LMFDB - Embedded newform 117.3.bd.c.28.1

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			28.1
Root			$2.22833 - 1.32913i$ of defining polynomial
Character	$\chi$	$=$	117.28
Dual form			117.3.bd.c.46.1

$q$-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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

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

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	−0.200603	−	0.979673i	$-0.564290\pi$
$2$	−1.72833	−	0.463105i	−0.864166	−	0.231553i	−0.663563	+	0.748120i	$0.730957\pi$
$3$		0			0
$3$		0			0
$4$	−0.691437	−	0.399201i	−0.172859	−	0.0998003i
$5$	−0.707764	+	0.707764i	−0.141553	+	0.141553i	−0.774332	−	0.632779i	$-0.781914\pi$
$5$	−0.707764	+	0.707764i	−0.141553	+	0.141553i	0.632779	+	0.774332i	$0.281914\pi$
$6$		0			0
$7$	−2.02673	+	0.543062i	−0.289534	+	0.0775803i	−0.400662	−	0.916226i	$-0.631220\pi$
$7$	−2.02673	+	0.543062i	−0.289534	+	0.0775803i	0.111129	+	0.993806i	$0.464553\pi$
$8$	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	0.721297	+	0.692626i	$0.243546\pi$
$11$	−2.74645	+	10.2499i	−0.249677	+	0.931809i	−0.970975	+	0.239183i	$0.923120\pi$
$12$		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	0.740314	−	0.672262i	$-0.234677\pi$
$17$	8.98068	+	5.18500i	0.528275	+	0.305000i	−0.212039	+	0.977261i	$0.568010\pi$
$18$		0			0
$19$	5.44333	+	20.3148i	0.286491	+	1.06920i	0.947743	+	0.319035i	$0.103359\pi$
$19$	5.44333	+	20.3148i	0.286491	+	1.06920i	−0.661252	+	0.750164i	$0.729975\pi$
$20$	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	−0.890092	−	0.455780i	$-0.849360\pi$
$23$	−21.6297	+	12.4879i	−0.940422	+	0.542953i	−0.0503292	+	0.998733i	$0.516027\pi$
$24$		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	0.577873	−	0.816127i	$-0.303883\pi$
$29$	−12.1176	−	20.9884i	−0.417850	−	0.723737i	−0.995723	+	0.0923897i	$0.970549\pi$
$30$		0			0
$31$	18.1124	−	18.1124i	0.584270	−	0.584270i	−0.351803	−	0.936074i	$-0.614431\pi$
$31$	18.1124	−	18.1124i	0.584270	−	0.584270i	0.936074	+	0.351803i	$0.114431\pi$
$32$	−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	−0.775818	−	0.630957i	$-0.782662\pi$
$37$	7.82694	−	29.2105i	0.211539	−	0.789474i	0.987356	−	0.158516i	$-0.0506710\pi$
$38$		−	37.6315i		−	0.990302i
$39$		0			0
$40$	−8.59377			−0.214844
$41$	−23.9995	−	6.43065i	−0.585354	−	0.156845i	−0.0460251	−	0.998940i	$-0.514655\pi$
$41$	−23.9995	−	6.43065i	−0.585354	−	0.156845i	−0.539329	+	0.842095i	$0.681322\pi$
$42$		0			0
$43$	−72.3974	−	41.7986i	−1.68366	−	0.972061i	−0.959193	−	0.282752i	$-0.908753\pi$
$43$	−72.3974	−	41.7986i	−1.68366	−	0.972061i	−0.724467	−	0.689310i	$-0.757914\pi$
$44$	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	0.999400	−	0.0346437i	$-0.0110297\pi$
$47$	45.3435	+	45.3435i	0.964756	+	0.964756i	−0.0346437	+	0.999400i	$0.511030\pi$
$48$		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	−0.827351	−	0.561686i	$-0.810153\pi$
$59$	−74.5178	+	19.9670i	−1.26301	+	0.338424i	−0.435664	+	0.900109i	$0.643486\pi$
$60$		0			0
$61$	13.2827	−	23.0063i	0.217749	−	0.377152i	−0.736371	−	0.676578i	$-0.763462\pi$
$61$	13.2827	−	23.0063i	0.217749	−	0.377152i	0.954119	+	0.299427i	$0.0967954\pi$
$62$	−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	0.770223	−	0.637774i	$-0.220145\pi$
$67$	74.9307	+	20.0776i	1.11837	+	0.299666i	0.348146	+	0.937440i	$0.386811\pi$
$68$	−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	0.835054	+	0.550168i	$0.185436\pi$
$71$	27.4742	+	102.535i	0.386960	+	1.44416i	−0.448094	+	0.893987i	$0.647897\pi$
$72$		0			0
$73$	82.5815	+	82.5815i	1.13125	+	1.13125i	0.989969	+	0.141285i	$0.0451233\pi$
$73$	82.5815	+	82.5815i	1.13125	+	1.13125i	0.141285	+	0.989969i	$0.454877\pi$
$74$	−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	−0.760296	−	0.649577i	$-0.774946\pi$
$83$	−9.18965	+	9.18965i	−0.110719	+	0.110719i	0.649577	+	0.760296i	$0.274946\pi$
$84$		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	−0.831832	−	0.555028i	$-0.812708\pi$
$89$	14.7802	−	55.1604i	0.166070	−	0.619780i	0.997901	−	0.0647522i	$-0.0206257\pi$
$90$		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	0.878951	−	0.476912i	$-0.158244\pi$
$97$	−11.7078	−	43.6941i	−0.120699	−	0.450455i	−0.999650	+	0.0264575i	$0.991577\pi$
$98$	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	−0.827875	−	0.560912i	$-0.810451\pi$
$101$	−76.3610	+	44.0870i	−0.756049	+	0.436505i	0.0718263	+	0.997417i	$0.477117\pi$
$102$		0			0
$103$			24.5513i			0.238363i	0.992873	+	0.119181i	$0.0380270\pi$
$103$			24.5513i			0.238363i	−0.992873	+	0.119181i	$0.961973\pi$
$104$	−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	0.596766	−	0.802415i	$-0.296452\pi$
$107$	−42.4286	−	73.4885i	−0.396529	−	0.686809i	−0.993295	+	0.115607i	$0.963119\pi$
$108$		0			0
$109$	46.7383	−	46.7383i	0.428792	−	0.428792i	−0.459425	−	0.888217i	$-0.651944\pi$
$109$	46.7383	−	46.7383i	0.428792	−	0.428792i	0.888217	+	0.459425i	$0.151944\pi$
$110$	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	0.110072	−	0.993924i	$-0.464892\pi$
$113$	103.485	−	179.242i	0.915799	−	1.58621i	0.805727	−	0.592287i	$-0.201775\pi$
$114$		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	−0.550171	−	0.835052i	$-0.685438\pi$
$127$	−12.9643	+	7.48492i	−0.102081	+	0.0589363i	0.448090	+	0.893988i	$0.352104\pi$
$128$	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	0.551642	−	0.834081i	$-0.314002\pi$
$137$	198.159	−	53.0966i	1.44642	−	0.387567i	0.894776	+	0.446515i	$0.147335\pi$
$138$		0			0
$139$	−29.8441	+	51.6915i	−0.214706	+	0.371881i	−0.953182	−	0.302399i	$-0.902213\pi$
$139$	−29.8441	+	51.6915i	−0.214706	+	0.371881i	0.738476	+	0.674280i	$0.235546\pi$
$140$	−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	0.997408	+	0.0719569i	$0.0229244\pi$
$149$	25.2713	+	94.3136i	0.169606	+	0.632977i	−0.827802	+	0.561020i	$0.810409\pi$
$150$		0			0
$151$	77.9592	+	77.9592i	0.516286	+	0.516286i	0.916445	−	0.400160i	$-0.131045\pi$
$151$	77.9592	+	77.9592i	0.516286	+	0.516286i	−0.400160	+	0.916445i	$0.631045\pi$
$152$	−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	−0.717857	−	0.696191i	$-0.754877\pi$
$163$	−161.605	+	43.3020i	−0.991444	+	0.265657i	−0.273587	+	0.961847i	$0.588210\pi$
$164$	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	−0.725551	−	0.688168i	$-0.758415\pi$
$167$	41.2288	−	153.868i	0.246879	−	0.921364i	0.972430	−	0.233196i	$-0.0749183\pi$
$168$		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	0.984396	−	0.175968i	$-0.0563056\pi$
$173$	229.087	+	132.263i	1.32420	+	0.764528i	0.339805	+	0.940496i	$0.389639\pi$
$174$		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	−0.578048	+	0.816003i	$0.696185\pi$
$179$	−281.701	+	162.640i	−1.57375	+	0.908606i	−0.995703	+	0.0926030i	$0.970481\pi$
$180$		0			0
$181$		−	299.624i		−	1.65538i	−0.561184	−	0.827691i	$-0.689654\pi$
$181$		−	299.624i		−	1.65538i	0.561184	−	0.827691i	$-0.310346\pi$
$182$	−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	−0.647290	−	0.762244i	$-0.724098\pi$
$191$	64.2673	−	111.314i	0.336478	−	0.582797i	0.983768	+	0.179447i	$0.0574309\pi$
$192$		0			0
$193$	5.65961	−	21.1220i	0.0293244	−	0.109440i	−0.949712	−	0.313124i	$-0.898625\pi$
$193$	5.65961	−	21.1220i	0.0293244	−	0.109440i	0.979037	+	0.203683i	$0.0652913\pi$
$194$			80.9398i			0.417216i
$195$		0			0
$196$	35.6067			0.181667
$197$	93.8465	+	25.1461i	0.476378	+	0.127645i	0.489016	−	0.872275i	$-0.337356\pi$
$197$	93.8465	+	25.1461i	0.476378	+	0.127645i	−0.0126375	+	0.999920i	$0.504023\pi$
$198$		0			0
$199$	41.6119	+	24.0246i	0.209105	+	0.120727i	0.600895	−	0.799328i	$-0.294811\pi$
$199$	41.6119	+	24.0246i	0.209105	+	0.120727i	−0.391790	+	0.920054i	$0.628144\pi$
$200$	−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	0.995758	−	0.0920098i	$-0.0293291\pi$
$211$	88.2394	+	152.835i	0.418196	+	0.724337i	−0.577562	+	0.816347i	$0.695996\pi$
$212$	−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	0.734400	−	0.678717i	$-0.237464\pi$
$223$	229.924	+	61.6080i	1.03105	+	0.276269i	0.296650	+	0.954986i	$0.404130\pi$
$224$	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	0.994445	−	0.105255i	$-0.0335658\pi$
$227$	18.2969	+	68.2850i	0.0806031	+	0.300815i	−0.913842	+	0.406069i	$0.866899\pi$
$228$		0			0
$229$	5.11731	+	5.11731i	0.0223463	+	0.0223463i	0.718192	−	0.695845i	$-0.244970\pi$
$229$	5.11731	+	5.11731i	0.0223463	+	0.0223463i	−0.695845	+	0.718192i	$0.744970\pi$
$230$	−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	$-0.939662\pi$
$233$		−	87.8062i		−	0.376851i	0.982088	−	0.188425i	$-0.0603383\pi$
$234$		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	−0.900915	−	0.433995i	$-0.857103\pi$
$239$	−111.594	+	111.594i	−0.466920	+	0.466920i	0.433995	+	0.900915i	$0.357103\pi$
$240$		0			0
$241$	45.8937	−	12.2972i	0.190430	−	0.0510256i	−0.162343	−	0.986734i	$-0.551905\pi$
$241$	45.8937	−	12.2972i	0.190430	−	0.0510256i	0.352774	+	0.935709i	$0.385239\pi$
$242$	−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	0.600026	−	0.799981i	$-0.295157\pi$
$251$	52.0159	+	30.0314i	0.207235	+	0.119647i	−0.392791	+	0.919628i	$0.628490\pi$
$252$		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	0.214438	−	0.976738i	$-0.431208\pi$
$257$	300.057	−	173.238i	1.16754	−	0.674077i	0.953098	+	0.302660i	$0.0978748\pi$
$258$		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	1.00000		0.000891166i	$-0.000283667\pi$
$263$	131.297	+	227.413i	0.499228	+	0.864688i	−0.500772	+	0.865579i	$0.666950\pi$
$264$		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	−0.784094	−	0.620641i	$-0.786872\pi$
$269$	39.1244	−	67.7655i	0.145444	−	0.251916i	0.929539	+	0.368725i	$0.120206\pi$
$270$		0			0
$271$	−30.7983	+	114.941i	−0.113647	+	0.424136i	−0.999182	−	0.0404365i	$-0.987125\pi$
$271$	−30.7983	+	114.941i	−0.113647	+	0.424136i	0.885535	+	0.464572i	$0.153792\pi$
$272$		−	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	0.933368	−	0.358921i	$-0.116855\pi$
$277$	301.713	+	174.194i	1.08922	+	0.628860i	0.155849	+	0.987781i	$0.450189\pi$
$278$	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	0.632128	−	0.774864i	$-0.282182\pi$
$281$	−40.1090	−	40.1090i	−0.142737	−	0.142737i	−0.774864	+	0.632128i	$0.782182\pi$
$282$		0			0
$283$	71.1179	−	41.0599i	0.251300	−	0.145088i	−0.369059	−	0.929406i	$-0.620320\pi$
$283$	71.1179	−	41.0599i	0.251300	−	0.145088i	0.620359	+	0.784318i	$0.286987\pi$
$284$	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	−0.982161	−	0.188044i	$-0.939785\pi$
$293$	−509.443	+	136.505i	−1.73871	+	0.465887i	−0.756554	+	0.653931i	$0.773119\pi$
$294$		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	0.0317217	−	0.999497i	$-0.489901\pi$
$307$	−297.107	−	297.107i	−0.967775	−	0.967775i	−0.999497	+	0.0317217i	$0.989901\pi$
$308$	−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	$-0.678224\pi$
$311$		−	527.024i		−	1.69461i	0.531107	−	0.847305i	$-0.321776\pi$
$312$		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	−0.592750	−	0.805386i	$-0.701958\pi$
$317$	67.4056	−	67.4056i	0.212636	−	0.212636i	0.805386	+	0.592750i	$0.201958\pi$
$318$		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	0.938133	−	0.346275i	$-0.112554\pi$
$331$	−15.7065	−	58.6175i	−0.0474517	−	0.177092i	−0.985585	+	0.169183i	$0.945887\pi$
$332$	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	$0.240152\pi$
$337$			461.619i			1.36979i	−0.728643	+	0.684894i	$0.759848\pi$
$338$	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	−0.995398	−	0.0958246i	$-0.969451\pi$
$347$	−143.905	+	249.251i	−0.414713	+	0.718303i	0.580686	+	0.814128i	$0.302785\pi$
$348$		0			0
$349$	−24.3973	+	91.0520i	−0.0699064	+	0.260894i	−0.992030	−	0.126001i	$-0.959786\pi$
$349$	−24.3973	+	91.0520i	−0.0699064	+	0.260894i	0.922124	+	0.386895i	$0.126452\pi$
$350$			90.0978i			0.257422i
$351$		0			0
$352$	133.378			0.378915
$353$	213.460	+	57.1964i	0.604703	+	0.162030i	0.548164	−	0.836371i	$-0.315327\pi$
$353$	213.460	+	57.1964i	0.604703	+	0.162030i	0.0565385	+	0.998400i	$0.481994\pi$
$354$		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	0.888588	−	0.458705i	$-0.151687\pi$
$359$	154.328	+	154.328i	0.429883	+	0.429883i	−0.458705	+	0.888588i	$0.651687\pi$
$360$		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	0.994058	+	0.108854i	$0.0347180\pi$
$367$	217.007	+	375.867i	0.591299	+	1.02416i	−0.402759	+	0.915306i	$0.631949\pi$
$368$	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	−0.648326	−	0.761363i	$-0.724531\pi$
$373$	125.028	−	216.555i	0.335196	−	0.580577i	0.983522	+	0.180786i	$0.0578641\pi$
$374$	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	−0.188039	−	0.982162i	$-0.560213\pi$
$379$	−319.105	−	85.5040i	−0.841966	−	0.225604i	−0.653927	+	0.756557i	$0.726880\pi$
$380$	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	0.808300	+	0.588770i	$0.200388\pi$
$383$	154.225	+	575.576i	0.402677	+	1.50281i	−0.405623	+	0.914040i	$0.632946\pi$
$384$		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	$0.195516\pi$
$389$			448.386i			1.15266i	−0.817216	+	0.576332i	$0.804484\pi$
$390$		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	−0.831727	−	0.555184i	$-0.812648\pi$
$397$	−505.950	+	135.569i	−1.27443	+	0.341483i	−0.442705	+	0.896667i	$0.645981\pi$
$398$	−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	0.782968	+	0.622062i	$0.213705\pi$
$401$	−82.6595	+	308.489i	−0.206133	+	0.769300i	−0.989101	+	0.147238i	$0.952962\pi$
$402$		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	0.689294	+	0.724481i	$0.257921\pi$
$409$	185.927	+	693.888i	0.454589	+	1.69655i	−0.234706	+	0.972066i	$0.575413\pi$
$410$	−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	0.981155	−	0.193225i	$-0.0618946\pi$
$419$	135.437	+	234.585i	0.323240	+	0.559868i	−0.657915	+	0.753092i	$0.728561\pi$
$420$		0			0
$421$	136.087	−	136.087i	0.323247	−	0.323247i	−0.526764	−	0.850011i	$-0.676595\pi$
$421$	136.087	−	136.087i	0.323247	−	0.323247i	0.850011	+	0.526764i	$0.176595\pi$
$422$	−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	0.715258	−	0.698861i	$-0.246309\pi$
$431$	424.646	+	113.784i	0.985259	+	0.263999i	0.270001	+	0.962860i	$0.412976\pi$
$432$		0			0
$433$	−311.613	−	179.910i	−0.719662	−	0.415497i	0.0949665	−	0.995480i	$-0.469726\pi$
$433$	−311.613	−	179.910i	−0.719662	−	0.415497i	−0.814628	+	0.579984i	$0.803059\pi$
$434$	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	0.176671	−	0.984270i	$-0.443467\pi$
$439$	490.543	−	283.215i	1.11741	−	0.645137i	0.940738	+	0.339133i	$0.110134\pi$
$440$	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	−0.768335	−	0.640047i	$-0.778915\pi$
$449$	−500.056	+	133.989i	−1.11371	+	0.298418i	−0.345374	+	0.938465i	$0.612248\pi$
$450$		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	0.318065	−	0.948069i	$-0.396967\pi$
$457$	54.6041	+	14.6311i	0.119484	+	0.0320156i	−0.198582	+	0.980084i	$0.563633\pi$
$458$	−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	−0.791747	−	0.610849i	$-0.790828\pi$
$461$	−189.701	−	707.973i	−0.411498	−	1.53573i	0.380249	−	0.924884i	$-0.375838\pi$
$462$		0			0
$463$	−231.348	−	231.348i	−0.499672	−	0.499672i	0.411664	−	0.911336i	$-0.364948\pi$
$463$	−231.348	−	231.348i	−0.499672	−	0.499672i	−0.911336	+	0.411664i	$0.864948\pi$
$464$	−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	$-0.990532\pi$
$467$		−	27.7760i		−	0.0594776i	0.999558	−	0.0297388i	$-0.00946755\pi$
$468$		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	−0.987413	−	0.158164i	$-0.949443\pi$
$479$	−25.4858	+	95.1144i	−0.0532063	+	0.198569i	0.934207	+	0.356733i	$0.116109\pi$
$480$		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	0.891621	−	0.452782i	$-0.149569\pi$
$487$	−52.0781	−	194.358i	−0.106937	−	0.399093i	−0.998558	+	0.0536896i	$0.982902\pi$
$488$	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	0.158745	−	0.987320i	$-0.449255\pi$
$491$	536.742	−	309.888i	1.09316	−	0.631137i	0.934416	+	0.356183i	$0.115922\pi$
$492$		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	0.0396281	−	0.999214i	$-0.487383\pi$
$499$	518.382	−	518.382i	1.03884	−	1.03884i	0.999214	−	0.0396281i	$-0.0126173\pi$
$500$	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	−0.0967843	−	0.995305i	$-0.530856\pi$
$503$	409.225	−	708.798i	0.813568	−	1.40914i	0.910352	−	0.413835i	$-0.135811\pi$
$504$		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	0.365315	−	0.930884i	$-0.380961\pi$
$509$	110.069	+	29.4928i	0.216245	+	0.0579426i	−0.149070	+	0.988827i	$0.547628\pi$
$510$		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	0.938598	−	0.345012i	$-0.112125\pi$
$523$	89.1769	+	154.459i	0.170510	+	0.295333i	−0.768088	+	0.640344i	$0.778792\pi$
$524$	−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	0.987972	+	0.154633i	$0.0494196\pi$
$541$	618.149	+	618.149i	1.14261	+	1.14261i	0.154633	+	0.987972i	$0.450580\pi$
$542$	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	0.468057	+	0.883698i	$0.344954\pi$
$557$	−211.182	+	788.141i	−0.379142	+	1.41498i	−0.847198	+	0.531277i	$0.821712\pi$
$558$		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	−0.437189	−	0.899370i	$-0.644026\pi$
$563$	−807.714	−	466.334i	−1.43466	−	0.828302i	−0.997471	+	0.0710682i	$0.977359\pi$
$564$		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	−0.483775	−	0.875192i	$-0.660735\pi$
$569$	18.3652	−	10.6031i	0.0322762	−	0.0186347i	0.516051	+	0.856558i	$0.327401\pi$
$570$		0			0
$571$			402.871i			0.705553i	0.935708	+	0.352776i	$0.114762\pi$
$571$			402.871i			0.705553i	−0.935708	+	0.352776i	$0.885238\pi$
$572$	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	−0.433221	−	0.901288i	$-0.642623\pi$
$577$	270.074	−	270.074i	0.468066	−	0.468066i	0.901288	+	0.433221i	$0.142623\pi$
$578$	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	0.645185	−	0.764026i	$-0.276780\pi$
$587$	482.466	+	129.276i	0.821918	+	0.220232i	0.176733	+	0.984259i	$0.443447\pi$
$588$		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	0.291276	−	0.956639i	$-0.405920\pi$
$593$	−394.560	−	394.560i	−0.665363	−	0.665363i	−0.956639	+	0.291276i	$0.905920\pi$
$594$		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	0.558283	−	0.829650i	$-0.311460\pi$
$601$	−264.053	−	457.354i	−0.439356	−	0.760988i	−0.997640	+	0.0686625i	$0.978127\pi$
$602$	−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	−0.681142	−	0.732151i	$-0.738516\pi$
$607$	178.149	−	308.563i	0.293491	−	0.508341i	0.974633	+	0.223811i	$0.0718497\pi$
$608$	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	−0.0683955	−	0.997658i	$-0.521788\pi$
$613$	−384.018	−	102.897i	−0.626457	−	0.167859i	−0.558061	+	0.829800i	$0.688455\pi$
$614$	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	0.582593	+	0.812764i	$0.302038\pi$
$617$	298.896	+	1115.50i	0.484435	+	1.80793i	−0.0981582	+	0.995171i	$0.531295\pi$
$618$		0			0
$619$	−305.402	−	305.402i	−0.493380	−	0.493380i	0.415989	−	0.909369i	$-0.363435\pi$
$619$	−305.402	−	305.402i	−0.493380	−	0.493380i	−0.909369	+	0.415989i	$0.863435\pi$
$620$	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	−0.601916	−	0.798559i	$-0.705596\pi$
$631$	−456.788	+	122.396i	−0.723911	+	0.193971i	−0.121995	+	0.992531i	$0.538929\pi$
$632$	−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	0.709720	−	0.704484i	$-0.248822\pi$
$641$	291.321	+	168.194i	0.454479	+	0.262393i	−0.255241	+	0.966877i	$0.582155\pi$
$642$		0			0
$643$	−6.42009	−	23.9601i	−0.00998458	−	0.0372630i	0.960754	−	0.277402i	$-0.0894735\pi$
$643$	−6.42009	−	23.9601i	−0.00998458	−	0.0372630i	−0.970738	+	0.240139i	$0.922807\pi$
$644$	−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	−0.133409	−	0.991061i	$-0.542592\pi$
$647$	425.837	−	245.857i	0.658171	−	0.379995i	0.791580	+	0.611066i	$0.209259\pi$
$648$		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	0.989309	−	0.145834i	$-0.0465867\pi$
$653$	240.538	+	416.624i	0.368358	+	0.638015i	−0.620951	+	0.783850i	$0.713253\pi$
$654$		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	−0.847227	−	0.531231i	$-0.821730\pi$
$659$	24.0182	−	41.6007i	0.0364464	−	0.0631271i	0.883673	+	0.468104i	$0.155063\pi$
$660$		0			0
$661$	126.623	−	472.565i	0.191563	−	0.714925i	−0.801566	−	0.597906i	$-0.796000\pi$
$661$	126.623	−	472.565i	0.191563	−	0.714925i	0.993130	−	0.117019i	$-0.0373337\pi$
$662$			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	−0.953343	−	0.301888i	$-0.902383\pi$
$673$	−786.449	+	454.057i	−1.16857	+	0.674675i	−0.215229	+	0.976564i	$0.569050\pi$
$674$	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	0.0173473	−	0.999850i	$-0.494478\pi$
$683$	363.558	−	97.4150i	0.532295	−	0.142628i	0.514948	+	0.857221i	$0.327811\pi$
$684$		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	−0.0220245	−	0.999757i	$-0.507011\pi$
$691$	−373.815	−	100.163i	−0.540977	−	0.144954i	−0.518953	+	0.854803i	$0.673678\pi$
$692$	−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	$-0.958905\pi$
$701$		−	180.499i		−	0.257489i	0.991678	−	0.128744i	$-0.0410946\pi$
$702$		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	0.169439	−	0.985541i	$-0.445805\pi$
$709$	573.543	−	153.680i	0.808947	−	0.216757i	0.639508	+	0.768784i	$0.279138\pi$
$710$	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	0.567726	−	0.823217i	$-0.307823\pi$
$719$	99.6984	+	57.5609i	0.138663	+	0.0800569i	−0.429064	+	0.903274i	$0.641156\pi$
$720$		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	$0.0299177\pi$
$727$			136.459i			0.187702i	−0.995586	+	0.0938509i	$0.970082\pi$
$728$	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	−0.295048	+	0.955482i	$0.595336\pi$
$733$	−916.639	+	916.639i	−1.25053	+	1.25053i	−0.955482	+	0.295048i	$0.904664\pi$
$734$	−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	0.496942	+	0.867784i	$0.334456\pi$
$739$	−271.445	+	1013.05i	−0.367314	+	1.37084i	−0.864256	+	0.503052i	$0.832210\pi$
$740$		−	24.1669i		−	0.0326580i
$741$		0			0
$742$	244.677			0.329754
$743$	42.7746	+	11.4614i	0.0575701	+	0.0154259i	0.287489	−	0.957784i	$-0.407179\pi$
$743$	42.7746	+	11.4614i	0.0575701	+	0.0154259i	−0.229919	+	0.973210i	$0.573846\pi$
$744$		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	0.450161	−	0.892948i	$-0.351367\pi$
$751$	1087.87	−	628.080i	1.44856	−	0.836324i	0.998396	+	0.0566233i	$0.0180334\pi$
$752$	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	0.986973	−	0.160886i	$-0.0514351\pi$
$757$	268.095	+	464.355i	0.354155	+	0.613415i	−0.632818	+	0.774301i	$0.718102\pi$
$758$	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	−0.853771	−	0.520649i	$-0.825690\pi$
$761$	−1014.29	+	271.777i	−1.33283	+	0.357132i	−0.479063	+	0.877780i	$0.659023\pi$
$762$		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	0.571573	−	0.820551i	$-0.306333\pi$
$769$	504.691	+	135.231i	0.656295	+	0.175854i	0.0847214	+	0.996405i	$0.473000\pi$
$770$	−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	−0.986914	−	0.161246i	$-0.948449\pi$
$773$	−164.529	−	614.030i	−0.212845	−	0.794347i	0.774070	−	0.633101i	$-0.218218\pi$
$774$		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	0.176109	−	0.984371i	$-0.443649\pi$
$787$	645.977	−	173.089i	0.820810	−	0.219935i	0.644700	+	0.764435i	$0.276982\pi$
$788$	−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	0.683974	−	0.729506i	$-0.260250\pi$
$797$	314.169	+	181.386i	0.394190	+	0.227586i	−0.289784	+	0.957092i	$0.593584\pi$
$798$		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	0.954335	−	0.298737i	$-0.0965655\pi$
$809$	176.729	+	306.103i	0.218453	+	0.378373i	−0.735882	+	0.677110i	$0.763232\pi$
$810$		0			0
$811$	−833.402	+	833.402i	−1.02762	+	1.02762i	−0.0280156	+	0.999607i	$0.508919\pi$
$811$	−833.402	+	833.402i	−1.02762	+	1.02762i	−0.999607	+	0.0280156i	$0.991081\pi$
$812$	−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	0.319650	−	0.947536i	$-0.396435\pi$
$821$	100.742	+	26.9938i	0.122707	+	0.0328792i	−0.196943	+	0.980415i	$0.563101\pi$
$822$		0			0
$823$	−236.250	−	136.399i	−0.287060	−	0.165734i	0.349555	−	0.936916i	$-0.386333\pi$
$823$	−236.250	−	136.399i	−0.287060	−	0.165734i	−0.636615	+	0.771182i	$0.719666\pi$
$824$	−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	0.935917	−	0.352219i	$-0.114573\pi$
$827$	482.718	+	482.718i	0.583698	+	0.583698i	−0.352219	+	0.935917i	$0.614573\pi$
$828$		0			0
$829$	64.6085	−	37.3017i	0.0779354	−	0.0449960i	−0.460526	−	0.887646i	$-0.652339\pi$
$829$	64.6085	−	37.3017i	0.0779354	−	0.0449960i	0.538461	+	0.842650i	$0.319006\pi$
$830$	−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	0.717251	−	0.696815i	$-0.245400\pi$
$839$	1415.24	−	379.212i	1.68682	−	0.451981i	0.969565	+	0.244834i	$0.0787334\pi$
$840$		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	0.163564	−	0.986533i	$-0.447701\pi$
$853$	−701.992	−	701.992i	−0.822968	−	0.822968i	−0.986533	+	0.163564i	$0.947701\pi$
$854$	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	$-0.877423\pi$
$857$		−	643.845i		−	0.751278i	0.926766	−	0.375639i	$-0.122577\pi$
$858$		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	−0.716823	−	0.697255i	$-0.754405\pi$
$863$	−16.8874	+	16.8874i	−0.0195682	+	0.0195682i	0.697255	+	0.716823i	$0.254405\pi$
$864$		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	0.531944	+	0.846780i	$0.321462\pi$
$877$	433.814	+	1619.02i	0.494657	+	1.84608i	−0.0372873	+	0.999305i	$0.511872\pi$
$878$	−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	−0.694446	−	0.719545i	$-0.744350\pi$
$881$	−368.720	+	212.880i	−0.418524	+	0.241635i	0.275922	+	0.961180i	$0.411017\pi$
$882$		0			0
$883$		−	990.748i		−	1.12203i	−0.827807	−	0.561013i	$-0.810412\pi$
$883$		−	990.748i		−	1.12203i	0.827807	−	0.561013i	$-0.189588\pi$
$884$	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	0.873188	−	0.487383i	$-0.162048\pi$
$887$	12.8689	+	22.2895i	0.0145083	+	0.0251291i	−0.858680	+	0.512512i	$0.828715\pi$
$888$		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	−0.323502	−	0.946228i	$-0.604860\pi$
$907$	303.123	−	175.008i	0.334204	−	0.192953i	0.657706	+	0.753275i	$0.271527\pi$
$908$	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	−0.996746	−	0.0806070i	$-0.974314\pi$
$919$	−393.851	+	682.171i	−0.428565	+	0.742297i	0.568181	+	0.822904i	$0.307647\pi$
$920$	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	−0.995756	−	0.0920304i	$-0.970664\pi$
$929$	−166.682	−	622.067i	−0.179421	−	0.669609i	0.816335	−	0.577579i	$-0.196002\pi$
$930$		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	−0.916864	−	0.399199i	$-0.869288\pi$
$941$	−487.123	+	487.123i	−0.517666	+	0.517666i	0.399199	+	0.916864i	$0.369288\pi$
$942$		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	−0.995140	−	0.0984720i	$-0.968605\pi$
$947$	−79.6308	+	297.186i	−0.0840874	+	0.313819i	0.911052	+	0.412291i	$0.135271\pi$
$948$		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	0.962440	−	0.271496i	$-0.0875182\pi$
$953$	1151.74	+	664.955i	1.20854	+	0.697749i	0.246098	+	0.969245i	$0.420852\pi$
$954$		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	−0.591190	−	0.806532i	$-0.701342\pi$
$967$	208.236	−	208.236i	0.215342	−	0.215342i	0.806532	+	0.591190i	$0.201342\pi$
$968$	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	−0.769417	−	0.638747i	$-0.779453\pi$
$971$	163.577	−	283.324i	0.168462	−	0.291785i	0.937879	+	0.346961i	$0.112786\pi$
$972$		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	0.273446	−	0.961887i	$-0.411837\pi$
$977$	28.6392	+	7.67384i	0.0293134	+	0.00785449i	−0.244133	+	0.969742i	$0.578503\pi$
$978$		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	0.999874	+	0.0159054i	$0.00506305\pi$
$983$	998.511	+	998.511i	1.01578	+	1.01578i	0.0159054	+	0.999874i	$0.494937\pi$
$984$		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	0.614111	−	0.789220i	$-0.289515\pi$
$991$	−373.041	−	646.126i	−0.376429	−	0.651994i	−0.990540	+	0.137226i	$0.956181\pi$
$992$	−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	−0.993781	−	0.111353i	$-0.964481\pi$
$997$	−399.254	+	691.529i	−0.400456	+	0.693610i	0.593325	+	0.804963i	$0.297815\pi$
$998$	−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.28.1		8
3.2	odd	2		39.3.l.a.28.2	yes	8
13.7	odd	12	inner	117.3.bd.c.46.1		8
39.20	even	12		39.3.l.a.7.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.l.a.7.2	✓	8	39.20	even	12
39.3.l.a.28.2	yes	8	3.2	odd	2
117.3.bd.c.28.1		8	1.1	even	1	trivial
117.3.bd.c.46.1		8	13.7	odd	12	inner

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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