LMFDB - Embedded newform 370.2.r.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.193
Dual form			370.2.r.a.347.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(-1.36603 - 1.36603i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000i q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(-1.36603 - 1.36603i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000i q^{8} +(-0.633975 + 0.366025i) q^{9} +(2.00000 + 1.00000i) q^{10} -2.00000i q^{11} +(1.86603 + 0.500000i) q^{12} +(-2.13397 - 1.23205i) q^{13} +(2.00000 + 2.00000i) q^{14} +(2.86603 - 3.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.09808 - 5.36603i) q^{17} +(0.366025 - 0.633975i) q^{18} +(-1.63397 - 6.09808i) q^{19} +(-2.23205 + 0.133975i) q^{20} +(4.73205 - 2.73205i) q^{21} +(1.00000 + 1.73205i) q^{22} +6.00000i q^{23} +(-1.86603 + 0.500000i) q^{24} +(-1.96410 + 4.59808i) q^{25} +2.46410 q^{26} +(3.09808 + 3.09808i) q^{27} +(-2.73205 - 0.732051i) q^{28} +(4.73205 + 4.73205i) q^{29} +(-0.866025 + 4.23205i) q^{30} +(6.83013 - 6.83013i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.73205 - 1.00000i) q^{33} +(5.36603 + 3.09808i) q^{34} +(-4.19615 + 4.73205i) q^{35} +0.732051i q^{36} +(2.59808 + 5.50000i) q^{37} +(4.46410 + 4.46410i) q^{38} +(1.23205 - 4.59808i) q^{39} +(1.86603 - 1.23205i) q^{40} +(-5.59808 - 3.23205i) q^{41} +(-2.73205 + 4.73205i) q^{42} -11.0000i q^{43} +(-1.73205 - 1.00000i) q^{44} +(1.46410 + 0.732051i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(-6.19615 + 6.19615i) q^{47} +(1.36603 - 1.36603i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.598076 - 4.96410i) q^{50} +(8.46410 - 8.46410i) q^{51} +(-2.13397 + 1.23205i) q^{52} +(-1.30385 + 4.86603i) q^{53} +(-4.23205 - 1.13397i) q^{54} +(-3.73205 + 2.46410i) q^{55} +(2.73205 - 0.732051i) q^{56} +(10.5622 - 6.09808i) q^{57} +(-6.46410 - 1.73205i) q^{58} +(-3.09808 - 0.830127i) q^{59} +(-1.36603 - 4.09808i) q^{60} +(0.464102 + 1.73205i) q^{61} +(-2.50000 + 9.33013i) q^{62} +(1.46410 + 1.46410i) q^{63} -1.00000 q^{64} +(0.330127 + 5.50000i) q^{65} +(-2.73205 + 2.73205i) q^{66} +(5.36603 - 1.43782i) q^{67} -6.19615 q^{68} +(-11.1962 + 3.00000i) q^{69} +(1.26795 - 6.19615i) q^{70} +(1.46410 - 2.53590i) q^{71} +(-0.366025 - 0.633975i) q^{72} +(-5.00000 - 3.46410i) q^{74} +(-9.56218 - 1.36603i) q^{75} +(-6.09808 - 1.63397i) q^{76} +(-5.46410 + 1.46410i) q^{77} +(1.23205 + 4.59808i) q^{78} +(-1.83013 - 6.83013i) q^{79} +(-1.00000 + 2.00000i) q^{80} +(-5.33013 + 9.23205i) q^{81} +6.46410 q^{82} +(4.16987 - 15.5622i) q^{83} -5.46410i q^{84} +(-6.19615 + 12.3923i) q^{85} +(5.50000 + 9.52628i) q^{86} +(-6.46410 + 11.1962i) q^{87} +2.00000 q^{88} +(-0.437822 + 1.63397i) q^{89} +(-1.63397 + 0.0980762i) q^{90} +(-1.80385 + 6.73205i) q^{91} +(5.19615 + 3.00000i) q^{92} +(16.1603 + 9.33013i) q^{93} +(2.26795 - 8.46410i) q^{94} +(-9.36603 + 10.5622i) q^{95} +(-0.500000 + 1.86603i) q^{96} -1.46410 q^{97} +(0.500000 - 0.866025i) q^{98} +(0.732051 + 1.26795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 6 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 6 q^{9} + 8 q^{10} + 4 q^{12} - 12 q^{13} + 8 q^{14} + 8 q^{15} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 10 q^{19} - 2 q^{20} + 12 q^{21} + 4 q^{22} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 2 q^{27} - 4 q^{28} + 12 q^{29} + 10 q^{31} + 8 q^{33} + 18 q^{34} + 4 q^{35} + 4 q^{38} - 2 q^{39} + 4 q^{40} - 12 q^{41} - 4 q^{42} - 8 q^{45} - 12 q^{46} - 4 q^{47} + 2 q^{48} + 8 q^{50} + 20 q^{51} - 12 q^{52} - 26 q^{53} - 10 q^{54} - 8 q^{55} + 4 q^{56} + 18 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} - 12 q^{61} - 10 q^{62} - 8 q^{63} - 4 q^{64} - 16 q^{65} - 4 q^{66} + 18 q^{67} - 4 q^{68} - 24 q^{69} + 12 q^{70} - 8 q^{71} + 2 q^{72} - 20 q^{74} - 14 q^{75} - 14 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} - 4 q^{80} - 4 q^{81} + 12 q^{82} + 34 q^{83} - 4 q^{85} + 22 q^{86} - 12 q^{87} + 8 q^{88} - 26 q^{89} - 10 q^{90} - 28 q^{91} + 30 q^{93} + 16 q^{94} - 34 q^{95} - 2 q^{96} + 8 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 6 * q^9 + 8 * q^10 + 4 * q^12 - 12 * q^13 + 8 * q^14 + 8 * q^15 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 10 * q^19 - 2 * q^20 + 12 * q^21 + 4 * q^22 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 2 * q^27 - 4 * q^28 + 12 * q^29 + 10 * q^31 + 8 * q^33 + 18 * q^34 + 4 * q^35 + 4 * q^38 - 2 * q^39 + 4 * q^40 - 12 * q^41 - 4 * q^42 - 8 * q^45 - 12 * q^46 - 4 * q^47 + 2 * q^48 + 8 * q^50 + 20 * q^51 - 12 * q^52 - 26 * q^53 - 10 * q^54 - 8 * q^55 + 4 * q^56 + 18 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 - 12 * q^61 - 10 * q^62 - 8 * q^63 - 4 * q^64 - 16 * q^65 - 4 * q^66 + 18 * q^67 - 4 * q^68 - 24 * q^69 + 12 * q^70 - 8 * q^71 + 2 * q^72 - 20 * q^74 - 14 * q^75 - 14 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 - 4 * q^80 - 4 * q^81 + 12 * q^82 + 34 * q^83 - 4 * q^85 + 22 * q^86 - 12 * q^87 + 8 * q^88 - 26 * q^89 - 10 * q^90 - 28 * q^91 + 30 * q^93 + 16 * q^94 - 34 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	0.946112	+	0.323840i	$0.104974\pi$
$3$	0.500000	+	1.86603i	0.288675	+	1.07735i	−0.657437	+	0.753510i	$0.728359\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$6$	−1.36603	−	1.36603i	−0.557678	−	0.557678i
$7$	−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	$-0.262842\pi$
$8$			1.00000i			0.353553i
$9$	−0.633975	+	0.366025i	−0.211325	+	0.122008i
$10$	2.00000	+	1.00000i	0.632456	+	0.316228i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$	1.86603	+	0.500000i	0.538675	+	0.144338i
$13$	−2.13397	−	1.23205i	−0.591858	−	0.341709i	0.173974	−	0.984750i	$-0.444339\pi$
$13$	−2.13397	−	1.23205i	−0.591858	−	0.341709i	−0.765832	+	0.643041i	$0.777673\pi$
$14$	2.00000	+	2.00000i	0.534522	+	0.534522i
$15$	2.86603	−	3.23205i	0.740005	−	0.834512i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.09808	−	5.36603i	−0.751394	−	1.30145i	−0.947147	−	0.320799i	$-0.896049\pi$
$17$	−3.09808	−	5.36603i	−0.751394	−	1.30145i	0.195753	−	0.980653i	$-0.437285\pi$
$18$	0.366025	−	0.633975i	0.0862730	−	0.149429i
$19$	−1.63397	−	6.09808i	−0.374859	−	1.39899i	−0.853550	−	0.521011i	$-0.825555\pi$
$19$	−1.63397	−	6.09808i	−0.374859	−	1.39899i	0.478691	−	0.877984i	$-0.341112\pi$
$20$	−2.23205	+	0.133975i	−0.499102	+	0.0299576i
$21$	4.73205	−	2.73205i	1.03262	−	0.596182i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−1.86603	+	0.500000i	−0.380901	+	0.102062i
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$	2.46410			0.483250
$27$	3.09808	+	3.09808i	0.596225	+	0.596225i
$28$	−2.73205	−	0.732051i	−0.516309	−	0.138345i
$29$	4.73205	+	4.73205i	0.878720	+	0.878720i	0.993402	−	0.114682i	$-0.0365850\pi$
$29$	4.73205	+	4.73205i	0.878720	+	0.878720i	−0.114682	+	0.993402i	$0.536585\pi$
$30$	−0.866025	+	4.23205i	−0.158114	+	0.772663i
$31$	6.83013	−	6.83013i	1.22673	−	1.22673i	0.261532	−	0.965195i	$-0.415772\pi$
$31$	6.83013	−	6.83013i	1.22673	−	1.22673i	0.965195	−	0.261532i	$-0.0842278\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	3.73205	−	1.00000i	0.649667	−	0.174078i
$34$	5.36603	+	3.09808i	0.920266	+	0.531316i
$35$	−4.19615	+	4.73205i	−0.709279	+	0.799863i
$36$			0.732051i			0.122008i
$37$	2.59808	+	5.50000i	0.427121	+	0.904194i
$37$	2.59808	+	5.50000i	0.427121	+	0.904194i
$38$	4.46410	+	4.46410i	0.724173	+	0.724173i
$39$	1.23205	−	4.59808i	0.197286	−	0.736281i
$40$	1.86603	−	1.23205i	0.295045	−	0.194804i
$41$	−5.59808	−	3.23205i	−0.874273	−	0.504762i	−0.00550690	−	0.999985i	$-0.501753\pi$
$41$	−5.59808	−	3.23205i	−0.874273	−	0.504762i	−0.868766	+	0.495223i	$0.835086\pi$
$42$	−2.73205	+	4.73205i	−0.421565	+	0.730171i
$43$		−	11.0000i		−	1.67748i	−0.544529	−	0.838742i	$-0.683292\pi$
$43$		−	11.0000i		−	1.67748i	0.544529	−	0.838742i	$-0.316708\pi$
$44$	−1.73205	−	1.00000i	−0.261116	−	0.150756i
$45$	1.46410	+	0.732051i	0.218255	+	0.109128i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$	−6.19615	+	6.19615i	−0.903802	+	0.903802i	−0.995763	−	0.0919609i	$-0.970687\pi$
$47$	−6.19615	+	6.19615i	−0.903802	+	0.903802i	0.0919609	+	0.995763i	$0.470687\pi$
$48$	1.36603	−	1.36603i	0.197169	−	0.197169i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−0.598076	−	4.96410i	−0.0845807	−	0.702030i
$51$	8.46410	−	8.46410i	1.18521	−	1.18521i
$52$	−2.13397	+	1.23205i	−0.295929	+	0.170855i
$53$	−1.30385	+	4.86603i	−0.179097	+	0.668400i	0.816720	+	0.577034i	$0.195790\pi$
$53$	−1.30385	+	4.86603i	−0.179097	+	0.668400i	−0.995817	+	0.0913660i	$0.970877\pi$
$54$	−4.23205	−	1.13397i	−0.575909	−	0.154314i
$55$	−3.73205	+	2.46410i	−0.503230	+	0.332259i
$56$	2.73205	−	0.732051i	0.365086	−	0.0978244i
$57$	10.5622	−	6.09808i	1.39899	−	0.807710i
$58$	−6.46410	−	1.73205i	−0.848778	−	0.227429i
$59$	−3.09808	−	0.830127i	−0.403335	−	0.108073i	0.0514477	−	0.998676i	$-0.483616\pi$
$59$	−3.09808	−	0.830127i	−0.403335	−	0.108073i	−0.454783	+	0.890602i	$0.650283\pi$
$60$	−1.36603	−	4.09808i	−0.176353	−	0.529059i
$61$	0.464102	+	1.73205i	0.0594221	+	0.221766i	0.989251	−	0.146225i	$-0.0467123\pi$
$61$	0.464102	+	1.73205i	0.0594221	+	0.221766i	−0.929829	+	0.367991i	$0.880046\pi$
$62$	−2.50000	+	9.33013i	−0.317500	+	1.18493i
$63$	1.46410	+	1.46410i	0.184459	+	0.184459i
$64$	−1.00000			−0.125000
$65$	0.330127	+	5.50000i	0.0409472	+	0.682191i
$66$	−2.73205	+	2.73205i	−0.336292	+	0.336292i
$67$	5.36603	−	1.43782i	0.655564	−	0.175658i	0.0843209	−	0.996439i	$-0.473128\pi$
$67$	5.36603	−	1.43782i	0.655564	−	0.175658i	0.571243	+	0.820781i	$0.306461\pi$
$68$	−6.19615			−0.751394
$69$	−11.1962	+	3.00000i	−1.34786	+	0.361158i
$70$	1.26795	−	6.19615i	0.151549	−	0.740582i
$71$	1.46410	−	2.53590i	0.173757	−	0.300956i	−0.765973	−	0.642872i	$-0.777743\pi$
$71$	1.46410	−	2.53590i	0.173757	−	0.300956i	0.939730	+	0.341916i	$0.111076\pi$
$72$	−0.366025	−	0.633975i	−0.0431365	−	0.0747146i
$73$		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
$75$	−9.56218	−	1.36603i	−1.10415	−	0.157735i
$76$	−6.09808	−	1.63397i	−0.699497	−	0.187430i
$77$	−5.46410	+	1.46410i	−0.622692	+	0.166850i
$78$	1.23205	+	4.59808i	0.139502	+	0.520630i
$79$	−1.83013	−	6.83013i	−0.205905	−	0.768449i	−0.989172	−	0.146763i	$-0.953115\pi$
$79$	−1.83013	−	6.83013i	−0.205905	−	0.768449i	0.783266	−	0.621686i	$-0.213552\pi$
$80$	−1.00000	+	2.00000i	−0.111803	+	0.223607i
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$	6.46410			0.713841
$83$	4.16987	−	15.5622i	0.457703	−	1.70817i	−0.222314	−	0.974975i	$-0.571361\pi$
$83$	4.16987	−	15.5622i	0.457703	−	1.70817i	0.680017	−	0.733196i	$-0.261972\pi$
$84$		−	5.46410i		−	0.596182i
$85$	−6.19615	+	12.3923i	−0.672067	+	1.34413i
$86$	5.50000	+	9.52628i	0.593080	+	1.02725i
$87$	−6.46410	+	11.1962i	−0.693024	+	1.20035i
$88$	2.00000			0.213201
$89$	−0.437822	+	1.63397i	−0.0464091	+	0.173201i	−0.985240	−	0.171176i	$-0.945243\pi$
$89$	−0.437822	+	1.63397i	−0.0464091	+	0.173201i	0.938831	+	0.344377i	$0.111910\pi$
$90$	−1.63397	+	0.0980762i	−0.172236	+	0.0103381i
$91$	−1.80385	+	6.73205i	−0.189095	+	0.705711i
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$	16.1603	+	9.33013i	1.67574	+	0.967489i
$94$	2.26795	−	8.46410i	0.233921	−	0.873005i
$95$	−9.36603	+	10.5622i	−0.960934	+	1.08366i
$96$	−0.500000	+	1.86603i	−0.0510310	+	0.190450i
$97$	−1.46410			−0.148657			−0.0743285	−	0.997234i	$-0.523681\pi$
$97$	−1.46410			−0.148657			−0.0743285	+	0.997234i	$0.523681\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	0.732051	+	1.26795i	0.0735739	+	0.127434i
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$		−	0.196152i		−	0.0195179i	−0.999952	−	0.00975895i	$-0.996894\pi$
$101$		−	0.196152i		−	0.0195179i	0.999952	−	0.00975895i	$-0.00310642\pi$
$102$	−3.09808	+	11.5622i	−0.306755	+	1.14483i
$103$	−6.19615			−0.610525			−0.305263	−	0.952268i	$-0.598744\pi$
$103$	−6.19615			−0.610525			−0.305263	+	0.952268i	$0.598744\pi$
$104$	1.23205	−	2.13397i	0.120813	−	0.209253i
$105$	−10.9282	−	5.46410i	−1.06648	−	0.533242i
$106$	−1.30385	−	4.86603i	−0.126641	−	0.472630i
$107$	3.59808	+	13.4282i	0.347839	+	1.29815i	0.889260	+	0.457402i	$0.151220\pi$
$107$	3.59808	+	13.4282i	0.347839	+	1.29815i	−0.541421	+	0.840752i	$0.682113\pi$
$108$	4.23205	−	1.13397i	0.407229	−	0.109117i
$109$	1.00000	+	0.267949i	0.0957826	+	0.0256649i	0.306392	−	0.951905i	$-0.400878\pi$
$109$	1.00000	+	0.267949i	0.0957826	+	0.0256649i	−0.210609	+	0.977570i	$0.567545\pi$
$110$	2.00000	−	4.00000i	0.190693	−	0.381385i
$111$	−8.96410	+	7.59808i	−0.850835	+	0.721177i
$112$	−2.00000	+	2.00000i	−0.188982	+	0.188982i
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	0.689714	−	0.724082i	$-0.257736\pi$
$113$	−3.00000	−	5.19615i	−0.282216	−	0.488813i	−0.971930	+	0.235269i	$0.924403\pi$
$114$	−6.09808	+	10.5622i	−0.571137	+	0.989239i
$115$	11.1962	−	7.39230i	1.04405	−	0.689336i
$116$	6.46410	−	1.73205i	0.600177	−	0.160817i
$117$	1.80385			0.166766
$118$	3.09808	−	0.830127i	0.285201	−	0.0764194i
$119$	−12.3923	+	12.3923i	−1.13600	+	1.13600i
$120$	3.23205	+	2.86603i	0.295045	+	0.261631i
$121$	7.00000			0.636364
$122$	−1.26795	−	1.26795i	−0.114795	−	0.114795i
$123$	3.23205	−	12.0622i	0.291424	−	1.08761i
$124$	−2.50000	−	9.33013i	−0.224507	−	0.837870i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	−2.00000	−	0.535898i	−0.178174	−	0.0477416i
$127$	−8.83013	−	2.36603i	−0.783547	−	0.209951i	−0.155199	−	0.987883i	$-0.549602\pi$
$127$	−8.83013	−	2.36603i	−0.783547	−	0.209951i	−0.628348	+	0.777932i	$0.716269\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	20.5263	−	5.50000i	1.80724	−	0.484248i
$130$	−3.03590	−	4.59808i	−0.266266	−	0.403278i
$131$	0.732051	+	0.196152i	0.0639596	+	0.0171379i	0.290657	−	0.956827i	$-0.406126\pi$
$131$	0.732051	+	0.196152i	0.0639596	+	0.0171379i	−0.226697	+	0.973965i	$0.572793\pi$
$132$	1.00000	−	3.73205i	0.0870388	−	0.324833i
$133$	−15.4641	+	8.92820i	−1.34091	+	0.774173i
$134$	−3.92820	+	3.92820i	−0.339345	+	0.339345i
$135$	1.96410	−	9.59808i	0.169043	−	0.826071i
$136$	5.36603	−	3.09808i	0.460133	−	0.265658i
$137$	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	$0.211446\pi$
$138$	8.19615	−	8.19615i	0.697703	−	0.697703i
$139$	5.46410	+	9.46410i	0.463459	+	0.802735i	0.999131	−	0.0416919i	$-0.0132748\pi$
$139$	5.46410	+	9.46410i	0.463459	+	0.802735i	−0.535671	+	0.844426i	$0.679941\pi$
$140$	2.00000	+	6.00000i	0.169031	+	0.507093i
$141$	−14.6603	−	8.46410i	−1.23462	−	0.712806i
$142$			2.92820i			0.245729i
$143$	−2.46410	+	4.26795i	−0.206059	+	0.356904i
$144$	0.633975	+	0.366025i	0.0528312	+	0.0305021i
$145$	3.00000	−	14.6603i	0.249136	−	1.21747i
$146$		0			0
$147$	−1.36603	−	1.36603i	−0.112668	−	0.112668i
$148$	6.06218	+	0.500000i	0.498308	+	0.0410997i
$149$			22.7321i			1.86228i	0.364659	+	0.931141i	$0.381186\pi$
$149$			22.7321i			1.86228i	−0.364659	+	0.931141i	$0.618814\pi$
$150$	8.96410	−	3.59808i	0.731916	−	0.293782i
$151$	−2.76795	−	1.59808i	−0.225253	−	0.130050i	0.383127	−	0.923695i	$-0.374847\pi$
$151$	−2.76795	−	1.59808i	−0.225253	−	0.130050i	−0.608380	+	0.793646i	$0.708180\pi$
$152$	6.09808	−	1.63397i	0.494619	−	0.132533i
$153$	3.92820	+	2.26795i	0.317576	+	0.183353i
$154$	4.00000	−	4.00000i	0.322329	−	0.322329i
$155$	−21.1603	−	4.33013i	−1.69963	−	0.347804i
$156$	−3.36603	−	3.36603i	−0.269498	−	0.269498i
$157$	19.6244	+	5.25833i	1.56619	+	0.419660i	0.934618	−	0.355653i	$-0.115742\pi$
$157$	19.6244	+	5.25833i	1.56619	+	0.419660i	0.631576	+	0.775314i	$0.282408\pi$
$158$	5.00000	+	5.00000i	0.397779	+	0.397779i
$159$	−9.73205			−0.771802
$160$	−0.133975	−	2.23205i	−0.0105916	−	0.176459i
$161$	16.3923	−	4.39230i	1.29189	−	0.346162i
$162$		−	10.6603i		−	0.837549i
$163$	1.76795	+	3.06218i	0.138476	+	0.239848i	0.926920	−	0.375259i	$-0.122446\pi$
$163$	1.76795	+	3.06218i	0.138476	+	0.239848i	−0.788444	+	0.615107i	$0.789113\pi$
$164$	−5.59808	+	3.23205i	−0.437136	+	0.252381i
$165$	−6.46410	−	5.73205i	−0.503230	−	0.446240i
$166$	4.16987	+	15.5622i	0.323645	+	1.20786i
$167$	10.3660	−	17.9545i	0.802147	−	1.38936i	−0.116053	−	0.993243i	$-0.537024\pi$
$167$	10.3660	−	17.9545i	0.802147	−	1.38936i	0.918200	−	0.396117i	$-0.129642\pi$
$168$	2.73205	+	4.73205i	0.210782	+	0.365086i
$169$	−3.46410	−	6.00000i	−0.266469	−	0.461538i
$170$	−0.830127	−	13.8301i	−0.0636678	−	1.06072i
$171$	3.26795	+	3.26795i	0.249906	+	0.249906i
$172$	−9.52628	−	5.50000i	−0.726372	−	0.419371i
$173$	23.4904	+	6.29423i	1.78594	+	0.478541i	0.991646	−	0.128991i	$-0.0411739\pi$
$173$	23.4904	+	6.29423i	1.78594	+	0.478541i	0.794295	+	0.607532i	$0.207841\pi$
$174$		−	12.9282i		−	0.980085i
$175$	14.0000	+	2.00000i	1.05830	+	0.151186i
$176$	−1.73205	+	1.00000i	−0.130558	+	0.0753778i
$177$		−	6.19615i		−	0.465731i
$178$	−0.437822	−	1.63397i	−0.0328162	−	0.122472i
$179$	−10.3923	−	10.3923i	−0.776757	−	0.776757i	0.202521	−	0.979278i	$-0.435087\pi$
$179$	−10.3923	−	10.3923i	−0.776757	−	0.776757i	−0.979278	+	0.202521i	$0.935087\pi$
$180$	1.36603	−	0.901924i	0.101818	−	0.0672254i
$181$	6.90192	−	11.9545i	0.513016	−	0.888570i	−0.486870	−	0.873474i	$-0.661861\pi$
$181$	6.90192	−	11.9545i	0.513016	−	0.888570i	0.999886	−	0.0150953i	$-0.00480517\pi$
$182$	−1.80385	−	6.73205i	−0.133710	−	0.499013i
$183$	−3.00000	+	1.73205i	−0.221766	+	0.128037i
$184$	−6.00000			−0.442326
$185$	7.06218	−	11.6244i	0.519222	−	0.854640i
$186$	−18.6603			−1.36824
$187$	−10.7321	+	6.19615i	−0.784805	+	0.453108i
$188$	2.26795	+	8.46410i	0.165407	+	0.617308i
$189$	6.19615	−	10.7321i	0.450704	−	0.780642i
$190$	2.83013	−	13.8301i	0.205319	−	1.00334i
$191$	−1.83013	−	1.83013i	−0.132423	−	0.132423i	0.637788	−	0.770212i	$-0.279849\pi$
$191$	−1.83013	−	1.83013i	−0.132423	−	0.132423i	−0.770212	+	0.637788i	$0.779849\pi$
$192$	−0.500000	−	1.86603i	−0.0360844	−	0.134669i
$193$		−	0.339746i		−	0.0244554i	−0.999925	−	0.0122277i	$-0.996108\pi$
$193$		−	0.339746i		−	0.0244554i	0.999925	−	0.0122277i	$-0.00389230\pi$
$194$	1.26795	−	0.732051i	0.0910334	−	0.0525582i
$195$	−10.0981	+	3.36603i	−0.723138	+	0.241046i
$196$			1.00000i			0.0714286i
$197$	7.86603	+	2.10770i	0.560431	+	0.150167i	0.527904	−	0.849304i	$-0.322978\pi$
$197$	7.86603	+	2.10770i	0.560431	+	0.150167i	0.0325267	+	0.999471i	$0.489645\pi$
$198$	−1.26795	−	0.732051i	−0.0901092	−	0.0520246i
$199$	14.7583	+	14.7583i	1.04619	+	1.04619i	0.998880	+	0.0473100i	$0.0150649\pi$
$199$	14.7583	+	14.7583i	1.04619	+	1.04619i	0.0473100	+	0.998880i	$0.484935\pi$
$200$	−4.59808	−	1.96410i	−0.325133	−	0.138883i
$201$	5.36603	+	9.29423i	0.378490	+	0.655564i
$202$	0.0980762	+	0.169873i	0.00690062	+	0.0119522i
$203$	9.46410	−	16.3923i	0.664250	−	1.15051i
$204$	−3.09808	−	11.5622i	−0.216909	−	0.809514i
$205$	0.866025	+	14.4282i	0.0604858	+	1.00771i
$206$	5.36603	−	3.09808i	0.373869	−	0.215853i
$207$	−2.19615	−	3.80385i	−0.152643	−	0.264386i
$208$			2.46410i			0.170855i
$209$	−12.1962	+	3.26795i	−0.843626	+	0.226049i
$210$	12.1962	−	0.732051i	0.841614	−	0.0505163i
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	3.56218	+	3.56218i	0.244651	+	0.244651i
$213$	5.46410	+	1.46410i	0.374394	+	0.100319i
$214$	−9.83013	−	9.83013i	−0.671974	−	0.671974i
$215$	−20.5263	+	13.5526i	−1.39988	+	0.924277i
$216$	−3.09808	+	3.09808i	−0.210797	+	0.210797i
$217$	−23.6603	−	13.6603i	−1.60616	−	0.927318i
$218$	−1.00000	+	0.267949i	−0.0677285	+	0.0181478i
$219$		0			0
$220$	0.267949	+	4.46410i	0.0180651	+	0.300970i
$221$			15.2679i			1.02703i
$222$	3.96410	−	11.0622i	0.266053	−	0.742445i
$223$	−12.9282	−	12.9282i	−0.865737	−	0.865737i	0.126261	−	0.991997i	$-0.459702\pi$
$223$	−12.9282	−	12.9282i	−0.865737	−	0.865737i	−0.991997	+	0.126261i	$0.959702\pi$
$224$	0.732051	−	2.73205i	0.0489122	−	0.182543i
$225$	−0.437822	−	3.63397i	−0.0291881	−	0.242265i
$226$	5.19615	+	3.00000i	0.345643	+	0.199557i
$227$	−1.33013	+	2.30385i	−0.0882836	+	0.152912i	−0.906786	−	0.421592i	$-0.861472\pi$
$227$	−1.33013	+	2.30385i	−0.0882836	+	0.152912i	0.818502	+	0.574504i	$0.194805\pi$
$228$		−	12.1962i		−	0.807710i
$229$	15.2942	+	8.83013i	1.01067	+	0.583511i	0.911388	−	0.411548i	$-0.135012\pi$
$229$	15.2942	+	8.83013i	1.01067	+	0.583511i	0.0992830	+	0.995059i	$0.468345\pi$
$230$	−6.00000	+	12.0000i	−0.395628	+	0.791257i
$231$	−5.46410	−	9.46410i	−0.359511	−	0.622692i
$232$	−4.73205	+	4.73205i	−0.310674	+	0.310674i
$233$	−15.8564	+	15.8564i	−1.03879	+	1.03879i	−0.0395710	+	0.999217i	$0.512599\pi$
$233$	−15.8564	+	15.8564i	−1.03879	+	1.03879i	−0.999217	+	0.0395710i	$0.987401\pi$
$234$	−1.56218	+	0.901924i	−0.102123	+	0.0589606i
$235$	19.1962	+	3.92820i	1.25222	+	0.256248i
$236$	−2.26795	+	2.26795i	−0.147631	+	0.147631i
$237$	11.8301	−	6.83013i	0.768449	−	0.443664i
$238$	4.53590	−	16.9282i	0.294019	−	1.09729i
$239$	14.8301	+	3.97372i	0.959281	+	0.257039i	0.704296	−	0.709906i	$-0.251263\pi$
$239$	14.8301	+	3.97372i	0.959281	+	0.257039i	0.254985	+	0.966945i	$0.417929\pi$
$240$	−4.23205	−	0.866025i	−0.273178	−	0.0559017i
$241$	18.0263	−	4.83013i	1.16117	−	0.311136i	0.373740	−	0.927534i	$-0.378075\pi$
$241$	18.0263	−	4.83013i	1.16117	−	0.311136i	0.787435	+	0.616398i	$0.211409\pi$
$242$	−6.06218	+	3.50000i	−0.389692	+	0.224989i
$243$	−7.19615	−	1.92820i	−0.461633	−	0.123694i
$244$	1.73205	+	0.464102i	0.110883	+	0.0297111i
$245$	2.00000	+	1.00000i	0.127775	+	0.0638877i
$246$	3.23205	+	12.0622i	0.206068	+	0.769056i
$247$	−4.02628	+	15.0263i	−0.256186	+	0.956099i
$248$	6.83013	+	6.83013i	0.433713	+	0.433713i
$249$	31.1244			1.97243
$250$	−8.52628	+	7.23205i	−0.539249	+	0.457395i
$251$	5.73205	−	5.73205i	0.361804	−	0.361804i	−0.502673	−	0.864477i	$-0.667650\pi$
$251$	5.73205	−	5.73205i	0.361804	−	0.361804i	0.864477	+	0.502673i	$0.167650\pi$
$252$	2.00000	−	0.535898i	0.125988	−	0.0337584i
$253$	12.0000			0.754434
$254$	8.83013	−	2.36603i	0.554051	−	0.148458i
$255$	−26.2224	−	5.36603i	−1.64211	−	0.336034i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.169873	−	0.294229i	−0.0105964	−	0.0183535i	0.860679	−	0.509149i	$-0.170040\pi$
$257$	−0.169873	−	0.294229i	−0.0105964	−	0.0183535i	−0.871275	+	0.490795i	$0.836706\pi$
$258$	−15.0263	+	15.0263i	−0.935495	+	0.935495i
$259$	13.1244	−	11.1244i	0.815508	−	0.691234i
$260$	4.92820	+	2.46410i	0.305634	+	0.152817i
$261$	−4.73205	−	1.26795i	−0.292907	−	0.0784841i
$262$	−0.732051	+	0.196152i	−0.0452262	+	0.0121183i
$263$	−0.0262794	−	0.0980762i	−0.00162046	−	0.00604764i	0.965111	−	0.261842i	$-0.0843298\pi$
$263$	−0.0262794	−	0.0980762i	−0.00162046	−	0.00604764i	−0.966731	+	0.255794i	$0.917663\pi$
$264$	1.00000	+	3.73205i	0.0615457	+	0.229692i
$265$	10.6865	−	3.56218i	0.656469	−	0.218823i
$266$	8.92820	−	15.4641i	0.547423	−	0.948165i
$267$	−3.26795			−0.199995
$268$	1.43782	−	5.36603i	0.0878290	−	0.327782i
$269$			6.58846i			0.401705i	0.979621	+	0.200853i	$0.0643712\pi$
$269$			6.58846i			0.401705i	−0.979621	+	0.200853i	$0.935629\pi$
$270$	3.09808	+	9.29423i	0.188543	+	0.565629i
$271$	5.23205	+	9.06218i	0.317824	+	0.550488i	0.980034	−	0.198831i	$-0.0637144\pi$
$271$	5.23205	+	9.06218i	0.317824	+	0.550488i	−0.662209	+	0.749319i	$0.730381\pi$
$272$	−3.09808	+	5.36603i	−0.187848	+	0.325363i
$273$	−13.4641			−0.814885
$274$	−0.732051	+	2.73205i	−0.0442248	+	0.165049i
$275$	9.19615	+	3.92820i	0.554549	+	0.236880i
$276$	−3.00000	+	11.1962i	−0.180579	+	0.673929i
$277$	−14.4282	−	8.33013i	−0.866907	−	0.500509i	−0.000587640	−	1.00000i	$-0.500187\pi$
$277$	−14.4282	−	8.33013i	−0.866907	−	0.500509i	−0.866319	+	0.499491i	$0.833520\pi$
$278$	−9.46410	−	5.46410i	−0.567619	−	0.327715i
$279$	−1.83013	+	6.83013i	−0.109567	+	0.408909i
$280$	−4.73205	−	4.19615i	−0.282794	−	0.250768i
$281$	−0.624356	+	2.33013i	−0.0372459	+	0.139004i	−0.982045	−	0.188646i	$-0.939590\pi$
$281$	−0.624356	+	2.33013i	−0.0372459	+	0.139004i	0.944799	+	0.327650i	$0.106257\pi$
$282$	16.9282			1.00806
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	−0.991960	−	0.126550i	$-0.959610\pi$
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	0.605575	+	0.795788i	$0.292943\pi$
$284$	−1.46410	−	2.53590i	−0.0868784	−	0.150478i
$285$	−24.3923	−	12.1962i	−1.44488	−	0.722438i
$286$		−	4.92820i		−	0.291411i
$287$	−4.73205	+	17.6603i	−0.279324	+	1.04245i
$288$	−0.732051			−0.0431365
$289$	−10.6962	+	18.5263i	−0.629185	+	1.08978i
$290$	4.73205	+	14.1962i	0.277876	+	0.833627i
$291$	−0.732051	−	2.73205i	−0.0429136	−	0.160156i
$292$		0			0
$293$	−3.13397	+	0.839746i	−0.183089	+	0.0490585i	−0.349198	−	0.937049i	$-0.613546\pi$
$293$	−3.13397	+	0.839746i	−0.183089	+	0.0490585i	0.166110	+	0.986107i	$0.446879\pi$
$294$	1.86603	+	0.500000i	0.108829	+	0.0291606i
$295$	2.26795	+	6.80385i	0.132045	+	0.396135i
$296$	−5.50000	+	2.59808i	−0.319681	+	0.151010i
$297$	6.19615	−	6.19615i	0.359537	−	0.359537i
$298$	−11.3660	−	19.6865i	−0.658416	−	1.14041i
$299$	7.39230	−	12.8038i	0.427508	−	0.740466i
$300$	−5.96410	+	7.59808i	−0.344338	+	0.438675i
$301$	−30.0526	+	8.05256i	−1.73220	+	0.464142i
$302$	3.19615			0.183918
$303$	0.366025	−	0.0980762i	0.0210276	−	0.00563433i
$304$	−4.46410	+	4.46410i	−0.256034	+	0.256034i
$305$	2.66025	−	3.00000i	0.152326	−	0.171780i
$306$	−4.53590			−0.259300
$307$	15.4186	+	15.4186i	0.879985	+	0.879985i	0.993533	−	0.113547i	$-0.0362214\pi$
$307$	15.4186	+	15.4186i	0.879985	+	0.879985i	−0.113547	+	0.993533i	$0.536221\pi$
$308$	−1.46410	+	5.46410i	−0.0834249	+	0.311346i
$309$	−3.09808	−	11.5622i	−0.176243	−	0.657749i
$310$	20.4904	−	6.83013i	1.16378	−	0.387925i
$311$	15.2583	+	4.08846i	0.865221	+	0.231835i	0.664020	−	0.747715i	$-0.268849\pi$
$311$	15.2583	+	4.08846i	0.865221	+	0.231835i	0.201201	+	0.979550i	$0.435516\pi$
$312$	4.59808	+	1.23205i	0.260315	+	0.0697511i
$313$	−15.1244	+	8.73205i	−0.854879	+	0.493565i	−0.862294	−	0.506408i	$-0.830973\pi$
$313$	−15.1244	+	8.73205i	−0.854879	+	0.493565i	0.00741498	+	0.999973i	$0.497640\pi$
$314$	−19.6244	+	5.25833i	−1.10747	+	0.296745i
$315$	0.928203	−	4.53590i	0.0522983	−	0.255569i
$316$	−6.83013	−	1.83013i	−0.384225	−	0.102953i
$317$	7.18653	−	26.8205i	0.403636	−	1.50639i	−0.402922	−	0.915234i	$-0.632005\pi$
$317$	7.18653	−	26.8205i	0.403636	−	1.50639i	0.806558	−	0.591155i	$-0.201328\pi$
$318$	8.42820	−	4.86603i	0.472630	−	0.272873i
$319$	9.46410	−	9.46410i	0.529888	−	0.529888i
$320$	1.23205	+	1.86603i	0.0688737	+	0.104314i
$321$	−23.2583	+	13.4282i	−1.29815	+	0.749489i
$322$	−12.0000	+	12.0000i	−0.668734	+	0.668734i
$323$	−27.6603	+	27.6603i	−1.53906	+	1.53906i
$324$	5.33013	+	9.23205i	0.296118	+	0.512892i
$325$	9.85641	−	7.39230i	0.546735	−	0.410051i
$326$	−3.06218	−	1.76795i	−0.169598	−	0.0979176i
$327$			2.00000i			0.110600i
$328$	3.23205	−	5.59808i	0.178460	−	0.309102i
$329$	21.4641	+	12.3923i	1.18335	+	0.683210i
$330$	8.46410	+	1.73205i	0.465933	+	0.0953463i
$331$	0.830127	−	3.09808i	0.0456279	−	0.170286i	−0.939352	−	0.342954i	$-0.888572\pi$
$331$	0.830127	−	3.09808i	0.0456279	−	0.170286i	0.984980	+	0.172669i	$0.0552390\pi$
$332$	−11.3923	−	11.3923i	−0.625234	−	0.625234i
$333$	−3.66025	−	2.53590i	−0.200581	−	0.138966i
$334$			20.7321i			1.13441i
$335$	−9.29423	−	8.24167i	−0.507798	−	0.450291i
$336$	−4.73205	−	2.73205i	−0.258155	−	0.149046i
$337$	7.56218	−	2.02628i	0.411938	−	0.110378i	−0.0468974	−	0.998900i	$-0.514933\pi$
$337$	7.56218	−	2.02628i	0.411938	−	0.110378i	0.458835	+	0.888521i	$0.348267\pi$
$338$	6.00000	+	3.46410i	0.326357	+	0.188422i
$339$	8.19615	−	8.19615i	0.445154	−	0.445154i
$340$	7.63397	+	11.5622i	0.414010	+	0.627047i
$341$	−13.6603	−	13.6603i	−0.739744	−	0.739744i
$342$	−4.46410	−	1.19615i	−0.241391	−	0.0646805i
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	11.0000			0.593080
$345$	19.3923	+	17.1962i	1.04405	+	0.925810i
$346$	−23.4904	+	6.29423i	−1.26285	+	0.338380i
$347$		−	19.8564i		−	1.06595i	−0.846132	−	0.532974i	$-0.821074\pi$
$347$		−	19.8564i		−	1.06595i	0.846132	−	0.532974i	$-0.178926\pi$
$348$	6.46410	+	11.1962i	0.346512	+	0.600177i
$349$	−31.0981	+	17.9545i	−1.66464	+	0.961081i	−0.694188	+	0.719793i	$0.744236\pi$
$349$	−31.0981	+	17.9545i	−1.66464	+	0.961081i	−0.970454	+	0.241288i	$0.922430\pi$
$350$	−13.1244	+	5.26795i	−0.701526	+	0.281584i
$351$	−2.79423	−	10.4282i	−0.149145	−	0.556616i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	−16.3923	−	28.3923i	−0.872474	−	1.51117i	−0.859429	−	0.511255i	$-0.829181\pi$
$353$	−16.3923	−	28.3923i	−0.872474	−	1.51117i	−0.0130453	−	0.999915i	$-0.504153\pi$
$354$	3.09808	+	5.36603i	0.164661	+	0.285201i
$355$	−6.53590	+	0.392305i	−0.346889	+	0.0208214i
$356$	1.19615	+	1.19615i	0.0633960	+	0.0633960i
$357$	−29.3205	−	16.9282i	−1.55181	−	0.895936i
$358$	14.1962	+	3.80385i	0.750290	+	0.201040i
$359$		−	3.39230i		−	0.179039i	−0.995985	−	0.0895195i	$-0.971467\pi$
$359$		−	3.39230i		−	0.179039i	0.995985	−	0.0895195i	$-0.0285331\pi$
$360$	−0.732051	+	1.46410i	−0.0385825	+	0.0771649i
$361$	−18.0622	+	10.4282i	−0.950641	+	0.548853i
$362$			13.8038i			0.725514i
$363$	3.50000	+	13.0622i	0.183702	+	0.685587i
$364$	4.92820	+	4.92820i	0.258308	+	0.258308i
$365$		0			0
$366$	1.73205	−	3.00000i	0.0905357	−	0.156813i
$367$	−9.32051	−	34.7846i	−0.486527	−	1.81574i	−0.573086	−	0.819495i	$-0.694254\pi$
$367$	−9.32051	−	34.7846i	−0.486527	−	1.81574i	0.0865595	−	0.996247i	$-0.472413\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$	4.73205			0.246341
$370$	−0.303848	+	13.5981i	−0.0157963	+	0.706930i
$371$	14.2487			0.739756
$372$	16.1603	−	9.33013i	0.837870	−	0.483745i
$373$	1.37564	+	5.13397i	0.0712282	+	0.265827i	0.992352	−	0.123443i	$-0.0393938\pi$
$373$	1.37564	+	5.13397i	0.0712282	+	0.265827i	−0.921123	+	0.389271i	$0.872727\pi$
$374$	6.19615	−	10.7321i	0.320395	−	0.554941i
$375$	9.23205	+	19.5263i	0.476741	+	1.00833i
$376$	−6.19615	−	6.19615i	−0.319542	−	0.319542i
$377$	−4.26795	−	15.9282i	−0.219811	−	0.820344i
$378$			12.3923i			0.637391i
$379$	12.5885	−	7.26795i	0.646626	−	0.373329i	−0.140537	−	0.990075i	$-0.544883\pi$
$379$	12.5885	−	7.26795i	0.646626	−	0.373329i	0.787162	+	0.616746i	$0.211549\pi$
$380$	4.46410	+	13.3923i	0.229004	+	0.687011i
$381$		−	17.6603i		−	0.904762i
$382$	2.50000	+	0.669873i	0.127911	+	0.0342737i
$383$	13.3923	+	7.73205i	0.684315	+	0.395089i	0.801479	−	0.598023i	$-0.204047\pi$
$383$	13.3923	+	7.73205i	0.684315	+	0.395089i	−0.117164	+	0.993113i	$0.537380\pi$
$384$	1.36603	+	1.36603i	0.0697097	+	0.0697097i
$385$	9.46410	+	8.39230i	0.482335	+	0.427711i
$386$	0.169873	+	0.294229i	0.00864631	+	0.0149758i
$387$	4.02628	+	6.97372i	0.204667	+	0.354494i
$388$	−0.732051	+	1.26795i	−0.0371642	+	0.0643704i
$389$	0.901924	+	3.36603i	0.0457294	+	0.170664i	0.985014	−	0.172475i	$-0.0551764\pi$
$389$	0.901924	+	3.36603i	0.0457294	+	0.170664i	−0.939285	+	0.343139i	$0.888510\pi$
$390$	7.06218	−	7.96410i	0.357607	−	0.403278i
$391$	32.1962	−	18.5885i	1.62823	−	0.940059i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$			1.46410i			0.0738542i
$394$	−7.86603	+	2.10770i	−0.396285	+	0.106184i
$395$	−10.4904	+	11.8301i	−0.527828	+	0.595238i
$396$	1.46410			0.0735739
$397$	−2.24167	−	2.24167i	−0.112506	−	0.112506i	0.648613	−	0.761119i	$-0.275350\pi$
$397$	−2.24167	−	2.24167i	−0.112506	−	0.112506i	−0.761119	+	0.648613i	$0.775350\pi$
$398$	−20.1603	−	5.40192i	−1.01054	−	0.270774i
$399$	−24.3923	−	24.3923i	−1.22114	−	1.22114i
$400$	4.96410	−	0.598076i	0.248205	−	0.0299038i
$401$	−16.1244	+	16.1244i	−0.805212	+	0.805212i	−0.983905	−	0.178693i	$-0.942813\pi$
$401$	−16.1244	+	16.1244i	−0.805212	+	0.805212i	0.178693	+	0.983905i	$0.442813\pi$
$402$	−9.29423	−	5.36603i	−0.463554	−	0.267633i
$403$	−22.9904	+	6.16025i	−1.14523	+	0.306864i
$404$	−0.169873	−	0.0980762i	−0.00845150	−	0.00487947i
$405$	23.7942	−	1.42820i	1.18234	−	0.0709680i
$406$			18.9282i			0.939391i
$407$	11.0000	−	5.19615i	0.545250	−	0.257564i
$408$	8.46410	+	8.46410i	0.419035	+	0.419035i
$409$	−7.10770	+	26.5263i	−0.351453	+	1.31164i	0.533437	+	0.845840i	$0.320900\pi$
$409$	−7.10770	+	26.5263i	−0.351453	+	1.31164i	−0.884890	+	0.465800i	$0.845767\pi$
$410$	−7.96410	−	12.0622i	−0.393319	−	0.595709i
$411$	4.73205	+	2.73205i	0.233415	+	0.134762i
$412$	−3.09808	+	5.36603i	−0.152631	+	0.264365i
$413$			9.07180i			0.446394i
$414$	3.80385	+	2.19615i	0.186949	+	0.107935i
$415$	−34.1769	+	11.3923i	−1.67768	+	0.559226i
$416$	−1.23205	−	2.13397i	−0.0604063	−	0.104627i
$417$	−14.9282	+	14.9282i	−0.731037	+	0.731037i
$418$	8.92820	−	8.92820i	0.436693	−	0.436693i
$419$	12.4186	−	7.16987i	0.606688	−	0.350271i	−0.164980	−	0.986297i	$-0.552756\pi$
$419$	12.4186	−	7.16987i	0.606688	−	0.350271i	0.771668	+	0.636026i	$0.219423\pi$
$420$	−10.1962	+	6.73205i	−0.497521	+	0.328490i
$421$	−8.66025	+	8.66025i	−0.422075	+	0.422075i	−0.885918	−	0.463843i	$-0.846470\pi$
$421$	−8.66025	+	8.66025i	−0.422075	+	0.422075i	0.463843	+	0.885918i	$0.346470\pi$
$422$	−3.46410	+	2.00000i	−0.168630	+	0.0973585i
$423$	1.66025	−	6.19615i	0.0807243	−	0.301267i
$424$	−4.86603	−	1.30385i	−0.236315	−	0.0633204i
$425$	30.7583	−	3.70577i	1.49200	−	0.179756i
$426$	−5.46410	+	1.46410i	−0.264737	+	0.0709360i
$427$	4.39230	−	2.53590i	0.212559	−	0.122721i
$428$	13.4282	+	3.59808i	0.649077	+	0.173920i
$429$	−9.19615	−	2.46410i	−0.443994	−	0.118968i
$430$	11.0000	−	22.0000i	0.530467	−	1.06093i
$431$	−4.10770	−	15.3301i	−0.197861	−	0.738426i	−0.991508	−	0.130048i	$-0.958487\pi$
$431$	−4.10770	−	15.3301i	−0.197861	−	0.738426i	0.793647	−	0.608379i	$-0.208180\pi$
$432$	1.13397	−	4.23205i	0.0545584	−	0.203615i
$433$	3.19615	+	3.19615i	0.153597	+	0.153597i	0.779723	−	0.626125i	$-0.215360\pi$
$433$	3.19615	+	3.19615i	0.153597	+	0.153597i	−0.626125	+	0.779723i	$0.715360\pi$
$434$	27.3205			1.31143
$435$	28.8564	−	1.73205i	1.38356	−	0.0830455i
$436$	0.732051	−	0.732051i	0.0350589	−	0.0350589i
$437$	36.5885	−	9.80385i	1.75026	−	0.468982i
$438$		0			0
$439$	0.866025	−	0.232051i	0.0413331	−	0.0110752i	−0.238093	−	0.971242i	$-0.576522\pi$
$439$	0.866025	−	0.232051i	0.0413331	−	0.0110752i	0.279426	+	0.960167i	$0.409856\pi$
$440$	−2.46410	−	3.73205i	−0.117471	−	0.177919i
$441$	0.366025	−	0.633975i	0.0174298	−	0.0301893i
$442$	−7.63397	−	13.2224i	−0.363111	−	0.628927i
$443$	18.7583	−	18.7583i	0.891235	−	0.891235i	−0.103404	−	0.994639i	$-0.532974\pi$
$443$	18.7583	−	18.7583i	0.891235	−	0.891235i	0.994639	+	0.103404i	$0.0329735\pi$
$444$	2.09808	+	11.5622i	0.0995703	+	0.548717i
$445$	3.58846	−	1.19615i	0.170109	−	0.0567031i
$446$	17.6603	+	4.73205i	0.836237	+	0.224069i
$447$	−42.4186	+	11.3660i	−2.00633	+	0.537595i
$448$	0.732051	+	2.73205i	0.0345861	+	0.129077i
$449$	−0.428203	−	1.59808i	−0.0202082	−	0.0754179i	0.955085	−	0.296331i	$-0.0957630\pi$
$449$	−0.428203	−	1.59808i	−0.0202082	−	0.0754179i	−0.975294	+	0.220913i	$0.929096\pi$
$450$	2.19615	+	2.92820i	0.103528	+	0.138037i
$451$	−6.46410	+	11.1962i	−0.304383	+	0.527206i
$452$	−6.00000			−0.282216
$453$	1.59808	−	5.96410i	0.0750842	−	0.280218i
$454$		−	2.66025i		−	0.124852i
$455$	14.7846	−	4.92820i	0.693113	−	0.231038i
$456$	6.09808	+	10.5622i	0.285569	+	0.494619i
$457$	−13.3923	+	23.1962i	−0.626466	+	1.08507i	0.361790	+	0.932260i	$0.382166\pi$
$457$	−13.3923	+	23.1962i	−0.626466	+	1.08507i	−0.988255	+	0.152811i	$0.951168\pi$
$458$	−17.6603			−0.825209
$459$	7.02628	−	26.2224i	0.327959	−	1.22396i
$460$	−0.803848	−	13.3923i	−0.0374796	−	0.624419i
$461$	−4.53590	+	16.9282i	−0.211258	+	0.788425i	0.776193	+	0.630496i	$0.217148\pi$
$461$	−4.53590	+	16.9282i	−0.211258	+	0.788425i	−0.987450	+	0.157929i	$0.949518\pi$
$462$	9.46410	+	5.46410i	0.440310	+	0.254213i
$463$	−7.22243	−	4.16987i	−0.335655	−	0.193790i	0.322694	−	0.946503i	$-0.395412\pi$
$463$	−7.22243	−	4.16987i	−0.335655	−	0.193790i	−0.658349	+	0.752713i	$0.728745\pi$
$464$	1.73205	−	6.46410i	0.0804084	−	0.300088i
$465$	−2.50000	−	41.6506i	−0.115935	−	1.93150i
$466$	5.80385	−	21.6603i	0.268858	−	1.00339i
$467$	29.9282			1.38491			0.692456	−	0.721460i	$-0.256529\pi$
$467$	29.9282			1.38491			0.692456	+	0.721460i	$0.256529\pi$
$468$	0.901924	−	1.56218i	0.0416914	−	0.0722117i
$469$	−7.85641	−	13.6077i	−0.362775	−	0.628345i
$470$	−18.5885	+	6.19615i	−0.857422	+	0.285807i
$471$			39.2487i			1.80849i
$472$	0.830127	−	3.09808i	0.0382097	−	0.142601i
$473$	−22.0000			−1.01156
$474$	−6.83013	+	11.8301i	−0.313718	+	0.543376i
$475$	31.2487	+	4.46410i	1.43379	+	0.204827i
$476$	4.53590	+	16.9282i	0.207903	+	0.775903i
$477$	−0.954483	−	3.56218i	−0.0437028	−	0.163101i
$478$	−14.8301	+	3.97372i	−0.678314	+	0.181754i
$479$	−3.96410	−	1.06218i	−0.181124	−	0.0485321i	0.167117	−	0.985937i	$-0.446554\pi$
$479$	−3.96410	−	1.06218i	−0.181124	−	0.0485321i	−0.348241	+	0.937405i	$0.613221\pi$
$480$	4.09808	−	1.36603i	0.187051	−	0.0623502i
$481$	1.23205	−	14.9378i	0.0561767	−	0.681106i
$482$	−13.1962	+	13.1962i	−0.601068	+	0.601068i
$483$	16.3923	+	28.3923i	0.745876	+	1.29189i
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	1.80385	+	2.73205i	0.0819085	+	0.124056i
$486$	7.19615	−	1.92820i	0.326424	−	0.0874651i
$487$	41.4641			1.87892			0.939459	−	0.342662i	$-0.111328\pi$
$487$	41.4641			1.87892			0.939459	+	0.342662i	$0.111328\pi$
$488$	−1.73205	+	0.464102i	−0.0784063	+	0.0210089i
$489$	−4.83013	+	4.83013i	−0.218426	+	0.218426i
$490$	−2.23205	+	0.133975i	−0.100834	+	0.00605236i
$491$	−8.19615			−0.369887			−0.184944	−	0.982749i	$-0.559210\pi$
$491$	−8.19615			−0.369887			−0.184944	+	0.982749i	$0.559210\pi$
$492$	−8.83013	−	8.83013i	−0.398093	−	0.398093i
$493$	10.7321	−	40.0526i	0.483347	−	1.80388i
$494$	−4.02628	−	15.0263i	−0.181151	−	0.676064i
$495$	1.46410	−	2.92820i	0.0658065	−	0.131613i
$496$	−9.33013	−	2.50000i	−0.418935	−	0.112253i
$497$	−8.00000	−	2.14359i	−0.358849	−	0.0961533i
$498$	−26.9545	+	15.5622i	−1.20786	+	0.697358i
$499$	−15.1962	+	4.07180i	−0.680273	+	0.182279i	−0.582378	−	0.812918i	$-0.697878\pi$
$499$	−15.1962	+	4.07180i	−0.680273	+	0.182279i	−0.0978952	+	0.995197i	$0.531211\pi$
$500$	3.76795	−	10.5263i	0.168508	−	0.470750i
$501$	38.6865	+	10.3660i	1.72839	+	0.463120i
$502$	−2.09808	+	7.83013i	−0.0936417	+	0.349476i
$503$	−2.49038	+	1.43782i	−0.111041	+	0.0641093i	−0.554492	−	0.832189i	$-0.687087\pi$
$503$	−2.49038	+	1.43782i	−0.111041	+	0.0641093i	0.443451	+	0.896299i	$0.353754\pi$
$504$	−1.46410	+	1.46410i	−0.0652163	+	0.0652163i
$505$	−0.366025	+	0.241670i	−0.0162879	+	0.0107542i
$506$	−10.3923	+	6.00000i	−0.461994	+	0.266733i
$507$	9.46410	−	9.46410i	0.420316	−	0.420316i
$508$	−6.46410	+	6.46410i	−0.286798	+	0.286798i
$509$	5.07180	+	8.78461i	0.224803	+	0.389371i	0.956260	−	0.292517i	$-0.0944927\pi$
$509$	5.07180	+	8.78461i	0.224803	+	0.389371i	−0.731457	+	0.681888i	$0.761159\pi$
$510$	25.3923	−	8.46410i	1.12439	−	0.374797i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	13.8301	−	23.9545i	0.610615	−	1.05762i
$514$	0.294229	+	0.169873i	0.0129779	+	0.00749278i
$515$	7.63397	+	11.5622i	0.336393	+	0.509490i
$516$	5.50000	−	20.5263i	0.242124	−	0.903619i
$517$	12.3923	+	12.3923i	0.545013	+	0.545013i
$518$	−5.80385	+	16.1962i	−0.255006	+	0.711618i
$519$			46.9808i			2.06223i
$520$	−5.50000	+	0.330127i	−0.241191	+	0.0144770i
$521$	−17.0885	−	9.86603i	−0.748659	−	0.432238i	0.0765502	−	0.997066i	$-0.475609\pi$
$521$	−17.0885	−	9.86603i	−0.748659	−	0.432238i	−0.825209	+	0.564827i	$0.808943\pi$
$522$	4.73205	−	1.26795i	0.207116	−	0.0554966i
$523$	−16.6244	−	9.59808i	−0.726932	−	0.419695i	0.0903665	−	0.995909i	$-0.471196\pi$
$523$	−16.6244	−	9.59808i	−0.726932	−	0.419695i	−0.817299	+	0.576214i	$0.804529\pi$
$524$	0.535898	−	0.535898i	0.0234108	−	0.0234108i
$525$	3.26795	+	27.1244i	0.142625	+	1.18380i
$526$	0.0717968	+	0.0717968i	0.00313049	+	0.00313049i
$527$	−57.8109	−	15.4904i	−2.51828	−	0.674772i
$528$	−2.73205	−	2.73205i	−0.118897	−	0.118897i
$529$	−13.0000			−0.565217
$530$	−7.47372	+	8.42820i	−0.324638	+	0.366098i
$531$	2.26795	−	0.607695i	0.0984206	−	0.0263717i
$532$			17.8564i			0.774173i
$533$	7.96410	+	13.7942i	0.344964	+	0.597494i
$534$	2.83013	−	1.63397i	0.122472	−	0.0707090i
$535$	20.6244	−	23.2583i	0.891669	−	1.00555i
$536$	1.43782	+	5.36603i	0.0621045	+	0.231777i
$537$	14.1962	−	24.5885i	0.612609	−	1.06107i
$538$	−3.29423	−	5.70577i	−0.142024	−	0.245993i
$539$	1.00000	+	1.73205i	0.0430730	+	0.0746047i
$540$	−7.33013	−	6.50000i	−0.315438	−	0.279715i
$541$	5.07180	+	5.07180i	0.218054	+	0.218054i	0.807678	−	0.589624i	$-0.200724\pi$
$541$	5.07180	+	5.07180i	0.218054	+	0.218054i	−0.589624	+	0.807678i	$0.700724\pi$
$542$	−9.06218	−	5.23205i	−0.389254	−	0.224736i
$543$	25.7583	+	6.90192i	1.10540	+	0.296190i
$544$		−	6.19615i		−	0.265658i
$545$	−0.732051	−	2.19615i	−0.0313576	−	0.0940728i
$546$	11.6603	−	6.73205i	0.499013	−	0.288105i
$547$		−	17.9808i		−	0.768802i	−0.923166	−	0.384401i	$-0.874408\pi$
$547$		−	17.9808i		−	0.768802i	0.923166	−	0.384401i	$-0.125592\pi$
$548$	−0.732051	−	2.73205i	−0.0312717	−	0.116707i
$549$	−0.928203	−	0.928203i	−0.0396147	−	0.0396147i
$550$	−9.92820	+	1.19615i	−0.423340	+	0.0510041i
$551$	21.1244	−	36.5885i	0.899928	−	1.55872i
$552$	−3.00000	−	11.1962i	−0.127688	−	0.476540i
$553$	−17.3205	+	10.0000i	−0.736543	+	0.425243i
$554$	16.6603			0.707826
$555$	25.2224	+	7.36603i	1.07063	+	0.312670i
$556$	10.9282			0.463459
$557$	32.3827	−	18.6962i	1.37210	−	0.792181i	0.380906	−	0.924614i	$-0.375612\pi$
$557$	32.3827	−	18.6962i	1.37210	−	0.792181i	0.991192	+	0.132432i	$0.0422787\pi$
$558$	−1.83013	−	6.83013i	−0.0774755	−	0.289142i
$559$	−13.5526	+	23.4737i	−0.573212	+	0.992833i
$560$	6.19615	+	1.26795i	0.261835	+	0.0535806i
$561$	−16.9282	−	16.9282i	−0.714709	−	0.714709i
$562$	−0.624356	−	2.33013i	−0.0263369	−	0.0982905i
$563$			15.6077i			0.657786i	0.944367	+	0.328893i	$0.106676\pi$
$563$			15.6077i			0.657786i	−0.944367	+	0.328893i	$0.893324\pi$
$564$	−14.6603	+	8.46410i	−0.617308	+	0.356403i
$565$	−6.00000	+	12.0000i	−0.252422	+	0.504844i
$566$		−	13.0000i		−	0.546431i
$567$	29.1244	+	7.80385i	1.22311	+	0.327731i
$568$	2.53590	+	1.46410i	0.106404	+	0.0614323i
$569$	−16.3660	−	16.3660i	−0.686099	−	0.686099i	0.275268	−	0.961368i	$-0.411233\pi$
$569$	−16.3660	−	16.3660i	−0.686099	−	0.686099i	−0.961368	+	0.275268i	$0.911233\pi$
$570$	27.2224	−	1.63397i	1.14022	−	0.0684397i
$571$	20.7583	+	35.9545i	0.868709	+	1.50465i	0.863317	+	0.504663i	$0.168383\pi$
$571$	20.7583	+	35.9545i	0.868709	+	1.50465i	0.00539254	+	0.999985i	$0.498283\pi$
$572$	2.46410	+	4.26795i	0.103029	+	0.178452i
$573$	2.50000	−	4.33013i	0.104439	−	0.180894i
$574$	−4.73205	−	17.6603i	−0.197512	−	0.737125i
$575$	−27.5885	−	11.7846i	−1.15052	−	0.491452i
$576$	0.633975	−	0.366025i	0.0264156	−	0.0152511i
$577$	−2.53590	−	4.39230i	−0.105571	−	0.182854i	0.808400	−	0.588633i	$-0.200334\pi$
$577$	−2.53590	−	4.39230i	−0.105571	−	0.182854i	−0.913971	+	0.405779i	$0.867000\pi$
$578$		−	21.3923i		−	0.889803i
$579$	0.633975	−	0.169873i	0.0263471	−	0.00705968i
$580$	−11.1962	−	9.92820i	−0.464895	−	0.412246i
$581$	−45.5692			−1.89053
$582$	2.00000	+	2.00000i	0.0829027	+	0.0829027i
$583$	9.73205	+	2.60770i	0.403060	+	0.108000i
$584$		0			0
$585$	−2.22243	−	3.36603i	−0.0918862	−	0.139168i
$586$	2.29423	−	2.29423i	0.0947737	−	0.0947737i
$587$	−12.4019	−	7.16025i	−0.511882	−	0.295535i	0.221725	−	0.975109i	$-0.428831\pi$
$587$	−12.4019	−	7.16025i	−0.511882	−	0.295535i	−0.733607	+	0.679574i	$0.762165\pi$
$588$	−1.86603	+	0.500000i	−0.0769536	+	0.0206197i
$589$	−52.8109	−	30.4904i	−2.17603	−	1.25633i
$590$	−5.36603	−	4.75833i	−0.220916	−	0.195897i
$591$			15.7321i			0.647130i
$592$	3.46410	−	5.00000i	0.142374	−	0.205499i
$593$	−18.6603	−	18.6603i	−0.766285	−	0.766285i	0.211166	−	0.977450i	$-0.432274\pi$
$593$	−18.6603	−	18.6603i	−0.766285	−	0.766285i	−0.977450	+	0.211166i	$0.932274\pi$
$594$	−2.26795	+	8.46410i	−0.0930551	+	0.347286i
$595$	38.3923	+	7.85641i	1.57393	+	0.322081i
$596$	19.6865	+	11.3660i	0.806392	+	0.465571i
$597$	−20.1603	+	34.9186i	−0.825104	+	1.42912i
$598$			14.7846i			0.604588i
$599$	−39.6051	−	22.8660i	−1.61822	−	0.934280i	−0.987380	−	0.158368i	$-0.949377\pi$
$599$	−39.6051	−	22.8660i	−1.61822	−	0.934280i	−0.630841	−	0.775912i	$-0.717290\pi$
$600$	1.36603	−	9.56218i	0.0557678	−	0.390374i
$601$	13.7942	+	23.8923i	0.562678	+	0.974587i	0.997262	+	0.0739558i	$0.0235624\pi$
$601$	13.7942	+	23.8923i	0.562678	+	0.974587i	−0.434583	+	0.900632i	$0.643104\pi$
$602$	22.0000	−	22.0000i	0.896653	−	0.896653i
$603$	−2.87564	+	2.87564i	−0.117105	+	0.117105i
$604$	−2.76795	+	1.59808i	−0.112626	+	0.0650248i
$605$	−8.62436	−	13.0622i	−0.350630	−	0.531053i
$606$	−0.267949	+	0.267949i	−0.0108847	+	0.0108847i
$607$	−12.1699	+	7.02628i	−0.493960	+	0.285188i	−0.726216	−	0.687467i	$-0.758723\pi$
$607$	−12.1699	+	7.02628i	−0.493960	+	0.285188i	0.232256	+	0.972655i	$0.425389\pi$
$608$	1.63397	−	6.09808i	0.0662664	−	0.247310i
$609$	35.3205	+	9.46410i	1.43126	+	0.383505i
$610$	−0.803848	+	3.92820i	−0.0325468	+	0.159048i
$611$	20.8564	−	5.58846i	0.843760	−	0.226085i
$612$	3.92820	−	2.26795i	0.158788	−	0.0916764i
$613$	28.4186	+	7.61474i	1.14782	+	0.307556i	0.782089	−	0.623166i	$-0.214154\pi$
$613$	28.4186	+	7.61474i	1.14782	+	0.307556i	0.365726	+	0.930722i	$0.380821\pi$
$614$	−21.0622	−	5.64359i	−0.850000	−	0.227757i
$615$	−26.4904	+	8.83013i	−1.06820	+	0.356065i
$616$	−1.46410	−	5.46410i	−0.0589903	−	0.220155i
$617$	−6.41858	+	23.9545i	−0.258402	+	0.964371i	0.707763	+	0.706450i	$0.249704\pi$
$617$	−6.41858	+	23.9545i	−0.258402	+	0.964371i	−0.966166	+	0.257922i	$0.916962\pi$
$618$	8.46410	+	8.46410i	0.340476	+	0.340476i
$619$	−13.0718			−0.525400			−0.262700	−	0.964878i	$-0.584613\pi$
$619$	−13.0718			−0.525400			−0.262700	+	0.964878i	$0.584613\pi$
$620$	−14.3301	+	16.1603i	−0.575512	+	0.649011i
$621$	−18.5885	+	18.5885i	−0.745929	+	0.745929i
$622$	−15.2583	+	4.08846i	−0.611803	+	0.163932i
$623$	4.78461			0.191691
$624$	−4.59808	+	1.23205i	−0.184070	+	0.0493215i
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$	8.73205	−	15.1244i	0.349003	−	0.604491i
$627$	−12.1962	−	21.1244i	−0.487067	−	0.843626i
$628$	14.3660	−	14.3660i	0.573267	−	0.573267i
$629$	21.4641	−	30.9808i	0.855830	−	1.23528i
$630$	1.46410	+	4.39230i	0.0583312	+	0.174994i
$631$	−5.06218	−	1.35641i	−0.201522	−	0.0539977i	0.156646	−	0.987655i	$-0.449932\pi$
$631$	−5.06218	−	1.35641i	−0.201522	−	0.0539977i	−0.358168	+	0.933657i	$0.616599\pi$
$632$	6.83013	−	1.83013i	0.271688	−	0.0727985i
$633$	2.00000	+	7.46410i	0.0794929	+	0.296671i
$634$	7.18653	+	26.8205i	0.285414	+	1.06518i
$635$	6.46410	+	19.3923i	0.256520	+	0.769560i
$636$	−4.86603	+	8.42820i	−0.192950	+	0.334200i
$637$	2.46410			0.0976313
$638$	−3.46410	+	12.9282i	−0.137145	+	0.511832i
$639$			2.14359i			0.0847992i
$640$	−2.00000	−	1.00000i	−0.0790569	−	0.0395285i
$641$	−21.9904	−	38.0885i	−0.868568	−	1.50440i	−0.863460	−	0.504417i	$-0.831708\pi$
$641$	−21.9904	−	38.0885i	−0.868568	−	1.50440i	−0.00510745	−	0.999987i	$-0.501626\pi$
$642$	13.4282	−	23.2583i	0.529969	−	0.917933i
$643$	−3.73205			−0.147178			−0.0735889	−	0.997289i	$-0.523445\pi$
$643$	−3.73205			−0.147178			−0.0735889	+	0.997289i	$0.523445\pi$
$644$	4.39230	−	16.3923i	0.173081	−	0.645947i
$645$	−35.5526	−	31.5263i	−1.39988	−	1.24135i
$646$	10.1244	−	37.7846i	0.398337	−	1.48662i
$647$	33.2942	+	19.2224i	1.30893	+	0.755712i	0.981918	−	0.189308i	$-0.0606244\pi$
$647$	33.2942	+	19.2224i	1.30893	+	0.755712i	0.327013	+	0.945020i	$0.393958\pi$
$648$	−9.23205	−	5.33013i	−0.362669	−	0.209387i
$649$	−1.66025	+	6.19615i	−0.0651707	+	0.243220i
$650$	−4.83975	+	11.3301i	−0.189830	+	0.444404i
$651$	13.6603	−	50.9808i	0.535388	−	1.99809i
$652$	3.53590			0.138476
$653$	7.62436	−	13.2058i	0.298364	−	0.516782i	−0.677398	−	0.735617i	$-0.736892\pi$
$653$	7.62436	−	13.2058i	0.298364	−	0.516782i	0.975762	+	0.218835i	$0.0702257\pi$
$654$	−1.00000	−	1.73205i	−0.0391031	−	0.0677285i
$655$	−0.535898	−	1.60770i	−0.0209393	−	0.0628178i
$656$			6.46410i			0.252381i
$657$		0			0
$658$	−24.7846			−0.966205
$659$	20.3923	−	35.3205i	0.794371	−	1.37589i	−0.128866	−	0.991662i	$-0.541134\pi$
$659$	20.3923	−	35.3205i	0.794371	−	1.37589i	0.923238	−	0.384230i	$-0.125533\pi$
$660$	−8.19615	+	2.73205i	−0.319035	+	0.106345i
$661$	6.41858	+	23.9545i	0.249654	+	0.931721i	0.970987	+	0.239133i	$0.0768631\pi$
$661$	6.41858	+	23.9545i	0.249654	+	0.931721i	−0.721333	+	0.692589i	$0.756470\pi$
$662$	0.830127	+	3.09808i	0.0322638	+	0.120410i
$663$	−28.4904	+	7.63397i	−1.10647	+	0.296479i
$664$	15.5622	+	4.16987i	0.603930	+	0.161822i
$665$	35.7128	+	17.8564i	1.38488	+	0.692442i
$666$	4.43782	+	0.366025i	0.171962	+	0.0141832i
$667$	−28.3923	+	28.3923i	−1.09935	+	1.09935i
$668$	−10.3660	−	17.9545i	−0.401074	−	0.694680i
$669$	17.6603	−	30.5885i	0.682785	−	1.18262i
$670$	12.1699	+	2.49038i	0.470163	+	0.0962118i
$671$	3.46410	−	0.928203i	0.133730	−	0.0358329i
$672$	5.46410			0.210782
$673$	30.4904	−	8.16987i	1.17532	−	0.314925i	0.382250	−	0.924059i	$-0.375149\pi$
$673$	30.4904	−	8.16987i	1.17532	−	0.314925i	0.793068	+	0.609133i	$0.208483\pi$
$674$	−5.53590	+	5.53590i	−0.213235	+	0.213235i
$675$	−20.3301	+	8.16025i	−0.782507	+	0.314088i
$676$	−6.92820			−0.266469
$677$	−11.3923	−	11.3923i	−0.437842	−	0.437842i	0.453443	−	0.891285i	$-0.350195\pi$
$677$	−11.3923	−	11.3923i	−0.437842	−	0.437842i	−0.891285	+	0.453443i	$0.850195\pi$
$678$	−3.00000	+	11.1962i	−0.115214	+	0.429986i
$679$	1.07180	+	4.00000i	0.0411318	+	0.153506i
$680$	−12.3923	−	6.19615i	−0.475223	−	0.237612i
$681$	−4.96410	−	1.33013i	−0.190225	−	0.0509706i
$682$	18.6603	+	5.00000i	0.714538	+	0.191460i
$683$	11.5981	−	6.69615i	0.443788	−	0.256221i	−0.261415	−	0.965226i	$-0.584189\pi$
$683$	11.5981	−	6.69615i	0.443788	−	0.256221i	0.705203	+	0.709005i	$0.250856\pi$
$684$	4.46410	−	1.19615i	0.170689	−	0.0457360i
$685$	−6.19615	−	1.26795i	−0.236743	−	0.0484458i
$686$	16.3923	+	4.39230i	0.625861	+	0.167699i
$687$	−8.83013	+	32.9545i	−0.336890	+	1.25729i
$688$	−9.52628	+	5.50000i	−0.363186	+	0.209686i
$689$	8.77757	−	8.77757i	0.334399	−	0.334399i
$690$	−25.3923	−	5.19615i	−0.966669	−	0.197814i
$691$	24.7583	−	14.2942i	0.941851	−	0.543778i	0.0513111	−	0.998683i	$-0.483660\pi$
$691$	24.7583	−	14.2942i	0.941851	−	0.543778i	0.890540	+	0.454905i	$0.150327\pi$
$692$	17.1962	−	17.1962i	0.653700	−	0.653700i
$693$	2.92820	−	2.92820i	0.111233	−	0.111233i
$694$	9.92820	+	17.1962i	0.376869	+	0.652757i
$695$	10.9282	−	21.8564i	0.414530	−	0.829061i
$696$	−11.1962	−	6.46410i	−0.424389	−	0.245021i
$697$			40.0526i			1.51710i
$698$	17.9545	−	31.0981i	0.679587	−	1.17708i
$699$	−37.5167	−	21.6603i	−1.41901	−	0.819266i
$700$	8.73205	−	11.1244i	0.330040	−	0.420461i
$701$	−1.50962	+	5.63397i	−0.0570175	+	0.212792i	−0.988557	−	0.150848i	$-0.951800\pi$
$701$	−1.50962	+	5.63397i	−0.0570175	+	0.212792i	0.931539	+	0.363640i	$0.118466\pi$
$702$	7.63397	+	7.63397i	0.288126	+	0.288126i
$703$	29.2942	−	24.8301i	1.10485	−	0.936486i
$704$			2.00000i			0.0753778i
$705$	2.26795	+	37.7846i	0.0854159	+	1.42305i
$706$	28.3923	+	16.3923i	1.06856	+	0.616933i
$707$	−0.535898	+	0.143594i	−0.0201545	+	0.00540039i
$708$	−5.36603	−	3.09808i	−0.201668	−	0.116433i
$709$	−20.0718	+	20.0718i	−0.753812	+	0.753812i	−0.975188	−	0.221376i	$-0.928945\pi$
$709$	−20.0718	+	20.0718i	−0.753812	+	0.753812i	0.221376	+	0.975188i	$0.428945\pi$
$710$	5.46410	−	3.60770i	0.205064	−	0.135394i
$711$	3.66025	+	3.66025i	0.137270	+	0.137270i
$712$	−1.63397	−	0.437822i	−0.0612358	−	0.0164081i
$713$	40.9808	+	40.9808i	1.53474	+	1.53474i
$714$	33.8564			1.26704
$715$	11.0000	−	0.660254i	0.411377	−	0.0246921i
$716$	−14.1962	+	3.80385i	−0.530535	+	0.142156i
$717$			29.6603i			1.10768i
$718$	1.69615	+	2.93782i	0.0632998	+	0.109639i
$719$	−44.4282	+	25.6506i	−1.65689	+	0.956607i	−0.682756	+	0.730646i	$0.739219\pi$
$719$	−44.4282	+	25.6506i	−1.65689	+	0.956607i	−0.974136	+	0.225961i	$0.927448\pi$
$720$	−0.0980762	−	1.63397i	−0.00365508	−	0.0608946i
$721$	4.53590	+	16.9282i	0.168926	+	0.630439i
$722$	10.4282	−	18.0622i	0.388098	−	0.672205i
$723$	18.0263	+	31.2224i	0.670405	+	1.16117i
$724$	−6.90192	−	11.9545i	−0.256508	−	0.444285i
$725$	−31.0526	+	12.4641i	−1.15326	+	0.462905i
$726$	−9.56218	−	9.56218i	−0.354886	−	0.354886i
$727$	35.1962	+	20.3205i	1.30535	+	0.753646i	0.981317	−	0.192399i	$-0.0616267\pi$
$727$	35.1962	+	20.3205i	1.30535	+	0.753646i	0.324036	+	0.946045i	$0.394960\pi$
$728$	−6.73205	−	1.80385i	−0.249506	−	0.0668550i
$729$			17.5885i			0.651424i
$730$		0			0
$731$	−59.0263	+	34.0788i	−2.18317	+	1.26045i
$732$			3.46410i			0.128037i
$733$	−11.2224	−	41.8827i	−0.414510	−	1.54697i	−0.785815	−	0.618461i	$-0.787756\pi$
$733$	−11.2224	−	41.8827i	−0.414510	−	1.54697i	0.371305	−	0.928511i	$-0.378910\pi$
$734$	25.4641	+	25.4641i	0.939897	+	0.939897i
$735$	−0.866025	+	4.23205i	−0.0319438	+	0.156102i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	−2.87564	−	10.7321i	−0.105926	−	0.395320i
$738$	−4.09808	+	2.36603i	−0.150852	+	0.0870946i
$739$	18.1962			0.669356			0.334678	−	0.942332i	$-0.391372\pi$
$739$	18.1962			0.669356			0.334678	+	0.942332i	$0.391372\pi$
$740$	−6.53590	−	11.9282i	−0.240264	−	0.438489i
$741$	−30.0526			−1.10401
$742$	−12.3397	+	7.12436i	−0.453006	+	0.261543i
$743$	−7.50962	−	28.0263i	−0.275501	−	1.02818i	−0.955505	−	0.294976i	$-0.904688\pi$
$743$	−7.50962	−	28.0263i	−0.275501	−	1.02818i	0.680004	−	0.733209i	$-0.261978\pi$
$744$	−9.33013	+	16.1603i	−0.342059	+	0.592464i
$745$	42.4186	−	28.0070i	1.55410	−	1.02610i
$746$	−3.75833	−	3.75833i	−0.137602	−	0.137602i
$747$	3.05256	+	11.3923i	0.111687	+	0.416823i
$748$			12.3923i			0.453108i
$749$	34.0526	−	19.6603i	1.24425	−	0.718370i
$750$	−17.7583	−	12.2942i	−0.648443	−	0.448922i
$751$			30.1769i			1.10117i	0.834779	+	0.550586i	$0.185596\pi$
$751$			30.1769i			1.10117i	−0.834779	+	0.550586i	$0.814404\pi$
$752$	8.46410	+	2.26795i	0.308654	+	0.0827036i
$753$	13.5622	+	7.83013i	0.494233	+	0.285346i
$754$	11.6603	+	11.6603i	0.424641	+	0.424641i
$755$	0.428203	+	7.13397i	0.0155839	+	0.259632i
$756$	−6.19615	−	10.7321i	−0.225352	−	0.390321i
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	0.669193	−	0.743089i	$-0.266640\pi$
$757$	−8.50000	−	14.7224i	−0.308938	−	0.535096i	−0.978130	+	0.207993i	$0.933307\pi$
$758$	−7.26795	+	12.5885i	−0.263984	+	0.457233i
$759$	6.00000	+	22.3923i	0.217786	+	0.812789i
$760$	−10.5622	−	9.36603i	−0.383130	−	0.339741i
$761$	−2.53590	+	1.46410i	−0.0919262	+	0.0530736i	−0.545258	−	0.838268i	$-0.683568\pi$
$761$	−2.53590	+	1.46410i	−0.0919262	+	0.0530736i	0.453332	+	0.891342i	$0.350235\pi$
$762$	8.83013	+	15.2942i	0.319882	+	0.554051i
$763$		−	2.92820i		−	0.106008i
$764$	−2.50000	+	0.669873i	−0.0904468	+	0.0242352i
$765$	−0.607695	−	10.1244i	−0.0219713	−	0.366047i
$766$	−15.4641			−0.558741
$767$	5.58846	+	5.58846i	0.201787	+	0.201787i
$768$	−1.86603	−	0.500000i	−0.0673344	−	0.0180422i
$769$	33.9282	+	33.9282i	1.22348	+	1.22348i	0.966386	+	0.257097i	$0.0827659\pi$
$769$	33.9282	+	33.9282i	1.22348	+	1.22348i	0.257097	+	0.966386i	$0.417234\pi$
$770$	−12.3923	−	2.53590i	−0.446588	−	0.0913874i
$771$	0.464102	−	0.464102i	0.0167142	−	0.0167142i
$772$	−0.294229	−	0.169873i	−0.0105895	−	0.00611386i
$773$	−15.6244	+	4.18653i	−0.561969	+	0.150579i	−0.528611	−	0.848864i	$-0.677287\pi$
$773$	−15.6244	+	4.18653i	−0.561969	+	0.150579i	−0.0333582	+	0.999443i	$0.510620\pi$
$774$	−6.97372	−	4.02628i	−0.250665	−	0.144722i
$775$	17.9904	+	44.8205i	0.646234	+	1.61000i
$776$		−	1.46410i		−	0.0525582i
$777$	27.3205	+	18.9282i	0.980118	+	0.679046i
$778$	−2.46410	−	2.46410i	−0.0883423	−	0.0883423i
$779$	−10.5622	+	39.4186i	−0.378429	+	1.41232i
$780$	−2.13397	+	10.4282i	−0.0764085	+	0.373390i
$781$	−5.07180	−	2.92820i	−0.181483	−	0.104779i
$782$	−18.5885	+	32.1962i	−0.664722	+	1.15133i
$783$			29.3205i			1.04783i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	−14.3660	−	43.0981i	−0.512745	−	1.53824i
$786$	−0.732051	−	1.26795i	−0.0261114	−	0.0452262i
$787$	−6.68653	+	6.68653i	−0.238349	+	0.238349i	−0.816166	−	0.577817i	$-0.803905\pi$
$787$	−6.68653	+	6.68653i	−0.238349	+	0.238349i	0.577817	+	0.816166i	$0.303905\pi$
$788$	5.75833	−	5.75833i	0.205132	−	0.205132i
$789$	0.169873	−	0.0980762i	0.00604764	−	0.00349161i
$790$	3.16987	−	15.4904i	0.112779	−	0.551123i
$791$	−12.0000	+	12.0000i	−0.426671	+	0.426671i
$792$	−1.26795	+	0.732051i	−0.0450546	+	0.0260123i
$793$	1.14359	−	4.26795i	0.0406102	−	0.151559i
$794$	3.06218	+	0.820508i	0.108673	+	0.0291187i
$795$	11.9904	+	18.1603i	0.425255	+	0.644078i
$796$	20.1603	−	5.40192i	0.714561	−	0.191466i
$797$	−19.0359	+	10.9904i	−0.674286	+	0.389299i	−0.797699	−	0.603056i	$-0.793949\pi$
$797$	−19.0359	+	10.9904i	−0.674286	+	0.389299i	0.123413	+	0.992355i	$0.460616\pi$
$798$	33.3205	+	8.92820i	1.17953	+	0.316055i
$799$	52.4449	+	14.0526i	1.85537	+	0.497144i
$800$	−4.00000	+	3.00000i	−0.141421	+	0.106066i
$801$	−0.320508	−	1.19615i	−0.0113246	−	0.0422640i
$802$	5.90192	−	22.0263i	0.208404	−	0.777775i
$803$		0			0
$804$	10.7321			0.378490
$805$	−28.3923	−	25.1769i	−1.00070	−	0.887370i
$806$	16.8301	−	16.8301i	0.592816	−	0.592816i
$807$	−12.2942	+	3.29423i	−0.432777	+	0.115962i
$808$	0.196152			0.00690062
$809$	−35.7224	+	9.57180i	−1.25593	+	0.336526i	−0.824626	−	0.565678i	$-0.808614\pi$
$809$	−35.7224	+	9.57180i	−1.25593	+	0.336526i	−0.431308	+	0.902205i	$0.641948\pi$
$810$	−19.8923	+	13.1340i	−0.698944	+	0.461481i
$811$	3.49038	−	6.04552i	0.122564	−	0.212287i	−0.798214	−	0.602374i	$-0.794222\pi$
$811$	3.49038	−	6.04552i	0.122564	−	0.212287i	0.920778	+	0.390087i	$0.127555\pi$
$812$	−9.46410	−	16.3923i	−0.332125	−	0.575257i
$813$	−14.2942	+	14.2942i	−0.501320	+	0.501320i
$814$	−6.92820	+	10.0000i	−0.242833	+	0.350500i
$815$	3.53590	−	7.07180i	0.123857	−	0.247714i
$816$	−11.5622	−	3.09808i	−0.404757	−	0.108454i
$817$	−67.0788	+	17.9737i	−2.34679	+	0.628821i
$818$	−7.10770	−	26.5263i	−0.248515	−	0.927470i
$819$	−1.32051	−	4.92820i	−0.0461423	−	0.172205i
$820$	12.9282	+	6.46410i	0.451472	+	0.225736i
$821$	10.5622	−	18.2942i	0.368623	−	0.638473i	−0.620728	−	0.784026i	$-0.713163\pi$
$821$	10.5622	−	18.2942i	0.368623	−	0.638473i	0.989350	+	0.145553i	$0.0464962\pi$
$822$	−5.46410			−0.190582
$823$	−8.97372	+	33.4904i	−0.312804	+	1.16740i	0.613212	+	0.789918i	$0.289877\pi$
$823$	−8.97372	+	33.4904i	−0.312804	+	1.16740i	−0.926016	+	0.377483i	$0.876790\pi$
$824$		−	6.19615i		−	0.215853i
$825$	−2.73205	+	19.1244i	−0.0951178	+	0.665825i
$826$	−4.53590	−	7.85641i	−0.157824	−	0.273359i
$827$	6.92820	−	12.0000i	0.240917	−	0.417281i	−0.720059	−	0.693913i	$-0.755885\pi$
$827$	6.92820	−	12.0000i	0.240917	−	0.417281i	0.960976	+	0.276632i	$0.0892184\pi$
$828$	−4.39230			−0.152643
$829$	12.4186	−	46.3468i	0.431315	−	1.60969i	−0.318418	−	0.947950i	$-0.603152\pi$
$829$	12.4186	−	46.3468i	0.431315	−	1.60969i	0.749733	−	0.661740i	$-0.230182\pi$
$830$	23.9019	−	26.9545i	0.829648	−	0.935604i
$831$	8.33013	−	31.0885i	0.288969	−	1.07845i
$832$	2.13397	+	1.23205i	0.0739823	+	0.0427137i
$833$	5.36603	+	3.09808i	0.185922	+	0.107342i
$834$	5.46410	−	20.3923i	0.189206	−	0.706128i
$835$	−46.2750	+	2.77757i	−1.60141	+	0.0961217i
$836$	−3.26795	+	12.1962i	−0.113024	+	0.421813i
$837$	42.3205			1.46281
$838$	−7.16987	+	12.4186i	−0.247679	+	0.428993i
$839$	−12.0622	−	20.8923i	−0.416433	−	0.721282i	0.579145	−	0.815225i	$-0.303386\pi$
$839$	−12.0622	−	20.8923i	−0.416433	−	0.721282i	−0.995578	+	0.0939421i	$0.970053\pi$
$840$	5.46410	−	10.9282i	0.188529	−	0.377059i
$841$			15.7846i			0.544297i
$842$	3.16987	−	11.8301i	0.109241	−	0.407693i
$843$	−4.66025			−0.160508
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	−6.92820	+	13.8564i	−0.238337	+	0.476675i
$846$	1.66025	+	6.19615i	0.0570807	+	0.213028i
$847$	−5.12436	−	19.1244i	−0.176075	−	0.657121i
$848$	4.86603	−	1.30385i	0.167100	−	0.0447743i
$849$	−24.2583	−	6.50000i	−0.832544	−	0.223079i
$850$	−24.7846	+	18.5885i	−0.850105	+	0.637579i
$851$	−33.0000	+	15.5885i	−1.13123	+	0.534365i
$852$	4.00000	−	4.00000i	0.137038	−	0.137038i
$853$	−3.03590	−	5.25833i	−0.103947	−	0.180042i	0.809360	−	0.587312i	$-0.199814\pi$
$853$	−3.03590	−	5.25833i	−0.103947	−	0.180042i	−0.913308	+	0.407271i	$0.866481\pi$
$854$	−2.53590	+	4.39230i	−0.0867767	+	0.150302i
$855$	2.07180	−	10.1244i	0.0708540	−	0.346246i
$856$	−13.4282	+	3.59808i	−0.458967	+	0.122980i
$857$	−10.7321			−0.366600			−0.183300	−	0.983057i	$-0.558678\pi$
$857$	−10.7321			−0.366600			−0.183300	+	0.983057i	$0.558678\pi$
$858$	9.19615	−	2.46410i	0.313951	−	0.0841230i
$859$	27.0000	−	27.0000i	0.921228	−	0.921228i	−0.0758882	−	0.997116i	$-0.524179\pi$
$859$	27.0000	−	27.0000i	0.921228	−	0.921228i	0.997116	+	0.0758882i	$0.0241792\pi$
$860$	1.47372	+	24.5526i	0.0502535	+	0.837235i
$861$	−35.3205			−1.20372
$862$	11.2224	+	11.2224i	0.382238	+	0.382238i
$863$	0.241670	−	0.901924i	0.00822653	−	0.0307018i	−0.961691	−	0.274137i	$-0.911608\pi$
$863$	0.241670	−	0.901924i	0.00822653	−	0.0307018i	0.969917	+	0.243435i	$0.0782744\pi$
$864$	1.13397	+	4.23205i	0.0385786	+	0.143977i
$865$	−17.1962	−	51.5885i	−0.584687	−	1.75406i
$866$	−4.36603	−	1.16987i	−0.148364	−	0.0397539i
$867$	−39.9186	−	10.6962i	−1.35571	−	0.363260i
$868$	−23.6603	+	13.6603i	−0.803081	+	0.463659i
$869$	−13.6603	+	3.66025i	−0.463392	+	0.124166i
$870$	−24.1244	+	15.9282i	−0.817892	+	0.540017i
$871$	−13.2224	−	3.54294i	−0.448025	−	0.120048i
$872$	−0.267949	+	1.00000i	−0.00907390	+	0.0338643i
$873$	0.928203	−	0.535898i	0.0314149	−	0.0181374i
$874$	−26.7846	+	26.7846i	−0.906003	+	0.906003i
$875$	−13.5167	−	28.5885i	−0.456947	−	0.966466i
$876$		0			0
$877$	−21.1699	+	21.1699i	−0.714856	+	0.714856i	−0.967547	−	0.252691i	$-0.918684\pi$
$877$	−21.1699	+	21.1699i	−0.714856	+	0.714856i	0.252691	+	0.967547i	$0.418684\pi$
$878$	−0.633975	+	0.633975i	−0.0213956	+	0.0213956i
$879$	−3.13397	−	5.42820i	−0.105706	−	0.183089i
$880$	4.00000	+	2.00000i	0.134840	+	0.0674200i
$881$	25.0526	+	14.4641i	0.844042	+	0.487308i	0.858636	−	0.512586i	$-0.171312\pi$
$881$	25.0526	+	14.4641i	0.844042	+	0.487308i	−0.0145940	+	0.999894i	$0.504646\pi$
$882$			0.732051i			0.0246494i
$883$	6.59808	−	11.4282i	0.222043	−	0.384590i	−0.733385	−	0.679813i	$-0.762061\pi$
$883$	6.59808	−	11.4282i	0.222043	−	0.384590i	0.955428	+	0.295224i	$0.0953941\pi$
$884$	13.2224	+	7.63397i	0.444719	+	0.256758i
$885$	−11.5622	+	7.63397i	−0.388658	+	0.256613i
$886$	−6.86603	+	25.6244i	−0.230669	+	0.860867i
$887$	−6.60770	−	6.60770i	−0.221865	−	0.221865i	0.587419	−	0.809283i	$-0.300144\pi$
$887$	−6.60770	−	6.60770i	−0.221865	−	0.221865i	−0.809283	+	0.587419i	$0.800144\pi$
$888$	−7.59808	−	8.96410i	−0.254975	−	0.300816i
$889$			25.8564i			0.867196i
$890$	−2.50962	+	2.83013i	−0.0841226	+	0.0948661i
$891$	18.4641	+	10.6603i	0.618571	+	0.357132i
$892$	−17.6603	+	4.73205i	−0.591309	+	0.158441i
$893$	47.9090	+	27.6603i	1.60321	+	0.925615i
$894$	31.0526	−	31.0526i	1.03855	−	1.03855i
$895$	−6.58846	+	32.1962i	−0.220228	+	1.07620i
$896$	−2.00000	−	2.00000i	−0.0668153	−	0.0668153i
$897$	27.5885	+	7.39230i	0.921152	+	0.246822i
$898$	1.16987	+	1.16987i	0.0390392	+	0.0390392i
$899$	64.6410			2.15590
$900$	−3.36603	−	1.43782i	−0.112201	−	0.0479274i
$901$	30.1506	−	8.07884i	1.00446	−	0.269145i
$902$		−	12.9282i		−	0.430462i
$903$	−30.0526	−	52.0526i	−1.00009	−	1.73220i
$904$	5.19615	−	3.00000i	0.172821	−	0.0997785i
$905$	−30.8109	+	1.84936i	−1.02419	+	0.0614750i
$906$	1.59808	+	5.96410i	0.0530925	+	0.198144i
$907$	18.5885	−	32.1962i	0.617220	−	1.06906i	−0.372771	−	0.927923i	$-0.621592\pi$
$907$	18.5885	−	32.1962i	0.617220	−	1.06906i	0.989991	−	0.141132i	$-0.0450743\pi$
$908$	1.33013	+	2.30385i	0.0441418	+	0.0764559i
$909$	0.0717968	+	0.124356i	0.00238135	+	0.00412462i
$910$	−10.3397	+	11.6603i	−0.342759	+	0.386534i
$911$	8.63397	+	8.63397i	0.286056	+	0.286056i	0.835519	−	0.549462i	$-0.185167\pi$
$911$	8.63397	+	8.63397i	0.286056	+	0.286056i	−0.549462	+	0.835519i	$0.685167\pi$
$912$	−10.5622	−	6.09808i	−0.349749	−	0.201927i
$913$	−31.1244	−	8.33975i	−1.03007	−	0.276005i
$914$		−	26.7846i		−	0.885956i
$915$	6.92820	+	3.46410i	0.229039	+	0.114520i
$916$	15.2942	−	8.83013i	0.505336	−	0.291756i
$917$		−	2.14359i		−	0.0707877i
$918$	7.02628	+	26.2224i	0.231902	+	0.865469i
$919$	−25.7846	−	25.7846i	−0.850556	−	0.850556i	0.139646	−	0.990202i	$-0.455404\pi$
$919$	−25.7846	−	25.7846i	−0.850556	−	0.850556i	−0.990202	+	0.139646i	$0.955404\pi$
$920$	7.39230	+	11.1962i	0.243717	+	0.369126i
$921$	−21.0622	+	36.4808i	−0.694022	+	1.20208i
$922$	−4.53590	−	16.9282i	−0.149382	−	0.557501i
$923$	−6.24871	+	3.60770i	−0.205679	+	0.118749i
$924$	−10.9282			−0.359511
$925$	−30.3923	+	1.14359i	−0.999293	+	0.0376011i
$926$	8.33975			0.274061
$927$	3.92820	−	2.26795i	0.129019	−	0.0744892i
$928$	1.73205	+	6.46410i	0.0568574	+	0.212195i
$929$	0.330127	−	0.571797i	0.0108311	−	0.0187600i	−0.860559	−	0.509351i	$-0.829886\pi$
$929$	0.330127	−	0.571797i	0.0108311	−	0.0187600i	0.871390	+	0.490591i	$0.163219\pi$
$930$	22.9904	+	34.8205i	0.753884	+	1.14181i
$931$	4.46410	+	4.46410i	0.146305	+	0.146305i
$932$	5.80385	+	21.6603i	0.190111	+	0.709505i
$933$			30.5167i			0.999071i
$934$	−25.9186	+	14.9641i	−0.848082	+	0.489640i
$935$	24.7846	+	12.3923i	0.810543	+	0.405272i
$936$			1.80385i			0.0589606i
$937$	−36.2224	−	9.70577i	−1.18334	−	0.317074i	−0.387087	−	0.922043i	$-0.626519\pi$
$937$	−36.2224	−	9.70577i	−1.18334	−	0.317074i	−0.796249	+	0.604970i	$0.793185\pi$
$938$	13.6077	+	7.85641i	0.444307	+	0.256521i
$939$	−23.8564	−	23.8564i	−0.778524	−	0.778524i
$940$	13.0000	−	14.6603i	0.424013	−	0.478165i
$941$	−16.5885	−	28.7321i	−0.540768	−	0.936638i	−0.998860	−	0.0477332i	$-0.984800\pi$
$941$	−16.5885	−	28.7321i	−0.540768	−	0.936638i	0.458092	−	0.888905i	$-0.348533\pi$
$942$	−19.6244	−	33.9904i	−0.639396	−	1.10747i
$943$	19.3923	−	33.5885i	0.631500	−	1.09379i
$944$	0.830127	+	3.09808i	0.0270183	+	0.100834i
$945$	−27.6603	+	1.66025i	−0.899788	+	0.0540081i
$946$	19.0526	−	11.0000i	0.619452	−	0.357641i
$947$	22.7679	+	39.4352i	0.739859	+	1.28147i	0.952558	+	0.304356i	$0.0984411\pi$
$947$	22.7679	+	39.4352i	0.739859	+	1.28147i	−0.212700	+	0.977118i	$0.568226\pi$
$948$		−	13.6603i		−	0.443664i
$949$		0			0
$950$	−29.2942	+	11.7583i	−0.950430	+	0.381491i
$951$	53.6410			1.73943
$952$	−12.3923	−	12.3923i	−0.401637	−	0.401637i
$953$	48.0526	+	12.8756i	1.55658	+	0.417083i	0.931577	−	0.363543i	$-0.118433\pi$
$953$	48.0526	+	12.8756i	1.55658	+	0.417083i	0.624998	+	0.780626i	$0.285100\pi$
$954$	2.60770	+	2.60770i	0.0844272	+	0.0844272i
$955$	−1.16025	+	5.66987i	−0.0375449	+	0.183473i
$956$	10.8564	−	10.8564i	0.351121	−	0.351121i
$957$	22.3923	+	12.9282i	0.723840	+	0.417909i
$958$	3.96410	−	1.06218i	0.128074	−	0.0343174i
$959$	−6.92820	−	4.00000i	−0.223723	−	0.129167i
$960$	−2.86603	+	3.23205i	−0.0925006	+	0.104314i
$961$		−	62.3013i		−	2.00972i
$962$	6.40192	+	13.5526i	0.206406	+	0.436952i
$963$	−7.19615	−	7.19615i	−0.231893	−	0.231893i
$964$	4.83013	−	18.0263i	0.155568	−	0.580587i
$965$	−0.633975	+	0.418584i	−0.0204084	+	0.0134747i
$966$	−28.3923	−	16.3923i	−0.913507	−	0.527414i
$967$	−19.0263	+	32.9545i	−0.611844	+	1.05974i	0.379086	+	0.925362i	$0.376239\pi$
$967$	−19.0263	+	32.9545i	−0.611844	+	1.05974i	−0.990929	+	0.134383i	$0.957095\pi$
$968$			7.00000i			0.224989i
$969$	−65.4449	−	37.7846i	−2.10239	−	1.21382i
$970$	−2.92820	−	1.46410i	−0.0940189	−	0.0470095i
$971$	12.4904	+	21.6340i	0.400835	+	0.694267i	0.993827	−	0.110941i	$-0.0353866\pi$
$971$	12.4904	+	21.6340i	0.400835	+	0.694267i	−0.592992	+	0.805209i	$0.702053\pi$
$972$	−5.26795	+	5.26795i	−0.168970	+	0.168970i
$973$	21.8564	−	21.8564i	0.700684	−	0.700684i
$974$	−35.9090	+	20.7321i	−1.15060	+	0.664298i
$975$	18.7224	+	14.6962i	0.599598	+	0.470654i
$976$	1.26795	−	1.26795i	0.0405861	−	0.0405861i
$977$	38.3660	−	22.1506i	1.22744	−	0.708662i	0.260945	−	0.965354i	$-0.415966\pi$
$977$	38.3660	−	22.1506i	1.22744	−	0.708662i	0.966493	+	0.256692i	$0.0826326\pi$
$978$	1.76795	−	6.59808i	0.0565328	−	0.210983i
$979$	3.26795	+	0.875644i	0.104444	+	0.0279857i
$980$	1.86603	−	1.23205i	0.0596080	−	0.0393564i
$981$	−0.732051	+	0.196152i	−0.0233726	+	0.00626266i
$982$	7.09808	−	4.09808i	0.226509	−	0.130775i
$983$	−30.1244	−	8.07180i	−0.960818	−	0.257450i	−0.255871	−	0.966711i	$-0.582362\pi$
$983$	−30.1244	−	8.07180i	−0.960818	−	0.257450i	−0.704946	+	0.709261i	$0.749029\pi$
$984$	12.0622	+	3.23205i	0.384528	+	0.103034i
$985$	−5.75833	−	17.2750i	−0.183476	−	0.550427i
$986$	10.7321	+	40.0526i	0.341778	+	1.27553i
$987$	−12.3923	+	46.2487i	−0.394451	+	1.47211i
$988$	11.0000	+	11.0000i	0.349957	+	0.349957i
$989$	66.0000			2.09868
$990$	0.196152	+	3.26795i	0.00623413	+	0.103862i
$991$	13.0981	−	13.0981i	0.416074	−	0.416074i	−0.467774	−	0.883848i	$-0.654944\pi$
$991$	13.0981	−	13.0981i	0.416074	−	0.416074i	0.883848	+	0.467774i	$0.154944\pi$
$992$	9.33013	−	2.50000i	0.296232	−	0.0793751i
$993$	6.19615			0.196629
$994$	8.00000	−	2.14359i	0.253745	−	0.0679907i
$995$	9.35641	−	45.7224i	0.296618	−	1.44950i
$996$	15.5622	−	26.9545i	0.493106	−	0.854085i
$997$	−15.0885	−	26.1340i	−0.477856	−	0.827671i	0.521822	−	0.853055i	$-0.325253\pi$
$997$	−15.0885	−	26.1340i	−0.477856	−	0.827671i	−0.999678	+	0.0253834i	$0.991919\pi$
$998$	11.1244	−	11.1244i	0.352135	−	0.352135i
$999$	−8.99038	+	25.0885i	−0.284443	+	0.793764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.a.193.1	yes	4
5.2	odd	4		370.2.q.a.267.1	✓	4
37.14	odd	12		370.2.q.a.273.1	yes	4
185.162	even	12	inner	370.2.r.a.347.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.a.267.1	✓	4	5.2	odd	4
370.2.q.a.273.1	yes	4	37.14	odd	12
370.2.r.a.193.1	yes	4	1.1	even	1	trivial
370.2.r.a.347.1	yes	4	185.162	even	12	inner

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.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(-1.36603 - 1.36603i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000i q^{8} +(-0.633975 + 0.366025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 1.86603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.23205 - 1.86603i) q^{5} +(-1.36603 - 1.36603i) q^{6} +(-0.732051 - 2.73205i) q^{7} +1.00000i q^{8} +(-0.633975 + 0.366025i) q^{9} +(2.00000 + 1.00000i) q^{10} -2.00000i q^{11} +(1.86603 + 0.500000i) q^{12} +(-2.13397 - 1.23205i) q^{13} +(2.00000 + 2.00000i) q^{14} +(2.86603 - 3.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.09808 - 5.36603i) q^{17} +(0.366025 - 0.633975i) q^{18} +(-1.63397 - 6.09808i) q^{19} +(-2.23205 + 0.133975i) q^{20} +(4.73205 - 2.73205i) q^{21} +(1.00000 + 1.73205i) q^{22} +6.00000i q^{23} +(-1.86603 + 0.500000i) q^{24} +(-1.96410 + 4.59808i) q^{25} +2.46410 q^{26} +(3.09808 + 3.09808i) q^{27} +(-2.73205 - 0.732051i) q^{28} +(4.73205 + 4.73205i) q^{29} +(-0.866025 + 4.23205i) q^{30} +(6.83013 - 6.83013i) q^{31} +(0.866025 + 0.500000i) q^{32} +(3.73205 - 1.00000i) q^{33} +(5.36603 + 3.09808i) q^{34} +(-4.19615 + 4.73205i) q^{35} +0.732051i q^{36} +(2.59808 + 5.50000i) q^{37} +(4.46410 + 4.46410i) q^{38} +(1.23205 - 4.59808i) q^{39} +(1.86603 - 1.23205i) q^{40} +(-5.59808 - 3.23205i) q^{41} +(-2.73205 + 4.73205i) q^{42} -11.0000i q^{43} +(-1.73205 - 1.00000i) q^{44} +(1.46410 + 0.732051i) q^{45} +(-3.00000 - 5.19615i) q^{46} +(-6.19615 + 6.19615i) q^{47} +(1.36603 - 1.36603i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.598076 - 4.96410i) q^{50} +(8.46410 - 8.46410i) q^{51} +(-2.13397 + 1.23205i) q^{52} +(-1.30385 + 4.86603i) q^{53} +(-4.23205 - 1.13397i) q^{54} +(-3.73205 + 2.46410i) q^{55} +(2.73205 - 0.732051i) q^{56} +(10.5622 - 6.09808i) q^{57} +(-6.46410 - 1.73205i) q^{58} +(-3.09808 - 0.830127i) q^{59} +(-1.36603 - 4.09808i) q^{60} +(0.464102 + 1.73205i) q^{61} +(-2.50000 + 9.33013i) q^{62} +(1.46410 + 1.46410i) q^{63} -1.00000 q^{64} +(0.330127 + 5.50000i) q^{65} +(-2.73205 + 2.73205i) q^{66} +(5.36603 - 1.43782i) q^{67} -6.19615 q^{68} +(-11.1962 + 3.00000i) q^{69} +(1.26795 - 6.19615i) q^{70} +(1.46410 - 2.53590i) q^{71} +(-0.366025 - 0.633975i) q^{72} +(-5.00000 - 3.46410i) q^{74} +(-9.56218 - 1.36603i) q^{75} +(-6.09808 - 1.63397i) q^{76} +(-5.46410 + 1.46410i) q^{77} +(1.23205 + 4.59808i) q^{78} +(-1.83013 - 6.83013i) q^{79} +(-1.00000 + 2.00000i) q^{80} +(-5.33013 + 9.23205i) q^{81} +6.46410 q^{82} +(4.16987 - 15.5622i) q^{83} -5.46410i q^{84} +(-6.19615 + 12.3923i) q^{85} +(5.50000 + 9.52628i) q^{86} +(-6.46410 + 11.1962i) q^{87} +2.00000 q^{88} +(-0.437822 + 1.63397i) q^{89} +(-1.63397 + 0.0980762i) q^{90} +(-1.80385 + 6.73205i) q^{91} +(5.19615 + 3.00000i) q^{92} +(16.1603 + 9.33013i) q^{93} +(2.26795 - 8.46410i) q^{94} +(-9.36603 + 10.5622i) q^{95} +(-0.500000 + 1.86603i) q^{96} -1.46410 q^{97} +(0.500000 - 0.866025i) q^{98} +(0.732051 + 1.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 6 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} - 6 q^{9} + 8 q^{10} + 4 q^{12} - 12 q^{13} + 8 q^{14} + 8 q^{15} - 2 q^{16} - 2 q^{17} - 2 q^{18} - 10 q^{19} - 2 q^{20} + 12 q^{21} + 4 q^{22} - 4 q^{24} + 6 q^{25} - 4 q^{26} + 2 q^{27} - 4 q^{28} + 12 q^{29} + 10 q^{31} + 8 q^{33} + 18 q^{34} + 4 q^{35} + 4 q^{38} - 2 q^{39} + 4 q^{40} - 12 q^{41} - 4 q^{42} - 8 q^{45} - 12 q^{46} - 4 q^{47} + 2 q^{48} + 8 q^{50} + 20 q^{51} - 12 q^{52} - 26 q^{53} - 10 q^{54} - 8 q^{55} + 4 q^{56} + 18 q^{57} - 12 q^{58} - 2 q^{59} - 2 q^{60} - 12 q^{61} - 10 q^{62} - 8 q^{63} - 4 q^{64} - 16 q^{65} - 4 q^{66} + 18 q^{67} - 4 q^{68} - 24 q^{69} + 12 q^{70} - 8 q^{71} + 2 q^{72} - 20 q^{74} - 14 q^{75} - 14 q^{76} - 8 q^{77} - 2 q^{78} + 10 q^{79} - 4 q^{80} - 4 q^{81} + 12 q^{82} + 34 q^{83} - 4 q^{85} + 22 q^{86} - 12 q^{87} + 8 q^{88} - 26 q^{89} - 10 q^{90} - 28 q^{91} + 30 q^{93} + 16 q^{94} - 34 q^{95} - 2 q^{96} + 8 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 - 6 * q^9 + 8 * q^10 + 4 * q^12 - 12 * q^13 + 8 * q^14 + 8 * q^15 - 2 * q^16 - 2 * q^17 - 2 * q^18 - 10 * q^19 - 2 * q^20 + 12 * q^21 + 4 * q^22 - 4 * q^24 + 6 * q^25 - 4 * q^26 + 2 * q^27 - 4 * q^28 + 12 * q^29 + 10 * q^31 + 8 * q^33 + 18 * q^34 + 4 * q^35 + 4 * q^38 - 2 * q^39 + 4 * q^40 - 12 * q^41 - 4 * q^42 - 8 * q^45 - 12 * q^46 - 4 * q^47 + 2 * q^48 + 8 * q^50 + 20 * q^51 - 12 * q^52 - 26 * q^53 - 10 * q^54 - 8 * q^55 + 4 * q^56 + 18 * q^57 - 12 * q^58 - 2 * q^59 - 2 * q^60 - 12 * q^61 - 10 * q^62 - 8 * q^63 - 4 * q^64 - 16 * q^65 - 4 * q^66 + 18 * q^67 - 4 * q^68 - 24 * q^69 + 12 * q^70 - 8 * q^71 + 2 * q^72 - 20 * q^74 - 14 * q^75 - 14 * q^76 - 8 * q^77 - 2 * q^78 + 10 * q^79 - 4 * q^80 - 4 * q^81 + 12 * q^82 + 34 * q^83 - 4 * q^85 + 22 * q^86 - 12 * q^87 + 8 * q^88 - 26 * q^89 - 10 * q^90 - 28 * q^91 + 30 * q^93 + 16 * q^94 - 34 * q^95 - 2 * q^96 + 8 * q^97 + 2 * q^98 - 4 * q^99

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