LMFDB - Embedded newform 143.4.q.a.48.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(3,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 10]))

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

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

chi := DirichletCharacter("143.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.q (of order $15$, degree $8$, 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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			48.18
Character	$\chi$	$=$	143.48
Dual form			143.4.q.a.3.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.868356 + 0.386617i) q^{2} +(2.30554 + 2.56056i) q^{3} +(-4.74848 + 5.27372i) q^{4} +(13.8209 - 10.0415i) q^{5} +(-2.99199 - 1.33212i) q^{6} +(9.48972 - 10.5394i) q^{7} +(4.43431 - 13.6474i) q^{8} +(1.58131 - 15.0451i) q^{9} +O(q^{10})$	\(q+(-0.868356 + 0.386617i) q^{2} +(2.30554 + 2.56056i) q^{3} +(-4.74848 + 5.27372i) q^{4} +(13.8209 - 10.0415i) q^{5} +(-2.99199 - 1.33212i) q^{6} +(9.48972 - 10.5394i) q^{7} +(4.43431 - 13.6474i) q^{8} +(1.58131 - 15.0451i) q^{9} +(-8.11928 + 14.0630i) q^{10} +(-25.2403 - 26.3425i) q^{11} -24.4515 q^{12} +(29.5165 + 36.4112i) q^{13} +(-4.16575 + 12.8208i) q^{14} +(57.5766 + 12.2383i) q^{15} +(-4.50852 - 42.8957i) q^{16} +(51.8537 + 23.0867i) q^{17} +(4.44357 + 13.6759i) q^{18} +(88.6267 - 18.8382i) q^{19} +(-12.6724 + 120.569i) q^{20} +48.8657 q^{21} +(32.1020 + 13.1164i) q^{22} +(-39.3337 + 68.1280i) q^{23} +(45.1685 - 20.1103i) q^{24} +(51.5595 - 158.684i) q^{25} +(-39.7080 - 20.2063i) q^{26} +(117.433 - 85.3201i) q^{27} +(10.5201 + 100.092i) q^{28} +(-226.658 - 48.1776i) q^{29} +(-54.7285 + 11.6329i) q^{30} +(157.454 + 114.397i) q^{31} +(77.8981 + 134.923i) q^{32} +(9.25921 - 125.363i) q^{33} -53.9532 q^{34} +(25.3254 - 240.955i) q^{35} +(71.8350 + 79.7808i) q^{36} +(312.174 + 66.3546i) q^{37} +(-69.6763 + 50.6228i) q^{38} +(-25.1817 + 159.526i) q^{39} +(-75.7540 - 233.147i) q^{40} +(-222.722 - 247.358i) q^{41} +(-42.4329 + 18.8923i) q^{42} +(-109.166 - 189.080i) q^{43} +(258.776 - 8.02319i) q^{44} +(-129.221 - 223.817i) q^{45} +(7.81623 - 74.3664i) q^{46} +(-187.739 + 577.800i) q^{47} +(99.4425 - 110.442i) q^{48} +(14.8291 + 141.089i) q^{49} +(16.5779 + 157.728i) q^{50} +(60.4357 + 186.002i) q^{51} +(-332.181 - 17.2362i) q^{52} +(147.007 + 106.807i) q^{53} +(-68.9875 + 119.490i) q^{54} +(-613.363 - 110.628i) q^{55} +(-101.755 - 176.245i) q^{56} +(252.569 + 183.502i) q^{57} +(215.446 - 45.7945i) q^{58} +(365.073 - 405.454i) q^{59} +(-337.942 + 245.529i) q^{60} +(-421.985 - 187.880i) q^{61} +(-180.954 - 38.4630i) q^{62} +(-143.561 - 159.440i) q^{63} +(159.349 + 115.774i) q^{64} +(773.569 + 206.847i) q^{65} +(40.4272 + 112.440i) q^{66} +(-268.915 + 465.774i) q^{67} +(-367.979 + 163.835i) q^{68} +(-265.131 + 56.3554i) q^{69} +(71.1660 + 219.026i) q^{70} +(-648.639 - 288.793i) q^{71} +(-198.315 - 88.2955i) q^{72} +(-191.613 - 589.724i) q^{73} +(-296.732 + 63.0723i) q^{74} +(525.192 - 233.831i) q^{75} +(-321.494 + 556.844i) q^{76} +(-517.158 + 16.0342i) q^{77} +(-39.8089 - 148.261i) q^{78} +(-223.524 - 162.400i) q^{79} +(-493.049 - 547.586i) q^{80} +(89.6835 + 19.0628i) q^{81} +(289.035 + 128.687i) q^{82} +(-1108.99 + 805.728i) q^{83} +(-232.038 + 257.704i) q^{84} +(948.492 - 201.608i) q^{85} +(167.896 + 121.984i) q^{86} +(-399.207 - 691.447i) q^{87} +(-471.430 + 227.653i) q^{88} +(779.964 - 1350.94i) q^{89} +(198.741 + 144.394i) q^{90} +(663.856 + 34.4461i) q^{91} +(-172.512 - 530.939i) q^{92} +(70.0959 + 666.918i) q^{93} +(-60.3634 - 574.319i) q^{94} +(1035.74 - 1150.31i) q^{95} +(-165.883 + 510.534i) q^{96} +(-37.7502 + 359.169i) q^{97} +(-67.4243 - 116.782i) q^{98} +(-436.240 + 338.088i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9}+O(q^{10}) $ 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9	\( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9} - 80 q^{10} + 30 q^{11} - 220 q^{12} - 114 q^{13} + 4 q^{14} - 33 q^{15} + 637 q^{16} + 143 q^{17} + 72 q^{18} + 17 q^{19} - 377 q^{20} - 524 q^{21} + 283 q^{22} + 196 q^{23} - 1137 q^{24} - 1324 q^{25} + 632 q^{26} + 192 q^{27} - 279 q^{28} + 943 q^{29} + 1617 q^{30} + 260 q^{31} - 52 q^{32} - 1244 q^{33} - 3508 q^{34} + 1253 q^{35} + 282 q^{36} + 333 q^{37} - 694 q^{38} - 1106 q^{39} - 296 q^{40} - 1751 q^{41} - 895 q^{42} - 2200 q^{43} - 252 q^{44} - 282 q^{45} + 485 q^{46} + 2116 q^{47} - 825 q^{48} + 1607 q^{49} + 348 q^{50} + 1768 q^{51} - 2431 q^{52} + 428 q^{53} + 8326 q^{54} - 1379 q^{55} + 7630 q^{56} - 888 q^{57} - 331 q^{58} - 1097 q^{59} - 1820 q^{60} + 885 q^{61} - 437 q^{62} + 540 q^{63} + 1148 q^{64} + 2324 q^{65} - 1686 q^{66} - 5184 q^{67} + 3834 q^{68} - 4905 q^{69} + 4078 q^{70} + 843 q^{71} + 1155 q^{72} - 972 q^{73} + 5631 q^{74} - 3431 q^{75} - 3090 q^{76} + 602 q^{77} + 1252 q^{78} + 1140 q^{79} + 8631 q^{80} - 3809 q^{81} + 4015 q^{82} - 5292 q^{83} - 5060 q^{84} + 391 q^{85} + 3388 q^{86} - 7600 q^{87} - 7229 q^{88} + 6276 q^{89} + 7374 q^{90} - 4602 q^{91} + 8158 q^{92} - 2599 q^{93} + 11081 q^{94} + 2305 q^{95} - 30114 q^{96} + 1377 q^{97} + 5102 q^{98} - 5812 q^{99}+O(q^{100}) \) 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9 - 80 * q^10 + 30 * q^11 - 220 * q^12 - 114 * q^13 + 4 * q^14 - 33 * q^15 + 637 * q^16 + 143 * q^17 + 72 * q^18 + 17 * q^19 - 377 * q^20 - 524 * q^21 + 283 * q^22 + 196 * q^23 - 1137 * q^24 - 1324 * q^25 + 632 * q^26 + 192 * q^27 - 279 * q^28 + 943 * q^29 + 1617 * q^30 + 260 * q^31 - 52 * q^32 - 1244 * q^33 - 3508 * q^34 + 1253 * q^35 + 282 * q^36 + 333 * q^37 - 694 * q^38 - 1106 * q^39 - 296 * q^40 - 1751 * q^41 - 895 * q^42 - 2200 * q^43 - 252 * q^44 - 282 * q^45 + 485 * q^46 + 2116 * q^47 - 825 * q^48 + 1607 * q^49 + 348 * q^50 + 1768 * q^51 - 2431 * q^52 + 428 * q^53 + 8326 * q^54 - 1379 * q^55 + 7630 * q^56 - 888 * q^57 - 331 * q^58 - 1097 * q^59 - 1820 * q^60 + 885 * q^61 - 437 * q^62 + 540 * q^63 + 1148 * q^64 + 2324 * q^65 - 1686 * q^66 - 5184 * q^67 + 3834 * q^68 - 4905 * q^69 + 4078 * q^70 + 843 * q^71 + 1155 * q^72 - 972 * q^73 + 5631 * q^74 - 3431 * q^75 - 3090 * q^76 + 602 * q^77 + 1252 * q^78 + 1140 * q^79 + 8631 * q^80 - 3809 * q^81 + 4015 * q^82 - 5292 * q^83 - 5060 * q^84 + 391 * q^85 + 3388 * q^86 - 7600 * q^87 - 7229 * q^88 + 6276 * q^89 + 7374 * q^90 - 4602 * q^91 + 8158 * q^92 - 2599 * q^93 + 11081 * q^94 + 2305 * q^95 - 30114 * q^96 + 1377 * q^97 + 5102 * q^98 - 5812 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.868356	+	0.386617i	−0.307010	+	0.136690i	−0.554459	−	0.832211i	$-0.687075\pi$
$2$	−0.868356	+	0.386617i	−0.307010	+	0.136690i	0.247448	+	0.968901i	$0.420408\pi$
$3$	2.30554	+	2.56056i	0.443701	+	0.492780i	0.922961	−	0.384893i	$-0.125762\pi$
$3$	2.30554	+	2.56056i	0.443701	+	0.492780i	−0.479260	+	0.877673i	$0.659095\pi$
$4$	−4.74848	+	5.27372i	−0.593559	+	0.659214i
$5$	13.8209	−	10.0415i	1.23618	−	0.898139i	0.238844	−	0.971058i	$-0.423231\pi$
$5$	13.8209	−	10.0415i	1.23618	−	0.898139i	0.997338	+	0.0729190i	$0.0232314\pi$
$6$	−2.99199	−	1.33212i	−0.203579	−	0.0906392i
$7$	9.48972	−	10.5394i	0.512397	−	0.569074i	−0.430317	−	0.902678i	$-0.641598\pi$
$7$	9.48972	−	10.5394i	0.512397	−	0.569074i	0.942713	+	0.333604i	$0.108265\pi$
$8$	4.43431	−	13.6474i	0.195971	−	0.603136i
$9$	1.58131	−	15.0451i	0.0585669	−	0.557227i
$10$	−8.11928	+	14.0630i	−0.256754	+	0.444711i
$11$	−25.2403	−	26.3425i	−0.691839	−	0.722052i
$11$	−25.2403	−	26.3425i	−0.691839	−	0.722052i
$12$	−24.4515			−0.588211
$13$	29.5165	+	36.4112i	0.629723	+	0.776820i
$13$	29.5165	+	36.4112i	0.629723	+	0.776820i
$14$	−4.16575	+	12.8208i	−0.0795244	+	0.244751i
$15$	57.5766	+	12.2383i	0.991081	+	0.210661i
$16$	−4.50852	−	42.8957i	−0.0704456	−	0.670245i
$17$	51.8537	+	23.0867i	0.739786	+	0.329374i	0.741797	−	0.670624i	$-0.233974\pi$
$17$	51.8537	+	23.0867i	0.739786	+	0.329374i	−0.00201149	+	0.999998i	$0.500640\pi$
$18$	4.44357	+	13.6759i	0.0581866	+	0.179080i
$19$	88.6267	−	18.8382i	1.07012	−	0.227462i	0.361014	−	0.932560i	$-0.382431\pi$
$19$	88.6267	−	18.8382i	1.07012	−	0.227462i	0.709109	+	0.705099i	$0.249097\pi$
$20$	−12.6724	+	120.569i	−0.141681	+	1.34801i
$21$	48.8657			0.507780
$22$	32.1020	+	13.1164i	0.311099	+	0.127110i
$23$	−39.3337	+	68.1280i	−0.356593	+	0.617638i	−0.987389	−	0.158311i	$-0.949395\pi$
$23$	−39.3337	+	68.1280i	−0.356593	+	0.617638i	0.630796	+	0.775949i	$0.282728\pi$
$24$	45.1685	−	20.1103i	0.384166	−	0.171042i
$25$	51.5595	−	158.684i	0.412476	−	1.26947i
$26$	−39.7080	−	20.2063i	−0.299515	−	0.152415i
$27$	117.433	−	85.3201i	0.837037	−	0.608143i
$28$	10.5201	+	100.092i	0.0710041	+	0.675559i
$29$	−226.658	−	48.1776i	−1.45136	−	0.308495i	−0.586269	−	0.810117i	$-0.699404\pi$
$29$	−226.658	−	48.1776i	−1.45136	−	0.308495i	−0.865087	+	0.501622i	$0.832737\pi$
$30$	−54.7285	+	11.6329i	−0.333067	+	0.0707956i
$31$	157.454	+	114.397i	0.912245	+	0.662785i	0.941582	−	0.336785i	$-0.109339\pi$
$31$	157.454	+	114.397i	0.912245	+	0.662785i	−0.0293367	+	0.999570i	$0.509339\pi$
$32$	77.8981	+	134.923i	0.430330	+	0.745354i
$33$	9.25921	−	125.363i	0.0488431	−	0.661300i
$34$	−53.9532			−0.272144
$35$	25.3254	−	240.955i	0.122308	−	1.16368i
$36$	71.8350	+	79.7808i	0.332569	+	0.369356i
$37$	312.174	+	66.3546i	1.38706	+	0.294828i	0.840145	−	0.542362i	$-0.182470\pi$
$37$	312.174	+	66.3546i	1.38706	+	0.294828i	0.546912	+	0.837190i	$0.315803\pi$
$38$	−69.6763	+	50.6228i	−0.297447	+	0.216108i
$39$	−25.1817	+	159.526i	−0.103392	+	0.654991i
$40$	−75.7540	−	233.147i	−0.299444	−	0.921594i
$41$	−222.722	−	247.358i	−0.848375	−	0.942215i	0.150549	−	0.988603i	$-0.451896\pi$
$41$	−222.722	−	247.358i	−0.848375	−	0.942215i	−0.998924	+	0.0463871i	$0.985229\pi$
$42$	−42.4329	+	18.8923i	−0.155894	+	0.0694083i
$43$	−109.166	−	189.080i	−0.387154	−	0.670570i	0.604912	−	0.796292i	$-0.293208\pi$
$43$	−109.166	−	189.080i	−0.387154	−	0.670570i	−0.992065	+	0.125723i	$0.959875\pi$
$44$	258.776	−	8.02319i	0.886635	−	0.0274896i
$45$	−129.221	−	223.817i	−0.428068	−	0.741436i
$46$	7.81623	−	74.3664i	0.0250530	−	0.238364i
$47$	−187.739	+	577.800i	−0.582649	+	1.79321i	0.0258646	+	0.999665i	$0.491766\pi$
$47$	−187.739	+	577.800i	−0.582649	+	1.79321i	−0.608513	+	0.793544i	$0.708234\pi$
$48$	99.4425	−	110.442i	0.299027	−	0.332103i
$49$	14.8291	+	141.089i	0.0432334	+	0.411338i
$50$	16.5779	+	157.728i	0.0468893	+	0.446122i
$51$	60.4357	+	186.002i	0.165935	+	0.510696i
$52$	−332.181	−	17.2362i	−0.885869	−	0.0459659i
$53$	147.007	+	106.807i	0.380999	+	0.276812i	0.761757	−	0.647862i	$-0.224337\pi$
$53$	147.007	+	106.807i	0.380999	+	0.276812i	−0.380758	+	0.924675i	$0.624337\pi$
$54$	−68.9875	+	119.490i	−0.173852	+	0.301121i
$55$	−613.363	−	110.628i	−1.50374	−	0.271220i
$56$	−101.755	−	176.245i	−0.242814	−	0.420567i
$57$	252.569	+	183.502i	0.586904	+	0.426411i
$58$	215.446	−	45.7945i	0.487749	−	0.103674i
$59$	365.073	−	405.454i	0.805567	−	0.894672i	−0.190643	−	0.981659i	$-0.561057\pi$
$59$	365.073	−	405.454i	0.805567	−	0.894672i	0.996209	+	0.0869871i	$0.0277239\pi$
$60$	−337.942	+	245.529i	−0.727136	+	0.528295i
$61$	−421.985	−	187.880i	−0.885732	−	0.394353i	−0.0871188	−	0.996198i	$-0.527766\pi$
$61$	−421.985	−	187.880i	−0.885732	−	0.394353i	−0.798613	+	0.601845i	$0.794433\pi$
$62$	−180.954	−	38.4630i	−0.370664	−	0.0787872i
$63$	−143.561	−	159.440i	−0.287094	−	0.318850i
$64$	159.349	+	115.774i	0.311228	+	0.226121i
$65$	773.569	+	206.847i	1.47614	+	0.394712i
$66$	40.4272	+	112.440i	0.0753976	+	0.209702i
$67$	−268.915	+	465.774i	−0.490346	+	0.849304i	−0.999938	−	0.0111118i	$-0.996463\pi$
$67$	−268.915	+	465.774i	−0.490346	+	0.849304i	0.509592	+	0.860416i	$0.329796\pi$
$68$	−367.979	+	163.835i	−0.656235	+	0.292175i
$69$	−265.131	+	56.3554i	−0.462581	+	0.0983245i
$70$	71.1660	+	219.026i	0.121514	+	0.373981i
$71$	−648.639	−	288.793i	−1.08421	−	0.482724i	−0.214725	−	0.976675i	$-0.568886\pi$
$71$	−648.639	−	288.793i	−1.08421	−	0.482724i	−0.869490	+	0.493951i	$0.835552\pi$
$72$	−198.315	−	88.2955i	−0.324606	−	0.144524i
$73$	−191.613	−	589.724i	−0.307214	−	0.945506i	−0.978842	−	0.204618i	$-0.934405\pi$
$73$	−191.613	−	589.724i	−0.307214	−	0.945506i	0.671628	−	0.740888i	$-0.265595\pi$
$74$	−296.732	+	63.0723i	−0.466141	+	0.0990812i
$75$	525.192	−	233.831i	0.808586	−	0.360006i
$76$	−321.494	+	556.844i	−0.485236	+	0.840453i
$77$	−517.158	+	16.0342i	−0.765397	+	0.0237307i
$78$	−39.8089	−	148.261i	−0.0577881	−	0.215222i
$79$	−223.524	−	162.400i	−0.318334	−	0.231283i	0.417130	−	0.908847i	$-0.363036\pi$
$79$	−223.524	−	162.400i	−0.318334	−	0.231283i	−0.735464	+	0.677563i	$0.763036\pi$
$80$	−493.049	−	547.586i	−0.689057	−	0.765275i
$81$	89.6835	+	19.0628i	0.123023	+	0.0261493i
$82$	289.035	+	128.687i	0.389251	+	0.173306i
$83$	−1108.99	+	805.728i	−1.46659	+	1.06554i	−0.485012	+	0.874508i	$0.661185\pi$
$83$	−1108.99	+	805.728i	−1.46659	+	1.06554i	−0.981583	+	0.191036i	$0.938815\pi$
$84$	−232.038	+	257.704i	−0.301397	+	0.334736i
$85$	948.492	−	201.608i	1.21033	−	0.257264i
$86$	167.896	+	121.984i	0.210520	+	0.152952i
$87$	−399.207	−	691.447i	−0.491948	−	0.852079i
$88$	−471.430	+	227.653i	−0.571075	+	0.275772i
$89$	779.964	−	1350.94i	0.928945	−	1.60898i	0.143853	−	0.989599i	$-0.454051\pi$
$89$	779.964	−	1350.94i	0.928945	−	1.60898i	0.785091	−	0.619380i	$-0.212616\pi$
$90$	198.741	+	144.394i	0.232768	+	0.169116i
$91$	663.856	+	34.4461i	0.764736	+	0.0396806i
$92$	−172.512	−	530.939i	−0.195496	−	0.601676i
$93$	70.0959	+	666.918i	0.0781571	+	0.743615i
$94$	−60.3634	−	574.319i	−0.0662341	−	0.630176i
$95$	1035.74	−	1150.31i	1.11858	−	1.24230i
$96$	−165.883	+	510.534i	−0.176358	+	0.542773i
$97$	−37.7502	+	359.169i	−0.0395149	+	0.375959i	0.956837	+	0.290624i	$0.0938629\pi$
$97$	−37.7502	+	359.169i	−0.0395149	+	0.375959i	−0.996352	+	0.0853354i	$0.972804\pi$
$98$	−67.4243	−	116.782i	−0.0694988	−	0.120375i
$99$	−436.240	+	338.088i	−0.442866	+	0.343223i
$100$	592.024	+	1025.42i	0.592024	+	1.02542i
$101$	471.999	−	210.148i	0.465007	−	0.207034i	−0.160840	−	0.986981i	$-0.551420\pi$
$101$	471.999	−	210.148i	0.465007	−	0.207034i	0.625847	+	0.779946i	$0.284754\pi$
$102$	−124.391	−	138.150i	−0.120751	−	0.134107i
$103$	358.994	+	1104.87i	0.343424	+	1.05695i	0.962422	+	0.271559i	$0.0875391\pi$
$103$	358.994	+	1104.87i	0.343424	+	1.05695i	−0.618997	+	0.785393i	$0.712461\pi$
$104$	627.804	−	241.365i	0.591935	−	0.227575i
$105$	675.370	−	490.685i	0.627708	−	0.456057i
$106$	−168.948	−	35.9110i	−0.154808	−	0.0329055i
$107$	323.979	+	359.815i	0.292712	+	0.325090i	0.871507	−	0.490384i	$-0.163143\pi$
$107$	323.979	+	359.815i	0.292712	+	0.325090i	−0.578794	+	0.815473i	$0.696477\pi$
$108$	−107.674	+	1024.45i	−0.0959345	+	0.912756i
$109$	1485.52			1.30539			0.652694	−	0.757621i	$-0.273639\pi$
$109$	1485.52			1.30539			0.652694	+	0.757621i	$0.273639\pi$
$110$	575.388	−	141.072i	0.498737	−	0.122279i
$111$	549.824	+	952.324i	0.470153	+	0.814330i
$112$	−494.880	−	359.551i	−0.417515	−	0.303343i
$113$	88.5197	−	18.8155i	0.0736924	−	0.0156638i	−0.170918	−	0.985285i	$-0.554673\pi$
$113$	88.5197	−	18.8155i	0.0736924	−	0.0156638i	0.244610	+	0.969621i	$0.421340\pi$
$114$	−290.264	−	61.6976i	−0.238472	−	0.0506887i
$115$	140.478	+	1336.56i	0.113910	+	1.08378i
$116$	1330.35	−	966.559i	1.06483	−	0.773645i
$117$	594.486	−	386.502i	0.469746	−	0.305403i
$118$	−160.258	+	493.222i	−0.125025	+	0.384786i
$119$	735.397	−	327.420i	0.566502	−	0.252223i
$120$	422.333	−	731.503i	0.321280	−	0.556473i
$121$	−56.8574	+	1329.79i	−0.0427178	+	0.999087i
$122$	439.071			0.325833
$123$	119.881	−	1140.59i	0.0878802	−	0.836125i
$124$	−1350.96	+	287.156i	−0.978389	+	0.207963i
$125$	−220.931	−	679.957i	−0.158086	−	0.486538i
$126$	186.304	+	82.9479i	0.131724	+	0.0586475i
$127$	34.0235	+	323.712i	0.0237724	+	0.226179i	0.999957	+	0.00923929i	$0.00294100\pi$
$127$	34.0235	+	323.712i	0.0237724	+	0.226179i	−0.976185	+	0.216940i	$0.930392\pi$
$128$	−1402.27	−	298.061i	−0.968312	−	0.205821i
$129$	232.466	−	715.458i	0.158663	−	0.488314i
$130$	−751.704	+	119.458i	−0.507145	+	0.0805934i
$131$	−884.608			−0.589989			−0.294994	−	0.955499i	$-0.595318\pi$
$131$	−884.608			−0.589989			−0.294994	+	0.955499i	$0.595318\pi$
$132$	617.162	+	644.114i	0.406947	+	0.424719i
$133$	642.499	−	1112.84i	0.418885	−	0.725531i
$134$	53.4376	−	508.425i	0.0344501	−	0.327770i
$135$	766.293	−	2358.41i	0.488533	−	1.50355i
$136$	545.009	−	605.294i	0.343633	−	0.381644i
$137$	385.074	+	171.446i	0.240139	+	0.106917i	0.523278	−	0.852162i	$-0.324709\pi$
$137$	385.074	+	171.446i	0.240139	+	0.106917i	−0.283139	+	0.959079i	$0.591376\pi$
$138$	208.440	−	151.441i	0.128577	−	0.0934167i
$139$	−494.258	+	548.929i	−0.301600	+	0.334961i	−0.874827	−	0.484436i	$-0.839025\pi$
$139$	−494.258	+	548.929i	−0.301600	+	0.334961i	0.573227	+	0.819397i	$0.305691\pi$
$140$	1150.47	+	1277.73i	0.694520	+	0.771342i
$141$	−1912.33	+	851.425i	−1.14218	+	0.508531i
$142$	674.902			0.398848
$143$	214.159	−	1696.57i	0.125237	−	0.992127i
$144$	−652.501			−0.377605
$145$	−3616.40	+	1610.13i	−2.07121	+	0.922163i
$146$	394.386	+	438.010i	0.223559	+	0.248287i
$147$	−327.078	+	363.257i	−0.183517	+	0.203816i
$148$	−1832.29	+	1331.23i	−1.01766	+	0.739370i
$149$	−1956.56	−	871.119i	−1.07576	−	0.478958i	−0.209117	−	0.977891i	$-0.567059\pi$
$149$	−1956.56	−	871.119i	−1.07576	−	0.478958i	−0.866641	+	0.498932i	$0.833726\pi$
$150$	−365.651	+	406.096i	−0.199035	+	0.221051i
$151$	−513.209	+	1579.49i	−0.276585	+	0.851241i	0.712211	+	0.701966i	$0.247694\pi$
$151$	−513.209	+	1579.49i	−0.276585	+	0.851241i	−0.988796	+	0.149275i	$0.952306\pi$
$152$	135.906	−	1293.06i	0.0725225	−	0.690005i
$153$	429.340	−	743.638i	0.226863	−	0.392938i
$154$	442.878	−	213.865i	0.231741	−	0.111908i
$155$	3324.88			1.72297
$156$	−721.722	−	890.308i	−0.370410	−	0.456934i
$157$	491.958	−	1514.09i	0.250080	−	0.769666i	−0.744680	−	0.667422i	$-0.767398\pi$
$157$	491.958	−	1514.09i	0.250080	−	0.769666i	0.994759	−	0.102244i	$-0.0326023\pi$
$158$	256.885	+	54.6026i	0.129346	+	0.0274933i
$159$	65.4451	+	622.668i	0.0326423	+	0.310571i
$160$	2431.46	+	1082.56i	1.20140	+	0.534897i
$161$	344.762	+	1061.07i	0.168764	+	0.519404i
$162$	−85.2473	+	18.1199i	−0.0413436	+	0.00878785i
$163$	−99.4256	+	945.971i	−0.0477768	+	0.454565i	0.944314	+	0.329045i	$0.106727\pi$
$163$	−99.4256	+	945.971i	−0.0477768	+	0.454565i	−0.992091	+	0.125521i	$0.959940\pi$
$164$	2362.09			1.12468
$165$	−1130.86	−	1825.61i	−0.533560	−	0.861355i
$166$	651.490	−	1128.41i	0.304611	−	0.527601i
$167$	−2831.89	+	1260.84i	−1.31220	+	0.584231i	−0.939127	−	0.343570i	$-0.888364\pi$
$167$	−2831.89	+	1260.84i	−1.31220	+	0.584231i	−0.373076	+	0.927801i	$0.621697\pi$
$168$	216.686	−	666.890i	0.0995099	−	0.306260i
$169$	−454.553	+	2149.46i	−0.206897	+	0.978363i
$170$	−745.683	+	541.771i	−0.336419	+	0.244423i
$171$	−143.277	−	1363.19i	−0.0640740	−	0.609624i
$172$	1515.53	+	322.135i	0.671848	+	0.142806i
$173$	1926.81	−	409.556i	0.846777	−	0.179988i	0.235963	−	0.971762i	$-0.424176\pi$
$173$	1926.81	−	409.556i	0.846777	−	0.179988i	0.610814	+	0.791774i	$0.290842\pi$
$174$	613.979	+	446.082i	0.267504	+	0.194353i
$175$	−1183.15	−	2049.27i	−0.511071	−	0.885202i
$176$	−1016.18	+	1201.46i	−0.435215	+	0.514567i
$177$	1879.88			0.798308
$178$	−154.991	+	1474.64i	−0.0652645	+	0.620950i
$179$	887.513	+	985.683i	0.370591	+	0.411583i	0.899378	−	0.437171i	$-0.144020\pi$
$179$	887.513	+	985.683i	0.370591	+	0.411583i	−0.528787	+	0.848754i	$0.677353\pi$
$180$	1793.95	+	381.315i	0.742849	+	0.157897i
$181$	−2415.83	+	1755.20i	−0.992083	+	0.720791i	−0.960376	−	0.278707i	$-0.910094\pi$
$181$	−2415.83	+	1755.20i	−0.992083	+	0.720791i	−0.0317069	+	0.999497i	$0.510094\pi$
$182$	−589.781	+	226.747i	−0.240206	+	0.0923493i
$183$	−491.826	−	1513.68i	−0.198671	−	0.611446i
$184$	755.352	+	838.903i	0.302637	+	0.336113i
$185$	4980.84	−	2217.61i	1.97945	−	0.881308i
$186$	−318.710	−	552.022i	−0.125640	−	0.217614i
$187$	−700.637	−	1948.67i	−0.273988	−	0.762037i
$188$	−2155.68	−	3733.75i	−0.836273	−	1.44847i
$189$	215.184	−	2047.34i	0.0828166	−	0.787947i
$190$	−454.663	+	1399.31i	−0.173604	+	0.534298i
$191$	−1927.78	+	2141.01i	−0.730309	+	0.811091i	−0.987888	−	0.155166i	$-0.950409\pi$
$191$	−1927.78	+	2141.01i	−0.730309	+	0.811091i	0.257579	+	0.966257i	$0.417075\pi$
$192$	70.9395	+	674.944i	0.0266647	+	0.253697i
$193$	328.678	+	3127.16i	0.122584	+	1.16631i	0.866899	+	0.498483i	$0.166109\pi$
$193$	328.678	+	3127.16i	0.122584	+	1.16631i	−0.744315	+	0.667828i	$0.767224\pi$
$194$	−106.080	−	326.481i	−0.0392583	−	0.120825i
$195$	1253.85	+	2457.67i	0.460461	+	0.902549i
$196$	−814.479	−	591.753i	−0.296822	−	0.215654i
$197$	−621.911	+	1077.18i	−0.224921	+	0.389574i	−0.956296	−	0.292402i	$-0.905546\pi$
$197$	−621.911	+	1077.18i	−0.224921	+	0.389574i	0.731375	+	0.681975i	$0.238879\pi$
$198$	248.101	−	462.238i	0.0890493	−	0.165908i
$199$	665.330	+	1152.39i	0.237005	+	0.410505i	0.959853	−	0.280502i	$-0.0905009\pi$
$199$	665.330	+	1152.39i	0.237005	+	0.410505i	−0.722849	+	0.691007i	$0.757168\pi$
$200$	−1936.99	−	1407.31i	−0.684829	−	0.497558i
$201$	−1812.64	+	385.288i	−0.636088	+	0.135205i
$202$	−328.617	+	364.966i	−0.114462	+	0.127123i
$203$	−2658.68	+	1931.65i	−0.919227	+	0.667857i
$204$	−1267.90	−	564.505i	−0.435150	−	0.193741i
$205$	−5562.07	−	1182.26i	−1.89499	−	0.402792i
$206$	−738.896	−	820.627i	−0.249909	−	0.277552i
$207$	962.796	+	699.512i	0.323280	+	0.234877i
$208$	1428.81	−	1430.29i	0.476298	−	0.476792i
$209$	−2733.21	−	1859.17i	−0.904592	−	0.615318i
$210$	−396.755	+	687.199i	−0.130375	+	0.225815i
$211$	−629.525	+	280.283i	−0.205395	+	0.0914477i	−0.506856	−	0.862031i	$-0.669192\pi$
$211$	−629.525	+	280.283i	−0.205395	+	0.0914477i	0.301461	+	0.953479i	$0.402526\pi$
$212$	−1261.33	+	268.104i	−0.408624	+	0.0868558i
$213$	−755.991	−	2326.70i	−0.243191	−	0.748465i
$214$	−420.440	−	187.192i	−0.134302	−	0.0597952i
$215$	−3407.42	−	1517.08i	−1.08086	−	0.481229i
$216$	−643.663	−	1980.99i	−0.202758	−	0.624025i
$217$	2699.87	−	573.876i	0.844605	−	0.179526i
$218$	−1289.96	+	574.329i	−0.400768	+	0.178433i
$219$	1068.25	−	1850.27i	0.329616	−	0.570911i
$220$	3495.96	−	2709.38i	1.07135	−	0.830303i
$221$	689.922	+	2569.49i	0.209996	+	0.782095i
$222$	−845.628	−	614.385i	−0.255652	−	0.185742i
$223$	1599.75	+	1776.71i	0.480392	+	0.533529i	0.933810	−	0.357769i	$-0.116462\pi$
$223$	1599.75	+	1776.71i	0.480392	+	0.533529i	−0.453418	+	0.891298i	$0.649796\pi$
$224$	2161.24	+	459.387i	0.644662	+	0.137027i
$225$	−2305.89	−	1026.65i	−0.683226	−	0.304192i
$226$	−69.5923	+	50.5618i	−0.0204832	+	0.0148819i
$227$	−673.002	+	747.444i	−0.196778	+	0.218544i	−0.833456	−	0.552585i	$-0.813641\pi$
$227$	−673.002	+	747.444i	−0.196778	+	0.218544i	0.636678	+	0.771130i	$0.280308\pi$
$228$	−2167.05	+	460.621i	−0.629459	+	0.133796i
$229$	−4442.16	−	3227.42i	−1.28186	−	0.931327i	−0.282254	−	0.959340i	$-0.591082\pi$
$229$	−4442.16	−	3227.42i	−1.28186	−	0.931327i	−0.999608	+	0.0280128i	$0.991082\pi$
$230$	−638.723	−	1106.30i	−0.183114	−	0.317162i
$231$	−1233.38	−	1287.25i	−0.351302	−	0.366643i
$232$	−1662.57	+	2879.66i	−0.470488	+	0.814908i
$233$	2986.49	+	2169.81i	0.839705	+	0.610082i	0.922288	−	0.386503i	$-0.126317\pi$
$233$	2986.49	+	2169.81i	0.839705	+	0.610082i	−0.0825831	+	0.996584i	$0.526317\pi$
$234$	−366.798	+	565.460i	−0.102471	+	0.157971i
$235$	3207.26	+	9870.92i	0.890291	+	2.74003i
$236$	404.712	+	3850.58i	0.111629	+	1.06208i
$237$	−99.5091	−	946.766i	−0.0272735	−	0.259490i
$238$	−512.001	+	568.634i	−0.139446	+	0.154870i
$239$	973.415	−	2995.86i	0.263452	−	0.810821i	−0.728594	−	0.684945i	$-0.759826\pi$
$239$	973.415	−	2995.86i	0.263452	−	0.810821i	0.992046	−	0.125876i	$-0.0401740\pi$
$240$	265.384	−	2524.96i	0.0713771	−	0.679107i
$241$	252.905	+	438.045i	0.0675978	+	0.117083i	0.897843	−	0.440315i	$-0.145133\pi$
$241$	252.905	+	438.045i	0.0675978	+	0.117083i	−0.830246	+	0.557398i	$0.811800\pi$
$242$	−464.745	−	1176.71i	−0.123450	−	0.312569i
$243$	−1801.64	−	3120.53i	−0.475618	−	0.823794i
$244$	2994.61	−	1333.29i	0.785698	−	0.349815i
$245$	1621.70	+	1801.08i	0.422883	+	0.469659i
$246$	336.872	+	1036.78i	0.0873096	+	0.268711i
$247$	3301.87	+	2670.97i	0.850578	+	0.688055i
$248$	2259.42	−	1641.57i	0.578522	−	0.420321i
$249$	−4619.93	−	981.997i	−1.17581	−	0.249926i
$250$	454.730	+	505.029i	0.115039	+	0.127763i
$251$	−478.286	+	4550.59i	−0.120275	+	1.14434i	0.753307	+	0.657669i	$0.228457\pi$
$251$	−478.286	+	4550.59i	−0.120275	+	1.14434i	−0.873583	+	0.486676i	$0.838209\pi$
$252$	1522.54			0.380598
$253$	2787.46	−	683.419i	0.692671	−	0.169827i
$254$	−154.697	−	267.943i	−0.0382148	−	0.0661900i
$255$	2703.02	+	1963.86i	0.663802	+	0.482280i
$256$	−208.394	+	44.2956i	−0.0508776	+	0.0108144i
$257$	417.136	+	88.6649i	0.101246	+	0.0215205i	0.258256	−	0.966077i	$-0.416852\pi$
$257$	417.136	+	88.6649i	0.101246	+	0.0215205i	−0.157010	+	0.987597i	$0.550186\pi$
$258$	74.7446	+	711.148i	0.0180364	+	0.171605i
$259$	3661.78	−	2660.44i	0.878502	−	0.638269i
$260$	−4764.13	+	3097.37i	−1.13638	+	0.738811i
$261$	−1083.25	+	3333.92i	−0.256903	+	0.790667i
$262$	768.155	−	342.005i	0.181133	−	0.0806455i
$263$	316.581	−	548.334i	0.0742252	−	0.128562i	−0.826524	−	0.562902i	$-0.809685\pi$
$263$	316.581	−	548.334i	0.0742252	−	0.128562i	0.900749	+	0.434340i	$0.143018\pi$
$264$	−1669.82	−	682.262i	−0.389282	−	0.159054i
$265$	3104.28			0.719601
$266$	−127.675	+	1214.74i	−0.0294295	+	0.280003i
$267$	5257.40	−	1117.49i	1.20505	−	0.256141i
$268$	−1179.43	−	3629.90i	−0.268824	−	0.827356i
$269$	−934.228	−	415.945i	−0.211751	−	0.0942774i	0.298121	−	0.954528i	$-0.403640\pi$
$269$	−934.228	−	415.945i	−0.211751	−	0.0942774i	−0.509871	+	0.860251i	$0.670307\pi$
$270$	246.385	+	2344.20i	0.0555353	+	0.528383i
$271$	4031.34	+	856.888i	0.903640	+	0.192075i	0.636222	−	0.771506i	$-0.280496\pi$
$271$	4031.34	+	856.888i	0.903640	+	0.192075i	0.267418	+	0.963581i	$0.413830\pi$
$272$	756.538	−	2328.39i	0.168647	−	0.519041i
$273$	1442.34	+	1779.26i	0.319761	+	0.394453i
$274$	−400.665			−0.0883397
$275$	−5481.51	+	2647.01i	−1.20199	+	0.580440i
$276$	961.767	−	1665.83i	0.209752	−	0.363301i
$277$	−202.387	+	1925.58i	−0.0438998	+	0.417679i	0.950398	+	0.311037i	$0.100676\pi$
$277$	−202.387	+	1925.58i	−0.0438998	+	0.417679i	−0.994298	+	0.106642i	$0.965990\pi$
$278$	216.966	−	667.754i	0.0468086	−	0.144062i
$279$	1970.10	−	2188.02i	0.422749	−	0.469510i
$280$	−3176.11	−	1414.10i	−0.677890	−	0.301816i
$281$	−1867.15	+	1356.56i	−0.396386	+	0.287992i	−0.768068	−	0.640369i	$-0.778781\pi$
$281$	−1867.15	+	1356.56i	−0.396386	+	0.287992i	0.371681	+	0.928360i	$0.378781\pi$
$282$	1331.41	−	1478.68i	0.281150	−	0.312249i
$283$	−3946.30	−	4382.81i	−0.828915	−	0.920603i	0.168969	−	0.985621i	$-0.445956\pi$
$283$	−3946.30	−	4382.81i	−0.828915	−	0.920603i	−0.997884	+	0.0650180i	$0.979290\pi$
$284$	4603.05	−	2049.41i	0.961764	−	0.428205i
$285$	5333.37			1.10850
$286$	469.956	+	1556.02i	0.0971646	+	0.321712i
$287$	−4720.58			−0.970895
$288$	2153.12	−	958.632i	0.440535	−	0.196139i
$289$	−1131.63	−	1256.81i	−0.230335	−	0.255813i
$290$	2517.82	−	2796.32i	0.509833	−	0.566227i
$291$	−1006.71	+	731.416i	−0.202798	+	0.147342i
$292$	4019.91	+	1789.78i	0.805641	+	0.358694i
$293$	3928.79	−	4363.36i	0.783353	−	0.870002i	−0.210850	−	0.977518i	$-0.567623\pi$
$293$	3928.79	−	4363.36i	0.783353	−	0.870002i	0.994203	+	0.107517i	$0.0342899\pi$
$294$	143.579	−	441.891i	0.0284820	−	0.0876584i
$295$	974.278	−	9269.64i	0.192287	−	1.82949i
$296$	2289.84	−	3966.13i	0.449643	−	0.778805i
$297$	−5211.59	−	939.981i	−1.01821	−	0.183647i
$298$	2035.78			0.395738
$299$	−3641.62	+	578.711i	−0.704348	+	0.111932i
$300$	−1260.71	+	3880.05i	−0.242623	+	0.746716i
$301$	−3028.75	−	643.780i	−0.579980	−	0.123279i
$302$	−165.011	−	1569.98i	−0.0314415	−	0.299146i
$303$	1626.31	+	724.079i	0.308347	+	0.137285i
$304$	−1207.65	−	3716.77i	−0.227841	−	0.701221i
$305$	−7718.82	+	1640.69i	−1.44911	+	0.308018i
$306$	−85.3166	+	811.733i	−0.0159386	+	0.151646i
$307$	−1602.07			−0.297835			−0.148917	−	0.988850i	$-0.547579\pi$
$307$	−1602.07			−0.297835			−0.148917	+	0.988850i	$0.547579\pi$
$308$	2371.15	−	2803.48i	0.438665	−	0.518646i
$309$	−2001.41	+	3466.55i	−0.368467	+	0.638204i
$310$	−2887.18	+	1285.46i	−0.528971	+	0.235513i
$311$	−821.635	+	2528.73i	−0.149809	+	0.461065i	−0.997598	−	0.0692687i	$-0.977933\pi$
$311$	−821.635	+	2528.73i	−0.149809	+	0.461065i	0.847789	+	0.530334i	$0.177933\pi$
$312$	2065.46	+	1051.05i	0.374787	+	0.190719i
$313$	2000.38	−	1453.36i	0.361241	−	0.262457i	−0.392329	−	0.919825i	$-0.628330\pi$
$313$	2000.38	−	1453.36i	0.361241	−	0.262457i	0.753569	+	0.657368i	$0.228330\pi$
$314$	158.179	+	1504.97i	0.0284285	+	0.270479i
$315$	−3585.16	−	762.049i	−0.641273	−	0.136307i
$316$	1917.85	−	407.651i	0.341416	−	0.0725701i
$317$	6487.91	+	4713.74i	1.14952	+	0.835174i	0.988417	−	0.151764i	$-0.0484952\pi$
$317$	6487.91	+	4713.74i	1.14952	+	0.835174i	0.161102	+	0.986938i	$0.448495\pi$
$318$	−297.564	−	515.396i	−0.0524734	−	0.0908866i
$319$	4451.79	+	7186.76i	0.781355	+	1.26138i
$320$	3364.89			0.587823
$321$	−174.382	+	1659.14i	−0.0303211	+	0.288486i
$322$	−709.604	−	788.095i	−0.122810	−	0.136394i
$323$	5030.53	+	1069.27i	0.866582	+	0.184198i
$324$	−526.392	+	382.446i	−0.0902592	+	0.0655772i
$325$	7299.72	−	2806.44i	1.24589	−	0.478995i
$326$	−279.392	−	859.879i	−0.0474665	−	0.146087i
$327$	3424.94	+	3803.78i	0.579203	+	0.643270i
$328$	−4363.41	+	1942.72i	−0.734540	+	0.327038i
$329$	4308.08	+	7461.82i	0.721922	+	1.25041i
$330$	1687.80	+	1148.07i	0.281547	+	0.191513i
$331$	−530.659	−	919.128i	−0.0881197	−	0.152628i	0.818597	−	0.574369i	$-0.194752\pi$
$331$	−530.659	−	919.128i	−0.0881197	−	0.152628i	−0.906716	+	0.421741i	$0.861419\pi$
$332$	1016.83	−	9674.47i	0.168089	−	1.59926i
$333$	1491.96	−	4591.77i	0.245522	−	0.755638i
$334$	1971.63	−	2189.71i	0.323002	−	0.358730i
$335$	960.416	+	9137.75i	0.156636	+	1.49029i
$336$	−220.312	−	2096.13i	−0.0357709	−	0.340337i
$337$	−2439.28	−	7507.32i	−0.394290	−	1.21350i	−0.929513	−	0.368790i	$-0.879772\pi$
$337$	−2439.28	−	7507.32i	−0.394290	−	1.21350i	0.535223	−	0.844711i	$-0.320228\pi$
$338$	−436.305	−	2042.24i	−0.0702126	−	0.328648i
$339$	252.264	+	183.280i	0.0404162	+	0.0293641i
$340$	−3440.66	+	5959.41i	−0.548813	+	0.950571i
$341$	−960.676	−	7035.15i	−0.152562	−	1.11723i
$342$	651.448	+	1128.34i	0.103001	+	0.178403i
$343$	5563.17	+	4041.88i	0.875752	+	0.636271i
$344$	−3064.53	+	651.386i	−0.480315	+	0.102094i
$345$	−3098.47	+	3441.20i	−0.483525	+	0.537009i
$346$	−1514.81	+	1100.58i	−0.235367	+	0.171004i
$347$	−467.647	−	208.210i	−0.0723476	−	0.0322112i	0.370244	−	0.928935i	$-0.379274\pi$
$347$	−467.647	−	208.210i	−0.0723476	−	0.0322112i	−0.442591	+	0.896723i	$0.645941\pi$
$348$	5542.12	+	1178.01i	0.853704	+	0.181460i
$349$	−1832.41	−	2035.10i	−0.281050	−	0.312138i	0.586047	−	0.810277i	$-0.300683\pi$
$349$	−1832.41	−	2035.10i	−0.281050	−	0.312138i	−0.867097	+	0.498139i	$0.834017\pi$
$350$	1819.68	+	1322.07i	0.277902	+	0.201908i
$351$	6572.82	+	1757.53i	0.999519	+	0.267265i
$352$	1588.06	−	5457.54i	0.240465	−	0.826386i
$353$	2441.51	−	4228.82i	0.368126	−	0.637613i	−0.621146	−	0.783695i	$-0.713333\pi$
$353$	2441.51	−	4228.82i	0.368126	−	0.637613i	0.989273	+	0.146081i	$0.0466661\pi$
$354$	−1632.41	+	726.794i	−0.245089	+	0.109121i
$355$	−11864.7	+	2521.92i	−1.77384	+	0.377041i
$356$	3420.82	+	10528.2i	0.509279	+	1.56740i
$357$	2533.87	+	1128.15i	0.375648	+	0.167249i
$358$	−1151.76	−	512.796i	−0.170034	−	0.0757042i
$359$	−849.909	−	2615.75i	−0.124948	−	0.384552i	0.868943	−	0.494912i	$-0.164800\pi$
$359$	−849.909	−	2615.75i	−0.124948	−	0.384552i	−0.993892	+	0.110360i	$0.964800\pi$
$360$	−3627.52	+	771.053i	−0.531075	+	0.112883i
$361$	1233.80	−	549.322i	0.179880	−	0.0800878i
$362$	1419.21	−	2458.14i	0.206055	−	0.356898i
$363$	−3536.08	+	2920.29i	−0.511284	+	0.422246i
$364$	−3333.96	+	3337.42i	−0.480074	+	0.480572i
$365$	−8569.98	−	6226.46i	−1.22897	−	0.892898i
$366$	1012.30	+	1124.27i	0.144573	+	0.160564i
$367$	8571.80	+	1821.99i	1.21919	+	0.259148i	0.772194	−	0.635386i	$-0.219159\pi$
$367$	8571.80	+	1821.99i	1.21919	+	0.259148i	0.447000	+	0.894534i	$0.352493\pi$
$368$	3099.73	+	1380.09i	0.439089	+	0.195495i
$369$	−4073.73	+	2959.74i	−0.574715	+	0.417555i
$370$	−3467.77	+	3851.35i	−0.487246	+	0.541141i
$371$	2520.74	−	535.799i	0.352750	−	0.0749793i
$372$	−3849.99	−	2797.18i	−0.536593	−	0.389857i
$373$	−1398.16	−	2421.69i	−0.194086	−	0.336167i	0.752514	−	0.658576i	$-0.228841\pi$
$373$	−1398.16	−	2421.69i	−0.194086	−	0.336167i	−0.946601	+	0.322409i	$0.895507\pi$
$374$	1361.79	+	1421.26i	0.188280	+	0.196502i
$375$	1231.71	−	2133.38i	0.169613	−	0.293779i
$376$	7052.98	+	5124.29i	0.967366	+	0.702833i
$377$	−4935.94	−	9674.93i	−0.674307	−	1.32171i
$378$	604.680	+	1861.01i	0.0822788	+	0.253228i
$379$	1463.49	+	13924.2i	0.198349	+	1.88717i	0.413376	+	0.910560i	$0.364350\pi$
$379$	1463.49	+	13924.2i	0.198349	+	1.88717i	−0.215027	+	0.976608i	$0.568984\pi$
$380$	1148.20	+	10924.4i	0.155004	+	1.47476i
$381$	−750.442	+	833.450i	−0.100909	+	0.112071i
$382$	846.245	−	2604.47i	0.113345	−	0.348839i
$383$	93.9148	−	893.540i	0.0125296	−	0.119211i	−0.986469	−	0.163946i	$-0.947578\pi$
$383$	93.9148	−	893.540i	0.0125296	−	0.119211i	0.998999	+	0.0447351i	$0.0142444\pi$
$384$	−2469.78	−	4277.78i	−0.328217	−	0.568488i
$385$	−6986.60	+	5414.64i	−0.924857	+	0.716768i
$386$	−1494.42	−	2588.42i	−0.197057	−	0.341314i
$387$	−3017.37	+	1343.42i	−0.396334	+	0.176459i
$388$	−1714.90	−	1904.59i	−0.224383	−	0.249203i
$389$	−2541.14	−	7820.81i	−0.331210	−	1.01936i	−0.968559	−	0.248784i	$-0.919969\pi$
$389$	−2541.14	−	7820.81i	−0.331210	−	1.01936i	0.637349	−	0.770575i	$-0.280031\pi$
$390$	−2038.96	−	1649.37i	−0.264736	−	0.214151i
$391$	−3612.45	+	2624.60i	−0.467236	+	0.339467i
$392$	1991.25	+	423.254i	0.256565	+	0.0545346i
$393$	−2039.50	−	2265.09i	−0.261779	−	0.290735i
$394$	123.584	−	1175.82i	0.0158022	−	0.150348i
$395$	−4720.05			−0.601244
$396$	288.494	−	3906.00i	0.0366095	−	0.495667i
$397$	−5422.99	−	9392.90i	−0.685572	−	1.18745i	−0.973257	−	0.229720i	$-0.926219\pi$
$397$	−5422.99	−	9392.90i	−0.685572	−	1.18745i	0.287685	−	0.957725i	$-0.407115\pi$
$398$	−1023.28	−	743.453i	−0.128875	−	0.0936330i
$399$	4330.81	−	920.541i	0.543387	−	0.115501i
$400$	−7039.31	−	1496.25i	−0.879913	−	0.187031i
$401$	−454.475	−	4324.04i	−0.0565970	−	0.538485i	−0.985682	−	0.168617i	$-0.946070\pi$
$401$	−454.475	−	4324.04i	−0.0565970	−	0.538485i	0.929085	−	0.369867i	$-0.120597\pi$
$402$	1425.06	−	1035.36i	0.176804	−	0.128456i
$403$	482.155	+	9109.70i	0.0595976	+	1.12602i
$404$	−1133.02	+	3487.07i	−0.139529	+	0.429426i
$405$	1430.93	−	637.091i	0.175564	−	0.0781662i
$406$	1561.88	−	2705.25i	0.190923	−	0.330688i
$407$	−6131.41	−	9898.26i	−0.746738	−	1.20550i
$408$	2806.43			0.340537
$409$	1387.81	−	13204.1i	0.167781	−	1.59633i	−0.509408	−	0.860525i	$-0.670136\pi$
$409$	1387.81	−	13204.1i	0.167781	−	1.59633i	0.677190	−	0.735809i	$-0.263198\pi$
$410$	5286.94	−	1123.77i	0.636838	−	0.135364i
$411$	448.805	+	1381.28i	0.0538636	+	0.165775i
$412$	−7531.44	−	3353.21i	−0.900601	−	0.400973i
$413$	−808.808	−	7695.30i	−0.0963653	−	0.916854i
$414$	−1106.49	−	235.192i	−0.131355	−	0.0279205i
$415$	−7236.55	+	22271.8i	−0.855972	+	2.63441i
$416$	−2613.45	+	6818.83i	−0.308017	+	0.803656i
$417$	−2545.10			−0.298882
$418$	3092.18	+	557.717i	0.361827	+	0.0652604i
$419$	4495.85	−	7787.04i	0.524193	−	0.907928i	−0.475411	−	0.879764i	$-0.657701\pi$
$419$	4495.85	−	7787.04i	0.524193	−	0.907928i	0.999603	−	0.0281643i	$-0.00896615\pi$
$420$	−619.244	+	5891.72i	−0.0719429	+	0.684491i
$421$	874.962	−	2692.86i	0.101290	−	0.311738i	−0.887552	−	0.460708i	$-0.847596\pi$
$421$	874.962	−	2692.86i	0.101290	−	0.311738i	0.988842	+	0.148970i	$0.0475956\pi$
$422$	438.290	−	486.770i	0.0505584	−	0.0561508i
$423$	8396.21	+	3738.23i	0.965101	+	0.429691i
$424$	2109.51	−	1532.65i	0.241620	−	0.175547i
$425$	6337.04	−	7037.99i	0.723274	−	0.803277i
$426$	1556.01	+	1728.13i	0.176970	+	0.196545i
$427$	−5984.66	+	2664.54i	−0.678263	+	0.301982i
$428$	−3435.97			−0.388046
$429$	4837.92	−	3363.14i	0.544468	−	0.378494i
$430$	3545.39			0.397613
$431$	−8036.98	+	3578.30i	−0.898208	+	0.399908i	−0.803298	−	0.595578i	$-0.796923\pi$
$431$	−8036.98	+	3578.30i	−0.898208	+	0.399908i	−0.0949106	+	0.995486i	$0.530257\pi$
$432$	−4189.31	−	4652.70i	−0.466571	−	0.518179i
$433$	1107.87	−	1230.41i	0.122958	−	0.136559i	−0.678522	−	0.734580i	$-0.737379\pi$
$433$	1107.87	−	1230.41i	0.122958	−	0.136559i	0.801480	+	0.598021i	$0.204046\pi$
$434$	−2122.58	+	1542.15i	−0.234763	+	0.170565i
$435$	−12460.6	−	5547.81i	−1.37342	−	0.611487i
$436$	−7053.97	+	7834.23i	−0.774826	+	0.860531i
$437$	−2202.61	+	6778.93i	−0.241110	+	0.742060i
$438$	−212.279	+	2019.70i	−0.0231577	+	0.220331i
$439$	−93.3050	+	161.609i	−0.0101440	+	0.0175699i	−0.871053	−	0.491189i	$-0.836562\pi$
$439$	−93.3050	+	161.609i	−0.0101440	+	0.0175699i	0.860909	+	0.508759i	$0.169896\pi$
$440$	−4229.63	+	7880.25i	−0.458272	+	0.853809i
$441$	2146.15			0.231741
$442$	−1592.51	−	1964.50i	−0.171375	−	0.211407i
$443$	233.556	−	718.812i	0.0250488	−	0.0770921i	−0.937751	−	0.347309i	$-0.887095\pi$
$443$	233.556	−	718.812i	0.0250488	−	0.0770921i	0.962799	+	0.270217i	$0.0870955\pi$
$444$	−7633.11	−	1622.47i	−0.815882	−	0.173421i
$445$	−2785.60	−	26503.2i	−0.296742	−	2.82331i
$446$	−2076.06	−	924.322i	−0.220413	−	0.0981343i
$447$	−2280.38	−	7018.30i	−0.241294	−	0.742627i
$448$	2732.36	−	580.782i	0.288152	−	0.0612486i
$449$	−469.160	+	4463.76i	−0.0493118	+	0.469171i	0.941803	+	0.336164i	$0.109130\pi$
$449$	−469.160	+	4463.76i	−0.0493118	+	0.469171i	−0.991115	+	0.133006i	$0.957537\pi$
$450$	2399.25			0.251337
$451$	−894.467	+	12110.4i	−0.0933899	+	1.26443i
$452$	−321.106	+	556.173i	−0.0334150	+	0.0578765i
$453$	−5227.62	+	2327.48i	−0.542196	+	0.241401i
$454$	295.430	−	909.242i	0.0305402	−	0.0939930i
$455$	9521.00	−	6190.03i	0.980992	−	0.637787i
$456$	3624.29	−	2633.20i	0.372199	−	0.270419i
$457$	−1.26927	−	12.0763i	−0.000129921	−	0.00123612i	0.994457	−	0.105147i	$-0.0335312\pi$
$457$	−1.26927	−	12.0763i	−0.000129921	−	0.00123612i	−0.994587	+	0.103910i	$0.966864\pi$
$458$	5105.15	+	1085.13i	0.520848	+	0.110710i
$459$	8059.10	−	1713.01i	0.819535	−	0.174197i
$460$	−7715.70	−	5605.79i	−0.782058	−	0.568198i
$461$	8590.00	+	14878.3i	0.867844	+	1.50315i	0.864195	+	0.503157i	$0.167828\pi$
$461$	8590.00	+	14878.3i	0.867844	+	1.50315i	0.00364929	+	0.999993i	$0.498838\pi$
$462$	1568.69	+	640.941i	0.157970	+	0.0645439i
$463$	6049.07			0.607179			0.303590	−	0.952803i	$-0.401815\pi$
$463$	6049.07			0.607179			0.303590	+	0.952803i	$0.401815\pi$
$464$	−1044.72	+	9939.86i	−0.104526	+	0.994496i
$465$	7665.65	+	8513.56i	0.764486	+	0.849048i
$466$	−3432.22	−	729.541i	−0.341190	−	0.0725222i
$467$	7621.39	−	5537.27i	0.755195	−	0.548681i	−0.142238	−	0.989833i	$-0.545430\pi$
$467$	7621.39	−	5537.27i	0.755195	−	0.548681i	0.897433	+	0.441151i	$0.145430\pi$
$468$	−784.600	+	4970.45i	−0.0774961	+	0.490938i
$469$	2357.06	+	7254.27i	0.232065	+	0.714224i
$470$	−6601.31	−	7331.49i	−0.647863	−	0.719525i
$471$	5011.15	−	2231.11i	0.490237	−	0.218268i
$472$	−3914.55	−	6780.20i	−0.381741	−	0.661195i
$473$	−2225.49	+	7648.14i	−0.216338	+	0.743471i
$474$	452.445	+	783.658i	0.0438428	+	0.0759380i
$475$	1580.23	−	15034.9i	0.152644	−	1.45231i
$476$	−1765.30	+	5433.02i	−0.169984	+	0.523156i
$477$	1839.39	−	2042.85i	0.176561	−	0.196091i
$478$	312.981	+	2977.81i	0.0299486	+	0.284942i
$479$	−60.2129	−	572.887i	−0.00574363	−	0.0546470i	0.991275	−	0.131812i	$-0.0420797\pi$
$479$	−60.2129	−	572.887i	−0.00574363	−	0.0546470i	−0.997018	+	0.0771655i	$0.975413\pi$
$480$	2833.88	+	8721.77i	0.269475	+	0.829360i
$481$	6798.23	+	13325.2i	0.644433	+	1.26315i
$482$	−388.968	−	282.602i	−0.0367572	−	0.0267057i
$483$	−1922.07	+	3329.12i	−0.181071	+	0.313624i
$484$	−6742.92	−	6614.30i	−0.633257	−	0.621178i
$485$	3084.85	+	5343.12i	0.288816	+	0.500244i
$486$	2770.91	+	2013.19i	0.258624	+	0.187901i
$487$	6416.91	−	1363.96i	0.597080	−	0.126913i	0.100549	−	0.994932i	$-0.467940\pi$
$487$	6416.91	−	1363.96i	0.597080	−	0.126913i	0.496531	+	0.868019i	$0.334607\pi$
$488$	−4435.28	+	4925.88i	−0.411426	+	0.456935i
$489$	−2651.45	+	1926.39i	−0.245200	+	0.178148i
$490$	−2104.54	−	937.000i	−0.194027	−	0.0863864i
$491$	−4471.74	−	950.497i	−0.411011	−	0.0873632i	−0.00223446	−	0.999998i	$-0.500711\pi$
$491$	−4471.74	−	950.497i	−0.411011	−	0.0873632i	−0.408777	+	0.912634i	$0.634045\pi$
$492$	5445.89	+	6048.27i	0.499023	+	0.554222i
$493$	−10640.8	−	7730.98i	−0.972082	−	0.706259i
$494$	−3899.84	−	1042.79i	−0.355186	−	0.0949746i
$495$	−2634.33	+	9053.19i	−0.239201	+	0.822041i
$496$	4197.26	−	7269.86i	0.379965	−	0.658118i
$497$	−9199.10	+	4095.70i	−0.830254	+	0.369653i
$498$	4391.41	−	933.422i	0.395148	−	0.0839913i
$499$	−1549.19	−	4767.93i	−0.138981	−	0.427739i	0.857207	−	0.514972i	$-0.172198\pi$
$499$	−1549.19	−	4767.93i	−0.138981	−	0.427739i	−0.996188	+	0.0872327i	$0.972198\pi$
$500$	4634.99	+	2063.63i	0.414566	+	0.184577i
$501$	−9757.48	−	4344.31i	−0.870124	−	0.387404i
$502$	−1344.01	−	4136.44i	−0.119494	−	0.367766i
$503$	−8134.89	+	1729.12i	−0.721107	+	0.153276i	−0.553825	−	0.832633i	$-0.686832\pi$
$503$	−8134.89	+	1729.12i	−0.721107	+	0.153276i	−0.167282	+	0.985909i	$0.553499\pi$
$504$	−2812.54	+	1252.22i	−0.248572	+	0.110671i
$505$	4413.27	−	7644.02i	0.388887	−	0.673573i
$506$	−2156.28	+	1671.13i	−0.189444	+	0.146820i
$507$	−6551.82	+	3791.76i	−0.573919	+	0.332146i
$508$	−1868.72	−	1357.71i	−0.163211	−	0.118580i
$509$	6451.07	+	7164.63i	0.561765	+	0.623903i	0.955383	−	0.295371i	$-0.0954432\pi$
$509$	6451.07	+	7164.63i	0.561765	+	0.623903i	−0.393617	+	0.919274i	$0.628777\pi$
$510$	−3106.44	−	660.294i	−0.269717	−	0.0573300i
$511$	−8033.69	−	3576.83i	−0.695479	−	0.309647i
$512$	9442.24	−	6860.19i	0.815024	−	0.592149i
$513$	8800.42	−	9773.86i	0.757404	−	0.841182i
$514$	−396.502	+	84.2791i	−0.0340252	+	0.00723228i
$515$	16056.2	+	11665.5i	1.37382	+	0.998142i
$516$	2669.26	+	4623.30i	0.227728	+	0.394437i
$517$	19959.3	−	9638.32i	1.69789	−	0.819909i
$518$	−2151.16	+	3725.92i	−0.182464	+	0.316037i
$519$	5491.02	+	3989.46i	0.464411	+	0.337414i
$520$	6253.17	−	9639.98i	0.527346	−	0.812963i
$521$	−6156.55	−	18947.9i	−0.517703	−	1.59333i	−0.778309	−	0.627881i	$-0.783922\pi$
$521$	−6156.55	−	18947.9i	−0.517703	−	1.59333i	0.260606	−	0.965445i	$-0.416078\pi$
$522$	−348.298	−	3313.83i	−0.0292042	−	0.277859i
$523$	1316.30	+	12523.7i	0.110053	+	1.04708i	0.900591	+	0.434669i	$0.143134\pi$
$523$	1316.30	+	12523.7i	0.110053	+	1.04708i	−0.790538	+	0.612413i	$0.790199\pi$
$524$	4200.54	−	4665.17i	0.350193	−	0.388929i
$525$	2519.49	−	7754.20i	0.209447	−	0.644611i
$526$	−62.9096	+	598.545i	−0.00521481	+	0.0496156i
$527$	5523.52	+	9567.01i	0.456562	+	0.790788i
$528$	−5419.28	+	168.021i	−0.446674	+	0.0138489i
$529$	2989.22	+	5177.48i	0.245683	+	0.425535i
$530$	−2695.62	+	1200.17i	−0.220925	+	0.0983621i
$531$	−5522.82	−	6133.72i	−0.451356	−	0.501282i
$532$	2817.92	+	8672.66i	0.229647	+	0.706781i
$533$	2432.63	−	15410.7i	0.197690	−	1.25237i
$534$	−4133.25	+	3002.98i	−0.334950	+	0.243355i
$535$	8090.77	+	1719.75i	0.653822	+	0.138974i
$536$	5164.16	+	5735.38i	0.416152	+	0.462184i
$537$	−477.705	+	4545.06i	−0.0383883	+	0.365240i
$538$	972.055			0.0778964
$539$	3342.35	−	3951.76i	0.267097	−	0.315797i
$540$	8798.85	+	15240.1i	0.701189	+	1.21450i
$541$	17601.0	+	12787.8i	1.39875	+	1.01625i	0.994840	+	0.101454i	$0.0323496\pi$
$541$	17601.0	+	12787.8i	1.39875	+	1.01625i	0.403911	+	0.914798i	$0.367650\pi$
$542$	−3831.93	+	814.501i	−0.303681	+	0.0645495i
$543$	−10064.1	−	2139.19i	−0.795380	−	0.169063i
$544$	924.359	+	8794.69i	0.0728522	+	0.693142i
$545$	20531.3	−	14916.9i	1.61370	−	1.17242i
$546$	−1940.36	−	987.397i	−0.152088	−	0.0773932i
$547$	7053.13	−	21707.3i	0.551316	−	1.69678i	−0.154163	−	0.988045i	$-0.549268\pi$
$547$	7053.13	−	21707.3i	0.551316	−	1.69678i	0.705479	−	0.708731i	$-0.250732\pi$
$548$	−2732.67	+	1216.66i	−0.213018	+	0.0948417i
$549$	−3493.97	+	6051.73i	−0.271619	+	0.470458i
$550$	3736.52	−	4417.80i	0.289683	−	0.342501i
$551$	−20995.5			−1.62330
$552$	−406.569	+	3868.25i	−0.0313492	+	0.298268i
$553$	−3832.78	+	814.682i	−0.294731	+	0.0626470i
$554$	−568.719	−	1750.34i	−0.0436147	−	0.134232i
$555$	17161.8	+	7640.95i	1.31258	+	0.584397i
$556$	−547.924	−	5213.15i	−0.0417934	−	0.397638i
$557$	6442.00	+	1369.29i	0.490047	+	0.104163i	0.446306	−	0.894880i	$-0.352739\pi$
$557$	6442.00	+	1369.29i	0.490047	+	0.104163i	0.0437406	+	0.999043i	$0.486072\pi$
$558$	−864.825	+	2661.66i	−0.0656110	+	0.201930i
$559$	3662.46	−	9555.85i	0.277112	−	0.723022i
$560$	−10450.1			−0.788569
$561$	3374.35	−	6286.77i	0.253948	−	0.473133i
$562$	1096.88	−	1899.85i	0.0823292	−	0.142598i
$563$	−691.188	+	6576.22i	−0.0517409	+	0.492282i	0.937711	+	0.347417i	$0.112941\pi$
$563$	−691.188	+	6576.22i	−0.0517409	+	0.492282i	−0.989452	+	0.144864i	$0.953725\pi$
$564$	4590.49	−	14128.1i	0.342721	−	1.05479i
$565$	1034.49	−	1148.92i	0.0770289	−	0.0855493i
$566$	5121.26	+	2280.13i	0.380323	+	0.169330i
$567$	1051.98	−	764.310i	0.0779173	−	0.0566102i
$568$	−6817.53	+	7571.64i	−0.503622	+	0.559329i
$569$	−5417.37	−	6016.60i	−0.399136	−	0.443285i	0.509755	−	0.860320i	$-0.329736\pi$
$569$	−5417.37	−	6016.60i	−0.399136	−	0.443285i	−0.908891	+	0.417035i	$0.863069\pi$
$570$	−4631.26	+	2061.97i	−0.340320	+	0.151520i
$571$	5098.10			0.373641			0.186820	−	0.982394i	$-0.440182\pi$
$571$	5098.10			0.373641			0.186820	+	0.982394i	$0.440182\pi$
$572$	7930.29	+	9185.53i	0.579689	+	0.671444i
$573$	−9926.77			−0.723729
$574$	4099.14	−	1825.06i	0.298075	−	0.132711i
$575$	8782.78	+	9754.26i	0.636986	+	0.707445i
$576$	1993.81	−	2214.35i	0.144228	−	0.160182i
$577$	−15939.6	+	11580.8i	−1.15004	+	0.835553i	−0.988486	−	0.151310i	$-0.951651\pi$
$577$	−15939.6	+	11580.8i	−1.15004	+	0.835553i	−0.161554	+	0.986864i	$0.551651\pi$
$578$	1468.56	+	653.847i	0.105682	+	0.0470527i
$579$	−7249.51	+	8051.40i	−0.520345	+	0.577901i
$580$	8681.04	−	26717.5i	0.621484	−	1.91273i
$581$	−2032.11	+	19334.2i	−0.145105	+	1.38058i
$582$	591.403	−	1024.34i	0.0421211	−	0.0729558i
$583$	−896.935	−	6568.37i	−0.0637174	−	0.466611i
$584$	−8897.87			−0.630473
$585$	4335.30	−	11311.4i	0.306397	−	0.799431i
$586$	−1724.64	+	5307.89i	−0.121577	+	0.374176i
$587$	−13001.0	−	2763.45i	−0.914155	−	0.194310i	−0.273262	−	0.961940i	$-0.588103\pi$
$587$	−13001.0	−	2763.45i	−0.914155	−	0.194310i	−0.640893	+	0.767630i	$0.721436\pi$
$588$	−362.592	−	3449.83i	−0.0254304	−	0.241954i
$589$	16109.7	+	7172.48i	1.12697	+	0.501761i
$590$	2737.78	+	8426.02i	0.191038	+	0.587956i
$591$	−4192.03	+	891.044i	−0.291772	+	0.0620180i
$592$	1438.89	−	13690.1i	0.0998950	−	0.950437i
$593$	−11459.8			−0.793588			−0.396794	−	0.917908i	$-0.629877\pi$
$593$	−11459.8			−0.793588			−0.396794	+	0.917908i	$0.629877\pi$
$594$	4888.93	−	1198.65i	0.337702	−	0.0827967i
$595$	6876.09	−	11909.7i	0.473769	−	0.820591i
$596$	13884.7	−	6181.88i	0.954263	−	0.424865i
$597$	−1416.81	+	4360.49i	−0.0971292	+	0.298933i
$598$	2938.48	−	1910.44i	0.200942	−	0.130641i
$599$	18732.4	−	13609.9i	1.27777	−	0.928357i	0.278291	−	0.960497i	$-0.410232\pi$
$599$	18732.4	−	13609.9i	1.27777	−	0.928357i	0.999483	+	0.0321393i	$0.0102320\pi$
$600$	−862.315	−	8204.38i	−0.0586731	−	0.558237i
$601$	18033.2	+	3833.07i	1.22394	+	0.260156i	0.774164	−	0.632985i	$-0.218171\pi$
$601$	18033.2	+	3833.07i	1.22394	+	0.260156i	0.449776	+	0.893141i	$0.351504\pi$
$602$	2878.93	−	611.935i	0.194911	−	0.0414296i
$603$	6582.40	+	4782.39i	0.444537	+	0.322975i
$604$	−5892.85	−	10206.7i	−0.396981	−	0.687591i
$605$	12567.2	+	18949.8i	0.844512	+	1.27342i
$606$	−1692.16			−0.113431
$607$	2314.92	−	22025.0i	0.154793	−	1.47276i	−0.591047	−	0.806637i	$-0.701285\pi$
$607$	2314.92	−	22025.0i	0.154793	−	1.47276i	0.745840	−	0.666125i	$-0.232048\pi$
$608$	9445.56	+	10490.4i	0.630046	+	0.699737i
$609$	−11075.8	−	2354.23i	−0.736969	−	0.156648i
$610$	6068.37	−	4408.93i	0.402789	−	0.292643i
$611$	−26579.8	+	10218.8i	−1.75991	+	0.676612i
$612$	1883.03	+	5795.36i	0.124374	+	0.382784i
$613$	−6805.46	−	7558.22i	−0.448401	−	0.498000i	0.475988	−	0.879452i	$-0.342091\pi$
$613$	−6805.46	−	7558.22i	−0.448401	−	0.498000i	−0.924389	+	0.381452i	$0.875424\pi$
$614$	1391.17	−	619.389i	0.0914383	−	0.0407109i
$615$	−9796.35	−	16967.8i	−0.642320	−	1.11253i
$616$	−2074.41	+	7128.96i	−0.135683	+	0.466289i
$617$	1917.37	+	3320.99i	0.125106	+	0.216690i	0.921774	−	0.387727i	$-0.126740\pi$
$617$	1917.37	+	3320.99i	0.125106	+	0.216690i	−0.796668	+	0.604417i	$0.793406\pi$
$618$	397.712	−	3783.98i	0.0258873	−	0.246301i
$619$	−3398.10	+	10458.3i	−0.220648	+	0.679085i	0.778056	+	0.628195i	$0.216206\pi$
$619$	−3398.10	+	10458.3i	−0.220648	+	0.679085i	−0.998704	+	0.0508900i	$0.983794\pi$
$620$	−15788.1	+	17534.5i	−1.02269	+	1.13581i
$621$	1193.61	+	11356.4i	0.0771302	+	0.733845i
$622$	−264.179	−	2513.50i	−0.0170299	−	0.162029i
$623$	−6836.44	−	21040.4i	−0.439640	−	1.35307i
$624$	6956.52	+	360.960i	0.446288	+	0.0231570i
$625$	6991.79	+	5079.84i	0.447475	+	0.325109i
$626$	−1175.15	+	2035.42i	−0.0750294	+	0.129955i
$627$	−1541.00	−	11284.9i	−0.0981524	−	0.718783i
$628$	5648.83	+	9784.07i	0.358938	+	0.621699i
$629$	14655.5	+	10647.8i	0.929016	+	0.674970i
$630$	3407.82	−	724.354i	0.215509	−	0.0458079i
$631$	−10761.1	+	11951.5i	−0.678913	+	0.754010i	−0.979872	−	0.199628i	$-0.936027\pi$
$631$	−10761.1	+	11951.5i	−0.678913	+	0.754010i	0.300959	+	0.953637i	$0.402693\pi$
$632$	−3207.51	+	2330.39i	−0.201879	+	0.146674i
$633$	−2169.08	−	965.735i	−0.136198	−	0.0606391i
$634$	−7456.23	−	1584.87i	−0.467074	−	0.0992796i
$635$	3720.79	+	4132.36i	0.232528	+	0.258248i
$636$	−3594.54	−	2611.59i	−0.224108	−	0.162824i
$637$	−4699.52	+	4704.40i	−0.292311	+	0.292614i
$638$	−6644.26	−	4519.53i	−0.412302	−	0.280454i
$639$	−5370.62	+	9302.19i	−0.332486	+	0.575882i
$640$	−22373.6	+	9961.37i	−1.38187	+	0.615246i
$641$	−18972.7	+	4032.78i	−1.16908	+	0.248495i	−0.751241	−	0.660028i	$-0.770544\pi$
$641$	−18972.7	+	4032.78i	−1.16908	+	0.248495i	−0.417835	+	0.908523i	$0.637211\pi$
$642$	−490.024	−	1508.14i	−0.0301242	−	0.0927127i
$643$	4752.30	+	2115.86i	0.291465	+	0.129769i	0.547261	−	0.836962i	$-0.315671\pi$
$643$	4752.30	+	2115.86i	0.291465	+	0.129769i	−0.255795	+	0.966731i	$0.582337\pi$
$644$	−7232.87	−	3220.28i	−0.442570	−	0.197045i
$645$	−3971.37	−	12222.6i	−0.242438	−	0.746147i
$646$	−4781.69	+	1016.38i	−0.291228	+	0.0619023i
$647$	6201.32	−	2761.01i	0.376815	−	0.167769i	−0.209585	−	0.977790i	$-0.567211\pi$
$647$	6201.32	−	2761.01i	0.376815	−	0.167769i	0.586400	+	0.810022i	$0.300545\pi$
$648$	657.842	−	1139.42i	0.0398804	−	0.0690749i
$649$	−19895.2	+	616.840i	−1.20332	+	0.0373083i
$650$	−5253.74	+	5259.19i	−0.317029	+	0.317358i
$651$	7694.11	+	5590.10i	0.463220	+	0.336549i
$652$	−4516.66	−	5016.26i	−0.271298	−	0.301307i
$653$	18968.5	+	4031.88i	1.13675	+	0.241623i	0.737582	−	0.675257i	$-0.235967\pi$
$653$	18968.5	+	4031.88i	1.13675	+	0.241623i	0.399163	+	0.916880i	$0.369301\pi$
$654$	−4444.67	−	1978.89i	−0.265750	−	0.118319i
$655$	−12226.1	+	8882.79i	−0.729334	+	0.529892i
$656$	−9606.45	+	10669.0i	−0.571751	+	0.634994i
$657$	−9175.48	+	1950.31i	−0.544854	+	0.115812i
$658$	−6625.82	−	4813.94i	−0.392555	−	0.285208i
$659$	−12868.0	−	22288.1i	−0.760648	−	1.31748i	−0.942517	−	0.334159i	$-0.891548\pi$
$659$	−12868.0	−	22288.1i	−0.760648	−	1.31748i	0.181869	−	0.983323i	$-0.441785\pi$
$660$	14997.6	+	2705.02i	0.884518	+	0.159535i
$661$	−11629.1	+	20142.3i	−0.684299	+	1.18524i	0.289358	+	0.957221i	$0.406558\pi$
$661$	−11629.1	+	20142.3i	−0.684299	+	1.18524i	−0.973657	+	0.228019i	$0.926775\pi$
$662$	816.151	+	592.968i	0.0479163	+	0.0348133i
$663$	−4988.71	+	7690.66i	−0.292225	+	0.450498i
$664$	6078.49	+	18707.7i	0.355258	+	1.09337i
$665$	−2294.65	−	21832.2i	−0.133809	−	1.27311i
$666$	479.707	+	4564.11i	0.0279103	+	0.265549i
$667$	12197.5	−	13546.7i	0.708082	−	0.786405i
$668$	6797.85	−	20921.6i	0.393737	−	1.21180i
$669$	−861.070	+	8192.53i	−0.0497622	+	0.473455i
$670$	−4366.79	−	7563.51i	−0.251797	−	0.436125i
$671$	5701.79	+	15858.3i	0.328040	+	0.912373i
$672$	3806.55	+	6593.13i	0.218513	+	0.378476i
$673$	10135.7	−	4512.68i	0.580536	−	0.258471i	−0.0953910	−	0.995440i	$-0.530410\pi$
$673$	10135.7	−	4512.68i	0.580536	−	0.258471i	0.675927	+	0.736969i	$0.263743\pi$
$674$	5020.62	+	5575.96i	0.286924	+	0.318662i
$675$	−7484.13	−	23033.8i	−0.426762	−	1.31344i
$676$	−9177.22	−	12603.9i	−0.522145	−	0.717106i
$677$	−13526.0	+	9827.25i	−0.767870	+	0.557891i	−0.901314	−	0.433166i	$-0.857396\pi$
$677$	−13526.0	+	9827.25i	−0.767870	+	0.557891i	0.133444	+	0.991056i	$0.457396\pi$
$678$	−289.914	−	61.6232i	−0.0164220	−	0.00349060i
$679$	3427.19	+	3806.28i	0.193702	+	0.215127i
$680$	1454.48	−	13838.4i	0.0820246	−	0.780412i
$681$	−3465.51			−0.195005
$682$	3554.12	+	5737.61i	0.199552	+	0.322147i
$683$	−4134.44	−	7161.06i	−0.231625	−	0.401186i	0.726661	−	0.686996i	$-0.241071\pi$
$683$	−4134.44	−	7161.06i	−0.231625	−	0.401186i	−0.958286	+	0.285809i	$0.907738\pi$
$684$	7869.42	+	5717.47i	0.439905	+	0.319609i
$685$	7043.65	−	1497.17i	0.392882	−	0.0835097i
$686$	−6393.47	−	1358.97i	−0.355836	−	0.0756354i
$687$	−1977.58	−	18815.4i	−0.109824	−	1.04491i
$688$	−7618.56	+	5535.21i	−0.422173	+	0.306727i
$689$	450.164	+	8505.27i	0.0248910	+	0.470283i
$690$	1360.15	−	4186.11i	0.0750435	−	0.230960i
$691$	17600.7	−	7836.34i	0.968977	−	0.431416i	0.139663	−	0.990199i	$-0.455398\pi$
$691$	17600.7	−	7836.34i	0.968977	−	0.431416i	0.829314	+	0.558783i	$0.188731\pi$
$692$	−6989.52	+	12106.2i	−0.383962	+	0.665041i
$693$	−576.549	+	7806.06i	−0.0316036	+	0.427890i
$694$	486.582			0.0266144
$695$	−1319.04	+	12549.8i	−0.0719912	+	0.684951i
$696$	−11206.7	+	2382.05i	−0.610327	+	0.129729i
$697$	−5838.27	−	17968.3i	−0.317274	−	0.976470i
$698$	2377.99	+	1058.75i	0.128951	+	0.0574129i
$699$	1329.53	+	12649.7i	0.0719422	+	0.684484i
$700$	16425.4	+	3491.33i	0.886889	+	0.188514i
$701$	4863.54	−	14968.4i	0.262045	−	0.806491i	−0.730315	−	0.683111i	$-0.760627\pi$
$701$	4863.54	−	14968.4i	0.262045	−	0.806491i	0.992360	−	0.123380i	$-0.0393734\pi$
$702$	−6387.04	+	1015.00i	−0.343395	+	0.0545709i
$703$	28916.9			1.55138
$704$	−972.237	−	7119.82i	−0.0520491	−	0.381162i
$705$	−17880.6	+	30970.2i	−0.955211	+	1.65447i
$706$	−485.167	+	4616.06i	−0.0258633	+	0.246073i
$707$	2264.31	−	6968.83i	0.120450	−	0.370707i
$708$	−8926.57	+	9913.96i	−0.473843	+	0.526256i
$709$	−14986.7	−	6672.49i	−0.793845	−	0.353443i	−0.0305835	−	0.999532i	$-0.509737\pi$
$709$	−14986.7	−	6672.49i	−0.793845	−	0.353443i	−0.763262	+	0.646090i	$0.776403\pi$
$710$	9327.77	−	6777.02i	0.493049	−	0.358221i
$711$	−2796.79	+	3106.14i	−0.147521	+	0.163839i
$712$	−14978.2	−	16635.0i	−0.788387	−	0.875592i
$713$	−13986.9	+	6227.37i	−0.734661	+	0.327092i
$714$	−2636.46			−0.138189
$715$	−14076.2	−	25598.6i	−0.736252	−	1.33893i
$716$	−9412.54			−0.491289
$717$	9915.34	−	4414.59i	0.516451	−	0.229939i
$718$	1749.32	+	1942.81i	0.0909247	+	0.100982i
$719$	16211.5	−	18004.7i	0.840874	−	0.933885i	−0.157688	−	0.987489i	$-0.550404\pi$
$719$	16211.5	−	18004.7i	0.840874	−	0.933885i	0.998562	+	0.0536036i	$0.0170707\pi$
$720$	−9018.17	+	6552.09i	−0.466788	+	0.339141i
$721$	15051.4	+	6701.32i	0.777454	+	0.346145i
$722$	−858.999	+	954.015i	−0.0442779	+	0.0491756i
$723$	−538.558	+	1657.51i	−0.0277029	+	0.0852607i
$724$	2215.06	−	21074.9i	0.113705	−	1.08183i
$725$	−19331.4	+	33482.9i	−0.990275	+	1.71521i
$726$	1941.55	−	3902.96i	0.0992529	−	0.199521i
$727$	−32044.3			−1.63474			−0.817371	−	0.576111i	$-0.804570\pi$
$727$	−32044.3			−1.63474			−0.817371	+	0.576111i	$0.804570\pi$
$728$	3413.84	−	8907.16i	0.173799	−	0.453463i
$729$	4601.55	−	14162.1i	0.233783	−	0.719509i
$730$	9849.05	+	2093.48i	0.499356	+	0.106141i
$731$	−1295.39	−	12324.8i	−0.0655426	−	0.623596i
$732$	10318.2	+	4593.94i	0.520997	+	0.231963i
$733$	11171.7	+	34383.0i	0.562942	+	1.73256i	0.673988	+	0.738742i	$0.264580\pi$
$733$	11171.7	+	34383.0i	0.562942	+	1.73256i	−0.111046	+	0.993815i	$0.535420\pi$
$734$	−8147.79	+	1731.87i	−0.409728	+	0.0870904i
$735$	−872.881	+	8304.91i	−0.0438050	+	0.416777i
$736$	−12256.1			−0.613812
$737$	19057.2	−	4672.37i	0.952482	−	0.233526i
$738$	2393.16	−	4145.08i	0.119368	−	0.206751i
$739$	16602.4	−	7391.89i	0.826429	−	0.367950i	0.0504639	−	0.998726i	$-0.483930\pi$
$739$	16602.4	−	7391.89i	0.826429	−	0.367950i	0.775965	+	0.630776i	$0.217263\pi$
$740$	−11956.3	+	36797.8i	−0.593950	+	1.82799i
$741$	773.414	+	14612.7i	0.0383429	+	0.724439i
$742$	−1981.75	+	1439.82i	−0.0980489	+	0.0712367i
$743$	−2023.69	−	19254.1i	−0.0999220	−	0.950694i	−0.923528	−	0.383531i	$-0.874708\pi$
$743$	−2023.69	−	19254.1i	−0.0999220	−	0.950694i	0.823606	−	0.567163i	$-0.191959\pi$
$744$	9412.52	+	2000.69i	0.463817	+	0.0985874i
$745$	−35788.9	+	7607.16i	−1.76000	+	0.374101i
$746$	2150.37	+	1562.33i	0.105537	+	0.0766771i
$747$	10368.6	+	17959.0i	0.507856	+	0.879632i
$748$	13603.7	+	5558.26i	0.664974	+	0.271698i
$749$	6866.70			0.334985
$750$	−244.759	+	2328.73i	−0.0119165	+	0.113378i
$751$	−12018.8	−	13348.2i	−0.583983	−	0.648579i	0.376664	−	0.926350i	$-0.377071\pi$
$751$	−12018.8	−	13348.2i	−0.583983	−	0.648579i	−0.960647	+	0.277771i	$0.910404\pi$
$752$	25631.6	+	5448.16i	1.24293	+	0.264194i
$753$	−12754.8	+	9266.88i	−0.617277	+	0.448478i
$754$	8026.65	+	6492.96i	0.387683	+	0.313607i
$755$	8767.46	+	26983.5i	0.422623	+	1.30070i
$756$	9775.29	+	10856.6i	0.470269	+	0.522287i
$757$	−16478.7	+	7336.79i	−0.791187	+	0.352259i	−0.762218	−	0.647321i	$-0.775889\pi$
$757$	−16478.7	+	7336.79i	−0.791187	+	0.352259i	−0.0289698	+	0.999580i	$0.509223\pi$
$758$	−6654.16	−	11525.3i	−0.318852	−	0.552268i
$759$	8176.53	+	5561.80i	0.391027	+	0.265982i
$760$	−11105.9	−	19236.0i	−0.530070	−	0.918108i
$761$	4228.29	−	40229.5i	0.201413	−	1.91632i	−0.165759	−	0.986166i	$-0.553007\pi$
$761$	4228.29	−	40229.5i	0.201413	−	1.91632i	0.367172	−	0.930153i	$-0.380326\pi$
$762$	329.425	−	1013.87i	0.0156612	−	0.0482001i
$763$	14097.2	−	15656.5i	0.668877	−	0.742863i
$764$	−2137.10	−	20333.1i	−0.101201	−	0.962861i
$765$	−1533.36	−	14589.0i	−0.0724692	−	0.689498i
$766$	263.906	+	812.220i	0.0124482	+	0.0383116i
$767$	25538.8	+	1325.15i	1.20228	+	0.0623840i
$768$	−593.883	−	431.482i	−0.0279035	−	0.0202731i
$769$	−1701.72	+	2947.46i	−0.0797990	+	0.138216i	−0.903163	−	0.429298i	$-0.858761\pi$
$769$	−1701.72	+	2947.46i	−0.0797990	+	0.138216i	0.823364	+	0.567513i	$0.192095\pi$
$770$	3973.46	−	7402.98i	0.185966	−	0.346474i
$771$	734.691	+	1272.52i	0.0343181	+	0.0594407i
$772$	−18052.5	−	13115.9i	−0.841610	−	0.611466i
$773$	−6546.39	+	1391.48i	−0.304602	+	0.0647452i	−0.357677	−	0.933845i	$-0.616431\pi$
$773$	−6546.39	+	1391.48i	−0.304602	+	0.0647452i	0.0530750	+	0.998591i	$0.483098\pi$
$774$	2100.76	−	2333.13i	0.0975585	−	0.108350i
$775$	26271.2	−	19087.2i	1.21766	−	0.884685i
$776$	4734.32	+	2107.86i	0.219011	+	0.0975099i
$777$	15254.6	+	3242.47i	0.704319	+	0.149708i
$778$	5230.27	+	5808.80i	0.241021	+	0.267681i
$779$	−24398.9	−	17726.8i	−1.12218	−	0.815314i
$780$	−18914.9	−	5057.72i	−0.868285	−	0.232174i
$781$	8764.29	+	24376.0i	0.401551	+	1.11683i
$782$	2122.18	−	3675.72i	0.0970447	−	0.168086i
$783$	−30727.7	+	13680.8i	−1.40245	+	0.624410i
$784$	5985.25	−	1272.20i	0.272652	−	0.0579539i
$785$	−8404.42	−	25866.1i	−0.382123	−	1.17605i
$786$	2646.74	+	1178.40i	0.120109	+	0.0534761i
$787$	−8491.22	−	3780.53i	−0.384599	−	0.171234i	0.205324	−	0.978694i	$-0.434175\pi$
$787$	−8491.22	−	3780.53i	−0.384599	−	0.171234i	−0.589923	+	0.807460i	$0.700842\pi$
$788$	−2727.62	−	8394.76i	−0.123309	−	0.379506i
$789$	2133.93	−	453.582i	0.0962865	−	0.0204663i
$790$	4098.68	−	1824.85i	0.184588	−	0.0821839i
$791$	641.724	−	1111.50i	0.0288459	−	0.0499625i
$792$	2679.60	+	7452.72i	0.120221	+	0.334370i
$793$	−5614.58	−	20910.5i	−0.251425	−	0.936387i
$794$	8340.54	+	6059.76i	0.372789	+	0.270847i
$795$	7157.03	+	7948.69i	0.319288	+	0.354605i
$796$	−9236.65	−	1963.31i	−0.411287	−	0.0874218i
$797$	−1039.28	−	462.719i	−0.0461899	−	0.0205651i	0.383512	−	0.923536i	$-0.374715\pi$
$797$	−1039.28	−	462.719i	−0.0461899	−	0.0205651i	−0.429702	+	0.902971i	$0.641381\pi$
$798$	−3404.79	+	2473.72i	−0.151038	+	0.109735i
$799$	−23074.5	+	25626.8i	−1.02167	+	1.13468i
$800$	25426.6	−	5404.58i	1.12371	−	0.238851i
$801$	−19091.7	−	13870.9i	−0.842162	−	0.611866i
$802$	2066.39	+	3579.10i	0.0909812	+	0.157584i
$803$	−10698.5	+	19932.4i	−0.470162	+	0.875962i
$804$	6575.37	−	11388.9i	0.288427	−	0.499570i
$805$	15419.7	+	11203.0i	0.675120	+	0.490503i
$806$	−3940.65	−	7724.05i	−0.172213	−	0.337554i
$807$	−1088.85	−	3351.13i	−0.0474960	−	0.146178i
$808$	−774.978	−	7373.42i	−0.0337421	−	0.321035i
$809$	3034.56	+	28872.0i	0.131878	+	1.25474i	0.837614	+	0.546263i	$0.183950\pi$
$809$	3034.56	+	28872.0i	0.131878	+	1.25474i	−0.705735	+	0.708476i	$0.749383\pi$
$810$	−996.246	+	1106.44i	−0.0432155	+	0.0479956i
$811$	1361.59	−	4190.53i	0.0589541	−	0.181442i	−0.917243	−	0.398329i	$-0.869590\pi$
$811$	1361.59	−	4190.53i	0.0589541	−	0.181442i	0.976197	+	0.216887i	$0.0695903\pi$
$812$	2437.74	−	23193.5i	0.105354	−	1.00238i
$813$	7100.30	+	12298.1i	0.306296	+	0.530520i
$814$	9151.08	+	6224.71i	0.394036	+	0.268029i
$815$	8124.81	+	14072.6i	0.349202	+	0.604836i
$816$	7706.20	−	3431.02i	0.330602	−	0.147193i
$817$	−13236.9	−	14701.1i	−0.566831	−	0.629530i
$818$	3899.82	+	12002.4i	0.166692	+	0.513025i
$819$	1568.01	−	9933.33i	0.0668994	−	0.423808i
$820$	32646.2	−	23718.9i	1.39031	−	1.01012i
$821$	12223.6	+	2598.21i	0.519619	+	0.110449i	0.460253	−	0.887788i	$-0.347759\pi$
$821$	12223.6	+	2598.21i	0.519619	+	0.110449i	0.0593663	+	0.998236i	$0.481092\pi$
$822$	−923.750	−	1025.93i	−0.0391964	−	0.0435320i
$823$	−3440.36	+	32732.8i	−0.145715	+	1.38639i	0.640275	+	0.768146i	$0.278820\pi$
$823$	−3440.36	+	32732.8i	−0.145715	+	1.38639i	−0.785990	+	0.618239i	$0.787846\pi$
$824$	16670.5			0.704786
$825$	−19415.7	−	7932.94i	−0.819354	−	0.334775i
$826$	3677.47	+	6369.56i	0.154910	+	0.268312i
$827$	13943.9	+	10130.9i	0.586310	+	0.425979i	0.840993	−	0.541046i	$-0.181971\pi$
$827$	13943.9	+	10130.9i	0.586310	+	0.425979i	−0.254684	+	0.967024i	$0.581971\pi$
$828$	−8260.84	+	1755.90i	−0.346720	+	0.0736976i
$829$	−34845.5	−	7406.64i	−1.45987	−	0.310306i	−0.591536	−	0.806279i	$-0.701478\pi$
$829$	−34845.5	−	7406.64i	−1.45987	−	0.310306i	−0.868338	+	0.495973i	$0.834811\pi$
$830$	−2326.76	−	22137.7i	−0.0973049	−	0.925794i
$831$	−5397.18	+	3921.28i	−0.225302	+	0.163692i
$832$	487.957	+	9219.33i	0.0203328	+	0.384162i
$833$	−2488.34	+	7658.34i	−0.103501	+	0.318542i
$834$	2210.05	−	983.978i	0.0917599	−	0.0408542i
$835$	−26478.6	+	45862.3i	−1.09740	+	1.90076i
$836$	22783.3	−	5585.93i	0.942556	−	0.231093i
$837$	28250.7			1.16665
$838$	−893.397	+	8500.10i	−0.0368280	+	0.350395i
$839$	8598.16	−	1827.59i	0.353804	−	0.0752033i	−0.0275814	−	0.999620i	$-0.508781\pi$
$839$	8598.16	−	1827.59i	0.353804	−	0.0752033i	0.381385	+	0.924416i	$0.375447\pi$
$840$	−3701.78	−	11392.9i	−0.152052	−	0.467967i
$841$	26772.3	+	11919.8i	1.09772	+	0.488736i
$842$	281.326	+	2676.63i	0.0115144	+	0.109552i
$843$	−7778.34	−	1653.34i	−0.317794	−	0.0675492i
$844$	1511.15	−	4650.85i	0.0616304	−	0.189679i
$845$	15301.5	+	34272.0i	0.622943	+	1.39526i
$846$	−8736.17			−0.355030
$847$	13475.6	+	13218.5i	0.546666	+	0.536239i
$848$	3918.77	−	6787.51i	0.158692	−	0.274863i
$849$	2124.10	−	20209.5i	0.0858645	−	0.816946i
$850$	−2781.80	+	8561.49i	−0.112253	+	0.345479i
$851$	−16799.6	+	18657.8i	−0.676712	+	0.751564i
$852$	15860.2	+	7061.40i	0.637747	+	0.283943i
$853$	−8020.61	+	5827.31i	−0.321947	+	0.233908i	−0.737006	−	0.675887i	$-0.763761\pi$
$853$	−8020.61	+	5827.31i	−0.321947	+	0.233908i	0.415059	+	0.909794i	$0.363761\pi$
$854$	4166.66	−	4627.55i	0.166956	−	0.185423i
$855$	−15668.7	−	17401.8i	−0.626734	−	0.696059i
$856$	6347.16	−	2825.94i	0.253436	−	0.112837i
$857$	−12603.2			−0.502353			−0.251176	−	0.967941i	$-0.580817\pi$
$857$	−12603.2			−0.502353			−0.251176	+	0.967941i	$0.580817\pi$
$858$	−2900.79	+	4790.82i	−0.115421	+	0.190625i
$859$	18001.8			0.715035			0.357517	−	0.933906i	$-0.383623\pi$
$859$	18001.8			0.715035			0.357517	+	0.933906i	$0.383623\pi$
$860$	24180.7	−	10766.0i	0.958786	−	0.426879i
$861$	−10883.5	−	12087.3i	−0.430787	−	0.478438i
$862$	5595.53	−	6214.47i	0.221096	−	0.245552i
$863$	−3848.25	+	2795.91i	−0.151791	+	0.110283i	−0.661089	−	0.750308i	$-0.729905\pi$
$863$	−3848.25	+	2795.91i	−0.151791	+	0.110283i	0.509297	+	0.860591i	$0.329905\pi$
$864$	20659.5	+	9198.20i	0.813484	+	0.362187i
$865$	22517.7	−	25008.5i	0.885117	−	0.983022i
$866$	−486.326	+	1496.76i	−0.0190832	+	0.0587320i
$867$	609.104	−	5795.24i	0.0238596	−	0.227009i
$868$	−9793.82	+	16963.4i	−0.382977	+	0.663336i
$869$	1363.79	+	9987.20i	0.0532374	+	0.389865i
$870$	12965.1			0.505239
$871$	−24896.8	+	3956.50i	−0.968539	+	0.153916i
$872$	6587.27	−	20273.5i	0.255818	−	0.787326i
$873$	5344.05	+	1135.91i	0.207181	+	0.0440376i
$874$	−708.202	−	6738.09i	−0.0274088	−	0.260777i
$875$	−9262.92	−	4124.12i	−0.357879	−	0.159338i
$876$	4685.22	+	14419.6i	0.180706	+	0.556157i
$877$	11029.2	−	2344.34i	0.424665	−	0.0902653i	0.00937849	−	0.999956i	$-0.497015\pi$
$877$	11029.2	−	2344.34i	0.424665	−	0.0902653i	0.415286	+	0.909691i	$0.363681\pi$
$878$	18.5412	−	176.408i	0.000712682	−	0.00678071i
$879$	20230.6			0.776295
$880$	−1980.12	+	26809.4i	−0.0758520	+	1.02698i
$881$	8321.38	−	14413.1i	0.318223	−	0.551178i	−0.661894	−	0.749597i	$-0.730247\pi$
$881$	8321.38	−	14413.1i	0.318223	−	0.551178i	0.980117	+	0.198419i	$0.0635806\pi$
$882$	−1863.62	+	829.739i	−0.0711468	+	0.0316766i
$883$	10430.1	−	32100.7i	0.397511	−	1.22341i	−0.529478	−	0.848324i	$-0.677612\pi$
$883$	10430.1	−	32100.7i	0.397511	−	1.22341i	0.926989	−	0.375089i	$-0.122388\pi$
$884$	−16826.9	−	8562.73i	−0.640213	−	0.325787i
$885$	25981.7	−	18876.8i	0.986854	−	0.716991i
$886$	75.0951	+	714.482i	0.00284748	+	0.0270920i
$887$	−45220.3	−	9611.88i	−1.71178	−	0.363850i	−0.755240	−	0.655448i	$-0.772480\pi$
$887$	−45220.3	−	9611.88i	−1.71178	−	0.363850i	−0.956541	+	0.291598i	$0.905813\pi$
$888$	15434.8	−	3280.78i	0.583287	−	0.123982i
$889$	3734.61	+	2713.35i	0.140894	+	0.102365i
$890$	12665.5	+	21937.3i	0.477021	+	0.826224i
$891$	−1761.47	−	2843.64i	−0.0662307	−	0.106920i
$892$	−16966.2			−0.636851
$893$	−5753.95	+	54745.2i	−0.215620	+	2.05149i
$894$	4693.58	+	5212.75i	0.175589	+	0.195012i
$895$	22164.0	+	4711.10i	0.827777	+	0.175949i
$896$	−16448.5	+	11950.5i	−0.613287	+	0.445579i
$897$	−9877.71	−	7990.34i	−0.367678	−	0.297424i
$898$	−1318.37	−	4057.52i	−0.0489916	−	0.150781i
$899$	−30176.8	−	33514.8i	−1.11953	−	1.24336i
$900$	16363.7	−	7285.59i	0.606063	−	0.269837i
$901$	5157.03	+	8932.24i	0.190683	+	0.330273i
$902$	−3905.39	−	10862.0i	−0.144163	−	0.400959i
$903$	−5334.46	−	9239.55i	−0.196589	−	0.340502i
$904$	135.742	−	1291.50i	0.00499415	−	0.0475161i
$905$	−15764.1	+	48517.1i	−0.579025	+	1.78206i
$906$	3639.59	−	4042.17i	0.133463	−	0.148225i
$907$	1465.94	+	13947.5i	0.0536668	+	0.510606i	0.988028	+	0.154277i	$0.0493049\pi$
$907$	1465.94	+	13947.5i	0.0536668	+	0.510606i	−0.934361	+	0.356328i	$0.884028\pi$
$908$	−746.076	−	7098.44i	−0.0272681	−	0.259438i
$909$	−2415.32	−	7433.60i	−0.0881312	−	0.271240i
$910$	−5874.45	+	9056.13i	−0.213996	+	0.329899i
$911$	−21897.6	−	15909.5i	−0.796377	−	0.578602i	0.113472	−	0.993541i	$-0.463803\pi$
$911$	−21897.6	−	15909.5i	−0.796377	−	0.578602i	−0.909849	+	0.414939i	$0.863803\pi$
$912$	6732.73	−	11661.4i	0.244455	−	0.423408i
$913$	49216.1	+	8876.79i	1.78403	+	0.321773i
$914$	5.77108	+	9.99581i	0.000208852	+	0.000361742i
$915$	−21997.1	−	15981.9i	−0.794757	−	0.577425i
$916$	38114.0	−	8101.38i	1.37481	−	0.292224i
$917$	−8394.68	+	9323.24i	−0.302308	+	0.335748i
$918$	−6335.89	+	4603.29i	−0.227795	+	0.165502i
$919$	5526.45	+	2460.53i	0.198369	+	0.0883194i	0.503517	−	0.863986i	$-0.332039\pi$
$919$	5526.45	+	2460.53i	0.198369	+	0.0883194i	−0.305148	+	0.952305i	$0.598706\pi$
$920$	18863.5	+	4009.56i	0.675991	+	0.143686i
$921$	−3693.65	−	4102.21i	−0.132150	−	0.146767i
$922$	−13211.4	−	9598.64i	−0.471902	−	0.342857i
$923$	−8630.25	−	32141.9i	−0.307766	−	1.14622i
$924$	12645.3	−	392.059i	0.450215	−	0.0139586i
$925$	26624.9	−	46115.7i	0.946402	−	1.63922i
$926$	−5252.75	+	2338.67i	−0.186410	+	0.0829952i
$927$	17190.6	−	3653.97i	0.609076	−	0.129463i
$928$	−11155.9	−	34334.4i	−0.394624	−	1.21453i
$929$	19907.2	+	8863.25i	0.703050	+	0.313018i	0.726944	−	0.686696i	$-0.240940\pi$
$929$	19907.2	+	8863.25i	0.703050	+	0.313018i	−0.0238942	+	0.999714i	$0.507606\pi$
$930$	−9948.00	−	4429.14i	−0.350761	−	0.156169i
$931$	3972.11	+	12224.9i	0.139829	+	0.430349i
$932$	−25624.2	+	5446.60i	−0.900590	+	0.191426i
$933$	−8369.29	+	3726.25i	−0.293674	+	0.130752i
$934$	−4477.28	+	7754.88i	−0.156854	+	0.271678i
$935$	−29251.1	−	19897.0i	−1.02311	−	0.695938i
$936$	−2638.62	−	9827.06i	−0.0921430	−	0.343171i
$937$	−19077.1	−	13860.3i	−0.665124	−	0.483241i	0.203266	−	0.979124i	$-0.434845\pi$
$937$	−19077.1	−	13860.3i	−0.665124	−	0.483241i	−0.868389	+	0.495883i	$0.834845\pi$
$938$	−4851.39	−	5388.01i	−0.168874	−	0.187553i
$939$	8333.39	+	1771.32i	0.289616	+	0.0615599i
$940$	−67286.0	−	29957.7i	−2.33471	−	1.03948i
$941$	8989.51	−	6531.26i	0.311424	−	0.226263i	−0.421083	−	0.907022i	$-0.638350\pi$
$941$	8989.51	−	6531.26i	0.311424	−	0.226263i	0.732507	+	0.680759i	$0.238350\pi$
$942$	−3488.88	+	3874.79i	−0.120673	+	0.134021i
$943$	25612.5	−	5444.10i	0.884472	−	0.188000i
$944$	−19038.2	−	13832.1i	−0.656398	−	0.476901i
$945$	−17584.3	−	30456.9i	−0.605309	−	1.04843i
$946$	−1024.39	−	7501.72i	−0.0352069	−	0.257825i
$947$	−2527.74	+	4378.18i	−0.0867377	+	0.150234i	−0.906130	−	0.422999i	$-0.860978\pi$
$947$	−2527.74	+	4378.18i	−0.0867377	+	0.150234i	0.819393	+	0.573233i	$0.194311\pi$
$948$	5465.49	+	3970.91i	0.187248	+	0.136043i
$949$	15816.8	−	24383.4i	0.541028	−	0.834057i
$950$	4440.54	+	13666.6i	0.151653	+	0.466740i
$951$	2888.31	+	27480.4i	0.0984856	+	0.937028i
$952$	−1207.45	−	11488.1i	−0.0411069	−	0.391106i
$953$	671.545	−	745.826i	0.0228263	−	0.0253512i	−0.731624	−	0.681709i	$-0.761237\pi$
$953$	671.545	−	745.826i	0.0228263	−	0.0253512i	0.754450	+	0.656358i	$0.227904\pi$
$954$	−807.444	+	2485.06i	−0.0274025	+	0.0843362i
$955$	−5144.70	+	48948.6i	−0.174323	+	1.65858i
$956$	11177.1	+	19359.3i	0.378131	+	0.654942i
$957$	−8138.37	+	27968.4i	−0.274897	+	0.944714i
$958$	273.774	+	474.191i	0.00923303	+	0.0159921i
$959$	5461.18	−	2431.47i	0.183890	−	0.0818732i
$960$	7757.90	+	8616.02i	0.260818	+	0.289668i
$961$	2499.17	+	7691.67i	0.0838902	+	0.258188i
$962$	−11055.0	−	8942.70i	−0.370508	−	0.299713i
$963$	5925.77	−	4305.33i	0.198292	−	0.144068i
$964$	−3511.04	−	746.294i	−0.117306	−	0.0249342i
$965$	35944.0	+	39919.9i	1.19905	+	1.33168i
$966$	381.946	−	3633.97i	0.0127214	−	0.121036i
$967$	−1922.76			−0.0639417			−0.0319709	−	0.999489i	$-0.510178\pi$
$967$	−1922.76			−0.0639417			−0.0319709	+	0.999489i	$0.510178\pi$
$968$	17896.0	+	6672.63i	0.594214	+	0.221556i
$969$	8860.15	+	15346.2i	0.293735	+	0.508764i
$970$	−4744.49	−	3447.07i	−0.157048	−	0.114102i
$971$	14520.6	−	3086.46i	0.479907	−	0.102007i	0.0383946	−	0.999263i	$-0.487776\pi$
$971$	14520.6	−	3086.46i	0.479907	−	0.102007i	0.441512	+	0.897255i	$0.354442\pi$
$972$	25011.8	+	5316.43i	0.825365	+	0.175437i
$973$	1095.01	+	10418.4i	0.0360787	+	0.343266i
$974$	−5044.83	+	3665.28i	−0.165962	+	0.120578i
$975$	24015.9	+	12221.0i	0.788845	+	0.401422i
$976$	−6156.71	+	18948.4i	−0.201917	+	0.621438i
$977$	35321.2	−	15726.0i	1.15663	−	0.514964i	0.263453	−	0.964672i	$-0.415139\pi$
$977$	35321.2	−	15726.0i	1.15663	−	0.514964i	0.893176	+	0.449708i	$0.148472\pi$
$978$	1557.63	−	2697.89i	0.0509278	−	0.0882095i
$979$	−55273.6	+	13551.8i	−1.80445	+	0.442408i
$980$	−17198.9			−0.560613
$981$	2349.07	−	22349.9i	0.0764526	−	0.727398i
$982$	4250.54	−	903.480i	0.138126	−	0.0293597i
$983$	−1485.22	−	4571.04i	−0.0481904	−	0.148315i	0.924066	−	0.382234i	$-0.124845\pi$
$983$	−1485.22	−	4571.04i	−0.0481904	−	0.148315i	−0.972256	+	0.233919i	$0.924845\pi$
$984$	−15034.5	−	6693.78i	−0.487075	−	0.216860i
$985$	2221.12	+	21132.6i	0.0718486	+	0.683594i
$986$	12228.9	+	2599.34i	0.394978	+	0.0839551i
$987$	−9173.99	+	28234.6i	−0.295857	+	0.910555i
$988$	−29764.8	+	4730.10i	−0.958445	+	0.152312i
$989$	17175.6			0.552225
$990$	−1212.58	−	8879.87i	−0.0389275	−	0.285071i
$991$	−283.864	+	491.666i	−0.00909912	+	0.0157601i	−0.870539	−	0.492099i	$-0.836230\pi$
$991$	−283.864	+	491.666i	−0.00909912	+	0.0157601i	0.861440	+	0.507859i	$0.169563\pi$
$992$	−3169.48	+	30155.6i	−0.101443	+	0.965162i
$993$	1130.03	−	3477.87i	0.0361132	−	0.111145i
$994$	6404.63	−	7113.06i	0.204369	−	0.226974i
$995$	20767.2	+	9246.13i	0.661671	+	0.294595i
$996$	27116.4	−	19701.2i	0.862667	−	0.626765i
$997$	23170.3	−	25733.3i	0.736020	−	0.817433i	−0.252647	−	0.967559i	$-0.581301\pi$
$997$	23170.3	−	25733.3i	0.736020	−	0.817433i	0.988667	+	0.150125i	$0.0479677\pi$
$998$	3188.62	+	3541.32i	0.101136	+	0.112323i
$999$	42320.9	−	18842.5i	1.34032	−	0.596747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.q.a.48.18	yes	320
11.3	even	5	inner	143.4.q.a.113.23	yes	320
13.3	even	3	inner	143.4.q.a.81.23	yes	320
143.3	even	15	inner	143.4.q.a.3.18	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.q.a.3.18	✓	320	143.3	even	15	inner
143.4.q.a.48.18	yes	320	1.1	even	1	trivial
143.4.q.a.81.23	yes	320	13.3	even	3	inner
143.4.q.a.113.23	yes	320	11.3	even	5	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.868356 + 0.386617i) q^{2} +(2.30554 + 2.56056i) q^{3} +(-4.74848 + 5.27372i) q^{4} +(13.8209 - 10.0415i) q^{5} +(-2.99199 - 1.33212i) q^{6} +(9.48972 - 10.5394i) q^{7} +(4.43431 - 13.6474i) q^{8} +(1.58131 - 15.0451i) q^{9} +O(q^{10})\)	\(q+(-0.868356 + 0.386617i) q^{2} +(2.30554 + 2.56056i) q^{3} +(-4.74848 + 5.27372i) q^{4} +(13.8209 - 10.0415i) q^{5} +(-2.99199 - 1.33212i) q^{6} +(9.48972 - 10.5394i) q^{7} +(4.43431 - 13.6474i) q^{8} +(1.58131 - 15.0451i) q^{9} +(-8.11928 + 14.0630i) q^{10} +(-25.2403 - 26.3425i) q^{11} -24.4515 q^{12} +(29.5165 + 36.4112i) q^{13} +(-4.16575 + 12.8208i) q^{14} +(57.5766 + 12.2383i) q^{15} +(-4.50852 - 42.8957i) q^{16} +(51.8537 + 23.0867i) q^{17} +(4.44357 + 13.6759i) q^{18} +(88.6267 - 18.8382i) q^{19} +(-12.6724 + 120.569i) q^{20} +48.8657 q^{21} +(32.1020 + 13.1164i) q^{22} +(-39.3337 + 68.1280i) q^{23} +(45.1685 - 20.1103i) q^{24} +(51.5595 - 158.684i) q^{25} +(-39.7080 - 20.2063i) q^{26} +(117.433 - 85.3201i) q^{27} +(10.5201 + 100.092i) q^{28} +(-226.658 - 48.1776i) q^{29} +(-54.7285 + 11.6329i) q^{30} +(157.454 + 114.397i) q^{31} +(77.8981 + 134.923i) q^{32} +(9.25921 - 125.363i) q^{33} -53.9532 q^{34} +(25.3254 - 240.955i) q^{35} +(71.8350 + 79.7808i) q^{36} +(312.174 + 66.3546i) q^{37} +(-69.6763 + 50.6228i) q^{38} +(-25.1817 + 159.526i) q^{39} +(-75.7540 - 233.147i) q^{40} +(-222.722 - 247.358i) q^{41} +(-42.4329 + 18.8923i) q^{42} +(-109.166 - 189.080i) q^{43} +(258.776 - 8.02319i) q^{44} +(-129.221 - 223.817i) q^{45} +(7.81623 - 74.3664i) q^{46} +(-187.739 + 577.800i) q^{47} +(99.4425 - 110.442i) q^{48} +(14.8291 + 141.089i) q^{49} +(16.5779 + 157.728i) q^{50} +(60.4357 + 186.002i) q^{51} +(-332.181 - 17.2362i) q^{52} +(147.007 + 106.807i) q^{53} +(-68.9875 + 119.490i) q^{54} +(-613.363 - 110.628i) q^{55} +(-101.755 - 176.245i) q^{56} +(252.569 + 183.502i) q^{57} +(215.446 - 45.7945i) q^{58} +(365.073 - 405.454i) q^{59} +(-337.942 + 245.529i) q^{60} +(-421.985 - 187.880i) q^{61} +(-180.954 - 38.4630i) q^{62} +(-143.561 - 159.440i) q^{63} +(159.349 + 115.774i) q^{64} +(773.569 + 206.847i) q^{65} +(40.4272 + 112.440i) q^{66} +(-268.915 + 465.774i) q^{67} +(-367.979 + 163.835i) q^{68} +(-265.131 + 56.3554i) q^{69} +(71.1660 + 219.026i) q^{70} +(-648.639 - 288.793i) q^{71} +(-198.315 - 88.2955i) q^{72} +(-191.613 - 589.724i) q^{73} +(-296.732 + 63.0723i) q^{74} +(525.192 - 233.831i) q^{75} +(-321.494 + 556.844i) q^{76} +(-517.158 + 16.0342i) q^{77} +(-39.8089 - 148.261i) q^{78} +(-223.524 - 162.400i) q^{79} +(-493.049 - 547.586i) q^{80} +(89.6835 + 19.0628i) q^{81} +(289.035 + 128.687i) q^{82} +(-1108.99 + 805.728i) q^{83} +(-232.038 + 257.704i) q^{84} +(948.492 - 201.608i) q^{85} +(167.896 + 121.984i) q^{86} +(-399.207 - 691.447i) q^{87} +(-471.430 + 227.653i) q^{88} +(779.964 - 1350.94i) q^{89} +(198.741 + 144.394i) q^{90} +(663.856 + 34.4461i) q^{91} +(-172.512 - 530.939i) q^{92} +(70.0959 + 666.918i) q^{93} +(-60.3634 - 574.319i) q^{94} +(1035.74 - 1150.31i) q^{95} +(-165.883 + 510.534i) q^{96} +(-37.7502 + 359.169i) q^{97} +(-67.4243 - 116.782i) q^{98} +(-436.240 + 338.088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9}+O(q^{10}) \) 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9	\( 320 q - 3 q^{2} - 3 q^{3} + 149 q^{4} - 12 q^{5} - 35 q^{6} - 3 q^{7} - 44 q^{8} + 369 q^{9} - 80 q^{10} + 30 q^{11} - 220 q^{12} - 114 q^{13} + 4 q^{14} - 33 q^{15} + 637 q^{16} + 143 q^{17} + 72 q^{18} + 17 q^{19} - 377 q^{20} - 524 q^{21} + 283 q^{22} + 196 q^{23} - 1137 q^{24} - 1324 q^{25} + 632 q^{26} + 192 q^{27} - 279 q^{28} + 943 q^{29} + 1617 q^{30} + 260 q^{31} - 52 q^{32} - 1244 q^{33} - 3508 q^{34} + 1253 q^{35} + 282 q^{36} + 333 q^{37} - 694 q^{38} - 1106 q^{39} - 296 q^{40} - 1751 q^{41} - 895 q^{42} - 2200 q^{43} - 252 q^{44} - 282 q^{45} + 485 q^{46} + 2116 q^{47} - 825 q^{48} + 1607 q^{49} + 348 q^{50} + 1768 q^{51} - 2431 q^{52} + 428 q^{53} + 8326 q^{54} - 1379 q^{55} + 7630 q^{56} - 888 q^{57} - 331 q^{58} - 1097 q^{59} - 1820 q^{60} + 885 q^{61} - 437 q^{62} + 540 q^{63} + 1148 q^{64} + 2324 q^{65} - 1686 q^{66} - 5184 q^{67} + 3834 q^{68} - 4905 q^{69} + 4078 q^{70} + 843 q^{71} + 1155 q^{72} - 972 q^{73} + 5631 q^{74} - 3431 q^{75} - 3090 q^{76} + 602 q^{77} + 1252 q^{78} + 1140 q^{79} + 8631 q^{80} - 3809 q^{81} + 4015 q^{82} - 5292 q^{83} - 5060 q^{84} + 391 q^{85} + 3388 q^{86} - 7600 q^{87} - 7229 q^{88} + 6276 q^{89} + 7374 q^{90} - 4602 q^{91} + 8158 q^{92} - 2599 q^{93} + 11081 q^{94} + 2305 q^{95} - 30114 q^{96} + 1377 q^{97} + 5102 q^{98} - 5812 q^{99}+O(q^{100}) \) 320 * q - 3 * q^2 - 3 * q^3 + 149 * q^4 - 12 * q^5 - 35 * q^6 - 3 * q^7 - 44 * q^8 + 369 * q^9 - 80 * q^10 + 30 * q^11 - 220 * q^12 - 114 * q^13 + 4 * q^14 - 33 * q^15 + 637 * q^16 + 143 * q^17 + 72 * q^18 + 17 * q^19 - 377 * q^20 - 524 * q^21 + 283 * q^22 + 196 * q^23 - 1137 * q^24 - 1324 * q^25 + 632 * q^26 + 192 * q^27 - 279 * q^28 + 943 * q^29 + 1617 * q^30 + 260 * q^31 - 52 * q^32 - 1244 * q^33 - 3508 * q^34 + 1253 * q^35 + 282 * q^36 + 333 * q^37 - 694 * q^38 - 1106 * q^39 - 296 * q^40 - 1751 * q^41 - 895 * q^42 - 2200 * q^43 - 252 * q^44 - 282 * q^45 + 485 * q^46 + 2116 * q^47 - 825 * q^48 + 1607 * q^49 + 348 * q^50 + 1768 * q^51 - 2431 * q^52 + 428 * q^53 + 8326 * q^54 - 1379 * q^55 + 7630 * q^56 - 888 * q^57 - 331 * q^58 - 1097 * q^59 - 1820 * q^60 + 885 * q^61 - 437 * q^62 + 540 * q^63 + 1148 * q^64 + 2324 * q^65 - 1686 * q^66 - 5184 * q^67 + 3834 * q^68 - 4905 * q^69 + 4078 * q^70 + 843 * q^71 + 1155 * q^72 - 972 * q^73 + 5631 * q^74 - 3431 * q^75 - 3090 * q^76 + 602 * q^77 + 1252 * q^78 + 1140 * q^79 + 8631 * q^80 - 3809 * q^81 + 4015 * q^82 - 5292 * q^83 - 5060 * q^84 + 391 * q^85 + 3388 * q^86 - 7600 * q^87 - 7229 * q^88 + 6276 * q^89 + 7374 * q^90 - 4602 * q^91 + 8158 * q^92 - 2599 * q^93 + 11081 * q^94 + 2305 * q^95 - 30114 * q^96 + 1377 * q^97 + 5102 * q^98 - 5812 * q^99

Introduction

L-functions

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