LMFDB - Embedded newform 35.2.f.a.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,2,Mod(13,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("35.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	35.f (of order $4$, 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:	$0.279476407074$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 25 $ x^4 + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Root			$-1.58114 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	35.13
Dual form			35.2.f.a.27.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.58114 + 1.58114i) q^{3} +(1.58114 - 1.58114i) q^{5} -3.16228i q^{6} +(2.58114 + 0.581139i) q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.58114 + 1.58114i) q^{3} +(1.58114 - 1.58114i) q^{5} -3.16228i q^{6} +(2.58114 + 0.581139i) q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{9} +3.16228i q^{10} -1.00000 q^{11} +(1.58114 - 1.58114i) q^{13} +(-3.16228 + 2.00000i) q^{14} +5.00000i q^{15} +4.00000 q^{16} +(-1.58114 - 1.58114i) q^{17} +(2.00000 + 2.00000i) q^{18} -3.16228 q^{19} +(-5.00000 + 3.16228i) q^{21} +(1.00000 - 1.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} +6.32456 q^{24} -5.00000i q^{25} +3.16228i q^{26} +(-1.58114 - 1.58114i) q^{27} -3.00000i q^{29} +(-5.00000 - 5.00000i) q^{30} -3.16228i q^{31} +(1.58114 - 1.58114i) q^{33} +3.16228 q^{34} +(5.00000 - 3.16228i) q^{35} +(-6.00000 + 6.00000i) q^{37} +(3.16228 - 3.16228i) q^{38} +5.00000i q^{39} -6.32456 q^{40} +9.48683i q^{41} +(1.83772 - 8.16228i) q^{42} +(-3.00000 - 3.00000i) q^{43} +(-3.16228 - 3.16228i) q^{45} -4.00000 q^{46} +(4.74342 + 4.74342i) q^{47} +(-6.32456 + 6.32456i) q^{48} +(6.32456 + 3.00000i) q^{49} +(5.00000 + 5.00000i) q^{50} +5.00000 q^{51} +(1.00000 + 1.00000i) q^{53} +3.16228 q^{54} +(-1.58114 + 1.58114i) q^{55} +(-4.00000 - 6.32456i) q^{56} +(5.00000 - 5.00000i) q^{57} +(3.00000 + 3.00000i) q^{58} -9.48683 q^{59} -6.32456i q^{61} +(3.16228 + 3.16228i) q^{62} +(1.16228 - 5.16228i) q^{63} +8.00000i q^{64} -5.00000i q^{65} +3.16228i q^{66} +(-1.00000 + 1.00000i) q^{67} -6.32456 q^{69} +(-1.83772 + 8.16228i) q^{70} -6.00000 q^{71} +(-4.00000 + 4.00000i) q^{72} -12.0000i q^{74} +(7.90569 + 7.90569i) q^{75} +(-2.58114 - 0.581139i) q^{77} +(-5.00000 - 5.00000i) q^{78} -13.0000i q^{79} +(6.32456 - 6.32456i) q^{80} +11.0000 q^{81} +(-9.48683 - 9.48683i) q^{82} +(3.16228 - 3.16228i) q^{83} -5.00000 q^{85} +6.00000 q^{86} +(4.74342 + 4.74342i) q^{87} +(2.00000 + 2.00000i) q^{88} +6.32456 q^{89} +6.32456 q^{90} +(5.00000 - 3.16228i) q^{91} +(5.00000 + 5.00000i) q^{93} -9.48683 q^{94} +(-5.00000 + 5.00000i) q^{95} +(1.58114 + 1.58114i) q^{97} +(-9.32456 + 3.32456i) q^{98} +2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{7} - 8 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^7 - 8 * q^8	$ 4 q - 4 q^{2} + 4 q^{7} - 8 q^{8} - 4 q^{11} + 16 q^{16} + 8 q^{18} - 20 q^{21} + 4 q^{22} + 8 q^{23} - 20 q^{30} + 20 q^{35} - 24 q^{37} + 20 q^{42} - 12 q^{43} - 16 q^{46} + 20 q^{50} + 20 q^{51} + 4 q^{53} - 16 q^{56} + 20 q^{57} + 12 q^{58} - 8 q^{63} - 4 q^{67} - 20 q^{70} - 24 q^{71} - 16 q^{72} - 4 q^{77} - 20 q^{78} + 44 q^{81} - 20 q^{85} + 24 q^{86} + 8 q^{88} + 20 q^{91} + 20 q^{93} - 20 q^{95} - 12 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^7 - 8 * q^8 - 4 * q^11 + 16 * q^16 + 8 * q^18 - 20 * q^21 + 4 * q^22 + 8 * q^23 - 20 * q^30 + 20 * q^35 - 24 * q^37 + 20 * q^42 - 12 * q^43 - 16 * q^46 + 20 * q^50 + 20 * q^51 + 4 * q^53 - 16 * q^56 + 20 * q^57 + 12 * q^58 - 8 * q^63 - 4 * q^67 - 20 * q^70 - 24 * q^71 - 16 * q^72 - 4 * q^77 - 20 * q^78 + 44 * q^81 - 20 * q^85 + 24 * q^86 + 8 * q^88 + 20 * q^91 + 20 * q^93 - 20 * q^95 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$3$	−1.58114	+	1.58114i	−0.912871	+	0.912871i	−0.996497	−	0.0836263i	$-0.973350\pi$
$3$	−1.58114	+	1.58114i	−0.912871	+	0.912871i	0.0836263	+	0.996497i	$0.473350\pi$
$4$		0			0
$5$	1.58114	−	1.58114i	0.707107	−	0.707107i
$5$	1.58114	−	1.58114i	0.707107	−	0.707107i
$6$		−	3.16228i		−	1.29099i
$7$	2.58114	+	0.581139i	0.975579	+	0.219650i
$7$	2.58114	+	0.581139i	0.975579	+	0.219650i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		−	2.00000i		−	0.666667i
$10$			3.16228i			1.00000i
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	1.58114	−	1.58114i	0.438529	−	0.438529i	−0.452988	−	0.891517i	$-0.649642\pi$
$13$	1.58114	−	1.58114i	0.438529	−	0.438529i	0.891517	+	0.452988i	$0.149642\pi$
$14$	−3.16228	+	2.00000i	−0.845154	+	0.534522i
$15$			5.00000i			1.29099i
$16$	4.00000			1.00000
$17$	−1.58114	−	1.58114i	−0.383482	−	0.383482i	0.488873	−	0.872355i	$-0.337408\pi$
$17$	−1.58114	−	1.58114i	−0.383482	−	0.383482i	−0.872355	+	0.488873i	$0.837408\pi$
$18$	2.00000	+	2.00000i	0.471405	+	0.471405i
$19$	−3.16228			−0.725476			−0.362738	−	0.931891i	$-0.618158\pi$
$19$	−3.16228			−0.725476			−0.362738	+	0.931891i	$0.618158\pi$
$20$		0			0
$21$	−5.00000	+	3.16228i	−1.09109	+	0.690066i
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	2.00000	+	2.00000i	0.417029	+	0.417029i	0.884178	−	0.467150i	$-0.154719\pi$
$23$	2.00000	+	2.00000i	0.417029	+	0.417029i	−0.467150	+	0.884178i	$0.654719\pi$
$24$	6.32456			1.29099
$25$		−	5.00000i		−	1.00000i
$26$			3.16228i			0.620174i
$27$	−1.58114	−	1.58114i	−0.304290	−	0.304290i
$28$		0			0
$29$		−	3.00000i		−	0.557086i	−0.960424	−	0.278543i	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$	−5.00000	−	5.00000i	−0.912871	−	0.912871i
$31$		−	3.16228i		−	0.567962i	−0.958830	−	0.283981i	$-0.908345\pi$
$31$		−	3.16228i		−	0.567962i	0.958830	−	0.283981i	$-0.0916552\pi$
$32$		0			0
$33$	1.58114	−	1.58114i	0.275241	−	0.275241i
$34$	3.16228			0.542326
$35$	5.00000	−	3.16228i	0.845154	−	0.534522i
$36$		0			0
$37$	−6.00000	+	6.00000i	−0.986394	+	0.986394i	−0.999909	−	0.0135147i	$-0.995698\pi$
$37$	−6.00000	+	6.00000i	−0.986394	+	0.986394i	0.0135147	+	0.999909i	$0.495698\pi$
$38$	3.16228	−	3.16228i	0.512989	−	0.512989i
$39$			5.00000i			0.800641i
$40$	−6.32456			−1.00000
$41$			9.48683i			1.48159i	0.671729	+	0.740797i	$0.265552\pi$
$41$			9.48683i			1.48159i	−0.671729	+	0.740797i	$0.734448\pi$
$42$	1.83772	−	8.16228i	0.283567	−	1.25947i
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	0.440337	−	0.897833i	$-0.354859\pi$
$43$	−3.00000	−	3.00000i	−0.457496	−	0.457496i	−0.897833	+	0.440337i	$0.854859\pi$
$44$		0			0
$45$	−3.16228	−	3.16228i	−0.471405	−	0.471405i
$46$	−4.00000			−0.589768
$47$	4.74342	+	4.74342i	0.691898	+	0.691898i	0.962649	−	0.270751i	$-0.0872720\pi$
$47$	4.74342	+	4.74342i	0.691898	+	0.691898i	−0.270751	+	0.962649i	$0.587272\pi$
$48$	−6.32456	+	6.32456i	−0.912871	+	0.912871i
$49$	6.32456	+	3.00000i	0.903508	+	0.428571i
$50$	5.00000	+	5.00000i	0.707107	+	0.707107i
$51$	5.00000			0.700140
$52$		0			0
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	0.772444	−	0.635083i	$-0.219034\pi$
$53$	1.00000	+	1.00000i	0.137361	+	0.137361i	−0.635083	+	0.772444i	$0.719034\pi$
$54$	3.16228			0.430331
$55$	−1.58114	+	1.58114i	−0.213201	+	0.213201i
$56$	−4.00000	−	6.32456i	−0.534522	−	0.845154i
$57$	5.00000	−	5.00000i	0.662266	−	0.662266i
$58$	3.00000	+	3.00000i	0.393919	+	0.393919i
$59$	−9.48683			−1.23508			−0.617540	−	0.786539i	$-0.711871\pi$
$59$	−9.48683			−1.23508			−0.617540	+	0.786539i	$0.711871\pi$
$60$		0			0
$61$		−	6.32456i		−	0.809776i	−0.914366	−	0.404888i	$-0.867310\pi$
$61$		−	6.32456i		−	0.809776i	0.914366	−	0.404888i	$-0.132690\pi$
$62$	3.16228	+	3.16228i	0.401610	+	0.401610i
$63$	1.16228	−	5.16228i	0.146433	−	0.650386i
$64$			8.00000i			1.00000i
$65$		−	5.00000i		−	0.620174i
$66$			3.16228i			0.389249i
$67$	−1.00000	+	1.00000i	−0.122169	+	0.122169i	−0.765548	−	0.643379i	$-0.777532\pi$
$67$	−1.00000	+	1.00000i	−0.122169	+	0.122169i	0.643379	+	0.765548i	$0.277532\pi$
$68$		0			0
$69$	−6.32456			−0.761387
$70$	−1.83772	+	8.16228i	−0.219650	+	0.975579i
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−4.00000	+	4.00000i	−0.471405	+	0.471405i
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		−	12.0000i		−	1.39497i
$75$	7.90569	+	7.90569i	0.912871	+	0.912871i
$76$		0			0
$77$	−2.58114	−	0.581139i	−0.294148	−	0.0662269i
$78$	−5.00000	−	5.00000i	−0.566139	−	0.566139i
$79$		−	13.0000i		−	1.46261i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$		−	13.0000i		−	1.46261i	0.682048	−	0.731307i	$-0.261089\pi$
$80$	6.32456	−	6.32456i	0.707107	−	0.707107i
$81$	11.0000			1.22222
$82$	−9.48683	−	9.48683i	−1.04765	−	1.04765i
$83$	3.16228	−	3.16228i	0.347105	−	0.347105i	−0.511925	−	0.859030i	$-0.671067\pi$
$83$	3.16228	−	3.16228i	0.347105	−	0.347105i	0.859030	+	0.511925i	$0.171067\pi$
$84$		0			0
$85$	−5.00000			−0.542326
$86$	6.00000			0.646997
$87$	4.74342	+	4.74342i	0.508548	+	0.508548i
$88$	2.00000	+	2.00000i	0.213201	+	0.213201i
$89$	6.32456			0.670402			0.335201	−	0.942147i	$-0.391196\pi$
$89$	6.32456			0.670402			0.335201	+	0.942147i	$0.391196\pi$
$90$	6.32456			0.666667
$91$	5.00000	−	3.16228i	0.524142	−	0.331497i
$92$		0			0
$93$	5.00000	+	5.00000i	0.518476	+	0.518476i
$94$	−9.48683			−0.978492
$95$	−5.00000	+	5.00000i	−0.512989	+	0.512989i
$96$		0			0
$97$	1.58114	+	1.58114i	0.160540	+	0.160540i	0.782806	−	0.622266i	$-0.213788\pi$
$97$	1.58114	+	1.58114i	0.160540	+	0.160540i	−0.622266	+	0.782806i	$0.713788\pi$
$98$	−9.32456	+	3.32456i	−0.941922	+	0.335831i
$99$			2.00000i			0.201008i
$100$		0			0
$101$			3.16228i			0.314658i	0.987546	+	0.157329i	$0.0502884\pi$
$101$			3.16228i			0.314658i	−0.987546	+	0.157329i	$0.949712\pi$
$102$	−5.00000	+	5.00000i	−0.495074	+	0.495074i
$103$	−11.0680	+	11.0680i	−1.09056	+	1.09056i	−0.0950911	+	0.995469i	$0.530314\pi$
$103$	−11.0680	+	11.0680i	−1.09056	+	1.09056i	−0.995469	+	0.0950911i	$0.969686\pi$
$104$	−6.32456			−0.620174
$105$	−2.90569	+	12.9057i	−0.283567	+	1.25947i
$106$	−2.00000			−0.194257
$107$	−3.00000	+	3.00000i	−0.290021	+	0.290021i	−0.837088	−	0.547068i	$-0.815744\pi$
$107$	−3.00000	+	3.00000i	−0.290021	+	0.290021i	0.547068	+	0.837088i	$0.315744\pi$
$108$		0			0
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		−	3.16228i		−	0.301511i
$111$		−	18.9737i		−	1.80090i
$112$	10.3246	+	2.32456i	0.975579	+	0.219650i
$113$	12.0000	+	12.0000i	1.12887	+	1.12887i	0.990362	+	0.138503i	$0.0442291\pi$
$113$	12.0000	+	12.0000i	1.12887	+	1.12887i	0.138503	+	0.990362i	$0.455771\pi$
$114$			10.0000i			0.936586i
$115$	6.32456			0.589768
$116$		0			0
$117$	−3.16228	−	3.16228i	−0.292353	−	0.292353i
$118$	9.48683	−	9.48683i	0.873334	−	0.873334i
$119$	−3.16228	−	5.00000i	−0.289886	−	0.458349i
$120$	10.0000	−	10.0000i	0.912871	−	0.912871i
$121$	−10.0000			−0.909091
$122$	6.32456	+	6.32456i	0.572598	+	0.572598i
$123$	−15.0000	−	15.0000i	−1.35250	−	1.35250i
$124$		0			0
$125$	−7.90569	−	7.90569i	−0.707107	−	0.707107i
$126$	4.00000	+	6.32456i	0.356348	+	0.563436i
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	9.48683			0.835269
$130$	5.00000	+	5.00000i	0.438529	+	0.438529i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	−8.16228	−	1.83772i	−0.707759	−	0.159351i
$134$		−	2.00000i		−	0.172774i
$135$	−5.00000			−0.430331
$136$			6.32456i			0.542326i
$137$	2.00000	−	2.00000i	0.170872	−	0.170872i	−0.616491	−	0.787362i	$-0.711446\pi$
$137$	2.00000	−	2.00000i	0.170872	−	0.170872i	0.787362	+	0.616491i	$0.211446\pi$
$138$	6.32456	−	6.32456i	0.538382	−	0.538382i
$139$	18.9737			1.60933			0.804663	−	0.593732i	$-0.202346\pi$
$139$	18.9737			1.60933			0.804663	+	0.593732i	$0.202346\pi$
$140$		0			0
$141$	−15.0000			−1.26323
$142$	6.00000	−	6.00000i	0.503509	−	0.503509i
$143$	−1.58114	+	1.58114i	−0.132221	+	0.132221i
$144$		−	8.00000i		−	0.666667i
$145$	−4.74342	−	4.74342i	−0.393919	−	0.393919i
$146$		0			0
$147$	−14.7434	+	5.25658i	−1.21602	+	0.433556i
$148$		0			0
$149$			12.0000i			0.983078i	0.870855	+	0.491539i	$0.163566\pi$
$149$			12.0000i			0.983078i	−0.870855	+	0.491539i	$0.836434\pi$
$150$	−15.8114			−1.29099
$151$	9.00000			0.732410			0.366205	−	0.930534i	$-0.380657\pi$
$151$	9.00000			0.732410			0.366205	+	0.930534i	$0.380657\pi$
$152$	6.32456	+	6.32456i	0.512989	+	0.512989i
$153$	−3.16228	+	3.16228i	−0.255655	+	0.255655i
$154$	3.16228	−	2.00000i	0.254824	−	0.161165i
$155$	−5.00000	−	5.00000i	−0.401610	−	0.401610i
$156$		0			0
$157$	−6.32456	−	6.32456i	−0.504754	−	0.504754i	0.408157	−	0.912912i	$-0.366172\pi$
$157$	−6.32456	−	6.32456i	−0.504754	−	0.504754i	−0.912912	+	0.408157i	$0.866172\pi$
$158$	13.0000	+	13.0000i	1.03422	+	1.03422i
$159$	−3.16228			−0.250785
$160$		0			0
$161$	4.00000	+	6.32456i	0.315244	+	0.498445i
$162$	−11.0000	+	11.0000i	−0.864242	+	0.864242i
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	0.901900	−	0.431944i	$-0.142172\pi$
$163$	6.00000	+	6.00000i	0.469956	+	0.469956i	−0.431944	+	0.901900i	$0.642172\pi$
$164$		0			0
$165$		−	5.00000i		−	0.389249i
$166$			6.32456i			0.490881i
$167$	−11.0680	−	11.0680i	−0.856465	−	0.856465i	0.134454	−	0.990920i	$-0.457072\pi$
$167$	−11.0680	−	11.0680i	−0.856465	−	0.856465i	−0.990920	+	0.134454i	$0.957072\pi$
$168$	16.3246	+	3.67544i	1.25947	+	0.283567i
$169$			8.00000i			0.615385i
$170$	5.00000	−	5.00000i	0.383482	−	0.383482i
$171$			6.32456i			0.483651i
$172$		0			0
$173$	11.0680	−	11.0680i	0.841482	−	0.841482i	−0.147569	−	0.989052i	$-0.547145\pi$
$173$	11.0680	−	11.0680i	0.841482	−	0.841482i	0.989052	+	0.147569i	$0.0471450\pi$
$174$	−9.48683			−0.719195
$175$	2.90569	−	12.9057i	0.219650	−	0.975579i
$176$	−4.00000			−0.301511
$177$	15.0000	−	15.0000i	1.12747	−	1.12747i
$178$	−6.32456	+	6.32456i	−0.474045	+	0.474045i
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$		0			0
$181$			22.1359i			1.64535i	0.568511	+	0.822676i	$0.307520\pi$
$181$			22.1359i			1.64535i	−0.568511	+	0.822676i	$0.692480\pi$
$182$	−1.83772	+	8.16228i	−0.136221	+	0.605028i
$183$	10.0000	+	10.0000i	0.739221	+	0.739221i
$184$		−	8.00000i		−	0.589768i
$185$			18.9737i			1.39497i
$186$	−10.0000			−0.733236
$187$	1.58114	+	1.58114i	0.115624	+	0.115624i
$188$		0			0
$189$	−3.16228	−	5.00000i	−0.230022	−	0.363696i
$190$		−	10.0000i		−	0.725476i
$191$	−3.00000			−0.217072			−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000			−0.217072			−0.108536	+	0.994092i	$0.534616\pi$
$192$	−12.6491	−	12.6491i	−0.912871	−	0.912871i
$193$	−8.00000	−	8.00000i	−0.575853	−	0.575853i	0.357905	−	0.933758i	$-0.383491\pi$
$193$	−8.00000	−	8.00000i	−0.575853	−	0.575853i	−0.933758	+	0.357905i	$0.883491\pi$
$194$	−3.16228			−0.227038
$195$	7.90569	+	7.90569i	0.566139	+	0.566139i
$196$		0			0
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	−0.741832	−	0.670585i	$-0.766043\pi$
$197$	−1.00000	+	1.00000i	−0.0712470	+	0.0712470i	0.670585	+	0.741832i	$0.266043\pi$
$198$	−2.00000	−	2.00000i	−0.142134	−	0.142134i
$199$	9.48683			0.672504			0.336252	−	0.941772i	$-0.390841\pi$
$199$	9.48683			0.672504			0.336252	+	0.941772i	$0.390841\pi$
$200$	−10.0000	+	10.0000i	−0.707107	+	0.707107i
$201$		−	3.16228i		−	0.223050i
$202$	−3.16228	−	3.16228i	−0.222497	−	0.222497i
$203$	1.74342	−	7.74342i	0.122364	−	0.543481i
$204$		0			0
$205$	15.0000	+	15.0000i	1.04765	+	1.04765i
$206$		−	22.1359i		−	1.54228i
$207$	4.00000	−	4.00000i	0.278019	−	0.278019i
$208$	6.32456	−	6.32456i	0.438529	−	0.438529i
$209$	3.16228			0.218739
$210$	−10.0000	−	15.8114i	−0.690066	−	1.09109i
$211$	17.0000			1.17033			0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000			1.17033			0.585164	+	0.810915i	$0.301030\pi$
$212$		0			0
$213$	9.48683	−	9.48683i	0.650027	−	0.650027i
$214$		−	6.00000i		−	0.410152i
$215$	−9.48683			−0.646997
$216$			6.32456i			0.430331i
$217$	1.83772	−	8.16228i	0.124753	−	0.554092i
$218$	−7.00000	−	7.00000i	−0.474100	−	0.474100i
$219$		0			0
$220$		0			0
$221$	−5.00000			−0.336336
$222$	18.9737	+	18.9737i	1.27343	+	1.27343i
$223$	−14.2302	+	14.2302i	−0.952928	+	0.952928i	−0.998941	−	0.0460129i	$-0.985348\pi$
$223$	−14.2302	+	14.2302i	−0.952928	+	0.952928i	0.0460129	+	0.998941i	$0.485348\pi$
$224$		0			0
$225$	−10.0000			−0.666667
$226$	−24.0000			−1.59646
$227$	1.58114	+	1.58114i	0.104944	+	0.104944i	0.757629	−	0.652685i	$-0.226358\pi$
$227$	1.58114	+	1.58114i	0.104944	+	0.104944i	−0.652685	+	0.757629i	$0.726358\pi$
$228$		0			0
$229$	−15.8114			−1.04485			−0.522423	−	0.852686i	$-0.674972\pi$
$229$	−15.8114			−1.04485			−0.522423	+	0.852686i	$0.674972\pi$
$230$	−6.32456	+	6.32456i	−0.417029	+	0.417029i
$231$	5.00000	−	3.16228i	0.328976	−	0.208063i
$232$	−6.00000	+	6.00000i	−0.393919	+	0.393919i
$233$	−18.0000	−	18.0000i	−1.17922	−	1.17922i	−0.979943	−	0.199276i	$-0.936141\pi$
$233$	−18.0000	−	18.0000i	−1.17922	−	1.17922i	−0.199276	−	0.979943i	$-0.563859\pi$
$234$	6.32456			0.413449
$235$	15.0000			0.978492
$236$		0			0
$237$	20.5548	+	20.5548i	1.33518	+	1.33518i
$238$	8.16228	+	1.83772i	0.529082	+	0.119122i
$239$		−	19.0000i		−	1.22901i	−0.788914	−	0.614504i	$-0.789356\pi$
$239$		−	19.0000i		−	1.22901i	0.788914	−	0.614504i	$-0.210644\pi$
$240$			20.0000i			1.29099i
$241$		−	25.2982i		−	1.62960i	−0.579741	−	0.814801i	$-0.696846\pi$
$241$		−	25.2982i		−	1.62960i	0.579741	−	0.814801i	$-0.303154\pi$
$242$	10.0000	−	10.0000i	0.642824	−	0.642824i
$243$	−12.6491	+	12.6491i	−0.811441	+	0.811441i
$244$		0			0
$245$	14.7434	−	5.25658i	0.941922	−	0.335831i
$246$	30.0000			1.91273
$247$	−5.00000	+	5.00000i	−0.318142	+	0.318142i
$248$	−6.32456	+	6.32456i	−0.401610	+	0.401610i
$249$			10.0000i			0.633724i
$250$	15.8114			1.00000
$251$		−	12.6491i		−	0.798405i	−0.916863	−	0.399202i	$-0.869287\pi$
$251$		−	12.6491i		−	0.798405i	0.916863	−	0.399202i	$-0.130713\pi$
$252$		0			0
$253$	−2.00000	−	2.00000i	−0.125739	−	0.125739i
$254$			18.0000i			1.12942i
$255$	7.90569	−	7.90569i	0.495074	−	0.495074i
$256$		0			0
$257$	−12.6491	−	12.6491i	−0.789030	−	0.789030i	0.192305	−	0.981335i	$-0.438404\pi$
$257$	−12.6491	−	12.6491i	−0.789030	−	0.789030i	−0.981335	+	0.192305i	$0.938404\pi$
$258$	−9.48683	+	9.48683i	−0.590624	+	0.590624i
$259$	−18.9737	+	12.0000i	−1.17897	+	0.745644i
$260$		0			0
$261$	−6.00000			−0.371391
$262$		0			0
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	0.889185	−	0.457547i	$-0.151272\pi$
$263$	7.00000	+	7.00000i	0.431638	+	0.431638i	−0.457547	+	0.889185i	$0.651272\pi$
$264$	−6.32456			−0.389249
$265$	3.16228			0.194257
$266$	10.0000	−	6.32456i	0.613139	−	0.387783i
$267$	−10.0000	+	10.0000i	−0.611990	+	0.611990i
$268$		0			0
$269$	18.9737			1.15684			0.578422	−	0.815737i	$-0.303669\pi$
$269$	18.9737			1.15684			0.578422	+	0.815737i	$0.303669\pi$
$270$	5.00000	−	5.00000i	0.304290	−	0.304290i
$271$			12.6491i			0.768379i	0.923254	+	0.384189i	$0.125519\pi$
$271$			12.6491i			0.768379i	−0.923254	+	0.384189i	$0.874481\pi$
$272$	−6.32456	−	6.32456i	−0.383482	−	0.383482i
$273$	−2.90569	+	12.9057i	−0.175861	+	0.781088i
$274$			4.00000i			0.241649i
$275$			5.00000i			0.301511i
$276$		0			0
$277$	−18.0000	+	18.0000i	−1.08152	+	1.08152i	−0.0851468	+	0.996368i	$0.527136\pi$
$277$	−18.0000	+	18.0000i	−1.08152	+	1.08152i	−0.996368	+	0.0851468i	$0.972864\pi$
$278$	−18.9737	+	18.9737i	−1.13796	+	1.13796i
$279$	−6.32456			−0.378641
$280$	−16.3246	−	3.67544i	−0.975579	−	0.219650i
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$	15.0000	−	15.0000i	0.893237	−	0.893237i
$283$	4.74342	−	4.74342i	0.281967	−	0.281967i	−0.551926	−	0.833893i	$-0.686107\pi$
$283$	4.74342	−	4.74342i	0.281967	−	0.281967i	0.833893	+	0.551926i	$0.186107\pi$
$284$		0			0
$285$		−	15.8114i		−	0.936586i
$286$		−	3.16228i		−	0.186989i
$287$	−5.51317	+	24.4868i	−0.325432	+	1.44541i
$288$		0			0
$289$		−	12.0000i		−	0.705882i
$290$	9.48683			0.557086
$291$	−5.00000			−0.293105
$292$		0			0
$293$	7.90569	−	7.90569i	0.461856	−	0.461856i	−0.437408	−	0.899263i	$-0.644103\pi$
$293$	7.90569	−	7.90569i	0.461856	−	0.461856i	0.899263	+	0.437408i	$0.144103\pi$
$294$	9.48683	−	20.0000i	0.553283	−	1.16642i
$295$	−15.0000	+	15.0000i	−0.873334	+	0.873334i
$296$	24.0000			1.39497
$297$	1.58114	+	1.58114i	0.0917470	+	0.0917470i
$298$	−12.0000	−	12.0000i	−0.695141	−	0.695141i
$299$	6.32456			0.365758
$300$		0			0
$301$	−6.00000	−	9.48683i	−0.345834	−	0.546812i
$302$	−9.00000	+	9.00000i	−0.517892	+	0.517892i
$303$	−5.00000	−	5.00000i	−0.287242	−	0.287242i
$304$	−12.6491			−0.725476
$305$	−10.0000	−	10.0000i	−0.572598	−	0.572598i
$306$		−	6.32456i		−	0.361551i
$307$	4.74342	+	4.74342i	0.270721	+	0.270721i	0.829390	−	0.558669i	$-0.188688\pi$
$307$	4.74342	+	4.74342i	0.270721	+	0.270721i	−0.558669	+	0.829390i	$0.688688\pi$
$308$		0			0
$309$		−	35.0000i		−	1.99108i
$310$	10.0000			0.567962
$311$			22.1359i			1.25521i	0.778530	+	0.627607i	$0.215966\pi$
$311$			22.1359i			1.25521i	−0.778530	+	0.627607i	$0.784034\pi$
$312$	10.0000	−	10.0000i	0.566139	−	0.566139i
$313$	14.2302	−	14.2302i	0.804341	−	0.804341i	−0.179430	−	0.983771i	$-0.557425\pi$
$313$	14.2302	−	14.2302i	0.804341	−	0.804341i	0.983771	+	0.179430i	$0.0574252\pi$
$314$	12.6491			0.713831
$315$	−6.32456	−	10.0000i	−0.356348	−	0.563436i
$316$		0			0
$317$	19.0000	−	19.0000i	1.06715	−	1.06715i	0.0695692	−	0.997577i	$-0.477838\pi$
$317$	19.0000	−	19.0000i	1.06715	−	1.06715i	0.997577	−	0.0695692i	$-0.0221625\pi$
$318$	3.16228	−	3.16228i	0.177332	−	0.177332i
$319$			3.00000i			0.167968i
$320$	12.6491	+	12.6491i	0.707107	+	0.707107i
$321$		−	9.48683i		−	0.529503i
$322$	−10.3246	−	2.32456i	−0.575365	−	0.129542i
$323$	5.00000	+	5.00000i	0.278207	+	0.278207i
$324$		0			0
$325$	−7.90569	−	7.90569i	−0.438529	−	0.438529i
$326$	−12.0000			−0.664619
$327$	−11.0680	−	11.0680i	−0.612060	−	0.612060i
$328$	18.9737	−	18.9737i	1.04765	−	1.04765i
$329$	9.48683	+	15.0000i	0.523026	+	0.826977i
$330$	5.00000	+	5.00000i	0.275241	+	0.275241i
$331$	−6.00000			−0.329790			−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000			−0.329790			−0.164895	+	0.986311i	$0.552728\pi$
$332$		0			0
$333$	12.0000	+	12.0000i	0.657596	+	0.657596i
$334$	22.1359			1.21122
$335$			3.16228i			0.172774i
$336$	−20.0000	+	12.6491i	−1.09109	+	0.690066i
$337$	−8.00000	+	8.00000i	−0.435788	+	0.435788i	−0.890592	−	0.454804i	$-0.849709\pi$
$337$	−8.00000	+	8.00000i	−0.435788	+	0.435788i	0.454804	+	0.890592i	$0.349709\pi$
$338$	−8.00000	−	8.00000i	−0.435143	−	0.435143i
$339$	−37.9473			−2.06102
$340$		0			0
$341$			3.16228i			0.171247i
$342$	−6.32456	−	6.32456i	−0.341993	−	0.341993i
$343$	14.5811	+	11.4189i	0.787307	+	0.616561i
$344$			12.0000i			0.646997i
$345$	−10.0000	+	10.0000i	−0.538382	+	0.538382i
$346$			22.1359i			1.19004i
$347$	24.0000	−	24.0000i	1.28839	−	1.28839i	0.352621	−	0.935766i	$-0.385290\pi$
$347$	24.0000	−	24.0000i	1.28839	−	1.28839i	0.935766	−	0.352621i	$-0.114710\pi$
$348$		0			0
$349$	−34.7851			−1.86200			−0.931001	−	0.365018i	$-0.881063\pi$
$349$	−34.7851			−1.86200			−0.931001	+	0.365018i	$0.881063\pi$
$350$	10.0000	+	15.8114i	0.534522	+	0.845154i
$351$	−5.00000			−0.266880
$352$		0			0
$353$	−14.2302	+	14.2302i	−0.757400	+	0.757400i	−0.975848	−	0.218449i	$-0.929900\pi$
$353$	−14.2302	+	14.2302i	−0.757400	+	0.757400i	0.218449	+	0.975848i	$0.429900\pi$
$354$			30.0000i			1.59448i
$355$	−9.48683	+	9.48683i	−0.503509	+	0.503509i
$356$		0			0
$357$	12.9057	+	2.90569i	0.683042	+	0.153786i
$358$	−6.00000	−	6.00000i	−0.317110	−	0.317110i
$359$			22.0000i			1.16112i	0.814219	+	0.580558i	$0.197165\pi$
$359$			22.0000i			1.16112i	−0.814219	+	0.580558i	$0.802835\pi$
$360$			12.6491i			0.666667i
$361$	−9.00000			−0.473684
$362$	−22.1359	−	22.1359i	−1.16344	−	1.16344i
$363$	15.8114	−	15.8114i	0.829883	−	0.829883i
$364$		0			0
$365$		0			0
$366$	−20.0000			−1.04542
$367$	17.3925	+	17.3925i	0.907883	+	0.907883i	0.996101	−	0.0882186i	$-0.0281174\pi$
$367$	17.3925	+	17.3925i	0.907883	+	0.907883i	−0.0882186	+	0.996101i	$0.528117\pi$
$368$	8.00000	+	8.00000i	0.417029	+	0.417029i
$369$	18.9737			0.987730
$370$	−18.9737	−	18.9737i	−0.986394	−	0.986394i
$371$	2.00000	+	3.16228i	0.103835	+	0.164177i
$372$		0			0
$373$	12.0000	+	12.0000i	0.621336	+	0.621336i	0.945873	−	0.324537i	$-0.105208\pi$
$373$	12.0000	+	12.0000i	0.621336	+	0.621336i	−0.324537	+	0.945873i	$0.605208\pi$
$374$	−3.16228			−0.163517
$375$	25.0000			1.29099
$376$		−	18.9737i		−	0.978492i
$377$	−4.74342	−	4.74342i	−0.244298	−	0.244298i
$378$	8.16228	+	1.83772i	0.419822	+	0.0945222i
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$		0			0
$381$			28.4605i			1.45808i
$382$	3.00000	−	3.00000i	0.153493	−	0.153493i
$383$	15.8114	−	15.8114i	0.807924	−	0.807924i	−0.176395	−	0.984319i	$-0.556444\pi$
$383$	15.8114	−	15.8114i	0.807924	−	0.807924i	0.984319	+	0.176395i	$0.0564437\pi$
$384$	25.2982			1.29099
$385$	−5.00000	+	3.16228i	−0.254824	+	0.161165i
$386$	16.0000			0.814379
$387$	−6.00000	+	6.00000i	−0.304997	+	0.304997i
$388$		0			0
$389$		−	23.0000i		−	1.16615i	−0.812420	−	0.583073i	$-0.801850\pi$
$389$		−	23.0000i		−	1.16615i	0.812420	−	0.583073i	$-0.198150\pi$
$390$	−15.8114			−0.800641
$391$		−	6.32456i		−	0.319847i
$392$	−6.64911	−	18.6491i	−0.335831	−	0.941922i
$393$		0			0
$394$		−	2.00000i		−	0.100759i
$395$	−20.5548	−	20.5548i	−1.03422	−	1.03422i
$396$		0			0
$397$	23.7171	+	23.7171i	1.19033	+	1.19033i	0.976976	+	0.213351i	$0.0684376\pi$
$397$	23.7171	+	23.7171i	1.19033	+	1.19033i	0.213351	+	0.976976i	$0.431562\pi$
$398$	−9.48683	+	9.48683i	−0.475532	+	0.475532i
$399$	15.8114	−	10.0000i	0.791559	−	0.500626i
$400$		−	20.0000i		−	1.00000i
$401$	−1.00000			−0.0499376			−0.0249688	−	0.999688i	$-0.507949\pi$
$401$	−1.00000			−0.0499376			−0.0249688	+	0.999688i	$0.507949\pi$
$402$	3.16228	+	3.16228i	0.157720	+	0.157720i
$403$	−5.00000	−	5.00000i	−0.249068	−	0.249068i
$404$		0			0
$405$	17.3925	−	17.3925i	0.864242	−	0.864242i
$406$	6.00000	+	9.48683i	0.297775	+	0.470824i
$407$	6.00000	−	6.00000i	0.297409	−	0.297409i
$408$	−10.0000	−	10.0000i	−0.495074	−	0.495074i
$409$	−3.16228			−0.156365			−0.0781823	−	0.996939i	$-0.524912\pi$
$409$	−3.16228			−0.156365			−0.0781823	+	0.996939i	$0.524912\pi$
$410$	−30.0000			−1.48159
$411$			6.32456i			0.311967i
$412$		0			0
$413$	−24.4868	−	5.51317i	−1.20492	−	0.271285i
$414$			8.00000i			0.393179i
$415$		−	10.0000i		−	0.490881i
$416$		0			0
$417$	−30.0000	+	30.0000i	−1.46911	+	1.46911i
$418$	−3.16228	+	3.16228i	−0.154672	+	0.154672i
$419$	15.8114			0.772437			0.386218	−	0.922407i	$-0.373781\pi$
$419$	15.8114			0.772437			0.386218	+	0.922407i	$0.373781\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−17.0000	+	17.0000i	−0.827547	+	0.827547i
$423$	9.48683	−	9.48683i	0.461266	−	0.461266i
$424$		−	4.00000i		−	0.194257i
$425$	−7.90569	+	7.90569i	−0.383482	+	0.383482i
$426$			18.9737i			0.919277i
$427$	3.67544	−	16.3246i	0.177867	−	0.790001i
$428$		0			0
$429$		−	5.00000i		−	0.241402i
$430$	9.48683	−	9.48683i	0.457496	−	0.457496i
$431$	−23.0000			−1.10787			−0.553936	−	0.832560i	$-0.686875\pi$
$431$	−23.0000			−1.10787			−0.553936	+	0.832560i	$0.686875\pi$
$432$	−6.32456	−	6.32456i	−0.304290	−	0.304290i
$433$	−9.48683	+	9.48683i	−0.455908	+	0.455908i	−0.897310	−	0.441402i	$-0.854481\pi$
$433$	−9.48683	+	9.48683i	−0.455908	+	0.455908i	0.441402	+	0.897310i	$0.354481\pi$
$434$	6.32456	+	10.0000i	0.303588	+	0.480015i
$435$	15.0000			0.719195
$436$		0			0
$437$	−6.32456	−	6.32456i	−0.302545	−	0.302545i
$438$		0			0
$439$	12.6491			0.603709			0.301855	−	0.953354i	$-0.402394\pi$
$439$	12.6491			0.603709			0.301855	+	0.953354i	$0.402394\pi$
$440$	6.32456			0.301511
$441$	6.00000	−	12.6491i	0.285714	−	0.602339i
$442$	5.00000	−	5.00000i	0.237826	−	0.237826i
$443$	1.00000	+	1.00000i	0.0475114	+	0.0475114i	0.730463	−	0.682952i	$-0.239304\pi$
$443$	1.00000	+	1.00000i	0.0475114	+	0.0475114i	−0.682952	+	0.730463i	$0.739304\pi$
$444$		0			0
$445$	10.0000	−	10.0000i	0.474045	−	0.474045i
$446$		−	28.4605i		−	1.34764i
$447$	−18.9737	−	18.9737i	−0.897424	−	0.897424i
$448$	−4.64911	+	20.6491i	−0.219650	+	0.975579i
$449$			17.0000i			0.802280i	0.916017	+	0.401140i	$0.131386\pi$
$449$			17.0000i			0.802280i	−0.916017	+	0.401140i	$0.868614\pi$
$450$	10.0000	−	10.0000i	0.471405	−	0.471405i
$451$		−	9.48683i		−	0.446718i
$452$		0			0
$453$	−14.2302	+	14.2302i	−0.668595	+	0.668595i
$454$	−3.16228			−0.148413
$455$	2.90569	−	12.9057i	0.136221	−	0.605028i
$456$	−20.0000			−0.936586
$457$	−1.00000	+	1.00000i	−0.0467780	+	0.0467780i	−0.730109	−	0.683331i	$-0.760531\pi$
$457$	−1.00000	+	1.00000i	−0.0467780	+	0.0467780i	0.683331	+	0.730109i	$0.260531\pi$
$458$	15.8114	−	15.8114i	0.738818	−	0.738818i
$459$			5.00000i			0.233380i
$460$		0			0
$461$			6.32456i			0.294564i	0.989095	+	0.147282i	$0.0470525\pi$
$461$			6.32456i			0.294564i	−0.989095	+	0.147282i	$0.952948\pi$
$462$	−1.83772	+	8.16228i	−0.0854986	+	0.379744i
$463$	−4.00000	−	4.00000i	−0.185896	−	0.185896i	0.608023	−	0.793919i	$-0.291963\pi$
$463$	−4.00000	−	4.00000i	−0.185896	−	0.185896i	−0.793919	+	0.608023i	$0.791963\pi$
$464$		−	12.0000i		−	0.557086i
$465$	15.8114			0.733236
$466$	36.0000			1.66767
$467$	11.0680	+	11.0680i	0.512165	+	0.512165i	0.915189	−	0.403025i	$-0.132041\pi$
$467$	11.0680	+	11.0680i	0.512165	+	0.512165i	−0.403025	+	0.915189i	$0.632041\pi$
$468$		0			0
$469$	−3.16228	+	2.00000i	−0.146020	+	0.0923514i
$470$	−15.0000	+	15.0000i	−0.691898	+	0.691898i
$471$	20.0000			0.921551
$472$	18.9737	+	18.9737i	0.873334	+	0.873334i
$473$	3.00000	+	3.00000i	0.137940	+	0.137940i
$474$	−41.1096			−1.88823
$475$			15.8114i			0.725476i
$476$		0			0
$477$	2.00000	−	2.00000i	0.0915737	−	0.0915737i
$478$	19.0000	+	19.0000i	0.869040	+	0.869040i
$479$	6.32456			0.288976			0.144488	−	0.989507i	$-0.453846\pi$
$479$	6.32456			0.288976			0.144488	+	0.989507i	$0.453846\pi$
$480$		0			0
$481$			18.9737i			0.865125i
$482$	25.2982	+	25.2982i	1.15230	+	1.15230i
$483$	−16.3246	−	3.67544i	−0.742793	−	0.167239i
$484$		0			0
$485$	5.00000			0.227038
$486$		−	25.2982i		−	1.14755i
$487$	4.00000	−	4.00000i	0.181257	−	0.181257i	−0.610646	−	0.791904i	$-0.709090\pi$
$487$	4.00000	−	4.00000i	0.181257	−	0.181257i	0.791904	+	0.610646i	$0.209090\pi$
$488$	−12.6491	+	12.6491i	−0.572598	+	0.572598i
$489$	−18.9737			−0.858019
$490$	−9.48683	+	20.0000i	−0.428571	+	0.903508i
$491$	−41.0000			−1.85030			−0.925152	−	0.379597i	$-0.876063\pi$
$491$	−41.0000			−1.85030			−0.925152	+	0.379597i	$0.876063\pi$
$492$		0			0
$493$	−4.74342	+	4.74342i	−0.213633	+	0.213633i
$494$		−	10.0000i		−	0.449921i
$495$	3.16228	+	3.16228i	0.142134	+	0.142134i
$496$		−	12.6491i		−	0.567962i
$497$	−15.4868	−	3.48683i	−0.694679	−	0.156406i
$498$	−10.0000	−	10.0000i	−0.448111	−	0.448111i
$499$		−	19.0000i		−	0.850557i	−0.905063	−	0.425278i	$-0.860176\pi$
$499$		−	19.0000i		−	0.850557i	0.905063	−	0.425278i	$-0.139824\pi$
$500$		0			0
$501$	35.0000			1.56368
$502$	12.6491	+	12.6491i	0.564557	+	0.564557i
$503$	−7.90569	+	7.90569i	−0.352497	+	0.352497i	−0.861038	−	0.508541i	$-0.830185\pi$
$503$	−7.90569	+	7.90569i	−0.352497	+	0.352497i	0.508541	+	0.861038i	$0.330185\pi$
$504$	−12.6491	+	8.00000i	−0.563436	+	0.356348i
$505$	5.00000	+	5.00000i	0.222497	+	0.222497i
$506$	4.00000			0.177822
$507$	−12.6491	−	12.6491i	−0.561767	−	0.561767i
$508$		0			0
$509$	−18.9737			−0.840993			−0.420496	−	0.907294i	$-0.638144\pi$
$509$	−18.9737			−0.840993			−0.420496	+	0.907294i	$0.638144\pi$
$510$			15.8114i			0.700140i
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	5.00000	+	5.00000i	0.220755	+	0.220755i
$514$	25.2982			1.11586
$515$			35.0000i			1.54228i
$516$		0			0
$517$	−4.74342	−	4.74342i	−0.208615	−	0.208615i
$518$	6.97367	−	30.9737i	0.306405	−	1.36090i
$519$			35.0000i			1.53633i
$520$	−10.0000	+	10.0000i	−0.438529	+	0.438529i
$521$		−	41.1096i		−	1.80104i	−0.434810	−	0.900522i	$-0.643184\pi$
$521$		−	41.1096i		−	1.80104i	0.434810	−	0.900522i	$-0.356816\pi$
$522$	6.00000	−	6.00000i	0.262613	−	0.262613i
$523$	18.9737	−	18.9737i	0.829660	−	0.829660i	−0.157809	−	0.987470i	$-0.550443\pi$
$523$	18.9737	−	18.9737i	0.829660	−	0.829660i	0.987470	+	0.157809i	$0.0504431\pi$
$524$		0			0
$525$	15.8114	+	25.0000i	0.690066	+	1.09109i
$526$	−14.0000			−0.610429
$527$	−5.00000	+	5.00000i	−0.217803	+	0.217803i
$528$	6.32456	−	6.32456i	0.275241	−	0.275241i
$529$		−	15.0000i		−	0.652174i
$530$	−3.16228	+	3.16228i	−0.137361	+	0.137361i
$531$			18.9737i			0.823387i
$532$		0			0
$533$	15.0000	+	15.0000i	0.649722	+	0.649722i
$534$		−	20.0000i		−	0.865485i
$535$			9.48683i			0.410152i
$536$	4.00000			0.172774
$537$	−9.48683	−	9.48683i	−0.409387	−	0.409387i
$538$	−18.9737	+	18.9737i	−0.818013	+	0.818013i
$539$	−6.32456	−	3.00000i	−0.272418	−	0.129219i
$540$		0			0
$541$	9.00000			0.386940			0.193470	−	0.981106i	$-0.438026\pi$
$541$	9.00000			0.386940			0.193470	+	0.981106i	$0.438026\pi$
$542$	−12.6491	−	12.6491i	−0.543326	−	0.543326i
$543$	−35.0000	−	35.0000i	−1.50199	−	1.50199i
$544$		0			0
$545$	11.0680	+	11.0680i	0.474100	+	0.474100i
$546$	−10.0000	−	15.8114i	−0.427960	−	0.676665i
$547$	14.0000	−	14.0000i	0.598597	−	0.598597i	−0.341342	−	0.939939i	$-0.610882\pi$
$547$	14.0000	−	14.0000i	0.598597	−	0.598597i	0.939939	+	0.341342i	$0.110882\pi$
$548$		0			0
$549$	−12.6491			−0.539851
$550$	−5.00000	−	5.00000i	−0.213201	−	0.213201i
$551$			9.48683i			0.404153i
$552$	12.6491	+	12.6491i	0.538382	+	0.538382i
$553$	7.55480	−	33.5548i	0.321263	−	1.42690i
$554$		−	36.0000i		−	1.52949i
$555$	−30.0000	−	30.0000i	−1.27343	−	1.27343i
$556$		0			0
$557$	−6.00000	+	6.00000i	−0.254228	+	0.254228i	−0.822702	−	0.568473i	$-0.807534\pi$
$557$	−6.00000	+	6.00000i	−0.254228	+	0.254228i	0.568473	+	0.822702i	$0.307534\pi$
$558$	6.32456	−	6.32456i	0.267740	−	0.267740i
$559$	−9.48683			−0.401250
$560$	20.0000	−	12.6491i	0.845154	−	0.534522i
$561$	−5.00000			−0.211100
$562$	−9.00000	+	9.00000i	−0.379642	+	0.379642i
$563$	−9.48683	+	9.48683i	−0.399822	+	0.399822i	−0.878170	−	0.478348i	$-0.841236\pi$
$563$	−9.48683	+	9.48683i	−0.399822	+	0.399822i	0.478348	+	0.878170i	$0.341236\pi$
$564$		0			0
$565$	37.9473			1.59646
$566$			9.48683i			0.398761i
$567$	28.3925	+	6.39253i	1.19237	+	0.268461i
$568$	12.0000	+	12.0000i	0.503509	+	0.503509i
$569$			32.0000i			1.34151i	0.741679	+	0.670755i	$0.234030\pi$
$569$			32.0000i			1.34151i	−0.741679	+	0.670755i	$0.765970\pi$
$570$	15.8114	+	15.8114i	0.662266	+	0.662266i
$571$	−26.0000			−1.08807			−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000			−1.08807			−0.544033	+	0.839064i	$0.683103\pi$
$572$		0			0
$573$	4.74342	−	4.74342i	0.198159	−	0.198159i
$574$	−18.9737	−	30.0000i	−0.791946	−	1.25218i
$575$	10.0000	−	10.0000i	0.417029	−	0.417029i
$576$	16.0000			0.666667
$577$	−20.5548	−	20.5548i	−0.855708	−	0.855708i	0.135121	−	0.990829i	$-0.456858\pi$
$577$	−20.5548	−	20.5548i	−0.855708	−	0.855708i	−0.990829	+	0.135121i	$0.956858\pi$
$578$	12.0000	+	12.0000i	0.499134	+	0.499134i
$579$	25.2982			1.05136
$580$		0			0
$581$	10.0000	−	6.32456i	0.414870	−	0.262387i
$582$	5.00000	−	5.00000i	0.207257	−	0.207257i
$583$	−1.00000	−	1.00000i	−0.0414158	−	0.0414158i
$584$		0			0
$585$	−10.0000			−0.413449
$586$			15.8114i			0.653162i
$587$	15.8114	+	15.8114i	0.652606	+	0.652606i	0.953620	−	0.301014i	$-0.0973251\pi$
$587$	15.8114	+	15.8114i	0.652606	+	0.652606i	−0.301014	+	0.953620i	$0.597325\pi$
$588$		0			0
$589$			10.0000i			0.412043i
$590$		−	30.0000i		−	1.23508i
$591$		−	3.16228i		−	0.130079i
$592$	−24.0000	+	24.0000i	−0.986394	+	0.986394i
$593$	−20.5548	+	20.5548i	−0.844085	+	0.844085i	−0.989387	−	0.145303i	$-0.953584\pi$
$593$	−20.5548	+	20.5548i	−0.844085	+	0.844085i	0.145303	+	0.989387i	$0.453584\pi$
$594$	−3.16228			−0.129750
$595$	−12.9057	−	2.90569i	−0.529082	−	0.119122i
$596$		0			0
$597$	−15.0000	+	15.0000i	−0.613909	+	0.613909i
$598$	−6.32456	+	6.32456i	−0.258630	+	0.258630i
$599$		−	13.0000i		−	0.531166i	−0.964088	−	0.265583i	$-0.914436\pi$
$599$		−	13.0000i		−	0.531166i	0.964088	−	0.265583i	$-0.0855644\pi$
$600$		−	31.6228i		−	1.29099i
$601$		−	22.1359i		−	0.902944i	−0.892285	−	0.451472i	$-0.850899\pi$
$601$		−	22.1359i		−	0.902944i	0.892285	−	0.451472i	$-0.149101\pi$
$602$	15.4868	+	3.48683i	0.631196	+	0.142113i
$603$	2.00000	+	2.00000i	0.0814463	+	0.0814463i
$604$		0			0
$605$	−15.8114	+	15.8114i	−0.642824	+	0.642824i
$606$	10.0000			0.406222
$607$	−14.2302	−	14.2302i	−0.577588	−	0.577588i	0.356650	−	0.934238i	$-0.383919\pi$
$607$	−14.2302	−	14.2302i	−0.577588	−	0.577588i	−0.934238	+	0.356650i	$0.883919\pi$
$608$		0			0
$609$	9.48683	+	15.0000i	0.384426	+	0.607831i
$610$	20.0000			0.809776
$611$	15.0000			0.606835
$612$		0			0
$613$	17.0000	+	17.0000i	0.686624	+	0.686624i	0.961484	−	0.274861i	$-0.0886317\pi$
$613$	17.0000	+	17.0000i	0.686624	+	0.686624i	−0.274861	+	0.961484i	$0.588632\pi$
$614$	−9.48683			−0.382857
$615$	−47.4342			−1.91273
$616$	4.00000	+	6.32456i	0.161165	+	0.254824i
$617$	4.00000	−	4.00000i	0.161034	−	0.161034i	−0.621991	−	0.783025i	$-0.713676\pi$
$617$	4.00000	−	4.00000i	0.161034	−	0.161034i	0.783025	+	0.621991i	$0.213676\pi$
$618$	35.0000	+	35.0000i	1.40791	+	1.40791i
$619$	25.2982			1.01682			0.508411	−	0.861115i	$-0.330233\pi$
$619$	25.2982			1.01682			0.508411	+	0.861115i	$0.330233\pi$
$620$		0			0
$621$		−	6.32456i		−	0.253796i
$622$	−22.1359	−	22.1359i	−0.887570	−	0.887570i
$623$	16.3246	+	3.67544i	0.654029	+	0.147254i
$624$			20.0000i			0.800641i
$625$	−25.0000			−1.00000
$626$			28.4605i			1.13751i
$627$	−5.00000	+	5.00000i	−0.199681	+	0.199681i
$628$		0			0
$629$	18.9737			0.756530
$630$	16.3246	+	3.67544i	0.650386	+	0.146433i
$631$	−31.0000			−1.23409			−0.617045	−	0.786928i	$-0.711670\pi$
$631$	−31.0000			−1.23409			−0.617045	+	0.786928i	$0.711670\pi$
$632$	−26.0000	+	26.0000i	−1.03422	+	1.03422i
$633$	−26.8794	+	26.8794i	−1.06836	+	1.06836i
$634$			38.0000i			1.50917i
$635$		−	28.4605i		−	1.12942i
$636$		0			0
$637$	14.7434	−	5.25658i	0.584155	−	0.208273i
$638$	−3.00000	−	3.00000i	−0.118771	−	0.118771i
$639$			12.0000i			0.474713i
$640$	−25.2982			−1.00000
$641$	44.0000			1.73790			0.868948	−	0.494904i	$-0.164797\pi$
$641$	44.0000			1.73790			0.868948	+	0.494904i	$0.164797\pi$
$642$	9.48683	+	9.48683i	0.374415	+	0.374415i
$643$	−4.74342	+	4.74342i	−0.187062	+	0.187062i	−0.794425	−	0.607363i	$-0.792228\pi$
$643$	−4.74342	+	4.74342i	−0.187062	+	0.187062i	0.607363	+	0.794425i	$0.292228\pi$
$644$		0			0
$645$	15.0000	−	15.0000i	0.590624	−	0.590624i
$646$	−10.0000			−0.393445
$647$	−12.6491	−	12.6491i	−0.497288	−	0.497288i	0.413305	−	0.910593i	$-0.364374\pi$
$647$	−12.6491	−	12.6491i	−0.497288	−	0.497288i	−0.910593	+	0.413305i	$0.864374\pi$
$648$	−22.0000	−	22.0000i	−0.864242	−	0.864242i
$649$	9.48683			0.372391
$650$	15.8114			0.620174
$651$	10.0000	+	15.8114i	0.391931	+	0.619697i
$652$		0			0
$653$	−19.0000	−	19.0000i	−0.743527	−	0.743527i	0.229728	−	0.973255i	$-0.426216\pi$
$653$	−19.0000	−	19.0000i	−0.743527	−	0.743527i	−0.973255	+	0.229728i	$0.926216\pi$
$654$	22.1359			0.865584
$655$		0			0
$656$			37.9473i			1.48159i
$657$		0			0
$658$	−24.4868	−	5.51317i	−0.954596	−	0.214926i
$659$			1.00000i			0.0389545i	0.999810	+	0.0194772i	$0.00620019\pi$
$659$			1.00000i			0.0389545i	−0.999810	+	0.0194772i	$0.993800\pi$
$660$		0			0
$661$			12.6491i			0.491993i	0.969271	+	0.245997i	$0.0791152\pi$
$661$			12.6491i			0.491993i	−0.969271	+	0.245997i	$0.920885\pi$
$662$	6.00000	−	6.00000i	0.233197	−	0.233197i
$663$	7.90569	−	7.90569i	0.307032	−	0.307032i
$664$	−12.6491			−0.490881
$665$	−15.8114	+	10.0000i	−0.613139	+	0.387783i
$666$	−24.0000			−0.929981
$667$	6.00000	−	6.00000i	0.232321	−	0.232321i
$668$		0			0
$669$		−	45.0000i		−	1.73980i
$670$	−3.16228	−	3.16228i	−0.122169	−	0.122169i
$671$			6.32456i			0.244157i
$672$		0			0
$673$	−24.0000	−	24.0000i	−0.925132	−	0.925132i	0.0722542	−	0.997386i	$-0.476981\pi$
$673$	−24.0000	−	24.0000i	−0.925132	−	0.925132i	−0.997386	+	0.0722542i	$0.976981\pi$
$674$		−	16.0000i		−	0.616297i
$675$	−7.90569	+	7.90569i	−0.304290	+	0.304290i
$676$		0			0
$677$	14.2302	+	14.2302i	0.546913	+	0.546913i	0.925547	−	0.378634i	$-0.123606\pi$
$677$	14.2302	+	14.2302i	0.546913	+	0.546913i	−0.378634	+	0.925547i	$0.623606\pi$
$678$	37.9473	−	37.9473i	1.45736	−	1.45736i
$679$	3.16228	+	5.00000i	0.121357	+	0.191882i
$680$	10.0000	+	10.0000i	0.383482	+	0.383482i
$681$	−5.00000			−0.191600
$682$	−3.16228	−	3.16228i	−0.121090	−	0.121090i
$683$	32.0000	+	32.0000i	1.22445	+	1.22445i	0.966035	+	0.258411i	$0.0831988\pi$
$683$	32.0000	+	32.0000i	1.22445	+	1.22445i	0.258411	+	0.966035i	$0.416801\pi$
$684$		0			0
$685$		−	6.32456i		−	0.241649i
$686$	−26.0000	+	3.16228i	−0.992685	+	0.120736i
$687$	25.0000	−	25.0000i	0.953809	−	0.953809i
$688$	−12.0000	−	12.0000i	−0.457496	−	0.457496i
$689$	3.16228			0.120473
$690$		−	20.0000i		−	0.761387i
$691$		−	31.6228i		−	1.20299i	−0.798878	−	0.601494i	$-0.794573\pi$
$691$		−	31.6228i		−	1.20299i	0.798878	−	0.601494i	$-0.205427\pi$
$692$		0			0
$693$	−1.16228	+	5.16228i	−0.0441513	+	0.196099i
$694$			48.0000i			1.82206i
$695$	30.0000	−	30.0000i	1.13796	−	1.13796i
$696$		−	18.9737i		−	0.719195i
$697$	15.0000	−	15.0000i	0.568166	−	0.568166i
$698$	34.7851	−	34.7851i	1.31663	−	1.31663i
$699$	56.9210			2.15295
$700$		0			0
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$	5.00000	−	5.00000i	0.188713	−	0.188713i
$703$	18.9737	−	18.9737i	0.715605	−	0.715605i
$704$		−	8.00000i		−	0.301511i
$705$	−23.7171	+	23.7171i	−0.893237	+	0.893237i
$706$		−	28.4605i		−	1.07113i
$707$	−1.83772	+	8.16228i	−0.0691147	+	0.306974i
$708$		0			0
$709$		−	9.00000i		−	0.338002i	−0.985616	−	0.169001i	$-0.945946\pi$
$709$		−	9.00000i		−	0.338002i	0.985616	−	0.169001i	$-0.0540541\pi$
$710$		−	18.9737i		−	0.712069i
$711$	−26.0000			−0.975076
$712$	−12.6491	−	12.6491i	−0.474045	−	0.474045i
$713$	6.32456	−	6.32456i	0.236856	−	0.236856i
$714$	−15.8114	+	10.0000i	−0.591726	+	0.374241i
$715$			5.00000i			0.186989i
$716$		0			0
$717$	30.0416	+	30.0416i	1.12193	+	1.12193i
$718$	−22.0000	−	22.0000i	−0.821033	−	0.821033i
$719$	−31.6228			−1.17933			−0.589665	−	0.807648i	$-0.700740\pi$
$719$	−31.6228			−1.17933			−0.589665	+	0.807648i	$0.700740\pi$
$720$	−12.6491	−	12.6491i	−0.471405	−	0.471405i
$721$	−35.0000	+	22.1359i	−1.30347	+	0.824386i
$722$	9.00000	−	9.00000i	0.334945	−	0.334945i
$723$	40.0000	+	40.0000i	1.48762	+	1.48762i
$724$		0			0
$725$	−15.0000			−0.557086
$726$			31.6228i			1.17363i
$727$	−9.48683	−	9.48683i	−0.351847	−	0.351847i	0.508949	−	0.860796i	$-0.330034\pi$
$727$	−9.48683	−	9.48683i	−0.351847	−	0.351847i	−0.860796	+	0.508949i	$0.830034\pi$
$728$	−16.3246	−	3.67544i	−0.605028	−	0.136221i
$729$		−	7.00000i		−	0.259259i
$730$		0			0
$731$			9.48683i			0.350883i
$732$		0			0
$733$	−17.3925	+	17.3925i	−0.642408	+	0.642408i	−0.951147	−	0.308739i	$-0.900093\pi$
$733$	−17.3925	+	17.3925i	−0.642408	+	0.642408i	0.308739	+	0.951147i	$0.400093\pi$
$734$	−34.7851			−1.28394
$735$	−15.0000	+	31.6228i	−0.553283	+	1.16642i
$736$		0			0
$737$	1.00000	−	1.00000i	0.0368355	−	0.0368355i
$738$	−18.9737	+	18.9737i	−0.698430	+	0.698430i
$739$			37.0000i			1.36107i	0.732717	+	0.680534i	$0.238252\pi$
$739$			37.0000i			1.36107i	−0.732717	+	0.680534i	$0.761748\pi$
$740$		0			0
$741$		−	15.8114i		−	0.580846i
$742$	−5.16228	−	1.16228i	−0.189513	−	0.0426686i
$743$	−9.00000	−	9.00000i	−0.330178	−	0.330178i	0.522476	−	0.852654i	$-0.325008\pi$
$743$	−9.00000	−	9.00000i	−0.330178	−	0.330178i	−0.852654	+	0.522476i	$0.825008\pi$
$744$		−	20.0000i		−	0.733236i
$745$	18.9737	+	18.9737i	0.695141	+	0.695141i
$746$	−24.0000			−0.878702
$747$	−6.32456	−	6.32456i	−0.231403	−	0.231403i
$748$		0			0
$749$	−9.48683	+	6.00000i	−0.346641	+	0.219235i
$750$	−25.0000	+	25.0000i	−0.912871	+	0.912871i
$751$	37.0000			1.35015			0.675075	−	0.737749i	$-0.264111\pi$
$751$	37.0000			1.35015			0.675075	+	0.737749i	$0.264111\pi$
$752$	18.9737	+	18.9737i	0.691898	+	0.691898i
$753$	20.0000	+	20.0000i	0.728841	+	0.728841i
$754$	9.48683			0.345490
$755$	14.2302	−	14.2302i	0.517892	−	0.517892i
$756$		0			0
$757$	−16.0000	+	16.0000i	−0.581530	+	0.581530i	−0.935324	−	0.353794i	$-0.884892\pi$
$757$	−16.0000	+	16.0000i	−0.581530	+	0.581530i	0.353794	+	0.935324i	$0.384892\pi$
$758$	8.00000	+	8.00000i	0.290573	+	0.290573i
$759$	6.32456			0.229567
$760$	20.0000			0.725476
$761$		−	25.2982i		−	0.917060i	−0.888679	−	0.458530i	$-0.848376\pi$
$761$		−	25.2982i		−	0.917060i	0.888679	−	0.458530i	$-0.151624\pi$
$762$	−28.4605	−	28.4605i	−1.03102	−	1.03102i
$763$	−4.06797	+	18.0680i	−0.147270	+	0.654104i
$764$		0			0
$765$			10.0000i			0.361551i
$766$			31.6228i			1.14258i
$767$	−15.0000	+	15.0000i	−0.541619	+	0.541619i
$768$		0			0
$769$	22.1359			0.798243			0.399121	−	0.916898i	$-0.369315\pi$
$769$	22.1359			0.798243			0.399121	+	0.916898i	$0.369315\pi$
$770$	1.83772	−	8.16228i	0.0662269	−	0.294148i
$771$	40.0000			1.44056
$772$		0			0
$773$	36.3662	−	36.3662i	1.30800	−	1.30800i	0.385145	−	0.922856i	$-0.374151\pi$
$773$	36.3662	−	36.3662i	1.30800	−	1.30800i	0.922856	−	0.385145i	$-0.125849\pi$
$774$		−	12.0000i		−	0.431331i
$775$	−15.8114			−0.567962
$776$		−	6.32456i		−	0.227038i
$777$	11.0263	−	48.9737i	0.395568	−	1.75692i
$778$	23.0000	+	23.0000i	0.824590	+	0.824590i
$779$		−	30.0000i		−	1.07486i
$780$		0			0
$781$	6.00000			0.214697
$782$	6.32456	+	6.32456i	0.226166	+	0.226166i
$783$	−4.74342	+	4.74342i	−0.169516	+	0.169516i
$784$	25.2982	+	12.0000i	0.903508	+	0.428571i
$785$	−20.0000			−0.713831
$786$		0			0
$787$	−17.3925	−	17.3925i	−0.619977	−	0.619977i	0.325549	−	0.945525i	$-0.394451\pi$
$787$	−17.3925	−	17.3925i	−0.619977	−	0.619977i	−0.945525	+	0.325549i	$0.894451\pi$
$788$		0			0
$789$	−22.1359			−0.788060
$790$	41.1096			1.46261
$791$	24.0000	+	37.9473i	0.853342	+	1.34925i
$792$	4.00000	−	4.00000i	0.142134	−	0.142134i
$793$	−10.0000	−	10.0000i	−0.355110	−	0.355110i
$794$	−47.4342			−1.68338
$795$	−5.00000	+	5.00000i	−0.177332	+	0.177332i
$796$		0			0
$797$	−1.58114	−	1.58114i	−0.0560068	−	0.0560068i	0.678549	−	0.734555i	$-0.262609\pi$
$797$	−1.58114	−	1.58114i	−0.0560068	−	0.0560068i	−0.734555	+	0.678549i	$0.762609\pi$
$798$	−5.81139	+	25.8114i	−0.205721	+	0.913713i
$799$		−	15.0000i		−	0.530662i
$800$		0			0
$801$		−	12.6491i		−	0.446934i
$802$	1.00000	−	1.00000i	0.0353112	−	0.0353112i
$803$		0			0
$804$		0			0
$805$	16.3246	+	3.67544i	0.575365	+	0.129542i
$806$	10.0000			0.352235
$807$	−30.0000	+	30.0000i	−1.05605	+	1.05605i
$808$	6.32456	−	6.32456i	0.222497	−	0.222497i
$809$		−	3.00000i		−	0.105474i	−0.998608	−	0.0527372i	$-0.983205\pi$
$809$		−	3.00000i		−	0.105474i	0.998608	−	0.0527372i	$-0.0167946\pi$
$810$			34.7851i			1.22222i
$811$			37.9473i			1.33251i	0.745724	+	0.666256i	$0.232104\pi$
$811$			37.9473i			1.33251i	−0.745724	+	0.666256i	$0.767896\pi$
$812$		0			0
$813$	−20.0000	−	20.0000i	−0.701431	−	0.701431i
$814$			12.0000i			0.420600i
$815$	18.9737			0.664619
$816$	20.0000			0.700140
$817$	9.48683	+	9.48683i	0.331902	+	0.331902i
$818$	3.16228	−	3.16228i	0.110566	−	0.110566i
$819$	−6.32456	−	10.0000i	−0.220998	−	0.349428i
$820$		0			0
$821$	−23.0000			−0.802706			−0.401353	−	0.915924i	$-0.631460\pi$
$821$	−23.0000			−0.802706			−0.401353	+	0.915924i	$0.631460\pi$
$822$	−6.32456	−	6.32456i	−0.220594	−	0.220594i
$823$	−3.00000	−	3.00000i	−0.104573	−	0.104573i	0.652884	−	0.757458i	$-0.273559\pi$
$823$	−3.00000	−	3.00000i	−0.104573	−	0.104573i	−0.757458	+	0.652884i	$0.773559\pi$
$824$	44.2719			1.54228
$825$	−7.90569	−	7.90569i	−0.275241	−	0.275241i
$826$	30.0000	−	18.9737i	1.04383	−	0.660178i
$827$	−26.0000	+	26.0000i	−0.904109	+	0.904109i	−0.995789	−	0.0916799i	$-0.970776\pi$
$827$	−26.0000	+	26.0000i	−0.904109	+	0.904109i	0.0916799	+	0.995789i	$0.470776\pi$
$828$		0			0
$829$	−28.4605			−0.988474			−0.494237	−	0.869327i	$-0.664552\pi$
$829$	−28.4605			−0.988474			−0.494237	+	0.869327i	$0.664552\pi$
$830$	10.0000	+	10.0000i	0.347105	+	0.347105i
$831$		−	56.9210i		−	1.97457i
$832$	12.6491	+	12.6491i	0.438529	+	0.438529i
$833$	−5.25658	−	14.7434i	−0.182130	−	0.510829i
$834$		−	60.0000i		−	2.07763i
$835$	−35.0000			−1.21122
$836$		0			0
$837$	−5.00000	+	5.00000i	−0.172825	+	0.172825i
$838$	−15.8114	+	15.8114i	−0.546195	+	0.546195i
$839$	−50.5964			−1.74678			−0.873392	−	0.487019i	$-0.838084\pi$
$839$	−50.5964			−1.74678			−0.873392	+	0.487019i	$0.838084\pi$
$840$	31.6228	−	20.0000i	1.09109	−	0.690066i
$841$	20.0000			0.689655
$842$	−19.0000	+	19.0000i	−0.654783	+	0.654783i
$843$	−14.2302	+	14.2302i	−0.490116	+	0.490116i
$844$		0			0
$845$	12.6491	+	12.6491i	0.435143	+	0.435143i
$846$			18.9737i			0.652328i
$847$	−25.8114	−	5.81139i	−0.886890	−	0.199682i
$848$	4.00000	+	4.00000i	0.137361	+	0.137361i
$849$			15.0000i			0.514799i
$850$		−	15.8114i		−	0.542326i
$851$	−24.0000			−0.822709
$852$		0			0
$853$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$853$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$854$	12.6491	+	20.0000i	0.432844	+	0.684386i
$855$	10.0000	+	10.0000i	0.341993	+	0.341993i
$856$	12.0000			0.410152
$857$	31.6228	+	31.6228i	1.08021	+	1.08021i	0.996489	+	0.0837245i	$0.0266816\pi$
$857$	31.6228	+	31.6228i	1.08021	+	1.08021i	0.0837245	+	0.996489i	$0.473318\pi$
$858$	5.00000	+	5.00000i	0.170697	+	0.170697i
$859$	−12.6491			−0.431582			−0.215791	−	0.976440i	$-0.569233\pi$
$859$	−12.6491			−0.431582			−0.215791	+	0.976440i	$0.569233\pi$
$860$		0			0
$861$	−30.0000	−	47.4342i	−1.02240	−	1.61655i
$862$	23.0000	−	23.0000i	0.783383	−	0.783383i
$863$	−13.0000	−	13.0000i	−0.442525	−	0.442525i	0.450335	−	0.892860i	$-0.351305\pi$
$863$	−13.0000	−	13.0000i	−0.442525	−	0.442525i	−0.892860	+	0.450335i	$0.851305\pi$
$864$		0			0
$865$		−	35.0000i		−	1.19004i
$866$		−	18.9737i		−	0.644751i
$867$	18.9737	+	18.9737i	0.644379	+	0.644379i
$868$		0			0
$869$			13.0000i			0.440995i
$870$	−15.0000	+	15.0000i	−0.508548	+	0.508548i
$871$			3.16228i			0.107150i
$872$	14.0000	−	14.0000i	0.474100	−	0.474100i
$873$	3.16228	−	3.16228i	0.107027	−	0.107027i
$874$	12.6491			0.427863
$875$	−15.8114	−	25.0000i	−0.534522	−	0.845154i
$876$		0			0
$877$	17.0000	−	17.0000i	0.574049	−	0.574049i	−0.359208	−	0.933257i	$-0.616953\pi$
$877$	17.0000	−	17.0000i	0.574049	−	0.574049i	0.933257	+	0.359208i	$0.116953\pi$
$878$	−12.6491	+	12.6491i	−0.426887	+	0.426887i
$879$			25.0000i			0.843229i
$880$	−6.32456	+	6.32456i	−0.213201	+	0.213201i
$881$		−	37.9473i		−	1.27848i	−0.769008	−	0.639239i	$-0.779249\pi$
$881$		−	37.9473i		−	1.27848i	0.769008	−	0.639239i	$-0.220751\pi$
$882$	6.64911	+	18.6491i	0.223887	+	0.627948i
$883$	−18.0000	−	18.0000i	−0.605748	−	0.605748i	0.336084	−	0.941832i	$-0.390897\pi$
$883$	−18.0000	−	18.0000i	−0.605748	−	0.605748i	−0.941832	+	0.336084i	$0.890897\pi$
$884$		0			0
$885$		−	47.4342i		−	1.59448i
$886$	−2.00000			−0.0671913
$887$	−3.16228	−	3.16228i	−0.106179	−	0.106179i	0.652022	−	0.758200i	$-0.273921\pi$
$887$	−3.16228	−	3.16228i	−0.106179	−	0.106179i	−0.758200	+	0.652022i	$0.773921\pi$
$888$	−37.9473	+	37.9473i	−1.27343	+	1.27343i
$889$	28.4605	−	18.0000i	0.954534	−	0.603701i
$890$			20.0000i			0.670402i
$891$	−11.0000			−0.368514
$892$		0			0
$893$	−15.0000	−	15.0000i	−0.501956	−	0.501956i
$894$	37.9473			1.26915
$895$	9.48683	+	9.48683i	0.317110	+	0.317110i
$896$	−16.0000	−	25.2982i	−0.534522	−	0.845154i
$897$	−10.0000	+	10.0000i	−0.333890	+	0.333890i
$898$	−17.0000	−	17.0000i	−0.567297	−	0.567297i
$899$	−9.48683			−0.316404
$900$		0			0
$901$		−	3.16228i		−	0.105351i
$902$	9.48683	+	9.48683i	0.315877	+	0.315877i
$903$	24.4868	+	5.51317i	0.814871	+	0.183467i
$904$		−	48.0000i		−	1.59646i
$905$	35.0000	+	35.0000i	1.16344	+	1.16344i
$906$		−	28.4605i		−	0.945537i
$907$	22.0000	−	22.0000i	0.730498	−	0.730498i	−0.240220	−	0.970718i	$-0.577220\pi$
$907$	22.0000	−	22.0000i	0.730498	−	0.730498i	0.970718	+	0.240220i	$0.0772197\pi$
$908$		0			0
$909$	6.32456			0.209772
$910$	10.0000	+	15.8114i	0.331497	+	0.524142i
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$	20.0000	−	20.0000i	0.662266	−	0.662266i
$913$	−3.16228	+	3.16228i	−0.104656	+	0.104656i
$914$		−	2.00000i		−	0.0661541i
$915$	31.6228			1.04542
$916$		0			0
$917$		0			0
$918$	−5.00000	−	5.00000i	−0.165025	−	0.165025i
$919$			27.0000i			0.890648i	0.895370	+	0.445324i	$0.146911\pi$
$919$			27.0000i			0.890648i	−0.895370	+	0.445324i	$0.853089\pi$
$920$	−12.6491	−	12.6491i	−0.417029	−	0.417029i
$921$	−15.0000			−0.494267
$922$	−6.32456	−	6.32456i	−0.208288	−	0.208288i
$923$	−9.48683	+	9.48683i	−0.312263	+	0.312263i
$924$		0			0
$925$	30.0000	+	30.0000i	0.986394	+	0.986394i
$926$	8.00000			0.262896
$927$	22.1359	+	22.1359i	0.727040	+	0.727040i
$928$		0			0
$929$	−3.16228			−0.103751			−0.0518755	−	0.998654i	$-0.516520\pi$
$929$	−3.16228			−0.103751			−0.0518755	+	0.998654i	$0.516520\pi$
$930$	−15.8114	+	15.8114i	−0.518476	+	0.518476i
$931$	−20.0000	−	9.48683i	−0.655474	−	0.310918i
$932$		0			0
$933$	−35.0000	−	35.0000i	−1.14585	−	1.14585i
$934$	−22.1359			−0.724310
$935$	5.00000			0.163517
$936$			12.6491i			0.413449i
$937$	14.2302	+	14.2302i	0.464882	+	0.464882i	0.900252	−	0.435370i	$-0.143382\pi$
$937$	14.2302	+	14.2302i	0.464882	+	0.464882i	−0.435370	+	0.900252i	$0.643382\pi$
$938$	1.16228	−	5.16228i	0.0379497	−	0.168554i
$939$			45.0000i			1.46852i
$940$		0			0
$941$			37.9473i			1.23705i	0.785766	+	0.618524i	$0.212269\pi$
$941$			37.9473i			1.23705i	−0.785766	+	0.618524i	$0.787731\pi$
$942$	−20.0000	+	20.0000i	−0.651635	+	0.651635i
$943$	−18.9737	+	18.9737i	−0.617868	+	0.617868i
$944$	−37.9473			−1.23508
$945$	−12.9057	−	2.90569i	−0.419822	−	0.0945222i
$946$	−6.00000			−0.195077
$947$	7.00000	−	7.00000i	0.227469	−	0.227469i	−0.584165	−	0.811635i	$-0.698578\pi$
$947$	7.00000	−	7.00000i	0.227469	−	0.227469i	0.811635	+	0.584165i	$0.198578\pi$
$948$		0			0
$949$		0			0
$950$	−15.8114	−	15.8114i	−0.512989	−	0.512989i
$951$			60.0833i			1.94833i
$952$	−3.67544	+	16.3246i	−0.119122	+	0.529082i
$953$	−3.00000	−	3.00000i	−0.0971795	−	0.0971795i	0.656846	−	0.754025i	$-0.271890\pi$
$953$	−3.00000	−	3.00000i	−0.0971795	−	0.0971795i	−0.754025	+	0.656846i	$0.771890\pi$
$954$			4.00000i			0.129505i
$955$	−4.74342	+	4.74342i	−0.153493	+	0.153493i
$956$		0			0
$957$	−4.74342	−	4.74342i	−0.153333	−	0.153333i
$958$	−6.32456	+	6.32456i	−0.204337	+	0.204337i
$959$	6.32456	−	4.00000i	0.204231	−	0.129167i
$960$	−40.0000			−1.29099
$961$	21.0000			0.677419
$962$	−18.9737	−	18.9737i	−0.611736	−	0.611736i
$963$	6.00000	+	6.00000i	0.193347	+	0.193347i
$964$		0			0
$965$	−25.2982			−0.814379
$966$	20.0000	−	12.6491i	0.643489	−	0.406978i
$967$	−33.0000	+	33.0000i	−1.06121	+	1.06121i	−0.0632081	+	0.998000i	$0.520133\pi$
$967$	−33.0000	+	33.0000i	−1.06121	+	1.06121i	−0.998000	+	0.0632081i	$0.979867\pi$
$968$	20.0000	+	20.0000i	0.642824	+	0.642824i
$969$	−15.8114			−0.507935
$970$	−5.00000	+	5.00000i	−0.160540	+	0.160540i
$971$			34.7851i			1.11631i	0.829738	+	0.558153i	$0.188490\pi$
$971$			34.7851i			1.11631i	−0.829738	+	0.558153i	$0.811510\pi$
$972$		0			0
$973$	48.9737	+	11.0263i	1.57002	+	0.353488i
$974$			8.00000i			0.256337i
$975$	25.0000			0.800641
$976$		−	25.2982i		−	0.809776i
$977$	−1.00000	+	1.00000i	−0.0319928	+	0.0319928i	−0.722922	−	0.690929i	$-0.757202\pi$
$977$	−1.00000	+	1.00000i	−0.0319928	+	0.0319928i	0.690929	+	0.722922i	$0.257202\pi$
$978$	18.9737	−	18.9737i	0.606711	−	0.606711i
$979$	−6.32456			−0.202134
$980$		0			0
$981$	14.0000			0.446986
$982$	41.0000	−	41.0000i	1.30836	−	1.30836i
$983$	20.5548	−	20.5548i	0.655596	−	0.655596i	−0.298739	−	0.954335i	$-0.596566\pi$
$983$	20.5548	−	20.5548i	0.655596	−	0.655596i	0.954335	+	0.298739i	$0.0965658\pi$
$984$			60.0000i			1.91273i
$985$			3.16228i			0.100759i
$986$		−	9.48683i		−	0.302122i
$987$	−38.7171	−	8.71708i	−1.23238	−	0.277468i
$988$		0			0
$989$		−	12.0000i		−	0.381578i
$990$	−6.32456			−0.201008
$991$	4.00000			0.127064			0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000			0.127064			0.0635321	+	0.997980i	$0.479763\pi$
$992$		0			0
$993$	9.48683	−	9.48683i	0.301056	−	0.301056i
$994$	18.9737	−	12.0000i	0.601808	−	0.380617i
$995$	15.0000	−	15.0000i	0.475532	−	0.475532i
$996$		0			0
$997$	−14.2302	−	14.2302i	−0.450677	−	0.450677i	0.444902	−	0.895579i	$-0.353238\pi$
$997$	−14.2302	−	14.2302i	−0.450677	−	0.450677i	−0.895579	+	0.444902i	$0.853238\pi$
$998$	19.0000	+	19.0000i	0.601434	+	0.601434i
$999$	18.9737			0.600300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.2.f.a.13.1	✓	4
3.2	odd	2		315.2.p.c.118.1		4
4.3	odd	2		560.2.bj.a.433.2		4
5.2	odd	4	inner	35.2.f.a.27.2	yes	4
5.3	odd	4		175.2.f.c.132.1		4
5.4	even	2		175.2.f.c.118.2		4
7.2	even	3		245.2.l.c.178.1		8
7.3	odd	6		245.2.l.c.68.1		8
7.4	even	3		245.2.l.c.68.2		8
7.5	odd	6		245.2.l.c.178.2		8
7.6	odd	2	inner	35.2.f.a.13.2	yes	4
15.2	even	4		315.2.p.c.307.2		4
20.7	even	4		560.2.bj.a.97.1		4
21.20	even	2		315.2.p.c.118.2		4
28.27	even	2		560.2.bj.a.433.1		4
35.2	odd	12		245.2.l.c.227.1		8
35.12	even	12		245.2.l.c.227.2		8
35.13	even	4		175.2.f.c.132.2		4
35.17	even	12		245.2.l.c.117.1		8
35.27	even	4	inner	35.2.f.a.27.1	yes	4
35.32	odd	12		245.2.l.c.117.2		8
35.34	odd	2		175.2.f.c.118.1		4
105.62	odd	4		315.2.p.c.307.1		4
140.27	odd	4		560.2.bj.a.97.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.f.a.13.1	✓	4	1.1	even	1	trivial
35.2.f.a.13.2	yes	4	7.6	odd	2	inner
35.2.f.a.27.1	yes	4	35.27	even	4	inner
35.2.f.a.27.2	yes	4	5.2	odd	4	inner
175.2.f.c.118.1		4	35.34	odd	2
175.2.f.c.118.2		4	5.4	even	2
175.2.f.c.132.1		4	5.3	odd	4
175.2.f.c.132.2		4	35.13	even	4
245.2.l.c.68.1		8	7.3	odd	6
245.2.l.c.68.2		8	7.4	even	3
245.2.l.c.117.1		8	35.17	even	12
245.2.l.c.117.2		8	35.32	odd	12
245.2.l.c.178.1		8	7.2	even	3
245.2.l.c.178.2		8	7.5	odd	6
245.2.l.c.227.1		8	35.2	odd	12
245.2.l.c.227.2		8	35.12	even	12
315.2.p.c.118.1		4	3.2	odd	2
315.2.p.c.118.2		4	21.20	even	2
315.2.p.c.307.1		4	105.62	odd	4
315.2.p.c.307.2		4	15.2	even	4
560.2.bj.a.97.1		4	20.7	even	4
560.2.bj.a.97.2		4	140.27	odd	4
560.2.bj.a.433.1		4	28.27	even	2
560.2.bj.a.433.2		4	4.3	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.58114 + 1.58114i) q^{3} +(1.58114 - 1.58114i) q^{5} -3.16228i q^{6} +(2.58114 + 0.581139i) q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.58114 + 1.58114i) q^{3} +(1.58114 - 1.58114i) q^{5} -3.16228i q^{6} +(2.58114 + 0.581139i) q^{7} +(-2.00000 - 2.00000i) q^{8} -2.00000i q^{9} +3.16228i q^{10} -1.00000 q^{11} +(1.58114 - 1.58114i) q^{13} +(-3.16228 + 2.00000i) q^{14} +5.00000i q^{15} +4.00000 q^{16} +(-1.58114 - 1.58114i) q^{17} +(2.00000 + 2.00000i) q^{18} -3.16228 q^{19} +(-5.00000 + 3.16228i) q^{21} +(1.00000 - 1.00000i) q^{22} +(2.00000 + 2.00000i) q^{23} +6.32456 q^{24} -5.00000i q^{25} +3.16228i q^{26} +(-1.58114 - 1.58114i) q^{27} -3.00000i q^{29} +(-5.00000 - 5.00000i) q^{30} -3.16228i q^{31} +(1.58114 - 1.58114i) q^{33} +3.16228 q^{34} +(5.00000 - 3.16228i) q^{35} +(-6.00000 + 6.00000i) q^{37} +(3.16228 - 3.16228i) q^{38} +5.00000i q^{39} -6.32456 q^{40} +9.48683i q^{41} +(1.83772 - 8.16228i) q^{42} +(-3.00000 - 3.00000i) q^{43} +(-3.16228 - 3.16228i) q^{45} -4.00000 q^{46} +(4.74342 + 4.74342i) q^{47} +(-6.32456 + 6.32456i) q^{48} +(6.32456 + 3.00000i) q^{49} +(5.00000 + 5.00000i) q^{50} +5.00000 q^{51} +(1.00000 + 1.00000i) q^{53} +3.16228 q^{54} +(-1.58114 + 1.58114i) q^{55} +(-4.00000 - 6.32456i) q^{56} +(5.00000 - 5.00000i) q^{57} +(3.00000 + 3.00000i) q^{58} -9.48683 q^{59} -6.32456i q^{61} +(3.16228 + 3.16228i) q^{62} +(1.16228 - 5.16228i) q^{63} +8.00000i q^{64} -5.00000i q^{65} +3.16228i q^{66} +(-1.00000 + 1.00000i) q^{67} -6.32456 q^{69} +(-1.83772 + 8.16228i) q^{70} -6.00000 q^{71} +(-4.00000 + 4.00000i) q^{72} -12.0000i q^{74} +(7.90569 + 7.90569i) q^{75} +(-2.58114 - 0.581139i) q^{77} +(-5.00000 - 5.00000i) q^{78} -13.0000i q^{79} +(6.32456 - 6.32456i) q^{80} +11.0000 q^{81} +(-9.48683 - 9.48683i) q^{82} +(3.16228 - 3.16228i) q^{83} -5.00000 q^{85} +6.00000 q^{86} +(4.74342 + 4.74342i) q^{87} +(2.00000 + 2.00000i) q^{88} +6.32456 q^{89} +6.32456 q^{90} +(5.00000 - 3.16228i) q^{91} +(5.00000 + 5.00000i) q^{93} -9.48683 q^{94} +(-5.00000 + 5.00000i) q^{95} +(1.58114 + 1.58114i) q^{97} +(-9.32456 + 3.32456i) q^{98} +2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{7} - 8 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^7 - 8 * q^8	\( 4 q - 4 q^{2} + 4 q^{7} - 8 q^{8} - 4 q^{11} + 16 q^{16} + 8 q^{18} - 20 q^{21} + 4 q^{22} + 8 q^{23} - 20 q^{30} + 20 q^{35} - 24 q^{37} + 20 q^{42} - 12 q^{43} - 16 q^{46} + 20 q^{50} + 20 q^{51} + 4 q^{53} - 16 q^{56} + 20 q^{57} + 12 q^{58} - 8 q^{63} - 4 q^{67} - 20 q^{70} - 24 q^{71} - 16 q^{72} - 4 q^{77} - 20 q^{78} + 44 q^{81} - 20 q^{85} + 24 q^{86} + 8 q^{88} + 20 q^{91} + 20 q^{93} - 20 q^{95} - 12 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^7 - 8 * q^8 - 4 * q^11 + 16 * q^16 + 8 * q^18 - 20 * q^21 + 4 * q^22 + 8 * q^23 - 20 * q^30 + 20 * q^35 - 24 * q^37 + 20 * q^42 - 12 * q^43 - 16 * q^46 + 20 * q^50 + 20 * q^51 + 4 * q^53 - 16 * q^56 + 20 * q^57 + 12 * q^58 - 8 * q^63 - 4 * q^67 - 20 * q^70 - 24 * q^71 - 16 * q^72 - 4 * q^77 - 20 * q^78 + 44 * q^81 - 20 * q^85 + 24 * q^86 + 8 * q^88 + 20 * q^91 + 20 * q^93 - 20 * q^95 - 12 * q^98

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