LMFDB - Embedded newform 105.3.r.a.19.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [105,3,Mod(19,105)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("105.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(105, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.r (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	105.19
Dual form			105.3.r.a.94.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.08943 - 1.20633i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.910488 + 1.57701i) q^{4} +(4.48539 + 2.20936i) q^{5} -4.17887i q^{6} +(-6.98737 + 0.420230i) q^{7} +5.25727i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-6.70671 - 10.0272i) q^{10} +(6.92139 + 11.9882i) q^{11} +(-1.57701 + 2.73146i) q^{12} +20.5470 q^{13} +(15.1066 + 7.55107i) q^{14} +(0.570430 + 8.64145i) q^{15} +(9.98398 - 17.2928i) q^{16} +(6.03626 + 10.4551i) q^{17} +(6.26830 - 3.61900i) q^{18} +(-10.7587 - 6.21151i) q^{19} +(0.599716 + 9.08511i) q^{20} +(-6.68159 - 10.1171i) q^{21} -33.3981i q^{22} +(16.5713 + 9.56747i) q^{23} +(-7.88590 + 4.55293i) q^{24} +(15.2375 + 19.8197i) q^{25} +(-42.9315 - 24.7865i) q^{26} -5.19615 q^{27} +(-7.02463 - 10.6366i) q^{28} -1.74604 q^{29} +(9.23261 - 18.7439i) q^{30} +(-42.2614 + 24.3997i) q^{31} +(-23.5100 + 13.5735i) q^{32} +(-11.9882 + 20.7642i) q^{33} -29.1270i q^{34} +(-32.2696 - 13.5527i) q^{35} -5.46293 q^{36} +(-20.4416 - 11.8020i) q^{37} +(14.9863 + 25.9571i) q^{38} +(17.7942 + 30.8204i) q^{39} +(-11.6152 + 23.5809i) q^{40} -70.2426i q^{41} +(1.75609 + 29.1993i) q^{42} -45.3054i q^{43} +(-12.6037 + 21.8302i) q^{44} +(-12.4682 + 8.33936i) q^{45} +(-23.0832 - 39.9812i) q^{46} +(8.98236 - 15.5579i) q^{47} +34.5855 q^{48} +(48.6468 - 5.87261i) q^{49} +(-7.92857 - 59.7934i) q^{50} +(-10.4551 + 18.1088i) q^{51} +(18.7078 + 32.4028i) q^{52} +(-57.9138 + 33.4366i) q^{53} +(10.8570 + 6.26830i) q^{54} +(4.55895 + 69.0636i) q^{55} +(-2.20926 - 36.7345i) q^{56} -21.5173i q^{57} +(3.64823 + 2.10630i) q^{58} +(-30.7390 + 17.7472i) q^{59} +(-13.1083 + 8.76751i) q^{60} +(51.9882 + 30.0154i) q^{61} +117.737 q^{62} +(9.38927 - 18.7841i) q^{63} -14.3750 q^{64} +(92.1611 + 45.3955i) q^{65} +(50.0971 - 28.9236i) q^{66} +(57.3961 - 33.1377i) q^{67} +(-10.9919 + 19.0385i) q^{68} +33.1427i q^{69} +(51.0760 + 67.2454i) q^{70} +31.6354 q^{71} +(-13.6588 - 7.88590i) q^{72} +(-9.99028 - 17.3037i) q^{73} +(28.4743 + 49.3189i) q^{74} +(-16.5334 + 40.0206i) q^{75} -22.6220i q^{76} +(-53.4002 - 80.8575i) q^{77} -85.8630i q^{78} +(49.4531 - 85.6553i) q^{79} +(82.9879 - 55.5066i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-84.7361 + 146.767i) q^{82} -92.2927 q^{83} +(9.87133 - 19.7485i) q^{84} +(3.97594 + 60.2316i) q^{85} +(-54.6535 + 94.6627i) q^{86} +(-1.51211 - 2.61905i) q^{87} +(-63.0251 + 36.3876i) q^{88} +(67.5949 + 39.0259i) q^{89} +(36.1115 - 2.38375i) q^{90} +(-143.569 + 8.63445i) q^{91} +34.8443i q^{92} +(-73.1990 - 42.2614i) q^{93} +(-37.5361 + 21.6715i) q^{94} +(-34.5334 - 51.6308i) q^{95} +(-40.7205 - 23.5100i) q^{96} +93.8717 q^{97} +(-108.729 - 46.4139i) q^{98} -41.5283 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39}+ \cdots + 168 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9 + 78 * q^10 - 28 * q^11 + 60 * q^14 - 24 * q^15 - 40 * q^16 - 60 * q^19 + 12 * q^21 - 34 * q^25 - 96 * q^26 - 88 * q^29 + 84 * q^31 - 170 * q^35 - 192 * q^36 + 36 * q^39 + 330 * q^40 + 320 * q^44 + 18 * q^45 - 60 * q^46 + 356 * q^49 + 12 * q^51 - 468 * q^56 - 804 * q^59 - 198 * q^60 + 336 * q^61 - 400 * q^64 - 46 * q^65 - 108 * q^66 - 438 * q^70 + 344 * q^71 + 900 * q^74 + 144 * q^75 - 20 * q^79 + 1140 * q^80 - 144 * q^81 + 780 * q^84 + 304 * q^85 + 144 * q^86 + 24 * q^89 - 224 * q^91 - 924 * q^94 - 342 * q^95 + 900 * q^96 + 168 * q^99

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.08943	−	1.20633i	−1.04472	−	0.603167i	−0.123551	−	0.992338i	$-0.539428\pi$
$2$	−2.08943	−	1.20633i	−1.04472	−	0.603167i	−0.921166	+	0.389171i	$0.872762\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	0.910488	+	1.57701i	0.227622	+	0.394253i
$5$	4.48539	+	2.20936i	0.897078	+	0.441871i
$5$	4.48539	+	2.20936i	0.897078	+	0.441871i
$6$		−	4.17887i		−	0.696478i
$7$	−6.98737	+	0.420230i	−0.998196	+	0.0600329i
$7$	−6.98737	+	0.420230i	−0.998196	+	0.0600329i
$8$			5.25727i			0.657158i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	−6.70671	−	10.0272i	−0.670671	−	1.00272i
$11$	6.92139	+	11.9882i	0.629217	+	1.08984i	0.987709	+	0.156303i	$0.0499578\pi$
$11$	6.92139	+	11.9882i	0.629217	+	1.08984i	−0.358492	+	0.933533i	$0.616709\pi$
$12$	−1.57701	+	2.73146i	−0.131418	+	0.227622i
$13$	20.5470			1.58053			0.790267	−	0.612762i	$-0.209942\pi$
$13$	20.5470			1.58053			0.790267	+	0.612762i	$0.209942\pi$
$14$	15.1066	+	7.55107i	1.07904	+	0.539362i
$15$	0.570430	+	8.64145i	0.0380286	+	0.576096i
$16$	9.98398	−	17.2928i	0.623998	−	1.08080i
$17$	6.03626	+	10.4551i	0.355074	+	0.615007i	0.987131	−	0.159916i	$-0.0511222\pi$
$17$	6.03626	+	10.4551i	0.355074	+	0.615007i	−0.632056	+	0.774922i	$0.717789\pi$
$18$	6.26830	−	3.61900i	0.348239	−	0.201056i
$19$	−10.7587	−	6.21151i	−0.566245	−	0.326922i	0.189403	−	0.981899i	$-0.439345\pi$
$19$	−10.7587	−	6.21151i	−0.566245	−	0.326922i	−0.755648	+	0.654978i	$0.772678\pi$
$20$	0.599716	+	9.08511i	0.0299858	+	0.454255i
$21$	−6.68159	−	10.1171i	−0.318171	−	0.481768i
$22$		−	33.3981i		−	1.51809i
$23$	16.5713	+	9.56747i	0.720493	+	0.415977i	0.814934	−	0.579553i	$-0.196773\pi$
$23$	16.5713	+	9.56747i	0.720493	+	0.415977i	−0.0944409	+	0.995530i	$0.530106\pi$
$24$	−7.88590	+	4.55293i	−0.328579	+	0.189705i
$25$	15.2375	+	19.8197i	0.609500	+	0.792786i
$26$	−42.9315	−	24.7865i	−1.65121	−	0.953327i
$27$	−5.19615			−0.192450
$28$	−7.02463	−	10.6366i	−0.250880	−	0.379877i
$29$	−1.74604			−0.0602081			−0.0301041	−	0.999547i	$-0.509584\pi$
$29$	−1.74604			−0.0602081			−0.0301041	+	0.999547i	$0.509584\pi$
$30$	9.23261	−	18.7439i	0.307754	−	0.624795i
$31$	−42.2614	+	24.3997i	−1.36327	+	0.787086i	−0.990058	−	0.140660i	$-0.955078\pi$
$31$	−42.2614	+	24.3997i	−1.36327	+	0.787086i	−0.373214	+	0.927745i	$0.621744\pi$
$32$	−23.5100	+	13.5735i	−0.734688	+	0.424172i
$33$	−11.9882	+	20.7642i	−0.363279	+	0.629217i
$34$		−	29.1270i		−	0.856677i
$35$	−32.2696	−	13.5527i	−0.921987	−	0.387220i
$36$	−5.46293			−0.151748
$37$	−20.4416	−	11.8020i	−0.552477	−	0.318973i	0.197643	−	0.980274i	$-0.436671\pi$
$37$	−20.4416	−	11.8020i	−0.552477	−	0.318973i	−0.750120	+	0.661301i	$0.770005\pi$
$38$	14.9863	+	25.9571i	0.394377	+	0.683081i
$39$	17.7942	+	30.8204i	0.456261	+	0.790267i
$40$	−11.6152	+	23.5809i	−0.290379	+	0.589522i
$41$		−	70.2426i		−	1.71323i	−0.515953	−	0.856617i	$-0.672562\pi$
$41$		−	70.2426i		−	1.71323i	0.515953	−	0.856617i	$-0.327438\pi$
$42$	1.75609	+	29.1993i	0.0418116	+	0.695222i
$43$		−	45.3054i		−	1.05361i	−0.849985	−	0.526807i	$-0.823389\pi$
$43$		−	45.3054i		−	1.05361i	0.849985	−	0.526807i	$-0.176611\pi$
$44$	−12.6037	+	21.8302i	−0.286447	+	0.496142i
$45$	−12.4682	+	8.33936i	−0.277070	+	0.185319i
$46$	−23.0832	−	39.9812i	−0.501808	−	0.869156i
$47$	8.98236	−	15.5579i	0.191114	−	0.331019i	−0.754506	−	0.656294i	$-0.772123\pi$
$47$	8.98236	−	15.5579i	0.191114	−	0.331019i	0.945620	+	0.325274i	$0.105457\pi$
$48$	34.5855			0.720531
$49$	48.6468	−	5.87261i	0.992792	−	0.119849i
$50$	−7.92857	−	59.7934i	−0.158571	−	1.19587i
$51$	−10.4551	+	18.1088i	−0.205002	+	0.355074i
$52$	18.7078	+	32.4028i	0.359765	+	0.623130i
$53$	−57.9138	+	33.4366i	−1.09271	+	0.630879i	−0.934298	−	0.356494i	$-0.883972\pi$
$53$	−57.9138	+	33.4366i	−1.09271	+	0.630879i	−0.158416	+	0.987372i	$0.550639\pi$
$54$	10.8570	+	6.26830i	0.201056	+	0.116080i
$55$	4.55895	+	69.0636i	0.0828900	+	1.25570i
$56$	−2.20926	−	36.7345i	−0.0394511	−	0.655973i
$57$		−	21.5173i		−	0.377497i
$58$	3.64823	+	2.10630i	0.0629004	+	0.0363156i
$59$	−30.7390	+	17.7472i	−0.521000	+	0.300799i	−0.737344	−	0.675518i	$-0.763920\pi$
$59$	−30.7390	+	17.7472i	−0.521000	+	0.300799i	0.216344	+	0.976317i	$0.430587\pi$
$60$	−13.1083	+	8.76751i	−0.218472	+	0.146125i
$61$	51.9882	+	30.0154i	0.852265	+	0.492055i	0.861414	−	0.507903i	$-0.169579\pi$
$61$	51.9882	+	30.0154i	0.852265	+	0.492055i	−0.00914943	+	0.999958i	$0.502912\pi$
$62$	117.737			1.89898
$63$	9.38927	−	18.7841i	0.149036	−	0.298160i
$64$	−14.3750			−0.224610
$65$	92.1611	+	45.3955i	1.41786	+	0.698393i
$66$	50.0971	−	28.9236i	0.759047	−	0.438236i
$67$	57.3961	−	33.1377i	0.856658	−	0.494592i	−0.00623342	−	0.999981i	$-0.501984\pi$
$67$	57.3961	−	33.1377i	0.856658	−	0.494592i	0.862892	+	0.505389i	$0.168651\pi$
$68$	−10.9919	+	19.0385i	−0.161645	+	0.279978i
$69$			33.1427i			0.480329i
$70$	51.0760	+	67.2454i	0.729657	+	0.960648i
$71$	31.6354			0.445569			0.222785	−	0.974868i	$-0.428485\pi$
$71$	31.6354			0.445569			0.222785	+	0.974868i	$0.428485\pi$
$72$	−13.6588	−	7.88590i	−0.189705	−	0.109526i
$73$	−9.99028	−	17.3037i	−0.136853	−	0.237037i	0.789451	−	0.613814i	$-0.210366\pi$
$73$	−9.99028	−	17.3037i	−0.136853	−	0.237037i	−0.926304	+	0.376777i	$0.877032\pi$
$74$	28.4743	+	49.3189i	0.384788	+	0.666472i
$75$	−16.5334	+	40.0206i	−0.220446	+	0.533608i
$76$		−	22.6220i		−	0.297658i
$77$	−53.4002	−	80.8575i	−0.693509	−	1.05010i
$78$		−	85.8630i		−	1.10081i
$79$	49.4531	−	85.6553i	0.625989	−	1.08424i	−0.362360	−	0.932038i	$-0.618029\pi$
$79$	49.4531	−	85.6553i	0.625989	−	1.08424i	0.988349	−	0.152207i	$-0.0486379\pi$
$80$	82.9879	−	55.5066i	1.03735	−	0.693833i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−84.7361	+	146.767i	−1.03337	+	1.78984i
$83$	−92.2927			−1.11196			−0.555980	−	0.831196i	$-0.687657\pi$
$83$	−92.2927			−1.11196			−0.555980	+	0.831196i	$0.687657\pi$
$84$	9.87133	−	19.7485i	0.117516	−	0.235101i
$85$	3.97594	+	60.2316i	0.0467757	+	0.708606i
$86$	−54.6535	+	94.6627i	−0.635506	+	1.10073i
$87$	−1.51211	−	2.61905i	−0.0173806	−	0.0301041i
$88$	−63.0251	+	36.3876i	−0.716195	+	0.413495i
$89$	67.5949	+	39.0259i	0.759493	+	0.438494i	0.829114	−	0.559080i	$-0.188846\pi$
$89$	67.5949	+	39.0259i	0.759493	+	0.438494i	−0.0696206	+	0.997574i	$0.522179\pi$
$90$	36.1115	−	2.38375i	0.401238	−	0.0264861i
$91$	−143.569	+	8.63445i	−1.57768	+	0.0948841i
$92$			34.8443i			0.378742i
$93$	−73.1990	−	42.2614i	−0.787086	−	0.454424i
$94$	−37.5361	+	21.6715i	−0.399320	+	0.230548i
$95$	−34.5334	−	51.6308i	−0.363509	−	0.543482i
$96$	−40.7205	−	23.5100i	−0.424172	−	0.244896i
$97$	93.8717			0.967749			0.483875	−	0.875137i	$-0.339229\pi$
$97$	93.8717			0.967749			0.483875	+	0.875137i	$0.339229\pi$
$98$	−108.729	−	46.4139i	−1.10948	−	0.473611i
$99$	−41.5283			−0.419478
$100$	−17.3823	+	42.0753i	−0.173823	+	0.420753i
$101$	37.2007	−	21.4778i	0.368324	−	0.212652i	−0.304402	−	0.952544i	$-0.598457\pi$
$101$	37.2007	−	21.4778i	0.368324	−	0.212652i	0.672726	+	0.739892i	$0.265123\pi$
$102$	43.6905	−	25.2247i	0.428339	−	0.247301i
$103$	8.70809	−	15.0829i	0.0845445	−	0.146435i	−0.820653	−	0.571428i	$-0.806390\pi$
$103$	8.70809	−	15.0829i	0.0845445	−	0.146435i	0.905197	+	0.424992i	$0.139723\pi$
$104$			108.021i			1.03866i
$105$	−7.61720	−	60.1413i	−0.0725448	−	0.572774i
$106$	161.343			1.52210
$107$	−22.8359	−	13.1843i	−0.213419	−	0.123218i	0.389480	−	0.921035i	$-0.372655\pi$
$107$	−22.8359	−	13.1843i	−0.213419	−	0.123218i	−0.602900	+	0.797817i	$0.705988\pi$
$108$	−4.73103	−	8.19439i	−0.0438059	−	0.0758740i
$109$	−93.8442	−	162.543i	−0.860956	−	1.49122i	−0.871007	−	0.491270i	$-0.836533\pi$
$109$	−93.8442	−	162.543i	−0.860956	−	1.49122i	0.0100510	−	0.999949i	$-0.496801\pi$
$110$	73.7882	−	149.803i	0.670802	−	1.36185i
$111$		−	40.8833i		−	0.368318i
$112$	−62.4948	+	125.027i	−0.557990	+	1.11631i
$113$			17.2000i			0.152212i	0.997100	+	0.0761061i	$0.0242488\pi$
$113$			17.2000i			0.152212i	−0.997100	+	0.0761061i	$0.975751\pi$
$114$	−25.9571	+	44.9590i	−0.227694	+	0.394377i
$115$	53.1910	+	79.5259i	0.462531	+	0.691529i
$116$	−1.58974	−	2.75352i	−0.0137047	−	0.0237372i
$117$	−30.8204	+	53.3825i	−0.263422	+	0.456261i
$118$	85.6361			0.725729
$119$	−46.5712	−	70.5172i	−0.391355	−	0.592581i
$120$	−45.4304	+	2.99890i	−0.378587	+	0.0249908i
$121$	−35.3113	+	61.1610i	−0.291829	+	0.505462i
$122$	−72.4172	−	125.430i	−0.593584	−	1.02812i
$123$	105.364	−	60.8319i	0.856617	−	0.494568i
$124$	−76.9571	−	44.4312i	−0.620622	−	0.358316i
$125$	24.5574	+	122.564i	0.196460	+	0.980512i
$126$	−42.2781	+	27.9215i	−0.335541	+	0.221599i
$127$		−	76.1776i		−	0.599824i	−0.953967	−	0.299912i	$-0.903043\pi$
$127$		−	76.1776i		−	0.599824i	0.953967	−	0.299912i	$-0.0969573\pi$
$128$	124.076	+	71.6351i	0.969341	+	0.559649i
$129$	67.9581	−	39.2357i	0.526807	−	0.304152i
$130$	−137.802	−	206.028i	−1.06002	−	1.58483i
$131$	78.3306	+	45.2242i	0.597943	+	0.345223i	0.768232	−	0.640172i	$-0.221137\pi$
$131$	78.3306	+	45.2242i	0.597943	+	0.345223i	−0.170289	+	0.985394i	$0.554470\pi$
$132$	−43.6605			−0.330761
$133$	77.7850	+	38.8811i	0.584850	+	0.292339i
$134$	−159.900			−1.19329
$135$	−23.3068	−	11.4802i	−0.172643	−	0.0850382i
$136$	−54.9653	+	31.7342i	−0.404157	+	0.233340i
$137$	83.3371	−	48.1147i	0.608300	−	0.351202i	−0.164000	−	0.986460i	$-0.552440\pi$
$137$	83.3371	−	48.1147i	0.608300	−	0.351202i	0.772300	+	0.635258i	$0.219106\pi$
$138$	39.9812	−	69.2495i	0.289719	−	0.501808i
$139$		−	33.5627i		−	0.241459i	−0.992685	−	0.120729i	$-0.961477\pi$
$139$		−	33.5627i		−	0.241459i	0.992685	−	0.120729i	$-0.0385233\pi$
$140$	−8.00828	−	63.2290i	−0.0572020	−	0.451636i
$141$	31.1158			0.220679
$142$	−66.1001	−	38.1629i	−0.465493	−	0.268753i
$143$	142.213	+	246.321i	0.994500	+	1.72252i
$144$	29.9519	+	51.8783i	0.207999	+	0.360266i
$145$	−7.83166	−	3.85762i	−0.0540114	−	0.0266042i
$146$			48.2065i			0.330182i
$147$	50.9383	+	67.8844i	0.346519	+	0.461799i
$148$		−	42.9823i		−	0.290421i
$149$	126.505	−	219.113i	0.849028	−	1.47056i	−0.0330491	−	0.999454i	$-0.510522\pi$
$149$	126.505	−	219.113i	0.849028	−	1.47056i	0.882077	−	0.471106i	$-0.156145\pi$
$150$	82.8237	−	63.6754i	0.552158	−	0.424503i
$151$	62.8703	+	108.895i	0.416360	+	0.721156i	0.995570	−	0.0940220i	$-0.0299724\pi$
$151$	62.8703	+	108.895i	0.416360	+	0.721156i	−0.579210	+	0.815178i	$0.696639\pi$
$152$	32.6556	−	56.5611i	0.214839	−	0.372113i
$153$	−36.2176			−0.236716
$154$	14.0349	+	233.365i	0.0911356	+	1.51536i
$155$	−243.467	+	16.0714i	−1.57075	+	0.103687i
$156$	−32.4028	+	56.1233i	−0.207710	+	0.359765i
$157$	−4.83207	−	8.36938i	−0.0307775	−	0.0533082i	0.850226	−	0.526417i	$-0.176465\pi$
$157$	−4.83207	−	8.36938i	−0.0307775	−	0.0533082i	−0.881004	+	0.473109i	$0.843132\pi$
$158$	−206.658	+	119.314i	−1.30796	+	0.755153i
$159$	−100.310	−	57.9138i	−0.630879	−	0.364238i
$160$	−135.440	+	8.94053i	−0.846502	+	0.0558783i
$161$	−119.811	−	59.8877i	−0.744166	−	0.371973i
$162$			21.7140i			0.134037i
$163$	6.51524	+	3.76157i	0.0399708	+	0.0230771i	0.519852	−	0.854256i	$-0.325987\pi$
$163$	6.51524	+	3.76157i	0.0399708	+	0.0230771i	−0.479881	+	0.877333i	$0.659320\pi$
$164$	110.773	−	63.9550i	0.675447	−	0.389970i
$165$	−99.6472	+	66.6493i	−0.603923	+	0.403935i
$166$	192.839	+	111.336i	1.16168	+	0.670698i
$167$	−254.798			−1.52574			−0.762869	−	0.646553i	$-0.776210\pi$
$167$	−254.798			−1.52574			−0.762869	+	0.646553i	$0.776210\pi$
$168$	53.1884	−	35.1269i	0.316598	−	0.209089i
$169$	253.177			1.49809
$170$	64.3520	−	130.646i	0.378541	−	0.768507i
$171$	32.2760	−	18.6345i	0.188748	−	0.108974i
$172$	71.4472	−	41.2501i	0.415391	−	0.239826i
$173$	−16.4662	+	28.5203i	−0.0951804	+	0.164857i	−0.909684	−	0.415301i	$-0.863676\pi$
$173$	−16.4662	+	28.5203i	−0.0951804	+	0.164857i	0.814503	+	0.580159i	$0.197009\pi$
$174$			7.29645i			0.0419336i
$175$	−114.799	−	132.084i	−0.655994	−	0.754766i
$176$	276.412			1.57052
$177$	−53.2415	−	30.7390i	−0.300799	−	0.173667i
$178$	−94.1567	−	163.084i	−0.528970	−	0.916203i
$179$	48.2811	+	83.6253i	0.269727	+	0.467180i	0.968791	−	0.247878i	$-0.0797333\pi$
$179$	48.2811	+	83.6253i	0.269727	+	0.467180i	−0.699064	+	0.715059i	$0.746400\pi$
$180$	−24.5034	−	12.0696i	−0.136130	−	0.0670531i
$181$		−	144.036i		−	0.795781i	−0.917433	−	0.397891i	$-0.869742\pi$
$181$		−	144.036i		−	0.795781i	0.917433	−	0.397891i	$-0.130258\pi$
$182$	310.394	+	155.151i	1.70546	+	0.852481i
$183$			103.976i			0.568177i
$184$	−50.2987	+	87.1200i	−0.273363	+	0.473478i
$185$	−65.6140	−	98.0994i	−0.354670	−	0.530267i
$186$	101.963	+	176.605i	0.548188	+	0.949489i
$187$	−83.5587	+	144.728i	−0.446838	+	0.773946i
$188$	32.7133			0.174007
$189$	36.3075	−	2.18358i	0.192103	−	0.0115533i
$190$	9.87113	+	149.538i	0.0519533	+	0.787041i
$191$	−119.933	+	207.730i	−0.627923	+	1.08759i	0.360045	+	0.932935i	$0.382761\pi$
$191$	−119.933	+	207.730i	−0.627923	+	1.08759i	−0.987968	+	0.154659i	$0.950572\pi$
$192$	−12.4491	−	21.5625i	−0.0648392	−	0.112305i
$193$	148.839	−	85.9324i	0.771188	−	0.445246i	−0.0621101	−	0.998069i	$-0.519783\pi$
$193$	148.839	−	85.9324i	0.771188	−	0.445246i	0.833298	+	0.552824i	$0.186450\pi$
$194$	−196.139	−	113.241i	−1.01102	−	0.583715i
$195$	11.7206	+	177.555i	0.0601056	+	0.910541i
$196$	53.5535	+	71.3696i	0.273232	+	0.364131i
$197$		−	129.725i		−	0.658503i	−0.944242	−	0.329252i	$-0.893204\pi$
$197$		−	129.725i		−	0.658503i	0.944242	−	0.329252i	$-0.106796\pi$
$198$	86.7707	+	50.0971i	0.438236	+	0.253016i
$199$	−170.323	+	98.3362i	−0.855896	+	0.494152i	−0.862636	−	0.505826i	$-0.831188\pi$
$199$	−170.323	+	98.3362i	−0.855896	+	0.494152i	0.00673987	+	0.999977i	$0.497855\pi$
$200$	−104.197	+	80.1075i	−0.520986	+	0.400538i
$201$	99.4130	+	57.3961i	0.494592	+	0.285553i
$202$	−103.638			−0.513058
$203$	12.2002	−	0.733737i	0.0600995	−	0.00361447i
$204$	−38.0770			−0.186652
$205$	155.191	−	315.066i	0.757029	−	1.53691i
$206$	−36.3899	+	21.0097i	−0.176650	+	0.101989i
$207$	−49.7140	+	28.7024i	−0.240164	+	0.138659i
$208$	205.140	−	355.313i	0.986251	−	1.70824i
$209$		−	171.969i		−	0.822819i
$210$	−56.6349	+	134.850i	−0.269690	+	0.642144i
$211$	164.720			0.780663			0.390332	−	0.920674i	$-0.372360\pi$
$211$	164.720			0.780663			0.390332	+	0.920674i	$0.372360\pi$
$212$	−105.460	−	60.8872i	−0.497451	−	0.287204i
$213$	27.3971	+	47.4531i	0.128625	+	0.222785i
$214$	31.8094	+	55.0955i	0.148642	+	0.257455i
$215$	100.096	−	203.213i	0.465562	−	0.945175i
$216$		−	27.3176i		−	0.126470i
$217$	285.043	−	188.249i	1.31356	−	0.867507i
$218$			452.830i			2.07720i
$219$	17.3037	−	29.9708i	0.0790122	−	0.136853i
$220$	−104.763	+	70.0711i	−0.476196	+	0.318505i
$221$	124.027	+	214.821i	0.561207	+	0.972040i
$222$	−49.3189	+	85.4229i	−0.222157	+	0.384788i
$223$	−89.1764			−0.399894			−0.199947	−	0.979807i	$-0.564077\pi$
$223$	−89.1764			−0.399894			−0.199947	+	0.979807i	$0.564077\pi$
$224$	158.569	−	104.723i	0.707898	−	0.467512i
$225$	−74.3492	+	9.85867i	−0.330441	+	0.0438163i
$226$	20.7489	−	35.9382i	0.0918095	−	0.159019i
$227$	38.5909	+	66.8415i	0.170004	+	0.294456i	0.938421	−	0.345494i	$-0.112289\pi$
$227$	38.5909	+	66.8415i	0.170004	+	0.294456i	−0.768417	+	0.639950i	$0.778955\pi$
$228$	33.9331	−	19.5913i	0.148829	−	0.0859266i
$229$	45.0755	+	26.0243i	0.196836	+	0.113643i	0.595179	−	0.803593i	$-0.297081\pi$
$229$	45.0755	+	26.0243i	0.196836	+	0.113643i	−0.398343	+	0.917237i	$0.630415\pi$
$230$	−15.2043	−	230.330i	−0.0661057	−	1.00144i
$231$	75.0403	−	150.125i	0.324850	−	0.649891i
$232$		−	9.17937i		−	0.0395663i
$233$	−18.0433	−	10.4173i	−0.0774389	−	0.0447094i	0.460781	−	0.887514i	$-0.347570\pi$
$233$	−18.0433	−	10.4173i	−0.0774389	−	0.0447094i	−0.538219	+	0.842805i	$0.680903\pi$
$234$	128.794	−	74.3595i	0.550404	−	0.317776i
$235$	74.6624	−	49.9381i	0.317712	−	0.212502i
$236$	−55.9749	−	32.3172i	−0.237182	−	0.136937i
$237$	171.311			0.722830
$238$	12.2401	+	203.521i	0.0514288	+	0.855132i
$239$	−302.275			−1.26475			−0.632375	−	0.774662i	$-0.717920\pi$
$239$	−302.275			−1.26475			−0.632375	+	0.774662i	$0.717920\pi$
$240$	155.130	+	76.4117i	0.646373	+	0.318382i
$241$	−314.222	+	181.416i	−1.30383	+	0.752764i	−0.981058	−	0.193714i	$-0.937947\pi$
$241$	−314.222	+	181.416i	−1.30383	+	0.752764i	−0.322768	+	0.946478i	$0.604613\pi$
$242$	147.561	−	85.1945i	0.609757	−	0.352043i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$			109.315i			0.448011i
$245$	231.175	+	81.1372i	0.943570	+	0.331172i
$246$	−293.534			−1.19323
$247$	−221.058	−	127.628i	−0.894970	−	0.516711i
$248$	−128.275	−	222.180i	−0.517240	−	0.895885i
$249$	−79.9278	−	138.439i	−0.320995	−	0.555980i
$250$	96.5421	−	285.714i	0.386168	−	1.14286i
$251$			57.4428i			0.228856i	0.993432	+	0.114428i	$0.0365035\pi$
$251$			57.4428i			0.228856i	−0.993432	+	0.114428i	$0.963497\pi$
$252$	38.1715	−	2.29569i	0.151474	−	0.00910987i
$253$			264.881i			1.04696i
$254$	−91.8957	+	159.168i	−0.361794	+	0.626646i
$255$	−86.9041	+	58.1260i	−0.340800	+	0.227945i
$256$	−144.082	−	249.557i	−0.562820	−	0.974832i
$257$	−178.172	+	308.602i	−0.693275	+	1.20079i	0.277484	+	0.960730i	$0.410500\pi$
$257$	−178.172	+	308.602i	−0.693275	+	1.20079i	−0.970759	+	0.240057i	$0.922834\pi$
$258$	−189.325			−0.733819
$259$	147.793	+	73.8747i	0.570629	+	0.285231i
$260$	12.3223	+	186.671i	0.0473936	+	0.717966i
$261$	2.61905	−	4.53633i	0.0100347	−	0.0173806i
$262$	−109.111	−	188.986i	−0.416454	−	0.721320i
$263$	326.440	−	188.470i	1.24121	−	0.716616i	0.271873	−	0.962333i	$-0.412357\pi$
$263$	326.440	−	188.470i	1.24121	−	0.716616i	0.969342	+	0.245717i	$0.0790235\pi$
$264$	−109.163	−	63.0251i	−0.413495	−	0.238732i
$265$	−333.640	+	22.0238i	−1.25902	+	0.0831088i
$266$	−115.623	−	175.074i	−0.434673	−	0.658174i
$267$			135.190i			0.506329i
$268$	104.517	+	60.3429i	0.389989	+	0.225160i
$269$	−93.7498	+	54.1265i	−0.348512	+	0.201214i	−0.664030	−	0.747706i	$-0.731155\pi$
$269$	−93.7498	+	54.1265i	−0.348512	+	0.201214i	0.315518	+	0.948920i	$0.397822\pi$
$270$	34.8491	+	52.1028i	0.129071	+	0.192973i
$271$	−211.425	−	122.066i	−0.780166	−	0.450429i	0.0563230	−	0.998413i	$-0.482062\pi$
$271$	−211.425	−	122.066i	−0.780166	−	0.450429i	−0.836489	+	0.547983i	$0.815396\pi$
$272$	241.064			0.886263
$273$	−137.286	−	207.876i	−0.502880	−	0.761451i
$274$	−232.170			−0.847335
$275$	−132.137	+	319.850i	−0.480500	+	1.16309i
$276$	−52.2664	+	30.1760i	−0.189371	+	0.109333i
$277$	146.489	−	84.5753i	0.528840	−	0.305326i	−0.211704	−	0.977334i	$-0.567901\pi$
$277$	146.489	−	84.5753i	0.528840	−	0.305326i	0.740544	+	0.672008i	$0.234568\pi$
$278$	−40.4879	+	70.1271i	−0.145640	+	0.252256i
$279$		−	146.398i		−	0.524724i
$280$	71.2501	−	169.650i	0.254465	−	0.605891i
$281$	110.103			0.391825			0.195913	−	0.980621i	$-0.437233\pi$
$281$	110.103			0.391825			0.195913	+	0.980621i	$0.437233\pi$
$282$	−65.0144	−	37.5361i	−0.230548	−	0.133107i
$283$	−241.547	−	418.372i	−0.853523	−	1.47834i	−0.878009	−	0.478645i	$-0.841128\pi$
$283$	−241.547	−	418.372i	−0.853523	−	1.47834i	0.0244860	−	0.999700i	$-0.492205\pi$
$284$	28.8037	+	49.8894i	0.101421	+	0.175667i
$285$	47.5394	−	96.5136i	0.166805	−	0.338644i
$286$		−	686.228i		−	2.39940i
$287$	29.5181	+	490.811i	0.102850	+	1.71014i
$288$		−	81.4410i		−	0.282781i
$289$	71.6270	−	124.062i	0.247844	−	0.429279i
$290$	11.7101	+	17.5078i	0.0403798	+	0.0603718i
$291$	81.2953	+	140.808i	0.279365	+	0.483875i
$292$	18.1921	−	31.5096i	0.0623016	−	0.107910i
$293$	−526.016			−1.79528			−0.897638	−	0.440733i	$-0.854719\pi$
$293$	−526.016			−1.79528			−0.897638	+	0.440733i	$0.854719\pi$
$294$	−24.5409	−	203.289i	−0.0834723	−	0.691458i
$295$	−177.086	+	11.6896i	−0.600292	+	0.0396258i
$296$	62.0462	−	107.467i	0.209616	−	0.363065i
$297$	−35.9646	−	62.2925i	−0.121093	−	0.209739i
$298$	−528.648	+	305.215i	−1.77399	+	1.02421i
$299$	340.491	+	196.582i	1.13876	+	0.657466i
$300$	−78.1664	+	10.3648i	−0.260555	+	0.0345494i
$301$	19.0387	+	316.566i	0.0632515	+	1.05171i
$302$		−	303.371i		−	1.00454i
$303$	64.4335	+	37.2007i	0.212652	+	0.122775i
$304$	−214.828	+	124.031i	−0.706672	+	0.407997i
$305$	166.873	+	249.491i	0.547123	+	0.818004i
$306$	75.6742	+	43.6905i	0.247301	+	0.142780i
$307$	−129.052			−0.420366			−0.210183	−	0.977662i	$-0.567406\pi$
$307$	−129.052			−0.420366			−0.210183	+	0.977662i	$0.567406\pi$
$308$	78.8930	−	157.832i	0.256146	−	0.512443i
$309$	30.1657			0.0976236
$310$	528.095	+	260.122i	1.70353	+	0.839104i
$311$	200.865	−	115.970i	0.645869	−	0.372893i	−0.141003	−	0.990009i	$-0.545033\pi$
$311$	200.865	−	115.970i	0.645869	−	0.372893i	0.786872	+	0.617116i	$0.211699\pi$
$312$	−162.031	+	93.5487i	−0.519331	+	0.299836i
$313$	92.1115	−	159.542i	0.294286	−	0.509718i	−0.680533	−	0.732718i	$-0.738252\pi$
$313$	92.1115	−	159.542i	0.294286	−	0.509718i	0.974819	+	0.223000i	$0.0715849\pi$
$314$			23.3164i			0.0742559i
$315$	83.6153	−	63.5097i	0.265445	−	0.201618i
$316$	180.106			0.569956
$317$	−247.246	−	142.747i	−0.779954	−	0.450307i	0.0564597	−	0.998405i	$-0.482019\pi$
$317$	−247.246	−	142.747i	−0.779954	−	0.450307i	−0.836414	+	0.548098i	$0.815352\pi$
$318$	139.727	+	242.014i	0.439393	+	0.761051i
$319$	−12.0850	−	20.9318i	−0.0378840	−	0.0656170i
$320$	−64.4776	−	31.7595i	−0.201493	−	0.0992486i
$321$		−	45.6718i		−	0.142280i
$322$	178.092	+	269.663i	0.553081	+	0.837464i
$323$		−	149.977i		−	0.464326i
$324$	8.19439	−	14.1931i	0.0252913	−	0.0438059i
$325$	313.084	+	407.234i	0.963335	+	1.25303i
$326$	−9.07544	−	15.7191i	−0.0278388	−	0.0482181i
$327$	162.543	−	281.533i	0.497073	−	0.860956i
$328$	369.284			1.12587
$329$	−56.2252	+	112.484i	−0.170897	+	0.341895i
$330$	288.608	−	19.0512i	0.874568	−	0.0577310i
$331$	−18.1747	+	31.4795i	−0.0549085	+	0.0951043i	−0.892173	−	0.451694i	$-0.850820\pi$
$331$	−18.1747	+	31.4795i	−0.0549085	+	0.0951043i	0.837265	+	0.546798i	$0.184153\pi$
$332$	−84.0314	−	145.547i	−0.253107	−	0.438394i
$333$	61.3249	−	35.4060i	0.184159	−	0.106324i
$334$	532.384	+	307.372i	1.59396	+	0.920276i
$335$	330.657	−	21.8270i	0.987036	−	0.0651551i
$336$	−241.662	+	14.5339i	−0.719232	+	0.0432556i
$337$			524.246i			1.55563i	0.628496	+	0.777813i	$0.283671\pi$
$337$			524.246i			1.55563i	−0.628496	+	0.777813i	$0.716329\pi$
$338$	−528.997	−	305.417i	−1.56508	−	0.903599i
$339$	−25.8000	+	14.8956i	−0.0761061	+	0.0439399i
$340$	−91.3658	+	61.1102i	−0.268723	+	0.179736i
$341$	−585.016	−	337.759i	−1.71559	−	0.990496i
$342$	−89.9180			−0.262918
$343$	−337.446	+	61.4770i	−0.983807	+	0.179233i
$344$	238.183			0.692391
$345$	−73.2240	+	148.658i	−0.212244	+	0.430893i
$346$	68.8101	−	39.7275i	0.198873	−	0.114819i
$347$	368.677	−	212.856i	1.06247	−	0.613417i	0.136355	−	0.990660i	$-0.456461\pi$
$347$	368.677	−	212.856i	1.06247	−	0.613417i	0.926114	+	0.377243i	$0.123128\pi$
$348$	2.75352	−	4.76923i	0.00791241	−	0.0137047i
$349$			516.742i			1.48064i	0.672257	+	0.740318i	$0.265325\pi$
$349$			516.742i			1.48064i	−0.672257	+	0.740318i	$0.734675\pi$
$350$	80.5269	+	414.467i	0.230077	+	1.18419i
$351$	−106.765			−0.304174
$352$	−325.444	−	187.895i	−0.924556	−	0.533793i
$353$	76.6693	+	132.795i	0.217193	+	0.376190i	0.953949	−	0.299969i	$-0.0969764\pi$
$353$	76.6693	+	132.795i	0.217193	+	0.376190i	−0.736755	+	0.676159i	$0.763643\pi$
$354$	74.1630	+	128.454i	0.209500	+	0.362865i
$355$	141.897	+	69.8939i	0.399710	+	0.196884i
$356$			142.131i			0.399243i
$357$	65.4439	−	130.926i	0.183316	−	0.366741i
$358$		−	232.973i		−	0.650762i
$359$	86.2580	−	149.403i	0.240273	−	0.416165i	−0.720519	−	0.693435i	$-0.756096\pi$
$359$	86.2580	−	149.403i	0.240273	−	0.416165i	0.960792	+	0.277270i	$0.0894297\pi$
$360$	−43.8422	−	65.5484i	−0.121784	−	0.182079i
$361$	−103.334	−	178.980i	−0.286244	−	0.495790i
$362$	−173.756	+	300.954i	−0.479989	+	0.831366i
$363$	−122.322			−0.336975
$364$	−144.335	−	218.549i	−0.396524	−	0.600409i
$365$	−6.58035	−	99.6859i	−0.0180284	−	0.273112i
$366$	125.430	−	217.252i	0.342706	−	0.593584i
$367$	337.212	+	584.068i	0.918834	+	1.59147i	0.801189	+	0.598411i	$0.204201\pi$
$367$	337.212	+	584.068i	0.918834	+	1.59147i	0.117645	+	0.993056i	$0.462465\pi$
$368$	330.896	−	191.043i	0.899174	−	0.519138i
$369$	182.496	+	105.364i	0.494568	+	0.285539i
$370$	18.7553	+	284.125i	0.0506901	+	0.767905i
$371$	390.615	−	257.971i	1.05287	−	0.695340i
$372$		−	153.914i		−	0.413748i
$373$	523.373	+	302.169i	1.40314	+	0.810106i	0.994714	−	0.102684i	$-0.0327429\pi$
$373$	523.373	+	302.169i	1.40314	+	0.810106i	0.408430	+	0.912789i	$0.366076\pi$
$374$	349.181	−	201.600i	0.933638	−	0.539036i
$375$	−162.579	+	142.980i	−0.433543	+	0.381279i
$376$	81.7920	+	47.2226i	0.217532	+	0.125592i
$377$	−35.8757			−0.0951611
$378$	−78.4962	−	39.2365i	−0.207662	−	0.103800i
$379$	335.031			0.883987			0.441994	−	0.897018i	$-0.354271\pi$
$379$	335.031			0.883987			0.441994	+	0.897018i	$0.354271\pi$
$380$	49.9801	−	101.469i	0.131527	−	0.267023i
$381$	114.266	−	65.9718i	0.299912	−	0.173154i
$382$	501.185	−	289.359i	1.31200	−	0.757485i
$383$	146.747	−	254.173i	0.383150	−	0.663636i	−0.608360	−	0.793661i	$-0.708172\pi$
$383$	146.747	−	254.173i	0.383150	−	0.663636i	0.991511	+	0.130025i	$0.0415057\pi$
$384$			248.151i			0.646227i
$385$	−60.8777	−	480.657i	−0.158124	−	1.24846i
$386$	−414.653			−1.07423
$387$	117.707	+	67.9581i	0.304152	+	0.175602i
$388$	85.4691	+	148.037i	0.220281	+	0.381538i
$389$	−256.067	−	443.521i	−0.658270	−	1.14016i	−0.981063	−	0.193688i	$-0.937955\pi$
$389$	−256.067	−	443.521i	−0.658270	−	1.14016i	0.322793	−	0.946470i	$-0.395378\pi$
$390$	189.702	−	385.129i	0.486415	−	0.987511i
$391$			231.007i			0.590811i
$392$	30.8739	+	255.749i	0.0787599	+	0.652421i
$393$			156.661i			0.398629i
$394$	−156.492	+	271.052i	−0.397188	+	0.687949i
$395$	411.060	−	274.938i	1.04066	−	0.696046i
$396$	−37.8111	−	65.4907i	−0.0954825	−	0.165381i
$397$	−232.830	+	403.273i	−0.586473	+	1.01580i	0.408217	+	0.912885i	$0.366151\pi$
$397$	−232.830	+	403.273i	−0.586473	+	1.01580i	−0.994690	+	0.102917i	$0.967183\pi$
$398$	474.506			1.19223
$399$	9.04223	+	150.350i	0.0226622	+	0.376816i
$400$	494.867	−	65.6192i	1.23717	−	0.164048i
$401$	−75.8880	+	131.442i	−0.189247	+	0.327785i	−0.944999	−	0.327072i	$-0.893938\pi$
$401$	−75.8880	+	131.442i	−0.189247	+	0.327785i	0.755752	+	0.654857i	$0.227271\pi$
$402$	−138.478	−	239.851i	−0.344472	−	0.596644i
$403$	−868.344	+	501.339i	−2.15470	+	1.24402i
$404$	67.7416	+	39.1106i	0.167677	+	0.0968084i
$405$	−2.96404	−	44.9023i	−0.00731861	−	0.110870i
$406$	−26.3767	−	13.1844i	−0.0649671	−	0.0324740i
$407$		−	326.745i		−	0.802813i
$408$	−95.2027	−	54.9653i	−0.233340	−	0.134719i
$409$	314.952	−	181.838i	0.770054	−	0.444591i	−0.0628396	−	0.998024i	$-0.520016\pi$
$409$	314.952	−	181.838i	0.770054	−	0.444591i	0.832894	+	0.553432i	$0.186682\pi$
$410$	−704.336	+	471.096i	−1.71789	+	1.14902i
$411$	144.344	+	83.3371i	0.351202	+	0.202767i
$412$	31.7144			0.0769768
$413$	207.327	−	136.923i	0.502002	−	0.331534i
$414$	138.499			0.334538
$415$	−413.969	−	203.907i	−0.997516	−	0.491343i
$416$	−483.059	+	278.894i	−1.16120	+	0.670419i
$417$	50.3441	−	29.0662i	0.120729	−	0.0697031i
$418$	−207.453	+	359.318i	−0.496298	+	0.859613i
$419$			28.2349i			0.0673863i	0.999432	+	0.0336932i	$0.0107269\pi$
$419$			28.2349i			0.0673863i	−0.999432	+	0.0336932i	$0.989273\pi$
$420$	87.9082	−	66.7704i	0.209305	−	0.158977i
$421$	−767.555			−1.82317			−0.911585	−	0.411111i	$-0.865141\pi$
$421$	−767.555			−1.82317			−0.911585	+	0.411111i	$0.865141\pi$
$422$	−344.171	−	198.707i	−0.815572	−	0.470871i
$423$	26.9471	+	46.6737i	0.0637047	+	0.110340i
$424$	−175.785	−	304.468i	−0.414587	−	0.718086i
$425$	−115.239	+	278.946i	−0.271151	+	0.656344i
$426$		−	132.200i		−	0.310329i
$427$	−375.874	−	187.882i	−0.880267	−	0.440004i
$428$		−	48.0166i		−	0.112188i
$429$	−246.321	+	426.640i	−0.574175	+	0.994500i
$430$	−454.286	+	303.850i	−1.05648	+	0.706628i
$431$	−376.304	−	651.777i	−0.873095	−	1.51224i	−0.858779	−	0.512347i	$-0.828776\pi$
$431$	−376.304	−	651.777i	−0.873095	−	1.51224i	−0.0143160	−	0.999898i	$-0.504557\pi$
$432$	−51.8783	+	89.8558i	−0.120089	+	0.207999i
$433$	240.850			0.556235			0.278117	−	0.960547i	$-0.410290\pi$
$433$	240.850			0.556235			0.278117	+	0.960547i	$0.410290\pi$
$434$	−822.670	+	49.4765i	−1.89555	+	0.114001i
$435$	−0.995990	−	15.0883i	−0.00228963	−	0.0346857i
$436$	170.888	−	295.987i	0.391945	−	0.678869i
$437$	−118.857	−	205.866i	−0.271984	−	0.471090i
$438$	−72.3098	+	41.7481i	−0.165091	+	0.0953152i
$439$	−620.395	−	358.185i	−1.41320	−	0.815912i	−0.417513	−	0.908671i	$-0.637098\pi$
$439$	−620.395	−	358.185i	−1.41320	−	0.815912i	−0.995689	+	0.0927587i	$0.970431\pi$
$440$	−363.086	+	23.9676i	−0.825195	+	0.0544718i
$441$	−57.7127	+	135.197i	−0.130868	+	0.306569i
$442$		−	598.472i		−	1.35401i
$443$	369.423	+	213.287i	0.833913	+	0.481460i	0.855190	−	0.518314i	$-0.173440\pi$
$443$	369.423	+	213.287i	0.833913	+	0.481460i	−0.0212777	+	0.999774i	$0.506773\pi$
$444$	64.4734	−	37.2238i	0.145210	−	0.0838373i
$445$	216.967	+	324.388i	0.487567	+	0.728961i
$446$	186.328	+	107.577i	0.417776	+	0.241203i
$447$	438.227			0.980373
$448$	100.444	−	6.04082i	0.224205	−	0.0134840i
$449$	262.992			0.585727			0.292864	−	0.956154i	$-0.405392\pi$
$449$	262.992			0.585727			0.292864	+	0.956154i	$0.405392\pi$
$450$	167.241	+	69.0910i	0.371646	+	0.153536i
$451$	842.082	−	486.176i	1.86714	−	1.07800i
$452$	−27.1246	+	15.6604i	−0.0600101	+	0.0346468i
$453$	−108.895	+	188.611i	−0.240385	+	0.416360i
$454$		−	186.214i		−	0.410164i
$455$	−663.041	−	278.467i	−1.45723	−	0.612015i
$456$	113.122			0.248075
$457$	57.8418	+	33.3950i	0.126569	+	0.0730744i	0.561948	−	0.827173i	$-0.310052\pi$
$457$	57.8418	+	33.3950i	0.126569	+	0.0730744i	−0.435379	+	0.900247i	$0.643386\pi$
$458$	−62.7881	−	108.752i	−0.137092	−	0.237450i
$459$	−31.3653	−	54.3264i	−0.0683341	−	0.118358i
$460$	−76.9834	+	156.290i	−0.167355	+	0.339761i
$461$			237.618i			0.515441i	0.966219	+	0.257721i	$0.0829714\pi$
$461$			237.618i			0.515441i	−0.966219	+	0.257721i	$0.917029\pi$
$462$	−337.893	+	223.152i	−0.731369	+	0.483013i
$463$			21.0733i			0.0455146i	0.999741	+	0.0227573i	$0.00724450\pi$
$463$			21.0733i			0.0455146i	−0.999741	+	0.0227573i	$0.992755\pi$
$464$	−17.4324	+	30.1938i	−0.0375698	+	0.0650728i
$465$	−234.955	−	351.282i	−0.505281	−	0.755445i
$466$	25.1335	+	43.5324i	0.0539345	+	0.0934172i
$467$	−283.926	+	491.774i	−0.607978	+	1.05305i	0.383595	+	0.923502i	$0.374686\pi$
$467$	−283.926	+	491.774i	−0.607978	+	1.05305i	−0.991573	+	0.129548i	$0.958647\pi$
$468$	−112.247			−0.239843
$469$	−387.123	+	255.665i	−0.825422	+	0.545128i
$470$	−216.244	+	14.2745i	−0.460094	+	0.0303712i
$471$	8.36938	−	14.4962i	0.0177694	−	0.0307775i
$472$	−93.3015	−	161.603i	−0.197673	−	0.342379i
$473$	543.131	−	313.577i	1.14827	−	0.662953i
$474$	−357.942	−	206.658i	−0.755153	−	0.435988i
$475$	−40.8249	−	307.881i	−0.0859471	−	0.648170i
$476$	68.8039	−	137.648i	0.144546	−	0.289177i
$477$		−	200.619i		−	0.420586i
$478$	631.584	+	364.645i	1.32131	+	0.762857i
$479$	−140.065	+	80.8663i	−0.292410	+	0.168823i	−0.639028	−	0.769183i	$-0.720663\pi$
$479$	−140.065	+	80.8663i	−0.292410	+	0.168823i	0.346618	+	0.938006i	$0.387330\pi$
$480$	−130.706	−	195.418i	−0.272303	−	0.407120i
$481$	−420.014	−	242.495i	−0.873209	−	0.504147i
$482$	875.394			1.81617
$483$	−13.9276	−	231.580i	−0.0288355	−	0.479463i
$484$	−128.602			−0.265707
$485$	421.051	+	207.396i	0.868147	+	0.427621i
$486$	−32.5710	+	18.8049i	−0.0670186	+	0.0386932i
$487$	248.735	−	143.607i	0.510750	−	0.294882i	−0.222392	−	0.974957i	$-0.571386\pi$
$487$	248.735	−	143.607i	0.510750	−	0.294882i	0.733142	+	0.680076i	$0.238053\pi$
$488$	−157.799	+	273.316i	−0.323358	+	0.560073i
$489$			13.0305i			0.0266472i
$490$	−385.146	−	448.405i	−0.786012	−	0.915112i
$491$	865.837			1.76342			0.881708	−	0.471796i	$-0.156394\pi$
$491$	865.837			1.76342			0.881708	+	0.471796i	$0.156394\pi$
$492$	191.865	+	110.773i	0.389970	+	0.225149i
$493$	−10.5395	−	18.2550i	−0.0213784	−	0.0370284i
$494$	307.923	+	533.339i	0.623327	+	1.07963i
$495$	−186.271	−	91.7509i	−0.376305	−	0.185355i
$496$			974.422i			1.96456i
$497$	−221.048	+	13.2942i	−0.444765	+	0.0267488i
$498$			385.679i			0.774456i
$499$	109.612	−	189.853i	0.219663	−	0.380467i	−0.735042	−	0.678022i	$-0.762838\pi$
$499$	109.612	−	189.853i	0.219663	−	0.380467i	0.954705	+	0.297554i	$0.0961709\pi$
$500$	−170.926	+	150.320i	−0.341851	+	0.300641i
$501$	−220.662	−	382.197i	−0.440443	−	0.762869i
$502$	69.2953	−	120.023i	0.138038	−	0.239089i
$503$	−52.3860			−0.104147			−0.0520735	−	0.998643i	$-0.516583\pi$
$503$	−52.3860			−0.104147			−0.0520735	+	0.998643i	$0.516583\pi$
$504$	98.7529	+	49.3619i	0.195938	+	0.0979403i
$505$	214.312	−	14.1469i	0.424380	−	0.0280137i
$506$	319.535	−	553.451i	0.631492	−	1.09378i
$507$	219.258	+	379.766i	0.432461	+	0.749045i
$508$	120.133	−	69.3588i	0.236482	−	0.136533i
$509$	169.522	+	97.8739i	0.333050	+	0.192287i	0.657194	−	0.753721i	$-0.271743\pi$
$509$	169.522	+	97.8739i	0.333050	+	0.192287i	−0.324144	+	0.946008i	$0.605076\pi$
$510$	251.700	−	16.6149i	0.493529	−	0.0325783i
$511$	77.0774	+	116.709i	0.150836	+	0.228393i
$512$			122.163i			0.238599i
$513$	55.9036	+	32.2760i	0.108974	+	0.0629161i
$514$	744.556	−	429.869i	1.44855	−	0.836322i
$515$	72.3826	−	48.4132i	0.140549	−	0.0940063i
$516$	123.750	+	71.4472i	0.239826	+	0.138464i
$517$	248.682			0.481009
$518$	−219.686	−	332.644i	−0.424104	−	0.642170i
$519$	−57.0406			−0.109905
$520$	−238.656	+	484.516i	−0.458955	+	0.931761i
$521$	−283.053	+	163.420i	−0.543287	+	0.313667i	−0.746410	−	0.665486i	$-0.768224\pi$
$521$	−283.053	+	163.420i	−0.543287	+	0.313667i	0.203123	+	0.979153i	$0.434891\pi$
$522$	−10.9447	+	6.31891i	−0.0209668	+	0.0121052i
$523$	342.951	−	594.009i	0.655739	−	1.13577i	−0.325970	−	0.945380i	$-0.605691\pi$
$523$	342.951	−	594.009i	0.655739	−	1.13577i	0.981708	−	0.190392i	$-0.0609760\pi$
$524$			164.704i			0.314321i
$525$	98.7075	−	286.587i	0.188014	−	0.545879i
$526$	−909.432			−1.72896
$527$	−510.202	−	294.565i	−0.968126	−	0.558948i
$528$	239.380	+	414.618i	0.453371	+	0.785261i
$529$	−81.4269	−	141.036i	−0.153926	−	0.266608i
$530$	723.686	+	356.464i	1.36544	+	0.672573i
$531$		−	106.483i		−	0.200533i
$532$	9.50647	+	158.069i	0.0178693	+	0.297122i
$533$		−	1443.27i		−	2.70783i
$534$	163.084	−	282.470i	0.305401	−	0.528970i
$535$	−73.2991	−	109.589i	−0.137008	−	0.204840i
$536$	174.213	+	301.747i	0.325025	+	0.562960i
$537$	−83.6253	+	144.843i	−0.155727	+	0.269727i
$538$	261.179			0.485462
$539$	407.106	+	542.541i	0.755298	+	1.00657i
$540$	−3.11622	−	47.2076i	−0.00577077	−	0.0874215i
$541$	−90.5573	+	156.850i	−0.167389	+	0.289926i	−0.937501	−	0.347983i	$-0.886867\pi$
$541$	−90.5573	+	156.850i	−0.167389	+	0.289926i	0.770112	+	0.637908i	$0.220200\pi$
$542$	294.506	+	510.099i	0.543368	+	0.941142i
$543$	216.055	−	124.739i	0.397891	−	0.229722i
$544$	−283.825	−	163.867i	−0.521737	−	0.301225i
$545$	−61.8129	−	936.404i	−0.113418	−	1.71817i
$546$	36.0822	+	599.957i	0.0660847	+	1.09882i
$547$		−	417.257i		−	0.762810i	−0.924408	−	0.381405i	$-0.875440\pi$
$547$		−	417.257i		−	0.762810i	0.924408	−	0.381405i	$-0.124560\pi$
$548$	151.755	+	87.6158i	0.276925	+	0.159883i
$549$	−155.964	+	90.0461i	−0.284088	+	0.164018i
$550$	661.938	−	508.903i	1.20352	−	0.925278i
$551$	18.7850	+	10.8455i	0.0340926	+	0.0196834i
$552$	−174.240			−0.315652
$553$	−309.553	+	619.288i	−0.559770	+	1.11987i
$554$	−408.105			−0.736651
$555$	90.3258	−	183.378i	0.162749	−	0.330410i
$556$	52.9288	−	30.5585i	0.0951957	−	0.0549613i
$557$	−736.087	+	424.980i	−1.32152	+	0.762980i	−0.983971	−	0.178327i	$-0.942931\pi$
$557$	−736.087	+	424.980i	−1.32152	+	0.762980i	−0.337550	+	0.941308i	$0.609598\pi$
$558$	−176.605	+	305.889i	−0.316496	+	0.548188i
$559$		−	930.889i		−	1.66527i
$560$	−556.542	+	422.720i	−0.993825	+	0.754856i
$561$	−289.456			−0.515964
$562$	−230.053	−	132.821i	−0.409347	−	0.236336i
$563$	497.281	+	861.316i	0.883270	+	1.52987i	0.847683	+	0.530503i	$0.177997\pi$
$563$	497.281	+	861.316i	0.883270	+	1.52987i	0.0355872	+	0.999367i	$0.488670\pi$
$564$	28.3306	+	49.0700i	0.0502315	+	0.0870035i
$565$	−38.0009	+	77.1487i	−0.0672582	+	0.136546i
$566$			1165.55i			2.05927i
$567$	34.7186	+	52.5702i	0.0612320	+	0.0927163i
$568$			166.316i			0.292809i
$569$	−358.617	+	621.142i	−0.630258	+	1.09164i	0.357241	+	0.934012i	$0.383717\pi$
$569$	−358.617	+	621.142i	−0.630258	+	1.09164i	−0.987499	+	0.157626i	$0.949616\pi$
$570$	−215.758	+	144.310i	−0.378523	+	0.253176i
$571$	496.542	+	860.037i	0.869601	+	1.50619i	0.862404	+	0.506220i	$0.168958\pi$
$571$	496.542	+	860.037i	0.869601	+	1.50619i	0.00719702	+	0.999974i	$0.497709\pi$
$572$	−258.967	+	448.545i	−0.452740	+	0.784169i
$573$	−415.461			−0.725063
$574$	530.407	−	1061.13i	0.924054	−	1.84865i
$575$	62.8817	+	474.223i	0.109360	+	0.824735i
$576$	21.5625	−	37.3474i	0.0374350	−	0.0648392i
$577$	−354.285	−	613.639i	−0.614011	−	1.06350i	−0.990557	−	0.137101i	$-0.956222\pi$
$577$	−354.285	−	613.639i	−0.614011	−	1.06350i	0.376546	−	0.926398i	$-0.377112\pi$
$578$	−299.320	+	172.812i	−0.517854	+	0.298983i
$579$	257.797	+	148.839i	0.445246	+	0.257063i
$580$	−1.04713	−	15.8629i	−0.00180539	−	0.0273499i
$581$	644.884	−	38.7842i	1.10995	−	0.0667542i
$582$		−	392.277i		−	0.674016i
$583$	−801.688	−	462.855i	−1.37511	−	0.793919i
$584$	90.9700	−	52.5216i	0.155771	−	0.0899342i
$585$	−256.183	+	171.348i	−0.437919	+	0.292903i
$586$	1099.08	+	634.551i	1.87556	+	1.08285i
$587$	51.3529			0.0874837			0.0437419	−	0.999043i	$-0.486072\pi$
$587$	51.3529			0.0874837			0.0437419	+	0.999043i	$0.486072\pi$
$588$	−60.6758	+	142.138i	−0.103190	+	0.241732i
$589$	606.235			1.02926
$590$	384.111	+	189.201i	0.651036	+	0.320679i
$591$	194.588	−	112.345i	0.329252	−	0.190094i
$592$	−408.178	+	235.662i	−0.689490	+	0.398077i
$593$	3.14448	−	5.44641i	0.00530267	−	0.00918450i	−0.863362	−	0.504585i	$-0.831645\pi$
$593$	3.14448	−	5.44641i	0.00530267	−	0.00918450i	0.868665	+	0.495401i	$0.164979\pi$
$594$			173.541i			0.292157i
$595$	−53.0925	−	419.190i	−0.0892311	−	0.704520i
$596$	460.726			0.773030
$597$	−295.009	−	170.323i	−0.494152	−	0.285299i
$598$	−474.288	−	821.492i	−0.793124	−	1.37373i
$599$	−83.2393	−	144.175i	−0.138964	−	0.240692i	0.788141	−	0.615495i	$-0.211044\pi$
$599$	−83.2393	−	144.175i	−0.138964	−	0.240692i	−0.927105	+	0.374803i	$0.877711\pi$
$600$	−210.399	−	86.9207i	−0.350665	−	0.144868i
$601$			31.0015i			0.0515833i	0.999667	+	0.0257916i	$0.00821064\pi$
$601$			31.0015i			0.0515833i	−0.999667	+	0.0257916i	$0.991789\pi$
$602$	342.105	−	684.411i	0.568280	−	1.13689i
$603$			198.826i			0.329728i
$604$	−114.485	+	198.294i	−0.189545	+	0.328302i
$605$	−293.511	+	196.316i	−0.485143	+	0.324489i
$606$	−89.7530	−	155.457i	−0.148107	−	0.256529i
$607$	16.7490	−	29.0101i	0.0275930	−	0.0477925i	−0.851899	−	0.523706i	$-0.824549\pi$
$607$	16.7490	−	29.0101i	0.0275930	−	0.0477925i	0.879492	+	0.475913i	$0.157882\pi$
$608$	337.248			0.554684
$609$	11.6663	+	17.6649i	0.0191565	+	0.0290064i
$610$	−47.6994	−	722.599i	−0.0781958	−	1.18459i
$611$	184.560	−	319.667i	0.302062	−	0.523187i
$612$	−32.9757	−	57.1155i	−0.0538818	−	0.0933261i
$613$	−835.234	+	482.223i	−1.36254	+	0.786660i	−0.989961	−	0.141342i	$-0.954858\pi$
$613$	−835.234	+	482.223i	−1.36254	+	0.786660i	−0.372575	+	0.928002i	$0.621525\pi$
$614$	269.646	+	155.680i	0.439163	+	0.253551i
$615$	606.998	−	40.0684i	0.986988	−	0.0651519i
$616$	425.089	−	280.739i	0.690080	−	0.455745i
$617$			691.561i			1.12084i	0.828207	+	0.560422i	$0.189361\pi$
$617$			691.561i			1.12084i	−0.828207	+	0.560422i	$0.810639\pi$
$618$	−63.0292	−	36.3899i	−0.101989	−	0.0588834i
$619$	−618.233	+	356.937i	−0.998761	+	0.576635i	−0.907882	−	0.419227i	$-0.862301\pi$
$619$	−618.233	+	356.937i	−0.998761	+	0.576635i	−0.0908798	+	0.995862i	$0.528968\pi$
$620$	−247.018	−	369.317i	−0.398417	−	0.595672i
$621$	−86.1073	−	49.7140i	−0.138659	−	0.0800548i
$622$	−559.593			−0.899667
$623$	−488.711	−	244.283i	−0.784447	−	0.392108i
$624$	710.627			1.13882
$625$	−160.638	+	604.004i	−0.257020	+	0.966406i
$626$	−384.922	+	222.235i	−0.614891	+	0.355007i
$627$	257.954	−	148.930i	0.411410	−	0.237527i
$628$	8.79908	−	15.2404i	0.0140113	−	0.0242682i
$629$		−	284.960i		−	0.453036i
$630$	−251.323	+	31.8313i	−0.398925	+	0.0505258i
$631$	−208.740			−0.330809			−0.165404	−	0.986226i	$-0.552893\pi$
$631$	−208.740			−0.330809			−0.165404	+	0.986226i	$0.552893\pi$
$632$	450.313	+	259.988i	0.712520	+	0.411374i
$633$	142.652	+	247.080i	0.225358	+	0.390332i
$634$	344.402	+	596.522i	0.543221	+	0.940886i
$635$	168.304	−	341.687i	0.265045	−	0.538089i
$636$		−	210.919i		−	0.331634i
$637$	999.544	−	120.664i	1.56914	−	0.189426i
$638$			58.3142i			0.0914016i
$639$	−47.4531	+	82.1912i	−0.0742615	+	0.128625i
$640$	398.261	+	595.439i	0.622282	+	0.930373i
$641$	11.3505	+	19.6597i	0.0177076	+	0.0306704i	0.874743	−	0.484586i	$-0.161030\pi$
$641$	11.3505	+	19.6597i	0.0177076	+	0.0306704i	−0.857036	+	0.515257i	$0.827697\pi$
$642$	−55.0955	+	95.4281i	−0.0858185	+	0.148642i
$643$	589.246			0.916401			0.458200	−	0.888849i	$-0.348494\pi$
$643$	589.246			0.916401			0.458200	+	0.888849i	$0.348494\pi$
$644$	−14.6426	−	243.470i	−0.0227370	−	0.378059i
$645$	391.504	−	25.8436i	0.606984	−	0.0400675i
$646$	−180.923	+	313.368i	−0.280066	+	0.485089i
$647$	−115.870	−	200.693i	−0.179088	−	0.310190i	0.762480	−	0.647011i	$-0.223981\pi$
$647$	−115.870	−	200.693i	−0.179088	−	0.310190i	−0.941568	+	0.336822i	$0.890648\pi$
$648$	40.9763	−	23.6577i	0.0632351	−	0.0365088i
$649$	−425.513	−	245.670i	−0.655644	−	0.378536i
$650$	−162.908	−	1228.57i	−0.250628	−	1.89011i
$651$	529.228	+	264.536i	0.812946	+	0.406353i
$652$			13.6995i			0.0210115i
$653$	317.714	+	183.432i	0.486545	+	0.280907i	0.723140	−	0.690701i	$-0.242698\pi$
$653$	317.714	+	183.432i	0.486545	+	0.280907i	−0.236595	+	0.971608i	$0.576031\pi$
$654$	−679.245	+	392.163i	−1.03860	+	0.599637i
$655$	251.427	+	375.908i	0.383858	+	0.573906i
$656$	−1214.69	−	701.300i	−1.85166	−	1.06906i
$657$	59.9417			0.0912355
$658$	253.172	−	167.200i	0.384759	−	0.254104i
$659$	−16.7125			−0.0253603			−0.0126802	−	0.999920i	$-0.504036\pi$
$659$	−16.7125			−0.0253603			−0.0126802	+	0.999920i	$0.504036\pi$
$660$	−195.834	−	96.4615i	−0.296719	−	0.146154i
$661$	144.634	−	83.5046i	0.218811	−	0.126331i	−0.386589	−	0.922252i	$-0.626347\pi$
$661$	144.634	−	83.5046i	0.218811	−	0.126331i	0.605400	+	0.795922i	$0.293013\pi$
$662$	75.9497	−	43.8496i	0.114728	−	0.0662380i
$663$	−214.821	+	372.080i	−0.324013	+	0.561207i
$664$		−	485.207i		−	0.730734i
$665$	262.994	+	346.252i	0.395480	+	0.520679i
$666$	−170.846			−0.256525
$667$	−28.9342	−	16.7052i	−0.0433796	−	0.0250452i
$668$	−231.991	−	401.820i	−0.347292	−	0.601527i
$669$	−77.2290	−	133.765i	−0.115439	−	0.199947i
$670$	−717.216	−	353.277i	−1.07047	−	0.527279i
$671$			830.993i			1.23844i
$672$	294.409	+	147.161i	0.438109	+	0.218990i
$673$		−	999.203i		−	1.48470i	−0.670012	−	0.742350i	$-0.733711\pi$
$673$		−	999.203i		−	1.48470i	0.670012	−	0.742350i	$-0.266289\pi$
$674$	632.416	−	1095.38i	0.938302	−	1.62519i
$675$	−79.1763	−	102.986i	−0.117298	−	0.152572i
$676$	230.515	+	399.263i	0.340998	+	0.590626i
$677$	448.288	−	776.458i	0.662169	−	1.14691i	−0.317876	−	0.948132i	$-0.602969\pi$
$677$	448.288	−	776.458i	0.662169	−	1.14691i	0.980045	−	0.198778i	$-0.0636972\pi$
$678$	71.8764			0.106012
$679$	−655.917	+	39.4477i	−0.966004	+	0.0580968i
$680$	−316.653	+	20.9026i	−0.465667	+	0.0307391i
$681$	−66.8415	+	115.773i	−0.0981519	+	0.170004i
$682$	814.901	+	1411.45i	1.19487	+	2.06958i
$683$	−41.3172	+	23.8545i	−0.0604938	+	0.0349261i	−0.529942	−	0.848034i	$-0.677786\pi$
$683$	−41.3172	+	23.8545i	−0.0604938	+	0.0349261i	0.469448	+	0.882960i	$0.344453\pi$
$684$	58.7738	+	33.9331i	0.0859266	+	0.0496097i
$685$	480.102	−	31.6920i	0.700879	−	0.0462657i
$686$	779.232	+	278.620i	1.13591	+	0.406152i
$687$			90.1509i			0.131224i
$688$	−783.456	−	452.328i	−1.13874	−	0.657454i
$689$	−1189.95	+	687.020i	−1.72707	+	0.997126i
$690$	332.328	−	222.278i	0.481635	−	0.322142i
$691$	366.434	+	211.560i	0.530295	+	0.306166i	0.741136	−	0.671354i	$-0.234287\pi$
$691$	366.434	+	211.560i	0.530295	+	0.306166i	−0.210842	+	0.977520i	$0.567621\pi$
$692$	−59.9692			−0.0866607
$693$	290.174	−	17.4515i	0.418722	−	0.0251825i
$694$	−1027.10			−1.47997
$695$	74.1520	−	150.542i	0.106694	−	0.216607i
$696$	13.7691	−	7.94957i	0.0197831	−	0.0114218i
$697$	734.394	−	424.003i	1.05365	−	0.608325i
$698$	623.364	−	1079.70i	0.893072	−	1.54685i
$699$		−	36.0865i		−	0.0516259i
$700$	103.775	−	301.300i	0.148250	−	0.430429i
$701$	−1051.65			−1.50021			−0.750105	−	0.661319i	$-0.769997\pi$
$701$	−1051.65			−1.50021			−0.750105	+	0.661319i	$0.769997\pi$
$702$	223.079	+	128.794i	0.317776	+	0.183468i
$703$	146.616	+	253.947i	0.208558	+	0.361233i
$704$	−99.4951	−	172.331i	−0.141328	−	0.244788i
$705$	139.567	+	68.7459i	0.197967	+	0.0975119i
$706$		−	369.955i		−	0.524016i
$707$	−250.909	+	165.706i	−0.354893	+	0.234380i
$708$		−	111.950i		−	0.158121i
$709$	91.8143	−	159.027i	0.129498	−	0.224298i	−0.793984	−	0.607939i	$-0.791997\pi$
$709$	91.8143	−	159.027i	0.129498	−	0.224298i	0.923482	+	0.383641i	$0.125330\pi$
$710$	−212.169	−	317.214i	−0.298830	−	0.446781i
$711$	148.359	+	256.966i	0.208663	+	0.361415i
$712$	−205.170	+	355.364i	−0.288160	+	0.499107i
$713$	−933.772			−1.30964
$714$	−294.682	+	194.615i	−0.412720	+	0.272570i
$715$	93.6725	+	1419.05i	0.131010	+	1.98468i
$716$	−87.9187	+	152.280i	−0.122791	+	0.212681i
$717$	−261.778	−	453.413i	−0.365102	−	0.632375i
$718$	−360.461	+	208.112i	−0.502034	+	0.289850i
$719$	−271.719	−	156.877i	−0.377913	−	0.218188i	0.298997	−	0.954254i	$-0.403348\pi$
$719$	−271.719	−	156.877i	−0.377913	−	0.218188i	−0.676910	+	0.736066i	$0.736681\pi$
$720$	19.7286	+	298.869i	0.0274008	+	0.415096i
$721$	−54.5084	+	109.049i	−0.0756011	+	0.151247i
$722$			498.623i			0.690613i
$723$	−544.248	−	314.222i	−0.752764	−	0.434609i
$724$	227.147	−	131.143i	0.313739	−	0.181137i
$725$	−26.6052	−	34.6058i	−0.0366968	−	0.0477322i
$726$	255.583	+	147.561i	0.352043	+	0.203252i
$727$	54.2935			0.0746816			0.0373408	−	0.999303i	$-0.488111\pi$
$727$	54.2935			0.0746816			0.0373408	+	0.999303i	$0.488111\pi$
$728$	−45.3936	−	754.782i	−0.0623539	−	1.03679i
$729$	27.0000			0.0370370
$730$	−106.505	+	216.225i	−0.145898	+	0.296199i
$731$	473.674	−	273.476i	0.647980	−	0.374112i
$732$	−163.972	+	94.6692i	−0.224005	+	0.129330i
$733$	−451.910	+	782.731i	−0.616521	+	1.06785i	0.373595	+	0.927592i	$0.378125\pi$
$733$	−451.910	+	782.731i	−0.616521	+	1.06785i	−0.990116	+	0.140254i	$0.955208\pi$
$734$		−	1627.16i		−	2.21684i
$735$	78.4975	+	417.029i	0.106799	+	0.567386i
$736$	−519.457			−0.705783
$737$	794.522	+	458.717i	1.07805	+	0.622412i
$738$	−254.208	−	440.302i	−0.344456	−	0.596615i
$739$	529.386	+	916.924i	0.716355	+	1.24076i	0.962435	+	0.271513i	$0.0875241\pi$
$739$	529.386	+	916.924i	0.716355	+	1.24076i	−0.246080	+	0.969250i	$0.579143\pi$
$740$	94.9632	−	192.792i	0.128329	−	0.260530i
$741$		−	442.115i		−	0.596647i
$742$	−1127.36	+	67.8011i	−1.51936	+	0.0913762i
$743$			893.251i			1.20222i	0.799165	+	0.601111i	$0.205275\pi$
$743$			893.251i			1.20222i	−0.799165	+	0.601111i	$0.794725\pi$
$744$	222.180	−	384.826i	0.298628	−	0.517240i
$745$	1051.52	−	703.314i	1.41144	−	0.944046i
$746$	−729.035	−	1262.73i	−0.977259	−	1.69266i
$747$	138.439	−	239.783i	0.185327	−	0.320995i
$748$	−304.317			−0.406841
$749$	165.103	+	82.5273i	0.220432	+	0.110183i
$750$	512.179	−	102.622i	0.682905	−	0.136830i
$751$	671.400	−	1162.90i	0.894008	−	1.54847i	0.0589799	−	0.998259i	$-0.481215\pi$
$751$	671.400	−	1162.90i	0.894008	−	1.54847i	0.835028	−	0.550208i	$-0.185451\pi$
$752$	−179.359	−	310.659i	−0.238510	−	0.413111i
$753$	−86.1642	+	49.7469i	−0.114428	+	0.0660650i
$754$	74.9599	+	43.2781i	0.0994163	+	0.0573981i
$755$	41.4111	+	627.338i	0.0548492	+	0.830911i
$756$	36.5010	+	55.2692i	0.0482818	+	0.0731074i
$757$		−	518.848i		−	0.685400i	−0.939445	−	0.342700i	$-0.888658\pi$
$757$		−	518.848i		−	0.685400i	0.939445	−	0.342700i	$-0.111342\pi$
$758$	−700.025	−	404.160i	−0.923516	−	0.533192i
$759$	−397.321	+	229.394i	−0.523480	+	0.302231i
$760$	271.437	−	181.551i	0.357154	−	0.238883i
$761$	119.379	+	68.9233i	0.156871	+	0.0905694i	0.576381	−	0.817181i	$-0.304465\pi$
$761$	119.379	+	68.9233i	0.156871	+	0.0905694i	−0.419510	+	0.907751i	$0.637798\pi$
$762$	−318.336			−0.417764
$763$	724.030	+	1096.31i	0.948926	+	1.43684i
$764$	−436.791			−0.571716
$765$	−162.450	−	80.0175i	−0.212353	−	0.104598i
$766$	−613.235	+	354.051i	−0.800567	+	0.462208i
$767$	−631.592	+	364.650i	−0.823458	+	0.475424i
$768$	249.557	−	432.246i	0.324944	−	0.562820i
$769$			1287.39i			1.67411i	0.547116	+	0.837057i	$0.315726\pi$
$769$			1287.39i			1.67411i	−0.547116	+	0.837057i	$0.684274\pi$
$770$	−452.634	+	1077.74i	−0.587836	+	1.39966i
$771$	−617.205			−0.800525
$772$	271.033	+	156.481i	0.351079	+	0.202695i
$773$	−258.628	−	447.957i	−0.334577	−	0.579504i	0.648827	−	0.760936i	$-0.275260\pi$
$773$	−258.628	−	447.957i	−0.334577	−	0.579504i	−0.983403	+	0.181432i	$0.941927\pi$
$774$	−163.961	−	283.988i	−0.211835	−	0.366910i
$775$	−1127.55	−	465.818i	−1.45490	−	0.601055i
$776$			493.508i			0.635964i
$777$	17.1804	+	285.667i	0.0221112	+	0.367654i
$778$			1235.61i			1.58819i
$779$	−436.313	+	755.716i	−0.560093	+	0.970110i
$780$	−269.335	+	180.146i	−0.345302	+	0.230956i
$781$	218.961	+	379.252i	0.280360	+	0.485597i
$782$	278.672	−	482.674i	0.356358	−	0.617230i
$783$	9.07267			0.0115871
$784$	384.135	−	899.869i	0.489968	−	1.14779i
$785$	−3.18276	−	48.2157i	−0.00405447	−	0.0614213i
$786$	188.986	−	327.333i	0.240440	−	0.416454i
$787$	−479.057	−	829.751i	−0.608712	−	1.05432i	−0.991453	−	0.130465i	$-0.958353\pi$
$787$	−479.057	−	829.751i	−0.608712	−	1.05432i	0.382740	−	0.923856i	$-0.374980\pi$
$788$	204.578	−	118.113i	0.259617	−	0.149890i
$789$	565.410	+	326.440i	0.716616	+	0.413738i
$790$	−1190.55	+	78.5892i	−1.50703	+	0.0994801i
$791$	−7.22795	−	120.183i	−0.00913774	−	0.151938i
$792$		−	218.326i		−	0.275664i
$793$	1068.20	+	616.725i	1.34703	+	0.777711i
$794$	972.965	−	561.742i	1.22540	−	0.707483i
$795$	−321.976	−	481.386i	−0.405001	−	0.605517i
$796$	−310.155	−	179.068i	−0.389642	−	0.224960i
$797$	−305.949			−0.383876			−0.191938	−	0.981407i	$-0.561477\pi$
$797$	−305.949			−0.383876			−0.191938	+	0.981407i	$0.561477\pi$
$798$	162.479	−	325.053i	0.203607	−	0.407335i
$799$	216.880			0.271439
$800$	−627.256	−	259.134i	−0.784070	−	0.323918i
$801$	−202.785	+	117.078i	−0.253164	+	0.146165i
$802$	317.126	−	183.093i	0.395419	−	0.228295i
$803$	138.293	−	239.531i	0.172221	−	0.298295i
$804$			209.034i			0.259992i
$805$	−405.085	−	533.325i	−0.503211	−	0.662515i
$806$	2419.13			3.00140
$807$	−162.379	−	93.7498i	−0.201214	−	0.116171i
$808$	112.915	+	195.574i	0.139746	+	0.242047i
$809$	321.894	+	557.536i	0.397891	+	0.689167i	0.993466	−	0.114133i	$-0.0364089\pi$
$809$	321.894	+	557.536i	0.397891	+	0.689167i	−0.595575	+	0.803300i	$0.703076\pi$
$810$	−47.9740	+	97.3959i	−0.0592272	+	0.120242i
$811$		−	338.901i		−	0.417881i	−0.977928	−	0.208940i	$-0.932999\pi$
$811$		−	338.901i		−	0.417881i	0.977928	−	0.208940i	$-0.0670015\pi$
$812$	12.2653	+	18.5718i	0.0151050	+	0.0228717i
$813$		−	422.850i		−	0.520111i
$814$	−394.164	+	682.711i	−0.484230	+	0.838712i
$815$	20.9127	+	31.2666i	0.0256598	+	0.0383639i
$816$	208.767	+	361.595i	0.255842	+	0.443132i
$817$	−281.415	+	487.426i	−0.344450	+	0.596604i
$818$	−877.429			−1.07265
$819$	192.921	−	385.956i	0.235557	−	0.471252i
$820$	638.162	−	42.1256i	0.778246	−	0.0513727i
$821$	−554.149	+	959.815i	−0.674969	+	1.16908i	0.301509	+	0.953463i	$0.402510\pi$
$821$	−554.149	+	959.815i	−0.674969	+	1.16908i	−0.976478	+	0.215617i	$0.930824\pi$
$822$	−201.065	−	348.255i	−0.244605	−	0.423668i
$823$	953.672	−	550.603i	1.15877	−	0.669019i	0.207765	−	0.978179i	$-0.433381\pi$
$823$	953.672	−	550.603i	1.15877	−	0.669019i	0.951010	+	0.309160i	$0.100048\pi$
$824$	79.2945	+	45.7807i	0.0962312	+	0.0555591i
$825$	−594.209	+	78.7918i	−0.720253	+	0.0955053i
$826$	−598.371	+	35.9869i	−0.724420	+	0.0435676i
$827$		−	174.811i		−	0.211379i	−0.994399	−	0.105690i	$-0.966295\pi$
$827$		−	174.811i		−	0.211379i	0.994399	−	0.105690i	$-0.0337050\pi$
$828$	−90.5281	−	52.2664i	−0.109333	−	0.0631237i
$829$	−221.752	+	128.029i	−0.267493	+	0.154437i	−0.627748	−	0.778417i	$-0.716023\pi$
$829$	−221.752	+	128.029i	−0.267493	+	0.154437i	0.360255	+	0.932854i	$0.382690\pi$
$830$	618.980	+	925.436i	0.745759	+	1.11498i
$831$	253.726	+	146.489i	0.305326	+	0.176280i
$832$	−295.363			−0.355003
$833$	355.044	+	473.159i	0.426223	+	0.568018i
$834$	−140.254			−0.168171
$835$	−1142.87	−	562.940i	−1.36871	−	0.674180i
$836$	271.197	−	156.576i	0.324399	−	0.187292i
$837$	219.597	−	126.784i	0.262362	−	0.151475i
$838$	34.0607	−	58.9949i	0.0406452	−	0.0703996i
$839$		−	488.850i		−	0.582658i	−0.956623	−	0.291329i	$-0.905903\pi$
$839$		−	488.850i		−	0.582658i	0.956623	−	0.291329i	$-0.0940974\pi$
$840$	316.179	−	40.0457i	0.376403	−	0.0476734i
$841$	−837.951			−0.996375
$842$	1603.75	+	925.928i	1.90470	+	1.09968i
$843$	95.3520	+	165.154i	0.113110	+	0.195913i
$844$	149.976	+	259.765i	0.177696	+	0.307779i
$845$	1135.60	+	559.359i	1.34390	+	0.661963i
$846$		−	130.029i		−	0.153698i
$847$	221.032	−	442.193i	0.260958	−	0.522070i
$848$			1335.32i			1.57467i
$849$	418.372	−	724.641i	0.492782	−	0.853523i
$850$	577.288	−	443.823i	0.679162	−	0.522144i
$851$	−225.830	−	391.150i	−0.265371	−	0.459635i
$852$	−49.8894	+	86.4110i	−0.0585556	+	0.101421i
$853$	155.926			0.182797			0.0913985	−	0.995814i	$-0.470866\pi$
$853$	155.926			0.182797			0.0913985	+	0.995814i	$0.470866\pi$
$854$	558.716	+	845.996i	0.654234	+	0.990628i
$855$	185.941	−	12.2741i	0.217475	−	0.0143557i
$856$	69.3134	−	120.054i	0.0809736	−	0.140250i
$857$	−597.245	−	1034.46i	−0.696902	−	1.20707i	−0.969535	−	0.244951i	$-0.921228\pi$
$857$	−597.245	−	1034.46i	−0.696902	−	1.20707i	0.272634	−	0.962118i	$-0.412105\pi$
$858$	1029.34	−	594.291i	1.19970	−	0.692647i
$859$	1002.34	+	578.702i	1.16687	+	0.673693i	0.952941	−	0.303156i	$-0.0980403\pi$
$859$	1002.34	+	578.702i	1.16687	+	0.673693i	0.213930	+	0.976849i	$0.431374\pi$
$860$	411.605	−	27.1704i	0.478610	−	0.0315935i
$861$	−710.654	+	469.332i	−0.825382	+	0.545101i
$862$			1815.79i			2.10649i
$863$	694.291	+	400.849i	0.804509	+	0.464483i	0.845045	−	0.534695i	$-0.179573\pi$
$863$	694.291	+	400.849i	0.804509	+	0.464483i	−0.0405365	+	0.999178i	$0.512907\pi$
$864$	122.162	−	70.5300i	0.141391	−	0.0816320i
$865$	−136.869	+	91.5451i	−0.158230	+	0.105832i
$866$	−503.239	−	290.545i	−0.581108	−	0.335503i
$867$	248.123			0.286186
$868$	556.399	+	278.118i	0.641013	+	0.320412i
$869$	1369.14			1.57553
$870$	−16.1205	+	32.7274i	−0.0185293	+	0.0376178i
$871$	1179.32	−	680.878i	1.35398	−	0.781720i
$872$	854.531	−	493.364i	0.979967	−	0.565784i
$873$	−140.808	+	243.886i	−0.161292	+	0.279365i
$874$			573.525i			0.656207i
$875$	−223.097	−	846.081i	−0.254968	−	0.966949i
$876$	63.0192			0.0719397
$877$	1079.03	+	622.980i	1.23037	+	0.710353i	0.967107	−	0.254371i	$-0.0818684\pi$
$877$	1079.03	+	622.980i	1.23037	+	0.710353i	0.263262	+	0.964724i	$0.415202\pi$
$878$	864.183	+	1496.81i	0.984264	+	1.70479i
$879$	−455.543	−	789.024i	−0.518252	−	0.897638i
$880$	1239.82	+	610.692i	1.40888	+	0.693969i
$881$			791.060i			0.897911i	0.893554	+	0.448956i	$0.148204\pi$
$881$			791.060i			0.897911i	−0.893554	+	0.448956i	$0.851796\pi$
$882$	283.680	−	212.864i	0.321632	−	0.241343i
$883$		−	343.428i		−	0.388933i	−0.980909	−	0.194467i	$-0.937702\pi$
$883$		−	343.428i		−	0.388933i	0.980909	−	0.194467i	$-0.0622976\pi$
$884$	−225.850	+	391.183i	−0.255486	+	0.442515i
$885$	−170.896	−	255.506i	−0.193102	−	0.288707i
$886$	−514.590	−	891.297i	−0.580802	−	1.00598i
$887$	754.185	−	1306.29i	0.850265	−	1.47270i	−0.0307048	−	0.999528i	$-0.509775\pi$
$887$	754.185	−	1306.29i	0.850265	−	1.47270i	0.880969	−	0.473173i	$-0.156891\pi$
$888$	214.934			0.242043
$889$	32.0121	+	532.282i	0.0360092	+	0.598742i
$890$	−62.0187	−	939.522i	−0.0696839	−	1.05564i
$891$	62.2925	−	107.894i	0.0699130	−	0.121093i
$892$	−81.1940	−	140.632i	−0.0910247	−	0.157659i
$893$	−193.276	+	111.588i	−0.216435	+	0.124959i
$894$	−915.645	−	528.648i	−1.02421	−	0.591329i
$895$	31.8016	+	481.762i	0.0355325	+	0.538282i
$896$	−897.066	−	448.401i	−1.00119	−	0.500448i
$897$			680.981i			0.759177i
$898$	−549.503	−	317.256i	−0.611919	−	0.353292i
$899$	73.7900	−	42.6027i	0.0820801	−	0.0473890i
$900$	−83.2413	−	108.273i	−0.0924904	−	0.120304i
$901$	−699.166	−	403.664i	−0.775989	−	0.448018i
$902$	−2345.97			−2.60085
$903$	−458.361	+	302.712i	−0.507598	+	0.335230i
$904$	−90.4249			−0.100027
$905$	318.228	−	646.060i	0.351633	−	0.713878i
$906$	455.056	−	262.727i	0.502269	−	0.289985i
$907$	−935.921	+	540.354i	−1.03189	+	0.595760i	−0.917524	−	0.397679i	$-0.869816\pi$
$907$	−935.921	+	540.354i	−1.03189	+	0.595760i	−0.114362	+	0.993439i	$0.536482\pi$
$908$	−70.2732	+	121.717i	−0.0773934	+	0.134049i
$909$			128.867i			0.141768i
$910$	1049.46	+	1381.69i	1.15325	+	1.51834i
$911$	315.550			0.346377			0.173189	−	0.984889i	$-0.444593\pi$
$911$	315.550			0.346377			0.173189	+	0.984889i	$0.444593\pi$
$912$	−372.094	−	214.828i	−0.407997	−	0.235557i
$913$	−638.794	−	1106.42i	−0.699665	−	1.21185i
$914$	−80.5711	−	139.553i	−0.0881522	−	0.152684i
$915$	−229.721	+	466.375i	−0.251061	+	0.509699i
$916$			94.7794i			0.103471i
$917$	−566.329	−	283.081i	−0.617589	−	0.308704i
$918$			151.348i			0.164868i
$919$	−252.321	+	437.032i	−0.274560	+	0.475552i	−0.970024	−	0.243009i	$-0.921866\pi$
$919$	−252.321	+	437.032i	−0.274560	+	0.475552i	0.695464	+	0.718561i	$0.255199\pi$
$920$	−418.089	+	279.639i	−0.454444	+	0.303956i
$921$	−111.763	−	193.579i	−0.121349	−	0.210183i
$922$	286.647	−	496.488i	0.310897	−	0.538490i
$923$	650.011			0.704237
$924$	305.072	−	18.3474i	0.330164	−	0.0198565i
$925$	−77.5680	−	584.979i	−0.0838573	−	0.632410i
$926$	25.4214	−	44.0312i	0.0274529	−	0.0475499i
$927$	26.1243	+	45.2486i	0.0281815	+	0.0488118i
$928$	41.0493	−	23.6998i	0.0442342	−	0.0255386i
$929$	41.7500	+	24.1044i	0.0449408	+	0.0259466i	0.522302	−	0.852761i	$-0.325073\pi$
$929$	41.7500	+	24.1044i	0.0449408	+	0.0259466i	−0.477361	+	0.878707i	$0.658407\pi$
$930$	67.1604	+	1017.41i	0.0722155	+	1.09399i
$931$	−559.852	−	238.989i	−0.601345	−	0.256701i
$932$		−	37.9392i		−	0.0407073i
$933$	347.909	+	200.865i	0.372893	+	0.215290i
$934$	1186.49	−	685.020i	1.27033	−	0.733426i
$935$	−694.549	+	464.550i	−0.742833	+	0.496845i
$936$	−280.646	−	162.031i	−0.299836	−	0.173110i
$937$	−730.647			−0.779773			−0.389887	−	0.920863i	$-0.627486\pi$
$937$	−730.647			−0.779773			−0.389887	+	0.920863i	$0.627486\pi$
$938$	1117.28	−	67.1950i	1.19113	−	0.0716365i
$939$	319.084			0.339812
$940$	146.732	+	72.2754i	0.156098	+	0.0768887i
$941$	−293.174	+	169.264i	−0.311556	+	0.179877i	−0.647622	−	0.761961i	$-0.724237\pi$
$941$	−293.174	+	169.264i	−0.311556	+	0.179877i	0.336067	+	0.941838i	$0.390903\pi$
$942$	−34.9745	+	20.1926i	−0.0371280	+	0.0214358i
$943$	672.044	−	1164.01i	0.712666	−	1.23437i
$944$			708.749i			0.750793i
$945$	167.678	+	70.4219i	0.177437	+	0.0745205i
$946$	−1513.11			−1.59949
$947$	−1605.75	−	927.082i	−1.69562	−	0.978967i	−0.949820	−	0.312798i	$-0.898734\pi$
$947$	−1605.75	−	927.082i	−1.69562	−	0.978967i	−0.745801	−	0.666169i	$-0.767933\pi$
$948$	155.976	+	270.159i	0.164532	+	0.284978i
$949$	−205.270	−	355.538i	−0.216301	−	0.374645i
$950$	−286.107	+	692.545i	−0.301165	+	0.728995i
$951$		−	494.491i		−	0.519970i
$952$	370.728	−	244.837i	0.389420	−	0.257182i
$953$			434.419i			0.455843i	0.973679	+	0.227922i	$0.0731930\pi$
$953$			434.419i			0.455843i	−0.973679	+	0.227922i	$0.926807\pi$
$954$	−242.014	+	419.181i	−0.253684	+	0.439393i
$955$	−996.898	+	666.777i	−1.04387	+	0.698196i
$956$	−275.218	−	476.692i	−0.287885	−	0.498632i
$957$	20.9318	−	36.2550i	0.0218723	−	0.0378840i
$958$	390.207			0.407315
$959$	−562.089	+	371.216i	−0.586119	+	0.387087i
$960$	−8.19994	−	124.221i	−0.00854160	−	0.129397i
$961$	710.186	−	1230.08i	0.739007	−	1.28000i
$962$	585.060	+	1013.35i	0.608171	+	1.05338i
$963$	68.5077	−	39.5529i	0.0711398	−	0.0410726i
$964$	−572.191	−	330.354i	−0.593559	−	0.342691i
$965$	857.458	−	56.6016i	0.888558	−	0.0586545i
$966$	−250.263	+	500.673i	−0.259071	+	0.518295i
$967$			1051.59i			1.08747i	0.839256	+	0.543737i	$0.182991\pi$
$967$			1051.59i			1.08747i	−0.839256	+	0.543737i	$0.817009\pi$
$968$	−321.539	−	185.641i	−0.332169	−	0.191778i
$969$	224.966	−	129.884i	0.232163	−	0.134039i
$970$	−629.570	−	941.269i	−0.649041	−	0.970381i
$971$	255.709	+	147.634i	0.263346	+	0.152043i	0.625860	−	0.779935i	$-0.284748\pi$
$971$	255.709	+	147.634i	0.263346	+	0.152043i	−0.362514	+	0.931978i	$0.618081\pi$
$972$	28.3862			0.0292039
$973$	14.1041	+	234.515i	0.0144955	+	0.241023i
$974$	−692.954			−0.711452
$975$	−339.712	+	822.301i	−0.348422	+	0.843385i
$976$	1038.10	−	599.346i	1.06362	−	0.614084i
$977$	−1131.35	+	653.187i	−1.15799	+	0.668564i	−0.950821	−	0.309742i	$-0.899757\pi$
$977$	−1131.35	+	653.187i	−1.15799	+	0.668564i	−0.207166	+	0.978306i	$0.566424\pi$
$978$	15.7191	−	27.2263i	0.0160727	−	0.0278388i
$979$			1080.45i			1.10363i
$980$	82.5276	+	438.440i	0.0842118	+	0.447387i
$981$	563.065			0.573971
$982$	−1809.11	−	1044.49i	−1.84227	−	1.06363i
$983$	−307.982	−	533.440i	−0.313308	−	0.542665i	0.665769	−	0.746158i	$-0.268104\pi$
$983$	−307.982	−	533.440i	−0.313308	−	0.542665i	−0.979076	+	0.203493i	$0.934770\pi$
$984$	319.809	+	553.926i	0.325009	+	0.562933i
$985$	286.609	−	581.868i	0.290974	−	0.590729i
$986$			50.8568i			0.0515789i
$987$	−217.418	+	13.0758i	−0.220281	+	0.0132480i
$988$		−	464.814i		−	0.470459i
$989$	433.458	−	750.772i	0.438280	−	0.759122i
$990$	278.518	+	416.413i	0.281332	+	0.420619i
$991$	−276.419	−	478.771i	−0.278929	−	0.483119i	0.692190	−	0.721715i	$-0.256646\pi$
$991$	−276.419	−	478.771i	−0.278929	−	0.483119i	−0.971119	+	0.238596i	$0.923313\pi$
$992$	662.378	−	1147.27i	0.667719	−	1.15652i
$993$	−62.9590			−0.0634029
$994$	477.903	+	238.881i	0.480788	+	0.240323i
$995$	−981.226	+	64.7716i	−0.986157	+	0.0650971i
$996$	145.547	−	252.094i	0.146131	−	0.253107i
$997$	458.012	+	793.300i	0.459390	+	0.795687i	0.998929	−	0.0462737i	$-0.0147346\pi$
$997$	458.012	+	793.300i	0.459390	+	0.795687i	−0.539539	+	0.841961i	$0.681401\pi$
$998$	−458.053	+	264.457i	−0.458971	+	0.264987i
$999$	106.218	+	61.3249i	0.106324	+	0.0613863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.r.a.19.4	✓	32
3.2	odd	2		315.3.bi.e.19.13		32
5.2	odd	4		525.3.o.q.376.7		16
5.3	odd	4		525.3.o.p.376.2		16
5.4	even	2	inner	105.3.r.a.19.13	yes	32
7.2	even	3		735.3.e.a.244.32		32
7.3	odd	6	inner	105.3.r.a.94.13	yes	32
7.5	odd	6		735.3.e.a.244.8		32
15.14	odd	2		315.3.bi.e.19.4		32
21.17	even	6		315.3.bi.e.199.4		32
35.3	even	12		525.3.o.p.451.2		16
35.9	even	6		735.3.e.a.244.7		32
35.17	even	12		525.3.o.q.451.7		16
35.19	odd	6		735.3.e.a.244.31		32
35.24	odd	6	inner	105.3.r.a.94.4	yes	32
105.59	even	6		315.3.bi.e.199.13		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.r.a.19.4	✓	32	1.1	even	1	trivial
105.3.r.a.19.13	yes	32	5.4	even	2	inner
105.3.r.a.94.4	yes	32	35.24	odd	6	inner
105.3.r.a.94.13	yes	32	7.3	odd	6	inner
315.3.bi.e.19.4		32	15.14	odd	2
315.3.bi.e.19.13		32	3.2	odd	2
315.3.bi.e.199.4		32	21.17	even	6
315.3.bi.e.199.13		32	105.59	even	6
525.3.o.p.376.2		16	5.3	odd	4
525.3.o.p.451.2		16	35.3	even	12
525.3.o.q.376.7		16	5.2	odd	4
525.3.o.q.451.7		16	35.17	even	12
735.3.e.a.244.7		32	35.9	even	6
735.3.e.a.244.8		32	7.5	odd	6
735.3.e.a.244.31		32	35.19	odd	6
735.3.e.a.244.32		32	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08943 - 1.20633i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.910488 + 1.57701i) q^{4} +(4.48539 + 2.20936i) q^{5} -4.17887i q^{6} +(-6.98737 + 0.420230i) q^{7} +5.25727i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-6.70671 - 10.0272i) q^{10} +(6.92139 + 11.9882i) q^{11} +(-1.57701 + 2.73146i) q^{12} +20.5470 q^{13} +(15.1066 + 7.55107i) q^{14} +(0.570430 + 8.64145i) q^{15} +(9.98398 - 17.2928i) q^{16} +(6.03626 + 10.4551i) q^{17} +(6.26830 - 3.61900i) q^{18} +(-10.7587 - 6.21151i) q^{19} +(0.599716 + 9.08511i) q^{20} +(-6.68159 - 10.1171i) q^{21} -33.3981i q^{22} +(16.5713 + 9.56747i) q^{23} +(-7.88590 + 4.55293i) q^{24} +(15.2375 + 19.8197i) q^{25} +(-42.9315 - 24.7865i) q^{26} -5.19615 q^{27} +(-7.02463 - 10.6366i) q^{28} -1.74604 q^{29} +(9.23261 - 18.7439i) q^{30} +(-42.2614 + 24.3997i) q^{31} +(-23.5100 + 13.5735i) q^{32} +(-11.9882 + 20.7642i) q^{33} -29.1270i q^{34} +(-32.2696 - 13.5527i) q^{35} -5.46293 q^{36} +(-20.4416 - 11.8020i) q^{37} +(14.9863 + 25.9571i) q^{38} +(17.7942 + 30.8204i) q^{39} +(-11.6152 + 23.5809i) q^{40} -70.2426i q^{41} +(1.75609 + 29.1993i) q^{42} -45.3054i q^{43} +(-12.6037 + 21.8302i) q^{44} +(-12.4682 + 8.33936i) q^{45} +(-23.0832 - 39.9812i) q^{46} +(8.98236 - 15.5579i) q^{47} +34.5855 q^{48} +(48.6468 - 5.87261i) q^{49} +(-7.92857 - 59.7934i) q^{50} +(-10.4551 + 18.1088i) q^{51} +(18.7078 + 32.4028i) q^{52} +(-57.9138 + 33.4366i) q^{53} +(10.8570 + 6.26830i) q^{54} +(4.55895 + 69.0636i) q^{55} +(-2.20926 - 36.7345i) q^{56} -21.5173i q^{57} +(3.64823 + 2.10630i) q^{58} +(-30.7390 + 17.7472i) q^{59} +(-13.1083 + 8.76751i) q^{60} +(51.9882 + 30.0154i) q^{61} +117.737 q^{62} +(9.38927 - 18.7841i) q^{63} -14.3750 q^{64} +(92.1611 + 45.3955i) q^{65} +(50.0971 - 28.9236i) q^{66} +(57.3961 - 33.1377i) q^{67} +(-10.9919 + 19.0385i) q^{68} +33.1427i q^{69} +(51.0760 + 67.2454i) q^{70} +31.6354 q^{71} +(-13.6588 - 7.88590i) q^{72} +(-9.99028 - 17.3037i) q^{73} +(28.4743 + 49.3189i) q^{74} +(-16.5334 + 40.0206i) q^{75} -22.6220i q^{76} +(-53.4002 - 80.8575i) q^{77} -85.8630i q^{78} +(49.4531 - 85.6553i) q^{79} +(82.9879 - 55.5066i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-84.7361 + 146.767i) q^{82} -92.2927 q^{83} +(9.87133 - 19.7485i) q^{84} +(3.97594 + 60.2316i) q^{85} +(-54.6535 + 94.6627i) q^{86} +(-1.51211 - 2.61905i) q^{87} +(-63.0251 + 36.3876i) q^{88} +(67.5949 + 39.0259i) q^{89} +(36.1115 - 2.38375i) q^{90} +(-143.569 + 8.63445i) q^{91} +34.8443i q^{92} +(-73.1990 - 42.2614i) q^{93} +(-37.5361 + 21.6715i) q^{94} +(-34.5334 - 51.6308i) q^{95} +(-40.7205 - 23.5100i) q^{96} +93.8717 q^{97} +(-108.729 - 46.4139i) q^{98} -41.5283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 6 q^{5} - 48 q^{9} + 78 q^{10} - 28 q^{11} + 60 q^{14} - 24 q^{15} - 40 q^{16} - 60 q^{19} + 12 q^{21} - 34 q^{25} - 96 q^{26} - 88 q^{29} + 84 q^{31} - 170 q^{35} - 192 q^{36} + 36 q^{39}+ \cdots + 168 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 6 * q^5 - 48 * q^9 + 78 * q^10 - 28 * q^11 + 60 * q^14 - 24 * q^15 - 40 * q^16 - 60 * q^19 + 12 * q^21 - 34 * q^25 - 96 * q^26 - 88 * q^29 + 84 * q^31 - 170 * q^35 - 192 * q^36 + 36 * q^39 + 330 * q^40 + 320 * q^44 + 18 * q^45 - 60 * q^46 + 356 * q^49 + 12 * q^51 - 468 * q^56 - 804 * q^59 - 198 * q^60 + 336 * q^61 - 400 * q^64 - 46 * q^65 - 108 * q^66 - 438 * q^70 + 344 * q^71 + 900 * q^74 + 144 * q^75 - 20 * q^79 + 1140 * q^80 - 144 * q^81 + 780 * q^84 + 304 * q^85 + 144 * q^86 + 24 * q^89 - 224 * q^91 - 924 * q^94 - 342 * q^95 + 900 * q^96 + 168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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