LMFDB - Embedded newform 75.3.h.a.14.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(14,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("75.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.h (of order $10$, degree $4$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			14.7
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.949573 + 0.689905i) q^{2} +(-0.131165 + 2.99713i) q^{3} +(-0.810348 + 2.49399i) q^{4} +(-4.82831 - 1.29902i) q^{5} +(-1.94319 - 2.93649i) q^{6} -4.52613i q^{7} +(-2.40195 - 7.39246i) q^{8} +(-8.96559 - 0.786239i) q^{9} +(5.48103 - 2.09756i) q^{10} +(9.16255 + 12.6112i) q^{11} +(-7.36854 - 2.75584i) q^{12} +(-11.4738 + 15.7924i) q^{13} +(3.12260 + 4.29789i) q^{14} +(4.52663 - 14.3007i) q^{15} +(-1.10515 - 0.802935i) q^{16} +(-2.55369 - 7.85945i) q^{17} +(9.05592 - 5.43882i) q^{18} +(10.2547 + 31.5607i) q^{19} +(7.15235 - 10.9891i) q^{20} +(13.5654 + 0.593671i) q^{21} +(-17.4010 - 5.65394i) q^{22} +(-10.6402 + 7.73056i) q^{23} +(22.4712 - 6.22934i) q^{24} +(21.6251 + 12.5441i) q^{25} -22.9119i q^{26} +(3.53244 - 26.7679i) q^{27} +(11.2881 + 3.66774i) q^{28} +(29.2705 + 9.51056i) q^{29} +(5.56775 + 16.7025i) q^{30} +(-11.2815 - 34.7209i) q^{31} +32.6949 q^{32} +(-38.9992 + 25.8072i) q^{33} +(7.84719 + 5.70132i) q^{34} +(-5.87952 + 21.8535i) q^{35} +(9.22612 - 21.7230i) q^{36} +(-9.54112 + 13.1322i) q^{37} +(-31.5115 - 22.8945i) q^{38} +(-45.8269 - 36.4600i) q^{39} +(1.99445 + 38.8132i) q^{40} +(-17.3303 + 23.8531i) q^{41} +(-13.2909 + 8.79511i) q^{42} -12.8584i q^{43} +(-38.8771 + 12.6319i) q^{44} +(42.2673 + 15.4427i) q^{45} +(4.77030 - 14.6815i) q^{46} +(-1.51095 + 4.65021i) q^{47} +(2.55146 - 3.20695i) q^{48} +28.5142 q^{49} +(-29.1889 + 3.00773i) q^{50} +(23.8908 - 6.62286i) q^{51} +(-30.0883 - 41.4131i) q^{52} +(-0.118940 + 0.366060i) q^{53} +(15.1130 + 27.8552i) q^{54} +(-27.8575 - 72.7929i) q^{55} +(-33.4592 + 10.8716i) q^{56} +(-95.9367 + 26.5950i) q^{57} +(-34.3559 + 11.1629i) q^{58} +(-24.3125 + 33.4633i) q^{59} +(31.9977 + 22.8779i) q^{60} +(21.8684 - 15.8883i) q^{61} +(34.6668 + 25.1869i) q^{62} +(-3.55862 + 40.5794i) q^{63} +(-26.6256 + 19.3447i) q^{64} +(75.9139 - 61.3458i) q^{65} +(19.2280 - 51.4116i) q^{66} +(55.6316 - 18.0758i) q^{67} +21.6708 q^{68} +(-21.7739 - 32.9041i) q^{69} +(-9.49384 - 24.8079i) q^{70} +(-15.6979 - 5.10057i) q^{71} +(15.7227 + 68.1662i) q^{72} +(37.5788 + 51.7228i) q^{73} -19.0525i q^{74} +(-40.4328 + 63.1679i) q^{75} -87.0222 q^{76} +(57.0798 - 41.4709i) q^{77} +(68.6700 + 3.00525i) q^{78} +(11.5206 - 35.4568i) q^{79} +(4.29296 + 5.31242i) q^{80} +(79.7637 + 14.0982i) q^{81} -34.6066i q^{82} +(-24.5328 - 75.5041i) q^{83} +(-12.4733 + 33.3510i) q^{84} +(2.12044 + 41.2651i) q^{85} +(8.87106 + 12.2100i) q^{86} +(-32.3437 + 86.4800i) q^{87} +(71.2195 - 98.0252i) q^{88} +(37.7114 + 51.9054i) q^{89} +(-50.7899 + 14.4965i) q^{90} +(71.4784 + 51.9321i) q^{91} +(-10.6577 - 32.8011i) q^{92} +(105.543 - 29.2580i) q^{93} +(-1.77345 - 5.45813i) q^{94} +(-8.51493 - 165.706i) q^{95} +(-4.28844 + 97.9910i) q^{96} +(8.05793 + 2.61818i) q^{97} +(-27.0763 + 19.6721i) q^{98} +(-72.2323 - 120.271i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) $ 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.949573	+	0.689905i	−0.474787	+	0.344953i	−0.799304	−	0.600927i	$-0.794798\pi$
$2$	−0.949573	+	0.689905i	−0.474787	+	0.344953i	0.324517	+	0.945880i	$0.394798\pi$
$3$	−0.131165	+	2.99713i	−0.0437218	+	0.999044i
$3$	−0.131165	+	2.99713i	−0.0437218	+	0.999044i
$4$	−0.810348	+	2.49399i	−0.202587	+	0.623499i
$5$	−4.82831	−	1.29902i	−0.965662	−	0.259803i
$5$	−4.82831	−	1.29902i	−0.965662	−	0.259803i
$6$	−1.94319	−	2.93649i	−0.323864	−	0.489415i
$7$		−	4.52613i		−	0.646590i	−0.946298	−	0.323295i	$-0.895209\pi$
$7$		−	4.52613i		−	0.646590i	0.946298	−	0.323295i	$-0.104791\pi$
$8$	−2.40195	−	7.39246i	−0.300244	−	0.924057i
$9$	−8.96559	−	0.786239i	−0.996177	−	0.0873599i
$10$	5.48103	−	2.09756i	0.548103	−	0.209756i
$11$	9.16255	+	12.6112i	0.832960	+	1.14647i	0.987365	+	0.158463i	$0.0506538\pi$
$11$	9.16255	+	12.6112i	0.832960	+	1.14647i	−0.154405	+	0.988008i	$0.549346\pi$
$12$	−7.36854	−	2.75584i	−0.614045	−	0.229654i
$13$	−11.4738	+	15.7924i	−0.882604	+	1.21480i	0.0930891	+	0.995658i	$0.470326\pi$
$13$	−11.4738	+	15.7924i	−0.882604	+	1.21480i	−0.975693	+	0.219142i	$0.929674\pi$
$14$	3.12260	+	4.29789i	0.223043	+	0.306992i
$15$	4.52663	−	14.3007i	0.301775	−	0.953379i
$16$	−1.10515	−	0.802935i	−0.0690716	−	0.0501834i
$17$	−2.55369	−	7.85945i	−0.150217	−	0.462320i	0.847428	−	0.530910i	$-0.178150\pi$
$17$	−2.55369	−	7.85945i	−0.150217	−	0.462320i	−0.997645	+	0.0685900i	$0.978150\pi$
$18$	9.05592	−	5.43882i	0.503107	−	0.302157i
$19$	10.2547	+	31.5607i	0.539721	+	1.66109i	0.733220	+	0.679991i	$0.238016\pi$
$19$	10.2547	+	31.5607i	0.539721	+	1.66109i	−0.193499	+	0.981100i	$0.561984\pi$
$20$	7.15235	−	10.9891i	0.357618	−	0.549456i
$21$	13.5654	+	0.593671i	0.645972	+	0.0282700i
$22$	−17.4010	−	5.65394i	−0.790956	−	0.256997i
$23$	−10.6402	+	7.73056i	−0.462618	+	0.336111i	−0.794557	−	0.607189i	$-0.792297\pi$
$23$	−10.6402	+	7.73056i	−0.462618	+	0.336111i	0.331940	+	0.943301i	$0.392297\pi$
$24$	22.4712	−	6.22934i	0.936301	−	0.259556i
$25$	21.6251	+	12.5441i	0.865004	+	0.501764i
$26$		−	22.9119i		−	0.881227i
$27$	3.53244	−	26.7679i	0.130831	−	0.991405i
$28$	11.2881	+	3.66774i	0.403148	+	0.130991i
$29$	29.2705	+	9.51056i	1.00933	+	0.327950i	0.766586	−	0.642141i	$-0.221954\pi$
$29$	29.2705	+	9.51056i	1.00933	+	0.327950i	0.242740	+	0.970091i	$0.421954\pi$
$30$	5.56775	+	16.7025i	0.185592	+	0.556750i
$31$	−11.2815	−	34.7209i	−0.363920	−	1.12003i	−0.950655	−	0.310251i	$-0.899587\pi$
$31$	−11.2815	−	34.7209i	−0.363920	−	1.12003i	0.586735	−	0.809779i	$-0.300413\pi$
$32$	32.6949			1.02172
$33$	−38.9992	+	25.8072i	−1.18179	+	0.782037i
$34$	7.84719	+	5.70132i	0.230800	+	0.167686i
$35$	−5.87952	+	21.8535i	−0.167986	+	0.624387i
$36$	9.22612	−	21.7230i	0.256281	−	0.603417i
$37$	−9.54112	+	13.1322i	−0.257868	+	0.354925i	−0.918247	−	0.396007i	$-0.870396\pi$
$37$	−9.54112	+	13.1322i	−0.257868	+	0.354925i	0.660379	+	0.750932i	$0.270396\pi$
$38$	−31.5115	−	22.8945i	−0.829251	−	0.602486i
$39$	−45.8269	−	36.4600i	−1.17505	−	0.934873i
$40$	1.99445	+	38.8132i	0.0498612	+	0.970331i
$41$	−17.3303	+	23.8531i	−0.422691	+	0.581784i	−0.966256	−	0.257583i	$-0.917074\pi$
$41$	−17.3303	+	23.8531i	−0.422691	+	0.581784i	0.543565	+	0.839367i	$0.317074\pi$
$42$	−13.2909	+	8.79511i	−0.316451	+	0.209407i
$43$		−	12.8584i		−	0.299032i	−0.988759	−	0.149516i	$-0.952228\pi$
$43$		−	12.8584i		−	0.299032i	0.988759	−	0.149516i	$-0.0477715\pi$
$44$	−38.8771	+	12.6319i	−0.883569	+	0.287089i
$45$	42.2673	+	15.4427i	0.939273	+	0.343170i
$46$	4.77030	−	14.6815i	0.103702	−	0.319163i
$47$	−1.51095	+	4.65021i	−0.0321478	+	0.0989407i	−0.965843	−	0.259128i	$-0.916565\pi$
$47$	−1.51095	+	4.65021i	−0.0321478	+	0.0989407i	0.933695	+	0.358069i	$0.116565\pi$
$48$	2.55146	−	3.20695i	0.0531554	−	0.0668114i
$49$	28.5142			0.581921
$50$	−29.1889	+	3.00773i	−0.583778	+	0.0601545i
$51$	23.8908	−	6.62286i	0.468446	−	0.129860i
$52$	−30.0883	−	41.4131i	−0.578622	−	0.796405i
$53$	−0.118940	+	0.366060i	−0.00224415	+	0.00690679i	−0.952172	−	0.305562i	$-0.901156\pi$
$53$	−0.118940	+	0.366060i	−0.00224415	+	0.00690679i	0.949928	+	0.312468i	$0.101156\pi$
$54$	15.1130	+	27.8552i	0.279871	+	0.515836i
$55$	−27.8575	−	72.7929i	−0.506500	−	1.32351i
$56$	−33.4592	+	10.8716i	−0.597486	+	0.194135i
$57$	−95.9367	+	26.5950i	−1.68310	+	0.466579i
$58$	−34.3559	+	11.1629i	−0.592342	+	0.192464i
$59$	−24.3125	+	33.4633i	−0.412076	+	0.567174i	−0.963723	−	0.266903i	$-0.914000\pi$
$59$	−24.3125	+	33.4633i	−0.412076	+	0.567174i	0.551647	+	0.834078i	$0.314000\pi$
$60$	31.9977	+	22.8779i	0.533295	+	0.381299i
$61$	21.8684	−	15.8883i	0.358498	−	0.260464i	−0.393927	−	0.919142i	$-0.628884\pi$
$61$	21.8684	−	15.8883i	0.358498	−	0.260464i	0.752425	+	0.658677i	$0.228884\pi$
$62$	34.6668	+	25.1869i	0.559142	+	0.406240i
$63$	−3.55862	+	40.5794i	−0.0564860	+	0.644118i
$64$	−26.6256	+	19.3447i	−0.416026	+	0.302260i
$65$	75.9139	−	61.3458i	1.16791	−	0.943782i
$66$	19.2280	−	51.4116i	0.291333	−	0.778963i
$67$	55.6316	−	18.0758i	0.830322	−	0.269788i	0.137141	−	0.990552i	$-0.456209\pi$
$67$	55.6316	−	18.0758i	0.830322	−	0.269788i	0.693181	+	0.720764i	$0.256209\pi$
$68$	21.6708			0.318688
$69$	−21.7739	−	32.9041i	−0.315564	−	0.476871i
$70$	−9.49384	−	24.8079i	−0.135626	−	0.354398i
$71$	−15.6979	−	5.10057i	−0.221098	−	0.0718390i	0.196373	−	0.980529i	$-0.437084\pi$
$71$	−15.6979	−	5.10057i	−0.221098	−	0.0718390i	−0.417471	+	0.908690i	$0.637084\pi$
$72$	15.7227	+	68.1662i	0.218371	+	0.946753i
$73$	37.5788	+	51.7228i	0.514778	+	0.708531i	0.984716	−	0.174168i	$-0.0557237\pi$
$73$	37.5788	+	51.7228i	0.514778	+	0.708531i	−0.469938	+	0.882700i	$0.655724\pi$
$74$		−	19.0525i		−	0.257466i
$75$	−40.4328	+	63.1679i	−0.539104	+	0.842239i
$76$	−87.0222			−1.14503
$77$	57.0798	−	41.4709i	0.741296	−	0.538583i
$78$	68.6700	+	3.00525i	0.880385	+	0.0385288i
$79$	11.5206	−	35.4568i	0.145830	−	0.448820i	−0.851286	−	0.524701i	$-0.824177\pi$
$79$	11.5206	−	35.4568i	0.145830	−	0.448820i	0.997117	+	0.0758813i	$0.0241770\pi$
$80$	4.29296	+	5.31242i	0.0536619	+	0.0664053i
$81$	79.7637	+	14.0982i	0.984737	+	0.174052i
$82$		−	34.6066i		−	0.422032i
$83$	−24.5328	−	75.5041i	−0.295575	−	0.909688i	−0.983028	−	0.183458i	$-0.941271\pi$
$83$	−24.5328	−	75.5041i	−0.295575	−	0.909688i	0.687452	−	0.726230i	$-0.258729\pi$
$84$	−12.4733	+	33.3510i	−0.148492	+	0.397035i
$85$	2.12044	+	41.2651i	0.0249463	+	0.485472i
$86$	8.87106	+	12.2100i	0.103152	+	0.141976i
$87$	−32.3437	+	86.4800i	−0.371766	+	0.994023i
$88$	71.2195	−	98.0252i	0.809313	−	1.11392i
$89$	37.7114	+	51.9054i	0.423724	+	0.583206i	0.966498	−	0.256672i	$-0.0826261\pi$
$89$	37.7114	+	51.9054i	0.423724	+	0.583206i	−0.542774	+	0.839879i	$0.682626\pi$
$90$	−50.7899	+	14.4965i	−0.564332	+	0.161072i
$91$	71.4784	+	51.9321i	0.785477	+	0.570683i
$92$	−10.6577	−	32.8011i	−0.115845	−	0.356533i
$93$	105.543	−	29.2580i	1.13487	−	0.314602i
$94$	−1.77345	−	5.45813i	−0.0188665	−	0.0580652i
$95$	−8.51493	−	165.706i	−0.0896308	−	1.74427i
$96$	−4.28844	+	97.9910i	−0.0446712	+	1.02074i
$97$	8.05793	+	2.61818i	0.0830715	+	0.0269916i	0.350258	−	0.936653i	$-0.386094\pi$
$97$	8.05793	+	2.61818i	0.0830715	+	0.0269916i	−0.267186	+	0.963645i	$0.586094\pi$
$98$	−27.0763	+	19.6721i	−0.276289	+	0.200735i
$99$	−72.2323	−	120.271i	−0.729619	−	1.21485i
$100$	−48.8088	+	43.7678i	−0.488088	+	0.437678i
$101$			71.0307i			0.703274i	0.936136	+	0.351637i	$0.114375\pi$
$101$			71.0307i			0.703274i	−0.936136	+	0.351637i	$0.885625\pi$
$102$	−18.1169	+	22.7712i	−0.177616	+	0.223248i
$103$	−53.5433	−	17.3973i	−0.519838	−	0.168906i	0.0373339	−	0.999303i	$-0.488113\pi$
$103$	−53.5433	−	17.3973i	−0.519838	−	0.168906i	−0.557172	+	0.830397i	$0.688113\pi$
$104$	144.304	+	46.8873i	1.38754	+	0.450839i
$105$	−64.7268	−	20.4881i	−0.616445	−	0.195125i
$106$	−0.139604	−	0.429658i	−0.00131702	−	0.00405338i
$107$	−66.8812			−0.625058			−0.312529	−	0.949908i	$-0.601176\pi$
$107$	−66.8812			−0.625058			−0.312529	+	0.949908i	$0.601176\pi$
$108$	63.8966	+	30.5012i	0.591635	+	0.282419i
$109$	−147.061	−	106.846i	−1.34919	−	0.980240i	−0.999052	−	0.0435407i	$-0.986136\pi$
$109$	−147.061	−	106.846i	−1.34919	−	0.980240i	−0.350134	−	0.936700i	$-0.613864\pi$
$110$	76.6730	+	49.9032i	0.697027	+	0.453665i
$111$	−38.1076	−	30.3185i	−0.343311	−	0.273140i
$112$	−3.63419	+	5.00203i	−0.0324481	+	0.0446610i
$113$	29.0363	+	21.0961i	0.256958	+	0.186691i	0.708805	−	0.705405i	$-0.249235\pi$
$113$	29.0363	+	21.0961i	0.256958	+	0.186691i	−0.451847	+	0.892096i	$0.649235\pi$
$114$	72.7509	−	91.4412i	0.638166	−	0.802116i
$115$	61.4163	−	23.5037i	0.534055	−	0.204380i
$116$	−47.4385	+	65.2936i	−0.408953	+	0.562875i
$117$	115.286	−	132.567i	0.985354	−	1.13305i
$118$		−	48.5492i		−	0.411434i
$119$	−35.5729	+	11.5583i	−0.298932	+	0.0971288i
$120$	−116.590	+	0.886673i	−0.971583	+	0.00738894i
$121$	−37.6983	+	116.023i	−0.311556	+	0.958870i
$122$	−9.80421	+	30.1742i	−0.0803623	+	0.247330i
$123$	−69.2179	−	55.0700i	−0.562747	−	0.447723i
$124$	95.7358			0.772063
$125$	−88.1177	−	88.6582i	−0.704941	−	0.709266i
$126$	−24.6168	−	40.9883i	−0.195371	−	0.325304i
$127$	109.767	+	151.081i	0.864304	+	1.18961i	0.980526	+	0.196389i	$0.0629216\pi$
$127$	109.767	+	151.081i	0.864304	+	1.18961i	−0.116222	+	0.993223i	$0.537078\pi$
$128$	−28.4761	+	87.6405i	−0.222470	+	0.684691i
$129$	38.5382	+	1.68657i	0.298746	+	0.0130742i
$130$	−29.7630	+	110.626i	−0.228946	+	0.850967i
$131$	−130.052	+	42.2566i	−0.992766	+	0.322569i	−0.759971	−	0.649957i	$-0.774787\pi$
$131$	−130.052	+	42.2566i	−0.992766	+	0.322569i	−0.232794	+	0.972526i	$0.574787\pi$
$132$	−32.7602	−	118.177i	−0.248183	−	0.895277i
$133$	142.848	−	46.4141i	1.07405	−	0.348978i
$134$	−40.3557	+	55.5448i	−0.301162	+	0.414514i
$135$	−51.8277	+	124.655i	−0.383909	+	0.923371i
$136$	−51.9668	+	37.7561i	−0.382109	+	0.277618i
$137$	117.368	+	85.2728i	0.856700	+	0.622429i	0.926985	−	0.375098i	$-0.122391\pi$
$137$	117.368	+	85.2728i	0.856700	+	0.622429i	−0.0702850	+	0.997527i	$0.522391\pi$
$138$	43.3766	+	16.2229i	0.314323	+	0.117557i
$139$	−3.34482	+	2.43015i	−0.0240635	+	0.0174831i	−0.599752	−	0.800186i	$-0.704734\pi$
$139$	−3.34482	+	2.43015i	−0.0240635	+	0.0174831i	0.575689	+	0.817669i	$0.304734\pi$
$140$	−49.7382	−	32.3725i	−0.355273	−	0.231232i
$141$	−13.7391	−	5.13845i	−0.0974405	−	0.0364429i
$142$	18.4253	−	5.98673i	0.129755	−	0.0421601i
$143$	−304.290			−2.12791
$144$	9.27698	+	8.06770i	0.0644235	+	0.0560257i
$145$	−128.973	−	83.9427i	−0.889466	−	0.578916i
$146$	−71.3677	−	23.1888i	−0.488820	−	0.158827i
$147$	−3.74007	+	85.4607i	−0.0254426	+	0.581365i
$148$	−25.0201	−	34.4372i	−0.169055	−	0.232684i
$149$		−	157.266i		−	1.05547i	−0.849408	−	0.527737i	$-0.823041\pi$
$149$		−	157.266i		−	1.05547i	0.849408	−	0.527737i	$-0.176959\pi$
$150$	−5.18599	−	87.8774i	−0.0345732	−	0.585849i
$151$	47.4259			0.314079			0.157039	−	0.987592i	$-0.449805\pi$
$151$	47.4259			0.314079			0.157039	+	0.987592i	$0.449805\pi$
$152$	208.680	−	151.615i	1.37290	−	0.997467i
$153$	16.7159	+	72.4724i	0.109254	+	0.473676i
$154$	−25.5905	+	78.7593i	−0.166172	+	0.511424i
$155$	9.36754	+	182.298i	0.0604357	+	1.17612i
$156$	128.067	−	84.7468i	0.820942	−	0.543248i
$157$			247.875i			1.57882i	0.613867	+	0.789410i	$0.289613\pi$
$157$			247.875i			1.57882i	−0.613867	+	0.789410i	$0.710387\pi$
$158$	13.5222	+	41.6170i	0.0855833	+	0.263398i
$159$	−1.08153	−	0.404493i	−0.00680206	−	0.00254398i
$160$	−157.861	−	42.4713i	−0.986632	−	0.265445i
$161$	34.9895	+	48.1590i	0.217326	+	0.299124i
$162$	−85.4679	+	41.6421i	−0.527579	+	0.257050i
$163$	−74.1290	+	102.030i	−0.454779	+	0.625950i	−0.973416	−	0.229045i	$-0.926440\pi$
$163$	−74.1290	+	102.030i	−0.454779	+	0.625950i	0.518637	+	0.854995i	$0.326440\pi$
$164$	−45.4460	−	62.5511i	−0.277110	−	0.381409i
$165$	221.824	−	73.9447i	1.34439	−	0.448150i
$166$	75.3863	+	54.7714i	0.454135	+	0.329948i
$167$	−3.00294	−	9.24211i	−0.0179817	−	0.0553420i	0.941663	−	0.336557i	$-0.109263\pi$
$167$	−3.00294	−	9.24211i	−0.0179817	−	0.0553420i	−0.959645	+	0.281215i	$0.909263\pi$
$168$	−28.1948	−	101.708i	−0.167826	−	0.605403i
$169$	−65.5268	−	201.671i	−0.387732	−	1.19332i
$170$	−30.4825	−	37.7214i	−0.179309	−	0.221890i
$171$	−67.1252	−	291.023i	−0.392545	−	1.70189i
$172$	32.0687	+	10.4198i	0.186446	+	0.0605799i
$173$	205.101	−	149.015i	1.18555	−	0.861356i	0.192767	−	0.981245i	$-0.438254\pi$
$173$	205.101	−	149.015i	1.18555	−	0.861356i	0.992787	+	0.119889i	$0.0382538\pi$
$174$	−28.9504	−	104.433i	−0.166381	−	0.600191i
$175$	56.7763	−	97.8780i	0.324436	−	0.559303i
$176$		−	21.2941i		−	0.120989i
$177$	−97.1049	−	77.2570i	−0.548615	−	0.436480i
$178$	−71.6196	−	23.2706i	−0.402357	−	0.130734i
$179$	337.748	+	109.741i	1.88686	+	0.613077i	0.982487	+	0.186331i	$0.0596598\pi$
$179$	337.748	+	109.741i	1.88686	+	0.613077i	0.904371	+	0.426746i	$0.140340\pi$
$180$	−72.7651	+	92.9005i	−0.404251	+	0.516114i
$181$	14.7839	+	45.5002i	0.0816791	+	0.251383i	0.983554	−	0.180615i	$-0.0578089\pi$
$181$	14.7839	+	45.5002i	0.0816791	+	0.251383i	−0.901875	+	0.431998i	$0.857809\pi$
$182$	−103.702			−0.569793
$183$	44.7510	+	67.6264i	0.244541	+	0.369543i
$184$	82.7052	+	60.0888i	0.449485	+	0.326570i
$185$	63.1265	−	51.0124i	0.341224	−	0.275742i
$186$	−80.0355	+	100.597i	−0.430299	+	0.540846i
$187$	75.7185	−	104.218i	0.404912	−	0.557314i
$188$	−10.3732	−	7.53658i	−0.0551766	−	0.0400882i
$189$	−121.155	−	15.9883i	−0.641032	−	0.0845940i
$190$	122.407	+	151.476i	0.644248	+	0.797240i
$191$	146.083	−	201.066i	0.764832	−	1.05270i	−0.231965	−	0.972724i	$-0.574515\pi$
$191$	146.083	−	201.066i	0.764832	−	1.05270i	0.996797	−	0.0799766i	$-0.0254845\pi$
$192$	−54.4861	−	82.3379i	−0.283782	−	0.428843i
$193$			314.212i			1.62804i	0.580835	+	0.814021i	$0.302726\pi$
$193$			314.212i			1.62804i	−0.580835	+	0.814021i	$0.697274\pi$
$194$	−9.45789	+	3.07306i	−0.0487520	+	0.0158405i
$195$	173.904	+	235.570i	0.891817	+	1.20805i
$196$	−23.1064	+	71.1141i	−0.117890	+	0.362827i
$197$	−71.6978	+	220.663i	−0.363948	+	1.12012i	0.586689	+	0.809813i	$0.300431\pi$
$197$	−71.6978	+	220.663i	−0.363948	+	1.12012i	−0.950637	+	0.310305i	$0.899569\pi$
$198$	151.565	+	64.3723i	0.765481	+	0.325113i
$199$	−14.9368			−0.0750595			−0.0375297	−	0.999296i	$-0.511949\pi$
$199$	−14.9368			−0.0750595			−0.0375297	+	0.999296i	$0.511949\pi$
$200$	40.7893	−	189.993i	0.203946	−	0.949965i
$201$	46.8786	+	169.106i	0.233227	+	0.841324i
$202$	−49.0045	−	67.4488i	−0.242596	−	0.333905i
$203$	43.0460	−	132.482i	0.212049	−	0.652621i
$204$	−2.84246	+	64.9502i	−0.0139336	+	0.318383i
$205$	114.662	−	92.6579i	0.559326	−	0.451990i
$206$	62.8458	−	20.4198i	0.305077	−	0.0991254i
$207$	101.474	−	60.9433i	0.490212	−	0.294412i
$208$	25.3605	−	8.24014i	0.121926	−	0.0396161i
$209$	−304.059	+	418.501i	−1.45483	+	2.00240i
$210$	75.5977	−	25.2004i	0.359989	−	0.120002i
$211$	194.813	−	141.540i	0.923286	−	0.670807i	−0.0210536	−	0.999778i	$-0.506702\pi$
$211$	194.813	−	141.540i	0.923286	−	0.670807i	0.944340	+	0.328972i	$0.106702\pi$
$212$	−0.816568	−	0.593271i	−0.00385174	−	0.00279845i
$213$	17.3461	−	46.3798i	0.0814371	−	0.217745i
$214$	63.5086	−	46.1417i	0.296769	−	0.215615i
$215$	−16.7032	+	62.0842i	−0.0776895	+	0.288763i
$216$	−206.365	+	38.1820i	−0.955396	+	0.176768i
$217$	−157.152	+	51.0616i	−0.724200	+	0.235307i
$218$	213.359			0.978712
$219$	−159.949	+	105.844i	−0.730361	+	0.483308i
$220$	204.119	−	10.4888i	0.927816	−	0.0476765i
$221$	153.420	+	49.8492i	0.694209	+	0.225562i
$222$	57.1028	+	2.49902i	0.257220	+	0.0112569i
$223$	−130.399	−	179.479i	−0.584750	−	0.804840i	0.409456	−	0.912330i	$-0.365719\pi$
$223$	−130.399	−	179.479i	−0.584750	−	0.804840i	−0.994206	+	0.107490i	$0.965719\pi$
$224$		−	147.981i		−	0.660631i
$225$	−184.019	−	129.468i	−0.817863	−	0.575413i
$226$	−42.1264			−0.186400
$227$	−23.8507	+	17.3285i	−0.105069	+	0.0763371i	−0.639079	−	0.769141i	$-0.720684\pi$
$227$	−23.8507	+	17.3285i	−0.105069	+	0.0763371i	0.534010	+	0.845478i	$0.320684\pi$
$228$	11.4143	−	260.817i	0.0500627	−	1.14393i
$229$	−64.2078	+	197.611i	−0.280383	+	0.862932i	0.707361	+	0.706852i	$0.249886\pi$
$229$	−64.2078	+	197.611i	−0.280383	+	0.862932i	−0.987745	+	0.156079i	$0.950114\pi$
$230$	−42.1040	+	64.6900i	−0.183061	+	0.281261i
$231$	116.807	+	176.515i	0.505657	+	0.764135i
$232$		−	239.225i		−	1.03114i
$233$	−37.4986	−	115.409i	−0.160938	−	0.495316i	0.837776	−	0.546014i	$-0.183855\pi$
$233$	−37.4986	−	115.409i	−0.160938	−	0.495316i	−0.998714	+	0.0506978i	$0.983855\pi$
$234$	−18.0142	+	205.419i	−0.0769839	+	0.877858i
$235$	13.3360	−	20.4899i	0.0567490	−	0.0871911i
$236$	−63.7557	−	87.7521i	−0.270151	−	0.371831i
$237$	104.758	+	39.1795i	0.442015	+	0.165314i
$238$	25.8049	−	35.5174i	0.108424	−	0.149233i
$239$	−64.3700	−	88.5977i	−0.269331	−	0.370702i	0.652833	−	0.757502i	$-0.273580\pi$
$239$	−64.3700	−	88.5977i	−0.269331	−	0.370702i	−0.922164	+	0.386800i	$0.873580\pi$
$240$	−16.4851	+	12.1697i	−0.0686880	+	0.0507073i
$241$	−175.497	−	127.506i	−0.728203	−	0.529070i	0.160791	−	0.986988i	$-0.448595\pi$
$241$	−175.497	−	127.506i	−0.728203	−	0.529070i	−0.888994	+	0.457918i	$0.848595\pi$
$242$	−44.2479	−	136.181i	−0.182842	−	0.562731i
$243$	−52.7164	+	237.213i	−0.216940	+	0.976185i
$244$	21.9044	+	67.4147i	0.0897720	+	0.276290i
$245$	−137.675	−	37.0404i	−0.561939	−	0.151185i
$246$	103.721	+	4.53918i	0.421628	+	0.0184520i
$247$	−616.081	−	200.177i	−2.49425	−	0.810432i
$248$	−229.575	+	166.796i	−0.925707	+	0.672566i
$249$	229.514	−	63.6244i	0.921741	−	0.255520i
$250$	144.840	+	23.3946i	0.579360	+	0.0935785i
$251$		−	163.018i		−	0.649476i	−0.945804	−	0.324738i	$-0.894724\pi$
$251$		−	163.018i		−	0.649476i	0.945804	−	0.324738i	$-0.105276\pi$
$252$	−98.3211	−	41.7586i	−0.390163	−	0.165709i
$253$	−194.983	−	63.3538i	−0.770684	−	0.250410i
$254$	−208.463	−	67.7337i	−0.820720	−	0.266668i
$255$	−123.955	+	0.942685i	−0.486098	+	0.00369680i
$256$	−74.1039	−	228.068i	−0.289468	−	0.890891i
$257$	−236.058			−0.918512			−0.459256	−	0.888304i	$-0.651884\pi$
$257$	−236.058			−0.918512			−0.459256	+	0.888304i	$0.651884\pi$
$258$	−37.7584	+	24.9862i	−0.146351	+	0.0968457i
$259$	59.4382	+	43.1844i	0.229491	+	0.166735i
$260$	91.4795	+	239.040i	0.351844	+	0.919386i
$261$	−254.950	−	108.281i	−0.976818	−	0.414871i
$262$	94.3412	−	129.849i	0.360081	−	0.495609i
$263$	71.2176	+	51.7426i	0.270789	+	0.196740i	0.714890	−	0.699237i	$-0.246477\pi$
$263$	71.2176	+	51.7426i	0.270789	+	0.196740i	−0.444101	+	0.895977i	$0.646477\pi$
$264$	284.453	+	226.312i	1.07747	+	0.857241i
$265$	1.04980	−	1.61294i	0.00396150	−	0.00608658i
$266$	−103.623	+	142.625i	−0.389561	+	0.536185i
$267$	−160.514	+	106.218i	−0.601174	+	0.397820i
$268$			153.393i			0.572360i
$269$	114.500	−	37.2032i	0.425650	−	0.138302i	−0.0883556	−	0.996089i	$-0.528161\pi$
$269$	114.500	−	37.2032i	0.425650	−	0.138302i	0.514005	+	0.857787i	$0.328161\pi$
$270$	−36.7860	−	154.125i	−0.136245	−	0.570835i
$271$	82.4311	−	253.697i	0.304174	−	0.936151i	−0.675810	−	0.737076i	$-0.736206\pi$
$271$	82.4311	−	253.697i	0.304174	−	0.936151i	0.979984	−	0.199075i	$-0.0637938\pi$
$272$	−3.48843	+	10.7363i	−0.0128251	+	0.0394716i
$273$	−165.023	+	207.419i	−0.604479	+	0.759775i
$274$	−170.280			−0.621459
$275$	39.9453	+	387.654i	0.145256	+	1.40965i
$276$	99.7070	−	27.6402i	0.361257	−	0.100146i
$277$	244.274	+	336.215i	0.881857	+	1.21377i	0.975903	+	0.218204i	$0.0700199\pi$
$277$	244.274	+	336.215i	0.881857	+	1.21377i	−0.0940459	+	0.995568i	$0.529980\pi$
$278$	1.49958	−	4.61522i	0.00539416	−	0.0166015i
$279$	73.8465	+	320.164i	0.264683	+	1.14754i
$280$	175.674	−	9.02713i	0.627406	−	0.0322397i
$281$	−134.339	+	43.6494i	−0.478075	+	0.155336i	−0.538135	−	0.842859i	$-0.680871\pi$
$281$	−134.339	+	43.6494i	−0.478075	+	0.155336i	0.0600598	+	0.998195i	$0.480871\pi$
$282$	16.5913	−	4.59935i	0.0588345	−	0.0163098i
$283$	−188.219	+	61.1562i	−0.665086	+	0.216100i	−0.622054	−	0.782974i	$-0.713702\pi$
$283$	−188.219	+	61.1562i	−0.665086	+	0.216100i	−0.0430320	+	0.999074i	$0.513702\pi$
$284$	25.4416	−	35.0173i	0.0895830	−	0.123300i
$285$	497.760	−	3.78549i	1.74652	−	0.0132824i
$286$	288.946	−	209.932i	1.01030	−	0.734027i
$287$	107.962	+	78.4393i	0.376176	+	0.273308i
$288$	−293.129	−	25.7060i	−1.01781	−	0.0892570i
$289$	178.556	−	129.729i	0.617842	−	0.448888i
$290$	180.381	−	9.26904i	0.622005	−	0.0319622i
$291$	−8.90395	+	23.8073i	−0.0305978	+	0.0818119i
$292$	−159.448	+	51.8079i	−0.546056	+	0.177424i
$293$	−68.8382			−0.234943			−0.117471	−	0.993076i	$-0.537479\pi$
$293$	−68.8382			−0.234943			−0.117471	+	0.993076i	$0.537479\pi$
$294$	−55.4083	−	83.7315i	−0.188464	−	0.284801i
$295$	160.858	−	129.989i	0.545280	−	0.440640i
$296$	119.997	+	38.9893i	0.405395	+	0.131721i
$297$	369.941	−	200.714i	1.24559	−	0.675806i
$298$	108.498	+	149.335i	0.364089	+	0.501125i
$299$		−	256.734i		−	0.858641i
$300$	−124.776	−	152.027i	−0.415919	−	0.506757i
$301$	−58.1986			−0.193351
$302$	−45.0343	+	32.7194i	−0.149120	+	0.108342i
$303$	−212.888	−	9.31676i	−0.702602	−	0.0307484i
$304$	14.0083	−	43.1131i	0.0460799	−	0.141819i
$305$	−126.227	+	48.3063i	−0.413857	+	0.158381i
$306$	−65.8721	−	57.2855i	−0.215268	−	0.187207i
$307$		−	141.263i		−	0.460138i	−0.973174	−	0.230069i	$-0.926105\pi$
$307$		−	141.263i		−	0.460138i	0.973174	−	0.230069i	$-0.0738953\pi$
$308$	57.1737	+	175.963i	0.185629	+	0.571307i
$309$	59.1649	−	158.194i	0.191472	−	0.511956i
$310$	−134.664	−	166.643i	−0.434399	−	0.537558i
$311$	317.649	+	437.206i	1.02138	+	1.40581i	0.911233	+	0.411892i	$0.135132\pi$
$311$	317.649	+	437.206i	1.02138	+	1.40581i	0.110146	+	0.993915i	$0.464868\pi$
$312$	−159.455	+	426.349i	−0.511074	+	1.36650i
$313$	80.5178	−	110.823i	0.257245	−	0.354068i	−0.660787	−	0.750574i	$-0.729777\pi$
$313$	80.5178	−	110.823i	0.257245	−	0.354068i	0.918032	+	0.396506i	$0.129777\pi$
$314$	−171.010	−	235.375i	−0.544618	−	0.749603i
$315$	69.8955	−	191.307i	0.221890	−	0.607325i
$316$	79.0933	+	57.4647i	0.250295	+	0.181850i
$317$	−84.7017	−	260.685i	−0.267198	−	0.822350i	−0.991179	−	0.132530i	$-0.957690\pi$
$317$	−84.7017	−	260.685i	−0.267198	−	0.822350i	0.723981	−	0.689820i	$-0.242310\pi$
$318$	1.30605	−	0.362056i	0.00410708	−	0.00113854i
$319$	148.253	+	456.276i	0.464743	+	1.43033i
$320$	153.686	−	58.8148i	0.480268	−	0.183796i
$321$	8.77248	−	200.452i	0.0273286	−	0.624460i
$322$	−66.4503	−	21.5910i	−0.206367	−	0.0670528i
$323$	221.863	−	161.193i	0.686881	−	0.499048i
$324$	−99.7971	+	187.506i	−0.308016	+	0.578721i
$325$	−446.225	+	197.583i	−1.37300	+	0.607948i
$326$		−	148.027i		−	0.454070i
$327$	339.521	−	426.747i	1.03829	−	1.30504i
$328$	217.960	+	70.8195i	0.664512	+	0.215913i
$329$	21.0475	+	6.83873i	0.0639740	+	0.0207864i
$330$	−159.623	+	223.253i	−0.483707	+	0.676526i
$331$	−28.7321	−	88.4284i	−0.0868040	−	0.267155i	0.898227	−	0.439532i	$-0.144856\pi$
$331$	−28.7321	−	88.4284i	−0.0868040	−	0.267155i	−0.985031	+	0.172376i	$0.944856\pi$
$332$	208.187			0.627069
$333$	95.8669	−	110.237i	0.287889	−	0.331041i
$334$	9.22770	+	6.70432i	0.0276278	+	0.0200728i
$335$	−292.087	+	15.0091i	−0.871902	+	0.0448033i
$336$	−14.5151	−	11.5482i	−0.0431996	−	0.0343697i
$337$	276.127	−	380.056i	0.819368	−	1.12776i	−0.170442	−	0.985368i	$-0.554519\pi$
$337$	276.127	−	380.056i	0.819368	−	1.12776i	0.989810	−	0.142396i	$-0.0454805\pi$
$338$	201.356	+	146.294i	0.595728	+	0.432822i
$339$	−67.0363	+	84.2584i	−0.197747	+	0.248550i
$340$	−104.633	−	28.1507i	−0.307745	−	0.0827963i
$341$	334.504	−	460.406i	0.980951	−	1.35016i
$342$	264.519	+	230.038i	0.773447	+	0.672626i
$343$		−	350.839i		−	1.02285i
$344$	−95.0549	+	30.8852i	−0.276322	+	0.0897826i
$345$	62.3881	+	187.156i	0.180835	+	0.542480i
$346$	−91.9524	+	283.001i	−0.265758	+	0.817921i
$347$	77.9057	−	239.769i	0.224512	−	0.690977i	−0.773829	−	0.633395i	$-0.781661\pi$
$347$	77.9057	−	239.769i	0.224512	−	0.690977i	0.998341	−	0.0575821i	$-0.0183391\pi$
$348$	−189.471	−	150.744i	−0.544457	−	0.433172i
$349$	123.827			0.354806			0.177403	−	0.984138i	$-0.443230\pi$
$349$	123.827			0.354806			0.177403	+	0.984138i	$0.443230\pi$
$350$	13.6134	+	132.113i	0.0388953	+	0.377465i
$351$	382.199	+	362.917i	1.08889	+	1.03395i
$352$	299.569	+	412.321i	0.851048	+	1.17137i
$353$	−127.446	+	392.238i	−0.361036	+	1.11116i	0.591390	+	0.806386i	$0.298579\pi$
$353$	−127.446	+	392.238i	−0.361036	+	1.11116i	−0.952426	+	0.304770i	$0.901421\pi$
$354$	145.508	+	6.36796i	0.411040	+	0.0179886i
$355$	69.1687	+	45.0190i	0.194842	+	0.126814i
$356$	−160.011	+	51.9907i	−0.449469	+	0.146041i
$357$	−29.9759	−	108.133i	−0.0839661	−	0.302893i
$358$	−396.427	+	128.807i	−1.10734	+	0.359796i
$359$	370.136	−	509.449i	1.03102	−	1.41908i	0.126841	−	0.991923i	$-0.459516\pi$
$359$	370.136	−	509.449i	1.03102	−	1.41908i	0.904179	−	0.427154i	$-0.140484\pi$
$360$	12.6351	−	349.552i	0.0350974	−	0.970977i
$361$	−598.866	+	435.102i	−1.65891	+	1.20527i
$362$	−45.4293	−	33.0063i	−0.125495	−	0.0911776i
$363$	−342.792	−	128.205i	−0.944332	−	0.353181i
$364$	−187.441	+	136.184i	−0.514947	+	0.374131i
$365$	−114.253	−	298.549i	−0.313022	−	0.817942i
$366$	−89.1502	−	33.3423i	−0.243580	−	0.0910992i
$367$	140.729	−	45.7256i	0.383458	−	0.124593i	−0.110944	−	0.993827i	$-0.535387\pi$
$367$	140.729	−	45.7256i	0.383458	−	0.124593i	0.494401	+	0.869234i	$0.335387\pi$
$368$	17.9661			0.0488210
$369$	174.131	−	200.232i	0.471899	−	0.542634i
$370$	−24.7495	+	91.9913i	−0.0668906	+	0.248625i
$371$	1.65683	+	0.538338i	0.00446586	+	0.00145105i
$372$	−12.5572	+	286.933i	−0.0337559	+	0.771325i
$373$	82.2542	+	113.213i	0.220521	+	0.303521i	0.904916	−	0.425591i	$-0.139934\pi$
$373$	82.2542	+	113.213i	0.220521	+	0.303521i	−0.684395	+	0.729111i	$0.739934\pi$
$374$			151.201i			0.404281i
$375$	277.278	−	252.471i	0.739409	−	0.673257i
$376$	38.0057			0.101079
$377$	−486.040	+	353.128i	−1.28923	+	0.936680i
$378$	126.076	−	68.4035i	0.333535	−	0.180962i
$379$	126.815	−	390.298i	0.334605	−	1.02981i	−0.632311	−	0.774715i	$-0.717893\pi$
$379$	126.815	−	390.298i	0.334605	−	1.02981i	0.966916	−	0.255094i	$-0.0821065\pi$
$380$	420.170	+	113.043i	1.10571	+	0.297482i
$381$	−467.206	+	309.168i	−1.22626	+	0.811466i
$382$			291.710i			0.763639i
$383$	50.5993	+	155.729i	0.132113	+	0.406602i	0.995130	−	0.0985732i	$-0.0314279\pi$
$383$	50.5993	+	155.729i	0.132113	+	0.406602i	−0.863017	+	0.505175i	$0.831428\pi$
$384$	−258.935	−	96.8421i	−0.674310	−	0.252193i
$385$	−329.470	+	126.087i	−0.855767	+	0.327498i
$386$	−216.777	−	298.368i	−0.561598	−	0.772973i
$387$	−10.1097	+	115.283i	−0.0261234	+	0.297889i
$388$	−13.0595	+	17.9748i	−0.0336584	+	0.0463268i
$389$	95.5239	+	131.477i	0.245563	+	0.337988i	0.913951	−	0.405824i	$-0.133016\pi$
$389$	95.5239	+	131.477i	0.245563	+	0.337988i	−0.668388	+	0.743812i	$0.733016\pi$
$390$	−327.656	−	103.714i	−0.840144	−	0.265933i
$391$	87.9298	+	63.8847i	0.224884	+	0.163388i
$392$	−68.4897	−	210.790i	−0.174719	−	0.537729i
$393$	−109.590	−	395.326i	−0.278855	−	1.00592i
$394$	−84.1544	−	259.001i	−0.213590	−	0.657362i
$395$	−101.684	+	156.231i	−0.257428	+	0.395521i
$396$	358.487	−	82.6860i	0.905271	−	0.208803i
$397$	−127.297	−	41.3613i	−0.320647	−	0.104185i	0.144271	−	0.989538i	$-0.453916\pi$
$397$	−127.297	−	41.3613i	−0.320647	−	0.104185i	−0.464918	+	0.885354i	$0.653916\pi$
$398$	14.1836	−	10.3050i	0.0356372	−	0.0258920i
$399$	120.373	+	434.222i	0.301686	+	1.08828i
$400$	−13.8268	−	31.2266i	−0.0345670	−	0.0780666i
$401$		−	451.210i		−	1.12521i	−0.826725	−	0.562606i	$-0.809799\pi$
$401$		−	451.210i		−	1.12521i	0.826725	−	0.562606i	$-0.190201\pi$
$402$	−161.182	−	128.237i	−0.400950	−	0.318997i
$403$	677.770	+	220.221i	1.68181	+	0.546453i
$404$	−177.150	−	57.5596i	−0.438490	−	0.142474i
$405$	−366.810	−	171.685i	−0.905703	−	0.423913i
$406$	50.5247	+	155.499i	0.124445	+	0.383003i
$407$	−253.034			−0.621705
$408$	−106.344	−	160.704i	−0.260646	−	0.393881i
$409$	15.8044	+	11.4826i	0.0386415	+	0.0280747i	0.606938	−	0.794749i	$-0.292397\pi$
$409$	15.8044	+	11.4826i	0.0386415	+	0.0280747i	−0.568297	+	0.822824i	$0.692397\pi$
$410$	−44.9546	+	167.091i	−0.109645	+	0.407540i
$411$	−270.968	+	340.582i	−0.659290	+	0.828667i
$412$	86.7774	−	119.439i	0.210625	−	0.289900i
$413$	151.459	+	110.042i	0.366729	+	0.266444i
$414$	−54.3117	+	127.878i	−0.131188	+	0.308883i
$415$	20.3706	+	396.425i	0.0490858	+	0.955242i
$416$	−375.137	+	516.331i	−0.901771	+	1.24118i
$417$	−6.84477	−	10.3436i	−0.0164143	−	0.0248048i
$418$		−	607.169i		−	1.45256i
$419$	−520.732	+	169.196i	−1.24280	+	0.403809i	−0.855334	−	0.518076i	$-0.826648\pi$
$419$	−520.732	+	169.196i	−1.24280	+	0.403809i	−0.387463	+	0.921885i	$0.626648\pi$
$420$	103.548	−	144.826i	0.246544	−	0.344823i
$421$	−173.380	+	533.609i	−0.411829	+	1.26748i	0.503227	+	0.864154i	$0.332146\pi$
$421$	−173.380	+	533.609i	−0.411829	+	1.26748i	−0.915056	+	0.403326i	$0.867854\pi$
$422$	−87.3402	+	268.806i	−0.206967	+	0.636980i
$423$	17.2027	−	40.5039i	0.0406683	−	0.0957540i
$424$	2.99177			0.00705606
$425$	43.3660	−	201.995i	0.102038	−	0.475283i
$426$	15.5263	+	56.0082i	0.0364466	+	0.131475i
$427$	−71.9126	−	98.9792i	−0.168414	−	0.231801i
$428$	54.1970	−	166.801i	0.126629	−	0.389722i
$429$	39.9123	−	911.998i	0.0930357	−	2.12587i
$430$	−26.9712	−	70.4771i	−0.0627238	−	0.163900i
$431$	432.742	−	140.606i	1.00404	−	0.326233i	0.239562	−	0.970881i	$-0.422996\pi$
$431$	432.742	−	140.606i	1.00404	−	0.326233i	0.764479	+	0.644648i	$0.222996\pi$
$432$	−25.3968	+	26.7461i	−0.0587888	+	0.0619123i
$433$	797.637	−	259.168i	1.84212	−	0.598541i	0.844061	−	0.536247i	$-0.180159\pi$
$433$	797.637	−	259.168i	1.84212	−	0.598541i	0.998058	−	0.0622933i	$-0.0198414\pi$
$434$	113.999	−	156.906i	0.262671	−	0.361536i
$435$	268.504	−	375.537i	0.617251	−	0.863304i
$436$	385.645	−	280.187i	0.884506	−	0.642631i
$437$	−353.095	−	256.538i	−0.807997	−	0.587044i
$438$	78.8607	−	210.857i	0.180047	−	0.481408i
$439$	−443.492	+	322.216i	−1.01023	+	0.733977i	−0.964258	−	0.264966i	$-0.914639\pi$
$439$	−443.492	+	322.216i	−1.01023	+	0.733977i	−0.0459747	+	0.998943i	$0.514639\pi$
$440$	−471.206	+	380.781i	−1.07092	+	0.865411i
$441$	−255.646	−	22.4189i	−0.579697	−	0.0508366i
$442$	−180.075	+	58.5099i	−0.407409	+	0.132375i
$443$	770.025			1.73820			0.869102	−	0.494632i	$-0.164697\pi$
$443$	770.025			1.73820			0.869102	+	0.494632i	$0.164697\pi$
$444$	106.495	−	70.4715i	0.239853	−	0.158720i
$445$	−114.657	−	299.603i	−0.257655	−	0.673265i
$446$	247.648	+	80.4656i	0.555263	+	0.180416i
$447$	471.346	+	20.6278i	1.05446	+	0.0461472i
$448$	87.5564	+	120.511i	0.195438	+	0.268998i
$449$			512.440i			1.14129i	0.821196	+	0.570646i	$0.193307\pi$
$449$			512.440i			1.14129i	−0.821196	+	0.570646i	$0.806693\pi$
$450$	264.060	−	4.01662i	0.586801	−	0.00892582i
$451$	−459.606			−1.01908
$452$	−76.1430	+	55.3211i	−0.168458	+	0.122392i
$453$	−6.22063	+	142.142i	−0.0137321	+	0.313778i
$454$	10.6929	−	32.9094i	0.0235527	−	0.0724877i
$455$	−277.659	−	343.596i	−0.610240	−	0.755156i
$456$	427.038	+	645.328i	0.936487	+	1.41519i
$457$			379.087i			0.829513i	0.909933	+	0.414756i	$0.136133\pi$
$457$			379.087i			0.829513i	−0.909933	+	0.414756i	$0.863867\pi$
$458$	−75.3631	−	231.944i	−0.164548	−	0.506427i
$459$	−219.402	+	40.5940i	−0.478000	+	0.0884400i
$460$	8.84956	+	172.218i	0.0192382	+	0.374387i
$461$	124.704	+	171.640i	0.270507	+	0.372321i	0.922561	−	0.385852i	$-0.126092\pi$
$461$	124.704	+	171.640i	0.270507	+	0.372321i	−0.652054	+	0.758173i	$0.726092\pi$
$462$	−232.696	−	87.0285i	−0.503670	−	0.188373i
$463$	−231.975	+	319.286i	−0.501025	+	0.689602i	−0.982374	−	0.186927i	$-0.940147\pi$
$463$	−231.975	+	319.286i	−0.501025	+	0.689602i	0.481348	+	0.876529i	$0.340147\pi$
$464$	−24.7118	−	34.0128i	−0.0532581	−	0.0733035i
$465$	−547.601	+	4.16453i	−1.17764	+	0.00895598i
$466$	115.229	+	83.7186i	0.247272	+	0.179654i
$467$	278.306	+	856.539i	0.595945	+	1.83413i	0.549965	+	0.835188i	$0.314641\pi$
$467$	278.306	+	856.539i	0.595945	+	1.83413i	0.0459797	+	0.998942i	$0.485359\pi$
$468$	237.199	+	394.949i	0.506836	+	0.843908i
$469$	−81.8134	−	251.796i	−0.174442	−	0.536878i
$470$	1.47257	+	28.6573i	0.00313314	+	0.0609729i
$471$	−742.913	−	32.5125i	−1.57731	−	0.0690288i
$472$	305.773	+	99.3518i	0.647825	+	0.210491i
$473$	162.159	−	117.815i	0.342831	−	0.249081i
$474$	−126.505	+	35.0690i	−0.266888	+	0.0739853i
$475$	−174.142	+	811.141i	−0.366615	+	1.70766i
$476$		−	98.0848i		−	0.206061i
$477$	1.35418	−	3.18843i	0.00283895	−	0.00668433i
$478$	122.248	+	39.7208i	0.255749	+	0.0830979i
$479$	−542.640	−	176.314i	−1.13286	−	0.368088i	−0.318197	−	0.948024i	$-0.603077\pi$
$479$	−542.640	−	176.314i	−1.13286	−	0.368088i	−0.814662	+	0.579936i	$0.803077\pi$
$480$	147.998	−	467.560i	0.308329	−	0.974083i
$481$	−97.9160	−	301.354i	−0.203568	−	0.626517i
$482$	254.614			0.528245
$483$	−148.928	+	98.5514i	−0.308340	+	0.204040i
$484$	−258.813	−	188.038i	−0.534737	−	0.388509i
$485$	−35.5051	−	23.1088i	−0.0732064	−	0.0476470i
$486$	−113.596	−	261.620i	−0.233738	−	0.538314i
$487$	457.802	−	630.110i	0.940045	−	1.29386i	−0.0157647	−	0.999876i	$-0.505018\pi$
$487$	457.802	−	630.110i	0.940045	−	1.29386i	0.955810	−	0.293985i	$-0.0949817\pi$
$488$	−169.981	−	123.498i	−0.348321	−	0.253070i
$489$	−296.074	−	235.557i	−0.605468	−	0.481712i
$490$	156.287	−	59.8102i	0.318953	−	0.122062i
$491$	306.359	−	421.667i	0.623949	−	0.858792i	−0.373684	−	0.927556i	$-0.621905\pi$
$491$	306.359	−	421.667i	0.623949	−	0.858792i	0.997633	+	0.0687637i	$0.0219055\pi$
$492$	193.435	−	128.003i	0.393160	−	0.260169i
$493$		−	254.337i		−	0.515896i
$494$	723.117	−	234.955i	1.46380	−	0.475617i
$495$	192.526	+	674.534i	0.388942	+	1.36270i
$496$	−15.4109	+	47.4300i	−0.0310705	+	0.0956250i
$497$	−23.0858	+	71.0509i	−0.0464504	+	0.142960i
$498$	−174.045	+	218.759i	−0.349488	+	0.439274i
$499$	92.9843			0.186341			0.0931706	−	0.995650i	$-0.470300\pi$
$499$	92.9843			0.186341			0.0931706	+	0.995650i	$0.470300\pi$
$500$	292.519	−	147.921i	0.585038	−	0.295842i
$501$	28.0937	−	7.78797i	0.0560753	−	0.0155449i
$502$	112.467	+	154.798i	0.224038	+	0.308363i
$503$	−57.9474	+	178.344i	−0.115204	+	0.354560i	−0.991989	−	0.126321i	$-0.959683\pi$
$503$	−57.9474	+	178.344i	−0.115204	+	0.354560i	0.876786	+	0.480881i	$0.159683\pi$
$504$	308.529	−	71.1630i	0.612161	−	0.141196i
$505$	92.2701	−	342.958i	0.182713	−	0.679125i
$506$	228.859	−	74.3607i	0.452290	−	0.146958i
$507$	613.028	−	169.940i	1.20913	−	0.335188i
$508$	−465.744	+	151.329i	−0.916818	+	0.297892i
$509$	253.712	−	349.204i	0.498452	−	0.686060i	−0.483467	−	0.875363i	$-0.660623\pi$
$509$	253.712	−	349.204i	0.498452	−	0.686060i	0.981919	+	0.189303i	$0.0606227\pi$
$510$	117.054	−	86.4125i	0.229518	−	0.169436i
$511$	234.104	−	170.087i	0.458129	−	0.332850i
$512$	−70.4933	−	51.2164i	−0.137682	−	0.100032i
$513$	881.040	−	163.011i	1.71743	−	0.317760i
$514$	224.154	−	162.857i	0.436097	−	0.316843i
$515$	235.924	+	153.553i	0.458105	+	0.298161i
$516$	−35.4357	+	94.7474i	−0.0686738	+	0.183619i
$517$	−72.4887	+	23.5530i	−0.140210	+	0.0455571i
$518$	−86.2340			−0.166475
$519$	419.714	+	634.260i	0.808698	+	1.22208i
$520$	−635.838	−	413.840i	−1.22277	−	0.795846i
$521$	−837.828	−	272.227i	−1.60812	−	0.522508i	−0.639019	−	0.769191i	$-0.720659\pi$
$521$	−837.828	−	272.227i	−1.60812	−	0.522508i	−0.969096	+	0.246683i	$0.920659\pi$
$522$	316.797	−	73.0700i	0.606891	−	0.139981i
$523$	−361.944	−	498.173i	−0.692053	−	0.952530i	−0.999999	−	0.00112582i	$-0.999642\pi$
$523$	−361.944	−	498.173i	−0.692053	−	0.952530i	0.307946	−	0.951404i	$-0.400358\pi$
$524$		−	358.592i		−	0.684336i
$525$	285.906	+	183.004i	0.544583	+	0.348579i
$526$	−103.324			−0.196433
$527$	−244.078	+	177.333i	−0.463146	+	0.336495i
$528$	63.8213	+	2.79305i	0.120874	+	0.00528986i
$529$	−110.018	+	338.599i	−0.207973	+	0.640074i
$530$	0.115920	+	2.25587i	0.000218716	+	0.00425636i
$531$	244.286	−	280.903i	0.460049	−	0.529007i
$532$			393.874i			0.740364i
$533$	−177.853	−	547.375i	−0.333683	−	1.02697i
$534$	79.1391	−	211.601i	0.148201	−	0.396256i
$535$	322.923	+	86.8798i	0.603594	+	0.162392i
$536$	−267.249	−	367.837i	−0.498599	−	0.686263i
$537$	−373.209	+	997.880i	−0.694988	+	1.85825i
$538$	−83.0592	+	114.321i	−0.154385	+	0.212493i
$539$	261.262	+	359.597i	0.484717	+	0.667156i
$540$	−268.891	−	230.272i	−0.497946	−	0.426430i
$541$	754.736	+	548.348i	1.39508	+	1.01358i	0.995287	+	0.0969753i	$0.0309168\pi$
$541$	754.736	+	548.348i	1.39508	+	1.01358i	0.399790	+	0.916607i	$0.369083\pi$
$542$	96.7525	+	297.773i	0.178510	+	0.549398i
$543$	−138.309	+	38.3413i	−0.254713	+	0.0706101i
$544$	−83.4927	−	256.964i	−0.153479	−	0.472360i
$545$	571.262	+	706.921i	1.04819	+	1.29710i
$546$	13.6021	−	310.809i	0.0249123	−	0.569248i
$547$	−322.894	−	104.915i	−0.590300	−	0.191800i	−0.00139024	−	0.999999i	$-0.500443\pi$
$547$	−322.894	−	104.915i	−0.590300	−	0.191800i	−0.588909	+	0.808199i	$0.700443\pi$
$548$	−307.779	+	223.614i	−0.561640	+	0.408055i
$549$	−208.555	+	125.254i	−0.379882	+	0.228150i
$550$	−305.376	−	340.548i	−0.555228	−	0.619177i
$551$			1021.33i			1.85359i
$552$	−190.942	+	239.997i	−0.345910	+	0.434777i
$553$	−160.482	−	52.1438i	−0.290203	−	0.0942925i
$554$	−463.913	−	150.734i	−0.837388	−	0.272084i
$555$	144.611	+	195.889i	0.260560	+	0.352954i
$556$	−3.35032	−	10.3112i	−0.00602576	−	0.0185454i
$557$	782.260			1.40442			0.702208	−	0.711972i	$-0.252198\pi$
$557$	782.260			1.40442			0.702208	+	0.711972i	$0.252198\pi$
$558$	−291.005	−	253.072i	−0.521515	−	0.453534i
$559$	203.064	+	147.535i	0.363264	+	0.263927i
$560$	24.0447	−	19.4305i	0.0429370	−	0.0346973i
$561$	302.422	+	240.608i	0.539077	+	0.428892i
$562$	97.4508	−	134.130i	0.173400	−	0.238665i
$563$	92.3487	+	67.0952i	0.164030	+	0.119174i	0.666772	−	0.745262i	$-0.267676\pi$
$563$	92.3487	+	67.0952i	0.164030	+	0.119174i	−0.502742	+	0.864436i	$0.667676\pi$
$564$	23.9487	−	30.1013i	0.0424623	−	0.0533712i
$565$	−112.792	−	139.577i	−0.199632	−	0.247039i
$566$	136.536	−	187.926i	0.241230	−	0.332025i
$567$	63.8103	−	361.021i	0.112540	−	0.636721i
$568$			128.298i			0.225876i
$569$	48.2487	−	15.6769i	0.0847956	−	0.0275518i	−0.266312	−	0.963887i	$-0.585805\pi$
$569$	48.2487	−	15.6769i	0.0847956	−	0.0275518i	0.351108	+	0.936335i	$0.385805\pi$
$570$	−470.048	+	347.002i	−0.824645	+	0.608775i
$571$	163.602	−	503.516i	0.286519	−	0.881814i	−0.699421	−	0.714710i	$-0.746559\pi$
$571$	163.602	−	503.516i	0.286519	−	0.881814i	0.985939	−	0.167103i	$-0.0534414\pi$
$572$	246.581	−	758.899i	0.431086	−	1.32675i
$573$	583.460	+	464.202i	1.01825	+	0.810126i
$574$	−156.634			−0.272881
$575$	−327.069	+	33.7023i	−0.568815	+	0.0586128i
$576$	253.924	−	152.502i	0.440841	−	0.264761i
$577$	−43.7565	−	60.2257i	−0.0758345	−	0.104377i	0.769415	−	0.638750i	$-0.220548\pi$
$577$	−43.7565	−	60.2257i	−0.0758345	−	0.104377i	−0.845249	+	0.534372i	$0.820548\pi$
$578$	−80.0518	+	246.374i	−0.138498	+	0.426253i
$579$	−941.735	−	41.2137i	−1.62649	−	0.0711809i
$580$	313.865	−	253.634i	0.541147	−	0.437300i
$581$	−341.741	+	111.038i	−0.588195	+	0.191116i
$582$	−7.96981	−	28.7496i	−0.0136938	−	0.0493980i
$583$	−5.70624	+	1.85407i	−0.00978771	+	0.00318022i
$584$	292.096	−	402.035i	0.500164	−	0.688417i
$585$	−728.845	+	490.315i	−1.24589	+	0.838146i
$586$	65.3669	−	47.4918i	0.111548	−	0.0810441i
$587$	−850.180	−	617.692i	−1.44835	−	1.05229i	−0.986214	−	0.165476i	$-0.947084\pi$
$587$	−850.180	−	617.692i	−1.44835	−	1.05229i	−0.462134	−	0.886810i	$-0.652916\pi$
$588$	−210.108	−	78.5806i	−0.357326	−	0.133640i
$589$	980.130	−	712.106i	1.66406	−	1.20901i
$590$	−63.0662	+	234.410i	−0.106892	+	0.397306i
$591$	−651.952	−	243.831i	−1.10313	−	0.412574i
$592$	21.0887	−	6.85212i	0.0356227	−	0.0115745i
$593$	−1079.90			−1.82108			−0.910540	−	0.413420i	$-0.864334\pi$
$593$	−1079.90			−1.82108			−0.910540	+	0.413420i	$0.864334\pi$
$594$	−212.812	+	445.817i	−0.358270	+	0.750534i
$595$	186.771	−	9.59738i	0.313901	−	0.0161301i
$596$	392.220	+	127.440i	0.658087	+	0.213825i
$597$	1.95919	−	44.7676i	0.00328173	−	0.0749877i
$598$	177.122	+	243.788i	0.296191	+	0.407671i
$599$			1066.05i			1.77972i	0.456229	+	0.889862i	$0.349200\pi$
$599$			1066.05i			1.77972i	−0.456229	+	0.889862i	$0.650800\pi$
$600$	564.084	+	147.171i	0.940140	+	0.245285i
$601$	−825.264			−1.37315			−0.686576	−	0.727058i	$-0.740887\pi$
$601$	−825.264			−1.37315			−0.686576	+	0.727058i	$0.740887\pi$
$602$	55.2639	−	40.1516i	0.0918005	−	0.0666969i
$603$	−512.982	+	118.320i	−0.850716	+	0.196220i
$604$	−38.4315	+	118.280i	−0.0636282	+	0.195828i
$605$	332.735	−	511.226i	0.549975	−	0.845001i
$606$	208.581	−	138.026i	0.344193	−	0.227765i
$607$		−	444.639i		−	0.732519i	−0.930513	−	0.366260i	$-0.880638\pi$
$607$		−	444.639i		−	0.732519i	0.930513	−	0.366260i	$-0.119362\pi$
$608$	335.277	+	1031.88i	0.551442	+	1.69716i
$609$	391.420	+	146.392i	0.642725	+	0.240380i
$610$	86.5346	−	132.955i	0.141860	−	0.217959i
$611$	−56.1016	−	77.2173i	−0.0918194	−	0.126379i
$612$	−194.291	−	17.0384i	−0.317470	−	0.0278406i
$613$	108.903	−	149.893i	0.177656	−	0.244523i	−0.710897	−	0.703296i	$-0.751711\pi$
$613$	108.903	−	149.893i	0.177656	−	0.244523i	0.888554	+	0.458773i	$0.151711\pi$
$614$	97.4578	+	134.139i	0.158726	+	0.218468i
$615$	262.668	+	355.810i	0.427103	+	0.578553i
$616$	−443.675	−	322.349i	−0.720252	−	0.523293i
$617$	129.854	+	399.648i	0.210460	+	0.647728i	0.999445	+	0.0333160i	$0.0106068\pi$
$617$	129.854	+	399.648i	0.210460	+	0.647728i	−0.788985	+	0.614412i	$0.789393\pi$
$618$	52.9577	+	191.035i	0.0856921	+	0.309119i
$619$	55.1731	+	169.805i	0.0891327	+	0.274322i	0.985680	−	0.168625i	$-0.0539328\pi$
$619$	55.1731	+	169.805i	0.0891327	+	0.274322i	−0.896548	+	0.442948i	$0.853933\pi$
$620$	−462.242	−	124.362i	−0.745551	−	0.200585i
$621$	169.345	+	312.124i	0.272698	+	0.502615i
$622$	−603.262	−	196.012i	−0.969874	−	0.315131i
$623$	234.930	−	170.687i	0.377095	−	0.273976i
$624$	21.3704	+	77.0897i	0.0342474	+	0.123541i
$625$	310.291	+	542.535i	0.496465	+	0.868057i
$626$			160.784i			0.256844i
$627$	−1214.42	−	966.197i	−1.93687	−	1.54098i
$628$	−618.198	−	200.865i	−0.984392	−	0.319848i
$629$	127.577	+	41.4523i	0.202825	+	0.0659020i
$630$	65.6130	+	229.882i	0.104148	+	0.364891i
$631$	−194.093	−	597.356i	−0.307596	−	0.946682i	−0.978696	−	0.205316i	$-0.934178\pi$
$631$	−194.093	−	597.356i	−0.307596	−	0.946682i	0.671100	−	0.741367i	$-0.265822\pi$
$632$	−289.785			−0.458520
$633$	398.662	+	602.446i	0.629798	+	0.951732i
$634$	260.278	+	189.103i	0.410534	+	0.298270i
$635$	−333.730	−	872.053i	−0.525560	−	1.37331i
$636$	1.88522	−	2.36954i	0.00296418	−	0.00372570i
$637$	−327.167	+	450.307i	−0.513606	+	0.706918i
$638$	−455.565	−	330.987i	−0.714051	−	0.518788i
$639$	136.731	+	58.0719i	0.213977	+	0.0908794i
$640$	251.338	−	386.164i	0.392716	−	0.603382i
$641$	−102.718	+	141.379i	−0.160246	+	0.220560i	−0.881589	−	0.472019i	$-0.843525\pi$
$641$	−102.718	+	141.379i	−0.160246	+	0.220560i	0.721342	+	0.692579i	$0.243525\pi$
$642$	129.963	+	196.396i	0.202434	+	0.305912i
$643$			441.290i			0.686298i	0.939281	+	0.343149i	$0.111494\pi$
$643$			441.290i			0.686298i	−0.939281	+	0.343149i	$0.888506\pi$
$644$	−148.462	+	48.2382i	−0.230531	+	0.0749040i
$645$	−183.883	−	58.2051i	−0.285091	−	0.0902404i
$646$	−99.4672	+	306.129i	−0.153974	+	0.473883i
$647$	191.495	−	589.361i	0.295974	−	0.910913i	−0.686919	−	0.726734i	$-0.741037\pi$
$647$	191.495	−	589.361i	0.295974	−	0.910913i	0.982893	−	0.184179i	$-0.0589627\pi$
$648$	−87.3684	−	623.513i	−0.134828	−	0.962211i
$649$	−644.776			−0.993491
$650$	287.410	−	495.473i	0.442169	−	0.762266i
$651$	−132.426	−	477.701i	−0.203419	−	0.733796i
$652$	−194.392	−	267.557i	−0.298147	−	0.410364i
$653$	240.005	−	738.661i	0.367543	−	1.13118i	−0.580831	−	0.814024i	$-0.697272\pi$
$653$	240.005	−	738.661i	0.367543	−	1.13118i	0.948373	−	0.317156i	$-0.102728\pi$
$654$	−27.9853	+	639.465i	−0.0427910	+	0.977776i
$655$	682.824	−	35.0875i	1.04248	−	0.0535686i
$656$	38.3051	−	12.4461i	0.0583919	−	0.0189727i
$657$	−296.250	−	493.271i	−0.450913	−	0.750793i
$658$	−24.7042	+	8.02688i	−0.0375444	+	0.0121989i
$659$	−157.285	+	216.484i	−0.238672	+	0.328504i	−0.911504	−	0.411292i	$-0.865078\pi$
$659$	−157.285	+	216.484i	−0.238672	+	0.328504i	0.672832	+	0.739796i	$0.265078\pi$
$660$	4.66303	+	613.149i	0.00706519	+	0.929013i
$661$	527.052	−	382.926i	0.797356	−	0.579313i	−0.112781	−	0.993620i	$-0.535976\pi$
$661$	527.052	−	382.926i	0.797356	−	0.579313i	0.910137	+	0.414307i	$0.135976\pi$
$662$	88.2905	+	64.1468i	0.133369	+	0.0968985i
$663$	−169.528	+	453.282i	−0.255699	+	0.683683i
$664$	−499.234	+	362.715i	−0.751859	+	0.546257i
$665$	−750.007	+	38.5397i	−1.12783	+	0.0579544i
$666$	−14.9798	+	170.817i	−0.0224922	+	0.256482i
$667$	−384.966	+	125.083i	−0.577160	+	0.187531i
$668$	25.4832			0.0381485
$669$	555.027	−	367.283i	0.829637	−	0.549002i
$670$	267.003	−	215.765i	0.398512	−	0.322037i
$671$	400.741	+	130.209i	0.597229	+	0.194051i
$672$	443.520	+	19.4100i	0.660000	+	0.0288840i
$673$	53.6995	+	73.9111i	0.0797913	+	0.109823i	0.847047	−	0.531518i	$-0.178378\pi$
$673$	53.6995	+	73.9111i	0.0797913	+	0.109823i	−0.767256	+	0.641341i	$0.778378\pi$
$674$			551.393i			0.818090i
$675$	412.169	−	534.548i	0.610621	−	0.791923i
$676$	556.065			0.822581
$677$	696.469	−	506.015i	1.02876	−	0.747437i	0.0606986	−	0.998156i	$-0.480667\pi$
$677$	696.469	−	506.015i	1.02876	−	0.747437i	0.968060	+	0.250719i	$0.0806672\pi$
$678$	5.52552	−	126.258i	0.00814973	−	0.186222i
$679$	11.8502	−	36.4712i	0.0174525	−	0.0537132i
$680$	299.957	−	114.792i	0.441114	−	0.168812i
$681$	−48.8075	−	73.7565i	−0.0716703	−	0.108306i
$682$			667.965i			0.979422i
$683$	−249.650	−	768.345i	−0.365520	−	1.12496i	−0.949655	−	0.313299i	$-0.898566\pi$
$683$	−249.650	−	768.345i	−0.365520	−	1.12496i	0.584134	−	0.811657i	$-0.301434\pi$
$684$	780.205	+	68.4202i	1.14065	+	0.100030i
$685$	−455.918	−	564.186i	−0.665573	−	0.823630i
$686$	242.046	+	333.147i	0.352836	+	0.485638i
$687$	−583.845	−	218.359i	−0.849848	−	0.317844i
$688$	−10.3244	+	14.2104i	−0.0150064	+	0.0206546i
$689$	−4.41626	−	6.07846i	−0.00640967	−	0.00882215i
$690$	−188.362	−	134.676i	−0.272988	−	0.195183i
$691$	873.560	+	634.678i	1.26420	+	0.918492i	0.998956	−	0.0456898i	$-0.0145486\pi$
$691$	873.560	+	634.678i	1.26420	+	0.918492i	0.265241	+	0.964182i	$0.414549\pi$
$692$	205.438	+	632.274i	0.296876	+	0.913691i
$693$	−544.360	+	326.933i	−0.785513	+	0.471765i
$694$	91.4408	+	281.426i	0.131759	+	0.405513i
$695$	19.3066	−	7.38855i	0.0277793	−	0.0106310i
$696$	716.988	+	31.3780i	1.03015	+	0.0450833i
$697$	231.729	+	75.2933i	0.332466	+	0.108025i
$698$	−117.583	+	85.4291i	−0.168457	+	0.122391i
$699$	350.814	−	97.2505i	0.501879	−	0.139128i
$700$	198.099	+	220.915i	0.282998	+	0.315593i
$701$			126.200i			0.180028i	0.995940	+	0.0900140i	$0.0286912\pi$
$701$			126.200i			0.180028i	−0.995940	+	0.0900140i	$0.971309\pi$
$702$	−613.304	−	80.9349i	−0.873653	−	0.115292i
$703$	−512.304	−	166.458i	−0.728740	−	0.236782i
$704$	−487.918	−	158.534i	−0.693065	−	0.225190i
$705$	59.6617	+	42.6573i	0.0846265	+	0.0605069i
$706$	−149.588	−	460.384i	−0.211881	−	0.652102i
$707$	321.494			0.454730
$708$	271.367	−	179.574i	0.383287	−	0.253636i
$709$	639.408	+	464.557i	0.901845	+	0.655229i	0.938939	−	0.344083i	$-0.111810\pi$
$709$	639.408	+	464.557i	0.901845	+	0.655229i	−0.0370940	+	0.999312i	$0.511810\pi$
$710$	−96.7397	+	4.97104i	−0.136253	+	0.00700146i
$711$	−131.167	+	308.833i	−0.184482	+	0.434364i
$712$	293.127	−	403.455i	0.411695	−	0.566650i
$713$	388.450	+	282.226i	0.544811	+	0.395828i
$714$	103.066	+	81.9993i	0.144350	+	0.114845i
$715$	1469.21	+	395.279i	2.05484	+	0.552837i
$716$	−547.386	+	753.412i	−0.764506	+	1.05225i
$717$	273.982	−	181.304i	0.382123	−	0.252865i
$718$			739.118i			1.02941i
$719$	595.621	−	193.529i	0.828402	−	0.269164i	0.136030	−	0.990705i	$-0.456566\pi$
$719$	595.621	−	193.529i	0.828402	−	0.269164i	0.692372	+	0.721540i	$0.256566\pi$
$720$	−34.3120	−	51.0043i	−0.0476556	−	0.0708393i
$721$	−78.7423	+	242.344i	−0.109213	+	0.336122i
$722$	268.488	−	826.322i	0.371868	−	1.14449i
$723$	405.171	−	509.263i	0.560403	−	0.704375i
$724$	−125.457			−0.173284
$725$	513.676	+	572.839i	0.708518	+	0.790123i
$726$	413.956	−	114.754i	0.570187	−	0.158064i
$727$	−196.370	−	270.281i	−0.270110	−	0.371775i	0.652317	−	0.757947i	$-0.273797\pi$
$727$	−196.370	−	270.281i	−0.270110	−	0.371775i	−0.922427	+	0.386171i	$0.873797\pi$
$728$	212.218	−	653.140i	0.291508	−	0.897170i
$729$	−704.044	−	189.112i	−0.965767	−	0.259413i
$730$	314.462	+	204.670i	0.430770	+	0.280370i
$731$	−101.060	+	32.8363i	−0.138249	+	0.0449197i
$732$	−204.924	+	56.8078i	−0.279951	+	0.0776063i
$733$	−253.600	+	82.3997i	−0.345976	+	0.112414i	−0.476850	−	0.878985i	$-0.658222\pi$
$733$	−253.600	+	82.3997i	−0.345976	+	0.112414i	0.130874	+	0.991399i	$0.458222\pi$
$734$	−102.086	+	140.509i	−0.139082	+	0.191430i
$735$	129.073	−	407.772i	0.175610	−	0.554792i
$736$	−347.881	+	252.750i	−0.472664	+	0.343411i
$737$	737.684	+	535.959i	1.00093	+	0.727217i
$738$	−27.2091	+	310.269i	−0.0368686	+	0.420418i
$739$	−895.612	+	650.700i	−1.21192	+	0.880515i	−0.995404	−	0.0957635i	$-0.969471\pi$
$739$	−895.612	+	650.700i	−1.21192	+	0.880515i	−0.216520	+	0.976278i	$0.569471\pi$
$740$	76.0701	+	198.775i	0.102797	+	0.268615i
$741$	680.764	−	1820.22i	0.918711	−	2.45644i
$742$	−1.94469	+	0.631867i	−0.00262087	+	0.000851573i
$743$	149.524			0.201244			0.100622	−	0.994925i	$-0.467917\pi$
$743$	149.524			0.201244			0.100622	+	0.994925i	$0.467917\pi$
$744$	−469.798	−	709.945i	−0.631449	−	0.954228i
$745$	−204.291	+	759.327i	−0.274216	+	1.01923i
$746$	−156.213	−	50.7566i	−0.209400	−	0.0680383i
$747$	160.586	+	696.227i	0.214975	+	0.932031i
$748$	198.560	+	273.294i	0.265454	+	0.365367i
$749$			302.713i			0.404156i
$750$	−89.1147	+	431.036i	−0.118820	+	0.574714i
$751$	−14.6660			−0.0195287			−0.00976434	−	0.999952i	$-0.503108\pi$
$751$	−14.6660			−0.0195287			−0.00976434	+	0.999952i	$0.503108\pi$
$752$	5.40363	−	3.92597i	0.00718568	−	0.00522070i
$753$	488.588	+	21.3824i	0.648855	+	0.0283962i
$754$	217.905	−	670.643i	0.288999	−	0.889447i
$755$	−228.987	−	61.6070i	−0.303294	−	0.0815987i
$756$	138.052	−	289.204i	0.182609	−	0.382545i
$757$			433.882i			0.573160i	0.958056	+	0.286580i	$0.0925185\pi$
$757$			433.882i			0.573160i	−0.958056	+	0.286580i	$0.907482\pi$
$758$	148.848	+	458.107i	0.196369	+	0.604363i
$759$	215.455	−	576.080i	0.283867	−	0.758998i
$760$	−1204.52	+	460.965i	−1.58490	+	0.606532i
$761$	148.426	+	204.291i	0.195041	+	0.268451i	0.895325	−	0.445414i	$-0.146943\pi$
$761$	148.426	+	204.291i	0.195041	+	0.268451i	−0.700284	+	0.713864i	$0.746943\pi$
$762$	230.350	−	615.906i	0.302296	−	0.808276i
$763$	−483.600	+	665.618i	−0.633814	+	0.872370i
$764$	383.079	+	527.263i	0.501412	+	0.690135i
$765$	13.4333	−	371.633i	0.0175598	−	0.485795i
$766$	−155.486	−	112.967i	−0.202984	−	0.147477i
$767$	−249.508	−	767.905i	−0.325303	−	1.00118i
$768$	693.270	−	192.184i	0.902696	−	0.250240i
$769$	110.577	+	340.322i	0.143794	+	0.442552i	0.996854	−	0.0792610i	$-0.0252560\pi$
$769$	110.577	+	340.322i	0.143794	+	0.442552i	−0.853060	+	0.521813i	$0.825256\pi$
$770$	225.868	−	347.032i	0.293336	−	0.450691i
$771$	30.9626	−	707.496i	0.0401590	−	0.917634i
$772$	−783.644	−	254.621i	−1.01508	−	0.329820i
$773$	−677.204	+	492.018i	−0.876073	+	0.636504i	−0.932210	−	0.361919i	$-0.882122\pi$
$773$	−677.204	+	492.018i	−0.876073	+	0.636504i	0.0561366	+	0.998423i	$0.482122\pi$
$774$	−69.9343	−	116.444i	−0.0903544	−	0.150445i
$775$	191.579	−	892.361i	0.247199	−	1.15143i
$776$		−	65.8567i		−	0.0848668i
$777$	−137.225	+	172.480i	−0.176609	+	0.221982i
$778$	−181.414	−	58.9449i	−0.233180	−	0.0757647i
$779$	−930.540	−	302.351i	−1.19453	−	0.388127i
$780$	−728.434	+	242.822i	−0.933890	+	0.311311i
$781$	−79.5090	−	244.704i	−0.101804	−	0.313321i
$782$	−127.570			−0.163133
$783$	357.974	−	749.915i	0.457183	−	0.957745i
$784$	−31.5123	−	22.8950i	−0.0401942	−	0.0292028i
$785$	321.993	−	1196.82i	0.410183	−	1.52461i
$786$	376.802	+	299.785i	0.479391	+	0.381405i
$787$	−95.1242	+	130.927i	−0.120869	+	0.166362i	−0.865164	−	0.501489i	$-0.832786\pi$
$787$	−95.1242	+	130.927i	−0.120869	+	0.166362i	0.744295	+	0.667851i	$0.232786\pi$
$788$	−492.233	−	357.628i	−0.624661	−	0.453843i
$789$	−164.421	+	206.662i	−0.208391	+	0.261928i
$790$	−11.2280	−	218.505i	−0.0142127	−	0.276589i
$791$	95.4836	−	131.422i	0.120713	−	0.166147i
$792$	−715.596	+	822.859i	−0.903531	+	1.03896i
$793$			527.654i			0.665390i
$794$	149.413	−	48.5473i	0.188178	−	0.0611427i
$795$	4.69651	+	3.35794i	0.00590755	+	0.00422382i
$796$	12.1040	−	37.2524i	0.0152061	−	0.0467995i
$797$	−254.920	+	784.563i	−0.319849	+	0.984395i	0.653863	+	0.756613i	$0.273147\pi$
$797$	−254.920	+	784.563i	−0.319849	+	0.984395i	−0.973712	+	0.227782i	$0.926853\pi$
$798$	−413.875	−	329.280i	−0.518640	−	0.412632i
$799$	40.4066			0.0505714
$800$	707.031	+	410.129i	0.883789	+	0.512661i
$801$	−297.295	−	495.012i	−0.371155	−	0.617993i
$802$	311.292	+	428.457i	0.388145	+	0.534236i
$803$	−307.967	+	947.826i	−0.383521	+	1.18036i
$804$	−459.738	−	20.1198i	−0.571813	−	0.0250246i
$805$	−106.381	−	277.978i	−0.132150	−	0.345315i
$806$	−795.523	+	258.481i	−0.987002	+	0.320696i
$807$	96.4846	+	348.051i	0.119560	+	0.431289i
$808$	525.091	−	170.612i	0.649865	−	0.211154i
$809$	−93.1201	+	128.169i	−0.115105	+	0.158429i	−0.862682	−	0.505746i	$-0.831217\pi$
$809$	−93.1201	+	128.169i	−0.115105	+	0.158429i	0.747577	+	0.664175i	$0.231217\pi$
$810$	466.759	−	90.0367i	0.576246	−	0.111156i
$811$	1067.58	−	775.641i	1.31637	−	0.956401i	0.316403	−	0.948625i	$-0.397525\pi$
$811$	1067.58	−	775.641i	1.31637	−	0.956401i	0.999970	−	0.00777589i	$-0.00247517\pi$
$812$	295.527	+	214.713i	0.363950	+	0.264425i
$813$	749.551	+	280.333i	0.921957	+	0.344813i
$814$	240.274	−	174.569i	0.295177	−	0.214459i
$815$	490.456	−	396.337i	0.601787	−	0.486303i
$816$	−31.7205	−	11.8635i	−0.0388731	−	0.0145386i
$817$	405.820	−	131.859i	0.496719	−	0.161394i
$818$	−22.9293			−0.0280309
$819$	−600.015	−	521.801i	−0.732620	−	0.637120i
$820$	138.172	+	361.051i	0.168503	+	0.440306i
$821$	−1045.16	−	339.592i	−1.27303	−	0.413632i	−0.406908	−	0.913469i	$-0.633393\pi$
$821$	−1045.16	−	339.592i	−1.27303	−	0.413632i	−0.866119	+	0.499837i	$0.833393\pi$
$822$	22.3348	−	510.350i	0.0271713	−	0.620864i
$823$	−281.353	−	387.249i	−0.341863	−	0.470534i	0.603122	−	0.797649i	$-0.293923\pi$
$823$	−281.353	−	387.249i	−0.341863	−	0.470534i	−0.944984	+	0.327116i	$0.893923\pi$
$824$			437.604i			0.531073i
$825$	−1167.09	+	68.8745i	−1.41465	+	0.0834842i
$826$	−219.740			−0.266029
$827$	−418.443	+	304.017i	−0.505977	+	0.367614i	−0.811295	−	0.584636i	$-0.801237\pi$
$827$	−418.443	+	304.017i	−0.505977	+	0.367614i	0.305318	+	0.952250i	$0.401237\pi$
$828$	69.7632	+	302.460i	0.0842551	+	0.365290i
$829$	114.037	−	350.971i	0.137560	−	0.423366i	−0.858419	−	0.512948i	$-0.828553\pi$
$829$	114.037	−	350.971i	0.137560	−	0.423366i	0.995979	+	0.0895823i	$0.0285532\pi$
$830$	−292.839	−	362.381i	−0.352819	−	0.436604i
$831$	−1039.72	+	688.023i	−1.25117	+	0.827946i
$832$		−	642.441i		−	0.772164i
$833$	−72.8163	−	224.105i	−0.0874145	−	0.269034i
$834$	13.6357	+	5.09978i	0.0163498	+	0.00611484i
$835$	2.49347	+	48.5246i	0.00298620	+	0.0581133i
$836$	−797.346	−	1097.45i	−0.953763	−	1.31274i
$837$	−969.259	+	179.333i	−1.15802	+	0.214257i
$838$	377.744	−	519.920i	0.450768	−	0.620430i
$839$	145.236	+	199.900i	0.173106	+	0.238260i	0.886751	−	0.462248i	$-0.152957\pi$
$839$	145.236	+	199.900i	0.173106	+	0.238260i	−0.713645	+	0.700508i	$0.752957\pi$
$840$	4.01320	+	527.701i	0.00477761	+	0.628216i
$841$	85.9271	+	62.4297i	0.102173	+	0.0742327i
$842$	−203.503	−	626.317i	−0.241690	−	0.743845i
$843$	−113.202	−	408.357i	−0.134285	−	0.484409i
$844$	195.134	+	600.560i	0.231201	+	0.711564i
$845$	54.4097	+	1058.85i	0.0643902	+	1.25308i
$846$	11.6087	+	50.3297i	0.0137218	+	0.0594914i
$847$	525.137	+	170.627i	0.619996	+	0.201449i
$848$	0.425368	−	0.309048i	0.000501613	−	0.000364443i
$849$	−158.605	−	572.140i	−0.186814	−	0.673899i
$850$	98.1784	+	221.728i	0.115504	+	0.260856i
$851$		−	213.488i		−	0.250867i
$852$	101.614	+	80.8448i	0.119266	+	0.0948883i
$853$	−5.05983	−	1.64404i	−0.00593181	−	0.00192736i	0.306050	−	0.952016i	$-0.400993\pi$
$853$	−5.05983	−	1.64404i	−0.00593181	−	0.00192736i	−0.311981	+	0.950088i	$0.600993\pi$
$854$	136.573	+	44.3751i	0.159921	+	0.0519615i
$855$	−53.9431	+	1492.35i	−0.0630914	+	1.74544i
$856$	160.645	+	494.416i	0.187670	+	0.577589i
$857$	941.563			1.09867			0.549337	−	0.835601i	$-0.314880\pi$
$857$	941.563			1.09867			0.549337	+	0.835601i	$0.314880\pi$
$858$	591.293	+	893.545i	0.689153	+	1.04143i
$859$	−131.977	−	95.8872i	−0.153641	−	0.111627i	0.508309	−	0.861175i	$-0.330271\pi$
$859$	−131.977	−	95.8872i	−0.153641	−	0.111627i	−0.661950	+	0.749548i	$0.730271\pi$
$860$	−141.302	−	91.9675i	−0.164305	−	0.106939i
$861$	−249.254	+	313.289i	−0.289493	+	0.363866i
$862$	−313.915	+	432.067i	−0.364171	+	0.501238i
$863$	−1130.37	−	821.258i	−1.30981	−	0.951632i	−1.00000		0.000833301i	$-0.999735\pi$
$863$	−1130.37	−	821.258i	−1.30981	−	0.951632i	−0.309809	−	0.950799i	$-0.600265\pi$
$864$	115.493	−	875.175i	0.133672	−	1.01293i
$865$	−1183.86	+	453.058i	−1.36863	+	0.523767i
$866$	−578.614	+	796.394i	−0.668145	+	0.919623i
$867$	365.394	+	552.173i	0.421446	+	0.636877i
$868$		−	433.313i		−	0.499208i
$869$	552.710	−	179.586i	0.636030	−	0.206659i
$870$	4.12074	+	541.843i	0.00473648	+	0.622808i
$871$	−352.848	+	1085.96i	−0.405107	+	1.24679i
$872$	−436.622	+	1343.78i	−0.500713	+	1.54104i
$873$	−70.1856	−	29.8090i	−0.0803959	−	0.0341455i
$874$	512.276			0.586128
$875$	−401.279	+	398.832i	−0.458604	+	0.455808i
$876$	−134.361	−	484.683i	−0.153380	−	0.553291i
$877$	568.890	+	783.010i	0.648678	+	0.892828i	0.999041	−	0.0437856i	$-0.0139418\pi$
$877$	568.890	+	783.010i	0.648678	+	0.892828i	−0.350363	+	0.936614i	$0.613942\pi$
$878$	198.830	−	611.935i	0.226458	−	0.696965i
$879$	9.02918	−	206.317i	0.0102721	−	0.234718i
$880$	−27.6614	+	102.815i	−0.0314334	+	0.116835i
$881$	1217.78	−	395.680i	1.38227	−	0.449126i	0.478853	−	0.877895i	$-0.341053\pi$
$881$	1217.78	−	395.680i	1.38227	−	0.449126i	0.903414	+	0.428770i	$0.141053\pi$
$882$	258.222	−	155.083i	0.292768	−	0.175831i
$883$	142.939	−	46.4437i	0.161879	−	0.0525976i	−0.226956	−	0.973905i	$-0.572878\pi$
$883$	142.939	−	46.4437i	0.161879	−	0.0525976i	0.388835	+	0.921307i	$0.372878\pi$
$884$	−248.647	+	342.234i	−0.281275	+	0.387142i
$885$	368.494	+	499.161i	0.416378	+	0.564024i
$886$	−731.195	+	531.244i	−0.825276	+	0.599598i
$887$	−186.253	−	135.321i	−0.209980	−	0.152560i	0.477824	−	0.878455i	$-0.341426\pi$
$887$	−186.253	−	135.321i	−0.209980	−	0.152560i	−0.687805	+	0.725896i	$0.741426\pi$
$888$	−132.596	+	354.532i	−0.149319	+	0.399248i
$889$	683.811	−	496.818i	0.769191	−	0.558850i
$890$	315.572	+	205.393i	0.354576	+	0.230778i
$891$	553.044	+	1135.09i	0.620700	+	1.27395i
$892$	553.289	−	179.775i	0.620279	−	0.201541i
$893$	−162.258			−0.181700
$894$	−461.809	+	305.596i	−0.516564	+	0.341830i
$895$	−1488.19	−	968.603i	−1.66279	−	1.08224i
$896$	396.672	+	128.887i	0.442715	+	0.143847i
$897$	769.465	+	33.6745i	0.857820	+	0.0375413i
$898$	−353.535	−	486.599i	−0.393692	−	0.541870i
$899$		−	1123.59i		−	1.24982i
$900$	472.012	−	354.029i	0.524457	−	0.393365i
$901$	3.18076			0.00353026
$902$	436.430	−	317.085i	0.483847	−	0.351535i
$903$	7.63364	−	174.429i	0.00845364	−	0.193166i
$904$	86.2081	−	265.321i	0.0953629	−	0.293497i
$905$	−12.2757	−	238.894i	−0.0135643	−	0.263971i
$906$	−92.1573	−	139.265i	−0.101719	−	0.153715i
$907$		−	410.452i		−	0.452539i	−0.974065	−	0.226269i	$-0.927347\pi$
$907$		−	410.452i		−	0.452539i	0.974065	−	0.226269i	$-0.0726529\pi$
$908$	−23.8899	−	73.5256i	−0.0263105	−	0.0809753i
$909$	55.8471	−	636.832i	0.0614379	−	0.700585i
$910$	500.707	+	134.711i	0.550227	+	0.148034i
$911$	292.830	+	403.046i	0.321438	+	0.442422i	0.938906	−	0.344175i	$-0.111841\pi$
$911$	292.830	+	403.046i	0.321438	+	0.442422i	−0.617467	+	0.786597i	$0.711841\pi$
$912$	127.378	+	47.6396i	0.139669	+	0.0522364i
$913$	727.412	−	1001.20i	0.796728	−	1.09660i
$914$	−261.534	−	359.971i	−0.286143	−	0.393842i
$915$	−128.224	−	384.654i	−0.140135	−	0.420386i
$916$	−440.811	−	320.268i	−0.481235	−	0.349637i
$917$	191.259	+	588.634i	0.208570	+	0.641912i
$918$	180.332	−	189.914i	0.196440	−	0.206877i
$919$	−330.073	−	1015.86i	−0.359165	−	1.10540i	−0.953555	−	0.301219i	$-0.902606\pi$
$919$	−330.073	−	1015.86i	−0.359165	−	1.10540i	0.594390	−	0.804177i	$-0.297394\pi$
$920$	−321.270	−	397.563i	−0.349206	−	0.432133i
$921$	423.382	+	18.5287i	0.459698	+	0.0201181i
$922$	−236.831	−	76.9509i	−0.256866	−	0.0834609i
$923$	260.666	−	189.385i	0.282412	−	0.205184i
$924$	−534.882	+	148.277i	−0.578877	+	0.160473i
$925$	−371.060	+	164.301i	−0.401146	+	0.177623i
$926$		−	463.226i		−	0.500244i
$927$	466.369	+	198.075i	0.503095	+	0.213673i
$928$	956.996	+	310.947i	1.03125	+	0.335072i
$929$	1704.04	+	553.677i	1.83428	+	0.595992i	0.998929	+	0.0462700i	$0.0147335\pi$
$929$	1704.04	+	553.677i	1.83428	+	0.595992i	0.835347	+	0.549723i	$0.185267\pi$
$930$	517.114	−	381.747i	0.556036	−	0.410481i
$931$	292.404	+	899.928i	0.314075	+	0.966625i
$932$	318.215			0.341433
$933$	−1352.03	+	894.689i	−1.44912	+	0.958938i
$934$	−855.203	−	621.341i	−0.915635	−	0.665248i
$935$	−500.973	+	404.835i	−0.535800	+	0.432979i
$936$	−1256.91	−	533.830i	−1.34285	−	0.570331i
$937$	776.352	−	1068.56i	0.828550	−	1.14040i	−0.159641	−	0.987175i	$-0.551034\pi$
$937$	776.352	−	1068.56i	0.828550	−	1.14040i	0.988191	−	0.153227i	$-0.0489665\pi$
$938$	251.403	+	182.655i	0.268020	+	0.194728i
$939$	321.591	+	255.859i	0.342482	+	0.272480i
$940$	40.2949	+	49.8639i	0.0428669	+	0.0530467i
$941$	−619.997	+	853.353i	−0.658871	+	0.906858i	−0.999443	−	0.0333605i	$-0.989379\pi$
$941$	−619.997	+	853.353i	−0.658871	+	0.906858i	0.340573	+	0.940218i	$0.389379\pi$
$942$	727.881	−	481.667i	0.772697	−	0.511323i
$943$		−	387.776i		−	0.411215i
$944$	53.7377	−	17.4604i	0.0569255	−	0.0184962i
$945$	564.205	+	234.579i	0.597042	+	0.248232i
$946$	−72.7004	+	223.749i	−0.0768503	+	0.236521i
$947$	163.200	−	502.277i	0.172333	−	0.530388i	−0.827168	−	0.561954i	$-0.810050\pi$
$947$	163.200	−	502.277i	0.172333	−	0.530388i	0.999502	+	0.0315667i	$0.0100497\pi$
$948$	−182.603	+	229.516i	−0.192620	+	0.242105i
$949$	−1248.00			−1.31507
$950$	−394.249	−	890.379i	−0.414999	−	0.937241i
$951$	792.417	−	219.669i	0.833246	−	0.230988i
$952$	170.889	+	235.208i	0.179505	+	0.247068i
$953$	215.591	−	663.520i	0.226223	−	0.696244i	−0.771942	−	0.635693i	$-0.780714\pi$
$953$	215.591	−	663.520i	0.226223	−	0.696244i	0.998165	−	0.0605505i	$-0.0192856\pi$
$954$	0.913821	+	3.96190i	0.000957884	+	0.00415293i
$955$	−966.521	+	781.044i	−1.01206	+	0.817847i
$956$	273.124	−	88.7435i	0.285695	−	0.0928279i
$957$	−1386.97	+	384.486i	−1.44928	+	0.401762i
$958$	636.916	−	206.947i	0.664840	−	0.216019i
$959$	385.956	−	531.222i	0.402456	−	0.553934i
$960$	156.117	+	468.331i	0.162622	+	0.487845i
$961$	−300.806	+	218.549i	−0.313014	+	0.227418i
$962$	300.885	+	218.605i	0.312770	+	0.227241i
$963$	599.629	+	52.5846i	0.622668	+	0.0546050i
$964$	460.213	−	334.364i	0.477399	−	0.346851i
$965$	408.167	−	1517.11i	0.422971	−	1.57214i
$966$	73.4270	−	196.328i	0.0760114	−	0.203238i
$967$	−1001.44	+	325.388i	−1.03562	+	0.336492i	−0.777009	−	0.629490i	$-0.783264\pi$
$967$	−1001.44	+	325.388i	−1.03562	+	0.336492i	−0.258609	+	0.965982i	$0.583264\pi$
$968$	948.247			0.979594
$969$	454.015	+	686.094i	0.468540	+	0.708044i
$970$	49.6576	−	2.55169i	0.0511934	−	0.00263061i
$971$	−220.610	−	71.6804i	−0.227198	−	0.0738212i	0.193206	−	0.981158i	$-0.438112\pi$
$971$	−220.610	−	71.6804i	−0.227198	−	0.0738212i	−0.420404	+	0.907337i	$0.638112\pi$
$972$	−548.889	−	323.699i	−0.564701	−	0.333024i
$973$	10.9992	+	15.1391i	0.0113044	+	0.0155592i
$974$			914.176i			0.938579i
$975$	−533.653	−	1363.31i	−0.547337	−	1.39827i
$976$	−36.9250			−0.0378330
$977$	−375.775	+	273.017i	−0.384622	+	0.279444i	−0.763248	−	0.646106i	$-0.776397\pi$
$977$	−375.775	+	273.017i	−0.384622	+	0.279444i	0.378626	+	0.925550i	$0.376397\pi$
$978$	443.656	+	19.4160i	0.453636	+	0.0198527i
$979$	−309.054	+	951.171i	−0.315684	+	0.971574i
$980$	203.943	−	313.345i	0.208105	−	0.319740i
$981$	1234.48	+	1073.56i	1.25839	+	1.09436i
$982$			611.763i			0.622976i
$983$	377.895	+	1163.04i	0.384431	+	1.18316i	0.936892	+	0.349618i	$0.113689\pi$
$983$	377.895	+	1163.04i	0.384431	+	1.18316i	−0.552462	+	0.833538i	$0.686311\pi$
$984$	−240.844	+	643.966i	−0.244760	+	0.654437i
$985$	632.825	−	972.293i	0.642461	−	0.987100i
$986$	175.468	+	241.511i	0.177960	+	0.244941i
$987$	−23.2573	+	62.1850i	−0.0235636	+	0.0630040i
$988$	998.480	−	1374.29i	1.01061	−	1.39098i
$989$	99.4024	+	136.816i	0.100508	+	0.138337i
$990$	−648.183	−	507.695i	−0.654730	−	0.512823i
$991$	−1298.79	−	943.625i	−1.31058	−	0.952195i	−0.999999	−	0.00164927i	$-0.999475\pi$
$991$	−1298.79	−	943.625i	−1.31058	−	0.952195i	−0.310585	−	0.950546i	$-0.600525\pi$
$992$	−368.848	−	1135.20i	−0.371823	−	1.14435i
$993$	268.800	−	74.5153i	0.270695	−	0.0750405i
$994$	−27.0967	−	83.3951i	−0.0272603	−	0.0838985i
$995$	72.1196	+	19.4032i	0.0724820	+	0.0195007i
$996$	−27.3069	+	623.963i	−0.0274165	+	0.626469i
$997$	372.060	+	120.890i	0.373179	+	0.121253i	0.489601	−	0.871947i	$-0.337142\pi$
$997$	372.060	+	120.890i	0.373179	+	0.121253i	−0.116422	+	0.993200i	$0.537142\pi$
$998$	−88.2954	+	64.1504i	−0.0884723	+	0.0642789i
$999$	317.819	+	301.785i	0.318137	+	0.302087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.7	✓	72
3.2	odd	2	inner	75.3.h.a.14.12	yes	72
5.2	odd	4		375.3.j.b.176.14		144
5.3	odd	4		375.3.j.b.176.23		144
5.4	even	2		375.3.h.a.74.12		72
15.2	even	4		375.3.j.b.176.24		144
15.8	even	4		375.3.j.b.176.13		144
15.14	odd	2		375.3.h.a.74.7		72
25.9	even	10	inner	75.3.h.a.59.12	yes	72
25.12	odd	20		375.3.j.b.326.24		144
25.13	odd	20		375.3.j.b.326.13		144
25.16	even	5		375.3.h.a.299.7		72
75.38	even	20		375.3.j.b.326.23		144
75.41	odd	10		375.3.h.a.299.12		72
75.59	odd	10	inner	75.3.h.a.59.7	yes	72
75.62	even	20		375.3.j.b.326.14		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.7	✓	72	1.1	even	1	trivial
75.3.h.a.14.12	yes	72	3.2	odd	2	inner
75.3.h.a.59.7	yes	72	75.59	odd	10	inner
75.3.h.a.59.12	yes	72	25.9	even	10	inner
375.3.h.a.74.7		72	15.14	odd	2
375.3.h.a.74.12		72	5.4	even	2
375.3.h.a.299.7		72	25.16	even	5
375.3.h.a.299.12		72	75.41	odd	10
375.3.j.b.176.13		144	15.8	even	4
375.3.j.b.176.14		144	5.2	odd	4
375.3.j.b.176.23		144	5.3	odd	4
375.3.j.b.176.24		144	15.2	even	4
375.3.j.b.326.13		144	25.13	odd	20
375.3.j.b.326.14		144	75.62	even	20
375.3.j.b.326.23		144	75.38	even	20
375.3.j.b.326.24		144	25.12	odd	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.949573 + 0.689905i) q^{2} +(-0.131165 + 2.99713i) q^{3} +(-0.810348 + 2.49399i) q^{4} +(-4.82831 - 1.29902i) q^{5} +(-1.94319 - 2.93649i) q^{6} -4.52613i q^{7} +(-2.40195 - 7.39246i) q^{8} +(-8.96559 - 0.786239i) q^{9} +(5.48103 - 2.09756i) q^{10} +(9.16255 + 12.6112i) q^{11} +(-7.36854 - 2.75584i) q^{12} +(-11.4738 + 15.7924i) q^{13} +(3.12260 + 4.29789i) q^{14} +(4.52663 - 14.3007i) q^{15} +(-1.10515 - 0.802935i) q^{16} +(-2.55369 - 7.85945i) q^{17} +(9.05592 - 5.43882i) q^{18} +(10.2547 + 31.5607i) q^{19} +(7.15235 - 10.9891i) q^{20} +(13.5654 + 0.593671i) q^{21} +(-17.4010 - 5.65394i) q^{22} +(-10.6402 + 7.73056i) q^{23} +(22.4712 - 6.22934i) q^{24} +(21.6251 + 12.5441i) q^{25} -22.9119i q^{26} +(3.53244 - 26.7679i) q^{27} +(11.2881 + 3.66774i) q^{28} +(29.2705 + 9.51056i) q^{29} +(5.56775 + 16.7025i) q^{30} +(-11.2815 - 34.7209i) q^{31} +32.6949 q^{32} +(-38.9992 + 25.8072i) q^{33} +(7.84719 + 5.70132i) q^{34} +(-5.87952 + 21.8535i) q^{35} +(9.22612 - 21.7230i) q^{36} +(-9.54112 + 13.1322i) q^{37} +(-31.5115 - 22.8945i) q^{38} +(-45.8269 - 36.4600i) q^{39} +(1.99445 + 38.8132i) q^{40} +(-17.3303 + 23.8531i) q^{41} +(-13.2909 + 8.79511i) q^{42} -12.8584i q^{43} +(-38.8771 + 12.6319i) q^{44} +(42.2673 + 15.4427i) q^{45} +(4.77030 - 14.6815i) q^{46} +(-1.51095 + 4.65021i) q^{47} +(2.55146 - 3.20695i) q^{48} +28.5142 q^{49} +(-29.1889 + 3.00773i) q^{50} +(23.8908 - 6.62286i) q^{51} +(-30.0883 - 41.4131i) q^{52} +(-0.118940 + 0.366060i) q^{53} +(15.1130 + 27.8552i) q^{54} +(-27.8575 - 72.7929i) q^{55} +(-33.4592 + 10.8716i) q^{56} +(-95.9367 + 26.5950i) q^{57} +(-34.3559 + 11.1629i) q^{58} +(-24.3125 + 33.4633i) q^{59} +(31.9977 + 22.8779i) q^{60} +(21.8684 - 15.8883i) q^{61} +(34.6668 + 25.1869i) q^{62} +(-3.55862 + 40.5794i) q^{63} +(-26.6256 + 19.3447i) q^{64} +(75.9139 - 61.3458i) q^{65} +(19.2280 - 51.4116i) q^{66} +(55.6316 - 18.0758i) q^{67} +21.6708 q^{68} +(-21.7739 - 32.9041i) q^{69} +(-9.49384 - 24.8079i) q^{70} +(-15.6979 - 5.10057i) q^{71} +(15.7227 + 68.1662i) q^{72} +(37.5788 + 51.7228i) q^{73} -19.0525i q^{74} +(-40.4328 + 63.1679i) q^{75} -87.0222 q^{76} +(57.0798 - 41.4709i) q^{77} +(68.6700 + 3.00525i) q^{78} +(11.5206 - 35.4568i) q^{79} +(4.29296 + 5.31242i) q^{80} +(79.7637 + 14.0982i) q^{81} -34.6066i q^{82} +(-24.5328 - 75.5041i) q^{83} +(-12.4733 + 33.3510i) q^{84} +(2.12044 + 41.2651i) q^{85} +(8.87106 + 12.2100i) q^{86} +(-32.3437 + 86.4800i) q^{87} +(71.2195 - 98.0252i) q^{88} +(37.7114 + 51.9054i) q^{89} +(-50.7899 + 14.4965i) q^{90} +(71.4784 + 51.9321i) q^{91} +(-10.6577 - 32.8011i) q^{92} +(105.543 - 29.2580i) q^{93} +(-1.77345 - 5.45813i) q^{94} +(-8.51493 - 165.706i) q^{95} +(-4.28844 + 97.9910i) q^{96} +(8.05793 + 2.61818i) q^{97} +(-27.0763 + 19.6721i) q^{98} +(-72.2323 - 120.271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) \) 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

Introduction

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