LMFDB - Embedded newform 1305.2.c.h.784.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1305,2,Mod(784,1305)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1305.784"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1305, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,-14,-3,0,0,0,0,-3,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.84345856.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 13x^{4} + 41x^{2} + 1 $ x^6 + 13x^4 + 41x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.1
Root			$-2.77035i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.h.784.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.77035i q^{2} -5.67486 q^{4} +(1.96358 - 1.06975i) q^{5} +1.86960i q^{7} +10.1807i q^{8} +(-2.96358 - 5.43981i) q^{10} +3.25230 q^{11} +3.40121i q^{13} +5.17945 q^{14} +16.8543 q^{16} -2.40939i q^{17} +0.674860 q^{19} +(-11.1430 + 6.07067i) q^{20} -9.01001i q^{22} -7.41031i q^{23} +(2.71128 - 4.20107i) q^{25} +9.42256 q^{26} -10.6097i q^{28} -1.00000 q^{29} +5.25230 q^{31} -26.3311i q^{32} -6.67486 q^{34} +(2.00000 + 3.67111i) q^{35} -1.86960i q^{37} -1.86960i q^{38} +(10.8907 + 19.9905i) q^{40} -3.46931i q^{43} -18.4563 q^{44} -20.5292 q^{46} +4.00910i q^{47} +3.50459 q^{49} +(-11.6384 - 7.51121i) q^{50} -19.3014i q^{52} -0.877777i q^{53} +(6.38614 - 3.47914i) q^{55} -19.0338 q^{56} +2.77035i q^{58} +10.0000 q^{59} +11.8543 q^{61} -14.5507i q^{62} -39.2378 q^{64} +(3.63844 + 6.67855i) q^{65} -7.95010i q^{67} +13.6729i q^{68} +(10.1703 - 5.54071i) q^{70} -2.00000 q^{71} -0.607882i q^{73} -5.17945 q^{74} -3.82973 q^{76} +6.08050i q^{77} -8.60202 q^{79} +(33.0948 - 18.0299i) q^{80} +2.40939i q^{83} +(-2.57744 - 4.73102i) q^{85} -9.61121 q^{86} +33.1105i q^{88} -8.50459 q^{89} -6.35891 q^{91} +42.0525i q^{92} +11.1066 q^{94} +(1.32514 - 0.721929i) q^{95} +13.1332i q^{97} -9.70897i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 14 q^{4} - 3 q^{5} - 3 q^{10} + 10 q^{11} - 8 q^{14} + 42 q^{16} - 16 q^{19} - 13 q^{20} + 11 q^{25} + 46 q^{26} - 6 q^{29} + 22 q^{31} - 20 q^{34} + 12 q^{35} + 21 q^{40} - 2 q^{44} - 44 q^{46} + 2 q^{49}+ \cdots + 28 q^{95}+O(q^{100}) $ 6 * q - 14 * q^4 - 3 * q^5 - 3 * q^10 + 10 * q^11 - 8 * q^14 + 42 * q^16 - 16 * q^19 - 13 * q^20 + 11 * q^25 + 46 * q^26 - 6 * q^29 + 22 * q^31 - 20 * q^34 + 12 * q^35 + 21 * q^40 - 2 * q^44 - 44 * q^46 + 2 * q^49 - 35 * q^50 + 13 * q^55 - 16 * q^56 + 60 * q^59 + 12 * q^61 - 38 * q^64 - 13 * q^65 + 60 * q^70 - 12 * q^71 + 8 * q^74 - 24 * q^76 - 2 * q^79 + 55 * q^80 - 26 * q^85 + 30 * q^86 - 32 * q^89 + 40 * q^91 - 2 * q^94 + 28 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	2.77035i		−	1.95894i	−0.201600	−	0.979468i	$-0.564614\pi$
$2$		−	2.77035i		−	1.95894i	0.201600	−	0.979468i	$-0.435386\pi$
$3$		0			0
$3$		0			0
$4$	−5.67486			−2.83743
$5$	1.96358	−	1.06975i	0.878139	−	0.478406i
$5$	1.96358	−	1.06975i	0.878139	−	0.478406i
$6$		0			0
$7$			1.86960i			0.706643i	0.935502	+	0.353321i	$0.114948\pi$
$7$			1.86960i			0.706643i	−0.935502	+	0.353321i	$0.885052\pi$
$8$			10.1807i			3.59941i
$9$		0			0
$10$	−2.96358	−	5.43981i	−0.937166	−	1.72022i
$11$	3.25230			0.980605			0.490302	−	0.871552i	$-0.336886\pi$
$11$	3.25230			0.980605			0.490302	+	0.871552i	$0.336886\pi$
$12$		0			0
$13$			3.40121i			0.943327i	0.881779	+	0.471663i	$0.156346\pi$
$13$			3.40121i			0.943327i	−0.881779	+	0.471663i	$0.843654\pi$
$14$	5.17945			1.38427
$15$		0			0
$16$	16.8543			4.21358
$17$		−	2.40939i		−	0.584363i	−0.956363	−	0.292181i	$-0.905619\pi$
$17$		−	2.40939i		−	0.584363i	0.956363	−	0.292181i	$-0.0943811\pi$
$18$		0			0
$19$	0.674860			0.154823			0.0774117	−	0.996999i	$-0.475334\pi$
$19$	0.674860			0.154823			0.0774117	+	0.996999i	$0.475334\pi$
$20$	−11.1430	+	6.07067i	−2.49166	+	1.35744i
$21$		0			0
$22$		−	9.01001i		−	1.92094i
$23$		−	7.41031i		−	1.54516i	−0.634920	−	0.772578i	$-0.718967\pi$
$23$		−	7.41031i		−	1.54516i	0.634920	−	0.772578i	$-0.281033\pi$
$24$		0			0
$25$	2.71128	−	4.20107i	0.542256	−	0.840213i
$26$	9.42256			1.84792
$27$		0			0
$28$		−	10.6097i		−	2.00505i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	5.25230			0.943340			0.471670	−	0.881775i	$-0.343651\pi$
$31$	5.25230			0.943340			0.471670	+	0.881775i	$0.343651\pi$
$32$		−	26.3311i		−	4.65472i
$33$		0			0
$34$	−6.67486			−1.14473
$35$	2.00000	+	3.67111i	0.338062	+	0.620530i
$36$		0			0
$37$		−	1.86960i		−	0.307360i	−0.988121	−	0.153680i	$-0.950887\pi$
$37$		−	1.86960i		−	0.307360i	0.988121	−	0.153680i	$-0.0491126\pi$
$38$		−	1.86960i		−	0.303289i
$39$		0			0
$40$	10.8907	+	19.9905i	1.72198	+	3.16078i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$		−	3.46931i		−	0.529064i	−0.964377	−	0.264532i	$-0.914782\pi$
$43$		−	3.46931i		−	0.529064i	0.964377	−	0.264532i	$-0.0852175\pi$
$44$	−18.4563			−2.78240
$45$		0			0
$46$	−20.5292			−3.02686
$47$			4.00910i			0.584787i	0.956298	+	0.292393i	$0.0944516\pi$
$47$			4.00910i			0.584787i	−0.956298	+	0.292393i	$0.905548\pi$
$48$		0			0
$49$	3.50459			0.500656
$50$	−11.6384	−	7.51121i	−1.64592	−	1.06225i
$51$		0			0
$52$		−	19.3014i		−	2.67662i
$53$		−	0.877777i		−	0.120572i	−0.998181	−	0.0602859i	$-0.980799\pi$
$53$		−	0.877777i		−	0.120572i	0.998181	−	0.0602859i	$-0.0192013\pi$
$54$		0			0
$55$	6.38614	−	3.47914i	0.861107	−	0.469127i
$56$	−19.0338			−2.54349
$57$		0			0
$58$			2.77035i			0.363765i
$59$	10.0000			1.30189			0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000			1.30189			0.650945	+	0.759125i	$0.274373\pi$
$60$		0			0
$61$	11.8543			1.51779			0.758895	−	0.651213i	$-0.225740\pi$
$61$	11.8543			1.51779			0.758895	+	0.651213i	$0.225740\pi$
$62$		−	14.5507i		−	1.84794i
$63$		0			0
$64$	−39.2378			−4.90473
$65$	3.63844	+	6.67855i	0.451293	+	0.828372i
$66$		0			0
$67$		−	7.95010i		−	0.971259i	−0.874165	−	0.485629i	$-0.838590\pi$
$67$		−	7.95010i		−	0.971259i	0.874165	−	0.485629i	$-0.161410\pi$
$68$			13.6729i			1.65809i
$69$		0			0
$70$	10.1703	−	5.54071i	1.21558	−	0.662241i
$71$	−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
$73$		−	0.607882i		−	0.0711472i	−0.999367	−	0.0355736i	$-0.988674\pi$
$73$		−	0.607882i		−	0.0711472i	0.999367	−	0.0355736i	$-0.0113258\pi$
$74$	−5.17945			−0.602099
$75$		0			0
$76$	−3.82973			−0.439301
$77$			6.08050i			0.692937i
$78$		0			0
$79$	−8.60202			−0.967803			−0.483901	−	0.875123i	$-0.660781\pi$
$79$	−8.60202			−0.967803			−0.483901	+	0.875123i	$0.660781\pi$
$80$	33.0948	−	18.0299i	3.70011	−	2.01580i
$81$		0			0
$82$		0			0
$83$			2.40939i			0.264465i	0.991219	+	0.132232i	$0.0422145\pi$
$83$			2.40939i			0.264465i	−0.991219	+	0.132232i	$0.957785\pi$
$84$		0			0
$85$	−2.57744	−	4.73102i	−0.279562	−	0.513152i
$86$	−9.61121			−1.03640
$87$		0			0
$88$			33.1105i			3.52960i
$89$	−8.50459			−0.901485			−0.450743	−	0.892654i	$-0.648841\pi$
$89$	−8.50459			−0.901485			−0.450743	+	0.892654i	$0.648841\pi$
$90$		0			0
$91$	−6.35891			−0.666595
$92$			42.0525i			4.38427i
$93$		0			0
$94$	11.1066			1.14556
$95$	1.32514	−	0.721929i	0.135957	−	0.0740684i
$96$		0			0
$97$			13.1332i			1.33347i	0.745295	+	0.666735i	$0.232309\pi$
$97$			13.1332i			1.33347i	−0.745295	+	0.666735i	$0.767691\pi$
$98$		−	9.70897i		−	0.980754i
$99$		0			0
$100$	−15.3861	+	23.8405i	−1.53861	+	2.38405i
$101$	−4.84513			−0.482108			−0.241054	−	0.970512i	$-0.577493\pi$
$101$	−4.84513			−0.482108			−0.241054	+	0.970512i	$0.577493\pi$
$102$		0			0
$103$			14.8887i			1.46703i	0.679674	+	0.733514i	$0.262121\pi$
$103$			14.8887i			1.46703i	−0.679674	+	0.733514i	$0.737879\pi$
$104$	−34.6266			−3.39542
$105$		0			0
$106$	−2.43175			−0.236193
$107$			1.86960i			0.180741i	0.995908	+	0.0903705i	$0.0288051\pi$
$107$			1.86960i			0.180741i	−0.995908	+	0.0903705i	$0.971195\pi$
$108$		0			0
$109$	8.77228			0.840232			0.420116	−	0.907470i	$-0.361989\pi$
$109$	8.77228			0.840232			0.420116	+	0.907470i	$0.361989\pi$
$110$	−9.63844	−	17.6919i	−0.918989	−	1.68685i
$111$		0			0
$112$			31.5108i			2.97749i
$113$		−	10.0699i		−	0.947299i	−0.880713	−	0.473650i	$-0.842936\pi$
$113$		−	10.0699i		−	0.947299i	0.880713	−	0.473650i	$-0.157064\pi$
$114$		0			0
$115$	−7.92716	−	14.5507i	−0.739211	−	1.35686i
$116$	5.67486			0.526898
$117$		0			0
$118$		−	27.7035i		−	2.55032i
$119$	4.50459			0.412936
$120$		0			0
$121$	−0.422563			−0.0384148
$122$		−	32.8406i		−	2.97325i
$123$		0			0
$124$	−29.8061			−2.67666
$125$	0.829735	−	11.1495i	0.0742137	−	0.997242i
$126$		0			0
$127$		−	18.6739i		−	1.65704i	−0.559961	−	0.828519i	$-0.689184\pi$
$127$		−	18.6739i		−	1.65704i	0.559961	−	0.828519i	$-0.310816\pi$
$128$			56.0404i			4.95332i
$129$		0			0
$130$	18.5019	−	10.0798i	1.62273	−	0.884054i
$131$	11.0338			0.964025			0.482012	−	0.876164i	$-0.339906\pi$
$131$	11.0338			0.964025			0.482012	+	0.876164i	$0.339906\pi$
$132$		0			0
$133$			1.26172i			0.109405i
$134$	−22.0246			−1.90263
$135$		0			0
$136$	24.5292			2.10336
$137$			11.8714i			1.01425i	0.861874	+	0.507123i	$0.169291\pi$
$137$			11.8714i			1.01425i	−0.861874	+	0.507123i	$0.830709\pi$
$138$		0			0
$139$	−14.8451			−1.25915			−0.629574	−	0.776941i	$-0.716770\pi$
$139$	−14.8451			−1.25915			−0.629574	+	0.776941i	$0.716770\pi$
$140$	−11.3497	−	20.8330i	−0.959226	−	1.76071i
$141$		0			0
$142$			5.54071i			0.464966i
$143$			11.0618i			0.925030i
$144$		0			0
$145$	−1.96358	+	1.06975i	−0.163066	+	0.0888377i
$146$	−1.68405			−0.139373
$147$		0			0
$148$			10.6097i			0.872114i
$149$	17.2769			1.41538			0.707688	−	0.706525i	$-0.249738\pi$
$149$	17.2769			1.41538			0.707688	+	0.706525i	$0.249738\pi$
$150$		0			0
$151$	0.504595			0.0410633			0.0205317	−	0.999789i	$-0.493464\pi$
$151$	0.504595			0.0410633			0.0205317	+	0.999789i	$0.493464\pi$
$152$			6.87052i			0.557273i
$153$		0			0
$154$	16.8451			1.35742
$155$	10.3133	−	5.61863i	0.828384	−	0.451299i
$156$		0			0
$157$			17.9519i			1.43272i	0.697731	+	0.716360i	$0.254193\pi$
$157$			17.9519i			1.43272i	−0.697731	+	0.716360i	$0.745807\pi$
$158$			23.8306i			1.89586i
$159$		0			0
$160$	−28.1676	−	51.7032i	−2.22685	−	4.08749i
$161$	13.8543			1.09187
$162$		0			0
$163$		−	5.45295i		−	0.427108i	−0.976931	−	0.213554i	$-0.931496\pi$
$163$		−	5.45295i		−	0.427108i	0.976931	−	0.213554i	$-0.0685040\pi$
$164$		0			0
$165$		0			0
$166$	6.67486			0.518070
$167$		−	1.51195i		−	0.116998i	−0.998287	−	0.0584992i	$-0.981368\pi$
$167$		−	1.51195i		−	0.116998i	0.998287	−	0.0584992i	$-0.0186315\pi$
$168$		0			0
$169$	1.43175			0.110135
$170$	−13.1066	+	7.14041i	−1.00523	+	0.547645i
$171$		0			0
$172$			19.6878i			1.50118i
$173$		−	8.74012i		−	0.664499i	−0.943192	−	0.332249i	$-0.892192\pi$
$173$		−	8.74012i		−	0.664499i	0.943192	−	0.332249i	$-0.107808\pi$
$174$		0			0
$175$	7.85431	+	5.06901i	0.593730	+	0.383181i
$176$	54.8152			4.13185
$177$		0			0
$178$			23.5607i			1.76595i
$179$	−9.49541			−0.709720			−0.354860	−	0.934919i	$-0.615471\pi$
$179$	−9.49541			−0.709720			−0.354860	+	0.934919i	$0.615471\pi$
$180$		0			0
$181$	14.9363			1.11021			0.555105	−	0.831780i	$-0.312678\pi$
$181$	14.9363			1.11021			0.555105	+	0.831780i	$0.312678\pi$
$182$			17.6164i			1.30582i
$183$		0			0
$184$	75.4418			5.56165
$185$	−2.00000	−	3.67111i	−0.147043	−	0.269905i
$186$		0			0
$187$		−	7.83605i		−	0.573029i
$188$		−	22.7511i		−	1.65929i
$189$		0			0
$190$	−2.00000	−	3.67111i	−0.145095	−	0.266330i
$191$	−10.5292			−0.761864			−0.380932	−	0.924603i	$-0.624397\pi$
$191$	−10.5292			−0.761864			−0.380932	+	0.924603i	$0.624397\pi$
$192$		0			0
$193$		−	18.1341i		−	1.30532i	−0.757651	−	0.652660i	$-0.773653\pi$
$193$		−	18.1341i		−	1.30532i	0.757651	−	0.652660i	$-0.226347\pi$
$194$	36.3835			2.61218
$195$		0			0
$196$	−19.8881			−1.42058
$197$			16.9798i			1.20976i	0.796317	+	0.604879i	$0.206779\pi$
$197$			16.9798i			1.20976i	−0.796317	+	0.604879i	$0.793221\pi$
$198$		0			0
$199$	−7.49541			−0.531335			−0.265668	−	0.964065i	$-0.585592\pi$
$199$	−7.49541			−0.531335			−0.265668	+	0.964065i	$0.585592\pi$
$200$	42.7696	+	27.6026i	3.02427	+	1.95180i
$201$		0			0
$202$			13.4227i			0.944419i
$203$		−	1.86960i		−	0.131220i
$204$		0			0
$205$		0			0
$206$	41.2470			2.87381
$207$		0			0
$208$			57.3251i			3.97478i
$209$	2.19484			0.151821
$210$		0			0
$211$	18.0974			1.24588			0.622939	−	0.782270i	$-0.285938\pi$
$211$	18.0974			1.24588			0.622939	+	0.782270i	$0.285938\pi$
$212$			4.98126i			0.342114i
$213$		0			0
$214$	5.17945			0.354060
$215$	−3.71128	−	6.81226i	−0.253107	−	0.464592i
$216$		0			0
$217$			9.81970i			0.666604i
$218$		−	24.3023i		−	1.64596i
$219$		0			0
$220$	−36.2405	+	19.7436i	−2.44333	+	1.33111i
$221$	8.19484			0.551245
$222$		0			0
$223$		−	6.33073i		−	0.423937i	−0.977276	−	0.211969i	$-0.932013\pi$
$223$		−	6.33073i		−	0.423937i	0.977276	−	0.211969i	$-0.0679874\pi$
$224$	49.2286			3.28923
$225$		0			0
$226$	−27.8973			−1.85570
$227$		−	24.8905i		−	1.65204i	−0.563638	−	0.826022i	$-0.690599\pi$
$227$		−	24.8905i		−	1.65204i	0.563638	−	0.826022i	$-0.309401\pi$
$228$		0			0
$229$	−2.14569			−0.141791			−0.0708955	−	0.997484i	$-0.522586\pi$
$229$	−2.14569			−0.141791			−0.0708955	+	0.997484i	$0.522586\pi$
$230$	−40.3106	+	21.9610i	−2.65801	+	1.44807i
$231$		0			0
$232$		−	10.1807i		−	0.668393i
$233$			5.33891i			0.349763i	0.984589	+	0.174882i	$0.0559543\pi$
$233$			5.33891i			0.349763i	−0.984589	+	0.174882i	$0.944046\pi$
$234$		0			0
$235$	4.28872	+	7.87217i	0.279765	+	0.513524i
$236$	−56.7486			−3.69402
$237$		0			0
$238$		−	12.4793i		−	0.808914i
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$		0			0
$241$	−6.77228			−0.436241			−0.218121	−	0.975922i	$-0.569993\pi$
$241$	−6.77228			−0.436241			−0.218121	+	0.975922i	$0.569993\pi$
$242$			1.17065i			0.0752521i
$243$		0			0
$244$	−67.2716			−4.30662
$245$	6.88155	−	3.74903i	0.439646	−	0.239517i
$246$		0			0
$247$			2.29534i			0.146049i
$248$			53.4719i			3.39547i
$249$		0			0
$250$	−30.8881	−	2.29866i	−1.95353	−	0.145380i
$251$	−20.2615			−1.27889			−0.639447	−	0.768835i	$-0.720837\pi$
$251$	−20.2615			−1.27889			−0.639447	+	0.768835i	$0.720837\pi$
$252$		0			0
$253$		−	24.1005i		−	1.51519i
$254$	−51.7332			−3.24603
$255$		0			0
$256$	76.7762			4.79851
$257$			19.4376i			1.21248i	0.795280	+	0.606242i	$0.207324\pi$
$257$			19.4376i			1.21248i	−0.795280	+	0.606242i	$0.792676\pi$
$258$		0			0
$259$	3.49541			0.217194
$260$	−20.6476	−	37.8998i	−1.28051	−	2.35045i
$261$		0			0
$262$		−	30.5674i		−	1.88846i
$263$			8.28808i			0.511065i	0.966800	+	0.255533i	$0.0822508\pi$
$263$			8.28808i			0.511065i	−0.966800	+	0.255533i	$0.917749\pi$
$264$		0			0
$265$	−0.938999	−	1.72358i	−0.0576823	−	0.105879i
$266$	3.49541			0.214317
$267$		0			0
$268$			45.1157i			2.75588i
$269$	−23.8543			−1.45442			−0.727212	−	0.686413i	$-0.759184\pi$
$269$	−23.8543			−1.45442			−0.727212	+	0.686413i	$0.759184\pi$
$270$		0			0
$271$	−0.893389			−0.0542695			−0.0271347	−	0.999632i	$-0.508638\pi$
$271$	−0.893389			−0.0542695			−0.0271347	+	0.999632i	$0.508638\pi$
$272$		−	40.6086i		−	2.46226i
$273$		0			0
$274$	32.8881			1.98684
$275$	8.81789	−	13.6631i	0.531739	−	0.823917i
$276$		0			0
$277$			3.55706i			0.213723i	0.994274	+	0.106862i	$0.0340801\pi$
$277$			3.55706i			0.213723i	−0.994274	+	0.106862i	$0.965920\pi$
$278$			41.1262i			2.46659i
$279$		0			0
$280$	−37.3743	+	20.3613i	−2.23354	+	1.21682i
$281$	−7.76309			−0.463107			−0.231554	−	0.972822i	$-0.574381\pi$
$281$	−7.76309			−0.463107			−0.231554	+	0.972822i	$0.574381\pi$
$282$		0			0
$283$		−	30.7889i		−	1.83021i	−0.403215	−	0.915105i	$-0.632107\pi$
$283$		−	30.7889i		−	1.83021i	0.403215	−	0.915105i	$-0.367893\pi$
$284$	11.3497			0.673482
$285$		0			0
$286$	30.6450			1.81208
$287$		0			0
$288$		0			0
$289$	11.1948			0.658520
$290$	2.96358	+	5.43981i	0.174027	+	0.319436i
$291$		0			0
$292$			3.44965i			0.201875i
$293$			6.33073i			0.369845i	0.982753	+	0.184923i	$0.0592034\pi$
$293$			6.33073i			0.369845i	−0.982753	+	0.184923i	$0.940797\pi$
$294$		0			0
$295$	19.6358	−	10.6975i	1.14324	−	0.622831i
$296$	19.0338			1.10632
$297$		0			0
$298$		−	47.8631i		−	2.77263i
$299$	25.2040			1.45759
$300$		0			0
$301$	6.48622			0.373859
$302$		−	1.39791i		−	0.0804404i
$303$		0			0
$304$	11.3743			0.652361
$305$	23.2769	−	12.6811i	1.33283	−	0.726119i
$306$		0			0
$307$			12.5671i			0.717241i	0.933483	+	0.358620i	$0.116753\pi$
$307$			12.5671i			0.717241i	−0.933483	+	0.358620i	$0.883247\pi$
$308$		−	34.5060i		−	1.96616i
$309$		0			0
$310$	−15.5656	−	28.5715i	−0.884066	−	1.62275i
$311$	−24.3835			−1.38266			−0.691330	−	0.722539i	$-0.742975\pi$
$311$	−24.3835			−1.38266			−0.691330	+	0.722539i	$0.742975\pi$
$312$		0			0
$313$			34.6618i			1.95920i	0.200954	+	0.979601i	$0.435596\pi$
$313$			34.6618i			1.95920i	−0.200954	+	0.979601i	$0.564404\pi$
$314$	49.7332			2.80661
$315$		0			0
$316$	48.8152			2.74607
$317$			25.7880i			1.44840i	0.689591	+	0.724199i	$0.257790\pi$
$317$			25.7880i			1.44840i	−0.689591	+	0.724199i	$0.742210\pi$
$318$		0			0
$319$	−3.25230			−0.182094
$320$	−77.0465	+	41.9745i	−4.30703	+	2.34645i
$321$		0			0
$322$		−	38.3814i		−	2.13891i
$323$		−	1.62600i		−	0.0904730i
$324$		0			0
$325$	14.2887	+	9.22164i	0.792596	+	0.511525i
$326$	−15.1066			−0.836678
$327$		0			0
$328$		0			0
$329$	−7.49541			−0.413235
$330$		0			0
$331$	−16.9609			−0.932257			−0.466128	−	0.884717i	$-0.654352\pi$
$331$	−16.9609			−0.932257			−0.466128	+	0.884717i	$0.654352\pi$
$332$		−	13.6729i		−	0.750400i
$333$		0			0
$334$	−4.18864			−0.229192
$335$	−8.50459	−	15.6106i	−0.464656	−	0.852900i
$336$		0			0
$337$		−	22.5952i		−	1.23084i	−0.788200	−	0.615420i	$-0.788987\pi$
$337$		−	22.5952i		−	1.23084i	0.788200	−	0.615420i	$-0.211013\pi$
$338$		−	3.96646i		−	0.215747i
$339$		0			0
$340$	14.6266	+	26.8479i	0.793239	+	1.45603i
$341$	17.0820			0.925044
$342$		0			0
$343$			19.6394i			1.06043i
$344$	35.3198			1.90432
$345$		0			0
$346$	−24.2132			−1.30171
$347$		−	12.0469i		−	0.646714i	−0.946277	−	0.323357i	$-0.895189\pi$
$347$		−	12.0469i		−	0.646714i	0.946277	−	0.323357i	$-0.104811\pi$
$348$		0			0
$349$	1.56825			0.0839464			0.0419732	−	0.999119i	$-0.486636\pi$
$349$	1.56825			0.0839464			0.0419732	+	0.999119i	$0.486636\pi$
$350$	14.0430	−	21.7592i	0.750628	−	1.16308i
$351$		0			0
$352$		−	85.6365i		−	4.56444i
$353$			7.66054i			0.407730i	0.978999	+	0.203865i	$0.0653503\pi$
$353$			7.66054i			0.407730i	−0.978999	+	0.203865i	$0.934650\pi$
$354$		0			0
$355$	−3.92716	+	2.13949i	−0.208432	+	0.113553i
$356$	48.2624			2.55790
$357$		0			0
$358$			26.3056i			1.39030i
$359$	17.5928			0.928514			0.464257	−	0.885701i	$-0.346321\pi$
$359$	17.5928			0.928514			0.464257	+	0.885701i	$0.346321\pi$
$360$		0			0
$361$	−18.5446			−0.976030
$362$		−	41.3790i		−	2.17483i
$363$		0			0
$364$	36.0859			1.89142
$365$	−0.650280	−	1.19362i	−0.0340372	−	0.0624772i
$366$		0			0
$367$		−	9.88779i		−	0.516138i	−0.966126	−	0.258069i	$-0.916914\pi$
$367$		−	9.88779i		−	0.516138i	0.966126	−	0.258069i	$-0.0830863\pi$
$368$		−	124.896i		−	6.51064i
$369$		0			0
$370$	−10.1703	+	5.54071i	−0.528727	+	0.288048i
$371$	1.64109			0.0852012
$372$		0			0
$373$		−	16.2841i		−	0.843161i	−0.906791	−	0.421580i	$-0.861476\pi$
$373$		−	16.2841i		−	0.843161i	0.906791	−	0.421580i	$-0.138524\pi$
$374$	−21.7086			−1.12253
$375$		0			0
$376$	−40.8152			−2.10489
$377$		−	3.40121i		−	0.175171i
$378$		0			0
$379$	2.52917			0.129915			0.0649575	−	0.997888i	$-0.479309\pi$
$379$	2.52917			0.129915			0.0649575	+	0.997888i	$0.479309\pi$
$380$	−7.51998	+	4.09685i	−0.385767	+	0.210164i
$381$		0			0
$382$			29.1695i			1.49244i
$383$		−	5.60880i		−	0.286596i	−0.989680	−	0.143298i	$-0.954229\pi$
$383$		−	5.60880i		−	0.286596i	0.989680	−	0.143298i	$-0.0457708\pi$
$384$		0			0
$385$	6.50459	+	11.9395i	0.331505	+	0.608495i
$386$	−50.2378			−2.55704
$387$		0			0
$388$		−	74.5288i		−	3.78363i
$389$	−12.0000			−0.608424			−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000			−0.608424			−0.304212	+	0.952604i	$0.598393\pi$
$390$		0			0
$391$	−17.8543			−0.902931
$392$			35.6791i			1.80207i
$393$		0			0
$394$	47.0400			2.36984
$395$	−16.8907	+	9.20198i	−0.849865	+	0.463002i
$396$		0			0
$397$			27.8660i			1.39856i	0.714850	+	0.699278i	$0.246495\pi$
$397$			27.8660i			1.39856i	−0.714850	+	0.699278i	$0.753505\pi$
$398$			20.7649i			1.04085i
$399$		0			0
$400$	45.6968	−	70.8061i	2.28484	−	3.54030i
$401$	15.6174			0.779896			0.389948	−	0.920837i	$-0.372493\pi$
$401$	15.6174			0.779896			0.389948	+	0.920837i	$0.372493\pi$
$402$		0			0
$403$			17.8642i			0.889878i
$404$	27.4954			1.36795
$405$		0			0
$406$	−5.17945			−0.257052
$407$		−	6.08050i		−	0.301399i
$408$		0			0
$409$	30.5538			1.51079			0.755393	−	0.655272i	$-0.227446\pi$
$409$	30.5538			1.51079			0.755393	+	0.655272i	$0.227446\pi$
$410$		0			0
$411$		0			0
$412$		−	84.4913i		−	4.16259i
$413$			18.6960i			0.919970i
$414$		0			0
$415$	2.57744	+	4.73102i	0.126521	+	0.232237i
$416$	89.5576			4.39092
$417$		0			0
$418$		−	6.08050i		−	0.297407i
$419$	−10.0492			−0.490934			−0.245467	−	0.969405i	$-0.578941\pi$
$419$	−10.0492			−0.490934			−0.245467	+	0.969405i	$0.578941\pi$
$420$		0			0
$421$	−16.1948			−0.789288			−0.394644	−	0.918834i	$-0.629132\pi$
$421$	−16.1948			−0.789288			−0.394644	+	0.918834i	$0.629132\pi$
$422$		−	50.1363i		−	2.44060i
$423$		0			0
$424$	8.93635			0.433987
$425$	−10.1220	−	6.53253i	−0.490989	−	0.316874i
$426$		0			0
$427$			22.1628i			1.07253i
$428$		−	10.6097i		−	0.512840i
$429$		0			0
$430$	−18.8724	+	10.2816i	−0.910106	+	0.495821i
$431$	−11.1857			−0.538794			−0.269397	−	0.963029i	$-0.586824\pi$
$431$	−11.1857			−0.538794			−0.269397	+	0.963029i	$0.586824\pi$
$432$		0			0
$433$		−	14.0306i		−	0.674267i	−0.941457	−	0.337134i	$-0.890543\pi$
$433$		−	14.0306i		−	0.674267i	0.941457	−	0.337134i	$-0.109457\pi$
$434$	27.2040			1.30584
$435$		0			0
$436$	−49.7815			−2.38410
$437$		−	5.00092i		−	0.239226i
$438$		0			0
$439$	−9.65947			−0.461021			−0.230511	−	0.973070i	$-0.574040\pi$
$439$	−9.65947			−0.461021			−0.230511	+	0.973070i	$0.574040\pi$
$440$	35.4199	+	65.0151i	1.68858	+	3.09948i
$441$		0			0
$442$		−	22.7026i		−	1.07985i
$443$		−	9.75160i		−	0.463313i	−0.972798	−	0.231656i	$-0.925586\pi$
$443$		−	9.75160i		−	0.463313i	0.972798	−	0.231656i	$-0.0744145\pi$
$444$		0			0
$445$	−16.6994	+	9.09777i	−0.791629	+	0.431276i
$446$	−17.5384			−0.830466
$447$		0			0
$448$		−	73.3590i		−	3.46589i
$449$	8.86350			0.418295			0.209147	−	0.977884i	$-0.432931\pi$
$449$	8.86350			0.418295			0.209147	+	0.977884i	$0.432931\pi$
$450$		0			0
$451$		0			0
$452$			57.1454i			2.68790i
$453$		0			0
$454$	−68.9556			−3.23625
$455$	−12.4862	+	6.80243i	−0.585363	+	0.318903i
$456$		0			0
$457$			24.5041i			1.14625i	0.819466	+	0.573127i	$0.194270\pi$
$457$			24.5041i			1.14625i	−0.819466	+	0.573127i	$0.805730\pi$
$458$			5.94431i			0.277759i
$459$		0			0
$460$	44.9855	+	82.5733i	2.09746	+	3.85000i
$461$	37.4173			1.74270			0.871348	−	0.490666i	$-0.163247\pi$
$461$	37.4173			1.74270			0.871348	+	0.490666i	$0.163247\pi$
$462$		0			0
$463$		−	2.45534i		−	0.114109i	−0.998371	−	0.0570547i	$-0.981829\pi$
$463$		−	2.45534i		−	0.114109i	0.998371	−	0.0570547i	$-0.0181710\pi$
$464$	−16.8543			−0.782442
$465$		0			0
$466$	14.7907			0.685164
$467$			34.4182i			1.59268i	0.604846	+	0.796342i	$0.293235\pi$
$467$			34.4182i			1.59268i	−0.604846	+	0.796342i	$0.706765\pi$
$468$		0			0
$469$	14.8635			0.686333
$470$	21.8087	−	11.8813i	1.00596	−	0.548042i
$471$		0			0
$472$			101.807i			4.68603i
$473$		−	11.2832i		−	0.518803i
$474$		0			0
$475$	1.82973	−	2.83513i	0.0839540	−	0.130085i
$476$	−25.5629			−1.17168
$477$		0			0
$478$			5.54071i			0.253426i
$479$	−9.41636			−0.430245			−0.215122	−	0.976587i	$-0.569015\pi$
$479$	−9.41636			−0.430245			−0.215122	+	0.976587i	$0.569015\pi$
$480$		0			0
$481$	6.35891			0.289941
$482$			18.7616i			0.854568i
$483$		0			0
$484$	2.39798			0.108999
$485$	14.0492	+	25.7880i	0.637939	+	1.17097i
$486$		0			0
$487$			33.0909i			1.49949i	0.661726	+	0.749745i	$0.269824\pi$
$487$			33.0909i			1.49949i	−0.661726	+	0.749745i	$0.730176\pi$
$488$			120.685i			5.46314i
$489$		0			0
$490$	−10.3861	−	19.0643i	−0.469198	−	0.861238i
$491$	−28.9609			−1.30699			−0.653494	−	0.756932i	$-0.726698\pi$
$491$	−28.9609			−1.30699			−0.653494	+	0.756932i	$0.726698\pi$
$492$		0			0
$493$			2.40939i			0.108513i
$494$	6.35891			0.286101
$495$		0			0
$496$	88.5239			3.97484
$497$		−	3.73920i		−	0.167726i
$498$		0			0
$499$	−33.8727			−1.51635			−0.758175	−	0.652051i	$-0.773909\pi$
$499$	−33.8727			−1.51635			−0.758175	+	0.652051i	$0.773909\pi$
$500$	−4.70863	+	63.2719i	−0.210576	+	2.82961i
$501$		0			0
$502$			56.1315i			2.50527i
$503$		−	0.945870i		−	0.0421743i	−0.999778	−	0.0210871i	$-0.993287\pi$
$503$		−	0.945870i		−	0.0421743i	0.999778	−	0.0210871i	$-0.00671274\pi$
$504$		0			0
$505$	−9.51378	+	5.18306i	−0.423358	+	0.230643i
$506$	−66.7670			−2.96815
$507$		0			0
$508$			105.972i			4.70173i
$509$	32.1404			1.42460			0.712299	−	0.701877i	$-0.247654\pi$
$509$	32.1404			1.42460			0.712299	+	0.701877i	$0.247654\pi$
$510$		0			0
$511$	1.13650			0.0502757
$512$		−	100.616i		−	4.44665i
$513$		0			0
$514$	53.8490			2.37518
$515$	15.9272	+	29.2351i	0.701834	+	1.28825i
$516$		0			0
$517$			13.0388i			0.573444i
$518$		−	9.68351i		−	0.425469i
$519$		0			0
$520$	−67.9920	+	37.0417i	−2.98165	+	1.62439i
$521$	8.43175			0.369402			0.184701	−	0.982795i	$-0.440868\pi$
$521$	8.43175			0.369402			0.184701	+	0.982795i	$0.440868\pi$
$522$		0			0
$523$			21.8273i			0.954442i	0.878783	+	0.477221i	$0.158356\pi$
$523$			21.8273i			0.954442i	−0.878783	+	0.477221i	$0.841644\pi$
$524$	−62.6151			−2.73535
$525$		0			0
$526$	22.9609			1.00114
$527$		−	12.6548i		−	0.551253i
$528$		0			0
$529$	−31.9127			−1.38751
$530$	−4.77494	+	2.60136i	−0.207410	+	0.112996i
$531$		0			0
$532$		−	7.16007i		−	0.310429i
$533$		0			0
$534$		0			0
$535$	2.00000	+	3.67111i	0.0864675	+	0.158716i
$536$	80.9372			3.49596
$537$		0			0
$538$			66.0849i			2.84912i
$539$	11.3980			0.490946
$540$		0			0
$541$	−25.5138			−1.09692			−0.548462	−	0.836176i	$-0.684786\pi$
$541$	−25.5138			−1.09692			−0.548462	+	0.836176i	$0.684786\pi$
$542$			2.47500i			0.106310i
$543$		0			0
$544$	−63.4418			−2.72005
$545$	17.2251	−	9.38413i	0.737841	−	0.401972i
$546$		0			0
$547$		−	17.7698i		−	0.759781i	−0.925031	−	0.379891i	$-0.875962\pi$
$547$		−	17.7698i		−	0.759781i	0.925031	−	0.379891i	$-0.124038\pi$
$548$		−	67.3687i		−	2.87785i
$549$		0			0
$550$	−37.8517	−	24.4287i	−1.61400	−	1.04164i
$551$	−0.674860			−0.0287500
$552$		0			0
$553$		−	16.0823i		−	0.683890i
$554$	9.85431			0.418670
$555$		0			0
$556$	84.2440			3.57274
$557$			42.1665i			1.78665i	0.449409	+	0.893326i	$0.351635\pi$
$557$			42.1665i			1.78665i	−0.449409	+	0.893326i	$0.648365\pi$
$558$		0			0
$559$	11.7998			0.499080
$560$	33.7086	+	61.8740i	1.42445	+	2.61465i
$561$		0			0
$562$			21.5065i			0.907198i
$563$		−	5.76465i		−	0.242951i	−0.992594	−	0.121475i	$-0.961237\pi$
$563$		−	5.76465i		−	0.242951i	0.992594	−	0.121475i	$-0.0387626\pi$
$564$		0			0
$565$	−10.7723	−	19.7731i	−0.453193	−	0.831861i
$566$	−85.2961			−3.58526
$567$		0			0
$568$		−	20.3613i		−	0.854342i
$569$	1.49541			0.0626907			0.0313453	−	0.999509i	$-0.490021\pi$
$569$	1.49541			0.0626907			0.0313453	+	0.999509i	$0.490021\pi$
$570$		0			0
$571$	−7.03997			−0.294614			−0.147307	−	0.989091i	$-0.547060\pi$
$571$	−7.03997			−0.294614			−0.147307	+	0.989091i	$0.547060\pi$
$572$		−	62.7739i		−	2.62471i
$573$		0			0
$574$		0			0
$575$	−31.1312	−	20.0914i	−1.29826	−	0.837870i
$576$		0			0
$577$		−	34.7102i		−	1.44501i	−0.691368	−	0.722503i	$-0.742991\pi$
$577$		−	34.7102i		−	1.44501i	0.691368	−	0.722503i	$-0.257009\pi$
$578$		−	31.0137i		−	1.29000i
$579$		0			0
$580$	11.1430	−	6.07067i	0.462689	−	0.252071i
$581$	−4.50459			−0.186882
$582$		0			0
$583$		−	2.85479i		−	0.118233i
$584$	6.18864			0.256088
$585$		0			0
$586$	17.5384			0.724503
$587$			37.4158i			1.54432i	0.635430	+	0.772158i	$0.280823\pi$
$587$			37.4158i			1.54432i	−0.635430	+	0.772158i	$0.719177\pi$
$588$		0			0
$589$	3.54456			0.146051
$590$	−29.6358	−	54.3981i	−1.22009	−	2.23953i
$591$		0			0
$592$		−	31.5108i		−	1.29509i
$593$			32.6388i			1.34032i	0.742218	+	0.670158i	$0.233774\pi$
$593$			32.6388i			1.34032i	−0.742218	+	0.670158i	$0.766226\pi$
$594$		0			0
$595$	8.84513	−	4.81878i	0.362615	−	0.197551i
$596$	−98.0439			−4.01603
$597$		0			0
$598$		−	69.8241i		−	2.85532i
$599$	−38.1466			−1.55863			−0.779314	−	0.626634i	$-0.784432\pi$
$599$	−38.1466			−1.55863			−0.779314	+	0.626634i	$0.784432\pi$
$600$		0			0
$601$	−16.7178			−0.681934			−0.340967	−	0.940075i	$-0.610754\pi$
$601$	−16.7178			−0.681934			−0.340967	+	0.940075i	$0.610754\pi$
$602$		−	17.9691i		−	0.732366i
$603$		0			0
$604$	−2.86350			−0.116514
$605$	−0.829735	+	0.452035i	−0.0337335	+	0.0183778i
$606$		0			0
$607$			0.673496i			0.0273364i	0.999907	+	0.0136682i	$0.00435085\pi$
$607$			0.673496i			0.0273364i	−0.999907	+	0.0136682i	$0.995649\pi$
$608$		−	17.7698i		−	0.720660i
$609$		0			0
$610$	−35.1312	−	64.4852i	−1.42242	−	2.61093i
$611$	−13.6358			−0.551645
$612$		0			0
$613$			26.4615i			1.06877i	0.845241	+	0.534385i	$0.179457\pi$
$613$			26.4615i			1.06877i	−0.845241	+	0.534385i	$0.820543\pi$
$614$	34.8152			1.40503
$615$		0			0
$616$	−61.9035			−2.49416
$617$			27.9538i			1.12538i	0.826669	+	0.562688i	$0.190233\pi$
$617$			27.9538i			1.12538i	−0.826669	+	0.562688i	$0.809767\pi$
$618$		0			0
$619$	−24.6512			−0.990814			−0.495407	−	0.868661i	$-0.664981\pi$
$619$	−24.6512			−0.990814			−0.495407	+	0.868661i	$0.664981\pi$
$620$	−58.5265	+	31.8849i	−2.35048	+	1.28053i
$621$		0			0
$622$			67.5509i			2.70854i
$623$		−	15.9002i		−	0.637028i
$624$		0			0
$625$	−10.2979	−	22.7805i	−0.411916	−	0.911222i
$626$	96.0255			3.83795
$627$		0			0
$628$		−	101.875i		−	4.06524i
$629$	−4.50459			−0.179610
$630$		0			0
$631$	11.8052			0.469956			0.234978	−	0.972001i	$-0.424498\pi$
$631$	11.8052			0.469956			0.234978	+	0.972001i	$0.424498\pi$
$632$		−	87.5742i		−	3.48352i
$633$		0			0
$634$	71.4418			2.83732
$635$	−19.9763	−	36.6676i	−0.792736	−	1.45511i
$636$		0			0
$637$			11.9199i			0.472283i
$638$			9.01001i			0.356710i
$639$		0			0
$640$	59.9491	+	110.040i	2.36970	+	4.34970i
$641$	−13.8727			−0.547938			−0.273969	−	0.961738i	$-0.588337\pi$
$641$	−13.8727			−0.547938			−0.273969	+	0.961738i	$0.588337\pi$
$642$		0			0
$643$			5.29047i			0.208636i	0.994544	+	0.104318i	$0.0332660\pi$
$643$			5.29047i			0.208636i	−0.994544	+	0.104318i	$0.966734\pi$
$644$	−78.6213			−3.09811
$645$		0			0
$646$	−4.50459			−0.177231
$647$			40.7448i			1.60184i	0.598769	+	0.800921i	$0.295657\pi$
$647$			40.7448i			1.60184i	−0.598769	+	0.800921i	$0.704343\pi$
$648$		0			0
$649$	32.5230			1.27664
$650$	25.5472	−	39.5848i	1.00204	−	1.55264i
$651$		0			0
$652$			30.9447i			1.21189i
$653$		−	26.8742i		−	1.05167i	−0.850587	−	0.525834i	$-0.823753\pi$
$653$		−	26.8742i		−	1.05167i	0.850587	−	0.525834i	$-0.176247\pi$
$654$		0			0
$655$	21.6657	−	11.8033i	0.846548	−	0.461195i
$656$		0			0
$657$		0			0
$658$			20.7649i			0.809501i
$659$	29.1558			1.13575			0.567874	−	0.823116i	$-0.307766\pi$
$659$	29.1558			1.13575			0.567874	+	0.823116i	$0.307766\pi$
$660$		0			0
$661$	19.9035			0.774155			0.387078	−	0.922047i	$-0.373485\pi$
$661$	19.9035			0.774155			0.387078	+	0.922047i	$0.373485\pi$
$662$			46.9878i			1.82623i
$663$		0			0
$664$	−24.5292			−0.951917
$665$	1.34972	+	2.47748i	0.0523399	+	0.0960727i
$666$		0			0
$667$			7.41031i			0.286928i
$668$			8.58012i			0.331975i
$669$		0			0
$670$	−43.2470	+	23.5607i	−1.67078	+	0.910231i
$671$	38.5538			1.48835
$672$		0			0
$673$		−	8.71383i		−	0.335893i	−0.985796	−	0.167947i	$-0.946286\pi$
$673$		−	8.71383i		−	0.335893i	0.985796	−	0.167947i	$-0.0537136\pi$
$674$	−62.5967			−2.41114
$675$		0			0
$676$	−8.12499			−0.312500
$677$			9.70565i			0.373018i	0.982453	+	0.186509i	$0.0597174\pi$
$677$			9.70565i			0.373018i	−0.982453	+	0.186509i	$0.940283\pi$
$678$		0			0
$679$	−24.5538			−0.942287
$680$	48.1650	−	26.2400i	1.84704	−	1.00626i
$681$		0			0
$682$		−	47.3233i		−	1.81210i
$683$			9.53014i			0.364661i	0.983237	+	0.182330i	$0.0583640\pi$
$683$			9.53014i			0.364661i	−0.983237	+	0.182330i	$0.941636\pi$
$684$		0			0
$685$	12.6994	+	23.3105i	0.485221	+	0.890648i
$686$	54.4081			2.07731
$687$		0			0
$688$		−	58.4728i		−	2.22925i
$689$	2.98550			0.113739
$690$		0			0
$691$	8.50459			0.323530			0.161765	−	0.986829i	$-0.448281\pi$
$691$	8.50459			0.323530			0.161765	+	0.986829i	$0.448281\pi$
$692$			49.5990i			1.88547i
$693$		0			0
$694$	−33.3743			−1.26687
$695$	−29.1496	+	15.8805i	−1.10571	+	0.602383i
$696$		0			0
$697$		0			0
$698$		−	4.34460i		−	0.164446i
$699$		0			0
$700$	−44.5721	−	28.7659i	−1.68467	−	1.08725i
$701$	28.6266			1.08121			0.540606	−	0.841276i	$-0.318195\pi$
$701$	28.6266			1.08121			0.540606	+	0.841276i	$0.318195\pi$
$702$		0			0
$703$		−	1.26172i		−	0.0475866i
$704$	−127.613			−4.80960
$705$		0			0
$706$	21.2224			0.798716
$707$		−	9.05845i		−	0.340678i
$708$		0			0
$709$	−14.9855			−0.562792			−0.281396	−	0.959592i	$-0.590798\pi$
$709$	−14.9855			−0.562792			−0.281396	+	0.959592i	$0.590798\pi$
$710$	5.92716	+	10.8796i	0.222442	+	0.408305i
$711$		0			0
$712$		−	86.5824i		−	3.24481i
$713$		−	38.9211i		−	1.45761i
$714$		0			0
$715$	11.8333	+	21.7206i	0.442540	+	0.812305i
$716$	53.8851			2.01378
$717$		0			0
$718$		−	48.7384i		−	1.81890i
$719$	−36.7486			−1.37049			−0.685246	−	0.728312i	$-0.740305\pi$
$719$	−36.7486			−1.37049			−0.685246	+	0.728312i	$0.740305\pi$
$720$		0			0
$721$	−27.8359			−1.03666
$722$			51.3750i			1.91198i
$723$		0			0
$724$	−84.7617			−3.15014
$725$	−2.71128	+	4.20107i	−0.100694	+	0.156024i
$726$		0			0
$727$			39.1647i			1.45254i	0.687410	+	0.726270i	$0.258748\pi$
$727$			39.1647i			1.45254i	−0.687410	+	0.726270i	$0.741252\pi$
$728$		−	64.7379i		−	2.39935i
$729$		0			0
$730$	−3.30676	+	1.80151i	−0.122389	+	0.0666768i
$731$	−8.35891			−0.309165
$732$		0			0
$733$			5.38071i			0.198741i	0.995051	+	0.0993705i	$0.0316829\pi$
$733$			5.38071i			0.198741i	−0.995051	+	0.0993705i	$0.968317\pi$
$734$	−27.3927			−1.01108
$735$		0			0
$736$	−195.121			−7.19227
$737$		−	25.8561i		−	0.952421i
$738$		0			0
$739$	9.93336			0.365404			0.182702	−	0.983168i	$-0.441516\pi$
$739$	9.93336			0.365404			0.182702	+	0.983168i	$0.441516\pi$
$740$	11.3497	+	20.8330i	0.417224	+	0.765837i
$741$		0			0
$742$		−	4.54640i		−	0.166904i
$743$		−	43.4963i		−	1.59573i	−0.602839	−	0.797863i	$-0.705964\pi$
$743$		−	43.4963i		−	1.59573i	0.602839	−	0.797863i	$-0.294036\pi$
$744$		0			0
$745$	33.9245	−	18.4819i	1.24290	−	0.677124i
$746$	−45.1128			−1.65170
$747$		0			0
$748$			44.4685i			1.62593i
$749$	−3.49541			−0.127719
$750$		0			0
$751$	11.3743			0.415054			0.207527	−	0.978229i	$-0.433459\pi$
$751$	11.3743			0.415054			0.207527	+	0.978229i	$0.433459\pi$
$752$			67.5705i			2.46404i
$753$		0			0
$754$	−9.42256			−0.343149
$755$	0.990811	−	0.539789i	0.0360593	−	0.0196449i
$756$		0			0
$757$			10.0699i			0.365998i	0.983113	+	0.182999i	$0.0585805\pi$
$757$			10.0699i			0.365998i	−0.983113	+	0.182999i	$0.941420\pi$
$758$		−	7.00671i		−	0.254495i
$759$		0			0
$760$	7.34972	+	13.4908i	0.266602	+	0.489363i
$761$	27.0092			0.979082			0.489541	−	0.871980i	$-0.337164\pi$
$761$	27.0092			0.979082			0.489541	+	0.871980i	$0.337164\pi$
$762$		0			0
$763$			16.4007i			0.593744i
$764$	59.7516			2.16174
$765$		0			0
$766$	−15.5384			−0.561424
$767$			34.0121i			1.22811i
$768$		0			0
$769$	−25.7086			−0.927077			−0.463538	−	0.886077i	$-0.653420\pi$
$769$	−25.7086			−0.927077			−0.463538	+	0.886077i	$0.653420\pi$
$770$	33.0767	−	18.0200i	1.19200	−	0.649397i
$771$		0			0
$772$			102.908i			3.70375i
$773$		−	32.8185i		−	1.18040i	−0.807257	−	0.590200i	$-0.799049\pi$
$773$		−	32.8185i		−	1.18040i	0.807257	−	0.590200i	$-0.200951\pi$
$774$		0			0
$775$	14.2405	−	22.0652i	0.511532	−	0.792607i
$776$	−133.704			−4.79970
$777$		0			0
$778$			33.2442i			1.19186i
$779$		0			0
$780$		0			0
$781$	−6.50459			−0.232753
$782$			49.4628i			1.76878i
$783$		0			0
$784$	59.0675			2.10955
$785$	19.2040	+	35.2500i	0.685421	+	1.25813i
$786$		0			0
$787$			21.1973i			0.755602i	0.925887	+	0.377801i	$0.123320\pi$
$787$			21.1973i			0.755602i	−0.925887	+	0.377801i	$0.876680\pi$
$788$		−	96.3578i		−	3.43261i
$789$		0			0
$790$	25.4928	+	46.7933i	0.906991	+	1.66483i
$791$	18.8267			0.669402
$792$		0			0
$793$			40.3190i			1.43177i
$794$	77.1987			2.73968
$795$		0			0
$796$	42.5354			1.50763
$797$			21.7305i			0.769732i	0.922972	+	0.384866i	$0.125752\pi$
$797$			21.7305i			0.769732i	−0.922972	+	0.384866i	$0.874248\pi$
$798$		0			0
$799$	9.65947			0.341727
$800$	−110.619	−	71.3910i	−3.91096	−	2.52405i
$801$		0			0
$802$		−	43.2657i		−	1.52777i
$803$		−	1.97701i		−	0.0697673i
$804$		0			0
$805$	27.2040	−	14.8206i	0.958816	−	0.522358i
$806$	49.4901			1.74321
$807$		0			0
$808$		−	49.3266i		−	1.73530i
$809$	−7.20403			−0.253280			−0.126640	−	0.991949i	$-0.540419\pi$
$809$	−7.20403			−0.253280			−0.126640	+	0.991949i	$0.540419\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$			10.6097i			0.372328i
$813$		0			0
$814$	−16.8451			−0.590421
$815$	−5.83328	−	10.7073i	−0.204331	−	0.375060i
$816$		0			0
$817$		−	2.34130i		−	0.0819116i
$818$		−	84.6447i		−	2.95953i
$819$		0			0
$820$		0			0
$821$	−24.1220			−0.841864			−0.420932	−	0.907092i	$-0.638297\pi$
$821$	−24.1220			−0.841864			−0.420932	+	0.907092i	$0.638297\pi$
$822$		0			0
$823$		−	17.2300i		−	0.600600i	−0.953845	−	0.300300i	$-0.902913\pi$
$823$		−	17.2300i		−	0.600600i	0.953845	−	0.300300i	$-0.0970868\pi$
$824$	−151.577			−5.28043
$825$		0			0
$826$	51.7945			1.80216
$827$			3.46931i			0.120640i	0.998179	+	0.0603198i	$0.0192121\pi$
$827$			3.46931i			0.120640i	−0.998179	+	0.0603198i	$0.980788\pi$
$828$		0			0
$829$	−7.52619			−0.261395			−0.130698	−	0.991422i	$-0.541722\pi$
$829$	−7.52619			−0.261395			−0.130698	+	0.991422i	$0.541722\pi$
$830$	13.1066	−	7.14041i	0.454937	−	0.247847i
$831$		0			0
$832$		−	133.456i		−	4.62676i
$833$		−	8.44393i		−	0.292565i
$834$		0			0
$835$	−1.61741	−	2.96884i	−0.0559727	−	0.102741i
$836$	−12.4554			−0.430780
$837$		0			0
$838$			27.8397i			0.961707i
$839$	−9.61121			−0.331816			−0.165908	−	0.986141i	$-0.553055\pi$
$839$	−9.61121			−0.331816			−0.165908	+	0.986141i	$0.553055\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			44.8654i			1.54617i
$843$		0			0
$844$	−102.700			−3.53509
$845$	2.81136	−	1.53161i	0.0967136	−	0.0526891i
$846$		0			0
$847$		−	0.790023i		−	0.0271455i
$848$		−	14.7943i		−	0.508039i
$849$		0			0
$850$	−18.0974	+	28.0415i	−0.620736	+	0.961816i
$851$	−13.8543			−0.474920
$852$		0			0
$853$			20.8330i			0.713309i	0.934236	+	0.356654i	$0.116083\pi$
$853$			20.8330i			0.713309i	−0.934236	+	0.356654i	$0.883917\pi$
$854$	61.3989			2.10103
$855$		0			0
$856$	−19.0338			−0.650561
$857$		−	33.0424i		−	1.12871i	−0.825533	−	0.564354i	$-0.809125\pi$
$857$		−	33.0424i		−	1.12871i	0.825533	−	0.564354i	$-0.190875\pi$
$858$		0			0
$859$	−49.8061			−1.69936			−0.849680	−	0.527298i	$-0.823205\pi$
$859$	−49.8061			−1.69936			−0.849680	+	0.527298i	$0.823205\pi$
$860$	21.0610	+	38.6586i	0.718174	+	1.31825i
$861$		0			0
$862$			30.9882i			1.05546i
$863$			9.03631i			0.307599i	0.988102	+	0.153800i	$0.0491511\pi$
$863$			9.03631i			0.307599i	−0.988102	+	0.153800i	$0.950849\pi$
$864$		0			0
$865$	−9.34972	−	17.1619i	−0.317900	−	0.583522i
$866$	−38.8697			−1.32085
$867$		0			0
$868$		−	55.7254i		−	1.89144i
$869$	−27.9763			−0.949032
$870$		0			0
$871$	27.0400			0.916214
$872$			89.3076i			3.02434i
$873$		0			0
$874$	−13.8543			−0.468629
$875$	20.8451	+	1.55127i	0.704694	+	0.0524426i
$876$		0			0
$877$			24.0809i			0.813153i	0.913617	+	0.406576i	$0.133278\pi$
$877$			24.0809i			0.813153i	−0.913617	+	0.406576i	$0.866722\pi$
$878$			26.7601i			0.903111i
$879$		0			0
$880$	107.634	−	58.6385i	3.62834	−	1.97670i
$881$	0.814344			0.0274360			0.0137180	−	0.999906i	$-0.495633\pi$
$881$	0.814344			0.0274360			0.0137180	+	0.999906i	$0.495633\pi$
$882$		0			0
$883$			31.8751i			1.07268i	0.844001	+	0.536341i	$0.180194\pi$
$883$			31.8751i			1.07268i	−0.844001	+	0.536341i	$0.819806\pi$
$884$	−46.5046			−1.56412
$885$		0			0
$886$	−27.0154			−0.907600
$887$		−	45.6358i		−	1.53230i	−0.642661	−	0.766150i	$-0.722170\pi$
$887$		−	45.6358i		−	1.53230i	0.642661	−	0.766150i	$-0.277830\pi$
$888$		0			0
$889$	34.9127			1.17093
$890$	25.2040	+	46.2634i	0.844841	+	1.55075i
$891$		0			0
$892$			35.9260i			1.20289i
$893$			2.70558i			0.0905387i
$894$		0			0
$895$	−18.6450	+	10.1577i	−0.623233	+	0.339534i
$896$	−104.773			−3.50023
$897$		0			0
$898$		−	24.5550i		−	0.819412i
$899$	−5.25230			−0.175174
$900$		0			0
$901$	−2.11491			−0.0704577
$902$		0			0
$903$		0			0
$904$	102.519			3.40972
$905$	29.3287	−	15.9781i	0.974919	−	0.531131i
$906$		0			0
$907$		−	18.5820i		−	0.617004i	−0.951224	−	0.308502i	$-0.900172\pi$
$907$		−	18.5820i		−	0.617004i	0.951224	−	0.308502i	$-0.0998276\pi$
$908$			141.250i			4.68756i
$909$		0			0
$910$	18.8451	+	34.5912i	0.624710	+	1.14669i
$911$	45.6296			1.51178			0.755888	−	0.654701i	$-0.227206\pi$
$911$	45.6296			1.51178			0.755888	+	0.654701i	$0.227206\pi$
$912$		0			0
$913$			7.83605i			0.259335i
$914$	67.8851			2.24544
$915$		0			0
$916$	12.1765			0.402322
$917$			20.6287i			0.681221i
$918$		0			0
$919$	−24.6994			−0.814759			−0.407380	−	0.913259i	$-0.633557\pi$
$919$	−24.6994			−0.814759			−0.407380	+	0.913259i	$0.633557\pi$
$920$	148.136	−	80.7037i	4.88390	−	2.66072i
$921$		0			0
$922$		−	103.659i		−	3.41383i
$923$		−	6.80243i		−	0.223905i
$924$		0			0
$925$	−7.85431	−	5.06901i	−0.258248	−	0.166668i
$926$	−6.80217			−0.223533
$927$		0			0
$928$			26.3311i			0.864360i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$	2.36511			0.0775133
$932$		−	30.2975i		−	0.992429i
$933$		0			0
$934$	95.3506			3.11997
$935$	−8.38259	−	15.3867i	−0.274140	−	0.503199i
$936$		0			0
$937$		−	46.4389i		−	1.51709i	−0.651620	−	0.758546i	$-0.725910\pi$
$937$		−	46.4389i		−	1.51709i	0.651620	−	0.758546i	$-0.274090\pi$
$938$		−	41.1772i		−	1.34448i
$939$		0			0
$940$	−24.3379	−	44.6735i	−0.793814	−	1.45709i
$941$	14.2861			0.465712			0.232856	−	0.972511i	$-0.425193\pi$
$941$	14.2861			0.465712			0.232856	+	0.972511i	$0.425193\pi$
$942$		0			0
$943$		0			0
$944$	168.543			5.48561
$945$		0			0
$946$	−31.2585			−1.01630
$947$			29.3713i			0.954440i	0.878784	+	0.477220i	$0.158356\pi$
$947$			29.3713i			0.954440i	−0.878784	+	0.477220i	$0.841644\pi$
$948$		0			0
$949$	2.06754			0.0671151
$950$	−7.85431	−	5.06901i	−0.254828	−	0.164460i
$951$		0			0
$952$			45.8598i			1.48632i
$953$			22.5911i			0.731796i	0.930655	+	0.365898i	$0.119238\pi$
$953$			22.5911i			0.731796i	−0.930655	+	0.365898i	$0.880762\pi$
$954$		0			0
$955$	−20.6749	+	11.2636i	−0.669023	+	0.364480i
$956$	11.3497			0.367076
$957$		0			0
$958$			26.0867i			0.842821i
$959$	−22.1948			−0.716709
$960$		0			0
$961$	−3.41337			−0.110109
$962$		−	17.6164i		−	0.567976i
$963$		0			0
$964$	38.4318			1.23780
$965$	−19.3989	−	35.6077i	−0.624472	−	1.14625i
$966$		0			0
$967$		−	48.4316i		−	1.55746i	−0.627362	−	0.778728i	$-0.715865\pi$
$967$		−	48.4316i		−	1.55746i	0.627362	−	0.778728i	$-0.284135\pi$
$968$		−	4.30197i		−	0.138270i
$969$		0			0
$970$	71.4418	−	38.9211i	2.29386	−	1.24968i
$971$	−47.0829			−1.51096			−0.755482	−	0.655170i	$-0.772597\pi$
$971$	−47.0829			−1.51096			−0.755482	+	0.655170i	$0.772597\pi$
$972$		0			0
$973$		−	27.7545i		−	0.889767i
$974$	91.6734			2.93741
$975$		0			0
$976$	199.796			6.39532
$977$		−	51.1987i		−	1.63799i	−0.573800	−	0.818995i	$-0.694532\pi$
$977$		−	51.1987i		−	1.63799i	0.573800	−	0.818995i	$-0.305468\pi$
$978$		0			0
$979$	−27.6595			−0.884000
$980$	−39.0518	+	21.2752i	−1.24746	+	0.679612i
$981$		0			0
$982$			80.2320i			2.56031i
$983$			23.5123i			0.749926i	0.927040	+	0.374963i	$0.122345\pi$
$983$			23.5123i			0.749926i	−0.927040	+	0.374963i	$0.877655\pi$
$984$		0			0
$985$	18.1641	+	33.3411i	0.578755	+	1.06234i
$986$	6.67486			0.212571
$987$		0			0
$988$		−	13.0257i		−	0.414404i
$989$	−25.7086			−0.817487
$990$		0			0
$991$	−7.64109			−0.242727			−0.121364	−	0.992608i	$-0.538727\pi$
$991$	−7.64109			−0.242727			−0.121364	+	0.992608i	$0.538727\pi$
$992$		−	138.299i		−	4.39099i
$993$		0			0
$994$	−10.3589			−0.328565
$995$	−14.7178	+	8.01819i	−0.466586	+	0.254194i
$996$		0			0
$997$		−	3.71043i		−	0.117510i	−0.998272	−	0.0587552i	$-0.981287\pi$
$997$		−	3.71043i		−	0.117510i	0.998272	−	0.0587552i	$-0.0187131\pi$
$998$			93.8393i			2.97043i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.h.784.1		6
3.2	odd	2		145.2.b.c.59.6	yes	6
5.2	odd	4		6525.2.a.bt.1.6		6
5.3	odd	4		6525.2.a.bt.1.1		6
5.4	even	2	inner	1305.2.c.h.784.6		6
12.11	even	2		2320.2.d.g.929.4		6
15.2	even	4		725.2.a.l.1.1		6
15.8	even	4		725.2.a.l.1.6		6
15.14	odd	2		145.2.b.c.59.1	✓	6
60.59	even	2		2320.2.d.g.929.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.c.59.1	✓	6	15.14	odd	2
145.2.b.c.59.6	yes	6	3.2	odd	2
725.2.a.l.1.1		6	15.2	even	4
725.2.a.l.1.6		6	15.8	even	4
1305.2.c.h.784.1		6	1.1	even	1	trivial
1305.2.c.h.784.6		6	5.4	even	2	inner
2320.2.d.g.929.3		6	60.59	even	2
2320.2.d.g.929.4		6	12.11	even	2
6525.2.a.bt.1.1		6	5.3	odd	4
6525.2.a.bt.1.6		6	5.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.77035i q^{2} -5.67486 q^{4} +(1.96358 - 1.06975i) q^{5} +1.86960i q^{7} +10.1807i q^{8} +(-2.96358 - 5.43981i) q^{10} +3.25230 q^{11} +3.40121i q^{13} +5.17945 q^{14} +16.8543 q^{16} -2.40939i q^{17} +0.674860 q^{19} +(-11.1430 + 6.07067i) q^{20} -9.01001i q^{22} -7.41031i q^{23} +(2.71128 - 4.20107i) q^{25} +9.42256 q^{26} -10.6097i q^{28} -1.00000 q^{29} +5.25230 q^{31} -26.3311i q^{32} -6.67486 q^{34} +(2.00000 + 3.67111i) q^{35} -1.86960i q^{37} -1.86960i q^{38} +(10.8907 + 19.9905i) q^{40} -3.46931i q^{43} -18.4563 q^{44} -20.5292 q^{46} +4.00910i q^{47} +3.50459 q^{49} +(-11.6384 - 7.51121i) q^{50} -19.3014i q^{52} -0.877777i q^{53} +(6.38614 - 3.47914i) q^{55} -19.0338 q^{56} +2.77035i q^{58} +10.0000 q^{59} +11.8543 q^{61} -14.5507i q^{62} -39.2378 q^{64} +(3.63844 + 6.67855i) q^{65} -7.95010i q^{67} +13.6729i q^{68} +(10.1703 - 5.54071i) q^{70} -2.00000 q^{71} -0.607882i q^{73} -5.17945 q^{74} -3.82973 q^{76} +6.08050i q^{77} -8.60202 q^{79} +(33.0948 - 18.0299i) q^{80} +2.40939i q^{83} +(-2.57744 - 4.73102i) q^{85} -9.61121 q^{86} +33.1105i q^{88} -8.50459 q^{89} -6.35891 q^{91} +42.0525i q^{92} +11.1066 q^{94} +(1.32514 - 0.721929i) q^{95} +13.1332i q^{97} -9.70897i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 14 q^{4} - 3 q^{5} - 3 q^{10} + 10 q^{11} - 8 q^{14} + 42 q^{16} - 16 q^{19} - 13 q^{20} + 11 q^{25} + 46 q^{26} - 6 q^{29} + 22 q^{31} - 20 q^{34} + 12 q^{35} + 21 q^{40} - 2 q^{44} - 44 q^{46} + 2 q^{49}+ \cdots + 28 q^{95}+O(q^{100}) \) 6 * q - 14 * q^4 - 3 * q^5 - 3 * q^10 + 10 * q^11 - 8 * q^14 + 42 * q^16 - 16 * q^19 - 13 * q^20 + 11 * q^25 + 46 * q^26 - 6 * q^29 + 22 * q^31 - 20 * q^34 + 12 * q^35 + 21 * q^40 - 2 * q^44 - 44 * q^46 + 2 * q^49 - 35 * q^50 + 13 * q^55 - 16 * q^56 + 60 * q^59 + 12 * q^61 - 38 * q^64 - 13 * q^65 + 60 * q^70 - 12 * q^71 + 8 * q^74 - 24 * q^76 - 2 * q^79 + 55 * q^80 - 26 * q^85 + 30 * q^86 - 32 * q^89 + 40 * q^91 - 2 * q^94 + 28 * q^95

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