LMFDB - Embedded newform 725.2.c.f.376.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(376,725)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("725.376"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,8,0,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1731891456.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 $ x^8 - 9x^6 + 65x^4 - 144*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			376.7
Root			$-2.21837 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	725.376
Dual form			725.2.c.f.376.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +2.56155i q^{3} +1.00000 q^{4} -2.56155 q^{6} -3.46410 q^{7} +3.00000i q^{8} -3.56155 q^{9} +0.972638i q^{11} +2.56155i q^{12} -4.43674 q^{13} -3.46410i q^{14} -1.00000 q^{16} -2.00000i q^{17} -3.56155i q^{18} -3.46410i q^{19} -8.87348i q^{21} -0.972638 q^{22} +3.46410 q^{23} -7.68466 q^{24} -4.43674i q^{26} -1.43845i q^{27} -3.46410 q^{28} +(-4.12311 + 3.46410i) q^{29} +7.90084i q^{31} +5.00000i q^{32} -2.49146 q^{33} +2.00000 q^{34} -3.56155 q^{36} +7.12311i q^{37} +3.46410 q^{38} -11.3649i q^{39} +8.87348i q^{41} +8.87348 q^{42} -5.43845i q^{43} +0.972638i q^{44} +3.46410i q^{46} -11.6847i q^{47} -2.56155i q^{48} +5.00000 q^{49} +5.12311 q^{51} -4.43674 q^{52} +4.43674 q^{53} +1.43845 q^{54} -10.3923i q^{56} +8.87348 q^{57} +(-3.46410 - 4.12311i) q^{58} +1.12311 q^{59} -1.94528i q^{61} -7.90084 q^{62} +12.3376 q^{63} -7.00000 q^{64} -2.49146i q^{66} +12.3376 q^{67} -2.00000i q^{68} +8.87348i q^{69} -2.24621 q^{71} -10.6847i q^{72} +7.12311i q^{73} -7.12311 q^{74} -3.46410i q^{76} -3.36932i q^{77} +11.3649 q^{78} +14.8290i q^{79} -7.00000 q^{81} -8.87348 q^{82} +10.3923 q^{83} -8.87348i q^{84} +5.43845 q^{86} +(-8.87348 - 10.5616i) q^{87} -2.91791 q^{88} -8.87348i q^{89} +15.3693 q^{91} +3.46410 q^{92} -20.2384 q^{93} +11.6847 q^{94} -12.8078 q^{96} +8.24621i q^{97} +5.00000i q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 4 q^{6} - 12 q^{9} - 8 q^{16} - 12 q^{24} + 16 q^{34} - 12 q^{36} + 40 q^{49} + 8 q^{51} + 28 q^{54} - 24 q^{59} - 56 q^{64} + 48 q^{71} - 24 q^{74} - 56 q^{81} + 60 q^{86} + 24 q^{91} + 44 q^{94}+ \cdots - 20 q^{96}+O(q^{100}) $ 8 * q + 8 * q^4 - 4 * q^6 - 12 * q^9 - 8 * q^16 - 12 * q^24 + 16 * q^34 - 12 * q^36 + 40 * q^49 + 8 * q^51 + 28 * q^54 - 24 * q^59 - 56 * q^64 + 48 * q^71 - 24 * q^74 - 56 * q^81 + 60 * q^86 + 24 * q^91 + 44 * q^94 - 20 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$			2.56155i			1.47891i	0.673204	+	0.739457i	$0.264917\pi$
$3$			2.56155i			1.47891i	−0.673204	+	0.739457i	$0.735083\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−2.56155			−1.04575
$7$	−3.46410			−1.30931			−0.654654	−	0.755929i	$-0.727186\pi$
$7$	−3.46410			−1.30931			−0.654654	+	0.755929i	$0.727186\pi$
$8$			3.00000i			1.06066i
$9$	−3.56155			−1.18718
$10$		0			0
$11$			0.972638i			0.293261i	0.989191	+	0.146631i	$0.0468429\pi$
$11$			0.972638i			0.293261i	−0.989191	+	0.146631i	$0.953157\pi$
$12$			2.56155i			0.739457i
$13$	−4.43674			−1.23053			−0.615265	−	0.788320i	$-0.710951\pi$
$13$	−4.43674			−1.23053			−0.615265	+	0.788320i	$0.710951\pi$
$14$		−	3.46410i		−	0.925820i
$15$		0			0
$16$	−1.00000			−0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$		−	3.56155i		−	0.839466i
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$		0			0
$21$		−	8.87348i		−	1.93635i
$22$	−0.972638			−0.207367
$23$	3.46410			0.722315			0.361158	−	0.932505i	$-0.382382\pi$
$23$	3.46410			0.722315			0.361158	+	0.932505i	$0.382382\pi$
$24$	−7.68466			−1.56862
$25$		0			0
$26$		−	4.43674i		−	0.870116i
$27$		−	1.43845i		−	0.276829i
$28$	−3.46410			−0.654654
$29$	−4.12311	+	3.46410i	−0.765641	+	0.643268i
$29$	−4.12311	+	3.46410i	−0.765641	+	0.643268i
$30$		0			0
$31$			7.90084i			1.41903i	0.704689	+	0.709516i	$0.251087\pi$
$31$			7.90084i			1.41903i	−0.704689	+	0.709516i	$0.748913\pi$
$32$			5.00000i			0.883883i
$33$	−2.49146			−0.433708
$34$	2.00000			0.342997
$35$		0			0
$36$	−3.56155			−0.593592
$37$			7.12311i			1.17103i	0.810661	+	0.585516i	$0.199108\pi$
$37$			7.12311i			1.17103i	−0.810661	+	0.585516i	$0.800892\pi$
$38$	3.46410			0.561951
$39$		−	11.3649i		−	1.81985i
$40$		0			0
$41$			8.87348i			1.38580i	0.721031	+	0.692902i	$0.243668\pi$
$41$			8.87348i			1.38580i	−0.721031	+	0.692902i	$0.756332\pi$
$42$	8.87348			1.36921
$43$		−	5.43845i		−	0.829355i	−0.909968	−	0.414678i	$-0.863894\pi$
$43$		−	5.43845i		−	0.829355i	0.909968	−	0.414678i	$-0.136106\pi$
$44$			0.972638i			0.146631i
$45$		0			0
$46$			3.46410i			0.510754i
$47$		−	11.6847i		−	1.70438i	−0.523230	−	0.852191i	$-0.675273\pi$
$47$		−	11.6847i		−	1.70438i	0.523230	−	0.852191i	$-0.324727\pi$
$48$		−	2.56155i		−	0.369728i
$49$	5.00000			0.714286
$50$		0			0
$51$	5.12311			0.717378
$52$	−4.43674			−0.615265
$53$	4.43674			0.609433			0.304717	−	0.952443i	$-0.401438\pi$
$53$	4.43674			0.609433			0.304717	+	0.952443i	$0.401438\pi$
$54$	1.43845			0.195748
$55$		0			0
$56$		−	10.3923i		−	1.38873i
$57$	8.87348			1.17532
$58$	−3.46410	−	4.12311i	−0.454859	−	0.541390i
$59$	1.12311			0.146216			0.0731079	−	0.997324i	$-0.476708\pi$
$59$	1.12311			0.146216			0.0731079	+	0.997324i	$0.476708\pi$
$60$		0			0
$61$		−	1.94528i		−	0.249067i	−0.992215	−	0.124534i	$-0.960257\pi$
$61$		−	1.94528i		−	0.249067i	0.992215	−	0.124534i	$-0.0397434\pi$
$62$	−7.90084			−1.00341
$63$	12.3376			1.55439
$64$	−7.00000			−0.875000
$65$		0			0
$66$		−	2.49146i		−	0.306678i
$67$	12.3376			1.50728			0.753638	−	0.657290i	$-0.228297\pi$
$67$	12.3376			1.50728			0.753638	+	0.657290i	$0.228297\pi$
$68$		−	2.00000i		−	0.242536i
$69$			8.87348i			1.06824i
$70$		0			0
$71$	−2.24621			−0.266576			−0.133288	−	0.991077i	$-0.542554\pi$
$71$	−2.24621			−0.266576			−0.133288	+	0.991077i	$0.542554\pi$
$72$		−	10.6847i		−	1.25920i
$73$			7.12311i			0.833696i	0.908976	+	0.416848i	$0.136865\pi$
$73$			7.12311i			0.833696i	−0.908976	+	0.416848i	$0.863135\pi$
$74$	−7.12311			−0.828044
$75$		0			0
$76$		−	3.46410i		−	0.397360i
$77$		−	3.36932i		−	0.383969i
$78$	11.3649			1.28683
$79$			14.8290i			1.66840i	0.551464	+	0.834199i	$0.314070\pi$
$79$			14.8290i			1.66840i	−0.551464	+	0.834199i	$0.685930\pi$
$80$		0			0
$81$	−7.00000			−0.777778
$82$	−8.87348			−0.979912
$83$	10.3923			1.14070			0.570352	−	0.821401i	$-0.306807\pi$
$83$	10.3923			1.14070			0.570352	+	0.821401i	$0.306807\pi$
$84$		−	8.87348i		−	0.968176i
$85$		0			0
$86$	5.43845			0.586443
$87$	−8.87348	−	10.5616i	−0.951337	−	1.13232i
$88$	−2.91791			−0.311051
$89$		−	8.87348i		−	0.940587i	−0.882510	−	0.470293i	$-0.844148\pi$
$89$		−	8.87348i		−	0.940587i	0.882510	−	0.470293i	$-0.155852\pi$
$90$		0			0
$91$	15.3693			1.61114
$92$	3.46410			0.361158
$93$	−20.2384			−2.09863
$94$	11.6847			1.20518
$95$		0			0
$96$	−12.8078			−1.30719
$97$			8.24621i			0.837276i	0.908153	+	0.418638i	$0.137492\pi$
$97$			8.24621i			0.837276i	−0.908153	+	0.418638i	$0.862508\pi$
$98$			5.00000i			0.505076i
$99$		−	3.46410i		−	0.348155i
$100$		0			0
$101$			6.92820i			0.689382i	0.938716	+	0.344691i	$0.112016\pi$
$101$			6.92820i			0.689382i	−0.938716	+	0.344691i	$0.887984\pi$
$102$			5.12311i			0.507263i
$103$	−1.51883			−0.149654			−0.0748272	−	0.997197i	$-0.523841\pi$
$103$	−1.51883			−0.149654			−0.0748272	+	0.997197i	$0.523841\pi$
$104$		−	13.3102i		−	1.30517i
$105$		0			0
$106$			4.43674i			0.430934i
$107$	−14.2829			−1.38078			−0.690388	−	0.723439i	$-0.742560\pi$
$107$	−14.2829			−1.38078			−0.690388	+	0.723439i	$0.742560\pi$
$108$		−	1.43845i		−	0.138415i
$109$	5.68466			0.544492			0.272246	−	0.962228i	$-0.412234\pi$
$109$	5.68466			0.544492			0.272246	+	0.962228i	$0.412234\pi$
$110$		0			0
$111$	−18.2462			−1.73185
$112$	3.46410			0.327327
$113$		−	5.36932i		−	0.505103i	−0.967583	−	0.252551i	$-0.918730\pi$
$113$		−	5.36932i		−	0.505103i	0.967583	−	0.252551i	$-0.0812697\pi$
$114$			8.87348i			0.831077i
$115$		0			0
$116$	−4.12311	+	3.46410i	−0.382821	+	0.321634i
$117$	15.8017			1.46087
$118$			1.12311i			0.103390i
$119$			6.92820i			0.635107i
$120$		0			0
$121$	10.0540			0.913998
$122$	1.94528			0.176117
$123$	−22.7299			−2.04948
$124$			7.90084i			0.709516i
$125$		0			0
$126$			12.3376i			1.09912i
$127$		−	2.24621i		−	0.199319i	−0.995022	−	0.0996595i	$-0.968225\pi$
$127$		−	2.24621i		−	0.199319i	0.995022	−	0.0996595i	$-0.0317754\pi$
$128$			3.00000i			0.265165i
$129$	13.9309			1.22654
$130$		0			0
$131$		−	14.2829i		−	1.24790i	−0.781465	−	0.623949i	$-0.785527\pi$
$131$		−	14.2829i		−	1.24790i	0.781465	−	0.623949i	$-0.214473\pi$
$132$	−2.49146			−0.216854
$133$			12.0000i			1.04053i
$134$			12.3376i			1.06580i
$135$		0			0
$136$	6.00000			0.514496
$137$			13.3693i			1.14222i	0.820874	+	0.571109i	$0.193487\pi$
$137$			13.3693i			1.14222i	−0.820874	+	0.571109i	$0.806513\pi$
$138$	−8.87348			−0.755361
$139$	−19.3693			−1.64288			−0.821442	−	0.570292i	$-0.806830\pi$
$139$	−19.3693			−1.64288			−0.821442	+	0.570292i	$0.806830\pi$
$140$		0			0
$141$	29.9309			2.52063
$142$		−	2.24621i		−	0.188498i
$143$		−	4.31534i		−	0.360867i
$144$	3.56155			0.296796
$145$		0			0
$146$	−7.12311			−0.589512
$147$			12.8078i			1.05637i
$148$			7.12311i			0.585516i
$149$	13.6847			1.12109			0.560545	−	0.828124i	$-0.310592\pi$
$149$	13.6847			1.12109			0.560545	+	0.828124i	$0.310592\pi$
$150$		0			0
$151$	15.3693			1.25074			0.625369	−	0.780329i	$-0.284949\pi$
$151$	15.3693			1.25074			0.625369	+	0.780329i	$0.284949\pi$
$152$	10.3923			0.842927
$153$			7.12311i			0.575869i
$154$	3.36932			0.271507
$155$		0			0
$156$		−	11.3649i		−	0.909924i
$157$			22.4924i			1.79509i	0.440922	+	0.897545i	$0.354651\pi$
$157$			22.4924i			1.79509i	−0.440922	+	0.897545i	$0.645349\pi$
$158$	−14.8290			−1.17974
$159$			11.3649i			0.901299i
$160$		0			0
$161$	−12.0000			−0.945732
$162$		−	7.00000i		−	0.549972i
$163$			5.43845i			0.425972i	0.977055	+	0.212986i	$0.0683189\pi$
$163$			5.43845i			0.425972i	−0.977055	+	0.212986i	$0.931681\pi$
$164$			8.87348i			0.692902i
$165$		0			0
$166$			10.3923i			0.806599i
$167$	−8.44703			−0.653651			−0.326825	−	0.945085i	$-0.605979\pi$
$167$	−8.44703			−0.653651			−0.326825	+	0.945085i	$0.605979\pi$
$168$	26.6204			2.05381
$169$	6.68466			0.514204
$170$		0			0
$171$			12.3376i			0.943478i
$172$		−	5.43845i		−	0.414678i
$173$	−10.8188			−0.822535			−0.411267	−	0.911515i	$-0.634914\pi$
$173$	−10.8188			−0.822535			−0.411267	+	0.911515i	$0.634914\pi$
$174$	10.5616	−	8.87348i	0.800669	−	0.672697i
$175$		0			0
$176$		−	0.972638i		−	0.0733153i
$177$			2.87689i			0.216241i
$178$	8.87348			0.665095
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−13.6847			−1.01717			−0.508586	−	0.861011i	$-0.669832\pi$
$181$	−13.6847			−1.01717			−0.508586	+	0.861011i	$0.669832\pi$
$182$			15.3693i			1.13925i
$183$	4.98293			0.368349
$184$			10.3923i			0.766131i
$185$		0			0
$186$		−	20.2384i		−	1.48395i
$187$	1.94528			0.142253
$188$		−	11.6847i		−	0.852191i
$189$			4.98293i			0.362455i
$190$		0			0
$191$		−	3.46410i		−	0.250654i	−0.992116	−	0.125327i	$-0.960002\pi$
$191$		−	3.46410i		−	0.250654i	0.992116	−	0.125327i	$-0.0399979\pi$
$192$		−	17.9309i		−	1.29405i
$193$		−	8.24621i		−	0.593575i	−0.954944	−	0.296788i	$-0.904085\pi$
$193$		−	8.24621i		−	0.593575i	0.954944	−	0.296788i	$-0.0959153\pi$
$194$	−8.24621			−0.592043
$195$		0			0
$196$	5.00000			0.357143
$197$	−10.8188			−0.770804			−0.385402	−	0.922749i	$-0.625937\pi$
$197$	−10.8188			−0.770804			−0.385402	+	0.922749i	$0.625937\pi$
$198$	3.46410			0.246183
$199$	15.3693			1.08950			0.544751	−	0.838598i	$-0.316624\pi$
$199$	15.3693			1.08950			0.544751	+	0.838598i	$0.316624\pi$
$200$		0			0
$201$			31.6034i			2.22913i
$202$	−6.92820			−0.487467
$203$	14.2829	−	12.0000i	1.00246	−	0.842235i
$204$	5.12311			0.358689
$205$		0			0
$206$		−	1.51883i		−	0.105822i
$207$	−12.3376			−0.857521
$208$	4.43674			0.307633
$209$	3.36932			0.233061
$210$		0			0
$211$			14.8290i			1.02087i	0.859915	+	0.510437i	$0.170516\pi$
$211$			14.8290i			1.02087i	−0.859915	+	0.510437i	$0.829484\pi$
$212$	4.43674			0.304717
$213$		−	5.75379i		−	0.394243i
$214$		−	14.2829i		−	0.976356i
$215$		0			0
$216$	4.31534			0.293622
$217$		−	27.3693i		−	1.85795i
$218$			5.68466i			0.385014i
$219$	−18.2462			−1.23296
$220$		0			0
$221$			8.87348i			0.596895i
$222$		−	18.2462i		−	1.22461i
$223$	12.3376			0.826186			0.413093	−	0.910689i	$-0.364449\pi$
$223$	12.3376			0.826186			0.413093	+	0.910689i	$0.364449\pi$
$224$		−	17.3205i		−	1.15728i
$225$		0			0
$226$	5.36932			0.357162
$227$	12.3376			0.818874			0.409437	−	0.912338i	$-0.365725\pi$
$227$	12.3376			0.818874			0.409437	+	0.912338i	$0.365725\pi$
$228$	8.87348			0.587661
$229$			15.8017i			1.04420i	0.852883	+	0.522102i	$0.174852\pi$
$229$			15.8017i			1.04420i	−0.852883	+	0.522102i	$0.825148\pi$
$230$		0			0
$231$	8.63068			0.567857
$232$	−10.3923	−	12.3693i	−0.682288	−	0.812085i
$233$	2.49146			0.163221			0.0816106	−	0.996664i	$-0.473994\pi$
$233$	2.49146			0.163221			0.0816106	+	0.996664i	$0.473994\pi$
$234$			15.8017i			1.03299i
$235$		0			0
$236$	1.12311			0.0731079
$237$	−37.9854			−2.46742
$238$	−6.92820			−0.449089
$239$	−13.1231			−0.848863			−0.424432	−	0.905460i	$-0.639526\pi$
$239$	−13.1231			−0.848863			−0.424432	+	0.905460i	$0.639526\pi$
$240$		0			0
$241$	−1.68466			−0.108518			−0.0542592	−	0.998527i	$-0.517280\pi$
$241$	−1.68466			−0.108518			−0.0542592	+	0.998527i	$0.517280\pi$
$242$			10.0540i			0.646294i
$243$		−	22.2462i		−	1.42710i
$244$		−	1.94528i		−	0.124534i
$245$		0			0
$246$		−	22.7299i		−	1.44920i
$247$			15.3693i			0.977926i
$248$	−23.7025			−1.50511
$249$			26.6204i			1.68700i
$250$		0			0
$251$		−	16.7743i		−	1.05879i	−0.848377	−	0.529393i	$-0.822420\pi$
$251$		−	16.7743i		−	1.05879i	0.848377	−	0.529393i	$-0.177580\pi$
$252$	12.3376			0.777195
$253$			3.36932i			0.211827i
$254$	2.24621			0.140940
$255$		0			0
$256$	−17.0000			−1.06250
$257$	11.3649			0.708926			0.354463	−	0.935070i	$-0.384664\pi$
$257$	11.3649			0.708926			0.354463	+	0.935070i	$0.384664\pi$
$258$			13.9309i			0.867298i
$259$		−	24.6752i		−	1.53324i
$260$		0			0
$261$	14.6847	−	12.3376i	0.908958	−	0.763677i
$262$	14.2829			0.882398
$263$		−	3.68466i		−	0.227206i	−0.993526	−	0.113603i	$-0.963761\pi$
$263$		−	3.68466i		−	0.227206i	0.993526	−	0.113603i	$-0.0362392\pi$
$264$		−	7.47439i		−	0.460017i
$265$		0			0
$266$	−12.0000			−0.735767
$267$	22.7299			1.39105
$268$	12.3376			0.753638
$269$		−	15.8017i		−	0.963446i	−0.876324	−	0.481723i	$-0.840011\pi$
$269$		−	15.8017i		−	0.963446i	0.876324	−	0.481723i	$-0.159989\pi$
$270$		0			0
$271$		−	14.8290i		−	0.900800i	−0.892827	−	0.450400i	$-0.851281\pi$
$271$		−	14.8290i		−	0.900800i	0.892827	−	0.450400i	$-0.148719\pi$
$272$			2.00000i			0.121268i
$273$			39.3693i			2.38274i
$274$	−13.3693			−0.807670
$275$		0			0
$276$			8.87348i			0.534121i
$277$	−10.8188			−0.650036			−0.325018	−	0.945708i	$-0.605370\pi$
$277$	−10.8188			−0.650036			−0.325018	+	0.945708i	$0.605370\pi$
$278$		−	19.3693i		−	1.16169i
$279$		−	28.1393i		−	1.68465i
$280$		0			0
$281$	13.6847			0.816358			0.408179	−	0.912902i	$-0.366164\pi$
$281$	13.6847			0.816358			0.408179	+	0.912902i	$0.366164\pi$
$282$			29.9309i			1.78236i
$283$	14.2829			0.849028			0.424514	−	0.905421i	$-0.360445\pi$
$283$	14.2829			0.849028			0.424514	+	0.905421i	$0.360445\pi$
$284$	−2.24621			−0.133288
$285$		0			0
$286$	4.31534			0.255171
$287$		−	30.7386i		−	1.81444i
$288$		−	17.8078i		−	1.04933i
$289$	13.0000			0.764706
$290$		0			0
$291$	−21.1231			−1.23826
$292$			7.12311i			0.416848i
$293$		−	1.36932i		−	0.0799963i	−0.999200	−	0.0399982i	$-0.987265\pi$
$293$		−	1.36932i		−	0.0799963i	0.999200	−	0.0399982i	$-0.0127352\pi$
$294$	−12.8078			−0.746964
$295$		0			0
$296$	−21.3693			−1.24207
$297$	1.39909			0.0811833
$298$			13.6847i			0.792731i
$299$	−15.3693			−0.888831
$300$		0			0
$301$			18.8393i			1.08588i
$302$			15.3693i			0.884405i
$303$	−17.7470			−1.01954
$304$			3.46410i			0.198680i
$305$		0			0
$306$	−7.12311			−0.407201
$307$			3.19224i			0.182191i	0.995842	+	0.0910953i	$0.0290368\pi$
$307$			3.19224i			0.182191i	−0.995842	+	0.0910953i	$0.970963\pi$
$308$		−	3.36932i		−	0.191985i
$309$		−	3.89055i		−	0.221326i
$310$		0			0
$311$			0.426450i			0.0241818i	0.999927	+	0.0120909i	$0.00384874\pi$
$311$			0.426450i			0.0241818i	−0.999927	+	0.0120909i	$0.996151\pi$
$312$	34.0948			1.93024
$313$	2.49146			0.140826			0.0704129	−	0.997518i	$-0.477568\pi$
$313$	2.49146			0.140826			0.0704129	+	0.997518i	$0.477568\pi$
$314$	−22.4924			−1.26932
$315$		0			0
$316$			14.8290i			0.834199i
$317$			2.00000i			0.112331i	0.998421	+	0.0561656i	$0.0178875\pi$
$317$			2.00000i			0.112331i	−0.998421	+	0.0561656i	$0.982113\pi$
$318$	−11.3649			−0.637314
$319$	−3.36932	−	4.01029i	−0.188646	−	0.224533i
$320$		0			0
$321$		−	36.5863i		−	2.04205i
$322$		−	12.0000i		−	0.668734i
$323$	−6.92820			−0.385496
$324$	−7.00000			−0.388889
$325$		0			0
$326$	−5.43845			−0.301208
$327$			14.5616i			0.805256i
$328$	−26.6204			−1.46987
$329$			40.4768i			2.23156i
$330$		0			0
$331$			5.95557i			0.327347i	0.986515	+	0.163674i	$0.0523344\pi$
$331$			5.95557i			0.327347i	−0.986515	+	0.163674i	$0.947666\pi$
$332$	10.3923			0.570352
$333$		−	25.3693i		−	1.39023i
$334$		−	8.44703i		−	0.462201i
$335$		0			0
$336$			8.87348i			0.484088i
$337$			3.75379i			0.204482i	0.994760	+	0.102241i	$0.0326013\pi$
$337$			3.75379i			0.204482i	−0.994760	+	0.102241i	$0.967399\pi$
$338$			6.68466i			0.363597i
$339$	13.7538			0.747003
$340$		0			0
$341$	−7.68466			−0.416148
$342$	−12.3376			−0.667140
$343$	6.92820			0.374088
$344$	16.3153			0.879664
$345$		0			0
$346$		−	10.8188i		−	0.581620i
$347$	26.1940			1.40617			0.703083	−	0.711107i	$-0.251806\pi$
$347$	26.1940			1.40617			0.703083	+	0.711107i	$0.251806\pi$
$348$	−8.87348	−	10.5616i	−0.475668	−	0.566159i
$349$	−10.3153			−0.552168			−0.276084	−	0.961134i	$-0.589037\pi$
$349$	−10.3153			−0.552168			−0.276084	+	0.961134i	$0.589037\pi$
$350$		0			0
$351$			6.38202i			0.340647i
$352$	−4.86319			−0.259209
$353$	17.7470			0.944575			0.472288	−	0.881444i	$-0.343428\pi$
$353$	17.7470			0.944575			0.472288	+	0.881444i	$0.343428\pi$
$354$	−2.87689			−0.152905
$355$		0			0
$356$		−	8.87348i		−	0.470293i
$357$	−17.7470			−0.939269
$358$			12.0000i			0.634220i
$359$		−	21.7572i		−	1.14830i	−0.818749	−	0.574152i	$-0.805332\pi$
$359$		−	21.7572i		−	1.14830i	0.818749	−	0.574152i	$-0.194668\pi$
$360$		0			0
$361$	7.00000			0.368421
$362$		−	13.6847i		−	0.719250i
$363$			25.7538i			1.35172i
$364$	15.3693			0.805571
$365$		0			0
$366$			4.98293i			0.260462i
$367$		−	28.4924i		−	1.48729i	−0.668573	−	0.743646i	$-0.733095\pi$
$367$		−	28.4924i		−	1.48729i	0.668573	−	0.743646i	$-0.266905\pi$
$368$	−3.46410			−0.180579
$369$		−	31.6034i		−	1.64521i
$370$		0			0
$371$	−15.3693			−0.797935
$372$	−20.2384			−1.04931
$373$	−36.0401			−1.86609			−0.933043	−	0.359765i	$-0.882857\pi$
$373$	−36.0401			−1.86609			−0.933043	+	0.359765i	$0.882857\pi$
$374$			1.94528i			0.100588i
$375$		0			0
$376$	35.0540			1.80777
$377$	18.2931	−	15.3693i	0.942145	−	0.791560i
$378$	−4.98293			−0.256294
$379$			0.426450i			0.0219053i	0.999940	+	0.0109526i	$0.00348640\pi$
$379$			0.426450i			0.0219053i	−0.999940	+	0.0109526i	$0.996514\pi$
$380$		0			0
$381$	5.75379			0.294776
$382$	3.46410			0.177239
$383$	17.3205			0.885037			0.442518	−	0.896759i	$-0.354085\pi$
$383$	17.3205			0.885037			0.442518	+	0.896759i	$0.354085\pi$
$384$	−7.68466			−0.392156
$385$		0			0
$386$	8.24621			0.419721
$387$			19.3693i			0.984598i
$388$			8.24621i			0.418638i
$389$			10.8188i			0.548533i	0.961654	+	0.274266i	$0.0884350\pi$
$389$			10.8188i			0.548533i	−0.961654	+	0.274266i	$0.911565\pi$
$390$		0			0
$391$		−	6.92820i		−	0.350374i
$392$			15.0000i			0.757614i
$393$	36.5863			1.84553
$394$		−	10.8188i		−	0.545041i
$395$		0			0
$396$		−	3.46410i		−	0.174078i
$397$	−0.546188			−0.0274124			−0.0137062	−	0.999906i	$-0.504363\pi$
$397$	−0.546188			−0.0274124			−0.0137062	+	0.999906i	$0.504363\pi$
$398$			15.3693i			0.770394i
$399$	−30.7386			−1.53886
$400$		0			0
$401$	15.9309			0.795550			0.397775	−	0.917483i	$-0.369783\pi$
$401$	15.9309			0.795550			0.397775	+	0.917483i	$0.369783\pi$
$402$	−31.6034			−1.57623
$403$		−	35.0540i		−	1.74616i
$404$			6.92820i			0.344691i
$405$		0			0
$406$	12.0000	+	14.2829i	0.595550	+	0.708846i
$407$	−6.92820			−0.343418
$408$			15.3693i			0.760895i
$409$		−	3.89055i		−	0.192375i	−0.995363	−	0.0961877i	$-0.969335\pi$
$409$		−	3.89055i		−	0.192375i	0.995363	−	0.0961877i	$-0.0306649\pi$
$410$		0			0
$411$	−34.2462			−1.68924
$412$	−1.51883			−0.0748272
$413$	−3.89055			−0.191442
$414$		−	12.3376i		−	0.606359i
$415$		0			0
$416$		−	22.1837i		−	1.08765i
$417$		−	49.6155i		−	2.42968i
$418$			3.36932i			0.164799i
$419$	−14.2462			−0.695973			−0.347986	−	0.937500i	$-0.613134\pi$
$419$	−14.2462			−0.695973			−0.347986	+	0.937500i	$0.613134\pi$
$420$		0			0
$421$			37.4392i			1.82467i	0.409439	+	0.912337i	$0.365724\pi$
$421$			37.4392i			1.82467i	−0.409439	+	0.912337i	$0.634276\pi$
$422$	−14.8290			−0.721867
$423$			41.6155i			2.02342i
$424$			13.3102i			0.646401i
$425$		0			0
$426$	5.75379			0.278772
$427$			6.73863i			0.326105i
$428$	−14.2829			−0.690388
$429$	11.0540			0.533691
$430$		0			0
$431$	8.63068			0.415725			0.207863	−	0.978158i	$-0.433349\pi$
$431$	8.63068			0.415725			0.207863	+	0.978158i	$0.433349\pi$
$432$			1.43845i			0.0692073i
$433$		−	16.8769i		−	0.811052i	−0.914084	−	0.405526i	$-0.867088\pi$
$433$		−	16.8769i		−	0.811052i	0.914084	−	0.405526i	$-0.132912\pi$
$434$	27.3693			1.31377
$435$		0			0
$436$	5.68466			0.272246
$437$		−	12.0000i		−	0.574038i
$438$		−	18.2462i		−	0.871838i
$439$	−15.3693			−0.733537			−0.366769	−	0.930312i	$-0.619536\pi$
$439$	−15.3693			−0.733537			−0.366769	+	0.930312i	$0.619536\pi$
$440$		0			0
$441$	−17.8078			−0.847989
$442$	−8.87348			−0.422068
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$	−18.2462			−0.865927
$445$		0			0
$446$			12.3376i			0.584201i
$447$			35.0540i			1.65800i
$448$	24.2487			1.14564
$449$		−	17.7470i		−	0.837531i	−0.908094	−	0.418765i	$-0.862463\pi$
$449$		−	17.7470i		−	0.837531i	0.908094	−	0.418765i	$-0.137537\pi$
$450$		0			0
$451$	−8.63068			−0.406403
$452$		−	5.36932i		−	0.252551i
$453$			39.3693i			1.84973i
$454$			12.3376i			0.579031i
$455$		0			0
$456$			26.6204i			1.24662i
$457$	−3.89055			−0.181992			−0.0909962	−	0.995851i	$-0.529005\pi$
$457$	−3.89055			−0.181992			−0.0909962	+	0.995851i	$0.529005\pi$
$458$	−15.8017			−0.738364
$459$	−2.87689			−0.134282
$460$		0			0
$461$		−	34.6410i		−	1.61339i	−0.590966	−	0.806696i	$-0.701253\pi$
$461$		−	34.6410i		−	1.61339i	0.590966	−	0.806696i	$-0.298747\pi$
$462$			8.63068i			0.401536i
$463$	7.35465			0.341800			0.170900	−	0.985288i	$-0.445333\pi$
$463$	7.35465			0.341800			0.170900	+	0.985288i	$0.445333\pi$
$464$	4.12311	−	3.46410i	0.191410	−	0.160817i
$465$		0			0
$466$			2.49146i			0.115415i
$467$		−	8.31534i		−	0.384788i	−0.981318	−	0.192394i	$-0.938375\pi$
$467$		−	8.31534i		−	0.384788i	0.981318	−	0.192394i	$-0.0616252\pi$
$468$	15.8017			0.730433
$469$	−42.7386			−1.97349
$470$		0			0
$471$	−57.6155			−2.65478
$472$			3.36932i			0.155085i
$473$	5.28964			0.243218
$474$		−	37.9854i		−	1.74473i
$475$		0			0
$476$			6.92820i			0.317554i
$477$	−15.8017			−0.723509
$478$		−	13.1231i		−	0.600237i
$479$		−	2.91791i		−	0.133323i	−0.997776	−	0.0666614i	$-0.978765\pi$
$479$		−	2.91791i		−	0.133323i	0.997776	−	0.0666614i	$-0.0212347\pi$
$480$		0			0
$481$		−	31.6034i		−	1.44099i
$482$		−	1.68466i		−	0.0767341i
$483$		−	30.7386i		−	1.39866i
$484$	10.0540			0.456999
$485$		0			0
$486$	22.2462			1.00911
$487$	32.0298			1.45141			0.725705	−	0.688006i	$-0.241514\pi$
$487$	32.0298			1.45141			0.725705	+	0.688006i	$0.241514\pi$
$488$	5.83583			0.264176
$489$	−13.9309			−0.629976
$490$		0			0
$491$		−	29.5384i		−	1.33305i	−0.745484	−	0.666524i	$-0.767782\pi$
$491$		−	29.5384i		−	1.33305i	0.745484	−	0.666524i	$-0.232218\pi$
$492$	−22.7299			−1.02474
$493$	6.92820	+	8.24621i	0.312031	+	0.371391i
$494$	−15.3693			−0.691498
$495$		0			0
$496$		−	7.90084i		−	0.354758i
$497$	7.78110			0.349030
$498$	−26.6204			−1.19289
$499$	4.63068			0.207298			0.103649	−	0.994614i	$-0.466948\pi$
$499$	4.63068			0.207298			0.103649	+	0.994614i	$0.466948\pi$
$500$		0			0
$501$		−	21.6375i		−	0.966693i
$502$	16.7743			0.748675
$503$		−	4.94602i		−	0.220532i	−0.993902	−	0.110266i	$-0.964830\pi$
$503$		−	4.94602i		−	0.220532i	0.993902	−	0.110266i	$-0.0351703\pi$
$504$			37.0127i			1.64868i
$505$		0			0
$506$	−3.36932			−0.149784
$507$			17.1231i			0.760464i
$508$		−	2.24621i		−	0.0996595i
$509$	29.0540			1.28779			0.643897	−	0.765112i	$-0.277316\pi$
$509$	29.0540			1.28779			0.643897	+	0.765112i	$0.277316\pi$
$510$		0			0
$511$		−	24.6752i		−	1.09156i
$512$		−	11.0000i		−	0.486136i
$513$	−4.98293			−0.220002
$514$			11.3649i			0.501286i
$515$		0			0
$516$	13.9309			0.613272
$517$	11.3649			0.499830
$518$	24.6752			1.08416
$519$		−	27.7128i		−	1.21646i
$520$		0			0
$521$	22.3153			0.977653			0.488826	−	0.872381i	$-0.337425\pi$
$521$	22.3153			0.977653			0.488826	+	0.872381i	$0.337425\pi$
$522$	12.3376	+	14.6847i	0.540001	+	0.642730i
$523$	−26.1940			−1.14538			−0.572692	−	0.819771i	$-0.694101\pi$
$523$	−26.1940			−1.14538			−0.572692	+	0.819771i	$0.694101\pi$
$524$		−	14.2829i		−	0.623949i
$525$		0			0
$526$	3.68466			0.160659
$527$	15.8017			0.688332
$528$	2.49146			0.108427
$529$	−11.0000			−0.478261
$530$		0			0
$531$	−4.00000			−0.173585
$532$			12.0000i			0.520266i
$533$		−	39.3693i		−	1.70527i
$534$			22.7299i			0.983618i
$535$		0			0
$536$			37.0127i			1.59871i
$537$			30.7386i			1.32647i
$538$	15.8017			0.681259
$539$			4.86319i			0.209472i
$540$		0			0
$541$			38.5316i			1.65660i	0.560284	+	0.828301i	$0.310692\pi$
$541$			38.5316i			1.65660i	−0.560284	+	0.828301i	$0.689308\pi$
$542$	14.8290			0.636962
$543$		−	35.0540i		−	1.50431i
$544$	10.0000			0.428746
$545$		0			0
$546$	−39.3693			−1.68485
$547$	7.35465			0.314462			0.157231	−	0.987562i	$-0.449743\pi$
$547$	7.35465			0.314462			0.157231	+	0.987562i	$0.449743\pi$
$548$			13.3693i			0.571109i
$549$			6.92820i			0.295689i
$550$		0			0
$551$	12.0000	+	14.2829i	0.511217	+	0.608470i
$552$	−26.6204			−1.13304
$553$		−	51.3693i		−	2.18445i
$554$		−	10.8188i		−	0.459645i
$555$		0			0
$556$	−19.3693			−0.821442
$557$	−6.92820			−0.293557			−0.146779	−	0.989169i	$-0.546891\pi$
$557$	−6.92820			−0.293557			−0.146779	+	0.989169i	$0.546891\pi$
$558$	28.1393			1.19123
$559$			24.1290i			1.02055i
$560$		0			0
$561$			4.98293i			0.210379i
$562$			13.6847i			0.577252i
$563$			15.6847i			0.661030i	0.943801	+	0.330515i	$0.107222\pi$
$563$			15.6847i			0.661030i	−0.943801	+	0.330515i	$0.892778\pi$
$564$	29.9309			1.26032
$565$		0			0
$566$			14.2829i			0.600353i
$567$	24.2487			1.01835
$568$		−	6.73863i		−	0.282747i
$569$		−	3.89055i		−	0.163100i	−0.996669	−	0.0815502i	$-0.974013\pi$
$569$		−	3.89055i		−	0.163100i	0.996669	−	0.0815502i	$-0.0259871\pi$
$570$		0			0
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$		−	4.31534i		−	0.180433i
$573$	8.87348			0.370695
$574$	30.7386			1.28301
$575$		0			0
$576$	24.9309			1.03879
$577$		−	44.2462i		−	1.84199i	−0.389570	−	0.920997i	$-0.627376\pi$
$577$		−	44.2462i		−	1.84199i	0.389570	−	0.920997i	$-0.372624\pi$
$578$			13.0000i			0.540729i
$579$	21.1231			0.877846
$580$		0			0
$581$	−36.0000			−1.49353
$582$		−	21.1231i		−	0.875581i
$583$			4.31534i			0.178723i
$584$	−21.3693			−0.884269
$585$		0			0
$586$	1.36932			0.0565660
$587$	13.4300			0.554314			0.277157	−	0.960825i	$-0.410608\pi$
$587$	13.4300			0.554314			0.277157	+	0.960825i	$0.410608\pi$
$588$			12.8078i			0.528183i
$589$	27.3693			1.12773
$590$		0			0
$591$		−	27.7128i		−	1.13995i
$592$		−	7.12311i		−	0.292758i
$593$	6.38202			0.262078			0.131039	−	0.991377i	$-0.458169\pi$
$593$	6.38202			0.262078			0.131039	+	0.991377i	$0.458169\pi$
$594$			1.39909i			0.0574053i
$595$		0			0
$596$	13.6847			0.560545
$597$			39.3693i			1.61128i
$598$		−	15.3693i		−	0.628498i
$599$			0.972638i			0.0397409i	0.999803	+	0.0198705i	$0.00632538\pi$
$599$			0.972638i			0.0397409i	−0.999803	+	0.0198705i	$0.993675\pi$
$600$		0			0
$601$		−	8.87348i		−	0.361957i	−0.983487	−	0.180978i	$-0.942074\pi$
$601$		−	8.87348i		−	0.361957i	0.983487	−	0.180978i	$-0.0579264\pi$
$602$	−18.8393			−0.767834
$603$	−43.9409			−1.78941
$604$	15.3693			0.625369
$605$		0			0
$606$		−	17.7470i		−	0.720921i
$607$			0.177081i			0.00718749i	0.999994	+	0.00359375i	$0.00114393\pi$
$607$			0.177081i			0.00718749i	−0.999994	+	0.00359375i	$0.998856\pi$
$608$	17.3205			0.702439
$609$	30.7386	+	36.5863i	1.24559	+	1.48255i
$610$		0			0
$611$			51.8418i			2.09729i
$612$			7.12311i			0.287934i
$613$	14.4026			0.581715			0.290858	−	0.956766i	$-0.406059\pi$
$613$	14.4026			0.581715			0.290858	+	0.956766i	$0.406059\pi$
$614$	−3.19224			−0.128828
$615$		0			0
$616$	10.1080			0.407261
$617$			13.3693i			0.538228i	0.963108	+	0.269114i	$0.0867309\pi$
$617$			13.3693i			0.538228i	−0.963108	+	0.269114i	$0.913269\pi$
$618$	3.89055			0.156501
$619$		−	10.9385i		−	0.439655i	−0.975539	−	0.219828i	$-0.929451\pi$
$619$		−	10.9385i		−	0.439655i	0.975539	−	0.219828i	$-0.0705495\pi$
$620$		0			0
$621$		−	4.98293i		−	0.199958i
$622$	−0.426450			−0.0170991
$623$			30.7386i			1.23152i
$624$			11.3649i			0.454962i
$625$		0			0
$626$			2.49146i			0.0995789i
$627$			8.63068i			0.344676i
$628$			22.4924i			0.897545i
$629$	14.2462			0.568034
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	−44.4871			−1.76960
$633$	−37.9854			−1.50978
$634$	−2.00000			−0.0794301
$635$		0			0
$636$			11.3649i			0.450649i
$637$	−22.1837			−0.878950
$638$	4.01029	−	3.36932i	0.158769	−	0.133393i
$639$	8.00000			0.316475
$640$		0			0
$641$			4.98293i			0.196814i	0.995146	+	0.0984069i	$0.0313747\pi$
$641$			4.98293i			0.196814i	−0.995146	+	0.0984069i	$0.968625\pi$
$642$	36.5863			1.44395
$643$	−35.0675			−1.38293			−0.691463	−	0.722412i	$-0.743033\pi$
$643$	−35.0675			−1.38293			−0.691463	+	0.722412i	$0.743033\pi$
$644$	−12.0000			−0.472866
$645$		0			0
$646$		−	6.92820i		−	0.272587i
$647$	−48.9239			−1.92340			−0.961698	−	0.274111i	$-0.911616\pi$
$647$	−48.9239			−1.92340			−0.961698	+	0.274111i	$0.911616\pi$
$648$		−	21.0000i		−	0.824958i
$649$			1.09238i			0.0428795i
$650$		0			0
$651$	70.1080			2.74775
$652$			5.43845i			0.212986i
$653$			28.7386i			1.12463i	0.826923	+	0.562315i	$0.190089\pi$
$653$			28.7386i			1.12463i	−0.826923	+	0.562315i	$0.809911\pi$
$654$	−14.5616			−0.569402
$655$		0			0
$656$		−	8.87348i		−	0.346451i
$657$		−	25.3693i		−	0.989751i
$658$	−40.4768			−1.57795
$659$			35.6137i			1.38731i	0.720307	+	0.693655i	$0.244001\pi$
$659$			35.6137i			1.38731i	−0.720307	+	0.693655i	$0.755999\pi$
$660$		0			0
$661$	−24.7386			−0.962221			−0.481111	−	0.876660i	$-0.659766\pi$
$661$	−24.7386			−0.962221			−0.481111	+	0.876660i	$0.659766\pi$
$662$	−5.95557			−0.231470
$663$	−22.7299			−0.882756
$664$			31.1769i			1.20990i
$665$		0			0
$666$	25.3693			0.983041
$667$	−14.2829	+	12.0000i	−0.553034	+	0.464642i
$668$	−8.44703			−0.326825
$669$			31.6034i			1.22186i
$670$		0			0
$671$	1.89205			0.0730418
$672$	44.3674			1.71151
$673$	29.1119			1.12218			0.561091	−	0.827754i	$-0.310382\pi$
$673$	29.1119			1.12218			0.561091	+	0.827754i	$0.310382\pi$
$674$	−3.75379			−0.144591
$675$		0			0
$676$	6.68466			0.257102
$677$		−	13.3693i		−	0.513825i	−0.966435	−	0.256912i	$-0.917295\pi$
$677$		−	13.3693i		−	0.513825i	0.966435	−	0.256912i	$-0.0827052\pi$
$678$			13.7538i			0.528211i
$679$		−	28.5657i		−	1.09625i
$680$		0			0
$681$			31.6034i			1.21104i
$682$		−	7.68466i		−	0.294261i
$683$	−16.2281			−0.620952			−0.310476	−	0.950581i	$-0.600488\pi$
$683$	−16.2281			−0.620952			−0.310476	+	0.950581i	$0.600488\pi$
$684$			12.3376i			0.471739i
$685$		0			0
$686$			6.92820i			0.264520i
$687$	−40.4768			−1.54429
$688$			5.43845i			0.207339i
$689$	−19.6847			−0.749926
$690$		0			0
$691$	18.7386			0.712851			0.356426	−	0.934324i	$-0.383995\pi$
$691$	18.7386			0.712851			0.356426	+	0.934324i	$0.383995\pi$
$692$	−10.8188			−0.411267
$693$			12.0000i			0.455842i
$694$			26.1940i			0.994310i
$695$		0			0
$696$	31.6847	−	26.6204i	1.20100	−	1.00905i
$697$	17.7470			0.672214
$698$		−	10.3153i		−	0.390441i
$699$			6.38202i			0.241390i
$700$		0			0
$701$	−50.8078			−1.91898			−0.959491	−	0.281738i	$-0.909089\pi$
$701$	−50.8078			−1.91898			−0.959491	+	0.281738i	$0.909089\pi$
$702$	−6.38202			−0.240874
$703$	24.6752			0.930641
$704$		−	6.80847i		−	0.256604i
$705$		0			0
$706$			17.7470i			0.667916i
$707$		−	24.0000i		−	0.902613i
$708$			2.87689i			0.108120i
$709$	6.31534			0.237178			0.118589	−	0.992943i	$-0.462163\pi$
$709$	6.31534			0.237178			0.118589	+	0.992943i	$0.462163\pi$
$710$		0			0
$711$		−	52.8144i		−	1.98070i
$712$	26.6204			0.997643
$713$			27.3693i			1.02499i
$714$		−	17.7470i		−	0.664163i
$715$		0			0
$716$	12.0000			0.448461
$717$		−	33.6155i		−	1.25539i
$718$	21.7572			0.811973
$719$	−26.2462			−0.978819			−0.489409	−	0.872054i	$-0.662788\pi$
$719$	−26.2462			−0.978819			−0.489409	+	0.872054i	$0.662788\pi$
$720$		0			0
$721$	5.26137			0.195944
$722$			7.00000i			0.260513i
$723$		−	4.31534i		−	0.160489i
$724$	−13.6847			−0.508586
$725$		0			0
$726$	−25.7538			−0.955813
$727$		−	4.49242i		−	0.166615i	−0.996524	−	0.0833074i	$-0.973452\pi$
$727$		−	4.49242i		−	0.166615i	0.996524	−	0.0833074i	$-0.0265483\pi$
$728$			46.1080i			1.70887i
$729$	35.9848			1.33277
$730$		0			0
$731$	−10.8769			−0.402296
$732$	4.98293			0.184174
$733$			16.8769i			0.623362i	0.950187	+	0.311681i	$0.100892\pi$
$733$			16.8769i			0.623362i	−0.950187	+	0.311681i	$0.899108\pi$
$734$	28.4924			1.05167
$735$		0			0
$736$			17.3205i			0.638442i
$737$			12.0000i			0.442026i
$738$	31.6034			1.16334
$739$		−	27.5931i		−	1.01503i	−0.861644	−	0.507514i	$-0.830565\pi$
$739$		−	27.5931i		−	1.01503i	0.861644	−	0.507514i	$-0.169435\pi$
$740$		0			0
$741$	−39.3693			−1.44627
$742$		−	15.3693i		−	0.564225i
$743$			32.0000i			1.17397i	0.809599	+	0.586983i	$0.199684\pi$
$743$			32.0000i			1.17397i	−0.809599	+	0.586983i	$0.800316\pi$
$744$		−	60.7153i		−	2.22593i
$745$		0			0
$746$		−	36.0401i		−	1.31952i
$747$	−37.0127			−1.35423
$748$	1.94528			0.0711263
$749$	49.4773			1.80786
$750$		0			0
$751$			6.50175i			0.237252i	0.992939	+	0.118626i	$0.0378490\pi$
$751$			6.50175i			0.237252i	−0.992939	+	0.118626i	$0.962151\pi$
$752$			11.6847i			0.426096i
$753$	42.9683			1.56585
$754$	15.3693	+	18.2931i	0.559718	+	0.666197i
$755$		0			0
$756$			4.98293i			0.181227i
$757$			15.7538i			0.572581i	0.958143	+	0.286291i	$0.0924223\pi$
$757$			15.7538i			0.572581i	−0.958143	+	0.286291i	$0.907578\pi$
$758$	−0.426450			−0.0154894
$759$	−8.63068			−0.313274
$760$		0			0
$761$	−1.50758			−0.0546496			−0.0273248	−	0.999627i	$-0.508699\pi$
$761$	−1.50758			−0.0546496			−0.0273248	+	0.999627i	$0.508699\pi$
$762$			5.75379i			0.208438i
$763$	−19.6922			−0.712907
$764$		−	3.46410i		−	0.125327i
$765$		0			0
$766$			17.3205i			0.625815i
$767$	−4.98293			−0.179923
$768$		−	43.5464i		−	1.57135i
$769$		−	32.6957i		−	1.17904i	−0.807754	−	0.589519i	$-0.799317\pi$
$769$		−	32.6957i		−	1.17904i	0.807754	−	0.589519i	$-0.200683\pi$
$770$		0			0
$771$			29.1119i			1.04844i
$772$		−	8.24621i		−	0.296788i
$773$		−	26.0000i		−	0.935155i	−0.883952	−	0.467578i	$-0.845127\pi$
$773$		−	26.0000i		−	0.935155i	0.883952	−	0.467578i	$-0.154873\pi$
$774$	−19.3693			−0.696216
$775$		0			0
$776$	−24.7386			−0.888065
$777$	63.2067			2.26753
$778$	−10.8188			−0.387871
$779$	30.7386			1.10133
$780$		0			0
$781$		−	2.18475i		−	0.0781765i
$782$	6.92820			0.247752
$783$	4.98293	+	5.93087i	0.178075	+	0.211952i
$784$	−5.00000			−0.178571
$785$		0			0
$786$			36.5863i			1.30499i
$787$	12.3376			0.439787			0.219894	−	0.975524i	$-0.429429\pi$
$787$	12.3376			0.439787			0.219894	+	0.975524i	$0.429429\pi$
$788$	−10.8188			−0.385402
$789$	9.43845			0.336018
$790$		0			0
$791$			18.5999i			0.661335i
$792$	10.3923			0.369274
$793$			8.63068i			0.306485i
$794$		−	0.546188i		−	0.0193835i
$795$		0			0
$796$	15.3693			0.544751
$797$			34.0000i			1.20434i	0.798367	+	0.602171i	$0.205697\pi$
$797$			34.0000i			1.20434i	−0.798367	+	0.602171i	$0.794303\pi$
$798$		−	30.7386i		−	1.08814i
$799$	−23.3693			−0.826747
$800$		0			0
$801$			31.6034i			1.11665i
$802$			15.9309i			0.562539i
$803$	−6.92820			−0.244491
$804$			31.6034i			1.11456i
$805$		0			0
$806$	35.0540			1.23472
$807$	40.4768			1.42485
$808$	−20.7846			−0.731200
$809$			31.6034i			1.11112i	0.831478	+	0.555558i	$0.187495\pi$
$809$			31.6034i			1.11112i	−0.831478	+	0.555558i	$0.812505\pi$
$810$		0			0
$811$	4.63068			0.162605			0.0813026	−	0.996689i	$-0.474092\pi$
$811$	4.63068			0.162605			0.0813026	+	0.996689i	$0.474092\pi$
$812$	14.2829	−	12.0000i	0.501230	−	0.421117i
$813$	37.9854			1.33221
$814$		−	6.92820i		−	0.242833i
$815$		0			0
$816$	−5.12311			−0.179345
$817$	−18.8393			−0.659105
$818$	3.89055			0.136030
$819$	−54.7386			−1.91272
$820$		0			0
$821$	47.7926			1.66797			0.833987	−	0.551784i	$-0.186053\pi$
$821$	47.7926			1.66797			0.833987	+	0.551784i	$0.186053\pi$
$822$		−	34.2462i		−	1.19447i
$823$			21.7538i			0.758289i	0.925337	+	0.379145i	$0.123782\pi$
$823$			21.7538i			0.758289i	−0.925337	+	0.379145i	$0.876218\pi$
$824$		−	4.55648i		−	0.158732i
$825$		0			0
$826$		−	3.89055i		−	0.135370i
$827$		−	15.0540i		−	0.523478i	−0.965139	−	0.261739i	$-0.915704\pi$
$827$		−	15.0540i		−	0.523478i	0.965139	−	0.261739i	$-0.0842960\pi$
$828$	−12.3376			−0.428761
$829$		−	23.5828i		−	0.819064i	−0.912296	−	0.409532i	$-0.865692\pi$
$829$		−	23.5828i		−	0.819064i	0.912296	−	0.409532i	$-0.134308\pi$
$830$		0			0
$831$		−	27.7128i		−	0.961347i
$832$	31.0572			1.07671
$833$		−	10.0000i		−	0.346479i
$834$	49.6155			1.71805
$835$		0			0
$836$	3.36932			0.116530
$837$	11.3649			0.392830
$838$		−	14.2462i		−	0.492127i
$839$			18.7196i			0.646272i	0.946352	+	0.323136i	$0.104737\pi$
$839$			18.7196i			0.646272i	−0.946352	+	0.323136i	$0.895263\pi$
$840$		0			0
$841$	5.00000	−	28.5657i	0.172414	−	0.985025i
$842$	−37.4392			−1.29024
$843$			35.0540i			1.20732i
$844$			14.8290i			0.510437i
$845$		0			0
$846$	−41.6155			−1.43077
$847$	−34.8280			−1.19670
$848$	−4.43674			−0.152358
$849$			36.5863i			1.25564i
$850$		0			0
$851$			24.6752i			0.845854i
$852$		−	5.75379i		−	0.197122i
$853$		−	37.8617i		−	1.29636i	−0.761487	−	0.648181i	$-0.775530\pi$
$853$		−	37.8617i		−	1.29636i	0.761487	−	0.648181i	$-0.224470\pi$
$854$	−6.73863			−0.230591
$855$		0			0
$856$		−	42.8486i		−	1.46453i
$857$	20.2384			0.691331			0.345666	−	0.938358i	$-0.387653\pi$
$857$	20.2384			0.691331			0.345666	+	0.938358i	$0.387653\pi$
$858$			11.0540i			0.377376i
$859$			52.2682i			1.78337i	0.452657	+	0.891685i	$0.350476\pi$
$859$			52.2682i			1.78337i	−0.452657	+	0.891685i	$0.649524\pi$
$860$		0			0
$861$	78.7386			2.68341
$862$			8.63068i			0.293962i
$863$	−15.3752			−0.523379			−0.261689	−	0.965152i	$-0.584280\pi$
$863$	−15.3752			−0.523379			−0.261689	+	0.965152i	$0.584280\pi$
$864$	7.19224			0.244685
$865$		0			0
$866$	16.8769			0.573500
$867$			33.3002i			1.13093i
$868$		−	27.3693i		−	0.928975i
$869$	−14.4233			−0.489277
$870$		0			0
$871$	−54.7386			−1.85475
$872$			17.0540i			0.577520i
$873$		−	29.3693i		−	0.994001i
$874$	12.0000			0.405906
$875$		0			0
$876$	−18.2462			−0.616482
$877$	−41.0230			−1.38525			−0.692625	−	0.721298i	$-0.743546\pi$
$877$	−41.0230			−1.38525			−0.692625	+	0.721298i	$0.743546\pi$
$878$		−	15.3693i		−	0.518689i
$879$	3.50758			0.118308
$880$		0			0
$881$		−	45.4598i		−	1.53158i	−0.643092	−	0.765789i	$-0.722349\pi$
$881$		−	45.4598i		−	1.53158i	0.643092	−	0.765789i	$-0.277651\pi$
$882$		−	17.8078i		−	0.599619i
$883$	35.9204			1.20882			0.604408	−	0.796675i	$-0.293410\pi$
$883$	35.9204			1.20882			0.604408	+	0.796675i	$0.293410\pi$
$884$			8.87348i			0.298447i
$885$		0			0
$886$	−4.00000			−0.134383
$887$		−	3.68466i		−	0.123719i	−0.998085	−	0.0618594i	$-0.980297\pi$
$887$		−	3.68466i		−	0.123719i	0.998085	−	0.0618594i	$-0.0197030\pi$
$888$		−	54.7386i		−	1.83691i
$889$			7.78110i			0.260970i
$890$		0			0
$891$		−	6.80847i		−	0.228092i
$892$	12.3376			0.413093
$893$	−40.4768			−1.35451
$894$	−35.0540			−1.17238
$895$		0			0
$896$		−	10.3923i		−	0.347183i
$897$		−	39.3693i		−	1.31450i
$898$	17.7470			0.592224
$899$	−27.3693	−	32.5760i	−0.912818	−	1.08647i
$900$		0			0
$901$		−	8.87348i		−	0.295618i
$902$		−	8.63068i		−	0.287370i
$903$	−48.2579			−1.60592
$904$	16.1080			0.535742
$905$		0			0
$906$	−39.3693			−1.30796
$907$		−	40.4924i		−	1.34453i	−0.740311	−	0.672264i	$-0.765322\pi$
$907$		−	40.4924i		−	1.34453i	0.740311	−	0.672264i	$-0.234678\pi$
$908$	12.3376			0.409437
$909$		−	24.6752i		−	0.818423i
$910$		0			0
$911$		−	9.84612i		−	0.326216i	−0.986608	−	0.163108i	$-0.947848\pi$
$911$		−	9.84612i		−	0.326216i	0.986608	−	0.163108i	$-0.0521520\pi$
$912$	−8.87348			−0.293830
$913$			10.1080i			0.334524i
$914$		−	3.89055i		−	0.128688i
$915$		0			0
$916$			15.8017i			0.522102i
$917$			49.4773i			1.63388i
$918$		−	2.87689i		−	0.0949517i
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$		0			0
$921$	−8.17708			−0.269444
$922$	34.6410			1.14084
$923$	9.96585			0.328030
$924$	8.63068			0.283929
$925$		0			0
$926$			7.35465i			0.241689i
$927$	5.40938			0.177667
$928$	−17.3205	−	20.6155i	−0.568574	−	0.676738i
$929$	−48.7386			−1.59906			−0.799531	−	0.600624i	$-0.794919\pi$
$929$	−48.7386			−1.59906			−0.799531	+	0.600624i	$0.794919\pi$
$930$		0			0
$931$		−	17.3205i		−	0.567657i
$932$	2.49146			0.0816106
$933$	−1.09238			−0.0357628
$934$	8.31534			0.272086
$935$		0			0
$936$			47.4050i			1.54948i
$937$	31.6034			1.03244			0.516218	−	0.856457i	$-0.327339\pi$
$937$	31.6034			1.03244			0.516218	+	0.856457i	$0.327339\pi$
$938$		−	42.7386i		−	1.39547i
$939$			6.38202i			0.208269i
$940$		0			0
$941$	32.4233			1.05697			0.528485	−	0.848943i	$-0.322760\pi$
$941$	32.4233			1.05697			0.528485	+	0.848943i	$0.322760\pi$
$942$		−	57.6155i		−	1.87722i
$943$			30.7386i			1.00099i
$944$	−1.12311			−0.0365540
$945$		0			0
$946$			5.28964i			0.171981i
$947$			23.6847i			0.769648i	0.922990	+	0.384824i	$0.125738\pi$
$947$			23.6847i			0.769648i	−0.922990	+	0.384824i	$0.874262\pi$
$948$	−37.9854			−1.23371
$949$		−	31.6034i		−	1.02589i
$950$		0			0
$951$	−5.12311			−0.166128
$952$	−20.7846			−0.673633
$953$	10.2726			0.332761			0.166381	−	0.986062i	$-0.446792\pi$
$953$	10.2726			0.332761			0.166381	+	0.986062i	$0.446792\pi$
$954$		−	15.8017i		−	0.511598i
$955$		0			0
$956$	−13.1231			−0.424432
$957$	10.2726	−	8.63068i	0.332065	−	0.278990i
$958$	2.91791			0.0942735
$959$		−	46.3127i		−	1.49551i
$960$		0			0
$961$	−31.4233			−1.01365
$962$	31.6034			1.01893
$963$	50.8691			1.63924
$964$	−1.68466			−0.0542592
$965$		0			0
$966$	30.7386			0.988999
$967$			45.9309i			1.47704i	0.674233	+	0.738519i	$0.264474\pi$
$967$			45.9309i			1.47704i	−0.674233	+	0.738519i	$0.735526\pi$
$968$			30.1619i			0.969441i
$969$		−	17.7470i		−	0.570114i
$970$		0			0
$971$		−	45.8862i		−	1.47256i	−0.676678	−	0.736279i	$-0.736581\pi$
$971$		−	45.8862i		−	1.47256i	0.676678	−	0.736279i	$-0.263419\pi$
$972$		−	22.2462i		−	0.713548i
$973$	67.0973			2.15104
$974$			32.0298i			1.02630i
$975$		0			0
$976$			1.94528i			0.0622668i
$977$	−6.38202			−0.204179			−0.102089	−	0.994775i	$-0.532553\pi$
$977$	−6.38202			−0.204179			−0.102089	+	0.994775i	$0.532553\pi$
$978$		−	13.9309i		−	0.445460i
$979$	8.63068			0.275838
$980$		0			0
$981$	−20.2462			−0.646412
$982$	29.5384			0.942607
$983$		−	27.0540i		−	0.862888i	−0.902140	−	0.431444i	$-0.858004\pi$
$983$		−	27.0540i		−	0.862888i	0.902140	−	0.431444i	$-0.141996\pi$
$984$		−	68.1897i		−	2.17381i
$985$		0			0
$986$	−8.24621	+	6.92820i	−0.262613	+	0.220639i
$987$	−103.684			−3.30028
$988$			15.3693i			0.488963i
$989$		−	18.8393i		−	0.599056i
$990$		0			0
$991$	−30.7386			−0.976445			−0.488222	−	0.872719i	$-0.662355\pi$
$991$	−30.7386			−0.976445			−0.488222	+	0.872719i	$0.662355\pi$
$992$	−39.5042			−1.25426
$993$	−15.2555			−0.484118
$994$			7.78110i			0.246802i
$995$		0			0
$996$			26.6204i			0.843501i
$997$			59.6155i			1.88804i	0.329884	+	0.944021i	$0.392990\pi$
$997$			59.6155i			1.88804i	−0.329884	+	0.944021i	$0.607010\pi$
$998$			4.63068i			0.146582i
$999$	10.2462			0.324176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.c.f.376.7		8
5.2	odd	4		145.2.d.a.144.3	✓	4
5.3	odd	4		145.2.d.c.144.2	yes	4
5.4	even	2	inner	725.2.c.f.376.2		8
15.2	even	4		1305.2.f.i.289.4		4
15.8	even	4		1305.2.f.e.289.3		4
20.3	even	4		2320.2.j.c.289.4		4
20.7	even	4		2320.2.j.a.289.1		4
29.28	even	2	inner	725.2.c.f.376.1		8
145.28	odd	4		145.2.d.a.144.4	yes	4
145.57	odd	4		145.2.d.c.144.1	yes	4
145.144	even	2	inner	725.2.c.f.376.8		8
435.173	even	4		1305.2.f.i.289.3		4
435.347	even	4		1305.2.f.e.289.4		4
580.347	even	4		2320.2.j.c.289.3		4
580.463	even	4		2320.2.j.a.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.d.a.144.3	✓	4	5.2	odd	4
145.2.d.a.144.4	yes	4	145.28	odd	4
145.2.d.c.144.1	yes	4	145.57	odd	4
145.2.d.c.144.2	yes	4	5.3	odd	4
725.2.c.f.376.1		8	29.28	even	2	inner
725.2.c.f.376.2		8	5.4	even	2	inner
725.2.c.f.376.7		8	1.1	even	1	trivial
725.2.c.f.376.8		8	145.144	even	2	inner
1305.2.f.e.289.3		4	15.8	even	4
1305.2.f.e.289.4		4	435.347	even	4
1305.2.f.i.289.3		4	435.173	even	4
1305.2.f.i.289.4		4	15.2	even	4
2320.2.j.a.289.1		4	20.7	even	4
2320.2.j.a.289.2		4	580.463	even	4
2320.2.j.c.289.3		4	580.347	even	4
2320.2.j.c.289.4		4	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +2.56155i q^{3} +1.00000 q^{4} -2.56155 q^{6} -3.46410 q^{7} +3.00000i q^{8} -3.56155 q^{9} +0.972638i q^{11} +2.56155i q^{12} -4.43674 q^{13} -3.46410i q^{14} -1.00000 q^{16} -2.00000i q^{17} -3.56155i q^{18} -3.46410i q^{19} -8.87348i q^{21} -0.972638 q^{22} +3.46410 q^{23} -7.68466 q^{24} -4.43674i q^{26} -1.43845i q^{27} -3.46410 q^{28} +(-4.12311 + 3.46410i) q^{29} +7.90084i q^{31} +5.00000i q^{32} -2.49146 q^{33} +2.00000 q^{34} -3.56155 q^{36} +7.12311i q^{37} +3.46410 q^{38} -11.3649i q^{39} +8.87348i q^{41} +8.87348 q^{42} -5.43845i q^{43} +0.972638i q^{44} +3.46410i q^{46} -11.6847i q^{47} -2.56155i q^{48} +5.00000 q^{49} +5.12311 q^{51} -4.43674 q^{52} +4.43674 q^{53} +1.43845 q^{54} -10.3923i q^{56} +8.87348 q^{57} +(-3.46410 - 4.12311i) q^{58} +1.12311 q^{59} -1.94528i q^{61} -7.90084 q^{62} +12.3376 q^{63} -7.00000 q^{64} -2.49146i q^{66} +12.3376 q^{67} -2.00000i q^{68} +8.87348i q^{69} -2.24621 q^{71} -10.6847i q^{72} +7.12311i q^{73} -7.12311 q^{74} -3.46410i q^{76} -3.36932i q^{77} +11.3649 q^{78} +14.8290i q^{79} -7.00000 q^{81} -8.87348 q^{82} +10.3923 q^{83} -8.87348i q^{84} +5.43845 q^{86} +(-8.87348 - 10.5616i) q^{87} -2.91791 q^{88} -8.87348i q^{89} +15.3693 q^{91} +3.46410 q^{92} -20.2384 q^{93} +11.6847 q^{94} -12.8078 q^{96} +8.24621i q^{97} +5.00000i q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 4 q^{6} - 12 q^{9} - 8 q^{16} - 12 q^{24} + 16 q^{34} - 12 q^{36} + 40 q^{49} + 8 q^{51} + 28 q^{54} - 24 q^{59} - 56 q^{64} + 48 q^{71} - 24 q^{74} - 56 q^{81} + 60 q^{86} + 24 q^{91} + 44 q^{94}+ \cdots - 20 q^{96}+O(q^{100}) \) 8 * q + 8 * q^4 - 4 * q^6 - 12 * q^9 - 8 * q^16 - 12 * q^24 + 16 * q^34 - 12 * q^36 + 40 * q^49 + 8 * q^51 + 28 * q^54 - 24 * q^59 - 56 * q^64 + 48 * q^71 - 24 * q^74 - 56 * q^81 + 60 * q^86 + 24 * q^91 + 44 * q^94 - 20 * q^96

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