LMFDB - Embedded newform 847.2.n.d.366.2

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			366.2
Character	$\chi$	$=$	847.366
Dual form			847.2.n.d.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0686355 + 0.653023i) q^{2} +(1.27953 - 1.42106i) q^{3} +(1.53457 - 0.326182i) q^{4} +(-3.26031 + 1.45158i) q^{5} +(1.01581 + 0.738028i) q^{6} +(-2.40923 + 1.09345i) q^{7} +(0.724144 + 2.22869i) q^{8} +(-0.0686355 - 0.653023i) q^{9} +O(q^{10})$	\(q+(0.0686355 + 0.653023i) q^{2} +(1.27953 - 1.42106i) q^{3} +(1.53457 - 0.326182i) q^{4} +(-3.26031 + 1.45158i) q^{5} +(1.01581 + 0.738028i) q^{6} +(-2.40923 + 1.09345i) q^{7} +(0.724144 + 2.22869i) q^{8} +(-0.0686355 - 0.653023i) q^{9} +(-1.17169 - 2.02943i) q^{10} +(1.50000 - 2.59808i) q^{12} +(-4.78309 + 3.47512i) q^{13} +(-0.879407 - 1.49823i) q^{14} +(-2.10887 + 6.49045i) q^{15} +(1.46075 - 0.650367i) q^{16} +(-0.173164 + 1.64755i) q^{17} +(0.421729 - 0.0896412i) q^{18} +(1.44871 + 0.307934i) q^{19} +(-4.52968 + 3.29100i) q^{20} +(-1.52882 + 4.82277i) q^{21} +(-1.67169 + 2.89545i) q^{23} +(4.09367 + 1.82262i) q^{24} +(5.17685 - 5.74948i) q^{25} +(-2.59763 - 2.88496i) q^{26} +(3.62527 + 2.63391i) q^{27} +(-3.34045 + 2.46382i) q^{28} +(-0.951793 + 2.92932i) q^{29} +(-4.38316 - 0.931669i) q^{30} +(-6.46796 - 2.87972i) q^{31} +(2.86834 + 4.96812i) q^{32} -1.08777 q^{34} +(6.26758 - 7.06217i) q^{35} +(-0.318330 - 0.979720i) q^{36} +(-3.01859 - 3.35249i) q^{37} +(-0.101655 + 0.967179i) q^{38} +(-1.18175 + 11.2436i) q^{39} +(-5.59605 - 6.21505i) q^{40} +(0.397318 + 1.22282i) q^{41} +(-3.25431 - 0.667340i) q^{42} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(-2.00553 - 0.892922i) q^{46} +(1.62042 + 0.344431i) q^{47} +(0.944860 - 2.90798i) q^{48} +(4.60873 - 5.26874i) q^{49} +(4.10986 + 2.98599i) q^{50} +(2.11970 + 2.35416i) q^{51} +(-6.20645 + 6.89296i) q^{52} +(8.42789 + 3.75234i) q^{53} +(-1.47118 + 2.54817i) q^{54} +(-4.18158 - 4.57759i) q^{56} +(2.29127 - 1.66470i) q^{57} +(-1.97824 - 0.420488i) q^{58} +(-8.65852 + 1.84042i) q^{59} +(-1.11914 + 10.6479i) q^{60} +(6.10866 - 2.71975i) q^{61} +(1.43659 - 4.42138i) q^{62} +(0.879407 + 1.49823i) q^{63} +(-0.460209 + 0.334361i) q^{64} +(10.5499 - 18.2730i) q^{65} +(4.91223 + 8.50823i) q^{67} +(0.271668 + 2.58475i) q^{68} +(1.97564 + 6.08040i) q^{69} +(5.04194 + 3.60816i) q^{70} +(6.97274 + 5.06599i) q^{71} +(1.40568 - 0.625850i) q^{72} +(4.46147 - 0.948316i) q^{73} +(1.98207 - 2.20131i) q^{74} +(-1.54643 - 14.7133i) q^{75} +2.32359 q^{76} -7.42345 q^{78} +(-0.668283 - 6.35828i) q^{79} +(-3.81843 + 4.24079i) q^{80} +(10.3084 - 2.19112i) q^{81} +(-0.771259 + 0.343387i) q^{82} +(0.135784 + 0.0986527i) q^{83} +(-0.772970 + 7.89953i) q^{84} +(-1.82698 - 5.62286i) q^{85} +(-0.109747 - 1.04418i) q^{86} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(-1.24484 + 0.904432i) q^{90} +(7.72368 - 13.6024i) q^{91} +(-1.62087 + 4.98854i) q^{92} +(-12.3682 + 5.50669i) q^{93} +(-0.113703 + 1.08181i) q^{94} +(-5.17024 + 1.09897i) q^{95} +(10.7301 + 2.28076i) q^{96} +(-7.87715 + 5.72308i) q^{97} +(3.75693 + 2.64799i) 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.0686355	+	0.653023i	0.0485326	+	0.461757i	0.991618	+	0.129206i	$0.0412428\pi$
$2$	0.0686355	+	0.653023i	0.0485326	+	0.461757i	−0.943085	+	0.332551i	$0.892091\pi$
$3$	1.27953	−	1.42106i	0.738738	−	0.820451i	−0.250292	−	0.968170i	$-0.580527\pi$
$3$	1.27953	−	1.42106i	0.738738	−	0.820451i	0.989029	+	0.147719i	$0.0471932\pi$
$4$	1.53457	−	0.326182i	0.767283	−	0.163091i
$5$	−3.26031	+	1.45158i	−1.45805	+	0.649167i	−0.974139	−	0.225948i	$-0.927452\pi$
$5$	−3.26031	+	1.45158i	−1.45805	+	0.649167i	−0.483914	+	0.875116i	$0.660785\pi$
$6$	1.01581	+	0.738028i	0.414702	+	0.301299i
$7$	−2.40923	+	1.09345i	−0.910602	+	0.413285i
$7$	−2.40923	+	1.09345i	−0.910602	+	0.413285i
$8$	0.724144	+	2.22869i	0.256024	+	0.787960i
$9$	−0.0686355	−	0.653023i	−0.0228785	−	0.217674i
$10$	−1.17169	−	2.02943i	−0.370521	−	0.641761i
$11$		0			0
$11$		0			0
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$	−4.78309	+	3.47512i	−1.32659	+	0.963825i	−0.326767	+	0.945105i	$0.605959\pi$
$13$	−4.78309	+	3.47512i	−1.32659	+	0.963825i	−0.999825	+	0.0187202i	$0.994041\pi$
$14$	−0.879407	−	1.49823i	−0.235031	−	0.400419i
$15$	−2.10887	+	6.49045i	−0.544509	+	1.67583i
$16$	1.46075	−	0.650367i	0.365187	−	0.162592i
$17$	−0.173164	+	1.64755i	−0.0419984	+	0.399588i	0.953247	+	0.302192i	$0.0977183\pi$
$17$	−0.173164	+	1.64755i	−0.0419984	+	0.399588i	−0.995246	+	0.0973968i	$0.968948\pi$
$18$	0.421729	−	0.0896412i	0.0994024	−	0.0211286i
$19$	1.44871	+	0.307934i	0.332358	+	0.0706448i	0.371068	−	0.928606i	$-0.378992\pi$
$19$	1.44871	+	0.307934i	0.332358	+	0.0706448i	−0.0387104	+	0.999250i	$0.512325\pi$
$20$	−4.52968	+	3.29100i	−1.01287	+	0.735891i
$21$	−1.52882	+	4.82277i	−0.333615	+	1.05241i
$22$		0			0
$23$	−1.67169	+	2.89545i	−0.348571	+	0.603743i	−0.985996	−	0.166769i	$-0.946666\pi$
$23$	−1.67169	+	2.89545i	−0.348571	+	0.603743i	0.637425	+	0.770513i	$0.280000\pi$
$24$	4.09367	+	1.82262i	0.835617	+	0.372041i
$25$	5.17685	−	5.74948i	1.03537	−	1.14990i
$26$	−2.59763	−	2.88496i	−0.509436	−	0.565786i
$27$	3.62527	+	2.63391i	0.697683	+	0.506897i
$28$	−3.34045	+	2.46382i	−0.631286	+	0.465618i
$29$	−0.951793	+	2.92932i	−0.176744	+	0.543961i	−0.999709	−	0.0241310i	$-0.992318\pi$
$29$	−0.951793	+	2.92932i	−0.176744	+	0.543961i	0.822965	+	0.568092i	$0.192318\pi$
$30$	−4.38316	−	0.931669i	−0.800251	−	0.170099i
$31$	−6.46796	−	2.87972i	−1.16168	−	0.517213i	−0.266902	−	0.963724i	$-0.586000\pi$
$31$	−6.46796	−	2.87972i	−1.16168	−	0.517213i	−0.894779	+	0.446510i	$0.852667\pi$
$32$	2.86834	+	4.96812i	0.507056	+	0.878247i
$33$		0			0
$34$	−1.08777			−0.186551
$35$	6.26758	−	7.06217i	1.05941	−	1.19372i
$36$	−0.318330	−	0.979720i	−0.0530551	−	0.163287i
$37$	−3.01859	−	3.35249i	−0.496254	−	0.551146i	0.442035	−	0.896998i	$-0.354257\pi$
$37$	−3.01859	−	3.35249i	−0.496254	−	0.551146i	−0.938289	+	0.345852i	$0.887590\pi$
$38$	−0.101655	+	0.967179i	−0.0164906	+	0.156897i
$39$	−1.18175	+	11.2436i	−0.189232	+	1.80042i
$40$	−5.59605	−	6.21505i	−0.884814	−	0.982685i
$41$	0.397318	+	1.22282i	0.0620506	+	0.190972i	0.977276	−	0.211969i	$-0.0679877\pi$
$41$	0.397318	+	1.22282i	0.0620506	+	0.190972i	−0.915226	+	0.402942i	$0.867988\pi$
$42$	−3.25431	−	0.667340i	−0.502151	−	0.102973i
$43$	−1.59899			−0.243843			−0.121922	−	0.992540i	$-0.538906\pi$
$43$	−1.59899			−0.243843			−0.121922	+	0.992540i	$0.538906\pi$
$44$		0			0
$45$	1.17169	+	2.02943i	0.174665	+	0.302529i
$46$	−2.00553	−	0.892922i	−0.295700	−	0.131654i
$47$	1.62042	+	0.344431i	0.236362	+	0.0502404i	0.324570	−	0.945862i	$-0.394780\pi$
$47$	1.62042	+	0.344431i	0.236362	+	0.0502404i	−0.0882074	+	0.996102i	$0.528114\pi$
$48$	0.944860	−	2.90798i	0.136379	−	0.419731i
$49$	4.60873	−	5.26874i	0.658390	−	0.752677i
$50$	4.10986	+	2.98599i	0.581222	+	0.422283i
$51$	2.11970	+	2.35416i	0.296817	+	0.329649i
$52$	−6.20645	+	6.89296i	−0.860680	+	0.955882i
$53$	8.42789	+	3.75234i	1.15766	+	0.515423i	0.893503	−	0.449057i	$-0.148240\pi$
$53$	8.42789	+	3.75234i	1.15766	+	0.515423i	0.264156	+	0.964480i	$0.414907\pi$
$54$	−1.47118	+	2.54817i	−0.200203	+	0.346761i
$55$		0			0
$56$	−4.18158	−	4.57759i	−0.558788	−	0.611706i
$57$	2.29127	−	1.66470i	0.303486	−	0.220495i
$58$	−1.97824	−	0.420488i	−0.259756	−	0.0552128i
$59$	−8.65852	+	1.84042i	−1.12724	+	0.239603i	−0.733547	−	0.679638i	$-0.762137\pi$
$59$	−8.65852	+	1.84042i	−1.12724	+	0.239603i	−0.393695	+	0.919241i	$0.628803\pi$
$60$	−1.11914	+	10.6479i	−0.144480	+	1.37464i
$61$	6.10866	−	2.71975i	0.782134	−	0.348228i	0.0234815	−	0.999724i	$-0.492525\pi$
$61$	6.10866	−	2.71975i	0.782134	−	0.348228i	0.758652	+	0.651496i	$0.225858\pi$
$62$	1.43659	−	4.42138i	0.182448	−	0.561516i
$63$	0.879407	+	1.49823i	0.110795	+	0.188759i
$64$	−0.460209	+	0.334361i	−0.0575261	+	0.0417952i
$65$	10.5499	−	18.2730i	1.30856	−	2.26649i
$66$		0			0
$67$	4.91223	+	8.50823i	0.600124	+	1.03945i	0.992802	+	0.119770i	$0.0382156\pi$
$67$	4.91223	+	8.50823i	0.600124	+	1.03945i	−0.392677	+	0.919676i	$0.628451\pi$
$68$	0.271668	+	2.58475i	0.0329446	+	0.313447i
$69$	1.97564	+	6.08040i	0.237839	+	0.731994i
$70$	5.04194	+	3.60816i	0.602627	+	0.431258i
$71$	6.97274	+	5.06599i	0.827512	+	0.601222i	0.918854	−	0.394597i	$-0.129116\pi$
$71$	6.97274	+	5.06599i	0.827512	+	0.601222i	−0.0913425	+	0.995820i	$0.529116\pi$
$72$	1.40568	−	0.625850i	0.165661	−	0.0737571i
$73$	4.46147	−	0.948316i	0.522176	−	0.110992i	0.0607197	−	0.998155i	$-0.480660\pi$
$73$	4.46147	−	0.948316i	0.522176	−	0.110992i	0.461456	+	0.887163i	$0.347327\pi$
$74$	1.98207	−	2.20131i	0.230411	−	0.255897i
$75$	−1.54643	−	14.7133i	−0.178566	−	1.69894i
$76$	2.32359			0.266534
$77$		0			0
$78$	−7.42345			−0.840540
$79$	−0.668283	−	6.35828i	−0.0751877	−	0.715363i	−0.965569	−	0.260147i	$-0.916229\pi$
$79$	−0.668283	−	6.35828i	−0.0751877	−	0.715363i	0.890381	−	0.455216i	$-0.150438\pi$
$80$	−3.81843	+	4.24079i	−0.426913	+	0.474135i
$81$	10.3084	−	2.19112i	1.14538	−	0.243458i
$82$	−0.771259	+	0.343387i	−0.0851713	+	0.0379207i
$83$	0.135784	+	0.0986527i	0.0149042	+	0.0108285i	0.595212	−	0.803568i	$-0.297068\pi$
$83$	0.135784	+	0.0986527i	0.0149042	+	0.0108285i	−0.580308	+	0.814397i	$0.697068\pi$
$84$	−0.772970	+	7.89953i	−0.0843379	+	0.861909i
$85$	−1.82698	−	5.62286i	−0.198164	−	0.609885i
$86$	−0.109747	−	1.04418i	−0.0118344	−	0.112596i
$87$	2.94490	+	5.10071i	0.315726	+	0.546854i
$88$		0			0
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	−0.789887	−	0.613252i	$-0.789861\pi$
$89$	1.28442	−	2.22469i	0.136149	−	0.235817i	0.926036	+	0.377436i	$0.123194\pi$
$90$	−1.24484	+	0.904432i	−0.131218	+	0.0953355i
$91$	7.72368	−	13.6024i	0.809661	−	1.42592i
$92$	−1.62087	+	4.98854i	−0.168988	+	0.520091i
$93$	−12.3682	+	5.50669i	−1.28253	+	0.571017i
$94$	−0.113703	+	1.08181i	−0.0117276	+	0.111580i
$95$	−5.17024	+	1.09897i	−0.530456	+	0.112752i
$96$	10.7301	+	2.28076i	1.09514	+	0.232779i
$97$	−7.87715	+	5.72308i	−0.799803	+	0.581091i	−0.910856	−	0.412724i	$-0.864578\pi$
$97$	−7.87715	+	5.72308i	−0.799803	+	0.581091i	0.111053	+	0.993814i	$0.464578\pi$
$98$	3.75693	+	2.64799i	0.379507	+	0.267487i
$99$		0			0
$100$	6.06885	−	10.5116i	0.606885	−	1.05116i
$101$	−1.69426	−	0.754333i	−0.168585	−	0.0750589i	0.320709	−	0.947178i	$-0.396079\pi$
$101$	−1.69426	−	0.754333i	−0.168585	−	0.0750589i	−0.489294	+	0.872119i	$0.662746\pi$
$102$	−1.39184	+	1.54579i	−0.137812	+	0.153056i
$103$	−2.11970	−	2.35416i	−0.208860	−	0.231963i	0.629609	−	0.776913i	$-0.283215\pi$
$103$	−2.11970	−	2.35416i	−0.208860	−	0.231963i	−0.838469	+	0.544950i	$0.816549\pi$
$104$	−11.2086	−	8.14353i	−1.09909	−	0.798539i
$105$	−2.01623	−	17.9429i	−0.196764	−	1.75105i
$106$	−1.87191	+	5.76115i	−0.181816	+	0.559572i
$107$	−4.66266	−	0.991079i	−0.450756	−	0.0958112i	−0.0230608	−	0.999734i	$-0.507341\pi$
$107$	−4.66266	−	0.991079i	−0.450756	−	0.0958112i	−0.427696	+	0.903923i	$0.640674\pi$
$108$	6.42235	+	2.85942i	0.617991	+	0.275147i
$109$	−7.44105	−	12.8883i	−0.712723	−	1.23447i	−0.963831	−	0.266513i	$-0.914128\pi$
$109$	−7.44105	−	12.8883i	−0.712723	−	1.23447i	0.251108	−	0.967959i	$-0.419205\pi$
$110$		0			0
$111$	−8.62648			−0.818789
$112$	−2.80813	+	3.16414i	−0.265343	+	0.298983i
$113$	3.84517	+	11.8342i	0.361723	+	1.11327i	0.952008	+	0.306074i	$0.0990156\pi$
$113$	3.84517	+	11.8342i	0.361723	+	1.11327i	−0.590284	+	0.807195i	$0.700984\pi$
$114$	1.24435	+	1.38199i	0.116544	+	0.129436i
$115$	1.24724	−	11.8667i	0.116305	−	1.10657i
$116$	−0.505098	+	4.80569i	−0.0468972	+	0.446197i
$117$	2.59763	+	2.88496i	0.240151	+	0.266714i
$118$	−1.79612	−	5.52789i	−0.165346	−	0.508884i
$119$	−1.38432	−	4.15865i	−0.126900	−	0.381223i
$120$	−15.9923			−1.45989
$121$		0			0
$122$	2.19533	+	3.80243i	0.198756	+	0.344255i
$123$	2.24608	+	1.00002i	0.202522	+	0.0901688i
$124$	−10.8648	−	2.30939i	−0.975691	−	0.207389i
$125$	−3.01812	+	9.28880i	−0.269948	+	0.830816i
$126$	−0.918021	+	0.677105i	−0.0817838	+	0.0603213i
$127$	−5.35684	−	3.89197i	−0.475343	−	0.345357i	0.324177	−	0.945996i	$-0.394913\pi$
$127$	−5.35684	−	3.89197i	−0.475343	−	0.345357i	−0.799520	+	0.600640i	$0.794913\pi$
$128$	7.42725	+	8.24880i	0.656483	+	0.729098i
$129$	−2.04596	+	2.27226i	−0.180136	+	0.200062i
$130$	12.6568	+	5.63517i	1.11008	+	0.494237i
$131$	−3.02882	+	5.24606i	−0.264629	+	0.458351i	−0.967466	−	0.253000i	$-0.918583\pi$
$131$	−3.02882	+	5.24606i	−0.264629	+	0.458351i	0.702837	+	0.711351i	$0.251916\pi$
$132$		0			0
$133$	−3.82699	+	0.842215i	−0.331842	+	0.0730293i
$134$	−5.21892	+	3.79177i	−0.450846	+	0.327559i
$135$	−15.6428	−	3.32499i	−1.34632	−	0.286169i
$136$	−3.79726	+	0.807132i	−0.325612	+	0.0692110i
$137$	0.775961	−	7.38278i	0.0662949	−	0.630753i	−0.910045	−	0.414510i	$-0.863953\pi$
$137$	0.775961	−	7.38278i	0.0662949	−	0.630753i	0.976340	−	0.216243i	$-0.0693804\pi$
$138$	−3.83504	+	1.70747i	−0.326460	+	0.145350i
$139$	3.34494	−	10.2947i	0.283714	−	0.873183i	−0.703067	−	0.711124i	$-0.748187\pi$
$139$	3.34494	−	10.2947i	0.283714	−	0.873183i	0.986781	−	0.162059i	$-0.0518135\pi$
$140$	7.31446	−	12.8817i	0.618185	−	1.08871i
$141$	2.56283	−	1.86201i	0.215830	−	0.156809i
$142$	−2.82963	+	4.90107i	−0.237458	+	0.411288i
$143$		0			0
$144$	−0.524964	−	0.909265i	−0.0437470	−	0.0757721i
$145$	−1.14901	−	10.9321i	−0.0954199	−	0.907860i
$146$	0.925488	+	2.84836i	0.0765939	+	0.235732i
$147$	−1.59019	−	13.2908i	−0.131157	−	1.09621i
$148$	−5.72575	−	4.16000i	−0.470654	−	0.341950i
$149$	0.913545	−	0.406737i	0.0748406	−	0.0333212i	−0.368975	−	0.929439i	$-0.620291\pi$
$149$	0.913545	−	0.406737i	0.0748406	−	0.0333212i	0.443816	+	0.896118i	$0.353625\pi$
$150$	9.50197	−	2.01971i	0.775833	−	0.164908i
$151$	−10.9894	+	12.2050i	−0.894307	+	0.993229i	−0.999999	−	0.00117014i	$-0.999628\pi$
$151$	−10.9894	+	12.2050i	−0.894307	+	0.993229i	0.105692	+	0.994399i	$0.466294\pi$
$152$	0.362790	+	3.45172i	0.0294262	+	0.279971i
$153$	1.08777			0.0879411
$154$		0			0
$155$	25.2677			2.02955
$156$	1.85399	+	17.6395i	0.148438	+	1.41229i
$157$	−7.66217	+	8.50971i	−0.611508	+	0.679149i	−0.966779	−	0.255615i	$-0.917722\pi$
$157$	−7.66217	+	8.50971i	−0.611508	+	0.679149i	0.355271	+	0.934764i	$0.384389\pi$
$158$	4.10624	−	0.872808i	0.326675	−	0.0694369i
$159$	16.1161	−	7.17533i	1.27809	−	0.569041i
$160$	−16.5633	−	12.0339i	−1.30944	−	0.951367i
$161$	0.861444	−	8.80371i	0.0678913	−	0.693829i
$162$	2.13838	+	6.58125i	0.168007	+	0.517072i
$163$	0.934455	+	8.89075i	0.0731922	+	0.696377i	0.968175	+	0.250276i	$0.0805213\pi$
$163$	0.934455	+	8.89075i	0.0731922	+	0.696377i	−0.894982	+	0.446101i	$0.852812\pi$
$164$	1.00857	+	1.74690i	0.0787563	+	0.136410i
$165$		0			0
$166$	−0.0551029	+	0.0954410i	−0.00427681	+	0.00740766i
$167$	−14.7385	+	10.7081i	−1.14050	+	0.828620i	−0.987189	−	0.159558i	$-0.948993\pi$
$167$	−14.7385	+	10.7081i	−1.14050	+	0.828620i	−0.153309	+	0.988178i	$0.548993\pi$
$168$	−11.8555	+	0.0851255i	−0.914673	+	0.00656757i
$169$	6.78430	−	20.8799i	0.521869	−	1.60615i
$170$	3.54647	−	1.57899i	0.272002	−	0.121103i
$171$	0.101655	−	0.967179i	0.00777372	−	0.0739620i
$172$	−2.45375	+	0.521561i	−0.187097	+	0.0397687i
$173$	19.1337	+	4.06699i	1.45471	+	0.309208i	0.866368	−	0.499406i	$-0.166449\pi$
$173$	19.1337	+	4.06699i	1.45471	+	0.309208i	0.588340	+	0.808614i	$0.299782\pi$
$174$	−3.12876	+	2.27318i	−0.237191	+	0.172329i
$175$	−6.18544	+	19.5124i	−0.467575	+	1.47500i
$176$		0			0
$177$	−8.46348	+	14.6592i	−0.636154	+	1.10185i
$178$	1.54093	+	0.686067i	0.115498	+	0.0514229i
$179$	2.17327	−	2.41366i	0.162438	−	0.180406i	−0.656431	−	0.754386i	$-0.727935\pi$
$179$	2.17327	−	2.41366i	0.162438	−	0.180406i	0.818869	+	0.573980i	$0.194601\pi$
$180$	2.46000	+	2.73211i	0.183357	+	0.203639i
$181$	8.36583	+	6.07813i	0.621827	+	0.451784i	0.853559	−	0.520996i	$-0.174439\pi$
$181$	8.36583	+	6.07813i	0.621827	+	0.451784i	−0.231732	+	0.972780i	$0.574439\pi$
$182$	9.41282	+	4.11013i	0.697725	+	0.304663i
$183$	3.95128	−	12.1608i	0.292087	−	0.898952i
$184$	−7.66360	−	1.62895i	−0.564968	−	0.120088i
$185$	14.7080	+	6.54840i	1.08135	+	0.481448i
$186$	−4.44490	−	7.69879i	−0.325916	−	0.564502i
$187$		0			0
$188$	2.59899			0.189551
$189$	−11.6141	−	2.38163i	−0.844804	−	0.173238i
$190$	−1.07251	−	3.30086i	−0.0778084	−	0.239470i
$191$	6.70632	+	7.44812i	0.485252	+	0.538927i	0.935196	−	0.354130i	$-0.115223\pi$
$191$	6.70632	+	7.44812i	0.485252	+	0.538927i	−0.449944	+	0.893057i	$0.648556\pi$
$192$	−0.113703	+	1.08181i	−0.00820581	+	0.0780730i
$193$	2.64722	−	25.1866i	0.190551	−	1.81297i	−0.313819	−	0.949483i	$-0.601609\pi$
$193$	2.64722	−	25.1866i	0.190551	−	1.81297i	0.504370	−	0.863488i	$-0.331725\pi$
$194$	−4.27796	−	4.75115i	−0.307139	−	0.341113i
$195$	−12.4681	−	38.3730i	−0.892862	−	2.74795i
$196$	5.35384	−	9.58851i	0.382417	−	0.684894i
$197$	24.5809			1.75132			0.875660	−	0.482929i	$-0.160427\pi$
$197$	24.5809			1.75132			0.875660	+	0.482929i	$0.160427\pi$
$198$		0			0
$199$	−2.79564	−	4.84219i	−0.198178	−	0.343254i	0.749760	−	0.661710i	$-0.230169\pi$
$199$	−2.79564	−	4.84219i	−0.198178	−	0.343254i	−0.947938	+	0.318456i	$0.896836\pi$
$200$	16.5626	+	7.37413i	1.17115	+	0.521430i
$201$	18.3761	+	3.90596i	1.29615	+	0.275505i
$202$	0.376310	−	1.15816i	0.0264771	−	0.0814882i
$203$	−0.909980	−	8.09813i	−0.0638681	−	0.568377i
$204$	4.02070	+	2.92121i	0.281505	+	0.204526i
$205$	−3.07040	−	3.41002i	−0.214446	−	0.238166i
$206$	1.39184	−	1.54579i	0.0969738	−	0.107700i
$207$	2.00553	+	0.892922i	0.139394	+	0.0620623i
$208$	−4.72679	+	8.18705i	−0.327744	+	0.567669i
$209$		0			0
$210$	11.5787	−	2.54817i	0.799009	−	0.175840i
$211$	9.78899	−	7.11212i	0.673902	−	0.489618i	−0.197427	−	0.980318i	$-0.563259\pi$
$211$	9.78899	−	7.11212i	0.673902	−	0.489618i	0.871329	+	0.490699i	$0.163259\pi$
$212$	14.1571	+	3.00918i	0.972313	+	0.206672i
$213$	16.1209	−	3.42661i	1.10459	−	0.234787i
$214$	0.327174	−	3.11285i	0.0223651	−	0.212790i
$215$	5.21319	−	2.32106i	0.355537	−	0.158295i
$216$	−3.24495	+	9.98692i	−0.220791	+	0.679524i
$217$	18.7316	−	0.134498i	1.27158	−	0.00913029i
$218$	7.90562	−	5.74377i	0.535436	−	0.389017i
$219$	4.36098	−	7.55344i	0.294688	−	0.510414i
$220$		0			0
$221$	−4.89716	−	8.48213i	−0.329419	−	0.570570i
$222$	−0.592083	−	5.63329i	−0.0397380	−	0.378082i
$223$	4.82885	+	14.8617i	0.323364	+	0.995211i	0.972174	+	0.234261i	$0.0752669\pi$
$223$	4.82885	+	14.8617i	0.323364	+	0.995211i	−0.648810	+	0.760950i	$0.724733\pi$
$224$	−12.3429	−	8.83292i	−0.824693	−	0.590174i
$225$	−4.10986	−	2.98599i	−0.273991	−	0.199066i
$226$	−7.46411	+	3.32323i	−0.496505	+	0.221058i
$227$	−15.3263	+	3.25771i	−1.01724	+	0.216222i	−0.686215	−	0.727399i	$-0.740729\pi$
$227$	−15.3263	+	3.25771i	−1.01724	+	0.216222i	−0.331028	+	0.943621i	$0.607396\pi$
$228$	2.97311	−	3.30197i	0.196899	−	0.218678i
$229$	0.582380	+	5.54097i	0.0384847	+	0.366158i	0.996768	+	0.0803369i	$0.0255996\pi$
$229$	0.582380	+	5.54097i	0.0384847	+	0.366158i	−0.958283	+	0.285821i	$0.907734\pi$
$230$	7.83481			0.516612
$231$		0			0
$232$	−7.21777			−0.473870
$233$	−2.01483	−	19.1698i	−0.131996	−	1.25586i	−0.837218	−	0.546869i	$-0.815819\pi$
$233$	−2.01483	−	19.1698i	−0.131996	−	1.25586i	0.705222	−	0.708986i	$-0.250847\pi$
$234$	−1.70565	+	1.89432i	−0.111502	+	0.123836i
$235$	−5.78303	+	1.22922i	−0.377243	+	0.0801856i
$236$	−12.6868	+	5.64851i	−0.825837	+	0.367686i
$237$	−9.89061	−	7.18595i	−0.642464	−	0.466778i
$238$	2.62068	−	1.18942i	0.169874	−	0.0770989i
$239$	6.84704	+	21.0730i	0.442898	+	1.36310i	0.884772	+	0.466024i	$0.154314\pi$
$239$	6.84704	+	21.0730i	0.442898	+	1.36310i	−0.441874	+	0.897077i	$0.645686\pi$
$240$	1.14064	+	10.8525i	0.0736279	+	0.700523i
$241$	−9.93719	−	17.2117i	−0.640111	−	1.10870i	−0.985408	−	0.170211i	$-0.945555\pi$
$241$	−9.93719	−	17.2117i	−0.640111	−	1.10870i	0.345297	−	0.938494i	$-0.387778\pi$
$242$		0			0
$243$	3.35460	−	5.81033i	0.215198	−	0.372733i
$244$	8.48701	−	6.16617i	0.543325	−	0.394749i
$245$	−7.37787	+	23.8676i	−0.471355	+	1.52485i
$246$	−0.498876	+	1.53538i	−0.0318072	+	0.0978924i
$247$	−7.99944	+	3.56158i	−0.508992	+	0.226618i
$248$	1.73426	−	16.5004i	0.110126	−	1.04778i
$249$	0.313931	−	0.0667281i	0.0198946	−	0.00422872i
$250$	−6.27296	−	1.33336i	−0.396737	−	0.0843290i
$251$	−17.8854	+	12.9945i	−1.12892	+	0.820205i	−0.985537	−	0.169462i	$-0.945797\pi$
$251$	−17.8854	+	12.9945i	−1.12892	+	0.820205i	−0.143379	+	0.989668i	$0.545797\pi$
$252$	1.83821	+	2.01229i	0.115796	+	0.126762i
$253$		0			0
$254$	2.17388	−	3.76527i	0.136401	−	0.236254i
$255$	−10.3281	−	4.59838i	−0.646772	−	0.287961i
$256$	−5.63816	+	6.26181i	−0.352385	+	0.391363i
$257$	19.4848	+	21.6401i	1.21543	+	1.34987i	0.918722	+	0.394906i	$0.129223\pi$
$257$	19.4848	+	21.6401i	1.21543	+	1.34987i	0.296710	+	0.954968i	$0.404111\pi$
$258$	−1.62427	−	1.18010i	−0.101122	−	0.0734697i
$259$	10.9383	+	4.77622i	0.679670	+	0.296780i
$260$	10.2292	−	31.4824i	0.634390	−	1.95245i
$261$	1.97824	+	0.420488i	0.122450	+	0.0260275i
$262$	−3.63369	−	1.61782i	−0.224490	−	0.0999493i
$263$	−7.75176	−	13.4264i	−0.477994	−	0.827910i	0.521688	−	0.853136i	$-0.325303\pi$
$263$	−7.75176	−	13.4264i	−0.477994	−	0.827910i	−0.999682	+	0.0252268i	$0.991969\pi$
$264$		0			0
$265$	−32.9243			−2.02252
$266$	−0.812654	−	2.44131i	−0.0498270	−	0.149686i
$267$	−1.51796	−	4.67181i	−0.0928978	−	0.285910i
$268$	10.3134	+	11.4542i	0.629990	+	0.699674i
$269$	−0.178383	+	1.69720i	−0.0108762	+	0.103480i	−0.998613	−	0.0526468i	$-0.983234\pi$
$269$	−0.178383	+	1.69720i	−0.0108762	+	0.103480i	0.987737	+	0.156127i	$0.0499009\pi$
$270$	1.09764	−	10.4433i	0.0668002	−	0.635562i
$271$	13.7362	+	15.2555i	0.834412	+	0.926708i	0.998211	−	0.0597853i	$-0.0190416\pi$
$271$	13.7362	+	15.2555i	0.834412	+	0.926708i	−0.163799	+	0.986494i	$0.552375\pi$
$272$	0.818560	+	2.51927i	0.0496325	+	0.152753i
$273$	−9.44722	−	28.3806i	−0.571772	−	1.71767i
$274$	4.87439			0.294472
$275$		0			0
$276$	5.01507	+	8.68635i	0.301872	+	0.522857i
$277$	24.3560	+	10.8440i	1.46341	+	0.651553i	0.975231	−	0.221189i	$-0.0709937\pi$
$277$	24.3560	+	10.8440i	1.46341	+	0.651553i	0.488182	+	0.872742i	$0.337660\pi$
$278$	6.95224	+	1.47774i	0.416968	+	0.0886293i
$279$	−1.43659	+	4.42138i	−0.0860066	+	0.264701i
$280$	20.2780	+	8.85444i	1.21184	+	0.529154i
$281$	12.7375	+	9.25432i	0.759854	+	0.552067i	0.898866	−	0.438224i	$-0.144392\pi$
$281$	12.7375	+	9.25432i	0.759854	+	0.552067i	−0.139011	+	0.990291i	$0.544392\pi$
$282$	1.39184	+	1.54579i	0.0828827	+	0.0920505i
$283$	10.7527	−	11.9421i	0.639184	−	0.709886i	−0.333309	−	0.942818i	$-0.608165\pi$
$283$	10.7527	−	11.9421i	0.639184	−	0.709886i	0.972493	+	0.232932i	$0.0748319\pi$
$284$	12.3526	+	5.49972i	0.732990	+	0.326348i
$285$	−5.05378	+	8.75340i	−0.299360	+	0.518507i
$286$		0			0
$287$	−2.29432	−	2.51160i	−0.135429	−	0.148255i
$288$	3.04743	−	2.21408i	0.179571	−	0.130466i
$289$	13.9441	+	2.96391i	0.820241	+	0.174348i
$290$	7.06004	−	1.50066i	0.414580	−	0.0881217i
$291$	−1.94619	+	18.5168i	−0.114088	+	1.08547i
$292$	6.53710	−	2.91051i	0.382555	−	0.170325i
$293$	−4.73898	+	14.5851i	−0.276854	+	0.852070i	0.711868	+	0.702313i	$0.247849\pi$
$293$	−4.73898	+	14.5851i	−0.276854	+	0.852070i	−0.988723	+	0.149757i	$0.952151\pi$
$294$	8.57007	−	1.95066i	0.499816	−	0.113765i
$295$	25.5579	−	18.5689i	1.48804	−	1.08112i
$296$	5.28575	−	9.15518i	0.307228	−	0.532134i
$297$		0			0
$298$	0.328310	+	0.568650i	0.0190185	+	0.0329410i
$299$	−2.06620	−	19.6585i	−0.119491	−	1.13688i
$300$	−7.17230	−	22.0741i	−0.414093	−	1.27445i
$301$	3.85232	−	1.74841i	0.222044	−	0.100777i
$302$	−8.72442	−	6.33866i	−0.502034	−	0.364749i
$303$	−3.23981	+	1.44246i	−0.186122	+	0.0828670i
$304$	2.31648	−	0.492382i	0.132859	−	0.0282401i
$305$	−15.9682	+	17.7344i	−0.914334	+	1.01547i
$306$	0.0746597	+	0.710340i	0.00426801	+	0.0406074i
$307$	16.4707			0.940034			0.470017	−	0.882657i	$-0.344248\pi$
$307$	16.4707			0.940034			0.470017	+	0.882657i	$0.344248\pi$
$308$		0			0
$309$	−6.05763			−0.344607
$310$	1.73426	+	16.5004i	0.0984994	+	0.937160i
$311$	14.4727	−	16.0736i	0.820672	−	0.911449i	−0.176673	−	0.984270i	$-0.556533\pi$
$311$	14.4727	−	16.0736i	0.820672	−	0.911449i	0.997345	+	0.0728209i	$0.0232001\pi$
$312$	−25.9142	+	5.50824i	−1.46710	+	0.311843i
$313$	14.9714	−	6.66570i	0.846234	−	0.376768i	0.0626366	−	0.998036i	$-0.480049\pi$
$313$	14.9714	−	6.66570i	0.846234	−	0.376768i	0.783598	+	0.621269i	$0.213382\pi$
$314$	−6.08294	−	4.41951i	−0.343280	−	0.249407i
$315$	−5.04194	−	3.60816i	−0.284081	−	0.203297i
$316$	−3.09948	−	9.53923i	−0.174360	−	0.536624i
$317$	−0.466332	−	4.43685i	−0.0261918	−	0.249198i	−0.999782	−	0.0208943i	$-0.993349\pi$
$317$	−0.466332	−	4.43685i	−0.0261918	−	0.249198i	0.973590	−	0.228304i	$-0.0733180\pi$
$318$	5.79179	+	10.0317i	0.324787	+	0.562548i
$319$		0			0
$320$	1.01507	−	1.75815i	0.0567441	−	0.0982837i
$321$	−7.37440	+	5.35782i	−0.411599	+	0.299044i
$322$	5.80815	−	0.0417039i	0.323676	−	0.00232407i
$323$	−0.758200	+	2.33350i	−0.0421874	+	0.129839i
$324$	15.1042	−	6.72484i	0.839125	−	0.373602i
$325$	−4.78124	+	45.4905i	−0.265216	+	2.52336i
$326$	−5.74173	+	1.22044i	−0.318005	+	0.0675941i
$327$	−27.8361	−	5.91674i	−1.53934	−	0.327197i
$328$	−2.43756	+	1.77099i	−0.134592	+	0.0977868i
$329$	−4.28057	+	0.942037i	−0.235996	+	0.0519362i
$330$		0			0
$331$	−9.51979	+	16.4888i	−0.523255	+	0.906304i	0.476379	+	0.879240i	$0.341949\pi$
$331$	−9.51979	+	16.4888i	−0.523255	+	0.906304i	−0.999634	+	0.0270640i	$0.991384\pi$
$332$	0.240548	+	0.107099i	0.0132018	+	0.00587781i
$333$	−1.98207	+	2.20131i	−0.108617	+	0.120631i
$334$	−8.00425	−	8.88962i	−0.437973	−	0.486418i
$335$	−28.3658	−	20.6089i	−1.54979	−	1.12599i
$336$	0.903352	+	8.03914i	0.0492819	+	0.438571i
$337$	−8.34801	+	25.6925i	−0.454745	+	1.39956i	0.416689	+	0.909049i	$0.363190\pi$
$337$	−8.34801	+	25.6925i	−0.454745	+	1.39956i	−0.871434	+	0.490513i	$0.836810\pi$
$338$	14.1007	+	2.99720i	0.766978	+	0.163026i
$339$	21.7372	+	9.67802i	1.18060	+	0.525638i
$340$	−4.63770	−	8.03273i	−0.251515	−	0.435636i
$341$		0			0
$342$	0.638568			0.0345298
$343$	−5.34237	+	17.7330i	−0.288461	+	0.957492i
$344$	−1.15790	−	3.56364i	−0.0624297	−	0.192139i
$345$	−15.2674	−	16.9562i	−0.821969	−	0.912889i
$346$	−1.34259	+	12.7739i	−0.0721781	+	0.686728i
$347$	−2.11333	+	20.1070i	−0.113450	+	1.07940i	0.778618	+	0.627499i	$0.215921\pi$
$347$	−2.11333	+	20.1070i	−0.113450	+	1.07940i	−0.892067	+	0.451902i	$0.850746\pi$
$348$	6.18290	+	6.86681i	0.331438	+	0.368100i
$349$	3.71514	+	11.4340i	0.198867	+	0.612049i	0.999910	+	0.0134419i	$0.00427882\pi$
$349$	3.71514	+	11.4340i	0.198867	+	0.612049i	−0.801043	+	0.598607i	$0.795721\pi$
$350$	−13.1666	−	2.69999i	−0.703785	−	0.144320i
$351$	−26.4932			−1.41410
$352$		0			0
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	0.972930	−	0.231101i	$-0.0742329\pi$
$353$	5.37956	+	9.31767i	0.286325	+	0.495930i	−0.686605	+	0.727031i	$0.740900\pi$
$354$	−10.1537	−	4.52071i	−0.539662	−	0.240273i
$355$	−30.0870	−	6.39518i	−1.59685	−	0.339421i
$356$	1.24538	−	3.83289i	0.0660051	−	0.203143i
$357$	−7.68099	−	3.35392i	−0.406521	−	0.177508i
$358$	1.72534	+	1.25353i	0.0911872	+	0.0662514i
$359$	−16.2533	−	18.0511i	−0.857815	−	0.952700i	0.141492	−	0.989939i	$-0.454810\pi$
$359$	−16.2533	−	18.0511i	−0.857815	−	0.952700i	−0.999306	+	0.0372397i	$0.988144\pi$
$360$	−3.67448	+	4.08093i	−0.193662	+	0.215084i
$361$	−15.3534	−	6.83578i	−0.808075	−	0.359778i
$362$	−3.39497	+	5.88026i	−0.178436	+	0.309060i
$363$		0			0
$364$	7.41563	−	23.3932i	0.388684	−	1.22613i
$365$	−13.1692	+	9.56799i	−0.689308	+	0.500812i
$366$	8.21248	+	1.74562i	0.429273	+	0.0912449i
$367$	−10.6073	+	2.25465i	−0.553695	+	0.117692i	−0.476258	−	0.879306i	$-0.658007\pi$
$367$	−10.6073	+	2.25465i	−0.553695	+	0.117692i	−0.0774374	+	0.996997i	$0.524674\pi$
$368$	−0.558812	+	5.31674i	−0.0291301	+	0.277154i
$369$	0.771259	−	0.343387i	0.0401501	−	0.0178760i
$370$	−3.26677	+	10.0541i	−0.169831	+	0.522687i
$371$	−24.4077	+	0.175253i	−1.26718	+	0.00909868i
$372$	−17.1837	+	12.4847i	−0.890933	+	0.647300i
$373$	−16.5121	+	28.5998i	−0.854963	+	1.48084i	0.0217156	+	0.999764i	$0.493087\pi$
$373$	−16.5121	+	28.5998i	−0.854963	+	1.48084i	−0.876679	+	0.481076i	$0.840246\pi$
$374$		0			0
$375$	9.33821	+	16.1742i	0.482223	+	0.835234i
$376$	0.405789	+	3.86082i	0.0209270	+	0.199107i
$377$	−5.62722	−	17.3188i	−0.289817	−	0.891964i
$378$	0.758121	−	7.74777i	0.0389935	−	0.398502i
$379$	17.7434	+	12.8913i	0.911416	+	0.662182i	0.941373	−	0.337369i	$-0.109537\pi$
$379$	17.7434	+	12.8913i	0.911416	+	0.662182i	−0.0299566	+	0.999551i	$0.509537\pi$
$380$	−7.57561	+	3.37288i	−0.388621	+	0.173025i
$381$	−12.3850	+	2.63251i	−0.634502	+	0.134868i
$382$	−4.40351	+	4.89059i	−0.225303	+	0.250224i
$383$	−3.81142	−	36.2633i	−0.194755	−	1.85297i	−0.458905	−	0.888485i	$-0.651758\pi$
$383$	−3.81142	−	36.2633i	−0.194755	−	1.85297i	0.264150	−	0.964482i	$-0.414909\pi$
$384$	21.2255			1.08316
$385$		0			0
$386$	16.6291			0.846400
$387$	0.109747	+	1.04418i	0.00557877	+	0.0530785i
$388$	−10.2212	+	11.3518i	−0.518905	+	0.576302i
$389$	−19.0504	+	4.04929i	−0.965895	+	0.205307i	−0.663750	−	0.747955i	$-0.731036\pi$
$389$	−19.0504	+	4.04929i	−0.965895	+	0.205307i	−0.302145	+	0.953262i	$0.597703\pi$
$390$	24.2027	−	10.7757i	1.22555	−	0.545651i
$391$	−4.48091	−	3.25557i	−0.226609	−	0.164641i
$392$	15.0797	+	6.45609i	0.761642	+	0.326082i
$393$	3.57952	+	11.0166i	0.180563	+	0.555716i
$394$	1.68713	+	16.0519i	0.0849962	+	0.808684i
$395$	11.4084	+	19.7599i	0.574018	+	0.994228i
$396$		0			0
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	−0.750732	−	0.660606i	$-0.770299\pi$
$397$	3.91993	−	6.78952i	0.196736	−	0.340756i	0.947468	+	0.319850i	$0.103633\pi$
$398$	2.97019	−	2.15797i	0.148882	−	0.108169i
$399$	−3.69991	+	6.51603i	−0.185227	+	0.326210i
$400$	3.82281	−	11.7654i	0.191140	−	0.588270i
$401$	−22.3324	+	9.94304i	−1.11523	+	0.496532i	−0.879792	−	0.475358i	$-0.842318\pi$
$401$	−22.3324	+	9.94304i	−1.11523	+	0.496532i	−0.235436	+	0.971890i	$0.575652\pi$
$402$	−1.28943	+	12.2681i	−0.0643109	+	0.611877i
$403$	40.9443	−	8.70297i	2.03958	−	0.433526i
$404$	−2.84600	−	0.604937i	−0.141594	−	0.0300967i
$405$	−30.4280	+	22.1072i	−1.51198	+	1.09852i
$406$	5.22581	−	1.15006i	0.259353	−	0.0570764i
$407$		0			0
$408$	−3.71172	+	6.42889i	−0.183758	+	0.318278i
$409$	2.15024	+	0.957348i	0.106322	+	0.0473378i	0.459209	−	0.888328i	$-0.348133\pi$
$409$	2.15024	+	0.957348i	0.106322	+	0.0473378i	−0.352886	+	0.935666i	$0.614800\pi$
$410$	2.01609	−	2.23909i	0.0995674	−	0.110581i
$411$	−9.49853	−	10.5492i	−0.468528	−	0.520353i
$412$	−4.02070	−	2.92121i	−0.198086	−	0.143918i
$413$	18.8479	−	13.9017i	0.927445	−	0.684056i
$414$	−0.445448	+	1.37095i	−0.0218926	+	0.0673784i
$415$	−0.585899	−	0.124537i	−0.0287606	−	0.00611326i
$416$	−30.9844	−	13.7951i	−1.51913	−	0.676362i
$417$	−10.3494	−	17.9257i	−0.506813	−	0.877827i
$418$		0			0
$419$	9.29081			0.453886			0.226943	−	0.973908i	$-0.427127\pi$
$419$	9.29081			0.453886			0.226943	+	0.973908i	$0.427127\pi$
$420$	−8.94669	−	26.8769i	−0.436554	−	1.31146i
$421$	−12.0615	−	37.1215i	−0.587842	−	1.80919i	−0.587544	−	0.809192i	$-0.699905\pi$
$421$	−12.0615	−	37.1215i	−0.587842	−	1.80919i	−0.000298162	−	1.00000i	$-0.500095\pi$
$422$	5.31625	+	5.90430i	0.258791	+	0.287417i
$423$	0.113703	−	1.08181i	0.00552843	−	0.0525995i
$424$	−2.25978	+	21.5003i	−0.109745	+	1.04415i
$425$	8.57608	+	9.52470i	0.416001	+	0.462016i
$426$	3.34412	+	10.2922i	0.162023	+	0.498657i
$427$	−11.7432	+	13.2320i	−0.568294	+	0.640342i
$428$	−7.47843			−0.361484
$429$		0			0
$430$	1.87352	+	3.24503i	0.0903491	+	0.156489i
$431$	3.47332	+	1.54642i	0.167304	+	0.0744885i	0.488680	−	0.872463i	$-0.337479\pi$
$431$	3.47332	+	1.54642i	0.167304	+	0.0744885i	−0.321376	+	0.946952i	$0.604145\pi$
$432$	7.00862	+	1.48973i	0.337202	+	0.0716745i
$433$	2.54025	−	7.81808i	0.122076	−	0.375713i	−0.871281	−	0.490785i	$-0.836710\pi$
$433$	2.54025	−	7.81808i	0.122076	−	0.375713i	0.993357	+	0.115072i	$0.0367100\pi$
$434$	1.37348	+	12.2230i	0.0659294	+	0.586720i
$435$	−17.0054	−	12.3551i	−0.815345	−	0.592383i
$436$	−15.6227	−	17.3508i	−0.748192	−	0.830951i
$437$	−3.31341	+	3.67991i	−0.158502	+	0.176034i
$438$	5.23189	+	2.32939i	0.249989	+	0.111302i
$439$	2.27068	−	3.93293i	0.108374	−	0.187708i	−0.806738	−	0.590909i	$-0.798769\pi$
$439$	2.27068	−	3.93293i	0.108374	−	0.187708i	0.915112	+	0.403201i	$0.132102\pi$
$440$		0			0
$441$	−3.75693	−	2.64799i	−0.178901	−	0.126095i
$442$	5.20291	−	3.78014i	0.247477	−	0.179803i
$443$	−13.4440	−	2.85762i	−0.638746	−	0.135770i	−0.122856	−	0.992425i	$-0.539205\pi$
$443$	−13.4440	−	2.85762i	−0.638746	−	0.135770i	−0.515890	+	0.856655i	$0.672539\pi$
$444$	−13.2379	+	2.81380i	−0.628243	+	0.133537i
$445$	−0.958300	+	9.11762i	−0.0454278	+	0.432216i
$446$	−9.37359	+	4.17339i	−0.443852	+	0.197616i
$447$	0.590911	−	1.81864i	0.0279491	−	0.0860186i
$448$	0.743139	−	1.30877i	0.0351100	−	0.0618335i
$449$	−17.4474	+	12.6763i	−0.823395	+	0.598231i	−0.917683	−	0.397314i	$-0.869943\pi$
$449$	−17.4474	+	12.6763i	−0.823395	+	0.598231i	0.0942880	+	0.995545i	$0.469943\pi$
$450$	1.66784	−	2.88878i	0.0786226	−	0.136178i
$451$		0			0
$452$	9.76078	+	16.9062i	0.459109	+	0.795199i
$453$	3.28276	+	31.2334i	0.154237	+	1.46747i
$454$	−3.17929	−	9.78484i	−0.149211	−	0.459225i
$455$	−5.43652	+	55.5596i	−0.254868	+	2.60468i
$456$	5.36931	+	3.90103i	0.251441	+	0.182683i
$457$	3.01976	−	1.34448i	0.141258	−	0.0628923i	−0.334890	−	0.942257i	$-0.608699\pi$
$457$	3.01976	−	1.34448i	0.141258	−	0.0628923i	0.476148	+	0.879365i	$0.342033\pi$
$458$	−3.57841	+	0.760615i	−0.167208	+	0.0355412i
$459$	−4.96726	+	5.51670i	−0.231852	+	0.257497i
$460$	−1.95673	−	18.6170i	−0.0912328	−	0.868022i
$461$	32.1524			1.49749			0.748744	−	0.662859i	$-0.230657\pi$
$461$	32.1524			1.49749			0.748744	+	0.662859i	$0.230657\pi$
$462$		0			0
$463$	5.82181			0.270563			0.135281	−	0.990807i	$-0.456806\pi$
$463$	5.82181			0.270563			0.135281	+	0.990807i	$0.456806\pi$
$464$	0.514802	+	4.89801i	0.0238991	+	0.227384i
$465$	32.3308	−	35.9070i	1.49930	−	1.66515i
$466$	12.3800	−	2.63146i	0.573494	−	0.121900i
$467$	−5.49473	+	2.44641i	−0.254266	+	0.113206i	−0.529912	−	0.848053i	$-0.677775\pi$
$467$	−5.49473	+	2.44641i	−0.254266	+	0.113206i	0.275646	+	0.961259i	$0.411108\pi$
$468$	4.92725	+	3.57986i	0.227762	+	0.165479i
$469$	−21.1380	−	15.1270i	−0.976062	−	0.698498i
$470$	−1.19963	−	3.69209i	−0.0553349	−	0.170303i
$471$	2.28884	+	21.7769i	0.105464	+	1.00343i
$472$	−10.3717	−	17.9644i	−0.477398	−	0.826878i
$473$		0			0
$474$	4.01375	−	6.95201i	0.184357	−	0.319317i
$475$	9.27024	−	6.73522i	0.425348	−	0.309033i
$476$	−3.48081	−	5.93019i	−0.159543	−	0.271810i
$477$	1.87191	−	5.76115i	0.0857089	−	0.263785i
$478$	−13.2912	+	5.91764i	−0.607927	+	0.270666i
$479$	1.79110	−	17.0412i	0.0818375	−	0.778632i	−0.874235	−	0.485502i	$-0.838637\pi$
$479$	1.79110	−	17.0412i	0.0818375	−	0.778632i	0.956073	−	0.293129i	$-0.0946966\pi$
$480$	−38.2943	+	8.13970i	−1.74789	+	0.371525i
$481$	26.0885	+	5.54529i	1.18953	+	0.252843i
$482$	10.5576	−	7.67056i	0.480886	−	0.349384i
$483$	−11.4084	−	12.4888i	−0.519099	−	0.568259i
$484$		0			0
$485$	17.3744	−	30.0933i	0.788930	−	1.36647i
$486$	4.02453	+	1.79184i	0.182556	+	0.0812793i
$487$	3.82358	−	4.24652i	0.173263	−	0.192428i	−0.650259	−	0.759713i	$-0.725339\pi$
$487$	3.82358	−	4.24652i	0.173263	−	0.192428i	0.823522	+	0.567285i	$0.192006\pi$
$488$	10.4850	+	11.6448i	0.474635	+	0.527135i
$489$	13.8300	+	10.0481i	0.625413	+	0.454389i
$490$	−16.0925	−	3.17976i	−0.726986	−	0.143647i
$491$	−7.43721	+	22.8894i	−0.335636	+	1.03298i	0.630771	+	0.775969i	$0.282739\pi$
$491$	−7.43721	+	22.8894i	−0.335636	+	1.03298i	−0.966408	+	0.257014i	$0.917261\pi$
$492$	3.77295	+	0.801966i	0.170098	+	0.0361554i
$493$	−4.66137	−	2.07537i	−0.209937	−	0.0934702i
$494$	−2.87484	−	4.97937i	−0.129345	−	0.224032i
$495$		0			0
$496$	−11.3209			−0.508325
$497$	−22.3383	−	4.58077i	−1.00201	−	0.205476i
$498$	0.0651219	+	0.200424i	0.00291818	+	0.00898124i
$499$	7.21942	+	8.01798i	0.323186	+	0.358934i	0.882742	−	0.469858i	$-0.155695\pi$
$499$	7.21942	+	8.01798i	0.323186	+	0.358934i	−0.559556	+	0.828793i	$0.689028\pi$
$500$	−1.60166	+	15.2387i	−0.0716282	+	0.681497i
$501$	−3.64141	+	34.6457i	−0.162686	+	1.54786i
$502$	−9.71328	−	10.7877i	−0.433525	−	0.481478i
$503$	−8.65621	−	26.6411i	−0.385961	−	1.18787i	−0.935780	−	0.352583i	$-0.885303\pi$
$503$	−8.65621	−	26.6411i	−0.385961	−	1.18787i	0.549819	−	0.835284i	$-0.314697\pi$
$504$	−2.70227	+	3.04486i	−0.120369	+	0.135629i
$505$	6.61878			0.294532
$506$		0			0
$507$	−20.9910	−	36.3574i	−0.932242	−	1.61469i
$508$	−9.48993	−	4.22519i	−0.421047	−	0.187462i
$509$	1.87303	+	0.398125i	0.0830206	+	0.0176466i	0.249235	−	0.968443i	$-0.419821\pi$
$509$	1.87303	+	0.398125i	0.0830206	+	0.0176466i	−0.166214	+	0.986090i	$0.553154\pi$
$510$	2.29397	−	7.06012i	0.101579	−	0.312627i
$511$	−9.71176	+	7.16311i	−0.429623	+	0.316877i
$512$	13.4839	+	9.79660i	0.595908	+	0.432953i
$513$	4.44091	+	4.93213i	0.196071	+	0.217759i
$514$	−12.7941	+	14.2093i	−0.564326	+	0.626747i
$515$	10.3281	+	4.59838i	0.455111	+	0.202629i
$516$	−2.39848	+	4.15429i	−0.105587	+	0.182883i
$517$		0			0
$518$	−2.36823	+	7.47075i	−0.104054	+	0.328246i
$519$	30.2616	−	21.9863i	1.32834	−	0.965093i
$520$	48.3645	+	10.2802i	2.12092	+	0.450816i
$521$	−1.54469	+	0.328334i	−0.0676741	+	0.0143846i	−0.241624	−	0.970370i	$-0.577680\pi$
$521$	−1.54469	+	0.328334i	−0.0676741	+	0.0143846i	0.173950	+	0.984754i	$0.444347\pi$
$522$	−0.138811	+	1.32070i	−0.00607559	+	0.0578054i
$523$	8.19438	−	3.64837i	0.358315	−	0.159532i	−0.219681	−	0.975572i	$-0.570502\pi$
$523$	8.19438	−	3.64837i	0.358315	−	0.159532i	0.577996	+	0.816040i	$0.303835\pi$
$524$	−2.93675	+	9.03838i	−0.128292	+	0.394843i
$525$	19.8139	+	33.7566i	0.864751	+	1.47326i
$526$	8.23573	−	5.98361i	0.359095	−	0.260898i
$527$	5.86449	−	10.1576i	0.255461	−	0.442472i
$528$		0			0
$529$	5.91091	+	10.2380i	0.256996	+	0.445130i
$530$	−2.25978	−	21.5003i	−0.0981585	−	0.933915i
$531$	1.79612	+	5.52789i	0.0779450	+	0.239890i
$532$	−5.59805	+	2.54073i	−0.242706	+	0.110155i
$533$	−6.14985	−	4.46813i	−0.266380	−	0.193536i
$534$	2.94661	−	1.31192i	0.127512	−	0.0567722i
$535$	16.6403	−	3.53701i	0.719424	−	0.152918i
$536$	−15.4050	+	17.1090i	−0.665395	+	0.738996i
$537$	−0.649199	−	6.17672i	−0.0280150	−	0.266545i
$538$	−1.12055			−0.0483105
$539$		0			0
$540$	−25.0895			−1.07968
$541$	1.89223	+	18.0033i	0.0813532	+	0.774024i	0.956807	+	0.290723i	$0.0938957\pi$
$541$	1.89223	+	18.0033i	0.0813532	+	0.774024i	−0.875454	+	0.483301i	$0.839438\pi$
$542$	−9.01944	+	10.0171i	−0.387418	+	0.430271i
$543$	19.3417	−	4.11122i	0.830034	−	0.176429i
$544$	−8.68189	+	3.86543i	−0.372233	+	0.165729i
$545$	42.9685	+	31.2184i	1.84057	+	1.33725i
$546$	17.8848	−	8.11717i	0.765397	−	0.347383i
$547$	−7.01113	−	21.5780i	−0.299774	−	0.922610i	−0.981576	−	0.191073i	$-0.938803\pi$
$547$	−7.01113	−	21.5780i	−0.299774	−	0.922610i	0.681801	−	0.731537i	$-0.261197\pi$
$548$	−1.21737	−	11.5825i	−0.0520033	−	0.494779i
$549$	−2.19533	−	3.80243i	−0.0936945	−	0.162284i
$550$		0			0
$551$	−2.28091	+	3.95065i	−0.0971701	+	0.168304i
$552$	−12.1206	+	8.80617i	−0.515889	+	0.374815i
$553$	8.56251	+	14.5878i	0.364115	+	0.620337i
$554$	−5.40970	+	16.6493i	−0.229836	+	0.707363i
$555$	28.1250	−	12.5220i	1.19384	−	0.531531i
$556$	1.77510	−	16.8889i	0.0752809	−	0.716250i
$557$	37.5173	−	7.97455i	1.58966	−	0.337893i	0.673650	−	0.739050i	$-0.264725\pi$
$557$	37.5173	−	7.97455i	1.58966	−	0.337893i	0.916009	+	0.401158i	$0.131392\pi$
$558$	−2.98587	−	0.634666i	−0.126402	−	0.0268675i
$559$	7.64811	−	5.55668i	0.323481	−	0.235022i
$560$	4.56235	−	14.3923i	0.192795	−	0.608185i
$561$		0			0
$562$	−5.16904	+	8.95305i	−0.218043	+	0.377662i
$563$	38.1623	+	16.9910i	1.60835	+	0.716083i	0.997154	−	0.0753957i	$-0.0240220\pi$
$563$	38.1623	+	16.9910i	1.60835	+	0.716083i	0.611196	+	0.791479i	$0.290689\pi$
$564$	3.32549	−	3.69333i	0.140028	−	0.155517i
$565$	−29.7148	−	33.0016i	−1.25011	−	1.38839i
$566$	8.53651	+	6.20214i	0.358816	+	0.260695i
$567$	−22.4394	+	16.5506i	−0.942367	+	0.695062i
$568$	−6.24124	+	19.2086i	−0.261877	+	0.805973i
$569$	−11.6106	−	2.46791i	−0.486742	−	0.103460i	−0.0419977	−	0.999118i	$-0.513372\pi$
$569$	−11.6106	−	2.46791i	−0.486742	−	0.103460i	−0.444745	+	0.895657i	$0.646706\pi$
$570$	−6.06305	−	2.69944i	−0.253953	−	0.113067i
$571$	9.90067	+	17.1485i	0.414330	+	0.717641i	0.995358	−	0.0962427i	$-0.0306825\pi$
$571$	9.90067	+	17.1485i	0.414330	+	0.717641i	−0.581028	+	0.813884i	$0.697349\pi$
$572$		0			0
$573$	19.1652			0.800637
$574$	1.48266	−	1.67063i	0.0618850	−	0.0697307i
$575$	7.99324	+	24.6007i	0.333341	+	1.02592i
$576$	0.249933	+	0.277578i	0.0104139	+	0.0115658i
$577$	−2.99778	+	28.5219i	−0.124799	+	1.18738i	0.735475	+	0.677552i	$0.236959\pi$
$577$	−2.99778	+	28.5219i	−0.124799	+	1.18738i	−0.860274	+	0.509832i	$0.829707\pi$
$578$	−0.978441	+	9.30925i	−0.0406978	+	0.387214i
$579$	−32.4045	−	35.9889i	−1.34669	−	1.49565i
$580$	−5.32908	−	16.4012i	−0.221278	−	0.681023i
$581$	−0.435005	−	0.0892037i	−0.0180471	−	0.00370079i
$582$	−12.2255			−0.506762
$583$		0			0
$584$	5.34425	+	9.25651i	0.221147	+	0.383037i
$585$	−12.6568	−	5.63517i	−0.523294	−	0.232986i
$586$	−9.84967	−	2.09361i	−0.406886	−	0.0864863i
$587$	0.312752	−	0.962551i	0.0129086	−	0.0397287i	−0.944395	−	0.328814i	$-0.893351\pi$
$587$	0.312752	−	0.962551i	0.0129086	−	0.0397287i	0.957303	+	0.289085i	$0.0933511\pi$
$588$	−6.77548	−	19.8769i	−0.279416	−	0.819711i
$589$	−8.48346	−	6.16360i	−0.349555	−	0.253967i
$590$	13.8801	+	15.4154i	0.571435	+	0.634642i
$591$	31.4521	−	34.9311i	1.29377	−	1.43687i
$592$	−6.58975	−	2.93395i	−0.270837	−	0.120585i
$593$	7.11659	−	12.3263i	0.292243	−	0.506180i	−0.682097	−	0.731262i	$-0.738932\pi$
$593$	7.11659	−	12.3263i	0.292243	−	0.506180i	0.974340	+	0.225082i	$0.0722650\pi$
$594$		0			0
$595$	10.5499	+	11.5490i	0.432505	+	0.473464i
$596$	1.26923	−	0.922147i	0.0519895	−	0.0377726i
$597$	−10.4582	−	2.22295i	−0.428025	−	0.0909794i
$598$	12.6957	−	2.69855i	0.519165	−	0.110352i
$599$	2.77479	−	26.4003i	0.113375	−	1.07869i	−0.778886	−	0.627166i	$-0.784215\pi$
$599$	2.77479	−	26.4003i	0.113375	−	1.07869i	0.892260	−	0.451522i	$-0.149119\pi$
$600$	31.6714	−	14.1010i	1.29298	−	0.575672i
$601$	3.75633	−	11.5608i	0.153224	−	0.471575i	−0.844753	−	0.535157i	$-0.820252\pi$
$601$	3.75633	−	11.5608i	0.153224	−	0.471575i	0.997977	+	0.0635819i	$0.0202524\pi$
$602$	1.40616	+	2.39565i	0.0573109	+	0.0976396i
$603$	5.21892	−	3.79177i	0.212531	−	0.154413i
$604$	−12.8830	+	22.3139i	−0.524200	+	0.907941i
$605$		0			0
$606$	−1.16432	−	2.01667i	−0.0472974	−	0.0819216i
$607$	1.45997	+	13.8907i	0.0592584	+	0.563806i	0.983361	+	0.181662i	$0.0581476\pi$
$607$	1.45997	+	13.8907i	0.0592584	+	0.563806i	−0.924103	+	0.382144i	$0.875186\pi$
$608$	2.62556	+	8.08064i	0.106480	+	0.327713i
$609$	−12.6723	−	9.06866i	−0.513507	−	0.367481i
$610$	−12.6770	−	9.21037i	−0.513276	−	0.372917i
$611$	−8.94756	+	3.98371i	−0.361979	+	0.161164i
$612$	1.66926	−	0.354811i	0.0674757	−	0.0143424i
$613$	−3.10603	+	3.44960i	−0.125451	+	0.139328i	−0.802598	−	0.596520i	$-0.796550\pi$
$613$	−3.10603	+	3.44960i	−0.125451	+	0.139328i	0.677147	+	0.735848i	$0.263216\pi$
$614$	1.13048	+	10.7558i	0.0456223	+	0.434068i
$615$	−8.77453			−0.353823
$616$		0			0
$617$	−26.3960			−1.06266			−0.531331	−	0.847165i	$-0.678308\pi$
$617$	−26.3960			−1.06266			−0.531331	+	0.847165i	$0.678308\pi$
$618$	−0.415769	−	3.95578i	−0.0167247	−	0.159125i
$619$	9.82382	−	10.9105i	0.394853	−	0.438528i	−0.512635	−	0.858606i	$-0.671331\pi$
$619$	9.82382	−	10.9105i	0.394853	−	0.438528i	0.907488	+	0.420078i	$0.137997\pi$
$620$	38.7750	−	8.24187i	1.55724	−	0.331002i
$621$	−13.6867	+	6.09371i	−0.549228	+	0.244532i
$622$	11.4898	+	8.34780i	0.460697	+	0.334716i
$623$	−0.661881	+	6.76423i	−0.0265177	+	0.271003i
$624$	5.58623	+	17.1926i	0.223628	+	0.688257i
$625$	0.400041	+	3.80614i	0.0160017	+	0.152246i
$626$	5.38043	+	9.31918i	0.215045	+	0.372469i
$627$		0			0
$628$	−8.98240	+	15.5580i	−0.358437	+	0.620831i
$629$	6.04609	−	4.39274i	0.241073	−	0.175150i
$630$	2.01016	−	3.54015i	0.0800866	−	0.141043i
$631$	−9.31680	+	28.6741i	−0.370896	+	1.14150i	0.575310	+	0.817935i	$0.304881\pi$
$631$	−9.31680	+	28.6741i	−0.370896	+	1.14150i	−0.946206	+	0.323565i	$0.895119\pi$
$632$	13.6867	−	6.09371i	0.544427	−	0.242395i
$633$	2.41855	−	23.0109i	0.0961287	−	0.914603i
$634$	2.86536	−	0.609051i	0.113798	−	0.0241885i
$635$	23.1145	+	4.91313i	0.917270	+	0.194972i
$636$	22.3907	−	16.2678i	0.887848	−	0.645060i
$637$	−3.73450	+	41.2168i	−0.147966	+	1.63307i
$638$		0			0
$639$	2.82963	−	4.90107i	0.111939	−	0.193883i
$640$	−36.1889	−	16.1124i	−1.43049	−	0.636897i
$641$	−10.8253	+	12.0227i	−0.427574	+	0.474870i	−0.917981	−	0.396624i	$-0.870182\pi$
$641$	−10.8253	+	12.0227i	−0.427574	+	0.474870i	0.490407	+	0.871494i	$0.336848\pi$
$642$	−4.00493	−	4.44792i	−0.158062	−	0.175545i
$643$	1.88960	+	1.37288i	0.0745186	+	0.0541409i	0.624421	−	0.781088i	$-0.285335\pi$
$643$	1.88960	+	1.37288i	0.0745186	+	0.0541409i	−0.549902	+	0.835229i	$0.685335\pi$
$644$	−1.54967	−	13.7909i	−0.0610655	−	0.543436i
$645$	3.37206	−	10.3781i	0.132775	−	0.408639i
$646$	−1.57587	−	0.334961i	−0.0620017	−	0.0131789i
$647$	13.6686	+	6.08566i	0.537369	+	0.239252i	0.657431	−	0.753514i	$-0.271643\pi$
$647$	13.6686	+	6.08566i	0.537369	+	0.239252i	−0.120063	+	0.992766i	$0.538310\pi$
$648$	12.3481	+	21.3875i	0.485079	+	0.840182i
$649$		0			0
$650$	−30.0345			−1.17805
$651$	23.7766	−	26.7909i	0.931877	−	1.05002i
$652$	4.33399	+	13.3386i	0.169732	+	0.522382i
$653$	−15.3163	−	17.0104i	−0.599372	−	0.665670i	0.364758	−	0.931102i	$-0.381152\pi$
$653$	−15.3163	−	17.0104i	−0.599372	−	0.665670i	−0.964129	+	0.265433i	$0.914485\pi$
$654$	1.95323	−	18.5837i	0.0763772	−	0.726681i
$655$	2.25978	−	21.5003i	0.0882968	−	0.840088i
$656$	1.37566	+	1.52783i	0.0537106	+	0.0596517i
$657$	−0.925488	−	2.84836i	−0.0361067	−	0.111125i
$658$	−0.908972	−	2.73066i	−0.0354354	−	0.106452i
$659$	2.20568			0.0859211			0.0429606	−	0.999077i	$-0.486321\pi$
$659$	2.20568			0.0859211			0.0429606	+	0.999077i	$0.486321\pi$
$660$		0			0
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	0.872584	−	0.488463i	$-0.162442\pi$
$661$	0.341188	+	0.590956i	0.0132707	+	0.0229855i	−0.859314	+	0.511449i	$0.829109\pi$
$662$	−11.4209	−	5.08493i	−0.443887	−	0.197631i
$663$	−18.3197	−	3.89397i	−0.711479	−	0.151229i
$664$	−0.121539	+	0.374058i	−0.00471662	+	0.0145163i
$665$	11.2546	−	8.30107i	0.436435	−	0.321902i
$666$	−1.57355	−	1.14325i	−0.0609738	−	0.0443000i
$667$	−6.89060	−	7.65278i	−0.266805	−	0.296317i
$668$	−19.1244	+	21.2398i	−0.739944	+	0.821792i
$669$	27.2980	+	12.1539i	1.05540	+	0.469896i
$670$	11.5112	−	19.9380i	0.444717	−	0.770273i
$671$		0			0
$672$	−28.3452	+	6.23801i	−1.09344	+	0.240637i
$673$	−8.80734	+	6.39891i	−0.339498	+	0.246660i	−0.744450	−	0.667678i	$-0.767288\pi$
$673$	−8.80734	+	6.39891i	−0.339498	+	0.246660i	0.404952	+	0.914338i	$0.367288\pi$
$674$	−17.3508	−	3.68803i	−0.668328	−	0.142057i
$675$	33.9111	−	7.20803i	1.30524	−	0.277437i
$676$	3.60030	−	34.2546i	0.138473	−	1.31748i
$677$	−41.7174	+	18.5738i	−1.60333	+	0.713849i	−0.996703	−	0.0811379i	$-0.974145\pi$
$677$	−41.7174	+	18.5738i	−1.60333	+	0.713849i	−0.606627	+	0.794986i	$0.707478\pi$
$678$	−4.82803	+	14.8592i	−0.185419	+	0.570662i
$679$	12.7199	−	22.4015i	0.488145	−	0.859689i
$680$	11.2086	−	8.14353i	0.429830	−	0.312290i
$681$	−14.9811	+	25.9480i	−0.574076	+	0.994329i
$682$		0			0
$683$	−3.24186	−	5.61507i	−0.124046	−	0.214855i	0.797313	−	0.603566i	$-0.206254\pi$
$683$	−3.24186	−	5.61507i	−0.124046	−	0.214855i	−0.921360	+	0.388711i	$0.872921\pi$
$684$	−0.159481	−	1.51736i	−0.00609790	−	0.0580177i
$685$	8.18684	+	25.1965i	0.312803	+	0.962709i
$686$	−11.9467	−	2.27158i	−0.456129	−	0.0867293i
$687$	8.61925	+	6.26225i	0.328845	+	0.238920i
$688$	−2.33572	+	1.03993i	−0.0890485	+	0.0396469i
$689$	−53.3512	+	11.3401i	−2.03252	+	0.432025i
$690$	10.0249	−	11.1338i	0.381641	−	0.423855i
$691$	−1.14425	−	10.8868i	−0.0435292	−	0.414153i	−0.994489	−	0.104839i	$-0.966567\pi$
$691$	−1.14425	−	10.8868i	−0.0435292	−	0.414153i	0.950960	−	0.309314i	$-0.100099\pi$
$692$	30.6885			1.16660
$693$		0			0
$694$	−13.2754			−0.503927
$695$	4.03802	+	38.4192i	0.153171	+	1.45732i
$696$	−9.23536	+	10.2569i	−0.350065	+	0.388787i
$697$	−2.08345	+	0.442851i	−0.0789163	+	0.0167742i
$698$	−7.21169	+	3.21085i	−0.272966	+	0.121532i
$699$	−29.8195	−	21.6652i	−1.12788	−	0.819452i
$700$	−3.12736	+	31.9607i	−0.118203	+	1.20800i
$701$	0.282712	+	0.870097i	0.0106779	+	0.0328631i	0.956253	−	0.292539i	$-0.0945002\pi$
$701$	0.282712	+	0.870097i	0.0106779	+	0.0328631i	−0.945576	+	0.325402i	$0.894500\pi$
$702$	−1.81837	−	17.3007i	−0.0686300	−	0.652971i
$703$	−3.34073	−	5.78632i	−0.125998	−	0.218235i
$704$		0			0
$705$	−5.65277	+	9.79088i	−0.212896	+	0.368746i
$706$	−5.71543	+	4.15250i	−0.215103	+	0.156282i
$707$	4.90668	−	0.0352311i	0.184535	−	0.00132500i
$708$	−8.20621	+	25.2561i	−0.308408	+	0.949183i
$709$	40.4813	−	18.0234i	1.52031	−	0.676885i	0.534563	−	0.845129i	$-0.320476\pi$
$709$	40.4813	−	18.0234i	1.52031	−	0.676885i	0.985745	+	0.168244i	$0.0538096\pi$
$710$	2.11117	−	20.0864i	0.0792307	−	0.753830i
$711$	−4.10624	+	0.872808i	−0.153996	+	0.0327329i
$712$	5.88824	+	1.25158i	0.220671	+	0.0469051i
$713$	19.1505	−	13.9137i	0.717193	−	0.521071i
$714$	1.66300	−	5.24606i	0.0622363	−	0.196329i
$715$		0			0
$716$	2.54774	−	4.41281i	0.0952134	−	0.164914i
$717$	38.7071	+	17.2335i	1.44554	+	0.643597i
$718$	10.6722	−	11.8527i	0.398284	−	0.442339i
$719$	−3.48106	−	3.86611i	−0.129822	−	0.144181i	0.674729	−	0.738065i	$-0.264260\pi$
$719$	−3.48106	−	3.86611i	−0.129822	−	0.144181i	−0.804551	+	0.593884i	$0.797594\pi$
$720$	3.03142	+	2.20245i	0.112974	+	0.0820806i
$721$	7.68099	+	3.35392i	0.286055	+	0.124907i
$722$	3.41014	−	10.4953i	0.126912	−	0.390595i
$723$	−37.1739	−	7.90156i	−1.38251	−	0.293862i
$724$	14.8205	+	6.59851i	0.550800	+	0.245232i
$725$	11.9148	+	20.6370i	0.442503	+	0.766438i
$726$		0			0
$727$	50.0871			1.85763			0.928814	−	0.370547i	$-0.120830\pi$
$727$	50.0871			1.85763			0.928814	+	0.370547i	$0.120830\pi$
$728$	35.9086	+	7.36354i	1.33086	+	0.272911i
$729$	5.80538	+	17.8671i	0.215014	+	0.661746i
$730$	−7.15200	−	7.94310i	−0.264707	−	0.293987i
$731$	0.276887	−	2.63441i	0.0102410	−	0.0974370i
$732$	2.09687	−	19.9504i	0.0775025	−	0.737387i
$733$	31.4958	+	34.9796i	1.16332	+	1.29200i	0.949013	+	0.315236i	$0.102084\pi$
$733$	31.4958	+	34.9796i	1.16332	+	1.29200i	0.214310	+	0.976766i	$0.431250\pi$
$734$	−2.20037	−	6.77205i	−0.0812172	−	0.249961i
$735$	24.4772	+	41.0238i	0.902856	+	1.51319i
$736$	−19.1799			−0.706981
$737$		0			0
$738$	0.277175	+	0.480082i	0.0102030	+	0.0176720i
$739$	−42.9288	−	19.1131i	−1.57916	−	0.703087i	−0.585003	−	0.811031i	$-0.698907\pi$
$739$	−42.9288	−	19.1131i	−1.57916	−	0.703087i	−0.994157	+	0.107943i	$0.965573\pi$
$740$	24.7063	+	5.25149i	0.908222	+	0.193048i
$741$	−5.17430	+	15.9249i	−0.190083	+	0.585014i
$742$	−1.78968	−	15.9268i	−0.0657011	−	0.584689i
$743$	−4.20311	−	3.05374i	−0.154197	−	0.112031i	0.508011	−	0.861350i	$-0.330381\pi$
$743$	−4.20311	−	3.05374i	−0.154197	−	0.112031i	−0.662209	+	0.749319i	$0.730381\pi$
$744$	−21.2291	−	23.5773i	−0.778295	−	0.864384i
$745$	−2.38803	+	2.65217i	−0.0874905	+	0.0971681i
$746$	−19.8096	−	8.81982i	−0.725282	−	0.322916i
$747$	0.0551029	−	0.0954410i	0.00201611	−	0.00349200i
$748$		0			0
$749$	12.3171	−	2.71066i	0.450057	−	0.0990452i
$750$	−9.92123	+	7.20819i	−0.362272	+	0.263206i
$751$	−32.7225	−	6.95539i	−1.19406	−	0.253806i	−0.432341	−	0.901710i	$-0.642312\pi$
$751$	−32.7225	−	6.95539i	−1.19406	−	0.253806i	−0.761722	+	0.647904i	$0.775646\pi$
$752$	2.59103	−	0.550741i	0.0944852	−	0.0200834i
$753$	−4.41891	+	42.0431i	−0.161034	+	1.53214i
$754$	10.9234	−	4.86339i	0.397805	−	0.177114i
$755$	18.1124	−	55.7441i	0.659176	−	2.02874i
$756$	−18.5995	+	0.133549i	−0.676458	+	0.00485713i
$757$	−32.3962	+	23.5373i	−1.17746	+	0.855476i	−0.991883	−	0.127154i	$-0.959416\pi$
$757$	−32.3962	+	23.5373i	−1.17746	+	0.855476i	−0.185579	+	0.982629i	$0.559416\pi$
$758$	−7.20051	+	12.4716i	−0.261534	+	0.452990i
$759$		0			0
$760$	−6.19326	−	10.7270i	−0.224653	−	0.389110i
$761$	−0.790078	−	7.51709i	−0.0286403	−	0.272494i	−0.999465	−	0.0327043i	$-0.989588\pi$
$761$	−0.790078	−	7.51709i	−0.0286403	−	0.272494i	0.970825	−	0.239790i	$-0.0770786\pi$
$762$	−2.56914	−	7.90700i	−0.0930702	−	0.286441i
$763$	32.0198	+	22.9143i	1.15920	+	0.829554i
$764$	12.7207	+	9.24215i	0.460220	+	0.334369i
$765$	−3.54647	+	1.57899i	−0.128223	+	0.0570884i
$766$	23.4192	−	4.97790i	0.846169	−	0.179859i
$767$	35.0188	−	38.8923i	1.26446	−	1.40432i
$768$	1.68423	+	16.0244i	0.0607743	+	0.578229i
$769$	−51.5407			−1.85860			−0.929302	−	0.369320i	$-0.879591\pi$
$769$	−51.5407			−1.85860			−0.929302	+	0.369320i	$0.879591\pi$
$770$		0			0
$771$	55.6834			2.00539
$772$	−4.15309	−	39.5140i	−0.149473	−	1.42214i
$773$	−10.3486	+	11.4932i	−0.372212	+	0.413383i	−0.899929	−	0.436037i	$-0.856382\pi$
$773$	−10.3486	+	11.4932i	−0.372212	+	0.413383i	0.527717	+	0.849420i	$0.323048\pi$
$774$	−0.674339	+	0.143335i	−0.0242386	+	0.00515208i
$775$	−50.0406	+	22.2795i	−1.79751	+	0.800304i
$776$	−18.4591	−	13.4114i	−0.662645	−	0.481439i
$777$	20.7831	−	9.43263i	0.745591	−	0.338394i
$778$	−3.95182	−	12.1624i	−0.141680	−	0.436045i
$779$	0.199053	+	1.89386i	0.00713181	+	0.0678546i
$780$	−31.6498	−	54.8190i	−1.13324	−	1.96284i
$781$		0			0
$782$	1.81842	−	3.14959i	0.0650264	−	0.112629i
$783$	−11.1661	+	8.11263i	−0.399043	+	0.289922i
$784$	3.30558	−	10.6937i	0.118057	−	0.381917i
$785$	12.6285	−	38.8665i	0.450730	−	1.38721i
$786$	−6.94844	+	3.09365i	−0.247843	+	0.110347i
$787$	2.29459	−	21.8316i	0.0817933	−	0.778211i	−0.874347	−	0.485301i	$-0.838710\pi$
$787$	2.29459	−	21.8316i	0.0817933	−	0.778211i	0.956140	−	0.292909i	$-0.0946235\pi$
$788$	37.7211	−	8.01786i	1.34376	−	0.285625i
$789$	−28.9984	−	6.16381i	−1.03237	−	0.219437i
$790$	−12.1206	+	8.80617i	−0.431233	+	0.313309i
$791$	−22.2040	−	24.3068i	−0.789484	−	0.864250i
$792$		0			0
$793$	−19.7668	+	34.2371i	−0.701941	+	1.21580i
$794$	4.70276	+	2.09381i	0.166895	+	0.0743064i
$795$	−42.1277	+	46.7875i	−1.49411	+	1.65938i
$796$	−5.86954	−	6.51878i	−0.208040	−	0.231052i
$797$	−34.4850	−	25.0548i	−1.22152	−	0.887487i	−0.225296	−	0.974290i	$-0.572335\pi$
$797$	−34.4850	−	25.0548i	−1.22152	−	0.887487i	−0.996225	+	0.0868031i	$0.972335\pi$
$798$	−4.50907	−	1.96890i	−0.159619	−	0.0696981i
$799$	−0.848064	+	2.61007i	−0.0300023	+	0.0923377i
$800$	43.4131	+	9.22774i	1.53488	+	0.326250i
$801$	−1.54093	−	0.686067i	−0.0544461	−	0.0242410i
$802$	−8.02583	−	13.9011i	−0.283402	−	0.490867i
$803$		0			0
$804$	29.4734			1.03945
$805$	9.97073	+	29.9532i	0.351422	+	1.05571i
$806$	8.49347	+	26.1402i	0.299170	+	0.920750i
$807$	2.18358	+	2.42511i	0.0768657	+	0.0853680i
$808$	0.454283	−	4.32222i	0.0159816	−	0.152055i
$809$	0.414711	−	3.94571i	0.0145805	−	0.138724i	−0.984810	−	0.173636i	$-0.944448\pi$
$809$	0.414711	−	3.94571i	0.0145805	−	0.138724i	0.999390	+	0.0349120i	$0.0111151\pi$
$810$	−16.5250	−	18.3529i	−0.580629	−	0.644854i
$811$	14.4996	+	44.6252i	0.509150	+	1.56700i	0.793681	+	0.608335i	$0.208162\pi$
$811$	14.4996	+	44.6252i	0.509150	+	1.56700i	−0.284531	+	0.958667i	$0.591838\pi$
$812$	−4.03789	−	12.1303i	−0.141702	−	0.425690i
$813$	39.2549			1.37673
$814$		0			0
$815$	−15.9523	−	27.6301i	−0.558783	−	0.967841i
$816$	4.62741	+	2.06026i	0.161992	+	0.0721234i
$817$	−2.31648	−	0.492382i	−0.0810432	−	0.0172263i
$818$	−0.477588	+	1.46986i	−0.0166985	+	0.0513926i
$819$	−9.41282	−	4.11013i	−0.328911	−	0.143620i
$820$	−5.82402	−	4.23140i	−0.203384	−	0.147767i
$821$	33.8580	+	37.6032i	1.18165	+	1.31236i	0.939671	+	0.342079i	$0.111131\pi$
$821$	33.8580	+	37.6032i	1.18165	+	1.31236i	0.241983	+	0.970281i	$0.422202\pi$
$822$	6.23693	−	6.92681i	0.217538	−	0.241600i
$823$	0.364138	+	0.162125i	0.0126930	+	0.00565131i	0.413073	−	0.910698i	$-0.364455\pi$
$823$	0.364138	+	0.162125i	0.0126930	+	0.00565131i	−0.400380	+	0.916349i	$0.631122\pi$
$824$	3.71172	−	6.42889i	0.129304	−	0.223961i
$825$		0			0
$826$	10.3717	+	11.3540i	0.360879	+	0.395055i
$827$	−16.5229	+	12.0046i	−0.574558	+	0.417441i	−0.836758	−	0.547573i	$-0.815552\pi$
$827$	−16.5229	+	12.0046i	−0.574558	+	0.417441i	0.262200	+	0.965014i	$0.415552\pi$
$828$	3.36888	+	0.716078i	0.117077	+	0.0248854i
$829$	22.7550	−	4.83671i	0.790312	−	0.167986i	0.204966	−	0.978769i	$-0.434292\pi$
$829$	22.7550	−	4.83671i	0.790312	−	0.167986i	0.585347	+	0.810783i	$0.300958\pi$
$830$	0.0411119	−	0.391153i	0.00142701	−	0.0135771i
$831$	46.5743	−	20.7362i	1.61565	−	0.719332i
$832$	1.03928	−	3.19856i	0.0360304	−	0.110890i
$833$	7.88242	+	8.50545i	0.273110	+	0.294696i
$834$	10.9956	−	7.98876i	0.380746	−	0.276628i
$835$	32.5082	−	56.3059i	1.12499	−	1.94855i
$836$		0			0
$837$	−15.8632	−	27.4758i	−0.548311	−	0.949703i
$838$	0.637679	+	6.06711i	0.0220283	+	0.209585i
$839$	−5.09450	−	15.6792i	−0.175882	−	0.541308i	0.823791	−	0.566894i	$-0.191855\pi$
$839$	−5.09450	−	15.6792i	−0.175882	−	0.541308i	−0.999673	+	0.0255858i	$0.991855\pi$
$840$	38.5290	−	17.4868i	1.32938	−	0.603351i
$841$	15.7865	+	11.4696i	0.544362	+	0.395502i
$842$	23.4134	−	10.4243i	0.806878	−	0.359245i
$843$	29.4490	−	6.25957i	1.01428	−	0.215591i
$844$	12.7020	−	14.1070i	0.437221	−	0.485583i
$845$	8.19003	+	77.9229i	0.281746	+	2.68063i
$846$	0.714253			0.0245565
$847$		0			0
$848$	14.7514			0.506566
$849$	−3.21205	−	30.5606i	−0.110237	−	1.04884i
$850$	−5.63123	+	6.25412i	−0.193150	+	0.214514i
$851$	14.7531	−	3.13587i	0.505730	−	0.107496i
$852$	23.6209	−	10.5167i	0.809240	−	0.360297i
$853$	−11.9989	−	8.71773i	−0.410835	−	0.298489i	0.363105	−	0.931748i	$-0.381717\pi$
$853$	−11.9989	−	8.71773i	−0.410835	−	0.298489i	−0.773940	+	0.633259i	$0.781717\pi$
$854$	−9.44681	−	6.76041i	−0.323263	−	0.231337i
$855$	1.07251	+	3.30086i	0.0366792	+	0.112887i
$856$	−1.16763	−	11.1093i	−0.0399089	−	0.379708i
$857$	−2.51594	−	4.35773i	−0.0859428	−	0.148857i	0.819850	−	0.572579i	$-0.194057\pi$
$857$	−2.51594	−	4.35773i	−0.0859428	−	0.148857i	−0.905793	+	0.423721i	$0.860724\pi$
$858$		0			0
$859$	28.0181	−	48.5288i	0.955966	−	1.65578i	0.223825	−	0.974629i	$-0.428146\pi$
$859$	28.0181	−	48.5288i	0.955966	−	1.65578i	0.732141	−	0.681153i	$-0.238521\pi$
$860$	7.24290	−	5.26227i	0.246981	−	0.179442i
$861$	−6.50479	+	0.0467060i	−0.221683	+	0.00159174i
$862$	−0.771457	+	2.37430i	−0.0262759	+	0.0808690i
$863$	−33.3225	+	14.8361i	−1.13431	+	0.505028i	−0.886015	−	0.463656i	$-0.846537\pi$
$863$	−33.3225	+	14.8361i	−1.13431	+	0.505028i	−0.248296	+	0.968684i	$0.579871\pi$
$864$	−2.68707	+	25.5657i	−0.0914158	+	0.869764i
$865$	−68.2853	+	14.5145i	−2.32177	+	0.493507i
$866$	5.27974	+	1.12224i	0.179413	+	0.0381354i
$867$	22.0538	−	16.0230i	0.748986	−	0.544170i
$868$	28.7010	−	6.31631i	0.974177	−	0.214390i
$869$		0			0
$870$	6.90101	−	11.9529i	0.233966	−	0.405241i
$871$	−53.0628	−	23.6251i	−1.79796	−	0.800505i
$872$	23.3355	−	25.9167i	0.790240	−	0.877651i
$873$	4.27796	+	4.75115i	0.144787	+	0.160802i
$874$	−2.63049	−	1.91116i	−0.0889775	−	0.0646459i
$875$	−2.88553	−	25.6790i	−0.0975487	−	0.868108i
$876$	4.22841	−	13.0137i	0.142865	−	0.439693i
$877$	−6.47155	−	1.37557i	−0.218529	−	0.0464497i	0.0973460	−	0.995251i	$-0.468965\pi$
$877$	−6.47155	−	1.37557i	−0.218529	−	0.0464497i	−0.315875	+	0.948801i	$0.602298\pi$
$878$	2.72414	+	1.21287i	0.0919354	+	0.0409323i
$879$	14.6627	+	25.3965i	0.494559	+	0.856602i
$880$		0			0
$881$	−22.5286			−0.759008			−0.379504	−	0.925190i	$-0.623905\pi$
$881$	−22.5286			−0.759008			−0.379504	+	0.925190i	$0.623905\pi$
$882$	1.47134	−	2.63511i	0.0495425	−	0.0887288i
$883$	−15.8109	−	48.6610i	−0.532080	−	1.63757i	−0.749876	−	0.661578i	$-0.769887\pi$
$883$	−15.8109	−	48.6610i	−0.532080	−	1.63757i	0.217796	−	0.975994i	$-0.430113\pi$
$884$	−10.2817	−	11.4190i	−0.345812	−	0.384063i
$885$	6.31454	−	60.0788i	0.212261	−	2.01953i
$886$	0.943354	−	8.97541i	0.0316926	−	0.301535i
$887$	4.24101	+	4.71012i	0.142399	+	0.158150i	0.810125	−	0.586257i	$-0.199399\pi$
$887$	4.24101	+	4.71012i	0.142399	+	0.158150i	−0.667726	+	0.744407i	$0.732732\pi$
$888$	−6.24682	−	19.2257i	−0.209629	−	0.645173i
$889$	17.1615	+	3.51920i	0.575579	+	0.118030i
$890$	−6.01979			−0.201784
$891$		0			0
$892$	12.2578	+	21.2311i	0.410421	+	0.710871i
$893$	2.24146	+	0.997963i	0.0750077	+	0.0333956i
$894$	1.22817	+	0.261056i	0.0410762	+	0.00873101i
$895$	−3.58190	+	11.0240i	−0.119730	+	0.368491i
$896$	−26.9136	−	11.7519i	−0.899120	−	0.392603i
$897$	−30.5798	−	22.2175i	−1.02103	−	0.741821i
$898$	−9.47543	−	10.5235i	−0.316199	−	0.351175i
$899$	14.5918	−	16.2058i	0.486663	−	0.540494i
$900$	−7.28083	−	3.24163i	−0.242694	−	0.108054i
$901$	−7.64155	+	13.2356i	−0.254577	+	0.440940i
$902$		0			0
$903$	2.44456	−	7.71155i	0.0813498	−	0.256624i
$904$	−23.5903	+	17.1394i	−0.784602	+	0.570047i
$905$	−36.0981	−	7.67288i	−1.19994	−	0.255055i
$906$	−20.1708	+	4.28743i	−0.670130	+	0.142440i
$907$	0.719651	−	6.84702i	0.0238956	−	0.227352i	−0.976056	−	0.217519i	$-0.930204\pi$
$907$	0.719651	−	6.84702i	0.0238956	−	0.227352i	0.999952	−	0.00983240i	$-0.00312980\pi$
$908$	−22.4566	+	9.99834i	−0.745250	+	0.331806i
$909$	−0.376310	+	1.15816i	−0.0124814	+	0.0384139i
$910$	−36.6549	+	0.263191i	−1.21510	+	0.00872469i
$911$	33.2359	−	24.1473i	1.10115	−	0.800035i	0.119906	−	0.992785i	$-0.461741\pi$
$911$	33.2359	−	24.1473i	1.10115	−	0.800035i	0.981248	+	0.192750i	$0.0617407\pi$
$912$	2.26430	−	3.92188i	0.0749784	−	0.129866i
$913$		0			0
$914$	1.08524	+	1.87969i	0.0358966	+	0.0621747i
$915$	4.77000	+	45.3835i	0.157691	+	1.50033i
$916$	2.70107	+	8.31303i	0.0892458	+	0.274670i
$917$	1.56079	−	15.9508i	0.0515418	−	0.526742i
$918$	−3.94346	−	2.86509i	−0.130154	−	0.0945621i
$919$	10.6213	−	4.72892i	0.350365	−	0.155993i	−0.224006	−	0.974588i	$-0.571913\pi$
$919$	10.6213	−	4.72892i	0.350365	−	0.155993i	0.574371	+	0.818595i	$0.305247\pi$
$920$	27.3502	−	5.81347i	0.901710	−	0.191664i
$921$	21.0748	−	23.4059i	0.694439	−	0.771252i
$922$	2.20680	+	20.9963i	0.0726771	+	0.691476i
$923$	−50.9562			−1.67724
$924$		0			0
$925$	−34.9019			−1.14757
$926$	0.399583	+	3.80178i	0.0131311	+	0.124934i
$927$	−1.39184	+	1.54579i	−0.0457139	+	0.0507704i
$928$	−17.2833	+	3.67367i	−0.567351	+	0.120594i
$929$	22.6256	−	10.0736i	0.742323	−	0.330503i	−0.000492574	−	1.00000i	$-0.500157\pi$
$929$	22.6256	−	10.0736i	0.742323	−	0.330503i	0.742815	+	0.669497i	$0.233490\pi$
$930$	25.6671	+	18.6483i	0.841659	+	0.611501i
$931$	8.29915	−	6.21371i	0.271994	−	0.203646i
$932$	−9.34474	−	28.7601i	−0.306097	−	0.942070i
$933$	−4.32328	−	41.1333i	−0.141538	−	1.34664i
$934$	−1.97470	−	3.42028i	−0.0646141	−	0.111915i
$935$		0			0
$936$	−4.54861	+	7.87842i	−0.148676	+	0.257514i
$937$	0.930743	−	0.676224i	0.0304060	−	0.0220913i	−0.572478	−	0.819920i	$-0.694018\pi$
$937$	0.930743	−	0.676224i	0.0304060	−	0.0220913i	0.602884	+	0.797828i	$0.294018\pi$
$938$	8.42744	−	14.8419i	0.275166	−	0.484604i
$939$	9.68400	−	29.8043i	0.316025	−	0.972626i
$940$	−8.47350	+	3.77264i	−0.276375	+	0.123050i
$941$	1.05680	−	10.0548i	0.0344508	−	0.327778i	−0.963700	−	0.266988i	$-0.913971\pi$
$941$	1.05680	−	10.0548i	0.0344508	−	0.327778i	0.998151	−	0.0607895i	$-0.0193618\pi$
$942$	−14.0637	+	2.98933i	−0.458220	+	0.0973978i
$943$	−4.20480	−	0.893759i	−0.136927	−	0.0291048i
$944$	−11.4510	+	8.31961i	−0.372697	+	0.270780i
$945$	41.3228	−	9.09402i	1.34423	−	0.295828i
$946$		0			0
$947$	12.2277	−	21.1789i	0.397346	−	0.688223i	−0.596052	−	0.802946i	$-0.703265\pi$
$947$	12.2277	−	21.1789i	0.397346	−	0.688223i	0.993398	+	0.114723i	$0.0365981\pi$
$948$	−17.5217	−	7.80118i	−0.569079	−	0.253370i
$949$	−18.0441	+	20.0400i	−0.585737	+	0.650527i
$950$	5.03453	+	5.59141i	0.163342	+	0.181409i
$951$	−6.90173	−	5.01440i	−0.223804	−	0.162603i
$952$	8.26589	−	6.09668i	0.267899	−	0.197594i
$953$	4.99667	−	15.3782i	0.161858	−	0.498148i	−0.836933	−	0.547305i	$-0.815654\pi$
$953$	4.99667	−	15.3782i	0.161858	−	0.498148i	0.998791	+	0.0491574i	$0.0156536\pi$
$954$	3.89065	+	0.826982i	0.125964	+	0.0267745i
$955$	−32.6762	−	14.5484i	−1.05738	−	0.470775i
$956$	17.3809	+	30.1046i	0.562138	+	0.973652i
$957$		0			0
$958$	11.2512			0.363511
$959$	6.20324	+	18.6353i	0.200313	+	0.601764i
$960$	−1.19963	−	3.69209i	−0.0387180	−	0.119162i
$961$	12.7987	+	14.2144i	0.412861	+	0.458529i
$962$	−1.83060	+	17.4170i	−0.0590210	+	0.561547i
$963$	−0.327174	+	3.11285i	−0.0105430	+	0.100310i
$964$	−20.8634	−	23.1712i	−0.671966	−	0.746294i
$965$	27.9297	+	85.9587i	0.899088	+	2.76711i
$966$	7.37245	−	8.30711i	0.237205	−	0.267277i
$967$	1.55941			0.0501472			0.0250736	−	0.999686i	$-0.492018\pi$
$967$	1.55941			0.0501472			0.0250736	+	0.999686i	$0.492018\pi$
$968$		0			0
$969$	2.34591	+	4.06323i	0.0753614	+	0.130530i
$970$	20.8441	+	9.28041i	0.669265	+	0.297976i
$971$	8.84958	+	1.88104i	0.283996	+	0.0603653i	0.347707	−	0.937603i	$-0.386960\pi$
$971$	8.84958	+	1.88104i	0.283996	+	0.0603653i	−0.0637110	+	0.997968i	$0.520294\pi$
$972$	3.25263	−	10.0106i	0.104328	−	0.321089i
$973$	3.19800	+	28.4597i	0.102523	+	0.912376i
$974$	3.03551	+	2.20543i	0.0972640	+	0.0706664i
$975$	58.5271	+	65.0010i	1.87437	+	2.08170i
$976$	7.15438	−	7.94574i	0.229006	−	0.254337i
$977$	−6.17235	−	2.74811i	−0.197471	−	0.0879197i	0.305619	−	0.952154i	$-0.401137\pi$
$977$	−6.17235	−	2.74811i	−0.197471	−	0.0879197i	−0.503090	+	0.864234i	$0.667803\pi$
$978$	−5.61240	+	9.72096i	−0.179465	+	0.310842i
$979$		0			0
$980$	−3.53664	+	39.0330i	−0.112974	+	1.24686i
$981$	−7.90562	+	5.74377i	−0.252407	+	0.183384i
$982$	−15.4577	−	3.28565i	−0.493277	−	0.104849i
$983$	−25.8529	+	5.49520i	−0.824580	+	0.175270i	−0.600830	−	0.799377i	$-0.705163\pi$
$983$	−25.8529	+	5.49520i	−0.824580	+	0.175270i	−0.223750	+	0.974647i	$0.571830\pi$
$984$	−0.602244	+	5.72997i	−0.0191989	+	0.182665i
$985$	−80.1414	+	35.6812i	−2.55352	+	1.13690i
$986$	1.03533	−	3.18643i	0.0329717	−	0.101476i
$987$	−4.13843	+	7.28833i	−0.131728	+	0.231990i
$988$	−11.1139	+	8.07476i	−0.353582	+	0.256892i
$989$	2.67301	−	4.62979i	0.0849969	−	0.147219i
$990$		0			0
$991$	0.317093	+	0.549221i	0.0100728	+	0.0174466i	0.871018	−	0.491251i	$-0.163460\pi$
$991$	0.317093	+	0.549221i	0.0100728	+	0.0174466i	−0.860945	+	0.508698i	$0.830127\pi$
$992$	−4.24554	−	40.3936i	−0.134796	−	1.28250i
$993$	11.2507	+	34.6261i	0.357030	+	1.09883i
$994$	1.45815	−	14.9018i	0.0462496	−	0.472658i
$995$	16.1435	+	11.7289i	0.511783	+	0.371832i
$996$	0.459983	−	0.204798i	0.0145751	−	0.00648926i
$997$	9.90604	−	2.10559i	0.313728	−	0.0666848i	−0.0483570	−	0.998830i	$-0.515399\pi$
$997$	9.90604	−	2.10559i	0.313728	−	0.0666848i	0.362085	+	0.932145i	$0.382065\pi$
$998$	−4.74042	+	5.26477i	−0.150055	+	0.166653i
$999$	−2.11306	−	20.1044i	−0.0668541	−	0.636074i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.n.d.366.2		24
7.4	even	3	inner	847.2.n.d.487.2		24
11.2	odd	10		77.2.e.b.23.2	✓	6
11.3	even	5	inner	847.2.n.d.632.2		24
11.4	even	5	inner	847.2.n.d.807.2		24
11.5	even	5	inner	847.2.n.d.9.2		24
11.6	odd	10		847.2.n.e.9.2		24
11.7	odd	10		847.2.n.e.807.2		24
11.8	odd	10		847.2.n.e.632.2		24
11.9	even	5		847.2.e.d.485.2		6
11.10	odd	2		847.2.n.e.366.2		24
33.2	even	10		693.2.i.g.100.2		6
44.35	even	10		1232.2.q.k.177.3		6
77.2	odd	30		539.2.a.h.1.2		3
77.4	even	15	inner	847.2.n.d.81.2		24
77.9	even	15		5929.2.a.v.1.2		3
77.13	even	10		539.2.e.l.177.2		6
77.18	odd	30		847.2.n.e.81.2		24
77.24	even	30		539.2.e.l.67.2		6
77.25	even	15	inner	847.2.n.d.753.2		24
77.32	odd	6		847.2.n.e.487.2		24
77.39	odd	30		847.2.n.e.130.2		24
77.46	odd	30		77.2.e.b.67.2	yes	6
77.53	even	15		847.2.e.d.606.2		6
77.60	even	15	inner	847.2.n.d.130.2		24
77.68	even	30		539.2.a.i.1.2		3
77.74	odd	30		847.2.n.e.753.2		24
77.75	odd	30		5929.2.a.w.1.2		3
231.2	even	30		4851.2.a.bo.1.2		3
231.68	odd	30		4851.2.a.bn.1.2		3
231.200	even	30		693.2.i.g.298.2		6
308.79	even	30		8624.2.a.cl.1.1		3
308.123	even	30		1232.2.q.k.529.3		6
308.299	odd	30		8624.2.a.ck.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.b.23.2	✓	6	11.2	odd	10
77.2.e.b.67.2	yes	6	77.46	odd	30
539.2.a.h.1.2		3	77.2	odd	30
539.2.a.i.1.2		3	77.68	even	30
539.2.e.l.67.2		6	77.24	even	30
539.2.e.l.177.2		6	77.13	even	10
693.2.i.g.100.2		6	33.2	even	10
693.2.i.g.298.2		6	231.200	even	30
847.2.e.d.485.2		6	11.9	even	5
847.2.e.d.606.2		6	77.53	even	15
847.2.n.d.9.2		24	11.5	even	5	inner
847.2.n.d.81.2		24	77.4	even	15	inner
847.2.n.d.130.2		24	77.60	even	15	inner
847.2.n.d.366.2		24	1.1	even	1	trivial
847.2.n.d.487.2		24	7.4	even	3	inner
847.2.n.d.632.2		24	11.3	even	5	inner
847.2.n.d.753.2		24	77.25	even	15	inner
847.2.n.d.807.2		24	11.4	even	5	inner
847.2.n.e.9.2		24	11.6	odd	10
847.2.n.e.81.2		24	77.18	odd	30
847.2.n.e.130.2		24	77.39	odd	30
847.2.n.e.366.2		24	11.10	odd	2
847.2.n.e.487.2		24	77.32	odd	6
847.2.n.e.632.2		24	11.8	odd	10
847.2.n.e.753.2		24	77.74	odd	30
847.2.n.e.807.2		24	11.7	odd	10
1232.2.q.k.177.3		6	44.35	even	10
1232.2.q.k.529.3		6	308.123	even	30
4851.2.a.bn.1.2		3	231.68	odd	30
4851.2.a.bo.1.2		3	231.2	even	30
5929.2.a.v.1.2		3	77.9	even	15
5929.2.a.w.1.2		3	77.75	odd	30
8624.2.a.ck.1.3		3	308.299	odd	30
8624.2.a.cl.1.1		3	308.79	even	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)

\(f(q)\)	\(=\)	\(q+(0.0686355 + 0.653023i) q^{2} +(1.27953 - 1.42106i) q^{3} +(1.53457 - 0.326182i) q^{4} +(-3.26031 + 1.45158i) q^{5} +(1.01581 + 0.738028i) q^{6} +(-2.40923 + 1.09345i) q^{7} +(0.724144 + 2.22869i) q^{8} +(-0.0686355 - 0.653023i) q^{9} +O(q^{10})\)	\(q+(0.0686355 + 0.653023i) q^{2} +(1.27953 - 1.42106i) q^{3} +(1.53457 - 0.326182i) q^{4} +(-3.26031 + 1.45158i) q^{5} +(1.01581 + 0.738028i) q^{6} +(-2.40923 + 1.09345i) q^{7} +(0.724144 + 2.22869i) q^{8} +(-0.0686355 - 0.653023i) q^{9} +(-1.17169 - 2.02943i) q^{10} +(1.50000 - 2.59808i) q^{12} +(-4.78309 + 3.47512i) q^{13} +(-0.879407 - 1.49823i) q^{14} +(-2.10887 + 6.49045i) q^{15} +(1.46075 - 0.650367i) q^{16} +(-0.173164 + 1.64755i) q^{17} +(0.421729 - 0.0896412i) q^{18} +(1.44871 + 0.307934i) q^{19} +(-4.52968 + 3.29100i) q^{20} +(-1.52882 + 4.82277i) q^{21} +(-1.67169 + 2.89545i) q^{23} +(4.09367 + 1.82262i) q^{24} +(5.17685 - 5.74948i) q^{25} +(-2.59763 - 2.88496i) q^{26} +(3.62527 + 2.63391i) q^{27} +(-3.34045 + 2.46382i) q^{28} +(-0.951793 + 2.92932i) q^{29} +(-4.38316 - 0.931669i) q^{30} +(-6.46796 - 2.87972i) q^{31} +(2.86834 + 4.96812i) q^{32} -1.08777 q^{34} +(6.26758 - 7.06217i) q^{35} +(-0.318330 - 0.979720i) q^{36} +(-3.01859 - 3.35249i) q^{37} +(-0.101655 + 0.967179i) q^{38} +(-1.18175 + 11.2436i) q^{39} +(-5.59605 - 6.21505i) q^{40} +(0.397318 + 1.22282i) q^{41} +(-3.25431 - 0.667340i) q^{42} -1.59899 q^{43} +(1.17169 + 2.02943i) q^{45} +(-2.00553 - 0.892922i) q^{46} +(1.62042 + 0.344431i) q^{47} +(0.944860 - 2.90798i) q^{48} +(4.60873 - 5.26874i) q^{49} +(4.10986 + 2.98599i) q^{50} +(2.11970 + 2.35416i) q^{51} +(-6.20645 + 6.89296i) q^{52} +(8.42789 + 3.75234i) q^{53} +(-1.47118 + 2.54817i) q^{54} +(-4.18158 - 4.57759i) q^{56} +(2.29127 - 1.66470i) q^{57} +(-1.97824 - 0.420488i) q^{58} +(-8.65852 + 1.84042i) q^{59} +(-1.11914 + 10.6479i) q^{60} +(6.10866 - 2.71975i) q^{61} +(1.43659 - 4.42138i) q^{62} +(0.879407 + 1.49823i) q^{63} +(-0.460209 + 0.334361i) q^{64} +(10.5499 - 18.2730i) q^{65} +(4.91223 + 8.50823i) q^{67} +(0.271668 + 2.58475i) q^{68} +(1.97564 + 6.08040i) q^{69} +(5.04194 + 3.60816i) q^{70} +(6.97274 + 5.06599i) q^{71} +(1.40568 - 0.625850i) q^{72} +(4.46147 - 0.948316i) q^{73} +(1.98207 - 2.20131i) q^{74} +(-1.54643 - 14.7133i) q^{75} +2.32359 q^{76} -7.42345 q^{78} +(-0.668283 - 6.35828i) q^{79} +(-3.81843 + 4.24079i) q^{80} +(10.3084 - 2.19112i) q^{81} +(-0.771259 + 0.343387i) q^{82} +(0.135784 + 0.0986527i) q^{83} +(-0.772970 + 7.89953i) q^{84} +(-1.82698 - 5.62286i) q^{85} +(-0.109747 - 1.04418i) q^{86} +(2.94490 + 5.10071i) q^{87} +(1.28442 - 2.22469i) q^{89} +(-1.24484 + 0.904432i) q^{90} +(7.72368 - 13.6024i) q^{91} +(-1.62087 + 4.98854i) q^{92} +(-12.3682 + 5.50669i) q^{93} +(-0.113703 + 1.08181i) q^{94} +(-5.17024 + 1.09897i) q^{95} +(10.7301 + 2.28076i) q^{96} +(-7.87715 + 5.72308i) q^{97} +(3.75693 + 2.64799i) 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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