LMFDB - Embedded newform 72.2.n.b.13.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [72,2,Mod(13,72)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(72, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("72.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$72 = 2^{3} \cdot 3^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	72.n (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.574922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256$ x^16 - x^15 + x^14 + 2x^12 - 4x^11 - 8x^9 + 4x^8 - 16x^7 - 32x^5 + 32x^4 + 64x^2 - 128*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$2^{2}\cdot 3^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			13.3
Root			$1.41411 - 0.0174668i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.b.61.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.722180 + 1.21592i) q^{2} +(0.294546 - 1.70682i) q^{3} +(-0.956913 - 1.75622i) q^{4} +(3.17262 + 1.83171i) q^{5} +(1.86264 + 1.59078i) q^{6} +(-0.191926 - 0.332426i) q^{7} +(2.82649 + 0.104780i) q^{8} +(-2.82649 - 1.00547i) q^{9} +(-4.51841 + 2.53482i) q^{10} +(-1.73849 + 1.00372i) q^{11} +(-3.27941 + 1.11599i) q^{12} +(-0.397799 - 0.229669i) q^{13} +(0.542808 + 0.00670468i) q^{14} +(4.06089 - 4.87557i) q^{15} +(-2.16863 + 3.36111i) q^{16} -4.08495 q^{17} +(3.26380 - 2.71064i) q^{18} -4.72398i q^{19} +(0.180973 - 7.32461i) q^{20} +(-0.623923 + 0.229669i) q^{21} +(0.0350635 - 2.83872i) q^{22} +(-2.97594 + 5.15447i) q^{23} +(1.01137 - 4.79345i) q^{24} +(4.21034 + 7.29252i) q^{25} +(0.566541 - 0.317828i) q^{26} +(-2.54870 + 4.52815i) q^{27} +(-0.400157 + 0.655168i) q^{28} +(-2.03783 + 1.17654i) q^{29} +(2.99561 + 8.45875i) q^{30} +(0.592083 - 1.02552i) q^{31} +(-2.52069 - 5.06420i) q^{32} +(1.20110 + 3.26293i) q^{33} +(2.95007 - 4.96697i) q^{34} -1.40621i q^{35} +(0.938865 + 5.92609i) q^{36} +5.74432i q^{37} +(5.74397 + 3.41156i) q^{38} +(-0.509175 + 0.611324i) q^{39} +(8.77543 + 5.50973i) q^{40} +(4.75281 - 8.23212i) q^{41} +(0.171325 - 0.924501i) q^{42} +(1.03633 - 0.598327i) q^{43} +(3.42633 + 2.09270i) q^{44} +(-7.12562 - 8.36729i) q^{45} +(-4.11825 - 7.34095i) q^{46} +(3.27688 + 5.67572i) q^{47} +(5.09805 + 4.69147i) q^{48} +(3.42633 - 5.93458i) q^{49} +(-11.9077 - 0.147082i) q^{50} +(-1.20321 + 6.97229i) q^{51} +(-0.0226913 + 0.918397i) q^{52} -7.63807i q^{53} +(-3.66524 - 6.36914i) q^{54} -7.35407 q^{55} +(-0.507645 - 0.959707i) q^{56} +(-8.06300 - 1.39143i) q^{57} +(0.0411010 - 3.32752i) q^{58} +(0.603703 + 0.348548i) q^{59} +(-12.4485 - 2.46632i) q^{60} +(4.23774 - 2.44666i) q^{61} +(0.819356 + 1.46053i) q^{62} +(0.208231 + 1.13257i) q^{63} +(7.97804 + 0.592316i) q^{64} +(-0.841376 - 1.45731i) q^{65} +(-4.83486 - 0.895980i) q^{66} +(8.87932 + 5.12648i) q^{67} +(3.90895 + 7.17409i) q^{68} +(7.92122 + 6.59762i) q^{69} +(1.70984 + 1.01554i) q^{70} -3.73792 q^{71} +(-7.88367 - 3.13812i) q^{72} -2.68275 q^{73} +(-6.98462 - 4.14843i) q^{74} +(13.6872 - 5.03832i) q^{75} +(-8.29636 + 4.52044i) q^{76} +(0.667322 + 0.385279i) q^{77} +(-0.375604 - 1.06060i) q^{78} +(-5.35979 - 9.28342i) q^{79} +(-13.0368 + 6.69119i) q^{80} +(6.97804 + 5.68392i) q^{81} +(6.57719 + 11.7241i) q^{82} +(-5.49039 + 3.16988i) q^{83} +(1.00039 + 0.875974i) q^{84} +(-12.9600 - 7.48246i) q^{85} +(-0.0209018 + 1.69220i) q^{86} +(1.40792 + 3.82477i) q^{87} +(-5.01898 + 2.65483i) q^{88} +7.56802 q^{89} +(15.3199 - 2.62148i) q^{90} +0.176318i q^{91} +(11.9001 + 0.294022i) q^{92} +(-1.57598 - 1.31264i) q^{93} +(-9.26771 - 0.114473i) q^{94} +(8.65297 - 14.9874i) q^{95} +(-9.38615 + 2.81072i) q^{96} +(-2.98511 - 5.17036i) q^{97} +(4.74153 + 8.45196i) q^{98} +(5.92302 - 1.08898i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + q^{2} - q^{4} - 7 q^{6} + 6 q^{7} - 2 q^{8} + 2 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{14} - 10 q^{15} - 9 q^{16} - 28 q^{17} + 4 q^{18} - 8 q^{20} + q^{22} - 10 q^{23} + 7 q^{24} + 2 q^{25} + 28 q^{26}+ \cdots + 66 q^{98}+O(q^{100})$ 16 * q + q^2 - q^4 - 7 * q^6 + 6 * q^7 - 2 * q^8 + 2 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^14 - 10 * q^15 - 9 * q^16 - 28 * q^17 + 4 * q^18 - 8 * q^20 + q^22 - 10 * q^23 + 7 * q^24 + 2 * q^25 + 28 * q^26 + 4 * q^28 + 22 * q^30 - 10 * q^31 + 11 * q^32 + q^34 + 27 * q^36 + 23 * q^38 + 2 * q^39 + 6 * q^40 - 8 * q^41 + 8 * q^42 + 18 * q^44 - 20 * q^46 + 6 * q^47 + 39 * q^48 + 18 * q^49 - 23 * q^50 - 8 * q^52 - 29 * q^54 - 4 * q^55 + 10 * q^56 + 10 * q^57 - 14 * q^58 + 6 * q^60 - 52 * q^62 + 2 * q^63 + 26 * q^64 - 14 * q^65 - 72 * q^66 - 39 * q^68 + 72 * q^71 - 77 * q^72 - 44 * q^73 - 38 * q^74 + 5 * q^76 + 10 * q^78 - 30 * q^79 - 96 * q^80 + 10 * q^81 + 38 * q^82 - 28 * q^84 + 7 * q^86 + 42 * q^87 + 31 * q^88 + 64 * q^89 + 64 * q^90 - 30 * q^92 - 12 * q^94 + 44 * q^95 - 26 * q^96 + 66 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$ .

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	−0.722180	+	1.21592i	−0.510658	+	0.859784i
$2$	−0.722180	+	1.21592i	−0.510658	+	0.859784i
$3$	0.294546	−	1.70682i	0.170056	−	0.985434i
$3$	0.294546	−	1.70682i	0.170056	−	0.985434i
$4$	−0.956913	−	1.75622i	−0.478457	−	0.878111i
$5$	3.17262	+	1.83171i	1.41884	+	0.819167i	0.996197	−	0.0871306i	$-0.0277697\pi$
$5$	3.17262	+	1.83171i	1.41884	+	0.819167i	0.422641	+	0.906297i	$0.361103\pi$
$6$	1.86264	+	1.59078i	0.760420	+	0.649431i
$7$	−0.191926	−	0.332426i	−0.0725413	−	0.125645i	0.827473	−	0.561505i	$-0.189778\pi$
$7$	−0.191926	−	0.332426i	−0.0725413	−	0.125645i	−0.900014	+	0.435860i	$0.856444\pi$
$8$	2.82649	+	0.104780i	0.999314	+	0.0370452i
$9$	−2.82649	−	1.00547i	−0.942162	−	0.335158i
$10$	−4.51841	+	2.53482i	−1.42885	+	0.801580i
$11$	−1.73849	+	1.00372i	−0.524173	+	0.302632i	−0.738640	−	0.674100i	$-0.764532\pi$
$11$	−1.73849	+	1.00372i	−0.524173	+	0.302632i	0.214467	+	0.976731i	$0.431199\pi$
$12$	−3.27941	+	1.11599i	−0.946685	+	0.322160i
$13$	−0.397799	−	0.229669i	−0.110330	−	0.0636988i	0.443820	−	0.896116i	$-0.353623\pi$
$13$	−0.397799	−	0.229669i	−0.110330	−	0.0636988i	−0.554149	+	0.832417i	$0.686956\pi$
$14$	0.542808	+	0.00670468i	0.145071	+	0.00179190i
$15$	4.06089	−	4.87557i	1.04852	−	1.25887i
$16$	−2.16863	+	3.36111i	−0.542158	+	0.840276i
$17$	−4.08495			−0.990747			−0.495373	−	0.868680i	$-0.664969\pi$
$17$	−4.08495			−0.990747			−0.495373	+	0.868680i	$0.664969\pi$
$18$	3.26380	−	2.71064i	0.769286	−	0.638904i
$19$		−	4.72398i		−	1.08376i	−0.840457	−	0.541878i	$-0.817714\pi$
$19$		−	4.72398i		−	1.08376i	0.840457	−	0.541878i	$-0.182286\pi$
$20$	0.180973	−	7.32461i	0.0404667	−	1.63783i
$21$	−0.623923	+	0.229669i	−0.136151	+	0.0501179i
$22$	0.0350635	−	2.83872i	0.00747555	−	0.605217i
$23$	−2.97594	+	5.15447i	−0.620525	+	1.07478i	0.368863	+	0.929484i	$0.379747\pi$
$23$	−2.97594	+	5.15447i	−0.620525	+	1.07478i	−0.989388	+	0.145298i	$0.953586\pi$
$24$	1.01137	−	4.79345i	0.206445	−	0.978458i
$25$	4.21034	+	7.29252i	0.842068	+	1.45850i
$26$	0.566541	−	0.317828i	0.111108	−	0.0623313i
$27$	−2.54870	+	4.52815i	−0.490497	+	0.871443i
$28$	−0.400157	+	0.655168i	−0.0756226	+	0.123815i
$29$	−2.03783	+	1.17654i	−0.378416	+	0.218479i	−0.677129	−	0.735864i	$-0.736776\pi$
$29$	−2.03783	+	1.17654i	−0.378416	+	0.218479i	0.298713	+	0.954343i	$0.403443\pi$
$30$	2.99561	+	8.45875i	0.546920	+	1.54435i
$31$	0.592083	−	1.02552i	0.106341	−	0.184188i	−0.807944	−	0.589259i	$-0.799420\pi$
$31$	0.592083	−	1.02552i	0.106341	−	0.184188i	0.914285	+	0.405071i	$0.132753\pi$
$32$	−2.52069	−	5.06420i	−0.445598	−	0.895233i
$33$	1.20110	+	3.26293i	0.209085	+	0.568003i
$34$	2.95007	−	4.96697i	0.505933	−	0.851828i
$35$		−	1.40621i		−	0.237693i
$36$	0.938865	+	5.92609i	0.156478	+	0.987682i
$37$			5.74432i			0.944360i	0.881502	+	0.472180i	$0.156533\pi$
$37$			5.74432i			0.944360i	−0.881502	+	0.472180i	$0.843467\pi$
$38$	5.74397	+	3.41156i	0.931795	+	0.553428i
$39$	−0.509175	+	0.611324i	−0.0815332	+	0.0978902i
$40$	8.77543	+	5.50973i	1.38752	+	0.871165i
$41$	4.75281	−	8.23212i	0.742265	−	1.28564i	−0.209197	−	0.977874i	$-0.567085\pi$
$41$	4.75281	−	8.23212i	0.742265	−	1.28564i	0.951462	−	0.307767i	$-0.0995817\pi$
$42$	0.171325	−	0.924501i	0.0264361	−	0.142654i
$43$	1.03633	−	0.598327i	0.158039	−	0.0912440i	−0.418895	−	0.908035i	$-0.637582\pi$
$43$	1.03633	−	0.598327i	0.158039	−	0.0912440i	0.576934	+	0.816791i	$0.304249\pi$
$44$	3.42633	+	2.09270i	0.516538	+	0.315486i
$45$	−7.12562	−	8.36729i	−1.06222	−	1.24732i
$46$	−4.11825	−	7.34095i	−0.607204	−	1.08236i
$47$	3.27688	+	5.67572i	0.477982	+	0.827889i	0.999681	−	0.0252403i	$-0.00803510\pi$
$47$	3.27688	+	5.67572i	0.477982	+	0.827889i	−0.521699	+	0.853129i	$0.674702\pi$
$48$	5.09805	+	4.69147i	0.735840	+	0.677156i
$49$	3.42633	−	5.93458i	0.489476	−	0.847796i
$50$	−11.9077	−	0.147082i	−1.68401	−	0.0208006i
$51$	−1.20321	+	6.97229i	−0.168482	+	0.976316i
$52$	−0.0226913	+	0.918397i	−0.00314671	+	0.127359i
$53$		−	7.63807i		−	1.04917i	−0.851358	−	0.524585i	$-0.824221\pi$
$53$		−	7.63807i		−	1.04917i	0.851358	−	0.524585i	$-0.175779\pi$
$54$	−3.66524	−	6.36914i	−0.498777	−	0.866731i
$55$	−7.35407			−0.991623
$56$	−0.507645	−	0.959707i	−0.0678369	−	0.128246i
$57$	−8.06300	−	1.39143i	−1.06797	−	0.184299i
$58$	0.0411010	−	3.32752i	0.00539682	−	0.436924i
$59$	0.603703	+	0.348548i	0.0785954	+	0.0453771i	0.538783	−	0.842445i	$-0.318884\pi$
$59$	0.603703	+	0.348548i	0.0785954	+	0.0453771i	−0.460187	+	0.887822i	$0.652218\pi$
$60$	−12.4485	−	2.46632i	−1.60710	−	0.318401i
$61$	4.23774	−	2.44666i	0.542587	−	0.313263i	−0.203540	−	0.979067i	$-0.565245\pi$
$61$	4.23774	−	2.44666i	0.542587	−	0.313263i	0.746127	+	0.665804i	$0.231911\pi$
$62$	0.819356	+	1.46053i	0.104058	+	0.185488i
$63$	0.208231	+	1.13257i	0.0262346	+	0.142691i
$64$	7.97804	+	0.592316i	0.997255	+	0.0740395i
$65$	−0.841376	−	1.45731i	−0.104360	−	0.180757i
$66$	−4.83486	−	0.895980i	−0.595131	−	0.110287i
$67$	8.87932	+	5.12648i	1.08478	+	0.626299i	0.932182	−	0.361989i	$-0.117902\pi$
$67$	8.87932	+	5.12648i	1.08478	+	0.626299i	0.152599	+	0.988288i	$0.451236\pi$
$68$	3.90895	+	7.17409i	0.474029	+	0.869986i
$69$	7.92122	+	6.59762i	0.953603	+	0.794260i
$70$	1.70984	+	1.01554i	0.204365	+	0.121380i
$71$	−3.73792			−0.443610			−0.221805	−	0.975091i	$-0.571195\pi$
$71$	−3.73792			−0.443610			−0.221805	+	0.975091i	$0.571195\pi$
$72$	−7.88367	−	3.13812i	−0.929099	−	0.369831i
$73$	−2.68275			−0.313992			−0.156996	−	0.987599i	$-0.550181\pi$
$73$	−2.68275			−0.313992			−0.156996	+	0.987599i	$0.550181\pi$
$74$	−6.98462	−	4.14843i	−0.811945	−	0.482245i
$75$	13.6872	−	5.03832i	1.58046	−	0.581775i
$76$	−8.29636	+	4.52044i	−0.951658	+	0.518530i
$77$	0.667322	+	0.385279i	0.0760484	+	0.0439066i
$78$	−0.375604	−	1.06060i	−0.0425288	−	0.120089i
$79$	−5.35979	−	9.28342i	−0.603023	−	1.04447i	−0.992361	−	0.123372i	$-0.960629\pi$
$79$	−5.35979	−	9.28342i	−0.603023	−	1.04447i	0.389337	−	0.921095i	$-0.372704\pi$
$80$	−13.0368	+	6.69119i	−1.45756	+	0.748098i
$81$	6.97804	+	5.68392i	0.775338	+	0.631546i
$82$	6.57719	+	11.7241i	0.726329	+	1.29471i
$83$	−5.49039	+	3.16988i	−0.602648	+	0.347939i	−0.770083	−	0.637944i	$-0.779785\pi$
$83$	−5.49039	+	3.16988i	−0.602648	+	0.347939i	0.167434	+	0.985883i	$0.446452\pi$
$84$	1.00039	+	0.875974i	0.109152	+	0.0955766i
$85$	−12.9600	−	7.48246i	−1.40571	−	0.811586i
$86$	−0.0209018	+	1.69220i	−0.00225389	+	0.182474i
$87$	1.40792	+	3.82477i	0.150945	+	0.410058i
$88$	−5.01898	+	2.65483i	−0.535025	+	0.283006i
$89$	7.56802			0.802208			0.401104	−	0.916032i	$-0.368627\pi$
$89$	7.56802			0.802208			0.401104	+	0.916032i	$0.368627\pi$
$90$	15.3199	−	2.62148i	1.61486	−	0.276328i
$91$			0.176318i			0.0184832i
$92$	11.9001	+	0.294022i	1.24067	+	0.0306539i
$93$	−1.57598	−	1.31264i	−0.163422	−	0.136115i
$94$	−9.26771	−	0.114473i	−0.955891	−	0.0118070i
$95$	8.65297	−	14.9874i	0.887776	−	1.53767i
$96$	−9.38615	+	2.81072i	−0.957970	+	0.286868i
$97$	−2.98511	−	5.17036i	−0.303092	−	0.524971i	0.673743	−	0.738966i	$-0.264686\pi$
$97$	−2.98511	−	5.17036i	−0.303092	−	0.524971i	−0.976835	+	0.213995i	$0.931352\pi$
$98$	4.74153	+	8.45196i	0.478967	+	0.853777i
$99$	5.92302	−	1.08898i	0.595286	−	0.109447i
$100$	8.77836	−	14.3726i	0.877836	−	1.43726i
$101$	4.81265	−	2.77859i	0.478877	−	0.276480i	−0.241071	−	0.970507i	$-0.577499\pi$
$101$	4.81265	−	2.77859i	0.478877	−	0.276480i	0.719948	+	0.694028i	$0.244165\pi$
$102$	−7.60880	−	6.49824i	−0.753384	−	0.643422i
$103$	−6.14380	+	10.6414i	−0.605366	+	1.04853i	0.386627	+	0.922236i	$0.373640\pi$
$103$	−6.14380	+	10.6414i	−0.605366	+	1.04853i	−0.991993	+	0.126289i	$0.959693\pi$
$104$	−1.10031	−	0.690838i	−0.107894	−	0.0677422i
$105$	−2.40016	−	0.414194i	−0.234231	−	0.0404212i
$106$	9.28726	+	5.51606i	0.902059	+	0.535767i
$107$		−	6.61773i		−	0.639760i	−0.947458	−	0.319880i	$-0.896357\pi$
$107$		−	6.61773i		−	0.639760i	0.947458	−	0.319880i	$-0.103643\pi$
$108$	10.3913	+	0.143028i	0.999905	+	0.0137628i
$109$			7.01563i			0.671975i	0.941866	+	0.335988i	$0.109070\pi$
$109$			7.01563i			0.671975i	−0.941866	+	0.335988i	$0.890930\pi$
$110$	5.31096	−	8.94195i	0.506380	−	0.852581i
$111$	9.80453	+	1.69196i	0.930605	+	0.160594i
$112$	1.53354	+	0.0758259i	0.144905	+	0.00716487i
$113$	−4.09419	+	7.09135i	−0.385149	+	0.667098i	−0.991790	−	0.127878i	$-0.959183\pi$
$113$	−4.09419	+	7.09135i	−0.385149	+	0.667098i	0.606641	+	0.794976i	$0.292517\pi$
$114$	7.51479	−	8.79908i	0.703825	−	0.824109i
$115$	−18.8830	+	10.9021i	−1.76085	+	1.01663i
$116$	4.01630	+	2.45304i	0.372905	+	0.227759i
$117$	0.893446	+	1.04913i	0.0825991	+	0.0969924i
$118$	−0.859788	+	0.482339i	−0.0791499	+	0.0444029i
$119$	0.784009	+	1.35794i	0.0718700	+	0.124483i
$120$	11.9889	−	13.3552i	1.09443	−	1.21916i
$121$	−3.48511	+	6.03639i	−0.316828	+	0.548762i
$122$	−0.0854708	+	6.91967i	−0.00773816	+	0.626478i
$123$	−12.6508	−	10.5369i	−1.14069	−	0.950084i
$124$	−2.36761	−	0.0584977i	−0.212618	−	0.00525325i
$125$			12.5314i			1.12084i
$126$	−1.52750	−	0.564730i	−0.136080	−	0.0503101i
$127$	21.0113			1.86445			0.932224	−	0.361882i	$-0.117866\pi$
$127$	21.0113			1.86445			0.932224	+	0.361882i	$0.117866\pi$
$128$	−6.48179	+	9.27289i	−0.572914	+	0.819615i
$129$	−0.715991	−	1.94507i	−0.0630395	−	0.171254i
$130$	2.37959	+	0.0293923i	0.208704	+	0.00257788i
$131$	5.49039	+	3.16988i	0.479697	+	0.276953i	0.720290	−	0.693673i	$-0.244009\pi$
$131$	5.49039	+	3.16988i	0.479697	+	0.276953i	−0.240593	+	0.970626i	$0.577342\pi$
$132$	4.58108	−	5.23174i	0.398732	−	0.455364i
$133$	−1.57037	+	0.906655i	−0.136169	+	0.0786170i
$134$	−12.6458	+	7.09429i	−1.09243	+	0.612853i
$135$	−16.3803	+	9.69762i	−1.40979	+	0.834638i
$136$	−11.5461	−	0.428020i	−0.990067	−	0.0367024i
$137$	0.483695	+	0.837785i	0.0413249	+	0.0715768i	0.885948	−	0.463784i	$-0.153509\pi$
$137$	0.483695	+	0.837785i	0.0413249	+	0.0715768i	−0.844623	+	0.535361i	$0.820175\pi$
$138$	−13.7427	+	4.86689i	−1.16986	+	0.414297i
$139$	−5.18167	−	2.99164i	−0.439503	−	0.253747i	0.263884	−	0.964554i	$-0.414996\pi$
$139$	−5.18167	−	2.99164i	−0.439503	−	0.253747i	−0.703387	+	0.710807i	$0.748330\pi$
$140$	−2.46962	+	1.34562i	−0.208721	+	0.113726i
$141$	10.6526	−	3.92129i	0.897114	−	0.330232i
$142$	2.69945	−	4.54501i	0.226533	−	0.381409i
$143$	0.922090			0.0771091
$144$	9.50912	−	7.31961i	0.792426	−	0.609968i
$145$	−8.62036			−0.715882
$146$	1.93743	−	3.26201i	0.160343	−	0.269966i
$147$	−9.12006	−	7.59614i	−0.752210	−	0.626519i
$148$	10.0883	−	5.49681i	0.829253	−	0.451835i
$149$	−6.43764	−	3.71678i	−0.527392	−	0.304490i	0.212562	−	0.977148i	$-0.431819\pi$
$149$	−6.43764	−	3.71678i	−0.527392	−	0.304490i	−0.739954	+	0.672658i	$0.765153\pi$
$150$	−3.75841	+	20.2811i	−0.306873	+	1.65594i
$151$	−0.492870	−	0.853676i	−0.0401092	−	0.0694711i	0.845274	−	0.534333i	$-0.179437\pi$
$151$	−0.492870	−	0.853676i	−0.0401092	−	0.0694711i	−0.885383	+	0.464862i	$0.846104\pi$
$152$	0.494977	−	13.3523i	0.0401479	−	1.08301i
$153$	11.5461	+	4.10732i	0.933444	+	0.332057i
$154$	−0.950393	+	0.533169i	−0.0765849	+	0.0429639i
$155$	3.75691	−	2.16905i	0.301762	−	0.174222i
$156$	1.56086	+	0.309240i	0.124969	+	0.0247590i
$157$	15.2336	+	8.79510i	1.21577	+	0.701925i	0.964010	−	0.265864i	$-0.0856573\pi$
$157$	15.2336	+	8.79510i	1.21577	+	0.701925i	0.251760	+	0.967790i	$0.418991\pi$
$158$	15.1586	+	0.187237i	1.20595	+	0.0148958i
$159$	−13.0368	−	2.24976i	−1.03389	−	0.178418i
$160$	1.27899	−	20.6840i	0.101113	−	1.63521i
$161$	2.28464			0.180055
$162$	−11.9506	+	4.37992i	−0.938926	+	0.344119i
$163$		−	17.8852i		−	1.40088i	−0.713711	−	0.700440i	$-0.752987\pi$
$163$		−	17.8852i		−	1.40088i	0.713711	−	0.700440i	$-0.247013\pi$
$164$	−19.0055	−	0.469577i	−1.48408	−	0.0366678i
$165$	−2.16611	+	12.5521i	−0.168631	+	0.977179i
$166$	0.110735	−	8.96508i	0.00859473	−	0.695825i
$167$	−1.04037	+	1.80197i	−0.0805062	+	0.139441i	−0.903467	−	0.428657i	$-0.858987\pi$
$167$	−1.04037	+	1.80197i	−0.0805062	+	0.139441i	0.822961	+	0.568097i	$0.192320\pi$
$168$	−1.78757	+	0.583782i	−0.137914	+	0.0450398i
$169$	−6.39450	−	11.0756i	−0.491885	−	0.851970i
$170$	18.4575	−	10.3546i	1.41563	−	0.794163i
$171$	−4.74984	+	13.3523i	−0.363229	+	1.02107i
$172$	−2.04248	−	1.24748i	−0.155737	−	0.0951198i
$173$	−16.4718	+	9.51000i	−1.25233	+	0.723032i	−0.971571	−	0.236747i	$-0.923919\pi$
$173$	−16.4718	+	9.51000i	−1.25233	+	0.723032i	−0.280757	+	0.959779i	$0.590585\pi$
$174$	−5.66737	−	1.05026i	−0.429642	−	0.0796198i
$175$	1.61615	−	2.79925i	0.122169	−	0.211603i
$176$	0.396546	−	8.01993i	0.0298908	−	0.604525i
$177$	0.772728	−	0.927750i	0.0580818	−	0.0697340i
$178$	−5.46547	+	9.20209i	−0.409654	+	0.689726i
$179$		−	2.12111i		−	0.158539i	−0.996853	−	0.0792697i	$-0.974741\pi$
$179$		−	2.12111i		−	0.158539i	0.996853	−	0.0792697i	$-0.0252588\pi$
$180$	−7.87623	+	20.5209i	−0.587059	+	1.52954i
$181$		−	1.66297i		−	0.123608i	−0.998088	−	0.0618039i	$-0.980315\pi$
$181$		−	1.66297i		−	0.123608i	0.998088	−	0.0618039i	$-0.0196853\pi$
$182$	−0.214388	−	0.127333i	−0.0158915	−	0.00943857i
$183$	−2.92781	−	7.95372i	−0.216430	−	0.587956i
$184$	−8.95152	+	14.2572i	−0.659915	+	1.05106i
$185$	−10.5219	+	18.2245i	−0.773588	+	1.33989i
$186$	2.73421	−	0.968301i	0.200482	−	0.0709993i
$187$	7.10164	−	4.10013i	0.519323	−	0.299831i
$188$	6.83214	−	11.1861i	0.498285	−	0.815830i
$189$	1.99444	−	0.0218184i	0.145074	−	0.00158705i
$190$	11.9744	+	21.3449i	0.868717	+	1.54852i
$191$	−8.69755	−	15.0646i	−0.629333	−	1.09004i	−0.987686	−	0.156450i	$-0.949995\pi$
$191$	−8.69755	−	15.0646i	−0.629333	−	1.09004i	0.358353	−	0.933586i	$-0.383338\pi$
$192$	3.36088	−	13.4426i	0.242550	−	0.970139i
$193$	−1.41709	+	2.45447i	−0.102004	+	0.176677i	−0.912510	−	0.409054i	$-0.865859\pi$
$193$	−1.41709	+	2.45447i	−0.102004	+	0.176677i	0.810506	+	0.585730i	$0.199192\pi$
$194$	8.44252	+	0.104281i	0.606138	+	0.00748692i
$195$	−2.73519	+	1.00684i	−0.195871	+	0.0721010i
$196$	−13.7011	−	0.338520i	−0.978652	−	0.0241800i
$197$		−	12.5991i		−	0.897646i	−0.893621	−	0.448823i	$-0.851843\pi$
$197$		−	12.5991i		−	0.897646i	0.893621	−	0.448823i	$-0.148157\pi$
$198$	−2.95337	+	7.98835i	−0.209887	+	0.567707i
$199$	17.2733			1.22447			0.612237	−	0.790674i	$-0.290270\pi$
$199$	17.2733			1.22447			0.612237	+	0.790674i	$0.290270\pi$
$200$	11.1364	+	21.0534i	0.787459	+	1.48870i
$201$	11.3654	−	13.6454i	0.801650	−	0.962475i
$202$	−0.0970662	+	7.85843i	−0.00682955	+	0.552917i
$203$	0.782227	+	0.451619i	0.0549016	+	0.0316975i
$204$	13.3963	−	4.55878i	0.937925	−	0.319178i
$205$	30.1577	−	17.4116i	2.10631	−	1.21608i
$206$	−8.50211	−	15.1553i	−0.592370	−	1.05592i
$207$	13.5941	−	11.5768i	0.944857	−	0.804644i
$208$	1.63462	−	0.838975i	0.113341	−	0.0581725i
$209$	4.74153	+	8.21258i	0.327979	+	0.568076i
$210$	2.23697	−	2.61927i	0.154366	−	0.180747i
$211$	15.2192	+	8.78678i	1.04773	+	0.604907i	0.922013	−	0.387159i	$-0.126544\pi$
$211$	15.2192	+	8.78678i	1.04773	+	0.604907i	0.125717	+	0.992066i	$0.459877\pi$
$212$	−13.4141	+	7.30897i	−0.921287	+	0.501982i
$213$	−1.10099	+	6.37997i	−0.0754386	+	0.437149i
$214$	8.04662	+	4.77919i	0.550055	+	0.326699i
$215$	4.38385			0.298976
$216$	−7.67831	+	12.5317i	−0.522443	+	0.852674i
$217$	−0.454545			−0.0308565
$218$	−8.53043	−	5.06654i	−0.577754	−	0.343150i
$219$	−0.790193	+	4.57898i	−0.0533963	+	0.309419i
$220$	7.03721	+	12.9154i	0.474449	+	0.870755i
$221$	1.62499	+	0.938188i	0.109309	+	0.0631094i
$222$	−9.13792	+	10.6996i	−0.613297	+	0.718110i
$223$	12.3137	+	21.3280i	0.824587	+	1.42823i	0.902235	+	0.431245i	$0.141926\pi$
$223$	12.3137	+	21.3280i	0.824587	+	1.42823i	−0.0776484	+	0.996981i	$0.524741\pi$
$224$	−1.19969	+	1.80989i	−0.0801574	+	0.120929i
$225$	−4.56802	−	24.8456i	−0.304535	−	1.65637i
$226$	−5.66575	−	10.0994i	−0.376880	−	0.671804i
$227$	16.9918	−	9.81024i	1.12779	−	0.651128i	0.184410	−	0.982849i	$-0.440963\pi$
$227$	16.9918	−	9.81024i	1.12779	−	0.651128i	0.943378	+	0.331721i	$0.107629\pi$
$228$	5.27193	+	15.4919i	0.349142	+	1.02598i
$229$	−21.3431	−	12.3224i	−1.41039	−	0.814289i	−0.414965	−	0.909837i	$-0.636206\pi$
$229$	−21.3431	−	12.3224i	−1.41039	−	0.814289i	−0.995425	+	0.0955486i	$0.969539\pi$
$230$	0.380851	−	30.8335i	0.0251125	−	2.03310i
$231$	0.854159	−	1.02552i	0.0561995	−	0.0674741i
$232$	−5.88319	+	3.11196i	−0.386250	+	0.204310i
$233$	−20.9222			−1.37066			−0.685330	−	0.728233i	$-0.740342\pi$
$233$	−20.9222			−1.37066			−0.685330	+	0.728233i	$0.740342\pi$
$234$	−1.92089	+	0.328695i	−0.125572	+	0.0214874i
$235$			24.0092i			1.56619i
$236$	0.0344365	−	1.39377i	0.00224162	−	0.0907265i
$237$	−17.4239	+	6.41381i	−1.13180	+	0.416622i
$238$	−2.21734	−	0.0273883i	−0.143729	−	0.00177532i
$239$	−5.14584	+	8.91286i	−0.332857	+	0.576525i	−0.983071	−	0.183226i	$-0.941346\pi$
$239$	−5.14584	+	8.91286i	−0.332857	+	0.576525i	0.650214	+	0.759751i	$0.274679\pi$
$240$	7.58074	+	24.2224i	0.489334	+	1.56355i
$241$	10.2379	+	17.7326i	0.659483	+	1.14226i	0.980750	+	0.195269i	$0.0625579\pi$
$241$	10.2379	+	17.7326i	0.659483	+	1.14226i	−0.321267	+	0.946989i	$0.604109\pi$
$242$	−4.82288	−	8.59696i	−0.310026	−	0.552634i
$243$	11.7568	−	10.2361i	0.754199	−	0.656646i
$244$	−8.35203	−	5.10117i	−0.534684	−	0.326569i
$245$	21.7409	−	12.5521i	1.38897	−	0.801924i
$246$	21.9482	−	7.77282i	1.39937	−	0.495577i
$247$	−1.08495	+	1.87919i	−0.0690339	+	0.119570i
$248$	1.78097	−	2.83657i	0.113092	−	0.180123i
$249$	3.79325	+	10.3048i	0.240387	+	0.653040i
$250$	−15.2371	−	9.04991i	−0.963681	−	0.572367i
$251$			28.0987i			1.77358i	0.462177	+	0.886788i	$0.347068\pi$
$251$			28.0987i			1.77358i	−0.462177	+	0.886788i	$0.652932\pi$
$252$	1.78979	−	1.44947i	0.112746	−	0.0913083i
$253$		−	11.9480i		−	0.751163i
$254$	−15.1739	+	25.5480i	−0.952095	+	1.60302i
$255$	−16.5885	+	19.9165i	−1.03881	+	1.24722i
$256$	−6.59406	−	14.5780i	−0.412129	−	0.911126i
$257$	5.53682	−	9.59006i	0.345378	−	0.598211i	−0.640045	−	0.768338i	$-0.721084\pi$
$257$	5.53682	−	9.59006i	0.345378	−	0.598211i	0.985422	+	0.170126i	$0.0544175\pi$
$258$	2.88212	+	0.534105i	0.179433	+	0.0332519i
$259$	1.90956	−	1.10248i	0.118654	−	0.0685050i
$260$	−1.75423	+	2.87216i	−0.108793	+	0.178124i
$261$	6.94290	−	1.27650i	0.429754	−	0.0790131i
$262$	−7.81936	+	4.38664i	−0.483081	+	0.271008i
$263$	−12.7620	−	22.1044i	−0.786938	−	1.36302i	−0.927834	−	0.372992i	$-0.878332\pi$
$263$	−12.7620	−	22.1044i	−0.786938	−	1.36302i	0.140897	−	0.990024i	$-0.455002\pi$
$264$	3.05301	+	9.34847i	0.187899	+	0.575359i
$265$	13.9907	−	24.2327i	0.859444	−	1.48860i
$266$	0.0316728	−	2.56421i	0.00194198	−	0.157222i
$267$	2.22913	−	12.9173i	0.136420	−	0.790524i
$268$	0.506495	−	20.4997i	0.0309391	−	1.25222i
$269$			18.3998i			1.12185i	0.827865	+	0.560927i	$0.189555\pi$
$269$			18.3998i			1.12185i	−0.827865	+	0.560927i	$0.810445\pi$
$270$	0.0380132	−	26.9205i	0.00231341	−	1.63833i
$271$	−22.4135			−1.36152			−0.680760	−	0.732506i	$-0.738350\pi$
$271$	−22.4135			−1.36152			−0.680760	+	0.732506i	$0.738350\pi$
$272$	8.85877	−	13.7300i	0.537142	−	0.832501i
$273$	0.300944	+	0.0519337i	0.0182139	+	0.00314317i
$274$	−1.36799	−	0.0168972i	−0.0826435	−	0.00102080i
$275$	−14.6392	−	8.45196i	−0.882779	−	0.509673i
$276$	4.00697	−	20.2248i	0.241191	−	1.21739i
$277$	−20.2421	+	11.6868i	−1.21623	+	0.702190i	−0.964109	−	0.265506i	$-0.914461\pi$
$277$	−20.2421	+	11.6868i	−1.21623	+	0.702190i	−0.252119	+	0.967696i	$0.581128\pi$
$278$	7.37968	−	4.13998i	0.442604	−	0.248300i
$279$	−2.70465	+	2.30329i	−0.161923	+	0.137894i
$280$	0.147343	−	3.97464i	0.00880540	−	0.237530i
$281$	5.29466	+	9.17062i	0.315853	+	0.547073i	0.979618	−	0.200867i	$-0.0643760\pi$
$281$	5.29466	+	9.17062i	0.315853	+	0.547073i	−0.663765	+	0.747941i	$0.731043\pi$
$282$	−2.92515	+	15.7846i	−0.174190	+	0.939960i
$283$	−7.69029	−	4.43999i	−0.457140	−	0.263930i	0.253701	−	0.967283i	$-0.418352\pi$
$283$	−7.69029	−	4.43999i	−0.457140	−	0.263930i	−0.710841	+	0.703353i	$0.751686\pi$
$284$	3.57687	+	6.56463i	0.212248	+	0.389539i
$285$	−23.0321	−	19.1836i	−1.36430	−	1.13634i
$286$	−0.665915	+	1.12119i	−0.0393764	+	0.0662971i
$287$	−3.64876			−0.215379
$288$	2.03276	+	16.8484i	0.119781	+	0.992800i
$289$	−0.313160			−0.0184212
$290$	6.22545	−	10.4817i	0.365571	−	0.615504i
$291$	−9.70414	+	3.57214i	−0.568867	+	0.209403i
$292$	2.56716	+	4.71151i	0.150232	+	0.275720i
$293$	−9.82117	−	5.67026i	−0.573759	−	0.331260i	0.184890	−	0.982759i	$-0.440807\pi$
$293$	−9.82117	−	5.67026i	−0.573759	−	0.331260i	−0.758649	+	0.651499i	$0.774140\pi$
$294$	15.8226	−	5.60346i	0.922793	−	0.326801i
$295$	1.27688	+	2.21162i	0.0743428	+	0.128765i
$296$	−0.601887	+	16.2362i	−0.0349840	+	0.943712i
$297$	−0.114103	−	10.4303i	−0.00662095	−	0.605227i
$298$	9.16843	−	5.14347i	0.531113	−	0.297953i
$299$	2.36765	−	1.36696i	0.136925	−	0.0790534i
$300$	−21.9458	−	19.2165i	−1.26704	−	1.10946i
$301$	−0.397799	−	0.229669i	−0.0229287	−	0.0132379i
$302$	1.39394	+	0.0172177i	0.0802122	+	0.000990770i
$303$	−3.32501	−	9.03277i	−0.191017	−	0.518919i
$304$	15.8778	+	10.2446i	0.910654	+	0.587567i
$305$	17.9263			1.02646
$306$	−13.3325	+	11.0728i	−0.762168	+	0.632992i
$307$			0.628678i			0.0358805i	0.999839	+	0.0179403i	$0.00571087\pi$
$307$			0.628678i			0.0358805i	−0.999839	+	0.0179403i	$0.994289\pi$
$308$	0.0380654	−	1.54064i	0.00216898	−	0.0877863i
$309$	16.3533	+	13.6207i	0.930307	+	0.774857i
$310$	−0.0757729	+	6.13454i	−0.00430361	+	0.348418i
$311$	−9.64443	+	16.7046i	−0.546885	+	0.947233i	0.451600	+	0.892220i	$0.350853\pi$
$311$	−9.64443	+	16.7046i	−0.546885	+	0.947233i	−0.998486	+	0.0550127i	$0.982480\pi$
$312$	−1.50323	+	1.67455i	−0.0851036	+	0.0948025i
$313$	−2.86959	−	4.97028i	−0.162199	−	0.280937i	0.773458	−	0.633847i	$-0.218525\pi$
$313$	−2.86959	−	4.97028i	−0.162199	−	0.280937i	−0.935657	+	0.352911i	$0.885192\pi$
$314$	−21.6955	+	12.1711i	−1.22435	+	0.686856i
$315$	−1.41391	+	3.97464i	−0.0796649	+	0.223946i
$316$	−11.1749	+	18.2964i	−0.628638	+	1.02925i
$317$	−10.8187	+	6.24618i	−0.607639	+	0.350821i	−0.772041	−	0.635573i	$-0.780764\pi$
$317$	−10.8187	+	6.24618i	−0.607639	+	0.350821i	0.164402	+	0.986393i	$0.447431\pi$
$318$	12.1505	−	14.2270i	0.681363	−	0.797809i
$319$	2.36183	−	4.09081i	0.132237	−	0.229042i
$320$	24.2263	+	16.4927i	1.35429	+	0.921968i
$321$	−11.2953	−	1.94922i	−0.630442	−	0.108795i
$322$	−1.64992	+	2.77793i	−0.0919464	+	0.154808i
$323$			19.2972i			1.07373i
$324$	3.30484	−	17.6940i	0.183602	−	0.983001i
$325$		−	3.86794i		−	0.214555i
$326$	21.7470	+	12.9164i	1.20445	+	0.715371i
$327$	11.9744	+	2.06642i	0.662188	+	0.114273i
$328$	14.2963	−	22.7700i	0.789382	−	1.25726i
$329$	1.25784	−	2.17864i	0.0693468	−	0.120112i
$330$	−13.6980	−	11.6987i	−0.754050	−	0.643991i
$331$	−3.00014	+	1.73213i	−0.164902	+	0.0952065i	−0.580180	−	0.814488i	$-0.697018\pi$
$331$	−3.00014	+	1.73213i	−0.164902	+	0.0952065i	0.415278	+	0.909695i	$0.363684\pi$
$332$	10.8208	+	6.60904i	0.593870	+	0.362718i
$333$	5.77576	−	16.2362i	0.316510	−	0.889740i
$334$	−1.43972	−	2.56635i	−0.0787778	−	0.140425i
$335$	18.7805	+	32.5287i	1.02609	+	1.77723i
$336$	0.581118	−	2.59514i	0.0317026	−	0.141576i
$337$	−9.30453	+	16.1159i	−0.506850	+	0.877890i	0.493119	+	0.869962i	$0.335857\pi$
$337$	−9.30453	+	16.1159i	−0.506850	+	0.877890i	−0.999969	+	0.00792778i	$0.997476\pi$
$338$	18.0850	+	0.223383i	0.983695	+	0.0121505i
$339$	10.8977	+	9.07678i	0.591884	+	0.492983i
$340$	−0.739265	+	29.9207i	−0.0400923	+	1.62268i
$341$			2.37713i			0.128729i
$342$	−12.8050	−	15.4181i	−0.692416	−	0.833718i
$343$	−5.31737			−0.287111
$344$	2.99187	−	1.58258i	0.161311	−	0.0853268i
$345$	13.0461	+	35.4411i	0.702376	+	1.90809i
$346$	0.332219	−	26.8963i	0.0178602	−	1.44595i
$347$	−0.0408752	−	0.0235993i	−0.00219430	−	0.00126688i	0.498902	−	0.866658i	$-0.333737\pi$
$347$	−0.0408752	−	0.0235993i	−0.00219430	−	0.00126688i	−0.501097	+	0.865391i	$0.667070\pi$
$348$	5.36989	−	6.13259i	0.287856	−	0.328741i
$349$	−12.8884	+	7.44113i	−0.689901	+	0.398314i	−0.803575	−	0.595204i	$-0.797071\pi$
$349$	−12.8884	+	7.44113i	−0.689901	+	0.398314i	0.113674	+	0.993518i	$0.463738\pi$
$350$	2.23651	+	3.98666i	0.119546	+	0.213096i
$351$	2.05384	−	1.21594i	0.109626	−	0.0649019i
$352$	9.46520	+	6.27400i	0.504497	+	0.334405i
$353$	−9.25423	−	16.0288i	−0.492553	−	0.853127i	0.507410	−	0.861705i	$-0.330603\pi$
$353$	−9.25423	−	16.0288i	−0.492553	−	0.853127i	−0.999963	+	0.00857792i	$0.997270\pi$
$354$	0.570020	+	1.60958i	0.0302962	+	0.0855480i
$355$	−11.8590	−	6.84680i	−0.629411	−	0.363390i
$356$	−7.24194	−	13.2911i	−0.383822	−	0.704428i
$357$	2.54870	−	0.938188i	0.134891	−	0.0496542i
$358$	2.57910	+	1.53182i	0.136310	+	0.0809594i
$359$	31.3426			1.65420			0.827101	−	0.562054i	$-0.189989\pi$
$359$	31.3426			1.65420			0.827101	+	0.562054i	$0.189989\pi$
$360$	−19.2637	−	24.3967i	−1.01529	−	1.28582i
$361$	−3.31599			−0.174526
$362$	2.02204	+	1.20096i	0.106276	+	0.0631213i
$363$	9.27652	+	7.72646i	0.486891	+	0.405534i
$364$	0.309654	−	0.168721i	0.0162303	−	0.00884339i
$365$	−8.51135	−	4.91403i	−0.445504	−	0.257212i
$366$	11.7855	+	2.18404i	0.616037	+	0.114162i
$367$	−10.2308	−	17.7203i	−0.534043	−	0.924990i	−0.999209	−	0.0397663i	$-0.987339\pi$
$367$	−10.2308	−	17.7203i	−0.534043	−	0.924990i	0.465166	−	0.885224i	$-0.345995\pi$
$368$	−10.8710	−	21.1806i	−0.566690	−	1.10411i
$369$	−21.7109	+	18.4891i	−1.13023	+	0.962505i
$370$	−14.5608	−	25.9552i	−0.756980	−	1.34935i
$371$	−2.53909	+	1.46594i	−0.131823	+	0.0761081i
$372$	−0.797214	+	4.02386i	−0.0413336	+	0.208627i
$373$	20.6021	+	11.8946i	1.06674	+	0.615880i	0.927288	−	0.374349i	$-0.122134\pi$
$373$	20.6021	+	11.8946i	1.06674	+	0.615880i	0.139448	+	0.990229i	$0.455467\pi$
$374$	−0.143233	+	11.5960i	−0.00740638	+	0.599617i
$375$	21.3889	+	3.69107i	1.10452	+	0.190606i
$376$	8.66735	+	16.3857i	0.446985	+	0.845028i
$377$	1.08086			0.0556673
$378$	−1.41381	+	2.44083i	−0.0727186	+	0.125543i
$379$		−	24.0988i		−	1.23787i	−0.785441	−	0.618937i	$-0.787564\pi$
$379$		−	24.0988i		−	1.23787i	0.785441	−	0.618937i	$-0.212436\pi$
$380$	−34.6013	−	0.854911i	−1.77501	−	0.0438560i
$381$	6.18878	−	35.8625i	0.317061	−	1.83729i
$382$	24.5985	+	0.303837i	1.25857	+	0.0155457i
$383$	9.39161	−	16.2667i	0.479889	−	0.831192i	−0.519845	−	0.854261i	$-0.674010\pi$
$383$	9.39161	−	16.2667i	0.479889	−	0.831192i	0.999734	+	0.0230686i	$0.00734361\pi$
$384$	13.9180	+	13.7945i	0.710249	+	0.703950i
$385$	1.41144	+	2.44468i	0.0719336	+	0.124593i
$386$	−1.96105	−	3.49564i	−0.0998146	−	0.177923i
$387$	−3.53078	+	0.649157i	−0.179480	+	0.0329985i
$388$	−6.22381	+	10.1901i	−0.315966	+	0.517324i
$389$	15.0467	−	8.68720i	0.762897	−	0.440459i	−0.0674382	−	0.997723i	$-0.521483\pi$
$389$	15.0467	−	8.68720i	0.762897	−	0.440459i	0.830335	+	0.557265i	$0.188149\pi$
$390$	0.751065	−	4.05288i	0.0380317	−	0.205225i
$391$	12.1566	−	21.0558i	0.614783	−	1.06484i
$392$	10.3063	−	16.4150i	0.520546	−	0.829082i
$393$	7.02759	−	8.43744i	0.354495	−	0.425613i
$394$	15.3194	+	9.09879i	0.771782	+	0.458390i
$395$		−	39.2703i		−	1.97591i
$396$	−7.58031	−	9.36007i	−0.380925	−	0.470361i
$397$			26.2401i			1.31696i	0.752600	+	0.658478i	$0.228799\pi$
$397$			26.2401i			1.31696i	−0.752600	+	0.658478i	$0.771201\pi$
$398$	−12.4744	+	21.0030i	−0.625288	+	1.05278i
$399$	1.08495	+	2.94740i	0.0543156	+	0.147555i
$400$	−33.6416	−	1.66341i	−1.68208	−	0.0831707i
$401$	10.8194	−	18.7398i	0.540296	−	0.935820i	−0.458591	−	0.888648i	$-0.651646\pi$
$401$	10.8194	−	18.7398i	0.540296	−	0.935820i	0.998887	−	0.0471725i	$-0.0150210\pi$
$402$	8.38391	+	23.6738i	0.418152	+	1.18074i
$403$	−0.471060	+	0.271967i	−0.0234652	+	0.0135476i
$404$	−9.48511	−	5.79322i	−0.471902	−	0.288224i
$405$	11.7274	+	30.8147i	0.582737	+	1.53119i
$406$	−1.11404	+	0.624974i	−0.0552889	+	0.0310170i
$407$	−5.76566	−	9.98642i	−0.285793	−	0.495008i
$408$	−4.13140	+	19.5810i	−0.204535	+	0.969404i
$409$	−6.00563	+	10.4021i	−0.296959	+	0.514348i	−0.975439	−	0.220271i	$-0.929306\pi$
$409$	−6.00563	+	10.4021i	−0.296959	+	0.514348i	0.678480	+	0.734619i	$0.262639\pi$
$410$	−0.608250	+	49.2436i	−0.0300393	+	2.43197i
$411$	1.57242	−	0.578816i	0.0775618	−	0.0285509i
$412$	24.5677	+	0.607006i	1.21036	+	0.0299050i
$413$		−	0.267582i		−	0.0131668i
$414$	4.25905	+	24.8899i	0.209321	+	1.22327i
$415$	−23.2252			−1.14008
$416$	−0.160366	+	2.59346i	−0.00786258	+	0.127155i
$417$	−6.63243	+	7.96301i	−0.324791	+	0.389950i
$418$	−13.4101	−	0.165639i	−0.655907	−	0.00810167i
$419$	−1.38092	−	0.797277i	−0.0674625	−	0.0389495i	0.465889	−	0.884843i	$-0.345734\pi$
$419$	−1.38092	−	0.797277i	−0.0674625	−	0.0389495i	−0.533352	+	0.845893i	$0.679068\pi$
$420$	1.56933	+	4.61156i	0.0765752	+	0.225021i
$421$	−15.6612	+	9.04197i	−0.763278	+	0.440679i	−0.830471	−	0.557061i	$-0.811929\pi$
$421$	−15.6612	+	9.04197i	−0.763278	+	0.440679i	0.0671934	+	0.997740i	$0.478596\pi$
$422$	−21.6750	+	12.1596i	−1.05512	+	0.591920i
$423$	−3.55526	−	19.3372i	−0.172863	−	0.940205i
$424$	0.800314	−	21.5889i	0.0388667	−	1.04845i
$425$	−17.1990	−	29.7896i	−0.834276	−	1.44501i
$426$	−6.96241	−	5.94620i	−0.337330	−	0.288094i
$427$	−1.62667	−	0.939156i	−0.0787199	−	0.0454489i
$428$	−11.6222	+	6.33259i	−0.561781	+	0.306098i
$429$	0.271598	−	1.57384i	0.0131129	−	0.0759859i
$430$	−3.16593	+	5.33041i	−0.152675	+	0.257055i
$431$	−34.7451			−1.67361			−0.836806	−	0.547499i	$-0.815580\pi$
$431$	−34.7451			−1.67361			−0.836806	+	0.547499i	$0.815580\pi$
$432$	−9.69241	−	18.3863i	−0.466326	−	0.884613i
$433$	12.7197			0.611270			0.305635	−	0.952149i	$-0.401131\pi$
$433$	12.7197			0.611270			0.305635	+	0.952149i	$0.401131\pi$
$434$	0.328263	−	0.552689i	0.0157571	−	0.0265299i
$435$	−2.53909	+	14.7134i	−0.121740	+	0.705455i
$436$	12.3210	−	6.71335i	0.590069	−	0.321511i
$437$	24.3496	+	14.0583i	1.16480	+	0.672498i
$438$	−4.99700	−	4.26766i	−0.238766	−	0.203916i
$439$	−7.45900	−	12.9194i	−0.355999	−	0.616608i	0.631290	−	0.775547i	$-0.282526\pi$
$439$	−7.45900	−	12.9194i	−0.355999	−	0.616608i	−0.987288	+	0.158939i	$0.949193\pi$
$440$	−20.7862	−	0.770557i	−0.990942	−	0.0367349i
$441$	−15.6515	+	13.3289i	−0.745311	+	0.634710i
$442$	−2.31429	+	1.29831i	−0.110080	+	0.0617545i
$443$	−3.48405	+	2.01152i	−0.165532	+	0.0955702i	−0.580478	−	0.814276i	$-0.697134\pi$
$443$	−3.48405	+	2.01152i	−0.165532	+	0.0955702i	0.414945	+	0.909846i	$0.363801\pi$
$444$	−6.41062	−	18.8380i	−0.304235	−	0.894012i
$445$	24.0104	+	13.8624i	1.13820	+	0.657142i
$446$	−34.8258	−	0.430163i	−1.64905	−	0.0203688i
$447$	−8.24006	+	9.89315i	−0.389741	+	0.467930i
$448$	−1.33429	−	2.76579i	−0.0630394	−	0.130671i
$449$	10.9179			0.515246			0.257623	−	0.966245i	$-0.417061\pi$
$449$	10.9179			0.515246			0.257623	+	0.966245i	$0.417061\pi$
$450$	33.5091	+	12.3886i	1.57964	+	0.584006i
$451$			19.0819i			0.898531i
$452$	16.3718	+	0.404505i	0.770063	+	0.0190263i
$453$	−1.60225	+	0.589795i	−0.0752801	+	0.0277110i
$454$	−0.342707	+	27.7454i	−0.0160841	+	1.30216i
$455$	−0.322964	+	0.559390i	−0.0151408	+	0.0262246i
$456$	−22.6441	−	4.77769i	−1.06041	−	0.223736i
$457$	−0.815204	−	1.41197i	−0.0381336	−	0.0660494i	0.846329	−	0.532661i	$-0.178808\pi$
$457$	−0.815204	−	1.41197i	−0.0381336	−	0.0660494i	−0.884462	+	0.466612i	$0.845475\pi$
$458$	30.3966	−	17.0524i	1.42034	−	0.796807i
$459$	10.4113	−	18.4973i	0.485958	−	0.863379i
$460$	37.2159	+	22.7304i	1.73520	+	1.05981i
$461$	10.1812	−	5.87811i	0.474185	−	0.273771i	−0.243805	−	0.969824i	$-0.578396\pi$
$461$	10.1812	−	5.87811i	0.474185	−	0.273771i	0.717990	+	0.696054i	$0.245062\pi$
$462$	0.630090	+	1.77920i	0.0293144	+	0.0827757i
$463$	−10.6473	+	18.4416i	−0.494820	+	0.857053i	−0.999982	−	0.00597113i	$-0.998099\pi$
$463$	−10.6473	+	18.4416i	−0.494820	+	0.857053i	0.505162	+	0.863024i	$0.331433\pi$
$464$	0.464827	−	9.40087i	0.0215791	−	0.436424i
$465$	−2.59560	−	7.05126i	−0.120368	−	0.326994i
$466$	15.1096	−	25.4397i	0.699939	−	1.17847i
$467$		−	18.9230i		−	0.875650i	−0.899060	−	0.437825i	$-0.855749\pi$
$467$		−	18.9230i		−	0.875650i	0.899060	−	0.437825i	$-0.144251\pi$
$468$	0.987561	−	2.57302i	0.0456500	−	0.118938i
$469$		−	3.93562i		−	0.181730i
$470$	−29.1932	−	17.3389i	−1.34658	−	0.799786i
$471$	19.4987	−	23.4104i	0.898451	−	1.07870i
$472$	1.66984	+	1.04842i	0.0768605	+	0.0482575i
$473$	−1.20110	+	2.08037i	−0.0552267	+	0.0956554i
$474$	4.78448	−	25.8179i	0.219759	−	1.18586i
$475$	34.4497	−	19.8896i	1.58066	−	0.912595i
$476$	1.63462	−	2.67633i	0.0749228	−	0.122669i
$477$	−7.67988	+	21.5889i	−0.351638	+	0.988487i
$478$	−7.12108	−	12.6936i	−0.325711	−	0.580592i
$479$	14.9759	+	25.9391i	0.684268	+	1.18519i	0.973666	+	0.227978i	$0.0732115\pi$
$479$	14.9759	+	25.9391i	0.684268	+	1.18519i	−0.289398	+	0.957209i	$0.593455\pi$
$480$	−34.9271	−	8.27537i	−1.59420	−	0.377717i
$481$	1.31929	−	2.28508i	0.0601546	−	0.104191i
$482$	−28.9550	−	0.357648i	−1.31886	−	0.0162904i
$483$	0.672931	−	3.89947i	0.0306194	−	0.177432i
$484$	13.9362	+	0.344328i	0.633463	+	0.0156513i
$485$		−	21.8714i		−	0.993131i
$486$	3.95575	+	21.6876i	0.179437	+	0.983770i
$487$	−17.3370			−0.785614			−0.392807	−	0.919621i	$-0.628496\pi$
$487$	−17.3370			−0.785614			−0.392807	+	0.919621i	$0.628496\pi$
$488$	12.2343	−	6.47142i	0.553819	−	0.292947i
$489$	−30.5269	−	5.26802i	−1.38048	−	0.238228i
$490$	−0.438491	+	35.5000i	−0.0198090	+	1.60373i
$491$	−31.1204	−	17.9674i	−1.40444	−	0.810856i	−0.409599	−	0.912265i	$-0.634332\pi$
$491$	−31.1204	−	17.9674i	−1.40444	−	0.810856i	−0.994845	+	0.101409i	$0.967665\pi$
$492$	−6.39946	+	32.3006i	−0.288510	+	1.45622i
$493$	8.32446	−	4.80613i	0.374915	−	0.216457i
$494$	−1.50141	−	2.67633i	−0.0675518	−	0.120414i
$495$	20.7862	+	7.39433i	0.934269	+	0.332350i
$496$	2.16286	+	4.21403i	0.0971154	+	0.189215i
$497$	0.717405	+	1.24258i	0.0321800	+	0.0557374i
$498$	−15.2692	−	2.82963i	−0.684229	−	0.126799i
$499$	−10.4956	−	6.05962i	−0.469846	−	0.271266i	0.246329	−	0.969186i	$-0.420776\pi$
$499$	−10.4956	−	6.05962i	−0.469846	−	0.271266i	−0.716175	+	0.697920i	$0.754109\pi$
$500$	22.0079	−	11.9915i	0.984223	−	0.536274i
$501$	2.76921	+	2.30649i	0.123719	+	0.103046i
$502$	−34.1657	−	20.2923i	−1.52489	−	0.905691i
$503$	32.3442			1.44215			0.721077	−	0.692855i	$-0.243647\pi$
$503$	32.3442			1.44215			0.721077	+	0.692855i	$0.243647\pi$
$504$	0.469891	+	3.22302i	0.0209306	+	0.143565i
$505$	20.3583			0.905932
$506$	14.5278	+	8.62858i	0.645837	+	0.383587i
$507$	−20.7876	+	7.65201i	−0.923208	+	0.339838i
$508$	−20.1060	−	36.9004i	−0.892057	−	1.63719i
$509$	−2.90310	−	1.67610i	−0.128677	−	0.0742919i	0.434280	−	0.900778i	$-0.357003\pi$
$509$	−2.90310	−	1.67610i	−0.128677	−	0.0742919i	−0.562957	+	0.826486i	$0.690336\pi$
$510$	−12.2369	−	34.5536i	−0.541860	−	1.53006i
$511$	0.514890	+	0.891816i	0.0227774	+	0.0394516i
$512$	22.4878	+	2.51011i	0.993828	+	0.110932i
$513$	21.3909	+	12.0400i	0.944431	+	0.531578i
$514$	7.66215	+	13.6581i	0.337963	+	0.602432i
$515$	−38.9838	+	22.5073i	−1.71783	+	0.991792i
$516$	−2.73084	+	3.11870i	−0.120218	+	0.137293i
$517$	−11.3936	−	6.57811i	−0.501091	−	0.289305i
$518$	−0.0385138	+	3.11806i	−0.00169220	+	0.137000i
$519$	11.3802	+	30.9156i	0.499535	+	1.35704i
$520$	−2.22544	−	4.20721i	−0.0975920	−	0.184498i
$521$	21.5651			0.944786			0.472393	−	0.881388i	$-0.343390\pi$
$521$	21.5651			0.944786			0.472393	+	0.881388i	$0.343390\pi$
$522$	−3.46190	+	9.36385i	−0.151523	+	0.409845i
$523$			24.9549i			1.09120i	0.838046	+	0.545600i	$0.183698\pi$
$523$			24.9549i			1.09120i	−0.838046	+	0.545600i	$0.816302\pi$
$524$	0.313183	−	12.6756i	0.0136815	−	0.553738i
$525$	−4.30179	−	3.58298i	−0.187746	−	0.156374i
$526$	36.0936	+	0.445823i	1.57376	+	0.0194388i
$527$	−2.41863	+	4.18919i	−0.105357	+	0.182484i
$528$	−13.5718	−	3.03907i	−0.590636	−	0.132259i
$529$	−6.21238	−	10.7602i	−0.270104	−	0.467833i
$530$	19.3611	+	34.5119i	0.840993	+	1.49910i
$531$	−1.35590	−	1.59217i	−0.0588411	−	0.0690944i
$532$	3.09500	+	1.89033i	0.134185	+	0.0819564i
$533$	−3.78133	+	2.18315i	−0.163787	+	0.0945627i
$534$	14.0965	+	12.0390i	0.610015	+	0.520979i
$535$	12.1218	−	20.9955i	0.524070	−	0.907716i
$536$	24.5601	+	15.4203i	1.06084	+	0.666055i
$537$	−3.62036	−	0.624764i	−0.156230	−	0.0269606i
$538$	−22.3726	−	13.2879i	−0.964552	−	0.572884i
$539$			13.7562i			0.592523i
$540$	32.7057	+	19.4877i	1.40743	+	0.838616i
$541$		−	41.9065i		−	1.80170i	−0.434131	−	0.900850i	$-0.642945\pi$
$541$		−	41.9065i		−	1.80170i	0.434131	−	0.900850i	$-0.357055\pi$
$542$	16.1865	−	27.2529i	0.695272	−	1.17061i
$543$	−2.83840	−	0.489821i	−0.121807	−	0.0210202i
$544$	10.2969	+	20.6870i	0.441475	+	0.886949i
$545$	−12.8506	+	22.2579i	−0.550460	+	0.953424i
$546$	−0.280483	+	0.328417i	−0.0120035	+	0.0140550i
$547$	25.7251	−	14.8524i	1.09993	−	0.635043i	0.163726	−	0.986506i	$-0.447649\pi$
$547$	25.7251	−	14.8524i	1.09993	−	0.635043i	0.936202	+	0.351462i	$0.114316\pi$
$548$	1.00848	−	1.65116i	0.0430802	−	0.0705342i
$549$	−14.4380	+	2.65451i	−0.616197	+	0.113292i
$550$	20.8490	−	11.6963i	0.889006	−	0.498731i
$551$	5.55797	+	9.62669i	0.236778	+	0.410111i
$552$	21.6979	+	19.4781i	0.923525	+	0.829041i
$553$	−2.05737	+	3.56346i	−0.0874881	+	0.151534i
$554$	0.408262	−	33.0527i	0.0173454	−	1.40427i
$555$	28.0068	+	23.3270i	1.18882	+	0.990177i
$556$	−0.295573	+	11.9629i	−0.0125351	+	0.507340i
$557$			21.9632i			0.930609i	0.885151	+	0.465305i	$0.154055\pi$
$557$			21.9632i			0.930609i	−0.885151	+	0.465305i	$0.845945\pi$
$558$	−0.847368	−	4.95202i	−0.0358720	−	0.209636i
$559$	−0.549669			−0.0232485
$560$	4.72643	+	3.04956i	0.199728	+	0.128868i
$561$	−4.90644	−	13.3289i	−0.207150	−	0.562747i
$562$	−14.9744	−	0.184962i	−0.631658	−	0.00780214i
$563$	23.8394	+	13.7637i	1.00471	+	0.580069i	0.909638	−	0.415401i	$-0.136359\pi$
$563$	23.8394	+	13.7637i	1.00471	+	0.580069i	0.0950710	+	0.995470i	$0.469692\pi$
$564$	−17.0803	−	14.9561i	−0.719211	−	0.629764i
$565$	−25.9786	+	14.9988i	−1.09293	+	0.631002i
$566$	10.9524	−	6.14429i	0.460365	−	0.258264i
$567$	0.550212	−	3.41057i	0.0231067	−	0.143231i
$568$	−10.5652	−	0.391658i	−0.443305	−	0.0164336i
$569$	8.83572	+	15.3039i	0.370413	+	0.641574i	0.989629	−	0.143647i	$-0.0458829\pi$
$569$	8.83572	+	15.3039i	0.370413	+	0.641574i	−0.619216	+	0.785221i	$0.712550\pi$
$570$	39.9590	−	14.1512i	1.67370	−	0.592728i
$571$	−3.92630	−	2.26685i	−0.164311	−	0.0948648i	0.415590	−	0.909552i	$-0.363575\pi$
$571$	−3.92630	−	2.26685i	−0.164311	−	0.0948648i	−0.579900	+	0.814687i	$0.696909\pi$
$572$	−0.882361	−	1.61940i	−0.0368934	−	0.0677103i
$573$	−28.2744	+	10.4080i	−1.18118	+	0.434799i
$574$	2.63506	−	4.43659i	0.109985	−	0.185180i
$575$	−50.1188			−2.09010
$576$	−21.9543	−	9.69589i	−0.914761	−	0.403995i
$577$	23.3909			0.973776			0.486888	−	0.873464i	$-0.338132\pi$
$577$	23.3909			0.973776			0.486888	+	0.873464i	$0.338132\pi$
$578$	0.226158	−	0.380776i	0.00940691	−	0.0158382i
$579$	3.77195	+	3.14168i	0.156757	+	0.130564i
$580$	8.24894	+	15.1393i	0.342519	+	0.628624i
$581$	2.10750	+	1.21676i	0.0874337	+	0.0504799i
$582$	2.66470	−	14.3792i	0.110455	−	0.596036i
$583$	7.66645	+	13.2787i	0.317512	+	0.549947i
$584$	−7.58276	−	0.281098i	−0.313777	−	0.0116319i
$585$	0.912853	+	4.96504i	0.0377418	+	0.205279i
$586$	13.9872	−	7.84680i	0.577807	−	0.324148i
$587$	−7.18259	+	4.14687i	−0.296457	+	0.171160i	−0.640850	−	0.767666i	$-0.721418\pi$
$587$	−7.18259	+	4.14687i	−0.296457	+	0.171160i	0.344393	+	0.938826i	$0.388085\pi$
$588$	−4.61340	+	23.2857i	−0.190254	+	0.960286i
$589$	−4.84453	−	2.79699i	−0.199615	−	0.115248i
$590$	−3.61128	−	0.0446060i	−0.148674	−	0.00183640i
$591$	−21.5044	−	3.71100i	−0.884572	−	0.152650i
$592$	−19.3073	−	12.4573i	−0.793523	−	0.511993i
$593$	−43.5169			−1.78702			−0.893512	−	0.449039i	$-0.851766\pi$
$593$	−43.5169			−1.78702			−0.893512	+	0.449039i	$0.851766\pi$
$594$	12.7648	+	7.39381i	0.523746	+	0.303372i
$595$			5.74432i			0.235494i
$596$	−0.367216	+	14.8626i	−0.0150418	+	0.608794i
$597$	5.08779	−	29.4825i	0.208229	−	1.20664i
$598$	−0.0477530	+	3.86606i	−0.00195276	+	0.158095i
$599$	0.527649	−	0.913915i	0.0215592	−	0.0373416i	−0.855045	−	0.518555i	$-0.826470\pi$
$599$	0.527649	−	0.913915i	0.0215592	−	0.0373416i	0.876604	+	0.481213i	$0.159804\pi$
$600$	39.2145	−	12.8066i	1.60093	−	0.522827i
$601$	17.9922	+	31.1633i	0.733915	+	1.27118i	0.955198	+	0.295969i	$0.0956424\pi$
$601$	17.9922	+	31.1633i	0.733915	+	1.27118i	−0.221282	+	0.975210i	$0.571024\pi$
$602$	0.566541	−	0.317828i	0.0230905	−	0.0129537i
$603$	−19.9427	−	23.4178i	−0.812131	−	0.953648i
$604$	−1.02761	+	1.68248i	−0.0418129	+	0.0684592i
$605$	−22.1138	+	12.7674i	−0.899056	+	0.519070i
$606$	13.3844	+	2.48034i	0.543702	+	0.100757i
$607$	−9.81512	+	17.0003i	−0.398383	+	0.690020i	−0.993527	−	0.113599i	$-0.963762\pi$
$607$	−9.81512	+	17.0003i	−0.398383	+	0.690020i	0.595143	+	0.803620i	$0.297095\pi$
$608$	−23.9232	+	11.9077i	−0.970214	+	0.482920i
$609$	1.00124	−	1.20210i	0.0405721	−	0.0487116i
$610$	−12.9460	+	21.7969i	−0.524169	+	0.882531i
$611$		−	3.01039i		−	0.121787i
$612$	−3.83522	−	24.2078i	−0.155030	−	0.978542i
$613$		−	0.0630655i		−	0.00254719i	−0.999999	−	0.00127360i	$-0.999595\pi$
$613$		−	0.0630655i		−	0.00254719i	0.999999	−	0.00127360i	$-0.000405399\pi$
$614$	−0.764421	−	0.454018i	−0.0308495	−	0.0183227i
$615$	−20.8356	−	56.6024i	−0.840174	−	2.28243i
$616$	1.84581	+	1.15891i	0.0743697	+	0.0466937i
$617$	15.0926	−	26.1412i	0.607606	−	1.05240i	−0.384028	−	0.923322i	$-0.625463\pi$
$617$	15.0926	−	26.1412i	0.607606	−	1.05240i	0.991634	−	0.129083i	$-0.0412034\pi$
$618$	−28.3717	+	10.0476i	−1.14128	+	0.404176i
$619$	−38.2663	+	22.0930i	−1.53805	+	0.887994i	−0.539099	+	0.842243i	$0.681235\pi$
$619$	−38.2663	+	22.0930i	−1.53805	+	0.887994i	−0.998953	+	0.0457517i	$0.985432\pi$
$620$	−7.40437	−	4.52237i	−0.297367	−	0.181623i
$621$	−15.7555	−	26.6127i	−0.632245	−	1.06793i
$622$	−13.3465	−	23.7906i	−0.535144	−	0.953915i
$623$	−1.45250	−	2.51580i	−0.0581932	−	0.100794i
$624$	−0.950511	−	3.03713i	−0.0380509	−	0.121582i
$625$	−1.90220	+	3.29471i	−0.0760881	+	0.131788i
$626$	8.11581	+	0.100245i	0.324373	+	0.00400661i
$627$	15.4140	−	5.67398i	0.615576	−	0.226597i
$628$	0.868954	−	35.1697i	0.0346750	−	1.40342i
$629$		−	23.4653i		−	0.935621i
$630$	−3.81174	−	4.58961i	−0.151863	−	0.182854i
$631$	19.6743			0.783221			0.391610	−	0.920131i	$-0.371918\pi$
$631$	19.6743			0.783221			0.391610	+	0.920131i	$0.371918\pi$
$632$	−14.1766	−	26.8011i	−0.563917	−	1.06609i
$633$	19.4802	−	23.3883i	0.774269	−	0.929601i
$634$	0.218202	−	17.6655i	0.00866591	−	0.701588i
$635$	66.6607	+	38.4866i	2.64535	+	1.52729i
$636$	8.52403	+	25.0484i	0.338000	+	0.993233i
$637$	−2.72598	+	1.57384i	−0.108007	+	0.0623580i
$638$	3.26843	+	5.82610i	0.129398	+	0.230657i
$639$	10.5652	+	3.75839i	0.417952	+	0.148679i
$640$	−37.5495	+	17.5466i	−1.48427	+	0.693589i
$641$	−0.994371	−	1.72230i	−0.0392753	−	0.0680268i	0.845720	−	0.533628i	$-0.179172\pi$
$641$	−0.994371	−	1.72230i	−0.0392753	−	0.0680268i	−0.884995	+	0.465601i	$0.845838\pi$
$642$	10.5273	−	12.3265i	0.415480	−	0.486486i
$643$	−12.9370	−	7.46917i	−0.510185	−	0.294555i	0.222725	−	0.974881i	$-0.428505\pi$
$643$	−12.9370	−	7.46917i	−0.510185	−	0.294555i	−0.732910	+	0.680326i	$0.761838\pi$
$644$	−2.18620	−	4.01233i	−0.0861484	−	0.158108i
$645$	1.29124	−	7.48246i	0.0508427	−	0.294621i
$646$	−23.4639	−	13.9361i	−0.923173	−	0.548307i
$647$	−8.81283			−0.346468			−0.173234	−	0.984881i	$-0.555422\pi$
$647$	−8.81283			−0.346468			−0.173234	+	0.984881i	$0.555422\pi$
$648$	19.1278	+	16.7967i	0.751410	+	0.659835i
$649$	−1.39937			−0.0549302
$650$	4.70310	+	2.79335i	0.184471	+	0.109564i
$651$	−0.133884	+	0.775827i	−0.00524734	+	0.0304071i
$652$	−31.4105	+	17.1146i	−1.23013	+	0.670261i
$653$	18.1802	+	10.4964i	0.711447	+	0.410754i	0.811597	−	0.584218i	$-0.198599\pi$
$653$	18.1802	+	10.4964i	0.711447	+	0.410754i	−0.100150	+	0.994972i	$0.531932\pi$
$654$	−11.1603	+	13.0676i	−0.436402	+	0.510984i
$655$	11.6126	+	20.1136i	0.453742	+	0.785904i
$656$	17.3619	+	33.8272i	0.677868	+	1.32073i
$657$	7.58276	+	2.69744i	0.295832	+	0.105237i
$658$	1.74066	+	3.10280i	0.0678580	+	0.120960i
$659$	40.6209	−	23.4525i	1.58237	−	0.913580i	0.587853	−	0.808968i	$-0.299973\pi$
$659$	40.6209	−	23.4525i	1.58237	−	0.913580i	0.994513	−	0.104612i	$-0.0333601\pi$
$660$	24.1170	−	8.20710i	0.938755	−	0.319461i
$661$	−0.736985	−	0.425498i	−0.0286654	−	0.0165500i	0.485599	−	0.874182i	$-0.338602\pi$
$661$	−0.736985	−	0.425498i	−0.0286654	−	0.0165500i	−0.514264	+	0.857632i	$0.671935\pi$
$662$	0.0605096	−	4.89883i	0.00235177	−	0.190398i
$663$	2.07995	−	2.49723i	0.0807787	−	0.0969843i
$664$	−15.8506	+	8.38433i	−0.615124	+	0.325375i
$665$	−6.64293			−0.257602
$666$	15.5708	+	18.7483i	0.603356	+	0.726483i
$667$		−	14.0053i		−	0.542287i
$668$	4.16021	+	0.102788i	0.160963	+	0.00397700i
$669$	40.0300	−	14.7352i	1.54765	−	0.569698i
$670$	−53.1151	−	0.656070i	−2.05202	−	0.0253462i
$671$	−4.91150	+	8.50697i	−0.189606	+	0.328408i
$672$	2.73580	+	2.58075i	0.105536	+	0.0995545i
$673$	−22.4873	−	38.9491i	−0.866820	−	1.50138i	−0.865229	−	0.501378i	$-0.832827\pi$
$673$	−22.4873	−	38.9491i	−0.866820	−	1.50138i	−0.00159139	−	0.999999i	$-0.500507\pi$
$674$	−12.8761	−	22.9521i	−0.495969	−	0.884083i
$675$	−43.7525	+	0.478635i	−1.68403	+	0.0184227i
$676$	−13.3322	+	21.8286i	−0.512778	+	0.839560i
$677$	−7.29713	+	4.21300i	−0.280451	+	0.161919i	−0.633628	−	0.773638i	$-0.718435\pi$
$677$	−7.29713	+	4.21300i	−0.280451	+	0.161919i	0.353176	+	0.935557i	$0.385102\pi$
$678$	−18.9067	+	6.69569i	−0.726109	+	0.257147i
$679$	−1.14584	+	1.98466i	−0.0439733	+	0.0761641i
$680$	−35.8472	−	22.5070i	−1.37468	−	0.863104i
$681$	−11.7395	−	31.8916i	−0.449857	−	1.22209i
$682$	−2.89040	−	1.71672i	−0.110679	−	0.0657365i
$683$			23.3602i			0.893853i	0.894571	+	0.446926i	$0.147481\pi$
$683$			23.3602i			0.893853i	−0.894571	+	0.446926i	$0.852519\pi$
$684$	27.9947	−	4.43518i	1.07041	−	0.169583i
$685$			3.54396i			0.135408i
$686$	3.84010	−	6.46549i	0.146616	−	0.246854i
$687$	−27.3187	+	32.7993i	−1.04227	+	1.25137i
$688$	−0.236386	+	4.78078i	−0.00901214	+	0.182265i
$689$	−1.75423	+	3.03841i	−0.0668308	+	0.115754i
$690$	−52.5151	−	9.73191i	−1.99922	−	0.370488i
$691$	25.9304	−	14.9709i	0.986439	−	0.569521i	0.0822311	−	0.996613i	$-0.473795\pi$
$691$	25.9304	−	14.9709i	0.986439	−	0.569521i	0.904208	+	0.427092i	$0.140462\pi$
$692$	32.4638	+	19.8279i	1.23409	+	0.753744i
$693$	−1.49879	−	1.75996i	−0.0569343	−	0.0668553i
$694$	0.0582141	−	0.0326580i	0.00220978	−	0.00123968i
$695$	−10.9596	−	18.9826i	−0.415722	−	0.720052i
$696$	3.57870	+	10.9582i	0.135650	+	0.415368i
$697$	−19.4150	+	33.6278i	−0.735396	+	1.27374i
$698$	0.259946	−	21.0451i	0.00983909	−	0.796568i
$699$	−6.16255	+	35.7105i	−0.233089	+	1.35070i
$700$	−6.46262	−	0.159675i	−0.244264	−	0.00603515i
$701$		−	0.718775i		−	0.0271478i	−0.999908	−	0.0135739i	$-0.995679\pi$
$701$		−	0.718775i		−	0.0271478i	0.999908	−	0.0135739i	$-0.00432083\pi$
$702$	−0.00476628	+	3.37543i	−0.000179892	+	0.127397i
$703$	27.1360			1.02346
$704$	−14.4642	+	6.97795i	−0.545141	+	0.262991i
$705$	40.9794	+	7.07181i	1.54337	+	0.266340i
$706$	26.1729	+	0.323284i	0.985031	+	0.0121670i
$707$	−1.84735	−	1.06657i	−0.0694767	−	0.0401124i
$708$	−2.36877	−	0.469305i	−0.0890238	−	0.0176376i
$709$	10.9918	−	6.34613i	0.412807	−	0.238334i	−0.279188	−	0.960236i	$-0.590065\pi$
$709$	10.9918	−	6.34613i	0.412807	−	0.238334i	0.691995	+	0.721902i	$0.256732\pi$
$710$	16.8895	−	9.47496i	0.633851	−	0.355589i
$711$	5.81512	+	31.6286i	0.218084	+	1.18616i
$712$	21.3909	+	0.792974i	0.801658	+	0.0297180i
$713$	3.52400	+	6.10375i	0.131975	+	0.228587i
$714$	−0.699856	+	3.77654i	−0.0261915	+	0.141334i
$715$	2.92544	+	1.68900i	0.109405	+	0.0631652i
$716$	−3.72514	+	2.02972i	−0.139215	+	0.0758542i
$717$	13.6970	+	11.4083i	0.511523	+	0.426050i
$718$	−22.6350	+	38.1101i	−0.844731	+	1.42226i
$719$	7.74226			0.288738			0.144369	−	0.989524i	$-0.453885\pi$
$719$	7.74226			0.288738			0.144369	+	0.989524i	$0.453885\pi$
$720$	43.5762	−	5.80436i	1.62399	−	0.216316i
$721$	4.71662			0.175656
$722$	2.39474	−	4.03197i	0.0891230	−	0.150054i
$723$	33.2819	−	12.2513i	1.23777	−	0.455629i
$724$	−2.92055	+	1.59132i	−0.108541	+	0.0591409i
$725$	−17.1599	−	9.90730i	−0.637304	−	0.367948i
$726$	−16.0940	+	5.69960i	−0.597306	+	0.211532i
$727$	9.91355	+	17.1708i	0.367673	+	0.636828i	0.989201	−	0.146563i	$-0.0468212\pi$
$727$	9.91355	+	17.1708i	0.367673	+	0.636828i	−0.621528	+	0.783392i	$0.713488\pi$
$728$	−0.0184745	+	0.498361i	−0.000684712	+	0.0184705i
$729$	−14.0083	−	23.0818i	−0.518826	−	0.854880i
$730$	12.1218	−	6.80029i	0.448647	−	0.251690i
$731$	−4.23337	+	2.44414i	−0.156577	+	0.0903997i
$732$	−11.1668	+	12.7529i	−0.412739	+	0.471361i
$733$	32.7535	+	18.9102i	1.20978	+	0.698466i	0.962711	−	0.270532i	$-0.0871997\pi$
$733$	32.7535	+	18.9102i	1.20978	+	0.698466i	0.247068	+	0.968998i	$0.420533\pi$
$734$	28.9348	+	0.357399i	1.06800	+	0.0131918i
$735$	−15.0205	−	40.8050i	−0.554040	−	1.50511i
$736$	33.6047	+	2.07794i	1.23869	+	0.0765938i
$737$	−20.5821			−0.758152
$738$	−6.80206	−	39.7512i	−0.250387	−	1.46326i
$739$			6.61431i			0.243311i	0.992572	+	0.121656i	$0.0388204\pi$
$739$			6.61431i			0.243311i	−0.992572	+	0.121656i	$0.961180\pi$
$740$	42.0749	+	1.03956i	1.54670	+	0.0382151i
$741$	2.88788	+	2.40533i	0.106089	+	0.0883620i
$742$	0.0512108	−	4.14600i	0.00188001	−	0.152204i
$743$	−3.30245	+	5.72000i	−0.121155	+	0.209847i	−0.920223	−	0.391394i	$-0.871993\pi$
$743$	−3.30245	+	5.72000i	−0.121155	+	0.209847i	0.799068	+	0.601240i	$0.205326\pi$
$744$	−4.31695	−	3.87530i	−0.158267	−	0.142075i
$745$	−13.6161	−	23.5838i	−0.498856	−	0.864044i
$746$	−29.3413	+	16.4604i	−1.07426	+	0.602658i
$747$	18.7057	−	3.43917i	0.684407	−	0.125833i
$748$	−13.9964	−	8.54858i	−0.511759	−	0.312567i
$749$	−2.19990	+	1.27012i	−0.0803828	+	0.0464090i
$750$	−19.9346	+	23.3415i	−0.727910	+	0.852310i
$751$	12.8675	−	22.2871i	0.469540	−	0.813268i	−0.529853	−	0.848089i	$-0.677753\pi$
$751$	12.8675	−	22.2871i	0.469540	−	0.813268i	0.999394	+	0.0348217i	$0.0110863\pi$
$752$	−26.1830	−	1.29462i	−0.954797	−	0.0472101i
$753$	47.9595	+	8.27636i	1.74774	+	0.301607i
$754$	−0.780578	+	1.31424i	−0.0284270	+	0.0478619i
$755$		−	3.61118i		−	0.131424i
$756$	−1.94682	−	3.48179i	−0.0708052	−	0.126632i
$757$		−	48.0424i		−	1.74613i	−0.487602	−	0.873066i	$-0.662128\pi$
$757$		−	48.0424i		−	1.74613i	0.487602	−	0.873066i	$-0.337872\pi$
$758$	29.3022	+	17.4037i	1.06430	+	0.632130i
$759$	−20.3931	−	3.51922i	−0.740221	−	0.127740i
$760$	26.0279	−	41.4550i	0.944130	−	1.50373i
$761$	−1.20688	+	2.09038i	−0.0437493	+	0.0757761i	−0.887071	−	0.461633i	$-0.847264\pi$
$761$	−1.20688	+	2.09038i	−0.0437493	+	0.0757761i	0.843322	+	0.537409i	$0.180597\pi$
$762$	39.1364	+	33.4242i	1.41776	+	1.21083i
$763$	2.33218	−	1.34648i	0.0844305	−	0.0487459i
$764$	−18.1340	+	29.6904i	−0.656065	+	1.07416i
$765$	29.1078	+	34.1800i	1.05240	+	1.23578i
$766$	12.9966	+	23.1669i	0.469586	+	0.837056i
$767$	−0.160101	−	0.277304i	−0.00578093	−	0.0100129i
$768$	−26.8243	+	6.96099i	−0.967940	+	0.251183i
$769$	16.8464	−	29.1788i	0.607496	−	1.05221i	−0.384156	−	0.923268i	$-0.625507\pi$
$769$	16.8464	−	29.1788i	0.607496	−	1.05221i	0.991652	−	0.128945i	$-0.0411592\pi$
$770$	−3.99185	−	0.0493067i	−0.143856	−	0.00177689i
$771$	−14.7377	−	12.2751i	−0.530765	−	0.442076i
$772$	5.66664	+	0.140008i	0.203947	+	0.00503901i
$773$			18.8545i			0.678149i	0.940759	+	0.339075i	$0.110114\pi$
$773$			18.8545i			0.678149i	−0.940759	+	0.339075i	$0.889886\pi$
$774$	1.76054	−	4.76195i	0.0632812	−	0.171165i
$775$	9.97148			0.358186
$776$	−7.89562	−	14.9267i	−0.283436	−	0.535838i
$777$	−1.31929	−	3.58401i	−0.0473294	−	0.128576i
$778$	−0.303476	+	24.5692i	−0.0108801	+	0.880850i
$779$	−38.8884	−	22.4522i	−1.39332	−	0.804434i
$780$	4.38556	+	3.84014i	0.157028	+	0.137499i
$781$	6.49833	−	3.75181i	0.232529	−	0.134250i
$782$	16.8229	+	29.9874i	0.601585	+	1.07235i
$783$	−0.133751	−	12.2263i	−0.00477986	−	0.436931i
$784$	12.5163	+	24.3862i	0.447010	+	0.870935i
$785$	32.2202	+	55.8070i	1.14999	+	1.99184i
$786$	5.18406	+	14.6383i	0.184909	+	0.522131i
$787$	−14.8124	−	8.55193i	−0.528004	−	0.304843i	0.212199	−	0.977226i	$-0.431937\pi$
$787$	−14.8124	−	8.55193i	−0.528004	−	0.304843i	−0.740203	+	0.672383i	$0.765271\pi$
$788$	−22.1268	+	12.0562i	−0.788233	+	0.429485i
$789$	−41.4873	+	15.2717i	−1.47699	+	0.543687i
$790$	47.7495	+	28.3602i	1.69885	+	1.00901i
$791$	3.14313			0.111757
$792$	16.8554	−	2.45739i	0.598932	−	0.0873194i
$793$	−2.24769			−0.0798178
$794$	−31.9059	−	18.9501i	−1.13230	−	0.672514i
$795$	−37.2400	−	31.0173i	−1.32077	−	1.10007i
$796$	−16.5291	−	30.3358i	−0.585858	−	1.07522i
$797$	3.11800	+	1.80018i	0.110445	+	0.0637656i	0.554205	−	0.832380i	$-0.313022\pi$
$797$	3.11800	+	1.80018i	0.110445	+	0.0637656i	−0.443760	+	0.896146i	$0.646356\pi$
$798$	−4.36733	−	0.809338i	−0.154602	−	0.0286502i
$799$	−13.3859	−	23.1851i	−0.473559	−	0.820228i
$800$	26.3179	−	39.7042i	0.930477	−	1.40375i
$801$	−21.3909	−	7.60945i	−0.755810	−	0.268867i
$802$	14.9725	+	26.6890i	0.528697	+	0.942422i
$803$	4.66393	−	2.69272i	0.164586	−	0.0950240i
$804$	−34.8401	−	6.90258i	−1.22872	−	0.243435i
$805$	7.24829	+	4.18480i	0.255469	+	0.147495i
$806$	0.00950078	−	0.769179i	0.000334651	−	0.0270932i
$807$	31.4052	+	5.41958i	1.10551	+	0.190778i
$808$	13.8940	−	7.34937i	0.488791	−	0.258550i
$809$	13.5918			0.477864			0.238932	−	0.971036i	$-0.423203\pi$
$809$	13.5918			0.477864			0.238932	+	0.971036i	$0.423203\pi$
$810$	−45.9374	−	7.99421i	−1.61407	−	0.280888i
$811$			10.0627i			0.353349i	0.984269	+	0.176674i	$0.0565339\pi$
$811$			10.0627i			0.353349i	−0.984269	+	0.176674i	$0.943466\pi$
$812$	0.0446199	−	1.80593i	0.00156585	−	0.0633756i
$813$	−6.60179	+	38.2558i	−0.231535	+	1.34169i
$814$	16.3065	+	0.201416i	0.571543	+	0.00705961i
$815$	32.7606	−	56.7430i	1.14755	−	1.98762i
$816$	−20.8253	−	19.1644i	−0.729031	−	0.670890i
$817$	−2.82649	−	4.89562i	−0.0988862	−	0.171276i
$818$	−8.31090	−	14.8145i	−0.290584	−	0.517977i
$819$	0.177283	−	0.498361i	0.00619478	−	0.0174141i
$820$	−59.4369	−	36.3023i	−2.07563	−	1.26773i
$821$	−33.4098	+	19.2891i	−1.16601	+	0.673196i	−0.952737	−	0.303797i	$-0.901746\pi$
$821$	−33.4098	+	19.2891i	−1.16601	+	0.673196i	−0.213273	+	0.976993i	$0.568412\pi$
$822$	−0.431777	+	2.32994i	−0.0150599	+	0.0812661i
$823$	−16.1120	+	27.9068i	−0.561628	+	0.972768i	0.435727	+	0.900079i	$0.356491\pi$
$823$	−16.1120	+	27.9068i	−0.561628	+	0.972768i	−0.997355	+	0.0726892i	$0.976842\pi$
$824$	−18.4804	+	29.4339i	−0.643794	+	1.02538i
$825$	−18.7379	+	22.4971i	−0.652371	+	0.783248i
$826$	0.325358	+	0.193242i	0.0113206	+	0.00672375i
$827$		−	27.7190i		−	0.963886i	−0.876203	−	0.481943i	$-0.839931\pi$
$827$		−	27.7190i		−	0.963886i	0.876203	−	0.481943i	$-0.160069\pi$
$828$	−33.3399	−	12.7963i	−1.15864	−	0.444702i
$829$			10.3137i			0.358208i	0.983830	+	0.179104i	$0.0573199\pi$
$829$			10.3137i			0.358208i	−0.983830	+	0.179104i	$0.942680\pi$
$830$	16.7728	−	28.2399i	0.582191	−	0.980223i
$831$	13.9850	+	37.9919i	0.485135	+	1.31793i
$832$	−3.03762	−	2.06793i	−0.105310	−	0.0716927i
$833$	−13.9964	+	24.2425i	−0.484946	+	0.839951i
$834$	−4.89256	−	13.8152i	−0.169416	−	0.478382i
$835$	−6.60139	+	3.81131i	−0.228451	+	0.131896i
$836$	9.88587	−	16.1859i	0.341910	−	0.559801i
$837$	3.13466	+	5.29477i	0.108350	+	0.183014i
$838$	1.96670	−	1.10331i	0.0679385	−	0.0381133i
$839$	−19.1961	−	33.2487i	−0.662724	−	1.14787i	−0.979897	−	0.199504i	$-0.936067\pi$
$839$	−19.1961	−	33.2487i	−0.662724	−	1.14787i	0.317173	−	0.948368i	$-0.397267\pi$
$840$	−6.74061	−	1.42220i	−0.232573	−	0.0490706i
$841$	−11.7315	+	20.3195i	−0.404534	+	0.700673i
$842$	0.315869	−	25.5726i	0.0108856	−	0.881290i
$843$	17.2121	−	6.33588i	0.592818	−	0.218219i
$844$	0.868132	−	35.1364i	0.0298823	−	1.20944i
$845$		−	46.8516i		−	1.61174i
$846$	26.0799	+	9.64200i	0.896647	+	0.331499i
$847$	2.67553			0.0919325
$848$	25.6723	+	16.5642i	0.881592	+	0.568816i
$849$	−9.84342	+	11.8182i	−0.337825	+	0.405599i
$850$	48.6425	+	0.600825i	1.66842	+	0.0206081i
$851$	−29.6089	−	17.0947i	−1.01498	−	0.585999i
$852$	12.2582	−	4.17150i	0.419959	−	0.142913i
$853$	24.4212	−	14.0996i	0.836166	−	0.482761i	−0.0197931	−	0.999804i	$-0.506301\pi$
$853$	24.4212	−	14.0996i	0.836166	−	0.482761i	0.855959	+	0.517043i	$0.172967\pi$
$854$	2.31668	−	1.29965i	0.0792752	−	0.0444732i
$855$	−39.5269	+	33.6613i	−1.35179	+	1.15119i
$856$	0.693403	−	18.7049i	0.0237000	−	0.639321i
$857$	15.7011	+	27.1951i	0.536339	+	0.928966i	0.999097	+	0.0424814i	$0.0135263\pi$
$857$	15.7011	+	27.1951i	0.536339	+	0.928966i	−0.462759	+	0.886484i	$0.653140\pi$
$858$	1.71752	+	1.46684i	0.0586353	+	0.0500771i
$859$	41.6368	+	24.0390i	1.42063	+	0.820201i	0.996353	−	0.0853309i	$-0.0271947\pi$
$859$	41.6368	+	24.0390i	1.42063	+	0.820201i	0.424278	+	0.905532i	$0.360528\pi$
$860$	−4.19497	−	7.69902i	−0.143047	−	0.262534i
$861$	−1.07473	+	6.22778i	−0.0366266	+	0.212242i
$862$	25.0922	−	42.2472i	0.854644	−	1.43894i
$863$	37.6968			1.28321			0.641607	−	0.767034i	$-0.278268\pi$
$863$	37.6968			1.28321			0.641607	+	0.767034i	$0.278268\pi$
$864$	29.3559	+	1.49306i	0.998709	+	0.0507951i
$865$	−69.6783			−2.36913
$866$	−9.18591	+	15.4661i	−0.312150	+	0.525560i
$867$	−0.0922398	+	0.534508i	−0.00313263	+	0.0181528i
$868$	0.434960	+	0.798282i	0.0147635	+	0.0270955i
$869$	18.6358	+	10.7594i	0.632177	+	0.364988i
$870$	−16.0566	−	13.7131i	−0.544371	−	0.464916i
$871$	−2.35479	−	4.07861i	−0.0797890	−	0.138199i
$872$	−0.735095	+	19.8296i	−0.0248935	+	0.671514i
$873$	3.23870	+	17.6154i	0.109614	+	0.596191i
$874$	−34.6785	+	19.4546i	−1.17302	+	0.658060i
$875$	4.16576	−	2.40510i	0.140828	−	0.0813072i
$876$	8.79785	−	2.99393i	0.297252	−	0.101156i
$877$	−21.6823	−	12.5183i	−0.732158	−	0.422711i	0.0870533	−	0.996204i	$-0.472255\pi$
$877$	−21.6823	−	12.5183i	−0.732158	−	0.422711i	−0.819211	+	0.573492i	$0.805588\pi$
$878$	21.0956	+	0.260570i	0.711943	+	0.00879382i
$879$	−12.5709	+	15.0928i	−0.424006	+	0.509069i
$880$	15.9483	−	24.7178i	0.537617	−	0.833237i
$881$	−21.0382			−0.708795			−0.354398	−	0.935095i	$-0.615314\pi$
$881$	−21.0382			−0.708795			−0.354398	+	0.935095i	$0.615314\pi$
$882$	−4.90364	−	28.6568i	−0.165114	−	0.964926i
$883$			55.5904i			1.87077i	0.353636	+	0.935383i	$0.384945\pi$
$883$			55.5904i			1.87077i	−0.353636	+	0.935383i	$0.615055\pi$
$884$	0.0926927	−	3.75161i	0.00311759	−	0.126180i
$885$	4.15094	−	1.52798i	0.139532	−	0.0513626i
$886$	0.0702697	−	5.68900i	0.00236076	−	0.191126i
$887$	0.695385	−	1.20444i	0.0233487	−	0.0404412i	−0.854115	−	0.520084i	$-0.825901\pi$
$887$	0.695385	−	1.20444i	0.0233487	−	0.0404412i	0.877464	+	0.479643i	$0.159234\pi$
$888$	27.5351	+	5.80963i	0.924017	+	0.194958i
$889$	−4.03261	−	6.98468i	−0.135249	−	0.234259i
$890$	−34.1954	+	19.1836i	−1.14623	+	0.643034i
$891$	−17.8363	−	2.87744i	−0.597538	−	0.0963980i
$892$	25.6735	−	42.0346i	0.859612	−	1.40742i
$893$	26.8120	−	15.4799i	0.897229	−	0.518015i
$894$	−6.07847	−	17.1639i	−0.203294	−	0.574046i
$895$	3.88527	−	6.72948i	0.129870	−	0.224942i
$896$	4.32657	+	0.375004i	0.144541	+	0.0125280i
$897$	−1.63578	−	4.44379i	−0.0546171	−	0.148374i
$898$	−7.88467	+	13.2752i	−0.263115	+	0.443001i
$899$			2.78645i			0.0929332i
$900$	−39.2632	+	31.7975i	−1.30877	+	1.05992i
$901$			31.2011i			1.03946i
$902$	−23.2020	−	13.7806i	−0.772543	−	0.458842i
$903$	−0.509175	+	0.611324i	−0.0169443	+	0.0203436i
$904$	−12.3152	+	19.6146i	−0.409597	+	0.652372i
$905$	3.04608	−	5.27597i	0.101255	−	0.175379i
$906$	0.439967	−	2.37414i	0.0146169	−	0.0788754i
$907$	−37.3197	+	21.5465i	−1.23918	+	0.715440i	−0.968926	−	0.247349i	$-0.920441\pi$
$907$	−37.3197	+	21.5465i	−1.23918	+	0.715440i	−0.270252	+	0.962789i	$0.587107\pi$
$908$	−33.4887	−	20.4539i	−1.11136	−	0.678786i
$909$	−16.3967	+	3.01464i	−0.543844	+	0.0999892i
$910$	−0.446934	−	0.796678i	−0.0148157	−	0.0264096i
$911$	−3.96463	−	6.86694i	−0.131354	−	0.227512i	0.792845	−	0.609424i	$-0.208599\pi$
$911$	−3.96463	−	6.86694i	−0.131354	−	0.227512i	−0.924199	+	0.381912i	$0.875266\pi$
$912$	22.1624	−	24.0831i	0.733871	−	0.797470i
$913$	6.36331	−	11.0216i	0.210595	−	0.364761i
$914$	2.30557	+	0.0284781i	0.0762615	+	0.000941970i
$915$	5.28012	−	30.5970i	0.174555	−	1.01151i
$916$	−1.21745	+	49.2747i	−0.0402258	+	1.62808i
$917$		−	2.43353i		−	0.0803622i
$918$	14.9724	+	26.0176i	0.494161	+	0.858710i
$919$	1.66862			0.0550426			0.0275213	−	0.999621i	$-0.491239\pi$
$919$	1.66862			0.0550426			0.0275213	+	0.999621i	$0.491239\pi$
$920$	−54.5149	+	28.8361i	−1.79730	+	0.950698i
$921$	1.07304	+	0.185174i	0.0353579	+	0.00610170i
$922$	−0.205344	+	16.6245i	−0.00676264	+	0.547500i
$923$	1.48694	+	0.858486i	0.0489433	+	0.0282574i
$924$	−2.61839	−	0.518761i	−0.0861388	−	0.0170660i
$925$	−41.8905	+	24.1855i	−1.37735	+	0.795215i
$926$	−14.7342	−	26.2643i	−0.484197	−	0.863099i
$927$	28.0650	−	23.9002i	0.921775	−	0.784987i
$928$	11.0950	+	7.35431i	0.364211	+	0.241417i
$929$	−23.3838	−	40.5020i	−0.767199	−	1.32883i	−0.939076	−	0.343709i	$-0.888317\pi$
$929$	−23.3838	−	40.5020i	−0.767199	−	1.32883i	0.171878	−	0.985118i	$-0.445017\pi$
$930$	10.4482	+	1.93623i	0.342611	+	0.0634915i
$931$	−28.0348	−	16.1859i	−0.918804	−	0.530472i
$932$	20.0207	+	36.7441i	0.655801	+	1.20359i
$933$	25.6711	+	21.3816i	0.840435	+	0.700002i
$934$	23.0088	+	13.6658i	0.752870	+	0.447158i
$935$	30.0410			0.982447
$936$	2.41538	+	3.05898i	0.0789493	+	0.0999857i
$937$	−9.30185			−0.303878			−0.151939	−	0.988390i	$-0.548552\pi$
$937$	−9.30185			−0.303878			−0.151939	+	0.988390i	$0.548552\pi$
$938$	4.78539	+	2.84222i	0.156249	+	0.0928019i
$939$	−9.32861	+	3.43391i	−0.304428	+	0.112061i
$940$	42.1655	−	22.9747i	1.37529	−	0.749353i
$941$	−5.42009	−	3.12929i	−0.176690	−	0.102012i	0.409047	−	0.912513i	$-0.365861\pi$
$941$	−5.42009	−	3.12929i	−0.176690	−	0.102012i	−0.585736	+	0.810502i	$0.699195\pi$
$942$	14.3836	+	40.6153i	0.468644	+	1.32332i
$943$	28.2881	+	48.9965i	0.921188	+	1.59555i
$944$	−2.48072	+	1.27324i	−0.0807404	+	0.0414403i
$945$	6.36755	+	3.58401i	0.207136	+	0.116588i
$946$	−1.66215	−	2.96284i	−0.0540410	−	0.0963302i
$947$	−38.4243	+	22.1843i	−1.24862	+	0.720893i	−0.970835	−	0.239749i	$-0.922935\pi$
$947$	−38.4243	+	22.1843i	−1.24862	+	0.720893i	−0.277789	+	0.960642i	$0.589601\pi$
$948$	27.9372	+	24.4627i	0.907358	+	0.794512i
$949$	1.06720	+	0.616146i	0.0346426	+	0.0200009i
$950$	−0.694815	+	56.2519i	−0.0225428	+	1.82505i
$951$	7.47452	+	20.3054i	0.242378	+	0.658448i
$952$	2.07371	+	3.92036i	0.0672092	+	0.127059i
$953$	6.11599			0.198116			0.0990582	−	0.995082i	$-0.468417\pi$
$953$	6.11599			0.198116			0.0990582	+	0.995082i	$0.468417\pi$
$954$	−20.7041	−	24.9292i	−0.670319	−	0.807111i
$955$		−	63.7257i		−	2.06211i
$956$	20.5771	+	0.508408i	0.665510	+	0.0164431i
$957$	−6.28662	−	5.23616i	−0.203218	−	0.169261i
$958$	−42.3551	−	0.523164i	−1.36843	−	0.0169027i
$959$	0.185668	−	0.321586i	0.00599552	−	0.0103845i
$960$	35.2858	−	36.4922i	1.13884	−	1.17778i
$961$	14.7989	+	25.6324i	0.477383	+	0.826852i
$962$	1.82571	+	3.25439i	0.0588631	+	0.104926i
$963$	−6.65396	+	18.7049i	−0.214421	+	0.602758i
$964$	21.3456	−	34.9486i	0.687495	−	1.12562i
$965$	−8.99178	+	5.19141i	−0.289456	+	0.167117i
$966$	4.25546	+	3.63435i	0.136917	+	0.116933i
$967$	16.9985	−	29.4423i	0.546635	−	0.946799i	−0.451867	−	0.892085i	$-0.649242\pi$
$967$	16.9985	−	29.4423i	0.546635	−	0.946799i	0.998502	−	0.0547141i	$-0.0174248\pi$
$968$	−10.4831	+	16.6966i	−0.336940	+	0.536649i
$969$	32.9370	+	5.68392i	1.05809	+	0.182594i
$970$	26.5939	+	15.7951i	0.853878	+	0.507150i
$971$		−	42.4798i		−	1.36324i	−0.731706	−	0.681621i	$-0.761275\pi$
$971$		−	42.4798i		−	1.36324i	0.731706	−	0.681621i	$-0.238725\pi$
$972$	−29.2271	−	10.8525i	−0.937460	−	0.348093i
$973$			2.29669i			0.0736286i
$974$	12.5204	−	21.0803i	0.401180	−	0.675458i
$975$	−6.60189	−	1.13929i	−0.211430	−	0.0364863i
$976$	−0.966623	+	19.5494i	−0.0309408	+	0.625761i
$977$	7.66569	−	13.2774i	0.245247	−	0.424781i	−0.716954	−	0.697121i	$-0.754464\pi$
$977$	7.66569	−	13.2774i	0.245247	−	0.424781i	0.962201	+	0.272340i	$0.0877975\pi$
$978$	28.4514	−	33.3138i	0.909776	−	1.06526i
$979$	−13.1569	+	7.59614i	−0.420496	+	0.242774i
$980$	−42.8484	−	26.1705i	−1.36874	−	0.835987i
$981$	7.05404	−	19.8296i	0.225218	−	0.633110i
$982$	44.3214	−	24.8642i	1.41435	−	0.793448i
$983$	−14.8653	−	25.7474i	−0.474129	−	0.821216i	0.525432	−	0.850836i	$-0.323904\pi$
$983$	−14.8653	−	25.7474i	−0.474129	−	0.821216i	−0.999561	+	0.0296198i	$0.990570\pi$
$984$	−34.6534	−	31.1081i	−1.10471	−	0.991689i
$985$	23.0779	−	39.9720i	0.735322	−	1.27361i
$986$	−0.167896	+	13.5927i	−0.00534689	+	0.432881i
$987$	−3.34806	−	2.78861i	−0.106570	−	0.0887626i
$988$	4.33849	+	0.107193i	0.138026	+	0.00341027i
$989$			7.12233i			0.226477i
$990$	−24.0023	+	19.9343i	−0.762842	+	0.633552i
$991$	−49.5495			−1.57399			−0.786996	−	0.616958i	$-0.788365\pi$
$991$	−49.5495			−1.57399			−0.786996	+	0.616958i	$0.788365\pi$
$992$	−6.68589	−	0.413420i	−0.212277	−	0.0131261i
$993$	2.07276	+	5.63089i	0.0657771	+	0.178691i
$994$	−2.02897	−	0.0250616i	−0.0643551	−	0.000794905i
$995$	54.8017	+	31.6398i	1.73733	+	1.00305i
$996$	14.4677	−	16.5226i	0.458426	−	0.523538i
$997$	34.4541	−	19.8921i	1.09117	−	0.629988i	0.157284	−	0.987553i	$-0.449726\pi$
$997$	34.4541	−	19.8921i	1.09117	−	0.629988i	0.933888	+	0.357565i	$0.116393\pi$
$998$	14.9477	−	8.38562i	0.473161	−	0.265442i
$999$	−26.0111	−	14.6405i	−0.822956	−	0.463205i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.2.n.b.13.3	✓	16
3.2	odd	2		216.2.n.b.37.6		16
4.3	odd	2		288.2.r.b.49.4		16
8.3	odd	2		288.2.r.b.49.5		16
8.5	even	2	inner	72.2.n.b.13.8	yes	16
9.2	odd	6		216.2.n.b.181.1		16
9.4	even	3		648.2.d.j.325.3		8
9.5	odd	6		648.2.d.k.325.6		8
9.7	even	3	inner	72.2.n.b.61.8	yes	16
12.11	even	2		864.2.r.b.145.1		16
24.5	odd	2		216.2.n.b.37.1		16
24.11	even	2		864.2.r.b.145.8		16
36.7	odd	6		288.2.r.b.241.5		16
36.11	even	6		864.2.r.b.721.8		16
36.23	even	6		2592.2.d.k.1297.8		8
36.31	odd	6		2592.2.d.j.1297.1		8
72.5	odd	6		648.2.d.k.325.5		8
72.11	even	6		864.2.r.b.721.1		16
72.13	even	6		648.2.d.j.325.4		8
72.29	odd	6		216.2.n.b.181.6		16
72.43	odd	6		288.2.r.b.241.4		16
72.59	even	6		2592.2.d.k.1297.1		8
72.61	even	6	inner	72.2.n.b.61.3	yes	16
72.67	odd	6		2592.2.d.j.1297.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.2.n.b.13.3	✓	16	1.1	even	1	trivial
72.2.n.b.13.8	yes	16	8.5	even	2	inner
72.2.n.b.61.3	yes	16	72.61	even	6	inner
72.2.n.b.61.8	yes	16	9.7	even	3	inner
216.2.n.b.37.1		16	24.5	odd	2
216.2.n.b.37.6		16	3.2	odd	2
216.2.n.b.181.1		16	9.2	odd	6
216.2.n.b.181.6		16	72.29	odd	6
288.2.r.b.49.4		16	4.3	odd	2
288.2.r.b.49.5		16	8.3	odd	2
288.2.r.b.241.4		16	72.43	odd	6
288.2.r.b.241.5		16	36.7	odd	6
648.2.d.j.325.3		8	9.4	even	3
648.2.d.j.325.4		8	72.13	even	6
648.2.d.k.325.5		8	72.5	odd	6
648.2.d.k.325.6		8	9.5	odd	6
864.2.r.b.145.1		16	12.11	even	2
864.2.r.b.145.8		16	24.11	even	2
864.2.r.b.721.1		16	72.11	even	6
864.2.r.b.721.8		16	36.11	even	6
2592.2.d.j.1297.1		8	36.31	odd	6
2592.2.d.j.1297.8		8	72.67	odd	6
2592.2.d.k.1297.1		8	72.59	even	6
2592.2.d.k.1297.8		8	36.23	even	6

Overview	Random
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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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	72.2.n.b.13.3

Level	$72$
Weight	$2$
Character	72.13
Analytic conductor	$0.575$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$