LMFDB - Embedded newform 75.3.h.a.14.4

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			14.4
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.05424 + 1.49250i) q^{2} +(0.392507 + 2.97421i) q^{3} +(0.756307 - 2.32767i) q^{4} +(4.44388 + 2.29172i) q^{5} +(-5.24530 - 5.52394i) q^{6} +6.97211i q^{7} +(-1.21820 - 3.74924i) q^{8} +(-8.69188 + 2.33480i) q^{9} +(-12.5492 + 1.92472i) q^{10} +(-7.98507 - 10.9905i) q^{11} +(7.21985 + 1.33579i) q^{12} +(0.259763 - 0.357533i) q^{13} +(-10.4058 - 14.3224i) q^{14} +(-5.07180 + 14.1165i) q^{15} +(16.0184 + 11.6380i) q^{16} +(7.94771 + 24.4605i) q^{17} +(14.3706 - 17.7688i) q^{18} +(-3.70606 - 11.4061i) q^{19} +(8.69531 - 8.61066i) q^{20} +(-20.7365 + 2.73660i) q^{21} +(32.8065 + 10.6595i) q^{22} +(19.1473 - 13.9113i) q^{23} +(10.6729 - 5.09479i) q^{24} +(14.4961 + 20.3682i) q^{25} +1.12216i q^{26} +(-10.3558 - 24.9351i) q^{27} +(16.2288 + 5.27306i) q^{28} +(32.2785 + 10.4879i) q^{29} +(-10.6502 - 36.5685i) q^{30} +(7.00881 + 21.5709i) q^{31} -34.5066 q^{32} +(29.5539 - 28.0631i) q^{33} +(-52.8338 - 38.3860i) q^{34} +(-15.9781 + 30.9832i) q^{35} +(-1.13908 + 21.9977i) q^{36} +(-24.1765 + 33.2760i) q^{37} +(24.6367 + 17.8996i) q^{38} +(1.16534 + 0.632257i) q^{39} +(3.17866 - 19.4529i) q^{40} +(11.1774 - 15.3843i) q^{41} +(38.5136 - 36.5709i) q^{42} -40.7478i q^{43} +(-31.6215 + 10.2744i) q^{44} +(-43.9763 - 9.54376i) q^{45} +(-18.5706 + 57.1545i) q^{46} +(-7.83781 + 24.1223i) q^{47} +(-28.3266 + 52.2100i) q^{48} +0.389632 q^{49} +(-60.1779 - 20.2060i) q^{50} +(-69.6313 + 33.2391i) q^{51} +(-0.635761 - 0.875050i) q^{52} +(-22.0806 + 67.9572i) q^{53} +(58.4888 + 35.7667i) q^{54} +(-10.2975 - 67.1399i) q^{55} +(26.1401 - 8.49344i) q^{56} +(32.4694 - 15.4996i) q^{57} +(-81.9612 + 26.6308i) q^{58} +(16.0556 - 22.0987i) q^{59} +(29.0229 + 22.4819i) q^{60} +(77.8653 - 56.5725i) q^{61} +(-46.5923 - 33.8513i) q^{62} +(-16.2785 - 60.6007i) q^{63} +(6.81151 - 4.94885i) q^{64} +(1.97372 - 0.993530i) q^{65} +(-18.8268 + 101.758i) q^{66} +(92.0681 - 29.9148i) q^{67} +62.9471 q^{68} +(48.8907 + 51.4878i) q^{69} +(-13.4194 - 87.4943i) q^{70} +(-15.2176 - 4.94450i) q^{71} +(19.3422 + 29.7437i) q^{72} +(-23.6157 - 32.5042i) q^{73} -104.440i q^{74} +(-54.8896 + 51.1090i) q^{75} -29.3526 q^{76} +(76.6270 - 55.6728i) q^{77} +(-3.33753 + 0.440454i) q^{78} +(-3.55591 + 10.9440i) q^{79} +(44.5125 + 88.4274i) q^{80} +(70.0974 - 40.5876i) q^{81} +48.2853i q^{82} +(-9.61536 - 29.5930i) q^{83} +(-9.31328 + 50.3376i) q^{84} +(-20.7380 + 126.913i) q^{85} +(60.8159 + 83.7059i) q^{86} +(-18.5238 + 100.120i) q^{87} +(-31.4786 + 43.3265i) q^{88} +(-35.6526 - 49.0716i) q^{89} +(104.582 - 46.0292i) q^{90} +(2.49276 + 1.81110i) q^{91} +(-17.8998 - 55.0899i) q^{92} +(-61.4054 + 29.3124i) q^{93} +(-19.9017 - 61.2510i) q^{94} +(9.67024 - 59.1804i) q^{95} +(-13.5441 - 102.630i) q^{96} +(-125.919 - 40.9136i) q^{97} +(-0.800399 + 0.581524i) q^{98} +(95.0658 + 76.8845i) 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 $

$2$	−2.05424	+	1.49250i	−1.02712	+	0.746248i	−0.967731	−	0.251987i	$-0.918916\pi$
$2$	−2.05424	+	1.49250i	−1.02712	+	0.746248i	−0.0593914	+	0.998235i	$0.518916\pi$
$3$	0.392507	+	2.97421i	0.130836	+	0.991404i
$3$	0.392507	+	2.97421i	0.130836	+	0.991404i
$4$	0.756307	−	2.32767i	0.189077	−	0.581919i
$5$	4.44388	+	2.29172i	0.888775	+	0.458343i
$5$	4.44388	+	2.29172i	0.888775	+	0.458343i
$6$	−5.24530	−	5.52394i	−0.874217	−	0.920657i
$7$			6.97211i			0.996016i	0.867172	+	0.498008i	$0.165935\pi$
$7$			6.97211i			0.996016i	−0.867172	+	0.498008i	$0.834065\pi$
$8$	−1.21820	−	3.74924i	−0.152275	−	0.468655i
$9$	−8.69188	+	2.33480i	−0.965764	+	0.259422i
$10$	−12.5492	+	1.92472i	−1.25492	+	0.192472i
$11$	−7.98507	−	10.9905i	−0.725915	−	0.999136i	−0.999307	−	0.0372335i	$-0.988145\pi$
$11$	−7.98507	−	10.9905i	−0.725915	−	0.999136i	0.273392	−	0.961903i	$-0.411855\pi$
$12$	7.21985	+	1.33579i	0.601655	+	0.111316i
$13$	0.259763	−	0.357533i	0.0199818	−	0.0275026i	−0.798909	−	0.601452i	$-0.794589\pi$
$13$	0.259763	−	0.357533i	0.0199818	−	0.0275026i	0.818891	+	0.573949i	$0.194589\pi$
$14$	−10.4058	−	14.3224i	−0.743275	−	1.02303i
$15$	−5.07180	+	14.1165i	−0.338120	+	0.941103i
$16$	16.0184	+	11.6380i	1.00115	+	0.727376i
$17$	7.94771	+	24.4605i	0.467512	+	1.43885i	0.855795	+	0.517314i	$0.173068\pi$
$17$	7.94771	+	24.4605i	0.467512	+	1.43885i	−0.388283	+	0.921540i	$0.626932\pi$
$18$	14.3706	−	17.7688i	0.798364	−	0.987158i
$19$	−3.70606	−	11.4061i	−0.195056	−	0.600320i	−0.999976	−	0.00693679i	$-0.997792\pi$
$19$	−3.70606	−	11.4061i	−0.195056	−	0.600320i	0.804920	−	0.593383i	$-0.202208\pi$
$20$	8.69531	−	8.61066i	0.434765	−	0.430533i
$21$	−20.7365	+	2.73660i	−0.987455	+	0.130315i
$22$	32.8065	+	10.6595i	1.49121	+	0.484522i
$23$	19.1473	−	13.9113i	0.832491	−	0.604840i	−0.0877718	−	0.996141i	$-0.527975\pi$
$23$	19.1473	−	13.9113i	0.832491	−	0.604840i	0.920263	+	0.391300i	$0.127975\pi$
$24$	10.6729	−	5.09479i	0.444703	−	0.212283i
$25$	14.4961	+	20.3682i	0.579843	+	0.814729i
$26$			1.12216i			0.0431599i
$27$	−10.3558	−	24.9351i	−0.383549	−	0.923521i
$28$	16.2288	+	5.27306i	0.579600	+	0.188324i
$29$	32.2785	+	10.4879i	1.11305	+	0.361653i	0.807112	−	0.590398i	$-0.201029\pi$
$29$	32.2785	+	10.4879i	1.11305	+	0.361653i	0.305941	+	0.952051i	$0.401029\pi$
$30$	−10.6502	−	36.5685i	−0.355006	−	1.21895i
$31$	7.00881	+	21.5709i	0.226091	+	0.695835i	0.998179	+	0.0603203i	$0.0192122\pi$
$31$	7.00881	+	21.5709i	0.226091	+	0.695835i	−0.772088	+	0.635515i	$0.780788\pi$
$32$	−34.5066			−1.07833
$33$	29.5539	−	28.0631i	0.895572	−	0.850398i
$34$	−52.8338	−	38.3860i	−1.55393	−	1.12900i
$35$	−15.9781	+	30.9832i	−0.456517	+	0.885234i
$36$	−1.13908	+	21.9977i	−0.0316410	+	0.611047i
$37$	−24.1765	+	33.2760i	−0.653418	+	0.899353i	−0.999241	−	0.0389470i	$-0.987600\pi$
$37$	−24.1765	+	33.2760i	−0.653418	+	0.899353i	0.345823	+	0.938300i	$0.387600\pi$
$38$	24.6367	+	17.8996i	0.648333	+	0.471042i
$39$	1.16534	+	0.632257i	0.0298805	+	0.0162117i
$40$	3.17866	−	19.4529i	0.0794664	−	0.486323i
$41$	11.1774	−	15.3843i	0.272619	−	0.375227i	−0.650653	−	0.759375i	$-0.725505\pi$
$41$	11.1774	−	15.3843i	0.272619	−	0.375227i	0.923272	+	0.384148i	$0.125505\pi$
$42$	38.5136	−	36.5709i	0.916989	−	0.870735i
$43$		−	40.7478i		−	0.947623i	−0.880626	−	0.473811i	$-0.842878\pi$
$43$		−	40.7478i		−	0.947623i	0.880626	−	0.473811i	$-0.157122\pi$
$44$	−31.6215	+	10.2744i	−0.718670	+	0.233510i
$45$	−43.9763	−	9.54376i	−0.977252	−	0.212084i
$46$	−18.5706	+	57.1545i	−0.403709	+	1.24249i
$47$	−7.83781	+	24.1223i	−0.166762	+	0.513240i	−0.999162	−	0.0409351i	$-0.986966\pi$
$47$	−7.83781	+	24.1223i	−0.166762	+	0.513240i	0.832400	+	0.554175i	$0.186966\pi$
$48$	−28.3266	+	52.2100i	−0.590138	+	1.08771i
$49$	0.389632			0.00795167
$50$	−60.1779	−	20.2060i	−1.20356	−	0.404119i
$51$	−69.6313	+	33.2391i	−1.36532	+	0.651747i
$52$	−0.635761	−	0.875050i	−0.0122262	−	0.0168279i
$53$	−22.0806	+	67.9572i	−0.416616	+	1.28221i	0.494182	+	0.869358i	$0.335468\pi$
$53$	−22.0806	+	67.9572i	−0.416616	+	1.28221i	−0.910798	+	0.412853i	$0.864532\pi$
$54$	58.4888	+	35.7667i	1.08313	+	0.662346i
$55$	−10.2975	−	67.1399i	−0.187228	−	1.22073i
$56$	26.1401	−	8.49344i	0.466788	−	0.151668i
$57$	32.4694	−	15.4996i	0.569639	−	0.271922i
$58$	−81.9612	+	26.6308i	−1.41312	+	0.459152i
$59$	16.0556	−	22.0987i	0.272129	−	0.374554i	−0.650978	−	0.759097i	$-0.725641\pi$
$59$	16.0556	−	22.0987i	0.272129	−	0.374554i	0.923107	+	0.384543i	$0.125641\pi$
$60$	29.0229	+	22.4819i	0.483715	+	0.374699i
$61$	77.8653	−	56.5725i	1.27648	−	0.927418i	0.277040	−	0.960858i	$-0.410647\pi$
$61$	77.8653	−	56.5725i	1.27648	−	0.927418i	0.999441	+	0.0334407i	$0.0106465\pi$
$62$	−46.5923	−	33.8513i	−0.751488	−	0.545988i
$63$	−16.2785	−	60.6007i	−0.258389	−	0.961917i
$64$	6.81151	−	4.94885i	0.106430	−	0.0773258i
$65$	1.97372	−	0.993530i	0.0303649	−	0.0152851i
$66$	−18.8268	+	101.758i	−0.285254	+	1.54178i
$67$	92.0681	−	29.9148i	1.37415	−	0.446489i	0.473409	−	0.880843i	$-0.343023\pi$
$67$	92.0681	−	29.9148i	1.37415	−	0.446489i	0.900742	+	0.434354i	$0.143023\pi$
$68$	62.9471			0.925692
$69$	48.8907	+	51.4878i	0.708561	+	0.746200i
$70$	−13.4194	−	87.4943i	−0.191705	−	1.24992i
$71$	−15.2176	−	4.94450i	−0.214333	−	0.0696409i	0.199883	−	0.979820i	$-0.435944\pi$
$71$	−15.2176	−	4.94450i	−0.214333	−	0.0696409i	−0.414215	+	0.910179i	$0.635944\pi$
$72$	19.3422	+	29.7437i	0.268641	+	0.413106i
$73$	−23.6157	−	32.5042i	−0.323502	−	0.445263i	0.616030	−	0.787723i	$-0.288740\pi$
$73$	−23.6157	−	32.5042i	−0.323502	−	0.445263i	−0.939533	+	0.342460i	$0.888740\pi$
$74$		−	104.440i		−	1.41136i
$75$	−54.8896	+	51.1090i	−0.731861	+	0.681454i
$76$	−29.3526			−0.386218
$77$	76.6270	−	55.6728i	0.995156	−	0.723023i
$78$	−3.33753	+	0.440454i	−0.0427889	+	0.00564685i
$79$	−3.55591	+	10.9440i	−0.0450115	+	0.138531i	−0.971037	−	0.238931i	$-0.923203\pi$
$79$	−3.55591	+	10.9440i	−0.0450115	+	0.138531i	0.926025	+	0.377462i	$0.123203\pi$
$80$	44.5125	+	88.4274i	0.556407	+	1.10534i
$81$	70.0974	−	40.5876i	0.865400	−	0.501081i
$82$			48.2853i			0.588845i
$83$	−9.61536	−	29.5930i	−0.115848	−	0.356543i	0.876275	−	0.481811i	$-0.160021\pi$
$83$	−9.61536	−	29.5930i	−0.115848	−	0.356543i	−0.992123	+	0.125268i	$0.960021\pi$
$84$	−9.31328	+	50.3376i	−0.110872	+	0.599258i
$85$	−20.7380	+	126.913i	−0.243976	+	1.49310i
$86$	60.8159	+	83.7059i	0.707162	+	0.973324i
$87$	−18.5238	+	100.120i	−0.212917	+	1.15080i
$88$	−31.4786	+	43.3265i	−0.357711	+	0.492347i
$89$	−35.6526	−	49.0716i	−0.400591	−	0.551367i	0.560301	−	0.828289i	$-0.310685\pi$
$89$	−35.6526	−	49.0716i	−0.400591	−	0.551367i	−0.960892	+	0.276923i	$0.910685\pi$
$90$	104.582	−	46.0292i	1.16202	−	0.511436i
$91$	2.49276	+	1.81110i	0.0273930	+	0.0199022i
$92$	−17.8998	−	55.0899i	−0.194563	−	0.598803i
$93$	−61.4054	+	29.3124i	−0.660273	+	0.315187i
$94$	−19.9017	−	61.2510i	−0.211720	−	0.651606i
$95$	9.67024	−	59.1804i	0.101792	−	0.622952i
$96$	−13.5441	−	102.630i	−0.141084	−	1.06906i
$97$	−125.919	−	40.9136i	−1.29813	−	0.421789i	−0.423202	−	0.906035i	$-0.639094\pi$
$97$	−125.919	−	40.9136i	−1.29813	−	0.421789i	−0.874932	+	0.484246i	$0.839094\pi$
$98$	−0.800399	+	0.581524i	−0.00816734	+	0.00593392i
$99$	95.0658	+	76.8845i	0.960261	+	0.776612i
$100$	58.3741	−	18.3375i	0.583741	−	0.183375i
$101$		−	182.040i		−	1.80238i	−0.433423	−	0.901191i	$-0.642694\pi$
$101$		−	182.040i		−	1.80238i	0.433423	−	0.901191i	$-0.357306\pi$
$102$	93.4304	−	172.206i	0.915984	−	1.68829i
$103$	33.2817	+	10.8139i	0.323123	+	0.104989i	0.466087	−	0.884739i	$-0.345663\pi$
$103$	33.2817	+	10.8139i	0.323123	+	0.104989i	−0.142964	+	0.989728i	$0.545663\pi$
$104$	−1.65692	−	0.538366i	−0.0159319	−	0.00517660i
$105$	−98.4222	−	35.3612i	−0.937354	−	0.336773i
$106$	−56.0668	−	172.556i	−0.528932	−	1.62789i
$107$	−142.508			−1.33185			−0.665925	−	0.746018i	$-0.731963\pi$
$107$	−142.508			−1.33185			−0.665925	+	0.746018i	$0.731963\pi$
$108$	−65.8729	+	5.24639i	−0.609934	+	0.0485777i
$109$	116.368	+	84.5460i	1.06759	+	0.775651i	0.975478	−	0.220097i	$-0.0706375\pi$
$109$	116.368	+	84.5460i	1.06759	+	0.775651i	0.0921144	+	0.995748i	$0.470637\pi$
$110$	121.360	+	122.553i	1.10327	+	1.11412i
$111$	−108.459	−	58.8448i	−0.977112	−	0.530134i
$112$	−81.1416	+	111.682i	−0.724478	+	0.997159i
$113$	58.5612	+	42.5472i	0.518240	+	0.376524i	0.815941	−	0.578136i	$-0.196220\pi$
$113$	58.5612	+	42.5472i	0.518240	+	0.376524i	−0.297700	+	0.954659i	$0.596220\pi$
$114$	−43.5671	+	80.3004i	−0.382168	+	0.704390i
$115$	116.969	−	17.9400i	1.01712	−	0.156000i
$116$	48.8250	−	67.2018i	0.420905	−	0.579326i
$117$	−1.42306	+	3.71413i	−0.0121629	+	0.0317447i
$118$			69.3590i			0.587788i
$119$	−170.542	+	55.4123i	−1.43312	+	0.465650i
$120$	59.1047	+	1.81859i	0.492540	+	0.0151549i
$121$	−19.6388	+	60.4419i	−0.162304	+	0.499520i
$122$	−75.5202	+	232.427i	−0.619018	+	1.90514i
$123$	50.1434	+	27.2054i	0.407670	+	0.221182i
$124$	55.5109			0.447668
$125$	17.7405	+	123.735i	0.141924	+	0.989878i
$126$	123.886	+	100.193i	0.983225	+	0.795184i
$127$	−104.138	−	143.334i	−0.819984	−	1.12861i	−0.989705	−	0.143119i	$-0.954287\pi$
$127$	−104.138	−	143.334i	−0.819984	−	1.12861i	0.169721	−	0.985492i	$-0.445713\pi$
$128$	36.0461	−	110.939i	0.281610	−	0.866707i
$129$	121.193	−	15.9938i	0.939477	−	0.123983i
$130$	−2.57167	+	4.98672i	−0.0197820	+	0.0383594i
$131$	−110.681	+	35.9623i	−0.844891	+	0.274522i	−0.699304	−	0.714824i	$-0.746507\pi$
$131$	−110.681	+	35.9623i	−0.844891	+	0.274522i	−0.145586	+	0.989346i	$0.546507\pi$
$132$	−42.9700	−	90.0162i	−0.325530	−	0.681941i
$133$	79.5245	−	25.8391i	0.597928	−	0.194279i
$134$	−144.483	+	198.864i	−1.07823	+	1.48406i
$135$	11.1242	−	134.541i	0.0824012	−	0.996599i
$136$	82.0264	−	59.5957i	0.603135	−	0.438203i
$137$	82.1209	+	59.6643i	0.599423	+	0.435506i	0.845674	−	0.533700i	$-0.179199\pi$
$137$	82.1209	+	59.6643i	0.599423	+	0.435506i	−0.246251	+	0.969206i	$0.579199\pi$
$138$	−177.279	−	32.7994i	−1.28463	−	0.237677i
$139$	−13.3673	+	9.71192i	−0.0961677	+	0.0698699i	−0.634830	−	0.772652i	$-0.718930\pi$
$139$	−13.3673	+	9.71192i	−0.0961677	+	0.0698699i	0.538662	+	0.842522i	$0.318930\pi$
$140$	60.0345	+	60.6247i	0.428818	+	0.433033i
$141$	−74.8212	−	13.8431i	−0.530647	−	0.0981783i
$142$	38.6403	−	12.5550i	0.272115	−	0.0884155i
$143$	−6.00370			−0.0419839
$144$	−166.402	−	63.7566i	−1.15557	−	0.442754i
$145$	119.406	+	120.580i	0.823493	+	0.831589i
$146$	97.0248	+	31.5253i	0.664553	+	0.215926i
$147$	0.152933	+	1.15885i	0.00104036	+	0.00788332i
$148$	59.1710	+	81.4419i	0.399804	+	0.550283i
$149$		−	163.472i		−	1.09713i	−0.836109	−	0.548563i	$-0.815175\pi$
$149$		−	163.472i		−	1.09713i	0.836109	−	0.548563i	$-0.184825\pi$
$150$	36.4766	−	186.913i	0.243177	−	1.24609i
$151$	−94.5637			−0.626250			−0.313125	−	0.949712i	$-0.601376\pi$
$151$	−94.5637			−0.626250			−0.313125	+	0.949712i	$0.601376\pi$
$152$	−38.2494	+	27.7898i	−0.251641	+	0.182828i
$153$	−126.191	−	194.052i	−0.824777	−	1.26831i
$154$	−74.3192	+	228.731i	−0.482592	+	1.48527i
$155$	−18.2881	+	111.921i	−0.117988	+	0.722068i
$156$	2.35304	−	2.23435i	0.0150836	−	0.0143228i
$157$		−	105.152i		−	0.669756i	−0.942262	−	0.334878i	$-0.891305\pi$
$157$		−	105.152i		−	0.669756i	0.942262	−	0.334878i	$-0.108695\pi$
$158$	−9.02911	−	27.7887i	−0.0571462	−	0.175878i
$159$	−210.786	−	38.9988i	−1.32570	−	0.245275i
$160$	−153.343	−	79.0793i	−0.958393	−	0.494246i
$161$	96.9913	+	133.497i	0.602431	+	0.829175i
$162$	−83.4204	+	187.997i	−0.514941	+	1.16047i
$163$	−36.7479	+	50.5791i	−0.225447	+	0.310301i	−0.906724	−	0.421725i	$-0.861425\pi$
$163$	−36.7479	+	50.5791i	−0.225447	+	0.310301i	0.681277	+	0.732026i	$0.261425\pi$
$164$	−27.3562	−	37.6525i	−0.166806	−	0.229589i
$165$	195.647	−	56.9799i	1.18574	−	0.345333i
$166$	63.9198	+	46.4404i	0.385059	+	0.279762i
$167$	−37.6809	−	115.970i	−0.225634	−	0.694431i	−0.998227	−	0.0595283i	$-0.981040\pi$
$167$	−37.6809	−	115.970i	−0.225634	−	0.694431i	0.772592	−	0.634902i	$-0.218960\pi$
$168$	35.5215	+	74.4125i	0.211437	+	0.442932i
$169$	52.1635	+	160.543i	0.308660	+	0.949957i
$170$	−146.817	−	291.663i	−0.863629	−	1.71566i
$171$	58.8435	+	90.4873i	0.344114	+	0.529166i
$172$	−94.8476	−	30.8179i	−0.551439	−	0.179174i
$173$	124.504	−	90.4577i	0.719678	−	0.522877i	−0.166603	−	0.986024i	$-0.553280\pi$
$173$	124.504	−	90.4577i	0.719678	−	0.522877i	0.886281	+	0.463147i	$0.153280\pi$
$174$	−111.376	−	233.317i	−0.640092	−	1.34090i
$175$	−142.009	+	101.068i	−0.811483	+	0.577533i
$176$		−	268.980i		−	1.52830i
$177$	72.0281	+	39.0789i	0.406938	+	0.220785i
$178$	146.478	+	47.5937i	0.822912	+	0.267380i
$179$	164.186	+	53.3472i	0.917239	+	0.298029i	0.729334	−	0.684158i	$-0.239830\pi$
$179$	164.186	+	53.3472i	0.917239	+	0.298029i	0.187905	+	0.982187i	$0.439830\pi$
$180$	−55.4744	+	95.1445i	−0.308191	+	0.528581i
$181$	−23.8974	−	73.5485i	−0.132030	−	0.406345i	0.863087	−	0.505056i	$-0.168528\pi$
$181$	−23.8974	−	73.5485i	−0.132030	−	0.406345i	−0.995116	+	0.0987106i	$0.968528\pi$
$182$	−7.82380			−0.0429879
$183$	198.821	+	209.383i	1.08645	+	1.14417i
$184$	−75.4821	−	54.8410i	−0.410229	−	0.298049i
$185$	−183.696	+	92.4690i	−0.992954	+	0.499832i
$186$	82.3931	−	151.862i	0.442973	−	0.816463i
$187$	205.370	−	282.668i	1.09824	−	1.51159i
$188$	50.2211	+	36.4877i	0.267133	+	0.194084i
$189$	173.850	−	72.2019i	0.919842	−	0.382021i
$190$	68.4615	+	136.004i	0.360324	+	0.715810i
$191$	51.5237	−	70.9163i	0.269758	−	0.371290i	−0.652550	−	0.757746i	$-0.726301\pi$
$191$	51.5237	−	70.9163i	0.269758	−	0.371290i	0.922308	+	0.386456i	$0.126301\pi$
$192$	17.3925	+	18.3164i	0.0905860	+	0.0953980i
$193$		−	32.0812i		−	0.166224i	−0.996540	−	0.0831119i	$-0.973514\pi$
$193$		−	32.0812i		−	0.166224i	0.996540	−	0.0831119i	$-0.0264859\pi$
$194$	319.732	−	103.887i	1.64810	−	0.535501i
$195$	3.72967	+	5.48030i	0.0191265	+	0.0281041i
$196$	0.294682	−	0.906937i	0.00150348	−	0.00462723i
$197$	90.4803	−	278.470i	0.459291	−	1.41355i	−0.406732	−	0.913547i	$-0.633332\pi$
$197$	90.4803	−	278.470i	0.459291	−	1.41355i	0.866023	−	0.500004i	$-0.166668\pi$
$198$	−310.038	−	16.0543i	−1.56585	−	0.0810823i
$199$	179.944			0.904241			0.452121	−	0.891957i	$-0.350668\pi$
$199$	179.944			0.904241			0.452121	+	0.891957i	$0.350668\pi$
$200$	58.7061	−	79.1618i	0.293531	−	0.395809i
$201$	125.110	+	262.088i	0.622439	+	1.30392i
$202$	271.695	+	373.956i	1.34502	+	1.85127i
$203$	−73.1231	+	225.050i	−0.360212	+	1.10862i
$204$	24.7072	+	187.218i	0.121114	+	0.917735i
$205$	84.9273	−	42.7506i	0.414280	−	0.208540i
$206$	−84.5083	+	27.4584i	−0.410235	+	0.133293i
$207$	−133.946	+	165.621i	−0.647081	+	0.800100i
$208$	8.32196	−	2.70397i	0.0400094	−	0.0129999i
$209$	−95.7654	+	131.810i	−0.458208	+	0.630669i
$210$	254.960	−	74.2542i	1.21409	−	0.353591i
$211$	−262.367	+	190.621i	−1.24344	+	0.903415i	−0.997823	−	0.0659506i	$-0.978992\pi$
$211$	−262.367	+	190.621i	−1.24344	+	0.903415i	−0.245621	+	0.969366i	$0.578992\pi$
$212$	141.482	+	102.793i	0.667370	+	0.484873i
$213$	8.73297	−	47.2012i	0.0409999	−	0.221602i
$214$	292.746	−	212.693i	1.36797	−	0.993891i
$215$	93.3824	−	181.078i	0.434337	−	0.842224i
$216$	−80.8720	+	69.2023i	−0.374407	+	0.320381i
$217$	−150.395	+	48.8662i	−0.693063	+	0.225190i
$218$	−365.232			−1.67538
$219$	87.4051	−	82.9962i	0.399110	−	0.378978i
$220$	−164.068	−	26.8091i	−0.745764	−	0.121860i
$221$	10.8100	+	3.51237i	0.0489139	+	0.0158931i
$222$	310.628	−	40.9936i	1.39922	−	0.184656i
$223$	−157.480	−	216.752i	−0.706187	−	0.971983i	−0.999871	−	0.0160803i	$-0.994881\pi$
$223$	−157.480	−	216.752i	−0.706187	−	0.971983i	0.293684	−	0.955903i	$-0.405119\pi$
$224$		−	240.584i		−	1.07403i
$225$	−173.554	−	143.193i	−0.771350	−	0.636411i
$226$	−183.800			−0.813276
$227$	−19.7762	+	14.3683i	−0.0871199	+	0.0632963i	−0.630493	−	0.776195i	$-0.717147\pi$
$227$	−19.7762	+	14.3683i	−0.0871199	+	0.0632963i	0.543373	+	0.839492i	$0.317147\pi$
$228$	−11.5211	−	87.3007i	−0.0505311	−	0.382898i
$229$	−54.2684	+	167.021i	−0.236980	+	0.729349i	0.759873	+	0.650072i	$0.225261\pi$
$229$	−54.2684	+	167.021i	−0.236980	+	0.729349i	−0.996853	+	0.0792770i	$0.974739\pi$
$230$	−213.508	+	211.429i	−0.928294	+	0.919256i
$231$	195.659	+	206.053i	0.847010	+	0.892004i
$232$		−	133.796i		−	0.576708i
$233$	28.6275	+	88.1063i	0.122865	+	0.378139i	0.993506	−	0.113780i	$-0.0362958\pi$
$233$	28.6275	+	88.1063i	0.122865	+	0.378139i	−0.870641	+	0.491918i	$0.836296\pi$
$234$	−2.62001	−	9.75365i	−0.0111966	−	0.0416822i
$235$	−90.1117	+	89.2344i	−0.383454	+	0.379721i
$236$	−39.2955	−	54.0856i	−0.166506	−	0.229176i
$237$	−33.9454	−	6.28044i	−0.143229	−	0.0264998i
$238$	267.631	−	368.363i	1.12450	−	1.54774i
$239$	−44.1110	−	60.7136i	−0.184565	−	0.254032i	0.706702	−	0.707512i	$-0.250182\pi$
$239$	−44.1110	−	60.7136i	−0.184565	−	0.254032i	−0.891266	+	0.453480i	$0.850182\pi$
$240$	−245.530	+	167.098i	−1.02304	+	0.696242i
$241$	−25.5230	−	18.5436i	−0.105905	−	0.0769443i	0.533572	−	0.845754i	$-0.320849\pi$
$241$	−25.5230	−	18.5436i	−0.105905	−	0.0769443i	−0.639477	+	0.768810i	$0.720849\pi$
$242$	−49.8665	−	153.473i	−0.206060	−	0.634187i
$243$	148.230	+	192.554i	0.609999	+	0.792402i
$244$	−72.7922	−	224.031i	−0.298329	−	0.918161i
$245$	1.73148	+	0.892926i	0.00706725	+	0.00364460i
$246$	−143.611	+	18.9523i	−0.583784	+	0.0770420i
$247$	−5.04075	−	1.63784i	−0.0204079	−	0.00663093i
$248$	72.3363	−	52.5554i	0.291679	−	0.211917i
$249$	84.2419	−	40.2136i	0.338321	−	0.161500i
$250$	−221.117	−	227.704i	−0.884467	−	0.910814i
$251$			349.893i			1.39400i	0.717072	+	0.696999i	$0.245482\pi$
$251$			349.893i			1.39400i	−0.717072	+	0.696999i	$0.754518\pi$
$252$	−153.370	−	7.94177i	−0.608613	−	0.0315150i
$253$	−305.785	−	99.3555i	−1.20864	−	0.392710i
$254$	427.850	+	139.017i	1.68445	+	0.547310i
$255$	−385.607	−	11.8647i	−1.51219	−	0.0465284i
$256$	101.935	+	313.723i	0.398183	+	1.22548i
$257$	5.11640			0.0199082			0.00995408	−	0.999950i	$-0.496831\pi$
$257$	5.11640			0.0199082			0.00995408	+	0.999950i	$0.496831\pi$
$258$	−225.088	+	213.735i	−0.872436	+	0.828428i
$259$	−232.004	−	168.561i	−0.895770	−	0.650815i
$260$	−0.819876	−	5.34560i	−0.00315337	−	0.0205600i
$261$	−305.048	−	15.7959i	−1.16877	−	0.0605207i
$262$	173.691	−	239.066i	0.662945	−	0.912465i
$263$	239.867	+	174.274i	0.912043	+	0.662638i	0.941531	−	0.336927i	$-0.109387\pi$
$263$	239.867	+	174.274i	0.912043	+	0.662638i	−0.0294874	+	0.999565i	$0.509387\pi$
$264$	−141.218	−	76.6180i	−0.534916	−	0.290220i
$265$	−253.862	+	251.391i	−0.957970	+	0.948644i
$266$	−124.798	+	171.770i	−0.469165	+	0.645751i
$267$	131.956	−	125.299i	0.494215	−	0.469286i
$268$		−	236.929i		−	0.884065i
$269$	−217.290	+	70.6018i	−0.807769	+	0.262460i	−0.683653	−	0.729808i	$-0.739610\pi$
$269$	−217.290	+	70.6018i	−0.807769	+	0.262460i	−0.124116	+	0.992268i	$0.539610\pi$
$270$	177.950	+	292.983i	0.659074	+	1.08512i
$271$	77.2828	−	237.852i	0.285176	−	0.877682i	−0.701170	−	0.712995i	$-0.747338\pi$
$271$	77.2828	−	237.852i	0.285176	−	0.877682i	0.986346	−	0.164688i	$-0.0526616\pi$
$272$	−157.363	+	484.313i	−0.578540	+	1.78056i
$273$	−4.40816	+	8.12488i	−0.0161471	+	0.0297615i
$274$	−257.745			−0.940676
$275$	108.105	−	321.961i	0.393108	−	1.17077i
$276$	156.823	−	74.8610i	0.568200	−	0.271235i
$277$	194.827	+	268.157i	0.703348	+	0.968075i	0.999915	+	0.0130633i	$0.00415828\pi$
$277$	194.827	+	268.157i	0.703348	+	0.968075i	−0.296567	+	0.955012i	$0.595842\pi$
$278$	12.9647	−	39.9013i	0.0466357	−	0.143530i
$279$	−111.283	−	171.127i	−0.398865	−	0.613360i
$280$	135.628	+	22.1620i	0.484386	+	0.0791499i
$281$	−460.102	+	149.496i	−1.63737	+	0.532015i	−0.975949	−	0.217998i	$-0.930047\pi$
$281$	−460.102	+	149.496i	−1.63737	+	0.532015i	−0.661423	+	0.750013i	$0.730047\pi$
$282$	174.362	−	83.2332i	0.618305	−	0.295153i
$283$	473.697	−	153.914i	1.67384	−	0.543864i	0.690141	−	0.723675i	$-0.257549\pi$
$283$	473.697	−	153.914i	1.67384	−	0.543864i	0.983701	+	0.179811i	$0.0575487\pi$
$284$	−23.0184	+	31.6821i	−0.0810506	+	0.111557i
$285$	179.811	+	5.53259i	0.630915	+	0.0194126i
$286$	12.3331	−	8.96049i	0.0431226	−	0.0313304i
$287$	107.261	+	77.9298i	0.373732	+	0.271533i
$288$	299.927	−	80.5659i	1.04141	−	0.279743i
$289$	−301.345	+	218.940i	−1.04272	+	0.757579i
$290$	−425.256	−	69.4879i	−1.46640	−	0.239613i
$291$	72.2615	−	390.569i	0.248321	−	1.34216i
$292$	−93.5199	+	30.3865i	−0.320274	+	0.104063i
$293$	−340.665			−1.16268			−0.581339	−	0.813662i	$-0.697471\pi$
$293$	−340.665			−1.16268			−0.581339	+	0.813662i	$0.697471\pi$
$294$	−2.04374	−	2.15230i	−0.00695149	−	0.00732076i
$295$	121.993	−	61.4088i	0.413536	−	0.208165i
$296$	154.212	+	50.1064i	0.520985	+	0.169278i
$297$	−191.357	+	312.924i	−0.644299	+	1.05361i
$298$	243.981	+	335.811i	0.818728	+	1.12688i
$299$		−	10.4595i		−	0.0349814i
$300$	77.4518	+	166.419i	0.258173	+	0.554731i
$301$	284.098			0.943848
$302$	194.257	−	141.136i	0.643235	−	0.467338i
$303$	541.427	−	71.4522i	1.78689	−	0.235816i
$304$	73.3792	−	225.838i	0.241379	−	0.742888i
$305$	475.672	−	72.9557i	1.55958	−	0.239199i
$306$	548.848	+	210.290i	1.79362	+	0.687222i
$307$			206.808i			0.673641i	0.941569	+	0.336821i	$0.109352\pi$
$307$			206.808i			0.673641i	−0.941569	+	0.336821i	$0.890648\pi$
$308$	−71.6346	−	220.469i	−0.232580	−	0.715807i
$309$	−19.0995	+	103.231i	−0.0618105	+	0.334082i
$310$	−129.473	−	257.207i	−0.417654	−	0.829701i
$311$	114.814	+	158.028i	0.369177	+	0.508128i	0.952677	−	0.303985i	$-0.0983172\pi$
$311$	114.814	+	158.028i	0.369177	+	0.508128i	−0.583500	+	0.812113i	$0.698317\pi$
$312$	0.950862	−	5.13935i	0.00304764	−	0.0164723i
$313$	−277.776	+	382.326i	−0.887464	+	1.22149i	0.0868331	+	0.996223i	$0.472325\pi$
$313$	−277.776	+	382.326i	−0.887464	+	1.22149i	−0.974297	+	0.225267i	$0.927675\pi$
$314$	156.938	+	216.007i	0.499804	+	0.687921i
$315$	66.5402	−	306.608i	0.211239	−	0.973358i
$316$	22.7846	+	16.5540i	0.0721032	+	0.0523860i
$317$	15.1899	+	46.7499i	0.0479178	+	0.147476i	0.972153	−	0.234349i	$-0.0752958\pi$
$317$	15.1899	+	46.7499i	0.0479178	+	0.147476i	−0.924235	+	0.381825i	$0.875296\pi$
$318$	491.211	−	234.484i	1.54469	−	0.737371i
$319$	−142.479	−	438.504i	−0.446641	−	1.37462i
$320$	41.6109	−	6.38203i	0.130034	−	0.0199438i
$321$	−55.9354	−	423.849i	−0.174254	−	1.32040i
$322$	−398.488	−	129.477i	−1.23754	−	0.402101i
$323$	249.544	−	181.304i	0.772582	−	0.561314i
$324$	−41.4595	−	193.861i	−0.127961	−	0.598335i
$325$	11.0479	+	0.108085i	0.0339934	+	0.000332570i
$326$		−	158.748i		−	0.486957i
$327$	−205.783	+	379.287i	−0.629305	+	1.15990i
$328$	−71.2957	−	23.1654i	−0.217365	−	0.0706262i
$329$	−168.183	−	54.6461i	−0.511196	−	0.166098i
$330$	−316.863	+	409.052i	−0.960192	+	1.23955i
$331$	6.07919	+	18.7098i	0.0183661	+	0.0565252i	0.959820	−	0.280618i	$-0.0905394\pi$
$331$	6.07919	+	18.7098i	0.0183661	+	0.0565252i	−0.941453	+	0.337143i	$0.890539\pi$
$332$	−76.1551			−0.229383
$333$	132.446	−	345.678i	0.397736	−	1.03807i
$334$	250.490	+	181.992i	0.749971	+	0.544886i
$335$	477.696	+	78.0567i	1.42596	+	0.233005i
$336$	−364.014	−	197.496i	−1.08338	−	0.587787i
$337$	274.595	−	377.948i	0.814822	−	1.12151i	−0.175739	−	0.984437i	$-0.556232\pi$
$337$	274.595	−	377.948i	0.814822	−	1.12151i	0.990561	−	0.137070i	$-0.0437684\pi$
$338$	−346.766	−	251.940i	−1.02594	−	0.745385i
$339$	−103.559	+	190.873i	−0.305483	+	0.563048i
$340$	279.729	+	144.257i	0.822732	+	0.424285i
$341$	181.109	−	249.275i	0.531112	−	0.731013i
$342$	−255.931	−	98.0593i	−0.748336	−	0.286723i
$343$			344.350i			1.00394i
$344$	−152.773	+	49.6390i	−0.444108	+	0.144299i
$345$	99.2686	+	340.849i	0.287735	+	0.987969i
$346$	−120.755	+	371.644i	−0.349002	+	1.07412i
$347$	79.0960	−	243.432i	0.227942	−	0.701534i	−0.770037	−	0.637999i	$-0.779762\pi$
$347$	79.0960	−	243.432i	0.227942	−	0.701534i	0.997980	−	0.0635354i	$-0.0202376\pi$
$348$	219.037	+	118.839i	0.629416	+	0.341491i
$349$	−17.4643			−0.0500411			−0.0250205	−	0.999687i	$-0.507965\pi$
$349$	−17.4643			−0.0500411			−0.0250205	+	0.999687i	$0.507965\pi$
$350$	140.878	−	419.567i	0.402509	−	1.19876i
$351$	−11.6052	−	2.77466i	−0.0330632	−	0.00790502i
$352$	275.537	+	379.245i	0.782776	+	1.07740i
$353$	−22.0131	+	67.7494i	−0.0623601	+	0.191925i	−0.977383	−	0.211478i	$-0.932172\pi$
$353$	−22.0131	+	67.7494i	−0.0623601	+	0.191925i	0.915023	+	0.403402i	$0.132172\pi$
$354$	−206.288	+	27.2239i	−0.582735	+	0.0769037i
$355$	−56.2938	−	56.8472i	−0.158574	−	0.160133i
$356$	−141.187	+	45.8745i	−0.396593	+	0.128861i
$357$	−231.747	−	485.477i	−0.649151	−	1.35988i
$358$	−416.898	+	135.458i	−1.16452	+	0.378375i
$359$	90.9521	−	125.185i	0.253348	−	0.348704i	−0.663332	−	0.748325i	$-0.730858\pi$
$359$	90.9521	−	125.185i	0.253348	−	0.348704i	0.916680	+	0.399621i	$0.130858\pi$
$360$	17.7902	+	176.504i	0.0494171	+	0.490289i
$361$	175.691	−	127.647i	0.486680	−	0.353594i
$362$	158.862	+	115.420i	0.438845	+	0.318840i
$363$	−187.475	−	34.6860i	−0.516461	−	0.0955536i
$364$	6.10094	−	4.43260i	0.0167608	−	0.0121775i
$365$	−30.4547	−	198.565i	−0.0834376	−	0.544014i
$366$	−720.930	−	133.384i	−1.96976	−	0.364437i
$367$	−421.585	+	136.981i	−1.14873	+	0.373246i	−0.820666	−	0.571408i	$-0.806397\pi$
$367$	−421.585	+	136.981i	−1.14873	+	0.373246i	−0.328067	+	0.944654i	$0.606397\pi$
$368$	468.608			1.27339
$369$	−61.2329	+	159.815i	−0.165943	+	0.433104i
$370$	239.348	−	464.120i	0.646886	−	1.25438i
$371$	−473.805	−	153.949i	−1.27710	−	0.414956i
$372$	21.7884	+	165.101i	0.0585710	+	0.443820i
$373$	−77.8079	−	107.093i	−0.208600	−	0.287114i	0.691878	−	0.722014i	$-0.256784\pi$
$373$	−77.8079	−	107.093i	−0.208600	−	0.287114i	−0.900478	+	0.434901i	$0.856784\pi$
$374$			887.184i			2.37215i
$375$	−361.050	+	101.331i	−0.962800	+	0.270216i
$376$	99.9882			0.265926
$377$	12.1346	−	8.81628i	0.0321872	−	0.0233854i
$378$	−249.369	+	407.791i	−0.659708	+	1.07881i
$379$	128.165	−	394.451i	0.338166	−	1.04077i	−0.626976	−	0.779039i	$-0.715707\pi$
$379$	128.165	−	394.451i	0.338166	−	1.04077i	0.965141	−	0.261729i	$-0.0842926\pi$
$380$	−130.439	−	67.2678i	−0.343261	−	0.177020i
$381$	385.430	−	365.988i	1.01163	−	0.960598i
$382$			222.578i			0.582666i
$383$	−101.612	−	312.730i	−0.265306	−	0.816527i	−0.991623	−	0.129167i	$-0.958770\pi$
$383$	−101.612	−	312.730i	−0.265306	−	0.816527i	0.726317	−	0.687360i	$-0.241230\pi$
$384$	344.103	+	63.6646i	0.896102	+	0.165793i
$385$	468.107	−	71.7955i	1.21586	−	0.186482i
$386$	47.8811	+	65.9026i	0.124044	+	0.170732i
$387$	95.1379	+	354.175i	0.245834	+	0.915180i
$388$	−190.467	+	262.155i	−0.490894	+	0.675658i
$389$	−88.8453	−	122.285i	−0.228394	−	0.314358i	0.679404	−	0.733764i	$-0.262238\pi$
$389$	−88.8453	−	122.285i	−0.228394	−	0.314358i	−0.907799	+	0.419406i	$0.862238\pi$
$390$	−15.8410	−	5.69135i	−0.0406179	−	0.0145932i
$391$	492.455	+	357.790i	1.25948	+	0.915063i
$392$	−0.474650	−	1.46082i	−0.00121084	−	0.00372659i
$393$	−150.403	−	315.072i	−0.382704	−	0.801711i
$394$	229.746	+	707.086i	0.583112	+	1.79463i
$395$	−40.8825	+	40.4845i	−0.103500	+	0.102492i
$396$	250.861	−	163.134i	0.633488	−	0.411954i
$397$	−559.798	−	181.889i	−1.41007	−	0.458159i	−0.497637	−	0.867386i	$-0.665799\pi$
$397$	−559.798	−	181.889i	−1.41007	−	0.458159i	−0.912433	+	0.409226i	$0.865799\pi$
$398$	−369.649	+	268.566i	−0.928766	+	0.674788i
$399$	108.065	+	226.381i	0.270839	+	0.567370i
$400$	−4.84247	+	494.971i	−0.0121062	+	1.23743i
$401$			28.4184i			0.0708688i	0.999372	+	0.0354344i	$0.0112815\pi$
$401$			28.4184i			0.0708688i	−0.999372	+	0.0354344i	$0.988719\pi$
$402$	−648.173	−	351.667i	−1.61237	−	0.874794i
$403$	9.53295	+	3.09744i	0.0236550	+	0.00768596i
$404$	−423.731	−	137.679i	−1.04884	−	0.340789i
$405$	404.519	−	19.7227i	0.998814	−	0.0486979i
$406$	−185.673	−	571.443i	−0.457323	−	1.40749i
$407$	558.771			1.37290
$408$	209.446	+	220.572i	0.513348	+	0.540618i
$409$	−208.962	−	151.820i	−0.510910	−	0.371198i	0.302258	−	0.953226i	$-0.402259\pi$
$409$	−208.962	−	151.820i	−0.510910	−	0.371198i	−0.813169	+	0.582028i	$0.802259\pi$
$410$	−110.656	+	214.574i	−0.269893	+	0.523351i
$411$	−145.221	+	267.664i	−0.353337	+	0.651250i
$412$	50.3423	−	69.2903i	0.122190	−	0.168180i
$413$	154.074	+	111.942i	0.373061	+	0.271045i
$414$	27.9693	−	540.139i	0.0675587	−	1.30468i
$415$	25.0894	−	153.543i	0.0604564	−	0.369984i
$416$	−8.96354	+	12.3373i	−0.0215470	+	0.0296569i
$417$	−34.1321	−	35.9452i	−0.0818515	−	0.0861996i
$418$		−	413.699i		−	0.989710i
$419$	225.854	−	73.3843i	0.539030	−	0.175141i	−0.0268343	−	0.999640i	$-0.508543\pi$
$419$	225.854	−	73.3843i	0.539030	−	0.175141i	0.565864	+	0.824498i	$0.308543\pi$
$420$	−156.747	+	202.351i	−0.373206	+	0.481788i
$421$	132.441	−	407.611i	0.314586	−	0.968197i	−0.661338	−	0.750088i	$-0.730011\pi$
$421$	132.441	−	407.611i	0.314586	−	0.968197i	0.975924	−	0.218109i	$-0.0699889\pi$
$422$	254.465	−	783.163i	0.602997	−	1.85584i
$423$	11.8045	−	227.968i	0.0279067	−	0.538931i
$424$	281.686			0.664354
$425$	−383.007	+	516.462i	−0.901192	+	1.21520i
$426$	52.5079	+	109.997i	0.123258	+	0.258208i
$427$	394.430	+	542.886i	0.923723	+	1.27140i
$428$	−107.780	+	331.712i	−0.251822	+	0.775029i
$429$	−2.35649	−	17.8563i	−0.00549299	−	0.0416230i
$430$	78.4280	+	511.351i	0.182391	+	1.18919i
$431$	−631.269	+	205.112i	−1.46466	+	0.475898i	−0.929491	−	0.368846i	$-0.879753\pi$
$431$	−631.269	+	205.112i	−1.46466	+	0.475898i	−0.535172	+	0.844743i	$0.679753\pi$
$432$	124.312	−	519.940i	0.287758	−	1.20356i
$433$	−559.669	+	181.848i	−1.29254	+	0.419971i	−0.872980	−	0.487756i	$-0.837815\pi$
$433$	−559.669	+	181.848i	−1.29254	+	0.419971i	−0.419559	+	0.907728i	$0.637815\pi$
$434$	236.015	−	324.847i	0.543813	−	0.748495i
$435$	−311.764	+	402.469i	−0.716698	+	0.925216i
$436$	284.805	−	206.923i	0.653223	−	0.474594i
$437$	−229.635	−	166.839i	−0.525480	−	0.381783i
$438$	−55.6799	+	300.946i	−0.127123	+	0.687092i
$439$	−248.454	+	180.512i	−0.565954	+	0.411190i	−0.833633	−	0.552318i	$-0.813743\pi$
$439$	−248.454	+	180.512i	−0.565954	+	0.411190i	0.267679	+	0.963508i	$0.413743\pi$
$440$	−239.179	+	120.398i	−0.543589	+	0.273631i
$441$	−3.38663	+	0.909712i	−0.00767944	+	0.00206284i
$442$	−27.4485	+	8.91857i	−0.0621008	+	0.0201778i
$443$	−567.297			−1.28058			−0.640290	−	0.768133i	$-0.721186\pi$
$443$	−567.297			−1.28058			−0.640290	+	0.768133i	$0.721186\pi$
$444$	−219.000	+	207.954i	−0.493244	+	0.468364i
$445$	−45.9775	−	299.774i	−0.103320	−	0.673649i
$446$	647.003	+	210.224i	1.45068	+	0.471355i
$447$	486.200	−	64.1639i	1.08770	−	0.143543i
$448$	34.5040	+	47.4906i	0.0770178	+	0.106006i
$449$		−	21.4607i		−	0.0477967i	−0.999714	−	0.0238983i	$-0.992392\pi$
$449$		−	21.4607i		−	0.0477967i	0.999714	−	0.0238983i	$-0.00760780\pi$
$450$	570.236	+	35.1244i	1.26719	+	0.0780542i
$451$	−258.333			−0.572801
$452$	143.326	−	104.133i	0.317093	−	0.230382i
$453$	−37.1169	−	281.253i	−0.0819359	−	0.620867i
$454$	19.1806	−	59.0318i	0.0422480	−	0.130026i
$455$	6.92701	+	13.7610i	0.0152242	+	0.0302440i
$456$	−97.6659	−	102.854i	−0.214180	−	0.225557i
$457$			442.410i			0.968075i	0.875047	+	0.484037i	$0.160830\pi$
$457$			442.410i			0.968075i	−0.875047	+	0.484037i	$0.839170\pi$
$458$	−137.797	−	424.097i	−0.300868	−	0.925976i
$459$	527.620	−	451.485i	1.14950	−	0.983628i
$460$	46.7060	−	285.834i	0.101535	−	0.621378i
$461$	270.395	+	372.166i	0.586540	+	0.807303i	0.994393	−	0.105745i	$-0.0337227\pi$
$461$	270.395	+	372.166i	0.586540	+	0.807303i	−0.407854	+	0.913047i	$0.633723\pi$
$462$	−709.465	−	131.263i	−1.53564	−	0.284118i
$463$	110.953	−	152.714i	0.239640	−	0.329836i	−0.672209	−	0.740361i	$-0.734655\pi$
$463$	110.953	−	152.714i	0.239640	−	0.329836i	0.911849	+	0.410525i	$0.134655\pi$
$464$	394.990	+	543.658i	0.851272	+	1.17168i
$465$	−340.054	−	10.4631i	−0.731299	−	0.0225013i
$466$	−190.306	−	138.266i	−0.408382	−	0.296707i
$467$	38.8708	+	119.632i	0.0832352	+	0.256172i	0.984010	−	0.178116i	$-0.0570002\pi$
$467$	38.8708	+	119.632i	0.0832352	+	0.256172i	−0.900774	+	0.434288i	$0.857000\pi$
$468$	7.56902	+	6.12145i	0.0161731	+	0.0130800i
$469$	208.569	+	641.910i	0.444710	+	1.36868i
$470$	51.9295	−	317.801i	0.110488	−	0.676172i
$471$	312.743	−	41.2728i	0.663999	−	0.0876280i
$472$	−102.412	−	33.2757i	−0.216975	−	0.0704994i
$473$	−447.839	+	325.374i	−0.946805	+	0.687894i
$474$	79.1056	−	37.7618i	0.166889	−	0.0796662i
$475$	178.598	−	240.829i	0.375996	−	0.507009i
$476$			438.874i			0.922004i
$477$	33.2557	−	642.229i	0.0697184	−	1.34639i
$478$	181.229	+	58.8850i	0.379141	+	0.123190i
$479$	518.995	+	168.632i	1.08350	+	0.352049i	0.795730	−	0.605651i	$-0.207087\pi$
$479$	518.995	+	168.632i	1.08350	+	0.352049i	0.287766	+	0.957701i	$0.407087\pi$
$480$	175.010	−	487.114i	0.364605	−	1.01482i
$481$	5.61714	+	17.2878i	0.0116781	+	0.0359413i
$482$	80.1068			0.166197
$483$	−358.979	+	340.871i	−0.743228	+	0.705738i
$484$	125.836	+	91.4253i	0.259992	+	0.188895i
$485$	−465.806	−	470.386i	−0.960425	−	0.969867i
$486$	−591.886	−	174.320i	−1.21787	−	0.358683i
$487$	−183.292	+	252.279i	−0.376369	+	0.518027i	−0.954618	−	0.297833i	$-0.903736\pi$
$487$	−183.292	+	252.279i	−0.376369	+	0.518027i	0.578249	+	0.815860i	$0.303736\pi$
$488$	−306.959	−	223.019i	−0.629015	−	0.457006i
$489$	−164.857	−	89.4433i	−0.337130	−	0.182911i
$490$	−4.88956	+	0.749932i	−0.00997870	+	0.00153047i
$491$	207.347	−	285.389i	0.422296	−	0.581241i	−0.543867	−	0.839171i	$-0.683041\pi$
$491$	207.347	−	285.389i	0.422296	−	0.581241i	0.966163	+	0.257931i	$0.0830406\pi$
$492$	101.249	−	96.1419i	0.205791	−	0.195410i
$493$			872.905i			1.77060i
$494$	12.7994	−	4.15878i	0.0259097	−	0.00841858i
$495$	246.263	+	559.529i	0.497501	+	1.13036i
$496$	−138.773	+	427.099i	−0.279784	+	0.861087i
$497$	34.4736	−	106.099i	0.0693634	−	0.213479i
$498$	−113.035	+	208.339i	−0.226977	+	0.418352i
$499$	80.4065			0.161135			0.0805677	−	0.996749i	$-0.474327\pi$
$499$	80.4065			0.161135			0.0805677	+	0.996749i	$0.474327\pi$
$500$	301.431	+	52.2873i	0.602863	+	0.104575i
$501$	330.129	−	157.590i	0.658940	−	0.314551i
$502$	−522.214	−	718.766i	−1.04027	−	1.43181i
$503$	−154.019	+	474.023i	−0.306201	+	0.942391i	0.673025	+	0.739620i	$0.264995\pi$
$503$	−154.019	+	474.023i	−0.306201	+	0.942391i	−0.979226	+	0.202771i	$0.935005\pi$
$504$	−207.376	+	134.856i	−0.411461	+	0.267571i
$505$	417.185	−	808.965i	0.826110	−	1.60191i
$506$	776.444	−	252.282i	1.53448	−	0.498581i
$507$	−457.014	+	218.160i	−0.901408	+	0.430295i
$508$	−412.394	+	133.995i	−0.811800	+	0.263770i
$509$	137.249	−	188.907i	0.269645	−	0.371134i	−0.652625	−	0.757681i	$-0.726332\pi$
$509$	137.249	−	188.907i	0.269645	−	0.371134i	0.922270	+	0.386547i	$0.126332\pi$
$510$	809.840	−	551.144i	1.58792	−	1.08067i
$511$	226.623	−	164.651i	0.443489	−	0.322214i
$512$	−300.150	−	218.071i	−0.586230	−	0.425921i
$513$	−246.032	+	210.530i	−0.479594	+	0.410390i
$514$	−10.5103	+	7.63620i	−0.0204481	+	0.0148564i
$515$	123.117	+	124.328i	0.239063	+	0.241413i
$516$	54.4305	−	294.193i	0.105485	−	0.570142i
$517$	327.702	−	106.477i	0.633852	−	0.205951i
$518$	728.170			1.40573
$519$	317.909	+	334.797i	0.612542	+	0.645081i
$520$	−6.12937	−	6.18963i	−0.0117873	−	0.0119031i
$521$	216.308	+	70.2826i	0.415178	+	0.134899i	0.509155	−	0.860675i	$-0.329958\pi$
$521$	216.308	+	70.2826i	0.415178	+	0.134899i	−0.0939771	+	0.995574i	$0.529958\pi$
$522$	650.219	−	422.835i	1.24563	−	0.810028i
$523$	−146.764	−	202.004i	−0.280620	−	0.386241i	0.645319	−	0.763913i	$-0.276725\pi$
$523$	−146.764	−	202.004i	−0.280620	−	0.386241i	−0.925939	+	0.377672i	$0.876725\pi$
$524$			284.827i			0.543563i
$525$	−356.338	−	382.696i	−0.678739	−	0.728945i
$526$	−752.849			−1.43127
$527$	−471.932	+	342.878i	−0.895506	+	0.650623i
$528$	800.004	−	105.577i	1.51516	−	0.199956i
$529$	9.62402	−	29.6197i	0.0181929	−	0.0559918i
$530$	146.295	−	895.306i	0.276029	−	1.68926i
$531$	−87.9575	+	229.565i	−0.165645	+	0.432327i
$532$		−	204.649i		−	0.384679i
$533$	−2.59694	−	7.99256i	−0.00487231	−	0.0149954i
$534$	−84.0600	+	454.339i	−0.157416	+	0.850821i
$535$	−633.288	−	326.588i	−1.18372	−	0.610445i
$536$	−224.315	−	308.743i	−0.418498	−	0.576013i
$537$	−94.2218	+	509.262i	−0.175460	+	0.948347i
$538$	340.994	−	469.337i	0.633817	−	0.872374i
$539$	−3.11124	−	4.28225i	−0.00577224	−	0.00794481i
$540$	−304.754	−	127.648i	−0.564360	−	0.236385i
$541$	95.2741	+	69.2207i	0.176107	+	0.127950i	0.672347	−	0.740236i	$-0.265286\pi$
$541$	95.2741	+	69.2207i	0.176107	+	0.127950i	−0.496240	+	0.868186i	$0.665286\pi$
$542$	196.235	+	603.950i	0.362058	+	1.11430i
$543$	209.369	−	99.9441i	0.385578	−	0.184059i
$544$	−274.248	−	844.049i	−0.504133	−	1.55156i
$545$	323.368	+	642.393i	0.593335	+	1.17870i
$546$	−3.07090	−	23.2696i	−0.00562436	−	0.0426184i
$547$	689.808	+	224.132i	1.26108	+	0.409748i	0.861877	−	0.507117i	$-0.169289\pi$
$547$	689.808	+	224.132i	1.26108	+	0.409748i	0.399198	+	0.916865i	$0.369289\pi$
$548$	200.988	−	146.026i	0.366766	−	0.266471i
$549$	−544.710	+	673.521i	−0.992187	+	1.22681i
$550$	258.451	+	822.731i	0.469911	+	1.49588i
$551$		−	407.040i		−	0.738730i
$552$	133.481	−	246.025i	0.241814	−	0.445698i
$553$	−76.3025	−	24.7922i	−0.137979	−	0.0448322i
$554$	−800.446	−	260.081i	−1.44485	−	0.469460i
$555$	−347.125	−	510.058i	−0.625450	−	0.919023i
$556$	12.4964	+	38.4600i	0.0224755	+	0.0691726i
$557$	66.5010			0.119391			0.0596957	−	0.998217i	$-0.480987\pi$
$557$	66.5010			0.119391			0.0596957	+	0.998217i	$0.480987\pi$
$558$	484.010	+	185.447i	0.867402	+	0.332343i
$559$	−14.5687	−	10.5848i	−0.0260621	−	0.0189352i
$560$	−616.526	+	310.347i	−1.10094	+	0.554190i
$561$	921.324	+	499.866i	1.64229	+	0.891027i
$562$	722.039	−	993.801i	1.28477	−	1.76833i
$563$	−420.897	−	305.800i	−0.747598	−	0.543161i	0.147484	−	0.989064i	$-0.452883\pi$
$563$	−420.897	−	305.800i	−0.747598	−	0.543161i	−0.895081	+	0.445903i	$0.852883\pi$
$564$	−88.8102	+	163.690i	−0.157465	+	0.290230i
$565$	162.732	+	323.280i	0.288022	+	0.572177i
$566$	−743.374	+	1023.17i	−1.31338	+	1.80772i
$567$	282.981	+	488.727i	0.499085	+	0.861953i
$568$			63.0778i			0.111053i
$569$	364.152	−	118.320i	0.639985	−	0.207944i	0.0289921	−	0.999580i	$-0.490770\pi$
$569$	364.152	−	118.320i	0.639985	−	0.207944i	0.610993	+	0.791636i	$0.290770\pi$
$570$	−377.633	+	257.002i	−0.662513	+	0.450880i
$571$	−276.902	+	852.217i	−0.484942	+	1.49250i	0.347122	+	0.937820i	$0.387159\pi$
$571$	−276.902	+	852.217i	−0.484942	+	1.49250i	−0.832065	+	0.554679i	$0.812841\pi$
$572$	−4.54064	+	13.9747i	−0.00793818	+	0.0244312i
$573$	231.144	+	125.407i	0.403392	+	0.218861i
$574$	−336.651			−0.586499
$575$	560.909	+	188.337i	0.975494	+	0.327542i
$576$	−47.6502	+	58.9183i	−0.0827261	+	0.102289i
$577$	−518.759	−	714.010i	−0.899062	−	1.23745i	−0.970766	−	0.240026i	$-0.922844\pi$
$577$	−518.759	−	714.010i	−0.899062	−	1.23745i	0.0717049	−	0.997426i	$-0.477156\pi$
$578$	292.270	−	899.513i	0.505657	−	1.55625i
$579$	95.4163	−	12.5921i	0.164795	−	0.0217480i
$580$	370.980	−	186.744i	0.639620	−	0.321972i
$581$	206.326	−	67.0394i	0.355122	−	0.115386i
$582$	434.479	+	910.174i	0.746528	+	1.56387i
$583$	923.199	−	299.965i	1.58353	−	0.514520i
$584$	−93.0973	+	128.137i	−0.159413	+	0.219413i
$585$	−14.8356	+	13.2439i	−0.0253601	+	0.0226391i
$586$	699.808	−	508.440i	1.19421	−	0.867646i
$587$	−313.505	−	227.774i	−0.534079	−	0.388031i	0.287802	−	0.957690i	$-0.407075\pi$
$587$	−313.505	−	227.774i	−0.534079	−	0.388031i	−0.821881	+	0.569659i	$0.807075\pi$
$588$	2.81309	+	0.520466i	0.00478416	+	0.000885147i
$589$	220.064	−	159.886i	0.373624	−	0.271453i
$590$	−158.951	+	308.223i	−0.269409	+	0.522411i
$591$	863.742	+	159.806i	1.46149	+	0.270400i
$592$	−774.534	+	251.661i	−1.30834	+	0.425104i
$593$	134.959			0.227586			0.113793	−	0.993504i	$-0.463700\pi$
$593$	134.959			0.227586			0.113793	+	0.993504i	$0.463700\pi$
$594$	−73.9433	−	928.421i	−0.124484	−	1.56300i
$595$	−884.855	−	144.588i	−1.48715	−	0.243004i
$596$	−380.509	−	123.635i	−0.638439	−	0.207441i
$597$	70.6293	+	535.192i	0.118307	+	0.896469i
$598$	15.6107	+	21.4863i	0.0261048	+	0.0359302i
$599$		−	279.184i		−	0.466083i	−0.972467	−	0.233041i	$-0.925132\pi$
$599$		−	279.184i		−	0.466083i	0.972467	−	0.233041i	$-0.0748678\pi$
$600$	258.486	+	143.533i	0.430811	+	0.239222i
$601$	−135.279			−0.225089			−0.112545	−	0.993647i	$-0.535900\pi$
$601$	−135.279			−0.225089			−0.112545	+	0.993647i	$0.535900\pi$
$602$	−583.607	+	424.015i	−0.969447	+	0.704344i
$603$	−730.400	+	474.976i	−1.21128	+	0.787688i
$604$	−71.5193	+	220.114i	−0.118409	+	0.364427i
$605$	−225.788	+	223.590i	−0.373203	+	0.369570i
$606$	−1005.58	+	954.858i	−1.65937	+	1.57567i
$607$			206.038i			0.339436i	0.985493	+	0.169718i	$0.0542857\pi$
$607$			206.038i			0.339436i	−0.985493	+	0.169718i	$0.945714\pi$
$608$	127.883	+	393.585i	0.210335	+	0.647343i
$609$	−698.047	−	129.150i	−1.14622	−	0.212069i
$610$	−868.260	+	859.807i	−1.42338	+	1.40952i
$611$	6.58855	+	9.06837i	0.0107832	+	0.0148418i
$612$	−547.128	+	146.969i	−0.894000	+	0.240145i
$613$	187.514	−	258.091i	0.305896	−	0.421030i	−0.628200	−	0.778052i	$-0.716208\pi$
$613$	187.514	−	258.091i	0.305896	−	0.421030i	0.934096	+	0.357022i	$0.116208\pi$
$614$	−308.660	−	424.834i	−0.502703	−	0.691912i
$615$	160.484	+	235.812i	0.260950	+	0.383434i
$616$	−302.078	−	219.472i	−0.490386	−	0.356286i
$617$	134.643	+	414.390i	0.218223	+	0.671620i	0.998909	+	0.0466971i	$0.0148696\pi$
$617$	134.643	+	414.390i	0.218223	+	0.671620i	−0.780687	+	0.624923i	$0.785130\pi$
$618$	−114.837	−	240.568i	−0.185821	−	0.389269i
$619$	67.3502	+	207.283i	0.108805	+	0.334867i	0.990605	−	0.136757i	$-0.0436679\pi$
$619$	67.3502	+	207.283i	0.108805	+	0.334867i	−0.881800	+	0.471624i	$0.843668\pi$
$620$	246.683	+	127.215i	0.397876	+	0.205186i
$621$	−545.166	−	333.376i	−0.877883	−	0.536837i
$622$	−471.712	−	153.268i	−0.758379	−	0.246412i
$623$	342.133	−	248.574i	0.549170	−	0.398995i
$624$	11.3086	+	23.6899i	0.0181228	+	0.0379647i
$625$	−204.728	+	590.518i	−0.327565	+	0.944829i
$626$		−	1199.97i		−	1.91689i
$627$	−429.619	−	233.090i	−0.685197	−	0.371755i
$628$	−244.759	−	79.5270i	−0.389743	−	0.126635i
$629$	−1006.10	−	326.901i	−1.59952	−	0.519715i
$630$	320.921	+	729.158i	0.509399	+	1.15739i
$631$	−327.690	−	1008.53i	−0.519319	−	1.59830i	−0.775283	−	0.631614i	$-0.782393\pi$
$631$	−327.690	−	1008.53i	−0.519319	−	1.59830i	0.255964	−	0.966686i	$-0.417607\pi$
$632$	45.3633			0.0717774
$633$	−669.927	−	705.514i	−1.05834	−	1.11456i
$634$	−100.978	−	73.3647i	−0.159271	−	0.115717i
$635$	−134.296	−	875.612i	−0.211490	−	1.37892i
$636$	−250.195	+	461.146i	−0.393389	+	0.725072i
$637$	0.101212	−	0.139306i	0.000158889	−	0.000218691i
$638$	947.151	+	688.146i	1.48456	+	1.07860i
$639$	143.814	+	7.44693i	0.225061	+	0.0116540i
$640$	414.424	−	410.390i	0.647538	−	0.641234i
$641$	2.10516	−	2.89750i	0.00328417	−	0.00452028i	−0.807372	−	0.590043i	$-0.799111\pi$
$641$	2.10516	−	2.89750i	0.00328417	−	0.00452028i	0.810656	+	0.585523i	$0.199111\pi$
$642$	747.498	+	787.206i	1.16433	+	1.22618i
$643$		−	885.019i		−	1.37639i	−0.725526	−	0.688195i	$-0.758403\pi$
$643$		−	885.019i		−	1.37639i	0.725526	−	0.688195i	$-0.241597\pi$
$644$	384.093	−	124.799i	0.596418	−	0.193788i
$645$	575.218	+	206.665i	0.891811	+	0.320410i
$646$	−242.028	+	744.887i	−0.374657	+	1.15308i
$647$	−195.799	+	602.607i	−0.302626	+	0.931386i	0.677927	+	0.735129i	$0.262879\pi$
$647$	−195.799	+	602.607i	−0.302626	+	0.931386i	−0.980553	+	0.196257i	$0.937121\pi$
$648$	−237.565	−	213.368i	−0.366613	−	0.329272i
$649$	−371.081			−0.571773
$650$	−22.8563	+	16.2669i	−0.0351636	+	0.0250259i
$651$	−204.370	−	428.126i	−0.313932	−	0.657643i
$652$	89.9390	+	123.790i	0.137943	+	0.189863i
$653$	193.035	−	594.101i	0.295612	−	0.909802i	−0.687403	−	0.726277i	$-0.741249\pi$
$653$	193.035	−	594.101i	0.295612	−	0.909802i	0.983015	−	0.183525i	$-0.0587508\pi$
$654$	−143.356	−	1086.28i	−0.219199	−	1.66097i
$655$	−574.267	−	93.8366i	−0.876743	−	0.143262i
$656$	358.086	−	116.349i	0.545863	−	0.177362i
$657$	281.155	+	227.385i	0.427938	+	0.346095i
$658$	427.049	−	138.757i	0.649010	−	0.210876i
$659$	319.722	−	440.059i	0.485162	−	0.667768i	−0.494325	−	0.869277i	$-0.664585\pi$
$659$	319.722	−	440.059i	0.485162	−	0.667768i	0.979487	+	0.201509i	$0.0645846\pi$
$660$	15.3382	−	498.496i	0.0232397	−	0.755297i
$661$	−138.017	+	100.275i	−0.208801	+	0.151703i	−0.687271	−	0.726401i	$-0.741191\pi$
$661$	−138.017	+	100.275i	−0.208801	+	0.151703i	0.478470	+	0.878104i	$0.341191\pi$
$662$	−40.4125	−	29.3614i	−0.0610461	−	0.0443526i
$663$	−6.20355	+	33.5298i	−0.00935679	+	0.0505729i
$664$	−99.2379	+	72.1005i	−0.149455	+	0.108585i
$665$	412.613	+	67.4220i	0.620470	+	0.101386i
$666$	243.847	+	907.783i	0.366137	+	1.36304i
$667$	763.948	−	248.222i	1.14535	−	0.372146i
$668$	−298.439			−0.446764
$669$	582.855	−	553.455i	0.871233	−	0.827287i
$670$	−1097.80	+	552.611i	−1.63851	+	0.824793i
$671$	−1243.52	−	404.044i	−1.85323	−	0.602152i
$672$	715.547	−	94.4309i	1.06480	−	0.140522i
$673$	251.764	+	346.524i	0.374092	+	0.514894i	0.954007	−	0.299783i	$-0.0969143\pi$
$673$	251.764	+	346.524i	0.374092	+	0.514894i	−0.579915	+	0.814677i	$0.696914\pi$
$674$			1186.23i			1.75998i
$675$	357.764	−	572.390i	0.530021	−	0.847985i
$676$	413.143			0.611158
$677$	391.318	−	284.309i	0.578018	−	0.419955i	−0.259991	−	0.965611i	$-0.583720\pi$
$677$	391.318	−	284.309i	0.578018	−	0.419955i	0.838009	+	0.545656i	$0.183720\pi$
$678$	−72.1430	−	546.661i	−0.106406	−	0.806285i
$679$	285.254	−	877.922i	0.420109	−	1.29296i
$680$	501.092	−	76.8545i	0.736899	−	0.113021i
$681$	−50.4966	−	53.1790i	−0.0741506	−	0.0780896i
$682$			782.377i			1.14718i
$683$	354.430	+	1090.82i	0.518931	+	1.59711i	0.776013	+	0.630716i	$0.217239\pi$
$683$	354.430	+	1090.82i	0.518931	+	1.59711i	−0.257082	+	0.966389i	$0.582761\pi$
$684$	255.129	−	68.5323i	0.372995	−	0.100193i
$685$	228.201	+	453.339i	0.333141	+	0.661809i
$686$	−513.941	−	707.379i	−0.749185	−	1.03117i
$687$	−518.056	−	95.8488i	−0.754085	−	0.139518i
$688$	474.223	−	652.713i	0.689278	−	0.948710i
$689$	18.5612	+	25.5473i	0.0269394	+	0.0370789i
$690$	−712.638	−	552.029i	−1.03281	−	0.800043i
$691$	350.566	+	254.701i	0.507331	+	0.368597i	0.811810	−	0.583922i	$-0.198482\pi$
$691$	350.566	+	254.701i	0.507331	+	0.368597i	−0.304479	+	0.952519i	$0.598482\pi$
$692$	−116.393	−	358.219i	−0.168197	−	0.517658i
$693$	−536.048	+	662.810i	−0.773518	+	0.956435i
$694$	200.839	+	618.120i	0.289394	+	0.890663i
$695$	−81.6597	+	12.5245i	−0.117496	+	0.0180208i
$696$	397.939	−	52.5160i	0.571751	−	0.0754540i
$697$	465.143	+	151.134i	0.667350	+	0.216835i
$698$	35.8760	−	26.0654i	0.0513983	−	0.0373430i
$699$	−250.810	+	119.727i	−0.358813	+	0.171283i
$700$	127.851	+	406.991i	0.182644	+	0.581415i
$701$			708.515i			1.01072i	0.862909	+	0.505360i	$0.168640\pi$
$701$			708.515i			1.01072i	−0.862909	+	0.505360i	$0.831360\pi$
$702$	27.9810	−	11.6208i	0.0398590	−	0.0165539i
$703$	469.149	+	152.436i	0.667352	+	0.216836i
$704$	−108.781	−	35.3450i	−0.154518	−	0.0502060i
$705$	−300.772	−	232.986i	−0.426627	−	0.330477i
$706$	−55.8954	−	172.028i	−0.0791719	−	0.243666i
$707$	1269.21			1.79520
$708$	145.438	−	138.102i	0.205421	−	0.195060i
$709$	869.199	+	631.510i	1.22595	+	0.890705i	0.996580	−	0.0826343i	$-0.0263333\pi$
$709$	869.199	+	631.510i	1.22595	+	0.890705i	0.229370	+	0.973339i	$0.426333\pi$
$710$	200.485	+	32.7598i	0.282374	+	0.0461406i
$711$	5.35556	−	103.426i	0.00753244	−	0.145465i
$712$	−140.549	+	193.449i	−0.197400	+	0.271698i
$713$	434.280	+	315.523i	0.609088	+	0.442528i
$714$	1200.64	+	651.407i	1.68156	+	0.912335i
$715$	−26.6797	−	13.7588i	−0.0373142	−	0.0192430i
$716$	248.350	−	341.824i	0.346857	−	0.477408i
$717$	163.261	−	155.026i	0.227700	−	0.216215i
$718$			392.906i			0.547223i
$719$	−1266.77	+	411.597i	−1.76184	+	0.572458i	−0.997389	−	0.0722178i	$-0.976992\pi$
$719$	−1266.77	+	411.597i	−1.76184	+	0.572458i	−0.764456	+	0.644676i	$0.776992\pi$
$720$	−593.358	−	664.673i	−0.824108	−	0.923156i
$721$	−75.3955	+	232.044i	−0.104571	+	0.321836i
$722$	−170.400	+	524.437i	−0.236011	+	0.726367i
$723$	45.1346	−	83.1895i	0.0624268	−	0.115061i
$724$	−189.271			−0.261424
$725$	254.291	+	809.490i	0.350747	+	1.11654i
$726$	436.889	−	208.553i	0.601775	−	0.287263i
$727$	319.388	+	439.600i	0.439323	+	0.604676i	0.970062	−	0.242859i	$-0.0780853\pi$
$727$	319.388	+	439.600i	0.439323	+	0.604676i	−0.530738	+	0.847536i	$0.678085\pi$
$728$	3.75355	−	11.5522i	0.00515598	−	0.0158685i
$729$	−514.514	+	516.446i	−0.705781	+	0.708430i
$730$	358.919	+	362.448i	0.491670	+	0.496504i
$731$	996.712	−	323.851i	1.36349	−	0.443025i
$732$	637.745	−	304.433i	0.871237	−	0.415893i
$733$	803.163	−	260.963i	1.09572	−	0.356021i	0.295266	−	0.955415i	$-0.404592\pi$
$733$	803.163	−	260.963i	1.09572	−	0.356021i	0.800454	+	0.599394i	$0.204592\pi$
$734$	661.595	−	910.607i	0.901355	−	1.24061i
$735$	−1.97614	+	5.50026i	−0.00268862	+	0.00748334i
$736$	−660.708	+	480.032i	−0.897701	+	0.652218i
$737$	−1063.95	−	773.004i	−1.44362	−	1.04885i
$738$	−112.736	−	419.690i	−0.152759	−	0.568685i
$739$	472.107	−	343.005i	0.638845	−	0.464148i	−0.220608	−	0.975363i	$-0.570804\pi$
$739$	472.107	−	343.005i	0.638845	−	0.464148i	0.859453	+	0.511214i	$0.170804\pi$
$740$	76.3068	+	497.521i	0.103117	+	0.672325i
$741$	2.89275	−	15.6351i	0.00390385	−	0.0211000i
$742$	1203.08	−	390.904i	1.62140	−	0.526825i
$743$	−96.0790			−0.129312			−0.0646561	−	0.997908i	$-0.520595\pi$
$743$	−96.0790			−0.129312			−0.0646561	+	0.997908i	$0.520595\pi$
$744$	184.703	+	194.515i	0.248257	+	0.261445i
$745$	374.631	−	726.449i	0.502861	−	0.975099i
$746$	319.673	+	103.868i	0.428516	+	0.139233i
$747$	152.669	+	234.769i	0.204377	+	0.314283i
$748$	−502.636	−	691.820i	−0.671974	−	0.924893i
$749$		−	993.582i		−	1.32654i
$750$	590.449	−	747.024i	0.787265	−	0.996032i
$751$	−665.080			−0.885592			−0.442796	−	0.896622i	$-0.646013\pi$
$751$	−665.080			−0.885592			−0.442796	+	0.896622i	$0.646013\pi$
$752$	−406.285	+	295.183i	−0.540272	+	0.392531i
$753$	−1040.66	+	137.336i	−1.38201	+	0.182385i
$754$	−11.7691	+	36.2216i	−0.0156089	+	0.0480392i
$755$	−420.229	−	216.713i	−0.556595	−	0.287038i
$756$	−36.5785	−	459.273i	−0.0483842	−	0.607504i
$757$		−	710.689i		−	0.938822i	−0.882980	−	0.469411i	$-0.844466\pi$
$757$		−	710.689i		−	0.938822i	0.882980	−	0.469411i	$-0.155534\pi$
$758$	325.434	+	1001.58i	0.429333	+	1.32135i
$759$	175.482	−	948.467i	0.231201	−	1.24963i
$760$	−233.662	+	35.8377i	−0.307450	+	0.0471548i
$761$	89.4370	+	123.099i	0.117526	+	0.161760i	0.863727	−	0.503960i	$-0.168124\pi$
$761$	89.4370	+	123.099i	0.117526	+	0.161760i	−0.746201	+	0.665721i	$0.768124\pi$
$762$	−245.531	+	1327.08i	−0.322220	+	1.74158i
$763$	−589.464	+	811.328i	−0.772561	+	1.06334i
$764$	−126.102	−	173.565i	−0.165055	−	0.227179i
$765$	−116.065	−	1151.53i	−0.151719	−	1.50527i
$766$	675.484	+	490.768i	0.881832	+	0.640689i
$767$	−3.73035	−	11.4808i	−0.00486356	−	0.0149685i
$768$	−893.069	+	426.314i	−1.16285	+	0.555097i
$769$	−298.261	−	917.953i	−0.387856	−	1.19370i	−0.934387	−	0.356259i	$-0.884052\pi$
$769$	−298.261	−	917.953i	−0.387856	−	1.19370i	0.546532	−	0.837439i	$-0.315948\pi$
$770$	−854.452	+	846.134i	−1.10968	+	1.09887i
$771$	2.00822	+	15.2173i	0.00260470	+	0.0197370i
$772$	−74.6746	−	24.2633i	−0.0967288	−	0.0314291i
$773$	728.420	−	529.228i	0.942329	−	0.684642i	−0.00665109	−	0.999978i	$-0.502117\pi$
$773$	728.420	−	529.228i	0.942329	−	0.684642i	0.948980	+	0.315336i	$0.102117\pi$
$774$	−724.041	−	585.568i	−0.935453	−	0.756548i
$775$	−337.760	+	455.450i	−0.435820	+	0.587678i
$776$			521.941i			0.672605i
$777$	410.273	−	756.192i	0.528022	−	0.973220i
$778$	365.020	+	118.602i	0.469177	+	0.152445i
$779$	−216.899	−	70.4747i	−0.278432	−	0.0904681i
$780$	15.5771	−	4.53667i	0.0199707	−	0.00581624i
$781$	67.1711	+	206.731i	0.0860065	+	0.264701i
$782$	−1545.62			−1.97650
$783$	−72.7533	−	913.478i	−0.0929160	−	1.16664i
$784$	6.24126	+	4.53454i	0.00796080	+	0.00578386i
$785$	240.978	−	467.281i	0.306978	−	0.595262i
$786$	779.208	+	422.760i	0.991358	+	0.537863i
$787$	−358.857	+	493.925i	−0.455981	+	0.627605i	−0.973669	−	0.227965i	$-0.926793\pi$
$787$	−358.857	+	493.925i	−0.455981	+	0.627605i	0.517688	+	0.855570i	$0.326793\pi$
$788$	−579.756	−	421.217i	−0.735731	−	0.534540i
$789$	−424.178	+	781.820i	−0.537615	+	0.990900i
$790$	23.5597	−	144.182i	0.0298224	−	0.182509i
$791$	−296.644	+	408.295i	−0.375024	+	0.516176i
$792$	172.449	−	450.085i	0.217739	−	0.568289i
$793$		−	42.5349i		−	0.0536380i
$794$	1421.43	−	461.851i	1.79021	−	0.581676i
$795$	−847.332	−	656.367i	−1.06583	−	0.825619i
$796$	136.093	−	418.851i	0.170971	−	0.526195i
$797$	181.689	−	559.182i	0.227966	−	0.701608i	−0.770011	−	0.638031i	$-0.779749\pi$
$797$	181.689	−	559.182i	0.227966	−	0.701608i	0.997977	−	0.0635770i	$-0.0202509\pi$
$798$	−559.864	−	303.755i	−0.701583	−	0.380645i
$799$	−652.337			−0.816441
$800$	−500.210	−	702.837i	−0.625262	−	0.878547i
$801$	424.461	+	343.283i	0.529913	+	0.428568i
$802$	−42.4143	−	58.3783i	−0.0528857	−	0.0727909i
$803$	−168.665	+	519.096i	−0.210043	+	0.646446i
$804$	704.678	−	92.9965i	0.876466	−	0.115667i
$805$	125.080	+	815.521i	0.155379	+	1.01307i
$806$	−24.2059	+	7.86498i	−0.0300322	+	0.00975804i
$807$	−295.272	−	618.554i	−0.365889	−	0.766486i
$808$	−682.513	+	221.762i	−0.844694	+	0.274458i
$809$	−324.701	+	446.913i	−0.401361	+	0.552426i	−0.961085	−	0.276253i	$-0.910907\pi$
$809$	−324.701	+	446.913i	−0.401361	+	0.552426i	0.559724	+	0.828679i	$0.310907\pi$
$810$	−801.546	+	644.259i	−0.989563	+	0.795381i
$811$	−52.3347	+	38.0234i	−0.0645311	+	0.0468846i	−0.619583	−	0.784931i	$-0.712698\pi$
$811$	−52.3347	+	38.0234i	−0.0645311	+	0.0468846i	0.555052	+	0.831816i	$0.312698\pi$
$812$	468.539	+	340.413i	0.577018	+	0.419228i
$813$	737.756	+	136.497i	0.907449	+	0.167893i
$814$	−1147.85	+	833.963i	−1.41014	+	1.02453i
$815$	−279.216	+	140.552i	−0.342596	+	0.172456i
$816$	−1502.22	−	277.934i	−1.84095	−	0.340606i
$817$	−464.772	+	151.014i	−0.568877	+	0.184839i
$818$	655.850			0.801773
$819$	−25.8953	−	9.92174i	−0.0316182	−	0.0121145i
$820$	−35.2785	−	230.016i	−0.0430225	−	0.280507i
$821$	253.051	+	82.2212i	0.308223	+	0.100148i	0.459044	−	0.888413i	$-0.348192\pi$
$821$	253.051	+	82.2212i	0.308223	+	0.100148i	−0.150822	+	0.988561i	$0.548192\pi$
$822$	−101.167	−	766.589i	−0.123074	−	0.932590i
$823$	215.463	+	296.559i	0.261802	+	0.360339i	0.919601	−	0.392854i	$-0.128512\pi$
$823$	215.463	+	296.559i	0.261802	+	0.360339i	−0.657799	+	0.753194i	$0.728512\pi$
$824$		−	137.954i		−	0.167420i
$825$	1000.01	+	195.155i	1.21213	+	0.236551i
$826$	−483.579			−0.585446
$827$	125.593	−	91.2487i	0.151866	−	0.110337i	−0.509258	−	0.860614i	$-0.670080\pi$
$827$	125.593	−	91.2487i	0.151866	−	0.110337i	0.661123	+	0.750277i	$0.270080\pi$
$828$	284.207	+	437.042i	0.343245	+	0.527829i
$829$	−255.989	+	787.854i	−0.308793	+	0.950367i	0.669441	+	0.742865i	$0.266533\pi$
$829$	−255.989	+	787.854i	−0.308793	+	0.950367i	−0.978235	+	0.207502i	$0.933467\pi$
$830$	177.623	+	352.862i	0.214004	+	0.425134i
$831$	−721.084	+	684.711i	−0.867731	+	0.823961i
$832$		−	3.72087i		−	0.00447220i
$833$	3.09668	+	9.53060i	0.00371750	+	0.0114413i
$834$	123.764	+	22.8983i	0.148398	+	0.0274560i
$835$	98.3210	−	601.710i	0.117750	−	0.720611i
$836$	234.382	+	322.599i	0.280361	+	0.385884i
$837$	465.290	−	398.149i	0.555902	−	0.475686i
$838$	−354.433	+	487.835i	−0.422951	+	0.582142i
$839$	555.403	+	764.447i	0.661982	+	0.911140i	0.999545	−	0.0301628i	$-0.00960258\pi$
$839$	555.403	+	764.447i	0.661982	+	0.911140i	−0.337563	+	0.941303i	$0.609603\pi$
$840$	−12.6794	+	412.085i	−0.0150946	+	0.490577i
$841$	251.524	+	182.743i	0.299077	+	0.217292i
$842$	336.292	+	1035.00i	0.399396	+	1.22922i
$843$	−625.226	−	1309.76i	−0.741668	−	1.55369i
$844$	245.273	+	754.872i	0.290608	+	0.894398i
$845$	−136.110	+	832.976i	−0.161078	+	0.985771i
$846$	315.991	+	485.920i	0.373512	+	0.574373i
$847$	−421.408	−	136.924i	−0.497530	−	0.161657i
$848$	−1144.58	+	831.588i	−1.34974	+	0.980646i
$849$	643.701	+	1348.46i	0.758187	+	1.58830i
$850$	15.9721	−	1632.57i	0.0187907	−	1.92068i
$851$			973.473i			1.14392i
$852$	−103.264	−	56.0261i	−0.121202	−	0.0657583i
$853$	−387.900	−	126.036i	−0.454748	−	0.147757i	0.0726819	−	0.997355i	$-0.476844\pi$
$853$	−387.900	−	126.036i	−0.454748	−	0.147757i	−0.527430	+	0.849599i	$0.676844\pi$
$854$	−1620.51	−	526.536i	−1.89755	−	0.616552i
$855$	54.1219	+	536.967i	0.0633005	+	0.628032i
$856$	173.603	+	534.296i	0.202808	+	0.624178i
$857$	−1424.88			−1.66264			−0.831320	−	0.555795i	$-0.812414\pi$
$857$	−1424.88			−1.66264			−0.831320	+	0.555795i	$0.812414\pi$
$858$	31.4912	+	33.1641i	0.0367031	+	0.0386528i
$859$	796.733	+	578.860i	0.927512	+	0.673877i	0.945382	−	0.325964i	$-0.105689\pi$
$859$	796.733	+	578.860i	0.927512	+	0.673877i	−0.0178705	+	0.999840i	$0.505689\pi$
$860$	−350.865	−	354.315i	−0.407983	−	0.411994i
$861$	−189.679	+	349.606i	−0.220301	+	0.406046i
$862$	990.653	−	1363.52i	1.14925	−	1.58181i
$863$	−135.978	−	98.7941i	−0.157565	−	0.114478i	0.506209	−	0.862411i	$-0.331046\pi$
$863$	−135.978	−	98.7941i	−0.157565	−	0.114478i	−0.663774	+	0.747933i	$0.731046\pi$
$864$	357.344	+	860.424i	0.413592	+	0.995861i
$865$	760.585	−	116.654i	0.879289	−	0.134860i
$866$	878.291	−	1208.86i	1.01419	−	1.39592i
$867$	−769.455	−	810.329i	−0.887491	−	0.934636i
$868$			387.028i			0.445885i
$869$	148.674	−	48.3070i	0.171086	−	0.0555892i
$870$	39.7558	−	1292.08i	0.0456963	−	1.48514i
$871$	13.2204	−	40.6882i	0.0151784	−	0.0467143i
$872$	175.224	−	539.284i	0.200945	−	0.618445i
$873$	1190.00	+	61.6201i	1.36311	+	0.0705843i
$874$	720.733			0.824637
$875$	−862.692	+	123.689i	−0.985934	+	0.141359i
$876$	−127.083	−	266.221i	−0.145072	−	0.303905i
$877$	−124.112	−	170.825i	−0.141519	−	0.194784i	0.732374	−	0.680902i	$-0.238412\pi$
$877$	−124.112	−	170.825i	−0.141519	−	0.194784i	−0.873893	+	0.486119i	$0.838412\pi$
$878$	240.971	−	741.632i	0.274454	−	0.844684i
$879$	−133.713	−	1013.21i	−0.152120	−	1.15268i
$880$	616.426	−	1195.31i	0.700484	−	1.35831i
$881$	1227.02	−	398.682i	1.39276	−	0.452534i	0.485914	−	0.874007i	$-0.338487\pi$
$881$	1227.02	−	398.682i	1.39276	−	0.452534i	0.906841	+	0.421473i	$0.138487\pi$
$882$	5.59923	−	6.92331i	0.00634833	−	0.00784955i
$883$	364.163	−	118.324i	0.412416	−	0.134002i	−0.0954580	−	0.995433i	$-0.530432\pi$
$883$	364.163	−	118.324i	0.412416	−	0.134002i	0.507874	+	0.861431i	$0.330432\pi$
$884$	16.3513	−	22.5057i	0.0184970	−	0.0254589i
$885$	230.526	+	338.730i	0.260481	+	0.382746i
$886$	1165.37	−	846.689i	1.31531	−	0.955631i
$887$	−100.370	−	72.9232i	−0.113157	−	0.0822133i	0.529768	−	0.848143i	$-0.322279\pi$
$887$	−100.370	−	72.9232i	−0.113157	−	0.0822133i	−0.642925	+	0.765930i	$0.722279\pi$
$888$	−88.4979	+	478.325i	−0.0996598	+	0.538654i
$889$	999.338	−	726.062i	1.12412	−	0.816717i
$890$	541.860	+	547.188i	0.608832	+	0.614817i
$891$	−1005.81	−	446.311i	−1.12886	−	0.500911i
$892$	−623.632	+	202.630i	−0.699139	+	0.227164i
$893$	304.188			0.340636
$894$	−903.009	+	857.460i	−1.01008	+	0.959127i
$895$	607.365	+	613.336i	0.678620	+	0.685291i
$896$	773.476	+	251.318i	0.863254	+	0.280488i
$897$	31.1086	−	4.10541i	0.0346807	−	0.00457682i
$898$	32.0300	+	44.0855i	0.0356682	+	0.0490930i
$899$			769.785i			0.856268i
$900$	−464.566	+	295.679i	−0.516184	+	0.328532i
$901$	−1837.76			−2.03969
$902$	530.680	−	385.561i	0.588337	−	0.427452i
$903$	111.511	+	844.968i	0.123489	+	0.935735i
$904$	88.1802	−	271.391i	0.0975444	−	0.300211i
$905$	62.3555	−	381.606i	0.0689011	−	0.421665i
$906$	496.016	+	522.365i	0.547479	+	0.576561i
$907$			479.783i			0.528978i	0.964389	+	0.264489i	$0.0852033\pi$
$907$			479.783i			0.528978i	−0.964389	+	0.264489i	$0.914797\pi$
$908$	18.4877	+	56.8994i	0.0203609	+	0.0626646i
$909$	425.028	+	1582.27i	0.467578	+	1.74067i
$910$	−34.7680	−	17.9299i	−0.0382066	−	0.0197032i
$911$	−576.910	−	794.048i	−0.633271	−	0.871623i	0.364963	−	0.931022i	$-0.381082\pi$
$911$	−576.910	−	794.048i	−0.633271	−	0.871623i	−0.998234	+	0.0593992i	$0.981082\pi$
$912$	700.491	+	129.602i	0.768083	+	0.142108i
$913$	−248.463	+	341.980i	−0.272139	+	0.374567i
$914$	−660.295	−	908.818i	−0.722424	−	0.994331i
$915$	403.691	+	1386.11i	0.441192	+	1.51488i
$916$	347.727	+	252.638i	0.379614	+	0.275806i
$917$	−250.733	−	771.678i	−0.273428	−	0.841525i
$918$	−410.020	+	1714.93i	−0.446645	+	1.86812i
$919$	−277.843	−	855.113i	−0.302332	−	0.930482i	−0.980659	−	0.195722i	$-0.937295\pi$
$919$	−277.843	−	855.113i	−0.302332	−	0.930482i	0.678327	−	0.734760i	$-0.262705\pi$
$920$	−209.753	−	416.690i	−0.227993	−	0.452924i
$921$	−615.091	+	81.1736i	−0.667851	+	0.0881364i
$922$	−1110.91	−	360.958i	−1.20490	−	0.391494i
$923$	−5.72080	+	4.15640i	−0.00619805	+	0.00450315i
$924$	627.603	−	299.592i	0.679224	−	0.324234i
$925$	−1028.24	−	10.0596i	−1.11161	−	0.0108753i
$926$			479.309i			0.517613i
$927$	−314.528	−	16.2868i	−0.339297	−	0.0175694i
$928$	−1113.82	−	361.903i	−1.20024	−	0.389981i
$929$	1487.83	+	483.425i	1.60154	+	0.520371i	0.967487	−	0.252920i	$-0.0813910\pi$
$929$	1487.83	+	483.425i	1.60154	+	0.520371i	0.634051	+	0.773291i	$0.281391\pi$
$930$	714.170	−	486.035i	0.767924	−	0.522618i
$931$	−1.44400	−	4.44417i	−0.00155102	−	0.00477355i
$932$	226.734			0.243277
$933$	−424.943	+	403.508i	−0.455459	+	0.432485i
$934$	−258.401	−	187.739i	−0.276660	−	0.201005i
$935$	1560.44	−	785.491i	1.66892	−	0.840098i
$936$	15.6587	+	0.810835i	0.0167294	+	0.000866277i
$937$	−374.955	+	516.081i	−0.400165	+	0.550780i	−0.960785	−	0.277293i	$-0.910563\pi$
$937$	−374.955	+	516.081i	−0.400165	+	0.550780i	0.560620	+	0.828073i	$0.310563\pi$
$938$	−1386.50	−	1007.35i	−1.47814	−	1.07393i
$939$	−1246.15	−	676.100i	−1.32710	−	0.720021i
$940$	139.557	+	277.239i	0.148464	+	0.294936i
$941$	419.935	−	577.992i	0.446265	−	0.614231i	−0.525325	−	0.850902i	$-0.676056\pi$
$941$	419.935	−	577.992i	0.446265	−	0.614231i	0.971590	+	0.236671i	$0.0760562\pi$
$942$	−580.852	+	551.552i	−0.616615	+	0.585512i
$943$		−	450.060i		−	0.477264i
$944$	514.369	−	167.129i	0.544883	−	0.177043i
$945$	938.034	+	77.5589i	0.992629	+	0.0820729i
$946$	434.351	−	1336.79i	0.459145	−	1.41310i
$947$	85.6580	−	263.628i	0.0904520	−	0.278383i	−0.895590	−	0.444881i	$-0.853246\pi$
$947$	85.6580	−	263.628i	0.0904520	−	0.278383i	0.986042	+	0.166498i	$0.0532460\pi$
$948$	−40.2920	+	74.2638i	−0.0425021	+	0.0783374i
$949$	−17.7558			−0.0187100
$950$	−7.44786	+	761.279i	−0.00783985	+	0.801346i
$951$	−133.082	+	63.5278i	−0.139939	+	0.0668010i
$952$	415.508	+	571.897i	0.436458	+	0.600733i
$953$	230.629	−	709.802i	0.242003	−	0.744808i	−0.754112	−	0.656745i	$-0.771933\pi$
$953$	230.629	−	709.802i	0.242003	−	0.744808i	0.996115	−	0.0880621i	$-0.0280674\pi$
$954$	890.209	+	1368.93i	0.933133	+	1.43494i
$955$	391.485	−	197.066i	0.409932	−	0.206351i
$956$	−174.683	+	56.7579i	−0.182723	+	0.0593702i
$957$	1248.28	−	595.878i	1.30437	−	0.622652i
$958$	−1317.82	+	428.187i	−1.37560	+	0.446959i
$959$	−415.987	+	572.556i	−0.433771	+	0.597035i
$960$	35.3141	+	121.255i	0.0367855	+	0.126307i
$961$	361.285	−	262.489i	0.375947	−	0.273141i
$962$	−37.3409	−	27.1298i	−0.0388159	−	0.0282014i
$963$	1238.66	−	332.728i	1.28625	−	0.345511i
$964$	−62.4667	+	45.3847i	−0.0647995	+	0.0470796i
$965$	73.5211	−	142.565i	0.0761876	−	0.147736i
$966$	228.681	−	1236.01i	0.236730	−	1.27951i
$967$	−1240.43	+	403.039i	−1.28276	+	0.416793i	−0.869551	−	0.493844i	$-0.835591\pi$
$967$	−1240.43	+	403.039i	−1.28276	+	0.416793i	−0.413207	+	0.910637i	$0.635591\pi$
$968$	250.535			0.258817
$969$	637.185	+	671.034i	0.657570	+	0.692501i
$970$	1658.93	+	271.073i	1.71024	+	0.279457i
$971$	−721.884	−	234.554i	−0.743444	−	0.241560i	−0.0872862	−	0.996183i	$-0.527819\pi$
$971$	−721.884	−	234.554i	−0.743444	−	0.241560i	−0.656158	+	0.754624i	$0.727819\pi$
$972$	560.310	−	199.401i	0.576450	−	0.205145i
$973$	−67.7126	−	93.1984i	−0.0695916	−	0.0957846i
$974$		−	791.805i		−	0.812942i
$975$	4.01490	+	32.9011i	0.00411784	+	0.0337447i
$976$	1905.67			1.95253
$977$	−961.944	+	698.893i	−0.984589	+	0.715346i	−0.958730	−	0.284319i	$-0.908232\pi$
$977$	−961.944	+	698.893i	−0.984589	+	0.715346i	−0.0258599	+	0.999666i	$0.508232\pi$
$978$	472.150	−	62.3097i	0.482771	−	0.0637113i
$979$	−254.633	+	783.680i	−0.260095	+	0.800491i
$980$	3.38797	−	3.35499i	0.00345711	−	0.00342346i
$981$	−1208.85	−	463.168i	−1.23226	−	0.472139i
$982$			895.724i			0.912143i
$983$	−441.654	−	1359.27i	−0.449292	−	1.38278i	−0.877708	−	0.479196i	$-0.840928\pi$
$983$	−441.654	−	1359.27i	−0.449292	−	1.38278i	0.428416	−	0.903581i	$-0.359072\pi$
$984$	40.9147	−	221.141i	0.0415800	−	0.224737i
$985$	1040.26	−	1030.13i	1.05610	−	1.04582i
$986$	−1302.81	−	1793.16i	−1.32131	−	1.81862i
$987$	96.5159	−	521.662i	0.0977871	−	0.528533i
$988$	−7.62472	+	10.4945i	−0.00771732	+	0.0106220i
$989$	−566.856	−	780.210i	−0.573160	−	0.788888i
$990$	−1340.98	−	781.863i	−1.35452	−	0.789761i
$991$	−751.395	−	545.920i	−0.758219	−	0.550878i	0.140145	−	0.990131i	$-0.455243\pi$
$991$	−751.395	−	545.920i	−0.758219	−	0.550878i	−0.898363	+	0.439253i	$0.855243\pi$
$992$	−241.850	−	744.338i	−0.243800	−	0.750341i
$993$	−53.2609	+	25.4246i	−0.0536363	+	0.0256038i
$994$	87.5349	+	269.405i	0.0880633	+	0.271031i
$995$	799.649	+	412.381i	0.803667	+	0.414453i
$996$	−29.8914	−	226.501i	−0.0300115	−	0.227411i
$997$	−695.228	−	225.893i	−0.697320	−	0.226573i	−0.0611574	−	0.998128i	$-0.519479\pi$
$997$	−695.228	−	225.893i	−0.697320	−	0.226573i	−0.636162	+	0.771555i	$0.719479\pi$
$998$	−165.175	+	120.006i	−0.165506	+	0.120247i
$999$	1080.11	+	258.241i	1.08119	+	0.258500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.4	✓	72
3.2	odd	2	inner	75.3.h.a.14.15	yes	72
5.2	odd	4		375.3.j.b.176.8		144
5.3	odd	4		375.3.j.b.176.29		144
5.4	even	2		375.3.h.a.74.15		72
15.2	even	4		375.3.j.b.176.30		144
15.8	even	4		375.3.j.b.176.7		144
15.14	odd	2		375.3.h.a.74.4		72
25.9	even	10	inner	75.3.h.a.59.15	yes	72
25.12	odd	20		375.3.j.b.326.30		144
25.13	odd	20		375.3.j.b.326.7		144
25.16	even	5		375.3.h.a.299.4		72
75.38	even	20		375.3.j.b.326.29		144
75.41	odd	10		375.3.h.a.299.15		72
75.59	odd	10	inner	75.3.h.a.59.4	yes	72
75.62	even	20		375.3.j.b.326.8		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.4	✓	72	1.1	even	1	trivial
75.3.h.a.14.15	yes	72	3.2	odd	2	inner
75.3.h.a.59.4	yes	72	75.59	odd	10	inner
75.3.h.a.59.15	yes	72	25.9	even	10	inner
375.3.h.a.74.4		72	15.14	odd	2
375.3.h.a.74.15		72	5.4	even	2
375.3.h.a.299.4		72	25.16	even	5
375.3.h.a.299.15		72	75.41	odd	10
375.3.j.b.176.7		144	15.8	even	4
375.3.j.b.176.8		144	5.2	odd	4
375.3.j.b.176.29		144	5.3	odd	4
375.3.j.b.176.30		144	15.2	even	4
375.3.j.b.326.7		144	25.13	odd	20
375.3.j.b.326.8		144	75.62	even	20
375.3.j.b.326.29		144	75.38	even	20
375.3.j.b.326.30		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+(-2.05424 + 1.49250i) q^{2} +(0.392507 + 2.97421i) q^{3} +(0.756307 - 2.32767i) q^{4} +(4.44388 + 2.29172i) q^{5} +(-5.24530 - 5.52394i) q^{6} +6.97211i q^{7} +(-1.21820 - 3.74924i) q^{8} +(-8.69188 + 2.33480i) q^{9} +(-12.5492 + 1.92472i) q^{10} +(-7.98507 - 10.9905i) q^{11} +(7.21985 + 1.33579i) q^{12} +(0.259763 - 0.357533i) q^{13} +(-10.4058 - 14.3224i) q^{14} +(-5.07180 + 14.1165i) q^{15} +(16.0184 + 11.6380i) q^{16} +(7.94771 + 24.4605i) q^{17} +(14.3706 - 17.7688i) q^{18} +(-3.70606 - 11.4061i) q^{19} +(8.69531 - 8.61066i) q^{20} +(-20.7365 + 2.73660i) q^{21} +(32.8065 + 10.6595i) q^{22} +(19.1473 - 13.9113i) q^{23} +(10.6729 - 5.09479i) q^{24} +(14.4961 + 20.3682i) q^{25} +1.12216i q^{26} +(-10.3558 - 24.9351i) q^{27} +(16.2288 + 5.27306i) q^{28} +(32.2785 + 10.4879i) q^{29} +(-10.6502 - 36.5685i) q^{30} +(7.00881 + 21.5709i) q^{31} -34.5066 q^{32} +(29.5539 - 28.0631i) q^{33} +(-52.8338 - 38.3860i) q^{34} +(-15.9781 + 30.9832i) q^{35} +(-1.13908 + 21.9977i) q^{36} +(-24.1765 + 33.2760i) q^{37} +(24.6367 + 17.8996i) q^{38} +(1.16534 + 0.632257i) q^{39} +(3.17866 - 19.4529i) q^{40} +(11.1774 - 15.3843i) q^{41} +(38.5136 - 36.5709i) q^{42} -40.7478i q^{43} +(-31.6215 + 10.2744i) q^{44} +(-43.9763 - 9.54376i) q^{45} +(-18.5706 + 57.1545i) q^{46} +(-7.83781 + 24.1223i) q^{47} +(-28.3266 + 52.2100i) q^{48} +0.389632 q^{49} +(-60.1779 - 20.2060i) q^{50} +(-69.6313 + 33.2391i) q^{51} +(-0.635761 - 0.875050i) q^{52} +(-22.0806 + 67.9572i) q^{53} +(58.4888 + 35.7667i) q^{54} +(-10.2975 - 67.1399i) q^{55} +(26.1401 - 8.49344i) q^{56} +(32.4694 - 15.4996i) q^{57} +(-81.9612 + 26.6308i) q^{58} +(16.0556 - 22.0987i) q^{59} +(29.0229 + 22.4819i) q^{60} +(77.8653 - 56.5725i) q^{61} +(-46.5923 - 33.8513i) q^{62} +(-16.2785 - 60.6007i) q^{63} +(6.81151 - 4.94885i) q^{64} +(1.97372 - 0.993530i) q^{65} +(-18.8268 + 101.758i) q^{66} +(92.0681 - 29.9148i) q^{67} +62.9471 q^{68} +(48.8907 + 51.4878i) q^{69} +(-13.4194 - 87.4943i) q^{70} +(-15.2176 - 4.94450i) q^{71} +(19.3422 + 29.7437i) q^{72} +(-23.6157 - 32.5042i) q^{73} -104.440i q^{74} +(-54.8896 + 51.1090i) q^{75} -29.3526 q^{76} +(76.6270 - 55.6728i) q^{77} +(-3.33753 + 0.440454i) q^{78} +(-3.55591 + 10.9440i) q^{79} +(44.5125 + 88.4274i) q^{80} +(70.0974 - 40.5876i) q^{81} +48.2853i q^{82} +(-9.61536 - 29.5930i) q^{83} +(-9.31328 + 50.3376i) q^{84} +(-20.7380 + 126.913i) q^{85} +(60.8159 + 83.7059i) q^{86} +(-18.5238 + 100.120i) q^{87} +(-31.4786 + 43.3265i) q^{88} +(-35.6526 - 49.0716i) q^{89} +(104.582 - 46.0292i) q^{90} +(2.49276 + 1.81110i) q^{91} +(-17.8998 - 55.0899i) q^{92} +(-61.4054 + 29.3124i) q^{93} +(-19.9017 - 61.2510i) q^{94} +(9.67024 - 59.1804i) q^{95} +(-13.5441 - 102.630i) q^{96} +(-125.919 - 40.9136i) q^{97} +(-0.800399 + 0.581524i) q^{98} +(95.0658 + 76.8845i) 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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