LMFDB - Embedded newform 63.4.o.a.20.12

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			20.12
Character	$\chi$	$=$	63.20
Dual form			63.4.o.a.41.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0847887 - 0.0489528i) q^{2} +(5.17293 + 0.490712i) q^{3} +(-3.99521 - 6.91990i) q^{4} +(-9.06347 - 15.6984i) q^{5} +(-0.414584 - 0.294836i) q^{6} +(-18.0075 - 4.32762i) q^{7} +1.56555i q^{8} +(26.5184 + 5.07683i) q^{9} +O(q^{10})$	\(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} +(-18.0075 - 4.32762i) 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} +(1.31499 + 1.24845i) 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} +(-91.0282 - 31.2230i) 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} +(6.18971 + 7.10344i) 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} +(305.543 + 155.860i) 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} +(6.77511 - 28.1917i) 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} +(-455.561 - 206.183i) 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} +(7.68035 - 31.9585i) 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} +(-497.120 - 471.968i) 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} +(147.616 + 754.648i) 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 $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

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

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	0.484936	−	0.874549i	$-0.338843\pi$
$2$	−0.0847887	−	0.0489528i	−0.0299773	−	0.0173074i	−0.514914	+	0.857242i	$0.672176\pi$
$3$	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	−0.912402	−	0.409296i	$-0.865774\pi$
$5$	−9.06347	−	15.6984i	−0.810661	−	1.40411i	0.101740	−	0.994811i	$-0.467559\pi$
$6$	−0.414584	−	0.294836i	−0.0282089	−	0.0200611i
$7$	−18.0075	−	4.32762i	−0.972316	−	0.233670i
$7$	−18.0075	−	4.32762i	−0.972316	−	0.233670i
$8$			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	0.870195	−	0.492707i	$-0.163993\pi$
$11$	32.0537	+	18.5062i	0.878595	+	0.507257i	0.00840042	+	0.999965i	$0.497326\pi$
$12$	−17.2713	−	37.7567i	−0.415482	−	0.908284i
$13$	16.3673	−	9.44964i	0.349189	−	0.201605i	−0.315139	−	0.949046i	$-0.602051\pi$
$13$	16.3673	−	9.44964i	0.349189	−	0.201605i	0.664328	+	0.747441i	$0.268718\pi$
$14$	1.31499	+	1.24845i	0.0251032	+	0.0238331i
$15$	−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	$-0.352859\pi$
$17$	62.5187			0.891941			0.445971	+	0.895048i	$0.352859\pi$
$18$	−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
$21$	−91.0282	−	31.2230i	−0.945903	−	0.324448i
$22$	−1.81186	−	3.13823i	−0.0175586	−	0.0304124i
$23$	140.692	−	81.2288i	1.27550	−	0.736408i	0.299479	−	0.954103i	$-0.403187\pi$
$23$	140.692	−	81.2288i	1.27550	−	0.736408i	0.976017	+	0.217695i	$0.0698539\pi$
$24$	−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	0.740316	−	0.672259i	$-0.234676\pi$
$29$	82.5015	+	47.6323i	0.528281	+	0.305003i	−0.212035	+	0.977262i	$0.568009\pi$
$30$	−0.870879	+	9.18054i	−0.00530000	+	0.0558710i
$31$	−110.611	+	63.8612i	−0.640848	+	0.369994i	−0.784941	−	0.619570i	$-0.787307\pi$
$31$	−110.611	+	63.8612i	−0.640848	+	0.369994i	0.144093	+	0.989564i	$0.453973\pi$
$32$	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	$-0.290000\pi$
$41$	−99.1937	−	171.809i	−0.377840	−	0.654439i	−0.990748	+	0.135716i	$0.956667\pi$
$42$	6.18971	+	7.10344i	0.0227403	+	0.0260972i
$43$	160.692	−	278.327i	0.569892	−	0.987081i	−0.426685	−	0.904401i	$-0.640319\pi$
$43$	160.692	−	278.327i	0.569892	−	0.987081i	0.996576	−	0.0826806i	$-0.0263481\pi$
$44$		−	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	$-0.912575\pi$
$47$	−79.3885	+	137.505i	−0.246383	+	0.426748i	0.716136	+	0.697960i	$0.245909\pi$
$48$	−192.039	+	270.036i	−0.577468	+	0.812008i
$49$	305.543	+	155.860i	0.890797	+	0.454401i
$50$	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	$0.0799440\pi$
$53$			191.780i			0.497039i	−0.968627	+	0.248519i	$0.920056\pi$
$54$	−9.49728	−	9.92336i	−0.0239336	−	0.0250074i
$55$		−	670.922i		−	1.64486i
$56$	6.77511	−	28.1917i	0.0161672	−	0.0672728i
$57$	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	$-0.0908551\pi$
$59$	106.918	+	185.187i	0.235924	+	0.408632i	−0.723617	+	0.690202i	$0.757522\pi$
$60$	−436.181	+	613.337i	−0.938513	+	1.31969i
$61$	190.929	+	110.233i	0.400754	+	0.231375i	0.686809	−	0.726838i	$-0.259011\pi$
$61$	190.929	+	110.233i	0.400754	+	0.231375i	−0.286055	+	0.958213i	$0.592344\pi$
$62$	12.5047			0.0256145
$63$	−455.561	−	206.183i	−0.911036	−	0.412327i
$64$	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	0.921549	−	0.388262i	$-0.126924\pi$
$67$	68.2947	+	118.290i	0.124530	+	0.215693i	−0.797019	+	0.603954i	$0.793591\pi$
$68$	−249.775	−	432.623i	−0.445436	−	0.771518i
$69$	767.652	−	351.151i	1.33934	−	0.612662i
$70$	7.68035	−	31.9585i	0.0131140	−	0.0545681i
$71$		−	458.924i		−	0.767102i	−0.923520	−	0.383551i	$-0.874701\pi$
$71$		−	458.924i		−	0.767102i	0.923520	−	0.383551i	$-0.125299\pi$
$72$	−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
$77$	−497.120	−	471.968i	−0.735742	−	0.698516i
$78$	−9.57170	−	0.907986i	−0.0138946	−	0.00131807i
$79$	298.318	−	516.702i	0.424853	−	0.735868i	−0.571553	−	0.820565i	$-0.693659\pi$
$79$	298.318	−	516.702i	0.424853	−	0.735868i	0.996407	+	0.0846971i	$0.0269923\pi$
$80$	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	$-0.910149\pi$
$83$	−180.715	+	313.007i	−0.238988	+	0.413940i	0.721436	+	0.692481i	$0.243482\pi$
$84$	147.616	+	754.648i	0.191741	+	0.980225i
$85$	−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	$-0.506729\pi$
$89$	−35.4987			−0.0422792			−0.0211396	+	0.999777i	$0.506729\pi$
$90$	−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	$-0.0883051\pi$
$97$	1151.63	+	664.894i	1.20547	+	0.695977i	0.243701	+	0.969850i	$0.421638\pi$
$98$	−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	$-0.982164\pi$
$101$	−457.491	+	792.398i	−0.450714	+	0.780659i	0.547717	+	0.836664i	$0.315497\pi$
$102$	−25.9193	−	18.4328i	−0.0251607	−	0.0178933i
$103$	721.873	−	416.774i	0.690566	−	0.398698i	−0.113258	−	0.993566i	$-0.536129\pi$
$103$	721.873	−	416.774i	0.690566	−	0.398698i	0.803824	+	0.594867i	$0.202795\pi$
$104$	14.7939	+	25.6238i	0.0139487	+	0.0241598i
$105$	334.880	+	1711.98i	0.311247	+	1.59117i
$106$	9.38818	−	16.2608i	0.00860246	−	0.0148999i
$107$			1686.33i			1.52358i	0.647822	+	0.761792i	$0.275680\pi$
$107$			1686.33i			1.52358i	−0.647822	+	0.761792i	$0.724320\pi$
$108$	−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
$112$	813.170	−	856.507i	0.686048	−	0.722610i
$113$	1245.30	−	718.974i	1.03671	−	0.598543i	0.117809	−	0.993036i	$-0.462413\pi$
$113$	1245.30	−	718.974i	1.03671	−	0.598543i	0.918899	+	0.394493i	$0.129080\pi$
$114$	−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
$119$	−1125.81	−	270.557i	−0.867249	−	0.208420i
$120$	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
$126$	28.5332	+	39.7829i	0.0201741	+	0.0281281i
$127$	−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	−0.955541	−	0.294858i	$-0.904728\pi$
$131$	−1099.22	−	1903.91i	−0.733125	−	1.26981i	0.222416	−	0.974952i	$-0.428606\pi$
$132$	145.125	−	1529.87i	0.0956934	−	1.00877i
$133$	−304.093	+	1265.35i	−0.198257	+	0.824963i
$134$		−	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	0.952720	−	0.303848i	$-0.0982716\pi$
$137$	1869.64	+	1079.44i	1.16594	+	0.673156i	0.213220	+	0.977004i	$0.431605\pi$
$138$	−82.2780	−	7.80501i	−0.0507534	−	0.00481454i
$139$	−2521.54	+	1455.81i	−1.53866	+	0.888348i	−0.539746	+	0.841828i	$0.681480\pi$
$139$	−2521.54	+	1455.81i	−1.53866	+	0.888348i	−0.998917	+	0.0465196i	$0.985187\pi$
$140$	1846.96	−	1945.40i	1.11498	−	1.17440i
$141$	−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
$147$	1504.07	+	956.185i	0.843903	+	0.536495i
$148$	1513.51	+	2621.48i	0.840608	+	1.45598i
$149$	−230.641	+	133.161i	−0.126811	+	0.0732144i	−0.562064	−	0.827094i	$-0.689992\pi$
$149$	−230.641	+	133.161i	−0.126811	+	0.0732144i	0.435253	+	0.900308i	$0.356659\pi$
$150$	94.1845	−	43.0834i	0.0512675	−	0.0234516i
$151$	467.757	−	810.180i	0.252090	−	0.436632i	−0.712011	−	0.702168i	$-0.752215\pi$
$151$	467.757	−	810.180i	0.252090	−	0.436632i	0.964101	+	0.265536i	$0.0855488\pi$
$152$	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	$-0.749118\pi$
$157$	−872.747	+	503.881i	−0.443648	+	0.256141i	0.261496	+	0.965205i	$0.415784\pi$
$158$	−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	$-0.0429390\pi$
$167$	817.899	+	1416.64i	0.378987	+	0.656425i	−0.611928	+	0.790914i	$0.709606\pi$
$168$	48.8812	−	142.509i	0.0224480	−	0.0654453i
$169$	−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	$-0.777120\pi$
$173$	399.759	−	692.402i	0.175683	−	0.304291i	0.940397	+	0.340078i	$0.110453\pi$
$174$	−20.1601	−	44.0720i	−0.00878353	−	0.0192017i
$175$	2596.05	−	2734.40i	1.12139	−	1.18115i
$176$	−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	$-0.789618\pi$
$179$		−	2940.19i		−	1.22771i	0.789418	−	0.613856i	$-0.210382\pi$
$180$	−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	$0.975340\pi$
$182$	33.3202	+	8.00759i	0.0135706	+	0.00326133i
$183$	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
$189$	−2255.41	−	1290.12i	−0.868025	−	0.496520i
$190$	124.707			0.0476167
$191$	1586.09	+	915.732i	0.600868	+	0.346911i	0.769383	−	0.638788i	$-0.220564\pi$
$191$	1586.09	+	915.732i	0.600868	+	0.346911i	−0.168515	+	0.985699i	$0.553897\pi$
$192$	2629.52	+	249.440i	0.988381	+	0.0937592i
$193$	190.008	+	329.104i	0.0708657	+	0.122743i	0.899281	−	0.437371i	$-0.144090\pi$
$193$	190.008	+	329.104i	0.0708657	+	0.122743i	−0.828415	+	0.560114i	$0.810757\pi$
$194$	−65.0968	−	112.751i	−0.0240911	−	0.0417270i
$195$	−1450.69	−	1031.68i	−0.532750	−	0.378871i
$196$	−142.175	−	2737.02i	−0.0518132	−	0.997457i
$197$			3579.56i			1.29458i	0.762243	+	0.647291i	$0.224098\pi$
$197$			3579.56i			1.29458i	−0.762243	+	0.647291i	$0.775902\pi$
$198$	−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
$203$	−1279.52	−	1214.78i	−0.442386	−	0.420003i
$204$	−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
$210$	55.4123	−	161.550i	0.0182086	−	0.0530858i
$211$	−418.581	−	725.004i	−0.136570	−	0.236547i	0.789626	−	0.613588i	$-0.210275\pi$
$211$	−418.581	−	725.004i	−0.136570	−	0.236547i	−0.926196	+	0.377042i	$0.876941\pi$
$212$	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	$-0.387782\pi$
$223$	−981.825	−	566.857i	−0.294834	−	0.170222i	−0.640120	+	0.768275i	$0.721115\pi$
$224$	−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	−0.487349	−	0.873207i	$-0.662036\pi$
$227$	1752.96	−	3036.21i	0.512545	−	0.887754i	0.999894	−	0.0145471i	$-0.00463065\pi$
$228$	−2653.09	+	1213.62i	−0.770635	+	0.352516i
$229$	2721.44	−	1571.23i	0.785319	−	0.453404i	−0.0529930	−	0.998595i	$-0.516876\pi$
$229$	2721.44	−	1571.23i	0.785319	−	0.453404i	0.838312	+	0.545191i	$0.183543\pi$
$230$	144.159	+	249.691i	0.0413285	+	0.0715831i
$231$	−2339.97	−	2685.40i	−0.666488	−	0.764875i
$232$	−74.5707	+	129.160i	−0.0211026	+	0.0365508i
$233$		−	6882.00i		−	1.93500i	−0.252872	−	0.967500i	$-0.581375\pi$
$233$		−	6882.00i		−	1.93500i	0.252872	−	0.967500i	$-0.418625\pi$
$234$	−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
$238$	82.2112	+	78.0516i	0.0223906	+	0.0212577i
$239$	−1036.14	+	598.217i	−0.280429	+	0.161906i	−0.633617	−	0.773646i	$-0.718431\pi$
$239$	−1036.14	+	598.217i	−0.280429	+	0.161906i	0.353189	+	0.935552i	$0.385097\pi$
$240$	5979.68	+	567.241i	1.60828	+	0.152563i
$241$	−3790.59	−	2188.50i	−1.01317	−	0.584953i	−0.101051	−	0.994881i	$-0.532220\pi$
$241$	−3790.59	−	2188.50i	−1.01317	−	0.584953i	−0.912118	+	0.409928i	$0.865554\pi$
$242$		−	3.81033i		−	0.00101214i
$243$	3372.28	+	1725.29i	0.890255	+	0.455463i
$244$		−	1761.62i		−	0.462196i
$245$	−322.537	−	6209.17i	−0.0841067	−	1.61914i
$246$	−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	$-0.759391\pi$
$251$	−5787.19			−1.45532			−0.727658	+	0.685940i	$0.759391\pi$
$252$	393.294	+	3976.18i	0.0983143	+	0.993951i
$253$	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	$-0.0826848\pi$
$257$	1074.45	+	1861.00i	0.260786	+	0.451695i	−0.705665	+	0.708546i	$0.749351\pi$
$258$	−148.681	+	68.0122i	−0.0358779	+	0.0164118i
$259$	6821.84	+	1639.44i	1.63663	+	0.393320i
$260$			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	0.370917	−	0.928666i	$-0.379043\pi$
$263$	−1057.21	−	610.380i	−0.247872	−	0.143109i	−0.618789	+	0.785557i	$0.712377\pi$
$264$	−174.497	+	245.369i	−0.0406801	+	0.0572024i
$265$	3010.64	−	1738.20i	0.697895	−	0.402930i
$266$	87.7263	−	92.4015i	0.0202212	−	0.0212989i
$267$	−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	$-0.332556\pi$
$269$	4430.56			1.00422			0.502112	+	0.864803i	$0.332556\pi$
$270$	−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
$273$	−1784.93	+	349.149i	−0.395710	+	0.0774045i
$274$	−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	−0.651124	−	0.758971i	$-0.725702\pi$
$277$	1529.33	−	2648.87i	0.331727	−	0.574567i	0.982850	+	0.184404i	$0.0590356\pi$
$278$	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	−0.00633670	−	0.999980i	$-0.502017\pi$
$281$	−4124.03	−	2381.01i	−0.875513	−	0.505478i	−0.869176	+	0.494502i	$0.835350\pi$
$282$	73.4547	−	33.6008i	0.0155112	−	0.00709538i
$283$	−3567.54	+	2059.72i	−0.749358	+	0.432642i	−0.825462	−	0.564458i	$-0.809085\pi$
$283$	−3567.54	+	2059.72i	−0.749358	+	0.432642i	0.0761041	+	0.997100i	$0.475752\pi$
$284$	−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	$-0.0765041\pi$
$293$	1401.70	+	2427.81i	0.279482	+	0.484076i	−0.691774	+	0.722114i	$0.743171\pi$
$294$	−80.7204	−	154.702i	−0.0160126	−	0.0306885i
$295$	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
$301$	−4098.17	+	4316.57i	−0.784766	+	0.826588i
$302$	−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	$0.880033\pi$
$308$	−1279.87	+	5325.63i	−0.236777	+	0.985247i
$309$	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	$-0.0165155\pi$
$311$	2492.25	+	4316.71i	0.454413	+	0.787067i	−0.544241	+	0.838929i	$0.683182\pi$
$312$	63.9539	+	139.809i	0.0116047	+	0.0253691i
$313$	−699.706	−	403.976i	−0.126357	−	0.0729522i	0.435489	−	0.900194i	$-0.356575\pi$
$313$	−699.706	−	403.976i	−0.126357	−	0.0729522i	−0.561846	+	0.827242i	$0.689909\pi$
$314$	98.6654			0.0177325
$315$	892.221	+	9020.30i	0.159590	+	1.61345i
$316$	−4767.37			−0.848689
$317$	2061.65	+	1190.29i	0.365280	+	0.210894i	0.671394	−	0.741100i	$-0.265696\pi$
$317$	2061.65	+	1190.29i	0.365280	+	0.210894i	−0.306115	+	0.951995i	$0.599029\pi$
$318$	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
$322$	286.419	+	68.8330i	0.0495699	+	0.0119128i
$323$		−	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
$329$	2024.66	−	2132.56i	0.339280	−	0.357362i
$330$	−197.812	+	278.154i	−0.0329975	+	0.0463995i
$331$	3727.74	−	6456.64i	0.619019	−	1.07217i	−0.370646	−	0.928774i	$-0.620864\pi$
$331$	3727.74	−	6456.64i	0.619019	−	1.07217i	0.989665	−	0.143398i	$-0.0458029\pi$
$332$	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
$336$	4626.77	−	4031.62i	0.751223	−	0.654592i
$337$	978.259	+	1694.39i	0.158128	+	0.273886i	0.934194	−	0.356766i	$-0.116121\pi$
$337$	978.259	+	1694.39i	0.158128	+	0.273886i	−0.776066	+	0.630652i	$0.782787\pi$
$338$	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	−0.589340	−	0.807885i	$-0.700612\pi$
$347$	−1191.69	+	688.024i	−0.184361	+	0.106441i	0.404979	+	0.914326i	$0.367279\pi$
$348$	373.531	−	3937.65i	0.0575384	−	0.606552i
$349$	−8098.04	−	4675.41i	−1.24206	−	0.717103i	−0.272546	−	0.962143i	$-0.587866\pi$
$349$	−8098.04	−	4675.41i	−1.24206	−	0.717103i	−0.969513	+	0.245040i	$0.921199\pi$
$350$	−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	$-0.849603\pi$
$353$	−338.836	+	586.881i	−0.0510890	+	0.0884887i	0.839350	+	0.543591i	$0.182936\pi$
$354$	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
$357$	−5690.96	−	1952.02i	−0.843690	−	0.289389i
$358$	−143.931	+	249.295i	−0.0212485	+	0.0368035i
$359$		−	1662.36i		−	0.244390i	−0.992506	−	0.122195i	$-0.961007\pi$
$359$		−	1662.36i		−	0.244390i	0.992506	−	0.122195i	$-0.0389933\pi$
$360$	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
$364$	2028.28	+	1925.66i	0.292063	+	0.277286i
$365$	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	$-0.263415\pi$
$367$	2653.41	+	1531.94i	0.377402	+	0.217893i	−0.299285	+	0.954164i	$0.596748\pi$
$368$			10359.9i			1.46752i
$369$	−1758.22	−	5059.68i	−0.248046	−	0.713811i
$370$		−	672.324i		−	0.0944661i
$371$	829.953	−	3453.49i	0.116143	−	0.483279i
$372$	4321.57	+	3073.33i	0.602320	+	0.428346i
$373$	3900.06	+	6755.10i	0.541387	+	0.937711i	0.998825	+	0.0484687i	$0.0154341\pi$
$373$	3900.06	+	6755.10i	0.541387	+	0.937711i	−0.457437	+	0.889242i	$0.651233\pi$
$374$	−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
$378$	128.078	+	219.796i	0.0174276	+	0.0299076i
$379$	−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	0.954588	+	0.297928i	$0.0962955\pi$
$383$	5511.46	+	9546.14i	0.735307	+	1.27359i	−0.219281	+	0.975662i	$0.570371\pi$
$384$	−846.527	−	602.017i	−0.112498	−	0.0800040i
$385$	−2903.50	+	12081.7i	−0.384353	+	1.59932i
$386$		−	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	0.967675	−	0.252200i	$-0.0811541\pi$
$389$	9460.70	+	5462.14i	1.23310	+	0.711931i	0.265426	+	0.964131i	$0.414487\pi$
$390$	72.4989	+	158.490i	0.00941314	+	0.0205781i
$391$	8795.90	−	5078.32i	1.13767	−	0.656833i
$392$	−244.006	+	478.343i	−0.0314392	+	0.0616326i
$393$	−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
$399$	−2193.98	+	6396.37i	−0.275279	+	0.802554i
$400$	−6491.34	−	11243.3i	−0.811418	−	1.40542i
$401$	−10633.1	+	6139.03i	−1.32417	+	0.764510i	−0.984391	−	0.175996i	$-0.943685\pi$
$401$	−10633.1	+	6139.03i	−1.32417	+	0.764510i	−0.339778	+	0.940506i	$0.610352\pi$
$402$	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	$-0.650318\pi$
$409$	735.497	−	424.639i	0.0889193	−	0.0513376i	0.543800	+	0.839215i	$0.316985\pi$
$410$	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	$-0.284771\pi$
$419$	−3109.74	−	5386.23i	−0.362579	−	0.628006i	−0.988385	+	0.151973i	$0.951437\pi$
$420$	10508.8	−	9157.07i	1.22090	−	1.06386i
$421$	−1012.07	+	1752.95i	−0.117162	+	0.202930i	−0.918642	−	0.395091i	$-0.870713\pi$
$421$	−1012.07	+	1752.95i	−0.117162	+	0.202930i	0.801480	+	0.598021i	$0.204046\pi$
$422$			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
$427$	−2961.12	−	2811.30i	−0.335594	−	0.318614i
$428$	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	$0.118697\pi$
$431$			6519.65i			0.728633i	−0.931275	+	0.364316i	$0.881303\pi$
$432$	−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	$0.553334\pi$
$434$	−225.179	−	54.1157i	−0.0249054	−	0.00598534i
$435$	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	$-0.358951\pi$
$439$	−1280.80	−	739.472i	−0.139247	−	0.0803942i	−0.568005	+	0.823025i	$0.692285\pi$
$440$	1050.36			0.113805
$441$	7311.25	+	5684.34i	0.789467	+	0.613794i
$442$	−115.681			−0.0124488
$443$	13484.2	+	7785.09i	1.44617	+	0.834945i	0.998250	−	0.0591295i	$-0.0188325\pi$
$443$	13484.2	+	7785.09i	1.44617	+	0.834945i	0.447918	+	0.894075i	$0.352166\pi$
$444$	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
$448$	−9153.65	−	2199.83i	−0.965333	−	0.231991i
$449$			6120.30i			0.643284i	0.946861	+	0.321642i	$0.104235\pi$
$449$			6120.30i			0.643284i	−0.946861	+	0.321642i	$0.895765\pi$
$450$	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
$455$	4601.34	+	4368.52i	0.474097	+	0.450109i
$456$	569.064	+	53.9822i	0.0584405	+	0.00554375i
$457$	−3498.22	+	6059.10i	−0.358074	+	0.620203i	−0.987639	−	0.156745i	$-0.949900\pi$
$457$	−3498.22	+	6059.10i	−0.358074	+	0.620203i	0.629565	+	0.776948i	$0.283233\pi$
$458$	−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	$-0.774038\pi$
$461$	1833.17	−	3175.15i	0.185205	−	0.320784i	0.943646	+	0.330958i	$0.107372\pi$
$462$	66.9452	+	342.239i	0.00674150	+	0.0344641i
$463$	3513.71	+	6085.92i	0.352691	+	0.610878i	0.986720	−	0.162431i	$-0.0519335\pi$
$463$	3513.71	+	6085.92i	0.352691	+	0.610878i	−0.634029	+	0.773309i	$0.718600\pi$
$464$	−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	$-0.269580\pi$
$467$	13367.8			1.32460			0.662301	+	0.749238i	$0.269580\pi$
$468$	−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	$-0.941594\pi$
$479$	−3497.20	+	6057.33i	−0.333593	+	0.577800i	0.649620	+	0.760259i	$0.274928\pi$
$480$	−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
$483$	−15343.2	+	3001.27i	−1.44542	+	0.282738i
$484$	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
$490$	−276.609	+	542.256i	−0.0255018	+	0.0499932i
$491$	−12925.9	+	7462.77i	−1.18806	+	0.685927i	−0.957865	−	0.287218i	$-0.907270\pi$
$491$	−12925.9	+	7462.77i	−1.18806	+	0.685927i	−0.230195	+	0.973145i	$0.573936\pi$
$492$	−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
$497$	−1986.05	+	8264.09i	−0.179248	+	0.745866i
$498$	167.207	−	76.4866i	0.0150457	−	0.00688242i
$499$	−4165.46	−	7214.80i	−0.373691	−	0.647252i	0.616439	−	0.787402i	$-0.288575\pi$
$499$	−4165.46	−	7214.80i	−0.373691	−	0.647252i	−0.990130	+	0.140151i	$0.955241\pi$
$500$	−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	$-0.258719\pi$
$503$	15511.0			1.37495			0.687475	+	0.726208i	$0.258719\pi$
$504$	322.790	−	713.203i	0.0285282	−	0.0630329i
$505$	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	$-0.217220\pi$
$509$	−1816.15	−	3145.66i	−0.158152	−	0.273927i	−0.934202	+	0.356744i	$0.883887\pi$
$510$	−54.4462	+	573.955i	−0.00472729	+	0.0498337i
$511$	4188.57	−	17428.9i	0.362606	−	1.50883i
$512$			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
$518$	−498.159	−	472.954i	−0.0422546	−	0.0401166i
$519$	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	$-0.507117\pi$
$521$	−531.760			−0.0447156			−0.0223578	+	0.999750i	$0.507117\pi$
$522$	−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
$525$	14771.0	−	12870.9i	1.22792	−	1.06997i
$526$	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
$546$	168.433	+	57.7733i	0.0132020	+	0.00452833i
$547$	6024.28	−	10434.4i	0.470895	−	0.815614i	−0.528551	−	0.848902i	$-0.677264\pi$
$547$	6024.28	−	10434.4i	0.470895	−	0.815614i	0.999446	+	0.0332874i	$0.0105977\pi$
$548$		−	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
$553$	−7608.07	+	8013.53i	−0.585042	+	0.616221i
$554$	−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	$-0.969117\pi$
$557$		−	2546.80i		−	0.193737i	0.995297	−	0.0968684i	$-0.0308826\pi$
$558$	331.605	+	63.4844i	0.0251577	+	0.00481632i
$559$		−	6073.94i		−	0.459571i
$560$	−20815.9	−	5002.54i	−1.57077	−	0.377493i
$561$	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	−0.868452	−	0.495772i	$-0.834885\pi$
$563$	−11536.2	−	19981.3i	−0.863578	−	1.49576i	0.00487467	−	0.999988i	$-0.498448\pi$
$564$	6562.87	+	622.563i	0.489976	+	0.0464799i
$565$	−22573.5	−	13032.8i	−1.68084	−	0.970432i
$566$	403.316			0.0299517
$567$	−11034.0	−	7780.45i	−0.817256	−	0.576275i
$568$	718.468			0.0530744
$569$	−5471.39	−	3158.91i	−0.403115	−	0.232739i	0.284712	−	0.958613i	$-0.408102\pi$
$569$	−5471.39	−	3158.91i	−0.403115	−	0.232739i	−0.687827	+	0.725874i	$0.741435\pi$
$570$	645.098	+	61.1950i	0.0474039	+	0.00449680i
$571$	−9276.07	−	16066.6i	−0.679845	−	1.17753i	−0.975027	−	0.222085i	$-0.928714\pi$
$571$	−9276.07	−	16066.6i	−0.679845	−	1.17753i	0.295182	−	0.955441i	$-0.404620\pi$
$572$	−2794.68	−	4840.53i	−0.204286	−	0.353833i
$573$	7755.39	+	5515.33i	0.565421	+	0.402105i
$574$	84.0564	−	349.765i	0.00611228	−	0.0254336i
$575$			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
$581$	4608.81	−	4854.43i	0.329097	−	0.346636i
$582$	−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	−0.343527	−	0.939143i	$-0.611622\pi$
$587$	9124.16	−	15803.5i	0.641558	−	1.11121i	0.985085	−	0.172068i	$-0.0550448\pi$
$588$	607.625	−	14228.2i	0.0426157	−	0.997892i
$589$	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	$-0.383549\pi$
$593$	10331.8			0.715473			0.357736	+	0.933823i	$0.383549\pi$
$594$	−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	−0.613129	−	0.789983i	$-0.710089\pi$
$599$	−3453.17	+	1993.69i	−0.235547	+	0.135993i	0.377581	+	0.925976i	$0.376756\pi$
$600$	−1349.65	−	959.816i	−0.0918319	−	0.0653072i
$601$	15935.6	+	9200.43i	1.08158	+	0.624448i	0.931321	−	0.364199i	$-0.118657\pi$
$601$	15935.6	+	9200.43i	1.08158	+	0.624448i	0.150255	+	0.988647i	$0.451990\pi$
$602$	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	$-0.823834\pi$
$607$	−12276.2	+	7087.68i	−0.820883	+	0.473937i	0.0298377	+	0.999555i	$0.490501\pi$
$608$	−659.389	−	1142.10i	−0.0439832	−	0.0761811i
$609$	−6022.74	−	6911.82i	−0.400745	−	0.459903i
$610$	−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
$616$	738.889	−	778.267i	0.0483290	−	0.0509047i
$617$	2799.72	−	1616.42i	0.182678	−	0.105469i	−0.405872	−	0.913930i	$-0.633032\pi$
$617$	2799.72	−	1616.42i	0.182678	−	0.105469i	0.588550	+	0.808460i	$0.299699\pi$
$618$	−422.157	−	40.0464i	−0.0274784	−	0.00260664i
$619$	−18943.3	−	10936.9i	−1.23004	−	0.710166i	−0.263005	−	0.964795i	$-0.584713\pi$
$619$	−18943.3	−	10936.9i	−1.23004	−	0.710166i	−0.967039	+	0.254629i	$0.918047\pi$
$620$		−	18499.5i		−	1.19832i
$621$	22139.6	−	5414.74i	1.43065	−	0.349897i
$622$		−	488.010i		−	0.0314589i
$623$	639.244	+	153.625i	0.0411088	+	0.00987937i
$624$	−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
$630$	365.919	−	808.496i	0.0231405	−	0.0511290i
$631$	−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
$637$	6473.73	−	336.280i	0.402666	−	0.0209166i
$638$		−	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	0.858375	−	0.513022i	$-0.171474\pi$
$641$	13685.3	+	7901.22i	0.843272	+	0.486864i	−0.0151029	+	0.999886i	$0.504808\pi$
$642$	497.190	−	699.125i	0.0305647	−	0.0429786i
$643$	10980.9	−	6339.83i	0.673476	−	0.388831i	−0.123917	−	0.992293i	$-0.539546\pi$
$643$	10980.9	−	6339.83i	0.673476	−	0.388831i	0.797392	+	0.603461i	$0.206212\pi$
$644$	17435.1	+	16552.9i	1.06683	+	1.01285i
$645$	−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	$-0.716630\pi$
$647$	−20710.7			−1.25846			−0.629230	+	0.777219i	$0.716630\pi$
$648$	−421.538	+	1060.58i	−0.0255549	+	0.0642958i
$649$			7914.57i			0.478696i
$650$	188.352	−	326.235i	0.0113658	−	0.0196862i
$651$	12062.6	−	2359.56i	0.726224	−	0.142056i
$652$	7196.45	+	12464.6i	0.432262	+	0.748699i
$653$	−1355.80	+	782.771i	−0.0812505	+	0.0469100i	−0.540075	−	0.841617i	$-0.681604\pi$
$653$	−1355.80	+	782.771i	−0.0812505	+	0.0469100i	0.458824	+	0.888527i	$0.348271\pi$
$654$	−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	−0.0330256	−	0.999455i	$-0.510514\pi$
$659$	−15480.8	−	8937.83i	−0.915091	−	0.528328i	−0.882066	+	0.471126i	$0.843848\pi$
$660$	−25331.8	+	11587.7i	−1.49400	+	0.683408i
$661$	21911.3	−	12650.5i	1.28934	−	0.744399i	0.310801	−	0.950475i	$-0.399403\pi$
$661$	21911.3	−	12650.5i	1.28934	−	0.744399i	0.978536	+	0.206076i	$0.0660695\pi$
$662$	−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
$672$	−1772.51	+	346.720i	−0.101750	+	0.0199033i
$673$	−16774.4	+	29054.1i	−0.960781	+	1.66412i	−0.240233	+	0.970715i	$0.577224\pi$
$673$	−16774.4	+	29054.1i	−0.960781	+	1.66412i	−0.720548	+	0.693405i	$0.756110\pi$
$674$		−	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	−0.110408	+	0.993886i	$0.535216\pi$
$677$	−16134.2	+	27945.3i	−0.915935	+	1.58645i	−0.805527	+	0.592559i	$0.798118\pi$
$678$	−728.261	−	69.0839i	−0.0412518	−	0.00391320i
$679$	−17860.6	−	16956.9i	−1.00947	−	0.958390i
$680$	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	$-0.862534\pi$
$683$		−	14942.5i		−	0.837126i	0.908188	−	0.418563i	$-0.137466\pi$
$684$	−14319.8	+	4976.05i	−0.800482	+	0.278164i
$685$		−	39133.7i		−	2.18281i
$686$	207.202	+	586.410i	0.0115321	+	0.0326374i
$687$	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	$-0.233202\pi$
$691$	9734.42	+	5620.17i	0.535912	+	0.309409i	−0.207509	+	0.978233i	$0.566536\pi$
$692$	−6388.47			−0.350944
$693$	−10786.7	−	15039.6i	−0.591276	−	0.824398i
$694$	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
$700$	−29293.5	−	7039.90i	−1.58170	−	0.380119i
$701$			19409.2i			1.04576i	0.852407	+	0.522879i	$0.175142\pi$
$701$			19409.2i			1.04576i	−0.852407	+	0.522879i	$0.824858\pi$
$702$	−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
$707$	11667.5	−	12289.3i	0.620652	−	0.653729i
$708$	5145.44	−	7235.27i	0.273132	−	0.384065i
$709$	866.108	−	1500.14i	0.0458778	−	0.0794627i	−0.842175	−	0.539205i	$-0.818725\pi$
$709$	866.108	−	1500.14i	0.0458778	−	0.0794627i	0.888052	+	0.459742i	$0.152058\pi$
$710$	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
$714$	386.972	+	444.097i	0.0202830	+	0.0232772i
$715$	−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	$-0.907638\pi$
$719$	−36946.9			−1.91639			−0.958197	+	0.286109i	$0.907638\pi$
$720$	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	$-0.316675\pi$
$727$	1776.00	+	1025.38i	0.0906029	+	0.0523096i	−0.454014	+	0.890995i	$0.650008\pi$
$728$	−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	$-0.956616\pi$
$733$	−27156.6	+	15678.9i	−1.36842	+	0.790058i	−0.377694	+	0.925931i	$0.623283\pi$
$734$	−149.986	−	259.783i	−0.00754234	−	0.0130637i
$735$	1378.45	−	32277.9i	0.0691767	−	1.61985i
$736$	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
$742$	−239.429	+	252.189i	−0.0118460	+	0.0124773i
$743$	26190.4	−	15121.0i	1.29318	−	0.746618i	0.313963	−	0.949435i	$-0.398343\pi$
$743$	26190.4	−	15121.0i	1.29318	−	0.746618i	0.979217	+	0.202818i	$0.0650098\pi$
$744$	−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
$749$	7297.79	−	30366.6i	0.356015	−	1.48140i
$750$	−590.585	−	420.001i	−0.0287535	−	0.0204483i
$751$	−2746.70	−	4757.42i	−0.133460	−	0.231159i	0.791548	−	0.611107i	$-0.209275\pi$
$751$	−2746.70	−	4757.42i	−0.133460	−	0.231159i	−0.925008	+	0.379947i	$0.875942\pi$
$752$	−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
$756$	83.3256	+	20761.5i	0.00400863	+	0.998794i
$757$	−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	$-0.0385949\pi$
$761$	8220.51	+	14238.3i	0.391581	+	0.678238i	−0.601077	+	0.799191i	$0.705262\pi$
$762$	764.921	+	543.982i	0.0363651	+	0.0258614i
$763$	−11547.5	−	2775.12i	−0.547899	−	0.131673i
$764$		−	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	$-0.677190\pi$
$769$	−1220.92	+	704.900i	−0.0572531	+	0.0330551i	0.471100	+	0.882080i	$0.343857\pi$
$770$	837.614	−	882.253i	0.0392020	−	0.0412912i
$771$	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	$-0.428492\pi$
$773$	9575.08			0.445526			0.222763	+	0.974873i	$0.428492\pi$
$774$	−802.492	+	278.863i	−0.0372674	+	0.0129503i
$775$		−	26002.5i		−	1.20521i
$776$	−1040.92	+	1802.93i	−0.0481534	+	0.0834041i
$777$	34484.4	+	11828.3i	1.59218	+	0.546122i
$778$	−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	$-0.674872\pi$
$787$	−985.646	+	569.063i	−0.0446436	+	0.0257750i	0.477512	+	0.878625i	$0.341539\pi$
$788$	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	$-0.324188\pi$
$797$	−10685.7	−	18508.2i	−0.474914	−	0.822576i	−0.999587	+	0.0287282i	$0.990854\pi$
$798$	499.144	−	434.938i	0.0221423	−	0.0192940i
$799$	−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
$805$	39552.9	+	37551.7i	1.73175	+	1.64413i
$806$	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	$0.119128\pi$
$809$			16824.0i			0.731150i	−0.930782	+	0.365575i	$0.880872\pi$
$810$	−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	$0.747039\pi$
$812$	−3294.20	+	13707.4i	−0.142369	+	0.592408i
$813$	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
$819$	−9404.64	+	930.237i	−0.401251	+	0.0396888i
$820$	28734.8			1.22373
$821$	−18735.6	−	10817.0i	−0.796438	−	0.459824i	0.0457860	−	0.998951i	$-0.485421\pi$
$821$	−18735.6	−	10817.0i	−0.796438	−	0.459824i	−0.842224	+	0.539127i	$0.818754\pi$
$822$	−456.865	−	998.753i	−0.0193857	−	0.0423790i
$823$	12194.5	+	21121.4i	0.516492	+	0.894590i	0.999817	+	0.0191488i	$0.00609561\pi$
$823$	12194.5	+	21121.4i	0.516492	+	0.894590i	−0.483325	+	0.875441i	$0.660571\pi$
$824$	652.480	+	1130.13i	0.0275852	+	0.0477790i
$825$	−35605.7	+	16287.3i	−1.50258	+	0.687335i
$826$	−90.6017	+	377.000i	−0.00381651	+	0.0158808i
$827$		−	29015.7i		−	1.22004i	−0.792385	−	0.610022i	$-0.791161\pi$
$827$		−	29015.7i		−	1.22004i	0.792385	−	0.610022i	$-0.208839\pi$
$828$	−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
$833$	19102.2	+	9744.14i	0.794539	+	0.405299i
$834$	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	−0.157124	−	0.987579i	$-0.550222\pi$
$839$	18875.6	−	32693.4i	0.776706	−	1.34529i	0.933831	−	0.357716i	$-0.116444\pi$
$840$	−2680.20	+	524.272i	−0.110090	+	0.0215346i
$841$	−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	$-0.183114\pi$
$853$	19616.3	+	11325.5i	0.787398	+	0.454605i	−0.0516476	+	0.998665i	$0.516447\pi$
$854$	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	$-0.911252\pi$
$857$	−6080.19	+	10531.2i	−0.242351	+	0.419765i	0.719032	+	0.694977i	$0.244585\pi$
$858$	−290.005	−	206.240i	−0.0115392	−	0.00820621i
$859$	12189.4	−	7037.53i	0.484163	−	0.279531i	−0.237987	−	0.971268i	$-0.576488\pi$
$859$	12189.4	−	7037.53i	0.484163	−	0.279531i	0.722150	+	0.691737i	$0.243154\pi$
$860$	23274.9	+	40313.4i	0.922871	+	1.59846i
$861$	3665.04	+	18736.5i	0.145069	+	0.741626i
$862$	319.155	−	552.793i	0.0126107	−	0.0218425i
$863$		−	8687.35i		−	0.342666i	−0.985213	−	0.171333i	$-0.945193\pi$
$863$		−	8687.35i		−	0.342666i	0.985213	−	0.171333i	$-0.0548074\pi$
$864$	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
$868$	−13707.3	−	13013.7i	−0.536007	−	0.508887i
$869$	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
$875$	−25652.2	−	6164.80i	−0.991087	−	0.238181i
$876$	36543.5	−	16716.3i	1.40946	−	0.644740i
$877$	−1604.18	−	2778.53i	−0.0617667	−	0.106983i	0.833488	−	0.552537i	$-0.186340\pi$
$877$	−1604.18	−	2778.53i	−0.0617667	−	0.106983i	−0.895255	+	0.445554i	$0.853007\pi$
$878$	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	$-0.254369\pi$
$881$	36469.9			1.39467			0.697334	+	0.716746i	$0.254369\pi$
$882$	−341.647	−	839.874i	−0.0130429	−	0.0320635i
$883$	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	−0.990098	−	0.140379i	$-0.955168\pi$
$887$	−16289.3	−	28214.0i	−0.616620	−	1.06802i	0.373478	−	0.927639i	$-0.378165\pi$
$888$	291.032	−	3067.97i	0.0109982	−	0.115939i
$889$	33224.5	+	7984.60i	1.25345	+	0.301232i
$890$		−	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
$896$	2685.03	+	2549.18i	0.100112	+	0.0950469i
$897$	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
$903$	−23317.7	+	20318.3i	−0.859319	+	0.748783i
$904$	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	−0.906933	−	0.421276i	$-0.861582\pi$
$907$	−2421.00	+	4193.30i	−0.0886307	+	0.153513i	0.818302	+	0.574789i	$0.194916\pi$
$908$	−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	−0.176160	−	0.984362i	$-0.556367\pi$
$911$	−30705.9	−	17728.1i	−1.11672	−	0.644740i	−0.940562	+	0.339622i	$0.889701\pi$
$912$	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
$924$	−9234.03	+	26921.1i	−0.328763	+	0.958483i
$925$	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	−0.242866	−	0.970060i	$-0.578087\pi$
$929$	20349.3	−	35246.0i	0.718664	−	1.24476i	0.961529	−	0.274702i	$-0.0885793\pi$
$930$	−489.952	−	1071.08i	−0.0172754	−	0.0377658i
$931$	10951.9	−	21469.9i	0.385538	−	0.755798i
$932$	−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	$0.921879\pi$
$938$	−57.8727	+	240.812i	−0.00201451	+	0.00838252i
$939$	−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	−0.997416	−	0.0718418i	$-0.977112\pi$
$941$	−16191.6	−	28044.6i	−0.560925	−	0.971550i	0.436491	−	0.899709i	$-0.356221\pi$
$942$	510.389	+	48.4163i	0.0176533	+	0.00167461i
$943$	−27911.6	−	16114.8i	−0.963868	−	0.556489i
$944$	−13636.3			−0.470152
$945$	189.031	+	47099.2i	0.00650707	+	1.62131i
$946$	−1164.61			−0.0400261
$947$	6500.78	+	3753.23i	0.223070	+	0.128789i	0.607371	−	0.794418i	$-0.292224\pi$
$947$	6500.78	+	3753.23i	0.223070	+	0.128789i	−0.384301	+	0.923208i	$0.625558\pi$
$948$	−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
$952$	423.571	−	1762.51i	0.0144202	−	0.0600034i
$953$		−	469.935i		−	0.0159735i	−0.999968	−	0.00798673i	$-0.997458\pi$
$953$		−	469.935i		−	0.0159735i	0.999968	−	0.00798673i	$-0.00254228\pi$
$954$	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
$959$	−28996.2	−	27529.1i	−0.976366	−	0.926965i
$960$	−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
$966$	1447.85	+	496.617i	0.0482233	+	0.0165408i
$967$	−16008.3	−	27727.1i	−0.532359	−	0.922073i	−0.999286	−	0.0377773i	$-0.987972\pi$
$967$	−16008.3	−	27727.1i	−0.532359	−	0.922073i	0.466927	−	0.884296i	$-0.345361\pi$
$968$	−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	$-0.486381\pi$
$971$	2588.27			0.0855424			0.0427712	+	0.999085i	$0.486381\pi$
$972$	−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	−0.919800	−	0.392387i	$-0.871649\pi$
$977$	−31756.0	+	18334.4i	−1.03988	+	0.600376i	−0.120083	+	0.992764i	$0.538316\pi$
$978$	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	$-0.880032\pi$
$983$	−4505.33	+	7803.46i	−0.146183	+	0.253196i	0.783631	+	0.621227i	$0.213365\pi$
$984$	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
$987$	11519.9	−	10038.1i	0.371512	−	0.323724i
$988$	−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
$994$	572.945	−	603.479i	0.0182824	−	0.0192567i
$995$	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	$-0.413886\pi$
$997$	−13651.7	−	7881.82i	−0.433655	−	0.250371i	−0.700902	+	0.713257i	$0.747219\pi$
$998$			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.20.12	yes	44
3.2	odd	2		189.4.o.a.62.12		44
7.6	odd	2	inner	63.4.o.a.20.11	✓	44
9.2	odd	6		567.4.c.c.566.3		44
9.4	even	3		189.4.o.a.125.11		44
9.5	odd	6	inner	63.4.o.a.41.11	yes	44
9.7	even	3		567.4.c.c.566.42		44
21.20	even	2		189.4.o.a.62.11		44
63.13	odd	6		189.4.o.a.125.12		44
63.20	even	6		567.4.c.c.566.41		44
63.34	odd	6		567.4.c.c.566.4		44
63.41	even	6	inner	63.4.o.a.41.12	yes	44

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

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

\(f(q)\)	\(=\)	\(q+(-0.0847887 - 0.0489528i) q^{2} +(5.17293 + 0.490712i) q^{3} +(-3.99521 - 6.91990i) q^{4} +(-9.06347 - 15.6984i) q^{5} +(-0.414584 - 0.294836i) q^{6} +(-18.0075 - 4.32762i) q^{7} +1.56555i q^{8} +(26.5184 + 5.07683i) q^{9} +O(q^{10})\)	\(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} +(-18.0075 - 4.32762i) 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} +(1.31499 + 1.24845i) 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} +(-91.0282 - 31.2230i) 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} +(6.18971 + 7.10344i) 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} +(305.543 + 155.860i) 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} +(6.77511 - 28.1917i) 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} +(-455.561 - 206.183i) 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} +(7.68035 - 31.9585i) 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} +(-497.120 - 471.968i) 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} +(147.616 + 754.648i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more