LMFDB - Embedded newform 75.3.h.a.14.9

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			14.9
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.624639 + 0.453826i) q^{2} +(2.99063 - 0.236895i) q^{3} +(-1.05185 + 3.23727i) q^{4} +(-2.07515 + 4.54904i) q^{5} +(-1.76055 + 1.50520i) q^{6} +1.71117i q^{7} +(-1.76649 - 5.43671i) q^{8} +(8.88776 - 1.41693i) q^{9} +(-0.768257 - 3.78326i) q^{10} +(3.68799 + 5.07609i) q^{11} +(-2.37881 + 9.93067i) q^{12} +(7.16998 - 9.86863i) q^{13} +(-0.776575 - 1.06886i) q^{14} +(-5.12836 + 14.0961i) q^{15} +(-7.44441 - 5.40868i) q^{16} +(4.51198 + 13.8864i) q^{17} +(-4.90860 + 4.91857i) q^{18} +(-4.19666 - 12.9160i) q^{19} +(-12.5437 - 11.5027i) q^{20} +(0.405369 + 5.11749i) q^{21} +(-4.60733 - 1.49701i) q^{22} +(31.0498 - 22.5590i) q^{23} +(-6.57086 - 15.8407i) q^{24} +(-16.3875 - 18.8799i) q^{25} +9.41826i q^{26} +(26.2444 - 6.34300i) q^{27} +(-5.53953 - 1.79990i) q^{28} +(-38.1684 - 12.4017i) q^{29} +(-3.19381 - 11.1323i) q^{30} +(-8.30364 - 25.5560i) q^{31} +29.9706 q^{32} +(12.2319 + 14.3070i) q^{33} +(-9.12039 - 6.62635i) q^{34} +(-7.78419 - 3.55093i) q^{35} +(-4.76162 + 30.2625i) q^{36} +(-1.16967 + 1.60991i) q^{37} +(8.48302 + 6.16327i) q^{38} +(19.1049 - 31.2120i) q^{39} +(28.3975 + 3.24612i) q^{40} +(-20.7006 + 28.4920i) q^{41} +(-2.57566 - 3.01261i) q^{42} +73.2513i q^{43} +(-20.3119 + 6.59974i) q^{44} +(-11.9977 + 43.3711i) q^{45} +(-9.15703 + 28.1824i) q^{46} +(-5.42185 + 16.6867i) q^{47} +(-23.5448 - 14.4118i) q^{48} +46.0719 q^{49} +(18.8045 + 4.35599i) q^{50} +(16.7833 + 40.4604i) q^{51} +(24.4057 + 33.5915i) q^{52} +(25.7997 - 79.4032i) q^{53} +(-13.5146 + 15.8725i) q^{54} +(-30.7445 + 6.24320i) q^{55} +(9.30315 - 3.02278i) q^{56} +(-15.6104 - 37.6328i) q^{57} +(29.4696 - 9.57527i) q^{58} +(-5.62764 + 7.74578i) q^{59} +(-40.2386 - 31.4289i) q^{60} +(-1.66280 + 1.20810i) q^{61} +(16.7847 + 12.1948i) q^{62} +(2.42462 + 15.2085i) q^{63} +(11.0568 - 8.03324i) q^{64} +(30.0140 + 53.0954i) q^{65} +(-14.1334 - 3.38555i) q^{66} +(25.3218 - 8.22755i) q^{67} -49.7001 q^{68} +(87.5144 - 74.8212i) q^{69} +(6.47381 - 1.31462i) q^{70} +(-81.8447 - 26.5930i) q^{71} +(-23.4036 - 45.8172i) q^{72} +(-5.68457 - 7.82414i) q^{73} -1.53644i q^{74} +(-53.4816 - 52.5806i) q^{75} +46.2269 q^{76} +(-8.68606 + 6.31079i) q^{77} +(2.23114 + 28.1665i) q^{78} +(-41.5338 + 127.828i) q^{79} +(40.0525 - 22.6411i) q^{80} +(76.9846 - 25.1867i) q^{81} -27.1917i q^{82} +(0.618811 + 1.90451i) q^{83} +(-16.9931 - 4.07056i) q^{84} +(-72.5330 - 8.29125i) q^{85} +(-33.2434 - 45.7556i) q^{86} +(-117.085 - 28.0469i) q^{87} +(21.0824 - 29.0174i) q^{88} +(62.4318 + 85.9300i) q^{89} +(-12.1887 - 32.5362i) q^{90} +(16.8869 + 12.2691i) q^{91} +(40.3698 + 124.245i) q^{92} +(-30.8872 - 74.4614i) q^{93} +(-4.18619 - 12.8838i) q^{94} +(67.4641 + 7.71182i) q^{95} +(89.6312 - 7.09990i) q^{96} +(-85.9955 - 27.9416i) q^{97} +(-28.7783 + 20.9086i) q^{98} +(39.9705 + 39.8894i) 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 $

$2$	−0.624639	+	0.453826i	−0.312319	+	0.226913i	−0.732891	−	0.680346i	$-0.761829\pi$
$2$	−0.624639	+	0.453826i	−0.312319	+	0.226913i	0.420572	+	0.907259i	$0.361829\pi$
$3$	2.99063	−	0.236895i	0.996877	−	0.0789651i
$3$	2.99063	−	0.236895i	0.996877	−	0.0789651i
$4$	−1.05185	+	3.23727i	−0.262963	+	0.809318i
$5$	−2.07515	+	4.54904i	−0.415030	+	0.909808i
$5$	−2.07515	+	4.54904i	−0.415030	+	0.909808i
$6$	−1.76055	+	1.50520i	−0.293426	+	0.250867i
$7$			1.71117i			0.244453i	0.992502	+	0.122227i	$0.0390035\pi$
$7$			1.71117i			0.244453i	−0.992502	+	0.122227i	$0.960997\pi$
$8$	−1.76649	−	5.43671i	−0.220812	−	0.679589i
$9$	8.88776	−	1.41693i	0.987529	−	0.157437i
$10$	−0.768257	−	3.78326i	−0.0768257	−	0.378326i
$11$	3.68799	+	5.07609i	0.335272	+	0.461462i	0.943053	−	0.332642i	$-0.107940\pi$
$11$	3.68799	+	5.07609i	0.335272	+	0.461462i	−0.607781	+	0.794105i	$0.707940\pi$
$12$	−2.37881	+	9.93067i	−0.198234	+	0.827556i
$13$	7.16998	−	9.86863i	0.551537	−	0.759126i	−0.438683	−	0.898642i	$-0.644555\pi$
$13$	7.16998	−	9.86863i	0.551537	−	0.759126i	0.990220	+	0.139516i	$0.0445548\pi$
$14$	−0.776575	−	1.06886i	−0.0554697	−	0.0763474i
$15$	−5.12836	+	14.0961i	−0.341890	+	0.939740i
$16$	−7.44441	−	5.40868i	−0.465275	−	0.338042i
$17$	4.51198	+	13.8864i	0.265411	+	0.816850i	0.991599	+	0.129353i	$0.0412902\pi$
$17$	4.51198	+	13.8864i	0.265411	+	0.816850i	−0.726188	+	0.687496i	$0.758710\pi$
$18$	−4.90860	+	4.91857i	−0.272700	+	0.273254i
$19$	−4.19666	−	12.9160i	−0.220877	−	0.679790i	−0.998684	−	0.0512863i	$-0.983668\pi$
$19$	−4.19666	−	12.9160i	−0.220877	−	0.679790i	0.777807	−	0.628503i	$-0.216332\pi$
$20$	−12.5437	−	11.5027i	−0.627186	−	0.575137i
$21$	0.405369	+	5.11749i	0.0193033	+	0.243690i
$22$	−4.60733	−	1.49701i	−0.209424	−	0.0680459i
$23$	31.0498	−	22.5590i	1.34999	−	0.980826i	0.350979	−	0.936383i	$-0.385849\pi$
$23$	31.0498	−	22.5590i	1.34999	−	0.980826i	0.999012	−	0.0444426i	$-0.0141512\pi$
$24$	−6.57086	−	15.8407i	−0.273786	−	0.660030i
$25$	−16.3875	−	18.8799i	−0.655501	−	0.755194i
$26$			9.41826i			0.362241i
$27$	26.2444	−	6.34300i	0.972013	−	0.234926i
$28$	−5.53953	−	1.79990i	−0.197840	−	0.0642822i
$29$	−38.1684	−	12.4017i	−1.31615	−	0.427643i	−0.434980	−	0.900440i	$-0.643244\pi$
$29$	−38.1684	−	12.4017i	−1.31615	−	0.427643i	−0.881171	+	0.472797i	$0.843244\pi$
$30$	−3.19381	−	11.1323i	−0.106460	−	0.371078i
$31$	−8.30364	−	25.5560i	−0.267859	−	0.824386i	−0.991021	−	0.133707i	$-0.957312\pi$
$31$	−8.30364	−	25.5560i	−0.267859	−	0.824386i	0.723162	−	0.690679i	$-0.242688\pi$
$32$	29.9706			0.936583
$33$	12.2319	+	14.3070i	0.370665	+	0.433547i
$34$	−9.12039	−	6.62635i	−0.268247	−	0.194893i
$35$	−7.78419	−	3.55093i	−0.222405	−	0.101455i
$36$	−4.76162	+	30.2625i	−0.132267	+	0.840625i
$37$	−1.16967	+	1.60991i	−0.0316126	+	0.0435110i	−0.824531	−	0.565817i	$-0.808561\pi$
$37$	−1.16967	+	1.60991i	−0.0316126	+	0.0435110i	0.792918	+	0.609328i	$0.208561\pi$
$38$	8.48302	+	6.16327i	0.223237	+	0.162191i
$39$	19.1049	−	31.2120i	0.489870	−	0.800307i
$40$	28.3975	+	3.24612i	0.709939	+	0.0811531i
$41$	−20.7006	+	28.4920i	−0.504893	+	0.694926i	−0.983048	−	0.183350i	$-0.941306\pi$
$41$	−20.7006	+	28.4920i	−0.504893	+	0.694926i	0.478155	+	0.878276i	$0.341306\pi$
$42$	−2.57566	−	3.01261i	−0.0613252	−	0.0717289i
$43$			73.2513i			1.70352i	0.523934	+	0.851759i	$0.324464\pi$
$43$			73.2513i			1.70352i	−0.523934	+	0.851759i	$0.675536\pi$
$44$	−20.3119	+	6.59974i	−0.461634	+	0.149994i
$45$	−11.9977	+	43.3711i	−0.266616	+	0.963803i
$46$	−9.15703	+	28.1824i	−0.199066	+	0.612662i
$47$	−5.42185	+	16.6867i	−0.115359	+	0.355037i	−0.992022	−	0.126068i	$-0.959764\pi$
$47$	−5.42185	+	16.6867i	−0.115359	+	0.355037i	0.876663	+	0.481105i	$0.159764\pi$
$48$	−23.5448	−	14.4118i	−0.490516	−	0.300246i
$49$	46.0719			0.940243
$50$	18.8045	+	4.35599i	0.376089	+	0.0871199i
$51$	16.7833	+	40.4604i	0.329084	+	0.793341i
$52$	24.4057	+	33.5915i	0.469340	+	0.645991i
$53$	25.7997	−	79.4032i	0.486786	−	1.49817i	−0.342591	−	0.939485i	$-0.611304\pi$
$53$	25.7997	−	79.4032i	0.486786	−	1.49817i	0.829377	−	0.558689i	$-0.188696\pi$
$54$	−13.5146	+	15.8725i	−0.250271	+	0.293935i
$55$	−30.7445	+	6.24320i	−0.558990	+	0.113513i
$56$	9.30315	−	3.02278i	0.166128	−	0.0539781i
$57$	−15.6104	−	37.6328i	−0.273867	−	0.660225i
$58$	29.4696	−	9.57527i	0.508097	−	0.165091i
$59$	−5.62764	+	7.74578i	−0.0953837	+	0.131284i	−0.854041	−	0.520205i	$-0.825856\pi$
$59$	−5.62764	+	7.74578i	−0.0953837	+	0.131284i	0.758658	+	0.651489i	$0.225856\pi$
$60$	−40.2386	−	31.4289i	−0.670644	−	0.523815i
$61$	−1.66280	+	1.20810i	−0.0272591	+	0.0198049i	−0.601331	−	0.799000i	$-0.705363\pi$
$61$	−1.66280	+	1.20810i	−0.0272591	+	0.0198049i	0.574072	+	0.818805i	$0.305363\pi$
$62$	16.7847	+	12.1948i	0.270722	+	0.196691i
$63$	2.42462	+	15.2085i	0.0384860	+	0.241405i
$64$	11.0568	−	8.03324i	0.172763	−	0.125519i
$65$	30.0140	+	53.0954i	0.461754	+	0.816852i
$66$	−14.1334	−	3.38555i	−0.214143	−	0.0512963i
$67$	25.3218	−	8.22755i	0.377937	−	0.122799i	−0.113887	−	0.993494i	$-0.536330\pi$
$67$	25.3218	−	8.22755i	0.377937	−	0.122799i	0.491824	+	0.870694i	$0.336330\pi$
$68$	−49.7001			−0.730884
$69$	87.5144	−	74.8212i	1.26832	−	1.08437i
$70$	6.47381	−	1.31462i	0.0924830	−	0.0187803i
$71$	−81.8447	−	26.5930i	−1.15274	−	0.374549i	−0.330567	−	0.943783i	$-0.607240\pi$
$71$	−81.8447	−	26.5930i	−1.15274	−	0.374549i	−0.822176	+	0.569234i	$0.807240\pi$
$72$	−23.4036	−	45.8172i	−0.325050	−	0.636350i
$73$	−5.68457	−	7.82414i	−0.0778709	−	0.107180i	0.768305	−	0.640084i	$-0.221101\pi$
$73$	−5.68457	−	7.82414i	−0.0778709	−	0.107180i	−0.846176	+	0.532904i	$0.821101\pi$
$74$		−	1.53644i		−	0.0207626i
$75$	−53.4816	−	52.5806i	−0.713088	−	0.701074i
$76$	46.2269			0.608248
$77$	−8.68606	+	6.31079i	−0.112806	+	0.0819583i
$78$	2.23114	+	28.1665i	0.0286044	+	0.361109i
$79$	−41.5338	+	127.828i	−0.525744	+	1.61807i	0.237096	+	0.971486i	$0.423805\pi$
$79$	−41.5338	+	127.828i	−0.525744	+	1.61807i	−0.762840	+	0.646588i	$0.776195\pi$
$80$	40.0525	−	22.6411i	0.500657	−	0.283014i
$81$	76.9846	−	25.1867i	0.950427	−	0.310947i
$82$		−	27.1917i		−	0.331606i
$83$	0.618811	+	1.90451i	0.00745556	+	0.0229459i	0.954715	−	0.297522i	$-0.0961600\pi$
$83$	0.618811	+	1.90451i	0.00745556	+	0.0229459i	−0.947260	+	0.320467i	$0.896160\pi$
$84$	−16.9931	−	4.07056i	−0.202299	−	0.0484590i
$85$	−72.5330	−	8.29125i	−0.853329	−	0.0975441i
$86$	−33.2434	−	45.7556i	−0.386551	−	0.532041i
$87$	−117.085	−	28.0469i	−1.34581	−	0.322378i
$88$	21.0824	−	29.0174i	0.239573	−	0.329743i
$89$	62.4318	+	85.9300i	0.701481	+	0.965505i	0.999939	+	0.0110825i	$0.00352775\pi$
$89$	62.4318	+	85.9300i	0.701481	+	0.965505i	−0.298458	+	0.954423i	$0.596472\pi$
$90$	−12.1887	−	32.5362i	−0.135430	−	0.361513i
$91$	16.8869	+	12.2691i	0.185571	+	0.134825i
$92$	40.3698	+	124.245i	0.438802	+	1.35049i
$93$	−30.8872	−	74.4614i	−0.332121	−	0.800660i
$94$	−4.18619	−	12.8838i	−0.0445339	−	0.137061i
$95$	67.4641	+	7.71182i	0.710148	+	0.0811771i
$96$	89.6312	−	7.09990i	0.933658	−	0.0739573i
$97$	−85.9955	−	27.9416i	−0.886552	−	0.288058i	−0.169877	−	0.985465i	$-0.554337\pi$
$97$	−85.9955	−	27.9416i	−0.886552	−	0.288058i	−0.716675	+	0.697407i	$0.754337\pi$
$98$	−28.7783	+	20.9086i	−0.293656	+	0.213353i
$99$	39.9705	+	39.8894i	0.403742	+	0.402923i
$100$	78.3565	−	33.1920i	0.783565	−	0.331920i
$101$		−	157.223i		−	1.55666i	−0.627856	−	0.778329i	$-0.716067\pi$
$101$		−	157.223i		−	1.55666i	0.627856	−	0.778329i	$-0.283933\pi$
$102$	−28.8455	−	17.6564i	−0.282799	−	0.173102i
$103$	−87.8915	−	28.5577i	−0.853315	−	0.277259i	−0.150481	−	0.988613i	$-0.548082\pi$
$103$	−87.8915	−	28.5577i	−0.853315	−	0.277259i	−0.702834	+	0.711354i	$0.748082\pi$
$104$	−66.3186	−	21.5482i	−0.637679	−	0.207194i
$105$	−24.1208	−	8.77550i	−0.229722	−	0.0835762i
$106$	19.9198	+	61.3069i	0.187923	+	0.578367i
$107$	−4.26071			−0.0398198			−0.0199099	−	0.999802i	$-0.506338\pi$
$107$	−4.26071			−0.0398198			−0.0199099	+	0.999802i	$0.506338\pi$
$108$	−7.07122	+	91.6320i	−0.0654742	+	0.848445i
$109$	−124.599	−	90.5264i	−1.14311	−	0.830518i	−0.155560	−	0.987826i	$-0.549718\pi$
$109$	−124.599	−	90.5264i	−1.14311	−	0.830518i	−0.987550	+	0.157309i	$0.949718\pi$
$110$	16.3708	−	17.8524i	0.148826	−	0.162294i
$111$	−3.11666	+	5.09173i	−0.0280780	+	0.0458714i
$112$	9.25518	−	12.7387i	0.0826355	−	0.113738i
$113$	−18.2003	−	13.2233i	−0.161064	−	0.117020i	0.504334	−	0.863509i	$-0.331738\pi$
$113$	−18.2003	−	13.2233i	−0.161064	−	0.117020i	−0.665398	+	0.746489i	$0.731738\pi$
$114$	26.8296	+	16.4225i	0.235348	+	0.144057i
$115$	38.1889	+	188.060i	0.332077	+	1.63530i
$116$	80.2951	−	110.517i	0.692199	−	0.952730i
$117$	49.7419	−	97.8694i	0.425144	−	0.836491i
$118$		−	7.39228i		−	0.0626464i
$119$	−23.7621	+	7.72077i	−0.199681	+	0.0648804i
$120$	85.6956	+	2.98071i	0.714130	+	0.0248393i
$121$	25.2257	−	77.6367i	0.208477	−	0.641626i
$122$	0.490384	−	1.50925i	0.00401954	−	0.0123709i
$123$	−55.1583	+	90.1128i	−0.448442	+	0.732625i
$124$	91.4658			0.737627
$125$	119.892	−	35.3690i	0.959134	−	0.282952i
$126$	−8.41652	−	8.39945i	−0.0667978	−	0.0666623i
$127$	90.4421	+	124.483i	0.712143	+	0.980180i	0.999748	+	0.0224315i	$0.00714076\pi$
$127$	90.4421	+	124.483i	0.712143	+	0.980180i	−0.287606	+	0.957749i	$0.592859\pi$
$128$	−40.3066	+	124.051i	−0.314895	+	0.969147i
$129$	17.3529	+	219.068i	0.134518	+	1.69820i
$130$	−42.8440	−	19.5443i	−0.329569	−	0.150341i
$131$	−159.091	+	51.6917i	−1.21443	+	0.394593i	−0.845052	−	0.534685i	$-0.820430\pi$
$131$	−159.091	+	51.6917i	−1.21443	+	0.394593i	−0.369381	+	0.929278i	$0.620430\pi$
$132$	−59.1820	+	24.5492i	−0.448348	+	0.185979i
$133$	22.1015	−	7.18121i	0.166177	−	0.0539941i
$134$	−12.0831	+	16.6310i	−0.0901724	+	0.124112i
$135$	−25.6064	+	132.549i	−0.189677	+	0.981847i
$136$	67.5262	−	49.0606i	0.496516	−	0.360740i
$137$	−154.827	−	112.488i	−1.13012	−	0.821081i	−0.144409	−	0.989518i	$-0.546128\pi$
$137$	−154.827	−	112.488i	−1.13012	−	0.821081i	−0.985712	+	0.168437i	$0.946128\pi$
$138$	−20.7090	+	86.4526i	−0.150065	+	0.626468i
$139$	−6.70525	+	4.87165i	−0.0482392	+	0.0350478i	−0.611644	−	0.791133i	$-0.709491\pi$
$139$	−6.70525	+	4.87165i	−0.0482392	+	0.0350478i	0.563404	+	0.826181i	$0.309491\pi$
$140$	19.6832	−	21.4645i	0.140594	−	0.153318i
$141$	−12.2618	+	51.1883i	−0.0869628	+	0.363038i
$142$	63.1920	−	20.5323i	0.445014	−	0.144594i
$143$	76.5369			0.535223
$144$	−73.8278	−	37.5228i	−0.512693	−	0.260575i
$145$	135.621	−	147.894i	0.935315	−	1.01996i
$146$	7.10161	+	2.30745i	0.0486411	+	0.0158045i
$147$	137.784	−	10.9142i	0.937307	−	0.0742464i
$148$	−3.98139	−	5.47991i	−0.0269013	−	0.0370264i
$149$			266.284i			1.78714i	0.448921	+	0.893571i	$0.351808\pi$
$149$			266.284i			1.78714i	−0.448921	+	0.893571i	$0.648192\pi$
$150$	57.2691	+	8.57249i	0.381794	+	0.0571499i
$151$	−209.240			−1.38570			−0.692849	−	0.721083i	$-0.743645\pi$
$151$	−209.240			−1.38570			−0.692849	+	0.721083i	$0.743645\pi$
$152$	−62.8072	+	45.6321i	−0.413205	+	0.300211i
$153$	59.7776	+	117.026i	0.390703	+	0.764877i
$154$	2.56164	−	7.88393i	0.0166340	−	0.0511943i
$155$	133.486	+	15.2588i	0.861202	+	0.0984440i
$156$	80.9461	+	94.6783i	0.518885	+	0.606912i
$157$		−	216.981i		−	1.38204i	−0.722835	−	0.691021i	$-0.757161\pi$
$157$		−	216.981i		−	1.38204i	0.722835	−	0.691021i	$-0.242839\pi$
$158$	−32.0681	−	98.6953i	−0.202962	−	0.624654i
$159$	58.3471	−	243.578i	0.366963	−	1.53193i
$160$	−62.1935	+	136.338i	−0.388709	+	0.852110i
$161$	38.6023	+	53.1315i	0.239766	+	0.330010i
$162$	−36.6571	+	50.6703i	−0.226279	+	0.312779i
$163$	8.35407	−	11.4984i	0.0512519	−	0.0705422i	−0.782622	−	0.622497i	$-0.786118\pi$
$163$	8.35407	−	11.4984i	0.0512519	−	0.0705422i	0.833874	+	0.551955i	$0.186118\pi$
$164$	−70.4622	−	96.9829i	−0.429647	−	0.591359i
$165$	−90.4664	+	25.9543i	−0.548281	+	0.157299i
$166$	−1.25085	−	0.908795i	−0.00753523	−	0.00547467i
$167$	−4.56813	−	14.0593i	−0.0273541	−	0.0841871i	0.936448	−	0.350808i	$-0.114093\pi$
$167$	−4.56813	−	14.0593i	−0.0273541	−	0.0841871i	−0.963802	+	0.266621i	$0.914093\pi$
$168$	27.1062	−	11.2439i	0.161346	−	0.0669279i
$169$	6.24259	+	19.2127i	0.0369384	+	0.113685i
$170$	49.0697	−	27.7384i	0.288645	−	0.163167i
$171$	−55.6001	−	108.848i	−0.325146	−	0.636538i
$172$	−237.134	−	77.0496i	−1.37869	−	0.447963i
$173$	114.125	−	82.9168i	0.659683	−	0.479288i	−0.206873	−	0.978368i	$-0.566329\pi$
$173$	114.125	−	82.9168i	0.659683	−	0.479288i	0.866556	+	0.499080i	$0.166329\pi$
$174$	85.8645	−	35.6173i	0.493474	−	0.204697i
$175$	32.3067	−	28.0419i	0.184610	−	0.160239i
$176$		−	57.7356i		−	0.328043i
$177$	−14.9953	+	24.4979i	−0.0847189	+	0.138406i
$178$	−77.9946	−	25.3420i	−0.438172	−	0.142371i
$179$	18.8274	+	6.11739i	0.105181	+	0.0341754i	0.361135	−	0.932514i	$-0.382389\pi$
$179$	18.8274	+	6.11739i	0.105181	+	0.0341754i	−0.255954	+	0.966689i	$0.582389\pi$
$180$	−127.784	−	84.4600i	−0.709912	−	0.469222i
$181$	−24.7103	−	76.0504i	−0.136521	−	0.420168i	0.859303	−	0.511467i	$-0.170898\pi$
$181$	−24.7103	−	76.0504i	−0.136521	−	0.420168i	−0.995823	+	0.0912996i	$0.970898\pi$
$182$	−16.1163			−0.0885509
$183$	−4.68664	+	4.00688i	−0.0256101	+	0.0218955i
$184$	−177.496	−	128.958i	−0.964652	−	0.700861i
$185$	−4.89630	−	8.66165i	−0.0264665	−	0.0468197i
$186$	53.0859	+	32.4940i	0.285408	+	0.174699i
$187$	−53.8486	+	74.1163i	−0.287961	+	0.396344i
$188$	−48.3165	−	35.1040i	−0.257003	−	0.186723i
$189$	10.8540	+	44.9086i	0.0574283	+	0.237612i
$190$	−45.6405	+	25.7999i	−0.240213	+	0.135789i
$191$	−82.2359	+	113.188i	−0.430554	+	0.592607i	−0.968080	−	0.250640i	$-0.919359\pi$
$191$	−82.2359	+	113.188i	−0.430554	+	0.592607i	0.537526	+	0.843247i	$0.319359\pi$
$192$	31.1638	−	26.6438i	0.162311	−	0.138770i
$193$		−	179.383i		−	0.929445i	−0.885456	−	0.464723i	$-0.846154\pi$
$193$		−	179.383i		−	0.929445i	0.885456	−	0.464723i	$-0.153846\pi$
$194$	66.3968	−	21.5736i	0.342251	−	0.111204i
$195$	102.339	+	151.679i	0.524815	+	0.777839i
$196$	−48.4609	+	149.147i	−0.247249	+	0.760955i
$197$	−4.98853	+	15.3531i	−0.0253225	+	0.0779346i	−0.962919	−	0.269790i	$-0.913046\pi$
$197$	−4.98853	+	15.3531i	−0.0253225	+	0.0779346i	0.937597	+	0.347725i	$0.113046\pi$
$198$	−43.0700	−	6.77680i	−0.217525	−	0.0342263i
$199$	344.397			1.73064			0.865318	−	0.501223i	$-0.167116\pi$
$199$	344.397			1.73064			0.865318	+	0.501223i	$0.167116\pi$
$200$	−73.6958	+	122.445i	−0.368479	+	0.612227i
$201$	73.7791	−	30.6042i	0.367060	−	0.152260i
$202$	71.3517	+	98.2072i	0.353226	+	0.486174i
$203$	21.2214	−	65.3127i	0.104539	−	0.321737i
$204$	−148.635	+	11.7737i	−0.728602	+	0.0577143i
$205$	−86.6542	−	153.293i	−0.422703	−	0.747770i
$206$	67.8606	−	22.0493i	0.329421	−	0.107035i
$207$	243.999	−	244.494i	1.17874	−	1.18113i
$208$	−106.753	+	34.6860i	−0.513233	+	0.166760i
$209$	50.0855	−	68.9367i	0.239643	−	0.329841i
$210$	19.0494	−	5.46516i	0.0907113	−	0.0260246i
$211$	30.9857	−	22.5124i	0.146852	−	0.106694i	−0.511934	−	0.859025i	$-0.671071\pi$
$211$	30.9857	−	22.5124i	0.146852	−	0.106694i	0.658785	+	0.752331i	$0.271071\pi$
$212$	229.912	+	167.041i	1.08449	+	0.787930i
$213$	−251.067	−	60.1411i	−1.17872	−	0.282353i
$214$	2.66141	−	1.93362i	0.0124365	−	0.00903563i
$215$	−333.223	−	152.007i	−1.54987	−	0.707010i
$216$	−80.8455	−	131.478i	−0.374285	−	0.608695i
$217$	43.7307	−	14.2090i	0.201524	−	0.0654790i
$218$	118.913			0.545471
$219$	−18.8540	−	22.0525i	−0.0860912	−	0.100696i
$220$	12.1277	−	106.095i	0.0551260	−	0.482250i
$221$	169.391	+	55.0385i	0.766475	+	0.249043i
$222$	−0.363974	−	4.59491i	−0.00163952	−	0.0206978i
$223$	147.749	+	203.359i	0.662550	+	0.911922i	0.999562	−	0.0295784i	$-0.00941647\pi$
$223$	147.749	+	203.359i	0.662550	+	0.911922i	−0.337013	+	0.941500i	$0.609416\pi$
$224$			51.2849i			0.228951i
$225$	−172.400	−	144.580i	−0.766222	−	0.642576i
$226$	17.3697			0.0768570
$227$	28.4124	−	20.6428i	0.125165	−	0.0909376i	−0.523442	−	0.852062i	$-0.675352\pi$
$227$	28.4124	−	20.6428i	0.125165	−	0.0909376i	0.648606	+	0.761124i	$0.275352\pi$
$228$	138.248	−	10.9509i	0.606349	−	0.0480304i
$229$	−45.0741	+	138.724i	−0.196830	+	0.605781i	0.803120	+	0.595817i	$0.203172\pi$
$229$	−45.0741	+	138.724i	−0.196830	+	0.605781i	−0.999950	+	0.00996408i	$0.996828\pi$
$230$	−109.201	−	100.138i	−0.474786	−	0.435384i
$231$	−24.4818	+	20.9309i	−0.105982	+	0.0906101i
$232$			229.418i			0.988870i
$233$	−40.5672	−	124.853i	−0.174108	−	0.535849i	0.825484	−	0.564426i	$-0.190902\pi$
$233$	−40.5672	−	124.853i	−0.174108	−	0.535849i	−0.999592	+	0.0285768i	$0.990902\pi$
$234$	13.3450	+	83.7072i	0.0570301	+	0.357723i
$235$	−64.6575	−	59.2917i	−0.275138	−	0.252305i
$236$	−19.1557	−	26.3656i	−0.0811684	−	0.111719i
$237$	−93.9305	+	392.125i	−0.396331	+	1.65454i
$238$	11.3388	−	15.6066i	0.0476421	−	0.0655738i
$239$	−100.919	−	138.903i	−0.422255	−	0.581185i	0.543899	−	0.839151i	$-0.316948\pi$
$239$	−100.919	−	138.903i	−0.422255	−	0.581185i	−0.966154	+	0.257966i	$0.916948\pi$
$240$	114.419	−	77.1994i	0.476745	−	0.321664i
$241$	324.422	+	235.706i	1.34615	+	0.978034i	0.999194	+	0.0401521i	$0.0127843\pi$
$241$	324.422	+	235.706i	1.34615	+	0.978034i	0.346955	+	0.937882i	$0.387216\pi$
$242$	19.4766	+	59.9430i	0.0804820	+	0.247698i
$243$	224.266	−	93.5615i	0.922905	−	0.385027i
$244$	−2.16191	−	6.65368i	−0.00886030	−	0.0272692i
$245$	−95.6060	+	209.583i	−0.390228	+	0.855440i
$246$	−6.44158	−	81.3202i	−0.0261853	−	0.330570i
$247$	−157.553	−	51.1922i	−0.637867	−	0.207256i
$248$	−124.272	+	90.2889i	−0.501097	+	0.364068i
$249$	2.30181	+	5.54908i	0.00924420	+	0.0222855i
$250$	−58.8376	+	76.5029i	−0.235350	+	0.306012i
$251$			365.146i			1.45476i	0.686233	+	0.727382i	$0.259263\pi$
$251$			365.146i			1.45476i	−0.686233	+	0.727382i	$0.740737\pi$
$252$	−51.7843	−	8.14795i	−0.205493	−	0.0323332i
$253$	229.023	+	74.4140i	0.905229	+	0.294127i
$254$	−112.987	−	36.7118i	−0.444832	−	0.144535i
$255$	−218.884	−	7.61334i	−0.858367	−	0.0298562i
$256$	−14.2272	−	43.7869i	−0.0555751	−	0.171043i
$257$	142.469			0.554354			0.277177	−	0.960819i	$-0.410601\pi$
$257$	142.469			0.554354			0.277177	+	0.960819i	$0.410601\pi$
$258$	−110.258	−	128.963i	−0.427356	−	0.499856i
$259$	−2.75483	−	2.00150i	−0.0106364	−	0.00772780i
$260$	−203.455	+	41.3150i	−0.782518	+	0.158904i
$261$	−356.804	−	56.1409i	−1.36706	−	0.215099i
$262$	75.9151	−	104.488i	0.289752	−	0.398810i
$263$	198.261	+	144.045i	0.753843	+	0.547699i	0.897016	−	0.441998i	$-0.145730\pi$
$263$	198.261	+	144.045i	0.753843	+	0.547699i	−0.143172	+	0.989698i	$0.545730\pi$
$264$	56.1756	−	91.7748i	0.212786	−	0.347632i
$265$	307.670	+	282.137i	1.16102	+	1.06467i
$266$	−10.5464	+	14.5159i	−0.0396482	+	0.0545711i
$267$	207.067	+	242.195i	0.775531	+	0.907098i
$268$			90.6277i			0.338163i
$269$	−110.951	+	36.0503i	−0.412459	+	0.134016i	−0.507894	−	0.861420i	$-0.669576\pi$
$269$	−110.951	+	36.0503i	−0.412459	+	0.134016i	0.0954349	+	0.995436i	$0.469576\pi$
$270$	−44.1596	−	94.4162i	−0.163554	−	0.349690i
$271$	−53.8737	+	165.806i	−0.198796	+	0.611831i	0.801115	+	0.598510i	$0.204240\pi$
$271$	−53.8737	+	165.806i	−0.198796	+	0.611831i	−0.999911	+	0.0133212i	$0.995760\pi$
$272$	41.5183	−	127.780i	0.152641	−	0.469780i
$273$	53.4091	+	32.6918i	0.195638	+	0.119750i
$274$	147.761			0.539273
$275$	35.3987	−	152.813i	0.128723	−	0.555685i
$276$	150.164	+	362.009i	0.544073	+	1.31163i
$277$	107.330	+	147.728i	0.387475	+	0.533313i	0.957545	−	0.288282i	$-0.0930842\pi$
$277$	107.330	+	147.728i	0.387475	+	0.533313i	−0.570071	+	0.821596i	$0.693084\pi$
$278$	1.97747	−	6.08604i	0.00711322	−	0.0218922i
$279$	−110.012	−	215.370i	−0.394308	−	0.771934i
$280$	−5.55468	+	48.5931i	−0.0198381	+	0.173547i
$281$	17.1449	−	5.57070i	0.0610137	−	0.0198246i	−0.278351	−	0.960479i	$-0.589788\pi$
$281$	17.1449	−	5.57070i	0.0610137	−	0.0198246i	0.339365	+	0.940655i	$0.389788\pi$
$282$	−15.5715	−	37.5389i	−0.0552179	−	0.133117i
$283$	19.2974	−	6.27010i	0.0681887	−	0.0221558i	−0.274724	−	0.961523i	$-0.588586\pi$
$283$	19.2974	−	6.27010i	0.0681887	−	0.0221558i	0.342913	+	0.939367i	$0.388586\pi$
$284$	172.177	−	236.982i	0.606258	−	0.834443i
$285$	203.587	+	7.08129i	0.714341	+	0.0248466i
$286$	−47.8079	+	34.7345i	−0.167160	+	0.121449i
$287$	−48.7546	−	35.4223i	−0.169877	−	0.123423i
$288$	266.372	−	42.4664i	0.924902	−	0.147453i
$289$	61.3306	−	44.5593i	0.212217	−	0.154184i
$290$	−17.5956	+	153.929i	−0.0606744	+	0.530788i
$291$	−263.800	−	63.1912i	−0.906530	−	0.217152i
$292$	31.3082	−	10.1727i	0.107220	−	0.0348379i
$293$	−121.001			−0.412971			−0.206486	−	0.978450i	$-0.566203\pi$
$293$	−121.001			−0.412971			−0.206486	+	0.978450i	$0.566203\pi$
$294$	−81.1121	+	69.3475i	−0.275891	+	0.235876i
$295$	−23.5577	−	41.6740i	−0.0798565	−	0.141268i
$296$	10.8188	+	3.51524i	0.0365500	+	0.0118758i
$297$	128.987	+	109.826i	0.434298	+	0.369784i
$298$	−120.847	−	166.331i	−0.405526	−	0.558159i
$299$		−	468.167i		−	1.56577i
$300$	226.472	−	117.827i	0.754908	−	0.392758i
$301$	−125.346			−0.416430
$302$	130.700	−	94.9588i	0.432780	−	0.314433i
$303$	−37.2453	−	470.195i	−0.122922	−	1.55180i
$304$	−38.6168	+	118.850i	−0.127029	+	0.390955i
$305$	−2.04512	−	10.0711i	−0.00670531	−	0.0330201i
$306$	−90.4490	−	45.9704i	−0.295585	−	0.150230i
$307$			186.483i			0.607435i	0.952762	+	0.303718i	$0.0982279\pi$
$307$			186.483i			0.607435i	−0.952762	+	0.303718i	$0.901772\pi$
$308$	−11.2933	−	34.7572i	−0.0366665	−	0.112848i
$309$	−269.616	−	64.5844i	−0.872545	−	0.209011i
$310$	−90.3056	+	51.0484i	−0.291308	+	0.164672i
$311$	188.941	+	260.055i	0.607526	+	0.836188i	0.996371	−	0.0851150i	$-0.0271258\pi$
$311$	188.941	+	260.055i	0.607526	+	0.836188i	−0.388845	+	0.921303i	$0.627126\pi$
$312$	−203.439	−	48.7322i	−0.652049	−	0.156193i
$313$	−117.969	+	162.371i	−0.376899	+	0.518757i	−0.954760	−	0.297378i	$-0.903888\pi$
$313$	−117.969	+	162.371i	−0.376899	+	0.518757i	0.577861	+	0.816135i	$0.303888\pi$
$314$	98.4715	+	135.534i	0.313603	+	0.431638i
$315$	−74.2155	−	20.5302i	−0.235605	−	0.0651752i
$316$	−370.126	−	268.912i	−1.17128	−	0.850988i
$317$	−124.913	−	384.444i	−0.394048	−	1.21276i	−0.929700	−	0.368317i	$-0.879934\pi$
$317$	−124.913	−	384.444i	−0.394048	−	1.21276i	0.535652	−	0.844439i	$-0.320066\pi$
$318$	74.0962	+	178.627i	0.233007	+	0.561721i
$319$	−77.8128	−	239.483i	−0.243927	−	0.750731i
$320$	13.5990	+	66.9680i	0.0424970	+	0.209275i
$321$	−12.7422	+	1.00934i	−0.0396954	+	0.00314437i
$322$	−48.2250	−	15.6693i	−0.149767	−	0.0486623i
$323$	160.422	−	116.553i	0.496663	−	0.360847i
$324$	0.559787	+	275.713i	0.00172774	+	0.850965i
$325$	−303.817	+	26.3542i	−0.934820	+	0.0810900i
$326$			10.9736i			0.0336614i
$327$	−394.075	−	241.214i	−1.20512	−	0.737659i
$328$	191.470	+	62.2124i	0.583750	+	0.189672i
$329$	−28.5539	−	9.27772i	−0.0867900	−	0.0281998i
$330$	44.7300	−	57.2681i	0.135545	−	0.173540i
$331$	−162.219	−	499.260i	−0.490089	−	1.50834i	−0.824473	−	0.565902i	$-0.808528\pi$
$331$	−162.219	−	499.260i	−0.490089	−	1.50834i	0.334384	−	0.942437i	$-0.391472\pi$
$332$	−6.81630			−0.0205310
$333$	−8.11458	+	15.9658i	−0.0243681	+	0.0479454i
$334$	9.23389	+	6.70881i	0.0276464	+	0.0200863i
$335$	−15.1190	+	132.263i	−0.0451314	+	0.394816i
$336$	24.6611	−	40.2892i	0.0733962	−	0.119908i
$337$	216.442	−	297.907i	0.642261	−	0.883996i	−0.356473	−	0.934306i	$-0.616021\pi$
$337$	216.442	−	297.907i	0.642261	−	0.883996i	0.998734	+	0.0503096i	$0.0160208\pi$
$338$	−12.6186	−	9.16795i	−0.0373331	−	0.0271241i
$339$	−57.5629	−	35.2344i	−0.169802	−	0.103936i
$340$	103.135	−	226.088i	0.303338	−	0.664964i
$341$	99.1005	−	136.400i	0.290617	−	0.400001i
$342$	84.1280	+	42.7578i	0.245988	+	0.125023i
$343$			162.684i			0.474298i
$344$	398.246	−	129.398i	1.15769	−	0.376157i
$345$	158.759	+	553.371i	0.460172	+	1.60398i
$346$	−33.6571	+	103.586i	−0.0972750	+	0.299382i
$347$	59.4858	−	183.079i	0.171429	−	0.527604i	−0.828024	−	0.560693i	$-0.810535\pi$
$347$	59.4858	−	183.079i	0.171429	−	0.527604i	0.999452	+	0.0330896i	$0.0105347\pi$
$348$	213.952	−	349.536i	0.614805	−	1.00441i
$349$	−293.490			−0.840945			−0.420473	−	0.907305i	$-0.638136\pi$
$349$	−293.490			−0.840945			−0.420473	+	0.907305i	$0.638136\pi$
$350$	−7.45386	+	32.1777i	−0.0212967	+	0.0919362i
$351$	125.575	−	304.475i	0.357763	−	0.867450i
$352$	110.532	+	152.134i	0.314010	+	0.432198i
$353$	−171.108	+	526.617i	−0.484726	+	1.49183i	0.347652	+	0.937624i	$0.386979\pi$
$353$	−171.108	+	526.617i	−0.484726	+	1.49183i	−0.832378	+	0.554209i	$0.813021\pi$
$354$	−1.75120	−	22.1076i	−0.00494688	−	0.0624508i
$355$	290.812	−	317.131i	0.819190	−	0.893326i
$356$	−343.848	+	111.723i	−0.965864	+	0.313828i
$357$	−69.2347	+	28.7191i	−0.193935	+	0.0804457i
$358$	−14.5366	+	4.72321i	−0.0406049	+	0.0131933i
$359$	−85.3501	+	117.474i	−0.237744	+	0.327227i	−0.911172	−	0.412026i	$-0.864821\pi$
$359$	−85.3501	+	117.474i	−0.237744	+	0.327227i	0.673428	+	0.739253i	$0.264821\pi$
$360$	256.990	−	11.3867i	0.713861	−	0.0316296i
$361$	142.844	−	103.782i	0.395690	−	0.287486i
$362$	49.9487	+	36.2898i	0.137980	+	0.100248i
$363$	57.0490	−	238.159i	0.157160	−	0.656084i
$364$	−57.4809	+	41.7623i	−0.157915	+	0.114732i
$365$	47.3887	−	9.62310i	0.129832	−	0.0263646i
$366$	1.10903	−	4.62977i	0.00303012	−	0.0126497i
$367$	−224.988	+	73.1032i	−0.613047	+	0.199191i	−0.599051	−	0.800711i	$-0.704455\pi$
$367$	−224.988	+	73.1032i	−0.613047	+	0.199191i	−0.0139964	+	0.999902i	$0.504455\pi$
$368$	−353.162			−0.959678
$369$	−143.611	+	282.561i	−0.389190	+	0.765748i
$370$	6.98931	+	3.18833i	0.0188900	+	0.00861711i
$371$	135.873	+	44.1477i	0.366233	+	0.118996i
$372$	273.541	−	21.6678i	0.735324	−	0.0582468i
$373$	−168.516	−	231.942i	−0.451784	−	0.621828i	0.520995	−	0.853559i	$-0.325561\pi$
$373$	−168.516	−	231.942i	−0.451784	−	0.621828i	−0.972780	+	0.231732i	$0.925561\pi$
$374$		−	70.7338i		−	0.189128i
$375$	350.173	−	134.178i	0.933796	−	0.357807i
$376$	100.299			0.266752
$377$	−396.054	+	287.750i	−1.05054	+	0.763263i
$378$	−27.1605	−	23.1258i	−0.0718532	−	0.0611795i
$379$	−38.5235	+	118.563i	−0.101645	+	0.312831i	−0.988928	−	0.148393i	$-0.952590\pi$
$379$	−38.5235	+	118.563i	−0.101645	+	0.312831i	0.887283	+	0.461225i	$0.152590\pi$
$380$	−95.9276	+	210.288i	−0.252441	+	0.553389i
$381$	299.969	+	350.857i	0.787319	+	0.920885i
$382$		−	108.022i		−	0.282781i
$383$	210.811	+	648.811i	0.550422	+	1.69402i	0.707738	+	0.706475i	$0.249716\pi$
$383$	210.811	+	648.811i	0.550422	+	1.69402i	−0.157316	+	0.987548i	$0.550284\pi$
$384$	−91.1550	+	380.539i	−0.237383	+	0.990987i
$385$	−10.6832	−	52.6090i	−0.0277485	−	0.136647i
$386$	81.4087	+	112.050i	0.210903	+	0.290284i
$387$	103.792	+	651.040i	0.268197	+	1.68227i
$388$	180.909	−	249.000i	0.466261	−	0.641753i
$389$	−16.7972	−	23.1194i	−0.0431805	−	0.0594329i	0.786881	−	0.617105i	$-0.211695\pi$
$389$	−16.7972	−	23.1194i	−0.0431805	−	0.0594329i	−0.830061	+	0.557672i	$0.811695\pi$
$390$	−132.761	−	48.3002i	−0.340412	−	0.123847i
$391$	453.360	+	329.385i	1.15949	+	0.842418i
$392$	−81.3857	−	250.479i	−0.207617	−	0.638978i
$393$	−463.536	+	192.279i	−1.17948	+	0.489259i
$394$	−3.85162	−	11.8541i	−0.00977569	−	0.0300865i
$395$	−495.305	−	454.200i	−1.25394	−	1.14987i
$396$	−171.176	+	87.4375i	−0.432262	+	0.220802i
$397$	−195.376	−	63.4815i	−0.492131	−	0.159903i	0.0524297	−	0.998625i	$-0.483303\pi$
$397$	−195.376	−	63.4815i	−0.492131	−	0.159903i	−0.544560	+	0.838722i	$0.683303\pi$
$398$	−215.123	+	156.296i	−0.540511	+	0.392704i
$399$	64.3963	−	26.7121i	0.161394	−	0.0669476i
$400$	19.8803	+	229.184i	0.0497008	+	0.572960i
$401$		−	396.678i		−	0.989222i	−0.869115	−	0.494611i	$-0.835311\pi$
$401$		−	396.678i		−	0.989222i	0.869115	−	0.494611i	$-0.164689\pi$
$402$	−32.1963	+	52.5995i	−0.0800903	+	0.130845i
$403$	−311.739	−	101.290i	−0.773547	−	0.251341i
$404$	508.972	+	165.375i	1.25983	+	0.409344i
$405$	−45.1790	+	402.472i	−0.111553	+	0.993758i
$406$	16.3849	+	50.4276i	0.0403570	+	0.124206i
$407$	−12.4858			−0.0306775
$408$	190.324	−	162.719i	0.466480	−	0.398821i
$409$	279.949	+	203.395i	0.684472	+	0.497298i	0.874838	−	0.484415i	$-0.160968\pi$
$409$	279.949	+	203.395i	0.684472	+	0.497298i	−0.190366	+	0.981713i	$0.560968\pi$
$410$	123.696	+	56.4267i	0.301697	+	0.137626i
$411$	−489.677	−	299.733i	−1.19143	−	0.729277i
$412$	184.898	−	254.490i	0.448781	−	0.617694i
$413$	−13.2544	−	9.62985i	−0.0320929	−	0.0233168i
$414$	−41.4528	+	263.454i	−0.100128	+	0.636361i
$415$	−9.94780	−	1.13713i	−0.0239706	−	0.00274008i
$416$	214.889	−	295.769i	0.516560	−	0.710984i
$417$	−18.8989	+	16.1578i	−0.0453210	+	0.0387476i
$418$			65.7907i			0.157394i
$419$	158.769	−	51.5871i	0.378923	−	0.123120i	−0.113362	−	0.993554i	$-0.536162\pi$
$419$	158.769	−	51.5871i	0.378923	−	0.123120i	0.492285	+	0.870434i	$0.336162\pi$
$420$	53.7803	−	68.8552i	0.128048	−	0.163941i
$421$	10.2098	−	31.4226i	0.0242514	−	0.0746380i	−0.938198	−	0.346098i	$-0.887506\pi$
$421$	10.2098	−	31.4226i	0.0242514	−	0.0746380i	0.962450	+	0.271460i	$0.0875065\pi$
$422$	−9.13812	+	28.1242i	−0.0216543	+	0.0666451i
$423$	−24.5441	+	155.990i	−0.0580239	+	0.368771i
$424$	−477.267			−1.12563
$425$	188.234	−	312.750i	0.442903	−	0.735882i
$426$	184.120	−	76.3745i	0.432206	−	0.179283i
$427$	−2.06726	−	2.84534i	−0.00484136	−	0.00666356i
$428$	4.48165	−	13.7931i	0.0104711	−	0.0322268i
$429$	228.894	−	18.1312i	0.533552	−	0.0422639i
$430$	277.129	−	56.2758i	0.644485	−	0.130874i
$431$	570.239	−	185.282i	1.32306	−	0.429888i	0.439516	−	0.898235i	$-0.355150\pi$
$431$	570.239	−	185.282i	1.32306	−	0.429888i	0.883545	+	0.468347i	$0.155150\pi$
$432$	−229.681	−	94.7274i	−0.531669	−	0.219277i
$433$	265.335	−	86.2124i	0.612782	−	0.199105i	0.0138489	−	0.999904i	$-0.495592\pi$
$433$	265.335	−	86.2124i	0.612782	−	0.199105i	0.598933	+	0.800799i	$0.295592\pi$
$434$	−20.8675	+	28.7216i	−0.0480817	+	0.0661788i
$435$	370.556	−	474.425i	0.851853	−	1.09063i
$436$	424.118	−	308.140i	0.972749	−	0.706743i
$437$	−421.678	−	306.367i	−0.964937	−	0.701068i
$438$	21.7849	+	5.21840i	0.0497373	+	0.0119142i
$439$	243.371	−	176.819i	0.554376	−	0.402778i	−0.275020	−	0.961438i	$-0.588685\pi$
$439$	243.371	−	176.819i	0.554376	−	0.402778i	0.829396	+	0.558661i	$0.188685\pi$
$440$	88.2523	+	156.120i	0.200574	+	0.354818i
$441$	409.476	−	65.2808i	0.928517	−	0.148029i
$442$	−130.786	+	42.4950i	−0.295896	+	0.0961425i
$443$	−225.255			−0.508477			−0.254239	−	0.967142i	$-0.581825\pi$
$443$	−225.255			−0.508477			−0.254239	+	0.967142i	$0.581825\pi$
$444$	−13.2050	−	15.4452i	−0.0297411	−	0.0347866i
$445$	−520.454	+	105.687i	−1.16956	+	0.237500i
$446$	−184.579	−	59.9733i	−0.413854	−	0.134469i
$447$	63.0815	+	796.358i	0.141122	+	1.78156i
$448$	13.7463	+	18.9201i	0.0306836	+	0.0422324i
$449$			544.155i			1.21193i	0.795493	+	0.605963i	$0.207212\pi$
$449$			544.155i			1.21193i	−0.795493	+	0.605963i	$0.792788\pi$
$450$	173.302	+	12.0704i	0.385115	+	0.0268230i
$451$	−220.971			−0.489959
$452$	61.9514	−	45.0103i	0.137061	−	0.0995803i
$453$	−625.761	+	49.5681i	−1.38137	+	0.109422i
$454$	−8.37923	+	25.7886i	−0.0184565	+	0.0568031i
$455$	−90.8554	+	51.3592i	−0.199682	+	0.112877i
$456$	−177.023	+	151.347i	−0.388209	+	0.331902i
$457$			166.755i			0.364890i	0.983216	+	0.182445i	$0.0584012\pi$
$457$			166.755i			0.364890i	−0.983216	+	0.182445i	$0.941599\pi$
$458$	−34.8015	−	107.108i	−0.0759859	−	0.233861i
$459$	206.496	+	335.821i	0.449882	+	0.731637i
$460$	−648.970	−	74.1838i	−1.41080	−	0.161269i
$461$	−82.9803	−	114.213i	−0.180001	−	0.247750i	0.709477	−	0.704729i	$-0.248931\pi$
$461$	−82.9803	−	114.213i	−0.180001	−	0.247750i	−0.889477	+	0.456979i	$0.848931\pi$
$462$	5.79327	−	24.1848i	0.0125395	−	0.0523480i
$463$	−275.071	+	378.603i	−0.594106	+	0.817717i	−0.995153	−	0.0983404i	$-0.968647\pi$
$463$	−275.071	+	378.603i	−0.594106	+	0.817717i	0.401046	+	0.916058i	$0.368647\pi$
$464$	217.064	+	298.763i	0.467811	+	0.643887i
$465$	402.823	+	14.0112i	0.866287	+	0.0301317i
$466$	82.0014	+	59.5775i	0.175969	+	0.127849i
$467$	36.4887	+	112.301i	0.0781342	+	0.240472i	0.982493	−	0.186301i	$-0.0596501\pi$
$467$	36.4887	+	112.301i	0.0781342	+	0.240472i	−0.904358	+	0.426774i	$0.859650\pi$
$468$	264.509	+	263.972i	0.565190	+	0.564043i
$469$	14.0788	+	43.3300i	0.0300187	+	0.0923880i
$470$	67.2957	+	7.69257i	0.143182	+	0.0163672i
$471$	−51.4017	−	648.909i	−0.109133	−	1.37773i
$472$	52.0527	+	16.9130i	0.110281	+	0.0358325i
$473$	−371.830	+	270.150i	−0.786110	+	0.571142i
$474$	−119.284	−	287.565i	−0.251654	−	0.606676i
$475$	−175.079	+	290.894i	−0.368588	+	0.612408i
$476$		−	85.0455i		−	0.178667i
$477$	116.792	−	742.273i	0.244847	−	1.55613i
$478$	126.076	+	40.9645i	0.263757	+	0.0856998i
$479$	3.93806	+	1.27955i	0.00822141	+	0.00267130i	0.313125	−	0.949712i	$-0.398624\pi$
$479$	3.93806	+	1.27955i	0.00822141	+	0.00267130i	−0.304903	+	0.952383i	$0.598624\pi$
$480$	−153.700	+	422.469i	−0.320209	+	0.880144i
$481$	7.50110	+	23.0860i	0.0155948	+	0.0479959i
$482$	−309.616			−0.642357
$483$	128.032	+	149.752i	0.265077	+	0.310046i
$484$	224.797	+	163.325i	0.464457	+	0.337448i
$485$	305.561	−	333.214i	0.630023	−	0.687039i
$486$	−97.6245	+	160.220i	−0.200873	+	0.329671i
$487$	481.749	−	663.071i	0.989218	−	1.36154i	0.0575051	−	0.998345i	$-0.481685\pi$
$487$	481.749	−	663.071i	0.989218	−	1.36154i	0.931713	−	0.363196i	$-0.118315\pi$
$488$	9.50540	+	6.90608i	0.0194783	+	0.0141518i
$489$	22.2600	−	36.3665i	0.0455215	−	0.0743691i
$490$	−35.3951	−	174.302i	−0.0722348	−	0.355718i
$491$	−229.669	+	316.113i	−0.467758	+	0.643814i	−0.976095	−	0.217344i	$-0.930261\pi$
$491$	−229.669	+	316.113i	−0.467758	+	0.643814i	0.508337	+	0.861158i	$0.330261\pi$
$492$	−233.701	−	273.348i	−0.475002	−	0.555585i
$493$		−	585.979i		−	1.18860i
$494$	121.646	−	39.5252i	0.246247	−	0.0800106i
$495$	−264.403	+	99.0509i	−0.534148	+	0.200103i
$496$	−76.4083	+	235.161i	−0.154049	+	0.474114i
$497$	45.5051	−	140.050i	0.0915596	−	0.281792i
$498$	−3.95612	−	2.42155i	−0.00794401	−	0.00486255i
$499$	−901.118			−1.80585			−0.902923	−	0.429801i	$-0.858584\pi$
$499$	−901.118			−1.80585			−0.902923	+	0.429801i	$0.858584\pi$
$500$	−11.6094	+	425.325i	−0.0232189	+	0.850650i
$501$	−16.9922	−	40.9639i	−0.0339165	−	0.0817642i
$502$	−165.713	−	228.084i	−0.330105	−	0.454351i
$503$	158.993	−	489.331i	0.316090	−	0.972825i	−0.659213	−	0.751956i	$-0.729111\pi$
$503$	158.993	−	489.331i	0.316090	−	0.972825i	0.975303	−	0.220869i	$-0.0708894\pi$
$504$	78.4011	−	40.0476i	0.155558	−	0.0794596i
$505$	715.212	+	326.260i	1.41626	+	0.646059i
$506$	−176.828	+	57.4548i	−0.349462	+	0.113547i
$507$	23.2207	+	55.9793i	0.0458002	+	0.110413i
$508$	−498.117	+	161.848i	−0.980545	+	0.318598i
$509$	−91.7524	+	126.286i	−0.180260	+	0.248107i	−0.889579	−	0.456781i	$-0.849002\pi$
$509$	−91.7524	+	126.286i	−0.180260	+	0.248107i	0.709319	+	0.704887i	$0.249002\pi$
$510$	140.178	−	94.5796i	0.274859	−	0.185450i
$511$	13.3885	−	9.72728i	0.0262005	−	0.0190358i
$512$	−393.337	−	285.776i	−0.768237	−	0.558157i
$513$	−192.065	−	312.353i	−0.374395	−	0.608875i
$514$	−88.9917	+	64.6562i	−0.173136	+	0.125790i
$515$	312.298	−	340.560i	0.606403	−	0.661282i
$516$	−727.434	−	174.251i	−1.40976	−	0.337696i
$517$	−104.699	+	34.0188i	−0.202513	+	0.0658004i
$518$	2.62911			0.00507549
$519$	321.664	−	275.009i	0.619776	−	0.529883i
$520$	235.645	−	256.970i	0.453163	−	0.494174i
$521$	749.697	+	243.591i	1.43896	+	0.467546i	0.921573	−	0.388206i	$-0.126905\pi$
$521$	749.697	+	243.591i	1.43896	+	0.467546i	0.517386	+	0.855752i	$0.326905\pi$
$522$	248.352	−	126.859i	0.475769	−	0.243025i
$523$	106.206	+	146.180i	0.203070	+	0.279503i	0.898390	−	0.439198i	$-0.144737\pi$
$523$	106.206	+	146.180i	0.203070	+	0.279503i	−0.695320	+	0.718700i	$0.744737\pi$
$524$		−	569.392i		−	1.08663i
$525$	89.9744	−	91.5162i	0.171380	−	0.174317i
$526$	−189.213			−0.359720
$527$	317.416	−	230.616i	0.602307	−	0.437601i
$528$	−13.6773	−	172.666i	−0.0259040	−	0.327019i
$529$	291.711	−	897.795i	0.551439	−	1.69716i
$530$	−320.224	−	36.6048i	−0.604196	−	0.0690657i
$531$	−39.0418	+	76.8166i	−0.0735251	+	0.144664i
$532$			79.1021i			0.148688i
$533$	132.754	+	408.574i	0.249069	+	0.766555i
$534$	−239.257	−	57.3120i	−0.448046	−	0.107326i
$535$	8.84161	−	19.3822i	0.0165264	−	0.0362283i
$536$	−89.4616	−	123.133i	−0.166906	−	0.229726i
$537$	57.7550	+	13.8348i	0.107551	+	0.0257630i
$538$	52.9440	−	72.8711i	0.0984089	−	0.135448i
$539$	169.913	+	233.865i	0.315237	+	0.433887i
$540$	−402.164	−	222.317i	−0.744748	−	0.411698i
$541$	107.419	+	78.0448i	0.198557	+	0.144260i	0.682621	−	0.730772i	$-0.260840\pi$
$541$	107.419	+	78.0448i	0.198557	+	0.144260i	−0.484064	+	0.875033i	$0.660840\pi$
$542$	−41.5957	−	128.018i	−0.0767448	−	0.236196i
$543$	−91.9153	−	221.585i	−0.169273	−	0.408075i
$544$	135.227	+	416.186i	0.248579	+	0.765047i
$545$	670.370	−	378.950i	1.23004	−	0.695321i
$546$	−48.1978	+	3.81787i	−0.0882744	+	0.00699243i
$547$	−113.633	−	36.9217i	−0.207739	−	0.0674986i	0.203299	−	0.979117i	$-0.434834\pi$
$547$	−113.633	−	36.9217i	−0.207739	−	0.0674986i	−0.411038	+	0.911618i	$0.634834\pi$
$548$	527.009	−	382.895i	0.961696	−	0.698713i
$549$	−13.0668	+	13.0934i	−0.0238011	+	0.0238495i
$550$	47.2393	+	111.518i	0.0858897	+	0.202760i
$551$			545.028i			0.989162i
$552$	−561.375	−	343.619i	−1.01698	−	0.622498i
$553$	−218.735	−	71.0715i	−0.395543	−	0.128520i
$554$	−134.086	−	43.5670i	−0.242032	−	0.0786408i
$555$	−16.6949	−	24.7439i	−0.0300810	−	0.0445836i
$556$	−8.71791	−	26.8310i	−0.0156797	−	0.0482571i
$557$	−619.206			−1.11168			−0.555841	−	0.831289i	$-0.687603\pi$
$557$	−619.206			−1.11168			−0.555841	+	0.831289i	$0.687603\pi$
$558$	166.458	+	84.6019i	0.298312	+	0.151616i
$559$	722.890	+	525.210i	1.29318	+	0.939553i
$560$	38.7428	+	68.5368i	0.0691836	+	0.122387i
$561$	−143.484	+	234.411i	−0.255764	+	0.417845i
$562$	−8.18121	+	11.2605i	−0.0145573	+	0.0200364i
$563$	102.281	+	74.3113i	0.181671	+	0.131992i	0.674904	−	0.737906i	$-0.264185\pi$
$563$	102.281	+	74.3113i	0.181671	+	0.131992i	−0.493233	+	0.869897i	$0.664185\pi$
$564$	−152.813	−	93.5372i	−0.270945	−	0.165846i
$565$	97.9215	−	55.3536i	0.173312	−	0.0979709i
$566$	−9.20836	+	12.6742i	−0.0162692	+	0.0223926i
$567$	43.0988	+	131.734i	0.0760121	+	0.232335i
$568$			491.942i			0.866096i
$569$	−937.859	+	304.729i	−1.64826	+	0.535552i	−0.978362	−	0.206903i	$-0.933662\pi$
$569$	−937.859	+	304.729i	−1.64826	+	0.535552i	−0.669897	+	0.742454i	$0.733662\pi$
$570$	−130.382	+	87.9700i	−0.228740	+	0.154333i
$571$	−12.9513	+	39.8601i	−0.0226819	+	0.0698076i	−0.961757	−	0.273905i	$-0.911685\pi$
$571$	−12.9513	+	39.8601i	−0.0226819	+	0.0698076i	0.939075	+	0.343713i	$0.111685\pi$
$572$	−80.5056	+	247.771i	−0.140744	+	0.433165i
$573$	−219.124	+	357.985i	−0.382415	+	0.624756i
$574$	46.5296			0.0810620
$575$	−934.740	−	216.530i	−1.62563	−	0.376573i
$576$	86.8877	−	87.0643i	0.150847	−	0.151153i
$577$	520.698	+	716.679i	0.902423	+	1.24208i	0.969689	+	0.244343i	$0.0785723\pi$
$577$	520.698	+	716.679i	0.902423	+	1.24208i	−0.0672662	+	0.997735i	$0.521428\pi$
$578$	−18.0873	+	55.6669i	−0.0312928	+	0.0963095i
$579$	−42.4950	−	536.468i	−0.0733938	−	0.926543i
$580$	336.121	+	594.604i	0.579518	+	1.02518i
$581$	−3.25894	+	1.05889i	−0.00560919	+	0.00182254i
$582$	193.458	−	80.2479i	0.332401	−	0.137883i
$583$	498.207	−	161.877i	0.854557	−	0.277662i
$584$	−32.4958	+	44.7267i	−0.0556435	+	0.0765868i
$585$	341.990	+	429.371i	0.584599	+	0.733968i
$586$	75.5817	−	54.9133i	0.128979	−	0.0937087i
$587$	806.259	+	585.781i	1.37352	+	0.997924i	0.997453	+	0.0713330i	$0.0227253\pi$
$587$	806.259	+	585.781i	1.37352	+	0.997924i	0.376071	+	0.926591i	$0.377275\pi$
$588$	−109.596	+	457.525i	−0.186388	+	0.778103i
$589$	−295.233	+	214.500i	−0.501245	+	0.364176i
$590$	33.6278	+	15.3401i	0.0569962	+	0.0260001i
$591$	−11.2818	+	47.0973i	−0.0190893	+	0.0796908i
$592$	17.4149	−	5.65846i	0.0294171	−	0.00955820i
$593$	507.055			0.855068			0.427534	−	0.903999i	$-0.359382\pi$
$593$	507.055			0.855068			0.427534	+	0.903999i	$0.359382\pi$
$594$	−130.412	−	10.0638i	−0.219549	−	0.0169425i
$595$	14.1878	−	124.116i	0.0238450	−	0.208599i
$596$	−862.034	−	280.092i	−1.44637	−	0.469953i
$597$	1029.96	−	81.5859i	1.72523	−	0.136660i
$598$	212.466	+	292.435i	0.355295	+	0.489022i
$599$		−	675.422i		−	1.12758i	−0.825917	−	0.563791i	$-0.809342\pi$
$599$		−	675.422i		−	1.12758i	0.825917	−	0.563791i	$-0.190658\pi$
$600$	−191.390	+	383.647i	−0.318984	+	0.639412i
$601$	−659.654			−1.09759			−0.548797	−	0.835956i	$-0.684914\pi$
$601$	−659.654			−1.09759			−0.548797	+	0.835956i	$0.684914\pi$
$602$	78.2956	−	56.8851i	0.130059	−	0.0944935i
$603$	213.396	−	109.004i	0.353891	−	0.180769i
$604$	220.090	−	677.368i	0.364388	−	1.12147i
$605$	300.825	+	275.860i	0.497232	+	0.455967i
$606$	236.652	+	276.799i	0.390514	+	0.456764i
$607$			1147.75i			1.89085i	0.325837	+	0.945426i	$0.394354\pi$
$607$			1147.75i			1.89085i	−0.325837	+	0.945426i	$0.605646\pi$
$608$	−125.777	−	387.101i	−0.206870	−	0.636679i
$609$	47.9931	−	200.353i	0.0788063	−	0.328988i
$610$	5.84801	+	5.36269i	0.00958690	+	0.00879129i
$611$	125.801	+	173.150i	0.205893	+	0.283388i
$612$	−441.723	+	70.4218i	−0.721769	+	0.115068i
$613$	−346.355	+	476.717i	−0.565016	+	0.777678i	−0.991953	−	0.126603i	$-0.959593\pi$
$613$	−346.355	+	476.717i	−0.565016	+	0.777678i	0.426937	+	0.904281i	$0.359593\pi$
$614$	−84.6307	−	116.484i	−0.137835	−	0.189714i
$615$	−295.465	−	437.915i	−0.480431	−	0.712057i
$616$	49.6538	+	36.0756i	0.0806068	+	0.0585643i
$617$	160.785	+	494.845i	0.260591	+	0.802017i	0.992676	+	0.120804i	$0.0385473\pi$
$617$	160.785	+	494.845i	0.260591	+	0.802017i	−0.732085	+	0.681213i	$0.761453\pi$
$618$	197.723	−	82.0171i	0.319940	−	0.132714i
$619$	25.3157	+	77.9139i	0.0408978	+	0.125871i	0.969421	−	0.245404i	$-0.0789207\pi$
$619$	25.3157	+	77.9139i	0.0408978	+	0.125871i	−0.928523	+	0.371275i	$0.878921\pi$
$620$	−189.805	+	416.082i	−0.306137	+	0.671099i
$621$	671.790	−	788.995i	1.08179	−	1.27052i
$622$	−236.039	−	76.6938i	−0.379484	−	0.123302i
$623$	−147.041	+	106.832i	−0.236021	+	0.171479i
$624$	−311.041	+	129.022i	−0.498462	+	0.206766i
$625$	−87.8980	+	618.788i	−0.140637	+	0.990061i
$626$		−	154.961i		−	0.247541i
$627$	133.456	−	218.029i	0.212849	−	0.347734i
$628$	702.425	+	228.232i	1.11851	+	0.363426i
$629$	−27.6334	−	8.97863i	−0.0439323	−	0.0142745i
$630$	55.6750	−	20.8570i	0.0883730	−	0.0331063i
$631$	80.8343	+	248.782i	0.128105	+	0.394267i	0.994454	−	0.105172i	$-0.0335394\pi$
$631$	80.8343	+	248.782i	0.128105	+	0.394267i	−0.866349	+	0.499439i	$0.833539\pi$
$632$	768.332			1.21572
$633$	87.3337	−	74.6667i	0.137968	−	0.117957i
$634$	252.496	+	183.449i	0.398259	+	0.289352i
$635$	−753.958	+	153.104i	−1.18734	+	0.241109i
$636$	727.154	+	445.093i	1.14332	+	0.699832i
$637$	330.335	−	454.667i	0.518579	−	0.713762i
$638$	157.289	+	114.277i	0.246534	+	0.179117i
$639$	−765.097	−	120.383i	−1.19733	−	0.188393i
$640$	−480.670	−	440.780i	−0.751047	−	0.688719i
$641$	−225.134	+	309.870i	−0.351222	+	0.483416i	−0.947677	−	0.319231i	$-0.896576\pi$
$641$	−225.134	+	309.870i	−0.351222	+	0.483416i	0.596455	+	0.802647i	$0.296576\pi$
$642$	7.50122	−	6.41323i	0.0116841	−	0.00998946i
$643$		−	657.068i		−	1.02188i	−0.859617	−	0.510940i	$-0.829298\pi$
$643$		−	657.068i		−	1.02188i	0.859617	−	0.510940i	$-0.170702\pi$
$644$	−212.605	+	69.0796i	−0.330132	+	0.107266i
$645$	−1032.56	−	375.659i	−1.60086	−	0.582416i
$646$	−47.3108	+	145.608i	−0.0732365	+	0.225399i
$647$	−228.875	+	704.403i	−0.353747	+	1.08872i	0.602985	+	0.797753i	$0.293978\pi$
$647$	−228.875	+	704.403i	−0.353747	+	1.08872i	−0.956732	+	0.290970i	$0.906022\pi$
$648$	−272.926	−	374.051i	−0.421182	−	0.577239i
$649$	−60.0729			−0.0925623
$650$	177.815	−	154.342i	0.273562	−	0.237449i
$651$	127.416	−	52.8533i	0.195724	−	0.0811879i
$652$	28.4361	+	39.1390i	0.0436137	+	0.0600291i
$653$	51.5318	−	158.599i	0.0789155	−	0.242877i	−0.903814	−	0.427926i	$-0.859244\pi$
$653$	51.5318	−	158.599i	0.0789155	−	0.242877i	0.982729	+	0.185049i	$0.0592444\pi$
$654$	355.624	−	28.1698i	0.543767	−	0.0430731i
$655$	94.9891	−	830.978i	0.145022	−	1.26867i
$656$	308.208	−	100.143i	0.469829	−	0.152657i
$657$	−61.6094	−	61.4845i	−0.0937739	−	0.0935837i
$658$	22.0463	−	7.16329i	0.0335051	−	0.0108865i
$659$	−93.6473	+	128.894i	−0.142105	+	0.195591i	−0.874137	−	0.485679i	$-0.838572\pi$
$659$	−93.6473	+	128.894i	−0.142105	+	0.195591i	0.732032	+	0.681270i	$0.238572\pi$
$660$	11.1361	−	320.164i	0.0168729	−	0.485097i
$661$	−302.488	+	219.770i	−0.457621	+	0.332481i	−0.792597	−	0.609745i	$-0.791272\pi$
$661$	−302.488	+	219.770i	−0.457621	+	0.332481i	0.334976	+	0.942227i	$0.391272\pi$
$662$	327.906	+	238.238i	0.495326	+	0.359876i
$663$	519.625	+	124.472i	0.783747	+	0.187740i
$664$	9.26112	−	6.72860i	0.0139475	−	0.0101334i
$665$	−13.1963	+	115.443i	−0.0198440	+	0.173598i
$666$	−2.17703	−	13.6555i	−0.00326881	−	0.0205037i
$667$	−1464.89	+	475.971i	−2.19624	+	0.713600i
$668$	50.3186			0.0753273
$669$	490.037	+	573.170i	0.732491	+	0.856756i
$670$	−50.5807	−	89.4782i	−0.0754935	−	0.133549i
$671$	−12.2648	−	3.98508i	−0.0182784	−	0.00593901i
$672$	12.1492	+	153.374i	0.0180791	+	0.228236i
$673$	−238.217	−	327.877i	−0.353962	−	0.487187i	0.594492	−	0.804102i	$-0.297353\pi$
$673$	−238.217	−	327.877i	−0.353962	−	0.487187i	−0.948454	+	0.316914i	$0.897353\pi$
$674$			284.311i			0.421826i
$675$	−549.835	−	391.544i	−0.814570	−	0.580065i
$676$	−68.7631			−0.101721
$677$	707.402	−	513.958i	1.04491	−	0.759169i	0.0736694	−	0.997283i	$-0.476529\pi$
$677$	707.402	−	513.958i	1.04491	−	0.759169i	0.971237	+	0.238114i	$0.0765290\pi$
$678$	51.9463	−	4.11479i	0.0766170	−	0.00606902i
$679$	47.8130	−	147.153i	0.0704167	−	0.216720i
$680$	83.0520	+	408.987i	0.122135	+	0.601452i
$681$	80.0809	−	68.4659i	0.117593	−	0.100537i
$682$			130.175i			0.190873i
$683$	−409.220	−	1259.45i	−0.599150	−	1.84399i	−0.532876	−	0.846193i	$-0.678889\pi$
$683$	−409.220	−	1259.45i	−0.599150	−	1.84399i	−0.0662740	−	0.997801i	$-0.521111\pi$
$684$	410.853	−	65.5004i	0.600663	−	0.0957608i
$685$	833.001	−	470.883i	1.21606	−	0.687420i
$686$	−73.8305	−	101.619i	−0.107625	−	0.148133i
$687$	−101.937	+	425.550i	−0.148380	+	0.619432i
$688$	396.193	−	545.312i	0.575861	−	0.792605i
$689$	−598.618	−	823.927i	−0.868822	−	1.19583i
$690$	−350.302	−	273.608i	−0.507684	−	0.396533i
$691$	131.537	+	95.5669i	0.190357	+	0.138302i	0.678882	−	0.734248i	$-0.262465\pi$
$691$	131.537	+	95.5669i	0.190357	+	0.138302i	−0.488525	+	0.872550i	$0.662465\pi$
$692$	148.381	+	456.670i	0.214424	+	0.659928i
$693$	−68.2576	+	68.3964i	−0.0984959	+	0.0986961i
$694$	45.9287	+	141.354i	0.0661797	+	0.203680i
$695$	−8.24694	−	40.6118i	−0.0118661	−	0.0584343i
$696$	54.3480	+	686.104i	0.0780862	+	0.985782i
$697$	−489.053	−	158.903i	−0.701654	−	0.227981i
$698$	183.325	−	133.193i	0.262643	−	0.190822i
$699$	−150.899	−	363.779i	−0.215878	−	0.520428i
$700$	56.7973	+	134.081i	0.0811390	+	0.191545i
$701$		−	556.658i		−	0.794091i	−0.917799	−	0.397046i	$-0.870035\pi$
$701$		−	556.658i		−	0.794091i	0.917799	−	0.397046i	$-0.129965\pi$
$702$	59.7400	+	247.176i	0.0850996	+	0.352103i
$703$	25.7023	+	8.35117i	0.0365608	+	0.0118793i
$704$	81.5549	+	26.4988i	0.115845	+	0.0376403i
$705$	−207.413	−	162.003i	−0.294203	−	0.229791i
$706$	−132.112	−	406.599i	−0.187127	−	0.575919i
$707$	269.035			0.380530
$708$	−63.5336	−	74.3119i	−0.0897368	−	0.104960i
$709$	−427.692	−	310.736i	−0.603233	−	0.438274i	0.243792	−	0.969828i	$-0.421609\pi$
$709$	−427.692	−	310.736i	−0.603233	−	0.438274i	−0.847025	+	0.531553i	$0.821609\pi$
$710$	−37.7303	+	330.070i	−0.0531413	+	0.464888i
$711$	−188.019	+	1194.95i	−0.264443	+	1.68067i
$712$	356.891	−	491.218i	0.501251	−	0.689913i
$713$	−834.343	−	606.186i	−1.17019	−	0.850190i
$714$	30.2131	−	49.3596i	0.0423153	−	0.0691311i
$715$	−158.825	+	348.169i	−0.222133	+	0.486950i
$716$	−39.6073	+	54.5148i	−0.0553175	+	0.0761380i
$717$	−334.717	−	391.501i	−0.466830	−	0.546026i
$718$		−	112.113i		−	0.156146i
$719$	41.8379	−	13.5940i	0.0581890	−	0.0189068i	−0.279778	−	0.960065i	$-0.590261\pi$
$719$	41.8379	−	13.5940i	0.0581890	−	0.0189068i	0.337967	+	0.941158i	$0.390261\pi$
$720$	323.896	−	257.980i	0.449856	−	0.358306i
$721$	48.8671	−	150.397i	0.0677768	−	0.208596i
$722$	−42.1268	+	129.653i	−0.0583473	+	0.179575i
$723$	1026.06	+	628.057i	1.41918	+	0.868681i
$724$	272.187			0.375949
$725$	391.344	+	923.846i	0.539784	+	1.27427i
$726$	72.4477	+	174.653i	0.0997902	+	0.240569i
$727$	−498.452	−	686.060i	−0.685628	−	0.943686i	0.314356	−	0.949305i	$-0.398211\pi$
$727$	−498.452	−	686.060i	−0.685628	−	0.943686i	−0.999984	+	0.00561920i	$0.998211\pi$
$728$	36.8727	−	113.483i	0.0506493	−	0.155883i
$729$	648.533	−	332.936i	0.889620	−	0.456702i
$730$	−25.2336	+	27.5172i	−0.0345665	+	0.0376948i
$731$	−1017.20	+	330.508i	−1.39152	+	0.452132i
$732$	−8.04171	−	19.3866i	−0.0109859	−	0.0264844i
$733$	−447.807	+	145.501i	−0.610924	+	0.198501i	−0.598107	−	0.801417i	$-0.704080\pi$
$733$	−447.807	+	145.501i	−0.610924	+	0.198501i	−0.0128176	+	0.999918i	$0.504080\pi$
$734$	107.360	−	147.769i	0.146267	−	0.201320i
$735$	−236.273	+	649.434i	−0.321460	+	0.883583i
$736$	930.582	−	676.108i	1.26438	−	0.918624i
$737$	135.150	+	98.1925i	0.183379	+	0.133233i
$738$	−38.5288	−	241.673i	−0.0522070	−	0.327470i
$739$	30.1447	−	21.9014i	0.0407912	−	0.0296366i	−0.567203	−	0.823578i	$-0.691974\pi$
$739$	30.1447	−	21.9014i	0.0407912	−	0.0296366i	0.607994	+	0.793942i	$0.291974\pi$
$740$	33.1903	−	6.73987i	0.0448518	−	0.00910794i
$741$	−483.311	−	115.773i	−0.652242	−	0.156239i
$742$	−104.907	+	34.0862i	−0.141384	+	0.0459383i
$743$	977.642			1.31580			0.657902	−	0.753104i	$-0.271444\pi$
$743$	977.642			1.31580			0.657902	+	0.753104i	$0.271444\pi$
$744$	−350.263	+	299.460i	−0.470783	+	0.402501i
$745$	−1211.34	−	552.579i	−1.62596	−	0.741717i
$746$	210.523	+	68.4029i	0.282202	+	0.0916930i
$747$	8.19841	+	16.0500i	0.0109751	+	0.0214859i
$748$	−183.294	−	252.282i	−0.245045	−	0.337276i
$749$		−	7.29081i		−	0.00973407i
$750$	−157.838	+	242.730i	−0.210451	+	0.323641i
$751$	110.601			0.147271			0.0736355	−	0.997285i	$-0.476540\pi$
$751$	110.601			0.147271			0.0736355	+	0.997285i	$0.476540\pi$
$752$	130.616	−	94.8979i	0.173691	−	0.126194i
$753$	86.5013	+	1092.02i	0.114876	+	1.45022i
$754$	116.802	−	359.480i	0.154910	−	0.476763i
$755$	434.205	−	951.843i	0.575105	−	1.26072i
$756$	−156.798	−	12.1001i	−0.207405	−	0.0160054i
$757$			193.534i			0.255659i	0.991796	+	0.127830i	$0.0408010\pi$
$757$			193.534i			0.255659i	−0.991796	+	0.127830i	$0.959199\pi$
$758$	−29.7438	−	91.5421i	−0.0392399	−	0.120768i
$759$	702.551	+	168.291i	0.925628	+	0.221727i
$760$	−77.2480	−	380.406i	−0.101642	−	0.500534i
$761$	−369.468	−	508.529i	−0.485503	−	0.668238i	0.494047	−	0.869435i	$-0.335517\pi$
$761$	−369.468	−	508.529i	−0.485503	−	0.668238i	−0.979551	+	0.201197i	$0.935517\pi$
$762$	−346.600	−	83.0253i	−0.454856	−	0.108957i
$763$	154.906	−	213.210i	0.203023	−	0.279437i
$764$	−279.920	−	385.277i	−0.366388	−	0.504289i
$765$	−656.404	+	29.0838i	−0.858045	+	0.0380181i
$766$	−426.129	−	309.601i	−0.556304	−	0.404178i
$767$	36.0902	+	111.074i	0.0470537	+	0.144816i
$768$	−52.9213	−	127.580i	−0.0689079	−	0.166120i
$769$	−17.4647	−	53.7507i	−0.0227109	−	0.0698969i	0.939059	−	0.343757i	$-0.111700\pi$
$769$	−17.4647	−	53.7507i	−0.0227109	−	0.0698969i	−0.961770	+	0.273860i	$0.911700\pi$
$770$	30.5485	+	28.0133i	0.0396734	+	0.0363809i
$771$	426.073	−	33.7503i	0.552623	−	0.0437746i
$772$	580.711	+	188.685i	0.752217	+	0.244410i
$773$	714.283	−	518.957i	0.924040	−	0.671354i	−0.0204865	−	0.999790i	$-0.506522\pi$
$773$	714.283	−	518.957i	0.924040	−	0.671354i	0.944526	+	0.328436i	$0.106522\pi$
$774$	−360.292	−	359.561i	−0.465493	−	0.464549i
$775$	−346.417	+	575.570i	−0.446990	+	0.742672i
$776$			516.891i			0.666097i
$777$	−8.71283	−	5.33314i	−0.0112134	−	0.00686376i
$778$	20.9844	+	6.81824i	0.0269722	+	0.00876381i
$779$	454.876	+	147.798i	0.583922	+	0.189728i
$780$	−598.670	+	171.755i	−0.767526	+	0.220199i
$781$	−166.855	−	513.526i	−0.213642	−	0.657523i
$782$	−432.670			−0.553287
$783$	−1080.37	−	83.3717i	−1.37978	−	0.106477i
$784$	−342.978	−	249.188i	−0.437472	−	0.317842i
$785$	987.053	+	450.267i	1.25739	+	0.573588i
$786$	202.281	−	330.470i	0.257356	−	0.420445i
$787$	476.013	−	655.176i	0.604845	−	0.832498i	−0.391296	−	0.920265i	$-0.627973\pi$
$787$	476.013	−	655.176i	0.604845	−	0.832498i	0.996141	+	0.0877672i	$0.0279732\pi$
$788$	−44.4550	−	32.2984i	−0.0564149	−	0.0409879i
$789$	627.049	+	383.818i	0.794739	+	0.486462i
$790$	515.515	+	58.9285i	0.652551	+	0.0745930i
$791$	22.6273	−	31.1438i	0.0286060	−	0.0393727i
$792$	146.260	−	287.772i	0.184671	−	0.363349i
$793$			25.0716i			0.0316162i
$794$	150.849	−	49.0138i	0.189986	−	0.0617302i
$795$	986.966	+	770.883i	1.24147	+	0.969664i
$796$	−362.255	+	1114.91i	−0.455094	+	1.40063i
$797$	71.4536	−	219.912i	0.0896532	−	0.275924i	−0.896170	−	0.443710i	$-0.853662\pi$
$797$	71.4536	−	219.912i	0.0896532	−	0.275924i	0.985823	+	0.167786i	$0.0536619\pi$
$798$	−28.1017	+	45.9101i	−0.0352152	+	0.0575315i
$799$	−256.183			−0.320629
$800$	−491.145	−	565.841i	−0.613931	−	0.707302i
$801$	676.636	+	675.263i	0.844739	+	0.843025i
$802$	180.023	+	247.780i	0.224468	+	0.308953i
$803$	18.7514	−	57.7108i	0.0233516	−	0.0718690i
$804$	21.4693	+	271.034i	0.0267031	+	0.337107i
$805$	−321.803	+	65.3477i	−0.399755	+	0.0811773i
$806$	240.693	−	78.2058i	0.298626	−	0.0970295i
$807$	−323.275	+	134.097i	−0.400588	+	0.166167i
$808$	−854.773	+	277.733i	−1.05789	+	0.343729i
$809$	−607.858	+	836.645i	−0.751370	+	1.03417i	0.246513	+	0.969139i	$0.420715\pi$
$809$	−607.858	+	836.645i	−0.751370	+	1.03417i	−0.997883	+	0.0650327i	$0.979285\pi$
$810$	−154.432	−	271.903i	−0.190657	−	0.335683i
$811$	−946.582	+	687.732i	−1.16718	+	0.848005i	−0.990669	−	0.136293i	$-0.956481\pi$
$811$	−946.582	+	687.732i	−1.16718	+	0.848005i	−0.176511	+	0.984299i	$0.556481\pi$
$812$	189.113	+	137.399i	0.232898	+	0.169210i
$813$	−121.838	+	508.628i	−0.149862	+	0.625619i
$814$	7.79908	−	5.66636i	0.00958118	−	0.00696113i
$815$	34.9707	+	61.8638i	0.0429088	+	0.0759065i
$816$	93.8954	−	391.979i	0.115068	−	0.480366i
$817$	946.113	−	307.411i	1.15803	−	0.376268i
$818$	−267.173			−0.326617
$819$	167.471	+	85.1169i	0.204483	+	0.103928i
$820$	587.398	−	119.281i	0.716339	−	0.145465i
$821$	−1378.21	−	447.806i	−1.67869	−	0.545440i	−0.694035	−	0.719941i	$-0.744169\pi$
$821$	−1378.21	−	447.806i	−1.67869	−	0.545440i	−0.984657	+	0.174501i	$0.944169\pi$
$822$	441.898	−	35.0038i	0.537589	−	0.0425837i
$823$	413.581	+	569.246i	0.502529	+	0.691672i	0.982637	−	0.185537i	$-0.0594026\pi$
$823$	413.581	+	569.246i	0.502529	+	0.691672i	−0.480108	+	0.877209i	$0.659403\pi$
$824$			528.287i			0.641126i
$825$	69.6638	−	465.394i	0.0844410	−	0.564114i
$826$	12.6495			0.0153141
$827$	−701.706	+	509.820i	−0.848496	+	0.616469i	−0.924731	−	0.380621i	$-0.875710\pi$
$827$	−701.706	+	509.820i	−0.848496	+	0.616469i	0.0762348	+	0.997090i	$0.475710\pi$
$828$	534.844	+	1047.06i	0.645947	+	1.26457i
$829$	59.4524	−	182.976i	0.0717158	−	0.220718i	−0.908774	−	0.417289i	$-0.862980\pi$
$829$	59.4524	−	182.976i	0.0717158	−	0.220718i	0.980490	+	0.196570i	$0.0629804\pi$
$830$	6.72984	−	3.80428i	0.00810824	−	0.00458347i
$831$	355.982	+	416.373i	0.428378	+	0.501051i
$832$		−	166.714i		−	0.200377i
$833$	207.875	+	639.775i	0.249550	+	0.768037i
$834$	4.47214	−	18.6696i	0.00536228	−	0.0223856i
$835$	73.4356	+	8.39443i	0.0879469	+	0.0100532i
$836$	170.484	+	234.652i	0.203929	+	0.280684i
$837$	−380.025	−	618.030i	−0.454032	−	0.738387i
$838$	−75.7615	+	104.277i	−0.0904075	+	0.124435i
$839$	−218.610	−	300.892i	−0.260561	−	0.358631i	0.658614	−	0.752481i	$-0.271143\pi$
$839$	−218.610	−	300.892i	−0.260561	−	0.358631i	−0.919175	+	0.393850i	$0.871143\pi$
$840$	−5.10052	+	146.640i	−0.00607204	+	0.174571i
$841$	622.641	+	452.375i	0.740358	+	0.537901i
$842$	7.88296	+	24.2613i	0.00936219	+	0.0288138i
$843$	49.9543	−	20.7215i	0.0592578	−	0.0245806i
$844$	40.2864	+	123.989i	0.0477327	+	0.146906i
$845$	−100.354	−	11.4714i	−0.118762	−	0.0135757i
$846$	−55.4613	−	108.576i	−0.0655571	−	0.128341i
$847$	132.850	+	43.1655i	0.156847	+	0.0509628i
$848$	−621.530	+	451.568i	−0.732936	+	0.532509i
$849$	56.2261	−	23.3230i	0.0662262	−	0.0274712i
$850$	24.3561	+	280.781i	0.0286542	+	0.330331i
$851$			76.3738i			0.0897459i
$852$	458.779	−	749.513i	0.538473	−	0.879710i
$853$	−0.0190880	−	0.00620206i	−2.23775e−5	−	7.27088e-6i	0.309006	−	0.951060i	$-0.400004\pi$
$853$	−0.0190880	−	0.00620206i	−2.23775e−5	−	7.27088e-6i	−0.309028	+	0.951053i	$0.600004\pi$
$854$	2.58258	+	0.839132i	0.00302410	+	0.000982590i
$855$	610.532	−	27.0513i	0.714072	−	0.0316390i
$856$	7.52653	+	23.1643i	0.00879267	+	0.0270611i
$857$	−56.5546			−0.0659913			−0.0329957	−	0.999455i	$-0.510505\pi$
$857$	−56.5546			−0.0659913			−0.0329957	+	0.999455i	$0.510505\pi$
$858$	−134.747	+	115.203i	−0.157048	+	0.134270i
$859$	482.719	+	350.716i	0.561955	+	0.408284i	0.832174	−	0.554515i	$-0.187096\pi$
$859$	482.719	+	350.716i	0.561955	+	0.408284i	−0.270219	+	0.962799i	$0.587096\pi$
$860$	842.590	−	918.844i	0.979756	−	1.06842i
$861$	−154.199	−	94.3854i	−0.179092	−	0.109623i
$862$	−272.107	+	374.524i	−0.315670	+	0.434482i
$863$	206.837	+	150.276i	0.239672	+	0.174132i	0.701137	−	0.713027i	$-0.252676\pi$
$863$	206.837	+	150.276i	0.239672	+	0.174132i	−0.461465	+	0.887158i	$0.652676\pi$
$864$	786.560	−	190.104i	0.910371	−	0.220027i
$865$	140.365	+	691.224i	0.162272	+	0.799103i
$866$	−126.613	+	174.267i	−0.146204	+	0.201233i
$867$	172.861	−	147.789i	0.199379	−	0.170461i
$868$			156.514i			0.180315i
$869$	−802.042	+	260.599i	−0.922948	+	0.299884i
$870$	−16.1569	+	464.512i	−0.0185712	+	0.533922i
$871$	100.362	−	308.883i	0.115226	−	0.354630i
$872$	−272.063	+	837.323i	−0.311998	+	0.960233i
$873$	−803.899	−	126.489i	−0.920847	−	0.144890i
$874$	402.433			0.460450
$875$	60.5225	+	205.155i	0.0691685	+	0.234463i
$876$	91.2215	−	37.8394i	0.104134	−	0.0431957i
$877$	−146.721	−	201.945i	−0.167299	−	0.230267i	0.717133	−	0.696936i	$-0.245454\pi$
$877$	−146.721	−	201.945i	−0.167299	−	0.230267i	−0.884432	+	0.466669i	$0.845454\pi$
$878$	−71.7736	+	220.897i	−0.0817467	+	0.251591i
$879$	−361.868	+	28.6645i	−0.411682	+	0.0326103i
$880$	262.642	+	119.810i	0.298456	+	0.136148i
$881$	1039.28	−	337.681i	1.17966	−	0.383293i	0.347417	−	0.937711i	$-0.387059\pi$
$881$	1039.28	−	337.681i	1.17966	−	0.383293i	0.832239	+	0.554418i	$0.187059\pi$
$882$	−226.148	+	226.608i	−0.256404	+	0.256925i
$883$	598.455	−	194.450i	0.677752	−	0.220215i	0.0501409	−	0.998742i	$-0.484033\pi$
$883$	598.455	−	194.450i	0.677752	−	0.220215i	0.627611	+	0.778527i	$0.284033\pi$
$884$	−356.349	+	490.472i	−0.403110	+	0.554833i
$885$	−80.3247	−	119.051i	−0.0907624	−	0.134521i
$886$	140.703	−	102.227i	0.158807	−	0.115380i
$887$	−436.537	−	317.163i	−0.492150	−	0.357568i	0.313861	−	0.949469i	$-0.398377\pi$
$887$	−436.537	−	317.163i	−0.492150	−	0.357568i	−0.806010	+	0.591901i	$0.798377\pi$
$888$	33.1878	+	7.94988i	0.0373737	+	0.00895256i
$889$	−213.012	+	154.762i	−0.239608	+	0.174086i
$890$	277.132	−	302.212i	0.311384	−	0.339564i
$891$	411.769	+	297.892i	0.462142	+	0.334334i
$892$	−813.737	+	264.399i	−0.912261	+	0.296412i
$893$	238.280			0.266831
$894$	−400.812	−	468.808i	−0.448335	−	0.524394i
$895$	−66.8979	+	72.9521i	−0.0747463	+	0.0815107i
$896$	−212.272	−	68.9715i	−0.236911	−	0.0769771i
$897$	−110.906	−	1400.11i	−0.123642	−	1.56089i
$898$	−246.952	−	339.900i	−0.275002	−	0.378508i
$899$			1078.41i			1.19956i
$900$	649.383	−	406.029i	0.721537	−	0.451143i
$901$	1219.04			1.35298
$902$	138.027	−	100.283i	0.153024	−	0.111178i
$903$	−374.862	+	29.6938i	−0.415130	+	0.0328835i
$904$	−39.7404	+	122.309i	−0.0439607	+	0.135297i
$905$	397.234	+	45.4078i	0.438932	+	0.0501743i
$906$	368.379	−	314.949i	0.406599	−	0.347626i
$907$		−	286.442i		−	0.315812i	−0.987454	−	0.157906i	$-0.949526\pi$
$907$		−	286.442i		−	0.315812i	0.987454	−	0.157906i	$-0.0504744\pi$
$908$	36.9408	+	113.692i	0.0406837	+	0.125211i
$909$	−222.774	−	1397.36i	−0.245076	−	1.53725i
$910$	33.4436	−	73.3135i	0.0367512	−	0.0805643i
$911$	−828.429	−	1140.23i	−0.909362	−	1.25163i	−0.967384	−	0.253314i	$-0.918479\pi$
$911$	−828.429	−	1140.23i	−0.909362	−	1.25163i	0.0580217	−	0.998315i	$-0.481521\pi$
$912$	−87.3336	+	364.586i	−0.0957605	+	0.399765i
$913$	−7.38526	+	10.1649i	−0.00808901	+	0.0111336i
$914$	−75.6777	−	104.161i	−0.0827984	−	0.113962i
$915$	−8.50201	−	29.6346i	−0.00929181	−	0.0323875i
$916$	−401.676	−	291.834i	−0.438510	−	0.318596i
$917$	−88.4534	−	272.232i	−0.0964596	−	0.296872i
$918$	−281.390	−	116.054i	−0.306525	−	0.126420i
$919$	−9.97272	−	30.6929i	−0.0108517	−	0.0333981i	0.945484	−	0.325668i	$-0.105589\pi$
$919$	−9.97272	−	30.6929i	−0.0108517	−	0.0333981i	−0.956336	+	0.292270i	$0.905589\pi$
$920$	954.967	−	539.829i	1.03801	−	0.586770i
$921$	44.1768	+	557.701i	0.0479662	+	0.605538i
$922$	103.665	+	33.6829i	0.112435	+	0.0365325i
$923$	−849.261	+	617.025i	−0.920110	+	0.668499i
$924$	−42.0079	−	101.271i	−0.0454631	−	0.109600i
$925$	49.5628	−	4.29927i	0.0535814	−	0.00464786i
$926$		−	361.325i		−	0.390199i
$927$	−821.623	−	129.277i	−0.886325	−	0.139458i
$928$	−1143.93	−	371.686i	−1.23268	−	0.400523i
$929$	477.883	+	155.274i	0.514406	+	0.167141i	0.554705	−	0.832047i	$-0.312831\pi$
$929$	477.883	+	155.274i	0.514406	+	0.167141i	−0.0402991	+	0.999188i	$0.512831\pi$
$930$	−257.978	+	174.060i	−0.277395	+	0.187161i
$931$	−193.348	−	595.065i	−0.207678	−	0.639167i
$932$	446.853			0.479456
$933$	626.658	+	732.968i	0.671659	+	0.785604i
$934$	−73.7572	−	53.5878i	−0.0789692	−	0.0573745i
$935$	−225.414	−	398.762i	−0.241085	−	0.426483i
$936$	−619.956	−	97.5464i	−0.662347	−	0.104216i
$937$	40.3942	−	55.5978i	0.0431101	−	0.0593360i	−0.786918	−	0.617058i	$-0.788324\pi$
$937$	40.3942	−	55.5978i	0.0431101	−	0.0593360i	0.830028	+	0.557722i	$0.188324\pi$
$938$	−28.4584	−	20.6763i	−0.0303395	−	0.0220429i
$939$	−314.338	+	513.538i	−0.334758	+	0.546899i
$940$	259.954	−	146.948i	0.276546	−	0.156327i
$941$	503.452	−	692.942i	0.535018	−	0.736389i	−0.452867	−	0.891578i	$-0.649599\pi$
$941$	503.452	−	692.942i	0.535018	−	0.736389i	0.987885	+	0.155189i	$0.0495988\pi$
$942$	326.599	+	382.006i	0.346709	+	0.405527i
$943$			1351.65i			1.43336i
$944$	83.7888	−	27.2246i	0.0887593	−	0.0288397i
$945$	−226.815	−	43.8169i	−0.240016	−	0.0463671i
$946$	109.658	−	337.492i	0.115917	−	0.356757i
$947$	220.744	−	679.381i	0.233098	−	0.717403i	−0.764270	−	0.644897i	$-0.776900\pi$
$947$	220.744	−	679.381i	0.233098	−	0.717403i	0.997368	−	0.0725062i	$-0.0230997\pi$
$948$	−1170.61	−	716.537i	−1.23483	−	0.755840i
$949$	−117.972			−0.124312
$950$	−22.6540	−	261.159i	−0.0238463	−	0.274904i
$951$	−464.643	−	1120.14i	−0.488583	−	1.17785i
$952$	83.9512	+	115.549i	0.0881840	+	0.121375i
$953$	319.010	−	981.811i	0.334743	−	1.03023i	−0.632106	−	0.774882i	$-0.717809\pi$
$953$	319.010	−	981.811i	0.334743	−	1.03023i	0.966849	−	0.255350i	$-0.0821908\pi$
$954$	263.910	+	516.656i	0.276636	+	0.541568i
$955$	−344.245	−	608.976i	−0.360466	−	0.637671i
$956$	555.819	−	180.597i	0.581401	−	0.188909i
$957$	−289.442	−	697.773i	−0.302447	−	0.729125i
$958$	−3.04056	+	0.987937i	−0.00317386	+	0.00103125i
$959$	192.487	−	264.935i	0.200716	−	0.276262i
$960$	56.5341	+	197.055i	0.0588897	+	0.205266i
$961$	193.308	−	140.447i	0.201153	−	0.146146i
$962$	−15.1625	−	11.0162i	−0.0157615	−	0.0114514i
$963$	−37.8682	+	6.03715i	−0.0393232	+	0.00626910i
$964$	−1104.29	+	802.313i	−1.14553	+	0.832275i
$965$	816.020	+	372.246i	0.845617	+	0.385747i
$966$	−147.935	−	35.4367i	−0.153142	−	0.0366839i
$967$	956.592	−	310.815i	0.989236	−	0.321422i	0.230680	−	0.973030i	$-0.425905\pi$
$967$	956.592	−	310.815i	0.989236	−	0.321422i	0.758556	+	0.651607i	$0.225905\pi$
$968$	−466.649			−0.482076
$969$	452.152	−	386.572i	0.466618	−	0.398939i
$970$	−39.6439	+	346.810i	−0.0408700	+	0.357536i
$971$	756.006	+	245.641i	0.778585	+	0.252977i	0.671236	−	0.741244i	$-0.265764\pi$
$971$	756.006	+	245.641i	0.778585	+	0.252977i	0.107349	+	0.994221i	$0.465764\pi$
$972$	66.9892	+	824.423i	0.0689189	+	0.848172i
$973$	−8.33623	−	11.4738i	−0.00856756	−	0.0117922i
$974$			632.810i			0.649702i
$975$	−902.361	+	150.789i	−0.925498	+	0.154655i
$976$	18.9128			0.0193779
$977$	−1195.65	+	868.690i	−1.22380	+	0.889140i	−0.996410	−	0.0846646i	$-0.973018\pi$
$977$	−1195.65	+	868.690i	−1.22380	+	0.889140i	−0.227387	+	0.973805i	$0.573018\pi$
$978$	2.59960	+	32.8181i	0.00265808	+	0.0335563i
$979$	−205.940	+	633.818i	−0.210358	+	0.647414i
$980$	−577.913	−	529.953i	−0.589707	−	0.540768i
$981$	−1235.68	−	628.029i	−1.25961	−	0.640193i
$982$		−	301.686i		−	0.307216i
$983$	32.7514	+	100.798i	0.0333178	+	0.102542i	0.966332	−	0.257297i	$-0.0828318\pi$
$983$	32.7514	+	100.798i	0.0333178	+	0.102542i	−0.933015	+	0.359838i	$0.882832\pi$
$984$	587.354	+	140.696i	0.596905	+	0.142984i
$985$	−59.4900	−	54.5530i	−0.0603959	−	0.0553837i
$986$	265.933	+	366.025i	0.269709	+	0.371222i
$987$	−87.5921	−	20.9820i	−0.0887458	−	0.0212583i
$988$	331.446	−	456.196i	0.335471	−	0.461737i
$989$	1652.47	+	2274.44i	1.67085	+	2.29973i
$990$	120.204	−	181.864i	0.121419	−	0.183701i
$991$	763.591	+	554.781i	0.770525	+	0.559819i	0.902121	−	0.431484i	$-0.142010\pi$
$991$	763.591	+	554.781i	0.770525	+	0.559819i	−0.131595	+	0.991304i	$0.542010\pi$
$992$	−248.865	−	765.929i	−0.250872	−	0.772106i
$993$	−603.411	−	1454.67i	−0.607665	−	1.46493i
$994$	35.1343	+	108.132i	0.0353464	+	0.108785i
$995$	−714.674	+	1566.67i	−0.718265	+	1.57455i
$996$	−20.3850	+	1.61475i	−0.0204669	+	0.00162123i
$997$	−560.352	−	182.069i	−0.562038	−	0.182617i	0.0142002	−	0.999899i	$-0.495480\pi$
$997$	−560.352	−	182.069i	−0.562038	−	0.182617i	−0.576238	+	0.817282i	$0.695480\pi$
$998$	562.873	−	408.951i	0.564001	−	0.409771i
$999$	−20.4855	+	49.6702i	−0.0205060	+	0.0497199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.9	✓	72
3.2	odd	2	inner	75.3.h.a.14.10	yes	72
5.2	odd	4		375.3.j.b.176.18		144
5.3	odd	4		375.3.j.b.176.19		144
5.4	even	2		375.3.h.a.74.10		72
15.2	even	4		375.3.j.b.176.20		144
15.8	even	4		375.3.j.b.176.17		144
15.14	odd	2		375.3.h.a.74.9		72
25.9	even	10	inner	75.3.h.a.59.10	yes	72
25.12	odd	20		375.3.j.b.326.20		144
25.13	odd	20		375.3.j.b.326.17		144
25.16	even	5		375.3.h.a.299.9		72
75.38	even	20		375.3.j.b.326.19		144
75.41	odd	10		375.3.h.a.299.10		72
75.59	odd	10	inner	75.3.h.a.59.9	yes	72
75.62	even	20		375.3.j.b.326.18		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.9	✓	72	1.1	even	1	trivial
75.3.h.a.14.10	yes	72	3.2	odd	2	inner
75.3.h.a.59.9	yes	72	75.59	odd	10	inner
75.3.h.a.59.10	yes	72	25.9	even	10	inner
375.3.h.a.74.9		72	15.14	odd	2
375.3.h.a.74.10		72	5.4	even	2
375.3.h.a.299.9		72	25.16	even	5
375.3.h.a.299.10		72	75.41	odd	10
375.3.j.b.176.17		144	15.8	even	4
375.3.j.b.176.18		144	5.2	odd	4
375.3.j.b.176.19		144	5.3	odd	4
375.3.j.b.176.20		144	15.2	even	4
375.3.j.b.326.17		144	25.13	odd	20
375.3.j.b.326.18		144	75.62	even	20
375.3.j.b.326.19		144	75.38	even	20
375.3.j.b.326.20		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+(-0.624639 + 0.453826i) q^{2} +(2.99063 - 0.236895i) q^{3} +(-1.05185 + 3.23727i) q^{4} +(-2.07515 + 4.54904i) q^{5} +(-1.76055 + 1.50520i) q^{6} +1.71117i q^{7} +(-1.76649 - 5.43671i) q^{8} +(8.88776 - 1.41693i) q^{9} +(-0.768257 - 3.78326i) q^{10} +(3.68799 + 5.07609i) q^{11} +(-2.37881 + 9.93067i) q^{12} +(7.16998 - 9.86863i) q^{13} +(-0.776575 - 1.06886i) q^{14} +(-5.12836 + 14.0961i) q^{15} +(-7.44441 - 5.40868i) q^{16} +(4.51198 + 13.8864i) q^{17} +(-4.90860 + 4.91857i) q^{18} +(-4.19666 - 12.9160i) q^{19} +(-12.5437 - 11.5027i) q^{20} +(0.405369 + 5.11749i) q^{21} +(-4.60733 - 1.49701i) q^{22} +(31.0498 - 22.5590i) q^{23} +(-6.57086 - 15.8407i) q^{24} +(-16.3875 - 18.8799i) q^{25} +9.41826i q^{26} +(26.2444 - 6.34300i) q^{27} +(-5.53953 - 1.79990i) q^{28} +(-38.1684 - 12.4017i) q^{29} +(-3.19381 - 11.1323i) q^{30} +(-8.30364 - 25.5560i) q^{31} +29.9706 q^{32} +(12.2319 + 14.3070i) q^{33} +(-9.12039 - 6.62635i) q^{34} +(-7.78419 - 3.55093i) q^{35} +(-4.76162 + 30.2625i) q^{36} +(-1.16967 + 1.60991i) q^{37} +(8.48302 + 6.16327i) q^{38} +(19.1049 - 31.2120i) q^{39} +(28.3975 + 3.24612i) q^{40} +(-20.7006 + 28.4920i) q^{41} +(-2.57566 - 3.01261i) q^{42} +73.2513i q^{43} +(-20.3119 + 6.59974i) q^{44} +(-11.9977 + 43.3711i) q^{45} +(-9.15703 + 28.1824i) q^{46} +(-5.42185 + 16.6867i) q^{47} +(-23.5448 - 14.4118i) q^{48} +46.0719 q^{49} +(18.8045 + 4.35599i) q^{50} +(16.7833 + 40.4604i) q^{51} +(24.4057 + 33.5915i) q^{52} +(25.7997 - 79.4032i) q^{53} +(-13.5146 + 15.8725i) q^{54} +(-30.7445 + 6.24320i) q^{55} +(9.30315 - 3.02278i) q^{56} +(-15.6104 - 37.6328i) q^{57} +(29.4696 - 9.57527i) q^{58} +(-5.62764 + 7.74578i) q^{59} +(-40.2386 - 31.4289i) q^{60} +(-1.66280 + 1.20810i) q^{61} +(16.7847 + 12.1948i) q^{62} +(2.42462 + 15.2085i) q^{63} +(11.0568 - 8.03324i) q^{64} +(30.0140 + 53.0954i) q^{65} +(-14.1334 - 3.38555i) q^{66} +(25.3218 - 8.22755i) q^{67} -49.7001 q^{68} +(87.5144 - 74.8212i) q^{69} +(6.47381 - 1.31462i) q^{70} +(-81.8447 - 26.5930i) q^{71} +(-23.4036 - 45.8172i) q^{72} +(-5.68457 - 7.82414i) q^{73} -1.53644i q^{74} +(-53.4816 - 52.5806i) q^{75} +46.2269 q^{76} +(-8.68606 + 6.31079i) q^{77} +(2.23114 + 28.1665i) q^{78} +(-41.5338 + 127.828i) q^{79} +(40.0525 - 22.6411i) q^{80} +(76.9846 - 25.1867i) q^{81} -27.1917i q^{82} +(0.618811 + 1.90451i) q^{83} +(-16.9931 - 4.07056i) q^{84} +(-72.5330 - 8.29125i) q^{85} +(-33.2434 - 45.7556i) q^{86} +(-117.085 - 28.0469i) q^{87} +(21.0824 - 29.0174i) q^{88} +(62.4318 + 85.9300i) q^{89} +(-12.1887 - 32.5362i) q^{90} +(16.8869 + 12.2691i) q^{91} +(40.3698 + 124.245i) q^{92} +(-30.8872 - 74.4614i) q^{93} +(-4.18619 - 12.8838i) q^{94} +(67.4641 + 7.71182i) q^{95} +(89.6312 - 7.09990i) q^{96} +(-85.9955 - 27.9416i) q^{97} +(-28.7783 + 20.9086i) q^{98} +(39.9705 + 39.8894i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more