LMFDB - Embedded newform 585.2.b.g.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(181,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("585.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.b (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5089536.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 16x^2 - 24*x + 18
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.1
Root			$1.66044 + 1.66044i$ of defining polynomial
Character	$\chi$	$=$	585.181
Dual form			585.2.b.g.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51414i q^{2} -4.32088 q^{4} +1.00000i q^{5} -3.32088i q^{7} +5.83502i q^{8} +O(q^{10})$	\(q-2.51414i q^{2} -4.32088 q^{4} +1.00000i q^{5} -3.32088i q^{7} +5.83502i q^{8} +2.51414 q^{10} -2.83502i q^{11} +(-3.51414 + 0.806748i) q^{13} -8.34916 q^{14} +6.02827 q^{16} -6.64177 q^{17} +2.19325i q^{19} -4.32088i q^{20} -7.12763 q^{22} -0.485863 q^{23} -1.00000 q^{25} +(2.02827 + 8.83502i) q^{26} +14.3492i q^{28} +3.32088 q^{29} +3.80675i q^{31} -3.48586i q^{32} +16.6983i q^{34} +3.32088 q^{35} -9.32088i q^{37} +5.51414 q^{38} -5.83502 q^{40} +1.61350i q^{41} +0.872368 q^{43} +12.2498i q^{44} +1.22153i q^{46} -3.32088i q^{47} -4.02827 q^{49} +2.51414i q^{50} +(15.1842 - 3.48586i) q^{52} -11.6700 q^{53} +2.83502 q^{55} +19.3774 q^{56} -8.34916i q^{58} -8.83502i q^{59} -3.70739 q^{61} +9.57068 q^{62} +3.29261 q^{64} +(-0.806748 - 3.51414i) q^{65} +4.29261i q^{67} +28.6983 q^{68} -8.34916i q^{70} -2.19325i q^{71} -12.7357i q^{73} -23.4340 q^{74} -9.47679i q^{76} -9.41478 q^{77} +0.585221 q^{79} +6.02827i q^{80} +4.05655 q^{82} -7.70739i q^{83} -6.64177i q^{85} -2.19325i q^{86} +16.5424 q^{88} +3.41478i q^{89} +(2.67912 + 11.6700i) q^{91} +2.09936 q^{92} -8.34916 q^{94} -2.19325 q^{95} +0.641769i q^{97} +10.1276i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{4}+O(q^{10}) $ 6 * q - 10 * q^4	$ 6 q - 10 q^{4} + 2 q^{10} - 8 q^{13} - 8 q^{14} + 10 q^{16} - 8 q^{17} - 24 q^{22} - 16 q^{23} - 6 q^{25} - 14 q^{26} + 4 q^{29} + 4 q^{35} + 20 q^{38} - 6 q^{40} + 24 q^{43} + 2 q^{49} + 20 q^{52} - 12 q^{53} - 12 q^{55} + 48 q^{56} - 12 q^{61} - 8 q^{62} + 30 q^{64} - 2 q^{65} + 88 q^{68} - 20 q^{74} - 36 q^{77} + 24 q^{79} - 28 q^{82} + 60 q^{88} + 32 q^{91} + 20 q^{92} - 8 q^{94} - 16 q^{95}+O(q^{100}) $ 6 * q - 10 * q^4 + 2 * q^10 - 8 * q^13 - 8 * q^14 + 10 * q^16 - 8 * q^17 - 24 * q^22 - 16 * q^23 - 6 * q^25 - 14 * q^26 + 4 * q^29 + 4 * q^35 + 20 * q^38 - 6 * q^40 + 24 * q^43 + 2 * q^49 + 20 * q^52 - 12 * q^53 - 12 * q^55 + 48 * q^56 - 12 * q^61 - 8 * q^62 + 30 * q^64 - 2 * q^65 + 88 * q^68 - 20 * q^74 - 36 * q^77 + 24 * q^79 - 28 * q^82 + 60 * q^88 + 32 * q^91 + 20 * q^92 - 8 * q^94 - 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$		−	2.51414i		−	1.77776i	−0.458137	−	0.888882i	$-0.651483\pi$
$2$		−	2.51414i		−	1.77776i	0.458137	−	0.888882i	$-0.348517\pi$
$3$		0			0
$3$		0			0
$4$	−4.32088			−2.16044
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$		−	3.32088i		−	1.25518i	−0.778545	−	0.627588i	$-0.784042\pi$
$7$		−	3.32088i		−	1.25518i	0.778545	−	0.627588i	$-0.215958\pi$
$8$			5.83502i			2.06299i
$9$		0			0
$10$	2.51414			0.795040
$11$		−	2.83502i		−	0.854791i	−0.904065	−	0.427396i	$-0.859431\pi$
$11$		−	2.83502i		−	0.854791i	0.904065	−	0.427396i	$-0.140569\pi$
$12$		0			0
$13$	−3.51414	+	0.806748i	−0.974646	+	0.223752i
$13$	−3.51414	+	0.806748i	−0.974646	+	0.223752i
$14$	−8.34916			−2.23141
$15$		0			0
$16$	6.02827			1.50707
$17$	−6.64177			−1.61087			−0.805433	−	0.592687i	$-0.798067\pi$
$17$	−6.64177			−1.61087			−0.805433	+	0.592687i	$0.798067\pi$
$18$		0			0
$19$			2.19325i			0.503167i	0.967836	+	0.251583i	$0.0809512\pi$
$19$			2.19325i			0.503167i	−0.967836	+	0.251583i	$0.919049\pi$
$20$		−	4.32088i		−	0.966179i
$21$		0			0
$22$	−7.12763			−1.51962
$23$	−0.485863			−0.101309			−0.0506547	−	0.998716i	$-0.516131\pi$
$23$	−0.485863			−0.101309			−0.0506547	+	0.998716i	$0.516131\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.02827	+	8.83502i	0.397777	+	1.73269i
$27$		0			0
$28$			14.3492i			2.71174i
$29$	3.32088			0.616673			0.308336	−	0.951277i	$-0.400228\pi$
$29$	3.32088			0.616673			0.308336	+	0.951277i	$0.400228\pi$
$30$		0			0
$31$			3.80675i			0.683712i	0.939752	+	0.341856i	$0.111056\pi$
$31$			3.80675i			0.683712i	−0.939752	+	0.341856i	$0.888944\pi$
$32$		−	3.48586i		−	0.616219i
$33$		0			0
$34$			16.6983i			2.86374i
$35$	3.32088			0.561332
$36$		0			0
$37$		−	9.32088i		−	1.53234i	−0.642636	−	0.766172i	$-0.722159\pi$
$37$		−	9.32088i		−	1.53234i	0.642636	−	0.766172i	$-0.277841\pi$
$38$	5.51414			0.894511
$39$		0			0
$40$	−5.83502			−0.922598
$41$			1.61350i			0.251986i	0.992031	+	0.125993i	$0.0402116\pi$
$41$			1.61350i			0.251986i	−0.992031	+	0.125993i	$0.959788\pi$
$42$		0			0
$43$	0.872368			0.133035			0.0665174	−	0.997785i	$-0.478811\pi$
$43$	0.872368			0.133035			0.0665174	+	0.997785i	$0.478811\pi$
$44$			12.2498i			1.84673i
$45$		0			0
$46$			1.22153i			0.180104i
$47$		−	3.32088i		−	0.484401i	−0.970226	−	0.242200i	$-0.922131\pi$
$47$		−	3.32088i		−	0.484401i	0.970226	−	0.242200i	$-0.0778691\pi$
$48$		0			0
$49$	−4.02827			−0.575468
$50$			2.51414i			0.355553i
$51$		0			0
$52$	15.1842	−	3.48586i	2.10567	−	0.483402i
$53$	−11.6700			−1.60300			−0.801502	−	0.597992i	$-0.795965\pi$
$53$	−11.6700			−1.60300			−0.801502	+	0.597992i	$0.795965\pi$
$54$		0			0
$55$	2.83502			0.382274
$56$	19.3774			2.58942
$57$		0			0
$58$		−	8.34916i		−	1.09630i
$59$		−	8.83502i		−	1.15022i	−0.818075	−	0.575111i	$-0.804959\pi$
$59$		−	8.83502i		−	1.15022i	0.818075	−	0.575111i	$-0.195041\pi$
$60$		0			0
$61$	−3.70739			−0.474683			−0.237341	−	0.971426i	$-0.576276\pi$
$61$	−3.70739			−0.474683			−0.237341	+	0.971426i	$0.576276\pi$
$62$	9.57068			1.21548
$63$		0			0
$64$	3.29261			0.411576
$65$	−0.806748	−	3.51414i	−0.100065	−	0.435875i
$66$		0			0
$67$			4.29261i			0.524426i	0.965010	+	0.262213i	$0.0844523\pi$
$67$			4.29261i			0.524426i	−0.965010	+	0.262213i	$0.915548\pi$
$68$	28.6983			3.48018
$69$		0			0
$70$		−	8.34916i		−	0.997915i
$71$		−	2.19325i		−	0.260291i	−0.991495	−	0.130146i	$-0.958456\pi$
$71$		−	2.19325i		−	0.260291i	0.991495	−	0.130146i	$-0.0415445\pi$
$72$		0			0
$73$		−	12.7357i		−	1.49060i	−0.666731	−	0.745298i	$-0.732307\pi$
$73$		−	12.7357i		−	1.49060i	0.666731	−	0.745298i	$-0.267693\pi$
$74$	−23.4340			−2.72414
$75$		0			0
$76$		−	9.47679i		−	1.08706i
$77$	−9.41478			−1.07291
$78$		0			0
$79$	0.585221			0.0658425			0.0329213	−	0.999458i	$-0.489519\pi$
$79$	0.585221			0.0658425			0.0329213	+	0.999458i	$0.489519\pi$
$80$			6.02827i			0.673982i
$81$		0			0
$82$	4.05655			0.447971
$83$		−	7.70739i		−	0.845996i	−0.906131	−	0.422998i	$-0.860978\pi$
$83$		−	7.70739i		−	0.845996i	0.906131	−	0.422998i	$-0.139022\pi$
$84$		0			0
$85$		−	6.64177i		−	0.720401i
$86$		−	2.19325i		−	0.236504i
$87$		0			0
$88$	16.5424			1.76343
$89$			3.41478i			0.361966i	0.983486	+	0.180983i	$0.0579279\pi$
$89$			3.41478i			0.361966i	−0.983486	+	0.180983i	$0.942072\pi$
$90$		0			0
$91$	2.67912	+	11.6700i	0.280848	+	1.22335i
$92$	2.09936			0.218873
$93$		0			0
$94$	−8.34916			−0.861150
$95$	−2.19325			−0.225023
$96$		0			0
$97$			0.641769i			0.0651618i	0.999469	+	0.0325809i	$0.0103727\pi$
$97$			0.641769i			0.0651618i	−0.999469	+	0.0325809i	$0.989627\pi$
$98$			10.1276i			1.02305i
$99$		0			0
$100$	4.32088			0.432088
$101$	6.97173			0.693713			0.346856	−	0.937918i	$-0.387249\pi$
$101$	6.97173			0.693713			0.346856	+	0.937918i	$0.387249\pi$
$102$		0			0
$103$	7.18418			0.707878			0.353939	−	0.935268i	$-0.384842\pi$
$103$	7.18418			0.707878			0.353939	+	0.935268i	$0.384842\pi$
$104$	−4.70739	−	20.5051i	−0.461598	−	2.01069i
$105$		0			0
$106$			29.3401i			2.84976i
$107$	9.57068			0.925233			0.462617	−	0.886558i	$-0.346911\pi$
$107$	9.57068			0.925233			0.462617	+	0.886558i	$0.346911\pi$
$108$		0			0
$109$		−	10.6983i		−	1.02471i	−0.858773	−	0.512356i	$-0.828773\pi$
$109$		−	10.6983i		−	1.02471i	0.858773	−	0.512356i	$-0.171227\pi$
$110$		−	7.12763i		−	0.679593i
$111$		0			0
$112$		−	20.0192i		−	1.89164i
$113$	3.22699			0.303570			0.151785	−	0.988414i	$-0.451498\pi$
$113$	3.22699			0.303570			0.151785	+	0.988414i	$0.451498\pi$
$114$		0			0
$115$		−	0.485863i		−	0.0453070i
$116$	−14.3492			−1.33229
$117$		0			0
$118$	−22.2125			−2.04482
$119$			22.0565i			2.02192i
$120$		0			0
$121$	2.96265			0.269332
$122$			9.32088i			0.843873i
$123$		0			0
$124$		−	16.4485i		−	1.47712i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$	−5.90064			−0.523597			−0.261799	−	0.965123i	$-0.584316\pi$
$127$	−5.90064			−0.523597			−0.261799	+	0.965123i	$0.584316\pi$
$128$		−	15.2498i		−	1.34790i
$129$		0			0
$130$	−8.83502	+	2.02827i	−0.774883	+	0.177891i
$131$	−3.41478			−0.298351			−0.149175	−	0.988811i	$-0.547662\pi$
$131$	−3.41478			−0.298351			−0.149175	+	0.988811i	$0.547662\pi$
$132$		0			0
$133$	7.28354			0.631563
$134$	10.7922			0.932305
$135$		0			0
$136$		−	38.7549i		−	3.32320i
$137$		−	15.0848i		−	1.28878i	−0.764696	−	0.644392i	$-0.777111\pi$
$137$		−	15.0848i		−	1.28878i	0.764696	−	0.644392i	$-0.222889\pi$
$138$		0			0
$139$	−20.6983			−1.75561			−0.877804	−	0.479020i	$-0.840992\pi$
$139$	−20.6983			−1.75561			−0.877804	+	0.479020i	$0.840992\pi$
$140$	−14.3492			−1.21273
$141$		0			0
$142$	−5.51414			−0.462736
$143$	2.28715	+	9.96265i	0.191261	+	0.833119i
$144$		0			0
$145$			3.32088i			0.275784i
$146$	−32.0192			−2.64993
$147$		0			0
$148$			40.2745i			3.31054i
$149$		−	0.641769i		−	0.0525758i	−0.999654	−	0.0262879i	$-0.991631\pi$
$149$		−	0.641769i		−	0.0525758i	0.999654	−	0.0262879i	$-0.00836866\pi$
$150$		0			0
$151$		−	16.6363i		−	1.35384i	−0.736055	−	0.676922i	$-0.763314\pi$
$151$		−	16.6363i		−	1.35384i	0.736055	−	0.676922i	$-0.236686\pi$
$152$	−12.7977			−1.03803
$153$		0			0
$154$			23.6700i			1.90739i
$155$	−3.80675			−0.305765
$156$		0			0
$157$	10.2553			0.818459			0.409230	−	0.912431i	$-0.365798\pi$
$157$	10.2553			0.818459			0.409230	+	0.912431i	$0.365798\pi$
$158$		−	1.47133i		−	0.117052i
$159$		0			0
$160$	3.48586			0.275582
$161$			1.61350i			0.127161i
$162$		0			0
$163$			1.37743i			0.107889i	0.998544	+	0.0539444i	$0.0171794\pi$
$163$			1.37743i			0.107889i	−0.998544	+	0.0539444i	$0.982821\pi$
$164$		−	6.97173i		−	0.544400i
$165$		0			0
$166$	−19.3774			−1.50398
$167$			17.5761i			1.36008i	0.733174	+	0.680042i	$0.238038\pi$
$167$			17.5761i			1.36008i	−0.733174	+	0.680042i	$0.761962\pi$
$168$		0			0
$169$	11.6983	−	5.67004i	0.899871	−	0.436157i
$170$	−16.6983			−1.28070
$171$		0			0
$172$	−3.76940			−0.287414
$173$	6.31181			0.479878			0.239939	−	0.970788i	$-0.422873\pi$
$173$	6.31181			0.479878			0.239939	+	0.970788i	$0.422873\pi$
$174$		0			0
$175$			3.32088i			0.251035i
$176$		−	17.0903i		−	1.28823i
$177$		0			0
$178$	8.58522			0.643490
$179$	−9.08482			−0.679031			−0.339516	−	0.940600i	$-0.610263\pi$
$179$	−9.08482			−0.679031			−0.339516	+	0.940600i	$0.610263\pi$
$180$		0			0
$181$	−12.0192			−0.893380			−0.446690	−	0.894689i	$-0.647397\pi$
$181$	−12.0192			−0.893380			−0.446690	+	0.894689i	$0.647397\pi$
$182$	29.3401	−	6.73566i	2.17483	−	0.499281i
$183$		0			0
$184$		−	2.83502i		−	0.209001i
$185$	9.32088			0.685285
$186$		0			0
$187$			18.8296i			1.37695i
$188$			14.3492i			1.04652i
$189$		0			0
$190$			5.51414i			0.400038i
$191$	−13.2835			−0.961163			−0.480582	−	0.876950i	$-0.659574\pi$
$191$	−13.2835			−0.961163			−0.480582	+	0.876950i	$0.659574\pi$
$192$		0			0
$193$		−	16.3684i		−	1.17822i	−0.808053	−	0.589110i	$-0.799478\pi$
$193$		−	16.3684i		−	1.17822i	0.808053	−	0.589110i	$-0.200522\pi$
$194$	1.61350			0.115842
$195$		0			0
$196$	17.4057			1.24326
$197$		−	14.8970i		−	1.06137i	−0.847569	−	0.530685i	$-0.821935\pi$
$197$		−	14.8970i		−	1.06137i	0.847569	−	0.530685i	$-0.178065\pi$
$198$		0			0
$199$	16.3118			1.15631			0.578157	−	0.815926i	$-0.303772\pi$
$199$	16.3118			1.15631			0.578157	+	0.815926i	$0.303772\pi$
$200$		−	5.83502i		−	0.412598i
$201$		0			0
$202$		−	17.5279i		−	1.23326i
$203$		−	11.0283i		−	0.774033i
$204$		0			0
$205$	−1.61350			−0.112691
$206$		−	18.0620i		−	1.25844i
$207$		0			0
$208$	−21.1842	+	4.86330i	−1.46886	+	0.337209i
$209$	6.21792			0.430102
$210$		0			0
$211$	11.8013			0.812434			0.406217	−	0.913777i	$-0.366848\pi$
$211$	11.8013			0.812434			0.406217	+	0.913777i	$0.366848\pi$
$212$	50.4249			3.46320
$213$		0			0
$214$		−	24.0620i		−	1.64485i
$215$			0.872368i			0.0594950i
$216$		0			0
$217$	12.6418			0.858179
$218$	−26.8970			−1.82170
$219$		0			0
$220$	−12.2498			−0.825881
$221$	23.3401	−	5.35823i	1.57002	−	0.360434i
$222$		0			0
$223$		−	20.0192i		−	1.34058i	−0.742097	−	0.670292i	$-0.766169\pi$
$223$		−	20.0192i		−	1.34058i	0.742097	−	0.670292i	$-0.233831\pi$
$224$	−11.5761			−0.773464
$225$		0			0
$226$		−	8.11310i		−	0.539675i
$227$			22.4623i			1.49087i	0.666577	+	0.745436i	$0.267759\pi$
$227$			22.4623i			1.49087i	−0.666577	+	0.745436i	$0.732241\pi$
$228$		0			0
$229$			10.3684i			0.685160i	0.939489	+	0.342580i	$0.111301\pi$
$229$			10.3684i			0.685160i	−0.939489	+	0.342580i	$0.888699\pi$
$230$	−1.22153			−0.0805451
$231$		0			0
$232$			19.3774i			1.27219i
$233$	11.3582			0.744102			0.372051	−	0.928212i	$-0.378655\pi$
$233$	11.3582			0.744102			0.372051	+	0.928212i	$0.378655\pi$
$234$		0			0
$235$	3.32088			0.216631
$236$			38.1751i			2.48499i
$237$		0			0
$238$	55.4532			3.59450
$239$		−	28.1186i		−	1.81884i	−0.415881	−	0.909419i	$-0.636527\pi$
$239$		−	28.1186i		−	1.81884i	0.415881	−	0.909419i	$-0.363473\pi$
$240$		0			0
$241$			15.0848i			0.971699i	0.874043	+	0.485849i	$0.161490\pi$
$241$			15.0848i			0.971699i	−0.874043	+	0.485849i	$0.838510\pi$
$242$		−	7.44852i		−	0.478809i
$243$		0			0
$244$	16.0192			1.02552
$245$		−	4.02827i		−	0.257357i
$246$		0			0
$247$	−1.76940	−	7.70739i	−0.112584	−	0.490409i
$248$	−22.2125			−1.41049
$249$		0			0
$250$	−2.51414			−0.159008
$251$	1.15951			0.0731879			0.0365940	−	0.999330i	$-0.488349\pi$
$251$	1.15951			0.0731879			0.0365940	+	0.999330i	$0.488349\pi$
$252$		0			0
$253$			1.37743i			0.0865984i
$254$			14.8350i			0.930832i
$255$		0			0
$256$	−31.7549			−1.98468
$257$	−0.829557			−0.0517464			−0.0258732	−	0.999665i	$-0.508237\pi$
$257$	−0.829557			−0.0517464			−0.0258732	+	0.999665i	$0.508237\pi$
$258$		0			0
$259$	−30.9536			−1.92336
$260$	3.48586	+	15.1842i	0.216184	+	0.941683i
$261$		0			0
$262$			8.58522i			0.530397i
$263$	25.6272			1.58024			0.790121	−	0.612950i	$-0.210017\pi$
$263$	25.6272			1.58024			0.790121	+	0.612950i	$0.210017\pi$
$264$		0			0
$265$		−	11.6700i		−	0.716885i
$266$		−	18.3118i		−	1.12277i
$267$		0			0
$268$		−	18.5479i		−	1.13299i
$269$	−5.02827			−0.306579			−0.153290	−	0.988181i	$-0.548987\pi$
$269$	−5.02827			−0.306579			−0.153290	+	0.988181i	$0.548987\pi$
$270$		0			0
$271$			18.8916i			1.14758i	0.819002	+	0.573791i	$0.194528\pi$
$271$			18.8916i			1.14758i	−0.819002	+	0.573791i	$0.805472\pi$
$272$	−40.0384			−2.42768
$273$		0			0
$274$	−37.9253			−2.29115
$275$			2.83502i			0.170958i
$276$		0			0
$277$	−23.7831			−1.42899			−0.714495	−	0.699640i	$-0.753344\pi$
$277$	−23.7831			−1.42899			−0.714495	+	0.699640i	$0.753344\pi$
$278$			52.0384i			3.12106i
$279$		0			0
$280$			19.3774i			1.15802i
$281$			31.5953i			1.88482i	0.334459	+	0.942410i	$0.391446\pi$
$281$			31.5953i			1.88482i	−0.334459	+	0.942410i	$0.608554\pi$
$282$		0			0
$283$	−6.35462			−0.377743			−0.188872	−	0.982002i	$-0.560483\pi$
$283$	−6.35462			−0.377743			−0.188872	+	0.982002i	$0.560483\pi$
$284$			9.47679i			0.562344i
$285$		0			0
$286$	25.0475	−	5.75020i	1.48109	−	0.340016i
$287$	5.35823			0.316286
$288$		0			0
$289$	27.1131			1.59489
$290$	8.34916			0.490279
$291$		0			0
$292$			55.0293i			3.22035i
$293$		−	8.03735i		−	0.469547i	−0.972050	−	0.234773i	$-0.924565\pi$
$293$		−	8.03735i		−	0.469547i	0.972050	−	0.234773i	$-0.0754348\pi$
$294$		0			0
$295$	8.83502			0.514395
$296$	54.3876			3.16121
$297$		0			0
$298$	−1.61350			−0.0934673
$299$	1.70739	−	0.391969i	0.0987409	−	0.0226681i
$300$		0			0
$301$		−	2.89703i		−	0.166982i
$302$	−41.8259			−2.40681
$303$		0			0
$304$			13.2215i			0.758307i
$305$		−	3.70739i		−	0.212284i
$306$		0			0
$307$			15.8205i			0.902923i	0.892291	+	0.451461i	$0.149097\pi$
$307$			15.8205i			0.902923i	−0.892291	+	0.451461i	$0.850903\pi$
$308$	40.6802			2.31797
$309$		0			0
$310$			9.57068i			0.543578i
$311$	24.3118			1.37860			0.689298	−	0.724478i	$-0.257919\pi$
$311$	24.3118			1.37860			0.689298	+	0.724478i	$0.257919\pi$
$312$		0			0
$313$	−11.2270			−0.634587			−0.317294	−	0.948327i	$-0.602774\pi$
$313$	−11.2270			−0.634587			−0.317294	+	0.948327i	$0.602774\pi$
$314$		−	25.7831i		−	1.45503i
$315$		0			0
$316$	−2.52867			−0.142249
$317$			16.1504i			0.907099i	0.891231	+	0.453550i	$0.149843\pi$
$317$			16.1504i			0.907099i	−0.891231	+	0.453550i	$0.850157\pi$
$318$		0			0
$319$		−	9.41478i		−	0.527126i
$320$			3.29261i			0.184063i
$321$		0			0
$322$	4.05655			0.226063
$323$		−	14.5671i		−	0.810534i
$324$		0			0
$325$	3.51414	−	0.806748i	0.194929	−	0.0447503i
$326$	3.46305			0.191801
$327$		0			0
$328$	−9.41478			−0.519844
$329$	−11.0283			−0.608008
$330$		0			0
$331$			30.0620i			1.65236i	0.563408	+	0.826179i	$0.309490\pi$
$331$			30.0620i			1.65236i	−0.563408	+	0.826179i	$0.690510\pi$
$332$			33.3027i			1.82773i
$333$		0			0
$334$	44.1888			2.41791
$335$	−4.29261			−0.234530
$336$		0			0
$337$	17.4713			0.951724			0.475862	−	0.879520i	$-0.342136\pi$
$337$	17.4713			0.951724			0.475862	+	0.879520i	$0.342136\pi$
$338$	−14.2553	−	29.4112i	−0.775384	−	1.59976i
$339$		0			0
$340$			28.6983i			1.55638i
$341$	10.7922			0.584431
$342$		0			0
$343$		−	9.86876i		−	0.532863i
$344$			5.09029i			0.274450i
$345$		0			0
$346$		−	15.8688i		−	0.853110i
$347$	−33.2407			−1.78446			−0.892228	−	0.451585i	$-0.850859\pi$
$347$	−33.2407			−1.78446			−0.892228	+	0.451585i	$0.850859\pi$
$348$		0			0
$349$			20.8970i			1.11859i	0.828968	+	0.559296i	$0.188929\pi$
$349$			20.8970i			1.11859i	−0.828968	+	0.559296i	$0.811071\pi$
$350$	8.34916			0.446281
$351$		0			0
$352$	−9.88250			−0.526739
$353$		−	12.5479i		−	0.667856i	−0.942599	−	0.333928i	$-0.891626\pi$
$353$		−	12.5479i		−	0.667856i	0.942599	−	0.333928i	$-0.108374\pi$
$354$		0			0
$355$	2.19325			0.116406
$356$		−	14.7549i		−	0.782006i
$357$		0			0
$358$			22.8405i			1.20716i
$359$		−	2.97719i		−	0.157130i	−0.996909	−	0.0785650i	$-0.974966\pi$
$359$		−	2.97719i		−	0.157130i	0.996909	−	0.0785650i	$-0.0250338\pi$
$360$		0			0
$361$	14.1896			0.746823
$362$			30.2179i			1.58822i
$363$		0			0
$364$	−11.5761	−	50.4249i	−0.606755	−	2.64298i
$365$	12.7357			0.666615
$366$		0			0
$367$	−30.5990			−1.59725			−0.798626	−	0.601827i	$-0.794440\pi$
$367$	−30.5990			−1.59725			−0.798626	+	0.601827i	$0.794440\pi$
$368$	−2.92892			−0.152680
$369$		0			0
$370$		−	23.4340i		−	1.21827i
$371$			38.7549i			2.01205i
$372$		0			0
$373$	18.2553			0.945222			0.472611	−	0.881271i	$-0.343312\pi$
$373$	18.2553			0.945222			0.472611	+	0.881271i	$0.343312\pi$
$374$	47.3401			2.44790
$375$		0			0
$376$	19.3774			0.999315
$377$	−11.6700	+	2.67912i	−0.601038	+	0.137981i
$378$		0			0
$379$			15.9945i			0.821584i	0.911729	+	0.410792i	$0.134748\pi$
$379$			15.9945i			0.821584i	−0.911729	+	0.410792i	$0.865252\pi$
$380$	9.47679			0.486149
$381$		0			0
$382$			33.3966i			1.70872i
$383$			2.16137i			0.110441i	0.998474	+	0.0552204i	$0.0175862\pi$
$383$			2.16137i			0.110441i	−0.998474	+	0.0552204i	$0.982414\pi$
$384$		0			0
$385$		−	9.41478i		−	0.479822i
$386$	−41.1523			−2.09460
$387$		0			0
$388$		−	2.77301i		−	0.140778i
$389$	−0.453981			−0.0230177			−0.0115089	−	0.999934i	$-0.503663\pi$
$389$	−0.453981			−0.0230177			−0.0115089	+	0.999934i	$0.503663\pi$
$390$		0			0
$391$	3.22699			0.163196
$392$		−	23.5051i		−	1.18719i
$393$		0			0
$394$	−37.4532			−1.88686
$395$			0.585221i			0.0294457i
$396$		0			0
$397$			29.2462i			1.46782i	0.679244	+	0.733912i	$0.262308\pi$
$397$			29.2462i			1.46782i	−0.679244	+	0.733912i	$0.737692\pi$
$398$		−	41.0101i		−	2.05565i
$399$		0			0
$400$	−6.02827			−0.301414
$401$			15.2270i			0.760400i	0.924904	+	0.380200i	$0.124145\pi$
$401$			15.2270i			0.760400i	−0.924904	+	0.380200i	$0.875855\pi$
$402$		0			0
$403$	−3.07108	−	13.3774i	−0.152982	−	0.666377i
$404$	−30.1240			−1.49873
$405$		0			0
$406$	−27.7266			−1.37605
$407$	−26.4249			−1.30983
$408$		0			0
$409$		−	23.6700i		−	1.17041i	−0.810886	−	0.585204i	$-0.801014\pi$
$409$		−	23.6700i		−	1.17041i	0.810886	−	0.585204i	$-0.198986\pi$
$410$			4.05655i			0.200339i
$411$		0			0
$412$	−31.0420			−1.52933
$413$	−29.3401			−1.44373
$414$		0			0
$415$	7.70739			0.378341
$416$	2.81221	+	12.2498i	0.137880	+	0.600596i
$417$		0			0
$418$		−	15.6327i		−	0.764620i
$419$	5.67004			0.277000			0.138500	−	0.990362i	$-0.455772\pi$
$419$	5.67004			0.277000			0.138500	+	0.990362i	$0.455772\pi$
$420$		0			0
$421$		−	26.3009i		−	1.28183i	−0.767613	−	0.640913i	$-0.778556\pi$
$421$		−	26.3009i		−	1.28183i	0.767613	−	0.640913i	$-0.221444\pi$
$422$		−	29.6700i		−	1.44432i
$423$		0			0
$424$		−	68.0950i		−	3.30698i
$425$	6.64177			0.322173
$426$		0			0
$427$			12.3118i			0.595810i
$428$	−41.3538			−1.99891
$429$		0			0
$430$	2.19325			0.105768
$431$		−	5.09029i		−	0.245190i	−0.992457	−	0.122595i	$-0.960878\pi$
$431$		−	5.09029i		−	0.245190i	0.992457	−	0.122595i	$-0.0391217\pi$
$432$		0			0
$433$	−24.0565			−1.15608			−0.578042	−	0.816007i	$-0.696183\pi$
$433$	−24.0565			−1.15608			−0.578042	+	0.816007i	$0.696183\pi$
$434$		−	31.7831i		−	1.52564i
$435$		0			0
$436$			46.2262i			2.21383i
$437$		−	1.06562i		−	0.0509755i
$438$		0			0
$439$	7.21606			0.344404			0.172202	−	0.985062i	$-0.444912\pi$
$439$	7.21606			0.344404			0.172202	+	0.985062i	$0.444912\pi$
$440$			16.5424i			0.788628i
$441$		0			0
$442$	−13.4713	−	58.6802i	−0.640766	−	2.79113i
$443$	−27.3829			−1.30100			−0.650500	−	0.759506i	$-0.725441\pi$
$443$	−27.3829			−1.30100			−0.650500	+	0.759506i	$0.725441\pi$
$444$		0			0
$445$	−3.41478			−0.161876
$446$	−50.3310			−2.38324
$447$		0			0
$448$		−	10.9344i		−	0.516601i
$449$			1.42571i			0.0672833i	0.999434	+	0.0336416i	$0.0107105\pi$
$449$			1.42571i			0.0672833i	−0.999434	+	0.0336416i	$0.989290\pi$
$450$		0			0
$451$	4.57429			0.215395
$452$	−13.9435			−0.655845
$453$		0			0
$454$	56.4732			2.65042
$455$	−11.6700	+	2.67912i	−0.547100	+	0.125599i
$456$		0			0
$457$		−	35.3219i		−	1.65229i	−0.563457	−	0.826145i	$-0.690529\pi$
$457$		−	35.3219i		−	1.65229i	0.563457	−	0.826145i	$-0.309471\pi$
$458$	26.0675			1.21805
$459$		0			0
$460$			2.09936i			0.0978831i
$461$		−	29.1979i		−	1.35988i	−0.733267	−	0.679941i	$-0.762005\pi$
$461$		−	29.1979i		−	1.35988i	0.733267	−	0.679941i	$-0.237995\pi$
$462$		0			0
$463$			3.32088i			0.154335i	0.997018	+	0.0771673i	$0.0245876\pi$
$463$			3.32088i			0.154335i	−0.997018	+	0.0771673i	$0.975412\pi$
$464$	20.0192			0.929368
$465$		0			0
$466$		−	28.5561i		−	1.32284i
$467$	21.5525			0.997333			0.498666	−	0.866794i	$-0.333823\pi$
$467$	21.5525			0.997333			0.498666	+	0.866794i	$0.333823\pi$
$468$		0			0
$469$	14.2553			0.658247
$470$		−	8.34916i		−	0.385118i
$471$		0			0
$472$	51.5525			2.37290
$473$		−	2.47318i		−	0.113717i
$474$		0			0
$475$		−	2.19325i		−	0.100633i
$476$		−	95.3038i		−	4.36824i
$477$		0			0
$478$	−70.6939			−3.23346
$479$			5.42024i			0.247657i	0.992304	+	0.123829i	$0.0395173\pi$
$479$			5.42024i			0.247657i	−0.992304	+	0.123829i	$0.960483\pi$
$480$		0			0
$481$	7.51960	+	32.7549i	0.342864	+	1.49349i
$482$	37.9253			1.72745
$483$		0			0
$484$	−12.8013			−0.581877
$485$	−0.641769			−0.0291412
$486$		0			0
$487$			17.4521i			0.790831i	0.918502	+	0.395416i	$0.129399\pi$
$487$			17.4521i			0.790831i	−0.918502	+	0.395416i	$0.870601\pi$
$488$		−	21.6327i		−	0.979266i
$489$		0			0
$490$	−10.1276			−0.457520
$491$	24.6236			1.11125			0.555624	−	0.831433i	$-0.312479\pi$
$491$	24.6236			1.11125			0.555624	+	0.831433i	$0.312479\pi$
$492$		0			0
$493$	−22.0565			−0.993377
$494$	−19.3774	+	4.44852i	−0.871832	+	0.200148i
$495$		0			0
$496$			22.9481i			1.03040i
$497$	−7.28354			−0.326711
$498$		0			0
$499$			32.3629i			1.44876i	0.689400	+	0.724381i	$0.257874\pi$
$499$			32.3629i			1.44876i	−0.689400	+	0.724381i	$0.742126\pi$
$500$			4.32088i			0.193236i
$501$		0			0
$502$		−	2.91518i		−	0.130111i
$503$	26.7411			1.19233			0.596164	−	0.802863i	$-0.296691\pi$
$503$	26.7411			1.19233			0.596164	+	0.802863i	$0.296691\pi$
$504$		0			0
$505$			6.97173i			0.310238i
$506$	3.46305			0.153951
$507$		0			0
$508$	25.4960			1.13120
$509$		−	9.74474i		−	0.431928i	−0.976401	−	0.215964i	$-0.930711\pi$
$509$		−	9.74474i		−	0.431928i	0.976401	−	0.215964i	$-0.0692894\pi$
$510$		0			0
$511$	−42.2937			−1.87096
$512$			49.3365i			2.18038i
$513$		0			0
$514$			2.08562i			0.0919928i
$515$			7.18418i			0.316573i
$516$		0			0
$517$	−9.41478			−0.414061
$518$			77.8215i			3.41928i
$519$		0			0
$520$	20.5051	−	4.70739i	0.899207	−	0.206433i
$521$	11.4340			0.500932			0.250466	−	0.968125i	$-0.419416\pi$
$521$	11.4340			0.500932			0.250466	+	0.968125i	$0.419416\pi$
$522$		0			0
$523$	33.6272			1.47042			0.735208	−	0.677841i	$-0.237084\pi$
$523$	33.6272			1.47042			0.735208	+	0.677841i	$0.237084\pi$
$524$	14.7549			0.644569
$525$		0			0
$526$		−	64.4304i		−	2.80930i
$527$		−	25.2835i		−	1.10137i
$528$		0			0
$529$	−22.7639			−0.989736
$530$	−29.3401			−1.27445
$531$		0			0
$532$	−31.4713			−1.36446
$533$	−1.30168	−	5.67004i	−0.0563822	−	0.245597i
$534$		0			0
$535$			9.57068i			0.413777i
$536$	−25.0475			−1.08189
$537$		0			0
$538$			12.6418i			0.545025i
$539$			11.4202i			0.491905i
$540$		0			0
$541$		−	26.4431i		−	1.13688i	−0.822726	−	0.568438i	$-0.807548\pi$
$541$		−	26.4431i		−	1.13688i	0.822726	−	0.568438i	$-0.192452\pi$
$542$	47.4960			2.04013
$543$		0			0
$544$			23.1523i			0.992647i
$545$	10.6983			0.458266
$546$		0			0
$547$	−21.9681			−0.939289			−0.469644	−	0.882856i	$-0.655618\pi$
$547$	−21.9681			−0.939289			−0.469644	+	0.882856i	$0.655618\pi$
$548$			65.1798i			2.78434i
$549$		0			0
$550$	7.12763			0.303923
$551$			7.28354i			0.310289i
$552$		0			0
$553$		−	1.94345i		−	0.0826440i
$554$			59.7941i			2.54041i
$555$		0			0
$556$	89.4350			3.79289
$557$		−	39.3027i		−	1.66531i	−0.553792	−	0.832655i	$-0.686820\pi$
$557$		−	39.3027i		−	1.66531i	0.553792	−	0.832655i	$-0.313180\pi$
$558$		0			0
$559$	−3.06562	+	0.703781i	−0.129662	+	0.0297668i
$560$	20.0192			0.845966
$561$		0			0
$562$	79.4350			3.35076
$563$	−23.0420			−0.971105			−0.485552	−	0.874208i	$-0.661382\pi$
$563$	−23.0420			−0.971105			−0.485552	+	0.874208i	$0.661382\pi$
$564$		0			0
$565$			3.22699i			0.135761i
$566$			15.9764i			0.671538i
$567$		0			0
$568$	12.7977			0.536979
$569$	−3.63270			−0.152291			−0.0761453	−	0.997097i	$-0.524261\pi$
$569$	−3.63270			−0.152291			−0.0761453	+	0.997097i	$0.524261\pi$
$570$		0			0
$571$	43.3785			1.81533			0.907667	−	0.419692i	$-0.137862\pi$
$571$	43.3785			1.81533			0.907667	+	0.419692i	$0.137862\pi$
$572$	−9.88250	−	43.0475i	−0.413208	−	1.79991i
$573$		0			0
$574$		−	13.4713i		−	0.562282i
$575$	0.485863			0.0202619
$576$		0			0
$577$			8.84876i			0.368379i	0.982891	+	0.184189i	$0.0589660\pi$
$577$			8.84876i			0.368379i	−0.982891	+	0.184189i	$0.941034\pi$
$578$		−	68.1660i		−	2.83533i
$579$		0			0
$580$		−	14.3492i		−	0.595816i
$581$	−25.5953			−1.06187
$582$		0			0
$583$			33.0848i			1.37023i
$584$	74.3129			3.07509
$585$		0			0
$586$	−20.2070			−0.834743
$587$			15.3209i			0.632361i	0.948699	+	0.316180i	$0.102400\pi$
$587$			15.3209i			0.632361i	−0.948699	+	0.316180i	$0.897600\pi$
$588$		0			0
$589$	−8.34916			−0.344021
$590$		−	22.2125i		−	0.914472i
$591$		0			0
$592$		−	56.1888i		−	2.30935i
$593$		−	4.52867i		−	0.185970i	−0.995667	−	0.0929852i	$-0.970359\pi$
$593$		−	4.52867i		−	0.185970i	0.995667	−	0.0929852i	$-0.0296409\pi$
$594$		0			0
$595$	−22.0565			−0.904230
$596$			2.77301i			0.113587i
$597$		0			0
$598$	−0.985463	−	4.29261i	−0.0402986	−	0.175538i
$599$	−23.0283			−0.940910			−0.470455	−	0.882424i	$-0.655910\pi$
$599$	−23.0283			−0.940910			−0.470455	+	0.882424i	$0.655910\pi$
$600$		0			0
$601$	−12.0565			−0.491797			−0.245898	−	0.969296i	$-0.579083\pi$
$601$	−12.0565			−0.491797			−0.245898	+	0.969296i	$0.579083\pi$
$602$	−7.28354			−0.296855
$603$		0			0
$604$			71.8836i			2.92490i
$605$			2.96265i			0.120449i
$606$		0			0
$607$	−8.99639			−0.365152			−0.182576	−	0.983192i	$-0.558444\pi$
$607$	−8.99639			−0.365152			−0.182576	+	0.983192i	$0.558444\pi$
$608$	7.64538			0.310061
$609$		0			0
$610$	−9.32088			−0.377392
$611$	2.67912	+	11.6700i	0.108385	+	0.472119i
$612$		0			0
$613$		−	14.1131i		−	0.570023i	−0.958524	−	0.285011i	$-0.908003\pi$
$613$		−	14.1131i		−	0.570023i	0.958524	−	0.285011i	$-0.0919973\pi$
$614$	39.7749			1.60518
$615$		0			0
$616$		−	54.9354i		−	2.21341i
$617$			2.46120i			0.0990841i	0.998772	+	0.0495420i	$0.0157762\pi$
$617$			2.46120i			0.0990841i	−0.998772	+	0.0495420i	$0.984224\pi$
$618$		0			0
$619$		−	5.73205i		−	0.230391i	−0.993343	−	0.115195i	$-0.963251\pi$
$619$		−	5.73205i		−	0.230391i	0.993343	−	0.115195i	$-0.0367494\pi$
$620$	16.4485			0.660588
$621$		0			0
$622$		−	61.1232i		−	2.45082i
$623$	11.3401			0.454331
$624$		0			0
$625$	1.00000			0.0400000
$626$			28.2262i			1.12815i
$627$		0			0
$628$	−44.3118			−1.76823
$629$			61.9072i			2.46840i
$630$		0			0
$631$			5.27807i			0.210117i	0.994466	+	0.105058i	$0.0335030\pi$
$631$			5.27807i			0.210117i	−0.994466	+	0.105058i	$0.966497\pi$
$632$			3.41478i			0.135833i
$633$		0			0
$634$	40.6044			1.61261
$635$		−	5.90064i		−	0.234160i
$636$		0			0
$637$	14.1559	−	3.24980i	0.560877	−	0.128762i
$638$	−23.6700			−0.937106
$639$		0			0
$640$	15.2498			0.602801
$641$	−42.9992			−1.69837			−0.849183	−	0.528098i	$-0.822905\pi$
$641$	−42.9992			−1.69837			−0.849183	+	0.528098i	$0.822905\pi$
$642$		0			0
$643$			43.3593i			1.70992i	0.518691	+	0.854962i	$0.326419\pi$
$643$			43.3593i			1.70992i	−0.518691	+	0.854962i	$0.673581\pi$
$644$		−	6.97173i		−	0.274724i
$645$		0			0
$646$	−36.6236			−1.44094
$647$	−19.6454			−0.772339			−0.386170	−	0.922428i	$-0.626202\pi$
$647$	−19.6454			−0.772339			−0.386170	+	0.922428i	$0.626202\pi$
$648$		0			0
$649$	−25.0475			−0.983199
$650$	−2.02827	−	8.83502i	−0.0795554	−	0.346538i
$651$		0			0
$652$		−	5.95173i		−	0.233088i
$653$	−9.93252			−0.388690			−0.194345	−	0.980933i	$-0.562258\pi$
$653$	−9.93252			−0.388690			−0.194345	+	0.980933i	$0.562258\pi$
$654$		0			0
$655$		−	3.41478i		−	0.133426i
$656$			9.72659i			0.379760i
$657$		0			0
$658$			27.7266i			1.08090i
$659$	−10.1806			−0.396579			−0.198289	−	0.980144i	$-0.563539\pi$
$659$	−10.1806			−0.396579			−0.198289	+	0.980144i	$0.563539\pi$
$660$		0			0
$661$			32.9427i			1.28132i	0.767824	+	0.640660i	$0.221339\pi$
$661$			32.9427i			1.28132i	−0.767824	+	0.640660i	$0.778661\pi$
$662$	75.5800			2.93750
$663$		0			0
$664$	44.9728			1.74528
$665$			7.28354i			0.282443i
$666$		0			0
$667$	−1.61350			−0.0624748
$668$		−	75.9445i		−	2.93838i
$669$		0			0
$670$			10.7922i			0.416939i
$671$			10.5105i			0.405754i
$672$		0			0
$673$	11.2270			0.432769			0.216384	−	0.976308i	$-0.430574\pi$
$673$	11.2270			0.432769			0.216384	+	0.976308i	$0.430574\pi$
$674$		−	43.9253i		−	1.69194i
$675$		0			0
$676$	−50.5471	+	24.4996i	−1.94412	+	0.942292i
$677$	15.7447			0.605119			0.302560	−	0.953130i	$-0.402159\pi$
$677$	15.7447			0.605119			0.302560	+	0.953130i	$0.402159\pi$
$678$		0			0
$679$	2.13124			0.0817895
$680$	38.7549			1.48618
$681$		0			0
$682$		−	27.1331i		−	1.03898i
$683$			50.3492i			1.92656i	0.268504	+	0.963279i	$0.413471\pi$
$683$			50.3492i			1.92656i	−0.268504	+	0.963279i	$0.586529\pi$
$684$		0			0
$685$	15.0848			0.576361
$686$	−24.8114			−0.947304
$687$		0			0
$688$	5.25887			0.200493
$689$	41.0101	−	9.41478i	1.56236	−	0.358675i
$690$		0			0
$691$			8.19325i			0.311686i	0.987782	+	0.155843i	$0.0498094\pi$
$691$			8.19325i			0.311686i	−0.987782	+	0.155843i	$0.950191\pi$
$692$	−27.2726			−1.03675
$693$		0			0
$694$			83.5717i			3.17234i
$695$		−	20.6983i		−	0.785132i
$696$		0			0
$697$		−	10.7165i		−	0.405915i
$698$	52.5380			1.98859
$699$		0			0
$700$		−	14.3492i		−	0.542347i
$701$	−8.25526			−0.311797			−0.155899	−	0.987773i	$-0.549827\pi$
$701$	−8.25526			−0.311797			−0.155899	+	0.987773i	$0.549827\pi$
$702$		0			0
$703$	20.4431			0.771024
$704$		−	9.33462i		−	0.351812i
$705$		0			0
$706$	−31.5471			−1.18729
$707$		−	23.1523i		−	0.870732i
$708$		0			0
$709$		−	37.7831i		−	1.41898i	−0.704718	−	0.709488i	$-0.748926\pi$
$709$		−	37.7831i		−	1.41898i	0.704718	−	0.709488i	$-0.251074\pi$
$710$		−	5.51414i		−	0.206942i
$711$		0			0
$712$	−19.9253			−0.746732
$713$		−	1.84956i		−	0.0692665i
$714$		0			0
$715$	−9.96265	+	2.28715i	−0.372582	+	0.0855344i
$716$	39.2545			1.46701
$717$		0			0
$718$	−7.48506			−0.279340
$719$	−22.2443			−0.829574			−0.414787	−	0.909919i	$-0.636144\pi$
$719$	−22.2443			−0.829574			−0.414787	+	0.909919i	$0.636144\pi$
$720$		0			0
$721$		−	23.8578i		−	0.888512i
$722$		−	35.6747i		−	1.32768i
$723$		0			0
$724$	51.9336			1.93010
$725$	−3.32088			−0.123335
$726$		0			0
$727$	30.0812			1.11565			0.557825	−	0.829958i	$-0.311636\pi$
$727$	30.0812			1.11565			0.557825	+	0.829958i	$0.311636\pi$
$728$	−68.0950	+	15.6327i	−2.52377	+	0.579386i
$729$		0			0
$730$		−	32.0192i		−	1.18508i
$731$	−5.79407			−0.214301
$732$		0			0
$733$		−	35.0101i		−	1.29313i	−0.762859	−	0.646564i	$-0.776205\pi$
$733$		−	35.0101i		−	1.29313i	0.762859	−	0.646564i	$-0.223795\pi$
$734$			76.9300i			2.83954i
$735$		0			0
$736$			1.69365i			0.0624288i
$737$	12.1696			0.448275
$738$		0			0
$739$		−	42.6856i		−	1.57022i	−0.619359	−	0.785108i	$-0.712607\pi$
$739$		−	42.6856i		−	1.57022i	0.619359	−	0.785108i	$-0.287393\pi$
$740$	−40.2745			−1.48052
$741$		0			0
$742$	97.4350			3.57695
$743$		−	13.6892i		−	0.502210i	−0.967960	−	0.251105i	$-0.919206\pi$
$743$		−	13.6892i		−	0.502210i	0.967960	−	0.251105i	$-0.0807939\pi$
$744$		0			0
$745$	0.641769			0.0235126
$746$		−	45.8962i		−	1.68038i
$747$		0			0
$748$		−	81.3603i		−	2.97483i
$749$		−	31.7831i		−	1.16133i
$750$		0			0
$751$	−17.7831			−0.648916			−0.324458	−	0.945900i	$-0.605182\pi$
$751$	−17.7831			−0.648916			−0.324458	+	0.945900i	$0.605182\pi$
$752$		−	20.0192i		−	0.730025i
$753$		0			0
$754$	6.73566	+	29.3401i	0.245298	+	1.06850i
$755$	16.6363			0.605457
$756$		0			0
$757$	−26.9717			−0.980304			−0.490152	−	0.871637i	$-0.663059\pi$
$757$	−26.9717			−0.980304			−0.490152	+	0.871637i	$0.663059\pi$
$758$	40.2125			1.46058
$759$		0			0
$760$		−	12.7977i		−	0.464220i
$761$		−	35.1523i		−	1.27427i	−0.770752	−	0.637135i	$-0.780119\pi$
$761$		−	35.1523i		−	1.27427i	0.770752	−	0.637135i	$-0.219881\pi$
$762$		0			0
$763$	−35.5279			−1.28620
$764$	57.3966			2.07654
$765$		0			0
$766$	5.43398			0.196338
$767$	7.12763	+	31.0475i	0.257364	+	1.12106i
$768$		0			0
$769$			23.1523i			0.834893i	0.908701	+	0.417447i	$0.137075\pi$
$769$			23.1523i			0.834893i	−0.908701	+	0.417447i	$0.862925\pi$
$770$	−23.6700			−0.853009
$771$		0			0
$772$			70.7258i			2.54548i
$773$			41.6218i			1.49703i	0.663117	+	0.748515i	$0.269233\pi$
$773$			41.6218i			1.49703i	−0.663117	+	0.748515i	$0.730767\pi$
$774$		0			0
$775$		−	3.80675i		−	0.136742i
$776$	−3.74474			−0.134428
$777$		0			0
$778$			1.14137i			0.0409201i
$779$	−3.53880			−0.126791
$780$		0			0
$781$	−6.21792			−0.222495
$782$		−	8.11310i		−	0.290124i
$783$		0			0
$784$	−24.2835			−0.867269
$785$			10.2553i			0.366026i
$786$		0			0
$787$		−	43.2353i		−	1.54117i	−0.637337	−	0.770585i	$-0.719964\pi$
$787$		−	43.2353i		−	1.54117i	0.637337	−	0.770585i	$-0.280036\pi$
$788$			64.3684i			2.29303i
$789$		0			0
$790$	1.47133			0.0523474
$791$		−	10.7165i		−	0.381034i
$792$		0			0
$793$	13.0283	−	2.99093i	0.462648	−	0.106211i
$794$	73.5289			2.60944
$795$		0			0
$796$	−70.4815			−2.49815
$797$	−14.4431			−0.511599			−0.255800	−	0.966730i	$-0.582339\pi$
$797$	−14.4431			−0.511599			−0.255800	+	0.966730i	$0.582339\pi$
$798$		0			0
$799$			22.0565i			0.780305i
$800$			3.48586i			0.123244i
$801$		0			0
$802$	38.2827			1.35181
$803$	−36.1059			−1.27415
$804$		0			0
$805$	−1.61350			−0.0568682
$806$	−33.6327	+	7.72113i	−1.18466	+	0.271965i
$807$		0			0
$808$			40.6802i			1.43112i
$809$	−17.8880			−0.628907			−0.314454	−	0.949273i	$-0.601821\pi$
$809$	−17.8880			−0.628907			−0.314454	+	0.949273i	$0.601821\pi$
$810$		0			0
$811$		−	8.69285i		−	0.305247i	−0.988284	−	0.152624i	$-0.951228\pi$
$811$		−	8.69285i		−	0.305247i	0.988284	−	0.152624i	$-0.0487722\pi$
$812$			47.6519i			1.67225i
$813$		0			0
$814$			66.4358i			2.32857i
$815$	−1.37743			−0.0482493
$816$		0			0
$817$			1.91332i			0.0669387i
$818$	−59.5097			−2.08071
$819$		0			0
$820$	6.97173			0.243463
$821$			9.41478i			0.328578i	0.986412	+	0.164289i	$0.0525330\pi$
$821$			9.41478i			0.328578i	−0.986412	+	0.164289i	$0.947467\pi$
$822$		0			0
$823$	30.3365			1.05746			0.528732	−	0.848789i	$-0.322668\pi$
$823$	30.3365			1.05746			0.528732	+	0.848789i	$0.322668\pi$
$824$			41.9198i			1.46035i
$825$		0			0
$826$			73.7650i			2.56661i
$827$		−	18.2361i		−	0.634130i	−0.948404	−	0.317065i	$-0.897303\pi$
$827$		−	18.2361i		−	0.634130i	0.948404	−	0.317065i	$-0.102697\pi$
$828$		0			0
$829$	−29.8023			−1.03508			−0.517539	−	0.855660i	$-0.673152\pi$
$829$	−29.8023			−1.03508			−0.517539	+	0.855660i	$0.673152\pi$
$830$		−	19.3774i		−	0.672600i
$831$		0			0
$832$	−11.5707	+	2.65631i	−0.401141	+	0.0920908i
$833$	26.7549			0.927001
$834$		0			0
$835$	−17.5761			−0.608248
$836$	−26.8669			−0.929211
$837$		0			0
$838$		−	14.2553i		−	0.492440i
$839$		−	46.1004i		−	1.59156i	−0.605584	−	0.795782i	$-0.707060\pi$
$839$		−	46.1004i		−	1.59156i	0.605584	−	0.795782i	$-0.292940\pi$
$840$		0			0
$841$	−17.9717			−0.619715
$842$	−66.1240			−2.27878
$843$		0			0
$844$	−50.9920			−1.75522
$845$	5.67004	+	11.6983i	0.195055	+	0.402434i
$846$		0			0
$847$		−	9.83863i		−	0.338059i
$848$	−70.3502			−2.41584
$849$		0			0
$850$		−	16.6983i		−	0.572748i
$851$			4.52867i			0.155241i
$852$		0			0
$853$			19.3774i			0.663471i	0.943373	+	0.331735i	$0.107634\pi$
$853$			19.3774i			0.663471i	−0.943373	+	0.331735i	$0.892366\pi$
$854$	30.9536			1.05921
$855$		0			0
$856$			55.8452i			1.90875i
$857$	−43.4713			−1.48495			−0.742476	−	0.669873i	$-0.766349\pi$
$857$	−43.4713			−1.48495			−0.742476	+	0.669873i	$0.766349\pi$
$858$		0			0
$859$	−27.7375			−0.946392			−0.473196	−	0.880957i	$-0.656900\pi$
$859$	−27.7375			−0.946392			−0.473196	+	0.880957i	$0.656900\pi$
$860$		−	3.76940i		−	0.128536i
$861$		0			0
$862$	−12.7977			−0.435891
$863$		−	3.69646i		−	0.125829i	−0.998019	−	0.0629145i	$-0.979960\pi$
$863$		−	3.69646i		−	0.125829i	0.998019	−	0.0629145i	$-0.0200395\pi$
$864$		0			0
$865$			6.31181i			0.214608i
$866$			60.4815i			2.05524i
$867$		0			0
$868$	−54.6236			−1.85405
$869$		−	1.65911i		−	0.0562816i
$870$		0			0
$871$	−3.46305	−	15.0848i	−0.117341	−	0.511130i
$872$	62.4249			2.11397
$873$		0			0
$874$	−2.67912			−0.0906224
$875$	−3.32088			−0.112266
$876$		0			0
$877$		−	20.5671i		−	0.694501i	−0.937772	−	0.347250i	$-0.887115\pi$
$877$		−	20.5671i		−	0.694501i	0.937772	−	0.347250i	$-0.112885\pi$
$878$		−	18.1422i		−	0.612269i
$879$		0			0
$880$	17.0903			0.576113
$881$	−14.5369			−0.489762			−0.244881	−	0.969553i	$-0.578749\pi$
$881$	−14.5369			−0.489762			−0.244881	+	0.969553i	$0.578749\pi$
$882$		0			0
$883$	36.2871			1.22116			0.610580	−	0.791955i	$-0.290936\pi$
$883$	36.2871			1.22116			0.610580	+	0.791955i	$0.290936\pi$
$884$	−100.850	+	23.1523i	−3.39195	+	0.778696i
$885$		0			0
$886$			68.8444i			2.31287i
$887$	45.2407			1.51903			0.759517	−	0.650487i	$-0.225435\pi$
$887$	45.2407			1.51903			0.759517	+	0.650487i	$0.225435\pi$
$888$		0			0
$889$			19.5953i			0.657207i
$890$			8.58522i			0.287777i
$891$		0			0
$892$			86.5007i			2.89626i
$893$	7.28354			0.243734
$894$		0			0
$895$		−	9.08482i		−	0.303672i
$896$	−50.6428			−1.69186
$897$		0			0
$898$	3.58442			0.119614
$899$			12.6418i			0.421627i
$900$		0			0
$901$	77.5097			2.58222
$902$		−	11.5004i		−	0.382921i
$903$		0			0
$904$			18.8296i			0.626262i
$905$		−	12.0192i		−	0.399532i
$906$		0			0
$907$	11.2973			0.375120			0.187560	−	0.982253i	$-0.439942\pi$
$907$	11.2973			0.375120			0.187560	+	0.982253i	$0.439942\pi$
$908$		−	97.0568i		−	3.22094i
$909$		0			0
$910$	6.73566	+	29.3401i	0.223285	+	0.972614i
$911$	41.1979			1.36495			0.682474	−	0.730910i	$-0.260904\pi$
$911$	41.1979			1.36495			0.682474	+	0.730910i	$0.260904\pi$
$912$		0			0
$913$	−21.8506			−0.723150
$914$	−88.8042			−2.93738
$915$		0			0
$916$		−	44.8005i		−	1.48025i
$917$			11.3401i			0.374483i
$918$		0			0
$919$	1.74474			0.0575535			0.0287768	−	0.999586i	$-0.490839\pi$
$919$	1.74474			0.0575535			0.0287768	+	0.999586i	$0.490839\pi$
$920$	2.83502			0.0934679
$921$		0			0
$922$	−73.4076			−2.41755
$923$	1.76940	+	7.70739i	0.0582405	+	0.253692i
$924$		0			0
$925$			9.32088i			0.306469i
$926$	8.34916			0.274370
$927$		0			0
$928$		−	11.5761i		−	0.380006i
$929$		−	15.5569i		−	0.510407i	−0.966887	−	0.255203i	$-0.917858\pi$
$929$		−	15.5569i		−	0.510407i	0.966887	−	0.255203i	$-0.0821424\pi$
$930$		0			0
$931$		−	8.83502i		−	0.289556i
$932$	−49.0776			−1.60759
$933$		0			0
$934$		−	54.1860i		−	1.77302i
$935$	−18.8296			−0.615792
$936$		0			0
$937$	26.0384			0.850638			0.425319	−	0.905044i	$-0.360162\pi$
$937$	26.0384			0.850638			0.425319	+	0.905044i	$0.360162\pi$
$938$		−	35.8397i		−	1.17021i
$939$		0			0
$940$	−14.3492			−0.468018
$941$		−	50.8789i		−	1.65860i	−0.558800	−	0.829302i	$-0.688738\pi$
$941$		−	50.8789i		−	1.65860i	0.558800	−	0.829302i	$-0.311262\pi$
$942$		0			0
$943$		−	0.783938i		−	0.0255285i
$944$		−	53.2599i		−	1.73346i
$945$		0			0
$946$	−6.21792			−0.202162
$947$			37.8770i			1.23084i	0.788200	+	0.615419i	$0.211013\pi$
$947$			37.8770i			1.23084i	−0.788200	+	0.615419i	$0.788987\pi$
$948$		0			0
$949$	10.2745	+	44.7549i	0.333523	+	1.45280i
$950$	−5.51414			−0.178902
$951$		0			0
$952$	−128.700			−4.17120
$953$	−32.0950			−1.03966			−0.519829	−	0.854271i	$-0.674004\pi$
$953$	−32.0950			−1.03966			−0.519829	+	0.854271i	$0.674004\pi$
$954$		0			0
$955$		−	13.2835i		−	0.429845i
$956$			121.497i			3.92950i
$957$		0			0
$958$	13.6272			0.440276
$959$	−50.0950			−1.61765
$960$		0			0
$961$	16.5087			0.532538
$962$	82.3502	−	18.9053i	2.65508	−	0.609532i
$963$		0			0
$964$		−	65.1798i		−	2.09930i
$965$	16.3684			0.526916
$966$		0			0
$967$		−	24.4057i		−	0.784835i	−0.919787	−	0.392417i	$-0.871639\pi$
$967$		−	24.4057i		−	0.784835i	0.919787	−	0.392417i	$-0.128361\pi$
$968$			17.2871i			0.555630i
$969$		0			0
$970$			1.61350i			0.0518062i
$971$	36.9354			1.18531			0.592657	−	0.805455i	$-0.298079\pi$
$971$	36.9354			1.18531			0.592657	+	0.805455i	$0.298079\pi$
$972$		0			0
$973$			68.7367i			2.20360i
$974$	43.8770			1.40591
$975$		0			0
$976$	−22.3492			−0.715379
$977$			25.1715i			0.805308i	0.915352	+	0.402654i	$0.131912\pi$
$977$			25.1715i			0.805308i	−0.915352	+	0.402654i	$0.868088\pi$
$978$		0			0
$979$	9.68097			0.309405
$980$			17.4057i			0.556005i
$981$		0			0
$982$		−	61.9072i		−	1.97554i
$983$			13.1896i			0.420684i	0.977628	+	0.210342i	$0.0674578\pi$
$983$			13.1896i			0.420684i	−0.977628	+	0.210342i	$0.932542\pi$
$984$		0			0
$985$	14.8970			0.474659
$986$			55.4532i			1.76599i
$987$		0			0
$988$	7.64538	+	33.3027i	0.243232	+	1.05950i
$989$	−0.423851			−0.0134777
$990$		0			0
$991$	23.0667			0.732737			0.366369	−	0.930470i	$-0.380601\pi$
$991$	23.0667			0.732737			0.366369	+	0.930470i	$0.380601\pi$
$992$	13.2698			0.421317
$993$		0			0
$994$			18.3118i			0.580815i
$995$			16.3118i			0.517119i
$996$		0			0
$997$	−0.630841			−0.0199789			−0.00998947	−	0.999950i	$-0.503180\pi$
$997$	−0.630841			−0.0199789			−0.00998947	+	0.999950i	$0.503180\pi$
$998$	81.3648			2.57556
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.b.g.181.1		6
3.2	odd	2		65.2.c.a.51.6	yes	6
12.11	even	2		1040.2.k.d.961.1		6
13.5	odd	4		7605.2.a.bs.1.1		3
13.8	odd	4		7605.2.a.cc.1.3		3
13.12	even	2	inner	585.2.b.g.181.6		6
15.2	even	4		325.2.d.e.324.1		6
15.8	even	4		325.2.d.f.324.6		6
15.14	odd	2		325.2.c.g.51.1		6
39.2	even	12		845.2.e.i.191.1		6
39.5	even	4		845.2.a.k.1.3		3
39.8	even	4		845.2.a.i.1.1		3
39.11	even	12		845.2.e.k.191.3		6
39.17	odd	6		845.2.m.h.361.1		12
39.20	even	12		845.2.e.k.146.3		6
39.23	odd	6		845.2.m.h.316.6		12
39.29	odd	6		845.2.m.h.316.1		12
39.32	even	12		845.2.e.i.146.1		6
39.35	odd	6		845.2.m.h.361.6		12
39.38	odd	2		65.2.c.a.51.1	✓	6
156.155	even	2		1040.2.k.d.961.2		6
195.38	even	4		325.2.d.e.324.2		6
195.44	even	4		4225.2.a.bc.1.1		3
195.77	even	4		325.2.d.f.324.5		6
195.164	even	4		4225.2.a.be.1.3		3
195.194	odd	2		325.2.c.g.51.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.1	✓	6	39.38	odd	2
65.2.c.a.51.6	yes	6	3.2	odd	2
325.2.c.g.51.1		6	15.14	odd	2
325.2.c.g.51.6		6	195.194	odd	2
325.2.d.e.324.1		6	15.2	even	4
325.2.d.e.324.2		6	195.38	even	4
325.2.d.f.324.5		6	195.77	even	4
325.2.d.f.324.6		6	15.8	even	4
585.2.b.g.181.1		6	1.1	even	1	trivial
585.2.b.g.181.6		6	13.12	even	2	inner
845.2.a.i.1.1		3	39.8	even	4
845.2.a.k.1.3		3	39.5	even	4
845.2.e.i.146.1		6	39.32	even	12
845.2.e.i.191.1		6	39.2	even	12
845.2.e.k.146.3		6	39.20	even	12
845.2.e.k.191.3		6	39.11	even	12
845.2.m.h.316.1		12	39.29	odd	6
845.2.m.h.316.6		12	39.23	odd	6
845.2.m.h.361.1		12	39.17	odd	6
845.2.m.h.361.6		12	39.35	odd	6
1040.2.k.d.961.1		6	12.11	even	2
1040.2.k.d.961.2		6	156.155	even	2
4225.2.a.bc.1.1		3	195.44	even	4
4225.2.a.be.1.3		3	195.164	even	4
7605.2.a.bs.1.1		3	13.5	odd	4
7605.2.a.cc.1.3		3	13.8	odd	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.51414i q^{2} -4.32088 q^{4} +1.00000i q^{5} -3.32088i q^{7} +5.83502i q^{8} +O(q^{10})\)	\(q-2.51414i q^{2} -4.32088 q^{4} +1.00000i q^{5} -3.32088i q^{7} +5.83502i q^{8} +2.51414 q^{10} -2.83502i q^{11} +(-3.51414 + 0.806748i) q^{13} -8.34916 q^{14} +6.02827 q^{16} -6.64177 q^{17} +2.19325i q^{19} -4.32088i q^{20} -7.12763 q^{22} -0.485863 q^{23} -1.00000 q^{25} +(2.02827 + 8.83502i) q^{26} +14.3492i q^{28} +3.32088 q^{29} +3.80675i q^{31} -3.48586i q^{32} +16.6983i q^{34} +3.32088 q^{35} -9.32088i q^{37} +5.51414 q^{38} -5.83502 q^{40} +1.61350i q^{41} +0.872368 q^{43} +12.2498i q^{44} +1.22153i q^{46} -3.32088i q^{47} -4.02827 q^{49} +2.51414i q^{50} +(15.1842 - 3.48586i) q^{52} -11.6700 q^{53} +2.83502 q^{55} +19.3774 q^{56} -8.34916i q^{58} -8.83502i q^{59} -3.70739 q^{61} +9.57068 q^{62} +3.29261 q^{64} +(-0.806748 - 3.51414i) q^{65} +4.29261i q^{67} +28.6983 q^{68} -8.34916i q^{70} -2.19325i q^{71} -12.7357i q^{73} -23.4340 q^{74} -9.47679i q^{76} -9.41478 q^{77} +0.585221 q^{79} +6.02827i q^{80} +4.05655 q^{82} -7.70739i q^{83} -6.64177i q^{85} -2.19325i q^{86} +16.5424 q^{88} +3.41478i q^{89} +(2.67912 + 11.6700i) q^{91} +2.09936 q^{92} -8.34916 q^{94} -2.19325 q^{95} +0.641769i q^{97} +10.1276i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{4}+O(q^{10}) \) 6 * q - 10 * q^4	\( 6 q - 10 q^{4} + 2 q^{10} - 8 q^{13} - 8 q^{14} + 10 q^{16} - 8 q^{17} - 24 q^{22} - 16 q^{23} - 6 q^{25} - 14 q^{26} + 4 q^{29} + 4 q^{35} + 20 q^{38} - 6 q^{40} + 24 q^{43} + 2 q^{49} + 20 q^{52} - 12 q^{53} - 12 q^{55} + 48 q^{56} - 12 q^{61} - 8 q^{62} + 30 q^{64} - 2 q^{65} + 88 q^{68} - 20 q^{74} - 36 q^{77} + 24 q^{79} - 28 q^{82} + 60 q^{88} + 32 q^{91} + 20 q^{92} - 8 q^{94} - 16 q^{95}+O(q^{100}) \) 6 * q - 10 * q^4 + 2 * q^10 - 8 * q^13 - 8 * q^14 + 10 * q^16 - 8 * q^17 - 24 * q^22 - 16 * q^23 - 6 * q^25 - 14 * q^26 + 4 * q^29 + 4 * q^35 + 20 * q^38 - 6 * q^40 + 24 * q^43 + 2 * q^49 + 20 * q^52 - 12 * q^53 - 12 * q^55 + 48 * q^56 - 12 * q^61 - 8 * q^62 + 30 * q^64 - 2 * q^65 + 88 * q^68 - 20 * q^74 - 36 * q^77 + 24 * q^79 - 28 * q^82 + 60 * q^88 + 32 * q^91 + 20 * q^92 - 8 * q^94 - 16 * q^95

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