LMFDB - Embedded newform 45.3.k.a.13.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(7,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([8, 3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.k (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			13.4
Character	$\chi$	$=$	45.13
Dual form			45.3.k.a.7.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.891829 - 0.238965i) q^{2} +(-2.93652 + 0.613889i) q^{3} +(-2.72585 - 1.57377i) q^{4} +(-1.31764 + 4.82326i) q^{5} +(2.76557 + 0.154241i) q^{6} +(-11.0534 - 2.96175i) q^{7} +(4.66637 + 4.66637i) q^{8} +(8.24628 - 3.60539i) q^{9} +(2.32770 - 3.98665i) q^{10} +(-1.30484 - 2.26005i) q^{11} +(8.97062 + 2.94803i) q^{12} +(2.85447 - 0.764853i) q^{13} +(9.15000 + 5.28276i) q^{14} +(0.908333 - 14.9725i) q^{15} +(3.24857 + 5.62669i) q^{16} +(-13.6850 + 13.6850i) q^{17} +(-8.21583 + 1.24482i) q^{18} -11.4465i q^{19} +(11.1824 - 11.0738i) q^{20} +(34.2768 + 1.91167i) q^{21} +(0.623621 + 2.32738i) q^{22} +(-10.7887 + 2.89082i) q^{23} +(-16.5675 - 10.8382i) q^{24} +(-21.5276 - 12.7107i) q^{25} -2.72847 q^{26} +(-22.0020 + 15.6496i) q^{27} +(25.4688 + 25.4688i) q^{28} +(-23.0262 + 13.2942i) q^{29} +(-4.38797 + 13.1358i) q^{30} +(-21.8787 + 37.8950i) q^{31} +(-8.38463 - 31.2919i) q^{32} +(5.21910 + 5.83564i) q^{33} +(15.4750 - 8.93448i) q^{34} +(28.8498 - 49.4110i) q^{35} +(-28.1522 - 3.14999i) q^{36} +(14.4324 - 14.4324i) q^{37} +(-2.73530 + 10.2083i) q^{38} +(-7.91267 + 3.99833i) q^{39} +(-28.6557 + 16.3585i) q^{40} +(-0.924605 + 1.60146i) q^{41} +(-30.1122 - 9.89582i) q^{42} +(13.1494 - 49.0742i) q^{43} +8.21405i q^{44} +(6.52410 + 44.5246i) q^{45} +10.3125 q^{46} +(61.3211 + 16.4309i) q^{47} +(-12.9936 - 14.5286i) q^{48} +(70.9709 + 40.9750i) q^{49} +(16.1616 + 16.4801i) q^{50} +(31.7853 - 48.5875i) q^{51} +(-8.98455 - 2.40740i) q^{52} +(6.43481 + 6.43481i) q^{53} +(23.3618 - 8.69905i) q^{54} +(12.6201 - 3.31564i) q^{55} +(-37.7587 - 65.4000i) q^{56} +(7.02686 + 33.6128i) q^{57} +(23.7122 - 6.35367i) q^{58} +(-49.5170 - 28.5886i) q^{59} +(-26.0392 + 39.3832i) q^{60} +(16.8393 + 29.1666i) q^{61} +(28.5676 - 28.5676i) q^{62} +(-101.828 + 15.4285i) q^{63} +3.92205i q^{64} +(-0.0720848 + 14.7757i) q^{65} +(-3.26003 - 6.45157i) q^{66} +(-8.41554 - 31.4072i) q^{67} +(58.8405 - 15.7663i) q^{68} +(29.9066 - 15.1120i) q^{69} +(-37.5365 + 37.1720i) q^{70} -63.3498 q^{71} +(55.3043 + 21.6561i) q^{72} +(-50.9063 - 50.9063i) q^{73} +(-16.3201 + 9.42239i) q^{74} +(71.0192 + 24.1095i) q^{75} +(-18.0141 + 31.2013i) q^{76} +(7.72922 + 28.8458i) q^{77} +(8.01221 - 1.67498i) q^{78} +(-59.5972 + 34.4084i) q^{79} +(-31.4194 + 8.25473i) q^{80} +(55.0023 - 59.4622i) q^{81} +(1.20728 - 1.20728i) q^{82} +(-27.2882 + 101.841i) q^{83} +(-90.4247 - 59.1546i) q^{84} +(-47.9745 - 84.0385i) q^{85} +(-23.4540 + 40.6236i) q^{86} +(59.4556 - 53.1740i) q^{87} +(4.45735 - 16.6351i) q^{88} +136.887i q^{89} +(4.82142 - 41.2673i) q^{90} -33.8170 q^{91} +(33.9578 + 9.09897i) q^{92} +(40.9838 - 124.710i) q^{93} +(-50.7615 - 29.3072i) q^{94} +(55.2093 + 15.0823i) q^{95} +(43.8313 + 86.7419i) q^{96} +(35.3034 + 9.45952i) q^{97} +(-53.5023 - 53.5023i) q^{98} +(-18.9084 - 13.9325i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.891829	−	0.238965i	−0.445914	−	0.119482i	0.0288727	−	0.999583i	$-0.490808\pi$
$2$	−0.891829	−	0.238965i	−0.445914	−	0.119482i	−0.474787	+	0.880101i	$0.657475\pi$
$3$	−2.93652	+	0.613889i	−0.978839	+	0.204630i
$3$	−2.93652	+	0.613889i	−0.978839	+	0.204630i
$4$	−2.72585	−	1.57377i	−0.681462	−	0.393442i
$5$	−1.31764	+	4.82326i	−0.263528	+	0.964652i
$5$	−1.31764	+	4.82326i	−0.263528	+	0.964652i
$6$	2.76557	+	0.154241i	0.460928	+	0.0257068i
$7$	−11.0534	−	2.96175i	−1.57906	−	0.423108i	−0.640425	−	0.768021i	$-0.721242\pi$
$7$	−11.0534	−	2.96175i	−1.57906	−	0.423108i	−0.938635	+	0.344913i	$0.887909\pi$
$8$	4.66637	+	4.66637i	0.583296	+	0.583296i
$9$	8.24628	−	3.60539i	0.916253	−	0.400599i
$10$	2.32770	−	3.98665i	0.232770	−	0.398665i
$11$	−1.30484	−	2.26005i	−0.118622	−	0.205459i	0.800600	−	0.599199i	$-0.204514\pi$
$11$	−1.30484	−	2.26005i	−0.118622	−	0.205459i	−0.919222	+	0.393740i	$0.871181\pi$
$12$	8.97062	+	2.94803i	0.747552	+	0.245669i
$13$	2.85447	−	0.764853i	0.219575	−	0.0588349i	−0.147354	−	0.989084i	$-0.547076\pi$
$13$	2.85447	−	0.764853i	0.219575	−	0.0588349i	0.366929	+	0.930249i	$0.380409\pi$
$14$	9.15000	+	5.28276i	0.653572	+	0.377340i
$15$	0.908333	−	14.9725i	0.0605555	−	0.998165i
$16$	3.24857	+	5.62669i	0.203036	+	0.351668i
$17$	−13.6850	+	13.6850i	−0.805003	+	0.805003i	−0.983873	−	0.178870i	$-0.942756\pi$
$17$	−13.6850	+	13.6850i	−0.805003	+	0.805003i	0.178870	+	0.983873i	$0.442756\pi$
$18$	−8.21583	+	1.24482i	−0.456435	+	0.0691568i
$19$		−	11.4465i		−	0.602446i	−0.953554	−	0.301223i	$-0.902605\pi$
$19$		−	11.4465i		−	0.602446i	0.953554	−	0.301223i	$-0.0973948\pi$
$20$	11.1824	−	11.0738i	0.559119	−	0.553690i
$21$	34.2768	+	1.91167i	1.63223	+	0.0910321i
$22$	0.623621	+	2.32738i	0.0283464	+	0.105790i
$23$	−10.7887	+	2.89082i	−0.469074	+	0.125688i	−0.485611	−	0.874175i	$-0.661403\pi$
$23$	−10.7887	+	2.89082i	−0.469074	+	0.125688i	0.0165366	+	0.999863i	$0.494736\pi$
$24$	−16.5675	−	10.8382i	−0.690313	−	0.451594i
$25$	−21.5276	−	12.7107i	−0.861106	−	0.508426i
$26$	−2.72847			−0.104941
$27$	−22.0020	+	15.6496i	−0.814890	+	0.579615i
$28$	25.4688	+	25.4688i	0.909601	+	0.909601i
$29$	−23.0262	+	13.2942i	−0.794005	+	0.458419i	−0.841371	−	0.540458i	$-0.818251\pi$
$29$	−23.0262	+	13.2942i	−0.794005	+	0.458419i	0.0473654	+	0.998878i	$0.484917\pi$
$30$	−4.38797	+	13.1358i	−0.146266	+	0.437861i
$31$	−21.8787	+	37.8950i	−0.705764	+	1.22242i	0.260652	+	0.965433i	$0.416063\pi$
$31$	−21.8787	+	37.8950i	−0.705764	+	1.22242i	−0.966415	+	0.256985i	$0.917271\pi$
$32$	−8.38463	−	31.2919i	−0.262020	−	0.977870i
$33$	5.21910	+	5.83564i	0.158154	+	0.176838i
$34$	15.4750	−	8.93448i	0.455146	−	0.262779i
$35$	28.8498	−	49.4110i	0.824279	−	1.41174i
$36$	−28.1522	−	3.14999i	−0.782004	−	0.0874996i
$37$	14.4324	−	14.4324i	0.390065	−	0.390065i	−0.484646	−	0.874711i	$-0.661051\pi$
$37$	14.4324	−	14.4324i	0.390065	−	0.390065i	0.874711	+	0.484646i	$0.161051\pi$
$38$	−2.73530	+	10.2083i	−0.0719817	+	0.268639i
$39$	−7.91267	+	3.99833i	−0.202889	+	0.102521i
$40$	−28.6557	+	16.3585i	−0.716393	+	0.408963i
$41$	−0.924605	+	1.60146i	−0.0225513	+	0.0390601i	−0.877081	−	0.480343i	$-0.840512\pi$
$41$	−0.924605	+	1.60146i	−0.0225513	+	0.0390601i	0.854529	+	0.519403i	$0.173846\pi$
$42$	−30.1122	−	9.89582i	−0.716957	−	0.235615i
$43$	13.1494	−	49.0742i	0.305800	−	1.14126i	−0.626455	−	0.779458i	$-0.715495\pi$
$43$	13.1494	−	49.0742i	0.305800	−	1.14126i	0.932255	−	0.361803i	$-0.117839\pi$
$44$			8.21405i			0.186683i
$45$	6.52410	+	44.5246i	0.144980	+	0.989435i
$46$	10.3125			0.224184
$47$	61.3211	+	16.4309i	1.30470	+	0.349594i	0.843227	−	0.537558i	$-0.180653\pi$
$47$	61.3211	+	16.4309i	1.30470	+	0.349594i	0.461477	+	0.887152i	$0.347320\pi$
$48$	−12.9936	−	14.5286i	−0.270701	−	0.302679i
$49$	70.9709	+	40.9750i	1.44838	+	0.836225i
$50$	16.1616	+	16.4801i	0.323231	+	0.329601i
$51$	31.7853	−	48.5875i	0.623241	−	0.952696i
$52$	−8.98455	−	2.40740i	−0.172780	−	0.0462962i
$53$	6.43481	+	6.43481i	0.121412	+	0.121412i	0.765202	−	0.643790i	$-0.222639\pi$
$53$	6.43481	+	6.43481i	0.121412	+	0.121412i	−0.643790	+	0.765202i	$0.722639\pi$
$54$	23.3618	−	8.69905i	0.432625	−	0.161094i
$55$	12.6201	−	3.31564i	0.229456	−	0.0602844i
$56$	−37.7587	−	65.4000i	−0.674262	−	1.16786i
$57$	7.02686	+	33.6128i	0.123278	+	0.589698i
$58$	23.7122	−	6.35367i	0.408831	−	0.109546i
$59$	−49.5170	−	28.5886i	−0.839271	−	0.484553i	0.0177457	−	0.999843i	$-0.494351\pi$
$59$	−49.5170	−	28.5886i	−0.839271	−	0.484553i	−0.857016	+	0.515289i	$0.827684\pi$
$60$	−26.0392	+	39.3832i	−0.433986	+	0.656386i
$61$	16.8393	+	29.1666i	0.276055	+	0.478141i	0.970401	−	0.241501i	$-0.0776396\pi$
$61$	16.8393	+	29.1666i	0.276055	+	0.478141i	−0.694346	+	0.719641i	$0.744306\pi$
$62$	28.5676	−	28.5676i	0.460768	−	0.460768i
$63$	−101.828	+	15.4285i	−1.61632	+	0.244896i
$64$			3.92205i			0.0612820i
$65$	−0.0720848	+	14.7757i	−0.00110900	+	0.227318i
$66$	−3.26003	−	6.45157i	−0.0493944	−	0.0977511i
$67$	−8.41554	−	31.4072i	−0.125605	−	0.468765i	0.874255	−	0.485466i	$-0.161350\pi$
$67$	−8.41554	−	31.4072i	−0.125605	−	0.468765i	−0.999861	+	0.0167016i	$0.994683\pi$
$68$	58.8405	−	15.7663i	0.865301	−	0.231857i
$69$	29.9066	−	15.1120i	0.433429	−	0.219015i
$70$	−37.5365	+	37.1720i	−0.536236	+	0.531029i
$71$	−63.3498			−0.892251			−0.446126	−	0.894970i	$-0.647197\pi$
$71$	−63.3498			−0.892251			−0.446126	+	0.894970i	$0.647197\pi$
$72$	55.3043	+	21.6561i	0.768115	+	0.300779i
$73$	−50.9063	−	50.9063i	−0.697347	−	0.697347i	0.266491	−	0.963838i	$-0.414136\pi$
$73$	−50.9063	−	50.9063i	−0.697347	−	0.697347i	−0.963838	+	0.266491i	$0.914136\pi$
$74$	−16.3201	+	9.42239i	−0.220541	+	0.127330i
$75$	71.0192	+	24.1095i	0.946923	+	0.321460i
$76$	−18.0141	+	31.2013i	−0.237028	+	0.410544i
$77$	7.72922	+	28.8458i	0.100379	+	0.374621i
$78$	8.01221	−	1.67498i	0.102721	−	0.0214741i
$79$	−59.5972	+	34.4084i	−0.754395	+	0.435550i	−0.827280	−	0.561790i	$-0.810113\pi$
$79$	−59.5972	+	34.4084i	−0.754395	+	0.435550i	0.0728850	+	0.997340i	$0.476779\pi$
$80$	−31.4194	+	8.25473i	−0.392743	+	0.103184i
$81$	55.0023	−	59.4622i	0.679040	−	0.734101i
$82$	1.20728	−	1.20728i	0.0147230	−	0.0147230i
$83$	−27.2882	+	101.841i	−0.328773	+	1.22700i	0.581691	+	0.813410i	$0.302391\pi$
$83$	−27.2882	+	101.841i	−0.328773	+	1.22700i	−0.910464	+	0.413589i	$0.864275\pi$
$84$	−90.4247	−	59.1546i	−1.07648	−	0.704222i
$85$	−47.9745	−	84.0385i	−0.564406	−	0.988688i
$86$	−23.4540	+	40.6236i	−0.272721	+	0.472367i
$87$	59.4556	−	53.1740i	0.683398	−	0.611196i
$88$	4.45735	−	16.6351i	0.0506517	−	0.189035i
$89$			136.887i			1.53806i	0.639213	+	0.769029i	$0.279260\pi$
$89$			136.887i			1.53806i	−0.639213	+	0.769029i	$0.720740\pi$
$90$	4.82142	−	41.2673i	0.0535713	−	0.458526i
$91$	−33.8170			−0.371615
$92$	33.9578	+	9.09897i	0.369107	+	0.0989019i
$93$	40.9838	−	124.710i	0.440686	−	1.34097i
$94$	−50.7615	−	29.3072i	−0.540016	−	0.311778i
$95$	55.2093	+	15.0823i	0.581150	+	0.158762i
$96$	43.8313	+	86.7419i	0.456576	+	0.903561i
$97$	35.3034	+	9.45952i	0.363953	+	0.0975209i	0.436161	−	0.899869i	$-0.356338\pi$
$97$	35.3034	+	9.45952i	0.363953	+	0.0975209i	−0.0722080	+	0.997390i	$0.523005\pi$
$98$	−53.5023	−	53.5023i	−0.545941	−	0.545941i
$99$	−18.9084	−	13.9325i	−0.190994	−	0.140732i
$100$	38.6774	+	68.5268i	0.386774	+	0.685268i
$101$	−48.3142	−	83.6827i	−0.478359	−	0.828541i	0.521334	−	0.853353i	$-0.325435\pi$
$101$	−48.3142	−	83.6827i	−0.478359	−	0.828541i	−0.999692	+	0.0248116i	$0.992101\pi$
$102$	−39.9577	+	35.7362i	−0.391743	+	0.350355i
$103$	25.6673	−	6.87754i	0.249198	−	0.0667723i	−0.132058	−	0.991242i	$-0.542158\pi$
$103$	25.6673	−	6.87754i	0.249198	−	0.0667723i	0.381255	+	0.924470i	$0.375492\pi$
$104$	16.8891	+	9.75093i	0.162395	+	0.0937589i
$105$	−54.3850	+	162.807i	−0.517952	+	1.55054i
$106$	−4.20106	−	7.27645i	−0.0396326	−	0.0686457i
$107$	−43.8389	+	43.8389i	−0.409709	+	0.409709i	−0.881637	−	0.471928i	$-0.843558\pi$
$107$	−43.8389	+	43.8389i	−0.409709	+	0.409709i	0.471928	+	0.881637i	$0.343558\pi$
$108$	84.6031	−	8.03231i	0.783362	−	0.0743732i
$109$		−	13.1212i		−	0.120378i	−0.998187	−	0.0601892i	$-0.980830\pi$
$109$		−	13.1212i		−	0.120378i	0.998187	−	0.0601892i	$-0.0191704\pi$
$110$	−12.0473	−	0.0587742i	−0.109521	−	0.000534311i
$111$	−33.5211	+	51.2409i	−0.301992	+	0.461630i
$112$	−19.2429	−	71.8156i	−0.171812	−	0.641211i
$113$	31.4100	−	8.41629i	0.277965	−	0.0744805i	−0.117143	−	0.993115i	$-0.537374\pi$
$113$	31.4100	−	8.41629i	0.277965	−	0.0744805i	0.395108	+	0.918635i	$0.370707\pi$
$114$	1.76551	−	31.6560i	0.0154869	−	0.277684i
$115$	0.272450	−	55.8458i	0.00236913	−	0.485615i
$116$	83.6877			0.721446
$117$	20.7812	−	16.5987i	0.177617	−	0.141869i
$118$	37.3290	+	37.3290i	0.316347	+	0.316347i
$119$	191.798	−	110.735i	1.61175	−	0.930545i
$120$	74.1057	−	65.6285i	0.617548	−	0.546904i
$121$	57.0948	−	98.8911i	0.471858	−	0.817282i
$122$	−8.04801	−	30.0356i	−0.0659673	−	0.246193i
$123$	1.73200	−	5.27033i	0.0140813	−	0.0428482i
$124$	119.276	−	68.8639i	0.961902	−	0.555354i
$125$	89.6725	−	87.0853i	0.717380	−	0.696682i
$126$	94.4999	+	10.5737i	0.749999	+	0.0839185i
$127$	−108.223	+	108.223i	−0.852153	+	0.852153i	−0.990398	−	0.138245i	$-0.955854\pi$
$127$	−108.223	+	108.223i	−0.852153	+	0.852153i	0.138245	+	0.990398i	$0.455854\pi$
$128$	−32.6013	+	121.670i	−0.254697	+	0.950544i
$129$	−8.48732	+	152.180i	−0.0657932	+	1.17969i
$130$	3.59515	−	13.1601i	0.0276550	−	0.101232i
$131$	−3.28859	+	5.69601i	−0.0251038	+	0.0434810i	−0.878304	−	0.478102i	$-0.841325\pi$
$131$	−3.28859	+	5.69601i	−0.0251038	+	0.0434810i	0.853201	+	0.521583i	$0.174658\pi$
$132$	−5.04252	−	24.1207i	−0.0382009	−	0.182733i
$133$	−33.9016	+	126.523i	−0.254900	+	0.951298i
$134$			30.0209i			0.224036i
$135$	−46.4913	−	126.742i	−0.344380	−	0.938830i
$136$	−127.719			−0.939110
$137$	−84.1178	−	22.5393i	−0.613998	−	0.164520i	−0.0616003	−	0.998101i	$-0.519620\pi$
$137$	−84.1178	−	22.5393i	−0.613998	−	0.164520i	−0.552398	+	0.833581i	$0.686287\pi$
$138$	−30.2828	+	6.33072i	−0.219440	+	0.0458748i
$139$	75.7500	+	43.7343i	0.544964	+	0.314635i	0.747088	−	0.664725i	$-0.231451\pi$
$139$	75.7500	+	43.7343i	0.544964	+	0.314635i	−0.202124	+	0.979360i	$0.564785\pi$
$140$	−156.401	+	89.2839i	−1.11715	+	0.637742i
$141$	−190.157	−	10.6054i	−1.34863	−	0.0752156i
$142$	56.4972	+	15.1384i	0.397868	+	0.106608i
$143$	−5.45322	−	5.45322i	−0.0381344	−	0.0381344i
$144$	47.0750	+	34.6869i	0.326910	+	0.240881i
$145$	−33.7809	−	128.578i	−0.232972	−	0.886745i
$146$	33.2349	+	57.5646i	0.227636	+	0.394278i
$147$	−233.561	−	76.7557i	−1.58885	−	0.522148i
$148$	−62.0538	+	16.6273i	−0.419282	+	0.112346i
$149$	−144.963	−	83.6946i	−0.972909	−	0.561709i	−0.0727869	−	0.997348i	$-0.523189\pi$
$149$	−144.963	−	83.6946i	−0.972909	−	0.561709i	−0.900122	+	0.435638i	$0.856523\pi$
$150$	−57.5757	−	38.4726i	−0.383838	−	0.256484i
$151$	124.775	+	216.117i	0.826325	+	1.43124i	0.900902	+	0.434022i	$0.142906\pi$
$151$	124.775	+	216.117i	0.826325	+	1.43124i	−0.0745766	+	0.997215i	$0.523761\pi$
$152$	53.4135	−	53.4135i	0.351404	−	0.351404i
$153$	−63.5108	+	162.191i	−0.415103	+	1.06007i
$154$		−	27.5726i		−	0.179043i
$155$	−153.949	−	155.458i	−0.993219	−	1.00296i
$156$	27.8612	+	1.55387i	0.178597	+	0.00996068i
$157$	12.9675	+	48.3954i	0.0825957	+	0.308251i	0.994848	−	0.101377i	$-0.0323250\pi$
$157$	12.9675	+	48.3954i	0.0825957	+	0.308251i	−0.912252	+	0.409629i	$0.865658\pi$
$158$	61.3729	−	16.4448i	0.388436	−	0.104081i
$159$	−22.8462	−	14.9457i	−0.143687	−	0.0939980i
$160$	161.977	+	0.790223i	1.01235	+	0.00493889i
$161$	127.814			0.793875
$162$	−63.2620	+	39.8865i	−0.390506	+	0.246213i
$163$	−23.5188	−	23.5188i	−0.144287	−	0.144287i	0.631273	−	0.775560i	$-0.282533\pi$
$163$	−23.5188	−	23.5188i	−0.144287	−	0.144287i	−0.775560	+	0.631273i	$0.782533\pi$
$164$	5.04066	−	2.91023i	0.0307358	−	0.0177453i
$165$	−35.0237	+	17.4838i	−0.212265	+	0.105962i
$166$	48.6728	−	84.3037i	0.293210	−	0.507854i
$167$	−28.6408	−	106.889i	−0.171502	−	0.640052i	−0.997121	−	0.0758252i	$-0.975841\pi$
$167$	−28.6408	−	106.889i	−0.171502	−	0.640052i	0.825620	−	0.564227i	$-0.190826\pi$
$168$	151.027	+	168.869i	0.898973	+	1.00517i
$169$	−138.795	+	80.1335i	−0.821274	+	0.474163i
$170$	22.7028	+	86.4122i	0.133546	+	0.508307i
$171$	−41.2690	−	94.3908i	−0.241339	−	0.551993i
$172$	−113.075	+	113.075i	−0.657411	+	0.657411i
$173$	17.6528	−	65.8811i	0.102039	−	0.380816i	−0.895953	−	0.444149i	$-0.853506\pi$
$173$	17.6528	−	65.8811i	0.102039	−	0.380816i	0.997992	+	0.0633327i	$0.0201729\pi$
$174$	−65.7309	+	33.2143i	−0.377764	+	0.190887i
$175$	200.308	+	204.256i	1.14462	+	1.16718i
$176$	8.47772	−	14.6838i	0.0481688	−	0.0834309i
$177$	162.958	+	53.5531i	0.920665	+	0.302560i
$178$	32.7112	−	122.080i	0.183771	−	0.685843i
$179$		−	303.920i		−	1.69788i	−0.528490	−	0.848939i	$-0.677242\pi$
$179$		−	303.920i		−	1.69788i	0.528490	−	0.848939i	$-0.322758\pi$
$180$	52.2876	−	131.635i	0.290487	−	0.731303i
$181$	172.576			0.953460			0.476730	−	0.879050i	$-0.341822\pi$
$181$	172.576			0.953460			0.476730	+	0.879050i	$0.341822\pi$
$182$	30.1589	+	8.08107i	0.165708	+	0.0444015i
$183$	−67.3540	−	75.3107i	−0.368055	−	0.411534i
$184$	−63.8337	−	36.8544i	−0.346922	−	0.200296i
$185$	50.5945	+	88.6279i	0.273484	+	0.479070i
$186$	−66.3519	+	101.427i	−0.356731	+	0.545304i
$187$	48.7856	+	13.0721i	0.260886	+	0.0699041i
$188$	−141.293	−	141.293i	−0.751561	−	0.751561i
$189$	289.548	−	107.817i	1.53200	−	0.570460i
$190$	−45.6331	−	26.6439i	−0.240174	−	0.140231i
$191$	143.618	+	248.754i	0.751927	+	1.30238i	0.946887	+	0.321565i	$0.104209\pi$
$191$	143.618	+	248.754i	0.751927	+	1.30238i	−0.194960	+	0.980811i	$0.562458\pi$
$192$	−2.40770	−	11.5172i	−0.0125401	−	0.0599852i
$193$	−35.5390	+	9.52264i	−0.184140	+	0.0493401i	−0.349711	−	0.936858i	$-0.613720\pi$
$193$	−35.5390	+	9.52264i	−0.184140	+	0.0493401i	0.165571	+	0.986198i	$0.447053\pi$
$194$	−29.2241	−	16.8725i	−0.150640	−	0.0869719i
$195$	−8.85893	−	43.4332i	−0.0454304	−	0.222734i
$196$	−128.970	−	223.383i	−0.658013	−	1.13971i
$197$	−226.659	+	226.659i	−1.15056	+	1.15056i	−0.164114	+	0.986441i	$0.552476\pi$
$197$	−226.659	+	226.659i	−1.15056	+	1.15056i	−0.986441	+	0.164114i	$0.947524\pi$
$198$	13.5337	+	16.9439i	0.0683520	+	0.0855751i
$199$			107.508i			0.540240i	0.962827	+	0.270120i	$0.0870633\pi$
$199$			107.508i			0.540240i	−0.962827	+	0.270120i	$0.912937\pi$
$200$	−41.1433	−	159.769i	−0.205717	−	0.798843i
$201$	43.9930	+	87.0617i	0.218870	+	0.433143i
$202$	23.0908	+	86.1760i	0.114311	+	0.426614i
$203$	293.892	−	78.7481i	1.44774	−	0.387922i
$204$	−163.107	+	82.4194i	−0.799546	+	0.404017i
$205$	−6.50597	−	6.56976i	−0.0317364	−	0.0320476i
$206$	−24.5344			−0.119099
$207$	−78.5441	+	62.7360i	−0.379440	+	0.303073i
$208$	13.5765	+	13.5765i	0.0652718	+	0.0652718i
$209$	−25.8695	+	14.9358i	−0.123778	+	0.0714631i
$210$	87.4072	−	132.200i	0.416225	−	0.629522i
$211$	45.5871	−	78.9591i	0.216053	−	0.374214i	−0.737545	−	0.675298i	$-0.764015\pi$
$211$	45.5871	−	78.9591i	0.216053	−	0.374214i	0.953598	+	0.301084i	$0.0973484\pi$
$212$	−7.41341	−	27.6672i	−0.0349689	−	0.130506i
$213$	186.028	−	38.8898i	0.873371	−	0.182581i
$214$	49.5727	−	28.6208i	0.231648	−	0.133742i
$215$	219.371	+	128.085i	1.02033	+	0.595745i
$216$	−175.697	−	29.6428i	−0.813410	−	0.137235i
$217$	354.070	−	354.070i	1.63166	−	1.63166i
$218$	−3.13551	+	11.7019i	−0.0143831	+	0.0536784i
$219$	180.738	+	118.237i	0.825289	+	0.539893i
$220$	−39.6185	−	10.8232i	−0.180084	−	0.0491963i
$221$	−28.5965	+	49.5306i	−0.129396	+	0.224120i
$222$	42.1399	−	37.6877i	0.189819	−	0.169765i
$223$	−61.4305	+	229.262i	−0.275473	+	1.02808i	0.680051	+	0.733165i	$0.261958\pi$
$223$	−61.4305	+	229.262i	−0.275473	+	1.02808i	−0.955524	+	0.294914i	$0.904709\pi$
$224$			370.715i			1.65498i
$225$	−223.350	−	27.2000i	−0.992666	−	0.120889i
$226$	−30.0236			−0.132848
$227$	118.644	+	31.7905i	0.522660	+	0.140046i	0.510497	−	0.859880i	$-0.329462\pi$
$227$	118.644	+	31.7905i	0.522660	+	0.140046i	0.0121631	+	0.999926i	$0.496128\pi$
$228$	33.7446	−	102.682i	0.148003	−	0.450359i
$229$	−285.203	−	164.662i	−1.24543	−	0.719048i	−0.275234	−	0.961377i	$-0.588755\pi$
$229$	−285.203	−	164.662i	−1.24543	−	0.719048i	−0.970194	+	0.242329i	$0.922089\pi$
$230$	−13.5881	+	49.7397i	−0.0590789	+	0.216260i
$231$	−40.4051	−	79.9615i	−0.174914	−	0.346154i
$232$	−169.484	−	45.4131i	−0.730534	−	0.195746i
$233$	−227.098	−	227.098i	−0.974670	−	0.974670i	0.0250170	−	0.999687i	$-0.492036\pi$
$233$	−227.098	−	227.098i	−0.974670	−	0.974670i	−0.999687	+	0.0250170i	$0.992036\pi$
$234$	−22.4997	+	9.83722i	−0.0961528	+	0.0420394i
$235$	−160.050	+	274.117i	−0.681063	+	1.16646i
$236$	89.9838	+	155.856i	0.381287	+	0.660409i
$237$	153.885	−	137.627i	0.649305	−	0.580705i
$238$	−197.513	+	52.9235i	−0.829887	+	0.222367i
$239$	123.443	+	71.2696i	0.516496	+	0.298199i	0.735500	−	0.677525i	$-0.236947\pi$
$239$	123.443	+	71.2696i	0.516496	+	0.298199i	−0.219004	+	0.975724i	$0.570281\pi$
$240$	87.1962	−	43.5282i	0.363318	−	0.181368i
$241$	−228.867	−	396.410i	−0.949656	−	1.64485i	−0.746148	−	0.665780i	$-0.768099\pi$
$241$	−228.867	−	396.410i	−0.949656	−	1.64485i	−0.203509	−	0.979073i	$-0.565234\pi$
$242$	−74.5503	+	74.5503i	−0.308059	+	0.308059i
$243$	−125.012	+	208.377i	−0.514453	+	0.857519i
$244$		−	106.005i		−	0.434446i
$245$	−291.147	+	288.320i	−1.18836	+	1.17682i
$246$	−2.80407	+	4.28634i	−0.0113987	+	0.0174242i
$247$	−8.75487	−	32.6736i	−0.0354448	−	0.132282i
$248$	−278.926	+	74.7380i	−1.12470	+	0.301363i
$249$	17.6132	−	315.810i	0.0707359	−	1.26831i
$250$	−100.783	+	56.2366i	−0.403131	+	0.224946i
$251$	102.580			0.408684			0.204342	−	0.978900i	$-0.434494\pi$
$251$	102.580			0.408684			0.204342	+	0.978900i	$0.434494\pi$
$252$	301.848	+	118.198i	1.19781	+	0.469039i
$253$	20.6109	+	20.6109i	0.0814660	+	0.0814660i
$254$	122.378	−	70.6552i	0.481805	−	0.278170i
$255$	192.468	+	217.330i	0.754778	+	0.852273i
$256$	65.9936	−	114.304i	0.257788	−	0.446501i
$257$	29.0526	+	108.426i	0.113045	+	0.421890i	0.999133	−	0.0416268i	$-0.0132541\pi$
$257$	29.0526	+	108.426i	0.113045	+	0.421890i	−0.886088	+	0.463517i	$0.846587\pi$
$258$	43.9348	−	133.690i	0.170290	−	0.518178i
$259$	−202.273	+	116.782i	−0.780975	+	0.450896i
$260$	23.4499	−	40.1627i	0.0901921	−	0.154472i
$261$	−141.949	+	192.646i	−0.543868	+	0.738106i
$262$	4.29401	−	4.29401i	0.0163893	−	0.0163893i
$263$	38.5609	−	143.911i	0.146619	−	0.547191i	−0.853059	−	0.521815i	$-0.825255\pi$
$263$	38.5609	−	143.911i	0.146619	−	0.547191i	0.999678	−	0.0253757i	$-0.00807820\pi$
$264$	−2.87701	+	51.5855i	−0.0108978	+	0.195400i
$265$	−39.5156	+	22.5580i	−0.149115	+	0.0851245i
$266$	60.4689	−	104.735i	0.227327	−	0.393742i
$267$	−84.0336	−	401.972i	−0.314733	−	1.50551i
$268$	−26.4882	+	98.8554i	−0.0988367	+	0.368864i
$269$		−	31.0843i		−	0.115555i	−0.998329	−	0.0577774i	$-0.981599\pi$
$269$		−	31.0843i		−	0.115555i	0.998329	−	0.0577774i	$-0.0184014\pi$
$270$	11.1754	+	124.142i	0.0413902	+	0.459785i
$271$	4.22458			0.0155889			0.00779444	−	0.999970i	$-0.497519\pi$
$271$	4.22458			0.0155889			0.00779444	+	0.999970i	$0.497519\pi$
$272$	−121.458	−	32.5447i	−0.446538	−	0.119650i
$273$	99.3042	−	20.7599i	0.363751	−	0.0760435i
$274$	69.6325	+	40.2024i	0.254133	+	0.146724i
$275$	−0.636566	+	65.2388i	−0.00231479	+	0.237232i
$276$	−105.304	−	5.87296i	−0.381535	−	0.0212788i
$277$	134.321	+	35.9912i	0.484913	+	0.129932i	0.492990	−	0.870035i	$-0.335904\pi$
$277$	134.321	+	35.9912i	0.484913	+	0.129932i	−0.00807616	+	0.999967i	$0.502571\pi$
$278$	−57.1051	−	57.1051i	−0.205414	−	0.205414i
$279$	−43.7914	+	391.374i	−0.156958	+	1.40277i
$280$	365.193	−	95.9462i	1.30426	−	0.342665i
$281$	−251.702	−	435.961i	−0.895737	−	1.55146i	−0.832890	−	0.553439i	$-0.813315\pi$
$281$	−251.702	−	435.961i	−0.895737	−	1.55146i	−0.0628471	−	0.998023i	$-0.520018\pi$
$282$	167.053	+	54.8991i	0.592388	+	0.194678i
$283$	141.561	−	37.9311i	0.500214	−	0.134032i	0.000114837	−	1.00000i	$-0.499963\pi$
$283$	141.561	−	37.9311i	0.500214	−	0.134032i	0.500099	+	0.865968i	$0.333297\pi$
$284$	172.682	+	99.6980i	0.608035	+	0.351049i
$285$	−171.382	−	10.3972i	−0.601340	−	0.0364814i
$286$	3.56021	+	6.16647i	0.0124483	+	0.0215611i
$287$	14.9632	−	14.9632i	0.0521365	−	0.0521365i
$288$	−181.961	−	227.812i	−0.631811	−	0.791012i
$289$		−	85.5611i		−	0.296059i
$290$	−0.598812	+	122.742i	−0.00206487	+	0.423248i
$291$	−109.476	−	6.10568i	−0.376207	−	0.0209817i
$292$	58.6481	+	218.878i	0.200850	+	0.749581i
$293$	331.315	−	88.7756i	1.13077	−	0.302988i	0.355535	−	0.934663i	$-0.384299\pi$
$293$	331.315	−	88.7756i	1.13077	−	0.302988i	0.775234	+	0.631675i	$0.217632\pi$
$294$	189.955	+	124.266i	0.646105	+	0.422673i
$295$	203.136	−	201.164i	0.688596	−	0.681910i
$296$	134.694			0.455047
$297$	64.0779	+	29.3054i	0.215751	+	0.0986714i
$298$	109.282	+	109.282i	0.366720	+	0.366720i
$299$	−28.5850	+	16.5035i	−0.0956019	+	0.0551958i
$300$	−155.645	−	177.487i	−0.518816	−	0.591622i
$301$	−290.692	+	503.493i	−0.965753	+	1.67273i
$302$	−59.6337	−	222.556i	−0.197463	−	0.736941i
$303$	193.247	+	216.076i	0.637780	+	0.713123i
$304$	64.4057	−	37.1847i	0.211861	−	0.122318i
$305$	−162.866	+	42.7894i	−0.533987	+	0.140293i
$306$	95.3986	−	129.470i	0.311760	−	0.423103i
$307$	−19.2282	+	19.2282i	−0.0626327	+	0.0626327i	−0.737729	−	0.675097i	$-0.764102\pi$
$307$	−19.2282	+	19.2282i	−0.0626327	+	0.0626327i	0.675097	+	0.737729i	$0.264102\pi$
$308$	24.3280	−	90.7934i	0.0789870	−	0.294784i
$309$	−71.1506	+	35.9529i	−0.230261	+	0.116353i
$310$	100.147	+	175.431i	0.323055	+	0.565906i
$311$	−275.689	+	477.507i	−0.886459	+	1.53539i	−0.0424271	+	0.999100i	$0.513509\pi$
$311$	−275.689	+	477.507i	−0.886459	+	1.53539i	−0.844032	+	0.536293i	$0.819824\pi$
$312$	−55.5811	−	18.2657i	−0.178145	−	0.0585440i
$313$	124.130	−	463.260i	0.396582	−	1.48006i	−0.422488	−	0.906368i	$-0.638843\pi$
$313$	124.130	−	463.260i	0.396582	−	1.48006i	0.819070	−	0.573694i	$-0.194490\pi$
$314$		−	46.2592i		−	0.147322i
$315$	59.7572	−	511.471i	0.189705	−	1.62372i
$316$	216.604			0.685455
$317$	270.009	+	72.3487i	0.851763	+	0.228229i	0.658186	−	0.752856i	$-0.271324\pi$
$317$	270.009	+	72.3487i	0.851763	+	0.228229i	0.193578	+	0.981085i	$0.437991\pi$
$318$	16.8034	+	18.7884i	0.0528409	+	0.0590831i
$319$	60.0908	+	34.6934i	0.188372	+	0.108757i
$320$	−18.9170	−	5.16785i	−0.0591157	−	0.0161495i
$321$	101.821	−	155.646i	0.317201	−	0.484878i
$322$	−113.988	−	30.5430i	−0.354000	−	0.0948541i
$323$	156.646	+	156.646i	0.484971	+	0.484971i
$324$	−243.508	+	75.5239i	−0.751566	+	0.233099i
$325$	−71.1718	−	19.8167i	−0.218990	−	0.0609744i
$326$	15.3545	+	26.5949i	0.0470998	+	0.0815793i
$327$	8.05498	+	38.5307i	0.0246330	+	0.117831i
$328$	−11.7876	+	3.15847i	−0.0359377	+	0.00962948i
$329$	−629.143	−	363.236i	−1.91229	−	1.10406i
$330$	35.4131	−	7.22310i	0.107313	−	0.0218882i
$331$	−61.1788	−	105.965i	−0.184830	−	0.320136i	0.758689	−	0.651453i	$-0.225840\pi$
$331$	−61.1788	−	105.965i	−0.184830	−	0.320136i	−0.943519	+	0.331317i	$0.892507\pi$
$332$	234.657	−	234.657i	0.706800	−	0.706800i
$333$	66.9791	−	171.048i	0.201139	−	0.513658i
$334$			102.171i			0.305900i
$335$	162.574	+	0.793137i	0.485295	+	0.00236757i
$336$	100.594	+	199.075i	0.299387	+	0.592485i
$337$	85.5276	+	319.193i	0.253791	+	0.947161i	0.968759	+	0.248004i	$0.0797746\pi$
$337$	85.5276	+	319.193i	0.253791	+	0.947161i	−0.714968	+	0.699157i	$0.753559\pi$
$338$	142.931	−	38.2982i	0.422872	−	0.113308i
$339$	−87.0694	+	43.9969i	−0.256842	+	0.129784i
$340$	−1.48592	+	304.577i	−0.00437034	+	0.895815i
$341$	114.192			0.334875
$342$	14.2488	+	94.0423i	0.0416632	+	0.274977i
$343$	−266.621	−	266.621i	−0.777321	−	0.777321i
$344$	290.358	−	167.638i	0.844065	−	0.487321i
$345$	33.4830	+	164.159i	0.0970523	+	0.475824i
$346$	−31.4865	+	54.5363i	−0.0910016	+	0.157619i
$347$	−92.1251	−	343.816i	−0.265490	−	0.990823i	−0.961950	−	0.273227i	$-0.911909\pi$
$347$	−92.1251	−	343.816i	−0.265490	−	0.990823i	0.696459	−	0.717596i	$-0.254758\pi$
$348$	−245.750	+	51.3750i	−0.706180	+	0.147629i
$349$	43.1516	−	24.9136i	0.123644	−	0.0713857i	−0.436903	−	0.899509i	$-0.643925\pi$
$349$	43.1516	−	24.9136i	0.123644	−	0.0713857i	0.560546	+	0.828123i	$0.310591\pi$
$350$	−129.831	−	230.028i	−0.370945	−	0.657222i
$351$	−50.8345	+	61.4997i	−0.144828	+	0.175213i
$352$	−59.7804	+	59.7804i	−0.169831	+	0.169831i
$353$	−162.600	+	606.831i	−0.460623	+	1.71907i	0.210385	+	0.977619i	$0.432528\pi$
$353$	−162.600	+	606.831i	−0.460623	+	1.71907i	−0.671008	+	0.741450i	$0.734138\pi$
$354$	−132.533	−	86.7014i	−0.374387	−	0.244919i
$355$	83.4724	−	305.553i	0.235133	−	0.860712i
$356$	215.429	−	373.134i	0.605137	−	1.04813i
$357$	−495.240	+	442.918i	−1.38723	+	1.24067i
$358$	−72.6263	+	271.045i	−0.202867	+	0.757109i
$359$		−	81.3046i		−	0.226475i	−0.993568	−	0.113238i	$-0.963878\pi$
$359$		−	81.3046i		−	0.226475i	0.993568	−	0.113238i	$-0.0361221\pi$
$360$	−177.324	+	238.212i	−0.492567	+	0.661700i
$361$	229.978			0.637059
$362$	−153.908	−	41.2397i	−0.425162	−	0.113922i
$363$	−106.952	+	325.445i	−0.294633	+	0.896544i
$364$	92.1799	+	53.2201i	0.253241	+	0.146209i
$365$	312.611	−	178.458i	0.856468	−	0.488926i
$366$	42.0717	+	83.2595i	0.114950	+	0.227485i
$367$	−58.0273	−	15.5484i	−0.158113	−	0.0423661i	0.178894	−	0.983868i	$-0.442748\pi$
$367$	−58.0273	−	15.5484i	−0.158113	−	0.0423661i	−0.337007	+	0.941502i	$0.609415\pi$
$368$	−51.3136	−	51.3136i	−0.139439	−	0.139439i
$369$	−1.85065	+	16.5397i	−0.00501531	+	0.0448230i
$370$	−23.9426	−	91.1312i	−0.0647098	−	0.246301i
$371$	−52.0684	−	90.1851i	−0.140346	−	0.243086i
$372$	−307.981	+	275.442i	−0.827906	+	0.740436i
$373$	188.424	−	50.4882i	0.505159	−	0.135357i	0.00276585	−	0.999996i	$-0.499120\pi$
$373$	188.424	−	50.4882i	0.505159	−	0.135357i	0.502393	+	0.864639i	$0.332453\pi$
$374$	−40.3846	−	23.3161i	−0.107980	−	0.0623425i
$375$	−209.864	+	310.777i	−0.559638	+	0.828737i
$376$	209.474	+	362.820i	0.557112	+	0.964946i
$377$	−55.5594	+	55.5594i	−0.147372	+	0.147372i
$378$	−283.992	+	26.9625i	−0.751301	+	0.0713294i
$379$			145.837i			0.384795i	0.981317	+	0.192398i	$0.0616263\pi$
$379$			145.837i			0.384795i	−0.981317	+	0.192398i	$0.938374\pi$
$380$	−126.756	−	127.999i	−0.333568	−	0.336839i
$381$	251.363	−	384.237i	0.659745	−	1.00850i
$382$	−68.6394	−	256.166i	−0.179684	−	0.670591i
$383$	−729.460	+	195.458i	−1.90459	+	0.510335i	−0.908973	+	0.416854i	$0.863133\pi$
$383$	−729.460	+	195.458i	−1.90459	+	0.510335i	−0.995621	+	0.0934803i	$0.970201\pi$
$384$	21.0426	−	377.299i	0.0547984	−	0.982549i
$385$	−149.315	−	0.728453i	−0.387832	−	0.00189209i
$386$	33.9703			0.0880059
$387$	−68.4982	−	452.088i	−0.176998	−	1.16819i
$388$	−81.3446	−	81.3446i	−0.209651	−	0.209651i
$389$	37.3613	−	21.5705i	0.0960444	−	0.0554512i	−0.451209	−	0.892419i	$-0.649007\pi$
$389$	37.3613	−	21.5705i	0.0960444	−	0.0554512i	0.547253	+	0.836967i	$0.315674\pi$
$390$	−2.47836	+	40.8520i	−0.00635477	+	0.104749i
$391$	108.083	−	187.205i	0.276427	−	0.478785i
$392$	139.972	+	522.381i	0.357070	+	1.33260i
$393$	6.16029	−	18.7453i	0.0156750	−	0.0476979i
$394$	256.305	−	147.978i	0.650520	−	0.375578i
$395$	−87.4331	−	332.791i	−0.221350	−	0.842508i
$396$	29.6149	+	67.7354i	0.0747851	+	0.171049i
$397$	−89.7953	+	89.7953i	−0.226185	+	0.226185i	−0.811097	−	0.584912i	$-0.801129\pi$
$397$	−89.7953	+	89.7953i	−0.226185	+	0.226185i	0.584912	+	0.811097i	$0.301129\pi$
$398$	25.6906	−	95.8785i	0.0645491	−	0.240901i
$399$	21.8819	−	392.348i	0.0548419	−	0.983328i
$400$	1.58482	−	162.421i	0.00396204	−	0.406052i
$401$	−144.777	+	250.762i	−0.361041	+	0.625341i	−0.988132	−	0.153604i	$-0.950912\pi$
$401$	−144.777	+	250.762i	−0.361041	+	0.625341i	0.627092	+	0.778946i	$0.284245\pi$
$402$	−18.4295	−	88.1569i	−0.0458445	−	0.219296i
$403$	−33.4679	+	124.904i	−0.0830470	+	0.309936i
$404$			304.142i			0.752826i
$405$	214.328	+	343.640i	0.529205	+	0.848494i
$406$	−280.919			−0.691919
$407$	−51.4498	−	13.7859i	−0.126412	−	0.0338721i
$408$	375.049	−	78.4053i	0.919238	−	0.192170i
$409$	178.588	+	103.108i	0.436646	+	0.252098i	0.702174	−	0.712006i	$-0.252213\pi$
$409$	178.588	+	103.108i	0.436646	+	0.252098i	−0.265528	+	0.964103i	$0.585546\pi$
$410$	4.23227	+	7.41380i	0.0103226	+	0.0180824i
$411$	260.850	+	14.5480i	0.634671	+	0.0353967i
$412$	−80.7889	−	21.6473i	−0.196090	−	0.0525421i
$413$	462.659	+	462.659i	1.12024	+	1.12024i
$414$	85.0396	−	37.1805i	0.205410	−	0.0898081i
$415$	−455.249	−	265.808i	−1.09699	−	0.640501i
$416$	−47.8673	−	82.9087i	−0.115066	−	0.199300i
$417$	−249.289	−	81.9244i	−0.597816	−	0.196461i
$418$	26.6403	−	7.13826i	0.0637329	−	0.0170772i
$419$	621.108	+	358.597i	1.48236	+	0.855839i	0.999799	−	0.0200248i	$-0.00637453\pi$
$419$	621.108	+	358.597i	1.48236	+	0.855839i	0.482558	+	0.875864i	$0.339708\pi$
$420$	404.465	−	358.197i	0.963013	−	0.852850i
$421$	124.562	+	215.747i	0.295871	+	0.512463i	0.975187	−	0.221382i	$-0.0710569\pi$
$421$	124.562	+	215.747i	0.295871	+	0.512463i	−0.679316	+	0.733846i	$0.737724\pi$
$422$	−59.5243	+	59.5243i	−0.141053	+	0.141053i
$423$	564.911	−	85.5925i	1.33549	−	0.202346i
$424$			60.0544i			0.141638i
$425$	468.553	−	120.661i	1.10248	−	0.283908i
$426$	−175.198	−	9.77111i	−0.411264	−	0.0229369i
$427$	−99.7479	−	372.264i	−0.233602	−	0.871814i
$428$	188.490	−	50.5058i	0.440398	−	0.118004i
$429$	19.3612	+	12.6658i	0.0451309	+	0.0295241i
$430$	−165.034	−	166.652i	−0.383800	−	0.387563i
$431$	−234.096			−0.543146			−0.271573	−	0.962418i	$-0.587544\pi$
$431$	−234.096			−0.543146			−0.271573	+	0.962418i	$0.587544\pi$
$432$	−159.531	−	72.9598i	−0.369284	−	0.168888i
$433$	372.915	+	372.915i	0.861236	+	0.861236i	0.991482	−	0.130245i	$-0.0415765\pi$
$433$	372.915	+	372.915i	0.861236	+	0.861236i	−0.130245	+	0.991482i	$0.541577\pi$
$434$	−400.380	+	231.159i	−0.922534	+	0.532625i
$435$	178.131	+	356.834i	0.409497	+	0.820308i
$436$	−20.6498	+	35.7665i	−0.0473619	+	0.0820332i
$437$	33.0897	+	123.493i	0.0757202	+	0.282592i
$438$	−132.933	−	148.637i	−0.303500	−	0.339353i
$439$	558.854	−	322.654i	1.27302	−	0.734976i	0.297461	−	0.954734i	$-0.403860\pi$
$439$	558.854	−	322.654i	1.27302	−	0.734976i	0.975554	+	0.219758i	$0.0705269\pi$
$440$	74.3620	+	43.4180i	0.169005	+	0.0986773i
$441$	732.977	+	82.0138i	1.66208	+	0.185972i
$442$	37.3393	−	37.3393i	0.0844780	−	0.0844780i
$443$	71.1633	−	265.585i	0.160640	−	0.599515i	−0.837917	−	0.545798i	$-0.816227\pi$
$443$	71.1633	−	265.585i	0.160640	−	0.599515i	0.998556	−	0.0537167i	$-0.0171068\pi$
$444$	172.015	−	86.9204i	0.387421	−	0.195767i
$445$	−660.242	−	180.368i	−1.48369	−	0.405322i
$446$	109.571	−	189.782i	0.245675	−	0.425521i
$447$	477.067	+	156.779i	1.06726	+	0.350737i
$448$	11.6161	−	43.3520i	0.0259289	−	0.0967679i
$449$		−	190.668i		−	0.424651i	−0.977199	−	0.212325i	$-0.931896\pi$
$449$		−	190.668i		−	0.424651i	0.977199	−	0.212325i	$-0.0681036\pi$
$450$	192.690	+	77.6305i	0.428200	+	0.172512i
$451$	4.82584			0.0107003
$452$	−98.8642	−	26.4906i	−0.218726	−	0.0586075i
$453$	−499.076	−	558.033i	−1.10171	−	1.23186i
$454$	−98.2131	−	56.7034i	−0.216328	−	0.124897i
$455$	44.5586	−	163.108i	0.0979311	−	0.358479i
$456$	−124.060	+	189.640i	−0.272061	+	0.415876i
$457$	−302.074	−	80.9404i	−0.660993	−	0.177112i	−0.0872988	−	0.996182i	$-0.527823\pi$
$457$	−302.074	−	80.9404i	−0.660993	−	0.177112i	−0.573694	+	0.819070i	$0.694490\pi$
$458$	215.004	+	215.004i	0.469441	+	0.469441i
$459$	86.9334	−	515.265i	0.189397	−	1.12258i
$460$	−88.6310	+	151.798i	−0.192676	+	0.329996i
$461$	−110.361	−	191.151i	−0.239395	−	0.414645i	0.721146	−	0.692784i	$-0.243616\pi$
$461$	−110.361	−	191.151i	−0.239395	−	0.414645i	−0.960541	+	0.278139i	$0.910283\pi$
$462$	16.9265	+	80.9673i	0.0366374	+	0.175254i
$463$	−279.010	+	74.7605i	−0.602613	+	0.161470i	−0.547211	−	0.836994i	$-0.684311\pi$
$463$	−279.010	+	74.7605i	−0.602613	+	0.161470i	−0.0554018	+	0.998464i	$0.517644\pi$
$464$	−149.604	−	86.3740i	−0.322423	−	0.186151i
$465$	547.508	+	361.999i	1.17744	+	0.778493i
$466$	148.264	+	256.801i	0.318163	+	0.551075i
$467$	−249.664	+	249.664i	−0.534613	+	0.534613i	−0.921942	−	0.387329i	$-0.873398\pi$
$467$	−249.664	+	249.664i	−0.534613	+	0.534613i	0.387329	+	0.921942i	$0.373398\pi$
$468$	−82.7688	+	12.5407i	−0.176856	+	0.0267964i
$469$			372.082i			0.793352i
$470$	208.241	−	206.219i	0.443067	−	0.438765i
$471$	−67.7888	−	134.153i	−0.143925	−	0.284827i
$472$	−97.6593	−	364.470i	−0.206905	−	0.772181i
$473$	−128.068	+	34.3157i	−0.270756	+	0.0725490i
$474$	−170.127	+	85.9666i	−0.358918	+	0.181364i
$475$	−145.492	+	246.416i	−0.306299	+	0.518770i
$476$	−697.084			−1.46446
$477$	76.2633	+	29.8632i	0.159881	+	0.0626064i
$478$	−93.0588	−	93.0588i	−0.194684	−	0.194684i
$479$	−757.971	+	437.615i	−1.58240	+	0.913600i	−0.587895	+	0.808938i	$0.700043\pi$
$479$	−757.971	+	437.615i	−1.58240	+	0.913600i	−0.994508	+	0.104663i	$0.966624\pi$
$480$	−476.132	+	97.1152i	−0.991943	+	0.202323i
$481$	30.1582	−	52.2355i	0.0626989	−	0.108598i
$482$	109.382	+	408.221i	0.226934	+	0.846931i
$483$	−375.328	+	78.4636i	−0.777077	+	0.162450i
$484$	−311.263	+	179.708i	−0.643106	+	0.371298i
$485$	−92.1430	+	157.813i	−0.189986	+	0.325388i
$486$	161.284	−	155.963i	0.331860	−	0.320912i
$487$	−241.500	+	241.500i	−0.495894	+	0.495894i	−0.910157	−	0.414263i	$-0.864039\pi$
$487$	−241.500	+	241.500i	−0.495894	+	0.495894i	0.414263	+	0.910157i	$0.364039\pi$
$488$	−57.5235	+	214.681i	−0.117876	+	0.439919i
$489$	83.5012	+	54.6253i	0.170759	+	0.111708i
$490$	328.552	−	187.558i	0.670514	−	0.382772i
$491$	−14.2377	+	24.6604i	−0.0289973	+	0.0502248i	−0.880160	−	0.474677i	$-0.842565\pi$
$491$	−14.2377	+	24.6604i	−0.0289973	+	0.0502248i	0.851163	+	0.524902i	$0.175898\pi$
$492$	−13.0154	+	11.6403i	−0.0264542	+	0.0236592i
$493$	133.183	−	497.045i	0.270148	−	1.00821i
$494$			31.2314i			0.0632214i
$495$	92.1146	−	72.8421i	0.186090	−	0.147156i
$496$	−284.298			−0.573181
$497$	700.232	+	187.627i	1.40892	+	0.377518i
$498$	−91.1754	+	277.439i	−0.183083	+	0.557107i
$499$	−409.907	−	236.660i	−0.821457	−	0.474269i	0.0294615	−	0.999566i	$-0.490621\pi$
$499$	−409.907	−	236.660i	−0.821457	−	0.474269i	−0.850919	+	0.525297i	$0.823954\pi$
$500$	−381.486	+	96.2575i	−0.762971	+	0.192515i
$501$	149.722	+	296.298i	0.298846	+	0.591414i
$502$	−91.4836	−	24.5130i	−0.182238	−	0.0488306i
$503$	58.9981	+	58.9981i	0.117292	+	0.117292i	0.763317	−	0.646024i	$-0.223570\pi$
$503$	58.9981	+	58.9981i	0.117292	+	0.117292i	−0.646024	+	0.763317i	$0.723570\pi$
$504$	−547.161	−	403.172i	−1.08564	−	0.799944i
$505$	467.284	−	122.768i	0.925315	−	0.243105i
$506$	−13.4561	−	23.3067i	−0.0265931	−	0.0460606i
$507$	358.382	−	320.518i	0.706868	−	0.632186i
$508$	465.319	−	124.682i	0.915983	−	0.245437i
$509$	388.655	+	224.390i	0.763565	+	0.440844i	0.830574	−	0.556908i	$-0.188012\pi$
$509$	388.655	+	224.390i	0.763565	+	0.440844i	−0.0670093	+	0.997752i	$0.521346\pi$
$510$	−119.715	−	239.814i	−0.234735	−	0.470223i
$511$	411.917	+	713.461i	0.806100	+	1.39621i
$512$	270.104	−	270.104i	0.527546	−	0.527546i
$513$	179.133	+	251.846i	0.349187	+	0.490927i
$514$		−	103.640i		−	0.201634i
$515$	−0.648185	+	132.862i	−0.00125861	+	0.257985i
$516$	262.631	−	401.461i	0.508974	−	0.778026i
$517$	−42.8794	−	160.028i	−0.0829389	−	0.309532i
$518$	208.299	−	55.8136i	0.402122	−	0.107748i
$519$	−11.3941	+	204.298i	−0.0219539	+	0.393638i
$520$	−69.2850	+	68.6123i	−0.133240	+	0.131947i
$521$	−548.131			−1.05208			−0.526038	−	0.850461i	$-0.676323\pi$
$521$	−548.131			−1.05208			−0.526038	+	0.850461i	$0.676323\pi$
$522$	172.630	−	137.886i	0.330709	−	0.264150i
$523$	−237.559	−	237.559i	−0.454224	−	0.454224i	0.442530	−	0.896754i	$-0.354081\pi$
$523$	−237.559	−	237.559i	−0.454224	−	0.454224i	−0.896754	+	0.442530i	$0.854081\pi$
$524$	17.9284	−	10.3510i	0.0342145	−	0.0197538i
$525$	−713.599	−	476.834i	−1.35924	−	0.908255i
$526$	−68.7794	+	119.129i	−0.130759	+	0.226482i
$527$	−219.184	−	818.005i	−0.415909	−	1.55219i
$528$	−15.8807	+	48.3237i	−0.0300771	+	0.0915222i
$529$	−350.088	+	202.124i	−0.661793	+	0.382086i
$530$	40.6317	−	10.6750i	0.0766635	−	0.0201416i
$531$	−511.404	−	57.2217i	−0.963096	−	0.107762i
$532$	291.528	−	291.528i	0.547985	−	0.547985i
$533$	−1.41437	+	5.27851i	−0.00265361	+	0.00990340i
$534$	−21.1136	+	378.571i	−0.0395385	+	0.708935i
$535$	−153.682	−	269.210i	−0.287257	−	0.503196i
$536$	107.288	−	185.828i	0.200164	−	0.346694i
$537$	186.573	+	892.468i	0.347436	+	1.66195i
$538$	−7.42804	+	27.7218i	−0.0138068	+	0.0515276i
$539$		−	213.863i		−	0.396778i
$540$	−72.7346	+	418.646i	−0.134694	+	0.775271i
$541$	−694.204			−1.28319			−0.641593	−	0.767045i	$-0.721726\pi$
$541$	−694.204			−1.28319			−0.641593	+	0.767045i	$0.721726\pi$
$542$	−3.76761	−	1.00953i	−0.00695130	−	0.00186260i
$543$	−506.773	+	105.943i	−0.933284	+	0.195106i
$544$	542.975	+	313.487i	0.998115	+	0.576262i
$545$	63.2871	+	17.2891i	0.116123	+	0.0317231i
$546$	−93.5232	−	5.21595i	−0.171288	−	0.00955302i
$547$	855.323	+	229.183i	1.56366	+	0.418982i	0.933820	−	0.357742i	$-0.116453\pi$
$547$	855.323	+	229.183i	1.56366	+	0.418982i	0.629841	+	0.776724i	$0.283120\pi$
$548$	193.821	+	193.821i	0.353687	+	0.353687i
$549$	244.019	+	179.803i	0.444479	+	0.327511i
$550$	16.1575	−	58.0297i	0.0293772	−	0.105509i
$551$	152.171	+	263.568i	0.276173	+	0.478345i
$552$	210.073	+	69.0368i	0.380568	+	0.125067i
$553$	760.662	−	203.819i	1.37552	−	0.368569i
$554$	−111.191	−	64.1960i	−0.200705	−	0.115877i
$555$	−202.979	−	229.198i	−0.365728	−	0.412970i
$556$	−137.655	−	238.426i	−0.247581	−	0.428824i
$557$	598.653	−	598.653i	1.07478	−	1.07478i	0.0778138	−	0.996968i	$-0.475206\pi$
$557$	598.653	−	598.653i	1.07478	−	1.07478i	0.996968	−	0.0778138i	$-0.0247940\pi$
$558$	132.579	−	338.574i	0.237597	−	0.606763i
$559$		−	150.138i		−	0.268584i
$560$	371.741	+	1.81358i	0.663822	+	0.00323854i
$561$	−151.285	−	8.43740i	−0.269670	−	0.0150399i
$562$	120.296	+	448.950i	0.214050	+	0.798844i
$563$	−300.796	+	80.5980i	−0.534273	+	0.143158i	−0.515861	−	0.856672i	$-0.672528\pi$
$563$	−300.796	+	80.5980i	−0.534273	+	0.143158i	−0.0184123	+	0.999830i	$0.505861\pi$
$564$	501.649	+	328.172i	0.889449	+	0.581866i
$565$	−0.793207	+	162.588i	−0.00140391	+	0.287767i
$566$	−135.312			−0.239067
$567$	−784.076	+	494.357i	−1.38285	+	0.871882i
$568$	−295.614	−	295.614i	−0.520447	−	0.520447i
$569$	−20.4998	+	11.8356i	−0.0360278	+	0.0208006i	−0.517906	−	0.855438i	$-0.673288\pi$
$569$	−20.4998	+	11.8356i	−0.0360278	+	0.0208006i	0.481878	+	0.876238i	$0.339955\pi$
$570$	150.359	+	50.2268i	0.263787	+	0.0881172i
$571$	22.7049	−	39.3260i	0.0397633	−	0.0688721i	−0.845459	−	0.534041i	$-0.820673\pi$
$571$	22.7049	−	39.3260i	0.0397633	−	0.0688721i	0.885222	+	0.465169i	$0.154006\pi$
$572$	6.28254	+	23.4468i	0.0109835	+	0.0409909i
$573$	−574.445	−	642.305i	−1.00252	−	1.12095i
$574$	−16.9203	+	9.76892i	−0.0294778	+	0.0170190i
$575$	269.000	+	74.8988i	0.467825	+	0.130259i
$576$	14.1405	+	32.3423i	0.0245495	+	0.0561498i
$577$	−333.577	+	333.577i	−0.578124	+	0.578124i	−0.934386	−	0.356262i	$-0.884051\pi$
$577$	−333.577	+	333.577i	−0.578124	+	0.578124i	0.356262	+	0.934386i	$0.384051\pi$
$578$	−20.4461	+	76.3059i	−0.0353739	+	0.132017i
$579$	98.5150	−	49.7804i	0.170147	−	0.0859765i
$580$	−110.270	+	403.647i	−0.190121	+	0.695944i
$581$	603.256	−	1044.87i	1.03831	−	1.79840i
$582$	96.1750	+	31.6062i	0.165249	+	0.0543062i
$583$	6.14658	−	22.9394i	0.0105430	−	0.0393471i
$584$		−	475.096i		−	0.813520i
$585$	52.6776	+	122.104i	0.0900472	+	0.208725i
$586$	−316.691			−0.540428
$587$	−751.967	−	201.489i	−1.28103	−	0.343252i	−0.446786	−	0.894641i	$-0.647432\pi$
$587$	−751.967	−	201.489i	−1.28103	−	0.343252i	−0.834249	+	0.551388i	$0.814098\pi$
$588$	515.857	+	576.796i	0.877307	+	0.980945i
$589$	433.764	+	250.434i	0.736441	+	0.425184i
$590$	−229.233	+	130.861i	−0.388531	+	0.221798i
$591$	526.446	−	804.733i	0.890771	−	1.36165i
$592$	128.091	+	34.3219i	0.216370	+	0.0579763i
$593$	−464.151	−	464.151i	−0.782717	−	0.782717i	0.197571	−	0.980289i	$-0.436695\pi$
$593$	−464.151	−	464.151i	−0.782717	−	0.782717i	−0.980289	+	0.197571i	$0.936695\pi$
$594$	−50.1436	−	41.4478i	−0.0844168	−	0.0697774i
$595$	281.381	+	1071.00i	0.472910	+	1.80000i
$596$	263.432	+	456.278i	0.442000	+	0.765567i
$597$	−65.9978	−	315.698i	−0.110549	−	0.528808i
$598$	29.4367	−	7.88753i	0.0492252	−	0.0131899i
$599$	402.592	+	232.437i	0.672108	+	0.388042i	0.796875	−	0.604145i	$-0.206485\pi$
$599$	402.592	+	232.437i	0.672108	+	0.388042i	−0.124767	+	0.992186i	$0.539818\pi$
$600$	218.898	+	443.906i	0.364831	+	0.739843i
$601$	−305.138	−	528.514i	−0.507717	−	0.879392i	−0.999960	−	0.00893383i	$-0.997156\pi$
$601$	−305.138	−	528.514i	−0.507717	−	0.879392i	0.492243	−	0.870458i	$-0.336177\pi$
$602$	379.564	−	379.564i	0.630505	−	0.630505i
$603$	−182.632	−	228.651i	−0.302873	−	0.379190i
$604$		−	785.469i		−	1.30045i
$605$	401.747	+	405.686i	0.664044	+	0.670555i
$606$	−120.709	−	238.882i	−0.199190	−	0.394195i
$607$	−21.8621	−	81.5905i	−0.0360167	−	0.134416i	0.945577	−	0.325400i	$-0.105499\pi$
$607$	−21.8621	−	81.5905i	−0.0360167	−	0.134416i	−0.981593	+	0.190984i	$0.938832\pi$
$608$	−358.181	+	95.9744i	−0.589114	+	0.157853i
$609$	−814.676	+	411.662i	−1.33773	+	0.675964i
$610$	155.474	+	0.758498i	0.254875	+	0.00124344i
$611$	187.606			0.307048
$612$	428.371	−	342.156i	0.699953	−	0.559078i
$613$	463.301	+	463.301i	0.755793	+	0.755793i	0.975554	−	0.219760i	$-0.0705276\pi$
$613$	463.301	+	463.301i	0.755793	+	0.755793i	−0.219760	+	0.975554i	$0.570528\pi$
$614$	21.7432	−	12.5534i	0.0354123	−	0.0204453i
$615$	23.1380	+	15.2983i	0.0376228	+	0.0248753i
$616$	−98.5380	+	170.673i	−0.159964	+	0.277066i
$617$	174.357	+	650.709i	0.282588	+	1.05463i	0.950584	+	0.310468i	$0.100486\pi$
$617$	174.357	+	650.709i	0.282588	+	1.05463i	−0.667995	+	0.744165i	$0.732847\pi$
$618$	72.0456	−	15.0614i	0.116579	−	0.0243712i
$619$	759.400	−	438.440i	1.22682	−	0.708303i	0.260455	−	0.965486i	$-0.416128\pi$
$619$	759.400	−	438.440i	1.22682	−	0.708303i	0.966363	+	0.257183i	$0.0827942\pi$
$620$	174.986	+	666.036i	0.282235	+	1.07425i
$621$	192.133	−	232.443i	0.309393	−	0.374304i
$622$	359.975	−	359.975i	0.578737	−	0.578737i
$623$	405.426	−	1513.07i	0.650765	−	2.42869i
$624$	−48.2022	−	31.5333i	−0.0772472	−	0.0505341i
$625$	301.879	+	547.261i	0.483006	+	0.875617i
$626$	−221.405	+	383.485i	−0.353683	+	0.612597i
$627$	66.7975	−	59.7403i	0.106535	−	0.0952795i
$628$	40.8157	−	152.326i	0.0649932	−	0.242558i
$629$			395.016i			0.628007i
$630$	−175.517	+	441.865i	−0.278598	+	0.701373i
$631$	1077.51			1.70762			0.853812	−	0.520581i	$-0.174285\pi$
$631$	1077.51			1.70762			0.853812	+	0.520581i	$0.174285\pi$
$632$	−438.665	−	117.540i	−0.694090	−	0.185981i
$633$	−85.3951	+	259.850i	−0.134905	+	0.410506i
$634$	−223.513	−	129.045i	−0.352544	−	0.203541i
$635$	−379.390	−	664.589i	−0.597464	−	1.04660i
$636$	38.7542	+	76.6943i	0.0609343	+	0.120589i
$637$	233.924	+	62.6798i	0.367228	+	0.0983984i
$638$	−45.3002	−	45.3002i	−0.0710034	−	0.0710034i
$639$	−522.400	+	228.401i	−0.817528	+	0.357435i
$640$	−543.887	−	317.561i	−0.849824	−	0.496190i
$641$	−332.614	−	576.105i	−0.518899	−	0.898759i	−0.999759	−	0.0219617i	$-0.993009\pi$
$641$	−332.614	−	576.105i	−0.518899	−	0.898759i	0.480860	−	0.876797i	$-0.340325\pi$
$642$	−128.001	+	114.478i	−0.199379	+	0.178314i
$643$	−1071.82	+	287.192i	−1.66690	+	0.446644i	−0.964272	−	0.264915i	$-0.914656\pi$
$643$	−1071.82	+	287.192i	−1.66690	+	0.446644i	−0.702626	+	0.711559i	$0.747989\pi$
$644$	−348.401	−	201.150i	−0.540996	−	0.312344i
$645$	−722.818	−	241.455i	−1.12065	−	0.374348i
$646$	−102.268	−	177.134i	−0.158310	−	0.274201i
$647$	−231.177	+	231.177i	−0.357306	+	0.357306i	−0.862819	−	0.505513i	$-0.831303\pi$
$647$	−231.177	+	231.177i	−0.357306	+	0.357306i	0.505513	+	0.862819i	$0.331303\pi$
$648$	534.133	−	20.8115i	0.824280	−	0.0321165i
$649$			149.214i			0.229914i
$650$	58.7376	+	34.6807i	0.0903655	+	0.0533549i
$651$	−822.373	+	1257.09i	−1.26325	+	1.93102i
$652$	27.0955	+	101.122i	0.0415574	+	0.155094i
$653$	−653.059	+	174.987i	−1.00009	+	0.267974i	−0.721484	−	0.692432i	$-0.756539\pi$
$653$	−653.059	+	174.987i	−1.00009	+	0.267974i	−0.278607	+	0.960405i	$0.589873\pi$
$654$	2.02383	−	36.2877i	0.00309454	−	0.0554858i
$655$	−23.1401	−	23.3670i	−0.0353285	−	0.0356748i
$656$	−12.0146			−0.0183149
$657$	−603.325	−	236.251i	−0.918303	−	0.359590i
$658$	474.287	+	474.287i	0.720802	+	0.720802i
$659$	−138.847	+	80.1633i	−0.210693	+	0.121644i	−0.601634	−	0.798772i	$-0.705483\pi$
$659$	−138.847	+	80.1633i	−0.210693	+	0.121644i	0.390940	+	0.920416i	$0.372150\pi$
$660$	122.985	+	7.46109i	0.186340	+	0.0113047i
$661$	−471.803	+	817.186i	−0.713771	+	1.23629i	0.249660	+	0.968333i	$0.419681\pi$
$661$	−471.803	+	817.186i	−0.713771	+	1.23629i	−0.963432	+	0.267954i	$0.913652\pi$
$662$	29.2392	+	109.122i	0.0441679	+	0.164837i
$663$	53.5679	−	163.003i	0.0807962	−	0.245856i
$664$	−602.564	+	347.891i	−0.907476	+	0.523931i
$665$	−565.581	−	330.228i	−0.850498	−	0.496583i
$666$	−100.608	+	136.540i	−0.151064	+	0.205015i
$667$	209.991	−	209.991i	0.314829	−	0.314829i
$668$	−90.1478	+	336.436i	−0.134952	+	0.503647i
$669$	39.6505	−	710.943i	0.0592683	−	1.06269i
$670$	−144.799	−	39.5568i	−0.216117	−	0.0590400i
$671$	43.9452	−	76.1153i	0.0654921	−	0.113436i
$672$	−227.578	−	1088.61i	−0.338658	−	1.61996i
$673$	−147.135	+	549.114i	−0.218625	+	0.815919i	0.766234	+	0.642562i	$0.222128\pi$
$673$	−147.135	+	549.114i	−0.218625	+	0.815919i	−0.984859	+	0.173358i	$0.944538\pi$
$674$		−	305.104i		−	0.452676i
$675$	672.569	−	57.2388i	0.996398	−	0.0847983i
$676$	504.446			0.746222
$677$	−284.520	−	76.2369i	−0.420266	−	0.112610i	0.0424873	−	0.999097i	$-0.486472\pi$
$677$	−284.520	−	76.2369i	−0.420266	−	0.112610i	−0.462753	+	0.886487i	$0.653138\pi$
$678$	88.1647	−	18.4311i	0.130036	−	0.0271846i
$679$	−362.207	−	209.120i	−0.533441	−	0.307983i
$680$	168.288	−	616.022i	0.247482	−	0.905914i
$681$	−367.915	−	20.5193i	−0.540258	−	0.0301311i
$682$	−101.840	−	27.2880i	−0.149326	−	0.0400117i
$683$	449.659	+	449.659i	0.658359	+	0.658359i	0.954992	−	0.296632i	$-0.0958636\pi$
$683$	449.659	+	449.659i	0.658359	+	0.658359i	−0.296632	+	0.954992i	$0.595864\pi$
$684$	−36.0562	+	322.243i	−0.0527138	+	0.471115i
$685$	219.550	−	376.023i	0.320511	−	0.548939i
$686$	174.067	+	301.493i	0.253742	+	0.439495i
$687$	938.588	+	308.450i	1.36621	+	0.448981i
$688$	318.842	−	85.4335i	0.463433	−	0.124177i
$689$	23.2897	+	13.4463i	0.0338021	+	0.0195157i
$690$	9.36716	−	154.403i	0.0135756	−	0.223773i
$691$	−465.762	−	806.723i	−0.674040	−	1.16747i	−0.976748	−	0.214388i	$-0.931224\pi$
$691$	−465.762	−	806.723i	−0.674040	−	1.16747i	0.302708	−	0.953083i	$-0.402109\pi$
$692$	−151.800	+	151.800i	−0.219365	+	0.219365i
$693$	167.738	+	210.004i	0.242046	+	0.303036i
$694$			328.639i			0.473544i
$695$	−310.753	+	307.736i	−0.447127	+	0.442785i
$696$	525.571	+	29.3120i	0.755131	+	0.0421150i
$697$	−9.26283	−	34.5694i	−0.0132896	−	0.0495974i
$698$	−44.4373	+	11.9069i	−0.0636638	+	0.0170587i
$699$	806.291	+	527.465i	1.15349	+	0.754599i
$700$	−224.558	−	872.009i	−0.320798	−	1.24573i
$701$	1256.95			1.79308			0.896539	−	0.442964i	$-0.146073\pi$
$701$	1256.95			1.79308			0.896539	+	0.442964i	$0.146073\pi$
$702$	60.0320	−	42.6995i	0.0855156	−	0.0608255i
$703$	−165.200	−	165.200i	−0.234993	−	0.234993i
$704$	8.86400	−	5.11763i	0.0125909	−	0.00726937i
$705$	301.712	−	903.204i	0.427960	−	1.28114i
$706$	290.023	−	502.334i	0.410797	−	0.711521i
$707$	286.190	+	1068.07i	0.404795	+	1.51071i
$708$	−359.918	−	402.435i	−0.508358	−	0.568412i
$709$	−631.908	+	364.832i	−0.891267	+	0.514573i	−0.874357	−	0.485284i	$-0.838716\pi$
$709$	−631.908	+	364.832i	−0.891267	+	0.514573i	−0.0169102	+	0.999857i	$0.505383\pi$
$710$	−147.459	+	252.554i	−0.207689	+	0.355709i
$711$	−367.399	+	498.613i	−0.516736	+	0.701284i
$712$	−638.766	+	638.766i	−0.897144	+	0.897144i
$713$	126.495	−	472.085i	0.177412	−	0.662111i
$714$	547.511	−	276.662i	0.766823	−	0.387481i
$715$	33.4877	−	19.1169i	0.0468360	−	0.0267369i
$716$	−478.300	+	828.440i	−0.668017	+	1.15704i
$717$	−406.243	−	133.505i	−0.566588	−	0.186199i
$718$	−19.4289	+	72.5097i	−0.0270598	+	0.100988i
$719$			806.713i			1.12199i	0.827818	+	0.560997i	$0.189582\pi$
$719$			806.713i			1.12199i	−0.827818	+	0.560997i	$0.810418\pi$
$720$	−229.332	+	181.350i	−0.318516	+	0.251875i
$721$	−304.082			−0.421750
$722$	−205.101	−	54.9567i	−0.284074	−	0.0761173i
$723$	915.424	+	1023.57i	1.26615	+	1.41572i
$724$	−470.417	−	271.595i	−0.649747	−	0.375131i
$725$	664.676	+	6.48556i	0.916795	+	0.00894561i
$726$	173.153	−	264.684i	0.238502	−	0.364578i
$727$	−1142.72	−	306.191i	−1.57183	−	0.421171i	−0.635446	−	0.772145i	$-0.719184\pi$
$727$	−1142.72	−	306.191i	−1.57183	−	0.421171i	−0.936385	+	0.350974i	$0.885850\pi$
$728$	−157.802	−	157.802i	−0.216762	−	0.216762i
$729$	239.180	−	688.647i	0.328093	−	0.944645i
$730$	−321.440	+	84.4511i	−0.440329	+	0.115686i
$731$	491.633	+	851.533i	0.672548	+	1.16489i
$732$	65.0752	+	311.285i	0.0889006	+	0.425253i
$733$	−987.760	+	264.670i	−1.34756	+	0.361077i	−0.859233	−	0.511585i	$-0.829059\pi$
$733$	−987.760	+	264.670i	−1.34756	+	0.361077i	−0.488325	+	0.872662i	$0.662392\pi$
$734$	48.0349	+	27.7330i	0.0654426	+	0.0377833i
$735$	677.963	−	1025.39i	0.922398	−	1.39509i
$736$	180.918	+	313.360i	0.245813	+	0.425761i
$737$	−60.0009	+	60.0009i	−0.0814123	+	0.0814123i
$738$	5.60286	−	14.3083i	0.00759195	−	0.0193880i
$739$		−	808.791i		−	1.09444i	−0.836989	−	0.547220i	$-0.815686\pi$
$739$		−	808.791i		−	1.09444i	0.836989	−	0.547220i	$-0.184314\pi$
$740$	1.56706	−	321.210i	0.00211765	−	0.434068i
$741$	45.7668	+	90.5722i	0.0617636	+	0.122230i
$742$	24.8850	+	92.8721i	0.0335378	+	0.125165i
$743$	614.769	−	164.727i	0.827415	−	0.221705i	0.179829	−	0.983698i	$-0.442445\pi$
$743$	614.769	−	164.727i	0.827415	−	0.221705i	0.647586	+	0.761993i	$0.275779\pi$
$744$	773.190	−	390.699i	1.03923	−	0.525133i
$745$	594.691	−	588.916i	0.798243	−	0.790492i
$746$	−180.107			−0.241431
$747$	142.150	+	938.193i	0.190295	+	1.25595i
$748$	−112.410	−	112.410i	−0.150280	−	0.150280i
$749$	614.409	−	354.729i	0.820306	−	0.473604i
$750$	261.428	−	227.009i	0.348570	−	0.302679i
$751$	709.826	−	1229.46i	0.945175	−	1.63709i	0.189774	−	0.981828i	$-0.439224\pi$
$751$	709.826	−	1229.46i	0.945175	−	1.63709i	0.755401	−	0.655263i	$-0.227442\pi$
$752$	106.754	+	398.412i	0.141960	+	0.529803i
$753$	−301.227	+	62.9726i	−0.400036	+	0.0836290i
$754$	62.8262	−	36.2727i	0.0833239	−	0.0481071i
$755$	−1206.80	+	317.058i	−1.59841	+	0.419945i
$756$	−958.943	−	161.789i	−1.26844	−	0.214007i
$757$	582.278	−	582.278i	0.769192	−	0.769192i	−0.208772	−	0.977964i	$-0.566947\pi$
$757$	582.278	−	582.278i	0.769192	−	0.769192i	0.977964	+	0.208772i	$0.0669467\pi$
$758$	34.8500	−	130.062i	0.0459762	−	0.171586i
$759$	−73.1771	−	47.8715i	−0.0964125	−	0.0630718i
$760$	187.247	+	328.007i	0.246378	+	0.431588i
$761$	−73.5291	+	127.356i	−0.0966217	+	0.167354i	−0.910284	−	0.413984i	$-0.864137\pi$
$761$	−73.5291	+	127.356i	−0.0966217	+	0.167354i	0.813663	+	0.581337i	$0.197470\pi$
$762$	−315.992	+	282.607i	−0.414687	+	0.370875i
$763$	−38.8619	+	145.035i	−0.0509330	+	0.190085i
$764$		−	904.087i		−	1.18336i
$765$	−698.603	−	520.038i	−0.913207	−	0.679788i
$766$	697.261			0.910262
$767$	−163.211	−	43.7322i	−0.212791	−	0.0570172i
$768$	−123.621	+	376.169i	−0.160965	+	0.489804i
$769$	798.259	+	460.875i	1.03805	+	0.599317i	0.919280	−	0.393605i	$-0.128772\pi$
$769$	798.259	+	460.875i	1.03805	+	0.599317i	0.118768	+	0.992922i	$0.462106\pi$
$770$	132.990	+	36.3308i	0.172714	+	0.0471828i
$771$	−151.875	−	300.559i	−0.196984	−	0.389830i
$772$	111.860	+	29.9729i	0.144897	+	0.0388250i
$773$	646.946	+	646.946i	0.836928	+	0.836928i	0.988453	−	0.151525i	$-0.0484185\pi$
$773$	646.946	+	646.946i	0.836928	+	0.836928i	−0.151525	+	0.988453i	$0.548418\pi$
$774$	−46.9445	+	419.554i	−0.0606518	+	0.542060i
$775$	952.666	−	537.697i	1.22925	−	0.693803i
$776$	120.597	+	208.880i	0.155409	+	0.269176i
$777$	522.286	−	467.106i	0.672183	−	0.601166i
$778$	−38.4744	+	10.3092i	−0.0494530	+	0.0132509i
$779$	18.3311	+	10.5835i	0.0235316	+	0.0135860i
$780$	−44.2057	+	132.334i	−0.0566740	+	0.169659i
$781$	82.6613	+	143.174i	0.105840	+	0.183321i
$782$	−141.127	+	141.127i	−0.180469	+	0.180469i
$783$	298.574	−	652.849i	0.381321	−	0.833779i
$784$			532.441i			0.679134i
$785$	−250.510	−	1.22215i	−0.319121	−	0.00155687i
$786$	−9.97338	+	15.2455i	−0.0126888	+	0.0193963i
$787$	28.2343	+	105.372i	0.0358758	+	0.133890i	0.981541	−	0.191251i	$-0.0612546\pi$
$787$	28.2343	+	105.372i	0.0358758	+	0.133890i	−0.945665	+	0.325142i	$0.894588\pi$
$788$	974.548	−	261.129i	1.23674	−	0.331382i
$789$	−24.8892	+	446.270i	−0.0315453	+	0.565614i
$790$	−1.54987	+	317.686i	−0.00196186	+	0.402134i
$791$	−372.115			−0.470436
$792$	−23.2194	−	153.248i	−0.0293174	−	0.193495i
$793$	70.3755	+	70.3755i	0.0887459	+	0.0887459i
$794$	101.540	−	58.6241i	0.127884	−	0.0738339i
$795$	102.190	−	90.5001i	0.128541	−	0.113837i
$796$	169.192	−	293.050i	0.212553	−	0.368153i
$797$	−231.377	−	863.511i	−0.290310	−	1.08345i	−0.944871	−	0.327443i	$-0.893813\pi$
$797$	−231.377	−	863.511i	−0.290310	−	1.08345i	0.654561	−	0.756009i	$-0.272854\pi$
$798$	−113.272	+	344.678i	−0.141945	+	0.431928i
$799$	−1064.04	+	614.324i	−1.33171	+	0.768866i
$800$	−217.239	+	780.214i	−0.271548	+	0.975267i
$801$	493.532	+	1128.81i	0.616145	+	1.40925i
$802$	189.040	−	189.040i	0.235711	−	0.235711i
$803$	−48.6261	+	181.475i	−0.0605556	+	0.225996i
$804$	17.0969	−	306.552i	0.0212648	−	0.381283i
$805$	−168.413	+	616.480i	−0.209209	+	0.765813i
$806$	59.6953	−	103.395i	0.0740637	−	0.128282i
$807$	19.0823	+	91.2795i	0.0236460	+	0.113110i
$808$	165.042	−	615.946i	0.204260	−	0.762310i
$809$		−	920.002i		−	1.13721i	−0.822611	−	0.568604i	$-0.807484\pi$
$809$		−	920.002i		−	1.13721i	0.822611	−	0.568604i	$-0.192516\pi$
$810$	−109.026	−	357.685i	−0.134600	−	0.441586i
$811$	−174.196			−0.214792			−0.107396	−	0.994216i	$-0.534251\pi$
$811$	−174.196			−0.214792			−0.107396	+	0.994216i	$0.534251\pi$
$812$	−925.035	−	247.862i	−1.13921	−	0.305249i
$813$	−12.4056	+	2.59343i	−0.0152590	+	0.00318995i
$814$	42.5901	+	24.5894i	0.0523220	+	0.0302081i
$815$	144.426	−	82.4477i	0.177210	−	0.101163i
$816$	376.643	+	21.0061i	0.461573	+	0.0257427i
$817$	−561.727	−	150.514i	−0.687548	−	0.184228i
$818$	−134.631	−	134.631i	−0.164585	−	0.164585i
$819$	−278.864	+	121.923i	−0.340494	+	0.148869i
$820$	7.39500	+	28.1471i	0.00901829	+	0.0343257i
$821$	425.992	+	737.840i	0.518869	+	0.898708i	0.999760	+	0.0219274i	$0.00698027\pi$
$821$	425.992	+	737.840i	0.518869	+	0.898708i	−0.480890	+	0.876781i	$0.659686\pi$
$822$	−229.157	−	75.3083i	−0.278780	−	0.0916160i
$823$	199.408	−	53.4313i	0.242295	−	0.0649226i	−0.135628	−	0.990760i	$-0.543305\pi$
$823$	199.408	−	53.4313i	0.242295	−	0.0649226i	0.377923	+	0.925837i	$0.376639\pi$
$824$	151.866	+	87.6802i	0.184304	+	0.106408i
$825$	−38.1801	−	191.966i	−0.0462789	−	0.232686i
$826$	−302.054	−	523.172i	−0.365682	−	0.633380i
$827$	−66.1579	+	66.1579i	−0.0799974	+	0.0799974i	−0.745973	−	0.665976i	$-0.768015\pi$
$827$	−66.1579	+	66.1579i	−0.0799974	+	0.0799974i	0.665976	+	0.745973i	$0.268015\pi$
$828$	312.831	−	47.3987i	0.377815	−	0.0572448i
$829$			71.1280i			0.0857998i	0.999079	+	0.0428999i	$0.0136596\pi$
$829$			71.1280i			0.0857998i	−0.999079	+	0.0428999i	$0.986340\pi$
$830$	342.485	+	345.843i	0.412633	+	0.416679i
$831$	−416.531	−	23.2306i	−0.501240	−	0.0279550i
$832$	2.99979	+	11.1954i	0.00360552	+	0.0134560i
$833$	−1531.98	+	410.494i	−1.83912	+	0.492790i
$834$	202.746	+	132.634i	0.243101	+	0.159033i
$835$	553.290	+	2.69929i	0.662623	+	0.00323269i
$836$	94.0219			0.112466
$837$	−111.666	−	1176.16i	−0.133412	−	1.40521i
$838$	−468.230	−	468.230i	−0.558747	−	0.558747i
$839$	327.523	−	189.096i	0.390373	−	0.225382i	−0.291949	−	0.956434i	$-0.594304\pi$
$839$	327.523	−	189.096i	0.390373	−	0.225382i	0.682322	+	0.731052i	$0.260970\pi$
$840$	−1013.50	+	505.936i	−1.20654	+	0.602305i
$841$	−67.0308	+	116.101i	−0.0797037	+	0.138051i
$842$	−59.5317	−	222.175i	−0.0707027	−	0.263866i
$843$	1006.76	+	1125.69i	1.19426	+	1.33534i
$844$	−248.527	+	143.487i	−0.294463	+	0.170008i
$845$	−203.622	−	775.033i	−0.240973	−	0.917199i
$846$	−524.257	−	58.6599i	−0.619690	−	0.0693380i
$847$	−923.984	+	923.984i	−1.09089	+	1.09089i
$848$	−15.3028	+	57.1106i	−0.0180457	+	0.0673475i
$849$	−392.410	+	198.288i	−0.462203	+	0.233555i
$850$	−446.702	−	4.35869i	−0.525532	−	0.00512787i
$851$	−113.985	+	197.428i	−0.133943	+	0.231996i
$852$	−568.287	−	186.757i	−0.667004	−	0.219199i
$853$	−168.733	+	629.719i	−0.197811	+	0.738240i	0.793711	+	0.608296i	$0.208146\pi$
$853$	−168.733	+	629.719i	−0.197811	+	0.738240i	−0.991521	+	0.129944i	$0.958520\pi$
$854$			355.832i			0.416665i
$855$	509.649	−	74.6780i	0.596081	−	0.0873426i
$856$	−409.137			−0.477963
$857$	542.809	+	145.445i	0.633382	+	0.169714i	0.561204	−	0.827677i	$-0.310338\pi$
$857$	542.809	+	145.445i	0.633382	+	0.169714i	0.0721782	+	0.997392i	$0.477005\pi$
$858$	−14.2402	−	15.9224i	−0.0165969	−	0.0185576i
$859$	−468.778	−	270.649i	−0.545725	−	0.315075i	0.201671	−	0.979453i	$-0.435363\pi$
$859$	−468.778	−	270.649i	−0.545725	−	0.315075i	−0.747396	+	0.664379i	$0.768696\pi$
$860$	−396.397	−	694.380i	−0.460926	−	0.807419i
$861$	−34.7539	+	53.1254i	−0.0403646	+	0.0617020i
$862$	208.774	+	55.9407i	0.242197	+	0.0648964i
$863$	24.2188	+	24.2188i	0.0280635	+	0.0280635i	0.720999	−	0.692936i	$-0.243683\pi$
$863$	24.2188	+	24.2188i	0.0280635	+	0.0280635i	−0.692936	+	0.720999i	$0.743683\pi$
$864$	674.184	+	557.269i	0.780306	+	0.644987i
$865$	294.502	+	171.952i	0.340464	+	0.198788i
$866$	−243.463	−	421.690i	−0.281135	−	0.486940i
$867$	52.5250	+	251.252i	0.0605825	+	0.289794i
$868$	−1522.36	+	407.916i	−1.75388	+	0.469950i
$869$	155.529	+	89.7949i	0.178975	+	0.103331i
$870$	−73.5916	−	360.802i	−0.0845880	−	0.414715i
$871$	−48.0438	−	83.2144i	−0.0551594	−	0.0955389i
$872$	61.2285	−	61.2285i	0.0702162	−	0.0702162i
$873$	325.227	−	49.2768i	0.372540	−	0.0564454i
$874$		−	118.041i		−	0.135059i
$875$	−1249.11	+	697.002i	−1.42756	+	0.796574i
$876$	−306.588	−	606.735i	−0.349986	−	0.692620i
$877$	321.735	+	1200.73i	0.366858	+	1.36913i	0.864884	+	0.501972i	$0.167392\pi$
$877$	321.735	+	1200.73i	0.366858	+	1.36913i	−0.498025	+	0.867162i	$0.665941\pi$
$878$	−575.505	+	154.206i	−0.655472	+	0.175633i
$879$	−918.415	+	464.082i	−1.04484	+	0.527966i
$880$	59.6533	+	60.2382i	0.0677879	+	0.0684525i
$881$	1074.75			1.21993			0.609963	−	0.792430i	$-0.291184\pi$
$881$	1074.75			1.21993			0.609963	+	0.792430i	$0.291184\pi$
$882$	−634.091	−	248.298i	−0.718924	−	0.281517i
$883$	285.903	+	285.903i	0.323786	+	0.323786i	0.850217	−	0.526432i	$-0.176470\pi$
$883$	285.903	+	285.903i	0.323786	+	0.323786i	−0.526432	+	0.850217i	$0.676470\pi$
$884$	155.899	−	90.0086i	0.176357	−	0.101820i
$885$	−473.020	+	715.423i	−0.534486	+	0.808388i
$886$	−126.931	+	219.851i	−0.143263	+	0.248139i
$887$	−277.751	−	1036.58i	−0.313135	−	1.16864i	−0.925713	−	0.378226i	$-0.876534\pi$
$887$	−277.751	−	1036.58i	−0.313135	−	1.16864i	0.612578	−	0.790410i	$-0.290132\pi$
$888$	−395.531	+	82.6871i	−0.445418	+	0.0931161i
$889$	1516.77	−	875.708i	1.70615	−	0.985048i
$890$	545.722	+	318.632i	0.613170	+	0.358014i
$891$	−206.156	−	46.7192i	−0.231376	−	0.0524345i
$892$	528.255	−	528.255i	0.592214	−	0.592214i
$893$	188.076	−	701.910i	0.210612	−	0.786013i
$894$	−387.997	−	253.823i	−0.434001	−	0.283918i
$895$	1465.89	+	400.458i	1.63786	+	0.447439i
$896$	720.711	−	1248.31i	0.804365	−	1.39320i
$897$	73.8090	−	66.0110i	0.0822842	−	0.0735908i
$898$	−45.5630	+	170.043i	−0.0507383	+	0.189358i
$899$		−	1163.43i		−	1.29414i
$900$	566.011	+	425.644i	0.628901	+	0.472938i
$901$	−176.122			−0.195473
$902$	−4.30382	−	1.15321i	−0.00477142	−	0.00127850i
$903$	544.533	−	1656.97i	0.603026	−	1.83496i
$904$	185.844	+	107.297i	0.205580	+	0.118692i
$905$	−227.394	+	832.380i	−0.251264	+	0.919757i
$906$	311.740	+	616.932i	0.344084	+	0.680940i
$907$	1652.08	+	442.672i	1.82147	+	0.488062i	0.996969	−	0.0777954i	$-0.0247881\pi$
$907$	1652.08	+	442.672i	1.82147	+	0.488062i	0.824503	+	0.565858i	$0.191455\pi$
$908$	−273.374	−	273.374i	−0.301073	−	0.301073i
$909$	−700.122	−	515.879i	−0.770211	−	0.567524i
$910$	−78.7157	+	134.816i	−0.0865008	+	0.148150i
$911$	−203.177	−	351.913i	−0.223026	−	0.386293i	0.732699	−	0.680553i	$-0.238260\pi$
$911$	−203.177	−	351.913i	−0.223026	−	0.386293i	−0.955726	+	0.294260i	$0.904927\pi$
$912$	−166.301	+	148.731i	−0.182348	+	0.163083i
$913$	265.772	−	71.2133i	0.291097	−	0.0779993i
$914$	250.056	+	144.370i	0.273584	+	0.157954i
$915$	451.991	−	225.633i	0.493980	−	0.246594i
$916$	518.280	+	897.687i	0.565808	+	0.980008i
$917$	53.2204	−	53.2204i	0.0580375	−	0.0580375i
$918$	−200.660	+	438.754i	−0.218584	+	0.477945i
$919$		−	975.596i		−	1.06158i	−0.847502	−	0.530792i	$-0.821895\pi$
$919$		−	975.596i		−	1.06158i	0.847502	−	0.530792i	$-0.178105\pi$
$920$	261.868	−	259.326i	0.284639	−	0.281876i
$921$	44.6600	−	68.2681i	0.0484908	−	0.0741238i
$922$	52.7449	+	196.847i	0.0572071	+	0.213500i
$923$	−180.830	+	48.4533i	−0.195916	+	0.0524955i
$924$	−15.7026	+	281.551i	−0.0169941	+	0.304709i
$925$	−494.141	+	127.250i	−0.534206	+	0.137568i
$926$	266.694			0.288007
$927$	186.864	−	149.255i	0.201579	−	0.161009i
$928$	609.065	+	609.065i	0.656320	+	0.656320i
$929$	−1121.09	+	647.262i	−1.20677	+	0.696730i	−0.962052	−	0.272864i	$-0.912029\pi$
$929$	−1121.09	+	647.262i	−1.20677	+	0.696730i	−0.244719	+	0.969594i	$0.578696\pi$
$930$	−401.779	−	453.676i	−0.432020	−	0.487824i
$931$	469.020	−	812.366i	0.503780	−	0.872573i
$932$	261.635	+	976.435i	0.280724	+	1.04768i
$933$	516.429	−	1571.45i	0.553514	−	1.68430i
$934$	282.319	−	162.997i	0.302269	−	0.174515i
$935$	−127.332	+	218.081i	−0.136184	+	0.233242i
$936$	174.428	+	19.5170i	0.186355	+	0.0208515i
$937$	−416.458	+	416.458i	−0.444459	+	0.444459i	−0.893507	−	0.449049i	$-0.851763\pi$
$937$	−416.458	+	416.458i	−0.444459	+	0.444459i	0.449049	+	0.893507i	$0.351763\pi$
$938$	88.9145	−	331.834i	0.0947916	−	0.353767i
$939$	−80.1201	+	1436.57i	−0.0853249	+	1.52990i
$940$	867.669	−	495.321i	0.923052	−	0.526937i
$941$	6.23741	−	10.8035i	0.00662849	−	0.0114809i	−0.862692	−	0.505729i	$-0.831223\pi$
$941$	6.23741	−	10.8035i	0.00662849	−	0.0114809i	0.869321	+	0.494249i	$0.164557\pi$
$942$	28.3980	+	135.841i	0.0301465	+	0.144205i
$943$	5.34574	−	19.9506i	0.00566886	−	0.0211565i
$944$		−	371.489i		−	0.393526i
$945$	138.509	+	1538.63i	0.146570	+	1.62818i
$946$	122.415			0.129403
$947$	1149.13	+	307.908i	1.21344	+	0.325140i	0.808111	−	0.589031i	$-0.200490\pi$
$947$	1149.13	+	307.908i	1.21344	+	0.325140i	0.405329	+	0.914171i	$0.367157\pi$
$948$	−636.061	+	132.971i	−0.670950	+	0.140264i
$949$	−184.246	−	106.375i	−0.194148	−	0.112091i
$950$	188.639	−	184.993i	0.198567	−	0.194729i
$951$	−837.300	−	46.6977i	−0.880442	−	0.0491038i
$952$	1411.73	+	378.272i	1.48291	+	0.397345i
$953$	−943.370	−	943.370i	−0.989895	−	0.989895i	0.0100546	−	0.999949i	$-0.496799\pi$
$953$	−943.370	−	943.370i	−0.989895	−	0.989895i	−0.999949	+	0.0100546i	$0.996799\pi$
$954$	−60.8776	−	44.8572i	−0.0638130	−	0.0470201i
$955$	−1389.04	+	364.939i	−1.45449	+	0.382135i
$956$	−224.324	−	388.540i	−0.234648	−	0.406423i
$957$	−197.756	−	64.9888i	−0.206641	−	0.0679089i
$958$	780.555	−	209.149i	0.814775	−	0.218318i
$959$	863.033	+	498.272i	0.899930	+	0.519575i
$960$	58.7227	+	3.56252i	0.0611695	+	0.00371096i
$961$	−476.853	−	825.933i	−0.496204	−	0.859451i
$962$	−39.3784	+	39.3784i	−0.0409339	+	0.0409339i
$963$	−203.451	+	519.564i	−0.211268	+	0.539526i
$964$			1440.74i			1.49454i
$965$	0.897477	−	183.961i	0.000930028	−	0.190633i
$966$	353.478	+	19.7141i	0.365920	+	0.0204080i
$967$	−71.4571	−	266.681i	−0.0738956	−	0.275782i	0.919085	−	0.394059i	$-0.128930\pi$
$967$	−71.4571	−	266.681i	−0.0738956	−	0.275782i	−0.992981	+	0.118277i	$0.962263\pi$
$968$	727.888	−	195.037i	0.751950	−	0.201484i
$969$	−556.155	−	363.829i	−0.573948	−	0.375469i
$970$	119.888	−	118.723i	0.123595	−	0.122395i
$971$	−311.097			−0.320388			−0.160194	−	0.987086i	$-0.551212\pi$
$971$	−311.097			−0.320388			−0.160194	+	0.987086i	$0.551212\pi$
$972$	668.701	−	371.264i	0.687964	−	0.381959i
$973$	−707.766	−	707.766i	−0.727406	−	0.727406i
$974$	273.087	−	157.667i	0.280377	−	0.161876i
$975$	221.163	+	14.5005i	0.226833	+	0.0148723i
$976$	−109.407	+	189.499i	−0.112098	+	0.194159i
$977$	−163.044	−	608.490i	−0.166883	−	0.622815i	−0.997793	−	0.0664079i	$-0.978846\pi$
$977$	−163.044	−	608.490i	−0.166883	−	0.622815i	0.830910	−	0.556407i	$-0.187821\pi$
$978$	−61.4152	−	68.6703i	−0.0627967	−	0.0702150i
$979$	309.371	−	178.616i	0.316008	−	0.182447i
$980$	1247.37	−	327.719i	1.27283	−	0.334407i
$981$	−47.3072	−	108.201i	−0.0482235	−	0.110297i
$982$	18.5905	−	18.5905i	0.0189313	−	0.0189313i
$983$	−81.8068	+	305.307i	−0.0832216	+	0.310587i	−0.994971	−	0.100159i	$-0.968065\pi$
$983$	−81.8068	+	305.307i	−0.0832216	+	0.310587i	0.911750	+	0.410746i	$0.134732\pi$
$984$	32.6754	−	16.5112i	0.0332068	−	0.0167796i
$985$	−794.581	−	1391.89i	−0.806681	−	1.41309i
$986$	−237.553	+	411.453i	−0.240926	+	0.417295i
$987$	2070.48	+	680.425i	2.09775	+	0.689387i
$988$	−27.5563	+	102.841i	−0.0278910	+	0.104091i
$989$			567.460i			0.573771i
$990$	−99.5572	+	42.9505i	−0.100563	+	0.0433844i
$991$	−1401.99			−1.41472			−0.707362	−	0.706852i	$-0.750115\pi$
$991$	−1401.99			−1.41472			−0.707362	+	0.706852i	$0.750115\pi$
$992$	1369.25	+	366.889i	1.38029	+	0.369848i
$993$	244.703	+	273.611i	0.246428	+	0.275539i
$994$	−579.651	−	334.662i	−0.583150	−	0.336682i
$995$	−518.538	−	141.657i	−0.521143	−	0.142368i
$996$	−545.022	+	833.130i	−0.547211	+	0.836475i
$997$	−1305.07	−	349.692i	−1.30900	−	0.350745i	−0.464152	−	0.885756i	$-0.653641\pi$
$997$	−1305.07	−	349.692i	−1.30900	−	0.350745i	−0.844845	+	0.535011i	$0.820307\pi$
$998$	309.014	+	309.014i	0.309633	+	0.309633i
$999$	−91.6809	+	543.404i	−0.0917727	+	0.543947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.k.a.13.4	yes	40
3.2	odd	2		135.3.l.a.118.7		40
5.2	odd	4	inner	45.3.k.a.22.7	yes	40
5.3	odd	4		225.3.o.b.157.4		40
5.4	even	2		225.3.o.b.193.7		40
9.2	odd	6		135.3.l.a.73.4		40
9.4	even	3		405.3.g.h.163.7		20
9.5	odd	6		405.3.g.g.163.4		20
9.7	even	3	inner	45.3.k.a.43.7	yes	40
15.2	even	4		135.3.l.a.37.4		40
45.2	even	12		135.3.l.a.127.7		40
45.7	odd	12	inner	45.3.k.a.7.4	✓	40
45.22	odd	12		405.3.g.h.82.7		20
45.32	even	12		405.3.g.g.82.4		20
45.34	even	6		225.3.o.b.43.4		40
45.43	odd	12		225.3.o.b.7.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.k.a.7.4	✓	40	45.7	odd	12	inner
45.3.k.a.13.4	yes	40	1.1	even	1	trivial
45.3.k.a.22.7	yes	40	5.2	odd	4	inner
45.3.k.a.43.7	yes	40	9.7	even	3	inner
135.3.l.a.37.4		40	15.2	even	4
135.3.l.a.73.4		40	9.2	odd	6
135.3.l.a.118.7		40	3.2	odd	2
135.3.l.a.127.7		40	45.2	even	12
225.3.o.b.7.7		40	45.43	odd	12
225.3.o.b.43.4		40	45.34	even	6
225.3.o.b.157.4		40	5.3	odd	4
225.3.o.b.193.7		40	5.4	even	2
405.3.g.g.82.4		20	45.32	even	12
405.3.g.g.163.4		20	9.5	odd	6
405.3.g.h.82.7		20	45.22	odd	12
405.3.g.h.163.7		20	9.4	even	3

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891829 - 0.238965i) q^{2} +(-2.93652 + 0.613889i) q^{3} +(-2.72585 - 1.57377i) q^{4} +(-1.31764 + 4.82326i) q^{5} +(2.76557 + 0.154241i) q^{6} +(-11.0534 - 2.96175i) q^{7} +(4.66637 + 4.66637i) q^{8} +(8.24628 - 3.60539i) q^{9} +(2.32770 - 3.98665i) q^{10} +(-1.30484 - 2.26005i) q^{11} +(8.97062 + 2.94803i) q^{12} +(2.85447 - 0.764853i) q^{13} +(9.15000 + 5.28276i) q^{14} +(0.908333 - 14.9725i) q^{15} +(3.24857 + 5.62669i) q^{16} +(-13.6850 + 13.6850i) q^{17} +(-8.21583 + 1.24482i) q^{18} -11.4465i q^{19} +(11.1824 - 11.0738i) q^{20} +(34.2768 + 1.91167i) q^{21} +(0.623621 + 2.32738i) q^{22} +(-10.7887 + 2.89082i) q^{23} +(-16.5675 - 10.8382i) q^{24} +(-21.5276 - 12.7107i) q^{25} -2.72847 q^{26} +(-22.0020 + 15.6496i) q^{27} +(25.4688 + 25.4688i) q^{28} +(-23.0262 + 13.2942i) q^{29} +(-4.38797 + 13.1358i) q^{30} +(-21.8787 + 37.8950i) q^{31} +(-8.38463 - 31.2919i) q^{32} +(5.21910 + 5.83564i) q^{33} +(15.4750 - 8.93448i) q^{34} +(28.8498 - 49.4110i) q^{35} +(-28.1522 - 3.14999i) q^{36} +(14.4324 - 14.4324i) q^{37} +(-2.73530 + 10.2083i) q^{38} +(-7.91267 + 3.99833i) q^{39} +(-28.6557 + 16.3585i) q^{40} +(-0.924605 + 1.60146i) q^{41} +(-30.1122 - 9.89582i) q^{42} +(13.1494 - 49.0742i) q^{43} +8.21405i q^{44} +(6.52410 + 44.5246i) q^{45} +10.3125 q^{46} +(61.3211 + 16.4309i) q^{47} +(-12.9936 - 14.5286i) q^{48} +(70.9709 + 40.9750i) q^{49} +(16.1616 + 16.4801i) q^{50} +(31.7853 - 48.5875i) q^{51} +(-8.98455 - 2.40740i) q^{52} +(6.43481 + 6.43481i) q^{53} +(23.3618 - 8.69905i) q^{54} +(12.6201 - 3.31564i) q^{55} +(-37.7587 - 65.4000i) q^{56} +(7.02686 + 33.6128i) q^{57} +(23.7122 - 6.35367i) q^{58} +(-49.5170 - 28.5886i) q^{59} +(-26.0392 + 39.3832i) q^{60} +(16.8393 + 29.1666i) q^{61} +(28.5676 - 28.5676i) q^{62} +(-101.828 + 15.4285i) q^{63} +3.92205i q^{64} +(-0.0720848 + 14.7757i) q^{65} +(-3.26003 - 6.45157i) q^{66} +(-8.41554 - 31.4072i) q^{67} +(58.8405 - 15.7663i) q^{68} +(29.9066 - 15.1120i) q^{69} +(-37.5365 + 37.1720i) q^{70} -63.3498 q^{71} +(55.3043 + 21.6561i) q^{72} +(-50.9063 - 50.9063i) q^{73} +(-16.3201 + 9.42239i) q^{74} +(71.0192 + 24.1095i) q^{75} +(-18.0141 + 31.2013i) q^{76} +(7.72922 + 28.8458i) q^{77} +(8.01221 - 1.67498i) q^{78} +(-59.5972 + 34.4084i) q^{79} +(-31.4194 + 8.25473i) q^{80} +(55.0023 - 59.4622i) q^{81} +(1.20728 - 1.20728i) q^{82} +(-27.2882 + 101.841i) q^{83} +(-90.4247 - 59.1546i) q^{84} +(-47.9745 - 84.0385i) q^{85} +(-23.4540 + 40.6236i) q^{86} +(59.4556 - 53.1740i) q^{87} +(4.45735 - 16.6351i) q^{88} +136.887i q^{89} +(4.82142 - 41.2673i) q^{90} -33.8170 q^{91} +(33.9578 + 9.09897i) q^{92} +(40.9838 - 124.710i) q^{93} +(-50.7615 - 29.3072i) q^{94} +(55.2093 + 15.0823i) q^{95} +(43.8313 + 86.7419i) q^{96} +(35.3034 + 9.45952i) q^{97} +(-53.5023 - 53.5023i) q^{98} +(-18.9084 - 13.9325i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 6 * q^3 - 2 * q^5 - 24 * q^6 - 2 * q^7 - 24 * q^8 - 8 * q^10 + 8 * q^11 - 30 * q^12 - 2 * q^13 - 30 * q^15 + 28 * q^16 + 28 * q^17 + 48 * q^18 - 114 * q^20 + 12 * q^21 + 14 * q^22 + 82 * q^23 - 8 * q^25 - 112 * q^26 - 198 * q^27 - 88 * q^28 + 162 * q^30 - 4 * q^31 - 14 * q^32 + 96 * q^33 + 352 * q^35 + 264 * q^36 - 92 * q^37 + 330 * q^38 + 30 * q^40 - 28 * q^41 + 498 * q^42 - 2 * q^43 - 72 * q^45 - 136 * q^46 + 64 * q^47 - 510 * q^48 - 458 * q^50 - 396 * q^51 - 74 * q^52 - 608 * q^53 + 224 * q^55 - 192 * q^56 - 114 * q^57 + 30 * q^58 - 798 * q^60 + 92 * q^61 - 100 * q^62 + 24 * q^63 - 326 * q^65 + 588 * q^66 - 80 * q^67 + 626 * q^68 - 102 * q^70 + 248 * q^71 - 162 * q^72 - 8 * q^73 + 810 * q^75 - 96 * q^76 + 338 * q^77 + 1062 * q^78 + 1444 * q^80 + 204 * q^81 + 104 * q^82 + 370 * q^83 - 98 * q^85 - 328 * q^86 + 534 * q^87 - 210 * q^88 + 462 * q^90 + 152 * q^91 + 388 * q^92 - 1062 * q^93 - 360 * q^95 - 876 * q^96 + 292 * q^97 - 1876 * q^98

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