LMFDB - Embedded newform 115.4.g.a.6.3

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			6.3
Character	$\chi$	$=$	115.6
Dual form			115.4.g.a.96.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54534 + 3.38383i) q^{2} +(4.29324 + 1.26061i) q^{3} +(-3.82332 - 4.41235i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-10.9002 + 12.5795i) q^{6} +(-1.59229 + 11.0746i) q^{7} +(-7.71551 + 2.26548i) q^{8} +(-5.87108 - 3.77311i) q^{9} +O(q^{10})$	\(q+(-1.54534 + 3.38383i) q^{2} +(4.29324 + 1.26061i) q^{3} +(-3.82332 - 4.41235i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-10.9002 + 12.5795i) q^{6} +(-1.59229 + 11.0746i) q^{7} +(-7.71551 + 2.26548i) q^{8} +(-5.87108 - 3.77311i) q^{9} +(2.64705 + 18.4107i) q^{10} +(16.8650 + 36.9291i) q^{11} +(-10.8522 - 23.7630i) q^{12} +(10.1224 + 70.4026i) q^{13} +(-35.0139 - 22.5021i) q^{14} +(21.4662 - 6.30304i) q^{15} +(10.9042 - 75.8405i) q^{16} +(-55.9075 + 64.5207i) q^{17} +(21.8404 - 14.0360i) q^{18} +(-5.60580 - 6.46943i) q^{19} +(-28.0094 - 8.22430i) q^{20} +(-20.7968 + 45.5386i) q^{21} -151.024 q^{22} +(79.7668 - 76.1856i) q^{23} -35.9804 q^{24} +(10.3854 - 22.7408i) q^{25} +(-253.873 - 74.5438i) q^{26} +(-99.5640 - 114.903i) q^{27} +(54.9528 - 35.3160i) q^{28} +(160.537 - 185.270i) q^{29} +(-11.8442 + 82.3783i) q^{30} +(-260.087 + 76.3684i) q^{31} +(185.663 + 119.318i) q^{32} +(25.8521 + 179.806i) q^{33} +(-131.931 - 288.888i) q^{34} +(23.2393 + 50.8870i) q^{35} +(5.79873 + 40.3311i) q^{36} +(301.945 + 194.048i) q^{37} +(30.5543 - 8.97156i) q^{38} +(-45.2924 + 315.015i) q^{39} +(-26.3294 + 30.3858i) q^{40} +(36.0852 - 23.1905i) q^{41} +(-121.957 - 140.746i) q^{42} +(319.198 + 93.7251i) q^{43} +(98.4639 - 215.606i) q^{44} -34.8948 q^{45} +(134.532 + 387.650i) q^{46} +27.2797 q^{47} +(142.420 - 311.855i) q^{48} +(208.995 + 61.3664i) q^{49} +(60.9020 + 70.2847i) q^{50} +(-321.360 + 206.525i) q^{51} +(271.940 - 313.835i) q^{52} +(100.461 - 698.725i) q^{53} +(542.672 - 159.343i) q^{54} +(170.765 + 109.744i) q^{55} +(-12.8039 - 89.0534i) q^{56} +(-15.9116 - 34.8415i) q^{57} +(378.837 + 829.537i) q^{58} +(49.5248 + 344.452i) q^{59} +(-109.883 - 70.6178i) q^{60} +(-147.816 + 43.4027i) q^{61} +(143.506 - 998.105i) q^{62} +(51.1341 - 59.0119i) q^{63} +(-175.007 + 112.470i) q^{64} +(232.890 + 268.769i) q^{65} +(-648.382 - 190.382i) q^{66} +(106.610 - 233.444i) q^{67} +498.440 q^{68} +(438.498 - 226.528i) q^{69} -208.105 q^{70} +(15.8496 - 34.7058i) q^{71} +(53.8462 + 15.8107i) q^{72} +(690.690 + 797.099i) q^{73} +(-1123.23 + 721.859i) q^{74} +(73.2542 - 84.5398i) q^{75} +(-7.11264 + 49.4695i) q^{76} +(-435.829 + 127.971i) q^{77} +(-995.966 - 640.068i) q^{78} +(-9.65990 - 67.1861i) q^{79} +(-159.146 - 348.482i) q^{80} +(-204.327 - 447.414i) q^{81} +(22.7088 + 157.943i) q^{82} +(-668.821 - 429.825i) q^{83} +(280.445 - 82.3462i) q^{84} +(-60.7493 + 422.521i) q^{85} +(-810.420 + 935.275i) q^{86} +(922.779 - 593.034i) q^{87} +(-213.784 - 246.720i) q^{88} +(-622.552 - 182.798i) q^{89} +(53.9244 - 118.078i) q^{90} -795.798 q^{91} +(-641.132 - 60.6768i) q^{92} -1212.89 q^{93} +(-42.1565 + 92.3098i) q^{94} +(-41.0677 - 12.0586i) q^{95} +(646.681 + 746.309i) q^{96} +(-571.497 + 367.279i) q^{97} +(-530.622 + 612.370i) q^{98} +(40.3222 - 280.447i) 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 $

$2$	−1.54534	+	3.38383i	−0.546361	+	1.19636i	0.412099	+	0.911139i	$0.364796\pi$
$2$	−1.54534	+	3.38383i	−0.546361	+	1.19636i	−0.958461	+	0.285225i	$0.907932\pi$
$3$	4.29324	+	1.26061i	0.826234	+	0.242604i	0.667399	−	0.744701i	$-0.267408\pi$
$3$	4.29324	+	1.26061i	0.826234	+	0.242604i	0.158836	+	0.987305i	$0.449226\pi$
$4$	−3.82332	−	4.41235i	−0.477915	−	0.551544i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$5$	4.20627	−	2.70320i	0.376220	−	0.241782i
$6$	−10.9002	+	12.5795i	−0.741665	+	0.855927i
$7$	−1.59229	+	11.0746i	−0.0859754	+	0.597972i	0.900598	+	0.434653i	$0.143129\pi$
$7$	−1.59229	+	11.0746i	−0.0859754	+	0.597972i	−0.986573	+	0.163319i	$0.947780\pi$
$8$	−7.71551	+	2.26548i	−0.340980	+	0.100121i
$9$	−5.87108	−	3.77311i	−0.217447	−	0.139745i
$10$	2.64705	+	18.4107i	0.0837072	+	0.582196i
$11$	16.8650	+	36.9291i	0.462270	+	1.01223i	0.986964	+	0.160940i	$0.0514526\pi$
$11$	16.8650	+	36.9291i	0.462270	+	1.01223i	−0.524694	+	0.851291i	$0.675820\pi$
$12$	−10.8522	−	23.7630i	−0.261063	−	0.571649i
$13$	10.1224	+	70.4026i	0.215957	+	1.50201i	0.752754	+	0.658301i	$0.228725\pi$
$13$	10.1224	+	70.4026i	0.215957	+	1.50201i	−0.536798	+	0.843711i	$0.680366\pi$
$14$	−35.0139	−	22.5021i	−0.668418	−	0.429566i
$15$	21.4662	−	6.30304i	0.369503	−	0.108496i
$16$	10.9042	−	75.8405i	0.170378	−	1.18501i
$17$	−55.9075	+	64.5207i	−0.797621	+	0.920504i	−0.998248	−	0.0591637i	$-0.981157\pi$
$17$	−55.9075	+	64.5207i	−0.797621	+	0.920504i	0.200627	+	0.979668i	$0.435702\pi$
$18$	21.8404	−	14.0360i	0.285990	−	0.183795i
$19$	−5.60580	−	6.46943i	−0.0676873	−	0.0781153i	0.720896	−	0.693043i	$-0.243731\pi$
$19$	−5.60580	−	6.46943i	−0.0676873	−	0.0781153i	−0.788583	+	0.614928i	$0.789185\pi$
$20$	−28.0094	−	8.22430i	−0.313155	−	0.0919505i
$21$	−20.7968	+	45.5386i	−0.216106	+	0.473207i
$22$	−151.024			−1.46356
$23$	79.7668	−	76.1856i	0.723154	−	0.690687i
$23$	79.7668	−	76.1856i	0.723154	−	0.690687i
$24$	−35.9804			−0.306019
$25$	10.3854	−	22.7408i	0.0830830	−	0.181926i
$26$	−253.873	−	74.5438i	−1.91494	−	0.562278i
$27$	−99.5640	−	114.903i	−0.709670	−	0.819003i
$28$	54.9528	−	35.3160i	0.370897	−	0.238361i
$29$	160.537	−	185.270i	1.02797	−	1.18634i	0.0456801	−	0.998956i	$-0.485455\pi$
$29$	160.537	−	185.270i	1.02797	−	1.18634i	0.982287	−	0.187381i	$-0.0600000\pi$
$30$	−11.8442	+	82.3783i	−0.0720816	+	0.501338i
$31$	−260.087	+	76.3684i	−1.50687	+	0.442457i	−0.927881	−	0.372877i	$-0.878371\pi$
$31$	−260.087	+	76.3684i	−1.50687	+	0.442457i	−0.578990	+	0.815334i	$0.696553\pi$
$32$	185.663	+	119.318i	1.02565	+	0.659146i
$33$	25.8521	+	179.806i	0.136372	+	0.948489i
$34$	−131.931	−	288.888i	−0.665469	−	1.45717i
$35$	23.2393	+	50.8870i	0.112233	+	0.245756i
$36$	5.79873	+	40.3311i	0.0268460	+	0.186718i
$37$	301.945	+	194.048i	1.34161	+	0.862199i	0.997064	−	0.0765720i	$-0.0243975\pi$
$37$	301.945	+	194.048i	1.34161	+	0.862199i	0.344543	+	0.938771i	$0.388034\pi$
$38$	30.5543	−	8.97156i	0.130436	−	0.0382995i
$39$	−45.2924	+	315.015i	−0.185964	+	1.29341i
$40$	−26.3294	+	30.3858i	−0.104076	+	0.120110i
$41$	36.0852	−	23.1905i	0.137453	−	0.0883354i	−0.470107	−	0.882609i	$-0.655785\pi$
$41$	36.0852	−	23.1905i	0.137453	−	0.0883354i	0.607560	+	0.794274i	$0.292148\pi$
$42$	−121.957	−	140.746i	−0.448056	−	0.517084i
$43$	319.198	+	93.7251i	1.13203	+	0.332394i	0.793505	−	0.608564i	$-0.208254\pi$
$43$	319.198	+	93.7251i	1.13203	+	0.332394i	0.338525	+	0.940958i	$0.390072\pi$
$44$	98.4639	−	215.606i	0.337364	−	0.738723i
$45$	−34.8948			−0.115596
$46$	134.532	+	387.650i	0.431210	+	1.24252i
$47$	27.2797			0.0846628			0.0423314	−	0.999104i	$-0.486521\pi$
$47$	27.2797			0.0846628			0.0423314	+	0.999104i	$0.486521\pi$
$48$	142.420	−	311.855i	0.428260	−	0.937759i
$49$	208.995	+	61.3664i	0.609314	+	0.178911i
$50$	60.9020	+	70.2847i	0.172257	+	0.198795i
$51$	−321.360	+	206.525i	−0.882340	+	0.567046i
$52$	271.940	−	313.835i	0.725217	−	0.836945i
$53$	100.461	−	698.725i	0.260367	−	1.81089i	−0.269710	−	0.962942i	$-0.586928\pi$
$53$	100.461	−	698.725i	0.260367	−	1.81089i	0.530077	−	0.847950i	$-0.322163\pi$
$54$	542.672	−	159.343i	1.36756	−	0.401553i
$55$	170.765	+	109.744i	0.418655	+	0.269053i
$56$	−12.8039	−	89.0534i	−0.0305536	−	0.212505i
$57$	−15.9116	−	34.8415i	−0.0369744	−	0.0809627i
$58$	378.837	+	829.537i	0.857650	+	1.87799i
$59$	49.5248	+	344.452i	0.109281	+	0.760066i	0.968600	+	0.248625i	$0.0799788\pi$
$59$	49.5248	+	344.452i	0.109281	+	0.760066i	−0.859319	+	0.511440i	$0.829112\pi$
$60$	−109.883	−	70.6178i	−0.236432	−	0.151945i
$61$	−147.816	+	43.4027i	−0.310261	+	0.0911007i	−0.433156	−	0.901319i	$-0.642600\pi$
$61$	−147.816	+	43.4027i	−0.310261	+	0.0911007i	0.122896	+	0.992420i	$0.460782\pi$
$62$	143.506	−	998.105i	0.293956	−	2.04451i
$63$	51.1341	−	59.0119i	0.102259	−	0.118013i
$64$	−175.007	+	112.470i	−0.341811	+	0.219669i
$65$	232.890	+	268.769i	0.444407	+	0.512873i
$66$	−648.382	−	190.382i	−1.20925	−	0.355067i
$67$	106.610	−	233.444i	0.194396	−	0.425668i	−0.787184	−	0.616718i	$-0.788462\pi$
$67$	106.610	−	233.444i	0.194396	−	0.425668i	0.981580	+	0.191050i	$0.0611892\pi$
$68$	498.440			0.888894
$69$	438.498	−	226.528i	0.765058	−	0.395229i
$70$	−208.105			−0.355334
$71$	15.8496	−	34.7058i	0.0264930	−	0.0580115i	−0.895923	−	0.444210i	$-0.853485\pi$
$71$	15.8496	−	34.7058i	0.0264930	−	0.0580115i	0.922416	+	0.386198i	$0.126212\pi$
$72$	53.8462	+	15.8107i	0.0881367	+	0.0258793i
$73$	690.690	+	797.099i	1.10739	+	1.27799i	0.957230	+	0.289330i	$0.0934324\pi$
$73$	690.690	+	797.099i	1.10739	+	1.27799i	0.150157	+	0.988662i	$0.452022\pi$
$74$	−1123.23	+	721.859i	−1.76451	+	1.13398i
$75$	73.2542	−	84.5398i	0.112782	−	0.130158i
$76$	−7.11264	+	49.4695i	−0.0107352	+	0.0746650i
$77$	−435.829	+	127.971i	−0.645030	+	0.189398i
$78$	−995.966	−	640.068i	−1.44578	−	0.929147i
$79$	−9.65990	−	67.1861i	−0.0137573	−	0.0956838i	0.981786	−	0.189990i	$-0.0608457\pi$
$79$	−9.65990	−	67.1861i	−0.0137573	−	0.0956838i	−0.995543	+	0.0943066i	$0.969937\pi$
$80$	−159.146	−	348.482i	−0.222414	−	0.487018i
$81$	−204.327	−	447.414i	−0.280284	−	0.613736i
$82$	22.7088	+	157.943i	0.0305826	+	0.212706i
$83$	−668.821	−	429.825i	−0.884489	−	0.568427i	0.0176632	−	0.999844i	$-0.494377\pi$
$83$	−668.821	−	429.825i	−0.884489	−	0.568427i	−0.902153	+	0.431417i	$0.858014\pi$
$84$	280.445	−	82.3462i	0.364275	−	0.106961i
$85$	−60.7493	+	422.521i	−0.0775199	+	0.539162i
$86$	−810.420	+	935.275i	−1.01616	+	1.17271i
$87$	922.779	−	593.034i	1.13715	−	0.730803i
$88$	−213.784	−	246.720i	−0.258971	−	0.298868i
$89$	−622.552	−	182.798i	−0.741465	−	0.217714i	−0.110880	−	0.993834i	$-0.535367\pi$
$89$	−622.552	−	182.798i	−0.741465	−	0.217714i	−0.630585	+	0.776120i	$0.717185\pi$
$90$	53.9244	−	118.078i	0.0631571	−	0.138295i
$91$	−795.798			−0.916728
$92$	−641.132	−	60.6768i	−0.726551	−	0.0687608i
$93$	−1212.89			−1.35237
$94$	−42.1565	+	92.3098i	−0.0462565	+	0.101288i
$95$	−41.0677	−	12.0586i	−0.0443522	−	0.0130230i
$96$	646.681	+	746.309i	0.687517	+	0.793436i
$97$	−571.497	+	367.279i	−0.598214	+	0.384449i	−0.804421	−	0.594060i	$-0.797524\pi$
$97$	−571.497	+	367.279i	−0.598214	+	0.384449i	0.206207	+	0.978508i	$0.433888\pi$
$98$	−530.622	+	612.370i	−0.546948	+	0.631212i
$99$	40.3222	−	280.447i	0.0409347	−	0.284707i
$100$	−140.047	+	41.1215i	−0.140047	+	0.0411215i
$101$	368.315	+	236.702i	0.362859	+	0.233195i	0.709347	−	0.704859i	$-0.248990\pi$
$101$	368.315	+	236.702i	0.362859	+	0.233195i	−0.346489	+	0.938054i	$0.612626\pi$
$102$	−202.235	−	1406.58i	−0.196317	−	1.36541i
$103$	−29.1591	−	63.8495i	−0.0278945	−	0.0610803i	0.895172	−	0.445721i	$-0.147053\pi$
$103$	−29.1591	−	63.8495i	−0.0278945	−	0.0610803i	−0.923066	+	0.384641i	$0.874325\pi$
$104$	−237.595	−	520.260i	−0.224020	−	0.490535i
$105$	35.6233	+	247.766i	0.0331093	+	0.230281i
$106$	2209.12	+	1419.71i	2.02423	+	1.30089i
$107$	1209.23	−	355.063i	1.09253	−	0.320796i	0.314651	−	0.949208i	$-0.398113\pi$
$107$	1209.23	−	355.063i	1.09253	−	0.320796i	0.777881	+	0.628411i	$0.216294\pi$
$108$	−126.327	+	878.623i	−0.112554	+	0.782829i
$109$	206.684	−	238.526i	0.181622	−	0.209603i	−0.657637	−	0.753335i	$-0.728444\pi$
$109$	206.684	−	238.526i	0.181622	−	0.209603i	0.839259	+	0.543732i	$0.182989\pi$
$110$	−635.247	+	408.248i	−0.550622	+	0.353863i
$111$	1051.70	+	1213.73i	0.899309	+	1.03786i
$112$	822.540	+	241.520i	0.693953	+	0.203763i
$113$	769.006	−	1683.89i	0.640195	−	1.40183i	−0.259686	−	0.965693i	$-0.583619\pi$
$113$	769.006	−	1683.89i	0.640195	−	1.40183i	0.899880	−	0.436137i	$-0.143654\pi$
$114$	142.487			0.117062
$115$	129.575	−	536.083i	0.105069	−	0.434696i
$116$	−1431.26			−1.14560
$117$	206.208	−	451.532i	0.162939	−	0.356787i
$118$	−1242.10	−	364.714i	−0.969022	−	0.284531i
$119$	−625.520	−	721.888i	−0.481860	−	0.556096i
$120$	−151.343	+	97.2624i	−0.115131	+	0.0739900i
$121$	−207.712	+	239.712i	−0.156057	+	0.180099i
$122$	81.5591	−	567.256i	0.0605247	−	0.420958i
$123$	184.156	−	54.0732i	0.134999	−	0.0396392i
$124$	1331.36	+	855.614i	0.964191	+	0.619648i
$125$	−17.7894	−	123.728i	−0.0127290	−	0.0885323i
$126$	120.666	+	264.223i	0.0853161	+	0.186816i
$127$	966.658	+	2116.69i	0.675410	+	1.47894i	0.867435	+	0.497551i	$0.165767\pi$
$127$	966.658	+	2116.69i	0.675410	+	1.47894i	−0.192025	+	0.981390i	$0.561505\pi$
$128$	141.134	+	981.610i	0.0974580	+	0.677835i
$129$	1252.24	+	804.768i	0.854682	+	0.549271i
$130$	−1269.36	+	372.719i	−0.856389	+	0.251458i
$131$	56.5310	−	393.182i	0.0377033	−	0.262232i	−0.962247	−	0.272177i	$-0.912256\pi$
$131$	56.5310	−	393.182i	0.0377033	−	0.262232i	0.999951	+	0.00994455i	$0.00316550\pi$
$132$	694.524	−	801.523i	0.457959	−	0.528513i
$133$	80.5724	−	51.7807i	0.0525302	−	0.0337591i
$134$	625.186	+	721.503i	0.403044	+	0.465137i
$135$	−729.399	−	214.171i	−0.465012	−	0.136540i
$136$	285.185	−	624.467i	0.179812	−	0.393732i
$137$	−544.617			−0.339633			−0.169817	−	0.985476i	$-0.554318\pi$
$137$	−544.617			−0.339633			−0.169817	+	0.985476i	$0.554318\pi$
$138$	88.9031	+	1833.87i	0.0548401	+	1.13123i
$139$	773.695			0.472115			0.236058	−	0.971739i	$-0.424145\pi$
$139$	773.695			0.472115			0.236058	+	0.971739i	$0.424145\pi$
$140$	135.680	−	297.097i	0.0819074	−	0.179352i
$141$	117.118	+	34.3890i	0.0699513	+	0.0205396i
$142$	92.9453	+	107.265i	0.0549282	+	0.0633905i
$143$	−2429.19	+	1561.15i	−1.42055	+	0.912934i
$144$	−350.174	+	404.122i	−0.202647	+	0.233867i
$145$	174.441	−	1213.26i	0.0999069	−	0.694868i
$146$	−3764.60	+	1105.39i	−2.13398	+	0.626592i
$147$	819.906	+	526.921i	0.460032	+	0.295645i
$148$	−298.224	−	2074.20i	−0.165634	−	1.15201i
$149$	−1423.77	−	3117.63i	−0.782818	−	1.71413i	−0.696150	−	0.717896i	$-0.745105\pi$
$149$	−1423.77	−	3117.63i	−0.782818	−	1.71413i	−0.0866682	−	0.996237i	$-0.527622\pi$
$150$	172.865	+	378.522i	0.0940960	+	0.206042i
$151$	−93.6415	−	651.291i	−0.0504665	−	0.351002i	−0.999372	−	0.0354410i	$-0.988716\pi$
$151$	−93.6415	−	651.291i	−0.0504665	−	0.351002i	0.948905	−	0.315561i	$-0.102193\pi$
$152$	57.9079	+	37.2152i	0.0309010	+	0.0198589i
$153$	571.681	−	167.861i	0.302076	−	0.0886976i
$154$	240.473	−	1672.53i	0.125830	−	0.875170i
$155$	−887.556	+	1024.29i	−0.459937	+	0.530795i
$156$	1563.13	−	1004.56i	0.802245	−	0.515572i
$157$	1108.59	+	1279.38i	0.563537	+	0.650356i	0.963983	−	0.265964i	$-0.0856902\pi$
$157$	1108.59	+	1279.38i	0.563537	+	0.650356i	−0.400446	+	0.916320i	$0.631145\pi$
$158$	242.274	+	71.1380i	0.121989	+	0.0358192i
$159$	1312.12	−	2873.15i	0.654454	−	1.43305i
$160$	1103.49			0.545240
$161$	716.714	+	1004.69i	0.350838	+	0.491808i
$162$	1829.73			0.887388
$163$	710.367	−	1555.49i	0.341351	−	0.747454i	−0.658636	−	0.752461i	$-0.728866\pi$
$163$	710.367	−	1555.49i	0.341351	−	0.747454i	0.999987	+	0.00500689i	$0.00159375\pi$
$164$	−240.290	−	70.5555i	−0.114412	−	0.0335943i
$165$	594.792	+	686.427i	0.280633	+	0.323868i
$166$	2488.01	−	1598.95i	1.16330	−	0.747605i
$167$	−1596.93	+	1842.96i	−0.739967	+	0.853967i	−0.993556	−	0.113345i	$-0.963844\pi$
$167$	−1596.93	+	1842.96i	−0.739967	+	0.853967i	0.253589	+	0.967312i	$0.418389\pi$
$168$	57.2911	−	398.468i	0.0263101	−	0.182991i
$169$	−2746.06	+	806.315i	−1.24991	+	0.367007i
$170$	−1335.86	−	858.504i	−0.602681	−	0.387319i
$171$	8.50216	+	59.1338i	0.00380220	+	0.0264449i
$172$	−806.850	−	1766.76i	−0.357685	−	0.783220i
$173$	−682.301	−	1494.03i	−0.299852	−	0.656584i	0.698399	−	0.715709i	$-0.253896\pi$
$173$	−682.301	−	1494.03i	−0.299852	−	0.656584i	−0.998251	+	0.0591249i	$0.981169\pi$
$174$	580.715	+	4038.96i	0.253011	+	1.75973i
$175$	235.309	+	151.224i	0.101644	+	0.0653225i
$176$	2984.62	−	876.363i	1.27826	−	0.375332i
$177$	−221.598	+	1541.25i	−0.0941035	+	0.654505i
$178$	1580.61	−	1824.12i	0.665573	−	0.768112i
$179$	2389.38	−	1535.56i	0.997712	−	0.641191i	0.0635273	−	0.997980i	$-0.479765\pi$
$179$	2389.38	−	1535.56i	0.997712	−	0.641191i	0.934185	+	0.356789i	$0.116129\pi$
$180$	133.414	+	153.968i	0.0552450	+	0.0637562i
$181$	−771.437	−	226.514i	−0.316798	−	0.0930203i	0.119468	−	0.992838i	$-0.461881\pi$
$181$	−771.437	−	226.514i	−0.316798	−	0.0930203i	−0.436266	+	0.899818i	$0.643699\pi$
$182$	1229.78	−	2692.84i	0.500865	−	1.09674i
$183$	−689.323			−0.278449
$184$	−442.845	+	768.521i	−0.177429	+	0.307914i
$185$	1794.61			0.713203
$186$	1874.32	−	4104.20i	0.738883	−	1.61793i
$187$	−3325.57	−	976.475i	−1.30048	−	0.381855i
$188$	−104.299	−	120.368i	−0.0404617	−	0.0466953i
$189$	1431.04	−	919.673i	0.550755	−	0.353949i
$190$	104.268	−	120.331i	0.0398125	−	0.0459461i
$191$	−489.575	+	3405.07i	−0.185468	+	1.28996i	0.658098	+	0.752932i	$0.271361\pi$
$191$	−489.575	+	3405.07i	−0.185468	+	1.28996i	−0.843566	+	0.537026i	$0.819548\pi$
$192$	−893.130	+	262.247i	−0.335709	+	0.0985730i
$193$	−2645.25	−	1700.00i	−0.986577	−	0.634034i	−0.0553471	−	0.998467i	$-0.517627\pi$
$193$	−2645.25	−	1700.00i	−0.986577	−	0.634034i	−0.931230	+	0.364433i	$0.881263\pi$
$194$	−359.650	−	2501.42i	−0.133100	−	0.925729i
$195$	661.039	+	1447.47i	0.242759	+	0.531568i
$196$	−528.285	−	1156.78i	−0.192524	−	0.421568i
$197$	550.352	+	3827.78i	0.199040	+	1.38436i	0.807077	+	0.590447i	$0.201048\pi$
$197$	550.352	+	3827.78i	0.199040	+	1.38436i	−0.608036	+	0.793909i	$0.708043\pi$
$198$	886.673	+	569.830i	0.318248	+	0.204525i
$199$	−4572.72	+	1342.67i	−1.62890	+	0.478289i	−0.963392	−	0.268098i	$-0.913605\pi$
$199$	−4572.72	+	1342.67i	−1.62890	+	0.478289i	−0.665512	+	0.746387i	$0.731787\pi$
$200$	−28.6097	+	198.985i	−0.0101150	+	0.0703517i
$201$	751.986	−	867.838i	0.263886	−	0.304540i
$202$	−1370.13	+	880.530i	−0.477238	+	0.306702i
$203$	1796.17	+	2072.89i	0.621017	+	0.716691i
$204$	2139.92	+	628.338i	0.734434	+	0.215649i
$205$	89.0951	−	195.091i	0.0303545	−	0.0664671i
$206$	261.116			0.0883148
$207$	−755.774	+	146.323i	−0.253768	+	0.0491310i
$208$	5449.74			1.81669
$209$	144.369	−	316.124i	0.0477809	−	0.104626i
$210$	−893.447	−	262.340i	−0.293589	−	0.0862055i
$211$	−1082.66	−	1249.46i	−0.353239	−	0.407660i	0.551124	−	0.834423i	$-0.314199\pi$
$211$	−1082.66	−	1249.46i	−0.353239	−	0.407660i	−0.904363	+	0.426763i	$0.859654\pi$
$212$	−3467.12	+	2228.18i	−1.12322	+	0.721849i
$213$	111.797	−	129.020i	0.0359632	−	0.0415038i
$214$	−667.207	+	4640.53i	−0.213128	+	1.48234i
$215$	1595.99	−	468.625i	0.506259	−	0.148651i
$216$	1028.50	+	660.975i	0.323983	+	0.208211i
$217$	−431.616	−	3001.96i	−0.135023	−	0.939107i
$218$	487.734	+	1067.99i	0.151530	+	0.331804i
$219$	1960.47	+	4292.83i	0.604914	+	1.32458i
$220$	−168.661	−	1173.06i	−0.0516870	−	0.359491i
$221$	−5108.34	−	3282.93i	−1.55486	−	0.999248i
$222$	−5732.30	+	1683.15i	−1.73300	+	0.508856i
$223$	−599.812	+	4171.79i	−0.180118	+	1.25275i	0.676361	+	0.736570i	$0.263556\pi$
$223$	−599.812	+	4171.79i	−0.180118	+	1.25275i	−0.856480	+	0.516181i	$0.827353\pi$
$224$	−1617.03	+	1866.15i	−0.482332	+	0.556640i
$225$	−146.777	+	94.3278i	−0.0434895	+	0.0279490i
$226$	4509.61	+	5204.37i	1.32732	+	1.53181i
$227$	2888.59	+	848.166i	0.844592	+	0.247995i	0.675274	−	0.737567i	$-0.264025\pi$
$227$	2888.59	+	848.166i	0.844592	+	0.247995i	0.169318	+	0.985562i	$0.445844\pi$
$228$	−92.8979	+	203.418i	−0.0269838	+	0.0590864i
$229$	1632.50			0.471087			0.235543	−	0.971864i	$-0.424313\pi$
$229$	1632.50			0.471087			0.235543	+	0.971864i	$0.424313\pi$
$230$	1613.78	+	1266.89i	0.462649	+	0.363202i
$231$	−2032.44			−0.578894
$232$	−818.903	+	1793.15i	−0.231740	+	0.507439i
$233$	−4792.31	−	1407.15i	−1.34745	−	0.395646i	−0.473125	−	0.880995i	$-0.656874\pi$
$233$	−4792.31	−	1407.15i	−1.34745	−	0.395646i	−0.874320	+	0.485350i	$0.838692\pi$
$234$	1209.24	+	1395.54i	0.337824	+	0.389869i
$235$	114.746	−	73.7426i	0.0318519	−	0.0204699i
$236$	1330.50	−	1535.47i	0.366983	−	0.423520i
$237$	43.2231	−	300.623i	0.0118466	−	0.0823948i
$238$	3409.39	−	1001.09i	0.928562	−	0.272650i
$239$	−1597.48	−	1026.64i	−0.432354	−	0.277857i	0.306309	−	0.951932i	$-0.400906\pi$
$239$	−1597.48	−	1026.64i	−0.432354	−	0.277857i	−0.738663	+	0.674075i	$0.764542\pi$
$240$	−243.954	−	1696.74i	−0.0656131	−	0.456349i
$241$	−1842.82	−	4035.22i	−0.492559	−	1.07855i	−0.978817	−	0.204739i	$-0.934366\pi$
$241$	−1842.82	−	4035.22i	−0.492559	−	1.07855i	0.486257	−	0.873816i	$-0.338362\pi$
$242$	−490.159	−	1073.30i	−0.130201	−	0.285100i
$243$	270.997	+	1884.82i	0.0715410	+	0.497579i
$244$	756.656	+	486.273i	0.198524	+	0.127584i
$245$	1044.97	−	306.832i	0.272494	−	0.0800114i
$246$	−101.610	+	706.715i	−0.0263351	+	0.183165i
$247$	398.721	−	460.149i	0.102713	−	0.118537i
$248$	1833.69	−	1178.44i	0.469514	−	0.301739i
$249$	−2329.57	−	2688.46i	−0.592893	−	0.684235i
$250$	446.164	+	131.006i	0.112872	+	0.0331421i
$251$	824.894	−	1806.27i	0.207438	−	0.454225i	−0.777105	−	0.629371i	$-0.783313\pi$
$251$	824.894	−	1806.27i	0.207438	−	0.454225i	0.984542	+	0.175146i	$0.0560398\pi$
$252$	−455.884			−0.113960
$253$	4158.73	+	1660.85i	1.03343	+	0.412714i
$254$	−8656.32			−2.13837
$255$	−793.445	+	1737.40i	−0.194853	+	0.426668i
$256$	−5136.54	−	1508.22i	−1.25404	−	0.368219i
$257$	1262.39	+	1456.88i	0.306404	+	0.353609i	0.887979	−	0.459884i	$-0.152109\pi$
$257$	1262.39	+	1456.88i	0.306404	+	0.353609i	−0.581575	+	0.813493i	$0.697563\pi$
$258$	−4658.34	+	2993.74i	−1.12409	+	0.722410i
$259$	−2629.79	+	3034.94i	−0.630916	+	0.728116i
$260$	295.491	−	2055.18i	0.0704829	−	0.490220i
$261$	−1641.57	+	482.009i	−0.389313	+	0.114313i
$262$	1243.10	+	798.891i	0.293126	+	0.188380i
$263$	115.412	+	802.706i	0.0270593	+	0.188201i	0.998868	−	0.0475695i	$-0.0151476\pi$
$263$	115.412	+	802.706i	0.0270593	+	0.188201i	−0.971809	+	0.235771i	$0.924238\pi$
$264$	−606.808	−	1328.72i	−0.141464	−	0.309762i
$265$	−1466.23	−	3210.59i	−0.339886	−	0.744245i
$266$	50.7052	+	352.662i	0.0116877	+	0.0812899i
$267$	−2442.33	−	1569.59i	−0.559806	−	0.359765i
$268$	−1437.64	+	422.131i	−0.327680	+	0.0962154i
$269$	383.813	−	2669.48i	0.0869945	−	0.605060i	−0.898958	−	0.438035i	$-0.855675\pi$
$269$	383.813	−	2669.48i	0.0869945	−	0.605060i	0.985953	−	0.167025i	$-0.0534162\pi$
$270$	1851.89	−	2137.19i	0.417416	−	0.481724i
$271$	3674.64	−	2361.55i	0.823685	−	0.529350i	−0.0595804	−	0.998224i	$-0.518976\pi$
$271$	3674.64	−	2361.55i	0.823685	−	0.529350i	0.883265	+	0.468873i	$0.155340\pi$
$272$	4283.65	+	4943.60i	0.954907	+	1.10202i
$273$	−3416.55	−	1003.19i	−0.757432	−	0.222402i
$274$	841.619	−	1842.89i	0.185562	−	0.406325i
$275$	1014.95			0.222558
$276$	−2676.04	−	1068.72i	−0.583619	−	0.233077i
$277$	−4560.64			−0.989251			−0.494625	−	0.869106i	$-0.664695\pi$
$277$	−4560.64			−0.989251			−0.494625	+	0.869106i	$0.664695\pi$
$278$	−1195.62	+	2618.05i	−0.257945	+	0.564821i
$279$	1815.14	+	532.972i	0.389496	+	0.114366i
$280$	−294.586	−	339.971i	−0.0628746	−	0.0725612i
$281$	612.430	−	393.585i	0.130016	−	0.0835563i	−0.474016	−	0.880516i	$-0.657196\pi$
$281$	612.430	−	393.585i	0.130016	−	0.0835563i	0.604032	+	0.796960i	$0.293560\pi$
$282$	−297.354	+	343.165i	−0.0627915	+	0.0724652i
$283$	173.834	−	1209.04i	0.0365136	−	0.253958i	−0.963386	−	0.268118i	$-0.913598\pi$
$283$	173.834	−	1209.04i	0.0365136	−	0.253958i	0.999900	+	0.0141601i	$0.00450744\pi$
$284$	−213.732	+	62.7574i	−0.0446573	+	0.0131126i
$285$	−161.112	−	103.541i	−0.0334859	−	0.0215201i
$286$	−1528.72	−	10632.5i	−0.316066	−	2.19829i
$287$	199.368	+	436.555i	0.0410046	+	0.0897874i
$288$	−639.839	−	1401.05i	−0.130913	−	0.286659i
$289$	−338.079	−	2351.39i	−0.0688131	−	0.478606i
$290$	3835.90	+	2465.18i	0.776730	+	0.499174i
$291$	−2916.57	+	856.382i	−0.587534	+	0.172515i
$292$	876.348	−	6095.14i	0.175632	−	1.22154i
$293$	2376.39	−	2742.49i	0.473822	−	0.546820i	−0.467649	−	0.883914i	$-0.654899\pi$
$293$	2376.39	−	2742.49i	0.473822	−	0.546820i	0.941471	+	0.337094i	$0.109444\pi$
$294$	−3050.05	+	1960.15i	−0.605042	+	0.388837i
$295$	1139.44	+	1314.98i	0.224884	+	0.259530i
$296$	−2769.27	−	813.131i	−0.543786	−	0.159670i
$297$	2564.12	−	5614.64i	0.500961	−	1.09695i
$298$	12749.7			2.47843
$299$	6171.10	+	4844.61i	1.19359	+	0.937027i
$300$	−653.094			−0.125688
$301$	−1546.22	+	3385.75i	−0.296089	+	0.648344i
$302$	2348.56	+	689.601i	0.447499	+	0.131398i
$303$	1282.88	+	1480.52i	0.243232	+	0.280705i
$304$	−551.772	+	354.602i	−0.104100	+	0.0669008i
$305$	−504.427	+	582.140i	−0.0946997	+	0.109289i
$306$	−315.431	+	2193.87i	−0.0589281	+	0.409854i
$307$	−7453.85	+	2188.65i	−1.38571	+	0.406882i	−0.887754	−	0.460319i	$-0.847735\pi$
$307$	−7453.85	+	2188.65i	−1.38571	+	0.406882i	−0.497959	+	0.867201i	$0.665917\pi$
$308$	2230.97	+	1433.75i	0.412731	+	0.265246i
$309$	−44.6977	−	310.879i	−0.00822900	−	0.0572340i
$310$	−2094.46	−	4586.22i	−0.383733	−	0.840258i
$311$	1147.90	+	2513.54i	0.209297	+	0.458296i	0.984945	−	0.172870i	$-0.0553041\pi$
$311$	1147.90	+	2513.54i	0.209297	+	0.458296i	−0.775648	+	0.631166i	$0.782577\pi$
$312$	−364.207	−	2533.11i	−0.0660870	−	0.459645i
$313$	−4068.16	−	2614.45i	−0.734652	−	0.472132i	0.119054	−	0.992888i	$-0.462014\pi$
$313$	−4068.16	−	2614.45i	−0.734652	−	0.472132i	−0.853706	+	0.520755i	$0.825650\pi$
$314$	−6042.37	+	1774.20i	−1.08596	+	0.318866i
$315$	55.5625	−	386.446i	0.00993839	−	0.0691230i
$316$	−259.516	+	299.497i	−0.0461990	+	0.0533165i
$317$	−578.120	+	371.535i	−0.102430	+	0.0658281i	−0.590853	−	0.806779i	$-0.701209\pi$
$317$	−578.120	+	371.535i	−0.102430	+	0.0658281i	0.488423	+	0.872607i	$0.337572\pi$
$318$	7694.57	+	8880.00i	1.35689	+	1.56593i
$319$	9549.31	+	2803.93i	1.67605	+	0.492132i
$320$	−432.097	+	946.161i	−0.0754843	+	0.165288i
$321$	5639.12			0.980514
$322$	−4507.28	+	872.638i	−0.780065	+	0.151026i
$323$	730.819			0.125894
$324$	−1192.94	+	2612.17i	−0.204550	+	0.447903i
$325$	1706.14	+	500.967i	0.291198	+	0.0855035i
$326$	4165.74	+	4807.52i	0.707727	+	0.816760i
$327$	1188.03	−	763.503i	0.200913	−	0.129119i
$328$	−225.878	+	260.677i	−0.0380244	+	0.0438825i
$329$	−43.4371	+	302.112i	−0.00727892	+	0.0506260i
$330$	−3241.91	+	951.910i	−0.540791	+	0.158791i
$331$	5905.09	+	3794.97i	0.980584	+	0.630183i	0.929621	−	0.368518i	$-0.120135\pi$
$331$	5905.09	+	3794.97i	0.980584	+	0.630183i	0.0509628	+	0.998701i	$0.483771\pi$
$332$	660.580	+	4594.43i	0.109199	+	0.759495i
$333$	−1040.58	−	2278.55i	−0.171241	−	0.374965i
$334$	−3768.45	−	8251.76i	−0.617367	−	1.35184i
$335$	−182.616	−	1270.12i	−0.0297832	−	0.207146i
$336$	3226.90	+	2073.80i	0.523934	+	0.336712i
$337$	10191.0	−	2992.36i	1.64730	−	0.483692i	0.679139	−	0.734010i	$-0.262354\pi$
$337$	10191.0	−	2992.36i	1.64730	−	0.483692i	0.968164	+	0.250319i	$0.0805353\pi$
$338$	1515.17	−	10538.2i	0.243829	−	1.69587i
$339$	5424.25	−	6259.92i	0.869041	−	1.00293i
$340$	2096.57	−	1347.39i	0.334420	−	0.214918i
$341$	−7206.57	−	8316.83i	−1.14445	−	1.32077i
$342$	−213.238	−	62.6122i	−0.0337151	−	0.00989965i
$343$	−2606.60	+	5707.67i	−0.410331	+	0.898499i
$344$	−2675.11			−0.419280
$345$	1232.09	−	2138.19i	0.192271	−	0.333670i
$346$	6109.93			0.949341
$347$	−1672.27	+	3661.77i	−0.258710	+	0.566496i	−0.993763	−	0.111514i	$-0.964430\pi$
$347$	−1672.27	+	3661.77i	−0.258710	+	0.566496i	0.735053	+	0.678010i	$0.237157\pi$
$348$	−6144.75	−	1804.26i	−0.946533	−	0.277927i
$349$	4883.14	+	5635.44i	0.748964	+	0.864350i	0.994467	−	0.105046i	$-0.0334988\pi$
$349$	4883.14	+	5635.44i	0.748964	+	0.864350i	−0.245504	+	0.969396i	$0.578953\pi$
$350$	−875.347	+	562.552i	−0.133684	+	0.0859133i
$351$	7081.64	−	8172.65i	1.07690	−	1.24280i
$352$	−1275.12	+	8868.65i	−0.193080	+	1.34290i
$353$	−6846.04	+	2010.18i	−1.03223	+	0.303091i	−0.753618	−	0.657312i	$-0.771693\pi$
$353$	−6846.04	+	2010.18i	−1.03223	+	0.303091i	−0.278614	+	0.960403i	$0.589875\pi$
$354$	−4872.87	−	3131.61i	−0.731611	−	0.470178i
$355$	−27.1491	−	188.826i	−0.00405895	−	0.0282306i
$356$	1573.65	+	3445.81i	0.234279	+	0.512999i
$357$	−1775.49	−	3887.77i	−0.263218	−	0.576367i
$358$	1503.66	+	10458.2i	0.221986	+	1.54395i
$359$	402.547	+	258.701i	0.0591800	+	0.0380327i	0.569896	−	0.821717i	$-0.306983\pi$
$359$	402.547	+	258.701i	0.0591800	+	0.0380327i	−0.510716	+	0.859749i	$0.670620\pi$
$360$	269.231	−	79.0534i	0.0394159	−	0.0115736i
$361$	965.709	−	6716.65i	0.140794	−	0.979247i
$362$	1958.62	−	2260.37i	0.284372	−	0.328183i
$363$	−1193.94	+	767.299i	−0.172633	+	0.110944i
$364$	3042.59	+	3511.34i	0.438119	+	0.505616i
$365$	5059.95	+	1485.74i	0.725616	+	0.213060i
$366$	1065.24	−	2332.55i	0.152134	−	0.333127i
$367$	−9342.01			−1.32874			−0.664372	−	0.747402i	$-0.731301\pi$
$367$	−9342.01			−1.32874			−0.664372	+	0.747402i	$0.731301\pi$
$368$	−4908.16	−	6880.30i	−0.695260	−	0.974621i
$369$	−299.359			−0.0422331
$370$	−2773.29	+	6072.67i	−0.389667	+	0.853251i
$371$	7578.13	+	2225.14i	1.06048	+	0.311384i
$372$	4637.26	+	5351.68i	0.646319	+	0.745892i
$373$	−613.218	+	394.092i	−0.0851240	+	0.0547059i	−0.582510	−	0.812823i	$-0.697929\pi$
$373$	−613.218	+	394.092i	−0.0851240	+	0.0547059i	0.497386	+	0.867529i	$0.334293\pi$
$374$	8443.37	−	9744.16i	1.16737	−	1.34722i
$375$	79.5982	−	553.618i	0.0109612	−	0.0762366i
$376$	−210.477	+	61.8015i	−0.0288684	+	0.00847652i
$377$	14668.5	+	9426.88i	2.00389	+	1.28782i
$378$	900.569	+	6263.60i	0.122540	+	0.852287i
$379$	2769.98	+	6065.40i	0.375420	+	0.822055i	0.999182	+	0.0404406i	$0.0128762\pi$
$379$	2769.98	+	6065.40i	0.375420	+	0.822055i	−0.623762	+	0.781614i	$0.714397\pi$
$380$	103.808	+	227.309i	0.0140138	+	0.0306860i
$381$	1481.78	+	10306.0i	0.199249	+	1.38581i
$382$	−10765.6	−	6918.63i	−1.44193	−	0.926670i
$383$	−5749.48	+	1688.20i	−0.767062	+	0.225230i	−0.641777	−	0.766891i	$-0.721803\pi$
$383$	−5749.48	+	1688.20i	−0.767062	+	0.225230i	−0.125285	+	0.992121i	$0.539984\pi$
$384$	−631.503	+	4392.20i	−0.0839226	+	0.583694i
$385$	−1487.28	+	1716.41i	−0.196880	+	0.227212i
$386$	9840.32	−	6323.99i	1.29756	−	0.833893i
$387$	−1520.40	−	1754.64i	−0.199706	−	0.230474i
$388$	3805.58	+	1117.42i	0.497936	+	0.146207i
$389$	3281.03	−	7184.45i	0.427647	−	0.936416i	−0.566056	−	0.824367i	$-0.691531\pi$
$389$	3281.03	−	7184.45i	0.427647	−	0.936416i	0.993703	−	0.112049i	$-0.0357415\pi$
$390$	−5919.53			−0.768583
$391$	455.987	+	9405.96i	0.0589776	+	1.21657i
$392$	−1751.53			−0.225677
$393$	738.349	−	1616.76i	0.0947705	−	0.207518i
$394$	−13803.0	−	4052.94i	−1.76494	−	0.518233i
$395$	−222.250	−	256.490i	−0.0283104	−	0.0326719i
$396$	−1391.59	+	894.324i	−0.176592	+	0.113489i
$397$	6201.76	−	7157.21i	0.784024	−	0.904812i	−0.213369	−	0.976972i	$-0.568444\pi$
$397$	6201.76	−	7157.21i	0.784024	−	0.904812i	0.997393	+	0.0721599i	$0.0229892\pi$
$398$	2523.05	−	17548.2i	0.317761	−	2.21008i
$399$	411.192	−	120.737i	0.0515923	−	0.0151489i
$400$	−1611.43	−	1035.60i	−0.201429	−	0.129450i
$401$	−1290.41	−	8974.97i	−0.160698	−	1.11768i	−0.897323	−	0.441375i	$-0.854491\pi$
$401$	−1290.41	−	8974.97i	−0.160698	−	1.11768i	0.736625	−	0.676302i	$-0.236418\pi$
$402$	1774.54	+	3885.70i	0.220164	+	0.482092i
$403$	−8009.23	−	17537.8i	−0.989995	−	2.16779i
$404$	−363.777	−	2530.12i	−0.0447985	−	0.311580i
$405$	−2068.90	−	1329.60i	−0.253839	−	0.163132i
$406$	−9790.00	+	2874.60i	−1.19672	+	0.351390i
$407$	−2073.74	+	14423.2i	−0.252559	+	1.75659i
$408$	2011.57	−	2321.48i	0.244088	−	0.281692i
$409$	−1738.86	+	1117.50i	−0.210223	+	0.135102i	−0.641516	−	0.767110i	$-0.721694\pi$
$409$	−1738.86	+	1117.50i	−0.210223	+	0.135102i	0.431293	+	0.902212i	$0.358058\pi$
$410$	522.472	+	602.965i	0.0629343	+	0.0726301i
$411$	−2338.17	−	686.549i	−0.280617	−	0.0823965i
$412$	−170.242	+	372.777i	−0.0203573	+	0.0445762i
$413$	−3893.53			−0.463894
$414$	672.799	−	2783.53i	0.0798703	−	0.330442i
$415$	−3975.14			−0.470198
$416$	−6520.96	+	14278.9i	−0.768549	+	1.68289i
$417$	3321.66	+	975.327i	0.390078	+	0.114537i
$418$	846.609	+	977.039i	0.0990646	+	0.114327i
$419$	4403.97	−	2830.26i	0.513480	−	0.329994i	−0.258108	−	0.966116i	$-0.583099\pi$
$419$	4403.97	−	2830.26i	0.513480	−	0.329994i	0.771588	+	0.636122i	$0.219463\pi$
$420$	957.029	−	1104.47i	0.111186	−	0.128316i
$421$	−470.833	+	3274.71i	−0.0545059	+	0.379097i	0.944250	+	0.329230i	$0.106789\pi$
$421$	−470.833	+	3274.71i	−0.0545059	+	0.379097i	−0.998756	+	0.0498675i	$0.984120\pi$
$422$	5901.04	−	1732.70i	0.680706	−	0.199873i
$423$	−160.161	−	102.929i	−0.0184097	−	0.0118312i
$424$	807.834	+	5618.61i	0.0925280	+	0.643547i
$425$	886.632	+	1941.45i	0.101195	+	0.221587i
$426$	263.818	+	577.680i	0.0300047	+	0.0657012i
$427$	−245.302	−	1706.11i	−0.0278009	−	0.193360i
$428$	−6189.95	−	3978.04i	−0.699071	−	0.449266i
$429$	−12397.1	+	3640.11i	−1.39519	+	0.409665i
$430$	−880.606	+	6124.75i	−0.0987595	+	0.686887i
$431$	−2390.36	+	2758.63i	−0.267146	+	0.308302i	−0.873434	−	0.486942i	$-0.838112\pi$
$431$	−2390.36	+	2758.63i	−0.267146	+	0.308302i	0.606289	+	0.795245i	$0.292658\pi$
$432$	−9799.97	+	6298.06i	−1.09144	+	0.701424i
$433$	−6181.64	−	7134.00i	−0.686076	−	0.791774i	0.300725	−	0.953711i	$-0.402771\pi$
$433$	−6181.64	−	7134.00i	−0.686076	−	0.791774i	−0.986801	+	0.161937i	$0.948226\pi$
$434$	10825.1	+	3178.54i	1.19729	+	0.351555i
$435$	2278.36	−	4988.92i	0.251124	−	0.549886i
$436$	−1842.68			−0.202405
$437$	−940.035	−	88.9650i	−0.102902	−	0.00973861i
$438$	−17555.8			−1.91518
$439$	−2823.39	+	6182.35i	−0.306954	+	0.672136i	−0.998751	−	0.0499561i	$-0.984092\pi$
$439$	−2823.39	+	6182.35i	−0.306954	+	0.672136i	0.691797	+	0.722092i	$0.256819\pi$
$440$	−1566.16	−	459.867i	−0.169691	−	0.0498257i
$441$	−995.482	−	1148.85i	−0.107492	−	0.124052i
$442$	19003.0	−	12212.5i	2.04498	−	1.31423i
$443$	−7271.08	+	8391.27i	−0.779818	+	0.899958i	−0.997096	−	0.0761517i	$-0.975737\pi$
$443$	−7271.08	+	8391.27i	−0.779818	+	0.899958i	0.217278	+	0.976110i	$0.430282\pi$
$444$	1334.40	−	9280.97i	0.142630	−	0.992016i
$445$	−3112.76	+	913.989i	−0.331593	+	0.0973646i
$446$	−13189.7	−	8476.50i	−1.40034	−	0.899941i
$447$	−2182.49	−	15179.5i	−0.230935	−	1.60619i
$448$	−966.902	−	2117.22i	−0.101968	−	0.223280i
$449$	3591.06	+	7863.33i	0.377445	+	0.826488i	0.999068	+	0.0431718i	$0.0137463\pi$
$449$	3591.06	+	7863.33i	0.377445	+	0.826488i	−0.621623	+	0.783317i	$0.713526\pi$
$450$	−92.3684	−	642.437i	−0.00967620	−	0.0672994i
$451$	1464.98	+	941.485i	0.152956	+	0.0982989i
$452$	−10370.1	+	3044.92i	−1.07913	+	0.316861i
$453$	418.998	−	2914.19i	0.0434574	−	0.302253i
$454$	−7333.91	+	8463.78i	−0.758144	+	0.874945i
$455$	−3347.34	+	2151.20i	−0.344892	+	0.221648i
$456$	201.699	+	232.773i	0.0207136	+	0.0239048i
$457$	−6086.32	−	1787.11i	−0.622989	−	0.182926i	−0.0450220	−	0.998986i	$-0.514336\pi$
$457$	−6086.32	−	1787.11i	−0.622989	−	0.182926i	−0.577967	+	0.816060i	$0.696154\pi$
$458$	−2522.78	+	5524.11i	−0.257383	+	0.563591i
$459$	12980.0			1.31994
$460$	−2860.80	+	1477.89i	−0.289968	+	0.149798i
$461$	3493.89			0.352986			0.176493	−	0.984302i	$-0.443525\pi$
$461$	3493.89			0.352986			0.176493	+	0.984302i	$0.443525\pi$
$462$	3140.81	−	6877.42i	0.316285	−	0.692568i
$463$	974.893	+	286.254i	0.0978555	+	0.0287330i	0.330294	−	0.943878i	$-0.392852\pi$
$463$	974.893	+	286.254i	0.0978555	+	0.0287330i	−0.232438	+	0.972611i	$0.574670\pi$
$464$	−12300.4	−	14195.5i	−1.23068	−	1.42028i
$465$	−5101.72	+	3278.68i	−0.508789	+	0.326979i
$466$	12167.3	−	14041.8i	1.20953	−	1.39587i
$467$	1758.69	−	12232.0i	0.174266	−	1.21205i	−0.695478	−	0.718548i	$-0.744807\pi$
$467$	1758.69	−	12232.0i	0.174266	−	1.21205i	0.869744	−	0.493503i	$-0.164284\pi$
$468$	−2780.71	+	816.492i	−0.274655	+	0.0806460i
$469$	2415.55	+	1552.38i	0.237824	+	0.152840i
$470$	72.2108	+	502.237i	0.00708689	+	0.0492904i
$471$	3146.65	+	6890.20i	0.307834	+	0.674063i
$472$	−1162.46	−	2545.43i	−0.113361	−	0.248226i
$473$	1922.08	+	13368.4i	0.186844	+	1.29953i
$474$	950.463	+	610.825i	0.0921017	+	0.0591902i
$475$	−205.338	+	60.2928i	−0.0198349	+	0.00582405i
$476$	−793.660	+	5520.02i	−0.0764230	+	0.531533i
$477$	−3226.18	+	3723.21i	−0.309679	+	0.357388i
$478$	5942.64	−	3819.10i	0.568640	−	0.365443i
$479$	1001.26	+	1155.52i	0.0955090	+	0.110223i	0.801492	−	0.598006i	$-0.204040\pi$
$479$	1001.26	+	1155.52i	0.0955090	+	0.110223i	−0.705983	+	0.708229i	$0.749495\pi$
$480$	4737.54	+	1391.07i	0.450496	+	0.132278i
$481$	−10605.1	+	23221.9i	−1.00530	+	2.20131i
$482$	16502.3			1.55946
$483$	1810.50	+	5216.89i	0.170560	+	0.491463i
$484$	1851.84			0.173915
$485$	−1411.04	+	3089.75i	−0.132107	+	0.289275i
$486$	−6796.71	−	1995.69i	−0.634372	−	0.186268i
$487$	8658.38	+	9992.30i	0.805644	+	0.929762i	0.998677	−	0.0514298i	$-0.0163778\pi$
$487$	8658.38	+	9992.30i	0.805644	+	0.929762i	−0.193033	+	0.981192i	$0.561832\pi$
$488$	1042.15	−	669.747i	0.0966717	−	0.0621271i
$489$	5010.63	−	5782.58i	0.463372	−	0.534759i
$490$	−576.576	+	4010.17i	−0.0531572	+	0.369717i
$491$	−1361.84	+	399.871i	−0.125171	+	0.0367534i	−0.343718	−	0.939073i	$-0.611686\pi$
$491$	−1361.84	+	399.871i	−0.125171	+	0.0367534i	0.218547	+	0.975826i	$0.429868\pi$
$492$	−942.679	−	605.823i	−0.0863806	−	0.0555135i
$493$	2978.51	+	20716.0i	0.272100	+	1.89250i
$494$	940.903	+	2060.29i	0.0856948	+	0.187645i
$495$	−588.499	−	1288.63i	−0.0534365	−	0.117010i
$496$	2955.77	+	20557.9i	0.267577	+	1.86104i
$497$	359.115	+	230.789i	0.0324115	+	0.0208296i
$498$	12697.3	−	3728.26i	1.14253	−	0.335476i
$499$	1272.33	−	8849.23i	0.114143	−	0.793880i	−0.849673	−	0.527310i	$-0.823201\pi$
$499$	1272.33	−	8849.23i	0.114143	−	0.793880i	0.963816	−	0.266570i	$-0.0858902\pi$
$500$	−477.915	+	551.544i	−0.0427461	+	0.0493316i
$501$	−9179.27	+	5899.16i	−0.818562	+	0.526058i
$502$	4837.35	+	5582.60i	0.430083	+	0.496342i
$503$	16868.3	+	4952.97i	1.49526	+	0.439049i	0.924217	−	0.381867i	$-0.124719\pi$
$503$	16868.3	+	4952.97i	1.49526	+	0.439049i	0.571048	+	0.820917i	$0.306537\pi$
$504$	−260.835	+	571.150i	−0.0230526	+	0.0504783i
$505$	2189.09			0.192897
$506$	−12046.7	+	11505.8i	−1.05838	+	1.01086i
$507$	−12805.9			−1.12176
$508$	5643.71	−	12358.0i	0.492912	−	1.07933i
$509$	14549.0	+	4271.96i	1.26694	+	0.372006i	0.845072	−	0.534652i	$-0.179557\pi$
$509$	14549.0	+	4271.96i	1.26694	+	0.372006i	0.421865	+	0.906659i	$0.361376\pi$
$510$	−4652.92	−	5369.76i	−0.403990	−	0.466229i
$511$	−9927.33	+	6379.91i	−0.859411	+	0.552310i
$512$	7845.86	−	9054.61i	0.677229	−	0.781564i
$513$	−185.222	+	1288.25i	−0.0159410	+	0.110872i
$514$	−6880.65	+	2020.34i	−0.590452	+	0.173372i
$515$	−295.249	−	189.745i	−0.0252626	−	0.0162353i
$516$	−1236.81	−	8602.23i	−0.105519	−	0.733899i
$517$	460.071	+	1007.41i	0.0391371	+	0.0856984i
$518$	−6205.79	−	13588.8i	−0.526383	−	1.15262i
$519$	−1045.89	−	7274.34i	−0.0884578	−	0.615238i
$520$	−2405.75	−	1546.08i	−0.202883	−	0.130385i
$521$	17623.3	−	5174.66i	1.48194	−	0.435137i	0.561980	−	0.827151i	$-0.310040\pi$
$521$	17623.3	−	5174.66i	1.48194	−	0.435137i	0.919959	+	0.392014i	$0.128222\pi$
$522$	905.755	−	6299.67i	0.0759461	−	0.528216i
$523$	−1585.02	+	1829.21i	−0.132520	+	0.152937i	−0.818131	−	0.575032i	$-0.804990\pi$
$523$	−1585.02	+	1829.21i	−0.132520	+	0.152937i	0.685611	+	0.727968i	$0.259535\pi$
$524$	−1950.99	+	1253.83i	−0.162652	+	0.104530i
$525$	819.602	+	945.872i	0.0681341	+	0.0786309i
$526$	−2894.57	−	849.922i	−0.239942	−	0.0704532i
$527$	9613.47	−	21050.6i	0.794629	−	1.73999i
$528$	13918.4			1.14720
$529$	558.494	−	12154.2i	0.0459024	−	0.998946i
$530$	13129.9			1.07609
$531$	1008.89	−	2209.17i	0.0824525	−	0.180546i
$532$	−536.529	−	157.539i	−0.0437246	−	0.0128387i
$533$	1997.94	+	2305.75i	0.162365	+	0.187379i
$534$	9085.46	−	5838.87i	0.736266	−	0.473170i
$535$	4126.55	−	4762.29i	0.333470	−	0.384844i
$536$	−293.691	+	2042.67i	−0.0236670	+	0.164608i
$537$	12193.9	−	3580.46i	0.979900	−	0.287724i
$538$	8439.94	+	5424.02i	0.676341	+	0.434658i
$539$	1258.48	+	8752.93i	0.100569	+	0.699472i
$540$	1843.73	+	4037.21i	0.146929	+	0.321729i
$541$	−7201.93	−	15770.0i	−0.572339	−	1.25325i	−0.945543	−	0.325498i	$-0.894468\pi$
$541$	−7201.93	−	15770.0i	−0.572339	−	1.25325i	0.373204	−	0.927749i	$-0.378259\pi$
$542$	2312.50	+	16083.8i	0.183266	+	1.27464i
$543$	−3026.42	−	1944.96i	−0.239182	−	0.153713i
$544$	−18078.4	+	5308.31i	−1.42483	+	0.418367i
$545$	224.584	−	1562.02i	0.0176516	−	0.122770i
$546$	8674.36	−	10010.7i	0.679905	−	0.784653i
$547$	−9800.77	+	6298.57i	−0.766089	+	0.492336i	−0.864390	−	0.502821i	$-0.832295\pi$
$547$	−9800.77	+	6298.57i	−0.766089	+	0.492336i	0.0983014	+	0.995157i	$0.468659\pi$
$548$	2082.25	+	2403.04i	0.162316	+	0.187323i
$549$	1031.60	+	302.906i	0.0801962	+	0.0235477i
$550$	−1568.44	+	3434.40i	−0.121597	+	0.266261i
$551$	−2098.53			−0.162251
$552$	−2870.04	+	2741.19i	−0.221299	+	0.211364i
$553$	759.440			0.0583990
$554$	7047.76	−	15432.4i	0.540488	−	1.18350i
$555$	7704.71	+	2262.31i	0.589273	+	0.173026i
$556$	−2958.09	−	3413.82i	−0.225631	−	0.260392i
$557$	−3971.35	+	2552.23i	−0.302103	+	0.194150i	−0.682906	−	0.730506i	$-0.739284\pi$
$557$	−3971.35	+	2552.23i	−0.302103	+	0.194150i	0.380803	+	0.924656i	$0.375648\pi$
$558$	−4608.50	+	5318.49i	−0.349629	+	0.403494i
$559$	−3367.45	+	23421.1i	−0.254790	+	1.77211i
$560$	4112.70	−	1207.60i	0.310345	−	0.0911256i
$561$	−13046.5	−	8384.48i	−0.981861	−	0.631004i
$562$	385.410	+	2680.58i	0.0289280	+	0.201199i
$563$	−2190.08	−	4795.62i	−0.163945	−	0.358990i	0.809774	−	0.586742i	$-0.199590\pi$
$563$	−2190.08	−	4795.62i	−0.163945	−	0.358990i	−0.973719	+	0.227752i	$0.926862\pi$
$564$	−296.045	−	648.247i	−0.0221024	−	0.0483974i
$565$	−1317.25	−	9161.66i	−0.0980833	−	0.682184i
$566$	3822.55	+	2456.61i	0.283876	+	0.182436i
$567$	5280.27	−	1550.43i	0.391094	−	0.114836i
$568$	−43.6625	+	303.680i	−0.00322542	+	0.0224333i
$569$	6962.62	−	8035.29i	0.512984	−	0.592015i	−0.438876	−	0.898548i	$-0.644623\pi$
$569$	6962.62	−	8035.29i	0.512984	−	0.592015i	0.951860	+	0.306532i	$0.0991687\pi$
$570$	599.337	−	385.171i	0.0440412	−	0.0283035i
$571$	−2960.81	−	3416.95i	−0.216998	−	0.250429i	0.636805	−	0.771025i	$-0.280255\pi$
$571$	−2960.81	−	3416.95i	−0.216998	−	0.250429i	−0.853804	+	0.520595i	$0.825710\pi$
$572$	16175.9	+	4749.67i	1.18243	+	0.347192i
$573$	−6394.32	+	14001.6i	−0.466189	+	1.02081i
$574$	−1785.32			−0.129822
$575$	−904.114	−	2605.18i	−0.0655725	−	0.188945i
$576$	1451.85			0.105024
$577$	3669.85	−	8035.85i	0.264780	−	0.579787i	−0.729812	−	0.683648i	$-0.760392\pi$
$577$	3669.85	−	8035.85i	0.264780	−	0.579787i	0.994592	+	0.103861i	$0.0331197\pi$
$578$	8479.14	+	2489.70i	0.610183	+	0.179166i
$579$	−9213.66	−	10633.1i	−0.661324	−	0.763209i
$580$	−6020.28	+	3869.00i	−0.430997	+	0.276985i
$581$	5825.09	−	6722.51i	0.415948	−	0.480029i
$582$	1609.25	−	11192.6i	0.114614	−	0.797160i
$583$	27497.6	−	8074.01i	1.95340	−	0.573570i
$584$	−7134.84	−	4585.28i	−0.505551	−	0.324898i
$585$	−353.218	−	2456.68i	−0.0249637	−	0.173626i
$586$	5607.80	+	12279.4i	0.395318	+	0.865625i
$587$	−10296.9	−	22547.1i	−0.724018	−	1.58538i	−0.808186	−	0.588927i	$-0.799551\pi$
$587$	−10296.9	−	22547.1i	−0.724018	−	1.58538i	0.0841680	−	0.996452i	$-0.473177\pi$
$588$	−809.803	−	5632.30i	−0.0567954	−	0.395021i
$589$	1952.06	+	1254.51i	0.136559	+	0.0877609i
$590$	−6210.50	+	1823.57i	−0.433360	+	0.127246i
$591$	−2462.54	+	17127.4i	−0.171397	+	1.19209i
$592$	18009.2	−	20783.7i	1.25029	−	1.44291i
$593$	11975.0	−	7695.85i	0.829263	−	0.532935i	−0.0557805	−	0.998443i	$-0.517765\pi$
$593$	11975.0	−	7695.85i	0.829263	−	0.532935i	0.885044	+	0.465508i	$0.154128\pi$
$594$	15036.5	+	17353.1i	1.03865	+	1.19866i
$595$	−4582.52	−	1345.55i	−0.315739	−	0.0927094i
$596$	−8312.52	+	18201.9i	−0.571299	+	1.25097i
$597$	−21324.4			−1.46189
$598$	−25929.8	+	13395.3i	−1.77316	+	0.916014i
$599$	−22188.2			−1.51350			−0.756748	−	0.653707i	$-0.773213\pi$
$599$	−22188.2			−1.51350			−0.756748	+	0.653707i	$0.773213\pi$
$600$	−373.670	+	818.223i	−0.0254250	+	0.0556730i
$601$	12008.2	+	3525.92i	0.815015	+	0.239310i	0.662568	−	0.749002i	$-0.269467\pi$
$601$	12008.2	+	3525.92i	0.815015	+	0.239310i	0.152447	+	0.988312i	$0.451285\pi$
$602$	−9067.37	−	10464.3i	−0.613884	−	0.708460i
$603$	−1506.73	+	968.317i	−0.101756	+	0.0653945i
$604$	−2515.70	+	2903.27i	−0.169474	+	0.195584i
$605$	−225.701	+	1569.78i	−0.0151670	+	0.105489i
$606$	−6992.31	+	2053.13i	−0.468718	+	0.137628i
$607$	−24271.5	−	15598.4i	−1.62298	−	1.04303i	−0.954025	−	0.299727i	$-0.903105\pi$
$607$	−24271.5	−	15598.4i	−1.62298	−	1.04303i	−0.668957	−	0.743301i	$-0.733259\pi$
$608$	−268.866	−	1870.01i	−0.0179342	−	0.124735i
$609$	5098.28	+	11163.7i	0.339233	+	0.742816i
$610$	−1190.35	−	2606.50i	−0.0790095	−	0.173007i
$611$	276.135	+	1920.56i	0.0182835	+	0.127165i
$612$	−2926.38	−	1880.67i	−0.193288	−	0.124218i
$613$	4722.74	−	1386.72i	0.311174	−	0.0913690i	−0.122417	−	0.992479i	$-0.539064\pi$
$613$	4722.74	−	1386.72i	0.311174	−	0.0913690i	0.433591	+	0.901110i	$0.357246\pi$
$614$	4112.74	−	28604.8i	0.270321	−	1.88012i
$615$	628.440	−	725.259i	0.0412051	−	0.0475533i
$616$	3072.72	−	1974.72i	0.200980	−	0.129162i
$617$	10009.1	+	11551.1i	0.653082	+	0.753697i	0.981631	−	0.190790i	$-0.0611050\pi$
$617$	10009.1	+	11551.1i	0.653082	+	0.753697i	−0.328549	+	0.944487i	$0.606560\pi$
$618$	1121.03	+	329.166i	0.0729687	+	0.0214255i
$619$	7485.99	−	16392.0i	0.486086	−	1.06438i	−0.494659	−	0.869087i	$-0.664707\pi$
$619$	7485.99	−	16392.0i	0.486086	−	1.06438i	0.980745	−	0.195293i	$-0.0625657\pi$
$620$	7912.96			0.512568
$621$	−16695.9	−	1580.10i	−1.07888	−	0.102105i
$622$	−10279.3			−0.662640
$623$	3015.69	−	6603.45i	0.193934	−	0.424657i
$624$	23397.0	+	6869.99i	1.50101	+	0.440737i
$625$	−409.288	−	472.343i	−0.0261944	−	0.0302300i
$626$	15133.6	−	9725.75i	0.966228	−	0.620957i
$627$	1018.32	−	1175.20i	0.0648608	−	0.0748534i
$628$	1406.58	−	9783.00i	0.0893770	−	0.621631i
$629$	−29401.1	+	8632.95i	−1.86375	+	0.547247i
$630$	1221.80	+	785.205i	0.0772664	+	0.0496561i
$631$	901.315	+	6268.79i	0.0568634	+	0.395494i	0.998299	+	0.0583009i	$0.0185683\pi$
$631$	901.315	+	6268.79i	0.0568634	+	0.395494i	−0.941436	+	0.337193i	$0.890523\pi$
$632$	226.739	+	496.490i	0.0142709	+	0.0312489i
$633$	−3073.05	−	6729.04i	−0.192958	−	0.422520i
$634$	−363.818	−	2530.41i	−0.0227903	−	0.158510i
$635$	9787.86	+	6290.27i	0.611684	+	0.393105i
$636$	−17694.0	+	5195.43i	−1.10317	+	0.323919i
$637$	−2204.83	+	15334.9i	−0.137141	+	0.953835i
$638$	−24245.0	+	27980.2i	−1.50450	+	1.73628i
$639$	−224.003	+	143.958i	−0.0138676	+	0.00891219i
$640$	3247.14	+	3747.40i	0.200554	+	0.231452i
$641$	−17100.1	−	5021.05i	−1.05369	−	0.309391i	−0.291381	−	0.956607i	$-0.594115\pi$
$641$	−17100.1	−	5021.05i	−1.05369	−	0.309391i	−0.762306	+	0.647216i	$0.775933\pi$
$642$	−8714.37	+	19081.8i	−0.535715	+	1.17305i
$643$	10064.2			0.617254			0.308627	−	0.951183i	$-0.400130\pi$
$643$	10064.2			0.617254			0.308627	+	0.951183i	$0.400130\pi$
$644$	1692.84	−	7003.66i	0.103583	−	0.428545i
$645$	7442.73			0.454352
$646$	−1129.36	+	2472.96i	−0.0687837	+	0.150615i
$647$	7364.69	+	2162.47i	0.447505	+	0.131399i	0.497718	−	0.867339i	$-0.334172\pi$
$647$	7364.69	+	2162.47i	0.447505	+	0.131399i	−0.0502123	+	0.998739i	$0.515990\pi$
$648$	2590.09	+	2989.12i	0.157019	+	0.181210i
$649$	−11885.1	+	7638.08i	−0.718845	+	0.461974i
$650$	−4331.75	+	4999.10i	−0.261393	+	0.301663i
$651$	1931.26	−	13432.2i	0.116271	−	0.808680i
$652$	−9579.31	+	2812.74i	−0.575391	+	0.168950i
$653$	23216.3	+	14920.2i	1.39131	+	0.894139i	0.999663	−	0.0259767i	$-0.00826957\pi$
$653$	23216.3	+	14920.2i	1.39131	+	0.894139i	0.391646	+	0.920116i	$0.371906\pi$
$654$	747.644	+	5199.98i	0.0447021	+	0.310910i
$655$	−825.066	−	1806.64i	−0.0492183	−	0.107773i
$656$	−1365.30	−	2989.59i	−0.0812592	−	0.177933i
$657$	−1047.55	−	7285.88i	−0.0622053	−	0.432647i
$658$	−955.169	−	613.850i	−0.0565902	−	0.0363683i
$659$	−1141.40	+	335.144i	−0.0674696	+	0.0198109i	−0.315293	−	0.948994i	$-0.602103\pi$
$659$	−1141.40	+	335.144i	−0.0674696	+	0.0198109i	0.247824	+	0.968805i	$0.420285\pi$
$660$	754.673	−	5248.86i	0.0445085	−	0.309563i
$661$	2979.91	−	3439.00i	0.175348	−	0.202363i	−0.661272	−	0.750147i	$-0.729983\pi$
$661$	2979.91	−	3439.00i	0.175348	−	0.202363i	0.836620	+	0.547784i	$0.184528\pi$
$662$	−21966.9	+	14117.3i	−1.28968	+	0.828827i
$663$	−17792.8	−	20534.0i	−1.04226	−	1.20283i
$664$	6134.05	+	1801.12i	0.358505	+	0.105267i
$665$	198.935	−	435.607i	0.0116006	−	0.0254017i
$666$	9318.25			0.542155
$667$	−1309.36	−	27009.1i	−0.0760098	−	1.56791i
$668$	14237.4			0.824642
$669$	−7834.13	+	17154.3i	−0.452743	+	0.991368i
$670$	4580.07	+	1344.83i	0.264095	+	0.0775452i
$671$	−4095.73	−	4726.73i	−0.235639	−	0.271942i
$672$	−9294.78	+	5973.39i	−0.533562	+	0.342900i
$673$	22531.8	−	26003.1i	1.29054	−	1.48937i	0.516419	−	0.856336i	$-0.327265\pi$
$673$	22531.8	−	26003.1i	1.29054	−	1.48937i	0.774126	−	0.633032i	$-0.218190\pi$
$674$	−5623.01	+	39108.9i	−0.321351	+	2.23504i
$675$	−3647.00	+	1070.85i	−0.207960	+	0.0610625i
$676$	14056.8	+	9033.76i	0.799772	+	0.513982i
$677$	3574.17	+	24858.9i	0.202905	+	1.41123i	0.795607	+	0.605813i	$0.207152\pi$
$677$	3574.17	+	24858.9i	0.202905	+	1.41123i	−0.592702	+	0.805422i	$0.701939\pi$
$678$	12800.2	+	28028.4i	0.725055	+	1.58765i
$679$	−3157.48	−	6913.91i	−0.178458	−	0.390768i
$680$	−488.499	−	3397.59i	−0.0275487	−	0.191605i
$681$	11332.2	+	7282.76i	0.637666	+	0.409803i
$682$	39279.3	−	11533.5i	2.20540	−	0.647564i
$683$	−1887.37	+	13127.0i	−0.105737	+	0.735416i	0.866119	+	0.499838i	$0.166607\pi$
$683$	−1887.37	+	13127.0i	−0.105737	+	0.735416i	−0.971856	+	0.235577i	$0.924302\pi$
$684$	228.413	−	263.602i	0.0127684	−	0.0147355i
$685$	−2290.80	+	1472.21i	−0.127777	+	0.0821172i
$686$	−15285.7	−	17640.6i	−0.850743	−	0.981809i
$687$	7008.73	+	2057.95i	0.389228	+	0.114288i
$688$	10588.8	−	23186.2i	0.586763	−	1.28483i
$689$	50208.9			2.77621
$690$	5331.27	+	7473.41i	0.294142	+	0.412330i
$691$	−25495.8			−1.40363			−0.701814	−	0.712360i	$-0.747626\pi$
$691$	−25495.8			−1.40363			−0.701814	+	0.712360i	$0.747626\pi$
$692$	−3983.53	+	8722.71i	−0.218831	+	0.479173i
$693$	3041.63	+	893.104i	0.166727	+	0.0489556i
$694$	−9806.56	−	11317.4i	−0.536386	−	0.619023i
$695$	3254.37	−	2091.46i	0.177619	−	0.114149i
$696$	−5776.20	+	6666.09i	−0.314578	+	0.363042i
$697$	−521.162	+	3624.76i	−0.0283220	+	0.196984i
$698$	−26615.5	+	7815.01i	−1.44328	+	0.423786i
$699$	−18800.7	−	12082.5i	−1.01732	−	0.653792i
$700$	−232.409	−	1616.44i	−0.0125489	−	0.0872796i
$701$	−4569.47	−	10005.8i	−0.246201	−	0.539104i	0.745676	−	0.666309i	$-0.232127\pi$
$701$	−4569.47	−	10005.8i	−0.246201	−	0.539104i	−0.991876	+	0.127205i	$0.959399\pi$
$702$	16711.3	+	36592.6i	0.898471	+	1.96738i
$703$	−437.260	−	3041.21i	−0.0234588	−	0.163160i
$704$	−7104.92	−	4566.06i	−0.380365	−	0.244446i
$705$	585.591	−	171.945i	0.0312832	−	0.00918557i
$706$	3777.38	−	26272.2i	0.201365	−	1.40052i
$707$	−3207.84	+	3702.05i	−0.170641	+	0.196930i
$708$	7647.77	−	4914.92i	0.405961	−	0.260896i
$709$	−19832.4	−	22887.8i	−1.05052	−	1.21237i	−0.976591	−	0.215103i	$-0.930991\pi$
$709$	−19832.4	−	22887.8i	−1.05052	−	1.21237i	−0.0739302	−	0.997263i	$-0.523554\pi$
$710$	680.911	+	199.934i	0.0359917	+	0.0105681i
$711$	−196.787	+	430.902i	−0.0103798	+	0.0227287i
$712$	5217.43			0.274623
$713$	−14928.1	+	25906.6i	−0.784100	+	1.36074i
$714$	15899.3			0.833356
$715$	−5997.73	+	13133.2i	−0.313710	+	0.686928i
$716$	−15910.8	−	4671.83i	−0.830467	−	0.243847i
$717$	−5564.19	−	6421.42i	−0.289817	−	0.334466i
$718$	−1497.47	+	962.368i	−0.0778346	+	0.0500213i
$719$	−7105.21	+	8199.85i	−0.368539	+	0.425317i	−0.909482	−	0.415742i	$-0.863522\pi$
$719$	−7105.21	+	8199.85i	−0.368539	+	0.425317i	0.540943	+	0.841059i	$0.318067\pi$
$720$	−380.501	+	2646.44i	−0.0196950	+	0.136982i
$721$	753.536	−	221.258i	0.0389226	−	0.0114287i
$722$	21235.6	+	13647.3i	1.09461	+	0.703464i
$723$	−2824.85	−	19647.3i	−0.145307	−	1.01064i
$724$	1949.99	+	4269.89i	0.100098	+	0.219184i
$725$	−2545.95	−	5574.85i	−0.130420	−	0.285579i
$726$	−751.361	−	5225.83i	−0.0384099	−	0.267147i
$727$	−7056.20	−	4534.74i	−0.359972	−	0.231340i	0.348136	−	0.937444i	$-0.386815\pi$
$727$	−7056.20	−	4534.74i	−0.359972	−	0.231340i	−0.708108	+	0.706104i	$0.750451\pi$
$728$	6139.98	−	1802.86i	0.312586	−	0.0917836i
$729$	−3102.55	+	21578.7i	−0.157626	+	1.09631i
$730$	−12846.8	+	14826.0i	−0.651346	+	0.751693i
$731$	−23892.8	+	15355.0i	−1.20890	+	0.776913i
$732$	2635.50	+	3041.53i	0.133075	+	0.153577i
$733$	−26176.1	−	7685.99i	−1.31901	−	0.387297i	−0.454875	−	0.890555i	$-0.650316\pi$
$733$	−26176.1	−	7685.99i	−1.31901	−	0.387297i	−0.864136	+	0.503259i	$0.832134\pi$
$734$	14436.6	−	31611.7i	0.725974	−	1.58966i
$735$	4873.12			0.244555
$736$	23900.1	−	4627.20i	1.19697	−	0.231740i
$737$	10418.9			0.520738
$738$	462.613	−	1012.98i	0.0230745	−	0.0505262i
$739$	21970.5	+	6451.12i	1.09364	+	0.321121i	0.778321	−	0.627866i	$-0.216071\pi$
$739$	21970.5	+	6451.12i	1.09364	+	0.321121i	0.315316	+	0.948987i	$0.397890\pi$
$740$	−6861.39	−	7918.47i	−0.340851	−	0.393363i
$741$	2291.87	−	1472.90i	0.113622	−	0.0730205i
$742$	−19240.3	+	22204.5i	−0.951932	+	1.09859i
$743$	3083.95	−	21449.4i	0.152274	−	1.05909i	−0.760123	−	0.649779i	$-0.774861\pi$
$743$	3083.95	−	21449.4i	0.152274	−	1.05909i	0.912397	−	0.409307i	$-0.134229\pi$
$744$	9358.03	−	2747.77i	0.461132	−	0.135401i
$745$	−14416.3	−	9264.82i	−0.708958	−	0.455620i
$746$	−385.906	−	2684.03i	−0.0189397	−	0.131728i
$747$	2304.92	+	5047.07i	0.112895	+	0.247206i
$748$	8406.17	+	18407.0i	0.410909	+	0.899766i
$749$	2006.73	+	13957.1i	0.0978963	+	0.680884i
$750$	1750.34	+	1124.88i	0.0852179	+	0.0547662i
$751$	24264.8	−	7124.80i	1.17901	−	0.346189i	0.367218	−	0.930135i	$-0.380310\pi$
$751$	24264.8	−	7124.80i	1.17901	−	0.346189i	0.811792	+	0.583946i	$0.198492\pi$
$752$	297.464	−	2068.91i	0.0144247	−	0.100326i
$753$	5818.46	−	6714.86i	0.281589	−	0.324971i
$754$	−54566.8	+	35068.0i	−2.63555	+	1.69377i
$755$	−2154.45	−	2486.37i	−0.103852	−	0.119852i
$756$	−9529.24	−	2798.04i	−0.458433	−	0.134608i
$757$	−4587.87	+	10046.0i	−0.220276	+	0.482337i	−0.987217	−	0.159380i	$-0.949050\pi$
$757$	−4587.87	+	10046.0i	−0.220276	+	0.482337i	0.766941	+	0.641717i	$0.221778\pi$
$758$	−24804.8			−1.18859
$759$	15760.7	+	12373.0i	0.753727	+	0.591713i
$760$	344.176			0.0164271
$761$	8842.06	−	19361.4i	0.421189	−	0.922274i	−0.573487	−	0.819215i	$-0.694410\pi$
$761$	8842.06	−	19361.4i	0.421189	−	0.922274i	0.994675	−	0.103059i	$-0.0328632\pi$
$762$	−37163.7	−	10912.2i	−1.76679	−	0.518778i
$763$	2312.48	+	2668.75i	0.109722	+	0.126625i
$764$	16896.2	−	10858.5i	0.800106	−	0.514197i
$765$

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)

\(f(q)\)	\(=\)	\(q+(-1.54534 + 3.38383i) q^{2} +(4.29324 + 1.26061i) q^{3} +(-3.82332 - 4.41235i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-10.9002 + 12.5795i) q^{6} +(-1.59229 + 11.0746i) q^{7} +(-7.71551 + 2.26548i) q^{8} +(-5.87108 - 3.77311i) q^{9} +O(q^{10})\)	\(q+(-1.54534 + 3.38383i) q^{2} +(4.29324 + 1.26061i) q^{3} +(-3.82332 - 4.41235i) q^{4} +(4.20627 - 2.70320i) q^{5} +(-10.9002 + 12.5795i) q^{6} +(-1.59229 + 11.0746i) q^{7} +(-7.71551 + 2.26548i) q^{8} +(-5.87108 - 3.77311i) q^{9} +(2.64705 + 18.4107i) q^{10} +(16.8650 + 36.9291i) q^{11} +(-10.8522 - 23.7630i) q^{12} +(10.1224 + 70.4026i) q^{13} +(-35.0139 - 22.5021i) q^{14} +(21.4662 - 6.30304i) q^{15} +(10.9042 - 75.8405i) q^{16} +(-55.9075 + 64.5207i) q^{17} +(21.8404 - 14.0360i) q^{18} +(-5.60580 - 6.46943i) q^{19} +(-28.0094 - 8.22430i) q^{20} +(-20.7968 + 45.5386i) q^{21} -151.024 q^{22} +(79.7668 - 76.1856i) q^{23} -35.9804 q^{24} +(10.3854 - 22.7408i) q^{25} +(-253.873 - 74.5438i) q^{26} +(-99.5640 - 114.903i) q^{27} +(54.9528 - 35.3160i) q^{28} +(160.537 - 185.270i) q^{29} +(-11.8442 + 82.3783i) q^{30} +(-260.087 + 76.3684i) q^{31} +(185.663 + 119.318i) q^{32} +(25.8521 + 179.806i) q^{33} +(-131.931 - 288.888i) q^{34} +(23.2393 + 50.8870i) q^{35} +(5.79873 + 40.3311i) q^{36} +(301.945 + 194.048i) q^{37} +(30.5543 - 8.97156i) q^{38} +(-45.2924 + 315.015i) q^{39} +(-26.3294 + 30.3858i) q^{40} +(36.0852 - 23.1905i) q^{41} +(-121.957 - 140.746i) q^{42} +(319.198 + 93.7251i) q^{43} +(98.4639 - 215.606i) q^{44} -34.8948 q^{45} +(134.532 + 387.650i) q^{46} +27.2797 q^{47} +(142.420 - 311.855i) q^{48} +(208.995 + 61.3664i) q^{49} +(60.9020 + 70.2847i) q^{50} +(-321.360 + 206.525i) q^{51} +(271.940 - 313.835i) q^{52} +(100.461 - 698.725i) q^{53} +(542.672 - 159.343i) q^{54} +(170.765 + 109.744i) q^{55} +(-12.8039 - 89.0534i) q^{56} +(-15.9116 - 34.8415i) q^{57} +(378.837 + 829.537i) q^{58} +(49.5248 + 344.452i) q^{59} +(-109.883 - 70.6178i) q^{60} +(-147.816 + 43.4027i) q^{61} +(143.506 - 998.105i) q^{62} +(51.1341 - 59.0119i) q^{63} +(-175.007 + 112.470i) q^{64} +(232.890 + 268.769i) q^{65} +(-648.382 - 190.382i) q^{66} +(106.610 - 233.444i) q^{67} +498.440 q^{68} +(438.498 - 226.528i) q^{69} -208.105 q^{70} +(15.8496 - 34.7058i) q^{71} +(53.8462 + 15.8107i) q^{72} +(690.690 + 797.099i) q^{73} +(-1123.23 + 721.859i) q^{74} +(73.2542 - 84.5398i) q^{75} +(-7.11264 + 49.4695i) q^{76} +(-435.829 + 127.971i) q^{77} +(-995.966 - 640.068i) q^{78} +(-9.65990 - 67.1861i) q^{79} +(-159.146 - 348.482i) q^{80} +(-204.327 - 447.414i) q^{81} +(22.7088 + 157.943i) q^{82} +(-668.821 - 429.825i) q^{83} +(280.445 - 82.3462i) q^{84} +(-60.7493 + 422.521i) q^{85} +(-810.420 + 935.275i) q^{86} +(922.779 - 593.034i) q^{87} +(-213.784 - 246.720i) q^{88} +(-622.552 - 182.798i) q^{89} +(53.9244 - 118.078i) q^{90} -795.798 q^{91} +(-641.132 - 60.6768i) q^{92} -1212.89 q^{93} +(-42.1565 + 92.3098i) q^{94} +(-41.0677 - 12.0586i) q^{95} +(646.681 + 746.309i) q^{96} +(-571.497 + 367.279i) q^{97} +(-530.622 + 612.370i) q^{98} +(40.3222 - 280.447i) 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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