LMFDB - Embedded newform 315.2.cg.a.187.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(157,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 3, 2]))

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

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

chi := DirichletCharacter("315.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cg (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:	$2.51528766367$
Analytic rank:	$1$
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			187.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	315.187
Dual form			315.2.cg.a.283.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 1.86603i) q^{2} -1.73205i q^{3} +(-1.50000 - 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-0.366025 + 0.366025i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 1.86603i) q^{2} -1.73205i q^{3} +(-1.50000 - 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-0.366025 + 0.366025i) q^{8} -3.00000 q^{9} +(-0.866025 - 4.23205i) q^{10} -5.46410 q^{11} +(-1.50000 + 2.59808i) q^{12} +(-1.00000 + 3.73205i) q^{13} +(4.23205 + 2.86603i) q^{14} +(1.73205 + 3.46410i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-2.73205 - 0.732051i) q^{17} +(1.50000 - 5.59808i) q^{18} +(-1.63397 + 2.83013i) q^{19} +(3.86603 + 0.232051i) q^{20} +(-4.33013 - 1.50000i) q^{21} +(2.73205 - 10.1962i) q^{22} +(3.36603 - 3.36603i) q^{23} +(0.633975 + 0.633975i) q^{24} +(3.00000 - 4.00000i) q^{25} +(-6.46410 - 3.73205i) q^{26} +5.19615i q^{27} +(-3.46410 + 3.00000i) q^{28} +(-6.00000 - 3.46410i) q^{29} +(-7.33013 + 1.50000i) q^{30} +(-0.169873 - 0.0980762i) q^{31} +(7.33013 - 1.96410i) q^{32} +9.46410i q^{33} +(2.73205 - 4.73205i) q^{34} +(0.767949 + 5.86603i) q^{35} +(4.50000 + 2.59808i) q^{36} +(-4.09808 + 1.09808i) q^{37} +(-4.46410 - 4.46410i) q^{38} +(6.46410 + 1.73205i) q^{39} +(0.366025 - 1.09808i) q^{40} +(2.19615 - 1.26795i) q^{41} +(4.96410 - 7.33013i) q^{42} +(-0.401924 - 1.50000i) q^{43} +(8.19615 + 4.73205i) q^{44} +(6.00000 - 3.00000i) q^{45} +(4.59808 + 7.96410i) q^{46} +(12.6962 + 3.40192i) q^{47} +(-6.69615 + 3.86603i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(5.96410 + 7.59808i) q^{50} +(-1.26795 + 4.73205i) q^{51} +(4.73205 - 4.73205i) q^{52} +(6.09808 + 1.63397i) q^{53} +(-9.69615 - 2.59808i) q^{54} +(10.9282 - 5.46410i) q^{55} +(0.598076 + 1.23205i) q^{56} +(4.90192 + 2.83013i) q^{57} +(9.46410 - 9.46410i) q^{58} +(-1.73205 + 3.00000i) q^{59} +(0.401924 - 6.69615i) q^{60} +(-9.86603 + 5.69615i) q^{61} +(0.267949 - 0.267949i) q^{62} +(-2.59808 + 7.50000i) q^{63} +5.73205i q^{64} +(-1.73205 - 8.46410i) q^{65} +(-17.6603 - 4.73205i) q^{66} +(-1.23205 + 0.330127i) q^{67} +(3.46410 + 3.46410i) q^{68} +(-5.83013 - 5.83013i) q^{69} +(-11.3301 - 1.50000i) q^{70} -6.00000 q^{71} +(1.09808 - 1.09808i) q^{72} +(-2.36603 + 8.83013i) q^{73} -8.19615i q^{74} +(-6.92820 - 5.19615i) q^{75} +(4.90192 - 2.83013i) q^{76} +(-4.73205 + 13.6603i) q^{77} +(-6.46410 + 11.1962i) q^{78} +(-3.92820 + 2.26795i) q^{79} +(8.33013 + 5.50000i) q^{80} +9.00000 q^{81} +(1.26795 + 4.73205i) q^{82} +(1.36603 - 0.366025i) q^{83} +(5.19615 + 6.00000i) q^{84} +(6.19615 - 1.26795i) q^{85} +3.00000 q^{86} +(-6.00000 + 10.3923i) q^{87} +(2.00000 - 2.00000i) q^{88} +(-4.59808 + 7.96410i) q^{89} +(2.59808 + 12.6962i) q^{90} +(8.46410 + 5.73205i) q^{91} +(-7.96410 + 2.13397i) q^{92} +(-0.169873 + 0.294229i) q^{93} +(-12.6962 + 21.9904i) q^{94} +(0.437822 - 7.29423i) q^{95} +(-3.40192 - 12.6962i) q^{96} +(-2.09808 - 7.83013i) q^{97} +(10.8301 - 8.09808i) q^{98} +16.3923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{4} - 8 q^{5} + 6 q^{6} + 2 q^{8} - 12 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^4 - 8 * q^5 + 6 * q^6 + 2 * q^8 - 12 * q^9	$ 4 q - 2 q^{2} - 6 q^{4} - 8 q^{5} + 6 q^{6} + 2 q^{8} - 12 q^{9} - 8 q^{11} - 6 q^{12} - 4 q^{13} + 10 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{18} - 10 q^{19} + 12 q^{20} + 4 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{25} - 12 q^{26} - 24 q^{29} - 12 q^{30} - 18 q^{31} + 12 q^{32} + 4 q^{34} + 10 q^{35} + 18 q^{36} - 6 q^{37} - 4 q^{38} + 12 q^{39} - 2 q^{40} - 12 q^{41} + 6 q^{42} - 12 q^{43} + 12 q^{44} + 24 q^{45} + 8 q^{46} + 30 q^{47} - 6 q^{48} - 22 q^{49} + 10 q^{50} - 12 q^{51} + 12 q^{52} + 14 q^{53} - 18 q^{54} + 16 q^{55} - 8 q^{56} + 30 q^{57} + 24 q^{58} + 12 q^{60} - 36 q^{61} + 8 q^{62} - 36 q^{66} + 2 q^{67} - 6 q^{69} - 28 q^{70} - 24 q^{71} - 6 q^{72} - 6 q^{73} + 30 q^{76} - 12 q^{77} - 12 q^{78} + 12 q^{79} + 16 q^{80} + 36 q^{81} + 12 q^{82} + 2 q^{83} + 4 q^{85} + 12 q^{86} - 24 q^{87} + 8 q^{88} - 8 q^{89} + 20 q^{91} - 18 q^{92} - 18 q^{93} - 30 q^{94} + 26 q^{95} - 24 q^{96} + 2 q^{97} + 26 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^4 - 8 * q^5 + 6 * q^6 + 2 * q^8 - 12 * q^9 - 8 * q^11 - 6 * q^12 - 4 * q^13 + 10 * q^14 - 2 * q^16 - 4 * q^17 + 6 * q^18 - 10 * q^19 + 12 * q^20 + 4 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^25 - 12 * q^26 - 24 * q^29 - 12 * q^30 - 18 * q^31 + 12 * q^32 + 4 * q^34 + 10 * q^35 + 18 * q^36 - 6 * q^37 - 4 * q^38 + 12 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^42 - 12 * q^43 + 12 * q^44 + 24 * q^45 + 8 * q^46 + 30 * q^47 - 6 * q^48 - 22 * q^49 + 10 * q^50 - 12 * q^51 + 12 * q^52 + 14 * q^53 - 18 * q^54 + 16 * q^55 - 8 * q^56 + 30 * q^57 + 24 * q^58 + 12 * q^60 - 36 * q^61 + 8 * q^62 - 36 * q^66 + 2 * q^67 - 6 * q^69 - 28 * q^70 - 24 * q^71 - 6 * q^72 - 6 * q^73 + 30 * q^76 - 12 * q^77 - 12 * q^78 + 12 * q^79 + 16 * q^80 + 36 * q^81 + 12 * q^82 + 2 * q^83 + 4 * q^85 + 12 * q^86 - 24 * q^87 + 8 * q^88 - 8 * q^89 + 20 * q^91 - 18 * q^92 - 18 * q^93 - 30 * q^94 + 26 * q^95 - 24 * q^96 + 2 * q^97 + 26 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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	+	1.86603i	−0.353553	+	1.31948i	0.528742	+	0.848783i	$0.322664\pi$
$2$	−0.500000	+	1.86603i	−0.353553	+	1.31948i	−0.882295	+	0.470696i	$0.844003\pi$
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−1.50000	−	0.866025i	−0.750000	−	0.433013i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$	3.23205	+	0.866025i	1.31948	+	0.353553i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$	−0.366025	+	0.366025i	−0.129410	+	0.129410i
$9$	−3.00000			−1.00000
$10$	−0.866025	−	4.23205i	−0.273861	−	1.33829i
$11$	−5.46410			−1.64749			−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410			−1.64749			−0.823744	+	0.566961i	$0.808119\pi$
$12$	−1.50000	+	2.59808i	−0.433013	+	0.750000i
$13$	−1.00000	+	3.73205i	−0.277350	+	1.03508i	0.676900	+	0.736075i	$0.263323\pi$
$13$	−1.00000	+	3.73205i	−0.277350	+	1.03508i	−0.954250	+	0.299010i	$0.903344\pi$
$14$	4.23205	+	2.86603i	1.13106	+	0.765978i
$15$	1.73205	+	3.46410i	0.447214	+	0.894427i
$16$	−2.23205	−	3.86603i	−0.558013	−	0.966506i
$17$	−2.73205	−	0.732051i	−0.662620	−	0.177548i	−0.0881917	−	0.996104i	$-0.528109\pi$
$17$	−2.73205	−	0.732051i	−0.662620	−	0.177548i	−0.574428	+	0.818555i	$0.694775\pi$
$18$	1.50000	−	5.59808i	0.353553	−	1.31948i
$19$	−1.63397	+	2.83013i	−0.374859	+	0.649276i	−0.990306	−	0.138903i	$-0.955642\pi$
$19$	−1.63397	+	2.83013i	−0.374859	+	0.649276i	0.615447	+	0.788179i	$0.288976\pi$
$20$	3.86603	+	0.232051i	0.864470	+	0.0518881i
$21$	−4.33013	−	1.50000i	−0.944911	−	0.327327i
$22$	2.73205	−	10.1962i	0.582475	−	2.17383i
$23$	3.36603	−	3.36603i	0.701865	−	0.701865i	−0.262946	−	0.964811i	$-0.584694\pi$
$23$	3.36603	−	3.36603i	0.701865	−	0.701865i	0.964811	+	0.262946i	$0.0846940\pi$
$24$	0.633975	+	0.633975i	0.129410	+	0.129410i
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$	−6.46410	−	3.73205i	−1.26771	−	0.731915i
$27$			5.19615i			1.00000i
$28$	−3.46410	+	3.00000i	−0.654654	+	0.566947i
$29$	−6.00000	−	3.46410i	−1.11417	−	0.643268i	−0.174265	−	0.984699i	$-0.555755\pi$
$29$	−6.00000	−	3.46410i	−1.11417	−	0.643268i	−0.939907	+	0.341431i	$0.889088\pi$
$30$	−7.33013	+	1.50000i	−1.33829	+	0.273861i
$31$	−0.169873	−	0.0980762i	−0.0305101	−	0.0176150i	0.484667	−	0.874699i	$-0.338941\pi$
$31$	−0.169873	−	0.0980762i	−0.0305101	−	0.0176150i	−0.515177	+	0.857084i	$0.672274\pi$
$32$	7.33013	−	1.96410i	1.29580	−	0.347207i
$33$			9.46410i			1.64749i
$34$	2.73205	−	4.73205i	0.468543	−	0.811540i
$35$	0.767949	+	5.86603i	0.129807	+	0.991539i
$36$	4.50000	+	2.59808i	0.750000	+	0.433013i
$37$	−4.09808	+	1.09808i	−0.673720	+	0.180523i	−0.579430	−	0.815022i	$-0.696725\pi$
$37$	−4.09808	+	1.09808i	−0.673720	+	0.180523i	−0.0942898	+	0.995545i	$0.530058\pi$
$38$	−4.46410	−	4.46410i	−0.724173	−	0.724173i
$39$	6.46410	+	1.73205i	1.03508	+	0.277350i
$40$	0.366025	−	1.09808i	0.0578737	−	0.173621i
$41$	2.19615	−	1.26795i	0.342981	−	0.198020i	−0.318608	−	0.947886i	$-0.603215\pi$
$41$	2.19615	−	1.26795i	0.342981	−	0.198020i	0.661590	+	0.749866i	$0.269882\pi$
$42$	4.96410	−	7.33013i	0.765978	−	1.13106i
$43$	−0.401924	−	1.50000i	−0.0612928	−	0.228748i	0.928484	−	0.371372i	$-0.121113\pi$
$43$	−0.401924	−	1.50000i	−0.0612928	−	0.228748i	−0.989777	+	0.142624i	$0.954446\pi$
$44$	8.19615	+	4.73205i	1.23562	+	0.713384i
$45$	6.00000	−	3.00000i	0.894427	−	0.447214i
$46$	4.59808	+	7.96410i	0.677949	+	1.17424i
$47$	12.6962	+	3.40192i	1.85192	+	0.496222i	0.999639	−	0.0268563i	$-0.00854967\pi$
$47$	12.6962	+	3.40192i	1.85192	+	0.496222i	0.852285	+	0.523078i	$0.175216\pi$
$48$	−6.69615	+	3.86603i	−0.966506	+	0.558013i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	5.96410	+	7.59808i	0.843451	+	1.07453i
$51$	−1.26795	+	4.73205i	−0.177548	+	0.662620i
$52$	4.73205	−	4.73205i	0.656217	−	0.656217i
$53$	6.09808	+	1.63397i	0.837635	+	0.224444i	0.652042	−	0.758183i	$-0.273913\pi$
$53$	6.09808	+	1.63397i	0.837635	+	0.224444i	0.185593	+	0.982627i	$0.440579\pi$
$54$	−9.69615	−	2.59808i	−1.31948	−	0.353553i
$55$	10.9282	−	5.46410i	1.47356	−	0.736779i
$56$	0.598076	+	1.23205i	0.0799213	+	0.164640i
$57$	4.90192	+	2.83013i	0.649276	+	0.374859i
$58$	9.46410	−	9.46410i	1.24270	−	1.24270i
$59$	−1.73205	+	3.00000i	−0.225494	+	0.390567i	−0.956467	−	0.291839i	$-0.905733\pi$
$59$	−1.73205	+	3.00000i	−0.225494	+	0.390567i	0.730974	+	0.682406i	$0.239066\pi$
$60$	0.401924	−	6.69615i	0.0518881	−	0.864470i
$61$	−9.86603	+	5.69615i	−1.26322	+	0.729318i	−0.973695	−	0.227854i	$-0.926829\pi$
$61$	−9.86603	+	5.69615i	−1.26322	+	0.729318i	−0.289520	+	0.957172i	$0.593496\pi$
$62$	0.267949	−	0.267949i	0.0340296	−	0.0340296i
$63$	−2.59808	+	7.50000i	−0.327327	+	0.944911i
$64$			5.73205i			0.716506i
$65$	−1.73205	−	8.46410i	−0.214834	−	1.04984i
$66$	−17.6603	−	4.73205i	−2.17383	−	0.582475i
$67$	−1.23205	+	0.330127i	−0.150519	+	0.0403314i	−0.333292	−	0.942824i	$-0.608159\pi$
$67$	−1.23205	+	0.330127i	−0.150519	+	0.0403314i	0.182773	+	0.983155i	$0.441493\pi$
$68$	3.46410	+	3.46410i	0.420084	+	0.420084i
$69$	−5.83013	−	5.83013i	−0.701865	−	0.701865i
$70$	−11.3301	−	1.50000i	−1.35421	−	0.179284i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	1.09808	−	1.09808i	0.129410	−	0.129410i
$73$	−2.36603	+	8.83013i	−0.276922	+	1.03349i	0.677620	+	0.735412i	$0.263012\pi$
$73$	−2.36603	+	8.83013i	−0.276922	+	1.03349i	−0.954542	+	0.298076i	$0.903655\pi$
$74$		−	8.19615i		−	0.952783i
$75$	−6.92820	−	5.19615i	−0.800000	−	0.600000i
$76$	4.90192	−	2.83013i	0.562289	−	0.324638i
$77$	−4.73205	+	13.6603i	−0.539267	+	1.55673i
$78$	−6.46410	+	11.1962i	−0.731915	+	1.26771i
$79$	−3.92820	+	2.26795i	−0.441957	+	0.255164i	−0.704428	−	0.709776i	$-0.748796\pi$
$79$	−3.92820	+	2.26795i	−0.441957	+	0.255164i	0.262470	+	0.964940i	$0.415463\pi$
$80$	8.33013	+	5.50000i	0.931337	+	0.614919i
$81$	9.00000			1.00000
$82$	1.26795	+	4.73205i	0.140022	+	0.522568i
$83$	1.36603	−	0.366025i	0.149941	−	0.0401765i	−0.183068	−	0.983100i	$-0.558603\pi$
$83$	1.36603	−	0.366025i	0.149941	−	0.0401765i	0.333009	+	0.942924i	$0.391936\pi$
$84$	5.19615	+	6.00000i	0.566947	+	0.654654i
$85$	6.19615	−	1.26795i	0.672067	−	0.137528i
$86$	3.00000			0.323498
$87$	−6.00000	+	10.3923i	−0.643268	+	1.11417i
$88$	2.00000	−	2.00000i	0.213201	−	0.213201i
$89$	−4.59808	+	7.96410i	−0.487395	+	0.844193i	−0.999895	−	0.0144942i	$-0.995386\pi$
$89$	−4.59808	+	7.96410i	−0.487395	+	0.844193i	0.512500	+	0.858687i	$0.328720\pi$
$90$	2.59808	+	12.6962i	0.273861	+	1.33829i
$91$	8.46410	+	5.73205i	0.887279	+	0.600882i
$92$	−7.96410	+	2.13397i	−0.830315	+	0.222482i
$93$	−0.169873	+	0.294229i	−0.0176150	+	0.0305101i
$94$	−12.6962	+	21.9904i	−1.30951	+	2.26813i
$95$	0.437822	−	7.29423i	0.0449196	−	0.748372i
$96$	−3.40192	−	12.6962i	−0.347207	−	1.29580i
$97$	−2.09808	−	7.83013i	−0.213027	−	0.795029i	−0.986852	−	0.161629i	$-0.948325\pi$
$97$	−2.09808	−	7.83013i	−0.213027	−	0.795029i	0.773824	−	0.633400i	$-0.218341\pi$
$98$	10.8301	−	8.09808i	1.09401	−	0.818029i
$99$	16.3923			1.64749
$100$	−7.96410	+	3.40192i	−0.796410	+	0.340192i
$101$		−	17.5885i		−	1.75012i	−0.484017	−	0.875058i	$-0.660823\pi$
$101$		−	17.5885i		−	1.75012i	0.484017	−	0.875058i	$-0.339177\pi$
$102$	−8.19615	−	4.73205i	−0.811540	−	0.468543i
$103$	2.90192	+	2.90192i	0.285935	+	0.285935i	0.835470	−	0.549535i	$-0.185195\pi$
$103$	2.90192	+	2.90192i	0.285935	+	0.285935i	−0.549535	+	0.835470i	$0.685195\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$	10.1603	−	1.33013i	0.991539	−	0.129807i
$106$	−6.09808	+	10.5622i	−0.592298	+	1.02589i
$107$	2.36603	−	0.633975i	0.228732	−	0.0612886i	−0.142632	−	0.989776i	$-0.545557\pi$
$107$	2.36603	−	0.633975i	0.228732	−	0.0612886i	0.371365	+	0.928487i	$0.378890\pi$
$108$	4.50000	−	7.79423i	0.433013	−	0.750000i
$109$	1.73205	−	1.00000i	0.165900	−	0.0957826i	−0.414751	−	0.909935i	$-0.636131\pi$
$109$	1.73205	−	1.00000i	0.165900	−	0.0957826i	0.580651	+	0.814152i	$0.302798\pi$
$110$	4.73205	+	23.1244i	0.451183	+	2.20482i
$111$	1.90192	+	7.09808i	0.180523	+	0.673720i
$112$	−11.5981	+	2.23205i	−1.09592	+	0.210909i
$113$	−7.09808	−	1.90192i	−0.667731	−	0.178918i	−0.0909984	−	0.995851i	$-0.529006\pi$
$113$	−7.09808	−	1.90192i	−0.667731	−	0.178918i	−0.576732	+	0.816933i	$0.695672\pi$
$114$	−7.73205	+	7.73205i	−0.724173	+	0.724173i
$115$	−3.36603	+	10.0981i	−0.313883	+	0.941650i
$116$	6.00000	+	10.3923i	0.557086	+	0.964901i
$117$	3.00000	−	11.1962i	0.277350	−	1.03508i
$118$	−4.73205	−	4.73205i	−0.435621	−	0.435621i
$119$	−4.19615	+	6.19615i	−0.384661	+	0.568000i
$120$	−1.90192	−	0.633975i	−0.173621	−	0.0578737i
$121$	18.8564			1.71422
$122$	−5.69615	−	21.2583i	−0.515705	−	1.92464i
$123$	−2.19615	−	3.80385i	−0.198020	−	0.342981i
$124$	0.169873	+	0.294229i	0.0152550	+	0.0264225i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−12.6962	−	8.59808i	−1.13106	−	0.765978i
$127$	−15.7583	−	15.7583i	−1.39833	−	1.39833i	−0.804857	−	0.593468i	$-0.797758\pi$
$127$	−15.7583	−	15.7583i	−1.39833	−	1.39833i	−0.593468	−	0.804857i	$-0.702242\pi$
$128$	3.96410	+	1.06218i	0.350380	+	0.0938841i
$129$	−2.59808	+	0.696152i	−0.228748	+	0.0612928i
$130$	16.6603	+	1.00000i	1.46120	+	0.0877058i
$131$		−	5.07180i		−	0.443125i	−0.975146	−	0.221562i	$-0.928884\pi$
$131$		−	5.07180i		−	0.443125i	0.975146	−	0.221562i	$-0.0711157\pi$
$132$	8.19615	−	14.1962i	0.713384	−	1.23562i
$133$	5.66025	+	6.53590i	0.490806	+	0.566734i
$134$		−	2.46410i		−	0.212866i
$135$	−5.19615	−	10.3923i	−0.447214	−	0.894427i
$136$	1.26795	−	0.732051i	0.108726	−	0.0627728i
$137$	1.46410	+	1.46410i	0.125087	+	0.125087i	0.766879	−	0.641792i	$-0.221809\pi$
$137$	1.46410	+	1.46410i	0.125087	+	0.125087i	−0.641792	+	0.766879i	$0.721809\pi$
$138$	13.7942	−	7.96410i	1.17424	−	0.677949i
$139$	3.46410	+	6.00000i	0.293821	+	0.508913i	0.974710	−	0.223474i	$-0.0717396\pi$
$139$	3.46410	+	6.00000i	0.293821	+	0.508913i	−0.680889	+	0.732387i	$0.738406\pi$
$140$	3.92820	−	9.46410i	0.331994	−	0.799863i
$141$	5.89230	−	21.9904i	0.496222	−	1.85192i
$142$	3.00000	−	11.1962i	0.251754	−	0.939560i
$143$	5.46410	−	20.3923i	0.456931	−	1.70529i
$144$	6.69615	+	11.5981i	0.558013	+	0.966506i
$145$	15.4641	+	0.928203i	1.28422	+	0.0770831i
$146$	−15.2942	−	8.83013i	−1.26576	−	0.730787i
$147$	−7.50000	+	9.52628i	−0.618590	+	0.785714i
$148$	7.09808	+	1.90192i	0.583458	+	0.156337i
$149$		−	3.33975i		−	0.273603i	−0.990599	−	0.136801i	$-0.956318\pi$
$149$		−	3.33975i		−	0.273603i	0.990599	−	0.136801i	$-0.0436822\pi$
$150$	13.1603	−	10.3301i	1.07453	−	0.843451i
$151$	4.73205			0.385089			0.192544	−	0.981288i	$-0.438326\pi$
$151$	4.73205			0.385089			0.192544	+	0.981288i	$0.438326\pi$
$152$	−0.437822	−	1.63397i	−0.0355121	−	0.132533i
$153$	8.19615	+	2.19615i	0.662620	+	0.177548i
$154$	−23.1244	−	15.6603i	−1.86341	−	1.26194i
$155$	0.437822	+	0.0262794i	0.0351667	+	0.00211082i
$156$	−8.19615	−	8.19615i	−0.656217	−	0.656217i
$157$	0.366025	+	1.36603i	0.0292120	+	0.109021i	0.978993	−	0.203896i	$-0.0653605\pi$
$157$	0.366025	+	1.36603i	0.0292120	+	0.109021i	−0.949780	+	0.312917i	$0.898694\pi$
$158$	−2.26795	−	8.46410i	−0.180428	−	0.673368i
$159$	2.83013	−	10.5622i	0.224444	−	0.837635i
$160$	−12.6962	+	11.2583i	−1.00372	+	0.890049i
$161$	−5.50000	−	11.3301i	−0.433461	−	0.892939i
$162$	−4.50000	+	16.7942i	−0.353553	+	1.31948i
$163$	2.36603	+	8.83013i	0.185321	+	0.691629i	0.994562	+	0.104151i	$0.0332125\pi$
$163$	2.36603	+	8.83013i	0.185321	+	0.691629i	−0.809240	+	0.587478i	$0.800121\pi$
$164$	−4.39230			−0.342981
$165$	−9.46410	−	18.9282i	−0.736779	−	1.47356i
$166$			2.73205i			0.212048i
$167$	−13.5263	−	3.62436i	−1.04669	−	0.280461i	−0.305810	−	0.952093i	$-0.598927\pi$
$167$	−13.5263	−	3.62436i	−1.04669	−	0.280461i	−0.740885	+	0.671632i	$0.765594\pi$
$168$	2.13397	−	1.03590i	0.164640	−	0.0799213i
$169$	−1.66987	−	0.964102i	−0.128452	−	0.0741617i
$170$	−0.732051	+	12.1962i	−0.0561457	+	0.935402i
$171$	4.90192	−	8.49038i	0.374859	−	0.649276i
$172$	−0.696152	+	2.59808i	−0.0530811	+	0.198101i
$173$	3.66025	−	13.6603i	0.278284	−	1.03857i	−0.675325	−	0.737521i	$-0.735996\pi$
$173$	3.66025	−	13.6603i	0.278284	−	1.03857i	0.953609	−	0.301049i	$-0.0973369\pi$
$174$	−16.3923	−	16.3923i	−1.24270	−	1.24270i
$175$	−7.40192	−	10.9641i	−0.559533	−	0.828808i
$176$	12.1962	+	21.1244i	0.919320	+	1.59231i
$177$	5.19615	+	3.00000i	0.390567	+	0.225494i
$178$	−12.5622	−	12.5622i	−0.941575	−	0.941575i
$179$	−10.9019	+	6.29423i	−0.814848	+	0.470453i	−0.848637	−	0.528976i	$-0.822576\pi$
$179$	−10.9019	+	6.29423i	−0.814848	+	0.470453i	0.0337886	+	0.999429i	$0.489243\pi$
$180$	−11.5981	−	0.696152i	−0.864470	−	0.0518881i
$181$			11.4641i			0.852120i	0.904695	+	0.426060i	$0.140099\pi$
$181$			11.4641i			0.852120i	−0.904695	+	0.426060i	$0.859901\pi$
$182$	−14.9282	+	12.9282i	−1.10655	+	0.958302i
$183$	9.86603	+	17.0885i	0.729318	+	1.26322i
$184$			2.46410i			0.181656i
$185$	7.09808	−	6.29423i	0.521861	−	0.462761i
$186$	−0.464102	−	0.464102i	−0.0340296	−	0.0340296i
$187$	14.9282	+	4.00000i	1.09166	+	0.292509i
$188$	−16.0981	−	16.0981i	−1.17407	−	1.17407i
$189$	12.9904	+	4.50000i	0.944911	+	0.327327i
$190$	13.3923	+	4.46410i	0.971580	+	0.323860i
$191$	8.83013	+	15.2942i	0.638926	+	1.10665i	0.985669	+	0.168691i	$0.0539542\pi$
$191$	8.83013	+	15.2942i	0.638926	+	1.10665i	−0.346743	+	0.937960i	$0.612713\pi$
$192$	9.92820			0.716506
$193$	−5.29423	−	19.7583i	−0.381087	−	1.42224i	−0.844244	−	0.535959i	$-0.819950\pi$
$193$	−5.29423	−	19.7583i	−0.381087	−	1.42224i	0.463157	−	0.886276i	$-0.346717\pi$
$194$	15.6603			1.12434
$195$	−14.6603	+	3.00000i	−1.04984	+	0.214834i
$196$	4.50000	+	11.2583i	0.321429	+	0.804166i
$197$	−17.4641	−	17.4641i	−1.24427	−	1.24427i	−0.958214	−	0.286051i	$-0.907657\pi$
$197$	−17.4641	−	17.4641i	−1.24427	−	1.24427i	−0.286051	−	0.958214i	$-0.592343\pi$
$198$	−8.19615	+	30.5885i	−0.582475	+	2.17383i
$199$	3.92820	+	6.80385i	0.278463	+	0.482312i	0.971003	−	0.239068i	$-0.0768417\pi$
$199$	3.92820	+	6.80385i	0.278463	+	0.482312i	−0.692540	+	0.721379i	$0.743508\pi$
$200$	0.366025	+	2.56218i	0.0258819	+	0.181173i
$201$	0.571797	+	2.13397i	0.0403314	+	0.150519i
$202$	32.8205	+	8.79423i	2.30924	+	0.618760i
$203$	−13.8564	+	12.0000i	−0.972529	+	0.842235i
$204$	6.00000	−	6.00000i	0.420084	−	0.420084i
$205$	−3.12436	+	4.73205i	−0.218214	+	0.330501i
$206$	−6.86603	+	3.96410i	−0.478379	+	0.276192i
$207$	−10.0981	+	10.0981i	−0.701865	+	0.701865i
$208$	16.6603	−	4.46410i	1.15518	−	0.309530i
$209$	8.92820	−	15.4641i	0.617577	−	1.06967i
$210$	−2.59808	+	19.6244i	−0.179284	+	1.35421i
$211$	−4.46410	−	7.73205i	−0.307321	−	0.532296i	0.670454	−	0.741951i	$-0.266099\pi$
$211$	−4.46410	−	7.73205i	−0.307321	−	0.532296i	−0.977775	+	0.209655i	$0.932766\pi$
$212$	−7.73205	−	7.73205i	−0.531039	−	0.531039i
$213$			10.3923i			0.712069i
$214$			4.73205i			0.323476i
$215$	2.30385	+	2.59808i	0.157121	+	0.177187i
$216$	−1.90192	−	1.90192i	−0.129410	−	0.129410i
$217$	−0.392305	+	0.339746i	−0.0266314	+	0.0230635i
$218$	1.00000	+	3.73205i	0.0677285	+	0.252766i
$219$	15.2942	+	4.09808i	1.03349	+	0.276922i
$220$	−21.1244	−	1.26795i	−1.42420	−	0.0854851i
$221$	5.46410	−	9.46410i	0.367555	−	0.636624i
$222$	−14.1962			−0.952783
$223$	−4.96410	+	1.33013i	−0.332421	+	0.0890719i	−0.421169	−	0.906982i	$-0.638380\pi$
$223$	−4.96410	+	1.33013i	−0.332421	+	0.0890719i	0.0887481	+	0.996054i	$0.471713\pi$
$224$	1.43782	−	20.0263i	0.0960685	−	1.33806i
$225$	−9.00000	+	12.0000i	−0.600000	+	0.800000i
$226$	7.09808	−	12.2942i	0.472157	−	0.817800i
$227$	−10.6603	+	10.6603i	−0.707546	+	0.707546i	−0.966019	−	0.258473i	$-0.916781\pi$
$227$	−10.6603	+	10.6603i	−0.707546	+	0.707546i	0.258473	+	0.966019i	$0.416781\pi$
$228$	−4.90192	−	8.49038i	−0.324638	−	0.562289i
$229$	−4.66025			−0.307958			−0.153979	−	0.988074i	$-0.549209\pi$
$229$	−4.66025			−0.307958			−0.153979	+	0.988074i	$0.549209\pi$
$230$	−17.1603	−	11.3301i	−1.13151	−	0.747086i
$231$	23.6603	+	8.19615i	1.55673	+	0.539267i
$232$	3.46410	−	0.928203i	0.227429	−	0.0609395i
$233$	3.16987	+	11.8301i	0.207665	+	0.775017i	0.988621	+	0.150430i	$0.0480660\pi$
$233$	3.16987	+	11.8301i	0.207665	+	0.775017i	−0.780955	+	0.624587i	$0.785267\pi$
$234$	19.3923	+	11.1962i	1.26771	+	0.731915i
$235$	−28.7942	+	5.89230i	−1.87833	+	0.384372i
$236$	5.19615	−	3.00000i	0.338241	−	0.195283i
$237$	3.92820	+	6.80385i	0.255164	+	0.441957i
$238$	−9.46410	−	10.9282i	−0.613467	−	0.708370i
$239$	−19.0526	+	11.0000i	−1.23241	+	0.711531i	−0.967531	−	0.252752i	$-0.918664\pi$
$239$	−19.0526	+	11.0000i	−1.23241	+	0.711531i	−0.264876	+	0.964282i	$0.585331\pi$
$240$	9.52628	−	14.4282i	0.614919	−	0.931337i
$241$		−	9.53590i		−	0.614261i	−0.951667	−	0.307131i	$-0.900631\pi$
$241$		−	9.53590i		−	0.614261i	0.951667	−	0.307131i	$-0.0993688\pi$
$242$	−9.42820	+	35.1865i	−0.606068	+	2.26188i
$243$		−	15.5885i		−	1.00000i
$244$	19.7321			1.26322
$245$	15.3301	+	3.16025i	0.979406	+	0.201901i
$246$	8.19615	−	2.19615i	0.522568	−	0.140022i
$247$	−8.92820	−	8.92820i	−0.568088	−	0.568088i
$248$	0.0980762	−	0.0262794i	0.00622785	−	0.00166875i
$249$	−0.633975	−	2.36603i	−0.0401765	−	0.149941i
$250$	−19.5263	−	9.23205i	−1.23495	−	0.583886i
$251$		−	5.85641i		−	0.369653i	−0.982771	−	0.184827i	$-0.940828\pi$
$251$		−	5.85641i		−	0.369653i	0.982771	−	0.184827i	$-0.0591723\pi$
$252$	10.3923	−	9.00000i	0.654654	−	0.566947i
$253$	−18.3923	+	18.3923i	−1.15631	+	1.15631i
$254$	37.2846	−	21.5263i	2.33944	−	1.35068i
$255$	−2.19615	−	10.7321i	−0.137528	−	0.672067i
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	−8.80385	+	8.80385i	−0.549169	+	0.549169i	−0.926200	−	0.377032i	$-0.876945\pi$
$257$	−8.80385	+	8.80385i	−0.549169	+	0.549169i	0.377032	+	0.926200i	$0.376945\pi$
$258$		−	5.19615i		−	0.323498i
$259$	−0.803848	+	11.1962i	−0.0499487	+	0.695695i
$260$	−4.73205	+	14.1962i	−0.293469	+	0.880408i
$261$	18.0000	+	10.3923i	1.11417	+	0.643268i
$262$	9.46410	+	2.53590i	0.584694	+	0.156668i
$263$	−20.0981	+	20.0981i	−1.23930	+	1.23930i	−0.279013	+	0.960287i	$0.590007\pi$
$263$	−20.0981	+	20.0981i	−1.23930	+	1.23930i	−0.960287	+	0.279013i	$0.909993\pi$
$264$	−3.46410	−	3.46410i	−0.213201	−	0.213201i
$265$	−13.8301	+	2.83013i	−0.849578	+	0.173853i
$266$	−15.0263	+	7.29423i	−0.921320	+	0.447238i
$267$	13.7942	+	7.96410i	0.844193	+	0.487395i
$268$	2.13397	+	0.571797i	0.130353	+	0.0349280i
$269$	−4.96410	−	8.59808i	−0.302667	−	0.524234i	0.674072	−	0.738665i	$-0.264544\pi$
$269$	−4.96410	−	8.59808i	−0.302667	−	0.524234i	−0.976739	+	0.214431i	$0.931210\pi$
$270$	21.9904	−	4.50000i	1.33829	−	0.273861i
$271$	−9.92820	−	5.73205i	−0.603095	−	0.348197i	0.167163	−	0.985929i	$-0.446539\pi$
$271$	−9.92820	−	5.73205i	−0.603095	−	0.348197i	−0.770258	+	0.637732i	$0.779873\pi$
$272$	3.26795	+	12.1962i	0.198149	+	0.739500i
$273$	9.92820	−	14.6603i	0.600882	−	0.887279i
$274$	−3.46410	+	2.00000i	−0.209274	+	0.120824i
$275$	−16.3923	+	21.8564i	−0.988493	+	1.31799i
$276$	3.69615	+	13.7942i	0.222482	+	0.830315i
$277$	−14.1962	−	14.1962i	−0.852964	−	0.852964i	0.137533	−	0.990497i	$-0.456083\pi$
$277$	−14.1962	−	14.1962i	−0.852964	−	0.852964i	−0.990497	+	0.137533i	$0.956083\pi$
$278$	−12.9282	+	3.46410i	−0.775382	+	0.207763i
$279$	0.509619	+	0.294229i	0.0305101	+	0.0176150i
$280$	−2.42820	−	1.86603i	−0.145113	−	0.111516i
$281$	6.86603	−	11.8923i	0.409593	−	0.709435i	−0.585251	−	0.810852i	$-0.699004\pi$
$281$	6.86603	−	11.8923i	0.409593	−	0.709435i	0.994844	+	0.101417i	$0.0323375\pi$
$282$	38.0885	+	21.9904i	2.26813	+	1.30951i
$283$	21.5263	−	5.76795i	1.27960	−	0.342869i	0.445901	−	0.895082i	$-0.352883\pi$
$283$	21.5263	−	5.76795i	1.27960	−	0.342869i	0.833703	+	0.552213i	$0.186217\pi$
$284$	9.00000	+	5.19615i	0.534052	+	0.308335i
$285$	−12.6340	−	0.758330i	−0.748372	−	0.0449196i
$286$	35.3205	+	20.3923i	2.08855	+	1.20582i
$287$	−1.26795	−	6.58846i	−0.0748447	−	0.388904i
$288$	−21.9904	+	5.89230i	−1.29580	+	0.347207i
$289$	−7.79423	−	4.50000i	−0.458484	−	0.264706i
$290$	−9.46410	+	28.3923i	−0.555751	+	1.66725i
$291$	−13.5622	+	3.63397i	−0.795029	+	0.213027i
$292$	11.1962	−	11.1962i	0.655205	−	0.655205i
$293$	−5.43782	+	20.2942i	−0.317681	+	1.18560i	0.603787	+	0.797146i	$0.293658\pi$
$293$	−5.43782	+	20.2942i	−0.317681	+	1.18560i	−0.921468	+	0.388455i	$0.873009\pi$
$294$	−14.0263	−	18.7583i	−0.818029	−	1.09401i
$295$	0.464102	−	7.73205i	0.0270210	−	0.450177i
$296$	1.09808	−	1.90192i	0.0638244	−	0.110547i
$297$		−	28.3923i		−	1.64749i
$298$	6.23205	+	1.66987i	0.361013	+	0.0967331i
$299$	9.19615	+	15.9282i	0.531827	+	0.921152i
$300$	5.89230	+	13.7942i	0.340192	+	0.796410i
$301$	−4.09808	−	0.294229i	−0.236209	−	0.0169591i
$302$	−2.36603	+	8.83013i	−0.136149	+	0.508117i
$303$	−30.4641			−1.75012
$304$	14.5885			0.836705
$305$	14.0359	−	21.2583i	0.803693	−	1.21725i
$306$	−8.19615	+	14.1962i	−0.468543	+	0.811540i
$307$	17.5359	−	17.5359i	1.00083	−	1.00083i	0.000826926	−	1.00000i	$-0.499737\pi$
$307$	17.5359	−	17.5359i	1.00083	−	1.00083i	1.00000		0.000826926i	$-0.000263219\pi$
$308$	18.9282	−	16.3923i	1.07853	−	0.934038i
$309$	5.02628	−	5.02628i	0.285935	−	0.285935i
$310$	−0.267949	+	0.803848i	−0.0152185	+	0.0456555i
$311$	−13.8564	−	8.00000i	−0.785725	−	0.453638i	0.0527306	−	0.998609i	$-0.483208\pi$
$311$	−13.8564	−	8.00000i	−0.785725	−	0.453638i	−0.838455	+	0.544970i	$0.816541\pi$
$312$	−3.00000	+	1.73205i	−0.169842	+	0.0980581i
$313$	−1.90192	+	7.09808i	−0.107503	+	0.401207i	−0.998617	−	0.0525725i	$-0.983258\pi$
$313$	−1.90192	+	7.09808i	−0.107503	+	0.401207i	0.891114	+	0.453779i	$0.149925\pi$
$314$	−2.73205			−0.154179
$315$	−2.30385	−	17.5981i	−0.129807	−	0.991539i
$316$	7.85641			0.441957
$317$	3.09808	−	11.5622i	0.174005	−	0.649397i	−0.822714	−	0.568456i	$-0.807541\pi$
$317$	3.09808	−	11.5622i	0.174005	−	0.649397i	0.996719	−	0.0809406i	$-0.0257924\pi$
$318$	18.2942	+	10.5622i	1.02589	+	0.592298i
$319$	32.7846	+	18.9282i	1.83559	+	1.05978i
$320$	−5.73205	−	11.4641i	−0.320431	−	0.640863i
$321$	−1.09808	−	4.09808i	−0.0612886	−	0.228732i
$322$	23.8923	−	4.59808i	1.33147	−	0.256241i
$323$	6.53590	−	6.53590i	0.363667	−	0.363667i
$324$	−13.5000	−	7.79423i	−0.750000	−	0.433013i
$325$	11.9282	+	15.1962i	0.661658	+	0.842931i
$326$	−17.6603			−0.978111
$327$	−1.73205	−	3.00000i	−0.0957826	−	0.165900i
$328$	−0.339746	+	1.26795i	−0.0187593	+	0.0700108i
$329$	19.5000	−	28.7942i	1.07507	−	1.58748i
$330$	40.0526	−	8.19615i	2.20482	−	0.451183i
$331$	−9.16987	−	15.8827i	−0.504022	−	0.872991i	−0.999989	−	0.00465022i	$-0.998520\pi$
$331$	−9.16987	−	15.8827i	−0.504022	−	0.872991i	0.495967	−	0.868341i	$-0.334814\pi$
$332$	−2.36603	−	0.633975i	−0.129853	−	0.0347939i
$333$	12.2942	−	3.29423i	0.673720	−	0.180523i
$334$	13.5263	−	23.4282i	0.740125	−	1.28193i
$335$	2.13397	−	1.89230i	0.116591	−	0.103388i
$336$	3.86603	+	20.0885i	0.210909	+	1.09592i
$337$	−1.19615	+	4.46410i	−0.0651586	+	0.243175i	−0.990822	−	0.135173i	$-0.956841\pi$
$337$	−1.19615	+	4.46410i	−0.0651586	+	0.243175i	0.925663	+	0.378348i	$0.123508\pi$
$338$	2.63397	−	2.63397i	0.143269	−	0.143269i
$339$	−3.29423	+	12.2942i	−0.178918	+	0.667731i
$340$	−10.3923	−	3.46410i	−0.563602	−	0.187867i
$341$	0.928203	+	0.535898i	0.0502650	+	0.0290205i
$342$	13.3923	+	13.3923i	0.724173	+	0.724173i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	0.696152	+	0.401924i	0.0375340	+	0.0216703i
$345$	17.4904	+	5.83013i	0.941650	+	0.313883i
$346$	23.6603	+	13.6603i	1.27198	+	0.734380i
$347$	20.2583	−	5.42820i	1.08752	−	0.291401i	0.329849	−	0.944034i	$-0.393002\pi$
$347$	20.2583	−	5.42820i	1.08752	−	0.291401i	0.757675	+	0.652632i	$0.226335\pi$
$348$	18.0000	−	10.3923i	0.964901	−	0.557086i
$349$	−17.0622	+	29.5526i	−0.913317	+	1.58191i	−0.103971	+	0.994580i	$0.533155\pi$
$349$	−17.0622	+	29.5526i	−0.913317	+	1.58191i	−0.809346	+	0.587332i	$0.800178\pi$
$350$	24.1603	−	8.33013i	1.29142	−	0.445264i
$351$	−19.3923	−	5.19615i	−1.03508	−	0.277350i
$352$	−40.0526	+	10.7321i	−2.13481	+	0.572020i
$353$	7.85641	+	7.85641i	0.418154	+	0.418154i	0.884567	−	0.466413i	$-0.154454\pi$
$353$	7.85641	+	7.85641i	0.418154	+	0.418154i	−0.466413	+	0.884567i	$0.654454\pi$
$354$	−8.19615	+	8.19615i	−0.435621	+	0.435621i
$355$	12.0000	−	6.00000i	0.636894	−	0.318447i
$356$	13.7942	−	7.96410i	0.731093	−	0.422097i
$357$	10.7321	+	7.26795i	0.568000	+	0.384661i
$358$	−6.29423	−	23.4904i	−0.332660	−	1.24151i
$359$	−17.9545	−	10.3660i	−0.947601	−	0.547098i	−0.0552664	−	0.998472i	$-0.517601\pi$
$359$	−17.9545	−	10.3660i	−0.947601	−	0.547098i	−0.892335	+	0.451374i	$0.850934\pi$
$360$	−1.09808	+	3.29423i	−0.0578737	+	0.173621i
$361$	4.16025	+	7.20577i	0.218961	+	0.379251i
$362$	−21.3923	−	5.73205i	−1.12435	−	0.301270i
$363$		−	32.6603i		−	1.71422i
$364$	−7.73205	−	15.9282i	−0.405270	−	0.834865i
$365$	−4.09808	−	20.0263i	−0.214503	−	1.04822i
$366$	−36.8205	+	9.86603i	−1.92464	+	0.515705i
$367$	−4.83013	+	4.83013i	−0.252131	+	0.252131i	−0.821844	−	0.569713i	$-0.807054\pi$
$367$	−4.83013	+	4.83013i	−0.252131	+	0.252131i	0.569713	+	0.821844i	$0.307054\pi$
$368$	−20.5263	−	5.50000i	−1.07001	−	0.286707i
$369$	−6.58846	+	3.80385i	−0.342981	+	0.198020i
$370$	8.19615	+	16.3923i	0.426098	+	0.852195i
$371$	9.36603	−	13.8301i	0.486260	−	0.718024i
$372$	0.509619	−	0.294229i	0.0264225	−	0.0152550i
$373$	3.00000	−	3.00000i	0.155334	−	0.155334i	−0.625161	−	0.780496i	$-0.714967\pi$
$373$	3.00000	−	3.00000i	0.155334	−	0.155334i	0.780496	+	0.625161i	$0.214967\pi$
$374$	−14.9282	+	25.8564i	−0.771919	+	1.33700i
$375$	19.0526	+	3.46410i	0.983870	+	0.178885i
$376$	−5.89230	+	3.40192i	−0.303872	+	0.175441i
$377$	18.9282	−	18.9282i	0.974852	−	0.974852i
$378$	−14.8923	+	21.9904i	−0.765978	+	1.13106i
$379$		−	12.5359i		−	0.643926i	−0.946752	−	0.321963i	$-0.895657\pi$
$379$		−	12.5359i		−	0.643926i	0.946752	−	0.321963i	$-0.104343\pi$
$380$	−6.97372	+	10.5622i	−0.357744	+	0.541828i
$381$	−27.2942	+	27.2942i	−1.39833	+	1.39833i
$382$	−32.9545	+	8.83013i	−1.68610	+	0.451789i
$383$	11.5622	+	11.5622i	0.590800	+	0.590800i	0.937847	−	0.347048i	$-0.112816\pi$
$383$	11.5622	+	11.5622i	0.590800	+	0.590800i	−0.347048	+	0.937847i	$0.612816\pi$
$384$	1.83975	−	6.86603i	0.0938841	−	0.350380i
$385$	−4.19615	−	32.0526i	−0.213856	−	1.63355i
$386$	39.5167			2.01135
$387$	1.20577	+	4.50000i	0.0612928	+	0.228748i
$388$	−3.63397	+	13.5622i	−0.184487	+	0.688515i
$389$		−	1.19615i		−	0.0606473i	−0.999540	−	0.0303237i	$-0.990346\pi$
$389$		−	1.19615i		−	0.0606473i	0.999540	−	0.0303237i	$-0.00965380\pi$
$390$	1.73205	−	28.8564i	0.0877058	−	1.46120i
$391$	−11.6603	+	6.73205i	−0.589684	+	0.340454i
$392$	3.59808	−	0.428203i	0.181730	−	0.0216275i
$393$	−8.78461			−0.443125
$394$	41.3205	−	23.8564i	2.08170	−	1.20187i
$395$	5.58846	−	8.46410i	0.281186	−	0.425875i
$396$	−24.5885	−	14.1962i	−1.23562	−	0.713384i
$397$	8.78461	+	32.7846i	0.440887	+	1.64541i	0.726573	+	0.687089i	$0.241112\pi$
$397$	8.78461	+	32.7846i	0.440887	+	1.64541i	−0.285686	+	0.958323i	$0.592221\pi$
$398$	−14.6603	+	3.92820i	−0.734852	+	0.196903i
$399$	11.3205	−	9.80385i	0.566734	−	0.490806i
$400$	−22.1603	−	2.66987i	−1.10801	−	0.133494i
$401$	23.3923			1.16816			0.584078	−	0.811698i	$-0.301456\pi$
$401$	23.3923			1.16816			0.584078	+	0.811698i	$0.301456\pi$
$402$	−4.26795			−0.212866
$403$	0.535898	−	0.535898i	0.0266950	−	0.0266950i
$404$	−15.2321	+	26.3827i	−0.757823	+	1.31259i
$405$	−18.0000	+	9.00000i	−0.894427	+	0.447214i
$406$	−15.4641	−	31.8564i	−0.767470	−	1.58101i
$407$	22.3923	−	6.00000i	1.10995	−	0.297409i
$408$	−1.26795	−	2.19615i	−0.0627728	−	0.108726i
$409$	2.69615	−	4.66987i	0.133316	−	0.230910i	−0.791637	−	0.610992i	$-0.790771\pi$
$409$	2.69615	−	4.66987i	0.133316	−	0.230910i	0.924953	+	0.380082i	$0.124104\pi$
$410$	−7.26795	−	8.19615i	−0.358938	−	0.404779i
$411$	2.53590	−	2.53590i	0.125087	−	0.125087i
$412$	−1.83975	−	6.86603i	−0.0906378	−	0.338265i
$413$	6.00000	+	6.92820i	0.295241	+	0.340915i
$414$	−13.7942	−	23.8923i	−0.677949	−	1.17424i
$415$	−2.36603	+	2.09808i	−0.116144	+	0.102991i
$416$			29.3205i			1.43756i
$417$	10.3923	−	6.00000i	0.508913	−	0.293821i
$418$	24.3923	+	24.3923i	1.19307	+	1.19307i
$419$	4.00000	+	6.92820i	0.195413	+	0.338465i	0.947036	−	0.321128i	$-0.104062\pi$
$419$	4.00000	+	6.92820i	0.195413	+	0.338465i	−0.751623	+	0.659593i	$0.770729\pi$
$420$	−16.3923	−	6.80385i	−0.799863	−	0.331994i
$421$	−11.5263	+	19.9641i	−0.561756	+	0.972991i	0.435587	+	0.900147i	$0.356541\pi$
$421$	−11.5263	+	19.9641i	−0.561756	+	0.972991i	−0.997343	+	0.0728441i	$0.976792\pi$
$422$	16.6603	−	4.46410i	0.811008	−	0.217309i
$423$	−38.0885	−	10.2058i	−1.85192	−	0.496222i
$424$	−2.83013	+	1.63397i	−0.137443	+	0.0793528i
$425$	−11.1244	+	8.73205i	−0.539611	+	0.423567i
$426$	−19.3923	−	5.19615i	−0.939560	−	0.251754i
$427$	5.69615	+	29.5981i	0.275656	+	1.43235i
$428$	−4.09808	−	1.09808i	−0.198088	−	0.0530775i
$429$	−35.3205	−	9.46410i	−1.70529	−	0.456931i
$430$	−6.00000	+	3.00000i	−0.289346	+	0.144673i
$431$	12.0981	+	20.9545i	0.582744	+	1.00934i	0.995153	+	0.0983430i	$0.0313542\pi$
$431$	12.0981	+	20.9545i	0.582744	+	1.00934i	−0.412409	+	0.910999i	$0.635312\pi$
$432$	20.0885	−	11.5981i	0.966506	−	0.558013i
$433$	−9.80385	−	9.80385i	−0.471143	−	0.471143i	0.431141	−	0.902284i	$-0.358111\pi$
$433$	−9.80385	−	9.80385i	−0.471143	−	0.471143i	−0.902284	+	0.431141i	$0.858111\pi$
$434$	−0.437822	−	0.901924i	−0.0210161	−	0.0432937i
$435$	1.60770	−	26.7846i	0.0770831	−	1.28422i
$436$	−3.46410			−0.165900
$437$	4.02628	+	15.0263i	0.192603	+	0.718804i
$438$	−15.2942	+	26.4904i	−0.730787	+	1.26576i
$439$	−2.92820	−	5.07180i	−0.139756	−	0.242064i	0.787649	−	0.616125i	$-0.211298\pi$
$439$	−2.92820	−	5.07180i	−0.139756	−	0.242064i	−0.927404	+	0.374061i	$0.877965\pi$
$440$	−2.00000	+	6.00000i	−0.0953463	+	0.286039i
$441$	16.5000	+	12.9904i	0.785714	+	0.618590i
$442$	14.9282	+	14.9282i	0.710062	+	0.710062i
$443$	0.901924	+	0.241670i	0.0428517	+	0.0114821i	0.280181	−	0.959947i	$-0.409605\pi$
$443$	0.901924	+	0.241670i	0.0428517	+	0.0114821i	−0.237330	+	0.971429i	$0.576272\pi$
$444$	3.29423	−	12.2942i	0.156337	−	0.583458i
$445$	1.23205	−	20.5263i	0.0584048	−	0.973039i
$446$		−	9.92820i		−	0.470114i
$447$	−5.78461			−0.273603
$448$	14.3301	+	4.96410i	0.677035	+	0.234532i
$449$		−	1.58846i		−	0.0749639i	−0.999297	−	0.0374820i	$-0.988066\pi$
$449$		−	1.58846i		−	0.0749639i	0.999297	−	0.0374820i	$-0.0119337\pi$
$450$	−17.8923	−	22.7942i	−0.843451	−	1.07453i
$451$	−12.0000	+	6.92820i	−0.565058	+	0.326236i
$452$	9.00000	+	9.00000i	0.423324	+	0.423324i
$453$		−	8.19615i		−	0.385089i
$454$	−14.5622	−	25.2224i	−0.683437	−	1.18375i
$455$	−22.6603	−	3.00000i	−1.06233	−	0.140642i
$456$	−2.83013	+	0.758330i	−0.132533	+	0.0355121i
$457$	−2.68653	+	10.0263i	−0.125671	+	0.469010i	−0.999863	−	0.0165709i	$-0.994725\pi$
$457$	−2.68653	+	10.0263i	−0.125671	+	0.469010i	0.874192	+	0.485581i	$0.161392\pi$
$458$	2.33013	−	8.69615i	0.108880	−	0.406345i
$459$	3.80385	−	14.1962i	0.177548	−	0.662620i
$460$	13.7942	−	12.2321i	0.643159	−	0.570322i
$461$	−1.03590	−	0.598076i	−0.0482466	−	0.0278552i	0.475683	−	0.879617i	$-0.342201\pi$
$461$	−1.03590	−	0.598076i	−0.0482466	−	0.0278552i	−0.523929	+	0.851762i	$0.675534\pi$
$462$	−27.1244	+	40.0526i	−1.26194	+	1.86341i
$463$	35.1865	+	9.42820i	1.63526	+	0.438166i	0.955433	−	0.295209i	$-0.0953894\pi$
$463$	35.1865	+	9.42820i	1.63526	+	0.438166i	0.679824	+	0.733375i	$0.262056\pi$
$464$			30.9282i			1.43581i
$465$	0.0455173	−	0.758330i	0.00211082	−	0.0351667i
$466$	−23.6603			−1.09604
$467$	3.47372	+	12.9641i	0.160745	+	0.599907i	0.998545	+	0.0539300i	$0.0171748\pi$
$467$	3.47372	+	12.9641i	0.160745	+	0.599907i	−0.837800	+	0.545977i	$0.816159\pi$
$468$	−14.1962	+	14.1962i	−0.656217	+	0.656217i
$469$	−0.241670	+	3.36603i	−0.0111593	+	0.155429i
$470$	3.40192	−	56.6769i	0.156919	−	2.61431i
$471$	2.36603	−	0.633975i	0.109021	−	0.0292120i
$472$	−0.464102	−	1.73205i	−0.0213620	−	0.0797241i
$473$	2.19615	+	8.19615i	0.100979	+	0.376859i
$474$	−14.6603	+	3.92820i	−0.673368	+	0.180428i
$475$	6.41858	+	15.0263i	0.294505	+	0.689453i
$476$	11.6603	−	5.66025i	0.534447	−	0.259437i
$477$	−18.2942	−	4.90192i	−0.837635	−	0.224444i
$478$	−11.0000	−	41.0526i	−0.503128	−	1.87770i
$479$	5.26795			0.240699			0.120349	−	0.992732i	$-0.461599\pi$
$479$	5.26795			0.240699			0.120349	+	0.992732i	$0.461599\pi$
$480$	19.5000	+	21.9904i	0.890049	+	1.00372i
$481$		−	16.3923i		−	0.747425i
$482$	17.7942	+	4.76795i	0.810505	+	0.217174i
$483$	−19.6244	+	9.52628i	−0.892939	+	0.433461i
$484$	−28.2846	−	16.3301i	−1.28566	−	0.742279i
$485$	12.0263	+	13.5622i	0.546085	+	0.615827i
$486$	29.0885	+	7.79423i	1.31948	+	0.353553i
$487$	8.68653	−	32.4186i	0.393624	−	1.46903i	−0.430486	−	0.902597i	$-0.641658\pi$
$487$	8.68653	−	32.4186i	0.393624	−	1.46903i	0.824110	−	0.566429i	$-0.191675\pi$
$488$	1.52628	−	5.69615i	0.0690914	−	0.257853i
$489$	15.2942	−	4.09808i	0.691629	−	0.185321i
$490$	−13.5622	+	27.0263i	−0.612677	+	1.22092i
$491$	8.46410	+	14.6603i	0.381980	+	0.661608i	0.991345	−	0.131281i	$-0.0419091\pi$
$491$	8.46410	+	14.6603i	0.381980	+	0.661608i	−0.609366	+	0.792889i	$0.708576\pi$
$492$			7.60770i			0.342981i
$493$	13.8564	+	13.8564i	0.624061	+	0.624061i
$494$	21.1244	−	12.1962i	0.950430	−	0.548731i
$495$	−32.7846	+	16.3923i	−1.47356	+	0.736779i
$496$			0.875644i			0.0393176i
$497$	−5.19615	+	15.0000i	−0.233079	+	0.672842i
$498$	4.73205			0.212048
$499$		−	7.07180i		−	0.316577i	−0.987393	−	0.158289i	$-0.949402\pi$
$499$		−	7.07180i		−	0.316577i	0.987393	−	0.158289i	$-0.0505976\pi$
$500$	12.5263	−	14.7679i	0.560192	−	0.660443i
$501$	−6.27757	+	23.4282i	−0.280461	+	1.04669i
$502$	10.9282	+	2.92820i	0.487750	+	0.130692i
$503$	−10.0718	−	10.0718i	−0.449079	−	0.449079i	0.445969	−	0.895048i	$-0.352859\pi$
$503$	−10.0718	−	10.0718i	−0.449079	−	0.449079i	−0.895048	+	0.445969i	$0.852859\pi$
$504$	−1.79423	−	3.69615i	−0.0799213	−	0.164640i
$505$	17.5885	+	35.1769i	0.782676	+	1.56535i
$506$	−25.1244	−	43.5167i	−1.11691	−	1.93455i
$507$	−1.66987	+	2.89230i	−0.0741617	+	0.128452i
$508$	9.99038	+	37.2846i	0.443251	+	1.65424i
$509$	−18.0000			−0.797836			−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000			−0.797836			−0.398918	+	0.916987i	$0.630614\pi$
$510$	21.1244	+	1.26795i	0.935402	+	0.0561457i
$511$	20.0263	+	13.5622i	0.885910	+	0.599955i
$512$	−20.6865	−	20.6865i	−0.914224	−	0.914224i
$513$	−14.7058	−	8.49038i	−0.649276	−	0.374859i
$514$	−12.0263	−	20.8301i	−0.530456	−	0.918778i
$515$	−8.70577	−	2.90192i	−0.383622	−	0.127874i
$516$	4.50000	+	1.20577i	0.198101	+	0.0530811i
$517$	−69.3731	−	18.5885i	−3.05102	−	0.817519i
$518$	−20.4904	−	7.09808i	−0.900296	−	0.311872i
$519$	−23.6603	−	6.33975i	−1.03857	−	0.278284i
$520$	3.73205	+	2.46410i	0.163661	+	0.108058i
$521$	37.6244	−	21.7224i	1.64835	−	0.951677i	0.670626	−	0.741796i	$-0.266026\pi$
$521$	37.6244	−	21.7224i	1.64835	−	0.951677i	0.977727	−	0.209881i	$-0.0673078\pi$
$522$	−28.3923	+	28.3923i	−1.24270	+	1.24270i
$523$	−4.96410	+	1.33013i	−0.217065	+	0.0581624i	−0.365713	−	0.930728i	$-0.619175\pi$
$523$	−4.96410	+	1.33013i	−0.217065	+	0.0581624i	0.148648	+	0.988890i	$0.452508\pi$
$524$	−4.39230	+	7.60770i	−0.191879	+	0.332344i
$525$	−18.9904	+	12.8205i	−0.828808	+	0.559533i
$526$	−27.4545	−	47.5526i	−1.19707	−	2.07339i
$527$	0.392305	+	0.392305i	0.0170891	+	0.0170891i
$528$	36.5885	−	21.1244i	1.59231	−	0.919320i
$529$			0.339746i			0.0147716i
$530$	1.63397	−	27.2224i	0.0709753	−	1.18247i
$531$	5.19615	−	9.00000i	0.225494	−	0.390567i
$532$	−2.83013	−	14.7058i	−0.122702	−	0.637576i
$533$	2.53590	+	9.46410i	0.109842	+	0.409936i
$534$	−21.7583	+	21.7583i	−0.941575	+	0.941575i
$535$	−4.09808	+	3.63397i	−0.177175	+	0.157110i
$536$	0.330127	−	0.571797i	0.0142593	−	0.0246979i
$537$	10.9019	+	18.8827i	0.470453	+	0.814848i
$538$	18.5263	−	4.96410i	0.798725	−	0.214018i
$539$	30.0526	+	23.6603i	1.29446	+	1.01912i
$540$	−1.20577	+	20.0885i	−0.0518881	+	0.864470i
$541$	4.96410	−	8.59808i	0.213423	−	0.369660i	−0.739360	−	0.673310i	$-0.764872\pi$
$541$	4.96410	−	8.59808i	0.213423	−	0.369660i	0.952784	+	0.303650i	$0.0982053\pi$
$542$	15.6603	−	15.6603i	0.672666	−	0.672666i
$543$	19.8564			0.852120
$544$	−21.4641			−0.920266
$545$	−2.46410	+	3.73205i	−0.105551	+	0.159863i
$546$	22.3923	+	25.8564i	0.958302	+	1.10655i
$547$	−12.3660	+	3.31347i	−0.528733	+	0.141674i	−0.513303	−	0.858207i	$-0.671578\pi$
$547$	−12.3660	+	3.31347i	−0.528733	+	0.141674i	−0.0154299	+	0.999881i	$0.504912\pi$
$548$	−0.928203	−	3.46410i	−0.0396509	−	0.147979i
$549$	29.5981	−	17.0885i	1.26322	−	0.729318i
$550$	−32.5885	−	41.5167i	−1.38958	−	1.77028i
$551$	19.6077	−	11.3205i	0.835316	−	0.482270i
$552$	4.26795			0.181656
$553$	2.26795	+	11.7846i	0.0964430	+	0.501133i
$554$	33.5885	−	19.3923i	1.42704	−	0.823900i
$555$	−10.9019	−	12.2942i	−0.462761	−	0.521861i
$556$		−	12.0000i		−	0.508913i
$557$	4.09808	−	15.2942i	0.173641	−	0.648037i	−0.823138	−	0.567841i	$-0.807779\pi$
$557$	4.09808	−	15.2942i	0.173641	−	0.648037i	0.996779	−	0.0801960i	$-0.0255546\pi$
$558$	−0.803848	+	0.803848i	−0.0340296	+	0.0340296i
$559$	6.00000			0.253773
$560$	20.9641	−	16.0622i	0.885895	−	0.678751i
$561$	6.92820	−	25.8564i	0.292509	−	1.09166i
$562$	18.7583	+	18.7583i	0.791272	+	0.791272i
$563$	20.7224	−	5.55256i	0.873346	−	0.234012i	0.205812	−	0.978592i	$-0.434016\pi$
$563$	20.7224	−	5.55256i	0.873346	−	0.234012i	0.667534	+	0.744579i	$0.267350\pi$
$564$	−27.8827	+	27.8827i	−1.17407	+	1.17407i
$565$	16.0981	−	3.29423i	0.677251	−	0.138589i
$566$			43.0526i			1.80963i
$567$	7.79423	−	22.5000i	0.327327	−	0.944911i
$568$	2.19615	−	2.19615i	0.0921485	−	0.0921485i
$569$	−16.2679	+	9.39230i	−0.681988	+	0.393746i	−0.800604	−	0.599194i	$-0.795488\pi$
$569$	−16.2679	+	9.39230i	−0.681988	+	0.393746i	0.118616	+	0.992940i	$0.462154\pi$
$570$	7.73205	−	23.1962i	0.323860	−	0.971580i
$571$	10.1244	−	17.5359i	0.423691	−	0.733855i	−0.572606	−	0.819831i	$-0.694068\pi$
$571$	10.1244	−	17.5359i	0.423691	−	0.733855i	0.996297	+	0.0859761i	$0.0274009\pi$
$572$	−25.8564	+	25.8564i	−1.08111	+	1.08111i
$573$	26.4904	−	15.2942i	1.10665	−	0.638926i
$574$	12.9282	+	0.928203i	0.539613	+	0.0387425i
$575$	−3.36603	−	23.5622i	−0.140373	−	0.982611i
$576$		−	17.1962i		−	0.716506i
$577$	4.92820	+	1.32051i	0.205164	+	0.0549735i	0.359937	−	0.932977i	$-0.382798\pi$
$577$	4.92820	+	1.32051i	0.205164	+	0.0549735i	−0.154773	+	0.987950i	$0.549465\pi$
$578$	12.2942	−	12.2942i	0.511372	−	0.511372i
$579$	−34.2224	+	9.16987i	−1.42224	+	0.381087i
$580$	−22.3923	−	14.7846i	−0.929790	−	0.613898i
$581$	0.267949	−	3.73205i	0.0111164	−	0.154832i
$582$		−	27.1244i		−	1.12434i
$583$	−33.3205	−	8.92820i	−1.37999	−	0.369768i
$584$	−2.36603	−	4.09808i	−0.0979068	−	0.169580i
$585$	5.19615	+	25.3923i	0.214834	+	1.04984i
$586$	−35.1506	−	20.2942i	−1.45206	−	0.838347i
$587$	8.62436	+	32.1865i	0.355965	+	1.32848i	0.879265	+	0.476332i	$0.158034\pi$
$587$	8.62436	+	32.1865i	0.355965	+	1.32848i	−0.523300	+	0.852148i	$0.675299\pi$
$588$	19.5000	−	7.79423i	0.804166	−	0.321429i
$589$	0.555136	−	0.320508i	0.0228740	−	0.0132063i
$590$	14.1962	+	4.73205i	0.584446	+	0.194815i
$591$	−30.2487	+	30.2487i	−1.24427	+	1.24427i
$592$	13.3923	+	13.3923i	0.550420	+	0.550420i
$593$	−2.73205	+	0.732051i	−0.112192	+	0.0300617i	−0.314478	−	0.949265i	$-0.601830\pi$
$593$	−2.73205	+	0.732051i	−0.112192	+	0.0300617i	0.202286	+	0.979326i	$0.435163\pi$
$594$	52.9808	+	14.1962i	2.17383	+	0.582475i
$595$	2.19615	−	16.5885i	0.0900335	−	0.680060i
$596$	−2.89230	+	5.00962i	−0.118473	+	0.205202i
$597$	11.7846	−	6.80385i	0.482312	−	0.278463i
$598$	−34.3205	+	9.19615i	−1.40347	+	0.376059i
$599$	−26.8301	−	15.4904i	−1.09625	−	0.632920i	−0.161016	−	0.986952i	$-0.551477\pi$
$599$	−26.8301	−	15.4904i	−1.09625	−	0.632920i	−0.935233	+	0.354032i	$0.884810\pi$
$600$	4.43782	−	0.633975i	0.181173	−	0.0258819i
$601$	−20.6603	−	11.9282i	−0.842749	−	0.486562i	0.0154485	−	0.999881i	$-0.495082\pi$
$601$	−20.6603	−	11.9282i	−0.842749	−	0.486562i	−0.858198	+	0.513319i	$0.828416\pi$
$602$	2.59808	−	7.50000i	0.105890	−	0.305677i
$603$	3.69615	−	0.990381i	0.150519	−	0.0403314i
$604$	−7.09808	−	4.09808i	−0.288817	−	0.166748i
$605$	−37.7128	+	18.8564i	−1.53324	+	0.766622i
$606$	15.2321	−	56.8468i	0.618760	−	2.30924i
$607$	3.00000	−	3.00000i	0.121766	−	0.121766i	−0.643598	−	0.765364i	$-0.722559\pi$
$607$	3.00000	−	3.00000i	0.121766	−	0.121766i	0.765364	+	0.643598i	$0.222559\pi$
$608$	−6.41858	+	23.9545i	−0.260308	+	0.971483i
$609$	20.7846	+	24.0000i	0.842235	+	0.972529i
$610$	32.6506	+	36.8205i	1.32199	+	1.49082i
$611$	−25.3923	+	43.9808i	−1.02726	+	1.77927i
$612$	−10.3923	−	10.3923i	−0.420084	−	0.420084i
$613$	41.4186	+	11.0981i	1.67288	+	0.448247i	0.965885	−	0.258971i	$-0.0833833\pi$
$613$	41.4186	+	11.0981i	1.67288	+	0.448247i	0.706996	+	0.707218i	$0.250050\pi$
$614$	23.9545	+	41.4904i	0.966724	+	1.67442i
$615$	8.19615	+	5.41154i	0.330501	+	0.218214i
$616$	−3.26795	−	6.73205i	−0.131669	−	0.271242i
$617$	0.562178	−	2.09808i	0.0226324	−	0.0844654i	−0.953686	−	0.300804i	$-0.902745\pi$
$617$	0.562178	−	2.09808i	0.0226324	−	0.0844654i	0.976318	+	0.216339i	$0.0694116\pi$
$618$	6.86603	+	11.8923i	0.276192	+	0.478379i
$619$	24.9808			1.00406			0.502031	−	0.864850i	$-0.332586\pi$
$619$	24.9808			1.00406			0.502031	+	0.864850i	$0.332586\pi$
$620$	−0.633975	−	0.418584i	−0.0254610	−	0.0168107i
$621$	17.4904	+	17.4904i	0.701865	+	0.701865i
$622$	21.8564	−	21.8564i	0.876362	−	0.876362i
$623$	15.9282	+	18.3923i	0.638150	+	0.736872i
$624$	−7.73205	−	28.8564i	−0.309530	−	1.15518i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−12.2942	−	7.09808i	−0.491376	−	0.283696i
$627$	−26.7846	−	15.4641i	−1.06967	−	0.617577i
$628$	0.633975	−	2.36603i	0.0252983	−	0.0944147i
$629$	12.0000			0.478471
$630$	33.9904	+	4.50000i	1.35421	+	0.179284i
$631$	37.3205			1.48571			0.742853	−	0.669455i	$-0.233472\pi$
$631$	37.3205			1.48571			0.742853	+	0.669455i	$0.233472\pi$
$632$	0.607695	−	2.26795i	0.0241728	−	0.0902142i
$633$	−13.3923	+	7.73205i	−0.532296	+	0.307321i
$634$	20.0263	+	11.5622i	0.795345	+	0.459193i
$635$	47.2750	+	15.7583i	1.87605	+	0.625350i
$636$	−13.3923	+	13.3923i	−0.531039	+	0.531039i
$637$	21.6603	−	16.1962i	0.858211	−	0.641715i
$638$	−51.7128	+	51.7128i	−2.04733	+	2.04733i
$639$	18.0000			0.712069
$640$	−8.99038	+	1.83975i	−0.355376	+	0.0727223i
$641$	−31.4449			−1.24200			−0.620999	−	0.783812i	$-0.713273\pi$
$641$	−31.4449			−1.24200			−0.620999	+	0.783812i	$0.713273\pi$
$642$	8.19615			0.323476
$643$	−0.186533	+	0.696152i	−0.00735616	+	0.0274536i	−0.969506	−	0.245066i	$-0.921190\pi$
$643$	−0.186533	+	0.696152i	−0.00735616	+	0.0274536i	0.962150	+	0.272520i	$0.0878570\pi$
$644$	−1.56218	+	21.7583i	−0.0615584	+	0.857398i
$645$	4.50000	−	3.99038i	0.177187	−	0.157121i
$646$	8.92820	+	15.4641i	0.351275	+	0.608427i
$647$	18.8301	+	5.04552i	0.740289	+	0.198360i	0.609206	−	0.793012i	$-0.291488\pi$
$647$	18.8301	+	5.04552i	0.740289	+	0.198360i	0.131082	+	0.991371i	$0.458155\pi$
$648$	−3.29423	+	3.29423i	−0.129410	+	0.129410i
$649$	9.46410	−	16.3923i	0.371498	−	0.643454i
$650$	−34.3205	+	14.6603i	−1.34616	+	0.575022i
$651$	0.588457	+	0.679492i	0.0230635	+	0.0266314i
$652$	4.09808	−	15.2942i	0.160493	−	0.598968i
$653$	17.7321	−	17.7321i	0.693909	−	0.693909i	−0.269181	−	0.963090i	$-0.586753\pi$
$653$	17.7321	−	17.7321i	0.693909	−	0.693909i	0.963090	+	0.269181i	$0.0867529\pi$
$654$	6.46410	−	1.73205i	0.252766	−	0.0677285i
$655$	5.07180	+	10.1436i	0.198171	+	0.396343i
$656$	−9.80385	−	5.66025i	−0.382776	−	0.220996i
$657$	7.09808	−	26.4904i	0.276922	−	1.03349i
$658$	43.9808	+	50.7846i	1.71455	+	1.97979i
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.869709	−	0.493564i	$-0.164306\pi$
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.00741531	+	0.999973i	$0.497640\pi$
$660$	−2.19615	+	36.5885i	−0.0854851	+	1.42420i
$661$	−9.52628	−	5.50000i	−0.370529	−	0.213925i	0.303160	−	0.952940i	$-0.401958\pi$
$661$	−9.52628	−	5.50000i	−0.370529	−	0.213925i	−0.673690	+	0.739014i	$0.735292\pi$
$662$	34.2224	−	9.16987i	1.33009	−	0.356397i
$663$	−16.3923	−	9.46410i	−0.636624	−	0.367555i
$664$	−0.366025	+	0.633975i	−0.0142045	+	0.0246030i
$665$	−17.8564	−	7.41154i	−0.692442	−	0.287407i
$666$			24.5885i			0.952783i
$667$	−31.8564	+	8.53590i	−1.23348	+	0.330511i
$668$	17.1506	+	17.1506i	0.663578	+	0.663578i
$669$	2.30385	+	8.59808i	0.0890719	+	0.332421i
$670$	2.46410	+	4.92820i	0.0951966	+	0.190393i
$671$	53.9090	−	31.1244i	2.08113	−	1.20154i
$672$	−34.6865	−	2.49038i	−1.33806	−	0.0960685i
$673$	−6.92820	−	25.8564i	−0.267063	−	0.996691i	−0.960976	−	0.276633i	$-0.910782\pi$
$673$	−6.92820	−	25.8564i	−0.267063	−	0.996691i	0.693913	−	0.720059i	$-0.255885\pi$
$674$	−7.73205	−	4.46410i	−0.297827	−	0.171951i
$675$	20.7846	+	15.5885i	0.800000	+	0.600000i
$676$	1.66987	+	2.89230i	0.0642259	+	0.111242i
$677$	−49.0526	−	13.1436i	−1.88524	−	0.505149i	−0.999131	−	0.0416780i	$-0.986730\pi$
$677$	−49.0526	−	13.1436i	−1.88524	−	0.505149i	−0.886112	−	0.463471i	$-0.846604\pi$
$678$	−21.2942	−	12.2942i	−0.817800	−	0.472157i
$679$	−21.3923	−	1.53590i	−0.820961	−	0.0589424i
$680$	−1.80385	+	2.73205i	−0.0691744	+	0.104769i
$681$	18.4641	+	18.4641i	0.707546	+	0.707546i
$682$	−1.46410	+	1.46410i	−0.0560633	+	0.0560633i
$683$	14.9641	+	4.00962i	0.572585	+	0.153424i	0.533482	−	0.845811i	$-0.320883\pi$
$683$	14.9641	+	4.00962i	0.572585	+	0.153424i	0.0391034	+	0.999235i	$0.487550\pi$
$684$	−14.7058	+	8.49038i	−0.562289	+	0.324638i
$685$	−4.39230	−	1.46410i	−0.167821	−	0.0559404i
$686$	−10.8660	−	34.0885i	−0.414867	−	1.30150i
$687$			8.07180i			0.307958i
$688$	−4.90192	+	4.90192i	−0.186884	+	0.186884i
$689$	−12.1962	+	21.1244i	−0.464636	+	0.804774i
$690$	−19.6244	+	29.7224i	−0.747086	+	1.13151i
$691$	9.16987	−	5.29423i	0.348838	−	0.201402i	−0.315335	−	0.948980i	$-0.602117\pi$
$691$	9.16987	−	5.29423i	0.348838	−	0.201402i	0.664174	+	0.747578i	$0.268784\pi$
$692$	−17.3205	+	17.3205i	−0.658427	+	0.658427i
$693$	14.1962	−	40.9808i	0.539267	−	1.55673i
$694$			40.5167i			1.53799i
$695$	−12.9282	−	8.53590i	−0.490395	−	0.323785i
$696$	−1.60770	−	6.00000i	−0.0609395	−	0.227429i
$697$	−6.92820	+	1.85641i	−0.262424	+	0.0703164i
$698$	−46.6147	−	46.6147i	−1.76439	−	1.76439i
$699$	20.4904	−	5.49038i	0.775017	−	0.207665i
$700$	1.60770	+	22.8564i	0.0607652	+	0.863891i
$701$	−47.4641			−1.79269			−0.896347	−	0.443353i	$-0.853789\pi$
$701$	−47.4641			−1.79269			−0.896347	+	0.443353i	$0.853789\pi$
$702$	19.3923	−	33.5885i	0.731915	−	1.26771i
$703$	3.58846	−	13.3923i	0.135341	−	0.505100i
$704$		−	31.3205i		−	1.18044i
$705$	10.2058	+	49.8731i	0.384372	+	1.87833i
$706$	−18.5885	+	10.7321i	−0.699586	+	0.403906i
$707$	−43.9711	−	15.2321i	−1.65371	−	0.572860i
$708$	−5.19615	−	9.00000i	−0.195283	−	0.338241i
$709$	5.81347	−	3.35641i	0.218329	−	0.126052i	−0.386847	−	0.922144i	$-0.626436\pi$
$709$	5.81347	−	3.35641i	0.218329	−	0.126052i	0.605176	+	0.796091i	$0.293103\pi$
$710$	5.19615	+	25.3923i	0.195008	+	0.952956i
$711$	11.7846	−	6.80385i	0.441957	−	0.255164i
$712$	−1.23205	−	4.59808i	−0.0461731	−	0.172320i
$713$	−0.901924	+	0.241670i	−0.0337773	+	0.00905060i
$714$	−18.9282	+	16.3923i	−0.708370	+	0.613467i
$715$	9.46410	+	46.2487i	0.353937	+	1.72960i
$716$	21.8038			0.814848
$717$	19.0526	+	33.0000i	0.711531	+	1.23241i
$718$	28.3205	−	28.3205i	1.05691	−	1.05691i
$719$	−15.5622	+	26.9545i	−0.580371	+	1.00523i	0.415064	+	0.909792i	$0.363759\pi$
$719$	−15.5622	+	26.9545i	−0.580371	+	1.00523i	−0.995435	+	0.0954403i	$0.969574\pi$
$720$	−24.9904	−	16.5000i	−0.931337	−	0.614919i
$721$	9.76795	−	4.74167i	0.363777	−	0.176589i
$722$	−15.5263	+	4.16025i	−0.577828	+	0.154829i
$723$	−16.5167			−0.614261
$724$	9.92820	−	17.1962i	0.368979	−	0.639090i
$725$	−31.8564	+	13.6077i	−1.18312	+	0.505377i
$726$	60.9449	+	16.3301i	2.26188	+	0.606068i
$727$	−1.37564	−	5.13397i	−0.0510198	−	0.190409i	0.935713	−	0.352763i	$-0.114758\pi$
$727$	−1.37564	−	5.13397i	−0.0510198	−	0.190409i	−0.986732	+	0.162355i	$0.948091\pi$
$728$	−5.19615	+	1.00000i	−0.192582	+	0.0370625i
$729$	−27.0000			−1.00000
$730$	39.4186	+	2.36603i	1.45895	+	0.0875705i
$731$			4.39230i			0.162455i
$732$		−	34.1769i		−	1.26322i
$733$	−15.6603	−	15.6603i	−0.578425	−	0.578425i	0.356044	−	0.934469i	$-0.384125\pi$
$733$	−15.6603	−	15.6603i	−0.578425	−	0.578425i	−0.934469	+	0.356044i	$0.884125\pi$
$734$	−6.59808	−	11.4282i	−0.243539	−	0.421823i
$735$	5.47372	−	26.5526i	0.201901	−	0.979406i
$736$	18.0622	−	31.2846i	0.665781	−	1.15317i
$737$	6.73205	−	1.80385i	0.247978	−	0.0664456i
$738$	−3.80385	−	14.1962i	−0.140022	−	0.522568i
$739$	21.1244	−	12.1962i	0.777072	−	0.448643i	−0.0583196	−	0.998298i	$-0.518574\pi$
$739$	21.1244	−	12.1962i	0.777072	−	0.448643i	0.835392	+	0.549655i	$0.185241\pi$
$740$	−16.0981	+	3.29423i	−0.591777	+	0.121098i
$741$	−15.4641	+	15.4641i	−0.568088	+	0.568088i
$742$	21.1244	+	24.3923i	0.775499	+	0.895470i
$743$	8.83013	+	2.36603i	0.323946	+	0.0868011i	0.417127	−	0.908848i	$-0.363037\pi$
$743$	8.83013	+	2.36603i	0.323946	+	0.0868011i	−0.0931813	+	0.995649i	$0.529704\pi$
$744$	−0.0455173	−	0.169873i	−0.00166875	−	0.00622785i
$745$	3.33975	+	6.67949i	0.122359	+	0.244718i
$746$	4.09808	+	7.09808i	0.150041	+	0.259879i
$747$	−4.09808	+	1.09808i	−0.149941	+	0.0401765i
$748$	−18.9282	−	18.9282i	−0.692084	−	0.692084i
$749$	0.464102	−	6.46410i	0.0169579	−	0.236193i
$750$	−15.9904	+	33.8205i	−0.583886	+	1.23495i
$751$	−47.1244			−1.71959			−0.859796	−	0.510638i	$-0.829409\pi$
$751$	−47.1244			−1.71959			−0.859796	+	0.510638i	$0.829409\pi$
$752$	−15.1865	−	56.6769i	−0.553796	−	2.06679i
$753$	−10.1436			−0.369653
$754$	25.8564	+	44.7846i	0.941635	+	1.63096i
$755$	−9.46410	+	4.73205i	−0.344434	+	0.172217i
$756$	−15.5885	−	18.0000i	−0.566947	−	0.654654i
$757$	−8.26795	−	8.26795i	−0.300504	−	0.300504i	0.540707	−	0.841211i	$-0.318157\pi$
$757$	−8.26795	−	8.26795i	−0.300504	−	0.300504i	−0.841211	+	0.540707i	$0.818157\pi$
$758$	23.3923	+	6.26795i	0.849647	+	0.227662i
$759$	31.8564	+	31.8564i	1.15631	+	1.15631i
$760$	2.50962	+	2.83013i	0.0910334	+	0.102659i
$761$			19.5885i			0.710081i	0.934851	+	0.355041i	$0.115533\pi$
$761$			19.5885i			0.710081i	−0.934851	+	0.355041i	$0.884467\pi$
$762$	−37.2846	−	64.5788i	−1.35068	−	2.33944i
$763$	−1.00000	−	5.19615i	−0.0362024	−	0.188113i
$764$		−	30.5885i		−	1.10665i
$765$	−18.5885	+	3.80385i	−0.672067	+	0.137528i
$766$	−27.3564	+	15.7942i	−0.988427	+	0.570669i
$767$	−9.46410	−	9.46410i	−0.341729	−	0.341729i
$768$	29.0885	+	16.7942i	1.04964	+	0.606010i
$769$	7.99038	+	13.8397i	0.288141	+	0.499074i	0.973366	−	0.229257i	$-0.0736296\pi$
$769$	7.99038	+	13.8397i	0.288141	+	0.499074i	−0.685225	+	0.728331i	$0.740296\pi$
$770$	61.9090	+	8.19615i	2.23104	+	0.295369i
$771$	15.2487	+	15.2487i	0.549169	+	0.549169i
$772$	−9.16987	+	34.2224i	−0.330031	+	1.23169i
$773$	−1.88269	+	7.02628i	−0.0677155	+	0.252718i	−0.991483	−	0.130236i	$-0.958426\pi$
$773$	−1.88269	+	7.02628i	−0.0677155	+	0.252718i	0.923768	+	0.382954i	$0.125093\pi$
$774$	−9.00000			−0.323498
$775$	−0.901924	+	0.385263i	−0.0323981	+	0.0138391i
$776$	3.63397	+	2.09808i	0.130452	+	0.0753165i
$777$	19.3923	+	1.39230i	0.695695	+	0.0499487i
$778$	2.23205	+	0.598076i	0.0800229	+	0.0214421i
$779$			8.28719i			0.296919i
$780$	24.5885	+	8.19615i	0.880408	+	0.293469i
$781$	32.7846			1.17313
$782$	−6.73205	−	25.1244i	−0.240738	−	0.898445i
$783$	18.0000	−	31.1769i	0.643268	−	1.11417i
$784$	−4.46410	+	30.9282i	−0.159432	+	1.10458i
$785$	−2.09808	−	2.36603i	−0.0748836	−	0.0844471i
$786$	4.39230	−	16.3923i	0.156668	−	0.584694i
$787$	4.13397	+	15.4282i	0.147360	+	0.549956i	0.999639	+	0.0268681i	$0.00855341\pi$
$787$	4.13397	+	15.4282i	0.147360	+	0.549956i	−0.852279	+	0.523088i	$0.824780\pi$
$788$	11.0718	+	41.3205i	0.394416	+	1.47198i
$789$	34.8109	+	34.8109i	1.23930	+	1.23930i
$790$	13.0000	+	14.6603i	0.462519	+	0.521588i
$791$	−10.9019	+	16.0981i	−0.387628	+	0.572382i
$792$	−6.00000	+	6.00000i	−0.213201	+	0.213201i
$793$	−11.3923	−	42.5167i	−0.404553	−	1.50981i
$794$	−65.5692			−2.32696
$795$	4.90192	+	23.9545i	0.173853	+	0.849578i
$796$		−	13.6077i		−	0.482312i
$797$	37.6147	+	10.0788i	1.33238	+	0.357011i	0.853603	−	0.520924i	$-0.174413\pi$
$797$	37.6147	+	10.0788i	1.33238	+	0.357011i	0.478780	+	0.877935i	$0.341079\pi$
$798$	12.6340	+	26.0263i	0.447238	+	0.921320i
$799$	−32.1962	−	18.5885i	−1.13902	−	0.657612i
$800$	14.1340	−	35.2128i	0.499711	−	1.24496i
$801$	13.7942	−	23.8923i	0.487395	−	0.844193i
$802$	−11.6962	+	43.6506i	−0.413005	+	1.54136i
$803$	12.9282	−	48.2487i	0.456226	−	1.70266i
$804$	0.990381	−	3.69615i	0.0349280	−	0.130353i
$805$	22.3301	+	17.1603i	0.787034	+	0.604819i
$806$	0.732051	+	1.26795i	0.0257854	+	0.0446616i
$807$	−14.8923	+	8.59808i	−0.524234	+	0.302667i
$808$	6.43782	+	6.43782i	0.226482	+	0.226482i
$809$	−36.4019	+	21.0167i	−1.27982	+	0.738906i	−0.976816	−	0.214082i	$-0.931324\pi$
$809$	−36.4019	+	21.0167i	−1.27982	+	0.738906i	−0.303008	+	0.952988i	$0.597991\pi$
$810$	−7.79423	−	38.0885i	−0.273861	−	1.33829i
$811$			1.85641i			0.0651872i	0.999469	+	0.0325936i	$0.0103767\pi$
$811$			1.85641i			0.0651872i	−0.999469	+	0.0325936i	$0.989623\pi$
$812$	31.1769	−	6.00000i	1.09410	−	0.210559i
$813$	−9.92820	+	17.1962i	−0.348197	+	0.603095i
$814$			44.7846i			1.56970i
$815$	−13.5622	−	15.2942i	−0.475062	−	0.535733i
$816$	21.1244	−	5.66025i	0.739500	−	0.198149i
$817$	4.90192	+	1.31347i	0.171497	+	0.0459524i
$818$	7.36603	+	7.36603i	0.257547	+	0.257547i
$819$	−25.3923	−	17.1962i	−0.887279	−	0.600882i
$820$	8.78461	−	4.39230i	0.306772	−	0.153386i
$821$	12.3301	+	21.3564i	0.430324	+	0.745344i	0.996901	−	0.0786653i	$-0.0250658\pi$
$821$	12.3301	+	21.3564i	0.430324	+	0.745344i	−0.566577	+	0.824009i	$0.691733\pi$
$822$	3.46410	+	6.00000i	0.120824	+	0.209274i
$823$	−5.15064	−	19.2224i	−0.179540	−	0.670052i	−0.995734	−	0.0922737i	$-0.970587\pi$
$823$	−5.15064	−	19.2224i	−0.179540	−	0.670052i	0.816194	−	0.577778i	$-0.196080\pi$
$824$	−2.12436			−0.0740054
$825$	37.8564	+	28.3923i	1.31799	+	0.988493i
$826$	−15.9282	+	7.73205i	−0.554213	+	0.269032i
$827$	21.3923	+	21.3923i	0.743883	+	0.743883i	0.973323	−	0.229440i	$-0.0736893\pi$
$827$	21.3923	+	21.3923i	0.743883	+	0.743883i	−0.229440	+	0.973323i	$0.573689\pi$
$828$	23.8923	−	6.40192i	0.830315	−	0.222482i
$829$	−22.1603	−	38.3827i	−0.769657	−	1.33309i	−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−22.1603	−	38.3827i	−0.769657	−	1.33309i	0.168091	−	0.985771i	$-0.446240\pi$
$830$	−2.73205	−	5.46410i	−0.0948309	−	0.189662i
$831$	−24.5885	+	24.5885i	−0.852964	+	0.852964i
$832$	−21.3923	−	5.73205i	−0.741645	−	0.198723i
$833$	11.8564	+	15.8564i	0.410800	+	0.549392i
$834$	6.00000	+	22.3923i	0.207763	+	0.775382i
$835$	30.6769	−	6.27757i	1.06162	−	0.217244i
$836$	−26.7846	+	15.4641i	−0.926365	+	0.534837i
$837$	0.509619	−	0.882686i	0.0176150	−	0.0305101i
$838$	−14.9282	+	4.00000i	−0.515686	+	0.138178i
$839$	0.0262794	−	0.0455173i	0.000907267	−	0.00157143i	−0.865571	−	0.500786i	$-0.833045\pi$
$839$	0.0262794	−	0.0455173i	0.000907267	−	0.00157143i	0.866479	+	0.499214i	$0.166378\pi$
$840$	−3.23205	+	4.20577i	−0.111516	+	0.145113i
$841$	9.50000	+	16.4545i	0.327586	+	0.567396i
$842$	−31.4904	−	31.4904i	−1.08523	−	1.08523i
$843$	−20.5981	−	11.8923i	−0.709435	−	0.409593i
$844$			15.4641i			0.532296i
$845$	4.30385	+	0.258330i	0.148057	+	0.00888683i
$846$	38.0885	−	65.9711i	1.30951	−	2.26813i
$847$	16.3301	−	47.1410i	0.561110	−	1.61978i
$848$	−7.29423	−	27.2224i	−0.250485	−	0.934822i
$849$	−9.99038	−	37.2846i	−0.342869	−	1.27960i
$850$	−10.7321	−	25.1244i	−0.368106	−	0.861758i
$851$	−10.0981	+	17.4904i	−0.346158	+	0.599563i
$852$	9.00000	−	15.5885i	0.308335	−	0.534052i
$853$	−40.5167	+	10.8564i	−1.38726	+	0.371716i	−0.873754	−	0.486368i	$-0.838322\pi$
$853$	−40.5167	+	10.8564i	−1.38726	+	0.371716i	−0.513510	+	0.858084i	$0.671655\pi$
$854$	−58.0788	−	4.16987i	−1.98742	−	0.142690i
$855$	−1.31347	+	21.8827i	−0.0449196	+	0.748372i
$856$	−0.633975	+	1.09808i	−0.0216688	+	0.0375315i
$857$	21.0526	−	21.0526i	0.719142	−	0.719142i	−0.249288	−	0.968429i	$-0.580196\pi$
$857$	21.0526	−	21.0526i	0.719142	−	0.719142i	0.968429	+	0.249288i	$0.0801965\pi$
$858$	35.3205	−	61.1769i	1.20582	−	2.08855i
$859$	42.9808			1.46648			0.733242	−	0.679967i	$-0.238006\pi$
$859$	42.9808			1.46648			0.733242	+	0.679967i	$0.238006\pi$
$860$	−1.20577	−	5.89230i	−0.0411165	−	0.200926i
$861$	−11.4115	+	2.19615i	−0.388904	+	0.0748447i
$862$	−45.1506	+	12.0981i	−1.53784	+	0.412062i
$863$	−6.54552	−	24.4282i	−0.222812	−	0.831546i	−0.983269	−	0.182158i	$-0.941692\pi$
$863$	−6.54552	−	24.4282i	−0.222812	−	0.831546i	0.760457	−	0.649388i	$-0.224975\pi$
$864$	10.2058	+	38.0885i	0.347207	+	1.29580i
$865$	6.33975	+	30.9808i	0.215558	+	1.05338i
$866$	23.1962	−	13.3923i	0.788237	−	0.455089i
$867$	−7.79423	+	13.5000i	−0.264706	+	0.458484i
$868$	0.882686	−	0.169873i	0.0299603	−	0.00576586i
$869$	21.4641	−	12.3923i	0.728120	−	0.420380i
$870$	49.1769	+	16.3923i	1.66725	+	0.555751i
$871$		−	4.92820i		−	0.166986i
$872$	−0.267949	+	1.00000i	−0.00907390	+	0.0338643i
$873$	6.29423	+	23.4904i	0.213027	+	0.795029i
$874$	−30.0526			−1.01654
$875$	25.7679	+	14.5263i	0.871116	+	0.491078i
$876$	−19.3923	−	19.3923i	−0.655205	−	0.655205i
$877$	8.46410	+	8.46410i	0.285812	+	0.285812i	0.835422	−	0.549609i	$-0.185223\pi$
$877$	8.46410	+	8.46410i	0.285812	+	0.285812i	−0.549609	+	0.835422i	$0.685223\pi$
$878$	10.9282	−	2.92820i	0.368809	−	0.0988221i
$879$	35.1506	+	9.41858i	1.18560	+	0.317681i
$880$	−45.5167	−	30.0526i	−1.53437	−	1.01307i
$881$			17.7846i			0.599179i	0.954068	+	0.299589i	$0.0968497\pi$
$881$			17.7846i			0.599179i	−0.954068	+	0.299589i	$0.903150\pi$
$882$	−32.4904	+	24.2942i	−1.09401	+	0.818029i
$883$	−24.5429	+	24.5429i	−0.825936	+	0.825936i	−0.986952	−	0.161016i	$-0.948523\pi$
$883$	−24.5429	+	24.5429i	−0.825936	+	0.825936i	0.161016	+	0.986952i	$0.448523\pi$
$884$	−16.3923	+	9.46410i	−0.551333	+	0.318312i
$885$	−13.3923	−	0.803848i	−0.450177	−	0.0270210i
$886$	−0.901924	+	1.56218i	−0.0303007	+	0.0524824i
$887$	−13.0263	+	13.0263i	−0.437380	+	0.437380i	−0.891129	−	0.453750i	$-0.850086\pi$
$887$	−13.0263	+	13.0263i	−0.437380	+	0.437380i	0.453750	+	0.891129i	$0.350086\pi$
$888$	−3.29423	−	1.90192i	−0.110547	−	0.0638244i
$889$	−53.0429	+	25.7487i	−1.77900	+	0.863584i
$890$	37.6865	+	12.5622i	1.26326	+	0.421085i
$891$	−49.1769			−1.64749
$892$	8.59808	+	2.30385i	0.287885	+	0.0771385i
$893$	−30.3731	+	30.3731i	−1.01640	+	1.01640i
$894$	2.89230	−	10.7942i	0.0967331	−	0.361013i
$895$	15.5096	−	23.4904i	0.518429	−	0.785197i
$896$	6.08846	−	8.99038i	0.203401	−	0.300348i
$897$	27.5885	−	15.9282i	0.921152	−	0.531827i
$898$	2.96410	+	0.794229i	0.0989134	+	0.0265038i
$899$	0.679492	+	1.17691i	0.0226623	+	0.0392523i
$900$	23.8923	−	10.2058i	0.796410	−	0.340192i
$901$	−15.4641	−	8.92820i	−0.515184	−	0.297442i
$902$	−6.92820	−	25.8564i	−0.230684	−	0.860924i
$903$	−0.509619	+	7.09808i	−0.0169591	+	0.236209i
$904$	3.29423	−	1.90192i	0.109564	−	0.0632570i
$905$	−11.4641	−	22.9282i	−0.381080	−	0.762159i
$906$	15.2942	+	4.09808i	0.508117	+	0.136149i
$907$	14.8564	+	14.8564i	0.493299	+	0.493299i	0.909344	−	0.416045i	$-0.136584\pi$
$907$	14.8564	+	14.8564i	0.493299	+	0.493299i	−0.416045	+	0.909344i	$0.636584\pi$
$908$	25.2224	−	6.75833i	0.837036	−	0.224283i
$909$			52.7654i			1.75012i
$910$	16.9282	−	40.7846i	0.561164	−	1.35200i
$911$	−7.43782	+	12.8827i	−0.246426	+	0.426822i	−0.962532	−	0.271170i	$-0.912590\pi$
$911$	−7.43782	+	12.8827i	−0.246426	+	0.426822i	0.716106	+	0.697992i	$0.245923\pi$
$912$		−	25.2679i		−	0.836705i
$913$	−7.46410	+	2.00000i	−0.247026	+	0.0661903i
$914$	−17.3660	−	10.0263i	−0.574417	−	0.331640i
$915$	−36.8205	−	24.3109i	−1.21725	−	0.803693i
$916$	6.99038	+	4.03590i	0.230969	+	0.133350i
$917$	−12.6795	−	4.39230i	−0.418714	−	0.145047i
$918$	24.5885	+	14.1962i	0.811540	+	0.468543i
$919$	45.3731	+	26.1962i	1.49672	+	0.864131i	0.999993	−	0.00377579i	$-0.00120188\pi$
$919$	45.3731	+	26.1962i	1.49672	+	0.864131i	0.496727	+	0.867907i	$0.334535\pi$
$920$	−2.46410	−	4.92820i	−0.0812390	−	0.162478i
$921$	−30.3731	−	30.3731i	−1.00083	−	1.00083i
$922$	1.63397	−	1.63397i	0.0538121	−	0.0538121i
$923$	6.00000	−	22.3923i	0.197492	−	0.737052i
$924$	−28.3923	−	32.7846i	−0.934038	−	1.07853i
$925$	−7.90192	+	19.6865i	−0.259814	+	0.647289i
$926$	−35.1865	+	60.9449i	−1.15630	+	2.00277i
$927$	−8.70577	−	8.70577i	−0.285935	−	0.285935i
$928$	−50.7846	−	13.6077i	−1.66709	−	0.446694i
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	−0.993431	−	0.114435i	$-0.963494\pi$
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	0.397612	−	0.917554i	$-0.369839\pi$
$930$	1.39230	+	0.464102i	0.0456555	+	0.0152185i
$931$	21.2417	−	8.49038i	0.696168	−	0.278261i
$932$	5.49038	−	20.4904i	0.179843	−	0.671185i
$933$	−13.8564	+	24.0000i	−0.453638	+	0.785725i
$934$	−25.9282			−0.848397
$935$	−33.8564	+	6.92820i	−1.10722	+	0.226576i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	9.46410	−	9.46410i	0.309179	−	0.309179i	−0.535412	−	0.844591i	$-0.679844\pi$
$937$	9.46410	−	9.46410i	0.309179	−	0.309179i	0.844591	+	0.535412i	$0.179844\pi$
$938$	−6.16025	−	2.13397i	−0.201139	−	0.0696767i
$939$	12.2942	+	3.29423i	0.401207	+	0.107503i
$940$	48.2942	+	16.0981i	1.57518	+	0.525061i
$941$	−32.8923	−	18.9904i	−1.07226	−	0.619069i	−0.143461	−	0.989656i	$-0.545823\pi$
$941$	−32.8923	−	18.9904i	−1.07226	−	0.619069i	−0.928798	+	0.370587i	$0.879156\pi$
$942$			4.73205i			0.154179i
$943$	3.12436	−	11.6603i	0.101743	−	0.379710i
$944$	15.4641			0.503314
$945$	−30.4808	+	3.99038i	−0.991539	+	0.129807i
$946$	−16.3923			−0.532960
$947$	6.66987	−	24.8923i	0.216742	−	0.808891i	−0.768804	−	0.639484i	$-0.779148\pi$
$947$	6.66987	−	24.8923i	0.216742	−	0.808891i	0.985546	−	0.169407i	$-0.0541853\pi$
$948$		−	13.6077i		−	0.441957i
$949$	−30.5885	−	17.6603i	−0.992943	−	0.573276i
$950$	−31.2487	+	4.46410i	−1.01384	+	0.144835i
$951$	−20.0263	−	5.36603i	−0.649397	−	0.174005i
$952$	−0.732051	−	3.80385i	−0.0237259	−	0.123283i
$953$	21.0000	−	21.0000i	0.680257	−	0.680257i	−0.279801	−	0.960058i	$-0.590269\pi$
$953$	21.0000	−	21.0000i	0.680257	−	0.680257i	0.960058	+	0.279801i	$0.0902686\pi$
$954$	18.2942	−	31.6865i	0.592298	−	1.02589i
$955$	−32.9545	−	21.7583i	−1.06638	−	0.704083i
$956$	38.1051			1.23241
$957$	32.7846	−	56.7846i	1.05978	−	1.83559i
$958$	−2.63397	+	9.83013i	−0.0850999	+	0.317597i
$959$	4.92820	−	2.39230i	0.159140	−	0.0772516i
$960$	−19.8564	+	9.92820i	−0.640863	+	0.320431i
$961$	−15.4808	−	26.8135i	−0.499379	−	0.864951i
$962$	30.5885	+	8.19615i	0.986211	+	0.264255i
$963$	−7.09808	+	1.90192i	−0.228732	+	0.0612886i
$964$	−8.25833	+	14.3038i	−0.265983	+	0.460696i
$965$	30.3468	+	34.2224i	0.976898	+	1.10166i
$966$	−7.96410	−	41.3827i	−0.256241	−	1.33147i
$967$	0.447441	−	1.66987i	0.0143887	−	0.0536995i	−0.958358	−	0.285569i	$-0.907817\pi$
$967$	0.447441	−	1.66987i	0.0143887	−	0.0536995i	0.972747	+	0.231869i	$0.0744842\pi$
$968$	−6.90192	+	6.90192i	−0.221836	+	0.221836i
$969$	−11.3205	−	11.3205i	−0.363667	−	0.363667i
$970$	−31.3205	+	15.6603i	−1.00564	+	0.502820i
$971$	−2.53590	−	1.46410i	−0.0813809	−	0.0469853i	0.458757	−	0.888562i	$-0.348295\pi$
$971$	−2.53590	−	1.46410i	−0.0813809	−	0.0469853i	−0.540138	+	0.841576i	$0.681628\pi$
$972$	−13.5000	+	23.3827i	−0.433013	+	0.750000i
$973$	18.0000	−	3.46410i	0.577054	−	0.111054i
$974$	56.1506	+	32.4186i	1.79918	+	1.03876i
$975$	26.3205	−	20.6603i	0.842931	−	0.661658i
$976$	44.0429	+	25.4282i	1.40978	+	0.813937i
$977$	45.3205	−	12.1436i	1.44993	−	0.388508i	0.553932	−	0.832562i	$-0.313127\pi$
$977$	45.3205	−	12.1436i	1.44993	−	0.388508i	0.896000	+	0.444054i	$0.146460\pi$
$978$			30.5885i			0.978111i
$979$	25.1244	−	43.5167i	0.802978	−	1.39080i
$980$	−20.2583	−	18.0167i	−0.647129	−	0.575521i
$981$	−5.19615	+	3.00000i	−0.165900	+	0.0957826i
$982$	−31.5885	+	8.46410i	−1.00803	+	0.270100i
$983$	2.60770	+	2.60770i	0.0831726	+	0.0831726i	0.747469	−	0.664297i	$-0.231269\pi$
$983$	2.60770	+	2.60770i	0.0831726	+	0.0831726i	−0.664297	+	0.747469i	$0.731269\pi$
$984$	2.19615	+	0.588457i	0.0700108	+	0.0187593i
$985$	52.3923	+	17.4641i	1.66936	+	0.556453i
$986$	−32.7846	+	18.9282i	−1.04407	+	0.602797i
$987$	−49.8731	−	33.7750i	−1.58748	−	1.07507i
$988$	5.66025	+	21.1244i	0.180077	+	0.672055i
$989$	−6.40192	−	3.69615i	−0.203569	−	0.117531i
$990$	−14.1962	−	69.3731i	−0.451183	−	2.20482i
$991$	8.73205	+	15.1244i	0.277383	+	0.480441i	0.970734	−	0.240159i	$-0.0771997\pi$
$991$	8.73205	+	15.1244i	0.277383	+	0.480441i	−0.693351	+	0.720600i	$0.743866\pi$
$992$	−1.43782	−	0.385263i	−0.0456509	−	0.0122321i
$993$	−27.5096	+	15.8827i	−0.872991	+	0.504022i
$994$	−25.3923	−	17.1962i	−0.805395	−	0.545429i
$995$	−14.6603	−	9.67949i	−0.464761	−	0.306861i
$996$	−1.09808	+	4.09808i	−0.0347939	+	0.129853i
$997$	−31.9808	+	31.9808i	−1.01284	+	1.01284i	−0.0129244	+	0.999916i	$0.504114\pi$
$997$	−31.9808	+	31.9808i	−1.01284	+	1.01284i	−0.999916	+	0.0129244i	$0.995886\pi$
$998$	13.1962	+	3.53590i	0.417717	+	0.111927i
$999$	−5.70577	−	21.2942i	−0.180523	−	0.673720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cg.a.187.1	yes	4
3.2	odd	2		945.2.cj.d.397.1		4
5.3	odd	4		315.2.cg.c.313.1	yes	4
7.3	odd	6		315.2.bs.c.52.1	yes	4
9.4	even	3		315.2.bs.b.292.1	yes	4
9.5	odd	6		945.2.bv.a.712.1		4
15.8	even	4		945.2.cj.a.208.1		4
21.17	even	6		945.2.bv.d.262.1		4
35.3	even	12		315.2.bs.b.178.1	✓	4
45.13	odd	12		315.2.bs.c.103.1	yes	4
45.23	even	12		945.2.bv.d.523.1		4
63.31	odd	6		315.2.cg.c.157.1	yes	4
63.59	even	6		945.2.cj.a.577.1		4
105.38	odd	12		945.2.bv.a.73.1		4
315.248	odd	12		945.2.cj.d.388.1		4
315.283	even	12	inner	315.2.cg.a.283.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bs.b.178.1	✓	4	35.3	even	12
315.2.bs.b.292.1	yes	4	9.4	even	3
315.2.bs.c.52.1	yes	4	7.3	odd	6
315.2.bs.c.103.1	yes	4	45.13	odd	12
315.2.cg.a.187.1	yes	4	1.1	even	1	trivial
315.2.cg.a.283.1	yes	4	315.283	even	12	inner
315.2.cg.c.157.1	yes	4	63.31	odd	6
315.2.cg.c.313.1	yes	4	5.3	odd	4
945.2.bv.a.73.1		4	105.38	odd	12
945.2.bv.a.712.1		4	9.5	odd	6
945.2.bv.d.262.1		4	21.17	even	6
945.2.bv.d.523.1		4	45.23	even	12
945.2.cj.a.208.1		4	15.8	even	4
945.2.cj.a.577.1		4	63.59	even	6
945.2.cj.d.388.1		4	315.248	odd	12
945.2.cj.d.397.1		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 1.86603i) q^{2} -1.73205i q^{3} +(-1.50000 - 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-0.366025 + 0.366025i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 1.86603i) q^{2} -1.73205i q^{3} +(-1.50000 - 0.866025i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(3.23205 + 0.866025i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-0.366025 + 0.366025i) q^{8} -3.00000 q^{9} +(-0.866025 - 4.23205i) q^{10} -5.46410 q^{11} +(-1.50000 + 2.59808i) q^{12} +(-1.00000 + 3.73205i) q^{13} +(4.23205 + 2.86603i) q^{14} +(1.73205 + 3.46410i) q^{15} +(-2.23205 - 3.86603i) q^{16} +(-2.73205 - 0.732051i) q^{17} +(1.50000 - 5.59808i) q^{18} +(-1.63397 + 2.83013i) q^{19} +(3.86603 + 0.232051i) q^{20} +(-4.33013 - 1.50000i) q^{21} +(2.73205 - 10.1962i) q^{22} +(3.36603 - 3.36603i) q^{23} +(0.633975 + 0.633975i) q^{24} +(3.00000 - 4.00000i) q^{25} +(-6.46410 - 3.73205i) q^{26} +5.19615i q^{27} +(-3.46410 + 3.00000i) q^{28} +(-6.00000 - 3.46410i) q^{29} +(-7.33013 + 1.50000i) q^{30} +(-0.169873 - 0.0980762i) q^{31} +(7.33013 - 1.96410i) q^{32} +9.46410i q^{33} +(2.73205 - 4.73205i) q^{34} +(0.767949 + 5.86603i) q^{35} +(4.50000 + 2.59808i) q^{36} +(-4.09808 + 1.09808i) q^{37} +(-4.46410 - 4.46410i) q^{38} +(6.46410 + 1.73205i) q^{39} +(0.366025 - 1.09808i) q^{40} +(2.19615 - 1.26795i) q^{41} +(4.96410 - 7.33013i) q^{42} +(-0.401924 - 1.50000i) q^{43} +(8.19615 + 4.73205i) q^{44} +(6.00000 - 3.00000i) q^{45} +(4.59808 + 7.96410i) q^{46} +(12.6962 + 3.40192i) q^{47} +(-6.69615 + 3.86603i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(5.96410 + 7.59808i) q^{50} +(-1.26795 + 4.73205i) q^{51} +(4.73205 - 4.73205i) q^{52} +(6.09808 + 1.63397i) q^{53} +(-9.69615 - 2.59808i) q^{54} +(10.9282 - 5.46410i) q^{55} +(0.598076 + 1.23205i) q^{56} +(4.90192 + 2.83013i) q^{57} +(9.46410 - 9.46410i) q^{58} +(-1.73205 + 3.00000i) q^{59} +(0.401924 - 6.69615i) q^{60} +(-9.86603 + 5.69615i) q^{61} +(0.267949 - 0.267949i) q^{62} +(-2.59808 + 7.50000i) q^{63} +5.73205i q^{64} +(-1.73205 - 8.46410i) q^{65} +(-17.6603 - 4.73205i) q^{66} +(-1.23205 + 0.330127i) q^{67} +(3.46410 + 3.46410i) q^{68} +(-5.83013 - 5.83013i) q^{69} +(-11.3301 - 1.50000i) q^{70} -6.00000 q^{71} +(1.09808 - 1.09808i) q^{72} +(-2.36603 + 8.83013i) q^{73} -8.19615i q^{74} +(-6.92820 - 5.19615i) q^{75} +(4.90192 - 2.83013i) q^{76} +(-4.73205 + 13.6603i) q^{77} +(-6.46410 + 11.1962i) q^{78} +(-3.92820 + 2.26795i) q^{79} +(8.33013 + 5.50000i) q^{80} +9.00000 q^{81} +(1.26795 + 4.73205i) q^{82} +(1.36603 - 0.366025i) q^{83} +(5.19615 + 6.00000i) q^{84} +(6.19615 - 1.26795i) q^{85} +3.00000 q^{86} +(-6.00000 + 10.3923i) q^{87} +(2.00000 - 2.00000i) q^{88} +(-4.59808 + 7.96410i) q^{89} +(2.59808 + 12.6962i) q^{90} +(8.46410 + 5.73205i) q^{91} +(-7.96410 + 2.13397i) q^{92} +(-0.169873 + 0.294229i) q^{93} +(-12.6962 + 21.9904i) q^{94} +(0.437822 - 7.29423i) q^{95} +(-3.40192 - 12.6962i) q^{96} +(-2.09808 - 7.83013i) q^{97} +(10.8301 - 8.09808i) q^{98} +16.3923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{4} - 8 q^{5} + 6 q^{6} + 2 q^{8} - 12 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^4 - 8 * q^5 + 6 * q^6 + 2 * q^8 - 12 * q^9	\( 4 q - 2 q^{2} - 6 q^{4} - 8 q^{5} + 6 q^{6} + 2 q^{8} - 12 q^{9} - 8 q^{11} - 6 q^{12} - 4 q^{13} + 10 q^{14} - 2 q^{16} - 4 q^{17} + 6 q^{18} - 10 q^{19} + 12 q^{20} + 4 q^{22} + 10 q^{23} + 6 q^{24} + 12 q^{25} - 12 q^{26} - 24 q^{29} - 12 q^{30} - 18 q^{31} + 12 q^{32} + 4 q^{34} + 10 q^{35} + 18 q^{36} - 6 q^{37} - 4 q^{38} + 12 q^{39} - 2 q^{40} - 12 q^{41} + 6 q^{42} - 12 q^{43} + 12 q^{44} + 24 q^{45} + 8 q^{46} + 30 q^{47} - 6 q^{48} - 22 q^{49} + 10 q^{50} - 12 q^{51} + 12 q^{52} + 14 q^{53} - 18 q^{54} + 16 q^{55} - 8 q^{56} + 30 q^{57} + 24 q^{58} + 12 q^{60} - 36 q^{61} + 8 q^{62} - 36 q^{66} + 2 q^{67} - 6 q^{69} - 28 q^{70} - 24 q^{71} - 6 q^{72} - 6 q^{73} + 30 q^{76} - 12 q^{77} - 12 q^{78} + 12 q^{79} + 16 q^{80} + 36 q^{81} + 12 q^{82} + 2 q^{83} + 4 q^{85} + 12 q^{86} - 24 q^{87} + 8 q^{88} - 8 q^{89} + 20 q^{91} - 18 q^{92} - 18 q^{93} - 30 q^{94} + 26 q^{95} - 24 q^{96} + 2 q^{97} + 26 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^4 - 8 * q^5 + 6 * q^6 + 2 * q^8 - 12 * q^9 - 8 * q^11 - 6 * q^12 - 4 * q^13 + 10 * q^14 - 2 * q^16 - 4 * q^17 + 6 * q^18 - 10 * q^19 + 12 * q^20 + 4 * q^22 + 10 * q^23 + 6 * q^24 + 12 * q^25 - 12 * q^26 - 24 * q^29 - 12 * q^30 - 18 * q^31 + 12 * q^32 + 4 * q^34 + 10 * q^35 + 18 * q^36 - 6 * q^37 - 4 * q^38 + 12 * q^39 - 2 * q^40 - 12 * q^41 + 6 * q^42 - 12 * q^43 + 12 * q^44 + 24 * q^45 + 8 * q^46 + 30 * q^47 - 6 * q^48 - 22 * q^49 + 10 * q^50 - 12 * q^51 + 12 * q^52 + 14 * q^53 - 18 * q^54 + 16 * q^55 - 8 * q^56 + 30 * q^57 + 24 * q^58 + 12 * q^60 - 36 * q^61 + 8 * q^62 - 36 * q^66 + 2 * q^67 - 6 * q^69 - 28 * q^70 - 24 * q^71 - 6 * q^72 - 6 * q^73 + 30 * q^76 - 12 * q^77 - 12 * q^78 + 12 * q^79 + 16 * q^80 + 36 * q^81 + 12 * q^82 + 2 * q^83 + 4 * q^85 + 12 * q^86 - 24 * q^87 + 8 * q^88 - 8 * q^89 + 20 * q^91 - 18 * q^92 - 18 * q^93 - 30 * q^94 + 26 * q^95 - 24 * q^96 + 2 * q^97 + 26 * q^98 + 24 * q^99

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