LMFDB - Embedded newform 105.3.f.a.29.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(29,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.f (of order $2$, degree $1$, 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:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.17
Character	$\chi$	$=$	105.29
Dual form			105.3.f.a.29.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.87229 q^{2} +(2.98471 - 0.302541i) q^{3} -0.494516 q^{4} +(2.18081 - 4.49934i) q^{5} +(5.58825 - 0.566446i) q^{6} -2.64575i q^{7} -8.41505 q^{8} +(8.81694 - 1.80599i) q^{9} +O(q^{10})$	\(q+1.87229 q^{2} +(2.98471 - 0.302541i) q^{3} -0.494516 q^{4} +(2.18081 - 4.49934i) q^{5} +(5.58825 - 0.566446i) q^{6} -2.64575i q^{7} -8.41505 q^{8} +(8.81694 - 1.80599i) q^{9} +(4.08312 - 8.42408i) q^{10} +20.6982i q^{11} +(-1.47598 + 0.149611i) q^{12} +8.03563i q^{13} -4.95362i q^{14} +(5.14785 - 14.0890i) q^{15} -13.7774 q^{16} -18.0807 q^{17} +(16.5079 - 3.38135i) q^{18} +13.9519 q^{19} +(-1.07845 + 2.22499i) q^{20} +(-0.800449 - 7.89679i) q^{21} +38.7531i q^{22} -18.8532 q^{23} +(-25.1165 + 2.54590i) q^{24} +(-15.4881 - 19.6244i) q^{25} +15.0451i q^{26} +(25.7696 - 8.05785i) q^{27} +1.30837i q^{28} -28.0643i q^{29} +(9.63829 - 26.3787i) q^{30} +14.1409 q^{31} +7.86489 q^{32} +(6.26205 + 61.7780i) q^{33} -33.8523 q^{34} +(-11.9041 - 5.76989i) q^{35} +(-4.36012 + 0.893092i) q^{36} -46.9161i q^{37} +26.1221 q^{38} +(2.43111 + 23.9840i) q^{39} +(-18.3517 + 37.8622i) q^{40} +66.4914i q^{41} +(-1.49868 - 14.7851i) q^{42} +2.30441i q^{43} -10.2356i q^{44} +(11.1023 - 43.6089i) q^{45} -35.2987 q^{46} -41.8354 q^{47} +(-41.1215 + 4.16823i) q^{48} -7.00000 q^{49} +(-28.9983 - 36.7427i) q^{50} +(-53.9655 + 5.47015i) q^{51} -3.97375i q^{52} -13.0099 q^{53} +(48.2482 - 15.0867i) q^{54} +(93.1281 + 45.1389i) q^{55} +22.2641i q^{56} +(41.6423 - 4.22103i) q^{57} -52.5447i q^{58} -24.5869i q^{59} +(-2.54569 + 6.96723i) q^{60} +68.2822 q^{61} +26.4760 q^{62} +(-4.77821 - 23.3274i) q^{63} +69.8350 q^{64} +(36.1550 + 17.5242i) q^{65} +(11.7244 + 115.667i) q^{66} -72.3360i q^{67} +8.94118 q^{68} +(-56.2713 + 5.70387i) q^{69} +(-22.2880 - 10.8029i) q^{70} +36.5402i q^{71} +(-74.1950 + 15.1975i) q^{72} -42.4661i q^{73} -87.8407i q^{74} +(-52.1646 - 53.8874i) q^{75} -6.89944 q^{76} +54.7622 q^{77} +(4.55175 + 44.9051i) q^{78} +75.4606 q^{79} +(-30.0459 + 61.9892i) q^{80} +(74.4768 - 31.8467i) q^{81} +124.491i q^{82} +45.9851 q^{83} +(0.395835 + 3.90509i) q^{84} +(-39.4306 + 81.3511i) q^{85} +4.31453i q^{86} +(-8.49062 - 83.7638i) q^{87} -174.176i q^{88} +14.4680i q^{89} +(20.7868 - 81.6487i) q^{90} +21.2603 q^{91} +9.32321 q^{92} +(42.2066 - 4.27822i) q^{93} -78.3282 q^{94} +(30.4265 - 62.7743i) q^{95} +(23.4744 - 2.37946i) q^{96} +132.492i q^{97} -13.1061 q^{98} +(37.3808 + 182.495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) $ 24 * q + 52 * q^4 - 22 * q^9	$ 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) $ 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	1.87229			0.936147			0.468073	−	0.883690i	$-0.344948\pi$
$2$	1.87229			0.936147			0.468073	+	0.883690i	$0.344948\pi$
$3$	2.98471	−	0.302541i	0.994902	−	0.100847i
$3$	2.98471	−	0.302541i	0.994902	−	0.100847i
$4$	−0.494516			−0.123629
$5$	2.18081	−	4.49934i	0.436163	−	0.899868i
$5$	2.18081	−	4.49934i	0.436163	−	0.899868i
$6$	5.58825	−	0.566446i	0.931374	−	0.0944077i
$7$		−	2.64575i		−	0.377964i
$7$		−	2.64575i		−	0.377964i
$8$	−8.41505			−1.05188
$9$	8.81694	−	1.80599i	0.979660	−	0.200666i
$10$	4.08312	−	8.42408i	0.408312	−	0.842408i
$11$			20.6982i			1.88165i	0.338889	+	0.940826i	$0.389949\pi$
$11$			20.6982i			1.88165i	−0.338889	+	0.940826i	$0.610051\pi$
$12$	−1.47598	+	0.149611i	−0.122999	+	0.0124676i
$13$			8.03563i			0.618125i	0.951042	+	0.309063i	$0.100015\pi$
$13$			8.03563i			0.618125i	−0.951042	+	0.309063i	$0.899985\pi$
$14$		−	4.95362i		−	0.353830i
$15$	5.14785	−	14.0890i	0.343190	−	0.939266i
$16$	−13.7774			−0.861087
$17$	−18.0807			−1.06357			−0.531784	−	0.846880i	$-0.678478\pi$
$17$	−18.0807			−1.06357			−0.531784	+	0.846880i	$0.678478\pi$
$18$	16.5079	−	3.38135i	0.917105	−	0.187853i
$19$	13.9519			0.734310			0.367155	−	0.930160i	$-0.380332\pi$
$19$	13.9519			0.734310			0.367155	+	0.930160i	$0.380332\pi$
$20$	−1.07845	+	2.22499i	−0.0539223	+	0.111250i
$21$	−0.800449	−	7.89679i	−0.0381166	−	0.376038i
$22$			38.7531i			1.76150i
$23$	−18.8532			−0.819704			−0.409852	−	0.912152i	$-0.634420\pi$
$23$	−18.8532			−0.819704			−0.409852	+	0.912152i	$0.634420\pi$
$24$	−25.1165	+	2.54590i	−1.04652	+	0.106079i
$25$	−15.4881	−	19.6244i	−0.619524	−	0.784978i
$26$			15.0451i			0.578656i
$27$	25.7696	−	8.05785i	0.954429	−	0.298439i
$28$			1.30837i			0.0467274i
$29$		−	28.0643i		−	0.967735i	−0.875141	−	0.483868i	$-0.839232\pi$
$29$		−	28.0643i		−	0.967735i	0.875141	−	0.483868i	$-0.160768\pi$
$30$	9.63829	−	26.3787i	0.321276	−	0.879291i
$31$	14.1409			0.456159			0.228080	−	0.973642i	$-0.426755\pi$
$31$	14.1409			0.456159			0.228080	+	0.973642i	$0.426755\pi$
$32$	7.86489			0.245778
$33$	6.26205	+	61.7780i	0.189759	+	1.87206i
$34$	−33.8523			−0.995657
$35$	−11.9041	−	5.76989i	−0.340118	−	0.164854i
$36$	−4.36012	+	0.893092i	−0.121114	+	0.0248081i
$37$		−	46.9161i		−	1.26800i	−0.773332	−	0.634001i	$-0.781411\pi$
$37$		−	46.9161i		−	1.26800i	0.773332	−	0.634001i	$-0.218589\pi$
$38$	26.1221			0.687422
$39$	2.43111	+	23.9840i	0.0623361	+	0.614974i
$40$	−18.3517	+	37.8622i	−0.458792	+	0.946555i
$41$			66.4914i			1.62174i	0.585225	+	0.810871i	$0.301006\pi$
$41$			66.4914i			1.62174i	−0.585225	+	0.810871i	$0.698994\pi$
$42$	−1.49868	−	14.7851i	−0.0356828	−	0.352026i
$43$			2.30441i			0.0535909i	0.999641	+	0.0267955i	$0.00853028\pi$
$43$			2.30441i			0.0535909i	−0.999641	+	0.0267955i	$0.991470\pi$
$44$		−	10.2356i		−	0.232627i
$45$	11.1023	−	43.6089i	0.246718	−	0.969087i
$46$	−35.2987			−0.767364
$47$	−41.8354			−0.890115			−0.445057	−	0.895502i	$-0.646817\pi$
$47$	−41.8354			−0.890115			−0.445057	+	0.895502i	$0.646817\pi$
$48$	−41.1215	+	4.16823i	−0.856697	+	0.0868381i
$49$	−7.00000			−0.142857
$50$	−28.9983	−	36.7427i	−0.579966	−	0.734854i
$51$	−53.9655	+	5.47015i	−1.05815	+	0.107258i
$52$		−	3.97375i		−	0.0764182i
$53$	−13.0099			−0.245470			−0.122735	−	0.992439i	$-0.539166\pi$
$53$	−13.0099			−0.245470			−0.122735	+	0.992439i	$0.539166\pi$
$54$	48.2482	−	15.0867i	0.893486	−	0.279383i
$55$	93.1281	+	45.1389i	1.69324	+	0.820707i
$56$			22.2641i			0.397574i
$57$	41.6423	−	4.22103i	0.730567	−	0.0740531i
$58$		−	52.5447i		−	0.905943i
$59$		−	24.5869i		−	0.416726i	−0.978052	−	0.208363i	$-0.933186\pi$
$59$		−	24.5869i		−	0.416726i	0.978052	−	0.208363i	$-0.0668136\pi$
$60$	−2.54569	+	6.96723i	−0.0424282	+	0.116120i
$61$	68.2822			1.11938			0.559690	−	0.828702i	$-0.310920\pi$
$61$	68.2822			1.11938			0.559690	+	0.828702i	$0.310920\pi$
$62$	26.4760			0.427032
$63$	−4.77821	−	23.3274i	−0.0758446	−	0.370277i
$64$	69.8350			1.09117
$65$	36.1550	+	17.5242i	0.556231	+	0.269603i
$66$	11.7244	+	115.667i	0.177642	+	1.75252i
$67$		−	72.3360i		−	1.07964i	−0.841780	−	0.539821i	$-0.818492\pi$
$67$		−	72.3360i		−	1.07964i	0.841780	−	0.539821i	$-0.181508\pi$
$68$	8.94118			0.131488
$69$	−56.2713	+	5.70387i	−0.815525	+	0.0826648i
$70$	−22.2880	−	10.8029i	−0.318400	−	0.154328i
$71$			36.5402i			0.514650i	0.966325	+	0.257325i	$0.0828411\pi$
$71$			36.5402i			0.514650i	−0.966325	+	0.257325i	$0.917159\pi$
$72$	−74.1950	+	15.1975i	−1.03049	+	0.211077i
$73$		−	42.4661i		−	0.581727i	−0.956765	−	0.290863i	$-0.906057\pi$
$73$		−	42.4661i		−	0.581727i	0.956765	−	0.290863i	$-0.0939425\pi$
$74$		−	87.8407i		−	1.18704i
$75$	−52.1646	−	53.8874i	−0.695529	−	0.718498i
$76$	−6.89944			−0.0907821
$77$	54.7622			0.711198
$78$	4.55175	+	44.9051i	0.0583558	+	0.575706i
$79$	75.4606			0.955198			0.477599	−	0.878578i	$-0.341507\pi$
$79$	75.4606			0.955198			0.477599	+	0.878578i	$0.341507\pi$
$80$	−30.0459	+	61.9892i	−0.375574	+	0.774864i
$81$	74.4768	−	31.8467i	0.919466	−	0.393169i
$82$			124.491i			1.51819i
$83$	45.9851			0.554037			0.277019	−	0.960865i	$-0.410654\pi$
$83$	45.9851			0.554037			0.277019	+	0.960865i	$0.410654\pi$
$84$	0.395835	+	3.90509i	0.00471232	+	0.0464891i
$85$	−39.4306	+	81.3511i	−0.463889	+	0.957071i
$86$			4.31453i			0.0501690i
$87$	−8.49062	−	83.7638i	−0.0975933	−	0.962802i
$88$		−	174.176i		−	1.97928i
$89$			14.4680i			0.162562i	0.996691	+	0.0812808i	$0.0259011\pi$
$89$			14.4680i			0.162562i	−0.996691	+	0.0812808i	$0.974099\pi$
$90$	20.7868	−	81.6487i	0.230964	−	0.907208i
$91$	21.2603			0.233629
$92$	9.32321			0.101339
$93$	42.2066	−	4.27822i	0.453834	−	0.0460024i
$94$	−78.3282			−0.833278
$95$	30.4265	−	62.7743i	0.320279	−	0.660782i
$96$	23.4744	−	2.37946i	0.244525	−	0.0247860i
$97$			132.492i			1.36589i	0.730469	+	0.682946i	$0.239302\pi$
$97$			132.492i			1.36589i	−0.730469	+	0.682946i	$0.760698\pi$
$98$	−13.1061			−0.133735
$99$	37.3808	+	182.495i	0.377584	+	1.84338i
$100$	7.65912	+	9.70460i	0.0765912	+	0.0970460i
$101$		−	149.346i		−	1.47867i	−0.673336	−	0.739336i	$-0.735139\pi$
$101$		−	149.346i		−	1.47867i	0.673336	−	0.739336i	$-0.264861\pi$
$102$	−101.039	+	10.2417i	−0.990581	+	0.100409i
$103$		−	21.3293i		−	0.207081i	−0.994625	−	0.103540i	$-0.966983\pi$
$103$		−	21.3293i		−	0.207081i	0.994625	−	0.103540i	$-0.0330171\pi$
$104$		−	67.6203i		−	0.650195i
$105$	−37.2760	−	13.6199i	−0.355009	−	0.129714i
$106$	−24.3584			−0.229796
$107$	35.3662			0.330525			0.165262	−	0.986250i	$-0.447153\pi$
$107$	35.3662			0.330525			0.165262	+	0.986250i	$0.447153\pi$
$108$	−12.7435	+	3.98473i	−0.117995	+	0.0368957i
$109$	−169.644			−1.55637			−0.778183	−	0.628037i	$-0.783858\pi$
$109$	−169.644			−1.55637			−0.778183	+	0.628037i	$0.783858\pi$
$110$	174.363	+	84.5132i	1.58512	+	0.768302i
$111$	−14.1941	−	140.031i	−0.127874	−	1.26154i
$112$			36.4515i			0.325460i
$113$	−23.4622			−0.207630			−0.103815	−	0.994597i	$-0.533105\pi$
$113$	−23.4622			−0.207630			−0.103815	+	0.994597i	$0.533105\pi$
$114$	77.9666	−	7.90300i	0.683918	−	0.0693246i
$115$	−41.1153	+	84.8269i	−0.357524	+	0.737626i
$116$			13.8783i			0.119640i
$117$	14.5123	+	70.8496i	0.124037	+	0.605553i
$118$		−	46.0338i		−	0.390117i
$119$			47.8370i			0.401991i
$120$	−43.3194	+	118.560i	−0.360995	+	0.987997i
$121$	−307.415			−2.54062
$122$	127.844			1.04790
$123$	20.1164	+	198.457i	0.163548	+	1.61347i
$124$	−6.99292			−0.0563945
$125$	−122.074	+	26.8890i	−0.976589	+	0.215112i
$126$	−8.94621	−	43.6758i	−0.0710017	−	0.346633i
$127$		−	72.2568i		−	0.568951i	−0.958683	−	0.284475i	$-0.908181\pi$
$127$		−	72.2568i		−	0.568951i	0.958683	−	0.284475i	$-0.0918194\pi$
$128$	99.2920			0.775719
$129$	0.697179	+	6.87799i	0.00540449	+	0.0533177i
$130$	67.6928	+	32.8105i	0.520714	+	0.252388i
$131$			40.8211i			0.311611i	0.987788	+	0.155806i	$0.0497974\pi$
$131$			40.8211i			0.311611i	−0.987788	+	0.155806i	$0.950203\pi$
$132$	−3.09669	−	30.5502i	−0.0234597	−	0.231441i
$133$		−	36.9133i		−	0.277543i
$134$		−	135.434i		−	1.01070i
$135$	19.9437	−	133.519i	0.147731	−	0.989028i
$136$	152.150			1.11875
$137$	−187.190			−1.36635			−0.683176	−	0.730254i	$-0.739402\pi$
$137$	−187.190			−1.36635			−0.683176	+	0.730254i	$0.739402\pi$
$138$	−105.356	+	10.6793i	−0.763452	+	0.0773864i
$139$	−16.1761			−0.116374			−0.0581872	−	0.998306i	$-0.518532\pi$
$139$	−16.1761			−0.116374			−0.0581872	+	0.998306i	$0.518532\pi$
$140$	5.88678	+	2.85330i	0.0420485	+	0.0203807i
$141$	−124.866	+	12.6569i	−0.885577	+	0.0897655i
$142$			68.4139i			0.481788i
$143$	−166.323			−1.16310
$144$	−121.474	+	24.8819i	−0.843572	+	0.172791i
$145$	−126.271	−	61.2031i	−0.870834	−	0.422090i
$146$		−	79.5089i		−	0.544582i
$147$	−20.8929	+	2.11779i	−0.142129	+	0.0144067i
$148$			23.2008i			0.156762i
$149$			208.667i			1.40045i	0.713923	+	0.700225i	$0.246917\pi$
$149$			208.667i			1.40045i	−0.713923	+	0.700225i	$0.753083\pi$
$150$	−97.6675	−	100.893i	−0.651117	−	0.672620i
$151$	173.305			1.14772			0.573859	−	0.818954i	$-0.305446\pi$
$151$	173.305			1.14772			0.573859	+	0.818954i	$0.305446\pi$
$152$	−117.406			−0.772408
$153$	−159.416	+	32.6536i	−1.04194	+	0.213422i
$154$	102.531			0.665786
$155$	30.8388	−	63.6249i	0.198960	−	0.410483i
$156$	−1.20222	−	11.8605i	−0.00770655	−	0.0760286i
$157$			158.683i			1.01072i	0.862908	+	0.505360i	$0.168640\pi$
$157$			158.683i			1.01072i	−0.862908	+	0.505360i	$0.831360\pi$
$158$	141.284			0.894206
$159$	−38.8307	+	3.93603i	−0.244218	+	0.0247549i
$160$	17.1519	−	35.3868i	0.107199	−	0.221168i
$161$			49.8809i			0.309819i
$162$	139.442	−	59.6263i	0.860756	−	0.368064i
$163$		−	36.1332i		−	0.221676i	−0.993838	−	0.110838i	$-0.964646\pi$
$163$		−	36.1332i		−	0.221676i	0.993838	−	0.110838i	$-0.0353535\pi$
$164$		−	32.8811i		−	0.200494i
$165$	291.616	+	106.551i	1.76737	+	0.645764i
$166$	86.0976			0.518660
$167$	120.996			0.724527			0.362264	−	0.932076i	$-0.382004\pi$
$167$	120.996			0.724527			0.362264	+	0.932076i	$0.382004\pi$
$168$	6.73582	+	66.4519i	0.0400942	+	0.395547i
$169$	104.429			0.617921
$170$	−73.8256	+	152.313i	−0.434268	+	0.895959i
$171$	123.013	−	25.1970i	0.719374	−	0.147351i
$172$		−	1.13957i		−	0.00662539i
$173$	141.578			0.818373			0.409186	−	0.912451i	$-0.365813\pi$
$173$	141.578			0.818373			0.409186	+	0.912451i	$0.365813\pi$
$174$	−15.8969	−	156.830i	−0.0913617	−	0.901324i
$175$	−51.9214	+	40.9777i	−0.296694	+	0.234158i
$176$		−	285.167i		−	1.62027i
$177$	−7.43854	−	73.3845i	−0.0420256	−	0.414602i
$178$			27.0883i			0.152182i
$179$			91.5789i			0.511614i	0.966728	+	0.255807i	$0.0823412\pi$
$179$			91.5789i			0.511614i	−0.966728	+	0.255807i	$0.917659\pi$
$180$	−5.49027	+	21.5653i	−0.0305015	+	0.119807i
$181$	44.3433			0.244990			0.122495	−	0.992469i	$-0.460910\pi$
$181$	44.3433			0.244990			0.122495	+	0.992469i	$0.460910\pi$
$182$	39.8055			0.218711
$183$	203.802	−	20.6582i	1.11367	−	0.112886i
$184$	158.651			0.862232
$185$	−211.091	−	102.315i	−1.14103	−	0.553055i
$186$	79.0231	−	8.01008i	0.424855	−	0.0430650i
$187$		−	374.237i		−	2.00127i
$188$	20.6883			0.110044
$189$	−21.3191	−	68.1799i	−0.112799	−	0.360740i
$190$	56.9673	−	117.532i	0.299828	−	0.618589i
$191$		−	162.070i		−	0.848535i	−0.905537	−	0.424267i	$-0.860532\pi$
$191$		−	162.070i		−	0.848535i	0.905537	−	0.424267i	$-0.139468\pi$
$192$	208.437	−	21.1280i	1.08561	−	0.110041i
$193$			85.1633i			0.441261i	0.975358	+	0.220630i	$0.0708114\pi$
$193$			85.1633i			0.441261i	−0.975358	+	0.220630i	$0.929189\pi$
$194$			248.063i			1.27868i
$195$	113.214	+	41.3662i	0.580584	+	0.212134i
$196$	3.46161			0.0176613
$197$	−137.697			−0.698971			−0.349486	−	0.936942i	$-0.613644\pi$
$197$	−137.697			−0.698971			−0.349486	+	0.936942i	$0.613644\pi$
$198$	69.9878	+	341.683i	0.353474	+	1.72567i
$199$	45.7142			0.229720			0.114860	−	0.993382i	$-0.463358\pi$
$199$	45.7142			0.229720			0.114860	+	0.993382i	$0.463358\pi$
$200$	130.333	+	165.141i	0.651666	+	0.825704i
$201$	−21.8846	−	215.902i	−0.108879	−	1.07414i
$202$		−	279.620i		−	1.38425i
$203$	−74.2512			−0.365770
$204$	26.6868	−	2.70508i	0.130818	−	0.0132602i
$205$	299.167	+	145.005i	1.45935	+	0.707343i
$206$		−	39.9348i		−	0.193858i
$207$	−166.227	+	34.0488i	−0.803031	+	0.164487i
$208$		−	110.710i		−	0.532260i
$209$			288.779i			1.38172i
$210$	−69.7916	−	25.5005i	−0.332341	−	0.121431i
$211$	−48.2681			−0.228759			−0.114379	−	0.993437i	$-0.536488\pi$
$211$	−48.2681			−0.228759			−0.114379	+	0.993437i	$0.536488\pi$
$212$	6.43360			0.0303472
$213$	11.0549	+	109.062i	0.0519010	+	0.512026i
$214$	66.2159			0.309420
$215$	10.3683	+	5.02549i	0.0482248	+	0.0233744i
$216$	−216.852	+	67.8072i	−1.00395	+	0.313922i
$217$		−	37.4134i		−	0.172412i
$218$	−317.623			−1.45699
$219$	−12.8477	−	126.749i	−0.0586654	−	0.578761i
$220$	−46.0533	−	22.3219i	−0.209333	−	0.101463i
$221$		−	145.290i		−	0.657419i
$222$	−26.5754	−	262.179i	−0.119709	−	1.18099i
$223$			56.7446i			0.254460i	0.991873	+	0.127230i	$0.0406087\pi$
$223$			56.7446i			0.254460i	−0.991873	+	0.127230i	$0.959391\pi$
$224$		−	20.8086i		−	0.0928953i
$225$	−171.999	−	145.056i	−0.764441	−	0.644693i
$226$	−43.9280			−0.194372
$227$	295.599			1.30220			0.651100	−	0.758992i	$-0.274308\pi$
$227$	295.599			1.30220			0.651100	+	0.758992i	$0.274308\pi$
$228$	−20.5928	+	2.08736i	−0.0903192	+	0.00915511i
$229$	−288.308			−1.25899			−0.629493	−	0.777006i	$-0.716737\pi$
$229$	−288.308			−1.25899			−0.629493	+	0.777006i	$0.716737\pi$
$230$	−76.9799	+	158.821i	−0.334695	+	0.690526i
$231$	163.449	−	16.5678i	0.707572	−	0.0717222i
$232$			236.163i			1.01794i
$233$	−353.925			−1.51899			−0.759495	−	0.650513i	$-0.774554\pi$
$233$	−353.925			−1.51899			−0.759495	+	0.650513i	$0.774554\pi$
$234$	27.1713	+	132.651i	0.116117	+	0.566886i
$235$	−91.2352	+	188.232i	−0.388235	+	0.800986i
$236$			12.1586i			0.0515194i
$237$	225.228	−	22.8300i	0.950328	−	0.0963289i
$238$			89.5648i			0.376323i
$239$			0.342767i			0.00143417i	1.00000		0.000717085i	$0.000228255\pi$
$239$			0.342767i			0.00143417i	−1.00000		0.000717085i	$0.999772\pi$
$240$	−70.9239	+	194.110i	−0.295516	+	0.808790i
$241$	−34.2211			−0.141996			−0.0709981	−	0.997476i	$-0.522618\pi$
$241$	−34.2211			−0.141996			−0.0709981	+	0.997476i	$0.522618\pi$
$242$	−575.571			−2.37839
$243$	212.656	−	117.585i	0.875129	−	0.483890i
$244$	−33.7666			−0.138388
$245$	−15.2657	+	31.4954i	−0.0623090	+	0.128553i
$246$	37.6638	+	371.570i	0.153105	+	1.51045i
$247$			112.112i			0.453896i
$248$	−118.997			−0.479826
$249$	137.252	−	13.9124i	0.551213	−	0.0558730i
$250$	−228.558	+	50.3441i	−0.914231	+	0.201377i
$251$			215.397i			0.858157i	0.903267	+	0.429078i	$0.141162\pi$
$251$			215.397i			0.858157i	−0.903267	+	0.429078i	$0.858838\pi$
$252$	2.36290	+	11.5358i	0.00937659	+	0.0457769i
$253$		−	390.227i		−	1.54240i
$254$		−	135.286i		−	0.532622i
$255$	−93.0766	+	254.738i	−0.365006	+	0.998974i
$256$	−93.4361			−0.364985
$257$	−116.993			−0.455227			−0.227614	−	0.973752i	$-0.573092\pi$
$257$	−116.993			−0.455227			−0.227614	+	0.973752i	$0.573092\pi$
$258$	1.30532	+	12.8776i	0.00505940	+	0.0499132i
$259$	−124.128			−0.479260
$260$	−17.8792	−	8.66600i	−0.0687663	−	0.0333308i
$261$	−50.6840	−	247.441i	−0.194192	−	0.948051i
$262$			76.4291i			0.291714i
$263$	352.692			1.34104			0.670518	−	0.741893i	$-0.266072\pi$
$263$	352.692			1.34104			0.670518	+	0.741893i	$0.266072\pi$
$264$	−52.6955	−	519.865i	−0.199604	−	1.96919i
$265$	−28.3722	+	58.5359i	−0.107065	+	0.220890i
$266$		−	69.1125i		−	0.259821i
$267$	4.37716	+	43.1827i	0.0163939	+	0.161733i
$268$			35.7713i			0.133475i
$269$			104.650i			0.389032i	0.980899	+	0.194516i	$0.0623136\pi$
$269$			104.650i			0.389032i	−0.980899	+	0.194516i	$0.937686\pi$
$270$	37.3404	−	249.986i	0.138298	−	0.925875i
$271$	151.602			0.559418			0.279709	−	0.960085i	$-0.409762\pi$
$271$	151.602			0.559418			0.279709	+	0.960085i	$0.409762\pi$
$272$	249.104			0.915825
$273$	63.4557	−	6.43211i	0.232438	−	0.0235608i
$274$	−350.475			−1.27911
$275$	406.190	−	320.576i	1.47706	−	1.16573i
$276$	27.8270	−	2.82065i	0.100823	−	0.0102198i
$277$			366.475i			1.32301i	0.749940	+	0.661506i	$0.230083\pi$
$277$			366.475i			1.32301i	−0.749940	+	0.661506i	$0.769917\pi$
$278$	−30.2863			−0.108944
$279$	124.680	−	25.5384i	0.446881	−	0.0915357i
$280$	100.174	+	48.5539i	0.357764	+	0.173407i
$281$		−	299.046i		−	1.06422i	−0.846675	−	0.532110i	$-0.821399\pi$
$281$		−	299.046i		−	1.06422i	0.846675	−	0.532110i	$-0.178601\pi$
$282$	−233.787	+	23.6975i	−0.829030	+	0.0840337i
$283$		−	83.7217i		−	0.295836i	−0.989000	−	0.147918i	$-0.952743\pi$
$283$		−	83.7217i		−	0.295836i	0.989000	−	0.147918i	$-0.0472572\pi$
$284$		−	18.0697i		−	0.0636257i
$285$	71.8223	−	196.568i	0.252008	−	0.689713i
$286$	−311.405			−1.08883
$287$	175.920			0.612961
$288$	69.3443	−	14.2039i	0.240779	−	0.0493193i
$289$	37.9107			0.131179
$290$	−236.416	−	114.590i	−0.815229	−	0.395138i
$291$	40.0842	+	395.448i	0.137746	+	1.35893i
$292$			21.0001i			0.0719183i
$293$	266.374			0.909127			0.454563	−	0.890714i	$-0.349795\pi$
$293$	266.374			0.909127			0.454563	+	0.890714i	$0.349795\pi$
$294$	−39.1177	+	3.96512i	−0.133053	+	0.0134868i
$295$	−110.625	−	53.6193i	−0.374999	−	0.181760i
$296$			394.802i			1.33379i
$297$	166.783	+	533.383i	0.561558	+	1.79590i
$298$			390.686i			1.31103i
$299$		−	151.497i		−	0.506680i
$300$	25.7962	+	26.6482i	0.0859875	+	0.0888272i
$301$	6.09690			0.0202555
$302$	324.479			1.07443
$303$	−45.1833	−	445.754i	−0.149120	−	1.47113i
$304$	−192.221			−0.632305
$305$	148.911	−	307.225i	0.488232	−	1.00729i
$306$	−298.474	+	61.1371i	−0.975405	+	0.199794i
$307$			346.521i			1.12873i	0.825525	+	0.564366i	$0.190879\pi$
$307$			346.521i			1.12873i	−0.825525	+	0.564366i	$0.809121\pi$
$308$	−27.0808			−0.0879247
$309$	−6.45300	−	63.6618i	−0.0208835	−	0.206025i
$310$	57.7392	−	119.125i	0.186256	−	0.384273i
$311$			459.024i			1.47596i	0.674822	+	0.737981i	$0.264221\pi$
$311$			459.024i			1.47596i	−0.674822	+	0.737981i	$0.735779\pi$
$312$	−20.4579	−	201.827i	−0.0655703	−	0.646880i
$313$		−	270.888i		−	0.865457i	−0.901524	−	0.432729i	$-0.857551\pi$
$313$		−	270.888i		−	0.865457i	0.901524	−	0.432729i	$-0.142449\pi$
$314$			297.101i			0.946183i
$315$	−115.378	−	29.3740i	−0.366281	−	0.0932507i
$316$	−37.3165			−0.118090
$317$	−127.077			−0.400875			−0.200437	−	0.979707i	$-0.564236\pi$
$317$	−127.077			−0.400875			−0.200437	+	0.979707i	$0.564236\pi$
$318$	−72.7025	+	7.36941i	−0.228624	+	0.0231742i
$319$	580.881			1.82094
$320$	152.297	−	314.211i	0.475928	−	0.981910i
$321$	105.558	−	10.6997i	0.328840	−	0.0333325i
$322$			93.3917i			0.290036i
$323$	−252.260			−0.780990
$324$	−36.8300	+	15.7487i	−0.113673	+	0.0486070i
$325$	157.695	−	124.457i	0.485214	−	0.382944i
$326$		−	67.6520i		−	0.207522i
$327$	−506.337	+	51.3243i	−1.54843	+	0.156955i
$328$		−	559.529i		−	1.70588i
$329$			110.686i			0.336432i
$330$	545.992	+	199.495i	1.65452	+	0.604530i
$331$	−73.9152			−0.223309			−0.111654	−	0.993747i	$-0.535615\pi$
$331$	−73.9152			−0.223309			−0.111654	+	0.993747i	$0.535615\pi$
$332$	−22.7404			−0.0684951
$333$	−84.7302	−	413.656i	−0.254445	−	1.24221i
$334$	226.540			0.678264
$335$	−325.464	−	157.751i	−0.971535	−	0.470899i
$336$	11.0281	+	108.797i	0.0328217	+	0.323801i
$337$		−	352.433i		−	1.04580i	−0.852395	−	0.522898i	$-0.824851\pi$
$337$		−	352.433i		−	1.04580i	0.852395	−	0.522898i	$-0.175149\pi$
$338$	195.521			0.578465
$339$	−70.0276	+	7.09827i	−0.206571	+	0.0209388i
$340$	19.4990	−	40.2294i	0.0573501	−	0.118322i
$341$			292.692i			0.858334i
$342$	230.317	−	47.1763i	0.673440	−	0.137942i
$343$			18.5203i			0.0539949i
$344$		−	19.3917i		−	0.0563713i
$345$	−97.0534	+	265.623i	−0.281314	+	0.769920i
$346$	265.076			0.766117
$347$	−611.555			−1.76241			−0.881203	−	0.472738i	$-0.843266\pi$
$347$	−611.555			−1.76241			−0.881203	+	0.472738i	$0.843266\pi$
$348$	4.19875	+	41.4225i	0.0120654	+	0.119030i
$349$	126.822			0.363386			0.181693	−	0.983355i	$-0.441842\pi$
$349$	126.822			0.363386			0.181693	+	0.983355i	$0.441842\pi$
$350$	−97.2121	+	76.7223i	−0.277749	+	0.219206i
$351$	64.7499	+	207.075i	0.184473	+	0.589957i
$352$			162.789i			0.462469i
$353$	437.477			1.23931			0.619656	−	0.784873i	$-0.287272\pi$
$353$	437.477			1.23931			0.619656	+	0.784873i	$0.287272\pi$
$354$	−13.9271	−	137.397i	−0.0393422	−	0.388128i
$355$	164.407	+	79.6873i	0.463117	+	0.224471i
$356$		−	7.15465i		−	0.0200973i
$357$	14.4727	+	142.779i	0.0405396	+	0.399942i
$358$			171.463i			0.478946i
$359$		−	149.721i		−	0.417050i	−0.978017	−	0.208525i	$-0.933134\pi$
$359$		−	149.721i		−	0.417050i	0.978017	−	0.208525i	$-0.0668662\pi$
$360$	−93.4266	+	366.971i	−0.259518	+	1.01937i
$361$	−166.345			−0.460788
$362$	83.0236			0.229347
$363$	−917.542	+	93.0056i	−2.52767	+	0.256214i
$364$	−10.5135			−0.0288834
$365$	−191.069	−	92.6105i	−0.523477	−	0.253727i
$366$	381.578	−	38.6782i	1.04256	−	0.105678i
$367$		−	691.449i		−	1.88406i	−0.335534	−	0.942028i	$-0.608917\pi$
$367$		−	691.449i		−	1.88406i	0.335534	−	0.942028i	$-0.391083\pi$
$368$	259.748			0.705837
$369$	120.083	+	586.251i	0.325428	+	1.58876i
$370$	−395.225	−	191.564i	−1.06818	−	0.517741i
$371$			34.4210i			0.0927789i
$372$	−20.8718	+	2.11565i	−0.0561070	+	0.00568722i
$373$			291.881i			0.782522i	0.920280	+	0.391261i	$0.127961\pi$
$373$			291.881i			0.782522i	−0.920280	+	0.391261i	$0.872039\pi$
$374$		−	700.682i		−	1.87348i
$375$	−356.219	+	117.188i	−0.949917	+	0.312502i
$376$	352.047			0.936296
$377$	225.515			0.598182
$378$	−39.9155	−	127.653i	−0.105597	−	0.337706i
$379$	−181.245			−0.478219			−0.239109	−	0.970993i	$-0.576855\pi$
$379$	−181.245			−0.478219			−0.239109	+	0.970993i	$0.576855\pi$
$380$	−15.0464	+	31.0429i	−0.0395957	+	0.0816919i
$381$	−21.8607	−	215.665i	−0.0573770	−	0.566050i
$382$		−	303.443i		−	0.794353i
$383$	109.263			0.285282			0.142641	−	0.989774i	$-0.454440\pi$
$383$	109.263			0.285282			0.142641	+	0.989774i	$0.454440\pi$
$384$	296.357	−	30.0399i	0.771764	−	0.0782290i
$385$	119.426	−	246.394i	0.310198	−	0.639984i
$386$			159.451i			0.413085i
$387$	4.16175	+	20.3178i	0.0107539	+	0.0525009i
$388$		−	65.5192i		−	0.168864i
$389$			57.2749i			0.147236i	0.997287	+	0.0736181i	$0.0234546\pi$
$389$			57.2749i			0.147236i	−0.997287	+	0.0736181i	$0.976545\pi$
$390$	211.970	+	77.4497i	0.543512	+	0.198589i
$391$	340.878			0.871812
$392$	58.9054			0.150269
$393$	12.3501	+	121.839i	0.0314251	+	0.310023i
$394$	−257.810			−0.654340
$395$	164.566	−	339.523i	0.416622	−	0.859552i
$396$	−18.4854	−	90.2465i	−0.0466803	−	0.227895i
$397$			399.556i			1.00644i	0.864159	+	0.503219i	$0.167851\pi$
$397$			399.556i			1.00644i	−0.864159	+	0.503219i	$0.832149\pi$
$398$	85.5905			0.215051
$399$	−11.1678	−	110.175i	−0.0279894	−	0.276128i
$400$	213.386	+	270.374i	0.533464	+	0.675934i
$401$			455.663i			1.13632i	0.822919	+	0.568158i	$0.192344\pi$
$401$			455.663i			1.13632i	−0.822919	+	0.568158i	$0.807656\pi$
$402$	−40.9744	−	404.231i	−0.101926	−	1.00555i
$403$			113.631i			0.281964i
$404$			73.8540i			0.182807i
$405$	19.1310	−	404.548i	0.0472371	−	0.998884i
$406$	−139.020			−0.342414
$407$	971.078			2.38594
$408$	454.122	−	46.0316i	1.11305	−	0.112823i
$409$	509.418			1.24552			0.622760	−	0.782413i	$-0.286011\pi$
$409$	509.418			1.24552			0.622760	+	0.782413i	$0.286011\pi$
$410$	560.129	+	271.493i	1.36617	+	0.662177i
$411$	−558.707	+	56.6327i	−1.35939	+	0.137793i
$412$			10.5477i			0.0256012i
$413$	−65.0507			−0.157508
$414$	−311.227	+	63.7493i	−0.751755	+	0.153984i
$415$	100.285	−	206.903i	0.241650	−	0.498560i
$416$			63.1994i			0.151922i
$417$	−48.2808	+	4.89392i	−0.115781	+	0.0117360i
$418$			540.679i			1.29349i
$419$		−	714.669i		−	1.70565i	−0.522194	−	0.852826i	$-0.674886\pi$
$419$		−	714.669i		−	1.70565i	0.522194	−	0.852826i	$-0.325114\pi$
$420$	18.4336	+	6.73527i	0.0438894	+	0.0160364i
$421$	465.974			1.10683			0.553414	−	0.832907i	$-0.313325\pi$
$421$	465.974			1.10683			0.553414	+	0.832907i	$0.313325\pi$
$422$	−90.3720			−0.214152
$423$	−368.860	+	75.5545i	−0.872010	+	0.178616i
$424$	109.479			0.258205
$425$	280.035	+	354.823i	0.658907	+	0.834878i
$426$	20.6980	+	204.195i	0.0485869	+	0.479332i
$427$		−	180.658i		−	0.423086i
$428$	−17.4891			−0.0408625
$429$	−496.425	+	50.3195i	−1.15717	+	0.117295i
$430$	19.4125	+	9.40919i	0.0451455	+	0.0218818i
$431$		−	132.795i		−	0.308108i	−0.988062	−	0.154054i	$-0.950767\pi$
$431$		−	132.795i		−	0.308108i	0.988062	−	0.154054i	$-0.0492330\pi$
$432$	−355.038	+	111.016i	−0.821846	+	0.256982i
$433$			648.834i			1.49846i	0.662308	+	0.749231i	$0.269577\pi$
$433$			648.834i			1.49846i	−0.662308	+	0.749231i	$0.730423\pi$
$434$		−	70.0489i		−	0.161403i
$435$	−395.398	−	144.471i	−0.908961	−	0.332117i
$436$	83.8916			0.192412
$437$	−263.038			−0.601917
$438$	−24.0547	−	237.311i	−0.0549195	−	0.541805i
$439$	−482.312			−1.09866			−0.549331	−	0.835605i	$-0.685117\pi$
$439$	−482.312			−1.09866			−0.549331	+	0.835605i	$0.685117\pi$
$440$	−783.678	−	379.846i	−1.78109	−	0.863286i
$441$	−61.7186	+	12.6420i	−0.139951	+	0.0286666i
$442$		−	272.025i		−	0.615441i
$443$	−86.6613			−0.195624			−0.0978119	−	0.995205i	$-0.531184\pi$
$443$	−86.6613			−0.195624			−0.0978119	+	0.995205i	$0.531184\pi$
$444$	7.01919	+	69.2474i	0.0158090	+	0.155963i
$445$	65.0964	+	31.5520i	0.146284	+	0.0709033i
$446$			106.243i			0.238212i
$447$	63.1304	+	622.809i	0.141231	+	1.39331i
$448$		−	184.766i		−	0.412424i
$449$		−	256.209i		−	0.570621i	−0.958435	−	0.285310i	$-0.907903\pi$
$449$		−	256.209i		−	0.570621i	0.958435	−	0.285310i	$-0.0920967\pi$
$450$	−322.033	−	271.587i	−0.715629	−	0.603528i
$451$	−1376.25			−3.05155
$452$	11.6024			0.0256690
$453$	517.266	−	52.4320i	1.14187	−	0.115744i
$454$	553.449			1.21905
$455$	46.3647	−	95.6572i	0.101900	−	0.210236i
$456$	−350.422	+	35.5202i	−0.768470	+	0.0778951i
$457$		−	512.729i		−	1.12195i	−0.827834	−	0.560973i	$-0.810427\pi$
$457$		−	512.729i		−	1.12195i	0.827834	−	0.560973i	$-0.189573\pi$
$458$	−539.797			−1.17860
$459$	−465.931	+	145.691i	−1.01510	+	0.317410i
$460$	20.3322	−	41.9483i	0.0442004	−	0.0911919i
$461$		−	520.250i		−	1.12852i	−0.825595	−	0.564262i	$-0.809161\pi$
$461$		−	520.250i		−	1.12852i	0.825595	−	0.564262i	$-0.190839\pi$
$462$	306.025	−	31.0199i	0.662391	−	0.0671426i
$463$			699.869i			1.51160i	0.654805	+	0.755798i	$0.272751\pi$
$463$			699.869i			1.51160i	−0.654805	+	0.755798i	$0.727249\pi$
$464$			386.653i			0.833304i
$465$	72.7955	−	199.232i	0.156549	−	0.428455i
$466$	−662.651			−1.42200
$467$	−33.4916			−0.0717165			−0.0358582	−	0.999357i	$-0.511416\pi$
$467$	−33.4916			−0.0717165			−0.0358582	+	0.999357i	$0.511416\pi$
$468$	−7.17656	−	35.0363i	−0.0153345	−	0.0748638i
$469$	−191.383			−0.408066
$470$	−170.819	+	352.425i	−0.363445	+	0.749840i
$471$	48.0082	+	473.623i	0.101928	+	1.00557i
$472$			206.900i			0.438347i
$473$	−47.6971			−0.100840
$474$	421.693	−	42.7444i	0.889647	−	0.0901780i
$475$	−216.088	−	273.798i	−0.454923	−	0.576417i
$476$		−	23.6561i		−	0.0496978i
$477$	−114.707	+	23.4958i	−0.240477	+	0.0492574i
$478$			0.641760i			0.00134259i
$479$			626.193i			1.30729i	0.756800	+	0.653646i	$0.226762\pi$
$479$			626.193i			1.30729i	−0.756800	+	0.653646i	$0.773238\pi$
$480$	40.4873	−	110.808i	0.0843485	−	0.230851i
$481$	377.000			0.783785
$482$	−64.0720			−0.132929
$483$	15.0910	+	148.880i	0.0312444	+	0.308240i
$484$	152.021			0.314094
$485$	596.124	+	288.939i	1.22912	+	0.595751i
$486$	398.155	−	220.154i	0.819249	−	0.452992i
$487$		−	474.081i		−	0.973473i	−0.873549	−	0.486736i	$-0.838187\pi$
$487$		−	474.081i		−	0.973473i	0.873549	−	0.486736i	$-0.161813\pi$
$488$	−574.599			−1.17746
$489$	−10.9318	−	107.847i	−0.0223554	−	0.220546i
$490$	−28.5819	+	58.9686i	−0.0583303	+	0.120344i
$491$			609.917i			1.24219i	0.783734	+	0.621097i	$0.213313\pi$
$491$			609.917i			1.24219i	−0.783734	+	0.621097i	$0.786687\pi$
$492$	−9.94788	−	98.1403i	−0.0202193	−	0.199472i
$493$			507.422i			1.02925i
$494$			209.907i			0.424913i
$495$	902.625	+	229.798i	1.82349	+	0.464238i
$496$	−194.825			−0.392793
$497$	96.6762			0.194519
$498$	256.976	−	26.0481i	0.516016	−	0.0523054i
$499$	−644.922			−1.29243			−0.646215	−	0.763155i	$-0.723649\pi$
$499$	−644.922			−1.29243			−0.646215	+	0.763155i	$0.723649\pi$
$500$	60.3674	−	13.2970i	0.120735	−	0.0265941i
$501$	361.138	−	36.6063i	0.720834	−	0.0730665i
$502$			403.287i			0.803361i
$503$	345.703			0.687283			0.343641	−	0.939101i	$-0.388340\pi$
$503$	345.703			0.687283			0.343641	+	0.939101i	$0.388340\pi$
$504$	40.2089	+	196.302i	0.0797795	+	0.389487i
$505$	−671.958	−	325.696i	−1.33061	−	0.644942i
$506$		−	730.619i		−	1.44391i
$507$	311.689	−	31.5940i	0.614771	−	0.0623155i
$508$			35.7321i			0.0703388i
$509$		−	619.093i		−	1.21629i	−0.793825	−	0.608147i	$-0.791913\pi$
$509$		−	619.093i		−	1.21629i	0.793825	−	0.608147i	$-0.208087\pi$
$510$	−174.267	+	476.945i	−0.341699	+	0.935187i
$511$	−112.355			−0.219872
$512$	−572.108			−1.11740
$513$	359.535	−	112.422i	0.700847	−	0.219147i
$514$	−219.046			−0.426160
$515$	−95.9679	−	46.5153i	−0.186345	−	0.0903210i
$516$	−0.344766	−	3.40127i	−0.000668152	−	0.00659162i
$517$		−	865.917i		−	1.67489i
$518$	−232.405			−0.448658
$519$	422.570	−	42.8333i	0.814200	−	0.0825305i
$520$	−304.246	−	147.467i	−0.585089	−	0.283591i
$521$		−	223.013i		−	0.428048i	−0.976828	−	0.214024i	$-0.931343\pi$
$521$		−	223.013i		−	0.428048i	0.976828	−	0.214024i	$-0.0686571\pi$
$522$	−94.8953	−	463.283i	−0.181792	−	0.887515i
$523$			1007.64i			1.92665i	0.268340	+	0.963324i	$0.413525\pi$
$523$			1007.64i			1.92665i	−0.268340	+	0.963324i	$0.586475\pi$
$524$		−	20.1867i		−	0.0385242i
$525$	−142.573	+	138.015i	−0.271567	+	0.262885i
$526$	660.344			1.25541
$527$	−255.678			−0.485157
$528$	−86.2748	−	851.139i	−0.163399	−	1.61201i
$529$	−173.557			−0.328085
$530$	−53.1210	+	109.596i	−0.100228	+	0.206786i
$531$	−44.4037	−	216.781i	−0.0836228	−	0.408250i
$532$			18.2542i			0.0343124i
$533$	−534.300			−1.00244
$534$	8.19534	+	80.8507i	0.0153471	+	0.151406i
$535$	77.1270	−	159.124i	0.144163	−	0.297429i
$536$			608.711i			1.13566i
$537$	27.7064	+	273.336i	0.0515948	+	0.509006i
$538$			195.935i			0.364191i
$539$		−	144.887i		−	0.268808i
$540$	−9.86245	+	66.0271i	−0.0182638	+	0.122272i
$541$	894.636			1.65367			0.826836	−	0.562444i	$-0.190139\pi$
$541$	894.636			1.65367			0.826836	+	0.562444i	$0.190139\pi$
$542$	283.844			0.523697
$543$	132.352	−	13.4157i	0.243741	−	0.0247066i
$544$	−142.203			−0.261402
$545$	−369.962	+	763.286i	−0.678829	+	1.40052i
$546$	118.808	−	12.0428i	0.217596	−	0.0220564i
$547$			965.766i			1.76557i	0.469779	+	0.882784i	$0.344333\pi$
$547$			965.766i			1.76557i	−0.469779	+	0.882784i	$0.655667\pi$
$548$	92.5685			0.168921
$549$	602.040	−	123.317i	1.09661	−	0.224622i
$550$	760.507	−	600.212i	1.38274	−	1.09129i
$551$		−	391.551i		−	0.710618i
$552$	473.526	−	47.9984i	0.857836	−	0.0869536i
$553$		−	199.650i		−	0.361031i
$554$			686.148i			1.23853i
$555$	−661.000	−	241.517i	−1.19099	−	0.435166i
$556$	7.99932			0.0143873
$557$	−494.156			−0.887174			−0.443587	−	0.896231i	$-0.646294\pi$
$557$	−494.156			−0.887174			−0.443587	+	0.896231i	$0.646294\pi$
$558$	233.437	−	47.8155i	0.418346	−	0.0856908i
$559$	−18.5174			−0.0331259
$560$	164.008	+	79.4940i	0.292871	+	0.141954i
$561$	−113.222	−	1116.99i	−0.201822	−	1.99106i
$562$		−	559.901i		−	0.996266i
$563$	688.775			1.22340			0.611701	−	0.791089i	$-0.290486\pi$
$563$	688.775			1.22340			0.611701	+	0.791089i	$0.290486\pi$
$564$	61.7484	−	6.25906i	0.109483	−	0.0110976i
$565$	−51.1666	+	105.564i	−0.0905603	+	0.186839i
$566$		−	156.752i		−	0.276946i
$567$	−84.2583	−	197.047i	−0.148604	−	0.347526i
$568$		−	307.487i		−	0.541351i
$569$		−	574.381i		−	1.00946i	−0.863278	−	0.504728i	$-0.831593\pi$
$569$		−	574.381i		−	1.00946i	0.863278	−	0.504728i	$-0.168407\pi$
$570$	134.472	−	368.033i	0.235917	−	0.645673i
$571$	−457.862			−0.801860			−0.400930	−	0.916109i	$-0.631313\pi$
$571$	−457.862			−0.801860			−0.400930	+	0.916109i	$0.631313\pi$
$572$	82.2493			0.143793
$573$	−49.0329	−	483.732i	−0.0855722	−	0.844209i
$574$	329.373			0.573821
$575$	292.000	+	369.983i	0.507827	+	0.643449i
$576$	615.730	−	126.121i	1.06898	−	0.218961i
$577$			385.014i			0.667268i	0.942703	+	0.333634i	$0.108275\pi$
$577$			385.014i			0.667268i	−0.942703	+	0.333634i	$0.891725\pi$
$578$	70.9799			0.122803
$579$	25.7654	+	254.187i	0.0444998	+	0.439011i
$580$	62.4430	+	30.2659i	0.107660	+	0.0521826i
$581$		−	121.665i		−	0.209406i
$582$	75.0493	+	740.395i	0.128951	+	1.27216i
$583$		−	269.281i		−	0.461889i
$584$			357.354i			0.611908i
$585$	350.425	+	89.2141i	0.599017	+	0.152503i
$586$	498.731			0.851076
$587$	−94.3210			−0.160683			−0.0803416	−	0.996767i	$-0.525601\pi$
$587$	−94.3210			−0.160683			−0.0803416	+	0.996767i	$0.525601\pi$
$588$	10.3319	−	1.04728i	0.0175712	−	0.00178109i
$589$	197.293			0.334963
$590$	−207.122	−	100.391i	−0.351054	−	0.170154i
$591$	−410.986	+	41.6591i	−0.695408	+	0.0704892i
$592$			646.381i			1.09186i
$593$	−599.091			−1.01027			−0.505135	−	0.863040i	$-0.668557\pi$
$593$	−599.091			−1.01027			−0.505135	+	0.863040i	$0.668557\pi$
$594$	312.266	+	998.650i	0.525701	+	1.68123i
$595$	215.235	+	104.323i	0.361739	+	0.175334i
$596$		−	103.189i		−	0.173136i
$597$	136.444	−	13.8304i	0.228549	−	0.0231666i
$598$		−	283.647i		−	0.474327i
$599$		−	1087.49i		−	1.81550i	−0.419509	−	0.907751i	$-0.637798\pi$
$599$		−	1087.49i		−	1.81550i	0.419509	−	0.907751i	$-0.362202\pi$
$600$	438.968	+	453.465i	0.731614	+	0.755775i
$601$	425.183			0.707459			0.353730	−	0.935348i	$-0.384913\pi$
$601$	425.183			0.707459			0.353730	+	0.935348i	$0.384913\pi$
$602$	11.4152			0.0189621
$603$	−130.638	−	637.782i	−0.216647	−	1.05768i
$604$	−85.7023			−0.141891
$605$	−670.414	+	1383.16i	−1.10812	+	2.28622i
$606$	−84.5964	−	834.582i	−0.139598	−	1.37720i
$607$		−	692.121i		−	1.14023i	−0.821564	−	0.570116i	$-0.806898\pi$
$607$		−	692.121i		−	1.14023i	0.821564	−	0.570116i	$-0.193102\pi$
$608$	109.730			0.180477
$609$	−221.618	+	22.4641i	−0.363905	+	0.0368868i
$610$	278.805	−	575.215i	0.457057	−	0.942976i
$611$		−	336.174i		−	0.550203i
$612$	78.8338	−	16.1477i	0.128813	−	0.0263851i
$613$		−	881.359i		−	1.43778i	−0.695124	−	0.718889i	$-0.744651\pi$
$613$		−	881.359i		−	1.43778i	0.695124	−	0.718889i	$-0.255349\pi$
$614$			648.789i			1.05666i
$615$	936.797	+	342.288i	1.52325	+	0.556566i
$616$	−460.827			−0.748096
$617$	464.296			0.752506			0.376253	−	0.926517i	$-0.377212\pi$
$617$	464.296			0.752506			0.376253	+	0.926517i	$0.377212\pi$
$618$	−12.0819	−	119.194i	−0.0195500	−	0.192870i
$619$	564.596			0.912110			0.456055	−	0.889952i	$-0.349262\pi$
$619$	564.596			0.912110			0.456055	+	0.889952i	$0.349262\pi$
$620$	−15.2503	+	31.4635i	−0.0245972	+	0.0507476i
$621$	−485.839	+	151.916i	−0.782349	+	0.244632i
$622$			859.428i			1.38172i
$623$	38.2787			0.0614425
$624$	−33.4943	−	330.437i	−0.0536768	−	0.529546i
$625$	−145.237	+	607.891i	−0.232379	+	0.972625i
$626$		−	507.182i		−	0.810195i
$627$	87.3675	+	861.920i	0.139342	+	1.37467i
$628$		−	78.4713i		−	0.124954i
$629$			848.275i			1.34861i
$630$	−216.022	−	54.9967i	−0.342892	−	0.0872964i
$631$	286.667			0.454306			0.227153	−	0.973859i	$-0.427058\pi$
$631$	286.667			0.454306			0.227153	+	0.973859i	$0.427058\pi$
$632$	−635.005			−1.00476
$633$	−144.066	+	14.6031i	−0.227592	+	0.0230696i
$634$	−237.926			−0.375278
$635$	−325.108	−	157.579i	−0.511981	−	0.248155i
$636$	19.2024	−	1.94643i	0.0301925	−	0.00306042i
$637$		−	56.2494i		−	0.0883036i
$638$	1087.58			1.70467
$639$	65.9913	+	322.172i	0.103273	+	0.504182i
$640$	216.537	−	446.748i	0.338339	−	0.698044i
$641$		−	542.483i		−	0.846307i	−0.906058	−	0.423153i	$-0.860923\pi$
$641$		−	542.483i		−	0.846307i	0.906058	−	0.423153i	$-0.139077\pi$
$642$	197.635	−	20.0330i	0.307842	−	0.0312041i
$643$			323.728i			0.503466i	0.967797	+	0.251733i	$0.0810004\pi$
$643$			323.728i			0.503466i	−0.967797	+	0.251733i	$0.919000\pi$
$644$		−	24.6669i		−	0.0383026i
$645$	32.4668	+	11.8628i	0.0503361	+	0.0183919i
$646$	−472.304			−0.731121
$647$	397.939			0.615053			0.307526	−	0.951540i	$-0.400499\pi$
$647$	397.939			0.615053			0.307526	+	0.951540i	$0.400499\pi$
$648$	−626.726	+	267.991i	−0.967170	+	0.413567i
$649$	508.903			0.784134
$650$	295.251	−	233.019i	0.454232	−	0.358492i
$651$	−11.3191	−	111.668i	−0.0173873	−	0.171533i
$652$			17.8685i			0.0274056i
$653$	−921.847			−1.41171			−0.705855	−	0.708356i	$-0.749437\pi$
$653$	−921.847			−1.41171			−0.705855	+	0.708356i	$0.749437\pi$
$654$	−948.012	+	96.0941i	−1.44956	+	0.146933i
$655$	183.668	+	89.0232i	0.280409	+	0.135913i
$656$		−	916.078i		−	1.39646i
$657$	−76.6934	−	374.421i	−0.116733	−	0.569894i
$658$			207.237i			0.314950i
$659$		−	63.7909i		−	0.0967995i	−0.998828	−	0.0483998i	$-0.984588\pi$
$659$		−	63.7909i		−	0.0967995i	0.998828	−	0.0483998i	$-0.0154121\pi$
$660$	−144.209	−	52.6912i	−0.218498	−	0.0798352i
$661$	−525.054			−0.794332			−0.397166	−	0.917747i	$-0.630006\pi$
$661$	−525.054			−0.794332			−0.397166	+	0.917747i	$0.630006\pi$
$662$	−138.391			−0.209050
$663$	−43.9561	−	433.647i	−0.0662988	−	0.654067i
$664$	−386.967			−0.582782
$665$	−166.085	−	80.5009i	−0.249752	−	0.121054i
$666$	−158.640	−	774.486i	−0.238198	−	1.16289i
$667$			529.102i			0.793257i
$668$	−59.8345			−0.0895726
$669$	17.1676	+	169.366i	0.0256616	+	0.253163i
$670$	−609.364	−	295.357i	−0.909499	−	0.440831i
$671$			1413.32i			2.10629i
$672$	−6.29545	−	62.1074i	−0.00936822	−	0.0924218i
$673$			243.515i			0.361835i	0.983498	+	0.180917i	$0.0579067\pi$
$673$			243.515i			0.361835i	−0.983498	+	0.180917i	$0.942093\pi$
$674$		−	659.859i		−	0.979019i
$675$	−557.253	−	380.913i	−0.825560	−	0.564315i
$676$	−51.6416			−0.0763930
$677$	−571.892			−0.844744			−0.422372	−	0.906423i	$-0.638802\pi$
$677$	−571.892			−0.844744			−0.422372	+	0.906423i	$0.638802\pi$
$678$	−131.112	+	13.2900i	−0.193381	+	0.0196018i
$679$	350.540			0.516259
$680$	331.810	−	684.574i	0.487956	−	1.00673i
$681$	882.277	−	89.4310i	1.29556	−	0.131323i
$682$			548.005i			0.803526i
$683$	1117.51			1.63618			0.818092	−	0.575088i	$-0.195032\pi$
$683$	1117.51			1.63618			0.818092	+	0.575088i	$0.195032\pi$
$684$	−60.8319	+	12.4603i	−0.0889355	+	0.0182169i
$685$	−408.227	+	842.232i	−0.595951	+	1.22954i
$686$			34.6754i			0.0505472i
$687$	−860.513	+	87.2250i	−1.25257	+	0.126965i
$688$		−	31.7488i		−	0.0461465i
$689$		−	104.543i		−	0.151731i
$690$	−181.713	+	497.323i	−0.263352	+	0.720759i
$691$	−148.853			−0.215417			−0.107708	−	0.994183i	$-0.534351\pi$
$691$	−148.853			−0.215417			−0.107708	+	0.994183i	$0.534351\pi$
$692$	−70.0128			−0.101175
$693$	482.835	−	98.9002i	0.696732	−	0.142713i
$694$	−1145.01			−1.64987
$695$	−35.2770	+	72.7816i	−0.0507582	+	0.104722i
$696$	71.4490	+	704.877i	0.102657	+	1.01275i
$697$		−	1202.21i		−	1.72483i
$698$	237.447			0.340182
$699$	−1056.36	+	107.077i	−1.51125	+	0.153186i
$700$	25.6759	−	20.2641i	0.0366799	−	0.0289487i
$701$			758.051i			1.08139i	0.841220	+	0.540693i	$0.181838\pi$
$701$			758.051i			1.08139i	−0.841220	+	0.540693i	$0.818162\pi$
$702$	121.231	+	387.705i	0.172693	+	0.552286i
$703$		−	654.569i		−	0.931108i
$704$			1445.46i			2.05321i
$705$	−215.362	+	589.419i	−0.305479	+	0.836055i
$706$	819.086			1.16018
$707$	−395.132			−0.558886
$708$	3.67848	+	36.2898i	0.00519559	+	0.0512568i
$709$	404.100			0.569958			0.284979	−	0.958534i	$-0.408013\pi$
$709$	404.100			0.569958			0.284979	+	0.958534i	$0.408013\pi$
$710$	307.817	+	149.198i	0.433546	+	0.210138i
$711$	665.332	−	136.281i	0.935769	−	0.191676i
$712$		−	121.749i		−	0.170996i
$713$	−266.602			−0.373916
$714$	27.0971	+	267.325i	0.0379511	+	0.374404i
$715$	−362.719	+	748.343i	−0.507300	+	1.04663i
$716$		−	45.2872i		−	0.0632503i
$717$	0.103701	+	1.02306i	0.000144632	+	0.00142686i
$718$		−	280.321i		−	0.390420i
$719$		−	891.404i		−	1.23978i	−0.784688	−	0.619892i	$-0.787177\pi$
$719$		−	891.404i		−	1.23978i	0.784688	−	0.619892i	$-0.212823\pi$
$720$	−152.961	+	600.817i	−0.212446	+	0.834468i
$721$	−56.4321			−0.0782692
$722$	−311.446			−0.431365
$723$	−102.140	+	10.3533i	−0.141272	+	0.0143199i
$724$	−21.9284			−0.0302879
$725$	−550.747	+	434.663i	−0.759651	+	0.599536i
$726$	−1717.91	+	174.134i	−2.36627	+	0.239854i
$727$		−	254.837i		−	0.350532i	−0.984521	−	0.175266i	$-0.943921\pi$
$727$		−	254.837i		−	0.350532i	0.984521	−	0.175266i	$-0.0560786\pi$
$728$	−178.906			−0.245751
$729$	599.142	−	415.295i	0.821869	−	0.569677i
$730$	−357.738	−	173.394i	−0.490052	−	0.237526i
$731$		−	41.6653i		−	0.0569977i
$732$	−100.784	+	10.2158i	−0.137682	+	0.0139560i
$733$		−	593.296i		−	0.809408i	−0.914448	−	0.404704i	$-0.867375\pi$
$733$		−	593.296i		−	0.809408i	0.914448	−	0.404704i	$-0.132625\pi$
$734$		−	1294.60i		−	1.76375i
$735$	−36.0350	+	98.6229i	−0.0490271	+	0.134181i
$736$	−148.278			−0.201465
$737$	1497.22			2.03151
$738$	224.831	+	1097.63i	0.304649	+	1.48731i
$739$	205.825			0.278518			0.139259	−	0.990256i	$-0.455528\pi$
$739$	205.825			0.278518			0.139259	+	0.990256i	$0.455528\pi$
$740$	104.388	+	50.5965i	0.141065	+	0.0683737i
$741$	33.9186	+	334.622i	0.0457741	+	0.451582i
$742$			64.4461i			0.0868546i
$743$	−992.549			−1.33587			−0.667933	−	0.744221i	$-0.732821\pi$
$743$	−992.549			−1.33587			−0.667933	+	0.744221i	$0.732821\pi$
$744$	−355.170	+	36.0014i	−0.477380	+	0.0483890i
$745$	938.863	+	455.064i	1.26022	+	0.610824i
$746$			546.486i			0.732556i
$747$	405.448	−	83.0488i	0.542768	−	0.111176i
$748$			185.066i			0.247415i
$749$		−	93.5701i		−	0.124927i
$750$	−666.947	+	219.411i	−0.889262	+	0.292547i
$751$	−367.868			−0.489838			−0.244919	−	0.969544i	$-0.578761\pi$
$751$	−367.868			−0.489838			−0.244919	+	0.969544i	$0.578761\pi$
$752$	576.383			0.766466
$753$	65.1666	+	642.898i	0.0865426	+	0.853782i
$754$	422.229			0.559986
$755$	377.947	−	779.760i	0.500592	−	1.03279i
$756$	10.5426	+	33.7160i	0.0139453	+	0.0445979i
$757$		−	1047.25i		−	1.38343i	−0.722172	−	0.691713i	$-0.756856\pi$
$757$		−	1047.25i		−	1.38343i	0.722172	−	0.691713i	$-0.243144\pi$
$758$	−339.344			−0.447683
$759$	−118.060	−	1164.71i	−0.155546	−	1.53454i
$760$	−256.041	+	528.249i	−0.336895	+	0.695065i
$761$		−	814.787i		−	1.07068i	−0.844637	−	0.535340i	$-0.820184\pi$
$761$		−	814.787i		−	1.07068i	0.844637	−	0.535340i	$-0.179816\pi$
$762$	−40.9296	−	403.789i	−0.0537133	−	0.529906i
$763$			448.836i			0.588251i
$764$			80.1463i			0.104903i
$765$	−200.737	+	788.479i	−0.262402	+	1.03069i
$766$	204.573			0.267066
$767$	197.571			0.257589
$768$	−278.879	+	28.2683i	−0.363124	+	0.0368076i
$769$	−1490.09			−1.93770			−0.968850	−	0.247647i	$-0.920343\pi$
$769$	−1490.09			−1.93770			−0.968850	+	0.247647i	$0.920343\pi$
$770$	223.601	−	461.322i	0.290391	−	0.599119i
$771$	−349.191	+	35.3953i	−0.452907	+	0.0459083i
$772$		−	42.1146i		−	0.0545526i
$773$	305.547			0.395275			0.197637	−	0.980275i	$-0.436673\pi$
$773$	305.547			0.395275			0.197637	+	0.980275i	$0.436673\pi$
$774$	7.79202	+	38.0410i	0.0100672	+	0.0491485i
$775$	−219.016	−	277.508i	−0.282602	−	0.358075i
$776$		−	1114.92i		−	1.43676i
$777$	−370.487	+	37.5539i	−0.476817	+	0.0483320i
$778$			107.235i			0.137835i
$779$			927.681i			1.19086i
$780$	−55.9861	−	20.4563i	−0.0717770	−	0.0262260i
$781$	−756.315			−0.968393
$782$	638.225			0.816144
$783$	−226.138	−	723.206i	−0.288810	−	0.923635i
$784$	96.4417			0.123012
$785$	713.969	+	346.058i	0.909515	+	0.440839i
$786$	23.1229	+	228.118i	0.0294185	+	0.290227i
$787$		−	927.227i		−	1.17818i	−0.808068	−	0.589090i	$-0.799486\pi$
$787$		−	927.227i		−	1.17818i	0.808068	−	0.589090i	$-0.200514\pi$
$788$	68.0935			0.0864131
$789$	1052.68	−	106.704i	1.33420	−	0.135240i
$790$	308.115	−	635.687i	0.390019	−	0.804667i
$791$			62.0750i			0.0784766i
$792$	−314.561	−	1535.70i	−0.397173	−	1.93902i
$793$			548.691i			0.691918i
$794$			748.086i			0.942173i
$795$	−66.9730	+	183.296i	−0.0842428	+	0.230561i
$796$	−22.6064			−0.0284000
$797$	−55.2054			−0.0692665			−0.0346332	−	0.999400i	$-0.511026\pi$
$797$	−55.2054			−0.0692665			−0.0346332	+	0.999400i	$0.511026\pi$
$798$	−20.9094	−	206.280i	−0.0262022	−	0.258497i
$799$	756.412			0.946699
$800$	−121.812	−	154.344i	−0.152265	−	0.192930i
$801$	26.1291	+	127.563i	0.0326206	+	0.159255i
$802$			853.135i			1.06376i
$803$	878.970			1.09461
$804$	10.8223	+	106.767i	0.0134606	+	0.132795i
$805$	224.431	+	108.781i	0.278796	+	0.135132i
$806$			212.751i			0.263959i
$807$	31.6608	+	312.348i	0.0392327	+	0.387048i
$808$			1256.75i			1.55539i
$809$		−	80.6259i		−	0.0996612i	−0.998758	−	0.0498306i	$-0.984132\pi$
$809$		−	80.6259i		−	0.0996612i	0.998758	−	0.0498306i	$-0.0158681\pi$
$810$	35.8189	−	757.433i	0.0442208	−	0.935102i
$811$	1217.85			1.50166			0.750831	−	0.660494i	$-0.229653\pi$
$811$	1217.85			1.50166			0.750831	+	0.660494i	$0.229653\pi$
$812$	36.7184			0.0452197
$813$	452.488	−	45.8659i	0.556566	−	0.0564157i
$814$	1818.14			2.23359
$815$	−162.576	−	78.7998i	−0.199479	−	0.0966869i
$816$	743.504	−	75.3644i	0.911156	−	0.0923583i
$817$			32.1509i			0.0393524i
$818$	953.780			1.16599
$819$	187.451	−	38.3959i	0.228877	−	0.0468815i
$820$	−147.943	−	71.7075i	−0.180418	−	0.0874481i
$821$		−	811.278i		−	0.988159i	−0.869417	−	0.494079i	$-0.835505\pi$
$821$		−	811.278i		−	0.988159i	0.869417	−	0.494079i	$-0.164495\pi$
$822$	−1046.06	+	106.033i	−1.27258	+	0.128994i
$823$			1587.38i			1.92877i	0.264504	+	0.964385i	$0.414792\pi$
$823$			1587.38i			1.92877i	−0.264504	+	0.964385i	$0.585208\pi$
$824$			179.488i			0.217825i
$825$	1115.37	−	1079.71i	1.35196	−	1.30874i
$826$	−121.794			−0.147450
$827$	199.624			0.241384			0.120692	−	0.992690i	$-0.461489\pi$
$827$	199.624			0.241384			0.120692	+	0.992690i	$0.461489\pi$
$828$	82.2021	−	16.8376i	0.0992779	−	0.0203353i
$829$	−62.1446			−0.0749633			−0.0374816	−	0.999297i	$-0.511934\pi$
$829$	−62.1446			−0.0749633			−0.0374816	+	0.999297i	$0.511934\pi$
$830$	187.763	−	387.382i	0.226220	−	0.466726i
$831$	110.874	+	1093.82i	0.133422	+	1.31627i
$832$			561.168i			0.674481i
$833$	126.565			0.151938
$834$	−90.3958	+	9.16286i	−0.108388	+	0.0109866i
$835$	263.870	−	544.402i	0.316012	−	0.651979i
$836$		−	142.806i		−	0.170820i
$837$	364.406	−	113.946i	0.435372	−	0.136136i
$838$		−	1338.07i		−	1.59674i
$839$		−	626.986i		−	0.747302i	−0.927569	−	0.373651i	$-0.878106\pi$
$839$		−	626.986i		−	0.747302i	0.927569	−	0.373651i	$-0.121894\pi$
$840$	313.679	+	114.612i	0.373428	+	0.136443i
$841$	53.3935			0.0634881
$842$	872.441			1.03615
$843$	−90.4736	−	892.563i	−0.107323	−	1.05879i
$844$	23.8693			0.0282812
$845$	227.739	−	469.860i	0.269514	−	0.556047i
$846$	−690.615	+	141.460i	−0.816329	+	0.167211i
$847$			813.343i			0.960263i
$848$	179.242			0.211371
$849$	−25.3293	−	249.885i	−0.0298342	−	0.294328i
$850$	524.308	+	664.333i	0.616834	+	0.781568i
$851$			884.519i			1.03939i
$852$	−5.46683	−	53.9327i	−0.00641646	−	0.0633013i
$853$		−	1501.49i		−	1.76025i	−0.474744	−	0.880124i	$-0.657459\pi$
$853$		−	1501.49i		−	1.76025i	0.474744	−	0.880124i	$-0.342541\pi$
$854$		−	338.244i		−	0.396071i
$855$	154.898	−	608.427i	0.181168	−	0.711611i
$856$	−297.608			−0.347673
$857$	−1141.54			−1.33202			−0.666010	−	0.745942i	$-0.731999\pi$
$857$	−1141.54			−1.33202			−0.666010	+	0.745942i	$0.731999\pi$
$858$	−929.453	+	94.2130i	−1.08328	+	0.109805i
$859$	−1673.77			−1.94851			−0.974254	−	0.225452i	$-0.927614\pi$
$859$	−1673.77			−1.94851			−0.974254	+	0.225452i	$0.927614\pi$
$860$	−5.12730	−	2.48518i	−0.00596198	−	0.00288975i
$861$	525.069	−	53.2230i	0.609836	−	0.0618153i
$862$		−	248.631i		−	0.288434i
$863$	−1042.44			−1.20792			−0.603962	−	0.797013i	$-0.706412\pi$
$863$	−1042.44			−1.20792			−0.603962	+	0.797013i	$0.706412\pi$
$864$	202.675	−	63.3741i	0.234578	−	0.0733497i
$865$	308.756	−	637.010i	0.356944	−	0.736427i
$866$			1214.81i			1.40278i
$867$	113.152	−	11.4695i	0.130510	−	0.0132290i
$868$			18.5015i			0.0213151i
$869$			1561.90i			1.79735i
$870$	−740.301	−	270.492i	−0.850921	−	0.310910i
$871$	581.265			0.667354
$872$	1427.56			1.63711
$873$	239.279	+	1168.17i	0.274088	+	1.33811i
$874$	−492.484			−0.563483
$875$	71.1416	+	322.977i	0.0813047	+	0.369116i
$876$	6.35341	+	62.6792i	0.00725275	+	0.0715516i
$877$			315.797i			0.360088i	0.983659	+	0.180044i	$0.0576241\pi$
$877$			315.797i			0.360088i	−0.983659	+	0.180044i	$0.942376\pi$
$878$	−903.030			−1.02851
$879$	795.048	−	80.5892i	0.904492	−	0.0916828i
$880$	−1283.06	−	621.896i	−1.45803	−	0.706700i
$881$		−	981.121i		−	1.11364i	−0.830632	−	0.556822i	$-0.812020\pi$
$881$		−	981.121i		−	1.11364i	0.830632	−	0.556822i	$-0.187980\pi$
$882$	−115.555	+	23.6695i	−0.131015	+	0.0268361i
$883$		−	473.207i		−	0.535908i	−0.963432	−	0.267954i	$-0.913652\pi$
$883$		−	473.207i		−	0.535908i	0.963432	−	0.267954i	$-0.0863476\pi$
$884$			71.8480i			0.0812760i
$885$	−346.404	−	126.569i	−0.391417	−	0.143016i
$886$	−162.256			−0.183133
$887$	−234.838			−0.264755			−0.132378	−	0.991199i	$-0.542261\pi$
$887$	−234.838			−0.264755			−0.132378	+	0.991199i	$0.542261\pi$
$888$	119.444	+	1178.37i	0.134509	+	1.32699i
$889$	−191.173			−0.215043
$890$	121.880	+	59.0746i	0.136943	+	0.0663759i
$891$	659.168	+	1541.53i	0.739807	+	1.73012i
$892$		−	28.0611i		−	0.0314586i
$893$	−583.683			−0.653621
$894$	118.199	+	1166.08i	0.132213	+	1.30434i
$895$	412.045	+	199.717i	0.460385	+	0.223147i
$896$		−	262.702i		−	0.293194i
$897$	−45.8342	−	452.175i	−0.0510972	−	0.504097i
$898$		−	479.698i		−	0.534185i
$899$		−	396.856i		−	0.441442i
$900$	85.0564	+	71.7325i	0.0945071	+	0.0797028i
$901$	235.228			0.261074
$902$	−2576.75			−2.85670
$903$	18.1974	−	1.84456i	0.0201522	−	0.00204271i
$904$	197.435			0.218402
$905$	96.7044	−	199.515i	0.106856	−	0.220459i
$906$	968.473	−	98.1682i	1.06895	−	0.108353i
$907$		−	30.8673i		−	0.0340323i	−0.999855	−	0.0170162i	$-0.994583\pi$
$907$		−	30.8673i		−	0.0340323i	0.999855	−	0.0170162i	$-0.00541667\pi$
$908$	−146.179			−0.160990
$909$	−269.718	−	1316.77i	−0.296719	−	1.44860i
$910$	86.8083	−	179.098i	0.0953938	−	0.196811i
$911$			250.101i			0.274534i	0.990534	+	0.137267i	$0.0438318\pi$
$911$			250.101i			0.274534i	−0.990534	+	0.137267i	$0.956168\pi$
$912$	−573.722	+	58.1547i	−0.629082	+	0.0637661i
$913$			951.808i			1.04251i
$914$		−	959.979i		−	1.05031i
$915$	351.507	−	962.028i	0.384160	−	1.05140i
$916$	142.573			0.155647
$917$	108.002			0.117778
$918$	−872.360	+	272.777i	−0.950283	+	0.297143i
$919$	501.139			0.545309			0.272654	−	0.962112i	$-0.412098\pi$
$919$	501.139			0.545309			0.272654	+	0.962112i	$0.412098\pi$
$920$	345.988	−	713.823i	0.376073	−	0.775895i
$921$	104.837	+	1034.26i	0.113829	+	1.12298i
$922$		−	974.061i		−	1.05647i
$923$	−293.623			−0.318118
$924$	−80.8282	+	8.19306i	−0.0874764	+	0.00886695i
$925$	−920.702	+	726.642i	−0.995354	+	0.785558i
$926$			1310.36i			1.41508i
$927$	−38.5206	−	188.059i	−0.0415541	−	0.202869i
$928$		−	220.723i		−	0.237848i
$929$			806.545i			0.868187i	0.900868	+	0.434093i	$0.142931\pi$
$929$			806.545i			0.868187i	−0.900868	+	0.434093i	$0.857069\pi$
$930$	136.294	−	373.020i	0.146553	−	0.401097i
$931$	−97.6633			−0.104901
$932$	175.021			0.187791
$933$	138.874	+	1370.05i	0.148846	+	1.46844i
$934$	−62.7061			−0.0671371
$935$	−1683.82	−	816.141i	−1.80088	−	0.872878i
$936$	−122.122	−	596.204i	−0.130472	−	0.636970i
$937$			13.2891i			0.0141826i	0.999975	+	0.00709129i	$0.00225725\pi$
$937$			13.2891i			0.0141826i	−0.999975	+	0.00709129i	$0.997743\pi$
$938$	−358.325			−0.382010
$939$	−81.9549	−	808.522i	−0.0872789	−	0.861045i
$940$	45.1173	−	93.0836i	0.0479971	−	0.0990251i
$941$			25.1716i			0.0267498i	0.999911	+	0.0133749i	$0.00425749\pi$
$941$			25.1716i			0.0267498i	−0.999911	+	0.0133749i	$0.995743\pi$
$942$	89.8855	+	886.761i	0.0954198	+	0.941359i
$943$		−	1253.58i		−	1.32935i
$944$			338.743i			0.358838i
$945$	−353.257	−	52.7659i	−0.373817	−	0.0558370i
$946$	−89.3030			−0.0944006
$947$	−766.174			−0.809054			−0.404527	−	0.914526i	$-0.632564\pi$
$947$	−766.174			−0.809054			−0.404527	+	0.914526i	$0.632564\pi$
$948$	−111.379	+	11.2898i	−0.117488	+	0.0119090i
$949$	341.241			0.359580
$950$	−404.581	−	512.631i	−0.425875	−	0.539611i
$951$	−379.288	+	38.4461i	−0.398831	+	0.0404270i
$952$		−	402.551i		−	0.422847i
$953$	1640.06			1.72095			0.860474	−	0.509495i	$-0.170168\pi$
$953$	1640.06			1.72095			0.860474	+	0.509495i	$0.170168\pi$
$954$	−214.766	+	43.9910i	−0.225122	+	0.0461122i
$955$	−729.208	−	353.445i	−0.763569	−	0.370099i
$956$		−	0.169504i		−	0.000177305i
$957$	1733.76	−	175.740i	1.81166	−	0.183637i
$958$			1172.42i			1.22382i
$959$			495.259i			0.516432i
$960$	359.500	−	983.904i	0.374479	−	1.02490i
$961$	−761.034			−0.791919
$962$	705.855			0.733738
$963$	311.821	−	63.8711i	0.323802	−	0.0663251i
$964$	16.9229			0.0175549
$965$	383.179	+	185.725i	0.397076	+	0.192461i
$966$	28.2548	+	278.747i	0.0292493	+	0.288558i
$967$			337.789i			0.349317i	0.984629	+	0.174658i	$0.0558821\pi$
$967$			337.789i			0.349317i	−0.984629	+	0.174658i	$0.944118\pi$
$968$	2586.91			2.67243
$969$	−752.921	+	76.3190i	−0.777008	+	0.0787605i
$970$	1116.12	+	540.979i	1.15064	+	0.557711i
$971$			642.396i			0.661582i	0.943704	+	0.330791i	$0.107316\pi$
$971$			642.396i			0.661582i	−0.943704	+	0.330791i	$0.892684\pi$
$972$	−105.162	+	58.1478i	−0.108191	+	0.0598228i
$973$			42.7978i			0.0439854i
$974$		−	887.619i		−	0.911313i
$975$	433.019	−	419.176i	0.444122	−	0.429924i
$976$	−940.751			−0.963884
$977$	1169.01			1.19653			0.598265	−	0.801299i	$-0.295857\pi$
$977$	1169.01			1.19653			0.598265	+	0.801299i	$0.295857\pi$
$978$	−20.4675	−	201.921i	−0.0209279	−	0.206464i
$979$	−299.461			−0.305885
$980$	7.54913	−	15.5750i	0.00770319	−	0.0158928i
$981$	−1495.74	+	306.376i	−1.52471	+	0.312310i
$982$			1141.94i			1.16288i
$983$	1538.19			1.56479			0.782396	−	0.622782i	$-0.213997\pi$
$983$	1538.19			1.56479			0.782396	+	0.622782i	$0.213997\pi$
$984$	−169.281	−	1670.03i	−0.172033	−	1.69718i
$985$	−300.292	+	619.547i	−0.304865	+	0.628982i
$986$			950.043i			0.963532i
$987$	33.4871	+	330.365i	0.0339282	+	0.334717i
$988$		−	55.4413i		−	0.0561147i
$989$		−	43.4455i		−	0.0439287i
$990$	1689.98	+	430.249i	1.70705	+	0.434595i
$991$	−889.089			−0.897163			−0.448582	−	0.893742i	$-0.648071\pi$
$991$	−889.089			−0.897163			−0.448582	+	0.893742i	$0.648071\pi$
$992$	111.217			0.112114
$993$	−220.615	+	22.3624i	−0.222170	+	0.0225200i
$994$	181.006			0.182099
$995$	99.6942	−	205.684i	0.100195	−	0.206717i
$996$	−67.8733	+	6.87990i	−0.0681459	+	0.00690753i
$997$			1345.70i			1.34975i	0.737932	+	0.674876i	$0.235803\pi$
$997$			1345.70i			1.34975i	−0.737932	+	0.674876i	$0.764197\pi$
$998$	−1207.48			−1.20990
$999$	−378.043	−	1209.01i	−0.378421	−	1.21022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.f.a.29.17	yes	24
3.2	odd	2	inner	105.3.f.a.29.7	✓	24
5.2	odd	4		525.3.c.e.176.17		24
5.3	odd	4		525.3.c.e.176.8		24
5.4	even	2	inner	105.3.f.a.29.8	yes	24
15.2	even	4		525.3.c.e.176.7		24
15.8	even	4		525.3.c.e.176.18		24
15.14	odd	2	inner	105.3.f.a.29.18	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.f.a.29.7	✓	24	3.2	odd	2	inner
105.3.f.a.29.8	yes	24	5.4	even	2	inner
105.3.f.a.29.17	yes	24	1.1	even	1	trivial
105.3.f.a.29.18	yes	24	15.14	odd	2	inner
525.3.c.e.176.7		24	15.2	even	4
525.3.c.e.176.8		24	5.3	odd	4
525.3.c.e.176.17		24	5.2	odd	4
525.3.c.e.176.18		24	15.8	even	4

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.87229 q^{2} +(2.98471 - 0.302541i) q^{3} -0.494516 q^{4} +(2.18081 - 4.49934i) q^{5} +(5.58825 - 0.566446i) q^{6} -2.64575i q^{7} -8.41505 q^{8} +(8.81694 - 1.80599i) q^{9} +O(q^{10})\)	\(q+1.87229 q^{2} +(2.98471 - 0.302541i) q^{3} -0.494516 q^{4} +(2.18081 - 4.49934i) q^{5} +(5.58825 - 0.566446i) q^{6} -2.64575i q^{7} -8.41505 q^{8} +(8.81694 - 1.80599i) q^{9} +(4.08312 - 8.42408i) q^{10} +20.6982i q^{11} +(-1.47598 + 0.149611i) q^{12} +8.03563i q^{13} -4.95362i q^{14} +(5.14785 - 14.0890i) q^{15} -13.7774 q^{16} -18.0807 q^{17} +(16.5079 - 3.38135i) q^{18} +13.9519 q^{19} +(-1.07845 + 2.22499i) q^{20} +(-0.800449 - 7.89679i) q^{21} +38.7531i q^{22} -18.8532 q^{23} +(-25.1165 + 2.54590i) q^{24} +(-15.4881 - 19.6244i) q^{25} +15.0451i q^{26} +(25.7696 - 8.05785i) q^{27} +1.30837i q^{28} -28.0643i q^{29} +(9.63829 - 26.3787i) q^{30} +14.1409 q^{31} +7.86489 q^{32} +(6.26205 + 61.7780i) q^{33} -33.8523 q^{34} +(-11.9041 - 5.76989i) q^{35} +(-4.36012 + 0.893092i) q^{36} -46.9161i q^{37} +26.1221 q^{38} +(2.43111 + 23.9840i) q^{39} +(-18.3517 + 37.8622i) q^{40} +66.4914i q^{41} +(-1.49868 - 14.7851i) q^{42} +2.30441i q^{43} -10.2356i q^{44} +(11.1023 - 43.6089i) q^{45} -35.2987 q^{46} -41.8354 q^{47} +(-41.1215 + 4.16823i) q^{48} -7.00000 q^{49} +(-28.9983 - 36.7427i) q^{50} +(-53.9655 + 5.47015i) q^{51} -3.97375i q^{52} -13.0099 q^{53} +(48.2482 - 15.0867i) q^{54} +(93.1281 + 45.1389i) q^{55} +22.2641i q^{56} +(41.6423 - 4.22103i) q^{57} -52.5447i q^{58} -24.5869i q^{59} +(-2.54569 + 6.96723i) q^{60} +68.2822 q^{61} +26.4760 q^{62} +(-4.77821 - 23.3274i) q^{63} +69.8350 q^{64} +(36.1550 + 17.5242i) q^{65} +(11.7244 + 115.667i) q^{66} -72.3360i q^{67} +8.94118 q^{68} +(-56.2713 + 5.70387i) q^{69} +(-22.2880 - 10.8029i) q^{70} +36.5402i q^{71} +(-74.1950 + 15.1975i) q^{72} -42.4661i q^{73} -87.8407i q^{74} +(-52.1646 - 53.8874i) q^{75} -6.89944 q^{76} +54.7622 q^{77} +(4.55175 + 44.9051i) q^{78} +75.4606 q^{79} +(-30.0459 + 61.9892i) q^{80} +(74.4768 - 31.8467i) q^{81} +124.491i q^{82} +45.9851 q^{83} +(0.395835 + 3.90509i) q^{84} +(-39.4306 + 81.3511i) q^{85} +4.31453i q^{86} +(-8.49062 - 83.7638i) q^{87} -174.176i q^{88} +14.4680i q^{89} +(20.7868 - 81.6487i) q^{90} +21.2603 q^{91} +9.32321 q^{92} +(42.2066 - 4.27822i) q^{93} -78.3282 q^{94} +(30.4265 - 62.7743i) q^{95} +(23.4744 - 2.37946i) q^{96} +132.492i q^{97} -13.1061 q^{98} +(37.3808 + 182.495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 52 q^{4} - 22 q^{9}+O(q^{10}) \) 24 * q + 52 * q^4 - 22 * q^9	\( 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46} - 168 q^{49} + 70 q^{51} + 60 q^{54} - 16 q^{55} - 348 q^{60} + 432 q^{61} - 364 q^{64} + 284 q^{66} + 404 q^{69} + 140 q^{70} + 204 q^{75} + 152 q^{76} + 108 q^{79} - 158 q^{81} + 112 q^{84} + 196 q^{85} - 152 q^{90} - 84 q^{91} + 808 q^{94} - 516 q^{96} + 582 q^{99}+O(q^{100}) \) 24 * q + 52 * q^4 - 22 * q^9 - 24 * q^10 + 26 * q^15 + 4 * q^16 + 72 * q^19 + 14 * q^21 - 156 * q^24 - 64 * q^25 - 32 * q^30 - 40 * q^31 - 144 * q^34 + 36 * q^36 + 62 * q^39 - 40 * q^40 + 120 * q^45 - 104 * q^46 - 168 * q^49 + 70 * q^51 + 60 * q^54 - 16 * q^55 - 348 * q^60 + 432 * q^61 - 364 * q^64 + 284 * q^66 + 404 * q^69 + 140 * q^70 + 204 * q^75 + 152 * q^76 + 108 * q^79 - 158 * q^81 + 112 * q^84 + 196 * q^85 - 152 * q^90 - 84 * q^91 + 808 * q^94 - 516 * q^96 + 582 * q^99

Introduction

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