LMFDB - Embedded newform 2175.2.f.c.724.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2175,2,Mod(724,2175)] 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("2175.724"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2175, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2175.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [10,-2,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$17.3674624396$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.281900339052544.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 17x^{8} + 104x^{6} + 273x^{4} + 281x^{2} + 64 $ x^10 + 17x^8 + 104x^6 + 273x^4 + 281x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 435)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.3
Root			$1.78296i$ of defining polynomial
Character	$\chi$	$=$	2175.724
Dual form			2175.2.f.c.724.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.78296 q^{2} -1.00000 q^{3} +1.17894 q^{4} +1.78296 q^{6} -2.60402i q^{7} +1.46391 q^{8} +1.00000 q^{9} +6.61083i q^{11} -1.17894 q^{12} +4.14692i q^{13} +4.64285i q^{14} -4.96798 q^{16} +3.78904 q^{17} -1.78296 q^{18} +7.10882i q^{19} +2.60402i q^{21} -11.7868i q^{22} -2.46391i q^{23} -1.46391 q^{24} -7.39379i q^{26} -1.00000 q^{27} -3.06999i q^{28} +(-4.42581 + 3.06793i) q^{29} -6.39305i q^{31} +5.92988 q^{32} -6.61083i q^{33} -6.75570 q^{34} +1.17894 q^{36} -4.64491 q^{37} -12.6747i q^{38} -4.14692i q^{39} -0.721109i q^{41} -4.64285i q^{42} -3.57274 q^{43} +7.79380i q^{44} +4.39305i q^{46} +1.85308 q^{47} +4.96798 q^{48} +0.219100 q^{49} -3.78904 q^{51} +4.88898i q^{52} +0.644913i q^{53} +1.78296 q^{54} -3.81205i q^{56} -7.10882i q^{57} +(7.89104 - 5.46999i) q^{58} +13.2217 q^{59} +5.92380i q^{61} +11.3986i q^{62} -2.60402i q^{63} -0.636777 q^{64} +11.7868i q^{66} +5.45564i q^{67} +4.46706 q^{68} +2.46391i q^{69} -3.13184 q^{71} +1.46391 q^{72} -15.7086 q^{73} +8.28169 q^{74} +8.38090i q^{76} +17.2147 q^{77} +7.39379i q^{78} +1.18502i q^{79} +1.00000 q^{81} +1.28571i q^{82} -10.5236i q^{83} +3.06999i q^{84} +6.37004 q^{86} +(4.42581 - 3.06793i) q^{87} +9.67767i q^{88} +4.34682i q^{89} +10.7987 q^{91} -2.90481i q^{92} +6.39305i q^{93} -3.30396 q^{94} -5.92988 q^{96} +6.44090 q^{97} -0.390646 q^{98} +6.61083i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 10 q^{3} + 14 q^{4} + 2 q^{6} + 10 q^{9} - 14 q^{12} - 2 q^{16} - 12 q^{17} - 2 q^{18} - 10 q^{27} - 16 q^{29} - 2 q^{32} + 6 q^{34} + 14 q^{36} - 2 q^{37} + 38 q^{43} + 64 q^{47} + 2 q^{48}+ \cdots - 48 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 10 * q^3 + 14 * q^4 + 2 * q^6 + 10 * q^9 - 14 * q^12 - 2 * q^16 - 12 * q^17 - 2 * q^18 - 10 * q^27 - 16 * q^29 - 2 * q^32 + 6 * q^34 + 14 * q^36 - 2 * q^37 + 38 * q^43 + 64 * q^47 + 2 * q^48 - 14 * q^49 + 12 * q^51 + 2 * q^54 + 12 * q^58 + 12 * q^59 - 28 * q^64 - 90 * q^68 + 32 * q^71 - 18 * q^73 + 60 * q^74 - 32 * q^77 + 10 * q^81 + 16 * q^87 - 24 * q^91 - 14 * q^94 + 2 * q^96 + 54 * q^97 - 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2175\mathbb{Z}\right)^\times$.

$n$	$901$	$1451$	$2002$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.78296			−1.26074			−0.630371	−	0.776294i	$-0.717097\pi$
$2$	−1.78296			−1.26074			−0.630371	+	0.776294i	$0.717097\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.17894			0.589471
$5$		0			0
$5$		0			0
$6$	1.78296			0.727890
$7$		−	2.60402i		−	0.984226i	−0.870531	−	0.492113i	$-0.836225\pi$
$7$		−	2.60402i		−	0.984226i	0.870531	−	0.492113i	$-0.163775\pi$
$8$	1.46391			0.517571
$9$	1.00000			0.333333
$10$		0			0
$11$			6.61083i			1.99324i	0.0821418	+	0.996621i	$0.473824\pi$
$11$			6.61083i			1.99324i	−0.0821418	+	0.996621i	$0.526176\pi$
$12$	−1.17894			−0.340331
$13$			4.14692i			1.15015i	0.818101	+	0.575075i	$0.195027\pi$
$13$			4.14692i			1.15015i	−0.818101	+	0.575075i	$0.804973\pi$
$14$			4.64285i			1.24085i
$15$		0			0
$16$	−4.96798			−1.24199
$17$	3.78904			0.918976			0.459488	−	0.888184i	$-0.348033\pi$
$17$	3.78904			0.918976			0.459488	+	0.888184i	$0.348033\pi$
$18$	−1.78296			−0.420247
$19$			7.10882i			1.63088i	0.578844	+	0.815438i	$0.303504\pi$
$19$			7.10882i			1.63088i	−0.578844	+	0.815438i	$0.696496\pi$
$20$		0			0
$21$			2.60402i			0.568243i
$22$		−	11.7868i		−	2.51296i
$23$		−	2.46391i		−	0.513761i	−0.966443	−	0.256881i	$-0.917305\pi$
$23$		−	2.46391i		−	0.513761i	0.966443	−	0.256881i	$-0.0826947\pi$
$24$	−1.46391			−0.298820
$25$		0			0
$26$		−	7.39379i		−	1.45004i
$27$	−1.00000			−0.192450
$28$		−	3.06999i		−	0.580173i
$29$	−4.42581	+	3.06793i	−0.821853	+	0.569700i
$29$	−4.42581	+	3.06793i	−0.821853	+	0.569700i
$30$		0			0
$31$		−	6.39305i		−	1.14823i	−0.818776	−	0.574113i	$-0.805347\pi$
$31$		−	6.39305i		−	1.14823i	0.818776	−	0.574113i	$-0.194653\pi$
$32$	5.92988			1.04826
$33$		−	6.61083i		−	1.15080i
$34$	−6.75570			−1.15859
$35$		0			0
$36$	1.17894			0.196490
$37$	−4.64491			−0.763619			−0.381809	−	0.924241i	$-0.624699\pi$
$37$	−4.64491			−0.763619			−0.381809	+	0.924241i	$0.624699\pi$
$38$		−	12.6747i		−	2.05611i
$39$		−	4.14692i		−	0.664039i
$40$		0			0
$41$		−	0.721109i		−	0.112618i	−0.998413	−	0.0563092i	$-0.982067\pi$
$41$		−	0.721109i		−	0.112618i	0.998413	−	0.0563092i	$-0.0179333\pi$
$42$		−	4.64285i		−	0.716408i
$43$	−3.57274			−0.544837			−0.272419	−	0.962179i	$-0.587824\pi$
$43$	−3.57274			−0.544837			−0.272419	+	0.962179i	$0.587824\pi$
$44$			7.79380i			1.17496i
$45$		0			0
$46$			4.39305i			0.647720i
$47$	1.85308			0.270299			0.135150	−	0.990825i	$-0.456849\pi$
$47$	1.85308			0.270299			0.135150	+	0.990825i	$0.456849\pi$
$48$	4.96798			0.717066
$49$	0.219100			0.0313000
$50$		0			0
$51$	−3.78904			−0.530571
$52$			4.88898i			0.677980i
$53$			0.644913i			0.0885856i	0.999019	+	0.0442928i	$0.0141035\pi$
$53$			0.644913i			0.0885856i	−0.999019	+	0.0442928i	$0.985897\pi$
$54$	1.78296			0.242630
$55$		0			0
$56$		−	3.81205i		−	0.509406i
$57$		−	7.10882i		−	0.941587i
$58$	7.89104	−	5.46999i	1.03614	−	0.718245i
$59$	13.2217			1.72131			0.860657	−	0.509185i	$-0.170053\pi$
$59$	13.2217			1.72131			0.860657	+	0.509185i	$0.170053\pi$
$60$		0			0
$61$			5.92380i			0.758465i	0.925301	+	0.379233i	$0.123812\pi$
$61$			5.92380i			0.758465i	−0.925301	+	0.379233i	$0.876188\pi$
$62$			11.3986i			1.44762i
$63$		−	2.60402i		−	0.328075i
$64$	−0.636777			−0.0795971
$65$		0			0
$66$			11.7868i			1.45086i
$67$			5.45564i			0.666513i	0.942836	+	0.333256i	$0.108147\pi$
$67$			5.45564i			0.666513i	−0.942836	+	0.333256i	$0.891853\pi$
$68$	4.46706			0.541710
$69$			2.46391i			0.296620i
$70$		0			0
$71$	−3.13184			−0.371681			−0.185840	−	0.982580i	$-0.559501\pi$
$71$	−3.13184			−0.371681			−0.185840	+	0.982580i	$0.559501\pi$
$72$	1.46391			0.172524
$73$	−15.7086			−1.83855			−0.919276	−	0.393614i	$-0.871225\pi$
$73$	−15.7086			−1.83855			−0.919276	+	0.393614i	$0.871225\pi$
$74$	8.28169			0.962727
$75$		0			0
$76$			8.38090i			0.961355i
$77$	17.2147			1.96180
$78$			7.39379i			0.837182i
$79$			1.18502i			0.133325i	0.997776	+	0.0666626i	$0.0212351\pi$
$79$			1.18502i			0.133325i	−0.997776	+	0.0666626i	$0.978765\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$			1.28571i			0.141983i
$83$		−	10.5236i		−	1.15511i	−0.816351	−	0.577556i	$-0.804007\pi$
$83$		−	10.5236i		−	1.15511i	0.816351	−	0.577556i	$-0.195993\pi$
$84$			3.06999i			0.334963i
$85$		0			0
$86$	6.37004			0.686899
$87$	4.42581	−	3.06793i	0.474497	−	0.328916i
$88$			9.67767i			1.03164i
$89$			4.34682i			0.460762i	0.973101	+	0.230381i	$0.0739972\pi$
$89$			4.34682i			0.460762i	−0.973101	+	0.230381i	$0.926003\pi$
$90$		0			0
$91$	10.7987			1.13201
$92$		−	2.90481i		−	0.302847i
$93$			6.39305i			0.662929i
$94$	−3.30396			−0.340778
$95$		0			0
$96$	−5.92988			−0.605216
$97$	6.44090			0.653974			0.326987	−	0.945029i	$-0.393967\pi$
$97$	6.44090			0.653974			0.326987	+	0.945029i	$0.393967\pi$
$98$	−0.390646			−0.0394612
$99$			6.61083i			0.664414i
$100$		0			0
$101$		−	17.6420i		−	1.75544i	−0.479171	−	0.877721i	$-0.659063\pi$
$101$		−	17.6420i		−	1.75544i	0.479171	−	0.877721i	$-0.340937\pi$
$102$	6.75570			0.668914
$103$			1.97699i			0.194798i	0.995245	+	0.0973992i	$0.0310524\pi$
$103$			1.97699i			0.194798i	−0.995245	+	0.0973992i	$0.968948\pi$
$104$			6.07073i			0.595284i
$105$		0			0
$106$		−	1.14985i		−	0.111684i
$107$		−	7.03263i		−	0.679870i	−0.940449	−	0.339935i	$-0.889595\pi$
$107$		−	7.03263i		−	0.679870i	0.940449	−	0.339935i	$-0.110405\pi$
$108$	−1.17894			−0.113444
$109$	−18.1357			−1.73709			−0.868544	−	0.495613i	$-0.834944\pi$
$109$	−18.1357			−1.73709			−0.868544	+	0.495613i	$0.834944\pi$
$110$		0			0
$111$	4.64491			0.440876
$112$			12.9367i			1.22240i
$113$	−4.99707			−0.470085			−0.235042	−	0.971985i	$-0.575523\pi$
$113$	−4.99707			−0.470085			−0.235042	+	0.971985i	$0.575523\pi$
$114$			12.6747i			1.18710i
$115$		0			0
$116$	−5.21778	+	3.61691i	−0.484459	+	0.335822i
$117$			4.14692i			0.383383i
$118$	−23.5737			−2.17013
$119$		−	9.86671i		−	0.904480i
$120$		0			0
$121$	−32.7031			−2.97301
$122$		−	10.5619i		−	0.956229i
$123$			0.721109i			0.0650202i
$124$		−	7.53704i		−	0.676847i
$125$		0			0
$126$			4.64285i			0.413618i
$127$	−4.93316			−0.437747			−0.218874	−	0.975753i	$-0.570238\pi$
$127$	−4.93316			−0.437747			−0.218874	+	0.975753i	$0.570238\pi$
$128$	−10.7244			−0.947913
$129$	3.57274			0.314562
$130$		0			0
$131$			8.09374i			0.707153i	0.935406	+	0.353577i	$0.115035\pi$
$131$			8.09374i			0.707153i	−0.935406	+	0.353577i	$0.884965\pi$
$132$		−	7.79380i		−	0.678363i
$133$	18.5115			1.60515
$134$		−	9.72719i		−	0.840301i
$135$		0			0
$136$	5.54681			0.475635
$137$	−9.08581			−0.776253			−0.388127	−	0.921606i	$-0.626878\pi$
$137$	−9.08581			−0.776253			−0.388127	+	0.921606i	$0.626878\pi$
$138$		−	4.39305i		−	0.373961i
$139$	13.9957			1.18710			0.593552	−	0.804796i	$-0.297725\pi$
$139$	13.9957			1.18710			0.593552	+	0.804796i	$0.297725\pi$
$140$		0			0
$141$	−1.85308			−0.156057
$142$	5.58394			0.468593
$143$	−27.4146			−2.29253
$144$	−4.96798			−0.413998
$145$		0			0
$146$	28.0078			2.31794
$147$	−0.219100			−0.0180711
$148$	−5.47609			−0.450132
$149$	6.57405			0.538568			0.269284	−	0.963061i	$-0.413213\pi$
$149$	6.57405			0.538568			0.269284	+	0.963061i	$0.413213\pi$
$150$		0			0
$151$	−10.8570			−0.883527			−0.441764	−	0.897131i	$-0.645647\pi$
$151$	−10.8570			−0.883527			−0.441764	+	0.897131i	$0.645647\pi$
$152$			10.4067i			0.844094i
$153$	3.78904			0.306325
$154$	−30.6931			−2.47332
$155$		0			0
$156$		−	4.88898i		−	0.391432i
$157$	−13.0637			−1.04259			−0.521297	−	0.853375i	$-0.674552\pi$
$157$	−13.0637			−1.04259			−0.521297	+	0.853375i	$0.674552\pi$
$158$		−	2.11284i		−	0.168089i
$159$		−	0.644913i		−	0.0511449i
$160$		0			0
$161$	−6.41606			−0.505657
$162$	−1.78296			−0.140082
$163$	−23.8666			−1.86937			−0.934687	−	0.355471i	$-0.884321\pi$
$163$	−23.8666			−1.86937			−0.934687	+	0.355471i	$0.884321\pi$
$164$		−	0.850147i		−	0.0663853i
$165$		0			0
$166$			18.7631i			1.45630i
$167$		−	18.5182i		−	1.43298i	−0.697595	−	0.716492i	$-0.745747\pi$
$167$		−	18.5182i		−	1.43298i	0.697595	−	0.716492i	$-0.254253\pi$
$168$			3.81205i			0.294106i
$169$	−4.19696			−0.322843
$170$		0			0
$171$			7.10882i			0.543625i
$172$	−4.21205			−0.321166
$173$			4.07086i			0.309502i	0.987954	+	0.154751i	$0.0494575\pi$
$173$			4.07086i			0.309502i	−0.987954	+	0.154751i	$0.950543\pi$
$174$	−7.89104	+	5.46999i	−0.598218	+	0.414679i
$175$		0			0
$176$		−	32.8425i		−	2.47560i
$177$	−13.2217			−0.993801
$178$		−	7.75020i		−	0.580902i
$179$	17.2677			1.29065			0.645324	−	0.763909i	$-0.276722\pi$
$179$	17.2677			1.29065			0.645324	+	0.763909i	$0.276722\pi$
$180$		0			0
$181$	−8.86803			−0.659156			−0.329578	−	0.944128i	$-0.606906\pi$
$181$	−8.86803			−0.659156			−0.329578	+	0.944128i	$0.606906\pi$
$182$	−19.2536			−1.42717
$183$		−	5.92380i		−	0.437900i
$184$		−	3.60695i		−	0.265908i
$185$		0			0
$186$		−	11.3986i		−	0.835782i
$187$			25.0487i			1.83174i
$188$	2.18467			0.159334
$189$			2.60402i			0.189414i
$190$		0			0
$191$		−	4.68446i		−	0.338956i	−0.985534	−	0.169478i	$-0.945792\pi$
$191$		−	4.68446i		−	0.338956i	0.985534	−	0.169478i	$-0.0542081\pi$
$192$	0.636777			0.0459554
$193$	19.5479			1.40709			0.703544	−	0.710651i	$-0.251600\pi$
$193$	19.5479			1.40709			0.703544	+	0.710651i	$0.251600\pi$
$194$	−11.4839			−0.824493
$195$		0			0
$196$	0.258306			0.0184504
$197$			25.5128i			1.81771i	0.417109	+	0.908856i	$0.363043\pi$
$197$			25.5128i			1.81771i	−0.417109	+	0.908856i	$0.636957\pi$
$198$		−	11.7868i		−	0.837655i
$199$	1.36177			0.0965335			0.0482667	−	0.998834i	$-0.484630\pi$
$199$	1.36177			0.0965335			0.0482667	+	0.998834i	$0.484630\pi$
$200$		0			0
$201$		−	5.45564i		−	0.384811i
$202$			31.4549i			2.21316i
$203$	7.98893	+	11.5249i	0.560713	+	0.808889i
$204$	−4.46706			−0.312757
$205$		0			0
$206$		−	3.52489i		−	0.245591i
$207$		−	2.46391i		−	0.171254i
$208$		−	20.6018i		−	1.42848i
$209$	−46.9953			−3.25073
$210$		0			0
$211$		−	0.904811i		−	0.0622897i	−0.999515	−	0.0311449i	$-0.990085\pi$
$211$		−	0.904811i		−	0.0622897i	0.999515	−	0.0311449i	$-0.00991532\pi$
$212$			0.760316i			0.0522187i
$213$	3.13184			0.214590
$214$			12.5389i			0.857141i
$215$		0			0
$216$	−1.46391			−0.0996065
$217$	−16.6476			−1.13011
$218$	32.3352			2.19002
$219$	15.7086			1.06149
$220$		0			0
$221$			15.7128i			1.05696i
$222$	−8.28169			−0.555831
$223$			26.9575i			1.80521i	0.430471	+	0.902605i	$0.358348\pi$
$223$			26.9575i			1.80521i	−0.430471	+	0.902605i	$0.641652\pi$
$224$		−	15.4415i		−	1.03173i
$225$		0			0
$226$	8.90957			0.592656
$227$			3.33208i			0.221158i	0.993867	+	0.110579i	$0.0352705\pi$
$227$			3.33208i			0.221158i	−0.993867	+	0.110579i	$0.964730\pi$
$228$		−	8.38090i		−	0.555039i
$229$		−	3.07218i		−	0.203015i	−0.994835	−	0.101508i	$-0.967633\pi$
$229$		−	3.07218i		−	0.203015i	0.994835	−	0.101508i	$-0.0323666\pi$
$230$		0			0
$231$	−17.2147			−1.13265
$232$	−6.47900	+	4.49117i	−0.425367	+	0.294860i
$233$			18.6744i			1.22340i	0.791090	+	0.611700i	$0.209514\pi$
$233$			18.6744i			1.22340i	−0.791090	+	0.611700i	$0.790486\pi$
$234$		−	7.39379i		−	0.483347i
$235$		0			0
$236$	15.5876			1.01467
$237$		−	1.18502i		−	0.0769753i
$238$			17.5919i			1.14032i
$239$	−13.5155			−0.874246			−0.437123	−	0.899402i	$-0.644003\pi$
$239$	−13.5155			−0.874246			−0.437123	+	0.899402i	$0.644003\pi$
$240$		0			0
$241$	9.28996			0.598419			0.299209	−	0.954187i	$-0.403277\pi$
$241$	9.28996			0.598419			0.299209	+	0.954187i	$0.403277\pi$
$242$	58.3083			3.74820
$243$	−1.00000			−0.0641500
$244$			6.98383i			0.447094i
$245$		0			0
$246$		−	1.28571i		−	0.0819738i
$247$	−29.4797			−1.87575
$248$		−	9.35886i		−	0.594288i
$249$			10.5236i			0.666904i
$250$		0			0
$251$			7.79989i			0.492325i	0.969229	+	0.246162i	$0.0791697\pi$
$251$			7.79989i			0.492325i	−0.969229	+	0.246162i	$0.920830\pi$
$252$		−	3.06999i		−	0.193391i
$253$	16.2885			1.02405
$254$	8.79562			0.551886
$255$		0			0
$256$	20.3947			1.27467
$257$		−	3.42838i		−	0.213856i	−0.994267	−	0.106928i	$-0.965898\pi$
$257$		−	3.42838i		−	0.213856i	0.994267	−	0.106928i	$-0.0341015\pi$
$258$	−6.37004			−0.396581
$259$			12.0954i			0.751573i
$260$		0			0
$261$	−4.42581	+	3.06793i	−0.273951	+	0.189900i
$262$		−	14.4308i		−	0.891538i
$263$	15.1455			0.933910			0.466955	−	0.884281i	$-0.345351\pi$
$263$	15.1455			0.933910			0.466955	+	0.884281i	$0.345351\pi$
$264$		−	9.67767i		−	0.595620i
$265$		0			0
$266$	−33.0052			−2.02368
$267$		−	4.34682i		−	0.266021i
$268$			6.43189i			0.392890i
$269$			25.6963i			1.56673i	0.621561	+	0.783366i	$0.286499\pi$
$269$			25.6963i			1.56673i	−0.621561	+	0.783366i	$0.713501\pi$
$270$		0			0
$271$		−	5.24468i		−	0.318592i	−0.987231	−	0.159296i	$-0.949078\pi$
$271$		−	5.24468i		−	0.318592i	0.987231	−	0.159296i	$-0.0509224\pi$
$272$	−18.8239			−1.14136
$273$	−10.7987			−0.653564
$274$	16.1996			0.978656
$275$		0			0
$276$			2.90481i			0.174849i
$277$		−	15.4448i		−	0.927987i	−0.885839	−	0.463994i	$-0.846416\pi$
$277$		−	15.4448i		−	0.927987i	0.885839	−	0.463994i	$-0.153584\pi$
$278$	−24.9538			−1.49663
$279$		−	6.39305i		−	0.382742i
$280$		0			0
$281$	−22.1658			−1.32230			−0.661149	−	0.750254i	$-0.729931\pi$
$281$	−22.1658			−1.32230			−0.661149	+	0.750254i	$0.729931\pi$
$282$	3.30396			0.196748
$283$		−	13.1225i		−	0.780049i	−0.920804	−	0.390025i	$-0.872466\pi$
$283$		−	13.1225i		−	0.780049i	0.920804	−	0.390025i	$-0.127534\pi$
$284$	−3.69226			−0.219095
$285$		0			0
$286$	48.8791			2.89028
$287$	−1.87778			−0.110842
$288$	5.92988			0.349422
$289$	−2.64320			−0.155482
$290$		0			0
$291$	−6.44090			−0.377572
$292$	−18.5195			−1.08377
$293$	−17.1631			−1.00268			−0.501339	−	0.865251i	$-0.667159\pi$
$293$	−17.1631			−1.00268			−0.501339	+	0.865251i	$0.667159\pi$
$294$	0.390646			0.0227829
$295$		0			0
$296$	−6.79974			−0.395227
$297$		−	6.61083i		−	0.383599i
$298$	−11.7213			−0.678995
$299$	10.2176			0.590902
$300$		0			0
$301$			9.30346i			0.536243i
$302$	19.3575			1.11390
$303$			17.6420i			1.01351i
$304$		−	35.3165i		−	2.02554i
$305$		0			0
$306$	−6.75570			−0.386197
$307$	−8.04069			−0.458906			−0.229453	−	0.973320i	$-0.573694\pi$
$307$	−8.04069			−0.458906			−0.229453	+	0.973320i	$0.573694\pi$
$308$	20.2952			1.15642
$309$		−	1.97699i		−	0.112467i
$310$		0			0
$311$			3.67741i			0.208527i	0.994550	+	0.104263i	$0.0332485\pi$
$311$			3.67741i			0.208527i	−0.994550	+	0.104263i	$0.966751\pi$
$312$		−	6.07073i		−	0.343687i
$313$			17.6267i			0.996318i	0.867086	+	0.498159i	$0.165990\pi$
$313$			17.6267i			0.996318i	−0.867086	+	0.498159i	$0.834010\pi$
$314$	23.2920			1.31444
$315$		0			0
$316$			1.39707i			0.0785914i
$317$	17.4787			0.981699			0.490850	−	0.871244i	$-0.336686\pi$
$317$	17.4787			0.981699			0.490850	+	0.871244i	$0.336686\pi$
$318$			1.14985i			0.0644806i
$319$	−20.2816	−	29.2583i	−1.13555	−	1.63815i
$320$		0			0
$321$			7.03263i			0.392523i
$322$	11.4396			0.637503
$323$			26.9356i			1.49874i
$324$	1.17894			0.0654968
$325$		0			0
$326$	42.5531			2.35680
$327$	18.1357			1.00291
$328$		−	1.05564i		−	0.0582880i
$329$		−	4.82544i		−	0.266035i
$330$		0			0
$331$			22.9479i			1.26133i	0.776054	+	0.630666i	$0.217218\pi$
$331$			22.9479i			1.26133i	−0.776054	+	0.630666i	$0.782782\pi$
$332$		−	12.4067i		−	0.680905i
$333$	−4.64491			−0.254540
$334$			33.0172i			1.80662i
$335$		0			0
$336$		−	12.9367i		−	0.705755i
$337$	−25.2051			−1.37301			−0.686505	−	0.727125i	$-0.740856\pi$
$337$	−25.2051			−1.37301			−0.686505	+	0.727125i	$0.740856\pi$
$338$	7.48302			0.407022
$339$	4.99707			0.271404
$340$		0			0
$341$	42.2634			2.28869
$342$		−	12.6747i		−	0.685372i
$343$		−	18.7987i		−	1.01503i
$344$	−5.23017			−0.281992
$345$		0			0
$346$		−	7.25817i		−	0.390202i
$347$			21.1875i			1.13740i	0.822544	+	0.568701i	$0.192554\pi$
$347$			21.1875i			1.13740i	−0.822544	+	0.568701i	$0.807446\pi$
$348$	5.21778	−	3.61691i	0.279702	−	0.193887i
$349$	−30.9222			−1.65523			−0.827614	−	0.561297i	$-0.810302\pi$
$349$	−30.9222			−1.65523			−0.827614	+	0.561297i	$0.810302\pi$
$350$		0			0
$351$		−	4.14692i		−	0.221346i
$352$			39.2015i			2.08944i
$353$			27.0800i			1.44132i	0.693288	+	0.720660i	$0.256161\pi$
$353$			27.0800i			1.44132i	−0.693288	+	0.720660i	$0.743839\pi$
$354$	23.5737			1.25293
$355$		0			0
$356$			5.12465i			0.271606i
$357$			9.86671i			0.522202i
$358$	−30.7876			−1.62717
$359$		−	4.10164i		−	0.216476i	−0.994125	−	0.108238i	$-0.965479\pi$
$359$		−	4.10164i		−	0.216476i	0.994125	−	0.108238i	$-0.0345209\pi$
$360$		0			0
$361$	−31.5354			−1.65976
$362$	15.8113			0.831025
$363$	32.7031			1.71647
$364$	12.7310			0.667285
$365$		0			0
$366$			10.5619i			0.552079i
$367$	3.44492			0.179823			0.0899116	−	0.995950i	$-0.471342\pi$
$367$	3.44492			0.179823			0.0899116	+	0.995950i	$0.471342\pi$
$368$			12.2407i			0.638089i
$369$		−	0.721109i		−	0.0375394i
$370$		0			0
$371$	1.67936			0.0871882
$372$			7.53704i			0.390778i
$373$		−	1.89363i		−	0.0980485i	−0.998798	−	0.0490243i	$-0.984389\pi$
$373$		−	1.89363i		−	0.0980485i	0.998798	−	0.0490243i	$-0.0156112\pi$
$374$		−	44.6608i		−	2.30935i
$375$		0			0
$376$	2.71274			0.139899
$377$	−12.7225	−	18.3535i	−0.655240	−	0.945254i
$378$		−	4.64285i		−	0.238803i
$379$		−	19.0161i		−	0.976791i	−0.872622	−	0.488395i	$-0.837582\pi$
$379$		−	19.0161i		−	0.976791i	0.872622	−	0.488395i	$-0.162418\pi$
$380$		0			0
$381$	4.93316			0.252733
$382$			8.35220i			0.427336i
$383$		−	33.6337i		−	1.71860i	−0.511471	−	0.859301i	$-0.670899\pi$
$383$		−	33.6337i		−	1.71860i	0.511471	−	0.859301i	$-0.329101\pi$
$384$	10.7244			0.547278
$385$		0			0
$386$	−34.8531			−1.77398
$387$	−3.57274			−0.181612
$388$	7.59345			0.385499
$389$			23.2259i			1.17760i	0.808278	+	0.588800i	$0.200400\pi$
$389$			23.2259i			1.17760i	−0.808278	+	0.588800i	$0.799600\pi$
$390$		0			0
$391$		−	9.33585i		−	0.472134i
$392$	0.320743			0.0162000
$393$		−	8.09374i		−	0.408275i
$394$		−	45.4883i		−	2.29167i
$395$		0			0
$396$			7.79380i			0.391653i
$397$		−	4.93046i		−	0.247453i	−0.992316	−	0.123726i	$-0.960515\pi$
$397$		−	4.93046i		−	0.247453i	0.992316	−	0.123726i	$-0.0394845\pi$
$398$	−2.42798			−0.121704
$399$	−18.5115			−0.926734
$400$		0			0
$401$	21.8391			1.09059			0.545296	−	0.838243i	$-0.316417\pi$
$401$	21.8391			1.09059			0.545296	+	0.838243i	$0.316417\pi$
$402$			9.72719i			0.485148i
$403$	26.5115			1.32063
$404$		−	20.7989i		−	1.03478i
$405$		0			0
$406$	−14.2439	−	20.5484i	−0.706915	−	1.01980i
$407$		−	30.7067i		−	1.52208i
$408$	−5.54681			−0.274608
$409$		−	14.0163i		−	0.693060i	−0.938039	−	0.346530i	$-0.887360\pi$
$409$		−	14.0163i		−	0.693060i	0.938039	−	0.346530i	$-0.112640\pi$
$410$		0			0
$411$	9.08581			0.448170
$412$			2.33076i			0.114828i
$413$		−	34.4294i		−	1.69416i
$414$			4.39305i			0.215907i
$415$		0			0
$416$			24.5908i			1.20566i
$417$	−13.9957			−0.685375
$418$	83.7906			4.09833
$419$	−12.0925			−0.590756			−0.295378	−	0.955381i	$-0.595446\pi$
$419$	−12.0925			−0.590756			−0.295378	+	0.955381i	$0.595446\pi$
$420$		0			0
$421$		−	32.3671i		−	1.57748i	−0.614728	−	0.788739i	$-0.710734\pi$
$421$		−	32.3671i		−	1.57748i	0.614728	−	0.788739i	$-0.289266\pi$
$422$			1.61324i			0.0785313i
$423$	1.85308			0.0900997
$424$			0.944095i			0.0458493i
$425$		0			0
$426$	−5.58394			−0.270543
$427$	15.4257			0.746501
$428$		−	8.29107i		−	0.400764i
$429$	27.4146			1.32359
$430$		0			0
$431$	−19.3797			−0.933485			−0.466743	−	0.884393i	$-0.654573\pi$
$431$	−19.3797			−0.933485			−0.466743	+	0.884393i	$0.654573\pi$
$432$	4.96798			0.239022
$433$	−20.3511			−0.978010			−0.489005	−	0.872281i	$-0.662640\pi$
$433$	−20.3511			−0.978010			−0.489005	+	0.872281i	$0.662640\pi$
$434$	29.6820			1.42478
$435$		0			0
$436$	−21.3810			−1.02396
$437$	17.5155			0.837881
$438$	−28.0078			−1.33826
$439$	8.42565			0.402134			0.201067	−	0.979577i	$-0.435559\pi$
$439$	8.42565			0.402134			0.201067	+	0.979577i	$0.435559\pi$
$440$		0			0
$441$	0.219100			0.0104333
$442$		−	28.0154i		−	1.33255i
$443$	−7.52948			−0.357736			−0.178868	−	0.983873i	$-0.557244\pi$
$443$	−7.52948			−0.357736			−0.178868	+	0.983873i	$0.557244\pi$
$444$	5.47609			0.259884
$445$		0			0
$446$		−	48.0642i		−	2.27590i
$447$	−6.57405			−0.310942
$448$			1.65818i			0.0783415i
$449$			31.1439i			1.46977i	0.678192	+	0.734885i	$0.262764\pi$
$449$			31.1439i			1.46977i	−0.678192	+	0.734885i	$0.737236\pi$
$450$		0			0
$451$	4.76713			0.224476
$452$	−5.89126			−0.277102
$453$	10.8570			0.510105
$454$		−	5.94095i		−	0.278823i
$455$		0			0
$456$		−	10.4067i		−	0.487338i
$457$			5.96504i			0.279033i	0.990220	+	0.139516i	$0.0445548\pi$
$457$			5.96504i			0.279033i	−0.990220	+	0.139516i	$0.955445\pi$
$458$			5.47757i			0.255950i
$459$	−3.78904			−0.176857
$460$		0			0
$461$			22.3287i			1.03995i	0.854182	+	0.519975i	$0.174059\pi$
$461$			22.3287i			1.03995i	−0.854182	+	0.519975i	$0.825941\pi$
$462$	30.6931			1.42797
$463$			12.1195i			0.563242i	0.959526	+	0.281621i	$0.0908721\pi$
$463$			12.1195i			0.563242i	−0.959526	+	0.281621i	$0.909128\pi$
$464$	21.9873	−	15.2414i	1.02074	−	0.707564i
$465$		0			0
$466$		−	33.2957i		−	1.54239i
$467$	−35.8252			−1.65779			−0.828896	−	0.559402i	$-0.811031\pi$
$467$	−35.8252			−1.65779			−0.828896	+	0.559402i	$0.811031\pi$
$468$			4.88898i			0.225993i
$469$	14.2066			0.655999
$470$		0			0
$471$	13.0637			0.601942
$472$	19.3553			0.890902
$473$		−	23.6188i		−	1.08599i
$474$			2.11284i			0.0970461i
$475$		0			0
$476$		−	11.6323i		−	0.533165i
$477$			0.644913i			0.0295285i
$478$	24.0976			1.10220
$479$		−	26.7495i		−	1.22222i	−0.791547	−	0.611108i	$-0.790724\pi$
$479$		−	26.7495i		−	1.22222i	0.791547	−	0.611108i	$-0.209276\pi$
$480$		0			0
$481$		−	19.2621i		−	0.878276i
$482$	−16.5636			−0.754452
$483$	6.41606			0.291941
$484$	−38.5551			−1.75251
$485$		0			0
$486$	1.78296			0.0808767
$487$			0.382377i			0.0173272i	0.999962	+	0.00866358i	$0.00275774\pi$
$487$			0.382377i			0.0173272i	−0.999962	+	0.00866358i	$0.997242\pi$
$488$			8.67192i			0.392560i
$489$	23.8666			1.07928
$490$		0			0
$491$			25.6067i			1.15561i	0.816174	+	0.577807i	$0.196091\pi$
$491$			25.6067i			1.15561i	−0.816174	+	0.577807i	$0.803909\pi$
$492$			0.850147i			0.0383276i
$493$	−16.7696	+	11.6245i	−0.755263	+	0.523541i
$494$	52.5612			2.36484
$495$		0			0
$496$			31.7606i			1.42609i
$497$			8.15535i			0.365818i
$498$		−	18.7631i		−	0.840794i
$499$	20.2051			0.904505			0.452252	−	0.891890i	$-0.350621\pi$
$499$	20.2051			0.904505			0.452252	+	0.891890i	$0.350621\pi$
$500$		0			0
$501$			18.5182i			0.827334i
$502$		−	13.9069i		−	0.620695i
$503$	−6.63918			−0.296027			−0.148013	−	0.988985i	$-0.547288\pi$
$503$	−6.63918			−0.296027			−0.148013	+	0.988985i	$0.547288\pi$
$504$		−	3.81205i		−	0.169802i
$505$		0			0
$506$	−29.0417			−1.29106
$507$	4.19696			0.186394
$508$	−5.81591			−0.258039
$509$	6.71577			0.297671			0.148836	−	0.988862i	$-0.452447\pi$
$509$	6.71577			0.297671			0.148836	+	0.988862i	$0.452447\pi$
$510$		0			0
$511$			40.9054i			1.80955i
$512$	−14.9142			−0.659119
$513$		−	7.10882i		−	0.313862i
$514$			6.11266i			0.269618i
$515$		0			0
$516$	4.21205			0.185425
$517$			12.2504i			0.538771i
$518$		−	21.5657i		−	0.947540i
$519$		−	4.07086i		−	0.178691i
$520$		0			0
$521$	43.7273			1.91573			0.957864	−	0.287223i	$-0.0927320\pi$
$521$	43.7273			1.91573			0.957864	+	0.287223i	$0.0927320\pi$
$522$	7.89104	−	5.46999i	0.345382	−	0.239415i
$523$			24.1412i			1.05562i	0.849362	+	0.527811i	$0.176987\pi$
$523$			24.1412i			1.05562i	−0.849362	+	0.527811i	$0.823013\pi$
$524$			9.54205i			0.416847i
$525$		0			0
$526$	−27.0038			−1.17742
$527$		−	24.2235i		−	1.05519i
$528$			32.8425i			1.42929i
$529$	16.9291			0.736050
$530$		0			0
$531$	13.2217			0.573771
$532$	21.8240			0.946190
$533$	2.99038			0.129528
$534$			7.75020i			0.335384i
$535$		0			0
$536$			7.98658i			0.344968i
$537$	−17.2677			−0.745156
$538$		−	45.8155i		−	1.97524i
$539$			1.44843i			0.0623884i
$540$		0			0
$541$		−	12.6252i		−	0.542800i	−0.962467	−	0.271400i	$-0.912513\pi$
$541$		−	12.6252i		−	0.542800i	0.962467	−	0.271400i	$-0.0874867\pi$
$542$			9.35105i			0.401662i
$543$	8.86803			0.380564
$544$	22.4685			0.963331
$545$		0			0
$546$	19.2536			0.823976
$547$		−	12.2476i		−	0.523670i	−0.965113	−	0.261835i	$-0.915672\pi$
$547$		−	12.2476i		−	0.523670i	0.965113	−	0.261835i	$-0.0843276\pi$
$548$	−10.7117			−0.457579
$549$			5.92380i			0.252822i
$550$		0			0
$551$	−21.8094	−	31.4623i	−0.929110	−	1.34034i
$552$			3.60695i			0.153522i
$553$	3.08581			0.131222
$554$			27.5374i			1.16995i
$555$		0			0
$556$	16.5002			0.699764
$557$		−	21.9729i		−	0.931024i	−0.885042	−	0.465512i	$-0.845870\pi$
$557$		−	21.9729i		−	0.931024i	0.885042	−	0.465512i	$-0.154130\pi$
$558$			11.3986i			0.482539i
$559$		−	14.8159i		−	0.626644i
$560$		0			0
$561$		−	25.0487i		−	1.05756i
$562$	39.5206			1.66708
$563$	32.5545			1.37201			0.686004	−	0.727598i	$-0.259363\pi$
$563$	32.5545			1.37201			0.686004	+	0.727598i	$0.259363\pi$
$564$	−2.18467			−0.0919913
$565$		0			0
$566$			23.3968i			0.983441i
$567$		−	2.60402i		−	0.109358i
$568$	−4.58473			−0.192371
$569$			33.2040i			1.39199i	0.718049	+	0.695993i	$0.245036\pi$
$569$			33.2040i			1.39199i	−0.718049	+	0.695993i	$0.754964\pi$
$570$		0			0
$571$	17.3794			0.727305			0.363653	−	0.931535i	$-0.381530\pi$
$571$	17.3794			0.727305			0.363653	+	0.931535i	$0.381530\pi$
$572$	−32.3203			−1.35138
$573$			4.68446i			0.195696i
$574$	3.34800			0.139743
$575$		0			0
$576$	−0.636777			−0.0265324
$577$	38.4323			1.59996			0.799980	−	0.600027i	$-0.204844\pi$
$577$	38.4323			1.59996			0.799980	+	0.600027i	$0.204844\pi$
$578$	4.71272			0.196023
$579$	−19.5479			−0.812383
$580$		0			0
$581$	−27.4035			−1.13689
$582$	11.4839			0.476021
$583$	−4.26341			−0.176573
$584$	−22.9960			−0.951580
$585$		0			0
$586$	30.6011			1.26412
$587$		−	16.8853i		−	0.696931i	−0.937322	−	0.348466i	$-0.886703\pi$
$587$		−	16.8853i		−	0.696931i	0.937322	−	0.348466i	$-0.113297\pi$
$588$	−0.258306			−0.0106524
$589$	45.4471			1.87261
$590$		0			0
$591$		−	25.5128i		−	1.04946i
$592$	23.0758			0.948411
$593$			12.1712i			0.499811i	0.968270	+	0.249906i	$0.0803996\pi$
$593$			12.1712i			0.499811i	−0.968270	+	0.249906i	$0.919600\pi$
$594$			11.7868i			0.483620i
$595$		0			0
$596$	7.75043			0.317470
$597$	−1.36177			−0.0557336
$598$	−18.2176			−0.744975
$599$			18.4881i			0.755403i	0.925927	+	0.377701i	$0.123285\pi$
$599$			18.4881i			0.755403i	−0.925927	+	0.377701i	$0.876715\pi$
$600$		0			0
$601$			25.7139i			1.04889i	0.851443	+	0.524446i	$0.175728\pi$
$601$			25.7139i			1.04889i	−0.851443	+	0.524446i	$0.824272\pi$
$602$		−	16.5877i		−	0.676064i
$603$			5.45564i			0.222171i
$604$	−12.7997			−0.520814
$605$		0			0
$606$		−	31.4549i		−	1.27777i
$607$	24.3863			0.989810			0.494905	−	0.868947i	$-0.335203\pi$
$607$	24.3863			0.989810			0.494905	+	0.868947i	$0.335203\pi$
$608$			42.1545i			1.70959i
$609$	−7.98893	−	11.5249i	−0.323728	−	0.467012i
$610$		0			0
$611$			7.68457i			0.310884i
$612$	4.46706			0.180570
$613$		−	13.4750i		−	0.544248i	−0.962262	−	0.272124i	$-0.912274\pi$
$613$		−	13.4750i		−	0.544248i	0.962262	−	0.272124i	$-0.0877262\pi$
$614$	14.3362			0.578562
$615$		0			0
$616$	25.2008			1.01537
$617$	−1.36560			−0.0549770			−0.0274885	−	0.999622i	$-0.508751\pi$
$617$	−1.36560			−0.0549770			−0.0274885	+	0.999622i	$0.508751\pi$
$618$			3.52489i			0.141792i
$619$		−	22.6187i		−	0.909124i	−0.890715	−	0.454562i	$-0.849796\pi$
$619$		−	22.6187i		−	0.909124i	0.890715	−	0.454562i	$-0.150204\pi$
$620$		0			0
$621$			2.46391i			0.0988734i
$622$		−	6.55668i		−	0.262899i
$623$	11.3192			0.453494
$624$			20.6018i			0.824733i
$625$		0			0
$626$		−	31.4276i		−	1.25610i
$627$	46.9953			1.87681
$628$	−15.4013			−0.614580
$629$	−17.5997			−0.701748
$630$		0			0
$631$	10.6701			0.424772			0.212386	−	0.977186i	$-0.431877\pi$
$631$	10.6701			0.424772			0.212386	+	0.977186i	$0.431877\pi$
$632$			1.73476i			0.0690052i
$633$			0.904811i			0.0359630i
$634$	−31.1637			−1.23767
$635$		0			0
$636$		−	0.760316i		−	0.0301485i
$637$			0.908590i			0.0359997i
$638$	36.1612	+	52.1664i	1.43164	+	2.06529i
$639$	−3.13184			−0.123894
$640$		0			0
$641$			11.7428i			0.463811i	0.972738	+	0.231905i	$0.0744960\pi$
$641$			11.7428i			0.463811i	−0.972738	+	0.231905i	$0.925504\pi$
$642$		−	12.5389i		−	0.494870i
$643$			37.2947i			1.47076i	0.677654	+	0.735381i	$0.262997\pi$
$643$			37.2947i			1.47076i	−0.677654	+	0.735381i	$0.737003\pi$
$644$	−7.56417			−0.298070
$645$		0			0
$646$		−	48.0251i		−	1.88952i
$647$		−	14.6160i		−	0.574616i	−0.957838	−	0.287308i	$-0.907240\pi$
$647$		−	14.6160i		−	0.574616i	0.957838	−	0.287308i	$-0.0927603\pi$
$648$	1.46391			0.0575079
$649$			87.4062i			3.43100i
$650$		0			0
$651$	16.6476			0.652471
$652$	−28.1373			−1.10194
$653$	−20.8225			−0.814849			−0.407425	−	0.913239i	$-0.633573\pi$
$653$	−20.8225			−0.814849			−0.407425	+	0.913239i	$0.633573\pi$
$654$	−32.3352			−1.26441
$655$		0			0
$656$			3.58246i			0.139871i
$657$	−15.7086			−0.612850
$658$			8.60357i			0.335402i
$659$		−	5.84686i		−	0.227761i	−0.993494	−	0.113881i	$-0.963672\pi$
$659$		−	5.84686i		−	0.227761i	0.993494	−	0.113881i	$-0.0363282\pi$
$660$		0			0
$661$	−16.9767			−0.660316			−0.330158	−	0.943926i	$-0.607102\pi$
$661$	−16.9767			−0.660316			−0.330158	+	0.943926i	$0.607102\pi$
$662$		−	40.9152i		−	1.59022i
$663$		−	15.7128i		−	0.610236i
$664$		−	15.4056i		−	0.597852i
$665$		0			0
$666$	8.28169			0.320909
$667$	7.55910	+	10.9048i	0.292690	+	0.422236i
$668$		−	21.8319i		−	0.844703i
$669$		−	26.9575i		−	1.04224i
$670$		0			0
$671$	−39.1613			−1.51180
$672$			15.4415i			0.595669i
$673$			18.2039i			0.701710i	0.936430	+	0.350855i	$0.114109\pi$
$673$			18.2039i			0.701710i	−0.936430	+	0.350855i	$0.885891\pi$
$674$	44.9397			1.73101
$675$		0			0
$676$	−4.94798			−0.190307
$677$	−16.5888			−0.637558			−0.318779	−	0.947829i	$-0.603273\pi$
$677$	−16.5888			−0.637558			−0.318779	+	0.947829i	$0.603273\pi$
$678$	−8.90957			−0.342170
$679$		−	16.7722i		−	0.643658i
$680$		0			0
$681$		−	3.33208i		−	0.127685i
$682$	−75.3539			−2.88545
$683$		−	36.6485i		−	1.40232i	−0.713006	−	0.701158i	$-0.752667\pi$
$683$		−	36.6485i		−	1.40232i	0.713006	−	0.701158i	$-0.247333\pi$
$684$			8.38090i			0.320452i
$685$		0			0
$686$			33.5172i			1.27969i
$687$			3.07218i			0.117211i
$688$	17.7493			0.676685
$689$	−2.67440			−0.101887
$690$		0			0
$691$	20.4746			0.778892			0.389446	−	0.921049i	$-0.372667\pi$
$691$	20.4746			0.778892			0.389446	+	0.921049i	$0.372667\pi$
$692$			4.79931i			0.182442i
$693$	17.2147			0.653933
$694$		−	37.7764i		−	1.43397i
$695$		0			0
$696$	6.47900	−	4.49117i	0.245586	−	0.170237i
$697$		−	2.73231i		−	0.103494i
$698$	55.1331			2.08682
$699$		−	18.6744i		−	0.706331i
$700$		0			0
$701$	−31.8417			−1.20265			−0.601323	−	0.799006i	$-0.705360\pi$
$701$	−31.8417			−1.20265			−0.601323	+	0.799006i	$0.705360\pi$
$702$			7.39379i			0.279061i
$703$		−	33.0199i		−	1.24537i
$704$		−	4.20962i		−	0.158656i
$705$		0			0
$706$		−	48.2824i		−	1.81713i
$707$	−45.9400			−1.72775
$708$	−15.5876			−0.585818
$709$	14.0789			0.528744			0.264372	−	0.964421i	$-0.414835\pi$
$709$	14.0789			0.528744			0.264372	+	0.964421i	$0.414835\pi$
$710$		0			0
$711$			1.18502i			0.0444417i
$712$			6.36336i			0.238477i
$713$	−15.7519			−0.589914
$714$		−	17.5919i		−	0.658362i
$715$		0			0
$716$	20.3576			0.760800
$717$	13.5155			0.504746
$718$			7.31306i			0.272921i
$719$	−5.94838			−0.221837			−0.110919	−	0.993830i	$-0.535379\pi$
$719$	−5.94838			−0.221837			−0.110919	+	0.993830i	$0.535379\pi$
$720$		0			0
$721$	5.14811			0.191726
$722$	56.2263			2.09253
$723$	−9.28996			−0.345497
$724$	−10.4549			−0.388553
$725$		0			0
$726$	−58.3083			−2.16402
$727$	12.3620			0.458481			0.229241	−	0.973370i	$-0.426376\pi$
$727$	12.3620			0.458481			0.229241	+	0.973370i	$0.426376\pi$
$728$	15.8083			0.585893
$729$	1.00000			0.0370370
$730$		0			0
$731$	−13.5372			−0.500692
$732$		−	6.98383i		−	0.258130i
$733$	−49.3006			−1.82096			−0.910479	−	0.413556i	$-0.864287\pi$
$733$	−49.3006			−1.82096			−0.910479	+	0.413556i	$0.864287\pi$
$734$	−6.14215			−0.226711
$735$		0			0
$736$		−	14.6107i		−	0.538558i
$737$	−36.0663			−1.32852
$738$			1.28571i			0.0473276i
$739$		−	8.72784i		−	0.321059i	−0.987031	−	0.160529i	$-0.948680\pi$
$739$		−	8.72784i		−	0.321059i	0.987031	−	0.160529i	$-0.0513202\pi$
$740$		0			0
$741$	29.4797			1.08297
$742$	−2.99424			−0.109922
$743$	41.6374			1.52753			0.763764	−	0.645496i	$-0.223349\pi$
$743$	41.6374			1.52753			0.763764	+	0.645496i	$0.223349\pi$
$744$			9.35886i			0.343113i
$745$		0			0
$746$			3.37627i			0.123614i
$747$		−	10.5236i		−	0.385037i
$748$			29.5310i			1.07976i
$749$	−18.3131			−0.669145
$750$		0			0
$751$		−	14.9756i		−	0.546468i	−0.961948	−	0.273234i	$-0.911907\pi$
$751$		−	14.9756i		−	0.546468i	0.961948	−	0.273234i	$-0.0880933\pi$
$752$	−9.20605			−0.335710
$753$		−	7.79989i		−	0.284244i
$754$	22.6836	+	32.7235i	0.826089	+	1.19172i
$755$		0			0
$756$			3.06999i			0.111654i
$757$	−7.16735			−0.260502			−0.130251	−	0.991481i	$-0.541578\pi$
$757$	−7.16735			−0.260502			−0.130251	+	0.991481i	$0.541578\pi$
$758$			33.9049i			1.23148i
$759$	−16.2885			−0.591235
$760$		0			0
$761$	−8.16312			−0.295913			−0.147957	−	0.988994i	$-0.547270\pi$
$761$	−8.16312			−0.295913			−0.147957	+	0.988994i	$0.547270\pi$
$762$	−8.79562			−0.318632
$763$			47.2257i			1.70969i
$764$		−	5.52271i		−	0.199805i
$765$		0			0
$766$			59.9675i			2.16671i
$767$			54.8292i			1.97977i
$768$	−20.3947			−0.735932
$769$			9.40091i			0.339005i	0.985530	+	0.169503i	$0.0542161\pi$
$769$			9.40091i			0.339005i	−0.985530	+	0.169503i	$0.945784\pi$
$770$		0			0
$771$			3.42838i			0.123470i
$772$	23.0459			0.829439
$773$	−14.0490			−0.505307			−0.252653	−	0.967557i	$-0.581303\pi$
$773$	−14.0490			−0.505307			−0.252653	+	0.967557i	$0.581303\pi$
$774$	6.37004			0.228966
$775$		0			0
$776$	9.42890			0.338478
$777$		−	12.0954i		−	0.433921i
$778$		−	41.4109i		−	1.48465i
$779$	5.12624			0.183667
$780$		0			0
$781$		−	20.7040i		−	0.740849i
$782$			16.6454i			0.595240i
$783$	4.42581	−	3.06793i	0.158166	−	0.109639i
$784$	−1.08848			−0.0388744
$785$		0			0
$786$			14.4308i			0.514730i
$787$		−	28.6760i		−	1.02219i	−0.859525	−	0.511094i	$-0.829240\pi$
$787$		−	28.6760i		−	1.02219i	0.859525	−	0.511094i	$-0.170760\pi$
$788$			30.0781i			1.07149i
$789$	−15.1455			−0.539193
$790$		0			0
$791$			13.0124i			0.462669i
$792$			9.67767i			0.343881i
$793$	−24.5656			−0.872348
$794$			8.79081i			0.311974i
$795$		0			0
$796$	1.60545			0.0569037
$797$	17.0067			0.602409			0.301204	−	0.953560i	$-0.402611\pi$
$797$	17.0067			0.602409			0.301204	+	0.953560i	$0.402611\pi$
$798$	33.0052			1.16837
$799$	7.02138			0.248399
$800$		0			0
$801$			4.34682i			0.153587i
$802$	−38.9382			−1.37496
$803$		−	103.847i		−	3.66468i
$804$		−	6.43189i		−	0.226835i
$805$		0			0
$806$	−47.2689			−1.66498
$807$		−	25.6963i		−	0.904553i
$808$		−	25.8263i		−	0.908566i
$809$		−	37.8813i		−	1.33184i	−0.746025	−	0.665918i	$-0.768040\pi$
$809$		−	37.8813i		−	1.33184i	0.746025	−	0.665918i	$-0.231960\pi$
$810$		0			0
$811$	−53.0728			−1.86364			−0.931819	−	0.362923i	$-0.881779\pi$
$811$	−53.0728			−1.86364			−0.931819	+	0.362923i	$0.881779\pi$
$812$	9.41849	+	13.5872i	0.330524	+	0.476817i
$813$			5.24468i			0.183939i
$814$			54.7489i			1.91895i
$815$		0			0
$816$	18.8239			0.658967
$817$		−	25.3979i		−	0.888562i
$818$			24.9904i			0.873770i
$819$	10.7987			0.377335
$820$		0			0
$821$	23.5402			0.821558			0.410779	−	0.911735i	$-0.365257\pi$
$821$	23.5402			0.821558			0.410779	+	0.911735i	$0.365257\pi$
$822$	−16.1996			−0.565027
$823$	5.33654			0.186020			0.0930100	−	0.995665i	$-0.470351\pi$
$823$	5.33654			0.186020			0.0930100	+	0.995665i	$0.470351\pi$
$824$			2.89414i			0.100822i
$825$		0			0
$826$			61.3863i			2.13590i
$827$	−16.3727			−0.569334			−0.284667	−	0.958626i	$-0.591883\pi$
$827$	−16.3727			−0.569334			−0.284667	+	0.958626i	$0.591883\pi$
$828$		−	2.90481i		−	0.100949i
$829$		−	4.76206i		−	0.165393i	−0.996575	−	0.0826966i	$-0.973647\pi$
$829$		−	4.76206i		−	0.165393i	0.996575	−	0.0826966i	$-0.0263532\pi$
$830$		0			0
$831$			15.4448i			0.535774i
$832$		−	2.64066i		−	0.0915485i
$833$	0.830177			0.0287639
$834$	24.9538			0.864081
$835$		0			0
$836$	−55.4047			−1.91621
$837$			6.39305i			0.220976i
$838$	21.5604			0.744791
$839$		−	1.38600i		−	0.0478502i	−0.999714	−	0.0239251i	$-0.992384\pi$
$839$		−	1.38600i		−	0.0478502i	0.999714	−	0.0239251i	$-0.00761632\pi$
$840$		0			0
$841$	10.1756	−	27.1561i	0.350884	−	0.936419i
$842$			57.7093i			1.98879i
$843$	22.1658			0.763429
$844$		−	1.06672i		−	0.0367180i
$845$		0			0
$846$	−3.30396			−0.113593
$847$			85.1595i			2.92611i
$848$		−	3.20391i		−	0.110023i
$849$			13.1225i			0.450362i
$850$		0			0
$851$			11.4447i			0.392318i
$852$	3.69226			0.126495
$853$	−36.3453			−1.24444			−0.622219	−	0.782843i	$-0.713769\pi$
$853$	−36.3453			−1.24444			−0.622219	+	0.782843i	$0.713769\pi$
$854$	−27.5034			−0.941145
$855$		0			0
$856$		−	10.2951i		−	0.351881i
$857$		−	42.3964i		−	1.44823i	−0.689678	−	0.724116i	$-0.742248\pi$
$857$		−	42.3964i		−	1.44823i	0.689678	−	0.724116i	$-0.257752\pi$
$858$	−48.8791			−1.66871
$859$		−	14.1971i		−	0.484398i	−0.970227	−	0.242199i	$-0.922131\pi$
$859$		−	14.1971i		−	0.484398i	0.970227	−	0.242199i	$-0.0778687\pi$
$860$		0			0
$861$	1.87778			0.0639946
$862$	34.5531			1.17688
$863$		−	23.0565i		−	0.784853i	−0.919783	−	0.392426i	$-0.871636\pi$
$863$		−	23.0565i		−	0.784853i	0.919783	−	0.392426i	$-0.128364\pi$
$864$	−5.92988			−0.201739
$865$		0			0
$866$	36.2851			1.23302
$867$	2.64320			0.0897678
$868$	−19.6266			−0.666170
$869$	−7.83397			−0.265749
$870$		0			0
$871$	−22.6241			−0.766589
$872$	−26.5491			−0.899066
$873$	6.44090			0.217991
$874$	−31.2294			−1.05635
$875$		0			0
$876$	18.5195			0.625717
$877$			31.7600i			1.07246i	0.844073	+	0.536229i	$0.180152\pi$
$877$			31.7600i			1.07246i	−0.844073	+	0.536229i	$0.819848\pi$
$878$	−15.0226			−0.506988
$879$	17.1631			0.578897
$880$		0			0
$881$			12.5647i			0.423316i	0.977344	+	0.211658i	$0.0678864\pi$
$881$			12.5647i			0.423316i	−0.977344	+	0.211658i	$0.932114\pi$
$882$	−0.390646			−0.0131537
$883$			39.7039i			1.33614i	0.744098	+	0.668071i	$0.232880\pi$
$883$			39.7039i			1.33614i	−0.744098	+	0.668071i	$0.767120\pi$
$884$			18.5245i			0.623048i
$885$		0			0
$886$	13.4248			0.451014
$887$	19.0472			0.639543			0.319771	−	0.947495i	$-0.396394\pi$
$887$	19.0472			0.639543			0.319771	+	0.947495i	$0.396394\pi$
$888$	6.79974			0.228184
$889$			12.8460i			0.430842i
$890$		0			0
$891$			6.61083i			0.221471i
$892$			31.7814i			1.06412i
$893$			13.1732i			0.440824i
$894$	11.7213			0.392018
$895$		0			0
$896$			27.9266i			0.932961i
$897$	−10.2176			−0.341157
$898$		−	55.5282i		−	1.85300i
$899$	19.6134	+	28.2945i	0.654144	+	0.943673i
$900$		0			0
$901$			2.44360i			0.0814081i
$902$	−8.49960			−0.283006
$903$		−	9.30346i		−	0.309600i
$904$	−7.31527			−0.243302
$905$		0			0
$906$	−19.3575			−0.643111
$907$	−9.30880			−0.309094			−0.154547	−	0.987985i	$-0.549392\pi$
$907$	−9.30880			−0.309094			−0.154547	+	0.987985i	$0.549392\pi$
$908$			3.92833i			0.130366i
$909$		−	17.6420i		−	0.585148i
$910$		0			0
$911$		−	15.8924i		−	0.526539i	−0.964722	−	0.263270i	$-0.915199\pi$
$911$		−	15.8924i		−	0.526539i	0.964722	−	0.263270i	$-0.0848009\pi$
$912$			35.3165i			1.16945i
$913$	69.5696			2.30242
$914$		−	10.6354i		−	0.351789i
$915$		0			0
$916$		−	3.62192i		−	0.119672i
$917$	21.0762			0.695998
$918$	6.75570			0.222971
$919$	−26.1892			−0.863904			−0.431952	−	0.901897i	$-0.642175\pi$
$919$	−26.1892			−0.863904			−0.431952	+	0.901897i	$0.642175\pi$
$920$		0			0
$921$	8.04069			0.264950
$922$		−	39.8111i		−	1.31111i
$923$		−	12.9875i		−	0.427488i
$924$	−20.2952			−0.667662
$925$		0			0
$926$		−	21.6086i		−	0.710103i
$927$			1.97699i			0.0649328i
$928$	−26.2445	+	18.1924i	−0.861519	+	0.597196i
$929$	−44.7041			−1.46669			−0.733347	−	0.679854i	$-0.762043\pi$
$929$	−44.7041			−1.46669			−0.733347	+	0.679854i	$0.762043\pi$
$930$		0			0
$931$			1.55754i			0.0510464i
$932$			22.0160i			0.721160i
$933$		−	3.67741i		−	0.120393i
$934$	63.8749			2.09005
$935$		0			0
$936$			6.07073i			0.198428i
$937$		−	28.9245i		−	0.944923i	−0.881351	−	0.472462i	$-0.843366\pi$
$937$		−	28.9245i		−	0.944923i	0.881351	−	0.472462i	$-0.156634\pi$
$938$	−25.3298			−0.827046
$939$		−	17.6267i		−	0.575224i
$940$		0			0
$941$	1.16465			0.0379664			0.0189832	−	0.999820i	$-0.493957\pi$
$941$	1.16465			0.0379664			0.0189832	+	0.999820i	$0.493957\pi$
$942$	−23.2920			−0.758894
$943$	−1.77675			−0.0578589
$944$	−65.6850			−2.13786
$945$		0			0
$946$			42.1113i			1.36916i
$947$	12.4430			0.404343			0.202171	−	0.979350i	$-0.435200\pi$
$947$	12.4430			0.404343			0.202171	+	0.979350i	$0.435200\pi$
$948$		−	1.39707i		−	0.0453748i
$949$		−	65.1423i		−	2.11461i
$950$		0			0
$951$	−17.4787			−0.566784
$952$		−	14.4440i		−	0.468132i
$953$			15.1160i			0.489655i	0.969567	+	0.244827i	$0.0787313\pi$
$953$			15.1160i			0.489655i	−0.969567	+	0.244827i	$0.921269\pi$
$954$		−	1.14985i		−	0.0372279i
$955$		0			0
$956$	−15.9340			−0.515343
$957$	20.2816	+	29.2583i	0.655610	+	0.945787i
$958$			47.6933i			1.54090i
$959$			23.6596i			0.764008i
$960$		0			0
$961$	−9.87112			−0.318423
$962$			34.3435i			1.10728i
$963$		−	7.03263i		−	0.226623i
$964$	10.9523			0.352751
$965$		0			0
$966$	−11.4396			−0.368062
$967$	−51.6458			−1.66082			−0.830408	−	0.557156i	$-0.811893\pi$
$967$	−51.6458			−1.66082			−0.830408	+	0.557156i	$0.811893\pi$
$968$	−47.8745			−1.53874
$969$		−	26.9356i		−	0.865296i
$970$		0			0
$971$		−	7.30486i		−	0.234424i	−0.993107	−	0.117212i	$-0.962604\pi$
$971$		−	7.30486i		−	0.234424i	0.993107	−	0.117212i	$-0.0373957\pi$
$972$	−1.17894			−0.0378146
$973$		−	36.4452i		−	1.16838i
$974$		−	0.681763i		−	0.0218451i
$975$		0			0
$976$		−	29.4293i		−	0.942010i
$977$			13.5367i			0.433077i	0.976274	+	0.216539i	$0.0694768\pi$
$977$			13.5367i			0.433077i	−0.976274	+	0.216539i	$0.930523\pi$
$978$	−42.5531			−1.36070
$979$	−28.7361			−0.918409
$980$		0			0
$981$	−18.1357			−0.579029
$982$		−	45.6557i		−	1.45693i
$983$	−17.1481			−0.546940			−0.273470	−	0.961881i	$-0.588171\pi$
$983$	−17.1481			−0.546940			−0.273470	+	0.961881i	$0.588171\pi$
$984$			1.05564i			0.0336526i
$985$		0			0
$986$	29.8995	−	20.7260i	0.952193	−	0.660050i
$987$			4.82544i			0.153596i
$988$	−34.7549			−1.10570
$989$			8.80290i			0.279916i
$990$		0			0
$991$	62.2864			1.97859			0.989296	−	0.145923i	$-0.0466153\pi$
$991$	62.2864			1.97859			0.989296	+	0.145923i	$0.0466153\pi$
$992$		−	37.9100i		−	1.20365i
$993$		−	22.9479i		−	0.728231i
$994$		−	14.5407i		−	0.461202i
$995$		0			0
$996$			12.4067i			0.393121i
$997$	17.0038			0.538516			0.269258	−	0.963068i	$-0.413222\pi$
$997$	17.0038			0.538516			0.269258	+	0.963068i	$0.413222\pi$
$998$	−36.0249			−1.14035
$999$	4.64491			0.146959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.2.f.c.724.3		10
5.2	odd	4		435.2.d.b.376.3	✓	10
5.3	odd	4		2175.2.d.g.376.8		10
5.4	even	2		2175.2.f.f.724.8		10
15.2	even	4		1305.2.d.c.811.8		10
29.28	even	2		2175.2.f.f.724.7		10
145.28	odd	4		2175.2.d.g.376.3		10
145.57	odd	4		435.2.d.b.376.8	yes	10
145.144	even	2	inner	2175.2.f.c.724.4		10
435.347	even	4		1305.2.d.c.811.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.d.b.376.3	✓	10	5.2	odd	4
435.2.d.b.376.8	yes	10	145.57	odd	4
1305.2.d.c.811.3		10	435.347	even	4
1305.2.d.c.811.8		10	15.2	even	4
2175.2.d.g.376.3		10	145.28	odd	4
2175.2.d.g.376.8		10	5.3	odd	4
2175.2.f.c.724.3		10	1.1	even	1	trivial
2175.2.f.c.724.4		10	145.144	even	2	inner
2175.2.f.f.724.7		10	29.28	even	2
2175.2.f.f.724.8		10	5.4	even	2

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:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2175.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.78296 q^{2} -1.00000 q^{3} +1.17894 q^{4} +1.78296 q^{6} -2.60402i q^{7} +1.46391 q^{8} +1.00000 q^{9} +6.61083i q^{11} -1.17894 q^{12} +4.14692i q^{13} +4.64285i q^{14} -4.96798 q^{16} +3.78904 q^{17} -1.78296 q^{18} +7.10882i q^{19} +2.60402i q^{21} -11.7868i q^{22} -2.46391i q^{23} -1.46391 q^{24} -7.39379i q^{26} -1.00000 q^{27} -3.06999i q^{28} +(-4.42581 + 3.06793i) q^{29} -6.39305i q^{31} +5.92988 q^{32} -6.61083i q^{33} -6.75570 q^{34} +1.17894 q^{36} -4.64491 q^{37} -12.6747i q^{38} -4.14692i q^{39} -0.721109i q^{41} -4.64285i q^{42} -3.57274 q^{43} +7.79380i q^{44} +4.39305i q^{46} +1.85308 q^{47} +4.96798 q^{48} +0.219100 q^{49} -3.78904 q^{51} +4.88898i q^{52} +0.644913i q^{53} +1.78296 q^{54} -3.81205i q^{56} -7.10882i q^{57} +(7.89104 - 5.46999i) q^{58} +13.2217 q^{59} +5.92380i q^{61} +11.3986i q^{62} -2.60402i q^{63} -0.636777 q^{64} +11.7868i q^{66} +5.45564i q^{67} +4.46706 q^{68} +2.46391i q^{69} -3.13184 q^{71} +1.46391 q^{72} -15.7086 q^{73} +8.28169 q^{74} +8.38090i q^{76} +17.2147 q^{77} +7.39379i q^{78} +1.18502i q^{79} +1.00000 q^{81} +1.28571i q^{82} -10.5236i q^{83} +3.06999i q^{84} +6.37004 q^{86} +(4.42581 - 3.06793i) q^{87} +9.67767i q^{88} +4.34682i q^{89} +10.7987 q^{91} -2.90481i q^{92} +6.39305i q^{93} -3.30396 q^{94} -5.92988 q^{96} +6.44090 q^{97} -0.390646 q^{98} +6.61083i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 10 q^{3} + 14 q^{4} + 2 q^{6} + 10 q^{9} - 14 q^{12} - 2 q^{16} - 12 q^{17} - 2 q^{18} - 10 q^{27} - 16 q^{29} - 2 q^{32} + 6 q^{34} + 14 q^{36} - 2 q^{37} + 38 q^{43} + 64 q^{47} + 2 q^{48}+ \cdots - 48 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 10 * q^3 + 14 * q^4 + 2 * q^6 + 10 * q^9 - 14 * q^12 - 2 * q^16 - 12 * q^17 - 2 * q^18 - 10 * q^27 - 16 * q^29 - 2 * q^32 + 6 * q^34 + 14 * q^36 - 2 * q^37 + 38 * q^43 + 64 * q^47 + 2 * q^48 - 14 * q^49 + 12 * q^51 + 2 * q^54 + 12 * q^58 + 12 * q^59 - 28 * q^64 - 90 * q^68 + 32 * q^71 - 18 * q^73 + 60 * q^74 - 32 * q^77 + 10 * q^81 + 16 * q^87 - 24 * q^91 - 14 * q^94 + 2 * q^96 + 54 * q^97 - 48 * q^98

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