LMFDB - Embedded newform 117.4.g.f.100.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.g (of order $3$, degree $2$, 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:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + 21016320 x^{2} + 24920064 $ x^16 + 52x^14 + 1899x^12 + 33440x^10 + 424113x^8 + 2869882x^6 + 13705540x^4 + 21016320*x^2 + 24920064
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.3
Root			$-1.37814 + 2.38701i$ of defining polynomial
Character	$\chi$	$=$	117.100
Dual form			117.4.g.f.55.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37814 + 2.38701i) q^{2} +(0.201468 + 0.348954i) q^{4} +0.313209 q^{5} +(-14.2830 - 24.7388i) q^{7} -23.1608 q^{8} +O(q^{10})$	\(q+(-1.37814 + 2.38701i) q^{2} +(0.201468 + 0.348954i) q^{4} +0.313209 q^{5} +(-14.2830 - 24.7388i) q^{7} -23.1608 q^{8} +(-0.431646 + 0.747632i) q^{10} +(-31.6086 + 54.7478i) q^{11} +(-2.26982 - 46.8172i) q^{13} +78.7357 q^{14} +(30.3071 - 52.4934i) q^{16} +(-49.4135 - 85.5867i) q^{17} +(7.24486 + 12.5485i) q^{19} +(0.0631018 + 0.109295i) q^{20} +(-87.1222 - 150.900i) q^{22} +(7.19499 - 12.4621i) q^{23} -124.902 q^{25} +(114.881 + 59.1025i) q^{26} +(5.75514 - 9.96819i) q^{28} +(98.1415 - 169.986i) q^{29} +118.691 q^{31} +(-9.10860 - 15.7766i) q^{32} +272.395 q^{34} +(-4.47356 - 7.74843i) q^{35} +(-159.557 + 276.361i) q^{37} -39.9377 q^{38} -7.25418 q^{40} +(-173.053 + 299.737i) q^{41} +(34.7427 + 60.1761i) q^{43} -25.4726 q^{44} +(19.8314 + 34.3490i) q^{46} -101.875 q^{47} +(-236.507 + 409.642i) q^{49} +(172.132 - 298.142i) q^{50} +(15.8797 - 10.2242i) q^{52} -594.823 q^{53} +(-9.90012 + 17.1475i) q^{55} +(330.806 + 572.972i) q^{56} +(270.505 + 468.529i) q^{58} +(102.237 + 177.079i) q^{59} +(107.989 + 187.043i) q^{61} +(-163.572 + 283.315i) q^{62} +535.125 q^{64} +(-0.710929 - 14.6636i) q^{65} +(-34.3025 + 59.4136i) q^{67} +(19.9105 - 34.4860i) q^{68} +24.6607 q^{70} +(-473.121 - 819.469i) q^{71} -779.872 q^{73} +(-439.784 - 761.727i) q^{74} +(-2.91922 + 5.05624i) q^{76} +1805.86 q^{77} +240.022 q^{79} +(9.49245 - 16.4414i) q^{80} +(-476.982 - 826.158i) q^{82} +855.576 q^{83} +(-15.4768 - 26.8065i) q^{85} -191.521 q^{86} +(732.082 - 1268.00i) q^{88} +(-632.029 + 1094.71i) q^{89} +(-1125.78 + 724.842i) q^{91} +5.79825 q^{92} +(140.398 - 243.176i) q^{94} +(2.26916 + 3.93030i) q^{95} +(-331.145 - 573.560i) q^{97} +(-651.879 - 1129.09i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 40 q^{4} + 22 q^{7}+O(q^{10}) $ 16 * q - 40 * q^4 + 22 * q^7	$ 16 q - 40 q^{4} + 22 q^{7} - 36 q^{10} + 36 q^{13} - 204 q^{16} - 244 q^{19} - 136 q^{22} + 708 q^{25} + 452 q^{28} + 484 q^{31} - 2584 q^{34} - 1018 q^{37} + 3400 q^{40} - 74 q^{43} + 896 q^{46} - 298 q^{49} - 1676 q^{52} - 1300 q^{55} - 812 q^{58} - 1148 q^{61} + 7272 q^{64} + 2198 q^{67} + 4400 q^{70} - 4352 q^{73} - 6936 q^{76} + 3724 q^{79} - 5436 q^{82} + 890 q^{85} - 3528 q^{88} - 4754 q^{91} + 3104 q^{94} + 4370 q^{97}+O(q^{100}) $ 16 * q - 40 * q^4 + 22 * q^7 - 36 * q^10 + 36 * q^13 - 204 * q^16 - 244 * q^19 - 136 * q^22 + 708 * q^25 + 452 * q^28 + 484 * q^31 - 2584 * q^34 - 1018 * q^37 + 3400 * q^40 - 74 * q^43 + 896 * q^46 - 298 * q^49 - 1676 * q^52 - 1300 * q^55 - 812 * q^58 - 1148 * q^61 + 7272 * q^64 + 2198 * q^67 + 4400 * q^70 - 4352 * q^73 - 6936 * q^76 + 3724 * q^79 - 5436 * q^82 + 890 * q^85 - 3528 * q^88 - 4754 * q^91 + 3104 * q^94 + 4370 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.37814	+	2.38701i	−0.487246	+	0.843934i	−0.999892	−	0.0146655i	$-0.995332\pi$
$2$	−1.37814	+	2.38701i	−0.487246	+	0.843934i	0.512647	+	0.858600i	$0.328665\pi$
$3$		0			0
$3$		0			0
$4$	0.201468	+	0.348954i	0.0251836	+	0.0436192i
$5$	0.313209			0.0280143			0.0140071	−	0.999902i	$-0.495541\pi$
$5$	0.313209			0.0280143			0.0140071	+	0.999902i	$0.495541\pi$
$6$		0			0
$7$	−14.2830	−	24.7388i	−0.771208	−	1.33577i	−0.936901	−	0.349595i	$-0.886319\pi$
$7$	−14.2830	−	24.7388i	−0.771208	−	1.33577i	0.165693	−	0.986177i	$-0.447014\pi$
$8$	−23.1608			−1.02357
$9$		0			0
$10$	−0.431646	+	0.747632i	−0.0136498	+	0.0236422i
$11$	−31.6086	+	54.7478i	−0.866397	+	1.50064i	−0.000743312		1.00000i	$0.500237\pi$
$11$	−31.6086	+	54.7478i	−0.866397	+	1.50064i	−0.865654	+	0.500644i	$0.833097\pi$
$12$		0			0
$13$	−2.26982	−	46.8172i	−0.0484258	−	0.998827i
$13$	−2.26982	−	46.8172i	−0.0484258	−	0.998827i
$14$	78.7357			1.50307
$15$		0			0
$16$	30.3071	−	52.4934i	0.473548	−	0.820209i
$17$	−49.4135	−	85.5867i	−0.704973	−	1.22105i	−0.966701	−	0.255907i	$-0.917626\pi$
$17$	−49.4135	−	85.5867i	−0.704973	−	1.22105i	0.261729	−	0.965142i	$-0.415708\pi$
$18$		0			0
$19$	7.24486	+	12.5485i	0.0874782	+	0.151517i	0.906445	−	0.422325i	$-0.138786\pi$
$19$	7.24486	+	12.5485i	0.0874782	+	0.151517i	−0.818966	+	0.573842i	$0.805453\pi$
$20$	0.0631018	+	0.109295i	0.000705499	+	0.00122196i
$21$		0			0
$22$	−87.1222	−	150.900i	−0.844296	−	1.46236i
$23$	7.19499	−	12.4621i	0.0652286	−	0.112979i	−0.831567	−	0.555425i	$-0.812556\pi$
$23$	7.19499	−	12.4621i	0.0652286	−	0.112979i	0.896795	+	0.442446i	$0.145889\pi$
$24$		0			0
$25$	−124.902			−0.999215
$26$	114.881	+	59.1025i	0.866539	+	0.445806i
$27$		0			0
$28$	5.75514	−	9.96819i	0.0388435	−	0.0672790i
$29$	98.1415	−	169.986i	0.628428	−	1.08847i	−0.359439	−	0.933169i	$-0.617032\pi$
$29$	98.1415	−	169.986i	0.628428	−	1.08847i	0.987867	−	0.155301i	$-0.0496347\pi$
$30$		0			0
$31$	118.691			0.687661			0.343830	−	0.939032i	$-0.388276\pi$
$31$	118.691			0.687661			0.343830	+	0.939032i	$0.388276\pi$
$32$	−9.10860	−	15.7766i	−0.0503184	−	0.0871540i
$33$		0			0
$34$	272.395			1.37398
$35$	−4.47356	−	7.74843i	−0.0216048	−	0.0374207i
$36$		0			0
$37$	−159.557	+	276.361i	−0.708947	+	1.22793i	0.256302	+	0.966597i	$0.417496\pi$
$37$	−159.557	+	276.361i	−0.708947	+	1.22793i	−0.965248	+	0.261335i	$0.915837\pi$
$38$	−39.9377			−0.170493
$39$		0			0
$40$	−7.25418			−0.0286747
$41$	−173.053	+	299.737i	−0.659180	+	1.14173i	0.321649	+	0.946859i	$0.395763\pi$
$41$	−173.053	+	299.737i	−0.659180	+	1.14173i	−0.980828	+	0.194873i	$0.937570\pi$
$42$		0			0
$43$	34.7427	+	60.1761i	0.123214	+	0.213413i	0.921033	−	0.389483i	$-0.127346\pi$
$43$	34.7427	+	60.1761i	0.123214	+	0.213413i	−0.797819	+	0.602897i	$0.794013\pi$
$44$	−25.4726			−0.0872758
$45$		0			0
$46$	19.8314	+	34.3490i	0.0635647	+	0.110097i
$47$	−101.875			−0.316170			−0.158085	−	0.987426i	$-0.550532\pi$
$47$	−101.875			−0.316170			−0.158085	+	0.987426i	$0.550532\pi$
$48$		0			0
$49$	−236.507	+	409.642i	−0.689525	+	1.19429i
$50$	172.132	−	298.142i	0.486863	−	0.843272i
$51$		0			0
$52$	15.8797	−	10.2242i	0.0423485	−	0.0272663i
$53$	−594.823			−1.54161			−0.770804	−	0.637072i	$-0.780145\pi$
$53$	−594.823			−1.54161			−0.770804	+	0.637072i	$0.780145\pi$
$54$		0			0
$55$	−9.90012	+	17.1475i	−0.0242715	+	0.0420394i
$56$	330.806	+	572.972i	0.789388	+	1.36726i
$57$		0			0
$58$	270.505	+	468.529i	0.612398	+	1.06070i
$59$	102.237	+	177.079i	0.225595	+	0.390741i	0.956498	−	0.291740i	$-0.0942342\pi$
$59$	102.237	+	177.079i	0.225595	+	0.390741i	−0.730903	+	0.682481i	$0.760901\pi$
$60$		0			0
$61$	107.989	+	187.043i	0.226666	+	0.392596i	0.956818	−	0.290688i	$-0.0938842\pi$
$61$	107.989	+	187.043i	0.226666	+	0.392596i	−0.730152	+	0.683285i	$0.760551\pi$
$62$	−163.572	+	283.315i	−0.335060	+	0.580340i
$63$		0			0
$64$	535.125			1.04517
$65$	−0.710929	−	14.6636i	−0.00135661	−	0.0279814i
$66$		0			0
$67$	−34.3025	+	59.4136i	−0.0625480	+	0.108336i	−0.895604	−	0.444853i	$-0.853256\pi$
$67$	−34.3025	+	59.4136i	−0.0625480	+	0.108336i	0.833056	+	0.553189i	$0.186589\pi$
$68$	19.9105	−	34.4860i	0.0355074	−	0.0615007i
$69$		0			0
$70$	24.6607			0.0421075
$71$	−473.121	−	819.469i	−0.790832	−	1.36976i	−0.925452	−	0.378864i	$-0.876315\pi$
$71$	−473.121	−	819.469i	−0.790832	−	1.36976i	0.134620	−	0.990897i	$-0.457019\pi$
$72$		0			0
$73$	−779.872			−1.25037			−0.625185	−	0.780476i	$-0.714977\pi$
$73$	−779.872			−1.25037			−0.625185	+	0.780476i	$0.714977\pi$
$74$	−439.784	−	761.727i	−0.690862	−	1.19661i
$75$		0			0
$76$	−2.91922	+	5.05624i	−0.00440602	+	0.00763145i
$77$	1805.86			2.67269
$78$		0			0
$79$	240.022			0.341831			0.170915	−	0.985286i	$-0.445328\pi$
$79$	240.022			0.341831			0.170915	+	0.985286i	$0.445328\pi$
$80$	9.49245	−	16.4414i	0.0132661	−	0.0229776i
$81$		0			0
$82$	−476.982	−	826.158i	−0.642365	−	1.11261i
$83$	855.576			1.13147			0.565733	−	0.824588i	$-0.308593\pi$
$83$	855.576			1.13147			0.565733	+	0.824588i	$0.308593\pi$
$84$		0			0
$85$	−15.4768	−	26.8065i	−0.0197493	−	0.0342068i
$86$	−191.521			−0.240142
$87$		0			0
$88$	732.082	−	1268.00i	0.886821	−	1.53602i
$89$	−632.029	+	1094.71i	−0.752753	+	1.30381i	0.193731	+	0.981055i	$0.437941\pi$
$89$	−632.029	+	1094.71i	−0.752753	+	1.30381i	−0.946484	+	0.322751i	$0.895392\pi$
$90$		0			0
$91$	−1125.78	+	724.842i	−1.29686	+	0.834989i
$92$	5.79825			0.00657075
$93$		0			0
$94$	140.398	−	243.176i	0.154052	−	0.266826i
$95$	2.26916	+	3.93030i	0.00245064	+	0.00424463i
$96$		0			0
$97$	−331.145	−	573.560i	−0.346625	−	0.600373i	0.639022	−	0.769188i	$-0.279339\pi$
$97$	−331.145	−	573.560i	−0.346625	−	0.600373i	−0.985648	+	0.168815i	$0.946006\pi$
$98$	−651.879	−	1129.09i	−0.671936	−	1.16383i
$99$		0			0
$100$	−25.1638	−	43.5850i	−0.0251638	−	0.0435850i
$101$	396.785	−	687.252i	0.390907	−	0.677071i	−0.601662	−	0.798751i	$-0.705495\pi$
$101$	396.785	−	687.252i	0.390907	−	0.677071i	0.992569	+	0.121680i	$0.0388281\pi$
$102$		0			0
$103$	980.791			0.938254			0.469127	−	0.883131i	$-0.344569\pi$
$103$	980.791			0.938254			0.469127	+	0.883131i	$0.344569\pi$
$104$	52.5710	+	1084.32i	0.0495674	+	1.02237i
$105$		0			0
$106$	819.749	−	1419.85i	0.751142	−	1.30102i
$107$	402.972	−	697.968i	0.364082	−	0.630609i	−0.624546	−	0.780988i	$-0.714716\pi$
$107$	402.972	−	697.968i	0.364082	−	0.630609i	0.988628	+	0.150379i	$0.0480494\pi$
$108$		0			0
$109$	845.184			0.742697			0.371348	−	0.928494i	$-0.378896\pi$
$109$	845.184			0.742697			0.371348	+	0.928494i	$0.378896\pi$
$110$	−27.2875	−	47.2633i	−0.0236523	−	0.0409671i
$111$		0			0
$112$	−1731.50			−1.46082
$113$	−28.1887	−	48.8243i	−0.0234670	−	0.0406460i	0.854053	−	0.520185i	$-0.174137\pi$
$113$	−28.1887	−	48.8243i	−0.0234670	−	0.0406460i	−0.877520	+	0.479539i	$0.840804\pi$
$114$		0			0
$115$	2.25354	−	3.90324i	0.00182733	−	0.00316503i
$116$	79.0896			0.0633042
$117$		0			0
$118$	−563.585			−0.439680
$119$	−1411.54	+	2444.87i	−1.08736	+	1.88337i
$120$		0			0
$121$	−1332.71	−	2308.33i	−1.00129	−	1.73428i
$122$	−595.296			−0.441767
$123$		0			0
$124$	23.9124	+	41.4175i	0.0173177	+	0.0299952i
$125$	−78.2716			−0.0560066
$126$		0			0
$127$	−833.323	+	1443.36i	−0.582248	+	1.00848i	0.412965	+	0.910747i	$0.364493\pi$
$127$	−833.323	+	1443.36i	−0.582248	+	1.00848i	−0.995212	+	0.0977357i	$0.968840\pi$
$128$	−664.607	+	1151.13i	−0.458934	+	0.794897i
$129$		0			0
$130$	35.9818	+	18.5114i	0.0242755	+	0.0124889i
$131$	−602.630			−0.401924			−0.200962	−	0.979599i	$-0.564407\pi$
$131$	−602.630			−0.401924			−0.200962	+	0.979599i	$0.564407\pi$
$132$		0			0
$133$	206.956	−	358.459i	0.134928	−	0.233702i
$134$	−94.5471	−	163.760i	−0.0609524	−	0.105573i
$135$		0			0
$136$	1144.46	+	1982.26i	0.721591	+	1.24983i
$137$	−210.827	−	365.163i	−0.131476	−	0.227722i	0.792770	−	0.609521i	$-0.208638\pi$
$137$	−210.827	−	365.163i	−0.131476	−	0.227722i	−0.924246	+	0.381799i	$0.875305\pi$
$138$		0			0
$139$	−14.5851	−	25.2622i	−0.00889995	−	0.0154152i	0.861541	−	0.507688i	$-0.169500\pi$
$139$	−14.5851	−	25.2622i	−0.00889995	−	0.0154152i	−0.870441	+	0.492273i	$0.836166\pi$
$140$	1.80256	−	3.12213i	0.00108817	−	0.00188477i
$141$		0			0
$142$	2608.10			1.54132
$143$	2634.88	+	1355.56i	1.54084	+	0.792710i
$144$		0			0
$145$	30.7388	−	53.2412i	0.0176050	−	0.0304927i
$146$	1074.77	−	1861.56i	0.609238	−	1.05523i
$147$		0			0
$148$	−128.583			−0.0714152
$149$	−1070.90	−	1854.85i	−0.588802	−	1.01983i	−0.994390	−	0.105778i	$-0.966267\pi$
$149$	−1070.90	−	1854.85i	−0.588802	−	1.01983i	0.405588	−	0.914056i	$-0.367067\pi$
$150$		0			0
$151$	1459.30			0.786462			0.393231	−	0.919440i	$-0.371357\pi$
$151$	1459.30			0.786462			0.393231	+	0.919440i	$0.371357\pi$
$152$	−167.797	−	290.633i	−0.0895403	−	0.155088i
$153$		0			0
$154$	−2488.73	+	4310.60i	−1.30226	+	2.25557i
$155$	37.1750			0.0192643
$156$		0			0
$157$	2008.20			1.02084			0.510419	−	0.859926i	$-0.329490\pi$
$157$	2008.20			1.02084			0.510419	+	0.859926i	$0.329490\pi$
$158$	−330.784	+	572.935i	−0.166555	+	0.288482i
$159$		0			0
$160$	−2.85290	−	4.94136i	−0.00140963	−	0.00244156i
$161$	−411.063			−0.201219
$162$		0			0
$163$	−274.248	−	475.011i	−0.131784	−	0.228256i	0.792581	−	0.609767i	$-0.208737\pi$
$163$	−274.248	−	475.011i	−0.131784	−	0.228256i	−0.924364	+	0.381511i	$0.875404\pi$
$164$	−139.459			−0.0664019
$165$		0			0
$166$	−1179.10	+	2042.27i	−0.551302	+	0.954883i
$167$	1981.29	−	3431.69i	0.918064	−	1.59013i	0.115712	−	0.993283i	$-0.463085\pi$
$167$	1981.29	−	3431.69i	0.918064	−	1.59013i	0.802352	−	0.596851i	$-0.203582\pi$
$168$		0			0
$169$	−2186.70	+	212.533i	−0.995310	+	0.0967380i
$170$	85.3165			0.0384910
$171$		0			0
$172$	−13.9991	+	24.2472i	−0.00620594	+	0.0107490i
$173$	864.771	+	1497.83i	0.380042	+	0.658252i	0.991068	−	0.133358i	$-0.0425762\pi$
$173$	864.771	+	1497.83i	0.380042	+	0.658252i	−0.611026	+	0.791611i	$0.709243\pi$
$174$		0			0
$175$	1783.97	+	3089.93i	0.770603	+	1.33472i
$176$	1915.93	+	3318.49i	0.820561	+	1.42125i
$177$		0			0
$178$	−1742.05	−	3017.32i	−0.733551	−	1.27055i
$179$	−726.456	+	1258.26i	−0.303340	+	0.525400i	−0.976890	−	0.213741i	$-0.931435\pi$
$179$	−726.456	+	1258.26i	−0.303340	+	0.525400i	0.673550	+	0.739141i	$0.264768\pi$
$180$		0			0
$181$	−550.329			−0.225998			−0.112999	−	0.993595i	$-0.536046\pi$
$181$	−550.329			−0.225998			−0.112999	+	0.993595i	$0.536046\pi$
$182$	−178.716	−	3686.18i	−0.0727875	−	1.50131i
$183$		0			0
$184$	−166.642	+	288.632i	−0.0667663	+	0.115643i
$185$	−49.9747	+	86.5588i	−0.0198606	+	0.0343996i
$186$		0			0
$187$	6247.58			2.44314
$188$	−20.5246	−	35.5496i	−0.00796228	−	0.0137911i
$189$		0			0
$190$	−12.5089			−0.00477625
$191$	−934.340	−	1618.32i	−0.353960	−	0.613078i	0.632979	−	0.774169i	$-0.281832\pi$
$191$	−934.340	−	1618.32i	−0.353960	−	0.613078i	−0.986939	+	0.161091i	$0.948499\pi$
$192$		0			0
$193$	−2078.26	+	3599.66i	−0.775112	+	1.34253i	0.159620	+	0.987179i	$0.448973\pi$
$193$	−2078.26	+	3599.66i	−0.775112	+	1.34253i	−0.934732	+	0.355354i	$0.884360\pi$
$194$	1825.45			0.675567
$195$		0			0
$196$	−190.595			−0.0694587
$197$	761.092	−	1318.25i	0.275257	−	0.476758i	−0.694943	−	0.719065i	$-0.744571\pi$
$197$	761.092	−	1318.25i	0.275257	−	0.476758i	0.970200	+	0.242306i	$0.0779038\pi$
$198$		0			0
$199$	−404.065	−	699.861i	−0.143937	−	0.249306i	0.785039	−	0.619446i	$-0.212643\pi$
$199$	−404.065	−	699.861i	−0.143937	−	0.249306i	−0.928976	+	0.370141i	$0.879309\pi$
$200$	2892.83			1.02277
$201$		0			0
$202$	1093.65	+	1894.26i	0.380935	+	0.659800i
$203$	−5607.01			−1.93860
$204$		0			0
$205$	−54.2018	+	93.8803i	−0.0184664	+	0.0319848i
$206$	−1351.67	+	2341.15i	−0.457160	+	0.791825i
$207$		0			0
$208$	−2526.38	−	1299.74i	−0.842179	−	0.433273i
$209$	−916.001			−0.303163
$210$		0			0
$211$	2630.02	−	4555.32i	0.858094	−	1.48626i	−0.0156511	−	0.999878i	$-0.504982\pi$
$211$	2630.02	−	4555.32i	0.858094	−	1.48626i	0.873745	−	0.486384i	$-0.161685\pi$
$212$	−119.838	−	207.566i	−0.0388232	−	0.0672437i
$213$		0			0
$214$	1110.70	+	1923.79i	0.354795	+	0.614523i
$215$	10.8817	+	18.8477i	0.00345176	+	0.00597862i
$216$		0			0
$217$	−1695.26	−	2936.27i	−0.530330	−	0.918558i
$218$	−1164.78	+	2017.46i	−0.361876	+	0.626787i
$219$		0			0
$220$	−7.97824			−0.00244497
$221$	−3894.77	+	2507.67i	−1.18548	+	0.763276i
$222$		0			0
$223$	2345.36	−	4062.28i	0.704290	−	1.21987i	−0.262657	−	0.964889i	$-0.584599\pi$
$223$	2345.36	−	4062.28i	0.704290	−	1.21987i	0.966947	−	0.254977i	$-0.0820678\pi$
$224$	−260.196	+	450.672i	−0.0776119	+	0.134428i
$225$		0			0
$226$	155.392			0.0457368
$227$	1780.31	+	3083.58i	0.520542	+	0.901606i	0.999715	+	0.0238849i	$0.00760352\pi$
$227$	1780.31	+	3083.58i	0.520542	+	0.901606i	−0.479172	+	0.877721i	$0.659063\pi$
$228$		0			0
$229$	−3144.82			−0.907490			−0.453745	−	0.891131i	$-0.649912\pi$
$229$	−3144.82			−0.907490			−0.453745	+	0.891131i	$0.649912\pi$
$230$	6.21137	+	10.7584i	0.00178072	+	0.00308430i
$231$		0			0
$232$	−2273.04	+	3937.02i	−0.643242	+	1.11413i
$233$	852.543			0.239708			0.119854	−	0.992792i	$-0.461757\pi$
$233$	852.543			0.239708			0.119854	+	0.992792i	$0.461757\pi$
$234$		0			0
$235$	−31.9081			−0.00885727
$236$	−41.1949	+	71.3517i	−0.0113625	+	0.0196805i
$237$		0			0
$238$	−3890.61	−	6738.73i	−1.05962	−	1.83532i
$239$	−2189.33			−0.592534			−0.296267	−	0.955105i	$-0.595742\pi$
$239$	−2189.33			−0.592534			−0.296267	+	0.955105i	$0.595742\pi$
$240$		0			0
$241$	−3164.99	−	5481.92i	−0.845954	−	1.46523i	−0.884791	−	0.465989i	$-0.845699\pi$
$241$	−3164.99	−	5481.92i	−0.845954	−	1.46523i	0.0388369	−	0.999246i	$-0.487635\pi$
$242$	7346.65			1.95149
$243$		0			0
$244$	−43.5128	+	75.3664i	−0.0114165	+	0.0197739i
$245$	−74.0762	+	128.304i	−0.0193165	+	0.0334572i
$246$		0			0
$247$	571.039	−	367.667i	0.147103	−	0.0947129i
$248$	−2748.97			−0.703871
$249$		0			0
$250$	107.869	−	186.835i	0.0272890	−	0.0472659i
$251$	−1801.49	−	3120.27i	−0.453023	−	0.784659i	0.545549	−	0.838079i	$-0.316321\pi$
$251$	−1801.49	−	3120.27i	−0.453023	−	0.784659i	−0.998572	+	0.0534200i	$0.982988\pi$
$252$		0			0
$253$	454.848	+	787.819i	0.113028	+	0.195770i
$254$	−2296.87	−	3978.29i	−0.567395	−	0.982757i
$255$		0			0
$256$	308.657	+	534.610i	0.0753558	+	0.130520i
$257$	1536.32	−	2660.98i	0.372891	−	0.645865i	−0.617118	−	0.786870i	$-0.711700\pi$
$257$	1536.32	−	2660.98i	0.372891	−	0.645865i	0.990009	+	0.141005i	$0.0450334\pi$
$258$		0			0
$259$	9115.80			2.18698
$260$	4.97367	−	3.20233i	0.00118636	−	0.000763846i
$261$		0			0
$262$	830.507	−	1438.48i	0.195836	−	0.339197i
$263$	−1771.60	+	3068.50i	−0.415367	+	0.719437i	−0.995467	−	0.0951084i	$-0.969680\pi$
$263$	−1771.60	+	3068.50i	−0.415367	+	0.719437i	0.580100	+	0.814545i	$0.303014\pi$
$264$		0			0
$265$	−186.304			−0.0431871
$266$	570.429	+	988.012i	0.131486	+	0.227740i
$267$		0			0
$268$	−27.6435			−0.00630072
$269$	2949.98	+	5109.52i	0.668638	+	1.15811i	0.978285	+	0.207263i	$0.0664557\pi$
$269$	2949.98	+	5109.52i	0.668638	+	1.15811i	−0.309647	+	0.950852i	$0.600211\pi$
$270$		0			0
$271$	1054.76	−	1826.90i	0.236429	−	0.409507i	−0.723258	−	0.690578i	$-0.757356\pi$
$271$	1054.76	−	1826.90i	0.236429	−	0.409507i	0.959687	+	0.281071i	$0.0906896\pi$
$272$	−5990.32			−1.33535
$273$		0			0
$274$	1162.19			0.256244
$275$	3947.98	−	6838.10i	0.865717	−	1.49947i
$276$		0			0
$277$	−3632.50	−	6291.67i	−0.787927	−	1.36473i	−0.927235	−	0.374480i	$-0.877821\pi$
$277$	−3632.50	−	6291.67i	−0.787927	−	1.36473i	0.139308	−	0.990249i	$-0.455512\pi$
$278$	80.4012			0.0173458
$279$		0			0
$280$	103.611	+	179.460i	0.0221141	+	0.0383028i
$281$	4771.36			1.01294			0.506469	−	0.862258i	$-0.330951\pi$
$281$	4771.36			1.01294			0.506469	+	0.862258i	$0.330951\pi$
$282$		0			0
$283$	−1018.13	+	1763.45i	−0.213857	+	0.370411i	−0.952918	−	0.303227i	$-0.901936\pi$
$283$	−1018.13	+	1763.45i	−0.213857	+	0.370411i	0.739061	+	0.673638i	$0.235269\pi$
$284$	190.638	−	330.194i	0.0398319	−	0.0689909i
$285$		0			0
$286$	−6866.96	+	4421.33i	−1.41976	+	0.914122i
$287$	9886.86			2.03346
$288$		0			0
$289$	−2426.89	+	4203.50i	−0.493973	+	0.855587i
$290$	84.7247	+	146.747i	0.0171559	+	0.0297148i
$291$		0			0
$292$	−157.119	−	272.139i	−0.0314888	−	0.0545402i
$293$	−1859.51	−	3220.77i	−0.370764	−	0.642182i	0.618920	−	0.785454i	$-0.287571\pi$
$293$	−1859.51	−	3220.77i	−0.370764	−	0.642182i	−0.989683	+	0.143273i	$0.954237\pi$
$294$		0			0
$295$	32.0215	+	55.4628i	0.00631987	+	0.0109463i
$296$	3695.47	−	6400.75i	0.725659	−	1.25688i
$297$		0			0
$298$	5903.39			1.14756
$299$	−599.771	−	308.562i	−0.116005	−	0.0596810i
$300$		0			0
$301$	992.458	−	1718.99i	0.190048	−	0.329172i
$302$	−2011.11	+	3483.35i	−0.383200	+	0.663722i
$303$		0			0
$304$	878.282			0.165700
$305$	33.8232	+	58.5835i	0.00634987	+	0.0109983i
$306$		0			0
$307$	−7282.24			−1.35381			−0.676905	−	0.736070i	$-0.736679\pi$
$307$	−7282.24			−1.35381			−0.676905	+	0.736070i	$0.736679\pi$
$308$	363.824	+	630.162i	0.0673078	+	0.116581i
$309$		0			0
$310$	−51.2323	+	88.7370i	−0.00938645	+	0.0162578i
$311$	−4569.28			−0.833120			−0.416560	−	0.909108i	$-0.636764\pi$
$311$	−4569.28			−0.833120			−0.416560	+	0.909108i	$0.636764\pi$
$312$		0			0
$313$	21.0294			0.00379761			0.00189880	−	0.999998i	$-0.499396\pi$
$313$	21.0294			0.00379761			0.00189880	+	0.999998i	$0.499396\pi$
$314$	−2767.57	+	4793.58i	−0.497399	+	0.861520i
$315$		0			0
$316$	48.3569	+	83.7566i	0.00860851	+	0.0149104i
$317$	−5159.17			−0.914095			−0.457047	−	0.889442i	$-0.651093\pi$
$317$	−5159.17			−0.914095			−0.457047	+	0.889442i	$0.651093\pi$
$318$		0			0
$319$	6204.24	+	10746.1i	1.08894	+	1.88609i
$320$	167.606			0.0292796
$321$		0			0
$322$	566.502	−	981.211i	0.0980433	−	0.169816i
$323$	715.988	−	1240.13i	0.123339	−	0.213630i
$324$		0			0
$325$	283.505	+	5847.55i	0.0483878	+	0.998043i
$326$	1511.80			0.256844
$327$		0			0
$328$	4008.05	−	6942.15i	0.674719	−	1.16865i
$329$	1455.08	+	2520.27i	0.243833	+	0.422331i
$330$		0			0
$331$	3788.76	+	6562.33i	0.629152	+	1.08972i	0.987722	+	0.156220i	$0.0499309\pi$
$331$	3788.76	+	6562.33i	0.629152	+	1.08972i	−0.358570	+	0.933503i	$0.616736\pi$
$332$	172.372	+	298.556i	0.0284943	+	0.0493536i
$333$		0			0
$334$	5460.98	+	9458.70i	0.894645	+	1.54957i
$335$	−10.7438	+	18.6089i	−0.00175224	+	0.00303496i
$336$		0			0
$337$	−2109.79			−0.341032			−0.170516	−	0.985355i	$-0.554543\pi$
$337$	−2109.79			−0.341032			−0.170516	+	0.985355i	$0.554543\pi$
$338$	2506.25	−	5512.56i	0.403320	−	0.887111i
$339$		0			0
$340$	6.23616	−	10.8013i	0.000994715	−	0.00172290i
$341$	−3751.65	+	6498.05i	−0.595787	+	1.03193i
$342$		0			0
$343$	3713.98			0.584653
$344$	−804.669	−	1393.73i	−0.126119	−	0.218444i
$345$		0			0
$346$	−4767.09			−0.740695
$347$	4053.95	+	7021.65i	0.627169	+	1.08629i	0.988117	+	0.153703i	$0.0491198\pi$
$347$	4053.95	+	7021.65i	0.627169	+	1.08629i	−0.360948	+	0.932586i	$0.617547\pi$
$348$		0			0
$349$	−4343.19	+	7522.62i	−0.666148	+	1.15380i	0.312825	+	0.949811i	$0.398725\pi$
$349$	−4343.19	+	7522.62i	−0.666148	+	1.15380i	−0.978973	+	0.203991i	$0.934609\pi$
$350$	−9834.24			−1.50189
$351$		0			0
$352$	1151.64			0.174383
$353$	4525.12	−	7837.73i	0.682288	−	1.18176i	−0.291993	−	0.956421i	$-0.594318\pi$
$353$	4525.12	−	7837.73i	0.682288	−	1.18176i	0.974281	−	0.225337i	$-0.0723483\pi$
$354$		0			0
$355$	−148.186	−	256.665i	−0.0221546	−	0.0383729i
$356$	−509.336			−0.0758279
$357$		0			0
$358$	−2002.31	−	3468.11i	−0.295602	−	0.511998i
$359$	−7043.80			−1.03554			−0.517768	−	0.855521i	$-0.673237\pi$
$359$	−7043.80			−1.03554			−0.517768	+	0.855521i	$0.673237\pi$
$360$		0			0
$361$	3324.52	−	5758.24i	0.484695	−	0.839517i
$362$	758.429	−	1313.64i	0.110116	−	0.190727i
$363$		0			0
$364$	−479.746	−	246.813i	−0.0690811	−	0.0355399i
$365$	−244.263			−0.0350282
$366$		0			0
$367$	−6912.55	+	11972.9i	−0.983194	+	1.70294i	−0.333491	+	0.942753i	$0.608227\pi$
$367$	−6912.55	+	11972.9i	−0.983194	+	1.70294i	−0.649703	+	0.760188i	$0.725107\pi$
$368$	−436.118	−	755.378i	−0.0617778	−	0.107002i
$369$		0			0
$370$	−137.744	−	238.580i	−0.0193540	−	0.0335221i
$371$	8495.85	+	14715.2i	1.18890	+	2.05924i
$372$		0			0
$373$	−3184.09	−	5515.01i	−0.442000	−	0.765567i	0.555837	−	0.831291i	$-0.312398\pi$
$373$	−3184.09	−	5515.01i	−0.442000	−	0.765567i	−0.997838	+	0.0657238i	$0.979064\pi$
$374$	−8610.03	+	14913.0i	−1.19041	+	2.06185i
$375$		0			0
$376$	2359.51			0.323623
$377$	−8181.03	−	4208.87i	−1.11762	−	0.574981i
$378$		0			0
$379$	−1225.83	+	2123.20i	−0.166139	+	0.287761i	−0.937059	−	0.349171i	$-0.886463\pi$
$379$	−1225.83	+	2123.20i	−0.166139	+	0.287761i	0.770920	+	0.636932i	$0.219797\pi$
$380$	−0.914327	+	1.58366i	−0.000123432	+	0.000213790i
$381$		0			0
$382$	5150.60			0.689863
$383$	5415.47	+	9379.87i	0.722500	+	1.25141i	0.959995	+	0.280018i	$0.0903405\pi$
$383$	5415.47	+	9379.87i	0.722500	+	1.25141i	−0.237494	+	0.971389i	$0.576326\pi$
$384$		0			0
$385$	565.613			0.0748735
$386$	−5728.27	−	9921.65i	−0.755340	−	1.30829i
$387$		0			0
$388$	133.430	−	231.108i	0.0174585	−	0.0302390i
$389$	4978.07			0.648838			0.324419	−	0.945914i	$-0.394831\pi$
$389$	4978.07			0.648838			0.324419	+	0.945914i	$0.394831\pi$
$390$		0			0
$391$	−1422.12			−0.183938
$392$	5477.70	−	9487.65i	0.705779	−	1.22245i
$393$		0			0
$394$	2097.78	+	3633.46i	0.268235	+	0.464597i
$395$	75.1772			0.00957614
$396$		0			0
$397$	−4725.34	−	8184.52i	−0.597375	−	1.03468i	−0.993207	−	0.116361i	$-0.962877\pi$
$397$	−4725.34	−	8184.52i	−0.597375	−	1.03468i	0.395832	−	0.918323i	$-0.370456\pi$
$398$	2227.43			0.280530
$399$		0			0
$400$	−3785.41	+	6556.52i	−0.473176	+	0.819566i
$401$	4388.39	−	7600.91i	0.546498	−	0.946562i	−0.452013	−	0.892011i	$-0.649294\pi$
$401$	4388.39	−	7600.91i	0.546498	−	0.946562i	0.998511	−	0.0545506i	$-0.0173726\pi$
$402$		0			0
$403$	−269.407	−	5556.76i	−0.0333005	−	0.686854i
$404$	319.759			0.0393777
$405$		0			0
$406$	7727.24	−	13384.0i	0.944572	−	1.63605i
$407$	−10086.8	−	17470.8i	−1.22846	−	2.12775i
$408$		0			0
$409$	2260.10	+	3914.60i	0.273238	+	0.473263i	0.969689	−	0.244342i	$-0.0785719\pi$
$409$	2260.10	+	3914.60i	0.273238	+	0.473263i	−0.696451	+	0.717605i	$0.745239\pi$
$410$	−149.395	−	258.760i	−0.0179954	−	0.0311689i
$411$		0			0
$412$	197.598	+	342.250i	0.0236286	+	0.0409259i
$413$	2920.49	−	5058.43i	0.347961	−	0.602686i
$414$		0			0
$415$	267.974			0.0316972
$416$	−717.939	+	462.249i	−0.0846150	+	0.0544798i
$417$		0			0
$418$	1262.38	−	2186.50i	0.147715	−	0.255850i
$419$	6003.22	−	10397.9i	0.699944	−	1.21234i	−0.268541	−	0.963268i	$-0.586542\pi$
$419$	6003.22	−	10397.9i	0.699944	−	1.21234i	0.968485	−	0.249070i	$-0.0801251\pi$
$420$		0			0
$421$	−9731.52			−1.12657			−0.563284	−	0.826263i	$-0.690462\pi$
$421$	−9731.52			−1.12657			−0.563284	+	0.826263i	$0.690462\pi$
$422$	7249.05	+	12555.7i	0.836205	+	1.44835i
$423$		0			0
$424$	13776.6			1.57795
$425$	6171.84	+	10689.9i	0.704420	+	1.22009i
$426$		0			0
$427$	3084.82	−	5343.06i	0.349613	−	0.605547i
$428$	324.745			0.0366755
$429$		0			0
$430$	−59.9861			−0.00672741
$431$	−2055.51	+	3560.25i	−0.229723	+	0.397892i	−0.957726	−	0.287682i	$-0.907115\pi$
$431$	−2055.51	+	3560.25i	−0.229723	+	0.397892i	0.728003	+	0.685574i	$0.240449\pi$
$432$		0			0
$433$	−1453.03	−	2516.72i	−0.161266	−	0.279321i	0.774057	−	0.633116i	$-0.218224\pi$
$433$	−1453.03	−	2516.72i	−0.161266	−	0.279321i	−0.935323	+	0.353795i	$0.884891\pi$
$434$	9345.19			1.03360
$435$		0			0
$436$	170.278	+	294.930i	0.0187037	+	0.0323958i
$437$	208.507			0.0228243
$438$		0			0
$439$	−4437.36	+	7685.73i	−0.482423	+	0.835581i	−0.999796	−	0.0201788i	$-0.993576\pi$
$439$	−4437.36	+	7685.73i	−0.482423	+	0.835581i	0.517374	+	0.855760i	$0.326910\pi$
$440$	229.295	−	397.150i	0.0248436	−	0.0430305i
$441$		0			0
$442$	−618.288	−	12752.7i	−0.0665361	−	1.37237i
$443$	−12640.5			−1.35569			−0.677843	−	0.735207i	$-0.737085\pi$
$443$	−12640.5			−1.35569			−0.677843	+	0.735207i	$0.737085\pi$
$444$		0			0
$445$	−197.957	+	342.872i	−0.0210878	+	0.0365252i
$446$	6464.45	+	11196.8i	0.686324	+	1.18875i
$447$		0			0
$448$	−7643.18	−	13238.4i	−0.806041	−	1.39610i
$449$	−887.147	−	1536.58i	−0.0932451	−	0.161505i	0.815630	−	0.578574i	$-0.196391\pi$
$449$	−887.147	−	1536.58i	−0.0932451	−	0.161505i	−0.908875	+	0.417069i	$0.863057\pi$
$450$		0			0
$451$	−10940.0	−	18948.6i	−1.14222	−	1.97839i
$452$	11.3583	−	19.6731i	0.00118197	−	0.00204722i
$453$		0			0
$454$	−9814.04			−1.01453
$455$	−352.606	+	227.027i	−0.0363306	+	0.0233916i
$456$		0			0
$457$	−3084.41	+	5342.35i	−0.315717	+	0.546837i	−0.979590	−	0.201008i	$-0.935578\pi$
$457$	−3084.41	+	5342.35i	−0.315717	+	0.546837i	0.663873	+	0.747845i	$0.268912\pi$
$458$	4333.99	−	7506.69i	0.442171	−	0.765862i
$459$		0			0
$460$	1.81607			0.000184075
$461$	−3727.69	−	6456.55i	−0.376607	−	0.652302i	0.613959	−	0.789338i	$-0.289576\pi$
$461$	−3727.69	−	6456.55i	−0.376607	−	0.652302i	−0.990566	+	0.137036i	$0.956243\pi$
$462$		0			0
$463$	5399.78			0.542006			0.271003	−	0.962578i	$-0.412645\pi$
$463$	5399.78			0.542006			0.271003	+	0.962578i	$0.412645\pi$
$464$	−5948.76	−	10303.6i	−0.595182	−	1.03088i
$465$		0			0
$466$	−1174.92	+	2035.03i	−0.116797	+	0.202298i
$467$	−3992.01			−0.395564			−0.197782	−	0.980246i	$-0.563374\pi$
$467$	−3992.01			−0.395564			−0.197782	+	0.980246i	$0.563374\pi$
$468$		0			0
$469$	1959.77			0.192950
$470$	43.9738	−	76.1649i	0.00431566	−	0.00747495i
$471$		0			0
$472$	−2367.89	−	4101.30i	−0.230913	−	0.399952i
$473$	−4392.68			−0.427009
$474$		0			0
$475$	−904.897	−	1567.33i	−0.0874095	−	0.151398i
$476$	−1137.53			−0.109535
$477$		0			0
$478$	3017.19	−	5225.93i	0.288710	−	0.500060i
$479$	1575.81	−	2729.39i	0.150315	−	0.260352i	−0.781029	−	0.624495i	$-0.785305\pi$
$479$	1575.81	−	2729.39i	0.150315	−	0.260352i	0.931343	+	0.364143i	$0.118638\pi$
$480$		0			0
$481$	13300.6	+	6842.72i	1.26082	+	0.648651i
$482$	17447.2			1.64875
$483$		0			0
$484$	536.999	−	930.110i	0.0504319	−	0.0873507i
$485$	−103.718	−	179.644i	−0.00971046	−	0.0168190i
$486$		0			0
$487$	1954.59	+	3385.45i	0.181870	+	0.315009i	0.942517	−	0.334157i	$-0.108452\pi$
$487$	1954.59	+	3385.45i	0.181870	+	0.315009i	−0.760647	+	0.649166i	$0.775118\pi$
$488$	−2501.12	−	4332.07i	−0.232009	−	0.401851i
$489$		0			0
$490$	−204.174	−	353.641i	−0.0188238	−	0.0326038i
$491$	3322.57	−	5754.86i	0.305388	−	0.528947i	−0.671960	−	0.740588i	$-0.734547\pi$
$491$	3322.57	−	5754.86i	0.305388	−	0.528947i	0.977348	+	0.211641i	$0.0678806\pi$
$492$		0			0
$493$	−19398.1			−1.77210
$494$	90.6515	+	1869.77i	0.00825628	+	0.170293i
$495$		0			0
$496$	3597.17	−	6230.48i	0.325640	−	0.564026i
$497$	−13515.1	+	23408.9i	−1.21979	+	2.11274i
$498$		0			0
$499$	6111.83			0.548303			0.274151	−	0.961687i	$-0.411603\pi$
$499$	6111.83			0.548303			0.274151	+	0.961687i	$0.411603\pi$
$500$	−15.7692	−	27.3131i	−0.00141044	−	0.00244296i
$501$		0			0
$502$	9930.79			0.882934
$503$	5477.03	+	9486.50i	0.485505	+	0.840919i	0.999861	−	0.0166575i	$-0.00530250\pi$
$503$	5477.03	+	9486.50i	0.485505	+	0.840919i	−0.514356	+	0.857576i	$0.671969\pi$
$504$		0			0
$505$	124.277	−	215.254i	0.0109510	−	0.0189677i
$506$	−2507.37			−0.220289
$507$		0			0
$508$	−671.553			−0.0586523
$509$	−5560.57	+	9631.18i	−0.484220	+	0.838693i	−0.999836	−	0.0181268i	$-0.994230\pi$
$509$	−5560.57	+	9631.18i	−0.484220	+	0.838693i	0.515616	+	0.856820i	$0.327563\pi$
$510$		0			0
$511$	11138.9	+	19293.1i	0.964296	+	1.67021i
$512$	−12335.2			−1.06473
$513$		0			0
$514$	4234.52	+	7334.40i	0.363379	+	0.629390i
$515$	307.193			0.0262845
$516$		0			0
$517$	3220.13	−	5577.42i	0.273928	−	0.474458i
$518$	−12562.8	+	21759.5i	−1.06560	+	1.84567i
$519$		0			0
$520$	16.4657	+	339.620i	0.00138859	+	0.0286410i
$521$	−2403.33			−0.202096			−0.101048	−	0.994882i	$-0.532220\pi$
$521$	−2403.33			−0.202096			−0.101048	+	0.994882i	$0.532220\pi$
$522$		0			0
$523$	−2125.86	+	3682.10i	−0.177739	+	0.307853i	−0.941106	−	0.338113i	$-0.890212\pi$
$523$	−2125.86	+	3682.10i	−0.177739	+	0.307853i	0.763367	+	0.645965i	$0.223545\pi$
$524$	−121.411	−	210.290i	−0.0101219	−	0.0175316i
$525$		0			0
$526$	−4883.02	−	8457.64i	−0.404772	−	0.701085i
$527$	−5864.92	−	10158.3i	−0.484782	−	0.839667i
$528$		0			0
$529$	5979.96	+	10357.6i	0.491490	+	0.851286i
$530$	256.753	−	444.709i	0.0210427	−	0.0364470i
$531$		0			0
$532$	166.781			0.0135918
$533$	14425.6	+	7421.51i	1.17231	+	0.603117i
$534$		0			0
$535$	126.215	−	218.610i	0.0101995	−	0.0176661i
$536$	794.473	−	1376.07i	0.0640224	−	0.110890i
$537$		0			0
$538$	−16261.9			−1.30316
$539$	−14951.3	−	25896.5i	−1.19480	−	2.06946i
$540$		0			0
$541$	−8924.44			−0.709227			−0.354613	−	0.935013i	$-0.615388\pi$
$541$	−8924.44			−0.709227			−0.354613	+	0.935013i	$0.615388\pi$
$542$	2907.22	+	5035.45i	0.230398	+	0.399061i
$543$		0			0
$544$	−900.176	+	1559.15i	−0.0709462	+	0.122882i
$545$	264.719			0.0208061
$546$		0			0
$547$	−14696.0			−1.14873			−0.574367	−	0.818598i	$-0.694752\pi$
$547$	−14696.0			−1.14873			−0.574367	+	0.818598i	$0.694752\pi$
$548$	84.9499	−	147.138i	0.00662204	−	0.0114697i
$549$		0			0
$550$	10881.7	+	18847.7i	0.843633	+	1.46122i
$551$	2844.09			0.219895
$552$		0			0
$553$	−3428.23	−	5937.87i	−0.263623	−	0.456608i
$554$	20024.3			1.53566
$555$		0			0
$556$	5.87688	−	10.1791i	0.000448265	−	0.000776417i
$557$	1232.01	−	2133.91i	0.0937202	−	0.162328i	−0.815354	−	0.578963i	$-0.803457\pi$
$557$	1232.01	−	2133.91i	0.0937202	−	0.162328i	0.909074	+	0.416635i	$0.136791\pi$
$558$		0			0
$559$	2738.41	−	1763.14i	0.207196	−	0.133404i
$560$	−542.322			−0.0409237
$561$		0			0
$562$	−6575.59	+	11389.3i	−0.493549	+	0.854852i
$563$	9014.61	+	15613.8i	0.674815	+	1.16881i	0.976523	+	0.215413i	$0.0691098\pi$
$563$	9014.61	+	15613.8i	0.674815	+	1.16881i	−0.301708	+	0.953400i	$0.597557\pi$
$564$		0			0
$565$	−8.82897	−	15.2922i	−0.000657411	−	0.00113867i
$566$	−2806.25	−	4860.57i	−0.208402	−	0.360963i
$567$		0			0
$568$	10957.9	+	18979.6i	0.809475	+	1.40205i
$569$	5962.32	−	10327.0i	0.439286	−	0.760865i	−0.558349	−	0.829606i	$-0.688565\pi$
$569$	5962.32	−	10327.0i	0.439286	−	0.760865i	0.997635	+	0.0687410i	$0.0218982\pi$
$570$		0			0
$571$	5834.77			0.427632			0.213816	−	0.976874i	$-0.431411\pi$
$571$	5834.77			0.427632			0.213816	+	0.976874i	$0.431411\pi$
$572$	57.8182	+	1192.55i	0.00422640	+	0.0871734i
$573$		0			0
$574$	−13625.5	+	23600.0i	−0.990794	+	1.71611i
$575$	−898.667	+	1556.54i	−0.0651774	+	0.112891i
$576$		0			0
$577$	15927.5			1.14917			0.574586	−	0.818444i	$-0.305163\pi$
$577$	15927.5			1.14917			0.574586	+	0.818444i	$0.305163\pi$
$578$	−6689.19	−	11586.0i	−0.481373	−	0.833762i
$579$		0			0
$580$	24.7716			0.00177342
$581$	−12220.2	−	21166.0i	−0.872596	−	1.51138i
$582$		0			0
$583$	18801.6	−	32565.3i	1.33564	−	2.31340i
$584$	18062.5			1.27985
$585$		0			0
$586$	10250.7			0.722612
$587$	−6755.55	+	11701.0i	−0.475011	+	0.822743i	−0.999590	−	0.0286184i	$-0.990889\pi$
$587$	−6755.55	+	11701.0i	−0.475011	+	0.822743i	0.524579	+	0.851362i	$0.324223\pi$
$588$		0			0
$589$	859.898	+	1489.39i	0.0601553	+	0.104192i
$590$	−176.520			−0.0123173
$591$		0			0
$592$	9671.42	+	16751.4i	0.671441	+	1.16297i
$593$	−15830.4			−1.09625			−0.548126	−	0.836396i	$-0.684659\pi$
$593$	−15830.4			−1.09625			−0.548126	+	0.836396i	$0.684659\pi$
$594$		0			0
$595$	−442.109	+	765.755i	−0.0304617	+	0.0527611i
$596$	431.505	−	747.388i	0.0296562	−	0.0513661i
$597$		0			0
$598$	1563.11	−	1006.42i	0.106890	−	0.0688217i
$599$	5914.12			0.403413			0.201706	−	0.979446i	$-0.435351\pi$
$599$	5914.12			0.403413			0.201706	+	0.979446i	$0.435351\pi$
$600$		0			0
$601$	−4946.10	+	8566.89i	−0.335700	+	0.581449i	−0.983619	−	0.180260i	$-0.942306\pi$
$601$	−4946.10	+	8566.89i	−0.335700	+	0.581449i	0.647919	+	0.761709i	$0.275639\pi$
$602$	2735.49	+	4738.01i	0.185200	+	0.320775i
$603$		0			0
$604$	294.002	+	509.226i	0.0198059	+	0.0343048i
$605$	−417.418	−	722.989i	−0.0280503	−	0.0485846i
$606$		0			0
$607$	8391.16	+	14533.9i	0.561098	+	0.971851i	0.997401	+	0.0720510i	$0.0229544\pi$
$607$	8391.16	+	14533.9i	0.561098	+	0.971851i	−0.436302	+	0.899800i	$0.643712\pi$
$608$	131.981	−	228.598i	0.00880352	−	0.0152481i
$609$		0			0
$610$	−186.452			−0.0123758
$611$	231.238	+	4769.49i	0.0153108	+	0.315799i
$612$		0			0
$613$	−6122.83	+	10605.0i	−0.403424	+	0.698750i	−0.994137	−	0.108132i	$-0.965513\pi$
$613$	−6122.83	+	10605.0i	−0.403424	+	0.698750i	0.590713	+	0.806882i	$0.298847\pi$
$614$	10035.9	−	17382.8i	0.659638	−	1.14253i
$615$		0			0
$616$	−41825.3			−2.73569
$617$	5021.86	+	8698.12i	0.327670	+	0.567542i	0.982049	−	0.188625i	$-0.0604031\pi$
$617$	5021.86	+	8698.12i	0.327670	+	0.567542i	−0.654379	+	0.756167i	$0.727070\pi$
$618$		0			0
$619$	−9942.69			−0.645607			−0.322803	−	0.946466i	$-0.604625\pi$
$619$	−9942.69			−0.645607			−0.322803	+	0.946466i	$0.604625\pi$
$620$	7.48959	+	12.9724i	0.000485144	+	0.000840294i
$621$		0			0
$622$	6297.10	−	10906.9i	0.405934	−	0.703098i
$623$	36109.1			2.32212
$624$		0			0
$625$	15588.2			0.997646
$626$	−28.9814	+	50.1973i	−0.00185037	+	0.00320493i
$627$		0			0
$628$	404.588	+	700.767i	0.0257083	+	0.0445281i
$629$	31537.1			1.99915
$630$		0			0
$631$	−5134.31	−	8892.89i	−0.323920	−	0.561047i	0.657373	−	0.753566i	$-0.271668\pi$
$631$	−5134.31	−	8892.89i	−0.323920	−	0.561047i	−0.981293	+	0.192519i	$0.938334\pi$
$632$	−5559.11			−0.349889
$633$		0			0
$634$	7110.05	−	12315.0i	0.445389	−	0.771436i
$635$	−261.004	+	452.073i	−0.0163113	+	0.0282519i
$636$		0			0
$637$	19715.1	+	10142.8i	1.22628	+	0.630881i
$638$	−34201.2			−2.12232
$639$		0			0
$640$	−208.161	+	360.546i	−0.0128567	+	0.0222685i
$641$	−6828.72	−	11827.7i	−0.420777	−	0.728808i	0.575238	−	0.817986i	$-0.304909\pi$
$641$	−6828.72	−	11827.7i	−0.420777	−	0.728808i	−0.996016	+	0.0891780i	$0.971576\pi$
$642$		0			0
$643$	−12335.8	−	21366.2i	−0.756572	−	1.31042i	−0.944589	−	0.328256i	$-0.893539\pi$
$643$	−12335.8	−	21366.2i	−0.756572	−	1.31042i	0.188017	−	0.982166i	$-0.439794\pi$
$644$	−82.8163	−	143.442i	−0.00506742	−	0.00877703i
$645$		0			0
$646$	1973.46	+	3418.14i	0.120193	+	0.208181i
$647$	−8256.13	+	14300.0i	−0.501672	+	0.868922i	0.498326	+	0.866990i	$0.333948\pi$
$647$	−8256.13	+	14300.0i	−0.501672	+	0.868922i	−0.999998	+	0.00193194i	$0.999385\pi$
$648$		0			0
$649$	−12926.3			−0.781818
$650$	−14348.9	−	7382.01i	−0.865859	−	0.445456i
$651$		0			0
$652$	110.504	−	191.399i	0.00663756	−	0.0114966i
$653$	15297.4	−	26495.8i	0.916742	−	1.58784i	0.112412	−	0.993662i	$-0.464142\pi$
$653$	15297.4	−	26495.8i	0.916742	−	1.58784i	0.804330	−	0.594182i	$-0.202524\pi$
$654$		0			0
$655$	−188.749			−0.0112596
$656$	10489.5	+	18168.3i	0.624306	+	1.08133i
$657$		0			0
$658$	−8021.19			−0.475226
$659$	−1153.89	−	1998.60i	−0.0682084	−	0.118140i	0.829904	−	0.557906i	$-0.188395\pi$
$659$	−1153.89	−	1998.60i	−0.0682084	−	0.118140i	−0.898113	+	0.439765i	$0.855062\pi$
$660$		0			0
$661$	13811.2	−	23921.7i	0.812700	−	1.40764i	−0.0982684	−	0.995160i	$-0.531330\pi$
$661$	13811.2	−	23921.7i	0.812700	−	1.40764i	0.910968	−	0.412477i	$-0.135336\pi$
$662$	−20885.8			−1.22621
$663$		0			0
$664$	−19815.9			−1.15814
$665$	64.8206	−	112.273i	0.00377991	−	0.00654699i
$666$		0			0
$667$	−1412.25	−	2446.09i	−0.0819830	−	0.141999i
$668$	1596.67			0.0924805
$669$		0			0
$670$	−29.6130	−	51.2913i	−0.00170754	−	0.00295754i
$671$	−13653.6			−0.785530
$672$		0			0
$673$	5652.94	−	9791.17i	0.323781	−	0.560805i	−0.657484	−	0.753469i	$-0.728379\pi$
$673$	5652.94	−	9791.17i	0.323781	−	0.560805i	0.981265	+	0.192663i	$0.0617125\pi$
$674$	2907.58	−	5036.08i	0.166166	−	0.287808i
$675$		0			0
$676$	−514.714	−	720.236i	−0.0292851	−	0.0409784i
$677$	−15455.8			−0.877419			−0.438710	−	0.898629i	$-0.644564\pi$
$677$	−15455.8			−0.877419			−0.438710	+	0.898629i	$0.644564\pi$
$678$		0			0
$679$	−9459.47	+	16384.3i	−0.534641	+	0.926025i
$680$	358.455	+	620.862i	0.0202149	+	0.0350132i
$681$		0			0
$682$	−10340.6	−	17910.4i	−0.580589	−	1.00561i
$683$	8420.96	+	14585.5i	0.471770	+	0.817130i	0.999478	−	0.0322958i	$-0.0102819\pi$
$683$	8420.96	+	14585.5i	0.471770	+	0.817130i	−0.527708	+	0.849426i	$0.676949\pi$
$684$		0			0
$685$	−66.0329	−	114.372i	−0.00368319	−	0.00637948i
$686$	−5118.37	+	8865.28i	−0.284869	+	0.493408i
$687$		0			0
$688$	4211.80			0.233391
$689$	1350.14	+	27847.9i	0.0746537	+	1.53980i
$690$		0			0
$691$	12520.8	−	21686.6i	0.689310	−	1.19392i	−0.282751	−	0.959193i	$-0.591247\pi$
$691$	12520.8	−	21686.6i	0.689310	−	1.19392i	0.972061	−	0.234727i	$-0.0754195\pi$
$692$	−348.448	+	603.529i	−0.0191416	+	0.0331543i
$693$		0			0
$694$	−22347.6			−1.22234
$695$	−4.56819	−	7.91234i	−0.000249326	−	0.000431845i
$696$		0			0
$697$	34204.7			1.85881
$698$	−11971.0	−	20734.4i	−0.649155	−	1.12437i
$699$		0			0
$700$	−718.828	+	1245.05i	−0.0388131	+	0.0672262i
$701$	28309.0			1.52527			0.762635	−	0.646829i	$-0.223905\pi$
$701$	28309.0			1.52527			0.762635	+	0.646829i	$0.223905\pi$
$702$		0			0
$703$	−4623.88			−0.248069
$704$	−16914.6	+	29296.9i	−0.905528	+	1.56842i
$705$		0			0
$706$	12472.5	+	21603.0i	0.664884	+	1.15161i
$707$	−22669.1			−1.20588
$708$		0			0
$709$	2520.59	+	4365.78i	0.133516	+	0.231256i	0.925029	−	0.379895i	$-0.124040\pi$
$709$	2520.59	+	4365.78i	0.133516	+	0.231256i	−0.791514	+	0.611151i	$0.790707\pi$
$710$	816.882			0.0431789
$711$		0			0
$712$	14638.3	−	25354.3i	0.770498	−	1.33454i
$713$	853.978	−	1479.13i	0.0448552	−	0.0776914i
$714$		0			0
$715$	825.269	+	424.574i	0.0431655	+	0.0222072i
$716$	−585.431			−0.0305567
$717$		0			0
$718$	9707.33	−	16813.6i	0.504560	−	0.873924i
$719$	5919.62	+	10253.1i	0.307044	+	0.531815i	0.977714	−	0.209940i	$-0.0673269\pi$
$719$	5919.62	+	10253.1i	0.307044	+	0.531815i	−0.670671	+	0.741755i	$0.733994\pi$
$720$		0			0
$721$	−14008.6	−	24263.6i	−0.723590	−	1.25329i
$722$	9163.31	+	15871.3i	0.472331	+	0.818101i
$723$		0			0
$724$	−110.874	−	192.039i	−0.00569143	−	0.00985784i
$725$	−12258.1	+	21231.6i	−0.627935	+	1.08762i
$726$		0			0
$727$	−31004.9			−1.58172			−0.790858	−	0.611999i	$-0.790365\pi$
$727$	−31004.9			−1.58172			−0.790858	+	0.611999i	$0.790365\pi$
$728$	26074.1	−	16787.9i	1.32743	−	0.854673i
$729$		0			0
$730$	336.628	−	583.057i	0.0170674	−	0.0295615i
$731$	3433.52	−	5947.02i	0.173725	−	0.300901i
$732$		0			0
$733$	15666.0			0.789411			0.394706	−	0.918808i	$-0.370847\pi$
$733$	15666.0			0.789411			0.394706	+	0.918808i	$0.370847\pi$
$734$	−19052.9	−	33000.6i	−0.958114	−	1.65950i
$735$		0			0
$736$	−262.145			−0.0131288
$737$	−2168.51	−	3755.97i	−0.108383	−	0.187724i
$738$		0			0
$739$	16669.7	−	28872.8i	0.829777	−	1.43722i	−0.0684357	−	0.997656i	$-0.521801\pi$
$739$	16669.7	−	28872.8i	0.829777	−	1.43722i	0.898213	−	0.439561i	$-0.144866\pi$
$740$	−40.2733			−0.00200064
$741$		0			0
$742$	−46833.8			−2.31715
$743$	1013.07	−	1754.69i	0.0500215	−	0.0866397i	−0.839931	−	0.542694i	$-0.817404\pi$
$743$	1013.07	−	1754.69i	0.0500215	−	0.0866397i	0.889952	+	0.456054i	$0.150738\pi$
$744$		0			0
$745$	−335.415	−	580.956i	−0.0164949	−	0.0285699i
$746$	17552.5			0.861451
$747$		0			0
$748$	1258.69	+	2180.11i	0.0615271	+	0.106568i
$749$	−23022.6			−1.12313
$750$		0			0
$751$	−17737.4	+	30722.0i	−0.861846	+	1.49276i	0.00829952	+	0.999966i	$0.497358\pi$
$751$	−17737.4	+	30722.0i	−0.861846	+	1.49276i	−0.870145	+	0.492795i	$0.835975\pi$
$752$	−3087.53	+	5347.76i	−0.149722	+	0.259325i
$753$		0			0
$754$	21321.2	−	13727.8i	1.02980	−	0.663044i
$755$	457.065			0.0220322
$756$		0			0
$757$	−1199.29	+	2077.23i	−0.0575811	+	0.0997333i	−0.893379	−	0.449304i	$-0.851672\pi$
$757$	−1199.29	+	2077.23i	−0.0575811	+	0.0997333i	0.835798	+	0.549037i	$0.185005\pi$
$758$	−3378.73	−	5852.13i	−0.161901	−	0.280421i
$759$		0			0
$760$	−52.5555	−	91.0289i	−0.00250841	−	0.00434469i
$761$	−2502.53	−	4334.52i	−0.119207	−	0.206473i	0.800246	−	0.599671i	$-0.204702\pi$
$761$	−2502.53	−	4334.52i	−0.119207	−	0.206473i	−0.919454	+	0.393198i	$0.871369\pi$
$762$		0			0
$763$	−12071.7	−	20908.9i	−0.572774	−	0.992074i
$764$	376.480	−	652.082i	0.0178280	−	0.0308789i
$765$		0			0
$766$	−29853.1			−1.40814
$767$	8058.28	−	5188.37i	0.379358	−	0.244252i
$768$		0			0
$769$	−7054.78	+	12219.2i	−0.330822	+	0.573000i	−0.982673	−	0.185346i	$-0.940659\pi$
$769$	−7054.78	+	12219.2i	−0.330822	+	0.573000i	0.651851	+	0.758347i	$0.273993\pi$
$770$	−779.493	+	1350.12i	−0.0364818	+	0.0631883i
$771$		0			0
$772$	−1674.82			−0.0780803
$773$	−6366.85	−	11027.7i	−0.296248	−	0.513116i	0.679027	−	0.734114i	$-0.262402\pi$
$773$	−6366.85	−	11027.7i	−0.296248	−	0.513116i	−0.975274	+	0.220997i	$0.929069\pi$
$774$		0			0
$775$	−14824.7			−0.687121
$776$	7669.59	+	13284.1i	0.354796	+	0.614526i
$777$		0			0
$778$	−6860.46	+	11882.7i	−0.316143	+	0.547576i
$779$	−5014.98			−0.230655
$780$		0			0
$781$	59818.8			2.74070
$782$	1959.88	−	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37814 + 2.38701i) q^{2} +(0.201468 + 0.348954i) q^{4} +0.313209 q^{5} +(-14.2830 - 24.7388i) q^{7} -23.1608 q^{8} +O(q^{10})\)	\(q+(-1.37814 + 2.38701i) q^{2} +(0.201468 + 0.348954i) q^{4} +0.313209 q^{5} +(-14.2830 - 24.7388i) q^{7} -23.1608 q^{8} +(-0.431646 + 0.747632i) q^{10} +(-31.6086 + 54.7478i) q^{11} +(-2.26982 - 46.8172i) q^{13} +78.7357 q^{14} +(30.3071 - 52.4934i) q^{16} +(-49.4135 - 85.5867i) q^{17} +(7.24486 + 12.5485i) q^{19} +(0.0631018 + 0.109295i) q^{20} +(-87.1222 - 150.900i) q^{22} +(7.19499 - 12.4621i) q^{23} -124.902 q^{25} +(114.881 + 59.1025i) q^{26} +(5.75514 - 9.96819i) q^{28} +(98.1415 - 169.986i) q^{29} +118.691 q^{31} +(-9.10860 - 15.7766i) q^{32} +272.395 q^{34} +(-4.47356 - 7.74843i) q^{35} +(-159.557 + 276.361i) q^{37} -39.9377 q^{38} -7.25418 q^{40} +(-173.053 + 299.737i) q^{41} +(34.7427 + 60.1761i) q^{43} -25.4726 q^{44} +(19.8314 + 34.3490i) q^{46} -101.875 q^{47} +(-236.507 + 409.642i) q^{49} +(172.132 - 298.142i) q^{50} +(15.8797 - 10.2242i) q^{52} -594.823 q^{53} +(-9.90012 + 17.1475i) q^{55} +(330.806 + 572.972i) q^{56} +(270.505 + 468.529i) q^{58} +(102.237 + 177.079i) q^{59} +(107.989 + 187.043i) q^{61} +(-163.572 + 283.315i) q^{62} +535.125 q^{64} +(-0.710929 - 14.6636i) q^{65} +(-34.3025 + 59.4136i) q^{67} +(19.9105 - 34.4860i) q^{68} +24.6607 q^{70} +(-473.121 - 819.469i) q^{71} -779.872 q^{73} +(-439.784 - 761.727i) q^{74} +(-2.91922 + 5.05624i) q^{76} +1805.86 q^{77} +240.022 q^{79} +(9.49245 - 16.4414i) q^{80} +(-476.982 - 826.158i) q^{82} +855.576 q^{83} +(-15.4768 - 26.8065i) q^{85} -191.521 q^{86} +(732.082 - 1268.00i) q^{88} +(-632.029 + 1094.71i) q^{89} +(-1125.78 + 724.842i) q^{91} +5.79825 q^{92} +(140.398 - 243.176i) q^{94} +(2.26916 + 3.93030i) q^{95} +(-331.145 - 573.560i) q^{97} +(-651.879 - 1129.09i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 40 q^{4} + 22 q^{7}+O(q^{10}) \) 16 * q - 40 * q^4 + 22 * q^7	\( 16 q - 40 q^{4} + 22 q^{7} - 36 q^{10} + 36 q^{13} - 204 q^{16} - 244 q^{19} - 136 q^{22} + 708 q^{25} + 452 q^{28} + 484 q^{31} - 2584 q^{34} - 1018 q^{37} + 3400 q^{40} - 74 q^{43} + 896 q^{46} - 298 q^{49} - 1676 q^{52} - 1300 q^{55} - 812 q^{58} - 1148 q^{61} + 7272 q^{64} + 2198 q^{67} + 4400 q^{70} - 4352 q^{73} - 6936 q^{76} + 3724 q^{79} - 5436 q^{82} + 890 q^{85} - 3528 q^{88} - 4754 q^{91} + 3104 q^{94} + 4370 q^{97}+O(q^{100}) \) 16 * q - 40 * q^4 + 22 * q^7 - 36 * q^10 + 36 * q^13 - 204 * q^16 - 244 * q^19 - 136 * q^22 + 708 * q^25 + 452 * q^28 + 484 * q^31 - 2584 * q^34 - 1018 * q^37 + 3400 * q^40 - 74 * q^43 + 896 * q^46 - 298 * q^49 - 1676 * q^52 - 1300 * q^55 - 812 * q^58 - 1148 * q^61 + 7272 * q^64 + 2198 * q^67 + 4400 * q^70 - 4352 * q^73 - 6936 * q^76 + 3724 * q^79 - 5436 * q^82 + 890 * q^85 - 3528 * q^88 - 4754 * q^91 + 3104 * q^94 + 4370 * q^97

Introduction

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