LMFDB - Embedded newform 322.2.c.b.321.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(321,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("322.321");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.c (of order $2$, degree $1$, 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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 9x^{2} - 8x + 2 $ x^4 - 2x^3 + 9x^2 - 8*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			321.3
Root			$0.500000 + 2.73709i$ of defining polynomial
Character	$\chi$	$=$	322.321
Dual form			322.2.c.b.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.41421i q^{3} +1.00000 q^{4} -3.74166 q^{5} -1.41421i q^{6} -2.64575i q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.41421i q^{3} +1.00000 q^{4} -3.74166 q^{5} -1.41421i q^{6} -2.64575i q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.74166 q^{10} +1.41421i q^{12} -5.65685i q^{13} +2.64575i q^{14} -5.29150i q^{15} +1.00000 q^{16} +3.74166 q^{17} -1.00000 q^{18} -3.74166 q^{20} +3.74166 q^{21} +(4.00000 - 2.64575i) q^{23} -1.41421i q^{24} +9.00000 q^{25} +5.65685i q^{26} +5.65685i q^{27} -2.64575i q^{28} -8.00000 q^{29} +5.29150i q^{30} -1.41421i q^{31} -1.00000 q^{32} -3.74166 q^{34} +9.89949i q^{35} +1.00000 q^{36} -10.5830i q^{37} +8.00000 q^{39} +3.74166 q^{40} -5.65685i q^{41} -3.74166 q^{42} -5.29150i q^{43} -3.74166 q^{45} +(-4.00000 + 2.64575i) q^{46} -7.07107i q^{47} +1.41421i q^{48} -7.00000 q^{49} -9.00000 q^{50} +5.29150i q^{51} -5.65685i q^{52} +10.5830i q^{53} -5.65685i q^{54} +2.64575i q^{56} +8.00000 q^{58} -9.89949i q^{59} -5.29150i q^{60} -3.74166 q^{61} +1.41421i q^{62} -2.64575i q^{63} +1.00000 q^{64} +21.1660i q^{65} +3.74166 q^{68} +(3.74166 + 5.65685i) q^{69} -9.89949i q^{70} -8.00000 q^{71} -1.00000 q^{72} +11.3137i q^{73} +10.5830i q^{74} +12.7279i q^{75} -8.00000 q^{78} +10.5830i q^{79} -3.74166 q^{80} -5.00000 q^{81} +5.65685i q^{82} +14.9666 q^{83} +3.74166 q^{84} -14.0000 q^{85} +5.29150i q^{86} -11.3137i q^{87} -11.2250 q^{89} +3.74166 q^{90} -14.9666 q^{91} +(4.00000 - 2.64575i) q^{92} +2.00000 q^{93} +7.07107i q^{94} -1.41421i q^{96} -3.74166 q^{97} +7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 4 q^{9} + 4 q^{16} - 4 q^{18} + 16 q^{23} + 36 q^{25} - 32 q^{29} - 4 q^{32} + 4 q^{36} + 32 q^{39} - 16 q^{46} - 28 q^{49} - 36 q^{50} + 32 q^{58} + 4 q^{64} - 32 q^{71} - 4 q^{72} - 32 q^{78} - 20 q^{81} - 56 q^{85} + 16 q^{92} + 8 q^{93} + 28 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 4 * q^9 + 4 * q^16 - 4 * q^18 + 16 * q^23 + 36 * q^25 - 32 * q^29 - 4 * q^32 + 4 * q^36 + 32 * q^39 - 16 * q^46 - 28 * q^49 - 36 * q^50 + 32 * q^58 + 4 * q^64 - 32 * q^71 - 4 * q^72 - 32 * q^78 - 20 * q^81 - 56 * q^85 + 16 * q^92 + 8 * q^93 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$-1$	$-1$

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			−0.707107
$2$	−1.00000			−0.707107
$3$			1.41421i			0.816497i	0.912871	+	0.408248i	$0.133860\pi$
$3$			1.41421i			0.816497i	−0.912871	+	0.408248i	$0.866140\pi$
$4$	1.00000			0.500000
$5$	−3.74166			−1.67332			−0.836660	−	0.547723i	$-0.815495\pi$
$5$	−3.74166			−1.67332			−0.836660	+	0.547723i	$0.815495\pi$
$6$		−	1.41421i		−	0.577350i
$7$		−	2.64575i		−	1.00000i
$7$		−	2.64575i		−	1.00000i
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	3.74166			1.18322
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$			1.41421i			0.408248i
$13$		−	5.65685i		−	1.56893i	−0.620174	−	0.784465i	$-0.712938\pi$
$13$		−	5.65685i		−	1.56893i	0.620174	−	0.784465i	$-0.287062\pi$
$14$			2.64575i			0.707107i
$15$		−	5.29150i		−	1.36626i
$16$	1.00000			0.250000
$17$	3.74166			0.907485			0.453743	−	0.891133i	$-0.350089\pi$
$17$	3.74166			0.907485			0.453743	+	0.891133i	$0.350089\pi$
$18$	−1.00000			−0.235702
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−3.74166			−0.836660
$21$	3.74166			0.816497
$22$		0			0
$23$	4.00000	−	2.64575i	0.834058	−	0.551677i
$23$	4.00000	−	2.64575i	0.834058	−	0.551677i
$24$		−	1.41421i		−	0.288675i
$25$	9.00000			1.80000
$26$			5.65685i			1.10940i
$27$			5.65685i			1.08866i
$28$		−	2.64575i		−	0.500000i
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$			5.29150i			0.966092i
$31$		−	1.41421i		−	0.254000i	−0.991903	−	0.127000i	$-0.959465\pi$
$31$		−	1.41421i		−	0.254000i	0.991903	−	0.127000i	$-0.0405349\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−3.74166			−0.641689
$35$			9.89949i			1.67332i
$36$	1.00000			0.166667
$37$		−	10.5830i		−	1.73984i	−0.493197	−	0.869918i	$-0.664172\pi$
$37$		−	10.5830i		−	1.73984i	0.493197	−	0.869918i	$-0.335828\pi$
$38$		0			0
$39$	8.00000			1.28103
$40$	3.74166			0.591608
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$	−3.74166			−0.577350
$43$		−	5.29150i		−	0.806947i	−0.914991	−	0.403473i	$-0.867803\pi$
$43$		−	5.29150i		−	0.806947i	0.914991	−	0.403473i	$-0.132197\pi$
$44$		0			0
$45$	−3.74166			−0.557773
$46$	−4.00000	+	2.64575i	−0.589768	+	0.390095i
$47$		−	7.07107i		−	1.03142i	−0.856763	−	0.515711i	$-0.827528\pi$
$47$		−	7.07107i		−	1.03142i	0.856763	−	0.515711i	$-0.172472\pi$
$48$			1.41421i			0.204124i
$49$	−7.00000			−1.00000
$50$	−9.00000			−1.27279
$51$			5.29150i			0.740959i
$52$		−	5.65685i		−	0.784465i
$53$			10.5830i			1.45369i	0.686803	+	0.726844i	$0.259014\pi$
$53$			10.5830i			1.45369i	−0.686803	+	0.726844i	$0.740986\pi$
$54$		−	5.65685i		−	0.769800i
$55$		0			0
$56$			2.64575i			0.353553i
$57$		0			0
$58$	8.00000			1.05045
$59$		−	9.89949i		−	1.28880i	−0.764687	−	0.644402i	$-0.777106\pi$
$59$		−	9.89949i		−	1.28880i	0.764687	−	0.644402i	$-0.222894\pi$
$60$		−	5.29150i		−	0.683130i
$61$	−3.74166			−0.479070			−0.239535	−	0.970888i	$-0.576995\pi$
$61$	−3.74166			−0.479070			−0.239535	+	0.970888i	$0.576995\pi$
$62$			1.41421i			0.179605i
$63$		−	2.64575i		−	0.333333i
$64$	1.00000			0.125000
$65$			21.1660i			2.62532i
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	3.74166			0.453743
$69$	3.74166	+	5.65685i	0.450443	+	0.681005i
$70$		−	9.89949i		−	1.18322i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.00000			−0.117851
$73$			11.3137i			1.32417i	0.749429	+	0.662085i	$0.230328\pi$
$73$			11.3137i			1.32417i	−0.749429	+	0.662085i	$0.769672\pi$
$74$			10.5830i			1.23025i
$75$			12.7279i			1.46969i
$76$		0			0
$77$		0			0
$78$	−8.00000			−0.905822
$79$			10.5830i			1.19068i	0.803473	+	0.595341i	$0.202983\pi$
$79$			10.5830i			1.19068i	−0.803473	+	0.595341i	$0.797017\pi$
$80$	−3.74166			−0.418330
$81$	−5.00000			−0.555556
$82$			5.65685i			0.624695i
$83$	14.9666			1.64280			0.821401	−	0.570352i	$-0.193193\pi$
$83$	14.9666			1.64280			0.821401	+	0.570352i	$0.193193\pi$
$84$	3.74166			0.408248
$85$	−14.0000			−1.51851
$86$			5.29150i			0.570597i
$87$		−	11.3137i		−	1.21296i
$88$		0			0
$89$	−11.2250			−1.18984			−0.594922	−	0.803783i	$-0.702817\pi$
$89$	−11.2250			−1.18984			−0.594922	+	0.803783i	$0.702817\pi$
$90$	3.74166			0.394405
$91$	−14.9666			−1.56893
$92$	4.00000	−	2.64575i	0.417029	−	0.275839i
$93$	2.00000			0.207390
$94$			7.07107i			0.729325i
$95$		0			0
$96$		−	1.41421i		−	0.144338i
$97$	−3.74166			−0.379908			−0.189954	−	0.981793i	$-0.560834\pi$
$97$	−3.74166			−0.379908			−0.189954	+	0.981793i	$0.560834\pi$
$98$	7.00000			0.707107
$99$		0			0
$100$	9.00000			0.900000
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		−	5.29150i		−	0.523937i
$103$	14.9666			1.47471			0.737353	−	0.675508i	$-0.236075\pi$
$103$	14.9666			1.47471			0.737353	+	0.675508i	$0.236075\pi$
$104$			5.65685i			0.554700i
$105$	−14.0000			−1.36626
$106$		−	10.5830i		−	1.02791i
$107$		−	5.29150i		−	0.511549i	−0.966736	−	0.255774i	$-0.917670\pi$
$107$		−	5.29150i		−	0.511549i	0.966736	−	0.255774i	$-0.0823304\pi$
$108$			5.65685i			0.544331i
$109$			10.5830i			1.01367i	0.862044	+	0.506834i	$0.169184\pi$
$109$			10.5830i			1.01367i	−0.862044	+	0.506834i	$0.830816\pi$
$110$		0			0
$111$	14.9666			1.42057
$112$		−	2.64575i		−	0.250000i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$	−14.9666	+	9.89949i	−1.39565	+	0.923133i
$116$	−8.00000			−0.742781
$117$		−	5.65685i		−	0.522976i
$118$			9.89949i			0.911322i
$119$		−	9.89949i		−	0.907485i
$120$			5.29150i			0.483046i
$121$	11.0000			1.00000
$122$	3.74166			0.338754
$123$	8.00000			0.721336
$124$		−	1.41421i		−	0.127000i
$125$	−14.9666			−1.33866
$126$			2.64575i			0.235702i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000			−0.0883883
$129$	7.48331			0.658869
$130$		−	21.1660i		−	1.85638i
$131$		−	12.7279i		−	1.11204i	−0.831168	−	0.556022i	$-0.812327\pi$
$131$		−	12.7279i		−	1.11204i	0.831168	−	0.556022i	$-0.187673\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		−	21.1660i		−	1.82168i
$136$	−3.74166			−0.320844
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	−3.74166	−	5.65685i	−0.318511	−	0.481543i
$139$		−	4.24264i		−	0.359856i	−0.983680	−	0.179928i	$-0.942414\pi$
$139$		−	4.24264i		−	0.359856i	0.983680	−	0.179928i	$-0.0575865\pi$
$140$			9.89949i			0.836660i
$141$	10.0000			0.842152
$142$	8.00000			0.671345
$143$		0			0
$144$	1.00000			0.0833333
$145$	29.9333			2.48582
$146$		−	11.3137i		−	0.936329i
$147$		−	9.89949i		−	0.816497i
$148$		−	10.5830i		−	0.869918i
$149$			10.5830i			0.866994i	0.901155	+	0.433497i	$0.142720\pi$
$149$			10.5830i			0.866994i	−0.901155	+	0.433497i	$0.857280\pi$
$150$		−	12.7279i		−	1.03923i
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$		0			0
$153$	3.74166			0.302495
$154$		0			0
$155$			5.29150i			0.425024i
$156$	8.00000			0.640513
$157$	−11.2250			−0.895850			−0.447925	−	0.894071i	$-0.647837\pi$
$157$	−11.2250			−0.895850			−0.447925	+	0.894071i	$0.647837\pi$
$158$		−	10.5830i		−	0.841939i
$159$	−14.9666			−1.18693
$160$	3.74166			0.295804
$161$	−7.00000	−	10.5830i	−0.551677	−	0.834058i
$162$	5.00000			0.392837
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$		−	5.65685i		−	0.441726i
$165$		0			0
$166$	−14.9666			−1.16164
$167$			9.89949i			0.766046i	0.923739	+	0.383023i	$0.125117\pi$
$167$			9.89949i			0.766046i	−0.923739	+	0.383023i	$0.874883\pi$
$168$	−3.74166			−0.288675
$169$	−19.0000			−1.46154
$170$	14.0000			1.07375
$171$		0			0
$172$		−	5.29150i		−	0.403473i
$173$		0			0		1.00000			$0$
$173$		0			0		−1.00000			$\pi$
$174$			11.3137i			0.857690i
$175$		−	23.8118i		−	1.80000i
$176$		0			0
$177$	14.0000			1.05230
$178$	11.2250			0.841347
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$	−3.74166			−0.278887
$181$	−11.2250			−0.834346			−0.417173	−	0.908827i	$-0.636979\pi$
$181$	−11.2250			−0.834346			−0.417173	+	0.908827i	$0.636979\pi$
$182$	14.9666			1.10940
$183$		−	5.29150i		−	0.391159i
$184$	−4.00000	+	2.64575i	−0.294884	+	0.195047i
$185$			39.5980i			2.91130i
$186$	−2.00000			−0.146647
$187$		0			0
$188$		−	7.07107i		−	0.515711i
$189$	14.9666			1.08866
$190$		0			0
$191$		−	15.8745i		−	1.14864i	−0.818631	−	0.574320i	$-0.805267\pi$
$191$		−	15.8745i		−	1.14864i	0.818631	−	0.574320i	$-0.194733\pi$
$192$			1.41421i			0.102062i
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$	3.74166			0.268635
$195$	−29.9333			−2.14357
$196$	−7.00000			−0.500000
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−9.00000			−0.636396
$201$		0			0
$202$		0			0
$203$			21.1660i			1.48556i
$204$			5.29150i			0.370479i
$205$			21.1660i			1.47830i
$206$	−14.9666			−1.04277
$207$	4.00000	−	2.64575i	0.278019	−	0.183892i
$208$		−	5.65685i		−	0.392232i
$209$		0			0
$210$	14.0000			0.966092
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$			10.5830i			0.726844i
$213$		−	11.3137i		−	0.775203i
$214$			5.29150i			0.361720i
$215$			19.7990i			1.35028i
$216$		−	5.65685i		−	0.384900i
$217$	−3.74166			−0.254000
$218$		−	10.5830i		−	0.716772i
$219$	−16.0000			−1.08118
$220$		0			0
$221$		−	21.1660i		−	1.42378i
$222$	−14.9666			−1.00449
$223$		−	9.89949i		−	0.662919i	−0.943469	−	0.331460i	$-0.892459\pi$
$223$		−	9.89949i		−	0.662919i	0.943469	−	0.331460i	$-0.107541\pi$
$224$			2.64575i			0.176777i
$225$	9.00000			0.600000
$226$		0			0
$227$	14.9666			0.993370			0.496685	−	0.867931i	$-0.334550\pi$
$227$	14.9666			0.993370			0.496685	+	0.867931i	$0.334550\pi$
$228$		0			0
$229$	18.7083			1.23628			0.618139	−	0.786069i	$-0.287887\pi$
$229$	18.7083			1.23628			0.618139	+	0.786069i	$0.287887\pi$
$230$	14.9666	−	9.89949i	0.986870	−	0.652753i
$231$		0			0
$232$	8.00000			0.525226
$233$	−4.00000			−0.262049			−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000			−0.262049			−0.131024	+	0.991379i	$0.541827\pi$
$234$			5.65685i			0.369800i
$235$			26.4575i			1.72590i
$236$		−	9.89949i		−	0.644402i
$237$	−14.9666			−0.972187
$238$			9.89949i			0.641689i
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		−	5.29150i		−	0.341565i
$241$	18.7083			1.20511			0.602553	−	0.798079i	$-0.294150\pi$
$241$	18.7083			1.20511			0.602553	+	0.798079i	$0.294150\pi$
$242$	−11.0000			−0.707107
$243$			9.89949i			0.635053i
$244$	−3.74166			−0.239535
$245$	26.1916			1.67332
$246$	−8.00000			−0.510061
$247$		0			0
$248$			1.41421i			0.0898027i
$249$			21.1660i			1.34134i
$250$	14.9666			0.946573
$251$	14.9666			0.944685			0.472343	−	0.881415i	$-0.343408\pi$
$251$	14.9666			0.944685			0.472343	+	0.881415i	$0.343408\pi$
$252$		−	2.64575i		−	0.166667i
$253$		0			0
$254$	−8.00000			−0.501965
$255$		−	19.7990i		−	1.23986i
$256$	1.00000			0.0625000
$257$		−	16.9706i		−	1.05859i	−0.848436	−	0.529297i	$-0.822456\pi$
$257$		−	16.9706i		−	1.05859i	0.848436	−	0.529297i	$-0.177544\pi$
$258$	−7.48331			−0.465891
$259$	−28.0000			−1.73984
$260$			21.1660i			1.31266i
$261$	−8.00000			−0.495188
$262$			12.7279i			0.786334i
$263$		−	10.5830i		−	0.652576i	−0.945270	−	0.326288i	$-0.894202\pi$
$263$		−	10.5830i		−	0.652576i	0.945270	−	0.326288i	$-0.105798\pi$
$264$		0			0
$265$		−	39.5980i		−	2.43248i
$266$		0			0
$267$		−	15.8745i		−	0.971504i
$268$		0			0
$269$			11.3137i			0.689809i	0.938638	+	0.344904i	$0.112089\pi$
$269$			11.3137i			0.689809i	−0.938638	+	0.344904i	$0.887911\pi$
$270$			21.1660i			1.28812i
$271$			29.6985i			1.80405i	0.431679	+	0.902027i	$0.357921\pi$
$271$			29.6985i			1.80405i	−0.431679	+	0.902027i	$0.642079\pi$
$272$	3.74166			0.226871
$273$		−	21.1660i		−	1.28103i
$274$		0			0
$275$		0			0
$276$	3.74166	+	5.65685i	0.225221	+	0.340503i
$277$	16.0000			0.961347			0.480673	−	0.876900i	$-0.340392\pi$
$277$	16.0000			0.961347			0.480673	+	0.876900i	$0.340392\pi$
$278$			4.24264i			0.254457i
$279$		−	1.41421i		−	0.0846668i
$280$		−	9.89949i		−	0.591608i
$281$			21.1660i			1.26266i	0.775515	+	0.631329i	$0.217490\pi$
$281$			21.1660i			1.26266i	−0.775515	+	0.631329i	$0.782510\pi$
$282$	−10.0000			−0.595491
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$	−8.00000			−0.474713
$285$		0			0
$286$		0			0
$287$	−14.9666			−0.883452
$288$	−1.00000			−0.0589256
$289$	−3.00000			−0.176471
$290$	−29.9333			−1.75774
$291$		−	5.29150i		−	0.310193i
$292$			11.3137i			0.662085i
$293$	−18.7083			−1.09295			−0.546475	−	0.837475i	$-0.684031\pi$
$293$	−18.7083			−1.09295			−0.546475	+	0.837475i	$0.684031\pi$
$294$			9.89949i			0.577350i
$295$			37.0405i			2.15658i
$296$			10.5830i			0.615125i
$297$		0			0
$298$		−	10.5830i		−	0.613057i
$299$	−14.9666	−	22.6274i	−0.865543	−	1.30858i
$300$			12.7279i			0.734847i
$301$	−14.0000			−0.806947
$302$	−16.0000			−0.920697
$303$		0			0
$304$		0			0
$305$	14.0000			0.801638
$306$	−3.74166			−0.213896
$307$			9.89949i			0.564994i	0.959268	+	0.282497i	$0.0911627\pi$
$307$			9.89949i			0.564994i	−0.959268	+	0.282497i	$0.908837\pi$
$308$		0			0
$309$			21.1660i			1.20409i
$310$		−	5.29150i		−	0.300537i
$311$			18.3848i			1.04251i	0.853402	+	0.521253i	$0.174535\pi$
$311$			18.3848i			1.04251i	−0.853402	+	0.521253i	$0.825465\pi$
$312$	−8.00000			−0.452911
$313$	−26.1916			−1.48044			−0.740218	−	0.672366i	$-0.765278\pi$
$313$	−26.1916			−1.48044			−0.740218	+	0.672366i	$0.765278\pi$
$314$	11.2250			0.633462
$315$			9.89949i			0.557773i
$316$			10.5830i			0.595341i
$317$	−8.00000			−0.449325			−0.224662	−	0.974437i	$-0.572128\pi$
$317$	−8.00000			−0.449325			−0.224662	+	0.974437i	$0.572128\pi$
$318$	14.9666			0.839287
$319$		0			0
$320$	−3.74166			−0.209165
$321$	7.48331			0.417678
$322$	7.00000	+	10.5830i	0.390095	+	0.589768i
$323$		0			0
$324$	−5.00000			−0.277778
$325$		−	50.9117i		−	2.82407i
$326$	4.00000			0.221540
$327$	−14.9666			−0.827657
$328$			5.65685i			0.312348i
$329$	−18.7083			−1.03142
$330$		0			0
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$	14.9666			0.821401
$333$		−	10.5830i		−	0.579945i
$334$		−	9.89949i		−	0.541676i
$335$		0			0
$336$	3.74166			0.204124
$337$		−	21.1660i		−	1.15299i	−0.817102	−	0.576493i	$-0.804421\pi$
$337$		−	21.1660i		−	1.15299i	0.817102	−	0.576493i	$-0.195579\pi$
$338$	19.0000			1.03346
$339$		0			0
$340$	−14.0000			−0.759257
$341$		0			0
$342$		0			0
$343$			18.5203i			1.00000i
$344$			5.29150i			0.285299i
$345$	−14.0000	−	21.1660i	−0.753735	−	1.13954i
$346$		0			0
$347$	−4.00000			−0.214731			−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000			−0.214731			−0.107366	+	0.994220i	$0.534242\pi$
$348$		−	11.3137i		−	0.606478i
$349$			33.9411i			1.81683i	0.418073	+	0.908413i	$0.362706\pi$
$349$			33.9411i			1.81683i	−0.418073	+	0.908413i	$0.637294\pi$
$350$			23.8118i			1.27279i
$351$	32.0000			1.70803
$352$		0			0
$353$		−	11.3137i		−	0.602168i	−0.953598	−	0.301084i	$-0.902652\pi$
$353$		−	11.3137i		−	0.602168i	0.953598	−	0.301084i	$-0.0973484\pi$
$354$	−14.0000			−0.744092
$355$	29.9333			1.58869
$356$	−11.2250			−0.594922
$357$	14.0000			0.740959
$358$	12.0000			0.634220
$359$		−	10.5830i		−	0.558550i	−0.960211	−	0.279275i	$-0.909906\pi$
$359$		−	10.5830i		−	0.558550i	0.960211	−	0.279275i	$-0.0900940\pi$
$360$	3.74166			0.197203
$361$	−19.0000			−1.00000
$362$	11.2250			0.589971
$363$			15.5563i			0.816497i
$364$	−14.9666			−0.784465
$365$		−	42.3320i		−	2.21576i
$366$			5.29150i			0.276591i
$367$	14.9666			0.781252			0.390626	−	0.920550i	$-0.372259\pi$
$367$	14.9666			0.781252			0.390626	+	0.920550i	$0.372259\pi$
$368$	4.00000	−	2.64575i	0.208514	−	0.137919i
$369$		−	5.65685i		−	0.294484i
$370$		−	39.5980i		−	2.05860i
$371$	28.0000			1.45369
$372$	2.00000			0.103695
$373$		−	10.5830i		−	0.547967i	−0.961734	−	0.273984i	$-0.911659\pi$
$373$		−	10.5830i		−	0.547967i	0.961734	−	0.273984i	$-0.0883414\pi$
$374$		0			0
$375$		−	21.1660i		−	1.09301i
$376$			7.07107i			0.364662i
$377$			45.2548i			2.33074i
$378$	−14.9666			−0.769800
$379$			21.1660i			1.08722i	0.839336	+	0.543612i	$0.182944\pi$
$379$			21.1660i			1.08722i	−0.839336	+	0.543612i	$0.817056\pi$
$380$		0			0
$381$			11.3137i			0.579619i
$382$			15.8745i			0.812210i
$383$	−29.9333			−1.52952			−0.764759	−	0.644316i	$-0.777142\pi$
$383$	−29.9333			−1.52952			−0.764759	+	0.644316i	$0.777142\pi$
$384$		−	1.41421i		−	0.0721688i
$385$		0			0
$386$	2.00000			0.101797
$387$		−	5.29150i		−	0.268982i
$388$	−3.74166			−0.189954
$389$			31.7490i			1.60974i	0.593452	+	0.804869i	$0.297765\pi$
$389$			31.7490i			1.60974i	−0.593452	+	0.804869i	$0.702235\pi$
$390$	29.9333			1.51573
$391$	14.9666	−	9.89949i	0.756895	−	0.500639i
$392$	7.00000			0.353553
$393$	18.0000			0.907980
$394$	−6.00000			−0.302276
$395$		−	39.5980i		−	1.99239i
$396$		0			0
$397$		−	16.9706i		−	0.851728i	−0.904787	−	0.425864i	$-0.859970\pi$
$397$		−	16.9706i		−	0.851728i	0.904787	−	0.425864i	$-0.140030\pi$
$398$		0			0
$399$		0			0
$400$	9.00000			0.450000
$401$		−	21.1660i		−	1.05698i	−0.848939	−	0.528490i	$-0.822758\pi$
$401$		−	21.1660i		−	1.05698i	0.848939	−	0.528490i	$-0.177242\pi$
$402$		0			0
$403$	−8.00000			−0.398508
$404$		0			0
$405$	18.7083			0.929622
$406$		−	21.1660i		−	1.05045i
$407$		0			0
$408$		−	5.29150i		−	0.261968i
$409$			11.3137i			0.559427i	0.960084	+	0.279713i	$0.0902395\pi$
$409$			11.3137i			0.559427i	−0.960084	+	0.279713i	$0.909761\pi$
$410$		−	21.1660i		−	1.04531i
$411$		0			0
$412$	14.9666			0.737353
$413$	−26.1916			−1.28880
$414$	−4.00000	+	2.64575i	−0.196589	+	0.130032i
$415$	−56.0000			−2.74893
$416$			5.65685i			0.277350i
$417$	6.00000			0.293821
$418$		0			0
$419$	29.9333			1.46234			0.731168	−	0.682198i	$-0.238976\pi$
$419$	29.9333			1.46234			0.731168	+	0.682198i	$0.238976\pi$
$420$	−14.0000			−0.683130
$421$		−	31.7490i		−	1.54735i	−0.633581	−	0.773676i	$-0.718416\pi$
$421$		−	31.7490i		−	1.54735i	0.633581	−	0.773676i	$-0.281584\pi$
$422$	−12.0000			−0.584151
$423$		−	7.07107i		−	0.343807i
$424$		−	10.5830i		−	0.513956i
$425$	33.6749			1.63347
$426$			11.3137i			0.548151i
$427$			9.89949i			0.479070i
$428$		−	5.29150i		−	0.255774i
$429$		0			0
$430$		−	19.7990i		−	0.954792i
$431$		−	26.4575i		−	1.27441i	−0.770693	−	0.637207i	$-0.780090\pi$
$431$		−	26.4575i		−	1.27441i	0.770693	−	0.637207i	$-0.219910\pi$
$432$			5.65685i			0.272166i
$433$	11.2250			0.539438			0.269719	−	0.962939i	$-0.413069\pi$
$433$	11.2250			0.539438			0.269719	+	0.962939i	$0.413069\pi$
$434$	3.74166			0.179605
$435$			42.3320i			2.02967i
$436$			10.5830i			0.506834i
$437$		0			0
$438$	16.0000			0.764510
$439$			12.7279i			0.607471i	0.952756	+	0.303735i	$0.0982338\pi$
$439$			12.7279i			0.607471i	−0.952756	+	0.303735i	$0.901766\pi$
$440$		0			0
$441$	−7.00000			−0.333333
$442$			21.1660i			1.00676i
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	14.9666			0.710285
$445$	42.0000			1.99099
$446$			9.89949i			0.468755i
$447$	−14.9666			−0.707897
$448$		−	2.64575i		−	0.125000i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$	−9.00000			−0.424264
$451$		0			0
$452$		0			0
$453$			22.6274i			1.06313i
$454$	−14.9666			−0.702419
$455$	56.0000			2.62532
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	−18.7083			−0.874181
$459$			21.1660i			0.987945i
$460$	−14.9666	+	9.89949i	−0.697823	+	0.461566i
$461$			5.65685i			0.263466i	0.991285	+	0.131733i	$0.0420541\pi$
$461$			5.65685i			0.263466i	−0.991285	+	0.131733i	$0.957946\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	−8.00000			−0.371391
$465$	−7.48331			−0.347030
$466$	4.00000			0.185296
$467$	29.9333			1.38515			0.692573	−	0.721348i	$-0.256477\pi$
$467$	29.9333			1.38515			0.692573	+	0.721348i	$0.256477\pi$
$468$		−	5.65685i		−	0.261488i
$469$		0			0
$470$		−	26.4575i		−	1.22039i
$471$		−	15.8745i		−	0.731459i
$472$			9.89949i			0.455661i
$473$		0			0
$474$	14.9666			0.687440
$475$		0			0
$476$		−	9.89949i		−	0.453743i
$477$			10.5830i			0.484563i
$478$	−8.00000			−0.365911
$479$	−29.9333			−1.36769			−0.683843	−	0.729629i	$-0.739693\pi$
$479$	−29.9333			−1.36769			−0.683843	+	0.729629i	$0.739693\pi$
$480$			5.29150i			0.241523i
$481$	−59.8665			−2.72968
$482$	−18.7083			−0.852139
$483$	14.9666	−	9.89949i	0.681005	−	0.450443i
$484$	11.0000			0.500000
$485$	14.0000			0.635707
$486$		−	9.89949i		−	0.449050i
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	3.74166			0.169377
$489$		−	5.65685i		−	0.255812i
$490$	−26.1916			−1.18322
$491$	20.0000			0.902587			0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000			0.902587			0.451294	+	0.892375i	$0.350963\pi$
$492$	8.00000			0.360668
$493$	−29.9333			−1.34813
$494$		0			0
$495$		0			0
$496$		−	1.41421i		−	0.0635001i
$497$			21.1660i			0.949425i
$498$		−	21.1660i		−	0.948472i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	−14.9666			−0.669328
$501$	−14.0000			−0.625474
$502$	−14.9666			−0.667993
$503$	29.9333			1.33466			0.667329	−	0.744763i	$-0.267437\pi$
$503$	29.9333			1.33466			0.667329	+	0.744763i	$0.267437\pi$
$504$			2.64575i			0.117851i
$505$		0			0
$506$		0			0
$507$		−	26.8701i		−	1.19334i
$508$	8.00000			0.354943
$509$			22.6274i			1.00294i	0.865174	+	0.501471i	$0.167208\pi$
$509$			22.6274i			1.00294i	−0.865174	+	0.501471i	$0.832792\pi$
$510$			19.7990i			0.876714i
$511$	29.9333			1.32417
$512$	−1.00000			−0.0441942
$513$		0			0
$514$			16.9706i			0.748539i
$515$	−56.0000			−2.46765
$516$	7.48331			0.329435
$517$		0			0
$518$	28.0000			1.23025
$519$		0			0
$520$		−	21.1660i		−	0.928191i
$521$	−3.74166			−0.163925			−0.0819625	−	0.996635i	$-0.526119\pi$
$521$	−3.74166			−0.163925			−0.0819625	+	0.996635i	$0.526119\pi$
$522$	8.00000			0.350150
$523$	−14.9666			−0.654445			−0.327223	−	0.944947i	$-0.606113\pi$
$523$	−14.9666			−0.654445			−0.327223	+	0.944947i	$0.606113\pi$
$524$		−	12.7279i		−	0.556022i
$525$	33.6749			1.46969
$526$			10.5830i			0.461441i
$527$		−	5.29150i		−	0.230501i
$528$		0			0
$529$	9.00000	−	21.1660i	0.391304	−	0.920261i
$530$			39.5980i			1.72003i
$531$		−	9.89949i		−	0.429601i
$532$		0			0
$533$	−32.0000			−1.38607
$534$			15.8745i			0.686957i
$535$			19.7990i			0.855985i
$536$		0			0
$537$		−	16.9706i		−	0.732334i
$538$		−	11.3137i		−	0.487769i
$539$		0			0
$540$		−	21.1660i		−	0.910840i
$541$	32.0000			1.37579			0.687894	−	0.725811i	$-0.258536\pi$
$541$	32.0000			1.37579			0.687894	+	0.725811i	$0.258536\pi$
$542$		−	29.6985i		−	1.27566i
$543$		−	15.8745i		−	0.681240i
$544$	−3.74166			−0.160422
$545$		−	39.5980i		−	1.69619i
$546$			21.1660i			0.905822i
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$		0			0
$549$	−3.74166			−0.159690
$550$		0			0
$551$		0			0
$552$	−3.74166	−	5.65685i	−0.159256	−	0.240772i
$553$	28.0000			1.19068
$554$	−16.0000			−0.679775
$555$	−56.0000			−2.37707
$556$		−	4.24264i		−	0.179928i
$557$		−	31.7490i		−	1.34525i	−0.739984	−	0.672624i	$-0.765167\pi$
$557$		−	31.7490i		−	1.34525i	0.739984	−	0.672624i	$-0.234833\pi$
$558$			1.41421i			0.0598684i
$559$	−29.9333			−1.26604
$560$			9.89949i			0.418330i
$561$		0			0
$562$		−	21.1660i		−	0.892834i
$563$	44.8999			1.89230			0.946152	−	0.323722i	$-0.104934\pi$
$563$	44.8999			1.89230			0.946152	+	0.323722i	$0.104934\pi$
$564$	10.0000			0.421076
$565$		0			0
$566$		0			0
$567$			13.2288i			0.555556i
$568$	8.00000			0.335673
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$			37.0405i			1.55010i	0.631901	+	0.775049i	$0.282275\pi$
$571$			37.0405i			1.55010i	−0.631901	+	0.775049i	$0.717725\pi$
$572$		0			0
$573$	22.4499			0.937860
$574$	14.9666			0.624695
$575$	36.0000	−	23.8118i	1.50130	−	0.993019i
$576$	1.00000			0.0416667
$577$			28.2843i			1.17749i	0.808319	+	0.588745i	$0.200378\pi$
$577$			28.2843i			1.17749i	−0.808319	+	0.588745i	$0.799622\pi$
$578$	3.00000			0.124784
$579$		−	2.82843i		−	0.117545i
$580$	29.9333			1.24291
$581$		−	39.5980i		−	1.64280i
$582$			5.29150i			0.219340i
$583$		0			0
$584$		−	11.3137i		−	0.468165i
$585$			21.1660i			0.875107i
$586$	18.7083			0.772832
$587$		−	15.5563i		−	0.642079i	−0.947066	−	0.321040i	$-0.895968\pi$
$587$		−	15.5563i		−	0.642079i	0.947066	−	0.321040i	$-0.104032\pi$
$588$		−	9.89949i		−	0.408248i
$589$		0			0
$590$		−	37.0405i		−	1.52493i
$591$			8.48528i			0.349038i
$592$		−	10.5830i		−	0.434959i
$593$		−	39.5980i		−	1.62609i	−0.582198	−	0.813047i	$-0.697807\pi$
$593$		−	39.5980i		−	1.62609i	0.582198	−	0.813047i	$-0.302193\pi$
$594$		0			0
$595$			37.0405i			1.51851i
$596$			10.5830i			0.433497i
$597$		0			0
$598$	14.9666	+	22.6274i	0.612031	+	0.925304i
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		−	12.7279i		−	0.519615i
$601$			45.2548i			1.84598i	0.384820	+	0.922992i	$0.374263\pi$
$601$			45.2548i			1.84598i	−0.384820	+	0.922992i	$0.625737\pi$
$602$	14.0000			0.570597
$603$		0			0
$604$	16.0000			0.651031
$605$	−41.1582			−1.67332
$606$		0			0
$607$		−	29.6985i		−	1.20542i	−0.797959	−	0.602712i	$-0.794087\pi$
$607$		−	29.6985i		−	1.20542i	0.797959	−	0.602712i	$-0.205913\pi$
$608$		0			0
$609$	−29.9333			−1.21296
$610$	−14.0000			−0.566843
$611$	−40.0000			−1.61823
$612$	3.74166			0.151248
$613$			10.5830i			0.427444i	0.976895	+	0.213722i	$0.0685586\pi$
$613$			10.5830i			0.427444i	−0.976895	+	0.213722i	$0.931441\pi$
$614$		−	9.89949i		−	0.399511i
$615$	−29.9333			−1.20703
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		−	21.1660i		−	0.851422i
$619$	14.9666			0.601560			0.300780	−	0.953694i	$-0.402753\pi$
$619$	14.9666			0.601560			0.300780	+	0.953694i	$0.402753\pi$
$620$			5.29150i			0.212512i
$621$	14.9666	+	22.6274i	0.600590	+	0.908007i
$622$		−	18.3848i		−	0.737162i
$623$			29.6985i			1.18984i
$624$	8.00000			0.320256
$625$	11.0000			0.440000
$626$	26.1916			1.04683
$627$		0			0
$628$	−11.2250			−0.447925
$629$		−	39.5980i		−	1.57887i
$630$		−	9.89949i		−	0.394405i
$631$		−	10.5830i		−	0.421303i	−0.977561	−	0.210651i	$-0.932442\pi$
$631$		−	10.5830i		−	0.421303i	0.977561	−	0.210651i	$-0.0675585\pi$
$632$		−	10.5830i		−	0.420969i
$633$			16.9706i			0.674519i
$634$	8.00000			0.317721
$635$	−29.9333			−1.18787
$636$	−14.9666			−0.593465
$637$			39.5980i			1.56893i
$638$		0			0
$639$	−8.00000			−0.316475
$640$	3.74166			0.147902
$641$		−	42.3320i		−	1.67201i	−0.548719	−	0.836007i	$-0.684884\pi$
$641$		−	42.3320i		−	1.67201i	0.548719	−	0.836007i	$-0.315116\pi$
$642$	−7.48331			−0.295343
$643$	−44.8999			−1.77068			−0.885339	−	0.464945i	$-0.846074\pi$
$643$	−44.8999			−1.77068			−0.885339	+	0.464945i	$0.846074\pi$
$644$	−7.00000	−	10.5830i	−0.275839	−	0.417029i
$645$	−28.0000			−1.10250
$646$		0			0
$647$			38.1838i			1.50116i	0.660780	+	0.750579i	$0.270226\pi$
$647$			38.1838i			1.50116i	−0.660780	+	0.750579i	$0.729774\pi$
$648$	5.00000			0.196419
$649$		0			0
$650$			50.9117i			1.99692i
$651$		−	5.29150i		−	0.207390i
$652$	−4.00000			−0.156652
$653$	46.0000			1.80012			0.900060	−	0.435767i	$-0.143523\pi$
$653$	46.0000			1.80012			0.900060	+	0.435767i	$0.143523\pi$
$654$	14.9666			0.585242
$655$			47.6235i			1.86081i
$656$		−	5.65685i		−	0.220863i
$657$			11.3137i			0.441390i
$658$	18.7083			0.729325
$659$			26.4575i			1.03064i	0.856998	+	0.515319i	$0.172327\pi$
$659$			26.4575i			1.03064i	−0.856998	+	0.515319i	$0.827673\pi$
$660$		0			0
$661$	11.2250			0.436601			0.218300	−	0.975882i	$-0.429949\pi$
$661$	11.2250			0.436601			0.218300	+	0.975882i	$0.429949\pi$
$662$	−4.00000			−0.155464
$663$	29.9333			1.16251
$664$	−14.9666			−0.580818
$665$		0			0
$666$			10.5830i			0.410083i
$667$	−32.0000	+	21.1660i	−1.23904	+	0.819551i
$668$			9.89949i			0.383023i
$669$	14.0000			0.541271
$670$		0			0
$671$		0			0
$672$	−3.74166			−0.144338
$673$	−36.0000			−1.38770			−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000			−1.38770			−0.693849	+	0.720121i	$0.744086\pi$
$674$			21.1660i			0.815284i
$675$			50.9117i			1.95959i
$676$	−19.0000			−0.730769
$677$	11.2250			0.431411			0.215705	−	0.976458i	$-0.430795\pi$
$677$	11.2250			0.431411			0.215705	+	0.976458i	$0.430795\pi$
$678$		0			0
$679$			9.89949i			0.379908i
$680$	14.0000			0.536875
$681$			21.1660i			0.811083i
$682$		0			0
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$		0			0
$686$		−	18.5203i		−	0.707107i
$687$			26.4575i			1.00942i
$688$		−	5.29150i		−	0.201737i
$689$	59.8665			2.28073
$690$	14.0000	+	21.1660i	0.532971	+	0.805776i
$691$		−	29.6985i		−	1.12978i	−0.825165	−	0.564892i	$-0.808918\pi$
$691$		−	29.6985i		−	1.12978i	0.825165	−	0.564892i	$-0.191082\pi$
$692$		0			0
$693$		0			0
$694$	4.00000			0.151838
$695$			15.8745i			0.602154i
$696$			11.3137i			0.428845i
$697$		−	21.1660i		−	0.801720i
$698$		−	33.9411i		−	1.28469i
$699$		−	5.65685i		−	0.213962i
$700$		−	23.8118i		−	0.900000i
$701$			10.5830i			0.399715i	0.979825	+	0.199857i	$0.0640479\pi$
$701$			10.5830i			0.399715i	−0.979825	+	0.199857i	$0.935952\pi$
$702$	−32.0000			−1.20776
$703$		0			0
$704$		0			0
$705$	−37.4166			−1.40919
$706$			11.3137i			0.425797i
$707$		0			0
$708$	14.0000			0.526152
$709$			10.5830i			0.397453i	0.980055	+	0.198727i	$0.0636806\pi$
$709$			10.5830i			0.397453i	−0.980055	+	0.198727i	$0.936319\pi$
$710$	−29.9333			−1.12338
$711$			10.5830i			0.396894i
$712$	11.2250			0.420674
$713$	−3.74166	−	5.65685i	−0.140126	−	0.211851i
$714$	−14.0000			−0.523937
$715$		0			0
$716$	−12.0000			−0.448461
$717$			11.3137i			0.422518i
$718$			10.5830i			0.394954i
$719$			9.89949i			0.369189i	0.982815	+	0.184594i	$0.0590972\pi$
$719$			9.89949i			0.369189i	−0.982815	+	0.184594i	$0.940903\pi$
$720$	−3.74166			−0.139443
$721$		−	39.5980i		−	1.47471i
$722$	19.0000			0.707107
$723$			26.4575i			0.983965i
$724$	−11.2250			−0.417173
$725$	−72.0000			−2.67401
$726$		−	15.5563i		−	0.577350i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	14.9666			0.554700
$729$	−29.0000			−1.07407
$730$			42.3320i			1.56678i
$731$		−	19.7990i		−	0.732292i
$732$		−	5.29150i		−	0.195580i
$733$	26.1916			0.967409			0.483704	−	0.875231i	$-0.339291\pi$
$733$	26.1916			0.967409			0.483704	+	0.875231i	$0.339291\pi$
$734$	−14.9666			−0.552428
$735$			37.0405i			1.36626i
$736$	−4.00000	+	2.64575i	−0.147442	+	0.0975237i
$737$		0			0
$738$			5.65685i			0.208232i
$739$	12.0000			0.441427			0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000			0.441427			0.220714	+	0.975339i	$0.429161\pi$
$740$			39.5980i			1.45565i
$741$		0			0
$742$	−28.0000			−1.02791
$743$		−	31.7490i		−	1.16476i	−0.812917	−	0.582379i	$-0.802122\pi$
$743$		−	31.7490i		−	1.16476i	0.812917	−	0.582379i	$-0.197878\pi$
$744$	−2.00000			−0.0733236
$745$		−	39.5980i		−	1.45076i
$746$			10.5830i			0.387471i
$747$	14.9666			0.547600
$748$		0			0
$749$	−14.0000			−0.511549
$750$			21.1660i			0.772873i
$751$		−	31.7490i		−	1.15854i	−0.815136	−	0.579269i	$-0.803338\pi$
$751$		−	31.7490i		−	1.15854i	0.815136	−	0.579269i	$-0.196662\pi$
$752$		−	7.07107i		−	0.257855i
$753$			21.1660i			0.771332i
$754$		−	45.2548i		−	1.64808i
$755$	−59.8665			−2.17877
$756$	14.9666			0.544331
$757$			10.5830i			0.384646i	0.981332	+	0.192323i	$0.0616021\pi$
$757$			10.5830i			0.384646i	−0.981332	+	0.192323i	$0.938398\pi$
$758$		−	21.1660i		−	0.768784i
$759$		0			0
$760$		0			0
$761$			22.6274i			0.820243i	0.912031	+	0.410122i	$0.134514\pi$
$761$			22.6274i			0.820243i	−0.912031	+	0.410122i	$0.865486\pi$
$762$		−	11.3137i		−	0.409852i
$763$	28.0000			1.01367
$764$		−	15.8745i		−	0.574320i
$765$	−14.0000			−0.506171
$766$	29.9333			1.08153
$767$	−56.0000			−2.02204
$768$			1.41421i			0.0510310i
$769$	33.6749			1.21435			0.607174	−	0.794569i	$-0.292303\pi$
$769$	33.6749			1.21435			0.607174	+	0.794569i	$0.292303\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	−2.00000			−0.0719816
$773$	3.74166			0.134578			0.0672890	−	0.997734i	$-0.478565\pi$
$773$	3.74166			0.134578			0.0672890	+	0.997734i	$0.478565\pi$
$774$			5.29150i			0.190199i
$775$		−	12.7279i		−	0.457200i
$776$	3.74166			0.134318
$777$		−	39.5980i		−	1.42057i
$778$		−	31.7490i		−	1.13826i
$779$		0			0
$780$	−29.9333			−1.07178
$781$		0			0
$782$	−14.9666	+	9.89949i	−0.535206	+	0.354005i
$783$		−	45.2548i		−	1.61728i
$784$	−7.00000			−0.250000
$785$	42.0000			1.49904
$786$	−18.0000			−0.642039
$787$	−29.9333			−1.06701			−0.533503	−	0.845798i	$-0.679125\pi$
$787$	−29.9333			−1.06701			−0.533503	+	0.845798i	$0.679125\pi$
$788$	6.00000			0.213741
$789$	14.9666			0.532826
$790$			39.5980i			1.40883i
$791$		0			0
$792$		0			0
$793$			21.1660i			0.751627i
$794$			16.9706i			0.602263i
$795$	56.0000			1.98612
$796$		0			0
$797$	33.6749			1.19283			0.596413	−	0.802677i	$-0.296592\pi$
$797$	33.6749			1.19283			0.596413	+	0.802677i	$0.296592\pi$
$798$		0			0
$799$		−	26.4575i		−	0.936000i
$800$	−9.00000			−0.318198
$801$	−11.2250			−0.396615
$802$			21.1660i			0.747398i
$803$		0			0
$804$		0			0
$805$	26.1916	+	39.5980i	0.923133	+	1.39565i
$806$	8.00000			0.281788
$807$	−16.0000			−0.563227
$808$		0			0
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$	−18.7083			−0.657342
$811$			4.24264i			0.148979i	0.997222	+	0.0744896i	$0.0237328\pi$
$811$			4.24264i			0.148979i	−0.997222	+	0.0744896i	$0.976267\pi$
$812$			21.1660i			0.742781i
$813$	−42.0000			−1.47300
$814$		0			0
$815$	14.9666			0.524258
$816$			5.29150i			0.185240i
$817$		0			0
$818$		−	11.3137i		−	0.395575i
$819$	−14.9666			−0.522976
$820$			21.1660i			0.739149i
$821$	48.0000			1.67521			0.837606	−	0.546275i	$-0.183955\pi$
$821$	48.0000			1.67521			0.837606	+	0.546275i	$0.183955\pi$
$822$		0			0
$823$	−16.0000			−0.557725			−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000			−0.557725			−0.278862	+	0.960331i	$0.589957\pi$
$824$	−14.9666			−0.521387
$825$		0			0
$826$	26.1916			0.911322
$827$			47.6235i			1.65603i	0.560704	+	0.828016i	$0.310530\pi$
$827$			47.6235i			1.65603i	−0.560704	+	0.828016i	$0.689470\pi$
$828$	4.00000	−	2.64575i	0.139010	−	0.0919462i
$829$		−	39.5980i		−	1.37529i	−0.726045	−	0.687647i	$-0.758644\pi$
$829$		−	39.5980i		−	1.37529i	0.726045	−	0.687647i	$-0.241356\pi$
$830$	56.0000			1.94379
$831$			22.6274i			0.784936i
$832$		−	5.65685i		−	0.196116i
$833$	−26.1916			−0.907485
$834$	−6.00000			−0.207763
$835$		−	37.0405i		−	1.28184i
$836$		0			0
$837$	8.00000			0.276520
$838$	−29.9333			−1.03403
$839$	−14.9666			−0.516705			−0.258353	−	0.966051i	$-0.583180\pi$
$839$	−14.9666			−0.516705			−0.258353	+	0.966051i	$0.583180\pi$
$840$	14.0000			0.483046
$841$	35.0000			1.20690
$842$			31.7490i			1.09414i
$843$	−29.9333			−1.03096
$844$	12.0000			0.413057
$845$	71.0915			2.44562
$846$			7.07107i			0.243108i
$847$		−	29.1033i		−	1.00000i
$848$			10.5830i			0.363422i
$849$		0			0
$850$	−33.6749			−1.15504
$851$	−28.0000	−	42.3320i	−0.959828	−	1.45112i
$852$		−	11.3137i		−	0.387601i
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		−	9.89949i		−	0.338754i
$855$		0			0
$856$			5.29150i			0.180860i
$857$			11.3137i			0.386469i	0.981153	+	0.193234i	$0.0618978\pi$
$857$			11.3137i			0.386469i	−0.981153	+	0.193234i	$0.938102\pi$
$858$		0			0
$859$		−	32.5269i		−	1.10980i	−0.831916	−	0.554902i	$-0.812756\pi$
$859$		−	32.5269i		−	1.10980i	0.831916	−	0.554902i	$-0.187244\pi$
$860$			19.7990i			0.675140i
$861$		−	21.1660i		−	0.721336i
$862$			26.4575i			0.901146i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		−	5.65685i		−	0.192450i
$865$		0			0
$866$	−11.2250			−0.381440
$867$		−	4.24264i		−	0.144088i
$868$	−3.74166			−0.127000
$869$		0			0
$870$		−	42.3320i		−	1.43519i
$871$		0			0
$872$		−	10.5830i		−	0.358386i
$873$	−3.74166			−0.126636
$874$		0			0
$875$			39.5980i			1.33866i
$876$	−16.0000			−0.540590
$877$	8.00000			0.270141			0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000			0.270141			0.135070	+	0.990836i	$0.456874\pi$
$878$		−	12.7279i		−	0.429547i
$879$		−	26.4575i		−	0.892390i
$880$		0			0
$881$	−11.2250			−0.378179			−0.189089	−	0.981960i	$-0.560554\pi$
$881$	−11.2250			−0.378179			−0.189089	+	0.981960i	$0.560554\pi$
$882$	7.00000			0.235702
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		−	21.1660i		−	0.711890i
$885$	−52.3832			−1.76084
$886$	4.00000			0.134383
$887$			7.07107i			0.237423i	0.992929	+	0.118712i	$0.0378764\pi$
$887$			7.07107i			0.237423i	−0.992929	+	0.118712i	$0.962124\pi$
$888$	−14.9666			−0.502247
$889$		−	21.1660i		−	0.709885i
$890$	−42.0000			−1.40784
$891$		0			0
$892$		−	9.89949i		−	0.331460i
$893$		0			0
$894$	14.9666			0.500559
$895$	44.8999			1.50084
$896$			2.64575i			0.0883883i
$897$	32.0000	−	21.1660i	1.06845	−	0.706713i
$898$	−12.0000			−0.400445
$899$			11.3137i			0.377333i
$900$	9.00000			0.300000
$901$			39.5980i			1.31920i
$902$		0			0
$903$		−	19.7990i		−	0.658869i
$904$		0			0
$905$	42.0000			1.39613
$906$		−	22.6274i		−	0.751746i
$907$			5.29150i			0.175701i	0.996134	+	0.0878507i	$0.0279999\pi$
$907$			5.29150i			0.175701i	−0.996134	+	0.0878507i	$0.972000\pi$
$908$	14.9666			0.496685
$909$		0			0
$910$	−56.0000			−1.85638
$911$			31.7490i			1.05189i	0.850518	+	0.525946i	$0.176289\pi$
$911$			31.7490i			1.05189i	−0.850518	+	0.525946i	$0.823711\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$			19.7990i			0.654534i
$916$	18.7083			0.618139
$917$	−33.6749			−1.11204
$918$		−	21.1660i		−	0.698582i
$919$			10.5830i			0.349101i	0.984648	+	0.174551i	$0.0558472\pi$
$919$			10.5830i			0.349101i	−0.984648	+	0.174551i	$0.944153\pi$
$920$	14.9666	−	9.89949i	0.493435	−	0.326377i
$921$	−14.0000			−0.461316
$922$		−	5.65685i		−	0.186299i
$923$			45.2548i			1.48958i
$924$		0			0
$925$		−	95.2470i		−	3.13170i
$926$	16.0000			0.525793
$927$	14.9666			0.491569
$928$	8.00000			0.262613
$929$			56.5685i			1.85595i	0.372638	+	0.927977i	$0.378453\pi$
$929$			56.5685i			1.85595i	−0.372638	+	0.927977i	$0.621547\pi$
$930$	7.48331			0.245388
$931$		0			0
$932$	−4.00000			−0.131024
$933$	−26.0000			−0.851202
$934$	−29.9333			−0.979446
$935$		0			0
$936$			5.65685i			0.184900i
$937$	48.6415			1.58905			0.794525	−	0.607231i	$-0.207720\pi$
$937$	48.6415			1.58905			0.794525	+	0.607231i	$0.207720\pi$
$938$		0			0
$939$		−	37.0405i		−	1.20877i
$940$			26.4575i			0.862949i
$941$	3.74166			0.121975			0.0609873	−	0.998139i	$-0.480575\pi$
$941$	3.74166			0.121975			0.0609873	+	0.998139i	$0.480575\pi$
$942$			15.8745i			0.517219i
$943$	−14.9666	−	22.6274i	−0.487381	−	0.736850i
$944$		−	9.89949i		−	0.322201i
$945$	−56.0000			−1.82168
$946$		0			0
$947$	60.0000			1.94974			0.974869	−	0.222779i	$-0.0715128\pi$
$947$	60.0000			1.94974			0.974869	+	0.222779i	$0.0715128\pi$
$948$	−14.9666			−0.486094
$949$	64.0000			2.07753
$950$		0			0
$951$		−	11.3137i		−	0.366872i
$952$			9.89949i			0.320844i
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		−	10.5830i		−	0.342637i
$955$			59.3970i			1.92204i
$956$	8.00000			0.258738
$957$		0			0
$958$	29.9333			0.967100
$959$		0			0
$960$		−	5.29150i		−	0.170783i
$961$	29.0000			0.935484
$962$	59.8665			1.93017
$963$		−	5.29150i		−	0.170516i
$964$	18.7083			0.602553
$965$	7.48331			0.240896
$966$	−14.9666	+	9.89949i	−0.481543	+	0.318511i
$967$	48.0000			1.54358			0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000			1.54358			0.771788	+	0.635880i	$0.219363\pi$
$968$	−11.0000			−0.353553
$969$		0			0
$970$	−14.0000			−0.449513
$971$	−14.9666			−0.480302			−0.240151	−	0.970736i	$-0.577197\pi$
$971$	−14.9666			−0.480302			−0.240151	+	0.970736i	$0.577197\pi$
$972$			9.89949i			0.317526i
$973$	−11.2250			−0.359856
$974$	16.0000			0.512673
$975$	72.0000			2.30585
$976$	−3.74166			−0.119768
$977$		−	21.1660i		−	0.677161i	−0.940937	−	0.338580i	$-0.890053\pi$
$977$		−	21.1660i		−	0.677161i	0.940937	−	0.338580i	$-0.109947\pi$
$978$			5.65685i			0.180886i
$979$		0			0
$980$	26.1916			0.836660
$981$			10.5830i			0.337889i
$982$	−20.0000			−0.638226
$983$	−29.9333			−0.954723			−0.477361	−	0.878707i	$-0.658407\pi$
$983$	−29.9333			−0.954723			−0.477361	+	0.878707i	$0.658407\pi$
$984$	−8.00000			−0.255031
$985$	−22.4499			−0.715315
$986$	29.9333			0.953269
$987$		−	26.4575i		−	0.842152i
$988$		0			0
$989$	−14.0000	−	21.1660i	−0.445174	−	0.673040i
$990$		0			0
$991$	32.0000			1.01651			0.508257	−	0.861206i	$-0.330290\pi$
$991$	32.0000			1.01651			0.508257	+	0.861206i	$0.330290\pi$
$992$			1.41421i			0.0449013i
$993$			5.65685i			0.179515i
$994$		−	21.1660i		−	0.671345i
$995$		0			0
$996$			21.1660i			0.670671i
$997$		0			0		1.00000			$0$
$997$		0			0		−1.00000			$\pi$
$998$	−4.00000			−0.126618
$999$	59.8665			1.89409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.c.b.321.3	yes	4
3.2	odd	2		2898.2.g.e.2575.3		4
4.3	odd	2		2576.2.f.c.321.1		4
7.6	odd	2	inner	322.2.c.b.321.2	yes	4
21.20	even	2		2898.2.g.e.2575.1		4
23.22	odd	2	inner	322.2.c.b.321.4	yes	4
28.27	even	2		2576.2.f.c.321.4		4
69.68	even	2		2898.2.g.e.2575.2		4
92.91	even	2		2576.2.f.c.321.2		4
161.160	even	2	inner	322.2.c.b.321.1	✓	4
483.482	odd	2		2898.2.g.e.2575.4		4
644.643	odd	2		2576.2.f.c.321.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.c.b.321.1	✓	4	161.160	even	2	inner
322.2.c.b.321.2	yes	4	7.6	odd	2	inner
322.2.c.b.321.3	yes	4	1.1	even	1	trivial
322.2.c.b.321.4	yes	4	23.22	odd	2	inner
2576.2.f.c.321.1		4	4.3	odd	2
2576.2.f.c.321.2		4	92.91	even	2
2576.2.f.c.321.3		4	644.643	odd	2
2576.2.f.c.321.4		4	28.27	even	2
2898.2.g.e.2575.1		4	21.20	even	2
2898.2.g.e.2575.2		4	69.68	even	2
2898.2.g.e.2575.3		4	3.2	odd	2
2898.2.g.e.2575.4		4	483.482	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.41421i q^{3} +1.00000 q^{4} -3.74166 q^{5} -1.41421i q^{6} -2.64575i q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.41421i q^{3} +1.00000 q^{4} -3.74166 q^{5} -1.41421i q^{6} -2.64575i q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.74166 q^{10} +1.41421i q^{12} -5.65685i q^{13} +2.64575i q^{14} -5.29150i q^{15} +1.00000 q^{16} +3.74166 q^{17} -1.00000 q^{18} -3.74166 q^{20} +3.74166 q^{21} +(4.00000 - 2.64575i) q^{23} -1.41421i q^{24} +9.00000 q^{25} +5.65685i q^{26} +5.65685i q^{27} -2.64575i q^{28} -8.00000 q^{29} +5.29150i q^{30} -1.41421i q^{31} -1.00000 q^{32} -3.74166 q^{34} +9.89949i q^{35} +1.00000 q^{36} -10.5830i q^{37} +8.00000 q^{39} +3.74166 q^{40} -5.65685i q^{41} -3.74166 q^{42} -5.29150i q^{43} -3.74166 q^{45} +(-4.00000 + 2.64575i) q^{46} -7.07107i q^{47} +1.41421i q^{48} -7.00000 q^{49} -9.00000 q^{50} +5.29150i q^{51} -5.65685i q^{52} +10.5830i q^{53} -5.65685i q^{54} +2.64575i q^{56} +8.00000 q^{58} -9.89949i q^{59} -5.29150i q^{60} -3.74166 q^{61} +1.41421i q^{62} -2.64575i q^{63} +1.00000 q^{64} +21.1660i q^{65} +3.74166 q^{68} +(3.74166 + 5.65685i) q^{69} -9.89949i q^{70} -8.00000 q^{71} -1.00000 q^{72} +11.3137i q^{73} +10.5830i q^{74} +12.7279i q^{75} -8.00000 q^{78} +10.5830i q^{79} -3.74166 q^{80} -5.00000 q^{81} +5.65685i q^{82} +14.9666 q^{83} +3.74166 q^{84} -14.0000 q^{85} +5.29150i q^{86} -11.3137i q^{87} -11.2250 q^{89} +3.74166 q^{90} -14.9666 q^{91} +(4.00000 - 2.64575i) q^{92} +2.00000 q^{93} +7.07107i q^{94} -1.41421i q^{96} -3.74166 q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 4 q^{9} + 4 q^{16} - 4 q^{18} + 16 q^{23} + 36 q^{25} - 32 q^{29} - 4 q^{32} + 4 q^{36} + 32 q^{39} - 16 q^{46} - 28 q^{49} - 36 q^{50} + 32 q^{58} + 4 q^{64} - 32 q^{71} - 4 q^{72} - 32 q^{78} - 20 q^{81} - 56 q^{85} + 16 q^{92} + 8 q^{93} + 28 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 4 * q^9 + 4 * q^16 - 4 * q^18 + 16 * q^23 + 36 * q^25 - 32 * q^29 - 4 * q^32 + 4 * q^36 + 32 * q^39 - 16 * q^46 - 28 * q^49 - 36 * q^50 + 32 * q^58 + 4 * q^64 - 32 * q^71 - 4 * q^72 - 32 * q^78 - 20 * q^81 - 56 * q^85 + 16 * q^92 + 8 * q^93 + 28 * q^98

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