LMFDB - Embedded newform 63.4.o.a.41.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,4,Mod(20,63)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("63.20");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	63.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.71712033036$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.11
Character	$\chi$	$=$	63.41
Dual form			63.4.o.a.20.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0847887 + 0.0489528i) q^{2} +(-5.17293 + 0.490712i) q^{3} +(-3.99521 + 6.91990i) q^{4} +(9.06347 - 15.6984i) q^{5} +(0.414584 - 0.294836i) q^{6} +(12.7516 - 13.4312i) q^{7} -1.56555i q^{8} +(26.5184 - 5.07683i) q^{9} +O(q^{10})$	\(q+(-0.0847887 + 0.0489528i) q^{2} +(-5.17293 + 0.490712i) q^{3} +(-3.99521 + 6.91990i) q^{4} +(9.06347 - 15.6984i) q^{5} +(0.414584 - 0.294836i) q^{6} +(12.7516 - 13.4312i) q^{7} -1.56555i q^{8} +(26.5184 - 5.07683i) q^{9} +1.77473i q^{10} +(32.0537 - 18.5062i) q^{11} +(17.2713 - 37.7567i) q^{12} +(-16.3673 - 9.44964i) q^{13} +(-0.423698 + 1.76304i) q^{14} +(-39.1813 + 85.6542i) q^{15} +(-31.8850 - 55.2265i) q^{16} -62.5187 q^{17} +(-1.99994 + 1.72861i) q^{18} -70.2680i q^{19} +(72.4209 + 125.437i) q^{20} +(-59.3723 + 75.7359i) q^{21} +(-1.81186 + 3.13823i) q^{22} +(140.692 + 81.2288i) q^{23} +(0.768234 + 8.09848i) q^{24} +(-101.793 - 176.311i) q^{25} +1.85034 q^{26} +(-134.687 + 39.2750i) q^{27} +(41.9972 + 141.900i) q^{28} +(82.5015 - 47.6323i) q^{29} +(-0.870879 - 9.18054i) q^{30} +(110.611 + 63.8612i) q^{31} +(16.2534 + 9.38392i) q^{32} +(-156.730 + 111.460i) q^{33} +(5.30088 - 3.06046i) q^{34} +(-95.2742 - 321.913i) q^{35} +(-70.8153 + 203.788i) q^{36} -378.832 q^{37} +(3.43981 + 5.95793i) q^{38} +(89.3037 + 40.8507i) q^{39} +(-24.5766 - 14.1893i) q^{40} +(99.1937 - 171.809i) q^{41} +(1.32662 - 9.32799i) q^{42} +(160.692 + 278.327i) q^{43} +295.744i q^{44} +(160.651 - 462.310i) q^{45} -15.9055 q^{46} +(79.3885 + 137.505i) q^{47} +(192.039 + 270.036i) q^{48} +(-17.7932 - 342.538i) q^{49} +(17.2618 + 9.96610i) q^{50} +(323.405 - 30.6786i) q^{51} +(130.781 - 75.5066i) q^{52} -191.780i q^{53} +(9.49728 - 9.92336i) q^{54} -670.922i q^{55} +(-21.0272 - 19.9633i) q^{56} +(34.4813 + 363.491i) q^{57} +(-4.66346 + 8.07736i) q^{58} +(-106.918 + 185.187i) q^{59} +(-436.181 - 613.337i) q^{60} +(-190.929 + 110.233i) q^{61} -12.5047 q^{62} +(269.964 - 420.911i) q^{63} +508.323 q^{64} +(-296.688 + 171.293i) q^{65} +(7.83266 - 17.1230i) q^{66} +(68.2947 - 118.290i) q^{67} +(249.775 - 432.623i) q^{68} +(-767.652 - 351.151i) q^{69} +(23.8367 + 22.6306i) q^{70} +458.924i q^{71} +(-7.94804 - 41.5159i) q^{72} +967.869i q^{73} +(32.1207 - 18.5449i) q^{74} +(613.086 + 862.091i) q^{75} +(486.248 + 280.735i) q^{76} +(160.176 - 666.503i) q^{77} +(-9.57170 + 0.907986i) q^{78} +(298.318 + 516.702i) q^{79} -1155.96 q^{80} +(677.452 - 269.259i) q^{81} +19.4232i q^{82} +(180.715 + 313.007i) q^{83} +(-286.880 - 713.431i) q^{84} +(-566.636 + 981.443i) q^{85} +(-27.2498 - 15.7327i) q^{86} +(-403.401 + 286.883i) q^{87} +(-28.9724 - 50.1817i) q^{88} +35.4987 q^{89} +(9.01000 + 47.0630i) q^{90} +(-335.629 + 99.3336i) q^{91} +(-1124.19 + 649.052i) q^{92} +(-603.519 - 276.071i) q^{93} +(-13.4625 - 7.77258i) q^{94} +(-1103.09 - 636.872i) q^{95} +(-88.6826 - 40.5666i) q^{96} +(-1151.63 + 664.894i) q^{97} +(18.2769 + 28.1723i) q^{98} +(756.060 - 653.486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) $ 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.0847887	+	0.0489528i	−0.0299773	+	0.0173074i	−0.514914	−	0.857242i	$-0.672176\pi$
$2$	−0.0847887	+	0.0489528i	−0.0299773	+	0.0173074i	0.484936	+	0.874549i	$0.338843\pi$
$3$	−5.17293	+	0.490712i	−0.995531	+	0.0944375i
$3$	−5.17293	+	0.490712i	−0.995531	+	0.0944375i
$4$	−3.99521	+	6.91990i	−0.499401	+	0.864988i
$5$	9.06347	−	15.6984i	0.810661	−	1.40411i	−0.101740	−	0.994811i	$-0.532441\pi$
$5$	9.06347	−	15.6984i	0.810661	−	1.40411i	0.912402	−	0.409296i	$-0.134226\pi$
$6$	0.414584	−	0.294836i	0.0282089	−	0.0200611i
$7$	12.7516	−	13.4312i	0.688522	−	0.725216i
$7$	12.7516	−	13.4312i	0.688522	−	0.725216i
$8$		−	1.56555i		−	0.0691882i
$9$	26.5184	−	5.07683i	0.982163	−	0.188031i
$10$			1.77473i			0.0561218i
$11$	32.0537	−	18.5062i	0.878595	−	0.507257i	0.00840042	−	0.999965i	$-0.497326\pi$
$11$	32.0537	−	18.5062i	0.878595	−	0.507257i	0.870195	+	0.492707i	$0.163993\pi$
$12$	17.2713	−	37.7567i	0.415482	−	0.908284i
$13$	−16.3673	−	9.44964i	−0.349189	−	0.201605i	0.315139	−	0.949046i	$-0.397949\pi$
$13$	−16.3673	−	9.44964i	−0.349189	−	0.201605i	−0.664328	+	0.747441i	$0.731282\pi$
$14$	−0.423698	+	1.76304i	−0.00808843	+	0.0336566i
$15$	−39.1813	+	85.6542i	−0.674438	+	1.47439i
$16$	−31.8850	−	55.2265i	−0.498203	−	0.862914i
$17$	−62.5187			−0.891941			−0.445971	−	0.895048i	$-0.647141\pi$
$17$	−62.5187			−0.891941			−0.445971	+	0.895048i	$0.647141\pi$
$18$	−1.99994	+	1.72861i	−0.0261883	+	0.0226354i
$19$		−	70.2680i		−	0.848452i	−0.905556	−	0.424226i	$-0.860546\pi$
$19$		−	70.2680i		−	0.848452i	0.905556	−	0.424226i	$-0.139454\pi$
$20$	72.4209	+	125.437i	0.809690	+	1.40242i
$21$	−59.3723	+	75.7359i	−0.616957	+	0.786997i
$22$	−1.81186	+	3.13823i	−0.0175586	+	0.0304124i
$23$	140.692	+	81.2288i	1.27550	+	0.736408i	0.976017	−	0.217695i	$-0.0698539\pi$
$23$	140.692	+	81.2288i	1.27550	+	0.736408i	0.299479	+	0.954103i	$0.403187\pi$
$24$	0.768234	+	8.09848i	0.00653396	+	0.0688790i
$25$	−101.793	−	176.311i	−0.814344	−	1.41048i
$26$	1.85034			0.0139570
$27$	−134.687	+	39.2750i	−0.960016	+	0.279944i
$28$	41.9972	+	141.900i	0.283454	+	0.957736i
$29$	82.5015	−	47.6323i	0.528281	−	0.305003i	−0.212035	−	0.977262i	$-0.568009\pi$
$29$	82.5015	−	47.6323i	0.528281	−	0.305003i	0.740316	+	0.672259i	$0.234676\pi$
$30$	−0.870879	−	9.18054i	−0.00530000	−	0.0558710i
$31$	110.611	+	63.8612i	0.640848	+	0.369994i	0.784941	−	0.619570i	$-0.212693\pi$
$31$	110.611	+	63.8612i	0.640848	+	0.369994i	−0.144093	+	0.989564i	$0.546027\pi$
$32$	16.2534	+	9.38392i	0.0897883	+	0.0518393i
$33$	−156.730	+	111.460i	−0.826765	+	0.587963i
$34$	5.30088	−	3.06046i	0.0267380	−	0.0154372i
$35$	−95.2742	−	321.913i	−0.460122	−	1.55466i
$36$	−70.8153	+	203.788i	−0.327849	+	0.943462i
$37$	−378.832			−1.68323			−0.841617	−	0.540075i	$-0.818396\pi$
$37$	−378.832			−1.68323			−0.841617	+	0.540075i	$0.818396\pi$
$38$	3.43981	+	5.95793i	0.0146845	+	0.0254343i
$39$	89.3037	+	40.8507i	0.366668	+	0.167727i
$40$	−24.5766	−	14.1893i	−0.0971476	−	0.0560882i
$41$	99.1937	−	171.809i	0.377840	−	0.654439i	−0.612907	−	0.790155i	$-0.710000\pi$
$41$	99.1937	−	171.809i	0.377840	−	0.654439i	0.990748	+	0.135716i	$0.0433334\pi$
$42$	1.32662	−	9.32799i	0.00487384	−	0.0342700i
$43$	160.692	+	278.327i	0.569892	+	0.987081i	0.996576	+	0.0826806i	$0.0263481\pi$
$43$	160.692	+	278.327i	0.569892	+	0.987081i	−0.426685	+	0.904401i	$0.640319\pi$
$44$			295.744i			1.01330i
$45$	160.651	−	462.310i	0.532186	−	1.53149i
$46$	−15.9055			−0.0509813
$47$	79.3885	+	137.505i	0.246383	+	0.426748i	0.962520	−	0.271212i	$-0.0874245\pi$
$47$	79.3885	+	137.505i	0.246383	+	0.426748i	−0.716136	+	0.697960i	$0.754091\pi$
$48$	192.039	+	270.036i	0.577468	+	0.812008i
$49$	−17.7932	−	342.538i	−0.0518754	−	0.998654i
$50$	17.2618	+	9.96610i	0.0488237	+	0.0281884i
$51$	323.405	−	30.6786i	0.887955	−	0.0842327i
$52$	130.781	−	75.5066i	0.348771	−	0.201363i
$53$		−	191.780i		−	0.497039i	−0.968627	−	0.248519i	$-0.920056\pi$
$53$		−	191.780i		−	0.497039i	0.968627	−	0.248519i	$-0.0799440\pi$
$54$	9.49728	−	9.92336i	0.0239336	−	0.0250074i
$55$		−	670.922i		−	1.64486i
$56$	−21.0272	−	19.9633i	−0.0501764	−	0.0476376i
$57$	34.4813	+	363.491i	0.0801257	+	0.844660i
$58$	−4.66346	+	8.07736i	−0.0105576	+	0.0182864i
$59$	−106.918	+	185.187i	−0.235924	+	0.408632i	−0.959541	−	0.281570i	$-0.909145\pi$
$59$	−106.918	+	185.187i	−0.235924	+	0.408632i	0.723617	+	0.690202i	$0.242478\pi$
$60$	−436.181	−	613.337i	−0.938513	−	1.31969i
$61$	−190.929	+	110.233i	−0.400754	+	0.231375i	−0.686809	−	0.726838i	$-0.740989\pi$
$61$	−190.929	+	110.233i	−0.400754	+	0.231375i	0.286055	+	0.958213i	$0.407656\pi$
$62$	−12.5047			−0.0256145
$63$	269.964	−	420.911i	0.539878	−	0.841743i
$64$	508.323			0.992818
$65$	−296.688	+	171.293i	−0.566149	+	0.326866i
$66$	7.83266	−	17.1230i	0.0146081	−	0.0319347i
$67$	68.2947	−	118.290i	0.124530	−	0.215693i	−0.797019	−	0.603954i	$-0.793591\pi$
$67$	68.2947	−	118.290i	0.124530	−	0.215693i	0.921549	+	0.388262i	$0.126924\pi$
$68$	249.775	−	432.623i	0.445436	−	0.771518i
$69$	−767.652	−	351.151i	−1.33934	−	0.612662i
$70$	23.8367	+	22.6306i	0.0407004	+	0.0386411i
$71$			458.924i			0.767102i	0.923520	+	0.383551i	$0.125299\pi$
$71$			458.924i			0.767102i	−0.923520	+	0.383551i	$0.874701\pi$
$72$	−7.94804	−	41.5159i	−0.0130095	−	0.0679541i
$73$			967.869i			1.55179i	0.630863	+	0.775894i	$0.282701\pi$
$73$			967.869i			1.55179i	−0.630863	+	0.775894i	$0.717299\pi$
$74$	32.1207	−	18.5449i	0.0504588	−	0.0291324i
$75$	613.086	+	862.091i	0.943907	+	1.32728i
$76$	486.248	+	280.735i	0.733900	+	0.423718i
$77$	160.176	−	666.503i	0.237061	−	0.986429i
$78$	−9.57170	+	0.907986i	−0.0138946	+	0.00131807i
$79$	298.318	+	516.702i	0.424853	+	0.735868i	0.996407	−	0.0846971i	$-0.0269923\pi$
$79$	298.318	+	516.702i	0.424853	+	0.735868i	−0.571553	+	0.820565i	$0.693659\pi$
$80$	−1155.96			−1.61550
$81$	677.452	−	269.259i	0.929289	−	0.369354i
$82$			19.4232i			0.0261578i
$83$	180.715	+	313.007i	0.238988	+	0.413940i	0.960424	−	0.278541i	$-0.0898509\pi$
$83$	180.715	+	313.007i	0.238988	+	0.413940i	−0.721436	+	0.692481i	$0.756518\pi$
$84$	−286.880	−	713.431i	−0.372634	−	0.926687i
$85$	−566.636	+	981.443i	−0.723063	+	1.25238i
$86$	−27.2498	−	15.7327i	−0.0341676	−	0.0197267i
$87$	−403.401	+	286.883i	−0.497116	+	0.353530i
$88$	−28.9724	−	50.1817i	−0.0350962	−	0.0607884i
$89$	35.4987			0.0422792			0.0211396	−	0.999777i	$-0.493271\pi$
$89$	35.4987			0.0422792			0.0211396	+	0.999777i	$0.493271\pi$
$90$	9.01000	+	47.0630i	0.0105526	+	0.0551208i
$91$	−335.629	+	99.3336i	−0.386631	+	0.114428i
$92$	−1124.19	+	649.052i	−1.27397	+	0.735525i
$93$	−603.519	−	276.071i	−0.672925	−	0.307820i
$94$	−13.4625	−	7.77258i	−0.0147718	−	0.00852851i
$95$	−1103.09	−	636.872i	−1.19132	−	0.687807i
$96$	−88.6826	−	40.5666i	−0.0942826	−	0.0431283i
$97$	−1151.63	+	664.894i	−1.20547	+	0.695977i	−0.961766	−	0.273874i	$-0.911695\pi$
$97$	−1151.63	+	664.894i	−1.20547	+	0.695977i	−0.243701	+	0.969850i	$0.578362\pi$
$98$	18.2769	+	28.1723i	0.0188392	+	0.0290391i
$99$	756.060	−	653.486i	0.767544	−	0.663413i
$100$	1626.74			1.62674
$101$	457.491	+	792.398i	0.450714	+	0.780659i	0.998430	−	0.0560049i	$-0.0178362\pi$
$101$	457.491	+	792.398i	0.450714	+	0.780659i	−0.547717	+	0.836664i	$0.684503\pi$
$102$	−25.9193	+	18.4328i	−0.0251607	+	0.0178933i
$103$	−721.873	−	416.774i	−0.690566	−	0.398698i	0.113258	−	0.993566i	$-0.463871\pi$
$103$	−721.873	−	416.774i	−0.690566	−	0.398698i	−0.803824	+	0.594867i	$0.797205\pi$
$104$	−14.7939	+	25.6238i	−0.0139487	+	0.0241598i
$105$	650.813	+	1618.48i	0.604884	+	1.50426i
$106$	9.38818	+	16.2608i	0.00860246	+	0.0148999i
$107$		−	1686.33i		−	1.52358i	−0.647822	−	0.761792i	$-0.724320\pi$
$107$		−	1686.33i		−	1.52358i	0.647822	−	0.761792i	$-0.275680\pi$
$108$	266.322	−	1088.93i	0.237285	−	0.970207i
$109$	641.258			0.563499			0.281750	−	0.959488i	$-0.409085\pi$
$109$	641.258			0.563499			0.281750	+	0.959488i	$0.409085\pi$
$110$	32.8435	+	56.8866i	0.0284682	+	0.0493084i
$111$	1959.67	−	185.897i	1.67571	−	0.158960i
$112$	−1148.34	−	275.973i	−0.968822	−	0.232830i
$113$	1245.30	+	718.974i	1.03671	+	0.598543i	0.918899	−	0.394493i	$-0.129080\pi$
$113$	1245.30	+	718.974i	1.03671	+	0.598543i	0.117809	+	0.993036i	$0.462413\pi$
$114$	−20.7175	−	29.1320i	−0.0170208	−	0.0239339i
$115$	2550.32	−	1472.43i	2.06799	−	1.19395i
$116$			761.203i			0.609275i
$117$	−482.008	−	167.496i	−0.380869	−	0.132350i
$118$		−	20.9357i		−	0.0163329i
$119$	−797.213	+	839.700i	−0.614121	+	0.646850i
$120$	134.096	+	61.3403i	0.102010	+	0.0466632i
$121$	19.4592	−	33.7044i	0.0146200	−	0.0253226i
$122$	10.7924	−	18.6930i	0.00800902	−	0.0138720i
$123$	−428.814	+	937.429i	−0.314348	+	0.687196i
$124$	−883.826	+	510.277i	−0.640080	+	0.369550i
$125$	−1424.52			−1.01931
$126$	−2.28515	+	48.9040i	−0.00161569	+	0.0345771i
$127$	−1845.03			−1.28914			−0.644568	−	0.764547i	$-0.722963\pi$
$127$	−1845.03			−1.28914			−0.644568	+	0.764547i	$0.722963\pi$
$128$	−173.127	+	99.9552i	−0.119550	+	0.0690224i
$129$	−967.828	−	1360.91i	−0.660562	−	0.928850i
$130$	16.7705	−	29.0474i	0.0113144	−	0.0195971i
$131$	1099.22	−	1903.91i	0.733125	−	1.26981i	−0.222416	−	0.974952i	$-0.571394\pi$
$131$	1099.22	−	1903.91i	0.733125	−	1.26981i	0.955541	−	0.294858i	$-0.0952724\pi$
$132$	−145.125	−	1529.87i	−0.0956934	−	1.00877i
$133$	−943.782	−	896.030i	−0.615311	−	0.584178i
$134$			13.3729i			0.00862119i
$135$	−604.174	+	2470.33i	−0.385178	+	1.57491i
$136$			97.8761i			0.0617118i
$137$	1869.64	−	1079.44i	1.16594	−	0.673156i	0.213220	−	0.977004i	$-0.431605\pi$
$137$	1869.64	−	1079.44i	1.16594	−	0.673156i	0.952720	+	0.303848i	$0.0982716\pi$
$138$	82.2780	−	7.80501i	0.0507534	−	0.00481454i
$139$	2521.54	+	1455.81i	1.53866	+	0.888348i	0.998917	+	0.0465196i	$0.0148130\pi$
$139$	2521.54	+	1455.81i	1.53866	+	0.888348i	0.539746	+	0.841828i	$0.318520\pi$
$140$	2608.24	+	626.820i	1.57455	+	0.378400i
$141$	−478.147	−	672.347i	−0.285583	−	0.401573i
$142$	−22.4656	−	38.9115i	−0.0132766	−	0.0229957i
$143$	−699.508			−0.409062
$144$	−1125.92	−	1302.64i	−0.651571	−	0.753844i
$145$		−	1726.85i		−	0.989017i
$146$	−47.3799	−	82.0644i	−0.0268574	−	0.0465185i
$147$	260.131	+	1763.19i	0.145954	+	0.989291i
$148$	1513.51	−	2621.48i	0.840608	−	1.45598i
$149$	−230.641	−	133.161i	−0.126811	−	0.0732144i	0.435253	−	0.900308i	$-0.356659\pi$
$149$	−230.641	−	133.161i	−0.126811	−	0.0732144i	−0.562064	+	0.827094i	$0.689992\pi$
$150$	−94.1845	−	43.0834i	−0.0512675	−	0.0234516i
$151$	467.757	+	810.180i	0.252090	+	0.436632i	0.964101	−	0.265536i	$-0.0855488\pi$
$151$	467.757	+	810.180i	0.252090	+	0.436632i	−0.712011	+	0.702168i	$0.752215\pi$
$152$	−110.008			−0.0587029
$153$	−1657.90	+	317.397i	−0.876032	+	0.167713i
$154$	19.0461	+	64.3529i	0.00996607	+	0.0336734i
$155$	2005.04	−	1157.61i	1.03902	−	0.599879i
$156$	−639.470	+	454.766i	−0.328196	+	0.233400i
$157$	872.747	+	503.881i	0.443648	+	0.256141i	0.705144	−	0.709064i	$-0.250882\pi$
$157$	872.747	+	503.881i	0.443648	+	0.256141i	−0.261496	+	0.965205i	$0.584216\pi$
$158$	−50.5880	−	29.2070i	−0.0254719	−	0.0147062i
$159$	94.1088	+	992.066i	0.0469391	+	0.494817i
$160$	294.625	−	170.102i	0.145576	−	0.0840483i
$161$	2885.05	−	853.868i	1.41226	−	0.417976i
$162$	−44.2592	+	55.9932i	−0.0214650	+	0.0271558i
$163$	−1801.27			−0.865561			−0.432780	−	0.901499i	$-0.642467\pi$
$163$	−1801.27			−0.865561			−0.432780	+	0.901499i	$0.642467\pi$
$164$	792.599	+	1372.82i	0.377388	+	0.653655i
$165$	329.229	+	3470.63i	0.155336	+	1.63750i
$166$	−30.6451	−	17.6930i	−0.0143285	−	0.00827254i
$167$	−817.899	+	1416.64i	−0.378987	+	0.656425i	−0.990915	−	0.134488i	$-0.957061\pi$
$167$	−817.899	+	1416.64i	−0.378987	+	0.656425i	0.611928	+	0.790914i	$0.290394\pi$
$168$	118.568	+	92.9503i	0.0544509	+	0.0426862i
$169$	−919.908	−	1593.33i	−0.418711	−	0.725229i
$170$		−	110.954i		−	0.0500574i
$171$	−356.739	−	1863.40i	−0.159535	−	0.833318i
$172$	−2568.00			−1.13842
$173$	−399.759	−	692.402i	−0.175683	−	0.304291i	0.764715	−	0.644369i	$-0.222880\pi$
$173$	−399.759	−	692.402i	−0.175683	−	0.304291i	−0.940397	+	0.340078i	$0.889547\pi$
$174$	20.1601	−	44.0720i	0.00878353	−	0.0192017i
$175$	−3666.08	−	881.043i	−1.58360	−	0.380575i
$176$	−2044.06	−	1180.14i	−0.875439	−	0.505435i
$177$	462.205	−	1010.42i	0.196279	−	0.429086i
$178$	−3.00989	+	1.73776i	−0.00126742	+	0.000731745i
$179$			2940.19i			1.22771i	0.789418	+	0.613856i	$0.210382\pi$
$179$			2940.19i			1.22771i	−0.789418	+	0.613856i	$0.789618\pi$
$180$	2557.31	+	2958.71i	1.05895	+	1.22516i
$181$			376.924i			0.154788i	0.997001	+	0.0773938i	$0.0246599\pi$
$181$			376.924i			0.154788i	−0.997001	+	0.0773938i	$0.975340\pi$
$182$	23.5949	−	24.8523i	0.00960971	−	0.0101218i
$183$	933.571	−	663.919i	0.377112	−	0.268188i
$184$	127.168	−	220.261i	0.0509507	−	0.0882492i
$185$	−3433.53	+	5947.06i	−1.36453	+	2.36344i
$186$	64.6861	−	6.13621i	0.0255001	−	0.00241897i
$187$	−2003.95	+	1156.98i	−0.783656	+	0.452444i
$188$	−1268.69			−0.492176
$189$	−1189.96	+	2309.82i	−0.457973	+	0.888966i
$190$	124.707			0.0476167
$191$	1586.09	−	915.732i	0.600868	−	0.346911i	−0.168515	−	0.985699i	$-0.553897\pi$
$191$	1586.09	−	915.732i	0.600868	−	0.346911i	0.769383	+	0.638788i	$0.220564\pi$
$192$	−2629.52	+	249.440i	−0.988381	+	0.0937592i
$193$	190.008	−	329.104i	0.0708657	−	0.122743i	−0.828415	−	0.560114i	$-0.810757\pi$
$193$	190.008	−	329.104i	0.0708657	−	0.122743i	0.899281	+	0.437371i	$0.144090\pi$
$194$	65.0968	−	112.751i	0.0240911	−	0.0417270i
$195$	1450.69	−	1031.68i	0.532750	−	0.378871i
$196$	2441.42	+	1245.38i	0.889730	+	0.453857i
$197$		−	3579.56i		−	1.29458i	−0.762243	−	0.647291i	$-0.775902\pi$
$197$		−	3579.56i		−	1.29458i	0.762243	−	0.647291i	$-0.224098\pi$
$198$	−32.1153	+	92.4195i	−0.0115270	+	0.0331715i
$199$			881.304i			0.313939i	0.987603	+	0.156970i	$0.0501725\pi$
$199$			881.304i			0.313939i	−0.987603	+	0.156970i	$0.949827\pi$
$200$	−276.023	+	159.362i	−0.0975889	+	0.0563430i
$201$	−295.237	+	645.418i	−0.103604	+	0.226489i
$202$	−77.5802	−	44.7909i	−0.0270224	−	0.0156014i
$203$	412.269	−	1715.48i	0.142540	−	0.593119i
$204$	−1079.78	+	2360.50i	−0.370585	+	0.810136i
$205$	−1798.08	−	3114.36i	−0.612601	−	1.06106i
$206$	81.6089			0.0276018
$207$	4143.32	+	1439.79i	1.39121	+	0.483440i
$208$			1205.21i			0.401760i
$209$	−1300.39	−	2252.35i	−0.430383	−	0.745446i
$210$	−134.411	−	105.370i	−0.0441677	−	0.0346248i
$211$	−418.581	+	725.004i	−0.136570	+	0.236547i	−0.926196	−	0.377042i	$-0.876941\pi$
$211$	−418.581	+	725.004i	−0.136570	+	0.236547i	0.789626	+	0.613588i	$0.210275\pi$
$212$	1327.10	+	766.202i	0.429932	+	0.248222i
$213$	−225.199	−	2373.98i	−0.0724432	−	0.763674i
$214$	82.5504	+	142.981i	0.0263693	+	0.0456730i
$215$	5825.72			1.84796
$216$	61.4870	+	210.859i	0.0193688	+	0.0664218i
$217$	2268.20	−	671.301i	0.709563	−	0.210004i
$218$	−54.3715	+	31.3914i	−0.0168922	+	0.00975272i
$219$	−474.945	−	5006.72i	−0.146547	−	1.54485i
$220$	4642.71	+	2680.47i	1.42278	+	0.821442i
$221$	1023.26	+	590.779i	0.311456	+	0.179819i
$222$	−157.058	+	111.693i	−0.0474821	+	0.0337674i
$223$	981.825	−	566.857i	0.294834	−	0.170222i	−0.345286	−	0.938497i	$-0.612218\pi$
$223$	981.825	−	566.857i	0.294834	−	0.170222i	0.640120	+	0.768275i	$0.278885\pi$
$224$	333.294	−	98.6427i	0.0994159	−	0.0294234i
$225$	−3594.49	−	4158.69i	−1.06503	−	1.23220i
$226$	−140.783			−0.0414370
$227$	−1752.96	−	3036.21i	−0.512545	−	0.887754i	−0.999894	−	0.0145471i	$-0.995369\pi$
$227$	−1752.96	−	3036.21i	−0.512545	−	0.887754i	0.487349	−	0.873207i	$-0.337964\pi$
$228$	−2653.09	−	1213.62i	−0.770635	−	0.352516i
$229$	−2721.44	−	1571.23i	−0.785319	−	0.453404i	0.0529930	−	0.998595i	$-0.483124\pi$
$229$	−2721.44	−	1571.23i	−0.785319	−	0.453404i	−0.838312	+	0.545191i	$0.816457\pi$
$230$	−144.159	+	249.691i	−0.0413285	+	0.0715831i
$231$	−501.517	+	3526.37i	−0.142846	+	1.00441i
$232$	−74.5707	−	129.160i	−0.0211026	−	0.0365508i
$233$			6882.00i			1.93500i	0.252872	+	0.967500i	$0.418625\pi$
$233$			6882.00i			1.93500i	−0.252872	+	0.967500i	$0.581375\pi$
$234$	49.0682	−	9.39389i	0.0137081	−	0.00262435i
$235$	2878.14			0.798933
$236$	−854.317	−	1479.72i	−0.235641	−	0.408142i
$237$	−1796.73	−	2526.48i	−0.492448	−	0.692457i
$238$	26.4890	−	110.223i	0.00721441	−	0.0300197i
$239$	−1036.14	−	598.217i	−0.280429	−	0.161906i	0.353189	−	0.935552i	$-0.385097\pi$
$239$	−1036.14	−	598.217i	−0.280429	−	0.161906i	−0.633617	+	0.773646i	$0.718431\pi$
$240$	5979.68	−	567.241i	1.60828	−	0.152563i
$241$	3790.59	−	2188.50i	1.01317	−	0.584953i	0.101051	−	0.994881i	$-0.467780\pi$
$241$	3790.59	−	2188.50i	1.01317	−	0.584953i	0.912118	+	0.409928i	$0.134446\pi$
$242$			3.81033i			0.00101214i
$243$	−3372.28	+	1725.29i	−0.890255	+	0.455463i
$244$		−	1761.62i		−	0.462196i
$245$	−5538.57	−	2825.26i	−1.44427	−	0.736731i
$246$	−9.53120	−	100.475i	−0.00247027	−	0.0260409i
$247$	−664.008	+	1150.09i	−0.171052	+	0.296270i
$248$	99.9779	−	173.167i	0.0255992	−	0.0443391i
$249$	−1088.42	−	1530.49i	−0.277012	−	0.389520i
$250$	120.783	−	69.7344i	0.0305561	−	0.0176416i
$251$	5787.19			1.45532			0.727658	−	0.685940i	$-0.240609\pi$
$251$	5787.19			1.45532			0.727658	+	0.685940i	$0.240609\pi$
$252$	1834.10	+	3549.75i	0.458482	+	0.887355i
$253$	6012.95			1.49419
$254$	156.438	−	90.3195i	0.0386448	−	0.0223116i
$255$	2449.56	−	5354.99i	0.601559	−	1.31507i
$256$	−2023.51	+	3504.81i	−0.494020	+	0.855667i
$257$	−1074.45	+	1861.00i	−0.260786	+	0.451695i	−0.966451	−	0.256851i	$-0.917315\pi$
$257$	−1074.45	+	1861.00i	−0.260786	+	0.451695i	0.705665	+	0.708546i	$0.250649\pi$
$258$	148.681	+	68.0122i	0.0358779	+	0.0164118i
$259$	−4830.72	+	5088.16i	−1.15894	+	1.22071i
$260$		−	2737.41i		−	0.652949i
$261$	1945.99	−	1681.98i	0.461508	−	0.398896i
$262$			215.240i			0.0507540i
$263$	−1057.21	+	610.380i	−0.247872	+	0.143109i	−0.618789	−	0.785557i	$-0.712377\pi$
$263$	−1057.21	+	610.380i	−0.247872	+	0.143109i	0.370917	+	0.928666i	$0.379043\pi$
$264$	174.497	+	245.369i	0.0406801	+	0.0572024i
$265$	−3010.64	−	1738.20i	−0.697895	−	0.402930i
$266$	123.885	+	29.7724i	0.0285560	+	0.00686265i
$267$	−183.632	+	17.4196i	−0.0420903	+	0.00399275i
$268$	545.703	+	945.185i	0.124381	+	0.215434i
$269$	−4430.56			−1.00422			−0.502112	−	0.864803i	$-0.667444\pi$
$269$	−4430.56			−1.00422			−0.502112	+	0.864803i	$0.667444\pi$
$270$	−69.7024	−	239.032i	−0.0157109	−	0.0538779i
$271$		−	111.259i		−	0.0249391i	−0.999922	−	0.0124695i	$-0.996031\pi$
$271$		−	111.259i		−	0.0249391i	0.999922	−	0.0124695i	$-0.00396928\pi$
$272$	1993.41	+	3452.69i	0.444368	+	0.769668i
$273$	1687.44	−	678.542i	0.374097	−	0.150430i
$274$	−105.683	+	183.048i	−0.0233012	+	0.0403588i
$275$	−6525.68	−	3767.60i	−1.43096	−	0.826164i
$276$	5496.86	−	3909.15i	1.19881	−	0.852548i
$277$	1529.33	+	2648.87i	0.331727	+	0.574567i	0.982850	−	0.184404i	$-0.0590356\pi$
$277$	1529.33	+	2648.87i	0.331727	+	0.574567i	−0.651124	+	0.758971i	$0.725702\pi$
$278$	−285.064			−0.0615000
$279$	3257.43	+	1131.94i	0.698987	+	0.242895i
$280$	−503.971	+	149.156i	−0.107564	+	0.0318350i
$281$	−4124.03	+	2381.01i	−0.875513	+	0.505478i	−0.869176	−	0.494502i	$-0.835350\pi$
$281$	−4124.03	+	2381.01i	−0.875513	+	0.505478i	−0.00633670	+	0.999980i	$0.502017\pi$
$282$	73.4547	+	33.6008i	0.0155112	+	0.00709538i
$283$	3567.54	+	2059.72i	0.749358	+	0.432642i	0.825462	−	0.564458i	$-0.190915\pi$
$283$	3567.54	+	2059.72i	0.749358	+	0.432642i	−0.0761041	+	0.997100i	$0.524248\pi$
$284$	−3175.71	−	1833.50i	−0.663534	−	0.383091i
$285$	6018.75	+	2753.19i	1.25095	+	0.572228i
$286$	59.3104	−	34.2429i	0.0122626	−	0.00707980i
$287$	−1042.71	−	3523.12i	−0.214458	−	0.724611i
$288$	478.656	+	166.331i	0.0979342	+	0.0340317i
$289$	−1004.42			−0.204440
$290$	84.5343	+	146.418i	0.0171173	+	0.0296481i
$291$	5631.03	−	4004.57i	1.13435	−	0.806707i
$292$	−6697.56	−	3866.84i	−1.34228	−	0.774964i
$293$	−1401.70	+	2427.81i	−0.279482	+	0.484076i	−0.971256	−	0.238037i	$-0.923496\pi$
$293$	−1401.70	+	2427.81i	−0.279482	+	0.484076i	0.691774	+	0.722114i	$0.256829\pi$
$294$	−108.369	−	136.765i	−0.0214974	−	0.0271302i
$295$	1938.09	+	3356.87i	0.382509	+	0.662524i
$296$			593.081i			0.116460i
$297$	−3590.37	+	3751.45i	−0.701463	+	0.732933i
$298$	26.0743			0.00506861
$299$	−1535.17	−	2658.99i	−0.296926	−	0.514291i
$300$	−8414.99	+	798.258i	−1.61947	+	0.153625i
$301$	5787.35	+	1390.83i	1.10823	+	0.266333i
$302$	−79.3211	−	45.7960i	−0.0151140	−	0.00872605i
$303$	−2755.41	−	3874.52i	−0.522423	−	0.734606i
$304$	−3880.65	+	2240.50i	−0.732141	+	0.422702i
$305$			3996.38i			0.750268i
$306$	125.033	−	108.070i	0.0233584	−	0.0201894i
$307$			3959.31i			0.736058i	0.929814	+	0.368029i	$0.119967\pi$
$307$			3959.31i			0.736058i	−0.929814	+	0.368029i	$0.880033\pi$
$308$	3972.20	+	3771.22i	0.734860	+	0.697679i
$309$	3938.71	+	1801.71i	0.725132	+	0.331701i
$310$	−113.336	+	196.304i	−0.0207647	+	0.0359656i
$311$	−2492.25	+	4316.71i	−0.454413	+	0.787067i	−0.998654	−	0.0518618i	$-0.983484\pi$
$311$	−2492.25	+	4316.71i	−0.454413	+	0.787067i	0.544241	+	0.838929i	$0.316818\pi$
$312$	63.9539	−	139.809i	0.0116047	−	0.0253691i
$313$	699.706	−	403.976i	0.126357	−	0.0729522i	−0.435489	−	0.900194i	$-0.643425\pi$
$313$	699.706	−	403.976i	0.126357	−	0.0729522i	0.561846	+	0.827242i	$0.310091\pi$
$314$	−98.6654			−0.0177325
$315$	−4160.82	−	8052.92i	−0.744239	−	1.44042i
$316$	−4767.37			−0.848689
$317$	2061.65	−	1190.29i	0.365280	−	0.210894i	−0.306115	−	0.951995i	$-0.599029\pi$
$317$	2061.65	−	1190.29i	0.365280	−	0.210894i	0.671394	+	0.741100i	$0.265696\pi$
$318$	−56.5437	−	79.5091i	−0.00997112	−	0.0140209i
$319$	1762.99	−	3053.58i	0.309430	−	0.535949i
$320$	4607.17	−	7979.85i	0.804839	−	1.39402i
$321$	827.500	+	8723.25i	0.143883	+	1.51677i
$322$	−202.821	+	213.630i	−0.0351017	+	0.0369724i
$323$			4393.06i			0.756769i
$324$	−843.313	+	5763.64i	−0.144601	+	0.988279i
$325$			3847.63i			0.656702i
$326$	152.727	−	88.1772i	0.0259472	−	0.0149806i
$327$	−3317.19	+	314.673i	−0.560981	+	0.0532155i
$328$	−268.975	−	155.293i	−0.0452794	−	0.0261421i
$329$	2859.19	+	687.127i	0.479125	+	0.115145i
$330$	−197.812	−	278.154i	−0.0329975	−	0.0463995i
$331$	3727.74	+	6456.64i	0.619019	+	1.07217i	0.989665	+	0.143398i	$0.0458029\pi$
$331$	3727.74	+	6456.64i	0.619019	+	1.07217i	−0.370646	+	0.928774i	$0.620864\pi$
$332$	−2887.97			−0.477404
$333$	−10046.0	+	1923.27i	−1.65321	+	0.316500i
$334$		−	160.154i		−	0.0262372i
$335$	−1237.97	−	2144.23i	−0.201904	−	0.349707i
$336$	6075.71	+	864.082i	0.986480	+	0.140296i
$337$	978.259	−	1694.39i	0.158128	−	0.273886i	−0.776066	−	0.630652i	$-0.782787\pi$
$337$	978.259	−	1694.39i	0.158128	−	0.273886i	0.934194	+	0.356766i	$0.116121\pi$
$338$	155.996	+	90.0641i	0.0251037	+	0.0144936i
$339$	−6794.66	−	3108.12i	−1.08860	−	0.497964i
$340$	−4527.66	−	7842.13i	−0.722196	−	1.25088i
$341$	4727.31			0.750728
$342$	121.466	+	140.531i	0.0192050	+	0.0222195i
$343$	−4827.58	−	4128.93i	−0.759956	−	0.649974i
$344$	435.735	−	251.572i	0.0682944	−	0.0394298i
$345$	−12470.1	+	8868.25i	−1.94599	+	1.38391i
$346$	67.7900	+	39.1386i	0.0105330	+	0.00608122i
$347$	−1191.69	−	688.024i	−0.184361	−	0.106441i	0.404979	−	0.914326i	$-0.367279\pi$
$347$	−1191.69	−	688.024i	−0.184361	−	0.106441i	−0.589340	+	0.807885i	$0.700612\pi$
$348$	−373.531	−	3937.65i	−0.0575384	−	0.606552i
$349$	8098.04	−	4675.41i	1.24206	−	0.717103i	0.272546	−	0.962143i	$-0.412134\pi$
$349$	8098.04	−	4675.41i	1.24206	−	0.717103i	0.969513	+	0.245040i	$0.0788011\pi$
$350$	353.972	−	104.762i	0.0540588	−	0.0159994i
$351$	2575.59	+	629.916i	0.391665	+	0.0957904i
$352$	694.643			0.105184
$353$	338.836	+	586.881i	0.0510890	+	0.0884887i	0.890439	−	0.455103i	$-0.150397\pi$
$353$	338.836	+	586.881i	0.0510890	+	0.0884887i	−0.839350	+	0.543591i	$0.817064\pi$
$354$	10.2734	+	108.299i	0.00154244	+	0.0162599i
$355$	7204.37	+	4159.44i	1.07709	+	0.621860i
$356$	−141.825	+	245.647i	−0.0211143	+	0.0365710i
$357$	3711.88	−	4734.91i	0.550290	−	0.701955i
$358$	−143.931	−	249.295i	−0.0212485	−	0.0368035i
$359$			1662.36i			0.244390i	0.992506	+	0.122195i	$0.0389933\pi$
$359$			1662.36i			0.244390i	−0.992506	+	0.122195i	$0.961007\pi$
$360$	−723.769	−	251.507i	−0.105961	−	0.0368210i
$361$	1921.41			0.280129
$362$	−18.4515	−	31.9589i	−0.00267897	−	0.00464012i
$363$	−84.1221	+	183.899i	−0.0121633	+	0.0265901i
$364$	653.528	−	2719.38i	0.0941048	−	0.391577i
$365$	15194.0	+	8772.25i	2.17888	+	1.25797i
$366$	−46.6556	+	101.994i	−0.00666319	+	0.0145664i
$367$	−2653.41	+	1531.94i	−0.377402	+	0.217893i	−0.676687	−	0.736270i	$-0.736585\pi$
$367$	−2653.41	+	1531.94i	−0.377402	+	0.217893i	0.299285	+	0.954164i	$0.403252\pi$
$368$		−	10359.9i		−	1.46752i
$369$	1758.22	−	5059.68i	0.248046	−	0.713811i
$370$		−	672.324i		−	0.0944661i
$371$	−2575.84	−	2445.51i	−0.360460	−	0.342222i
$372$	4321.57	−	3073.33i	0.602320	−	0.428346i
$373$	3900.06	−	6755.10i	0.541387	−	0.937711i	−0.457437	−	0.889242i	$-0.651233\pi$
$373$	3900.06	−	6755.10i	0.541387	−	0.937711i	0.998825	−	0.0484687i	$-0.0154341\pi$
$374$	113.275	−	196.198i	0.0156613	−	0.0271261i
$375$	7368.96	−	699.030i	1.01475	−	0.0962607i
$376$	215.271	−	124.287i	0.0295259	−	0.0170468i
$377$	−1800.43			−0.245960
$378$	−12.1769	−	254.098i	−0.00165691	−	0.0345752i
$379$	−6855.89			−0.929191			−0.464595	−	0.885523i	$-0.653800\pi$
$379$	−6855.89			−0.929191			−0.464595	+	0.885523i	$0.653800\pi$
$380$	8814.18	−	5088.87i	1.18989	−	0.686983i
$381$	9544.22	−	905.379i	1.28337	−	0.121743i
$382$	−89.6552	+	155.287i	−0.0120083	+	0.0207989i
$383$	−5511.46	+	9546.14i	−0.735307	+	1.27359i	0.219281	+	0.975662i	$0.429629\pi$
$383$	−5511.46	+	9546.14i	−0.735307	+	1.27359i	−0.954588	+	0.297928i	$0.903705\pi$
$384$	846.527	−	602.017i	0.112498	−	0.0800040i
$385$	−9011.27	−	8555.33i	−1.19288	−	1.13252i
$386$			37.2057i			0.00490601i
$387$	5674.32	+	6564.98i	0.745328	+	0.862317i
$388$		−	10625.6i		−	1.39029i
$389$	9460.70	−	5462.14i	1.23310	−	0.711931i	0.265426	−	0.964131i	$-0.414487\pi$
$389$	9460.70	−	5462.14i	1.23310	−	0.711931i	0.967675	+	0.252200i	$0.0811541\pi$
$390$	−72.4989	+	158.490i	−0.00941314	+	0.0205781i
$391$	−8795.90	−	5078.32i	−1.13767	−	0.656833i
$392$	−536.261	+	27.8562i	−0.0690950	+	0.00358916i
$393$	−4751.93	+	10388.2i	−0.609931	+	1.33337i
$394$	175.229	+	303.506i	0.0224059	+	0.0388081i
$395$	10815.2			1.37765
$396$	1501.45	+	7842.67i	0.190531	+	0.995225i
$397$		−	7203.22i		−	0.910627i	−0.890331	−	0.455314i	$-0.849527\pi$
$397$		−	7203.22i		−	0.910627i	0.890331	−	0.455314i	$-0.150473\pi$
$398$	−43.1423	−	74.7246i	−0.00543348	−	0.00941107i
$399$	5321.81	+	4171.97i	0.667729	+	0.523458i
$400$	−6491.34	+	11243.3i	−0.811418	+	1.40542i
$401$	−10633.1	−	6139.03i	−1.32417	−	0.764510i	−0.339778	−	0.940506i	$-0.610352\pi$
$401$	−10633.1	−	6139.03i	−1.32417	−	0.764510i	−0.984391	+	0.175996i	$0.943685\pi$
$402$	−6.56222	−	69.1768i	−0.000814163	−	0.00858266i
$403$	−1206.93	−	2090.46i	−0.149185	−	0.258396i
$404$	−7311.09			−0.900347
$405$	1913.13	−	13075.3i	0.234726	−	1.60424i
$406$	49.0218	+	165.635i	0.00599239	+	0.0202471i
$407$	−12143.0	+	7010.75i	−1.47888	+	0.853832i
$408$	−48.0289	−	506.306i	−0.00582791	−	0.0614360i
$409$	−735.497	−	424.639i	−0.0889193	−	0.0513376i	0.454881	−	0.890552i	$-0.349682\pi$
$409$	−735.497	−	424.639i	−0.0889193	−	0.0513376i	−0.543800	+	0.839215i	$0.683015\pi$
$410$	304.913	+	176.042i	0.0367283	+	0.0212051i
$411$	−9141.81	+	6501.29i	−1.09716	+	0.780256i
$412$	5768.07	−	3330.19i	0.689738	−	0.398221i
$413$	1123.91	+	3797.46i	0.133908	+	0.452448i
$414$	−421.788	+	80.7496i	−0.0500719	+	0.00958605i
$415$	6551.61			0.774954
$416$	−177.349	−	307.178i	−0.0209021	−	0.0362035i
$417$	−13758.1	−	6293.46i	−1.61568	−	0.739070i
$418$	220.517	+	127.316i	0.0258035	+	0.0148977i
$419$	3109.74	−	5386.23i	0.362579	−	0.628006i	−0.625805	−	0.779979i	$-0.715229\pi$
$419$	3109.74	−	5386.23i	0.362579	−	0.628006i	0.988385	+	0.151973i	$0.0485628\pi$
$420$	−13799.9	−	1962.60i	−1.60325	−	0.228012i
$421$	−1012.07	−	1752.95i	−0.117162	−	0.202930i	0.801480	−	0.598021i	$-0.204046\pi$
$421$	−1012.07	−	1752.95i	−0.117162	−	0.202930i	−0.918642	+	0.395091i	$0.870713\pi$
$422$		−	81.9628i		−	0.00945471i
$423$	2803.35	+	3243.37i	0.322230	+	0.372809i
$424$	−300.242			−0.0343892
$425$	6363.96	+	11022.7i	0.726347	+	1.25807i
$426$	135.307	+	190.263i	0.0153889	+	0.0216391i
$427$	−954.094	+	3970.05i	−0.108131	+	0.449940i
$428$	11669.2	+	6737.23i	1.31788	+	0.760879i
$429$	3618.51	−	343.257i	0.407233	−	0.0386307i
$430$	−493.955	+	285.185i	−0.0553968	+	0.0319834i
$431$		−	6519.65i		−	0.728633i	−0.931275	−	0.364316i	$-0.881303\pi$
$431$		−	6519.65i		−	0.728633i	0.931275	−	0.364316i	$-0.118697\pi$
$432$	6463.50	+	6185.98i	0.719851	+	0.688943i
$433$			17767.9i			1.97199i	0.166772	+	0.985996i	$0.446666\pi$
$433$			17767.9i			1.97199i	−0.166772	+	0.985996i	$0.553334\pi$
$434$	−159.455	+	167.953i	−0.0176362	+	0.0185761i
$435$	847.388	+	8932.90i	0.0934003	+	0.984597i
$436$	−2561.96	+	4437.45i	−0.281412	+	0.487420i
$437$	5707.79	−	9886.17i	0.624806	−	1.08220i
$438$	285.363	+	401.263i	0.0311305	+	0.0437742i
$439$	1280.80	−	739.472i	0.139247	−	0.0803942i	−0.428758	−	0.903419i	$-0.641049\pi$
$439$	1280.80	−	739.472i	0.139247	−	0.0803942i	0.568005	+	0.823025i	$0.307715\pi$
$440$	−1050.36			−0.113805
$441$	−2210.86	−	8993.23i	−0.238728	−	0.971087i
$442$	−115.681			−0.0124488
$443$	13484.2	−	7785.09i	1.44617	−	0.834945i	0.447918	−	0.894075i	$-0.352166\pi$
$443$	13484.2	−	7785.09i	1.44617	−	0.834945i	0.998250	+	0.0591295i	$0.0188325\pi$
$444$	−6542.91	+	14303.4i	−0.699353	+	1.52885i
$445$	321.741	−	557.272i	0.0342742	−	0.0593646i
$446$	−55.4985	+	96.1262i	−0.00589222	+	0.0102056i
$447$	1258.43	+	575.652i	0.133158	+	0.0609114i
$448$	6481.93	−	6827.38i	0.683577	−	0.720007i
$449$		−	6120.30i		−	0.643284i	−0.946861	−	0.321642i	$-0.895765\pi$
$449$		−	6120.30i		−	0.643284i	0.946861	−	0.321642i	$-0.104235\pi$
$450$	508.351	+	176.650i	0.0532531	+	0.0185052i
$451$		−	7342.80i		−	0.766649i
$452$	−9950.46	+	5744.90i	−1.03547	+	0.597826i
$453$	−2817.24	−	3961.47i	−0.292198	−	0.410874i
$454$	297.262	+	171.624i	0.0307295	+	0.0177417i
$455$	−1482.58	+	6169.14i	−0.152757	+	0.635634i
$456$	569.064	−	53.9822i	0.0584405	−	0.00554375i
$457$	−3498.22	−	6059.10i	−0.358074	−	0.620203i	0.629565	−	0.776948i	$-0.283233\pi$
$457$	−3498.22	−	6059.10i	−0.358074	−	0.620203i	−0.987639	+	0.156745i	$0.949900\pi$
$458$	307.663			0.0313890
$459$	8420.43	−	2455.42i	0.856278	−	0.249693i
$460$			23530.6i			2.38505i
$461$	−1833.17	−	3175.15i	−0.185205	−	0.320784i	0.758441	−	0.651742i	$-0.225962\pi$
$461$	−1833.17	−	3175.15i	−0.185205	−	0.320784i	−0.943646	+	0.330958i	$0.892628\pi$
$462$	−130.103	−	323.547i	−0.0131016	−	0.0325818i
$463$	3513.71	−	6085.92i	0.352691	−	0.610878i	−0.634029	−	0.773309i	$-0.718600\pi$
$463$	3513.71	−	6085.92i	0.352691	−	0.610878i	0.986720	+	0.162431i	$0.0519335\pi$
$464$	−5261.13	−	3037.51i	−0.526383	−	0.303907i
$465$	−9803.85	+	6972.12i	−0.977727	+	0.695321i
$466$	−336.893	−	583.516i	−0.0334898	−	0.0580061i
$467$	−13367.8			−1.32460			−0.662301	−	0.749238i	$-0.730420\pi$
$467$	−13367.8			−1.32460			−0.662301	+	0.749238i	$0.730420\pi$
$468$	3084.77	−	2666.27i	0.304688	−	0.263351i
$469$	−717.906	−	2425.66i	−0.0706819	−	0.238820i
$470$	−244.034	+	140.893i	−0.0239499	+	0.0138275i
$471$	−4761.92	−	2178.27i	−0.465855	−	0.213099i
$472$	289.919	+	167.385i	0.0282725	+	0.0163231i
$473$	10301.6	+	5947.61i	1.00141	+	0.578163i
$474$	276.021	+	126.262i	0.0267469	+	0.0122350i
$475$	−12389.0	+	7152.79i	−1.19673	+	0.690932i
$476$	−2625.61	−	8871.41i	−0.252825	−	0.854245i
$477$	−973.637	−	5085.71i	−0.0934586	−	0.488173i
$478$	117.138			0.0112087
$479$	3497.20	+	6057.33i	0.333593	+	0.577800i	0.983214	−	0.182458i	$-0.0584055\pi$
$479$	3497.20	+	6057.33i	0.333593	+	0.577800i	−0.649620	+	0.760259i	$0.725072\pi$
$480$	−1440.60	+	1024.50i	−0.136988	+	0.0974205i
$481$	6200.45	+	3579.83i	0.587767	+	0.339348i
$482$	−214.266	+	371.120i	−0.0202481	+	0.0350707i
$483$	−14505.2	+	5832.73i	−1.36648	+	0.549479i
$484$	155.487	+	269.312i	0.0146025	+	0.0252923i
$485$			24105.0i			2.25681i
$486$	201.473	−	311.368i	0.0188046	−	0.0290616i
$487$	−8233.24			−0.766086			−0.383043	−	0.923731i	$-0.625124\pi$
$487$	−8233.24			−0.766086			−0.383043	+	0.923731i	$0.625124\pi$
$488$	172.575	+	298.909i	0.0160084	+	0.0277274i
$489$	9317.84	−	883.904i	0.861692	−	0.0817414i
$490$	607.912	−	31.5782i	0.0560463	−	0.00291134i
$491$	−12925.9	−	7462.77i	−1.18806	−	0.685927i	−0.230195	−	0.973145i	$-0.573936\pi$
$491$	−12925.9	−	7462.77i	−1.18806	−	0.685927i	−0.957865	+	0.287218i	$0.907270\pi$
$492$	−4773.72	−	6712.57i	−0.437431	−	0.615094i
$493$	−5157.89	+	2977.91i	−0.471196	+	0.272045i
$494$		−	130.020i		−	0.0118419i
$495$	−3406.16	−	17791.8i	−0.309284	−	1.61552i
$496$		−	8144.86i		−	0.737329i
$497$	6163.89	+	5852.01i	0.556314	+	0.528166i
$498$	167.207	+	76.4866i	0.0150457	+	0.00688242i
$499$	−4165.46	+	7214.80i	−0.373691	+	0.647252i	−0.990130	−	0.140151i	$-0.955241\pi$
$499$	−4165.46	+	7214.80i	−0.373691	+	0.647252i	0.616439	+	0.787402i	$0.288575\pi$
$500$	5691.27	−	9857.56i	0.509042	−	0.881687i
$501$	3535.77	−	7729.54i	0.315302	−	0.689282i
$502$	−490.688	+	283.299i	−0.0436265	+	0.0251878i
$503$	−15511.0			−1.37495			−0.687475	−	0.726208i	$-0.741281\pi$
$503$	−15511.0			−1.37495			−0.687475	+	0.726208i	$0.741281\pi$
$504$	−658.958	−	422.643i	−0.0582387	−	0.0373532i
$505$	16585.8			1.46150
$506$	−509.830	+	294.350i	−0.0447919	+	0.0258606i
$507$	5540.49	+	7790.77i	0.485329	+	0.682446i
$508$	7371.29	−	12767.4i	0.643795	−	1.11509i
$509$	1816.15	−	3145.66i	0.158152	−	0.273927i	−0.776050	−	0.630671i	$-0.782780\pi$
$509$	1816.15	−	3145.66i	0.158152	−	0.273927i	0.934202	+	0.356744i	$0.116113\pi$
$510$	54.4462	+	573.955i	0.00472729	+	0.0498337i
$511$	12999.6	+	12341.9i	1.12538	+	1.06844i
$512$		−	1995.51i		−	0.172246i
$513$	2759.77	+	9464.16i	0.237519	+	0.814528i
$514$		−	210.388i		−	0.0180542i
$515$	−13085.4	+	7554.83i	−1.11963	+	0.646419i
$516$	13284.1	−	1260.14i	1.13333	−	0.107509i
$517$	5089.39	+	2938.36i	0.432942	+	0.249959i
$518$	160.510	−	667.896i	0.0136147	−	0.0566518i
$519$	2407.69	+	3385.58i	0.203634	+	0.286340i
$520$	268.168	+	464.481i	0.0226153	+	0.0391708i
$521$	531.760			0.0447156			0.0223578	−	0.999750i	$-0.492883\pi$
$521$	531.760			0.0447156			0.0223578	+	0.999750i	$0.492883\pi$
$522$	−82.6602	+	237.874i	−0.00693092	+	0.0199453i
$523$		−	14041.2i		−	1.17395i	−0.809604	−	0.586977i	$-0.800318\pi$
$523$		−	14041.2i		−	1.17395i	0.809604	−	0.586977i	$-0.199682\pi$
$524$	8783.23	+	15213.0i	0.732247	+	1.26829i
$525$	19396.7	+	2758.58i	1.61246	+	0.229323i
$526$	59.7596	−	103.507i	0.00495369	−	0.00858005i
$527$	−6915.24	−	3992.52i	−0.571599	−	0.330013i
$528$	11152.9	+	5101.74i	0.919258	+	0.420502i
$529$	7112.74	+	12319.6i	0.584592	+	1.01254i
$530$	340.358			0.0278947
$531$	−1895.12	+	5453.67i	−0.154880	+	0.445704i
$532$	9971.04	−	2951.06i	0.812593	−	0.240497i
$533$	−3247.06	+	1874.69i	−0.263876	+	0.152349i
$534$	14.7172	−	10.4663i	0.00119265	−	0.000848166i
$535$	−26472.6	−	15284.0i	−2.13927	−	1.23511i
$536$	−185.189	−	106.919i	−0.0149234	−	0.00861602i
$537$	−1442.79	−	15209.4i	−0.115942	−	1.22222i
$538$	375.662	−	216.888i	0.0301040	−	0.0173805i
$539$	−6909.42	−	10650.3i	−0.552152	−	0.851098i
$540$	−14680.6	−	14050.3i	−1.16992	−	1.11968i
$541$	−11065.4			−0.879372			−0.439686	−	0.898151i	$-0.644910\pi$
$541$	−11065.4			−0.879372			−0.439686	+	0.898151i	$0.644910\pi$
$542$	5.44642	+	9.43348i	0.000431631	+	0.000747606i
$543$	−184.961	−	1949.80i	−0.0146177	−	0.154096i
$544$	−1016.14	−	586.670i	−0.0800860	−	0.0462376i
$545$	5812.03	−	10066.7i	0.456807	−	0.791213i
$546$	−109.859	+	140.138i	−0.00861088	+	0.0109841i
$547$	6024.28	+	10434.4i	0.470895	+	0.815614i	0.999446	−	0.0332874i	$-0.0105977\pi$
$547$	6024.28	+	10434.4i	0.470895	+	0.815614i	−0.528551	+	0.848902i	$0.677264\pi$
$548$			17250.3i			1.34470i
$549$	−4503.50	+	3892.52i	−0.350100	+	0.302602i
$550$	737.739			0.0571950
$551$	−3347.02	−	5797.22i	−0.258780	−	0.448221i
$552$	−549.745	+	1201.80i	−0.0423890	+	0.0926665i
$553$	10744.0	+	2582.02i	0.826184	+	0.198551i
$554$	−259.339	−	149.729i	−0.0198885	−	0.0114827i
$555$	14843.1	−	32448.6i	1.13524	−	2.48174i
$556$	−20148.1	+	11632.5i	−1.53682	+	0.887283i
$557$			2546.80i			0.193737i	0.995297	+	0.0968684i	$0.0308826\pi$
$557$			2546.80i			0.193737i	−0.995297	+	0.0968684i	$0.969117\pi$
$558$	−331.605	+	63.4844i	−0.0251577	+	0.00481632i
$559$		−	6073.94i		−	0.459571i
$560$	−14740.3	+	15525.9i	−1.11231	+	1.17158i
$561$	9798.57	−	6968.36i	0.737426	−	0.524428i
$562$	233.114	−	403.766i	0.0174970	−	0.0303057i
$563$	11536.2	−	19981.3i	0.863578	−	1.49576i	−0.00487467	−	0.999988i	$-0.501552\pi$
$563$	11536.2	−	19981.3i	0.863578	−	1.49576i	0.868452	−	0.495772i	$-0.165115\pi$
$564$	6562.87	−	622.563i	0.489976	−	0.0464799i
$565$	22573.5	−	13032.8i	1.68084	−	0.970432i
$566$	−403.316			−0.0299517
$567$	5022.13	−	12532.5i	0.371974	−	0.928243i
$568$	718.468			0.0530744
$569$	−5471.39	+	3158.91i	−0.403115	+	0.232739i	−0.687827	−	0.725874i	$-0.741435\pi$
$569$	−5471.39	+	3158.91i	−0.403115	+	0.232739i	0.284712	+	0.958613i	$0.408102\pi$
$570$	−645.098	+	61.1950i	−0.0474039	+	0.00449680i
$571$	−9276.07	+	16066.6i	−0.679845	+	1.17753i	0.295182	+	0.955441i	$0.404620\pi$
$571$	−9276.07	+	16066.6i	−0.679845	+	1.17753i	−0.975027	+	0.222085i	$0.928714\pi$
$572$	2794.68	−	4840.53i	0.204286	−	0.353833i
$573$	−7755.39	+	5515.33i	−0.565421	+	0.402105i
$574$	260.877	+	247.677i	0.0189700	+	0.0180102i
$575$		−	33074.1i		−	2.39876i
$576$	13479.9	−	2580.67i	0.975109	−	0.186680i
$577$			2684.61i			0.193695i	0.995299	+	0.0968473i	$0.0308758\pi$
$577$			2684.61i			0.193695i	−0.995299	+	0.0968473i	$0.969124\pi$
$578$	85.1631	−	49.1689i	0.00612858	−	0.00353834i
$579$	−821.404	+	1795.67i	−0.0589575	+	0.128887i
$580$	11949.7	+	6899.14i	0.855488	+	0.493916i
$581$	6508.46	+	1564.13i	0.464744	+	0.111689i
$582$	−281.413	+	615.196i	−0.0200429	+	0.0438157i
$583$	−3549.13	−	6147.27i	−0.252127	−	0.436696i
$584$	1515.25			0.107365
$585$	−6998.08	+	6048.66i	−0.494589	+	0.427489i
$586$		−	274.468i		−	0.0193484i
$587$	−9124.16	−	15803.5i	−0.641558	−	1.11121i	−0.985085	−	0.172068i	$-0.944955\pi$
$587$	−9124.16	−	15803.5i	−0.641558	−	1.11121i	0.343527	−	0.939143i	$-0.388378\pi$
$588$	−13240.4	−	5244.25i	−0.928614	−	0.367805i
$589$	4487.40	−	7772.40i	0.313922	−	0.543729i
$590$	−328.656	−	189.750i	−0.0229332	−	0.0132405i
$591$	1756.53	+	18516.8i	0.122257	+	1.28880i
$592$	12079.1	+	20921.6i	0.838593	+	1.45249i
$593$	−10331.8			−0.715473			−0.357736	−	0.933823i	$-0.616451\pi$
$593$	−10331.8			−0.715473			−0.357736	+	0.933823i	$0.616451\pi$
$594$	120.779	−	493.839i	0.00834281	−	0.0341119i
$595$	5956.41	+	20125.6i	0.410402	+	1.38667i
$596$	1842.92	−	1064.01i	0.126659	−	0.0731266i
$597$	−432.466	−	4558.92i	−0.0296477	−	0.312536i
$598$	260.329	+	150.301i	0.0178021	+	0.0102781i
$599$	−3453.17	−	1993.69i	−0.235547	−	0.135993i	0.377581	−	0.925976i	$-0.376756\pi$
$599$	−3453.17	−	1993.69i	−0.235547	−	0.135993i	−0.613129	+	0.789983i	$0.710089\pi$
$600$	1349.65	−	959.816i	0.0918319	−	0.0653072i
$601$	−15935.6	+	9200.43i	−1.08158	+	0.624448i	−0.931321	−	0.364199i	$-0.881343\pi$
$601$	−15935.6	+	9200.43i	−1.08158	+	0.624448i	−0.150255	+	0.988647i	$0.548010\pi$
$602$	−558.786	+	165.380i	−0.0378313	+	0.0111966i
$603$	1210.53	−	3483.58i	0.0817521	−	0.235261i
$604$	−7475.15			−0.503576
$605$	−352.736	−	610.957i	−0.0237038	−	0.0410561i
$606$	423.296	+	193.631i	0.0283750	+	0.0129797i
$607$	12276.2	+	7087.68i	0.820883	+	0.473937i	0.850721	−	0.525618i	$-0.176166\pi$
$607$	12276.2	+	7087.68i	0.820883	+	0.473937i	−0.0298377	+	0.999555i	$0.509499\pi$
$608$	659.389	−	1142.10i	0.0439832	−	0.0761811i
$609$	−1290.83	+	9076.37i	−0.0858902	+	0.603929i
$610$	−195.634	−	338.848i	−0.0129852	−	0.0224910i
$611$		−	3000.77i		−	0.198688i
$612$	4427.28	−	12740.5i	0.292422	−	0.841513i
$613$	−2164.43			−0.142611			−0.0713054	−	0.997455i	$-0.522716\pi$
$613$	−2164.43			−0.142611			−0.0713054	+	0.997455i	$0.522716\pi$
$614$	−193.819	−	335.705i	−0.0127393	−	0.0220650i
$615$	10829.6	+	15228.0i	0.710067	+	0.998462i
$616$	−1043.44	−	250.763i	−0.0682492	−	0.0164018i
$617$	2799.72	+	1616.42i	0.182678	+	0.105469i	0.588550	−	0.808460i	$-0.299699\pi$
$617$	2799.72	+	1616.42i	0.182678	+	0.105469i	−0.405872	+	0.913930i	$0.633032\pi$
$618$	−422.157	+	40.0464i	−0.0274784	+	0.00260664i
$619$	18943.3	−	10936.9i	1.23004	−	0.710166i	0.263005	−	0.964795i	$-0.415287\pi$
$619$	18943.3	−	10936.9i	1.23004	−	0.710166i	0.967039	+	0.254629i	$0.0819532\pi$
$620$			18499.5i			1.19832i
$621$	−22139.6	−	5414.74i	−1.43065	−	0.349897i
$622$		−	488.010i		−	0.0314589i
$623$	452.665	−	476.789i	0.0291102	−	0.0306616i
$624$	−591.410	−	6234.46i	−0.0379412	−	0.399965i
$625$	−187.001	+	323.895i	−0.0119680	+	0.0207292i
$626$	−39.5514	+	68.5051i	−0.00252523	+	0.00437383i
$627$	7832.10	+	11013.1i	0.498858	+	0.701470i
$628$	−6973.61	+	4026.22i	−0.443117	+	0.255834i
$629$	23684.1			1.50135
$630$	747.003	+	479.113i	0.0472402	+	0.0302989i
$631$	−9979.57			−0.629604			−0.314802	−	0.949157i	$-0.601938\pi$
$631$	−9979.57			−0.629604			−0.314802	+	0.949157i	$0.601938\pi$
$632$	808.923	−	467.032i	0.0509134	−	0.0293948i
$633$	1809.52	−	3955.80i	0.113621	−	0.248387i
$634$	−116.536	+	201.847i	−0.00730007	+	0.0126441i
$635$	−16722.4	+	28964.0i	−1.04505	+	1.81008i
$636$	−7240.98	−	3312.29i	−0.451452	−	0.206511i
$637$	−2945.64	+	5774.55i	−0.183219	+	0.359178i
$638$			345.212i			0.0214217i
$639$	2329.88	+	12169.9i	0.144239	+	0.753419i
$640$			3623.76i			0.223815i
$641$	13685.3	−	7901.22i	0.843272	−	0.486864i	−0.0151029	−	0.999886i	$-0.504808\pi$
$641$	13685.3	−	7901.22i	0.843272	−	0.486864i	0.858375	+	0.513022i	$0.171474\pi$
$642$	−497.190	−	699.125i	−0.0305647	−	0.0429786i
$643$	−10980.9	−	6339.83i	−0.673476	−	0.388831i	0.123917	−	0.992293i	$-0.460454\pi$
$643$	−10980.9	−	6339.83i	−0.673476	−	0.388831i	−0.797392	+	0.603461i	$0.793788\pi$
$644$	−5617.70	+	23375.7i	−0.343740	+	1.43033i
$645$	−30136.0	+	2858.75i	−1.83970	+	0.174516i
$646$	−215.053	−	372.482i	−0.0130977	−	0.0226859i
$647$	20710.7			1.25846			0.629230	−	0.777219i	$-0.283370\pi$
$647$	20710.7			1.25846			0.629230	+	0.777219i	$0.283370\pi$
$648$	−421.538	−	1060.58i	−0.0255549	−	0.0642958i
$649$			7914.57i			0.478696i
$650$	−188.352	−	326.235i	−0.0113658	−	0.0196862i
$651$	−11403.8	+	4585.62i	−0.686560	+	0.276075i
$652$	7196.45	−	12464.6i	0.432262	−	0.748699i
$653$	−1355.80	−	782.771i	−0.0812505	−	0.0469100i	0.458824	−	0.888527i	$-0.348271\pi$
$653$	−1355.80	−	782.771i	−0.0812505	−	0.0469100i	−0.540075	+	0.841617i	$0.681604\pi$
$654$	265.856	−	189.066i	0.0158957	−	0.0113044i
$655$	−19925.5	−	34512.0i	−1.18863	−	2.05877i
$656$	−12651.2			−0.752966
$657$	4913.71	+	25666.3i	0.291784	+	1.52411i
$658$	−276.063	+	81.7044i	−0.0163557	+	0.00484069i
$659$	−15480.8	+	8937.83i	−0.915091	+	0.528328i	−0.882066	−	0.471126i	$-0.843848\pi$
$659$	−15480.8	+	8937.83i	−0.915091	+	0.528328i	−0.0330256	+	0.999455i	$0.510514\pi$
$660$	−25331.8	−	11587.7i	−1.49400	−	0.683408i
$661$	−21911.3	−	12650.5i	−1.28934	−	0.744399i	−0.310801	−	0.950475i	$-0.600597\pi$
$661$	−21911.3	−	12650.5i	−1.28934	−	0.744399i	−0.978536	+	0.206076i	$0.933930\pi$
$662$	−632.141	−	364.967i	−0.0371131	−	0.0214272i
$663$	−5583.15	−	2553.93i	−0.327046	−	0.149603i
$664$	490.028	−	282.918i	0.0286397	−	0.0165352i
$665$	−22620.2	+	6694.72i	−1.31906	+	0.390391i
$666$	757.640	−	654.852i	0.0440810	−	0.0381006i
$667$	15476.4			0.898427
$668$	−6535.35	−	11319.6i	−0.378533	−	0.655639i
$669$	−4800.75	+	3414.11i	−0.277441	+	0.197305i
$670$	209.932	+	121.204i	0.0121051	+	0.00698886i
$671$	−4079.99	+	7066.75i	−0.234734	+	0.406571i
$672$	−1675.70	+	673.823i	−0.0961929	+	0.0386805i
$673$	−16774.4	−	29054.1i	−0.960781	−	1.66412i	−0.720548	−	0.693405i	$-0.756110\pi$
$673$	−16774.4	−	29054.1i	−0.960781	−	1.66412i	−0.240233	−	0.970715i	$-0.577224\pi$
$674$			191.554i			0.0109472i
$675$	20634.7	+	19748.8i	1.17664	+	1.12612i
$676$	14700.9			0.836419
$677$	16134.2	+	27945.3i	0.915935	+	1.58645i	0.805527	+	0.592559i	$0.201882\pi$
$677$	16134.2	+	27945.3i	0.915935	+	1.58645i	0.110408	+	0.993886i	$0.464784\pi$
$678$	728.261	−	69.0839i	0.0412518	−	0.00391320i
$679$	−5754.82	+	23946.2i	−0.325257	+	1.35342i
$680$	1536.50	+	887.097i	0.0866500	+	0.0500274i
$681$	10557.8	+	14845.9i	0.594092	+	0.835383i
$682$	−400.823	+	231.415i	−0.0225048	+	0.0129932i
$683$			14942.5i			0.837126i	0.908188	+	0.418563i	$0.137466\pi$
$683$			14942.5i			0.837126i	−0.908188	+	0.418563i	$0.862534\pi$
$684$	14319.8	+	4976.05i	0.800482	+	0.278164i
$685$		−	39133.7i		−	2.18281i
$686$	611.447	+	113.763i	0.0340308	+	0.00633160i
$687$	14848.9	+	6792.40i	0.824628	+	0.377214i
$688$	10247.4	−	17748.9i	0.567844	−	0.983534i
$689$	−1812.26	+	3138.92i	−0.100205	+	0.173561i
$690$	623.198	−	1362.37i	0.0343837	−	0.0751662i
$691$	−9734.42	+	5620.17i	−0.535912	+	0.309409i	−0.743420	−	0.668824i	$-0.766798\pi$
$691$	−9734.42	+	5620.17i	−0.535912	+	0.309409i	0.207509	+	0.978233i	$0.433464\pi$
$692$	6388.47			0.350944
$693$	863.881	−	18487.8i	0.0473537	−	1.01341i
$694$	134.723			0.00736889
$695$	45707.8	−	26389.4i	2.49467	−	1.44030i
$696$	449.129	+	631.544i	0.0244601	+	0.0343946i
$697$	−6201.46	+	10741.2i	−0.337012	+	0.583721i
$698$	−457.748	+	792.843i	−0.0248224	+	0.0429936i
$699$	−3377.08	−	35600.1i	−0.182737	−	1.92635i
$700$	20743.5	−	21849.0i	1.12004	−	1.17973i
$701$		−	19409.2i		−	1.04576i	−0.852407	−	0.522879i	$-0.824858\pi$
$701$		−	19409.2i		−	1.04576i	0.852407	−	0.522879i	$-0.175142\pi$
$702$	−249.217	+	72.6723i	−0.0133990	+	0.00390718i
$703$			26619.8i			1.42814i
$704$	16293.6	−	9407.13i	0.872285	−	0.503614i
$705$	−14888.4	+	1412.34i	−0.795363	+	0.0754493i
$706$	−57.4589	−	33.1739i	−0.00306302	−	0.00176844i
$707$	16476.6	+	3959.70i	0.876472	+	0.210636i
$708$	5145.44	+	7235.27i	0.273132	+	0.384065i
$709$	866.108	+	1500.14i	0.0458778	+	0.0794627i	0.888052	−	0.459742i	$-0.152058\pi$
$709$	866.108	+	1500.14i	0.0458778	+	0.0794627i	−0.842175	+	0.539205i	$0.818725\pi$
$710$	−814.465			−0.0430512
$711$	10534.1	+	12187.6i	0.555641	+	0.642857i
$712$		−	55.5750i		−	0.00292522i
$713$	10374.7	+	17969.6i	0.544932	+	0.943851i
$714$	−82.9383	+	583.173i	−0.00434718	+	0.0305668i
$715$	−6339.97	+	10981.2i	−0.331610	+	0.574366i
$716$	−20345.8	−	11746.7i	−1.06196	−	0.613120i
$717$	5653.44	+	2586.09i	0.294465	+	0.134699i
$718$	−81.3772	−	140.949i	−0.00422976	−	0.00732616i
$719$	36946.9			1.91639			0.958197	−	0.286109i	$-0.0923620\pi$
$719$	36946.9			1.91639			0.958197	+	0.286109i	$0.0923620\pi$
$720$	−30654.1	+	5868.59i	−1.58668	+	0.303763i
$721$	−14802.8	+	4381.08i	−0.764612	+	0.226297i
$722$	−162.914	+	94.0582i	−0.00839753	+	0.00484832i
$723$	−18534.6	+	13181.0i	−0.953399	+	0.678020i
$724$	−2608.28	−	1505.89i	−0.133889	−	0.0773011i
$725$	−16796.2	−	9697.26i	−0.860405	−	0.496755i
$726$	−1.86977	−	19.7106i	−9.55838e−5	−	0.00100762i
$727$	−1776.00	+	1025.38i	−0.0906029	+	0.0523096i	−0.544617	−	0.838685i	$-0.683325\pi$
$727$	−1776.00	+	1025.38i	−0.0906029	+	0.0523096i	0.454014	+	0.890995i	$0.349992\pi$
$728$	155.512	+	525.444i	0.00791710	+	0.0267503i
$729$	16598.0	−	10579.6i	0.843263	−	0.537501i
$730$	−1717.70			−0.0870892
$731$	−10046.3	−	17400.6i	−0.508310	−	0.880419i
$732$	864.445	+	9112.71i	0.0436487	+	0.460131i
$733$	27156.6	+	15678.9i	1.36842	+	0.790058i	0.990726	−	0.135873i	$-0.0433839\pi$
$733$	27156.6	+	15678.9i	1.36842	+	0.790058i	0.377694	+	0.925931i	$0.376717\pi$
$734$	149.986	−	259.783i	0.00754234	−	0.0130637i
$735$	30037.0	+	11897.0i	1.50739	+	0.597046i
$736$	1524.49	+	2640.49i	0.0763498	+	0.132242i
$737$		−	5055.50i		−	0.252675i
$738$	98.6085	+	515.073i	0.00491847	+	0.0256912i
$739$	1233.93			0.0614219			0.0307109	−	0.999528i	$-0.490223\pi$
$739$	1233.93			0.0614219			0.0307109	+	0.999528i	$0.490223\pi$
$740$	−27435.4	−	47519.4i	−1.36290	−	2.36061i
$741$	2870.50	−	6275.20i	0.142308	−	0.311100i
$742$	338.116	+	81.2570i	0.0167286	+	0.00402027i
$743$	26190.4	+	15121.0i	1.29318	+	0.746618i	0.979217	−	0.202818i	$-0.0650098\pi$
$743$	26190.4	+	15121.0i	1.29318	+	0.746618i	0.313963	+	0.949435i	$0.398343\pi$
$744$	−432.204	+	944.840i	−0.0212975	+	0.0465585i
$745$	−4180.81	+	2413.79i	−0.205602	+	0.118704i
$746$			763.675i			0.0374801i
$747$	6381.35	+	7382.99i	0.312559	+	0.361619i
$748$		−	18489.6i		−	0.903803i
$749$	−22649.4	−	21503.4i	−1.10493	−	1.04902i
$750$	−590.585	+	420.001i	−0.0287535	+	0.0204483i
$751$	−2746.70	+	4757.42i	−0.133460	+	0.231159i	−0.925008	−	0.379947i	$-0.875942\pi$
$751$	−2746.70	+	4757.42i	−0.133460	+	0.231159i	0.791548	+	0.611107i	$0.209275\pi$
$752$	5062.61	−	8768.70i	0.245498	−	0.425215i
$753$	−29936.7	+	2839.84i	−1.44881	+	0.137436i
$754$	152.656	−	88.1361i	0.00737323	−	0.00425693i
$755$	16958.0			0.817438
$756$	−11229.6	−	17462.6i	−0.540233	−	0.840091i
$757$	−31971.7			−1.53505			−0.767523	−	0.641021i	$-0.778511\pi$
$757$	−31971.7			−1.53505			−0.767523	+	0.641021i	$0.778511\pi$
$758$	581.302	−	335.615i	0.0278547	−	0.0160819i
$759$	−31104.6	+	2950.62i	−1.48751	+	0.141108i
$760$	−997.055	+	1726.95i	−0.0475881	+	0.0824251i
$761$	−8220.51	+	14238.3i	−0.391581	+	0.678238i	−0.992658	−	0.120953i	$-0.961405\pi$
$761$	−8220.51	+	14238.3i	−0.391581	+	0.678238i	0.601077	+	0.799191i	$0.294738\pi$
$762$	−764.921	+	543.982i	−0.0363651	+	0.0258614i
$763$	8177.07	−	8612.86i	0.387982	−	0.408658i
$764$			14634.2i			0.692991i
$765$	−10043.7	+	28903.0i	−0.474679	+	1.36600i
$766$		−	1079.21i		−	0.0509051i
$767$	3499.90	−	2020.67i	0.164764	−	0.0951266i
$768$	8747.60	−	19123.1i	0.411005	−	0.898497i
$769$	1220.92	+	704.900i	0.0572531	+	0.0330551i	0.528353	−	0.849025i	$-0.322810\pi$
$769$	1220.92	+	704.900i	0.0572531	+	0.0330551i	−0.471100	+	0.882080i	$0.656143\pi$
$770$	1182.86	+	284.268i	0.0553602	+	0.0133043i
$771$	4644.82	−	10154.0i	0.216964	−	0.474305i
$772$	1518.24	+	2629.67i	0.0707808	+	0.122596i
$773$	−9575.08			−0.445526			−0.222763	−	0.974873i	$-0.571508\pi$
$773$	−9575.08			−0.445526			−0.222763	+	0.974873i	$0.571508\pi$
$774$	−802.492	−	278.863i	−0.0372674	−	0.0129503i
$775$		−	26002.5i		−	1.20521i
$776$	1040.92	+	1802.93i	0.0481534	+	0.0834041i
$777$	22492.1	−	28691.2i	1.03848	−	1.32470i
$778$	−534.773	+	926.255i	−0.0246434	+	0.0426836i
$779$	−12072.6	−	6970.15i	−0.555260	−	0.320579i
$780$	1343.28	+	14160.4i	0.0616629	+	0.650031i
$781$	8492.94	+	14710.2i	0.389118	+	0.673972i
$782$	994.391			0.0454723
$783$	−9241.09	+	9655.67i	−0.421775	+	0.440697i
$784$	−18349.8	+	11904.5i	−0.835907	+	0.542297i
$785$	15820.2	−	9133.82i	0.719297	−	0.415286i
$786$	−105.621	−	1113.42i	−0.00479308	−	0.0505272i
$787$	985.646	+	569.063i	0.0446436	+	0.0257750i	0.522156	−	0.852850i	$-0.325128\pi$
$787$	985.646	+	569.063i	0.0446436	+	0.0257750i	−0.477512	+	0.878625i	$0.658461\pi$
$788$	24770.2	+	14301.1i	1.11980	+	0.646516i
$789$	5169.35	−	3676.24i	0.233249	−	0.165878i
$790$	−917.006	+	529.434i	−0.0412982	+	0.0238436i
$791$	25536.2	−	7557.78i	1.14787	−	0.339726i
$792$	−1023.07	−	1183.65i	−0.0459003	−	0.0531050i
$793$	4166.65			0.186585
$794$	352.617	+	610.751i	0.0157606	+	0.0272982i
$795$	16426.8	+	7514.21i	0.732828	+	0.335222i
$796$	−6098.53	−	3520.99i	−0.271554	−	0.156782i
$797$	10685.7	−	18508.2i	0.474914	−	0.822576i	−0.524673	−	0.851304i	$-0.675812\pi$
$797$	10685.7	−	18508.2i	0.474914	−	0.822576i	0.999587	+	0.0287282i	$0.00914573\pi$
$798$	−655.459	−	93.2187i	−0.0290764	−	0.00413522i
$799$	−4963.27	−	8596.63i	−0.219759	−	0.380634i
$800$		−	3820.87i		−	0.168860i
$801$	941.368	−	180.221i	0.0415251	−	0.00794980i
$802$	1202.09			0.0529267
$803$	17911.6	+	31023.8i	0.787156	+	1.36339i
$804$	−3286.70	−	4621.59i	−0.144170	−	0.202725i
$805$	12744.2	−	53029.7i	0.557982	−	2.32180i
$806$	204.668	+	118.165i	0.00894433	+	0.00516401i
$807$	22919.0	−	2174.13i	0.999736	−	0.0948364i
$808$	1240.54	−	716.225i	0.0540124	−	0.0311841i
$809$		−	16824.0i		−	0.731150i	−0.930782	−	0.365575i	$-0.880872\pi$
$809$		−	16824.0i		−	0.731150i	0.930782	−	0.365575i	$-0.119128\pi$
$810$	477.861	+	1202.29i	0.0207288	+	0.0521534i
$811$			32964.6i			1.42731i	0.700500	+	0.713653i	$0.252961\pi$
$811$			32964.6i			1.42731i	−0.700500	+	0.713653i	$0.747039\pi$
$812$	10223.9	+	9706.56i	0.441856	+	0.419499i
$813$	54.5959	+	575.533i	0.00235518	+	0.0248276i
$814$	686.391	−	1188.86i	0.0295553	−	0.0511912i
$815$	−16325.8	+	28277.0i	−0.701677	+	1.21534i
$816$	−12006.0	−	16882.3i	−0.515068	−	0.724264i
$817$	19557.5	−	11291.5i	0.837491	−	0.483526i
$818$	83.1491			0.00355408
$819$	−8396.04	+	4338.10i	−0.358219	+	0.185086i
$820$	28734.8			1.22373
$821$	−18735.6	+	10817.0i	−0.796438	+	0.459824i	−0.842224	−	0.539127i	$-0.818754\pi$
$821$	−18735.6	+	10817.0i	−0.796438	+	0.459824i	0.0457860	+	0.998951i	$0.485421\pi$
$822$	456.865	−	998.753i	0.0193857	−	0.0423790i
$823$	12194.5	−	21121.4i	0.516492	−	0.894590i	−0.483325	−	0.875441i	$-0.660571\pi$
$823$	12194.5	−	21121.4i	0.516492	−	0.894590i	0.999817	−	0.0191488i	$-0.00609561\pi$
$824$	−652.480	+	1130.13i	−0.0275852	+	0.0477790i
$825$	35605.7	+	16287.3i	1.50258	+	0.687335i
$826$	−281.191	−	266.963i	−0.0118449	−	0.0112456i
$827$			29015.7i			1.22004i	0.792385	+	0.610022i	$0.208839\pi$
$827$			29015.7i			1.22004i	−0.792385	+	0.610022i	$0.791161\pi$
$828$	−26516.6	+	22919.1i	−1.11294	+	0.961951i
$829$		−	17685.2i		−	0.740931i	−0.928846	−	0.370466i	$-0.879198\pi$
$829$		−	17685.2i		−	0.740931i	0.928846	−	0.370466i	$-0.120802\pi$
$830$	−555.502	+	320.720i	−0.0232311	+	0.0134125i
$831$	−9210.92	−	12952.0i	−0.384505	−	0.540672i
$832$	−8319.85	−	4803.47i	−0.346682	−	0.200157i
$833$	1112.41	+	21415.0i	0.0462698	+	0.890741i
$834$	1474.62	−	139.884i	0.0612252	−	0.00580791i
$835$	14826.0	+	25679.4i	0.614461	+	1.06428i
$836$	20781.4			0.859735
$837$	−17405.9	−	4257.01i	−0.718802	−	0.175799i
$838$			608.922i			0.0251013i
$839$	−18875.6	−	32693.4i	−0.776706	−	1.34529i	−0.933831	−	0.357716i	$-0.883556\pi$
$839$	−18875.6	−	32693.4i	−0.776706	−	1.34529i	0.157124	−	0.987579i	$-0.449778\pi$
$840$	2533.81	−	1018.88i	0.104077	−	0.0418508i
$841$	−7656.83	+	13262.0i	−0.313946	+	0.543771i
$842$	171.623	+	99.0869i	0.00702439	+	0.00405553i
$843$	20164.9	−	14340.5i	0.823864	−	0.585900i
$844$	−3344.64	−	5793.08i	−0.136407	−	0.236263i
$845$	−33350.3			−1.35773
$846$	−396.464	−	137.769i	−0.0161120	−	0.00559883i
$847$	−204.553	−	691.145i	−0.00829815	−	0.0280378i
$848$	−10591.4	+	6114.92i	−0.428902	+	0.247626i
$849$	−19465.4	−	8904.15i	−0.786866	−	0.359941i
$850$	−1079.18	−	623.067i	−0.0435479	−	0.0251424i
$851$	−53298.8	−	30772.1i	−2.14696	−	1.23955i
$852$	17327.4	+	7926.19i	0.696747	+	0.318717i
$853$	−19616.3	+	11325.5i	−0.787398	+	0.454605i	−0.839046	−	0.544061i	$-0.816886\pi$
$853$	−19616.3	+	11325.5i	−0.787398	+	0.454605i	0.0516476	+	0.998665i	$0.483553\pi$
$854$	−113.449	−	383.321i	−0.00454583	−	0.0153595i
$855$	−32485.6	−	11288.6i	−1.29940	−	0.451535i
$856$	−2640.03			−0.105414
$857$	6080.19	+	10531.2i	0.242351	+	0.419765i	0.961384	−	0.275212i	$-0.0887480\pi$
$857$	6080.19	+	10531.2i	0.242351	+	0.419765i	−0.719032	+	0.694977i	$0.755415\pi$
$858$	−290.005	+	206.240i	−0.0115392	+	0.00820621i
$859$	−12189.4	−	7037.53i	−0.484163	−	0.279531i	0.237987	−	0.971268i	$-0.423512\pi$
$859$	−12189.4	−	7037.53i	−0.484163	−	0.279531i	−0.722150	+	0.691737i	$0.756846\pi$
$860$	−23274.9	+	40313.4i	−0.922871	+	1.59846i
$861$	7122.72	+	17713.2i	0.281930	+	0.701120i
$862$	319.155	+	552.793i	0.0126107	+	0.0218425i
$863$			8687.35i			0.342666i	0.985213	+	0.171333i	$0.0548074\pi$
$863$			8687.35i			0.342666i	−0.985213	+	0.171333i	$0.945193\pi$
$864$	−2557.67	−	625.535i	−0.100710	−	0.0246309i
$865$	−14492.8			−0.569676
$866$	−869.789	−	1506.52i	−0.0341301	−	0.0591150i
$867$	5195.77	−	492.878i	0.203527	−	0.0193068i
$868$	−4416.57	+	18377.7i	−0.172705	+	0.718640i
$869$	19124.4	+	11041.5i	0.746549	+	0.431020i
$870$	−509.139	−	715.927i	−0.0198407	−	0.0278991i
$871$	−2235.59	+	1290.72i	−0.0869692	+	0.0502117i
$872$		−	1003.92i		−	0.0389875i
$873$	−27163.8	+	23478.6i	−1.05310	+	0.910227i
$874$			1117.65i			0.0432551i
$875$	−18165.0	+	19133.0i	−0.701814	+	0.739217i
$876$	36543.5	+	16716.3i	1.40946	+	0.644740i
$877$	−1604.18	+	2778.53i	−0.0617667	+	0.106983i	−0.895255	−	0.445554i	$-0.853007\pi$
$877$	−1604.18	+	2778.53i	−0.0617667	+	0.106983i	0.833488	+	0.552537i	$0.186340\pi$
$878$	−72.3984	+	125.398i	−0.00278283	+	0.00482001i
$879$	6059.53	−	13246.7i	0.232518	−	0.508306i
$880$	−37052.6	+	21392.4i	−1.41937	+	0.819473i
$881$	−36469.9			−1.39467			−0.697334	−	0.716746i	$-0.745631\pi$
$881$	−36469.9			−1.39467			−0.697334	+	0.716746i	$0.745631\pi$
$882$	627.699	+	654.297i	0.0239634	+	0.0249788i
$883$	4262.90			0.162467			0.0812333	−	0.996695i	$-0.474114\pi$
$883$	4262.90			0.162467			0.0812333	+	0.996695i	$0.474114\pi$
$884$	−8176.27	+	4720.57i	−0.311083	+	0.179604i
$885$	−11672.9	−	16413.8i	−0.443366	−	0.623440i
$886$	−762.203	+	1320.18i	−0.0289015	+	0.0500589i
$887$	16289.3	−	28214.0i	0.616620	−	1.06802i	−0.373478	−	0.927639i	$-0.621835\pi$
$887$	16289.3	−	28214.0i	0.616620	−	1.06802i	0.990098	−	0.140379i	$-0.0448320\pi$
$888$	−291.032	−	3067.97i	−0.0109982	−	0.115939i
$889$	−23527.1	+	24781.0i	−0.887598	+	0.934901i
$890$			63.0005i			0.00237279i
$891$	16731.9	−	21167.8i	0.629111	−	0.795901i
$892$			9058.85i			0.340037i
$893$	9662.20	−	5578.47i	0.362075	−	0.209044i
$894$	−134.881	+	12.7950i	−0.00504595	+	0.000478666i
$895$	46156.3	+	26648.4i	1.72384	+	0.995258i
$896$	−865.136	+	3599.89i	−0.0322569	+	0.134223i
$897$	9246.10	+	13001.4i	0.344168	+	0.483952i
$898$	299.605	+	518.932i	0.0111336	+	0.0192839i
$899$	12167.4			0.451397
$900$	43138.5	−	8258.67i	1.59772	−	0.305877i
$901$			11989.9i			0.443329i
$902$	359.450	+	622.586i	0.0132687	+	0.0229821i
$903$	−30620.0	−	4354.75i	−1.12843	−	0.160484i
$904$	1125.59	−	1949.58i	0.0414121	−	0.0717279i
$905$	5917.10	+	3416.24i	0.217338	+	0.125480i
$906$	432.795	+	197.976i	0.0158705	+	0.00725972i
$907$	−2421.00	−	4193.30i	−0.0886307	−	0.153513i	0.818302	−	0.574789i	$-0.194916\pi$
$907$	−2421.00	−	4193.30i	−0.0886307	−	0.153513i	−0.906933	+	0.421276i	$0.861582\pi$
$908$	28013.7			1.02386
$909$	16154.8	+	18690.5i	0.589462	+	0.681986i
$910$	−176.290	−	595.650i	−0.00642193	−	0.0216985i
$911$	−30705.9	+	17728.1i	−1.11672	+	0.644740i	−0.940562	−	0.339622i	$-0.889701\pi$
$911$	−30705.9	+	17728.1i	−1.11672	+	0.644740i	−0.176160	+	0.984362i	$0.556367\pi$
$912$	18974.9	−	13494.2i	0.688950	−	0.489954i
$913$	11585.1	+	6688.69i	0.419948	+	0.242457i
$914$	593.219	+	342.495i	0.0214682	+	0.0123947i
$915$	−1961.07	−	20673.0i	−0.0708535	−	0.746915i
$916$	21745.5	−	12554.7i	0.784378	−	0.452861i
$917$	−11554.9	−	39041.7i	−0.416113	−	1.40597i
$918$	−593.757	+	620.395i	−0.0213474	+	0.0223051i
$919$	16541.1			0.593732			0.296866	−	0.954919i	$-0.404059\pi$
$919$	16541.1			0.593732			0.296866	+	0.954919i	$0.404059\pi$
$920$	−2305.16	−	3992.66i	−0.0826076	−	0.143080i
$921$	−1942.88	−	20481.2i	−0.0695115	−	0.732768i
$922$	310.865	+	179.478i	0.0111039	+	0.00641084i
$923$	4336.67	−	7511.33i	0.154651	−	0.267864i
$924$	−22398.5	−	17559.0i	−0.797463	−	0.625162i
$925$	38562.5	+	66792.1i	1.37073	+	2.37418i
$926$			688.023i			0.0244167i
$927$	−21258.8	−	7387.34i	−0.753216	−	0.261739i
$928$	1787.91			0.0632446
$929$	−20349.3	−	35246.0i	−0.718664	−	1.24476i	−0.961529	−	0.274702i	$-0.911421\pi$
$929$	−20349.3	−	35246.0i	−0.718664	−	1.24476i	0.242866	−	0.970060i	$-0.421913\pi$
$930$	489.952	−	1071.08i	0.0172754	−	0.0377658i
$931$	−24069.5	+	1250.30i	−0.847309	+	0.0440137i
$932$	−47622.8	−	27495.0i	−1.67375	−	0.966341i
$933$	10774.0	−	23553.0i	0.378054	−	0.826463i
$934$	1133.44	−	654.392i	0.0397080	−	0.0229254i
$935$			41945.1i			1.46712i
$936$	−262.223	+	754.608i	−0.00915707	+	0.0263516i
$937$			13937.5i			0.485933i	0.970035	+	0.242967i	$0.0781205\pi$
$937$			13937.5i			0.485933i	−0.970035	+	0.242967i	$0.921879\pi$
$938$	179.613	+	170.525i	0.00625222	+	0.00593587i
$939$	−3421.30	+	2433.09i	−0.118903	+	0.0845590i
$940$	−11498.8	+	19916.5i	−0.398988	+	0.691068i
$941$	16191.6	−	28044.6i	0.560925	−	0.971550i	−0.436491	−	0.899709i	$-0.643779\pi$
$941$	16191.6	−	28044.6i	0.560925	−	0.971550i	0.997416	−	0.0718418i	$-0.0228877\pi$
$942$	510.389	−	48.4163i	0.0176533	−	0.00167461i
$943$	27911.6	−	16114.8i	0.963868	−	0.556489i
$944$	13636.3			0.470152
$945$	25475.3	+	39615.4i	0.876942	+	1.36369i
$946$	−1164.61			−0.0400261
$947$	6500.78	−	3753.23i	0.223070	−	0.128789i	−0.384301	−	0.923208i	$-0.625558\pi$
$947$	6500.78	−	3753.23i	0.223070	−	0.128789i	0.607371	+	0.794418i	$0.292224\pi$
$948$	24661.3	−	2339.41i	0.844896	−	0.0801480i
$949$	9146.02	−	15841.4i	0.312848	−	0.541868i
$950$	700.298	−	1212.95i	0.0239165	−	0.0414246i
$951$	−10080.7	+	7168.97i	−0.343731	+	0.244448i
$952$	1314.59	+	1248.08i	0.0447544	+	0.0424899i
$953$			469.935i			0.0159735i	0.999968	+	0.00798673i	$0.00254228\pi$
$953$			469.935i			0.0159735i	−0.999968	+	0.00798673i	$0.997458\pi$
$954$	331.513	+	383.548i	0.0112507	+	0.0130166i
$955$		−	33198.8i		−	1.12491i
$956$	8279.21	−	4780.00i	0.280093	−	0.161712i
$957$	−7621.37	+	16661.1i	−0.257434	+	0.562775i
$958$	−593.046	−	342.395i	−0.0200005	−	0.0115473i
$959$	9342.77	−	38876.0i	0.314592	−	1.30904i
$960$	−19916.8	+	43540.0i	−0.669594	+	1.46380i
$961$	−6739.00	−	11672.3i	−0.226209	−	0.391806i
$962$	−700.970			−0.0234929
$963$	−8561.20	−	44718.7i	−0.286481	−	1.49641i
$964$			34974.1i			1.16850i
$965$	−3444.27	−	5965.64i	−0.114896	−	0.199006i
$966$	944.346	−	1204.62i	0.0314533	−	0.0401221i
$967$	−16008.3	+	27727.1i	−0.532359	+	0.922073i	0.466927	+	0.884296i	$0.345361\pi$
$967$	−16008.3	+	27727.1i	−0.532359	+	0.922073i	−0.999286	+	0.0377773i	$0.987972\pi$
$968$	−52.7659	−	30.4644i	−0.00175203	−	0.00101153i
$969$	−2155.73	−	22725.0i	−0.0714674	−	0.753387i
$970$	−1180.01	−	2043.83i	−0.0390595	−	0.0676530i
$971$	−2588.27			−0.0855424			−0.0427712	−	0.999085i	$-0.513619\pi$
$971$	−2588.27			−0.0855424			−0.0427712	+	0.999085i	$0.513619\pi$
$972$	1534.11	−	30228.7i	0.0506242	−	0.997518i
$973$	51706.9	−	15303.3i	1.70365	−	0.504216i
$974$	698.086	−	403.040i	0.0229652	−	0.0132590i
$975$	−1888.08	−	19903.5i	−0.0620173	−	0.653767i
$976$	12175.6	+	7029.57i	0.399314	+	0.230544i
$977$	−31756.0	−	18334.4i	−1.03988	−	0.600376i	−0.120083	−	0.992764i	$-0.538316\pi$
$977$	−31756.0	−	18334.4i	−1.03988	−	0.600376i	−0.919800	+	0.392387i	$0.871649\pi$
$978$	−746.778	+	531.079i	−0.0244165	+	0.0173641i
$979$	1137.86	−	656.946i	0.0371464	−	0.0214465i
$980$	41678.2	−	27038.8i	1.35853	−	0.881351i
$981$	17005.2	−	3255.56i	0.553448	−	0.105955i
$982$	1461.29			0.0474865
$983$	4505.33	+	7803.46i	0.146183	+	0.253196i	0.929814	−	0.368031i	$-0.119968\pi$
$983$	4505.33	+	7803.46i	0.146183	+	0.253196i	−0.783631	+	0.621227i	$0.786635\pi$
$984$	1467.59	+	671.329i	0.0475459	+	0.0217492i
$985$	−56193.3	−	32443.2i	−1.81773	−	1.04947i
$986$	291.554	−	504.986i	0.00941679	−	0.0163104i
$987$	−15127.5	−	2151.42i	−0.487857	−	0.0693826i
$988$	−5305.70	−	9189.73i	−0.170847	−	0.295915i
$989$			52211.4i			1.67869i
$990$	1159.76	+	1341.80i	0.0372319	+	0.0430760i
$991$	13431.5			0.430540			0.215270	−	0.976555i	$-0.430937\pi$
$991$	13431.5			0.430540			0.215270	+	0.976555i	$0.430937\pi$
$992$	1198.54	+	2075.93i	0.0383604	+	0.0664422i
$993$	−22451.7	−	31570.5i	−0.717506	−	1.00892i
$994$	−809.100	−	194.445i	−0.0258180	−	0.00620465i
$995$	13835.0	+	7987.67i	0.440805	+	0.254499i
$996$	14939.3	−	1417.16i	0.475270	−	0.0450848i
$997$	13651.7	−	7881.82i	0.433655	−	0.250371i	−0.267248	−	0.963628i	$-0.586114\pi$
$997$	13651.7	−	7881.82i	0.433655	−	0.250371i	0.700902	+	0.713257i	$0.252781\pi$
$998$		−	815.644i		−	0.0258705i
$999$	51023.6	−	14878.6i	1.61593	−	0.471210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.4.o.a.41.11	yes	44
3.2	odd	2		189.4.o.a.125.11		44
7.6	odd	2	inner	63.4.o.a.41.12	yes	44
9.2	odd	6	inner	63.4.o.a.20.12	yes	44
9.4	even	3		567.4.c.c.566.3		44
9.5	odd	6		567.4.c.c.566.42		44
9.7	even	3		189.4.o.a.62.12		44
21.20	even	2		189.4.o.a.125.12		44
63.13	odd	6		567.4.c.c.566.41		44
63.20	even	6	inner	63.4.o.a.20.11	✓	44
63.34	odd	6		189.4.o.a.62.11		44
63.41	even	6		567.4.c.c.566.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.11	✓	44	63.20	even	6	inner
63.4.o.a.20.12	yes	44	9.2	odd	6	inner
63.4.o.a.41.11	yes	44	1.1	even	1	trivial
63.4.o.a.41.12	yes	44	7.6	odd	2	inner
189.4.o.a.62.11		44	63.34	odd	6
189.4.o.a.62.12		44	9.7	even	3
189.4.o.a.125.11		44	3.2	odd	2
189.4.o.a.125.12		44	21.20	even	2
567.4.c.c.566.3		44	9.4	even	3
567.4.c.c.566.4		44	63.41	even	6
567.4.c.c.566.41		44	63.13	odd	6
567.4.c.c.566.42		44	9.5	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0847887 + 0.0489528i) q^{2} +(-5.17293 + 0.490712i) q^{3} +(-3.99521 + 6.91990i) q^{4} +(9.06347 - 15.6984i) q^{5} +(0.414584 - 0.294836i) q^{6} +(12.7516 - 13.4312i) q^{7} -1.56555i q^{8} +(26.5184 - 5.07683i) q^{9} +O(q^{10})\)	\(q+(-0.0847887 + 0.0489528i) q^{2} +(-5.17293 + 0.490712i) q^{3} +(-3.99521 + 6.91990i) q^{4} +(9.06347 - 15.6984i) q^{5} +(0.414584 - 0.294836i) q^{6} +(12.7516 - 13.4312i) q^{7} -1.56555i q^{8} +(26.5184 - 5.07683i) q^{9} +1.77473i q^{10} +(32.0537 - 18.5062i) q^{11} +(17.2713 - 37.7567i) q^{12} +(-16.3673 - 9.44964i) q^{13} +(-0.423698 + 1.76304i) q^{14} +(-39.1813 + 85.6542i) q^{15} +(-31.8850 - 55.2265i) q^{16} -62.5187 q^{17} +(-1.99994 + 1.72861i) q^{18} -70.2680i q^{19} +(72.4209 + 125.437i) q^{20} +(-59.3723 + 75.7359i) q^{21} +(-1.81186 + 3.13823i) q^{22} +(140.692 + 81.2288i) q^{23} +(0.768234 + 8.09848i) q^{24} +(-101.793 - 176.311i) q^{25} +1.85034 q^{26} +(-134.687 + 39.2750i) q^{27} +(41.9972 + 141.900i) q^{28} +(82.5015 - 47.6323i) q^{29} +(-0.870879 - 9.18054i) q^{30} +(110.611 + 63.8612i) q^{31} +(16.2534 + 9.38392i) q^{32} +(-156.730 + 111.460i) q^{33} +(5.30088 - 3.06046i) q^{34} +(-95.2742 - 321.913i) q^{35} +(-70.8153 + 203.788i) q^{36} -378.832 q^{37} +(3.43981 + 5.95793i) q^{38} +(89.3037 + 40.8507i) q^{39} +(-24.5766 - 14.1893i) q^{40} +(99.1937 - 171.809i) q^{41} +(1.32662 - 9.32799i) q^{42} +(160.692 + 278.327i) q^{43} +295.744i q^{44} +(160.651 - 462.310i) q^{45} -15.9055 q^{46} +(79.3885 + 137.505i) q^{47} +(192.039 + 270.036i) q^{48} +(-17.7932 - 342.538i) q^{49} +(17.2618 + 9.96610i) q^{50} +(323.405 - 30.6786i) q^{51} +(130.781 - 75.5066i) q^{52} -191.780i q^{53} +(9.49728 - 9.92336i) q^{54} -670.922i q^{55} +(-21.0272 - 19.9633i) q^{56} +(34.4813 + 363.491i) q^{57} +(-4.66346 + 8.07736i) q^{58} +(-106.918 + 185.187i) q^{59} +(-436.181 - 613.337i) q^{60} +(-190.929 + 110.233i) q^{61} -12.5047 q^{62} +(269.964 - 420.911i) q^{63} +508.323 q^{64} +(-296.688 + 171.293i) q^{65} +(7.83266 - 17.1230i) q^{66} +(68.2947 - 118.290i) q^{67} +(249.775 - 432.623i) q^{68} +(-767.652 - 351.151i) q^{69} +(23.8367 + 22.6306i) q^{70} +458.924i q^{71} +(-7.94804 - 41.5159i) q^{72} +967.869i q^{73} +(32.1207 - 18.5449i) q^{74} +(613.086 + 862.091i) q^{75} +(486.248 + 280.735i) q^{76} +(160.176 - 666.503i) q^{77} +(-9.57170 + 0.907986i) q^{78} +(298.318 + 516.702i) q^{79} -1155.96 q^{80} +(677.452 - 269.259i) q^{81} +19.4232i q^{82} +(180.715 + 313.007i) q^{83} +(-286.880 - 713.431i) q^{84} +(-566.636 + 981.443i) q^{85} +(-27.2498 - 15.7327i) q^{86} +(-403.401 + 286.883i) q^{87} +(-28.9724 - 50.1817i) q^{88} +35.4987 q^{89} +(9.01000 + 47.0630i) q^{90} +(-335.629 + 99.3336i) q^{91} +(-1124.19 + 649.052i) q^{92} +(-603.519 - 276.071i) q^{93} +(-13.4625 - 7.77258i) q^{94} +(-1103.09 - 636.872i) q^{95} +(-88.6826 - 40.5666i) q^{96} +(-1151.63 + 664.894i) q^{97} +(18.2769 + 28.1723i) q^{98} +(756.060 - 653.486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q - 6 q^{2} + 78 q^{4} + 5 q^{7} - 18 q^{11} + 204 q^{14} + 66 q^{15} - 242 q^{16} - 210 q^{18} - 57 q^{21} - 34 q^{22} - 102 q^{23} - 352 q^{25} + 300 q^{28} + 246 q^{29} - 144 q^{30} + 1068 q^{32} - 1818 q^{36} + 328 q^{37} - 798 q^{39} - 1158 q^{42} - 170 q^{43} + 968 q^{46} - 79 q^{49} + 288 q^{50} - 204 q^{51} + 1212 q^{56} + 324 q^{57} - 538 q^{58} + 5316 q^{60} + 783 q^{63} - 808 q^{64} + 4350 q^{65} - 590 q^{67} + 384 q^{70} + 4284 q^{72} - 5304 q^{74} - 2787 q^{77} + 612 q^{78} - 302 q^{79} - 3720 q^{81} + 7050 q^{84} - 612 q^{85} - 13692 q^{86} + 1294 q^{88} + 210 q^{91} - 10194 q^{92} - 4266 q^{93} + 6336 q^{95} + 1014 q^{99}+O(q^{100}) \) 44 * q - 6 * q^2 + 78 * q^4 + 5 * q^7 - 18 * q^11 + 204 * q^14 + 66 * q^15 - 242 * q^16 - 210 * q^18 - 57 * q^21 - 34 * q^22 - 102 * q^23 - 352 * q^25 + 300 * q^28 + 246 * q^29 - 144 * q^30 + 1068 * q^32 - 1818 * q^36 + 328 * q^37 - 798 * q^39 - 1158 * q^42 - 170 * q^43 + 968 * q^46 - 79 * q^49 + 288 * q^50 - 204 * q^51 + 1212 * q^56 + 324 * q^57 - 538 * q^58 + 5316 * q^60 + 783 * q^63 - 808 * q^64 + 4350 * q^65 - 590 * q^67 + 384 * q^70 + 4284 * q^72 - 5304 * q^74 - 2787 * q^77 + 612 * q^78 - 302 * q^79 - 3720 * q^81 + 7050 * q^84 - 612 * q^85 - 13692 * q^86 + 1294 * q^88 + 210 * q^91 - 10194 * q^92 - 4266 * q^93 + 6336 * q^95 + 1014 * q^99

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