LMFDB - Embedded newform 847.2.n.e.9.3

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			9.3
Character	$\chi$	$=$	847.9
Dual form			847.2.n.e.753.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22735 + 1.36311i) q^{2} +(-2.00860 - 0.894288i) q^{3} +(-0.142624 + 1.35697i) q^{4} +(0.621664 + 0.132139i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(-1.80096 + 1.93818i) q^{7} +(0.943117 - 0.685215i) q^{8} +(1.22735 + 1.36311i) q^{9} +O(q^{10})$	\(q+(1.22735 + 1.36311i) q^{2} +(-2.00860 - 0.894288i) q^{3} +(-0.142624 + 1.35697i) q^{4} +(0.621664 + 0.132139i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(-1.80096 + 1.93818i) q^{7} +(0.943117 - 0.685215i) q^{8} +(1.22735 + 1.36311i) q^{9} +(0.582878 + 1.00958i) q^{10} +(1.50000 - 2.59808i) q^{12} +(-0.556635 + 1.71315i) q^{13} +(-4.85235 - 0.0760860i) q^{14} +(-1.13051 - 0.821361i) q^{15} +(4.76082 + 1.01194i) q^{16} +(-1.89648 + 2.10625i) q^{17} +(-0.351681 + 3.34602i) q^{18} +(0.581506 + 5.53266i) q^{19} +(-0.267973 + 0.824735i) q^{20} +(5.35071 - 2.28245i) q^{21} +(-1.08288 + 1.87560i) q^{23} +(-2.50713 + 0.532907i) q^{24} +(-4.19872 - 1.86939i) q^{25} +(-3.01839 + 1.34387i) q^{26} +(0.792054 + 2.43769i) q^{27} +(-2.37320 - 2.72029i) q^{28} +(8.43830 + 6.13079i) q^{29} +(-0.267921 - 2.54910i) q^{30} +(-6.28980 + 1.33694i) q^{31} +(3.29804 + 5.71237i) q^{32} -5.19869 q^{34} +(-1.37570 + 0.966918i) q^{35} +(-2.02475 + 1.47107i) q^{36} +(5.54145 - 2.46721i) q^{37} +(-6.82791 + 7.58316i) q^{38} +(2.65011 - 2.94324i) q^{39} +(0.676845 - 0.301351i) q^{40} +(-6.09648 + 4.42935i) q^{41} +(9.67842 + 4.49223i) q^{42} -4.86718 q^{43} +(0.582878 + 1.00958i) q^{45} +(-3.88572 + 0.825934i) q^{46} +(0.296259 + 2.81872i) q^{47} +(-8.65763 - 6.29014i) q^{48} +(-0.513073 - 6.98117i) q^{49} +(-2.60511 - 8.01771i) q^{50} +(5.69287 - 2.53463i) q^{51} +(-2.24530 - 0.999674i) q^{52} +(-7.30656 + 1.55306i) q^{53} +(-2.35071 + 4.07155i) q^{54} +(-0.370450 + 3.06197i) q^{56} +(3.77978 - 11.6330i) q^{57} +(1.99981 + 19.0269i) q^{58} +(-1.23414 + 11.7421i) q^{59} +(1.27580 - 1.41692i) q^{60} +(4.23686 + 0.900572i) q^{61} +(-9.54217 - 6.93279i) q^{62} +(-4.85235 - 0.0760860i) q^{63} +(-0.730655 + 2.24872i) q^{64} +(-0.572413 + 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(-2.58765 - 2.87387i) q^{68} +(3.85240 - 2.79893i) q^{69} +(-3.00648 - 0.688484i) q^{70} +(1.32631 + 4.08197i) q^{71} +(2.09155 + 0.444574i) q^{72} +(1.67177 - 15.9058i) q^{73} +(10.1644 + 4.52547i) q^{74} +(6.76180 + 7.50974i) q^{75} -7.59061 q^{76} +7.26456 q^{78} +(3.18629 + 3.53873i) q^{79} +(2.82591 + 1.25818i) q^{80} +(1.16427 - 11.0773i) q^{81} +(-13.5202 - 2.87381i) q^{82} +(-2.85273 - 8.77980i) q^{83} +(2.33409 + 7.58630i) q^{84} +(-1.45729 + 1.05878i) q^{85} +(-5.97372 - 6.63449i) q^{86} +(-11.4665 - 19.8606i) q^{87} +(-0.182224 + 0.315621i) q^{89} +(-0.660765 + 2.03363i) q^{90} +(-2.31791 - 4.16417i) q^{91} +(-2.39070 - 1.73694i) q^{92} +(13.8293 + 2.93951i) q^{93} +(-3.47860 + 3.86338i) q^{94} +(-0.369578 + 3.51630i) q^{95} +(-1.51595 - 14.4233i) q^{96} +(-0.802231 + 2.46901i) q^{97} +(8.88637 - 9.26770i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	1.22735	+	1.36311i	0.867866	+	0.963863i	0.999624	−	0.0274188i	$-0.00872877\pi$
$2$	1.22735	+	1.36311i	0.867866	+	0.963863i	−0.131758	+	0.991282i	$0.542062\pi$
$3$	−2.00860	−	0.894288i	−1.15967	−	0.516318i	−0.265527	−	0.964103i	$-0.585546\pi$
$3$	−2.00860	−	0.894288i	−1.15967	−	0.516318i	−0.894141	+	0.447786i	$0.852213\pi$
$4$	−0.142624	+	1.35697i	−0.0713118	+	0.678487i
$5$	0.621664	+	0.132139i	0.278016	+	0.0590942i	0.344810	−	0.938673i	$-0.387943\pi$
$5$	0.621664	+	0.132139i	0.278016	+	0.0590942i	−0.0667932	+	0.997767i	$0.521277\pi$
$6$	−1.24625	−	3.83555i	−0.508778	−	1.56586i
$7$	−1.80096	+	1.93818i	−0.680700	+	0.732563i
$7$	−1.80096	+	1.93818i	−0.680700	+	0.732563i
$8$	0.943117	−	0.685215i	0.333442	−	0.242260i
$9$	1.22735	+	1.36311i	0.409116	+	0.454369i
$10$	0.582878	+	1.00958i	0.184322	+	0.319256i
$11$		0			0
$11$		0			0
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	−0.556635	+	1.71315i	−0.154383	+	0.475141i	−0.998098	−	0.0616500i	$-0.980364\pi$
$13$	−0.556635	+	1.71315i	−0.154383	+	0.475141i	0.843715	+	0.536791i	$0.180364\pi$
$14$	−4.85235	−	0.0760860i	−1.29685	−	0.0203348i
$15$	−1.13051	−	0.821361i	−0.291895	−	0.212074i
$16$	4.76082	+	1.01194i	1.19020	+	0.252986i
$17$	−1.89648	+	2.10625i	−0.459964	+	0.510841i	−0.927853	−	0.372946i	$-0.878348\pi$
$17$	−1.89648	+	2.10625i	−0.459964	+	0.510841i	0.467890	+	0.883787i	$0.345014\pi$
$18$	−0.351681	+	3.34602i	−0.0828919	+	0.788664i
$19$	0.581506	+	5.53266i	0.133407	+	1.26928i	0.832409	+	0.554161i	$0.186961\pi$
$19$	0.581506	+	5.53266i	0.133407	+	1.26928i	−0.699003	+	0.715119i	$0.746372\pi$
$20$	−0.267973	+	0.824735i	−0.0599205	+	0.184416i
$21$	5.35071	−	2.28245i	1.16762	−	0.498073i
$22$		0			0
$23$	−1.08288	+	1.87560i	−0.225796	+	0.391090i	−0.956558	−	0.291542i	$-0.905832\pi$
$23$	−1.08288	+	1.87560i	−0.225796	+	0.391090i	0.730762	+	0.682632i	$0.239165\pi$
$24$	−2.50713	+	0.532907i	−0.511765	+	0.108779i
$25$	−4.19872	−	1.86939i	−0.839744	−	0.373878i
$26$	−3.01839	+	1.34387i	−0.591955	+	0.263555i
$27$	0.792054	+	2.43769i	0.152431	+	0.469134i
$28$	−2.37320	−	2.72029i	−0.448492	−	0.514086i
$29$	8.43830	+	6.13079i	1.56695	+	1.13846i	0.930002	+	0.367555i	$0.119805\pi$
$29$	8.43830	+	6.13079i	1.56695	+	1.13846i	0.636952	+	0.770904i	$0.280195\pi$
$30$	−0.267921	−	2.54910i	−0.0489155	−	0.465400i
$31$	−6.28980	+	1.33694i	−1.12968	+	0.240121i	−0.734584	−	0.678518i	$-0.762623\pi$
$31$	−6.28980	+	1.33694i	−1.12968	+	0.240121i	−0.395098	+	0.918639i	$0.629289\pi$
$32$	3.29804	+	5.71237i	0.583016	+	1.00981i
$33$		0			0
$34$	−5.19869			−0.891568
$35$	−1.37570	+	0.966918i	−0.232536	+	0.163439i
$36$	−2.02475	+	1.47107i	−0.337458	+	0.245178i
$37$	5.54145	−	2.46721i	0.911008	−	0.405607i	0.102934	−	0.994688i	$-0.467177\pi$
$37$	5.54145	−	2.46721i	0.911008	−	0.405607i	0.808074	+	0.589081i	$0.200510\pi$
$38$	−6.82791	+	7.58316i	−1.10763	+	1.23015i
$39$	2.65011	−	2.94324i	0.424357	−	0.471296i
$40$	0.676845	−	0.301351i	0.107019	−	0.0476477i
$41$	−6.09648	+	4.42935i	−0.952110	+	0.691749i	−0.951305	−	0.308251i	$-0.900256\pi$
$41$	−6.09648	+	4.42935i	−0.952110	+	0.691749i	−0.000805217		1.00000i	$0.500256\pi$
$42$	9.67842	+	4.49223i	1.49341	+	0.693166i
$43$	−4.86718			−0.742238			−0.371119	−	0.928585i	$-0.621026\pi$
$43$	−4.86718			−0.742238			−0.371119	+	0.928585i	$0.621026\pi$
$44$		0			0
$45$	0.582878	+	1.00958i	0.0868904	+	0.150499i
$46$	−3.88572	+	0.825934i	−0.572917	+	0.121777i
$47$	0.296259	+	2.81872i	0.0432138	+	0.411152i	0.994650	+	0.103305i	$0.0329418\pi$
$47$	0.296259	+	2.81872i	0.0432138	+	0.411152i	−0.951436	+	0.307847i	$0.900392\pi$
$48$	−8.65763	−	6.29014i	−1.24962	−	0.907903i
$49$	−0.513073	−	6.98117i	−0.0732961	−	0.997310i
$50$	−2.60511	−	8.01771i	−0.368418	−	1.13388i
$51$	5.69287	−	2.53463i	0.797162	−	0.354919i
$52$	−2.24530	−	0.999674i	−0.311368	−	0.138630i
$53$	−7.30656	+	1.55306i	−1.00363	+	0.213329i	−0.680282	−	0.732950i	$-0.738143\pi$
$53$	−7.30656	+	1.55306i	−1.00363	+	0.213329i	−0.323351	+	0.946279i	$0.604810\pi$
$54$	−2.35071	+	4.07155i	−0.319891	+	0.554068i
$55$		0			0
$56$	−0.370450	+	3.06197i	−0.0495034	+	0.409174i
$57$	3.77978	−	11.6330i	0.500644	−	1.54082i
$58$	1.99981	+	19.0269i	0.262588	+	2.49836i
$59$	−1.23414	+	11.7421i	−0.160672	+	1.52869i	0.555943	+	0.831220i	$0.312357\pi$
$59$	−1.23414	+	11.7421i	−0.160672	+	1.52869i	−0.716615	+	0.697469i	$0.754309\pi$
$60$	1.27580	−	1.41692i	0.164705	−	0.182924i
$61$	4.23686	+	0.900572i	0.542474	+	0.115306i	0.470995	−	0.882136i	$-0.343895\pi$
$61$	4.23686	+	0.900572i	0.542474	+	0.115306i	0.0714789	+	0.997442i	$0.477228\pi$
$62$	−9.54217	−	6.93279i	−1.21186	−	0.880465i
$63$	−4.85235	−	0.0760860i	−0.611339	−	0.00958594i
$64$	−0.730655	+	2.24872i	−0.0913318	+	0.281090i
$65$	−0.572413	+	0.991448i	−0.0709990	+	0.122974i
$66$		0			0
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	0.910813	−	0.412818i	$-0.135456\pi$
$67$	0.801309	+	1.38791i	0.0978954	+	0.169560i	−0.812918	+	0.582378i	$0.802122\pi$
$68$	−2.58765	−	2.87387i	−0.313798	−	0.348508i
$69$	3.85240	−	2.79893i	0.463775	−	0.336952i
$70$	−3.00648	−	0.688484i	−0.359343	−	0.0822895i
$71$	1.32631	+	4.08197i	0.157404	+	0.484441i	0.998397	−	0.0566066i	$-0.0180281\pi$
$71$	1.32631	+	4.08197i	0.157404	+	0.484441i	−0.840992	+	0.541047i	$0.818028\pi$
$72$	2.09155	+	0.444574i	0.246492	+	0.0523935i
$73$	1.67177	−	15.9058i	0.195666	−	1.86164i	−0.252381	−	0.967628i	$-0.581214\pi$
$73$	1.67177	−	15.9058i	0.195666	−	1.86164i	0.448047	−	0.894010i	$-0.352120\pi$
$74$	10.1644	+	4.52547i	1.18158	+	0.526075i
$75$	6.76180	+	7.50974i	0.780785	+	0.867150i
$76$	−7.59061			−0.870703
$77$		0			0
$78$	7.26456			0.822549
$79$	3.18629	+	3.53873i	0.358485	+	0.398138i	0.895228	−	0.445607i	$-0.147012\pi$
$79$	3.18629	+	3.53873i	0.358485	+	0.398138i	−0.536743	+	0.843746i	$0.680346\pi$
$80$	2.82591	+	1.25818i	0.315946	+	0.140668i
$81$	1.16427	−	11.0773i	0.129363	−	1.23081i
$82$	−13.5202	−	2.87381i	−1.49306	−	0.317359i
$83$	−2.85273	−	8.77980i	−0.313128	−	0.963708i	−0.976518	−	0.215435i	$-0.930883\pi$
$83$	−2.85273	−	8.77980i	−0.313128	−	0.963708i	0.663391	−	0.748273i	$-0.269117\pi$
$84$	2.33409	+	7.58630i	0.254670	+	0.827734i
$85$	−1.45729	+	1.05878i	−0.158065	+	0.114841i
$86$	−5.97372	−	6.63449i	−0.644163	−	0.715415i
$87$	−11.4665	−	19.8606i	−1.22934	−	2.12928i
$88$		0			0
$89$	−0.182224	+	0.315621i	−0.0193157	+	0.0334558i	−0.875522	−	0.483179i	$-0.839482\pi$
$89$	−0.182224	+	0.315621i	−0.0193157	+	0.0334558i	0.856206	+	0.516635i	$0.172815\pi$
$90$	−0.660765	+	2.03363i	−0.0696508	+	0.214363i
$91$	−2.31791	−	4.16417i	−0.242982	−	0.436524i
$92$	−2.39070	−	1.73694i	−0.249247	−	0.181089i
$93$	13.8293	+	2.93951i	1.43403	+	0.304813i
$94$	−3.47860	+	3.86338i	−0.358791	+	0.398477i
$95$	−0.369578	+	3.51630i	−0.0379179	+	0.360764i
$96$	−1.51595	−	14.4233i	−0.154721	−	1.47207i
$97$	−0.802231	+	2.46901i	−0.0814542	+	0.250690i	−0.983487	−	0.180976i	$-0.942074\pi$
$97$	−0.802231	+	2.46901i	−0.0814542	+	0.250690i	0.902033	+	0.431667i	$0.142074\pi$
$98$	8.88637	−	9.26770i	0.897659	−	0.936179i
$99$		0			0
$100$	3.13555	−	5.43094i	0.313555	−	0.543094i
$101$	9.68377	−	2.05835i	0.963571	−	0.204813i	0.300843	−	0.953674i	$-0.402732\pi$
$101$	9.68377	−	2.05835i	0.963571	−	0.204813i	0.662728	+	0.748860i	$0.269399\pi$
$102$	10.4421	+	4.64913i	1.03392	+	0.460332i
$103$	5.69287	−	2.53463i	0.560935	−	0.249745i	−0.106626	−	0.994299i	$-0.534005\pi$
$103$	5.69287	−	2.53463i	0.560935	−	0.249745i	0.667562	+	0.744555i	$0.267338\pi$
$104$	0.648901	+	1.99711i	0.0636300	+	0.195833i
$105$	3.62794	−	0.711883i	0.354051	−	0.0694727i
$106$	−11.0847	−	8.05349i	−1.07664	−	0.782224i
$107$	−1.16014	−	11.0380i	−0.112155	−	1.06708i	−0.895367	−	0.445329i	$-0.853087\pi$
$107$	−1.16014	−	11.0380i	−0.112155	−	1.06708i	0.783212	−	0.621755i	$-0.213580\pi$
$108$	−3.42085	+	0.727123i	−0.329171	+	0.0699675i
$109$	7.15202	+	12.3877i	0.685039	+	1.18652i	0.973424	+	0.229008i	$0.0735483\pi$
$109$	7.15202	+	12.3877i	0.685039	+	1.18652i	−0.288385	+	0.957514i	$0.593118\pi$
$110$		0			0
$111$	−13.3370			−1.26589
$112$	−10.5354	+	7.40484i	−0.995500	+	0.699692i
$113$	7.02989	−	5.10751i	0.661316	−	0.480474i	−0.205791	−	0.978596i	$-0.565977\pi$
$113$	7.02989	−	5.10751i	0.661316	−	0.480474i	0.867107	+	0.498122i	$0.165977\pi$
$114$	20.4961	−	9.12545i	1.91964	−	0.854677i
$115$	−0.921025	+	1.02290i	−0.0858861	+	0.0953861i
$116$	−9.52282	+	10.5762i	−0.884171	+	0.981972i
$117$	−3.01839	+	1.34387i	−0.279050	+	0.124241i
$118$	−17.5205	+	12.7294i	−1.61289	+	1.17183i
$119$	−0.666809	−	7.46900i	−0.0611262	−	0.684682i
$120$	−1.62901			−0.148707
$121$		0			0
$122$	3.97252	+	6.88061i	0.359655	+	0.622942i
$123$	16.2065	−	3.44481i	1.46129	−	0.310608i
$124$	−0.917115	−	8.72577i	−0.0823594	−	0.783597i
$125$	−4.93404	−	3.58479i	−0.441314	−	0.320633i
$126$	−5.85182	−	6.70767i	−0.521321	−	0.597567i
$127$	6.48902	+	19.9712i	0.575808	+	1.77215i	0.633413	+	0.773814i	$0.281654\pi$
$127$	6.48902	+	19.9712i	0.575808	+	1.77215i	−0.0576053	+	0.998339i	$0.518346\pi$
$128$	8.08960	−	3.60172i	0.715027	−	0.318350i
$129$	9.77623	+	4.35266i	0.860749	+	0.383230i
$130$	−2.05400	+	0.436591i	−0.180148	+	0.0382916i
$131$	6.85071	−	11.8658i	0.598549	−	1.03672i	−0.394486	−	0.918902i	$-0.629077\pi$
$131$	6.85071	−	11.8658i	0.598549	−	1.03672i	0.993035	−	0.117816i	$-0.0375893\pi$
$132$		0			0
$133$	−11.7706	−	8.83705i	−1.02064	−	0.766270i
$134$	−0.908383	+	2.79572i	−0.0784724	+	0.241513i
$135$	0.170278	+	1.62008i	0.0146552	+	0.139435i
$136$	−0.345366	+	3.28594i	−0.0296149	+	0.281767i
$137$	4.86094	−	5.39862i	0.415298	−	0.461235i	−0.498807	−	0.866713i	$-0.666228\pi$
$137$	4.86094	−	5.39862i	0.415298	−	0.461235i	0.914105	+	0.405478i	$0.132895\pi$
$138$	8.54349	+	1.81597i	0.727270	+	0.154586i
$139$	2.10556	+	1.52978i	0.178591	+	0.129754i	0.673490	−	0.739197i	$-0.264795\pi$
$139$	2.10556	+	1.52978i	0.178591	+	0.129754i	−0.494898	+	0.868951i	$0.664795\pi$
$140$	−1.11588	−	2.00469i	−0.0943087	−	0.169428i
$141$	1.92568	−	5.92663i	0.162171	−	0.499112i
$142$	−3.93632	+	6.81790i	−0.330328	+	0.572146i
$143$		0			0
$144$	4.46379	+	7.73152i	0.371983	+	0.644293i
$145$	4.43567	+	4.92631i	0.368363	+	0.409108i
$146$	23.7332	−	17.2432i	1.96418	−	1.42706i
$147$	−5.21262	+	14.4812i	−0.429930	+	1.19439i
$148$	2.55760	+	7.87148i	0.210233	+	0.647032i
$149$	0.978148	+	0.207912i	0.0801330	+	0.0170328i	0.247804	−	0.968810i	$-0.420291\pi$
$149$	0.978148	+	0.207912i	0.0801330	+	0.0170328i	−0.167671	+	0.985843i	$0.553625\pi$
$150$	−1.93750	+	18.4341i	−0.158197	+	1.50514i
$151$	1.58540	+	0.705867i	0.129018	+	0.0574426i	0.470230	−	0.882544i	$-0.344171\pi$
$151$	1.58540	+	0.705867i	0.129018	+	0.0574426i	−0.341212	+	0.939986i	$0.610837\pi$
$152$	4.33949	+	4.81949i	0.351979	+	0.390913i
$153$	−5.19869			−0.420289
$154$		0			0
$155$	−4.08680			−0.328260
$156$	3.61593	+	4.01590i	0.289506	+	0.321529i
$157$	−7.25318	−	3.22932i	−0.578867	−	0.257728i	0.0963501	−	0.995348i	$-0.469283\pi$
$157$	−7.25318	−	3.22932i	−0.578867	−	0.257728i	−0.675217	+	0.737620i	$0.735950\pi$
$158$	−0.912989	+	8.68651i	−0.0726335	+	0.691061i
$159$	16.0649	+	3.41469i	1.27403	+	0.270803i
$160$	1.29544	+	3.98697i	0.102414	+	0.315198i
$161$	−1.68503	−	5.47670i	−0.132799	−	0.431624i
$162$	16.5285	−	12.0086i	1.29860	−	0.943488i
$163$	−10.7097	−	11.8944i	−0.838852	−	0.931639i	0.159605	−	0.987181i	$-0.448978\pi$
$163$	−10.7097	−	11.8944i	−0.838852	−	0.931639i	−0.998456	+	0.0555417i	$0.982311\pi$
$164$	−5.14101	−	8.90449i	−0.401446	−	0.695324i
$165$		0			0
$166$	8.46652	−	14.6644i	0.657130	−	1.13818i
$167$	0.358217	−	1.10248i	0.0277196	−	0.0853122i	−0.936240	−	0.351362i	$-0.885719\pi$
$167$	0.358217	−	1.10248i	0.0277196	−	0.0853122i	0.963959	+	0.266050i	$0.0857186\pi$
$168$	3.48237	−	5.81901i	0.268671	−	0.448946i
$169$	7.89219	+	5.73401i	0.607092	+	0.441078i
$170$	−3.23184	−	0.686948i	−0.247871	−	0.0526865i
$171$	−6.82791	+	7.58316i	−0.522143	+	0.579899i
$172$	0.694175	−	6.60463i	0.0529303	−	0.503598i
$173$	0.103844	+	0.988014i	0.00789515	+	0.0751173i	0.997760	−	0.0668952i	$-0.0213093\pi$
$173$	0.103844	+	0.988014i	0.00789515	+	0.0751173i	−0.989865	+	0.142013i	$0.954643\pi$
$174$	12.9987	−	40.0060i	0.985431	−	3.03285i
$175$	11.1850	−	4.77117i	0.845503	−	0.360667i
$176$		0			0
$177$	12.9797	−	22.4815i	0.975615	−	1.68982i
$178$	−0.653878	+	0.138986i	−0.0490103	+	0.0104175i
$179$	−17.9621	−	7.99723i	−1.34255	−	0.597741i	−0.395392	−	0.918512i	$-0.629391\pi$
$179$	−17.9621	−	7.99723i	−1.34255	−	0.597741i	−0.947157	+	0.320771i	$0.896058\pi$
$180$	−1.45310	+	0.646961i	−0.108308	+	0.0482216i
$181$	−7.37705	−	22.7042i	−0.548332	−	1.68759i	−0.712933	−	0.701232i	$-0.752634\pi$
$181$	−7.37705	−	22.7042i	−0.548332	−	1.68759i	0.164602	−	0.986360i	$-0.447366\pi$
$182$	2.83134	−	8.27044i	0.209873	−	0.613046i
$183$	−7.70480	−	5.59787i	−0.569555	−	0.413806i
$184$	0.263908	+	2.51091i	0.0194555	+	0.185107i
$185$	3.77093	−	0.801536i	0.277244	−	0.0589301i
$186$	12.9665	+	22.4587i	0.950752	+	1.64675i
$187$		0			0
$188$	−3.86718			−0.282043
$189$	−6.15114	−	2.85505i	−0.447429	−	0.207674i
$190$	−5.24669	+	3.81194i	−0.380635	+	0.276548i
$191$	−10.1693	+	4.52769i	−0.735828	+	0.327612i	−0.740207	−	0.672379i	$-0.765273\pi$
$191$	−10.1693	+	4.52769i	−0.735828	+	0.327612i	0.00437921	+	0.999990i	$0.498606\pi$
$192$	3.47860	−	3.86338i	0.251047	−	0.278815i
$193$	2.41865	−	2.68619i	0.174098	−	0.193356i	−0.649780	−	0.760122i	$-0.725139\pi$
$193$	2.41865	−	2.68619i	0.174098	−	0.193356i	0.823879	+	0.566766i	$0.191806\pi$
$194$	−4.35015	+	1.93681i	−0.312322	+	0.139055i
$195$	2.03639	−	1.47952i	0.145829	−	0.105951i
$196$	9.54644	+	0.299454i	0.681889	+	0.0213896i
$197$	2.41831			0.172298			0.0861489	−	0.996282i	$-0.472544\pi$
$197$	2.41831			0.172298			0.0861489	+	0.996282i	$0.472544\pi$
$198$		0			0
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	0.981748	+	0.190186i	$0.0609091\pi$
$199$	9.24809	+	16.0182i	0.655580	+	1.13550i	−0.326168	+	0.945312i	$0.605758\pi$
$200$	−5.24082	+	1.11397i	−0.370582	+	0.0787696i
$201$	−0.368323	−	3.50436i	−0.0259795	−	0.247178i
$202$	14.6911	+	10.6737i	1.03366	+	0.751000i
$203$	−27.0796	+	5.31363i	−1.90062	+	0.372943i
$204$	2.62749	+	8.08658i	0.183961	+	0.566174i
$205$	−4.37525	+	1.94799i	−0.305581	+	0.136053i
$206$	10.4421	+	4.64913i	0.727537	+	0.323920i
$207$	−3.88572	+	0.825934i	−0.270076	+	0.0574064i
$208$	−4.38364	+	7.59270i	−0.303951	+	0.526459i
$209$		0			0
$210$	5.42312	+	4.07155i	0.374231	+	0.280964i
$211$	−2.42738	+	7.47072i	−0.167108	+	0.514305i	−0.999185	−	0.0403541i	$-0.987151\pi$
$211$	−2.42738	+	7.47072i	−0.167108	+	0.514305i	0.832078	+	0.554659i	$0.187151\pi$
$212$	−1.06537	−	10.1363i	−0.0731699	−	0.696165i
$213$	0.986421	−	9.38516i	0.0675884	−	0.643061i
$214$	13.6221	−	15.1289i	0.931187	−	1.03419i
$215$	−3.02575	−	0.643142i	−0.206354	−	0.0438619i
$216$	2.41734	+	1.75630i	0.164479	+	0.119501i
$217$	8.73646	−	14.5985i	0.593070	−	0.991013i
$218$	−8.10771	+	24.9530i	−0.549123	+	1.69003i
$219$	−17.5823	+	30.4535i	−1.18810	+	2.05786i
$220$		0			0
$221$	−2.55267	−	4.42136i	−0.171711	−	0.297413i
$222$	−16.3691	−	18.1797i	−1.09862	−	1.22014i
$223$	−16.4530	+	11.9538i	−1.10177	+	0.800484i	−0.981348	−	0.192239i	$-0.938425\pi$
$223$	−16.4530	+	11.9538i	−1.10177	+	0.800484i	−0.120423	+	0.992723i	$0.538425\pi$
$224$	−17.0112	−	3.89557i	−1.13661	−	0.260284i
$225$	−2.60511	−	8.01771i	−0.173674	−	0.534514i
$226$	15.5902	+	3.31380i	1.03705	+	0.220431i
$227$	−0.754656	+	7.18007i	−0.0500883	+	0.476558i	0.940511	+	0.339763i	$0.110347\pi$
$227$	−0.754656	+	7.18007i	−0.0500883	+	0.476558i	−0.990599	+	0.136795i	$0.956320\pi$
$228$	15.2465	+	6.78820i	1.00973	+	0.449559i
$229$	8.07729	+	8.97074i	0.533763	+	0.592804i	0.948358	−	0.317202i	$-0.102743\pi$
$229$	8.07729	+	8.97074i	0.533763	+	0.592804i	−0.414595	+	0.910006i	$0.636077\pi$
$230$	−2.52475			−0.166477
$231$		0			0
$232$	12.1592			0.798291
$233$	−5.04672	−	5.60495i	−0.330622	−	0.367193i	0.554798	−	0.831985i	$-0.312796\pi$
$233$	−5.04672	−	5.60495i	−0.330622	−	0.367193i	−0.885420	+	0.464793i	$0.846129\pi$
$234$	−5.53646	−	2.46499i	−0.361930	−	0.161141i
$235$	−0.188288	+	1.79144i	−0.0122826	+	0.116861i
$236$	−15.7577	−	3.34940i	−1.02574	−	0.218027i
$237$	−3.23534	−	9.95737i	−0.210158	−	0.646800i
$238$	9.36264	−	10.0760i	0.606890	−	0.653130i
$239$	7.96578	−	5.78748i	0.515264	−	0.374361i	−0.299553	−	0.954080i	$-0.596838\pi$
$239$	7.96578	−	5.78748i	0.515264	−	0.374361i	0.814817	+	0.579719i	$0.196838\pi$
$240$	−4.55096	−	5.05436i	−0.293763	−	0.326257i
$241$	0.837515	+	1.45062i	0.0539491	+	0.0934426i	0.891739	−	0.452551i	$-0.149486\pi$
$241$	0.837515	+	1.45062i	0.0539491	+	0.0934426i	−0.837790	+	0.545993i	$0.816152\pi$
$242$		0			0
$243$	−8.40011	+	14.5494i	−0.538867	+	0.933346i
$244$	−1.82633	+	5.62086i	−0.116919	+	0.359839i
$245$	0.603524	−	4.40774i	0.0385577	−	0.281600i
$246$	24.5867	+	17.8633i	1.56759	+	1.13892i
$247$	−9.80195	−	2.08347i	−0.623683	−	0.132568i
$248$	−5.01593	+	5.57075i	−0.318512	+	0.353743i
$249$	−2.12167	+	20.1863i	−0.134455	+	1.27925i
$250$	−1.16933	−	11.1254i	−0.0739548	−	0.703632i
$251$	6.11045	−	18.8060i	0.385688	−	1.18703i	−0.550292	−	0.834973i	$-0.685483\pi$
$251$	6.11045	−	18.8060i	0.385688	−	1.18703i	0.935980	−	0.352054i	$-0.114517\pi$
$252$	0.795307	−	6.57367i	0.0500997	−	0.414102i
$253$		0			0
$254$	−19.2586	+	33.3568i	−1.20839	+	2.09299i
$255$	3.87397	−	0.823439i	0.242598	−	0.0515657i
$256$	19.1584	+	8.52985i	1.19740	+	0.533116i
$257$	2.48481	−	1.10631i	0.154998	−	0.0690097i	−0.327771	−	0.944757i	$-0.606298\pi$
$257$	2.48481	−	1.10631i	0.154998	−	0.0690097i	0.482770	+	0.875747i	$0.339631\pi$
$258$	6.06570	+	18.6683i	0.377634	+	1.16224i
$259$	−5.19804	+	15.1837i	−0.322990	+	0.943467i
$260$	−1.26373	−	0.918153i	−0.0783731	−	0.0569414i
$261$	1.99981	+	19.0269i	0.123785	+	1.17774i
$262$	24.5825	−	5.22518i	1.51871	−	0.322813i
$263$	−6.34744	−	10.9941i	−0.391400	−	0.677924i	0.601235	−	0.799073i	$-0.294676\pi$
$263$	−6.34744	−	10.9941i	−0.391400	−	0.677924i	−0.992634	+	0.121148i	$0.961342\pi$
$264$		0			0
$265$	−4.74744			−0.291633
$266$	−2.40072	−	26.8907i	−0.147197	−	1.64877i
$267$	0.648272	−	0.470997i	0.0396736	−	0.0288246i
$268$	−1.99764	+	0.889406i	−0.122025	+	0.0543291i
$269$	−4.74637	+	5.27138i	−0.289392	+	0.321402i	−0.870257	−	0.492598i	$-0.836047\pi$
$269$	−4.74637	+	5.27138i	−0.289392	+	0.321402i	0.580866	+	0.813999i	$0.302714\pi$
$270$	−1.99936	+	2.22051i	−0.121677	+	0.135136i
$271$	−16.6413	+	7.40918i	−1.01089	+	0.450075i	−0.844254	−	0.535944i	$-0.819956\pi$
$271$	−16.6413	+	7.40918i	−1.01089	+	0.450075i	−0.166632	+	0.986019i	$0.553289\pi$
$272$	−11.1602	+	8.10836i	−0.676686	+	0.491642i
$273$	0.931787	+	10.4370i	0.0563943	+	0.631679i
$274$	13.3250			0.804991
$275$		0			0
$276$	3.24864	+	5.62680i	0.195545	+	0.338694i
$277$	−13.5460	+	2.87929i	−0.813901	+	0.173000i	−0.596014	−	0.802974i	$-0.703250\pi$
$277$	−13.5460	+	2.87929i	−0.813901	+	0.173000i	−0.217887	+	0.975974i	$0.569916\pi$
$278$	0.499001	+	4.74768i	0.0299281	+	0.284747i
$279$	−9.54217	−	6.93279i	−0.571274	−	0.415055i
$280$	−0.634900	+	1.85457i	−0.0379425	+	0.110832i
$281$	6.49953	+	20.0035i	0.387730	+	1.19331i	0.934481	+	0.356014i	$0.115864\pi$
$281$	6.49953	+	20.0035i	0.387730	+	1.19331i	−0.546751	+	0.837295i	$0.684136\pi$
$282$	10.4421	−	4.64913i	0.621819	−	0.276852i
$283$	0.321975	+	0.143352i	0.0191394	+	0.00852141i	0.416284	−	0.909235i	$-0.363332\pi$
$283$	0.321975	+	0.143352i	0.0191394	+	0.00852141i	−0.397145	+	0.917756i	$0.629999\pi$
$284$	−5.72829	+	1.21758i	−0.339911	+	0.0722504i
$285$	3.88692	−	6.73234i	0.230241	−	0.398789i
$286$		0			0
$287$	2.39465	−	19.7932i	0.141352	−	1.16835i
$288$	−3.73874	+	11.5066i	−0.220307	+	0.678036i
$289$	0.937314	+	8.91794i	0.0551361	+	0.524585i
$290$	−1.27098	+	12.0926i	−0.0746347	+	0.710102i
$291$	3.81937	−	4.24184i	0.223896	−	0.248661i
$292$	21.3454	+	4.53710i	1.24914	+	0.265514i
$293$	2.80183	+	2.03565i	0.163685	+	0.118924i	0.666612	−	0.745405i	$-0.267744\pi$
$293$	2.80183	+	2.03565i	0.163685	+	0.118924i	−0.502928	+	0.864329i	$0.667744\pi$
$294$	−26.1372	+	10.6682i	−1.52435	+	0.622180i
$295$	−2.31881	+	7.13655i	−0.135006	+	0.415506i
$296$	3.53566	−	6.12395i	0.205506	−	0.355947i
$297$		0			0
$298$	0.917122	+	1.58850i	0.0531274	+	0.0920194i
$299$	−2.61041	−	2.89915i	−0.150964	−	0.167662i
$300$	−11.1549	+	8.10451i	−0.644029	+	0.467914i
$301$	8.76560	−	9.43346i	0.505241	−	0.543736i
$302$	0.983669	+	3.02742i	0.0566038	+	0.174209i
$303$	−21.2916	−	4.52567i	−1.22317	−	0.259993i
$304$	−2.83029	+	26.9285i	−0.162329	+	1.54445i
$305$	2.51490	+	1.11971i	0.144003	+	0.0641142i
$306$	−6.38060	−	7.08638i	−0.364755	−	0.405101i
$307$	−6.51473			−0.371815			−0.185908	−	0.982567i	$-0.559523\pi$
$307$	−6.51473			−0.371815			−0.185908	+	0.982567i	$0.559523\pi$
$308$		0			0
$309$	−13.7014			−0.779447
$310$	−5.01593	−	5.57075i	−0.284886	−	0.316397i
$311$	10.6246	+	4.73038i	0.602467	+	0.268236i	0.685222	−	0.728334i	$-0.259705\pi$
$311$	10.6246	+	4.73038i	0.602467	+	0.268236i	−0.0827550	+	0.996570i	$0.526372\pi$
$312$	0.482608	−	4.59171i	0.0273223	−	0.259955i
$313$	26.5056	+	5.63393i	1.49818	+	0.318449i	0.882789	−	0.469770i	$-0.155663\pi$
$313$	26.5056	+	5.63393i	1.49818	+	0.318449i	0.615395	+	0.788219i	$0.288997\pi$
$314$	−4.50026	−	13.8504i	−0.253964	−	0.781622i
$315$	−3.00648	−	0.688484i	−0.169396	−	0.0387917i
$316$	−5.25640	+	3.81900i	−0.295696	+	0.214836i
$317$	2.58399	+	2.86982i	0.145132	+	0.161185i	0.811328	−	0.584592i	$-0.198745\pi$
$317$	2.58399	+	2.86982i	0.145132	+	0.161185i	−0.666196	+	0.745777i	$0.732079\pi$
$318$	15.0626	+	26.0892i	0.844668	+	1.46301i
$319$		0			0
$320$	−0.751365	+	1.30140i	−0.0420026	+	0.0727506i
$321$	−7.54089	+	23.2085i	−0.420892	+	1.29537i
$322$	5.39722	−	9.01869i	0.300775	−	0.502592i
$323$	−12.7560	−	9.26778i	−0.709763	−	0.515673i
$324$	14.8655	+	3.15976i	0.825861	+	0.175542i
$325$	5.53970	−	6.15246i	0.307287	−	0.341277i
$326$	3.06874	−	29.1971i	0.169962	−	1.61708i
$327$	−3.28744	−	31.2779i	−0.181796	−	1.72967i
$328$	−2.71464	+	8.35480i	−0.149891	+	0.461316i
$329$	−5.99673	−	4.50220i	−0.330610	−	0.248214i
$330$		0			0
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	−0.938077	−	0.346426i	$-0.887395\pi$
$331$	−3.07514	+	5.32630i	−0.169025	+	0.292760i	0.769052	+	0.639186i	$0.220729\pi$
$332$	12.3208	−	2.61887i	0.676193	−	0.143729i
$333$	10.1644	+	4.52547i	0.557004	+	0.247994i
$334$	1.94245	−	0.864835i	0.106286	−	0.0473217i
$335$	0.314748	+	0.968695i	0.0171965	+	0.0529255i
$336$	27.7835	−	5.45174i	1.51571	−	0.297417i
$337$	9.51464	+	6.91279i	0.518296	+	0.376564i	0.815961	−	0.578106i	$-0.196208\pi$
$337$	9.51464	+	6.91279i	0.518296	+	0.376564i	−0.297666	+	0.954670i	$0.596208\pi$
$338$	1.87039	+	17.7955i	0.101736	+	0.967950i
$339$	−18.6878	+	3.97223i	−1.01498	+	0.215742i
$340$	−1.22890	−	2.12851i	−0.0666462	−	0.115435i
$341$		0			0
$342$	−18.7169			−1.01209
$343$	14.4548	+	11.5784i	0.780485	+	0.625175i
$344$	−4.59032	+	3.33506i	−0.247493	+	0.179814i
$345$	2.76475	−	1.23094i	0.148849	−	0.0662718i
$346$	−1.21932	+	1.35419i	−0.0655509	+	0.0728016i
$347$	−0.562596	+	0.624826i	−0.0302018	+	0.0335424i	−0.758056	−	0.652189i	$-0.773851\pi$
$347$	−0.562596	+	0.624826i	−0.0302018	+	0.0335424i	0.727855	+	0.685731i	$0.240518\pi$
$348$	28.5857	−	12.7272i	1.53235	−	0.682248i
$349$	−7.38773	+	5.36750i	−0.395456	+	0.287316i	−0.767688	−	0.640824i	$-0.778593\pi$
$349$	−7.38773	+	5.36750i	−0.395456	+	0.287316i	0.372231	+	0.928140i	$0.378593\pi$
$350$	20.2315	+	9.39042i	1.08142	+	0.501939i
$351$	−4.61701			−0.246438
$352$		0			0
$353$	−11.3639	−	19.6829i	−0.604840	−	1.04761i	−0.992077	−	0.125633i	$-0.959904\pi$
$353$	−11.3639	−	19.6829i	−0.604840	−	1.04761i	0.387237	−	0.921980i	$-0.373429\pi$
$354$	46.5754	−	9.89991i	2.47545	−	0.526174i
$355$	0.285134	+	2.71287i	0.0151333	+	0.143984i
$356$	−0.402300	−	0.292288i	−0.0213219	−	0.0154912i
$357$	−5.34008	+	15.5986i	−0.282627	+	0.825564i
$358$	−11.1446	−	34.2996i	−0.589012	−	1.81279i
$359$	−23.9518	+	10.6640i	−1.26413	+	0.562827i	−0.925733	−	0.378177i	$-0.876551\pi$
$359$	−23.9518	+	10.6640i	−1.26413	+	0.562827i	−0.338396	+	0.941004i	$0.609884\pi$
$360$	1.24150	+	0.552751i	0.0654327	+	0.0291325i
$361$	−11.6874	+	2.48424i	−0.615127	+	0.130749i
$362$	21.8941	−	37.9217i	1.15073	−	1.99312i
$363$		0			0
$364$	5.98126	−	2.55143i	0.313503	−	0.133731i
$365$	3.14106	−	9.66718i	0.164410	−	0.506003i
$366$	−1.82598	−	17.3730i	−0.0954454	−	0.908102i
$367$	0.399533	−	3.80130i	0.0208554	−	0.198426i	−0.979133	−	0.203220i	$-0.934859\pi$
$367$	0.399533	−	3.80130i	0.0208554	−	0.198426i	0.999989	+	0.00479386i	$0.00152594\pi$
$368$	−7.05339	+	7.83358i	−0.367683	+	0.408354i
$369$	−13.5202	−	2.87381i	−0.703833	−	0.149604i
$370$	5.72082	+	4.15642i	0.297412	+	0.216082i
$371$	10.1487	−	16.9584i	0.526896	−	0.880437i
$372$	−5.96123	+	18.3468i	−0.309075	+	0.951236i
$373$	−7.55387	+	13.0837i	−0.391124	+	0.677447i	−0.992598	−	0.121445i	$-0.961247\pi$
$373$	−7.55387	+	13.0837i	−0.391124	+	0.677447i	0.601474	+	0.798893i	$0.294580\pi$
$374$		0			0
$375$	6.70469	+	11.6129i	0.346229	+	0.599686i
$376$	2.21083	+	2.45538i	0.114015	+	0.126627i
$377$	−15.2000	+	11.0434i	−0.782839	+	0.568766i
$378$	−3.65785	−	11.8888i	−0.188140	−	0.611494i
$379$	−3.51552	−	10.8196i	−0.180580	−	0.555768i	0.819264	−	0.573416i	$-0.194382\pi$
$379$	−3.51552	−	10.8196i	−0.180580	−	0.555768i	−0.999844	+	0.0176481i	$0.994382\pi$
$380$	−4.71881	−	1.00301i	−0.242070	−	0.0514535i
$381$	4.82609	−	45.9172i	0.247248	−	2.35241i
$382$	−18.6531	−	8.30488i	−0.954373	−	0.424914i
$383$	5.94571	+	6.60338i	0.303812	+	0.337417i	0.875647	−	0.482951i	$-0.160435\pi$
$383$	5.94571	+	6.60338i	0.303812	+	0.337417i	−0.571836	+	0.820368i	$0.693769\pi$
$384$	−19.4698			−0.993564
$385$		0			0
$386$	6.63009			0.337463
$387$	−5.97372	−	6.63449i	−0.303661	−	0.337250i
$388$	−3.23597	−	1.44075i	−0.164281	−	0.0731428i
$389$	2.08001	−	19.7900i	0.105461	−	1.00339i	−0.805974	−	0.591950i	$-0.798358\pi$
$389$	2.08001	−	19.7900i	0.105461	−	1.00339i	0.911435	−	0.411443i	$-0.134975\pi$
$390$	4.51611	+	0.959929i	0.228682	+	0.0486079i
$391$	−1.89683	−	5.83785i	−0.0959270	−	0.295233i
$392$	−5.26749	−	6.23250i	−0.266048	−	0.314789i
$393$	−24.3718	+	17.7071i	−1.22939	+	0.893207i
$394$	2.96811	+	3.29642i	0.149531	+	0.166071i
$395$	1.51320	+	2.62093i	0.0761371	+	0.131873i
$396$		0			0
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.0178296	−	0.999841i	$-0.494324\pi$
$397$	17.4303	−	30.1902i	0.874803	−	1.51520i	0.856973	−	0.515361i	$-0.172342\pi$
$398$	−10.4839	+	32.2660i	−0.525509	+	1.61735i
$399$	15.7395	+	28.2764i	0.787962	+	1.41559i
$400$	−18.0976	−	13.1487i	−0.904882	−	0.657435i
$401$	−11.1473	−	2.36942i	−0.556668	−	0.118323i	−0.0790171	−	0.996873i	$-0.525178\pi$
$401$	−11.1473	−	2.36942i	−0.556668	−	0.118323i	−0.477651	+	0.878550i	$0.658511\pi$
$402$	4.32476	−	4.80313i	0.215699	−	0.239558i
$403$	1.21075	−	11.5195i	0.0603118	−	0.573829i
$404$	1.41199	+	13.4342i	0.0702491	+	0.668376i
$405$	2.18752	−	6.73249i	0.108699	−	0.334540i
$406$	−40.4792	−	30.3908i	−2.00895	−	1.50827i
$407$		0			0
$408$	3.63228	−	6.29129i	0.179825	−	0.311465i
$409$	3.99855	−	0.849919i	0.197716	−	0.0420258i	−0.107989	−	0.994152i	$-0.534441\pi$
$409$	3.99855	−	0.849919i	0.197716	−	0.0420258i	0.305705	+	0.952126i	$0.401108\pi$
$410$	−8.02527	−	3.57308i	−0.396340	−	0.176462i
$411$	−14.5916	+	6.49661i	−0.719752	+	0.320454i
$412$	2.62749	+	8.08658i	0.129447	+	0.398397i
$413$	−20.5356	−	23.5390i	−1.01049	−	1.15828i
$414$	−5.89496	−	4.28294i	−0.289722	−	0.210495i
$415$	−0.613287	−	5.83504i	−0.0301051	−	0.286431i
$416$	−11.6219	+	2.47032i	−0.569812	+	0.121117i
$417$	−2.86118	−	4.95570i	−0.140112	−	0.242682i
$418$		0			0
$419$	32.8002			1.60240			0.801198	−	0.598399i	$-0.204196\pi$
$419$	32.8002			1.60240			0.801198	+	0.598399i	$0.204196\pi$
$420$	0.448576	+	5.02455i	0.0218883	+	0.245173i
$421$	6.89386	−	5.00868i	0.335986	−	0.244108i	−0.406980	−	0.913437i	$-0.633418\pi$
$421$	6.89386	−	5.00868i	0.335986	−	0.244108i	0.742966	+	0.669329i	$0.233418\pi$
$422$	−13.1626	+	5.86038i	−0.640747	+	0.285279i
$423$	−3.47860	+	3.86338i	−0.169135	+	0.187844i
$424$	−5.82677	+	6.47128i	−0.282973	+	0.314273i
$425$	11.9002	−	5.29831i	0.577244	−	0.257006i
$426$	14.0037	−	10.1743i	0.678480	−	0.492945i
$427$	−9.37589	+	6.58989i	−0.453731	+	0.318907i
$428$	15.1437			0.732000
$429$		0			0
$430$	−2.83697	−	4.91378i	−0.136811	−	0.236964i
$431$	16.3687	−	3.47927i	0.788451	−	0.167590i	0.203948	−	0.978982i	$-0.434623\pi$
$431$	16.3687	−	3.47927i	0.788451	−	0.167590i	0.584503	+	0.811391i	$0.301289\pi$
$432$	1.30402	+	12.4069i	0.0627397	+	0.596928i
$433$	20.9261	+	15.2037i	1.00564	+	0.730644i	0.963291	−	0.268459i	$-0.0865144\pi$
$433$	20.9261	+	15.2037i	1.00564	+	0.730644i	0.0423535	+	0.999103i	$0.486514\pi$
$434$	30.6221	−	6.00873i	1.46991	−	0.288428i
$435$	−4.50397	−	13.8618i	−0.215949	−	0.664622i
$436$	−17.8298	+	7.93833i	−0.853891	+	0.380177i
$437$	−11.0068	−	4.90053i	−0.526525	−	0.234424i
$438$	−63.0911	+	13.4104i	−3.01461	+	0.640775i
$439$	4.78430	−	8.28665i	0.228342	−	0.395500i	−0.728975	−	0.684541i	$-0.760003\pi$
$439$	4.78430	−	8.28665i	0.228342	−	0.395500i	0.957317	+	0.289040i	$0.0933362\pi$
$440$		0			0
$441$	8.88637	−	9.26770i	0.423161	−	0.441319i
$442$	2.89377	−	8.90612i	0.137643	−	0.423621i
$443$	−1.98948	−	18.9287i	−0.0945232	−	0.899328i	−0.934322	−	0.356430i	$-0.883994\pi$
$443$	−1.98948	−	18.9287i	−0.0945232	−	0.899328i	0.839799	−	0.542898i	$-0.182673\pi$
$444$	1.90217	−	18.0979i	0.0902729	−	0.858889i
$445$	−0.154988	+	0.172131i	−0.00734713	+	0.00815981i
$446$	−36.4878	−	7.75572i	−1.72775	−	0.367244i
$447$	−1.77878	−	1.29236i	−0.0841333	−	0.0611264i
$448$	−3.04255	−	5.46600i	−0.143747	−	0.258244i
$449$	10.3034	−	31.7105i	0.486246	−	1.49651i	−0.343921	−	0.938999i	$-0.611755\pi$
$449$	10.3034	−	31.7105i	0.486246	−	1.49651i	0.830167	−	0.557514i	$-0.188245\pi$
$450$	7.73163	−	13.3916i	0.364472	−	0.631285i
$451$		0			0
$452$	5.92813	+	10.2678i	0.278836	+	0.482958i
$453$	−2.55320	−	2.83562i	−0.119960	−	0.133229i
$454$	−10.7134	+	7.78377i	−0.502807	+	0.365311i
$455$	−0.890710	−	2.89500i	−0.0417571	−	0.135720i
$456$	−4.40630	−	13.5612i	−0.206344	−	0.635062i
$457$	−11.6992	−	2.48673i	−0.547263	−	0.116324i	−0.0740210	−	0.997257i	$-0.523583\pi$
$457$	−11.6992	−	2.48673i	−0.547263	−	0.116324i	−0.473242	+	0.880932i	$0.656917\pi$
$458$	−2.31444	+	22.0205i	−0.108147	+	1.02895i
$459$	−6.63651	−	2.95476i	−0.309766	−	0.137917i
$460$	−1.25669	−	1.39570i	−0.0585935	−	0.0650747i
$461$	12.4896			0.581701			0.290850	−	0.956769i	$-0.406062\pi$
$461$	12.4896			0.581701			0.290850	+	0.956769i	$0.406062\pi$
$462$		0			0
$463$	12.3095			0.572071			0.286035	−	0.958219i	$-0.407662\pi$
$463$	12.3095			0.572071			0.286035	+	0.958219i	$0.407662\pi$
$464$	33.9692	+	37.7266i	1.57698	+	1.75142i
$465$	8.20877	+	3.65478i	0.380672	+	0.169486i
$466$	1.44607	−	13.7585i	0.0669880	−	0.637348i
$467$	−32.0448	−	6.81134i	−1.48286	−	0.315191i	−0.605816	−	0.795605i	$-0.707153\pi$
$467$	−32.0448	−	6.81134i	−1.48286	−	0.315191i	−0.877042	+	0.480413i	$0.840487\pi$
$468$	−1.39311	−	4.28754i	−0.0643964	−	0.198192i
$469$	−4.13314	−	0.946489i	−0.190851	−	0.0437048i
$470$	−2.67302	+	1.94206i	−0.123297	+	0.0895808i
$471$	11.6808	+	12.9729i	0.538224	+	0.597758i
$472$	6.88191	+	11.9198i	0.316766	+	0.548654i
$473$		0			0
$474$	9.60208	−	16.6313i	0.441038	−	0.763900i
$475$	7.90113	−	24.3172i	0.362529	−	1.11575i
$476$	10.2303	+	0.160414i	0.468907	+	0.00735256i
$477$	−11.0847	−	8.05349i	−0.507533	−	0.368744i
$478$	17.6657	+	3.75497i	0.808012	+	0.171748i
$479$	17.3827	−	19.3054i	0.794234	−	0.882086i	−0.201001	−	0.979591i	$-0.564419\pi$
$479$	17.3827	−	19.3054i	0.794234	−	0.882086i	0.995235	+	0.0975046i	$0.0310861\pi$
$480$	0.963464	−	9.16674i	0.0439759	−	0.418403i
$481$	1.14213	+	10.8666i	0.0520767	+	0.495476i
$482$	−0.949428	+	2.92204i	−0.0432452	+	0.133095i
$483$	−1.51320	+	12.5074i	−0.0688528	+	0.569107i
$484$		0			0
$485$	−0.824970	+	1.42889i	−0.0374600	+	0.0648825i
$486$	−30.1423	+	6.40694i	−1.36728	+	0.290625i
$487$	13.2790	+	5.91219i	0.601728	+	0.267907i	0.684910	−	0.728628i	$-0.259841\pi$
$487$	13.2790	+	5.91219i	0.601728	+	0.267907i	−0.0831816	+	0.996534i	$0.526508\pi$
$488$	4.61294	−	2.05381i	0.208818	−	0.0929718i
$489$	10.8746	+	33.4687i	0.491768	+	1.51351i
$490$	6.74896	−	4.58716i	0.304887	−	0.207227i
$491$	31.8714	+	23.1559i	1.43834	+	1.04501i	0.988387	+	0.151958i	$0.0485579\pi$
$491$	31.8714	+	23.1559i	1.43834	+	1.04501i	0.449949	+	0.893054i	$0.351442\pi$
$492$	2.36307	+	22.4831i	0.106536	+	1.01362i
$493$	−28.9161	+	6.14630i	−1.30231	+	0.276815i
$494$	−9.19041	−	15.9183i	−0.413496	−	0.716196i
$495$		0			0
$496$	−31.2975			−1.40530
$497$	−10.3002	−	4.78084i	−0.462028	−	0.214450i
$498$	−30.1201	+	21.8836i	−1.34972	+	0.980626i
$499$	−23.9628	+	10.6689i	−1.07272	+	0.477607i	−0.865614	−	0.500712i	$-0.833072\pi$
$499$	−23.9628	+	10.6689i	−1.07272	+	0.477607i	−0.207108	+	0.978318i	$0.566405\pi$
$500$	5.56817	−	6.18408i	0.249016	−	0.276560i
$501$	−1.70545	+	1.89409i	−0.0761938	+	0.0846218i
$502$	33.1343	−	14.7523i	1.47886	−	0.658429i
$503$	−3.19249	+	2.31948i	−0.142346	+	0.103420i	−0.656679	−	0.754170i	$-0.728039\pi$
$503$	−3.19249	+	2.31948i	−0.142346	+	0.103420i	0.514333	+	0.857590i	$0.328039\pi$
$504$	−4.62847	+	3.25315i	−0.206169	+	0.144907i
$505$	6.29204			0.279992
$506$		0			0
$507$	−10.7244	−	18.5753i	−0.476289	−	0.824956i
$508$	−28.0258	+	5.95707i	−1.24344	+	0.264302i
$509$	−1.76711	−	16.8130i	−0.0783259	−	0.745221i	−0.961245	−	0.275696i	$-0.911092\pi$
$509$	−1.76711	−	16.8130i	−0.0783259	−	0.745221i	0.882919	−	0.469525i	$-0.155575\pi$
$510$	5.87715	+	4.27000i	0.260245	+	0.189079i
$511$	27.8176	+	31.8860i	1.23058	+	1.41055i
$512$	6.41407	+	19.7405i	0.283465	+	0.872414i
$513$	−13.0263	+	5.79970i	−0.575127	+	0.256063i
$514$	4.55775	+	2.02924i	0.201034	+	0.0895060i
$515$	3.87397	−	0.823439i	0.170708	−	0.0362850i
$516$	−7.30077	+	12.6453i	−0.321398	+	0.556678i
$517$		0			0
$518$	−27.0768	+	11.5502i	−1.18969	+	0.507485i
$519$	0.674987	−	2.07740i	0.0296286	−	0.0911876i
$520$	0.139502	+	1.32728i	0.00611759	+	0.0582049i
$521$	−0.162822	+	1.54915i	−0.00713336	+	0.0678694i	−0.997509	−	0.0705329i	$-0.977530\pi$
$521$	−0.162822	+	1.54915i	−0.00713336	+	0.0678694i	0.990376	+	0.138402i	$0.0441967\pi$
$522$	−23.4813	+	26.0786i	−1.02775	+	1.14143i
$523$	12.2295	+	2.59946i	0.534759	+	0.113667i	0.467373	−	0.884060i	$-0.345201\pi$
$523$	12.2295	+	2.59946i	0.534759	+	0.113667i	0.0673866	+	0.997727i	$0.478534\pi$
$524$	15.1245	+	10.9886i	0.660716	+	0.480038i
$525$	−26.7329	−	0.419179i	−1.16672	−	0.0182945i
$526$	7.19561	−	22.1458i	0.313744	−	0.965604i
$527$	9.11254	−	15.7834i	0.396949	−	0.687535i
$528$		0			0
$529$	9.15475	+	15.8565i	0.398033	+	0.689413i
$530$	−5.82677	−	6.47128i	−0.253099	−	0.281094i
$531$	−17.5205	+	12.7294i	−0.760323	+	0.552407i
$532$	13.6704	−	14.7120i	0.592687	−	0.637845i
$533$	−4.19461	−	12.9097i	−0.181689	−	0.559181i
$534$	1.43768	+	0.305588i	0.0622144	+	0.0132241i
$535$	0.737330	−	7.01522i	0.0318775	−	0.303295i
$536$	1.70674	+	0.759891i	0.0737200	+	0.0328223i
$537$	28.9269	+	32.1266i	1.24829	+	1.38636i
$538$	−13.0109			−0.560941
$539$		0			0
$540$	−2.22270			−0.0956497
$541$	−11.0822	−	12.3080i	−0.476460	−	0.529162i	0.456220	−	0.889867i	$-0.349203\pi$
$541$	−11.0822	−	12.3080i	−0.476460	−	0.529162i	−0.932680	+	0.360704i	$0.882536\pi$
$542$	−30.5242	−	13.5902i	−1.31113	−	0.583750i
$543$	−5.48655	+	52.2010i	−0.235450	+	2.24016i
$544$	−18.2863	−	3.88688i	−0.784021	−	0.166649i
$545$	2.80926	+	8.64602i	0.120336	+	0.370355i
$546$	−13.0832	+	14.0800i	−0.559909	+	0.602569i
$547$	5.37550	−	3.90553i	0.229840	−	0.166988i	−0.466905	−	0.884307i	$-0.654631\pi$
$547$	5.37550	−	3.90553i	0.229840	−	0.166988i	0.696745	+	0.717319i	$0.254631\pi$
$548$	6.63250	+	7.36614i	0.283326	+	0.314666i
$549$	3.97252	+	6.88061i	0.169543	+	0.293657i
$550$		0			0
$551$	−29.0127	+	50.2514i	−1.23598	+	2.14078i
$552$	1.71540	−	5.27944i	0.0730121	−	0.224708i
$553$	−12.5971	−	0.197525i	−0.535682	−	0.00839961i
$554$	−20.5505	−	14.9308i	−0.873105	−	0.634348i
$555$	−8.29111	−	1.76233i	−0.351938	−	0.0748067i
$556$	−2.37617	+	2.63901i	−0.100772	+	0.111919i
$557$	−1.37057	+	13.0401i	−0.0580727	+	0.552525i	0.926345	+	0.376677i	$0.122933\pi$
$557$	−1.37057	+	13.0401i	−0.0580727	+	0.552525i	−0.984417	+	0.175848i	$0.943733\pi$
$558$	−2.26142	−	21.5160i	−0.0957334	−	0.910843i
$559$	2.70924	−	8.33819i	0.114589	−	0.352668i
$560$	−7.52793	+	3.21119i	−0.318113	+	0.135698i
$561$		0			0
$562$	−19.2898	+	33.4108i	−0.813689	+	1.40935i
$563$	−29.8223	+	6.33893i	−1.25686	+	0.267154i	−0.787755	−	0.615988i	$-0.788757\pi$
$563$	−29.8223	+	6.33893i	−1.25686	+	0.267154i	−0.469105	+	0.883142i	$0.655423\pi$
$564$	7.76763	+	3.45837i	0.327076	+	0.145624i
$565$	5.04512	−	2.24623i	0.212250	−	0.0944998i
$566$	0.199770	+	0.614830i	0.00839697	+	0.0258432i
$567$	19.3729	+	22.2063i	0.813586	+	0.932577i
$568$	4.04789	+	2.94097i	0.169846	+	0.123400i
$569$	3.69591	+	35.1642i	0.154940	+	1.47416i	0.745143	+	0.666905i	$0.232381\pi$
$569$	3.69591	+	35.1642i	0.154940	+	1.47416i	−0.590202	+	0.807255i	$0.700952\pi$
$570$	13.9475	−	2.96463i	0.584197	−	0.124175i
$571$	20.6422	+	35.7533i	0.863849	+	1.49623i	0.868185	+	0.496240i	$0.165287\pi$
$571$	20.6422	+	35.7533i	0.863849	+	1.49623i	−0.00433587	+	0.999991i	$0.501380\pi$
$572$		0			0
$573$	24.4753			1.02247
$574$	29.9193	−	21.0289i	1.24881	−	0.877731i
$575$	8.05294	−	5.85080i	0.335831	−	0.243995i
$576$	−3.96202	+	1.76401i	−0.165084	+	0.0735002i
$577$	5.82311	−	6.46722i	0.242419	−	0.269234i	−0.609641	−	0.792678i	$-0.708686\pi$
$577$	5.82311	−	6.46722i	0.242419	−	0.269234i	0.852060	+	0.523444i	$0.175353\pi$
$578$	−11.0057	+	12.2231i	−0.457777	+	0.508413i
$579$	−7.26034	+	3.23251i	−0.301730	+	0.134339i
$580$	−7.31751	+	5.31648i	−0.303843	+	0.220755i
$581$	22.1545	+	10.2830i	0.919122	+	0.426610i
$582$	10.4698			0.433987
$583$		0			0
$584$	−9.32224	−	16.1466i	−0.385757	−	0.668151i
$585$	−2.05400	+	0.436591i	−0.0849225	+	0.0180508i
$586$	0.664011	+	6.31765i	0.0274301	+	0.260980i
$587$	18.6510	+	13.5507i	0.769808	+	0.559298i	0.901903	−	0.431939i	$-0.142170\pi$
$587$	18.6510	+	13.5507i	0.769808	+	0.559298i	−0.132095	+	0.991237i	$0.542170\pi$
$588$	−18.9072	−	9.13876i	−0.779721	−	0.376876i
$589$	−11.0544	−	34.0219i	−0.455488	−	1.40185i
$590$	−12.5739	+	5.59825i	−0.517658	+	0.230476i
$591$	−4.85744	−	2.16267i	−0.199808	−	0.0889604i
$592$	28.8785	−	6.13831i	1.18690	−	0.252283i
$593$	−15.0494	+	26.0663i	−0.618005	+	1.07042i	0.371844	+	0.928295i	$0.378725\pi$
$593$	−15.0494	+	26.0663i	−0.618005	+	1.07042i	−0.989849	+	0.142121i	$0.954608\pi$
$594$		0			0
$595$	0.572413	−	4.73131i	0.0234666	−	0.193965i
$596$	−0.421638	+	1.29767i	−0.0172710	+	0.0531545i
$597$	−4.25090	−	40.4446i	−0.173978	−	1.65529i
$598$	0.747979	−	7.11654i	0.0305871	−	0.291017i
$599$	19.5731	−	21.7381i	0.799733	−	0.888194i	−0.195987	−	0.980606i	$-0.562791\pi$
$599$	19.5731	−	21.7381i	0.799733	−	0.888194i	0.995721	+	0.0924125i	$0.0294578\pi$
$600$	11.5229	+	2.44928i	0.470422	+	0.0999914i
$601$	21.6996	+	15.7657i	0.885147	+	0.643097i	0.934608	−	0.355679i	$-0.115750\pi$
$601$	21.6996	+	15.7657i	0.885147	+	0.643097i	−0.0494611	+	0.998776i	$0.515750\pi$
$602$	23.6173	+	0.370324i	0.962568	+	0.0150933i
$603$	−0.908383	+	2.79572i	−0.0369922	+	0.113850i
$604$	−1.18396	+	2.05068i	−0.0481746	+	0.0834409i
$605$		0			0
$606$	−19.9633	−	34.5774i	−0.810952	−	1.40461i
$607$	21.5524	+	23.9364i	0.874786	+	0.971549i	0.999788	−	0.0206079i	$-0.00656016\pi$
$607$	21.5524	+	23.9364i	0.874786	+	0.971549i	−0.125001	+	0.992157i	$0.539893\pi$
$608$	−29.6868	+	21.5687i	−1.20396	+	0.874727i
$609$	59.1442	+	13.5440i	2.39664	+	0.548831i
$610$	1.56038	+	4.80235i	0.0631779	+	0.194442i
$611$	−4.99378	−	1.06146i	−0.202027	−	0.0429421i
$612$	0.741456	−	7.05449i	0.0299716	−	0.285161i
$613$	40.7395	+	18.1384i	1.64545	+	0.732604i	0.999526	−	0.0307936i	$-0.00980347\pi$
$613$	40.7395	+	18.1384i	1.64545	+	0.732604i	0.645929	+	0.763397i	$0.276470\pi$
$614$	−7.99585	−	8.88029i	−0.322686	−	0.358379i
$615$	10.5302			0.424619
$616$		0			0
$617$	−0.531290			−0.0213889			−0.0106945	−	0.999943i	$-0.503404\pi$
$617$	−0.531290			−0.0213889			−0.0106945	+	0.999943i	$0.503404\pi$
$618$	−16.8164	−	18.6765i	−0.676455	−	0.751280i
$619$	38.1362	+	16.9793i	1.53282	+	0.682457i	0.987766	−	0.155942i	$-0.0498412\pi$
$619$	38.1362	+	16.9793i	1.53282	+	0.682457i	0.545057	+	0.838399i	$0.316508\pi$
$620$	0.582874	−	5.54568i	0.0234088	−	0.222720i
$621$	−5.42983	−	1.15415i	−0.217892	−	0.0463143i
$622$	6.59208	+	20.2883i	0.264318	+	0.813488i
$623$	−0.283552	−	0.921605i	−0.0113603	−	0.0369233i
$624$	15.5951	−	11.3305i	0.624302	−	0.453582i
$625$	12.7832	+	14.1972i	0.511330	+	0.567889i
$626$	24.8519	+	43.0448i	0.993282	+	1.72041i
$627$		0			0
$628$	5.41658	−	9.38179i	0.216145	−	0.374374i
$629$	−5.31267	+	16.3507i	−0.211830	+	0.651945i
$630$	−2.75152	−	4.94317i	−0.109623	−	0.196940i
$631$	0.175749	+	0.127689i	0.00699646	+	0.00508323i	0.591278	−	0.806468i	$-0.298624\pi$
$631$	0.175749	+	0.127689i	0.00699646	+	0.00508323i	−0.584282	+	0.811551i	$0.698624\pi$
$632$	5.42983	+	1.15415i	0.215987	+	0.0459095i
$633$	11.5566	−	12.8349i	0.459335	−	0.510143i
$634$	−0.740410	+	7.04453i	−0.0294054	+	0.279774i
$635$	1.39503	+	13.2728i	0.0553599	+	0.526715i
$636$	−6.92488	+	21.3126i	−0.274589	+	0.845099i
$637$	12.2454	+	3.00700i	0.485179	+	0.119142i
$638$		0			0
$639$	−3.93632	+	6.81790i	−0.155718	+	0.269712i
$640$	5.50494	−	1.17011i	0.217602	−	0.0462527i
$641$	−8.85271	−	3.94148i	−0.349661	−	0.155679i	0.224388	−	0.974500i	$-0.427962\pi$
$641$	−8.85271	−	3.94148i	−0.349661	−	0.155679i	−0.574049	+	0.818821i	$0.694628\pi$
$642$	−40.8910	+	18.2058i	−1.61384	+	0.718527i
$643$	5.08742	+	15.6575i	0.200628	+	0.617471i	0.999865	+	0.0164538i	$0.00523763\pi$
$643$	5.08742	+	15.6575i	0.200628	+	0.617471i	−0.799236	+	0.601017i	$0.794762\pi$
$644$	7.67206	−	1.50543i	0.302321	−	0.0593222i
$645$	5.50237	+	3.99771i	0.216656	+	0.157410i
$646$	−3.02307	−	28.7626i	−0.118941	−	1.13165i
$647$	−0.854628	+	0.181657i	−0.0335989	+	0.00714167i	−0.224680	−	0.974432i	$-0.572134\pi$
$647$	−0.854628	+	0.181657i	−0.0335989	+	0.00714167i	0.191082	+	0.981574i	$0.438801\pi$
$648$	−6.49226	−	11.2449i	−0.255040	−	0.441743i
$649$		0			0
$650$	15.1856			0.595628
$651$	−30.6034	+	21.5098i	−1.19944	+	0.843034i
$652$	17.6678	−	12.8364i	0.691925	−	0.502713i
$653$	−36.4807	+	16.2422i	−1.42760	+	0.635608i	−0.967640	−	0.252333i	$-0.918802\pi$
$653$	−36.4807	+	16.2422i	−1.42760	+	0.635608i	−0.459958	+	0.887941i	$0.652135\pi$
$654$	38.6003	−	42.8700i	1.50939	−	1.67635i
$655$	5.82677	−	6.47128i	0.227671	−	0.252854i
$656$	−33.5065	+	14.9180i	−1.30821	+	0.582452i
$657$	23.7332	−	17.2432i	0.925922	−	0.672721i
$658$	−1.22309	−	13.7000i	−0.0476810	−	0.534080i
$659$	−6.89465			−0.268578			−0.134289	−	0.990942i	$-0.542875\pi$
$659$	−6.89465			−0.268578			−0.134289	+	0.990942i	$0.542875\pi$
$660$		0			0
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	0.932984	+	0.359917i	$0.117195\pi$
$661$	20.0072	+	34.6535i	0.778190	+	1.34786i	−0.154795	+	0.987947i	$0.549472\pi$
$662$	−11.0346	+	2.34548i	−0.428872	+	0.0911595i
$663$	1.17334	+	11.1636i	0.0455688	+	0.433558i
$664$	−8.70650	−	6.32565i	−0.337878	−	0.245483i
$665$	−6.14961	−	7.04902i	−0.238472	−	0.273349i
$666$	6.30651	+	19.4094i	0.244372	+	0.752101i
$667$	−20.6366	+	9.18799i	−0.799051	+	0.355760i
$668$	1.44494	+	0.643330i	0.0559065	+	0.0248912i
$669$	43.7376	−	9.29671i	1.69099	−	0.359432i
$670$	−0.934131	+	1.61796i	−0.0360886	+	0.0625073i
$671$		0			0
$672$	30.6851	+	23.0376i	1.18370	+	0.888695i
$673$	9.69659	−	29.8430i	0.373776	−	1.15036i	−0.570524	−	0.821281i	$-0.693260\pi$
$673$	9.69659	−	29.8430i	0.373776	−	1.15036i	0.944301	−	0.329084i	$-0.106740\pi$
$674$	2.25490	+	21.4539i	0.0868553	+	0.826373i
$675$	1.23138	−	11.7158i	0.0473960	−	0.450943i
$676$	−8.90652	+	9.89169i	−0.342558	+	0.380450i
$677$	35.7332	+	7.59533i	1.37334	+	0.291912i	0.834737	−	0.550649i	$-0.185620\pi$
$677$	35.7332	+	7.59533i	1.37334	+	0.291912i	0.538601	+	0.842561i	$0.318953\pi$
$678$	−28.3511	−	20.5983i	−1.08882	−	0.791071i
$679$	−3.34060	−	6.00146i	−0.128200	−	0.230315i
$680$	−0.648901	+	1.99711i	−0.0248842	+	0.0765858i
$681$	7.93686	−	13.7470i	0.304141	−	0.526788i
$682$		0			0
$683$	7.63501	+	13.2242i	0.292146	+	0.506011i	0.974317	−	0.225181i	$-0.0722975\pi$
$683$	7.63501	+	13.2242i	0.292146	+	0.506011i	−0.682171	+	0.731192i	$0.738964\pi$
$684$	−9.31633	−	10.3468i	−0.356219	−	0.395621i
$685$	3.73524	−	2.71381i	0.142716	−	0.103689i
$686$	1.95844	+	33.9142i	0.0747736	+	1.29485i
$687$	−8.20166	−	25.2421i	−0.312913	−	0.963046i
$688$	−23.1717	−	4.92531i	−0.883415	−	0.187776i
$689$	1.40647	−	13.3817i	0.0535824	−	0.509802i
$690$	5.07122	+	2.25785i	0.193058	+	0.0859549i
$691$	−25.6841	−	28.5251i	−0.977069	−	1.08515i	−0.996353	−	0.0853315i	$-0.972805\pi$
$691$	−25.6841	−	28.5251i	−0.977069	−	1.08515i	0.0192832	−	0.999814i	$-0.493862\pi$
$692$	−1.35552			−0.0515291
$693$		0			0
$694$	−1.54221			−0.0585414
$695$	1.10681	+	1.22923i	0.0419836	+	0.0466275i
$696$	−24.4230	−	10.8738i	−0.925753	−	0.412172i
$697$	2.23251	−	21.2409i	0.0845623	−	0.804557i
$698$	−16.3838	−	3.48248i	−0.620136	−	0.131814i
$699$	5.12442	+	15.7714i	0.193824	+	0.596528i
$700$	4.87911	+	15.8582i	0.184413	+	0.599382i
$701$	−14.4859	+	10.5246i	−0.547125	+	0.397510i	−0.826724	−	0.562607i	$-0.809798\pi$
$701$	−14.4859	+	10.5246i	−0.547125	+	0.397510i	0.279599	+	0.960117i	$0.409798\pi$
$702$	−5.66667	−	6.29348i	−0.213875	−	0.237532i
$703$	16.8726	+	29.2243i	0.636364	+	1.10221i
$704$		0			0
$705$	1.98026	−	3.42991i	0.0745809	−	0.129178i
$706$	12.8824	−	39.6480i	0.484836	−	1.49217i
$707$	−13.4507	+	22.4759i	−0.505864	+	0.845293i
$708$	28.6556	+	20.8195i	1.07694	+	0.782446i
$709$	−33.6477	−	7.15203i	−1.26366	−	0.268600i	−0.473116	−	0.881000i	$-0.656871\pi$
$709$	−33.6477	−	7.15203i	−1.26366	−	0.268600i	−0.790548	+	0.612400i	$0.790204\pi$
$710$	−3.34797	+	3.71830i	−0.125647	+	0.139545i
$711$	−0.912989	+	8.68651i	−0.0342398	+	0.325769i
$712$	0.0444097	+	0.422530i	0.00166433	+	0.0158350i
$713$	4.30353	−	13.2449i	0.161168	−	0.496025i
$714$	−27.8167	+	11.8658i	−1.04101	+	0.444066i
$715$		0			0
$716$	13.4138	−	23.2335i	0.501299	−	0.868276i
$717$	−21.1758	+	4.50105i	−0.790824	+	0.168095i
$718$	−43.9335	−	19.5604i	−1.63958	−	0.729989i
$719$	45.1449	−	20.0998i	1.68362	−	0.749596i	0.683819	−	0.729652i	$-0.260318\pi$
$719$	45.1449	−	20.0998i	1.68362	−	0.749596i	0.999801	−	0.0199443i	$-0.00634890\pi$
$720$	1.75335	+	5.39624i	0.0653433	+	0.201106i
$721$	−5.34008	+	15.5986i	−0.198875	+	0.580921i
$722$	−17.7308	−	12.8822i	−0.659873	−	0.479425i
$723$	−0.384965	−	3.66270i	−0.0143170	−	0.136217i
$724$	31.8612	−	6.77230i	1.18411	−	0.251691i
$725$	−23.9693	−	41.5160i	−0.890196	−	1.54186i
$726$		0			0
$727$	−19.8201			−0.735086			−0.367543	−	0.930007i	$-0.619801\pi$
$727$	−19.8201			−0.735086			−0.367543	+	0.930007i	$0.619801\pi$
$728$	−5.03941	−	2.33904i	−0.186773	−	0.0866905i
$729$	2.85070	−	2.07116i	0.105582	−	0.0767095i
$730$	17.0326	−	7.58339i	0.630404	−	0.280674i
$731$	9.23050	−	10.2515i	0.341402	−	0.379166i
$732$	8.69505	−	9.65683i	0.321378	−	0.356927i
$733$	−27.9979	+	12.4655i	−1.03413	+	0.460423i	−0.852380	−	0.522922i	$-0.824842\pi$
$733$	−27.9979	+	12.4655i	−1.03413	+	0.460423i	−0.181747	+	0.983345i	$0.558175\pi$
$734$	5.67195	−	4.12091i	0.209356	−	0.152106i
$735$	−5.15403	+	8.31368i	−0.190109	+	0.306655i
$736$	−14.2855			−0.526570
$737$		0			0
$738$	−12.6767	−	21.9566i	−0.466635	−	0.808235i
$739$	−16.7282	+	3.55568i	−0.615355	+	0.130798i	−0.505036	−	0.863098i	$-0.668521\pi$
$739$	−16.7282	+	3.55568i	−0.615355	+	0.130798i	−0.110319	+	0.993896i	$0.535187\pi$
$740$	0.549839	+	5.23137i	0.0202125	+	0.192309i
$741$	17.8250	+	12.9506i	0.654818	+	0.475753i
$742$	35.5722	−	6.98006i	1.30590	−	0.256246i
$743$	−2.15463	−	6.63127i	−0.0790457	−	0.243278i	0.903723	−	0.428118i	$-0.140823\pi$
$743$	−2.15463	−	6.63127i	−0.0790457	−	0.243278i	−0.982769	+	0.184840i	$0.940823\pi$
$744$	15.0569	−	6.70375i	0.552012	−	0.245771i
$745$	0.580606	+	0.258502i	0.0212717	+	0.00947079i
$746$	−27.1057	+	5.76149i	−0.992410	+	0.210943i
$747$	8.46652	−	14.6644i	0.309774	−	0.536544i
$748$		0			0
$749$	23.4830	+	17.6305i	0.858050	+	0.644203i
$750$	−7.60060	+	23.3923i	−0.277535	+	0.854164i
$751$	−1.59225	−	15.1493i	−0.0581021	−	0.552804i	−0.984392	−	0.175992i	$-0.943687\pi$
$751$	−1.59225	−	15.1493i	−0.0581021	−	0.552804i	0.926290	−	0.376813i	$-0.122980\pi$
$752$	−1.44195	+	13.7192i	−0.0525823	+	0.500288i
$753$	−29.0915	+	32.3094i	−1.06015	+	1.17742i
$754$	−33.7091	−	7.16509i	−1.22761	−	0.260937i
$755$	0.892315	+	0.648305i	0.0324747	+	0.0235942i
$756$	4.75152	−	7.93973i	0.172811	−	0.288765i
$757$	−4.49082	+	13.8213i	−0.163222	+	0.502344i	−0.998901	−	0.0468735i	$-0.985074\pi$
$757$	−4.49082	+	13.8213i	−0.163222	+	0.502344i	0.835679	+	0.549218i	$0.185074\pi$
$758$	10.4336	−	18.0715i	0.378965	−	0.656387i
$759$		0			0
$760$	2.06086	+	3.56952i	0.0747553	+	0.129480i
$761$	−1.14650	−	1.27332i	−0.0415607	−	0.0461579i	0.722006	−	0.691887i	$-0.243220\pi$
$761$	−1.14650	−	1.27332i	−0.0415607	−	0.0461579i	−0.763567	+	0.645729i	$0.776554\pi$
$762$	68.5134	−	49.7779i	2.48198	−	1.80326i
$763$	−36.8900	−	8.44781i	−1.33551	−	0.305831i
$764$	−4.69356	−	14.4453i	−0.169807	−	0.522612i
$765$	−3.23184	−	0.686948i	−0.116847	−	0.0248367i
$766$	−1.70367	+	16.2093i	−0.0615559	+	0.585666i
$767$	−19.4290	−	8.65033i	−0.701539	−	0.312345i
$768$	−30.8534	−	34.2662i	−1.11333	−	1.23648i
$769$	−36.5874			−1.31937			−0.659687	−	0.751540i	$-0.729311\pi$
$769$	−36.5874			−1.31937			−0.659687	+	0.751540i	$0.729311\pi$
$770$		0			0
$771$	−5.98037			−0.215378
$772$	3.30013	+	3.66516i	0.118774	+	0.131912i
$773$	24.5023	+	10.9091i	0.881288	+	0.392375i	0.796938	−	0.604061i	$-0.206452\pi$
$773$	24.5023	+	10.9091i	0.881288	+	0.392375i	0.0843503	+	0.996436i	$0.473119\pi$
$774$	1.71169	−	16.2857i	0.0615255	−	0.585376i
$775$	28.9084	+	6.14467i	1.03842	+	0.220723i
$776$	0.935206	+	2.87827i	0.0335719	+	0.103324i
$777$	24.0194	−	25.8494i	0.861690	−	0.927343i
$778$	29.5288	−	21.4540i	1.05866	−	0.769162i
$779$	−28.0513	−	31.1541i	−1.00504	−	1.11621i
$780$	1.71724	+	2.97434i	0.0614870	+	0.106499i
$781$		0			0
$782$	5.62955	−	9.75067i	0.201312	−	0.348683i
$783$	−8.26137	+	25.4259i	−0.295237	+	0.908647i
$784$	4.62190	−	33.7553i	0.165068	−	1.20555i
$785$	−4.08232	−	2.96598i	−0.145704	−	0.105860i
$786$	−54.0494	−	11.4886i	−1.92788	−	0.409783i
$787$	3.31326	−	3.67975i	0.118105	−	0.131169i	−0.681193	−	0.732104i	$-0.738538\pi$
$787$	3.31326	−	3.67975i	0.118105	−	0.131169i	0.799298	+	0.600935i	$0.205205\pi$
$788$	−0.344909	+	3.28159i	−0.0122869	+	0.116902i
$789$	2.91761	+	27.7592i	0.103870	+	0.988254i
$790$	−1.71540	+	5.27944i	−0.0610310	+	0.187834i
$791$	−2.76129	+	22.8236i	−0.0981801	+	0.811514i
$792$		0			0
$793$	−3.90120	+	6.75707i	−0.138536	+	0.239951i
$794$	62.5456	−	13.2945i	2.21966	−	0.471803i
$795$	9.53573	+	4.24558i	0.338198	+	0.150575i
$796$	−23.0552	+	10.2648i	−0.817171	+	0.363828i
$797$	−8.24513	−	25.3759i	−0.292057	−	0.898860i	−0.984194	−	0.177094i	$-0.943330\pi$
$797$	−8.24513	−	25.3759i	−0.292057	−	0.898860i	0.692137	−	0.721766i	$-0.256670\pi$
$798$	−19.2259	+	56.1597i	−0.680591	+	1.98803i
$799$	−6.49878	−	4.72164i	−0.229910	−	0.167040i
$800$	−3.16889	−	30.1500i	−0.112037	−	1.06596i
$801$	−0.653878	+	0.138986i	−0.0231037	+	0.00491083i
$802$	−10.4518	−	18.1030i	−0.369066	−	0.639240i
$803$		0			0
$804$	4.80785			0.169560
$805$	−0.323836	−	3.62732i	−0.0114137	−	0.127846i
$806$	17.1884	−	12.4881i	0.605435	−	0.439874i
$807$	14.2477	−	6.34349i	0.501544	−	0.223302i
$808$	7.72252	−	8.57673i	0.271677	−	0.301728i
$809$	−26.4574	+	29.3840i	−0.930194	+	1.03309i	0.0691759	+	0.997604i	$0.477963\pi$
$809$	−26.4574	+	29.3840i	−0.930194	+	1.03309i	−0.999370	+	0.0354811i	$0.988704\pi$
$810$	11.8620	−	5.28128i	0.416787	−	0.185565i
$811$	27.0651	−	19.6640i	0.950385	−	0.690495i	−0.000513088	−	1.00000i	$-0.500163\pi$
$811$	27.0651	−	19.6640i	0.950385	−	0.690495i	0.950898	+	0.309505i	$0.100163\pi$
$812$	−3.34826	−	37.5042i	−0.117501	−	1.31614i
$813$	40.0517			1.40467
$814$		0			0
$815$	−5.08615	−	8.80947i	−0.178160	−	0.308582i
$816$	29.6676	−	6.30605i	1.03858	−	0.220756i
$817$	−2.83029	−	26.9285i	−0.0990195	−	0.942107i
$818$	6.06615	+	4.40732i	0.212098	+	0.154098i
$819$	2.83134	−	8.27044i	0.0989349	−	0.288993i
$820$	−2.01935	−	6.21493i	−0.0705188	−	0.217035i
$821$	51.9460	−	23.1278i	1.81293	−	0.807167i	0.855915	−	0.517116i	$-0.172994\pi$
$821$	51.9460	−	23.1278i	1.81293	−	0.807167i	0.957011	−	0.290051i	$-0.0936723\pi$
$822$	−26.7646	−	11.9164i	−0.933522	−	0.415631i
$823$	39.2977	−	8.35297i	1.36983	−	0.291166i	0.536481	−	0.843913i	$-0.319753\pi$
$823$	39.2977	−	8.35297i	1.36983	−	0.291166i	0.833350	+	0.552746i	$0.186420\pi$
$824$	3.63228	−	6.29129i	0.126536	−	0.219168i
$825$		0			0
$826$	6.88191	−	56.8829i	0.239452	−	1.97921i
$827$	−1.77235	+	5.45473i	−0.0616306	+	0.189679i	−0.977131	−	0.212637i	$-0.931795\pi$
$827$	−1.77235	+	5.45473i	−0.0616306	+	0.189679i	0.915501	+	0.402316i	$0.131795\pi$
$828$	−0.566576	−	5.39061i	−0.0196899	−	0.187337i
$829$	3.72080	−	35.4011i	0.129229	−	1.22953i	−0.717139	−	0.696931i	$-0.754549\pi$
$829$	3.72080	−	35.4011i	0.129229	−	1.22953i	0.846367	−	0.532600i	$-0.178785\pi$
$830$	7.20107	−	7.99760i	0.249953	−	0.277601i
$831$	29.7835	+	6.33067i	1.03318	+	0.219609i
$832$	−3.44569	−	2.50344i	−0.119458	−	0.0867911i
$833$	15.6771	+	12.1590i	0.543181	+	0.421284i
$834$	3.24350	−	9.98247i	0.112313	−	0.345665i
$835$	0.368370	−	0.638036i	0.0127480	−	0.0220801i
$836$		0			0
$837$	−8.24090	−	14.2737i	−0.284847	−	0.493370i
$838$	40.2573	+	44.7103i	1.39067	+	1.54449i
$839$	33.7949	−	24.5534i	1.16673	−	0.847678i	0.176115	−	0.984370i	$-0.443647\pi$
$839$	33.7949	−	24.5534i	1.16673	−	0.847678i	0.990614	+	0.136692i	$0.0436471\pi$
$840$	2.93378	−	3.15731i	0.101225	−	0.108938i
$841$	24.6569	+	75.8862i	0.850239	+	2.61677i
$842$	15.2885	+	3.24968i	0.526878	+	0.111991i
$843$	4.83391	−	45.9916i	0.166489	−	1.58403i
$844$	−9.79136	−	4.35939i	−0.337033	−	0.150057i
$845$	4.14860	+	4.60749i	0.142716	+	0.158503i
$846$	−9.53566			−0.327843
$847$		0			0
$848$	−36.3568			−1.24850
$849$	−0.518521	−	0.575876i	−0.0177956	−	0.0197640i
$850$	21.8279	+	9.71839i	0.748689	+	0.333338i
$851$	−1.37321	+	13.0652i	−0.0470731	+	0.447870i
$852$	12.5947	+	2.67709i	0.431488	+	0.0917157i
$853$	15.3851	+	47.3504i	0.526775	+	1.62125i	0.760779	+	0.649011i	$0.224817\pi$
$853$	15.3851	+	47.3504i	0.526775	+	1.62125i	−0.234005	+	0.972236i	$0.575183\pi$
$854$	−20.4902	−	4.69226i	−0.701161	−	0.160566i
$855$	−5.24669	+	3.81194i	−0.179433	+	0.130366i
$856$	−8.65755	−	9.61518i	−0.295909	−	0.328640i
$857$	−12.7394	−	22.0652i	−0.435168	−	0.753734i	0.562141	−	0.827041i	$-0.309978\pi$
$857$	−12.7394	−	22.0652i	−0.435168	−	0.753734i	−0.997309	+	0.0733077i	$0.976644\pi$
$858$		0			0
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	−0.970315	−	0.241845i	$-0.922247\pi$
$859$	−8.08080	+	13.9964i	−0.275713	+	0.477549i	0.694602	+	0.719395i	$0.255581\pi$
$860$	1.30427	−	4.01413i	0.0444752	−	0.136881i
$861$	−22.5107	+	37.6151i	−0.767163	+	1.28192i
$862$	24.8327	+	18.0420i	0.845804	+	0.614513i
$863$	−2.83568	−	0.602742i	−0.0965276	−	0.0205176i	0.159395	−	0.987215i	$-0.449046\pi$
$863$	−2.83568	−	0.602742i	−0.0965276	−	0.0205176i	−0.255922	+	0.966697i	$0.582379\pi$
$864$	−11.3128	+	12.5641i	−0.384868	+	0.427439i
$865$	−0.0659985	+	0.627934i	−0.00224402	+	0.0213504i
$866$	4.95932	+	47.1848i	0.168525	+	1.60340i
$867$	6.09252	−	18.7508i	0.206913	−	0.636812i
$868$	18.5638	+	13.9372i	0.630096	+	0.473061i
$869$		0			0
$870$	13.3672	−	23.1526i	0.453190	−	0.784948i
$871$	−2.82373	+	0.600201i	−0.0956783	+	0.0203370i
$872$	15.2334	+	6.78235i	0.515868	+	0.229679i
$873$	−4.35015	+	1.93681i	−0.147230	+	0.0655511i
$874$	−6.82919	−	21.0181i	−0.231001	−	0.710947i
$875$	15.8340	−	3.10698i	0.535286	−	0.105035i
$876$	−38.8169	−	28.2022i	−1.31150	−	0.952862i
$877$	0.879591	+	8.36875i	0.0297017	+	0.282593i	0.999284	+	0.0378281i	$0.0120439\pi$
$877$	0.879591	+	8.36875i	0.0297017	+	0.282593i	−0.969583	+	0.244764i	$0.921289\pi$
$878$	17.1676	−	3.64909i	0.579379	−	0.123151i
$879$	−3.80731	−	6.59445i	−0.128417	−	0.222425i
$880$		0			0
$881$	41.5335			1.39930			0.699649	−	0.714486i	$-0.253340\pi$
$881$	41.5335			1.39930			0.699649	+	0.714486i	$0.253340\pi$
$882$	23.5396	+	0.738393i	0.792618	+	0.0248630i
$883$	45.6894	−	33.1953i	1.53757	−	1.11711i	0.585737	−	0.810501i	$-0.300805\pi$
$883$	45.6894	−	33.1953i	1.53757	−	1.11711i	0.951835	−	0.306610i	$-0.0991948\pi$
$884$	6.36374	−	2.83332i	0.214036	−	0.0952949i
$885$	11.0397	−	12.2608i	0.371095	−	0.412143i
$886$	23.3600	−	25.9440i	0.784796	−	0.871604i
$887$	−31.5900	+	14.0648i	−1.06069	+	0.472248i	−0.861523	−	0.507718i	$-0.830489\pi$
$887$	−31.5900	+	14.0648i	−1.06069	+	0.472248i	−0.199164	+	0.979966i	$0.563823\pi$
$888$	−12.5783	+	9.13869i	−0.422101	+	0.306674i
$889$	−50.3941	−	23.3904i	−1.69017	−	0.784489i
$890$	−0.424858			−0.0142413
$891$		0			0
$892$	−13.8744	−	24.0311i	−0.464548	−	0.804621i
$893$	−15.4227	+	3.27820i	−0.516102	+	0.109701i
$894$	−0.421556	−	4.01084i	−0.0140990	−	0.134143i
$895$	−10.1096	−	7.34507i	−0.337928	−	0.245519i
$896$	−7.58829	+	22.1657i	−0.253507	+	0.740503i
$897$	2.65060	+	8.15771i	0.0885010	+	0.272378i
$898$	55.8707	−	24.8753i	1.86443	−	0.830098i
$899$	−61.2717	−	27.2799i	−2.04353	−	0.909836i
$900$	11.2514	−	2.39155i	0.375046	−	0.0797184i
$901$	10.5856	−	18.3348i	0.352658	−	0.610821i
$902$		0			0
$903$	−26.0429	+	11.1091i	−0.866652	+	0.369688i
$904$	3.13026	−	9.63396i	0.104111	−	0.320421i
$905$	−1.58594	−	15.0892i	−0.0527183	−	0.501581i
$906$	0.731586	−	6.96057i	0.0243053	−	0.231250i
$907$	5.62260	−	6.24453i	0.186695	−	0.207346i	−0.642530	−	0.766260i	$-0.722115\pi$
$907$	5.62260	−	6.24453i	0.186695	−	0.207346i	0.829225	+	0.558914i	$0.188782\pi$
$908$	−9.63554	−	2.04810i	−0.319767	−	0.0679685i
$909$	14.6911	+	10.6737i	0.487273	+	0.354025i
$910$	2.85298	−	4.76730i	0.0945755	−	0.158035i
$911$	−0.183460	+	0.564632i	−0.00607830	+	0.0187071i	−0.954050	−	0.299649i	$-0.903131\pi$
$911$	−0.183460	+	0.564632i	−0.00607830	+	0.0187071i	0.947971	+	0.318356i	$0.103131\pi$
$912$	29.7667	−	51.5575i	0.985675	−	1.70724i
$913$		0			0
$914$	−10.9693	−	18.9993i	−0.362831	−	0.628441i
$915$	−4.05010	−	4.49809i	−0.133892	−	0.148702i
$916$	−13.3251	+	9.68123i	−0.440273	+	0.319877i
$917$	10.6601	+	34.6477i	0.352028	+	1.14417i
$918$	−4.11764	−	12.6728i	−0.135902	−	0.418265i
$919$	15.9800	+	3.39665i	0.527131	+	0.112045i	0.463787	−	0.885947i	$-0.346490\pi$
$919$	15.9800	+	3.39665i	0.527131	+	0.112045i	0.0633436	+	0.997992i	$0.479824\pi$
$920$	−0.167727	+	1.59582i	−0.00552980	+	0.0526125i
$921$	13.0855	+	5.82605i	0.431183	+	0.191975i
$922$	15.3291	+	17.0247i	0.504838	+	0.560680i
$923$	−7.73128			−0.254478
$924$		0			0
$925$	−27.8792			−0.916662
$926$	15.1080	+	16.7792i	0.496481	+	0.551398i
$927$	10.4421	+	4.64913i	0.342964	+	0.152697i
$928$	−7.19147	+	68.4223i	−0.236072	+	2.24607i
$929$	−8.70668	−	1.85066i	−0.285657	−	0.0607183i	0.0628547	−	0.998023i	$-0.479980\pi$
$929$	−8.70668	−	1.85066i	−0.285657	−	0.0607183i	−0.348512	+	0.937304i	$0.613313\pi$
$930$	5.09316	+	15.6751i	0.167011	+	0.514007i
$931$	38.3261	−	6.89825i	1.25609	−	0.226081i
$932$	8.32555	−	6.04887i	0.272713	−	0.198137i
$933$	−17.1103	−	19.0029i	−0.560167	−	0.622128i
$934$	−30.0456	−	52.0405i	−0.983122	−	1.70282i
$935$		0			0
$936$	−1.92585	+	3.33567i	−0.0629485	+	0.109030i
$937$	13.9787	−	43.0220i	0.456664	−	1.40547i	−0.412506	−	0.910955i	$-0.635347\pi$
$937$	13.9787	−	43.0220i	0.456664	−	1.40547i	0.869170	−	0.494513i	$-0.164653\pi$
$938$	−3.78263	−	6.79559i	−0.123507	−	0.221884i
$939$	−48.2008	−	35.0200i	−1.57298	−	1.14283i
$940$	−2.40408	−	0.511004i	−0.0784126	−	0.0166671i
$941$	−4.63911	+	5.15226i	−0.151231	+	0.167959i	−0.814000	−	0.580865i	$-0.802714\pi$
$941$	−4.63911	+	5.15226i	−0.151231	+	0.167959i	0.662769	+	0.748824i	$0.269381\pi$
$942$	−3.34699	+	31.8444i	−0.109051	+	1.03755i
$943$	−1.70595	−	16.2310i	−0.0555533	−	0.528554i
$944$	−17.7579	+	54.6531i	−0.577969	+	1.77881i
$945$	−3.44668	−	2.58768i	−0.112120	−	0.0841773i
$946$		0			0
$947$	−10.3716	+	17.9642i	−0.337033	+	0.583758i	−0.983873	−	0.178867i	$-0.942757\pi$
$947$	−10.3716	+	17.9642i	−0.337033	+	0.583758i	0.646840	+	0.762626i	$0.276090\pi$
$948$	13.9733	−	2.97012i	0.453832	−	0.0964650i
$949$	26.3185	+	11.7177i	0.854334	+	0.380374i
$950$	42.8444	−	19.0756i	1.39006	−	0.618893i
$951$	−2.62378	−	8.07516i	−0.0850819	−	0.261855i
$952$	−5.74674	−	6.58723i	−0.186253	−	0.213493i
$953$	−16.3483	−	11.8777i	−0.529574	−	0.384758i	0.290625	−	0.956837i	$-0.406137\pi$
$953$	−16.3483	−	11.8777i	−0.529574	−	0.384758i	−0.820198	+	0.572079i	$0.806137\pi$
$954$	−2.62698	−	24.9941i	−0.0850517	−	0.809213i
$955$	−6.92020	+	1.47093i	−0.223932	+	0.0475983i
$956$	6.71735	+	11.6348i	0.217254	+	0.376296i
$957$		0			0
$958$	47.6499			1.53950
$959$	1.70912	+	19.1441i	0.0551905	+	0.618195i
$960$	2.67302	−	1.94206i	0.0862715	−	0.0626799i
$961$	9.45426	−	4.20931i	0.304976	−	0.135784i
$962$	−13.4106	+	14.8940i	−0.432376	+	0.480202i
$963$	13.6221	−	15.1289i	0.438966	−	0.487521i
$964$	−2.08790	+	0.929593i	−0.0672467	+	0.0299402i
$965$	1.85854	−	1.35031i	0.0598284	−	0.0434679i
$966$	−18.9062	+	13.2883i	−0.608296	+	0.427544i
$967$	−7.98254			−0.256701			−0.128351	−	0.991729i	$-0.540968\pi$
$967$	−7.98254			−0.256701			−0.128351	+	0.991729i	$0.540968\pi$
$968$		0			0
$969$	17.3337	+	30.0229i	0.556839	+	0.964473i
$970$	−2.96026	+	0.629222i	−0.0950481	+	0.0202031i
$971$	1.44033	+	13.7038i	0.0462223	+	0.439776i	0.993020	+	0.117947i	$0.0376311\pi$
$971$	1.44033	+	13.7038i	0.0462223	+	0.439776i	−0.946798	+	0.321830i	$0.895702\pi$
$972$	−18.5451	−	13.4738i	−0.594835	−	0.432173i
$973$	−6.75702	+	1.32588i	−0.216620	+	0.0425057i
$974$	8.23899	+	25.3570i	0.263994	+	0.812491i
$975$	−16.6291	+	7.40377i	−0.532558	+	0.237110i
$976$	19.2596	+	8.57492i	0.616484	+	0.274477i
$977$	−11.7582	+	2.49929i	−0.376180	+	0.0799594i	−0.392121	−	0.919913i	$-0.628259\pi$
$977$	−11.7582	+	2.49929i	−0.376180	+	0.0799594i	0.0159418	+	0.999873i	$0.494925\pi$
$978$	−32.2745	+	55.9010i	−1.03202	+	1.78752i
$979$		0			0
$980$	5.89511	+	1.44761i	0.188312	+	0.0462423i
$981$	−8.10771	+	24.9530i	−0.258859	+	0.796686i
$982$	7.55327	+	71.8646i	0.241034	+	2.29329i
$983$	4.66765	−	44.4097i	0.148875	−	1.41645i	−0.623769	−	0.781609i	$-0.714399\pi$
$983$	4.66765	−	44.4097i	0.148875	−	1.41645i	0.772643	−	0.634840i	$-0.218934\pi$
$984$	12.9242	−	14.3538i	0.412009	−	0.457583i
$985$	1.50338	+	0.319553i	0.0479016	+	0.0101818i
$986$	−43.8681	−	31.8721i	−1.39705	−	1.01501i
$987$	8.01879	+	14.4059i	0.255241	+	0.458546i
$988$	4.22520	−	13.0038i	0.134422	−	0.413707i
$989$	5.27056	−	9.12888i	0.167594	−	0.290282i
$990$		0			0
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	0.988739	−	0.149650i	$-0.0478146\pi$
$991$	11.4830	+	19.8891i	0.364769	+	0.631799i	−0.623970	+	0.781448i	$0.714481\pi$
$992$	−28.3811	−	31.5204i	−0.901100	−	1.00077i
$993$	10.9400	−	7.94837i	0.347170	−	0.252234i
$994$	−6.12516	−	19.9081i	−0.194278	−	0.631446i
$995$	3.63258	+	11.1799i	0.115161	+	0.354428i
$996$	−27.0897	−	5.75809i	−0.858369	−	0.182452i
$997$	−0.141006	+	1.34159i	−0.00446572	+	0.0424884i	−0.996528	−	0.0832604i	$-0.973467\pi$
$997$	−0.141006	+	1.34159i	−0.00446572	+	0.0424884i	0.992062	+	0.125749i	$0.0401333\pi$
$998$	−43.9536	−	19.5694i	−1.39133	−	0.619458i
$999$	10.4034	+	11.5542i	0.329150	+	0.365558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.e.9.3		24
7.4	even	3	inner	847.2.n.e.130.1		24
11.2	odd	10		847.2.n.d.366.3		24
11.3	even	5	inner	847.2.n.e.807.3		24
11.4	even	5		77.2.e.b.23.1	✓	6
11.5	even	5	inner	847.2.n.e.632.1		24
11.6	odd	10		847.2.n.d.632.3		24
11.7	odd	10		847.2.e.d.485.3		6
11.8	odd	10		847.2.n.d.807.1		24
11.9	even	5	inner	847.2.n.e.366.1		24
11.10	odd	2		847.2.n.d.9.1		24
33.26	odd	10		693.2.i.g.100.3		6
44.15	odd	10		1232.2.q.k.177.1		6
77.4	even	15		77.2.e.b.67.1	yes	6
77.18	odd	30		847.2.e.d.606.3		6
77.25	even	15	inner	847.2.n.e.81.1		24
77.26	odd	30		539.2.a.i.1.3		3
77.32	odd	6		847.2.n.d.130.3		24
77.37	even	15		539.2.a.h.1.3		3
77.39	odd	30		847.2.n.d.753.1		24
77.40	even	30		5929.2.a.w.1.1		3
77.46	odd	30		847.2.n.d.487.1		24
77.48	odd	10		539.2.e.l.177.1		6
77.51	odd	30		5929.2.a.v.1.1		3
77.53	even	15	inner	847.2.n.e.487.3		24
77.59	odd	30		539.2.e.l.67.1		6
77.60	even	15	inner	847.2.n.e.753.3		24
77.74	odd	30		847.2.n.d.81.3		24
231.26	even	30		4851.2.a.bn.1.1		3
231.158	odd	30		693.2.i.g.298.3		6
231.191	odd	30		4851.2.a.bo.1.1		3
308.103	even	30		8624.2.a.ck.1.1		3
308.191	odd	30		8624.2.a.cl.1.3		3
308.235	odd	30		1232.2.q.k.529.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.1	✓	6	11.4	even	5
77.2.e.b.67.1	yes	6	77.4	even	15
539.2.a.h.1.3		3	77.37	even	15
539.2.a.i.1.3		3	77.26	odd	30
539.2.e.l.67.1		6	77.59	odd	30
539.2.e.l.177.1		6	77.48	odd	10
693.2.i.g.100.3		6	33.26	odd	10
693.2.i.g.298.3		6	231.158	odd	30
847.2.e.d.485.3		6	11.7	odd	10
847.2.e.d.606.3		6	77.18	odd	30
847.2.n.d.9.1		24	11.10	odd	2
847.2.n.d.81.3		24	77.74	odd	30
847.2.n.d.130.3		24	77.32	odd	6
847.2.n.d.366.3		24	11.2	odd	10
847.2.n.d.487.1		24	77.46	odd	30
847.2.n.d.632.3		24	11.6	odd	10
847.2.n.d.753.1		24	77.39	odd	30
847.2.n.d.807.1		24	11.8	odd	10
847.2.n.e.9.3		24	1.1	even	1	trivial
847.2.n.e.81.1		24	77.25	even	15	inner
847.2.n.e.130.1		24	7.4	even	3	inner
847.2.n.e.366.1		24	11.9	even	5	inner
847.2.n.e.487.3		24	77.53	even	15	inner
847.2.n.e.632.1		24	11.5	even	5	inner
847.2.n.e.753.3		24	77.60	even	15	inner
847.2.n.e.807.3		24	11.3	even	5	inner
1232.2.q.k.177.1		6	44.15	odd	10
1232.2.q.k.529.1		6	308.235	odd	30
4851.2.a.bn.1.1		3	231.26	even	30
4851.2.a.bo.1.1		3	231.191	odd	30
5929.2.a.v.1.1		3	77.51	odd	30
5929.2.a.w.1.1		3	77.40	even	30
8624.2.a.ck.1.1		3	308.103	even	30
8624.2.a.cl.1.3		3	308.191	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)

\(f(q)\)	\(=\)	\(q+(1.22735 + 1.36311i) q^{2} +(-2.00860 - 0.894288i) q^{3} +(-0.142624 + 1.35697i) q^{4} +(0.621664 + 0.132139i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(-1.80096 + 1.93818i) q^{7} +(0.943117 - 0.685215i) q^{8} +(1.22735 + 1.36311i) q^{9} +O(q^{10})\)	\(q+(1.22735 + 1.36311i) q^{2} +(-2.00860 - 0.894288i) q^{3} +(-0.142624 + 1.35697i) q^{4} +(0.621664 + 0.132139i) q^{5} +(-1.24625 - 3.83555i) q^{6} +(-1.80096 + 1.93818i) q^{7} +(0.943117 - 0.685215i) q^{8} +(1.22735 + 1.36311i) q^{9} +(0.582878 + 1.00958i) q^{10} +(1.50000 - 2.59808i) q^{12} +(-0.556635 + 1.71315i) q^{13} +(-4.85235 - 0.0760860i) q^{14} +(-1.13051 - 0.821361i) q^{15} +(4.76082 + 1.01194i) q^{16} +(-1.89648 + 2.10625i) q^{17} +(-0.351681 + 3.34602i) q^{18} +(0.581506 + 5.53266i) q^{19} +(-0.267973 + 0.824735i) q^{20} +(5.35071 - 2.28245i) q^{21} +(-1.08288 + 1.87560i) q^{23} +(-2.50713 + 0.532907i) q^{24} +(-4.19872 - 1.86939i) q^{25} +(-3.01839 + 1.34387i) q^{26} +(0.792054 + 2.43769i) q^{27} +(-2.37320 - 2.72029i) q^{28} +(8.43830 + 6.13079i) q^{29} +(-0.267921 - 2.54910i) q^{30} +(-6.28980 + 1.33694i) q^{31} +(3.29804 + 5.71237i) q^{32} -5.19869 q^{34} +(-1.37570 + 0.966918i) q^{35} +(-2.02475 + 1.47107i) q^{36} +(5.54145 - 2.46721i) q^{37} +(-6.82791 + 7.58316i) q^{38} +(2.65011 - 2.94324i) q^{39} +(0.676845 - 0.301351i) q^{40} +(-6.09648 + 4.42935i) q^{41} +(9.67842 + 4.49223i) q^{42} -4.86718 q^{43} +(0.582878 + 1.00958i) q^{45} +(-3.88572 + 0.825934i) q^{46} +(0.296259 + 2.81872i) q^{47} +(-8.65763 - 6.29014i) q^{48} +(-0.513073 - 6.98117i) q^{49} +(-2.60511 - 8.01771i) q^{50} +(5.69287 - 2.53463i) q^{51} +(-2.24530 - 0.999674i) q^{52} +(-7.30656 + 1.55306i) q^{53} +(-2.35071 + 4.07155i) q^{54} +(-0.370450 + 3.06197i) q^{56} +(3.77978 - 11.6330i) q^{57} +(1.99981 + 19.0269i) q^{58} +(-1.23414 + 11.7421i) q^{59} +(1.27580 - 1.41692i) q^{60} +(4.23686 + 0.900572i) q^{61} +(-9.54217 - 6.93279i) q^{62} +(-4.85235 - 0.0760860i) q^{63} +(-0.730655 + 2.24872i) q^{64} +(-0.572413 + 0.991448i) q^{65} +(0.801309 + 1.38791i) q^{67} +(-2.58765 - 2.87387i) q^{68} +(3.85240 - 2.79893i) q^{69} +(-3.00648 - 0.688484i) q^{70} +(1.32631 + 4.08197i) q^{71} +(2.09155 + 0.444574i) q^{72} +(1.67177 - 15.9058i) q^{73} +(10.1644 + 4.52547i) q^{74} +(6.76180 + 7.50974i) q^{75} -7.59061 q^{76} +7.26456 q^{78} +(3.18629 + 3.53873i) q^{79} +(2.82591 + 1.25818i) q^{80} +(1.16427 - 11.0773i) q^{81} +(-13.5202 - 2.87381i) q^{82} +(-2.85273 - 8.77980i) q^{83} +(2.33409 + 7.58630i) q^{84} +(-1.45729 + 1.05878i) q^{85} +(-5.97372 - 6.63449i) q^{86} +(-11.4665 - 19.8606i) q^{87} +(-0.182224 + 0.315621i) q^{89} +(-0.660765 + 2.03363i) q^{90} +(-2.31791 - 4.16417i) q^{91} +(-2.39070 - 1.73694i) q^{92} +(13.8293 + 2.93951i) q^{93} +(-3.47860 + 3.86338i) q^{94} +(-0.369578 + 3.51630i) q^{95} +(-1.51595 - 14.4233i) q^{96} +(-0.802231 + 2.46901i) q^{97} +(8.88637 - 9.26770i) 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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