LMFDB - Embedded newform 2205.2.d.l.1324.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2205,2,Mod(1324,2205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("2205.1324");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2205 = 3^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2205.d (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:	$17.6070136457$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1324.2
Root			$1.45161 + 1.45161i$ of defining polynomial
Character	$\chi$	$=$	2205.1324
Dual form			2205.2.d.l.1324.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.90321i q^{2} -1.62222 q^{4} +(0.311108 + 2.21432i) q^{5} -0.719004i q^{8} +O(q^{10})$	\(q-1.90321i q^{2} -1.62222 q^{4} +(0.311108 + 2.21432i) q^{5} -0.719004i q^{8} +(4.21432 - 0.592104i) q^{10} -2.00000 q^{11} +6.42864i q^{13} -4.61285 q^{16} -4.42864i q^{17} -2.42864 q^{19} +(-0.504684 - 3.59210i) q^{20} +3.80642i q^{22} -1.37778i q^{23} +(-4.80642 + 1.37778i) q^{25} +12.2351 q^{26} +0.755569 q^{29} -5.18421 q^{31} +7.34122i q^{32} -8.42864 q^{34} -7.61285i q^{37} +4.62222i q^{38} +(1.59210 - 0.223688i) q^{40} -8.23506 q^{41} +10.1017i q^{43} +3.24443 q^{44} -2.62222 q^{46} -2.75557i q^{47} +(2.62222 + 9.14764i) q^{50} -10.4286i q^{52} -9.18421i q^{53} +(-0.622216 - 4.42864i) q^{55} -1.43801i q^{58} -14.1017 q^{59} -6.85728 q^{61} +9.86665i q^{62} +4.74620 q^{64} +(-14.2351 + 2.00000i) q^{65} -2.75557i q^{67} +7.18421i q^{68} -2.00000 q^{71} +1.57136i q^{73} -14.4889 q^{74} +3.93978 q^{76} +4.85728 q^{79} +(-1.43509 - 10.2143i) q^{80} +15.6731i q^{82} +11.6128i q^{83} +(9.80642 - 1.37778i) q^{85} +19.2257 q^{86} +1.43801i q^{88} -4.62222 q^{89} +2.23506i q^{92} -5.24443 q^{94} +(-0.755569 - 5.37778i) q^{95} -11.9398i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4} + 2 q^{5}+O(q^{10}) $ 6 * q - 10 * q^4 + 2 * q^5	$ 6 q - 10 q^{4} + 2 q^{5} + 12 q^{10} - 12 q^{11} + 26 q^{16} + 12 q^{19} - 30 q^{20} - 2 q^{25} + 20 q^{26} + 4 q^{29} - 4 q^{31} - 24 q^{34} - 4 q^{40} + 4 q^{41} + 20 q^{44} - 16 q^{46} + 16 q^{50} - 4 q^{55} - 32 q^{59} + 12 q^{61} - 26 q^{64} - 32 q^{65} - 12 q^{71} - 88 q^{74} - 4 q^{76} - 24 q^{79} + 46 q^{80} + 32 q^{85} + 8 q^{86} - 28 q^{89} - 32 q^{94} - 4 q^{95}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^5 + 12 * q^10 - 12 * q^11 + 26 * q^16 + 12 * q^19 - 30 * q^20 - 2 * q^25 + 20 * q^26 + 4 * q^29 - 4 * q^31 - 24 * q^34 - 4 * q^40 + 4 * q^41 + 20 * q^44 - 16 * q^46 + 16 * q^50 - 4 * q^55 - 32 * q^59 + 12 * q^61 - 26 * q^64 - 32 * q^65 - 12 * q^71 - 88 * q^74 - 4 * q^76 - 24 * q^79 + 46 * q^80 + 32 * q^85 + 8 * q^86 - 28 * q^89 - 32 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times$.

$n$	$442$	$1081$	$1226$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	1.90321i		−	1.34577i	−0.739745	−	0.672887i	$-0.765054\pi$
$2$		−	1.90321i		−	1.34577i	0.739745	−	0.672887i	$-0.234946\pi$
$3$		0			0
$3$		0			0
$4$	−1.62222			−0.811108
$5$	0.311108	+	2.21432i	0.139132	+	0.990274i
$5$	0.311108	+	2.21432i	0.139132	+	0.990274i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	0.719004i		−	0.254206i
$9$		0			0
$10$	4.21432	−	0.592104i	1.33268	−	0.187240i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$			6.42864i			1.78298i	0.453037	+	0.891492i	$0.350341\pi$
$13$			6.42864i			1.78298i	−0.453037	+	0.891492i	$0.649659\pi$
$14$		0			0
$15$		0			0
$16$	−4.61285			−1.15321
$17$		−	4.42864i		−	1.07410i	−0.843550	−	0.537051i	$-0.819538\pi$
$17$		−	4.42864i		−	1.07410i	0.843550	−	0.537051i	$-0.180462\pi$
$18$		0			0
$19$	−2.42864			−0.557168			−0.278584	−	0.960412i	$-0.589865\pi$
$19$	−2.42864			−0.557168			−0.278584	+	0.960412i	$0.589865\pi$
$20$	−0.504684	−	3.59210i	−0.112851	−	0.803219i
$21$		0			0
$22$			3.80642i			0.811532i
$23$		−	1.37778i		−	0.287288i	−0.989629	−	0.143644i	$-0.954118\pi$
$23$		−	1.37778i		−	0.287288i	0.989629	−	0.143644i	$-0.0458820\pi$
$24$		0			0
$25$	−4.80642	+	1.37778i	−0.961285	+	0.275557i
$26$	12.2351			2.39949
$27$		0			0
$28$		0			0
$29$	0.755569			0.140306			0.0701528	−	0.997536i	$-0.477651\pi$
$29$	0.755569			0.140306			0.0701528	+	0.997536i	$0.477651\pi$
$30$		0			0
$31$	−5.18421			−0.931111			−0.465556	−	0.885019i	$-0.654145\pi$
$31$	−5.18421			−0.931111			−0.465556	+	0.885019i	$0.654145\pi$
$32$			7.34122i			1.29776i
$33$		0			0
$34$	−8.42864			−1.44550
$35$		0			0
$36$		0			0
$37$		−	7.61285i		−	1.25154i	−0.780006	−	0.625772i	$-0.784784\pi$
$37$		−	7.61285i		−	1.25154i	0.780006	−	0.625772i	$-0.215216\pi$
$38$			4.62222i			0.749822i
$39$		0			0
$40$	1.59210	−	0.223688i	0.251734	−	0.0353681i
$41$	−8.23506			−1.28610			−0.643050	−	0.765824i	$-0.722331\pi$
$41$	−8.23506			−1.28610			−0.643050	+	0.765824i	$0.722331\pi$
$42$		0			0
$43$			10.1017i			1.54050i	0.637744	+	0.770248i	$0.279868\pi$
$43$			10.1017i			1.54050i	−0.637744	+	0.770248i	$0.720132\pi$
$44$	3.24443			0.489116
$45$		0			0
$46$	−2.62222			−0.386625
$47$		−	2.75557i		−	0.401941i	−0.979597	−	0.200971i	$-0.935590\pi$
$47$		−	2.75557i		−	0.401941i	0.979597	−	0.200971i	$-0.0644095\pi$
$48$		0			0
$49$		0			0
$50$	2.62222	+	9.14764i	0.370837	+	1.29367i
$51$		0			0
$52$		−	10.4286i		−	1.44619i
$53$		−	9.18421i		−	1.26155i	−0.775967	−	0.630774i	$-0.782737\pi$
$53$		−	9.18421i		−	1.26155i	0.775967	−	0.630774i	$-0.217263\pi$
$54$		0			0
$55$	−0.622216	−	4.42864i	−0.0838995	−	0.597158i
$56$		0			0
$57$		0			0
$58$		−	1.43801i		−	0.188820i
$59$	−14.1017			−1.83589			−0.917943	−	0.396712i	$-0.870151\pi$
$59$	−14.1017			−1.83589			−0.917943	+	0.396712i	$0.870151\pi$
$60$		0			0
$61$	−6.85728			−0.877985			−0.438992	−	0.898491i	$-0.644664\pi$
$61$	−6.85728			−0.877985			−0.438992	+	0.898491i	$0.644664\pi$
$62$			9.86665i			1.25307i
$63$		0			0
$64$	4.74620			0.593275
$65$	−14.2351	+	2.00000i	−1.76564	+	0.248069i
$66$		0			0
$67$		−	2.75557i		−	0.336646i	−0.985732	−	0.168323i	$-0.946165\pi$
$67$		−	2.75557i		−	0.336646i	0.985732	−	0.168323i	$-0.0538352\pi$
$68$			7.18421i			0.871213i
$69$		0			0
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$			1.57136i			0.183914i	0.995763	+	0.0919569i	$0.0293122\pi$
$73$			1.57136i			0.183914i	−0.995763	+	0.0919569i	$0.970688\pi$
$74$	−14.4889			−1.68430
$75$		0			0
$76$	3.93978			0.451923
$77$		0			0
$78$		0			0
$79$	4.85728			0.546487			0.273243	−	0.961945i	$-0.411904\pi$
$79$	4.85728			0.546487			0.273243	+	0.961945i	$0.411904\pi$
$80$	−1.43509	−	10.2143i	−0.160448	−	1.14200i
$81$		0			0
$82$			15.6731i			1.73080i
$83$			11.6128i			1.27468i	0.770585	+	0.637338i	$0.219964\pi$
$83$			11.6128i			1.27468i	−0.770585	+	0.637338i	$0.780036\pi$
$84$		0			0
$85$	9.80642	−	1.37778i	1.06366	−	0.149442i
$86$	19.2257			2.07316
$87$		0			0
$88$			1.43801i			0.153292i
$89$	−4.62222			−0.489954			−0.244977	−	0.969529i	$-0.578780\pi$
$89$	−4.62222			−0.489954			−0.244977	+	0.969529i	$0.578780\pi$
$90$		0			0
$91$		0			0
$92$			2.23506i			0.233021i
$93$		0			0
$94$	−5.24443			−0.540922
$95$	−0.755569	−	5.37778i	−0.0775197	−	0.551749i
$96$		0			0
$97$		−	11.9398i		−	1.21230i	−0.795350	−	0.606150i	$-0.792713\pi$
$97$		−	11.9398i		−	1.21230i	0.795350	−	0.606150i	$-0.207287\pi$
$98$		0			0
$99$		0			0
$100$	7.79706	−	2.23506i	0.779706	−	0.223506i
$101$	1.47949			0.147215			0.0736076	−	0.997287i	$-0.476549\pi$
$101$	1.47949			0.147215			0.0736076	+	0.997287i	$0.476549\pi$
$102$		0			0
$103$			8.85728i			0.872734i	0.899769	+	0.436367i	$0.143735\pi$
$103$			8.85728i			0.872734i	−0.899769	+	0.436367i	$0.856265\pi$
$104$	4.62222			0.453246
$105$		0			0
$106$	−17.4795			−1.69776
$107$			1.76494i			0.170623i	0.996354	+	0.0853114i	$0.0271885\pi$
$107$			1.76494i			0.170623i	−0.996354	+	0.0853114i	$0.972811\pi$
$108$		0			0
$109$	−5.61285			−0.537613			−0.268807	−	0.963194i	$-0.586629\pi$
$109$	−5.61285			−0.537613			−0.268807	+	0.963194i	$0.586629\pi$
$110$	−8.42864	+	1.18421i	−0.803639	+	0.112910i
$111$		0			0
$112$		0			0
$113$			11.2859i			1.06169i	0.847469	+	0.530845i	$0.178125\pi$
$113$			11.2859i			1.06169i	−0.847469	+	0.530845i	$0.821875\pi$
$114$		0			0
$115$	3.05086	−	0.428639i	0.284494	−	0.0399708i
$116$	−1.22570			−0.113803
$117$		0			0
$118$			26.8385i			2.47069i
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$			13.0509i			1.18157i
$123$		0			0
$124$	8.40990			0.755232
$125$	−4.54617	−	10.2143i	−0.406622	−	0.913597i
$126$		0			0
$127$			12.8573i			1.14090i	0.821333	+	0.570450i	$0.193231\pi$
$127$			12.8573i			1.14090i	−0.821333	+	0.570450i	$0.806769\pi$
$128$			5.64941i			0.499342i
$129$		0			0
$130$	3.80642	+	27.0923i	0.333845	+	2.37616i
$131$	−2.10171			−0.183627			−0.0918136	−	0.995776i	$-0.529266\pi$
$131$	−2.10171			−0.183627			−0.0918136	+	0.995776i	$0.529266\pi$
$132$		0			0
$133$		0			0
$134$	−5.24443			−0.453050
$135$		0			0
$136$	−3.18421			−0.273044
$137$			15.9398i			1.36183i	0.732364	+	0.680914i	$0.238417\pi$
$137$			15.9398i			1.36183i	−0.732364	+	0.680914i	$0.761583\pi$
$138$		0			0
$139$	11.6731			0.990097			0.495048	−	0.868865i	$-0.335150\pi$
$139$	11.6731			0.990097			0.495048	+	0.868865i	$0.335150\pi$
$140$		0			0
$141$		0			0
$142$			3.80642i			0.319428i
$143$		−	12.8573i		−	1.07518i
$144$		0			0
$145$	0.235063	+	1.67307i	0.0195209	+	0.138941i
$146$	2.99063			0.247506
$147$		0			0
$148$			12.3497i			1.01514i
$149$	−21.2257			−1.73888			−0.869438	−	0.494041i	$-0.835519\pi$
$149$	−21.2257			−1.73888			−0.869438	+	0.494041i	$0.835519\pi$
$150$		0			0
$151$	16.8573			1.37183			0.685913	−	0.727684i	$-0.259403\pi$
$151$	16.8573			1.37183			0.685913	+	0.727684i	$0.259403\pi$
$152$			1.74620i			0.141636i
$153$		0			0
$154$		0			0
$155$	−1.61285	−	11.4795i	−0.129547	−	0.922055i
$156$		0			0
$157$		−	10.4286i		−	0.832296i	−0.909297	−	0.416148i	$-0.863380\pi$
$157$		−	10.4286i		−	0.832296i	0.909297	−	0.416148i	$-0.136620\pi$
$158$		−	9.24443i		−	0.735447i
$159$		0			0
$160$	−16.2558	+	2.28391i	−1.28513	+	0.180559i
$161$		0			0
$162$		0			0
$163$			20.8573i			1.63367i	0.576873	+	0.816834i	$0.304273\pi$
$163$			20.8573i			1.63367i	−0.576873	+	0.816834i	$0.695727\pi$
$164$	13.3590			1.04317
$165$		0			0
$166$	22.1017			1.71543
$167$		−	15.3461i		−	1.18752i	−0.804642	−	0.593760i	$-0.797643\pi$
$167$		−	15.3461i		−	1.18752i	0.804642	−	0.593760i	$-0.202357\pi$
$168$		0			0
$169$	−28.3274			−2.17903
$170$	−2.62222	−	18.6637i	−0.201115	−	1.43144i
$171$		0			0
$172$		−	16.3872i		−	1.24951i
$173$			2.06022i			0.156636i	0.996928	+	0.0783179i	$0.0249549\pi$
$173$			2.06022i			0.156636i	−0.996928	+	0.0783179i	$0.975045\pi$
$174$		0			0
$175$		0			0
$176$	9.22570			0.695413
$177$		0			0
$178$			8.79706i			0.659367i
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		0			0
$181$	12.1017			0.899513			0.449757	−	0.893151i	$-0.351511\pi$
$181$	12.1017			0.899513			0.449757	+	0.893151i	$0.351511\pi$
$182$		0			0
$183$		0			0
$184$	−0.990632			−0.0730304
$185$	16.8573	−	2.36842i	1.23937	−	0.174129i
$186$		0			0
$187$			8.85728i			0.647708i
$188$			4.47013i			0.326017i
$189$		0			0
$190$	−10.2351	+	1.43801i	−0.742530	+	0.104324i
$191$	−0.488863			−0.0353729			−0.0176864	−	0.999844i	$-0.505630\pi$
$191$	−0.488863			−0.0353729			−0.0176864	+	0.999844i	$0.505630\pi$
$192$		0			0
$193$		−	22.9590i		−	1.65262i	−0.563212	−	0.826312i	$-0.690435\pi$
$193$		−	22.9590i		−	1.65262i	0.563212	−	0.826312i	$-0.309565\pi$
$194$	−22.7239			−1.63148
$195$		0			0
$196$		0			0
$197$		−	1.18421i		−	0.0843713i	−0.999110	−	0.0421857i	$-0.986568\pi$
$197$		−	1.18421i		−	0.0843713i	0.999110	−	0.0421857i	$-0.0134321\pi$
$198$		0			0
$199$	8.79706			0.623607			0.311803	−	0.950147i	$-0.399067\pi$
$199$	8.79706			0.623607			0.311803	+	0.950147i	$0.399067\pi$
$200$	0.990632	+	3.45584i	0.0700483	+	0.244365i
$201$		0			0
$202$		−	2.81579i		−	0.198118i
$203$		0			0
$204$		0			0
$205$	−2.56199	−	18.2351i	−0.178937	−	1.27359i
$206$	16.8573			1.17450
$207$		0			0
$208$		−	29.6543i		−	2.05616i
$209$	4.85728			0.335985
$210$		0			0
$211$	23.2257			1.59892			0.799461	−	0.600717i	$-0.205118\pi$
$211$	23.2257			1.59892			0.799461	+	0.600717i	$0.205118\pi$
$212$			14.8988i			1.02325i
$213$		0			0
$214$	3.35905			0.229620
$215$	−22.3684	+	3.14272i	−1.52551	+	0.214332i
$216$		0			0
$217$		0			0
$218$			10.6824i			0.723506i
$219$		0			0
$220$	1.00937	+	7.18421i	0.0680516	+	0.484359i
$221$	28.4701			1.91511
$222$		0			0
$223$			15.2257i			1.01959i	0.860297	+	0.509794i	$0.170278\pi$
$223$			15.2257i			1.01959i	−0.860297	+	0.509794i	$0.829722\pi$
$224$		0			0
$225$		0			0
$226$	21.4795			1.42879
$227$			14.3684i			0.953665i	0.878994	+	0.476833i	$0.158215\pi$
$227$			14.3684i			0.953665i	−0.878994	+	0.476833i	$0.841785\pi$
$228$		0			0
$229$	−5.61285			−0.370907			−0.185454	−	0.982653i	$-0.559375\pi$
$229$	−5.61285			−0.370907			−0.185454	+	0.982653i	$0.559375\pi$
$230$	−0.815792	−	5.80642i	−0.0537917	−	0.382864i
$231$		0			0
$232$		−	0.543257i		−	0.0356666i
$233$		−	23.2859i		−	1.52551i	−0.646687	−	0.762756i	$-0.723846\pi$
$233$		−	23.2859i		−	1.52551i	0.646687	−	0.762756i	$-0.276154\pi$
$234$		0			0
$235$	6.10171	−	0.857279i	0.398032	−	0.0559227i
$236$	22.8760			1.48910
$237$		0			0
$238$		0			0
$239$	−8.48886			−0.549099			−0.274549	−	0.961573i	$-0.588529\pi$
$239$	−8.48886			−0.549099			−0.274549	+	0.961573i	$0.588529\pi$
$240$		0			0
$241$	7.24443			0.466655			0.233327	−	0.972398i	$-0.425039\pi$
$241$	7.24443			0.466655			0.233327	+	0.972398i	$0.425039\pi$
$242$			13.3225i			0.856402i
$243$		0			0
$244$	11.1240			0.712140
$245$		0			0
$246$		0			0
$247$		−	15.6128i		−	0.993422i
$248$			3.72746i			0.236694i
$249$		0			0
$250$	−19.4400	+	8.65233i	−1.22949	+	0.547221i
$251$	27.6128			1.74291			0.871454	−	0.490478i	$-0.163178\pi$
$251$	27.6128			1.74291			0.871454	+	0.490478i	$0.163178\pi$
$252$		0			0
$253$			2.75557i			0.173241i
$254$	24.4701			1.53539
$255$		0			0
$256$	20.2444			1.26528
$257$			0.428639i			0.0267378i	0.999911	+	0.0133689i	$0.00425558\pi$
$257$			0.428639i			0.0267378i	−0.999911	+	0.0133689i	$0.995744\pi$
$258$		0			0
$259$		0			0
$260$	23.0923	−	3.24443i	1.43213	−	0.201211i
$261$		0			0
$262$			4.00000i			0.247121i
$263$			9.37778i			0.578259i	0.957290	+	0.289129i	$0.0933658\pi$
$263$			9.37778i			0.578259i	−0.957290	+	0.289129i	$0.906634\pi$
$264$		0			0
$265$	20.3368	−	2.85728i	1.24928	−	0.175521i
$266$		0			0
$267$		0			0
$268$			4.47013i			0.273056i
$269$	−1.74620			−0.106468			−0.0532339	−	0.998582i	$-0.516953\pi$
$269$	−1.74620			−0.106468			−0.0532339	+	0.998582i	$0.516953\pi$
$270$		0			0
$271$	2.69535			0.163731			0.0818653	−	0.996643i	$-0.473912\pi$
$271$	2.69535			0.163731			0.0818653	+	0.996643i	$0.473912\pi$
$272$			20.4286i			1.23867i
$273$		0			0
$274$	30.3368			1.83271
$275$	9.61285	−	2.75557i	0.579677	−	0.166167i
$276$		0			0
$277$			5.12399i			0.307870i	0.988081	+	0.153935i	$0.0491947\pi$
$277$			5.12399i			0.307870i	−0.988081	+	0.153935i	$0.950805\pi$
$278$		−	22.2163i		−	1.33245i
$279$		0			0
$280$		0			0
$281$	−23.9813			−1.43060			−0.715301	−	0.698816i	$-0.753710\pi$
$281$	−23.9813			−1.43060			−0.715301	+	0.698816i	$0.753710\pi$
$282$		0			0
$283$		−	2.36842i		−	0.140788i	−0.997519	−	0.0703939i	$-0.977574\pi$
$283$		−	2.36842i		−	0.140788i	0.997519	−	0.0703939i	$-0.0224256\pi$
$284$	3.24443			0.192522
$285$		0			0
$286$	−24.4701			−1.44695
$287$		0			0
$288$		0			0
$289$	−2.61285			−0.153697
$290$	3.18421	−	0.447375i	0.186983	−	0.0262708i
$291$		0			0
$292$		−	2.54909i		−	0.149174i
$293$			8.42864i			0.492406i	0.969218	+	0.246203i	$0.0791831\pi$
$293$			8.42864i			0.492406i	−0.969218	+	0.246203i	$0.920817\pi$
$294$		0			0
$295$	−4.38715	−	31.2257i	−0.255430	−	1.81803i
$296$	−5.47367			−0.318150
$297$		0			0
$298$			40.3970i			2.34014i
$299$	8.85728			0.512230
$300$		0			0
$301$		0			0
$302$		−	32.0830i		−	1.84617i
$303$		0			0
$304$	11.2029			0.642533
$305$	−2.13335	−	15.1842i	−0.122155	−	0.869445i
$306$		0			0
$307$		−	22.5718i		−	1.28824i	−0.764923	−	0.644121i	$-0.777223\pi$
$307$		−	22.5718i		−	1.28824i	0.764923	−	0.644121i	$-0.222777\pi$
$308$		0			0
$309$		0			0
$310$	−21.8479	+	3.06959i	−1.24088	+	0.174341i
$311$	−24.0830			−1.36562			−0.682810	−	0.730596i	$-0.739242\pi$
$311$	−24.0830			−1.36562			−0.682810	+	0.730596i	$0.739242\pi$
$312$		0			0
$313$		−	9.65433i		−	0.545695i	−0.962057	−	0.272848i	$-0.912035\pi$
$313$		−	9.65433i		−	0.545695i	0.962057	−	0.272848i	$-0.0879655\pi$
$314$	−19.8479			−1.12008
$315$		0			0
$316$	−7.87955			−0.443260
$317$		−	6.04149i		−	0.339324i	−0.985502	−	0.169662i	$-0.945732\pi$
$317$		−	6.04149i		−	0.339324i	0.985502	−	0.169662i	$-0.0542676\pi$
$318$		0			0
$319$	−1.51114			−0.0846075
$320$	1.47658	+	10.5096i	0.0825433	+	0.587505i
$321$		0			0
$322$		0			0
$323$			10.7556i			0.598456i
$324$		0			0
$325$	−8.85728	−	30.8988i	−0.491313	−	1.71396i
$326$	39.6958			2.19855
$327$		0			0
$328$			5.92104i			0.326935i
$329$		0			0
$330$		0			0
$331$	13.5111			0.742639			0.371320	−	0.928505i	$-0.378905\pi$
$331$	13.5111			0.742639			0.371320	+	0.928505i	$0.378905\pi$
$332$		−	18.8385i		−	1.03390i
$333$		0			0
$334$	−29.2070			−1.59813
$335$	6.10171	−	0.857279i	0.333372	−	0.0468382i
$336$		0			0
$337$		−	10.4889i		−	0.571365i	−0.958324	−	0.285682i	$-0.907780\pi$
$337$		−	10.4889i		−	0.571365i	0.958324	−	0.285682i	$-0.0922202\pi$
$338$			53.9131i			2.93248i
$339$		0			0
$340$	−15.9081	+	2.23506i	−0.862740	+	0.121213i
$341$	10.3684			0.561481
$342$		0			0
$343$		0			0
$344$	7.26317			0.391604
$345$		0			0
$346$	3.92104			0.210796
$347$		−	16.7239i		−	0.897787i	−0.893585	−	0.448894i	$-0.851818\pi$
$347$		−	16.7239i		−	0.897787i	0.893585	−	0.448894i	$-0.148182\pi$
$348$		0			0
$349$	−16.3684			−0.876181			−0.438091	−	0.898931i	$-0.644345\pi$
$349$	−16.3684			−0.876181			−0.438091	+	0.898931i	$0.644345\pi$
$350$		0			0
$351$		0			0
$352$		−	14.6824i		−	0.782577i
$353$			0.549086i			0.0292249i	0.999893	+	0.0146124i	$0.00465145\pi$
$353$			0.549086i			0.0292249i	−0.999893	+	0.0146124i	$0.995349\pi$
$354$		0			0
$355$	−0.622216	−	4.42864i	−0.0330238	−	0.235048i
$356$	7.49823			0.397405
$357$		0			0
$358$		−	19.0321i		−	1.00588i
$359$	−0.285442			−0.0150651			−0.00753253	−	0.999972i	$-0.502398\pi$
$359$	−0.285442			−0.0150651			−0.00753253	+	0.999972i	$0.502398\pi$
$360$		0			0
$361$	−13.1017			−0.689564
$362$		−	23.0321i		−	1.21054i
$363$		0			0
$364$		0			0
$365$	−3.47949	+	0.488863i	−0.182125	+	0.0255882i
$366$		0			0
$367$			1.71456i			0.0894992i	0.998998	+	0.0447496i	$0.0142490\pi$
$367$			1.71456i			0.0894992i	−0.998998	+	0.0447496i	$0.985751\pi$
$368$			6.35551i			0.331304i
$369$		0			0
$370$	−4.50760	−	32.0830i	−0.234339	−	1.66791i
$371$		0			0
$372$		0			0
$373$			16.0000i			0.828449i	0.910175	+	0.414224i	$0.135947\pi$
$373$			16.0000i			0.828449i	−0.910175	+	0.414224i	$0.864053\pi$
$374$	16.8573			0.871669
$375$		0			0
$376$	−1.98126			−0.102176
$377$			4.85728i			0.250163i
$378$		0			0
$379$	4.85728			0.249502			0.124751	−	0.992188i	$-0.460187\pi$
$379$	4.85728			0.249502			0.124751	+	0.992188i	$0.460187\pi$
$380$	1.22570	+	8.72393i	0.0628768	+	0.447528i
$381$		0			0
$382$			0.930409i			0.0476039i
$383$		−	8.38715i		−	0.428563i	−0.976772	−	0.214282i	$-0.931259\pi$
$383$		−	8.38715i		−	0.428563i	0.976772	−	0.214282i	$-0.0687411\pi$
$384$		0			0
$385$		0			0
$386$	−43.6958			−2.22406
$387$		0			0
$388$			19.3689i			0.983307i
$389$	8.95899			0.454239			0.227119	−	0.973867i	$-0.427069\pi$
$389$	8.95899			0.454239			0.227119	+	0.973867i	$0.427069\pi$
$390$		0			0
$391$	−6.10171			−0.308577
$392$		0			0
$393$		0			0
$394$	−2.25380			−0.113545
$395$	1.51114	+	10.7556i	0.0760336	+	0.541171i
$396$		0			0
$397$		−	2.54909i		−	0.127935i	−0.997952	−	0.0639675i	$-0.979625\pi$
$397$		−	2.54909i		−	0.127935i	0.997952	−	0.0639675i	$-0.0203754\pi$
$398$		−	16.7427i		−	0.839234i
$399$		0			0
$400$	22.1713	−	6.35551i	1.10857	−	0.317775i
$401$	−0.958989			−0.0478896			−0.0239448	−	0.999713i	$-0.507623\pi$
$401$	−0.958989			−0.0478896			−0.0239448	+	0.999713i	$0.507623\pi$
$402$		0			0
$403$		−	33.3274i		−	1.66016i
$404$	−2.40006			−0.119407
$405$		0			0
$406$		0			0
$407$			15.2257i			0.754710i
$408$		0			0
$409$	−31.9813			−1.58137			−0.790686	−	0.612222i	$-0.790276\pi$
$409$	−31.9813			−1.58137			−0.790686	+	0.612222i	$0.790276\pi$
$410$	−34.7052	+	4.87601i	−1.71397	+	0.240809i
$411$		0			0
$412$		−	14.3684i		−	0.707881i
$413$		0			0
$414$		0			0
$415$	−25.7146	+	3.61285i	−1.26228	+	0.177348i
$416$	−47.1941			−2.31388
$417$		0			0
$418$		−	9.24443i		−	0.452160i
$419$	0.470127			0.0229672			0.0114836	−	0.999934i	$-0.496345\pi$
$419$	0.470127			0.0229672			0.0114836	+	0.999934i	$0.496345\pi$
$420$		0			0
$421$	−33.6128			−1.63819			−0.819095	−	0.573658i	$-0.805524\pi$
$421$	−33.6128			−1.63819			−0.819095	+	0.573658i	$0.805524\pi$
$422$		−	44.2034i		−	2.15179i
$423$		0			0
$424$	−6.60348			−0.320693
$425$	6.10171	+	21.2859i	0.295976	+	1.03252i
$426$		0			0
$427$		0			0
$428$		−	2.86311i		−	0.138394i
$429$		0			0
$430$	5.98126	+	42.5718i	0.288442	+	2.05300i
$431$	−11.7146			−0.564270			−0.282135	−	0.959375i	$-0.591043\pi$
$431$	−11.7146			−0.564270			−0.282135	+	0.959375i	$0.591043\pi$
$432$		0			0
$433$			0.0602231i			0.00289414i	0.999999	+	0.00144707i	$0.000460616\pi$
$433$			0.0602231i			0.00289414i	−0.999999	+	0.00144707i	$0.999539\pi$
$434$		0			0
$435$		0			0
$436$	9.10525			0.436062
$437$			3.34614i			0.160068i
$438$		0			0
$439$	−22.4286			−1.07046			−0.535230	−	0.844706i	$-0.679775\pi$
$439$	−22.4286			−1.07046			−0.535230	+	0.844706i	$0.679775\pi$
$440$	−3.18421	+	0.447375i	−0.151801	+	0.0213278i
$441$		0			0
$442$		−	54.1847i		−	2.57730i
$443$			23.9496i			1.13788i	0.822379	+	0.568940i	$0.192647\pi$
$443$			23.9496i			1.13788i	−0.822379	+	0.568940i	$0.807353\pi$
$444$		0			0
$445$	−1.43801	−	10.2351i	−0.0681681	−	0.485189i
$446$	28.9777			1.37214
$447$		0			0
$448$		0			0
$449$	29.4291			1.38885			0.694423	−	0.719567i	$-0.255660\pi$
$449$	29.4291			1.38885			0.694423	+	0.719567i	$0.255660\pi$
$450$		0			0
$451$	16.4701			0.775548
$452$		−	18.3082i		−	0.861145i
$453$		0			0
$454$	27.3461			1.28342
$455$		0			0
$456$		0			0
$457$			3.14272i			0.147010i	0.997295	+	0.0735051i	$0.0234185\pi$
$457$			3.14272i			0.147010i	−0.997295	+	0.0735051i	$0.976581\pi$
$458$			10.6824i			0.499158i
$459$		0			0
$460$	−4.94914	+	0.695346i	−0.230755	+	0.0324207i
$461$	−3.37778			−0.157319			−0.0786596	−	0.996902i	$-0.525064\pi$
$461$	−3.37778			−0.157319			−0.0786596	+	0.996902i	$0.525064\pi$
$462$		0			0
$463$			20.8573i			0.969320i	0.874703	+	0.484660i	$0.161057\pi$
$463$			20.8573i			0.969320i	−0.874703	+	0.484660i	$0.838943\pi$
$464$	−3.48532			−0.161802
$465$		0			0
$466$	−44.3180			−2.05299
$467$			14.3684i			0.664891i	0.943122	+	0.332446i	$0.107874\pi$
$467$			14.3684i			0.664891i	−0.943122	+	0.332446i	$0.892126\pi$
$468$		0			0
$469$		0			0
$470$	−1.63158	−	11.6128i	−0.0752593	−	0.535661i
$471$		0			0
$472$			10.1392i			0.466694i
$473$		−	20.2034i		−	0.928954i
$474$		0			0
$475$	11.6731	−	3.34614i	0.535597	−	0.153532i
$476$		0			0
$477$		0			0
$478$			16.1561i			0.738963i
$479$	−6.36842			−0.290980			−0.145490	−	0.989360i	$-0.546476\pi$
$479$	−6.36842			−0.290980			−0.145490	+	0.989360i	$0.546476\pi$
$480$		0			0
$481$	48.9403			2.23148
$482$		−	13.7877i		−	0.628012i
$483$		0			0
$484$	11.3555			0.516160
$485$	26.4385	−	3.71456i	1.20051	−	0.168669i
$486$		0			0
$487$		−	17.3274i		−	0.785180i	−0.919714	−	0.392590i	$-0.871579\pi$
$487$		−	17.3274i		−	0.785180i	0.919714	−	0.392590i	$-0.128421\pi$
$488$			4.93041i			0.223189i
$489$		0			0
$490$		0			0
$491$	−2.00000			−0.0902587			−0.0451294	−	0.998981i	$-0.514370\pi$
$491$	−2.00000			−0.0902587			−0.0451294	+	0.998981i	$0.514370\pi$
$492$		0			0
$493$		−	3.34614i		−	0.150703i
$494$	−29.7146			−1.33692
$495$		0			0
$496$	23.9140			1.07377
$497$		0			0
$498$		0			0
$499$	−23.3461			−1.04512			−0.522558	−	0.852603i	$-0.675022\pi$
$499$	−23.3461			−1.04512			−0.522558	+	0.852603i	$0.675022\pi$
$500$	7.37487	+	16.5698i	0.329814	+	0.741025i
$501$		0			0
$502$		−	52.5531i		−	2.34556i
$503$			0.387152i			0.0172623i	0.999963	+	0.00863113i	$0.00274741\pi$
$503$			0.387152i			0.0172623i	−0.999963	+	0.00863113i	$0.997253\pi$
$504$		0			0
$505$	0.460282	+	3.27607i	0.0204823	+	0.145783i
$506$	5.24443			0.233143
$507$		0			0
$508$		−	20.8573i		−	0.925392i
$509$	29.9496			1.32749			0.663747	−	0.747957i	$-0.268965\pi$
$509$	29.9496			1.32749			0.663747	+	0.747957i	$0.268965\pi$
$510$		0			0
$511$		0			0
$512$		−	27.2306i		−	1.20343i
$513$		0			0
$514$	0.815792			0.0359830
$515$	−19.6128	+	2.75557i	−0.864245	+	0.121425i
$516$		0			0
$517$			5.51114i			0.242380i
$518$		0			0
$519$		0			0
$520$	1.43801	+	10.2351i	0.0630608	+	0.448837i
$521$	−18.5205			−0.811398			−0.405699	−	0.914007i	$-0.632972\pi$
$521$	−18.5205			−0.811398			−0.405699	+	0.914007i	$0.632972\pi$
$522$		0			0
$523$			4.00000i			0.174908i	0.996169	+	0.0874539i	$0.0278730\pi$
$523$			4.00000i			0.174908i	−0.996169	+	0.0874539i	$0.972127\pi$
$524$	3.40943			0.148942
$525$		0			0
$526$	17.8479			0.778206
$527$			22.9590i			1.00011i
$528$		0			0
$529$	21.1017			0.917466
$530$	−5.43801	−	38.7052i	−0.236212	−	1.68125i
$531$		0			0
$532$		0			0
$533$		−	52.9403i		−	2.29310i
$534$		0			0
$535$	−3.90813	+	0.549086i	−0.168963	+	0.0237390i
$536$	−1.98126			−0.0855776
$537$		0			0
$538$			3.32339i			0.143282i
$539$		0			0
$540$		0			0
$541$	14.5906			0.627298			0.313649	−	0.949539i	$-0.398449\pi$
$541$	14.5906			0.627298			0.313649	+	0.949539i	$0.398449\pi$
$542$		−	5.12981i		−	0.220344i
$543$		0			0
$544$	32.5116			1.39392
$545$	−1.74620	−	12.4286i	−0.0747990	−	0.532384i
$546$		0			0
$547$			18.7556i			0.801930i	0.916093	+	0.400965i	$0.131325\pi$
$547$			18.7556i			0.801930i	−0.916093	+	0.400965i	$0.868675\pi$
$548$		−	25.8578i		−	1.10459i
$549$		0			0
$550$	−5.24443	−	18.2953i	−0.223623	−	0.780114i
$551$	−1.83500			−0.0781738
$552$		0			0
$553$		0			0
$554$	9.75203			0.414324
$555$		0			0
$556$	−18.9362			−0.803075
$557$			31.8765i			1.35065i	0.737520	+	0.675325i	$0.235997\pi$
$557$			31.8765i			1.35065i	−0.737520	+	0.675325i	$0.764003\pi$
$558$		0			0
$559$	−64.9403			−2.74668
$560$		0			0
$561$		0			0
$562$			45.6414i			1.92527i
$563$		−	2.01874i		−	0.0850796i	−0.999095	−	0.0425398i	$-0.986455\pi$
$563$		−	2.01874i		−	0.0850796i	0.999095	−	0.0425398i	$-0.0135449\pi$
$564$		0			0
$565$	−24.9906	+	3.51114i	−1.05136	+	0.147715i
$566$	−4.50760			−0.189468
$567$		0			0
$568$			1.43801i			0.0603375i
$569$	−28.9590			−1.21402			−0.607012	−	0.794693i	$-0.707632\pi$
$569$	−28.9590			−1.21402			−0.607012	+	0.794693i	$0.707632\pi$
$570$		0			0
$571$	8.97773			0.375706			0.187853	−	0.982197i	$-0.439847\pi$
$571$	8.97773			0.375706			0.187853	+	0.982197i	$0.439847\pi$
$572$			20.8573i			0.872087i
$573$		0			0
$574$		0			0
$575$	1.89829	+	6.62222i	0.0791642	+	0.276165i
$576$		0			0
$577$			28.6766i			1.19382i	0.802307	+	0.596911i	$0.203606\pi$
$577$			28.6766i			1.19382i	−0.802307	+	0.596911i	$0.796394\pi$
$578$			4.97280i			0.206841i
$579$		0			0
$580$	−0.381323	−	2.71408i	−0.0158336	−	0.112696i
$581$		0			0
$582$		0			0
$583$			18.3684i			0.760742i
$584$	1.12981			0.0467520
$585$		0			0
$586$	16.0415			0.662668
$587$		−	45.2070i		−	1.86589i	−0.360018	−	0.932945i	$-0.617229\pi$
$587$		−	45.2070i		−	1.86589i	0.360018	−	0.932945i	$-0.382771\pi$
$588$		0			0
$589$	12.5906			0.518786
$590$	−59.4291	+	8.34968i	−2.44666	+	0.343751i
$591$		0			0
$592$			35.1169i			1.44330i
$593$		−	18.2636i		−	0.749998i	−0.927025	−	0.374999i	$-0.877643\pi$
$593$		−	18.2636i		−	0.749998i	0.927025	−	0.374999i	$-0.122357\pi$
$594$		0			0
$595$		0			0
$596$	34.4327			1.41042
$597$		0			0
$598$		−	16.8573i		−	0.689345i
$599$	−22.7368			−0.929002			−0.464501	−	0.885573i	$-0.653766\pi$
$599$	−22.7368			−0.929002			−0.464501	+	0.885573i	$0.653766\pi$
$600$		0			0
$601$	−0.488863			−0.0199411			−0.00997056	−	0.999950i	$-0.503174\pi$
$601$	−0.488863			−0.0199411			−0.00997056	+	0.999950i	$0.503174\pi$
$602$		0			0
$603$		0			0
$604$	−27.3461			−1.11270
$605$	−2.17775	−	15.5002i	−0.0885383	−	0.630174i
$606$		0			0
$607$			20.2034i			0.820032i	0.912078	+	0.410016i	$0.134477\pi$
$607$			20.2034i			0.820032i	−0.912078	+	0.410016i	$0.865523\pi$
$608$		−	17.8292i		−	0.723069i
$609$		0			0
$610$	−28.8988	+	4.06022i	−1.17008	+	0.164394i
$611$	17.7146			0.716654
$612$		0			0
$613$		−	10.3684i		−	0.418776i	−0.977833	−	0.209388i	$-0.932853\pi$
$613$		−	10.3684i		−	0.418776i	0.977833	−	0.209388i	$-0.0671472\pi$
$614$	−42.9590			−1.73368
$615$		0			0
$616$		0			0
$617$			39.2859i			1.58159i	0.612080	+	0.790796i	$0.290333\pi$
$617$			39.2859i			1.58159i	−0.612080	+	0.790796i	$0.709667\pi$
$618$		0			0
$619$	42.8988			1.72425			0.862123	−	0.506698i	$-0.169134\pi$
$619$	42.8988			1.72425			0.862123	+	0.506698i	$0.169134\pi$
$620$	2.61639	+	18.6222i	0.105077	+	0.747886i
$621$		0			0
$622$			45.8350i			1.83782i
$623$		0			0
$624$		0			0
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$	−18.3742			−0.734383
$627$		0			0
$628$			16.9175i			0.675082i
$629$	−33.7146			−1.34429
$630$		0			0
$631$	15.3461			0.610920			0.305460	−	0.952205i	$-0.401190\pi$
$631$	15.3461			0.610920			0.305460	+	0.952205i	$0.401190\pi$
$632$		−	3.49240i		−	0.138920i
$633$		0			0
$634$	−11.4982			−0.456653
$635$	−28.4701	+	4.00000i	−1.12980	+	0.158735i
$636$		0			0
$637$		0			0
$638$			2.87601i			0.113863i
$639$		0			0
$640$	−12.5096	+	1.75758i	−0.494486	+	0.0694743i
$641$	−30.6735			−1.21153			−0.605766	−	0.795643i	$-0.707133\pi$
$641$	−30.6735			−1.21153			−0.605766	+	0.795643i	$0.707133\pi$
$642$		0			0
$643$		−	49.0607i		−	1.93477i	−0.253320	−	0.967383i	$-0.581523\pi$
$643$		−	49.0607i		−	1.93477i	0.253320	−	0.967383i	$-0.418477\pi$
$644$		0			0
$645$		0			0
$646$	20.4701			0.805386
$647$		−	15.3461i		−	0.603319i	−0.953416	−	0.301660i	$-0.902459\pi$
$647$		−	15.3461i		−	0.603319i	0.953416	−	0.301660i	$-0.0975406\pi$
$648$		0			0
$649$	28.2034			1.10708
$650$	−58.8069	+	16.8573i	−2.30660	+	0.661197i
$651$		0			0
$652$		−	33.8350i		−	1.32508i
$653$		−	19.4697i		−	0.761906i	−0.924594	−	0.380953i	$-0.875596\pi$
$653$		−	19.4697i		−	0.761906i	0.924594	−	0.380953i	$-0.124404\pi$
$654$		0			0
$655$	−0.653858	−	4.65386i	−0.0255484	−	0.181841i
$656$	37.9871			1.48315
$657$		0			0
$658$		0			0
$659$	30.9403			1.20526			0.602631	−	0.798020i	$-0.294119\pi$
$659$	30.9403			1.20526			0.602631	+	0.798020i	$0.294119\pi$
$660$		0			0
$661$	−47.7975			−1.85911			−0.929554	−	0.368685i	$-0.879808\pi$
$661$	−47.7975			−1.85911			−0.929554	+	0.368685i	$0.879808\pi$
$662$		−	25.7146i		−	0.999425i
$663$		0			0
$664$	8.34968			0.324030
$665$		0			0
$666$		0			0
$667$		−	1.04101i		−	0.0403081i
$668$			24.8948i			0.963207i
$669$		0			0
$670$	−1.63158	−	11.6128i	−0.0630336	−	0.448643i
$671$	13.7146			0.529445
$672$		0			0
$673$		−	27.8163i		−	1.07224i	−0.844142	−	0.536119i	$-0.819890\pi$
$673$		−	27.8163i		−	1.07224i	0.844142	−	0.536119i	$-0.180110\pi$
$674$	−19.9625			−0.768928
$675$		0			0
$676$	45.9532			1.76743
$677$		−	19.0005i		−	0.730248i	−0.930959	−	0.365124i	$-0.881027\pi$
$677$		−	19.0005i		−	0.730248i	0.930959	−	0.365124i	$-0.118973\pi$
$678$		0			0
$679$		0			0
$680$	−0.990632	−	7.05086i	−0.0379890	−	0.270388i
$681$		0			0
$682$		−	19.7333i		−	0.755627i
$683$			4.52051i			0.172972i	0.996253	+	0.0864862i	$0.0275638\pi$
$683$			4.52051i			0.172972i	−0.996253	+	0.0864862i	$0.972436\pi$
$684$		0			0
$685$	−35.2958	+	4.95899i	−1.34858	+	0.189473i
$686$		0			0
$687$		0			0
$688$		−	46.5977i		−	1.77652i
$689$	59.0420			2.24932
$690$		0			0
$691$	1.18421			0.0450494			0.0225247	−	0.999746i	$-0.492830\pi$
$691$	1.18421			0.0450494			0.0225247	+	0.999746i	$0.492830\pi$
$692$		−	3.34213i		−	0.127049i
$693$		0			0
$694$	−31.8292			−1.20822
$695$	3.63158	+	25.8479i	0.137754	+	0.980467i
$696$		0			0
$697$			36.4701i			1.38140i
$698$			31.1526i			1.17914i
$699$		0			0
$700$		0			0
$701$	26.6735			1.00745			0.503723	−	0.863865i	$-0.331963\pi$
$701$	26.6735			1.00745			0.503723	+	0.863865i	$0.331963\pi$
$702$		0			0
$703$			18.4889i			0.697321i
$704$	−9.49240			−0.357758
$705$		0			0
$706$	1.04503			0.0393301
$707$		0			0
$708$		0			0
$709$	18.2034			0.683644			0.341822	−	0.939765i	$-0.388956\pi$
$709$	18.2034			0.683644			0.341822	+	0.939765i	$0.388956\pi$
$710$	−8.42864	+	1.18421i	−0.316321	+	0.0444425i
$711$		0			0
$712$			3.32339i			0.124549i
$713$			7.14272i			0.267497i
$714$		0			0
$715$	28.4701	−	4.00000i	1.06472	−	0.149592i
$716$	−16.2222			−0.606250
$717$		0			0
$718$			0.543257i			0.0202742i
$719$	−4.85728			−0.181146			−0.0905730	−	0.995890i	$-0.528870\pi$
$719$	−4.85728			−0.181146			−0.0905730	+	0.995890i	$0.528870\pi$
$720$		0			0
$721$		0			0
$722$			24.9353i			0.927997i
$723$		0			0
$724$	−19.6316			−0.729602
$725$	−3.63158	+	1.04101i	−0.134874	+	0.0386622i
$726$		0			0
$727$		−	21.0607i		−	0.781098i	−0.920582	−	0.390549i	$-0.872285\pi$
$727$		−	21.0607i		−	0.781098i	0.920582	−	0.390549i	$-0.127715\pi$
$728$		0			0
$729$		0			0
$730$	0.930409	+	6.62222i	0.0344360	+	0.245099i
$731$	44.7368			1.65465
$732$		0			0
$733$			9.45091i			0.349077i	0.984650	+	0.174539i	$0.0558434\pi$
$733$			9.45091i			0.349077i	−0.984650	+	0.174539i	$0.944157\pi$
$734$	3.26317			0.120446
$735$		0			0
$736$	10.1146			0.372830
$737$			5.51114i			0.203005i
$738$		0			0
$739$	8.20342			0.301768			0.150884	−	0.988551i	$-0.451788\pi$
$739$	8.20342			0.301768			0.150884	+	0.988551i	$0.451788\pi$
$740$	−27.3461	+	3.84208i	−1.00526	+	0.141238i
$741$		0			0
$742$		0			0
$743$			8.33677i			0.305847i	0.988238	+	0.152923i	$0.0488687\pi$
$743$			8.33677i			0.305847i	−0.988238	+	0.152923i	$0.951131\pi$
$744$		0			0
$745$	−6.60348	−	47.0005i	−0.241933	−	1.72196i
$746$	30.4514			1.11490
$747$		0			0
$748$		−	14.3684i		−	0.525361i
$749$		0			0
$750$		0			0
$751$	−25.9180			−0.945760			−0.472880	−	0.881127i	$-0.656786\pi$
$751$	−25.9180			−0.945760			−0.472880	+	0.881127i	$0.656786\pi$
$752$			12.7110i			0.463523i
$753$		0			0
$754$	9.24443			0.336662
$755$	5.24443	+	37.3274i	0.190864	+	1.35848i
$756$		0			0
$757$			8.94025i			0.324939i	0.986714	+	0.162470i	$0.0519459\pi$
$757$			8.94025i			0.324939i	−0.986714	+	0.162470i	$0.948054\pi$
$758$		−	9.24443i		−	0.335773i
$759$		0			0
$760$	−3.86665	+	0.543257i	−0.140258	+	0.0197060i
$761$	−0.825636			−0.0299293			−0.0149646	−	0.999888i	$-0.504764\pi$
$761$	−0.825636			−0.0299293			−0.0149646	+	0.999888i	$0.504764\pi$
$762$		0			0
$763$		0			0
$764$	0.793040			0.0286912
$765$		0			0
$766$	−15.9625			−0.576750
$767$		−	90.6548i		−	3.27336i
$768$		0			0
$769$	21.2257			0.765418			0.382709	−	0.923869i	$-0.374991\pi$
$769$	21.2257			0.765418			0.382709	+	0.923869i	$0.374991\pi$
$770$		0			0
$771$		0			0
$772$			37.2444i			1.34046i
$773$		−	29.4893i		−	1.06066i	−0.847792	−	0.530329i	$-0.822068\pi$
$773$		−	29.4893i		−	1.06066i	0.847792	−	0.530329i	$-0.177932\pi$
$774$		0			0
$775$	24.9175	−	7.14272i	0.895063	−	0.256574i
$776$	−8.58474			−0.308174
$777$		0			0
$778$		−	17.0509i		−	0.611303i
$779$	20.0000			0.716574
$780$		0			0
$781$	4.00000			0.143131
$782$			11.6128i			0.415275i
$783$		0			0
$784$		0			0
$785$	23.0923	−	3.24443i	0.824201	−	0.115799i
$786$		0			0
$787$			34.4514i			1.22806i	0.789283	+	0.614030i	$0.210453\pi$
$787$			34.4514i			1.22806i	−0.789283	+	0.614030i	$0.789547\pi$
$788$			1.92104i			0.0684343i
$789$		0			0
$790$	20.4701	−	2.87601i	0.728294	−	0.102324i
$791$		0			0
$792$		0			0
$793$		−	44.0830i		−	1.56543i
$794$	−4.85145			−0.172172
$795$		0			0
$796$	−14.2707			−0.505812
$797$			18.9175i			0.670092i	0.942202	+	0.335046i	$0.108752\pi$
$797$			18.9175i			0.670092i	−0.942202	+	0.335046i	$0.891248\pi$
$798$		0			0
$799$	−12.2034			−0.431726
$800$	−10.1146	−	35.2850i	−0.357606	−	1.24751i
$801$		0			0
$802$			1.82516i			0.0644486i
$803$		−	3.14272i		−	0.110904i
$804$		0			0
$805$		0			0
$806$	−63.4291			−2.23420
$807$		0			0
$808$		−	1.06376i		−	0.0374230i
$809$	21.2257			0.746256			0.373128	−	0.927780i	$-0.378285\pi$
$809$	21.2257			0.746256			0.373128	+	0.927780i	$0.378285\pi$
$810$		0			0
$811$	21.5081			0.755251			0.377625	−	0.925958i	$-0.376741\pi$
$811$	21.5081			0.755251			0.377625	+	0.925958i	$0.376741\pi$
$812$		0			0
$813$		0			0
$814$	28.9777			1.01567
$815$	−46.1847	+	6.48886i	−1.61778	+	0.227295i
$816$		0			0
$817$		−	24.5334i		−	0.858315i
$818$			60.8671i			2.12817i
$819$		0			0
$820$	4.15610	+	29.5812i	0.145137	+	1.03302i
$821$	46.2034			1.61251			0.806255	−	0.591568i	$-0.201491\pi$
$821$	46.2034			1.61251			0.806255	+	0.591568i	$0.201491\pi$
$822$		0			0
$823$			17.8350i			0.621689i	0.950461	+	0.310845i	$0.100612\pi$
$823$			17.8350i			0.621689i	−0.950461	+	0.310845i	$0.899388\pi$
$824$	6.36842			0.221854
$825$		0			0
$826$		0			0
$827$		−	35.2128i		−	1.22447i	−0.790676	−	0.612234i	$-0.790271\pi$
$827$		−	35.2128i		−	1.22447i	0.790676	−	0.612234i	$-0.209729\pi$
$828$		0			0
$829$	14.3872			0.499686			0.249843	−	0.968286i	$-0.419621\pi$
$829$	14.3872			0.499686			0.249843	+	0.968286i	$0.419621\pi$
$830$	6.87601	+	48.9403i	0.238670	+	1.69874i
$831$		0			0
$832$			30.5116i			1.05780i
$833$		0			0
$834$		0			0
$835$	33.9813	−	4.77430i	1.17597	−	0.165222i
$836$	−7.87955			−0.272520
$837$		0			0
$838$		−	0.894751i		−	0.0309087i
$839$	−1.51114			−0.0521703			−0.0260851	−	0.999660i	$-0.508304\pi$
$839$	−1.51114			−0.0521703			−0.0260851	+	0.999660i	$0.508304\pi$
$840$		0			0
$841$	−28.4291			−0.980314
$842$			63.9724i			2.20463i
$843$		0			0
$844$	−37.6771			−1.29690
$845$	−8.81288	−	62.7259i	−0.303172	−	2.15784i
$846$		0			0
$847$		0			0
$848$			42.3654i			1.45483i
$849$		0			0
$850$	40.5116	−	11.6128i	1.38954	−	0.398317i
$851$	−10.4889			−0.359554
$852$		0			0
$853$		−	15.4064i		−	0.527504i	−0.964591	−	0.263752i	$-0.915040\pi$
$853$		−	15.4064i		−	0.527504i	0.964591	−	0.263752i	$-0.0849600\pi$
$854$		0			0
$855$		0			0
$856$	1.26900			0.0433734
$857$			19.8578i			0.678328i	0.940727	+	0.339164i	$0.110144\pi$
$857$			19.8578i			0.678328i	−0.940727	+	0.339164i	$0.889856\pi$
$858$		0			0
$859$	2.42864			0.0828641			0.0414321	−	0.999141i	$-0.486808\pi$
$859$	2.42864			0.0828641			0.0414321	+	0.999141i	$0.486808\pi$
$860$	36.2864	−	5.09817i	1.23736	−	0.173846i
$861$		0			0
$862$			22.2953i			0.759380i
$863$		−	39.2958i		−	1.33764i	−0.743423	−	0.668822i	$-0.766799\pi$
$863$		−	39.2958i		−	1.33764i	0.743423	−	0.668822i	$-0.233201\pi$
$864$		0			0
$865$	−4.56199	+	0.640951i	−0.155112	+	0.0217930i
$866$	0.114617			0.00389485
$867$		0			0
$868$		0			0
$869$	−9.71456			−0.329544
$870$		0			0
$871$	17.7146			0.600235
$872$			4.03566i			0.136665i
$873$		0			0
$874$	6.36842			0.215415
$875$		0			0
$876$		0			0
$877$		−	56.2864i		−	1.90066i	−0.311249	−	0.950328i	$-0.600747\pi$
$877$		−	56.2864i		−	1.90066i	0.311249	−	0.950328i	$-0.399253\pi$
$878$			42.6865i			1.44060i
$879$		0			0
$880$	2.87019	+	20.4286i	0.0967539	+	0.688649i
$881$	−2.33677			−0.0787279			−0.0393640	−	0.999225i	$-0.512533\pi$
$881$	−2.33677			−0.0787279			−0.0393640	+	0.999225i	$0.512533\pi$
$882$		0			0
$883$		−	33.7146i		−	1.13459i	−0.823516	−	0.567293i	$-0.807991\pi$
$883$		−	33.7146i		−	1.13459i	0.823516	−	0.567293i	$-0.192009\pi$
$884$	−46.1847			−1.55336
$885$		0			0
$886$	45.5812			1.53133
$887$			47.8992i			1.60830i	0.594427	+	0.804150i	$0.297379\pi$
$887$			47.8992i			1.60830i	−0.594427	+	0.804150i	$0.702621\pi$
$888$		0			0
$889$		0			0
$890$	−19.4795	+	2.73683i	−0.652954	+	0.0917388i
$891$		0			0
$892$		−	24.6994i		−	0.826996i
$893$			6.69228i			0.223949i
$894$		0			0
$895$	3.11108	+	22.1432i	0.103992	+	0.740165i
$896$		0			0
$897$		0			0
$898$		−	56.0098i		−	1.86907i
$899$	−3.91703			−0.130640
$900$		0			0
$901$	−40.6735			−1.35503
$902$		−	31.3461i		−	1.04371i
$903$		0			0
$904$	8.11462			0.269888
$905$	3.76494	+	26.7971i	0.125151	+	0.890764i
$906$		0			0
$907$			23.7591i			0.788908i	0.918916	+	0.394454i	$0.129066\pi$
$907$			23.7591i			0.788908i	−0.918916	+	0.394454i	$0.870934\pi$
$908$		−	23.3087i		−	0.773525i
$909$		0			0
$910$		0			0
$911$	−22.9403			−0.760045			−0.380022	−	0.924977i	$-0.624084\pi$
$911$	−22.9403			−0.760045			−0.380022	+	0.924977i	$0.624084\pi$
$912$		0			0
$913$		−	23.2257i		−	0.768658i
$914$	5.98126			0.197843
$915$		0			0
$916$	9.10525			0.300846
$917$		0			0
$918$		0			0
$919$	−16.9777			−0.560043			−0.280022	−	0.959994i	$-0.590342\pi$
$919$	−16.9777			−0.560043			−0.280022	+	0.959994i	$0.590342\pi$
$920$	−0.308193	−	2.19358i	−0.0101608	−	0.0723201i
$921$		0			0
$922$			6.42864i			0.211716i
$923$		−	12.8573i		−	0.423202i
$924$		0			0
$925$	10.4889	+	36.5906i	0.344872	+	1.20309i
$926$	39.6958			1.30449
$927$		0			0
$928$			5.54680i			0.182082i
$929$	−39.3403			−1.29071			−0.645357	−	0.763881i	$-0.723291\pi$
$929$	−39.3403			−1.29071			−0.645357	+	0.763881i	$0.723291\pi$
$930$		0			0
$931$		0			0
$932$			37.7748i			1.23735i
$933$		0			0
$934$	27.3461			0.894793
$935$	−19.6128	+	2.75557i	−0.641409	+	0.0901167i
$936$		0			0
$937$			17.7748i			0.580677i	0.956924	+	0.290338i	$0.0937679\pi$
$937$			17.7748i			0.580677i	−0.956924	+	0.290338i	$0.906232\pi$
$938$		0			0
$939$		0			0
$940$	−9.89829	+	1.39069i	−0.322847	+	0.0453594i
$941$	35.5812			1.15991			0.579957	−	0.814647i	$-0.303069\pi$
$941$	35.5812			1.15991			0.579957	+	0.814647i	$0.303069\pi$
$942$		0			0
$943$			11.3461i			0.369481i
$944$	65.0490			2.11717
$945$		0			0
$946$	−38.4514			−1.25016
$947$		−	30.5018i		−	0.991174i	−0.868558	−	0.495587i	$-0.834953\pi$
$947$		−	30.5018i		−	0.991174i	0.868558	−	0.495587i	$-0.165047\pi$
$948$		0			0
$949$	−10.1017			−0.327915
$950$	−6.36842	−	22.2163i	−0.206619	−	0.720793i
$951$		0			0
$952$		0			0
$953$		−	51.1655i		−	1.65741i	−0.559684	−	0.828706i	$-0.689077\pi$
$953$		−	51.1655i		−	1.65741i	0.559684	−	0.828706i	$-0.310923\pi$
$954$		0			0
$955$	−0.152089	−	1.08250i	−0.00492148	−	0.0350288i
$956$	13.7708			0.445378
$957$		0			0
$958$			12.1204i			0.391594i
$959$		0			0
$960$		0			0
$961$	−4.12399			−0.133032
$962$		−	93.1437i		−	3.00307i
$963$		0			0
$964$	−11.7520			−0.378507
$965$	50.8385	−	7.14272i	1.63655	−	0.229932i
$966$		0			0
$967$			47.8992i			1.54034i	0.637841	+	0.770168i	$0.279828\pi$
$967$			47.8992i			1.54034i	−0.637841	+	0.770168i	$0.720172\pi$
$968$			5.03303i			0.161768i
$969$		0			0
$970$	−7.06959	−	50.3180i	−0.226991	−	1.61561i
$971$	40.6735			1.30528			0.652638	−	0.757670i	$-0.273662\pi$
$971$	40.6735			1.30528			0.652638	+	0.757670i	$0.273662\pi$
$972$		0			0
$973$		0			0
$974$	−32.9777			−1.05667
$975$		0			0
$976$	31.6316			1.01250
$977$			27.4893i			0.879462i	0.898130	+	0.439731i	$0.144926\pi$
$977$			27.4893i			0.879462i	−0.898130	+	0.439731i	$0.855074\pi$
$978$		0			0
$979$	9.24443			0.295453
$980$		0			0
$981$		0			0
$982$			3.80642i			0.121468i
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$		0			0
$985$	2.62222	−	0.368416i	0.0835507	−	0.0117387i
$986$	−6.36842			−0.202812
$987$		0			0
$988$			25.3274i			0.805772i
$989$	13.9180			0.442566
$990$		0			0
$991$	−34.6923			−1.10204			−0.551018	−	0.834493i	$-0.685761\pi$
$991$	−34.6923			−1.10204			−0.551018	+	0.834493i	$0.685761\pi$
$992$		−	38.0584i		−	1.20836i
$993$		0			0
$994$		0			0
$995$	2.73683	+	19.4795i	0.0867634	+	0.617541i
$996$		0			0
$997$			28.6766i			0.908197i	0.890951	+	0.454099i	$0.150039\pi$
$997$			28.6766i			0.908197i	−0.890951	+	0.454099i	$0.849961\pi$
$998$			44.4327i			1.40649i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2205.2.d.l.1324.2		6
3.2	odd	2		735.2.d.b.589.5		6
5.4	even	2	inner	2205.2.d.l.1324.5		6
7.6	odd	2		315.2.d.e.64.2		6
15.2	even	4		3675.2.a.bj.1.1		3
15.8	even	4		3675.2.a.bi.1.3		3
15.14	odd	2		735.2.d.b.589.2		6
21.2	odd	6		735.2.q.f.214.5		12
21.5	even	6		735.2.q.e.214.5		12
21.11	odd	6		735.2.q.f.79.2		12
21.17	even	6		735.2.q.e.79.2		12
21.20	even	2		105.2.d.b.64.5	yes	6
28.27	even	2		5040.2.t.v.1009.3		6
35.13	even	4		1575.2.a.x.1.1		3
35.27	even	4		1575.2.a.w.1.3		3
35.34	odd	2		315.2.d.e.64.5		6
84.83	odd	2		1680.2.t.k.1009.5		6
105.44	odd	6		735.2.q.f.214.2		12
105.59	even	6		735.2.q.e.79.5		12
105.62	odd	4		525.2.a.k.1.1		3
105.74	odd	6		735.2.q.f.79.5		12
105.83	odd	4		525.2.a.j.1.3		3
105.89	even	6		735.2.q.e.214.2		12
105.104	even	2		105.2.d.b.64.2	✓	6
140.139	even	2		5040.2.t.v.1009.4		6
420.83	even	4		8400.2.a.dg.1.3		3
420.167	even	4		8400.2.a.dj.1.1		3
420.419	odd	2		1680.2.t.k.1009.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.d.b.64.2	✓	6	105.104	even	2
105.2.d.b.64.5	yes	6	21.20	even	2
315.2.d.e.64.2		6	7.6	odd	2
315.2.d.e.64.5		6	35.34	odd	2
525.2.a.j.1.3		3	105.83	odd	4
525.2.a.k.1.1		3	105.62	odd	4
735.2.d.b.589.2		6	15.14	odd	2
735.2.d.b.589.5		6	3.2	odd	2
735.2.q.e.79.2		12	21.17	even	6
735.2.q.e.79.5		12	105.59	even	6
735.2.q.e.214.2		12	105.89	even	6
735.2.q.e.214.5		12	21.5	even	6
735.2.q.f.79.2		12	21.11	odd	6
735.2.q.f.79.5		12	105.74	odd	6
735.2.q.f.214.2		12	105.44	odd	6
735.2.q.f.214.5		12	21.2	odd	6
1575.2.a.w.1.3		3	35.27	even	4
1575.2.a.x.1.1		3	35.13	even	4
1680.2.t.k.1009.2		6	420.419	odd	2
1680.2.t.k.1009.5		6	84.83	odd	2
2205.2.d.l.1324.2		6	1.1	even	1	trivial
2205.2.d.l.1324.5		6	5.4	even	2	inner
3675.2.a.bi.1.3		3	15.8	even	4
3675.2.a.bj.1.1		3	15.2	even	4
5040.2.t.v.1009.3		6	28.27	even	2
5040.2.t.v.1009.4		6	140.139	even	2
8400.2.a.dg.1.3		3	420.83	even	4
8400.2.a.dj.1.1		3	420.167	even	4

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:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.90321i q^{2} -1.62222 q^{4} +(0.311108 + 2.21432i) q^{5} -0.719004i q^{8} +O(q^{10})\)	\(q-1.90321i q^{2} -1.62222 q^{4} +(0.311108 + 2.21432i) q^{5} -0.719004i q^{8} +(4.21432 - 0.592104i) q^{10} -2.00000 q^{11} +6.42864i q^{13} -4.61285 q^{16} -4.42864i q^{17} -2.42864 q^{19} +(-0.504684 - 3.59210i) q^{20} +3.80642i q^{22} -1.37778i q^{23} +(-4.80642 + 1.37778i) q^{25} +12.2351 q^{26} +0.755569 q^{29} -5.18421 q^{31} +7.34122i q^{32} -8.42864 q^{34} -7.61285i q^{37} +4.62222i q^{38} +(1.59210 - 0.223688i) q^{40} -8.23506 q^{41} +10.1017i q^{43} +3.24443 q^{44} -2.62222 q^{46} -2.75557i q^{47} +(2.62222 + 9.14764i) q^{50} -10.4286i q^{52} -9.18421i q^{53} +(-0.622216 - 4.42864i) q^{55} -1.43801i q^{58} -14.1017 q^{59} -6.85728 q^{61} +9.86665i q^{62} +4.74620 q^{64} +(-14.2351 + 2.00000i) q^{65} -2.75557i q^{67} +7.18421i q^{68} -2.00000 q^{71} +1.57136i q^{73} -14.4889 q^{74} +3.93978 q^{76} +4.85728 q^{79} +(-1.43509 - 10.2143i) q^{80} +15.6731i q^{82} +11.6128i q^{83} +(9.80642 - 1.37778i) q^{85} +19.2257 q^{86} +1.43801i q^{88} -4.62222 q^{89} +2.23506i q^{92} -5.24443 q^{94} +(-0.755569 - 5.37778i) q^{95} -11.9398i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4} + 2 q^{5}+O(q^{10}) \) 6 * q - 10 * q^4 + 2 * q^5	\( 6 q - 10 q^{4} + 2 q^{5} + 12 q^{10} - 12 q^{11} + 26 q^{16} + 12 q^{19} - 30 q^{20} - 2 q^{25} + 20 q^{26} + 4 q^{29} - 4 q^{31} - 24 q^{34} - 4 q^{40} + 4 q^{41} + 20 q^{44} - 16 q^{46} + 16 q^{50} - 4 q^{55} - 32 q^{59} + 12 q^{61} - 26 q^{64} - 32 q^{65} - 12 q^{71} - 88 q^{74} - 4 q^{76} - 24 q^{79} + 46 q^{80} + 32 q^{85} + 8 q^{86} - 28 q^{89} - 32 q^{94} - 4 q^{95}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^5 + 12 * q^10 - 12 * q^11 + 26 * q^16 + 12 * q^19 - 30 * q^20 - 2 * q^25 + 20 * q^26 + 4 * q^29 - 4 * q^31 - 24 * q^34 - 4 * q^40 + 4 * q^41 + 20 * q^44 - 16 * q^46 + 16 * q^50 - 4 * q^55 - 32 * q^59 + 12 * q^61 - 26 * q^64 - 32 * q^65 - 12 * q^71 - 88 * q^74 - 4 * q^76 - 24 * q^79 + 46 * q^80 + 32 * q^85 + 8 * q^86 - 28 * q^89 - 32 * q^94 - 4 * q^95

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