LMFDB - Embedded newform 115.4.g.a.6.1

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			6.1
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30963 + 5.05739i) q^{2} +(-3.54080 - 1.03967i) q^{3} +(-15.0039 - 17.3154i) q^{4} +(4.20627 - 2.70320i) q^{5} +(13.4360 - 15.5060i) q^{6} +(-0.413013 + 2.87257i) q^{7} +(79.5474 - 23.3572i) q^{8} +(-11.2575 - 7.23474i) q^{9} +O(q^{10})$	\(q+(-2.30963 + 5.05739i) q^{2} +(-3.54080 - 1.03967i) q^{3} +(-15.0039 - 17.3154i) q^{4} +(4.20627 - 2.70320i) q^{5} +(13.4360 - 15.5060i) q^{6} +(-0.413013 + 2.87257i) q^{7} +(79.5474 - 23.3572i) q^{8} +(-11.2575 - 7.23474i) q^{9} +(3.95622 + 27.5161i) q^{10} +(12.3183 + 26.9733i) q^{11} +(35.1235 + 76.9096i) q^{12} +(2.25124 + 15.6577i) q^{13} +(-13.5738 - 8.72334i) q^{14} +(-17.7040 + 5.19837i) q^{15} +(-39.5134 + 274.822i) q^{16} +(70.6504 - 81.5349i) q^{17} +(62.5895 - 40.2239i) q^{18} +(-18.4918 - 21.3407i) q^{19} +(-109.918 - 32.2747i) q^{20} +(4.44893 - 9.74179i) q^{21} -164.865 q^{22} +(99.7449 + 47.0953i) q^{23} -305.946 q^{24} +(10.3854 - 22.7408i) q^{25} +(-84.3869 - 24.7782i) q^{26} +(97.5876 + 112.622i) q^{27} +(55.9365 - 35.9482i) q^{28} +(-132.925 + 153.404i) q^{29} +(14.5996 - 101.542i) q^{30} +(173.575 - 50.9661i) q^{31} +(-740.662 - 475.995i) q^{32} +(-15.5733 - 108.314i) q^{33} +(249.177 + 545.622i) q^{34} +(6.02789 + 13.1992i) q^{35} +(43.6335 + 303.477i) q^{36} +(169.563 + 108.972i) q^{37} +(150.637 - 44.2311i) q^{38} +(8.30773 - 57.7816i) q^{39} +(271.458 - 313.280i) q^{40} +(212.862 - 136.798i) q^{41} +(38.9926 + 44.9999i) q^{42} +(395.764 + 116.207i) q^{43} +(282.232 - 618.002i) q^{44} -66.9090 q^{45} +(-468.553 + 395.676i) q^{46} -29.5595 q^{47} +(425.634 - 932.009i) q^{48} +(321.025 + 94.2615i) q^{49} +(91.0227 + 105.046i) q^{50} +(-334.929 + 215.246i) q^{51} +(237.343 - 273.908i) q^{52} +(-9.40198 + 65.3922i) q^{53} +(-794.965 + 233.423i) q^{54} +(124.729 + 80.1582i) q^{55} +(34.2411 + 238.152i) q^{56} +(43.2885 + 94.7885i) q^{57} +(-468.814 - 1026.56i) q^{58} +(-74.5739 - 518.673i) q^{59} +(355.641 + 228.557i) q^{60} +(-159.479 + 46.8274i) q^{61} +(-143.138 + 995.547i) q^{62} +(25.4318 - 29.3498i) q^{63} +(2249.37 - 1445.58i) q^{64} +(51.7954 + 59.7751i) q^{65} +(583.756 + 171.406i) q^{66} +(206.940 - 453.135i) q^{67} -2471.84 q^{68} +(-304.213 - 270.457i) q^{69} -80.6759 q^{70} +(370.749 - 811.828i) q^{71} +(-1064.49 - 312.562i) q^{72} +(-510.565 - 589.224i) q^{73} +(-942.741 + 605.863i) q^{74} +(-60.4156 + 69.7233i) q^{75} +(-92.0737 + 640.386i) q^{76} +(-82.5703 + 24.2448i) q^{77} +(273.036 + 175.470i) q^{78} +(147.577 + 1026.42i) q^{79} +(576.696 + 1262.79i) q^{80} +(-78.3553 - 171.574i) q^{81} +(200.208 + 1392.48i) q^{82} +(868.547 + 558.181i) q^{83} +(-235.434 + 69.1298i) q^{84} +(76.7690 - 533.940i) q^{85} +(-1501.77 + 1733.14i) q^{86} +(630.151 - 404.974i) q^{87} +(1609.91 + 1857.94i) q^{88} +(-651.924 - 191.422i) q^{89} +(154.535 - 338.385i) q^{90} -45.9077 q^{91} +(-681.087 - 2433.74i) q^{92} -667.581 q^{93} +(68.2715 - 149.494i) q^{94} +(-135.470 - 39.7775i) q^{95} +(2127.66 + 2455.45i) q^{96} +(-69.4174 + 44.6119i) q^{97} +(-1218.17 + 1405.84i) q^{98} +(56.4721 - 392.772i) 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 $

$2$	−2.30963	+	5.05739i	−0.816578	+	1.78806i	−0.240529	+	0.970642i	$0.577321\pi$
$2$	−2.30963	+	5.05739i	−0.816578	+	1.78806i	−0.576049	+	0.817415i	$0.695406\pi$
$3$	−3.54080	−	1.03967i	−0.681428	−	0.200085i	−0.0773421	−	0.997005i	$-0.524643\pi$
$3$	−3.54080	−	1.03967i	−0.681428	−	0.200085i	−0.604086	+	0.796919i	$0.706462\pi$
$4$	−15.0039	−	17.3154i	−1.87549	−	2.16443i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	13.4360	−	15.5060i	0.914203	−	1.05505i
$7$	−0.413013	+	2.87257i	−0.0223006	+	0.155104i	−0.997929	−	0.0643254i	$-0.979510\pi$
$7$	−0.413013	+	2.87257i	−0.0223006	+	0.155104i	0.975628	+	0.219429i	$0.0704195\pi$
$8$	79.5474	−	23.3572i	3.51553	−	1.03225i
$9$	−11.2575	−	7.23474i	−0.416944	−	0.267953i
$10$	3.95622	+	27.5161i	0.125107	+	0.870137i
$11$	12.3183	+	26.9733i	0.337647	+	0.739343i	0.999951	−	0.00989199i	$-0.00314877\pi$
$11$	12.3183	+	26.9733i	0.337647	+	0.739343i	−0.662305	+	0.749235i	$0.730421\pi$
$12$	35.1235	+	76.9096i	0.844939	+	1.85016i
$13$	2.25124	+	15.6577i	0.0480294	+	0.334052i	0.999642	+	0.0267520i	$0.00851645\pi$
$13$	2.25124	+	15.6577i	0.0480294	+	0.334052i	−0.951613	+	0.307300i	$0.900574\pi$
$14$	−13.5738	−	8.72334i	−0.259125	−	0.166529i
$15$	−17.7040	+	5.19837i	−0.304744	+	0.0894809i
$16$	−39.5134	+	274.822i	−0.617397	+	4.29409i
$17$	70.6504	−	81.5349i	1.00796	−	1.16324i	0.0214078	−	0.999771i	$-0.493185\pi$
$17$	70.6504	−	81.5349i	1.00796	−	1.16324i	0.986548	−	0.163472i	$-0.0522694\pi$
$18$	62.5895	−	40.2239i	0.819583	−	0.526714i
$19$	−18.4918	−	21.3407i	−0.223279	−	0.257678i	0.633047	−	0.774114i	$-0.281804\pi$
$19$	−18.4918	−	21.3407i	−0.223279	−	0.257678i	−0.856326	+	0.516435i	$0.827259\pi$
$20$	−109.918	−	32.2747i	−1.22892	−	0.360842i
$21$	4.44893	−	9.74179i	0.0462303	−	0.101230i
$22$	−164.865			−1.59770
$23$	99.7449	+	47.0953i	0.904271	+	0.426958i
$23$	99.7449	+	47.0953i	0.904271	+	0.426958i
$24$	−305.946			−2.60212
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	−84.3869	−	24.7782i	−0.636524	−	0.186900i
$27$	97.5876	+	112.622i	0.695583	+	0.802745i
$28$	55.9365	−	35.9482i	0.377536	−	0.242628i
$29$	−132.925	+	153.404i	−0.851158	+	0.982288i	−0.999978	−	0.00657590i	$-0.997907\pi$
$29$	−132.925	+	153.404i	−0.851158	+	0.982288i	0.148821	+	0.988864i	$0.452452\pi$
$30$	14.5996	−	101.542i	0.0888503	−	0.617967i
$31$	173.575	−	50.9661i	1.00564	−	0.295283i	0.262873	−	0.964830i	$-0.415330\pi$
$31$	173.575	−	50.9661i	1.00564	−	0.295283i	0.742769	+	0.669547i	$0.233512\pi$
$32$	−740.662	−	475.995i	−4.09162	−	2.62952i
$33$	−15.5733	−	108.314i	−0.0821502	−	0.571367i
$34$	249.177	+	545.622i	1.25687	+	2.75216i
$35$	6.02789	+	13.1992i	0.0291114	+	0.0637451i
$36$	43.6335	+	303.477i	0.202007	+	1.40499i
$37$	169.563	+	108.972i	0.753406	+	0.484185i	0.860112	−	0.510106i	$-0.170394\pi$
$37$	169.563	+	108.972i	0.753406	+	0.484185i	−0.106705	+	0.994291i	$0.534030\pi$
$38$	150.637	−	44.2311i	0.643068	−	0.188822i
$39$	8.30773	−	57.7816i	0.0341103	−	0.237242i
$40$	271.458	−	313.280i	1.07303	−	1.23835i
$41$	212.862	−	136.798i	0.810814	−	0.521079i	−0.0683140	−	0.997664i	$-0.521762\pi$
$41$	212.862	−	136.798i	0.810814	−	0.521079i	0.879128	+	0.476585i	$0.158126\pi$
$42$	38.9926	+	44.9999i	0.143255	+	0.165325i
$43$	395.764	+	116.207i	1.40357	+	0.412125i	0.893908	−	0.448250i	$-0.147953\pi$
$43$	395.764	+	116.207i	1.40357	+	0.412125i	0.509661	+	0.860375i	$0.329771\pi$
$44$	282.232	−	618.002i	0.967002	−	2.11744i
$45$	−66.9090			−0.221649
$46$	−468.553	+	395.676i	−1.50183	+	1.26824i
$47$	−29.5595			−0.0917381			−0.0458690	−	0.998947i	$-0.514606\pi$
$47$	−29.5595			−0.0917381			−0.0458690	+	0.998947i	$0.514606\pi$
$48$	425.634	−	932.009i	1.27990	−	2.80258i
$49$	321.025	+	94.2615i	0.935933	+	0.274815i
$50$	91.0227	+	105.046i	0.257451	+	0.297114i
$51$	−334.929	+	215.246i	−0.919597	+	0.590989i
$52$	237.343	−	273.908i	0.632953	−	0.730467i
$53$	−9.40198	+	65.3922i	−0.0243672	+	0.169478i	−0.998371	−	0.0570536i	$-0.981829\pi$
$53$	−9.40198	+	65.3922i	−0.0243672	+	0.169478i	0.974004	+	0.226531i	$0.0727385\pi$
$54$	−794.965	+	233.423i	−2.00335	+	0.588237i
$55$	124.729	+	80.1582i	0.305789	+	0.196519i
$56$	34.2411	+	238.152i	0.0817082	+	0.568293i
$57$	43.2885	+	94.7885i	0.100591	+	0.220264i
$58$	−468.814	−	1026.56i	−1.06135	−	2.32403i
$59$	−74.5739	−	518.673i	−0.164554	−	1.14450i	−0.889914	−	0.456129i	$-0.849236\pi$
$59$	−74.5739	−	518.673i	−0.164554	−	1.14450i	0.725360	−	0.688370i	$-0.241673\pi$
$60$	355.641	+	228.557i	0.765218	+	0.491776i
$61$	−159.479	+	46.8274i	−0.334742	+	0.0982890i	−0.444784	−	0.895638i	$-0.646720\pi$
$61$	−159.479	+	46.8274i	−0.334742	+	0.0982890i	0.110042	+	0.993927i	$0.464901\pi$
$62$	−143.138	+	995.547i	−0.293202	+	2.03927i
$63$	25.4318	−	29.3498i	0.0508587	−	0.0586941i
$64$	2249.37	−	1445.58i	4.39330	−	2.82340i
$65$	51.7954	+	59.7751i	0.0988374	+	0.114064i
$66$	583.756	+	171.406i	1.08872	+	0.319677i
$67$	206.940	−	453.135i	0.377339	−	0.826258i	−0.621735	−	0.783228i	$-0.713572\pi$
$67$	206.940	−	453.135i	0.377339	−	0.826258i	0.999074	−	0.0430297i	$-0.0137010\pi$
$68$	−2471.84			−4.40816
$69$	−304.213	−	270.457i	−0.530768	−	0.471873i
$70$	−80.6759			−0.137752
$71$	370.749	−	811.828i	0.619716	−	1.35699i	−0.296009	−	0.955185i	$-0.595656\pi$
$71$	370.749	−	811.828i	0.619716	−	1.35699i	0.915726	−	0.401804i	$-0.131617\pi$
$72$	−1064.49	−	312.562i	−1.74238	−	0.511608i
$73$	−510.565	−	589.224i	−0.818591	−	0.944704i	0.180654	−	0.983547i	$-0.442178\pi$
$73$	−510.565	−	589.224i	−0.818591	−	0.944704i	−0.999245	+	0.0388423i	$0.987633\pi$
$74$	−942.741	+	605.863i	−1.48097	+	0.951759i
$75$	−60.4156	+	69.7233i	−0.0930159	+	0.107346i
$76$	−92.0737	+	640.386i	−0.138968	+	0.966544i
$77$	−82.5703	+	24.2448i	−0.122205	+	0.0358825i
$78$	273.036	+	175.470i	0.396349	+	0.254718i
$79$	147.577	+	1026.42i	0.210174	+	1.46179i	0.772572	+	0.634927i	$0.218970\pi$
$79$	147.577	+	1026.42i	0.210174	+	1.46179i	−0.562398	+	0.826867i	$0.690121\pi$
$80$	576.696	+	1262.79i	0.805957	+	1.76480i
$81$	−78.3553	−	171.574i	−0.107483	−	0.235355i
$82$	200.208	+	1392.48i	0.269625	+	1.87528i
$83$	868.547	+	558.181i	1.14862	+	0.738173i	0.969364	−	0.245629i	$-0.0789946\pi$
$83$	868.547	+	558.181i	1.14862	+	0.738173i	0.179256	+	0.983802i	$0.442631\pi$
$84$	−235.434	+	69.1298i	−0.305810	+	0.0897938i
$85$	76.7690	−	533.940i	0.0979620	−	0.681341i
$86$	−1501.77	+	1733.14i	−1.88303	+	2.17313i
$87$	630.151	−	404.974i	0.776544	−	0.499055i
$88$	1609.91	+	1857.94i	1.95020	+	2.25065i
$89$	−651.924	−	191.422i	−0.776447	−	0.227986i	−0.130583	−	0.991437i	$-0.541685\pi$
$89$	−651.924	−	191.422i	−0.776447	−	0.227986i	−0.645865	+	0.763452i	$0.723503\pi$
$90$	154.535	−	338.385i	0.180994	−	0.396321i
$91$	−45.9077			−0.0528839
$92$	−681.087	−	2433.74i	−0.771829	−	2.75798i
$93$	−667.581			−0.744355
$94$	68.2715	−	149.494i	0.0749113	−	0.164033i
$95$	−135.470	−	39.7775i	−0.146304	−	0.0429588i
$96$	2127.66	+	2455.45i	2.26201	+	2.61050i
$97$	−69.4174	+	44.6119i	−0.0726626	+	0.0466974i	−0.576468	−	0.817120i	$-0.695569\pi$
$97$	−69.4174	+	44.6119i	−0.0726626	+	0.0466974i	0.503805	+	0.863817i	$0.331933\pi$
$98$	−1218.17	+	1405.84i	−1.25565	+	1.44909i
$99$	56.4721	−	392.772i	0.0573298	−	0.398738i
$100$	−549.588	+	161.373i	−0.549588	+	0.161373i
$101$	−879.765	−	565.391i	−0.866732	−	0.557015i	0.0300198	−	0.999549i	$-0.490443\pi$
$101$	−879.765	−	565.391i	−0.866732	−	0.557015i	−0.896751	+	0.442535i	$0.854079\pi$
$102$	−315.019	−	2191.00i	−0.305799	−	2.12688i
$103$	−249.816	−	547.021i	−0.238982	−	0.523297i	0.751698	−	0.659507i	$-0.229235\pi$
$103$	−249.816	−	547.021i	−0.238982	−	0.523297i	−0.990680	+	0.136211i	$0.956508\pi$
$104$	544.802	+	1192.95i	0.513676	+	1.12479i
$105$	−7.62067	−	53.0029i	−0.00708287	−	0.0492625i
$106$	−308.999	−	198.581i	−0.283138	−	0.181962i
$107$	1656.70	−	486.450i	1.49681	−	0.439504i	0.572104	−	0.820181i	$-0.306127\pi$
$107$	1656.70	−	486.450i	1.49681	−	0.439504i	0.924708	+	0.380678i	$0.124309\pi$
$108$	485.904	−	3379.54i	0.432928	−	3.01108i
$109$	−322.975	+	372.733i	−0.283811	+	0.327535i	−0.879698	−	0.475533i	$-0.842255\pi$
$109$	−322.975	+	372.733i	−0.283811	+	0.327535i	0.595887	+	0.803068i	$0.296801\pi$
$110$	−693.468	+	445.665i	−0.601087	+	0.386295i
$111$	−487.095	−	562.138i	−0.416514	−	0.480682i
$112$	−773.125	−	227.010i	−0.652263	−	0.191522i
$113$	−766.735	+	1678.91i	−0.638304	+	1.39769i	0.263125	+	0.964762i	$0.415247\pi$
$113$	−766.735	+	1678.91i	−0.638304	+	1.39769i	−0.901428	+	0.432928i	$0.857480\pi$
$114$	−579.363			−0.475985
$115$	546.862	−	71.5355i	0.443436	−	0.0580062i
$116$	4650.64			3.72243
$117$	87.9364	−	192.554i	0.0694848	−	0.152151i
$118$	2795.37	+	820.794i	2.18080	+	0.640341i
$119$	205.035	+	236.623i	0.157946	+	0.182279i
$120$	−1286.89	+	827.034i	−0.978970	+	0.629146i
$121$	295.799	−	341.370i	0.222238	−	0.256477i
$122$	131.514	−	914.703i	0.0975964	−	0.678798i
$123$	−895.926	+	263.068i	−0.656772	+	0.192846i
$124$	−3486.79	−	2240.83i	−2.52519	−	1.62284i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	89.6954	+	196.406i	0.0634183	+	0.138867i
$127$	195.125	+	427.265i	0.136335	+	0.298532i	0.965469	−	0.260518i	$-0.0838932\pi$
$127$	195.125	+	427.265i	0.136335	+	0.298532i	−0.829134	+	0.559050i	$0.811166\pi$
$128$	1113.27	+	7742.97i	0.768752	+	5.34679i
$129$	−1280.51	−	822.931i	−0.873971	−	0.561667i
$130$	−421.934	+	123.891i	−0.284662	+	0.0835844i
$131$	56.5118	−	393.048i	0.0376906	−	0.262144i	−0.962260	−	0.272133i	$-0.912271\pi$
$131$	56.5118	−	393.048i	0.0376906	−	0.262144i	0.999950	+	0.00998981i	$0.00317991\pi$
$132$	−1641.85	+	1894.79i	−1.08261	+	1.24940i
$133$	68.9398	−	44.3049i	0.0449462	−	0.0288852i
$134$	1813.73	+	2093.15i	1.16927	+	1.34941i
$135$	714.920	+	209.919i	0.455782	+	0.133830i
$136$	3715.63	−	8136.10i	2.34274	−	5.12989i
$137$	479.211			0.298845			0.149423	−	0.988773i	$-0.452259\pi$
$137$	479.211			0.298845			0.149423	+	0.988773i	$0.452259\pi$
$138$	2070.43	−	913.868i	1.27715	−	0.563722i
$139$	−2389.57			−1.45814			−0.729068	−	0.684441i	$-0.760046\pi$
$139$	−2389.57			−1.45814			−0.729068	+	0.684441i	$0.760046\pi$
$140$	138.109	−	302.415i	0.0833736	−	0.182563i
$141$	104.664	+	30.7322i	0.0625129	+	0.0183554i
$142$	3249.43	+	3750.05i	1.92033	+	2.21618i
$143$	−394.610	+	253.601i	−0.230762	+	0.148302i
$144$	2433.09	−	2807.93i	1.40804	−	1.62496i
$145$	−144.437	+	1004.58i	−0.0827230	+	0.575351i
$146$	4159.15	−	1221.24i	2.35763	−	0.692262i
$147$	−1038.69	−	667.523i	−0.582784	−	0.374533i
$148$	−657.219	−	4571.06i	−0.365021	−	2.53878i
$149$	−674.243	−	1476.39i	−0.370712	−	0.811747i	−0.999418	−	0.0341037i	$-0.989142\pi$
$149$	−674.243	−	1476.39i	−0.370712	−	0.811747i	0.628706	−	0.777643i	$-0.283585\pi$
$150$	−213.080	−	466.580i	−0.115986	−	0.253974i
$151$	223.743	+	1556.17i	0.120583	+	0.838670i	0.956899	+	0.290422i	$0.0937957\pi$
$151$	223.743	+	1556.17i	0.120583	+	0.838670i	−0.836316	+	0.548248i	$0.815295\pi$
$152$	−1969.43	−	1265.68i	−1.05094	−	0.675395i
$153$	−1385.23	+	406.740i	−0.731956	+	0.214922i
$154$	68.0915	−	473.587i	0.0356297	−	0.247810i
$155$	592.329	−	683.584i	0.306949	−	0.354238i
$156$	−1125.16	+	723.097i	−0.577467	+	0.371116i
$157$	2396.56	+	2765.77i	1.21826	+	1.40594i	0.886597	+	0.462542i	$0.153063\pi$
$157$	2396.56	+	2765.77i	1.21826	+	1.40594i	0.331658	+	0.943400i	$0.392392\pi$
$158$	−5531.87	−	1624.30i	−2.78539	−	0.817866i
$159$	101.277	−	221.766i	0.0505145	−	0.110611i
$160$	−4402.14			−2.17512
$161$	−176.480	+	267.073i	−0.0863887	+	0.130735i
$162$	1048.69			0.508597
$163$	−1284.41	+	2812.48i	−0.617197	+	1.35147i	0.300343	+	0.953831i	$0.402899\pi$
$163$	−1284.41	+	2812.48i	−0.617197	+	1.35147i	−0.917541	+	0.397642i	$0.869829\pi$
$164$	−5562.46	−	1633.29i	−2.64851	−	0.777672i
$165$	−358.301	−	413.501i	−0.169053	−	0.195097i
$166$	−4828.97	+	3103.39i	−2.25783	+	1.45102i
$167$	560.892	−	647.304i	0.259899	−	0.299939i	−0.610771	−	0.791807i	$-0.709140\pi$
$167$	560.892	−	647.304i	0.259899	−	0.299939i	0.870670	+	0.491868i	$0.163686\pi$
$168$	126.359	−	878.849i	0.0580288	−	0.403599i
$169$	1867.91	−	548.468i	0.850209	−	0.249644i
$170$	2523.04	+	1621.46i	1.13828	+	0.731530i
$171$	53.7768	+	374.026i	0.0240492	+	0.167266i
$172$	−3925.84	−	8596.38i	−1.74036	−	3.81086i
$173$	77.1866	+	169.015i	0.0339213	+	0.0742773i	0.925834	−	0.377930i	$-0.123364\pi$
$173$	77.1866	+	169.015i	0.0339213	+	0.0742773i	−0.891913	+	0.452207i	$0.850637\pi$
$174$	592.692	+	4122.26i	0.258229	+	1.79602i
$175$	61.0352	+	39.2249i	0.0263647	+	0.0169436i
$176$	−7899.61	+	2319.53i	−3.38327	+	0.993417i
$177$	−275.199	+	1914.05i	−0.116866	+	0.812818i
$178$	2473.80	−	2854.92i	1.04168	−	1.20216i
$179$	283.692	−	182.318i	0.118459	−	0.0761289i	−0.480070	−	0.877230i	$-0.659389\pi$
$179$	283.692	−	182.318i	0.118459	−	0.0761289i	0.598529	+	0.801101i	$0.295752\pi$
$180$	1003.90	+	1158.56i	0.415700	+	0.479743i
$181$	−3603.72	−	1058.15i	−1.47990	−	0.434538i	−0.560598	−	0.828088i	$-0.689429\pi$
$181$	−3603.72	−	1058.15i	−1.47990	−	0.434538i	−0.919303	+	0.393550i	$0.871247\pi$
$182$	106.030	−	232.173i	0.0431838	−	0.0945594i
$183$	613.370			0.247769
$184$	9034.46	+	1416.54i	3.61973	+	0.567549i
$185$	1007.80			0.400514
$186$	1541.87	−	3376.22i	0.607824	−	1.33095i
$187$	3069.56	+	901.306i	1.20037	+	0.352460i
$188$	443.507	+	511.834i	0.172054	+	0.198560i
$189$	−363.819	+	233.812i	−0.140021	+	0.0899860i
$190$	514.055	−	593.251i	0.196281	−	0.226521i
$191$	−185.925	+	1293.14i	−0.0704350	+	0.489886i	0.923818	+	0.382832i	$0.125051\pi$
$191$	−185.925	+	1293.14i	−0.0704350	+	0.489886i	−0.994253	+	0.107055i	$0.965858\pi$
$192$	−9467.51	+	2779.91i	−3.55864	+	1.04491i
$193$	1733.60	+	1114.12i	0.646566	+	0.415522i	0.822410	−	0.568896i	$-0.192629\pi$
$193$	1733.60	+	1114.12i	0.646566	+	0.415522i	−0.175844	+	0.984418i	$0.556265\pi$
$194$	−65.2909	−	454.108i	−0.0241629	−	0.168057i
$195$	−121.251	−	265.502i	−0.0445279	−	0.0975026i
$196$	−3184.45	−	6972.97i	−1.16051	−	2.54117i
$197$	−370.106	−	2574.14i	−0.133853	−	0.930965i	−0.940466	−	0.339886i	$-0.889611\pi$
$197$	−370.106	−	2574.14i	−0.133853	−	0.930965i	0.806614	−	0.591079i	$-0.201298\pi$
$198$	1855.97	+	1192.76i	0.666152	+	0.428110i
$199$	1641.06	−	481.858i	0.584581	−	0.171648i	0.0239483	−	0.999713i	$-0.492376\pi$
$199$	1641.06	−	481.858i	0.584581	−	0.171648i	0.560632	+	0.828065i	$0.310558\pi$
$200$	294.968	−	2051.55i	0.104287	−	0.725331i
$201$	−1203.85	+	1389.31i	−0.422451	+	0.487535i
$202$	4891.33	−	3143.47i	1.70373	−	1.09492i
$203$	−385.763	−	445.194i	−0.133376	−	0.153924i
$204$	8752.31	+	2569.91i	3.00385	+	0.882009i
$205$	525.560	−	1150.82i	0.179057	−	0.392080i
$206$	3343.48			1.13083
$207$	−782.154	−	1251.80i	−0.262625	−	0.420320i
$208$	−4392.05			−1.46410
$209$	347.842	−	761.667i	0.115123	−	0.252084i
$210$	285.657	+	83.8766i	0.0938678	+	0.0275621i
$211$	3539.10	+	4084.34i	1.15470	+	1.33259i	0.934009	+	0.357250i	$0.116285\pi$
$211$	3539.10	+	4084.34i	1.15470	+	1.33259i	0.220690	+	0.975344i	$0.429169\pi$
$212$	1273.36	−	818.339i	0.412522	−	0.265112i
$213$	−2156.79	+	2489.06i	−0.693806	+	0.800694i
$214$	−1366.19	+	9502.08i	−0.436406	+	3.03527i
$215$	1978.82	−	581.034i	0.627695	−	0.184308i
$216$	10393.4	+	6679.42i	3.27398	+	2.10406i
$217$	74.7150	+	519.654i	0.0233732	+	0.162564i
$218$	−1139.10	−	2494.28i	−0.353898	−	0.774927i
$219$	1195.21	+	2617.15i	0.368789	+	0.807536i
$220$	−483.442	−	3362.41i	−0.148153	−	1.03043i
$221$	1435.70	+	922.672i	0.436995	+	0.280840i
$222$	3967.96	−	1165.10i	1.19960	−	0.352235i
$223$	−42.2358	+	293.757i	−0.0126830	+	0.0882125i	−0.995180	−	0.0980672i	$-0.968734\pi$
$223$	−42.2358	+	293.757i	−0.0126830	+	0.0882125i	0.982497	+	0.186280i	$0.0596431\pi$
$224$	1673.23	−	1931.01i	0.499095	−	0.575987i
$225$	−281.437	+	180.869i	−0.0833887	+	0.0535907i
$226$	−6720.05	−	7755.35i	−1.97792	−	2.28265i
$227$	3381.42	+	992.875i	0.988691	+	0.290306i	0.735807	−	0.677191i	$-0.236803\pi$
$227$	3381.42	+	992.875i	0.988691	+	0.290306i	0.252883	+	0.967497i	$0.418621\pi$
$228$	991.808	−	2171.76i	0.288088	−	0.630825i
$229$	119.789			0.0345671			0.0172835	−	0.999851i	$-0.494498\pi$
$229$	119.789			0.0345671			0.0172835	+	0.999851i	$0.494498\pi$
$230$	−901.267	+	2930.91i	−0.258382	+	0.840255i
$231$	317.572			0.0904533
$232$	−6990.76	+	15307.6i	−1.97830	+	4.33188i
$233$	−2478.19	−	727.663i	−0.696789	−	0.204596i	−0.0858905	−	0.996305i	$-0.527374\pi$
$233$	−2478.19	−	727.663i	−0.696789	−	0.204596i	−0.610899	+	0.791709i	$0.709192\pi$
$234$	770.719	+	889.458i	0.215314	+	0.248486i
$235$	−124.335	+	79.9053i	−0.0345137	+	0.0221806i
$236$	−7862.14	+	9073.39i	−2.16857	+	2.50266i
$237$	544.603	−	3787.80i	0.149265	−	1.03816i
$238$	−1670.25	+	490.430i	−0.454900	+	0.133571i
$239$	−3563.19	−	2289.92i	−0.964367	−	0.619761i	−0.0391635	−	0.999233i	$-0.512469\pi$
$239$	−3563.19	−	2289.92i	−0.964367	−	0.619761i	−0.925203	+	0.379472i	$0.876106\pi$
$240$	−729.079	−	5070.86i	−0.196091	−	1.36384i
$241$	910.659	+	1994.07i	0.243405	+	0.532984i	0.991422	−	0.130696i	$-0.0417212\pi$
$241$	910.659	+	1994.07i	0.243405	+	0.532984i	−0.748017	+	0.663679i	$0.768994\pi$
$242$	1043.26	+	2284.41i	0.277120	+	0.606808i
$243$	−473.551	−	3293.62i	−0.125014	−	0.869489i
$244$	3203.65	+	2058.86i	0.840543	+	0.540184i
$245$	1605.13	−	471.307i	0.418562	−	0.122901i
$246$	738.824	−	5138.63i	0.191487	−	1.33182i
$247$	292.517	−	337.583i	0.0753540	−	0.0869631i
$248$	12617.0	−	8108.44i	3.23056	−	2.07616i
$249$	−2495.03	−	2879.42i	−0.635004	−	0.732834i
$250$	666.826	+	195.798i	0.168695	+	0.0495333i
$251$	1534.83	−	3360.82i	0.385967	−	0.845151i	−0.612535	−	0.790443i	$-0.709850\pi$
$251$	1534.83	−	3360.82i	0.385967	−	0.845151i	0.998502	−	0.0547073i	$-0.0174226\pi$
$252$	−889.780			−0.222424
$253$	−41.6281	+	3270.59i	−0.0103444	+	0.812727i
$254$	−2611.51			−0.645121
$255$	−826.948	+	1810.76i	−0.203080	+	0.444684i
$256$	−21206.3	−	6226.73i	−5.17732	−	1.52020i
$257$	−2079.09	−	2399.39i	−0.504630	−	0.582373i	0.445086	−	0.895488i	$-0.353173\pi$
$257$	−2079.09	−	2399.39i	−0.504630	−	0.582373i	−0.949715	+	0.313114i	$0.898628\pi$
$258$	7119.38	−	4575.35i	1.71796	−	1.10407i
$259$	−383.060	+	442.075i	−0.0919004	+	0.106059i
$260$	257.898	−	1793.72i	0.0615159	−	0.427853i
$261$	2606.24	−	765.261i	0.618092	−	0.181488i
$262$	1857.28	+	1193.60i	0.437950	+	0.281454i
$263$	−230.133	−	1600.61i	−0.0539567	−	0.375277i	−0.998852	−	0.0479041i	$-0.984746\pi$
$263$	−230.133	−	1600.61i	−0.0539567	−	0.375277i	0.944895	−	0.327373i	$-0.106163\pi$
$264$	−3768.74	−	8252.38i	−0.878597	−	1.92386i
$265$	137.221	+	300.473i	0.0318092	+	0.0696524i
$266$	64.8417	+	450.984i	0.0149462	+	0.103953i
$267$	2109.32	+	1355.58i	0.483476	+	0.310711i
$268$	−10951.1	+	3215.54i	−2.49607	+	0.732912i
$269$	−96.3596	+	670.196i	−0.0218407	+	0.151905i	−0.997823	−	0.0659425i	$-0.978995\pi$
$269$	−96.3596	+	670.196i	−0.0218407	+	0.151905i	0.975983	+	0.217848i	$0.0699037\pi$
$270$	−2712.85	+	3130.79i	−0.611476	+	0.705681i
$271$	−2395.92	+	1539.76i	−0.537053	+	0.345143i	−0.780886	−	0.624674i	$-0.785232\pi$
$271$	−2395.92	+	1539.76i	−0.537053	+	0.345143i	0.243832	+	0.969817i	$0.421595\pi$
$272$	19616.0	+	22638.0i	4.37276	+	5.04644i
$273$	162.550	+	47.7290i	0.0360366	+	0.0105813i
$274$	−1106.80	+	2423.56i	−0.244030	+	0.534352i
$275$	741.326			0.162559
$276$	−118.695	+	9325.49i	−0.0258863	+	2.03380i
$277$	−7190.21			−1.55963			−0.779816	−	0.626009i	$-0.784687\pi$
$277$	−7190.21			−1.55963			−0.779816	+	0.626009i	$0.784687\pi$
$278$	5519.04	−	12085.0i	1.19068	−	2.60723i
$279$	−2322.74	−	682.018i	−0.498418	−	0.146349i
$280$	787.801	+	909.171i	0.168143	+	0.194048i
$281$	−6222.81	+	3999.15i	−1.32107	+	0.849002i	−0.995337	−	0.0964590i	$-0.969248\pi$
$281$	−6222.81	+	3999.15i	−1.32107	+	0.849002i	−0.325736	+	0.945461i	$0.605612\pi$
$282$	−397.161	+	458.348i	−0.0838672	+	0.0967880i
$283$	−884.570	+	6152.32i	−0.185803	+	1.29229i	0.656928	+	0.753953i	$0.271855\pi$
$283$	−884.570	+	6152.32i	−0.185803	+	1.29229i	−0.842731	+	0.538335i	$0.819054\pi$
$284$	−19619.8	+	5760.90i	−4.09938	+	1.20369i
$285$	438.316	+	281.688i	0.0911003	+	0.0585466i
$286$	−371.152	−	2581.42i	−0.0767367	−	0.533716i
$287$	305.046	+	667.958i	0.0627397	+	0.137381i
$288$	4894.29	+	10717.0i	1.00139	+	2.19273i
$289$	−957.271	−	6657.97i	−0.194845	−	1.35517i
$290$	−4746.96	−	3050.69i	−0.961211	−	0.617733i
$291$	292.175	−	85.7904i	0.0588578	−	0.0172822i
$292$	−2542.19	+	17681.3i	−0.509487	+	3.54356i
$293$	2872.80	−	3315.39i	0.572802	−	0.661049i	−0.393239	−	0.919436i	$-0.628646\pi$
$293$	2872.80	−	3315.39i	0.572802	−	0.661049i	0.966041	+	0.258387i	$0.0831911\pi$
$294$	5774.90	−	3711.30i	1.14558	−	0.736217i
$295$	−1715.76	−	1980.09i	−0.338628	−	0.390797i
$296$	16033.6	+	4707.89i	3.14843	+	0.924461i
$297$	−1835.68	+	4019.58i	−0.358643	+	0.785318i
$298$	9023.91			1.75417
$299$	−512.856	+	1667.80i	−0.0991947	+	0.322580i
$300$	2113.76			0.406793
$301$	−497.268	+	1088.86i	−0.0952227	+	0.208509i
$302$	−8386.91	−	2462.62i	−1.59805	−	0.469231i
$303$	2527.25	+	2916.61i	0.479165	+	0.552985i
$304$	6595.56	−	4238.71i	1.24435	−	0.799693i
$305$	−544.229	+	628.074i	−0.102172	+	0.117913i
$306$	1142.33	−	7945.07i	0.213407	−	1.48428i
$307$	5533.31	−	1624.73i	1.02867	−	0.302046i	0.276502	−	0.961013i	$-0.410825\pi$
$307$	5533.31	−	1624.73i	1.02867	−	0.302046i	0.752171	+	0.658967i	$0.229007\pi$
$308$	1658.69	+	1065.97i	0.306859	+	0.197206i
$309$	315.826	+	2196.62i	0.0581447	+	0.404406i
$310$	2089.09	+	4574.47i	0.382749	+	0.838104i
$311$	−1603.28	−	3510.69i	−0.292326	−	0.640106i	0.705304	−	0.708905i	$-0.250810\pi$
$311$	−1603.28	−	3510.69i	−0.292326	−	0.640106i	−0.997631	+	0.0687993i	$0.978083\pi$
$312$	−688.759	−	4790.42i	−0.124978	−	0.869244i
$313$	−5385.26	−	3460.89i	−0.972501	−	0.624988i	−0.0450702	−	0.998984i	$-0.514351\pi$
$313$	−5385.26	−	3460.89i	−0.972501	−	0.624988i	−0.927431	+	0.373996i	$0.877988\pi$
$314$	−19522.8	+	5732.40i	−3.50870	+	1.03025i
$315$	27.6342	−	192.200i	0.00494290	−	0.0343786i
$316$	15558.7	−	17955.7i	2.76977	−	3.19648i
$317$	−2535.78	+	1629.64i	−0.449285	+	0.288738i	−0.745651	−	0.666336i	$-0.767862\pi$
$317$	−2535.78	+	1629.64i	−0.449285	+	0.288738i	0.296366	+	0.955074i	$0.404225\pi$
$318$	887.644	+	1024.40i	0.156530	+	0.180645i
$319$	−5775.23	−	1695.76i	−1.01364	−	0.297631i
$320$	5553.75	−	12161.0i	0.970200	−	2.12444i
$321$	−6371.78			−1.10791
$322$	−943.087	−	1509.37i	−0.163218	−	0.261223i
$323$	−3046.46			−0.524798
$324$	−1795.24	+	3931.03i	−0.307826	+	0.674046i
$325$	379.450	+	111.416i	0.0647633	+	0.0190162i
$326$	−11257.3	−	12991.6i	−1.91252	−	2.20717i
$327$	1531.11	−	983.984i	0.258931	−	0.166405i
$328$	13737.4	−	15853.8i	2.31256	−	2.66884i
$329$	12.2084	−	84.9115i	0.00204581	−	0.0142289i
$330$	2918.78	−	857.031i	0.486890	−	0.142964i
$331$	5826.34	+	3744.36i	0.967506	+	0.621778i	0.926066	−	0.377363i	$-0.123169\pi$
$331$	5826.34	+	3744.36i	0.967506	+	0.621778i	0.0414404	+	0.999141i	$0.486805\pi$
$332$	−3366.45	−	23414.2i	−0.556499	−	3.87054i
$333$	−1120.47	−	2453.49i	−0.184389	−	0.403756i
$334$	1978.21	+	4331.68i	0.324081	+	0.709638i
$335$	−354.472	−	2465.41i	−0.0578116	−	0.402089i
$336$	2501.47	+	1607.59i	0.406149	+	0.261016i
$337$	4587.03	−	1346.87i	0.741458	−	0.217712i	0.110876	−	0.993834i	$-0.464634\pi$
$337$	4587.03	−	1346.87i	0.741458	−	0.217712i	0.630582	+	0.776123i	$0.282816\pi$
$338$	−1540.37	+	10713.5i	−0.247885	+	1.72408i
$339$	4460.38	−	5147.55i	0.714615	−	0.824710i
$340$	−10397.2	+	6681.90i	−1.65844	+	1.06581i
$341$	3512.87	+	4054.07i	0.557867	+	0.643813i
$342$	−2015.80	−	591.892i	−0.318719	−	0.0935843i
$343$	−816.873	+	1788.70i	−0.128592	+	0.281577i
$344$	34196.3			5.35971
$345$	−2010.70	−	315.265i	−0.313776	−	0.0491979i
$346$	−1033.05			−0.160512
$347$	−1444.49	+	3162.99i	−0.223471	+	0.489332i	−0.987845	−	0.155440i	$-0.950320\pi$
$347$	−1444.49	+	3162.99i	−0.223471	+	0.489332i	0.764375	+	0.644772i	$0.223048\pi$
$348$	−16467.0	−	4835.15i	−2.53657	−	0.744803i
$349$	2854.61	+	3294.40i	0.437833	+	0.505286i	0.931187	−	0.364542i	$-0.118775\pi$
$349$	2854.61	+	3294.40i	0.437833	+	0.505286i	−0.493354	+	0.869829i	$0.664229\pi$
$350$	−339.344	+	218.083i	−0.0518249	+	0.0333059i
$351$	−1543.71	+	1781.54i	−0.234750	+	0.270916i
$352$	3715.46	−	25841.6i	0.562599	−	3.91296i
$353$	7649.67	−	2246.15i	1.15340	−	0.338670i	0.351537	−	0.936174i	$-0.385659\pi$
$353$	7649.67	−	2246.15i	1.15340	−	0.338670i	0.801866	+	0.597504i	$0.203841\pi$
$354$	−9044.49	−	5812.54i	−1.35794	−	0.872692i
$355$	−635.065	−	4416.98i	−0.0949458	−	0.660363i
$356$	6466.85	+	14160.4i	0.962759	+	2.10815i
$357$	−479.978	−	1051.00i	−0.0711572	−	0.155813i
$358$	266.828	+	1855.83i	0.0393919	+	0.273977i
$359$	4246.47	+	2729.04i	0.624290	+	0.401207i	0.814192	−	0.580596i	$-0.197180\pi$
$359$	4246.47	+	2729.04i	0.624290	+	0.401207i	−0.189901	+	0.981803i	$0.560817\pi$
$360$	−5322.44	+	1562.81i	−0.779214	+	0.228798i
$361$	862.660	−	5999.93i	0.125770	−	0.874753i
$362$	13674.7	−	15781.5i	1.98543	−	2.29131i
$363$	−1402.28	+	901.191i	−0.202757	+	0.130304i
$364$	688.794	+	794.911i	0.0991831	+	0.114463i
$365$	−3740.37	−	1098.27i	−0.536383	−	0.157496i
$366$	−1416.66	+	3102.05i	−0.202322	+	0.443024i
$367$	−9887.28			−1.40630			−0.703150	−	0.711042i	$-0.748224\pi$
$367$	−9887.28			−1.40630			−0.703150	+	0.711042i	$0.748224\pi$
$368$	−16884.1	+	25551.2i	−2.39169	+	3.61942i
$369$	−3385.98			−0.477689
$370$	−2327.65	+	5096.84i	−0.327051	+	0.716141i
$371$	−183.960	−	54.0156i	−0.0257432	−	0.00755890i
$372$	10016.3	+	11559.5i	1.39603	+	1.61110i
$373$	1769.69	−	1137.31i	0.245660	−	0.157876i	−0.412017	−	0.911176i	$-0.635176\pi$
$373$	1769.69	−	1137.31i	0.245660	−	0.157876i	0.657677	+	0.753300i	$0.271539\pi$
$374$	−11647.8	+	13442.3i	−1.61041	+	1.85852i
$375$	−65.6478	+	456.590i	−0.00904010	+	0.0628753i
$376$	−2351.38	+	690.427i	−0.322508	+	0.0946970i
$377$	−2701.20	−	1735.96i	−0.369016	−	0.237152i
$378$	−342.192	−	2380.00i	−0.0465620	−	0.323846i
$379$	−307.420	−	673.155i	−0.0416652	−	0.0912340i	0.887655	−	0.460509i	$-0.152333\pi$
$379$	−307.420	−	673.155i	−0.0416652	−	0.0912340i	−0.929320	+	0.369275i	$0.879606\pi$
$380$	1343.81	+	2942.53i	0.181410	+	0.397233i
$381$	−246.684	−	1715.73i	−0.0331706	−	0.230707i
$382$	−6110.49	−	3926.97i	−0.818429	−	0.525972i
$383$	7751.75	−	2276.12i	1.03419	−	0.303666i	0.279778	−	0.960065i	$-0.409739\pi$
$383$	7751.75	−	2276.12i	1.03419	−	0.303666i	0.754415	+	0.656398i	$0.227921\pi$
$384$	4108.29	−	28573.8i	0.545964	−	3.79727i
$385$	−281.774	+	325.185i	−0.0373001	+	0.0430466i
$386$	−9638.49	+	6194.28i	−1.27095	+	0.816790i
$387$	−3614.58	−	4171.45i	−0.474779	−	0.547924i
$388$	1814.01	+	532.640i	0.237351	+	0.0696925i
$389$	1477.51	−	3235.29i	0.192577	−	0.421686i	−0.788570	−	0.614944i	$-0.789178\pi$
$389$	1477.51	−	3235.29i	0.192577	−	0.421686i	0.981148	+	0.193259i	$0.0619057\pi$
$390$	1622.79			0.210701
$391$	10886.9	−	4805.39i	1.40812	−	0.621532i
$392$	27738.4			3.57398
$393$	−608.739	+	1332.95i	−0.0781345	+	0.171091i
$394$	13873.3	+	4073.56i	1.77392	+	0.520870i
$395$	3395.38	+	3918.48i	0.432507	+	0.499140i
$396$	−7648.31	+	4915.27i	−0.970561	+	0.623741i
$397$	−1138.31	+	1313.67i	−0.143904	+	0.166074i	−0.823126	−	0.567859i	$-0.807772\pi$
$397$	−1138.31	+	1313.67i	−0.143904	+	0.166074i	0.679222	+	0.733933i	$0.262317\pi$
$398$	−1353.30	+	9412.39i	−0.170439	+	1.18543i
$399$	−290.165	+	85.2001i	−0.0364071	+	0.0106901i
$400$	5839.31	+	3752.70i	0.729914	+	0.469087i
$401$	−220.890	−	1536.33i	−0.0275081	−	0.191323i	0.971434	−	0.237310i	$-0.0762657\pi$
$401$	−220.890	−	1536.33i	−0.0275081	−	0.191323i	−0.998942	+	0.0459873i	$0.985357\pi$
$402$	−4245.85	−	9297.12i	−0.526776	−	1.15348i
$403$	1188.77	+	2603.05i	0.146940	+	0.321755i
$404$	3409.93	+	23716.6i	0.419926	+	2.92065i
$405$	−793.383	−	509.876i	−0.0973420	−	0.0625579i
$406$	3142.49	−	922.718i	0.384136	−	0.112792i
$407$	−850.598	+	5916.04i	−0.103594	+	0.720509i
$408$	−21615.2	+	24945.3i	−2.62282	+	3.02690i
$409$	7134.54	−	4585.09i	0.862544	−	0.554323i	−0.0329200	−	0.999458i	$-0.510481\pi$
$409$	7134.54	−	4585.09i	0.862544	−	0.554323i	0.895464	+	0.445135i	$0.146844\pi$
$410$	4606.27	+	5315.92i	0.554848	+	0.640329i
$411$	−1696.79	−	498.223i	−0.203641	−	0.0597945i
$412$	−5723.68	+	12533.1i	−0.684431	+	1.49869i
$413$	1520.72			0.181186
$414$	8137.34	−	1064.45i	0.966011	−	0.126365i
$415$	5162.22			0.610611
$416$	5785.59	−	12668.7i	0.681880	−	1.49311i
$417$	8461.01	+	2484.38i	0.993615	+	0.291752i
$418$	3048.66	+	3518.34i	0.356734	+	0.411693i
$419$	9290.54	−	5970.67i	1.08323	−	0.696149i	0.127927	−	0.991784i	$-0.459168\pi$
$419$	9290.54	−	5970.67i	1.08323	−	0.696149i	0.955301	+	0.295635i	$0.0955312\pi$
$420$	−803.428	+	927.206i	−0.0933412	+	0.107721i
$421$	−1748.00	+	12157.6i	−0.202357	+	1.40742i	0.594909	+	0.803793i	$0.297188\pi$
$421$	−1748.00	+	12157.6i	−0.202357	+	1.40742i	−0.797266	+	0.603629i	$0.793721\pi$
$422$	−28830.1	+	8465.28i	−3.32566	+	0.976501i
$423$	332.765	+	213.855i	0.0382496	+	0.0245815i
$424$	779.478	+	5421.39i	0.0892802	+	0.620957i
$425$	−1120.44	−	2453.42i	−0.127881	−	0.280019i
$426$	−7606.78	−	16656.5i	−0.865140	−	1.89439i
$427$	−68.6477	−	477.455i	−0.00778008	−	0.0541117i
$428$	−33280.0	−	21387.7i	−3.75852	−	2.41546i
$429$	1660.90	−	487.684i	0.186921	−	0.0548849i
$430$	−1631.83	+	11349.6i	−0.183009	+	1.27286i
$431$	245.844	−	283.719i	0.0274753	−	0.0317082i	−0.741846	−	0.670571i	$-0.766049\pi$
$431$	245.844	−	283.719i	0.0274753	−	0.0317082i	0.769321	+	0.638863i	$0.220595\pi$
$432$	−34807.0	+	22369.1i	−3.87651	+	2.49128i
$433$	−6429.68	−	7420.25i	−0.713605	−	0.823543i	0.276918	−	0.960894i	$-0.410687\pi$
$433$	−6429.68	−	7420.25i	−0.713605	−	0.823543i	−0.990523	+	0.137350i	$0.956141\pi$
$434$	−2800.66	−	822.347i	−0.309760	−	0.0909537i
$435$	1555.86	−	3406.86i	0.171489	−	0.375509i
$436$	11299.9			1.24121
$437$	−839.417	−	2999.50i	−0.0918874	−	0.328342i
$438$	−15996.4			−1.74507
$439$	−343.428	+	752.002i	−0.0373369	+	0.0817564i	−0.927381	−	0.374117i	$-0.877946\pi$
$439$	−343.428	+	752.002i	−0.0373369	+	0.0817564i	0.890045	+	0.455874i	$0.150673\pi$
$440$	11794.1	+	3463.06i	1.27787	+	0.375216i
$441$	−2931.98	−	3383.68i	−0.316594	−	0.365369i
$442$	−7982.26	+	5129.89i	−0.858999	+	0.552045i
$443$	−1151.50	+	1328.90i	−0.123497	+	0.142523i	−0.814131	−	0.580681i	$-0.802786\pi$
$443$	−1151.50	+	1328.90i	−0.123497	+	0.142523i	0.690634	+	0.723205i	$0.257332\pi$
$444$	−2425.33	+	16868.5i	−0.259236	+	1.80303i
$445$	−3259.62	+	957.111i	−0.347238	+	0.101958i
$446$	−1388.09	−	892.073i	−0.147372	−	0.0947105i
$447$	852.402	+	5928.59i	0.0901951	+	0.627321i
$448$	3223.51	+	7058.51i	0.339948	+	0.744382i
$449$	−6002.44	−	13143.5i	−0.630897	−	1.38147i	−0.907322	−	0.420436i	$-0.861877\pi$
$449$	−6002.44	−	13143.5i	−0.630897	−	1.38147i	0.276426	−	0.961035i	$-0.410850\pi$
$450$	−264.707	−	1841.08i	−0.0277298	−	0.192865i
$451$	6311.99	+	4056.47i	0.659024	+	0.423529i
$452$	40575.1	−	11913.9i	4.22233	−	1.23979i
$453$	825.676	−	5742.70i	0.0856372	−	0.595620i
$454$	−12831.2	+	14808.0i	−1.32643	+	1.53078i
$455$	−193.100	+	124.098i	−0.0198960	+	0.0127864i
$456$	5657.49	+	6529.09i	0.581000	+	0.670510i
$457$	−2245.15	−	659.235i	−0.229811	−	0.0674785i	0.164800	−	0.986327i	$-0.447302\pi$
$457$	−2245.15	−	659.235i	−0.229811	−	0.0674785i	−0.394610	+	0.918849i	$0.629120\pi$
$458$	−276.668	+	605.818i	−0.0282267	+	0.0618079i
$459$	16077.2			1.63490
$460$	−9443.72	−	8395.83i	−0.957208	−	0.850995i
$461$	−375.906			−0.0379777			−0.0189888	−	0.999820i	$-0.506045\pi$
$461$	−375.906			−0.0379777			−0.0189888	+	0.999820i	$0.506045\pi$
$462$	−733.475	+	1606.09i	−0.0738622	+	0.161736i
$463$	6424.71	+	1886.47i	0.644885	+	0.189355i	0.587790	−	0.809013i	$-0.299998\pi$
$463$	6424.71	+	1886.47i	0.644885	+	0.189355i	0.0570949	+	0.998369i	$0.481816\pi$
$464$	−36906.4	−	42592.2i	−3.69254	−	4.26141i
$465$	−2808.03	+	1804.61i	−0.280041	+	0.179971i
$466$	9403.79	−	10852.6i	0.934812	−	1.07883i
$467$	−1229.30	+	8549.96i	−0.121810	+	0.847206i	0.833694	+	0.552227i	$0.186222\pi$
$467$	−1229.30	+	8549.96i	−0.121810	+	0.847206i	−0.955504	+	0.294979i	$0.904687\pi$
$468$	−4653.54	+	1366.40i	−0.459637	+	0.134962i
$469$	1216.19	+	781.599i	0.119741	+	0.0769528i
$470$	−116.944	−	813.362i	−0.0114771	−	0.0798247i
$471$	−5610.23	−	12284.7i	−0.548845	−	1.20180i
$472$	−18046.9	−	39517.2i	−1.75991	−	3.85366i
$473$	1740.66	+	12106.6i	0.169209	+	1.17687i
$474$	17898.5	+	11502.7i	1.73440	+	1.11463i
$475$	−677.348	+	198.887i	−0.0654292	+	0.0192117i
$476$	1020.90	−	7100.53i	0.0983046	−	0.683724i
$477$	578.939	−	668.131i	0.0555719	−	0.0641333i
$478$	19810.7	−	12731.6i	1.89565	−	1.21826i
$479$	−1182.94	−	1365.19i	−0.112839	−	0.130223i	0.696520	−	0.717537i	$-0.254731\pi$
$479$	−1182.94	−	1365.19i	−0.112839	−	0.130223i	−0.809359	+	0.587314i	$0.800185\pi$
$480$	15587.1	+	4576.78i	1.48219	+	0.435210i
$481$	−1324.52	+	2900.30i	−0.125557	+	0.274932i
$482$	−12188.1			−1.15176
$483$	902.550	−	762.170i	0.0850257	−	0.0718011i
$484$	−10349.1			−0.971930
$485$	−171.393	+	375.299i	−0.0160465	+	0.0351370i
$486$	17750.9	+	5212.12i	1.65678	+	0.486475i
$487$	−2163.44	−	2496.74i	−0.201304	−	0.232317i	0.646118	−	0.763238i	$-0.276392\pi$
$487$	−2163.44	−	2496.74i	−0.201304	−	0.232317i	−0.847421	+	0.530921i	$0.821846\pi$
$488$	−11592.4	+	7450.00i	−1.07534	+	0.691077i
$489$	7471.92	−	8623.05i	0.690985	−	0.797439i
$490$	−1323.66	+	9206.29i	−0.122035	+	0.848771i
$491$	−2828.35	+	830.477i	−0.259962	+	0.0763318i	−0.409117	−	0.912482i	$-0.634163\pi$
$491$	−2828.35	+	830.477i	−0.259962	+	0.0763318i	0.149154	+	0.988814i	$0.452345\pi$
$492$	17997.5	+	11566.3i	1.64917	+	1.05986i
$493$	3116.55	+	21676.1i	0.284711	+	1.98021i
$494$	1031.68	+	2259.07i	0.0939626	+	0.205749i
$495$	−824.206	−	1804.76i	−0.0748390	−	0.163874i
$496$	7148.07	+	49716.0i	0.647093	+	4.50063i
$497$	2178.90	+	1400.30i	0.196654	+	0.126382i
$498$	20324.9	−	5967.94i	1.82888	−	0.537007i
$499$	536.771	−	3733.32i	0.0481546	−	0.334923i	−0.951475	−	0.307725i	$-0.900432\pi$
$499$	536.771	−	3733.32i	0.0481546	−	0.334923i	0.999630	−	0.0271981i	$-0.00865849\pi$
$500$	−1875.49	+	2164.43i	−0.167749	+	0.193592i
$501$	−2658.99	+	1708.83i	−0.237116	+	0.152385i
$502$	13452.1	+	15524.5i	1.19601	+	1.38026i
$503$	−9230.07	−	2710.19i	−0.818188	−	0.240242i	−0.154253	−	0.988031i	$-0.549297\pi$
$503$	−9230.07	−	2710.19i	−0.818188	−	0.240242i	−0.663936	+	0.747790i	$0.731115\pi$
$504$	1337.50	−	2928.72i	0.118208	−	0.258840i
$505$	−5228.89			−0.460758
$506$	−16444.5	−	7764.38i	−1.44476	−	0.682152i
$507$	−7184.13			−0.629306
$508$	4470.63	−	9789.31i	0.390457	−	0.854981i
$509$	17379.6	+	5103.10i	1.51343	+	0.444383i	0.929932	−	0.367731i	$-0.119865\pi$
$509$	17379.6	+	5103.10i	1.51343	+	0.444383i	0.583498	+	0.812114i	$0.301683\pi$
$510$	−7247.79	−	8364.39i	−0.629289	−	0.726238i
$511$	1903.45	−	1223.28i	0.164782	−	0.105899i
$512$	39488.1	−	45571.7i	3.40848	−	3.93360i
$513$	598.861	−	4165.17i	0.0515406	−	0.358473i
$514$	16936.6	−	4973.03i	1.45339	−	0.426753i
$515$	−2529.50	−	1625.61i	−0.216433	−	0.139093i
$516$	4963.18	+	34519.7i	0.423434	+	2.94505i
$517$	−364.123	−	797.318i	−0.0309750	−	0.0678259i
$518$	−1351.02	−	2958.31i	−0.114595	−	0.250928i
$519$	−97.5821	−	678.698i	−0.00825313	−	0.0574018i
$520$	5516.37	+	3545.16i	0.465210	+	0.298972i
$521$	18562.0	−	5450.30i	1.56088	−	0.458315i	0.616549	−	0.787317i	$-0.288530\pi$
$521$	18562.0	−	5450.30i	1.56088	−	0.458315i	0.944329	+	0.329002i	$0.106712\pi$
$522$	−2149.23	+	14948.2i	−0.180209	+	1.25338i
$523$	3723.78	−	4297.47i	0.311338	−	0.359303i	−0.578417	−	0.815741i	$-0.696330\pi$
$523$	3723.78	−	4297.47i	0.311338	−	0.359303i	0.889755	+	0.456438i	$0.150875\pi$
$524$	−7653.70	+	4918.73i	−0.638079	+	0.410068i
$525$	−175.332	−	202.344i	−0.0145755	−	0.0168210i
$526$	8626.43	+	2532.95i	0.715076	+	0.209965i
$527$	8107.60	−	17753.2i	0.670157	−	1.46744i
$528$	30382.5			2.50422
$529$	7731.07	+	9395.02i	0.635413	+	0.772172i
$530$	−1836.54			−0.150517
$531$	−2912.95	+	6378.47i	−0.238063	+	0.521284i
$532$	−1801.52	−	528.975i	−0.146816	−	0.0431090i
$533$	2621.15	+	3024.97i	0.213010	+	0.245827i
$534$	−11727.4	+	7536.76i	−0.950366	+	0.610763i
$535$	5653.53	−	6524.53i	0.456867	−	0.527252i
$536$	5877.55	−	40879.3i	0.473641	−	3.29425i
$537$	−1194.05	+	350.604i	−0.0959535	+	0.0281745i
$538$	−3166.88	−	2035.23i	−0.253781	−	0.163095i
$539$	1411.94	+	9820.26i	0.112832	+	0.784766i
$540$	−7091.74	−	15528.7i	−0.565148	−	1.23750i
$541$	1888.80	+	4135.89i	0.150103	+	0.328680i	0.969715	−	0.244239i	$-0.0785382\pi$
$541$	1888.80	+	4135.89i	0.150103	+	0.328680i	−0.819612	+	0.572919i	$0.805811\pi$
$542$	−2253.49	−	15673.4i	−0.178590	−	1.24212i
$543$	11659.9	+	7493.38i	0.921501	+	0.592213i
$544$	−91138.3	+	26760.6i	−7.18295	+	2.10910i
$545$	−350.945	+	2440.88i	−0.0275832	+	0.191845i
$546$	−616.815	+	711.843i	−0.0483466	+	0.0557950i
$547$	−4570.17	+	2937.07i	−0.357233	+	0.229580i	−0.706930	−	0.707283i	$-0.749921\pi$
$547$	−4570.17	+	2937.07i	−0.357233	+	0.229580i	0.349698	+	0.936863i	$0.386284\pi$
$548$	−7190.04	−	8297.75i	−0.560480	−	0.646829i
$549$	2134.12	+	626.634i	0.165905	+	0.0487142i
$550$	−1712.19	+	3749.17i	−0.132742	+	0.290664i
$551$	5731.76			0.443160
$552$	−30516.5	−	14408.6i	−2.35302	−	1.11100i
$553$	−3009.42			−0.231417
$554$	16606.7	−	36363.7i	1.27356	−	2.78871i
$555$	−3568.43	−	1047.78i	−0.272921	−	0.0801369i
$556$	35852.9	+	41376.5i	2.73472	+	3.15603i
$557$	−13039.2	+	8379.78i	−0.991900	+	0.637455i	−0.932648	−	0.360788i	$-0.882508\pi$
$557$	−13039.2	+	8379.78i	−0.991900	+	0.637455i	−0.0592520	+	0.998243i	$0.518872\pi$
$558$	8813.90	−	10171.8i	0.668678	−	0.771695i
$559$	−928.576	+	6458.39i	−0.0702586	+	0.488660i
$560$	−3865.62	+	1135.05i	−0.291701	+	0.0856511i
$561$	−9931.66	−	6382.69i	−0.747442	−	0.480352i
$562$	−5852.89	−	40707.7i	−0.439304	−	3.05543i
$563$	5514.51	+	12075.1i	0.412804	+	0.903916i	0.995810	+	0.0914474i	$0.0291493\pi$
$563$	5514.51	+	12075.1i	0.412804	+	0.903916i	−0.583005	+	0.812468i	$0.698123\pi$
$564$	−1038.23	−	2273.41i	−0.0775131	−	0.169730i
$565$	1313.36	+	9134.60i	0.0977936	+	0.680169i
$566$	−29071.6	−	18683.2i	−2.15896	−	1.38748i
$567$	525.220	−	154.218i	0.0389015	−	0.0114225i
$568$	10530.1	−	73238.5i	0.777876	−	5.41025i
$569$	−1270.39	+	1466.11i	−0.0935984	+	0.108018i	−0.800616	−	0.599177i	$-0.795494\pi$
$569$	−1270.39	+	1466.11i	−0.0935984	+	0.108018i	0.707018	+	0.707196i	$0.250040\pi$
$570$	−2436.96	+	1566.14i	−0.179075	+	0.115085i
$571$	−5477.09	−	6320.90i	−0.401417	−	0.463260i	0.518670	−	0.854975i	$-0.326427\pi$
$571$	−5477.09	−	6320.90i	−0.401417	−	0.463260i	−0.920087	+	0.391715i	$0.871882\pi$
$572$	10311.9	+	3027.85i	0.753780	+	0.221330i
$573$	2002.77	−	4385.45i	0.146015	−	0.319729i
$574$	−4082.67			−0.296877
$575$	2106.87	−	1779.18i	0.152805	−	0.129038i
$576$	−35780.6			−2.58830
$577$	−11182.3	+	24485.9i	−0.806805	+	1.76666i	−0.186234	+	0.982505i	$0.559628\pi$
$577$	−11182.3	+	24485.9i	−0.806805	+	1.76666i	−0.620571	+	0.784151i	$0.713099\pi$
$578$	35882.9	+	10536.2i	2.58223	+	0.758212i
$579$	−4980.01	−	5747.24i	−0.357448	−	0.412517i
$580$	19561.9	−	12571.6i	1.40045	−	0.900016i
$581$	−1962.13	+	2264.42i	−0.140108	+	0.161694i
$582$	−240.942	+	1675.79i	−0.0171604	+	0.119353i
$583$	−1879.66	+	551.919i	−0.133530	+	0.0392078i
$584$	−54376.8	−	34945.8i	−3.85296	−	2.47615i
$585$	−150.628	−	1047.64i	−0.0106457	−	0.0740423i
$586$	10132.1	+	22186.2i	0.714255	+	1.56400i
$587$	−1493.83	−	3271.02i	−0.105037	−	0.229999i	0.849815	−	0.527081i	$-0.176714\pi$
$587$	−1493.83	−	3271.02i	−0.105037	−	0.229999i	−0.954852	+	0.297082i	$0.903986\pi$
$588$	4025.89	+	28000.7i	0.282356	+	1.96383i
$589$	−4297.36	−	2761.74i	−0.300627	−	0.193201i
$590$	13976.8	−	4103.97i	0.975284	−	0.286369i
$591$	−1365.80	+	9499.33i	−0.0950615	+	0.661168i
$592$	−36647.8	+	42293.9i	−2.54429	+	2.93626i
$593$	−3670.54	+	2358.91i	−0.254184	+	0.163354i	−0.661527	−	0.749921i	$-0.730091\pi$
$593$	−3670.54	+	2358.91i	−0.254184	+	0.163354i	0.407344	+	0.913275i	$0.366455\pi$
$594$	−16088.8	−	18567.5i	−1.11133	−	1.28255i
$595$	1502.07	+	441.048i	0.103494	+	0.0303886i
$596$	−15448.0	+	33826.3i	−1.06170	+	2.32480i
$597$	−6311.64			−0.432694
$598$	−7250.22	−	6445.72i	−0.495792	−	0.440778i
$599$	−1150.64			−0.0784875			−0.0392437	−	0.999230i	$-0.512495\pi$
$599$	−1150.64			−0.0784875			−0.0392437	+	0.999230i	$0.512495\pi$
$600$	−3177.36	+	6957.45i	−0.216192	+	0.473395i
$601$	−4954.22	−	1454.69i	−0.336251	−	0.0987323i	0.109248	−	0.994015i	$-0.465156\pi$
$601$	−4954.22	−	1454.69i	−0.336251	−	0.0987323i	−0.445499	+	0.895282i	$0.646974\pi$
$602$	−4358.30	−	5029.75i	−0.295068	−	0.340527i
$603$	−5607.94	+	3604.00i	−0.378728	+	0.243394i
$604$	23588.7	−	27222.8i	1.58909	−	1.83391i
$605$	321.416	−	2235.50i	0.0215991	−	0.150225i
$606$	−20587.4	+	6045.02i	−1.38005	+	0.405218i
$607$	−940.100	−	604.166i	−0.0628624	−	0.0403992i	0.508832	−	0.860866i	$-0.330077\pi$
$607$	−940.100	−	604.166i	−0.0628624	−	0.0403992i	−0.571695	+	0.820467i	$0.693714\pi$
$608$	3538.13	+	24608.2i	0.236003	+	1.64144i
$609$	903.053	+	1977.41i	0.0600880	+	0.131574i
$610$	−1919.44	−	4203.00i	−0.127403	−	0.278974i
$611$	−66.5456	−	462.835i	−0.00440613	−	0.0306453i
$612$	27826.7	+	17883.2i	1.83796	+	1.18118i
$613$	−423.967	+	124.488i	−0.0279345	+	0.00820231i	−0.295670	−	0.955290i	$-0.595543\pi$
$613$	−423.967	+	124.488i	−0.0279345	+	0.00820231i	0.267735	+	0.963492i	$0.413725\pi$
$614$	−4563.04	+	31736.6i	−0.299917	+	2.08597i
$615$	−3057.38	+	3528.40i	−0.200464	+	0.231348i
$616$	−6001.97	+	3857.23i	−0.392575	+	0.252293i
$617$	−15631.6	−	18039.9i	−1.01995	−	1.17708i	−0.984081	−	0.177723i	$-0.943127\pi$
$617$	−15631.6	−	18039.9i	−1.01995	−	1.17708i	−0.0358650	−	0.999357i	$-0.511419\pi$
$618$	−11838.6	−	3476.13i	−0.770580	−	0.226263i
$619$	4319.12	−	9457.56i	0.280453	−	0.614106i	−0.716015	−	0.698085i	$-0.754036\pi$
$619$	4319.12	−	9457.56i	0.280453	−	0.614106i	0.996468	+	0.0839792i	$0.0267629\pi$
$620$	−20723.8			−1.34240
$621$	4429.89	+	15829.4i	0.286257	+	1.02288i
$622$	21457.9			1.38325
$623$	819.126	−	1793.64i	0.0526767	−	0.115346i
$624$	15551.4	+	4566.30i	0.997681	+	0.292946i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	29941.1	−	19241.9i	1.91164	−	1.22853i
$627$	−2023.52	+	2335.27i	−0.128886	+	0.148743i
$628$	11932.8	−	82994.8i	0.758237	−	5.27365i
$629$	20864.7	−	6126.43i	1.32262	−	0.388358i
$630$	908.207	+	583.669i	0.0574347	+	0.0369110i
$631$	1575.68	+	10959.1i	0.0994086	+	0.691402i	0.977194	+	0.212348i	$0.0681111\pi$
$631$	1575.68	+	10959.1i	0.0994086	+	0.691402i	−0.877786	+	0.479054i	$0.840980\pi$
$632$	35713.8	+	78202.4i	2.24782	+	4.92203i
$633$	−8284.87	−	18141.3i	−0.520212	−	1.13910i
$634$	−2385.04	−	16588.3i	−0.149404	−	1.03912i
$635$	1975.73	+	1269.73i	0.123472	+	0.0793505i
$636$	−5359.52	+	1573.70i	−0.334149	+	0.0981151i
$637$	−753.216	+	5238.73i	−0.0468501	+	0.325850i
$638$	21914.8	−	25291.0i	1.35990	−	1.56940i
$639$	−10047.1	+	6456.86i	−0.621997	+	0.399733i
$640$	25613.6	+	29559.6i	1.58198	+	1.82570i
$641$	−24336.4	−	7145.81i	−1.49958	−	0.440316i	−0.573994	−	0.818859i	$-0.694607\pi$
$641$	−24336.4	−	7145.81i	−1.49958	−	0.440316i	−0.925584	+	0.378543i	$0.876425\pi$
$642$	14716.5	−	32224.6i	0.904693	−	1.98100i
$643$	−29088.2			−1.78402			−0.892010	−	0.452016i	$-0.850705\pi$
$643$	−29088.2			−1.78402			−0.892010	+	0.452016i	$0.850705\pi$
$644$	7272.37	−	951.305i	0.444987	−	0.0582091i
$645$	−7610.70			−0.464606
$646$	7036.21	−	15407.2i	0.428539	−	0.938369i
$647$	−4134.66	−	1214.04i	−0.251237	−	0.0737698i	0.153689	−	0.988119i	$-0.450885\pi$
$647$	−4134.66	−	1214.04i	−0.251237	−	0.0737698i	−0.404926	+	0.914349i	$0.632703\pi$
$648$	−10240.5	−	11818.1i	−0.620807	−	0.716450i
$649$	13071.7	−	8400.68i	0.790616	−	0.508098i
$650$	−1439.87	+	1661.69i	−0.0868864	+	0.100272i
$651$	275.720	−	1917.67i	0.0165995	−	0.115452i
$652$	67970.4	−	19957.9i	4.08271	−	1.19879i
$653$	932.290	+	599.147i	0.0558704	+	0.0359057i	0.568278	−	0.822837i	$-0.307610\pi$
$653$	932.290	+	599.147i	0.0558704	+	0.0359057i	−0.512407	+	0.858742i	$0.671246\pi$
$654$	1440.09	+	10016.1i	0.0861041	+	0.598867i
$655$	−824.786	−	1806.03i	−0.0492016	−	0.107737i
$656$	29184.2	+	63904.4i	1.73697	+	3.80342i
$657$	1484.80	+	10327.0i	0.0881696	+	0.613233i
$658$	401.233	+	257.857i	0.0237716	+	0.0152771i
$659$	−14845.7	+	4359.09i	−0.877552	+	0.257672i	−0.689324	−	0.724453i	$-0.742092\pi$
$659$	−14845.7	+	4359.09i	−0.877552	+	0.257672i	−0.188228	+	0.982125i	$0.560274\pi$
$660$	−1784.04	+	12408.3i	−0.105218	+	0.731805i
$661$	5461.60	−	6303.02i	0.321379	−	0.370891i	−0.571954	−	0.820285i	$-0.693815\pi$
$661$	5461.60	−	6303.02i	0.321379	−	0.370891i	0.893334	+	0.449394i	$0.148360\pi$
$662$	−32393.4	+	20818.0i	−1.90182	+	1.22223i
$663$	−4124.27	−	4759.66i	−0.241589	−	0.278808i
$664$	82128.3	+	24115.0i	4.79999	+	1.40941i
$665$	170.214	−	372.717i	0.00992574	−	0.0217343i
$666$	14996.2			0.872506
$667$	−20483.2	+	9041.09i	−1.18907	+	0.524846i
$668$	−19623.9			−1.13663
$669$	454.960	−	996.223i	0.0262926	−	0.0575728i
$670$	13287.2	+	3901.48i	0.766165	+	0.224966i
$671$	−3227.61	−	3724.86i	−0.185694	−	0.214302i
$672$	−7932.20	+	5097.71i	−0.455344	+	0.292632i
$673$	6050.12	−	6982.21i	0.346531	−	0.399918i	−0.555551	−	0.831482i	$-0.687493\pi$
$673$	6050.12	−	6982.21i	0.346531	−	0.399918i	0.902082	+	0.431564i	$0.142038\pi$
$674$	−3782.69	+	26309.2i	−0.216177	+	1.50355i
$675$	3574.60	−	1049.60i	0.203832	−	0.0598504i
$676$	−37522.9	−	24114.5i	−2.13489	−	1.37201i
$677$	806.441	+	5608.92i	0.0457815	+	0.318417i	0.999824	+	0.0187467i	$0.00596762\pi$
$677$	806.441	+	5608.92i	0.0457815	+	0.318417i	−0.954043	+	0.299670i	$0.903123\pi$
$678$	15731.3	+	34446.8i	0.891089	+	1.95121i
$679$	−99.4803	−	217.831i	−0.00562254	−	0.0123116i
$680$	−6364.59	−	44266.7i	−0.358928	−	2.49640i
$681$	−10940.7	−	7031.15i	−0.615635	−	0.395645i
$682$	−28616.5	+	8402.55i	−1.60672	+	0.471775i
$683$	−1290.61	+	8976.40i	−0.0723044	+	0.502888i	0.921200	+	0.389090i	$0.127211\pi$
$683$	−1290.61	+	8976.40i	−0.0723044	+	0.502888i	−0.993504	+	0.113798i	$0.963698\pi$
$684$	5669.55	−	6543.01i	0.316931	−	0.365758i
$685$	2015.69	−	1295.41i	0.112432	−	0.0722554i
$686$	−7159.49	−	8262.49i	−0.398470	−	0.459859i
$687$	−424.148	−	124.541i	−0.0235550	−	0.00691636i
$688$	−47574.2	+	104173.i	−2.63626	+	5.77261i
$689$	−1045.06			−0.0577847
$690$	6238.40	−	9440.76i	0.344191	−	0.520875i
$691$	−21376.2			−1.17683			−0.588415	−	0.808559i	$-0.700248\pi$
$691$	−21376.2			−1.17683			−0.588415	+	0.808559i	$0.700248\pi$
$692$	1768.47	−	3872.40i	0.0971489	−	0.212726i
$693$	1104.94	+	324.439i	0.0605673	+	0.0177842i
$694$	−12660.2	−	14610.7i	−0.692473	−	0.799156i
$695$	−10051.2	+	6459.51i	−0.548580	+	0.352551i
$696$	40667.9	−	46933.2i	2.21482	−	2.55603i
$697$	3884.96	−	27020.5i	0.211124	−	1.46840i
$698$	−23254.1	+	6828.03i	−1.26101	+	0.370265i
$699$	8018.26	+	5153.02i	0.433875	+	0.278834i
$700$	−236.569	−	1645.38i	−0.0127735	−	0.0888419i
$701$	−9501.10	−	20804.5i	−0.511914	−	1.12093i	−0.972411	−	0.233274i	$-0.925056\pi$
$701$	−9501.10	−	20804.5i	−0.511914	−	1.12093i	0.460498	−	0.887661i	$-0.347671\pi$
$702$	−5444.53	−	11921.9i	−0.292722	−	0.640971i
$703$	−810.000	−	5633.68i	−0.0434562	−	0.302245i
$704$	66700.6	+	42865.9i	3.57084	+	2.29484i
$705$	523.321	−	153.661i	0.0279566	−	0.00820880i
$706$	−6308.29	+	43875.2i	−0.336283	+	2.33890i
$707$	1987.48	−	2293.67i	0.105724	−	0.122012i
$708$	37271.6	−	23953.0i	1.97847	−	1.27148i
$709$	−13591.6	−	15685.5i	−0.719947	−	0.830863i	0.271354	−	0.962480i	$-0.412529\pi$
$709$	−13591.6	−	15685.5i	−0.719947	−	0.830863i	−0.991301	+	0.131616i	$0.957983\pi$
$710$	23805.1	+	6989.82i	1.25830	+	0.369469i
$711$	5764.56	−	12622.6i	0.304062	−	0.665803i
$712$	−56330.0			−2.96497
$713$	19713.4	+	3090.93i	1.03545	+	0.162351i
$714$	6423.91			0.336707
$715$	−974.302	+	2133.42i	−0.0509606	+	0.111588i
$716$	−7413.40	−	2176.77i	−0.386944	−	0.113617i
$717$	10235.8	+	11812.7i	0.533141	+	0.615278i
$718$	−23609.6	+	15173.0i	−1.22716	+	0.788650i
$719$	−19764.8	+	22809.8i	−1.02518	+	1.18312i	−0.0422513	+	0.999107i	$0.513453\pi$
$719$	−19764.8	+	22809.8i	−1.02518	+	1.18312i	−0.982925	+	0.184009i	$0.941092\pi$
$720$	2643.80	−	18388.1i	0.136845	−	0.951781i
$721$	1674.53	−	491.686i	0.0864948	−	0.0253972i
$722$	28351.6	+	18220.4i	1.46141	+	0.939189i
$723$	−1151.29	−	8007.38i	−0.0592211	−	0.411892i
$724$	35747.5	+	78276.2i	1.83501	+	4.01811i
$725$	2108.05	+	4615.98i	0.107987	+	0.236460i
$726$	−1318.92	−	9173.29i	−0.0674239	−	0.468943i
$727$	−20186.4	−	12973.0i	−1.02981	−	0.661820i	−0.0873650	−	0.996176i	$-0.527845\pi$
$727$	−20186.4	−	12973.0i	−1.02981	−	0.661820i	−0.942447	+	0.334357i	$0.891481\pi$
$728$	−3651.84	+	1072.28i	−0.185915	+	0.0545896i
$729$	−2472.31	+	17195.3i	−0.125606	+	0.873611i
$730$	14193.3	−	16379.9i	0.719611	−	0.830475i
$731$	37435.8	−	24058.6i	1.89414	−	1.21729i
$732$	−9202.95	−	10620.8i	−0.464687	−	0.536277i
$733$	−4596.20	−	1349.57i	−0.231602	−	0.0680046i	0.163872	−	0.986482i	$-0.447602\pi$
$733$	−4596.20	−	1349.57i	−0.231602	−	0.0680046i	−0.395474	+	0.918477i	$0.629420\pi$
$734$	22836.0	−	50003.8i	1.14835	−	2.51454i
$735$	−6173.44			−0.309810
$736$	−51460.2	−	82359.7i	−2.57724	−	4.12475i
$737$	14771.7			0.738295
$738$	7820.37	−	17124.2i	0.390070	−	0.854135i
$739$	−7674.27	−	2253.37i	−0.382006	−	0.112167i	0.0850910	−	0.996373i	$-0.472882\pi$
$739$	−7674.27	−	2253.37i	−0.382006	−	0.112167i	−0.467097	+	0.884206i	$0.654700\pi$
$740$	−15120.9	−	17450.5i	−0.751158	−	0.866883i
$741$	−1386.72	+	891.192i	−0.0687483	+	0.0441819i
$742$	698.059	−	805.603i	0.0345371	−	0.0398580i
$743$	−2492.13	+	17333.2i	−0.123052	+	0.855844i	0.831015	+	0.556250i	$0.187760\pi$
$743$	−2492.13	+	17333.2i	−0.123052	+	0.855844i	−0.954067	+	0.299594i	$0.903149\pi$
$744$	−53104.4	+	15592.9i	−2.61680	+	0.768363i
$745$	−6827.02	−	4387.46i	−0.335735	−	0.215764i
$746$	1664.49	+	11576.8i	0.0816907	+	0.568171i
$747$	−5739.35	−	12567.4i	−0.281114	−	0.615553i
$748$	−30448.9	−	66673.9i	−1.48840	−	3.25914i
$749$	713.123	+	4959.88i	0.0347890	+	0.241963i
$750$	−2157.53	−	1386.56i	−0.105043	−	0.0675068i
$751$	5669.84	−	1664.82i	0.275493	−	0.0808922i	−0.141067	−	0.990000i	$-0.545053\pi$
$751$	5669.84	−	1664.82i	0.275493	−	0.0808922i	0.416561	+	0.909108i	$0.363235\pi$
$752$	1168.00	−	8123.59i	0.0566389	−	0.393932i
$753$	−8928.69	+	10304.3i	−0.432111	+	0.498683i
$754$	15018.2	−	9651.61i	0.725372	−	0.466168i
$755$	5147.76	+	5940.83i	0.248141	+	0.286370i
$756$	9507.27	+	2791.59i	0.457376	+	0.134298i
$757$	983.518	−	2153.60i	0.0472214	−	0.103400i	−0.884551	−	0.466444i	$-0.845535\pi$
$757$	983.518	−	2153.60i	0.0472214	−	0.103400i	0.931772	+	0.363043i	$0.118262\pi$
$758$	4114.44			0.197154
$759$	3547.74	−	11537.2i	0.169664	−	0.551745i
$760$	−11705.4			−0.558681
$761$	−12065.9	+	26420.6i	−0.574754	+	1.25854i	0.369473	+	0.929242i	$0.379538\pi$
$761$	−12065.9	+	26420.6i	−0.574754	+	1.25854i	−0.944227	+	0.329295i	$0.893189\pi$
$762$	9246.85	+	2715.12i	0.439604	+	0.129079i
$763$	−937.306	−	1081.71i	−0.0444728	−	0.0513244i
$764$	25180.8	−	16182.7i	1.19242	−	0.766324i

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)

\(f(q)\)	\(=\)	\(q+(-2.30963 + 5.05739i) q^{2} +(-3.54080 - 1.03967i) q^{3} +(-15.0039 - 17.3154i) q^{4} +(4.20627 - 2.70320i) q^{5} +(13.4360 - 15.5060i) q^{6} +(-0.413013 + 2.87257i) q^{7} +(79.5474 - 23.3572i) q^{8} +(-11.2575 - 7.23474i) q^{9} +O(q^{10})\)	\(q+(-2.30963 + 5.05739i) q^{2} +(-3.54080 - 1.03967i) q^{3} +(-15.0039 - 17.3154i) q^{4} +(4.20627 - 2.70320i) q^{5} +(13.4360 - 15.5060i) q^{6} +(-0.413013 + 2.87257i) q^{7} +(79.5474 - 23.3572i) q^{8} +(-11.2575 - 7.23474i) q^{9} +(3.95622 + 27.5161i) q^{10} +(12.3183 + 26.9733i) q^{11} +(35.1235 + 76.9096i) q^{12} +(2.25124 + 15.6577i) q^{13} +(-13.5738 - 8.72334i) q^{14} +(-17.7040 + 5.19837i) q^{15} +(-39.5134 + 274.822i) q^{16} +(70.6504 - 81.5349i) q^{17} +(62.5895 - 40.2239i) q^{18} +(-18.4918 - 21.3407i) q^{19} +(-109.918 - 32.2747i) q^{20} +(4.44893 - 9.74179i) q^{21} -164.865 q^{22} +(99.7449 + 47.0953i) q^{23} -305.946 q^{24} +(10.3854 - 22.7408i) q^{25} +(-84.3869 - 24.7782i) q^{26} +(97.5876 + 112.622i) q^{27} +(55.9365 - 35.9482i) q^{28} +(-132.925 + 153.404i) q^{29} +(14.5996 - 101.542i) q^{30} +(173.575 - 50.9661i) q^{31} +(-740.662 - 475.995i) q^{32} +(-15.5733 - 108.314i) q^{33} +(249.177 + 545.622i) q^{34} +(6.02789 + 13.1992i) q^{35} +(43.6335 + 303.477i) q^{36} +(169.563 + 108.972i) q^{37} +(150.637 - 44.2311i) q^{38} +(8.30773 - 57.7816i) q^{39} +(271.458 - 313.280i) q^{40} +(212.862 - 136.798i) q^{41} +(38.9926 + 44.9999i) q^{42} +(395.764 + 116.207i) q^{43} +(282.232 - 618.002i) q^{44} -66.9090 q^{45} +(-468.553 + 395.676i) q^{46} -29.5595 q^{47} +(425.634 - 932.009i) q^{48} +(321.025 + 94.2615i) q^{49} +(91.0227 + 105.046i) q^{50} +(-334.929 + 215.246i) q^{51} +(237.343 - 273.908i) q^{52} +(-9.40198 + 65.3922i) q^{53} +(-794.965 + 233.423i) q^{54} +(124.729 + 80.1582i) q^{55} +(34.2411 + 238.152i) q^{56} +(43.2885 + 94.7885i) q^{57} +(-468.814 - 1026.56i) q^{58} +(-74.5739 - 518.673i) q^{59} +(355.641 + 228.557i) q^{60} +(-159.479 + 46.8274i) q^{61} +(-143.138 + 995.547i) q^{62} +(25.4318 - 29.3498i) q^{63} +(2249.37 - 1445.58i) q^{64} +(51.7954 + 59.7751i) q^{65} +(583.756 + 171.406i) q^{66} +(206.940 - 453.135i) q^{67} -2471.84 q^{68} +(-304.213 - 270.457i) q^{69} -80.6759 q^{70} +(370.749 - 811.828i) q^{71} +(-1064.49 - 312.562i) q^{72} +(-510.565 - 589.224i) q^{73} +(-942.741 + 605.863i) q^{74} +(-60.4156 + 69.7233i) q^{75} +(-92.0737 + 640.386i) q^{76} +(-82.5703 + 24.2448i) q^{77} +(273.036 + 175.470i) q^{78} +(147.577 + 1026.42i) q^{79} +(576.696 + 1262.79i) q^{80} +(-78.3553 - 171.574i) q^{81} +(200.208 + 1392.48i) q^{82} +(868.547 + 558.181i) q^{83} +(-235.434 + 69.1298i) q^{84} +(76.7690 - 533.940i) q^{85} +(-1501.77 + 1733.14i) q^{86} +(630.151 - 404.974i) q^{87} +(1609.91 + 1857.94i) q^{88} +(-651.924 - 191.422i) q^{89} +(154.535 - 338.385i) q^{90} -45.9077 q^{91} +(-681.087 - 2433.74i) q^{92} -667.581 q^{93} +(68.2715 - 149.494i) q^{94} +(-135.470 - 39.7775i) q^{95} +(2127.66 + 2455.45i) q^{96} +(-69.4174 + 44.6119i) q^{97} +(-1218.17 + 1405.84i) q^{98} +(56.4721 - 392.772i) 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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