LMFDB - Embedded newform 72.2.n.b.13.8

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			13.8
Root			$-0.722180 + 1.21592i$ of defining polynomial
Character	$\chi$	$=$	72.13
Dual form			72.2.n.b.61.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41411 - 0.0174668i) q^{2} +(-0.294546 + 1.70682i) q^{3} +(1.99939 - 0.0493999i) q^{4} +(-3.17262 - 1.83171i) q^{5} +(-0.386706 + 2.41877i) 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} +(-0.504595 + 3.42715i) q^{12} +(0.397799 + 0.229669i) q^{13} +(-0.277210 - 0.466733i) q^{14} +(4.06089 - 4.87557i) q^{15} +(3.99512 - 0.197539i) q^{16} -4.08495 q^{17} +(-4.01451 - 1.37248i) q^{18} +4.72398i q^{19} +(-6.43379 - 3.50558i) q^{20} +(0.623923 - 0.229669i) q^{21} +(2.44087 - 1.44973i) q^{22} +(-2.97594 + 5.15447i) q^{23} +(-0.653689 + 4.85517i) 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} +(5.65736 - 6.96551i) q^{30} +(0.592083 - 1.02552i) q^{31} +(5.64607 - 0.349123i) q^{32} +(1.20110 + 3.26293i) q^{33} +(-5.77656 + 0.0713512i) q^{34} +1.40621i q^{35} +(-5.70092 - 1.87071i) q^{36} -5.74432i q^{37} +(0.0825129 + 6.68021i) q^{38} +(-0.509175 + 0.611324i) q^{39} +(-9.15929 - 4.84488i) q^{40} +(4.75281 - 8.23212i) q^{41} +(0.878281 - 0.335675i) 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} +(-0.839581 + 6.87714i) q^{48} +(3.42633 - 5.93458i) q^{49} +(6.08124 + 10.2389i) q^{50} +(1.20321 - 6.97229i) q^{51} +(0.806700 + 0.439547i) q^{52} +7.63807i q^{53} +(3.52503 - 6.44780i) q^{54} -7.35407 q^{55} +(-0.577308 - 0.919487i) q^{56} +(-8.06300 - 1.39143i) q^{57} +(2.86116 - 1.69935i) q^{58} +(-0.603703 - 0.348548i) q^{59} +(7.87845 - 9.94878i) 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} +(1.75548 + 4.59315i) q^{66} +(-8.87932 - 5.12648i) q^{67} +(-8.16741 + 0.201796i) q^{68} +(-7.92122 - 6.59762i) q^{69} +(0.0245621 + 1.98853i) q^{70} -3.73792 q^{71} +(-8.09437 - 2.54580i) q^{72} -2.68275 q^{73} +(-0.100335 - 8.12307i) q^{74} +(-13.6872 + 5.03832i) q^{75} +(0.233364 + 9.44508i) q^{76} +(-0.667322 - 0.385279i) q^{77} +(-0.709349 + 0.873370i) 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} +(1.23612 - 0.490020i) q^{84} +(12.9600 + 7.48246i) q^{85} +(-1.45503 + 0.864199i) q^{86} +(1.40792 + 3.82477i) q^{87} +(4.80864 - 3.01915i) q^{88} +7.56802 q^{89} +(10.2225 + 11.7078i) q^{90} -0.176318i q^{91} +(-5.69542 + 10.4528i) q^{92} +(1.57598 + 1.31264i) q^{93} +(4.73299 + 7.96883i) q^{94} +(8.65297 - 14.9874i) q^{95} +(-1.06713 + 9.73967i) 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 $

$2$	1.41411	−	0.0174668i	0.999924	−	0.0123509i
$2$	1.41411	−	0.0174668i	0.999924	−	0.0123509i
$3$	−0.294546	+	1.70682i	−0.170056	+	0.985434i
$3$	−0.294546	+	1.70682i	−0.170056	+	0.985434i
$4$	1.99939	−	0.0493999i	0.999695	−	0.0246999i
$5$	−3.17262	−	1.83171i	−1.41884	−	0.819167i	−0.422641	−	0.906297i	$-0.638897\pi$
$5$	−3.17262	−	1.83171i	−1.41884	−	0.819167i	−0.996197	+	0.0871306i	$0.972230\pi$
$6$	−0.386706	+	2.41877i	−0.157872	+	0.987460i
$7$	−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	−0.214467	−	0.976731i	$-0.568801\pi$
$11$	1.73849	−	1.00372i	0.524173	−	0.302632i	0.738640	+	0.674100i	$0.235468\pi$
$12$	−0.504595	+	3.42715i	−0.145664	+	0.989334i
$13$	0.397799	+	0.229669i	0.110330	+	0.0636988i	0.554149	−	0.832417i	$-0.313044\pi$
$13$	0.397799	+	0.229669i	0.110330	+	0.0636988i	−0.443820	+	0.896116i	$0.646377\pi$
$14$	−0.277210	−	0.466733i	−0.0740876	−	0.124740i
$15$	4.06089	−	4.87557i	1.04852	−	1.25887i
$16$	3.99512	−	0.197539i	0.998780	−	0.0493848i
$17$	−4.08495			−0.990747			−0.495373	−	0.868680i	$-0.664969\pi$
$17$	−4.08495			−0.990747			−0.495373	+	0.868680i	$0.664969\pi$
$18$	−4.01451	−	1.37248i	−0.946230	−	0.323496i
$19$			4.72398i			1.08376i	0.840457	+	0.541878i	$0.182286\pi$
$19$			4.72398i			1.08376i	−0.840457	+	0.541878i	$0.817714\pi$
$20$	−6.43379	−	3.50558i	−1.43864	−	0.783871i
$21$	0.623923	−	0.229669i	0.136151	−	0.0501179i
$22$	2.44087	−	1.44973i	0.520396	−	0.309083i
$23$	−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	$0.953586\pi$
$24$	−0.653689	+	4.85517i	−0.133434	+	0.991058i
$25$	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	−0.298713	−	0.954343i	$-0.596557\pi$
$29$	2.03783	−	1.17654i	0.378416	−	0.218479i	0.677129	+	0.735864i	$0.263224\pi$
$30$	5.65736	−	6.96551i	1.03289	−	1.27172i
$31$	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	$0.132753\pi$
$32$	5.64607	−	0.349123i	0.998094	−	0.0617169i
$33$	1.20110	+	3.26293i	0.209085	+	0.568003i
$34$	−5.77656	+	0.0713512i	−0.990671	+	0.0122366i
$35$			1.40621i			0.237693i
$36$	−5.70092	−	1.87071i	−0.950153	−	0.311785i
$37$		−	5.74432i		−	0.944360i	−0.881502	−	0.472180i	$-0.843467\pi$
$37$		−	5.74432i		−	0.944360i	0.881502	−	0.472180i	$-0.156533\pi$
$38$	0.0825129	+	6.68021i	0.0133854	+	1.08367i
$39$	−0.509175	+	0.611324i	−0.0815332	+	0.0978902i
$40$	−9.15929	−	4.84488i	−1.44821	−	0.766043i
$41$	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	$-0.0995817\pi$
$42$	0.878281	−	0.335675i	0.135522	−	0.0517957i
$43$	−1.03633	+	0.598327i	−0.158039	+	0.0912440i	−0.576934	−	0.816791i	$-0.695751\pi$
$43$	−1.03633	+	0.598327i	−0.158039	+	0.0912440i	0.418895	+	0.908035i	$0.362418\pi$
$44$	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	$0.674702\pi$
$48$	−0.839581	+	6.87714i	−0.121183	+	0.992630i
$49$	3.42633	−	5.93458i	0.489476	−	0.847796i
$50$	6.08124	+	10.2389i	0.860017	+	1.44799i
$51$	1.20321	−	6.97229i	0.168482	−	0.976316i
$52$	0.806700	+	0.439547i	0.111869	+	0.0609542i
$53$			7.63807i			1.04917i	0.851358	+	0.524585i	$0.175779\pi$
$53$			7.63807i			1.04917i	−0.851358	+	0.524585i	$0.824221\pi$
$54$	3.52503	−	6.44780i	0.479696	−	0.877435i
$55$	−7.35407			−0.991623
$56$	−0.577308	−	0.919487i	−0.0771460	−	0.122872i
$57$	−8.06300	−	1.39143i	−1.06797	−	0.184299i
$58$	2.86116	−	1.69935i	0.375689	−	0.223136i
$59$	−0.603703	−	0.348548i	−0.0785954	−	0.0453771i	0.460187	−	0.887822i	$-0.347782\pi$
$59$	−0.603703	−	0.348548i	−0.0785954	−	0.0453771i	−0.538783	+	0.842445i	$0.681116\pi$
$60$	7.87845	−	9.94878i	1.01710	−	1.28438i
$61$	−4.23774	+	2.44666i	−0.542587	+	0.313263i	−0.746127	−	0.665804i	$-0.768089\pi$
$61$	−4.23774	+	2.44666i	−0.542587	+	0.313263i	0.203540	+	0.979067i	$0.434755\pi$
$62$	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
$66$	1.75548	+	4.59315i	0.216084	+	0.565377i
$67$	−8.87932	−	5.12648i	−1.08478	−	0.626299i	−0.152599	−	0.988288i	$-0.548764\pi$
$67$	−8.87932	−	5.12648i	−1.08478	−	0.626299i	−0.932182	+	0.361989i	$0.882098\pi$
$68$	−8.16741	+	0.201796i	−0.990444	+	0.0244714i
$69$	−7.92122	−	6.59762i	−0.953603	−	0.794260i
$70$	0.0245621	+	1.98853i	0.00293573	+	0.237675i
$71$	−3.73792			−0.443610			−0.221805	−	0.975091i	$-0.571195\pi$
$71$	−3.73792			−0.443610			−0.221805	+	0.975091i	$0.571195\pi$
$72$	−8.09437	−	2.54580i	−0.953931	−	0.300026i
$73$	−2.68275			−0.313992			−0.156996	−	0.987599i	$-0.550181\pi$
$73$	−2.68275			−0.313992			−0.156996	+	0.987599i	$0.550181\pi$
$74$	−0.100335	−	8.12307i	−0.0116637	−	0.944288i
$75$	−13.6872	+	5.03832i	−1.58046	+	0.581775i
$76$	0.233364	+	9.44508i	0.0267687	+	1.08342i
$77$	−0.667322	−	0.385279i	−0.0760484	−	0.0439066i
$78$	−0.709349	+	0.873370i	−0.0803179	+	0.0988897i
$79$	−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	−0.167434	−	0.985883i	$-0.553548\pi$
$83$	5.49039	−	3.16988i	0.602648	−	0.347939i	0.770083	+	0.637944i	$0.220215\pi$
$84$	1.23612	−	0.490020i	0.134872	−	0.0534656i
$85$	12.9600	+	7.48246i	1.40571	+	0.811586i
$86$	−1.45503	+	0.864199i	−0.156900	+	0.0931890i
$87$	1.40792	+	3.82477i	0.150945	+	0.410058i
$88$	4.80864	−	3.01915i	0.512603	−	0.321842i
$89$	7.56802			0.802208			0.401104	−	0.916032i	$-0.368627\pi$
$89$	7.56802			0.802208			0.401104	+	0.916032i	$0.368627\pi$
$90$	10.2225	+	11.7078i	1.07755	+	1.23411i
$91$		−	0.176318i		−	0.0184832i
$92$	−5.69542	+	10.4528i	−0.593789	+	1.08978i
$93$	1.57598	+	1.31264i	0.163422	+	0.136115i
$94$	4.73299	+	7.96883i	0.488171	+	0.821922i
$95$	8.65297	−	14.9874i	0.887776	−	1.53767i
$96$	−1.06713	+	9.73967i	−0.108914	+	0.994051i
$97$	−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	−0.719948	−	0.694028i	$-0.755835\pi$
$101$	−4.81265	+	2.77859i	−0.478877	+	0.276480i	0.241071	+	0.970507i	$0.422501\pi$
$102$	1.57968	−	9.88057i	0.156411	−	0.978322i
$103$	−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	$0.959693\pi$
$104$	1.14844	+	0.607476i	0.112614	+	0.0595679i
$105$	−2.40016	−	0.414194i	−0.234231	−	0.0404212i
$106$	0.133413	+	10.8010i	0.0129582	+	1.04909i
$107$			6.61773i			0.639760i	0.947458	+	0.319880i	$0.103643\pi$
$107$			6.61773i			0.639760i	−0.947458	+	0.319880i	$0.896357\pi$
$108$	4.87215	−	9.17944i	0.468822	−	0.883292i
$109$		−	7.01563i		−	0.671975i	−0.941866	−	0.335988i	$-0.890930\pi$
$109$		−	7.01563i		−	0.671975i	0.941866	−	0.335988i	$-0.109070\pi$
$110$	−10.3994	+	0.128452i	−0.991547	+	0.0122474i
$111$	9.80453	+	1.69196i	0.930605	+	0.160594i
$112$	−0.832435	−	1.29017i	−0.0786577	−	0.121909i
$113$	−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	$0.292517\pi$
$114$	−11.4262	−	1.82679i	−1.07016	−	0.171095i
$115$	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
$120$	10.9672	−	14.2062i	1.00116	−	1.29685i
$121$	−3.48511	+	6.03639i	−0.316828	+	0.548762i
$122$	−5.94988	+	3.53386i	−0.538676	+	0.319940i
$123$	12.6508	+	10.5369i	1.14069	+	0.950084i
$124$	1.13314	−	2.07966i	0.101759	−	0.186759i
$125$		−	12.5314i		−	1.12084i
$126$	0.314243	+	1.59794i	0.0279950	+	0.142356i
$127$	21.0113			1.86445			0.932224	−	0.361882i	$-0.117866\pi$
$127$	21.0113			1.86445			0.932224	+	0.361882i	$0.117866\pi$
$128$	11.2714	−	0.976949i	0.996265	−	0.0863509i
$129$	−0.715991	−	1.94507i	−0.0630395	−	0.171254i
$130$	−1.21525	−	2.04609i	−0.106584	−	0.179454i
$131$	−5.49039	−	3.16988i	−0.479697	−	0.276953i	0.240593	−	0.970626i	$-0.422658\pi$
$131$	−5.49039	−	3.16988i	−0.479697	−	0.276953i	−0.720290	+	0.693673i	$0.755991\pi$
$132$	2.56266	+	6.46453i	0.223051	+	0.562665i
$133$	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	$0.820175\pi$
$138$	−11.3167	−	9.19137i	−0.963340	−	0.782422i
$139$	5.18167	+	2.99164i	0.439503	+	0.253747i	0.703387	−	0.710807i	$-0.251670\pi$
$139$	5.18167	+	2.99164i	0.439503	+	0.253747i	−0.263884	+	0.964554i	$0.585004\pi$
$140$	0.0694668	+	2.81157i	0.00587101	+	0.237621i
$141$	−10.6526	+	3.92129i	−0.897114	+	0.330232i
$142$	−5.28582	+	0.0652897i	−0.443576	+	0.00547899i
$143$	0.922090			0.0771091
$144$	−11.4908	−	3.45865i	−0.957564	−	0.288221i
$145$	−8.62036			−0.715882
$146$	−3.79369	+	0.0468592i	−0.313968	+	0.00387809i
$147$	9.12006	+	7.59614i	0.752210	+	0.626519i
$148$	−0.283769	−	11.4851i	−0.0233256	−	0.944072i
$149$	6.43764	+	3.71678i	0.527392	+	0.304490i	0.739954	−	0.672658i	$-0.234847\pi$
$149$	6.43764	+	3.71678i	0.527392	+	0.304490i	−0.212562	+	0.977148i	$0.568181\pi$
$150$	−19.2671	+	7.36379i	−1.57315	+	0.601251i
$151$	−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
$156$	−0.987839	+	1.24743i	−0.0790904	+	0.0998742i
$157$	−15.2336	−	8.79510i	−1.21577	−	0.701925i	−0.251760	−	0.967790i	$-0.581009\pi$
$157$	−15.2336	−	8.79510i	−1.21577	−	0.701925i	−0.964010	+	0.265864i	$0.914343\pi$
$158$	−7.74146	−	13.0341i	−0.615877	−	1.03694i
$159$	−13.0368	−	2.24976i	−1.03389	−	0.178418i
$160$	−18.5523	−	9.23434i	−1.46669	−	0.730039i
$161$	2.28464			0.180055
$162$	9.96697	+	7.91578i	0.783079	+	0.621922i
$163$			17.8852i			1.40088i	0.713711	+	0.700440i	$0.247013\pi$
$163$			17.8852i			1.40088i	−0.713711	+	0.700440i	$0.752987\pi$
$164$	9.09606	−	16.6940i	0.710283	−	1.30358i
$165$	2.16611	−	12.5521i	0.168631	−	0.977179i
$166$	7.70862	−	4.57844i	0.598305	−	0.355356i
$167$	−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	$0.192320\pi$
$168$	1.73944	−	0.714531i	0.134201	−	0.0551273i
$169$	−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	0.280757	−	0.959779i	$-0.409415\pi$
$173$	16.4718	−	9.51000i	1.25233	−	0.723032i	0.971571	+	0.236747i	$0.0760813\pi$
$174$	2.05775	+	5.38403i	0.155998	+	0.408163i
$175$	1.61615	−	2.79925i	0.122169	−	0.211603i
$176$	6.74719	−	4.35338i	0.508588	−	0.328149i
$177$	0.772728	−	0.927750i	0.0580818	−	0.0697340i
$178$	10.7020	−	0.132189i	0.802147	−	0.00990800i
$179$			2.12111i			0.158539i	0.996853	+	0.0792697i	$0.0252588\pi$
$179$			2.12111i			0.158539i	−0.996853	+	0.0792697i	$0.974741\pi$
$180$	14.6602	+	16.3775i	1.09271	+	1.22071i
$181$			1.66297i			0.123608i	0.998088	+	0.0618039i	$0.0196853\pi$
$181$			1.66297i			0.123608i	−0.998088	+	0.0618039i	$0.980315\pi$
$182$	−0.00307972	−	0.249332i	−0.000228284	−	0.0184818i
$183$	−2.92781	−	7.95372i	−0.216430	−	0.587956i
$184$	−7.87135	+	14.8809i	−0.580284	+	1.09703i
$185$	−10.5219	+	18.2245i	−0.773588	+	1.33989i
$186$	2.25153	+	1.82869i	0.165090	+	0.134086i
$187$	−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	$-0.383338\pi$
$192$	−1.33892	+	13.7916i	−0.0966282	+	0.995321i
$193$	−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	$0.199192\pi$
$194$	−4.31157	−	7.25930i	−0.309553	−	0.521187i
$195$	2.73519	−	1.00684i	0.195871	−	0.0721010i
$196$	6.55740	−	12.0348i	0.468386	−	0.859628i
$197$			12.5991i			0.897646i	0.893621	+	0.448823i	$0.148157\pi$
$197$			12.5991i			0.897646i	−0.893621	+	0.448823i	$0.851843\pi$
$198$	−8.35675	+	1.64340i	−0.593888	+	0.116791i
$199$	17.2733			1.22447			0.612237	−	0.790674i	$-0.290270\pi$
$199$	17.2733			1.22447			0.612237	+	0.790674i	$0.290270\pi$
$200$	12.6646	+	20.1710i	0.895520	+	1.42631i
$201$	11.3654	−	13.6454i	0.801650	−	0.962475i
$202$	−6.75707	+	4.01328i	−0.475426	+	0.282373i
$203$	−0.782227	−	0.451619i	−0.0549016	−	0.0316975i
$204$	2.06125	−	13.9998i	0.144316	−	0.980179i
$205$	−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
$210$	−3.40131	−	0.543791i	−0.234713	−	0.0375252i
$211$	−15.2192	−	8.78678i	−1.04773	−	0.604907i	−0.125717	−	0.992066i	$-0.540123\pi$
$211$	−15.2192	−	8.78678i	−1.04773	−	0.604907i	−0.922013	+	0.387159i	$0.873456\pi$
$212$	0.377320	+	15.2715i	0.0259144	+	1.04885i
$213$	1.10099	−	6.37997i	0.0754386	−	0.437149i
$214$	0.115591	+	9.35817i	0.00790162	+	0.639711i
$215$	4.38385			0.298976
$216$	6.72939	−	13.0658i	0.457877	−	0.889015i
$217$	−0.454545			−0.0308565
$218$	−0.122541	−	9.92084i	−0.00829951	−	0.671924i
$219$	0.790193	−	4.57898i	0.0533963	−	0.309419i
$220$	−14.7037	+	0.363290i	−0.991320	+	0.0244930i
$221$	−1.62499	−	0.938188i	−0.109309	−	0.0631094i
$222$	13.8942	+	2.22136i	0.932517	+	0.149088i
$223$	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	−0.943378	−	0.331721i	$-0.892371\pi$
$227$	−16.9918	+	9.81024i	−1.12779	+	0.651128i	−0.184410	+	0.982849i	$0.559037\pi$
$228$	−16.1898	−	2.38370i	−1.07220	−	0.157864i
$229$	21.3431	+	12.3224i	1.41039	+	0.814289i	0.995425	−	0.0955486i	$-0.0304605\pi$
$229$	21.3431	+	12.3224i	1.41039	+	0.814289i	0.414965	+	0.909837i	$0.363794\pi$
$230$	26.5122	−	15.7466i	1.74816	−	1.03830i
$231$	0.854159	−	1.02552i	0.0561995	−	0.0674741i
$232$	5.63663	−	3.53901i	0.370063	−	0.232347i
$233$	−20.9222			−1.37066			−0.685330	−	0.728233i	$-0.740342\pi$
$233$	−20.9222			−1.37066			−0.685330	+	0.728233i	$0.740342\pi$
$234$	−1.28175	−	1.46798i	−0.0837908	−	0.0959648i
$235$		−	24.0092i		−	1.56619i
$236$	−1.22426	−	0.667060i	−0.0796922	−	0.0434219i
$237$	17.4239	−	6.41381i	1.13180	−	0.416622i
$238$	1.13239	+	1.90658i	0.0734020	+	0.123585i
$239$	−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	$0.274679\pi$
$240$	15.2606	−	20.2807i	0.985069	−	1.30911i
$241$	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
$246$	18.0737	+	14.6794i	1.15234	+	0.935923i
$247$	−1.08495	+	1.87919i	−0.0690339	+	0.119570i
$248$	1.56606	−	2.96065i	0.0994450	−	0.188001i
$249$	3.79325	+	10.3048i	0.240387	+	0.653040i
$250$	−0.218884	−	17.7207i	−0.0138434	−	1.12076i
$251$		−	28.0987i		−	1.77358i	−0.462177	−	0.886788i	$-0.652932\pi$
$251$		−	28.0987i		−	1.77358i	0.462177	−	0.886788i	$-0.347068\pi$
$252$	0.472284	+	2.25417i	0.0297511	+	0.141999i
$253$			11.9480i			0.751163i
$254$	29.7121	−	0.367000i	1.86431	−	0.0230276i
$255$	−16.5885	+	19.9165i	−1.03881	+	1.24722i
$256$	15.9220	−	1.57839i	0.995122	−	0.0986491i
$257$	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	$0.0544175\pi$
$258$	−1.04646	−	2.73803i	−0.0651498	−	0.170462i
$259$	−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	$-0.455002\pi$
$264$	3.73678	+	9.09677i	0.229983	+	0.559867i
$265$	13.9907	−	24.2327i	0.859444	−	1.48860i
$266$	2.20484	−	1.30954i	0.135187	−	0.0802928i
$267$	−2.22913	+	12.9173i	−0.136420	+	0.790524i
$268$	−18.0065	−	9.81119i	−1.09992	−	0.599314i
$269$		−	18.3998i		−	1.12185i	−0.827865	−	0.560927i	$-0.810445\pi$
$269$		−	18.3998i		−	1.12185i	0.827865	−	0.560927i	$-0.189555\pi$
$270$	−22.9941	+	13.9996i	−1.39938	+	0.851987i
$271$	−22.4135			−1.36152			−0.680760	−	0.732506i	$-0.738350\pi$
$271$	−22.4135			−1.36152			−0.680760	+	0.732506i	$0.738350\pi$
$272$	−16.3199	+	0.806938i	−0.989538	+	0.0489278i
$273$	0.300944	+	0.0519337i	0.0182139	+	0.00314317i
$274$	0.698630	+	1.17627i	0.0422058	+	0.0710609i
$275$	14.6392	+	8.45196i	0.882779	+	0.509673i
$276$	−16.1635	−	12.7999i	−0.972930	−	0.770464i
$277$	20.2421	−	11.6868i	1.21623	−	0.702190i	0.252119	−	0.967696i	$-0.418872\pi$
$277$	20.2421	−	11.6868i	1.21623	−	0.702190i	0.964109	+	0.265506i	$0.0855391\pi$
$278$	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	$0.731043\pi$
$282$	−14.9955	+	5.73119i	−0.892967	+	0.341287i
$283$	7.69029	+	4.43999i	0.457140	+	0.263930i	0.710841	−	0.703353i	$-0.248314\pi$
$283$	7.69029	+	4.43999i	0.457140	+	0.263930i	−0.253701	+	0.967283i	$0.581648\pi$
$284$	−7.47357	+	0.184653i	−0.443475	+	0.0109571i
$285$	23.0321	+	19.1836i	1.36430	+	1.13634i
$286$	1.30393	−	0.0161060i	0.0771032	−	0.000952367i
$287$	−3.64876			−0.215379
$288$	−16.3096	−	4.69019i	−0.961051	−	0.276372i
$289$	−0.313160			−0.0184212
$290$	−12.1901	+	0.150570i	−0.715827	+	0.00884180i
$291$	9.70414	−	3.57214i	0.568867	−	0.209403i
$292$	−5.36387	+	0.132528i	−0.313897	+	0.00775559i
$293$	9.82117	+	5.67026i	0.573759	+	0.331260i	0.758649	−	0.651499i	$-0.225860\pi$
$293$	9.82117	+	5.67026i	0.573759	+	0.331260i	−0.184890	+	0.982759i	$0.559193\pi$
$294$	13.0294	+	10.5824i	0.759890	+	0.617181i
$295$	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
$300$	−27.1171	+	10.7497i	−1.56561	+	0.620635i
$301$	0.397799	+	0.229669i	0.0229287	+	0.0132379i
$302$	−0.711881	−	1.19858i	−0.0409642	−	0.0689705i
$303$	−3.32501	−	9.03277i	−0.191017	−	0.518919i
$304$	0.933171	+	18.8729i	0.0535210	+	1.08243i
$305$	17.9263			1.02646
$306$	16.3991	+	5.60651i	0.937474	+	0.320503i
$307$		−	0.628678i		−	0.0358805i	−0.999839	−	0.0179403i	$-0.994289\pi$
$307$		−	0.628678i		−	0.0358805i	0.999839	−	0.0179403i	$-0.00571087\pi$
$308$	−1.35327	−	0.737356i	−0.0771097	−	0.0420148i
$309$	−16.3533	−	13.6207i	−0.930307	−	0.774857i
$310$	−5.27478	+	3.13289i	−0.299587	+	0.177936i
$311$	−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	$0.982480\pi$
$312$	−1.37512	+	1.78125i	−0.0778509	+	0.100843i
$313$	−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	−0.164402	−	0.986393i	$-0.552569\pi$
$317$	10.8187	−	6.24618i	0.607639	−	0.350821i	0.772041	+	0.635573i	$0.219236\pi$
$318$	−18.4747	−	2.95369i	−1.03601	−	0.165634i
$319$	2.36183	−	4.09081i	0.132237	−	0.229042i
$320$	−26.3962	−	12.7343i	−1.47559	−	0.711868i
$321$	−11.2953	−	1.94922i	−0.630442	−	0.108795i
$322$	3.23072	−	0.0399054i	0.180041	−	0.00222384i
$323$		−	19.2972i		−	1.07373i
$324$	14.2326	+	11.0197i	0.790701	+	0.612203i
$325$			3.86794i			0.214555i
$326$	0.312398	+	25.2916i	0.0173021	+	1.40077i
$327$	11.9744	+	2.06642i	0.662188	+	0.114273i
$328$	12.5712	−	23.7660i	0.694129	−	1.31226i
$329$	1.25784	−	2.17864i	0.0693468	−	0.120112i
$330$	2.84386	−	17.7878i	0.156550	−	0.979187i
$331$	3.00014	−	1.73213i	0.164902	−	0.0952065i	−0.415278	−	0.909695i	$-0.636316\pi$
$331$	3.00014	−	1.73213i	0.164902	−	0.0952065i	0.580180	+	0.814488i	$0.302982\pi$
$332$	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
$336$	2.44728	−	1.04081i	0.133510	−	0.0567806i
$337$	−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	$0.997476\pi$
$338$	−9.23596	−	15.5504i	−0.502370	−	0.845829i
$339$	−10.8977	−	9.07678i	−0.591884	−	0.492983i
$340$	26.2817	+	14.3201i	1.42533	+	0.776618i
$341$		−	2.37713i		−	0.128729i
$342$	6.48356	−	18.9645i	0.350591	−	1.02548i
$343$	−5.31737			−0.287111
$344$	−2.86649	+	1.79975i	−0.154551	+	0.0970360i
$345$	13.0461	+	35.4411i	0.702376	+	1.90809i
$346$	23.1268	−	13.7359i	1.24330	−	0.738444i
$347$	0.0408752	+	0.0235993i	0.00219430	+	0.00126688i	0.501097	−	0.865391i	$-0.332930\pi$
$347$	0.0408752	+	0.0235993i	0.00219430	+	0.00126688i	−0.498902	+	0.866658i	$0.666263\pi$
$348$	3.00392	+	7.57765i	0.161027	+	0.406205i
$349$	12.8884	−	7.44113i	0.689901	−	0.398314i	−0.113674	−	0.993518i	$-0.536262\pi$
$349$	12.8884	−	7.44113i	0.689901	−	0.398314i	0.803575	+	0.595204i	$0.202929\pi$
$350$	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	$0.997270\pi$
$354$	1.07651	−	1.32543i	0.0572161	−	0.0704460i
$355$	11.8590	+	6.84680i	0.629411	+	0.363390i
$356$	15.1314	−	0.373859i	0.801964	−	0.0198145i
$357$	−2.54870	+	0.938188i	−0.134891	+	0.0496542i
$358$	0.0370491	+	2.99948i	0.00195811	+	0.158527i
$359$	31.3426			1.65420			0.827101	−	0.562054i	$-0.189989\pi$
$359$	31.3426			1.65420			0.827101	+	0.562054i	$0.189989\pi$
$360$	21.0172	+	22.9034i	1.10770	+	1.20712i
$361$	−3.31599			−0.174526
$362$	0.0290468	+	2.35162i	0.00152667	+	0.123598i
$363$	−9.27652	−	7.72646i	−0.486891	−	0.405534i
$364$	−0.00871009	−	0.352529i	−0.000456533	−	0.0184775i
$365$	8.51135	+	4.91403i	0.445504	+	0.257212i
$366$	−4.27915	−	11.1963i	−0.223675	−	0.585238i
$367$	−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
$372$	3.21585	+	2.54663i	0.166734	+	0.132037i
$373$	−20.6021	−	11.8946i	−1.06674	−	0.615880i	−0.139448	−	0.990229i	$-0.544533\pi$
$373$	−20.6021	−	11.8946i	−1.06674	−	0.615880i	−0.927288	+	0.374349i	$0.877866\pi$
$374$	−9.97085	+	5.92206i	−0.515580	+	0.306223i
$375$	21.3889	+	3.69107i	1.10452	+	0.190606i
$376$	9.85675	+	15.6990i	0.508323	+	0.809614i
$377$	1.08086			0.0556673
$378$	−2.81996	+	0.0656899i	−0.145043	+	0.00337872i
$379$			24.0988i			1.23787i	0.785441	+	0.618937i	$0.212436\pi$
$379$			24.0988i			1.23787i	−0.785441	+	0.618937i	$0.787564\pi$
$380$	16.5603	−	30.3931i	0.849525	−	1.55913i
$381$	−6.18878	+	35.8625i	−0.317061	+	1.83729i
$382$	−12.5624	−	21.1510i	−0.642748	−	1.08218i
$383$	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	$0.00734361\pi$
$384$	−1.65248	+	19.5261i	−0.0843277	+	0.996438i
$385$	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	−0.830335	−	0.557265i	$-0.811851\pi$
$389$	−15.0467	+	8.68720i	−0.762897	+	0.440459i	0.0674382	+	0.997723i	$0.478517\pi$
$390$	3.85026	−	1.47155i	0.194965	−	0.0745147i
$391$	12.1566	−	21.0558i	0.614783	−	1.06484i
$392$	9.06265	−	17.1330i	0.457733	−	0.865347i
$393$	7.02759	−	8.43744i	0.354495	−	0.425613i
$394$	0.220066	+	17.8164i	0.0110867	+	0.897578i
$395$			39.2703i			1.97591i
$396$	−11.7886	+	2.46990i	−0.592401	+	0.124117i
$397$		−	26.2401i		−	1.31696i	−0.752600	−	0.658478i	$-0.771201\pi$
$397$		−	26.2401i		−	1.31696i	0.752600	−	0.658478i	$-0.228799\pi$
$398$	24.4263	−	0.301710i	1.22438	−	0.0151234i
$399$	1.08495	+	2.94740i	0.0543156	+	0.147555i
$400$	18.2614	+	28.3028i	0.913068	+	1.41514i
$401$	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	$-0.0150210\pi$
$402$	15.8335	−	19.4946i	0.789702	−	0.972303i
$403$	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
$408$	2.67029	−	19.8331i	0.132199	−	0.981887i
$409$	−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	$0.262639\pi$
$410$	−42.3421	+	25.1486i	−2.09113	+	1.24200i
$411$	−1.57242	+	0.578816i	−0.0775618	+	0.0285509i
$412$	−11.7582	+	21.5797i	−0.579283	+	1.06316i
$413$			0.267582i			0.0131668i
$414$	19.0213	−	16.6083i	0.934847	−	0.816253i
$415$	−23.2252			−1.14008
$416$	2.32618	+	1.15785i	0.114051	+	0.0567682i
$417$	−6.63243	+	7.96301i	−0.324791	+	0.389950i
$418$	6.84848	+	11.5306i	0.334970	+	0.563982i
$419$	1.38092	+	0.797277i	0.0674625	+	0.0389495i	0.533352	−	0.845893i	$-0.320932\pi$
$419$	1.38092	+	0.797277i	0.0674625	+	0.0389495i	−0.465889	+	0.884843i	$0.654266\pi$
$420$	−4.81931	−	0.709568i	−0.235158	−	0.0346234i
$421$	15.6612	−	9.04197i	0.763278	−	0.440679i	−0.0671934	−	0.997740i	$-0.521404\pi$
$421$	15.6612	−	9.04197i	0.763278	−	0.440679i	0.830471	+	0.557061i	$0.188071\pi$
$422$	−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
$426$	1.44548	−	9.04119i	0.0700336	−	0.438047i
$427$	1.62667	+	0.939156i	0.0787199	+	0.0454489i
$428$	0.326915	+	13.2314i	0.0158020	+	0.639565i
$429$	−0.271598	+	1.57384i	−0.0131129	+	0.0759859i
$430$	6.19923	−	0.0765720i	0.298953	−	0.00369263i
$431$	−34.7451			−1.67361			−0.836806	−	0.547499i	$-0.815580\pi$
$431$	−34.7451			−1.67361			−0.836806	+	0.547499i	$0.815580\pi$
$432$	9.28785	−	18.5940i	0.446862	−	0.894603i
$433$	12.7197			0.611270			0.305635	−	0.952149i	$-0.401131\pi$
$433$	12.7197			0.611270			0.305635	+	0.952149i	$0.401131\pi$
$434$	−0.642774	+	0.00793946i	−0.0308542	+	0.000381106i
$435$	2.53909	−	14.7134i	0.121740	−	0.705455i
$436$	−0.346571	−	14.0270i	−0.0165978	−	0.671770i
$437$	−24.3496	−	14.0583i	−1.16480	−	0.672498i
$438$	1.03744	−	6.48896i	0.0495706	−	0.310055i
$439$	−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	−0.414945	−	0.909846i	$-0.636199\pi$
$443$	3.48405	−	2.01152i	0.165532	−	0.0955702i	0.580478	+	0.814276i	$0.302866\pi$
$444$	19.6867	+	2.89855i	0.934287	+	0.137559i
$445$	−24.0104	−	13.8624i	−1.13820	−	0.657142i
$446$	17.7854	+	29.9449i	0.842164	+	1.41793i
$447$	−8.24006	+	9.89315i	−0.389741	+	0.467930i
$448$	−1.72810	−	2.53843i	−0.0816449	−	0.119929i
$449$	10.9179			0.515246			0.257623	−	0.966245i	$-0.417061\pi$
$449$	10.9179			0.515246			0.257623	+	0.966245i	$0.417061\pi$
$450$	−6.89363	−	35.0545i	−0.324969	−	1.65248i
$451$		−	19.0819i		−	0.898531i
$452$	−7.83557	+	14.3806i	−0.368554	+	0.676407i
$453$	1.60225	−	0.589795i	0.0752801	−	0.0277110i
$454$	−23.8569	+	14.1695i	−1.11966	+	0.665008i
$455$	−0.322964	+	0.559390i	−0.0151408	+	0.0262246i
$456$	−22.9357	−	3.08801i	−1.07406	−	0.144609i
$457$	−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	−0.717990	−	0.696054i	$-0.754938\pi$
$461$	−10.1812	+	5.87811i	−0.474185	+	0.273771i	0.243805	+	0.969824i	$0.421604\pi$
$462$	1.18996	−	1.46511i	0.0553619	−	0.0681631i
$463$	−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	$0.331433\pi$
$464$	7.90898	−	5.10299i	0.367165	−	0.236900i
$465$	−2.59560	−	7.05126i	−0.120368	−	0.326994i
$466$	−29.5862	+	0.365445i	−1.37056	+	0.0169289i
$467$			18.9230i			0.875650i	0.899060	+	0.437825i	$0.144251\pi$
$467$			18.9230i			0.875650i	−0.899060	+	0.437825i	$0.855749\pi$
$468$	−1.83817	−	2.05349i	−0.0849696	−	0.0949226i
$469$			3.93562i			0.181730i
$470$	−0.419364	−	33.9515i	−0.0193438	−	1.56607i
$471$	19.4987	−	23.4104i	0.898451	−	1.07870i
$472$	−1.74288	−	0.921910i	−0.0802225	−	0.0424344i
$473$	−1.20110	+	2.08037i	−0.0552267	+	0.0956554i
$474$	24.5271	−	9.37415i	1.12657	−	0.430569i
$475$	−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	$0.593455\pi$
$480$	21.2259	−	28.9456i	0.968825	−	1.32118i
$481$	1.31929	−	2.28508i	0.0601546	−	0.104191i
$482$	14.7872	+	24.8970i	0.673540	+	1.13403i
$483$	−0.672931	+	3.89947i	−0.0306194	+	0.177432i
$484$	−6.66990	+	12.2413i	−0.303177	+	0.556421i
$485$			21.8714i			0.993131i
$486$	−16.4466	+	14.6803i	−0.746031	+	0.665911i
$487$	−17.3370			−0.785614			−0.392807	−	0.919621i	$-0.628496\pi$
$487$	−17.3370			−0.785614			−0.392807	+	0.919621i	$0.628496\pi$
$488$	−11.7215	+	7.35948i	−0.530610	+	0.333148i
$489$	−30.5269	−	5.26802i	−1.38048	−	0.238228i
$490$	−30.5246	+	18.1297i	−1.37896	+	0.819018i
$491$	31.1204	+	17.9674i	1.40444	+	0.810856i	0.994845	−	0.101409i	$-0.0323351\pi$
$491$	31.1204	+	17.9674i	1.40444	+	0.810856i	0.409599	+	0.912265i	$0.365668\pi$
$492$	25.8145	+	20.4425i	1.16381	+	0.921620i
$493$	−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
$498$	5.54404	+	14.5058i	0.248435	+	0.650021i
$499$	10.4956	+	6.05962i	0.469846	+	0.271266i	0.716175	−	0.697920i	$-0.245891\pi$
$499$	10.4956	+	6.05962i	0.469846	+	0.271266i	−0.246329	+	0.969186i	$0.579224\pi$
$500$	−0.619049	−	25.0551i	−0.0276847	−	1.12050i
$501$	−2.76921	−	2.30649i	−0.123719	−	0.103046i
$502$	−0.490795	−	39.7346i	−0.0219053	−	1.77344i
$503$	32.3442			1.44215			0.721077	−	0.692855i	$-0.243647\pi$
$503$	32.3442			1.44215			0.721077	+	0.692855i	$0.243647\pi$
$504$	0.707232	+	3.17938i	0.0315026	+	0.141621i
$505$	20.3583			0.905932
$506$	0.208693	+	16.8957i	0.00927754	+	0.751105i
$507$	20.7876	−	7.65201i	0.923208	−	0.339838i
$508$	42.0097	−	1.03795i	1.86388	−	0.0460517i
$509$	2.90310	+	1.67610i	0.128677	+	0.0742919i	0.562957	−	0.826486i	$-0.309664\pi$
$509$	2.90310	+	1.67610i	0.128677	+	0.0742919i	−0.434280	+	0.900778i	$0.642997\pi$
$510$	−23.1101	+	28.4538i	−1.02333	+	1.25995i
$511$	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
$516$	−1.52763	−	3.85359i	−0.0672502	−	0.169645i
$517$	11.3936	+	6.57811i	0.501091	+	0.289305i
$518$	−2.68106	+	1.59238i	−0.117799	+	0.0699653i
$519$	11.3802	+	30.9156i	0.499535	+	1.35704i
$520$	−2.53083	−	4.03089i	−0.110984	−	0.176766i
$521$	21.5651			0.944786			0.472393	−	0.881388i	$-0.343390\pi$
$521$	21.5651			0.944786			0.472393	+	0.881388i	$0.343390\pi$
$522$	−9.79569	+	1.92637i	−0.428746	+	0.0843149i
$523$		−	24.9549i		−	1.09120i	−0.838046	−	0.545600i	$-0.816302\pi$
$523$		−	24.9549i		−	1.09120i	0.838046	−	0.545600i	$-0.183698\pi$
$524$	−11.1340	−	6.06659i	−0.486392	−	0.265020i
$525$	4.30179	+	3.58298i	0.187746	+	0.156374i
$526$	−18.4329	−	31.0351i	−0.803712	−	1.35319i
$527$	−2.41863	+	4.18919i	−0.105357	+	0.182484i
$528$	5.44310	+	12.7985i	0.236880	+	0.556984i
$529$	−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
$534$	−2.92660	+	18.3053i	−0.126646	+	0.792148i
$535$	12.1218	−	20.9955i	0.524070	−	0.907716i
$536$	−25.6344	−	13.5595i	−1.10724	−	0.585683i
$537$	−3.62036	−	0.624764i	−0.156230	−	0.0269606i
$538$	−0.321386	−	26.0192i	−0.0138559	−	1.12177i
$539$		−	13.7562i		−	0.592523i
$540$	−32.2716	+	20.1985i	−1.38875	+	0.869205i
$541$			41.9065i			1.80170i	0.434131	+	0.900850i	$0.357055\pi$
$541$			41.9065i			1.80170i	−0.434131	+	0.900850i	$0.642945\pi$
$542$	−31.6950	+	0.391492i	−1.36142	+	0.0168160i
$543$	−2.83840	−	0.489821i	−0.121807	−	0.0210202i
$544$	−23.0639	+	1.42615i	−0.988858	+	0.0611458i
$545$	−12.8506	+	22.2579i	−0.550460	+	0.953424i
$546$	0.426473	+	0.0681833i	0.0182514	+	0.00291797i
$547$	−25.7251	+	14.8524i	−1.09993	+	0.635043i	−0.936202	−	0.351462i	$-0.885684\pi$
$547$	−25.7251	+	14.8524i	−1.09993	+	0.635043i	−0.163726	+	0.986506i	$0.552351\pi$
$548$	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
$552$	−23.0805	−	17.8181i	−0.982372	−	0.758389i
$553$	−2.05737	+	3.56346i	−0.0874881	+	0.151534i
$554$	28.4203	−	16.8799i	1.20746	−	0.717158i
$555$	−28.0068	−	23.3270i	−1.18882	−	0.990177i
$556$	10.5080	+	5.72547i	0.445637	+	0.242814i
$557$		−	21.9632i		−	0.930609i	−0.885151	−	0.465305i	$-0.845945\pi$
$557$		−	21.9632i		−	0.930609i	0.885151	−	0.465305i	$-0.154055\pi$
$558$	−3.78442	+	3.30433i	−0.160207	+	0.139884i
$559$	−0.549669			−0.0232485
$560$	0.277782	+	5.61799i	0.0117384	+	0.237403i
$561$	−4.90644	−	13.3289i	−0.207150	−	0.562747i
$562$	7.64739	+	12.8757i	0.322586	+	0.543131i
$563$	−23.8394	−	13.7637i	−1.00471	−	0.580069i	−0.0950710	−	0.995470i	$-0.530308\pi$
$563$	−23.8394	−	13.7637i	−1.00471	−	0.580069i	−0.909638	+	0.415401i	$0.863641\pi$
$564$	−21.1051	+	8.36643i	−0.888684	+	0.352290i
$565$	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	$0.712550\pi$
$570$	32.9049	+	26.7253i	1.37824	+	1.11940i
$571$	3.92630	+	2.26685i	0.164311	+	0.0948648i	0.579900	−	0.814687i	$-0.303091\pi$
$571$	3.92630	+	2.26685i	0.164311	+	0.0948648i	−0.415590	+	0.909552i	$0.636425\pi$
$572$	1.84362	−	0.0455512i	0.0770855	−	0.00190459i
$573$	28.2744	−	10.4080i	1.18118	−	0.434799i
$574$	−5.15973	+	0.0637322i	−0.215363	+	0.00266013i
$575$	−50.1188			−2.09010
$576$	−23.1454	−	6.34754i	−0.964391	−	0.264481i
$577$	23.3909			0.973776			0.486888	−	0.873464i	$-0.338132\pi$
$577$	23.3909			0.973776			0.486888	+	0.873464i	$0.338132\pi$
$578$	−0.442841	+	0.00546991i	−0.0184198	+	0.000227518i
$579$	−3.77195	−	3.14168i	−0.156757	−	0.130564i
$580$	−17.2355	+	0.425845i	−0.715664	+	0.0176822i
$581$	−2.10750	−	1.21676i	−0.0874337	−	0.0504799i
$582$	13.6603	−	5.22089i	0.566237	−	0.216413i
$583$	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	−0.344393	−	0.938826i	$-0.611915\pi$
$587$	7.18259	−	4.14687i	0.296457	−	0.171160i	0.640850	+	0.767666i	$0.278582\pi$
$588$	18.6098	+	14.7371i	0.767455	+	0.607748i
$589$	4.84453	+	2.79699i	0.199615	+	0.115248i
$590$	1.84427	+	3.10516i	0.0759275	+	0.127837i
$591$	−21.5044	−	3.71100i	−0.884572	−	0.152650i
$592$	−1.13473	−	22.9492i	−0.0466370	−	0.943208i
$593$	−43.5169			−1.78702			−0.893512	−	0.449039i	$-0.851766\pi$
$593$	−43.5169			−1.78702			−0.893512	+	0.449039i	$0.851766\pi$
$594$	−0.343538	−	14.7475i	−0.0140956	−	0.605099i
$595$		−	5.74432i		−	0.235494i
$596$	13.0550	+	7.11326i	0.534752	+	0.291371i
$597$	−5.08779	+	29.4825i	−0.208229	+	1.20664i
$598$	−3.32423	+	1.97438i	−0.135938	+	0.0807385i
$599$	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	$0.159804\pi$
$600$	−38.1587	+	15.6749i	−1.55782	+	0.639924i
$601$	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
$606$	−4.85969	−	12.7152i	−0.197411	−	0.516520i
$607$	−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	$0.297095\pi$
$608$	1.64925	+	26.6719i	0.0668860	+	1.08169i
$609$	1.00124	−	1.20210i	0.0405721	−	0.0487116i
$610$	25.3497	−	0.313116i	1.02638	−	0.0126777i
$611$			3.01039i			0.121787i
$612$	23.2880	+	7.64175i	0.941361	+	0.308899i
$613$			0.0630655i			0.00254719i	0.999999	+	0.00127360i	$0.000405399\pi$
$613$			0.0630655i			0.00254719i	−0.999999	+	0.00127360i	$0.999595\pi$
$614$	−0.0109810	−	0.889017i	−0.000443157	−	0.0358778i
$615$	−20.8356	−	56.6024i	−0.840174	−	2.28243i
$616$	−1.92655	−	1.01906i	−0.0776227	−	0.0410592i
$617$	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	$-0.0412034\pi$
$618$	−23.3632	−	18.9755i	−0.939806	−	0.763308i
$619$	38.2663	−	22.0930i	1.53805	−	0.887994i	0.539099	−	0.842243i	$-0.318765\pi$
$619$	38.2663	−	22.0930i	1.53805	−	0.887994i	0.998953	−	0.0457517i	$-0.0145683\pi$
$620$	−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
$624$	−1.91345	+	2.54289i	−0.0765994	+	0.101797i
$625$	−1.90220	+	3.29471i	−0.0760881	+	0.131788i
$626$	−4.14472	−	6.97838i	−0.165656	−	0.278912i
$627$	−15.4140	+	5.67398i	−0.615576	+	0.226597i
$628$	−30.8923	−	16.8323i	−1.23274	−	0.671682i
$629$			23.4653i			0.935621i
$630$	1.93000	−	5.64526i	0.0768929	−	0.224913i
$631$	19.6743			0.783221			0.391610	−	0.920131i	$-0.371918\pi$
$631$	19.6743			0.783221			0.391610	+	0.920131i	$0.371918\pi$
$632$	−16.1221	−	25.6779i	−0.641302	−	1.02141i
$633$	19.4802	−	23.3883i	0.774269	−	0.929601i
$634$	15.1897	−	9.02173i	0.603260	−	0.358299i
$635$	−66.6607	−	38.4866i	−2.64535	−	1.52729i
$636$	−26.1768	−	3.85413i	−1.03798	−	0.152826i
$637$	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	$0.845838\pi$
$642$	−16.0068	−	2.55912i	−0.631737	−	0.101000i
$643$	12.9370	+	7.46917i	0.510185	+	0.294555i	0.732910	−	0.680326i	$-0.238162\pi$
$643$	12.9370	+	7.46917i	0.510185	+	0.294555i	−0.222725	+	0.974881i	$0.571495\pi$
$644$	4.56788	−	0.112861i	0.180000	−	0.00444734i
$645$	−1.29124	+	7.48246i	−0.0508427	+	0.294621i
$646$	−0.337061	−	27.2883i	−0.0132615	−	1.07365i
$647$	−8.81283			−0.346468			−0.173234	−	0.984881i	$-0.555422\pi$
$647$	−8.81283			−0.346468			−0.173234	+	0.984881i	$0.555422\pi$
$648$	20.3189	+	15.3344i	0.798202	+	0.602390i
$649$	−1.39937			−0.0549302
$650$	0.0675606	+	5.46968i	0.00264995	+	0.214538i
$651$	0.133884	−	0.775827i	0.00524734	−	0.0304071i
$652$	0.883529	+	35.7596i	0.0346017	+	1.40045i
$653$	−18.1802	−	10.4964i	−0.711447	−	0.410754i	0.100150	−	0.994972i	$-0.468068\pi$
$653$	−18.1802	−	10.4964i	−0.711447	−	0.410754i	−0.811597	+	0.584218i	$0.801401\pi$
$654$	16.9692	+	2.71299i	0.663549	+	0.106086i
$655$	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	$0.700027\pi$
$659$	−40.6209	+	23.4525i	−1.58237	+	0.913580i	−0.994513	+	0.104612i	$0.966640\pi$
$660$	3.71083	−	25.2035i	0.144444	−	0.981046i
$661$	0.736985	+	0.425498i	0.0286654	+	0.0165500i	0.514264	−	0.857632i	$-0.328065\pi$
$661$	0.736985	+	0.425498i	0.0286654	+	0.0165500i	−0.485599	+	0.874182i	$0.661398\pi$
$662$	4.21226	−	2.50182i	0.163714	−	0.0972359i
$663$	2.07995	−	2.49723i	0.0807787	−	0.0969843i
$664$	15.1864	−	9.53489i	0.589345	−	0.370026i
$665$	−6.64293			−0.257602
$666$	−7.88394	+	23.0606i	−0.305497	+	0.893581i
$667$			14.0053i			0.542287i
$668$	−1.99109	+	3.65424i	−0.0770375	+	0.141387i
$669$	−40.0300	+	14.7352i	−1.54765	+	0.569698i
$670$	27.1257	+	45.6710i	1.04796	+	1.76442i
$671$	−4.91150	+	8.50697i	−0.189606	+	0.328408i
$672$	3.44253	−	1.51455i	0.132798	−	0.0584252i
$673$	−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	−0.353176	−	0.935557i	$-0.614898\pi$
$677$	7.29713	−	4.21300i	0.280451	−	0.161919i	0.633628	+	0.773638i	$0.281565\pi$
$678$	−15.5691	−	12.6452i	−0.597928	−	0.485635i
$679$	−1.14584	+	1.98466i	−0.0439733	+	0.0761641i
$680$	37.4153	+	19.7911i	1.43481	+	0.758955i
$681$	−11.7395	−	31.8916i	−0.449857	−	1.22209i
$682$	−0.0415210	−	3.36152i	−0.00158992	−	0.128719i
$683$		−	23.3602i		−	0.893853i	−0.894571	−	0.446926i	$-0.852519\pi$
$683$		−	23.3602i		−	0.893853i	0.894571	−	0.446926i	$-0.147481\pi$
$684$	8.83718	−	26.9310i	0.337898	−	1.02973i
$685$		−	3.54396i		−	0.135408i
$686$	−7.51933	+	0.0928776i	−0.287089	+	0.00354609i
$687$	−27.3187	+	32.7993i	−1.04227	+	1.25137i
$688$	−4.02208	+	2.59510i	−0.153340	+	0.0989374i
$689$	−1.75423	+	3.03841i	−0.0668308	+	0.115754i
$690$	19.0676	+	49.8896i	0.725889	+	1.89927i
$691$	−25.9304	+	14.9709i	−0.986439	+	0.569521i	−0.904208	−	0.427092i	$-0.859538\pi$
$691$	−25.9304	+	14.9709i	−0.986439	+	0.569521i	−0.0822311	+	0.996613i	$0.526205\pi$
$692$	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
$696$	4.38021	+	10.6631i	0.166032	+	0.404185i
$697$	−19.4150	+	33.6278i	−0.735396	+	1.27374i
$698$	18.0956	−	10.7477i	0.684929	−	0.406805i
$699$	6.16255	−	35.7105i	0.233089	−	1.35070i
$700$	3.09303	−	5.67663i	0.116905	−	0.214556i
$701$			0.718775i			0.0271478i	0.999908	+	0.0135739i	$0.00432083\pi$
$701$			0.718775i			0.0271478i	−0.999908	+	0.0135739i	$0.995679\pi$
$702$	2.88312	−	1.75534i	0.108816	−	0.0662509i
$703$	27.1360			1.02346
$704$	13.2752	−	9.03742i	0.500328	−	0.340611i
$705$	40.9794	+	7.07181i	1.54337	+	0.266340i
$706$	−13.3664	−	22.5048i	−0.503052	−	0.846978i
$707$	1.84735	+	1.06657i	0.0694767	+	0.0401124i
$708$	1.49915	−	1.89311i	0.0563416	−	0.0711473i
$709$	−10.9918	+	6.34613i	−0.412807	+	0.238334i	−0.691995	−	0.721902i	$-0.743268\pi$
$709$	−10.9918	+	6.34613i	−0.412807	+	0.238334i	0.279188	+	0.960236i	$0.409935\pi$
$710$	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
$714$	−3.58774	+	1.37121i	−0.134268	+	0.0513164i
$715$	−2.92544	−	1.68900i	−0.109405	−	0.0631652i
$716$	0.104783	+	4.24093i	0.00391591	+	0.158491i
$717$	−13.6970	−	11.4083i	−0.511523	−	0.426050i
$718$	44.3218	−	0.547456i	1.65408	−	0.0204309i
$719$	7.74226			0.288738			0.144369	−	0.989524i	$-0.453885\pi$
$719$	7.74226			0.288738			0.144369	+	0.989524i	$0.453885\pi$
$720$	30.1206	+	32.0207i	1.12253	+	1.19334i
$721$	4.71662			0.175656
$722$	−4.68916	+	0.0579198i	−0.174512	+	0.00215555i
$723$	−33.2819	+	12.2513i	−1.23777	+	0.455629i
$724$	0.0821506	+	3.32493i	0.00305310	+	0.123570i
$725$	17.1599	+	9.90730i	0.637304	+	0.367948i
$726$	−13.2529	−	10.7640i	−0.491862	−	0.399489i
$727$	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
$732$	−6.24674	−	15.7580i	−0.230886	−	0.582431i
$733$	−32.7535	−	18.9102i	−1.20978	−	0.698466i	−0.247068	−	0.968998i	$-0.579467\pi$
$733$	−32.7535	−	18.9102i	−1.20978	−	0.698466i	−0.962711	+	0.270532i	$0.912800\pi$
$734$	−14.7769	−	24.8796i	−0.545427	−	0.918323i
$735$	−15.0205	−	40.8050i	−0.554040	−	1.50511i
$736$	−15.0028	+	30.1415i	−0.553010	+	1.11103i
$737$	−20.5821			−0.758152
$738$	−30.3786	+	26.5248i	−1.11825	+	0.976391i
$739$		−	6.61431i		−	0.243311i	−0.992572	−	0.121656i	$-0.961180\pi$
$739$		−	6.61431i		−	0.243311i	0.992572	−	0.121656i	$-0.0388204\pi$
$740$	−20.1372	+	36.9577i	−0.740257	+	1.35859i
$741$	−2.88788	−	2.40533i	−0.106089	−	0.0883620i
$742$	3.56494	−	2.11735i	0.130873	−	0.0777304i
$743$	−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	$0.205326\pi$
$744$	4.59203	+	3.54503i	0.168352	+	0.129967i
$745$	−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
$750$	30.3106	+	4.84596i	1.10679	+	0.176950i
$751$	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	$0.0110863\pi$
$752$	14.2127	+	22.0279i	0.518284	+	0.803274i
$753$	47.9595	+	8.27636i	1.74774	+	0.301607i
$754$	1.52846	−	0.0188793i	0.0556631	−	0.000687542i
$755$			3.61118i			0.131424i
$756$	−3.98658	+	0.142148i	−0.144990	+	0.00516988i
$757$			48.0424i			1.74613i	0.487602	+	0.873066i	$0.337872\pi$
$757$			48.0424i			1.74613i	−0.487602	+	0.873066i	$0.662128\pi$
$758$	0.420930	+	34.0783i	0.0152889	+	1.23778i
$759$	−20.3931	−	3.51922i	−0.740221	−	0.127740i
$760$	22.8871	−	43.2683i	0.830203	−	1.56951i
$761$	−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	$0.180597\pi$
$762$	−8.12518	+	50.8214i	−0.294344	+	1.84107i
$763$	−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
$768$	−1.99572	+	27.6409i	−0.0720143	+	0.997404i
$769$	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	$-0.0411592\pi$
$770$	2.03862	+	3.43239i	0.0734669	+	0.123695i
$771$	14.7377	+	12.2751i	0.530765	+	0.442076i
$772$	−2.71207	+	4.97746i	−0.0976094	+	0.179143i
$773$		−	18.8545i		−	0.678149i	−0.940759	−	0.339075i	$-0.889886\pi$
$773$		−	18.8545i		−	0.678149i	0.940759	−	0.339075i	$-0.110114\pi$
$774$	4.98156	−	0.979648i	0.179059	−	0.0352127i
$775$	9.97148			0.358186
$776$	−8.97912	−	14.3012i	−0.322332	−	0.513382i
$777$	−1.31929	−	3.58401i	−0.0473294	−	0.128576i
$778$	−21.1258	+	12.5474i	−0.757398	+	0.449847i
$779$	38.8884	+	22.4522i	1.39332	+	0.804434i
$780$	5.41896	−	2.14818i	0.194030	−	0.0769170i
$781$	−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
$786$	9.79037	−	12.0542i	0.349211	−	0.429959i
$787$	14.8124	+	8.55193i	0.528004	+	0.304843i	0.740203	−	0.672383i	$-0.234729\pi$
$787$	14.8124	+	8.55193i	0.528004	+	0.304843i	−0.212199	+	0.977226i	$0.568063\pi$
$788$	0.622392	+	25.1904i	0.0221718	+	0.897372i
$789$	41.4873	−	15.2717i	1.47699	−	0.543687i
$790$	0.685928	+	55.5324i	0.0244042	+	1.97576i
$791$	3.14313			0.111757
$792$	−16.6272	+	3.69861i	−0.590823	+	0.131424i
$793$	−2.24769			−0.0798178
$794$	−0.458332	−	37.1063i	−0.0162656	−	1.31685i
$795$	37.2400	+	31.0173i	1.32077	+	1.10007i
$796$	34.5361	−	0.853301i	1.22410	−	0.0302444i
$797$	−3.11800	−	1.80018i	−0.110445	−	0.0637656i	0.443760	−	0.896146i	$-0.353644\pi$
$797$	−3.11800	−	1.80018i	−0.110445	−	0.0637656i	−0.554205	+	0.832380i	$0.686978\pi$
$798$	1.58572	+	4.14898i	0.0561339	+	0.146872i
$799$	−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
$804$	22.0497	−	27.8440i	0.777633	−	0.981982i
$805$	−7.24829	−	4.18480i	−0.255469	−	0.147495i
$806$	0.661378	−	0.392817i	0.0232960	−	0.0138364i
$807$	31.4052	+	5.41958i	1.10551	+	0.190778i
$808$	−13.3118	+	8.35790i	−0.468306	+	0.294030i
$809$	13.5918			0.477864			0.238932	−	0.971036i	$-0.423203\pi$
$809$	13.5918			0.477864			0.238932	+	0.971036i	$0.423203\pi$
$810$	−17.1220	−	43.3704i	−0.601605	−	1.52388i
$811$		−	10.0627i		−	0.353349i	−0.984269	−	0.176674i	$-0.943466\pi$
$811$		−	10.0627i		−	0.353349i	0.984269	−	0.176674i	$-0.0565339\pi$
$812$	−1.58629	−	0.864321i	−0.0556678	−	0.0303317i
$813$	6.60179	−	38.2558i	0.231535	−	1.34169i
$814$	−8.32768	−	14.0211i	−0.291885	−	0.491441i
$815$	32.7606	−	56.7430i	1.14755	−	1.98762i
$816$	3.42965	−	28.0928i	0.120062	−	0.983445i
$817$	−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	0.213273	−	0.976993i	$-0.431588\pi$
$821$	33.4098	−	19.2891i	1.16601	−	0.673196i	0.952737	+	0.303797i	$0.0982544\pi$
$822$	−2.21346	+	0.845972i	−0.0772032	+	0.0295067i
$823$	−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	$0.976842\pi$
$824$	−16.2504	+	30.7214i	−0.566108	+	1.07023i
$825$	−18.7379	+	22.4971i	−0.652371	+	0.783248i
$826$	0.00467381	+	0.378389i	0.000162623	+	0.0131658i
$827$			27.7190i			0.963886i	0.876203	+	0.481943i	$0.160069\pi$
$827$			27.7190i			0.963886i	−0.876203	+	0.481943i	$0.839931\pi$
$828$	26.6081	−	23.8181i	0.924694	−	0.827736i
$829$		−	10.3137i		−	0.358208i	−0.983830	−	0.179104i	$-0.942680\pi$
$829$		−	10.3137i		−	0.358208i	0.983830	−	0.179104i	$-0.0573199\pi$
$830$	−32.8429	+	0.405671i	−1.13999	+	0.0140810i
$831$	13.9850	+	37.9919i	0.485135	+	1.31793i
$832$	3.30969	+	1.59669i	0.114743	+	0.0553552i
$833$	−13.9964	+	24.2425i	−0.484946	+	0.839951i
$834$	−9.23987	+	11.3764i	−0.319950	+	0.393932i
$835$	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	$-0.397267\pi$
$840$	−6.82741	−	0.919226i	−0.235568	−	0.0317163i
$841$	−11.7315	+	20.3195i	−0.404534	+	0.700673i
$842$	21.9886	−	13.0599i	0.757777	−	0.450072i
$843$	−17.2121	+	6.33588i	−0.592818	+	0.218219i
$844$	−30.8631	−	16.8164i	−1.06235	−	0.578844i
$845$			46.8516i			1.61174i
$846$	−5.36527	−	27.2827i	−0.184462	−	0.937998i
$847$	2.67553			0.0919325
$848$	1.50882	+	30.5150i	0.0518130	+	1.04789i
$849$	−9.84342	+	11.8182i	−0.337825	+	0.405599i
$850$	−24.8416	−	41.8252i	−0.852059	−	1.43459i
$851$	29.6089	+	17.0947i	1.01498	+	0.585999i
$852$	1.88614	−	12.8104i	0.0646180	−	0.438879i
$853$	−24.4212	+	14.0996i	−0.836166	+	0.482761i	−0.855959	−	0.517043i	$-0.827033\pi$
$853$	−24.4212	+	14.0996i	−0.836166	+	0.482761i	0.0197931	+	0.999804i	$0.493699\pi$
$854$	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	$0.653140\pi$
$858$	−0.356578	+	2.23033i	−0.0121734	+	0.0761421i
$859$	−41.6368	−	24.0390i	−1.42063	−	0.820201i	−0.424278	−	0.905532i	$-0.639472\pi$
$859$	−41.6368	−	24.0390i	−1.42063	−	0.820201i	−0.996353	+	0.0853309i	$0.972805\pi$
$860$	8.76503	−	0.216562i	0.298885	−	0.00738469i
$861$	1.07473	−	6.22778i	0.0366266	−	0.212242i
$862$	−49.1332	+	0.606887i	−1.67348	+	0.0206706i
$863$	37.6968			1.28321			0.641607	−	0.767034i	$-0.278268\pi$
$863$	37.6968			1.28321			0.641607	+	0.767034i	$0.278268\pi$
$864$	12.8092	−	26.4561i	0.435779	−	0.900054i
$865$	−69.6783			−2.36913
$866$	17.9870	−	0.222173i	0.611223	−	0.00754974i
$867$	0.0922398	−	0.534508i	0.00313263	−	0.0181528i
$868$	−0.908812	+	0.0224545i	−0.0308471	+	0.000762154i
$869$	−18.6358	−	10.7594i	−0.632177	−	0.364988i
$870$	3.33355	−	20.8507i	0.113018	−	0.706905i
$871$	−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
$876$	1.35370	−	9.19420i	0.0457374	−	0.310643i
$877$	21.6823	+	12.5183i	0.732158	+	0.422711i	0.819211	−	0.573492i	$-0.194412\pi$
$877$	21.6823	+	12.5183i	0.732158	+	0.422711i	−0.0870533	+	0.996204i	$0.527745\pi$
$878$	−10.7735	−	18.1391i	−0.363587	−	0.612164i
$879$	−12.5709	+	15.0928i	−0.424006	+	0.509069i
$880$	−29.3804	+	1.45272i	−0.990413	+	0.0489711i
$881$	−21.0382			−0.708795			−0.354398	−	0.935095i	$-0.615314\pi$
$881$	−21.0382			−0.708795			−0.354398	+	0.935095i	$0.615314\pi$
$882$	−21.9001	+	19.1219i	−0.737415	+	0.643867i
$883$		−	55.5904i		−	1.87077i	−0.353636	−	0.935383i	$-0.615055\pi$
$883$		−	55.5904i		−	1.87077i	0.353636	−	0.935383i	$-0.384945\pi$
$884$	−3.29533	−	1.79553i	−0.110834	−	0.0603902i
$885$	−4.15094	+	1.52798i	−0.139532	+	0.0513626i
$886$	4.89169	−	2.90536i	0.164339	−	0.0976074i
$887$	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	$0.159234\pi$
$888$	27.8896	+	3.75500i	0.935915	+	0.126009i
$889$	−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
$894$	−11.4795	+	14.1339i	−0.383932	+	0.472708i
$895$	3.88527	−	6.72948i	0.129870	−	0.224942i
$896$	−2.48805	−	3.55942i	−0.0831199	−	0.118912i
$897$	−1.63578	−	4.44379i	−0.0546171	−	0.148374i
$898$	15.4390	−	0.190701i	0.515207	−	0.00636376i
$899$		−	2.78645i		−	0.0929332i
$900$	−10.3606	−	49.4504i	−0.345354	−	1.64835i
$901$		−	31.2011i		−	1.03946i
$902$	−0.333300	−	26.9838i	−0.0110977	−	0.898463i
$903$	−0.509175	+	0.611324i	−0.0169443	+	0.0203436i
$904$	−10.8291	+	20.4726i	−0.360172	+	0.680908i
$905$	3.04608	−	5.27597i	0.101255	−	0.175379i
$906$	2.25544	−	0.862018i	0.0749321	−	0.0286386i
$907$	37.3197	−	21.5465i	1.23918	−	0.715440i	0.270252	−	0.962789i	$-0.412893\pi$
$907$	37.3197	−	21.5465i	1.23918	−	0.715440i	0.968926	+	0.247349i	$0.0795595\pi$
$908$	−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	$0.875266\pi$
$912$	−32.4875	−	3.96616i	−1.07577	−	0.131333i
$913$	6.36331	−	11.0216i	0.210595	−	0.364761i
$914$	−1.17745	−	1.98244i	−0.0389465	−	0.0655734i
$915$	−5.28012	+	30.5970i	−0.174555	+	1.01151i
$916$	43.2818	+	23.5830i	1.43007	+	0.779204i
$917$			2.43353i			0.0803622i
$918$	−14.3996	+	26.3390i	−0.475257	+	0.869315i
$919$	1.66862			0.0550426			0.0275213	−	0.999621i	$-0.491239\pi$
$919$	1.66862			0.0550426			0.0275213	+	0.999621i	$0.491239\pi$
$920$	52.2302	−	32.7932i	1.72198	−	1.08116i
$921$	1.07304	+	0.185174i	0.0353579	+	0.00610170i
$922$	−14.2946	+	8.49010i	−0.470767	+	0.279606i
$923$	−1.48694	−	0.858486i	−0.0489433	−	0.0282574i
$924$	1.65714	−	2.09261i	0.0545158	−	0.0688417i
$925$	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	$-0.445017\pi$
$930$	−3.79362	−	9.92589i	−0.124398	−	0.325483i
$931$	28.0348	+	16.1859i	0.918804	+	0.530472i
$932$	−41.8317	+	1.03355i	−1.37024	+	0.0338552i
$933$	−25.6711	−	21.3816i	−0.840435	−	0.700002i
$934$	0.330524	+	26.7591i	0.0108151	+	0.875583i
$935$	30.0410			0.982447
$936$	−2.63524	−	2.87175i	−0.0861355	−	0.0938659i
$937$	−9.30185			−0.303878			−0.151939	−	0.988390i	$-0.548552\pi$
$937$	−9.30185			−0.303878			−0.151939	+	0.988390i	$0.548552\pi$
$938$	0.0687428	+	5.56538i	0.00224453	+	0.181716i
$939$	9.32861	−	3.43391i	0.304428	−	0.112061i
$940$	−1.18605	−	48.0037i	−0.0386847	−	1.56571i
$941$	5.42009	+	3.12929i	0.176690	+	0.102012i	0.585736	−	0.810502i	$-0.300805\pi$
$941$	5.42009	+	3.12929i	0.176690	+	0.102012i	−0.409047	+	0.912513i	$0.634139\pi$
$942$	27.1643	−	33.4454i	0.885059	−	1.08971i
$943$	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	0.277789	−	0.960642i	$-0.410399\pi$
$947$	38.4243	−	22.1843i	1.24862	−	0.720893i	0.970835	+	0.239749i	$0.0770652\pi$
$948$	34.5202	−	13.6844i	1.12117	−	0.444450i
$949$	−1.06720	−	0.616146i	−0.0346426	−	0.0200009i
$950$	−48.3681	+	28.7277i	−1.56927	+	0.932048i
$951$	7.47452	+	20.3054i	0.242378	+	0.658448i
$952$	2.35828	+	3.75606i	0.0764322	+	0.121735i
$953$	6.11599			0.198116			0.0990582	−	0.995082i	$-0.468417\pi$
$953$	6.11599			0.198116			0.0990582	+	0.995082i	$0.468417\pi$
$954$	10.4831	−	30.6631i	0.339402	−	0.992755i
$955$			63.7257i			2.06211i
$956$	−9.84825	+	18.0745i	−0.318515	+	0.584571i
$957$	6.28662	+	5.23616i	0.203218	+	0.169261i
$958$	21.6306	+	36.4190i	0.698854	+	1.17665i
$959$	0.185668	−	0.321586i	0.00599552	−	0.0103845i
$960$	29.5101	−	41.3029i	0.952433	−	1.33304i
$961$	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
$966$	−0.883484	+	5.52602i	−0.0284256	+	0.177797i
$967$	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	$-0.0174248\pi$
$968$	−9.21812	+	17.4269i	−0.296282	+	0.560123i
$969$	32.9370	+	5.68392i	1.05809	+	0.182594i
$970$	0.382025	+	30.9285i	0.0122661	+	0.993055i
$971$			42.4798i			1.36324i	0.731706	+	0.681621i	$0.238725\pi$
$971$			42.4798i			1.36324i	−0.731706	+	0.681621i	$0.761275\pi$
$972$	−23.0007	+	21.0467i	−0.737749	+	0.675075i
$973$		−	2.29669i		−	0.0736286i
$974$	−24.5163	+	0.302822i	−0.785554	+	0.00970304i
$975$	−6.60189	−	1.13929i	−0.211430	−	0.0364863i
$976$	−16.4470	+	10.6118i	−0.526454	+	0.339676i
$977$	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	$0.0877975\pi$
$978$	−43.2603	−	6.91633i	−1.38331	−	0.221160i
$979$	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	$0.990570\pi$
$984$	36.8615	+	28.4570i	1.17510	+	0.907175i
$985$	23.0779	−	39.9720i	0.735322	−	1.27361i
$986$	−11.6877	+	6.94178i	−0.372213	+	0.221071i
$987$	3.34806	+	2.78861i	0.106570	+	0.0887626i
$988$	−2.07641	+	3.81084i	−0.0660595	+	0.121239i
$989$		−	7.12233i		−	0.226477i
$990$	29.5230	+	10.0933i	0.938303	+	0.320786i
$991$	−49.5495			−1.57399			−0.786996	−	0.616958i	$-0.788365\pi$
$991$	−49.5495			−1.57399			−0.786996	+	0.616958i	$0.788365\pi$
$992$	2.98491	−	5.99686i	0.0947710	−	0.190400i
$993$	2.07276	+	5.63089i	0.0657771	+	0.178691i
$994$	1.03619	+	1.74461i	0.0328660	+	0.0553357i
$995$	−54.8017	−	31.6398i	−1.73733	−	1.00305i
$996$	8.09323	+	20.4159i	0.256444	+	0.646903i
$997$	−34.4541	+	19.8921i	−1.09117	+	0.629988i	−0.933888	−	0.357565i	$-0.883607\pi$
$997$	−34.4541	+	19.8921i	−1.09117	+	0.629988i	−0.157284	+	0.987553i	$0.550274\pi$
$998$	14.9477	+	8.38562i	0.473161	+	0.265442i
$999$	−26.0111	−	14.6405i	−0.822956	−	0.463205i

Twists

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

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

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

\(f(q)\)	\(=\)	\(q+(1.41411 - 0.0174668i) q^{2} +(-0.294546 + 1.70682i) q^{3} +(1.99939 - 0.0493999i) q^{4} +(-3.17262 - 1.83171i) q^{5} +(-0.386706 + 2.41877i) 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} +(-0.504595 + 3.42715i) q^{12} +(0.397799 + 0.229669i) q^{13} +(-0.277210 - 0.466733i) q^{14} +(4.06089 - 4.87557i) q^{15} +(3.99512 - 0.197539i) q^{16} -4.08495 q^{17} +(-4.01451 - 1.37248i) q^{18} +4.72398i q^{19} +(-6.43379 - 3.50558i) q^{20} +(0.623923 - 0.229669i) q^{21} +(2.44087 - 1.44973i) q^{22} +(-2.97594 + 5.15447i) q^{23} +(-0.653689 + 4.85517i) 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} +(5.65736 - 6.96551i) q^{30} +(0.592083 - 1.02552i) q^{31} +(5.64607 - 0.349123i) q^{32} +(1.20110 + 3.26293i) q^{33} +(-5.77656 + 0.0713512i) q^{34} +1.40621i q^{35} +(-5.70092 - 1.87071i) q^{36} -5.74432i q^{37} +(0.0825129 + 6.68021i) q^{38} +(-0.509175 + 0.611324i) q^{39} +(-9.15929 - 4.84488i) q^{40} +(4.75281 - 8.23212i) q^{41} +(0.878281 - 0.335675i) 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} +(-0.839581 + 6.87714i) q^{48} +(3.42633 - 5.93458i) q^{49} +(6.08124 + 10.2389i) q^{50} +(1.20321 - 6.97229i) q^{51} +(0.806700 + 0.439547i) q^{52} +7.63807i q^{53} +(3.52503 - 6.44780i) q^{54} -7.35407 q^{55} +(-0.577308 - 0.919487i) q^{56} +(-8.06300 - 1.39143i) q^{57} +(2.86116 - 1.69935i) q^{58} +(-0.603703 - 0.348548i) q^{59} +(7.87845 - 9.94878i) 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} +(1.75548 + 4.59315i) q^{66} +(-8.87932 - 5.12648i) q^{67} +(-8.16741 + 0.201796i) q^{68} +(-7.92122 - 6.59762i) q^{69} +(0.0245621 + 1.98853i) q^{70} -3.73792 q^{71} +(-8.09437 - 2.54580i) q^{72} -2.68275 q^{73} +(-0.100335 - 8.12307i) q^{74} +(-13.6872 + 5.03832i) q^{75} +(0.233364 + 9.44508i) q^{76} +(-0.667322 - 0.385279i) q^{77} +(-0.709349 + 0.873370i) 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} +(1.23612 - 0.490020i) q^{84} +(12.9600 + 7.48246i) q^{85} +(-1.45503 + 0.864199i) q^{86} +(1.40792 + 3.82477i) q^{87} +(4.80864 - 3.01915i) q^{88} +7.56802 q^{89} +(10.2225 + 11.7078i) q^{90} -0.176318i q^{91} +(-5.69542 + 10.4528i) q^{92} +(1.57598 + 1.31264i) q^{93} +(4.73299 + 7.96883i) q^{94} +(8.65297 - 14.9874i) q^{95} +(-1.06713 + 9.73967i) 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

Introduction

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