LMFDB - Embedded newform 115.4.g.a.96.8

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			96.8
Character	$\chi$	$=$	115.96
Dual form			115.4.g.a.6.8

$q$-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 $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$

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	0.962172	−	0.272442i	$-0.0878311\pi$
$2$	0.356908	+	0.781519i	0.126186	+	0.276309i	−0.835986	+	0.548750i	$0.815104\pi$
$3$	5.20863	−	1.52939i	1.00240	−	0.294331i	0.260960	−	0.965350i	$-0.415961\pi$
$3$	5.20863	−	1.52939i	1.00240	−	0.294331i	0.741441	+	0.671018i	$0.234143\pi$
$4$	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	0.830183	+	0.557491i	$0.188236\pi$
$7$	3.53166	+	24.5632i	0.190692	+	1.32629i	−0.639491	+	0.768798i	$0.720855\pi$
$8$	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	−0.909024	−	0.416745i	$-0.863171\pi$
$11$	0.0443232	−	0.0970542i	0.00121490	−	0.00266027i	0.910238	+	0.414084i	$0.135898\pi$
$12$	16.3761	−	35.8587i	0.393948	−	0.862626i
$13$	12.1879	−	84.7689i	0.260025	−	1.80851i	−0.272563	−	0.962138i	$-0.587871\pi$
$13$	12.1879	−	84.7689i	0.260025	−	1.80851i	0.532588	−	0.846375i	$-0.321220\pi$
$14$	−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	0.961638	−	0.274320i	$-0.0884528\pi$
$17$	38.7792	+	44.7536i	0.553255	+	0.638490i	−0.408384	+	0.912810i	$0.633907\pi$
$18$	1.78440	+	1.14677i	0.0233660	+	0.0150164i
$19$	−48.9282	+	56.4661i	−0.590784	+	0.681801i	−0.969888	−	0.243553i	$-0.921687\pi$
$19$	−48.9282	+	56.4661i	−0.590784	+	0.681801i	0.379104	+	0.925354i	$0.376232\pi$
$20$	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	0.664079	−	0.747663i	$-0.268824\pi$
$29$	−26.6242	−	30.7259i	−0.170482	−	0.196747i	−0.834561	+	0.550916i	$0.814279\pi$
$30$	3.31876	+	23.0825i	0.0201973	+	0.140475i
$31$	−33.2448	−	9.76157i	−0.192611	−	0.0565558i	0.184004	−	0.982925i	$-0.441094\pi$
$31$	−33.2448	−	9.76157i	−0.192611	−	0.0565558i	−0.376615	+	0.926370i	$0.622912\pi$
$32$	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	−0.491622	−	0.870809i	$-0.663596\pi$
$37$	21.6659	−	13.9238i	0.0962664	−	0.0618666i	0.587888	+	0.808942i	$0.299959\pi$
$38$	−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	0.501230	−	0.865314i	$-0.332881\pi$
$41$	−20.3901	−	13.1039i	−0.0776681	−	0.0499143i	−0.578899	+	0.815400i	$0.696517\pi$
$42$	−75.7936	+	87.4705i	−0.278457	+	0.321357i
$43$	−310.070	+	91.0447i	−1.09966	+	0.322888i	−0.780715	−	0.624887i	$-0.785145\pi$
$43$	−310.070	+	91.0447i	−1.09966	+	0.322888i	−0.318940	+	0.947775i	$0.603327\pi$
$44$	−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	0.997988	+	0.0634007i	$0.0201946\pi$
$53$	22.4900	+	156.421i	0.0582876	+	0.405399i	−0.939701	+	0.341998i	$0.888896\pi$
$54$	−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	0.950683	+	0.310165i	$0.100384\pi$
$59$	−22.1492	+	154.051i	−0.0488742	+	0.339928i	−0.999557	+	0.0297628i	$0.990525\pi$
$60$	165.816	−	106.563i	0.356778	−	0.229288i
$61$	−262.606	−	77.1081i	−0.551201	−	0.161847i	−0.00574026	−	0.999984i	$-0.501827\pi$
$61$	−262.606	−	77.1081i	−0.551201	−	0.161847i	−0.545461	+	0.838136i	$0.683645\pi$
$62$	−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	−0.825368	−	0.564595i	$-0.809033\pi$
$67$	−390.232	−	854.490i	−0.711559	−	1.55810i	0.113809	−	0.993503i	$-0.463695\pi$
$68$	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	0.794555	+	0.607192i	$0.207704\pi$
$71$	438.592	+	960.383i	0.733117	+	1.60530i	−0.0614378	+	0.998111i	$0.519569\pi$
$72$	31.0609	−	9.12031i	0.0508412	−	0.0149283i
$73$	−374.820	+	432.565i	−0.600950	+	0.693533i	−0.971974	−	0.235090i	$-0.924461\pi$
$73$	−374.820	+	432.565i	−0.600950	+	0.693533i	0.371024	+	0.928623i	$0.379007\pi$
$74$	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	0.941159	+	0.337963i	$0.109738\pi$
$79$	−40.0879	+	278.817i	−0.0570916	+	0.397081i	−0.998251	+	0.0591179i	$0.981171\pi$
$80$	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	0.193418	−	0.981116i	$-0.438043\pi$
$83$	881.857	−	566.735i	1.16622	−	0.749485i	0.972804	+	0.231631i	$0.0744063\pi$
$84$	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	−0.0911438	−	0.995838i	$-0.529052\pi$
$89$	311.141	−	91.3592i	0.370572	−	0.108810i	0.461715	+	0.887028i	$0.347234\pi$
$90$	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	−0.288338	−	0.957529i	$-0.593103\pi$
$97$	−1221.99	−	785.326i	−1.27912	−	0.822039i	−0.990779	+	0.135490i	$0.956739\pi$
$98$	−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	0.362353	−	0.932041i	$-0.381973\pi$
$101$	1381.16	−	887.615i	1.36069	−	0.874465i	0.998341	+	0.0575759i	$0.0183371\pi$
$102$	−39.3056	+	273.377i	−0.0381553	+	0.265376i
$103$	−643.920	+	1409.99i	−0.615994	+	1.34884i	0.302404	+	0.953180i	$0.402211\pi$
$103$	−643.920	+	1409.99i	−0.615994	+	1.34884i	−0.918398	+	0.395658i	$0.870517\pi$
$104$	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	0.0347794	−	0.999395i	$-0.488927\pi$
$107$	−527.150	−	154.785i	−0.476276	−	0.139847i	−0.511055	+	0.859548i	$0.670745\pi$
$108$	137.625	+	957.202i	0.122620	+	0.852841i
$109$	980.239	+	1131.26i	0.861375	+	0.994080i	0.999993	+	0.00373378i	$0.00118850\pi$
$109$	980.239	+	1131.26i	0.861375	+	0.994080i	−0.138618	+	0.990346i	$0.544266\pi$
$110$	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	0.844972	−	0.534810i	$-0.179617\pi$
$113$	−135.195	−	296.036i	−0.112549	−	0.246449i	−0.957522	+	0.288361i	$0.906890\pi$
$114$	−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	−0.138109	−	0.990417i	$-0.544102\pi$
$127$	1003.06	−	2196.38i	0.700840	−	1.53463i	0.838949	−	0.544210i	$-0.183170\pi$
$128$	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	−0.985378	−	0.170382i	$-0.945500\pi$
$131$	−131.819	−	916.823i	−0.0879168	−	0.611475i	0.897461	−	0.441093i	$-0.145409\pi$
$132$	−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	−0.469147	−	0.883120i	$-0.655438\pi$
$149$	919.386	−	2013.17i	0.505497	−	1.10688i	0.974644	−	0.223763i	$-0.0718342\pi$
$150$	−48.4370	+	106.062i	−0.0263658	+	0.0577330i
$151$	−279.928	+	1946.94i	−0.150862	+	1.04927i	0.763917	+	0.645315i	$0.223274\pi$
$151$	−279.928	+	1946.94i	−0.150862	+	1.04927i	−0.914779	+	0.403955i	$0.867635\pi$
$152$	−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	−0.920473	−	0.390807i	$-0.872196\pi$
$157$	−792.089	+	914.120i	−0.402647	+	0.464680i	0.517826	+	0.855486i	$0.326742\pi$
$158$	−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	−0.997681	−	0.0680601i	$-0.978319\pi$
$163$	−823.626	−	1803.49i	−0.395775	−	0.866627i	0.601906	−	0.798567i	$-0.294408\pi$
$164$	−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	0.983722	+	0.179699i	$0.0575123\pi$
$167$	2204.72	+	2544.38i	1.02159	+	1.17898i	0.0378716	+	0.999283i	$0.487942\pi$
$168$	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	−0.967404	−	0.253236i	$-0.918505\pi$
$173$	−324.267	+	710.045i	−0.142506	+	0.312045i	0.824898	+	0.565281i	$0.191232\pi$
$174$	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	0.599551	−	0.800336i	$-0.295346\pi$
$179$	288.825	+	185.617i	0.120602	+	0.0775063i	−0.478949	+	0.877843i	$0.658982\pi$
$180$	58.7027	−	67.7465i	0.0243080	−	0.0280529i
$181$	−2585.20	+	759.082i	−1.06164	+	0.311724i	−0.765510	−	0.643424i	$-0.777513\pi$
$181$	−2585.20	+	759.082i	−1.06164	+	0.311724i	−0.296126	+	0.955149i	$0.595695\pi$
$182$	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	0.999316	−	0.0369905i	$-0.0117771\pi$
$191$	79.3429	+	551.842i	0.0300579	+	0.209057i	−0.969258	+	0.246048i	$0.920868\pi$
$192$	−1301.85	−	382.258i	−0.489339	−	0.143683i
$193$	3395.41	−	2182.10i	1.26636	−	0.813839i	0.277217	−	0.960807i	$-0.410588\pi$
$193$	3395.41	−	2182.10i	1.26636	−	0.813839i	0.989141	+	0.146969i	$0.0469516\pi$
$194$	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	−0.442292	−	0.896871i	$-0.645834\pi$
$197$	649.123	−	4514.75i	0.234762	−	1.63280i	0.677054	−	0.735934i	$-0.263256\pi$
$198$	0.190389	−	0.122355i	6.83350e−5	−	4.39163e-5i
$199$	3742.99	+	1099.04i	1.33333	+	0.391502i	0.869287	−	0.494308i	$-0.164579\pi$
$199$	3742.99	+	1099.04i	1.33333	+	0.391502i	0.464047	+	0.885810i	$0.346397\pi$
$200$	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	−0.747162	−	0.664642i	$-0.768584\pi$
$211$	52.2497	−	60.2994i	0.0170475	−	0.0196738i	0.764209	+	0.644968i	$0.223129\pi$
$212$	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	−0.997519	−	0.0703948i	$-0.977574\pi$
$223$	−200.602	−	1395.22i	−0.0602390	−	0.418972i	0.937280	−	0.348577i	$-0.113335\pi$
$224$	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	0.523283	−	0.852159i	$-0.324707\pi$
$227$	4870.94	−	1430.24i	1.42421	−	0.418185i	0.900926	+	0.433974i	$0.142889\pi$
$228$	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	0.674474	−	0.738298i	$-0.264370\pi$
$233$	5836.48	−	1713.75i	1.64103	−	0.481851i	0.966558	+	0.256448i	$0.0825521\pi$
$234$	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	−0.936562	−	0.350503i	$-0.886011\pi$
$239$	−3719.96	+	2390.67i	−1.00679	+	0.647028i	−0.0702331	+	0.997531i	$0.522374\pi$
$240$	180.891	−	1258.13i	0.0486521	−	0.338383i
$241$	1086.62	−	2379.37i	0.290437	−	0.635968i	−0.707023	−	0.707190i	$-0.749963\pi$
$241$	1086.62	−	2379.37i	0.290437	−	0.635968i	0.997461	+	0.0712217i	$0.0226898\pi$
$242$	−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	0.920498	−	0.390748i	$-0.127784\pi$
$251$	89.0459	+	194.983i	0.0223925	+	0.0490328i	−0.898105	+	0.439781i	$0.855056\pi$
$252$	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	−0.807370	−	0.590045i	$-0.799110\pi$
$257$	−446.735	+	515.560i	−0.108430	+	0.125135i	0.698940	+	0.715180i	$0.253655\pi$
$258$	−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	0.535031	+	0.844832i	$0.320300\pi$
$263$	−922.739	+	6417.79i	−0.216344	+	1.50471i	−0.751375	+	0.659875i	$0.770609\pi$
$264$	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	0.999261	+	0.0384475i	$0.0122412\pi$
$269$	226.372	+	1574.45i	0.0513090	+	0.356862i	−0.947952	+	0.318414i	$0.896850\pi$
$270$	−374.621	−	432.336i	−0.0844397	−	0.0974486i
$271$	686.484	+	441.176i	0.153878	+	0.0988913i	0.615314	−	0.788282i	$-0.289029\pi$
$271$	686.484	+	441.176i	0.153878	+	0.0988913i	−0.461436	+	0.887173i	$0.652666\pi$
$272$	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	−0.206276	−	0.978494i	$-0.566134\pi$
$281$	−5567.88	−	3578.26i	−1.18203	−	0.759648i	−0.975759	+	0.218846i	$0.929771\pi$
$282$	−487.857	−	563.017i	−0.103019	−	0.118891i
$283$	538.424	+	3744.82i	0.113095	+	0.786596i	0.964878	+	0.262700i	$0.0846129\pi$
$283$	538.424	+	3744.82i	0.113095	+	0.786596i	−0.851782	+	0.523896i	$0.824478\pi$
$284$	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	−0.999424	−	0.0339445i	$-0.989193\pi$
$293$	−4467.63	−	5155.91i	−0.890790	−	1.02803i	0.108634	−	0.994082i	$-0.465352\pi$
$294$	−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	−0.0500717	−	0.998746i	$-0.515945\pi$
$307$	−3400.42	−	998.454i	−0.632157	−	0.185618i	−0.582086	+	0.813127i	$0.697763\pi$
$308$	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	0.199107	+	0.979978i	$0.436196\pi$
$311$	−3685.06	+	8069.15i	−0.671898	+	1.47125i	−0.871005	+	0.491274i	$0.836531\pi$
$312$	867.545	−	6033.91i	0.157420	−	1.09488i
$313$	−1278.80	+	821.835i	−0.230933	+	0.148412i	−0.650991	−	0.759086i	$-0.725646\pi$
$313$	−1278.80	+	821.835i	−0.230933	+	0.148412i	0.420058	+	0.907497i	$0.362010\pi$
$314$	−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	0.532217	−	0.846608i	$-0.321359\pi$
$317$	−94.7847	−	60.9144i	−0.0167938	−	0.0107927i	−0.549011	+	0.835815i	$0.684995\pi$
$318$	−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	−0.721081	−	0.692851i	$-0.756354\pi$
$331$	−2350.93	+	1510.85i	−0.390390	+	0.250888i	0.330691	+	0.943739i	$0.392718\pi$
$332$	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	−0.494654	−	0.869090i	$-0.664705\pi$
$337$	−8541.38	−	2507.98i	−1.38065	−	0.405395i	−0.885995	+	0.463695i	$0.846523\pi$
$338$	−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	0.961964	+	0.273175i	$0.0880737\pi$
$347$	3480.57	+	7621.39i	0.538463	+	1.17907i	−0.423501	+	0.905896i	$0.639199\pi$
$348$	−1537.79	+	451.536i	−0.236880	+	0.0695542i
$349$	3375.59	−	3895.63i	0.517739	−	0.597503i	−0.435324	−	0.900274i	$-0.643366\pi$
$349$	3375.59	−	3895.63i	0.517739	−	0.597503i	0.953063	+	0.302771i	$0.0979117\pi$
$350$	−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	0.253603	−	0.967308i	$-0.418384\pi$
$353$	−371.529	−	109.091i	−0.0560184	−	0.0164485i	−0.309622	+	0.950860i	$0.600202\pi$
$354$	−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	−0.992844	−	0.119415i	$-0.961898\pi$
$359$	−8820.01	+	5668.27i	−1.29666	+	0.833315i	−0.303819	+	0.952730i	$0.598262\pi$
$360$	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	0.645448	−	0.763804i	$-0.276671\pi$
$373$	1576.17	+	1012.95i	0.218797	+	0.140612i	−0.426652	+	0.904416i	$0.640307\pi$
$374$	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	−0.815397	−	0.578902i	$-0.803482\pi$
$379$	1151.60	−	2521.66i	0.156079	−	0.341765i	0.971476	+	0.237136i	$0.0762088\pi$
$380$	−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	−0.0609679	−	0.998140i	$-0.519419\pi$
$383$	−4886.23	−	1434.73i	−0.651892	−	0.191413i	−0.590924	+	0.806727i	$0.701237\pi$
$384$	−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	0.906178	−	0.422897i	$-0.138987\pi$
$389$	−52.5300	−	115.025i	−0.00684673	−	0.0149923i	−0.913024	+	0.407905i	$0.866260\pi$
$390$	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	0.705722	−	0.708489i	$-0.250623\pi$
$397$	−759.304	−	876.283i	−0.0959908	−	0.110779i	−0.801712	+	0.597710i	$0.796077\pi$
$398$	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	0.507703	+	0.861532i	$0.330495\pi$
$401$	−1783.92	+	12407.4i	−0.222156	+	1.54513i	−0.729859	+	0.683597i	$0.760414\pi$
$402$	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	−0.0515418	−	0.998671i	$-0.516414\pi$
$409$	−8117.46	−	5216.78i	−0.981376	−	0.630692i	−0.929834	+	0.367979i	$0.880050\pi$
$410$	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	0.694155	−	0.719826i	$-0.255778\pi$
$419$	2810.94	+	1806.48i	0.327740	+	0.210626i	−0.366414	+	0.930452i	$0.619415\pi$
$420$	3203.14	+	3696.62i	0.372136	+	0.429468i
$421$	548.271	+	3813.31i	0.0634705	+	0.441447i	0.996633	+	0.0819922i	$0.0261283\pi$
$421$	548.271	+	3813.31i	0.0634705	+	0.441447i	−0.933162	+	0.359455i	$0.882963\pi$
$422$	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	0.974410	+	0.224778i	$0.0721658\pi$
$431$	9468.80	+	10927.6i	1.05823	+	1.22126i	0.0838173	+	0.996481i	$0.473289\pi$
$432$	5246.18	+	3371.51i	0.584275	+	0.375491i
$433$	3800.18	−	4385.64i	0.421767	−	0.486745i	−0.504608	−	0.863349i	$-0.668363\pi$
$433$	3800.18	−	4385.64i	0.421767	−	0.486745i	0.926374	+	0.376604i	$0.122908\pi$
$434$	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	0.870571	−	0.492043i	$-0.163750\pi$
$439$	−656.677	−	1437.92i	−0.0713929	−	0.156329i	−0.941964	+	0.335714i	$0.891022\pi$
$440$	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	0.975647	+	0.219347i	$0.0703928\pi$
$443$	9826.76	+	11340.7i	1.05391	+	1.21628i	0.0782656	+	0.996933i	$0.475062\pi$
$444$	−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	0.194569	+	0.980889i	$0.437669\pi$
$449$	−6413.98	+	14044.7i	−0.674153	+	1.47619i	−0.868722	+	0.495300i	$0.835058\pi$
$450$	−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	−0.282059	−	0.959397i	$-0.591017\pi$
$457$	−6.37136	+	1.87080i	−0.000652165	+	0.000191493i	0.281406	+	0.959589i	$0.409199\pi$
$458$	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	−0.536870	−	0.843665i	$-0.680394\pi$
$463$	−5304.02	+	1557.40i	−0.532395	+	0.156325i	0.00447547	+	0.999990i	$0.498575\pi$
$464$	−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	−0.933311	−	0.359068i	$-0.883095\pi$
$467$	−1402.45	−	9754.24i	−0.138967	−	0.966536i	0.794344	−	0.607468i	$-0.207815\pi$
$468$	−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	−0.579521	−	0.814957i	$-0.696760\pi$
$479$	3245.84	−	3745.90i	0.309616	−	0.357316i	0.889137	+	0.457642i	$0.151306\pi$
$480$	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	0.107223	−	0.994235i	$-0.465804\pi$
$487$	11564.8	−	13346.5i	1.07608	−	1.24186i	0.968856	−	0.247626i	$-0.0796503\pi$
$488$	−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	−0.544573	−	0.838714i	$-0.683308\pi$
$491$	−15842.6	−	4651.79i	−1.45614	−	0.427561i	−0.911566	+	0.411153i	$0.865126\pi$
$492$	−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	0.974805	−	0.223058i	$-0.0716040\pi$
$499$	−260.348	−	1810.76i	−0.0233563	−	0.162446i	−0.998161	+	0.0606117i	$0.980695\pi$
$500$	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	0.615308	−	0.788287i	$-0.289032\pi$
$503$	17588.6	−	5164.48i	1.55912	−	0.457798i	0.943810	+	0.330488i	$0.107213\pi$
$504$	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	−0.749739	−	0.661734i	$-0.769821\pi$
$509$	−11744.2	+	3448.42i	−1.02270	+	0.300291i	−0.272960	+	0.962025i	$0.588003\pi$
$510$	−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	0.563548	−	0.826083i	$-0.309436\pi$
$521$	7028.44	+	2063.74i	0.591021	+	0.173539i	0.0274725	+	0.999623i	$0.491254\pi$
$522$	−12.2728	−	85.3590i	−0.00102905	−	0.00715721i
$523$	−2070.34	−	2389.29i	−0.173096	−	0.199764i	0.662572	−	0.748998i	$-0.269465\pi$
$523$	−2070.34	−	2389.29i	−0.173096	−	0.199764i	−0.835668	+	0.549234i	$0.814919\pi$
$524$	−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	−0.745776	−	0.666196i	$-0.767921\pi$
$541$	3096.52	−	6780.43i	0.246081	−	0.538842i	0.991857	+	0.127354i	$0.0406485\pi$
$542$	−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	−0.260167	−	0.965564i	$-0.583778\pi$
$547$	−15947.5	−	10248.8i	−1.24655	−	0.801110i	−0.986385	+	0.164453i	$0.947414\pi$
$548$	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	−0.0301251	−	0.999546i	$-0.509591\pi$
$557$	−12512.8	−	8041.50i	−0.951859	−	0.611722i	−0.921734	+	0.387824i	$0.873227\pi$
$558$	−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	−0.988963	−	0.148161i	$-0.952665\pi$
$563$	−3063.90	+	6709.01i	−0.229357	+	0.502222i	0.759606	+	0.650384i	$0.225392\pi$
$564$	−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	0.825236	−	0.564789i	$-0.191042\pi$
$569$	2018.98	+	2330.03i	0.148753	+	0.171670i	−0.676483	+	0.736458i	$0.736497\pi$
$570$	−1465.76	−	941.985i	−0.107708	−	0.0692200i
$571$	−2325.93	+	2684.26i	−0.170468	+	0.196730i	−0.834555	−	0.550925i	$-0.814275\pi$
$571$	−2325.93	+	2684.26i	−0.170468	+	0.196730i	0.664087	+	0.747655i	$0.268820\pi$
$572$	−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	0.924124	+	0.382093i	$0.124797\pi$
$577$	8422.98	+	18443.8i	0.607718	+	1.33072i	−0.316406	+	0.948624i	$0.602476\pi$
$578$	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	−0.434764	−	0.900544i	$-0.643168\pi$
$587$	7545.16	−	16521.6i	0.530532	−	1.16170i	0.965296	−	0.261158i	$-0.0841045\pi$
$588$	−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	0.252804	−	0.967517i	$-0.418647\pi$
$593$	−7541.72	−	4846.77i	−0.522262	−	0.335637i	−0.775066	+	0.631880i	$0.782284\pi$
$594$	−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	−0.315695	−	0.948861i	$-0.602237\pi$
$601$	−1006.03	+	295.396i	−0.0682807	+	0.0200490i	0.247414	+	0.968910i	$0.420419\pi$
$602$	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	0.0474833	−	0.998872i	$-0.484880\pi$
$607$	14593.2	−	9378.48i	0.975815	−	0.627118i	0.928331	+	0.371754i	$0.121244\pi$
$608$	−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	0.180127	−	0.983643i	$-0.442349\pi$
$613$	−3037.53	−	891.901i	−0.200138	−	0.0587660i	−0.380265	+	0.924877i	$0.624167\pi$
$614$	−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	−0.714381	−	0.699757i	$-0.753292\pi$
$617$	1224.85	−	1413.55i	0.0799200	−	0.0922325i	0.794301	+	0.607524i	$0.207837\pi$
$618$	−6936.60	+	2036.77i	−0.451506	+	0.132574i
$619$	5074.02	+	11110.5i	0.329470	+	0.721439i	0.999787	−	0.0206361i	$-0.00656914\pi$
$619$	5074.02	+	11110.5i	0.329470	+	0.721439i	−0.670317	+	0.742075i	$0.733842\pi$
$620$	−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	0.730118	+	0.683321i	$0.239465\pi$
$631$	−2582.67	+	17962.8i	−0.162939	+	1.13326i	−0.893057	+	0.449943i	$0.851444\pi$
$632$	−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	−0.454008	−	0.890997i	$-0.650006\pi$
$641$	−5748.81	+	1688.00i	−0.354235	+	0.104013i	0.0997736	+	0.995010i	$0.468188\pi$
$642$	−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	−0.545176	−	0.838322i	$-0.683537\pi$
$647$	−9060.96	+	2660.54i	−0.550577	+	0.161664i	−0.00540054	+	0.999985i	$0.501719\pi$
$648$	−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	−0.293795	−	0.955868i	$-0.594918\pi$
$653$	7569.84	−	4864.84i	0.453646	−	0.291541i	0.747441	+	0.664328i	$0.231282\pi$
$654$	−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	−0.409443	−	0.912336i	$-0.634277\pi$
$659$	−21098.0	−	6194.93i	−1.24713	−	0.366192i	−0.837691	+	0.546144i	$0.816095\pi$
$660$	−2.99294	−	20.8163i	−0.000176515	−	0.00122769i
$661$	−17387.5	−	20066.2i	−1.02314	−	1.18076i	−0.983381	−	0.181555i	$-0.941887\pi$
$661$	−17387.5	−	20066.2i	−1.02314	−	1.18076i	−0.0397574	−	0.999209i	$-0.512658\pi$
$662$	−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	−0.998240	−	0.0593015i	$-0.981113\pi$
$673$	−15972.9	−	18433.7i	−0.914874	−	1.05582i	0.0833665	−	0.996519i	$-0.473433\pi$
$674$	−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	0.900713	+	0.434414i	$0.143045\pi$
$677$	−1513.19	+	10524.5i	−0.0859034	+	0.597471i	−0.986617	+	0.163057i	$0.947865\pi$
$678$	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	−0.970325	−	0.241806i	$-0.922260\pi$
$683$	−1917.59	−	13337.1i	−0.107430	−	0.747190i	0.862895	−	0.505384i	$-0.168649\pi$
$684$	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	−0.999938	−	0.0111262i	$-0.996458\pi$
$701$	−6249.31	+	13684.1i	−0.336709	+	0.737291i	0.663229	+	0.748417i	$0.269186\pi$
$702$	−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	−0.988476	−	0.151380i	$-0.951628\pi$
$709$	−13176.5	+	15206.5i	−0.697962	+	0.805491i	0.290514	+	0.956871i	$0.406174\pi$
$710$	−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	0.773322	−	0.634014i	$-0.218594\pi$
$719$	688.396	+	794.452i	0.0357063	+	0.0412073i	−0.737616	+	0.675221i	$0.764048\pi$
$720$	−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	0.386556	−	0.922266i	$-0.373665\pi$
$727$	27169.6	−	17460.9i	1.38606	−	0.890766i	0.999504	+	0.0314997i	$0.0100283\pi$
$728$	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	−0.100351	−	0.994952i	$-0.531997\pi$
$733$	7008.14	−	2057.77i	0.353140	−	0.103691i	0.453491	+	0.891261i	$0.350178\pi$
$734$	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	0.569786	−	0.821793i	$-0.307026\pi$
$739$	30001.8	−	8809.32i	1.49342	−	0.438506i	0.923629	+	0.383287i	$0.125208\pi$
$740$	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	0.986768	+	0.162137i	$0.0518387\pi$
$743$	1734.65	+	12064.8i	0.0856503	+	0.595711i	−0.901118	+	0.433574i	$0.857252\pi$
$744$	−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	0.281193	−	0.959651i	$-0.409270\pi$
$751$	−22.2159	−	6.52317i	−0.00107945	−	0.000316956i	−0.282272	+	0.959334i	$0.591088\pi$
$752$	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	0.845037	+	0.534707i	$0.179578\pi$
$757$	14491.2	+	31731.2i	0.695760	+	1.52350i	−0.149277	+	0.988795i	$0.547695\pi$
$758$	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	0.778835	−	0.627228i	$-0.215811\pi$
$761$	−4308.23	−	9433.70i	−0.205221	−	0.449371i	−0.984056	+	0.177857i	$0.943083\pi$
$762$	10805.4	−	3172.74i	0.513697	−	0.150835i
$763$	−24325.4	+	28073.0i	−1.15418	+	1.33200i
$764$	3405.90	+	2188.84i	0.161284	+	0.103651i
$765$	478.697	+	552.446i	0.0226240	+	0.0261094i
$766$	−622.667	−	4330.75i	−0.0293706	−	0.204277i
$767$	12788.8	+	3755.13i	0.602055	+	0.176779i
$768$	−3733.33	+	2399.27i	−0.175410	+	0.112729i
$769$	658.109	−	4577.25i	0.0308609	−	0.214642i	−0.968556	−	0.248797i	$-0.919965\pi$
$769$	658.109	−	4577.25i	0.0308609	−	0.214642i	0.999417	+	0.0341548i	$0.0108739\pi$
$770$	−4.72501	+	10.3463i	−0.000221140	+	0.000484229i
$771$	−1538.39	+	3368.59i	−0.0718594	+	0.157350i
$772$	4171.22	−	29011.4i	0.194463	−	1.35252i
$773$	−14438.6	+	9279.15i	−0.671826	+	0.431756i	−0.831583	−	0.555400i	$-0.812565\pi$
$773$	−14438.6	+	9279.15i	−0.671826	+	0.431756i	0.159757	+	0.987156i	$0.448929\pi$
$774$	−657.696	−	193.117i	−0.0305431	−	0.00896827i
$775$	−123.274	−	857.392i	−0.00571374	−	0.0397399i
$776$	−12473.0	−	14394.6i	−0.577003	−	0.665897i
$777$	2918.69	+	1875.73i	0.134758	+	0.0866040i
$778$	71.1456	−	82.1064i	0.00327853	−	0.00378362i
$779$	1737.57	−	510.198i	0.0799166	−	0.0234656i
$780$	−7012.30	−	15354.8i	−0.321898	−	0.704859i
$781$	112.649			0.00516120
$782$	5591.45	−	479.420i	0.255690	−	0.0219233i
$783$	5414.10			0.247106
$784$	5307.41	+	11621.6i	0.241773	+	0.529410i
$785$	−5802.79	+	1703.85i	−0.263835	+	0.0774690i
$786$	2829.00	−	3264.84i	0.128380	−	0.148159i
$787$	−8439.58	−	5423.79i	−0.382260	−	0.245664i	0.335372	−	0.942086i	$-0.391138\pi$
$787$	−8439.58	−	5423.79i	−0.382260	−	0.245664i	−0.717632	+	0.696422i	$0.754774\pi$
$788$	−21690.7	−	25032.4i	−0.980581	−	1.13165i
$789$	5009.11	+	34839.1i	0.226019	+	1.57200i
$790$	−1161.04	−	340.913i	−0.0522887	−	0.0153533i
$791$	6794.14	−	4366.33i	0.305400	−	0.196269i
$792$	0.491554	−	3.41884i	2.20538e−5	−	0.000153388i
$793$	−9737.00	+	21321.0i	−0.436029	+	0.954770i
$794$	413.830	−	906.162i	0.0184966	−	0.0405019i
$795$	−610.438	+	4245.69i	−0.0272327	+	0.189408i
$796$	23831.5	−	15315.6i	1.06116	−	0.681967i
$797$	5737.43	+	1684.66i	0.254994	+	0.0748730i	0.406731	−	0.913548i	$-0.366669\pi$
$797$	5737.43	+	1684.66i	0.254994	+	0.0748730i	−0.151737	+	0.988421i	$0.548487\pi$
$798$	−1230.68	−	8559.54i	−0.0545933	−	0.379705i
$799$	−6194.23	−	7148.52i	−0.274263	−	0.316516i
$800$	3052.33	+	1961.61i	0.134895	+	0.0866919i
$801$	524.272	−	605.042i	0.0231264	−	0.0266893i
$802$	−10333.3	+	3034.14i	−0.454965	+	0.133590i
$803$	25.3691	+	55.5505i	0.00111489	+	0.00244126i
$804$	−37031.3			−1.62437
$805$	13636.4	−	1169.21i	0.597044	−	0.0511915i
$806$	−2549.39			−0.111412
$807$	3587.03	+	7854.51i	0.156468	+	0.342617i
$808$	20655.6	−	6065.04i	0.899334	−	0.264068i
$809$	−97.1077	+	112.068i	−0.00422018	+	0.00487035i	−0.757856	−	0.652422i	$-0.773753\pi$
$809$	−97.1077	+	112.068i	−0.00422018	+	0.00487035i	0.753636	+	0.657293i	$0.228298\pi$
$810$	−2853.37	−	1833.75i	−0.123774	−	0.0795448i
$811$	−3590.53	−	4143.69i	−0.155463	−	0.179414i	0.672675	−	0.739938i	$-0.265145\pi$
$811$	−3590.53	−	4143.69i	−0.155463	−	0.179414i	−0.828138	+	0.560524i	$0.810600\pi$
$812$	−1042.68	−	7252.03i	−0.0450629	−	0.313419i
$813$	4250.37	+	1248.02i	0.183354	+	0.0538376i
$814$	1.98609	−	1.27638i	8.55191e−5	−	5.49598e-5i
$815$	1410.81	−	9812.39i	0.0606362	−	0.421734i
$816$	6253.60	−	13693.5i	0.268284	−	0.587460i
$817$	10030.2	−	21963.1i	0.429514	−	0.940503i
$818$	1179.82	−	8205.86i	0.0504298	−	0.350747i
$819$	4413.95	−	2836.67i	0.188322	−	0.121027i
$820$	−844.404	−	247.939i	−0.0359608	−	0.0105591i
$821$	−5568.96	−	38733.0i	−0.236733	−	1.64652i	−0.667905	−	0.744246i	$-0.732809\pi$
$821$	−5568.96	−	38733.0i	−0.236733	−	1.64652i	0.431172	−	0.902270i	$-0.358100\pi$
$822$	8050.42	+	9290.68i	0.341595	+	0.394221i
$823$	−12653.8	−	8132.07i	−0.535944	−	0.344430i	0.244507	−	0.969648i	$-0.421374\pi$
$823$	−12653.8	−	8132.07i	−0.535944	−	0.344430i	−0.780451	+	0.625217i	$0.785010\pi$
$824$	−13310.0	+	15360.6i	−0.562715	+	0.649408i
$825$	13.8935	−	4.07950i	0.000586315	−	0.000172158i
$826$	−1378.45	−	3018.39i	−0.0580660	−	0.127147i
$827$	−15592.9			−0.655645			−0.327823	−	0.944739i	$-0.606315\pi$
$827$	−15592.9			−0.655645			−0.327823	+	0.944739i	$0.606315\pi$
$828$	−1842.93	+	717.204i	−0.0773504	+	0.0301021i
$829$	−24223.0			−1.01484			−0.507419	−	0.861700i	$-0.669400\pi$
$829$	−24223.0			−1.01484			−0.507419	+	0.861700i	$0.669400\pi$
$830$	1870.67	+	4096.20i	0.0782312	+	0.171302i
$831$	−31400.1	+	9219.90i	−1.31078	+	0.384879i
$832$	−14017.4	+	16176.9i	−0.584093	+	0.674079i
$833$	−13591.3	−	8734.59i	−0.565318	−	0.363308i
$834$	51.3513	+	59.2626i	0.00213208	+	0.00246055i
$835$	2395.65	+	16662.1i	0.0992874	+	0.690559i
$836$	55.5453	+	16.3096i	0.00229794	+	0.000674735i
$837$	3881.59	−	2494.54i	0.160295	−	0.103016i
$838$	−408.552	+	2841.54i	−0.0168415	+	0.117135i
$839$	−7407.80	+	16220.8i	−0.304822	+	0.667467i	−0.998610	−	0.0527124i	$-0.983213\pi$
$839$	−7407.80	+	16220.8i	−0.304822	+	0.667467i	0.693788	+	0.720180i	$0.255941\pi$
$840$	−3668.96	+	8033.90i	−0.150704	+	0.329995i
$841$	3235.68	−	22504.7i	0.132670	−	0.922738i
$842$	−2784.49	+	1789.48i	−0.113967	+	0.0732418i
$843$	−34473.6	−	10122.4i	−1.40846	−	0.413561i
$844$	−82.4578	−	573.507i	−0.00336293	−	0.0233897i
$845$	−16821.1	−	19412.6i	−0.684810	−	0.790313i
$846$	−285.024	−	183.174i	−0.0115831	−	0.00744402i
$847$	−21629.8	+	24962.1i	−0.877459	+	1.01264i
$848$	7100.65	−	2084.94i	0.287544	−	0.0844305i
$849$	8531.75	+	18681.9i	0.344887	+	0.755197i
$850$	−1271.93			−0.0513257
$851$	−2512.31	−	1326.08i	−0.101200	−	0.0534166i
$852$	41620.5			1.67359
$853$	12140.2	+	26583.4i	0.487308	+	1.06706i	0.980389	+	0.197072i	$0.0631433\pi$
$853$	12140.2	+	26583.4i	0.487308	+	1.06706i	−0.493081	+	0.869983i	$0.664129\pi$
$854$	5598.96	−	1644.00i	0.224347	−	0.0658742i
$855$	−603.978	+	697.028i	−0.0241586	+	0.0278805i
$856$	−6060.38	−	3894.77i	−0.241986	−	0.155515i
$857$	−8450.45	−	9752.34i	−0.336828	−	0.388720i	0.561916	−	0.827195i	$-0.310065\pi$
$857$	−8450.45	−	9752.34i	−0.336828	−	0.388720i	−0.898744	+	0.438474i	$0.855519\pi$
$858$	−6.06504	−	42.1833i	−0.000241325	−	0.00167845i
$859$	31284.5	+	9185.96i	1.24262	+	0.364867i	0.836001	−	0.548728i	$-0.184888\pi$
$859$	31284.5	+	9185.96i	1.24262	+	0.364867i	0.406623	+	0.913596i	$0.366706\pi$
$860$	−9871.01	+	6343.71i	−0.391394	+	0.251534i
$861$	464.678	−	3231.90i	0.0183928	−	0.127925i
$862$	−5160.62	+	11300.2i	−0.203911	+	0.446503i
$863$	−8501.67	+	18616.1i	−0.335342	+	0.734297i	−0.999916	−	0.0129255i	$-0.995886\pi$
$863$	−8501.67	+	18616.1i	−0.335342	+	0.734297i	0.664574	+	0.747222i	$0.268613\pi$
$864$	−2750.52	+	19130.3i	−0.108304	+	0.753270i
$865$	−3283.35	+	2110.08i	−0.129060	+	0.0829420i
$866$	4783.77	+	1404.64i	0.187713	+	0.0551174i
$867$	−1086.45	−	7556.39i	−0.0425578	−	0.295996i
$868$	−4088.91	−	4718.85i	−0.159892	−	0.184526i
$869$	25.2836	+	16.2488i	0.000986981	+	0.000634294i
$870$	620.870	−	716.523i	0.0241948	−	0.0279223i
$871$	−77190.3	+	22665.1i	−3.00286	+	0.881720i
$872$	8153.53	+	17853.7i	0.316644	+	0.693353i
$873$	−3586.19			−0.139031
$874$	1602.74	+	6896.91i	0.0620290	+	0.266924i
$875$	−3101.98			−0.119847
$876$	9373.12	+	20524.3i	0.361517	+	0.791611i
$877$	6816.81	−	2001.60i	0.262471	−	0.0770685i	−0.147849	−	0.989010i	$-0.547235\pi$
$877$	6816.81	−	2001.60i	0.262471	−	0.0770685i	0.410320	+	0.911941i	$0.365417\pi$
$878$	889.390	−	1026.41i	0.0341862	−	0.0394529i
$879$	−31155.6	−	20022.5i	−1.19551	−	0.768307i
$880$	−16.3600	−	18.8805i	−0.000626701	−	0.000723251i
$881$	−3767.39	−	26202.8i	−0.144071	−	1.00204i	−0.925691	−	0.378282i	$-0.876515\pi$
$881$	−3767.39	−	26202.8i	−0.144071	−	1.00204i	0.781619	−	0.623756i	$-0.214394\pi$
$882$	−555.254	−	163.037i	−0.0211977	−	0.00622420i
$883$	−28425.8	+	18268.1i	−1.08336	+	0.696231i	−0.955331	−	0.295540i	$-0.904501\pi$
$883$	−28425.8	+	18268.1i	−1.08336	+	0.696231i	−0.128026	+	0.991771i	$0.540864\pi$
$884$	5241.15	−	36453.0i	0.199411	−	1.38693i
$885$	−1754.86	+	3842.60i	−0.0666541	+	0.145952i
$886$	−5355.71	+	11727.4i	−0.203080	+	0.444682i
$887$	2282.40	−	15874.5i	0.0863987	−	0.600916i	−0.899919	−	0.436058i	$-0.856374\pi$
$887$	2282.40	−	15874.5i	0.0863987	−	0.600916i	0.986317	−	0.164858i	$-0.0527166\pi$
$888$	1542.20	−	991.109i	0.0582800	−	0.0374543i
$889$	57492.7	+	16881.4i	2.16900	+	0.636877i
$890$	198.248	+	1378.85i	0.00746662	+	0.0519315i
$891$	55.1677	+	63.6669i	0.00207428	+	0.00239385i
$892$	−8611.11	−	5534.02i	−0.323230	−	0.207727i
$893$	7815.33	−	9019.37i	0.292867	−	0.337986i
$894$	9904.04	−	2908.09i	0.370515	−	0.108793i
$895$	713.116	+	1561.51i	0.0266333	+	0.0583189i
$896$	34141.6			1.27298
$897$	−40613.8	+	31308.4i	−1.51177	+	1.16539i
$898$	−13265.4			−0.492952
$899$	585.183	+	1281.37i	0.0217096	+	0.0475374i
$900$	430.052	−	126.275i	0.0159278	−	0.00467684i
$901$	−6128.27	+	7072.41i	−0.226595	+	0.261505i
$902$	−1.86914	−	1.20122i	−6.89971e−5	−	4.43418e-5i
$903$	−28508.7	−	32900.7i	−1.05062	−	1.21248i
$904$	−607.309	−	4223.92i	−0.0223438	−	0.155404i
$905$	−12926.0	−	3795.41i	−0.474778	−	0.139407i
$906$	−7717.51	+	4959.75i	−0.282999	+	0.181873i
$907$	4043.91	−	28126.0i	0.148044	−	1.02967i	−0.771373	−	0.636383i	$-0.780430\pi$
$907$	4043.91	−	28126.0i	0.148044	−	1.02967i	0.919417	−	0.393284i	$-0.128661\pi$
$908$	15314.4	−	33533.8i	0.559720	−	1.22562i
$909$	1683.80	−	3687.00i	0.0614390	−	0.134533i
$910$	−1299.28	+	9036.68i	−0.0473304	+	0.329190i
$911$	16821.8	−	10810.7i	0.611781	−	0.393167i	−0.197744	−	0.980254i	$-0.563361\pi$
$911$	16821.8	−	10810.7i	0.611781	−	0.393167i	0.809524	+	0.587086i	$0.199725\pi$
$912$	18224.3	+	5351.12i	0.661695	+	0.194291i
$913$	−15.9173	−	110.707i	−0.000576984	−	0.00401301i
$914$	−3.73605	−	4.31163i	−0.000135205	−	0.000156035i
$915$	−6249.45	−	4016.27i	−0.225793	−	0.145108i
$916$	27470.4	−	31702.5i	0.990880	−	1.14354i
$917$	22054.6	−	6475.81i	0.794228	−	0.233206i
$918$	−2814.52	−	6162.95i	−0.101191	−	0.221577i
$919$	−13891.1			−0.498613			−0.249307	−	0.968425i	$-0.580203\pi$
$919$	−13891.1			−0.498613			−0.249307	+	0.968425i	$0.580203\pi$
$920$	2431.22	−	6810.81i	0.0871251	−	0.244071i
$921$	−19238.6			−0.688308
$922$	6601.42	+	14455.1i	0.235799	+	0.516327i
$923$	86756.2	−	25473.9i	3.09384	−	0.908433i
$924$	68.3526	−	78.8831i	0.00243359	−	0.00280851i
$925$	541.648	+	348.096i	0.0192533	+	0.0123733i
$926$	−3110.18	−	3589.34i	−0.110375	−	0.127379i
$927$	544.618	+	3787.90i	0.0192962	+	0.134208i
$928$	−5661.53	−	1662.37i	−0.200268	−	0.0588040i
$929$	7288.25	−	4683.88i	0.257395	−	0.165418i	−0.405579	−	0.914060i	$-0.632930\pi$
$929$	7288.25	−	4683.88i	0.257395	−	0.165418i	0.662974	+	0.748642i	$0.269294\pi$
$930$	114.989	−	799.769i	0.00405446	−	0.0281994i
$931$	8467.91	−	18542.1i	0.298093	−	0.652732i
$932$	18350.1	−	40181.1i	0.644933	−	1.41221i
$933$	−6853.20	+	47665.1i	−0.240476	+	1.67254i
$934$	7122.57	−	4577.40i	0.249526	−	0.160361i
$935$	30.3117	+	8.90032i	0.00106021	+	0.000311306i
$936$	−394.551	−	2744.16i	−0.0137781	−	0.0958287i
$937$	−31098.7	−	35889.8i	−1.08426	−	1.25130i	−0.966062	−	0.258309i	$-0.916835\pi$
$937$	−31098.7	−	35889.8i	−1.08426	−	1.25130i	−0.118195	−	0.992990i	$-0.537711\pi$
$938$	16848.8	+	10828.1i	0.586497	+	0.376919i
$939$	−5403.89	+	6236.42i	−0.187805	+	0.216739i
$940$	−5564.77	+	1633.96i	−0.193088	+	0.0566958i
$941$	−4220.07	−	9240.66i	−0.146196	−	0.320124i	0.822341	−	0.568995i	$-0.192668\pi$
$941$	−4220.07	−	9240.66i	−0.146196	−	0.320124i	−0.968537	+	0.248871i	$0.919940\pi$
$942$	−5641.31			−0.195121
$943$	−153.022	+	2669.14i	−0.00528427	+	0.0921729i
$944$	7288.27			0.251285
$945$	−6864.05	−	15030.2i	−0.236283	−	0.517388i
$946$	−28.4238	+	8.34597i	−0.000976889	+	0.000286840i
$947$	14041.2	−	16204.4i	0.481814	−	0.556043i	−0.461846	−	0.886960i	$-0.652813\pi$
$947$	14041.2	−	16204.4i	0.481814	−	0.556043i	0.943660	+	0.330917i	$0.107358\pi$
$948$	9341.53	+	6003.44i	0.320041	+	0.205678i
$949$	32099.8	+	37045.1i	1.09800	+	1.26716i
$950$	−228.388	−	1588.48i	−0.00779989	−	0.0542494i
$951$	−586.860	−	172.318i	−0.0200108	−	0.00587569i
$952$	−16210.1	+	10417.6i	−0.551862	+	0.354660i
$953$	−5102.36	+	35487.7i	−0.173433	+	1.20625i	0.698131	+	0.715970i	$0.254015\pi$
$953$	−5102.36	+	35487.7i	−0.173433	+	1.20625i	−0.871564	+	0.490282i	$0.836894\pi$
$954$	−139.247	+	304.909i	−0.00472569	+	0.0103478i
$955$	−1158.00	+	2535.68i	−0.0392378	+	0.0859189i
$956$	−4569.91	+	31784.5i	−0.154604	+	1.07530i
$957$	−19.8100	+	12.7311i	−0.000669139	+	0.000430029i
$958$	4085.95	+	1199.74i	0.137799	+	0.0404613i
$959$	9308.79	+	64744.1i	0.313448	+	2.18008i
$960$	−4442.61	−	5127.05i	−0.149359	−	0.172370i
$961$	−24051.9	−	15457.2i	−0.807353	−	0.518854i
$962$	1240.95	−	1432.13i	0.0415901	−	0.0479975i
$963$	−1301.45	+	382.139i	−0.0435499	+	0.0127874i
$964$	−7890.86	−	17278.6i	−0.263639	−	0.577288i
$965$	20180.7			0.673201
$966$	12512.0	+	2537.17i	0.416734	+	0.0845053i
$967$	3664.89			0.121877			0.0609384	−	0.998142i	$-0.480591\pi$
$967$	3664.89			0.121877			0.0609384	+	0.998142i	$0.480591\pi$
$968$	7249.99	+	15875.3i	0.240727	+	0.527118i
$969$	−23045.3	+	6766.72i	−0.764007	+	0.224333i
$970$	4086.33	−	4715.88i	0.135262	−	0.156101i
$971$	43690.4	+	28078.1i	1.44397	+	0.927981i	0.999482	+	0.0321941i	$0.0102495\pi$
$971$	43690.4	+	28078.1i	1.44397	+	0.927981i	0.444484	+	0.895787i	$0.353387\pi$
$972$	3284.27	+	3790.25i	0.108378	+	0.125075i
$973$	59.3781	+	412.984i	0.00195640	+	0.0136070i
$974$	14558.1	+	4274.64i	0.478923	+	0.140624i
$975$	9777.51	−	6283.62i	0.321160	−	0.206397i
$976$	−1824.02	+	12686.3i	−0.0598212	+	0.416065i
$977$	−9571.13	+	20957.9i	−0.313416	+	0.686286i	−0.999135	−	0.0415807i	$-0.986761\pi$
$977$	−9571.13	+	20957.9i	−0.313416	+	0.686286i	0.685719	+	0.727866i	$0.259488\pi$
$978$	3841.36	−	8411.41i	0.125596	−	0.275018i
$979$	4.92396	−	34.2469i	0.000160746	−	0.00111801i
$980$	−8333.51	+	5355.62i	−0.271637	+	0.174570i
$981$	3545.82	+	1041.15i	0.115402	+	0.0338851i
$982$	−2018.86	−	14041.5i	−0.0656054	−	0.456296i
$983$	−16961.2	−	19574.2i	−0.550332	−	0.635117i	0.410628	−	0.911803i	$-0.365309\pi$
$983$	−16961.2	−	19574.2i	−0.550332	−	0.635117i	−0.960961	+	0.276685i	$0.910764\pi$
$984$	−1451.38	−	932.744i	−0.0470206	−	0.0302183i
$985$	14934.7	−	17235.5i	0.483105	−	0.557533i
$986$	1984.69	−	582.757i	0.0641027	−	0.0188223i
$987$	−8938.83	−	19573.3i	−0.288274	−	0.631231i
$988$	46466.2			1.49624
$989$	25559.1	+	24846.7i	0.821773	+	0.798867i
$990$	1.13158			3.63272e−5
$991$	11722.4	+	25668.4i	0.375755	+	0.822788i	0.999164	+	0.0408918i	$0.0130199\pi$
$991$	11722.4	+	25668.4i	0.375755	+	0.822788i	−0.623409	+	0.781896i	$0.714253\pi$
$992$	−4824.91	+	1416.72i	−0.154426	+	0.0453437i
$993$	−9934.45	+	11465.0i	−0.317483	+	0.366395i
$994$	−18936.9	−	12170.0i	−0.604266	−	0.388338i
$995$	12773.1	+	14740.9i	0.406969	+	0.469667i
$996$	−5880.98	−	40903.1i	−0.187094	−	1.30127i
$997$	33242.4	+	9760.86i	1.05597	+	0.310060i	0.763226	−	0.646132i	$-0.223614\pi$
$997$	33242.4	+	9760.86i	1.05597	+	0.310060i	0.292741	+	0.956192i	$0.405433\pi$
$998$	1322.22	−	849.741i	0.0419381	−	0.0269520i
$999$	−488.090	+	3394.74i	−0.0154580	+	0.107512i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.4.g.a.96.8	yes	110
23.6	even	11	inner	115.4.g.a.6.8	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.4.g.a.6.8	✓	110	23.6	even	11	inner
115.4.g.a.96.8	yes	110	1.1	even	1	trivial

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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