LMFDB - Embedded newform 370.2.n.b.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (of order $6$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.269
Dual form			370.2.n.b.359.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.00000 - 2.00000i) q^{10} -3.00000 q^{11} +(-0.866025 + 0.500000i) q^{13} +4.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-1.50000 - 2.59808i) q^{19} +(-0.133975 + 2.23205i) q^{20} +(2.59808 + 1.50000i) q^{22} +1.00000i q^{23} +(1.96410 + 4.59808i) q^{25} +1.00000 q^{26} +(-3.46410 - 2.00000i) q^{28} +6.00000 q^{29} -4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(3.00000 + 5.19615i) q^{34} +(-8.92820 - 0.535898i) q^{35} -3.00000 q^{36} +(2.59808 + 5.50000i) q^{37} +3.00000i q^{38} +(1.23205 - 1.86603i) q^{40} +(5.00000 + 8.66025i) q^{41} +2.00000i q^{43} +(-1.50000 - 2.59808i) q^{44} +(-6.00000 + 3.00000i) q^{45} +(0.500000 - 0.866025i) q^{46} +11.0000i q^{47} +(4.50000 - 7.79423i) q^{49} +(0.598076 - 4.96410i) q^{50} +(-0.866025 - 0.500000i) q^{52} +(8.66025 + 5.00000i) q^{53} +(-5.59808 - 3.69615i) q^{55} +(2.00000 + 3.46410i) q^{56} +(-5.19615 - 3.00000i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-6.00000 - 10.3923i) q^{61} +(3.46410 + 2.00000i) q^{62} -12.0000i q^{63} -1.00000 q^{64} +(-2.23205 - 0.133975i) q^{65} +(-1.73205 + 1.00000i) q^{67} -6.00000i q^{68} +(7.46410 + 4.92820i) q^{70} +(3.00000 + 5.19615i) q^{71} +(2.59808 + 1.50000i) q^{72} +2.00000i q^{73} +(0.500000 - 6.06218i) q^{74} +(1.50000 - 2.59808i) q^{76} +(10.3923 - 6.00000i) q^{77} +(2.00000 + 3.46410i) q^{79} +(-2.00000 + 1.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} -10.0000i q^{82} +(5.19615 + 3.00000i) q^{83} +(-6.00000 - 12.0000i) q^{85} +(1.00000 - 1.73205i) q^{86} +3.00000i q^{88} +(-7.50000 + 12.9904i) q^{89} +(6.69615 + 0.401924i) q^{90} +(2.00000 - 3.46410i) q^{91} +(-0.866025 + 0.500000i) q^{92} +(5.50000 - 9.52628i) q^{94} +(0.401924 - 6.69615i) q^{95} -2.00000i q^{97} +(-7.79423 + 4.50000i) q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{5} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^5 - 6 * q^9	$ 4 q + 2 q^{4} + 4 q^{5} - 6 q^{9} - 4 q^{10} - 12 q^{11} + 16 q^{14} - 2 q^{16} - 6 q^{19} - 4 q^{20} - 6 q^{25} + 4 q^{26} + 24 q^{29} - 16 q^{31} + 12 q^{34} - 8 q^{35} - 12 q^{36} - 2 q^{40} + 20 q^{41} - 6 q^{44} - 24 q^{45} + 2 q^{46} + 18 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{56} + 30 q^{59} - 24 q^{61} - 4 q^{64} - 2 q^{65} + 16 q^{70} + 12 q^{71} + 2 q^{74} + 6 q^{76} + 8 q^{79} - 8 q^{80} - 18 q^{81} - 24 q^{85} + 4 q^{86} - 30 q^{89} + 6 q^{90} + 8 q^{91} + 22 q^{94} + 12 q^{95} + 18 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^5 - 6 * q^9 - 4 * q^10 - 12 * q^11 + 16 * q^14 - 2 * q^16 - 6 * q^19 - 4 * q^20 - 6 * q^25 + 4 * q^26 + 24 * q^29 - 16 * q^31 + 12 * q^34 - 8 * q^35 - 12 * q^36 - 2 * q^40 + 20 * q^41 - 6 * q^44 - 24 * q^45 + 2 * q^46 + 18 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^56 + 30 * q^59 - 24 * q^61 - 4 * q^64 - 2 * q^65 + 16 * q^70 + 12 * q^71 + 2 * q^74 + 6 * q^76 + 8 * q^79 - 8 * q^80 - 18 * q^81 - 24 * q^85 + 4 * q^86 - 30 * q^89 + 6 * q^90 + 8 * q^91 + 22 * q^94 + 12 * q^95 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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			0		−0.500000	−	0.866025i	$-0.666667\pi$
$3$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$5$	1.86603	+	1.23205i	0.834512	+	0.550990i
$6$		0			0
$7$	−3.46410	+	2.00000i	−1.30931	+	0.755929i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	−3.46410	+	2.00000i	−1.30931	+	0.755929i	−0.327327	+	0.944911i	$0.606148\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	−0.615265	−	0.788320i	$-0.710951\pi$
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i	0.375073	+	0.926995i	$0.377618\pi$
$14$	4.00000			1.06904
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.287129	−	0.957892i	$-0.592701\pi$
$17$	−5.19615	−	3.00000i	−1.26025	−	0.727607i	−0.973123	+	0.230285i	$0.926034\pi$
$18$	2.59808	−	1.50000i	0.612372	−	0.353553i
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	0.641071	−	0.767482i	$-0.278491\pi$
$19$	−1.50000	−	2.59808i	−0.344124	−	0.596040i	−0.985194	+	0.171442i	$0.945157\pi$
$20$	−0.133975	+	2.23205i	−0.0299576	+	0.499102i
$21$		0			0
$22$	2.59808	+	1.50000i	0.553912	+	0.319801i
$23$			1.00000i			0.208514i	0.994550	+	0.104257i	$0.0332465\pi$
$23$			1.00000i			0.208514i	−0.994550	+	0.104257i	$0.966753\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	1.00000			0.196116
$27$		0			0
$28$	−3.46410	−	2.00000i	−0.654654	−	0.377964i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$	−8.92820	−	0.535898i	−1.50914	−	0.0905834i
$36$	−3.00000			−0.500000
$37$	2.59808	+	5.50000i	0.427121	+	0.904194i
$37$	2.59808	+	5.50000i	0.427121	+	0.904194i
$38$			3.00000i			0.486664i
$39$		0			0
$40$	1.23205	−	1.86603i	0.194804	−	0.295045i
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	0.931436	+	0.363905i	$0.118557\pi$
$41$	5.00000	+	8.66025i	0.780869	+	1.35250i	−0.150567	+	0.988600i	$0.548110\pi$
$42$		0			0
$43$			2.00000i			0.304997i	0.988304	+	0.152499i	$0.0487319\pi$
$43$			2.00000i			0.304997i	−0.988304	+	0.152499i	$0.951268\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$	−6.00000	+	3.00000i	−0.894427	+	0.447214i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$			11.0000i			1.60451i	0.596978	+	0.802257i	$0.296368\pi$
$47$			11.0000i			1.60451i	−0.596978	+	0.802257i	$0.703632\pi$
$48$		0			0
$49$	4.50000	−	7.79423i	0.642857	−	1.11346i
$50$	0.598076	−	4.96410i	0.0845807	−	0.702030i
$51$		0			0
$52$	−0.866025	−	0.500000i	−0.120096	−	0.0693375i
$53$	8.66025	+	5.00000i	1.18958	+	0.686803i	0.958211	−	0.286064i	$-0.0923469\pi$
$53$	8.66025	+	5.00000i	1.18958	+	0.686803i	0.231367	+	0.972867i	$0.425680\pi$
$54$		0			0
$55$	−5.59808	−	3.69615i	−0.754844	−	0.498389i
$56$	2.00000	+	3.46410i	0.267261	+	0.462910i
$57$		0			0
$58$	−5.19615	−	3.00000i	−0.682288	−	0.393919i
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.301239	−	0.953549i	$-0.402600\pi$
$59$	7.50000	−	12.9904i	0.976417	−	1.69120i	0.675178	−	0.737655i	$-0.264067\pi$
$60$		0			0
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	−0.938527	−	0.345207i	$-0.887809\pi$
$61$	−6.00000	−	10.3923i	−0.768221	−	1.33060i	0.170305	−	0.985391i	$-0.445525\pi$
$62$	3.46410	+	2.00000i	0.439941	+	0.254000i
$63$		−	12.0000i		−	1.51186i
$64$	−1.00000			−0.125000
$65$	−2.23205	−	0.133975i	−0.276852	−	0.0166175i
$66$		0			0
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	−0.602056	−	0.798454i	$-0.705652\pi$
$67$	−1.73205	+	1.00000i	−0.211604	+	0.122169i	0.390453	+	0.920623i	$0.372318\pi$
$68$		−	6.00000i		−	0.727607i
$69$		0			0
$70$	7.46410	+	4.92820i	0.892131	+	0.589033i
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	0.500000	−	6.06218i	0.0581238	−	0.704714i
$75$		0			0
$76$	1.50000	−	2.59808i	0.172062	−	0.298020i
$77$	10.3923	−	6.00000i	1.18431	−	0.683763i
$78$		0			0
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−2.00000	+	1.00000i	−0.223607	+	0.111803i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		−	10.0000i		−	1.10432i
$83$	5.19615	+	3.00000i	0.570352	+	0.329293i	0.757290	−	0.653079i	$-0.226523\pi$
$83$	5.19615	+	3.00000i	0.570352	+	0.329293i	−0.186938	+	0.982372i	$0.559856\pi$
$84$		0			0
$85$	−6.00000	−	12.0000i	−0.650791	−	1.30158i
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$		0			0
$88$			3.00000i			0.319801i
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$	6.69615	+	0.401924i	0.705836	+	0.0423665i
$91$	2.00000	−	3.46410i	0.209657	−	0.363137i
$92$	−0.866025	+	0.500000i	−0.0902894	+	0.0521286i
$93$		0			0
$94$	5.50000	−	9.52628i	0.567282	−	0.982561i
$95$	0.401924	−	6.69615i	0.0412365	−	0.687011i
$96$		0			0
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$	−7.79423	+	4.50000i	−0.787336	+	0.454569i
$99$	4.50000	−	7.79423i	0.452267	−	0.783349i
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−4.00000			−0.398015			−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000			−0.398015			−0.199007	+	0.979998i	$0.563772\pi$
$102$		0			0
$103$		−	9.00000i		−	0.886796i	−0.896325	−	0.443398i	$-0.853773\pi$
$103$		−	9.00000i		−	0.886796i	0.896325	−	0.443398i	$-0.146227\pi$
$104$	0.500000	+	0.866025i	0.0490290	+	0.0849208i
$105$		0			0
$106$	−5.00000	−	8.66025i	−0.485643	−	0.841158i
$107$	−6.92820	+	4.00000i	−0.669775	+	0.386695i	−0.795991	−	0.605308i	$-0.793050\pi$
$107$	−6.92820	+	4.00000i	−0.669775	+	0.386695i	0.126217	+	0.992003i	$0.459717\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	3.00000	+	6.00000i	0.286039	+	0.572078i
$111$		0			0
$112$		−	4.00000i		−	0.377964i
$113$	8.66025	+	5.00000i	0.814688	+	0.470360i	0.848581	−	0.529065i	$-0.177457\pi$
$113$	8.66025	+	5.00000i	0.814688	+	0.470360i	−0.0338931	+	0.999425i	$0.510791\pi$
$114$		0			0
$115$	−1.23205	+	1.86603i	−0.114889	+	0.174008i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		−	3.00000i		−	0.277350i
$118$	−12.9904	+	7.50000i	−1.19586	+	0.690431i
$119$	24.0000			2.20008
$120$		0			0
$121$	−2.00000			−0.181818
$122$			12.0000i			1.08643i
$123$		0			0
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−6.00000	+	10.3923i	−0.534522	+	0.925820i
$127$	−14.7224	−	8.50000i	−1.30640	−	0.754253i	−0.324910	−	0.945745i	$-0.605334\pi$
$127$	−14.7224	−	8.50000i	−1.30640	−	0.754253i	−0.981494	+	0.191492i	$0.938667\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	1.86603	+	1.23205i	0.163661	+	0.108058i
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.0155672	+	0.999879i	$0.504955\pi$
$131$	−10.0000	+	17.3205i	−0.873704	+	1.51330i	−0.858137	+	0.513421i	$0.828378\pi$
$132$		0			0
$133$	10.3923	+	6.00000i	0.901127	+	0.520266i
$134$	2.00000			0.172774
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$		−	6.00000i		−	0.512615i	−0.966595	−	0.256307i	$-0.917494\pi$
$137$		−	6.00000i		−	0.512615i	0.966595	−	0.256307i	$-0.0825059\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$	−4.00000	−	8.00000i	−0.338062	−	0.676123i
$141$		0			0
$142$		−	6.00000i		−	0.503509i
$143$	2.59808	−	1.50000i	0.217262	−	0.125436i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	11.1962	+	7.39230i	0.929790	+	0.613898i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$		0			0
$148$	−3.46410	+	5.00000i	−0.284747	+	0.410997i
$149$	16.0000			1.31077			0.655386	−	0.755295i	$-0.272506\pi$
$149$	16.0000			1.31077			0.655386	+	0.755295i	$0.272506\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−2.59808	+	1.50000i	−0.210732	+	0.121666i
$153$	15.5885	−	9.00000i	1.26025	−	0.727607i
$154$	−12.0000			−0.966988
$155$	−7.46410	−	4.92820i	−0.599531	−	0.395843i
$156$		0			0
$157$	−4.33013	−	2.50000i	−0.345582	−	0.199522i	0.317156	−	0.948373i	$-0.397272\pi$
$157$	−4.33013	−	2.50000i	−0.345582	−	0.199522i	−0.662738	+	0.748852i	$0.730606\pi$
$158$		−	4.00000i		−	0.318223i
$159$		0			0
$160$	2.23205	+	0.133975i	0.176459	+	0.0105916i
$161$	−2.00000	−	3.46410i	−0.157622	−	0.273009i
$162$			9.00000i			0.707107i
$163$	−5.19615	−	3.00000i	−0.406994	−	0.234978i	0.282503	−	0.959266i	$-0.408835\pi$
$163$	−5.19615	−	3.00000i	−0.406994	−	0.234978i	−0.689497	+	0.724288i	$0.742169\pi$
$164$	−5.00000	+	8.66025i	−0.390434	+	0.676252i
$165$		0			0
$166$	−3.00000	−	5.19615i	−0.232845	−	0.403300i
$167$	6.92820	−	4.00000i	0.536120	−	0.309529i	−0.207385	−	0.978259i	$-0.566495\pi$
$167$	6.92820	−	4.00000i	0.536120	−	0.309529i	0.743505	+	0.668730i	$0.233162\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	−0.803848	+	13.3923i	−0.0616523	+	1.02714i
$171$	9.00000			0.688247
$172$	−1.73205	+	1.00000i	−0.132068	+	0.0762493i
$173$	−4.33013	−	2.50000i	−0.329213	−	0.190071i	0.326278	−	0.945274i	$-0.394205\pi$
$173$	−4.33013	−	2.50000i	−0.329213	−	0.190071i	−0.655492	+	0.755202i	$0.727539\pi$
$174$		0			0
$175$	−16.0000	−	12.0000i	−1.20949	−	0.907115i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$		0			0
$178$	12.9904	−	7.50000i	0.973670	−	0.562149i
$179$	−1.00000			−0.0747435			−0.0373718	−	0.999301i	$-0.511899\pi$
$179$	−1.00000			−0.0747435			−0.0373718	+	0.999301i	$0.511899\pi$
$180$	−5.59808	−	3.69615i	−0.417256	−	0.275495i
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	0.993598	+	0.112972i	$0.0360369\pi$
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	−0.398963	+	0.916967i	$0.630630\pi$
$182$	−3.46410	+	2.00000i	−0.256776	+	0.148250i
$183$		0			0
$184$	1.00000			0.0737210
$185$	−1.92820	+	13.4641i	−0.141764	+	0.989900i
$186$		0			0
$187$	15.5885	+	9.00000i	1.13994	+	0.658145i
$188$	−9.52628	+	5.50000i	−0.694775	+	0.401129i
$189$		0			0
$190$	−3.69615	+	5.59808i	−0.268147	+	0.406127i
$191$	4.00000			0.289430			0.144715	−	0.989473i	$-0.453773\pi$
$191$	4.00000			0.289430			0.144715	+	0.989473i	$0.453773\pi$
$192$		0			0
$193$			16.0000i			1.15171i	0.817554	+	0.575853i	$0.195330\pi$
$193$			16.0000i			1.15171i	−0.817554	+	0.575853i	$0.804670\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$	9.00000			0.642857
$197$	−19.0526	−	11.0000i	−1.35744	−	0.783718i	−0.368161	−	0.929762i	$-0.620012\pi$
$197$	−19.0526	−	11.0000i	−1.35744	−	0.783718i	−0.989278	+	0.146045i	$0.953346\pi$
$198$	−7.79423	+	4.50000i	−0.553912	+	0.319801i
$199$	−22.0000			−1.55954			−0.779769	−	0.626067i	$-0.784664\pi$
$199$	−22.0000			−1.55954			−0.779769	+	0.626067i	$0.784664\pi$
$200$	4.59808	−	1.96410i	0.325133	−	0.138883i
$201$		0			0
$202$	3.46410	+	2.00000i	0.243733	+	0.140720i
$203$	−20.7846	+	12.0000i	−1.45879	+	0.842235i
$204$		0			0
$205$	−1.33975	+	22.3205i	−0.0935719	+	1.55893i
$206$	−4.50000	+	7.79423i	−0.313530	+	0.543050i
$207$	−2.59808	−	1.50000i	−0.180579	−	0.104257i
$208$		−	1.00000i		−	0.0693375i
$209$	4.50000	+	7.79423i	0.311272	+	0.539138i
$210$		0			0
$211$	−1.00000			−0.0688428			−0.0344214	−	0.999407i	$-0.510959\pi$
$211$	−1.00000			−0.0688428			−0.0344214	+	0.999407i	$0.510959\pi$
$212$			10.0000i			0.686803i
$213$		0			0
$214$	8.00000			0.546869
$215$	−2.46410	+	3.73205i	−0.168050	+	0.254524i
$216$		0			0
$217$	13.8564	−	8.00000i	0.940634	−	0.543075i
$218$	−8.66025	+	5.00000i	−0.586546	+	0.338643i
$219$		0			0
$220$	0.401924	−	6.69615i	0.0270977	−	0.451455i
$221$	6.00000			0.403604
$222$		0			0
$223$			5.00000i			0.334825i	0.985887	+	0.167412i	$0.0535411\pi$
$223$			5.00000i			0.334825i	−0.985887	+	0.167412i	$0.946459\pi$
$224$	−2.00000	+	3.46410i	−0.133631	+	0.231455i
$225$	−14.8923	−	1.79423i	−0.992820	−	0.119615i
$226$	−5.00000	−	8.66025i	−0.332595	−	0.576072i
$227$	24.2487	−	14.0000i	1.60944	−	0.929213i	0.619949	−	0.784642i	$-0.287153\pi$
$227$	24.2487	−	14.0000i	1.60944	−	0.929213i	0.989494	−	0.144571i	$-0.0461801\pi$
$228$		0			0
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	0.897173	−	0.441679i	$-0.145617\pi$
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	−0.831092	+	0.556136i	$0.812283\pi$
$230$	2.00000	−	1.00000i	0.131876	−	0.0659380i
$231$		0			0
$232$		−	6.00000i		−	0.393919i
$233$		−	18.0000i		−	1.17922i	−0.807688	−	0.589610i	$-0.799282\pi$
$233$		−	18.0000i		−	1.17922i	0.807688	−	0.589610i	$-0.200718\pi$
$234$	−1.50000	+	2.59808i	−0.0980581	+	0.169842i
$235$	−13.5526	+	20.5263i	−0.884071	+	1.33899i
$236$	15.0000			0.976417
$237$		0			0
$238$	−20.7846	−	12.0000i	−1.34727	−	0.777844i
$239$	−10.0000	+	17.3205i	−0.646846	+	1.12037i	0.337026	+	0.941495i	$0.390579\pi$
$239$	−10.0000	+	17.3205i	−0.646846	+	1.12037i	−0.983872	+	0.178875i	$0.942754\pi$
$240$		0			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	1.73205	+	1.00000i	0.111340	+	0.0642824i
$243$		0			0
$244$	6.00000	−	10.3923i	0.384111	−	0.665299i
$245$	18.0000	−	9.00000i	1.14998	−	0.574989i
$246$		0			0
$247$	2.59808	+	1.50000i	0.165312	+	0.0954427i
$248$			4.00000i			0.254000i
$249$		0			0
$250$	7.23205	−	8.52628i	0.457395	−	0.539249i
$251$	−1.00000			−0.0631194			−0.0315597	−	0.999502i	$-0.510047\pi$
$251$	−1.00000			−0.0631194			−0.0315597	+	0.999502i	$0.510047\pi$
$252$	10.3923	−	6.00000i	0.654654	−	0.377964i
$253$		−	3.00000i		−	0.188608i
$254$	8.50000	+	14.7224i	0.533337	+	0.923768i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$	−20.0000	−	13.8564i	−1.24274	−	0.860995i
$260$	−1.00000	−	2.00000i	−0.0620174	−	0.124035i
$261$	−9.00000	+	15.5885i	−0.557086	+	0.964901i
$262$	17.3205	−	10.0000i	1.07006	−	0.617802i
$263$	16.4545	−	9.50000i	1.01463	−	0.585795i	0.102084	−	0.994776i	$-0.467449\pi$
$263$	16.4545	−	9.50000i	1.01463	−	0.585795i	0.912543	+	0.408981i	$0.134116\pi$
$264$		0			0
$265$	10.0000	+	20.0000i	0.614295	+	1.22859i
$266$	−6.00000	−	10.3923i	−0.367884	−	0.637193i
$267$		0			0
$268$	−1.73205	−	1.00000i	−0.105802	−	0.0610847i
$269$	−14.0000			−0.853595			−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000			−0.853595			−0.426798	+	0.904347i	$0.640358\pi$
$270$		0			0
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	5.19615	−	3.00000i	0.315063	−	0.181902i
$273$		0			0
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	−5.89230	−	13.7942i	−0.355319	−	0.831823i
$276$		0			0
$277$	5.19615	−	3.00000i	0.312207	−	0.180253i	−0.335707	−	0.941966i	$-0.608975\pi$
$277$	5.19615	−	3.00000i	0.312207	−	0.180253i	0.647913	+	0.761714i	$0.275642\pi$
$278$	4.33013	−	2.50000i	0.259704	−	0.149940i
$279$	6.00000	−	10.3923i	0.359211	−	0.622171i
$280$	−0.535898	+	8.92820i	−0.0320261	+	0.533562i
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−3.00000			−0.177394
$287$	−34.6410	−	20.0000i	−2.04479	−	1.18056i
$288$			3.00000i			0.176777i
$289$	9.50000	+	16.4545i	0.558824	+	0.967911i
$290$	−6.00000	−	12.0000i	−0.352332	−	0.704664i
$291$		0			0
$292$	−1.73205	+	1.00000i	−0.101361	+	0.0585206i
$293$	2.59808	−	1.50000i	0.151781	−	0.0876309i	−0.422186	−	0.906509i	$-0.638737\pi$
$293$	2.59808	−	1.50000i	0.151781	−	0.0876309i	0.573967	+	0.818878i	$0.305404\pi$
$294$		0			0
$295$	30.0000	−	15.0000i	1.74667	−	0.873334i
$296$	5.50000	−	2.59808i	0.319681	−	0.151010i
$297$		0			0
$298$	−13.8564	−	8.00000i	−0.802680	−	0.463428i
$299$	−0.500000	−	0.866025i	−0.0289157	−	0.0500835i
$300$		0			0
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$		−	2.00000i		−	0.115087i
$303$		0			0
$304$	3.00000			0.172062
$305$	1.60770	−	26.7846i	0.0920564	−	1.53368i
$306$	−18.0000			−1.02899
$307$			32.0000i			1.82634i	0.407583	+	0.913168i	$0.366372\pi$
$307$			32.0000i			1.82634i	−0.407583	+	0.913168i	$0.633628\pi$
$308$	10.3923	+	6.00000i	0.592157	+	0.341882i
$309$		0			0
$310$	4.00000	+	8.00000i	0.227185	+	0.454369i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	27.7128	+	16.0000i	1.56642	+	0.904373i	0.996581	+	0.0826174i	$0.0263280\pi$
$313$	27.7128	+	16.0000i	1.56642	+	0.904373i	0.569839	+	0.821756i	$0.307005\pi$
$314$	2.50000	+	4.33013i	0.141083	+	0.244363i
$315$	14.7846	−	22.3923i	0.833018	−	1.26166i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$	7.79423	+	4.50000i	0.437767	+	0.252745i	0.702650	−	0.711535i	$-0.252000\pi$
$317$	7.79423	+	4.50000i	0.437767	+	0.252745i	−0.264883	+	0.964281i	$0.585333\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$	−1.86603	−	1.23205i	−0.104314	−	0.0688737i
$321$		0			0
$322$			4.00000i			0.222911i
$323$			18.0000i			1.00155i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	−4.00000	−	3.00000i	−0.221880	−	0.166410i
$326$	3.00000	+	5.19615i	0.166155	+	0.287788i
$327$		0			0
$328$	8.66025	−	5.00000i	0.478183	−	0.276079i
$329$	−22.0000	−	38.1051i	−1.21290	−	2.10080i
$330$		0			0
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	−0.630232	−	0.776407i	$-0.717040\pi$
$331$	6.50000	−	11.2583i	0.357272	−	0.618814i	0.987504	+	0.157593i	$0.0503735\pi$
$332$			6.00000i			0.329293i
$333$	−18.1865	−	1.50000i	−0.996616	−	0.0821995i
$334$	−8.00000			−0.437741
$335$	−4.46410	−	0.267949i	−0.243900	−	0.0146396i
$336$		0			0
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	−0.676688	−	0.736270i	$-0.736585\pi$
$337$	−6.92820	+	4.00000i	−0.377403	+	0.217894i	0.299285	+	0.954164i	$0.403252\pi$
$338$	10.3923	−	6.00000i	0.565267	−	0.326357i
$339$		0			0
$340$	7.39230	−	11.1962i	0.400904	−	0.607197i
$341$	12.0000			0.649836
$342$	−7.79423	−	4.50000i	−0.421464	−	0.243332i
$343$			8.00000i			0.431959i
$344$	2.00000			0.107833
$345$		0			0
$346$	2.50000	+	4.33013i	0.134401	+	0.232789i
$347$			30.0000i			1.61048i	0.592946	+	0.805242i	$0.297965\pi$
$347$			30.0000i			1.61048i	−0.592946	+	0.805242i	$0.702035\pi$
$348$		0			0
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	−0.774493	−	0.632583i	$-0.781995\pi$
$349$	3.00000	−	5.19615i	0.160586	−	0.278144i	0.935079	+	0.354439i	$0.115328\pi$
$350$	7.85641	+	18.3923i	0.419943	+	0.983110i
$351$		0			0
$352$	−2.59808	+	1.50000i	−0.138478	+	0.0799503i
$353$	−15.5885	−	9.00000i	−0.829690	−	0.479022i	0.0240566	−	0.999711i	$-0.492342\pi$
$353$	−15.5885	−	9.00000i	−0.829690	−	0.479022i	−0.853746	+	0.520689i	$0.825675\pi$
$354$		0			0
$355$	−0.803848	+	13.3923i	−0.0426638	+	0.710790i
$356$	−15.0000			−0.794998
$357$		0			0
$358$	0.866025	+	0.500000i	0.0457709	+	0.0264258i
$359$	26.0000			1.37223			0.686114	−	0.727494i	$-0.259315\pi$
$359$	26.0000			1.37223			0.686114	+	0.727494i	$0.259315\pi$
$360$	3.00000	+	6.00000i	0.158114	+	0.316228i
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$		−	16.0000i		−	0.840941i
$363$		0			0
$364$	4.00000			0.209657
$365$	−2.46410	+	3.73205i	−0.128977	+	0.195344i
$366$		0			0
$367$	−11.2583	+	6.50000i	−0.587680	+	0.339297i	−0.764180	−	0.645003i	$-0.776856\pi$
$367$	−11.2583	+	6.50000i	−0.587680	+	0.339297i	0.176500	+	0.984301i	$0.443523\pi$
$368$	−0.866025	−	0.500000i	−0.0451447	−	0.0260643i
$369$	−30.0000			−1.56174
$370$	8.40192	−	10.6962i	0.436795	−	0.556066i
$371$	−40.0000			−2.07670
$372$		0			0
$373$	19.9186	−	11.5000i	1.03135	−	0.595447i	0.113975	−	0.993484i	$-0.463641\pi$
$373$	19.9186	−	11.5000i	1.03135	−	0.595447i	0.917370	+	0.398036i	$0.130308\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$		0			0
$376$	11.0000			0.567282
$377$	−5.19615	+	3.00000i	−0.267615	+	0.154508i
$378$		0			0
$379$	−12.0000	+	20.7846i	−0.616399	+	1.06763i	0.373739	+	0.927534i	$0.378076\pi$
$379$	−12.0000	+	20.7846i	−0.616399	+	1.06763i	−0.990137	+	0.140100i	$0.955258\pi$
$380$	6.00000	−	3.00000i	0.307794	−	0.153897i
$381$		0			0
$382$	−3.46410	−	2.00000i	−0.177239	−	0.102329i
$383$	14.7224	−	8.50000i	0.752281	−	0.434330i	−0.0742364	−	0.997241i	$-0.523652\pi$
$383$	14.7224	−	8.50000i	0.752281	−	0.434330i	0.826518	+	0.562911i	$0.190319\pi$
$384$		0			0
$385$	26.7846	+	1.60770i	1.36507	+	0.0819357i
$386$	8.00000	−	13.8564i	0.407189	−	0.705273i
$387$	−5.19615	−	3.00000i	−0.264135	−	0.152499i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	−2.00000	−	3.46410i	−0.101404	−	0.175637i	0.810859	−	0.585241i	$-0.199000\pi$
$389$	−2.00000	−	3.46410i	−0.101404	−	0.175637i	−0.912263	+	0.409604i	$0.865667\pi$
$390$		0			0
$391$	3.00000	−	5.19615i	0.151717	−	0.262781i
$392$	−7.79423	−	4.50000i	−0.393668	−	0.227284i
$393$		0			0
$394$	11.0000	+	19.0526i	0.554172	+	0.959854i
$395$	−0.535898	+	8.92820i	−0.0269640	+	0.449227i
$396$	9.00000			0.452267
$397$		−	5.00000i		−	0.250943i	−0.992097	−	0.125471i	$-0.959956\pi$
$397$		−	5.00000i		−	0.250943i	0.992097	−	0.125471i	$-0.0400443\pi$
$398$	19.0526	+	11.0000i	0.955018	+	0.551380i
$399$		0			0
$400$	−4.96410	−	0.598076i	−0.248205	−	0.0299038i
$401$	25.0000			1.24844			0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000			1.24844			0.624220	+	0.781248i	$0.285417\pi$
$402$		0			0
$403$	3.46410	−	2.00000i	0.172559	−	0.0996271i
$404$	−2.00000	−	3.46410i	−0.0995037	−	0.172345i
$405$	1.20577	−	20.0885i	0.0599153	−	0.998203i
$406$	24.0000			1.19110
$407$	−7.79423	−	16.5000i	−0.386346	−	0.817875i
$408$		0			0
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	0.454759	+	0.890614i	$0.349725\pi$
$409$	−11.0000	+	19.0526i	−0.543915	+	0.942088i	−0.998674	+	0.0514740i	$0.983608\pi$
$410$	12.3205	−	18.6603i	0.608467	−	0.921564i
$411$		0			0
$412$	7.79423	−	4.50000i	0.383994	−	0.221699i
$413$			60.0000i			2.95241i
$414$	1.50000	+	2.59808i	0.0737210	+	0.127688i
$415$	6.00000	+	12.0000i	0.294528	+	0.589057i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$		0			0
$418$		−	9.00000i		−	0.440204i
$419$	−12.5000	+	21.6506i	−0.610665	+	1.05770i	0.380464	+	0.924796i	$0.375764\pi$
$419$	−12.5000	+	21.6506i	−0.610665	+	1.05770i	−0.991129	+	0.132907i	$0.957569\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	0.866025	+	0.500000i	0.0421575	+	0.0243396i
$423$	−28.5788	−	16.5000i	−1.38955	−	0.802257i
$424$	5.00000	−	8.66025i	0.242821	−	0.420579i
$425$	3.58846	−	29.7846i	0.174066	−	1.44477i
$426$		0			0
$427$	41.5692	+	24.0000i	2.01168	+	1.16144i
$428$	−6.92820	−	4.00000i	−0.334887	−	0.193347i
$429$		0			0
$430$	4.00000	−	2.00000i	0.192897	−	0.0964486i
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	0.991817	−	0.127666i	$-0.0407486\pi$
$431$	8.00000	+	13.8564i	0.385346	+	0.667440i	−0.606471	+	0.795106i	$0.707415\pi$
$432$		0			0
$433$		−	34.0000i		−	1.63394i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$		−	34.0000i		−	1.63394i	0.576683	−	0.816968i	$-0.304347\pi$
$434$	−16.0000			−0.768025
$435$		0			0
$436$	10.0000			0.478913
$437$	2.59808	−	1.50000i	0.124283	−	0.0717547i
$438$		0			0
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	0.841175	−	0.540763i	$-0.181865\pi$
$439$	−1.00000	−	1.73205i	−0.0477274	−	0.0826663i	−0.888902	+	0.458097i	$0.848531\pi$
$440$	−3.69615	+	5.59808i	−0.176207	+	0.266878i
$441$	13.5000	+	23.3827i	0.642857	+	1.11346i
$442$	−5.19615	−	3.00000i	−0.247156	−	0.142695i
$443$			34.0000i			1.61539i	0.589601	+	0.807694i	$0.299285\pi$
$443$			34.0000i			1.61539i	−0.589601	+	0.807694i	$0.700715\pi$
$444$		0			0
$445$	−30.0000	+	15.0000i	−1.42214	+	0.711068i
$446$	2.50000	−	4.33013i	0.118378	−	0.205037i
$447$		0			0
$448$	3.46410	−	2.00000i	0.163663	−	0.0944911i
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	−0.965637	−	0.259895i	$-0.916312\pi$
$449$	−15.0000	−	25.9808i	−0.707894	−	1.22611i	0.257743	−	0.966213i	$-0.417021\pi$
$450$	12.0000	+	9.00000i	0.565685	+	0.424264i
$451$	−15.0000	−	25.9808i	−0.706322	−	1.22339i
$452$			10.0000i			0.470360i
$453$		0			0
$454$	−28.0000			−1.31411
$455$	8.00000	−	4.00000i	0.375046	−	0.187523i
$456$		0			0
$457$	−22.5167	+	13.0000i	−1.05328	+	0.608114i	−0.923567	−	0.383437i	$-0.874740\pi$
$457$	−22.5167	+	13.0000i	−1.05328	+	0.608114i	−0.129718	+	0.991551i	$0.541407\pi$
$458$		−	2.00000i		−	0.0934539i
$459$		0			0
$460$	−2.23205	−	0.133975i	−0.104070	−	0.00624660i
$461$	−18.0000	+	31.1769i	−0.838344	+	1.45205i	0.0529352	+	0.998598i	$0.483142\pi$
$461$	−18.0000	+	31.1769i	−0.838344	+	1.45205i	−0.891279	+	0.453456i	$0.850191\pi$
$462$		0			0
$463$	6.92820	−	4.00000i	0.321981	−	0.185896i	−0.330294	−	0.943878i	$-0.607148\pi$
$463$	6.92820	−	4.00000i	0.321981	−	0.185896i	0.652275	+	0.757982i	$0.273815\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	−9.00000	+	15.5885i	−0.416917	+	0.722121i
$467$			6.00000i			0.277647i	0.990317	+	0.138823i	$0.0443321\pi$
$467$			6.00000i			0.277647i	−0.990317	+	0.138823i	$0.955668\pi$
$468$	2.59808	−	1.50000i	0.120096	−	0.0693375i
$469$	4.00000	−	6.92820i	0.184703	−	0.319915i
$470$	22.0000	−	11.0000i	1.01478	−	0.507392i
$471$		0			0
$472$	−12.9904	−	7.50000i	−0.597931	−	0.345215i
$473$		−	6.00000i		−	0.275880i
$474$		0			0
$475$	9.00000	−	12.0000i	0.412948	−	0.550598i
$476$	12.0000	+	20.7846i	0.550019	+	0.952661i
$477$	−25.9808	+	15.0000i	−1.18958	+	0.686803i
$478$	17.3205	−	10.0000i	0.792222	−	0.457389i
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	−0.789314	−	0.613990i	$-0.789564\pi$
$479$	3.00000	−	5.19615i	0.137073	−	0.237418i	0.926388	+	0.376571i	$0.122897\pi$
$480$		0			0
$481$	−5.00000	−	3.46410i	−0.227980	−	0.157949i
$482$			7.00000i			0.318841i
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	2.46410	−	3.73205i	0.111889	−	0.169464i
$486$		0			0
$487$			24.0000i			1.08754i	0.839233	+	0.543772i	$0.183004\pi$
$487$			24.0000i			1.08754i	−0.839233	+	0.543772i	$0.816996\pi$
$488$	−10.3923	+	6.00000i	−0.470438	+	0.271607i
$489$		0			0
$490$	−20.0885	−	1.20577i	−0.907504	−	0.0544712i
$491$	15.0000			0.676941			0.338470	−	0.940977i	$-0.390091\pi$
$491$	15.0000			0.676941			0.338470	+	0.940977i	$0.390091\pi$
$492$		0			0
$493$	−31.1769	−	18.0000i	−1.40414	−	0.810679i
$494$	−1.50000	−	2.59808i	−0.0674882	−	0.116893i
$495$	18.0000	−	9.00000i	0.809040	−	0.404520i
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$		0			0
$499$	18.0000	+	31.1769i	0.805791	+	1.39567i	0.915756	+	0.401735i	$0.131593\pi$
$499$	18.0000	+	31.1769i	0.805791	+	1.39567i	−0.109965	+	0.993935i	$0.535074\pi$
$500$	−10.5263	+	3.76795i	−0.470750	+	0.168508i
$501$		0			0
$502$	0.866025	+	0.500000i	0.0386526	+	0.0223161i
$503$	−13.8564	−	8.00000i	−0.617827	−	0.356702i	0.158196	−	0.987408i	$-0.449432\pi$
$503$	−13.8564	−	8.00000i	−0.617827	−	0.356702i	−0.776022	+	0.630705i	$0.782766\pi$
$504$	−12.0000			−0.534522
$505$	−7.46410	−	4.92820i	−0.332148	−	0.219302i
$506$	−1.50000	+	2.59808i	−0.0666831	+	0.115499i
$507$		0			0
$508$		−	17.0000i		−	0.754253i
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	0.123187	+	0.992384i	$0.460689\pi$
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	−0.921023	+	0.389509i	$0.872645\pi$
$510$		0			0
$511$	−4.00000	−	6.92820i	−0.176950	−	0.306486i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$		0			0
$515$	11.0885	−	16.7942i	0.488616	−	0.740042i
$516$		0			0
$517$		−	33.0000i		−	1.45134i
$518$	10.3923	+	22.0000i	0.456612	+	0.966625i
$519$		0			0
$520$	−0.133975	+	2.23205i	−0.00587517	+	0.0978819i
$521$	−2.50000	−	4.33013i	−0.109527	−	0.189706i	0.806052	−	0.591845i	$-0.201600\pi$
$521$	−2.50000	−	4.33013i	−0.109527	−	0.189706i	−0.915579	+	0.402139i	$0.868267\pi$
$522$	15.5885	−	9.00000i	0.682288	−	0.393919i
$523$	13.8564	−	8.00000i	0.605898	−	0.349816i	−0.165460	−	0.986216i	$-0.552911\pi$
$523$	13.8564	−	8.00000i	0.605898	−	0.349816i	0.771358	+	0.636401i	$0.219578\pi$
$524$	−20.0000			−0.873704
$525$		0			0
$526$	−19.0000			−0.828439
$527$	20.7846	+	12.0000i	0.905392	+	0.522728i
$528$		0			0
$529$	22.0000			0.956522
$530$	1.33975	−	22.3205i	0.0581948	−	0.969541i
$531$	22.5000	+	38.9711i	0.976417	+	1.69120i
$532$			12.0000i			0.520266i
$533$	−8.66025	−	5.00000i	−0.375117	−	0.216574i
$534$		0			0
$535$	−17.8564	−	1.07180i	−0.772000	−	0.0463378i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$		0			0
$538$	12.1244	+	7.00000i	0.522718	+	0.301791i
$539$	−13.5000	+	23.3827i	−0.581486	+	1.00716i
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	−17.3205	+	10.0000i	−0.743980	+	0.429537i
$543$		0			0
$544$	−6.00000			−0.257248
$545$	20.0000	−	10.0000i	0.856706	−	0.428353i
$546$		0			0
$547$			10.0000i			0.427569i	0.976881	+	0.213785i	$0.0685791\pi$
$547$			10.0000i			0.427569i	−0.976881	+	0.213785i	$0.931421\pi$
$548$	5.19615	−	3.00000i	0.221969	−	0.128154i
$549$	36.0000			1.53644
$550$	−1.79423	+	14.8923i	−0.0765062	+	0.635010i
$551$	−9.00000	−	15.5885i	−0.383413	−	0.664091i
$552$		0			0
$553$	−13.8564	−	8.00000i	−0.589234	−	0.340195i
$554$	−6.00000			−0.254916
$555$		0			0
$556$	−5.00000			−0.212047
$557$	−28.5788	−	16.5000i	−1.21092	−	0.699127i	−0.247964	−	0.968769i	$-0.579761\pi$
$557$	−28.5788	−	16.5000i	−1.21092	−	0.699127i	−0.962961	+	0.269642i	$0.913095\pi$
$558$	−10.3923	+	6.00000i	−0.439941	+	0.254000i
$559$	−1.00000	−	1.73205i	−0.0422955	−	0.0732579i
$560$	4.92820	−	7.46410i	0.208255	−	0.315416i
$561$		0			0
$562$	−2.59808	+	1.50000i	−0.109593	+	0.0632737i
$563$		−	4.00000i		−	0.168580i	−0.996441	−	0.0842900i	$-0.973138\pi$
$563$		−	4.00000i		−	0.168580i	0.996441	−	0.0842900i	$-0.0268622\pi$
$564$		0			0
$565$	10.0000	+	20.0000i	0.420703	+	0.841406i
$566$	−4.00000			−0.168133
$567$	31.1769	+	18.0000i	1.30931	+	0.755929i
$568$	5.19615	−	3.00000i	0.218026	−	0.125877i
$569$	−5.00000			−0.209611			−0.104805	−	0.994493i	$-0.533422\pi$
$569$	−5.00000			−0.209611			−0.104805	+	0.994493i	$0.533422\pi$
$570$		0			0
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	−0.969378	−	0.245573i	$-0.921024\pi$
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	0.697362	+	0.716720i	$0.254357\pi$
$572$	2.59808	+	1.50000i	0.108631	+	0.0627182i
$573$		0			0
$574$	20.0000	+	34.6410i	0.834784	+	1.44589i
$575$	−4.59808	+	1.96410i	−0.191753	+	0.0819087i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−17.3205	−	10.0000i	−0.721062	−	0.416305i	0.0940813	−	0.995565i	$-0.470009\pi$
$577$	−17.3205	−	10.0000i	−0.721062	−	0.416305i	−0.815144	+	0.579259i	$0.803342\pi$
$578$		−	19.0000i		−	0.790296i
$579$		0			0
$580$	−0.803848	+	13.3923i	−0.0333780	+	0.556085i
$581$	−24.0000			−0.995688
$582$		0			0
$583$	−25.9808	−	15.0000i	−1.07601	−	0.621237i
$584$	2.00000			0.0827606
$585$	3.69615	−	5.59808i	0.152817	−	0.231452i
$586$	−3.00000			−0.123929
$587$	31.1769	−	18.0000i	1.28681	−	0.742940i	0.308725	−	0.951151i	$-0.400098\pi$
$587$	31.1769	−	18.0000i	1.28681	−	0.742940i	0.978084	+	0.208212i	$0.0667643\pi$
$588$		0			0
$589$	6.00000	+	10.3923i	0.247226	+	0.428207i
$590$	−33.4808	−	2.00962i	−1.37838	−	0.0827347i
$591$		0			0
$592$	−6.06218	−	0.500000i	−0.249154	−	0.0205499i
$593$			42.0000i			1.72473i	0.506284	+	0.862367i	$0.331019\pi$
$593$			42.0000i			1.72473i	−0.506284	+	0.862367i	$0.668981\pi$
$594$		0			0
$595$	44.7846	+	29.5692i	1.83599	+	1.21222i
$596$	8.00000	+	13.8564i	0.327693	+	0.567581i
$597$		0			0
$598$			1.00000i			0.0408930i
$599$	−7.00000	−	12.1244i	−0.286012	−	0.495388i	0.686842	−	0.726807i	$-0.258996\pi$
$599$	−7.00000	−	12.1244i	−0.286012	−	0.495388i	−0.972854	+	0.231419i	$0.925663\pi$
$600$		0			0
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	−0.249565	−	0.968358i	$-0.580288\pi$
$601$	17.5000	−	30.3109i	0.713840	−	1.23641i	0.963405	−	0.268049i	$-0.0863789\pi$
$602$			8.00000i			0.326056i
$603$		−	6.00000i		−	0.244339i
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	−3.73205	−	2.46410i	−0.151729	−	0.100180i
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	−2.59808	−	1.50000i	−0.105366	−	0.0608330i
$609$		0			0
$610$	−14.7846	+	22.3923i	−0.598611	+	0.906638i
$611$	−5.50000	−	9.52628i	−0.222506	−	0.385392i
$612$	15.5885	+	9.00000i	0.630126	+	0.363803i
$613$	−7.79423	−	4.50000i	−0.314806	−	0.181753i	0.334269	−	0.942478i	$-0.391511\pi$
$613$	−7.79423	−	4.50000i	−0.314806	−	0.181753i	−0.649075	+	0.760724i	$0.724844\pi$
$614$	16.0000	−	27.7128i	0.645707	−	1.11840i
$615$		0			0
$616$	−6.00000	−	10.3923i	−0.241747	−	0.418718i
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	0.779809	−	0.626017i	$-0.215316\pi$
$617$	15.5885	+	9.00000i	0.627568	+	0.362326i	−0.152242	+	0.988343i	$0.548649\pi$
$618$		0			0
$619$	−4.00000			−0.160774			−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000			−0.160774			−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0.535898	−	8.92820i	0.0215222	−	0.358565i
$621$		0			0
$622$	−20.7846	+	12.0000i	−0.833387	+	0.481156i
$623$		−	60.0000i		−	2.40385i
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	−16.0000	−	27.7128i	−0.639489	−	1.10763i
$627$		0			0
$628$		−	5.00000i		−	0.199522i
$629$	3.00000	−	36.3731i	0.119618	−	1.45029i
$630$	−24.0000	+	12.0000i	−0.956183	+	0.478091i
$631$	1.00000	−	1.73205i	0.0398094	−	0.0689519i	−0.845434	−	0.534080i	$-0.820658\pi$
$631$	1.00000	−	1.73205i	0.0398094	−	0.0689519i	0.885244	+	0.465128i	$0.153992\pi$
$632$	3.46410	−	2.00000i	0.137795	−	0.0795557i
$633$		0			0
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$	−17.0000	−	34.0000i	−0.674624	−	1.34925i
$636$		0			0
$637$			9.00000i			0.356593i
$638$	15.5885	+	9.00000i	0.617153	+	0.356313i
$639$	−18.0000			−0.712069
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	0.280234	+	0.959932i	$0.409588\pi$
$641$	−17.5000	+	30.3109i	−0.691208	+	1.19721i	−0.971442	+	0.237276i	$0.923745\pi$
$642$		0			0
$643$			16.0000i			0.630978i	0.948929	+	0.315489i	$0.102169\pi$
$643$			16.0000i			0.630978i	−0.948929	+	0.315489i	$0.897831\pi$
$644$	2.00000	−	3.46410i	0.0788110	−	0.136505i
$645$		0			0
$646$	9.00000	−	15.5885i	0.354100	−	0.613320i
$647$	42.4352	−	24.5000i	1.66830	−	0.963194i	0.699748	−	0.714390i	$-0.253296\pi$
$647$	42.4352	−	24.5000i	1.66830	−	0.963194i	0.968554	−	0.248805i	$-0.0800377\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$	−22.5000	+	38.9711i	−0.883202	+	1.52975i
$650$	1.96410	+	4.59808i	0.0770384	+	0.180351i
$651$		0			0
$652$		−	6.00000i		−	0.234978i
$653$	−21.6506	+	12.5000i	−0.847255	+	0.489163i	−0.859724	−	0.510759i	$-0.829364\pi$
$653$	−21.6506	+	12.5000i	−0.847255	+	0.489163i	0.0124688	+	0.999922i	$0.496031\pi$
$654$		0			0
$655$	−40.0000	+	20.0000i	−1.56293	+	0.781465i
$656$	−10.0000			−0.390434
$657$	−5.19615	−	3.00000i	−0.202721	−	0.117041i
$658$			44.0000i			1.71530i
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	0.999545	+	0.0301523i	$0.00959924\pi$
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	−0.473660	+	0.880708i	$0.657067\pi$
$660$		0			0
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	−11.2583	+	6.50000i	−0.437567	+	0.252630i
$663$		0			0
$664$	3.00000	−	5.19615i	0.116423	−	0.201650i
$665$	12.0000	+	24.0000i	0.465340	+	0.930680i
$666$	15.0000	+	10.3923i	0.581238	+	0.402694i
$667$			6.00000i			0.232321i
$668$	6.92820	+	4.00000i	0.268060	+	0.154765i
$669$		0			0
$670$	3.73205	+	2.46410i	0.144182	+	0.0951966i
$671$	18.0000	+	31.1769i	0.694882	+	1.20357i
$672$		0			0
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	−0.843886	−	0.536522i	$-0.819738\pi$
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	0.0426985	+	0.999088i	$0.486405\pi$
$674$	8.00000			0.308148
$675$		0			0
$676$	−12.0000			−0.461538
$677$		−	27.0000i		−	1.03769i	−0.854867	−	0.518847i	$-0.826361\pi$
$677$		−	27.0000i		−	1.03769i	0.854867	−	0.518847i	$-0.173639\pi$
$678$		0			0
$679$	4.00000	+	6.92820i	0.153506	+	0.265880i
$680$	−12.0000	+	6.00000i	−0.460179	+	0.230089i
$681$		0			0
$682$	−10.3923	−	6.00000i	−0.397942	−	0.229752i
$683$	22.5167	+	13.0000i	0.861576	+	0.497431i	0.864540	−	0.502564i	$-0.167610\pi$
$683$	22.5167	+	13.0000i	0.861576	+	0.497431i	−0.00296369	+	0.999996i	$0.500943\pi$
$684$	4.50000	+	7.79423i	0.172062	+	0.298020i
$685$	7.39230	−	11.1962i	0.282445	−	0.427783i
$686$	4.00000	−	6.92820i	0.152721	−	0.264520i
$687$		0			0
$688$	−1.73205	−	1.00000i	−0.0660338	−	0.0381246i
$689$	−10.0000			−0.380970
$690$		0			0
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	−0.382791	−	0.923835i	$-0.625037\pi$
$691$	16.0000	−	27.7128i	0.608669	−	1.05425i	0.991460	−	0.130410i	$-0.0416295\pi$
$692$		−	5.00000i		−	0.190071i
$693$			36.0000i			1.36753i
$694$	15.0000	−	25.9808i	0.569392	−	0.986216i
$695$	−10.0000	+	5.00000i	−0.379322	+	0.189661i
$696$		0			0
$697$		−	60.0000i		−	2.27266i
$698$	−5.19615	+	3.00000i	−0.196677	+	0.113552i
$699$		0			0
$700$	2.39230	−	19.8564i	0.0904206	−	0.750502i
$701$	8.00000	−	13.8564i	0.302156	−	0.523349i	−0.674468	−	0.738304i	$-0.735627\pi$
$701$	8.00000	−	13.8564i	0.302156	−	0.523349i	0.976624	+	0.214955i	$0.0689604\pi$
$702$		0			0
$703$	10.3923	−	15.0000i	0.391953	−	0.565736i
$704$	3.00000			0.113067
$705$		0			0
$706$	9.00000	+	15.5885i	0.338719	+	0.586679i
$707$	13.8564	−	8.00000i	0.521124	−	0.300871i
$708$		0			0
$709$	16.0000			0.600893			0.300446	−	0.953799i	$-0.402864\pi$
$709$	16.0000			0.600893			0.300446	+	0.953799i	$0.402864\pi$
$710$	7.39230	−	11.1962i	0.277428	−	0.420184i
$711$	−12.0000			−0.450035
$712$	12.9904	+	7.50000i	0.486835	+	0.281074i
$713$		−	4.00000i		−	0.149801i
$714$		0			0
$715$	6.69615	+	0.401924i	0.250422	+	0.0150311i
$716$	−0.500000	−	0.866025i	−0.0186859	−	0.0323649i
$717$		0			0
$718$	−22.5167	−	13.0000i	−0.840314	−	0.485156i
$719$	19.0000	−	32.9090i	0.708580	−	1.22730i	−0.256803	−	0.966464i	$-0.582669\pi$
$719$	19.0000	−	32.9090i	0.708580	−	1.22730i	0.965384	−	0.260834i	$-0.0839974\pi$
$720$	0.401924	−	6.69615i	0.0149788	−	0.249551i
$721$	18.0000	+	31.1769i	0.670355	+	1.16109i
$722$	−8.66025	+	5.00000i	−0.322301	+	0.186081i
$723$		0			0
$724$	−8.00000	+	13.8564i	−0.297318	+	0.514969i
$725$	11.7846	+	27.5885i	0.437669	+	1.02461i
$726$		0			0
$727$	−37.2391	+	21.5000i	−1.38112	+	0.797391i	−0.992292	−	0.123919i	$-0.960454\pi$
$727$	−37.2391	+	21.5000i	−1.38112	+	0.797391i	−0.388829	+	0.921310i	$0.627120\pi$
$728$	−3.46410	−	2.00000i	−0.128388	−	0.0741249i
$729$	27.0000			1.00000
$730$	4.00000	−	2.00000i	0.148047	−	0.0740233i
$731$	6.00000	−	10.3923i	0.221918	−	0.384373i
$732$		0			0
$733$	32.0429	−	18.5000i	1.18353	−	0.683313i	0.226704	−	0.973964i	$-0.427205\pi$
$733$	32.0429	−	18.5000i	1.18353	−	0.683313i	0.956829	+	0.290651i	$0.0938717\pi$
$734$	13.0000			0.479839
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	5.19615	−	3.00000i	0.191403	−	0.110506i
$738$	25.9808	+	15.0000i	0.956365	+	0.552158i
$739$	−15.0000			−0.551784			−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000			−0.551784			−0.275892	+	0.961189i	$0.588973\pi$
$740$	−12.6244	+	5.06218i	−0.464081	+	0.186089i
$741$		0			0
$742$	34.6410	+	20.0000i	1.27171	+	0.734223i
$743$	35.5070	−	20.5000i	1.30263	−	0.752072i	0.321773	−	0.946817i	$-0.395721\pi$
$743$	35.5070	−	20.5000i	1.30263	−	0.752072i	0.980854	+	0.194745i	$0.0623879\pi$
$744$		0			0
$745$	29.8564	+	19.7128i	1.09385	+	0.722222i
$746$	−23.0000			−0.842090
$747$	−15.5885	+	9.00000i	−0.570352	+	0.329293i
$748$			18.0000i			0.658145i
$749$	16.0000	−	27.7128i	0.584627	−	1.01260i
$750$		0			0
$751$	10.0000			0.364905			0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000			0.364905			0.182453	+	0.983215i	$0.441596\pi$
$752$	−9.52628	−	5.50000i	−0.347388	−	0.200564i
$753$		0			0
$754$	6.00000			0.218507
$755$	−0.267949	+	4.46410i	−0.00975167	+	0.162465i
$756$		0			0
$757$	25.1147	+	14.5000i	0.912811	+	0.527011i	0.881334	−	0.472493i	$-0.156646\pi$
$757$	25.1147	+	14.5000i	0.912811	+	0.527011i	0.0314762	+	0.999505i	$0.489979\pi$
$758$	20.7846	−	12.0000i	0.754931	−	0.435860i
$759$		0			0
$760$	−6.69615	−	0.401924i	−0.242895	−	0.0145793i
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	−0.874946	−	0.484221i	$-0.839103\pi$
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	0.856821	+	0.515615i	$0.172436\pi$
$762$		0			0
$763$			40.0000i			1.44810i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$	40.1769	+	2.41154i	1.45260	+	0.0871895i
$766$	−17.0000			−0.614235
$767$			15.0000i			0.541619i
$768$		0			0
$769$	−22.0000			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$	−22.3923	−	14.7846i	−0.806963	−	0.532800i
$771$		0			0
$772$	−13.8564	+	8.00000i	−0.498703	+	0.287926i
$773$	7.79423	−	4.50000i	0.280339	−	0.161854i	−0.353238	−	0.935534i	$-0.614919\pi$
$773$	7.79423	−	4.50000i	0.280339	−	0.161854i	0.633577	+	0.773680i	$0.281586\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	−7.85641	−	18.3923i	−0.282210	−	0.660671i
$776$	−2.00000			−0.0717958
$777$		0			0
$778$			4.00000i			0.143407i
$779$	15.0000	−	25.9808i	0.537431	−	0.930857i
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$	−5.19615	+	3.00000i	−0.185814	+	0.107280i
$783$		0			0
$784$	4.50000	+	7.79423i	0.160714	+	0.278365i
$785$	−5.00000	−	10.0000i	−0.178458	−	0.356915i
$786$		0			0
$787$			38.0000i			1.35455i	0.735728	+	0.677277i	$0.236840\pi$
$787$			38.0000i			1.35455i	−0.735728	+	0.677277i	$0.763160\pi$
$788$		−	22.0000i		−	0.783718i
$789$		0			0
$790$	4.92820	−	7.46410i	0.175338	−	0.265561i
$791$	−40.0000			−1.42224
$792$	−7.79423	−	4.50000i	−0.276956	−	0.159901i
$793$	10.3923	+	6.00000i	0.369042	+	0.213066i
$794$	−2.50000	+	4.33013i	−0.0887217	+	0.153670i
$795$		0			0
$796$	−11.0000	−	19.0526i	−0.389885	−	0.675300i
$797$	−12.9904	−	7.50000i	−0.460143	−	0.265664i	0.251961	−	0.967737i	$-0.418924\pi$
$797$	−12.9904	−	7.50000i	−0.460143	−	0.265664i	−0.712104	+	0.702074i	$0.752258\pi$
$798$		0			0
$799$	33.0000	−	57.1577i	1.16746	−	2.02209i
$800$	4.00000	+	3.00000i	0.141421	+	0.106066i
$801$	−22.5000	−	38.9711i	−0.794998	−	1.37698i
$802$	−21.6506	−	12.5000i	−0.764511	−	0.441390i
$803$		−	6.00000i		−	0.211735i
$804$		0			0
$805$	0.535898	−	8.92820i	0.0188879	−	0.314678i
$806$	−4.00000			−0.140894
$807$		0			0
$808$			4.00000i			0.140720i
$809$	−22.5000	−	38.9711i	−0.791058	−	1.37015i	−0.925312	−	0.379206i	$-0.876197\pi$
$809$	−22.5000	−	38.9711i	−0.791058	−	1.37015i	0.134255	−	0.990947i	$-0.457136\pi$
$810$	−11.0885	+	16.7942i	−0.389609	+	0.590089i
$811$	16.5000	+	28.5788i	0.579393	+	1.00354i	0.995549	+	0.0942453i	$0.0300438\pi$
$811$	16.5000	+	28.5788i	0.579393	+	1.00354i	−0.416156	+	0.909293i	$0.636623\pi$
$812$	−20.7846	−	12.0000i	−0.729397	−	0.421117i
$813$		0			0
$814$	−1.50000	+	18.1865i	−0.0525750	+	0.637438i
$815$	−6.00000	−	12.0000i	−0.210171	−	0.420342i
$816$		0			0
$817$	5.19615	−	3.00000i	0.181790	−	0.104957i
$818$	19.0526	−	11.0000i	0.666157	−	0.384606i
$819$	6.00000	+	10.3923i	0.209657	+	0.363137i
$820$	−20.0000	+	10.0000i	−0.698430	+	0.349215i
$821$	19.0000	+	32.9090i	0.663105	+	1.14853i	0.979795	+	0.200002i	$0.0640949\pi$
$821$	19.0000	+	32.9090i	0.663105	+	1.14853i	−0.316691	+	0.948529i	$0.602572\pi$
$822$		0			0
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	0.238664	−	0.971102i	$-0.423291\pi$
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	−0.721668	+	0.692240i	$0.756624\pi$
$824$	−9.00000			−0.313530
$825$		0			0
$826$	30.0000	−	51.9615i	1.04383	−	1.80797i
$827$	10.3923	−	6.00000i	0.361376	−	0.208640i	−0.308308	−	0.951286i	$-0.599763\pi$
$827$	10.3923	−	6.00000i	0.361376	−	0.208640i	0.669684	+	0.742646i	$0.266429\pi$
$828$		−	3.00000i		−	0.104257i
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	−0.829202	−	0.558949i	$-0.811205\pi$
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	0.898665	+	0.438636i	$0.144538\pi$
$830$	0.803848	−	13.3923i	0.0279020	−	0.464854i
$831$		0			0
$832$	0.866025	−	0.500000i	0.0300240	−	0.0173344i
$833$	−46.7654	+	27.0000i	−1.62032	+	0.935495i
$834$		0			0
$835$	17.8564	+	1.07180i	0.617946	+	0.0370911i
$836$	−4.50000	+	7.79423i	−0.155636	+	0.269569i
$837$		0			0
$838$	21.6506	−	12.5000i	0.747909	−	0.431805i
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$839$	−6.00000	+	10.3923i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	5.19615	+	3.00000i	0.179071	+	0.103387i
$843$		0			0
$844$	−0.500000	−	0.866025i	−0.0172107	−	0.0298098i
$845$	−24.0000	+	12.0000i	−0.825625	+	0.412813i
$846$	16.5000	+	28.5788i	0.567282	+	0.982561i
$847$	6.92820	−	4.00000i	0.238056	−	0.137442i
$848$	−8.66025	+	5.00000i	−0.297394	+	0.171701i
$849$		0			0
$850$	−18.0000	+	24.0000i	−0.617395	+	0.823193i
$851$	−5.50000	+	2.59808i	−0.188538	+	0.0890609i
$852$		0			0
$853$	−18.1865	−	10.5000i	−0.622695	−	0.359513i	0.155222	−	0.987880i	$-0.450391\pi$
$853$	−18.1865	−	10.5000i	−0.622695	−	0.359513i	−0.777918	+	0.628366i	$0.783724\pi$
$854$	−24.0000	−	41.5692i	−0.821263	−	1.42247i
$855$	16.7942	+	11.0885i	0.574351	+	0.379217i
$856$	4.00000	+	6.92820i	0.136717	+	0.236801i
$857$		−	22.0000i		−	0.751506i	−0.926720	−	0.375753i	$-0.877384\pi$
$857$		−	22.0000i		−	0.751506i	0.926720	−	0.375753i	$-0.122616\pi$
$858$		0			0
$859$	−19.0000			−0.648272			−0.324136	−	0.946011i	$-0.605073\pi$
$859$	−19.0000			−0.648272			−0.324136	+	0.946011i	$0.605073\pi$
$860$	−4.46410	−	0.267949i	−0.152225	−	0.00913699i
$861$		0			0
$862$		−	16.0000i		−	0.544962i
$863$	−38.9711	−	22.5000i	−1.32659	−	0.765909i	−0.341822	−	0.939765i	$-0.611044\pi$
$863$	−38.9711	−	22.5000i	−1.32659	−	0.765909i	−0.984771	+	0.173856i	$0.944377\pi$
$864$		0			0
$865$	−5.00000	−	10.0000i	−0.170005	−	0.340010i
$866$	−17.0000	+	29.4449i	−0.577684	+	1.00058i
$867$		0			0
$868$	13.8564	+	8.00000i	0.470317	+	0.271538i
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	1.00000	−	1.73205i	0.0338837	−	0.0586883i
$872$	−8.66025	−	5.00000i	−0.293273	−	0.169321i
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	−3.00000			−0.101477
$875$	−15.0718	−	42.1051i	−0.509520	−	1.42341i
$876$		0			0
$877$		−	11.0000i		−	0.371444i	−0.982602	−	0.185722i	$-0.940538\pi$
$877$		−	11.0000i		−	0.371444i	0.982602	−	0.185722i	$-0.0594623\pi$
$878$			2.00000i			0.0674967i
$879$		0			0
$880$	6.00000	−	3.00000i	0.202260	−	0.101130i
$881$	−4.50000	−	7.79423i	−0.151609	−	0.262594i	0.780210	−	0.625517i	$-0.215112\pi$
$881$	−4.50000	−	7.79423i	−0.151609	−	0.262594i	−0.931819	+	0.362923i	$0.881779\pi$
$882$		−	27.0000i		−	0.909137i
$883$	1.73205	−	1.00000i	0.0582882	−	0.0336527i	−0.470573	−	0.882361i	$-0.655953\pi$
$883$	1.73205	−	1.00000i	0.0582882	−	0.0336527i	0.528861	+	0.848709i	$0.322619\pi$
$884$	3.00000	+	5.19615i	0.100901	+	0.174766i
$885$		0			0
$886$	17.0000	−	29.4449i	0.571126	−	0.989220i
$887$			8.00000i			0.268614i	0.990940	+	0.134307i	$0.0428808\pi$
$887$			8.00000i			0.268614i	−0.990940	+	0.134307i	$0.957119\pi$
$888$		0			0
$889$	68.0000			2.28065
$890$	33.4808	+	2.00962i	1.12228	+	0.0673626i
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$	−4.33013	+	2.50000i	−0.144983	+	0.0837062i
$893$	28.5788	−	16.5000i	0.956354	−	0.552151i
$894$		0			0
$895$	−1.86603	−	1.23205i	−0.0623744	−	0.0411829i
$896$	−4.00000			−0.133631
$897$		0			0
$898$			30.0000i			1.00111i
$899$	−24.0000			−0.800445
$900$	−5.89230	−	13.7942i	−0.196410	−	0.459808i
$901$	−30.0000	−	51.9615i	−0.999445	−	1.73109i
$902$			30.0000i			0.998891i
$903$		0			0
$904$	5.00000	−	8.66025i	0.166298	−	0.288036i
$905$	−2.14359	+	35.7128i	−0.0712555	+	1.18713i
$906$		0			0
$907$	48.4974	−	28.0000i	1.61033	−	0.929725i	0.621038	−	0.783781i	$-0.286711\pi$
$907$	48.4974	−	28.0000i	1.61033	−	0.929725i	0.989293	−	0.145944i	$-0.0466219\pi$
$908$	24.2487	+	14.0000i	0.804722	+	0.464606i
$909$	6.00000	−	10.3923i	0.199007	−	0.344691i
$910$	−8.92820	−	0.535898i	−0.295967	−	0.0177649i
$911$	36.0000			1.19273			0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000			1.19273			0.596367	+	0.802712i	$0.296610\pi$
$912$		0			0
$913$	−15.5885	−	9.00000i	−0.515903	−	0.297857i
$914$	26.0000			0.860004
$915$		0			0
$916$	−1.00000	+	1.73205i	−0.0330409	+	0.0572286i
$917$		−	80.0000i		−	2.64183i
$918$		0			0
$919$	34.0000			1.12156			0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000			1.12156			0.560778	+	0.827966i	$0.310502\pi$
$920$	1.86603	+	1.23205i	0.0615210	+	0.0406195i
$921$		0			0
$922$	31.1769	−	18.0000i	1.02676	−	0.592798i
$923$	−5.19615	−	3.00000i	−0.171033	−	0.0987462i
$924$		0			0
$925$	−20.1865	+	22.7487i	−0.663729	+	0.747973i
$926$	−8.00000			−0.262896
$927$	23.3827	+	13.5000i	0.767988	+	0.443398i
$928$	5.19615	−	3.00000i	0.170572	−	0.0984798i
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$		0			0
$931$	−27.0000			−0.884889
$932$	15.5885	−	9.00000i	0.510617	−	0.294805i
$933$		0			0
$934$	3.00000	−	5.19615i	0.0981630	−	0.170023i
$935$	18.0000	+	36.0000i	0.588663	+	1.17733i
$936$	−3.00000			−0.0980581
$937$	−12.1244	−	7.00000i	−0.396085	−	0.228680i	0.288708	−	0.957417i	$-0.406774\pi$
$937$	−12.1244	−	7.00000i	−0.396085	−	0.228680i	−0.684794	+	0.728737i	$0.740108\pi$
$938$	−6.92820	+	4.00000i	−0.226214	+	0.130605i
$939$		0			0
$940$	−24.5526	−	1.47372i	−0.800816	−	0.0480675i
$941$	20.0000	−	34.6410i	0.651981	−	1.12926i	−0.330660	−	0.943750i	$-0.607271\pi$
$941$	20.0000	−	34.6410i	0.651981	−	1.12926i	0.982641	−	0.185515i	$-0.0593953\pi$
$942$		0			0
$943$	−8.66025	+	5.00000i	−0.282017	+	0.162822i
$944$	7.50000	+	12.9904i	0.244104	+	0.422801i
$945$		0			0
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	39.8372	+	23.0000i	1.29453	+	0.747400i	0.979454	−	0.201666i	$-0.0646354\pi$
$947$	39.8372	+	23.0000i	1.29453	+	0.747400i	0.315080	+	0.949065i	$0.397969\pi$
$948$		0			0
$949$	−1.00000	−	1.73205i	−0.0324614	−	0.0562247i
$950$	−13.7942	+	5.89230i	−0.447544	+	0.191172i
$951$		0			0
$952$		−	24.0000i		−	0.777844i
$953$	−31.1769	−	18.0000i	−1.00992	−	0.583077i	−0.0987513	−	0.995112i	$-0.531485\pi$
$953$	−31.1769	−	18.0000i	−1.00992	−	0.583077i	−0.911168	+	0.412035i	$0.864818\pi$
$954$	30.0000			0.971286
$955$	7.46410	+	4.92820i	0.241533	+	0.159473i
$956$	−20.0000			−0.646846
$957$		0			0
$958$	−5.19615	+	3.00000i	−0.167880	+	0.0969256i
$959$	12.0000	+	20.7846i	0.387500	+	0.671170i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	2.59808	+	5.50000i	0.0837653	+	0.177327i
$963$		−	24.0000i		−	0.773389i
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$	−19.7128	+	29.8564i	−0.634578	+	0.961112i
$966$		0			0
$967$	−35.5070	+	20.5000i	−1.14183	+	0.659236i	−0.946883	−	0.321578i	$-0.895787\pi$
$967$	−35.5070	+	20.5000i	−1.14183	+	0.659236i	−0.194946	+	0.980814i	$0.562453\pi$
$968$			2.00000i			0.0642824i
$969$		0			0
$970$	−4.00000	+	2.00000i	−0.128432	+	0.0642161i
$971$	−26.5000	+	45.8993i	−0.850425	+	1.47298i	0.0303994	+	0.999538i	$0.490322\pi$
$971$	−26.5000	+	45.8993i	−0.850425	+	1.47298i	−0.880825	+	0.473442i	$0.843011\pi$
$972$		0			0
$973$		−	20.0000i		−	0.641171i
$974$	12.0000	−	20.7846i	0.384505	−	0.665982i
$975$		0			0
$976$	12.0000			0.384111
$977$	51.9615	+	30.0000i	1.66240	+	0.959785i	0.971566	+	0.236768i	$0.0760881\pi$
$977$	51.9615	+	30.0000i	1.66240	+	0.959785i	0.690830	+	0.723017i	$0.257245\pi$
$978$		0			0
$979$	22.5000	−	38.9711i	0.719103	−	1.24552i
$980$	16.7942	+	11.0885i	0.536472	+	0.354208i
$981$	15.0000	+	25.9808i	0.478913	+	0.829502i
$982$	−12.9904	−	7.50000i	−0.414540	−	0.239335i
$983$	14.7224	+	8.50000i	0.469573	+	0.271108i	0.716061	−	0.698038i	$-0.245943\pi$
$983$	14.7224	+	8.50000i	0.469573	+	0.271108i	−0.246488	+	0.969146i	$0.579277\pi$
$984$		0			0
$985$	−22.0000	−	44.0000i	−0.700978	−	1.40196i
$986$	18.0000	+	31.1769i	0.573237	+	0.992875i
$987$		0			0
$988$			3.00000i			0.0954427i
$989$	−2.00000			−0.0635963
$990$	−20.0885	−	1.20577i	−0.638453	−	0.0383219i
$991$	−18.0000			−0.571789			−0.285894	−	0.958261i	$-0.592291\pi$
$991$	−18.0000			−0.571789			−0.285894	+	0.958261i	$0.592291\pi$
$992$	−3.46410	+	2.00000i	−0.109985	+	0.0635001i
$993$		0			0
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$	−41.0526	−	27.1051i	−1.30145	−	0.859290i
$996$		0			0
$997$	−14.7224	−	8.50000i	−0.466264	−	0.269198i	0.248410	−	0.968655i	$-0.420092\pi$
$997$	−14.7224	−	8.50000i	−0.466264	−	0.269198i	−0.714675	+	0.699457i	$0.753425\pi$
$998$		−	36.0000i		−	1.13956i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.b.269.1	✓	4
5.4	even	2	inner	370.2.n.b.269.2	yes	4
37.26	even	3	inner	370.2.n.b.359.2	yes	4
185.174	even	6	inner	370.2.n.b.359.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.b.269.1	✓	4	1.1	even	1	trivial
370.2.n.b.269.2	yes	4	5.4	even	2	inner
370.2.n.b.359.1	yes	4	185.174	even	6	inner
370.2.n.b.359.2	yes	4	37.26	even	3	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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.86603 + 1.23205i) q^{5} +(-3.46410 + 2.00000i) q^{7} -1.00000i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.00000 - 2.00000i) q^{10} -3.00000 q^{11} +(-0.866025 + 0.500000i) q^{13} +4.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 - 3.00000i) q^{17} +(2.59808 - 1.50000i) q^{18} +(-1.50000 - 2.59808i) q^{19} +(-0.133975 + 2.23205i) q^{20} +(2.59808 + 1.50000i) q^{22} +1.00000i q^{23} +(1.96410 + 4.59808i) q^{25} +1.00000 q^{26} +(-3.46410 - 2.00000i) q^{28} +6.00000 q^{29} -4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(3.00000 + 5.19615i) q^{34} +(-8.92820 - 0.535898i) q^{35} -3.00000 q^{36} +(2.59808 + 5.50000i) q^{37} +3.00000i q^{38} +(1.23205 - 1.86603i) q^{40} +(5.00000 + 8.66025i) q^{41} +2.00000i q^{43} +(-1.50000 - 2.59808i) q^{44} +(-6.00000 + 3.00000i) q^{45} +(0.500000 - 0.866025i) q^{46} +11.0000i q^{47} +(4.50000 - 7.79423i) q^{49} +(0.598076 - 4.96410i) q^{50} +(-0.866025 - 0.500000i) q^{52} +(8.66025 + 5.00000i) q^{53} +(-5.59808 - 3.69615i) q^{55} +(2.00000 + 3.46410i) q^{56} +(-5.19615 - 3.00000i) q^{58} +(7.50000 - 12.9904i) q^{59} +(-6.00000 - 10.3923i) q^{61} +(3.46410 + 2.00000i) q^{62} -12.0000i q^{63} -1.00000 q^{64} +(-2.23205 - 0.133975i) q^{65} +(-1.73205 + 1.00000i) q^{67} -6.00000i q^{68} +(7.46410 + 4.92820i) q^{70} +(3.00000 + 5.19615i) q^{71} +(2.59808 + 1.50000i) q^{72} +2.00000i q^{73} +(0.500000 - 6.06218i) q^{74} +(1.50000 - 2.59808i) q^{76} +(10.3923 - 6.00000i) q^{77} +(2.00000 + 3.46410i) q^{79} +(-2.00000 + 1.00000i) q^{80} +(-4.50000 - 7.79423i) q^{81} -10.0000i q^{82} +(5.19615 + 3.00000i) q^{83} +(-6.00000 - 12.0000i) q^{85} +(1.00000 - 1.73205i) q^{86} +3.00000i q^{88} +(-7.50000 + 12.9904i) q^{89} +(6.69615 + 0.401924i) q^{90} +(2.00000 - 3.46410i) q^{91} +(-0.866025 + 0.500000i) q^{92} +(5.50000 - 9.52628i) q^{94} +(0.401924 - 6.69615i) q^{95} -2.00000i q^{97} +(-7.79423 + 4.50000i) q^{98} +(4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{5} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^5 - 6 * q^9	\( 4 q + 2 q^{4} + 4 q^{5} - 6 q^{9} - 4 q^{10} - 12 q^{11} + 16 q^{14} - 2 q^{16} - 6 q^{19} - 4 q^{20} - 6 q^{25} + 4 q^{26} + 24 q^{29} - 16 q^{31} + 12 q^{34} - 8 q^{35} - 12 q^{36} - 2 q^{40} + 20 q^{41} - 6 q^{44} - 24 q^{45} + 2 q^{46} + 18 q^{49} - 8 q^{50} - 12 q^{55} + 8 q^{56} + 30 q^{59} - 24 q^{61} - 4 q^{64} - 2 q^{65} + 16 q^{70} + 12 q^{71} + 2 q^{74} + 6 q^{76} + 8 q^{79} - 8 q^{80} - 18 q^{81} - 24 q^{85} + 4 q^{86} - 30 q^{89} + 6 q^{90} + 8 q^{91} + 22 q^{94} + 12 q^{95} + 18 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^5 - 6 * q^9 - 4 * q^10 - 12 * q^11 + 16 * q^14 - 2 * q^16 - 6 * q^19 - 4 * q^20 - 6 * q^25 + 4 * q^26 + 24 * q^29 - 16 * q^31 + 12 * q^34 - 8 * q^35 - 12 * q^36 - 2 * q^40 + 20 * q^41 - 6 * q^44 - 24 * q^45 + 2 * q^46 + 18 * q^49 - 8 * q^50 - 12 * q^55 + 8 * q^56 + 30 * q^59 - 24 * q^61 - 4 * q^64 - 2 * q^65 + 16 * q^70 + 12 * q^71 + 2 * q^74 + 6 * q^76 + 8 * q^79 - 8 * q^80 - 18 * q^81 - 24 * q^85 + 4 * q^86 - 30 * q^89 + 6 * q^90 + 8 * q^91 + 22 * q^94 + 12 * q^95 + 18 * q^99

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