LMFDB - Embedded newform 75.3.h.a.14.1

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			14.1
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.91455 + 2.11754i) q^{2} +(0.529130 - 2.95297i) q^{3} +(2.77453 - 8.53912i) q^{4} +(-2.30619 + 4.43638i) q^{5} +(4.71086 + 9.72702i) q^{6} +9.61929i q^{7} +(5.54243 + 17.0578i) q^{8} +(-8.44004 - 3.12501i) q^{9} +(-2.67273 - 17.8135i) q^{10} +(1.54093 + 2.12091i) q^{11} +(-23.7477 - 12.7114i) q^{12} +(-11.1781 + 15.3854i) q^{13} +(-20.3692 - 28.0359i) q^{14} +(11.8802 + 9.15753i) q^{15} +(-23.2191 - 16.8697i) q^{16} +(0.622226 + 1.91502i) q^{17} +(31.2162 - 8.76416i) q^{18} +(4.29962 + 13.2329i) q^{19} +(31.4842 + 32.0017i) q^{20} +(28.4055 + 5.08986i) q^{21} +(-8.98221 - 2.91850i) q^{22} +(-4.75610 + 3.45551i) q^{23} +(53.3039 - 7.34080i) q^{24} +(-14.3630 - 20.4623i) q^{25} -68.5115i q^{26} +(-13.6939 + 23.2696i) q^{27} +(82.1403 + 26.6890i) q^{28} +(23.5609 + 7.65541i) q^{29} +(-54.0169 - 1.53316i) q^{30} +(-4.27699 - 13.1632i) q^{31} +31.6527 q^{32} +(7.07832 - 3.42808i) q^{33} +(-5.86863 - 4.26381i) q^{34} +(-42.6748 - 22.1839i) q^{35} +(-50.1020 + 63.4001i) q^{36} +(34.1022 - 46.9377i) q^{37} +(-40.5526 - 29.4632i) q^{38} +(39.5178 + 41.1495i) q^{39} +(-88.4570 - 14.7503i) q^{40} +(-11.5675 + 15.9213i) q^{41} +(-93.5670 + 45.3151i) q^{42} -12.7377i q^{43} +(22.3860 - 7.27366i) q^{44} +(33.3281 - 30.2364i) q^{45} +(6.54469 - 20.1425i) q^{46} +(-4.86299 + 14.9667i) q^{47} +(-62.1015 + 59.6390i) q^{48} -43.5307 q^{49} +(85.1913 + 29.2240i) q^{50} +(5.98422 - 0.824122i) q^{51} +(100.363 + 138.138i) q^{52} +(15.7029 - 48.3285i) q^{53} +(-9.36283 - 96.8179i) q^{54} +(-12.9628 + 1.94494i) q^{55} +(-164.084 + 53.3142i) q^{56} +(41.3513 - 5.69473i) q^{57} +(-84.8800 + 27.5792i) q^{58} +(-32.8435 + 45.2053i) q^{59} +(111.159 - 76.0389i) q^{60} +(3.13551 - 2.27808i) q^{61} +(40.3392 + 29.3081i) q^{62} +(30.0604 - 81.1872i) q^{63} +(0.623150 - 0.452745i) q^{64} +(-42.4765 - 85.0720i) q^{65} +(-13.3710 + 24.9799i) q^{66} +(-60.1212 + 19.5346i) q^{67} +18.0789 q^{68} +(7.68741 + 15.8730i) q^{69} +(171.353 - 25.7098i) q^{70} +(74.3554 + 24.1595i) q^{71} +(6.52758 - 161.289i) q^{72} +(48.7077 + 67.0405i) q^{73} +209.015i q^{74} +(-68.0243 + 31.5862i) q^{75} +124.926 q^{76} +(-20.4016 + 14.8226i) q^{77} +(-202.312 - 36.2515i) q^{78} +(-32.2869 + 99.3689i) q^{79} +(128.388 - 64.1042i) q^{80} +(61.4686 + 52.7504i) q^{81} -70.8982i q^{82} +(-34.6732 - 106.713i) q^{83} +(122.275 - 228.436i) q^{84} +(-9.93071 - 1.65595i) q^{85} +(26.9727 + 37.1247i) q^{86} +(35.0730 - 65.5239i) q^{87} +(-27.6376 + 38.0399i) q^{88} +(15.7364 + 21.6593i) q^{89} +(-33.1094 + 158.699i) q^{90} +(-147.996 - 107.526i) q^{91} +(16.3111 + 50.2004i) q^{92} +(-41.1337 + 5.66476i) q^{93} +(-17.5193 - 53.9188i) q^{94} +(-68.6218 - 11.4427i) q^{95} +(16.7484 - 93.4694i) q^{96} +(-45.8531 - 14.8986i) q^{97} +(126.872 - 92.1781i) q^{98} +(-6.37765 - 22.7160i) 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 $

$2$	−2.91455	+	2.11754i	−1.45727	+	1.05877i	−0.473211	+	0.880949i	$0.656905\pi$
$2$	−2.91455	+	2.11754i	−1.45727	+	1.05877i	−0.984063	+	0.177822i	$0.943095\pi$
$3$	0.529130	−	2.95297i	0.176377	−	0.984323i
$3$	0.529130	−	2.95297i	0.176377	−	0.984323i
$4$	2.77453	−	8.53912i	0.693632	−	2.13478i
$5$	−2.30619	+	4.43638i	−0.461238	+	0.887277i
$5$	−2.30619	+	4.43638i	−0.461238	+	0.887277i
$6$	4.71086	+	9.72702i	0.785143	+	1.62117i
$7$			9.61929i			1.37418i	0.726570	+	0.687092i	$0.241113\pi$
$7$			9.61929i			1.37418i	−0.726570	+	0.687092i	$0.758887\pi$
$8$	5.54243	+	17.0578i	0.692803	+	2.13223i
$9$	−8.44004	−	3.12501i	−0.937782	−	0.347223i
$10$	−2.67273	−	17.8135i	−0.267273	−	1.78135i
$11$	1.54093	+	2.12091i	0.140084	+	0.192810i	0.873295	−	0.487192i	$-0.161979\pi$
$11$	1.54093	+	2.12091i	0.140084	+	0.192810i	−0.733210	+	0.680002i	$0.761979\pi$
$12$	−23.7477	−	12.7114i	−1.97897	−	1.05928i
$13$	−11.1781	+	15.3854i	−0.859855	+	1.18349i	0.121749	+	0.992561i	$0.461150\pi$
$13$	−11.1781	+	15.3854i	−0.859855	+	1.18349i	−0.981604	+	0.190928i	$0.938850\pi$
$14$	−20.3692	−	28.0359i	−1.45495	−	2.00256i
$15$	11.8802	+	9.15753i	0.792015	+	0.610502i
$16$	−23.2191	−	16.8697i	−1.45119	−	1.05435i
$17$	0.622226	+	1.91502i	0.0366015	+	0.112648i	0.967688	−	0.252151i	$-0.0811378\pi$
$17$	0.622226	+	1.91502i	0.0366015	+	0.112648i	−0.931086	+	0.364799i	$0.881138\pi$
$18$	31.2162	−	8.76416i	1.73424	−	0.486898i
$19$	4.29962	+	13.2329i	0.226296	+	0.696466i	0.998158	+	0.0606761i	$0.0193257\pi$
$19$	4.29962	+	13.2329i	0.226296	+	0.696466i	−0.771862	+	0.635790i	$0.780674\pi$
$20$	31.4842	+	32.0017i	1.57421	+	1.60009i
$21$	28.4055	+	5.08986i	1.35264	+	0.242374i
$22$	−8.98221	−	2.91850i	−0.408282	−	0.132659i
$23$	−4.75610	+	3.45551i	−0.206787	+	0.150240i	−0.686359	−	0.727263i	$-0.740792\pi$
$23$	−4.75610	+	3.45551i	−0.206787	+	0.150240i	0.479572	+	0.877503i	$0.340792\pi$
$24$	53.3039	−	7.34080i	2.22100	−	0.305866i
$25$	−14.3630	−	20.4623i	−0.574519	−	0.818491i
$26$		−	68.5115i		−	2.63506i
$27$	−13.6939	+	23.2696i	−0.507183	+	0.861839i
$28$	82.1403	+	26.6890i	2.93358	+	0.953179i
$29$	23.5609	+	7.65541i	0.812445	+	0.263980i	0.685633	−	0.727947i	$-0.259525\pi$
$29$	23.5609	+	7.65541i	0.812445	+	0.263980i	0.126812	+	0.991927i	$0.459525\pi$
$30$	−54.0169	−	1.53316i	−1.80056	−	0.0511054i
$31$	−4.27699	−	13.1632i	−0.137967	−	0.424620i	0.858072	−	0.513529i	$-0.171662\pi$
$31$	−4.27699	−	13.1632i	−0.137967	−	0.424620i	−0.996040	+	0.0889087i	$0.971662\pi$
$32$	31.6527			0.989147
$33$	7.07832	−	3.42808i	0.214495	−	0.103881i
$34$	−5.86863	−	4.26381i	−0.172607	−	0.125406i
$35$	−42.6748	−	22.1839i	−1.21928	−	0.633826i
$36$	−50.1020	+	63.4001i	−1.39172	+	1.76112i
$37$	34.1022	−	46.9377i	0.921682	−	1.26859i	−0.0413355	−	0.999145i	$-0.513161\pi$
$37$	34.1022	−	46.9377i	0.921682	−	1.26859i	0.963017	−	0.269441i	$-0.0868388\pi$
$38$	−40.5526	−	29.4632i	−1.06717	−	0.775347i
$39$	39.5178	+	41.1495i	1.01328	+	1.05511i
$40$	−88.4570	−	14.7503i	−2.21142	−	0.368757i
$41$	−11.5675	+	15.9213i	−0.282135	+	0.388325i	−0.926439	−	0.376444i	$-0.877147\pi$
$41$	−11.5675	+	15.9213i	−0.282135	+	0.388325i	0.644305	+	0.764769i	$0.277147\pi$
$42$	−93.5670	+	45.3151i	−2.22779	+	1.07893i
$43$		−	12.7377i		−	0.296226i	−0.988970	−	0.148113i	$-0.952680\pi$
$43$		−	12.7377i		−	0.296226i	0.988970	−	0.148113i	$-0.0473200\pi$
$44$	22.3860	−	7.27366i	0.508773	−	0.165311i
$45$	33.3281	−	30.2364i	0.740624	−	0.671920i
$46$	6.54469	−	20.1425i	0.142276	−	0.437880i
$47$	−4.86299	+	14.9667i	−0.103468	+	0.318441i	−0.989368	−	0.145435i	$-0.953542\pi$
$47$	−4.86299	+	14.9667i	−0.103468	+	0.318441i	0.885900	+	0.463876i	$0.153542\pi$
$48$	−62.1015	+	59.6390i	−1.29378	+	1.24248i
$49$	−43.5307			−0.888382
$50$	85.1913	+	29.2240i	1.70383	+	0.584480i
$51$	5.98422	−	0.824122i	0.117338	−	0.0161592i
$52$	100.363	+	138.138i	1.93007	+	2.65651i
$53$	15.7029	−	48.3285i	0.296281	−	0.911859i	−0.686507	−	0.727123i	$-0.740857\pi$
$53$	15.7029	−	48.3285i	0.296281	−	0.911859i	0.982788	−	0.184736i	$-0.0591430\pi$
$54$	−9.36283	−	96.8179i	−0.173386	−	1.79292i
$55$	−12.9628	+	1.94494i	−0.235688	+	0.0353625i
$56$	−164.084	+	53.3142i	−2.93008	+	0.952039i
$57$	41.3513	−	5.69473i	0.725461	−	0.0999075i
$58$	−84.8800	+	27.5792i	−1.46345	+	0.475503i
$59$	−32.8435	+	45.2053i	−0.556670	+	0.766191i	−0.990898	−	0.134612i	$-0.957021\pi$
$59$	−32.8435	+	45.2053i	−0.556670	+	0.766191i	0.434228	+	0.900803i	$0.357021\pi$
$60$	111.159	−	76.0389i	1.85265	−	1.26731i
$61$	3.13551	−	2.27808i	0.0514018	−	0.0373456i	−0.561788	−	0.827281i	$-0.689886\pi$
$61$	3.13551	−	2.27808i	0.0514018	−	0.0373456i	0.613190	+	0.789936i	$0.289886\pi$
$62$	40.3392	+	29.3081i	0.650632	+	0.472712i
$63$	30.0604	−	81.1872i	0.477149	−	1.28869i
$64$	0.623150	−	0.452745i	0.00973672	−	0.00707414i
$65$	−42.4765	−	85.0720i	−0.653485	−	1.30880i
$66$	−13.3710	+	24.9799i	−0.202591	+	0.378484i
$67$	−60.1212	+	19.5346i	−0.897331	+	0.291560i	−0.721135	−	0.692795i	$-0.756379\pi$
$67$	−60.1212	+	19.5346i	−0.897331	+	0.291560i	−0.176196	+	0.984355i	$0.556379\pi$
$68$	18.0789			0.265867
$69$	7.68741	+	15.8730i	0.111412	+	0.230044i
$70$	171.353	−	25.7098i	2.44790	−	0.367283i
$71$	74.3554	+	24.1595i	1.04726	+	0.340275i	0.781592	−	0.623789i	$-0.214408\pi$
$71$	74.3554	+	24.1595i	1.04726	+	0.340275i	0.265667	+	0.964065i	$0.414408\pi$
$72$	6.52758	−	161.289i	0.0906608	−	2.24013i
$73$	48.7077	+	67.0405i	0.667229	+	0.918362i	0.999694	−	0.0247534i	$-0.00788007\pi$
$73$	48.7077	+	67.0405i	0.667229	+	0.918362i	−0.332464	+	0.943116i	$0.607880\pi$
$74$			209.015i			2.82453i
$75$	−68.0243	+	31.5862i	−0.906991	+	0.421150i
$76$	124.926			1.64377
$77$	−20.4016	+	14.8226i	−0.264956	+	0.192502i
$78$	−202.312	−	36.2515i	−2.59375	−	0.464763i
$79$	−32.2869	+	99.3689i	−0.408695	+	1.25783i	0.509075	+	0.860722i	$0.329988\pi$
$79$	−32.2869	+	99.3689i	−0.408695	+	1.25783i	−0.917770	+	0.397112i	$0.870012\pi$
$80$	128.388	−	64.1042i	1.60485	−	0.801303i
$81$	61.4686	+	52.7504i	0.758872	+	0.651240i
$82$		−	70.8982i		−	0.864612i
$83$	−34.6732	−	106.713i	−0.417749	−	1.28570i	−0.909769	−	0.415115i	$-0.863741\pi$
$83$	−34.6732	−	106.713i	−0.417749	−	1.28570i	0.492020	−	0.870584i	$-0.336259\pi$
$84$	122.275	−	228.436i	1.45565	−	2.71947i
$85$	−9.93071	−	1.65595i	−0.116832	−	0.0194818i
$86$	26.9727	+	37.1247i	0.313636	+	0.431683i
$87$	35.0730	−	65.5239i	0.403138	−	0.753149i
$88$	−27.6376	+	38.0399i	−0.314063	+	0.432271i
$89$	15.7364	+	21.6593i	0.176813	+	0.243363i	0.888221	−	0.459417i	$-0.151942\pi$
$89$	15.7364	+	21.6593i	0.176813	+	0.243363i	−0.711407	+	0.702780i	$0.751942\pi$
$90$	−33.1094	+	158.699i	−0.367882	+	1.76332i
$91$	−147.996	−	107.526i	−1.62633	−	1.18160i
$92$	16.3111	+	50.2004i	0.177294	+	0.545656i
$93$	−41.1337	+	5.66476i	−0.442297	+	0.0609114i
$94$	−17.5193	−	53.9188i	−0.186375	−	0.573605i
$95$	−68.6218	−	11.4427i	−0.722334	−	0.120450i
$96$	16.7484	−	93.4694i	0.174462	−	0.973640i
$97$	−45.8531	−	14.8986i	−0.472712	−	0.153593i	0.0629661	−	0.998016i	$-0.479944\pi$
$97$	−45.8531	−	14.8986i	−0.472712	−	0.153593i	−0.535678	+	0.844422i	$0.679944\pi$
$98$	126.872	−	92.1781i	1.29462	−	0.940593i
$99$	−6.37765	−	22.7160i	−0.0644207	−	0.229454i
$100$	−214.580	+	65.8742i	−2.14580	+	0.658742i
$101$			20.4266i			0.202244i	0.994874	+	0.101122i	$0.0322432\pi$
$101$			20.4266i			0.202244i	−0.994874	+	0.101122i	$0.967757\pi$
$102$	−15.6962	+	15.0738i	−0.153884	+	0.147782i
$103$	130.063	+	42.2602i	1.26275	+	0.410293i	0.862474	−	0.506101i	$-0.168914\pi$
$103$	130.063	+	42.2602i	1.26275	+	0.410293i	0.400278	+	0.916394i	$0.368914\pi$
$104$	−324.395	−	105.402i	−3.11918	−	1.01348i
$105$	−88.0889	+	114.279i	−0.838942	+	1.08837i
$106$	56.5709	+	174.107i	0.533688	+	1.64252i
$107$	−130.632			−1.22086			−0.610429	−	0.792071i	$-0.709003\pi$
$107$	−130.632			−1.22086			−0.610429	+	0.792071i	$0.709003\pi$
$108$	160.708	+	181.497i	1.48804	+	1.68052i
$109$	134.451	+	97.6842i	1.23349	+	0.896185i	0.997147	−	0.0754837i	$-0.0240501\pi$
$109$	134.451	+	97.6842i	1.23349	+	0.896185i	0.236346	+	0.971669i	$0.424050\pi$
$110$	33.6623	−	33.1179i	0.306021	−	0.301072i
$111$	−120.561	−	125.539i	−1.08613	−	1.13098i
$112$	162.274	−	223.351i	1.44888	−	1.99421i
$113$	167.682	+	121.828i	1.48391	+	1.07812i	0.976270	+	0.216555i	$0.0694821\pi$
$113$	167.682	+	121.828i	1.48391	+	1.07812i	0.507640	+	0.861569i	$0.330518\pi$
$114$	−108.461	+	104.161i	−0.951416	+	0.913690i
$115$	−4.36150	−	29.0689i	−0.0379261	−	0.252773i
$116$	130.741	−	179.949i	1.12708	−	1.55129i
$117$	142.423	−	94.9214i	1.21729	−	0.811294i
$118$		−	201.300i		−	1.70594i
$119$	−18.4211	+	5.98537i	−0.154799	+	0.0502972i
$120$	−90.3623	+	253.406i	−0.753019	+	2.11172i
$121$	35.2673	−	108.542i	0.291465	−	0.897037i
$122$	−4.31466	+	13.2792i	−0.0353661	+	0.108846i
$123$	40.8944	+	42.5830i	0.332475	+	0.346203i
$124$	−124.269			−1.00217
$125$	123.902	−	16.5299i	0.991218	−	0.132239i
$126$	84.3050	+	300.278i	0.669087	+	2.38316i
$127$	0.760056	+	1.04613i	0.00598469	+	0.00823722i	0.811999	−	0.583659i	$-0.198380\pi$
$127$	0.760056	+	1.04613i	0.00598469	+	0.00823722i	−0.806014	+	0.591896i	$0.798380\pi$
$128$	−39.9824	+	123.053i	−0.312362	+	0.961352i
$129$	−37.6141	−	6.73992i	−0.291582	−	0.0522474i
$130$	303.943	+	158.000i	2.33802	+	1.21539i
$131$	169.449	−	55.0573i	1.29350	−	0.420285i	0.420187	−	0.907437i	$-0.361964\pi$
$131$	169.449	−	55.0573i	1.29350	−	0.420285i	0.873317	+	0.487152i	$0.161964\pi$
$132$	−9.63377	−	69.9539i	−0.0729831	−	0.529954i
$133$	−127.291	+	41.3593i	−0.957073	+	0.310972i
$134$	133.861	−	184.243i	0.998961	−	1.37495i
$135$	−71.6522	−	114.416i	−0.530757	−	0.847524i
$136$	−29.2174	+	21.2277i	−0.214834	+	0.156086i
$137$	8.30822	+	6.03627i	0.0606439	+	0.0440604i	0.617694	−	0.786418i	$-0.288067\pi$
$137$	8.30822	+	6.03627i	0.0606439	+	0.0440604i	−0.557050	+	0.830479i	$0.688067\pi$
$138$	−56.0171	−	29.9843i	−0.405921	−	0.217277i
$139$	−1.72900	+	1.25619i	−0.0124389	+	0.00903736i	−0.593987	−	0.804474i	$-0.702447\pi$
$139$	−1.72900	+	1.25619i	−0.0124389	+	0.00903736i	0.581548	+	0.813512i	$0.302447\pi$
$140$	−307.834	+	302.856i	−2.19881	+	2.16326i
$141$	41.6231	+	22.2796i	0.295200	+	0.158011i
$142$	−267.871	+	87.0366i	−1.88642	+	0.612934i
$143$	−49.8556			−0.348640
$144$	143.252	+	214.941i	0.994808	+	1.49264i
$145$	−88.2982	+	86.8704i	−0.608953	+	0.599107i
$146$	−283.922	−	92.2518i	−1.94467	−	0.631862i
$147$	−23.0334	+	128.545i	−0.156690	+	0.874454i
$148$	−306.189	−	421.433i	−2.06884	−	2.84752i
$149$		−	88.6286i		−	0.594823i	−0.954749	−	0.297411i	$-0.903877\pi$
$149$		−	88.6286i		−	0.594823i	0.954749	−	0.297411i	$-0.0961233\pi$
$150$	131.375	−	236.104i	0.875833	−	1.57403i
$151$	38.2237			0.253137			0.126569	−	0.991958i	$-0.459604\pi$
$151$	38.2237			0.253137			0.126569	+	0.991958i	$0.459604\pi$
$152$	−201.894	+	146.684i	−1.32825	+	0.965029i
$153$	0.732825	−	18.1073i	0.00478971	−	0.118348i
$154$	28.0739	−	86.4025i	0.182298	−	0.561055i
$155$	68.2606	+	11.3825i	0.440391	+	0.0734355i
$156$	461.024	−	223.277i	2.95528	−	1.43126i
$157$		−	24.0420i		−	0.153134i	−0.997064	−	0.0765670i	$-0.975604\pi$
$157$		−	24.0420i		−	0.153134i	0.997064	−	0.0765670i	$-0.0243959\pi$
$158$	−116.316	−	357.984i	−0.736178	−	2.26572i
$159$	−134.404	−	71.9422i	−0.845306	−	0.452467i
$160$	−72.9971	+	140.423i	−0.456232	+	0.877647i
$161$	−33.2395	−	45.7503i	−0.206457	−	0.284163i
$162$	−290.854	−	23.5811i	−1.79540	−	0.145563i
$163$	−127.234	+	175.122i	−0.780576	+	1.07437i	0.214642	+	0.976693i	$0.431141\pi$
$163$	−127.234	+	175.122i	−0.780576	+	1.07437i	−0.995218	+	0.0976777i	$0.968859\pi$
$164$	103.860	+	142.951i	0.633291	+	0.871651i
$165$	−1.11568	+	39.3079i	−0.00676168	+	0.238230i
$166$	327.026	+	237.598i	1.97004	+	1.43132i
$167$	52.1758	+	160.581i	0.312430	+	0.961561i	0.976799	+	0.214157i	$0.0687003\pi$
$167$	52.1758	+	160.581i	0.312430	+	0.961561i	−0.664369	+	0.747405i	$0.731300\pi$
$168$	70.6132	+	512.746i	0.420317	+	3.05206i
$169$	−59.5351	−	183.230i	−0.352279	−	1.08420i
$170$	32.4501	−	16.2023i	0.190883	−	0.0953079i
$171$	5.06386	−	125.122i	0.0296132	−	0.731709i
$172$	−108.769	−	35.3412i	−0.632378	−	0.205472i
$173$	37.1446	−	26.9871i	0.214709	−	0.155995i	−0.475233	−	0.879860i	$-0.657636\pi$
$173$	37.1446	−	26.9871i	0.214709	−	0.155995i	0.689942	+	0.723865i	$0.257636\pi$
$174$	36.5279	+	265.241i	0.209930	+	1.52437i
$175$	196.832	−	138.162i	1.12476	−	0.789496i
$176$		−	75.2405i		−	0.427503i
$177$	116.111	+	120.905i	0.655995	+	0.683081i
$178$	−91.7289	−	29.8045i	−0.515331	−	0.167441i
$179$	−63.4653	−	20.6211i	−0.354555	−	0.115202i	0.126324	−	0.991989i	$-0.459682\pi$
$179$	−63.4653	−	20.6211i	−0.354555	−	0.115202i	−0.480878	+	0.876787i	$0.659682\pi$
$180$	−165.723	−	368.484i	−0.920681	−	2.04714i
$181$	−27.4507	−	84.4846i	−0.151661	−	0.466766i	0.846146	−	0.532951i	$-0.178917\pi$
$181$	−27.4507	−	84.4846i	−0.151661	−	0.466766i	−0.997807	+	0.0661856i	$0.978917\pi$
$182$	659.032			3.62105
$183$	−5.06801	−	10.4645i	−0.0276941	−	0.0571829i
$184$	−85.3039	−	61.9769i	−0.463608	−	0.336831i
$185$	129.587	+	259.538i	0.700472	+	1.40291i
$186$	107.891	−	103.612i	0.580057	−	0.557056i
$187$	−3.10276	+	4.27058i	−0.0165923	+	0.0228373i
$188$	114.310	+	83.0513i	0.608034	+	0.441762i
$189$	−223.837	−	131.726i	−1.18432	−	0.696962i
$190$	224.232	−	111.959i	1.18017	−	0.589259i
$191$	−155.312	+	213.768i	−0.813151	+	1.11921i	0.177679	+	0.984089i	$0.443141\pi$
$191$	−155.312	+	213.768i	−0.813151	+	1.11921i	−0.990830	+	0.135118i	$0.956859\pi$
$192$	−1.00721	−	2.07970i	−0.00524591	−	0.0108318i
$193$		−	217.844i		−	1.12872i	−0.825527	−	0.564362i	$-0.809122\pi$
$193$		−	217.844i		−	1.12872i	0.825527	−	0.564362i	$-0.190878\pi$
$194$	165.189	−	53.6732i	0.851491	−	0.276666i
$195$	−273.690	+	80.4176i	−1.40354	+	0.412398i
$196$	−120.777	+	371.714i	−0.616210	+	1.89650i
$197$	106.780	−	328.635i	0.542031	−	1.66820i	−0.185916	−	0.982566i	$-0.559525\pi$
$197$	106.780	−	328.635i	0.542031	−	1.66820i	0.727947	−	0.685633i	$-0.240475\pi$
$198$	66.6899	+	52.7018i	0.336818	+	0.266170i
$199$	120.507			0.605564			0.302782	−	0.953060i	$-0.402085\pi$
$199$	120.507			0.605564			0.302782	+	0.953060i	$0.402085\pi$
$200$	269.436	−	358.412i	1.34718	−	1.79206i
$201$	25.8730	+	187.872i	0.128721	+	0.934688i
$202$	−43.2543	−	59.5344i	−0.214130	−	0.294725i
$203$	−73.6396	+	226.639i	−0.362756	+	1.11645i
$204$	9.56611	−	53.3865i	0.0468927	−	0.261699i
$205$	−43.9562	−	88.0355i	−0.214421	−	0.429442i
$206$	−468.564	+	152.246i	−2.27458	+	0.739056i
$207$	50.9402	−	14.3018i	0.246088	−	0.0690908i
$208$	519.092	−	168.663i	2.49563	−	0.810880i
$209$	−21.4403	+	29.5100i	−0.102585	+	0.141196i
$210$	14.7479	−	519.604i	0.0702283	−	2.47431i
$211$	8.98786	−	6.53006i	0.0425965	−	0.0309482i	−0.566283	−	0.824211i	$-0.691619\pi$
$211$	8.98786	−	6.53006i	0.0425965	−	0.0309482i	0.608880	+	0.793263i	$0.291619\pi$
$212$	−369.115	−	268.178i	−1.74111	−	1.26499i
$213$	110.686	−	206.786i	0.519653	−	0.970825i
$214$	380.733	−	276.618i	1.77912	−	1.29261i
$215$	56.5094	+	29.3756i	0.262835	+	0.136631i
$216$	−472.827	−	104.619i	−2.18902	−	0.484345i
$217$	126.621	−	41.1416i	0.583506	−	0.189593i
$218$	−598.713			−2.74639
$219$	223.741	−	108.359i	1.02165	−	0.494791i
$220$	−19.3577	+	116.087i	−0.0879894	+	0.527670i
$221$	−36.4185	−	11.8331i	−0.164790	−	0.0535434i
$222$	617.214	+	110.596i	2.78025	+	0.498181i
$223$	252.876	+	348.053i	1.13397	+	1.56078i	0.780297	+	0.625409i	$0.215068\pi$
$223$	252.876	+	348.053i	1.13397	+	1.56078i	0.353675	+	0.935368i	$0.384932\pi$
$224$			304.476i			1.35927i
$225$	57.2794	+	217.587i	0.254575	+	0.967053i
$226$	−746.693			−3.30395
$227$	99.6999	−	72.4362i	0.439207	−	0.319102i	−0.346113	−	0.938193i	$-0.612499\pi$
$227$	99.6999	−	72.4362i	0.439207	−	0.319102i	0.785320	+	0.619090i	$0.212499\pi$
$228$	66.1024	−	368.904i	0.289923	−	1.61800i
$229$	−83.9328	+	258.319i	−0.366519	+	1.12803i	0.582506	+	0.812827i	$0.302072\pi$
$229$	−83.9328	+	258.319i	−0.366519	+	1.12803i	−0.949025	+	0.315202i	$0.897928\pi$
$230$	74.2665	+	75.4871i	0.322898	+	0.328205i
$231$	32.9757	+	68.0884i	0.142752	+	0.294755i
$232$			444.328i			1.91521i
$233$	90.9554	+	279.932i	0.390367	+	1.20142i	0.932512	+	0.361140i	$0.117612\pi$
$233$	90.9554	+	279.932i	0.390367	+	1.20142i	−0.542145	+	0.840285i	$0.682388\pi$
$234$	−214.099	+	578.240i	−0.914953	+	2.47111i
$235$	−55.1832	−	56.0902i	−0.234822	−	0.238682i
$236$	294.888	+	405.878i	1.24953	+	1.71982i
$237$	276.349	+	147.921i	1.16603	+	0.624141i
$238$	41.0148	−	56.4521i	0.172331	−	0.237194i
$239$	27.6341	+	38.0351i	0.115624	+	0.159143i	0.862906	−	0.505364i	$-0.168642\pi$
$239$	27.6341	+	38.0351i	0.115624	+	0.159143i	−0.747282	+	0.664507i	$0.768642\pi$
$240$	−121.364	−	413.045i	−0.505682	−	1.72102i
$241$	−82.7901	−	60.1506i	−0.343528	−	0.249587i	0.402621	−	0.915367i	$-0.368099\pi$
$241$	−82.7901	−	60.1506i	−0.343528	−	0.249587i	−0.746149	+	0.665779i	$0.768099\pi$
$242$	127.053	+	391.029i	0.525013	+	1.61582i
$243$	188.295	−	153.603i	0.774877	−	0.632111i
$244$	−10.7533	−	33.0951i	−0.0440708	−	0.135636i
$245$	100.390	−	193.119i	0.409755	−	0.788240i
$246$	−209.360	−	37.5144i	−0.851057	−	0.152497i
$247$	−251.654	−	81.7673i	−1.01884	−	0.331042i
$248$	200.831	−	145.912i	0.809803	−	0.588357i
$249$	−333.467	+	45.9237i	−1.33922	+	0.184432i
$250$	−326.116	+	310.545i	−1.30446	+	1.24218i
$251$		−	324.851i		−	1.29423i	−0.762394	−	0.647113i	$-0.775976\pi$
$251$		−	324.851i		−	1.29423i	0.762394	−	0.647113i	$-0.224024\pi$
$252$	−609.864	−	481.945i	−2.42010	−	1.91248i
$253$	−14.6576	−	4.76255i	−0.0579353	−	0.0188243i
$254$	−4.43044	−	1.43954i	−0.0174427	−	0.00566746i
$255$	−10.1446	+	28.4489i	−0.0397828	+	0.111564i
$256$	−143.088	−	440.378i	−0.558936	−	1.72023i
$257$	10.6951			0.0416150			0.0208075	−	0.999784i	$-0.493376\pi$
$257$	10.6951			0.0416150			0.0208075	+	0.999784i	$0.493376\pi$
$258$	123.900	−	60.0057i	0.480233	−	0.232580i
$259$	451.507	+	328.039i	1.74327	+	1.26656i
$260$	−844.292	+	126.677i	−3.24728	+	0.487221i
$261$	−174.932	−	138.240i	−0.670237	−	0.529655i
$262$	−377.281	+	519.283i	−1.44000	+	1.98200i
$263$	−220.942	−	160.524i	−0.840083	−	0.610356i	0.0823105	−	0.996607i	$-0.473770\pi$
$263$	−220.942	−	160.524i	−0.840083	−	0.610356i	−0.922394	+	0.386250i	$0.873770\pi$
$264$	97.7067	+	101.741i	0.370101	+	0.385382i
$265$	178.190	+	181.119i	0.672415	+	0.683467i
$266$	283.415	−	390.087i	1.06547	−	1.46649i
$267$	72.2858	−	35.0085i	0.270733	−	0.131118i
$268$			567.581i			2.11784i
$269$	−310.812	+	100.989i	−1.15544	+	0.375424i	−0.823189	−	0.567768i	$-0.807807\pi$
$269$	−310.812	+	100.989i	−1.15544	+	0.375424i	−0.332248	+	0.943192i	$0.607807\pi$
$270$	451.114	+	181.743i	1.67079	+	0.673123i
$271$	−30.9515	+	95.2590i	−0.114212	+	0.351509i	−0.991782	−	0.127940i	$-0.959164\pi$
$271$	−30.9515	+	95.2590i	−0.114212	+	0.351509i	0.877570	+	0.479449i	$0.159164\pi$
$272$	17.8581	−	54.9617i	0.0656549	−	0.202065i
$273$	−395.829	+	380.133i	−1.44992	+	1.39243i
$274$	−36.9968			−0.135025
$275$	21.2662	−	61.9934i	0.0773317	−	0.225431i
$276$	156.871	−	21.6036i	0.568372	−	0.0782739i
$277$	−144.606	−	199.033i	−0.522043	−	0.718530i	0.463849	−	0.885914i	$-0.346468\pi$
$277$	−144.606	−	199.033i	−0.522043	−	0.718530i	−0.985892	+	0.167384i	$0.946468\pi$
$278$	2.37921	−	7.32246i	0.00855832	−	0.0263398i
$279$	−5.03721	+	124.464i	−0.0180545	+	0.446107i
$280$	141.887	−	850.893i	0.506739	−	3.03890i
$281$	−492.907	+	160.155i	−1.75412	+	0.569948i	−0.996564	−	0.0828247i	$-0.973606\pi$
$281$	−492.907	+	160.155i	−1.75412	+	0.569948i	−0.757554	+	0.652772i	$0.773606\pi$
$282$	−168.491	+	23.2038i	−0.597484	+	0.0822831i
$283$	−342.705	+	111.352i	−1.21097	+	0.393468i	−0.843786	−	0.536680i	$-0.819678\pi$
$283$	−342.705	+	111.352i	−1.21097	+	0.393468i	−0.367185	+	0.930148i	$0.619678\pi$
$284$	412.603	−	567.899i	1.45283	−	1.99964i
$285$	−70.0999	+	196.583i	−0.245964	+	0.689766i
$286$	145.306	−	105.571i	0.508064	−	0.369130i
$287$	−153.152	−	111.271i	−0.533630	−	0.387705i
$288$	−267.150	−	98.9150i	−0.927605	−	0.343455i
$289$	230.526	−	167.487i	0.797667	−	0.579539i
$290$	73.3975	−	440.163i	0.253095	−	1.51780i
$291$	−68.2572	+	127.519i	−0.234561	+	0.438211i
$292$	707.608	−	229.916i	2.42331	−	0.787383i
$293$	257.869			0.880100			0.440050	−	0.897973i	$-0.354961\pi$
$293$	257.869			0.880100			0.440050	+	0.897973i	$0.354961\pi$
$294$	−205.067	−	423.424i	−0.697507	−	1.44022i
$295$	−124.804	−	249.958i	−0.423066	−	0.847316i
$296$	989.664	+	321.561i	3.34346	+	1.08636i
$297$	−70.4541	+	6.81330i	−0.237219	+	0.0229404i
$298$	187.675	+	258.312i	0.629781	+	0.866819i
$299$		−	111.800i		−	0.373914i
$300$	80.9833	+	668.505i	0.269944	+	2.22835i
$301$	122.528			0.407069
$302$	−111.405	+	80.9404i	−0.368890	+	0.268015i
$303$	60.3192	+	10.8083i	0.199073	+	0.0356711i
$304$	123.401	−	379.788i	0.405923	−	1.24930i
$305$	2.87537	+	19.1640i	0.00942743	+	0.0628329i
$306$	36.2071	+	54.3263i	0.118324	+	0.177537i
$307$			439.331i			1.43105i	0.698589	+	0.715524i	$0.253812\pi$
$307$			439.331i			1.43105i	−0.698589	+	0.715524i	$0.746188\pi$
$308$	69.9675	+	215.338i	0.227167	+	0.699148i
$309$	193.613	−	361.712i	0.626581	−	1.17059i
$310$	−223.052	+	111.370i	−0.719522	+	0.359258i
$311$	189.558	+	260.904i	0.609512	+	0.838921i	0.996537	−	0.0831483i	$-0.0264975\pi$
$311$	189.558	+	260.904i	0.609512	+	0.838921i	−0.387026	+	0.922069i	$0.626498\pi$
$312$	−482.897	+	902.156i	−1.54775	+	2.89153i
$313$	299.621	−	412.393i	0.957255	−	1.31755i	0.00902650	−	0.999959i	$-0.497127\pi$
$313$	299.621	−	412.393i	0.957255	−	1.31755i	0.948228	−	0.317589i	$-0.102873\pi$
$314$	50.9100	+	70.0716i	0.162134	+	0.223158i
$315$	290.853	+	320.592i	0.923342	+	1.01775i
$316$	758.942	+	551.404i	2.40172	+	1.74495i
$317$	−110.243	−	339.293i	−0.347770	−	1.07032i	−0.960084	−	0.279711i	$-0.909761\pi$
$317$	−110.243	−	339.293i	−0.347770	−	1.07032i	0.612315	−	0.790614i	$-0.290239\pi$
$318$	544.067	−	74.9266i	1.71090	−	0.235618i
$319$	20.0693	+	61.7669i	0.0629131	+	0.193627i
$320$	0.571449	+	3.80865i	0.00178578	+	0.0119020i
$321$	−69.1212	+	385.752i	−0.215331	+	1.20172i
$322$	193.756	+	62.9553i	0.601728	+	0.195513i
$323$	−22.6658	+	16.4677i	−0.0701727	+	0.0509835i
$324$	620.989	−	378.531i	1.91663	−	1.16830i
$325$	475.371	+	7.74997i	1.46268	+	0.0238461i
$326$		−	779.825i		−	2.39210i
$327$	359.600	−	345.341i	1.09969	−	1.05609i
$328$	−335.696	−	109.074i	−1.02346	−	0.332543i
$329$	−143.969	−	46.7785i	−0.437597	−	0.142184i
$330$	−79.9845	−	116.927i	−0.242377	−	0.354325i
$331$	−78.1687	−	240.579i	−0.236159	−	0.726824i	−0.996966	−	0.0778445i	$-0.975196\pi$
$331$	−78.1687	−	240.579i	−0.236159	−	0.726824i	0.760806	−	0.648979i	$-0.224804\pi$
$332$	−1007.44			−3.03445
$333$	−434.505	+	289.586i	−1.30482	+	0.869628i
$334$	−492.105	−	357.536i	−1.47337	−	1.07047i
$335$	51.9880	−	311.771i	0.155188	−	0.930659i
$336$	−573.685	−	597.372i	−1.70740	−	1.77789i
$337$	125.926	−	173.322i	0.373667	−	0.514308i	−0.580226	−	0.814455i	$-0.697036\pi$
$337$	125.926	−	173.322i	0.373667	−	0.514308i	0.953893	+	0.300147i	$0.0970358\pi$
$338$	561.515	+	407.965i	1.66129	+	1.20700i
$339$	448.480	−	430.696i	1.32295	−	1.27049i
$340$	−41.6934	+	80.2051i	−0.122628	+	0.235897i
$341$	21.3274	−	29.3547i	0.0625438	−	0.0860841i
$342$	250.193	+	375.398i	0.731558	+	1.09765i
$343$			52.6107i			0.153384i
$344$	217.278	−	70.5979i	0.631622	−	0.205227i
$345$	−88.1475	−	2.50189i	−0.255500	−	0.00725186i
$346$	−51.1133	+	157.310i	−0.147726	+	0.454655i
$347$	−5.40910	+	16.6475i	−0.0155882	+	0.0479755i	−0.958548	−	0.284931i	$-0.908029\pi$
$347$	−5.40910	+	16.6475i	−0.0155882	+	0.0479755i	0.942960	+	0.332906i	$0.108029\pi$
$348$	−462.206	−	481.291i	−1.32818	−	1.38302i
$349$	−498.785			−1.42918			−0.714591	−	0.699542i	$-0.753387\pi$
$349$	−498.785			−1.42918			−0.714591	+	0.699542i	$0.753387\pi$
$350$	−281.114	+	819.480i	−0.803184	+	2.34137i
$351$	−204.939	−	470.797i	−0.583873	−	1.34130i
$352$	48.7745	+	67.1324i	0.138564	+	0.190717i
$353$	115.543	−	355.604i	0.327317	−	1.00738i	−0.643067	−	0.765810i	$-0.722339\pi$
$353$	115.543	−	355.604i	0.327317	−	1.00738i	0.970384	−	0.241567i	$-0.0776615\pi$
$354$	−594.434	−	106.514i	−1.67919	−	0.300887i
$355$	−278.659	+	274.153i	−0.784954	+	0.772261i
$356$	228.612	−	74.2807i	0.642170	−	0.208654i
$357$	7.92746	+	57.5639i	0.0222058	+	0.161243i
$358$	228.639	−	74.2892i	0.638655	−	0.207512i
$359$	−49.4120	+	68.0098i	−0.137638	+	0.189442i	−0.872272	−	0.489021i	$-0.837354\pi$
$359$	−49.4120	+	68.0098i	−0.137638	+	0.189442i	0.734634	+	0.678464i	$0.237354\pi$
$360$	700.486	+	400.922i	1.94579	+	1.11367i
$361$	135.433	−	98.3980i	0.375161	−	0.272571i
$362$	258.906	+	188.106i	0.715210	+	0.519630i
$363$	−301.859	−	161.576i	−0.831567	−	0.445112i
$364$	−1328.79	+	965.425i	−3.65053	+	2.65227i
$365$	−409.746	+	61.4783i	−1.12259	+	0.168434i
$366$	36.9299	+	19.7675i	0.100901	+	0.0540095i
$367$	−212.024	+	68.8908i	−0.577722	+	0.187713i	−0.583280	−	0.812271i	$-0.698231\pi$
$367$	−212.024	+	68.8908i	−0.577722	+	0.187713i	0.00555765	+	0.999985i	$0.498231\pi$
$368$	168.726			0.458494
$369$	147.385	−	98.2281i	0.399416	−	0.266201i
$370$	−927.270	−	482.028i	−2.50614	−	1.30278i
$371$	464.886	+	151.051i	1.25306	+	0.407144i
$372$	−65.7545	+	366.962i	−0.176759	+	0.986458i
$373$	−79.9562	−	110.050i	−0.214360	−	0.295041i	0.688274	−	0.725451i	$-0.258369\pi$
$373$	−79.9562	−	110.050i	−0.214360	−	0.295041i	−0.902633	+	0.430410i	$0.858369\pi$
$374$		−	19.0170i		−	0.0508477i
$375$	16.7483	−	374.626i	0.0446621	−	0.999002i
$376$	−282.253			−0.750673
$377$	−381.148	+	276.920i	−1.01100	+	0.734536i
$378$	931.320	−	90.0638i	2.46381	−	0.238264i
$379$	146.003	−	449.351i	0.385232	−	1.18562i	−0.551079	−	0.834453i	$-0.685784\pi$
$379$	146.003	−	449.351i	0.385232	−	1.18562i	0.936312	−	0.351170i	$-0.114216\pi$
$380$	−288.104	+	554.222i	−0.758168	+	1.45848i
$381$	3.49135	−	1.69088i	0.00916364	−	0.00443801i
$382$		−	951.917i		−	2.49193i
$383$	50.3576	+	154.985i	0.131482	+	0.404660i	0.995026	−	0.0996130i	$-0.0317605\pi$
$383$	50.3576	+	154.985i	0.131482	+	0.404660i	−0.863544	+	0.504273i	$0.831760\pi$
$384$	342.216	+	183.178i	0.891188	+	0.477026i
$385$	−18.7089	−	124.693i	−0.0485946	−	0.323878i
$386$	461.293	+	634.916i	1.19506	+	1.64486i
$387$	−39.8055	+	107.507i	−0.102857	+	0.277796i
$388$	−254.441	+	350.209i	−0.655777	+	0.902599i
$389$	35.3689	+	48.6811i	0.0909226	+	0.125144i	0.852055	−	0.523452i	$-0.175356\pi$
$389$	35.3689	+	48.6811i	0.0909226	+	0.125144i	−0.761132	+	0.648597i	$0.775356\pi$
$390$	627.396	−	813.932i	1.60871	−	2.08700i
$391$	−9.57672	−	6.95790i	−0.0244929	−	0.0177951i
$392$	−241.266	−	742.540i	−0.615474	−	1.89423i
$393$	−72.9220	−	529.510i	−0.185552	−	1.34735i
$394$	384.683	+	1183.93i	0.976354	+	3.00491i
$395$	−366.379	−	372.401i	−0.927541	−	0.942786i
$396$	−211.669	−	8.56654i	−0.534518	−	0.0216327i
$397$	475.722	+	154.572i	1.19829	+	0.389349i	0.839133	−	0.543927i	$-0.183063\pi$
$397$	475.722	+	154.572i	1.19829	+	0.389349i	0.359160	+	0.933276i	$0.383063\pi$
$398$	−351.224	+	255.179i	−0.882473	+	0.641154i
$399$	54.7792	+	397.770i	0.137291	+	0.996917i
$400$	−11.6960	+	717.414i	−0.0292400	+	1.79354i
$401$			369.579i			0.921644i	0.887493	+	0.460822i	$0.152445\pi$
$401$			369.579i			0.921644i	−0.887493	+	0.460822i	$0.847555\pi$
$402$	−473.235	−	492.775i	−1.17720	−	1.22581i
$403$	250.330	+	81.3370i	0.621165	+	0.201829i
$404$	174.426	+	56.6743i	0.431746	+	0.140283i
$405$	−375.779	+	151.046i	−0.927850	+	0.372953i
$406$	−265.292	−	816.486i	−0.653429	−	2.01105i
$407$	152.099			0.373709
$408$	47.2248	+	97.5102i	0.115747	+	0.238996i
$409$	−220.737	−	160.375i	−0.539700	−	0.392115i	0.284274	−	0.958743i	$-0.408248\pi$
$409$	−220.737	−	160.375i	−0.539700	−	0.392115i	−0.823974	+	0.566628i	$0.808248\pi$
$410$	314.531	+	163.505i	0.767150	+	0.398792i
$411$	22.2211	−	21.3399i	0.0540658	−	0.0519220i
$412$	721.730	−	993.376i	1.75177	−	2.41111i
$413$	−434.842	−	315.931i	−1.05289	−	0.764967i
$414$	−118.183	+	149.551i	−0.285466	+	0.361235i
$415$	553.383	+	92.2770i	1.33345	+	0.222354i
$416$	−353.818	+	486.988i	−0.850523	+	1.17064i
$417$	2.79463	+	5.77037i	0.00670175	+	0.0138378i
$418$		−	131.409i		−	0.314375i
$419$	54.2295	−	17.6202i	0.129426	−	0.0420531i	−0.243588	−	0.969879i	$-0.578324\pi$
$419$	54.2295	−	17.6202i	0.129426	−	0.0420531i	0.373014	+	0.927826i	$0.378324\pi$
$420$	731.440	+	1069.27i	1.74152	+	2.54589i
$421$	111.392	−	342.830i	0.264590	−	0.814323i	−0.727198	−	0.686428i	$-0.759178\pi$
$421$	111.392	−	342.830i	0.264590	−	0.814323i	0.991788	−	0.127896i	$-0.0408222\pi$
$422$	−12.3679	+	38.0643i	−0.0293077	+	0.0901998i
$423$	87.8150	−	111.123i	0.207600	−	0.262702i
$424$	911.412			2.14956
$425$	30.2485	−	40.2375i	0.0711730	−	0.0946765i
$426$	115.278	+	837.069i	0.270605	+	1.96495i
$427$	21.9135	+	30.1614i	0.0513198	+	0.0706356i
$428$	−362.442	+	1115.48i	−0.846827	+	2.60626i
$429$	−26.3801	+	147.222i	−0.0614921	+	0.343175i
$430$	−226.903	+	34.0445i	−0.527682	+	0.0791734i
$431$	−236.795	+	76.9394i	−0.549408	+	0.178514i	−0.570550	−	0.821263i	$-0.693270\pi$
$431$	−236.795	+	76.9394i	−0.549408	+	0.178514i	0.0211416	+	0.999776i	$0.493270\pi$
$432$	710.512	−	309.288i	1.64470	−	0.715945i
$433$	−350.943	+	114.028i	−0.810491	+	0.263345i	−0.684806	−	0.728726i	$-0.740113\pi$
$433$	−350.943	+	114.028i	−0.810491	+	0.263345i	−0.125685	+	0.992070i	$0.540113\pi$
$434$	−281.923	+	388.034i	−0.649593	+	0.894088i
$435$	209.804	+	306.708i	0.482309	+	0.705075i
$436$	1207.18	−	877.064i	2.76875	−	2.01161i
$437$	−66.1757	−	48.0795i	−0.151432	−	0.110022i
$438$	−422.648	+	789.599i	−0.964951	+	1.80274i
$439$	−83.8726	+	60.9370i	−0.191054	+	0.138809i	−0.679200	−	0.733953i	$-0.737673\pi$
$439$	−83.8726	+	60.9370i	−0.191054	+	0.138809i	0.488146	+	0.872762i	$0.337673\pi$
$440$	−105.022	−	210.338i	−0.238686	−	0.478041i
$441$	367.401	+	136.034i	0.833109	+	0.308467i
$442$	131.201	−	42.6296i	0.296834	−	0.0964471i
$443$	610.142			1.37730			0.688648	−	0.725096i	$-0.258205\pi$
$443$	610.142			1.37730			0.688648	+	0.725096i	$0.258205\pi$
$444$	−1406.49	+	681.174i	−3.16778	+	1.53417i
$445$	−132.380	+	19.8623i	−0.297483	+	0.0446343i
$446$	−1474.04	−	478.943i	−3.30501	−	1.07386i
$447$	−261.717	−	46.8961i	−0.585497	−	0.104913i
$448$	4.35509	+	5.99426i	0.00972117	+	0.0133800i
$449$			16.8743i			0.0375821i	0.999823	+	0.0187910i	$0.00598172\pi$
$449$			16.8743i			0.0375821i	−0.999823	+	0.0187910i	$0.994018\pi$
$450$	−627.693	−	512.876i	−1.39487	−	1.13972i
$451$	−51.5924			−0.114395
$452$	1505.54	−	1093.84i	3.33085	−	2.42000i
$453$	20.2253	−	112.873i	0.0446475	−	0.249169i
$454$	−137.193	+	422.238i	−0.302188	+	0.930039i
$455$	818.332	−	408.594i	1.79853	−	0.898008i
$456$	326.326	+	673.801i	0.715628	+	1.47763i
$457$			4.80448i			0.0105131i	0.999986	+	0.00525654i	$0.00167322\pi$
$457$			4.80448i			0.0105131i	−0.999986	+	0.00525654i	$0.998327\pi$
$458$	−302.374	−	930.613i	−0.660206	−	2.03191i
$459$	−53.0824	−	11.7451i	−0.115648	−	0.0255885i
$460$	−260.324	−	43.4093i	−0.565923	−	0.0943680i
$461$	−111.308	−	153.203i	−0.241449	−	0.332327i	0.671044	−	0.741417i	$-0.265846\pi$
$461$	−111.308	−	153.203i	−0.241449	−	0.332327i	−0.912494	+	0.409091i	$0.865846\pi$
$462$	−240.289	−	128.619i	−0.520106	−	0.278397i
$463$	−106.344	+	146.370i	−0.229685	+	0.316134i	−0.908268	−	0.418390i	$-0.862595\pi$
$463$	−106.344	+	146.370i	−0.229685	+	0.316134i	0.678582	+	0.734524i	$0.262595\pi$
$464$	−417.919	−	575.217i	−0.900688	−	1.23969i
$465$	69.7310	−	195.549i	0.149959	−	0.420535i
$466$	−857.861	−	623.273i	−1.84090	−	1.33750i
$467$	16.2208	+	49.9225i	0.0347341	+	0.106900i	0.966920	−	0.255078i	$-0.0821013\pi$
$467$	16.2208	+	49.9225i	0.0347341	+	0.106900i	−0.932186	+	0.361979i	$0.882101\pi$
$468$	−415.388	−	1479.53i	−0.887581	−	3.16139i
$469$	−187.908	−	578.323i	−0.400658	−	1.23310i
$470$	279.607	+	46.6247i	0.594909	+	0.0992015i
$471$	−70.9954	−	12.7214i	−0.150733	−	0.0270093i
$472$	−953.137	−	309.693i	−2.01936	−	0.656129i
$473$	27.0155	−	19.6279i	0.0571153	−	0.0414967i
$474$	−1118.66	+	154.058i	−2.36005	+	0.325016i
$475$	209.019	−	278.043i	0.440040	−	0.585354i
$476$			173.907i			0.365350i
$477$	−283.560	+	358.823i	−0.594466	+	0.752250i
$478$	−161.082	−	52.3386i	−0.336991	−	0.109495i
$479$	817.603	+	265.655i	1.70690	+	0.554604i	0.989812	−	0.142382i	$-0.0454761\pi$
$479$	817.603	+	265.655i	1.70690	+	0.554604i	0.717085	+	0.696986i	$0.245476\pi$
$480$	376.041	+	289.860i	0.783419	+	0.603876i
$481$	340.954	+	1049.35i	0.708845	+	2.18160i
$482$	368.667			0.764869
$483$	−152.687	+	73.9474i	−0.316123	+	0.153100i
$484$	−828.999	−	602.303i	−1.71281	−	1.24443i
$485$	171.842	−	169.063i	0.354313	−	0.348583i
$486$	−223.534	+	846.406i	−0.459947	+	1.74158i
$487$	−470.715	+	647.883i	−0.966560	+	1.33036i	−0.0227947	+	0.999740i	$0.507256\pi$
$487$	−470.715	+	647.883i	−0.966560	+	1.33036i	−0.943765	+	0.330616i	$0.892744\pi$
$488$	56.2375	+	40.8590i	0.115241	+	0.0837274i
$489$	449.808	+	468.380i	0.919852	+	0.957832i
$490$	116.346	+	775.434i	0.237441	+	1.58252i
$491$	−29.2083	+	40.2018i	−0.0594874	+	0.0818773i	−0.837724	−	0.546094i	$-0.816114\pi$
$491$	−29.2083	+	40.2018i	−0.0594874	+	0.0818773i	0.778237	+	0.627971i	$0.216114\pi$
$492$	477.084	−	231.055i	0.969683	−	0.469624i
$493$			49.8829i			0.101182i
$494$	906.603	−	294.573i	1.83523	−	0.596302i
$495$	115.485	+	24.0936i	0.233302	+	0.0486739i
$496$	−122.751	+	377.790i	−0.247482	+	0.761673i
$497$	−232.398	+	715.246i	−0.467601	+	1.43913i
$498$	874.660	−	839.977i	1.75634	−	1.68670i
$499$	197.958			0.396709			0.198354	−	0.980130i	$-0.436440\pi$
$499$	197.958			0.396709			0.198354	+	0.980130i	$0.436440\pi$
$500$	202.620	−	1103.88i	0.405240	−	2.20776i
$501$	501.798	−	69.1055i	1.00159	−	0.137935i
$502$	687.885	+	946.792i	1.37029	+	1.88604i
$503$	108.467	−	333.826i	0.215640	−	0.663671i	−0.783468	−	0.621432i	$-0.786551\pi$
$503$	108.467	−	333.826i	0.215640	−	0.663671i	0.999108	−	0.0422385i	$-0.0134489\pi$
$504$	1551.49	+	62.7907i	3.07834	+	0.124585i
$505$	−90.6204	−	47.1077i	−0.179446	−	0.0932825i
$506$	52.8052	−	17.1575i	0.104358	−	0.0339080i
$507$	−572.575	+	78.8526i	−1.12934	+	0.155528i
$508$	11.0418	−	3.58770i	0.0217358	−	0.00706240i
$509$	−314.518	+	432.897i	−0.617913	+	0.850485i	−0.997199	−	0.0747949i	$-0.976170\pi$
$509$	−314.518	+	432.897i	−0.617913	+	0.850485i	0.379286	+	0.925280i	$0.376170\pi$
$510$	−30.6747	−	104.397i	−0.0601465	−	0.204700i
$511$	−644.881	+	468.534i	−1.26200	+	0.916896i
$512$	930.854	+	676.305i	1.81807	+	1.32091i
$513$	−366.803	−	81.1594i	−0.715015	−	0.158205i
$514$	−31.1712	+	22.6472i	−0.0606444	+	0.0440608i
$515$	−487.433	+	479.551i	−0.946472	+	0.931168i
$516$	−161.914	+	302.491i	−0.313788	+	0.586224i
$517$	−39.2366	+	12.7487i	−0.0758927	+	0.0246590i
$518$	−2010.57			−3.88142
$519$	−60.0378	−	123.967i	−0.115680	−	0.238856i
$520$	1215.72	−	1196.06i	2.33792	−	2.30012i
$521$	585.168	+	190.133i	1.12316	+	0.364938i	0.810974	−	0.585082i	$-0.198938\pi$
$521$	585.168	+	190.133i	1.12316	+	0.364938i	0.312189	+	0.950020i	$0.398938\pi$
$522$	802.576	+	32.4813i	1.53750	+	0.0622248i
$523$	−1.70712	−	2.34966i	−0.00326410	−	0.00449265i	0.807382	−	0.590029i	$-0.200884\pi$
$523$	−1.70712	−	2.34966i	−0.00326410	−	0.00449265i	−0.810646	+	0.585537i	$0.800884\pi$
$524$		−	1599.70i		−	3.05287i
$525$	−303.837	−	654.346i	−0.578737	−	1.24637i
$526$	983.861			1.87046
$527$	22.5465	−	16.3810i	0.0427828	−	0.0310835i
$528$	−222.183	−	39.8120i	−0.420801	−	0.0754015i
$529$	−152.790	+	470.239i	−0.288828	+	0.888921i
$530$	−902.870	−	150.554i	−1.70353	−	0.284064i
$531$	418.468	−	278.898i	0.788075	−	0.525231i
$532$			1201.70i			2.25884i
$533$	−115.652	−	355.941i	−0.216984	−	0.667807i
$534$	−136.548	+	255.102i	−0.255708	+	0.477719i
$535$	301.262	−	579.533i	0.563106	−	1.08324i
$536$	−666.434	−	917.268i	−1.24335	−	1.71132i
$537$	−94.4749	+	176.500i	−0.175931	+	0.328677i
$538$	692.029	−	952.496i	1.28630	−	1.77044i
$539$	−67.0777	−	92.3245i	−0.124448	−	0.171289i
$540$	−1175.81	+	294.398i	−2.17743	+	0.545181i
$541$	684.816	+	497.548i	1.26583	+	0.919682i	0.999029	−	0.0440682i	$-0.0140319\pi$
$541$	684.816	+	497.548i	1.26583	+	0.919682i	0.266805	+	0.963750i	$0.414032\pi$
$542$	−111.505	−	343.178i	−0.205729	−	0.633170i
$543$	−264.005	+	36.3577i	−0.486197	+	0.0669571i
$544$	19.6951	+	60.6154i	0.0362043	+	0.111425i
$545$	−743.433	+	371.197i	−1.36410	+	0.681095i
$546$	348.714	−	1946.10i	0.638670	−	3.56429i
$547$	−265.366	−	86.2225i	−0.485129	−	0.157628i	0.0562327	−	0.998418i	$-0.482091\pi$
$547$	−265.366	−	86.2225i	−0.485129	−	0.157628i	−0.541362	+	0.840790i	$0.682091\pi$
$548$	74.5959	−	54.1971i	0.136124	−	0.0988998i
$549$	−33.5829	+	9.42861i	−0.0611710	+	0.0171742i
$550$	69.2923	+	225.715i	0.125986	+	0.410391i
$551$			344.694i			0.625578i
$552$	−228.153	+	219.106i	−0.413320	+	0.396931i
$553$	−955.858	−	310.577i	−1.72850	−	0.561622i
$554$	842.921	+	273.882i	1.52152	+	0.494371i
$555$	834.975	−	245.338i	1.50446	−	0.442051i
$556$	5.92962	+	18.2495i	0.0106648	+	0.0328228i
$557$	415.319			0.745635			0.372818	−	0.927905i	$-0.378392\pi$
$557$	415.319			0.745635			0.372818	+	0.927905i	$0.378392\pi$
$558$	−248.876	−	373.422i	−0.446015	−	0.669215i
$559$	195.975	+	142.384i	0.350581	+	0.254712i
$560$	616.637	+	1235.00i	1.10114	+	2.20536i
$561$	10.9691	+	11.4220i	0.0195528	+	0.0203602i
$562$	1097.47	−	1510.53i	1.95279	−	2.68778i
$563$	758.639	+	551.183i	1.34749	+	0.979011i	0.999132	+	0.0416505i	$0.0132616\pi$
$563$	758.639	+	551.183i	1.34749	+	0.979011i	0.348361	+	0.937361i	$0.386738\pi$
$564$	305.733	−	293.610i	0.542080	−	0.520585i
$565$	−927.182	+	462.943i	−1.64103	+	0.819368i
$566$	763.037	−	1050.23i	1.34812	−	1.85553i
$567$	−507.422	+	591.285i	−0.894923	+	1.04283i
$568$			1402.25i			2.46874i
$569$	−517.157	+	168.035i	−0.908888	+	0.295316i	−0.725901	−	0.687800i	$-0.758577\pi$
$569$	−517.157	+	168.035i	−0.908888	+	0.295316i	−0.182988	+	0.983115i	$0.558577\pi$
$570$	−211.964	−	721.390i	−0.371867	−	1.26560i
$571$	−96.1700	+	295.981i	−0.168424	+	0.518355i	−0.999272	−	0.0381437i	$-0.987856\pi$
$571$	−96.1700	+	295.981i	−0.168424	+	0.518355i	0.830849	+	0.556499i	$0.187856\pi$
$572$	−138.326	+	425.723i	−0.241828	+	0.744271i
$573$	549.071	+	571.742i	0.958239	+	0.997805i
$574$	681.990			1.18814
$575$	139.019	+	47.6892i	0.241773	+	0.0829377i
$576$	−6.67425	+	1.87384i	−0.0115872	+	0.00325319i
$577$	−222.653	−	306.455i	−0.385880	−	0.531118i	0.571250	−	0.820776i	$-0.306459\pi$
$577$	−222.653	−	306.455i	−0.385880	−	0.531118i	−0.957130	+	0.289658i	$0.906459\pi$
$578$	−317.218	+	976.296i	−0.548820	+	1.68909i
$579$	−643.286	−	115.268i	−1.11103	−	0.199081i
$580$	496.811	+	995.014i	0.856571	+	1.71554i
$581$	1026.50	−	333.531i	1.76679	−	0.574064i
$582$	−71.0888	−	516.199i	−0.122146	−	0.886939i
$583$	126.697	−	41.1664i	0.217319	−	0.0706114i
$584$	−873.606	+	1202.42i	−1.49590	+	2.05893i
$585$	92.6528	+	850.750i	0.158381	+	1.45427i
$586$	−751.572	+	546.049i	−1.28255	+	0.931824i
$587$	−747.086	−	542.790i	−1.27272	−	0.924684i	−0.273411	−	0.961897i	$-0.588152\pi$
$587$	−747.086	−	542.790i	−1.27272	−	0.924684i	−0.999307	+	0.0372128i	$0.988152\pi$
$588$	1033.75	+	553.337i	1.75808	+	0.941048i
$589$	155.798	−	113.194i	0.264512	−	0.192179i
$590$	893.046	+	464.237i	1.51364	+	0.786842i
$591$	−913.949	−	489.209i	−1.54644	−	0.827765i
$592$	−1583.65	+	514.558i	−2.67508	+	0.869185i
$593$	758.601			1.27926			0.639630	−	0.768683i	$-0.279088\pi$
$593$	758.601			1.27926			0.639630	+	0.768683i	$0.279088\pi$
$594$	190.914	−	169.047i	0.321405	−	0.284591i
$595$	15.9291	−	95.5264i	0.0267716	−	0.160549i
$596$	−756.810	−	245.903i	−1.26982	−	0.412588i
$597$	63.7641	−	355.854i	0.106807	−	0.596071i
$598$	236.742	+	325.848i	0.395890	+	0.544896i
$599$			8.98283i			0.0149964i	0.999972	+	0.00749819i	$0.00238677\pi$
$599$			8.98283i			0.0149964i	−0.999972	+	0.00749819i	$0.997613\pi$
$600$	−915.813	−	985.284i	−1.52635	−	1.64214i
$601$	−112.394			−0.187012			−0.0935062	−	0.995619i	$-0.529807\pi$
$601$	−112.394			−0.187012			−0.0935062	+	0.995619i	$0.529807\pi$
$602$	−357.113	+	259.458i	−0.593211	+	0.430993i
$603$	568.471	+	23.0068i	0.942738	+	0.0381538i
$604$	106.053	−	326.397i	0.175584	−	0.540393i
$605$	400.199	+	406.776i	0.661485	+	0.672358i
$606$	−198.690	+	96.2270i	−0.327872	+	0.158790i
$607$		−	465.006i		−	0.766073i	−0.923733	−	0.383037i	$-0.874878\pi$
$607$		−	465.006i		−	0.766073i	0.923733	−	0.383037i	$-0.125122\pi$
$608$	136.094	+	418.856i	0.223840	+	0.688908i
$609$	630.294	+	337.377i	1.03496	+	0.553985i
$610$	−48.9610	−	49.7657i	−0.0802640	−	0.0815832i
$611$	−175.910	−	242.119i	−0.287904	−	0.396266i
$612$	−152.587	−	56.4968i	−0.249325	−	0.0923151i
$613$	642.929	−	884.916i	1.04882	−	1.44358i	0.158999	−	0.987279i	$-0.449173\pi$
$613$	642.929	−	884.916i	1.04882	−	1.44358i	0.889825	−	0.456303i	$-0.150827\pi$
$614$	−930.303	−	1280.45i	−1.51515	−	2.08543i
$615$	−283.225	+	83.2191i	−0.460528	+	0.135316i
$616$	−365.917	−	265.854i	−0.594020	−	0.431581i
$617$	184.628	+	568.228i	0.299236	+	0.920953i	0.981766	+	0.190095i	$0.0608797\pi$
$617$	184.628	+	568.228i	0.299236	+	0.920953i	−0.682530	+	0.730858i	$0.739120\pi$
$618$	201.645	+	1464.21i	0.326287	+	2.36927i
$619$	−130.565	−	401.836i	−0.210928	−	0.649170i	−0.999418	−	0.0341221i	$-0.989136\pi$
$619$	−130.565	−	401.836i	−0.210928	−	0.649170i	0.788489	−	0.615048i	$-0.210864\pi$
$620$	286.588	−	551.305i	0.462238	−	0.889202i
$621$	−15.2787	−	157.992i	−0.0246034	−	0.254416i
$622$	−1104.95	−	359.021i	−1.77645	−	0.577204i
$623$	−208.347	+	151.373i	−0.334425	+	0.242974i
$624$	−223.390	−	1622.11i	−0.357996	−	2.59953i
$625$	−212.409	+	587.799i	−0.339855	+	0.940478i
$626$			1836.40i			2.93354i
$627$	75.7973	+	78.9270i	0.120889	+	0.125880i
$628$	−205.298	−	66.7054i	−0.326908	−	0.106219i
$629$	111.106	+	36.1004i	0.176639	+	0.0573933i
$630$	−1526.57	−	318.489i	−2.42313	−	0.505537i
$631$	−83.0085	−	255.474i	−0.131551	−	0.404871i	0.863487	−	0.504371i	$-0.168276\pi$
$631$	−83.0085	−	255.474i	−0.131551	−	0.404871i	−0.995038	+	0.0994999i	$0.968276\pi$
$632$	−1873.97			−2.96514
$633$	−14.5273	−	29.9961i	−0.0229499	−	0.0473872i
$634$	1039.78	+	755.441i	1.64002	+	1.19155i
$635$	−6.39385	+	0.959332i	−0.0100691	+	0.00151076i
$636$	−987.231	+	948.084i	−1.55225	+	1.49070i
$637$	486.591	−	669.736i	0.763880	−	1.05139i
$638$	−189.287	−	137.525i	−0.296688	−	0.215556i
$639$	−552.064	−	436.269i	−0.863950	−	0.682737i
$640$	−453.704	−	461.161i	−0.708912	−	0.720564i
$641$	−82.4863	+	113.533i	−0.128684	+	0.177118i	−0.868497	−	0.495694i	$-0.834914\pi$
$641$	−82.4863	+	113.533i	−0.128684	+	0.177118i	0.739813	+	0.672812i	$0.234914\pi$
$642$	−615.388	−	1270.66i	−0.958549	−	1.97922i
$643$		−	541.595i		−	0.842293i	−0.906993	−	0.421147i	$-0.861628\pi$
$643$		−	541.595i		−	0.842293i	0.906993	−	0.421147i	$-0.138372\pi$
$644$	−482.892	+	156.901i	−0.749832	+	0.243635i
$645$	116.646	−	151.327i	0.180847	−	0.234616i
$646$	31.1895	−	95.9915i	0.0482810	−	0.148594i
$647$	219.433	−	675.344i	0.339154	−	1.04381i	−0.625485	−	0.780236i	$-0.715099\pi$
$647$	219.433	−	675.344i	0.339154	−	1.04381i	0.964639	−	0.263573i	$-0.0849010\pi$
$648$	−559.123	+	1340.89i	−0.862844	+	2.06927i
$649$	−146.486			−0.225710
$650$	−1401.90	+	984.030i	−2.15677	+	1.51389i
$651$	−54.4909	−	395.677i	−0.0837034	−	0.607798i
$652$	1142.38	+	1572.35i	1.75211	+	2.41158i
$653$	206.777	−	636.394i	0.316657	−	0.974570i	−0.658410	−	0.752660i	$-0.728771\pi$
$653$	206.777	−	636.394i	0.316657	−	0.974570i	0.975067	−	0.221911i	$-0.0712294\pi$
$654$	−316.797	+	1767.98i	−0.484400	+	2.70334i
$655$	−146.526	+	878.714i	−0.223704	+	1.34155i
$656$	537.175	−	174.539i	0.818864	−	0.266065i
$657$	−201.593	−	718.036i	−0.306839	−	1.09290i
$658$	518.661	−	168.523i	0.788238	−	0.256114i
$659$	−149.113	+	205.236i	−0.226271	+	0.311436i	−0.907025	−	0.421076i	$-0.861652\pi$
$659$	−149.113	+	205.236i	−0.226271	+	0.311436i	0.680754	+	0.732512i	$0.261652\pi$
$660$	332.560	+	118.588i	0.503878	+	0.179679i
$661$	378.243	−	274.810i	0.572228	−	0.415748i	−0.263686	−	0.964609i	$-0.584938\pi$
$661$	378.243	−	274.810i	0.572228	−	0.415748i	0.835914	+	0.548860i	$0.184938\pi$
$662$	737.262	+	535.652i	1.11369	+	0.809142i
$663$	−54.2129	+	101.281i	−0.0817691	+	0.152762i
$664$	1628.12	−	1182.90i	2.45199	−	1.78147i
$665$	110.071	−	660.093i	0.165520	−	0.992620i
$666$	653.174	−	1764.09i	0.980741	−	2.64879i
$667$	−138.511	+	45.0051i	−0.207663	+	0.0674739i
$668$	1515.98			2.26943
$669$	1161.59	−	562.568i	1.73632	−	0.840909i
$670$	508.667	+	1018.76i	0.759204	+	1.52053i
$671$	9.66320	+	3.13976i	0.0144012	+	0.00467923i
$672$	899.109	+	161.108i	1.33796	+	0.239744i
$673$	−467.186	−	643.026i	−0.694184	−	0.955462i	−0.999994	−	0.00336953i	$-0.998927\pi$
$673$	−467.186	−	643.026i	−0.694184	−	0.955462i	0.305811	−	0.952092i	$-0.401073\pi$
$674$			771.808i			1.14512i
$675$	672.836	−	54.0125i	0.996793	−	0.0800186i
$676$	−1729.81			−2.55889
$677$	−1011.31	+	734.760i	−1.49381	+	1.08532i	−0.521045	+	0.853529i	$0.674458\pi$
$677$	−1011.31	+	734.760i	−1.49381	+	1.08532i	−0.972766	+	0.231789i	$0.925542\pi$
$678$	−395.098	+	2204.96i	−0.582740	+	3.25215i
$679$	143.314	−	441.074i	0.211066	−	0.649593i
$680$	−26.7933	−	178.574i	−0.0394019	−	0.262610i
$681$	−161.148	−	332.739i	−0.236634	−	0.488603i
$682$			130.717i			0.191668i
$683$	129.140	+	397.451i	0.189077	+	0.581920i	0.999995	−	0.00324052i	$-0.00103149\pi$
$683$	129.140	+	397.451i	0.189077	+	0.581920i	−0.810917	+	0.585161i	$0.801031\pi$
$684$	−1054.38	−	390.396i	−1.54150	−	0.570755i
$685$	−45.9395	+	22.9377i	−0.0670650	+	0.0334856i
$686$	−111.405	−	153.336i	−0.162399	−	0.223522i
$687$	718.395	+	384.535i	1.04570	+	0.559731i
$688$	−214.881	+	295.759i	−0.312327	+	0.429882i
$689$	568.023	+	781.816i	0.824416	+	1.13471i
$690$	262.208	−	179.364i	0.380011	−	0.259948i
$691$	−223.108	−	162.097i	−0.322877	−	0.234584i	0.414525	−	0.910038i	$-0.363948\pi$
$691$	−223.108	−	162.097i	−0.322877	−	0.234584i	−0.737402	+	0.675454i	$0.763948\pi$
$692$	−127.388	−	392.059i	−0.184086	−	0.566559i
$693$	218.511	−	61.3485i	0.315312	−	0.0885259i
$694$	−19.4867	−	59.9739i	−0.0280788	−	0.0864177i
$695$	−1.58555	−	10.5675i	−0.00228137	−	0.0152051i
$696$	1312.09	+	235.107i	1.88518	+	0.337798i
$697$	−37.6872	−	12.2453i	−0.0540706	−	0.0175686i
$698$	1453.73	−	1056.20i	2.08271	−	1.51318i
$699$	874.757	−	120.468i	1.25144	−	0.172343i
$700$	−633.662	−	2064.11i	−0.905232	−	2.94873i
$701$		−	817.743i		−	1.16654i	−0.812279	−	0.583269i	$-0.801773\pi$
$701$		−	817.743i		−	1.16654i	0.812279	−	0.583269i	$-0.198227\pi$
$702$	1594.24	+	938.192i	2.27099	+	1.33646i
$703$	767.746	+	249.456i	1.09210	+	0.354845i
$704$	1.92046	+	0.623995i	0.00272793	+	0.000886357i
$705$	−194.832	+	133.275i	−0.276357	+	0.189043i
$706$	416.252	+	1281.09i	0.589592	+	1.81458i
$707$	−196.490			−0.277920
$708$	1354.58	−	656.032i	1.91325	−	0.926599i
$709$	−530.616	−	385.515i	−0.748401	−	0.543745i	0.146930	−	0.989147i	$-0.453061\pi$
$709$	−530.616	−	385.515i	−0.748401	−	0.543745i	−0.895331	+	0.445402i	$0.853061\pi$
$710$	231.634	−	1389.10i	0.326245	−	1.95648i
$711$	583.032	−	737.781i	0.820017	−	1.03767i
$712$	−282.243	+	388.474i	−0.396408	+	0.545609i
$713$	65.8274	+	47.8264i	0.0923246	+	0.0670777i
$714$	−144.999	−	150.986i	−0.203080	−	0.211465i
$715$	114.976	−	221.178i	0.160806	−	0.309340i
$716$	−352.173	+	484.724i	−0.491861	+	0.676989i
$717$	126.938	−	61.4771i	0.177041	−	0.0857421i
$718$		−	302.850i		−	0.421796i
$719$	−810.675	+	263.404i	−1.12750	+	0.366348i	−0.812627	−	0.582785i	$-0.801963\pi$
$719$	−810.675	+	263.404i	−1.12750	+	0.366348i	−0.314877	+	0.949133i	$0.601963\pi$
$720$	−1283.93	+	139.829i	−1.78323	+	0.194207i
$721$	−406.513	+	1251.12i	−0.563818	+	1.73525i
$722$	−186.365	+	573.571i	−0.258123	+	0.794420i
$723$	−221.429	+	212.649i	−0.306265	+	0.294121i
$724$	−797.587			−1.10164
$725$	−181.758	−	592.064i	−0.250701	−	0.816641i
$726$	1221.92	−	168.278i	1.68309	−	0.231788i
$727$	791.959	+	1090.04i	1.08935	+	1.49937i	0.848789	+	0.528732i	$0.177332\pi$
$727$	791.959	+	1090.04i	1.08935	+	1.49937i	0.240564	+	0.970633i	$0.422668\pi$
$728$	1013.90	−	3120.45i	1.39271	−	4.28633i
$729$	−353.952	−	637.306i	−0.485531	−	0.874219i
$730$	1064.04	−	1046.84i	1.45759	−	1.43402i
$731$	24.3929	−	7.92575i	0.0333693	−	0.0108423i
$732$	−103.419	+	14.2424i	−0.141282	+	0.0194568i
$733$	62.6609	−	20.3598i	0.0854855	−	0.0277759i	−0.265962	−	0.963984i	$-0.585690\pi$
$733$	62.6609	−	20.3598i	0.0854855	−	0.0277759i	0.351448	+	0.936208i	$0.385690\pi$
$734$	472.075	−	649.755i	0.643154	−	0.885225i
$735$	−517.155	−	398.634i	−0.703612	−	0.542359i
$736$	−150.543	+	109.376i	−0.204543	+	0.148609i
$737$	−134.073	−	97.4100i	−0.181918	−	0.132171i
$738$	−221.557	+	598.384i	−0.300213	+	0.810818i
$739$	−107.932	+	78.4173i	−0.146052	+	0.106113i	−0.658412	−	0.752658i	$-0.728771\pi$
$739$	−107.932	+	78.4173i	−0.146052	+	0.106113i	0.512360	+	0.858771i	$0.328771\pi$
$740$	2575.77	−	386.468i	3.48077	−	0.522254i
$741$	−374.614	+	699.861i	−0.505552	+	0.944481i
$742$	−1674.79	+	544.172i	−2.25713	+	0.733385i
$743$	−1069.77			−1.43980			−0.719899	−	0.694079i	$-0.755812\pi$
$743$	−1069.77			−1.43980			−0.719899	+	0.694079i	$0.755812\pi$
$744$	−324.609	−	670.255i	−0.436302	−	0.900880i
$745$	393.190	+	204.394i	0.527772	+	0.274355i
$746$	466.072	+	151.436i	0.624762	+	0.202997i
$747$	−40.8362	+	1009.02i	−0.0546670	+	1.35076i
$748$	27.8583	+	38.3437i	0.0372438	+	0.0512617i
$749$		−	1256.59i		−	1.67768i
$750$	744.472	+	1127.33i	0.992630	+	1.50311i
$751$	6.50034			0.00865559			0.00432779	−	0.999991i	$-0.498622\pi$
$751$	6.50034			0.00865559			0.00432779	+	0.999991i	$0.498622\pi$
$752$	365.398	−	265.477i	0.485902	−	0.353028i
$753$	−959.274	−	171.888i	−1.27394	−	0.228271i
$754$	524.483	−	1614.19i	0.695601	−	2.14084i
$755$	−88.1512	+	169.575i	−0.116757	+	0.224603i
$756$	−1745.87	+	1545.90i	−2.30935	+	2.04484i
$757$		−	156.229i		−	0.206380i	−0.994662	−	0.103190i	$-0.967095\pi$
$757$		−	156.229i		−	0.206380i	0.994662	−	0.103190i	$-0.0329049\pi$
$758$	525.987	+	1618.82i	0.693915	+	2.13565i
$759$	−21.8194	+	40.7635i	−0.0287476	+	0.0537068i
$760$	−185.143	−	1233.96i	−0.243609	−	1.62363i
$761$	−609.523	−	838.937i	−0.800950	−	1.10241i	−0.992657	−	0.120961i	$-0.961402\pi$
$761$	−609.523	−	838.937i	−0.800950	−	1.10241i	0.191707	−	0.981452i	$-0.438598\pi$
$762$	−6.59518	+	12.3212i	−0.00865509	+	0.0161696i
$763$	−939.652	+	1293.32i	−1.23152	+	1.69505i
$764$	1394.48	+	1919.33i	1.82523	+	2.51222i
$765$	78.6408	+	45.0099i	0.102798	+	0.0588364i
$766$	−474.957	−	345.076i	−0.620048	−	0.450491i
$767$	−328.370	−	1010.62i	−0.428123	−	1.31763i
$768$	−1376.13	+	189.516i	−1.79184	+	0.246765i
$769$	−98.3002	−	302.537i	−0.127829	−	0.393416i	0.866577	−	0.499043i	$-0.166315\pi$
$769$	−98.3002	−	302.537i	−0.127829	−	0.393416i	−0.994406	+	0.105627i	$0.966315\pi$
$770$	318.571	+	323.807i	0.413729	+	0.420529i
$771$	5.65908	−	31.5822i	0.00733992	−	0.0409626i
$772$	−1860.19	−	604.414i	−2.40958	−	0.782920i
$773$	−511.311	+	371.489i	−0.661464	+	0.480581i	−0.867157	−	0.498035i	$-0.834055\pi$
$773$	−511.311	+	371.489i	−0.661464	+	0.480581i	0.205693	+	0.978617i	$0.434055\pi$
$774$	−111.635	−	397.624i	−0.144232	−	0.513726i
$775$	−207.919	+	276.580i	−0.268283	+	0.356878i
$776$		−	864.729i		−	1.11434i
$777$	1207.59	−	1159.71i	1.55418	−	1.49255i
$778$	−206.169	−	66.9882i	−0.264998	−	0.0861031i
$779$	−260.421	−	84.6158i	−0.334301	−	0.108621i
$780$	−72.6661	+	2560.20i	−0.0931617	+	3.28230i
$781$	63.3363	+	194.929i	0.0810964	+	0.249589i
$782$	42.6454			0.0545338
$783$	−500.780	+	443.421i	−0.639566	+	0.566311i
$784$	1010.74	+	734.349i	1.28921	+	0.936669i
$785$	106.660	+	55.4455i	0.135872	+	0.0706312i
$786$	1333.79	+	1388.87i	1.69694	+	1.76701i
$787$	−289.858	+	398.956i	−0.368308	+	0.506933i	−0.952440	−	0.304726i	$-0.901435\pi$
$787$	−289.858	+	398.956i	−0.368308	+	0.506933i	0.584132	+	0.811659i	$0.301435\pi$
$788$	−2509.99	−	1823.62i	−3.18527	−	2.31423i
$789$	−590.928	+	567.497i	−0.748959	+	0.719261i
$790$	1856.40	+	309.556i	2.34988	+	0.391843i
$791$	−1171.90	+	1612.98i	−1.48154	+	2.03917i
$792$	352.137	−	234.690i	0.444618	−	0.296326i
$793$			73.7057i			0.0929454i
$794$	−1713.83	+	556.856i	−2.15847	+	0.701330i
$795$	629.124	−	430.354i	0.791350	−	0.541326i
$796$	334.351	−	1029.03i	0.420039	−	1.29275i
$797$	358.323	−	1102.81i	0.449590	−	1.38370i	−0.427781	−	0.903883i	$-0.640704\pi$
$797$	358.323	−	1102.81i	0.449590	−	1.38370i	0.877371	−	0.479813i	$-0.159296\pi$
$798$	−1001.95	−	1043.32i	−1.25558	−	1.30742i
$799$	−31.6874			−0.0396588
$800$	−454.627	−	647.686i	−0.568284	−	0.809608i
$801$	−65.1303	−	231.982i	−0.0813113	−	0.289615i
$802$	−782.599	−	1077.16i	−0.975810	−	1.34309i
$803$	−67.1314	+	206.609i	−0.0836007	+	0.257296i
$804$	1676.05	+	300.324i	2.08464	+	0.373538i
$805$	279.623	−	41.9545i	0.347357	−	0.0521174i
$806$	−901.832	+	293.023i	−1.11890	+	0.363552i
$807$	133.757	+	971.256i	0.165746	+	1.20354i
$808$	−348.434	+	113.213i	−0.431231	+	0.140115i
$809$	563.323	−	775.348i	0.696320	−	0.958402i	−0.303664	−	0.952779i	$-0.598210\pi$
$809$	563.323	−	775.348i	0.696320	−	0.958402i	0.999984	−	0.00562325i	$-0.00178995\pi$
$810$	775.380	−	1235.96i	0.957260	−	1.52588i
$811$	189.458	−	137.649i	0.233610	−	0.169727i	−0.464822	−	0.885404i	$-0.653882\pi$
$811$	189.458	−	137.649i	0.233610	−	0.169727i	0.698432	+	0.715677i	$0.253882\pi$
$812$	1730.99	+	1257.63i	2.13176	+	1.54881i
$813$	264.919	+	141.803i	0.325854	+	0.174420i
$814$	−443.301	+	322.077i	−0.544596	+	0.395672i
$815$	−483.485	−	968.323i	−0.593233	−	1.18813i
$816$	−152.851	−	81.8164i	−0.187317	−	0.100265i
$817$	168.557	−	54.7674i	0.206312	−	0.0670347i
$818$	982.950			1.20165
$819$	913.076	+	1370.01i	1.11487	+	1.67278i
$820$	−873.704	+	131.090i	−1.06549	+	0.159866i
$821$	532.681	+	173.079i	0.648820	+	0.210814i	0.614894	−	0.788610i	$-0.289199\pi$
$821$	532.681	+	173.079i	0.648820	+	0.210814i	0.0339260	+	0.999424i	$0.489199\pi$
$822$	−19.5761	+	109.250i	−0.0238152	+	0.132908i
$823$	−534.506	−	735.685i	−0.649461	−	0.893906i	0.349615	−	0.936894i	$-0.386312\pi$
$823$	−534.506	−	735.685i	−0.649461	−	0.893906i	−0.999076	+	0.0429873i	$0.986312\pi$
$824$			2452.83i			2.97673i
$825$	−171.812	−	95.6011i	−0.208257	−	0.115880i
$826$	1936.37			2.34427
$827$	687.080	−	499.193i	0.830810	−	0.603619i	−0.0889782	−	0.996034i	$-0.528360\pi$
$827$	687.080	−	499.193i	0.830810	−	0.603619i	0.919788	+	0.392415i	$0.128360\pi$
$828$	19.2103	−	474.665i	0.0232009	−	0.573267i
$829$	−270.730	+	833.223i	−0.326575	+	1.00509i	0.644150	+	0.764899i	$0.277211\pi$
$829$	−270.730	+	833.223i	−0.326575	+	1.00509i	−0.970725	+	0.240194i	$0.922789\pi$
$830$	−1808.26	+	902.866i	−2.17863	+	1.08779i
$831$	−664.253	+	321.702i	−0.799342	+	0.387126i
$832$			14.6482i			0.0176060i
$833$	−27.0859	−	83.3620i	−0.0325161	−	0.100074i
$834$	−20.3641	−	10.9003i	−0.0244174	−	0.0130699i
$835$	−832.725	−	138.857i	−0.997275	−	0.166296i
$836$	192.503	+	264.957i	0.230266	+	0.316935i
$837$	364.872	+	80.7323i	0.435929	+	0.0964543i
$838$	−120.743	+	166.188i	−0.144084	+	0.198315i
$839$	−130.501	−	179.620i	−0.155544	−	0.214088i	0.724132	−	0.689661i	$-0.242241\pi$
$839$	−130.501	−	179.620i	−0.155544	−	0.214088i	−0.879676	+	0.475573i	$0.842241\pi$
$840$	−2437.58	−	869.221i	−2.90189	−	1.03479i
$841$	−183.872	−	133.591i	−0.218635	−	0.158847i
$842$	401.299	+	1235.07i	0.476603	+	1.46683i
$843$	212.121	+	1540.28i	0.251627	+	1.82714i
$844$	−30.8239	−	94.8663i	−0.0365212	−	0.112401i
$845$	950.178	+	158.443i	1.12447	+	0.187506i
$846$	−20.6333	+	509.825i	−0.0243892	+	0.602630i
$847$	1044.09	+	339.246i	1.23269	+	0.400527i
$848$	−1179.89	+	857.242i	−1.39138	+	1.01090i
$849$	147.482	+	1070.92i	0.173713	+	1.26138i
$850$	−2.95617	+	181.327i	−0.00347785	+	0.213325i
$851$			341.081i			0.400800i
$852$	−1458.67	−	1518.90i	−1.71205	−	1.78274i
$853$	922.928	+	299.877i	1.08198	+	0.351556i	0.795142	−	0.606423i	$-0.207396\pi$
$853$	922.928	+	299.877i	1.08198	+	0.351556i	0.286837	+	0.957980i	$0.407396\pi$
$854$	−127.736	−	41.5040i	−0.149574	−	0.0485995i
$855$	543.412	+	311.021i	0.635570	+	0.363767i
$856$	−724.017	−	2228.30i	−0.845815	−	2.60315i
$857$	856.183			0.999046			0.499523	−	0.866300i	$-0.333509\pi$
$857$	856.183			0.999046			0.499523	+	0.866300i	$0.333509\pi$
$858$	−234.863	−	484.946i	−0.273733	−	0.565205i
$859$	−688.166	−	499.982i	−0.801125	−	0.582051i	0.110119	−	0.993918i	$-0.464877\pi$
$859$	−688.166	−	499.982i	−0.801125	−	0.582051i	−0.911244	+	0.411867i	$0.864877\pi$
$860$	407.629	−	401.038i	0.473987	−	0.466323i
$861$	−409.618	+	393.376i	−0.475747	+	0.456882i
$862$	527.228	−	725.667i	0.611633	−	0.841841i
$863$	−1204.33	−	874.998i	−1.39552	−	1.01390i	−0.995234	−	0.0975119i	$-0.968912\pi$
$863$	−1204.33	−	874.998i	−1.39552	−	1.01390i	−0.400284	−	0.916391i	$-0.631088\pi$
$864$	−433.450	+	736.547i	−0.501678	+	0.852485i
$865$	34.0628	+	227.025i	0.0393789	+	0.262457i
$866$	781.379	−	1075.48i	0.902286	−	1.24189i
$867$	−372.605	−	769.358i	−0.429764	−	0.887379i
$868$		−	1195.38i		−	1.37717i
$869$	−260.504	+	84.6429i	−0.299774	+	0.0974026i
$870$	−1260.95	−	449.644i	−1.44937	−	0.516832i
$871$	371.495	−	1143.35i	0.426516	−	1.31268i
$872$	−921.098	+	2834.85i	−1.05630	+	3.25097i
$873$	340.444	+	269.036i	0.389970	+	0.308174i
$874$	294.682			0.337165
$875$	159.005	+	1191.85i	0.181720	+	1.36212i
$876$	−304.517	−	2211.20i	−0.347622	−	2.52420i
$877$	269.400	+	370.798i	0.307184	+	0.422802i	0.934500	−	0.355962i	$-0.115847\pi$
$877$	269.400	+	370.798i	0.307184	+	0.422802i	−0.627317	+	0.778764i	$0.715847\pi$
$878$	115.414	−	355.208i	0.131451	−	0.404565i
$879$	136.446	−	761.480i	0.155229	−	0.866302i
$880$	333.796	+	173.519i	0.379313	+	0.197180i
$881$	−107.500	+	34.9287i	−0.122020	+	0.0396467i	−0.369390	−	0.929274i	$-0.620433\pi$
$881$	−107.500	+	34.9287i	−0.122020	+	0.0396467i	0.247371	+	0.968921i	$0.420433\pi$
$882$	−1358.86	+	381.510i	−1.54066	+	0.432551i
$883$	1390.39	−	451.764i	1.57462	−	0.511624i	0.613953	−	0.789342i	$-0.289578\pi$
$883$	1390.39	−	451.764i	1.57462	−	0.511624i	0.960663	+	0.277718i	$0.0895782\pi$
$884$	−202.088	+	278.151i	−0.228607	+	0.314650i
$885$	−804.157	+	236.283i	−0.908652	+	0.266986i
$886$	−1778.29	+	1292.00i	−2.00710	+	1.45824i
$887$	−3.82980	−	2.78251i	−0.00431770	−	0.00313699i	0.585624	−	0.810583i	$-0.300849\pi$
$887$	−3.82980	−	2.78251i	−0.00431770	−	0.00313699i	−0.589942	+	0.807446i	$0.700849\pi$
$888$	1473.22	−	2752.30i	1.65903	−	3.09944i
$889$	−10.0630	+	7.31120i	−0.0113195	+	0.00822407i
$890$	343.768	−	338.210i	0.386257	−	0.380011i
$891$	−17.1599	+	211.654i	−0.0192592	+	0.237546i
$892$	3673.68	−	1193.65i	4.11848	−	1.33817i
$893$	−218.962			−0.245198
$894$	862.092	−	417.517i	0.964308	−	0.467021i
$895$	237.846	−	234.000i	0.265750	−	0.261453i
$896$	−1183.68	−	384.602i	−1.32108	−	0.429243i
$897$	−330.143	−	59.1570i	−0.368052	−	0.0659498i
$898$	−35.7321	−	49.1811i	−0.0397908	−	0.0547673i
$899$		−	342.880i		−	0.381401i
$900$	2016.93	+	114.585i	2.24103	+	0.127317i
$901$	102.321			0.113563
$902$	150.368	−	109.249i	0.166705	−	0.121119i
$903$	64.8332	−	361.821i	0.0717976	−	0.400688i
$904$	−1148.76	+	3535.51i	−1.27075	+	3.91097i
$905$	438.112	+	73.0555i	0.484102	+	0.0807243i
$906$	180.067	+	371.803i	0.198749	+	0.410379i
$907$		−	1145.45i		−	1.26290i	−0.775416	−	0.631451i	$-0.782460\pi$
$907$		−	1145.45i		−	1.26290i	0.775416	−	0.631451i	$-0.217540\pi$
$908$	−341.922	−	1052.33i	−0.376566	−	1.15895i
$909$	63.8334	−	172.402i	0.0702238	−	0.189661i
$910$	−1519.85	+	2923.72i	−1.67017	+	3.21288i
$911$	−534.006	−	734.996i	−0.586176	−	0.806802i	0.408180	−	0.912902i	$-0.366164\pi$
$911$	−534.006	−	734.996i	−0.586176	−	0.806802i	−0.994355	+	0.106100i	$0.966164\pi$
$912$	−1056.21	−	565.356i	−1.15812	−	0.619908i
$913$	172.899	−	237.976i	0.189375	−	0.260652i
$914$	−10.1737	−	14.0029i	−0.0111309	−	0.0153204i
$915$	58.1122	+	1.64940i	0.0635106	+	0.00180262i
$916$	1972.94	+	1433.43i	2.15387	+	1.56487i
$917$	529.612	+	1629.98i	0.577549	+	1.77751i
$918$	179.582	−	78.1726i	0.195623	−	0.0851554i
$919$	342.604	+	1054.43i	0.372801	+	1.14736i	0.944950	+	0.327215i	$0.106110\pi$
$919$	342.604	+	1054.43i	0.372801	+	1.14736i	−0.572149	+	0.820150i	$0.693890\pi$
$920$	471.680	−	235.510i	0.512696	−	0.255989i
$921$	1297.33	+	232.464i	1.40861	+	0.252403i
$922$	648.826	+	210.816i	0.703716	+	0.228651i
$923$	−1202.86	+	873.927i	−1.30320	+	0.946833i
$924$	672.907	−	92.6700i	0.728255	−	0.100292i
$925$	−1450.26	−	23.6436i	−1.56785	−	0.0255607i
$926$		−	651.791i		−	0.703878i
$927$	−965.678	−	763.127i	−1.04172	−	0.823223i
$928$	745.767	+	242.314i	0.803628	+	0.261115i
$929$	−342.348	−	111.235i	−0.368512	−	0.119737i	0.118906	−	0.992905i	$-0.462061\pi$
$929$	−342.348	−	111.235i	−0.368512	−	0.119737i	−0.487418	+	0.873169i	$0.662061\pi$
$930$	210.848	+	717.594i	0.226719	+	0.771606i
$931$	−187.165	−	576.036i	−0.201037	−	0.618728i
$932$	2642.73			2.83555
$933$	870.743	−	421.707i	0.933272	−	0.451990i
$934$	−152.989	−	111.153i	−0.163800	−	0.119008i
$935$	−11.7904	−	23.6138i	−0.0126100	−	0.0252554i
$936$	2408.52	+	1903.34i	2.57321	+	2.03348i
$937$	−326.208	+	448.987i	−0.348141	+	0.479175i	−0.946797	−	0.321831i	$-0.895702\pi$
$937$	−326.208	+	448.987i	−0.348141	+	0.479175i	0.598656	+	0.801006i	$0.295702\pi$
$938$	1772.29	+	1287.64i	1.88944	+	1.37276i
$939$	−1059.24	−	1102.98i	−1.12806	−	1.17463i
$940$	−632.069	+	315.592i	−0.672413	+	0.335737i
$941$	−701.066	+	964.935i	−0.745023	+	1.02544i	0.253291	+	0.967390i	$0.418487\pi$
$941$	−701.066	+	964.935i	−0.745023	+	1.02544i	−0.998314	+	0.0580458i	$0.981513\pi$
$942$	233.857	−	113.259i	0.248256	−	0.120232i
$943$		−	115.695i		−	0.122688i
$944$	1525.20	−	495.566i	1.61567	−	0.524964i
$945$	1100.60	−	689.244i	1.16465	−	0.729358i
$946$	−37.1750	+	114.413i	−0.0392971	+	0.120944i
$947$	98.6599	−	303.644i	0.104181	−	0.320638i	−0.885356	−	0.464914i	$-0.846085\pi$
$947$	98.6599	−	303.644i	0.104181	−	0.320638i	0.989537	+	0.144276i	$0.0460853\pi$
$948$	2029.86	−	1949.37i	2.14120	−	2.05630i
$949$	−1575.90			−1.66059
$950$	−20.4273	+	1252.98i	−0.0215024	+	1.31892i
$951$	−1060.25	+	146.014i	−1.11488	+	0.153537i
$952$	−204.195	−	281.050i	−0.214491	−	0.295221i
$953$	−257.735	+	793.227i	−0.270446	+	0.832347i	0.719943	+	0.694034i	$0.244168\pi$
$953$	−257.735	+	793.227i	−0.270446	+	0.832347i	−0.990389	+	0.138313i	$0.955832\pi$
$954$	66.6262	−	1646.26i	0.0698388	−	1.72564i
$955$	−590.180	−	1182.01i	−0.617990	−	1.23771i
$956$	401.458	−	130.442i	0.419935	−	0.136445i
$957$	193.015	−	26.5812i	0.201688	−	0.0277756i
$958$	−2945.48	+	957.044i	−3.07461	+	0.999002i
$959$	−58.0647	+	79.9192i	−0.0605471	+	0.0833359i
$960$	11.5492	+	0.327801i	0.0120304	+	0.000341459i
$961$	622.488	−	452.264i	0.647750	−	0.470618i
$962$	−3215.77	−	2336.39i	−3.34280	−	2.42868i
$963$	1102.54	+	408.226i	1.14490	+	0.423910i
$964$	−743.337	+	540.066i	−0.771096	+	0.560234i
$965$	966.438	+	502.389i	1.00149	+	0.520610i
$966$	288.427	−	538.845i	0.298579	−	0.557810i
$967$	314.182	−	102.084i	0.324904	−	0.105568i	−0.142024	−	0.989863i	$-0.545361\pi$
$967$	314.182	−	102.084i	0.324904	−	0.105568i	0.466927	+	0.884296i	$0.345361\pi$
$968$	2046.95			2.11462
$969$	36.6353	+	75.6449i	0.0378074	+	0.0780649i
$970$	−142.843	+	856.623i	−0.147260	+	0.883117i
$971$	−189.425	−	61.5480i	−0.195083	−	0.0633862i	0.209846	−	0.977734i	$-0.432704\pi$
$971$	−189.425	−	61.5480i	−0.195083	−	0.0633862i	−0.404929	+	0.914348i	$0.632704\pi$
$972$	−789.205	−	2034.05i	−0.811939	−	2.09265i
$973$	−12.0837	−	16.6318i	−0.0124190	−	0.0170933i
$974$		−	2885.04i		−	2.96206i
$975$	274.418	−	1399.65i	0.281455	−	1.43554i
$976$	−111.234			−0.113970
$977$	224.931	−	163.422i	0.230226	−	0.167269i	−0.466691	−	0.884420i	$-0.654554\pi$
$977$	224.931	−	163.422i	0.230226	−	0.167269i	0.696918	+	0.717151i	$0.254554\pi$
$978$	−2302.80	−	412.629i	−2.35460	−	0.421911i
$979$	−21.6887	+	66.7508i	−0.0221539	+	0.0681826i
$980$	−1370.53	−	1393.06i	−1.39850	−	1.42149i
$981$	−829.506	−	1244.62i	−0.845572	−	1.26872i
$982$		−	179.020i		−	0.182301i
$983$	505.381	+	1555.40i	0.514121	+	1.58230i	0.784875	+	0.619654i	$0.212727\pi$
$983$	505.381	+	1555.40i	0.514121	+	1.58230i	−0.270754	+	0.962648i	$0.587273\pi$
$984$	−499.719	+	933.584i	−0.507845	+	0.948764i
$985$	1211.70	+	1231.61i	1.23015	+	1.25037i
$986$	−105.629	−	145.386i	−0.107129	−	0.147450i
$987$	−214.314	+	400.385i	−0.217137	+	0.405659i
$988$	−1396.44	+	1922.04i	−1.41340	+	1.94538i
$989$	44.0153	+	60.5819i	0.0445049	+	0.0612557i
$990$	−387.605	+	174.322i	−0.391520	+	0.176083i
$991$	714.008	+	518.757i	0.720492	+	0.523468i	0.886541	−	0.462649i	$-0.153101\pi$
$991$	714.008	+	518.757i	0.720492	+	0.523468i	−0.166049	+	0.986117i	$0.553101\pi$
$992$	−135.378	−	416.652i	−0.136470	−	0.420012i
$993$	−751.782	+	103.532i	−0.757082	+	0.104262i
$994$	−837.231	−	2576.73i	−0.842284	−	2.59228i
$995$	−277.913	+	534.617i	−0.279309	+	0.537303i
$996$	−533.066	+	2974.93i	−0.535207	+	2.98688i
$997$	1601.51	+	520.361i	1.60632	+	0.521927i	0.968661	−	0.248388i	$-0.0799007\pi$
$997$	1601.51	+	520.361i	1.60632	+	0.521927i	0.637664	+	0.770314i	$0.279901\pi$
$998$	−576.957	+	419.184i	−0.578113	+	0.420024i
$999$	625.229	+	1436.31i	0.625855	+	1.43775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.1	✓	72
3.2	odd	2	inner	75.3.h.a.14.18	yes	72
5.2	odd	4		375.3.j.b.176.1		144
5.3	odd	4		375.3.j.b.176.36		144
5.4	even	2		375.3.h.a.74.18		72
15.2	even	4		375.3.j.b.176.35		144
15.8	even	4		375.3.j.b.176.2		144
15.14	odd	2		375.3.h.a.74.1		72
25.9	even	10	inner	75.3.h.a.59.18	yes	72
25.12	odd	20		375.3.j.b.326.35		144
25.13	odd	20		375.3.j.b.326.2		144
25.16	even	5		375.3.h.a.299.1		72
75.38	even	20		375.3.j.b.326.36		144
75.41	odd	10		375.3.h.a.299.18		72
75.59	odd	10	inner	75.3.h.a.59.1	yes	72
75.62	even	20		375.3.j.b.326.1		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.1	✓	72	1.1	even	1	trivial
75.3.h.a.14.18	yes	72	3.2	odd	2	inner
75.3.h.a.59.1	yes	72	75.59	odd	10	inner
75.3.h.a.59.18	yes	72	25.9	even	10	inner
375.3.h.a.74.1		72	15.14	odd	2
375.3.h.a.74.18		72	5.4	even	2
375.3.h.a.299.1		72	25.16	even	5
375.3.h.a.299.18		72	75.41	odd	10
375.3.j.b.176.1		144	5.2	odd	4
375.3.j.b.176.2		144	15.8	even	4
375.3.j.b.176.35		144	15.2	even	4
375.3.j.b.176.36		144	5.3	odd	4
375.3.j.b.326.1		144	75.62	even	20
375.3.j.b.326.2		144	25.13	odd	20
375.3.j.b.326.35		144	25.12	odd	20
375.3.j.b.326.36		144	75.38	even	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+(-2.91455 + 2.11754i) q^{2} +(0.529130 - 2.95297i) q^{3} +(2.77453 - 8.53912i) q^{4} +(-2.30619 + 4.43638i) q^{5} +(4.71086 + 9.72702i) q^{6} +9.61929i q^{7} +(5.54243 + 17.0578i) q^{8} +(-8.44004 - 3.12501i) q^{9} +(-2.67273 - 17.8135i) q^{10} +(1.54093 + 2.12091i) q^{11} +(-23.7477 - 12.7114i) q^{12} +(-11.1781 + 15.3854i) q^{13} +(-20.3692 - 28.0359i) q^{14} +(11.8802 + 9.15753i) q^{15} +(-23.2191 - 16.8697i) q^{16} +(0.622226 + 1.91502i) q^{17} +(31.2162 - 8.76416i) q^{18} +(4.29962 + 13.2329i) q^{19} +(31.4842 + 32.0017i) q^{20} +(28.4055 + 5.08986i) q^{21} +(-8.98221 - 2.91850i) q^{22} +(-4.75610 + 3.45551i) q^{23} +(53.3039 - 7.34080i) q^{24} +(-14.3630 - 20.4623i) q^{25} -68.5115i q^{26} +(-13.6939 + 23.2696i) q^{27} +(82.1403 + 26.6890i) q^{28} +(23.5609 + 7.65541i) q^{29} +(-54.0169 - 1.53316i) q^{30} +(-4.27699 - 13.1632i) q^{31} +31.6527 q^{32} +(7.07832 - 3.42808i) q^{33} +(-5.86863 - 4.26381i) q^{34} +(-42.6748 - 22.1839i) q^{35} +(-50.1020 + 63.4001i) q^{36} +(34.1022 - 46.9377i) q^{37} +(-40.5526 - 29.4632i) q^{38} +(39.5178 + 41.1495i) q^{39} +(-88.4570 - 14.7503i) q^{40} +(-11.5675 + 15.9213i) q^{41} +(-93.5670 + 45.3151i) q^{42} -12.7377i q^{43} +(22.3860 - 7.27366i) q^{44} +(33.3281 - 30.2364i) q^{45} +(6.54469 - 20.1425i) q^{46} +(-4.86299 + 14.9667i) q^{47} +(-62.1015 + 59.6390i) q^{48} -43.5307 q^{49} +(85.1913 + 29.2240i) q^{50} +(5.98422 - 0.824122i) q^{51} +(100.363 + 138.138i) q^{52} +(15.7029 - 48.3285i) q^{53} +(-9.36283 - 96.8179i) q^{54} +(-12.9628 + 1.94494i) q^{55} +(-164.084 + 53.3142i) q^{56} +(41.3513 - 5.69473i) q^{57} +(-84.8800 + 27.5792i) q^{58} +(-32.8435 + 45.2053i) q^{59} +(111.159 - 76.0389i) q^{60} +(3.13551 - 2.27808i) q^{61} +(40.3392 + 29.3081i) q^{62} +(30.0604 - 81.1872i) q^{63} +(0.623150 - 0.452745i) q^{64} +(-42.4765 - 85.0720i) q^{65} +(-13.3710 + 24.9799i) q^{66} +(-60.1212 + 19.5346i) q^{67} +18.0789 q^{68} +(7.68741 + 15.8730i) q^{69} +(171.353 - 25.7098i) q^{70} +(74.3554 + 24.1595i) q^{71} +(6.52758 - 161.289i) q^{72} +(48.7077 + 67.0405i) q^{73} +209.015i q^{74} +(-68.0243 + 31.5862i) q^{75} +124.926 q^{76} +(-20.4016 + 14.8226i) q^{77} +(-202.312 - 36.2515i) q^{78} +(-32.2869 + 99.3689i) q^{79} +(128.388 - 64.1042i) q^{80} +(61.4686 + 52.7504i) q^{81} -70.8982i q^{82} +(-34.6732 - 106.713i) q^{83} +(122.275 - 228.436i) q^{84} +(-9.93071 - 1.65595i) q^{85} +(26.9727 + 37.1247i) q^{86} +(35.0730 - 65.5239i) q^{87} +(-27.6376 + 38.0399i) q^{88} +(15.7364 + 21.6593i) q^{89} +(-33.1094 + 158.699i) q^{90} +(-147.996 - 107.526i) q^{91} +(16.3111 + 50.2004i) q^{92} +(-41.1337 + 5.66476i) q^{93} +(-17.5193 - 53.9188i) q^{94} +(-68.6218 - 11.4427i) q^{95} +(16.7484 - 93.4694i) q^{96} +(-45.8531 - 14.8986i) q^{97} +(126.872 - 92.1781i) q^{98} +(-6.37765 - 22.7160i) 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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