LMFDB - Embedded newform 27.4.e.a.22.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, degree $6$, 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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			22.7
Character	$\chi$	$=$	27.22
Dual form			27.4.e.a.16.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.44194 - 2.04903i) q^{2} +(-2.73751 - 4.41656i) q^{3} +(0.375355 - 2.12875i) q^{4} +(6.73772 - 2.45233i) q^{5} +(-15.7345 - 5.17572i) q^{6} +(0.843459 + 4.78350i) q^{7} +(9.30563 + 16.1178i) q^{8} +(-12.0120 + 24.1808i) q^{9} +O(q^{10})$	\(q+(2.44194 - 2.04903i) q^{2} +(-2.73751 - 4.41656i) q^{3} +(0.375355 - 2.12875i) q^{4} +(6.73772 - 2.45233i) q^{5} +(-15.7345 - 5.17572i) q^{6} +(0.843459 + 4.78350i) q^{7} +(9.30563 + 16.1178i) q^{8} +(-12.0120 + 24.1808i) q^{9} +(11.4282 - 19.7942i) q^{10} +(20.1875 + 7.34765i) q^{11} +(-10.4293 + 4.16969i) q^{12} +(-26.7394 - 22.4370i) q^{13} +(11.8612 + 9.95273i) q^{14} +(-29.2755 - 23.0443i) q^{15} +(71.9995 + 26.2057i) q^{16} +(-57.1928 + 99.0609i) q^{17} +(20.2145 + 83.6610i) q^{18} +(-75.8961 - 131.456i) q^{19} +(-2.69135 - 15.2634i) q^{20} +(18.8176 - 16.8201i) q^{21} +(64.3522 - 23.4223i) q^{22} +(16.1288 - 91.4708i) q^{23} +(45.7111 - 85.2216i) q^{24} +(-56.3726 + 47.3022i) q^{25} -111.270 q^{26} +(139.679 - 13.1434i) q^{27} +10.4994 q^{28} +(144.206 - 121.003i) q^{29} +(-118.707 + 3.71361i) q^{30} +(-1.10912 + 6.29012i) q^{31} +(89.6036 - 32.6130i) q^{32} +(-22.8122 - 109.274i) q^{33} +(63.3173 + 359.090i) q^{34} +(17.4137 + 30.1614i) q^{35} +(46.9660 + 34.6470i) q^{36} +(-196.391 + 340.159i) q^{37} +(-454.691 - 165.494i) q^{38} +(-25.8950 + 179.518i) q^{39} +(102.225 + 85.7769i) q^{40} +(159.914 + 134.184i) q^{41} +(11.4866 - 79.6314i) q^{42} +(-142.747 - 51.9557i) q^{43} +(23.2188 - 40.2161i) q^{44} +(-21.6345 + 192.381i) q^{45} +(-148.041 - 256.414i) q^{46} +(-29.2530 - 165.902i) q^{47} +(-81.3606 - 389.728i) q^{48} +(300.144 - 109.244i) q^{49} +(-40.7347 + 231.018i) q^{50} +(594.075 - 18.5849i) q^{51} +(-57.7995 + 48.4995i) q^{52} -2.81647 q^{53} +(314.157 - 318.302i) q^{54} +154.037 q^{55} +(-69.2506 + 58.1082i) q^{56} +(-372.817 + 695.062i) q^{57} +(104.203 - 590.964i) q^{58} +(231.135 - 84.1261i) q^{59} +(-60.0441 + 53.6703i) q^{60} +(-123.808 - 702.150i) q^{61} +(10.1803 + 17.6327i) q^{62} +(-125.800 - 37.0640i) q^{63} +(-154.500 + 267.601i) q^{64} +(-235.186 - 85.6006i) q^{65} +(-279.611 - 220.096i) q^{66} +(181.688 + 152.454i) q^{67} +(189.408 + 158.932i) q^{68} +(-448.139 + 179.169i) q^{69} +(104.325 + 37.9711i) q^{70} +(-61.2324 + 106.058i) q^{71} +(-501.521 + 31.4097i) q^{72} +(-137.653 - 238.422i) q^{73} +(217.421 + 1233.06i) q^{74} +(363.234 + 119.482i) q^{75} +(-308.324 + 112.221i) q^{76} +(-18.1201 + 102.764i) q^{77} +(304.603 + 491.431i) q^{78} +(197.859 - 166.024i) q^{79} +549.377 q^{80} +(-440.422 - 580.921i) q^{81} +665.446 q^{82} +(1019.13 - 855.148i) q^{83} +(-28.7424 - 46.3714i) q^{84} +(-142.419 + 807.701i) q^{85} +(-455.038 + 165.620i) q^{86} +(-929.183 - 305.647i) q^{87} +(69.4292 + 393.753i) q^{88} +(-41.5833 - 72.0243i) q^{89} +(341.364 + 514.112i) q^{90} +(84.7738 - 146.832i) q^{91} +(-188.664 - 68.6681i) q^{92} +(30.8169 - 12.3208i) q^{93} +(-411.372 - 345.182i) q^{94} +(-833.741 - 699.591i) q^{95} +(-389.328 - 306.461i) q^{96} +(34.8364 + 12.6794i) q^{97} +(509.090 - 881.770i) q^{98} +(-420.165 + 399.889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	2.44194	−	2.04903i	0.863356	−	0.724441i	−0.0993326	−	0.995054i	$-0.531671\pi$
$2$	2.44194	−	2.04903i	0.863356	−	0.724441i	0.962688	+	0.270613i	$0.0872263\pi$
$3$	−2.73751	−	4.41656i	−0.526835	−	0.849968i
$3$	−2.73751	−	4.41656i	−0.526835	−	0.849968i
$4$	0.375355	−	2.12875i	0.0469194	−	0.266093i
$5$	6.73772	−	2.45233i	0.602640	−	0.219343i	−0.0226396	−	0.999744i	$-0.507207\pi$
$5$	6.73772	−	2.45233i	0.602640	−	0.219343i	0.625280	+	0.780401i	$0.284985\pi$
$6$	−15.7345	−	5.17572i	−1.07060	−	0.352163i
$7$	0.843459	+	4.78350i	0.0455425	+	0.258284i	0.999075	−	0.0430064i	$-0.0136936\pi$
$7$	0.843459	+	4.78350i	0.0455425	+	0.258284i	−0.953532	+	0.301291i	$0.902582\pi$
$8$	9.30563	+	16.1178i	0.411255	+	0.712314i
$9$	−12.0120	+	24.1808i	−0.444890	+	0.895585i
$10$	11.4282	−	19.7942i	0.361392	−	0.625949i
$11$	20.1875	+	7.34765i	0.553342	+	0.201400i	0.603531	−	0.797340i	$-0.293760\pi$
$11$	20.1875	+	7.34765i	0.553342	+	0.201400i	−0.0501890	+	0.998740i	$0.515982\pi$
$12$	−10.4293	+	4.16969i	−0.250889	+	0.100307i
$13$	−26.7394	−	22.4370i	−0.570475	−	0.478685i	0.311329	−	0.950302i	$-0.399226\pi$
$13$	−26.7394	−	22.4370i	−0.570475	−	0.478685i	−0.881803	+	0.471617i	$0.843670\pi$
$14$	11.8612	+	9.95273i	0.226431	+	0.189998i
$15$	−29.2755	−	23.0443i	−0.503926	−	0.396667i
$16$	71.9995	+	26.2057i	1.12499	+	0.409463i
$17$	−57.1928	+	99.0609i	−0.815959	+	1.41328i	0.0926783	+	0.995696i	$0.470457\pi$
$17$	−57.1928	+	99.0609i	−0.815959	+	1.41328i	−0.908637	+	0.417586i	$0.862876\pi$
$18$	20.2145	+	83.6610i	0.264700	+	1.09551i
$19$	−75.8961	−	131.456i	−0.916409	−	1.58727i	−0.804826	−	0.593511i	$-0.797741\pi$
$19$	−75.8961	−	131.456i	−0.916409	−	1.58727i	−0.111583	−	0.993755i	$-0.535592\pi$
$20$	−2.69135	−	15.2634i	−0.0300902	−	0.170650i
$21$	18.8176	−	16.8201i	0.195540	−	0.174783i
$22$	64.3522	−	23.4223i	0.623633	−	0.226984i
$23$	16.1288	−	91.4708i	0.146221	−	0.829260i	−0.820158	−	0.572137i	$-0.806114\pi$
$23$	16.1288	−	91.4708i	0.146221	−	0.829260i	0.966379	−	0.257123i	$-0.0827744\pi$
$24$	45.7111	−	85.2216i	0.388780	−	0.724825i
$25$	−56.3726	+	47.3022i	−0.450980	+	0.378418i
$26$	−111.270			−0.839302
$27$	139.679	−	13.1434i	0.995602	−	0.0936831i
$28$	10.4994			0.0708646
$29$	144.206	−	121.003i	0.923392	−	0.774818i	−0.0512273	−	0.998687i	$-0.516313\pi$
$29$	144.206	−	121.003i	0.923392	−	0.774818i	0.974619	+	0.223869i	$0.0718689\pi$
$30$	−118.707	+	3.71361i	−0.722430	+	0.0226003i
$31$	−1.10912	+	6.29012i	−0.00642592	+	0.0364432i	−0.987852	−	0.155397i	$-0.950334\pi$
$31$	−1.10912	+	6.29012i	−0.00642592	+	0.0364432i	0.981426	+	0.191840i	$0.0614455\pi$
$32$	89.6036	−	32.6130i	0.494994	−	0.180163i
$33$	−22.8122	−	109.274i	−0.120336	−	0.576427i
$34$	63.3173	+	359.090i	0.319377	+	1.81128i
$35$	17.4137	+	30.1614i	0.0840987	+	0.145663i
$36$	46.9660	+	34.6470i	0.217435	+	0.160403i
$37$	−196.391	+	340.159i	−0.872607	+	1.51140i	−0.0133160	+	0.999911i	$0.504239\pi$
$37$	−196.391	+	340.159i	−0.872607	+	1.51140i	−0.859291	+	0.511488i	$0.829095\pi$
$38$	−454.691	−	165.494i	−1.94107	−	0.706491i
$39$	−25.8950	+	179.518i	−0.106321	+	0.737073i
$40$	102.225	+	85.7769i	0.404080	+	0.339063i
$41$	159.914	+	134.184i	0.609131	+	0.511121i	0.894366	−	0.447336i	$-0.147627\pi$
$41$	159.914	+	134.184i	0.609131	+	0.511121i	−0.285235	+	0.958458i	$0.592072\pi$
$42$	11.4866	−	79.6314i	0.0422006	−	0.292557i
$43$	−142.747	−	51.9557i	−0.506250	−	0.184260i	0.0762532	−	0.997088i	$-0.475704\pi$
$43$	−142.747	−	51.9557i	−0.506250	−	0.184260i	−0.582503	+	0.812829i	$0.697926\pi$
$44$	23.2188	−	40.2161i	0.0795536	−	0.137791i
$45$	−21.6345	+	192.381i	−0.0716683	+	0.637299i
$46$	−148.041	−	256.414i	−0.474510	−	0.821875i
$47$	−29.2530	−	165.902i	−0.0907870	−	0.514879i	−0.995957	−	0.0898293i	$-0.971368\pi$
$47$	−29.2530	−	165.902i	−0.0907870	−	0.514879i	0.905170	−	0.425049i	$-0.139743\pi$
$48$	−81.3606	−	389.728i	−0.244654	−	1.17193i
$49$	300.144	−	109.244i	0.875056	−	0.318494i
$50$	−40.7347	+	231.018i	−0.115215	+	0.653418i
$51$	594.075	−	18.5849i	1.63112	−	0.0510276i
$52$	−57.7995	+	48.4995i	−0.154141	+	0.129340i
$53$	−2.81647			−0.00729946			−0.00364973	−	0.999993i	$-0.501162\pi$
$53$	−2.81647			−0.00729946			−0.00364973	+	0.999993i	$0.501162\pi$
$54$	314.157	−	318.302i	0.791691	−	0.802137i
$55$	154.037			0.377642
$56$	−69.2506	+	58.1082i	−0.165250	+	0.138661i
$57$	−372.817	+	695.062i	−0.866329	+	1.61514i
$58$	104.203	−	590.964i	0.235905	−	1.33789i
$59$	231.135	−	84.1261i	0.510019	−	0.185632i	−0.0741756	−	0.997245i	$-0.523633\pi$
$59$	231.135	−	84.1261i	0.510019	−	0.185632i	0.584195	+	0.811613i	$0.301410\pi$
$60$	−60.0441	+	53.6703i	−0.129194	+	0.115480i
$61$	−123.808	−	702.150i	−0.259869	−	1.47379i	−0.783259	−	0.621695i	$-0.786444\pi$
$61$	−123.808	−	702.150i	−0.259869	−	1.47379i	0.523391	−	0.852093i	$-0.324667\pi$
$62$	10.1803	+	17.6327i	0.0208531	+	0.0361187i
$63$	−125.800	−	37.0640i	−0.251577	−	0.0741210i
$64$	−154.500	+	267.601i	−0.301757	+	0.522659i
$65$	−235.186	−	85.6006i	−0.448788	−	0.163345i
$66$	−279.611	−	220.096i	−0.521480	−	0.410485i
$67$	181.688	+	152.454i	0.331295	+	0.277989i	0.793227	−	0.608926i	$-0.208399\pi$
$67$	181.688	+	152.454i	0.331295	+	0.277989i	−0.461932	+	0.886915i	$0.652844\pi$
$68$	189.408	+	158.932i	0.337781	+	0.283432i
$69$	−448.139	+	179.169i	−0.781878	+	0.312600i
$70$	104.325	+	37.9711i	0.178132	+	0.0648346i
$71$	−61.2324	+	106.058i	−0.102351	+	0.177278i	−0.912653	−	0.408735i	$-0.865970\pi$
$71$	−61.2324	+	106.058i	−0.102351	+	0.177278i	0.810302	+	0.586013i	$0.199303\pi$
$72$	−501.521	+	31.4097i	−0.820901	+	0.0514120i
$73$	−137.653	−	238.422i	−0.220700	−	0.382263i	0.734321	−	0.678802i	$-0.237501\pi$
$73$	−137.653	−	238.422i	−0.220700	−	0.382263i	−0.955021	+	0.296539i	$0.904167\pi$
$74$	217.421	+	1233.06i	0.341550	+	1.93703i
$75$	363.234	+	119.482i	0.559235	+	0.183955i
$76$	−308.324	+	112.221i	−0.465358	+	0.169377i
$77$	−18.1201	+	102.764i	−0.0268179	+	0.152092i
$78$	304.603	+	491.431i	0.442174	+	0.713380i
$79$	197.859	−	166.024i	0.281784	−	0.236445i	−0.490930	−	0.871199i	$-0.663343\pi$
$79$	197.859	−	166.024i	0.281784	−	0.236445i	0.772714	+	0.634754i	$0.218899\pi$
$80$	549.377			0.767778
$81$	−440.422	−	580.921i	−0.604145	−	0.796874i
$82$	665.446			0.896174
$83$	1019.13	−	855.148i	1.34775	−	1.13090i	0.368193	−	0.929749i	$-0.379976\pi$
$83$	1019.13	−	855.148i	1.34775	−	1.13090i	0.979560	−	0.201150i	$-0.0644679\pi$
$84$	−28.7424	−	46.3714i	−0.0373339	−	0.0602326i
$85$	−142.419	+	807.701i	−0.181736	+	1.03068i
$86$	−455.038	+	165.620i	−0.570559	+	0.207666i
$87$	−929.183	−	305.647i	−1.14505	−	0.376652i
$88$	69.4292	+	393.753i	0.0841043	+	0.476979i
$89$	−41.5833	−	72.0243i	−0.0495261	−	0.0857816i	0.840200	−	0.542277i	$-0.182438\pi$
$89$	−41.5833	−	72.0243i	−0.0495261	−	0.0857816i	−0.889726	+	0.456496i	$0.849104\pi$
$90$	341.364	+	514.112i	0.399811	+	0.602135i
$91$	84.7738	−	146.832i	0.0976561	−	0.169145i
$92$	−188.664	−	68.6681i	−0.213800	−	0.0778168i
$93$	30.8169	−	12.3208i	0.0343610	−	0.0137377i
$94$	−411.372	−	345.182i	−0.451381	−	0.378753i
$95$	−833.741	−	699.591i	−0.900421	−	0.755543i
$96$	−389.328	−	306.461i	−0.413913	−	0.325813i
$97$	34.8364	+	12.6794i	0.0364650	+	0.0132722i	0.360188	−	0.932880i	$-0.382712\pi$
$97$	34.8364	+	12.6794i	0.0364650	+	0.0132722i	−0.323723	+	0.946152i	$0.604935\pi$
$98$	509.090	−	881.770i	0.524754	−	0.908900i
$99$	−420.165	+	399.889i	−0.426547	+	0.405964i
$100$	79.5346	+	137.758i	0.0795346	+	0.137758i
$101$	193.821	+	1099.21i	0.190950	+	1.08293i	0.918070	+	0.396419i	$0.129747\pi$
$101$	193.821	+	1099.21i	0.190950	+	1.08293i	−0.727120	+	0.686510i	$0.759142\pi$
$102$	1412.61	−	1262.66i	1.37127	−	1.22571i
$103$	−1160.96	+	422.555i	−1.11061	+	0.404228i	−0.831217	−	0.555949i	$-0.812355\pi$
$103$	−1160.96	+	422.555i	−1.11061	+	0.404228i	−0.279392	+	0.960177i	$0.590133\pi$
$104$	112.809	−	639.771i	0.106364	−	0.603219i
$105$	85.5395	−	159.476i	0.0795029	−	0.148222i
$106$	−6.87764	+	5.77102i	−0.00630203	+	0.00528803i
$107$	−738.624			−0.667341			−0.333670	−	0.942690i	$-0.608287\pi$
$107$	−738.624			−0.667341			−0.333670	+	0.942690i	$0.608287\pi$
$108$	24.4504	−	302.275i	0.0217846	−	0.269319i
$109$	879.581			0.772923			0.386461	−	0.922306i	$-0.373697\pi$
$109$	879.581			0.772923			0.386461	+	0.922306i	$0.373697\pi$
$110$	376.148	−	315.626i	0.326039	−	0.273579i
$111$	2039.95	−	63.8175i	1.74436	−	0.0545701i
$112$	−64.6260	+	366.513i	−0.0545231	+	0.309216i
$113$	−837.528	+	304.835i	−0.697239	+	0.253774i	−0.666232	−	0.745745i	$-0.732094\pi$
$113$	−837.528	+	304.835i	−0.697239	+	0.253774i	−0.0310074	+	0.999519i	$0.509872\pi$
$114$	513.808	+	2461.21i	0.422128	+	2.02205i
$115$	−115.645	−	655.858i	−0.0937739	−	0.531818i
$116$	−203.456	−	352.397i	−0.162849	−	0.282062i
$117$	863.740	−	377.066i	0.682502	−	0.297946i
$118$	392.039	−	679.032i	0.305849	−	0.529746i
$119$	−522.097	−	190.028i	−0.402190	−	0.146385i
$120$	98.9969	−	686.298i	0.0753095	−	0.522085i
$121$	−666.058	−	558.889i	−0.500419	−	0.419902i
$122$	−1741.06	−	1460.92i	−1.29203	−	1.08414i
$123$	154.864	−	1073.60i	0.113525	−	0.787018i
$124$	12.9738	+	4.72206i	0.00939579	+	0.00341979i
$125$	−711.956	+	1233.14i	−0.509434	+	0.882365i
$126$	−383.142	+	167.261i	−0.270897	+	0.118260i
$127$	1102.29	+	1909.23i	0.770179	+	1.33399i	0.937464	+	0.348081i	$0.113167\pi$
$127$	1102.29	+	1909.23i	0.770179	+	1.33399i	−0.167285	+	0.985909i	$0.553500\pi$
$128$	303.509	+	1721.28i	0.209583	+	1.18860i
$129$	161.307	+	772.681i	0.110095	+	0.527370i
$130$	−749.707	+	272.871i	−0.505797	+	0.184095i
$131$	−63.8555	+	362.143i	−0.0425884	+	0.241531i	−0.998669	−	0.0515721i	$-0.983577\pi$
$131$	−63.8555	+	362.143i	−0.0425884	+	0.241531i	0.956081	+	0.293103i	$0.0946879\pi$
$132$	−241.178	+	7.54497i	−0.159029	+	0.00497504i
$133$	564.804	−	473.926i	0.368231	−	0.308982i
$134$	756.055			0.487412
$135$	908.887	−	431.096i	0.579441	−	0.274836i
$136$	−2128.86			−1.34227
$137$	764.565	−	641.546i	0.476797	−	0.400080i	−0.372470	−	0.928044i	$-0.621489\pi$
$137$	764.565	−	641.546i	0.476797	−	0.400080i	0.849267	+	0.527964i	$0.177045\pi$
$138$	−727.206	+	1355.77i	−0.448579	+	0.836310i
$139$	−439.429	+	2492.12i	−0.268143	+	1.52071i	0.491791	+	0.870713i	$0.336342\pi$
$139$	−439.429	+	2492.12i	−0.268143	+	1.52071i	−0.759934	+	0.650001i	$0.774769\pi$
$140$	70.7423	−	25.7481i	0.0427059	−	0.0155437i
$141$	−652.636	+	583.357i	−0.389800	+	0.348422i
$142$	67.7895	+	384.453i	0.0400617	+	0.227201i
$143$	−374.942	−	649.419i	−0.219260	−	0.379770i
$144$	−1498.53	+	1426.22i	−0.867207	+	0.825359i
$145$	674.880	−	1168.93i	0.386522	−	0.669476i
$146$	−824.674	−	300.157i	−0.467469	−	0.170145i
$147$	−1304.13	−	1026.55i	−0.731720	−	0.575975i
$148$	650.395	+	545.747i	0.361231	+	0.303109i
$149$	2584.06	+	2168.28i	1.42077	+	1.19216i	0.950929	+	0.309410i	$0.100132\pi$
$149$	2584.06	+	2168.28i	1.42077	+	1.19216i	0.469837	+	0.882753i	$0.344313\pi$
$150$	1131.82	−	452.508i	0.616083	−	0.246314i
$151$	−1008.56	−	367.085i	−0.543545	−	0.197834i	0.0556312	−	0.998451i	$-0.482283\pi$
$151$	−1008.56	−	367.085i	−0.543545	−	0.197834i	−0.599176	+	0.800617i	$0.704505\pi$
$152$	1412.52	−	2446.56i	0.753754	−	1.30554i
$153$	−1708.37	−	2572.89i	−0.902703	−	1.35952i
$154$	166.319	+	288.072i	0.0870282	+	0.150737i
$155$	7.95253	+	45.1010i	0.00412105	+	0.0233716i
$156$	372.428	+	122.507i	0.191142	+	0.0628744i
$157$	2569.60	−	935.260i	1.30622	−	0.475426i	0.407204	−	0.913337i	$-0.366504\pi$
$157$	2569.60	−	935.260i	1.30622	−	0.475426i	0.899018	+	0.437912i	$0.144282\pi$
$158$	142.973	−	810.839i	0.0719893	−	0.408272i
$159$	7.71011	+	12.4391i	0.00384561	+	0.00620430i
$160$	523.746	−	439.475i	0.258786	−	0.217147i
$161$	451.154			0.220844
$162$	−2265.81	−	516.136i	−1.09888	−	0.250318i
$163$	−503.590			−0.241989			−0.120995	−	0.992653i	$-0.538608\pi$
$163$	−503.590			−0.241989			−0.120995	+	0.992653i	$0.538608\pi$
$164$	345.668	−	290.050i	0.164586	−	0.138104i
$165$	−421.677	−	680.312i	−0.198955	−	0.320983i
$166$	736.418	−	4176.44i	0.344320	−	1.95274i
$167$	497.259	−	180.987i	0.230413	−	0.0838636i	−0.224233	−	0.974536i	$-0.571988\pi$
$167$	497.259	−	180.987i	0.230413	−	0.0838636i	0.454647	+	0.890672i	$0.349766\pi$
$168$	446.213	+	146.778i	0.204917	+	0.0674056i
$169$	−169.930	−	963.718i	−0.0773462	−	0.438652i
$170$	1307.22	+	2264.18i	0.589762	+	1.02150i
$171$	4090.38	−	256.175i	1.82923	−	0.114563i
$172$	−164.181	+	284.371i	−0.0727832	+	0.126064i
$173$	−865.997	−	315.197i	−0.380581	−	0.138520i	0.144644	−	0.989484i	$-0.453796\pi$
$173$	−865.997	−	315.197i	−0.380581	−	0.138520i	−0.525225	+	0.850964i	$0.676019\pi$
$174$	−2895.29	+	1157.55i	−1.26144	+	0.504333i
$175$	−273.818	−	229.760i	−0.118278	−	0.0992472i
$176$	1260.94	+	1058.05i	0.540039	+	0.453146i
$177$	−1004.28	−	790.524i	−0.426477	−	0.335703i
$178$	−249.124	−	90.6737i	−0.104902	−	0.0381813i
$179$	−257.731	+	446.403i	−0.107618	+	0.186401i	−0.914805	−	0.403896i	$-0.867656\pi$
$179$	−257.731	+	446.403i	−0.107618	+	0.186401i	0.807187	+	0.590296i	$0.200989\pi$
$180$	401.410	+	118.266i	0.166218	+	0.0489722i
$181$	840.670	+	1456.08i	0.345230	+	0.597955i	0.985395	−	0.170282i	$-0.0544677\pi$
$181$	840.670	+	1456.08i	0.345230	+	0.597955i	−0.640166	+	0.768237i	$0.721134\pi$
$182$	−93.8518	−	532.260i	−0.0382239	−	0.216779i
$183$	−2762.16	+	2468.95i	−1.11576	+	0.997323i
$184$	1624.40	−	591.233i	0.650827	−	0.236882i
$185$	−489.045	+	2773.51i	−0.194353	+	1.10223i
$186$	50.0074	−	93.2315i	0.0197135	−	0.0367530i
$187$	−1882.44	+	1579.56i	−0.736139	+	0.617694i
$188$	−364.143			−0.141265
$189$	180.685	+	657.068i	0.0695391	+	0.252882i
$190$	−3469.43			−1.32473
$191$	−1942.91	+	1630.30i	−0.736044	+	0.617614i	−0.931772	−	0.363044i	$-0.881737\pi$
$191$	−1942.91	+	1630.30i	−0.736044	+	0.617614i	0.195728	+	0.980658i	$0.437293\pi$
$192$	1604.82	−	50.2049i	0.603219	−	0.0188710i
$193$	326.965	−	1854.31i	0.121945	−	0.691587i	−0.861130	−	0.508385i	$-0.830243\pi$
$193$	326.965	−	1854.31i	0.121945	−	0.691587i	0.983075	−	0.183202i	$-0.0586462\pi$
$194$	111.049	−	40.4185i	0.0410972	−	0.0149581i
$195$	265.764	+	1273.04i	0.0975987	+	0.467511i
$196$	−119.891	−	679.936i	−0.0436921	−	0.247790i
$197$	−780.979	−	1352.70i	−0.282449	−	0.489216i	0.689538	−	0.724249i	$-0.257813\pi$
$197$	−780.979	−	1352.70i	−0.282449	−	0.489216i	−0.971987	+	0.235033i	$0.924480\pi$
$198$	−206.631	+	1837.44i	−0.0741648	+	0.659499i
$199$	1008.11	−	1746.09i	0.359110	−	0.621996i	−0.628703	−	0.777646i	$-0.716414\pi$
$199$	1008.11	−	1746.09i	0.359110	−	0.621996i	0.987812	+	0.155650i	$0.0497471\pi$
$200$	−1286.99	−	468.426i	−0.455020	−	0.165614i
$201$	175.951	−	1219.78i	0.0617443	−	0.428044i
$202$	2725.62	+	2287.07i	0.949376	+	0.796621i
$203$	700.450	+	587.747i	0.242177	+	0.203211i
$204$	183.427	−	1271.61i	0.0629531	−	0.436424i
$205$	1406.52	+	511.931i	0.479198	+	0.174414i
$206$	−1969.16	+	3410.69i	−0.666010	+	1.15356i
$207$	2018.10	+	1488.76i	0.677621	+	0.499883i
$208$	−1337.25	−	2316.18i	−0.445775	−	0.772106i
$209$	−566.261	−	3211.42i	−0.187412	−	1.06287i
$210$	−117.889	−	564.704i	−0.0387386	−	0.185563i
$211$	−720.357	+	262.189i	−0.235031	+	0.0855441i	−0.456850	−	0.889544i	$-0.651023\pi$
$211$	−720.357	+	262.189i	−0.235031	+	0.0855441i	0.221820	+	0.975088i	$0.428800\pi$
$212$	−1.05718	+	5.99554i	−0.000342486	+	0.00194234i
$213$	636.035	−	19.8976i	0.204603	−	0.00640074i
$214$	−1803.67	+	1513.46i	−0.576152	+	0.483449i
$215$	−1089.20			−0.345503
$216$	1511.64	+	2129.02i	0.476178	+	0.670653i
$217$	−31.0243			−0.00970537
$218$	2147.88	−	1802.29i	0.667307	−	0.559937i
$219$	−676.179	+	1260.64i	−0.208639	+	0.388977i
$220$	57.8185	−	327.905i	0.0177187	−	0.100488i
$221$	3751.93	−	1365.59i	1.14200	−	0.415655i
$222$	4850.68	−	4335.77i	1.46647	−	1.31080i
$223$	670.069	+	3800.15i	0.201216	+	1.14115i	0.903285	+	0.429042i	$0.141149\pi$
$223$	670.069	+	3800.15i	0.201216	+	1.14115i	−0.702069	+	0.712109i	$0.747740\pi$
$224$	231.581	+	401.110i	0.0690767	+	0.119644i
$225$	−466.656	−	1931.33i	−0.138268	−	0.572246i
$226$	−1420.58	+	2460.51i	−0.418121	+	0.724206i
$227$	−2921.06	−	1063.18i	−0.854085	−	0.310862i	−0.122381	−	0.992483i	$-0.539053\pi$
$227$	−2921.06	−	1063.18i	−0.854085	−	0.310862i	−0.731705	+	0.681622i	$0.761275\pi$
$228$	1339.67	+	1054.53i	0.389131	+	0.306306i
$229$	−2032.93	−	1705.83i	−0.586636	−	0.492246i	0.300483	−	0.953787i	$-0.402852\pi$
$229$	−2032.93	−	1705.83i	−0.586636	−	0.492246i	−0.887119	+	0.461541i	$0.847297\pi$
$230$	−1626.27	−	1364.60i	−0.466231	−	0.391214i
$231$	503.468	−	201.290i	0.143402	−	0.0573329i
$232$	3292.23	+	1198.27i	0.931662	+	0.339097i
$233$	−786.716	+	1362.63i	−0.221200	+	0.383129i	−0.955173	−	0.296050i	$-0.904331\pi$
$233$	−786.716	+	1362.63i	−0.221200	+	0.383129i	0.733973	+	0.679179i	$0.237664\pi$
$234$	1336.58	−	2690.60i	0.373397	−	0.751667i
$235$	−603.945	−	1046.06i	−0.167647	−	0.290373i
$236$	−92.3255	−	523.604i	−0.0254656	−	0.144422i
$237$	−1274.90	−	419.366i	−0.349424	−	0.114940i
$238$	−1664.30	+	605.756i	−0.453280	+	0.164980i
$239$	873.066	−	4951.40i	0.236293	−	1.34008i	−0.603581	−	0.797301i	$-0.706260\pi$
$239$	873.066	−	4951.40i	0.236293	−	1.34008i	0.839874	−	0.542781i	$-0.182629\pi$
$240$	−1503.93	−	2426.36i	−0.404492	−	0.652587i
$241$	1513.53	−	1270.01i	0.404545	−	0.339453i	−0.417702	−	0.908584i	$-0.637165\pi$
$241$	1513.53	−	1270.01i	0.404545	−	0.339453i	0.822247	+	0.569130i	$0.192720\pi$
$242$	−2771.65			−0.736234
$243$	−1360.01	+	3535.43i	−0.359032	+	0.933325i
$244$	−1541.17			−0.404358
$245$	1754.39	−	1472.11i	0.457484	−	0.383875i
$246$	−1821.67	−	2938.98i	−0.472136	−	0.761719i
$247$	−920.063	+	5217.93i	−0.237013	+	1.34417i
$248$	−111.704	+	40.6570i	−0.0286017	+	0.0104102i
$249$	−6566.68	−	2160.05i	−1.67127	−	0.549750i
$250$	788.195	+	4470.08i	0.199399	+	1.13085i
$251$	−1098.18	−	1902.11i	−0.276162	−	0.478326i	0.694266	−	0.719719i	$-0.255729\pi$
$251$	−1098.18	−	1902.11i	−0.276162	−	0.478326i	−0.970428	+	0.241392i	$0.922396\pi$
$252$	−126.120	+	253.885i	−0.0315270	+	0.0634653i
$253$	997.694	−	1728.06i	0.247923	−	0.429415i
$254$	6603.80	+	2403.59i	1.63134	+	0.593758i
$255$	3957.14	−	1582.09i	0.971786	−	0.388526i
$256$	2374.45	+	1992.40i	0.579701	+	0.486427i
$257$	−1840.98	−	1544.77i	−0.446838	−	0.374941i	0.391423	−	0.920211i	$-0.371983\pi$
$257$	−1840.98	−	1544.77i	−0.446838	−	0.374941i	−0.838261	+	0.545270i	$0.816427\pi$
$258$	1977.15	+	1556.32i	0.477100	+	0.375551i
$259$	−1792.80	−	652.524i	−0.430112	−	0.156548i
$260$	−270.500	+	468.520i	−0.0645219	+	0.111755i
$261$	1193.75	+	4940.51i	0.283107	+	1.17168i
$262$	586.110	+	1015.17i	0.138206	+	0.239380i
$263$	−708.982	−	4020.83i	−0.166227	−	0.942720i	−0.947790	−	0.318894i	$-0.896689\pi$
$263$	−708.982	−	4020.83i	−0.166227	−	0.942720i	0.781564	−	0.623826i	$-0.214422\pi$
$264$	1548.97	−	1384.54i	0.361108	−	0.322775i
$265$	−18.9766	+	6.90691i	−0.00439895	+	0.00160109i
$266$	408.126	−	2314.60i	0.0940745	−	0.533523i
$267$	−204.265	+	380.823i	−0.0468196	+	0.0872883i
$268$	392.735	−	329.543i	0.0895152	−	0.0751122i
$269$	1962.92			0.444911			0.222456	−	0.974943i	$-0.428593\pi$
$269$	1962.92			0.444911			0.222456	+	0.974943i	$0.428593\pi$
$270$	1336.12	−	2915.05i	0.301161	−	0.657052i
$271$	1628.04			0.364930			0.182465	−	0.983212i	$-0.441592\pi$
$271$	1628.04			0.364930			0.182465	+	0.983212i	$0.441592\pi$
$272$	−6713.81	+	5633.56i	−1.49663	+	1.25583i
$273$	−880.564	+	27.5474i	−0.195217	+	0.00610711i
$274$	552.473	−	3133.23i	0.121811	−	0.690823i
$275$	−1485.58	+	540.707i	−0.325760	+	0.118567i
$276$	213.194	+	1021.23i	0.0464955	+	0.222720i
$277$	630.670	+	3576.71i	0.136799	+	0.775825i	0.973590	+	0.228303i	$0.0733177\pi$
$277$	630.670	+	3576.71i	0.136799	+	0.775825i	−0.836791	+	0.547522i	$0.815571\pi$
$278$	4033.38	+	6986.02i	0.870165	+	1.50717i
$279$	−138.777	−	102.377i	−0.0297792	−	0.0219682i
$280$	−324.091	+	561.342i	−0.0691719	+	0.119809i
$281$	7854.93	+	2858.96i	1.66757	+	0.606944i	0.991525	−	0.129919i	$-0.0414719\pi$
$281$	7854.93	+	2858.96i	1.66757	+	0.606944i	0.676041	+	0.736864i	$0.263694\pi$
$282$	−398.382	+	2761.79i	−0.0841251	+	0.583200i
$283$	−5226.77	−	4385.78i	−1.09788	−	0.921229i	−0.100598	−	0.994927i	$-0.532075\pi$
$283$	−5226.77	−	4385.78i	−1.09788	−	0.921229i	−0.997281	+	0.0736981i	$0.976520\pi$
$284$	202.786	+	170.158i	0.0423702	+	0.0355528i
$285$	−807.412	+	5597.41i	−0.167814	+	1.16337i
$286$	−2246.26	−	817.573i	−0.464421	−	0.169035i
$287$	−506.986	+	878.126i	−0.104273	+	0.180607i
$288$	−287.712	+	2558.43i	−0.0588667	+	0.523463i
$289$	−4085.54	−	7076.37i	−0.831578	−	1.44034i
$290$	−747.149	−	4237.29i	−0.151290	−	0.858009i
$291$	−39.3658	−	188.567i	−0.00793011	−	0.0379863i
$292$	−559.209	+	203.535i	−0.112073	+	0.0407911i
$293$	−1414.12	+	8019.84i	−0.281957	+	1.59906i	0.433999	+	0.900914i	$0.357102\pi$
$293$	−1414.12	+	8019.84i	−0.281957	+	1.59906i	−0.715956	+	0.698146i	$0.754009\pi$
$294$	−5288.03	+	165.430i	−1.04899	+	0.0328165i
$295$	1351.02	−	1133.64i	0.266641	−	0.223739i
$296$	−7310.16			−1.43545
$297$	2916.34	+	760.981i	0.569776	+	0.148675i
$298$	10753.0			2.09028
$299$	−2483.61	+	2083.99i	−0.480370	+	0.403078i
$300$	390.690	−	728.384i	0.0751882	−	0.140178i
$301$	128.128	−	726.653i	0.0245356	−	0.139148i
$302$	−3215.00	+	1170.17i	−0.612592	+	0.222965i
$303$	4324.16	−	3865.13i	0.819856	−	0.732826i
$304$	−2019.59	−	11453.7i	−0.381024	−	2.16090i
$305$	−2556.09	−	4427.27i	−0.479873	−	0.831164i
$306$	−9443.66	−	2782.34i	−1.76424	−	0.519791i
$307$	−2325.36	+	4027.64i	−0.432297	+	0.748761i	−0.997071	−	0.0764852i	$-0.975630\pi$
$307$	−2325.36	+	4027.64i	−0.432297	+	0.748761i	0.564773	+	0.825246i	$0.308964\pi$
$308$	211.957	+	77.1462i	0.0392123	+	0.0142721i
$309$	5044.38	+	3970.70i	0.928688	+	0.731020i
$310$	111.833	+	93.8390i	0.0204893	+	0.0171926i
$311$	2205.80	+	1850.88i	0.402184	+	0.337472i	0.821337	−	0.570443i	$-0.193229\pi$
$311$	2205.80	+	1850.88i	0.402184	+	0.337472i	−0.419153	+	0.907916i	$0.637673\pi$
$312$	−3134.41	+	1253.16i	−0.568752	+	0.227391i
$313$	818.697	+	297.981i	0.147845	+	0.0538112i	0.414883	−	0.909875i	$-0.363823\pi$
$313$	818.697	+	297.981i	0.147845	+	0.0538112i	−0.267038	+	0.963686i	$0.586045\pi$
$314$	4358.44	−	7549.04i	0.783316	−	1.35674i
$315$	−938.502	+	58.7772i	−0.167868	+	0.0105134i
$316$	−279.155	−	483.510i	−0.0496952	−	0.0860746i
$317$	1155.64	+	6553.97i	0.204755	+	1.16122i	0.897825	+	0.440352i	$0.145146\pi$
$317$	1155.64	+	6553.97i	0.204755	+	1.16122i	−0.693070	+	0.720870i	$0.743743\pi$
$318$	44.3157	+	14.5773i	0.00781478	+	0.00257060i
$319$	3800.24	−	1383.18i	0.666999	−	0.242768i
$320$	−384.729	+	2181.91i	−0.0672094	+	0.381163i
$321$	2021.99	+	3262.18i	0.351578	+	0.567218i
$322$	1101.69	−	924.428i	0.190667	−	0.159989i
$323$	17362.9			2.99101
$324$	−1401.95	+	719.495i	−0.240389	+	0.123370i
$325$	2568.69			0.438416
$326$	−1229.74	+	1031.87i	−0.208923	+	0.175307i
$327$	−2407.86	−	3884.72i	−0.407203	−	0.656959i
$328$	−674.649	+	3826.13i	−0.113571	+	0.644093i
$329$	768.918	−	279.863i	0.128850	−	0.0468977i
$330$	−2423.69	−	797.251i	−0.404302	−	0.132992i
$331$	−1550.58	−	8793.78i	−0.257485	−	1.46027i	−0.789612	−	0.613607i	$-0.789718\pi$
$331$	−1550.58	−	8793.78i	−0.257485	−	1.46027i	0.532127	−	0.846665i	$-0.321393\pi$
$332$	−1437.86	−	2490.44i	−0.237689	−	0.411689i
$333$	−5866.26	−	8834.89i	−0.965372	−	1.45390i
$334$	843.427	−	1460.86i	0.138174	−	0.239325i
$335$	1598.03	+	581.637i	0.260627	+	0.0948603i
$336$	1795.64	−	717.908i	0.291548	−	0.116563i
$337$	885.644	+	743.143i	0.143158	+	0.120123i	0.711554	−	0.702631i	$-0.247992\pi$
$337$	885.644	+	743.143i	0.143158	+	0.120123i	−0.568397	+	0.822755i	$0.692436\pi$
$338$	−2389.64	−	2005.15i	−0.384555	−	0.322680i
$339$	3639.07	+	2864.50i	0.583030	+	0.458934i
$340$	1665.93	+	606.350i	0.265729	+	0.0967174i
$341$	−68.6079	+	118.832i	−0.0108954	+	0.0188714i
$342$	9463.54	−	9006.87i	1.49628	−	1.42408i
$343$	1608.75	+	2786.44i	0.253249	+	0.438640i
$344$	−490.939	−	2784.25i	−0.0769467	−	0.436386i
$345$	−2580.06	+	2306.18i	−0.402625	+	0.359885i
$346$	−2760.56	+	1004.76i	−0.428926	+	0.156116i
$347$	1188.95	−	6742.88i	0.183937	−	1.04316i	−0.743376	−	0.668874i	$-0.766776\pi$
$347$	1188.95	−	6742.88i	0.183937	−	1.04316i	0.927313	−	0.374287i	$-0.122112\pi$
$348$	−999.418	+	1863.27i	−0.153949	+	0.287016i
$349$	−1732.21	+	1453.49i	−0.265681	+	0.222933i	−0.765890	−	0.642972i	$-0.777701\pi$
$349$	−1732.21	+	1453.49i	−0.265681	+	0.222933i	0.500208	+	0.865905i	$0.333257\pi$
$350$	−1139.43			−0.174015
$351$	−4029.83	−	2782.54i	−0.612811	−	0.423136i
$352$	2048.50			0.310186
$353$	−4093.57	+	3434.91i	−0.617220	+	0.517909i	−0.896928	−	0.442176i	$-0.854207\pi$
$353$	−4093.57	+	3434.91i	−0.617220	+	0.517909i	0.279709	+	0.960085i	$0.409762\pi$
$354$	−4072.20	+	127.394i	−0.611398	+	0.0191268i
$355$	−152.479	+	864.749i	−0.0227964	+	0.129285i
$356$	−168.930	+	61.4855i	−0.0251496	+	0.00915372i
$357$	589.979	+	2826.08i	0.0874649	+	0.418969i
$358$	285.330	+	1618.19i	0.0421233	+	0.238893i
$359$	183.124	+	317.180i	0.0269217	+	0.0466298i	0.879172	−	0.476504i	$-0.158096\pi$
$359$	183.124	+	317.180i	0.0269217	+	0.0466298i	−0.852251	+	0.523134i	$0.824763\pi$
$360$	−3302.08	+	1441.53i	−0.483431	+	0.211042i
$361$	−8090.94	+	14013.9i	−1.17961	+	2.04314i
$362$	5036.42	+	1833.11i	0.731239	+	0.266149i
$363$	−645.025	+	4471.65i	−0.0932646	+	0.646559i
$364$	−280.749	−	235.576i	−0.0404265	−	0.0339218i
$365$	−1512.16	−	1268.85i	−0.216849	−	0.181958i
$366$	−1686.08	+	11688.8i	−0.240800	+	1.66935i
$367$	−7699.52	−	2802.40i	−1.09513	−	0.398594i	−0.269609	−	0.962970i	$-0.586895\pi$
$367$	−7699.52	−	2802.40i	−1.09513	−	0.398594i	−0.825518	+	0.564376i	$0.809117\pi$
$368$	3558.32	−	6163.18i	0.504049	−	0.873038i
$369$	−5165.56	+	2255.03i	−0.728749	+	0.318135i
$370$	4488.79	+	7774.81i	0.630706	+	1.09241i
$371$	−2.37557	−	13.4726i	−0.000332436	−	0.00188534i
$372$	−14.6606	−	70.2261i	−0.00204332	−	0.00978778i
$373$	−2422.87	+	881.852i	−0.336331	+	0.122414i	−0.504664	−	0.863316i	$-0.668384\pi$
$373$	−2422.87	+	881.852i	−0.336331	+	0.122414i	0.168333	+	0.985730i	$0.446161\pi$
$374$	−1360.25	+	7714.37i	−0.188067	+	1.06658i
$375$	7395.24	−	231.351i	1.01837	−	0.0318584i
$376$	2401.76	−	2015.32i	0.329419	−	0.276415i
$377$	−6570.93			−0.897666
$378$	1787.57	+	1234.29i	0.243235	+	0.167950i
$379$	1973.04			0.267410			0.133705	−	0.991021i	$-0.457313\pi$
$379$	1973.04			0.267410			0.133705	+	0.991021i	$0.457313\pi$
$380$	−1802.20	+	1512.23i	−0.243292	+	0.204146i
$381$	5414.68	−	10094.9i	0.728091	−	1.35742i
$382$	−1403.95	+	7962.18i	−0.188042	+	1.06644i
$383$	−7465.36	+	2717.17i	−0.995985	+	0.362509i	−0.788035	−	0.615631i	$-0.788901\pi$
$383$	−7465.36	+	2717.17i	−0.995985	+	0.362509i	−0.207950	+	0.978139i	$0.566679\pi$
$384$	6771.30	−	6052.50i	0.899860	−	0.804337i
$385$	129.924	+	736.833i	0.0171988	+	0.0975390i
$386$	−3001.11	−	5198.08i	−0.395732	−	0.685428i
$387$	2971.01	−	2827.65i	0.390246	−	0.371414i
$388$	40.0673	−	69.3986i	0.00524255	−	0.00908037i
$389$	−306.811	−	111.670i	−0.0399895	−	0.0145550i	0.321948	−	0.946757i	$-0.395662\pi$
$389$	−306.811	−	111.670i	−0.0399895	−	0.0145550i	−0.361937	+	0.932202i	$0.617885\pi$
$390$	3257.48	+	2564.14i	0.422947	+	0.332924i
$391$	8138.73	+	6829.21i	1.05267	+	0.883293i
$392$	4553.80	+	3821.09i	0.586739	+	0.492332i
$393$	1774.23	−	709.349i	0.227731	−	0.0910481i
$394$	−4678.82	−	1702.95i	−0.598262	−	0.217750i
$395$	925.976	−	1603.84i	0.117952	−	0.204298i
$396$	693.552	+	1044.52i	0.0880109	+	0.132549i
$397$	−2203.97	−	3817.39i	−0.278625	−	0.482592i	0.692418	−	0.721496i	$-0.256545\pi$
$397$	−2203.97	−	3817.39i	−0.278625	−	0.482592i	−0.971043	+	0.238904i	$0.923212\pi$
$398$	−1116.06	−	6329.49i	−0.140560	−	0.797158i
$399$	−3639.28	−	1197.11i	−0.456622	−	0.150202i
$400$	−5298.38	+	1928.45i	−0.662297	+	0.241057i
$401$	1422.73	−	8068.72i	0.177177	−	1.00482i	−0.758424	−	0.651761i	$-0.774030\pi$
$401$	1422.73	−	8068.72i	0.177177	−	1.00482i	0.935601	−	0.353059i	$-0.114858\pi$
$402$	−2069.71	−	3339.16i	−0.256786	−	0.414284i
$403$	170.789	−	143.309i	0.0211107	−	0.0177139i
$404$	2412.70			0.297119
$405$	−4392.05	−	2834.03i	−0.538871	−	0.347713i
$406$	2914.77			0.356299
$407$	−6464.00	+	5423.94i	−0.787245	+	0.660577i
$408$	5827.79	+	9402.25i	0.707153	+	1.14088i
$409$	1671.81	−	9481.29i	0.202116	−	1.14626i	−0.699797	−	0.714341i	$-0.746726\pi$
$409$	1671.81	−	9481.29i	0.202116	−	1.14626i	0.901914	−	0.431917i	$-0.142162\pi$
$410$	4483.59	−	1631.89i	0.540070	−	0.196570i
$411$	−4926.43	−	1620.51i	−0.591248	−	0.194486i
$412$	463.739	+	2629.99i	0.0554534	+	0.314492i
$413$	597.369	+	1034.67i	0.0711734	+	0.123276i
$414$	7978.58	−	499.689i	0.947163	−	0.0593197i
$415$	4769.48	−	8260.98i	0.564156	−	0.977146i
$416$	−3127.68	−	1138.38i	−0.368623	−	0.134168i
$417$	12209.6	−	4881.46i	1.43382	−	0.573252i
$418$	−7963.07	−	6681.81i	−0.931786	−	0.781862i
$419$	−10521.3	−	8828.44i	−1.22673	−	1.02935i	−0.998444	−	0.0557553i	$-0.982243\pi$
$419$	−10521.3	−	8828.44i	−1.22673	−	1.02935i	−0.228286	−	0.973594i	$-0.573312\pi$
$420$	−307.376	−	241.952i	−0.0357105	−	0.0281097i
$421$	10081.3	+	3669.30i	1.16706	+	0.424776i	0.851615	−	0.524167i	$-0.175623\pi$
$421$	10081.3	+	3669.30i	1.16706	+	0.424776i	0.315447	+	0.948943i	$0.397846\pi$
$422$	−1221.84	+	2116.28i	−0.140943	+	0.244121i
$423$	4363.03	+	1285.46i	0.501508	+	0.147757i
$424$	−26.2090	−	45.3953i	−0.00300194	−	0.00519950i
$425$	−1461.69	−	8289.66i	−0.166829	−	0.946136i
$426$	1512.39	−	1351.84i	0.172008	−	0.153749i
$427$	3254.30	−	1184.47i	0.368821	−	0.134240i
$428$	−277.246	+	1572.34i	−0.0313112	+	0.177575i
$429$	−1841.79	+	3433.75i	−0.207278	+	0.386440i
$430$	−2659.77	+	2231.81i	−0.298292	+	0.250296i
$431$	1902.52			0.212624			0.106312	−	0.994333i	$-0.466096\pi$
$431$	1902.52			0.212624			0.106312	+	0.994333i	$0.466096\pi$
$432$	10401.3	+	2714.07i	1.15840	+	0.302270i
$433$	−12218.4			−1.35607			−0.678034	−	0.735031i	$-0.737168\pi$
$433$	−12218.4			−1.35607			−0.678034	+	0.735031i	$0.737168\pi$
$434$	−75.7594	+	63.5697i	−0.00837918	+	0.00703097i
$435$	−7010.13	+	219.303i	−0.772666	+	0.0241719i
$436$	330.155	−	1872.40i	0.0362651	−	0.205669i
$437$	−13248.5	+	4822.06i	−1.45025	+	0.527849i
$438$	931.896	+	4463.91i	0.101661	+	0.486972i
$439$	213.898	+	1213.08i	0.0232547	+	0.131884i	0.994225	−	0.107317i	$-0.0342258\pi$
$439$	213.898	+	1213.08i	0.0232547	+	0.131884i	−0.970970	+	0.239200i	$0.923115\pi$
$440$	1433.41	+	2482.73i	0.155307	+	0.268999i
$441$	−963.746	+	8569.96i	−0.104065	+	0.925382i
$442$	6363.85	−	11022.5i	0.684836	−	1.18617i
$443$	10371.8	+	3775.04i	1.11237	+	0.404871i	0.831863	−	0.554981i	$-0.187274\pi$
$443$	10371.8	+	3775.04i	1.11237	+	0.404871i	0.280510	+	0.959851i	$0.409497\pi$
$444$	629.857	−	4366.50i	0.0673236	−	0.466723i
$445$	−456.804	−	383.304i	−0.0486620	−	0.0408323i
$446$	9422.88	+	7906.74i	1.00042	+	0.839450i
$447$	2502.45	−	17348.3i	0.264792	−	1.83568i
$448$	−1410.38	−	513.337i	−0.148737	−	0.0541360i
$449$	−6640.39	+	11501.5i	−0.697950	+	1.20888i	0.271227	+	0.962516i	$0.412571\pi$
$449$	−6640.39	+	11501.5i	−0.697950	+	1.20888i	−0.969176	+	0.246369i	$0.920763\pi$
$450$	−5096.89	−	3760.00i	−0.533933	−	0.393884i
$451$	2242.33	+	3883.82i	0.234118	+	0.405504i
$452$	334.546	+	1897.31i	0.0348136	+	0.197438i
$453$	1139.69	+	5459.26i	0.118206	+	0.566222i
$454$	−9311.53	+	3389.12i	−0.962581	+	0.350351i
$455$	211.100	−	1197.21i	0.0217506	−	0.123354i
$456$	−14672.2	+	459.001i	−1.50677	+	0.0471375i
$457$	635.660	−	533.382i	0.0650654	−	0.0545964i	−0.609675	−	0.792652i	$-0.708700\pi$
$457$	635.660	−	533.382i	0.0650654	−	0.0545964i	0.674740	+	0.738055i	$0.264256\pi$
$458$	−8459.58			−0.863079
$459$	−6686.65	+	14588.4i	−0.679970	+	1.48351i
$460$	−1439.56			−0.145913
$461$	10779.2	−	9044.81i	1.08902	−	0.913793i	0.0923782	−	0.995724i	$-0.470553\pi$
$461$	10779.2	−	9044.81i	1.08902	−	0.913793i	0.996638	+	0.0819309i	$0.0261087\pi$
$462$	816.990	−	1523.16i	0.0822723	−	0.153385i
$463$	−218.864	+	1241.24i	−0.0219686	+	0.124590i	−0.993820	−	0.111005i	$-0.964593\pi$
$463$	−218.864	+	1241.24i	−0.0219686	+	0.124590i	0.971851	+	0.235595i	$0.0757040\pi$
$464$	13553.7	−	4933.15i	1.35607	−	0.493568i
$465$	177.421	−	158.588i	0.0176940	−	0.0158157i
$466$	870.962	+	4939.47i	0.0865805	+	0.491023i
$467$	523.513	+	906.752i	0.0518743	+	0.0898490i	0.890797	−	0.454402i	$-0.150147\pi$
$467$	523.513	+	906.752i	0.0518743	+	0.0898490i	−0.838922	+	0.544251i	$0.816814\pi$
$468$	−478.468	−	1980.22i	−0.0472589	−	0.195589i
$469$	−576.019	+	997.694i	−0.0567123	+	0.0982286i
$470$	−3618.21	−	1316.92i	−0.355097	−	0.129245i
$471$	−11165.0	−	8788.53i	−1.09226	−	0.859775i
$472$	3506.78	+	2942.54i	0.341976	+	0.286952i
$473$	−2499.95	−	2097.71i	−0.243019	−	0.203917i
$474$	−3972.51	+	1588.24i	−0.384944	+	0.153903i
$475$	10496.6	+	3820.45i	1.01393	+	0.369041i
$476$	−600.493	+	1040.08i	−0.0578226	+	0.100152i
$477$	33.8315	−	68.1044i	0.00324746	−	0.00653729i
$478$	−8013.60	−	13880.0i	−0.766807	−	1.32815i
$479$	2585.05	+	14660.6i	0.246585	+	1.39845i	0.816783	+	0.576945i	$0.195755\pi$
$479$	2585.05	+	14660.6i	0.246585	+	1.39845i	−0.570198	+	0.821507i	$0.693134\pi$
$480$	−3374.73	−	1110.09i	−0.320906	−	0.105559i
$481$	12883.5	−	4689.22i	1.22128	−	0.444511i
$482$	1093.68	−	6202.55i	0.103352	−	0.586138i
$483$	−1235.04	−	1992.55i	−0.116348	−	0.187710i
$484$	−1439.74	+	1208.09i	−0.135212	+	0.113457i
$485$	265.812			0.0248864
$486$	3923.13	+	11420.0i	0.366167	+	1.06589i
$487$	−5554.29			−0.516815			−0.258408	−	0.966036i	$-0.583198\pi$
$487$	−5554.29			−0.516815			−0.258408	+	0.966036i	$0.583198\pi$
$488$	10165.0	−	8529.46i	0.942927	−	0.791210i
$489$	1378.59	+	2224.14i	0.127488	+	0.205683i
$490$	1267.72	−	7189.58i	0.116877	−	0.662841i
$491$	19584.3	−	7128.09i	1.80005	−	0.655165i	0.801702	−	0.597723i	$-0.203928\pi$
$491$	19584.3	−	7128.09i	1.80005	−	0.655165i	0.998349	−	0.0574416i	$-0.0182943\pi$
$492$	−2227.29	−	732.648i	−0.204094	−	0.0671348i
$493$	3739.13	+	21205.7i	0.341586	+	1.93723i
$494$	8444.97	+	14627.1i	0.769144	+	1.33220i
$495$	−1850.29	+	3724.73i	−0.168009	+	0.338210i
$496$	−244.693	+	423.820i	−0.0221513	+	0.0383671i
$497$	−558.973	−	203.450i	−0.0504495	−	0.0183621i
$498$	−20461.4	+	8180.62i	−1.84116	+	0.736109i
$499$	4643.93	+	3896.72i	0.416615	+	0.349581i	0.826874	−	0.562388i	$-0.190117\pi$
$499$	4643.93	+	3896.72i	0.416615	+	0.349581i	−0.410259	+	0.911969i	$0.634562\pi$
$500$	2357.81	+	1978.44i	0.210889	+	0.176957i
$501$	−2160.59	−	1700.72i	−0.192671	−	0.151662i
$502$	−6579.16	−	2394.62i	−0.584945	−	0.212903i
$503$	−7450.91	+	12905.4i	−0.660477	+	1.14398i	0.320014	+	0.947413i	$0.396312\pi$
$503$	−7450.91	+	12905.4i	−0.660477	+	1.14398i	−0.980491	+	0.196566i	$0.937021\pi$
$504$	−573.261	−	2372.53i	−0.0506648	−	0.209684i
$505$	4001.55	+	6930.88i	0.352607	+	0.610733i
$506$	−1104.53	−	6264.11i	−0.0970404	−	0.550344i
$507$	−3791.14	+	3388.70i	−0.332091	+	0.296839i
$508$	4478.02	−	1629.86i	0.391102	−	0.142350i
$509$	−972.211	+	5513.68i	−0.0846611	+	0.480137i	0.912768	+	0.408478i	$0.133940\pi$
$509$	−972.211	+	5513.68i	−0.0846611	+	0.480137i	−0.997429	+	0.0716588i	$0.977171\pi$
$510$	6421.34	−	11971.6i	0.557533	−	1.03944i
$511$	1024.39	−	859.562i	0.0886814	−	0.0744125i
$512$	−4101.93			−0.354066
$513$	−12328.9	−	17364.1i	−1.06108	−	1.49443i
$514$	−7660.84			−0.657403
$515$	−6785.98	+	5694.11i	−0.580633	+	0.487209i
$516$	1705.39	−	53.3510i	0.145495	−	0.00455164i
$517$	628.444	−	3564.09i	0.0534603	−	0.303188i
$518$	−5714.94	+	2080.07i	−0.484749	+	0.176434i
$519$	978.591	+	4687.58i	0.0827657	+	0.396459i
$520$	−808.855	−	4587.25i	−0.0682128	−	0.386854i
$521$	−3084.48	−	5342.47i	−0.259373	−	0.449248i	0.706701	−	0.707512i	$-0.250183\pi$
$521$	−3084.48	−	5342.47i	−0.259373	−	0.449248i	−0.966074	+	0.258265i	$0.916849\pi$
$522$	13038.3	+	9618.39i	1.09324	+	0.806486i
$523$	11712.8	−	20287.2i	0.979285	−	1.69617i	0.314283	−	0.949329i	$-0.398236\pi$
$523$	11712.8	−	20287.2i	0.979285	−	1.69617i	0.665002	−	0.746842i	$-0.268431\pi$
$524$	746.941	+	271.864i	0.0622715	+	0.0226650i
$525$	−265.171	+	1838.31i	−0.0220438	+	0.152819i
$526$	−9970.10	−	8365.90i	−0.826458	−	0.693481i
$527$	−559.672	−	469.620i	−0.0462613	−	0.0388178i
$528$	1221.12	−	8465.45i	0.100649	−	0.697749i
$529$	3326.47	+	1210.74i	0.273401	+	0.0995099i
$530$	−32.1872	+	55.7498i	−0.00263796	+	0.00456909i
$531$	−742.160	+	6599.54i	−0.0606535	+	0.539352i
$532$	−796.867	−	1380.21i	−0.0649409	−	0.112481i
$533$	−1265.32	−	7175.98i	−0.102828	−	0.583164i
$534$	281.514	+	1348.49i	0.0228133	+	0.109279i
$535$	−4976.64	+	1811.35i	−0.402166	+	0.146377i
$536$	−766.511	+	4347.10i	−0.0617691	+	0.350310i
$537$	2677.11	−	83.7500i	0.215132	−	0.00673013i
$538$	4793.32	−	4022.07i	0.384117	−	0.322312i
$539$	6861.84			0.548350
$540$	−576.538	−	2096.60i	−0.0459449	−	0.167081i
$541$	−17748.3			−1.41046			−0.705230	−	0.708979i	$-0.749156\pi$
$541$	−17748.3			−1.41046			−0.705230	+	0.708979i	$0.749156\pi$
$542$	3975.56	−	3335.89i	0.315065	−	0.264371i
$543$	4129.54	−	7698.92i	0.326364	−	0.608457i
$544$	−1894.01	+	10741.4i	−0.149274	+	0.846573i
$545$	5926.37	−	2157.02i	0.465794	−	0.169535i
$546$	−2093.84	+	1871.57i	−0.164117	+	0.146696i
$547$	−3488.54	−	19784.5i	−0.272686	−	1.54648i	−0.746219	−	0.665701i	$-0.768133\pi$
$547$	−3488.54	−	19784.5i	−0.272686	−	1.54648i	0.473533	−	0.880776i	$-0.342978\pi$
$548$	−1078.70	−	1868.37i	−0.0840876	−	0.145644i
$549$	18465.7	+	5440.47i	1.43552	+	0.422939i
$550$	−2519.77	+	4364.37i	−0.195352	+	0.338359i
$551$	−26851.2	−	9773.05i	−2.07605	−	0.755619i
$552$	−7058.03	−	5555.75i	−0.544220	−	0.428385i
$553$	961.060	+	806.425i	0.0739031	+	0.0620121i
$554$	8868.84	+	7441.84i	0.680146	+	0.570710i
$555$	13588.2	−	5432.63i	1.03925	−	0.415500i
$556$	5140.16	+	1870.86i	0.392071	+	0.142702i
$557$	6968.42	−	12069.7i	0.530093	−	0.918147i	−0.469291	−	0.883043i	$-0.655491\pi$
$557$	6968.42	−	12069.7i	0.530093	−	0.918147i	0.999384	−	0.0351037i	$-0.0111761\pi$
$558$	−548.659	+	34.3618i	−0.0416247	+	0.00260690i
$559$	2651.24	+	4592.08i	0.200600	+	0.347450i
$560$	463.378	+	2627.94i	0.0349666	+	0.198305i
$561$	12129.4	+	3989.87i	0.912843	+	0.300272i
$562$	25039.4	−	9113.58i	1.87940	−	0.684045i
$563$	−533.880	+	3027.78i	−0.0399651	+	0.226653i	−0.998248	−	0.0591679i	$-0.981155\pi$
$563$	−533.880	+	3027.78i	−0.0399651	+	0.226653i	0.958283	+	0.285821i	$0.0922664\pi$
$564$	996.848	+	1608.26i	0.0744235	+	0.120071i
$565$	−4895.48	+	4107.79i	−0.364521	+	0.305869i
$566$	−21750.1			−1.61524
$567$	2407.36	−	2596.74i	0.178306	−	0.192333i
$568$	−2279.22			−0.168370
$569$	4846.04	−	4066.31i	0.357041	−	0.299593i	−0.446569	−	0.894749i	$-0.647354\pi$
$569$	4846.04	−	4066.31i	0.357041	−	0.299593i	0.803610	+	0.595156i	$0.202910\pi$
$570$	9497.60	+	15322.9i	0.697914	+	1.12598i
$571$	2157.30	−	12234.6i	0.158109	−	0.896679i	−0.797780	−	0.602949i	$-0.793992\pi$
$571$	2157.30	−	12234.6i	0.158109	−	0.896679i	0.955888	−	0.293730i	$-0.0948967\pi$
$572$	−1523.18	+	554.394i	−0.111342	+	0.0405251i
$573$	12519.1	+	4118.04i	0.912726	+	0.300233i
$574$	561.277	+	3183.16i	0.0408140	+	0.231468i
$575$	3417.55	+	5919.37i	0.247864	+	0.429313i
$576$	−4614.96	−	6950.36i	−0.333836	−	0.502775i
$577$	−4666.09	+	8081.90i	−0.336658	+	0.583109i	−0.983802	−	0.179259i	$-0.942630\pi$
$577$	−4666.09	+	8081.90i	−0.336658	+	0.583109i	0.647144	+	0.762368i	$0.275963\pi$
$578$	−24476.3	−	8908.66i	−1.76139	−	0.641092i
$579$	−9084.76	+	3632.14i	−0.652072	+	0.260702i
$580$	−2235.03	−	1875.41i	−0.160008	−	0.134262i
$581$	4950.19	+	4153.70i	0.353474	+	0.296600i
$582$	−482.509	−	379.808i	−0.0343654	−	0.0270508i
$583$	−56.8574	−	20.6944i	−0.00403909	−	0.00147011i
$584$	2561.90	−	4437.33i	0.181527	−	0.314415i
$585$	4894.95	−	4658.74i	0.345951	−	0.329257i
$586$	12979.7	+	22481.5i	0.914995	+	1.58482i
$587$	1645.20	+	9330.41i	0.115681	+	0.656060i	0.986411	+	0.164298i	$0.0525359\pi$
$587$	1645.20	+	9330.41i	0.115681	+	0.656060i	−0.870730	+	0.491762i	$0.836353\pi$
$588$	−2674.78	+	2390.84i	−0.187595	+	0.167681i
$589$	911.052	−	331.596i	0.0637339	−	0.0231972i
$590$	976.242	−	5536.54i	0.0681207	−	0.386332i
$591$	−3836.32	+	7152.27i	−0.267014	+	0.497809i
$592$	−23054.1	+	19344.7i	−1.60054	+	1.34301i
$593$	15625.3			1.08204			0.541022	−	0.841008i	$-0.318037\pi$
$593$	15625.3			1.08204			0.541022	+	0.841008i	$0.318037\pi$
$594$	8680.80	−	4117.41i	0.599626	−	0.284409i
$595$	−3983.76			−0.274484
$596$	5585.66	−	4686.92i	0.383888	−	0.322120i
$597$	−10471.4	+	327.586i	−0.717868	+	0.0224576i
$598$	−1794.65	+	10178.0i	−0.122724	+	0.696000i
$599$	−18383.8	+	6691.17i	−1.25400	+	0.456417i	−0.881750	−	0.471717i	$-0.843634\pi$
$599$	−18383.8	+	6691.17i	−1.25400	+	0.456417i	−0.372246	+	0.928134i	$0.621412\pi$
$600$	1454.32	+	6966.40i	0.0989540	+	0.474003i
$601$	1170.18	+	6636.41i	0.0794219	+	0.450424i	0.998421	+	0.0561655i	$0.0178874\pi$
$601$	1170.18	+	6636.41i	0.0794219	+	0.450424i	−0.919000	+	0.394259i	$0.871001\pi$
$602$	−1176.05	−	2036.98i	−0.0796217	−	0.137909i
$603$	−5868.92	+	2562.08i	−0.396353	+	0.173028i
$604$	−1160.00	+	2009.18i	−0.0781452	+	0.135351i
$605$	−5858.30	−	2132.25i	−0.393676	−	0.143286i
$606$	2639.55	−	18298.7i	0.176938	−	1.22663i
$607$	6250.46	+	5244.76i	0.417954	+	0.350705i	0.827384	−	0.561636i	$-0.189828\pi$
$607$	6250.46	+	5244.76i	0.417954	+	0.350705i	−0.409430	+	0.912342i	$0.634272\pi$
$608$	−11087.7	−	9303.72i	−0.739584	−	0.620585i
$609$	678.330	−	4702.54i	0.0451352	−	0.312901i
$610$	−15313.4	−	5573.63i	−1.01643	−	0.369950i
$611$	−2940.14	+	5092.47i	−0.194673	+	0.337184i
$612$	−6118.28	+	2670.94i	−0.404112	+	0.176415i
$613$	−2100.86	−	3638.80i	−0.138423	−	0.239755i	0.788477	−	0.615064i	$-0.210870\pi$
$613$	−2100.86	−	3638.80i	−0.138423	−	0.239755i	−0.926900	+	0.375309i	$0.877537\pi$
$614$	2574.37	+	14600.0i	0.169207	+	0.959621i
$615$	−1589.39	−	7613.39i	−0.104212	−	0.499190i
$616$	−1824.95	+	664.229i	−0.119366	+	0.0434457i
$617$	−1694.73	+	9611.32i	−0.110579	+	0.627127i	0.878265	+	0.478174i	$0.158701\pi$
$617$	−1694.73	+	9611.32i	−0.110579	+	0.627127i	−0.988844	+	0.148952i	$0.952410\pi$
$618$	20454.1	−	639.882i	1.33137	−	0.0416502i
$619$	−10114.5	+	8487.05i	−0.656761	+	0.551088i	−0.909114	−	0.416547i	$-0.863240\pi$
$619$	−10114.5	+	8487.05i	−0.656761	+	0.551088i	0.252353	+	0.967635i	$0.418796\pi$
$620$	98.9937			0.00641239
$621$	1050.62	−	12988.5i	0.0678902	−	0.839311i
$622$	9178.93			0.591707
$623$	309.454	−	259.663i	0.0199005	−	0.0166985i
$624$	−6568.81	+	12246.6i	−0.421415	+	0.785667i
$625$	−175.557	+	995.633i	−0.0112356	+	0.0637205i
$626$	2609.78	−	949.883i	0.166626	−	0.0606469i
$627$	−12633.3	+	11292.2i	−0.804666	+	0.719248i
$628$	−1026.42	−	5821.09i	−0.0652204	−	0.369883i
$629$	−22464.3	−	38909.3i	−1.42402	−	2.46648i
$630$	−2171.33	+	2066.55i	−0.137314	+	0.130688i
$631$	−8133.90	+	14088.3i	−0.513162	+	0.888823i	0.486721	+	0.873557i	$0.338193\pi$
$631$	−8133.90	+	14088.3i	−0.513162	+	0.888823i	−0.999883	+	0.0152658i	$0.995141\pi$
$632$	4517.14	+	1644.11i	0.284308	+	0.103479i
$633$	3129.96	+	2463.76i	0.196532	+	0.154701i
$634$	16251.3	+	13636.4i	1.01801	+	0.854215i
$635$	12109.0	+	10160.7i	0.756743	+	0.634982i
$636$	29.3737	−	11.7438i	0.00183136	−	0.000732188i
$637$	−10476.8	−	3813.23i	−0.651656	−	0.237183i
$638$	6445.79	−	11164.4i	0.399986	−	0.692797i
$639$	−1829.03	−	2754.62i	−0.113232	−	0.170534i
$640$	6266.12	+	10853.2i	0.387016	+	0.670331i
$641$	967.776	+	5488.53i	0.0596331	+	0.338196i	0.999998	−	0.00197102i	$-0.000627395\pi$
$641$	967.776	+	5488.53i	0.0596331	+	0.338196i	−0.940365	+	0.340167i	$0.889516\pi$
$642$	11621.9	+	3822.91i	0.714453	+	0.235013i
$643$	−22952.9	+	8354.19i	−1.40774	+	0.512375i	−0.930465	−	0.366380i	$-0.880597\pi$
$643$	−22952.9	+	8354.19i	−1.40774	+	0.512375i	−0.477273	+	0.878755i	$0.658375\pi$
$644$	169.343	−	960.392i	0.0103619	−	0.0587652i
$645$	2981.71	+	4810.53i	0.182023	+	0.293666i
$646$	42399.0	−	35577.0i	2.58230	−	2.16681i
$647$	25936.4			1.57599			0.787994	−	0.615683i	$-0.211120\pi$
$647$	25936.4			1.57599			0.787994	+	0.615683i	$0.211120\pi$
$648$	5264.78	−	12504.5i	0.319167	−	0.758059i
$649$	5284.15			0.319601
$650$	6272.58	−	5263.32i	0.378509	−	0.317607i
$651$	84.9294	+	137.021i	0.00511313	+	0.00824925i
$652$	−189.025	+	1072.02i	−0.0113540	+	0.0643917i
$653$	14132.2	−	5143.69i	0.846913	−	0.308251i	0.118132	−	0.992998i	$-0.462309\pi$
$653$	14132.2	−	5143.69i	0.846913	−	0.308251i	0.728781	+	0.684747i	$0.240087\pi$
$654$	−13839.8	−	4552.47i	−0.827489	−	0.272195i
$655$	457.853	+	2596.61i	0.0273127	+	0.154898i
$656$	7997.34	+	13851.8i	0.475981	+	0.824424i
$657$	7418.73	−	464.626i	0.440536	−	0.0275902i
$658$	1304.20	−	2258.94i	0.0772691	−	0.133834i
$659$	8234.48	+	2997.10i	0.486752	+	0.177163i	0.573726	−	0.819047i	$-0.305497\pi$
$659$	8234.48	+	2997.10i	0.486752	+	0.177163i	−0.0869738	+	0.996211i	$0.527720\pi$
$660$	−1606.49	+	642.285i	−0.0947463	+	0.0378802i
$661$	−11054.9	−	9276.12i	−0.650505	−	0.545839i	0.256719	−	0.966486i	$-0.417359\pi$
$661$	−11054.9	−	9276.12i	−0.650505	−	0.545839i	−0.907224	+	0.420647i	$0.861803\pi$
$662$	−21805.1	−	18296.7i	−1.28018	−	1.07420i
$663$	−16302.2	−	12832.3i	−0.954939	−	0.751683i
$664$	23266.7	+	8468.39i	1.35983	+	0.494936i
$665$	2643.27	−	4578.27i	0.154138	−	0.266974i
$666$	−32428.0	−	9554.11i	−1.88673	−	0.555877i
$667$	−8742.39	−	15142.3i	−0.507506	−	0.879026i
$668$	−198.627	−	1126.47i	−0.0115047	−	0.0652463i
$669$	14949.3	−	13362.4i	0.863934	−	0.772225i
$670$	5094.09	−	1854.10i	0.293734	−	0.106910i
$671$	2659.78	−	15084.3i	0.153025	−	0.867846i
$672$	1137.57	−	2120.84i	0.0653018	−	0.121746i
$673$	4937.34	−	4142.92i	0.282794	−	0.237292i	−0.490346	−	0.871528i	$-0.663130\pi$
$673$	4937.34	−	4142.92i	0.282794	−	0.237292i	0.773140	+	0.634236i	$0.218685\pi$
$674$	3685.41			0.210618
$675$	−7252.36	+	7348.05i	−0.413546	+	0.419003i
$676$	−2115.30			−0.120351
$677$	5427.06	−	4553.85i	0.308093	−	0.258521i	−0.475610	−	0.879656i	$-0.657773\pi$
$677$	5427.06	−	4553.85i	0.308093	−	0.258521i	0.783703	+	0.621135i	$0.213328\pi$
$678$	14755.8	−	461.618i	0.835832	−	0.0261480i
$679$	−31.2689	+	177.335i	−0.00176729	+	0.0100228i
$680$	−14343.7	+	5220.67i	−0.808904	+	0.294417i
$681$	3300.84	+	15811.5i	0.185740	+	0.889718i
$682$	75.9548	+	430.761i	0.00426460	+	0.0241858i
$683$	9702.06	+	16804.5i	0.543542	+	0.941442i	0.998697	+	0.0510297i	$0.0162503\pi$
$683$	9702.06	+	16804.5i	0.543542	+	0.941442i	−0.455156	+	0.890412i	$0.650416\pi$
$684$	990.012	−	8803.53i	0.0553422	−	0.492122i
$685$	3578.14	−	6197.52i	0.199582	−	0.345686i
$686$	9637.96	+	3507.93i	0.536413	+	0.195238i
$687$	−1968.73	+	13648.3i	−0.109333	+	0.757954i
$688$	−8916.18	−	7481.57i	−0.494079	−	0.414581i
$689$	75.3106	+	63.1931i	0.00416416	+	0.00349414i
$690$	−1574.92	+	10918.2i	−0.0868928	+	0.602387i
$691$	−27872.8	−	10144.9i	−1.53449	−	0.558508i	−0.569772	−	0.821803i	$-0.692968\pi$
$691$	−27872.8	−	10144.9i	−1.53449	−	0.558508i	−0.964715	+	0.263295i	$0.915191\pi$
$692$	−996.031	+	1725.18i	−0.0547159	+	0.0947708i
$693$	−2267.26	−	1672.57i	−0.124280	−	0.0916818i
$694$	−10913.0	−	18901.9i	−0.596906	−	1.03387i
$695$	3150.76	+	17868.9i	0.171964	+	0.975259i
$696$	−3720.28	−	17820.6i	−0.202610	−	0.970531i
$697$	−22438.3	+	8166.87i	−1.21938	+	0.443820i
$698$	−1251.69	+	7098.68i	−0.0678755	+	0.384941i
$699$	8171.80	−	255.645i	0.442183	−	0.0138331i
$700$	−591.881	+	496.647i	−0.0319585	+	0.0268164i
$701$	−29123.5			−1.56916			−0.784579	−	0.620029i	$-0.787121\pi$
$701$	−29123.5			−1.56916			−0.784579	+	0.620029i	$0.787121\pi$
$702$	−15542.1	+	1462.46i	−0.835611	+	0.0786284i
$703$	59621.2			3.19866
$704$	−5085.20	+	4266.99i	−0.272238	+	0.228435i
$705$	−2966.70	+	5530.98i	−0.158485	+	0.295473i
$706$	−2958.00	+	16775.7i	−0.157685	+	0.894279i
$707$	−5094.60	+	1854.28i	−0.271007	+	0.0986386i
$708$	−2059.79	+	1841.13i	−0.109338	+	0.0977317i
$709$	−3531.60	−	20028.7i	−0.187069	−	1.06092i	−0.923268	−	0.384156i	$-0.874492\pi$
$709$	−3531.60	−	20028.7i	−0.187069	−	1.06092i	0.736199	−	0.676765i	$-0.236619\pi$
$710$	1399.55	+	2424.10i	0.0739779	+	0.128133i
$711$	1637.89	+	6778.68i	0.0863935	+	0.357553i
$712$	773.917	−	1340.46i	0.0407356	−	0.0705562i
$713$	557.474	+	202.904i	0.0292813	+	0.0106575i
$714$	7231.41	+	5692.23i	0.379032	+	0.298356i
$715$	−4118.85	−	3456.12i	−0.215435	−	0.180771i
$716$	853.537	+	716.203i	0.0445505	+	0.0373823i
$717$	−24258.2	+	9698.59i	−1.26351	+	0.505161i
$718$	1097.09	+	399.307i	0.0570236	+	0.0207549i
$719$	727.763	−	1260.52i	0.0377482	−	0.0653819i	−0.846534	−	0.532335i	$-0.821315\pi$
$719$	727.763	−	1260.52i	0.0377482	−	0.0653819i	0.884282	+	0.466953i	$0.154648\pi$
$720$	−6599.14	+	13284.4i	−0.341577	+	0.687611i
$721$	−3000.51	−	5197.03i	−0.154986	−	0.268443i
$722$	8957.36	+	50799.7i	0.461715	+	2.61852i
$723$	−9752.38	−	3207.96i	−0.501653	−	0.165014i
$724$	3415.18	−	1243.02i	0.175310	−	0.0638075i
$725$	−2405.54	+	13642.5i	−0.123227	+	0.698855i
$726$	7587.44	+	12241.2i	0.387874	+	0.625775i
$727$	12410.8	−	10413.9i	0.633136	−	0.531264i	−0.268766	−	0.963206i	$-0.586616\pi$
$727$	12410.8	−	10413.9i	0.633136	−	0.531264i	0.901902	+	0.431941i	$0.142171\pi$
$728$	3155.49			0.160646
$729$	19337.5	−	3671.71i	0.982447	−	0.186542i
$730$	−6292.51			−0.319036
$731$	13310.9	−	11169.2i	0.673490	−	0.565125i
$732$	4218.98	+	6806.67i	0.213030	+	0.343691i
$733$	2366.89	−	13423.3i	0.119268	−	0.676401i	−0.865281	−	0.501288i	$-0.832860\pi$
$733$	2366.89	−	13423.3i	0.119268	−	0.676401i	0.984548	−	0.175113i	$-0.0560290\pi$
$734$	−24543.9	+	8933.26i	−1.23424	+	0.449227i
$735$	−11304.3	−	3718.45i	−0.567300	−	0.186608i
$736$	−1537.94	−	8722.12i	−0.0770236	−	0.436823i
$737$	2547.65	+	4412.65i	0.127332	+	0.220546i
$738$	−7993.36	+	16091.0i	−0.398699	+	0.802600i
$739$	9649.92	−	16714.2i	0.480349	−	0.831989i	−0.519397	−	0.854533i	$-0.673843\pi$
$739$	9649.92	−	16714.2i	0.480349	−	0.831989i	0.999746	+	0.0225441i	$0.00717661\pi$
$740$	5720.54	+	2082.10i	0.284177	+	0.103432i
$741$	25564.0	−	10220.7i	1.26737	−	0.506701i
$742$	−33.4067	−	28.0315i	−0.00165283	−	0.00138689i
$743$	−4709.23	−	3951.52i	−0.232524	−	0.195110i	0.519080	−	0.854726i	$-0.326275\pi$
$743$	−4709.23	−	3951.52i	−0.232524	−	0.195110i	−0.751603	+	0.659615i	$0.770719\pi$
$744$	485.356	+	382.049i	0.0239167	+	0.0188261i
$745$	22728.0	+	8272.31i	1.11770	+	0.406811i
$746$	−4109.56	+	7117.96i	−0.201691	+	0.349339i
$747$	8436.38	+	34915.3i	0.413214	+	1.71015i
$748$	2655.89	+	4600.14i	0.129825	+	0.224863i
$749$	−622.999	−	3533.20i	−0.0303924	−	0.172364i
$750$	17584.7	−	15718.0i	0.856136	−	0.765254i
$751$	−25622.3	+	9325.75i	−1.24497	+	0.453131i	−0.878698	−	0.477378i	$-0.841587\pi$
$751$	−25622.3	+	9325.75i	−1.24497	+	0.453131i	−0.366269	+	0.930509i	$0.619365\pi$
$752$	2241.37	−	12711.4i	0.108689	−	0.616408i
$753$	−5394.48	+	10057.2i	−0.261070	+	0.486727i
$754$	−16045.8	+	13464.0i	−0.775005	+	0.650306i
$755$	−7695.60			−0.370956
$756$	1466.55	−	137.998i	0.0705529	−	0.00663881i
$757$	4412.15			0.211839			0.105920	−	0.994375i	$-0.466221\pi$
$757$	4412.15			0.211839			0.105920	+	0.994375i	$0.466221\pi$
$758$	4818.05	−	4042.82i	0.230870	−	0.193723i
$759$	−10363.3	+	324.202i	−0.495603	+	0.0155043i
$760$	3517.41	−	19948.2i	0.167881	−	0.952102i
$761$	8146.13	−	2964.95i	0.388038	−	0.141234i	−0.140632	−	0.990062i	$-0.544913\pi$
$761$	8146.13	−	2964.95i	0.388038	−	0.141234i	0.528670	+	0.848828i	$0.322691\pi$
$762$	−7462.41	−	35746.0i	−0.354770	−	1.69940i
$763$	741.891	+	4207.47i	0.0352008	+	0.199634i
$764$	2741.21	+	4747.91i	0.129808	+	0.224834i
$765$	−17820.1	−	13145.9i	−0.842206	−	0.621298i
$766$	−12662.4	+	21931.9i	−0.597273	+	1.03451i
$767$	−8067.94	−	2936.49i	−0.379813	−	0.138240i
$768$	2299.47	−	15941.2i	0.108040	−	0.748993i
$769$	−2532.05	−	2124.64i	−0.118736	−	0.0996315i	0.581486	−	0.813556i	$-0.302471\pi$
$769$	−2532.05	−	2124.64i	−0.118736	−	0.0996315i	−0.700222	+	0.713925i	$0.746916\pi$
$770$	1827.06	+	1533.08i	0.0855099	+	0.0717513i
$771$	−1782.85	+	12359.6i	−0.0832784	+	0.577330i
$772$	−3824.63	−	1392.05i	−0.178305	−	0.0648977i
$773$	1480.29	−	2563.93i	0.0688774	−	0.119299i	−0.829530	−	0.558462i	$-0.811392\pi$
$773$	1480.29	−	2563.93i	0.0688774	−	0.119299i	0.898407	+	0.439163i	$0.144725\pi$
$774$	1461.10	−	12992.6i	0.0678531	−	0.603373i
$775$	−235.013	−	407.054i	−0.0108928	−	0.0188669i
$776$	119.810	+	679.477i	0.00554244	+	0.0314328i
$777$	2025.89	+	9704.29i	0.0935372	+	0.448056i
$778$	−978.028	+	355.973i	−0.0450694	+	0.0164039i
$779$	5502.40	−	31205.7i	0.253073	−	1.43525i
$780$	2809.74	−	87.8994i	0.128981	−	0.00403500i
$781$	−2015.40	+	1691.12i	−0.0923390	+	0.0774817i
$782$	33867.5			1.54872
$783$	18552.2	−	18797.0i	0.846744	−	0.857916i
$784$	24473.0			1.11484
$785$	15019.7	−	12603.0i	0.682900	−	0.573022i
$786$	2879.09	−	5367.64i	0.130653	−	0.243584i
$787$	−3426.94	+	19435.1i	−0.155219	+	0.880289i	0.803367	+	0.595484i	$0.203040\pi$
$787$	−3426.94	+	19435.1i	−0.155219	+	0.880289i	−0.958586	+	0.284805i	$0.908071\pi$
$788$	−3172.69	+	1154.76i	−0.143429	+	0.0522041i
$789$	−15817.4	+	14138.3i	−0.713707	+	0.637945i
$790$	−1025.13	−	5813.83i	−0.0461679	−	0.261831i
$791$	−2164.60	−	3749.20i	−0.0973000	−	0.168528i
$792$	−10355.2	−	3050.92i	−0.464593	−	0.136881i
$793$	−12443.6	+	21552.9i	−0.557232	+	0.965154i
$794$	−13203.9	−	4805.83i	−0.590162	−	0.214802i
$795$	82.4534	+	64.9034i	0.00367839	+	0.00289546i
$796$	−3338.59	−	2801.41i	−0.148660	−	0.124740i
$797$	−6578.60	−	5520.10i	−0.292379	−	0.245335i	0.484785	−	0.874633i	$-0.338898\pi$
$797$	−6578.60	−	5520.10i	−0.292379	−	0.245335i	−0.777164	+	0.629298i	$0.783342\pi$
$798$	−11339.8	+	4533.73i	−0.503039	+	0.201118i
$799$	18107.5	+	6590.58i	0.801747	+	0.291812i
$800$	−3508.51	+	6076.93i	−0.155056	+	0.268565i
$801$	2241.11	−	140.358i	0.0988584	−	0.00619138i
$802$	−13058.8	−	22618.5i	−0.574966	−	0.995871i
$803$	−1027.03	−	5824.57i	−0.0451346	−	0.255971i
$804$	−2530.56	−	832.407i	−0.111003	−	0.0365133i
$805$	3039.75	−	1106.38i	0.133090	−	0.0484407i
$806$	123.412	−	699.902i	0.00539329	−	0.0305869i
$807$	−5373.51	−	8669.34i	−0.234395	−	0.378160i
$808$	−15913.3	+	13352.8i	−0.692856	+	0.581376i
$809$	−2823.95			−0.122725			−0.0613626	−	0.998116i	$-0.519545\pi$
$809$	−2823.95			−0.122725			−0.0613626	+	0.998116i	$0.519545\pi$
$810$	−16532.1	+	2078.93i	−0.717135	+	0.0901804i
$811$	8173.40			0.353892			0.176946	−	0.984221i	$-0.443378\pi$
$811$	8173.40			0.353892			0.176946	+	0.984221i	$0.443378\pi$
$812$	1514.08	−	1270.47i	0.0654358	−	0.0549071i
$813$	−4456.77	−	7190.32i	−0.192258	−	0.310179i
$814$	−4670.88	+	26489.9i	−0.201123	+	1.14063i
$815$	−3393.05	+	1234.97i	−0.145832	+	0.0530787i
$816$	43260.1	+	14230.0i	1.85589	+	0.610478i
$817$	4004.07	+	22708.2i	0.171462	+	0.972410i
$818$	−15345.0	−	26578.3i	−0.655898	−	1.13605i
$819$	2532.22	+	3813.65i	0.108038	+	0.162710i
$820$	1617.72	−	2801.96i	0.0688940	−	0.119328i
$821$	9318.94	+	3391.82i	0.396143	+	0.144184i	0.532407	−	0.846488i	$-0.321287\pi$
$821$	9318.94	+	3391.82i	0.396143	+	0.144184i	−0.136265	+	0.990672i	$0.543510\pi$
$822$	−15350.5	+	6137.23i	−0.651351	+	0.260414i
$823$	21772.3	+	18269.1i	0.922157	+	0.773782i	0.974393	−	0.224853i	$-0.0721903\pi$
$823$	21772.3	+	18269.1i	0.922157	+	0.773782i	−0.0522357	+	0.998635i	$0.516635\pi$
$824$	−17614.1	−	14780.0i	−0.744680	−	0.624861i
$825$	6454.86	+	5080.96i	0.272399	+	0.214420i
$826$	3578.82	+	1302.58i	0.150754	+	0.0548700i
$827$	13118.2	−	22721.5i	0.551591	−	0.955384i	−0.446569	−	0.894749i	$-0.647354\pi$
$827$	13118.2	−	22721.5i	0.551591	−	0.955384i	0.998160	−	0.0606348i	$-0.0193125\pi$
$828$	3926.69	−	3737.20i	0.164809	−	0.156856i
$829$	13091.4	+	22675.0i	0.548472	+	0.949982i	0.998380	+	0.0569066i	$0.0181237\pi$
$829$	13091.4	+	22675.0i	0.548472	+	0.949982i	−0.449907	+	0.893075i	$0.648543\pi$
$830$	−5280.22	−	29945.6i	−0.220818	−	1.25232i
$831$	14070.3	−	12576.7i	0.587356	−	0.525006i
$832$	10135.4	−	3688.98i	0.422334	−	0.153717i
$833$	−6344.33	+	35980.5i	−0.263887	+	1.49658i
$834$	19812.7	−	36938.0i	0.822613	−	1.53364i
$835$	2906.55	−	2438.89i	0.120462	−	0.101079i
$836$	−7048.85			−0.291614
$837$	−72.2472	+	893.176i	−0.00298355	+	0.0368849i
$838$	−43782.1			−1.80481
$839$	−17808.7	+	14943.3i	−0.732806	+	0.614898i	−0.930895	−	0.365287i	$-0.880971\pi$
$839$	−17808.7	+	14943.3i	−0.732806	+	0.614898i	0.198089	+	0.980184i	$0.436527\pi$
$840$	3366.41	−	105.314i	0.138276	−	0.00432580i
$841$	1918.48	−	10880.3i	0.0786618	−	0.446113i
$842$	32136.5	−	11696.7i	1.31532	−	0.478736i
$843$	−8876.21	−	42518.2i	−0.362649	−	1.73714i
$844$	287.743	+	1631.87i	0.0117352	+	0.0665537i
$845$	−3508.29	−	6076.54i	−0.142827	−	0.247384i
$846$	13288.2	−	5800.97i	0.540021	−	0.235746i
$847$	2111.65	−	3657.49i	0.0856637	−	0.148374i
$848$	−202.784	−	73.8074i	−0.00821183	−	0.00298886i
$849$	−5061.72	+	35090.5i	−0.204615	+	1.41850i
$850$	−20555.1	−	17247.8i	−0.829453	−	0.695994i
$851$	27947.1	+	23450.4i	1.12575	+	0.944616i
$852$	196.382	−	1361.43i	0.00789665	−	0.0547437i
$853$	−28176.8	−	10255.5i	−1.13101	−	0.411655i	−0.292353	−	0.956310i	$-0.594438\pi$
$853$	−28176.8	−	10255.5i	−1.13101	−	0.411655i	−0.838660	+	0.544655i	$0.816660\pi$
$854$	5519.79	−	9560.57i	0.221175	−	0.383086i
$855$	26931.6	−	11757.0i	1.07724	−	0.470270i
$856$	−6873.36	−	11905.0i	−0.274447	−	0.475356i
$857$	−5502.33	−	31205.3i	−0.219319	−	1.24382i	−0.873253	−	0.487267i	$-0.837994\pi$
$857$	−5502.33	−	31205.3i	−0.219319	−	1.24382i	0.653934	−	0.756551i	$-0.273117\pi$
$858$	2538.32	+	12158.9i	0.100998	+	0.483796i
$859$	15776.5	−	5742.18i	0.626644	−	0.228080i	−0.00912597	−	0.999958i	$-0.502905\pi$
$859$	15776.5	−	5742.18i	0.626644	−	0.228080i	0.635770	+	0.771879i	$0.280683\pi$
$860$	−408.838	+	2318.64i	−0.0162108	+	0.0919359i
$861$	5266.18	−	164.746i	0.208445	−	0.00652093i
$862$	4645.83	−	3898.31i	0.183570	−	0.154034i
$863$	−30224.1			−1.19217			−0.596083	−	0.802923i	$-0.703277\pi$
$863$	−30224.1			−1.19217			−0.596083	+	0.802923i	$0.703277\pi$
$864$	12087.1	−	5733.05i	0.475939	−	0.225744i
$865$	−6607.81			−0.259737
$866$	−29836.5	+	25035.8i	−1.17077	+	0.982391i
$867$	−20069.0	+	37415.7i	−0.786134	+	1.46563i
$868$	−11.6451	+	66.0428i	−0.000455370	+	0.00258253i
$869$	5214.17	−	1897.80i	0.203543	−	0.0740834i
$870$	−16668.9	+	14899.5i	−0.649575	+	0.580620i
$871$	−1437.61	−	8153.08i	−0.0559259	−	0.317172i
$872$	8185.05	+	14176.9i	0.317868	+	0.550563i
$873$	−725.055	+	690.067i	−0.0281093	+	0.0267528i
$874$	−22471.5	+	38921.7i	−0.869689	+	1.50635i
$875$	−6499.24	−	2365.53i	−0.251102	−	0.0913937i
$876$	2429.77	+	1912.60i	0.0937149	+	0.0737680i
$877$	35266.7	+	29592.3i	1.35789	+	1.13941i	0.976626	+	0.214944i	$0.0689570\pi$
$877$	35266.7	+	29592.3i	1.35789	+	1.13941i	0.381268	+	0.924464i	$0.375487\pi$
$878$	3007.95	+	2523.97i	0.115619	+	0.0970159i
$879$	39291.3	−	15708.9i	1.50769	−	0.602785i
$880$	11090.6	+	4036.63i	0.424844	+	0.154630i
$881$	−20745.8	+	35932.8i	−0.793354	+	1.37413i	0.130526	+	0.991445i	$0.458333\pi$
$881$	−20745.8	+	35932.8i	−0.793354	+	1.37413i	−0.923879	+	0.382684i	$0.875000\pi$
$882$	15206.7	+	22902.1i	0.580540	+	0.874323i
$883$	−4380.65	−	7587.50i	−0.166954	−	0.289173i	0.770393	−	0.637569i	$-0.220060\pi$
$883$	−4380.65	−	7587.50i	−0.166954	−	0.289173i	−0.937348	+	0.348396i	$0.886727\pi$
$884$	−1498.69	−	8499.50i	−0.0570208	−	0.323381i
$885$	−8705.20	−	2863.50i	−0.330646	−	0.108763i
$886$	33062.6	−	12033.8i	1.25368	−	0.456302i
$887$	78.0143	−	442.441i	0.00295317	−	0.0167483i	−0.983296	−	0.182016i	$-0.941738\pi$
$887$	78.0143	−	442.441i	0.00295317	−	0.0167483i	0.986249	+	0.165268i	$0.0528488\pi$
$888$	20011.7	+	32285.8i	0.756247	+	1.22009i
$889$	−8203.05	+	6883.18i	−0.309473	+	0.259679i
$890$	−1900.89			−0.0715932
$891$	−4622.61	−	14963.4i	−0.173808	−	0.562618i
$892$	8341.06			0.313094
$893$	−19588.6	+	16436.8i	−0.734051	+	0.615942i
$894$	−29436.4	−	47491.2i	−1.10123	−	1.77667i
$895$	−641.791	+	3639.78i	−0.0239695	+	0.135938i
$896$	−7977.76	+	2903.67i	−0.297453	+	0.108264i
$897$	16003.0	+	5264.04i	0.595679	+	0.195943i
$898$	7351.48	+	41692.3i	0.273187	+	1.54932i
$899$	601.183	+	1041.28i	0.0223032	+	0.0386303i
$900$	−4286.47	+	268.457i	−0.158758	+	0.00994284i
$901$	161.082	−	279.002i	0.00595606	−	0.0103162i
$902$	13433.7	+	4889.46i	0.495890	+	0.180489i
$903$	−3560.06	+	1423.33i	−0.131198	+	0.0524536i
$904$	−12707.0	−	10662.4i	−0.467510	−	0.392287i
$905$	9235.00	+	7749.09i	0.339207	+	0.284628i
$906$	13969.2	+	10995.9i	0.512248	+	0.403217i
$907$	−35939.2	−	13080.8i	−1.31570	−	0.478876i	−0.413622	−	0.910449i	$-0.635736\pi$
$907$	−35939.2	−	13080.8i	−1.31570	−	0.478876i	−0.902078	+	0.431573i	$0.857959\pi$
$908$	−3359.67	+	5819.12i	−0.122791	+	0.212681i
$909$	−28908.0	−	8517.05i	−1.05481	−	0.310773i
$910$	−1937.62	−	3356.06i	−0.0705842	−	0.122255i
$911$	−4918.25	−	27892.8i	−0.178868	−	1.01441i	−0.933584	−	0.358359i	$-0.883336\pi$
$911$	−4918.25	−	27892.8i	−0.178868	−	1.01441i	0.754716	−	0.656052i	$-0.227775\pi$
$912$	−45057.2	+	40274.2i	−1.63596	+	1.46229i
$913$	26856.9	−	9775.11i	0.973531	−	0.354336i
$914$	459.327	−	2604.97i	0.0166227	−	0.0942722i
$915$	−12556.0	+	23408.8i	−0.453649	+	0.845762i
$916$	−4394.35	+	3687.29i	−0.158508	+	0.133004i
$917$	−1786.17			−0.0643233
$918$	13563.8	+	49325.2i	0.487659	+	1.77339i
$919$	−15767.9			−0.565981			−0.282990	−	0.959123i	$-0.591326\pi$
$919$	−15767.9			−0.565981			−0.282990	+	0.959123i	$0.591326\pi$
$920$	9494.85	−	7967.12i	0.340256	−	0.285509i
$921$	24154.0	−	755.629i	0.864172	−	0.0270345i
$922$	7789.02	−	44173.7i	0.278219	−	1.57786i
$923$	4016.94	−	1462.04i	0.143249	−	0.0521385i
$924$	−239.515	−	1147.31i	−0.00852758	−	0.0408483i
$925$	−5019.21	−	28465.3i	−0.178411	−	1.01182i
$926$	2008.88	+	3479.48i	0.0712915	+	0.123480i
$927$	3727.78	−	33148.7i	0.132078	−	1.17448i
$928$	8975.08	−	15545.3i	0.317480	−	0.549892i
$929$	−18422.6	−	6705.29i	−0.650621	−	0.236807i	−0.00443926	−	0.999990i	$-0.501413\pi$
$929$	−18422.6	−	6705.29i	−0.650621	−	0.236807i	−0.646182	+	0.763183i	$0.723635\pi$
$930$	108.301	−	750.803i	0.00381865	−	0.0264729i
$931$	−37140.5	−	31164.6i	−1.30744	−	1.09708i
$932$	2605.40	+	2186.19i	0.0915695	+	0.0768359i
$933$	2136.14	−	14808.8i	0.0749561	−	0.519635i
$934$	3136.35	+	1141.54i	0.109876	+	0.0399917i
$935$	−8809.79	+	15259.0i	−0.308140	+	0.533714i
$936$	14115.1	+	10412.8i	0.492913	+	0.363624i
$937$	−3867.23	−	6698.24i	−0.134831	−	0.233535i	0.790702	−	0.612202i	$-0.209716\pi$
$937$	−3867.23	−	6698.24i	−0.134831	−	0.233535i	−0.925533	+	0.378667i	$0.876383\pi$
$938$	637.702	+	3616.59i	0.0221980	+	0.125891i
$939$	−925.142	−	4431.56i	−0.0321521	−	0.154013i
$940$	−2453.50	+	893.000i	−0.0851322	+	0.0309856i
$941$	−6244.94	+	35416.8i	−0.216343	+	1.22694i	0.662216	+	0.749313i	$0.269616\pi$
$941$	−6244.94	+	35416.8i	−0.216343	+	1.22694i	−0.878560	+	0.477632i	$0.841495\pi$
$942$	−45272.1	+	1416.28i	−1.56587	+	0.0489861i
$943$	14853.1	−	12463.2i	0.512920	−	0.430391i
$944$	18846.1			0.649777
$945$	2828.75	+	3984.05i	0.0973750	+	0.137144i
$946$	−10403.0			−0.357538
$947$	6635.32	−	5567.69i	0.227686	−	0.191051i	−0.521807	−	0.853064i	$-0.674742\pi$
$947$	6635.32	−	5567.69i	0.227686	−	0.191051i	0.749493	+	0.662012i	$0.230297\pi$
$948$	−1371.26	+	2556.52i	−0.0469795	+	0.0875864i
$949$	−1668.72	+	9463.79i	−0.0570800	+	0.323717i
$950$	33460.3	−	12178.6i	1.14273	−	0.415921i
$951$	25782.4	−	23045.5i	0.879129	−	0.785807i
$952$	−1795.61	−	10183.4i	−0.0611302	−	0.346687i
$953$	15182.6	+	26297.0i	0.516067	+	0.893855i	0.999826	+	0.0186534i	$0.00593791\pi$
$953$	15182.6	+	26297.0i	0.516067	+	0.893855i	−0.483759	+	0.875201i	$0.660729\pi$
$954$	−56.9335	−	235.628i	−0.00193217	−	0.00799660i
$955$	−9092.79	+	15749.2i	−0.308100	+	0.533645i
$956$	−10212.6	−	3717.07i	−0.345500	−	0.125752i
$957$	−16512.1	−	12997.5i	−0.557743	−	0.439029i
$958$	36352.5	+	30503.4i	1.22599	+	1.02873i
$959$	3713.71	+	3116.17i	0.125049	+	0.104929i
$960$	10689.7	−	4273.82i	0.359385	−	0.143684i
$961$	27956.0	+	10175.2i	0.938406	+	0.341552i
$962$	21852.4	−	37849.5i	0.732381	−	1.26852i
$963$	8872.37	−	17860.5i	0.296893	−	0.597660i
$964$	−2135.41	−	3698.63i	−0.0713453	−	0.123574i
$965$	−2344.39	−	13295.7i	−0.0782056	−	0.443526i
$966$	−7098.69	−	2335.05i	−0.236435	−	0.0777733i
$967$	22797.4	−	8297.57i	0.758133	−	0.275938i	0.0661090	−	0.997812i	$-0.478941\pi$
$967$	22797.4	−	8297.57i	0.758133	−	0.275938i	0.692024	+	0.721875i	$0.256719\pi$
$968$	2809.99	−	15936.2i	0.0933020	−	0.529142i
$969$	−47531.1	−	76684.1i	−1.57577	−	2.54226i
$970$	649.098	−	544.658i	0.0214858	−	0.0180288i
$971$	5488.24			0.181386			0.0906931	−	0.995879i	$-0.471092\pi$
$971$	5488.24			0.181386			0.0906931	+	0.995879i	$0.471092\pi$
$972$	7015.55	+	4222.17i	0.231506	+	0.139327i
$973$	−12291.7			−0.404989
$974$	−13563.2	+	11380.9i	−0.446195	+	0.374402i
$975$	−7031.82	−	11344.8i	−0.230973	−	0.372639i
$976$	9486.19	−	53798.9i	0.311112	−	1.76441i
$977$	16386.5	−	5964.20i	0.536593	−	0.195304i	−0.0594869	−	0.998229i	$-0.518946\pi$
$977$	16386.5	−	5964.20i	0.536593	−	0.195304i	0.596080	+	0.802925i	$0.296724\pi$
$978$	7923.75	+	2606.44i	0.259073	+	0.0852198i
$979$	−310.253	−	1759.53i	−0.0101284	−	0.0574411i
$980$	−2475.22	−	4287.21i	−0.0806816	−	0.139745i
$981$	−10565.6	+	21269.0i	−0.343866	+	0.692218i
$982$	33217.9	−	57535.1i	1.07946	−	1.86967i
$983$	9369.48	+	3410.21i	0.304008	+	0.110650i	0.489520	−	0.871992i	$-0.337172\pi$
$983$	9369.48	+	3410.21i	0.304008	+	0.110650i	−0.185512	+	0.982642i	$0.559394\pi$
$984$	18745.2	−	7494.45i	0.607291	−	0.242799i
$985$	−8579.28	−	7198.87i	−0.277521	−	0.232868i
$986$	52581.8	+	44121.4i	1.69832	+	1.42506i
$987$	−3340.96	−	2629.84i	−0.107744	−	0.0848114i
$988$	10762.3	+	3917.16i	0.346553	+	0.126135i
$989$	−7054.76	+	12219.2i	−0.226824	+	0.392870i
$990$	3113.78	+	12886.9i	0.0999619	+	0.413708i
$991$	17398.7	+	30135.4i	0.557706	+	0.965975i	0.997687	+	0.0679682i	$0.0216516\pi$
$991$	17398.7	+	30135.4i	0.557706	+	0.965975i	−0.439982	+	0.898007i	$0.645015\pi$
$992$	105.759	+	599.789i	0.00338493	+	0.0191969i
$993$	−34593.5	+	30921.3i	−1.10553	+	0.988176i
$994$	−1781.85	+	648.541i	−0.0568581	+	0.0206947i
$995$	2510.35	−	14236.9i	0.0799834	−	0.453608i
$996$	−7063.04	+	13168.0i	−0.224700	+	0.418920i
$997$	−6390.12	+	5361.95i	−0.202986	+	0.170326i	−0.738614	−	0.674128i	$-0.764519\pi$
$997$	−6390.12	+	5361.95i	−0.202986	+	0.170326i	0.535628	+	0.844454i	$0.320075\pi$
$998$	19324.7			0.612938
$999$	−22960.9	+	50094.3i	−0.727176	+	1.58650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.22.7	yes	48
3.2	odd	2		81.4.e.a.37.2		48
9.2	odd	6		243.4.e.b.190.7		48
9.4	even	3		243.4.e.d.28.7		48
9.5	odd	6		243.4.e.a.28.2		48
9.7	even	3		243.4.e.c.190.2		48
27.2	odd	18		243.4.e.b.55.7		48
27.4	even	9		729.4.a.d.1.18		24
27.7	even	9		243.4.e.d.217.7		48
27.11	odd	18		81.4.e.a.46.2		48
27.16	even	9	inner	27.4.e.a.16.7	✓	48
27.20	odd	18		243.4.e.a.217.2		48
27.23	odd	18		729.4.a.c.1.7		24
27.25	even	9		243.4.e.c.55.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.16.7	✓	48	27.16	even	9	inner
27.4.e.a.22.7	yes	48	1.1	even	1	trivial
81.4.e.a.37.2		48	3.2	odd	2
81.4.e.a.46.2		48	27.11	odd	18
243.4.e.a.28.2		48	9.5	odd	6
243.4.e.a.217.2		48	27.20	odd	18
243.4.e.b.55.7		48	27.2	odd	18
243.4.e.b.190.7		48	9.2	odd	6
243.4.e.c.55.2		48	27.25	even	9
243.4.e.c.190.2		48	9.7	even	3
243.4.e.d.28.7		48	9.4	even	3
243.4.e.d.217.7		48	27.7	even	9
729.4.a.c.1.7		24	27.23	odd	18
729.4.a.d.1.18		24	27.4	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44194 - 2.04903i) q^{2} +(-2.73751 - 4.41656i) q^{3} +(0.375355 - 2.12875i) q^{4} +(6.73772 - 2.45233i) q^{5} +(-15.7345 - 5.17572i) q^{6} +(0.843459 + 4.78350i) q^{7} +(9.30563 + 16.1178i) q^{8} +(-12.0120 + 24.1808i) q^{9} +O(q^{10})\)	\(q+(2.44194 - 2.04903i) q^{2} +(-2.73751 - 4.41656i) q^{3} +(0.375355 - 2.12875i) q^{4} +(6.73772 - 2.45233i) q^{5} +(-15.7345 - 5.17572i) q^{6} +(0.843459 + 4.78350i) q^{7} +(9.30563 + 16.1178i) q^{8} +(-12.0120 + 24.1808i) q^{9} +(11.4282 - 19.7942i) q^{10} +(20.1875 + 7.34765i) q^{11} +(-10.4293 + 4.16969i) q^{12} +(-26.7394 - 22.4370i) q^{13} +(11.8612 + 9.95273i) q^{14} +(-29.2755 - 23.0443i) q^{15} +(71.9995 + 26.2057i) q^{16} +(-57.1928 + 99.0609i) q^{17} +(20.2145 + 83.6610i) q^{18} +(-75.8961 - 131.456i) q^{19} +(-2.69135 - 15.2634i) q^{20} +(18.8176 - 16.8201i) q^{21} +(64.3522 - 23.4223i) q^{22} +(16.1288 - 91.4708i) q^{23} +(45.7111 - 85.2216i) q^{24} +(-56.3726 + 47.3022i) q^{25} -111.270 q^{26} +(139.679 - 13.1434i) q^{27} +10.4994 q^{28} +(144.206 - 121.003i) q^{29} +(-118.707 + 3.71361i) q^{30} +(-1.10912 + 6.29012i) q^{31} +(89.6036 - 32.6130i) q^{32} +(-22.8122 - 109.274i) q^{33} +(63.3173 + 359.090i) q^{34} +(17.4137 + 30.1614i) q^{35} +(46.9660 + 34.6470i) q^{36} +(-196.391 + 340.159i) q^{37} +(-454.691 - 165.494i) q^{38} +(-25.8950 + 179.518i) q^{39} +(102.225 + 85.7769i) q^{40} +(159.914 + 134.184i) q^{41} +(11.4866 - 79.6314i) q^{42} +(-142.747 - 51.9557i) q^{43} +(23.2188 - 40.2161i) q^{44} +(-21.6345 + 192.381i) q^{45} +(-148.041 - 256.414i) q^{46} +(-29.2530 - 165.902i) q^{47} +(-81.3606 - 389.728i) q^{48} +(300.144 - 109.244i) q^{49} +(-40.7347 + 231.018i) q^{50} +(594.075 - 18.5849i) q^{51} +(-57.7995 + 48.4995i) q^{52} -2.81647 q^{53} +(314.157 - 318.302i) q^{54} +154.037 q^{55} +(-69.2506 + 58.1082i) q^{56} +(-372.817 + 695.062i) q^{57} +(104.203 - 590.964i) q^{58} +(231.135 - 84.1261i) q^{59} +(-60.0441 + 53.6703i) q^{60} +(-123.808 - 702.150i) q^{61} +(10.1803 + 17.6327i) q^{62} +(-125.800 - 37.0640i) q^{63} +(-154.500 + 267.601i) q^{64} +(-235.186 - 85.6006i) q^{65} +(-279.611 - 220.096i) q^{66} +(181.688 + 152.454i) q^{67} +(189.408 + 158.932i) q^{68} +(-448.139 + 179.169i) q^{69} +(104.325 + 37.9711i) q^{70} +(-61.2324 + 106.058i) q^{71} +(-501.521 + 31.4097i) q^{72} +(-137.653 - 238.422i) q^{73} +(217.421 + 1233.06i) q^{74} +(363.234 + 119.482i) q^{75} +(-308.324 + 112.221i) q^{76} +(-18.1201 + 102.764i) q^{77} +(304.603 + 491.431i) q^{78} +(197.859 - 166.024i) q^{79} +549.377 q^{80} +(-440.422 - 580.921i) q^{81} +665.446 q^{82} +(1019.13 - 855.148i) q^{83} +(-28.7424 - 46.3714i) q^{84} +(-142.419 + 807.701i) q^{85} +(-455.038 + 165.620i) q^{86} +(-929.183 - 305.647i) q^{87} +(69.4292 + 393.753i) q^{88} +(-41.5833 - 72.0243i) q^{89} +(341.364 + 514.112i) q^{90} +(84.7738 - 146.832i) q^{91} +(-188.664 - 68.6681i) q^{92} +(30.8169 - 12.3208i) q^{93} +(-411.372 - 345.182i) q^{94} +(-833.741 - 699.591i) q^{95} +(-389.328 - 306.461i) q^{96} +(34.8364 + 12.6794i) q^{97} +(509.090 - 881.770i) q^{98} +(-420.165 + 399.889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

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