LMFDB - Embedded newform 1305.2.c.h.784.5

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			784.5
Root			$2.30229i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.h.784.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.30229i q^{2} -3.30056 q^{4} +(-2.17686 - 0.511167i) q^{5} +3.91261i q^{7} -2.99427i q^{8} +(1.17686 - 5.01177i) q^{10} -2.65427 q^{11} -5.62692i q^{13} -9.00799 q^{14} +0.292570 q^{16} +1.86794i q^{17} -1.69944 q^{19} +(7.18485 + 1.68714i) q^{20} -6.11092i q^{22} +0.691975i q^{23} +(4.47742 + 2.22548i) q^{25} +12.9548 q^{26} -12.9138i q^{28} -1.00000 q^{29} -0.654273 q^{31} -5.31495i q^{32} -4.30056 q^{34} +(2.00000 - 8.51720i) q^{35} -3.91261i q^{37} -3.91261i q^{38} +(-1.53057 + 6.51810i) q^{40} -10.7155i q^{43} +8.76059 q^{44} -1.59313 q^{46} +4.93495i q^{47} -8.30855 q^{49} +(-5.12370 + 10.3083i) q^{50} +18.5720i q^{52} -7.67159i q^{53} +(5.77797 + 1.35678i) q^{55} +11.7154 q^{56} -2.30229i q^{58} +10.0000 q^{59} -4.70743 q^{61} -1.50633i q^{62} +12.8217 q^{64} +(-2.87630 + 12.2490i) q^{65} +6.47253i q^{67} -6.16526i q^{68} +(19.6091 + 4.60459i) q^{70} -2.00000 q^{71} -10.5619i q^{73} +9.00799 q^{74} +5.60911 q^{76} -10.3851i q^{77} +2.05316 q^{79} +(-0.636884 - 0.149552i) q^{80} -1.86794i q^{83} +(0.954832 - 4.06625i) q^{85} +24.6703 q^{86} +7.94761i q^{88} +3.30855 q^{89} +22.0160 q^{91} -2.28390i q^{92} -11.3617 q^{94} +(3.69944 + 0.868699i) q^{95} -0.384703i q^{97} -19.1287i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.30229i			1.62797i	0.580887	+	0.813984i	$0.302706\pi$
$2$			2.30229i			1.62797i	−0.580887	+	0.813984i	$0.697294\pi$
$3$		0			0
$3$		0			0
$4$	−3.30056			−1.65028
$5$	−2.17686	−	0.511167i	−0.973520	−	0.228601i
$5$	−2.17686	−	0.511167i	−0.973520	−	0.228601i
$6$		0			0
$7$			3.91261i			1.47883i	0.673250	+	0.739415i	$0.264898\pi$
$7$			3.91261i			1.47883i	−0.673250	+	0.739415i	$0.735102\pi$
$8$		−	2.99427i		−	1.05863i
$9$		0			0
$10$	1.17686	−	5.01177i	0.372155	−	1.58486i
$11$	−2.65427			−0.800294			−0.400147	−	0.916451i	$-0.631041\pi$
$11$	−2.65427			−0.800294			−0.400147	+	0.916451i	$0.631041\pi$
$12$		0			0
$13$		−	5.62692i		−	1.56063i	−0.625388	−	0.780314i	$-0.715059\pi$
$13$		−	5.62692i		−	1.56063i	0.625388	−	0.780314i	$-0.284941\pi$
$14$	−9.00799			−2.40749
$15$		0			0
$16$	0.292570			0.0731426
$17$			1.86794i			0.453043i	0.974006	+	0.226522i	$0.0727354\pi$
$17$			1.86794i			0.453043i	−0.974006	+	0.226522i	$0.927265\pi$
$18$		0			0
$19$	−1.69944			−0.389879			−0.194939	−	0.980815i	$-0.562451\pi$
$19$	−1.69944			−0.389879			−0.194939	+	0.980815i	$0.562451\pi$
$20$	7.18485	+	1.68714i	1.60658	+	0.377255i
$21$		0			0
$22$		−	6.11092i		−	1.30285i
$23$			0.691975i			0.144287i	0.997394	+	0.0721433i	$0.0229839\pi$
$23$			0.691975i			0.144287i	−0.997394	+	0.0721433i	$0.977016\pi$
$24$		0			0
$25$	4.47742	+	2.22548i	0.895483	+	0.445095i
$26$	12.9548			2.54065
$27$		0			0
$28$		−	12.9138i		−	2.44048i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	−0.654273			−0.117511			−0.0587555	−	0.998272i	$-0.518713\pi$
$31$	−0.654273			−0.117511			−0.0587555	+	0.998272i	$0.518713\pi$
$32$		−	5.31495i		−	0.939560i
$33$		0			0
$34$	−4.30056			−0.737540
$35$	2.00000	−	8.51720i	0.338062	−	1.43967i
$36$		0			0
$37$		−	3.91261i		−	0.643230i	−0.946871	−	0.321615i	$-0.895774\pi$
$37$		−	3.91261i		−	0.643230i	0.946871	−	0.321615i	$-0.104226\pi$
$38$		−	3.91261i		−	0.634710i
$39$		0			0
$40$	−1.53057	+	6.51810i	−0.242005	+	1.03060i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$		−	10.7155i		−	1.63410i	−0.576567	−	0.817050i	$-0.695608\pi$
$43$		−	10.7155i		−	1.63410i	0.576567	−	0.817050i	$-0.304392\pi$
$44$	8.76059			1.32071
$45$		0			0
$46$	−1.59313			−0.234894
$47$			4.93495i			0.719836i	0.932984	+	0.359918i	$0.117195\pi$
$47$			4.93495i			0.719836i	−0.932984	+	0.359918i	$0.882805\pi$
$48$		0			0
$49$	−8.30855			−1.18694
$50$	−5.12370	+	10.3083i	−0.724601	+	1.45782i
$51$		0			0
$52$			18.5720i			2.57547i
$53$		−	7.67159i		−	1.05377i	−0.849935	−	0.526887i	$-0.823359\pi$
$53$		−	7.67159i		−	1.05377i	0.849935	−	0.526887i	$-0.176641\pi$
$54$		0			0
$55$	5.77797	+	1.35678i	0.779102	+	0.182948i
$56$	11.7154			1.56554
$57$		0			0
$58$		−	2.30229i		−	0.302306i
$59$	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
$61$	−4.70743			−0.602725			−0.301362	−	0.953510i	$-0.597441\pi$
$61$	−4.70743			−0.602725			−0.301362	+	0.953510i	$0.597441\pi$
$62$		−	1.50633i		−	0.191304i
$63$		0			0
$64$	12.8217			1.60272
$65$	−2.87630	+	12.2490i	−0.356761	+	1.51930i
$66$		0			0
$67$			6.47253i			0.790746i	0.918521	+	0.395373i	$0.129385\pi$
$67$			6.47253i			0.790746i	−0.918521	+	0.395373i	$0.870615\pi$
$68$		−	6.16526i		−	0.747648i
$69$		0			0
$70$	19.6091	+	4.60459i	2.34374	+	0.550354i
$71$	−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
$73$		−	10.5619i		−	1.23617i	−0.786110	−	0.618087i	$-0.787908\pi$
$73$		−	10.5619i		−	1.23617i	0.786110	−	0.618087i	$-0.212092\pi$
$74$	9.00799			1.04716
$75$		0			0
$76$	5.60911			0.643409
$77$		−	10.3851i		−	1.18350i
$78$		0			0
$79$	2.05316			0.230998			0.115499	−	0.993308i	$-0.463153\pi$
$79$	2.05316			0.230998			0.115499	+	0.993308i	$0.463153\pi$
$80$	−0.636884	−	0.149552i	−0.0712058	−	0.0167205i
$81$		0			0
$82$		0			0
$83$		−	1.86794i		−	0.205034i	−0.994731	−	0.102517i	$-0.967310\pi$
$83$		−	1.86794i		−	0.205034i	0.994731	−	0.102517i	$-0.0326895\pi$
$84$		0			0
$85$	0.954832	−	4.06625i	0.103566	−	0.441047i
$86$	24.6703			2.66026
$87$		0			0
$88$			7.94761i			0.847218i
$89$	3.30855			0.350705			0.175353	−	0.984506i	$-0.443893\pi$
$89$	3.30855			0.350705			0.175353	+	0.984506i	$0.443893\pi$
$90$		0			0
$91$	22.0160			2.30790
$92$		−	2.28390i		−	0.238113i
$93$		0			0
$94$	−11.3617			−1.17187
$95$	3.69944	+	0.868699i	0.379555	+	0.0891266i
$96$		0			0
$97$		−	0.384703i		−	0.0390607i	−0.999809	−	0.0195303i	$-0.993783\pi$
$97$		−	0.384703i		−	0.0390607i	0.999809	−	0.0195303i	$-0.00621710\pi$
$98$		−	19.1287i		−	1.93229i
$99$		0			0
$100$	−14.7780	−	7.34532i	−1.47780	−	0.734532i
$101$	−11.9097			−1.18506			−0.592528	−	0.805550i	$-0.701870\pi$
$101$	−11.9097			−1.18506			−0.592528	+	0.805550i	$0.701870\pi$
$102$		0			0
$103$			14.9585i			1.47390i	0.675946	+	0.736951i	$0.263735\pi$
$103$			14.9585i			1.47390i	−0.675946	+	0.736951i	$0.736265\pi$
$104$	−16.8485			−1.65213
$105$		0			0
$106$	17.6623			1.71551
$107$			3.91261i			0.378247i	0.981953	+	0.189123i	$0.0605646\pi$
$107$			3.91261i			0.378247i	−0.981953	+	0.189123i	$0.939435\pi$
$108$		0			0
$109$	7.55595			0.723729			0.361864	−	0.932231i	$-0.382140\pi$
$109$	7.55595			0.723729			0.361864	+	0.932231i	$0.382140\pi$
$110$	−3.12370	+	13.3026i	−0.297833	+	1.26835i
$111$		0			0
$112$			1.14472i			0.108165i
$113$		−	18.6944i		−	1.75862i	−0.476251	−	0.879309i	$-0.658005\pi$
$113$		−	18.6944i		−	1.75862i	0.476251	−	0.879309i	$-0.341995\pi$
$114$		0			0
$115$	0.353715	−	1.50633i	0.0329841	−	0.140466i
$116$	3.30056			0.306449
$117$		0			0
$118$			23.0229i			2.11943i
$119$	−7.30855			−0.669973
$120$		0			0
$121$	−3.95483			−0.359530
$122$		−	10.8379i		−	0.981216i
$123$		0			0
$124$	2.15947			0.193926
$125$	−8.60911	−	7.13325i	−0.770022	−	0.638018i
$126$		0			0
$127$			4.98929i			0.442728i	0.975191	+	0.221364i	$0.0710509\pi$
$127$			4.98929i			0.442728i	−0.975191	+	0.221364i	$0.928949\pi$
$128$			18.8895i			1.66961i
$129$		0			0
$130$	−28.2008	−	6.62209i	−2.47338	−	0.580795i
$131$	−19.7154			−1.72254			−0.861272	−	0.508144i	$-0.830332\pi$
$131$	−19.7154			−1.72254			−0.861272	+	0.508144i	$0.830332\pi$
$132$		0			0
$133$		−	6.64926i		−	0.576564i
$134$	−14.9017			−1.28731
$135$		0			0
$136$	5.59313			0.479607
$137$			6.26455i			0.535217i	0.963528	+	0.267608i	$0.0862334\pi$
$137$			6.26455i			0.535217i	−0.963528	+	0.267608i	$0.913767\pi$
$138$		0			0
$139$	−21.9097			−1.85835			−0.929177	−	0.369636i	$-0.879482\pi$
$139$	−21.9097			−1.85835			−0.929177	+	0.369636i	$0.879482\pi$
$140$	−6.60112	+	28.1115i	−0.557896	+	2.37586i
$141$		0			0
$142$		−	4.60459i		−	0.386408i
$143$			14.9354i			1.24896i
$144$		0			0
$145$	2.17686	+	0.511167i	0.180778	+	0.0424501i
$146$	24.3165			2.01245
$147$		0			0
$148$			12.9138i			1.06151i
$149$	4.24740			0.347961			0.173980	−	0.984749i	$-0.444337\pi$
$149$	4.24740			0.347961			0.173980	+	0.984749i	$0.444337\pi$
$150$		0			0
$151$	−11.3085			−0.920277			−0.460138	−	0.887847i	$-0.652200\pi$
$151$	−11.3085			−0.920277			−0.460138	+	0.887847i	$0.652200\pi$
$152$			5.08858i			0.412739i
$153$		0			0
$154$	23.9097			1.92670
$155$	1.42426	+	0.334443i	0.114399	+	0.0268631i
$156$		0			0
$157$		−	4.12059i		−	0.328859i	−0.986389	−	0.164430i	$-0.947422\pi$
$157$		−	4.12059i		−	0.328859i	0.986389	−	0.164430i	$-0.0525783\pi$
$158$			4.72697i			0.376057i
$159$		0			0
$160$	−2.71683	+	11.5699i	−0.214784	+	0.914681i
$161$	−2.70743			−0.213375
$162$		0			0
$163$		−	3.19755i		−	0.250452i	−0.992128	−	0.125226i	$-0.960034\pi$
$163$		−	3.19755i		−	0.250452i	0.992128	−	0.125226i	$-0.0399655\pi$
$164$		0			0
$165$		0			0
$166$	4.30056			0.333788
$167$		−	14.6050i		−	1.13017i	−0.825032	−	0.565086i	$-0.808843\pi$
$167$		−	14.6050i		−	1.13017i	0.825032	−	0.565086i	$-0.191157\pi$
$168$		0			0
$169$	−18.6623			−1.43556
$170$	9.36170	+	2.19830i	0.718010	+	0.168602i
$171$		0			0
$172$			35.3672i			2.69672i
$173$		−	9.00120i		−	0.684348i	−0.939637	−	0.342174i	$-0.888837\pi$
$173$		−	9.00120i		−	0.684348i	0.939637	−	0.342174i	$-0.111163\pi$
$174$		0			0
$175$	−8.70743	+	17.5184i	−0.658220	+	1.32427i
$176$	−0.776562			−0.0585356
$177$		0			0
$178$			7.61725i			0.570937i
$179$	−21.3085			−1.59268			−0.796338	−	0.604852i	$-0.793232\pi$
$179$	−21.3085			−1.59268			−0.796338	+	0.604852i	$0.793232\pi$
$180$		0			0
$181$	−16.9708			−1.26143			−0.630715	−	0.776014i	$-0.717238\pi$
$181$	−16.9708			−1.26143			−0.630715	+	0.776014i	$0.717238\pi$
$182$			50.6873i			3.75719i
$183$		0			0
$184$	2.07196			0.152747
$185$	−2.00000	+	8.51720i	−0.147043	+	0.626197i
$186$		0			0
$187$		−	4.95804i		−	0.362568i
$188$		−	16.2881i		−	1.18793i
$189$		0			0
$190$	−2.00000	+	8.51720i	−0.145095	+	0.617903i
$191$	8.40687			0.608300			0.304150	−	0.952624i	$-0.401628\pi$
$191$	8.40687			0.608300			0.304150	+	0.952624i	$0.401628\pi$
$192$		0			0
$193$		−	0.791267i		−	0.0569567i	−0.999594	−	0.0284783i	$-0.990934\pi$
$193$		−	0.791267i		−	0.0569567i	0.999594	−	0.0284783i	$-0.00906616\pi$
$194$	0.885700			0.0635895
$195$		0			0
$196$	27.4228			1.95877
$197$		−	24.5062i		−	1.74599i	−0.487726	−	0.872997i	$-0.662174\pi$
$197$		−	24.5062i		−	1.74599i	0.487726	−	0.872997i	$-0.337826\pi$
$198$		0			0
$199$	−19.3085			−1.36875			−0.684373	−	0.729132i	$-0.739924\pi$
$199$	−19.3085			−1.36875			−0.684373	+	0.729132i	$0.739924\pi$
$200$	6.66367	−	13.4066i	0.471193	−	0.947989i
$201$		0			0
$202$		−	27.4196i		−	1.92923i
$203$		−	3.91261i		−	0.274612i
$204$		0			0
$205$		0			0
$206$	−34.4388			−2.39947
$207$		0			0
$208$		−	1.64627i		−	0.114148i
$209$	4.51078			0.312017
$210$		0			0
$211$	19.2554			1.32560			0.662798	−	0.748798i	$-0.269369\pi$
$211$	19.2554			1.32560			0.662798	+	0.748798i	$0.269369\pi$
$212$			25.3205i			1.73902i
$213$		0			0
$214$	−9.00799			−0.615773
$215$	−5.47742	+	23.3261i	−0.373557	+	1.59083i
$216$		0			0
$217$		−	2.55992i		−	0.173779i
$218$			17.3960i			1.17821i
$219$		0			0
$220$	−19.0705	−	4.47812i	−1.28574	−	0.301915i
$221$	10.5108			0.707032
$222$		0			0
$223$		−	10.8691i		−	0.727852i	−0.931428	−	0.363926i	$-0.881436\pi$
$223$		−	10.8691i		−	0.727852i	0.931428	−	0.363926i	$-0.118564\pi$
$224$	20.7954			1.38945
$225$		0			0
$226$	43.0399			2.86297
$227$		−	17.3104i		−	1.14893i	−0.818528	−	0.574467i	$-0.805210\pi$
$227$		−	17.3104i		−	1.14893i	0.818528	−	0.574467i	$-0.194790\pi$
$228$		0			0
$229$	−18.7074			−1.23622			−0.618111	−	0.786091i	$-0.712102\pi$
$229$	−18.7074			−1.23622			−0.618111	+	0.786091i	$0.712102\pi$
$230$	3.46802	+	0.814355i	0.228674	+	0.0536970i
$231$		0			0
$232$			2.99427i			0.196583i
$233$			14.6281i			0.958320i	0.877728	+	0.479160i	$0.159059\pi$
$233$			14.6281i			0.958320i	−0.877728	+	0.479160i	$0.840941\pi$
$234$		0			0
$235$	2.52258	−	10.7427i	0.164555	−	0.700775i
$236$	−33.0056			−2.14848
$237$		0			0
$238$		−	16.8264i		−	1.09070i
$239$	−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
$241$	−5.55595			−0.357890			−0.178945	−	0.983859i	$-0.557268\pi$
$241$	−5.55595			−0.357890			−0.178945	+	0.983859i	$0.557268\pi$
$242$		−	9.10519i		−	0.585304i
$243$		0			0
$244$	15.5371			0.994664
$245$	18.0865	+	4.24706i	1.15551	+	0.271335i
$246$		0			0
$247$			9.56263i			0.608455i
$248$			1.95907i			0.124401i
$249$		0			0
$250$	16.4228	−	19.8207i	1.03867	−	1.25357i
$251$	9.27137			0.585204			0.292602	−	0.956234i	$-0.405479\pi$
$251$	9.27137			0.585204			0.292602	+	0.956234i	$0.405479\pi$
$252$		0			0
$253$		−	1.83669i		−	0.115472i
$254$	−11.4868			−0.720747
$255$		0			0
$256$	−17.8457			−1.11536
$257$			14.1129i			0.880337i	0.897915	+	0.440168i	$0.145081\pi$
$257$			14.1129i			0.880337i	−0.897915	+	0.440168i	$0.854919\pi$
$258$		0			0
$259$	15.3085			0.951227
$260$	9.49339	−	40.4286i	0.588755	−	2.50727i
$261$		0			0
$262$		−	45.3907i		−	2.80425i
$263$			6.97962i			0.430382i	0.976572	+	0.215191i	$0.0690373\pi$
$263$			6.97962i			0.430382i	−0.976572	+	0.215191i	$0.930963\pi$
$264$		0			0
$265$	−3.92147	+	16.7000i	−0.240894	+	1.02587i
$266$	15.3085			0.938627
$267$		0			0
$268$		−	21.3630i		−	1.30495i
$269$	−7.29257			−0.444636			−0.222318	−	0.974974i	$-0.571362\pi$
$269$	−7.29257			−0.444636			−0.222318	+	0.974974i	$0.571362\pi$
$270$		0			0
$271$	−23.3617			−1.41912			−0.709561	−	0.704644i	$-0.751107\pi$
$271$	−23.3617			−1.41912			−0.709561	+	0.704644i	$0.751107\pi$
$272$			0.546506i			0.0331368i
$273$		0			0
$274$	−14.4228			−0.871316
$275$	−11.8843	−	5.90702i	−0.716649	−	0.356207i
$276$		0			0
$277$			2.91337i			0.175047i	0.996162	+	0.0875236i	$0.0278953\pi$
$277$			2.91337i			0.175047i	−0.996162	+	0.0875236i	$0.972105\pi$
$278$		−	50.4425i		−	3.02534i
$279$		0			0
$280$	−25.5028	−	5.98854i	−1.52408	−	0.357884i
$281$	−30.1730			−1.79997			−0.899986	−	0.435918i	$-0.856424\pi$
$281$	−30.1730			−1.79997			−0.899986	+	0.435918i	$0.856424\pi$
$282$		0			0
$283$		−	2.01341i		−	0.119685i	−0.998208	−	0.0598425i	$-0.980940\pi$
$283$		−	2.01341i		−	0.119685i	0.998208	−	0.0598425i	$-0.0190599\pi$
$284$	6.60112			0.391704
$285$		0			0
$286$	−34.3857			−2.03327
$287$		0			0
$288$		0			0
$289$	13.5108			0.794752
$290$	−1.17686	+	5.01177i	−0.0691074	+	0.294301i
$291$		0			0
$292$			34.8601i			2.04003i
$293$			10.8691i			0.634982i	0.948261	+	0.317491i	$0.102840\pi$
$293$			10.8691i			0.634982i	−0.948261	+	0.317491i	$0.897160\pi$
$294$		0			0
$295$	−21.7686	−	5.11167i	−1.26742	−	0.297613i
$296$	−11.7154			−0.680945
$297$		0			0
$298$			9.77877i			0.566469i
$299$	3.89369			0.225178
$300$		0			0
$301$	41.9256			2.41655
$302$		−	26.0356i		−	1.49818i
$303$		0			0
$304$	−0.497206			−0.0285167
$305$	10.2474	+	2.40628i	0.586765	+	0.137783i
$306$		0			0
$307$			9.02429i			0.515043i	0.966273	+	0.257522i	$0.0829059\pi$
$307$			9.02429i			0.515043i	−0.966273	+	0.257522i	$0.917094\pi$
$308$			34.2768i			1.95310i
$309$		0			0
$310$	−0.769987	+	3.27907i	−0.0437323	+	0.186238i
$311$	11.1143			0.630234			0.315117	−	0.949053i	$-0.397956\pi$
$311$	11.1143			0.630234			0.315117	+	0.949053i	$0.397956\pi$
$312$		0			0
$313$		−	25.7365i		−	1.45471i	−0.686260	−	0.727356i	$-0.740749\pi$
$313$		−	25.7365i		−	1.45471i	0.686260	−	0.727356i	$-0.259251\pi$
$314$	9.48682			0.535372
$315$		0			0
$316$	−6.77656			−0.381211
$317$			0.837444i			0.0470355i	0.999723	+	0.0235178i	$0.00748663\pi$
$317$			0.837444i			0.0470355i	−0.999723	+	0.0235178i	$0.992513\pi$
$318$		0			0
$319$	2.65427			0.148611
$320$	−27.9111	−	6.55405i	−1.56028	−	0.366382i
$321$		0			0
$322$		−	6.23330i		−	0.347368i
$323$		−	3.17446i		−	0.176632i
$324$		0			0
$325$	12.5226	−	25.1941i	0.694628	−	1.39752i
$326$	7.36170			0.407727
$327$		0			0
$328$		0			0
$329$	−19.3085			−1.06451
$330$		0			0
$331$	22.0691			1.21303			0.606515	−	0.795072i	$-0.292567\pi$
$331$	22.0691			1.21303			0.606515	+	0.795072i	$0.292567\pi$
$332$			6.16526i			0.338363i
$333$		0			0
$334$	33.6251			1.83988
$335$	3.30855	−	14.0898i	0.180765	−	0.769807i
$336$		0			0
$337$		−	7.74780i		−	0.422049i	−0.977481	−	0.211025i	$-0.932320\pi$
$337$		−	7.74780i		−	0.422049i	0.977481	−	0.211025i	$-0.0676800\pi$
$338$		−	42.9660i		−	2.33704i
$339$		0			0
$340$	−3.15148	+	13.4209i	−0.170913	+	0.727850i
$341$	1.73662			0.0940433
$342$		0			0
$343$		−	5.11984i		−	0.276445i
$344$	−32.0851			−1.72991
$345$		0			0
$346$	20.7234			1.11410
$347$			9.33972i			0.501383i	0.968067	+	0.250691i	$0.0806579\pi$
$347$			9.33972i			0.501383i	−0.968067	+	0.250691i	$0.919342\pi$
$348$		0			0
$349$	21.6623			1.15955			0.579777	−	0.814775i	$-0.303140\pi$
$349$	21.6623			1.15955			0.579777	+	0.814775i	$0.303140\pi$
$350$	−40.3325	−	20.0471i	−2.15586	−	1.07156i
$351$		0			0
$352$			14.1073i			0.751924i
$353$			20.5623i			1.09442i	0.836995	+	0.547211i	$0.184310\pi$
$353$			20.5623i			1.09442i	−0.836995	+	0.547211i	$0.815690\pi$
$354$		0			0
$355$	4.35371	+	1.02233i	0.231071	+	0.0542599i
$356$	−10.9201			−0.578762
$357$		0			0
$358$		−	49.0585i		−	2.59282i
$359$	30.5639			1.61310			0.806551	−	0.591164i	$-0.201331\pi$
$359$	30.5639			1.61310			0.806551	+	0.591164i	$0.201331\pi$
$360$		0			0
$361$	−16.1119			−0.847995
$362$		−	39.0718i		−	2.05357i
$363$		0			0
$364$	−72.6650			−3.80868
$365$	−5.39888	+	22.9917i	−0.282590	+	1.20344i
$366$		0			0
$367$		−	13.7825i		−	0.719441i	−0.933060	−	0.359721i	$-0.882872\pi$
$367$		−	13.7825i		−	0.719441i	0.933060	−	0.359721i	$-0.117128\pi$
$368$			0.202451i			0.0105535i
$369$		0			0
$370$	−19.6091	−	4.60459i	−1.01943	−	0.239381i
$371$	30.0160			1.55835
$372$		0			0
$373$			27.2659i			1.41178i	0.708324	+	0.705888i	$0.249452\pi$
$373$			27.2659i			1.41178i	−0.708324	+	0.705888i	$0.750548\pi$
$374$	11.4149			0.590248
$375$		0			0
$376$	14.7766			0.762043
$377$			5.62692i			0.289801i
$378$		0			0
$379$	−16.4069			−0.842764			−0.421382	−	0.906883i	$-0.638455\pi$
$379$	−16.4069			−0.842764			−0.421382	+	0.906883i	$0.638455\pi$
$380$	−12.2102	−	2.86719i	−0.626371	−	0.147084i
$381$		0			0
$382$			19.3551i			0.990293i
$383$		−	11.7378i		−	0.599776i	−0.953974	−	0.299888i	$-0.903051\pi$
$383$		−	11.7378i		−	0.599776i	0.953974	−	0.299888i	$-0.0969493\pi$
$384$		0			0
$385$	−5.30855	+	22.6070i	−0.270549	+	1.15216i
$386$	1.82173			0.0927236
$387$		0			0
$388$			1.26974i			0.0644610i
$389$	−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
$391$	−1.29257			−0.0653681
$392$			24.8780i			1.25653i
$393$		0			0
$394$	56.4204			2.84242
$395$	−4.46943	−	1.04951i	−0.224881	−	0.0528064i
$396$		0			0
$397$			6.03349i			0.302812i	0.988472	+	0.151406i	$0.0483801\pi$
$397$			6.03349i			0.302812i	−0.988472	+	0.151406i	$0.951620\pi$
$398$		−	44.4540i		−	2.22828i
$399$		0			0
$400$	1.30996	+	0.651109i	0.0654980	+	0.0325554i
$401$	21.4656			1.07194			0.535971	−	0.844237i	$-0.319946\pi$
$401$	21.4656			1.07194			0.535971	+	0.844237i	$0.319946\pi$
$402$		0			0
$403$			3.68155i			0.183391i
$404$	39.3085			1.95567
$405$		0			0
$406$	9.00799			0.447059
$407$			10.3851i			0.514773i
$408$		0			0
$409$	4.49481			0.222254			0.111127	−	0.993806i	$-0.464554\pi$
$409$	4.49481			0.222254			0.111127	+	0.993806i	$0.464554\pi$
$410$		0			0
$411$		0			0
$412$		−	49.3713i		−	2.43235i
$413$			39.1261i			1.92527i
$414$		0			0
$415$	−0.954832	+	4.06625i	−0.0468709	+	0.199604i
$416$	−29.9068			−1.46630
$417$		0			0
$418$			10.3851i			0.507954i
$419$	4.19665			0.205020			0.102510	−	0.994732i	$-0.467313\pi$
$419$	4.19665			0.205020			0.102510	+	0.994732i	$0.467313\pi$
$420$		0			0
$421$	−18.5108			−0.902160			−0.451080	−	0.892483i	$-0.648961\pi$
$421$	−18.5108			−0.902160			−0.451080	+	0.892483i	$0.648961\pi$
$422$			44.3316i			2.15803i
$423$		0			0
$424$	−22.9708			−1.11556
$425$	−4.15707	+	8.36357i	−0.201647	+	0.405693i
$426$		0			0
$427$		−	18.4184i		−	0.891327i
$428$		−	12.9138i		−	0.624213i
$429$		0			0
$430$	−53.7036	−	12.6106i	−2.58982	−	0.608138i
$431$	−37.1279			−1.78839			−0.894193	−	0.447681i	$-0.852250\pi$
$431$	−37.1279			−1.78839			−0.894193	+	0.447681i	$0.852250\pi$
$432$		0			0
$433$			16.8577i			0.810128i	0.914288	+	0.405064i	$0.132751\pi$
$433$			16.8577i			0.810128i	−0.914288	+	0.405064i	$0.867249\pi$
$434$	5.89369			0.282906
$435$		0			0
$436$	−24.9389			−1.19435
$437$		−	1.17597i		−	0.0562543i
$438$		0			0
$439$	9.21821			0.439961			0.219981	−	0.975504i	$-0.429401\pi$
$439$	9.21821			0.439961			0.219981	+	0.975504i	$0.429401\pi$
$440$	4.06256	−	17.3008i	0.193675	−	0.824784i
$441$		0			0
$442$			24.1989i			1.15102i
$443$			18.9023i			0.898078i	0.893512	+	0.449039i	$0.148234\pi$
$443$			18.9023i			0.898078i	−0.893512	+	0.449039i	$0.851766\pi$
$444$		0			0
$445$	−7.20223	−	1.69122i	−0.341419	−	0.0801716i
$446$	25.0240			1.18492
$447$		0			0
$448$			50.1665i			2.37014i
$449$	−31.3245			−1.47830			−0.739148	−	0.673543i	$-0.764772\pi$
$449$	−31.3245			−1.47830			−0.739148	+	0.673543i	$0.764772\pi$
$450$		0			0
$451$		0			0
$452$			61.7019i			2.90221i
$453$		0			0
$454$	39.8537			1.87043
$455$	−47.9256	−	11.2538i	−2.24679	−	0.527588i
$456$		0			0
$457$		−	36.6287i		−	1.71342i	−0.515799	−	0.856710i	$-0.672505\pi$
$457$		−	36.6287i		−	1.71342i	0.515799	−	0.856710i	$-0.327495\pi$
$458$		−	43.0700i		−	2.01253i
$459$		0			0
$460$	−1.16746	+	4.97173i	−0.0544329	+	0.231808i
$461$	−28.8297			−1.34273			−0.671367	−	0.741125i	$-0.734293\pi$
$461$	−28.8297			−1.34273			−0.671367	+	0.741125i	$0.734293\pi$
$462$		0			0
$463$			29.6409i			1.37753i	0.724984	+	0.688766i	$0.241847\pi$
$463$			29.6409i			1.37753i	−0.724984	+	0.688766i	$0.758153\pi$
$464$	−0.292570			−0.0135822
$465$		0			0
$466$	−33.6782			−1.56011
$467$		−	26.4746i		−	1.22510i	−0.790432	−	0.612550i	$-0.790144\pi$
$467$		−	26.4746i		−	1.22510i	0.790432	−	0.612550i	$-0.209856\pi$
$468$		0			0
$469$	−25.3245			−1.16938
$470$	24.7328	+	5.80773i	1.14084	+	0.267891i
$471$		0			0
$472$		−	29.9427i		−	1.37822i
$473$			28.4419i			1.30776i
$474$		0			0
$475$	−7.60911	−	3.78207i	−0.349130	−	0.173533i
$476$	24.1223			1.10564
$477$		0			0
$478$		−	4.60459i		−	0.210609i
$479$	27.1810			1.24193			0.620967	−	0.783837i	$-0.286740\pi$
$479$	27.1810			1.24193			0.620967	+	0.783837i	$0.286740\pi$
$480$		0			0
$481$	−22.0160			−1.00384
$482$		−	12.7914i		−	0.582634i
$483$		0			0
$484$	13.0532			0.593325
$485$	−0.196648	+	0.837444i	−0.00892931	+	0.0380264i
$486$		0			0
$487$			32.0922i			1.45424i	0.686513	+	0.727118i	$0.259141\pi$
$487$			32.0922i			1.45424i	−0.686513	+	0.727118i	$0.740859\pi$
$488$			14.0953i			0.638065i
$489$		0			0
$490$	−9.77797	+	41.6405i	−0.441724	+	1.88113i
$491$	10.0691			0.454414			0.227207	−	0.973847i	$-0.427041\pi$
$491$	10.0691			0.454414			0.227207	+	0.973847i	$0.427041\pi$
$492$		0			0
$493$		−	1.86794i		−	0.0841280i
$494$	−22.0160			−0.990546
$495$		0			0
$496$	−0.191421			−0.00859506
$497$		−	7.82523i		−	0.351009i
$498$		0			0
$499$	29.9416			1.34037			0.670185	−	0.742194i	$-0.266215\pi$
$499$	29.9416			1.34037			0.670185	+	0.742194i	$0.266215\pi$
$500$	28.4149	+	23.5437i	1.27075	+	1.05291i
$501$		0			0
$502$			21.3454i			0.952693i
$503$		−	24.0140i		−	1.07073i	−0.844620	−	0.535366i	$-0.820174\pi$
$503$		−	24.0140i		−	1.07073i	0.844620	−	0.535366i	$-0.179826\pi$
$504$		0			0
$505$	25.9256	+	6.08783i	1.15368	+	0.270905i
$506$	4.22860			0.187984
$507$		0			0
$508$		−	16.4674i		−	0.730625i
$509$	−21.0771			−0.934227			−0.467113	−	0.884197i	$-0.654706\pi$
$509$	−21.0771			−0.934227			−0.467113	+	0.884197i	$0.654706\pi$
$510$		0			0
$511$	41.3245			1.82809
$512$		−	3.30707i		−	0.146153i
$513$		0			0
$514$	−32.4920			−1.43316
$515$	7.64629	−	32.5625i	0.336936	−	1.43487i
$516$		0			0
$517$		−	13.0987i		−	0.576080i
$518$			35.2448i			1.54857i
$519$		0			0
$520$	36.6768	+	8.61241i	1.60839	+	0.377679i
$521$	−11.6623			−0.510933			−0.255466	−	0.966818i	$-0.582229\pi$
$521$	−11.6623			−0.510933			−0.255466	+	0.966818i	$0.582229\pi$
$522$		0			0
$523$			36.3895i			1.59120i	0.605821	+	0.795601i	$0.292845\pi$
$523$			36.3895i			1.59120i	−0.605821	+	0.795601i	$0.707155\pi$
$524$	65.0719			2.84268
$525$		0			0
$526$	−16.0691			−0.700647
$527$		−	1.22215i		−	0.0532376i
$528$		0			0
$529$	22.5212			0.979181
$530$	−38.4482	−	9.02837i	−1.67008	−	0.392167i
$531$		0			0
$532$			21.9463i			0.951491i
$533$		0			0
$534$		0			0
$535$	2.00000	−	8.51720i	0.0864675	−	0.368231i
$536$	19.3805			0.837110
$537$		0			0
$538$		−	16.7896i		−	0.723853i
$539$	22.0532			0.949897
$540$		0			0
$541$	9.92564			0.426737			0.213368	−	0.976972i	$-0.431557\pi$
$541$	9.92564			0.426737			0.213368	+	0.976972i	$0.431557\pi$
$542$		−	53.7855i		−	2.31029i
$543$		0			0
$544$	9.92804			0.425661
$545$	−16.4482	−	3.86235i	−0.704565	−	0.165445i
$546$		0			0
$547$			9.03245i			0.386200i	0.981179	+	0.193100i	$0.0618541\pi$
$547$			9.03245i			0.386200i	−0.981179	+	0.193100i	$0.938146\pi$
$548$		−	20.6765i		−	0.883258i
$549$		0			0
$550$	13.5997	−	27.3611i	0.579893	−	1.16668i
$551$	1.69944			0.0723986
$552$		0			0
$553$			8.03321i			0.341607i
$554$	−6.70743			−0.284971
$555$		0			0
$556$	72.3141			3.06680
$557$		−	13.7145i		−	0.581101i	−0.956860	−	0.290550i	$-0.906162\pi$
$557$		−	13.7145i		−	0.581101i	0.956860	−	0.290550i	$-0.0938384\pi$
$558$		0			0
$559$	−60.2953			−2.55022
$560$	0.585141	−	2.49188i	0.0247267	−	0.105301i
$561$		0			0
$562$		−	69.4672i		−	2.93030i
$563$		−	20.2781i		−	0.854621i	−0.904105	−	0.427311i	$-0.859461\pi$
$563$		−	20.2781i		−	0.854621i	0.904105	−	0.427311i	$-0.140539\pi$
$564$		0			0
$565$	−9.55595	+	40.6950i	−0.402022	+	1.71205i
$566$	4.63547			0.194843
$567$		0			0
$568$			5.98854i			0.251273i
$569$	13.3085			0.557923			0.278962	−	0.960302i	$-0.410010\pi$
$569$	13.3085			0.557923			0.278962	+	0.960302i	$0.410010\pi$
$570$		0			0
$571$	−16.4204			−0.687174			−0.343587	−	0.939121i	$-0.611642\pi$
$571$	−16.4204			−0.687174			−0.343587	+	0.939121i	$0.611642\pi$
$572$		−	49.2951i		−	2.06113i
$573$		0			0
$574$		0			0
$575$	−1.53997	+	3.09826i	−0.0642213	+	0.129206i
$576$		0			0
$577$		−	14.7505i		−	0.614071i	−0.951698	−	0.307036i	$-0.900663\pi$
$577$		−	14.7505i		−	0.614071i	0.951698	−	0.307036i	$-0.0993371\pi$
$578$			31.1058i			1.29383i
$579$		0			0
$580$	−7.18485	−	1.68714i	−0.298334	−	0.0700546i
$581$	7.30855			0.303210
$582$		0			0
$583$			20.3625i			0.843329i
$584$	−31.6251			−1.30866
$585$		0			0
$586$	−25.0240			−1.03373
$587$			6.36385i			0.262664i	0.991338	+	0.131332i	$0.0419254\pi$
$587$			6.36385i			0.262664i	−0.991338	+	0.131332i	$0.958075\pi$
$588$		0			0
$589$	1.11190			0.0458150
$590$	11.7686	−	50.1177i	0.484505	−	2.06331i
$591$		0			0
$592$		−	1.14472i		−	0.0470475i
$593$			30.0706i			1.23485i	0.786629	+	0.617426i	$0.211824\pi$
$593$			30.0706i			1.23485i	−0.786629	+	0.617426i	$0.788176\pi$
$594$		0			0
$595$	15.9097	+	3.73589i	0.652233	+	0.153157i
$596$	−14.0188			−0.574233
$597$		0			0
$598$			8.96442i			0.366582i
$599$	−25.0587			−1.02387			−0.511936	−	0.859023i	$-0.671072\pi$
$599$	−25.0587			−1.02387			−0.511936	+	0.859023i	$0.671072\pi$
$600$		0			0
$601$	40.0320			1.63294			0.816469	−	0.577390i	$-0.195929\pi$
$601$	40.0320			1.63294			0.816469	+	0.577390i	$0.195929\pi$
$602$			96.5252i			3.93407i
$603$		0			0
$604$	37.3245			1.51871
$605$	8.60911	+	2.02158i	0.350010	+	0.0821889i
$606$		0			0
$607$		−	41.3557i		−	1.67858i	−0.543687	−	0.839288i	$-0.682972\pi$
$607$		−	41.3557i		−	1.67858i	0.543687	−	0.839288i	$-0.317028\pi$
$608$			9.03245i			0.366314i
$609$		0			0
$610$	−5.53997	+	23.5925i	−0.224307	+	0.955234i
$611$	27.7686			1.12340
$612$		0			0
$613$		−	40.5183i		−	1.63652i	−0.574851	−	0.818258i	$-0.694940\pi$
$613$		−	40.5183i		−	1.63652i	0.574851	−	0.818258i	$-0.305060\pi$
$614$	−20.7766			−0.838474
$615$		0			0
$616$	−31.0959			−1.25289
$617$		−	1.76865i		−	0.0712033i	−0.999366	−	0.0356016i	$-0.988665\pi$
$617$		−	1.76865i		−	0.0712033i	0.999366	−	0.0356016i	$-0.0113347\pi$
$618$		0			0
$619$	0.249804			0.0100405			0.00502023	−	0.999987i	$-0.498402\pi$
$619$	0.249804			0.0100405			0.00502023	+	0.999987i	$0.498402\pi$
$620$	−4.70085	−	1.10385i	−0.188791	−	0.0443317i
$621$		0			0
$622$			25.5884i			1.02600i
$623$			12.9451i			0.518633i
$624$		0			0
$625$	15.0945	+	19.9288i	0.603780	+	0.797151i
$626$	59.2530			2.36823
$627$		0			0
$628$			13.6003i			0.542709i
$629$	7.30855			0.291411
$630$		0			0
$631$	9.48922			0.377760			0.188880	−	0.982000i	$-0.439514\pi$
$631$	9.48922			0.377760			0.188880	+	0.982000i	$0.439514\pi$
$632$		−	6.14770i		−	0.244542i
$633$		0			0
$634$	−1.92804			−0.0765723
$635$	2.55036	−	10.8610i	0.101208	−	0.431005i
$636$		0			0
$637$			46.7516i			1.85236i
$638$			6.11092i			0.241934i
$639$		0			0
$640$	9.65569	−	41.1197i	0.381675	−	1.62540i
$641$	49.9416			1.97258			0.986288	−	0.165035i	$-0.0527738\pi$
$641$	49.9416			1.97258			0.986288	+	0.165035i	$0.0527738\pi$
$642$		0			0
$643$		−	25.8589i		−	1.01977i	−0.860241	−	0.509887i	$-0.829687\pi$
$643$		−	25.8589i		−	1.01977i	0.860241	−	0.509887i	$-0.170313\pi$
$644$	8.93603			0.352129
$645$		0			0
$646$	7.30855			0.287551
$647$			32.1384i			1.26349i	0.775177	+	0.631745i	$0.217661\pi$
$647$			32.1384i			1.26349i	−0.775177	+	0.631745i	$0.782339\pi$
$648$		0			0
$649$	−26.5427			−1.04189
$650$	58.0042	+	28.8307i	2.27511	+	1.13083i
$651$		0			0
$652$			10.5537i			0.413315i
$653$		−	9.79247i		−	0.383209i	−0.981472	−	0.191604i	$-0.938631\pi$
$653$		−	9.79247i		−	0.383209i	0.981472	−	0.191604i	$-0.0613691\pi$
$654$		0			0
$655$	42.9177	+	10.0779i	1.67693	+	0.393775i
$656$		0			0
$657$		0			0
$658$		−	44.4540i		−	1.73300i
$659$	−7.55835			−0.294432			−0.147216	−	0.989104i	$-0.547031\pi$
$659$	−7.55835			−0.294432			−0.147216	+	0.989104i	$0.547031\pi$
$660$		0			0
$661$	−10.9041			−0.424119			−0.212060	−	0.977257i	$-0.568017\pi$
$661$	−10.9041			−0.424119			−0.212060	+	0.977257i	$0.568017\pi$
$662$			50.8096i			1.97477i
$663$		0			0
$664$	−5.59313			−0.217056
$665$	−3.39888	+	14.4745i	−0.131803	+	0.561296i
$666$		0			0
$667$		−	0.691975i		−	0.0267934i
$668$			48.2048i			1.86510i
$669$		0			0
$670$	32.4388	+	7.61725i	1.25322	+	0.294280i
$671$	12.4948			0.482357
$672$		0			0
$673$		−	12.6296i		−	0.486836i	−0.969921	−	0.243418i	$-0.921731\pi$
$673$		−	12.6296i		−	0.486836i	0.969921	−	0.243418i	$-0.0782687\pi$
$674$	17.8377			0.687083
$675$		0			0
$676$	61.5959			2.36907
$677$			8.87065i			0.340927i	0.985364	+	0.170463i	$0.0545265\pi$
$677$			8.87065i			0.340927i	−0.985364	+	0.170463i	$0.945474\pi$
$678$		0			0
$679$	1.50519			0.0577641
$680$	−12.1754	−	2.85902i	−0.466907	−	0.109639i
$681$		0			0
$682$			3.99821i			0.153099i
$683$			24.4749i			0.936507i	0.883594	+	0.468254i	$0.155117\pi$
$683$			24.4749i			0.936507i	−0.883594	+	0.468254i	$0.844883\pi$
$684$		0			0
$685$	3.20223	−	13.6370i	0.122351	−	0.521045i
$686$	11.7874			0.450044
$687$		0			0
$688$		−	3.13504i		−	0.119522i
$689$	−43.1675			−1.64455
$690$		0			0
$691$	−3.30855			−0.125863			−0.0629315	−	0.998018i	$-0.520045\pi$
$691$	−3.30855			−0.125863			−0.0629315	+	0.998018i	$0.520045\pi$
$692$			29.7090i			1.12937i
$693$		0			0
$694$	−21.5028			−0.816235
$695$	47.6942	+	11.1995i	1.80914	+	0.424821i
$696$		0			0
$697$		0			0
$698$			49.8729i			1.88772i
$699$		0			0
$700$	28.7394	−	57.8205i	1.08625	−	2.18541i
$701$	10.8485			0.409743			0.204871	−	0.978789i	$-0.434322\pi$
$701$	10.8485			0.409743			0.204871	+	0.978789i	$0.434322\pi$
$702$		0			0
$703$			6.64926i			0.250781i
$704$	−34.0324			−1.28264
$705$		0			0
$706$	−47.3405			−1.78168
$707$		−	46.5979i		−	1.75250i
$708$		0			0
$709$	31.1675			1.17052			0.585259	−	0.810846i	$-0.300993\pi$
$709$	31.1675			1.17052			0.585259	+	0.810846i	$0.300993\pi$
$710$	−2.35371	+	10.0235i	−0.0883333	+	0.376176i
$711$		0			0
$712$		−	9.90668i		−	0.371269i
$713$		−	0.452741i		−	0.0169553i
$714$		0			0
$715$	7.63448	−	32.5122i	0.285513	−	1.21589i
$716$	70.3301			2.62836
$717$		0			0
$718$			70.3672i			2.62608i
$719$	−13.0056			−0.485027			−0.242513	−	0.970148i	$-0.577972\pi$
$719$	−13.0056			−0.485027			−0.242513	+	0.970148i	$0.577972\pi$
$720$		0			0
$721$	−58.5268			−2.17965
$722$		−	37.0943i		−	1.38051i
$723$		0			0
$724$	56.0132			2.08171
$725$	−4.47742	−	2.22548i	−0.166287	−	0.0826521i
$726$		0			0
$727$			1.19089i			0.0441677i	0.999756	+	0.0220839i	$0.00703008\pi$
$727$			1.19089i			0.0441677i	−0.999756	+	0.0220839i	$0.992970\pi$
$728$		−	65.9218i		−	2.44322i
$729$		0			0
$730$	−52.9336	−	12.4298i	−1.95916	−	0.460048i
$731$	20.0160			0.740318
$732$		0			0
$733$			34.5990i			1.27794i	0.769231	+	0.638971i	$0.220640\pi$
$733$			34.5990i			1.27794i	−0.769231	+	0.638971i	$0.779360\pi$
$734$	31.7314			1.17123
$735$		0			0
$736$	3.67781			0.135566
$737$		−	17.1799i		−	0.632829i
$738$		0			0
$739$	41.7821			1.53698			0.768491	−	0.639861i	$-0.221008\pi$
$739$	41.7821			1.53698			0.768491	+	0.639861i	$0.221008\pi$
$740$	6.60112	−	28.1115i	0.242662	−	1.03340i
$741$		0			0
$742$			69.1056i			2.53695i
$743$			4.02130i			0.147527i	0.997276	+	0.0737636i	$0.0235010\pi$
$743$			4.02130i			0.147527i	−0.997276	+	0.0737636i	$0.976499\pi$
$744$		0			0
$745$	−9.24599	−	2.17113i	−0.338747	−	0.0795442i
$746$	−62.7742			−2.29833
$747$		0			0
$748$			16.3643i			0.598338i
$749$	−15.3085			−0.559362
$750$		0			0
$751$	−0.497206			−0.0181433			−0.00907166	−	0.999959i	$-0.502888\pi$
$751$	−0.497206			−0.0181433			−0.00907166	+	0.999959i	$0.502888\pi$
$752$			1.44382i			0.0526507i
$753$		0			0
$754$	−12.9548			−0.471787
$755$	24.6171	+	5.78056i	0.895908	+	0.210376i
$756$		0			0
$757$			18.6944i			0.679458i	0.940523	+	0.339729i	$0.110335\pi$
$757$			18.6944i			0.679458i	−0.940523	+	0.339729i	$0.889665\pi$
$758$		−	37.7734i		−	1.37199i
$759$		0			0
$760$	2.60112	−	11.0771i	0.0943524	−	0.401809i
$761$	3.38291			0.122630			0.0613151	−	0.998118i	$-0.480471\pi$
$761$	3.38291			0.122630			0.0613151	+	0.998118i	$0.480471\pi$
$762$		0			0
$763$			29.5635i			1.07027i
$764$	−27.7474			−1.00386
$765$		0			0
$766$	27.0240			0.976416
$767$		−	56.2692i		−	2.03176i
$768$		0			0
$769$	7.41486			0.267387			0.133693	−	0.991023i	$-0.457316\pi$
$769$	7.41486			0.267387			0.133693	+	0.991023i	$0.457316\pi$
$770$	−52.0479	−	12.2218i	−1.87568	−	0.440444i
$771$		0			0
$772$			2.61162i			0.0939944i
$773$			33.2775i			1.19691i	0.801156	+	0.598455i	$0.204218\pi$
$773$			33.2775i			1.19691i	−0.801156	+	0.598455i	$0.795782\pi$
$774$		0			0
$775$	−2.92945	−	1.45607i	−0.105229	−	0.0523036i
$776$	−1.15190			−0.0413510
$777$		0			0
$778$		−	27.6275i		−	0.990495i
$779$		0			0
$780$		0			0
$781$	5.30855			0.189955
$782$		−	2.97588i		−	0.106417i
$783$		0			0
$784$	−2.43084			−0.0868156
$785$	−2.10631	+	8.96994i	−0.0751775	+	0.320151i
$786$		0			0
$787$		−	18.2878i		−	0.651890i	−0.945389	−	0.325945i	$-0.894318\pi$
$787$		−	18.2878i		−	0.651890i	0.945389	−	0.325945i	$-0.105682\pi$
$788$			80.8841i			2.88138i
$789$		0			0
$790$	2.41627	−	10.2899i	0.0859671	−	0.366100i
$791$	73.1439			2.60070
$792$		0			0
$793$			26.4883i			0.940629i
$794$	−13.8909			−0.492968
$795$		0			0
$796$	63.7290			2.25881
$797$		−	44.5845i		−	1.57926i	−0.613581	−	0.789632i	$-0.710271\pi$
$797$		−	44.5845i		−	1.57926i	0.613581	−	0.789632i	$-0.289729\pi$
$798$		0			0
$799$	−9.21821			−0.326117
$800$	11.8283	−	23.7973i	0.418194	−	0.841360i
$801$		0			0
$802$			49.4202i			1.74509i
$803$			28.0341i			0.989302i
$804$		0			0
$805$	5.89369	+	1.38395i	0.207725	+	0.0487778i
$806$	−8.47600			−0.298554
$807$		0			0
$808$			35.6607i			1.25454i
$809$	14.1063			0.495952			0.247976	−	0.968766i	$-0.420235\pi$
$809$	14.1063			0.495952			0.247976	+	0.968766i	$0.420235\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$			12.9138i			0.453186i
$813$		0			0
$814$	−23.9097			−0.838033
$815$	−1.63448	+	6.96061i	−0.0572535	+	0.243820i
$816$		0			0
$817$			18.2104i			0.637100i
$818$			10.3484i			0.361822i
$819$		0			0
$820$		0			0
$821$	−18.1571			−0.633686			−0.316843	−	0.948478i	$-0.602623\pi$
$821$	−18.1571			−0.633686			−0.316843	+	0.948478i	$0.602623\pi$
$822$		0			0
$823$			3.25189i			0.113354i	0.998393	+	0.0566770i	$0.0180505\pi$
$823$			3.25189i			0.113354i	−0.998393	+	0.0566770i	$0.981949\pi$
$824$	44.7897			1.56032
$825$		0			0
$826$	−90.0799			−3.13428
$827$			10.7155i			0.372615i	0.982492	+	0.186307i	$0.0596520\pi$
$827$			10.7155i			0.372615i	−0.982492	+	0.186307i	$0.940348\pi$
$828$		0			0
$829$	−52.3461			−1.81805			−0.909027	−	0.416736i	$-0.863174\pi$
$829$	−52.3461			−1.81805			−0.909027	+	0.416736i	$0.863174\pi$
$830$	−9.36170	−	2.19830i	−0.324949	−	0.0763043i
$831$		0			0
$832$		−	72.1469i		−	2.50124i
$833$		−	15.5199i		−	0.537733i
$834$		0			0
$835$	−7.46561	+	31.7931i	−0.258358	+	1.10024i
$836$	−14.8881			−0.514916
$837$		0			0
$838$			9.66192i			0.333765i
$839$	24.6703			0.851712			0.425856	−	0.904791i	$-0.359973\pi$
$839$	24.6703			0.851712			0.425856	+	0.904791i	$0.359973\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		−	42.6173i		−	1.46869i
$843$		0			0
$844$	−63.5535			−2.18760
$845$	40.6251	+	9.53954i	1.39755	+	0.328170i
$846$		0			0
$847$		−	15.4737i		−	0.531684i
$848$		−	2.24448i		−	0.0770758i
$849$		0			0
$850$	−19.2554	−	9.57079i	−0.660454	−	0.328275i
$851$	2.70743			0.0928095
$852$		0			0
$853$		−	28.1115i		−	0.962520i	−0.876578	−	0.481260i	$-0.840179\pi$
$853$		−	28.1115i		−	0.962520i	0.876578	−	0.481260i	$-0.159821\pi$
$854$	42.4045			1.45105
$855$		0			0
$856$	11.7154			0.400425
$857$			8.39482i			0.286762i	0.989668	+	0.143381i	$0.0457974\pi$
$857$			8.39482i			0.286762i	−0.989668	+	0.143381i	$0.954203\pi$
$858$		0			0
$859$	−17.8405			−0.608711			−0.304356	−	0.952559i	$-0.598441\pi$
$859$	−17.8405			−0.608711			−0.304356	+	0.952559i	$0.598441\pi$
$860$	18.0785	−	76.9893i	0.616473	−	2.62531i
$861$		0			0
$862$		−	85.4793i		−	2.91144i
$863$			2.48249i			0.0845049i	0.999107	+	0.0422524i	$0.0134534\pi$
$863$			2.48249i			0.0845049i	−0.999107	+	0.0422524i	$0.986547\pi$
$864$		0			0
$865$	−4.60112	+	19.5943i	−0.156443	+	0.666227i
$866$	−38.8113			−1.31886
$867$		0			0
$868$			8.44916i			0.286783i
$869$	−5.44964			−0.184866
$870$		0			0
$871$	36.4204			1.23406
$872$		−	22.6245i		−	0.766164i
$873$		0			0
$874$	2.70743			0.0915802
$875$	27.9097	−	33.6841i	0.943519	−	1.13873i
$876$		0			0
$877$			25.9813i			0.877325i	0.898652	+	0.438662i	$0.144548\pi$
$877$			25.9813i			0.877325i	−0.898652	+	0.438662i	$0.855452\pi$
$878$			21.2230i			0.716243i
$879$		0			0
$880$	1.69046	+	0.396953i	0.0569856	+	0.0133813i
$881$	−25.1279			−0.846580			−0.423290	−	0.905994i	$-0.639125\pi$
$881$	−25.1279			−0.846580			−0.423290	+	0.905994i	$0.639125\pi$
$882$		0			0
$883$			10.9684i			0.369117i	0.982822	+	0.184559i	$0.0590856\pi$
$883$			10.9684i			0.369117i	−0.982822	+	0.184559i	$0.940914\pi$
$884$	−34.6915			−1.16680
$885$		0			0
$886$	−43.5188			−1.46204
$887$			2.99897i			0.100695i	0.998732	+	0.0503477i	$0.0160330\pi$
$887$			2.99897i			0.100695i	−0.998732	+	0.0503477i	$0.983967\pi$
$888$		0			0
$889$	−19.5212			−0.654719
$890$	3.89369	−	16.5817i	0.130517	−	0.555819i
$891$		0			0
$892$			35.8742i			1.20116i
$893$		−	8.38665i		−	0.280649i
$894$		0			0
$895$	46.3857	+	10.8922i	1.55050	+	0.364087i
$896$	−73.9073			−2.46907
$897$		0			0
$898$		−	72.1183i		−	2.40662i
$899$	0.654273			0.0218212
$900$		0			0
$901$	14.3301			0.477405
$902$		0			0
$903$		0			0
$904$	−55.9760			−1.86173
$905$	36.9430	+	8.67492i	1.22803	+	0.288364i
$906$		0			0
$907$		−	50.5567i		−	1.67871i	−0.543585	−	0.839354i	$-0.682934\pi$
$907$		−	50.5567i		−	1.67871i	0.543585	−	0.839354i	$-0.317066\pi$
$908$			57.1341i			1.89606i
$909$		0			0
$910$	25.9097	−	110.339i	0.858897	−	3.65770i
$911$	−35.9044			−1.18957			−0.594784	−	0.803886i	$-0.702762\pi$
$911$	−35.9044			−1.18957			−0.594784	+	0.803886i	$0.702762\pi$
$912$		0			0
$913$			4.95804i			0.164087i
$914$	84.3301			2.78939
$915$		0			0
$916$	61.7450			2.04011
$917$		−	77.1388i		−	2.54735i
$918$		0			0
$919$	−15.2022			−0.501475			−0.250738	−	0.968055i	$-0.580673\pi$
$919$	−15.2022			−0.501475			−0.250738	+	0.968055i	$0.580673\pi$
$920$	−4.51036	−	1.05912i	−0.148702	−	0.0349181i
$921$		0			0
$922$		−	66.3745i		−	2.18593i
$923$			11.2538i			0.370425i
$924$		0			0
$925$	8.70743	−	17.5184i	0.286299	−	0.576001i
$926$	−68.2422			−2.24258
$927$		0			0
$928$			5.31495i			0.174472i
$929$	−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
$931$	14.1199			0.462761
$932$		−	48.2810i		−	1.58150i
$933$		0			0
$934$	60.9524			1.99442
$935$	−2.53439	+	10.7929i	−0.0828833	+	0.352967i
$936$		0			0
$937$			32.1859i			1.05147i	0.850649	+	0.525734i	$0.176209\pi$
$937$			32.1859i			1.05147i	−0.850649	+	0.525734i	$0.823791\pi$
$938$		−	58.3045i		−	1.90371i
$939$		0			0
$940$	−8.32594	+	35.4568i	−0.271562	+	1.15647i
$941$	−22.3697			−0.729231			−0.364616	−	0.931158i	$-0.618800\pi$
$941$	−22.3697			−0.729231			−0.364616	+	0.931158i	$0.618800\pi$
$942$		0			0
$943$		0			0
$944$	2.92570			0.0952236
$945$		0			0
$946$	−65.4816			−2.12899
$947$			0.122381i			0.00397684i	0.999998	+	0.00198842i	$0.000632935\pi$
$947$			0.122381i			0.00397684i	−0.999998	+	0.00198842i	$0.999367\pi$
$948$		0			0
$949$	−59.4308			−1.92921
$950$	8.70743	−	17.5184i	0.282506	−	0.568372i
$951$		0			0
$952$			21.8838i			0.709257i
$953$			55.4917i			1.79755i	0.438409	+	0.898776i	$0.355542\pi$
$953$			55.4917i			1.79755i	−0.438409	+	0.898776i	$0.644458\pi$
$954$		0			0
$955$	−18.3006	−	4.29732i	−0.592192	−	0.139058i
$956$	6.60112			0.213495
$957$		0			0
$958$			62.5787i			2.02183i
$959$	−24.5108			−0.791494
$960$		0			0
$961$	−30.5719			−0.986191
$962$		−	50.6873i		−	1.63422i
$963$		0			0
$964$	18.3377			0.590619
$965$	−0.404470	+	1.72248i	−0.0130203	+	0.0554485i
$966$		0			0
$967$		−	49.0722i		−	1.57806i	−0.614357	−	0.789028i	$-0.710584\pi$
$967$		−	49.0722i		−	1.57806i	0.614357	−	0.789028i	$-0.289416\pi$
$968$			11.8418i			0.380611i
$969$		0			0
$970$	−1.92804	−	0.452741i	−0.0619057	−	0.0145366i
$971$	−2.08793			−0.0670050			−0.0335025	−	0.999439i	$-0.510666\pi$
$971$	−2.08793			−0.0670050			−0.0335025	+	0.999439i	$0.510666\pi$
$972$		0			0
$973$		−	85.7241i		−	2.74819i
$974$	−73.8856			−2.36745
$975$		0			0
$976$	−1.37725			−0.0440849
$977$		−	36.5119i		−	1.16812i	−0.811711	−	0.584059i	$-0.801464\pi$
$977$		−	36.5119i		−	1.16812i	0.811711	−	0.584059i	$-0.198536\pi$
$978$		0			0
$979$	−8.78179			−0.280667
$980$	−59.6956	−	14.0177i	−1.90691	−	0.447778i
$981$		0			0
$982$			23.1821i			0.739771i
$983$		−	32.8698i		−	1.04838i	−0.851601	−	0.524191i	$-0.824368\pi$
$983$		−	32.8698i		−	1.04838i	0.851601	−	0.524191i	$-0.175632\pi$
$984$		0			0
$985$	−12.5268	+	53.3465i	−0.399136	+	1.69976i
$986$	4.30056			0.136958
$987$		0			0
$988$		−	31.5620i		−	1.00412i
$989$	7.41486			0.235779
$990$		0			0
$991$	−36.0160			−1.14409			−0.572043	−	0.820224i	$-0.693849\pi$
$991$	−36.0160			−1.14409			−0.572043	+	0.820224i	$0.693849\pi$
$992$			3.47743i			0.110409i
$993$		0			0
$994$	18.0160			0.571432
$995$	42.0320	+	9.86990i	1.33250	+	0.312897i
$996$		0			0
$997$			56.8063i			1.79907i	0.436844	+	0.899537i	$0.356096\pi$
$997$			56.8063i			1.79907i	−0.436844	+	0.899537i	$0.643904\pi$
$998$			68.9344i			2.18208i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.h.784.5		6
3.2	odd	2		145.2.b.c.59.2	✓	6
5.2	odd	4		6525.2.a.bt.1.2		6
5.3	odd	4		6525.2.a.bt.1.5		6
5.4	even	2	inner	1305.2.c.h.784.2		6
12.11	even	2		2320.2.d.g.929.1		6
15.2	even	4		725.2.a.l.1.5		6
15.8	even	4		725.2.a.l.1.2		6
15.14	odd	2		145.2.b.c.59.5	yes	6
60.59	even	2		2320.2.d.g.929.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.c.59.2	✓	6	3.2	odd	2
145.2.b.c.59.5	yes	6	15.14	odd	2
725.2.a.l.1.2		6	15.8	even	4
725.2.a.l.1.5		6	15.2	even	4
1305.2.c.h.784.2		6	5.4	even	2	inner
1305.2.c.h.784.5		6	1.1	even	1	trivial
2320.2.d.g.929.1		6	12.11	even	2
2320.2.d.g.929.6		6	60.59	even	2
6525.2.a.bt.1.2		6	5.2	odd	4
6525.2.a.bt.1.5		6	5.3	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)

\(f(q)\)	\(=\)	\(q+2.30229i q^{2} -3.30056 q^{4} +(-2.17686 - 0.511167i) q^{5} +3.91261i q^{7} -2.99427i q^{8} +(1.17686 - 5.01177i) q^{10} -2.65427 q^{11} -5.62692i q^{13} -9.00799 q^{14} +0.292570 q^{16} +1.86794i q^{17} -1.69944 q^{19} +(7.18485 + 1.68714i) q^{20} -6.11092i q^{22} +0.691975i q^{23} +(4.47742 + 2.22548i) q^{25} +12.9548 q^{26} -12.9138i q^{28} -1.00000 q^{29} -0.654273 q^{31} -5.31495i q^{32} -4.30056 q^{34} +(2.00000 - 8.51720i) q^{35} -3.91261i q^{37} -3.91261i q^{38} +(-1.53057 + 6.51810i) q^{40} -10.7155i q^{43} +8.76059 q^{44} -1.59313 q^{46} +4.93495i q^{47} -8.30855 q^{49} +(-5.12370 + 10.3083i) q^{50} +18.5720i q^{52} -7.67159i q^{53} +(5.77797 + 1.35678i) q^{55} +11.7154 q^{56} -2.30229i q^{58} +10.0000 q^{59} -4.70743 q^{61} -1.50633i q^{62} +12.8217 q^{64} +(-2.87630 + 12.2490i) q^{65} +6.47253i q^{67} -6.16526i q^{68} +(19.6091 + 4.60459i) q^{70} -2.00000 q^{71} -10.5619i q^{73} +9.00799 q^{74} +5.60911 q^{76} -10.3851i q^{77} +2.05316 q^{79} +(-0.636884 - 0.149552i) q^{80} -1.86794i q^{83} +(0.954832 - 4.06625i) q^{85} +24.6703 q^{86} +7.94761i q^{88} +3.30855 q^{89} +22.0160 q^{91} -2.28390i q^{92} -11.3617 q^{94} +(3.69944 + 0.868699i) q^{95} -0.384703i q^{97} -19.1287i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 14 q^{4} - 3 q^{5} - 3 q^{10} + 10 q^{11} - 8 q^{14} + 42 q^{16} - 16 q^{19} - 13 q^{20} + 11 q^{25} + 46 q^{26} - 6 q^{29} + 22 q^{31} - 20 q^{34} + 12 q^{35} + 21 q^{40} - 2 q^{44} - 44 q^{46} + 2 q^{49}+ \cdots + 28 q^{95}+O(q^{100}) \) 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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