LMFDB - Embedded newform 370.2.q.a.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.103
Dual form			370.2.q.a.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.133975 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(0.366025 - 0.366025i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000 q^{8} +(2.36603 - 1.36603i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.133975 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(0.366025 - 0.366025i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000 q^{8} +(2.36603 - 1.36603i) q^{9} +(2.00000 + 1.00000i) q^{10} +2.00000i q^{11} +(-0.500000 - 0.133975i) q^{12} +(2.23205 - 3.86603i) q^{13} +(-2.00000 + 2.00000i) q^{14} +(-0.866025 - 0.767949i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.63397 - 2.09808i) q^{17} +(-2.36603 - 1.36603i) q^{18} +(3.36603 - 0.901924i) q^{19} +(-0.133975 - 2.23205i) q^{20} +(1.26795 - 0.732051i) q^{21} +(1.73205 - 1.00000i) q^{22} +6.00000 q^{23} +(0.133975 + 0.500000i) q^{24} +(1.96410 - 4.59808i) q^{25} -4.46410 q^{26} +(2.09808 + 2.09808i) q^{27} +(2.73205 + 0.732051i) q^{28} +(-1.26795 + 1.26795i) q^{29} +(-0.232051 + 1.13397i) q^{30} +(-1.83013 - 1.83013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 0.267949i) q^{33} +(-3.63397 - 2.09808i) q^{34} +(4.73205 + 4.19615i) q^{35} +2.73205i q^{36} +(-5.50000 + 2.59808i) q^{37} +(-2.46410 - 2.46410i) q^{38} +(2.23205 + 0.598076i) q^{39} +(-1.86603 + 1.23205i) q^{40} +(-0.401924 - 0.232051i) q^{41} +(-1.26795 - 0.732051i) q^{42} -11.0000 q^{43} +(-1.73205 - 1.00000i) q^{44} +(-2.73205 + 5.46410i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(4.19615 - 4.19615i) q^{47} +(0.366025 - 0.366025i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-4.96410 + 0.598076i) q^{50} +(1.53590 + 1.53590i) q^{51} +(2.23205 + 3.86603i) q^{52} +(3.13397 - 11.6962i) q^{53} +(0.767949 - 2.86603i) q^{54} +(-2.46410 - 3.73205i) q^{55} +(-0.732051 - 2.73205i) q^{56} +(0.901924 + 1.56218i) q^{57} +(1.73205 + 0.464102i) q^{58} +(-2.09808 + 7.83013i) q^{59} +(1.09808 - 0.366025i) q^{60} +(-6.46410 + 1.73205i) q^{61} +(-0.669873 + 2.50000i) q^{62} +(-5.46410 - 5.46410i) q^{63} +1.00000 q^{64} +(0.598076 + 9.96410i) q^{65} +(0.732051 + 0.732051i) q^{66} +(13.5622 - 3.63397i) q^{67} +4.19615i q^{68} +(0.803848 + 3.00000i) q^{69} +(1.26795 - 6.19615i) q^{70} +(-5.46410 + 9.46410i) q^{71} +(2.36603 - 1.36603i) q^{72} +(5.00000 + 3.46410i) q^{74} +(2.56218 + 0.366025i) q^{75} +(-0.901924 + 3.36603i) q^{76} +(5.46410 - 1.46410i) q^{77} +(-0.598076 - 2.23205i) q^{78} +(-6.83013 + 1.83013i) q^{79} +(2.00000 + 1.00000i) q^{80} +(3.33013 - 5.76795i) q^{81} +0.464102i q^{82} +(-3.43782 + 12.8301i) q^{83} +1.46410i q^{84} +(-4.19615 + 8.39230i) q^{85} +(5.50000 + 9.52628i) q^{86} +(-0.803848 - 0.464102i) q^{87} +2.00000i q^{88} +(12.5622 + 3.36603i) q^{89} +(6.09808 - 0.366025i) q^{90} +(-12.1962 - 3.26795i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(0.669873 - 1.16025i) q^{93} +(-5.73205 - 1.53590i) q^{94} +(-5.16987 + 5.83013i) q^{95} +(-0.500000 - 0.133975i) q^{96} -5.46410i q^{97} +(0.866025 + 0.500000i) q^{98} +(2.73205 + 4.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} + 6 q^{9} + 8 q^{10} - 2 q^{12} + 2 q^{13} - 8 q^{14} - 2 q^{16} + 18 q^{17} - 6 q^{18} + 10 q^{19} - 4 q^{20} + 12 q^{21} + 24 q^{23} + 4 q^{24} - 6 q^{25} - 4 q^{26} - 2 q^{27} + 4 q^{28} - 12 q^{29} + 6 q^{30} + 10 q^{31} - 2 q^{32} - 4 q^{33} - 18 q^{34} + 12 q^{35} - 22 q^{37} + 4 q^{38} + 2 q^{39} - 4 q^{40} - 12 q^{41} - 12 q^{42} - 44 q^{43} - 4 q^{45} - 12 q^{46} - 4 q^{47} - 2 q^{48} - 6 q^{50} + 20 q^{51} + 2 q^{52} + 16 q^{53} + 10 q^{54} + 4 q^{55} + 4 q^{56} + 14 q^{57} + 2 q^{59} - 6 q^{60} - 12 q^{61} - 20 q^{62} - 8 q^{63} + 4 q^{64} - 8 q^{65} - 4 q^{66} + 30 q^{67} + 24 q^{69} + 12 q^{70} - 8 q^{71} + 6 q^{72} + 20 q^{74} - 14 q^{75} - 14 q^{76} + 8 q^{77} + 8 q^{78} - 10 q^{79} + 8 q^{80} - 4 q^{81} - 38 q^{83} + 4 q^{85} + 22 q^{86} - 24 q^{87} + 26 q^{89} + 14 q^{90} - 28 q^{91} - 12 q^{92} + 20 q^{93} - 16 q^{94} - 38 q^{95} - 2 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 + 6 * q^9 + 8 * q^10 - 2 * q^12 + 2 * q^13 - 8 * q^14 - 2 * q^16 + 18 * q^17 - 6 * q^18 + 10 * q^19 - 4 * q^20 + 12 * q^21 + 24 * q^23 + 4 * q^24 - 6 * q^25 - 4 * q^26 - 2 * q^27 + 4 * q^28 - 12 * q^29 + 6 * q^30 + 10 * q^31 - 2 * q^32 - 4 * q^33 - 18 * q^34 + 12 * q^35 - 22 * q^37 + 4 * q^38 + 2 * q^39 - 4 * q^40 - 12 * q^41 - 12 * q^42 - 44 * q^43 - 4 * q^45 - 12 * q^46 - 4 * q^47 - 2 * q^48 - 6 * q^50 + 20 * q^51 + 2 * q^52 + 16 * q^53 + 10 * q^54 + 4 * q^55 + 4 * q^56 + 14 * q^57 + 2 * q^59 - 6 * q^60 - 12 * q^61 - 20 * q^62 - 8 * q^63 + 4 * q^64 - 8 * q^65 - 4 * q^66 + 30 * q^67 + 24 * q^69 + 12 * q^70 - 8 * q^71 + 6 * q^72 + 20 * q^74 - 14 * q^75 - 14 * q^76 + 8 * q^77 + 8 * q^78 - 10 * q^79 + 8 * q^80 - 4 * q^81 - 38 * q^83 + 4 * q^85 + 22 * q^86 - 24 * q^87 + 26 * q^89 + 14 * q^90 - 28 * q^91 - 12 * q^92 + 20 * q^93 - 16 * q^94 - 38 * q^95 - 2 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.133975	+	0.500000i	0.0773503	+	0.288675i	0.993756	−	0.111576i	$-0.0355897\pi$
$3$	0.133975	+	0.500000i	0.0773503	+	0.288675i	−0.916406	+	0.400251i	$0.868923\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$5$	−1.86603	+	1.23205i	−0.834512	+	0.550990i
$6$	0.366025	−	0.366025i	0.149429	−	0.149429i
$7$	−0.732051	−	2.73205i	−0.276689	−	1.03262i	−0.954701	−	0.297567i	$-0.903825\pi$
$7$	−0.732051	−	2.73205i	−0.276689	−	1.03262i	0.678012	−	0.735051i	$-0.262842\pi$
$8$	1.00000			0.353553
$9$	2.36603	−	1.36603i	0.788675	−	0.455342i
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$			2.00000i			0.603023i	0.953463	+	0.301511i	$0.0974911\pi$
$11$			2.00000i			0.603023i	−0.953463	+	0.301511i	$0.902509\pi$
$12$	−0.500000	−	0.133975i	−0.144338	−	0.0386751i
$13$	2.23205	−	3.86603i	0.619060	−	1.07224i	−0.370598	−	0.928793i	$-0.620847\pi$
$13$	2.23205	−	3.86603i	0.619060	−	1.07224i	0.989658	−	0.143449i	$-0.0458194\pi$
$14$	−2.00000	+	2.00000i	−0.534522	+	0.534522i
$15$	−0.866025	−	0.767949i	−0.223607	−	0.198284i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.63397	−	2.09808i	0.881368	−	0.508858i	0.0102590	−	0.999947i	$-0.496734\pi$
$17$	3.63397	−	2.09808i	0.881368	−	0.508858i	0.871109	+	0.491089i	$0.163401\pi$
$18$	−2.36603	−	1.36603i	−0.557678	−	0.321975i
$19$	3.36603	−	0.901924i	0.772219	−	0.206916i	0.148868	−	0.988857i	$-0.452437\pi$
$19$	3.36603	−	0.901924i	0.772219	−	0.206916i	0.623352	+	0.781942i	$0.285771\pi$
$20$	−0.133975	−	2.23205i	−0.0299576	−	0.499102i
$21$	1.26795	−	0.732051i	0.276689	−	0.159747i
$22$	1.73205	−	1.00000i	0.369274	−	0.213201i
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	0.133975	+	0.500000i	0.0273474	+	0.102062i
$25$	1.96410	−	4.59808i	0.392820	−	0.919615i
$26$	−4.46410			−0.875482
$27$	2.09808	+	2.09808i	0.403775	+	0.403775i
$28$	2.73205	+	0.732051i	0.516309	+	0.138345i
$29$	−1.26795	+	1.26795i	−0.235452	+	0.235452i	−0.814964	−	0.579512i	$-0.803243\pi$
$29$	−1.26795	+	1.26795i	−0.235452	+	0.235452i	0.579512	+	0.814964i	$0.303243\pi$
$30$	−0.232051	+	1.13397i	−0.0423665	+	0.207034i
$31$	−1.83013	−	1.83013i	−0.328701	−	0.328701i	0.523392	−	0.852092i	$-0.324666\pi$
$31$	−1.83013	−	1.83013i	−0.328701	−	0.328701i	−0.852092	+	0.523392i	$0.824666\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.00000	+	0.267949i	−0.174078	+	0.0466440i
$34$	−3.63397	−	2.09808i	−0.623222	−	0.359817i
$35$	4.73205	+	4.19615i	0.799863	+	0.709279i
$36$			2.73205i			0.455342i
$37$	−5.50000	+	2.59808i	−0.904194	+	0.427121i
$37$	−5.50000	+	2.59808i	−0.904194	+	0.427121i
$38$	−2.46410	−	2.46410i	−0.399730	−	0.399730i
$39$	2.23205	+	0.598076i	0.357414	+	0.0957688i
$40$	−1.86603	+	1.23205i	−0.295045	+	0.194804i
$41$	−0.401924	−	0.232051i	−0.0627700	−	0.0362402i	0.468287	−	0.883577i	$-0.344871\pi$
$41$	−0.401924	−	0.232051i	−0.0627700	−	0.0362402i	−0.531057	+	0.847336i	$0.678205\pi$
$42$	−1.26795	−	0.732051i	−0.195649	−	0.112958i
$43$	−11.0000			−1.67748			−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000			−1.67748			−0.838742	+	0.544529i	$0.816708\pi$
$44$	−1.73205	−	1.00000i	−0.261116	−	0.150756i
$45$	−2.73205	+	5.46410i	−0.407270	+	0.814540i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	4.19615	−	4.19615i	0.612072	−	0.612072i	−0.331414	−	0.943486i	$-0.607526\pi$
$47$	4.19615	−	4.19615i	0.612072	−	0.612072i	0.943486	+	0.331414i	$0.107526\pi$
$48$	0.366025	−	0.366025i	0.0528312	−	0.0528312i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−4.96410	+	0.598076i	−0.702030	+	0.0845807i
$51$	1.53590	+	1.53590i	0.215069	+	0.215069i
$52$	2.23205	+	3.86603i	0.309530	+	0.536121i
$53$	3.13397	−	11.6962i	0.430485	−	1.60659i	−0.321162	−	0.947024i	$-0.604073\pi$
$53$	3.13397	−	11.6962i	0.430485	−	1.60659i	0.751647	−	0.659566i	$-0.229260\pi$
$54$	0.767949	−	2.86603i	0.104505	−	0.390017i
$55$	−2.46410	−	3.73205i	−0.332259	−	0.503230i
$56$	−0.732051	−	2.73205i	−0.0978244	−	0.365086i
$57$	0.901924	+	1.56218i	0.119463	+	0.206916i
$58$	1.73205	+	0.464102i	0.227429	+	0.0609395i
$59$	−2.09808	+	7.83013i	−0.273146	+	1.01940i	0.683927	+	0.729550i	$0.260271\pi$
$59$	−2.09808	+	7.83013i	−0.273146	+	1.01940i	−0.957073	+	0.289845i	$0.906396\pi$
$60$	1.09808	−	0.366025i	0.141761	−	0.0472537i
$61$	−6.46410	+	1.73205i	−0.827643	+	0.221766i	−0.647685	−	0.761908i	$-0.724263\pi$
$61$	−6.46410	+	1.73205i	−0.827643	+	0.221766i	−0.179958	+	0.983674i	$0.557596\pi$
$62$	−0.669873	+	2.50000i	−0.0850740	+	0.317500i
$63$	−5.46410	−	5.46410i	−0.688412	−	0.688412i
$64$	1.00000			0.125000
$65$	0.598076	+	9.96410i	0.0741822	+	1.23589i
$66$	0.732051	+	0.732051i	0.0901092	+	0.0901092i
$67$	13.5622	−	3.63397i	1.65688	−	0.443961i	0.695355	−	0.718666i	$-0.255247\pi$
$67$	13.5622	−	3.63397i	1.65688	−	0.443961i	0.961528	+	0.274705i	$0.0885803\pi$
$68$			4.19615i			0.508858i
$69$	0.803848	+	3.00000i	0.0967719	+	0.361158i
$70$	1.26795	−	6.19615i	0.151549	−	0.740582i
$71$	−5.46410	+	9.46410i	−0.648470	+	1.12318i	0.335019	+	0.942211i	$0.391257\pi$
$71$	−5.46410	+	9.46410i	−0.648470	+	1.12318i	−0.983488	+	0.180971i	$0.942076\pi$
$72$	2.36603	−	1.36603i	0.278839	−	0.160988i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	2.56218	+	0.366025i	0.295855	+	0.0422650i
$76$	−0.901924	+	3.36603i	−0.103458	+	0.386110i
$77$	5.46410	−	1.46410i	0.622692	−	0.166850i
$78$	−0.598076	−	2.23205i	−0.0677188	−	0.252730i
$79$	−6.83013	+	1.83013i	−0.768449	+	0.205905i	−0.621686	−	0.783266i	$-0.713552\pi$
$79$	−6.83013	+	1.83013i	−0.768449	+	0.205905i	−0.146763	+	0.989172i	$0.546885\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$			0.464102i			0.0512514i
$83$	−3.43782	+	12.8301i	−0.377350	+	1.40829i	0.472531	+	0.881314i	$0.343341\pi$
$83$	−3.43782	+	12.8301i	−0.377350	+	1.40829i	−0.849881	+	0.526975i	$0.823326\pi$
$84$			1.46410i			0.159747i
$85$	−4.19615	+	8.39230i	−0.455137	+	0.910273i
$86$	5.50000	+	9.52628i	0.593080	+	1.02725i
$87$	−0.803848	−	0.464102i	−0.0861815	−	0.0497569i
$88$			2.00000i			0.213201i
$89$	12.5622	+	3.36603i	1.33159	+	0.356798i	0.853307	−	0.521409i	$-0.174593\pi$
$89$	12.5622	+	3.36603i	1.33159	+	0.356798i	0.478281	+	0.878207i	$0.341260\pi$
$90$	6.09808	−	0.366025i	0.642794	−	0.0385825i
$91$	−12.1962	−	3.26795i	−1.27850	−	0.342574i
$92$	−3.00000	+	5.19615i	−0.312772	+	0.541736i
$93$	0.669873	−	1.16025i	0.0694626	−	0.120313i
$94$	−5.73205	−	1.53590i	−0.591216	−	0.158416i
$95$	−5.16987	+	5.83013i	−0.530418	+	0.598158i
$96$	−0.500000	−	0.133975i	−0.0510310	−	0.0136737i
$97$		−	5.46410i		−	0.554795i	−0.960755	−	0.277398i	$-0.910528\pi$
$97$		−	5.46410i		−	0.554795i	0.960755	−	0.277398i	$-0.0894720\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$	2.73205	+	4.73205i	0.274581	+	0.475589i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	10.1962i		−	1.01456i	−0.861783	−	0.507278i	$-0.830652\pi$
$101$		−	10.1962i		−	1.01456i	0.861783	−	0.507278i	$-0.169348\pi$
$102$	0.562178	−	2.09808i	0.0556639	−	0.207741i
$103$			4.19615i			0.413459i	0.978398	+	0.206730i	$0.0662820\pi$
$103$			4.19615i			0.413459i	−0.978398	+	0.206730i	$0.933718\pi$
$104$	2.23205	−	3.86603i	0.218871	−	0.379095i
$105$	−1.46410	+	2.92820i	−0.142882	+	0.285763i
$106$	−11.6962	+	3.13397i	−1.13603	+	0.304399i
$107$	0.428203	+	1.59808i	0.0413960	+	0.154492i	0.983530	−	0.180744i	$-0.0578506\pi$
$107$	0.428203	+	1.59808i	0.0413960	+	0.154492i	−0.942134	+	0.335236i	$0.891184\pi$
$108$	−2.86603	+	0.767949i	−0.275783	+	0.0738959i
$109$	−1.00000	+	3.73205i	−0.0957826	+	0.357466i	−0.997137	−	0.0756168i	$-0.975907\pi$
$109$	−1.00000	+	3.73205i	−0.0957826	+	0.357466i	0.901354	+	0.433082i	$0.142574\pi$
$110$	−2.00000	+	4.00000i	−0.190693	+	0.381385i
$111$	−2.03590	−	2.40192i	−0.193239	−	0.227981i
$112$	−2.00000	+	2.00000i	−0.188982	+	0.188982i
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	−0.235269	−	0.971930i	$-0.575597\pi$
$113$	5.19615	−	3.00000i	0.488813	−	0.282216i	0.724082	+	0.689714i	$0.242264\pi$
$114$	0.901924	−	1.56218i	0.0844729	−	0.146311i
$115$	−11.1962	+	7.39230i	−1.04405	+	0.689336i
$116$	−0.464102	−	1.73205i	−0.0430908	−	0.160817i
$117$		−	12.1962i		−	1.12753i
$118$	7.83013	−	2.09808i	0.720822	−	0.193144i
$119$	−8.39230	−	8.39230i	−0.769321	−	0.769321i
$120$	−0.866025	−	0.767949i	−0.0790569	−	0.0701038i
$121$	7.00000			0.636364
$122$	4.73205	+	4.73205i	0.428420	+	0.428420i
$123$	0.0621778	−	0.232051i	0.00560639	−	0.0209233i
$124$	2.50000	−	0.669873i	0.224507	−	0.0601564i
$125$	2.00000	+	11.0000i	0.178885	+	0.983870i
$126$	−2.00000	+	7.46410i	−0.178174	+	0.664955i
$127$	0.633975	+	0.169873i	0.0562561	+	0.0150738i	0.286837	−	0.957979i	$-0.407396\pi$
$127$	0.633975	+	0.169873i	0.0562561	+	0.0150738i	−0.230581	+	0.973053i	$0.574063\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.47372	−	5.50000i	−0.129754	−	0.484248i
$130$	8.33013	−	5.50000i	0.730600	−	0.482382i
$131$	−2.73205	+	10.1962i	−0.238700	+	0.890842i	0.737745	+	0.675079i	$0.235890\pi$
$131$	−2.73205	+	10.1962i	−0.238700	+	0.890842i	−0.976446	+	0.215763i	$0.930776\pi$
$132$	0.267949	−	1.00000i	0.0233220	−	0.0870388i
$133$	−4.92820	−	8.53590i	−0.427329	−	0.740156i
$134$	−9.92820	−	9.92820i	−0.857666	−	0.857666i
$135$	−6.50000	−	1.33013i	−0.559431	−	0.114479i
$136$	3.63397	−	2.09808i	0.311611	−	0.179909i
$137$	2.00000	−	2.00000i	0.170872	−	0.170872i	−0.616491	−	0.787362i	$-0.711446\pi$
$137$	2.00000	−	2.00000i	0.170872	−	0.170872i	0.787362	+	0.616491i	$0.211446\pi$
$138$	2.19615	−	2.19615i	0.186949	−	0.186949i
$139$	1.46410	+	2.53590i	0.124183	+	0.215092i	0.921413	−	0.388584i	$-0.127036\pi$
$139$	1.46410	+	2.53590i	0.124183	+	0.215092i	−0.797230	+	0.603676i	$0.793702\pi$
$140$	−6.00000	+	2.00000i	−0.507093	+	0.169031i
$141$	2.66025	+	1.53590i	0.224034	+	0.129346i
$142$	10.9282			0.917074
$143$	7.73205	+	4.46410i	0.646587	+	0.373307i
$144$	−2.36603	−	1.36603i	−0.197169	−	0.113835i
$145$	0.803848	−	3.92820i	0.0667559	−	0.326220i
$146$		0			0
$147$	−0.366025	−	0.366025i	−0.0301893	−	0.0301893i
$148$	0.500000	−	6.06218i	0.0410997	−	0.498308i
$149$			19.2679i			1.57849i	0.614077	+	0.789246i	$0.289528\pi$
$149$			19.2679i			1.57849i	−0.614077	+	0.789246i	$0.710472\pi$
$150$	−0.964102	−	2.40192i	−0.0787186	−	0.196116i
$151$	−6.23205	−	3.59808i	−0.507157	−	0.292807i	0.224507	−	0.974472i	$-0.427923\pi$
$151$	−6.23205	−	3.59808i	−0.507157	−	0.292807i	−0.731664	+	0.681665i	$0.761256\pi$
$152$	3.36603	−	0.901924i	0.273021	−	0.0731557i
$153$	5.73205	−	9.92820i	0.463409	−	0.802648i
$154$	−4.00000	−	4.00000i	−0.322329	−	0.322329i
$155$	5.66987	+	1.16025i	0.455415	+	0.0931938i
$156$	−1.63397	+	1.63397i	−0.130823	+	0.130823i
$157$	17.2583	+	4.62436i	1.37736	+	0.369064i	0.870163	−	0.492764i	$-0.164013\pi$
$157$	17.2583	+	4.62436i	1.37736	+	0.369064i	0.507202	+	0.861827i	$0.330680\pi$
$158$	5.00000	+	5.00000i	0.397779	+	0.397779i
$159$	6.26795			0.497081
$160$	−0.133975	−	2.23205i	−0.0105916	−	0.176459i
$161$	−4.39230	−	16.3923i	−0.346162	−	1.29189i
$162$	−6.66025			−0.523279
$163$	−9.06218	+	5.23205i	−0.709805	+	0.409806i	−0.810989	−	0.585062i	$-0.801070\pi$
$163$	−9.06218	+	5.23205i	−0.709805	+	0.409806i	0.101184	+	0.994868i	$0.467737\pi$
$164$	0.401924	−	0.232051i	0.0313850	−	0.0181201i
$165$	1.53590	−	1.73205i	0.119570	−	0.134840i
$166$	12.8301	−	3.43782i	0.995811	−	0.266827i
$167$	−14.9545	−	8.63397i	−1.15721	−	0.668117i	−0.206578	−	0.978430i	$-0.566233\pi$
$167$	−14.9545	−	8.63397i	−1.15721	−	0.668117i	−0.950634	+	0.310313i	$0.899566\pi$
$168$	1.26795	−	0.732051i	0.0978244	−	0.0564789i
$169$	−3.46410	−	6.00000i	−0.266469	−	0.461538i
$170$	9.36603	−	0.562178i	0.718341	−	0.0431171i
$171$	6.73205	−	6.73205i	0.514813	−	0.514813i
$172$	5.50000	−	9.52628i	0.419371	−	0.726372i
$173$	−9.29423	−	2.49038i	−0.706627	−	0.189340i	−0.112430	−	0.993660i	$-0.535863\pi$
$173$	−9.29423	−	2.49038i	−0.706627	−	0.189340i	−0.594197	+	0.804319i	$0.702530\pi$
$174$			0.928203i			0.0703669i
$175$	−14.0000	−	2.00000i	−1.05830	−	0.151186i
$176$	1.73205	−	1.00000i	0.130558	−	0.0753778i
$177$	−4.19615			−0.315402
$178$	−3.36603	−	12.5622i	−0.252294	−	0.941575i
$179$	−10.3923	+	10.3923i	−0.776757	+	0.776757i	−0.979278	−	0.202521i	$-0.935087\pi$
$179$	−10.3923	+	10.3923i	−0.776757	+	0.776757i	0.202521	+	0.979278i	$0.435087\pi$
$180$	−3.36603	−	5.09808i	−0.250889	−	0.379988i
$181$	12.0981	−	20.9545i	0.899243	−	1.55753i	0.0707790	−	0.997492i	$-0.477451\pi$
$181$	12.0981	−	20.9545i	0.899243	−	1.55753i	0.828464	−	0.560042i	$-0.189215\pi$
$182$	3.26795	+	12.1962i	0.242237	+	0.904039i
$183$	−1.73205	−	3.00000i	−0.128037	−	0.221766i
$184$	6.00000			0.442326
$185$	7.06218	−	11.6244i	0.519222	−	0.854640i
$186$	−1.33975			−0.0982349
$187$	4.19615	+	7.26795i	0.306853	+	0.531485i
$188$	1.53590	+	5.73205i	0.112017	+	0.418053i
$189$	4.19615	−	7.26795i	0.305225	−	0.528666i
$190$	7.63397	+	1.56218i	0.553827	+	0.113332i
$191$	6.83013	−	6.83013i	0.494211	−	0.494211i	−0.415419	−	0.909630i	$-0.636365\pi$
$191$	6.83013	−	6.83013i	0.494211	−	0.494211i	0.909630	+	0.415419i	$0.136365\pi$
$192$	0.133975	+	0.500000i	0.00966878	+	0.0360844i
$193$	−17.6603			−1.27121			−0.635606	−	0.772013i	$-0.719250\pi$
$193$	−17.6603			−1.27121			−0.635606	+	0.772013i	$0.719250\pi$
$194$	−4.73205	+	2.73205i	−0.339741	+	0.196150i
$195$	−4.90192	+	1.63397i	−0.351034	+	0.117011i
$196$		−	1.00000i		−	0.0714286i
$197$	−22.8923	−	6.13397i	−1.63101	−	0.437028i	−0.676800	−	0.736167i	$-0.736634\pi$
$197$	−22.8923	−	6.13397i	−1.63101	−	0.437028i	−0.954209	+	0.299140i	$0.903300\pi$
$198$	2.73205	−	4.73205i	0.194158	−	0.336292i
$199$	7.75833	−	7.75833i	0.549973	−	0.549973i	−0.376460	−	0.926433i	$-0.622859\pi$
$199$	7.75833	−	7.75833i	0.549973	−	0.549973i	0.926433	+	0.376460i	$0.122859\pi$
$200$	1.96410	−	4.59808i	0.138883	−	0.325133i
$201$	3.63397	+	6.29423i	0.256321	+	0.443961i
$202$	−8.83013	+	5.09808i	−0.621286	+	0.358699i
$203$	4.39230	+	2.53590i	0.308279	+	0.177985i
$204$	−2.09808	+	0.562178i	−0.146895	+	0.0393603i
$205$	1.03590	−	0.0621778i	0.0723503	−	0.00434269i
$206$	3.63397	−	2.09808i	0.253191	−	0.146180i
$207$	14.1962	−	8.19615i	0.986701	−	0.569672i
$208$	−4.46410			−0.309530
$209$	1.80385	+	6.73205i	0.124775	+	0.465666i
$210$	3.26795	−	0.196152i	0.225510	−	0.0135358i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	8.56218	+	8.56218i	0.588053	+	0.588053i
$213$	−5.46410	−	1.46410i	−0.374394	−	0.100319i
$214$	1.16987	−	1.16987i	0.0799709	−	0.0799709i
$215$	20.5263	−	13.5526i	1.39988	−	0.924277i
$216$	2.09808	+	2.09808i	0.142756	+	0.142756i
$217$	−3.66025	+	6.33975i	−0.248474	+	0.430370i
$218$	3.73205	−	1.00000i	0.252766	−	0.0677285i
$219$		0			0
$220$	4.46410	−	0.267949i	0.300970	−	0.0180651i
$221$		−	18.7321i		−	1.26005i
$222$	−1.06218	+	2.96410i	−0.0712887	+	0.198937i
$223$	0.928203	+	0.928203i	0.0621571	+	0.0621571i	0.737502	−	0.675345i	$-0.236005\pi$
$223$	0.928203	+	0.928203i	0.0621571	+	0.0621571i	−0.675345	+	0.737502i	$0.736005\pi$
$224$	2.73205	+	0.732051i	0.182543	+	0.0489122i
$225$	−1.63397	−	13.5622i	−0.108932	−	0.904145i
$226$	−5.19615	−	3.00000i	−0.345643	−	0.199557i
$227$	−12.6962	−	7.33013i	−0.842673	−	0.486518i	0.0154988	−	0.999880i	$-0.495066\pi$
$227$	−12.6962	−	7.33013i	−0.842673	−	0.486518i	−0.858172	+	0.513362i	$0.828400\pi$
$228$	−1.80385			−0.119463
$229$	0.294229	+	0.169873i	0.0194432	+	0.0112255i	0.509690	−	0.860358i	$-0.329760\pi$
$229$	0.294229	+	0.169873i	0.0194432	+	0.0112255i	−0.490247	+	0.871584i	$0.663093\pi$
$230$	12.0000	+	6.00000i	0.791257	+	0.395628i
$231$	1.46410	+	2.53590i	0.0963308	+	0.166850i
$232$	−1.26795	+	1.26795i	−0.0832449	+	0.0832449i
$233$	−11.8564	+	11.8564i	−0.776739	+	0.776739i	−0.979275	−	0.202536i	$-0.935082\pi$
$233$	−11.8564	+	11.8564i	−0.776739	+	0.776739i	0.202536	+	0.979275i	$0.435082\pi$
$234$	−10.5622	+	6.09808i	−0.690471	+	0.398644i
$235$	−2.66025	+	13.0000i	−0.173536	+	0.848026i
$236$	−5.73205	−	5.73205i	−0.373125	−	0.373125i
$237$	−1.83013	−	3.16987i	−0.118880	−	0.205905i
$238$	−3.07180	+	11.4641i	−0.199115	+	0.743107i
$239$	−6.16987	+	23.0263i	−0.399096	+	1.48945i	0.415594	+	0.909550i	$0.363574\pi$
$239$	−6.16987	+	23.0263i	−0.399096	+	1.48945i	−0.814690	+	0.579896i	$0.803093\pi$
$240$	−0.232051	+	1.13397i	−0.0149788	+	0.0731977i
$241$	−1.02628	−	3.83013i	−0.0661085	−	0.246720i	0.924962	−	0.380060i	$-0.124097\pi$
$241$	−1.02628	−	3.83013i	−0.0661085	−	0.246720i	−0.991070	+	0.133340i	$0.957430\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	11.9282	+	3.19615i	0.765195	+	0.205033i
$244$	1.73205	−	6.46410i	0.110883	−	0.413822i
$245$	1.00000	−	2.00000i	0.0638877	−	0.127775i
$246$	−0.232051	+	0.0621778i	−0.0147950	+	0.00396431i
$247$	4.02628	−	15.0263i	0.256186	−	0.956099i
$248$	−1.83013	−	1.83013i	−0.116213	−	0.116213i
$249$	−6.87564			−0.435726
$250$	8.52628	−	7.23205i	0.539249	−	0.457395i
$251$	2.26795	+	2.26795i	0.143152	+	0.143152i	0.775051	−	0.631899i	$-0.217724\pi$
$251$	2.26795	+	2.26795i	0.143152	+	0.143152i	−0.631899	+	0.775051i	$0.717724\pi$
$252$	7.46410	−	2.00000i	0.470194	−	0.125988i
$253$			12.0000i			0.754434i
$254$	−0.169873	−	0.633975i	−0.0106588	−	0.0397791i
$255$	−4.75833	−	0.973721i	−0.297978	−	0.0609767i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.2942	+	8.83013i	−0.954028	+	0.550808i	−0.894330	−	0.447408i	$-0.852347\pi$
$257$	−15.2942	+	8.83013i	−0.954028	+	0.550808i	−0.0596980	+	0.998216i	$0.519014\pi$
$258$	−4.02628	+	4.02628i	−0.250665	+	0.250665i
$259$	11.1244	+	13.1244i	0.691234	+	0.815508i
$260$	−8.92820	−	4.46410i	−0.553704	−	0.276852i
$261$	−1.26795	+	4.73205i	−0.0784841	+	0.292907i
$262$	10.1962	−	2.73205i	0.629920	−	0.168787i
$263$	5.09808	+	19.0263i	0.314361	+	1.17321i	0.924583	+	0.380980i	$0.124413\pi$
$263$	5.09808	+	19.0263i	0.314361	+	1.17321i	−0.610222	+	0.792230i	$0.708920\pi$
$264$	−1.00000	+	0.267949i	−0.0615457	+	0.0164911i
$265$	8.56218	+	25.6865i	0.525970	+	1.57791i
$266$	−4.92820	+	8.53590i	−0.302168	+	0.523370i
$267$			6.73205i			0.411995i
$268$	−3.63397	+	13.5622i	−0.221980	+	0.828442i
$269$		−	24.5885i		−	1.49918i	−0.661900	−	0.749592i	$-0.730250\pi$
$269$		−	24.5885i		−	1.49918i	0.661900	−	0.749592i	$-0.269750\pi$
$270$	2.09808	+	6.29423i	0.127685	+	0.383055i
$271$	1.76795	+	3.06218i	0.107395	+	0.186014i	0.914714	−	0.404101i	$-0.132416\pi$
$271$	1.76795	+	3.06218i	0.107395	+	0.186014i	−0.807319	+	0.590115i	$0.799082\pi$
$272$	−3.63397	−	2.09808i	−0.220342	−	0.127215i
$273$		−	6.53590i		−	0.395571i
$274$	−2.73205	−	0.732051i	−0.165049	−	0.0442248i
$275$	9.19615	+	3.92820i	0.554549	+	0.236880i
$276$	−3.00000	−	0.803848i	−0.180579	−	0.0483859i
$277$	−0.330127	+	0.571797i	−0.0198354	+	0.0343559i	−0.875773	−	0.482724i	$-0.839648\pi$
$277$	−0.330127	+	0.571797i	−0.0198354	+	0.0343559i	0.855937	+	0.517080i	$0.172981\pi$
$278$	1.46410	−	2.53590i	0.0878110	−	0.152093i
$279$	−6.83013	−	1.83013i	−0.408909	−	0.109567i
$280$	4.73205	+	4.19615i	0.282794	+	0.250768i
$281$	23.6244	+	6.33013i	1.40931	+	0.377624i	0.881679	−	0.471849i	$-0.156413\pi$
$281$	23.6244	+	6.33013i	1.40931	+	0.377624i	0.527632	+	0.849473i	$0.323080\pi$
$282$		−	3.07180i		−	0.182923i
$283$	−11.2583	−	6.50000i	−0.669238	−	0.386385i	0.126550	−	0.991960i	$-0.459610\pi$
$283$	−11.2583	−	6.50000i	−0.669238	−	0.386385i	−0.795788	+	0.605575i	$0.792943\pi$
$284$	−5.46410	−	9.46410i	−0.324235	−	0.561591i
$285$	−3.60770	−	1.80385i	−0.213701	−	0.106851i
$286$		−	8.92820i		−	0.527936i
$287$	−0.339746	+	1.26795i	−0.0200546	+	0.0748447i
$288$			2.73205i			0.160988i
$289$	0.303848	−	0.526279i	0.0178734	−	0.0309576i
$290$	−3.80385	+	1.26795i	−0.223370	+	0.0744565i
$291$	2.73205	−	0.732051i	0.160156	−	0.0429136i
$292$		0			0
$293$	18.1603	−	4.86603i	1.06093	−	0.284276i	0.314170	−	0.949367i	$-0.398274\pi$
$293$	18.1603	−	4.86603i	1.06093	−	0.284276i	0.746763	+	0.665090i	$0.231607\pi$
$294$	−0.133975	+	0.500000i	−0.00781356	+	0.0291606i
$295$	−5.73205	−	17.1962i	−0.333733	−	1.00120i
$296$	−5.50000	+	2.59808i	−0.319681	+	0.151010i
$297$	−4.19615	+	4.19615i	−0.243485	+	0.243485i
$298$	16.6865	−	9.63397i	0.966625	−	0.558081i
$299$	13.3923	−	23.1962i	0.774497	−	1.34147i
$300$	−1.59808	+	2.03590i	−0.0922650	+	0.117543i
$301$	8.05256	+	30.0526i	0.464142	+	1.73220i
$302$			7.19615i			0.414092i
$303$	5.09808	−	1.36603i	0.292877	−	0.0784761i
$304$	−2.46410	−	2.46410i	−0.141326	−	0.141326i
$305$	9.92820	−	11.1962i	0.568487	−	0.641090i
$306$	−11.4641			−0.655359
$307$	24.4186	+	24.4186i	1.39364	+	1.39364i	0.816989	+	0.576653i	$0.195642\pi$
$307$	24.4186	+	24.4186i	1.39364	+	1.39364i	0.576653	+	0.816989i	$0.304358\pi$
$308$	−1.46410	+	5.46410i	−0.0834249	+	0.311346i
$309$	−2.09808	+	0.562178i	−0.119355	+	0.0319812i
$310$	−1.83013	−	5.49038i	−0.103944	−	0.311833i
$311$	−7.25833	+	27.0885i	−0.411582	+	1.53605i	0.380002	+	0.924986i	$0.375923\pi$
$311$	−7.25833	+	27.0885i	−0.411582	+	1.53605i	−0.791584	+	0.611060i	$0.790743\pi$
$312$	2.23205	+	0.598076i	0.126365	+	0.0338594i
$313$	5.26795	+	9.12436i	0.297762	+	0.515739i	0.975624	−	0.219451i	$-0.0704265\pi$
$313$	5.26795	+	9.12436i	0.297762	+	0.515739i	−0.677862	+	0.735190i	$0.737093\pi$
$314$	−4.62436	−	17.2583i	−0.260967	−	0.973944i
$315$	16.9282	+	3.46410i	0.953796	+	0.195180i
$316$	1.83013	−	6.83013i	0.102953	−	0.384225i
$317$	−7.82051	+	29.1865i	−0.439243	+	1.63928i	0.291459	+	0.956583i	$0.405859\pi$
$317$	−7.82051	+	29.1865i	−0.439243	+	1.63928i	−0.730703	+	0.682696i	$0.760807\pi$
$318$	−3.13397	−	5.42820i	−0.175745	−	0.304399i
$319$	−2.53590	−	2.53590i	−0.141983	−	0.141983i
$320$	−1.86603	+	1.23205i	−0.104314	+	0.0688737i
$321$	−0.741670	+	0.428203i	−0.0413960	+	0.0239000i
$322$	−12.0000	+	12.0000i	−0.668734	+	0.668734i
$323$	10.3397	−	10.3397i	0.575319	−	0.575319i
$324$	3.33013	+	5.76795i	0.185007	+	0.320442i
$325$	−13.3923	−	17.8564i	−0.742871	−	0.990495i
$326$	9.06218	+	5.23205i	0.501908	+	0.289776i
$327$	−2.00000			−0.110600
$328$	−0.401924	−	0.232051i	−0.0221925	−	0.0128129i
$329$	−14.5359	−	8.39230i	−0.801390	−	0.462683i
$330$	−2.26795	−	0.464102i	−0.124846	−	0.0255480i
$331$	−7.83013	−	2.09808i	−0.430383	−	0.115321i	0.0371231	−	0.999311i	$-0.488181\pi$
$331$	−7.83013	−	2.09808i	−0.430383	−	0.115321i	−0.467506	+	0.883990i	$0.654847\pi$
$332$	−9.39230	−	9.39230i	−0.515470	−	0.515470i
$333$	−9.46410	+	13.6603i	−0.518630	+	0.748577i
$334$			17.2679i			0.944860i
$335$	−20.8301	+	23.4904i	−1.13807	+	1.28342i
$336$	−1.26795	−	0.732051i	−0.0691723	−	0.0399366i
$337$	−17.0263	+	4.56218i	−0.927481	+	0.248518i	−0.690780	−	0.723065i	$-0.742733\pi$
$337$	−17.0263	+	4.56218i	−0.927481	+	0.248518i	−0.236701	+	0.971583i	$0.576066\pi$
$338$	−3.46410	+	6.00000i	−0.188422	+	0.326357i
$339$	2.19615	+	2.19615i	0.119279	+	0.119279i
$340$	−5.16987	−	7.83013i	−0.280376	−	0.424648i
$341$	3.66025	−	3.66025i	0.198214	−	0.198214i
$342$	−9.19615	−	2.46410i	−0.497271	−	0.133243i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	−11.0000			−0.593080
$345$	−5.19615	−	4.60770i	−0.279751	−	0.248070i
$346$	2.49038	+	9.29423i	0.133884	+	0.499661i
$347$	−7.85641			−0.421754			−0.210877	−	0.977513i	$-0.567632\pi$
$347$	−7.85641			−0.421754			−0.210877	+	0.977513i	$0.567632\pi$
$348$	0.803848	−	0.464102i	0.0430908	−	0.0248785i
$349$	25.9019	−	14.9545i	1.38650	−	0.800495i	0.393579	−	0.919291i	$-0.371237\pi$
$349$	25.9019	−	14.9545i	1.38650	−	0.800495i	0.992919	+	0.118796i	$0.0379033\pi$
$350$	5.26795	+	13.1244i	0.281584	+	0.701526i
$351$	12.7942	−	3.42820i	0.682905	−	0.182984i
$352$	−1.73205	−	1.00000i	−0.0923186	−	0.0533002i
$353$	−7.60770	+	4.39230i	−0.404917	+	0.233779i	−0.688603	−	0.725138i	$-0.741776\pi$
$353$	−7.60770	+	4.39230i	−0.404917	+	0.233779i	0.283687	+	0.958917i	$0.408442\pi$
$354$	2.09808	+	3.63397i	0.111511	+	0.193144i
$355$	−1.46410	−	24.3923i	−0.0777064	−	1.29461i
$356$	−9.19615	+	9.19615i	−0.487395	+	0.487395i
$357$	3.07180	−	5.32051i	0.162577	−	0.281591i
$358$	14.1962	+	3.80385i	0.750290	+	0.201040i
$359$			17.3923i			0.917931i	0.888454	+	0.458965i	$0.151780\pi$
$359$			17.3923i			0.917931i	−0.888454	+	0.458965i	$0.848220\pi$
$360$	−2.73205	+	5.46410i	−0.143992	+	0.287983i
$361$	−5.93782	+	3.42820i	−0.312517	+	0.180432i
$362$	−24.1962			−1.27172
$363$	0.937822	+	3.50000i	0.0492229	+	0.183702i
$364$	8.92820	−	8.92820i	0.467965	−	0.467965i
$365$		0			0
$366$	−1.73205	+	3.00000i	−0.0905357	+	0.156813i
$367$	−6.78461	−	25.3205i	−0.354154	−	1.32172i	−0.881546	−	0.472098i	$-0.843497\pi$
$367$	−6.78461	−	25.3205i	−0.354154	−	1.32172i	0.527392	−	0.849622i	$-0.323170\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$	−1.26795			−0.0660068
$370$	−13.5981	−	0.303848i	−0.706930	−	0.0157963i
$371$	−34.2487			−1.77810
$372$	0.669873	+	1.16025i	0.0347313	+	0.0601564i
$373$	6.86603	+	25.6244i	0.355509	+	1.32678i	0.879842	+	0.475266i	$0.157648\pi$
$373$	6.86603	+	25.6244i	0.355509	+	1.32678i	−0.524333	+	0.851513i	$0.675685\pi$
$374$	4.19615	−	7.26795i	0.216978	−	0.375817i
$375$	−5.23205	+	2.47372i	−0.270182	+	0.127742i
$376$	4.19615	−	4.19615i	0.216400	−	0.216400i
$377$	2.07180	+	7.73205i	0.106703	+	0.398221i
$378$	−8.39230			−0.431654
$379$	18.5885	−	10.7321i	0.954825	−	0.551268i	0.0602485	−	0.998183i	$-0.480811\pi$
$379$	18.5885	−	10.7321i	0.954825	−	0.551268i	0.894576	+	0.446915i	$0.147477\pi$
$380$	−2.46410	−	7.39230i	−0.126406	−	0.379217i
$381$			0.339746i			0.0174057i
$382$	−9.33013	−	2.50000i	−0.477371	−	0.127911i
$383$	4.26795	−	7.39230i	0.218082	−	0.377729i	−0.736140	−	0.676830i	$-0.763353\pi$
$383$	4.26795	−	7.39230i	0.218082	−	0.377729i	0.954222	+	0.299101i	$0.0966866\pi$
$384$	0.366025	−	0.366025i	0.0186787	−	0.0186787i
$385$	−8.39230	+	9.46410i	−0.427711	+	0.482335i
$386$	8.83013	+	15.2942i	0.449442	+	0.778456i
$387$	−26.0263	+	15.0263i	−1.32299	+	0.763829i
$388$	4.73205	+	2.73205i	0.240233	+	0.138699i
$389$	−6.09808	+	1.63397i	−0.309185	+	0.0828458i	−0.410075	−	0.912052i	$-0.634498\pi$
$389$	−6.09808	+	1.63397i	−0.309185	+	0.0828458i	0.100890	+	0.994898i	$0.467831\pi$
$390$	3.86603	+	3.42820i	0.195764	+	0.173594i
$391$	21.8038	−	12.5885i	1.10267	−	0.636626i
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$	−5.46410			−0.275627
$394$	6.13397	+	22.8923i	0.309025	+	1.15330i
$395$	10.4904	−	11.8301i	0.527828	−	0.595238i
$396$	−5.46410			−0.274581
$397$	24.7583	+	24.7583i	1.24258	+	1.24258i	0.958925	+	0.283660i	$0.0915487\pi$
$397$	24.7583	+	24.7583i	1.24258	+	1.24258i	0.283660	+	0.958925i	$0.408451\pi$
$398$	−10.5981	−	2.83975i	−0.531234	−	0.142344i
$399$	3.60770	−	3.60770i	0.180611	−	0.180611i
$400$	−4.96410	+	0.598076i	−0.248205	+	0.0299038i
$401$	8.12436	+	8.12436i	0.405711	+	0.405711i	0.880240	−	0.474529i	$-0.157382\pi$
$401$	8.12436	+	8.12436i	0.405711	+	0.405711i	−0.474529	+	0.880240i	$0.657382\pi$
$402$	3.63397	−	6.29423i	0.181246	−	0.313928i
$403$	−11.1603	+	2.99038i	−0.555932	+	0.148961i
$404$	8.83013	+	5.09808i	0.439315	+	0.253639i
$405$	0.892305	+	14.8660i	0.0443390	+	0.738699i
$406$		−	5.07180i		−	0.251709i
$407$	−5.19615	−	11.0000i	−0.257564	−	0.545250i
$408$	1.53590	+	1.53590i	0.0760383	+	0.0760383i
$409$	27.8923	+	7.47372i	1.37919	+	0.369552i	0.870825	−	0.491593i	$-0.163585\pi$
$409$	27.8923	+	7.47372i	1.37919	+	0.369552i	0.508360	+	0.861144i	$0.330252\pi$
$410$	−0.571797	−	0.866025i	−0.0282390	−	0.0427699i
$411$	1.26795	+	0.732051i	0.0625433	+	0.0361094i
$412$	−3.63397	−	2.09808i	−0.179033	−	0.103365i
$413$	22.9282			1.12822
$414$	−14.1962	−	8.19615i	−0.697703	−	0.402819i
$415$	−9.39230	−	28.1769i	−0.461050	−	1.38315i
$416$	2.23205	+	3.86603i	0.109435	+	0.189547i
$417$	−1.07180	+	1.07180i	−0.0524861	+	0.0524861i
$418$	4.92820	−	4.92820i	0.241046	−	0.241046i
$419$	27.4186	−	15.8301i	1.33949	−	0.773352i	0.352754	−	0.935716i	$-0.385245\pi$
$419$	27.4186	−	15.8301i	1.33949	−	0.773352i	0.986731	+	0.162364i	$0.0519117\pi$
$420$	−1.80385	−	2.73205i	−0.0880187	−	0.133310i
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	0.885918	−	0.463843i	$-0.153530\pi$
$421$	8.66025	+	8.66025i	0.422075	+	0.422075i	−0.463843	+	0.885918i	$0.653530\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$	4.19615	−	15.6603i	0.204024	−	0.761428i
$424$	3.13397	−	11.6962i	0.152199	−	0.568015i
$425$	−2.50962	−	20.8301i	−0.121734	−	1.01041i
$426$	1.46410	+	5.46410i	0.0709360	+	0.264737i
$427$	9.46410	+	16.3923i	0.458000	+	0.793279i
$428$	−1.59808	−	0.428203i	−0.0772459	−	0.0206980i
$429$	−1.19615	+	4.46410i	−0.0577508	+	0.215529i
$430$	−22.0000	−	11.0000i	−1.06093	−	0.530467i
$431$	−24.8923	+	6.66987i	−1.19902	+	0.321276i	−0.802445	−	0.596726i	$-0.796468\pi$
$431$	−24.8923	+	6.66987i	−1.19902	+	0.321276i	−0.396575	+	0.918002i	$0.629801\pi$
$432$	0.767949	−	2.86603i	0.0369480	−	0.137892i
$433$	−7.19615	−	7.19615i	−0.345825	−	0.345825i	0.512727	−	0.858552i	$-0.328635\pi$
$433$	−7.19615	−	7.19615i	−0.345825	−	0.345825i	−0.858552	+	0.512727i	$0.828635\pi$
$434$	7.32051			0.351396
$435$	2.07180	−	0.124356i	0.0993351	−	0.00596240i
$436$	−2.73205	−	2.73205i	−0.130842	−	0.130842i
$437$	20.1962	−	5.41154i	0.966113	−	0.258869i
$438$		0			0
$439$	0.866025	+	3.23205i	0.0413331	+	0.154257i	0.983508	−	0.180864i	$-0.0578894\pi$
$439$	0.866025	+	3.23205i	0.0413331	+	0.154257i	−0.942175	+	0.335121i	$0.891223\pi$
$440$	−2.46410	−	3.73205i	−0.117471	−	0.177919i
$441$	−1.36603	+	2.36603i	−0.0650488	+	0.112668i
$442$	−16.2224	+	9.36603i	−0.771622	+	0.445496i
$443$	3.75833	−	3.75833i	0.178564	−	0.178564i	−0.612166	−	0.790729i	$-0.709701\pi$
$443$	3.75833	−	3.75833i	0.178564	−	0.178564i	0.790729	+	0.612166i	$0.209701\pi$
$444$	3.09808	−	0.562178i	0.147028	−	0.0266798i
$445$	−27.5885	+	9.19615i	−1.30782	+	0.435939i
$446$	0.339746	−	1.26795i	0.0160874	−	0.0600391i
$447$	−9.63397	+	2.58142i	−0.455671	+	0.122097i
$448$	−0.732051	−	2.73205i	−0.0345861	−	0.129077i
$449$	−13.4282	+	3.59808i	−0.633716	+	0.169804i	−0.561355	−	0.827575i	$-0.689720\pi$
$449$	−13.4282	+	3.59808i	−0.633716	+	0.169804i	−0.0723607	+	0.997379i	$0.523053\pi$
$450$	−10.9282	+	8.19615i	−0.515160	+	0.386370i
$451$	0.464102	−	0.803848i	0.0218537	−	0.0378517i
$452$			6.00000i			0.282216i
$453$	0.964102	−	3.59808i	0.0452974	−	0.169052i
$454$			14.6603i			0.688040i
$455$	26.7846	−	8.92820i	1.25568	−	0.418561i
$456$	0.901924	+	1.56218i	0.0422365	+	0.0731557i
$457$	−12.8038	−	7.39230i	−0.598939	−	0.345797i	0.169685	−	0.985498i	$-0.445725\pi$
$457$	−12.8038	−	7.39230i	−0.598939	−	0.345797i	−0.768624	+	0.639701i	$0.779058\pi$
$458$		−	0.339746i		−	0.0158753i
$459$	12.0263	+	3.22243i	0.561339	+	0.150410i
$460$	−0.803848	−	13.3923i	−0.0374796	−	0.624419i
$461$	−11.4641	−	3.07180i	−0.533936	−	0.143068i	−0.0182310	−	0.999834i	$-0.505803\pi$
$461$	−11.4641	−	3.07180i	−0.533936	−	0.143068i	−0.515705	+	0.856766i	$0.672470\pi$
$462$	1.46410	−	2.53590i	0.0681162	−	0.117981i
$463$	−12.8301	+	22.2224i	−0.596267	+	1.03276i	0.397100	+	0.917775i	$0.370017\pi$
$463$	−12.8301	+	22.2224i	−0.596267	+	1.03276i	−0.993367	+	0.114989i	$0.963317\pi$
$464$	1.73205	+	0.464102i	0.0804084	+	0.0215454i
$465$	0.179492	+	2.99038i	0.00832374	+	0.138676i
$466$	16.1962	+	4.33975i	0.750272	+	0.201035i
$467$		−	16.0718i		−	0.743714i	−0.928290	−	0.371857i	$-0.878721\pi$
$467$		−	16.0718i		−	0.743714i	0.928290	−	0.371857i	$-0.121279\pi$
$468$	10.5622	+	6.09808i	0.488237	+	0.281884i
$469$	−19.8564	−	34.3923i	−0.916884	−	1.58809i
$470$	12.5885	−	4.19615i	0.580662	−	0.193554i
$471$			9.24871i			0.426158i
$472$	−2.09808	+	7.83013i	−0.0965718	+	0.360411i
$473$		−	22.0000i		−	1.01156i
$474$	−1.83013	+	3.16987i	−0.0840605	+	0.145597i
$475$	2.46410	−	17.2487i	0.113061	−	0.791425i
$476$	11.4641	−	3.07180i	0.525456	−	0.140796i
$477$	−8.56218	−	31.9545i	−0.392035	−	1.46310i
$478$	23.0263	−	6.16987i	1.05320	−	0.282203i
$479$	−2.96410	+	11.0622i	−0.135433	+	0.505444i	0.864562	+	0.502525i	$0.167596\pi$
$479$	−2.96410	+	11.0622i	−0.135433	+	0.505444i	−0.999996	+	0.00291847i	$0.999071\pi$
$480$	1.09808	−	0.366025i	0.0501201	−	0.0167067i
$481$	−2.23205	+	27.0622i	−0.101773	+	1.23393i
$482$	−2.80385	+	2.80385i	−0.127712	+	0.127712i
$483$	7.60770	−	4.39230i	0.346162	−	0.199857i
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	6.73205	+	10.1962i	0.305687	+	0.462983i
$486$	−3.19615	−	11.9282i	−0.144980	−	0.541074i
$487$		−	34.5359i		−	1.56497i	−0.622669	−	0.782485i	$-0.713952\pi$
$487$		−	34.5359i		−	1.56497i	0.622669	−	0.782485i	$-0.286048\pi$
$488$	−6.46410	+	1.73205i	−0.292616	+	0.0784063i
$489$	−3.83013	−	3.83013i	−0.173204	−	0.173204i
$490$	−2.23205	+	0.133975i	−0.100834	+	0.00605236i
$491$	2.19615			0.0991110			0.0495555	−	0.998771i	$-0.484220\pi$
$491$	2.19615			0.0991110			0.0495555	+	0.998771i	$0.484220\pi$
$492$	0.169873	+	0.169873i	0.00765847	+	0.00765847i
$493$	−1.94744	+	7.26795i	−0.0877083	+	0.327332i
$494$	−15.0263	+	4.02628i	−0.676064	+	0.181151i
$495$	−10.9282	−	5.46410i	−0.491186	−	0.245593i
$496$	−0.669873	+	2.50000i	−0.0300782	+	0.112253i
$497$	29.8564	+	8.00000i	1.33924	+	0.358849i
$498$	3.43782	+	5.95448i	0.154052	+	0.266827i
$499$	4.80385	+	17.9282i	0.215050	+	0.802577i	0.986149	+	0.165862i	$0.0530405\pi$
$499$	4.80385	+	17.9282i	0.215050	+	0.802577i	−0.771099	+	0.636715i	$0.780293\pi$
$500$	−10.5263	−	3.76795i	−0.470750	−	0.168508i
$501$	2.31347	−	8.63397i	0.103358	−	0.385738i
$502$	0.830127	−	3.09808i	0.0370504	−	0.138274i
$503$	13.5622	+	23.4904i	0.604708	+	1.04738i	0.992098	+	0.125468i	$0.0400434\pi$
$503$	13.5622	+	23.4904i	0.604708	+	1.04738i	−0.387390	+	0.921916i	$0.626623\pi$
$504$	−5.46410	−	5.46410i	−0.243390	−	0.243390i
$505$	12.5622	+	19.0263i	0.559010	+	0.846658i
$506$	10.3923	−	6.00000i	0.461994	−	0.266733i
$507$	2.53590	−	2.53590i	0.112623	−	0.112623i
$508$	−0.464102	+	0.464102i	−0.0205912	+	0.0205912i
$509$	−18.9282	−	32.7846i	−0.838978	−	1.45315i	−0.890750	−	0.454493i	$-0.849820\pi$
$509$	−18.9282	−	32.7846i	−0.838978	−	1.45315i	0.0517723	−	0.998659i	$-0.483513\pi$
$510$	1.53590	+	4.60770i	0.0680107	+	0.204032i
$511$		0			0
$512$	1.00000			0.0441942
$513$	8.95448	+	5.16987i	0.395350	+	0.228255i
$514$	15.2942	+	8.83013i	0.674600	+	0.389480i
$515$	−5.16987	−	7.83013i	−0.227812	−	0.345037i
$516$	5.50000	+	1.47372i	0.242124	+	0.0648769i
$517$	8.39230	+	8.39230i	0.369093	+	0.369093i
$518$	5.80385	−	16.1962i	0.255006	−	0.711618i
$519$		−	4.98076i		−	0.218631i
$520$	0.598076	+	9.96410i	0.0262274	+	0.436955i
$521$	14.0885	+	8.13397i	0.617227	+	0.356356i	0.775788	−	0.630993i	$-0.217352\pi$
$521$	14.0885	+	8.13397i	0.617227	+	0.356356i	−0.158562	+	0.987349i	$0.550686\pi$
$522$	4.73205	−	1.26795i	0.207116	−	0.0554966i
$523$	−4.40192	+	7.62436i	−0.192483	+	0.333390i	−0.946072	−	0.323955i	$-0.894987\pi$
$523$	−4.40192	+	7.62436i	−0.192483	+	0.333390i	0.753590	+	0.657345i	$0.228321\pi$
$524$	−7.46410	−	7.46410i	−0.326071	−	0.326071i
$525$	−0.875644	−	7.26795i	−0.0382163	−	0.317199i
$526$	13.9282	−	13.9282i	0.607299	−	0.607299i
$527$	−10.4904	−	2.81089i	−0.456968	−	0.122444i
$528$	0.732051	+	0.732051i	0.0318584	+	0.0318584i
$529$	13.0000			0.565217
$530$	17.9641	−	20.2583i	0.780311	−	0.879966i
$531$	5.73205	+	21.3923i	0.248750	+	0.928347i
$532$	9.85641			0.427329
$533$	−1.79423	+	1.03590i	−0.0777167	+	0.0448697i
$534$	5.83013	−	3.36603i	0.252294	−	0.145662i
$535$	−2.76795	−	2.45448i	−0.119669	−	0.106117i
$536$	13.5622	−	3.63397i	0.585797	−	0.156964i
$537$	−6.58846	−	3.80385i	−0.284313	−	0.164148i
$538$	−21.2942	+	12.2942i	−0.918059	+	0.530042i
$539$	−1.00000	−	1.73205i	−0.0430730	−	0.0746047i
$540$	4.40192	−	4.96410i	0.189429	−	0.213621i
$541$	18.9282	−	18.9282i	0.813787	−	0.813787i	−0.171412	−	0.985199i	$-0.554833\pi$
$541$	18.9282	−	18.9282i	0.813787	−	0.813787i	0.985199	+	0.171412i	$0.0548330\pi$
$542$	1.76795	−	3.06218i	0.0759399	−	0.131532i
$543$	12.0981	+	3.24167i	0.519178	+	0.139113i
$544$			4.19615i			0.179909i
$545$	−2.73205	−	8.19615i	−0.117028	−	0.351085i
$546$	−5.66025	+	3.26795i	−0.242237	+	0.139855i
$547$	−33.9808			−1.45291			−0.726456	−	0.687213i	$-0.758834\pi$
$547$	−33.9808			−1.45291			−0.726456	+	0.687213i	$0.758834\pi$
$548$	0.732051	+	2.73205i	0.0312717	+	0.116707i
$549$	−12.9282	+	12.9282i	−0.551762	+	0.551762i
$550$	−1.19615	−	9.92820i	−0.0510041	−	0.423340i
$551$	−3.12436	+	5.41154i	−0.133102	+	0.230539i
$552$	0.803848	+	3.00000i	0.0342140	+	0.127688i
$553$	10.0000	+	17.3205i	0.425243	+	0.736543i
$554$	0.660254			0.0280515
$555$	6.75833	+	1.97372i	0.286875	+	0.0837798i
$556$	−2.92820			−0.124183
$557$	8.30385	+	14.3827i	0.351845	+	0.609414i	0.986573	−	0.163322i	$-0.0522210\pi$
$557$	8.30385	+	14.3827i	0.351845	+	0.609414i	−0.634727	+	0.772736i	$0.718888\pi$
$558$	1.83013	+	6.83013i	0.0774755	+	0.289142i
$559$	−24.5526	+	42.5263i	−1.03846	+	1.79867i
$560$	1.26795	−	6.19615i	0.0535806	−	0.261835i
$561$	−3.07180	+	3.07180i	−0.129691	+	0.129691i
$562$	−6.33013	−	23.6244i	−0.267020	−	0.996533i
$563$	36.3923			1.53375			0.766876	−	0.641795i	$-0.221810\pi$
$563$	36.3923			1.53375			0.766876	+	0.641795i	$0.221810\pi$
$564$	−2.66025	+	1.53590i	−0.112017	+	0.0646730i
$565$	−6.00000	+	12.0000i	−0.252422	+	0.504844i
$566$			13.0000i			0.546431i
$567$	−18.1962	−	4.87564i	−0.764167	−	0.204758i
$568$	−5.46410	+	9.46410i	−0.229269	+	0.397105i
$569$	14.6340	−	14.6340i	0.613488	−	0.613488i	−0.330365	−	0.943853i	$-0.607172\pi$
$569$	14.6340	−	14.6340i	0.613488	−	0.613488i	0.943853	+	0.330365i	$0.107172\pi$
$570$	0.241670	+	4.02628i	0.0101224	+	0.168642i
$571$	−1.75833	−	3.04552i	−0.0735838	−	0.127451i	0.826886	−	0.562370i	$-0.190110\pi$
$571$	−1.75833	−	3.04552i	−0.0735838	−	0.127451i	−0.900470	+	0.434919i	$0.856777\pi$
$572$	−7.73205	+	4.46410i	−0.323293	+	0.186653i
$573$	4.33013	+	2.50000i	0.180894	+	0.104439i
$574$	1.26795	−	0.339746i	0.0529232	−	0.0141807i
$575$	11.7846	−	27.5885i	0.491452	−	1.15052i
$576$	2.36603	−	1.36603i	0.0985844	−	0.0569177i
$577$	−16.3923	+	9.46410i	−0.682421	+	0.393996i	−0.800766	−	0.598977i	$-0.795574\pi$
$577$	−16.3923	+	9.46410i	−0.682421	+	0.393996i	0.118346	+	0.992972i	$0.462241\pi$
$578$	−0.607695			−0.0252768
$579$	−2.36603	−	8.83013i	−0.0983287	−	0.366968i
$580$	3.00000	+	2.66025i	0.124568	+	0.110461i
$581$	37.5692			1.55863
$582$	−2.00000	−	2.00000i	−0.0829027	−	0.0829027i
$583$	23.3923	+	6.26795i	0.968810	+	0.259592i
$584$		0			0
$585$	15.0263	+	22.7583i	0.621260	+	0.940941i
$586$	−13.2942	−	13.2942i	−0.549180	−	0.549180i
$587$	−10.1603	+	17.5981i	−0.419359	+	0.726350i	−0.995875	−	0.0907352i	$-0.971078\pi$
$587$	−10.1603	+	17.5981i	−0.419359	+	0.726350i	0.576516	+	0.817086i	$0.304412\pi$
$588$	0.500000	−	0.133975i	0.0206197	−	0.00552502i
$589$	−7.81089	−	4.50962i	−0.321842	−	0.185816i
$590$	−12.0263	+	13.5622i	−0.495114	+	0.558346i
$591$		−	12.2679i		−	0.504636i
$592$	5.00000	+	3.46410i	0.205499	+	0.142374i
$593$	−1.33975	−	1.33975i	−0.0550168	−	0.0550168i	0.679063	−	0.734080i	$-0.262386\pi$
$593$	−1.33975	−	1.33975i	−0.0550168	−	0.0550168i	−0.734080	+	0.679063i	$0.762386\pi$
$594$	5.73205	+	1.53590i	0.235189	+	0.0630187i
$595$	26.0000	+	5.32051i	1.06590	+	0.218120i
$596$	−16.6865	−	9.63397i	−0.683507	−	0.394623i
$597$	4.91858	+	2.83975i	0.201304	+	0.116223i
$598$	−26.7846			−1.09530
$599$	−36.6051	−	21.1340i	−1.49564	−	0.863511i	−0.495657	−	0.868518i	$-0.665073\pi$
$599$	−36.6051	−	21.1340i	−1.49564	−	0.863511i	−0.999987	+	0.00500751i	$0.998406\pi$
$600$	2.56218	+	0.366025i	0.104600	+	0.0149429i
$601$	−1.79423	−	3.10770i	−0.0731881	−	0.126766i	0.827109	−	0.562042i	$-0.189984\pi$
$601$	−1.79423	−	3.10770i	−0.0731881	−	0.126766i	−0.900297	+	0.435276i	$0.856651\pi$
$602$	22.0000	−	22.0000i	0.896653	−	0.896653i
$603$	27.1244	−	27.1244i	1.10459	−	1.10459i
$604$	6.23205	−	3.59808i	0.253579	−	0.146404i
$605$	−13.0622	+	8.62436i	−0.531053	+	0.350630i
$606$	−3.73205	−	3.73205i	−0.151604	−	0.151604i
$607$	12.0263	+	20.8301i	0.488132	+	0.845469i	0.999907	−	0.0136506i	$-0.00434526\pi$
$607$	12.0263	+	20.8301i	0.488132	+	0.845469i	−0.511775	+	0.859119i	$0.671012\pi$
$608$	−0.901924	+	3.36603i	−0.0365778	+	0.136510i
$609$	−0.679492	+	2.53590i	−0.0275344	+	0.102760i
$610$	−14.6603	−	3.00000i	−0.593576	−	0.121466i
$611$	−6.85641	−	25.5885i	−0.277381	−	1.03520i
$612$	5.73205	+	9.92820i	0.231704	+	0.401324i
$613$	−42.6147	−	11.4186i	−1.72119	−	0.461192i	−0.743069	−	0.669215i	$-0.766631\pi$
$613$	−42.6147	−	11.4186i	−1.72119	−	0.461192i	−0.978124	+	0.208023i	$0.933297\pi$
$614$	8.93782	−	33.3564i	0.360701	−	1.34616i
$615$	0.169873	+	0.509619i	0.00684994	+	0.0205498i
$616$	5.46410	−	1.46410i	0.220155	−	0.0589903i
$617$	8.95448	−	33.4186i	0.360494	−	1.34538i	−0.512934	−	0.858428i	$-0.671441\pi$
$617$	8.95448	−	33.4186i	0.360494	−	1.34538i	0.873428	−	0.486953i	$-0.161892\pi$
$618$	1.53590	+	1.53590i	0.0617829	+	0.0617829i
$619$	26.9282			1.08234			0.541168	−	0.840915i	$-0.317982\pi$
$619$	26.9282			1.08234			0.541168	+	0.840915i	$0.317982\pi$
$620$	−3.83975	+	4.33013i	−0.154208	+	0.173902i
$621$	12.5885	+	12.5885i	0.505157	+	0.505157i
$622$	27.0885	−	7.25833i	1.08615	−	0.291033i
$623$		−	36.7846i		−	1.47374i
$624$	−0.598076	−	2.23205i	−0.0239422	−	0.0893535i
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	5.26795	−	9.12436i	0.210550	−	0.364683i
$627$	−3.12436	+	1.80385i	−0.124775	+	0.0720387i
$628$	−12.6340	+	12.6340i	−0.504150	+	0.504150i
$629$	−14.5359	+	20.9808i	−0.579584	+	0.836558i
$630$	−5.46410	−	16.3923i	−0.217695	−	0.653085i
$631$	7.06218	−	26.3564i	0.281141	−	1.04923i	−0.670473	−	0.741934i	$-0.733909\pi$
$631$	7.06218	−	26.3564i	0.281141	−	1.04923i	0.951613	−	0.307298i	$-0.0994247\pi$
$632$	−6.83013	+	1.83013i	−0.271688	+	0.0727985i
$633$	0.535898	+	2.00000i	0.0213000	+	0.0794929i
$634$	29.1865	−	7.82051i	1.15915	−	0.310592i
$635$	−1.39230	+	0.464102i	−0.0552519	+	0.0184173i
$636$	−3.13397	+	5.42820i	−0.124270	+	0.215242i
$637$			4.46410i			0.176874i
$638$	−0.928203	+	3.46410i	−0.0367479	+	0.137145i
$639$			29.8564i			1.18110i
$640$	2.00000	+	1.00000i	0.0790569	+	0.0395285i
$641$	3.99038	+	6.91154i	0.157611	+	0.272990i	0.934007	−	0.357256i	$-0.116288\pi$
$641$	3.99038	+	6.91154i	0.157611	+	0.272990i	−0.776396	+	0.630245i	$0.782954\pi$
$642$	0.741670	+	0.428203i	0.0292714	+	0.0168998i
$643$		−	0.267949i		−	0.0105669i	−0.999986	−	0.00528344i	$-0.998318\pi$
$643$		−	0.267949i		−	0.0105669i	0.999986	−	0.00528344i	$-0.00168178\pi$
$644$	16.3923	+	4.39230i	0.645947	+	0.173081i
$645$	9.52628	+	8.44744i	0.375097	+	0.332618i
$646$	−14.1244	−	3.78461i	−0.555715	−	0.148903i
$647$	10.2224	−	17.7058i	0.401885	−	0.696086i	−0.592068	−	0.805888i	$-0.701688\pi$
$647$	10.2224	−	17.7058i	0.401885	−	0.696086i	0.993953	+	0.109802i	$0.0350217\pi$
$648$	3.33013	−	5.76795i	0.130820	−	0.226586i
$649$	−15.6603	−	4.19615i	−0.614719	−	0.164713i
$650$	−8.76795	+	20.5263i	−0.343907	+	0.805107i
$651$	−3.66025	−	0.980762i	−0.143457	−	0.0384391i
$652$		−	10.4641i		−	0.409806i
$653$	−28.7942	−	16.6244i	−1.12681	−	0.650561i	−0.183676	−	0.982987i	$-0.558800\pi$
$653$	−28.7942	−	16.6244i	−1.12681	−	0.650561i	−0.943129	+	0.332426i	$0.892133\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$	−7.46410	−	22.3923i	−0.291647	−	0.874940i
$656$			0.464102i			0.0181201i
$657$		0			0
$658$			16.7846i			0.654332i
$659$	0.392305	−	0.679492i	0.0152820	−	0.0264692i	−0.858283	−	0.513176i	$-0.828469\pi$
$659$	0.392305	−	0.679492i	0.0152820	−	0.0264692i	0.873565	+	0.486707i	$0.161802\pi$
$660$	0.732051	+	2.19615i	0.0284950	+	0.0854851i
$661$	−33.4186	+	8.95448i	−1.29983	+	0.348289i	−0.841387	−	0.540433i	$-0.818260\pi$
$661$	−33.4186	+	8.95448i	−1.29983	+	0.348289i	−0.458446	+	0.888723i	$0.651594\pi$
$662$	2.09808	+	7.83013i	0.0815440	+	0.304327i
$663$	9.36603	−	2.50962i	0.363746	−	0.0974655i
$664$	−3.43782	+	12.8301i	−0.133413	+	0.497905i
$665$	19.7128	+	9.85641i	0.764430	+	0.382215i
$666$	16.5622	+	1.36603i	0.641771	+	0.0529324i
$667$	−7.60770	+	7.60770i	−0.294571	+	0.294571i
$668$	14.9545	−	8.63397i	0.578606	−	0.334059i
$669$	−0.339746	+	0.588457i	−0.0131353	+	0.0227511i
$670$	30.7583	+	6.29423i	1.18830	+	0.243167i
$671$	−3.46410	−	12.9282i	−0.133730	−	0.499088i
$672$			1.46410i			0.0564789i
$673$	−16.8301	+	4.50962i	−0.648754	+	0.173833i	−0.568165	−	0.822914i	$-0.692347\pi$
$673$	−16.8301	+	4.50962i	−0.648754	+	0.173833i	−0.0805884	+	0.996747i	$0.525680\pi$
$674$	12.4641	+	12.4641i	0.480099	+	0.480099i
$675$	13.7679	−	5.52628i	0.529929	−	0.212707i
$676$	6.92820			0.266469
$677$	−9.39230	−	9.39230i	−0.360976	−	0.360976i	0.503196	−	0.864172i	$-0.332157\pi$
$677$	−9.39230	−	9.39230i	−0.360976	−	0.360976i	−0.864172	+	0.503196i	$0.832157\pi$
$678$	0.803848	−	3.00000i	0.0308716	−	0.115214i
$679$	−14.9282	+	4.00000i	−0.572892	+	0.153506i
$680$	−4.19615	+	8.39230i	−0.160915	+	0.321830i
$681$	1.96410	−	7.33013i	0.0752645	−	0.280891i
$682$	−5.00000	−	1.33975i	−0.191460	−	0.0513015i
$683$	3.69615	+	6.40192i	0.141429	+	0.244963i	0.928035	−	0.372493i	$-0.121497\pi$
$683$	3.69615	+	6.40192i	0.141429	+	0.244963i	−0.786606	+	0.617456i	$0.788164\pi$
$684$	2.46410	+	9.19615i	0.0942173	+	0.351624i
$685$	−1.26795	+	6.19615i	−0.0484458	+	0.236743i
$686$	−4.39230	+	16.3923i	−0.167699	+	0.625861i
$687$	−0.0455173	+	0.169873i	−0.00173659	+	0.00648106i
$688$	5.50000	+	9.52628i	0.209686	+	0.363186i
$689$	−38.2224	−	38.2224i	−1.45616	−	1.45616i
$690$	−1.39230	+	6.80385i	−0.0530041	+	0.259018i
$691$	2.24167	−	1.29423i	0.0852771	−	0.0492348i	−0.456755	−	0.889593i	$-0.650988\pi$
$691$	2.24167	−	1.29423i	0.0852771	−	0.0492348i	0.542032	+	0.840358i	$0.317655\pi$
$692$	6.80385	−	6.80385i	0.258643	−	0.258643i
$693$	10.9282	−	10.9282i	0.415128	−	0.415128i
$694$	3.92820	+	6.80385i	0.149113	+	0.258271i
$695$	−5.85641	−	2.92820i	−0.222146	−	0.111073i
$696$	−0.803848	−	0.464102i	−0.0304698	−	0.0175917i
$697$	−1.94744			−0.0737646
$698$	−25.9019	−	14.9545i	−0.980402	−	0.566036i
$699$	−7.51666	−	4.33975i	−0.284306	−	0.164144i
$700$	8.73205	−	11.1244i	0.330040	−	0.420461i
$701$	−27.4904	−	7.36603i	−1.03830	−	0.278211i	−0.300890	−	0.953659i	$-0.597284\pi$
$701$	−27.4904	−	7.36603i	−1.03830	−	0.278211i	−0.737408	+	0.675448i	$0.763950\pi$
$702$	−9.36603	−	9.36603i	−0.353498	−	0.353498i
$703$	−16.1699	+	13.7058i	−0.609858	+	0.516923i
$704$			2.00000i			0.0753778i
$705$	−6.85641	+	0.411543i	−0.258227	+	0.0154996i
$706$	7.60770	+	4.39230i	0.286319	+	0.165307i
$707$	−27.8564	+	7.46410i	−1.04765	+	0.280716i
$708$	2.09808	−	3.63397i	0.0788505	−	0.136573i
$709$	33.9282	+	33.9282i	1.27420	+	1.27420i	0.943863	+	0.330338i	$0.107163\pi$
$709$	33.9282	+	33.9282i	1.27420	+	1.27420i	0.330338	+	0.943863i	$0.392837\pi$
$710$	−20.3923	+	13.4641i	−0.765310	+	0.505299i
$711$	−13.6603	+	13.6603i	−0.512300	+	0.512300i
$712$	12.5622	+	3.36603i	0.470788	+	0.126147i
$713$	−10.9808	−	10.9808i	−0.411233	−	0.411233i
$714$	−6.14359			−0.229918
$715$	−19.9282	+	1.19615i	−0.745273	+	0.0447336i
$716$	−3.80385	−	14.1962i	−0.142156	−	0.530535i
$717$	−12.3397			−0.460836
$718$	15.0622	−	8.69615i	0.562115	−	0.324538i
$719$	30.5718	−	17.6506i	1.14014	−	0.658258i	0.193671	−	0.981066i	$-0.437960\pi$
$719$	30.5718	−	17.6506i	1.14014	−	0.658258i	0.946464	+	0.322809i	$0.104627\pi$
$720$	6.09808	−	0.366025i	0.227262	−	0.0136410i
$721$	11.4641	−	3.07180i	0.426945	−	0.114400i
$722$	5.93782	+	3.42820i	0.220983	+	0.127585i
$723$	1.77757	−	1.02628i	0.0661085	−	0.0381677i
$724$	12.0981	+	20.9545i	0.449621	+	0.778767i
$725$	3.33975	+	8.32051i	0.124035	+	0.309016i
$726$	2.56218	−	2.56218i	0.0950913	−	0.0950913i
$727$	14.3205	−	24.8038i	0.531118	−	0.919924i	−0.468222	−	0.883611i	$-0.655105\pi$
$727$	14.3205	−	24.8038i	0.531118	−	0.919924i	0.999340	−	0.0363130i	$-0.0115613\pi$
$728$	−12.1962	−	3.26795i	−0.452019	−	0.121118i
$729$		−	13.5885i		−	0.503276i
$730$		0			0
$731$	−39.9737	+	23.0788i	−1.47848	+	0.853602i
$732$	3.46410			0.128037
$733$	4.88269	+	18.2224i	0.180346	+	0.673061i	0.995579	+	0.0939276i	$0.0299422\pi$
$733$	4.88269	+	18.2224i	0.180346	+	0.673061i	−0.815233	+	0.579133i	$0.803391\pi$
$734$	−18.5359	+	18.5359i	−0.684172	+	0.684172i
$735$	1.13397	+	0.232051i	0.0418273	+	0.00855932i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	7.26795	+	27.1244i	0.267718	+	0.999138i
$738$	0.633975	+	1.09808i	0.0233369	+	0.0404207i
$739$	−7.80385			−0.287069			−0.143535	−	0.989645i	$-0.545847\pi$
$739$	−7.80385			−0.287069			−0.143535	+	0.989645i	$0.545847\pi$
$740$	6.53590	+	11.9282i	0.240264	+	0.438489i
$741$	8.05256			0.295818
$742$	17.1244	+	29.6603i	0.628655	+	1.08886i
$743$	−8.97372	−	33.4904i	−0.329214	−	1.22864i	−0.910007	−	0.414592i	$-0.863924\pi$
$743$	−8.97372	−	33.4904i	−0.329214	−	1.22864i	0.580794	−	0.814051i	$-0.302742\pi$
$744$	0.669873	−	1.16025i	0.0245587	−	0.0425370i
$745$	−23.7391	−	35.9545i	−0.869733	−	1.31727i
$746$	18.7583	−	18.7583i	0.686791	−	0.686791i
$747$	9.39230	+	35.0526i	0.343646	+	1.28251i
$748$	−8.39230			−0.306853
$749$	4.05256	−	2.33975i	0.148077	−	0.0854925i
$750$	4.75833	+	3.29423i	0.173750	+	0.120288i
$751$			32.1769i			1.17415i	0.809532	+	0.587076i	$0.199721\pi$
$751$			32.1769i			1.17415i	−0.809532	+	0.587076i	$0.800279\pi$
$752$	−5.73205	−	1.53590i	−0.209026	−	0.0560085i
$753$	−0.830127	+	1.43782i	−0.0302515	+	0.0523972i
$754$	5.66025	−	5.66025i	0.206134	−	0.206134i
$755$	16.0622	−	0.964102i	0.584563	−	0.0350873i
$756$	4.19615	+	7.26795i	0.152613	+	0.264333i
$757$	−14.7224	+	8.50000i	−0.535096	+	0.308938i	−0.743089	−	0.669193i	$-0.766640\pi$
$757$	−14.7224	+	8.50000i	−0.535096	+	0.308938i	0.207993	+	0.978130i	$0.433307\pi$
$758$	−18.5885	−	10.7321i	−0.675163	−	0.389806i
$759$	−6.00000	+	1.60770i	−0.217786	+	0.0583556i
$760$	−5.16987	+	5.83013i	−0.187531	+	0.211481i
$761$	−9.46410	+	5.46410i	−0.343073	+	0.198074i	−0.661630	−	0.749830i	$-0.730135\pi$
$761$	−9.46410	+	5.46410i	−0.343073	+	0.198074i	0.318557	+	0.947904i	$0.396802\pi$
$762$	0.294229	−	0.169873i	0.0106588	−	0.00615385i
$763$	10.9282			0.395628
$764$	2.50000	+	9.33013i	0.0904468	+	0.337552i
$765$	1.53590	+	25.5885i	0.0555305	+	0.925153i
$766$	−8.53590			−0.308415
$767$	25.5885	+	25.5885i	0.923946	+	0.923946i
$768$	−0.500000	−	0.133975i	−0.0180422	−	0.00483439i
$769$	−20.0718	+	20.0718i	−0.723808	+	0.723808i	−0.969379	−	0.245571i	$-0.921025\pi$
$769$	−20.0718	+	20.0718i	−0.723808	+	0.723808i	0.245571	+	0.969379i	$0.421025\pi$
$770$	12.3923	+	2.53590i	0.446588	+	0.0913874i
$771$	−6.46410	−	6.46410i	−0.232799	−	0.232799i
$772$	8.83013	−	15.2942i	0.317803	−	0.550451i
$773$	−32.1865	+	8.62436i	−1.15767	+	0.310197i	−0.786035	−	0.618183i	$-0.787869\pi$
$773$	−32.1865	+	8.62436i	−1.15767	+	0.310197i	−0.371635	+	0.928379i	$0.621203\pi$
$774$	26.0263	+	15.0263i	0.935495	+	0.540108i
$775$	−12.0096	+	4.82051i	−0.431398	+	0.173158i
$776$		−	5.46410i		−	0.196150i
$777$	−5.07180	+	7.32051i	−0.181950	+	0.262622i
$778$	4.46410	+	4.46410i	0.160046	+	0.160046i
$779$	−1.56218	−	0.418584i	−0.0559708	−	0.0149973i
$780$	1.03590	−	5.06218i	0.0370911	−	0.181255i
$781$	−18.9282	−	10.9282i	−0.677304	−	0.391042i
$782$	−21.8038	−	12.5885i	−0.779704	−	0.450162i
$783$	−5.32051			−0.190139
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	−37.9019	+	12.6340i	−1.35278	+	0.450926i
$786$	2.73205	+	4.73205i	0.0974490	+	0.168787i
$787$	29.6865	−	29.6865i	1.05821	−	1.05821i	0.0600130	−	0.998198i	$-0.480886\pi$
$787$	29.6865	−	29.6865i	1.05821	−	1.05821i	0.998198	−	0.0600130i	$-0.0191142\pi$
$788$	16.7583	−	16.7583i	0.596991	−	0.596991i
$789$	−8.83013	+	5.09808i	−0.314361	+	0.181496i
$790$	−15.4904	−	3.16987i	−0.551123	−	0.112779i
$791$	−12.0000	−	12.0000i	−0.426671	−	0.426671i
$792$	2.73205	+	4.73205i	0.0970792	+	0.168146i
$793$	−7.73205	+	28.8564i	−0.274573	+	1.02472i
$794$	9.06218	−	33.8205i	0.321605	−	1.20024i
$795$	−11.6962	+	7.72243i	−0.414820	+	0.273886i
$796$	2.83975	+	10.5981i	0.100652	+	0.375639i
$797$	14.9904	+	25.9641i	0.530987	+	0.919696i	0.999346	+	0.0361577i	$0.0115119\pi$
$797$	14.9904	+	25.9641i	0.530987	+	0.919696i	−0.468360	+	0.883538i	$0.655155\pi$
$798$	−4.92820	−	1.32051i	−0.174457	−	0.0467455i
$799$	6.44486	−	24.0526i	0.228003	−	0.850918i
$800$	3.00000	+	4.00000i	0.106066	+	0.141421i
$801$	34.3205	−	9.19615i	1.21266	−	0.324930i
$802$	2.97372	−	11.0981i	0.105006	−	0.391887i
$803$		0			0
$804$	−7.26795			−0.256321
$805$	28.3923	+	25.1769i	1.00070	+	0.887370i
$806$	8.16987	+	8.16987i	0.287772	+	0.287772i
$807$	12.2942	−	3.29423i	0.432777	−	0.115962i
$808$		−	10.1962i		−	0.358699i
$809$	6.27757	+	23.4282i	0.220708	+	0.823692i	0.984079	+	0.177732i	$0.0568760\pi$
$809$	6.27757	+	23.4282i	0.220708	+	0.823692i	−0.763371	+	0.645960i	$0.776457\pi$
$810$	12.4282	−	8.20577i	0.436683	−	0.288321i
$811$	−22.4904	+	38.9545i	−0.789744	+	1.36788i	0.136379	+	0.990657i	$0.456453\pi$
$811$	−22.4904	+	38.9545i	−0.789744	+	1.36788i	−0.926124	+	0.377220i	$0.876880\pi$
$812$	−4.39230	+	2.53590i	−0.154140	+	0.0889926i
$813$	−1.29423	+	1.29423i	−0.0453906	+	0.0453906i
$814$	−6.92820	+	10.0000i	−0.242833	+	0.350500i
$815$	10.4641	−	20.9282i	0.366541	−	0.733083i
$816$	0.562178	−	2.09808i	0.0196802	−	0.0734474i
$817$	−37.0263	+	9.92116i	−1.29539	+	0.347098i
$818$	−7.47372	−	27.8923i	−0.261313	−	0.975232i
$819$	−33.3205	+	8.92820i	−1.16431	+	0.311977i
$820$	−0.464102	+	0.928203i	−0.0162071	+	0.0324143i
$821$	−1.56218	+	2.70577i	−0.0545204	+	0.0944321i	−0.891998	−	0.452040i	$-0.850696\pi$
$821$	−1.56218	+	2.70577i	−0.0545204	+	0.0944321i	0.837477	+	0.546472i	$0.184030\pi$
$822$		−	1.46410i		−	0.0510664i
$823$	7.50962	−	28.0263i	0.261769	−	0.976935i	−0.702430	−	0.711753i	$-0.747901\pi$
$823$	7.50962	−	28.0263i	0.261769	−	0.976935i	0.964199	−	0.265182i	$-0.0854319\pi$
$824$			4.19615i			0.146180i
$825$	−0.732051	+	5.12436i	−0.0254867	+	0.178407i
$826$	−11.4641	−	19.8564i	−0.398887	−	0.690893i
$827$	12.0000	+	6.92820i	0.417281	+	0.240917i	0.693913	−	0.720059i	$-0.255885\pi$
$827$	12.0000	+	6.92820i	0.417281	+	0.240917i	−0.276632	+	0.960976i	$0.589218\pi$
$828$			16.3923i			0.569672i
$829$	27.4186	+	7.34679i	0.952287	+	0.255164i	0.701332	−	0.712834i	$-0.252589\pi$
$829$	27.4186	+	7.34679i	0.952287	+	0.255164i	0.250954	+	0.967999i	$0.419256\pi$
$830$	−19.7058	+	22.2224i	−0.683997	+	0.771352i
$831$	−0.330127	−	0.0884573i	−0.0114520	−	0.00306855i
$832$	2.23205	−	3.86603i	0.0773824	−	0.134030i
$833$	−2.09808	+	3.63397i	−0.0726940	+	0.125910i
$834$	1.46410	+	0.392305i	0.0506977	+	0.0135844i
$835$	38.5429	−	2.31347i	1.33383	−	0.0800608i
$836$	−6.73205	−	1.80385i	−0.232833	−	0.0623874i
$837$		−	7.67949i		−	0.265442i
$838$	−27.4186	−	15.8301i	−0.947159	−	0.546843i
$839$	−0.0621778	−	0.107695i	−0.00214662	−	0.00371805i	0.864950	−	0.501858i	$-0.167350\pi$
$839$	−0.0621778	−	0.107695i	−0.00214662	−	0.00371805i	−0.867097	+	0.498140i	$0.834017\pi$
$840$	−1.46410	+	2.92820i	−0.0505163	+	0.101033i
$841$			25.7846i			0.889124i
$842$	3.16987	−	11.8301i	0.109241	−	0.407693i
$843$			12.6603i			0.436042i
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$	13.8564	+	6.92820i	0.476675	+	0.238337i
$846$	−15.6603	+	4.19615i	−0.538411	+	0.144267i
$847$	−5.12436	−	19.1244i	−0.176075	−	0.657121i
$848$	−11.6962	+	3.13397i	−0.401648	+	0.107621i
$849$	1.74167	−	6.50000i	0.0597740	−	0.223079i
$850$	−16.7846	+	12.5885i	−0.575707	+	0.431781i
$851$	−33.0000	+	15.5885i	−1.13123	+	0.534365i
$852$	4.00000	−	4.00000i	0.137038	−	0.137038i
$853$	17.2583	−	9.96410i	0.590914	−	0.341164i	−0.174545	−	0.984649i	$-0.555845\pi$
$853$	17.2583	−	9.96410i	0.590914	−	0.341164i	0.765459	+	0.643485i	$0.222512\pi$
$854$	9.46410	−	16.3923i	0.323855	−	0.560933i
$855$	−4.26795	+	20.8564i	−0.145961	+	0.713274i
$856$	0.428203	+	1.59808i	0.0146357	+	0.0546211i
$857$			7.26795i			0.248268i	0.992265	+	0.124134i	$0.0396153\pi$
$857$			7.26795i			0.248268i	−0.992265	+	0.124134i	$0.960385\pi$
$858$	4.46410	−	1.19615i	0.152402	−	0.0408360i
$859$	−27.0000	−	27.0000i	−0.921228	−	0.921228i	0.0758882	−	0.997116i	$-0.475821\pi$
$859$	−27.0000	−	27.0000i	−0.921228	−	0.921228i	−0.997116	+	0.0758882i	$0.975821\pi$
$860$	1.47372	+	24.5526i	0.0502535	+	0.837235i
$861$	−0.679492			−0.0231570
$862$	18.2224	+	18.2224i	0.620658	+	0.620658i
$863$	−6.09808	+	22.7583i	−0.207581	+	0.774703i	0.781066	+	0.624448i	$0.214676\pi$
$863$	−6.09808	+	22.7583i	−0.207581	+	0.774703i	−0.988647	+	0.150255i	$0.951991\pi$
$864$	−2.86603	+	0.767949i	−0.0975042	+	0.0261262i
$865$	20.4115	−	6.80385i	0.694013	−	0.231338i
$866$	−2.63397	+	9.83013i	−0.0895061	+	0.334041i
$867$	0.303848	+	0.0814157i	0.0103192	+	0.00276502i
$868$	−3.66025	−	6.33975i	−0.124237	−	0.215185i
$869$	−3.66025	−	13.6603i	−0.124166	−	0.463392i
$870$	−1.14359	−	1.73205i	−0.0387715	−	0.0587220i
$871$	16.2224	−	60.5429i	0.549676	−	2.05142i
$872$	−1.00000	+	3.73205i	−0.0338643	+	0.126383i
$873$	−7.46410	−	12.9282i	−0.252622	−	0.437553i
$874$	−14.7846	−	14.7846i	−0.500097	−	0.500097i
$875$	28.5885	−	13.5167i	0.966466	−	0.456947i
$876$		0			0
$877$	−29.8301	+	29.8301i	−1.00729	+	1.00729i	−0.00731860	+	0.999973i	$0.502330\pi$
$877$	−29.8301	+	29.8301i	−1.00729	+	1.00729i	−0.999973	+	0.00731860i	$0.997670\pi$
$878$	2.36603	−	2.36603i	0.0798495	−	0.0798495i
$879$	4.86603	+	8.42820i	0.164127	+	0.284276i
$880$	−2.00000	+	4.00000i	−0.0674200	+	0.134840i
$881$	−13.0526	−	7.53590i	−0.439752	−	0.253891i	0.263740	−	0.964594i	$-0.415044\pi$
$881$	−13.0526	−	7.53590i	−0.439752	−	0.253891i	−0.703492	+	0.710703i	$0.748377\pi$
$882$	2.73205			0.0919929
$883$	2.42820	+	1.40192i	0.0817155	+	0.0471785i	0.540301	−	0.841472i	$-0.318310\pi$
$883$	2.42820	+	1.40192i	0.0817155	+	0.0471785i	−0.458585	+	0.888650i	$0.651644\pi$
$884$	16.2224	+	9.36603i	0.545619	+	0.315014i
$885$	7.83013	−	5.16987i	0.263207	−	0.173783i
$886$	−5.13397	−	1.37564i	−0.172479	−	0.0462157i
$887$	27.3923	+	27.3923i	0.919744	+	0.919744i	0.997010	−	0.0772669i	$-0.0246193\pi$
$887$	27.3923	+	27.3923i	0.919744	+	0.919744i	−0.0772669	+	0.997010i	$0.524619\pi$
$888$	−2.03590	−	2.40192i	−0.0683203	−	0.0806033i
$889$		−	1.85641i		−	0.0622619i
$890$	21.7583	+	19.2942i	0.729341	+	0.646744i
$891$	11.5359	+	6.66025i	0.386467	+	0.223127i
$892$	−1.26795	+	0.339746i	−0.0424541	+	0.0113755i
$893$	10.3397	−	17.9090i	0.346006	−	0.599301i
$894$	7.05256	+	7.05256i	0.235873	+	0.235873i
$895$	6.58846	−	32.1962i	0.220228	−	1.07620i
$896$	−2.00000	+	2.00000i	−0.0668153	+	0.0668153i
$897$	13.3923	+	3.58846i	0.447156	+	0.119815i
$898$	9.83013	+	9.83013i	0.328036	+	0.328036i
$899$	4.64102			0.154787
$900$	12.5622	+	5.36603i	0.418739	+	0.178868i
$901$	−13.1506	−	49.0788i	−0.438111	−	1.63505i
$902$	−0.928203			−0.0309058
$903$	−13.9474	+	8.05256i	−0.464142	+	0.267972i
$904$	5.19615	−	3.00000i	0.172821	−	0.0997785i
$905$	3.24167	+	54.0070i	0.107757	+	1.79525i
$906$	−3.59808	+	0.964102i	−0.119538	+	0.0320301i
$907$	21.8038	+	12.5885i	0.723985	+	0.417993i	0.816218	−	0.577745i	$-0.196067\pi$
$907$	21.8038	+	12.5885i	0.723985	+	0.417993i	−0.0922327	+	0.995737i	$0.529400\pi$
$908$	12.6962	−	7.33013i	0.421337	−	0.243259i
$909$	−13.9282	−	24.1244i	−0.461969	−	0.800154i
$910$	−21.1244	−	18.7321i	−0.700266	−	0.620961i
$911$	10.3660	−	10.3660i	0.343442	−	0.343442i	−0.514218	−	0.857660i	$-0.671918\pi$
$911$	10.3660	−	10.3660i	0.343442	−	0.343442i	0.857660	+	0.514218i	$0.171918\pi$
$912$	0.901924	−	1.56218i	0.0298657	−	0.0517289i
$913$	−25.6603	−	6.87564i	−0.849230	−	0.227551i
$914$			14.7846i			0.489031i
$915$	6.92820	+	3.46410i	0.229039	+	0.114520i
$916$	−0.294229	+	0.169873i	−0.00972159	+	0.00561276i
$917$	29.8564			0.985945
$918$	−3.22243	−	12.0263i	−0.106356	−	0.396926i
$919$	−15.7846	+	15.7846i	−0.520686	+	0.520686i	−0.917779	−	0.397092i	$-0.870019\pi$
$919$	−15.7846	+	15.7846i	−0.520686	+	0.520686i	0.397092	+	0.917779i	$0.370019\pi$
$920$	−11.1962	+	7.39230i	−0.369126	+	0.243717i
$921$	−8.93782	+	15.4808i	−0.294511	+	0.510108i
$922$	3.07180	+	11.4641i	0.101164	+	0.377550i
$923$	24.3923	+	42.2487i	0.802882	+	1.39063i
$924$	−2.92820			−0.0963308
$925$	1.14359	+	30.3923i	0.0376011	+	0.999293i
$926$	25.6603			0.843248
$927$	5.73205	+	9.92820i	0.188265	+	0.326085i
$928$	−0.464102	−	1.73205i	−0.0152349	−	0.0568574i
$929$	8.33013	−	14.4282i	0.273303	−	0.473374i	−0.696403	−	0.717651i	$-0.745217\pi$
$929$	8.33013	−	14.4282i	0.273303	−	0.473374i	0.969705	+	0.244277i	$0.0785506\pi$
$930$	2.50000	−	1.65064i	0.0819782	−	0.0541265i
$931$	−2.46410	+	2.46410i	−0.0807577	+	0.0807577i
$932$	−4.33975	−	16.1962i	−0.142153	−	0.530523i
$933$	−14.5167			−0.475254
$934$	−13.9186	+	8.03590i	−0.455430	+	0.262943i
$935$	−16.7846	−	8.39230i	−0.548915	−	0.274458i
$936$		−	12.1962i		−	0.398644i
$937$	25.2942	+	6.77757i	0.826326	+	0.221413i	0.647110	−	0.762396i	$-0.275977\pi$
$937$	25.2942	+	6.77757i	0.826326	+	0.221413i	0.179216	+	0.983810i	$0.442644\pi$
$938$	−19.8564	+	34.3923i	−0.648335	+	1.12295i
$939$	−3.85641	+	3.85641i	−0.125849	+	0.125849i
$940$	−9.92820	−	8.80385i	−0.323822	−	0.287150i
$941$	14.5885	+	25.2679i	0.475570	+	0.823712i	0.999608	−	0.0279831i	$-0.00890846\pi$
$941$	14.5885	+	25.2679i	0.475570	+	0.823712i	−0.524038	+	0.851695i	$0.675575\pi$
$942$	8.00962	−	4.62436i	0.260967	−	0.150670i
$943$	−2.41154	−	1.39230i	−0.0785306	−	0.0453397i
$944$	7.83013	−	2.09808i	0.254849	−	0.0682866i
$945$	1.12436	+	18.7321i	0.0365753	+	0.609354i
$946$	−19.0526	+	11.0000i	−0.619452	+	0.357641i
$947$	45.4352	−	26.2321i	1.47645	−	0.852427i	0.476800	−	0.879012i	$-0.341796\pi$
$947$	45.4352	−	26.2321i	1.47645	−	0.852427i	0.999647	+	0.0265844i	$0.00846308\pi$
$948$	3.66025			0.118880
$949$		0			0
$950$	−16.1699	+	6.49038i	−0.524620	+	0.210576i
$951$	−15.6410			−0.507195
$952$	−8.39230	−	8.39230i	−0.271996	−	0.271996i
$953$	37.1244	+	9.94744i	1.20258	+	0.322229i	0.803845	−	0.594839i	$-0.202784\pi$
$953$	37.1244	+	9.94744i	1.20258	+	0.322229i	0.398731	+	0.917068i	$0.369451\pi$
$954$	−23.3923	+	23.3923i	−0.757354	+	0.757354i
$955$	−4.33013	+	21.1603i	−0.140120	+	0.684730i
$956$	−16.8564	−	16.8564i	−0.545175	−	0.545175i
$957$	0.928203	−	1.60770i	0.0300045	−	0.0519694i
$958$	11.0622	−	2.96410i	0.357403	−	0.0957658i
$959$	−6.92820	−	4.00000i	−0.223723	−	0.129167i
$960$	−0.866025	−	0.767949i	−0.0279508	−	0.0247855i
$961$		−	24.3013i		−	0.783912i
$962$	24.5526	−	11.5981i	0.791606	−	0.373937i
$963$	3.19615	+	3.19615i	0.102995	+	0.102995i
$964$	3.83013	+	1.02628i	0.123360	+	0.0330542i
$965$	32.9545	−	21.7583i	1.06084	−	0.700425i
$966$	−7.60770	−	4.39230i	−0.244774	−	0.141320i
$967$	−0.0455173	−	0.0262794i	−0.00146374	−	0.000845090i	0.499268	−	0.866448i	$-0.333602\pi$
$967$	−0.0455173	−	0.0262794i	−0.00146374	−	0.000845090i	−0.500732	+	0.865603i	$0.666936\pi$
$968$	7.00000			0.224989
$969$	6.55514	+	3.78461i	0.210581	+	0.121579i
$970$	5.46410	−	10.9282i	0.175442	−	0.350883i
$971$	−13.4904	−	23.3660i	−0.432927	−	0.749851i	0.564197	−	0.825640i	$-0.309186\pi$
$971$	−13.4904	−	23.3660i	−0.432927	−	0.749851i	−0.997124	+	0.0757888i	$0.975853\pi$
$972$	−8.73205	+	8.73205i	−0.280081	+	0.280081i
$973$	5.85641	−	5.85641i	0.187748	−	0.187748i
$974$	−29.9090	+	17.2679i	−0.958345	+	0.553301i
$975$	7.13397	−	9.08846i	0.228470	−	0.291064i
$976$	4.73205	+	4.73205i	0.151469	+	0.151469i
$977$	−21.1506	−	36.6340i	−0.676669	−	1.17202i	−0.975978	−	0.217869i	$-0.930090\pi$
$977$	−21.1506	−	36.6340i	−0.676669	−	1.17202i	0.299309	−	0.954156i	$-0.403244\pi$
$978$	−1.40192	+	5.23205i	−0.0448286	+	0.167303i
$979$	−6.73205	+	25.1244i	−0.215157	+	0.802978i
$980$	1.23205	+	1.86603i	0.0393564	+	0.0596080i
$981$	2.73205	+	10.1962i	0.0872277	+	0.325538i
$982$	−1.09808	−	1.90192i	−0.0350410	−	0.0606928i
$983$	−21.9282	−	5.87564i	−0.699401	−	0.187404i	−0.108439	−	0.994103i	$-0.534585\pi$
$983$	−21.9282	−	5.87564i	−0.699401	−	0.187404i	−0.590962	+	0.806699i	$0.701252\pi$
$984$	0.0621778	−	0.232051i	0.00198216	−	0.00739751i
$985$	50.2750	−	16.7583i	1.60189	−	0.533965i
$986$	7.26795	−	1.94744i	0.231459	−	0.0620192i
$987$	2.24871	−	8.39230i	0.0715773	−	0.267130i
$988$	11.0000	+	11.0000i	0.349957	+	0.349957i
$989$	−66.0000			−2.09868
$990$	0.732051	+	12.1962i	0.0232661	+	0.387619i
$991$	7.90192	+	7.90192i	0.251013	+	0.251013i	0.821386	−	0.570373i	$-0.193201\pi$
$991$	7.90192	+	7.90192i	0.251013	+	0.251013i	−0.570373	+	0.821386i	$0.693201\pi$
$992$	2.50000	−	0.669873i	0.0793751	−	0.0212685i
$993$		−	4.19615i		−	0.133161i
$994$	−8.00000	−	29.8564i	−0.253745	−	0.946988i
$995$	−4.91858	+	24.0359i	−0.155930	+	0.761989i
$996$	3.43782	−	5.95448i	0.108932	−	0.188675i
$997$	27.8660	−	16.0885i	0.882526	−	0.509527i	0.0110355	−	0.999939i	$-0.496487\pi$
$997$	27.8660	−	16.0885i	0.882526	−	0.509527i	0.871490	+	0.490413i	$0.163154\pi$
$998$	13.1244	−	13.1244i	0.415444	−	0.415444i
$999$	−16.9904	−	6.08846i	−0.537552	−	0.192630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.a.103.1	yes	4
5.2	odd	4		370.2.r.a.177.1	yes	4
37.23	odd	12		370.2.r.a.23.1	yes	4
185.97	even	12	inner	370.2.q.a.97.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.a.97.1	✓	4	185.97	even	12	inner
370.2.q.a.103.1	yes	4	1.1	even	1	trivial
370.2.r.a.23.1	yes	4	37.23	odd	12
370.2.r.a.177.1	yes	4	5.2	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.133975 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(0.366025 - 0.366025i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000 q^{8} +(2.36603 - 1.36603i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.133975 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.86603 + 1.23205i) q^{5} +(0.366025 - 0.366025i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000 q^{8} +(2.36603 - 1.36603i) q^{9} +(2.00000 + 1.00000i) q^{10} +2.00000i q^{11} +(-0.500000 - 0.133975i) q^{12} +(2.23205 - 3.86603i) q^{13} +(-2.00000 + 2.00000i) q^{14} +(-0.866025 - 0.767949i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.63397 - 2.09808i) q^{17} +(-2.36603 - 1.36603i) q^{18} +(3.36603 - 0.901924i) q^{19} +(-0.133975 - 2.23205i) q^{20} +(1.26795 - 0.732051i) q^{21} +(1.73205 - 1.00000i) q^{22} +6.00000 q^{23} +(0.133975 + 0.500000i) q^{24} +(1.96410 - 4.59808i) q^{25} -4.46410 q^{26} +(2.09808 + 2.09808i) q^{27} +(2.73205 + 0.732051i) q^{28} +(-1.26795 + 1.26795i) q^{29} +(-0.232051 + 1.13397i) q^{30} +(-1.83013 - 1.83013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 0.267949i) q^{33} +(-3.63397 - 2.09808i) q^{34} +(4.73205 + 4.19615i) q^{35} +2.73205i q^{36} +(-5.50000 + 2.59808i) q^{37} +(-2.46410 - 2.46410i) q^{38} +(2.23205 + 0.598076i) q^{39} +(-1.86603 + 1.23205i) q^{40} +(-0.401924 - 0.232051i) q^{41} +(-1.26795 - 0.732051i) q^{42} -11.0000 q^{43} +(-1.73205 - 1.00000i) q^{44} +(-2.73205 + 5.46410i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(4.19615 - 4.19615i) q^{47} +(0.366025 - 0.366025i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-4.96410 + 0.598076i) q^{50} +(1.53590 + 1.53590i) q^{51} +(2.23205 + 3.86603i) q^{52} +(3.13397 - 11.6962i) q^{53} +(0.767949 - 2.86603i) q^{54} +(-2.46410 - 3.73205i) q^{55} +(-0.732051 - 2.73205i) q^{56} +(0.901924 + 1.56218i) q^{57} +(1.73205 + 0.464102i) q^{58} +(-2.09808 + 7.83013i) q^{59} +(1.09808 - 0.366025i) q^{60} +(-6.46410 + 1.73205i) q^{61} +(-0.669873 + 2.50000i) q^{62} +(-5.46410 - 5.46410i) q^{63} +1.00000 q^{64} +(0.598076 + 9.96410i) q^{65} +(0.732051 + 0.732051i) q^{66} +(13.5622 - 3.63397i) q^{67} +4.19615i q^{68} +(0.803848 + 3.00000i) q^{69} +(1.26795 - 6.19615i) q^{70} +(-5.46410 + 9.46410i) q^{71} +(2.36603 - 1.36603i) q^{72} +(5.00000 + 3.46410i) q^{74} +(2.56218 + 0.366025i) q^{75} +(-0.901924 + 3.36603i) q^{76} +(5.46410 - 1.46410i) q^{77} +(-0.598076 - 2.23205i) q^{78} +(-6.83013 + 1.83013i) q^{79} +(2.00000 + 1.00000i) q^{80} +(3.33013 - 5.76795i) q^{81} +0.464102i q^{82} +(-3.43782 + 12.8301i) q^{83} +1.46410i q^{84} +(-4.19615 + 8.39230i) q^{85} +(5.50000 + 9.52628i) q^{86} +(-0.803848 - 0.464102i) q^{87} +2.00000i q^{88} +(12.5622 + 3.36603i) q^{89} +(6.09808 - 0.366025i) q^{90} +(-12.1962 - 3.26795i) q^{91} +(-3.00000 + 5.19615i) q^{92} +(0.669873 - 1.16025i) q^{93} +(-5.73205 - 1.53590i) q^{94} +(-5.16987 + 5.83013i) q^{95} +(-0.500000 - 0.133975i) q^{96} -5.46410i q^{97} +(0.866025 + 0.500000i) q^{98} +(2.73205 + 4.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 + 6 * q^9	\( 4 q - 2 q^{2} + 4 q^{3} - 2 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} + 6 q^{9} + 8 q^{10} - 2 q^{12} + 2 q^{13} - 8 q^{14} - 2 q^{16} + 18 q^{17} - 6 q^{18} + 10 q^{19} - 4 q^{20} + 12 q^{21} + 24 q^{23} + 4 q^{24} - 6 q^{25} - 4 q^{26} - 2 q^{27} + 4 q^{28} - 12 q^{29} + 6 q^{30} + 10 q^{31} - 2 q^{32} - 4 q^{33} - 18 q^{34} + 12 q^{35} - 22 q^{37} + 4 q^{38} + 2 q^{39} - 4 q^{40} - 12 q^{41} - 12 q^{42} - 44 q^{43} - 4 q^{45} - 12 q^{46} - 4 q^{47} - 2 q^{48} - 6 q^{50} + 20 q^{51} + 2 q^{52} + 16 q^{53} + 10 q^{54} + 4 q^{55} + 4 q^{56} + 14 q^{57} + 2 q^{59} - 6 q^{60} - 12 q^{61} - 20 q^{62} - 8 q^{63} + 4 q^{64} - 8 q^{65} - 4 q^{66} + 30 q^{67} + 24 q^{69} + 12 q^{70} - 8 q^{71} + 6 q^{72} + 20 q^{74} - 14 q^{75} - 14 q^{76} + 8 q^{77} + 8 q^{78} - 10 q^{79} + 8 q^{80} - 4 q^{81} - 38 q^{83} + 4 q^{85} + 22 q^{86} - 24 q^{87} + 26 q^{89} + 14 q^{90} - 28 q^{91} - 12 q^{92} + 20 q^{93} - 16 q^{94} - 38 q^{95} - 2 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 - 2 * q^4 - 4 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 + 6 * q^9 + 8 * q^10 - 2 * q^12 + 2 * q^13 - 8 * q^14 - 2 * q^16 + 18 * q^17 - 6 * q^18 + 10 * q^19 - 4 * q^20 + 12 * q^21 + 24 * q^23 + 4 * q^24 - 6 * q^25 - 4 * q^26 - 2 * q^27 + 4 * q^28 - 12 * q^29 + 6 * q^30 + 10 * q^31 - 2 * q^32 - 4 * q^33 - 18 * q^34 + 12 * q^35 - 22 * q^37 + 4 * q^38 + 2 * q^39 - 4 * q^40 - 12 * q^41 - 12 * q^42 - 44 * q^43 - 4 * q^45 - 12 * q^46 - 4 * q^47 - 2 * q^48 - 6 * q^50 + 20 * q^51 + 2 * q^52 + 16 * q^53 + 10 * q^54 + 4 * q^55 + 4 * q^56 + 14 * q^57 + 2 * q^59 - 6 * q^60 - 12 * q^61 - 20 * q^62 - 8 * q^63 + 4 * q^64 - 8 * q^65 - 4 * q^66 + 30 * q^67 + 24 * q^69 + 12 * q^70 - 8 * q^71 + 6 * q^72 + 20 * q^74 - 14 * q^75 - 14 * q^76 + 8 * q^77 + 8 * q^78 - 10 * q^79 + 8 * q^80 - 4 * q^81 - 38 * q^83 + 4 * q^85 + 22 * q^86 - 24 * q^87 + 26 * q^89 + 14 * q^90 - 28 * q^91 - 12 * q^92 + 20 * q^93 - 16 * q^94 - 38 * q^95 - 2 * q^96 + 4 * q^99

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