LMFDB - Embedded newform 2205.2.d.s.1324.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2205,2,Mod(1324,2205)] 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("2205.1324"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2205, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,2,0,0,0,0,4,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$17.6070136457$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2058981376.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1324.6
Root			$-1.43917 - 1.43917i$ of defining polynomial
Character	$\chi$	$=$	2205.1324
Dual form			2205.2.d.s.1324.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.55241i q^{2} -0.409975 q^{4} +(-0.0917505 + 2.23418i) q^{5} +2.46837i q^{8} +(-3.46837 - 0.142434i) q^{10} -4.43075 q^{11} -1.73246i q^{13} -4.65187 q^{16} +2.73246i q^{17} +0.305156 q^{19} +(0.0376154 - 0.915960i) q^{20} -6.87834i q^{22} -7.02423i q^{23} +(-4.98316 - 0.409975i) q^{25} +2.68949 q^{26} -7.79430 q^{29} -5.28487 q^{31} -2.28487i q^{32} -4.24190 q^{34} -3.67406i q^{37} +0.473727i q^{38} +(-5.51479 - 0.226474i) q^{40} +6.71562 q^{41} +9.71562i q^{43} +1.81650 q^{44} +10.9045 q^{46} -1.81650i q^{47} +(0.636449 - 7.73591i) q^{50} +0.710265i q^{52} -1.71513i q^{53} +(0.406524 - 9.89912i) q^{55} -12.1000i q^{58} -1.14243 q^{59} +9.55635 q^{61} -8.20428i q^{62} -5.75669 q^{64} +(3.87063 + 0.158954i) q^{65} -8.38433i q^{67} -1.12024i q^{68} -10.2888 q^{71} +12.8204i q^{73} +5.70365 q^{74} -0.125106 q^{76} -6.71372 q^{79} +(0.426811 - 10.3931i) q^{80} +10.4254i q^{82} +5.09946i q^{83} +(-6.10482 - 0.250704i) q^{85} -15.0826 q^{86} -10.9367i q^{88} +4.07065 q^{89} +2.87976i q^{92} +2.81995 q^{94} +(-0.0279982 + 0.681775i) q^{95} -2.87834i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 2 q^{5} + 4 q^{10} + 24 q^{19} + 4 q^{20} + 4 q^{25} - 12 q^{26} - 12 q^{29} - 16 q^{31} + 8 q^{34} - 32 q^{40} - 8 q^{41} + 20 q^{44} + 32 q^{46} + 20 q^{50} + 4 q^{55} + 4 q^{59} - 16 q^{61}+ \cdots - 22 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^10 + 24 * q^19 + 4 * q^20 + 4 * q^25 - 12 * q^26 - 12 * q^29 - 16 * q^31 + 8 * q^34 - 32 * q^40 - 8 * q^41 + 20 * q^44 + 32 * q^46 + 20 * q^50 + 4 * q^55 + 4 * q^59 - 16 * q^61 + 8 * q^64 + 30 * q^65 + 28 * q^71 + 40 * q^74 - 32 * q^76 + 16 * q^79 + 52 * q^80 - 32 * q^85 - 48 * q^86 + 16 * q^89 + 32 * q^94 - 22 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$			1.55241i			1.09772i	0.835915	+	0.548860i	$0.184938\pi$
$2$			1.55241i			1.09772i	−0.835915	+	0.548860i	$0.815062\pi$
$3$		0			0
$3$		0			0
$4$	−0.409975			−0.204988
$5$	−0.0917505	+	2.23418i	−0.0410321	+	0.999158i
$5$	−0.0917505	+	2.23418i	−0.0410321	+	0.999158i
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.46837i			0.872700i
$9$		0			0
$10$	−3.46837	−	0.142434i	−1.09679	−	0.0450417i
$11$	−4.43075			−1.33592			−0.667961	−	0.744196i	$-0.732833\pi$
$11$	−4.43075			−1.33592			−0.667961	+	0.744196i	$0.732833\pi$
$12$		0			0
$13$		−	1.73246i		−	0.480498i	−0.970711	−	0.240249i	$-0.922771\pi$
$13$		−	1.73246i		−	0.480498i	0.970711	−	0.240249i	$-0.0772291\pi$
$14$		0			0
$15$		0			0
$16$	−4.65187			−1.16297
$17$			2.73246i			0.662719i	0.943505	+	0.331359i	$0.107507\pi$
$17$			2.73246i			0.662719i	−0.943505	+	0.331359i	$0.892493\pi$
$18$		0			0
$19$	0.305156			0.0700076			0.0350038	−	0.999387i	$-0.488856\pi$
$19$	0.305156			0.0700076			0.0350038	+	0.999387i	$0.488856\pi$
$20$	0.0376154	−	0.915960i	0.00841106	−	0.204815i
$21$		0			0
$22$		−	6.87834i		−	1.46647i
$23$		−	7.02423i		−	1.46465i	−0.680954	−	0.732327i	$-0.738434\pi$
$23$		−	7.02423i		−	1.46465i	0.680954	−	0.732327i	$-0.261566\pi$
$24$		0			0
$25$	−4.98316	−	0.409975i	−0.996633	−	0.0819950i
$26$	2.68949			0.527452
$27$		0			0
$28$		0			0
$29$	−7.79430			−1.44737			−0.723683	−	0.690132i	$-0.757552\pi$
$29$	−7.79430			−1.44737			−0.723683	+	0.690132i	$0.757552\pi$
$30$		0			0
$31$	−5.28487			−0.949190			−0.474595	−	0.880204i	$-0.657406\pi$
$31$	−5.28487			−0.949190			−0.474595	+	0.880204i	$0.657406\pi$
$32$		−	2.28487i		−	0.403912i
$33$		0			0
$34$	−4.24190			−0.727479
$35$		0			0
$36$		0			0
$37$		−	3.67406i		−	0.604013i	−0.953306	−	0.302006i	$-0.902344\pi$
$37$		−	3.67406i		−	0.604013i	0.953306	−	0.302006i	$-0.0976564\pi$
$38$			0.473727i			0.0768487i
$39$		0			0
$40$	−5.51479	−	0.226474i	−0.871965	−	0.0358087i
$41$	6.71562			1.04880			0.524402	−	0.851471i	$-0.324289\pi$
$41$	6.71562			1.04880			0.524402	+	0.851471i	$0.324289\pi$
$42$		0			0
$43$			9.71562i			1.48162i	0.671715	+	0.740809i	$0.265558\pi$
$43$			9.71562i			1.48162i	−0.671715	+	0.740809i	$0.734442\pi$
$44$	1.81650			0.273848
$45$		0			0
$46$	10.9045			1.60778
$47$		−	1.81650i		−	0.264964i	−0.991185	−	0.132482i	$-0.957705\pi$
$47$		−	1.81650i		−	0.264964i	0.991185	−	0.132482i	$-0.0422946\pi$
$48$		0			0
$49$		0			0
$50$	0.636449	−	7.73591i	0.0900075	−	1.09402i
$51$		0			0
$52$			0.710265i			0.0984961i
$53$		−	1.71513i		−	0.235591i	−0.993038	−	0.117796i	$-0.962417\pi$
$53$		−	1.71513i		−	0.235591i	0.993038	−	0.117796i	$-0.0375828\pi$
$54$		0			0
$55$	0.406524	−	9.89912i	0.0548157	−	1.33480i
$56$		0			0
$57$		0			0
$58$		−	12.1000i		−	1.58880i
$59$	−1.14243			−0.148732			−0.0743661	−	0.997231i	$-0.523693\pi$
$59$	−1.14243			−0.148732			−0.0743661	+	0.997231i	$0.523693\pi$
$60$		0			0
$61$	9.55635			1.22357			0.611783	−	0.791026i	$-0.290453\pi$
$61$	9.55635			1.22357			0.611783	+	0.791026i	$0.290453\pi$
$62$		−	8.20428i		−	1.04194i
$63$		0			0
$64$	−5.75669			−0.719586
$65$	3.87063	+	0.158954i	0.480093	+	0.0197158i
$66$		0			0
$67$		−	8.38433i		−	1.02431i	−0.858893	−	0.512154i	$-0.828848\pi$
$67$		−	8.38433i		−	1.02431i	0.858893	−	0.512154i	$-0.171152\pi$
$68$		−	1.12024i		−	0.135849i
$69$		0			0
$70$		0			0
$71$	−10.2888			−1.22106			−0.610529	−	0.791994i	$-0.709043\pi$
$71$	−10.2888			−1.22106			−0.610529	+	0.791994i	$0.709043\pi$
$72$		0			0
$73$			12.8204i			1.50052i	0.661143	+	0.750260i	$0.270072\pi$
$73$			12.8204i			1.50052i	−0.661143	+	0.750260i	$0.729928\pi$
$74$	5.70365			0.663036
$75$		0			0
$76$	−0.125106			−0.0143507
$77$		0			0
$78$		0			0
$79$	−6.71372			−0.755352			−0.377676	−	0.925938i	$-0.623277\pi$
$79$	−6.71372			−0.755352			−0.377676	+	0.925938i	$0.623277\pi$
$80$	0.426811	−	10.3931i	0.0477190	−	1.16199i
$81$		0			0
$82$			10.4254i			1.15129i
$83$			5.09946i			0.559739i	0.960038	+	0.279869i	$0.0902911\pi$
$83$			5.09946i			0.559739i	−0.960038	+	0.279869i	$0.909709\pi$
$84$		0			0
$85$	−6.10482	−	0.250704i	−0.662161	−	0.0271927i
$86$	−15.0826			−1.62640
$87$		0			0
$88$		−	10.9367i		−	1.16586i
$89$	4.07065			0.431489			0.215744	−	0.976450i	$-0.430782\pi$
$89$	4.07065			0.431489			0.215744	+	0.976450i	$0.430782\pi$
$90$		0			0
$91$		0			0
$92$			2.87976i			0.300236i
$93$		0			0
$94$	2.81995			0.290856
$95$	−0.0279982	+	0.681775i	−0.00287256	+	0.0699487i
$96$		0			0
$97$		−	2.87834i		−	0.292252i	−0.989266	−	0.146126i	$-0.953320\pi$
$97$		−	2.87834i		−	0.292252i	0.989266	−	0.146126i	$-0.0466804\pi$
$98$		0			0
$99$		0			0
$100$	2.04297	+	0.168080i	0.204297	+	0.0168080i
$101$	−7.21767			−0.718185			−0.359092	−	0.933302i	$-0.616914\pi$
$101$	−7.21767			−0.718185			−0.359092	+	0.933302i	$0.616914\pi$
$102$		0			0
$103$			11.2734i			1.11080i	0.831583	+	0.555400i	$0.187435\pi$
$103$			11.2734i			1.11080i	−0.831583	+	0.555400i	$0.812565\pi$
$104$	4.27635			0.419331
$105$		0			0
$106$	2.66259			0.258613
$107$			6.91596i			0.668591i	0.942468	+	0.334296i	$0.108498\pi$
$107$			6.91596i			0.668591i	−0.942468	+	0.334296i	$0.891502\pi$
$108$		0			0
$109$	−4.42195			−0.423546			−0.211773	−	0.977319i	$-0.567924\pi$
$109$	−4.42195			−0.423546			−0.211773	+	0.977319i	$0.567924\pi$
$110$	15.3675	+	0.631092i	1.46523	+	0.0601722i
$111$		0			0
$112$		0			0
$113$			2.86151i			0.269188i	0.990901	+	0.134594i	$0.0429730\pi$
$113$			2.86151i			0.269188i	−0.990901	+	0.134594i	$0.957027\pi$
$114$		0			0
$115$	15.6934	+	0.644477i	1.46342	+	0.0600978i
$116$	3.19547			0.296692
$117$		0			0
$118$		−	1.77353i		−	0.163266i
$119$		0			0
$120$		0			0
$121$	8.63158			0.784689
$122$			14.8354i			1.34313i
$123$		0			0
$124$	2.16666			0.194572
$125$	1.37317	−	11.0957i	0.122820	−	0.992429i
$126$		0			0
$127$		−	13.7325i		−	1.21856i	−0.792956	−	0.609279i	$-0.791459\pi$
$127$		−	13.7325i		−	1.21856i	0.792956	−	0.609279i	$-0.208541\pi$
$128$		−	13.5065i		−	1.19382i
$129$		0			0
$130$	−0.246762	+	6.00881i	−0.0216424	+	0.527007i
$131$	−21.9817			−1.92055			−0.960277	−	0.279048i	$-0.909981\pi$
$131$	−21.9817			−1.92055			−0.960277	+	0.279048i	$0.909981\pi$
$132$		0			0
$133$		0			0
$134$	13.0159			1.12440
$135$		0			0
$136$	−6.74472			−0.578355
$137$			3.00191i			0.256470i	0.991744	+	0.128235i	$0.0409312\pi$
$137$			3.00191i			0.256470i	−0.991744	+	0.128235i	$0.959069\pi$
$138$		0			0
$139$	21.7364			1.84366			0.921829	−	0.387597i	$-0.126695\pi$
$139$	21.7364			1.84366			0.921829	+	0.387597i	$0.126695\pi$
$140$		0			0
$141$		0			0
$142$		−	15.9724i		−	1.34038i
$143$			7.67610i			0.641908i
$144$		0			0
$145$	0.715131	−	17.4139i	0.0593884	−	1.44615i
$146$	−19.9026			−1.64715
$147$		0			0
$148$			1.50628i			0.123815i
$149$	−5.21309			−0.427073			−0.213536	−	0.976935i	$-0.568498\pi$
$149$	−5.21309			−0.427073			−0.213536	+	0.976935i	$0.568498\pi$
$150$		0			0
$151$	−9.71372			−0.790491			−0.395246	−	0.918576i	$-0.629340\pi$
$151$	−9.71372			−0.790491			−0.395246	+	0.918576i	$0.629340\pi$
$152$			0.753238i			0.0610957i
$153$		0			0
$154$		0			0
$155$	0.484889	−	11.8074i	0.0389472	−	0.948391i
$156$		0			0
$157$		−	9.47182i		−	0.755934i	−0.925819	−	0.377967i	$-0.876623\pi$
$157$		−	9.47182i		−	0.755934i	0.925819	−	0.377967i	$-0.123377\pi$
$158$		−	10.4224i		−	0.829165i
$159$		0			0
$160$	5.10482	+	0.209638i	0.403571	+	0.0165733i
$161$		0			0
$162$		0			0
$163$		−	5.39659i		−	0.422694i	−0.977411	−	0.211347i	$-0.932215\pi$
$163$		−	5.39659i		−	0.422694i	0.977411	−	0.211347i	$-0.0677849\pi$
$164$	−2.75324			−0.214992
$165$		0			0
$166$	−7.91645			−0.614436
$167$			0.312550i			0.0241859i	0.999927	+	0.0120929i	$0.00384939\pi$
$167$			0.312550i			0.0241859i	−0.999927	+	0.0120929i	$0.996151\pi$
$168$		0			0
$169$	9.99859			0.769122
$170$	0.389196	−	9.47718i	0.0298500	−	0.726866i
$171$		0			0
$172$		−	3.98316i		−	0.303713i
$173$			9.61475i			0.730996i	0.930812	+	0.365498i	$0.119101\pi$
$173$			9.61475i			0.730996i	−0.930812	+	0.365498i	$0.880899\pi$
$174$		0			0
$175$		0			0
$176$	20.6113			1.55363
$177$		0			0
$178$			6.31932i			0.473653i
$179$	−8.85461			−0.661824			−0.330912	−	0.943662i	$-0.607356\pi$
$179$	−8.85461			−0.661824			−0.330912	+	0.943662i	$0.607356\pi$
$180$		0			0
$181$	−16.9234			−1.25790			−0.628952	−	0.777445i	$-0.716516\pi$
$181$	−16.9234			−1.25790			−0.628952	+	0.777445i	$0.716516\pi$
$182$		0			0
$183$		0			0
$184$	17.3384			1.27820
$185$	8.20854	+	0.337097i	0.603504	+	0.0247839i
$186$		0			0
$187$		−	12.1069i		−	0.885341i
$188$			0.744719i			0.0543142i
$189$		0			0
$190$	−1.05839	−	0.0434647i	−0.0767840	−	0.00315326i
$191$	−0.318541			−0.0230488			−0.0115244	−	0.999934i	$-0.503668\pi$
$191$	−0.318541			−0.0230488			−0.0115244	+	0.999934i	$0.503668\pi$
$192$		0			0
$193$		−	2.09334i		−	0.150682i	−0.997158	−	0.0753410i	$-0.975995\pi$
$193$		−	2.09334i		−	0.150682i	0.997158	−	0.0753410i	$-0.0240045\pi$
$194$	4.46837			0.320810
$195$		0			0
$196$		0			0
$197$			22.5798i			1.60874i	0.594126	+	0.804372i	$0.297498\pi$
$197$			22.5798i			1.60874i	−0.594126	+	0.804372i	$0.702502\pi$
$198$		0			0
$199$	7.50408			0.531950			0.265975	−	0.963980i	$-0.414306\pi$
$199$	7.50408			0.531950			0.265975	+	0.963980i	$0.414306\pi$
$200$	1.01197	−	12.3003i	0.0715571	−	0.869762i
$201$		0			0
$202$		−	11.2048i		−	0.788365i
$203$		0			0
$204$		0			0
$205$	−0.616162	+	15.0039i	−0.0430346	+	1.04792i
$206$	−17.5009			−1.21935
$207$		0			0
$208$			8.05918i			0.558803i
$209$	−1.35207			−0.0935248
$210$		0			0
$211$	7.67216			0.528173			0.264087	−	0.964499i	$-0.414930\pi$
$211$	7.67216			0.528173			0.264087	+	0.964499i	$0.414930\pi$
$212$			0.703161i			0.0482933i
$213$		0			0
$214$	−10.7364			−0.733925
$215$	−21.7065	−	0.891413i	−1.48037	−	0.0607939i
$216$		0			0
$217$		0			0
$218$		−	6.86467i		−	0.464934i
$219$		0			0
$220$	−0.166665	+	4.05839i	−0.0112365	+	0.273617i
$221$	4.73387			0.318435
$222$		0			0
$223$		−	6.90208i		−	0.462198i	−0.972930	−	0.231099i	$-0.925768\pi$
$223$		−	6.90208i		−	0.462198i	0.972930	−	0.231099i	$-0.0742321\pi$
$224$		0			0
$225$		0			0
$226$	−4.44223			−0.295493
$227$		−	6.34721i		−	0.421279i	−0.977564	−	0.210639i	$-0.932445\pi$
$227$		−	6.34721i		−	0.421279i	0.977564	−	0.210639i	$-0.0675546\pi$
$228$		0			0
$229$	−6.75669			−0.446495			−0.223247	−	0.974762i	$-0.571666\pi$
$229$	−6.75669			−0.446495			−0.223247	+	0.974762i	$0.571666\pi$
$230$	−1.00049	+	24.3626i	−0.0659705	+	1.60642i
$231$		0			0
$232$		−	19.2392i		−	1.26312i
$233$			7.41201i			0.485577i	0.970079	+	0.242789i	$0.0780621\pi$
$233$			7.41201i			0.485577i	−0.970079	+	0.242789i	$0.921938\pi$
$234$		0			0
$235$	4.05839	+	0.166665i	0.264740	+	0.0108720i
$236$	0.468370			0.0304883
$237$		0			0
$238$		0			0
$239$	7.36355			0.476309			0.238154	−	0.971227i	$-0.423458\pi$
$239$	7.36355			0.476309			0.238154	+	0.971227i	$0.423458\pi$
$240$		0			0
$241$	13.6800			0.881209			0.440605	−	0.897701i	$-0.354764\pi$
$241$	13.6800			0.881209			0.440605	+	0.897701i	$0.354764\pi$
$242$			13.3998i			0.861369i
$243$		0			0
$244$	−3.91787			−0.250816
$245$		0			0
$246$		0			0
$247$		−	0.528671i		−	0.0336385i
$248$		−	13.0450i		−	0.828359i
$249$		0			0
$250$	17.2251	+	2.13172i	1.08941	+	0.134822i
$251$	−23.4843			−1.48231			−0.741157	−	0.671331i	$-0.765723\pi$
$251$	−23.4843			−1.48231			−0.741157	+	0.671331i	$0.765723\pi$
$252$		0			0
$253$			31.1226i			1.95666i
$254$	21.3184			1.33764
$255$		0			0
$256$	9.45420			0.590888
$257$		−	14.5974i		−	0.910562i	−0.890348	−	0.455281i	$-0.849539\pi$
$257$		−	14.5974i		−	0.910562i	0.890348	−	0.455281i	$-0.150461\pi$
$258$		0			0
$259$		0			0
$260$	−1.58686	−	0.0651672i	−0.0984131	−	0.00404150i
$261$		0			0
$262$		−	34.1247i		−	2.10823i
$263$		−	5.08940i		−	0.313826i	−0.987612	−	0.156913i	$-0.949846\pi$
$263$		−	5.08940i		−	0.313826i	0.987612	−	0.156913i	$-0.0501542\pi$
$264$		0			0
$265$	3.83192	+	0.157364i	0.235393	+	0.00966680i
$266$		0			0
$267$		0			0
$268$			3.43737i			0.209971i
$269$	30.5099			1.86022			0.930112	−	0.367277i	$-0.119710\pi$
$269$	30.5099			1.86022			0.930112	+	0.367277i	$0.119710\pi$
$270$		0			0
$271$	−19.4880			−1.18381			−0.591907	−	0.806007i	$-0.701625\pi$
$271$	−19.4880			−1.18381			−0.591907	+	0.806007i	$0.701625\pi$
$272$		−	12.7110i		−	0.770720i
$273$		0			0
$274$	−4.66019			−0.281532
$275$	22.0792	+	1.81650i	1.33142	+	0.109539i
$276$		0			0
$277$			25.4802i			1.53096i	0.643462	+	0.765478i	$0.277498\pi$
$277$			25.4802i			1.53096i	−0.643462	+	0.765478i	$0.722502\pi$
$278$			33.7438i			2.02382i
$279$		0			0
$280$		0			0
$281$	22.1914			1.32383			0.661914	−	0.749580i	$-0.269745\pi$
$281$	22.1914			1.32383			0.661914	+	0.749580i	$0.269745\pi$
$282$		0			0
$283$			18.1242i			1.07737i	0.842507	+	0.538685i	$0.181079\pi$
$283$			18.1242i			1.07737i	−0.842507	+	0.538685i	$0.818921\pi$
$284$	4.21816			0.250302
$285$		0			0
$286$	−11.9165			−0.704635
$287$		0			0
$288$		0			0
$289$	9.53367			0.560804
$290$	27.0335	+	1.11018i	1.58746	+	0.0651918i
$291$		0			0
$292$		−	5.25606i		−	0.307588i
$293$		−	13.8958i		−	0.811801i	−0.913917	−	0.405901i	$-0.866958\pi$
$293$		−	13.8958i		−	0.811801i	0.913917	−	0.405901i	$-0.133042\pi$
$294$		0			0
$295$	0.104819	−	2.55241i	0.00610279	−	0.148607i
$296$	9.06895			0.527122
$297$		0			0
$298$		−	8.09285i		−	0.468806i
$299$	−12.1692			−0.703763
$300$		0			0
$301$		0			0
$302$		−	15.0797i		−	0.867737i
$303$		0			0
$304$	−1.41955			−0.0814166
$305$	−0.876800	+	21.3507i	−0.0502054	+	1.22254i
$306$		0			0
$307$			29.8332i			1.70267i	0.524622	+	0.851335i	$0.324207\pi$
$307$			29.8332i			1.70267i	−0.524622	+	0.851335i	$0.675793\pi$
$308$		0			0
$309$		0			0
$310$	18.3299	+	0.752747i	1.04107	+	0.0427531i
$311$	−13.5132			−0.766266			−0.383133	−	0.923693i	$-0.625155\pi$
$311$	−13.5132			−0.766266			−0.383133	+	0.923693i	$0.625155\pi$
$312$		0			0
$313$			28.9857i			1.63837i	0.573531	+	0.819184i	$0.305573\pi$
$313$			28.9857i			1.63837i	−0.573531	+	0.819184i	$0.694427\pi$
$314$	14.7041			0.829803
$315$		0			0
$316$	2.75246			0.154838
$317$		−	1.15864i		−	0.0650756i	−0.999471	−	0.0325378i	$-0.989641\pi$
$317$		−	1.15864i		−	0.0650756i	0.999471	−	0.0325378i	$-0.0103589\pi$
$318$		0			0
$319$	34.5346			1.93357
$320$	0.528179	−	12.8615i	0.0295261	−	0.718980i
$321$		0			0
$322$		0			0
$323$			0.833827i			0.0463954i
$324$		0			0
$325$	−0.710265	+	8.63313i	−0.0393984	+	0.478880i
$326$	8.37772			0.463999
$327$		0			0
$328$			16.5766i			0.915292i
$329$		0			0
$330$		0			0
$331$	−28.3491			−1.55821			−0.779104	−	0.626895i	$-0.784326\pi$
$331$	−28.3491			−1.55821			−0.779104	+	0.626895i	$0.784326\pi$
$332$		−	2.09065i		−	0.114739i
$333$		0			0
$334$	−0.485206			−0.0265493
$335$	18.7321	+	0.769266i	1.02345	+	0.0420295i
$336$		0			0
$337$			15.9729i			0.870101i	0.900406	+	0.435051i	$0.143270\pi$
$337$			15.9729i			0.870101i	−0.900406	+	0.435051i	$0.856730\pi$
$338$			15.5219i			0.844280i
$339$		0			0
$340$	2.50282	+	0.102783i	0.135735	+	0.00557417i
$341$	23.4160			1.26805
$342$		0			0
$343$		0			0
$344$	−23.9817			−1.29301
$345$		0			0
$346$	−14.9260			−0.802428
$347$		−	13.0120i		−	0.698519i	−0.937026	−	0.349260i	$-0.886433\pi$
$347$		−	13.0120i		−	0.698519i	0.937026	−	0.349260i	$-0.113567\pi$
$348$		0			0
$349$	−32.0724			−1.71680			−0.858398	−	0.512984i	$-0.828540\pi$
$349$	−32.0724			−1.71680			−0.858398	+	0.512984i	$0.828540\pi$
$350$		0			0
$351$		0			0
$352$			10.1237i			0.539595i
$353$			13.3689i			0.711555i	0.934571	+	0.355778i	$0.115784\pi$
$353$			13.3689i			0.711555i	−0.934571	+	0.355778i	$0.884216\pi$
$354$		0			0
$355$	0.944004	−	22.9871i	0.0501025	−	1.22003i
$356$	−1.66887			−0.0884498
$357$		0			0
$358$		−	13.7460i		−	0.726497i
$359$	−13.1195			−0.692420			−0.346210	−	0.938157i	$-0.612531\pi$
$359$	−13.1195			−0.692420			−0.346210	+	0.938157i	$0.612531\pi$
$360$		0			0
$361$	−18.9069			−0.995099
$362$		−	26.2720i		−	1.38082i
$363$		0			0
$364$		0			0
$365$	−28.6432	−	1.17628i	−1.49926	−	0.0615694i
$366$		0			0
$367$			13.1360i			0.685691i	0.939392	+	0.342846i	$0.111391\pi$
$367$			13.1360i			0.685691i	−0.939392	+	0.342846i	$0.888609\pi$
$368$			32.6758i			1.70334i
$369$		0			0
$370$	−0.523313	+	12.7430i	−0.0272057	+	0.662478i
$371$		0			0
$372$		0			0
$373$			29.6197i			1.53365i	0.641855	+	0.766826i	$0.278165\pi$
$373$			29.6197i			1.53365i	−0.641855	+	0.766826i	$0.721835\pi$
$374$	18.7948			0.971856
$375$		0			0
$376$	4.48379			0.231234
$377$			13.5033i			0.695456i
$378$		0			0
$379$	−7.47689			−0.384062			−0.192031	−	0.981389i	$-0.561507\pi$
$379$	−7.47689			−0.384062			−0.192031	+	0.981389i	$0.561507\pi$
$380$	0.0114786	−	0.279511i	0.000588839	−	0.0143386i
$381$		0			0
$382$		−	0.494506i		−	0.0253012i
$383$		−	23.7391i		−	1.21301i	−0.795080	−	0.606505i	$-0.792571\pi$
$383$		−	23.7391i		−	1.21301i	0.795080	−	0.606505i	$-0.207429\pi$
$384$		0			0
$385$		0			0
$386$	3.24972			0.165406
$387$		0			0
$388$			1.18005i			0.0599079i
$389$	−14.1305			−0.716443			−0.358221	−	0.933637i	$-0.616617\pi$
$389$	−14.1305			−0.716443			−0.358221	+	0.933637i	$0.616617\pi$
$390$		0			0
$391$	19.1934			0.970653
$392$		0			0
$393$		0			0
$394$	−35.0531			−1.76595
$395$	0.615987	−	14.9997i	0.0309937	−	0.754716i
$396$		0			0
$397$			11.2696i			0.565604i	0.959178	+	0.282802i	$0.0912639\pi$
$397$			11.2696i			0.565604i	−0.959178	+	0.282802i	$0.908736\pi$
$398$			11.6494i			0.583932i
$399$		0			0
$400$	23.1810	+	1.90715i	1.15905	+	0.0953576i
$401$	−23.2968			−1.16339			−0.581694	−	0.813407i	$-0.697610\pi$
$401$	−23.2968			−1.16339			−0.581694	+	0.813407i	$0.697610\pi$
$402$		0			0
$403$			9.15582i			0.456084i
$404$	2.95906			0.147219
$405$		0			0
$406$		0			0
$407$			16.2789i			0.806914i
$408$		0			0
$409$	−20.6478			−1.02097			−0.510484	−	0.859887i	$-0.670534\pi$
$409$	−20.6478			−1.02097			−0.510484	+	0.859887i	$0.670534\pi$
$410$	−23.2923	−	0.956535i	−1.15032	−	0.0472399i
$411$		0			0
$412$		−	4.62181i		−	0.227700i
$413$		0			0
$414$		0			0
$415$	−11.3931	−	0.467878i	−0.559267	−	0.0229672i
$416$	−3.95844			−0.194079
$417$		0			0
$418$		−	2.09897i		−	0.102664i
$419$	−5.48254			−0.267839			−0.133920	−	0.990992i	$-0.542756\pi$
$419$	−5.48254			−0.267839			−0.133920	+	0.990992i	$0.542756\pi$
$420$		0			0
$421$	−3.78079			−0.184264			−0.0921322	−	0.995747i	$-0.529368\pi$
$421$	−3.78079			−0.184264			−0.0921322	+	0.995747i	$0.529368\pi$
$422$			11.9103i			0.579786i
$423$		0			0
$424$	4.23358			0.205601
$425$	1.12024	−	13.6163i	0.0543396	−	0.660487i
$426$		0			0
$427$		0			0
$428$		−	2.83537i		−	0.137053i
$429$		0			0
$430$	1.38384	−	33.6974i	0.0667346	−	1.62503i
$431$	27.5127			1.32524			0.662621	−	0.748955i	$-0.269444\pi$
$431$	27.5127			1.32524			0.662621	+	0.748955i	$0.269444\pi$
$432$		0			0
$433$		−	8.75514i		−	0.420745i	−0.977621	−	0.210373i	$-0.932532\pi$
$433$		−	8.75514i		−	0.420745i	0.977621	−	0.210373i	$-0.0674677\pi$
$434$		0			0
$435$		0			0
$436$	1.81289			0.0868216
$437$		−	2.14349i		−	0.102537i
$438$		0			0
$439$	10.6127			0.506517			0.253259	−	0.967399i	$-0.418498\pi$
$439$	10.6127			0.506517			0.253259	+	0.967399i	$0.418498\pi$
$440$	24.4347	+	1.00345i	1.16488	+	0.0478377i
$441$		0			0
$442$			7.34891i			0.349552i
$443$			19.9856i			0.949543i	0.880109	+	0.474771i	$0.157469\pi$
$443$			19.9856i			0.949543i	−0.880109	+	0.474771i	$0.842531\pi$
$444$		0			0
$445$	−0.373485	+	9.09460i	−0.0177049	+	0.431125i
$446$	10.7149			0.507363
$447$		0			0
$448$		0			0
$449$	3.02578			0.142795			0.0713976	−	0.997448i	$-0.477254\pi$
$449$	3.02578			0.142795			0.0713976	+	0.997448i	$0.477254\pi$
$450$		0			0
$451$	−29.7553			−1.40112
$452$		−	1.17315i		−	0.0551802i
$453$		0			0
$454$	9.85346			0.462446
$455$		0			0
$456$		0			0
$457$		−	2.28135i		−	0.106717i	−0.998575	−	0.0533584i	$-0.983007\pi$
$457$		−	2.28135i		−	0.106717i	0.998575	−	0.0533584i	$-0.0169926\pi$
$458$		−	10.4891i		−	0.490126i
$459$		0			0
$460$	−6.43392	−	0.264219i	−0.299983	−	0.0123193i
$461$	24.0678			1.12095			0.560475	−	0.828171i	$-0.310619\pi$
$461$	24.0678			1.12095			0.560475	+	0.828171i	$0.310619\pi$
$462$		0			0
$463$			11.1290i			0.517211i	0.965983	+	0.258605i	$0.0832629\pi$
$463$			11.1290i			0.517211i	−0.965983	+	0.258605i	$0.916737\pi$
$464$	36.2581			1.68324
$465$		0			0
$466$	−11.5065			−0.533027
$467$			28.5766i			1.32237i	0.750223	+	0.661185i	$0.229946\pi$
$467$			28.5766i			1.32237i	−0.750223	+	0.661185i	$0.770054\pi$
$468$		0			0
$469$		0			0
$470$	−0.258732	+	6.30029i	−0.0119344	+	0.290611i
$471$		0			0
$472$		−	2.81995i		−	0.129799i
$473$		−	43.0475i		−	1.97933i
$474$		0			0
$475$	−1.52064	−	0.125106i	−0.0697719	−	0.00574028i
$476$		0			0
$477$		0			0
$478$			11.4312i			0.522853i
$479$	−5.58009			−0.254961			−0.127480	−	0.991841i	$-0.540689\pi$
$479$	−5.58009			−0.254961			−0.127480	+	0.991841i	$0.540689\pi$
$480$		0			0
$481$	−6.36517			−0.290227
$482$			21.2370i			0.967320i
$483$		0			0
$484$	−3.53873			−0.160852
$485$	6.43075	+	0.264090i	0.292006	+	0.0119917i
$486$		0			0
$487$		−	8.34684i		−	0.378232i	−0.981955	−	0.189116i	$-0.939438\pi$
$487$		−	8.34684i		−	0.378232i	0.981955	−	0.189116i	$-0.0605622\pi$
$488$			23.5886i			1.06781i
$489$		0			0
$490$		0			0
$491$	−0.557405			−0.0251554			−0.0125777	−	0.999921i	$-0.504004\pi$
$491$	−0.557405			−0.0251554			−0.0125777	+	0.999921i	$0.504004\pi$
$492$		0			0
$493$		−	21.2976i		−	0.959197i
$494$	0.820713			0.0369256
$495$		0			0
$496$	24.5845			1.10388
$497$		0			0
$498$		0			0
$499$	26.0337			1.16543			0.582713	−	0.812678i	$-0.301991\pi$
$499$	26.0337			1.16543			0.582713	+	0.812678i	$0.301991\pi$
$500$	−0.562965	+	4.54896i	−0.0251765	+	0.203436i
$501$		0			0
$502$		−	36.4572i		−	1.62717i
$503$		−	5.52409i		−	0.246307i	−0.992388	−	0.123154i	$-0.960699\pi$
$503$		−	5.52409i		−	0.246307i	0.992388	−	0.123154i	$-0.0393008\pi$
$504$		0			0
$505$	0.662224	−	16.1256i	0.0294686	−	0.717580i
$506$	−48.3151			−2.14787
$507$		0			0
$508$			5.62997i			0.249789i
$509$	22.8893			1.01455			0.507274	−	0.861785i	$-0.330653\pi$
$509$	22.8893			1.01455			0.507274	+	0.861785i	$0.330653\pi$
$510$		0			0
$511$		0			0
$512$		−	12.3362i		−	0.545186i
$513$		0			0
$514$	22.6612			0.999541
$515$	−25.1868	−	1.03434i	−1.10986	−	0.0455784i
$516$		0			0
$517$			8.04846i			0.353971i
$518$		0			0
$519$		0			0
$520$	−0.392357	+	9.55416i	−0.0172060	+	0.418977i
$521$	−26.1989			−1.14780			−0.573898	−	0.818927i	$-0.694569\pi$
$521$	−26.1989			−1.14780			−0.573898	+	0.818927i	$0.694569\pi$
$522$		0			0
$523$		−	26.8760i		−	1.17521i	−0.809149	−	0.587603i	$-0.800072\pi$
$523$		−	26.8760i		−	1.17521i	0.809149	−	0.587603i	$-0.199928\pi$
$524$	9.01197			0.393690
$525$		0			0
$526$	7.90083			0.344493
$527$		−	14.4407i		−	0.629046i
$528$		0			0
$529$	−26.3398			−1.14521
$530$	−0.244294	+	5.94871i	−0.0106114	+	0.258395i
$531$		0			0
$532$		0			0
$533$		−	11.6345i		−	0.503948i
$534$		0			0
$535$	−15.4515	−	0.634543i	−0.668028	−	0.0274337i
$536$	20.6956			0.893915
$537$		0			0
$538$			47.3639i			2.04200i
$539$		0			0
$540$		0			0
$541$	−18.7844			−0.807606			−0.403803	−	0.914846i	$-0.632312\pi$
$541$	−18.7844			−0.807606			−0.403803	+	0.914846i	$0.632312\pi$
$542$		−	30.2534i		−	1.29949i
$543$		0			0
$544$	6.24331			0.267680
$545$	0.405716	−	9.87944i	0.0173789	−	0.423189i
$546$		0			0
$547$			13.4126i			0.573483i	0.958008	+	0.286742i	$0.0925721\pi$
$547$			13.4126i			0.573483i	−0.958008	+	0.286742i	$0.907428\pi$
$548$		−	1.23071i		−	0.0525732i
$549$		0			0
$550$	−2.81995	+	34.2759i	−0.120243	+	1.46153i
$551$	−2.37848			−0.101327
$552$		0			0
$553$		0			0
$554$	−39.5557			−1.68056
$555$		0			0
$556$	−8.91138			−0.377927
$557$			40.1845i			1.70267i	0.524621	+	0.851336i	$0.324207\pi$
$557$			40.1845i			1.70267i	−0.524621	+	0.851336i	$0.675793\pi$
$558$		0			0
$559$	16.8319			0.711914
$560$		0			0
$561$		0			0
$562$			34.4501i			1.45319i
$563$			25.1879i			1.06154i	0.847514	+	0.530772i	$0.178098\pi$
$563$			25.1879i			1.06154i	−0.847514	+	0.530772i	$0.821902\pi$
$564$		0			0
$565$	−6.39314	−	0.262545i	−0.268961	−	0.0110453i
$566$	−28.1362			−1.18265
$567$		0			0
$568$		−	25.3966i		−	1.06562i
$569$	−11.0351			−0.462617			−0.231309	−	0.972880i	$-0.574301\pi$
$569$	−11.0351			−0.462617			−0.231309	+	0.972880i	$0.574301\pi$
$570$		0			0
$571$	28.7147			1.20167			0.600836	−	0.799372i	$-0.294834\pi$
$571$	28.7147			1.20167			0.600836	+	0.799372i	$0.294834\pi$
$572$		−	3.14701i		−	0.131583i
$573$		0			0
$574$		0			0
$575$	−2.87976	+	35.0029i	−0.120094	+	1.45972i
$576$		0			0
$577$			6.86405i			0.285754i	0.989740	+	0.142877i	$0.0456353\pi$
$577$			6.86405i			0.285754i	−0.989740	+	0.142877i	$0.954365\pi$
$578$			14.8002i			0.615605i
$579$		0			0
$580$	−0.293186	+	7.13927i	−0.0121739	+	0.296442i
$581$		0			0
$582$		0			0
$583$			7.59933i			0.314732i
$584$	−31.6456			−1.30950
$585$		0			0
$586$	21.5720			0.891130
$587$			9.03965i			0.373106i	0.982445	+	0.186553i	$0.0597317\pi$
$587$			9.03965i			0.373106i	−0.982445	+	0.186553i	$0.940268\pi$
$588$		0			0
$589$	−1.61271			−0.0664506
$590$	3.96238	+	0.162722i	0.163129	+	0.00669915i
$591$		0			0
$592$			17.0913i			0.702447i
$593$			5.10798i			0.209760i	0.994485	+	0.104880i	$0.0334458\pi$
$593$			5.10798i			0.209760i	−0.994485	+	0.104880i	$0.966554\pi$
$594$		0			0
$595$		0			0
$596$	2.13724			0.0875446
$597$		0			0
$598$		−	18.8916i		−	0.772534i
$599$	−29.9443			−1.22349			−0.611745	−	0.791055i	$-0.709532\pi$
$599$	−29.9443			−1.22349			−0.611745	+	0.791055i	$0.709532\pi$
$600$		0			0
$601$	−12.5387			−0.511466			−0.255733	−	0.966747i	$-0.582317\pi$
$601$	−12.5387			−0.511466			−0.255733	+	0.966747i	$0.582317\pi$
$602$		0			0
$603$		0			0
$604$	3.98238			0.162041
$605$	−0.791952	+	19.2846i	−0.0321974	+	0.784029i
$606$		0			0
$607$		−	9.59805i		−	0.389573i	−0.980846	−	0.194786i	$-0.937599\pi$
$607$		−	9.59805i		−	0.389573i	0.980846	−	0.194786i	$-0.0624014\pi$
$608$		−	0.697242i		−	0.0282769i
$609$		0			0
$610$	−33.1450	−	1.36115i	−1.34200	−	0.0551115i
$611$	−3.14701			−0.127314
$612$		0			0
$613$			27.6646i			1.11736i	0.829382	+	0.558682i	$0.188693\pi$
$613$			27.6646i			1.11736i	−0.829382	+	0.558682i	$0.811307\pi$
$614$	−46.3133			−1.86905
$615$		0			0
$616$		0			0
$617$		−	20.4155i		−	0.821896i	−0.911659	−	0.410948i	$-0.865198\pi$
$617$		−	20.4155i		−	0.821896i	0.911659	−	0.410948i	$-0.134802\pi$
$618$		0			0
$619$	15.4422			0.620676			0.310338	−	0.950626i	$-0.399558\pi$
$619$	15.4422			0.620676			0.310338	+	0.950626i	$0.399558\pi$
$620$	−0.198793	+	4.84073i	−0.00798370	+	0.194408i
$621$		0			0
$622$		−	20.9781i		−	0.841145i
$623$		0			0
$624$		0			0
$625$	24.6638	+	4.08595i	0.986554	+	0.163438i
$626$	−44.9977			−1.79847
$627$		0			0
$628$			3.88321i			0.154957i
$629$	10.0392			0.400290
$630$		0			0
$631$	−38.1722			−1.51961			−0.759805	−	0.650151i	$-0.774705\pi$
$631$	−38.1722			−1.51961			−0.759805	+	0.650151i	$0.774705\pi$
$632$		−	16.5719i		−	0.659196i
$633$		0			0
$634$	1.79868			0.0714347
$635$	30.6809	+	1.25996i	1.21753	+	0.0500000i
$636$		0			0
$637$		0			0
$638$			53.6119i			2.12252i
$639$		0			0
$640$	30.1760	+	1.23923i	1.19281	+	0.0489847i
$641$	16.7801			0.662776			0.331388	−	0.943495i	$-0.392483\pi$
$641$	16.7801			0.662776			0.331388	+	0.943495i	$0.392483\pi$
$642$		0			0
$643$		−	14.2002i		−	0.560001i	−0.960000	−	0.280001i	$-0.909665\pi$
$643$		−	14.2002i		−	0.560001i	0.960000	−	0.280001i	$-0.0903346\pi$
$644$		0			0
$645$		0			0
$646$	−1.29444			−0.0509291
$647$			14.4885i			0.569602i	0.958587	+	0.284801i	$0.0919276\pi$
$647$			14.4885i			0.569602i	−0.958587	+	0.284801i	$0.908072\pi$
$648$		0			0
$649$	5.06185			0.198695
$650$	−13.4021	−	1.10262i	−0.525676	−	0.0432484i
$651$		0			0
$652$			2.21247i			0.0866469i
$653$		−	10.2833i		−	0.402418i	−0.979548	−	0.201209i	$-0.935513\pi$
$653$		−	10.2833i		−	0.402418i	0.979548	−	0.201209i	$-0.0644870\pi$
$654$		0			0
$655$	2.01684	−	49.1113i	0.0788043	−	1.91894i
$656$	−31.2402			−1.21973
$657$		0			0
$658$		0			0
$659$	14.9773			0.583433			0.291717	−	0.956505i	$-0.405774\pi$
$659$	14.9773			0.583433			0.291717	+	0.956505i	$0.405774\pi$
$660$		0			0
$661$	2.44647			0.0951565			0.0475782	−	0.998868i	$-0.484850\pi$
$661$	2.44647			0.0951565			0.0475782	+	0.998868i	$0.484850\pi$
$662$		−	44.0094i		−	1.71048i
$663$		0			0
$664$	−12.5874			−0.488484
$665$		0			0
$666$		0			0
$667$			54.7490i			2.11989i
$668$		−	0.128138i		−	0.00495780i
$669$		0			0
$670$	−1.19422	+	29.0800i	−0.0461366	+	1.12346i
$671$	−42.3418			−1.63459
$672$		0			0
$673$			17.2596i			0.665310i	0.943049	+	0.332655i	$0.107945\pi$
$673$			17.2596i			0.665310i	−0.943049	+	0.332655i	$0.892055\pi$
$674$	−24.7965			−0.955127
$675$		0			0
$676$	−4.09917			−0.157660
$677$			11.6384i			0.447298i	0.974670	+	0.223649i	$0.0717970\pi$
$677$			11.6384i			0.447298i	−0.974670	+	0.223649i	$0.928203\pi$
$678$		0			0
$679$		0			0
$680$	0.618831	−	15.0689i	0.0237311	−	0.577868i
$681$		0			0
$682$			36.3511i			1.39196i
$683$			31.0960i			1.18986i	0.803779	+	0.594928i	$0.202819\pi$
$683$			31.0960i			1.18986i	−0.803779	+	0.594928i	$0.797181\pi$
$684$		0			0
$685$	−6.70681	−	0.275426i	−0.256254	−	0.0105235i
$686$		0			0
$687$		0			0
$688$		−	45.1958i		−	1.72307i
$689$	−2.97140			−0.113201
$690$		0			0
$691$	−17.9339			−0.682238			−0.341119	−	0.940020i	$-0.610806\pi$
$691$	−17.9339			−0.682238			−0.341119	+	0.940020i	$0.610806\pi$
$692$		−	3.94181i		−	0.149845i
$693$		0			0
$694$	20.1999			0.766778
$695$	−1.99433	+	48.5631i	−0.0756491	+	1.84210i
$696$		0			0
$697$			18.3502i			0.695062i
$698$		−	49.7895i		−	1.88456i
$699$		0			0
$700$		0			0
$701$	−7.04488			−0.266081			−0.133041	−	0.991111i	$-0.542474\pi$
$701$	−7.04488			−0.266081			−0.133041	+	0.991111i	$0.542474\pi$
$702$		0			0
$703$		−	1.12116i		−	0.0422855i
$704$	25.5065			0.961312
$705$		0			0
$706$	−20.7540			−0.781088
$707$		0			0
$708$		0			0
$709$	25.9243			0.973609			0.486804	−	0.873511i	$-0.338162\pi$
$709$	25.9243			0.973609			0.486804	+	0.873511i	$0.338162\pi$
$710$	35.6854	+	1.46548i	1.33925	+	0.0549985i
$711$		0			0
$712$			10.0479i			0.376560i
$713$			37.1221i			1.39023i
$714$		0			0
$715$	−17.1498	−	0.704286i	−0.641367	−	0.0263388i
$716$	3.63017			0.135666
$717$		0			0
$718$		−	20.3668i		−	0.760082i
$719$	31.2855			1.16675			0.583376	−	0.812202i	$-0.301731\pi$
$719$	31.2855			1.16675			0.583376	+	0.812202i	$0.301731\pi$
$720$		0			0
$721$		0			0
$722$		−	29.3512i		−	1.09234i
$723$		0			0
$724$	6.93815			0.257854
$725$	38.8403	+	3.19547i	1.44249	+	0.118677i
$726$		0			0
$727$			22.8312i			0.846761i	0.905952	+	0.423380i	$0.139157\pi$
$727$			22.8312i			0.846761i	−0.905952	+	0.423380i	$0.860843\pi$
$728$		0			0
$729$		0			0
$730$	1.82607	−	44.4660i	0.0675859	−	1.64576i
$731$	−26.5475			−0.981896
$732$		0			0
$733$			5.95434i			0.219929i	0.993936	+	0.109964i	$0.0350736\pi$
$733$			5.95434i			0.219929i	−0.993936	+	0.109964i	$0.964926\pi$
$734$	−20.3924			−0.752696
$735$		0			0
$736$	−16.0494			−0.591590
$737$			37.1489i			1.36840i
$738$		0			0
$739$	−41.5079			−1.52689			−0.763446	−	0.645872i	$-0.776494\pi$
$739$	−41.5079			−1.52689			−0.763446	+	0.645872i	$0.776494\pi$
$740$	−3.36530	−	0.138201i	−0.123711	−	0.00508039i
$741$		0			0
$742$		0			0
$743$		−	6.80015i		−	0.249473i	−0.992190	−	0.124737i	$-0.960191\pi$
$743$		−	6.80015i		−	0.249473i	0.992190	−	0.124737i	$-0.0398086\pi$
$744$		0			0
$745$	0.478303	−	11.6470i	0.0175237	−	0.426713i
$746$	−45.9820			−1.68352
$747$		0			0
$748$			4.96351i			0.181484i
$749$		0			0
$750$		0			0
$751$	23.6113			0.861588			0.430794	−	0.902450i	$-0.358233\pi$
$751$	23.6113			0.861588			0.430794	+	0.902450i	$0.358233\pi$
$752$			8.45012i			0.308144i
$753$		0			0
$754$	−20.9627			−0.763416
$755$	0.891238	−	21.7022i	0.0324355	−	0.789825i
$756$		0			0
$757$			16.2267i			0.589769i	0.955533	+	0.294884i	$0.0952811\pi$
$757$			16.2267i			0.589769i	−0.955533	+	0.294884i	$0.904719\pi$
$758$		−	11.6072i		−	0.421592i
$759$		0			0
$760$	−1.68287	−	0.0691100i	−0.0610442	−	0.00250688i
$761$	2.55508			0.0926215			0.0463108	−	0.998927i	$-0.485254\pi$
$761$	2.55508			0.0926215			0.0463108	+	0.998927i	$0.485254\pi$
$762$		0			0
$763$		0			0
$764$	0.130594			0.00472473
$765$		0			0
$766$	36.8528			1.33154
$767$			1.97922i			0.0714655i
$768$		0			0
$769$	45.4525			1.63906			0.819530	−	0.573037i	$-0.194235\pi$
$769$	45.4525			1.63906			0.819530	+	0.573037i	$0.194235\pi$
$770$		0			0
$771$		0			0
$772$			0.858217i			0.0308879i
$773$		−	51.4891i		−	1.85194i	−0.377603	−	0.925968i	$-0.623251\pi$
$773$		−	51.4891i		−	1.85194i	0.377603	−	0.925968i	$-0.376749\pi$
$774$		0			0
$775$	26.3354	+	2.16666i	0.945994	+	0.0778289i
$776$	7.10482			0.255048
$777$		0			0
$778$		−	21.9363i		−	0.786453i
$779$	2.04931			0.0734243
$780$		0			0
$781$	45.5872			1.63124
$782$			29.7961i			1.06550i
$783$		0			0
$784$		0			0
$785$	21.1618	+	0.869044i	0.755297	+	0.0310175i
$786$		0			0
$787$			20.1514i			0.718321i	0.933276	+	0.359161i	$0.116937\pi$
$787$			20.1514i			0.718321i	−0.933276	+	0.359161i	$0.883063\pi$
$788$		−	9.25716i		−	0.329773i
$789$		0			0
$790$	23.2857	+	0.956264i	0.828466	+	0.0340223i
$791$		0			0
$792$		0			0
$793$		−	16.5560i		−	0.587920i
$794$	−17.4950			−0.620874
$795$		0			0
$796$	−3.07649			−0.109043
$797$			13.0702i			0.462971i	0.972838	+	0.231486i	$0.0743587\pi$
$797$			13.0702i			0.462971i	−0.972838	+	0.231486i	$0.925641\pi$
$798$		0			0
$799$	4.96351			0.175596
$800$	−0.936739	+	11.3859i	−0.0331187	+	0.402551i
$801$		0			0
$802$		−	36.1662i		−	1.27707i
$803$		−	56.8042i		−	2.00458i
$804$		0			0
$805$		0			0
$806$	−14.2136			−0.500652
$807$		0			0
$808$		−	17.8159i		−	0.626760i
$809$	−1.73720			−0.0610765			−0.0305383	−	0.999534i	$-0.509722\pi$
$809$	−1.73720			−0.0610765			−0.0305383	+	0.999534i	$0.509722\pi$
$810$		0			0
$811$	−27.9004			−0.979715			−0.489858	−	0.871802i	$-0.662951\pi$
$811$	−27.9004			−0.979715			−0.489858	+	0.871802i	$0.662951\pi$
$812$		0			0
$813$		0			0
$814$	−25.2715			−0.885765
$815$	12.0570	+	0.495140i	0.422338	+	0.0173440i
$816$		0			0
$817$			2.96478i			0.103725i
$818$		−	32.0538i		−	1.12074i
$819$		0			0
$820$	0.252611	−	6.15124i	0.00882156	−	0.214811i
$821$	−16.9360			−0.591070			−0.295535	−	0.955332i	$-0.595498\pi$
$821$	−16.9360			−0.591070			−0.295535	+	0.955332i	$0.595498\pi$
$822$		0			0
$823$		−	9.89031i		−	0.344755i	−0.985031	−	0.172377i	$-0.944855\pi$
$823$		−	9.89031i		−	0.344755i	0.985031	−	0.172377i	$-0.0551448\pi$
$824$	−27.8269			−0.969396
$825$		0			0
$826$		0			0
$827$		−	35.3201i		−	1.22820i	−0.789228	−	0.614101i	$-0.789519\pi$
$827$		−	35.3201i		−	1.22820i	0.789228	−	0.614101i	$-0.210481\pi$
$828$		0			0
$829$	−9.29951			−0.322985			−0.161493	−	0.986874i	$-0.551631\pi$
$829$	−9.29951			−0.322985			−0.161493	+	0.986874i	$0.551631\pi$
$830$	0.726338	−	17.6868i	0.0252116	−	0.613918i
$831$		0			0
$832$			9.97323i			0.345760i
$833$		0			0
$834$		0			0
$835$	−0.698295	−	0.0286766i	−0.0241655	−	0.000992396i
$836$	0.554316			0.0191714
$837$		0			0
$838$		−	8.51114i		−	0.294012i
$839$	−7.93405			−0.273914			−0.136957	−	0.990577i	$-0.543732\pi$
$839$	−7.93405			−0.273914			−0.136957	+	0.990577i	$0.543732\pi$
$840$		0			0
$841$	31.7512			1.09487
$842$		−	5.86933i		−	0.202271i
$843$		0			0
$844$	−3.14539			−0.108269
$845$	−0.917375	+	22.3387i	−0.0315587	+	0.768474i
$846$		0			0
$847$		0			0
$848$			7.97857i			0.273985i
$849$		0			0
$850$	21.1381	+	1.73907i	0.725029	+	0.0596497i
$851$	−25.8075			−0.884669
$852$		0			0
$853$		−	30.0757i		−	1.02977i	−0.857258	−	0.514887i	$-0.827834\pi$
$853$		−	30.0757i		−	1.02977i	0.857258	−	0.514887i	$-0.172166\pi$
$854$		0			0
$855$		0			0
$856$	−17.0711			−0.583480
$857$		−	47.1373i		−	1.61018i	−0.593153	−	0.805090i	$-0.702117\pi$
$857$		−	47.1373i		−	1.61018i	0.593153	−	0.805090i	$-0.297883\pi$
$858$		0			0
$859$	32.6367			1.11355			0.556774	−	0.830664i	$-0.312039\pi$
$859$	32.6367			1.11355			0.556774	+	0.830664i	$0.312039\pi$
$860$	8.89912	+	0.365457i	0.303458	+	0.0124620i
$861$		0			0
$862$			42.7110i			1.45474i
$863$		−	37.4102i		−	1.27346i	−0.771088	−	0.636728i	$-0.780287\pi$
$863$		−	37.4102i		−	1.27346i	0.771088	−	0.636728i	$-0.219713\pi$
$864$		0			0
$865$	−21.4811	−	0.882158i	−0.730380	−	0.0299943i
$866$	13.5916			0.461860
$867$		0			0
$868$		0			0
$869$	29.7468			1.00909
$870$		0			0
$871$	−14.5255			−0.492178
$872$		−	10.9150i		−	0.369628i
$873$		0			0
$874$	3.32757			0.112557
$875$		0			0
$876$		0			0
$877$		−	33.5657i		−	1.13343i	−0.823913	−	0.566716i	$-0.808214\pi$
$877$		−	33.5657i		−	1.13343i	0.823913	−	0.566716i	$-0.191786\pi$
$878$			16.4753i			0.556014i
$879$		0			0
$880$	−1.89110	+	46.0494i	−0.0637489	+	1.55233i
$881$	12.1952			0.410867			0.205433	−	0.978671i	$-0.434140\pi$
$881$	12.1952			0.410867			0.205433	+	0.978671i	$0.434140\pi$
$882$		0			0
$883$		−	11.0408i		−	0.371552i	−0.982592	−	0.185776i	$-0.940520\pi$
$883$		−	11.0408i		−	0.371552i	0.982592	−	0.185776i	$-0.0594799\pi$
$884$	−1.94077			−0.0652752
$885$		0			0
$886$	−31.0258			−1.04233
$887$			1.56093i			0.0524108i	0.999657	+	0.0262054i	$0.00834240\pi$
$887$			1.56093i			0.0524108i	−0.999657	+	0.0262054i	$0.991658\pi$
$888$		0			0
$889$		0			0
$890$	−14.1185	−	0.579801i	−0.473254	−	0.0194350i
$891$		0			0
$892$			2.82968i			0.0947448i
$893$		−	0.554316i		−	0.0185495i
$894$		0			0
$895$	0.812414	−	19.7828i	0.0271560	−	0.661267i
$896$		0			0
$897$		0			0
$898$			4.69724i			0.156749i
$899$	41.1919			1.37383
$900$		0			0
$901$	4.68653			0.156131
$902$		−	46.1924i		−	1.53804i
$903$		0			0
$904$	−7.06326			−0.234921
$905$	1.55273	−	37.8099i	0.0516144	−	1.25684i
$906$		0			0
$907$			17.4078i			0.578016i	0.957327	+	0.289008i	$0.0933255\pi$
$907$			17.4078i			0.578016i	−0.957327	+	0.289008i	$0.906675\pi$
$908$			2.60220i			0.0863569i
$909$		0			0
$910$		0			0
$911$	18.3203			0.606978			0.303489	−	0.952835i	$-0.401848\pi$
$911$	18.3203			0.606978			0.303489	+	0.952835i	$0.401848\pi$
$912$		0			0
$913$		−	22.5945i		−	0.747767i
$914$	3.54158			0.117145
$915$		0			0
$916$	2.77007			0.0915258
$917$		0			0
$918$		0			0
$919$	−22.5927			−0.745264			−0.372632	−	0.927979i	$-0.621545\pi$
$919$	−22.5927			−0.745264			−0.372632	+	0.927979i	$0.621545\pi$
$920$	−1.59081	+	38.7372i	−0.0524473	+	1.27713i
$921$		0			0
$922$			37.3631i			1.23049i
$923$			17.8249i			0.586715i
$924$		0			0
$925$	−1.50628	+	18.3085i	−0.0495260	+	0.601979i
$926$	−17.2768			−0.567752
$927$		0			0
$928$			17.8090i			0.584608i
$929$	38.6712			1.26876			0.634381	−	0.773021i	$-0.281255\pi$
$929$	38.6712			1.26876			0.634381	+	0.773021i	$0.281255\pi$
$930$		0			0
$931$		0			0
$932$		−	3.03874i		−	0.0995372i
$933$		0			0
$934$	−44.3626			−1.45159
$935$	27.0490	+	1.11081i	0.884595	+	0.0363274i
$936$		0			0
$937$		−	46.7921i		−	1.52863i	−0.644842	−	0.764316i	$-0.723077\pi$
$937$		−	46.7921i		−	1.52863i	0.644842	−	0.764316i	$-0.276923\pi$
$938$		0			0
$939$		0			0
$940$	−1.66384	−	0.0683284i	−0.0542685	−	0.00222863i
$941$	41.8922			1.36565			0.682824	−	0.730583i	$-0.260752\pi$
$941$	41.8922			1.36565			0.682824	+	0.730583i	$0.260752\pi$
$942$		0			0
$943$		−	47.1721i		−	1.53613i
$944$	5.31446			0.172971
$945$		0			0
$946$	66.8274			2.17275
$947$		−	56.1146i		−	1.82348i	−0.410768	−	0.911740i	$-0.634739\pi$
$947$		−	56.1146i		−	1.82348i	0.410768	−	0.911740i	$-0.365261\pi$
$948$		0			0
$949$	22.2109			0.720996
$950$	0.194216	−	2.36066i	0.00630121	−	0.0765900i
$951$		0			0
$952$		0			0
$953$			17.7705i			0.575643i	0.957684	+	0.287821i	$0.0929309\pi$
$953$			17.7705i			0.575643i	−0.957684	+	0.287821i	$0.907069\pi$
$954$		0			0
$955$	0.0292263	−	0.711680i	0.000945742	−	0.0230294i
$956$	−3.01887			−0.0976373
$957$		0			0
$958$		−	8.66259i		−	0.279875i
$959$		0			0
$960$		0			0
$961$	−3.07016			−0.0990375
$962$		−	9.88135i		−	0.318587i
$963$		0			0
$964$	−5.60848			−0.180637
$965$	4.67691	+	0.192065i	0.150555	+	0.00618279i
$966$		0			0
$967$		−	22.5942i		−	0.726579i	−0.931676	−	0.363290i	$-0.881654\pi$
$967$		−	22.5942i		−	0.726579i	0.931676	−	0.363290i	$-0.118346\pi$
$968$			21.3059i			0.684799i
$969$		0			0
$970$	−0.409975	+	9.98316i	−0.0131635	+	0.320540i
$971$	−41.0488			−1.31732			−0.658660	−	0.752441i	$-0.728876\pi$
$971$	−41.0488			−1.31732			−0.658660	+	0.752441i	$0.728876\pi$
$972$		0			0
$973$		0			0
$974$	12.9577			0.415192
$975$		0			0
$976$	−44.4549			−1.42297
$977$			19.4734i			0.623008i	0.950245	+	0.311504i	$0.100833\pi$
$977$			19.4734i			0.623008i	−0.950245	+	0.311504i	$0.899167\pi$
$978$		0			0
$979$	−18.0361			−0.576435
$980$		0			0
$981$		0			0
$982$		−	0.865321i		−	0.0276135i
$983$			51.7272i			1.64984i	0.565249	+	0.824920i	$0.308780\pi$
$983$			51.7272i			1.64984i	−0.565249	+	0.824920i	$0.691220\pi$
$984$		0			0
$985$	−50.4474	−	2.07171i	−1.60739	−	0.0660101i
$986$	33.0626			1.05293
$987$		0			0
$988$			0.216742i			0.00689548i
$989$	68.2448			2.17006
$990$		0			0
$991$	35.9499			1.14198			0.570992	−	0.820955i	$-0.306559\pi$
$991$	35.9499			1.14198			0.570992	+	0.820955i	$0.306559\pi$
$992$			12.0752i			0.383389i
$993$		0			0
$994$		0			0
$995$	−0.688503	+	16.7655i	−0.0218270	+	0.531502i
$996$		0			0
$997$			56.0599i			1.77544i	0.460388	+	0.887718i	$0.347710\pi$
$997$			56.0599i			1.77544i	−0.460388	+	0.887718i	$0.652290\pi$
$998$			40.4149i			1.27931i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2205.2.d.s.1324.6		8
3.2	odd	2		735.2.d.d.589.3		8
5.4	even	2	inner	2205.2.d.s.1324.3		8
7.2	even	3		315.2.bf.b.109.6		16
7.4	even	3		315.2.bf.b.289.3		16
7.6	odd	2		2205.2.d.o.1324.6		8
15.2	even	4		3675.2.a.bz.1.3		4
15.8	even	4		3675.2.a.bp.1.2		4
15.14	odd	2		735.2.d.d.589.6		8
21.2	odd	6		105.2.q.a.4.3	✓	16
21.5	even	6		735.2.q.g.214.3		16
21.11	odd	6		105.2.q.a.79.6	yes	16
21.17	even	6		735.2.q.g.79.6		16
21.20	even	2		735.2.d.e.589.3		8
35.4	even	6		315.2.bf.b.289.6		16
35.9	even	6		315.2.bf.b.109.3		16
35.34	odd	2		2205.2.d.o.1324.3		8
84.11	even	6		1680.2.di.d.289.8		16
84.23	even	6		1680.2.di.d.529.1		16
105.2	even	12		525.2.i.h.151.2		8
105.23	even	12		525.2.i.k.151.3		8
105.32	even	12		525.2.i.h.226.2		8
105.44	odd	6		105.2.q.a.4.6	yes	16
105.53	even	12		525.2.i.k.226.3		8
105.59	even	6		735.2.q.g.79.3		16
105.62	odd	4		3675.2.a.cb.1.3		4
105.74	odd	6		105.2.q.a.79.3	yes	16
105.83	odd	4		3675.2.a.bn.1.2		4
105.89	even	6		735.2.q.g.214.6		16
105.104	even	2		735.2.d.e.589.6		8
420.179	even	6		1680.2.di.d.289.1		16
420.359	even	6		1680.2.di.d.529.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.q.a.4.3	✓	16	21.2	odd	6
105.2.q.a.4.6	yes	16	105.44	odd	6
105.2.q.a.79.3	yes	16	105.74	odd	6
105.2.q.a.79.6	yes	16	21.11	odd	6
315.2.bf.b.109.3		16	35.9	even	6
315.2.bf.b.109.6		16	7.2	even	3
315.2.bf.b.289.3		16	7.4	even	3
315.2.bf.b.289.6		16	35.4	even	6
525.2.i.h.151.2		8	105.2	even	12
525.2.i.h.226.2		8	105.32	even	12
525.2.i.k.151.3		8	105.23	even	12
525.2.i.k.226.3		8	105.53	even	12
735.2.d.d.589.3		8	3.2	odd	2
735.2.d.d.589.6		8	15.14	odd	2
735.2.d.e.589.3		8	21.20	even	2
735.2.d.e.589.6		8	105.104	even	2
735.2.q.g.79.3		16	105.59	even	6
735.2.q.g.79.6		16	21.17	even	6
735.2.q.g.214.3		16	21.5	even	6
735.2.q.g.214.6		16	105.89	even	6
1680.2.di.d.289.1		16	420.179	even	6
1680.2.di.d.289.8		16	84.11	even	6
1680.2.di.d.529.1		16	84.23	even	6
1680.2.di.d.529.8		16	420.359	even	6
2205.2.d.o.1324.3		8	35.34	odd	2
2205.2.d.o.1324.6		8	7.6	odd	2
2205.2.d.s.1324.3		8	5.4	even	2	inner
2205.2.d.s.1324.6		8	1.1	even	1	trivial
3675.2.a.bn.1.2		4	105.83	odd	4
3675.2.a.bp.1.2		4	15.8	even	4
3675.2.a.bz.1.3		4	15.2	even	4
3675.2.a.cb.1.3		4	105.62	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:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2205.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.55241i q^{2} -0.409975 q^{4} +(-0.0917505 + 2.23418i) q^{5} +2.46837i q^{8} +(-3.46837 - 0.142434i) q^{10} -4.43075 q^{11} -1.73246i q^{13} -4.65187 q^{16} +2.73246i q^{17} +0.305156 q^{19} +(0.0376154 - 0.915960i) q^{20} -6.87834i q^{22} -7.02423i q^{23} +(-4.98316 - 0.409975i) q^{25} +2.68949 q^{26} -7.79430 q^{29} -5.28487 q^{31} -2.28487i q^{32} -4.24190 q^{34} -3.67406i q^{37} +0.473727i q^{38} +(-5.51479 - 0.226474i) q^{40} +6.71562 q^{41} +9.71562i q^{43} +1.81650 q^{44} +10.9045 q^{46} -1.81650i q^{47} +(0.636449 - 7.73591i) q^{50} +0.710265i q^{52} -1.71513i q^{53} +(0.406524 - 9.89912i) q^{55} -12.1000i q^{58} -1.14243 q^{59} +9.55635 q^{61} -8.20428i q^{62} -5.75669 q^{64} +(3.87063 + 0.158954i) q^{65} -8.38433i q^{67} -1.12024i q^{68} -10.2888 q^{71} +12.8204i q^{73} +5.70365 q^{74} -0.125106 q^{76} -6.71372 q^{79} +(0.426811 - 10.3931i) q^{80} +10.4254i q^{82} +5.09946i q^{83} +(-6.10482 - 0.250704i) q^{85} -15.0826 q^{86} -10.9367i q^{88} +4.07065 q^{89} +2.87976i q^{92} +2.81995 q^{94} +(-0.0279982 + 0.681775i) q^{95} -2.87834i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 2 q^{5} + 4 q^{10} + 24 q^{19} + 4 q^{20} + 4 q^{25} - 12 q^{26} - 12 q^{29} - 16 q^{31} + 8 q^{34} - 32 q^{40} - 8 q^{41} + 20 q^{44} + 32 q^{46} + 20 q^{50} + 4 q^{55} + 4 q^{59} - 16 q^{61}+ \cdots - 22 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 + 2 * q^5 + 4 * q^10 + 24 * q^19 + 4 * q^20 + 4 * q^25 - 12 * q^26 - 12 * q^29 - 16 * q^31 + 8 * q^34 - 32 * q^40 - 8 * q^41 + 20 * q^44 + 32 * q^46 + 20 * q^50 + 4 * q^55 + 4 * q^59 - 16 * q^61 + 8 * q^64 + 30 * q^65 + 28 * q^71 + 40 * q^74 - 32 * q^76 + 16 * q^79 + 52 * q^80 - 32 * q^85 - 48 * q^86 + 16 * q^89 + 32 * q^94 - 22 * q^95

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