	−0.974105	−	0.226098i	$-0.927403\pi$
$103$	−304.450	+	527.322i	−0.291246	+	0.504453i	0.682859	+	0.730550i	$0.260736\pi$
$104$	2070.97			1.95265
$105$	2295.30	−	783.184i	2.13332	−	0.727914i
$106$	1475.57			1.35207
$107$	−841.363	+	1457.28i	−0.760165	+	1.31664i	0.182601	+	0.983187i	$0.441548\pi$
$107$	−841.363	+	1457.28i	−0.760165	+	1.31664i	−0.942765	+	0.333457i	$0.891785\pi$
$108$	−393.500	−	681.562i	−0.350598	−	0.607253i
$109$	−397.398	−	688.314i	−0.349210	−	0.604849i	0.636900	−	0.770947i	$-0.280217\pi$
$109$	−397.398	−	688.314i	−0.349210	−	0.604849i	−0.986109	+	0.166098i	$0.946883\pi$
$110$	2569.94	−	4451.27i	2.22758	−	3.85829i
$111$	−118.202			−0.101074
$112$	225.989	−	1145.55i	0.190660	−	0.966464i
$113$	204.282			0.170064			0.0850321	−	0.996378i	$-0.472901\pi$
$113$	204.282			0.170064			0.0850321	+	0.996378i	$0.472901\pi$
$114$	1462.02	−	2532.29i	1.20114	−	2.08044i
$115$	220.152	+	381.315i	0.178516	+	0.309198i
$116$	−2281.13	−	3951.04i	−1.82584	−	3.16245i
$117$	−525.959	+	910.987i	−0.415597	+	0.719836i
$118$	−839.179			−0.654683
$119$	382.799	+	334.640i	0.294883	+	0.257785i
$120$	−5102.42			−3.88154
$121$	−838.804	+	1452.85i	−0.630206	+	1.09155i
$122$	−1199.86	−	2078.22i	−0.890411	−	1.54224i
$123$	−38.8652	−	67.3165i	−0.0284907	−	0.0493473i
$124$	449.245	−	778.115i	0.325350	−	0.563523i
$125$	2229.86			1.59556
$126$	1350.80	+	1180.86i	0.955071	+	0.834918i
$127$	−1564.48			−1.09311			−0.546557	−	0.837422i	$-0.684062\pi$
$127$	−1564.48			−1.09311			−0.546557	+	0.837422i	$0.684062\pi$
$128$	1259.24	−	2181.07i	0.869550	−	1.50610i
$129$	−531.461	−	920.518i	−0.362733	−	0.628272i
$130$	−2490.27	−	4313.28i	−1.68009	−	2.91000i
$131$	−295.278	+	511.436i	−0.196935	+	0.341102i	−0.947533	−	0.319657i	$-0.896432\pi$
$131$	−295.278	+	511.436i	−0.196935	+	0.341102i	0.750598	+	0.660759i	$0.229766\pi$
$132$	5988.30			3.94859
$133$	313.029	−	1586.76i	0.204083	−	1.03451i
$134$	5001.26			3.22420
$135$	−471.990	+	817.510i	−0.300907	+	0.521186i
$136$	−534.856	−	926.398i	−0.337232	−	0.584103i
$137$	1368.68	+	2370.62i	0.853533	+	1.47836i	0.877999	+	0.478662i	$0.158878\pi$
$137$	1368.68	+	2370.62i	0.853533	+	1.47836i	−0.0244659	+	0.999701i	$0.507789\pi$
$138$	−385.057	+	666.939i	−0.237524	+	0.411403i
$139$	2286.52			1.39525			0.697625	−	0.716463i	$-0.254240\pi$
$139$	2286.52			1.39525			0.697625	+	0.716463i	$0.254240\pi$
$140$	−5355.44	+	1827.34i	−3.23298	+	1.10313i
$141$	−930.224			−0.555596
$142$	78.3837	−	135.765i	0.0463226	−	0.0802332i
$143$	1457.67	+	2524.76i	0.852423	+	1.47644i
$144$	−623.881	−	1080.59i	−0.361042	−	0.625343i
$145$	−2736.14	+	4739.13i	−1.56706	+	2.71423i
$146$	−3518.82			−1.99465
$147$	2170.48	+	891.045i	1.21781	+	0.499946i
$148$	275.791			0.153175
$149$	970.352	−	1680.70i	0.533519	−	0.924082i	−0.465715	−	0.884935i	$-0.654203\pi$
$149$	970.352	−	1680.70i	0.533519	−	0.924082i	0.999233	−	0.0391468i	$-0.0124640\pi$
$150$	4042.77	+	7002.29i	2.20061	+	3.81156i
$151$	−542.628	−	939.859i	−0.292440	−	0.506521i	0.681946	−	0.731402i	$-0.261134\pi$
$151$	−542.628	−	939.859i	−0.292440	−	0.506521i	−0.974386	+	0.224882i	$0.927800\pi$
$152$	−1701.34	+	2946.81i	−0.907876	+	1.57249i
$153$	543.343			0.287103
$154$	4706.09	−	1605.77i	2.46252	−	0.840239i
$155$	−1077.71			−0.558475
$156$	2901.33	−	5025.25i	1.48905	−	2.57911i
$157$	426.739	+	739.133i	0.216926	+	0.375728i	0.953867	−	0.300230i	$-0.0970635\pi$
$157$	426.739	+	739.133i	0.216926	+	0.375728i	−0.736940	+	0.675958i	$0.763730\pi$
$158$	2690.81	+	4660.62i	1.35487	+	2.34670i
$159$	1031.02	−	1785.78i	0.514246	−	0.890701i
$160$	−59.5593			−0.0294286
$161$	−82.4438	+	417.911i	−0.0403570	+	0.204572i
$162$	−4266.74			−2.06930
$163$	−674.756	+	1168.71i	−0.324239	+	0.561598i	−0.981358	−	0.192188i	$-0.938442\pi$
$163$	−674.756	+	1168.71i	−0.324239	+	0.561598i	0.657119	+	0.753787i	$0.271775\pi$
$164$	90.6809	+	157.064i	0.0431768	+	0.0747843i
$165$	−3591.38	−	6220.45i	−1.69447	−	2.93492i
$166$	1061.85	−	1839.17i	0.496478	−	0.859925i
$167$	2110.64			0.978003			0.489001	−	0.872283i	$-0.337361\pi$
$167$	2110.64			0.978003			0.489001	+	0.872283i	$0.337361\pi$
$168$	−3716.39	−	3248.85i	−1.70670	−	1.49199i
$169$	627.964			0.285828
$170$	−1286.29	+	2227.92i	−0.580318	+	1.00514i
$171$	−864.171	−	1496.79i	−0.386461	−	0.669369i
$172$	1240.01	+	2147.77i	0.549710	+	0.952126i
$173$	1381.17	−	2392.25i	0.606983	−	1.05133i	−0.384752	−	0.923020i	$-0.625713\pi$
$173$	1381.17	−	2392.25i	0.606983	−	1.05133i	0.991735	−	0.128305i	$-0.0409538\pi$
$174$	−9571.30			−4.17010
$175$	3367.08	+	2943.48i	1.45444	+	1.27146i
$176$	−3458.11			−1.48105
$177$	−586.357	+	1015.60i	−0.249002	+	0.431284i
$178$	−15.9895	−	27.6946i	−0.00673293	−	0.0116618i
$179$	1909.16	+	3306.76i	0.797192	+	1.38078i	0.921438	+	0.388526i	$0.127016\pi$
$179$	1909.16	+	3306.76i	0.797192	+	1.38078i	−0.124246	+	0.992252i	$0.539651\pi$
$180$	−3023.49	+	5236.83i	−1.25199	+	2.16850i
$181$	2586.79			1.06229			0.531145	−	0.847281i	$-0.321762\pi$
$181$	2586.79			1.06229			0.531145	+	0.847281i	$0.321762\pi$
$182$	932.570	−	4727.24i	0.379817	−	1.92531i
$183$	−3353.50			−1.35463
$184$	448.090	−	776.115i	0.179531	−	0.310956i
$185$	−165.401	−	286.483i	−0.0657326	−	0.113852i
$186$	−942.483	−	1632.43i	−0.371539	−	0.643524i
$187$	752.925	−	1304.11i	0.294435	−	0.509977i
$188$	2170.41			0.841988
$189$	−864.310	+	294.912i	−0.332642	+	0.113501i
$190$	8183.23			3.12460
$191$	314.111	−	544.056i	0.118996	−	0.206107i	−0.800374	−	0.599501i	$-0.795366\pi$
$191$	314.111	−	544.056i	0.118996	−	0.206107i	0.919370	+	0.393394i	$0.128699\pi$
$192$	−1777.13	−	3078.07i	−0.667984	−	1.15698i
$193$	1323.97	+	2293.19i	0.493791	+	0.855271i	0.999974	−	0.00715483i	$-0.00227747\pi$
$193$	1323.97	+	2293.19i	0.493791	+	0.855271i	−0.506183	+	0.862426i	$0.668944\pi$
$194$	−1715.00	+	2970.47i	−0.634691	+	1.09932i
$195$	−6960.08			−2.55601
$196$	−5064.20	−	2079.00i	−1.84556	−	0.757653i
$197$	−1833.43			−0.663077			−0.331539	−	0.943442i	$-0.607568\pi$
$197$	−1833.43			−0.663077			−0.331539	+	0.943442i	$0.607568\pi$
$198$	2656.89	−	4601.86i	0.953620	−	1.65172i
$199$	1022.33	+	1770.73i	0.364177	+	0.630772i	0.988644	−	0.150279i	$-0.0480171\pi$
$199$	1022.33	+	1770.73i	0.364177	+	0.630772i	−0.624467	+	0.781051i	$0.714684\pi$
$200$	−4704.57	−	8148.55i	−1.66332	−	2.88095i
$201$	3494.51	−	6052.68i	1.22629	−	2.12399i
$202$	9025.75			3.14381
$203$	−5010.43	+	1709.62i	−1.73233	+	0.591092i
$204$	−2997.23			−1.02867
$205$	108.769	−	188.393i	0.0370572	−	0.0641850i
$206$	−1490.26	−	2581.20i	−0.504034	−	0.873012i
$207$	227.600	+	394.215i	0.0764218	+	0.132367i
$208$	−1675.45	+	2901.97i	−0.558519	+	0.967383i
$209$	−4790.02			−1.58532
$210$	−2297.65	+	11646.9i	−0.755013	+	3.82720i
$211$	1439.40			0.469633			0.234816	−	0.972040i	$-0.424551\pi$
$211$	1439.40			0.469633			0.234816	+	0.972040i	$0.424551\pi$
$212$	−2405.59	+	4166.61i	−0.779324	+	1.34983i
$213$	−109.538	−	189.725i	−0.0352366	−	0.0610316i
$214$	−4118.40	−	7133.27i	−1.31555	−	2.27860i
$215$	1487.35	−	2576.17i	0.471798	−	0.817179i
$216$	1921.34			0.605235
$217$	−784.959	−	686.207i	−0.245560	−	0.214667i
$218$	3890.46			1.20869
$219$	−2458.69	+	4258.58i	−0.758644	+	1.31401i
$220$	8379.46	+	14513.6i	2.56792	+	4.44777i
$221$	−729.584	−	1263.68i	−0.222069	−	0.384634i
$222$	289.295	−	501.073i	0.0874603	−	0.151486i
$223$	−4933.06			−1.48136			−0.740678	−	0.671860i	$-0.765496\pi$
$223$	−4933.06			−1.48136			−0.740678	+	0.671860i	$0.765496\pi$
$224$	−43.3806	−	37.9231i	−0.0129397	−	0.0113118i
$225$	4779.22			1.41607
$226$	−499.972	+	865.977i	−0.147158	+	0.254885i
$227$	2311.59	+	4003.80i	0.675885	+	1.17067i	0.976209	+	0.216830i	$0.0695718\pi$
$227$	2311.59	+	4003.80i	0.675885	+	1.17067i	−0.300324	+	0.953837i	$0.597095\pi$
$228$	4766.99	+	8256.68i	1.38466	+	2.39830i
$229$	769.323	−	1332.51i	0.222001	−	0.384517i	−0.733414	−	0.679782i	$-0.762074\pi$
$229$	769.323	−	1332.51i	0.222001	−	0.384517i	0.955416	+	0.295265i	$0.0954078\pi$
$230$	−2155.25			−0.617883
$231$	1344.92	−	6817.45i	0.383070	−	1.94180i
$232$	11138.1			3.15195
$233$	669.373	−	1159.39i	0.188206	−	0.325983i	−0.756446	−	0.654056i	$-0.773066\pi$
$233$	669.373	−	1159.39i	0.188206	−	0.325983i	0.944652	+	0.328073i	$0.106399\pi$
$234$	−2574.52	−	4459.20i	−0.719238	−	1.24576i
$235$	−1301.67	−	2254.55i	−0.361325	−	0.625834i
$236$	1368.10	−	2369.61i	0.377354	−	0.653596i
$237$	7520.57			2.06124
$238$	−2355.46	+	803.711i	−0.641521	+	0.218894i
$239$	233.746			0.0632626			0.0316313	−	0.999500i	$-0.489930\pi$
$239$	233.746			0.0632626			0.0316313	+	0.999500i	$0.489930\pi$
$240$	4127.95	−	7149.82i	1.11024	−	1.92299i
$241$	−580.269	−	1005.06i	−0.155097	−	0.268636i	0.777997	−	0.628268i	$-0.216236\pi$
$241$	−580.269	−	1005.06i	−0.155097	−	0.268636i	−0.933094	+	0.359632i	$0.882902\pi$
$242$	−4105.87	−	7111.58i	−1.09064	−	1.88905i
$243$	−2315.60	+	4010.74i	−0.611300	+	1.05880i
$244$	7824.43			2.05290
$245$	877.572	+	6507.37i	0.228841	+	1.69690i
$246$	380.483			0.0986128
$247$	−2320.76	+	4019.68i	−0.597840	+	1.03549i
$248$	1096.76	+	1899.65i	0.280825	+	0.486403i
$249$	−1483.88	−	2570.16i	−0.377660	−	0.654126i
$250$	−5457.49	+	9452.65i	−1.38065	+	2.39135i
$251$	3065.67			0.770930			0.385465	−	0.922723i	$-0.374041\pi$
$251$	3065.67			0.770930			0.385465	+	0.922723i	$0.374041\pi$
$252$	−5536.62	+	1889.16i	−1.38403	+	0.472246i
$253$	1261.57			0.313494
$254$	3829.01	−	6632.04i	0.945879	−	1.63831i
$255$	1797.53	+	3113.42i	0.441435	+	0.764588i
$256$	4085.50	+	7076.30i	0.997437	+	1.72761i
$257$	−2328.49	+	4033.07i	−0.565165	+	0.978894i	0.431869	+	0.901936i	$0.357854\pi$
$257$	−2328.49	+	4033.07i	−0.565165	+	0.978894i	−0.997034	+	0.0769582i	$0.975479\pi$
$258$	5202.91			1.25550
$259$	61.9403	−	313.978i	0.0148602	−	0.0753268i
$260$	16239.4			3.87355
$261$	−2828.71	+	4899.47i	−0.670853	+	1.16195i
$262$	−1445.36	−	2503.44i	−0.340819	−	0.590316i
$263$	774.932	+	1342.22i	0.181690	+	0.314696i	0.942456	−	0.334330i	$-0.108510\pi$
$263$	774.932	+	1342.22i	0.181690	+	0.314696i	−0.760766	+	0.649026i	$0.775177\pi$
$264$	−7309.76	+	12660.9i	−1.70411	+	2.95160i
$265$	5770.85			1.33774
$266$	5960.33	+	5210.49i	1.37388	+	1.20104i
$267$	−44.6891			−0.0102432
$268$	−8153.46	+	14122.2i	−1.85840	+	3.21885i
$269$	2303.44	+	3989.68i	0.522095	+	0.904294i	0.999670	+	0.0257035i	$0.00818256\pi$
$269$	2303.44	+	3989.68i	0.522095	+	0.904294i	−0.477575	+	0.878591i	$0.658484\pi$
$270$	−2310.35	−	4001.64i	−0.520753	−	0.901971i
$271$	499.021	−	864.330i	0.111857	−	0.193743i	−0.804662	−	0.593734i	$-0.797653\pi$
$271$	499.021	−	864.330i	0.111857	−	0.193743i	0.916519	+	0.399991i	$0.130987\pi$
$272$	1730.83			0.385835
$273$	−5069.44	−	4431.68i	−1.12387	−	0.982482i
$274$	−13399.1			−2.95427
$275$	6622.69	−	11470.8i	1.45223	−	2.51534i
$276$	−1255.50	−	2174.60i	−0.273813	−	0.474259i
$277$	−1979.01	−	3427.75i	−0.429269	−	0.743515i	0.567540	−	0.823346i	$-0.307895\pi$
$277$	−1979.01	−	3427.75i	−0.429269	−	0.743515i	−0.996808	+	0.0798308i	$0.974562\pi$
$278$	−5596.15	+	9692.82i	−1.20732	+	2.09114i
$279$	−1114.17			−0.239081
$280$	2673.77	−	13553.4i	0.570672	−	2.89276i
$281$	−1602.60			−0.340224			−0.170112	−	0.985425i	$-0.554413\pi$
$281$	−1602.60			−0.340224			−0.170112	+	0.985425i	$0.554413\pi$
$282$	2276.68	−	3943.33i	0.480761	−	0.832702i
$283$	−2413.32	−	4180.00i	−0.506916	−	0.878004i	−0.999968	−	0.00800390i	$-0.997452\pi$
$283$	−2413.32	−	4180.00i	−0.506916	−	0.878004i	0.493052	−	0.870000i	$-0.335881\pi$
$284$	255.575	+	442.669i	0.0534000	+	0.0924914i
$285$	5717.84	−	9903.60i	1.18841	−	2.05838i
$286$	−14270.3			−2.95043
$287$	199.177	−	67.9616i	0.0409654	−	0.0139779i
$288$	−61.5743			−0.0125983
$289$	2079.65	−	3602.06i	0.423295	−	0.733169i
$290$	−13393.2	−	23197.7i	−2.71198	−	4.69729i
$291$	2396.64	+	4151.10i	0.482796	+	0.836227i
$292$	5736.66	−	9936.19i	1.14970	−	1.99134i
$293$	−8325.17			−1.65994			−0.829969	−	0.557810i	$-0.811642\pi$
$293$	−8325.17			−1.65994			−0.829969	+	0.557810i	$0.811642\pi$
$294$	−9089.41	+	7020.14i	−1.80308	+	1.39259i
$295$	−3281.97			−0.647741
$296$	−336.652	+	583.098i	−0.0661063	+	0.114500i
$297$	1352.35	+	2342.34i	0.264214	+	0.457632i
$298$	4749.79	+	8226.87i	0.923315	+	1.59923i
$299$	611.229	−	1058.68i	0.118222	−	0.204766i
$300$	−26363.5			−5.07365
$301$	2723.65	−	929.340i	0.521556	−	0.177961i
$302$	5312.23			1.01220
$303$	6306.54	−	10923.2i	1.19571	−	2.07104i
$304$	−2752.84	−	4768.05i	−0.519362	−	0.899561i
$305$	−4692.57	−	8127.77i	−0.880969	−	1.52588i
$306$	−1329.81	+	2303.30i	−0.248432	+	0.430297i
$307$	1243.64			0.231199			0.115600	−	0.993296i	$-0.463121\pi$
$307$	1243.64			0.231199			0.115600	+	0.993296i	$0.463121\pi$
$308$	−3137.98	+	15906.6i	−0.580530	+	2.94273i
$309$	−4165.13			−0.766815
$310$	2637.64	−	4568.53i	0.483252	−	0.837017i
$311$	2908.81	+	5038.21i	0.530365	+	0.918619i	0.999372	+	0.0354246i	$0.0112784\pi$
$311$	2908.81	+	5038.21i	0.530365	+	0.918619i	−0.469008	+	0.883194i	$0.655388\pi$
$312$	7083.16	+	12268.4i	1.28527	+	2.22616i
$313$	1499.07	−	2596.47i	0.270711	−	0.468886i	−0.698333	−	0.715773i	$-0.746074\pi$
$313$	1499.07	−	2596.47i	0.270711	−	0.468886i	0.969044	+	0.246887i	$0.0794078\pi$
$314$	−4177.70			−0.750831
$315$	5282.89	+	4618.27i	0.944944	+	0.826064i
$316$	−17547.1			−3.12374
$317$	1358.16	−	2352.40i	0.240636	−	0.416795i	−0.720259	−	0.693705i	$-0.755977\pi$
$317$	1358.16	−	2352.40i	0.240636	−	0.416795i	0.960896	+	0.276910i	$0.0893105\pi$
$318$	5046.75	+	8741.23i	0.889962	+	1.54146i
$319$	7839.64	+	13578.6i	1.37597	+	2.38325i
$320$	4973.48	−	8614.33i	0.868832	−	1.50486i
$321$	−11510.5			−2.00142
$322$	−1569.80	−	1372.31i	−0.271682	−	0.237503i
$323$	2397.47			0.413000
$324$	6956.00	−	12048.1i	1.19273	−	2.06587i
$325$	−6417.39	−	11115.2i	−1.09530	−	1.89712i
$326$	−3302.87	−	5720.74i	−0.561132	−	0.971909i
$327$	2718.37	−	4708.36i	0.459713	−	0.796247i
$328$	−442.767			−0.0745358
$329$	487.456	−	2470.93i	0.0816848	−	0.414064i
$330$	35159.0			5.86496
$331$	181.634	−	314.599i	0.0301617	−	0.0522415i	−0.850551	−	0.525893i	$-0.823731\pi$
$331$	181.634	−	314.599i	0.0301617	−	0.0522415i	0.880712	+	0.473652i	$0.157064\pi$
$332$	3462.22	+	5996.74i	0.572331	+	0.991307i
$333$	−170.997	−	296.175i	−0.0281398	−	0.0487396i
$334$	−5165.71	+	8947.27i	−0.846272	+	1.46579i
$335$	19559.6			3.19001
$336$	7559.12	−	2579.26i	1.22733	−	0.418780i
$337$	−6841.06			−1.10581			−0.552903	−	0.833246i	$-0.686480\pi$
$337$	−6841.06			−1.10581			−0.552903	+	0.833246i	$0.686480\pi$
$338$	−1536.91	+	2662.01i	−0.247329	+	0.428386i
$339$	698.688	+	1210.16i	0.111940	+	0.193885i
$340$	−4194.04	−	7264.28i	−0.668981	−	1.15871i
$341$	−1543.93	+	2674.17i	−0.245187	+	0.424676i
$342$	8460.08			1.33763
$343$	−3504.24	+	5298.48i	−0.551636	+	0.834085i
$344$	−6054.61			−0.948962
$345$	−1505.93	+	2608.35i	−0.235005	+	0.407041i
$346$	6760.69	+	11709.9i	1.05045	+	1.81944i
$347$	−1377.97	−	2386.72i	−0.213180	−	0.369239i	0.739528	−	0.673126i	$-0.235049\pi$
$347$	−1377.97	−	2386.72i	−0.213180	−	0.369239i	−0.952708	+	0.303887i	$0.901715\pi$
$348$	15603.9	−	27026.8i	2.40361	−	4.16318i
$349$	855.088			0.131151			0.0655757	−	0.997848i	$-0.479112\pi$
$349$	855.088			0.131151			0.0655757	+	0.997848i	$0.479112\pi$
$350$	−20718.5	+	7069.40i	−3.16415	+	1.07964i
$351$	2620.86			0.398550
$352$	−85.3252	+	147.788i	−0.0129200	+	0.0223781i
$353$	−1438.35	−	2491.29i	−0.216871	−	0.375632i	0.736978	−	0.675916i	$-0.236252\pi$
$353$	−1438.35	−	2491.29i	−0.216871	−	0.375632i	−0.953850	+	0.300284i	$0.902919\pi$
$354$	−2870.17	−	4971.27i	−0.430926	−	0.746385i
$355$	306.553	−	530.966i	0.0458314	−	0.0793824i
$356$	104.269			0.0155232
$357$	−673.150	+	3412.23i	−0.0997952	+	0.505867i
$358$	−18690.4			−2.75926
$359$	−231.708	+	401.331i	−0.0340643	+	0.0590012i	−0.882555	−	0.470209i	$-0.844178\pi$
$359$	−231.708	+	401.331i	−0.0340643	+	0.0590012i	0.848491	+	0.529210i	$0.177512\pi$
$360$	−7381.39	−	12784.9i	−1.08065	−	1.87174i
$361$	−383.603	−	664.419i	−0.0559269	−	0.0968682i
$362$	−6331.05	+	10965.7i	−0.919206	+	1.59211i
$363$	−11475.5			−1.65926
$364$	11828.1	+	10340.1i	1.70319	+	1.48892i
$365$	−13761.9			−1.97350
$366$	8207.54	−	14215.9i	1.17217	−	2.03026i
$367$	388.493	+	672.889i	0.0552566	+	0.0957072i	0.892331	−	0.451383i	$-0.149069\pi$
$367$	388.493	+	672.889i	0.0552566	+	0.0957072i	−0.837074	+	0.547090i	$0.815736\pi$
$368$	725.027	+	1255.78i	0.102703	+	0.177887i
$369$	112.448	−	194.766i	0.0158640	−	0.0274773i
$370$	1619.25			0.227515
$371$	4203.25	+	3674.46i	0.588199	+	0.514201i
$372$	6146.05			0.856607
$373$	6136.35	−	10628.5i	0.851819	−	1.47539i	−0.0277468	−	0.999615i	$-0.508833\pi$
$373$	6136.35	−	10628.5i	0.851819	−	1.47539i	0.879565	−	0.475778i	$-0.157833\pi$
$374$	3685.50	+	6383.48i	0.509553	+	0.882572i
$375$	7626.60	+	13209.7i	1.05023	+	1.81905i
$376$	−2649.37	+	4588.84i	−0.363380	+	0.629392i
$377$	15193.2			2.07557
$378$	865.192	−	4385.70i	0.117727	−	0.596762i
$379$	−9613.48			−1.30293			−0.651466	−	0.758678i	$-0.725846\pi$
$379$	−9613.48			−1.30293			−0.651466	+	0.758678i	$0.725846\pi$
$380$	−13341.0	+	23107.2i	−1.80099	+	3.11941i
$381$	−5350.87	−	9267.97i	−0.719510	−	1.24623i
$382$	1537.54	+	2663.10i	0.205936	+	0.356692i
$383$	6521.99	−	11296.4i	0.870125	−	1.50710i	0.00825885	−	0.999966i	$-0.497371\pi$
$383$	6521.99	−	11296.4i	0.870125	−	1.50710i	0.861866	−	0.507135i	$-0.169296\pi$
$384$	17227.5			2.28942
$385$	18405.2	−	6280.06i	2.43640	−	0.831329i
$386$	−12961.5			−1.70912
$387$	1537.67	−	2663.33i	0.201975	−	0.349831i
$388$	−5591.88	−	9685.42i	−0.731662	−	1.26728i
$389$	−2963.02	−	5132.11i	−0.386199	−	0.668916i	0.605736	−	0.795666i	$-0.292879\pi$
$389$	−2963.02	−	5132.11i	−0.386199	−	0.668916i	−0.991935	+	0.126750i	$0.959545\pi$
$390$	17034.5	−	29504.6i	2.21173	−	3.83083i
$391$	−631.433			−0.0816699
$392$	10577.3	−	8169.32i	1.36284	−	1.05258i
$393$	−4039.65			−0.518507
$394$	4487.23	−	7772.11i	0.573765	−	0.993790i
$395$	10523.6	+	18227.4i	1.34050	+	2.32182i
$396$	8662.95	+	15004.7i	1.09932	+	1.90407i
$397$	−2786.90	+	4827.05i	−0.352318	+	0.610233i	−0.986655	−	0.162823i	$-0.947940\pi$
$397$	−2786.90	+	4827.05i	−0.352318	+	0.610233i	0.634337	+	0.773057i	$0.281273\pi$
$398$	−10008.4			−1.26050
$399$	10470.5	−	3572.67i	1.31374	−	0.448264i
$400$	15224.3			1.90304
$401$	−7421.87	+	12855.1i	−0.924265	+	1.60087i	−0.131527	+	0.991313i	$0.541988\pi$
$401$	−7421.87	+	12855.1i	−0.924265	+	1.60087i	−0.792739	+	0.609562i	$0.791345\pi$
$402$	17105.3	+	29627.3i	2.12223	+	3.67581i
$403$	1496.07	+	2591.27i	0.184925	+	0.320299i
$404$	−14714.5	+	25486.3i	−1.81207	+	3.13859i
$405$	−16687.0			−2.04736
$406$	5015.55	−	25424.0i	0.613097	−	3.10782i
$407$	−947.820			−0.115434
$408$	3658.64	−	6336.95i	0.443945	−	0.768936i
$409$	−593.035	−	1027.17i	−0.0716961	−	0.124181i	0.827949	−	0.560804i	$-0.189508\pi$
$409$	−593.035	−	1027.17i	−0.0716961	−	0.124181i	−0.899645	+	0.436623i	$0.856175\pi$
$410$	532.413	+	922.166i	0.0641317	+	0.111079i
$411$	−9362.33	+	16216.0i	−1.12362	+	1.94618i
$412$	9718.14			1.16208
$413$	−2390.46	−	2089.72i	−0.284810	−	0.248979i
$414$	−2228.17			−0.264513
$415$	4152.81	−	7192.88i	0.491213	−	0.850807i
$416$	82.6801	+	143.206i	0.00974453	+	0.0168780i
$417$	7820.37	+	13545.3i	0.918381	+	1.59068i
$418$	11723.4	−	20305.5i	1.37179	−	2.37601i
$419$	11020.8			1.28496			0.642482	−	0.766301i	$-0.277905\pi$
$419$	11020.8			1.28496			0.642482	+	0.766301i	$0.277905\pi$
$420$	−29141.8	−	25475.6i	−3.38566	−	2.95972i
$421$	−6818.68			−0.789364			−0.394682	−	0.918818i	$-0.629145\pi$
$421$	−6818.68			−0.789364			−0.394682	+	0.918818i	$0.629145\pi$
$422$	−3522.88	+	6101.80i	−0.406377	+	0.703865i
$423$	−1345.71	−	2330.83i	−0.154682	−	0.267917i
$424$	−5872.89	−	10172.1i	−0.672672	−	1.16510i
$425$	−3314.75	+	5741.32i	−0.378327	+	0.655282i
$426$	1072.35			0.121962
$427$	1757.30	−	8907.82i	0.199161	−	1.00955i
$428$	26856.6			3.03309
$429$	−9971.08	+	17270.4i	−1.12216	+	1.94364i
$430$	7280.47	+	12610.1i	0.816501	+	1.41422i
$431$	3287.06	+	5693.36i	0.367360	+	0.636287i	0.989152	−	0.146896i	$-0.0469282\pi$
$431$	3287.06	+	5693.36i	0.367360	+	0.636287i	−0.621792	+	0.783183i	$0.713595\pi$
$432$	−1554.40	+	2692.30i	−0.173116	+	0.299846i
$433$	−10894.2			−1.20910			−0.604551	−	0.796566i	$-0.706647\pi$
$433$	−10894.2			−1.20910			−0.604551	+	0.796566i	$0.706647\pi$
$434$	4830.06	−	1648.07i	0.534218	−	0.182281i
$435$	−37432.7			−4.12589
$436$	−6342.55	+	10985.6i	−0.696681	+	1.20669i
$437$	1004.27	+	1739.45i	0.109933	+	0.190410i
$438$	−12035.1	−	20845.4i	−1.31292	−	2.27404i
$439$	4481.05	−	7761.41i	0.487173	−	0.843808i	−0.512718	−	0.858557i	$-0.671361\pi$
$439$	4481.05	−	7761.41i	0.487173	−	0.843808i	0.999891	+	0.0147486i	$0.00469481\pi$
$440$	−40914.4			−4.43299
$441$	907.261	+	6727.53i	0.0979658	+	0.726437i
$442$	7142.51			0.768630
$443$	−5284.44	+	9152.93i	−0.566753	+	0.981645i	0.430131	+	0.902766i	$0.358467\pi$
$443$	−5284.44	+	9152.93i	−0.566753	+	0.981645i	−0.996884	+	0.0788784i	$0.974866\pi$
$444$	943.264	+	1633.78i	0.100823	+	0.174630i
$445$	−62.5338	−	108.312i	−0.00666154	−	0.0115381i
$446$	12073.5	−	20911.8i	1.28183	−	2.22019i
$447$	13275.2			1.40469
$448$	9107.47	−	3107.57i	0.960463	−	0.327721i
$449$	499.154			0.0524644			0.0262322	−	0.999656i	$-0.491649\pi$
$449$	499.154			0.0524644			0.0262322	+	0.999656i	$0.491649\pi$
$450$	−11696.9	+	20259.7i	−1.22533	+	2.12233i
$451$	−311.646	−	539.786i	−0.0325384	−	0.0563581i
$452$	−1630.19	−	2823.57i	−0.169641	−	0.293827i
$453$	3711.80	−	6429.03i	0.384979	−	0.666804i
$454$	−22630.1			−2.33939
$455$	3647.22	−	18487.9i	0.375790	−	1.90490i
$456$	−23275.8			−2.39033
$457$	−3176.86	+	5502.49i	−0.325180	+	0.563229i	−0.981549	−	0.191212i	$-0.938758\pi$
$457$	−3176.86	+	5502.49i	−0.325180	+	0.563229i	0.656369	+	0.754440i	$0.272092\pi$
$458$	3765.77	+	6522.50i	0.384198	+	0.665451i
$459$	−676.872	−	1172.38i	−0.0688315	−	0.119220i
$460$	3513.67	−	6085.85i	0.356143	−	0.616857i
$461$	−1563.98			−0.158009			−0.0790043	−	0.996874i	$-0.525174\pi$
$461$	−1563.98			−0.158009			−0.0790043	+	0.996874i	$0.525174\pi$
$462$	25608.4	+	22386.7i	2.57881	+	2.25438i
$463$	−14141.0			−1.41941			−0.709705	−	0.704499i	$-0.751172\pi$
$463$	−14141.0			−1.41941			−0.709705	+	0.704499i	$0.751172\pi$
$464$	−9010.92	+	15607.4i	−0.901555	+	1.56154i
$465$	−3685.99	−	6384.32i	−0.367599	−	0.636700i
$466$	3276.52	+	5675.10i	0.325712	+	0.564150i
$467$	2795.98	−	4842.79i	0.277051	−	0.479866i	−0.693600	−	0.720361i	$-0.743976\pi$
$467$	2795.98	−	4842.79i	0.277051	−	0.479866i	0.970650	+	0.240495i	$0.0773096\pi$
$468$	16788.8			1.65825
$469$	14246.4	+	12454.1i	1.40264	+	1.22618i
$470$	12743.1			1.25063
$471$	−2919.07	+	5055.98i	−0.285570	+	0.494623i
$472$	3340.00	+	5785.06i	0.325712	+	0.564150i
$473$	−4261.59	−	7381.29i	−0.414267	−	0.717531i
$474$	−18406.3	+	31880.6i	−1.78360	+	3.08929i
$475$	21088.0			2.03702
$476$	1570.61	−	7961.47i	0.151237	−	0.766625i
$477$	5966.08			0.572680
$478$	−572.083	+	990.877i	−0.0547416	+	0.0948151i
$479$	5125.68	+	8877.93i	0.488931	+	0.846854i	0.999919	−	0.0127342i	$-0.00405353\pi$
$479$	5125.68	+	8877.93i	0.488931	+	0.846854i	−0.510988	+	0.859588i	$0.670720\pi$
$480$	−203.705	−	352.828i	−0.0193705	−	0.0335507i
$481$	−459.218	+	795.390i	−0.0435313	+	0.0753984i
$482$	5680.73			0.536826
$483$	−2757.67	+	940.950i	−0.259790	+	0.0886433i
$484$	26774.9			2.51455
$485$	−6707.27	+	11617.3i	−0.627961	+	1.08766i
$486$	−11334.7	−	19632.2i	−1.05792	−	1.83238i
$487$	2387.29	+	4134.90i	0.222132	+	0.384744i	0.955455	−	0.295136i	$-0.0953651\pi$
$487$	2387.29	+	4134.90i	0.222132	+	0.384744i	−0.733323	+	0.679880i	$0.762032\pi$
$488$	−9551.09	+	16543.0i	−0.885978	+	1.53456i
$489$	−9231.22			−0.853682
$490$	−29733.4	−	12206.4i	−2.74126	−	1.12536i
$491$	218.570			0.0200895			0.0100447	−	0.999950i	$-0.496803\pi$
$491$	218.570			0.0200895			0.0100447	+	0.999950i	$0.496803\pi$
$492$	−620.295	+	1074.38i	−0.0568396	+	0.0984490i
$493$	−3923.85	−	6796.30i	−0.358461	−	0.620872i
$494$	−11359.9	−	19676.0i	−1.03463	−	1.79203i
$495$	10390.9	−	17997.6i	0.943508	−	1.63420i
$496$	−3549.21			−0.321299
$497$	561.362	−	191.543i	0.0506650	−	0.0172875i
$498$	14527.0			1.30717
$499$	−8528.29	+	14771.4i	−0.765087	+	1.32517i	0.175113	+	0.984548i	$0.443971\pi$
$499$	−8528.29	+	14771.4i	−0.765087	+	1.32517i	−0.940200	+	0.340622i	$0.889362\pi$
$500$	−17794.5	−	30821.0i	−1.59159	−	2.75671i
$501$	7218.84	+	12503.4i	0.643741	+	1.11499i
$502$	−7503.09	+	12995.7i	−0.667090	+	1.15543i
$503$	6640.40			0.588630			0.294315	−	0.955708i	$-0.404909\pi$
$503$	6640.40			0.588630			0.294315	+	0.955708i	$0.404909\pi$
$504$	2764.22	−	14012.0i	0.244302	−	1.23838i
$505$	35299.1			3.11047
$506$	−3087.63	+	5347.94i	−0.271269	+	0.469851i
$507$	2147.77	+	3720.04i	0.188137	+	0.325864i
$508$	12484.7	+	21624.2i	1.09039	+	1.88862i
$509$	10194.7	−	17657.8i	0.887767	−	1.53766i	0.0452590	−	0.998975i	$-0.485589\pi$
$509$	10194.7	−	17657.8i	0.887767	−	1.53766i	0.842508	−	0.538683i	$-0.181078\pi$
$510$	−17597.6			−1.52791
$511$	−10023.6	−	8762.56i	−0.867744	−	0.758577i
$512$	−19848.5			−1.71326
$513$	−2153.09	+	3729.26i	−0.185304	+	0.320956i
$514$	−11397.8	−	19741.5i	−0.978082	−	1.69409i
$515$	−5828.29	−	10094.9i	−0.498689	−	0.863755i
$516$	−8482.21	+	14691.6i	−0.723660	+	1.25342i
$517$	−7459.12			−0.634530
$518$	1179.39	+	1031.02i	0.100038	+	0.0874525i
$519$	18895.5			1.59811
$520$	−19823.0	+	34334.5i	−1.67172	+	2.89551i
$521$	1155.15	+	2000.78i	0.0971366	+	0.168246i	0.910498	−	0.413513i	$-0.135698\pi$
$521$	1155.15	+	2000.78i	0.0971366	+	0.168246i	−0.813362	+	0.581758i	$0.802365\pi$
$522$	−13846.3	−	23982.5i	−1.16099	−	2.01089i
$523$	−5897.82	+	10215.3i	−0.493104	+	0.854082i	−0.999968	−	0.00794420i	$-0.997471\pi$
$523$	−5897.82	+	10215.3i	−0.493104	+	0.854082i	0.506864	+	0.862026i	$0.330805\pi$
$524$	9425.37			0.785781
$525$	−5921.00	+	30013.8i	−0.492216	+	2.49507i
$526$	−7586.45			−0.628869
$527$	772.760	−	1338.46i	0.0638747	−	0.110634i
$528$	−11827.5	−	20485.8i	−0.974857	−	1.68850i
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$	−14123.9	+	24463.3i	−1.15755	+	2.00494i
$531$	−3393.01			−0.277295
$532$	−24430.0	+	8335.81i	−1.99093	+	0.679329i
$533$	−603.969			−0.0490822
$534$	109.375	−	189.443i	0.00886350	−	0.0153520i
$535$	−16106.8	−	27897.8i	−1.30160	−	2.25444i
$536$	−19905.4	−	34477.2i	−1.60407	−	2.77834i
$537$	−13059.5	+	22619.7i	−1.04946	+	1.81771i
$538$	−22550.3			−1.80709
$539$	17404.3	+	7144.96i	1.39083	+	0.570974i
$540$	15066.1			1.20063
$541$	5379.31	−	9317.24i	0.427495	−	0.740443i	−0.569155	−	0.822230i	$-0.692730\pi$
$541$	5379.31	−	9317.24i	0.427495	−	0.740443i	0.996650	+	0.0817874i	$0.0260628\pi$
$542$	2442.67	+	4230.82i	0.193582	+	0.335294i
$543$	8847.36	+	15324.1i	0.699220	+	1.21108i
$544$	42.7065	−	73.9698i	0.00336585	−	0.00582983i
$545$	15215.3			1.19588
$546$	31193.7	−	10643.6i	2.44499	−	0.834259i
$547$	−5351.69			−0.418322			−0.209161	−	0.977881i	$-0.567073\pi$
$547$	−5351.69			−0.418322			−0.209161	+	0.977881i	$0.567073\pi$
$548$	21844.3	−	37835.5i	1.70282	−	2.94937i
$549$	−4851.32	−	8402.74i	−0.377139	−	0.653225i
$550$	32417.5	+	56148.8i	2.51325	+	4.35308i
$551$	−12481.5	+	21618.6i	−0.965028	+	1.67148i
$552$	6130.25			0.472683
$553$	−3940.92	+	19976.7i	−0.303047	+	1.53616i
$554$	19374.2			1.48580
$555$	1131.41	−	1959.66i	0.0865329	−	0.149879i
$556$	−18246.6	−	31604.1i	−1.39178	−	2.41063i
$557$	−2835.84	−	4911.81i	−0.215724	−	0.373645i	0.737772	−	0.675050i	$-0.235878\pi$
$557$	−2835.84	−	4911.81i	−0.215724	−	0.373645i	−0.953496	+	0.301405i	$0.902544\pi$
$558$	2726.88	−	4723.09i	0.206878	−	0.358323i
$559$	−8258.96			−0.624896
$560$	16828.8	+	14711.6i	1.26990	+	1.11014i
$561$	10300.7			0.775212
$562$	3922.29	−	6793.60i	0.294398	−	0.509912i
$563$	7559.25	+	13093.0i	0.565869	+	0.980114i	0.996968	+	0.0778093i	$0.0247925\pi$
$563$	7559.25	+	13093.0i	0.565869	+	0.980114i	−0.431099	+	0.902304i	$0.641874\pi$
$564$	7423.27	+	12857.5i	0.554213	+	0.959925i
$565$	−1955.36	+	3386.78i	−0.145597	+	0.252182i
$566$	23626.0			1.75455
$567$	−12154.1	−	10625.0i	−0.900219	−	0.786966i
$568$	−1247.90			−0.0921841
$569$	7723.53	−	13377.5i	0.569046	−	0.985616i	−0.427615	−	0.903961i	$-0.640646\pi$
$569$	7723.53	−	13377.5i	0.569046	−	0.985616i	0.996661	−	0.0816553i	$-0.0260206\pi$
$570$	27988.4	+	48477.2i	2.05667	+	3.56226i
$571$	4104.71	+	7109.56i	0.300835	+	0.521061i	0.976325	−	0.216308i	$-0.0694014\pi$
$571$	4104.71	+	7109.56i	0.300835	+	0.521061i	−0.675490	+	0.737369i	$0.736068\pi$
$572$	23264.7	−	40295.6i	1.70060	−	2.94553i
$573$	4297.30			0.313302
$574$	−199.381	+	1010.67i	−0.0144982	+	0.0734923i
$575$	−5554.05			−0.402817
$576$	5141.75	−	8905.76i	0.371943	−	0.644225i
$577$	−9990.94	−	17304.8i	−0.720846	−	1.24854i	−0.960661	−	0.277723i	$-0.910420\pi$
$577$	−9990.94	−	17304.8i	−0.720846	−	1.24854i	0.239815	−	0.970819i	$-0.422913\pi$
$578$	10179.7	+	17631.8i	0.732561	+	1.26883i
$579$	−9056.53	+	15686.4i	−0.650046	+	1.12591i
$580$	87338.6			6.25265
$581$	7604.65	−	2594.79i	0.543019	−	0.185284i
$582$	−23462.7			−1.67107
$583$	8267.36	−	14319.5i	0.587306	−	1.01724i
$584$	14005.2	+	24257.7i	0.992362	+	1.71882i
$585$	−10068.8	−	17439.6i	−0.711612	−	1.23255i
$586$	20375.5	−	35291.4i	1.43635	−	2.48784i
$587$	−16605.5			−1.16760			−0.583799	−	0.811898i	$-0.698435\pi$
$587$	−16605.5			−1.16760			−0.583799	+	0.811898i	$0.698435\pi$
$588$	−5004.69	−	37110.8i	−0.351004	−	2.60276i
$589$	−4916.20			−0.343920
$590$	8032.48	−	13912.7i	0.560495	−	0.970806i
$591$	−6270.70	−	10861.2i	−0.436450	−	0.755954i
$592$	−544.715	−	943.474i	−0.0378170	−	0.0655009i
$593$	6013.78	−	10416.2i	0.416452	−	0.721317i	−0.579127	−	0.815237i	$-0.696607\pi$
$593$	6013.78	−	10416.2i	0.416452	−	0.721317i	0.995580	+	0.0939205i	$0.0299400\pi$
$594$	−13239.3			−0.914504
$595$	−9212.06	+	3143.26i	−0.634719	+	0.216573i
$596$	−30974.0			−2.12876
$597$	−6993.17	+	12112.5i	−0.479416	+	0.830374i
$598$	2991.92	+	5182.15i	0.204596	+	0.354371i
$599$	−2517.64	−	4360.68i	−0.171733	−	0.297450i	0.767293	−	0.641297i	$-0.221603\pi$
$599$	−2517.64	−	4360.68i	−0.171733	−	0.297450i	−0.939026	+	0.343847i	$0.888270\pi$
$600$	32181.2	−	55739.5i	2.18965	−	3.79259i
$601$	−1516.67			−0.102939			−0.0514693	−	0.998675i	$-0.516390\pi$
$601$	−1516.67			−0.102939			−0.0514693	+	0.998675i	$0.516390\pi$
$602$	−2726.43	+	13820.4i	−0.184586	+	0.935676i
$603$	20221.3			1.36563
$604$	−8660.43	+	15000.3i	−0.583424	+	1.01052i
$605$	−16057.8	−	27812.9i	−1.07908	−	1.86902i
$606$	30870.0	+	53468.4i	2.06932	+	3.58416i
$607$	−8270.84	+	14325.5i	−0.553053	+	0.957916i	0.444999	+	0.895531i	$0.353204\pi$
$607$	−8270.84	+	14325.5i	−0.553053	+	0.957916i	−0.998052	+	0.0623848i	$0.980129\pi$
$608$	−271.693			−0.0181227
$609$	−27264.5	−	23834.4i	−1.81414	−	1.58591i
$610$	45939.4			3.04923
$611$	−3613.94	+	6259.53i	−0.239287	+	0.414458i
$612$	−4335.93	−	7510.05i	−0.286388	−	0.496039i
$613$	−11662.4	−	20199.9i	−0.768419	−	1.33094i	−0.938420	−	0.345497i	$-0.887711\pi$
$613$	−11662.4	−	20199.9i	−0.768419	−	1.33094i	0.170001	−	0.985444i	$-0.445623\pi$
$614$	−3043.75	+	5271.93i	−0.200058	+	0.346511i
$615$	1488.05			0.0975671
$616$	−29800.4	−	26051.3i	−1.94917	−	1.70396i
$617$	15775.5			1.02933			0.514666	−	0.857391i	$-0.327916\pi$
$617$	15775.5			1.02933			0.514666	+	0.857391i	$0.327916\pi$
$618$	10194.0	−	17656.5i	0.663530	−	1.14927i
$619$	−11058.4	−	19153.7i	−0.718051	−	1.24370i	−0.961771	−	0.273855i	$-0.911701\pi$
$619$	−11058.4	−	19153.7i	−0.718051	−	1.24370i	0.243720	−	0.969846i	$-0.421632\pi$
$620$	8600.20	+	14896.0i	0.557085	+	0.964899i
$621$	567.068	−	982.191i	0.0366436	−	0.0634685i
$622$	−28476.7			−1.83571
$623$	23.4180	−	118.707i	0.00150597	−	0.00763385i
$624$	−22921.6			−1.47051
$625$	−6251.36	+	10827.7i	−0.400087	+	0.692971i
$626$	7337.83	+	12709.5i	0.468497	+	0.811460i
$627$	−16382.9	−	28376.0i	−1.04349	−	1.80738i
$628$	6810.82	−	11796.7i	0.432773	−	0.749585i
$629$	474.397			0.0300723
$630$	−32507.1	+	11091.8i	−2.05573	+	0.701440i
$631$	7915.33			0.499373			0.249686	−	0.968327i	$-0.419672\pi$
$631$	7915.33			0.499373			0.249686	+	0.968327i	$0.419672\pi$
$632$	21419.3	−	37099.3i	1.34812	−	2.33502i
$633$	4923.06	+	8526.99i	0.309122	+	0.535414i
$634$	6648.07	+	11514.8i	0.416449	+	0.721310i
$635$	14975.0	−	25937.4i	0.935850	−	1.62094i
$636$	−32910.5			−2.05187
$637$	14428.3	−	11143.6i	0.897439	−	0.693131i
$638$	−76748.7			−4.76255
$639$	316.925	−	548.929i	0.0196203	−	0.0339833i
$640$	24106.5	+	41753.7i	1.48890	+	2.57885i
$641$	10104.4	+	17501.4i	0.622622	+	1.07841i	0.988996	+	0.147945i	$0.0472660\pi$
$641$	10104.4	+	17501.4i	0.622622	+	1.07841i	−0.366373	+	0.930468i	$0.619401\pi$
$642$	28171.6	−	48794.6i	1.73184	−	2.99964i
$643$	22713.9			1.39308			0.696538	−	0.717520i	$-0.254723\pi$
$643$	22713.9			1.39308			0.696538	+	0.717520i	$0.254723\pi$
$644$	6434.25	−	2195.44i	0.393703	−	0.134336i
$645$	20348.2			1.24219
$646$	−5867.71	+	10163.2i	−0.357371	+	0.618985i
$647$	3743.97	+	6484.74i	0.227497	+	0.394037i	0.957066	−	0.289871i	$-0.0936124\pi$
$647$	3743.97	+	6484.74i	0.227497	+	0.394037i	−0.729569	+	0.683908i	$0.760279\pi$
$648$	16982.0	+	29413.7i	1.02950	+	1.78315i
$649$	−4701.78	+	8143.72i	−0.284377	+	0.492556i
$650$	62825.1			3.79108
$651$	1380.35	−	6997.05i	0.0831031	−	0.421253i
$652$	21538.4			1.29373
$653$	−4486.19	+	7770.31i	−0.268849	+	0.465660i	−0.968565	−	0.248761i	$-0.919977\pi$
$653$	−4486.19	+	7770.31i	−0.268849	+	0.465660i	0.699716	+	0.714421i	$0.253310\pi$
$654$	13306.2	+	23047.0i	0.795586	+	1.37800i
$655$	−5652.70	−	9790.77i	−0.337205	−	0.584056i
$656$	358.207	−	620.433i	0.0213196	−	0.0369266i
$657$	−14227.4			−0.844849
$658$	9281.56	+	8113.89i	0.549898	+	0.480718i
$659$	7083.63			0.418724			0.209362	−	0.977838i	$-0.432861\pi$
$659$	7083.63			0.418724			0.209362	+	0.977838i	$0.432861\pi$
$660$	−57319.0	+	99279.4i	−3.38051	+	5.85522i
$661$	−681.138	−	1179.77i	−0.0400805	−	0.0694214i	0.845289	−	0.534309i	$-0.179428\pi$
$661$	−681.138	−	1179.77i	−0.0400805	−	0.0694214i	−0.885370	+	0.464888i	$0.846095\pi$
$662$	889.083	+	1539.94i	0.0521982	+	0.0904099i
$663$	4990.66	−	8644.08i	0.292340	−	0.506347i
$664$	−16905.0			−0.988013
$665$	23310.5	+	20377.9i	1.35931	+	1.18830i
$666$	1674.03			0.0973984
$667$	3287.31	−	5693.79i	0.190832	−	0.330531i
$668$	−16843.1	−	29173.1i	−0.975568	−	1.68973i
$669$	−16872.1	−	29223.4i	−0.975058	−	1.68885i
$670$	−47871.2	+	82915.4i	−2.76034	+	4.78104i
$671$	−26890.4			−1.54709
$672$	76.2847	−	386.691i	0.00437909	−	0.0221978i
$673$	−24689.0			−1.41410			−0.707052	−	0.707162i	$-0.749975\pi$
$673$	−24689.0			−1.41410			−0.707052	+	0.707162i	$0.749975\pi$
$674$	16743.2	−	29000.1i	0.956861	−	1.65733i
$675$	−5953.73	−	10312.2i	−0.339495	−	0.588023i
$676$	−5011.20	−	8679.66i	−0.285116	−	0.493836i
$677$	−4097.45	+	7097.00i	−0.232611	+	0.402895i	−0.958576	−	0.284837i	$-0.908060\pi$
$677$	−4097.45	+	7097.00i	−0.232611	+	0.402895i	0.725964	+	0.687732i	$0.241394\pi$
$678$	−6840.04			−0.387448
$679$	−12282.4	+	4190.89i	−0.694189	+	0.236865i
$680$	20478.2			1.15486
$681$	−15812.3	+	27387.7i	−0.889762	+	1.54111i
$682$	−7557.42	−	13089.8i	−0.424323	−	0.734950i
$683$	−7917.18	−	13712.9i	−0.443547	−	0.768245i	0.554403	−	0.832248i	$-0.312947\pi$
$683$	−7917.18	−	13712.9i	−0.443547	−	0.768245i	−0.997950	+	0.0640031i	$0.979613\pi$
$684$	−13792.3	+	23889.0i	−0.770998	+	1.33541i
$685$	−52403.1			−2.92295
$686$	−13884.4	−	27822.7i	−0.772755	−	1.54851i
$687$	10525.0			0.584502
$688$	4898.30	−	8484.10i	0.271433	−	0.470135i
$689$	−8011.07	−	13875.6i	−0.442957	−	0.767224i
$690$	−7371.42	−	12767.7i	−0.406703	−	0.704430i
$691$	1164.34	−	2016.69i	0.0641004	−	0.111025i	−0.832194	−	0.554484i	$-0.812916\pi$
$691$	1164.34	−	2016.69i	0.0641004	−	0.111025i	0.896295	+	0.443459i	$0.146249\pi$
$692$	−44087.3			−2.42189
$693$	19027.9	−	6492.53i	1.04301	−	0.355889i
$694$	13490.1			0.737865
$695$	−21886.2	+	37908.0i	−1.19452	+	2.06897i
$696$	38094.6	+	65981.8i	2.07467	+	3.59344i
$697$	155.983	+	270.170i	0.00847672	+	0.0146821i
$698$	−2092.79	+	3624.82i	−0.113486	+	0.196564i
$699$	9157.58			0.495524
$700$	13815.0	−	70028.7i	0.745938	−	3.78119i
$701$	23597.8			1.27144			0.635718	−	0.771921i	$-0.280704\pi$
$701$	23597.8			1.27144			0.635718	+	0.771921i	$0.280704\pi$
$702$	−6414.44	+	11110.1i	−0.344868	+	0.597329i
$703$	−754.514	−	1306.86i	−0.0404794	−	0.0701124i
$704$	−14250.1	−	24681.9i	−0.762885	−	1.32136i
$705$	8903.95	−	15422.1i	0.475663	−	0.823872i
$706$	14081.2			0.750641
$707$	25710.4	+	22475.9i	1.36767	+	1.19561i
$708$	18716.7			0.993528
$709$	9257.99	−	16035.3i	0.490397	−	0.849392i	−0.509542	−	0.860446i	$-0.670185\pi$
$709$	9257.99	−	16035.3i	0.490397	−	0.849392i	0.999939	+	0.0110538i	$0.00351860\pi$
$710$	1500.55	+	2599.03i	0.0793165	+	0.137380i
$711$	10879.6	+	18844.0i	0.573864	+	0.993961i
$712$	−127.279	+	220.454i	−0.00669942	+	0.0116037i
$713$	1294.80			0.0680094
$714$	−12817.3	−	11204.9i	−0.671817	−	0.587298i
$715$	−55810.3			−2.91914
$716$	30470.5	−	52776.5i	1.59042	−	2.75468i
$717$	799.460	+	1384.71i	0.0416407	+	0.0721238i
$718$	−1134.19	−	1964.48i	−0.0589522	−	0.102108i
$719$	−14487.0	+	25092.3i	−0.751426	+	1.30151i	0.195705	+	0.980663i	$0.437300\pi$
$719$	−14487.0	+	25092.3i	−0.751426	+	1.30151i	−0.947131	+	0.320846i	$0.896033\pi$
$720$	23886.7			1.23640
$721$	2182.61	−	11063.7i	0.112739	−	0.571478i
$722$	3755.40			0.193576
$723$	3969.28	−	6875.00i	0.204176	−	0.353643i
$724$	−20642.8	−	35754.4i	−1.05965	−	1.83536i
$725$	−34514.0	−	59779.9i	−1.76802	−	3.06231i
$726$	28085.9	−	48646.2i	1.43577	−	2.48682i
$727$	−12185.1			−0.621625			−0.310812	−	0.950471i	$-0.600601\pi$
$727$	−12185.1			−0.621625			−0.310812	+	0.950471i	$0.600601\pi$
$728$	−36300.0	+	12386.0i	−1.84803	+	0.630569i
$729$	−8144.32			−0.413774
$730$	33681.6	−	58338.2i	1.70769	−	2.95780i
$731$	2132.99	+	3694.44i	0.107922	+	0.186927i
$732$	26761.2	+	46351.8i	1.35126	+	2.34045i
$733$	7229.65	−	12522.1i	0.364302	−	0.630989i	−0.624362	−	0.781135i	$-0.714641\pi$
$733$	7229.65	−	12522.1i	0.364302	−	0.630989i	0.988664	+	0.150146i	$0.0479744\pi$
$734$	−3803.28			−0.191255
$735$	−35548.1	+	27455.3i	−1.78396	+	1.37783i
$736$	71.5570			0.00358373
$737$	28021.2	−	48534.2i	1.40051	−	2.42575i
$738$	550.425	+	953.364i	0.0274545	+	0.0475526i
$739$	5263.30	+	9116.30i	0.261994	+	0.453787i	0.966772	−	0.255641i	$-0.0822866\pi$
$739$	5263.30	+	9116.30i	0.261994	+	0.453787i	−0.704778	+	0.709428i	$0.748953\pi$
$740$	−2639.83	+	4572.32i	−0.131138	+	0.227138i
$741$	−31750.0			−1.57404
$742$	−25863.7	+	8825.01i	−1.27963	+	0.436626i
$743$	22130.3			1.09271			0.546355	−	0.837554i	$-0.316015\pi$
$743$	22130.3			1.09271			0.546355	+	0.837554i	$0.316015\pi$
$744$	−7502.33	+	12994.4i	−0.369689	+	0.640320i
$745$	18576.1	+	32174.7i	0.913524	+	1.58227i
$746$	30036.9	+	52025.5i	1.47417	+	2.55333i
$747$	4293.31	−	7436.23i	0.210286	−	0.364227i
$748$	−24033.6			−1.17481
$749$	6031.75	−	30575.2i	0.294253	−	1.49158i
$750$	−74663.1			−3.63508
$751$	−4952.69	+	8578.31i	−0.240647	+	0.416814i	−0.960899	−	0.276900i	$-0.910693\pi$
$751$	−4952.69	+	8578.31i	−0.240647	+	0.416814i	0.720251	+	0.693713i	$0.244026\pi$
$752$	−4286.78	−	7424.92i	−0.207876	−	0.360052i
$753$	10485.2	+	18161.0i	0.507441	+	0.878914i
$754$	−37184.7	+	64405.8i	−1.79600	+	3.11077i
$755$	20775.8			1.00147
$756$	10973.5	+	9592.99i	0.527914	+	0.461500i
$757$	28503.4			1.36853			0.684263	−	0.729235i	$-0.260124\pi$
$757$	28503.4			1.36853			0.684263	+	0.729235i	$0.260124\pi$
$758$	23528.6	−	40752.7i	1.12744	−	1.95278i
$759$	4314.83	+	7473.50i	0.206348	+	0.357406i
$760$	−32570.0	−	56412.8i	−1.55452	−	2.69251i
$761$	−5284.04	+	9152.22i	−0.251703	+	0.435963i	−0.963995	−	0.265921i	$-0.914324\pi$
$761$	−5284.04	+	9152.22i	−0.251703	+	0.435963i	0.712292	+	0.701884i	$0.247657\pi$
$762$	52384.0			2.49039
$763$	11082.2	+	9688.02i	0.525824	+	0.459672i
$764$	−10026.5			−0.474800
$765$	−5200.79	+	9008.04i	−0.245798	+	0.425734i
$766$	31924.6	+	55295.0i	1.50585	+	2.60821i
$767$	4556.02	+	7891.26i	0.214483	+	0.371495i
$768$	−27946.5	+	48404.8i	−1.31307	+	2.27430i
$769$	21117.2			0.990254			0.495127	−	0.868821i	$-0.335122\pi$
$769$	21117.2			0.990254			0.495127	+	0.868821i	$0.335122\pi$
$770$	−18424.0	+	93392.0i	−0.862278	+	4.37093i
$771$	−31855.7			−1.48801
$772$	21130.8	−	36599.7i	0.985124	−	1.70628i
$773$	13028.6	+	22566.2i	0.606218	+	1.05000i	0.991858	+	0.127351i	$0.0406475\pi$
$773$	13028.6	+	22566.2i	0.606218	+	1.05000i	−0.385640	+	0.922649i	$0.626019\pi$
$774$	7526.78	+	13036.8i	0.349541	+	0.605422i
$775$	6797.16	−	11773.0i	0.315047	−	0.545677i
$776$	27303.5			1.26306
$777$	2071.85	−	706.938i	0.0956591	−	0.0326400i
$778$	29007.5			1.33672
$779$	496.172	−	859.395i	0.0228205	−	0.0395264i
$780$	55542.1	+	96201.7i	2.54965	+	4.41612i
$781$	−878.342	−	1521.33i	−0.0402427	−	0.0697024i
$782$	1545.40	−	2676.72i	0.0706695	−	0.122403i
$783$	14095.5			0.643336
$784$	2890.10	+	21430.7i	0.131656	+	0.976253i
$785$	−16338.7			−0.742870
$786$	9886.86	−	17124.5i	0.448668	−	0.777115i
$787$	5988.00	+	10371.5i	0.271219	+	0.469765i	0.969174	−	0.246377i	$-0.0792400\pi$
$787$	5988.00	+	10371.5i	0.271219	+	0.469765i	−0.697955	+	0.716141i	$0.745907\pi$
$788$	14630.9	+	25341.5i	0.661427	+	1.14562i
$789$	−5300.86	+	9181.36i	−0.239183	+	0.414278i
$790$	−103024.			−4.63978
$791$	−3580.66	+	1221.76i	−0.160953	+	0.0549189i
$792$	−42298.6			−1.89775
$793$	−13028.4	+	22565.9i	−0.583421	+	1.01051i
$794$	−13641.6	−	23628.0i	−0.609727	−	1.05608i
$795$	19737.5	+	34186.4i	0.880525	+	1.52511i
$796$	16316.6	−	28261.2i	0.726540	−	1.25840i
$797$	30252.6			1.34455			0.672273	−	0.740303i	$-0.265318\pi$
$797$	30252.6			1.34455			0.672273	+	0.740303i	$0.265318\pi$
$798$	−10481.2	+	53129.8i	−0.464952	+	2.35686i
$799$	3733.40			0.165304
$800$	375.644	−	650.634i	0.0166013	−	0.0287542i
$801$	−64.6494	−	111.976i	−0.00285178	−	0.00493942i
$802$	−36329.4	−	62924.4i	−1.59955	−	2.77049i
$803$	−19715.4	+	34148.0i	−0.866426	+	1.50069i
$804$	−111546.			−4.89295
$805$	−6139.38	−	5367.01i	−0.268801	−	0.234984i
$806$	−14646.3			−0.640066
$807$	−15756.5	+	27291.1i	−0.687306	+	1.19045i
$808$	−35923.3	−	62221.0i	−1.56408	−	2.70907i
$809$	−7338.44	−	12710.6i	−0.318920	−	0.552385i	0.661343	−	0.750083i	$-0.269987\pi$
$809$	−7338.44	−	12710.6i	−0.318920	−	0.552385i	−0.980263	+	0.197698i	$0.936653\pi$
$810$	40840.6	−	70738.0i	1.77160	−	3.06849i
$811$	42627.3			1.84568			0.922839	−	0.385185i	$-0.125862\pi$
$811$	42627.3			1.84568			0.922839	+	0.385185i	$0.125862\pi$
$812$	63613.9	+	55610.9i	2.74927	+	2.40340i
$813$	6827.03			0.294507
$814$	2319.75	−	4017.92i	0.0998859	−	0.173007i
$815$	−12917.3	−	22373.4i	−0.555182	−	0.961604i
$816$	5919.82	+	10253.4i	0.253964	+	0.439879i
$817$	6784.89	−	11751.8i	0.290543	−	0.503235i
$818$	5805.71			0.248157
$819$	3770.61	−	19113.4i	0.160874	−	0.815478i
$820$	−3471.93			−0.147860
$821$	7932.25	−	13739.1i	0.337195	−	0.584039i	−0.646709	−	0.762737i	$-0.723855\pi$
$821$	7932.25	−	13739.1i	0.337195	−	0.584039i	0.983904	+	0.178698i	$0.0571884\pi$
$822$	−45827.8	−	79376.1i	−1.94456	−	3.36808i
$823$	13306.9	+	23048.1i	0.563606	+	0.976194i	0.997178	+	0.0750751i	$0.0239197\pi$
$823$	13306.9	+	23048.1i	0.563606	+	0.976194i	−0.433572	+	0.901119i	$0.642747\pi$
$824$	−11862.7	+	20546.8i	−0.501525	+	0.868667i
$825$	90604.0			3.82355
$826$	14709.1	−	5018.92i	0.619607	−	0.211417i
$827$	−28187.8			−1.18523			−0.592615	−	0.805486i	$-0.701904\pi$
$827$	−28187.8			−1.18523			−0.592615	+	0.805486i	$0.701904\pi$
$828$	3632.54	−	6291.75i	0.152463	−	0.264074i
$829$	18684.4	+	32362.3i	0.782793	+	1.35584i	0.930308	+	0.366778i	$0.119539\pi$
$829$	18684.4	+	32362.3i	0.782793	+	1.35584i	−0.147515	+	0.989060i	$0.547127\pi$
$830$	20327.7	+	35208.5i	0.850100	+	1.47242i
$831$	13537.3	−	23447.3i	0.565106	−	0.978793i
$832$	−27616.7			−1.15077
$833$	−8711.09	−	3576.15i	−0.362331	−	0.148747i
$834$	−76560.0			−3.17873
$835$	−20202.7	+	34992.2i	−0.837299	+	1.45024i
$836$	38224.8	+	66207.2i	1.58138	+	2.73902i
$837$	1387.98	+	2404.05i	0.0573185	+	0.0992786i
$838$	−26972.9	+	46718.4i	−1.11189	+	1.92585i
$839$	−2241.69			−0.0922427			−0.0461213	−	0.998936i	$-0.514686\pi$
$839$	−2241.69			−0.0922427			−0.0461213	+	0.998936i	$0.514686\pi$
$840$	89435.1	−	30516.3i	3.67358	−	1.25347i
$841$	57323.0			2.35036
$842$	16688.4	−	28905.2i	0.683042	−	1.18306i
$843$	−5481.22	−	9493.74i	−0.223942	−	0.387879i
$844$	−11486.6	−	19895.3i	−0.468464	−	0.811404i
$845$	−6010.77	+	10411.0i	−0.244706	+	0.423843i
$846$	13174.2			0.535389
$847$	6013.41	−	30482.3i	0.243947	−	1.23658i
$848$	19005.1			0.769621
$849$	16508.1	−	28592.9i	0.667324	−	1.15584i
$850$	−16225.4	−	28103.3i	−0.654738	−	1.13404i
$851$	198.720	+	344.192i	0.00800472	+	0.0138646i
$852$	−1748.24	+	3028.04i	−0.0702978	+	0.121759i
$853$	−13238.3			−0.531386			−0.265693	−	0.964058i	$-0.585601\pi$
$853$	−13238.3			−0.531386			−0.265693	+	0.964058i	$0.585601\pi$
$854$	33460.4	+	29250.9i	1.34074	+	1.17207i
$855$	33086.8			1.32344
$856$	−32783.2	+	56782.1i	−1.30900	+	2.26726i
$857$	671.451	+	1162.99i	0.0267635	+	0.0463558i	0.879097	−	0.476643i	$-0.158147\pi$
$857$	671.451	+	1162.99i	0.0267635	+	0.0463558i	−0.852333	+	0.522999i	$0.824813\pi$
$858$	−48807.6	−	84537.2i	−1.94203	−	3.36370i
$859$	9392.26	−	16267.9i	0.373061	−	0.646161i	−0.616973	−	0.786984i	$-0.711641\pi$
$859$	9392.26	−	16267.9i	0.373061	−	0.646161i	0.990035	+	0.140823i	$0.0449747\pi$
$860$	−47476.8			−1.88250
$861$	1083.83	+	947.480i	0.0429000	+	0.0375029i
$862$	−32179.8			−1.27152
$863$	−12054.8	+	20879.5i	−0.475493	+	0.823577i	−0.999606	−	0.0280711i	$-0.991064\pi$
$863$	−12054.8	+	20879.5i	−0.475493	+	0.823577i	0.524113	+	0.851649i	$0.324397\pi$
$864$	76.7064	+	132.859i	0.00302038	+	0.00523145i
$865$	26440.6	+	45796.4i	1.03931	+	1.80015i
$866$	26663.0	−	46181.7i	1.04624	−	1.81215i
$867$	28451.4			1.11449
$868$	−3220.65	+	16325.6i	−0.125940	+	0.638396i
$869$	60304.6			2.35408
$870$	91614.9	−	158682.i	3.57016	−	6.18369i
$871$	−27152.5	−	47029.6i	−1.05629	−	1.82955i
$872$	−15484.4	−	26819.7i	−0.601338	−	1.04155i
$873$	−6934.18	+	12010.4i	−0.268828	+	0.465623i
$874$	−9831.67			−0.380505
$875$	−39085.0	+	13336.3i	−1.51007	+	0.515255i
$876$	78482.4			3.02702
$877$	−512.984	+	888.514i	−0.0197517	+	0.0342109i	−0.875732	−	0.482797i	$-0.839621\pi$
$877$	−512.984	+	888.514i	−0.0197517	+	0.0342109i	0.855981	+	0.517008i	$0.172954\pi$
$878$	21934.4	+	37991.4i	0.843108	+	1.46031i
$879$	−28473.8	−	49318.1i	−1.09260	−	1.89244i
$880$	33100.5	−	57331.7i	1.26797	−	2.19620i
$881$	−29534.1			−1.12943			−0.564715	−	0.825286i	$-0.691014\pi$
$881$	−29534.1			−1.12943			−0.564715	+	0.825286i	$0.691014\pi$
$882$	−30739.3	−	12619.3i	−1.17352	−	0.481764i
$883$	−10448.5			−0.398210			−0.199105	−	0.979978i	$-0.563803\pi$
$883$	−10448.5			−0.398210			−0.199105	+	0.979978i	$0.563803\pi$
$884$	−11644.3	+	20168.5i	−0.443032	+	0.767353i
$885$	−11225.0	−	19442.3i	−0.426356	−	0.738471i
$886$	−25866.9	−	44802.8i	−0.980830	−	1.69885i
$887$	3006.62	−	5207.61i	0.113813	−	0.197130i	−0.803492	−	0.595316i	$-0.797027\pi$
$887$	3006.62	−	5207.61i	0.113813	−	0.197130i	0.917305	+	0.398186i	$0.130360\pi$
$888$	−4605.68			−0.174050
$889$	27422.3	−	9356.80i	1.03455	−	0.353000i
$890$	612.195			0.0230571
$891$	−23905.9	+	41406.2i	−0.898851	+	1.55686i
$892$	39366.3	+	68184.4i	1.47767	+	2.55940i
$893$	−5937.85	−	10284.7i	−0.222511	−	0.385401i
$894$	−32490.5	+	56275.3i	−1.21549	+	2.10529i
$895$	−73096.7			−2.73000
$896$	−9027.55	+	45761.0i	−0.336595	+	1.70622i
$897$	8362.13			0.311264
$898$	−1221.66	+	2115.97i	−0.0453978	+	0.0786313i
$899$	8046.16	+	13936.4i	0.298503	+	0.517023i
$900$	−38138.6	−	66058.0i	−1.41254	−	2.44659i
$901$	−4137.93	+	7167.11i	−0.153002	+	0.265007i
$902$	3050.96			0.112623
$903$	14820.8	+	12956.3i	0.546187	+	0.477473i
$904$	7959.73			0.292850
$905$	−24760.3	+	42886.1i	−0.909459	+	1.57523i
$906$	18168.9	+	31469.5i	0.666250	+	1.15398i
$907$	2407.19	+	4169.37i	0.0881249	+	0.152637i	0.906719	−	0.421736i	$-0.138579\pi$
$907$	2407.19	+	4169.37i	0.0881249	+	0.152637i	−0.818594	+	0.574373i	$0.805246\pi$
$908$	36893.5	−	63901.4i	1.34841	−	2.33551i
$909$	36493.3			1.33158
$910$	69446.1	+	60709.4i	2.52980	+	2.21154i
$911$	−30090.6			−1.09434			−0.547171	−	0.837021i	$-0.684295\pi$
$911$	−30090.6			−1.09434			−0.547171	+	0.837021i	$0.684295\pi$
$912$	18830.6	−	32615.5i	0.683709	−	1.18422i
$913$	−11898.7	−	20609.2i	−0.431314	−	0.747058i
$914$	−15550.5	−	26934.2i	−0.562761	−	0.974731i
$915$	32099.1	−	55597.3i	1.15974	−	2.00873i
$916$	−24557.1			−0.885795
$917$	2116.85	−	10730.4i	0.0762319	−	0.386423i
$918$	6626.46			0.238242
$919$	10289.7	−	17822.2i	0.369342	−	0.639719i	−0.620121	−	0.784506i	$-0.712917\pi$
$919$	10289.7	−	17822.2i	0.369342	−	0.639719i	0.989463	+	0.144787i	$0.0462498\pi$
$920$	8578.10	+	14857.7i	0.307404	+	0.532439i
$921$	4253.50	+	7367.29i	0.152180	+	0.263583i
$922$	3827.78	−	6629.91i	0.136726	−	0.236816i
$923$	−1702.23			−0.0607036
$924$	−104963.	+	35814.5i	−3.73704	+	1.27512i
$925$	4172.77			0.148324
$926$	34609.4	−	59945.3i	1.22823	−	2.12735i
$927$	−6025.47	−	10436.4i	−0.213487	−	0.369770i
$928$	444.670	+	770.190i	0.0157295	+	0.0272443i
$929$	−520.581	+	901.673i	−0.0183850	+	0.0318438i	−0.875072	−	0.483994i	$-0.839186\pi$
$929$	−520.581	+	901.673i	−0.0183850	+	0.0318438i	0.856687	+	0.515837i	$0.172519\pi$
$930$	36085.2			1.27234
$931$	4003.24	+	29684.8i	0.140925	+	1.04499i
$932$	−21366.6			−0.750952
$933$	−19897.5	+	34463.4i	−0.698193	+	1.20931i
$934$	13686.1	+	23705.0i	0.479468	+	0.830463i
$935$	14413.8	+	24965.4i	0.504150	+	0.873214i
$936$	−20493.6	+	35496.0i	−0.715658	+	1.23956i
$937$	30155.5			1.05137			0.525686	−	0.850678i	$-0.323809\pi$
$937$	30155.5			1.05137			0.525686	+	0.850678i	$0.323809\pi$
$938$	−87662.0	+	29911.3i	−3.05146	+	1.04119i
$939$	20508.6			0.712750
$940$	−20774.8	+	35983.1i	−0.720852	+	1.24855i
$941$	−8860.49	−	15346.8i	−0.306954	−	0.531660i	0.670740	−	0.741692i	$-0.265976\pi$
$941$	−8860.49	−	15346.8i	−0.306954	−	0.531660i	−0.977694	+	0.210032i	$0.932643\pi$
$942$	−14288.6	−	24748.6i	−0.494212	−	0.856000i
$943$	−130.679	+	226.343i	−0.00451272	+	0.00781626i
$944$	−10808.5			−0.372656
$945$	3383.71	−	17152.2i	0.116478	−	0.590434i
$946$	41720.2			1.43387
$947$	19866.3	−	34409.4i	0.681697	−	1.18073i	−0.292765	−	0.956184i	$-0.594575\pi$
$947$	19866.3	−	34409.4i	0.681697	−	1.18073i	0.974463	−	0.224550i	$-0.0720912\pi$
$948$	−60014.8	−	103949.i	−2.05611	−	3.56128i
$949$	19104.2	+	33089.4i	0.653475	+	1.13185i
$950$	−51612.0	+	89394.7i	−1.76265	+	3.05300i
$951$	18580.7			0.633567
$952$	14915.5	+	13039.1i	0.507788	+	0.443906i
$953$	−44870.2			−1.52517			−0.762585	−	0.646888i	$-0.776070\pi$
$953$	−44870.2			−1.52517			−0.762585	+	0.646888i	$0.776070\pi$
$954$	−14601.7	+	25290.9i	−0.495544	+	0.858307i
$955$	6013.23	+	10415.2i	0.203752	+	0.352910i
$956$	−1865.31	−	3230.82i	−0.0631051	−	0.109301i
$957$	−53626.4	+	92883.6i	−1.81138	+	3.13741i
$958$	−50179.5			−1.69230
$959$	−38168.3	−	33366.5i	−1.28521	−	1.12352i
$960$	68041.4			2.28753
$961$	13310.9	−	23055.1i	0.446809	−	0.773896i
$962$	−2247.83	−	3893.36i	−0.0753359	−	0.130486i
$963$	−16651.7	−	28841.6i	−0.557210	−	0.965116i
$964$	−9261.19	+	16040.9i	−0.309422	+	0.535935i
$965$	−50691.4			−1.69100
$966$	2760.49	−	13993.0i	0.0919433	−	0.466065i
$967$	−29153.1			−0.969493			−0.484746	−	0.874655i	$-0.661088\pi$
$967$	−29153.1			−0.969493			−0.484746	+	0.874655i	$0.661088\pi$
$968$	−32683.5	+	56609.5i	−1.08521	+	1.87965i
$969$	8199.85	+	14202.6i	0.271844	+	0.470848i
$970$	−32831.5	−	56865.8i	−1.08676	−	1.88232i
$971$	−29569.1	+	51215.2i	−0.977259	+	1.69266i	−0.304991	+	0.952355i	$0.598653\pi$
$971$	−29569.1	+	51215.2i	−0.977259	+	1.69266i	−0.672268	+	0.740307i	$0.734680\pi$
$972$	73914.8			2.43912
$973$	−40078.1	+	13675.1i	−1.32050	+	0.450569i
$974$	−23371.1			−0.768849
$975$	43897.6	−	76032.9i	1.44190	−	2.49744i
$976$	−15454.0	−	26767.1i	−0.506835	−	0.877864i
$977$	11143.1	+	19300.5i	0.364893	+	0.632013i	0.988759	−	0.149518i	$-0.0477722\pi$
$977$	11143.1	+	19300.5i	0.364893	+	0.632013i	−0.623866	+	0.781531i	$0.714439\pi$
$978$	22593.0	−	39132.3i	0.738696	−	1.27946i
$979$	−358.346			−0.0116984
$980$	82941.3	−	64059.1i	2.70353	−	2.08806i
$981$	15730.1			0.511950
$982$	−534.941	+	926.544i	−0.0173835	+	0.0301092i
$983$	8555.76	+	14819.0i	0.277606	+	0.480827i	0.970789	−	0.239934i	$-0.0771258\pi$
$983$	8555.76	+	14819.0i	0.277606	+	0.480827i	−0.693183	+	0.720761i	$0.743792\pi$
$984$	−1514.36	−	2622.94i	−0.0490609	−	0.0849760i
$985$	17549.3	−	30396.2i	0.567681	−	0.983252i
$986$	38413.8			1.24071
$987$	16305.0	−	5563.44i	0.525828	−	0.179419i
$988$	74079.6			2.38541
$989$	−1786.97	+	3095.12i	−0.0574543	+	0.0995137i
$990$	50862.6	+	88096.6i	1.63285	+	2.82817i
$991$	12757.7	+	22096.9i	0.408941	+	0.708307i	0.994771	−	0.102127i	$-0.0325648\pi$
$991$	12757.7	+	22096.9i	0.408941	+	0.708307i	−0.585830	+	0.810434i	$0.699231\pi$
$992$	−87.5730	+	151.681i	−0.00280287	+	0.00485471i
$993$	2484.91			0.0794120
$994$	−561.935	+	2848.47i	−0.0179311	+	0.0908935i
$995$	−39142.4			−1.24713
$996$	−23683.0	+	41020.2i	−0.753440	+	1.30500i
$997$	−674.943	−	1169.04i	−0.0214400	−	0.0371352i	0.855106	−	0.518453i	$-0.173492\pi$
$997$	−674.943	−	1169.04i	−0.0214400	−	0.0371352i	−0.876546	+	0.481317i	$0.840158\pi$
$998$	−41745.2	−	72304.9i	−1.32407	−	2.29336i
$999$	−426.040	+	737.923i	−0.0134928	+	0.0233702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.e.a.93.3	✓	44
7.2	even	3		1127.4.a.l.1.20		22
7.4	even	3	inner	161.4.e.a.116.3	yes	44
7.5	odd	6		1127.4.a.k.1.20		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.e.a.93.3	✓	44	1.1	even	1	trivial
161.4.e.a.116.3	yes	44	7.4	even	3	inner
1127.4.a.k.1.20		22	7.5	odd	6
1127.4.a.l.1.20		22	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.44746 + 4.23912i) q^{2} +(3.42021 + 5.92398i) q^{3} +(-7.98009 - 13.8219i) q^{4} +(-9.57184 + 16.5789i) q^{5} -33.4833 q^{6} +(-17.5280 + 5.98075i) q^{7} +38.9644 q^{8} +(-9.89567 + 17.1398i) q^{9} +(-46.8533 - 81.1523i) q^{10} +(27.4254 + 47.5022i) q^{11} +(54.5872 - 94.5477i) q^{12} +53.1504 q^{13} +(17.5459 - 88.9409i) q^{14} -130.951 q^{15} +(-31.5229 + 54.5993i) q^{16} +(-13.7268 - 23.7755i) q^{17} +(-48.4384 - 83.8978i) q^{18} +(-43.6641 + 75.6284i) q^{19} +305.536 q^{20} +(-95.3793 - 83.3800i) q^{21} -268.490 q^{22} +(11.5000 - 19.9186i) q^{23} +(133.266 + 230.824i) q^{24} +(-120.740 - 209.128i) q^{25} +(-130.083 + 225.311i) q^{26} +49.3103 q^{27} +(222.540 + 194.544i) q^{28} +285.853 q^{29} +(320.496 - 555.116i) q^{30} +(28.1479 + 48.7536i) q^{31} +(1.55559 + 2.69436i) q^{32} +(-187.601 + 324.935i) q^{33} +134.383 q^{34} +(68.6208 - 347.842i) q^{35} +315.873 q^{36} +(-8.63998 + 14.9649i) q^{37} +(-213.732 - 370.194i) q^{38} +(181.785 + 314.862i) q^{39} +(-372.961 + 645.987i) q^{40} -11.3634 q^{41} +(586.894 - 200.255i) q^{42} -155.388 q^{43} +(437.714 - 758.143i) q^{44} +(-189.440 - 328.119i) q^{45} +(56.2915 + 97.4997i) q^{46} +(-67.9947 + 117.770i) q^{47} -431.260 q^{48} +(271.461 - 209.661i) q^{49} +1182.03 q^{50} +(93.8970 - 162.634i) q^{51} +(-424.145 - 734.640i) q^{52} +(-150.725 - 261.063i) q^{53} +(-120.685 + 209.032i) q^{54} -1050.05 q^{55} +(-682.967 + 233.036i) q^{56} -597.361 q^{57} +(-699.613 + 1211.77i) q^{58} +(85.7195 + 148.470i) q^{59} +(1045.00 + 1809.99i) q^{60} +(-245.124 + 424.567i) q^{61} -275.563 q^{62} +(70.9423 - 359.610i) q^{63} -519.595 q^{64} +(-508.747 + 881.175i) q^{65} +(-918.292 - 1590.53i) q^{66} +(-510.862 - 884.840i) q^{67} +(-219.082 + 379.461i) q^{68} +157.330 q^{69} +(1306.60 + 1142.22i) q^{70} -32.0266 q^{71} +(-385.579 + 667.842i) q^{72} +(359.436 + 622.562i) q^{73} +(-42.2920 - 73.2518i) q^{74} +(825.913 - 1430.52i) q^{75} +1393.77 q^{76} +(-764.811 - 668.593i) q^{77} -1779.65 q^{78} +(549.715 - 952.135i) q^{79} +(-603.464 - 1045.23i) q^{80} +(435.835 + 754.888i) q^{81} +(27.8114 - 48.1708i) q^{82} -433.857 q^{83} +(-391.337 + 1983.70i) q^{84} +525.563 q^{85} +(380.307 - 658.710i) q^{86} +(977.678 + 1693.39i) q^{87} +(1068.61 + 1850.89i) q^{88} +(-3.26655 + 5.65783i) q^{89} +1854.58 q^{90} +(-931.620 + 317.879i) q^{91} -367.084 q^{92} +(-192.543 + 333.495i) q^{93} +(-332.828 - 576.475i) q^{94} +(-835.891 - 1447.81i) q^{95} +(-10.6409 + 18.4305i) q^{96} +700.729 q^{97} +(224.389 + 1663.89i) q^{98} -1085.57 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{3} - 88 q^{4} - 20 q^{5} + 24 q^{6} - 12 q^{7} + 42 q^{8} - 238 q^{9} - 182 q^{10} + 28 q^{11} - 127 q^{12} + 440 q^{13} + 16 q^{14} + 40 q^{15} - 436 q^{16} - 294 q^{17} + 155 q^{18} - 252 q^{19}+ \cdots - 5764 q^{99}+O(q^{100}) \) 44 * q - 6 * q^3 - 88 * q^4 - 20 * q^5 + 24 * q^6 - 12 * q^7 + 42 * q^8 - 238 * q^9 - 182 * q^10 + 28 * q^11 - 127 * q^12 + 440 * q^13 + 16 * q^14 + 40 * q^15 - 436 * q^16 - 294 * q^17 + 155 * q^18 - 252 * q^19 + 708 * q^20 + 110 * q^21 + 28 * q^22 + 506 * q^23 - 458 * q^24 - 684 * q^25 - 396 * q^26 + 972 * q^27 - 354 * q^28 + 628 * q^29 + 905 * q^30 - 172 * q^31 + 127 * q^32 - 1524 * q^33 + 800 * q^34 - 1588 * q^35 + 2644 * q^36 + 710 * q^37 + 323 * q^38 + 136 * q^39 - 1808 * q^40 + 784 * q^41 - 2775 * q^42 + 504 * q^43 + 1106 * q^44 - 658 * q^45 - 448 * q^47 + 2730 * q^48 - 570 * q^49 + 738 * q^50 + 896 * q^51 - 1224 * q^52 - 308 * q^53 - 945 * q^54 + 4324 * q^55 - 481 * q^56 - 124 * q^57 + 1153 * q^58 + 282 * q^59 - 4442 * q^60 - 3076 * q^61 + 3500 * q^62 - 732 * q^63 - 4354 * q^64 + 1024 * q^65 + 549 * q^66 - 1056 * q^67 - 2478 * q^68 - 276 * q^69 + 2071 * q^70 - 96 * q^71 + 1922 * q^72 - 4430 * q^73 - 3322 * q^74 - 2540 * q^75 + 15026 * q^76 - 1116 * q^77 - 3990 * q^78 + 530 * q^79 - 296 * q^80 - 3446 * q^81 - 1570 * q^82 + 3572 * q^83 - 4571 * q^84 - 2624 * q^85 + 397 * q^86 + 1724 * q^87 - 5375 * q^88 - 658 * q^89 + 13620 * q^90 - 1098 * q^91 - 4048 * q^92 + 1722 * q^93 + 1944 * q^94 - 1742 * q^95 - 1142 * q^96 + 21364 * q^97 + 2001 * q^98 - 5764 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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