LMFDB - Embedded newform 115.4.g.a.6.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,4,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, 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:	$6.78521965066$
Analytic rank:	$0$
Dimension:	$110$
Relative dimension:	$11$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			6.8
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.356908 - 0.781519i) q^{2} +(5.20863 + 1.52939i) q^{3} +(4.75550 + 5.48814i) q^{4} +(4.20627 - 2.70320i) q^{5} +(3.05425 - 3.52479i) q^{6} +(3.53166 - 24.5632i) q^{7} +(12.5812 - 3.69418i) q^{8} +(2.07692 + 1.33475i) q^{9} +O(q^{10})$	\(q+(0.356908 - 0.781519i) q^{2} +(5.20863 + 1.52939i) q^{3} +(4.75550 + 5.48814i) q^{4} +(4.20627 - 2.70320i) q^{5} +(3.05425 - 3.52479i) q^{6} +(3.53166 - 24.5632i) q^{7} +(12.5812 - 3.69418i) q^{8} +(2.07692 + 1.33475i) q^{9} +(-0.611355 - 4.25207i) q^{10} +(0.0443232 + 0.0970542i) q^{11} +(16.3761 + 35.8587i) q^{12} +(12.1879 + 84.7689i) q^{13} +(-17.9361 - 11.5269i) q^{14} +(26.0431 - 7.64695i) q^{15} +(-6.66449 + 46.3525i) q^{16} +(38.7792 - 44.7536i) q^{17} +(1.78440 - 1.14677i) q^{18} +(-48.9282 - 56.4661i) q^{19} +(34.8384 + 10.2295i) q^{20} +(55.9619 - 122.539i) q^{21} +0.0916690 q^{22} +(-54.2260 + 96.0549i) q^{23} +71.1807 q^{24} +(10.3854 - 22.7408i) q^{25} +(70.5984 + 20.7296i) q^{26} +(-87.2065 - 100.642i) q^{27} +(151.601 - 97.4282i) q^{28} +(-26.6242 + 30.7259i) q^{29} +(3.31876 - 23.0825i) q^{30} +(-33.2448 + 9.76157i) q^{31} +(122.093 + 78.4646i) q^{32} +(0.0824291 + 0.573307i) q^{33} +(-21.1352 - 46.2795i) q^{34} +(-51.5443 - 112.866i) q^{35} +(2.55146 + 17.7458i) q^{36} +(21.6659 + 13.9238i) q^{37} +(-61.5922 + 18.0851i) q^{38} +(-66.1624 + 460.170i) q^{39} +(42.9338 - 49.5483i) q^{40} +(-20.3901 + 13.1039i) q^{41} +(-75.7936 - 87.4705i) q^{42} +(-310.070 - 91.0447i) q^{43} +(-0.321868 + 0.704793i) q^{44} +12.3442 q^{45} +(55.7150 + 76.6614i) q^{46} -159.731 q^{47} +(-105.604 + 231.240i) q^{48} +(-261.774 - 76.8636i) q^{49} +(-14.0657 - 16.2327i) q^{50} +(270.432 - 173.796i) q^{51} +(-407.264 + 470.007i) q^{52} +(22.4900 - 156.421i) q^{53} +(-109.778 + 32.2337i) q^{54} +(0.448793 + 0.288421i) q^{55} +(-46.3084 - 322.082i) q^{56} +(-168.490 - 368.941i) q^{57} +(14.5105 + 31.7736i) q^{58} +(-22.1492 - 154.051i) q^{59} +(165.816 + 106.563i) q^{60} +(-262.606 + 77.1081i) q^{61} +(-4.23649 + 29.4654i) q^{62} +(40.1208 - 46.3019i) q^{63} +(-210.264 + 135.129i) q^{64} +(280.413 + 323.614i) q^{65} +(0.477469 + 0.140198i) q^{66} +(-390.232 + 854.490i) q^{67} +430.028 q^{68} +(-429.349 + 417.381i) q^{69} -106.604 q^{70} +(438.592 - 960.383i) q^{71} +(31.0609 + 9.12031i) q^{72} +(-374.820 - 432.565i) q^{73} +(18.6145 - 11.9628i) q^{74} +(88.8731 - 102.565i) q^{75} +(77.2160 - 537.049i) q^{76} +(2.54050 - 0.745958i) q^{77} +(336.017 + 215.945i) q^{78} +(-40.0879 - 278.817i) q^{79} +(97.2677 + 212.987i) q^{80} +(-327.996 - 718.212i) q^{81} +(2.96357 + 20.6121i) q^{82} +(881.857 + 566.735i) q^{83} +(938.640 - 275.609i) q^{84} +(42.1376 - 293.073i) q^{85} +(-181.819 + 209.831i) q^{86} +(-185.667 + 119.321i) q^{87} +(0.916175 + 1.05732i) q^{88} +(311.141 + 91.3592i) q^{89} +(4.40573 - 9.64720i) q^{90} +2125.24 q^{91} +(-785.034 + 159.189i) q^{92} -188.089 q^{93} +(-57.0091 + 124.833i) q^{94} +(-358.444 - 105.249i) q^{95} +(515.935 + 595.421i) q^{96} +(-1221.99 + 785.326i) q^{97} +(-153.499 + 177.148i) q^{98} +(-0.0374879 + 0.260734i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) $ 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.356908	−	0.781519i	0.126186	−	0.276309i	−0.835986	−	0.548750i	$-0.815104\pi$
$2$	0.356908	−	0.781519i	0.126186	−	0.276309i	0.962172	+	0.272442i	$0.0878311\pi$
$3$	5.20863	+	1.52939i	1.00240	+	0.294331i	0.741441	−	0.671018i	$-0.234143\pi$
$3$	5.20863	+	1.52939i	1.00240	+	0.294331i	0.260960	+	0.965350i	$0.415961\pi$
$4$	4.75550	+	5.48814i	0.594437	+	0.686017i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	3.05425	−	3.52479i	0.207815	−	0.239831i
$7$	3.53166	−	24.5632i	0.190692	−	1.32629i	−0.639491	−	0.768798i	$-0.720855\pi$
$7$	3.53166	−	24.5632i	0.190692	−	1.32629i	0.830183	−	0.557491i	$-0.188236\pi$
$8$	12.5812	−	3.69418i	0.556016	−	0.163261i
$9$	2.07692	+	1.33475i	0.0769228	+	0.0494353i
$10$	−0.611355	−	4.25207i	−0.0193328	−	0.134462i
$11$	0.0443232	+	0.0970542i	0.00121490	+	0.00266027i	0.910238	−	0.414084i	$-0.135898\pi$
$11$	0.0443232	+	0.0970542i	0.00121490	+	0.00266027i	−0.909024	+	0.416745i	$0.863171\pi$
$12$	16.3761	+	35.8587i	0.393948	+	0.862626i
$13$	12.1879	+	84.7689i	0.260025	+	1.80851i	0.532588	+	0.846375i	$0.321220\pi$
$13$	12.1879	+	84.7689i	0.260025	+	1.80851i	−0.272563	+	0.962138i	$0.587871\pi$
$14$	−17.9361	−	11.5269i	−0.342403	−	0.220049i
$15$	26.0431	−	7.64695i	0.448287	−	0.131629i
$16$	−6.66449	+	46.3525i	−0.104133	+	0.724258i
$17$	38.7792	−	44.7536i	0.553255	−	0.638490i	−0.408384	−	0.912810i	$-0.633907\pi$
$17$	38.7792	−	44.7536i	0.553255	−	0.638490i	0.961638	+	0.274320i	$0.0884528\pi$
$18$	1.78440	−	1.14677i	0.0233660	−	0.0150164i
$19$	−48.9282	−	56.4661i	−0.590784	−	0.681801i	0.379104	−	0.925354i	$-0.376232\pi$
$19$	−48.9282	−	56.4661i	−0.590784	−	0.681801i	−0.969888	+	0.243553i	$0.921687\pi$
$20$	34.8384	+	10.2295i	0.389506	+	0.114369i
$21$	55.9619	−	122.539i	0.581518	−	1.27335i
$22$	0.0916690			0.000888359
$23$	−54.2260	+	96.0549i	−0.491605	+	0.870819i
$23$	−54.2260	+	96.0549i	−0.491605	+	0.870819i
$24$	71.1807			0.605404
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	70.5984	+	20.7296i	0.532519	+	0.156362i
$27$	−87.2065	−	100.642i	−0.621588	−	0.717351i
$28$	151.601	−	97.4282i	1.02321	−	0.657578i
$29$	−26.6242	+	30.7259i	−0.170482	+	0.196747i	−0.834561	−	0.550916i	$-0.814279\pi$
$29$	−26.6242	+	30.7259i	−0.170482	+	0.196747i	0.664079	+	0.747663i	$0.268824\pi$
$30$	3.31876	−	23.0825i	0.0201973	−	0.140475i
$31$	−33.2448	+	9.76157i	−0.192611	+	0.0565558i	−0.376615	−	0.926370i	$-0.622912\pi$
$31$	−33.2448	+	9.76157i	−0.192611	+	0.0565558i	0.184004	+	0.982925i	$0.441094\pi$
$32$	122.093	+	78.4646i	0.674476	+	0.433460i
$33$	0.0824291	+	0.573307i	0.000434820	+	0.00302424i
$34$	−21.1352	−	46.2795i	−0.106607	−	0.233437i
$35$	−51.5443	−	112.866i	−0.248931	−	0.545083i
$36$	2.55146	+	17.7458i	0.0118123	+	0.0821565i
$37$	21.6659	+	13.9238i	0.0962664	+	0.0618666i	0.587888	−	0.808942i	$-0.299959\pi$
$37$	21.6659	+	13.9238i	0.0962664	+	0.0618666i	−0.491622	+	0.870809i	$0.663596\pi$
$38$	−61.5922	+	18.0851i	−0.262936	+	0.0772050i
$39$	−66.1624	+	460.170i	−0.271653	+	1.88939i
$40$	42.9338	−	49.5483i	0.169711	−	0.195857i
$41$	−20.3901	+	13.1039i	−0.0776681	+	0.0499143i	−0.578899	−	0.815400i	$-0.696517\pi$
$41$	−20.3901	+	13.1039i	−0.0776681	+	0.0499143i	0.501230	+	0.865314i	$0.332881\pi$
$42$	−75.7936	−	87.4705i	−0.278457	−	0.321357i
$43$	−310.070	−	91.0447i	−1.09966	−	0.322888i	−0.318940	−	0.947775i	$-0.603327\pi$
$43$	−310.070	−	91.0447i	−1.09966	−	0.322888i	−0.780715	+	0.624887i	$0.785145\pi$
$44$	−0.321868	+	0.704793i	−0.00110281	+	0.00241481i
$45$	12.3442			0.0408925
$46$	55.7150	+	76.6614i	0.178581	+	0.245720i
$47$	−159.731			−0.495726			−0.247863	−	0.968795i	$-0.579728\pi$
$47$	−159.731			−0.495726			−0.247863	+	0.968795i	$0.579728\pi$
$48$	−105.604	+	231.240i	−0.317554	+	0.695347i
$49$	−261.774	−	76.8636i	−0.763188	−	0.224092i
$50$	−14.0657	−	16.2327i	−0.0397839	−	0.0459131i
$51$	270.432	−	173.796i	0.742511	−	0.477183i
$52$	−407.264	+	470.007i	−1.08610	+	1.25343i
$53$	22.4900	−	156.421i	0.0582876	−	0.405399i	−0.939701	−	0.341998i	$-0.888896\pi$
$53$	22.4900	−	156.421i	0.0582876	−	0.405399i	0.997988	−	0.0634007i	$-0.0201946\pi$
$54$	−109.778	+	32.2337i	−0.276646	+	0.0812306i
$55$	0.448793	+	0.288421i	0.00110028	+	0.000707104i
$56$	−46.3084	−	322.082i	−0.110504	−	0.768571i
$57$	−168.490	−	368.941i	−0.391527	−	0.857324i
$58$	14.5105	+	31.7736i	0.0328504	+	0.0719324i
$59$	−22.1492	−	154.051i	−0.0488742	−	0.339928i	−0.999557	−	0.0297628i	$-0.990525\pi$
$59$	−22.1492	−	154.051i	−0.0488742	−	0.339928i	0.950683	−	0.310165i	$-0.100384\pi$
$60$	165.816	+	106.563i	0.356778	+	0.229288i
$61$	−262.606	+	77.1081i	−0.551201	+	0.161847i	−0.545461	−	0.838136i	$-0.683645\pi$
$61$	−262.606	+	77.1081i	−0.551201	+	0.161847i	−0.00574026	+	0.999984i	$0.501827\pi$
$62$	−4.23649	+	29.4654i	−0.00867798	+	0.0603567i
$63$	40.1208	−	46.3019i	0.0802341	−	0.0925950i
$64$	−210.264	+	135.129i	−0.410672	+	0.263923i
$65$	280.413	+	323.614i	0.535092	+	0.617529i
$66$	0.477469	+	0.140198i	0.000890491	+	0.000261472i
$67$	−390.232	+	854.490i	−0.711559	+	1.55810i	0.113809	+	0.993503i	$0.463695\pi$
$67$	−390.232	+	854.490i	−0.711559	+	1.55810i	−0.825368	+	0.564595i	$0.809033\pi$
$68$	430.028			0.766890
$69$	−429.349	+	417.381i	−0.749094	+	0.728215i
$70$	−106.604			−0.182023
$71$	438.592	−	960.383i	0.733117	−	1.60530i	−0.0614378	−	0.998111i	$-0.519569\pi$
$71$	438.592	−	960.383i	0.733117	−	1.60530i	0.794555	−	0.607192i	$-0.207704\pi$
$72$	31.0609	+	9.12031i	0.0508412	+	0.0149283i
$73$	−374.820	−	432.565i	−0.600950	−	0.693533i	0.371024	−	0.928623i	$-0.379007\pi$
$73$	−374.820	−	432.565i	−0.600950	−	0.693533i	−0.971974	+	0.235090i	$0.924461\pi$
$74$	18.6145	−	11.9628i	0.0292417	−	0.0187925i
$75$	88.8731	−	102.565i	0.136829	−	0.157909i
$76$	77.2160	−	537.049i	0.116543	−	0.810576i
$77$	2.54050	−	0.745958i	0.00375996	−	0.00110402i
$78$	336.017	+	215.945i	0.487775	+	0.313474i
$79$	−40.0879	−	278.817i	−0.0570916	−	0.397081i	−0.998251	−	0.0591179i	$-0.981171\pi$
$79$	−40.0879	−	278.817i	−0.0570916	−	0.397081i	0.941159	−	0.337963i	$-0.109738\pi$
$80$	97.2677	+	212.987i	0.135936	+	0.297658i
$81$	−327.996	−	718.212i	−0.449927	−	0.985202i
$82$	2.96357	+	20.6121i	0.00399112	+	0.0277588i
$83$	881.857	+	566.735i	1.16622	+	0.749485i	0.972804	−	0.231631i	$-0.0744063\pi$
$83$	881.857	+	566.735i	1.16622	+	0.749485i	0.193418	+	0.981116i	$0.438043\pi$
$84$	938.640	−	275.609i	1.21921	−	0.357994i
$85$	42.1376	−	293.073i	0.0537702	−	0.373980i
$86$	−181.819	+	209.831i	−0.227978	+	0.263100i
$87$	−185.667	+	119.321i	−0.228800	+	0.147041i
$88$	0.916175	+	1.05732i	0.00110982	+	0.00128081i
$89$	311.141	+	91.3592i	0.370572	+	0.108810i	0.461715	−	0.887028i	$-0.347234\pi$
$89$	311.141	+	91.3592i	0.370572	+	0.108810i	−0.0911438	+	0.995838i	$0.529052\pi$
$90$	4.40573	−	9.64720i	0.00516005	−	0.0112989i
$91$	2125.24			2.44820
$92$	−785.034	+	159.189i	−0.889624	+	0.180398i
$93$	−188.089			−0.209720
$94$	−57.0091	+	124.833i	−0.0625536	+	0.136973i
$95$	−358.444	−	105.249i	−0.387112	−	0.113666i
$96$	515.935	+	595.421i	0.548515	+	0.633020i
$97$	−1221.99	+	785.326i	−1.27912	+	0.822039i	−0.990779	−	0.135490i	$-0.956739\pi$
$97$	−1221.99	+	785.326i	−1.27912	+	0.822039i	−0.288338	+	0.957529i	$0.593103\pi$
$98$	−153.499	+	177.148i	−0.158222	+	0.182598i
$99$	−0.0374879	+	0.260734i	−3.80573e−5	+	0.000264694i
$100$	174.192	−	51.1475i	0.174192	−	0.0511475i
$101$	1381.16	+	887.615i	1.36069	+	0.874465i	0.998341	−	0.0575759i	$-0.0183371\pi$
$101$	1381.16	+	887.615i	1.36069	+	0.874465i	0.362353	+	0.932041i	$0.381973\pi$
$102$	−39.3056	−	273.377i	−0.0381553	−	0.265376i
$103$	−643.920	−	1409.99i	−0.615994	−	1.34884i	−0.918398	−	0.395658i	$-0.870517\pi$
$103$	−643.920	−	1409.99i	−0.615994	−	1.34884i	0.302404	−	0.953180i	$-0.402211\pi$
$104$	466.490	+	1021.47i	0.439838	+	0.963110i
$105$	−95.8584	−	666.710i	−0.0890936	−	0.619659i
$106$	−114.219	−	73.4044i	−0.104660	−	0.0672610i
$107$	−527.150	+	154.785i	−0.476276	+	0.139847i	−0.511055	−	0.859548i	$-0.670745\pi$
$107$	−527.150	+	154.785i	−0.476276	+	0.139847i	0.0347794	+	0.999395i	$0.488927\pi$
$108$	137.625	−	957.202i	0.122620	−	0.852841i
$109$	980.239	−	1131.26i	0.861375	−	0.994080i	−0.138618	−	0.990346i	$-0.544266\pi$
$109$	980.239	−	1131.26i	0.861375	−	0.994080i	0.999993	−	0.00373378i	$-0.00118850\pi$
$110$	0.385584	−	0.247800i	0.000334218	−	0.000214789i
$111$	91.5547	+	105.660i	0.0782882	+	0.0903494i
$112$	1115.03	+	327.403i	0.940719	+	0.276220i
$113$	−135.195	+	296.036i	−0.112549	+	0.246449i	−0.957522	−	0.288361i	$-0.906890\pi$
$113$	−135.195	+	296.036i	−0.112549	+	0.246449i	0.844972	+	0.534810i	$0.179617\pi$
$114$	−348.470			−0.286291
$115$	31.5668	+	550.617i	0.0255967	+	0.446480i
$116$	−295.239			−0.236313
$117$	−87.8322	+	192.326i	−0.0694025	+	0.151970i
$118$	−128.299	−	37.6720i	−0.100092	−	0.0293897i
$119$	−962.337	−	1110.60i	−0.741322	−	0.855531i
$120$	299.405	−	192.416i	0.227765	−	0.146376i
$121$	871.612	−	1005.89i	0.654855	−	0.755743i
$122$	−33.4647	+	232.752i	−0.0248340	+	0.172724i
$123$	−126.245	+	37.0689i	−0.0925459	+	0.0271739i
$124$	−211.669	−	136.031i	−0.153294	−	0.0985158i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	−21.8664	−	47.8806i	−0.0154604	−	0.0338535i
$127$	1003.06	+	2196.38i	0.700840	+	1.53463i	0.838949	+	0.544210i	$0.183170\pi$
$127$	1003.06	+	2196.38i	0.700840	+	1.53463i	−0.138109	+	0.990417i	$0.544102\pi$
$128$	195.797	+	1361.80i	0.135204	+	0.940366i
$129$	−1475.80	−	948.436i	−1.00726	−	0.647327i
$130$	352.992	−	103.648i	0.238150	−	0.0699271i
$131$	−131.819	+	916.823i	−0.0879168	+	0.611475i	0.897461	+	0.441093i	$0.145409\pi$
$131$	−131.819	+	916.823i	−0.0879168	+	0.611475i	−0.985378	+	0.170382i	$0.945500\pi$
$132$	−2.75439	+	3.17874i	−0.00181621	+	0.00209601i
$133$	−1559.79	+	1002.41i	−1.01692	+	0.653537i
$134$	528.523	+	609.948i	0.340727	+	0.393220i
$135$	−638.868	−	187.589i	−0.407297	−	0.119593i
$136$	322.561	−	706.311i	0.203378	−	0.445336i
$137$	2635.81			1.64374			0.821871	−	0.569673i	$-0.192930\pi$
$137$	2635.81			1.64374			0.821871	+	0.569673i	$0.192930\pi$
$138$	172.953	+	484.510i	0.106687	+	0.298871i
$139$	16.8131			0.0102595			0.00512974	−	0.999987i	$-0.498367\pi$
$139$	16.8131			0.0102595			0.00512974	+	0.999987i	$0.498367\pi$
$140$	374.307	−	819.618i	0.225962	−	0.494788i
$141$	−831.978	−	244.291i	−0.496916	−	0.145908i
$142$	−594.020	−	685.536i	−0.351050	−	0.405133i
$143$	−7.68697	+	4.94012i	−0.00449522	+	0.00288890i
$144$	−75.7107	+	87.3748i	−0.0438141	+	0.0505641i
$145$	−28.9299	+	201.212i	−0.0165690	+	0.115240i
$146$	−471.834	+	138.543i	−0.267461	+	0.0785335i
$147$	−1245.93	−	800.708i	−0.699063	−	0.449261i
$148$	26.6163	+	185.120i	0.0147827	+	0.102816i
$149$	919.386	+	2013.17i	0.505497	+	1.10688i	0.974644	+	0.223763i	$0.0718342\pi$
$149$	919.386	+	2013.17i	0.505497	+	1.10688i	−0.469147	+	0.883120i	$0.655438\pi$
$150$	−48.4370	−	106.062i	−0.0263658	−	0.0577330i
$151$	−279.928	−	1946.94i	−0.150862	−	1.04927i	−0.914779	−	0.403955i	$-0.867635\pi$
$151$	−279.928	−	1946.94i	−0.150862	−	1.04927i	0.763917	−	0.645315i	$-0.223274\pi$
$152$	−824.172	−	529.663i	−0.439797	−	0.282640i
$153$	140.276	−	41.1888i	0.0741219	−	0.0217641i
$154$	0.323744	−	2.25169i	0.000169403	−	0.00117822i
$155$	−113.449	+	130.927i	−0.0587901	+	0.0678474i
$156$	−2840.11	+	1825.23i	−1.45763	+	0.936764i
$157$	−792.089	−	914.120i	−0.402647	−	0.464680i	0.517826	−	0.855486i	$-0.326742\pi$
$157$	−792.089	−	914.120i	−0.402647	−	0.464680i	−0.920473	+	0.390807i	$0.872196\pi$
$158$	−232.209	−	68.1826i	−0.116921	−	0.0343311i
$159$	356.372	−	780.345i	0.177749	−	0.389216i
$160$	725.663			0.358554
$161$	2167.91	+	1671.20i	1.06121	+	0.818068i
$162$	−678.361			−0.328994
$163$	−823.626	+	1803.49i	−0.395775	+	0.866627i	0.601906	+	0.798567i	$0.294408\pi$
$163$	−823.626	+	1803.49i	−0.395775	+	0.866627i	−0.997681	+	0.0680601i	$0.978319\pi$
$164$	−168.881	−	49.5879i	−0.0804108	−	0.0236108i
$165$	1.89648	+	2.18866i	0.000894794	+	0.00103265i
$166$	757.656	−	486.916i	0.354250	−	0.227663i
$167$	2204.72	−	2544.38i	1.02159	−	1.17898i	0.0378716	−	0.999283i	$-0.487942\pi$
$167$	2204.72	−	2544.38i	1.02159	−	1.17898i	0.983722	−	0.179699i	$-0.0575123\pi$
$168$	251.386	−	1748.43i	0.115445	−	0.802941i
$169$	−4929.22	+	1447.35i	−2.24361	+	0.658784i
$170$	−214.003	−	137.531i	−0.0965488	−	0.0620481i
$171$	−26.2514	−	182.582i	−0.0117397	−	0.0816516i
$172$	−974.870	−	2134.67i	−0.432170	−	0.946319i
$173$	−324.267	−	710.045i	−0.142506	−	0.312045i	0.824898	−	0.565281i	$-0.191232\pi$
$173$	−324.267	−	710.045i	−0.142506	−	0.312045i	−0.967404	+	0.253236i	$0.918505\pi$
$174$	26.9856	+	187.689i	0.0117573	+	0.0817740i
$175$	−521.910	−	335.411i	−0.225444	−	0.144884i
$176$	−4.79410	+	1.40767i	−0.00205323	+	0.000602883i
$177$	120.237	−	836.269i	0.0510599	−	0.355129i
$178$	182.448	−	210.556i	0.0768260	−	0.0886619i
$179$	288.825	−	185.617i	0.120602	−	0.0775063i	−0.478949	−	0.877843i	$-0.658982\pi$
$179$	288.825	−	185.617i	0.120602	−	0.0775063i	0.599551	+	0.800336i	$0.295346\pi$
$180$	58.7027	+	67.7465i	0.0243080	+	0.0280529i
$181$	−2585.20	−	759.082i	−1.06164	−	0.311724i	−0.296126	−	0.955149i	$-0.595695\pi$
$181$	−2585.20	−	759.082i	−1.06164	−	0.311724i	−0.765510	+	0.643424i	$0.777513\pi$
$182$	758.515	−	1660.92i	0.308928	−	0.676458i
$183$	−1485.75			−0.600161
$184$	−327.385	+	1408.81i	−0.131169	+	0.564449i
$185$	128.772			0.0511756
$186$	−67.1305	+	146.995i	−0.0264637	+	0.0579474i
$187$	6.06234	+	1.78006i	0.00237071	+	0.000696102i
$188$	−759.599	−	876.624i	−0.294678	−	0.340076i
$189$	−2780.07	+	1786.64i	−1.06995	+	0.687614i
$190$	−210.185	+	242.567i	−0.0802550	+	0.0926192i
$191$	79.3429	−	551.842i	0.0300579	−	0.209057i	−0.969258	−	0.246048i	$-0.920868\pi$
$191$	79.3429	−	551.842i	0.0300579	−	0.209057i	0.999316	+	0.0369905i	$0.0117771\pi$
$192$	−1301.85	+	382.258i	−0.489339	+	0.143683i
$193$	3395.41	+	2182.10i	1.26636	+	0.813839i	0.989141	−	0.146969i	$-0.0469516\pi$
$193$	3395.41	+	2182.10i	1.26636	+	0.813839i	0.277217	+	0.960807i	$0.410588\pi$
$194$	177.609	+	1235.30i	0.0657298	+	0.457161i
$195$	965.636	+	2114.45i	0.354619	+	0.776506i
$196$	−823.025	−	1802.17i	−0.299936	−	0.656769i
$197$	649.123	+	4514.75i	0.234762	+	1.63280i	0.677054	+	0.735934i	$0.263256\pi$
$197$	649.123	+	4514.75i	0.234762	+	1.63280i	−0.442292	+	0.896871i	$0.645834\pi$
$198$	0.190389	+	0.122355i	6.83350e−5	+	4.39163e-5i
$199$	3742.99	−	1099.04i	1.33333	−	0.391502i	0.464047	−	0.885810i	$-0.346397\pi$
$199$	3742.99	−	1099.04i	1.33333	−	0.391502i	0.869287	+	0.494308i	$0.164579\pi$
$200$	46.6521	−	324.472i	0.0164940	−	0.114718i
$201$	−3339.42	+	3853.90i	−1.17186	+	1.35240i
$202$	1186.63	−	762.602i	0.413323	−	0.265626i
$203$	660.700	+	762.489i	0.228434	+	0.263627i
$204$	2239.86	+	657.681i	0.768732	+	0.225720i
$205$	−50.3435	+	110.237i	−0.0171519	+	0.0375575i
$206$	−1331.75			−0.450425
$207$	−240.832	+	127.120i	−0.0808648	+	0.0426832i
$208$	−4010.48			−1.33691
$209$	3.31162	−	7.25144i	0.00109603	−	0.00239997i
$210$	−555.259	−	163.039i	−0.182460	−	0.0535750i
$211$	52.2497	+	60.2994i	0.0170475	+	0.0196738i	0.764209	−	0.644968i	$-0.223129\pi$
$211$	52.2497	+	60.2994i	0.0170475	+	0.0196738i	−0.747162	+	0.664642i	$0.768584\pi$
$212$	965.414	−	620.434i	0.312759	−	0.200998i
$213$	3753.27	−	4331.50i	1.20737	−	1.39338i
$214$	−67.1764	+	467.222i	−0.0214583	+	0.149246i
$215$	−1550.35	+	455.224i	−0.491781	+	0.144400i
$216$	−1468.95	−	944.037i	−0.462729	−	0.297378i
$217$	122.366	+	851.075i	0.0382800	+	0.266243i
$218$	−534.243	−	1169.83i	−0.165979	−	0.363444i
$219$	−1290.74	−	2826.32i	−0.398264	−	0.872077i
$220$	0.551335	+	3.83462i	0.000168959	+	0.00117514i
$221$	4266.35	+	2741.82i	1.29858	+	0.834545i
$222$	115.252	−	33.8409i	0.0348432	−	0.0102309i
$223$	−200.602	+	1395.22i	−0.0602390	+	0.418972i	0.937280	+	0.348577i	$0.113335\pi$
$223$	−200.602	+	1395.22i	−0.0602390	+	0.418972i	−0.997519	+	0.0703948i	$0.977574\pi$
$224$	2358.54	−	2721.89i	0.703510	−	0.811894i
$225$	51.9229	−	33.3688i	0.0153846	−	0.00988706i
$226$	183.105	+	211.315i	0.0538938	+	0.0621967i
$227$	4870.94	+	1430.24i	1.42421	+	0.418185i	0.900926	−	0.433974i	$-0.142889\pi$
$227$	4870.94	+	1430.24i	1.42421	+	0.418185i	0.523283	+	0.852159i	$0.324707\pi$
$228$	1223.55	−	2679.19i	0.355401	−	0.778219i
$229$	5776.55			1.66692			0.833461	−	0.552579i	$-0.186356\pi$
$229$	5776.55			1.66692			0.833461	+	0.552579i	$0.186356\pi$
$230$	441.583	+	171.849i	0.126596	+	0.0492669i
$231$	14.3734			0.00409393
$232$	−221.457	+	484.924i	−0.0626697	+	0.137228i
$233$	5836.48	+	1713.75i	1.64103	+	0.481851i	0.966558	−	0.256448i	$-0.0825521\pi$
$233$	5836.48	+	1713.75i	1.64103	+	0.481851i	0.674474	+	0.738298i	$0.264370\pi$
$234$	118.958	+	137.285i	0.0332331	+	0.0383530i
$235$	−671.870	+	431.785i	−0.186502	+	0.119858i
$236$	740.123	−	854.147i	0.204144	−	0.235594i
$237$	217.618	−	1513.57i	0.0596447	−	0.414838i
$238$	−1211.42	+	355.704i	−0.329935	+	0.0968776i
$239$	−3719.96	−	2390.67i	−1.00679	−	0.647028i	−0.0702331	−	0.997531i	$-0.522374\pi$
$239$	−3719.96	−	2390.67i	−1.00679	−	0.647028i	−0.936562	+	0.350503i	$0.886011\pi$
$240$	180.891	+	1258.13i	0.0486521	+	0.338383i
$241$	1086.62	+	2379.37i	0.290437	+	0.635968i	0.997461	−	0.0712217i	$-0.0226898\pi$
$241$	1086.62	+	2379.37i	0.290437	+	0.635968i	−0.707023	+	0.707190i	$0.749963\pi$
$242$	−475.040	−	1040.19i	−0.126185	−	0.276306i
$243$	−98.2865	−	683.597i	−0.0259468	−	0.180464i
$244$	−1672.00	−	1074.53i	−0.438684	−	0.281925i
$245$	−1308.87	+	384.318i	−0.341308	+	0.100217i
$246$	−16.0878	+	111.893i	−0.00416960	+	0.0290002i
$247$	4190.24	−	4835.79i	1.07943	−	1.24573i
$248$	−382.199	+	245.625i	−0.0978617	+	0.0628919i
$249$	3726.51	+	4300.62i	0.948424	+	1.09454i
$250$	−103.045	−	30.2566i	−0.0260685	−	0.00765439i
$251$	89.0459	−	194.983i	0.0223925	−	0.0490328i	−0.898105	−	0.439781i	$-0.855056\pi$
$251$	89.0459	−	194.983i	0.0223925	−	0.0490328i	0.920498	+	0.390748i	$0.127784\pi$
$252$	444.905			0.111216
$253$	−11.7260	−	1.00541i	−0.00291386	−	0.000249839i
$254$	2074.51			0.512467
$255$	667.703	−	1462.07i	0.163973	−	0.359051i
$256$	−784.386	−	230.317i	−0.191500	−	0.0562296i
$257$	−446.735	−	515.560i	−0.108430	−	0.125135i	0.698940	−	0.715180i	$-0.253655\pi$
$257$	−446.735	−	515.560i	−0.108430	−	0.125135i	−0.807370	+	0.590045i	$0.799110\pi$
$258$	−1267.94	+	814.857i	−0.305964	+	0.196631i
$259$	418.531	−	483.011i	0.100410	−	0.115880i
$260$	−442.534	+	3077.89i	−0.105557	+	0.734165i
$261$	−96.3076	+	28.2785i	−0.0228402	+	0.00670649i
$262$	669.467	+	430.240i	0.157862	+	0.101452i
$263$	−922.739	−	6417.79i	−0.216344	−	1.50471i	−0.751375	−	0.659875i	$-0.770609\pi$
$263$	−922.739	−	6417.79i	−0.216344	−	1.50471i	0.535031	−	0.844832i	$-0.320300\pi$
$264$	3.15495	+	6.90839i	0.000735508	+	0.00161054i
$265$	−328.240	−	718.746i	−0.0760892	−	0.166612i
$266$	226.706	+	1576.77i	0.0522565	+	0.363452i
$267$	1480.89	+	951.713i	0.339435	+	0.218142i
$268$	−6545.30	+	1921.87i	−1.49186	+	0.438049i
$269$	226.372	−	1574.45i	0.0513090	−	0.356862i	−0.947952	−	0.318414i	$-0.896850\pi$
$269$	226.372	−	1574.45i	0.0513090	−	0.356862i	0.999261	−	0.0384475i	$-0.0122412\pi$
$270$	−374.621	+	432.336i	−0.0844397	+	0.0974486i
$271$	686.484	−	441.176i	0.153878	−	0.0988913i	−0.461436	−	0.887173i	$-0.652666\pi$
$271$	686.484	−	441.176i	0.153878	−	0.0988913i	0.615314	+	0.788282i	$0.289029\pi$
$272$	1816.00	+	2095.77i	0.404820	+	0.467187i
$273$	11069.6	+	3250.33i	2.45407	+	0.720581i
$274$	940.742	−	2059.94i	0.207417	−	0.454180i
$275$	2.66740			0.000584911
$276$	−4332.41	−	371.468i	−0.944857	−	0.0810135i
$277$	−6028.48			−1.30764			−0.653820	−	0.756650i	$-0.726835\pi$
$277$	−6028.48			−1.30764			−0.653820	+	0.756650i	$0.726835\pi$
$278$	6.00072	−	13.1397i	0.00129460	−	0.00283478i
$279$	−82.0760	−	24.0997i	−0.0176121	−	0.00517137i
$280$	−1065.44	−	1229.58i	−0.227400	−	0.262434i
$281$	−5567.88	+	3578.26i	−1.18203	+	0.759648i	−0.975759	−	0.218846i	$-0.929771\pi$
$281$	−5567.88	+	3578.26i	−1.18203	+	0.759648i	−0.206276	+	0.978494i	$0.566134\pi$
$282$	−487.857	+	563.017i	−0.103019	+	0.118891i
$283$	538.424	−	3744.82i	0.113095	−	0.786596i	−0.851782	−	0.523896i	$-0.824478\pi$
$283$	538.424	−	3744.82i	0.113095	−	0.786596i	0.964878	−	0.262700i	$-0.0846129\pi$
$284$	7356.44	−	2160.05i	1.53706	−	0.451321i
$285$	−1706.04	−	1096.40i	−0.354586	−	0.227878i
$286$	1.11725	+	7.77068i	0.000230995	+	0.00160661i
$287$	249.863	+	547.124i	0.0513901	+	0.112529i
$288$	148.847	+	325.929i	0.0304544	+	0.0666859i
$289$	200.137	+	1391.98i	0.0407361	+	0.283326i
$290$	146.926	+	94.4233i	0.0297509	+	0.0191198i
$291$	−7565.96	+	2221.57i	−1.52414	+	0.447528i
$292$	591.522	−	4114.13i	0.118549	−	0.824524i
$293$	−4467.63	+	5155.91i	−0.890790	+	1.02803i	0.108634	+	0.994082i	$0.465352\pi$
$293$	−4467.63	+	5155.91i	−0.890790	+	1.02803i	−0.999424	+	0.0339445i	$0.989193\pi$
$294$	−1070.45	+	687.936i	−0.212346	+	0.136467i
$295$	−509.597	−	588.106i	−0.100576	−	0.116071i
$296$	324.021	+	95.1411i	0.0636261	+	0.0186823i
$297$	5.90243	−	12.9245i	0.00115318	−	0.00252510i
$298$	1901.47			0.369628
$299$	−8803.37	−	3425.97i	−1.70272	−	0.662639i
$300$	985.527			0.189665
$301$	−3331.41	+	7294.78i	−0.637938	+	1.39689i
$302$	−1621.48	−	476.109i	−0.308959	−	0.0907185i
$303$	5836.41	+	6735.58i	1.10658	+	1.27706i
$304$	2943.43	−	1891.63i	0.555320	−	0.356882i
$305$	−896.153	+	1034.22i	−0.168241	+	0.194161i
$306$	17.8758	−	124.329i	0.00333951	−	0.0232268i
$307$	−3400.42	+	998.454i	−0.632157	+	0.185618i	−0.582086	−	0.813127i	$-0.697763\pi$
$307$	−3400.42	+	998.454i	−0.632157	+	0.185618i	−0.0500717	+	0.998746i	$0.515945\pi$
$308$	16.1753	+	10.3952i	0.00299244	+	0.00192312i
$309$	−1197.52	−	8328.91i	−0.220467	−	1.53338i
$310$	61.8313	+	135.392i	0.0113283	+	0.0248056i
$311$	−3685.06	−	8069.15i	−0.671898	−	1.47125i	−0.871005	−	0.491274i	$-0.836531\pi$
$311$	−3685.06	−	8069.15i	−0.671898	−	1.47125i	0.199107	−	0.979978i	$-0.436196\pi$
$312$	867.545	+	6033.91i	0.157420	+	1.09488i
$313$	−1278.80	−	821.835i	−0.230933	−	0.148412i	0.420058	−	0.907497i	$-0.362010\pi$
$313$	−1278.80	−	821.835i	−0.230933	−	0.148412i	−0.650991	+	0.759086i	$0.725646\pi$
$314$	−997.104	+	292.776i	−0.179203	+	0.0526188i
$315$	43.5954	−	303.213i	0.00779785	−	0.0542353i
$316$	1339.55	−	1545.92i	0.238467	−	0.275205i
$317$	−94.7847	+	60.9144i	−0.0167938	+	0.0107927i	−0.549011	−	0.835815i	$-0.684995\pi$
$317$	−94.7847	+	60.9144i	−0.0167938	+	0.0107927i	0.532217	+	0.846608i	$0.321359\pi$
$318$	−482.663	−	557.022i	−0.0851144	−	0.0982272i
$319$	−4.16215	−	1.22212i	−0.000730519	−	0.000214500i
$320$	−519.147	+	1136.77i	−0.0906913	+	0.198586i
$321$	−2982.46			−0.518581
$322$	2079.82	−	1097.80i	0.359949	−	0.189994i
$323$	−4424.45			−0.762177
$324$	2381.86	−	5215.55i	0.408412	−	0.894298i
$325$	2054.29	+	603.194i	0.350620	+	0.102951i
$326$	1115.50	+	1287.36i	0.189515	+	0.218712i
$327$	6835.83	−	4393.12i	1.15603	−	0.742937i
$328$	−208.124	+	240.187i	−0.0350357	+	0.0404333i
$329$	−564.114	+	3923.50i	−0.0945308	+	0.657476i
$330$	2.38735	−	0.700988i	0.000398240	−	0.000116934i
$331$	−2350.93	−	1510.85i	−0.390390	−	0.250888i	0.330691	−	0.943739i	$-0.392718\pi$
$331$	−2350.93	−	1510.85i	−0.390390	−	0.250888i	−0.721081	+	0.692851i	$0.756354\pi$
$332$	1083.35	+	7534.86i	0.179086	+	1.24557i
$333$	26.4134	+	57.8373i	0.00434669	+	0.00951791i
$334$	−1201.60	−	2631.13i	−0.196852	−	0.431046i
$335$	668.438	+	4649.09i	0.109017	+	0.758229i
$336$	5307.05	+	3410.64i	0.861677	+	0.553766i
$337$	−8541.38	+	2507.98i	−1.38065	+	0.405395i	−0.885995	−	0.463695i	$-0.846523\pi$
$337$	−8541.38	+	2507.98i	−1.38065	+	0.405395i	−0.494654	+	0.869090i	$0.664705\pi$
$338$	−628.145	+	4368.84i	−0.101085	+	0.703058i
$339$	−1156.94	+	1335.17i	−0.185357	+	0.213914i
$340$	1808.81	−	1162.45i	0.288520	−	0.185420i
$341$	−2.42092	−	2.79389i	−0.000384458	−	0.000443688i
$342$	−152.061	−	44.6491i	−0.0240424	−	0.00705949i
$343$	723.426	−	1584.08i	0.113881	−	0.249365i
$344$	−4237.39			−0.664142
$345$	−677.688	+	2916.23i	−0.105755	+	0.455086i
$346$	−670.646			−0.104203
$347$	3480.57	−	7621.39i	0.538463	−	1.17907i	−0.423501	−	0.905896i	$-0.639199\pi$
$347$	3480.57	−	7621.39i	0.538463	−	1.17907i	0.961964	−	0.273175i	$-0.0880737\pi$
$348$	−1537.79	−	451.536i	−0.236880	−	0.0695542i
$349$	3375.59	+	3895.63i	0.517739	+	0.597503i	0.953063	−	0.302771i	$-0.0979117\pi$
$349$	3375.59	+	3895.63i	0.517739	+	0.597503i	−0.435324	+	0.900274i	$0.643366\pi$
$350$	−448.404	+	288.172i	−0.0684805	+	0.0440098i
$351$	7468.41	−	8619.01i	1.13571	−	1.31068i
$352$	−2.20376	+	15.3275i	−0.000333695	+	0.00232090i
$353$	−371.529	+	109.091i	−0.0560184	+	0.0164485i	−0.309622	−	0.950860i	$-0.600202\pi$
$353$	−371.529	+	109.091i	−0.0560184	+	0.0164485i	0.253603	+	0.967308i	$0.418384\pi$
$354$	−610.646	−	392.439i	−0.0916822	−	0.0589206i
$355$	−751.275	−	5225.23i	−0.112320	−	0.781202i
$356$	978.238	+	2142.04i	0.145636	+	0.318899i
$357$	−3313.92	−	7256.47i	−0.491292	−	1.07578i
$358$	−41.9790	−	291.970i	−0.00619736	−	0.0431036i
$359$	−8820.01	−	5668.27i	−1.29666	−	0.833315i	−0.303819	−	0.952730i	$-0.598262\pi$
$359$	−8820.01	−	5668.27i	−1.29666	−	0.833315i	−0.992844	+	0.119415i	$0.961898\pi$
$360$	155.305	−	45.6016i	0.0227369	−	0.00667615i
$361$	181.681	−	1263.62i	0.0264879	−	0.184228i
$362$	−1515.91	+	1749.46i	−0.220096	+	0.254004i
$363$	6078.31	−	3906.29i	0.878866	−	0.564813i
$364$	10106.6	+	11663.6i	1.45530	+	1.67950i
$365$	−2745.90	−	806.270i	−0.393773	−	0.115622i
$366$	−530.274	+	1161.14i	−0.0757319	+	0.165830i
$367$	5455.14			0.775901			0.387951	−	0.921680i	$-0.373183\pi$
$367$	5455.14			0.775901			0.387951	+	0.921680i	$0.373183\pi$
$368$	−4091.00	−	3153.67i	−0.579505	−	0.446729i
$369$	−59.8389			−0.00844198
$370$	45.9596	−	100.637i	0.00645764	−	0.0141402i
$371$	−3762.79	−	1104.85i	−0.526562	−	0.154612i
$372$	−894.458	−	1032.26i	−0.124665	−	0.143871i
$373$	1576.17	−	1012.95i	0.218797	−	0.140612i	−0.426652	−	0.904416i	$-0.640307\pi$
$373$	1576.17	−	1012.95i	0.218797	−	0.140612i	0.645448	+	0.763804i	$0.276671\pi$
$374$	3.55485	−	4.10251i	0.000491489	−	0.000567208i
$375$	96.5699	−	671.658i	0.0132983	−	0.0924914i
$376$	−2009.61	+	590.074i	−0.275632	+	0.0809328i
$377$	−2929.10	−	1882.42i	−0.400149	−	0.257160i
$378$	404.066	+	2810.34i	0.0549812	+	0.382403i
$379$	1151.60	+	2521.66i	0.156079	+	0.341765i	0.971476	−	0.237136i	$-0.0762088\pi$
$379$	1151.60	+	2521.66i	0.156079	+	0.341765i	−0.815397	+	0.578902i	$0.803482\pi$
$380$	−1126.96	−	2467.70i	−0.152137	−	0.333133i
$381$	1865.41	+	12974.2i	0.250834	+	1.74459i
$382$	−402.957	−	258.965i	−0.0539714	−	0.0346853i
$383$	−4886.23	+	1434.73i	−0.651892	+	0.191413i	−0.590924	−	0.806727i	$-0.701237\pi$
$383$	−4886.23	+	1434.73i	−0.651892	+	0.191413i	−0.0609679	+	0.998140i	$0.519419\pi$
$384$	−1062.89	+	7392.54i	−0.141251	+	0.982419i
$385$	8.66954	−	10.0052i	0.00114764	−	0.00132445i
$386$	2917.20	−	1874.77i	0.384667	−	0.247211i
$387$	−522.467	−	602.959i	−0.0686266	−	0.0791993i
$388$	−10121.1	−	2971.84i	−1.32429	−	0.388846i
$389$	−52.5300	+	115.025i	−0.00684673	+	0.0149923i	−0.913024	−	0.407905i	$-0.866260\pi$
$389$	−52.5300	+	115.025i	−0.00684673	+	0.0149923i	0.906178	+	0.422897i	$0.138987\pi$
$390$	1997.12			0.259303
$391$	2195.96	+	6151.74i	0.284026	+	0.795669i
$392$	−3577.38			−0.460931
$393$	−2088.78	+	4573.79i	−0.268104	+	0.587066i
$394$	3760.04	+	1104.05i	0.480782	+	0.141170i
$395$	−922.320	−	1064.41i	−0.117486	−	0.135586i
$396$	−1.60922	+	1.03418i	−0.000204208	+	0.000131236i
$397$	−759.304	+	876.283i	−0.0959908	+	0.110779i	−0.801712	−	0.597710i	$-0.796077\pi$
$397$	−759.304	+	876.283i	−0.0959908	+	0.110779i	0.705722	+	0.708489i	$0.250623\pi$
$398$	476.980	−	3317.47i	0.0600725	−	0.417814i
$399$	−9657.44	+	2835.68i	−1.21172	+	0.355793i
$400$	984.880	+	632.944i	0.123110	+	0.0791180i
$401$	−1783.92	−	12407.4i	−0.222156	−	1.54513i	−0.729859	−	0.683597i	$-0.760414\pi$
$401$	−1783.92	−	12407.4i	−0.222156	−	1.54513i	0.507703	−	0.861532i	$-0.330495\pi$
$402$	1820.03	+	3985.31i	0.225808	+	0.494450i
$403$	−1232.66	−	2699.16i	−0.152366	−	0.333634i
$404$	1696.73	+	11801.0i	0.208949	+	1.45327i
$405$	−3321.11	−	2134.35i	−0.407475	−	0.261869i
$406$	831.708	−	244.212i	0.101667	−	0.0298523i
$407$	−0.391065	+	2.71992i	−4.76275e−5	+	0.000331256i
$408$	2760.33	−	3185.59i	0.334943	−	0.386544i
$409$	−8117.46	+	5216.78i	−0.981376	+	0.630692i	−0.929834	−	0.367979i	$-0.880050\pi$
$409$	−8117.46	+	5216.78i	−0.981376	+	0.630692i	−0.0515418	+	0.998671i	$0.516414\pi$
$410$	68.1843	+	78.6888i	0.00821312	+	0.00947845i
$411$	13729.0	+	4031.19i	1.64769	+	0.483805i
$412$	4676.05	−	10239.1i	0.559156	−	1.22438i
$413$	−3862.21			−0.460163
$414$	13.3914	+	233.585i	0.00158974	+	0.0277296i
$415$	5241.33			0.619968
$416$	−5163.29	+	11306.0i	−0.608537	+	1.33251i
$417$	87.5731	+	25.7138i	0.0102841	+	0.00301969i
$418$	−4.48519	−	5.17619i	−0.000524828	−	0.000605684i
$419$	2810.94	−	1806.48i	0.327740	−	0.210626i	−0.366414	−	0.930452i	$-0.619415\pi$
$419$	2810.94	−	1806.48i	0.327740	−	0.210626i	0.694155	+	0.719826i	$0.255778\pi$
$420$	3203.14	−	3696.62i	0.372136	−	0.429468i
$421$	548.271	−	3813.31i	0.0634705	−	0.441447i	−0.933162	−	0.359455i	$-0.882963\pi$
$421$	548.271	−	3813.31i	0.0634705	−	0.441447i	0.996633	−	0.0819922i	$-0.0261283\pi$
$422$	65.7734	−	19.3128i	0.00758720	−	0.00222780i
$423$	−331.747	−	213.201i	−0.0381326	−	0.0245064i
$424$	−294.897	−	2051.05i	−0.0337770	−	0.234924i
$425$	−614.995	−	1346.65i	−0.0701921	−	0.153699i
$426$	−2045.58	−	4479.19i	−0.232649	−	0.509431i
$427$	966.589	+	6722.77i	0.109547	+	0.761915i
$428$	−3356.34	−	2156.99i	−0.379054	−	0.243603i
$429$	−47.5939	+	13.9748i	−0.00535631	+	0.00157275i
$430$	−197.566	+	1374.10i	−0.0221569	+	0.154105i
$431$	9468.80	−	10927.6i	1.05823	−	1.22126i	0.0838173	−	0.996481i	$-0.473289\pi$
$431$	9468.80	−	10927.6i	1.05823	−	1.22126i	0.974410	−	0.224778i	$-0.0721658\pi$
$432$	5246.18	−	3371.51i	0.584275	−	0.375491i
$433$	3800.18	+	4385.64i	0.421767	+	0.486745i	0.926374	−	0.376604i	$-0.122908\pi$
$433$	3800.18	+	4385.64i	0.421767	+	0.486745i	−0.504608	+	0.863349i	$0.668363\pi$
$434$	708.805	+	208.124i	0.0783956	+	0.0230190i
$435$	−458.417	+	1003.79i	−0.0505274	+	0.110640i
$436$	10870.0			1.19399
$437$	8077.03	−	1637.86i	0.884157	−	0.179289i
$438$	−2669.49			−0.291218
$439$	−656.677	+	1437.92i	−0.0713929	+	0.156329i	−0.941964	−	0.335714i	$-0.891022\pi$
$439$	−656.677	+	1437.92i	−0.0713929	+	0.156329i	0.870571	+	0.492043i	$0.163750\pi$
$440$	6.71183	+	1.97077i	0.000727214	+	0.000213529i
$441$	−441.088	−	509.042i	−0.0476285	−	0.0549662i
$442$	3665.47	−	2355.66i	0.394454	−	0.253500i
$443$	9826.76	−	11340.7i	1.05391	−	1.21628i	0.0782656	−	0.996933i	$-0.475062\pi$
$443$	9826.76	−	11340.7i	1.05391	−	1.21628i	0.975647	−	0.219347i	$-0.0703928\pi$
$444$	−144.487	+	1004.93i	−0.0154438	+	0.107414i
$445$	1555.71	−	456.796i	0.165725	−	0.0486612i
$446$	1018.79	+	654.738i	0.108164	+	0.0695129i
$447$	1709.81	+	11892.0i	0.180920	+	1.25832i
$448$	2576.61	+	5641.99i	0.271727	+	0.594998i
$449$	−6413.98	−	14044.7i	−0.674153	−	1.47619i	−0.868722	−	0.495300i	$-0.835058\pi$
$449$	−6413.98	−	14044.7i	−0.674153	−	1.47619i	0.194569	−	0.980889i	$-0.437669\pi$
$450$	−7.54668	−	52.4883i	−0.000790564	−	0.00549849i
$451$	−2.17554	−	1.39814i	−0.000227145	−	0.000145977i
$452$	−2267.61	+	665.829i	−0.235972	+	0.0692875i
$453$	1519.59	−	10569.0i	0.157609	−	1.09619i
$454$	2856.23	−	3296.26i	0.295263	−	0.340752i
$455$	8939.34	−	5744.96i	0.921061	−	0.591930i
$456$	−3482.74	−	4019.30i	−0.357663	−	0.412765i
$457$	−6.37136	−	1.87080i	−0.000652165	−	0.000191493i	0.281406	−	0.959589i	$-0.409199\pi$
$457$	−6.37136	−	1.87080i	−0.000652165	−	0.000191493i	−0.282059	+	0.959397i	$0.591017\pi$
$458$	2061.69	−	4514.48i	0.210342	−	0.460585i
$459$	−7885.86			−0.801919
$460$	−2871.74	+	2791.70i	−0.291078	+	0.282964i
$461$	18496.2			1.86866			0.934330	−	0.356408i	$-0.115999\pi$
$461$	18496.2			1.86866			0.934330	+	0.356408i	$0.115999\pi$
$462$	5.12997	−	11.2331i	0.000516597	−	0.00113119i
$463$	−5304.02	−	1557.40i	−0.532395	−	0.156325i	0.00447547	−	0.999990i	$-0.498575\pi$
$463$	−5304.02	−	1557.40i	−0.532395	−	0.156325i	−0.536870	+	0.843665i	$0.680394\pi$
$464$	−1246.79	−	1438.87i	−0.124743	−	0.143961i
$465$	−791.154	+	508.444i	−0.0789008	+	0.0507065i
$466$	3422.41	−	3949.67i	0.340215	−	0.392629i
$467$	−1402.45	+	9754.24i	−0.138967	+	0.966536i	0.794344	+	0.607468i	$0.207815\pi$
$467$	−1402.45	+	9754.24i	−0.138967	+	0.966536i	−0.933311	+	0.359068i	$0.883095\pi$
$468$	−1473.20	+	432.569i	−0.145510	+	0.0427255i
$469$	19610.9	+	12603.1i	1.93080	+	1.24085i
$470$	97.6522	+	679.186i	0.00958375	+	0.0666564i
$471$	−2727.65	−	5972.72i	−0.266844	−	0.584307i
$472$	−847.756	−	1856.33i	−0.0826718	−	0.181026i
$473$	−4.90701	−	34.1290i	−0.000477007	−	0.00331766i
$474$	−1105.21	−	710.275i	−0.107097	−	0.0688271i
$475$	−1792.22	+	526.244i	−0.173122	+	0.0508331i
$476$	1518.71	−	10562.9i	0.146240	−	1.01712i
$477$	255.494	−	294.856i	0.0245247	−	0.0283030i
$478$	−3196.03	+	2053.97i	−0.305823	+	0.196540i
$479$	3245.84	+	3745.90i	0.309616	+	0.357316i	0.889137	−	0.457642i	$-0.151306\pi$
$479$	3245.84	+	3745.90i	0.309616	+	0.357316i	−0.579521	+	0.814957i	$0.696760\pi$
$480$	3779.71	+	1109.82i	0.359415	+	0.105534i
$481$	−916.246	+	2006.30i	−0.0868550	+	0.190186i
$482$	2247.34			0.212373
$483$	8735.92	+	12020.2i	0.822977	+	1.13238i
$484$	9665.43			0.907723
$485$	−3017.12	+	6606.58i	−0.282475	+	0.618535i
$486$	−569.323	−	167.168i	−0.0531379	−	0.0156027i
$487$	11564.8	+	13346.5i	1.07608	+	1.24186i	0.968856	+	0.247626i	$0.0796503\pi$
$487$	11564.8	+	13346.5i	1.07608	+	1.24186i	0.107223	+	0.994235i	$0.465804\pi$
$488$	−3019.05	+	1940.23i	−0.280053	+	0.179979i
$489$	−7048.20	+	8134.06i	−0.651801	+	0.752219i
$490$	−166.793	+	1160.07i	−0.0153774	+	0.106952i
$491$	−15842.6	+	4651.79i	−1.45614	+	0.427561i	−0.911566	−	0.411153i	$-0.865126\pi$
$491$	−15842.6	+	4651.79i	−1.45614	+	0.427561i	−0.544573	+	0.838714i	$0.683308\pi$
$492$	−803.798	−	516.570i	−0.0736545	−	0.0473349i
$493$	342.631	+	2383.05i	0.0313009	+	0.217702i
$494$	−2283.73	−	5000.68i	−0.207996	−	0.455448i
$495$	0.547133	+	1.19805i	4.96804e−5	+	0.000108785i
$496$	−230.913	−	1606.04i	−0.0209039	−	0.145390i
$497$	−22041.2	−	14165.0i	−1.98930	−	1.27844i
$498$	4691.03	−	1377.41i	0.422109	−	0.123942i
$499$	−260.348	+	1810.76i	−0.0233563	+	0.162446i	−0.998161	−	0.0606117i	$-0.980695\pi$
$499$	−260.348	+	1810.76i	−0.0233563	+	0.162446i	0.974805	+	0.223058i	$0.0716040\pi$
$500$	594.437	−	686.017i	0.0531681	−	0.0613592i
$501$	15374.9	−	9880.85i	1.37106	−	0.881125i
$502$	−120.602	−	139.182i	−0.0107226	−	0.0123745i
$503$	17588.6	+	5164.48i	1.55912	+	0.457798i	0.943810	−	0.330488i	$-0.107213\pi$
$503$	17588.6	+	5164.48i	1.55912	+	0.457798i	0.615308	+	0.788287i	$0.289032\pi$
$504$	333.721	−	730.747i	0.0294943	−	0.0645834i
$505$	8208.91			0.723350
$506$	−4.97084	+	8.80525i	−0.000436721	+	0.000773599i
$507$	−27888.0			−2.44290
$508$	−7284.03	+	15949.8i	−0.636174	+	1.39303i
$509$	−11744.2	−	3448.42i	−1.02270	−	0.300291i	−0.272960	−	0.962025i	$-0.588003\pi$
$509$	−11744.2	−	3448.42i	−1.02270	−	0.300291i	−0.749739	+	0.661734i	$0.769821\pi$
$510$	−904.323	−	1043.64i	−0.0785179	−	0.0906144i
$511$	−11948.9	+	7679.11i	−1.03442	+	0.664783i
$512$	−7667.61	+	8848.89i	−0.661843	+	0.763807i
$513$	−1415.99	+	9848.42i	−0.121866	+	0.847599i
$514$	−562.363	+	165.125i	−0.0482583	+	0.0141699i
$515$	−6519.99	−	4190.14i	−0.557874	−	0.358524i
$516$	−1812.99	−	12609.7i	−0.154676	−	1.07579i
$517$	−7.07977	−	15.5025i	−0.000602259	−	0.00131876i
$518$	−228.105	−	499.480i	−0.0193482	−	0.0423666i
$519$	−603.048	−	4194.29i	−0.0510036	−	0.354738i
$520$	4723.43	+	3035.56i	0.398338	+	0.255997i
$521$	7028.44	−	2063.74i	0.591021	−	0.173539i	0.0274725	−	0.999623i	$-0.491254\pi$
$521$	7028.44	−	2063.74i	0.591021	−	0.173539i	0.563548	+	0.826083i	$0.309436\pi$
$522$	−12.2728	+	85.3590i	−0.00102905	+	0.00715721i
$523$	−2070.34	+	2389.29i	−0.173096	+	0.199764i	−0.835668	−	0.549234i	$-0.814919\pi$
$523$	−2070.34	+	2389.29i	−0.173096	+	0.199764i	0.662572	+	0.748998i	$0.269465\pi$
$524$	−5658.52	+	3636.51i	−0.471743	+	0.303171i
$525$	−2205.46	−	2545.24i	−0.183341	−	0.211587i
$526$	−5344.96	−	1569.42i	−0.443063	−	0.130095i
$527$	−852.343	+	1866.37i	−0.0704528	+	0.154270i
$528$	−27.1236			−0.00223561
$529$	−6286.08	−	10417.3i	−0.516650	−	0.856197i
$530$	−678.865			−0.0556377
$531$	159.618	−	349.515i	0.0130449	−	0.0285643i
$532$	−12919.0	−	3793.35i	−1.05283	−	0.309140i
$533$	−1359.32	−	1568.73i	−0.110466	−	0.127485i
$534$	1272.32	−	817.672i	0.103106	−	0.0662624i
$535$	−1798.92	+	2076.06i	−0.145372	+	0.167768i
$536$	−1752.96	+	12192.1i	−0.141262	+	0.982497i
$537$	1788.26	−	525.081i	0.143704	−	0.0421954i
$538$	−1149.67	−	738.846i	−0.0921295	−	0.0592080i
$539$	−4.14269	−	28.8131i	−0.000331055	−	0.00230254i
$540$	−2008.63	−	4398.28i	−0.160069	−	0.350503i
$541$	3096.52	+	6780.43i	0.246081	+	0.538842i	0.991857	−	0.127354i	$-0.0406485\pi$
$541$	3096.52	+	6780.43i	0.246081	+	0.538842i	−0.745776	+	0.666196i	$0.767921\pi$
$542$	−99.7762	−	693.959i	−0.00790730	−	0.0549965i
$543$	−12304.4	−	7907.55i	−0.972434	−	0.624946i
$544$	8246.25	−	2421.32i	0.649917	−	0.190833i
$545$	1065.13	−	7408.15i	0.0837160	−	0.582258i
$546$	6491.01	−	7491.03i	0.508772	−	0.587154i
$547$	−15947.5	+	10248.8i	−1.24655	+	0.801110i	−0.986385	−	0.164453i	$-0.947414\pi$
$547$	−15947.5	+	10248.8i	−1.24655	+	0.801110i	−0.260167	+	0.965564i	$0.583778\pi$
$548$	12534.6	+	14465.7i	0.977102	+	1.12764i
$549$	−648.331	−	190.367i	−0.0504009	−	0.0147990i
$550$	0.952017	−	2.08463i	7.38075e−5	−	0.000161616i
$551$	3037.64			0.234860
$552$	−3859.84	+	6837.25i	−0.297619	+	0.527197i
$553$	−6990.23			−0.537531
$554$	−2151.61	+	4711.37i	−0.165006	+	0.361312i
$555$	670.724	+	196.942i	0.0512984	+	0.0150626i
$556$	79.9546	+	92.2726i	0.00609862	+	0.00703818i
$557$	−12512.8	+	8041.50i	−0.951859	+	0.611722i	−0.921734	−	0.387824i	$-0.873227\pi$
$557$	−12512.8	+	8041.50i	−0.951859	+	0.611722i	−0.0301251	+	0.999546i	$0.509591\pi$
$558$	−48.1279	+	55.5426i	−0.00365129	+	0.00421381i
$559$	3938.65	−	27393.9i	0.298009	−	2.07270i
$560$	5575.15	−	1637.01i	0.420702	−	0.123529i
$561$	28.8540	+	18.5434i	0.00217151	+	0.00139555i
$562$	809.257	+	5628.51i	0.0607410	+	0.422463i
$563$	−3063.90	−	6709.01i	−0.229357	−	0.502222i	0.759606	−	0.650384i	$-0.225392\pi$
$563$	−3063.90	−	6709.01i	−0.229357	−	0.502222i	−0.988963	+	0.148161i	$0.952665\pi$
$564$	−2615.77	−	5727.73i	−0.195290	−	0.427626i
$565$	231.579	+	1610.67i	0.0172435	+	0.119931i
$566$	−2734.48	−	1757.34i	−0.203072	−	0.130507i
$567$	−18800.0	+	5520.17i	−1.39246	+	0.408863i
$568$	1970.20	−	13703.0i	0.145542	−	1.01226i
$569$	2018.98	−	2330.03i	0.148753	−	0.171670i	−0.676483	−	0.736458i	$-0.736497\pi$
$569$	2018.98	−	2330.03i	0.148753	−	0.171670i	0.825236	+	0.564789i	$0.191042\pi$
$570$	−1465.76	+	941.985i	−0.107708	+	0.0692200i
$571$	−2325.93	−	2684.26i	−0.170468	−	0.196730i	0.664087	−	0.747655i	$-0.268820\pi$
$571$	−2325.93	−	2684.26i	−0.170468	−	0.196730i	−0.834555	+	0.550925i	$0.814275\pi$
$572$	−63.6674	−	18.6944i	−0.00465397	−	0.00136653i
$573$	1257.25	−	2752.99i	0.0916621	−	0.200712i
$574$	516.766			0.0375773
$575$	1621.21	+	2230.71i	0.117581	+	0.161786i
$576$	−617.064			−0.0446372
$577$	8422.98	−	18443.8i	0.607718	−	1.33072i	−0.316406	−	0.948624i	$-0.602476\pi$
$577$	8422.98	−	18443.8i	0.607718	−	1.33072i	0.924124	−	0.382093i	$-0.124797\pi$
$578$	1159.29	+	340.398i	0.0834257	+	0.0244960i
$579$	14348.2	+	16558.6i	1.02986	+	1.18852i
$580$	−1241.85	+	798.092i	−0.0889055	+	0.0571361i
$581$	17035.3	−	19659.7i	1.21642	−	1.40383i
$582$	−964.154	+	6705.84i	−0.0686692	+	0.477605i
$583$	16.1782	−	4.75035i	0.00114928	−	0.000337460i
$584$	−6313.66	−	4057.54i	−0.447365	−	0.287504i
$585$	150.450	+	1046.40i	0.0106331	+	0.0739545i
$586$	2434.91	+	5331.72i	0.171647	+	0.375855i
$587$	7545.16	+	16521.6i	0.530532	+	1.16170i	0.965296	+	0.261158i	$0.0841045\pi$
$587$	7545.16	+	16521.6i	0.530532	+	1.16170i	−0.434764	+	0.900544i	$0.643168\pi$
$588$	−1530.60	−	10645.6i	−0.107349	−	0.746626i
$589$	2177.81	+	1399.59i	0.152351	+	0.0979103i
$590$	−641.495	+	188.360i	−0.0447626	+	0.0131435i
$591$	−3523.78	+	24508.4i	−0.245260	+	1.70582i
$592$	−789.797	+	911.475i	−0.0548319	+	0.0632794i
$593$	−7541.72	+	4846.77i	−0.522262	+	0.335637i	−0.775066	−	0.631880i	$-0.782284\pi$
$593$	−7541.72	+	4846.77i	−0.522262	+	0.335637i	0.252804	+	0.967517i	$0.418647\pi$
$594$	−7.99412	−	9.22571i	−0.000552193	−	0.000637265i
$595$	−7050.02	−	2070.07i	−0.485752	−	0.142630i
$596$	−6676.44	+	14619.4i	−0.458855	+	1.00475i
$597$	21176.7			1.45177
$598$	−5819.45	+	5657.24i	−0.397951	+	0.386859i
$599$	−20599.5			−1.40513			−0.702564	−	0.711621i	$-0.747961\pi$
$599$	−20599.5			−1.40513			−0.702564	+	0.711621i	$0.747961\pi$
$600$	739.238	−	1618.71i	0.0502988	−	0.110139i
$601$	−1006.03	−	295.396i	−0.0682807	−	0.0200490i	0.247414	−	0.968910i	$-0.420419\pi$
$601$	−1006.03	−	295.396i	−0.0682807	−	0.0200490i	−0.315695	+	0.948861i	$0.602237\pi$
$602$	4512.00	+	5207.12i	0.305474	+	0.352536i
$603$	−1951.01	+	1253.84i	−0.131760	+	0.0846771i
$604$	9353.87	−	10794.9i	0.630139	−	0.727219i
$605$	947.097	−	6587.21i	0.0636446	−	0.442658i
$606$	7347.04	−	2157.29i	0.492497	−	0.144610i
$607$	14593.2	+	9378.48i	0.975815	+	0.627118i	0.928331	−	0.371754i	$-0.121244\pi$
$607$	14593.2	+	9378.48i	0.975815	+	0.627118i	0.0474833	+	0.998872i	$0.484880\pi$
$608$	−1543.21	−	10733.3i	−0.102937	−	0.715939i
$609$	2275.20	+	4981.99i	0.151389	+	0.331495i
$610$	488.415	+	1069.48i	0.0324186	+	0.0709868i
$611$	−1946.79	−	13540.2i	−0.128901	−	0.896527i
$612$	893.132	+	573.981i	0.0589914	+	0.0379115i
$613$	−3037.53	+	891.901i	−0.200138	+	0.0587660i	−0.380265	−	0.924877i	$-0.624167\pi$
$613$	−3037.53	+	891.901i	−0.200138	+	0.0587660i	0.180127	+	0.983643i	$0.442349\pi$
$614$	−433.326	+	3013.85i	−0.0284815	+	0.198093i
$615$	−430.816	+	497.188i	−0.0282475	+	0.0325993i
$616$	29.2069	−	18.7701i	0.00191035	−	0.00122771i
$617$	1224.85	+	1413.55i	0.0799200	+	0.0922325i	0.794301	−	0.607524i	$-0.207837\pi$
$617$	1224.85	+	1413.55i	0.0799200	+	0.0922325i	−0.714381	+	0.699757i	$0.753292\pi$
$618$	−6936.60	−	2036.77i	−0.451506	−	0.132574i
$619$	5074.02	−	11110.5i	0.329470	−	0.721439i	−0.670317	−	0.742075i	$-0.733842\pi$
$619$	5074.02	−	11110.5i	0.329470	−	0.721439i	0.999787	+	0.0206361i	$0.00656914\pi$
$620$	−1258.05			−0.0814914
$621$	14396.0	−	2919.21i	0.930259	−	0.188638i
$622$	−7621.41			−0.491303
$623$	3342.92	−	7319.98i	0.214978	−	0.470736i
$624$	−20889.1	−	6133.59i	−1.34012	−	0.393494i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	−1098.69	+	706.087i	−0.0701479	+	0.0450813i
$627$	28.3393	−	32.7053i	0.00180504	−	0.00208313i
$628$	1250.04	−	8694.19i	0.0794297	−	0.552446i
$629$	1463.33	−	429.672i	0.0927611	−	0.0272371i
$630$	−221.407	−	142.290i	−0.0140017	−	0.00899834i
$631$	−2582.67	−	17962.8i	−0.162939	−	1.13326i	−0.893057	−	0.449943i	$-0.851444\pi$
$631$	−2582.67	−	17962.8i	−0.162939	−	1.13326i	0.730118	−	0.683321i	$-0.239465\pi$
$632$	−1534.35	−	3359.77i	−0.0965717	−	0.211463i
$633$	179.928	+	393.987i	0.0112978	+	0.0247387i
$634$	13.7764	+	95.8168i	0.000862981	+	0.00600217i
$635$	10156.4	+	6527.12i	0.634715	+	0.407907i
$636$	5977.37	−	1755.11i	0.372670	−	0.109426i
$637$	3325.17	−	23127.1i	0.206826	−	1.43851i
$638$	−2.44061	+	2.81661i	−0.000151449	+	0.000174782i
$639$	2192.79	−	1409.22i	0.135752	−	0.0872426i
$640$	4504.79	+	5198.80i	0.278230	+	0.321095i
$641$	−5748.81	−	1688.00i	−0.354235	−	0.104013i	0.0997736	−	0.995010i	$-0.468188\pi$
$641$	−5748.81	−	1688.00i	−0.354235	−	0.104013i	−0.454008	+	0.890997i	$0.650006\pi$
$642$	−1064.46	+	2330.85i	−0.0654376	+	0.143288i
$643$	2721.74			0.166929			0.0834643	−	0.996511i	$-0.473402\pi$
$643$	2721.74			0.166929			0.0834643	+	0.996511i	$0.473402\pi$
$644$	1137.72	+	19845.2i	0.0696158	+	1.21430i
$645$	−8771.41			−0.535463
$646$	−1579.12	+	3457.79i	−0.0961760	+	0.210596i
$647$	−9060.96	−	2660.54i	−0.550577	−	0.161664i	−0.00540054	−	0.999985i	$-0.501719\pi$
$647$	−9060.96	−	2660.54i	−0.550577	−	0.161664i	−0.545176	+	0.838322i	$0.683537\pi$
$648$	−6779.80	−	7824.30i	−0.411012	−	0.474333i
$649$	13.9696	−	8.97771i	0.000844922	−	0.000542998i
$650$	1204.60	−	1390.18i	0.0726896	−	0.0838883i
$651$	−664.267	+	4620.08i	−0.0399918	+	0.278149i
$652$	−13814.6	+	4056.32i	−0.829785	+	0.243647i
$653$	7569.84	+	4864.84i	0.453646	+	0.291541i	0.747441	−	0.664328i	$-0.231282\pi$
$653$	7569.84	+	4864.84i	0.453646	+	0.291541i	−0.293795	+	0.955868i	$0.594918\pi$
$654$	−993.547	−	6910.27i	−0.0594048	−	0.413170i
$655$	1923.89	+	4212.74i	0.114767	+	0.251306i
$656$	−471.509	−	1032.46i	−0.0280630	−	0.0614495i
$657$	−201.102	−	1398.69i	−0.0119417	−	0.0830567i
$658$	2864.95	+	1841.19i	0.169738	+	0.109084i
$659$	−21098.0	+	6194.93i	−1.24713	+	0.366192i	−0.837691	−	0.546144i	$-0.816095\pi$
$659$	−21098.0	+	6194.93i	−1.24713	+	0.366192i	−0.409443	+	0.912336i	$0.634277\pi$
$660$	−2.99294	+	20.8163i	−0.000176515	+	0.00122769i
$661$	−17387.5	+	20066.2i	−1.02314	+	1.18076i	−0.0397574	+	0.999209i	$0.512658\pi$
$661$	−17387.5	+	20066.2i	−1.02314	+	1.18076i	−0.983381	+	0.181555i	$0.941887\pi$
$662$	−2019.83	+	1298.06i	−0.118584	+	0.0762095i
$663$	18028.5	+	20806.0i	1.05606	+	1.21876i
$664$	13188.5	+	3872.48i	0.770800	+	0.226327i
$665$	−3851.15	+	8432.85i	−0.224573	+	0.491747i
$666$	54.6281			0.00317837
$667$	−1507.65	−	4223.52i	−0.0875210	−	0.245181i
$668$	24448.4			1.41607
$669$	−3178.70	+	6960.37i	−0.183700	+	0.402247i
$670$	3871.92	+	1136.90i	0.223262	+	0.0655555i
$671$	−19.1232	−	22.0694i	−0.00110021	−	0.00126971i
$672$	16447.6	−	10570.2i	0.944165	−	0.606778i
$673$	−15972.9	+	18433.7i	−0.914874	+	1.05582i	0.0833665	+	0.996519i	$0.473433\pi$
$673$	−15972.9	+	18433.7i	−0.914874	+	1.05582i	−0.998240	+	0.0593015i	$0.981113\pi$
$674$	−1088.45	+	7570.36i	−0.0622043	+	0.432640i
$675$	−3194.34	+	937.944i	−0.182149	+	0.0534837i
$676$	−31384.1	−	20169.4i	−1.78562	−	1.14755i
$677$	−1513.19	−	10524.5i	−0.0859034	−	0.597471i	−0.986617	−	0.163057i	$-0.947865\pi$
$677$	−1513.19	−	10524.5i	−0.0859034	−	0.597471i	0.900713	−	0.434414i	$-0.143045\pi$
$678$	630.545	+	1380.70i	0.0357167	+	0.0782087i
$679$	14974.5	+	32789.5i	0.846344	+	1.85324i
$680$	−552.523	−	3842.88i	−0.0311593	−	0.216717i
$681$	23183.5	+	14899.1i	1.30454	+	0.838379i
$682$	−3.04752	+	0.894833i	−0.000171108	+	5.02418e-5i
$683$	−1917.59	+	13337.1i	−0.107430	+	0.747190i	0.862895	+	0.505384i	$0.168649\pi$
$683$	−1917.59	+	13337.1i	−0.107430	+	0.747190i	−0.970325	+	0.241806i	$0.922260\pi$
$684$	877.199	−	1012.34i	0.0490359	−	0.0565904i
$685$	11086.9	−	7125.14i	0.618409	−	0.397427i
$686$	−979.793	−	1130.74i	−0.0545316	−	0.0629328i
$687$	30087.9	+	8834.60i	1.67092	+	0.490627i
$688$	6286.61	−	13765.7i	0.348364	−	0.762811i
$689$	13533.8			0.748325
$690$	2037.22	+	1570.45i	0.112399	+	0.0866465i
$691$	27419.5			1.50953			0.754765	−	0.655995i	$-0.227751\pi$
$691$	27419.5			1.50953			0.754765	+	0.655995i	$0.227751\pi$
$692$	2354.77	−	5156.24i	0.129357	−	0.283252i
$693$	6.27207	+	1.84165i	0.000343804	+	0.000100950i
$694$	−4714.01	−	5440.26i	−0.257841	−	0.297564i
$695$	70.7204	−	45.4492i	0.00385982	−	0.00248056i
$696$	−1895.13	+	2187.09i	−0.103211	+	0.119111i
$697$	−204.264	+	1420.69i	−0.0111005	+	0.0772056i
$698$	4249.28	−	1247.70i	0.230427	−	0.0676593i
$699$	27779.1	+	17852.5i	1.50315	+	0.966015i
$700$	−641.159	−	4459.36i	−0.0346193	−	0.240783i
$701$	−6249.31	−	13684.1i	−0.336709	−	0.737291i	0.663229	−	0.748417i	$-0.269186\pi$
$701$	−6249.31	−	13684.1i	−0.336709	−	0.737291i	−0.999938	+	0.0111262i	$0.996458\pi$
$702$	−4070.38	−	8912.89i	−0.218841	−	0.479196i
$703$	−273.849	−	1904.66i	−0.0146919	−	0.102184i
$704$	−22.4344	−	14.4177i	−0.00120103	−	0.000771857i
$705$	−4159.89	+	1221.45i	−0.222228	+	0.0652519i
$706$	−47.3451	+	329.292i	−0.00252387	+	0.0175539i
$707$	26680.5	−	30790.9i	1.41927	−	1.63792i
$708$	5161.35	−	3317.00i	0.273977	−	0.176074i
$709$	−13176.5	−	15206.5i	−0.697962	−	0.805491i	0.290514	−	0.956871i	$-0.406174\pi$
$709$	−13176.5	−	15206.5i	−0.697962	−	0.805491i	−0.988476	+	0.151380i	$0.951628\pi$
$710$	−4351.75	−	1277.79i	−0.230026	−	0.0675417i
$711$	288.893	−	632.587i	0.0152382	−	0.0333669i
$712$	4252.03			0.223808
$713$	865.089	−	3722.66i	0.0454388	−	0.195533i
$714$	−6853.83			−0.359241
$715$	−18.9793	+	41.5589i	−0.000992708	+	0.00217373i
$716$	2392.20	+	702.412i	0.124861	+	0.0366625i
$717$	−15719.6	−	18141.4i	−0.818771	−	0.944912i
$718$	−7577.79	+	4869.95i	−0.393873	+	0.253127i
$719$	688.396	−	794.452i	0.0357063	−	0.0412073i	−0.737616	−	0.675221i	$-0.764048\pi$
$719$	688.396	−	794.452i	0.0357063	−	0.0412073i	0.773322	+	0.634014i	$0.218594\pi$
$720$	−82.2676	+	572.184i	−0.00425824	+	0.0296167i
$721$	−36908.0	+	10837.2i	−1.90641	+	0.559774i
$722$	−922.697	−	592.981i	−0.0475612	−	0.0305658i
$723$	2020.82	+	14055.1i	0.103949	+	0.722980i
$724$	−8127.95	−	17797.7i	−0.417228	−	0.913601i
$725$	422.230	+	924.555i	0.0216293	+	0.0473615i
$726$	−883.445	−	6144.50i	−0.0451622	−	0.314110i
$727$	27169.6	+	17460.9i	1.38606	+	0.890766i	0.999504	−	0.0314997i	$-0.0100283\pi$
$727$	27169.6	+	17460.9i	1.38606	+	0.890766i	0.386556	+	0.922266i	$0.373665\pi$
$728$	26738.1	−	7851.02i	1.36124	−	0.399695i
$729$	−2500.35	+	17390.3i	−0.127031	+	0.883519i
$730$	−1610.15	+	1858.21i	−0.0816360	+	0.0942130i
$731$	−16098.8	+	10346.1i	−0.814551	+	0.523480i
$732$	−7065.46	−	8153.98i	−0.356758	−	0.411721i
$733$	7008.14	+	2057.77i	0.353140	+	0.103691i	0.453491	−	0.891261i	$-0.350178\pi$
$733$	7008.14	+	2057.77i	0.353140	+	0.103691i	−0.100351	+	0.994952i	$0.531997\pi$
$734$	1946.98	−	4263.29i	0.0979078	−	0.214388i
$735$	−7405.18			−0.371625
$736$	−14157.5	+	7472.83i	−0.709040	+	0.374256i
$737$	−100.228			−0.00500943
$738$	−21.3570	+	46.7652i	−0.00106526	+	0.00233259i
$739$	30001.8	+	8809.32i	1.49342	+	0.438506i	0.923629	−	0.383287i	$-0.125208\pi$
$739$	30001.8	+	8809.32i	1.49342	+	0.438506i	0.569786	+	0.821793i	$0.307026\pi$
$740$	612.373	+	706.717i	0.0304207	+	0.0351073i
$741$	29221.2	−	18779.3i	1.44867	−	0.931007i
$742$	−2206.43	+	2546.36i	−0.109165	+	0.125984i
$743$	1734.65	−	12064.8i	0.0856503	−	0.595711i	−0.901118	−	0.433574i	$-0.857252\pi$
$743$	1734.65	−	12064.8i	0.0856503	−	0.595711i	0.986768	−	0.162137i	$-0.0518387\pi$
$744$	−2366.39	+	694.835i	−0.116608	+	0.0342391i
$745$	9309.20	+	5982.66i	0.457802	+	0.294212i
$746$	−229.087	−	1593.34i	−0.0112433	−	0.0781987i
$747$	1075.09	+	2354.12i	0.0526580	+	0.115305i
$748$	19.0602	+	41.7360i	0.000931698	+	0.00204013i
$749$	1940.31	+	13495.2i	0.0946561	+	0.658348i
$750$	−490.447	−	315.191i	−0.0238781	−	0.0153455i
$751$	−22.2159	+	6.52317i	−0.00107945	+	0.000316956i	−0.282272	−	0.959334i	$-0.591088\pi$
$751$	−22.2159	+	6.52317i	−0.00107945	+	0.000316956i	0.281193	+	0.959651i	$0.409270\pi$
$752$	1064.52	−	7403.92i	0.0516212	−	0.359034i
$753$	762.012	−	879.409i	0.0368782	−	0.0425597i
$754$	−2516.56	+	1617.29i	−0.121549	+	0.0781146i
$755$	−6440.42	−	7432.65i	−0.310452	−	0.358280i
$756$	−23025.9	−	6761.02i	−1.10773	−	0.325259i
$757$	14491.2	−	31731.2i	0.695760	−	1.52350i	−0.149277	−	0.988795i	$-0.547695\pi$
$757$	14491.2	−	31731.2i	0.695760	−	1.52350i	0.845037	−	0.534707i	$-0.179578\pi$
$758$	2381.74			0.114128
$759$	−59.5387	−	23.1704i	−0.00284732	−	0.00110808i
$760$	−4898.47			−0.233798
$761$	−4308.23	+	9433.70i	−0.205221	+	0.449371i	−0.984056	−	0.177857i	$-0.943083\pi$
$761$	−4308.23	+	9433.70i	−0.205221	+	0.449371i	0.778835	+	0.627228i	$0.215811\pi$
$762$	10805.4	+	3172.74i	0.513697	+	0.150835i
$763$	−24325.4	−	28073.0i	−1.15418	−	1.33200i
$764$	3405.90

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.356908 - 0.781519i) q^{2} +(5.20863 + 1.52939i) q^{3} +(4.75550 + 5.48814i) q^{4} +(4.20627 - 2.70320i) q^{5} +(3.05425 - 3.52479i) q^{6} +(3.53166 - 24.5632i) q^{7} +(12.5812 - 3.69418i) q^{8} +(2.07692 + 1.33475i) q^{9} +O(q^{10})\)	\(q+(0.356908 - 0.781519i) q^{2} +(5.20863 + 1.52939i) q^{3} +(4.75550 + 5.48814i) q^{4} +(4.20627 - 2.70320i) q^{5} +(3.05425 - 3.52479i) q^{6} +(3.53166 - 24.5632i) q^{7} +(12.5812 - 3.69418i) q^{8} +(2.07692 + 1.33475i) q^{9} +(-0.611355 - 4.25207i) q^{10} +(0.0443232 + 0.0970542i) q^{11} +(16.3761 + 35.8587i) q^{12} +(12.1879 + 84.7689i) q^{13} +(-17.9361 - 11.5269i) q^{14} +(26.0431 - 7.64695i) q^{15} +(-6.66449 + 46.3525i) q^{16} +(38.7792 - 44.7536i) q^{17} +(1.78440 - 1.14677i) q^{18} +(-48.9282 - 56.4661i) q^{19} +(34.8384 + 10.2295i) q^{20} +(55.9619 - 122.539i) q^{21} +0.0916690 q^{22} +(-54.2260 + 96.0549i) q^{23} +71.1807 q^{24} +(10.3854 - 22.7408i) q^{25} +(70.5984 + 20.7296i) q^{26} +(-87.2065 - 100.642i) q^{27} +(151.601 - 97.4282i) q^{28} +(-26.6242 + 30.7259i) q^{29} +(3.31876 - 23.0825i) q^{30} +(-33.2448 + 9.76157i) q^{31} +(122.093 + 78.4646i) q^{32} +(0.0824291 + 0.573307i) q^{33} +(-21.1352 - 46.2795i) q^{34} +(-51.5443 - 112.866i) q^{35} +(2.55146 + 17.7458i) q^{36} +(21.6659 + 13.9238i) q^{37} +(-61.5922 + 18.0851i) q^{38} +(-66.1624 + 460.170i) q^{39} +(42.9338 - 49.5483i) q^{40} +(-20.3901 + 13.1039i) q^{41} +(-75.7936 - 87.4705i) q^{42} +(-310.070 - 91.0447i) q^{43} +(-0.321868 + 0.704793i) q^{44} +12.3442 q^{45} +(55.7150 + 76.6614i) q^{46} -159.731 q^{47} +(-105.604 + 231.240i) q^{48} +(-261.774 - 76.8636i) q^{49} +(-14.0657 - 16.2327i) q^{50} +(270.432 - 173.796i) q^{51} +(-407.264 + 470.007i) q^{52} +(22.4900 - 156.421i) q^{53} +(-109.778 + 32.2337i) q^{54} +(0.448793 + 0.288421i) q^{55} +(-46.3084 - 322.082i) q^{56} +(-168.490 - 368.941i) q^{57} +(14.5105 + 31.7736i) q^{58} +(-22.1492 - 154.051i) q^{59} +(165.816 + 106.563i) q^{60} +(-262.606 + 77.1081i) q^{61} +(-4.23649 + 29.4654i) q^{62} +(40.1208 - 46.3019i) q^{63} +(-210.264 + 135.129i) q^{64} +(280.413 + 323.614i) q^{65} +(0.477469 + 0.140198i) q^{66} +(-390.232 + 854.490i) q^{67} +430.028 q^{68} +(-429.349 + 417.381i) q^{69} -106.604 q^{70} +(438.592 - 960.383i) q^{71} +(31.0609 + 9.12031i) q^{72} +(-374.820 - 432.565i) q^{73} +(18.6145 - 11.9628i) q^{74} +(88.8731 - 102.565i) q^{75} +(77.2160 - 537.049i) q^{76} +(2.54050 - 0.745958i) q^{77} +(336.017 + 215.945i) q^{78} +(-40.0879 - 278.817i) q^{79} +(97.2677 + 212.987i) q^{80} +(-327.996 - 718.212i) q^{81} +(2.96357 + 20.6121i) q^{82} +(881.857 + 566.735i) q^{83} +(938.640 - 275.609i) q^{84} +(42.1376 - 293.073i) q^{85} +(-181.819 + 209.831i) q^{86} +(-185.667 + 119.321i) q^{87} +(0.916175 + 1.05732i) q^{88} +(311.141 + 91.3592i) q^{89} +(4.40573 - 9.64720i) q^{90} +2125.24 q^{91} +(-785.034 + 159.189i) q^{92} -188.089 q^{93} +(-57.0091 + 124.833i) q^{94} +(-358.444 - 105.249i) q^{95} +(515.935 + 595.421i) q^{96} +(-1221.99 + 785.326i) q^{97} +(-153.499 + 177.148i) q^{98} +(-0.0374879 + 0.260734i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9}+O(q^{10}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9	\( 110 q - 2 q^{2} + 6 q^{3} - 40 q^{4} - 55 q^{5} - 3 q^{6} - 10 q^{7} + 243 q^{8} - 233 q^{9} - 10 q^{10} + 2 q^{11} - 57 q^{12} + 34 q^{13} - 154 q^{14} + 30 q^{15} + 16 q^{16} + 252 q^{17} - 33 q^{18} - 160 q^{19} - 200 q^{20} - 684 q^{21} - 704 q^{22} + 127 q^{23} - 3090 q^{24} - 275 q^{25} - 567 q^{26} + 384 q^{27} - 188 q^{28} + 340 q^{29} - 15 q^{30} + 582 q^{31} - 1364 q^{32} + 1760 q^{33} + 1819 q^{34} + 665 q^{35} + 2794 q^{36} + 312 q^{37} + 3123 q^{38} - 1560 q^{39} - 1205 q^{40} + 1324 q^{41} + 1454 q^{42} - 1740 q^{43} - 369 q^{44} + 3730 q^{45} - 4322 q^{46} - 2858 q^{47} - 2686 q^{48} + 2015 q^{49} - 325 q^{50} - 1426 q^{51} + 1717 q^{52} + 882 q^{53} + 2541 q^{54} + 450 q^{55} + 7755 q^{56} + 3688 q^{57} + 6622 q^{58} + 2605 q^{59} + 1530 q^{60} - 104 q^{61} - 9360 q^{62} - 7618 q^{63} + 3483 q^{64} + 170 q^{65} - 1766 q^{66} - 166 q^{67} - 5018 q^{68} - 1194 q^{69} - 770 q^{70} - 1222 q^{71} + 3303 q^{72} - 922 q^{73} + 1245 q^{74} + 150 q^{75} + 1360 q^{76} - 3093 q^{77} - 1600 q^{78} + 2448 q^{79} + 2115 q^{80} - 1371 q^{81} + 6609 q^{82} + 6704 q^{83} + 3894 q^{84} - 720 q^{85} - 5074 q^{86} - 6324 q^{87} + 1918 q^{88} - 5380 q^{89} - 165 q^{90} + 7828 q^{91} - 16225 q^{92} - 24948 q^{93} - 16490 q^{94} + 685 q^{95} + 675 q^{96} - 4400 q^{97} + 8790 q^{98} - 3626 q^{99}+O(q^{100}) \) 110 * q - 2 * q^2 + 6 * q^3 - 40 * q^4 - 55 * q^5 - 3 * q^6 - 10 * q^7 + 243 * q^8 - 233 * q^9 - 10 * q^10 + 2 * q^11 - 57 * q^12 + 34 * q^13 - 154 * q^14 + 30 * q^15 + 16 * q^16 + 252 * q^17 - 33 * q^18 - 160 * q^19 - 200 * q^20 - 684 * q^21 - 704 * q^22 + 127 * q^23 - 3090 * q^24 - 275 * q^25 - 567 * q^26 + 384 * q^27 - 188 * q^28 + 340 * q^29 - 15 * q^30 + 582 * q^31 - 1364 * q^32 + 1760 * q^33 + 1819 * q^34 + 665 * q^35 + 2794 * q^36 + 312 * q^37 + 3123 * q^38 - 1560 * q^39 - 1205 * q^40 + 1324 * q^41 + 1454 * q^42 - 1740 * q^43 - 369 * q^44 + 3730 * q^45 - 4322 * q^46 - 2858 * q^47 - 2686 * q^48 + 2015 * q^49 - 325 * q^50 - 1426 * q^51 + 1717 * q^52 + 882 * q^53 + 2541 * q^54 + 450 * q^55 + 7755 * q^56 + 3688 * q^57 + 6622 * q^58 + 2605 * q^59 + 1530 * q^60 - 104 * q^61 - 9360 * q^62 - 7618 * q^63 + 3483 * q^64 + 170 * q^65 - 1766 * q^66 - 166 * q^67 - 5018 * q^68 - 1194 * q^69 - 770 * q^70 - 1222 * q^71 + 3303 * q^72 - 922 * q^73 + 1245 * q^74 + 150 * q^75 + 1360 * q^76 - 3093 * q^77 - 1600 * q^78 + 2448 * q^79 + 2115 * q^80 - 1371 * q^81 + 6609 * q^82 + 6704 * q^83 + 3894 * q^84 - 720 * q^85 - 5074 * q^86 - 6324 * q^87 + 1918 * q^88 - 5380 * q^89 - 165 * q^90 + 7828 * q^91 - 16225 * q^92 - 24948 * q^93 - 16490 * q^94 + 685 * q^95 + 675 * q^96 - 4400 * q^97 + 8790 * q^98 - 3626 * q^99

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