LMFDB - Embedded newform 847.2.n.e.753.1

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			753.1
Character	$\chi$	$=$	847.753
Dual form			847.2.n.e.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.66671 + 1.85107i) q^{2} +(-0.651849 + 0.290222i) q^{3} +(-0.439480 - 4.18137i) q^{4} +(-2.15623 + 0.458321i) q^{5} +(0.549224 - 1.69034i) q^{6} +(2.30546 + 1.29802i) q^{7} +(4.44220 + 3.22745i) q^{8} +(-1.66671 + 1.85107i) q^{9} +O(q^{10})$	\(q+(-1.66671 + 1.85107i) q^{2} +(-0.651849 + 0.290222i) q^{3} +(-0.439480 - 4.18137i) q^{4} +(-2.15623 + 0.458321i) q^{5} +(0.549224 - 1.69034i) q^{6} +(2.30546 + 1.29802i) q^{7} +(4.44220 + 3.22745i) q^{8} +(-1.66671 + 1.85107i) q^{9} +(2.74543 - 4.75523i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-1.01557 - 3.12561i) q^{13} +(-6.24527 + 2.10415i) q^{14} +(1.27252 - 0.924542i) q^{15} +(-5.15307 + 1.09532i) q^{16} +(0.997582 + 1.10793i) q^{17} +(-0.648537 - 6.17041i) q^{18} +(0.723122 - 6.88004i) q^{19} +(2.86403 + 8.81457i) q^{20} +(-1.87953 - 0.177017i) q^{21} +(-3.24543 - 5.62125i) q^{23} +(-3.83232 - 0.814585i) q^{24} +(-0.128457 + 0.0571928i) q^{25} +(7.47840 + 3.32960i) q^{26} +(1.21071 - 3.72618i) q^{27} +(4.41429 - 10.2104i) q^{28} +(1.33468 - 0.969699i) q^{29} +(-0.409536 + 3.89648i) q^{30} +(2.29889 + 0.488644i) q^{31} +(1.07031 - 1.85383i) q^{32} -3.71354 q^{34} +(-5.56601 - 1.74219i) q^{35} +(8.47250 + 6.15563i) q^{36} +(-5.07443 - 2.25928i) q^{37} +(11.5302 + 12.8056i) q^{38} +(1.56912 + 1.74269i) q^{39} +(-11.0576 - 4.92317i) q^{40} +(9.10137 + 6.61254i) q^{41} +(3.46030 - 3.18410i) q^{42} +5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(15.8145 + 3.36149i) q^{46} +(-0.155838 + 1.48270i) q^{47} +(3.04114 - 2.20952i) q^{48} +(3.63030 + 5.98506i) q^{49} +(0.108233 - 0.333107i) q^{50} +(-0.971818 - 0.432681i) q^{51} +(-12.6230 + 5.62013i) q^{52} +(-0.298076 - 0.0633579i) q^{53} +(4.87953 + 8.45159i) q^{54} +(6.05203 + 13.2068i) q^{56} +(1.52537 + 4.69462i) q^{57} +(-0.429539 + 4.08679i) q^{58} +(1.32320 + 12.5894i) q^{59} +(-4.42510 - 4.91457i) q^{60} +(12.6980 - 2.69905i) q^{61} +(-4.73611 + 3.44098i) q^{62} +(-6.24527 + 2.10415i) q^{63} +(-1.60825 - 4.94968i) q^{64} +(3.62234 + 6.27408i) q^{65} +(2.28646 - 3.96027i) q^{67} +(4.19424 - 4.65817i) q^{68} +(3.74694 + 2.72231i) q^{69} +(12.5019 - 7.39937i) q^{70} +(3.50016 - 10.7724i) q^{71} +(-13.3781 + 2.84361i) q^{72} +(0.895567 + 8.52075i) q^{73} +(12.6397 - 5.62756i) q^{74} +(0.0671361 - 0.0745622i) q^{75} -29.0858 q^{76} -5.84111 q^{78} +(3.09906 - 3.44186i) q^{79} +(10.6092 - 4.72352i) q^{80} +(-0.488879 - 4.65137i) q^{81} +(-27.4097 + 5.82610i) q^{82} +(-0.598322 + 1.84145i) q^{83} +(0.0858404 + 7.93679i) q^{84} +(-2.65880 - 1.93173i) q^{85} +(-8.78056 + 9.75180i) q^{86} +(-0.588580 + 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} +(4.22642 + 13.0076i) q^{90} +(1.71574 - 8.52421i) q^{91} +(-22.0782 + 16.0408i) q^{92} +(-1.64035 + 0.348666i) q^{93} +(-2.48484 - 2.75970i) q^{94} +(1.59405 + 15.1664i) q^{95} +(-0.159658 + 1.51904i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.66671	+	1.85107i	−1.17854	+	1.30891i	−0.237199	+	0.971461i	$0.576229\pi$
$2$	−1.66671	+	1.85107i	−1.17854	+	1.30891i	−0.941345	+	0.337445i	$0.890437\pi$
$3$	−0.651849	+	0.290222i	−0.376345	+	0.167560i	−0.586187	−	0.810176i	$-0.699372\pi$
$3$	−0.651849	+	0.290222i	−0.376345	+	0.167560i	0.209842	+	0.977735i	$0.432705\pi$
$4$	−0.439480	−	4.18137i	−0.219740	−	2.09068i
$5$	−2.15623	+	0.458321i	−0.964295	+	0.204967i	−0.663046	−	0.748578i	$-0.730737\pi$
$5$	−2.15623	+	0.458321i	−0.964295	+	0.204967i	−0.301249	+	0.953546i	$0.597404\pi$
$6$	0.549224	−	1.69034i	0.224220	−	0.690077i
$7$	2.30546	+	1.29802i	0.871382	+	0.490605i
$7$	2.30546	+	1.29802i	0.871382	+	0.490605i
$8$	4.44220	+	3.22745i	1.57056	+	1.14108i
$9$	−1.66671	+	1.85107i	−0.555571	+	0.617024i
$10$	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	−0.987377	−	0.158386i	$-0.949371\pi$
$13$	−1.01557	−	3.12561i	−0.281669	−	0.866889i	0.705708	−	0.708503i	$-0.250629\pi$
$14$	−6.24527	+	2.10415i	−1.66912	+	0.562358i
$15$	1.27252	−	0.924542i	0.328564	−	0.238716i
$16$	−5.15307	+	1.09532i	−1.28827	+	0.273830i
$17$	0.997582	+	1.10793i	0.241949	+	0.268712i	0.851873	−	0.523748i	$-0.175467\pi$
$17$	0.997582	+	1.10793i	0.241949	+	0.268712i	−0.609924	+	0.792460i	$0.708800\pi$
$18$	−0.648537	−	6.17041i	−0.152862	−	1.45438i
$19$	0.723122	−	6.88004i	0.165895	−	1.57839i	−0.522234	−	0.852802i	$-0.674901\pi$
$19$	0.723122	−	6.88004i	0.165895	−	1.57839i	0.688130	−	0.725588i	$-0.258432\pi$
$20$	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	$-0.403266\pi$
$24$	−3.83232	−	0.814585i	−0.782270	−	0.166277i
$25$	−0.128457	+	0.0571928i	−0.0256914	+	0.0114386i
$26$	7.47840	+	3.32960i	1.46664	+	0.652988i
$27$	1.21071	−	3.72618i	0.233001	−	0.717104i
$28$	4.41429	−	10.2104i	0.834223	−	1.92959i
$29$	1.33468	−	0.969699i	0.247843	−	0.180069i	−0.456927	−	0.889504i	$-0.651050\pi$
$29$	1.33468	−	0.969699i	0.247843	−	0.180069i	0.704770	+	0.709436i	$0.251050\pi$
$30$	−0.409536	+	3.89648i	−0.0747707	+	0.711396i
$31$	2.29889	+	0.488644i	0.412893	+	0.0877631i	0.409675	−	0.912232i	$-0.365642\pi$
$31$	2.29889	+	0.488644i	0.412893	+	0.0877631i	0.00321838	+	0.999995i	$0.498976\pi$
$32$	1.07031	−	1.85383i	0.189205	−	0.327713i
$33$		0			0
$34$	−3.71354			−0.636867
$35$	−5.56601	−	1.74219i	−0.940828	−	0.294483i
$36$	8.47250	+	6.15563i	1.41208	+	1.02594i
$37$	−5.07443	−	2.25928i	−0.834231	−	0.371423i	−0.0552509	−	0.998473i	$-0.517596\pi$
$37$	−5.07443	−	2.25928i	−0.834231	−	0.371423i	−0.778980	+	0.627049i	$0.784263\pi$
$38$	11.5302	+	12.8056i	1.87045	+	2.07734i
$39$	1.56912	+	1.74269i	0.251261	+	0.279053i
$40$	−11.0576	−	4.92317i	−1.74836	−	0.778421i
$41$	9.10137	+	6.61254i	1.42140	+	1.03270i	0.991539	+	0.129807i	$0.0414359\pi$
$41$	9.10137	+	6.61254i	1.42140	+	1.03270i	0.429857	+	0.902897i	$0.358564\pi$
$42$	3.46030	−	3.18410i	0.533936	−	0.491318i
$43$	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
$46$	15.8145	+	3.36149i	2.33173	+	0.495624i
$47$	−0.155838	+	1.48270i	−0.0227313	+	0.216274i	0.977260	+	0.212045i	$0.0680125\pi$
$47$	−0.155838	+	1.48270i	−0.0227313	+	0.216274i	−0.999991	+	0.00422804i	$0.998654\pi$
$48$	3.04114	−	2.20952i	0.438950	−	0.318916i
$49$	3.63030	+	5.98506i	0.518614	+	0.855009i
$50$	0.108233	−	0.333107i	0.0153065	−	0.0471085i
$51$	−0.971818	−	0.432681i	−0.136082	−	0.0605875i
$52$	−12.6230	+	5.62013i	−1.75050	+	0.779371i
$53$	−0.298076	−	0.0633579i	−0.0409438	−	0.00870288i	0.187394	−	0.982285i	$-0.439996\pi$
$53$	−0.298076	−	0.0633579i	−0.0409438	−	0.00870288i	−0.228338	+	0.973582i	$0.573329\pi$
$54$	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
$58$	−0.429539	+	4.08679i	−0.0564012	+	0.536622i
$59$	1.32320	+	12.5894i	0.172266	+	1.63900i	0.649601	+	0.760276i	$0.274936\pi$
$59$	1.32320	+	12.5894i	0.172266	+	1.63900i	−0.477335	+	0.878721i	$0.658397\pi$
$60$	−4.42510	−	4.91457i	−0.571278	−	0.634468i
$61$	12.6980	−	2.69905i	1.62582	−	0.345578i	0.697275	−	0.716803i	$-0.254396\pi$
$61$	12.6980	−	2.69905i	1.62582	−	0.345578i	0.928543	+	0.371225i	$0.121062\pi$
$62$	−4.73611	+	3.44098i	−0.601486	+	0.437005i
$63$	−6.24527	+	2.10415i	−0.786830	+	0.265098i
$64$	−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	$0.0765524\pi$
$68$	4.19424	−	4.65817i	0.508626	−	0.564886i
$69$	3.74694	+	2.72231i	0.451079	+	0.327728i
$70$	12.5019	−	7.39937i	1.49426	−	0.884394i
$71$	3.50016	−	10.7724i	0.415392	−	1.27845i	−0.496508	−	0.868032i	$-0.665385\pi$
$71$	3.50016	−	10.7724i	0.415392	−	1.27845i	0.911900	−	0.410413i	$-0.134615\pi$
$72$	−13.3781	+	2.84361i	−1.57663	+	0.335122i
$73$	0.895567	+	8.52075i	0.104818	+	0.997279i	0.912893	+	0.408199i	$0.133843\pi$
$73$	0.895567	+	8.52075i	0.104818	+	0.997279i	−0.808075	+	0.589080i	$0.799490\pi$
$74$	12.6397	−	5.62756i	1.46934	−	0.654190i
$75$	0.0671361	−	0.0745622i	0.00775221	−	0.00860970i
$76$	−29.0858			−3.33637
$77$		0			0
$78$	−5.84111			−0.661376
$79$	3.09906	−	3.44186i	0.348672	−	0.387239i	−0.543143	−	0.839640i	$-0.682766\pi$
$79$	3.09906	−	3.44186i	0.348672	−	0.387239i	0.891815	+	0.452401i	$0.149432\pi$
$80$	10.6092	−	4.72352i	1.18614	−	0.528105i
$81$	−0.488879	−	4.65137i	−0.0543199	−	0.516819i
$82$	−27.4097	+	5.82610i	−3.02689	+	0.643385i
$83$	−0.598322	+	1.84145i	−0.0656744	+	0.202125i	−0.978509	−	0.206205i	$-0.933889\pi$
$83$	−0.598322	+	1.84145i	−0.0656744	+	0.202125i	0.912834	+	0.408330i	$0.133889\pi$
$84$	0.0858404	+	7.93679i	0.00936596	+	0.865975i
$85$	−2.65880	−	1.93173i	−0.288388	−	0.209526i
$86$	−8.78056	+	9.75180i	−0.946832	+	1.05156i
$87$	−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
$91$	1.71574	−	8.52421i	0.179858	−	0.893580i
$92$	−22.0782	+	16.0408i	−2.30181	+	1.67237i
$93$	−1.64035	+	0.348666i	−0.170096	+	0.0361550i
$94$	−2.48484	−	2.75970i	−0.256292	−	0.284641i
$95$	1.59405	+	15.1664i	0.163546	+	1.55604i
$96$	−0.159658	+	1.51904i	−0.0162950	+	0.155037i
$97$	0.574582	+	1.76838i	0.0583400	+	0.179552i	0.975980	−	0.217861i	$-0.0699080\pi$
$97$	0.574582	+	1.76838i	0.0583400	+	0.179552i	−0.917640	+	0.397413i	$0.869908\pi$
$98$	−17.1294	−	3.25544i	−1.73034	−	0.328849i
$99$		0			0
$100$	0.295598	+	0.511992i	0.0295598	+	0.0511992i
$101$	−5.91341	−	1.25693i	−0.588406	−	0.125070i	−0.0959186	−	0.995389i	$-0.530579\pi$
$101$	−5.91341	−	1.25693i	−0.588406	−	0.125070i	−0.492487	+	0.870320i	$0.663912\pi$
$102$	2.42067	−	1.07775i	0.239682	−	0.106713i
$103$	−0.971818	−	0.432681i	−0.0957561	−	0.0426334i	0.358300	−	0.933607i	$-0.383357\pi$
$103$	−0.971818	−	0.432681i	−0.0957561	−	0.0426334i	−0.454056	+	0.890973i	$0.650023\pi$
$104$	5.57637	−	17.1623i	0.546808	−	1.68290i
$105$	4.13382	−	0.479737i	0.403420	−	0.0468175i
$106$	0.614087	−	0.446160i	0.0596454	−	0.0433349i
$107$	0.661872	−	6.29729i	0.0639856	−	0.608782i	−0.914802	−	0.403903i	$-0.867653\pi$
$107$	0.661872	−	6.29729i	0.0639856	−	0.608782i	0.978787	−	0.204879i	$-0.0656800\pi$
$108$	−16.1126	−	3.42484i	−1.55044	−	0.329556i
$109$	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
$112$	−13.3019	−	4.16356i	−1.25691	−	0.393420i
$113$	10.3181	+	7.49651i	0.970641	+	0.705212i	0.955598	−	0.294675i	$-0.0952113\pi$
$113$	10.3181	+	7.49651i	0.970641	+	0.705212i	0.0150435	+	0.999887i	$0.495211\pi$
$114$	−11.2324	−	5.00100i	−1.05201	−	0.468387i
$115$	9.57424	+	10.6333i	0.892802	+	0.991557i
$116$	−4.64123	−	5.15461i	−0.430928	−	0.478594i
$117$	7.47840	+	3.32960i	0.691378	+	0.307821i
$118$	−25.5092	−	18.5335i	−2.34832	−	1.70615i
$119$	0.861777	+	3.84916i	0.0789989	+	0.352852i
$120$	8.63671			0.788420
$121$		0			0
$122$	−16.1679	+	28.0035i	−1.46377	+	2.53532i
$123$	−7.85183	−	1.66896i	−0.707975	−	0.150485i
$124$	1.03289	−	9.82726i	0.0927560	−	0.882514i
$125$	9.16776	−	6.66077i	0.819990	−	0.595757i
$126$	6.51413	−	15.0675i	0.580325	−	1.34232i
$127$	−3.82486	+	11.7717i	−0.339401	+	1.04457i	0.625112	+	0.780535i	$0.285053\pi$
$127$	−3.82486	+	11.7717i	−0.339401	+	1.04457i	−0.964513	+	0.264034i	$0.914947\pi$
$128$	15.7538	+	7.01404i	1.39245	+	0.619960i
$129$	−3.43407	+	1.52894i	−0.302353	+	0.134616i
$130$	−17.6512	−	3.75187i	−1.54811	−	0.329061i
$131$	−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
$135$	−0.902782	+	8.58940i	−0.0776991	+	0.739258i
$136$	0.855683	+	8.14128i	0.0733743	+	0.698109i
$137$	−3.90847	−	4.34079i	−0.333923	−	0.370859i	0.552677	−	0.833395i	$-0.313606\pi$
$137$	−3.90847	−	4.34079i	−0.333923	−	0.370859i	−0.886600	+	0.462536i	$0.846940\pi$
$138$	−11.2843	+	2.39855i	−0.960582	+	0.204178i
$139$	4.50859	−	3.27568i	0.382414	−	0.277840i	−0.379926	−	0.925017i	$-0.624051\pi$
$139$	4.50859	−	3.27568i	0.382414	−	0.277840i	0.762340	+	0.647177i	$0.224051\pi$
$140$	−4.83857	+	24.0392i	−0.408934	+	2.03168i
$141$	−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
$145$	−2.43344	+	2.70260i	−0.202086	+	0.224439i
$146$	−17.2652	−	12.5439i	−1.42888	−	1.03814i
$147$	−4.10340	−	2.84777i	−0.338443	−	0.234880i
$148$	−7.21678	+	22.2110i	−0.593216	+	1.82573i
$149$	0.978148	−	0.207912i	0.0801330	−	0.0170328i	−0.167671	−	0.985843i	$-0.553625\pi$
$149$	0.978148	−	0.207912i	0.0801330	−	0.0170328i	0.247804	+	0.968810i	$0.420291\pi$
$150$	0.0261234	+	0.248547i	0.00213297	+	0.0202938i
$151$	13.5580	−	6.03642i	1.10334	−	0.491237i	0.227468	−	0.973786i	$-0.426955\pi$
$151$	13.5580	−	6.03642i	1.10334	−	0.491237i	0.875869	+	0.482548i	$0.160289\pi$
$152$	25.4172	−	28.2287i	2.06161	−	2.28965i
$153$	−3.71354			−0.300222
$154$		0			0
$155$	−5.18089			−0.416139
$156$	6.59722	−	7.32695i	0.528200	−	0.586626i
$157$	5.83804	−	2.59926i	0.465926	−	0.207444i	−0.160326	−	0.987064i	$-0.551255\pi$
$157$	5.83804	−	2.59926i	0.465926	−	0.207444i	0.626252	+	0.779620i	$0.284588\pi$
$158$	1.20588	+	11.4732i	0.0959347	+	0.912757i
$159$	0.212688	−	0.0452083i	0.0168673	−	0.00358525i
$160$	−1.45818	+	4.48782i	−0.115279	+	0.354793i
$161$	−0.185726	−	17.1722i	−0.0146373	−	1.35336i
$162$	9.42485	+	6.84755i	0.740486	+	0.537994i
$163$	6.65463	−	7.39071i	0.521230	−	0.578885i	−0.423846	−	0.905734i	$-0.639320\pi$
$163$	6.65463	−	7.39071i	0.521230	−	0.578885i	0.945077	+	0.326849i	$0.105987\pi$
$164$	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	0.925157	−	0.379584i	$-0.123933\pi$
$167$	−0.599940	−	1.84643i	−0.0464248	−	0.142881i	−0.971582	+	0.236704i	$0.923933\pi$
$168$	−7.77792	−	6.85242i	−0.600080	−	0.528676i
$169$	1.77916	−	1.29264i	0.136859	−	0.0994337i
$170$	8.00724	−	1.70199i	0.614127	−	0.130537i
$171$	11.5302	+	12.8056i	0.881738	+	0.979269i
$172$	−2.31526	−	22.0282i	−0.176537	−	1.67964i
$173$	−0.672360	+	6.39707i	−0.0511185	+	0.486360i	0.938773	+	0.344536i	$0.111964\pi$
$173$	−0.672360	+	6.39707i	−0.0511185	+	0.486360i	−0.989892	+	0.141825i	$0.954703\pi$
$174$	−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
$178$	7.80731	+	1.65949i	0.585182	+	0.124384i
$179$	−3.27594	+	1.45854i	−0.244855	+	0.109017i	−0.525495	−	0.850797i	$-0.676120\pi$
$179$	−3.27594	+	1.45854i	−0.244855	+	0.109017i	0.280640	+	0.959813i	$0.409453\pi$
$180$	−21.0899	−	9.38984i	−1.57195	−	0.699877i
$181$	3.77414	−	11.6156i	0.280530	−	0.863381i	−0.707174	−	0.707040i	$-0.750030\pi$
$181$	3.77414	−	11.6156i	0.280530	−	0.863381i	0.987703	−	0.156341i	$-0.0499699\pi$
$182$	12.9193	+	17.3834i	0.957641	+	1.28854i
$183$	−7.49389	+	5.44463i	−0.553964	+	0.402479i
$184$	3.72544	−	35.4452i	0.274643	−	2.61306i
$185$	11.9771	+	2.54581i	0.880574	+	0.187172i
$186$	2.08858	−	3.61753i	0.153142	−	0.265250i
$187$		0			0
$188$	6.26819			0.457155
$189$	7.62790	−	7.01904i	0.554848	−	0.510560i
$190$	−30.7309	−	22.3273i	−2.22945	−	1.61979i
$191$	11.0624	+	4.92530i	0.800447	+	0.356382i	0.765850	−	0.643019i	$-0.222319\pi$
$191$	11.0624	+	4.92530i	0.800447	+	0.356382i	0.0345971	+	0.999401i	$0.488985\pi$
$192$	2.48484	+	2.75970i	0.179328	+	0.199164i
$193$	−7.98938	−	8.87311i	−0.575088	−	0.638700i	0.383485	−	0.923547i	$-0.374724\pi$
$193$	−7.98938	−	8.87311i	−0.575088	−	0.638700i	−0.958573	+	0.284847i	$0.908057\pi$
$194$	−4.23107	−	1.88379i	−0.303773	−	0.135248i
$195$	−4.18210	−	3.03847i	−0.299486	−	0.217589i
$196$	23.4303	−	17.8099i	1.67359	−	1.27214i
$197$	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	$0.188174\pi$
$200$	−0.755219	−	0.160527i	−0.0534021	−	0.0113510i
$201$	−0.341072	+	3.24508i	−0.0240573	+	0.228890i
$202$	12.1826	−	8.85120i	0.857167	−	0.622768i
$203$	4.33573	−	0.503169i	0.304309	−	0.0353155i
$204$	−1.38211	+	4.25369i	−0.0967668	+	0.297818i
$205$	−22.6553	−	10.0868i	−1.58232	−	0.704493i
$206$	2.42067	−	1.07775i	0.168656	−	0.0750904i
$207$	15.8145	+	3.36149i	1.09919	+	0.233639i
$208$	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	−0.961271	−	0.275605i	$-0.911122\pi$
$211$	−5.01988	−	15.4496i	−0.345583	−	1.06360i	0.615688	−	0.787990i	$-0.288878\pi$
$212$	−0.133925	+	1.27421i	−0.00919799	+	0.0875130i
$213$	0.844805	+	8.03779i	0.0578851	+	0.550740i
$214$	10.5536	+	11.7209i	0.721428	+	0.801228i
$215$	−11.3594	+	2.41452i	−0.774707	+	0.164669i
$216$	17.4043	−	12.6449i	1.18421	−	0.860380i
$217$	4.66573	+	4.11055i	0.316731	+	0.279043i
$218$	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
$222$	−6.60594	+	7.33664i	−0.443362	+	0.492403i
$223$	−2.45662	−	1.78484i	−0.164507	−	0.119522i	0.502486	−	0.864585i	$-0.332419\pi$
$223$	−2.45662	−	1.78484i	−0.164507	−	0.119522i	−0.666993	+	0.745064i	$0.732419\pi$
$224$	4.87385	−	2.88464i	0.325648	−	0.192738i
$225$	0.108233	−	0.333107i	0.00721554	−	0.0222072i
$226$	−31.0738	+	6.60494i	−2.06700	+	0.439354i
$227$	−1.92845	−	18.3480i	−0.127996	−	1.21780i	−0.850328	−	0.526254i	$-0.823596\pi$
$227$	−1.92845	−	18.3480i	−0.127996	−	1.21780i	0.722332	−	0.691547i	$-0.243070\pi$
$228$	18.9596	−	8.44134i	1.25563	−	0.559041i
$229$	−17.0627	+	18.9501i	−1.12754	+	1.25226i	−0.163483	+	0.986546i	$0.552273\pi$
$229$	−17.0627	+	18.9501i	−1.12754	+	1.25226i	−0.964053	+	0.265710i	$0.914394\pi$
$230$	−35.6404			−2.35006
$231$		0			0
$232$	9.05855			0.594723
$233$	2.55448	−	2.83703i	0.167349	−	0.185860i	−0.653637	−	0.756808i	$-0.726758\pi$
$233$	2.55448	−	2.83703i	0.167349	−	0.185860i	0.820986	+	0.570948i	$0.193424\pi$
$234$	−18.6277	+	8.29358i	−1.21773	+	0.542168i
$235$	−0.343529	−	3.26846i	−0.0224093	−	0.213211i
$236$	52.0593	−	11.0655i	3.38877	−	0.720306i
$237$	−1.02122	+	3.14299i	−0.0663353	+	0.204159i
$238$	−8.56142	−	4.82024i	−0.554954	−	0.312450i
$239$	−10.5202	−	7.64340i	−0.680498	−	0.494411i	0.193025	−	0.981194i	$-0.438170\pi$
$239$	−10.5202	−	7.64340i	−0.680498	−	0.494411i	−0.873523	+	0.486783i	$0.838170\pi$
$240$	−5.54473	+	6.15804i	−0.357910	+	0.397500i
$241$	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
$245$	−10.5708	−	11.2413i	−0.675346	−	0.718182i
$246$	16.1761	−	11.7526i	1.03135	−	0.749320i
$247$	−22.2387	+	4.72699i	−1.41502	+	0.300771i
$248$	8.63506	+	9.59021i	0.548327	+	0.608979i
$249$	−0.144412	−	1.37399i	−0.00915177	−	0.0870732i
$250$	−2.95046	+	28.0718i	−0.186604	+	1.77542i
$251$	0.345668	+	1.06386i	0.0218184	+	0.0671501i	0.961373	−	0.275249i	$-0.0887604\pi$
$251$	0.345668	+	1.06386i	0.0218184	+	0.0671501i	−0.939554	+	0.342399i	$0.888760\pi$
$252$	11.5429	+	25.1890i	0.727134	+	1.58676i
$253$		0			0
$254$	−15.4153	−	26.7001i	−0.967243	−	1.67531i
$255$	2.29377	+	0.487556i	0.143642	+	0.0305319i
$256$	−29.7317	+	13.2374i	−1.85823	+	0.827337i
$257$	−20.8650	−	9.28971i	−1.30152	−	0.579476i	−0.365304	−	0.930888i	$-0.619035\pi$
$257$	−20.8650	−	9.28971i	−1.30152	−	0.579476i	−0.936221	+	0.351412i	$0.885702\pi$
$258$	2.89342	−	8.90502i	0.180136	−	0.554402i
$259$	−8.76630	−	11.7954i	−0.544712	−	0.732929i
$260$	24.6423	−	17.9037i	1.52825	−	1.11034i
$261$	−0.429539	+	4.08679i	−0.0265878	+	0.252966i
$262$	1.84938	+	0.393098i	0.114255	+	0.0242857i
$263$	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
$266$	9.96056	+	44.4893i	0.610721	+	2.72781i
$267$	1.84979	+	1.34395i	0.113205	+	0.0822483i
$268$	−17.5642	−	7.82009i	−1.07290	−	0.477688i
$269$	−10.4473	−	11.6029i	−0.636981	−	0.707440i	0.335074	−	0.942192i	$-0.391239\pi$
$269$	−10.4473	−	11.6029i	−0.636981	−	0.707440i	−0.972055	+	0.234752i	$0.924572\pi$
$270$	−14.3949	−	15.9872i	−0.876047	−	0.972949i
$271$	25.3459	+	11.2847i	1.53965	+	0.685497i	0.988819	−	0.149118i	$-0.0476435\pi$
$271$	25.3459	+	11.2847i	1.53965	+	0.685497i	0.550833	+	0.834616i	$0.314310\pi$
$272$	−6.35414	−	4.61655i	−0.385276	−	0.279920i
$273$	1.35551	+	6.05444i	0.0820392	+	0.366432i
$274$	14.5494			0.878962
$275$		0			0
$276$	9.73630	−	16.8638i	0.586056	−	1.01508i
$277$	−14.4887	−	3.07967i	−0.870541	−	0.185039i	−0.249079	−	0.968483i	$-0.580128\pi$
$277$	−14.4887	−	3.07967i	−0.870541	−	0.185039i	−0.621462	+	0.783444i	$0.713461\pi$
$278$	−1.45100	+	13.8054i	−0.0870252	+	0.827990i
$279$	−4.73611	+	3.44098i	−0.283543	+	0.206006i
$280$	−19.1025	−	25.7032i	−1.14159	−	1.53606i
$281$	4.70407	−	14.4776i	0.280621	−	0.863663i	−0.707056	−	0.707157i	$-0.749977\pi$
$281$	4.70407	−	14.4776i	0.280621	−	0.863663i	0.987677	−	0.156505i	$-0.0500228\pi$
$282$	2.42067	+	1.07775i	0.144149	+	0.0641791i
$283$	19.8397	−	8.83321i	1.17935	−	0.525080i	0.279018	−	0.960286i	$-0.409991\pi$
$283$	19.8397	−	8.83321i	1.17935	−	0.525080i	0.900331	+	0.435206i	$0.143324\pi$
$284$	−46.5815	−	9.90121i	−2.76410	−	0.587529i
$285$	−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
$289$	1.54465	−	14.6964i	0.0908618	−	0.864493i
$290$	−0.946877	−	9.00893i	−0.0556025	−	0.529023i
$291$	−0.887764	−	0.985962i	−0.0520417	−	0.0577981i
$292$	35.2348	−	7.48940i	2.06196	−	0.438284i
$293$	−9.00240	+	6.54062i	−0.525926	+	0.382107i	−0.818832	−	0.574034i	$-0.805378\pi$
$293$	−9.00240	+	6.54062i	−0.525926	+	0.382107i	0.292906	+	0.956141i	$0.405378\pi$
$294$	12.1106	−	2.84929i	0.706305	−	0.166174i
$295$	−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
$299$	−14.2739	+	15.8527i	−0.825480	+	0.916788i
$300$	−0.341277	−	0.247952i	−0.0197036	−	0.0143155i
$301$	12.1456	+	6.83821i	0.700061	+	0.394148i
$302$	−11.4235	+	35.1579i	−0.657348	+	2.02311i
$303$	4.21944	−	0.896870i	0.242400	−	0.0515238i
$304$	3.80954	+	36.2454i	0.218492	+	2.07881i
$305$	−26.1429	+	11.6396i	−1.49694	+	0.666479i
$306$	6.18940	−	6.87403i	0.353825	−	0.392962i
$307$	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
$310$	8.63506	−	9.59021i	0.490439	−	0.544687i
$311$	31.7373	−	14.1303i	1.79966	−	0.801259i	0.829608	−	0.558347i	$-0.188564\pi$
$311$	31.7373	−	14.1303i	1.79966	−	0.801259i	0.970048	−	0.242912i	$-0.0781026\pi$
$312$	1.34593	+	12.8056i	0.0761980	+	0.724976i
$313$	−23.1914	+	4.92948i	−1.31085	+	0.278630i	−0.809759	−	0.586762i	$-0.800402\pi$
$313$	−23.1914	+	4.92948i	−1.31085	+	0.278630i	−0.501094	+	0.865393i	$0.667069\pi$
$314$	−4.91891	+	15.1389i	−0.277590	+	0.854335i
$315$	12.5019	−	7.39937i	0.704400	−	0.416907i
$316$	−15.7537	−	11.4457i	−0.886212	−	0.643871i
$317$	13.1665	−	14.6229i	0.739503	−	0.821301i	−0.249627	−	0.968342i	$-0.580308\pi$
$317$	13.1665	−	14.6229i	0.739503	−	0.821301i	0.989130	+	0.147041i	$0.0469748\pi$
$318$	−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
$322$	32.0965	+	28.2773i	1.78867	+	1.57584i
$323$	8.34396	−	6.06224i	0.464270	−	0.337312i
$324$	−19.2342	+	4.08837i	−1.06857	+	0.227131i
$325$	0.309220	+	0.343424i	0.0171524	+	0.0190497i
$326$	2.58939	+	24.6364i	0.143413	+	1.36448i
$327$	−0.209873	+	1.99680i	−0.0116060	+	0.110424i
$328$	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	$0.551220\pi$
$332$	7.96272	+	1.69253i	0.437011	+	0.0928896i
$333$	12.6397	−	5.62756i	0.692652	−	0.308388i
$334$	4.41780	+	1.96693i	0.241731	+	0.107626i
$335$	−3.11506	+	9.58718i	−0.170194	+	0.523804i
$336$	9.87922	−	1.14650i	0.538955	−	0.0625467i
$337$	−17.5929	+	12.7820i	−0.958346	+	0.696279i	−0.952766	−	0.303705i	$-0.901776\pi$
$337$	−17.5929	+	12.7820i	−0.958346	+	0.696279i	−0.00558004	+	0.999984i	$0.501776\pi$
$338$	−0.572589	+	5.44782i	−0.0311447	+	0.296322i
$339$	−8.90147	−	1.89207i	−0.483461	−	0.102763i
$340$	−6.90880	+	11.9664i	−0.374682	+	0.648969i
$341$		0			0
$342$	−42.9217			−2.32094
$343$	0.600789	+	18.5105i	0.0324396	+	0.999474i
$344$	23.4024	+	17.0028i	1.26177	+	0.916730i
$345$	−9.32697	−	4.15263i	−0.502147	−	0.223570i
$346$	−10.7208	−	11.9067i	−0.576355	−	0.640107i
$347$	−2.63734	−	2.92907i	−0.141580	−	0.157240i	0.668184	−	0.743996i	$-0.267072\pi$
$347$	−2.63734	−	2.92907i	−0.141580	−	0.157240i	−0.809764	+	0.586755i	$0.800405\pi$
$348$	4.52137	+	2.01304i	0.242371	+	0.107910i
$349$	11.4147	+	8.29324i	0.611013	+	0.443927i	0.849771	−	0.527152i	$-0.176740\pi$
$349$	11.4147	+	8.29324i	0.611013	+	0.443927i	−0.238758	+	0.971079i	$0.576740\pi$
$350$	0.681907	−	0.627477i	0.0364494	−	0.0335401i
$351$	−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	$0.124453\pi$
$354$	22.0070	+	4.67774i	1.16966	+	0.248619i
$355$	−2.60994	+	24.8319i	−0.138521	+	1.31794i
$356$	−10.8996	+	7.91899i	−0.577675	+	0.419706i
$357$	−1.67886	−	2.25897i	−0.0888547	−	0.119557i
$358$	2.76018	−	8.49497i	0.145880	−	0.448973i
$359$	−3.71958	−	1.65607i	−0.196312	−	0.0874038i	0.306226	−	0.951959i	$-0.400934\pi$
$359$	−3.71958	−	1.65607i	−0.196312	−	0.0874038i	−0.502538	+	0.864555i	$0.667600\pi$
$360$	27.5430	−	12.2629i	1.45164	−	0.646314i
$361$	−28.2273	−	5.99989i	−1.48565	−	0.315784i
$362$	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
$366$	2.41176	−	22.9464i	0.126065	−	1.19943i
$367$	1.88381	+	17.9233i	0.0983342	+	0.935588i	0.926802	+	0.375551i	$0.122546\pi$
$367$	1.88381	+	17.9233i	0.0983342	+	0.935588i	−0.828468	+	0.560037i	$0.810787\pi$
$368$	22.8810	+	25.4119i	1.19275	+	1.32469i
$369$	−27.4097	+	5.82610i	−1.42689	+	0.303295i
$370$	−24.6749	+	17.9274i	−1.28279	+	0.931999i
$371$	−0.604962	−	0.532977i	−0.0314081	−	0.0276708i
$372$	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
$376$	−5.47759	+	6.08348i	−0.282485	+	0.313731i
$377$	−4.38636	−	3.18688i	−0.225909	−	0.164133i
$378$	0.279240	+	25.8185i	0.0143626	+	1.32796i
$379$	1.33139	−	4.09760i	0.0683889	−	0.210479i	−0.911021	−	0.412359i	$-0.864705\pi$
$379$	1.33139	−	4.09760i	0.0683889	−	0.210479i	0.979410	+	0.201880i	$0.0647049\pi$
$380$	62.7157	−	13.3306i	3.21725	−	0.683847i
$381$	−0.923176	−	8.78343i	−0.0472957	−	0.449989i
$382$	−27.5549	+	12.2682i	−1.40983	+	0.627698i
$383$	−8.26293	+	9.17691i	−0.422216	+	0.468918i	−0.916298	−	0.400497i	$-0.868837\pi$
$383$	−8.26293	+	9.17691i	−0.422216	+	0.468918i	0.494082	+	0.869415i	$0.335504\pi$
$384$	−12.3047			−0.627923
$385$		0			0
$386$	29.7408			1.51377
$387$	−8.78056	+	9.75180i	−0.446341	+	0.495712i
$388$	7.14174	−	3.17971i	0.362567	−	0.161425i
$389$	−3.07554	−	29.2618i	−0.155936	−	1.48363i	−0.740374	−	0.672195i	$-0.765352\pi$
$389$	−3.07554	−	29.2618i	−0.155936	−	1.48363i	0.584438	−	0.811438i	$-0.301315\pi$
$390$	12.5948	−	2.67710i	0.637762	−	0.135560i
$391$	2.99036	−	9.20337i	0.151229	−	0.465434i
$392$	−3.18996	+	38.3034i	−0.161117	+	1.93462i
$393$	0.438174	+	0.318352i	0.0221030	+	0.0160587i
$394$	−20.2716	+	22.5139i	−1.02127	+	1.13423i
$395$	−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
$399$	−2.57701	+	12.8032i	−0.129012	+	0.640963i
$400$	0.599304	−	0.435420i	0.0299652	−	0.0217710i
$401$	24.4052	−	5.18748i	1.21874	−	0.259051i	0.446732	−	0.894668i	$-0.352588\pi$
$401$	24.4052	−	5.18748i	1.21874	−	0.259051i	0.772005	+	0.635617i	$0.219254\pi$
$402$	−5.43841	−	6.03997i	−0.271243	−	0.301246i
$403$	−0.807379	−	7.68169i	−0.0402184	−	0.382652i
$404$	−2.65688	+	25.2785i	−0.132185	+	1.25765i
$405$	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
$409$	37.7158	+	8.01674i	1.86493	+	0.396402i	0.995261	−	0.0972401i	$-0.0310015\pi$
$409$	37.7158	+	8.01674i	1.86493	+	0.396402i	0.869665	+	0.493642i	$0.164335\pi$
$410$	56.4313	−	25.1248i	2.78694	−	1.24083i
$411$	3.80753	+	1.69522i	0.187811	+	0.0836190i
$412$	−1.38211	+	4.25369i	−0.0680915	+	0.209564i
$413$	−13.2907	+	30.7418i	−0.653991	+	1.51271i
$414$	−32.5807	+	23.6712i	−1.60125	+	1.16338i
$415$	0.446147	−	4.24481i	0.0219005	−	0.208369i
$416$	−6.88131	−	1.46267i	−0.337384	−	0.0717132i
$417$	−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	$0.492932\pi$
$420$	−3.82269	−	17.0742i	−0.186528	−	0.833136i
$421$	−12.5828	−	9.14191i	−0.613246	−	0.445550i	0.237310	−	0.971434i	$-0.423734\pi$
$421$	−12.5828	−	9.14191i	−0.613246	−	0.445550i	−0.850556	+	0.525884i	$0.823734\pi$
$422$	36.9651	+	16.4579i	1.79943	+	0.801158i
$423$	−2.48484	−	2.75970i	−0.120817	−	0.134181i
$424$	−1.11963	−	1.24347i	−0.0543739	−	0.0603884i
$425$	−0.191512	−	0.0852666i	−0.00928970	−	0.00413604i
$426$	−16.2866	−	11.8329i	−0.789087	−	0.573305i
$427$	32.7783	+	10.2597i	1.58625	+	0.496503i
$428$	−26.6222			−1.28683
$429$		0			0
$430$	14.4635	−	25.0514i	0.697490	−	1.20809i
$431$	−3.45910	−	0.735254i	−0.166619	−	0.0354160i	0.123847	−	0.992301i	$-0.460477\pi$
$431$	−3.45910	−	0.735254i	−0.166619	−	0.0354160i	−0.290466	+	0.956885i	$0.593810\pi$
$432$	−2.15751	+	20.5274i	−0.103803	+	0.987624i
$433$	−14.2757	+	10.3719i	−0.686044	+	0.498440i	−0.875357	−	0.483476i	$-0.839374\pi$
$433$	−14.2757	+	10.3719i	−0.686044	+	0.498440i	0.189313	+	0.981917i	$0.439374\pi$
$434$	−15.3854	+	1.78550i	−0.738521	+	0.0857066i
$435$	0.801878	−	2.46793i	0.0384471	−	0.118328i
$436$	−10.8078	−	4.81196i	−0.517601	−	0.230451i
$437$	−41.0213	+	18.2639i	−1.96231	+	0.873679i
$438$	14.8948	+	3.16599i	0.711702	+	0.151277i
$439$	−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
$443$	−1.38215	+	13.1502i	−0.0656677	+	0.624787i	0.911351	+	0.411631i	$0.135041\pi$
$443$	−1.38215	+	13.1502i	−0.0656677	+	0.624787i	−0.977018	+	0.213156i	$0.931626\pi$
$444$	−1.74186	−	16.5727i	−0.0826649	−	0.786504i
$445$	4.72660	+	5.24942i	0.224062	+	0.248846i
$446$	7.39834	−	1.57257i	0.350321	−	0.0744631i
$447$	−0.577264	+	0.419407i	−0.0273037	+	0.0198373i
$448$	2.71702	−	13.4988i	0.128367	−	0.637760i
$449$	−3.06194	−	9.42367i	−0.144502	−	0.444731i	0.852445	−	0.522817i	$-0.175119\pi$
$449$	−3.06194	−	9.42367i	−0.144502	−	0.444731i	−0.996947	+	0.0780865i	$0.975119\pi$
$450$	0.436212	+	0.755542i	0.0205632	+	0.0356166i
$451$		0			0
$452$	26.8111	−	46.4382i	1.26109	−	2.18427i
$453$	−7.08589	+	7.86968i	−0.332924	+	0.369750i
$454$	37.1777	+	27.0112i	1.74484	+	1.26770i
$455$	0.207295	+	19.1665i	0.00971816	+	0.898540i
$456$	−8.37562	+	25.7775i	−0.392224	+	1.20714i
$457$	−10.1190	+	2.15085i	−0.473345	+	0.100613i	−0.438406	−	0.898777i	$-0.644457\pi$
$457$	−10.1190	+	2.15085i	−0.473345	+	0.100613i	−0.0349384	+	0.999389i	$0.511124\pi$
$458$	−6.63929	−	63.1687i	−0.310234	−	2.95168i
$459$	5.33612	−	2.37579i	0.249069	−	0.110893i
$460$	40.2539	−	44.7065i	1.87685	−	2.08445i
$461$	−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	$0.698504\pi$
$464$	−5.81555	+	6.45882i	−0.269980	+	0.299843i
$465$	3.37716	−	1.50361i	0.156612	−	0.0697282i
$466$	0.993975	+	9.45704i	0.0460450	+	0.438089i
$467$	0.729712	−	0.155105i	0.0337671	−	0.00717741i	−0.190997	−	0.981591i	$-0.561172\pi$
$467$	0.729712	−	0.155105i	0.0337671	−	0.00717741i	0.224764	+	0.974413i	$0.427839\pi$
$468$	10.6357	−	32.7332i	0.491634	−	1.51309i
$469$	10.4118	−	6.16237i	0.480775	−	0.284552i
$470$	6.62272	+	4.81169i	0.305483	+	0.221947i
$471$	−3.05116	+	3.38866i	−0.140590	+	0.156141i
$472$	−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
$476$	15.7160	−	5.29504i	0.720344	−	0.242698i
$477$	0.614087	−	0.446160i	0.0281171	−	0.0204283i
$478$	31.6827	−	6.73437i	1.44913	−	0.308023i
$479$	−13.4582	−	14.9469i	−0.614923	−	0.682941i	0.352585	−	0.935780i	$-0.385303\pi$
$479$	−13.4582	−	14.9469i	−0.614923	−	0.682941i	−0.967509	+	0.252838i	$0.918636\pi$
$480$	−0.351950	−	3.34858i	−0.0160642	−	0.152841i
$481$	−1.90818	+	18.1551i	−0.0870057	+	0.827803i
$482$	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
$486$	−36.7683	−	7.81534i	−1.66784	−	0.354511i
$487$	−3.88249	+	1.72860i	−0.175933	+	0.0783302i	−0.492813	−	0.870135i	$-0.664031\pi$
$487$	−3.88249	+	1.72860i	−0.175933	+	0.0783302i	0.316880	+	0.948466i	$0.397365\pi$
$488$	65.1183	+	28.9926i	2.94777	+	1.31243i
$489$	−2.19287	+	6.74895i	−0.0991648	+	0.305198i
$490$	38.4271	−	0.831313i	1.73596	−	0.0375549i
$491$	−24.5358	+	17.8263i	−1.10728	+	0.804490i	−0.982234	−	0.187661i	$-0.939909\pi$
$491$	−24.5358	+	17.8263i	−1.10728	+	0.804490i	−0.125051	+	0.992150i	$0.539909\pi$
$492$	−3.52781	+	33.5649i	−0.159046	+	1.51322i
$493$	2.40581	+	0.511370i	0.108352	+	0.0230309i
$494$	28.3156	−	49.0440i	1.27398	−	2.20659i
$495$		0			0
$496$	−12.3816			−0.555948
$497$	22.0522	−	20.2920i	0.989177	−	0.910221i
$498$	2.78405	+	2.02273i	0.124756	+	0.0906409i
$499$	13.1928	+	5.87380i	0.590589	+	0.262947i	0.680196	−	0.733030i	$-0.261894\pi$
$499$	13.1928	+	5.87380i	0.590589	+	0.262947i	−0.0896071	+	0.995977i	$0.528561\pi$
$500$	−31.8802	−	35.4065i	−1.42573	−	1.58343i
$501$	0.926944	+	1.02948i	0.0414128	+	0.0459936i
$502$	−2.54541	−	1.13329i	−0.113607	−	0.0505811i
$503$	2.39325	+	1.73880i	0.106710	+	0.0775292i	0.639860	−	0.768491i	$-0.278992\pi$
$503$	2.39325	+	1.73880i	0.106710	+	0.0775292i	−0.533151	+	0.846020i	$0.678992\pi$
$504$	−34.5338	−	10.8092i	−1.53826	−	0.481481i
$505$	13.3267			0.593032
$506$		0			0
$507$	−0.784595	+	1.35896i	−0.0348451	+	0.0603534i
$508$	50.9027	+	10.8197i	2.25844	+	0.480047i
$509$	2.61224	−	24.8538i	0.115785	−	1.10163i	−0.770165	−	0.637845i	$-0.779826\pi$
$509$	2.61224	−	24.8538i	0.115785	−	1.10163i	0.885950	−	0.463780i	$-0.153507\pi$
$510$	−4.72556	+	3.43332i	−0.209251	+	0.152030i
$511$	−8.99540	+	20.8067i	−0.397933	+	0.920435i
$512$	14.3930	−	44.2970i	0.636086	−	1.95767i
$513$	−24.7608	−	11.0242i	−1.09322	−	0.486731i
$514$	51.9719	−	23.1394i	2.29238	−	1.02063i
$515$	2.29377	+	0.487556i	0.101076	+	0.0214843i
$516$	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
$520$	−4.15810	+	39.5616i	−0.182345	+	1.73489i
$521$	−3.01702	−	28.7050i	−0.132178	−	1.25759i	−0.836603	−	0.547810i	$-0.815462\pi$
$521$	−3.01702	−	28.7050i	−0.132178	−	1.25759i	0.704425	−	0.709779i	$-0.251205\pi$
$522$	−6.84903	−	7.60662i	−0.299774	−	0.332933i
$523$	−0.462264	+	0.0982572i	−0.0202134	+	0.00429649i	−0.218007	−	0.975947i	$-0.569956\pi$
$523$	−0.462264	+	0.0982572i	−0.0202134	+	0.00429649i	0.197794	+	0.980244i	$0.436622\pi$
$524$	−2.58187	+	1.87584i	−0.112789	+	0.0819463i
$525$	0.251563	−	0.0847563i	0.0109791	−	0.00369907i
$526$	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
$530$	−1.11963	+	1.24347i	−0.0486335	+	0.0540130i
$531$	−25.5092	−	18.5335i	−1.10701	−	0.804287i
$532$	−67.0562	−	37.7539i	−2.90725	−	1.63684i
$533$	11.4251	−	35.1629i	0.494876	−	1.52307i
$534$	−5.57081	+	1.18411i	−0.241073	+	0.0512415i
$535$	1.45903	+	13.8818i	0.0630794	+	0.600161i
$536$	22.9385	−	10.2129i	0.990792	−	0.441129i
$537$	1.71212	−	1.90150i	0.0738833	−	0.0820558i
$538$	38.8904			1.67668
$539$		0			0
$540$	36.3122			1.56263
$541$	10.3445	−	11.4887i	0.444743	−	0.493937i	−0.478536	−	0.878068i	$-0.658832\pi$
$541$	10.3445	−	11.4887i	0.444743	−	0.493937i	0.923279	+	0.384131i	$0.125499\pi$
$542$	−63.1331	+	28.1087i	−2.71180	+	1.20737i
$543$	0.910935	+	8.66696i	0.0390919	+	0.371935i
$544$	3.12162	−	0.663522i	0.133839	−	0.0284483i
$545$	−1.91680	+	5.89931i	−0.0821068	+	0.252699i
$546$	−13.4665	−	7.58187i	−0.576311	−	0.324474i
$547$	28.3512	+	20.5984i	1.21221	+	0.880722i	0.995430	−	0.0954983i	$-0.0304445\pi$
$547$	28.3512	+	20.5984i	1.21221	+	0.880722i	0.216780	+	0.976220i	$0.430444\pi$
$548$	−16.4328	+	18.2504i	−0.701973	+	0.779620i
$549$	−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
$553$	11.6124	−	3.91243i	0.493808	−	0.166373i
$554$	29.8492	−	21.6867i	1.26817	−	0.921379i
$555$	−8.54612	+	1.81653i	−0.362763	+	0.0771076i
$556$	−15.6783	−	17.4125i	−0.664907	−	0.738454i
$557$	−1.10096	−	10.4749i	−0.0466492	−	0.443838i	−0.992771	−	0.120026i	$-0.961702\pi$
$557$	−1.10096	−	10.4749i	−0.0466492	−	0.443838i	0.946122	−	0.323812i	$-0.104964\pi$
$558$	1.52422	−	14.5020i	0.0645255	−	0.613919i
$559$	−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
$563$	30.0435	+	6.38595i	1.26618	+	0.269136i	0.791581	−	0.611065i	$-0.209258\pi$
$563$	30.0435	+	6.38595i	1.26618	+	0.269136i	0.474602	+	0.880200i	$0.342592\pi$
$564$	−4.08592	+	1.81917i	−0.172048	+	0.0766007i
$565$	−25.6839	−	11.4352i	−1.08053	−	0.481083i
$566$	−16.7162	+	51.4472i	−0.702634	+	2.16249i
$567$	4.91047	−	11.3581i	0.206221	−	0.476996i
$568$	50.3157	−	36.5565i	2.11120	−	1.53388i
$569$	3.21656	−	30.6035i	0.134845	−	1.28297i	−0.692560	−	0.721360i	$-0.743517\pi$
$569$	3.21656	−	30.6035i	0.134845	−	1.28297i	0.827405	−	0.561606i	$-0.189816\pi$
$570$	26.5118	+	5.63525i	1.11046	+	0.236035i
$571$	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
$574$	−70.7543	−	22.1464i	−2.95323	−	0.924372i
$575$	0.738394	+	0.536475i	0.0307932	+	0.0223725i
$576$	11.8427	+	5.27271i	0.493446	+	0.219696i
$577$	18.4803	+	20.5245i	0.769347	+	0.854446i	0.992740	−	0.120282i	$-0.0383800\pi$
$577$	18.4803	+	20.5245i	0.769347	+	0.854446i	−0.223393	+	0.974728i	$0.571713\pi$
$578$	24.6296	+	27.3539i	1.02445	+	1.13777i
$579$	7.78305	+	3.46524i	0.323452	+	0.144010i
$580$	12.3700	+	8.98735i	0.513638	+	0.373179i
$581$	−3.76964	+	3.46875i	−0.156391	+	0.143908i
$582$	3.30473			0.136986
$583$		0			0
$584$	−23.5220	+	40.7413i	−0.973348	+	1.68589i
$585$	−17.6512	−	3.75187i	−0.729786	−	0.155121i
$586$	2.89724	−	27.5654i	0.119684	−	1.13872i
$587$	24.2367	−	17.6090i	1.00036	−	0.726801i	0.0381915	−	0.999270i	$-0.487840\pi$
$587$	24.2367	−	17.6090i	1.00036	−	0.726801i	0.962164	+	0.272469i	$0.0878403\pi$
$588$	−10.1042	+	18.4094i	−0.416690	+	0.759190i
$589$	5.02427	−	15.4631i	0.207022	−	0.637147i
$590$	63.4981	+	28.2712i	2.61417	+	1.16391i
$591$	−7.92820	+	3.52986i	−0.326122	+	0.145199i
$592$	28.6235	+	6.08411i	1.17642	+	0.250055i
$593$	−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
$597$	0.142077	−	1.35177i	0.00581483	−	0.0553244i
$598$	−5.55412	−	52.8440i	−0.227125	−	2.16095i
$599$	0.866033	+	0.961827i	0.0353851	+	0.0392992i	0.760578	−	0.649247i	$-0.224916\pi$
$599$	0.866033	+	0.961827i	0.0353851	+	0.0392992i	−0.725192	+	0.688546i	$0.758249\pi$
$600$	0.538878	−	0.114542i	0.0219996	−	0.00467616i
$601$	33.1875	−	24.1121i	1.35375	−	0.983554i	0.354931	−	0.934892i	$-0.384504\pi$
$601$	33.1875	−	24.1121i	1.35375	−	0.983554i	0.998815	−	0.0486619i	$-0.0154957\pi$
$602$	−32.9012	+	11.0851i	−1.34095	+	0.451793i
$603$	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
$607$	−14.1701	+	15.7374i	−0.575145	+	0.638763i	−0.958586	−	0.284802i	$-0.908072\pi$
$607$	−14.1701	+	15.7374i	−0.575145	+	0.638763i	0.383441	+	0.923565i	$0.374739\pi$
$608$	−11.9804	−	8.70430i	−0.485871	−	0.353006i
$609$	−2.68021	+	1.58631i	−0.108608	+	0.0642807i
$610$	22.0270	−	67.7922i	0.891847	−	2.74482i
$611$	4.79260	−	1.01870i	0.193888	−	0.0412121i
$612$	1.63202	+	15.5277i	0.0659707	+	0.627669i
$613$	6.17842	−	2.75081i	0.249544	−	0.111104i	−0.278153	−	0.960537i	$-0.589722\pi$
$613$	6.17842	−	2.75081i	0.249544	−	0.111104i	0.527697	+	0.849433i	$0.323056\pi$
$614$	−41.6436	+	46.2499i	−1.68060	+	1.86649i
$615$	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	$0.809820\pi$
$618$	−1.26512	+	1.40506i	−0.0508907	+	0.0565199i
$619$	−27.7962	+	12.3757i	−1.11722	+	0.497420i	−0.880447	−	0.474144i	$-0.842758\pi$
$619$	−27.7962	+	12.3757i	−1.11722	+	0.497420i	−0.236777	+	0.971564i	$0.576091\pi$
$620$	2.27690	+	21.6632i	0.0914424	+	0.870016i
$621$	−24.8751	+	5.28736i	−0.998203	+	0.212175i
$622$	−26.7406	+	82.2992i	−1.07220	+	3.29990i
$623$	−0.0916890	−	8.47755i	−0.00367344	−	0.339646i
$624$	−9.99458	−	7.26149i	−0.400104	−	0.290692i
$625$	−16.2446	+	18.0414i	−0.649784	+	0.721658i
$626$	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
$630$	−7.14024	+	35.4745i	−0.284474	+	1.41334i
$631$	−10.0051	+	7.26915i	−0.398298	+	0.289380i	−0.768847	−	0.639432i	$-0.779169\pi$
$631$	−10.0051	+	7.26915i	−0.398298	+	0.289380i	0.370549	+	0.928813i	$0.379169\pi$
$632$	24.8751	−	5.28736i	0.989478	−	0.210320i
$633$	7.75602	+	8.61394i	0.308274	+	0.342373i
$634$	5.12322	+	48.7442i	0.203469	+	1.93588i
$635$	2.85206	−	27.1355i	0.113180	−	1.07684i
$636$	−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
$640$	−37.1835	−	7.90360i	−1.46981	−	0.312417i
$641$	−43.0566	+	19.1700i	−1.70063	+	0.757171i	−0.701630	+	0.712542i	$0.747544\pi$
$641$	−43.0566	+	19.1700i	−1.70063	+	0.757171i	−0.999004	+	0.0446288i	$0.985789\pi$
$642$	−10.2810	−	4.57741i	−0.405760	−	0.180656i
$643$	0.578611	−	1.78078i	0.0228182	−	0.0702272i	−0.938999	−	0.343920i	$-0.888245\pi$
$643$	0.578611	−	1.78078i	0.0228182	−	0.0702272i	0.961817	+	0.273693i	$0.0882451\pi$
$644$	−71.7217	+	8.32342i	−2.82623	+	0.327989i
$645$	6.70389	−	4.87066i	0.263965	−	0.191782i
$646$	−2.68534	+	25.5493i	−0.105653	+	1.00522i
$647$	1.79576	+	0.381701i	0.0705986	+	0.0150062i	0.243076	−	0.970007i	$-0.421844\pi$
$647$	1.79576	+	0.381701i	0.0705986	+	0.0150062i	−0.172477	+	0.985014i	$0.555177\pi$
$648$	12.8404	−	22.2402i	0.504417	−	0.873676i
$649$		0			0
$650$	−1.15108			−0.0451492
$651$	−4.23433	−	1.32536i	−0.165956	−	0.0519451i
$652$	−33.8279	−	24.5774i	−1.32480	−	0.962525i
$653$	−16.6057	−	7.39332i	−0.649830	−	0.289323i	0.0552269	−	0.998474i	$-0.482412\pi$
$653$	−16.6057	−	7.39332i	−0.649830	−	0.289323i	−0.705057	+	0.709151i	$0.749078\pi$
$654$	−3.34643	−	3.71659i	−0.130856	−	0.145330i
$655$	1.11963	+	1.24347i	0.0437475	+	0.0485865i
$656$	−54.1428	−	24.1059i	−2.11392	−	0.941179i
$657$	−17.2652	−	12.5439i	−0.673579	−	0.489384i
$658$	−2.14657	−	9.58774i	−0.0836820	−	0.373769i
$659$	−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	$-0.176493\pi$
$662$	−68.6827	−	14.5990i	−2.66943	−	0.567405i
$663$	−0.365442	+	3.47695i	−0.0141926	+	0.135033i
$664$	−8.60105	+	6.24903i	−0.333785	+	0.242509i
$665$	−16.0112	+	37.0346i	−0.620888	+	1.43614i
$666$	−10.6497	+	32.7765i	−0.412669	+	1.27006i
$667$	−9.78252	−	4.35546i	−0.378781	−	0.168644i
$668$	−7.45693	+	3.32004i	−0.288517	+	0.128456i
$669$	2.11934	+	0.450480i	0.0819385	+	0.0174166i
$670$	−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	0.851795	+	0.523875i	$0.175514\pi$
$673$	12.2085	+	37.5740i	0.470604	+	1.44837i	−0.381191	+	0.924496i	$0.624486\pi$
$674$	5.66193	−	53.8696i	0.218089	−	2.07498i
$675$	0.0575864	+	0.547898i	0.00221650	+	0.0210886i
$676$	−6.18690	−	6.87125i	−0.237958	−	0.264279i
$677$	33.3880	−	7.09683i	1.28320	−	0.272753i	0.484667	−	0.874699i	$-0.338941\pi$
$677$	33.3880	−	7.09683i	1.28320	−	0.272753i	0.798537	+	0.601945i	$0.205608\pi$
$678$	18.3385	−	13.3237i	0.704288	−	0.511695i
$679$	−0.970715	+	4.82275i	−0.0372526	+	0.185080i
$680$	−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	$0.317056\pi$
$684$	48.4777	−	53.8399i	1.85359	−	2.05862i
$685$	10.4170	+	7.56842i	0.398014	+	0.289174i
$686$	−35.2656	−	29.7396i	−1.34645	−	1.13546i
$687$	5.62259	−	17.3046i	0.214515	−	0.660210i
$688$	−27.1473	+	5.77034i	−1.03498	+	0.219992i
$689$	0.104685	+	0.996013i	0.00398819	+	0.0379451i
$690$	23.2322	−	10.3436i	0.884435	−	0.393776i
$691$	−13.7590	+	15.2809i	−0.523416	+	0.581312i	−0.945655	−	0.325172i	$-0.894578\pi$
$691$	−13.7590	+	15.2809i	−0.523416	+	0.581312i	0.422239	+	0.906485i	$0.361244\pi$
$692$	27.0440			1.02806
$693$		0			0
$694$	9.81761			0.372671
$695$	−8.22024	+	9.12951i	−0.311812	+	0.346302i
$696$	−5.90481	+	2.62899i	−0.223821	+	0.0996517i
$697$	1.75316	+	16.6802i	0.0664057	+	0.631808i
$698$	−34.3764	+	7.30692i	−1.30116	+	0.276571i
$699$	−0.841764	+	2.59068i	−0.0318385	+	0.0979887i
$700$	0.0169162	+	1.56407i	0.000639372	+	0.0591162i
$701$	19.4089	+	14.1014i	0.733063	+	0.532602i	0.890531	−	0.454922i	$-0.150333\pi$
$701$	19.4089	+	14.1014i	0.733063	+	0.532602i	−0.157468	+	0.987524i	$0.550333\pi$
$702$	21.4609	−	23.8347i	0.809988	−	0.899583i
$703$	−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
$707$	−12.0016	−	10.5735i	−0.451367	−	0.397658i
$708$	−30.7234	+	22.3218i	−1.15465	+	0.838906i
$709$	50.5817	−	10.7515i	1.89963	−	0.403780i	0.900141	−	0.435598i	$-0.143463\pi$
$709$	50.5817	−	10.7515i	1.89963	−	0.403780i	0.999494	+	0.0318184i	$0.0101298\pi$
$710$	−41.6156	−	46.2189i	−1.56181	−	1.73456i
$711$	1.20588	+	11.4732i	0.0452240	+	0.430278i
$712$	1.83917	−	17.4985i	0.0689259	−	0.655786i
$713$	−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
$717$	9.07590	+	1.92914i	0.338946	+	0.0720451i
$718$	9.26498	−	4.12503i	0.345766	−	0.153945i
$719$	23.5559	+	10.4878i	0.878486	+	0.391127i	0.795880	−	0.605455i	$-0.207009\pi$
$719$	23.5559	+	10.4878i	0.878486	+	0.391127i	0.0826068	+	0.996582i	$0.473675\pi$
$720$	−8.93891	+	27.5111i	−0.333133	+	1.02528i
$721$	−1.67886	−	2.25897i	−0.0625240	−	0.0841284i
$722$	58.1530	−	42.2506i	2.16423	−	1.57241i
$723$	−0.0336068	+	0.319747i	−0.00124985	+	0.0118915i
$724$	−50.2278	−	10.6762i	−1.86670	−	0.396780i
$725$	−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	$0.292373\pi$
$728$	35.1331	−	32.3288i	1.30212	−	1.19818i
$729$	2.63979	+	1.91792i	0.0977698	+	0.0710340i
$730$	42.9768	+	19.1345i	1.59064	+	0.708201i
$731$	5.25545	+	5.83677i	0.194380	+	0.215881i
$732$	26.0594	+	28.9419i	0.963184	+	1.06972i
$733$	−8.48019	−	3.77563i	−0.313223	−	0.139456i	0.244104	−	0.969749i	$-0.421506\pi$
$733$	−8.48019	−	3.77563i	−0.313223	−	0.139456i	−0.557327	+	0.830293i	$0.688173\pi$
$734$	−36.3171	−	26.3859i	−1.34049	−	0.973921i
$735$	10.1531	+	4.25976i	0.374502	+	0.157124i
$736$	−13.8944			−0.512156
$737$		0			0
$738$	34.8995	−	60.4477i	1.28467	−	2.22511i
$739$	48.9986	+	10.4150i	1.80244	+	0.383121i	0.982041	−	0.188667i	$-0.0604165\pi$
$739$	48.9986	+	10.4150i	1.80244	+	0.383121i	0.820402	+	0.571788i	$0.193750\pi$
$740$	5.38129	−	51.1995i	0.197820	−	1.88213i
$741$	13.1244	−	9.53545i	0.482138	−	0.350293i
$742$	1.99488	−	0.231509i	0.0732342	−	0.00849895i
$743$	4.06909	−	12.5234i	0.149280	−	0.459438i	−0.848256	−	0.529586i	$-0.822347\pi$
$743$	4.06909	−	12.5234i	0.149280	−	0.459438i	0.997537	+	0.0701482i	$0.0223472\pi$
$744$	−8.41205	−	3.74529i	−0.308401	−	0.137309i
$745$	−2.01382	+	0.896611i	−0.0737807	+	0.0328493i
$746$	70.4529	+	14.9752i	2.57947	+	0.548282i
$747$	−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
$751$	−4.31846	+	41.0874i	−0.157583	+	1.49930i	0.574737	+	0.818339i	$0.305105\pi$
$751$	−4.31846	+	41.0874i	−0.157583	+	1.49930i	−0.732319	+	0.680961i	$0.761562\pi$
$752$	−0.820982	−	7.81113i	−0.0299381	−	0.284842i
$753$	−0.534079	−	0.593154i	−0.0194629	−	0.0216157i
$754$	13.2099	−	2.80786i	0.481078	−	0.102256i
$755$	−26.4676	+	19.2298i	−0.963255	+	0.699846i
$756$	−32.7015	−	28.8103i	−1.18934	−	1.04782i
$757$	−14.0638	−	43.2839i	−0.511157	−	1.57318i	−0.790167	−	0.612891i	$-0.790006\pi$
$757$	−14.0638	−	43.2839i	−0.511157	−	1.57318i	0.279010	−	0.960288i	$-0.409994\pi$
$758$	5.36591	+	9.29402i	0.194898	+	0.337574i
$759$		0			0
$760$	−41.8676	+	72.5168i	−1.51870	+	2.63046i
$761$	20.9250	−	23.2396i	0.758531	−	0.842434i	−0.232977	−	0.972482i	$-0.574847\pi$
$761$	20.9250	−	23.2396i	0.758531	−	0.842434i	0.991508	+	0.130049i	$0.0415133\pi$
$762$	17.7974	+	12.9306i	0.644733	+	0.468426i
$763$	6.40675	−	3.79191i	0.231940	−	0.137276i
$764$	15.7328	−	48.4205i	0.569192	−	1.75179i
$765$	8.00724	−	1.70199i	0.289502	−	0.0615356i
$766$	−3.21520	−	30.5906i	−0.116170	−	1.10528i
$767$	38.0057	−	16.9212i	1.37231	−	0.610990i
$768$	15.5388	−	17.2576i	0.560707	−	0.622729i
$769$	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
$772$	−33.5906	+	37.3061i	−1.20895	+	1.34268i
$773$	6.98361	−	3.10930i	0.251183	−	0.111834i	−0.277283	−	0.960788i	$-0.589434\pi$
$773$	6.98361	−	3.10930i	0.251183	−	0.111834i	0.528466	+	0.848954i	$0.322767\pi$
$774$	−3.41661	−	32.5069i	−0.122808	−	1.16844i
$775$	−0.323256	+	0.0687102i	−0.0116117	+	0.00246814i
$776$	−3.15495	+	9.70994i	−0.113256	+	0.348567i
$777$	9.13759	+	5.14464i	0.327809	+	0.184563i
$778$	59.2918	+	43.0780i	2.12571	+	1.54442i
$779$	52.0759	−	57.8362i	1.86581	−	2.07220i
$780$	−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
$784$	−25.2627	−	26.8651i	−0.902240	−	0.959467i
$785$	−11.3969	+	8.28030i	−0.406771	+	0.295537i
$786$	−1.31960	+	0.280490i	−0.0470687	+	0.0100048i
$787$	−18.6710	−	20.7363i	−0.665550	−	0.739168i	0.311951	−	0.950098i	$-0.399017\pi$
$787$	−18.6710	−	20.7363i	−0.665550	−	0.739168i	−0.977501	+	0.210930i	$0.932351\pi$
$788$	−5.34522	−	50.8564i	−0.190416	−	1.81168i
$789$	−0.685538	+	6.52246i	−0.0244058	+	0.232206i
$790$	−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
$794$	−42.1491	−	8.95906i	−1.49581	−	0.317945i
$795$	−0.437885	+	0.194959i	−0.0155302	+	0.00691448i
$796$	7.31656	+	3.25754i	0.259329	+	0.115460i
$797$	3.10747	−	9.56381i	0.110072	−	0.338767i	−0.880815	−	0.473460i	$-0.843005\pi$
$797$	3.10747	−	9.56381i	0.110072	−	0.338767i	0.990887	+	0.134693i	$0.0430047\pi$
$798$	−19.4045	−	26.1095i	−0.686913	−	0.924267i
$799$	−1.79818	+	1.30646i	−0.0636151	+	0.0462191i
$800$	−0.0314631	+	0.299351i	−0.00111239	+	0.0105837i
$801$	7.80731	+	1.65949i	0.275858	+	0.0586354i
$802$	−31.0740	+	53.8218i	−1.09726	+	1.90051i
$803$		0			0
$804$	13.7188			0.483824
$805$	8.27085	+	36.9421i	0.291509	+	1.30204i
$806$	15.5650	+	11.3087i	0.548255	+	0.398331i
$807$	10.1775	+	4.53130i	0.358263	+	0.159509i
$808$	−22.2119	−	24.6688i	−0.781410	−	0.867844i
$809$	25.8101	+	28.6650i	0.907435	+	1.00781i	0.999927	+	0.0120950i	$0.00385006\pi$
$809$	25.8101	+	28.6650i	0.907435	+	1.00781i	−0.0924920	+	0.995713i	$0.529483\pi$
$810$	−23.4605	−	10.4453i	−0.824318	−	0.367010i
$811$	−10.0124	−	7.27443i	−0.351583	−	0.255440i	0.397950	−	0.917407i	$-0.369722\pi$
$811$	−10.0124	−	7.27443i	−0.351583	−	0.255440i	−0.749533	+	0.661967i	$0.769722\pi$
$812$	−4.00940	−	17.9082i	−0.140702	−	0.628453i
$813$	−19.7968			−0.694303
$814$		0			0
$815$	−10.9616	+	18.9860i	−0.383968	+	0.665051i
$816$	5.48177	+	1.16519i	0.191900	+	0.0407897i
$817$	3.80954	−	36.2454i	0.133279	−	1.26806i
$818$	−77.7010	+	56.4531i	−2.71675	+	1.97383i
$819$	12.9193	+	17.3834i	0.451436	+	0.607424i
$820$	−32.2201	+	99.1632i	−1.12517	+	3.46293i
$821$	27.1671	+	12.0956i	0.948139	+	0.422139i	0.821754	−	0.569843i	$-0.192996\pi$
$821$	27.1671	+	12.0956i	0.948139	+	0.422139i	0.126385	+	0.991981i	$0.459662\pi$
$822$	−9.48403	+	4.22256i	−0.330793	+	0.147279i
$823$	−39.8859	−	8.47801i	−1.39034	−	0.295525i	−0.548903	−	0.835886i	$-0.684954\pi$
$823$	−39.8859	−	8.47801i	−1.39034	−	0.295525i	−0.841433	+	0.540361i	$0.818288\pi$
$824$	−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	−0.999808	−	0.0195857i	$-0.993765\pi$
$827$	−5.82222	−	17.9190i	−0.202459	−	0.623103i	0.797350	−	0.603518i	$-0.206235\pi$
$828$	7.10544	−	67.6038i	0.246931	−	2.34939i
$829$	3.25508	+	30.9700i	0.113054	+	1.07563i	0.893083	+	0.449891i	$0.148537\pi$
$829$	3.25508	+	30.9700i	0.113054	+	1.07563i	−0.780030	+	0.625742i	$0.784796\pi$
$830$	7.11385	+	7.90073i	0.246925	+	0.274238i
$831$	10.3382	−	2.19746i	0.358629	−	0.0762290i
$832$	−13.8375	+	10.0535i	−0.479728	+	0.348543i
$833$	−3.00949	+	9.99270i	−0.104273	+	0.346226i
$834$	−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
$838$	−1.51499	+	1.68257i	−0.0523345	+	0.0581234i
$839$	−8.29961	−	6.03002i	−0.286534	−	0.208179i	0.435228	−	0.900320i	$-0.356668\pi$
$839$	−8.29961	−	6.03002i	−0.286534	−	0.208179i	−0.721763	+	0.692141i	$0.756668\pi$
$840$	19.9116	+	11.2106i	0.687015	+	0.386803i
$841$	−8.12045	+	24.9922i	−0.280015	+	0.861799i
$842$	37.8942	−	8.05466i	1.30592	−	0.277582i
$843$	1.13538	+	10.8025i	0.0391047	+	0.372056i
$844$	−62.3944	+	27.7798i	−2.14770	+	0.956219i
$845$	−3.24384	+	3.60265i	−0.111592	+	0.123935i
$846$	9.24992			0.318019
$847$		0			0
$848$	1.60540			0.0551297
$849$	−10.3689	+	11.5158i	−0.355860	+	0.395223i
$850$	0.477030	−	0.212388i	0.0163620	−	0.00728483i
$851$	3.76872	+	35.8570i	0.129190	+	1.22916i
$852$	33.2377	−	7.06489i	1.13870	−	0.242039i
$853$	0.940756	−	2.89535i	0.0322109	−	0.0991348i	−0.933659	−	0.358164i	$-0.883403\pi$
$853$	0.940756	−	2.89535i	0.0322109	−	0.0991348i	0.965869	+	0.259030i	$0.0834027\pi$
$854$	−73.6235	+	43.5749i	−2.51934	+	1.49110i
$855$	−30.7309	−	22.3273i	−1.05097	−	0.763577i
$856$	23.2643	−	25.8377i	0.795159	−	0.883114i
$857$	−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
$861$	−15.9357	−	14.0395i	−0.543089	−	0.478466i
$862$	7.12634	−	5.17759i	0.242724	−	0.176349i
$863$	45.4086	−	9.65189i	1.54573	−	0.328554i	0.645425	−	0.763824i	$-0.276680\pi$
$863$	45.4086	−	9.65189i	1.54573	−	0.328554i	0.900300	+	0.435270i	$0.143347\pi$
$864$	−5.61186	−	6.23260i	−0.190919	−	0.212037i
$865$	−1.48215	−	14.1017i	−0.0503946	−	0.479473i
$866$	4.59434	−	43.7122i	0.156122	−	1.48540i
$867$	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
$871$	−14.7003	−	3.12465i	−0.498102	−	0.105875i
$872$	14.1148	−	6.28432i	0.477988	−	0.212814i
$873$	−4.23107	−	1.88379i	−0.143200	−	0.0637567i
$874$	34.5630	−	106.374i	1.16911	−	3.59815i
$875$	29.7817	−	3.45622i	1.00681	−	0.116841i
$876$	−20.7942	+	15.1079i	−0.702572	+	0.510448i
$877$	−4.07985	+	38.8172i	−0.137767	+	1.31076i	0.679147	+	0.734002i	$0.262350\pi$
$877$	−4.07985	+	38.8172i	−0.137767	+	1.31076i	−0.816914	+	0.576760i	$0.804317\pi$
$878$	36.6129	+	7.78230i	1.23562	+	0.262640i
$879$	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	$0.765782\pi$
$882$	34.5759	−	26.2820i	1.16423	−	0.884960i
$883$	18.8983	+	13.7304i	0.635978	+	0.462065i	0.858466	−	0.512871i	$-0.171418\pi$
$883$	18.8983	+	13.7304i	0.635978	+	0.462065i	−0.222488	+	0.974935i	$0.571418\pi$
$884$	−18.8192	−	8.37884i	−0.632958	−	0.281811i
$885$	13.3232	+	14.7969i	0.447854	+	0.497393i
$886$	−22.0384	−	24.4761i	−0.740395	−	0.822292i
$887$	38.2936	+	17.0494i	1.28577	+	0.572464i	0.931861	−	0.362815i	$-0.118184\pi$
$887$	38.2936	+	17.0494i	1.28577	+	0.572464i	0.353913	+	0.935278i	$0.384851\pi$
$888$	17.6065	+	12.7918i	0.590834	+	0.429266i
$889$	−24.0979	+	22.1744i	−0.808219	+	0.743707i
$890$	−17.5949			−0.589783
$891$		0			0
$892$	−6.38343	+	11.0564i	−0.213733	+	0.370196i
$893$	10.0883	+	2.14434i	0.337593	+	0.0717576i
$894$	0.185781	−	1.76759i	0.00621345	−	0.0591170i
$895$	6.39520	−	4.64638i	0.213768	−	0.155311i
$896$	27.2154	+	36.6193i	0.909203	+	1.22337i
$897$	4.70360	−	14.4762i	0.157049	−	0.483346i
$898$	22.5473	+	10.0387i	0.752412	+	0.334995i
$899$	3.54211	−	1.57705i	0.118136	−	0.0525976i
$900$	−1.44041	−	0.306169i	−0.0480137	−	0.0102056i
$901$	−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
$905$	−2.81424	+	26.7757i	−0.0935484	+	0.890054i
$906$	−2.75720	−	26.2330i	−0.0916018	−	0.871533i
$907$	−13.7293	−	15.2479i	−0.455874	−	0.506299i	0.470762	−	0.882260i	$-0.343979\pi$
$907$	−13.7293	−	15.2479i	−0.455874	−	0.506299i	−0.926635	+	0.375961i	$0.877313\pi$
$908$	−75.8723	+	16.1272i	−2.51791	+	0.535199i
$909$	12.1826	−	8.85120i	0.404072	−	0.293576i
$910$	−35.8241	−	31.5613i	−1.18756	−	1.04625i
$911$	8.55220	+	26.3210i	0.283347	+	0.872052i	0.986889	+	0.161399i	$0.0516006\pi$
$911$	8.55220	+	26.3210i	0.283347	+	0.872052i	−0.703542	+	0.710653i	$0.748399\pi$
$912$	−13.0025	−	22.5209i	−0.430554	−	0.745742i
$913$		0			0
$914$	12.8840	−	22.3158i	0.426165	−	0.738140i
$915$	13.6632	−	15.1745i	0.451690	−	0.501653i
$916$	86.7360	+	63.0174i	2.86584	+	2.08215i
$917$	−0.0217191	−	2.00815i	−0.000717229	−	0.0663149i
$918$	−4.49602	+	13.8373i	−0.148391	+	0.456700i
$919$	−0.942401	+	0.200313i	−0.0310869	+	0.00660773i	−0.223429	−	0.974720i	$-0.571725\pi$
$919$	−0.942401	+	0.200313i	−0.0310869	+	0.00660773i	0.192342	+	0.981328i	$0.438392\pi$
$920$	8.21237	+	78.1355i	0.270754	+	2.57605i
$921$	−16.2868	+	7.25133i	−0.536667	+	0.238939i
$922$	25.5627	−	28.3903i	0.841864	−	0.934984i
$923$	−37.2249			−1.22527
$924$		0			0
$925$	0.781061			0.0256811
$926$	41.8867	−	46.5199i	1.37648	−	1.52874i
$927$	2.42067	−	1.07775i	0.0795051	−	0.0353980i
$928$	−0.369140	−	3.51213i	−0.0121176	−	0.115291i
$929$	−25.7566	+	5.47473i	−0.845045	+	0.179620i	−0.610037	−	0.792373i	$-0.708845\pi$
$929$	−25.7566	+	5.47473i	−0.845045	+	0.179620i	−0.235009	+	0.971993i	$0.575512\pi$
$930$	−2.84547	+	8.75746i	−0.0933067	+	0.287168i
$931$	43.8026	−	20.6487i	1.43557	−	0.676733i
$932$	−12.9853	−	9.43439i	−0.425349	−	0.309034i
$933$	−16.5870	+	18.4217i	−0.543034	+	0.603100i
$934$	−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	−0.999089	−	0.0426865i	$-0.986408\pi$
$937$	−6.60878	−	20.3397i	−0.215899	−	0.664470i	0.783189	−	0.621784i	$-0.213592\pi$
$938$	−5.94657	+	29.5440i	−0.194162	+	0.964646i
$939$	13.6866	−	9.94392i	0.446646	−	0.324508i
$940$	−13.5157	+	2.87284i	−0.440832	+	0.0937018i
$941$	9.91842	+	11.0155i	0.323331	+	0.359096i	0.882794	−	0.469760i	$-0.155659\pi$
$941$	9.91842	+	11.0155i	0.323331	+	0.359096i	−0.559463	+	0.828855i	$0.688993\pi$
$942$	−1.18724	−	11.2958i	−0.0386824	−	0.368038i
$943$	7.63284	−	72.6217i	0.248560	−	2.36489i
$944$	−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	$-0.338968\pi$
$948$	13.5908	+	2.88881i	0.441409	+	0.0938243i
$949$	25.7231	−	11.4526i	0.835006	−	0.371768i
$950$	−2.21353	−	0.985526i	−0.0718163	−	0.0319747i
$951$	−4.33869	+	13.3531i	−0.140692	+	0.433004i
$952$	−8.59479	+	19.8801i	−0.278559	+	0.644318i
$953$	−40.4201	+	29.3669i	−1.30933	+	0.951287i	−0.309335	+	0.950953i	$0.600106\pi$
$953$	−40.4201	+	29.3669i	−1.30933	+	0.951287i	−1.00000		0.000333943i	$0.999894\pi$
$954$	−0.197632	+	1.88034i	−0.00639856	+	0.0608783i
$955$	−26.1104	−	5.54995i	−0.844914	−	0.179592i
$956$	−27.3365	+	47.3481i	−0.884124	+	1.53135i
$957$		0			0
$958$	50.0988			1.61862
$959$	−3.37639	−	15.0808i	−0.109029	−	0.486984i
$960$	−6.62272	−	4.81169i	−0.213747	−	0.155296i
$961$	−23.2738	−	10.3622i	−0.750767	−	0.334263i
$962$	−30.4261	−	33.7916i	−0.980977	−	1.08949i
$963$	10.5536	+	11.7209i	0.340085	+	0.377702i
$964$	−1.73065	−	0.770535i	−0.0557405	−	0.0248173i
$965$	21.2937	+	15.4708i	0.685468	+	0.498022i
$966$	−29.1288	−	9.11745i	−0.937205	−	0.293349i
$967$	−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
$970$	9.98653	+	2.12270i	0.320648	+	0.0681559i
$971$	−3.22225	+	30.6577i	−0.103407	+	0.983853i	0.812636	+	0.582772i	$0.198032\pi$
$971$	−3.22225	+	30.6577i	−0.103407	+	0.983853i	−0.916043	+	0.401081i	$0.868635\pi$
$972$	51.3311	−	37.2942i	1.64645	−	1.19621i
$973$	14.6463	−	1.69972i	0.469538	−	0.0544907i
$974$	3.27124	−	10.0678i	0.104817	−	0.322595i
$975$	−0.301234	−	0.134118i	−0.00964720	−	0.00429521i
$976$	−62.4776	+	27.8168i	−1.99986	+	0.890394i
$977$	−24.1950	−	5.14281i	−0.774067	−	0.164533i	−0.196090	−	0.980586i	$-0.562824\pi$
$977$	−24.1950	−	5.14281i	−0.774067	−	0.164533i	−0.577977	+	0.816053i	$0.696158\pi$
$978$	−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
$982$	7.89636	−	75.1289i	0.251983	−	2.39746i
$983$	−1.27774	−	12.1569i	−0.0407536	−	0.387744i	−0.995819	−	0.0913490i	$-0.970882\pi$
$983$	−1.27774	−	12.1569i	−0.0407536	−	0.387744i	0.955065	−	0.296395i	$-0.0957845\pi$
$984$	−29.4929	−	32.7552i	−0.940200	−	1.04420i
$985$	−26.2254	+	5.57438i	−0.835611	+	0.177615i
$986$	−4.95637	+	3.60101i	−0.157843	+	0.114680i
$987$	0.555363	−	2.75918i	0.0176774	−	0.0878257i
$988$	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	$0.189945\pi$
$992$	3.36638	−	3.73874i	0.106883	−	0.118705i
$993$	−16.2730	−	11.8230i	−0.516408	−	0.375192i
$994$	0.807282	+	74.6412i	0.0256054	+	2.36748i
$995$	1.29761	−	3.99365i	0.0411371	−	0.126607i
$996$	−5.68170	+	1.20768i	−0.180032	+	0.0382669i
$997$	3.60376	+	34.2875i	0.114132	+	1.08589i	0.890302	+	0.455371i	$0.150493\pi$
$997$	3.60376	+	34.2875i	0.114132	+	1.08589i	−0.776170	+	0.630524i	$0.782840\pi$
$998$	−32.8614	+	14.6308i	−1.04021	+	0.463131i
$999$	−14.5621	+	16.1729i	−0.460726	+	0.511688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.e.753.1		24
7.2	even	3	inner	847.2.n.e.632.3		24
11.2	odd	10		847.2.n.d.130.1		24
11.3	even	5		77.2.e.b.67.3	yes	6
11.4	even	5	inner	847.2.n.e.487.1		24
11.5	even	5	inner	847.2.n.e.81.3		24
11.6	odd	10		847.2.n.d.81.1		24
11.7	odd	10		847.2.n.d.487.3		24
11.8	odd	10		847.2.e.d.606.1		6
11.9	even	5	inner	847.2.n.e.130.3		24
11.10	odd	2		847.2.n.d.753.3		24
33.14	odd	10		693.2.i.g.298.1		6
44.3	odd	10		1232.2.q.k.529.2		6
77.2	odd	30		847.2.n.d.9.3		24
77.3	odd	30		539.2.a.i.1.1		3
77.9	even	15	inner	847.2.n.e.9.1		24
77.16	even	15	inner	847.2.n.e.807.1		24
77.25	even	15		539.2.a.h.1.1		3
77.30	odd	30		847.2.e.d.485.1		6
77.37	even	15	inner	847.2.n.e.366.3		24
77.47	odd	30		539.2.e.l.177.3		6
77.51	odd	30		847.2.n.d.366.1		24
77.52	even	30		5929.2.a.w.1.3		3
77.58	even	15		77.2.e.b.23.3	✓	6
77.65	odd	6		847.2.n.d.632.1		24
77.69	odd	10		539.2.e.l.67.3		6
77.72	odd	30		847.2.n.d.807.3		24
77.74	odd	30		5929.2.a.v.1.3		3
231.80	even	30		4851.2.a.bn.1.3		3
231.179	odd	30		4851.2.a.bo.1.3		3
231.212	odd	30		693.2.i.g.100.1		6
308.3	even	30		8624.2.a.ck.1.2		3
308.135	odd	30		1232.2.q.k.177.2		6
308.179	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	77.58	even	15
77.2.e.b.67.3	yes	6	11.3	even	5
539.2.a.h.1.1		3	77.25	even	15
539.2.a.i.1.1		3	77.3	odd	30
539.2.e.l.67.3		6	77.69	odd	10
539.2.e.l.177.3		6	77.47	odd	30
693.2.i.g.100.1		6	231.212	odd	30
693.2.i.g.298.1		6	33.14	odd	10
847.2.e.d.485.1		6	77.30	odd	30
847.2.e.d.606.1		6	11.8	odd	10
847.2.n.d.9.3		24	77.2	odd	30
847.2.n.d.81.1		24	11.6	odd	10
847.2.n.d.130.1		24	11.2	odd	10
847.2.n.d.366.1		24	77.51	odd	30
847.2.n.d.487.3		24	11.7	odd	10
847.2.n.d.632.1		24	77.65	odd	6
847.2.n.d.753.3		24	11.10	odd	2
847.2.n.d.807.3		24	77.72	odd	30
847.2.n.e.9.1		24	77.9	even	15	inner
847.2.n.e.81.3		24	11.5	even	5	inner
847.2.n.e.130.3		24	11.9	even	5	inner
847.2.n.e.366.3		24	77.37	even	15	inner
847.2.n.e.487.1		24	11.4	even	5	inner
847.2.n.e.632.3		24	7.2	even	3	inner
847.2.n.e.753.1		24	1.1	even	1	trivial
847.2.n.e.807.1		24	77.16	even	15	inner
1232.2.q.k.177.2		6	308.135	odd	30
1232.2.q.k.529.2		6	44.3	odd	10
4851.2.a.bn.1.3		3	231.80	even	30
4851.2.a.bo.1.3		3	231.179	odd	30
5929.2.a.v.1.3		3	77.74	odd	30
5929.2.a.w.1.3		3	77.52	even	30
8624.2.a.ck.1.2		3	308.3	even	30
8624.2.a.cl.1.2		3	308.179	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)

\(f(q)\)	\(=\)	\(q+(-1.66671 + 1.85107i) q^{2} +(-0.651849 + 0.290222i) q^{3} +(-0.439480 - 4.18137i) q^{4} +(-2.15623 + 0.458321i) q^{5} +(0.549224 - 1.69034i) q^{6} +(2.30546 + 1.29802i) q^{7} +(4.44220 + 3.22745i) q^{8} +(-1.66671 + 1.85107i) q^{9} +O(q^{10})\)	\(q+(-1.66671 + 1.85107i) q^{2} +(-0.651849 + 0.290222i) q^{3} +(-0.439480 - 4.18137i) q^{4} +(-2.15623 + 0.458321i) q^{5} +(0.549224 - 1.69034i) q^{6} +(2.30546 + 1.29802i) q^{7} +(4.44220 + 3.22745i) q^{8} +(-1.66671 + 1.85107i) q^{9} +(2.74543 - 4.75523i) q^{10} +(1.50000 + 2.59808i) q^{12} +(-1.01557 - 3.12561i) q^{13} +(-6.24527 + 2.10415i) q^{14} +(1.27252 - 0.924542i) q^{15} +(-5.15307 + 1.09532i) q^{16} +(0.997582 + 1.10793i) q^{17} +(-0.648537 - 6.17041i) q^{18} +(0.723122 - 6.88004i) q^{19} +(2.86403 + 8.81457i) q^{20} +(-1.87953 - 0.177017i) q^{21} +(-3.24543 - 5.62125i) q^{23} +(-3.83232 - 0.814585i) q^{24} +(-0.128457 + 0.0571928i) q^{25} +(7.47840 + 3.32960i) q^{26} +(1.21071 - 3.72618i) q^{27} +(4.41429 - 10.2104i) q^{28} +(1.33468 - 0.969699i) q^{29} +(-0.409536 + 3.89648i) q^{30} +(2.29889 + 0.488644i) q^{31} +(1.07031 - 1.85383i) q^{32} -3.71354 q^{34} +(-5.56601 - 1.74219i) q^{35} +(8.47250 + 6.15563i) q^{36} +(-5.07443 - 2.25928i) q^{37} +(11.5302 + 12.8056i) q^{38} +(1.56912 + 1.74269i) q^{39} +(-11.0576 - 4.92317i) q^{40} +(9.10137 + 6.61254i) q^{41} +(3.46030 - 3.18410i) q^{42} +5.26819 q^{43} +(2.74543 - 4.75523i) q^{45} +(15.8145 + 3.36149i) q^{46} +(-0.155838 + 1.48270i) q^{47} +(3.04114 - 2.20952i) q^{48} +(3.63030 + 5.98506i) q^{49} +(0.108233 - 0.333107i) q^{50} +(-0.971818 - 0.432681i) q^{51} +(-12.6230 + 5.62013i) q^{52} +(-0.298076 - 0.0633579i) q^{53} +(4.87953 + 8.45159i) q^{54} +(6.05203 + 13.2068i) q^{56} +(1.52537 + 4.69462i) q^{57} +(-0.429539 + 4.08679i) q^{58} +(1.32320 + 12.5894i) q^{59} +(-4.42510 - 4.91457i) q^{60} +(12.6980 - 2.69905i) q^{61} +(-4.73611 + 3.44098i) q^{62} +(-6.24527 + 2.10415i) q^{63} +(-1.60825 - 4.94968i) q^{64} +(3.62234 + 6.27408i) q^{65} +(2.28646 - 3.96027i) q^{67} +(4.19424 - 4.65817i) q^{68} +(3.74694 + 2.72231i) q^{69} +(12.5019 - 7.39937i) q^{70} +(3.50016 - 10.7724i) q^{71} +(-13.3781 + 2.84361i) q^{72} +(0.895567 + 8.52075i) q^{73} +(12.6397 - 5.62756i) q^{74} +(0.0671361 - 0.0745622i) q^{75} -29.0858 q^{76} -5.84111 q^{78} +(3.09906 - 3.44186i) q^{79} +(10.6092 - 4.72352i) q^{80} +(-0.488879 - 4.65137i) q^{81} +(-27.4097 + 5.82610i) q^{82} +(-0.598322 + 1.84145i) q^{83} +(0.0858404 + 7.93679i) q^{84} +(-2.65880 - 1.93173i) q^{85} +(-8.78056 + 9.75180i) q^{86} +(-0.588580 + 1.01945i) q^{87} +(-1.60220 - 2.77509i) q^{89} +(4.22642 + 13.0076i) q^{90} +(1.71574 - 8.52421i) q^{91} +(-22.0782 + 16.0408i) q^{92} +(-1.64035 + 0.348666i) q^{93} +(-2.48484 - 2.75970i) q^{94} +(1.59405 + 15.1664i) q^{95} +(-0.159658 + 1.51904i) 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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