LMFDB - Embedded newform 847.2.n.e.130.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(9,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 18]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("847.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			130.3
Character	$\chi$	$=$	847.130
Dual form			847.2.n.e.632.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.43643 - 0.517880i) q^{2} +(0.0745850 + 0.709629i) q^{3} +(3.84091 - 1.71008i) q^{4} +(1.47503 - 1.63819i) q^{5} +(0.549224 + 1.69034i) q^{6} +(-0.522062 + 2.59373i) q^{7} +(4.44220 - 3.22745i) q^{8} +(2.43643 - 0.517880i) q^{9} +O(q^{10})$	\(q+(2.43643 - 0.517880i) q^{2} +(0.0745850 + 0.709629i) q^{3} +(3.84091 - 1.71008i) q^{4} +(1.47503 - 1.63819i) q^{5} +(0.549224 + 1.69034i) q^{6} +(-0.522062 + 2.59373i) q^{7} +(4.44220 - 3.22745i) q^{8} +(2.43643 - 0.517880i) q^{9} +(2.74543 - 4.75523i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-1.01557 + 3.12561i) q^{13} +(0.0712722 + 6.58982i) q^{14} +(1.27252 + 0.924542i) q^{15} +(3.52511 - 3.91503i) q^{16} +(-1.45828 - 0.309968i) q^{17} +(5.66800 - 2.52356i) q^{18} +(-6.31985 - 2.81378i) q^{19} +(2.86403 - 8.81457i) q^{20} +(-1.87953 - 0.177017i) q^{21} +(-3.24543 - 5.62125i) q^{23} +(2.62161 + 2.91160i) q^{24} +(0.0146981 + 0.139844i) q^{25} +(-0.855683 + 8.14128i) q^{26} +(1.21071 + 3.72618i) q^{27} +(2.43031 + 10.8551i) q^{28} +(1.33468 + 0.969699i) q^{29} +(3.57922 + 1.59357i) q^{30} +(-1.57262 - 1.74658i) q^{31} +(1.07031 - 1.85383i) q^{32} -3.71354 q^{34} +(3.47897 + 4.68108i) q^{35} +(8.47250 - 6.15563i) q^{36} +(0.580619 - 5.52422i) q^{37} +(-16.8551 - 3.58266i) q^{38} +(-2.29377 - 0.487556i) q^{39} +(1.26522 - 12.0378i) q^{40} +(9.10137 - 6.61254i) q^{41} +(-4.67101 + 0.542079i) q^{42} +5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(-10.8184 - 12.0151i) q^{46} +(1.36197 + 0.606389i) q^{47} +(3.04114 + 2.20952i) q^{48} +(-6.45490 - 2.70818i) q^{49} +(0.108233 + 0.333107i) q^{50} +(0.111196 - 1.05796i) q^{51} +(1.44433 + 13.7419i) q^{52} +(0.203907 + 0.226462i) q^{53} +(4.87953 + 8.45159i) q^{54} +(6.05203 + 13.2068i) q^{56} +(1.52537 - 4.69462i) q^{57} +(3.75403 + 1.67140i) q^{58} +(-11.5643 + 5.14877i) q^{59} +(6.46869 + 1.37496i) q^{60} +(-8.68647 + 9.64730i) q^{61} +(-4.73611 - 3.44098i) q^{62} +(0.0712722 + 6.58982i) q^{63} +(-1.60825 + 4.94968i) q^{64} +(3.62234 + 6.27408i) q^{65} +(2.28646 - 3.96027i) q^{67} +(-6.13121 + 1.30323i) q^{68} +(3.74694 - 2.72231i) q^{69} +(10.9005 + 9.60344i) q^{70} +(3.50016 + 10.7724i) q^{71} +(9.15169 - 10.1640i) q^{72} +(-7.82697 + 3.48479i) q^{73} +(-1.44624 - 13.7601i) q^{74} +(-0.0981408 + 0.0208605i) q^{75} -29.0858 q^{76} -5.84111 q^{78} +(-4.53027 + 0.962938i) q^{79} +(-1.21391 - 11.5496i) q^{80} +(4.27265 - 1.90230i) q^{81} +(18.7504 - 20.8244i) q^{82} +(-0.598322 - 1.84145i) q^{83} +(-7.52181 + 2.53424i) q^{84} +(-2.65880 + 1.93173i) q^{85} +(12.8356 - 2.72829i) q^{86} +(-0.588580 + 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} +(4.22642 - 13.0076i) q^{90} +(-7.57681 - 4.26589i) q^{91} +(-22.0782 - 16.0408i) q^{92} +(1.12213 - 1.24625i) q^{93} +(3.63239 + 0.772088i) q^{94} +(-13.9315 + 6.20270i) q^{95} +(1.39536 + 0.621253i) q^{96} +(0.574582 - 1.76838i) q^{97} +(-17.1294 - 3.25544i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) $ 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.43643	−	0.517880i	1.72282	−	0.366196i	0.762908	−	0.646507i	$-0.223771\pi$
$2$	2.43643	−	0.517880i	1.72282	−	0.366196i	0.959909	+	0.280310i	$0.0904374\pi$
$3$	0.0745850	+	0.709629i	0.0430617	+	0.409705i	0.994726	+	0.102565i	$0.0327051\pi$
$3$	0.0745850	+	0.709629i	0.0430617	+	0.409705i	−0.951665	+	0.307139i	$0.900628\pi$
$4$	3.84091	−	1.71008i	1.92046	−	0.855042i
$5$	1.47503	−	1.63819i	0.659655	−	0.732621i	−0.316765	−	0.948504i	$-0.602596\pi$
$5$	1.47503	−	1.63819i	0.659655	−	0.732621i	0.976419	+	0.215884i	$0.0692632\pi$
$6$	0.549224	+	1.69034i	0.224220	+	0.690077i
$7$	−0.522062	+	2.59373i	−0.197321	+	0.980339i
$7$	−0.522062	+	2.59373i	−0.197321	+	0.980339i
$8$	4.44220	−	3.22745i	1.57056	−	1.14108i
$9$	2.43643	−	0.517880i	0.812144	−	0.172627i
$10$	2.74543	−	4.75523i	0.868182	−	1.50373i
$11$		0			0
$11$		0			0
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$	−1.01557	+	3.12561i	−0.281669	+	0.866889i	0.705708	+	0.708503i	$0.250629\pi$
$13$	−1.01557	+	3.12561i	−0.281669	+	0.866889i	−0.987377	+	0.158386i	$0.949371\pi$
$14$	0.0712722	+	6.58982i	0.0190483	+	1.76120i
$15$	1.27252	+	0.924542i	0.328564	+	0.238716i
$16$	3.52511	−	3.91503i	0.881277	−	0.978757i
$17$	−1.45828	−	0.309968i	−0.353686	−	0.0751783i	0.0276425	−	0.999618i	$-0.491200\pi$
$17$	−1.45828	−	0.309968i	−0.353686	−	0.0751783i	−0.381329	+	0.924440i	$0.624533\pi$
$18$	5.66800	−	2.52356i	1.33596	−	0.594808i
$19$	−6.31985	−	2.81378i	−1.44987	−	0.645525i	−0.477431	−	0.878669i	$-0.658432\pi$
$19$	−6.31985	−	2.81378i	−1.44987	−	0.645525i	−0.972442	+	0.233144i	$0.925099\pi$
$20$	2.86403	−	8.81457i	0.640416	−	1.97100i
$21$	−1.87953	−	0.177017i	−0.410146	−	0.0386283i
$22$		0			0
$23$	−3.24543	−	5.62125i	−0.676719	−	1.17211i	−0.975963	−	0.217936i	$-0.930068\pi$
$23$	−3.24543	−	5.62125i	−0.676719	−	1.17211i	0.299244	−	0.954177i	$-0.403266\pi$
$24$	2.62161	+	2.91160i	0.535135	+	0.594327i
$25$	0.0146981	+	0.139844i	0.00293963	+	0.0279687i
$26$	−0.855683	+	8.14128i	−0.167813	+	1.59664i
$27$	1.21071	+	3.72618i	0.233001	+	0.717104i
$28$	2.43031	+	10.8551i	0.459285	+	2.05142i
$29$	1.33468	+	0.969699i	0.247843	+	0.180069i	0.704770	−	0.709436i	$-0.251050\pi$
$29$	1.33468	+	0.969699i	0.247843	+	0.180069i	−0.456927	+	0.889504i	$0.651050\pi$
$30$	3.57922	+	1.59357i	0.653472	+	0.290945i
$31$	−1.57262	−	1.74658i	−0.282452	−	0.313694i	0.585178	−	0.810905i	$-0.301024\pi$
$31$	−1.57262	−	1.74658i	−0.282452	−	0.313694i	−0.867630	+	0.497210i	$0.834358\pi$
$32$	1.07031	−	1.85383i	0.189205	−	0.327713i
$33$		0			0
$34$	−3.71354			−0.636867
$35$	3.47897	+	4.68108i	0.588053	+	0.791247i
$36$	8.47250	−	6.15563i	1.41208	−	1.02594i
$37$	0.580619	−	5.52422i	0.0954532	−	0.908177i	−0.837077	−	0.547085i	$-0.815737\pi$
$37$	0.580619	−	5.52422i	0.0954532	−	0.908177i	0.932530	−	0.361092i	$-0.117596\pi$
$38$	−16.8551	−	3.58266i	−2.73426	−	0.581184i
$39$	−2.29377	−	0.487556i	−0.367297	−	0.0780715i
$40$	1.26522	−	12.0378i	0.200049	−	1.90334i
$41$	9.10137	−	6.61254i	1.42140	−	1.03270i	0.429857	−	0.902897i	$-0.358564\pi$
$41$	9.10137	−	6.61254i	1.42140	−	1.03270i	0.991539	−	0.129807i	$-0.0414359\pi$
$42$	−4.67101	+	0.542079i	−0.720753	+	0.0836446i
$43$	5.26819			0.803391			0.401696	−	0.915773i	$-0.368421\pi$
$43$	5.26819			0.803391			0.401696	+	0.915773i	$0.368421\pi$
$44$		0			0
$45$	2.74543	−	4.75523i	0.409265	−	0.708867i
$46$	−10.8184	−	12.0151i	−1.59509	−	1.77152i
$47$	1.36197	+	0.606389i	0.198664	+	0.0884509i	0.503657	−	0.863904i	$-0.331988\pi$
$47$	1.36197	+	0.606389i	0.198664	+	0.0884509i	−0.304993	+	0.952355i	$0.598654\pi$
$48$	3.04114	+	2.20952i	0.438950	+	0.318916i
$49$	−6.45490	−	2.70818i	−0.922129	−	0.386883i
$50$	0.108233	+	0.333107i	0.0153065	+	0.0471085i
$51$	0.111196	−	1.05796i	0.0155706	−	0.148144i
$52$	1.44433	+	13.7419i	0.200293	+	1.90566i
$53$	0.203907	+	0.226462i	0.0280088	+	0.0311070i	0.756986	−	0.653431i	$-0.226671\pi$
$53$	0.203907	+	0.226462i	0.0280088	+	0.0311070i	−0.728978	+	0.684538i	$0.760004\pi$
$54$	4.87953	+	8.45159i	0.664019	+	1.15012i
$55$		0			0
$56$	6.05203	+	13.2068i	0.808737	+	1.76483i
$57$	1.52537	−	4.69462i	0.202041	−	0.621817i
$58$	3.75403	+	1.67140i	0.492929	+	0.219466i
$59$	−11.5643	+	5.14877i	−1.50555	+	0.670312i	−0.983218	−	0.182433i	$-0.941603\pi$
$59$	−11.5643	+	5.14877i	−1.50555	+	0.670312i	−0.522327	+	0.852745i	$0.674936\pi$
$60$	6.46869	+	1.37496i	0.835104	+	0.177507i
$61$	−8.68647	+	9.64730i	−1.11219	+	1.23521i	−0.142781	+	0.989754i	$0.545604\pi$
$61$	−8.68647	+	9.64730i	−1.11219	+	1.23521i	−0.969408	+	0.245456i	$0.921062\pi$
$62$	−4.73611	−	3.44098i	−0.601486	−	0.437005i
$63$	0.0712722	+	6.58982i	0.00897946	+	0.830239i
$64$	−1.60825	+	4.94968i	−0.201031	+	0.618710i
$65$	3.62234	+	6.27408i	0.449296	+	0.778204i
$66$		0			0
$67$	2.28646	−	3.96027i	0.279336	−	0.483824i	−0.691884	−	0.722009i	$-0.743219\pi$
$67$	2.28646	−	3.96027i	0.279336	−	0.483824i	0.971220	+	0.238185i	$0.0765524\pi$
$68$	−6.13121	+	1.30323i	−0.743519	+	0.158040i
$69$	3.74694	−	2.72231i	0.451079	−	0.327728i
$70$	10.9005	+	9.60344i	1.30286	+	1.14783i
$71$	3.50016	+	10.7724i	0.415392	+	1.27845i	0.911900	+	0.410413i	$0.134615\pi$
$71$	3.50016	+	10.7724i	0.415392	+	1.27845i	−0.496508	+	0.868032i	$0.665385\pi$
$72$	9.15169	−	10.1640i	1.07854	−	1.19784i
$73$	−7.82697	+	3.48479i	−0.916078	+	0.407864i	−0.809957	−	0.586489i	$-0.800510\pi$
$73$	−7.82697	+	3.48479i	−0.916078	+	0.407864i	−0.106121	+	0.994353i	$0.533843\pi$
$74$	−1.44624	−	13.7601i	−0.168122	−	1.59958i
$75$	−0.0981408	+	0.0208605i	−0.0113323	+	0.00240876i
$76$	−29.0858			−3.33637
$77$		0			0
$78$	−5.84111			−0.661376
$79$	−4.53027	+	0.962938i	−0.509695	+	0.108339i	−0.455579	−	0.890196i	$-0.650568\pi$
$79$	−4.53027	+	0.962938i	−0.509695	+	0.108339i	−0.0541165	+	0.998535i	$0.517234\pi$
$80$	−1.21391	−	11.5496i	−0.135719	−	1.29128i
$81$	4.27265	−	1.90230i	0.474738	−	0.211367i
$82$	18.7504	−	20.8244i	2.07063	−	2.29967i
$83$	−0.598322	−	1.84145i	−0.0656744	−	0.202125i	0.912834	−	0.408330i	$-0.133889\pi$
$83$	−0.598322	−	1.84145i	−0.0656744	−	0.202125i	−0.978509	+	0.206205i	$0.933889\pi$
$84$	−7.52181	+	2.53424i	−0.820697	+	0.276508i
$85$	−2.65880	+	1.93173i	−0.288388	+	0.209526i
$86$	12.8356	−	2.72829i	1.38410	−	0.294199i
$87$	−0.588580	+	1.01945i	−0.0631024	+	0.109297i
$88$		0			0
$89$	−1.60220	−	2.77509i	−0.169833	−	0.294159i	0.768528	−	0.639816i	$-0.220989\pi$
$89$	−1.60220	−	2.77509i	−0.169833	−	0.294159i	−0.938361	+	0.345657i	$0.887656\pi$
$90$	4.22642	−	13.0076i	0.445504	−	1.37112i
$91$	−7.57681	−	4.26589i	−0.794265	−	0.447187i
$92$	−22.0782	−	16.0408i	−2.30181	−	1.67237i
$93$	1.12213	−	1.24625i	0.116359	−	0.129230i
$94$	3.63239	+	0.772088i	0.374652	+	0.0796348i
$95$	−13.9315	+	6.20270i	−1.42934	+	0.636384i
$96$	1.39536	+	0.621253i	0.142413	+	0.0634064i
$97$	0.574582	−	1.76838i	0.0583400	−	0.179552i	−0.917640	−	0.397413i	$-0.869908\pi$
$97$	0.574582	−	1.76838i	0.0583400	−	0.179552i	0.975980	+	0.217861i	$0.0699080\pi$
$98$	−17.1294	−	3.25544i	−1.73034	−	0.328849i
$99$		0			0
$100$	0.295598	+	0.511992i	0.0295598	+	0.0511992i
$101$	4.04524	+	4.49269i	0.402516	+	0.447040i	0.909992	−	0.414627i	$-0.136088\pi$
$101$	4.04524	+	4.49269i	0.402516	+	0.447040i	−0.507475	+	0.861666i	$0.669421\pi$
$102$	−0.276974	−	2.63523i	−0.0274245	−	0.260927i
$103$	0.111196	−	1.05796i	0.0109565	−	0.104244i	−0.987677	−	0.156507i	$-0.949977\pi$
$103$	0.111196	−	1.05796i	0.0109565	−	0.104244i	0.998633	+	0.0522629i	$0.0166434\pi$
$104$	5.57637	+	17.1623i	0.546808	+	1.68290i
$105$	−3.06235	+	2.81791i	−0.298855	+	0.275000i
$106$	0.614087	+	0.446160i	0.0596454	+	0.0433349i
$107$	−5.78455	−	2.57545i	−0.559213	−	0.248978i	0.107611	−	0.994193i	$-0.465680\pi$
$107$	−5.78455	−	2.57545i	−0.559213	−	0.248978i	−0.666824	+	0.745215i	$0.732347\pi$
$108$	11.0223	+	12.2415i	1.06062	+	1.17794i
$109$	1.40694	−	2.43688i	0.134760	−	0.233411i	−0.790746	−	0.612145i	$-0.790307\pi$
$109$	1.40694	−	2.43688i	0.134760	−	0.233411i	0.925506	+	0.378734i	$0.123640\pi$
$110$		0			0
$111$	3.96345			0.376194
$112$	8.31421	+	11.1871i	0.785619	+	1.05708i
$113$	10.3181	−	7.49651i	0.970641	−	0.705212i	0.0150435	−	0.999887i	$-0.495211\pi$
$113$	10.3181	−	7.49651i	0.970641	−	0.705212i	0.955598	+	0.294675i	$0.0952113\pi$
$114$	1.28522	−	12.2281i	0.120372	−	1.14526i
$115$	−13.9958	−	2.97490i	−1.30511	−	0.277411i
$116$	6.78464	+	1.44212i	0.629938	+	0.133897i
$117$	−0.855683	+	8.14128i	−0.0791080	+	0.752662i
$118$	−25.5092	+	18.5335i	−2.34832	+	1.70615i
$119$	1.56529	−	3.62058i	0.143490	−	0.331898i
$120$	8.63671			0.788420
$121$		0			0
$122$	−16.1679	+	28.0035i	−1.46377	+	2.53532i
$123$	5.37127	+	5.96540i	0.484311	+	0.537882i
$124$	−9.02710	−	4.01913i	−0.810658	−	0.360928i
$125$	9.16776	+	6.66077i	0.819990	+	0.595757i
$126$	3.58638	+	16.0187i	0.319500	+	1.42706i
$127$	−3.82486	−	11.7717i	−0.339401	−	1.04457i	−0.964513	−	0.264034i	$-0.914947\pi$
$127$	−3.82486	−	11.7717i	−0.339401	−	1.04457i	0.625112	−	0.780535i	$-0.285053\pi$
$128$	−1.80256	+	17.1502i	−0.159325	+	1.51588i
$129$	0.392928	+	3.73846i	0.0345954	+	0.329153i
$130$	12.0748	+	13.4104i	1.05903	+	1.17617i
$131$	−0.379526	−	0.657359i	−0.0331594	−	0.0574337i	0.848969	−	0.528442i	$-0.177224\pi$
$131$	−0.379526	−	0.657359i	−0.0331594	−	0.0574337i	−0.882129	+	0.471008i	$0.843890\pi$
$132$		0			0
$133$	10.5975	−	14.9230i	0.918924	−	1.29399i
$134$	3.51987	−	10.8330i	0.304070	−	0.935832i
$135$	7.89003	+	3.51287i	0.679066	+	0.302339i
$136$	−7.47840	+	3.32960i	−0.641268	+	0.285511i
$137$	5.71347	+	1.21444i	0.488135	+	0.103756i	0.445403	−	0.895330i	$-0.353060\pi$
$137$	5.71347	+	1.21444i	0.488135	+	0.103756i	0.0427320	+	0.999087i	$0.486394\pi$
$138$	7.71934	−	8.57320i	0.657114	−	0.729799i
$139$	4.50859	+	3.27568i	0.382414	+	0.277840i	0.762340	−	0.647177i	$-0.224051\pi$
$139$	4.50859	+	3.27568i	0.382414	+	0.277840i	−0.379926	+	0.925017i	$0.624051\pi$
$140$	21.3674	+	12.0303i	1.80588	+	1.01674i
$141$	−0.328728	+	1.01172i	−0.0276839	+	0.0852024i
$142$	14.1067	+	24.4335i	1.18381	+	2.05041i
$143$		0			0
$144$	6.56117	−	11.3643i	0.546764	−	0.947023i
$145$	3.55724	−	0.756115i	0.295413	−	0.0627919i
$146$	−17.2652	+	12.5439i	−1.42888	+	1.03814i
$147$	1.44036	−	4.78258i	0.118799	−	0.394460i
$148$	−7.21678	−	22.2110i	−0.593216	−	1.82573i
$149$	−0.669131	+	0.743145i	−0.0548173	+	0.0608808i	−0.769930	−	0.638129i	$-0.779709\pi$
$149$	−0.669131	+	0.743145i	−0.0548173	+	0.0608808i	0.715112	+	0.699009i	$0.246375\pi$
$150$	−0.228310	+	0.101650i	−0.0186414	+	0.00829970i
$151$	−1.55132	−	14.7598i	−0.126245	−	1.20114i	−0.855834	−	0.517251i	$-0.826955\pi$
$151$	−1.55132	−	14.7598i	−0.126245	−	1.20114i	0.729589	−	0.683886i	$-0.239711\pi$
$152$	−37.1554	+	7.89762i	−3.01370	+	0.640582i
$153$	−3.71354			−0.300222
$154$		0			0
$155$	−5.18089			−0.416139
$156$	−9.64393	+	2.04988i	−0.772133	+	0.164122i
$157$	−0.667992	−	6.35552i	−0.0533116	−	0.507226i	−0.988297	−	0.152540i	$-0.951255\pi$
$157$	−0.667992	−	6.35552i	−0.0533116	−	0.507226i	0.934986	−	0.354686i	$-0.115412\pi$
$158$	−10.5390	+	4.69227i	−0.838438	+	0.373297i
$159$	−0.145496	+	0.161589i	−0.0115386	+	0.0128149i
$160$	−1.45818	−	4.48782i	−0.115279	−	0.354793i
$161$	16.2743	−	5.48314i	1.28260	−	0.432132i
$162$	9.42485	−	6.84755i	0.740486	−	0.537994i
$163$	−9.72786	+	2.06772i	−0.761944	+	0.161956i	−0.572466	−	0.819929i	$-0.694013\pi$
$163$	−9.72786	+	2.06772i	−0.761944	+	0.161956i	−0.189479	+	0.981885i	$0.560680\pi$
$164$	23.6496	−	40.9623i	1.84672	−	3.19862i
$165$		0			0
$166$	−2.41142	−	4.17670i	−0.187163	−	0.324175i
$167$	−0.599940	+	1.84643i	−0.0464248	+	0.142881i	−0.971582	−	0.236704i	$-0.923933\pi$
$167$	−0.599940	+	1.84643i	−0.0464248	+	0.142881i	0.925157	+	0.379584i	$0.123933\pi$
$168$	−8.92055	+	5.27973i	−0.688235	+	0.407340i
$169$	1.77916	+	1.29264i	0.136859	+	0.0994337i
$170$	−5.47759	+	6.08348i	−0.420112	+	0.466582i
$171$	−16.8551	−	3.58266i	−1.28894	−	0.273973i
$172$	20.2347	−	9.00905i	1.54288	−	0.686933i
$173$	5.87621	+	2.61626i	0.446760	+	0.198910i	0.617770	−	0.786359i	$-0.288036\pi$
$173$	5.87621	+	2.61626i	0.446760	+	0.198910i	−0.171010	+	0.985269i	$0.554703\pi$
$174$	−0.906082	+	2.78863i	−0.0686899	+	0.211406i
$175$	−0.370390	−	0.0348840i	−0.0279989	−	0.00263698i
$176$		0			0
$177$	−4.51624	−	7.82235i	−0.339461	−	0.587964i
$178$	−5.34082	−	5.93158i	−0.400311	−	0.444591i
$179$	0.374835	+	3.56632i	0.0280165	+	0.266559i	0.999559	+	0.0296940i	$0.00945329\pi$
$179$	0.374835	+	3.56632i	0.0280165	+	0.266559i	−0.971543	+	0.236865i	$0.923880\pi$
$180$	2.41312	−	22.9593i	0.179864	−	1.71129i
$181$	3.77414	+	11.6156i	0.280530	+	0.863381i	0.987703	+	0.156341i	$0.0499699\pi$
$181$	3.77414	+	11.6156i	0.280530	+	0.863381i	−0.707174	+	0.707040i	$0.750030\pi$
$182$	−20.6696	−	6.46967i	−1.53213	−	0.479564i
$183$	−7.49389	−	5.44463i	−0.553964	−	0.402479i
$184$	−32.5592	−	14.4963i	−2.40029	−	1.06868i
$185$	−8.19329	−	9.09957i	−0.602383	−	0.669014i
$186$	2.08858	−	3.61753i	0.153142	−	0.265250i
$187$		0			0
$188$	6.26819			0.457155
$189$	−10.2968	+	1.19496i	−0.748981	+	0.0869205i
$190$	−30.7309	+	22.3273i	−2.22945	+	1.61979i
$191$	−1.26577	+	12.0430i	−0.0915877	+	0.871398i	0.848208	+	0.529663i	$0.177681\pi$
$191$	−1.26577	+	12.0430i	−0.0915877	+	0.871398i	−0.939796	+	0.341736i	$0.888985\pi$
$192$	−3.63239	−	0.772088i	−0.262145	−	0.0557206i
$193$	11.6790	+	2.48245i	0.840675	+	0.178691i	0.608073	−	0.793881i	$-0.291943\pi$
$193$	11.6790	+	2.48245i	0.840675	+	0.178691i	0.232602	+	0.972572i	$0.425276\pi$
$194$	0.484121	−	4.60611i	0.0347579	−	0.330699i
$195$	−4.18210	+	3.03847i	−0.299486	+	0.217589i
$196$	−29.4239	+	0.636544i	−2.10171	+	0.0454674i
$197$	12.1626			0.866551			0.433275	−	0.901262i	$-0.357358\pi$
$197$	12.1626			0.866551			0.433275	+	0.901262i	$0.357358\pi$
$198$		0			0
$199$	−0.952451	+	1.64969i	−0.0675174	+	0.116944i	−0.897808	−	0.440387i	$-0.854841\pi$
$199$	−0.952451	+	1.64969i	−0.0675174	+	0.116944i	0.830290	+	0.557331i	$0.188174\pi$
$200$	0.516630	+	0.573776i	0.0365312	+	0.0405721i
$201$	2.98086	+	1.32716i	0.210253	+	0.0936109i
$202$	12.1826	+	8.85120i	0.857167	+	0.622768i
$203$	−3.21192	+	2.95555i	−0.225433	+	0.207439i
$204$	−1.38211	−	4.25369i	−0.0967668	−	0.297818i
$205$	2.59224	−	24.6635i	0.181050	−	1.72257i
$206$	−0.276974	−	2.63523i	−0.0192977	−	0.183605i
$207$	−10.8184	−	12.0151i	−0.751931	−	0.835104i
$208$	8.65685	+	14.9941i	0.600245	+	1.03965i
$209$		0			0
$210$	−6.00187	+	8.45159i	−0.414168	+	0.583215i
$211$	−5.01988	+	15.4496i	−0.345583	+	1.06360i	0.615688	+	0.787990i	$0.288878\pi$
$211$	−5.01988	+	15.4496i	−0.345583	+	1.06360i	−0.961271	+	0.275605i	$0.911122\pi$
$212$	1.17046	+	0.521122i	0.0803875	+	0.0357908i
$213$	−7.38333	+	3.28727i	−0.505897	+	0.225240i
$214$	−15.4274	−	3.27920i	−1.05460	−	0.224162i
$215$	7.77075	−	8.63029i	0.529961	−	0.588581i
$216$	17.4043	+	12.6449i	1.18421	+	0.860380i
$217$	5.35116	−	3.16715i	0.363260	−	0.215000i
$218$	2.16589	−	6.66593i	0.146693	−	0.451473i
$219$	−3.05669	−	5.29434i	−0.206552	−	0.357758i
$220$		0			0
$221$	2.44983	−	4.24324i	0.164794	−	0.285431i
$222$	9.65669	−	2.05259i	0.648114	−	0.137761i
$223$	−2.45662	+	1.78484i	−0.164507	+	0.119522i	−0.666993	−	0.745064i	$-0.732419\pi$
$223$	−2.45662	+	1.78484i	−0.164507	+	0.119522i	0.502486	+	0.864585i	$0.332419\pi$
$224$	4.24956	+	3.74390i	0.283936	+	0.250150i
$225$	0.108233	+	0.333107i	0.00721554	+	0.0222072i
$226$	21.2570	−	23.6082i	1.41399	−	1.57040i
$227$	16.8541	−	7.50392i	1.11864	−	0.498053i	0.237731	−	0.971331i	$-0.423596\pi$
$227$	16.8541	−	7.50392i	1.11864	−	0.498053i	0.880913	+	0.473278i	$0.156930\pi$
$228$	−2.16936	−	20.6401i	−0.143670	−	1.36693i
$229$	24.9426	−	5.30171i	1.64825	−	0.350347i	0.712138	−	0.702040i	$-0.247727\pi$
$229$	24.9426	−	5.30171i	1.64825	−	0.350347i	0.936116	+	0.351693i	$0.114394\pi$
$230$	−35.6404			−2.35006
$231$		0			0
$232$	9.05855			0.594723
$233$	−3.73418	+	0.793725i	−0.244634	+	0.0519987i	−0.328597	−	0.944470i	$-0.606576\pi$
$233$	−3.73418	+	0.793725i	−0.244634	+	0.0519987i	0.0839625	+	0.996469i	$0.473242\pi$
$234$	2.13139	+	20.2788i	0.139333	+	1.32567i
$235$	3.00233	−	1.33672i	0.195851	−	0.0871983i
$236$	−35.6127	+	39.5519i	−2.31819	+	2.57461i
$237$	−1.02122	−	3.14299i	−0.0663353	−	0.204159i
$238$	1.93870	−	9.63193i	0.125667	−	0.624345i
$239$	−10.5202	+	7.64340i	−0.680498	+	0.494411i	−0.873523	−	0.486783i	$-0.838170\pi$
$239$	−10.5202	+	7.64340i	−0.680498	+	0.494411i	0.193025	+	0.981194i	$0.438170\pi$
$240$	8.10538	−	1.72285i	0.523200	−	0.111210i
$241$	0.225292	−	0.390216i	0.0145123	−	0.0251360i	−0.858678	−	0.512515i	$-0.828714\pi$
$241$	0.225292	−	0.390216i	0.0145123	−	0.0251360i	0.873190	+	0.487379i	$0.162047\pi$
$242$		0			0
$243$	7.54551	+	13.0692i	0.484045	+	0.838391i
$244$	−16.8663	+	51.9090i	−1.07975	+	3.32314i
$245$	−13.9577	+	6.57970i	−0.891725	+	0.420362i
$246$	16.1761	+	11.7526i	1.03135	+	0.749320i
$247$	15.2130	−	16.8958i	0.967983	−	1.07505i
$248$	−12.6229	−	2.68308i	−0.801555	−	0.170376i
$249$	1.26212	−	0.561931i	0.0799835	−	0.0356110i
$250$	25.7861	+	11.4807i	1.63086	+	0.726104i
$251$	0.345668	−	1.06386i	0.0218184	−	0.0671501i	−0.939554	−	0.342399i	$-0.888760\pi$
$251$	0.345668	−	1.06386i	0.0218184	−	0.0671501i	0.961373	+	0.275249i	$0.0887604\pi$
$252$	11.5429	+	25.1890i	0.727134	+	1.58676i
$253$		0			0
$254$	−15.4153	−	26.7001i	−0.967243	−	1.67531i
$255$	−1.56912	−	1.74269i	−0.0982622	−	0.109131i
$256$	3.40192	+	32.3671i	0.212620	+	2.02294i
$257$	2.38739	−	22.7145i	0.148921	−	1.41689i	−0.623521	−	0.781807i	$-0.714298\pi$
$257$	2.38739	−	22.7145i	0.148921	−	1.41689i	0.772442	−	0.635085i	$-0.219035\pi$
$258$	2.89342	+	8.90502i	0.180136	+	0.554402i
$259$	14.0252	+	4.38996i	0.871486	+	0.272779i
$260$	24.6423	+	17.9037i	1.52825	+	1.11034i
$261$	3.75403	+	1.67140i	0.232369	+	0.103457i
$262$	−1.26512	−	1.40506i	−0.0781596	−	0.0868050i
$263$	4.59568	−	7.95995i	0.283382	−	0.490832i	−0.688834	−	0.724919i	$-0.741877\pi$
$263$	4.59568	−	7.95995i	0.283382	−	0.490832i	0.972215	+	0.234088i	$0.0752103\pi$
$264$		0			0
$265$	0.671758			0.0412658
$266$	18.0919	−	41.8472i	1.10928	−	2.56582i
$267$	1.84979	−	1.34395i	0.113205	−	0.0822483i
$268$	2.00971	−	19.1211i	0.122762	−	1.16801i
$269$	15.2720	+	3.24617i	0.931151	+	0.197922i	0.648425	−	0.761278i	$-0.275428\pi$
$269$	15.2720	+	3.24617i	0.931151	+	0.197922i	0.282726	+	0.959201i	$0.408761\pi$
$270$	21.0428	+	4.47278i	1.28062	+	0.272205i
$271$	−2.90009	+	27.5925i	−0.176168	+	1.67613i	0.447382	+	0.894343i	$0.352357\pi$
$271$	−2.90009	+	27.5925i	−0.176168	+	1.67613i	−0.623550	+	0.781784i	$0.714310\pi$
$272$	−6.35414	+	4.61655i	−0.385276	+	0.279920i
$273$	2.46208	−	5.69490i	0.149012	−	0.344671i
$274$	14.5494			0.878962
$275$		0			0
$276$	9.73630	−	16.8638i	0.586056	−	1.01508i
$277$	9.91141	+	11.0077i	0.595519	+	0.661391i	0.963270	−	0.268533i	$-0.0865389\pi$
$277$	9.91141	+	11.0077i	0.595519	+	0.661391i	−0.367751	+	0.929924i	$0.619872\pi$
$278$	12.6813	+	5.64607i	0.760573	+	0.338629i
$279$	−4.73611	−	3.44098i	−0.283543	−	0.206006i
$280$	30.5622	+	9.56610i	1.82644	+	0.571684i
$281$	4.70407	+	14.4776i	0.280621	+	0.863663i	0.987677	+	0.156505i	$0.0500228\pi$
$281$	4.70407	+	14.4776i	0.280621	+	0.863663i	−0.707056	+	0.707157i	$0.749977\pi$
$282$	−0.276974	+	2.63523i	−0.0164936	+	0.156926i
$283$	−2.27007	−	21.5983i	−0.134942	−	1.28389i	−0.827065	−	0.562106i	$-0.809991\pi$
$283$	−2.27007	−	21.5983i	−0.134942	−	1.28389i	0.692123	−	0.721779i	$-0.256676\pi$
$284$	31.8655	+	35.3902i	1.89087	+	2.10002i
$285$	−5.44070	−	9.42356i	−0.322279	−	0.558204i
$286$		0			0
$287$	12.3997	+	27.0587i	0.731929	+	1.59722i
$288$	1.64767	−	5.07101i	0.0970900	−	0.298812i
$289$	−13.4998	−	6.01048i	−0.794103	−	0.353558i
$290$	8.27540	−	3.68445i	0.485948	−	0.216358i
$291$	1.29775	+	0.275845i	0.0760755	+	0.0161703i
$292$	−24.1034	+	26.7696i	−1.41055	+	1.56657i
$293$	−9.00240	−	6.54062i	−0.525926	−	0.382107i	0.292906	−	0.956141i	$-0.405378\pi$
$293$	−9.00240	−	6.54062i	−0.525926	−	0.382107i	−0.818832	+	0.574034i	$0.805378\pi$
$294$	1.03255	−	12.3984i	0.0602196	−	0.723087i
$295$	−8.62309	+	26.5391i	−0.502056	+	1.54517i
$296$	−15.2499	−	26.4136i	−0.886383	−	1.53526i
$297$		0			0
$298$	−1.24543	+	2.15715i	−0.0721459	+	0.124960i
$299$	20.8658	−	4.43517i	1.20670	−	0.256492i
$300$	−0.341277	+	0.247952i	−0.0197036	+	0.0143155i
$301$	−2.75032	+	13.6643i	−0.158526	+	0.787596i
$302$	−11.4235	−	35.1579i	−0.657348	−	2.02311i
$303$	−2.88643	+	3.20571i	−0.165821	+	0.184163i
$304$	−33.2942	+	14.8235i	−1.90955	+	0.850187i
$305$	2.99128	+	28.4602i	0.171280	+	1.62962i
$306$	−9.04778	+	1.92317i	−0.517227	+	0.109940i
$307$	24.9855			1.42600			0.712998	−	0.701166i	$-0.247337\pi$
$307$	24.9855			1.42600			0.712998	+	0.701166i	$0.247337\pi$
$308$		0			0
$309$	0.759053			0.0431810
$310$	−12.6229	+	2.68308i	−0.716932	+	0.152389i
$311$	−3.63140	−	34.5505i	−0.205918	−	1.95918i	−0.274656	−	0.961542i	$-0.588564\pi$
$311$	−3.63140	−	34.5505i	−0.205918	−	1.95918i	0.0687384	−	0.997635i	$-0.478103\pi$
$312$	−11.7630	+	5.23721i	−0.665946	+	0.296498i
$313$	15.8647	−	17.6196i	0.896728	−	0.995917i	−0.103272	−	0.994653i	$-0.532931\pi$
$313$	15.8647	−	17.6196i	0.896728	−	0.995917i	0.999999	−	0.00126374i	$-0.000402261\pi$
$314$	−4.91891	−	15.1389i	−0.277590	−	0.854335i
$315$	10.9005	+	9.60344i	0.614174	+	0.541093i
$316$	−15.7537	+	11.4457i	−0.886212	+	0.643871i
$317$	−19.2470	+	4.09108i	−1.08102	+	0.229778i	−0.713795	−	0.700355i	$-0.753025\pi$
$317$	−19.2470	+	4.09108i	−1.08102	+	0.229778i	−0.367224	+	0.930132i	$0.619692\pi$
$318$	−0.270807	+	0.469051i	−0.0151861	+	0.0263031i
$319$		0			0
$320$	5.73630	+	9.93556i	0.320669	+	0.555414i
$321$	1.39617	−	4.29697i	0.0779267	−	0.239834i
$322$	36.8117	−	21.7875i	2.05144	−	1.21417i
$323$	8.34396	+	6.06224i	0.464270	+	0.337312i
$324$	13.1578	−	14.6132i	0.730986	−	0.811843i
$325$	−0.452023	−	0.0960806i	−0.0250738	−	0.00532959i
$326$	−22.6304	+	10.0757i	−1.25338	+	0.558042i
$327$	1.83422	+	0.816647i	0.101433	+	0.0451607i
$328$	19.0885	−	58.7484i	1.05399	−	3.24384i
$329$	−2.28384	+	3.21602i	−0.125912	+	0.177305i
$330$		0			0
$331$	14.0949	+	24.4131i	0.774728	+	1.34187i	0.934947	+	0.354786i	$0.115446\pi$
$331$	14.0949	+	24.4131i	0.774728	+	1.34187i	−0.160220	+	0.987081i	$0.551220\pi$
$332$	−5.44713	−	6.04966i	−0.298950	−	0.332018i
$333$	−1.44624	−	13.7601i	−0.0792536	−	0.754048i
$334$	−0.505487	+	4.80939i	−0.0276590	+	0.263158i
$335$	−3.11506	−	9.58718i	−0.170194	−	0.523804i
$336$	−7.31856	+	6.73439i	−0.399260	+	0.367391i
$337$	−17.5929	−	12.7820i	−0.958346	−	0.696279i	−0.00558004	−	0.999984i	$-0.501776\pi$
$337$	−17.5929	−	12.7820i	−0.958346	−	0.696279i	−0.952766	+	0.303705i	$0.901776\pi$
$338$	5.00424	+	2.22803i	0.272195	+	0.121189i
$339$	6.08931	+	6.76287i	0.330726	+	0.367308i
$340$	−6.90880	+	11.9664i	−0.374682	+	0.648969i
$341$		0			0
$342$	−42.9217			−2.32094
$343$	10.3942	−	15.3285i	0.561232	−	0.827659i
$344$	23.4024	−	17.0028i	1.26177	−	0.916730i
$345$	1.06720	−	10.1537i	0.0574560	−	0.546657i
$346$	15.6719	+	3.33116i	0.842526	+	0.179084i
$347$	3.85532	+	0.819473i	0.206964	+	0.0439916i	0.310227	−	0.950663i	$-0.399595\pi$
$347$	3.85532	+	0.819473i	0.206964	+	0.0439916i	−0.103263	+	0.994654i	$0.532928\pi$
$348$	−0.517338	+	4.92214i	−0.0277322	+	0.263854i
$349$	11.4147	−	8.29324i	0.611013	−	0.443927i	−0.238758	−	0.971079i	$-0.576740\pi$
$349$	11.4147	−	8.29324i	0.611013	−	0.443927i	0.849771	+	0.527152i	$0.176740\pi$
$350$	−0.920496	+	0.106825i	−0.0492026	+	0.00571004i
$351$	−12.8762			−0.687279
$352$		0			0
$353$	2.48434	−	4.30301i	0.132228	−	0.229026i	−0.792307	−	0.610123i	$-0.791120\pi$
$353$	2.48434	−	4.30301i	0.132228	−	0.229026i	0.924535	+	0.381097i	$0.124453\pi$
$354$	−15.0545	−	16.7198i	−0.800140	−	0.888646i
$355$	22.8100	+	10.1557i	1.21063	+	0.539008i
$356$	−10.8996	−	7.91899i	−0.577675	−	0.419706i
$357$	2.68602	+	0.840734i	0.142159	+	0.0444964i
$358$	2.76018	+	8.49497i	0.145880	+	0.448973i
$359$	0.425597	−	4.04929i	0.0224622	−	0.213713i	−0.977534	−	0.210780i	$-0.932400\pi$
$359$	0.425597	−	4.04929i	0.0224622	−	0.213713i	0.999996	−	0.00293325i	$-0.000933683\pi$
$360$	−3.15149	−	29.9844i	−0.166098	−	1.58032i
$361$	19.3097	+	21.4456i	1.01630	+	1.12872i
$362$	15.2109	+	26.3461i	0.799468	+	1.38472i
$363$		0			0
$364$	−36.3969	−	3.42792i	−1.90772	−	0.179672i
$365$	−5.83629	+	17.9623i	−0.305485	+	0.940187i
$366$	−21.0780	−	9.38454i	−1.10177	−	0.490538i
$367$	−16.4639	+	7.33021i	−0.859410	+	0.382634i	−0.788637	−	0.614859i	$-0.789213\pi$
$367$	−16.4639	+	7.33021i	−0.859410	+	0.382634i	−0.0707724	+	0.997492i	$0.522546\pi$
$368$	−33.4479	−	7.10956i	−1.74359	−	0.370611i
$369$	18.7504	−	20.8244i	0.976106	−	1.08408i
$370$	−24.6749	−	17.9274i	−1.28279	−	0.931999i
$371$	−0.693835	+	0.410654i	−0.0360221	+	0.0213201i
$372$	2.17880	−	6.70566i	0.112966	−	0.347672i
$373$	−14.4582	−	25.0424i	−0.748618	−	1.29664i	−0.948485	−	0.316822i	$-0.897384\pi$
$373$	−14.4582	−	25.0424i	−0.748618	−	1.29664i	0.199867	−	0.979823i	$-0.435949\pi$
$374$		0			0
$375$	−4.04290	+	7.00250i	−0.208774	+	0.361608i
$376$	8.00724	−	1.70199i	0.412942	−	0.0877735i
$377$	−4.38636	+	3.18688i	−0.225909	+	0.164133i
$378$	−24.4686	+	8.24393i	−1.25853	+	0.424022i
$379$	1.33139	+	4.09760i	0.0683889	+	0.210479i	0.979410	−	0.201880i	$-0.0647049\pi$
$379$	1.33139	+	4.09760i	0.0683889	+	0.210479i	−0.911021	+	0.412359i	$0.864705\pi$
$380$	−42.9025	+	47.6480i	−2.20085	+	2.44429i
$381$	8.06826	−	3.59222i	0.413349	−	0.184035i
$382$	3.15285	+	29.9974i	0.161314	+	1.53480i
$383$	12.0789	−	2.56745i	0.617203	−	0.131191i	0.111308	−	0.993786i	$-0.464496\pi$
$383$	12.0789	−	2.56745i	0.617203	−	0.131191i	0.505895	+	0.862595i	$0.331163\pi$
$384$	−12.3047			−0.627923
$385$		0			0
$386$	29.7408			1.51377
$387$	12.8356	−	2.72829i	0.652470	−	0.138687i
$388$	−0.817162	−	7.77478i	−0.0414851	−	0.394705i
$389$	26.8793	−	11.9674i	1.36283	−	0.606772i	0.410507	−	0.911857i	$-0.365352\pi$
$389$	26.8793	−	11.9674i	1.36283	−	0.606772i	0.952325	+	0.305085i	$0.0986850\pi$
$390$	−8.61583	+	9.56885i	−0.436280	+	0.484538i
$391$	2.99036	+	9.20337i	0.151229	+	0.465434i
$392$	−37.4145	+	8.80258i	−1.88972	+	0.444597i
$393$	0.438174	−	0.318352i	0.0221030	−	0.0160587i
$394$	29.6334	−	6.29877i	1.49291	−	0.317328i
$395$	−5.10482	+	8.84180i	−0.256851	+	0.444879i
$396$		0			0
$397$	8.64975	+	14.9818i	0.434119	+	0.751915i	0.997223	−	0.0744702i	$-0.0237266\pi$
$397$	8.64975	+	14.9818i	0.434119	+	0.751915i	−0.563105	+	0.826386i	$0.690393\pi$
$398$	−1.46624	+	4.51262i	−0.0734959	+	0.226197i
$399$	11.3802	+	6.40729i	0.569725	+	0.320766i
$400$	0.599304	+	0.435420i	0.0299652	+	0.0217710i
$401$	−16.6951	+	18.5418i	−0.833713	+	0.925932i	−0.998171	−	0.0604521i	$-0.980746\pi$
$401$	−16.6951	+	18.5418i	−0.833713	+	0.925932i	0.164458	+	0.986384i	$0.447412\pi$
$402$	7.94997	+	1.68982i	0.396508	+	0.0842805i
$403$	7.05623	−	3.14164i	0.351496	−	0.156496i
$404$	23.2203	+	10.3383i	1.15525	+	0.514352i
$405$	3.18596	−	9.80536i	0.158311	−	0.487232i
$406$	−6.29502	+	8.86439i	−0.312416	+	0.439932i
$407$		0			0
$408$	−2.92056	−	5.05855i	−0.144589	−	0.250436i
$409$	−25.8006	−	28.6545i	−1.27576	−	1.41687i	−0.862339	−	0.506331i	$-0.831001\pi$
$409$	−25.8006	−	28.6545i	−1.27576	−	1.41687i	−0.413418	−	0.910541i	$-0.635665\pi$
$410$	−6.45691	−	61.4334i	−0.318884	−	3.03398i
$411$	−0.435660	+	4.14502i	−0.0214895	+	0.204459i
$412$	−1.38211	−	4.25369i	−0.0680915	−	0.209564i
$413$	−7.31723	−	32.6827i	−0.360057	−	1.60821i
$414$	−32.5807	−	23.6712i	−1.60125	−	1.16338i
$415$	−3.89918	−	1.73603i	−0.191403	−	0.0852183i
$416$	4.70736	+	5.22806i	0.230798	+	0.256327i
$417$	−1.98825	+	3.44374i	−0.0973648	+	0.168641i
$418$		0			0
$419$	0.908970			0.0444061			0.0222030	−	0.999753i	$-0.492932\pi$
$419$	0.908970			0.0444061			0.0222030	+	0.999753i	$0.492932\pi$
$420$	−6.94334	+	16.0602i	−0.338801	+	0.783659i
$421$	−12.5828	+	9.14191i	−0.613246	+	0.445550i	−0.850556	−	0.525884i	$-0.823734\pi$
$421$	−12.5828	+	9.14191i	−0.613246	+	0.445550i	0.237310	+	0.971434i	$0.423734\pi$
$422$	−4.22957	+	40.2416i	−0.205892	+	1.95893i
$423$	3.63239	+	0.772088i	0.176613	+	0.0375402i
$424$	1.63669	+	0.347890i	0.0794848	+	0.0168950i
$425$	0.0219129	−	0.208488i	0.00106293	−	0.0101131i
$426$	−16.2866	+	11.8329i	−0.789087	+	0.573305i
$427$	−20.4877	−	27.5669i	−0.991467	−	1.33405i
$428$	−26.6222			−1.28683
$429$		0			0
$430$	14.4635	−	25.0514i	0.697490	−	1.20809i
$431$	2.36630	+	2.62804i	0.113981	+	0.126588i	0.797435	−	0.603405i	$-0.206190\pi$
$431$	2.36630	+	2.62804i	0.113981	+	0.126588i	−0.683454	+	0.729993i	$0.739523\pi$
$432$	18.8560	+	8.39523i	0.907209	+	0.403916i
$433$	−14.2757	−	10.3719i	−0.686044	−	0.498440i	0.189313	−	0.981917i	$-0.439374\pi$
$433$	−14.2757	−	10.3719i	−0.686044	−	0.498440i	−0.875357	+	0.483476i	$0.839374\pi$
$434$	11.3975	−	10.4878i	0.547099	−	0.503430i
$435$	0.801878	+	2.46793i	0.0384471	+	0.118328i
$436$	1.23664	−	11.7658i	0.0592243	−	0.563481i
$437$	4.69368	+	44.6574i	0.224529	+	2.13625i
$438$	−10.1892	−	11.3163i	−0.486861	−	0.540713i
$439$	−7.51362	−	13.0140i	−0.358606	−	0.621123i	0.629123	−	0.777306i	$-0.283414\pi$
$439$	−7.51362	−	13.0140i	−0.358606	−	0.621123i	−0.987728	+	0.156183i	$0.950081\pi$
$440$		0			0
$441$	−17.1294	−	3.25544i	−0.815688	−	0.155021i
$442$	3.77137	−	11.6071i	0.179386	−	0.552092i
$443$	12.0795	+	5.37815i	0.573915	+	0.255523i	0.673107	−	0.739545i	$-0.264959\pi$
$443$	12.0795	+	5.37815i	0.573915	+	0.255523i	−0.0991922	+	0.995068i	$0.531626\pi$
$444$	15.2233	−	6.77784i	0.722465	−	0.321662i
$445$	−6.90943	−	1.46864i	−0.327538	−	0.0696204i
$446$	−5.06105	+	5.62087i	−0.239648	+	0.266156i
$447$	−0.577264	−	0.419407i	−0.0273037	−	0.0198373i
$448$	−11.9985	−	6.75541i	−0.566878	−	0.319163i
$449$	−3.06194	+	9.42367i	−0.144502	+	0.444731i	−0.996947	−	0.0780865i	$-0.975119\pi$
$449$	−3.06194	+	9.42367i	−0.144502	+	0.444731i	0.852445	+	0.522817i	$0.175119\pi$
$450$	0.436212	+	0.755542i	0.0205632	+	0.0356166i
$451$		0			0
$452$	26.8111	−	46.4382i	1.26109	−	2.18427i
$453$	10.3583	−	2.20172i	0.486675	−	0.103446i
$454$	37.1777	−	27.0112i	1.74484	−	1.26770i
$455$	−18.1644	+	6.11993i	−0.851559	+	0.286907i
$456$	−8.37562	−	25.7775i	−0.392224	−	1.20714i
$457$	6.92217	−	7.68784i	0.323805	−	0.359622i	−0.559161	−	0.829059i	$-0.688876\pi$
$457$	6.92217	−	7.68784i	0.323805	−	0.359622i	0.882966	+	0.469437i	$0.155543\pi$
$458$	58.0253	−	25.8345i	2.71134	−	1.20717i
$459$	−0.610563	−	5.80912i	−0.0284986	−	0.271146i
$460$	−58.8439	+	12.5077i	−2.74361	+	0.583173i
$461$	−15.3372			−0.714325			−0.357163	−	0.934042i	$-0.616256\pi$
$461$	−15.3372			−0.714325			−0.357163	+	0.934042i	$0.616256\pi$
$462$		0			0
$463$	−25.1313			−1.16795			−0.583976	−	0.811771i	$-0.698504\pi$
$463$	−25.1313			−1.16795			−0.583976	+	0.811771i	$0.698504\pi$
$464$	8.50127	−	1.80700i	0.394662	−	0.0838879i
$465$	−0.386417	−	3.67651i	−0.0179197	−	0.170494i
$466$	−8.68703	+	3.86771i	−0.402419	+	0.179168i
$467$	−0.499181	+	0.554397i	−0.0230994	+	0.0256544i	−0.754584	−	0.656204i	$-0.772161\pi$
$467$	−0.499181	+	0.554397i	−0.0230994	+	0.0256544i	0.731484	+	0.681858i	$0.238828\pi$
$468$	10.6357	+	32.7332i	0.491634	+	1.51309i
$469$	9.07820	+	7.99798i	0.419192	+	0.369312i
$470$	6.62272	−	4.81169i	0.305483	−	0.221947i
$471$	4.46024	−	0.948054i	0.205517	−	0.0436840i
$472$	−34.7537	+	60.1951i	−1.59967	+	2.77070i
$473$		0			0
$474$	−4.11582	−	7.12881i	−0.189046	−	0.327437i
$475$	0.300599	−	0.925148i	0.0137924	−	0.0424487i
$476$	−0.179355	−	16.5831i	−0.00822071	−	0.760085i
$477$	0.614087	+	0.446160i	0.0281171	+	0.0204283i
$478$	−21.6735	+	24.0709i	−0.991323	+	1.10098i
$479$	19.6735	+	4.18174i	0.898906	+	0.191068i	0.634116	−	0.773238i	$-0.281364\pi$
$479$	19.6735	+	4.18174i	0.898906	+	0.191068i	0.264790	+	0.964306i	$0.414697\pi$
$480$	3.07593	−	1.36949i	0.140396	−	0.0625085i
$481$	16.6769	+	7.42504i	0.760402	+	0.338553i
$482$	0.346822	−	1.06741i	0.0157973	−	0.0486192i
$483$	5.10482	+	11.1398i	0.232277	+	0.506878i
$484$		0			0
$485$	−2.04942	−	3.54969i	−0.0930592	−	0.161183i
$486$	25.1524	+	27.9346i	1.14094	+	1.26714i
$487$	0.444237	+	4.22664i	0.0201303	+	0.191527i	0.999966	−	0.00827918i	$-0.00263538\pi$
$487$	0.444237	+	4.22664i	0.0201303	+	0.191527i	−0.979835	+	0.199806i	$0.935969\pi$
$488$	−7.45088	+	70.8904i	−0.337286	+	3.20906i
$489$	−2.19287	−	6.74895i	−0.0991648	−	0.305198i
$490$	−30.5995	+	23.2594i	−1.38234	+	1.05075i
$491$	−24.5358	−	17.8263i	−1.10728	−	0.804490i	−0.125051	−	0.992150i	$-0.539909\pi$
$491$	−24.5358	−	17.8263i	−1.10728	−	0.804490i	−0.982234	+	0.187661i	$0.939909\pi$
$492$	30.8319	+	13.7273i	1.39001	+	0.618873i
$493$	−1.64576	−	1.82780i	−0.0741214	−	0.0823201i
$494$	28.3156	−	49.0440i	1.27398	−	2.20659i
$495$		0			0
$496$	−12.3816			−0.555948
$497$	−29.7680	+	3.45462i	−1.33528	+	0.154961i
$498$	2.78405	−	2.02273i	0.124756	−	0.0906409i
$499$	−1.50952	+	14.3622i	−0.0675756	+	0.642939i	0.907345	+	0.420387i	$0.138106\pi$
$499$	−1.50952	+	14.3622i	−0.0675756	+	0.642939i	−0.974921	+	0.222552i	$0.928561\pi$
$500$	46.6030	+	9.90578i	2.08415	+	0.443000i
$501$	−1.35502	−	0.288019i	−0.0605380	−	0.0128677i
$502$	0.291247	−	2.77103i	0.0129990	−	0.123677i
$503$	2.39325	−	1.73880i	0.106710	−	0.0775292i	−0.533151	−	0.846020i	$-0.678992\pi$
$503$	2.39325	−	1.73880i	0.106710	−	0.0775292i	0.639860	+	0.768491i	$0.278992\pi$
$504$	21.5849	+	29.0433i	0.961468	+	1.29369i
$505$	13.3267			0.593032
$506$		0			0
$507$	−0.784595	+	1.35896i	−0.0348451	+	0.0603534i
$508$	−34.8215	−	38.6732i	−1.54496	−	1.71585i
$509$	−22.8301	−	10.1646i	−1.01193	−	0.450539i	−0.167307	−	0.985905i	$-0.553507\pi$
$509$	−22.8301	−	10.1646i	−1.01193	−	0.450539i	−0.844621	+	0.535365i	$0.820174\pi$
$510$	−4.72556	−	3.43332i	−0.209251	−	0.152030i
$511$	−4.95246	−	22.1204i	−0.219084	−	0.978547i
$512$	14.3930	+	44.2970i	0.636086	+	1.95767i
$513$	2.83315	−	26.9556i	0.125086	−	1.19012i
$514$	−5.94666	−	56.5787i	−0.262296	−	2.49558i
$515$	−1.56912	−	1.74269i	−0.0691438	−	0.0767919i
$516$	7.90228	+	13.6872i	0.347879	+	0.602544i
$517$		0			0
$518$	36.4450	+	3.43245i	1.60130	+	0.150813i
$519$	−1.41829	+	4.36506i	−0.0622562	+	0.191605i
$520$	36.3404	+	16.1798i	1.59363	+	0.709531i
$521$	26.3678	−	11.7397i	1.15519	−	0.514325i	0.262474	−	0.964939i	$-0.415462\pi$
$521$	26.3678	−	11.7397i	1.15519	−	0.514325i	0.892719	+	0.450614i	$0.148795\pi$
$522$	10.0120	+	2.12812i	0.438215	+	0.0931455i
$523$	0.316225	−	0.351203i	0.0138276	−	0.0153571i	−0.736191	−	0.676773i	$-0.763378\pi$
$523$	0.316225	−	0.351203i	0.0138276	−	0.0153571i	0.750019	+	0.661416i	$0.230044\pi$
$524$	−2.58187	−	1.87584i	−0.112789	−	0.0819463i
$525$	−0.00287088	−	0.265441i	−0.000125296	−	0.0115848i
$526$	7.07477	−	21.7739i	0.308475	−	0.949387i
$527$	1.75195	+	3.03447i	0.0763162	+	0.132184i
$528$		0			0
$529$	−9.56566	+	16.5682i	−0.415898	+	0.720357i
$530$	1.63669	−	0.347890i	0.0710934	−	0.0151114i
$531$	−25.5092	+	18.5335i	−1.10701	+	0.804287i
$532$	15.1846	−	75.4408i	0.658336	−	3.27077i
$533$	11.4251	+	35.1629i	0.494876	+	1.52307i
$534$	3.81088	−	4.23241i	0.164913	−	0.183154i
$535$	−12.7515	+	5.67732i	−0.551294	+	0.245452i
$536$	−2.62464	−	24.9718i	−0.113367	−	1.07862i
$537$	−2.50281	+	0.531988i	−0.108004	+	0.0229570i
$538$	38.8904			1.67668
$539$		0			0
$540$	36.3122			1.56263
$541$	−15.1217	+	3.21422i	−0.650134	+	0.138190i	−0.521162	−	0.853458i	$-0.674501\pi$
$541$	−15.1217	+	3.21422i	−0.650134	+	0.138190i	−0.128972	+	0.991648i	$0.541168\pi$
$542$	7.22373	+	68.7292i	0.310286	+	2.95217i
$543$	−7.96128	+	3.54459i	−0.341651	+	0.152113i
$544$	−2.13544	+	2.37165i	−0.0915562	+	0.101683i
$545$	−1.91680	−	5.89931i	−0.0821068	−	0.252699i
$546$	3.04942	−	15.1503i	0.130503	−	0.648373i
$547$	28.3512	−	20.5984i	1.21221	−	0.880722i	0.216780	−	0.976220i	$-0.430444\pi$
$547$	28.3512	−	20.5984i	1.21221	−	0.880722i	0.995430	+	0.0954983i	$0.0304445\pi$
$548$	24.0217	−	5.10598i	1.02616	−	0.218116i
$549$	−16.1679	+	28.0035i	−0.690027	+	1.19516i
$550$		0			0
$551$	−5.70644	−	9.88384i	−0.243102	−	0.421066i
$552$	7.85855	−	24.1861i	0.334482	−	1.02943i
$553$	−0.132523	−	12.2530i	−0.00563544	−	0.521051i
$554$	29.8492	+	21.6867i	1.26817	+	0.921379i
$555$	5.84622	−	6.49289i	0.248158	−	0.275608i
$556$	22.9188	+	4.87154i	0.971973	+	0.206599i
$557$	9.62205	−	4.28401i	0.407699	−	0.181519i	−0.192632	−	0.981271i	$-0.561702\pi$
$557$	9.62205	−	4.28401i	0.407699	−	0.181519i	0.600331	+	0.799752i	$0.295036\pi$
$558$	−13.3212	−	5.93099i	−0.563932	−	0.251079i
$559$	−5.35023	+	16.4663i	−0.226291	+	0.696451i
$560$	30.5903	+	2.88104i	1.29268	+	0.121746i
$561$		0			0
$562$	18.9588	+	32.8376i	0.799729	+	1.38517i
$563$	−20.5521	−	22.8255i	−0.866170	−	0.961979i	0.133407	−	0.991061i	$-0.457408\pi$
$563$	−20.5521	−	22.8255i	−0.866170	−	0.961979i	−0.999577	+	0.0290823i	$0.990742\pi$
$564$	0.467513	+	4.44809i	0.0196859	+	0.187298i
$565$	2.93877	−	27.9605i	0.123635	−	1.17631i
$566$	−16.7162	−	51.4472i	−0.702634	−	2.16249i
$567$	2.70348	+	12.0752i	0.113536	+	0.507112i
$568$	50.3157	+	36.5565i	2.11120	+	1.53388i
$569$	−28.1117	−	12.5161i	−1.17850	−	0.524704i	−0.278437	−	0.960455i	$-0.589816\pi$
$569$	−28.1117	−	12.5161i	−1.17850	−	0.524704i	−0.900067	+	0.435751i	$0.856483\pi$
$570$	−18.1362	−	20.1422i	−0.759640	−	0.843666i
$571$	3.75847	−	6.50986i	0.157287	−	0.272429i	−0.776602	−	0.629991i	$-0.783059\pi$
$571$	3.75847	−	6.50986i	0.157287	−	0.272429i	0.933889	+	0.357562i	$0.116392\pi$
$572$		0			0
$573$	−8.64045			−0.360960
$574$	44.2241	+	59.5051i	1.84588	+	2.48370i
$575$	0.738394	−	0.536475i	0.0307932	−	0.0223725i
$576$	−1.35505	+	12.8924i	−0.0564604	+	0.537185i
$577$	−27.0149	−	5.74220i	−1.12465	−	0.239051i	−0.392202	−	0.919879i	$-0.628287\pi$
$577$	−27.0149	−	5.74220i	−1.12465	−	0.239051i	−0.732443	+	0.680828i	$0.761620\pi$
$578$	−36.0040	−	7.65288i	−1.49757	−	0.318318i
$579$	−0.890541	+	8.47293i	−0.0370096	+	0.352123i
$580$	12.3700	−	8.98735i	0.513638	−	0.373179i
$581$	5.08858	−	0.590539i	0.211110	−	0.0244997i
$582$	3.30473			0.136986
$583$		0			0
$584$	−23.5220	+	40.7413i	−0.973348	+	1.68589i
$585$	12.0748	+	13.4104i	0.499232	+	0.554453i
$586$	−25.3210	−	11.2736i	−1.04600	−	0.465709i
$587$	24.2367	+	17.6090i	1.00036	+	0.726801i	0.962164	−	0.272469i	$-0.0878403\pi$
$587$	24.2367	+	17.6090i	1.00036	+	0.726801i	0.0381915	+	0.999270i	$0.487840\pi$
$588$	−2.64629	−	20.8326i	−0.109131	−	0.859122i
$589$	5.02427	+	15.4631i	0.207022	+	0.637147i
$590$	−7.26549	+	69.1265i	−0.299116	+	2.84589i
$591$	0.907149	+	8.63095i	0.0373151	+	0.355030i
$592$	−19.5807	−	21.7466i	−0.804763	−	0.893780i
$593$	−6.33401	−	10.9708i	−0.260107	−	0.450518i	0.706163	−	0.708049i	$-0.250424\pi$
$593$	−6.33401	−	10.9708i	−0.260107	−	0.450518i	−0.966270	+	0.257531i	$0.917091\pi$
$594$		0			0
$595$	−3.62234	−	7.90471i	−0.148502	−	0.324062i
$596$	−1.29923	+	3.99862i	−0.0532186	+	0.163790i
$597$	−1.24171	−	0.552844i	−0.0508197	−	0.0226264i
$598$	48.5413	−	21.6120i	1.98500	−	0.883779i
$599$	−1.26598	−	0.269093i	−0.0517267	−	0.0109948i	0.181976	−	0.983303i	$-0.441751\pi$
$599$	−1.26598	−	0.269093i	−0.0517267	−	0.0109948i	−0.233702	+	0.972308i	$0.575084\pi$
$600$	−0.368635	+	0.409411i	−0.0150495	+	0.0167141i
$601$	33.1875	+	24.1121i	1.35375	+	0.983554i	0.998815	+	0.0486619i	$0.0154957\pi$
$601$	33.1875	+	24.1121i	1.35375	+	0.983554i	0.354931	+	0.934892i	$0.384504\pi$
$602$	0.375476	+	34.7164i	0.0153032	+	1.41494i
$603$	3.51987	−	10.8330i	0.143340	−	0.441155i
$604$	−31.1990	−	54.0383i	−1.26947	−	2.19879i
$605$		0			0
$606$	−5.37242	+	9.30531i	−0.218240	+	0.378002i
$607$	20.7141	−	4.40291i	0.840758	−	0.178709i	0.232647	−	0.972561i	$-0.425261\pi$
$607$	20.7141	−	4.40291i	0.840758	−	0.178709i	0.608110	+	0.793853i	$0.291928\pi$
$608$	−11.9804	+	8.70430i	−0.485871	+	0.353006i
$609$	−2.33691	−	2.05883i	−0.0946962	−	0.0834282i
$610$	22.0270	+	67.7922i	0.891847	+	2.74482i
$611$	−3.27852	+	3.64116i	−0.132635	+	0.147306i
$612$	−14.2634	+	6.35046i	−0.576563	+	0.256702i
$613$	−0.706939	−	6.72607i	−0.0285530	−	0.271664i	−0.999479	−	0.0322828i	$-0.989722\pi$
$613$	−0.706939	−	6.72607i	−0.0285530	−	0.271664i	0.970926	−	0.239381i	$-0.0769444\pi$
$614$	60.8754	−	12.9395i	2.45673	−	0.522194i
$615$	17.6953			0.713542
$616$		0			0
$617$	−41.0728			−1.65353			−0.826763	−	0.562550i	$-0.809820\pi$
$617$	−41.0728			−1.65353			−0.826763	+	0.562550i	$0.809820\pi$
$618$	1.84938	−	0.393098i	0.0743930	−	0.0158127i
$619$	3.18046	+	30.2601i	0.127834	+	1.21625i	0.850844	+	0.525418i	$0.176091\pi$
$619$	3.18046	+	30.2601i	0.127834	+	1.21625i	−0.723011	+	0.690837i	$0.757242\pi$
$620$	−19.8994	+	8.85977i	−0.799177	+	0.355817i
$621$	17.0165	−	18.8988i	0.682850	−	0.758382i
$622$	−26.7406	−	82.2992i	−1.07220	−	3.29990i
$623$	8.03430	−	2.70691i	0.321887	−	0.108450i
$624$	−9.99458	+	7.26149i	−0.400104	+	0.290692i
$625$	23.7466	−	5.04751i	0.949866	−	0.201900i
$626$	29.5285	−	51.1449i	1.18020	−	2.04416i
$627$		0			0
$628$	−13.4342	−	23.2687i	−0.536082	−	0.928521i
$629$	−2.55904	+	7.87592i	−0.102036	+	0.314033i
$630$	31.5318	+	17.7530i	1.25626	+	0.707296i
$631$	−10.0051	−	7.26915i	−0.398298	−	0.289380i	0.370549	−	0.928813i	$-0.379169\pi$
$631$	−10.0051	−	7.26915i	−0.398298	−	0.289380i	−0.768847	+	0.639432i	$0.779169\pi$
$632$	−17.0165	+	18.8988i	−0.676881	+	0.751753i
$633$	−11.3379	−	2.40995i	−0.450641	−	0.0957867i
$634$	−44.7753	+	19.9353i	−1.77826	+	0.791730i
$635$	−24.9261	−	11.0978i	−0.989160	−	0.440403i
$636$	−0.282505	+	0.869460i	−0.0112020	+	0.0344763i
$637$	15.0201	−	17.4252i	0.595120	−	0.690410i
$638$		0			0
$639$	14.1067	+	24.4335i	0.558052	+	0.966574i
$640$	25.4365	+	28.2501i	1.00546	+	1.11668i
$641$	4.92656	+	46.8731i	0.194588	+	1.85138i	0.460852	+	0.887477i	$0.347544\pi$
$641$	4.92656	+	46.8731i	0.194588	+	1.85138i	−0.266265	+	0.963900i	$0.585789\pi$
$642$	1.17636	−	11.1923i	0.0464273	−	0.441726i
$643$	0.578611	+	1.78078i	0.0228182	+	0.0702272i	0.961817	−	0.273693i	$-0.0882451\pi$
$643$	0.578611	+	1.78078i	0.0228182	+	0.0702272i	−0.938999	+	0.343920i	$0.888245\pi$
$644$	53.1317	−	48.8908i	2.09368	−	1.92657i
$645$	6.70389	+	4.87066i	0.263965	+	0.191782i
$646$	23.4690	+	10.4491i	0.923376	+	0.411113i
$647$	−1.22844	−	1.36432i	−0.0482951	−	0.0536371i	0.718513	−	0.695513i	$-0.244823\pi$
$647$	−1.22844	−	1.36432i	−0.0482951	−	0.0536371i	−0.766808	+	0.641876i	$0.778156\pi$
$648$	12.8404	−	22.2402i	0.504417	−	0.873676i
$649$		0			0
$650$	−1.15108			−0.0451492
$651$	2.64662	+	3.56112i	0.103729	+	0.139571i
$652$	−33.8279	+	24.5774i	−1.32480	+	0.962525i
$653$	1.90003	−	18.0776i	0.0743539	−	0.707430i	−0.892317	−	0.451409i	$-0.850922\pi$
$653$	1.90003	−	18.0776i	0.0743539	−	0.707430i	0.966671	−	0.256021i	$-0.0824118\pi$
$654$	4.89188	+	1.03980i	0.191288	+	0.0406594i
$655$	−1.63669	−	0.347890i	−0.0639509	−	0.0135932i
$656$	6.19506	−	58.9420i	0.241876	−	2.30130i
$657$	−17.2652	+	12.5439i	−0.673579	+	0.489384i
$658$	−3.89892	+	9.01837i	−0.151996	+	0.351573i
$659$	−16.8997			−0.658318			−0.329159	−	0.944275i	$-0.606765\pi$
$659$	−16.8997			−0.658318			−0.329159	+	0.944275i	$0.606765\pi$
$660$		0			0
$661$	22.6516	−	39.2338i	0.881046	−	1.52602i	0.0308661	−	0.999524i	$-0.490173\pi$
$661$	22.6516	−	39.2338i	0.881046	−	1.52602i	0.850180	−	0.526493i	$-0.176493\pi$
$662$	46.9844	+	52.1815i	1.82610	+	2.02809i
$663$	3.19384	+	1.42199i	0.124039	+	0.0552256i
$664$	−8.60105	−	6.24903i	−0.333785	−	0.242509i
$665$	−8.81504	−	39.3728i	−0.341833	−	1.52681i
$666$	−10.6497	−	32.7765i	−0.412669	−	1.27006i
$667$	1.11932	−	10.6496i	0.0433403	−	0.412356i
$668$	0.853226	+	8.11791i	0.0330123	+	0.314091i
$669$	−1.44980	−	1.61016i	−0.0560525	−	0.0622526i
$670$	−12.5547	−	21.7453i	−0.485028	−	0.840094i
$671$		0			0
$672$	−2.33983	+	3.29485i	−0.0902609	+	0.127102i
$673$	12.2085	−	37.5740i	0.470604	−	1.44837i	−0.381191	−	0.924496i	$-0.624486\pi$
$673$	12.2085	−	37.5740i	0.470604	−	1.44837i	0.851795	−	0.523875i	$-0.175514\pi$
$674$	−49.4834	−	22.0314i	−1.90603	−	0.848619i
$675$	−0.503287	+	0.224078i	−0.0193715	+	0.00862476i
$676$	9.04413	+	1.92239i	0.347851	+	0.0739380i
$677$	−22.8400	+	25.3664i	−0.877813	+	0.974911i	−0.999845	−	0.0176157i	$-0.994392\pi$
$677$	−22.8400	+	25.3664i	−0.877813	+	0.974911i	0.122031	+	0.992526i	$0.461059\pi$
$678$	18.3385	+	13.3237i	0.704288	+	0.511695i
$679$	4.28674	+	2.41352i	0.164510	+	0.0926223i
$680$	−5.57637	+	17.1623i	−0.213844	+	0.658144i
$681$	6.58206	+	11.4005i	0.252225	+	0.436867i
$682$		0			0
$683$	−11.8931	+	20.5995i	−0.455079	+	0.788219i	−0.998693	−	0.0511160i	$-0.983722\pi$
$683$	−11.8931	+	20.5995i	−0.455079	+	0.788219i	0.543614	+	0.839335i	$0.317056\pi$
$684$	−70.8656	+	15.0629i	−2.70961	+	0.575946i
$685$	10.4170	−	7.56842i	0.398014	−	0.289174i
$686$	17.3864	−	42.7297i	0.663815	−	1.63143i
$687$	5.62259	+	17.3046i	0.214515	+	0.660210i
$688$	18.5709	−	20.6251i	0.708010	−	0.786325i
$689$	−0.914915	+	0.407347i	−0.0348555	+	0.0155187i
$690$	−2.65824	−	25.2915i	−0.101198	−	0.962831i
$691$	20.1131	−	4.27517i	0.765139	−	0.162635i	0.191220	−	0.981547i	$-0.438756\pi$
$691$	20.1131	−	4.27517i	0.765139	−	0.162635i	0.573919	+	0.818912i	$0.305422\pi$
$692$	27.0440			1.02806
$693$		0			0
$694$	9.81761			0.372671
$695$	12.0165	−	2.55419i	0.455812	−	0.0968858i
$696$	0.675632	+	6.42821i	0.0256098	+	0.243661i
$697$	−15.3221	+	6.82182i	−0.580365	+	0.258395i
$698$	23.5162	−	26.1173i	0.890100	−	0.988556i
$699$	−0.841764	−	2.59068i	−0.0318385	−	0.0979887i
$700$	−1.48229	+	0.499412i	−0.0560253	+	0.0188760i
$701$	19.4089	−	14.1014i	0.733063	−	0.532602i	−0.157468	−	0.987524i	$-0.550333\pi$
$701$	19.4089	−	14.1014i	0.733063	−	0.532602i	0.890531	+	0.454922i	$0.150333\pi$
$702$	−31.3719	+	6.66830i	−1.18406	+	0.251679i
$703$	−19.2134	+	33.2785i	−0.724646	+	1.25512i
$704$		0			0
$705$	1.17251	+	2.03084i	0.0441592	+	0.0764860i
$706$	3.82450	−	11.7706i	0.143937	−	0.442992i
$707$	−13.7647	+	8.14680i	−0.517675	+	0.306392i
$708$	−30.7234	−	22.3218i	−1.15465	−	0.838906i
$709$	−34.6019	+	38.4293i	−1.29950	+	1.44324i	−0.472191	+	0.881496i	$0.656537\pi$
$709$	−34.6019	+	38.4293i	−1.29950	+	1.44324i	−0.827310	+	0.561746i	$0.810130\pi$
$710$	60.8345	+	12.9308i	2.28308	+	0.485283i
$711$	−10.5390	+	4.69227i	−0.395244	+	0.175974i
$712$	−16.0738	−	7.15650i	−0.602390	−	0.268201i
$713$	−4.71410	+	14.5085i	−0.176544	+	0.543348i
$714$	6.97969	+	0.657359i	0.261208	+	0.0246010i
$715$		0			0
$716$	7.53841	+	13.0569i	0.281724	+	0.487960i
$717$	−6.20863	−	6.89539i	−0.231866	−	0.257513i
$718$	−1.06010	−	10.0862i	−0.0395628	−	0.376414i
$719$	−2.69528	+	25.6439i	−0.100517	+	0.956355i	0.821762	+	0.569831i	$0.192991\pi$
$719$	−2.69528	+	25.6439i	−0.100517	+	0.956355i	−0.922279	+	0.386525i	$0.873675\pi$
$720$	−8.93891	−	27.5111i	−0.333133	−	1.02528i
$721$	2.68602	+	0.840734i	0.100032	+	0.0313106i
$722$	58.1530	+	42.2506i	2.16423	+	1.57241i
$723$	0.293712	+	0.130769i	0.0109233	+	0.00486336i
$724$	34.3598	+	38.1604i	1.27697	+	1.41822i
$725$	−0.115989	+	0.200899i	−0.00430772	+	0.00746118i
$726$		0			0
$727$	32.7330			1.21400			0.606999	−	0.794702i	$-0.292373\pi$
$727$	32.7330			1.21400			0.606999	+	0.794702i	$0.292373\pi$
$728$	−47.4256	+	5.50383i	−1.75771	+	0.203985i
$729$	2.63979	−	1.91792i	0.0977698	−	0.0710340i
$730$	−4.91744	+	46.7863i	−0.182003	+	1.73164i
$731$	−7.68252	−	1.63297i	−0.284148	−	0.0603976i
$732$	−38.0941	−	8.09716i	−1.40800	−	0.299280i
$733$	0.970309	−	9.23188i	0.0358392	−	0.340987i	−0.961879	−	0.273475i	$-0.911827\pi$
$733$	0.970309	−	9.23188i	0.0358392	−	0.340987i	0.997718	−	0.0675125i	$-0.0215063\pi$
$734$	−36.3171	+	26.3859i	−1.34049	+	0.973921i
$735$	−5.71018	−	9.41405i	−0.210623	−	0.347242i
$736$	−13.8944			−0.512156
$737$		0			0
$738$	34.8995	−	60.4477i	1.28467	−	2.22511i
$739$	−33.5189	−	37.2266i	−1.23301	−	1.36940i	−0.905383	−	0.424595i	$-0.860417\pi$
$739$	−33.5189	−	37.2266i	−1.23301	−	1.36940i	−0.327631	−	0.944806i	$-0.606250\pi$
$740$	−47.0307	−	20.9394i	−1.72888	−	0.769749i
$741$	13.1244	+	9.53545i	0.482138	+	0.350293i
$742$	−1.47781	+	1.35985i	−0.0542522	+	0.0499218i
$743$	4.06909	+	12.5234i	0.149280	+	0.459438i	0.997537	−	0.0701482i	$-0.0223472\pi$
$743$	4.06909	+	12.5234i	0.149280	+	0.459438i	−0.848256	+	0.529586i	$0.822347\pi$
$744$	0.962512	−	9.15769i	0.0352874	−	0.335737i
$745$	0.230423	+	2.19233i	0.00844203	+	0.0803206i
$746$	−48.1954	−	53.5264i	−1.76456	−	1.95974i
$747$	−2.41142	−	4.17670i	−0.0882293	−	0.152818i
$748$		0			0
$749$	9.69992	−	13.6590i	0.354427	−	0.499090i
$750$	−6.22379	+	19.1549i	−0.227261	+	0.699437i
$751$	37.7419	+	16.8038i	1.37722	+	0.613179i	0.955890	−	0.293726i	$-0.0948955\pi$
$751$	37.7419	+	16.8038i	1.37722	+	0.613179i	0.421334	+	0.906906i	$0.361562\pi$
$752$	7.17512	−	3.19457i	0.261650	−	0.116494i
$753$	0.780726	+	0.165948i	0.0284512	+	0.00604750i
$754$	−9.03665	+	10.0362i	−0.329096	+	0.365498i
$755$	−26.4676	−	19.2298i	−0.963255	−	0.699846i
$756$	−37.5056	+	22.1981i	−1.36406	+	0.807337i
$757$	−14.0638	+	43.2839i	−0.511157	+	1.57318i	0.279010	+	0.960288i	$0.409994\pi$
$757$	−14.0638	+	43.2839i	−0.511157	+	1.57318i	−0.790167	+	0.612891i	$0.790006\pi$
$758$	5.36591	+	9.29402i	0.194898	+	0.337574i
$759$		0			0
$760$	−41.8676	+	72.5168i	−1.51870	+	2.63046i
$761$	−30.5886	+	6.50180i	−1.10883	+	0.235690i	−0.725706	−	0.688005i	$-0.758487\pi$
$761$	−30.5886	+	6.50180i	−1.10883	+	0.235690i	−0.383128	+	0.923695i	$0.625153\pi$
$762$	17.7974	−	12.9306i	0.644733	−	0.468426i
$763$	5.58612	+	4.92142i	0.202231	+	0.178167i
$764$	15.7328	+	48.4205i	0.569192	+	1.75179i
$765$	−5.47759	+	6.08348i	−0.198043	+	0.219949i
$766$	28.0998	−	12.5108i	1.01529	−	0.452035i
$767$	−4.34864	−	41.3745i	−0.157020	−	1.49395i
$768$	−22.7149	+	4.82820i	−0.819653	+	0.174223i
$769$	42.0467			1.51624			0.758121	−	0.652114i	$-0.226118\pi$
$769$	42.0467			1.51624			0.758121	+	0.652114i	$0.226118\pi$
$770$		0			0
$771$	16.2969			0.586920
$772$	49.1033	−	10.4372i	1.76727	−	0.375644i
$773$	−0.799069	−	7.60264i	−0.0287405	−	0.273448i	−0.999449	−	0.0331880i	$-0.989434\pi$
$773$	−0.799069	−	7.60264i	−0.0287405	−	0.273448i	0.970709	−	0.240260i	$-0.0772327\pi$
$774$	29.8601	−	13.2946i	1.07330	−	0.477864i
$775$	0.221133	−	0.245593i	0.00794332	−	0.00882195i
$776$	−3.15495	−	9.70994i	−0.113256	−	0.348567i
$777$	−2.06917	+	10.2801i	−0.0742311	+	0.368798i
$778$	59.2918	−	43.0780i	2.12571	−	1.54442i
$779$	−76.1256	+	16.1810i	−2.72748	+	0.579744i
$780$	−10.8670	+	18.8222i	−0.389102	+	0.673944i
$781$		0			0
$782$	12.0520	+	20.8747i	0.430980	+	0.746479i
$783$	−1.99737	+	6.14727i	−0.0713801	+	0.219685i
$784$	−33.3568	+	15.7245i	−1.19131	+	0.561589i
$785$	−11.3969	−	8.28030i	−0.406771	−	0.295537i
$786$	0.902714	−	1.00256i	0.0321987	−	0.0357603i
$787$	27.2936	+	5.80144i	0.972913	+	0.206799i	0.666834	−	0.745207i	$-0.267649\pi$
$787$	27.2936	+	5.80144i	0.972913	+	0.206799i	0.306080	+	0.952006i	$0.400983\pi$
$788$	46.7156	−	20.7991i	1.66417	−	0.740937i
$789$	5.99138	+	2.66754i	0.213299	+	0.0949668i
$790$	−7.85855	+	24.1861i	−0.279595	+	0.860504i
$791$	14.0573	+	30.6759i	0.499819	+	1.09071i
$792$		0			0
$793$	−21.3320	−	36.9481i	−0.757521	−	1.31206i
$794$	28.8333	+	32.0226i	1.02326	+	1.13644i
$795$	0.0501031	+	0.476699i	0.00177697	+	0.0169068i
$796$	−0.837165	+	7.96510i	−0.0296725	+	0.282315i
$797$	3.10747	+	9.56381i	0.110072	+	0.338767i	0.990887	−	0.134693i	$-0.0430047\pi$
$797$	3.10747	+	9.56381i	0.110072	+	0.338767i	−0.880815	+	0.473460i	$0.843005\pi$
$798$	31.0454	+	9.71734i	1.09900	+	0.343990i
$799$	−1.79818	−	1.30646i	−0.0636151	−	0.0462191i
$800$	0.274977	+	0.122428i	0.00972191	+	0.00432847i
$801$	−5.34082	−	5.93158i	−0.188709	−	0.209582i
$802$	−31.0740	+	53.8218i	−1.09726	+	1.90051i
$803$		0			0
$804$	13.7188			0.483824
$805$	15.0228	−	34.7483i	0.529483	−	1.22472i
$806$	15.5650	−	11.3087i	0.548255	−	0.398331i
$807$	−1.16451	+	11.0796i	−0.0409927	+	0.390020i
$808$	32.4697	+	6.90165i	1.14228	+	0.242799i
$809$	−37.7297	−	8.01969i	−1.32651	−	0.281957i	−0.510438	−	0.859915i	$-0.670517\pi$
$809$	−37.7297	−	8.01969i	−1.32651	−	0.281957i	−0.816067	+	0.577957i	$0.803850\pi$
$810$	2.68437	−	25.5400i	0.0943190	−	0.897386i
$811$	−10.0124	+	7.27443i	−0.351583	+	0.255440i	−0.749533	−	0.661967i	$-0.769722\pi$
$811$	−10.0124	+	7.27443i	−0.351583	+	0.255440i	0.397950	+	0.917407i	$0.369722\pi$
$812$	−7.28248	+	16.8447i	−0.255565	+	0.591132i
$813$	−19.7968			−0.694303
$814$		0			0
$815$	−10.9616	+	18.9860i	−0.383968	+	0.665051i
$816$	−3.74997	−	4.16476i	−0.131275	−	0.145796i
$817$	−33.2942	−	14.8235i	−1.16482	−	0.518609i
$818$	−77.7010	−	56.4531i	−2.71675	−	1.97383i
$819$	−20.6696	−	6.46967i	−0.722254	−	0.226069i
$820$	−32.2201	−	99.1632i	−1.12517	−	3.46293i
$821$	−3.10848	+	29.5752i	−0.108487	+	1.03218i	0.795888	+	0.605443i	$0.207004\pi$
$821$	−3.10848	+	29.5752i	−0.108487	+	1.03218i	−0.904375	+	0.426738i	$0.859662\pi$
$822$	1.08517	+	10.3247i	0.0378496	+	0.360115i
$823$	27.2851	+	30.3032i	0.951100	+	1.05630i	0.998350	+	0.0574204i	$0.0182875\pi$
$823$	27.2851	+	30.3032i	0.951100	+	1.05630i	−0.0472501	+	0.998883i	$0.515046\pi$
$824$	−2.92056	−	5.05855i	−0.101742	−	0.176223i
$825$		0			0
$826$	−34.7537	−	75.8398i	−1.20923	−	2.63880i
$827$	−5.82222	+	17.9190i	−0.202459	+	0.623103i	0.797350	+	0.603518i	$0.206235\pi$
$827$	−5.82222	+	17.9190i	−0.202459	+	0.623103i	−0.999808	+	0.0195857i	$0.993765\pi$
$828$	−62.0993	−	27.6484i	−2.15810	−	0.960848i
$829$	−28.4484	+	12.6660i	−0.988053	+	0.439909i	−0.836159	−	0.548487i	$-0.815204\pi$
$829$	−28.4484	+	12.6660i	−0.988053	+	0.439909i	−0.151894	+	0.988397i	$0.548537\pi$
$830$	−10.3992	−	2.21041i	−0.360960	−	0.0767244i
$831$	−7.07217	+	7.85444i	−0.245331	+	0.272467i
$832$	−13.8375	−	10.0535i	−0.479728	−	0.348543i
$833$	8.57364	+	5.95011i	0.297059	+	0.206159i
$834$	−3.06078	+	9.42012i	−0.105986	+	0.326192i
$835$	2.13986	+	3.70635i	0.0740530	+	0.128264i
$836$		0			0
$837$	4.60407	−	7.97448i	0.159140	−	0.275638i
$838$	2.21464	−	0.470737i	0.0765036	−	0.0162613i
$839$	−8.29961	+	6.03002i	−0.286534	+	0.208179i	−0.721763	−	0.692141i	$-0.756668\pi$
$839$	−8.29961	+	6.03002i	−0.286534	+	0.208179i	0.435228	+	0.900320i	$0.356668\pi$
$840$	−4.50890	+	22.4013i	−0.155572	+	0.772919i
$841$	−8.12045	−	24.9922i	−0.280015	−	0.861799i
$842$	−25.9226	+	28.7900i	−0.893353	+	0.992169i
$843$	−9.92289	+	4.41796i	−0.341762	+	0.152162i
$844$	7.13921	+	67.9250i	0.245742	+	2.33808i
$845$	4.74191	−	1.00792i	0.163127	−	0.0346736i
$846$	9.24992			0.318019
$847$		0			0
$848$	1.60540			0.0551297
$849$	15.1575	−	3.22182i	0.520203	−	0.110573i
$850$	−0.0545821	−	0.519314i	−0.00187215	−	0.0178123i
$851$	−32.9374	+	14.6647i	−1.12908	+	0.502699i
$852$	−22.7372	+	25.2522i	−0.778964	+	0.865127i
$853$	0.940756	+	2.89535i	0.0322109	+	0.0991348i	0.965869	−	0.259030i	$-0.0834027\pi$
$853$	0.940756	+	2.89535i	0.0322109	+	0.0991348i	−0.933659	+	0.358164i	$0.883403\pi$
$854$	−64.1931	−	56.5547i	−2.19664	−	1.93526i
$855$	−30.7309	+	22.3273i	−1.05097	+	0.763577i
$856$	−34.0083	+	7.22868i	−1.16238	+	0.247071i
$857$	−24.7766	+	42.9143i	−0.846352	+	1.46592i	0.0380904	+	0.999274i	$0.487873\pi$
$857$	−24.7766	+	42.9143i	−0.846352	+	1.46592i	−0.884442	+	0.466650i	$0.845461\pi$
$858$		0			0
$859$	−18.4373	−	31.9344i	−0.629074	−	1.08959i	−0.987738	−	0.156121i	$-0.950101\pi$
$859$	−18.4373	−	31.9344i	−0.629074	−	1.08959i	0.358664	−	0.933467i	$-0.383232\pi$
$860$	15.0882	−	46.4368i	0.514505	−	1.58348i
$861$	−18.2768	+	10.8173i	−0.622872	+	0.368654i
$862$	7.12634	+	5.17759i	0.242724	+	0.176349i
$863$	−31.0631	+	34.4990i	−1.05740	+	1.17436i	−0.0731955	+	0.997318i	$0.523320\pi$
$863$	−31.0631	+	34.4990i	−1.05740	+	1.17436i	−0.984203	+	0.177043i	$0.943347\pi$
$864$	8.20352	+	1.74371i	0.279090	+	0.0593223i
$865$	12.9535	−	5.76728i	0.440433	−	0.196093i
$866$	−40.1531	−	17.8773i	−1.36446	−	0.607495i
$867$	3.25833	−	10.0281i	0.110659	−	0.340573i
$868$	15.1372	−	21.3157i	0.513792	−	0.723501i
$869$		0			0
$870$	3.23181	+	5.59766i	0.109569	+	0.189778i
$871$	10.0562	+	11.1685i	0.340741	+	0.378431i
$872$	−1.61503	−	15.3659i	−0.0546917	−	0.520356i
$873$	0.484121	−	4.60611i	0.0163850	−	0.155893i
$874$	34.5630	+	106.374i	1.16911	+	3.59815i
$875$	−22.0624	+	20.3014i	−0.745845	+	0.686312i
$876$	−20.7942	−	15.1079i	−0.702572	−	0.510448i
$877$	35.6566	+	15.8753i	1.20404	+	0.536072i	0.907946	−	0.419088i	$-0.137650\pi$
$877$	35.6566	+	15.8753i	1.20404	+	0.536072i	0.296091	+	0.955160i	$0.404317\pi$
$878$	−25.0461	−	27.8165i	−0.845265	−	0.938762i
$879$	3.96997	−	6.87620i	0.133904	−	0.231928i
$880$		0			0
$881$	−44.0049			−1.48256			−0.741281	−	0.671194i	$-0.765782\pi$
$881$	−44.0049			−1.48256			−0.741281	+	0.671194i	$0.765782\pi$
$882$	−43.4207	+	0.939343i	−1.46205	+	0.0316293i
$883$	18.8983	−	13.7304i	0.635978	−	0.462065i	−0.222488	−	0.974935i	$-0.571418\pi$
$883$	18.8983	−	13.7304i	0.635978	−	0.462065i	0.858466	+	0.512871i	$0.171418\pi$
$884$	2.15330	−	20.4873i	0.0724234	−	0.689063i
$885$	−19.4761	−	4.13977i	−0.654682	−	0.139157i
$886$	32.2162	+	6.84775i	1.08232	+	0.230055i
$887$	−4.38158	+	41.6880i	−0.147119	+	1.39975i	0.633018	+	0.774137i	$0.281816\pi$
$887$	−4.38158	+	41.6880i	−0.147119	+	1.39975i	−0.780137	+	0.625608i	$0.784851\pi$
$888$	17.6065	−	12.7918i	0.590834	−	0.429266i
$889$	32.5294	−	3.77510i	1.09100	−	0.126613i
$890$	−17.5949			−0.589783
$891$		0			0
$892$	−6.38343	+	11.0564i	−0.213733	+	0.370196i
$893$	−6.90122	−	7.66458i	−0.230940	−	0.256485i
$894$	−1.62367	−	0.722903i	−0.0543036	−	0.0241775i
$895$	6.39520	+	4.64638i	0.213768	+	0.155311i
$896$	−43.5420	−	13.6288i	−1.45464	−	0.455308i
$897$	4.70360	+	14.4762i	0.157049	+	0.483346i
$898$	−2.57987	+	24.5459i	−0.0860915	+	0.819106i
$899$	−0.405291	−	3.85608i	−0.0135172	−	0.128608i
$900$	0.985356	+	1.09435i	0.0328452	+	0.0364783i
$901$	−0.227159	−	0.393451i	−0.00756776	−	0.0131078i
$902$		0			0
$903$	−9.90170	−	0.932559i	−0.329508	−	0.0310336i
$904$	21.6403	−	66.6020i	0.719746	−	2.21515i
$905$	24.5955	+	10.9506i	0.817584	+	0.364012i
$906$	24.0970	−	10.7287i	0.800570	−	0.356437i
$907$	20.0697	+	4.26595i	0.666405	+	0.141649i	0.528679	−	0.848822i	$-0.322687\pi$
$907$	20.0697	+	4.26595i	0.666405	+	0.141649i	0.137726	+	0.990470i	$0.456021\pi$
$908$	51.9027	−	57.6438i	1.72245	−	1.91298i
$909$	12.1826	+	8.85120i	0.404072	+	0.293576i
$910$	−41.0869	+	24.3177i	−1.36202	+	0.806125i
$911$	8.55220	−	26.3210i	0.283347	−	0.872052i	−0.703542	−	0.710653i	$-0.748399\pi$
$911$	8.55220	−	26.3210i	0.283347	−	0.872052i	0.986889	−	0.161399i	$-0.0516006\pi$
$912$	−13.0025	−	22.5209i	−0.430554	−	0.745742i
$913$		0			0
$914$	12.8840	−	22.3158i	0.426165	−	0.738140i
$915$	−19.9731	+	4.24541i	−0.660289	+	0.140349i
$916$	86.7360	−	63.0174i	2.86584	−	2.08215i
$917$	1.90315	−	0.641208i	0.0628476	−	0.0211746i
$918$	−4.49602	−	13.8373i	−0.148391	−	0.456700i
$919$	0.644677	−	0.715986i	0.0212659	−	0.0236182i	−0.732418	−	0.680855i	$-0.761608\pi$
$919$	0.644677	−	0.715986i	0.0212659	−	0.0236182i	0.753684	+	0.657237i	$0.228275\pi$
$920$	−71.7735	+	31.9556i	−2.36630	+	1.05355i
$921$	1.86354	+	17.7304i	0.0614058	+	0.584237i
$922$	−37.3681	+	7.94283i	−1.23065	+	0.261583i
$923$	−37.2249			−1.22527
$924$		0			0
$925$	0.781061			0.0256811
$926$	−61.2307	+	13.0150i	−2.01217	+	0.427699i
$927$	−0.276974	−	2.63523i	−0.00909703	−	0.0865525i
$928$	3.22617	−	1.43638i	0.105904	−	0.0471515i
$929$	17.6195	−	19.5685i	0.578078	−	0.642021i	−0.381197	−	0.924494i	$-0.624488\pi$
$929$	17.6195	−	19.5685i	0.578078	−	0.642021i	0.959275	+	0.282473i	$0.0911548\pi$
$930$	−2.84547	−	8.75746i	−0.0933067	−	0.287168i
$931$	33.1738	+	35.2780i	1.08723	+	1.15619i
$932$	−12.9853	+	9.43439i	−0.425349	+	0.309034i
$933$	24.2472	−	5.15389i	0.793817	−	0.168731i
$934$	−0.929110	+	1.60927i	−0.0304014	+	0.0526568i
$935$		0			0
$936$	22.4745	+	38.9269i	0.734601	+	1.27237i
$937$	−6.60878	+	20.3397i	−0.215899	+	0.664470i	0.783189	+	0.621784i	$0.213592\pi$
$937$	−6.60878	+	20.3397i	−0.215899	+	0.664470i	−0.999089	+	0.0426865i	$0.986408\pi$
$938$	26.2604	+	14.7851i	0.857433	+	0.482751i
$939$	13.6866	+	9.94392i	0.446646	+	0.324508i
$940$	9.24578	−	10.2685i	0.301564	−	0.334921i
$941$	−14.4989	−	3.08184i	−0.472651	−	0.100465i	−0.0345735	−	0.999402i	$-0.511007\pi$
$941$	−14.4989	−	3.08184i	−0.472651	−	0.100465i	−0.438078	+	0.898937i	$0.644341\pi$
$942$	10.3761	−	4.61974i	0.338072	−	0.150519i
$943$	−66.7086	−	29.7006i	−2.17233	−	0.967184i
$944$	−20.6079	+	63.4246i	−0.670730	+	2.06429i
$945$	−13.2305	+	18.6307i	−0.430389	+	0.606056i
$946$		0			0
$947$	−15.8560	−	27.4634i	−0.515251	−	0.892442i	−0.999843	−	0.0177013i	$-0.994365\pi$
$947$	−15.8560	−	27.4634i	−0.515251	−	0.892442i	0.484592	−	0.874740i	$-0.338968\pi$
$948$	−9.29719	−	10.3256i	−0.301959	−	0.335359i
$949$	−2.94325	−	28.0031i	−0.0955419	−	0.909020i
$950$	0.253273	−	2.40973i	0.00821727	−	0.0781821i
$951$	−4.33869	−	13.3531i	−0.140692	−	0.433004i
$952$	−4.73190	−	21.1352i	−0.153362	−	0.684997i
$953$	−40.4201	−	29.3669i	−1.30933	−	0.951287i	−1.00000		0.000333943i	$-0.999894\pi$
$953$	−40.4201	−	29.3669i	−1.30933	−	0.951287i	−0.309335	−	0.950953i	$-0.600106\pi$
$954$	1.72724	+	0.769016i	0.0559214	+	0.0248978i
$955$	17.8616	+	19.8373i	0.577988	+	0.641921i
$956$	−27.3365	+	47.3481i	−0.884124	+	1.53135i
$957$		0			0
$958$	50.0988			1.61862
$959$	−6.13271	+	14.1852i	−0.198036	+	0.458064i
$960$	−6.62272	+	4.81169i	−0.213747	+	0.155296i
$961$	2.66300	−	25.3368i	0.0859033	−	0.817315i
$962$	44.4774	+	9.45397i	1.43401	+	0.304808i
$963$	−15.4274	−	3.27920i	−0.497142	−	0.105671i
$964$	0.198022	−	1.88405i	0.00637786	−	0.0606813i
$965$	21.2937	−	15.4708i	0.685468	−	0.498022i
$966$	18.2066	+	24.4977i	0.585788	+	0.788199i
$967$	−52.4581			−1.68694			−0.843469	−	0.537178i	$-0.819490\pi$
$967$	−52.4581			−1.68694			−0.843469	+	0.537178i	$0.819490\pi$
$968$		0			0
$969$	−3.67961	+	6.37327i	−0.118206	+	0.204739i
$970$	−6.83158	−	7.58724i	−0.219349	−	0.243612i
$971$	28.1615	+	12.5383i	0.903745	+	0.402373i	0.805367	−	0.592776i	$-0.201968\pi$
$971$	28.1615	+	12.5383i	0.903745	+	0.402373i	0.0983775	+	0.995149i	$0.468635\pi$
$972$	51.3311	+	37.2942i	1.64645	+	1.19621i
$973$	−10.8500	+	9.98397i	−0.347835	+	0.320071i
$974$	3.27124	+	10.0678i	0.104817	+	0.322595i
$975$	0.0344674	−	0.327935i	0.00110384	−	0.0105023i
$976$	7.14872	+	68.0155i	0.228825	+	2.17712i
$977$	16.5513	+	18.3821i	0.529523	+	0.588095i	0.947257	−	0.320474i	$-0.103842\pi$
$977$	16.5513	+	18.3821i	0.529523	+	0.588095i	−0.417734	+	0.908569i	$0.637176\pi$
$978$	−8.83791	−	15.3077i	−0.282605	−	0.489487i
$979$		0			0
$980$	−42.3585	+	49.1409i	−1.35309	+	1.56975i
$981$	2.16589	−	6.66593i	0.0691516	−	0.212827i
$982$	−69.0117	−	30.7260i	−2.20225	−	0.980505i
$983$	11.1670	−	4.97188i	0.356173	−	0.158578i	−0.220847	−	0.975308i	$-0.570882\pi$
$983$	11.1670	−	4.97188i	0.356173	−	0.158578i	0.577020	+	0.816730i	$0.304215\pi$
$984$	43.1133	+	9.16402i	1.37440	+	0.292138i
$985$	17.9403	−	19.9247i	0.571624	−	0.634853i
$986$	−4.95637	−	3.60101i	−0.157843	−	0.114680i
$987$	−2.45252	−	1.38082i	−0.0780646	−	0.0439519i
$988$	29.5387	−	90.9109i	0.939752	−	2.89226i
$989$	−17.0975	−	29.6138i	−0.543670	−	0.941665i
$990$		0			0
$991$	−2.30008	+	3.98386i	−0.0730645	+	0.126552i	−0.900243	−	0.435388i	$-0.856611\pi$
$991$	−2.30008	+	3.98386i	−0.0730645	+	0.126552i	0.827178	+	0.561939i	$0.189945\pi$
$992$	−4.92104	+	1.04600i	−0.156243	+	0.0332105i
$993$	−16.2730	+	11.8230i	−0.516408	+	0.375192i
$994$	−70.7385	+	23.8332i	−2.24369	+	0.755942i
$995$	1.29761	+	3.99365i	0.0411371	+	0.126607i
$996$	3.88674	−	4.31666i	0.123156	−	0.136779i
$997$	−31.4957	+	14.0228i	−0.997479	+	0.444106i	−0.839514	−	0.543339i	$-0.817160\pi$
$997$	−31.4957	+	14.0228i	−0.997479	+	0.444106i	−0.157965	+	0.987445i	$0.550493\pi$
$998$	3.76002	+	35.7742i	0.119021	+	1.13241i
$999$	21.2872	−	4.52474i	0.673498	−	0.143156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.e.130.3		24
7.2	even	3	inner	847.2.n.e.9.1		24
11.2	odd	10		847.2.n.d.487.3		24
11.3	even	5	inner	847.2.n.e.81.3		24
11.4	even	5		77.2.e.b.67.3	yes	6
11.5	even	5	inner	847.2.n.e.753.1		24
11.6	odd	10		847.2.n.d.753.3		24
11.7	odd	10		847.2.e.d.606.1		6
11.8	odd	10		847.2.n.d.81.1		24
11.9	even	5	inner	847.2.n.e.487.1		24
11.10	odd	2		847.2.n.d.130.1		24
33.26	odd	10		693.2.i.g.298.1		6
44.15	odd	10		1232.2.q.k.529.2		6
77.2	odd	30		847.2.n.d.366.1		24
77.4	even	15		539.2.a.h.1.1		3
77.9	even	15	inner	847.2.n.e.366.3		24
77.16	even	15	inner	847.2.n.e.632.3		24
77.18	odd	30		5929.2.a.v.1.3		3
77.26	odd	30		539.2.e.l.177.3		6
77.30	odd	30		847.2.n.d.807.3		24
77.37	even	15		77.2.e.b.23.3	✓	6
77.48	odd	10		539.2.e.l.67.3		6
77.51	odd	30		847.2.e.d.485.1		6
77.58	even	15	inner	847.2.n.e.807.1		24
77.59	odd	30		539.2.a.i.1.1		3
77.65	odd	6		847.2.n.d.9.3		24
77.72	odd	30		847.2.n.d.632.1		24
77.73	even	30		5929.2.a.w.1.3		3
231.59	even	30		4851.2.a.bn.1.3		3
231.158	odd	30		4851.2.a.bo.1.3		3
231.191	odd	30		693.2.i.g.100.1		6
308.59	even	30		8624.2.a.ck.1.2		3
308.191	odd	30		1232.2.q.k.177.2		6
308.235	odd	30		8624.2.a.cl.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.3	✓	6	77.37	even	15
77.2.e.b.67.3	yes	6	11.4	even	5
539.2.a.h.1.1		3	77.4	even	15
539.2.a.i.1.1		3	77.59	odd	30
539.2.e.l.67.3		6	77.48	odd	10
539.2.e.l.177.3		6	77.26	odd	30
693.2.i.g.100.1		6	231.191	odd	30
693.2.i.g.298.1		6	33.26	odd	10
847.2.e.d.485.1		6	77.51	odd	30
847.2.e.d.606.1		6	11.7	odd	10
847.2.n.d.9.3		24	77.65	odd	6
847.2.n.d.81.1		24	11.8	odd	10
847.2.n.d.130.1		24	11.10	odd	2
847.2.n.d.366.1		24	77.2	odd	30
847.2.n.d.487.3		24	11.2	odd	10
847.2.n.d.632.1		24	77.72	odd	30
847.2.n.d.753.3		24	11.6	odd	10
847.2.n.d.807.3		24	77.30	odd	30
847.2.n.e.9.1		24	7.2	even	3	inner
847.2.n.e.81.3		24	11.3	even	5	inner
847.2.n.e.130.3		24	1.1	even	1	trivial
847.2.n.e.366.3		24	77.9	even	15	inner
847.2.n.e.487.1		24	11.9	even	5	inner
847.2.n.e.632.3		24	77.16	even	15	inner
847.2.n.e.753.1		24	11.5	even	5	inner
847.2.n.e.807.1		24	77.58	even	15	inner
1232.2.q.k.177.2		6	308.191	odd	30
1232.2.q.k.529.2		6	44.15	odd	10
4851.2.a.bn.1.3		3	231.59	even	30
4851.2.a.bo.1.3		3	231.158	odd	30
5929.2.a.v.1.3		3	77.18	odd	30
5929.2.a.w.1.3		3	77.73	even	30
8624.2.a.ck.1.2		3	308.59	even	30
8624.2.a.cl.1.2		3	308.235	odd	30

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.43643 - 0.517880i) q^{2} +(0.0745850 + 0.709629i) q^{3} +(3.84091 - 1.71008i) q^{4} +(1.47503 - 1.63819i) q^{5} +(0.549224 + 1.69034i) q^{6} +(-0.522062 + 2.59373i) q^{7} +(4.44220 - 3.22745i) q^{8} +(2.43643 - 0.517880i) q^{9} +O(q^{10})\)	\(q+(2.43643 - 0.517880i) q^{2} +(0.0745850 + 0.709629i) q^{3} +(3.84091 - 1.71008i) q^{4} +(1.47503 - 1.63819i) q^{5} +(0.549224 + 1.69034i) q^{6} +(-0.522062 + 2.59373i) q^{7} +(4.44220 - 3.22745i) q^{8} +(2.43643 - 0.517880i) q^{9} +(2.74543 - 4.75523i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-1.01557 + 3.12561i) q^{13} +(0.0712722 + 6.58982i) q^{14} +(1.27252 + 0.924542i) q^{15} +(3.52511 - 3.91503i) q^{16} +(-1.45828 - 0.309968i) q^{17} +(5.66800 - 2.52356i) q^{18} +(-6.31985 - 2.81378i) q^{19} +(2.86403 - 8.81457i) q^{20} +(-1.87953 - 0.177017i) q^{21} +(-3.24543 - 5.62125i) q^{23} +(2.62161 + 2.91160i) q^{24} +(0.0146981 + 0.139844i) q^{25} +(-0.855683 + 8.14128i) q^{26} +(1.21071 + 3.72618i) q^{27} +(2.43031 + 10.8551i) q^{28} +(1.33468 + 0.969699i) q^{29} +(3.57922 + 1.59357i) q^{30} +(-1.57262 - 1.74658i) q^{31} +(1.07031 - 1.85383i) q^{32} -3.71354 q^{34} +(3.47897 + 4.68108i) q^{35} +(8.47250 - 6.15563i) q^{36} +(0.580619 - 5.52422i) q^{37} +(-16.8551 - 3.58266i) q^{38} +(-2.29377 - 0.487556i) q^{39} +(1.26522 - 12.0378i) q^{40} +(9.10137 - 6.61254i) q^{41} +(-4.67101 + 0.542079i) q^{42} +5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(-10.8184 - 12.0151i) q^{46} +(1.36197 + 0.606389i) q^{47} +(3.04114 + 2.20952i) q^{48} +(-6.45490 - 2.70818i) q^{49} +(0.108233 + 0.333107i) q^{50} +(0.111196 - 1.05796i) q^{51} +(1.44433 + 13.7419i) q^{52} +(0.203907 + 0.226462i) q^{53} +(4.87953 + 8.45159i) q^{54} +(6.05203 + 13.2068i) q^{56} +(1.52537 - 4.69462i) q^{57} +(3.75403 + 1.67140i) q^{58} +(-11.5643 + 5.14877i) q^{59} +(6.46869 + 1.37496i) q^{60} +(-8.68647 + 9.64730i) q^{61} +(-4.73611 - 3.44098i) q^{62} +(0.0712722 + 6.58982i) q^{63} +(-1.60825 + 4.94968i) q^{64} +(3.62234 + 6.27408i) q^{65} +(2.28646 - 3.96027i) q^{67} +(-6.13121 + 1.30323i) q^{68} +(3.74694 - 2.72231i) q^{69} +(10.9005 + 9.60344i) q^{70} +(3.50016 + 10.7724i) q^{71} +(9.15169 - 10.1640i) q^{72} +(-7.82697 + 3.48479i) q^{73} +(-1.44624 - 13.7601i) q^{74} +(-0.0981408 + 0.0208605i) q^{75} -29.0858 q^{76} -5.84111 q^{78} +(-4.53027 + 0.962938i) q^{79} +(-1.21391 - 11.5496i) q^{80} +(4.27265 - 1.90230i) q^{81} +(18.7504 - 20.8244i) q^{82} +(-0.598322 - 1.84145i) q^{83} +(-7.52181 + 2.53424i) q^{84} +(-2.65880 + 1.93173i) q^{85} +(12.8356 - 2.72829i) q^{86} +(-0.588580 + 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} +(4.22642 - 13.0076i) q^{90} +(-7.57681 - 4.26589i) q^{91} +(-22.0782 - 16.0408i) q^{92} +(1.12213 - 1.24625i) q^{93} +(3.63239 + 0.772088i) q^{94} +(-13.9315 + 6.20270i) q^{95} +(1.39536 + 0.621253i) q^{96} +(0.574582 - 1.76838i) q^{97} +(-17.1294 - 3.25544i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8}+O(q^{10}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8	\( 24 q - q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} + 36 q^{10} + 36 q^{12} + 22 q^{13} - 12 q^{14} + 14 q^{15} + 2 q^{16} - 3 q^{17} + 10 q^{18} - 11 q^{19} - 28 q^{20} + 40 q^{21} - 48 q^{23} + 2 q^{24} + 3 q^{25} + q^{26} - 4 q^{27} - 13 q^{28} + 18 q^{29} + 2 q^{30} - 3 q^{31} + 12 q^{32} - 80 q^{34} - 9 q^{35} + 18 q^{36} - 4 q^{37} + 8 q^{38} - 5 q^{39} - 3 q^{40} + 10 q^{41} + 2 q^{42} + 16 q^{43} + 36 q^{45} - 10 q^{46} - 3 q^{47} - 20 q^{48} + 24 q^{49} + 6 q^{50} + 2 q^{51} - 7 q^{52} + 17 q^{53} + 32 q^{54} + 12 q^{56} - 40 q^{57} - 13 q^{58} + 8 q^{59} + 6 q^{60} - 24 q^{61} - 26 q^{62} - 12 q^{63} + 14 q^{64} - 60 q^{65} + 64 q^{67} + 5 q^{68} + 6 q^{69} + 27 q^{70} - 14 q^{71} + 10 q^{72} - 20 q^{73} + 22 q^{74} + 25 q^{75} - 312 q^{76} - 48 q^{78} + 3 q^{79} + 9 q^{80} - 17 q^{81} + 41 q^{82} + 22 q^{83} - 12 q^{84} - 22 q^{85} - 21 q^{86} - 120 q^{87} - 4 q^{89} - 20 q^{90} + 15 q^{91} - 50 q^{92} - 26 q^{93} - 10 q^{94} - 17 q^{95} + 27 q^{96} - 18 q^{97} - 96 q^{98}+O(q^{100}) \) 24 * q - q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 + 36 * q^10 + 36 * q^12 + 22 * q^13 - 12 * q^14 + 14 * q^15 + 2 * q^16 - 3 * q^17 + 10 * q^18 - 11 * q^19 - 28 * q^20 + 40 * q^21 - 48 * q^23 + 2 * q^24 + 3 * q^25 + q^26 - 4 * q^27 - 13 * q^28 + 18 * q^29 + 2 * q^30 - 3 * q^31 + 12 * q^32 - 80 * q^34 - 9 * q^35 + 18 * q^36 - 4 * q^37 + 8 * q^38 - 5 * q^39 - 3 * q^40 + 10 * q^41 + 2 * q^42 + 16 * q^43 + 36 * q^45 - 10 * q^46 - 3 * q^47 - 20 * q^48 + 24 * q^49 + 6 * q^50 + 2 * q^51 - 7 * q^52 + 17 * q^53 + 32 * q^54 + 12 * q^56 - 40 * q^57 - 13 * q^58 + 8 * q^59 + 6 * q^60 - 24 * q^61 - 26 * q^62 - 12 * q^63 + 14 * q^64 - 60 * q^65 + 64 * q^67 + 5 * q^68 + 6 * q^69 + 27 * q^70 - 14 * q^71 + 10 * q^72 - 20 * q^73 + 22 * q^74 + 25 * q^75 - 312 * q^76 - 48 * q^78 + 3 * q^79 + 9 * q^80 - 17 * q^81 + 41 * q^82 + 22 * q^83 - 12 * q^84 - 22 * q^85 - 21 * q^86 - 120 * q^87 - 4 * q^89 - 20 * q^90 + 15 * q^91 - 50 * q^92 - 26 * q^93 - 10 * q^94 - 17 * q^95 + 27 * q^96 - 18 * q^97 - 96 * q^98

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