LMFDB - Embedded newform 117.3.bd.c.46.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(19,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.bd (of order $12$, degree $4$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.1579585536.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 4x^{6} + 28x^{5} - 38x^{4} + 8x^{3} + 200x^{2} - 352x + 484 $ x^8 - 2x^7 - 4x^6 + 28x^5 - 38x^4 + 8x^3 + 200x^2 - 352*x + 484
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			46.1
Root			$2.22833 + 1.32913i$ of defining polynomial
Character	$\chi$	$=$	117.46
Dual form			117.3.bd.c.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72833 + 0.463105i) q^{2} +(-0.691437 + 0.399201i) q^{4} +(-0.707764 - 0.707764i) q^{5} +(-2.02673 - 0.543062i) q^{7} +(6.07107 - 6.07107i) q^{8} +O(q^{10})$	\(q+(-1.72833 + 0.463105i) q^{2} +(-0.691437 + 0.399201i) q^{4} +(-0.707764 - 0.707764i) q^{5} +(-2.02673 - 0.543062i) q^{7} +(6.07107 - 6.07107i) q^{8} +(1.55102 + 0.895482i) q^{10} +(-2.74645 - 10.2499i) q^{11} +(-1.20259 - 12.9443i) q^{13} +3.75436 q^{14} +(-6.08447 + 10.5386i) q^{16} +(8.98068 - 5.18500i) q^{17} +(5.44333 - 20.3148i) q^{19} +(0.771915 + 0.206834i) q^{20} +(9.49356 + 16.4433i) q^{22} +(-21.6297 - 12.4879i) q^{23} -23.9981i q^{25} +(8.07303 + 21.8150i) q^{26} +(1.61815 - 0.433582i) q^{28} +(-12.1176 + 20.9884i) q^{29} +(18.1124 + 18.1124i) q^{31} +(-3.25316 + 12.1410i) q^{32} +(-13.1204 + 13.1204i) q^{34} +(1.05009 + 1.81881i) q^{35} +(7.82694 + 29.2105i) q^{37} +37.6315i q^{38} -8.59377 q^{40} +(-23.9995 + 6.43065i) q^{41} +(-72.3974 + 41.7986i) q^{43} +(5.99077 + 5.99077i) q^{44} +(43.1665 + 11.5664i) q^{46} +(45.3435 - 45.3435i) q^{47} +(-38.6225 - 22.2987i) q^{49} +(11.1137 + 41.4767i) q^{50} +(5.99888 + 8.47006i) q^{52} +65.1714 q^{53} +(-5.31067 + 9.19835i) q^{55} +(-15.6014 + 9.00748i) q^{56} +(11.2235 - 41.8866i) q^{58} +(-74.5178 - 19.9670i) q^{59} +(13.2827 + 23.0063i) q^{61} +(-39.6921 - 22.9163i) q^{62} -71.1659i q^{64} +(-8.31033 + 10.0126i) q^{65} +(74.9307 - 20.0776i) q^{67} +(-4.13971 + 7.17020i) q^{68} +(-2.65721 - 2.65721i) q^{70} +(27.4742 - 102.535i) q^{71} +(82.5815 - 82.5815i) q^{73} +(-27.0551 - 46.8608i) q^{74} +(4.34597 + 16.2194i) q^{76} +22.2653i q^{77} -70.2833 q^{79} +(11.7652 - 3.15248i) q^{80} +(38.5011 - 22.2286i) q^{82} +(-9.18965 - 9.18965i) q^{83} +(-10.0260 - 2.68645i) q^{85} +(105.770 - 105.770i) q^{86} +(-78.9017 - 45.5539i) q^{88} +(14.7802 + 55.1604i) q^{89} +(-4.59219 + 26.8877i) q^{91} +19.9408 q^{92} +(-57.3698 + 99.3675i) q^{94} +(-18.2307 + 10.5255i) q^{95} +(-11.7078 + 43.6941i) q^{97} +(77.0792 + 20.6533i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 12 q^{4} - 16 q^{5} + 14 q^{7} + 24 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 + 12 * q^4 - 16 * q^5 + 14 * q^7 + 24 * q^8	$ 8 q + 2 q^{2} + 12 q^{4} - 16 q^{5} + 14 q^{7} + 24 q^{8} - 42 q^{10} + 14 q^{11} + 2 q^{13} + 28 q^{14} - 28 q^{16} - 18 q^{17} - 94 q^{19} - 68 q^{20} + 46 q^{22} + 30 q^{23} - 136 q^{26} + 146 q^{28} + 64 q^{29} + 80 q^{31} + 86 q^{32} - 96 q^{34} - 122 q^{35} + 110 q^{37} - 204 q^{40} - 22 q^{41} - 54 q^{43} + 92 q^{44} + 294 q^{46} + 332 q^{47} - 12 q^{49} + 172 q^{50} - 72 q^{52} - 32 q^{53} - 122 q^{55} - 66 q^{56} - 134 q^{58} - 52 q^{59} + 46 q^{61} - 288 q^{62} - 214 q^{65} + 86 q^{67} - 114 q^{68} - 164 q^{70} - 94 q^{71} + 56 q^{73} - 236 q^{74} + 46 q^{76} - 80 q^{79} + 80 q^{80} + 180 q^{82} - 136 q^{83} + 138 q^{85} + 396 q^{86} + 66 q^{88} + 128 q^{89} - 496 q^{91} + 108 q^{92} + 202 q^{94} + 486 q^{95} - 40 q^{97} + 530 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 + 12 * q^4 - 16 * q^5 + 14 * q^7 + 24 * q^8 - 42 * q^10 + 14 * q^11 + 2 * q^13 + 28 * q^14 - 28 * q^16 - 18 * q^17 - 94 * q^19 - 68 * q^20 + 46 * q^22 + 30 * q^23 - 136 * q^26 + 146 * q^28 + 64 * q^29 + 80 * q^31 + 86 * q^32 - 96 * q^34 - 122 * q^35 + 110 * q^37 - 204 * q^40 - 22 * q^41 - 54 * q^43 + 92 * q^44 + 294 * q^46 + 332 * q^47 - 12 * q^49 + 172 * q^50 - 72 * q^52 - 32 * q^53 - 122 * q^55 - 66 * q^56 - 134 * q^58 - 52 * q^59 + 46 * q^61 - 288 * q^62 - 214 * q^65 + 86 * q^67 - 114 * q^68 - 164 * q^70 - 94 * q^71 + 56 * q^73 - 236 * q^74 + 46 * q^76 - 80 * q^79 + 80 * q^80 + 180 * q^82 - 136 * q^83 + 138 * q^85 + 396 * q^86 + 66 * q^88 + 128 * q^89 - 496 * q^91 + 108 * q^92 + 202 * q^94 + 486 * q^95 - 40 * q^97 + 530 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$

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 $

$2$	−1.72833	+	0.463105i	−0.864166	+	0.231553i	−0.663563	−	0.748120i	$-0.730957\pi$
$2$	−1.72833	+	0.463105i	−0.864166	+	0.231553i	−0.200603	+	0.979673i	$0.564290\pi$
$3$		0			0
$3$		0			0
$4$	−0.691437	+	0.399201i	−0.172859	+	0.0998003i
$5$	−0.707764	−	0.707764i	−0.141553	−	0.141553i	0.632779	−	0.774332i	$-0.281914\pi$
$5$	−0.707764	−	0.707764i	−0.141553	−	0.141553i	−0.774332	+	0.632779i	$0.781914\pi$
$6$		0			0
$7$	−2.02673	−	0.543062i	−0.289534	−	0.0775803i	0.111129	−	0.993806i	$-0.464553\pi$
$7$	−2.02673	−	0.543062i	−0.289534	−	0.0775803i	−0.400662	+	0.916226i	$0.631220\pi$
$8$	6.07107	−	6.07107i	0.758883	−	0.758883i
$9$		0			0
$10$	1.55102	+	0.895482i	0.155102	+	0.0895482i
$11$	−2.74645	−	10.2499i	−0.249677	−	0.931809i	−0.970975	−	0.239183i	$-0.923120\pi$
$11$	−2.74645	−	10.2499i	−0.249677	−	0.931809i	0.721297	−	0.692626i	$-0.243546\pi$
$12$		0			0
$13$	−1.20259	−	12.9443i	−0.0925072	−	0.995712i
$13$	−1.20259	−	12.9443i	−0.0925072	−	0.995712i
$14$	3.75436			0.268169
$15$		0			0
$16$	−6.08447	+	10.5386i	−0.380279	+	0.658663i
$17$	8.98068	−	5.18500i	0.528275	−	0.305000i	−0.212039	−	0.977261i	$-0.568010\pi$
$17$	8.98068	−	5.18500i	0.528275	−	0.305000i	0.740314	+	0.672262i	$0.234677\pi$
$18$		0			0
$19$	5.44333	−	20.3148i	0.286491	−	1.06920i	−0.661252	−	0.750164i	$-0.729975\pi$
$19$	5.44333	−	20.3148i	0.286491	−	1.06920i	0.947743	−	0.319035i	$-0.103359\pi$
$20$	0.771915	+	0.206834i	0.0385957	+	0.0103417i
$21$		0			0
$22$	9.49356	+	16.4433i	0.431525	+	0.747424i
$23$	−21.6297	−	12.4879i	−0.940422	−	0.542953i	−0.0503292	−	0.998733i	$-0.516027\pi$
$23$	−21.6297	−	12.4879i	−0.940422	−	0.542953i	−0.890092	+	0.455780i	$0.849360\pi$
$24$		0			0
$25$		−	23.9981i		−	0.959926i
$26$	8.07303	+	21.8150i	0.310501	+	0.839040i
$27$		0			0
$28$	1.61815	−	0.433582i	0.0577911	−	0.0154851i
$29$	−12.1176	+	20.9884i	−0.417850	+	0.723737i	−0.995723	−	0.0923897i	$-0.970549\pi$
$29$	−12.1176	+	20.9884i	−0.417850	+	0.723737i	0.577873	+	0.816127i	$0.303883\pi$
$30$		0			0
$31$	18.1124	+	18.1124i	0.584270	+	0.584270i	0.936074	−	0.351803i	$-0.114431\pi$
$31$	18.1124	+	18.1124i	0.584270	+	0.584270i	−0.351803	+	0.936074i	$0.614431\pi$
$32$	−3.25316	+	12.1410i	−0.101661	+	0.379405i
$33$		0			0
$34$	−13.1204	+	13.1204i	−0.385894	+	0.385894i
$35$	1.05009	+	1.81881i	0.0300026	+	0.0519660i
$36$		0			0
$37$	7.82694	+	29.2105i	0.211539	+	0.789474i	0.987356	+	0.158516i	$0.0506710\pi$
$37$	7.82694	+	29.2105i	0.211539	+	0.789474i	−0.775818	+	0.630957i	$0.782662\pi$
$38$			37.6315i			0.990302i
$39$		0			0
$40$	−8.59377			−0.214844
$41$	−23.9995	+	6.43065i	−0.585354	+	0.156845i	−0.539329	−	0.842095i	$-0.681322\pi$
$41$	−23.9995	+	6.43065i	−0.585354	+	0.156845i	−0.0460251	+	0.998940i	$0.514655\pi$
$42$		0			0
$43$	−72.3974	+	41.7986i	−1.68366	+	0.972061i	−0.724467	+	0.689310i	$0.757914\pi$
$43$	−72.3974	+	41.7986i	−1.68366	+	0.972061i	−0.959193	+	0.282752i	$0.908753\pi$
$44$	5.99077	+	5.99077i	0.136154	+	0.136154i
$45$		0			0
$46$	43.1665	+	11.5664i	0.938402	+	0.251444i
$47$	45.3435	−	45.3435i	0.964756	−	0.964756i	−0.0346437	−	0.999400i	$-0.511030\pi$
$47$	45.3435	−	45.3435i	0.964756	−	0.964756i	0.999400	+	0.0346437i	$0.0110297\pi$
$48$		0			0
$49$	−38.6225	−	22.2987i	−0.788214	−	0.455076i
$50$	11.1137	+	41.4767i	0.222273	+	0.829535i
$51$		0			0
$52$	5.99888	+	8.47006i	0.115363	+	0.162886i
$53$	65.1714			1.22965			0.614825	−	0.788664i	$-0.289227\pi$
$53$	65.1714			1.22965			0.614825	+	0.788664i	$0.289227\pi$
$54$		0			0
$55$	−5.31067	+	9.19835i	−0.0965576	+	0.167243i
$56$	−15.6014	+	9.00748i	−0.278597	+	0.160848i
$57$		0			0
$58$	11.2235	−	41.8866i	0.193508	−	0.722183i
$59$	−74.5178	−	19.9670i	−1.26301	−	0.338424i	−0.435664	−	0.900109i	$-0.643486\pi$
$59$	−74.5178	−	19.9670i	−1.26301	−	0.338424i	−0.827351	+	0.561686i	$0.810153\pi$
$60$		0			0
$61$	13.2827	+	23.0063i	0.217749	+	0.377152i	0.954119	−	0.299427i	$-0.0967954\pi$
$61$	13.2827	+	23.0063i	0.217749	+	0.377152i	−0.736371	+	0.676578i	$0.763462\pi$
$62$	−39.6921	−	22.9163i	−0.640196	−	0.369617i
$63$		0			0
$64$		−	71.1659i		−	1.11197i
$65$	−8.31033	+	10.0126i	−0.127851	+	0.154041i
$66$		0			0
$67$	74.9307	−	20.0776i	1.11837	−	0.299666i	0.348146	−	0.937440i	$-0.386811\pi$
$67$	74.9307	−	20.0776i	1.11837	−	0.299666i	0.770223	+	0.637774i	$0.220145\pi$
$68$	−4.13971	+	7.17020i	−0.0608781	+	0.105444i
$69$		0			0
$70$	−2.65721	−	2.65721i	−0.0379601	−	0.0379601i
$71$	27.4742	−	102.535i	0.386960	−	1.44416i	−0.448094	−	0.893987i	$-0.647897\pi$
$71$	27.4742	−	102.535i	0.386960	−	1.44416i	0.835054	−	0.550168i	$-0.185436\pi$
$72$		0			0
$73$	82.5815	−	82.5815i	1.13125	−	1.13125i	0.141285	−	0.989969i	$-0.454877\pi$
$73$	82.5815	−	82.5815i	1.13125	−	1.13125i	0.989969	−	0.141285i	$-0.0451233\pi$
$74$	−27.0551	−	46.8608i	−0.365609	−	0.633254i
$75$		0			0
$76$	4.34597	+	16.2194i	0.0571838	+	0.213413i
$77$			22.2653i			0.289160i
$78$		0			0
$79$	−70.2833			−0.889662			−0.444831	−	0.895614i	$-0.646736\pi$
$79$	−70.2833			−0.889662			−0.444831	+	0.895614i	$0.646736\pi$
$80$	11.7652	−	3.15248i	0.147065	−	0.0394060i
$81$		0			0
$82$	38.5011	−	22.2286i	0.469525	−	0.271080i
$83$	−9.18965	−	9.18965i	−0.110719	−	0.110719i	0.649577	−	0.760296i	$-0.274946\pi$
$83$	−9.18965	−	9.18965i	−0.110719	−	0.110719i	−0.760296	+	0.649577i	$0.774946\pi$
$84$		0			0
$85$	−10.0260	−	2.68645i	−0.117952	−	0.0316053i
$86$	105.770	−	105.770i	1.22988	−	1.22988i
$87$		0			0
$88$	−78.9017	−	45.5539i	−0.896610	−	0.517658i
$89$	14.7802	+	55.1604i	0.166070	+	0.619780i	0.997901	+	0.0647522i	$0.0206257\pi$
$89$	14.7802	+	55.1604i	0.166070	+	0.619780i	−0.831832	+	0.555028i	$0.812708\pi$
$90$		0			0
$91$	−4.59219	+	26.8877i	−0.0504637	+	0.295469i
$92$	19.9408			0.216747
$93$		0			0
$94$	−57.3698	+	99.3675i	−0.610318	+	1.05710i
$95$	−18.2307	+	10.5255i	−0.191902	+	0.110794i
$96$		0			0
$97$	−11.7078	+	43.6941i	−0.120699	+	0.450455i	−0.999650	−	0.0264575i	$-0.991577\pi$
$97$	−11.7078	+	43.6941i	−0.120699	+	0.450455i	0.878951	+	0.476912i	$0.158244\pi$
$98$	77.0792	+	20.6533i	0.786522	+	0.210748i
$99$		0			0
$100$	9.58009	+	16.5932i	0.0958009	+	0.165932i
$101$	−76.3610	−	44.0870i	−0.756049	−	0.436505i	0.0718263	−	0.997417i	$-0.477117\pi$
$101$	−76.3610	−	44.0870i	−0.756049	−	0.436505i	−0.827875	+	0.560912i	$0.810451\pi$
$102$		0			0
$103$		−	24.5513i		−	0.238363i	−0.992873	−	0.119181i	$-0.961973\pi$
$103$		−	24.5513i		−	0.238363i	0.992873	−	0.119181i	$-0.0380270\pi$
$104$	−85.8865	−	71.2844i	−0.825832	−	0.685427i
$105$		0			0
$106$	−112.638	+	30.1812i	−1.06262	+	0.284728i
$107$	−42.4286	+	73.4885i	−0.396529	+	0.686809i	−0.993295	−	0.115607i	$-0.963119\pi$
$107$	−42.4286	+	73.4885i	−0.396529	+	0.686809i	0.596766	+	0.802415i	$0.296452\pi$
$108$		0			0
$109$	46.7383	+	46.7383i	0.428792	+	0.428792i	0.888217	−	0.459425i	$-0.151944\pi$
$109$	46.7383	+	46.7383i	0.428792	+	0.428792i	−0.459425	+	0.888217i	$0.651944\pi$
$110$	4.91880	−	18.3572i	0.0447163	−	0.166884i
$111$		0			0
$112$	18.0547	−	18.0547i	0.161203	−	0.161203i
$113$	103.485	+	179.242i	0.915799	+	1.58621i	0.805727	+	0.592287i	$0.201775\pi$
$113$	103.485	+	179.242i	0.915799	+	1.58621i	0.110072	+	0.993924i	$0.464892\pi$
$114$		0			0
$115$	6.47023	+	24.1472i	0.0562629	+	0.209976i
$116$		−	19.3495i		−	0.166806i
$117$		0			0
$118$	138.038			1.16982
$119$	−21.0172	+	5.63155i	−0.176615	+	0.0473239i
$120$		0			0
$121$	7.27170	−	4.19832i	0.0600967	−	0.0346969i
$122$	−33.6112	−	33.6112i	−0.275501	−	0.275501i
$123$		0			0
$124$	−19.7541	−	5.29308i	−0.159307	−	0.0426862i
$125$	−34.6791	+	34.6791i	−0.277433	+	0.277433i
$126$		0			0
$127$	−12.9643	−	7.48492i	−0.102081	−	0.0589363i	0.448090	−	0.893988i	$-0.352104\pi$
$127$	−12.9643	−	7.48492i	−0.102081	−	0.0589363i	−0.550171	+	0.835052i	$0.685438\pi$
$128$	19.9447	+	74.4345i	0.155818	+	0.581520i
$129$		0			0
$130$	9.72610	−	21.1537i	0.0748162	−	0.162721i
$131$	8.61156			0.0657371			0.0328685	−	0.999460i	$-0.489536\pi$
$131$	8.61156			0.0657371			0.0328685	+	0.999460i	$0.489536\pi$
$132$		0			0
$133$	−22.0644	+	38.2166i	−0.165897	+	0.287343i
$134$	−120.207	+	69.4016i	−0.897068	+	0.517922i
$135$		0			0
$136$	23.0438	−	86.0007i	0.169440	−	0.632358i
$137$	198.159	+	53.0966i	1.44642	+	0.387567i	0.894776	−	0.446515i	$-0.147335\pi$
$137$	198.159	+	53.0966i	1.44642	+	0.387567i	0.551642	+	0.834081i	$0.314002\pi$
$138$		0			0
$139$	−29.8441	−	51.6915i	−0.214706	−	0.371881i	0.738476	−	0.674280i	$-0.235546\pi$
$139$	−29.8441	−	51.6915i	−0.214706	−	0.371881i	−0.953182	+	0.302399i	$0.902213\pi$
$140$	−1.45214	−	0.838395i	−0.0103724	−	0.00598854i
$141$		0			0
$142$			189.938i			1.33759i
$143$	−129.374	+	47.8772i	−0.904716	+	0.334806i
$144$		0			0
$145$	23.4313	−	6.27839i	0.161595	−	0.0432992i
$146$	−104.484	+	180.972i	−0.715646	+	1.23954i
$147$		0			0
$148$	−17.0727	−	17.0727i	−0.115356	−	0.115356i
$149$	25.2713	−	94.3136i	0.169606	−	0.632977i	−0.827802	−	0.561020i	$-0.810409\pi$
$149$	25.2713	−	94.3136i	0.169606	−	0.632977i	0.997408	−	0.0719569i	$-0.0229244\pi$
$150$		0			0
$151$	77.9592	−	77.9592i	0.516286	−	0.516286i	−0.400160	−	0.916445i	$-0.631045\pi$
$151$	77.9592	−	77.9592i	0.516286	−	0.516286i	0.916445	+	0.400160i	$0.131045\pi$
$152$	−90.2855	−	156.379i	−0.593984	−	1.02881i
$153$		0			0
$154$	−10.3112	−	38.4818i	−0.0669557	−	0.249882i
$155$		−	25.6386i		−	0.165410i
$156$		0			0
$157$	189.915			1.20965			0.604823	−	0.796360i	$-0.293244\pi$
$157$	189.915			1.20965			0.604823	+	0.796360i	$0.293244\pi$
$158$	121.473	−	32.5486i	0.768816	−	0.206004i
$159$		0			0
$160$	10.8954	−	6.29047i	0.0680963	−	0.0393154i
$161$	37.0559	+	37.0559i	0.230161	+	0.230161i
$162$		0			0
$163$	−161.605	−	43.3020i	−0.991444	−	0.265657i	−0.273587	−	0.961847i	$-0.588210\pi$
$163$	−161.605	−	43.3020i	−0.991444	−	0.265657i	−0.717857	+	0.696191i	$0.754877\pi$
$164$	14.0270	−	14.0270i	0.0855307	−	0.0855307i
$165$		0			0
$166$	20.1385	+	11.6270i	0.121317	+	0.0700421i
$167$	41.2288	+	153.868i	0.246879	+	0.921364i	0.972430	+	0.233196i	$0.0749183\pi$
$167$	41.2288	+	153.868i	0.246879	+	0.921364i	−0.725551	+	0.688168i	$0.758415\pi$
$168$		0			0
$169$	−166.108	+	31.1334i	−0.982885	+	0.184221i
$170$	18.5723			0.109249
$171$		0			0
$172$	33.3721	−	57.8023i	0.194024	−	0.336060i
$173$	229.087	−	132.263i	1.32420	−	0.764528i	0.339805	−	0.940496i	$-0.389639\pi$
$173$	229.087	−	132.263i	1.32420	−	0.764528i	0.984396	+	0.175968i	$0.0563056\pi$
$174$		0			0
$175$	−13.0325	+	48.6379i	−0.0744713	+	0.277931i
$176$	124.730	+	33.4214i	0.708695	+	0.189894i
$177$		0			0
$178$	−51.0901	−	88.4907i	−0.287023	−	0.497139i
$179$	−281.701	−	162.640i	−1.57375	−	0.908606i	−0.995703	−	0.0926030i	$-0.970481\pi$
$179$	−281.701	−	162.640i	−1.57375	−	0.908606i	−0.578048	−	0.816003i	$-0.696185\pi$
$180$		0			0
$181$			299.624i			1.65538i	0.561184	+	0.827691i	$0.310346\pi$
$181$			299.624i			1.65538i	−0.561184	+	0.827691i	$0.689654\pi$
$182$	−4.51498	−	48.5975i	−0.0248076	−	0.267019i
$183$		0			0
$184$	−207.130	+	55.5004i	−1.12571	+	0.301633i
$185$	15.1345	−	26.2138i	0.0818083	−	0.141696i
$186$		0			0
$187$	−77.8107	−	77.8107i	−0.416100	−	0.416100i
$188$	−13.2510	+	49.4534i	−0.0704840	+	0.263050i
$189$		0			0
$190$	26.6342	−	26.6342i	0.140180	−	0.140180i
$191$	64.2673	+	111.314i	0.336478	+	0.582797i	0.983768	−	0.179447i	$-0.0574309\pi$
$191$	64.2673	+	111.314i	0.336478	+	0.582797i	−0.647290	+	0.762244i	$0.724098\pi$
$192$		0			0
$193$	5.65961	+	21.1220i	0.0293244	+	0.109440i	0.979037	−	0.203683i	$-0.0652913\pi$
$193$	5.65961	+	21.1220i	0.0293244	+	0.109440i	−0.949712	+	0.313124i	$0.898625\pi$
$194$		−	80.9398i		−	0.417216i
$195$		0			0
$196$	35.6067			0.181667
$197$	93.8465	−	25.1461i	0.476378	−	0.127645i	−0.0126375	−	0.999920i	$-0.504023\pi$
$197$	93.8465	−	25.1461i	0.476378	−	0.127645i	0.489016	+	0.872275i	$0.337356\pi$
$198$		0			0
$199$	41.6119	−	24.0246i	0.209105	−	0.120727i	−0.391790	−	0.920054i	$-0.628144\pi$
$199$	41.6119	−	24.0246i	0.209105	−	0.120727i	0.600895	+	0.799328i	$0.294811\pi$
$200$	−145.694	−	145.694i	−0.728472	−	0.728472i
$201$		0			0
$202$	152.394	+	40.8339i	0.754426	+	0.202148i
$203$	35.9572	−	35.9572i	0.177129	−	0.177129i
$204$		0			0
$205$	21.5374	+	12.4346i	0.105060	+	0.0606567i
$206$	11.3699	+	42.4329i	0.0551935	+	0.205985i
$207$		0			0
$208$	143.732	+	66.0853i	0.691018	+	0.317718i
$209$	−223.174			−1.06782
$210$		0			0
$211$	88.2394	−	152.835i	0.418196	−	0.724337i	−0.577562	−	0.816347i	$-0.695996\pi$
$211$	88.2394	−	152.835i	0.418196	−	0.724337i	0.995758	+	0.0920098i	$0.0293291\pi$
$212$	−45.0619	+	26.0165i	−0.212556	+	0.122719i
$213$		0			0
$214$	39.2978	−	146.662i	0.183635	−	0.685334i
$215$	80.8239	+	21.6567i	0.375925	+	0.100729i
$216$		0			0
$217$	−26.8728	−	46.5451i	−0.123838	−	0.214494i
$218$	−102.424	−	59.1346i	−0.469835	−	0.271260i
$219$		0			0
$220$		−	8.48011i		−	0.0385459i
$221$	−77.9160	−	110.013i	−0.352561	−	0.497795i
$222$		0			0
$223$	229.924	−	61.6080i	1.03105	−	0.276269i	0.296650	−	0.954986i	$-0.404130\pi$
$223$	229.924	−	61.6080i	1.03105	−	0.276269i	0.734400	+	0.678717i	$0.237464\pi$
$224$	13.1866	−	22.8398i	0.0588687	−	0.101964i
$225$		0			0
$226$	−261.865	−	261.865i	−1.15869	−	1.15869i
$227$	18.2969	−	68.2850i	0.0806031	−	0.300815i	−0.913842	−	0.406069i	$-0.866899\pi$
$227$	18.2969	−	68.2850i	0.0806031	−	0.300815i	0.994445	+	0.105255i	$0.0335658\pi$
$228$		0			0
$229$	5.11731	−	5.11731i	0.0223463	−	0.0223463i	−0.695845	−	0.718192i	$-0.744970\pi$
$229$	5.11731	−	5.11731i	0.0223463	−	0.0223463i	0.718192	+	0.695845i	$0.244970\pi$
$230$	−22.3654	−	38.7380i	−0.0972409	−	0.168426i
$231$		0			0
$232$	53.8548	+	200.989i	0.232133	+	0.866331i
$233$			87.8062i			0.376851i	0.982088	+	0.188425i	$0.0603383\pi$
$233$			87.8062i			0.376851i	−0.982088	+	0.188425i	$0.939662\pi$
$234$		0			0
$235$	−64.1851			−0.273128
$236$	59.4952	−	15.9417i	0.252099	−	0.0675496i
$237$		0			0
$238$	33.7167	−	19.4664i	0.141667	−	0.0817914i
$239$	−111.594	−	111.594i	−0.466920	−	0.466920i	0.433995	−	0.900915i	$-0.357103\pi$
$239$	−111.594	−	111.594i	−0.466920	−	0.466920i	−0.900915	+	0.433995i	$0.857103\pi$
$240$		0			0
$241$	45.8937	+	12.2972i	0.190430	+	0.0510256i	0.352774	−	0.935709i	$-0.385239\pi$
$241$	45.8937	+	12.2972i	0.190430	+	0.0510256i	−0.162343	+	0.986734i	$0.551905\pi$
$242$	−10.6237	+	10.6237i	−0.0438994	+	0.0438994i
$243$		0			0
$244$	−18.3683	−	10.6049i	−0.0752797	−	0.0434628i
$245$	11.5534	+	43.1179i	0.0471567	+	0.175991i
$246$		0			0
$247$	−269.506	−	46.0294i	−1.09112	−	0.186354i
$248$	219.923			0.886786
$249$		0			0
$250$	43.8770	−	75.9971i	0.175508	−	0.303989i
$251$	52.0159	−	30.0314i	0.207235	−	0.119647i	−0.392791	−	0.919628i	$-0.628490\pi$
$251$	52.0159	−	30.0314i	0.207235	−	0.119647i	0.600026	+	0.799981i	$0.295157\pi$
$252$		0			0
$253$	−68.5949	+	256.000i	−0.271126	+	1.01186i
$254$	25.8728	+	6.93261i	0.101862	+	0.0272937i
$255$		0			0
$256$	73.3898	+	127.115i	0.286679	+	0.496543i
$257$	300.057	+	173.238i	1.16754	+	0.674077i	0.953098	−	0.302660i	$-0.0978748\pi$
$257$	300.057	+	173.238i	1.16754	+	0.674077i	0.214438	+	0.976738i	$0.431208\pi$
$258$		0			0
$259$		−	63.4525i		−	0.244990i
$260$	1.74901	−	10.2406i	0.00672697	−	0.0393869i
$261$		0			0
$262$	−14.8836	+	3.98806i	−0.0568077	+	0.0152216i
$263$	131.297	−	227.413i	0.499228	−	0.864688i	−0.500772	−	0.865579i	$-0.666950\pi$
$263$	131.297	−	227.413i	0.499228	−	0.864688i	1.00000		0.000891166i	$0.000283667\pi$
$264$		0			0
$265$	−46.1260	−	46.1260i	−0.174060	−	0.174060i
$266$	20.4362	−	76.2690i	0.0768279	−	0.286726i
$267$		0			0
$268$	−43.7949	+	43.7949i	−0.163414	+	0.163414i
$269$	39.1244	+	67.7655i	0.145444	+	0.251916i	0.929539	−	0.368725i	$-0.120206\pi$
$269$	39.1244	+	67.7655i	0.145444	+	0.251916i	−0.784094	+	0.620641i	$0.786872\pi$
$270$		0			0
$271$	−30.7983	−	114.941i	−0.113647	−	0.424136i	0.885535	−	0.464572i	$-0.153792\pi$
$271$	−30.7983	−	114.941i	−0.113647	−	0.424136i	−0.999182	+	0.0404365i	$0.987125\pi$
$272$			126.192i			0.463941i
$273$		0			0
$274$	−367.074			−1.33969
$275$	−245.978	+	65.9097i	−0.894467	+	0.239672i
$276$		0			0
$277$	301.713	−	174.194i	1.08922	−	0.628860i	0.155849	−	0.987781i	$-0.450189\pi$
$277$	301.713	−	174.194i	1.08922	−	0.628860i	0.933368	+	0.358921i	$0.116855\pi$
$278$	75.5191	+	75.5191i	0.271651	+	0.271651i
$279$		0			0
$280$	17.4173	+	4.66695i	0.0622046	+	0.0166677i
$281$	−40.1090	+	40.1090i	−0.142737	+	0.142737i	−0.774864	−	0.632128i	$-0.782182\pi$
$281$	−40.1090	+	40.1090i	−0.142737	+	0.142737i	0.632128	+	0.774864i	$0.282182\pi$
$282$		0			0
$283$	71.1179	+	41.0599i	0.251300	+	0.145088i	0.620359	−	0.784318i	$-0.286987\pi$
$283$	71.1179	+	41.0599i	0.251300	+	0.145088i	−0.369059	+	0.929406i	$0.620320\pi$
$284$	21.9355	+	81.8642i	0.0772375	+	0.288254i
$285$		0			0
$286$	201.430	−	142.662i	0.704300	−	0.498817i
$287$	52.1329			0.181648
$288$		0			0
$289$	−90.7316	+	157.152i	−0.313950	+	0.543778i
$290$	−37.5894	+	21.7023i	−0.129619	+	0.0748354i
$291$		0			0
$292$	−24.1333	+	90.0666i	−0.0826482	+	0.308447i
$293$	−509.443	−	136.505i	−1.73871	−	0.465887i	−0.756554	−	0.653931i	$-0.773119\pi$
$293$	−509.443	−	136.505i	−1.73871	−	0.465887i	−0.982161	+	0.188044i	$0.939785\pi$
$294$		0			0
$295$	38.6091	+	66.8730i	0.130878	+	0.226688i
$296$	224.857	+	129.821i	0.759652	+	0.438585i
$297$		0			0
$298$			174.708i			0.586270i
$299$	−135.635	+	294.998i	−0.453629	+	0.986616i
$300$		0			0
$301$	169.429	−	45.3985i	0.562889	−	0.150826i
$302$	−98.6360	+	170.843i	−0.326609	+	0.565704i
$303$		0			0
$304$	180.970	+	180.970i	0.595295	+	0.595295i
$305$	6.88201	−	25.6840i	0.0225640	−	0.0842099i
$306$		0			0
$307$	−297.107	+	297.107i	−0.967775	+	0.967775i	−0.999497	−	0.0317217i	$-0.989901\pi$
$307$	−297.107	+	297.107i	−0.967775	+	0.967775i	0.0317217	+	0.999497i	$0.489901\pi$
$308$	−8.88834	−	15.3951i	−0.0288583	−	0.0499840i
$309$		0			0
$310$	11.8734	+	44.3120i	0.0383012	+	0.142942i
$311$			527.024i			1.69461i	0.531107	+	0.847305i	$0.321776\pi$
$311$			527.024i			1.69461i	−0.531107	+	0.847305i	$0.678224\pi$
$312$		0			0
$313$	87.6743			0.280110			0.140055	−	0.990144i	$-0.455272\pi$
$313$	87.6743			0.280110			0.140055	+	0.990144i	$0.455272\pi$
$314$	−328.235	+	87.9504i	−1.04534	+	0.280097i
$315$		0			0
$316$	48.5965	−	28.0572i	0.153786	−	0.0887886i
$317$	67.4056	+	67.4056i	0.212636	+	0.212636i	0.805386	−	0.592750i	$-0.201958\pi$
$317$	67.4056	+	67.4056i	0.212636	+	0.212636i	−0.592750	+	0.805386i	$0.701958\pi$
$318$		0			0
$319$	248.409	+	66.5610i	0.778712	+	0.208655i
$320$	−50.3687	+	50.3687i	−0.157402	+	0.157402i
$321$		0			0
$322$	−81.2058	−	46.8842i	−0.252192	−	0.145603i
$323$	−56.4472	−	210.664i	−0.174759	−	0.652210i
$324$		0			0
$325$	−310.638	+	28.8600i	−0.955809	+	0.0888000i
$326$	299.361			0.918285
$327$		0			0
$328$	−106.662	+	184.744i	−0.325188	+	0.563243i
$329$	−116.524	+	67.2750i	−0.354175	+	0.204483i
$330$		0			0
$331$	−15.7065	+	58.6175i	−0.0474517	+	0.177092i	−0.985585	−	0.169183i	$-0.945887\pi$
$331$	−15.7065	+	58.6175i	−0.0474517	+	0.177092i	0.938133	+	0.346275i	$0.112554\pi$
$332$	10.0226	+	2.68554i	0.0301885	+	0.00808899i
$333$		0			0
$334$	−142.514	−	246.841i	−0.426688	−	0.739046i
$335$	−67.2435	−	38.8231i	−0.200727	−	0.115890i
$336$		0			0
$337$		−	461.619i		−	1.36979i	−0.728643	−	0.684894i	$-0.759848\pi$
$337$		−	461.619i		−	1.36979i	0.728643	−	0.684894i	$-0.240152\pi$
$338$	272.671	−	130.734i	0.806719	−	0.386787i
$339$		0			0
$340$	8.00475	−	2.14487i	0.0235434	−	0.00630843i
$341$	135.905	−	235.395i	0.398549	−	0.690307i
$342$		0			0
$343$	138.868	+	138.868i	0.404863	+	0.404863i
$344$	−185.767	+	693.292i	−0.540020	+	2.01538i
$345$		0			0
$346$	−334.686	+	334.686i	−0.967301	+	0.967301i
$347$	−143.905	−	249.251i	−0.414713	−	0.718303i	0.580686	−	0.814128i	$-0.302785\pi$
$347$	−143.905	−	249.251i	−0.414713	−	0.718303i	−0.995398	+	0.0958246i	$0.969451\pi$
$348$		0			0
$349$	−24.3973	−	91.0520i	−0.0699064	−	0.260894i	0.922124	−	0.386895i	$-0.126452\pi$
$349$	−24.3973	−	91.0520i	−0.0699064	−	0.260894i	−0.992030	+	0.126001i	$0.959786\pi$
$350$		−	90.0978i		−	0.257422i
$351$		0			0
$352$	133.378			0.378915
$353$	213.460	−	57.1964i	0.604703	−	0.162030i	0.0565385	−	0.998400i	$-0.481994\pi$
$353$	213.460	−	57.1964i	0.604703	−	0.162030i	0.548164	+	0.836371i	$0.315327\pi$
$354$		0			0
$355$	−92.0159	+	53.1254i	−0.259200	+	0.149649i
$356$	−32.2397	−	32.2397i	−0.0905609	−	0.0905609i
$357$		0			0
$358$	562.193	+	150.639i	1.57037	+	0.420780i
$359$	154.328	−	154.328i	0.429883	−	0.429883i	−0.458705	−	0.888588i	$-0.651687\pi$
$359$	154.328	−	154.328i	0.429883	−	0.429883i	0.888588	+	0.458705i	$0.151687\pi$
$360$		0			0
$361$	−70.4249	−	40.6598i	−0.195083	−	0.112631i
$362$	−138.757	−	517.850i	−0.383308	−	1.43052i
$363$		0			0
$364$	−7.55837	−	20.4243i	−0.0207648	−	0.0561108i
$365$	−116.897			−0.320264
$366$		0			0
$367$	217.007	−	375.867i	0.591299	−	1.02416i	−0.402759	−	0.915306i	$-0.631949\pi$
$367$	217.007	−	375.867i	0.591299	−	1.02416i	0.994058	−	0.108854i	$-0.0347180\pi$
$368$	263.211	−	151.965i	0.715246	−	0.412948i
$369$		0			0
$370$	−14.0178	+	52.3150i	−0.0378859	+	0.141392i
$371$	−132.085	−	35.3921i	−0.356025	−	0.0953965i
$372$		0			0
$373$	125.028	+	216.555i	0.335196	+	0.580577i	0.983522	−	0.180786i	$-0.0578641\pi$
$373$	125.028	+	216.555i	0.335196	+	0.580577i	−0.648326	+	0.761363i	$0.724531\pi$
$374$	170.517	+	98.4481i	0.455928	+	0.263230i
$375$		0			0
$376$		−	550.567i		−	1.46427i
$377$	286.251	+	131.613i	0.759288	+	0.349107i
$378$		0			0
$379$	−319.105	+	85.5040i	−0.841966	+	0.225604i	−0.653927	−	0.756557i	$-0.726880\pi$
$379$	−319.105	+	85.5040i	−0.841966	+	0.225604i	−0.188039	+	0.982162i	$0.560213\pi$
$380$	8.40357	−	14.5554i	0.0221147	−	0.0383037i
$381$		0			0
$382$	−162.625	−	162.625i	−0.425721	−	0.425721i
$383$	154.225	−	575.576i	0.402677	−	1.50281i	−0.405623	−	0.914040i	$-0.632946\pi$
$383$	154.225	−	575.576i	0.402677	−	1.50281i	0.808300	−	0.588770i	$-0.200388\pi$
$384$		0			0
$385$	15.7586	−	15.7586i	0.0409314	−	0.0409314i
$386$	−19.5634	−	33.8848i	−0.0506823	−	0.0877844i
$387$		0			0
$388$	−9.34754	−	34.8855i	−0.0240916	−	0.0899110i
$389$		−	448.386i		−	1.15266i	−0.817216	−	0.576332i	$-0.804484\pi$
$389$		−	448.386i		−	1.15266i	0.817216	−	0.576332i	$-0.195516\pi$
$390$		0			0
$391$	−258.999			−0.662402
$392$	−369.857	+	99.1028i	−0.943512	+	0.252813i
$393$		0			0
$394$	−150.553	+	86.9216i	−0.382113	+	0.220613i
$395$	49.7440	+	49.7440i	0.125934	+	0.125934i
$396$		0			0
$397$	−505.950	−	135.569i	−1.27443	−	0.341483i	−0.442705	−	0.896667i	$-0.645981\pi$
$397$	−505.950	−	135.569i	−1.27443	−	0.341483i	−0.831727	+	0.555184i	$0.812648\pi$
$398$	−60.7932	+	60.7932i	−0.152747	+	0.152747i
$399$		0			0
$400$	252.907	+	146.016i	0.632268	+	0.365040i
$401$	−82.6595	−	308.489i	−0.206133	−	0.769300i	−0.989101	−	0.147238i	$-0.952962\pi$
$401$	−82.6595	−	308.489i	−0.206133	−	0.769300i	0.782968	−	0.622062i	$-0.213705\pi$
$402$		0			0
$403$	212.669	−	256.233i	0.527716	−	0.635814i
$404$	70.3984			0.174253
$405$		0			0
$406$	−45.4940	+	78.7980i	−0.112054	+	0.194084i
$407$	277.909	−	160.451i	0.682822	−	0.394227i
$408$		0			0
$409$	185.927	−	693.888i	0.454589	−	1.69655i	−0.234706	−	0.972066i	$-0.575413\pi$
$409$	185.927	−	693.888i	0.454589	−	1.69655i	0.689294	−	0.724481i	$-0.257921\pi$
$410$	−42.9823	−	11.5171i	−0.104835	−	0.0280904i
$411$		0			0
$412$	9.80093	+	16.9757i	0.0237887	+	0.0412032i
$413$	140.185	+	80.9356i	0.339430	+	0.195970i
$414$		0			0
$415$			13.0082i			0.0313451i
$416$	161.068	+	27.5091i	0.387182	+	0.0661276i
$417$		0			0
$418$	385.719	−	103.353i	0.922772	−	0.247256i
$419$	135.437	−	234.585i	0.323240	−	0.559868i	−0.657915	−	0.753092i	$-0.728561\pi$
$419$	135.437	−	234.585i	0.323240	−	0.559868i	0.981155	+	0.193225i	$0.0618946\pi$
$420$		0			0
$421$	136.087	+	136.087i	0.323247	+	0.323247i	0.850011	−	0.526764i	$-0.176595\pi$
$421$	136.087	+	136.087i	0.323247	+	0.323247i	−0.526764	+	0.850011i	$0.676595\pi$
$422$	−81.7282	+	305.014i	−0.193669	+	0.722782i
$423$		0			0
$424$	395.660	−	395.660i	0.933160	−	0.933160i
$425$	−124.430	−	215.520i	−0.292777	−	0.507105i
$426$		0			0
$427$	−14.4266	−	53.8409i	−0.0337860	−	0.126091i
$428$		−	67.7503i		−	0.158295i
$429$		0			0
$430$	−149.720			−0.348186
$431$	424.646	−	113.784i	0.985259	−	0.263999i	0.270001	−	0.962860i	$-0.412976\pi$
$431$	424.646	−	113.784i	0.985259	−	0.263999i	0.715258	+	0.698861i	$0.246309\pi$
$432$		0			0
$433$	−311.613	+	179.910i	−0.719662	+	0.415497i	−0.814628	−	0.579984i	$-0.803059\pi$
$433$	−311.613	+	179.910i	−0.719662	+	0.415497i	0.0949665	+	0.995480i	$0.469726\pi$
$434$	68.0005	+	68.0005i	0.156683	+	0.156683i
$435$		0			0
$436$	−50.9746	−	13.6586i	−0.116914	−	0.0313271i
$437$	−371.427	+	371.427i	−0.849946	+	0.849946i
$438$		0			0
$439$	490.543	+	283.215i	1.11741	+	0.645137i	0.940738	−	0.339133i	$-0.110134\pi$
$439$	490.543	+	283.215i	1.11741	+	0.645137i	0.176671	+	0.984270i	$0.443467\pi$
$440$	23.6024	+	88.0852i	0.0536418	+	0.200194i
$441$		0			0
$442$	185.612	+	154.055i	0.419937	+	0.348541i
$443$	−621.478			−1.40288			−0.701442	−	0.712727i	$-0.747460\pi$
$443$	−621.478			−1.40288			−0.701442	+	0.712727i	$0.747460\pi$
$444$		0			0
$445$	28.5797	−	49.5015i	0.0642240	−	0.111239i
$446$	−368.854	+	212.958i	−0.827028	+	0.477485i
$447$		0			0
$448$	−38.6475	+	144.234i	−0.0862667	+	0.321952i
$449$	−500.056	−	133.989i	−1.11371	−	0.298418i	−0.345374	−	0.938465i	$-0.612248\pi$
$449$	−500.056	−	133.989i	−1.11371	−	0.298418i	−0.768335	+	0.640047i	$0.778915\pi$
$450$		0			0
$451$	131.827	+	228.331i	0.292299	+	0.506277i
$452$	−143.107	−	82.6229i	−0.316609	−	0.182794i
$453$		0			0
$454$			126.492i			0.278618i
$455$	22.2803	−	15.7799i	0.0489677	−	0.0346812i
$456$		0			0
$457$	54.6041	−	14.6311i	0.119484	−	0.0320156i	−0.198582	−	0.980084i	$-0.563633\pi$
$457$	54.6041	−	14.6311i	0.119484	−	0.0320156i	0.318065	+	0.948069i	$0.396967\pi$
$458$	−6.47455	+	11.2143i	−0.0141366	+	0.0244853i
$459$		0			0
$460$	−14.1134	−	14.1134i	−0.0306812	−	0.0306812i
$461$	−189.701	+	707.973i	−0.411498	+	1.53573i	0.380249	+	0.924884i	$0.375838\pi$
$461$	−189.701	+	707.973i	−0.411498	+	1.53573i	−0.791747	+	0.610849i	$0.790828\pi$
$462$		0			0
$463$	−231.348	+	231.348i	−0.499672	+	0.499672i	−0.911336	−	0.411664i	$-0.864948\pi$
$463$	−231.348	+	231.348i	−0.499672	+	0.499672i	0.411664	+	0.911336i	$0.364948\pi$
$464$	−147.459	−	255.406i	−0.317799	−	0.550444i
$465$		0			0
$466$	−40.6635	−	151.758i	−0.0872607	−	0.325661i
$467$			27.7760i			0.0594776i	0.999558	+	0.0297388i	$0.00946755\pi$
$467$			27.7760i			0.0594776i	−0.999558	+	0.0297388i	$0.990532\pi$
$468$		0			0
$469$	−162.768			−0.347053
$470$	110.933	−	29.7244i	0.236028	−	0.0632435i
$471$		0			0
$472$	−573.624	+	331.182i	−1.21530	+	0.701657i
$473$	627.268	+	627.268i	1.32615	+	1.32615i
$474$		0			0
$475$	−487.517	−	130.630i	−1.02635	−	0.275010i
$476$	12.2840	−	12.2840i	0.0258066	−	0.0258066i
$477$		0			0
$478$	244.551	+	141.191i	0.511612	+	0.295380i
$479$	−25.4858	−	95.1144i	−0.0532063	−	0.198569i	0.934207	−	0.356733i	$-0.116109\pi$
$479$	−25.4858	−	95.1144i	−0.0532063	−	0.198569i	−0.987413	+	0.158164i	$0.949443\pi$
$480$		0			0
$481$	368.696	−	136.442i	0.766520	−	0.283664i
$482$	−85.0144			−0.176378
$483$		0			0
$484$	−3.35195	+	5.80575i	−0.00692552	+	0.0119953i
$485$	39.2115	−	22.6388i	0.0808484	−	0.0466779i
$486$		0			0
$487$	−52.0781	+	194.358i	−0.106937	+	0.399093i	−0.998558	−	0.0536896i	$-0.982902\pi$
$487$	−52.0781	+	194.358i	−0.106937	+	0.399093i	0.891621	+	0.452782i	$0.149569\pi$
$488$	220.313	+	59.0326i	0.451460	+	0.120968i
$489$		0			0
$490$	−39.9362	−	69.1716i	−0.0815025	−	0.141166i
$491$	536.742	+	309.888i	1.09316	+	0.631137i	0.934416	−	0.356183i	$-0.115922\pi$
$491$	536.742	+	309.888i	1.09316	+	0.631137i	0.158745	+	0.987320i	$0.449255\pi$
$492$		0			0
$493$			251.320i			0.509776i
$494$	487.112	−	45.2554i	0.986056	−	0.0916101i
$495$		0			0
$496$	−301.084	+	80.6751i	−0.607024	+	0.162651i
$497$	−111.366	+	192.891i	−0.224076	+	0.388111i
$498$		0			0
$499$	518.382	+	518.382i	1.03884	+	1.03884i	0.999214	+	0.0396281i	$0.0126173\pi$
$499$	518.382	+	518.382i	1.03884	+	1.03884i	0.0396281	+	0.999214i	$0.487383\pi$
$500$	10.1345	−	37.8224i	0.0202690	−	0.0756448i
$501$		0			0
$502$	−75.9931	+	75.9931i	−0.151381	+	0.151381i
$503$	409.225	+	708.798i	0.813568	+	1.40914i	0.910352	+	0.413835i	$0.135811\pi$
$503$	409.225	+	708.798i	0.813568	+	1.40914i	−0.0967843	+	0.995305i	$0.530856\pi$
$504$		0			0
$505$	22.8423	+	85.2488i	0.0452324	+	0.168809i
$506$		−	474.219i		−	0.937192i
$507$		0			0
$508$	11.9520			0.0235275
$509$	110.069	−	29.4928i	0.216245	−	0.0579426i	−0.149070	−	0.988827i	$-0.547628\pi$
$509$	110.069	−	29.4928i	0.216245	−	0.0579426i	0.365315	+	0.930884i	$0.380961\pi$
$510$		0			0
$511$	−212.218	+	122.524i	−0.415299	+	0.239773i
$512$	−403.669	−	403.669i	−0.788416	−	0.788416i
$513$		0			0
$514$	−598.825	−	160.455i	−1.16503	−	0.312169i
$515$	−17.3766	+	17.3766i	−0.0337409	+	0.0337409i
$516$		0			0
$517$	−589.300	−	340.233i	−1.13985	−	0.658090i
$518$	29.3852	+	109.667i	0.0567281	+	0.211712i
$519$		0			0
$520$	10.3348	+	111.240i	0.0198746	+	0.213923i
$521$	−898.048			−1.72370			−0.861850	−	0.507163i	$-0.830694\pi$
$521$	−898.048			−1.72370			−0.861850	+	0.507163i	$0.830694\pi$
$522$		0			0
$523$	89.1769	−	154.459i	0.170510	−	0.295333i	−0.768088	−	0.640344i	$-0.778792\pi$
$523$	89.1769	−	154.459i	0.170510	−	0.295333i	0.938598	+	0.345012i	$0.112125\pi$
$524$	−5.95435	+	3.43774i	−0.0113633	+	0.00656058i
$525$		0			0
$526$	−121.609	+	453.849i	−0.231195	+	0.862832i
$527$	256.574	+	68.7488i	0.486858	+	0.130453i
$528$		0			0
$529$	47.3959	+	82.0922i	0.0895953	+	0.155184i
$530$	101.082	+	58.3599i	0.190721	+	0.110113i
$531$		0			0
$532$		−	35.2325i		−	0.0662265i
$533$	112.102	+	302.922i	0.210322	+	0.568335i
$534$		0			0
$535$	82.0420	−	21.9831i	0.153350	−	0.0410899i
$536$	333.017	−	576.802i	0.621300	−	1.07612i
$537$		0			0
$538$	−99.0026	−	99.0026i	−0.184020	−	0.184020i
$539$	−122.485	+	457.119i	−0.227244	+	0.848087i
$540$		0			0
$541$	618.149	−	618.149i	1.14261	−	1.14261i	0.154633	−	0.987972i	$-0.450580\pi$
$541$	618.149	−	618.149i	1.14261	−	1.14261i	0.987972	−	0.154633i	$-0.0494196\pi$
$542$	106.459	+	184.393i	0.196419	+	0.340208i
$543$		0			0
$544$	33.7352	+	125.902i	0.0620133	+	0.231437i
$545$		−	66.1594i		−	0.121393i
$546$		0			0
$547$	64.0914			0.117169			0.0585844	−	0.998282i	$-0.481341\pi$
$547$	64.0914			0.117169			0.0585844	+	0.998282i	$0.481341\pi$
$548$	−158.211	+	42.3925i	−0.288706	+	0.0773585i
$549$		0			0
$550$	394.609	−	227.828i	0.717471	−	0.414232i
$551$	360.414	+	360.414i	0.654108	+	0.654108i
$552$		0			0
$553$	142.446	+	38.1682i	0.257587	+	0.0690202i
$554$	−440.790	+	440.790i	−0.795650	+	0.795650i
$555$		0			0
$556$	41.2706	+	23.8276i	0.0742278	+	0.0428554i
$557$	−211.182	−	788.141i	−0.379142	−	1.41498i	−0.847198	−	0.531277i	$-0.821712\pi$
$557$	−211.182	−	788.141i	−0.379142	−	1.41498i	0.468057	−	0.883698i	$-0.344954\pi$
$558$		0			0
$559$	628.117	+	886.863i	1.12364	+	1.58652i
$560$	−25.5570			−0.0456375
$561$		0			0
$562$	50.7470	−	87.8963i	0.0902971	−	0.156399i
$563$	−807.714	+	466.334i	−1.43466	+	0.828302i	−0.997471	−	0.0710682i	$-0.977359\pi$
$563$	−807.714	+	466.334i	−1.43466	+	0.828302i	−0.437189	+	0.899370i	$0.644026\pi$
$564$		0			0
$565$	53.6177	−	200.104i	0.0948987	−	0.354167i
$566$	−141.930	−	38.0301i	−0.250760	−	0.0671911i
$567$		0			0
$568$	−455.699	−	789.295i	−0.802288	−	1.38960i
$569$	18.3652	+	10.6031i	0.0322762	+	0.0186347i	0.516051	−	0.856558i	$-0.327401\pi$
$569$	18.3652	+	10.6031i	0.0322762	+	0.0186347i	−0.483775	+	0.875192i	$0.660735\pi$
$570$		0			0
$571$		−	402.871i		−	0.705553i	−0.935708	−	0.352776i	$-0.885238\pi$
$571$		−	402.871i		−	0.705553i	0.935708	−	0.352776i	$-0.114762\pi$
$572$	70.3416	−	84.7505i	0.122975	−	0.148165i
$573$		0			0
$574$	−90.1029	+	24.1430i	−0.156974	+	0.0420610i
$575$	−299.687	+	519.073i	−0.521194	+	0.902735i
$576$		0			0
$577$	270.074	+	270.074i	0.468066	+	0.468066i	0.901288	−	0.433221i	$-0.142623\pi$
$577$	270.074	+	270.074i	0.468066	+	0.468066i	−0.433221	+	0.901288i	$0.642623\pi$
$578$	84.0366	−	313.629i	0.145392	−	0.542610i
$579$		0			0
$580$	−13.6949	+	13.6949i	−0.0236119	+	0.0236119i
$581$	13.6344	+	23.6155i	0.0234672	+	0.0406464i
$582$		0			0
$583$	−178.990	−	668.000i	−0.307016	−	1.14580i
$584$		−	1002.72i		−	1.71698i
$585$		0			0
$586$	943.703			1.61042
$587$	482.466	−	129.276i	0.821918	−	0.220232i	0.176733	−	0.984259i	$-0.443447\pi$
$587$	482.466	−	129.276i	0.821918	−	0.220232i	0.645185	+	0.764026i	$0.276780\pi$
$588$		0			0
$589$	466.540	−	269.357i	0.792089	−	0.457313i
$590$	−97.6987	−	97.6987i	−0.165591	−	0.165591i
$591$		0			0
$592$	−355.461	−	95.2455i	−0.600441	−	0.160888i
$593$	−394.560	+	394.560i	−0.665363	+	0.665363i	−0.956639	−	0.291276i	$-0.905920\pi$
$593$	−394.560	+	394.560i	−0.665363	+	0.665363i	0.291276	+	0.956639i	$0.405920\pi$
$594$		0			0
$595$	18.8610	+	10.8894i	0.0316992	+	0.0183016i
$596$	20.1766	+	75.3002i	0.0338534	+	0.126343i
$597$		0			0
$598$	97.8071	−	572.668i	0.163557	−	0.957639i
$599$	1136.88			1.89796			0.948980	−	0.315335i	$-0.102117\pi$
$599$	1136.88			1.89796			0.948980	+	0.315335i	$0.102117\pi$
$600$		0			0
$601$	−264.053	+	457.354i	−0.439356	+	0.760988i	−0.997640	−	0.0686625i	$-0.978127\pi$
$601$	−264.053	+	457.354i	−0.439356	+	0.760988i	0.558283	+	0.829650i	$0.311460\pi$
$602$	−271.806	+	156.927i	−0.451505	+	0.260677i
$603$		0			0
$604$	−22.7824	+	85.0252i	−0.0377193	+	0.140770i
$605$	−8.11807	−	2.17523i	−0.0134183	−	0.00359542i
$606$		0			0
$607$	178.149	+	308.563i	0.293491	+	0.508341i	0.974633	−	0.223811i	$-0.0718497\pi$
$607$	178.149	+	308.563i	0.293491	+	0.508341i	−0.681142	+	0.732151i	$0.738516\pi$
$608$	228.933	+	132.174i	0.376534	+	0.217392i
$609$		0			0
$610$			47.5776i			0.0779960i
$611$	−641.468	−	532.408i	−1.04987	−	0.871372i
$612$		0			0
$613$	−384.018	+	102.897i	−0.626457	+	0.167859i	−0.558061	−	0.829800i	$-0.688455\pi$
$613$	−384.018	+	102.897i	−0.626457	+	0.167859i	−0.0683955	+	0.997658i	$0.521788\pi$
$614$	375.908	−	651.091i	0.612227	−	1.06041i
$615$		0			0
$616$	135.174	+	135.174i	0.219439	+	0.219439i
$617$	298.896	−	1115.50i	0.484435	−	1.80793i	−0.0981582	−	0.995171i	$-0.531295\pi$
$617$	298.896	−	1115.50i	0.484435	−	1.80793i	0.582593	−	0.812764i	$-0.302038\pi$
$618$		0			0
$619$	−305.402	+	305.402i	−0.493380	+	0.493380i	−0.909369	−	0.415989i	$-0.863435\pi$
$619$	−305.402	+	305.402i	−0.493380	+	0.493380i	0.415989	+	0.909369i	$0.363435\pi$
$620$	10.2350	+	17.7275i	0.0165080	+	0.0285927i
$621$		0			0
$622$	−244.067	−	910.872i	−0.392391	−	1.46442i
$623$		−	119.822i		−	0.192331i
$624$		0			0
$625$	−550.864			−0.881383
$626$	−151.530	+	40.6024i	−0.242061	+	0.0648601i
$627$		0			0
$628$	−131.314	+	75.8141i	−0.209099	+	0.120723i
$629$	221.748	+	221.748i	0.352540	+	0.352540i
$630$		0			0
$631$	−456.788	−	122.396i	−0.723911	−	0.193971i	−0.121995	−	0.992531i	$-0.538929\pi$
$631$	−456.788	−	122.396i	−0.723911	−	0.193971i	−0.601916	+	0.798559i	$0.705596\pi$
$632$	−426.695	+	426.695i	−0.675150	+	0.675150i
$633$		0			0
$634$	−147.715	−	85.2833i	−0.232989	−	0.134516i
$635$	3.87808	+	14.4732i	0.00610721	+	0.0227924i
$636$		0			0
$637$	−242.193	+	526.756i	−0.380209	+	0.826932i
$638$	−460.158			−0.721251
$639$		0			0
$640$	38.5660	−	66.7982i	0.0602593	−	0.104372i
$641$	291.321	−	168.194i	0.454479	−	0.262393i	−0.255241	−	0.966877i	$-0.582155\pi$
$641$	291.321	−	168.194i	0.454479	−	0.262393i	0.709720	+	0.704484i	$0.248822\pi$
$642$		0			0
$643$	−6.42009	+	23.9601i	−0.00998458	+	0.0372630i	−0.970738	−	0.240139i	$-0.922807\pi$
$643$	−6.42009	+	23.9601i	−0.00998458	+	0.0372630i	0.960754	+	0.277402i	$0.0894735\pi$
$644$	−40.4146	−	10.8291i	−0.0627556	−	0.0168153i
$645$		0			0
$646$	195.119	+	337.956i	0.302042	+	0.523152i
$647$	425.837	+	245.857i	0.658171	+	0.379995i	0.791580	−	0.611066i	$-0.209259\pi$
$647$	425.837	+	245.857i	0.658171	+	0.379995i	−0.133409	+	0.991061i	$0.542592\pi$
$648$		0			0
$649$			818.639i			1.26138i
$650$	523.520	−	193.738i	0.805416	−	0.298058i
$651$		0			0
$652$	129.026	−	34.5724i	0.197893	−	0.0530252i
$653$	240.538	−	416.624i	0.368358	−	0.638015i	−0.620951	−	0.783850i	$-0.713253\pi$
$653$	240.538	−	416.624i	0.368358	−	0.638015i	0.989309	+	0.145834i	$0.0465867\pi$
$654$		0			0
$655$	−6.09495	−	6.09495i	−0.00930527	−	0.00930527i
$656$	78.2542	−	292.049i	0.119290	−	0.445196i
$657$		0			0
$658$	170.236	−	170.236i	0.258718	−	0.258718i
$659$	24.0182	+	41.6007i	0.0364464	+	0.0631271i	0.883673	−	0.468104i	$-0.155063\pi$
$659$	24.0182	+	41.6007i	0.0364464	+	0.0631271i	−0.847227	+	0.531231i	$0.821730\pi$
$660$		0			0
$661$	126.623	+	472.565i	0.191563	+	0.714925i	0.993130	+	0.117019i	$0.0373337\pi$
$661$	126.623	+	472.565i	0.191563	+	0.714925i	−0.801566	+	0.597906i	$0.796000\pi$
$662$		−	108.584i		−	0.164024i
$663$		0			0
$664$	−111.582			−0.168045
$665$	42.6647	−	11.4320i	0.0641574	−	0.0171909i
$666$		0			0
$667$	524.202	−	302.648i	0.785910	−	0.453745i
$668$	−89.9313	−	89.9313i	−0.134628	−	0.134628i
$669$		0			0
$670$	134.198	+	35.9583i	0.200296	+	0.0536691i
$671$	199.332	−	199.332i	0.297066	−	0.297066i
$672$		0			0
$673$	−786.449	−	454.057i	−1.16857	−	0.674675i	−0.215229	−	0.976564i	$-0.569050\pi$
$673$	−786.449	−	454.057i	−1.16857	−	0.674675i	−0.953343	+	0.301888i	$0.902383\pi$
$674$	213.778	+	797.830i	0.317178	+	1.18372i
$675$		0			0
$676$	102.424	−	87.8371i	0.151515	−	0.129937i
$677$	−775.791			−1.14592			−0.572962	−	0.819582i	$-0.694206\pi$
$677$	−775.791			−1.14592			−0.572962	+	0.819582i	$0.694206\pi$
$678$		0			0
$679$	47.4572	−	82.1983i	0.0698928	−	0.121058i
$680$	−77.1779	+	44.5587i	−0.113497	+	0.0655274i
$681$		0			0
$682$	−125.877	+	469.779i	−0.184570	+	0.688825i
$683$	363.558	+	97.4150i	0.532295	+	0.142628i	0.514948	−	0.857221i	$-0.327811\pi$
$683$	363.558	+	97.4150i	0.532295	+	0.142628i	0.0173473	+	0.999850i	$0.494478\pi$
$684$		0			0
$685$	−102.670	−	177.830i	−0.149883	−	0.259606i
$686$	−304.320	−	175.699i	−0.443616	−	0.256122i
$687$		0			0
$688$		−	1017.29i		−	1.47862i
$689$	−78.3747	−	843.595i	−0.113751	−	1.22438i
$690$		0			0
$691$	−373.815	+	100.163i	−0.540977	+	0.144954i	−0.518953	−	0.854803i	$-0.673678\pi$
$691$	−373.815	+	100.163i	−0.540977	+	0.144954i	−0.0220245	+	0.999757i	$0.507011\pi$
$692$	−105.599	+	182.903i	−0.152600	+	0.264311i
$693$		0			0
$694$	364.146	+	364.146i	0.524705	+	0.524705i
$695$	−15.4628	+	57.7080i	−0.0222486	+	0.0830331i
$696$		0			0
$697$	−182.189	+	182.189i	−0.261390	+	0.261390i
$698$	84.3333	+	146.070i	0.120821	+	0.209269i
$699$		0			0
$700$	−10.4052	−	38.8326i	−0.0148645	−	0.0554751i
$701$			180.499i			0.257489i	0.991678	+	0.128744i	$0.0410946\pi$
$701$			180.499i			0.257489i	−0.991678	+	0.128744i	$0.958905\pi$
$702$		0			0
$703$	636.010			0.904708
$704$	−729.443	+	195.454i	−1.03614	+	0.277633i
$705$		0			0
$706$	−342.442	+	197.709i	−0.485045	+	0.280041i
$707$	130.821	+	130.821i	0.185037	+	0.185037i
$708$		0			0
$709$	573.543	+	153.680i	0.808947	+	0.216757i	0.639508	−	0.768784i	$-0.279138\pi$
$709$	573.543	+	153.680i	0.808947	+	0.216757i	0.169439	+	0.985541i	$0.445805\pi$
$710$	134.431	−	134.431i	0.189340	−	0.189340i
$711$		0			0
$712$	424.614	+	245.151i	0.596368	+	0.344313i
$713$	−165.580	−	617.951i	−0.232229	−	0.866692i
$714$		0			0
$715$	125.452	+	57.6808i	0.175458	+	0.0806724i
$716$	259.705			0.362717
$717$		0			0
$718$	−195.260	+	338.200i	−0.271950	+	0.471031i
$719$	99.6984	−	57.5609i	0.138663	−	0.0800569i	−0.429064	−	0.903274i	$-0.641156\pi$
$719$	99.6984	−	57.5609i	0.138663	−	0.0800569i	0.567726	+	0.823217i	$0.307823\pi$
$720$		0			0
$721$	−13.3329	+	49.7591i	−0.0184922	+	0.0690140i
$722$	140.547	+	37.6595i	0.194664	+	0.0521600i
$723$		0			0
$724$	−119.610	−	207.171i	−0.165208	−	0.286148i
$725$	503.682	+	290.801i	0.694733	+	0.401105i
$726$		0			0
$727$		−	136.459i		−	0.187702i	−0.995586	−	0.0938509i	$-0.970082\pi$
$727$		−	136.459i		−	0.187702i	0.995586	−	0.0938509i	$-0.0299177\pi$
$728$	135.357	+	191.116i	0.185930	+	0.262522i
$729$		0			0
$730$	202.036	−	54.1354i	0.276762	−	0.0741580i
$731$	−433.452	+	750.760i	−0.592957	+	1.02703i
$732$		0			0
$733$	−916.639	−	916.639i	−1.25053	−	1.25053i	−0.955482	−	0.295048i	$-0.904664\pi$
$733$	−916.639	−	916.639i	−1.25053	−	1.25053i	−0.295048	−	0.955482i	$-0.595336\pi$
$734$	−200.994	+	750.119i	−0.273834	+	1.02196i
$735$		0			0
$736$	221.980	−	221.980i	0.301603	−	0.301603i
$737$	−411.587	−	712.890i	−0.558463	−	0.967286i
$738$		0			0
$739$	−271.445	−	1013.05i	−0.367314	−	1.37084i	−0.864256	−	0.503052i	$-0.832210\pi$
$739$	−271.445	−	1013.05i	−0.367314	−	1.37084i	0.496942	−	0.867784i	$-0.334456\pi$
$740$			24.1669i			0.0326580i
$741$		0			0
$742$	244.677			0.329754
$743$	42.7746	−	11.4614i	0.0575701	−	0.0154259i	−0.229919	−	0.973210i	$-0.573846\pi$
$743$	42.7746	−	11.4614i	0.0575701	−	0.0154259i	0.287489	+	0.957784i	$0.407179\pi$
$744$		0			0
$745$	−84.6379	+	48.8657i	−0.113608	+	0.0655916i
$746$	−316.378	−	316.378i	−0.424099	−	0.424099i
$747$		0			0
$748$	84.8633	+	22.7390i	0.113454	+	0.0303998i
$749$	125.900	−	125.900i	0.168091	−	0.168091i
$750$		0			0
$751$	1087.87	+	628.080i	1.44856	+	0.836324i	0.998396	−	0.0566233i	$-0.0180334\pi$
$751$	1087.87	+	628.080i	1.44856	+	0.836324i	0.450161	+	0.892948i	$0.351367\pi$
$752$	201.967	+	753.749i	0.268573	+	1.00233i
$753$		0			0
$754$	−555.688	−	94.9071i	−0.736987	−	0.125871i
$755$	−110.353			−0.146163
$756$		0			0
$757$	268.095	−	464.355i	0.354155	−	0.613415i	−0.632818	−	0.774301i	$-0.718102\pi$
$757$	268.095	−	464.355i	0.354155	−	0.613415i	0.986973	+	0.160886i	$0.0514351\pi$
$758$	511.922	−	295.558i	0.675359	−	0.389919i
$759$		0			0
$760$	−46.7787	+	174.580i	−0.0615509	+	0.229711i
$761$	−1014.29	−	271.777i	−1.33283	−	0.357132i	−0.479063	−	0.877780i	$-0.659023\pi$
$761$	−1014.29	−	271.777i	−1.33283	−	0.357132i	−0.853771	+	0.520649i	$0.825690\pi$
$762$		0			0
$763$	−69.3444	−	120.108i	−0.0908838	−	0.157415i
$764$	−88.8736	−	51.3112i	−0.116327	−	0.0671612i
$765$		0			0
$766$			1066.21i			1.39192i
$767$	−168.843	+	988.590i	−0.220135	+	1.28891i
$768$		0			0
$769$	504.691	−	135.231i	0.656295	−	0.175854i	0.0847214	−	0.996405i	$-0.473000\pi$
$769$	504.691	−	135.231i	0.656295	−	0.175854i	0.571573	+	0.820551i	$0.306333\pi$
$770$	−19.9382	+	34.5340i	−0.0258938	+	0.0448493i
$771$		0			0
$772$	−12.3452	−	12.3452i	−0.0159912	−	0.0159912i
$773$	−164.529	+	614.030i	−0.212845	+	0.794347i	0.774070	+	0.633101i	$0.218218\pi$
$773$	−164.529	+	614.030i	−0.212845	+	0.794347i	−0.986914	+	0.161246i	$0.948449\pi$
$774$		0			0
$775$	434.663	−	434.663i	0.560856	−	0.560856i
$776$	194.191	+	336.349i	0.250246	+	0.433439i
$777$		0			0
$778$	207.650	+	774.960i	0.266902	+	0.996092i
$779$			522.549i			0.670794i
$780$		0			0
$781$	−1126.43			−1.44229
$782$	447.636	−	119.944i	0.572425	−	0.153381i
$783$		0			0
$784$	469.995	−	271.352i	0.599484	−	0.346112i
$785$	−134.415	−	134.415i	−0.171229	−	0.171229i
$786$		0			0
$787$	645.977	+	173.089i	0.820810	+	0.219935i	0.644700	−	0.764435i	$-0.276982\pi$
$787$	645.977	+	173.089i	0.820810	+	0.219935i	0.176109	+	0.984371i	$0.443649\pi$
$788$	−54.8506	+	54.8506i	−0.0696073	+	0.0696073i
$789$		0			0
$790$	−109.011	−	62.9375i	−0.137989	−	0.0796677i
$791$	−112.398	−	419.474i	−0.142096	−	0.530309i
$792$		0			0
$793$	281.825	−	199.601i	0.355391	−	0.251704i
$794$	937.232			1.18039
$795$		0			0
$796$	−19.1813	+	33.2230i	−0.0240971	+	0.0417375i
$797$	314.169	−	181.386i	0.394190	−	0.227586i	−0.289784	−	0.957092i	$-0.593584\pi$
$797$	314.169	−	181.386i	0.394190	−	0.227586i	0.683974	+	0.729506i	$0.260250\pi$
$798$		0			0
$799$	172.110	−	642.322i	0.215406	−	0.803907i
$800$	291.360	+	78.0698i	0.364200	+	0.0975872i
$801$		0			0
$802$	285.726	+	494.892i	0.356267	+	0.617072i
$803$	−1073.26	−	619.646i	−1.33656	−	0.771664i
$804$		0			0
$805$		−	52.4538i		−	0.0651599i
$806$	−248.901	+	541.344i	−0.308810	+	0.671643i
$807$		0			0
$808$	−731.248	+	195.937i	−0.905010	+	0.242497i
$809$	176.729	−	306.103i	0.218453	−	0.378373i	−0.735882	−	0.677110i	$-0.763232\pi$
$809$	176.729	−	306.103i	0.218453	−	0.378373i	0.954335	+	0.298737i	$0.0965655\pi$
$810$		0			0
$811$	−833.402	−	833.402i	−1.02762	−	1.02762i	−0.999607	−	0.0280156i	$-0.991081\pi$
$811$	−833.402	−	833.402i	−1.02762	−	1.02762i	−0.0280156	−	0.999607i	$-0.508919\pi$
$812$	−10.5080	+	39.2163i	−0.0129409	+	0.0482960i
$813$		0			0
$814$	−406.013	+	406.013i	−0.498787	+	0.498787i
$815$	83.7309	+	145.026i	0.102737	+	0.177946i
$816$		0			0
$817$	455.047	+	1698.26i	0.556973	+	2.07865i
$818$			1285.37i			1.57136i
$819$		0			0
$820$	−19.8557			−0.0242142
$821$	100.742	−	26.9938i	0.122707	−	0.0328792i	−0.196943	−	0.980415i	$-0.563101\pi$
$821$	100.742	−	26.9938i	0.122707	−	0.0328792i	0.319650	+	0.947536i	$0.396435\pi$
$822$		0			0
$823$	−236.250	+	136.399i	−0.287060	+	0.165734i	−0.636615	−	0.771182i	$-0.719666\pi$
$823$	−236.250	+	136.399i	−0.287060	+	0.165734i	0.349555	+	0.936916i	$0.386333\pi$
$824$	−149.053	−	149.053i	−0.180889	−	0.180889i
$825$		0			0
$826$	−279.767	−	74.9634i	−0.338701	−	0.0907547i
$827$	482.718	−	482.718i	0.583698	−	0.583698i	−0.352219	−	0.935917i	$-0.614573\pi$
$827$	482.718	−	482.718i	0.583698	−	0.583698i	0.935917	+	0.352219i	$0.114573\pi$
$828$		0			0
$829$	64.6085	+	37.3017i	0.0779354	+	0.0449960i	0.538461	−	0.842650i	$-0.319006\pi$
$829$	64.6085	+	37.3017i	0.0779354	+	0.0449960i	−0.460526	+	0.887646i	$0.652339\pi$
$830$	−6.02417	−	22.4825i	−0.00725804	−	0.0270874i
$831$		0			0
$832$	−921.190	+	85.5837i	−1.10720	+	0.102865i
$833$	−462.475			−0.555192
$834$		0			0
$835$	79.7219	−	138.082i	0.0954753	−	0.165368i
$836$	154.311	−	89.0914i	0.184582	−	0.106569i
$837$		0			0
$838$	−125.444	+	468.162i	−0.149694	+	0.558666i
$839$	1415.24	+	379.212i	1.68682	+	0.451981i	0.969565	−	0.244834i	$-0.0787334\pi$
$839$	1415.24	+	379.212i	1.68682	+	0.451981i	0.717251	+	0.696815i	$0.245400\pi$
$840$		0			0
$841$	126.826	+	219.668i	0.150803	+	0.261199i
$842$	−298.226	−	172.181i	−0.354188	−	0.204491i
$843$		0			0
$844$			140.901i			0.166945i
$845$	139.600	+	95.5299i	0.165207	+	0.113053i
$846$		0			0
$847$	−17.0178	+	4.55990i	−0.0200918	+	0.00538358i
$848$	−396.534	+	686.816i	−0.467610	+	0.809925i
$849$		0			0
$850$	314.865	+	314.865i	0.370429	+	0.370429i
$851$	195.484	−	729.557i	0.229711	−	0.857294i
$852$		0			0
$853$	−701.992	+	701.992i	−0.822968	+	0.822968i	−0.986533	−	0.163564i	$-0.947701\pi$
$853$	−701.992	+	701.992i	−0.822968	+	0.822968i	0.163564	+	0.986533i	$0.447701\pi$
$854$	49.8680	+	86.3739i	0.0583934	+	0.101140i
$855$		0			0
$856$	188.567	+	703.741i	0.220288	+	0.822127i
$857$			643.845i			0.751278i	0.926766	+	0.375639i	$0.122577\pi$
$857$			643.845i			0.751278i	−0.926766	+	0.375639i	$0.877423\pi$
$858$		0			0
$859$	−1511.39			−1.75948			−0.879738	−	0.475460i	$-0.842282\pi$
$859$	−1511.39			−1.75948			−0.879738	+	0.475460i	$0.842282\pi$
$860$	−64.5300	+	17.2908i	−0.0750349	+	0.0201055i
$861$		0			0
$862$	−681.236	+	393.312i	−0.790297	+	0.456278i
$863$	−16.8874	−	16.8874i	−0.0195682	−	0.0195682i	0.697255	−	0.716823i	$-0.254405\pi$
$863$	−16.8874	−	16.8874i	−0.0195682	−	0.0195682i	−0.716823	+	0.697255i	$0.754405\pi$
$864$		0			0
$865$	−255.751	−	68.5282i	−0.295665	−	0.0792233i
$866$	455.254	−	455.254i	0.525698	−	0.525698i
$867$		0			0
$868$	37.1618	+	21.4554i	0.0428131	+	0.0247181i
$869$	193.030	+	720.397i	0.222129	+	0.828995i
$870$		0			0
$871$	−350.001	−	945.777i	−0.401838	−	1.08585i
$872$	567.503			0.650806
$873$		0			0
$874$	469.939	−	813.958i	0.537687	−	0.931302i
$875$	89.1183	−	51.4525i	0.101850	−	0.0588028i
$876$		0			0
$877$	433.814	−	1619.02i	0.494657	−	1.84608i	−0.0372873	−	0.999305i	$-0.511872\pi$
$877$	433.814	−	1619.02i	0.494657	−	1.84608i	0.531944	−	0.846780i	$-0.321462\pi$
$878$	−978.979	−	262.317i	−1.11501	−	0.298766i
$879$		0			0
$880$	−64.6252	−	111.934i	−0.0734378	−	0.127198i
$881$	−368.720	−	212.880i	−0.418524	−	0.241635i	0.275922	−	0.961180i	$-0.411017\pi$
$881$	−368.720	−	212.880i	−0.418524	−	0.241635i	−0.694446	+	0.719545i	$0.744350\pi$
$882$		0			0
$883$			990.748i			1.12203i	0.827807	+	0.561013i	$0.189588\pi$
$883$			990.748i			1.12203i	−0.827807	+	0.561013i	$0.810412\pi$
$884$	97.7912	+	44.9627i	0.110624	+	0.0508628i
$885$		0			0
$886$	1074.12	−	287.809i	1.21232	−	0.324841i
$887$	12.8689	−	22.2895i	0.0145083	−	0.0251291i	−0.858680	−	0.512512i	$-0.828715\pi$
$887$	12.8689	−	22.2895i	0.0145083	−	0.0251291i	0.873188	+	0.487383i	$0.162048\pi$
$888$		0			0
$889$	22.2103	+	22.2103i	0.0249835	+	0.0249835i
$890$	−26.4708	+	98.7904i	−0.0297425	+	0.111000i
$891$		0			0
$892$	−134.384	+	134.384i	−0.150655	+	0.150655i
$893$	−674.324	−	1167.96i	−0.755122	−	1.30791i
$894$		0			0
$895$	84.2672	+	314.489i	0.0941533	+	0.351385i
$896$		−	161.690i		−	0.180458i
$897$		0			0
$898$	926.313			1.03153
$899$	−599.629	+	160.670i	−0.666995	+	0.178721i
$900$		0			0
$901$	585.283	−	337.913i	0.649593	−	0.375043i
$902$	−333.582	−	333.582i	−0.369825	−	0.369825i
$903$		0			0
$904$	1716.46	+	459.923i	1.89873	+	0.508764i
$905$	212.063	−	212.063i	0.234324	−	0.234324i
$906$		0			0
$907$	303.123	+	175.008i	0.334204	+	0.192953i	0.657706	−	0.753275i	$-0.271527\pi$
$907$	303.123	+	175.008i	0.334204	+	0.192953i	−0.323502	+	0.946228i	$0.604860\pi$
$908$	14.6083	+	54.5189i	0.0160884	+	0.0600428i
$909$		0			0
$910$	−31.2000	+	37.5911i	−0.0342857	+	0.0413089i
$911$	−572.122			−0.628016			−0.314008	−	0.949420i	$-0.601672\pi$
$911$	−572.122			−0.628016			−0.314008	+	0.949420i	$0.601672\pi$
$912$		0			0
$913$	−68.9540	+	119.432i	−0.0755247	+	0.130813i
$914$	−87.5983	+	50.5749i	−0.0958405	+	0.0553336i
$915$		0			0
$916$	−1.49546	+	5.58113i	−0.00163260	+	0.00609294i
$917$	−17.4533	−	4.67661i	−0.0190331	−	0.00509990i
$918$		0			0
$919$	−393.851	−	682.171i	−0.428565	−	0.742297i	0.568181	−	0.822904i	$-0.307647\pi$
$919$	−393.851	−	682.171i	−0.428565	−	0.742297i	−0.996746	+	0.0806070i	$0.974314\pi$
$920$	185.881	+	107.318i	0.202044	+	0.116650i
$921$		0			0
$922$		−	1311.46i		−	1.42241i
$923$	−1360.28	−	232.325i	−1.47376	−	0.251706i
$924$		0			0
$925$	700.998	−	187.832i	0.757836	−	0.203062i
$926$	292.708	−	506.985i	0.316099	−	0.547500i
$927$		0			0
$928$	−215.398	−	215.398i	−0.232110	−	0.232110i
$929$	−166.682	+	622.067i	−0.179421	+	0.669609i	0.816335	+	0.577579i	$0.196002\pi$
$929$	−166.682	+	622.067i	−0.179421	+	0.669609i	−0.995756	+	0.0920304i	$0.970664\pi$
$930$		0			0
$931$	−663.228	+	663.228i	−0.712383	+	0.712383i
$932$	−35.0523	−	60.7124i	−0.0376098	−	0.0651421i
$933$		0			0
$934$	−12.8632	−	48.0062i	−0.0137722	−	0.0513985i
$935$			110.143i			0.117800i
$936$		0			0
$937$	1760.44			1.87880			0.939401	−	0.342821i	$-0.111382\pi$
$937$	1760.44			1.87880			0.939401	+	0.342821i	$0.111382\pi$
$938$	281.317	−	75.3787i	0.299912	−	0.0803611i
$939$		0			0
$940$	44.3799	−	25.6228i	0.0472127	−	0.0272583i
$941$	−487.123	−	487.123i	−0.517666	−	0.517666i	0.399199	−	0.916864i	$-0.369288\pi$
$941$	−487.123	−	487.123i	−0.517666	−	0.517666i	−0.916864	+	0.399199i	$0.869288\pi$
$942$		0			0
$943$	599.408	+	160.611i	0.635639	+	0.170319i
$944$	663.826	−	663.826i	0.703206	−	0.703206i
$945$		0			0
$946$	−1374.62	−	793.636i	−1.45308	−	0.838938i
$947$	−79.6308	−	297.186i	−0.0840874	−	0.313819i	0.911052	−	0.412291i	$-0.135271\pi$
$947$	−79.6308	−	297.186i	−0.0840874	−	0.313819i	−0.995140	+	0.0984720i	$0.968605\pi$
$948$		0			0
$949$	−1168.27	−	969.644i	−1.23105	−	1.02175i
$950$	903.086			0.950617
$951$		0			0
$952$	−93.4074	+	161.786i	−0.0981171	+	0.169944i
$953$	1151.74	−	664.955i	1.20854	−	0.697749i	0.246098	−	0.969245i	$-0.420852\pi$
$953$	1151.74	−	664.955i	1.20854	−	0.697749i	0.962440	+	0.271496i	$0.0875182\pi$
$954$		0			0
$955$	33.2981	−	124.270i	0.0348672	−	0.130126i
$956$	121.708	+	32.6117i	0.127310	+	0.0341126i
$957$		0			0
$958$	88.0960	+	152.587i	0.0919582	+	0.159276i
$959$	−372.781	−	215.225i	−0.388719	−	0.224427i
$960$		0			0
$961$		−	304.883i		−	0.317256i
$962$	−574.042	+	406.562i	−0.596717	+	0.422622i
$963$		0			0
$964$	−36.6417	+	9.81810i	−0.0380100	+	0.0101848i
$965$	10.9437	−	18.9550i	0.0113406	−	0.0196425i
$966$		0			0
$967$	208.236	+	208.236i	0.215342	+	0.215342i	0.806532	−	0.591190i	$-0.201342\pi$
$967$	208.236	+	208.236i	0.215342	+	0.215342i	−0.591190	+	0.806532i	$0.701342\pi$
$968$	18.6587	−	69.6353i	0.0192755	−	0.0719373i
$969$		0			0
$970$	−57.2863	+	57.2863i	−0.0590581	+	0.0590581i
$971$	163.577	+	283.324i	0.168462	+	0.291785i	0.937879	−	0.346961i	$-0.112786\pi$
$971$	163.577	+	283.324i	0.168462	+	0.291785i	−0.769417	+	0.638747i	$0.779453\pi$
$972$		0			0
$973$	32.4144	+	120.972i	0.0333139	+	0.124329i
$974$		−	360.033i		−	0.369644i
$975$		0			0
$976$	−323.272			−0.331221
$977$	28.6392	−	7.67384i	0.0293134	−	0.00785449i	−0.244133	−	0.969742i	$-0.578503\pi$
$977$	28.6392	−	7.67384i	0.0293134	−	0.00785449i	0.273446	+	0.961887i	$0.411837\pi$
$978$		0			0
$979$	524.795	−	302.991i	0.536053	−	0.309490i
$980$	−25.2012	−	25.2012i	−0.0257155	−	0.0257155i
$981$		0			0
$982$	−1071.18	−	287.022i	−1.09081	−	0.292283i
$983$	998.511	−	998.511i	1.01578	−	1.01578i	0.0159054	−	0.999874i	$-0.494937\pi$
$983$	998.511	−	998.511i	1.01578	−	1.01578i	0.999874	−	0.0159054i	$-0.00506305\pi$
$984$		0			0
$985$	−84.2187	−	48.6237i	−0.0855012	−	0.0493642i
$986$	−116.387	−	434.364i	−0.118040	−	0.440531i
$987$		0			0
$988$	204.721	−	75.7606i	0.207208	−	0.0766808i
$989$	2087.91			2.11113
$990$		0			0
$991$	−373.041	+	646.126i	−0.376429	+	0.651994i	−0.990540	−	0.137226i	$-0.956181\pi$
$991$	−373.041	+	646.126i	−0.376429	+	0.651994i	0.614111	+	0.789220i	$0.289515\pi$
$992$	−278.824	+	160.979i	−0.281073	+	0.162277i
$993$		0			0
$994$	103.148	−	384.954i	0.103771	−	0.387277i
$995$	−46.4552	−	12.4476i	−0.0466886	−	0.0125102i
$996$		0			0
$997$	−399.254	−	691.529i	−0.400456	−	0.693610i	0.593325	−	0.804963i	$-0.297815\pi$
$997$	−399.254	−	691.529i	−0.400456	−	0.693610i	−0.993781	+	0.111353i	$0.964481\pi$
$998$	−1136.00	−	655.871i	−1.13828	−	0.657186i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.bd.c.46.1		8
3.2	odd	2		39.3.l.a.7.2	✓	8
13.2	odd	12	inner	117.3.bd.c.28.1		8
39.2	even	12		39.3.l.a.28.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.l.a.7.2	✓	8	3.2	odd	2
39.3.l.a.28.2	yes	8	39.2	even	12
117.3.bd.c.28.1		8	13.2	odd	12	inner
117.3.bd.c.46.1		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72833 + 0.463105i) q^{2} +(-0.691437 + 0.399201i) q^{4} +(-0.707764 - 0.707764i) q^{5} +(-2.02673 - 0.543062i) q^{7} +(6.07107 - 6.07107i) q^{8} +O(q^{10})\)	\(q+(-1.72833 + 0.463105i) q^{2} +(-0.691437 + 0.399201i) q^{4} +(-0.707764 - 0.707764i) q^{5} +(-2.02673 - 0.543062i) q^{7} +(6.07107 - 6.07107i) q^{8} +(1.55102 + 0.895482i) q^{10} +(-2.74645 - 10.2499i) q^{11} +(-1.20259 - 12.9443i) q^{13} +3.75436 q^{14} +(-6.08447 + 10.5386i) q^{16} +(8.98068 - 5.18500i) q^{17} +(5.44333 - 20.3148i) q^{19} +(0.771915 + 0.206834i) q^{20} +(9.49356 + 16.4433i) q^{22} +(-21.6297 - 12.4879i) q^{23} -23.9981i q^{25} +(8.07303 + 21.8150i) q^{26} +(1.61815 - 0.433582i) q^{28} +(-12.1176 + 20.9884i) q^{29} +(18.1124 + 18.1124i) q^{31} +(-3.25316 + 12.1410i) q^{32} +(-13.1204 + 13.1204i) q^{34} +(1.05009 + 1.81881i) q^{35} +(7.82694 + 29.2105i) q^{37} +37.6315i q^{38} -8.59377 q^{40} +(-23.9995 + 6.43065i) q^{41} +(-72.3974 + 41.7986i) q^{43} +(5.99077 + 5.99077i) q^{44} +(43.1665 + 11.5664i) q^{46} +(45.3435 - 45.3435i) q^{47} +(-38.6225 - 22.2987i) q^{49} +(11.1137 + 41.4767i) q^{50} +(5.99888 + 8.47006i) q^{52} +65.1714 q^{53} +(-5.31067 + 9.19835i) q^{55} +(-15.6014 + 9.00748i) q^{56} +(11.2235 - 41.8866i) q^{58} +(-74.5178 - 19.9670i) q^{59} +(13.2827 + 23.0063i) q^{61} +(-39.6921 - 22.9163i) q^{62} -71.1659i q^{64} +(-8.31033 + 10.0126i) q^{65} +(74.9307 - 20.0776i) q^{67} +(-4.13971 + 7.17020i) q^{68} +(-2.65721 - 2.65721i) q^{70} +(27.4742 - 102.535i) q^{71} +(82.5815 - 82.5815i) q^{73} +(-27.0551 - 46.8608i) q^{74} +(4.34597 + 16.2194i) q^{76} +22.2653i q^{77} -70.2833 q^{79} +(11.7652 - 3.15248i) q^{80} +(38.5011 - 22.2286i) q^{82} +(-9.18965 - 9.18965i) q^{83} +(-10.0260 - 2.68645i) q^{85} +(105.770 - 105.770i) q^{86} +(-78.9017 - 45.5539i) q^{88} +(14.7802 + 55.1604i) q^{89} +(-4.59219 + 26.8877i) q^{91} +19.9408 q^{92} +(-57.3698 + 99.3675i) q^{94} +(-18.2307 + 10.5255i) q^{95} +(-11.7078 + 43.6941i) q^{97} +(77.0792 + 20.6533i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 12 q^{4} - 16 q^{5} + 14 q^{7} + 24 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 + 12 * q^4 - 16 * q^5 + 14 * q^7 + 24 * q^8	\( 8 q + 2 q^{2} + 12 q^{4} - 16 q^{5} + 14 q^{7} + 24 q^{8} - 42 q^{10} + 14 q^{11} + 2 q^{13} + 28 q^{14} - 28 q^{16} - 18 q^{17} - 94 q^{19} - 68 q^{20} + 46 q^{22} + 30 q^{23} - 136 q^{26} + 146 q^{28} + 64 q^{29} + 80 q^{31} + 86 q^{32} - 96 q^{34} - 122 q^{35} + 110 q^{37} - 204 q^{40} - 22 q^{41} - 54 q^{43} + 92 q^{44} + 294 q^{46} + 332 q^{47} - 12 q^{49} + 172 q^{50} - 72 q^{52} - 32 q^{53} - 122 q^{55} - 66 q^{56} - 134 q^{58} - 52 q^{59} + 46 q^{61} - 288 q^{62} - 214 q^{65} + 86 q^{67} - 114 q^{68} - 164 q^{70} - 94 q^{71} + 56 q^{73} - 236 q^{74} + 46 q^{76} - 80 q^{79} + 80 q^{80} + 180 q^{82} - 136 q^{83} + 138 q^{85} + 396 q^{86} + 66 q^{88} + 128 q^{89} - 496 q^{91} + 108 q^{92} + 202 q^{94} + 486 q^{95} - 40 q^{97} + 530 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 + 12 * q^4 - 16 * q^5 + 14 * q^7 + 24 * q^8 - 42 * q^10 + 14 * q^11 + 2 * q^13 + 28 * q^14 - 28 * q^16 - 18 * q^17 - 94 * q^19 - 68 * q^20 + 46 * q^22 + 30 * q^23 - 136 * q^26 + 146 * q^28 + 64 * q^29 + 80 * q^31 + 86 * q^32 - 96 * q^34 - 122 * q^35 + 110 * q^37 - 204 * q^40 - 22 * q^41 - 54 * q^43 + 92 * q^44 + 294 * q^46 + 332 * q^47 - 12 * q^49 + 172 * q^50 - 72 * q^52 - 32 * q^53 - 122 * q^55 - 66 * q^56 - 134 * q^58 - 52 * q^59 + 46 * q^61 - 288 * q^62 - 214 * q^65 + 86 * q^67 - 114 * q^68 - 164 * q^70 - 94 * q^71 + 56 * q^73 - 236 * q^74 + 46 * q^76 - 80 * q^79 + 80 * q^80 + 180 * q^82 - 136 * q^83 + 138 * q^85 + 396 * q^86 + 66 * q^88 + 128 * q^89 - 496 * q^91 + 108 * q^92 + 202 * q^94 + 486 * q^95 - 40 * q^97 + 530 * q^98

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