LMFDB - Embedded newform 1275.2.d.i.424.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1275,2,Mod(424,1275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1275, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1275.424"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1275 = 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1275.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-12,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1809262577$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 144x^{8} + 452x^{6} + 604x^{4} + 268x^{2} + 36 $ x^12 + 20x^10 + 144x^8 + 452x^6 + 604x^4 + 268*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			424.4
Root			$-1.54662i$ of defining polynomial
Character	$\chi$	$=$	1275.424
Dual form			1275.2.d.i.424.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.54662i q^{2} -1.00000 q^{3} -0.392039 q^{4} +1.54662i q^{6} -0.429930 q^{7} -2.48691i q^{8} +1.00000 q^{9} +0.976552i q^{11} +0.392039 q^{12} -5.16256i q^{13} +0.664939i q^{14} -4.63038 q^{16} +(4.00903 + 0.963160i) q^{17} -1.54662i q^{18} +3.67728 q^{19} +0.429930 q^{21} +1.51036 q^{22} -0.477303 q^{23} +2.48691i q^{24} -7.98453 q^{26} -1.00000 q^{27} +0.168549 q^{28} -6.61594i q^{29} +9.07940i q^{31} +2.18764i q^{32} -0.976552i q^{33} +(1.48964 - 6.20045i) q^{34} -0.392039 q^{36} -7.72152 q^{37} -5.68736i q^{38} +5.16256i q^{39} -8.75942i q^{41} -0.664939i q^{42} -6.80650i q^{43} -0.382846i q^{44} +0.738207i q^{46} -4.76254i q^{47} +4.63038 q^{48} -6.81516 q^{49} +(-4.00903 - 0.963160i) q^{51} +2.02392i q^{52} -7.93763i q^{53} +1.54662i q^{54} +1.06920i q^{56} -3.67728 q^{57} -10.2324 q^{58} +0.842970 q^{59} +4.24945i q^{61} +14.0424 q^{62} -0.429930 q^{63} -5.87732 q^{64} -1.51036 q^{66} +4.43839i q^{67} +(-1.57170 - 0.377596i) q^{68} +0.477303 q^{69} -8.61804i q^{71} -2.48691i q^{72} -7.06754 q^{73} +11.9423i q^{74} -1.44164 q^{76} -0.419849i q^{77} +7.98453 q^{78} -2.47389i q^{79} +1.00000 q^{81} -13.5475 q^{82} -6.29370i q^{83} -0.168549 q^{84} -10.5271 q^{86} +6.61594i q^{87} +2.42859 q^{88} -5.57341 q^{89} +2.21954i q^{91} +0.187121 q^{92} -9.07940i q^{93} -7.36585 q^{94} -2.18764i q^{96} -3.74952 q^{97} +10.5405i q^{98} +0.976552i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{3} - 16 q^{4} + 12 q^{9} + 16 q^{12} + 32 q^{16} - 6 q^{17} + 4 q^{19} + 12 q^{22} - 16 q^{23} - 36 q^{26} - 12 q^{27} - 36 q^{28} + 24 q^{34} - 16 q^{36} - 4 q^{37} - 32 q^{48} + 16 q^{49}+ \cdots - 16 q^{97}+O(q^{100}) $ 12 * q - 12 * q^3 - 16 * q^4 + 12 * q^9 + 16 * q^12 + 32 * q^16 - 6 * q^17 + 4 * q^19 + 12 * q^22 - 16 * q^23 - 36 * q^26 - 12 * q^27 - 36 * q^28 + 24 * q^34 - 16 * q^36 - 4 * q^37 - 32 * q^48 + 16 * q^49 + 6 * q^51 - 4 * q^57 + 4 * q^58 - 32 * q^59 - 56 * q^62 - 56 * q^64 - 12 * q^66 - 20 * q^68 + 16 * q^69 + 44 * q^73 + 64 * q^76 + 36 * q^78 + 12 * q^81 - 40 * q^82 + 36 * q^84 + 20 * q^86 - 8 * q^88 - 4 * q^89 - 40 * q^94 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1275\mathbb{Z}\right)^\times$.

$n$	$52$	$751$	$851$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.54662i		−	1.09363i	−0.837255	−	0.546813i	$-0.815841\pi$
$2$		−	1.54662i		−	1.09363i	0.837255	−	0.546813i	$-0.184159\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.392039			−0.196019
$5$		0			0
$5$		0			0
$6$			1.54662i			0.631406i
$7$	−0.429930			−0.162498			−0.0812491	−	0.996694i	$-0.525891\pi$
$7$	−0.429930			−0.162498			−0.0812491	+	0.996694i	$0.525891\pi$
$8$		−	2.48691i		−	0.879255i
$9$	1.00000			0.333333
$10$		0			0
$11$			0.976552i			0.294441i	0.989104	+	0.147221i	$0.0470328\pi$
$11$			0.976552i			0.294441i	−0.989104	+	0.147221i	$0.952967\pi$
$12$	0.392039			0.113172
$13$		−	5.16256i		−	1.43184i	−0.698184	−	0.715919i	$-0.746008\pi$
$13$		−	5.16256i		−	1.43184i	0.698184	−	0.715919i	$-0.253992\pi$
$14$			0.664939i			0.177712i
$15$		0			0
$16$	−4.63038			−1.15760
$17$	4.00903	+	0.963160i	0.972333	+	0.233601i
$17$	4.00903	+	0.963160i	0.972333	+	0.233601i
$18$		−	1.54662i		−	0.364542i
$19$	3.67728			0.843626			0.421813	−	0.906683i	$-0.361394\pi$
$19$	3.67728			0.843626			0.421813	+	0.906683i	$0.361394\pi$
$20$		0			0
$21$	0.429930			0.0938184
$22$	1.51036			0.322009
$23$	−0.477303			−0.0995246			−0.0497623	−	0.998761i	$-0.515846\pi$
$23$	−0.477303			−0.0995246			−0.0497623	+	0.998761i	$0.515846\pi$
$24$			2.48691i			0.507638i
$25$		0			0
$26$	−7.98453			−1.56590
$27$	−1.00000			−0.192450
$28$	0.168549			0.0318528
$29$		−	6.61594i		−	1.22855i	−0.789092	−	0.614275i	$-0.789449\pi$
$29$		−	6.61594i		−	1.22855i	0.789092	−	0.614275i	$-0.210551\pi$
$30$		0			0
$31$			9.07940i			1.63071i	0.578962	+	0.815354i	$0.303458\pi$
$31$			9.07940i			1.63071i	−0.578962	+	0.815354i	$0.696542\pi$
$32$			2.18764i			0.386723i
$33$		−	0.976552i		−	0.169996i
$34$	1.48964	−	6.20045i	0.255472	−	1.06337i
$35$		0			0
$36$	−0.392039			−0.0653398
$37$	−7.72152			−1.26941			−0.634705	−	0.772754i	$-0.718879\pi$
$37$	−7.72152			−1.26941			−0.634705	+	0.772754i	$0.718879\pi$
$38$		−	5.68736i		−	0.922612i
$39$			5.16256i			0.826672i
$40$		0			0
$41$		−	8.75942i		−	1.36799i	−0.729486	−	0.683995i	$-0.760241\pi$
$41$		−	8.75942i		−	1.36799i	0.729486	−	0.683995i	$-0.239759\pi$
$42$		−	0.664939i		−	0.102602i
$43$		−	6.80650i		−	1.03798i	−0.854780	−	0.518991i	$-0.826308\pi$
$43$		−	6.80650i		−	1.03798i	0.854780	−	0.518991i	$-0.173692\pi$
$44$		−	0.382846i		−	0.0577162i
$45$		0			0
$46$			0.738207i			0.108843i
$47$		−	4.76254i		−	0.694688i	−0.937738	−	0.347344i	$-0.887084\pi$
$47$		−	4.76254i		−	0.694688i	0.937738	−	0.347344i	$-0.112916\pi$
$48$	4.63038			0.668338
$49$	−6.81516			−0.973594
$50$		0			0
$51$	−4.00903	−	0.963160i	−0.561377	−	0.134869i
$52$			2.02392i			0.280668i
$53$		−	7.93763i		−	1.09032i	−0.838333	−	0.545159i	$-0.816469\pi$
$53$		−	7.93763i		−	1.09032i	0.838333	−	0.545159i	$-0.183531\pi$
$54$			1.54662i			0.210469i
$55$		0			0
$56$			1.06920i			0.142877i
$57$	−3.67728			−0.487068
$58$	−10.2324			−1.34357
$59$	0.842970			0.109745			0.0548727	−	0.998493i	$-0.482525\pi$
$59$	0.842970			0.109745			0.0548727	+	0.998493i	$0.482525\pi$
$60$		0			0
$61$			4.24945i			0.544087i	0.962285	+	0.272043i	$0.0876994\pi$
$61$			4.24945i			0.544087i	−0.962285	+	0.272043i	$0.912301\pi$
$62$	14.0424			1.78339
$63$	−0.429930			−0.0541661
$64$	−5.87732			−0.734665
$65$		0			0
$66$	−1.51036			−0.185912
$67$			4.43839i			0.542235i	0.962546	+	0.271118i	$0.0873932\pi$
$67$			4.43839i			0.542235i	−0.962546	+	0.271118i	$0.912607\pi$
$68$	−1.57170	−	0.377596i	−0.190596	−	0.0457902i
$69$	0.477303			0.0574605
$70$		0			0
$71$		−	8.61804i		−	1.02277i	−0.859351	−	0.511387i	$-0.829132\pi$
$71$		−	8.61804i		−	1.02277i	0.859351	−	0.511387i	$-0.170868\pi$
$72$		−	2.48691i		−	0.293085i
$73$	−7.06754			−0.827192			−0.413596	−	0.910460i	$-0.635727\pi$
$73$	−7.06754			−0.827192			−0.413596	+	0.910460i	$0.635727\pi$
$74$			11.9423i			1.38826i
$75$		0			0
$76$	−1.44164			−0.165367
$77$		−	0.419849i		−	0.0478462i
$78$	7.98453			0.904070
$79$		−	2.47389i		−	0.278334i	−0.990269	−	0.139167i	$-0.955558\pi$
$79$		−	2.47389i		−	0.278334i	0.990269	−	0.139167i	$-0.0444425\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−13.5475			−1.49607
$83$		−	6.29370i		−	0.690823i	−0.938451	−	0.345411i	$-0.887739\pi$
$83$		−	6.29370i		−	0.690823i	0.938451	−	0.345411i	$-0.112261\pi$
$84$	−0.168549			−0.0183902
$85$		0			0
$86$	−10.5271			−1.13516
$87$			6.61594i			0.709303i
$88$	2.42859			0.258889
$89$	−5.57341			−0.590780			−0.295390	−	0.955377i	$-0.595450\pi$
$89$	−5.57341			−0.590780			−0.295390	+	0.955377i	$0.595450\pi$
$90$		0			0
$91$			2.21954i			0.232671i
$92$	0.187121			0.0195087
$93$		−	9.07940i		−	0.941490i
$94$	−7.36585			−0.759730
$95$		0			0
$96$		−	2.18764i		−	0.223275i
$97$	−3.74952			−0.380706			−0.190353	−	0.981716i	$-0.560963\pi$
$97$	−3.74952			−0.380706			−0.190353	+	0.981716i	$0.560963\pi$
$98$			10.5405i			1.06475i
$99$			0.976552i			0.0981471i
$100$		0			0
$101$	7.69515			0.765696			0.382848	−	0.923811i	$-0.374943\pi$
$101$	7.69515			0.765696			0.382848	+	0.923811i	$0.374943\pi$
$102$	−1.48964	+	6.20045i	−0.147497	+	0.613936i
$103$			5.66786i			0.558471i	0.960223	+	0.279236i	$0.0900810\pi$
$103$			5.66786i			0.558471i	−0.960223	+	0.279236i	$0.909919\pi$
$104$	−12.8388			−1.25895
$105$		0			0
$106$	−12.2765			−1.19240
$107$	11.2117			1.08388			0.541940	−	0.840417i	$-0.317690\pi$
$107$	11.2117			1.08388			0.541940	+	0.840417i	$0.317690\pi$
$108$	0.392039			0.0377240
$109$			3.24392i			0.310711i	0.987859	+	0.155356i	$0.0496523\pi$
$109$			3.24392i			0.310711i	−0.987859	+	0.155356i	$0.950348\pi$
$110$		0			0
$111$	7.72152			0.732895
$112$	1.99074			0.188107
$113$	−16.6770			−1.56884			−0.784421	−	0.620229i	$-0.787040\pi$
$113$	−16.6770			−1.56884			−0.784421	+	0.620229i	$0.787040\pi$
$114$			5.68736i			0.532670i
$115$		0			0
$116$			2.59371i			0.240820i
$117$		−	5.16256i		−	0.477279i
$118$		−	1.30376i		−	0.120020i
$119$	−1.72360	−	0.414091i	−0.158002	−	0.0379597i
$120$		0			0
$121$	10.0463			0.913304
$122$	6.57229			0.595028
$123$			8.75942i			0.789810i
$124$		−	3.55948i		−	0.319650i
$125$		0			0
$126$			0.664939i			0.0592375i
$127$			10.2257i			0.907385i	0.891158	+	0.453693i	$0.149894\pi$
$127$			10.2257i			0.907385i	−0.891158	+	0.453693i	$0.850106\pi$
$128$			13.4653i			1.19017i
$129$			6.80650i			0.599279i
$130$		0			0
$131$		−	9.04036i		−	0.789860i	−0.918711	−	0.394930i	$-0.870769\pi$
$131$		−	9.04036i		−	0.789860i	0.918711	−	0.394930i	$-0.129231\pi$
$132$			0.382846i			0.0333225i
$133$	−1.58097			−0.137088
$134$	6.86450			0.593003
$135$		0			0
$136$	2.39529	−	9.97009i	0.205394	−	0.854928i
$137$			14.8099i			1.26530i	0.774439	+	0.632649i	$0.218032\pi$
$137$			14.8099i			1.26530i	−0.774439	+	0.632649i	$0.781968\pi$
$138$		−	0.738207i		−	0.0628404i
$139$		−	12.1919i		−	1.03410i	−0.855954	−	0.517052i	$-0.827029\pi$
$139$		−	12.1919i		−	1.03410i	0.855954	−	0.517052i	$-0.172971\pi$
$140$		0			0
$141$			4.76254i			0.401079i
$142$	−13.3289			−1.11853
$143$	5.04151			0.421592
$144$	−4.63038			−0.385865
$145$		0			0
$146$			10.9308i			0.904640i
$147$	6.81516			0.562105
$148$	3.02714			0.248829
$149$	2.53733			0.207866			0.103933	−	0.994584i	$-0.466857\pi$
$149$	2.53733			0.207866			0.103933	+	0.994584i	$0.466857\pi$
$150$		0			0
$151$	20.1805			1.64226			0.821131	−	0.570739i	$-0.193343\pi$
$151$	20.1805			1.64226			0.821131	+	0.570739i	$0.193343\pi$
$152$		−	9.14506i		−	0.741762i
$153$	4.00903	+	0.963160i	0.324111	+	0.0778669i
$154$	−0.649347			−0.0523259
$155$		0			0
$156$		−	2.02392i		−	0.162044i
$157$			8.08452i			0.645215i	0.946533	+	0.322607i	$0.104559\pi$
$157$			8.08452i			0.645215i	−0.946533	+	0.322607i	$0.895441\pi$
$158$	−3.82617			−0.304393
$159$			7.93763i			0.629495i
$160$		0			0
$161$	0.205207			0.0161726
$162$		−	1.54662i		−	0.121514i
$163$	14.8181			1.16064			0.580321	−	0.814388i	$-0.302927\pi$
$163$	14.8181			1.16064			0.580321	+	0.814388i	$0.302927\pi$
$164$			3.43403i			0.268153i
$165$		0			0
$166$	−9.73397			−0.755502
$167$	−1.83612			−0.142083			−0.0710417	−	0.997473i	$-0.522632\pi$
$167$	−1.83612			−0.142083			−0.0710417	+	0.997473i	$0.522632\pi$
$168$		−	1.06920i		−	0.0824903i
$169$	−13.6520			−1.05016
$170$		0			0
$171$	3.67728			0.281209
$172$			2.66841i			0.203465i
$173$	16.5137			1.25551			0.627757	−	0.778409i	$-0.283973\pi$
$173$	16.5137			1.25551			0.627757	+	0.778409i	$0.283973\pi$
$174$	10.2324			0.775713
$175$		0			0
$176$		−	4.52181i		−	0.340844i
$177$	−0.842970			−0.0633615
$178$			8.61995i			0.646093i
$179$	−8.48016			−0.633837			−0.316919	−	0.948453i	$-0.602648\pi$
$179$	−8.48016			−0.633837			−0.316919	+	0.948453i	$0.602648\pi$
$180$		0			0
$181$			11.2829i			0.838649i	0.907836	+	0.419325i	$0.137733\pi$
$181$			11.2829i			0.838649i	−0.907836	+	0.419325i	$0.862267\pi$
$182$	3.43279			0.254455
$183$		−	4.24945i		−	0.314129i
$184$			1.18701i			0.0875074i
$185$		0			0
$186$	−14.0424			−1.02964
$187$	−0.940575	+	3.91503i	−0.0687817	+	0.286295i
$188$			1.86710i			0.136172i
$189$	0.429930			0.0312728
$190$		0			0
$191$	3.03667			0.219726			0.109863	−	0.993947i	$-0.464959\pi$
$191$	3.03667			0.219726			0.109863	+	0.993947i	$0.464959\pi$
$192$	5.87732			0.424159
$193$	−23.9780			−1.72598			−0.862988	−	0.505225i	$-0.831409\pi$
$193$	−23.9780			−1.72598			−0.862988	+	0.505225i	$0.831409\pi$
$194$			5.79909i			0.416351i
$195$		0			0
$196$	2.67181			0.190843
$197$	8.42347			0.600147			0.300074	−	0.953916i	$-0.402989\pi$
$197$	8.42347			0.600147			0.300074	+	0.953916i	$0.402989\pi$
$198$	1.51036			0.107336
$199$		−	26.2107i		−	1.85803i	−0.370042	−	0.929015i	$-0.620657\pi$
$199$		−	26.2107i		−	1.85803i	0.370042	−	0.929015i	$-0.379343\pi$
$200$		0			0
$201$		−	4.43839i		−	0.313060i
$202$		−	11.9015i		−	0.837386i
$203$			2.84439i			0.199637i
$204$	1.57170	+	0.377596i	0.110041	+	0.0264370i
$205$		0			0
$206$	8.76604			0.610759
$207$	−0.477303			−0.0331749
$208$			23.9046i			1.65749i
$209$			3.59105i			0.248398i
$210$		0			0
$211$			4.35210i			0.299611i	0.988716	+	0.149805i	$0.0478647\pi$
$211$			4.35210i			0.299611i	−0.988716	+	0.149805i	$0.952135\pi$
$212$			3.11186i			0.213723i
$213$			8.61804i			0.590499i
$214$		−	17.3403i		−	1.18536i
$215$		0			0
$216$			2.48691i			0.169213i
$217$		−	3.90351i		−	0.264987i
$218$	5.01712			0.339802
$219$	7.06754			0.477580
$220$		0			0
$221$	4.97237	−	20.6969i	0.334478	−	1.39222i
$222$		−	11.9423i		−	0.801513i
$223$			3.48378i			0.233291i	0.993174	+	0.116646i	$0.0372142\pi$
$223$			3.48378i			0.233291i	−0.993174	+	0.116646i	$0.962786\pi$
$224$		−	0.940530i		−	0.0628418i
$225$		0			0
$226$			25.7930i			1.71573i
$227$	1.89538			0.125801			0.0629004	−	0.998020i	$-0.479965\pi$
$227$	1.89538			0.125801			0.0629004	+	0.998020i	$0.479965\pi$
$228$	1.44164			0.0954747
$229$	8.85340			0.585049			0.292524	−	0.956258i	$-0.405505\pi$
$229$	8.85340			0.585049			0.292524	+	0.956258i	$0.405505\pi$
$230$		0			0
$231$			0.419849i			0.0276240i
$232$	−16.4532			−1.08021
$233$	26.0340			1.70554			0.852771	−	0.522285i	$-0.174920\pi$
$233$	26.0340			1.70554			0.852771	+	0.522285i	$0.174920\pi$
$234$	−7.98453			−0.521965
$235$		0			0
$236$	−0.330477			−0.0215122
$237$			2.47389i			0.160696i
$238$	−0.640443	+	2.66576i	−0.0415137	+	0.172796i
$239$	24.0664			1.55673			0.778363	−	0.627815i	$-0.216050\pi$
$239$	24.0664			1.55673			0.778363	+	0.627815i	$0.216050\pi$
$240$		0			0
$241$		−	11.2091i		−	0.722042i	−0.932558	−	0.361021i	$-0.882428\pi$
$241$		−	11.2091i		−	0.722042i	0.932558	−	0.361021i	$-0.117572\pi$
$242$		−	15.5379i		−	0.998814i
$243$	−1.00000			−0.0641500
$244$		−	1.66595i		−	0.106652i
$245$		0			0
$246$	13.5475			0.863757
$247$		−	18.9842i		−	1.20793i
$248$	22.5796			1.43381
$249$			6.29370i			0.398847i
$250$		0			0
$251$	28.2730			1.78458			0.892289	−	0.451465i	$-0.149098\pi$
$251$	28.2730			1.78458			0.892289	+	0.451465i	$0.149098\pi$
$252$	0.168549			0.0106176
$253$		−	0.466111i		−	0.0293042i
$254$	15.8153			0.992341
$255$		0			0
$256$	9.07103			0.566939
$257$			5.51730i			0.344159i	0.985083	+	0.172080i	$0.0550487\pi$
$257$			5.51730i			0.344159i	−0.985083	+	0.172080i	$0.944951\pi$
$258$	10.5271			0.655387
$259$	3.31971			0.206277
$260$		0			0
$261$		−	6.61594i		−	0.409516i
$262$	−13.9820			−0.863812
$263$			16.0439i			0.989310i	0.869089	+	0.494655i	$0.164706\pi$
$263$			16.0439i			0.989310i	−0.869089	+	0.494655i	$0.835294\pi$
$264$	−2.42859			−0.149470
$265$		0			0
$266$			2.44517i			0.149923i
$267$	5.57341			0.341087
$268$		−	1.74002i		−	0.106289i
$269$		−	7.17003i		−	0.437165i	−0.975819	−	0.218582i	$-0.929857\pi$
$269$		−	7.17003i		−	0.437165i	0.975819	−	0.218582i	$-0.0701432\pi$
$270$		0			0
$271$	7.17160			0.435643			0.217822	−	0.975989i	$-0.430105\pi$
$271$	7.17160			0.435643			0.217822	+	0.975989i	$0.430105\pi$
$272$	−18.5633	−	4.45980i	−1.12557	−	0.270415i
$273$		−	2.21954i		−	0.134333i
$274$	22.9054			1.38376
$275$		0			0
$276$	−0.187121			−0.0112634
$277$	24.1787			1.45275			0.726377	−	0.687296i	$-0.241203\pi$
$277$	24.1787			1.45275			0.726377	+	0.687296i	$0.241203\pi$
$278$	−18.8563			−1.13092
$279$			9.07940i			0.543569i
$280$		0			0
$281$	−28.2491			−1.68520			−0.842601	−	0.538539i	$-0.818976\pi$
$281$	−28.2491			−1.68520			−0.842601	+	0.538539i	$0.818976\pi$
$282$	7.36585			0.438630
$283$	−32.2601			−1.91766			−0.958832	−	0.283973i	$-0.908347\pi$
$283$	−32.2601			−1.91766			−0.958832	+	0.283973i	$0.908347\pi$
$284$			3.37861i			0.200483i
$285$		0			0
$286$		−	7.79731i		−	0.461064i
$287$			3.76594i			0.222296i
$288$			2.18764i			0.128908i
$289$	15.1446	+	7.72267i	0.890862	+	0.454275i
$290$		0			0
$291$	3.74952			0.219801
$292$	2.77075			0.162146
$293$		−	26.0057i		−	1.51927i	−0.650349	−	0.759636i	$-0.725377\pi$
$293$		−	26.0057i		−	1.51927i	0.650349	−	0.759636i	$-0.274623\pi$
$294$		−	10.5405i		−	0.614733i
$295$		0			0
$296$			19.2027i			1.11614i
$297$		−	0.976552i		−	0.0566653i
$298$		−	3.92428i		−	0.227328i
$299$			2.46411i			0.142503i
$300$		0			0
$301$			2.92632i			0.168670i
$302$		−	31.2115i		−	1.79602i
$303$	−7.69515			−0.442075
$304$	−17.0272			−0.976578
$305$		0			0
$306$	1.48964	−	6.20045i	0.0851573	−	0.354456i
$307$		−	5.76186i		−	0.328847i	−0.986390	−	0.164423i	$-0.947424\pi$
$307$		−	5.76186i		−	0.328847i	0.986390	−	0.164423i	$-0.0525763\pi$
$308$			0.164597i			0.00937879i
$309$		−	5.66786i		−	0.322433i
$310$		0			0
$311$			24.9984i			1.41753i	0.705444	+	0.708766i	$0.250748\pi$
$311$			24.9984i			1.41753i	−0.705444	+	0.708766i	$0.749252\pi$
$312$	12.8388			0.726855
$313$	3.42518			0.193602			0.0968012	−	0.995304i	$-0.469139\pi$
$313$	3.42518			0.193602			0.0968012	+	0.995304i	$0.469139\pi$
$314$	12.5037			0.705624
$315$		0			0
$316$			0.969859i			0.0545588i
$317$	−23.7739			−1.33527			−0.667637	−	0.744487i	$-0.732694\pi$
$317$	−23.7739			−1.33527			−0.667637	+	0.744487i	$0.732694\pi$
$318$	12.2765			0.688433
$319$	6.46081			0.361736
$320$		0			0
$321$	−11.2117			−0.625779
$322$		−	0.317377i		−	0.0176868i
$323$	14.7423	+	3.54181i	0.820285	+	0.197071i
$324$	−0.392039			−0.0217799
$325$		0			0
$326$		−	22.9180i		−	1.26931i
$327$		−	3.24392i		−	0.179389i
$328$	−21.7839			−1.20281
$329$			2.04756i			0.112886i
$330$		0			0
$331$	9.57377			0.526222			0.263111	−	0.964766i	$-0.415251\pi$
$331$	9.57377			0.526222			0.263111	+	0.964766i	$0.415251\pi$
$332$			2.46737i			0.135415i
$333$	−7.72152			−0.423137
$334$			2.83979i			0.155386i
$335$		0			0
$336$	−1.99074			−0.108604
$337$	18.1726			0.989927			0.494963	−	0.868914i	$-0.335181\pi$
$337$	18.1726			0.989927			0.494963	+	0.868914i	$0.335181\pi$
$338$			21.1146i			1.14848i
$339$	16.6770			0.905771
$340$		0			0
$341$	−8.86650			−0.480148
$342$		−	5.68736i		−	0.307537i
$343$	5.93955			0.320706
$344$	−16.9271			−0.912650
$345$		0			0
$346$		−	25.5405i		−	1.37306i
$347$	−23.2530			−1.24828			−0.624142	−	0.781311i	$-0.714551\pi$
$347$	−23.2530			−1.24828			−0.624142	+	0.781311i	$0.714551\pi$
$348$		−	2.59371i		−	0.139037i
$349$	32.9277			1.76258			0.881290	−	0.472575i	$-0.156676\pi$
$349$	32.9277			1.76258			0.881290	+	0.472575i	$0.156676\pi$
$350$		0			0
$351$			5.16256i			0.275557i
$352$	−2.13634			−0.113867
$353$			6.76112i			0.359858i	0.983680	+	0.179929i	$0.0575868\pi$
$353$			6.76112i			0.359858i	−0.983680	+	0.179929i	$0.942413\pi$
$354$			1.30376i			0.0692939i
$355$		0			0
$356$	2.18499			0.115804
$357$	1.72360	+	0.414091i	0.0912227	+	0.0219160i
$358$			13.1156i			0.693181i
$359$	25.2197			1.33104			0.665521	−	0.746379i	$-0.268209\pi$
$359$	25.2197			1.33104			0.665521	+	0.746379i	$0.268209\pi$
$360$		0			0
$361$	−5.47761			−0.288295
$362$	17.4503			0.917169
$363$	−10.0463			−0.527296
$364$		−	0.870146i		−	0.0456080i
$365$		0			0
$366$	−6.57229			−0.343539
$367$	−8.08168			−0.421860			−0.210930	−	0.977501i	$-0.567649\pi$
$367$	−8.08168			−0.421860			−0.210930	+	0.977501i	$0.567649\pi$
$368$	2.21010			0.115209
$369$		−	8.75942i		−	0.455997i
$370$		0			0
$371$			3.41263i			0.177175i
$372$			3.55948i			0.184550i
$373$			17.1991i			0.890537i	0.895397	+	0.445268i	$0.146892\pi$
$373$			17.1991i			0.890537i	−0.895397	+	0.445268i	$0.853108\pi$
$374$	6.05506	+	1.45471i	0.313100	+	0.0752215i
$375$		0			0
$376$	−11.8440			−0.610808
$377$	−34.1552			−1.75908
$378$		−	0.664939i		−	0.0342008i
$379$		−	0.531420i		−	0.0272972i	−0.999907	−	0.0136486i	$-0.995655\pi$
$379$		−	0.531420i		−	0.0272972i	0.999907	−	0.0136486i	$-0.00434462\pi$
$380$		0			0
$381$		−	10.2257i		−	0.523879i
$382$		−	4.69658i		−	0.240298i
$383$			0.874772i			0.0446988i	0.999750	+	0.0223494i	$0.00711462\pi$
$383$			0.874772i			0.0446988i	−0.999750	+	0.0223494i	$0.992885\pi$
$384$		−	13.4653i		−	0.687146i
$385$		0			0
$386$			37.0849i			1.88757i
$387$		−	6.80650i		−	0.345994i
$388$	1.46996			0.0746258
$389$	24.9537			1.26520			0.632602	−	0.774477i	$-0.281987\pi$
$389$	24.9537			1.26520			0.632602	+	0.774477i	$0.281987\pi$
$390$		0			0
$391$	−1.91352	−	0.459719i	−0.0967710	−	0.0232490i
$392$			16.9487i			0.856037i
$393$			9.04036i			0.456026i
$394$		−	13.0279i		−	0.656337i
$395$		0			0
$396$		−	0.382846i		−	0.0192387i
$397$	15.7628			0.791111			0.395555	−	0.918442i	$-0.370552\pi$
$397$	15.7628			0.791111			0.395555	+	0.918442i	$0.370552\pi$
$398$	−40.5381			−2.03199
$399$	1.58097			0.0791476
$400$		0			0
$401$		−	10.7657i		−	0.537615i	−0.963194	−	0.268807i	$-0.913370\pi$
$401$		−	10.7657i		−	0.537615i	0.963194	−	0.268807i	$-0.0866295\pi$
$402$	−6.86450			−0.342370
$403$	46.8730			2.33491
$404$	−3.01680			−0.150091
$405$		0			0
$406$	4.39920			0.218328
$407$		−	7.54047i		−	0.373767i
$408$	−2.39529	+	9.97009i	−0.118585	+	0.493593i
$409$	−10.2591			−0.507282			−0.253641	−	0.967298i	$-0.581628\pi$
$409$	−10.2591			−0.507282			−0.253641	+	0.967298i	$0.581628\pi$
$410$		0			0
$411$		−	14.8099i		−	0.730520i
$412$		−	2.22202i		−	0.109471i
$413$	−0.362418			−0.0178334
$414$			0.738207i			0.0362809i
$415$		0			0
$416$	11.2938			0.553724
$417$			12.1919i			0.597041i
$418$	5.55400			0.271655
$419$			32.3428i			1.58005i	0.613074	+	0.790026i	$0.289933\pi$
$419$			32.3428i			1.58005i	−0.613074	+	0.790026i	$0.710067\pi$
$420$		0			0
$421$	−26.4919			−1.29114			−0.645568	−	0.763703i	$-0.723379\pi$
$421$	−26.4919			−1.29114			−0.645568	+	0.763703i	$0.723379\pi$
$422$	6.73104			0.327662
$423$		−	4.76254i		−	0.231563i
$424$	−19.7402			−0.958667
$425$		0			0
$426$	13.3289			0.645785
$427$		−	1.82697i		−	0.0884131i
$428$	−4.39544			−0.212462
$429$	−5.04151			−0.243406
$430$		0			0
$431$		−	15.5752i		−	0.750233i	−0.926978	−	0.375116i	$-0.877603\pi$
$431$		−	15.5752i		−	0.750233i	0.926978	−	0.375116i	$-0.122397\pi$
$432$	4.63038			0.222779
$433$		−	36.6438i		−	1.76099i	−0.474057	−	0.880494i	$-0.657211\pi$
$433$		−	36.6438i		−	1.76099i	0.474057	−	0.880494i	$-0.342789\pi$
$434$	−6.03725			−0.289797
$435$		0			0
$436$		−	1.27174i		−	0.0609054i
$437$	−1.75518			−0.0839615
$438$		−	10.9308i		−	0.522294i
$439$		−	35.7519i		−	1.70634i	−0.521630	−	0.853172i	$-0.674676\pi$
$439$		−	35.7519i		−	1.70634i	0.521630	−	0.853172i	$-0.325324\pi$
$440$		0			0
$441$	−6.81516			−0.324531
$442$	−32.0102	−	7.69038i	−1.52257	−	0.365794i
$443$		−	16.8118i		−	0.798753i	−0.916787	−	0.399377i	$-0.869227\pi$
$443$		−	16.8118i		−	0.798753i	0.916787	−	0.399377i	$-0.130773\pi$
$444$	−3.02714			−0.143662
$445$		0			0
$446$	5.38809			0.255133
$447$	−2.53733			−0.120011
$448$	2.52684			0.119382
$449$			18.0607i			0.852337i	0.904644	+	0.426169i	$0.140137\pi$
$449$			18.0607i			0.852337i	−0.904644	+	0.426169i	$0.859863\pi$
$450$		0			0
$451$	8.55402			0.402793
$452$	6.53804			0.307523
$453$	−20.1805			−0.948161
$454$		−	2.93144i		−	0.137579i
$455$		0			0
$456$			9.14506i			0.428256i
$457$			28.9103i			1.35237i	0.736733	+	0.676184i	$0.236368\pi$
$457$			28.9103i			1.35237i	−0.736733	+	0.676184i	$0.763632\pi$
$458$		−	13.6929i		−	0.639825i
$459$	−4.00903	−	0.963160i	−0.187126	−	0.0449565i
$460$		0			0
$461$	15.8971			0.740401			0.370201	−	0.928952i	$-0.379289\pi$
$461$	15.8971			0.740401			0.370201	+	0.928952i	$0.379289\pi$
$462$	0.649347			0.0302104
$463$			29.7924i			1.38457i	0.721624	+	0.692285i	$0.243396\pi$
$463$			29.7924i			1.38457i	−0.721624	+	0.692285i	$0.756604\pi$
$464$			30.6343i			1.42216i
$465$		0			0
$466$		−	40.2647i		−	1.86523i
$467$		−	2.48308i		−	0.114903i	−0.998348	−	0.0574516i	$-0.981703\pi$
$467$		−	2.48308i		−	0.114903i	0.998348	−	0.0574516i	$-0.0182975\pi$
$468$			2.02392i			0.0935560i
$469$		−	1.90819i		−	0.0881122i
$470$		0			0
$471$		−	8.08452i		−	0.372515i
$472$		−	2.09639i		−	0.0964941i
$473$	6.64690			0.305625
$474$	3.82617			0.175742
$475$		0			0
$476$	0.675719	+	0.162340i	0.0309715	+	0.00744083i
$477$		−	7.93763i		−	0.363439i
$478$		−	37.2216i		−	1.70248i
$479$		−	21.3380i		−	0.974960i	−0.873134	−	0.487480i	$-0.837916\pi$
$479$		−	21.3380i		−	0.974960i	0.873134	−	0.487480i	$-0.162084\pi$
$480$		0			0
$481$			39.8629i			1.81759i
$482$	−17.3363			−0.789645
$483$	−0.205207			−0.00933724
$484$	−3.93856			−0.179025
$485$		0			0
$486$			1.54662i			0.0701562i
$487$	41.3883			1.87548			0.937742	−	0.347333i	$-0.112913\pi$
$487$	41.3883			1.87548			0.937742	+	0.347333i	$0.112913\pi$
$488$	10.5680			0.478391
$489$	−14.8181			−0.670097
$490$		0			0
$491$	−15.5703			−0.702677			−0.351338	−	0.936249i	$-0.614273\pi$
$491$	−15.5703			−0.702677			−0.351338	+	0.936249i	$0.614273\pi$
$492$		−	3.43403i		−	0.154818i
$493$	6.37221	−	26.5235i	0.286990	−	1.19456i
$494$	−29.3614			−1.32103
$495$		0			0
$496$		−	42.0411i		−	1.88770i
$497$			3.70515i			0.166199i
$498$	9.73397			0.436190
$499$			28.3452i			1.26891i	0.772961	+	0.634453i	$0.218775\pi$
$499$			28.3452i			1.26891i	−0.772961	+	0.634453i	$0.781225\pi$
$500$		0			0
$501$	1.83612			0.0820319
$502$		−	43.7277i		−	1.95166i
$503$	28.3949			1.26606			0.633032	−	0.774125i	$-0.281810\pi$
$503$	28.3949			1.26606			0.633032	+	0.774125i	$0.281810\pi$
$504$			1.06920i			0.0476258i
$505$		0			0
$506$	−0.720898			−0.0320478
$507$	13.6520			0.606309
$508$		−	4.00888i		−	0.177865i
$509$	−15.6779			−0.694909			−0.347454	−	0.937697i	$-0.612954\pi$
$509$	−15.6779			−0.694909			−0.347454	+	0.937697i	$0.612954\pi$
$510$		0			0
$511$	3.03854			0.134417
$512$			12.9011i			0.570153i
$513$	−3.67728			−0.162356
$514$	8.53317			0.376382
$515$		0			0
$516$		−	2.66841i		−	0.117470i
$517$	4.65087			0.204545
$518$		−	5.13434i		−	0.225590i
$519$	−16.5137			−0.724872
$520$		0			0
$521$			22.7228i			0.995504i	0.867319	+	0.497752i	$0.165841\pi$
$521$			22.7228i			0.995504i	−0.867319	+	0.497752i	$0.834159\pi$
$522$	−10.2324			−0.447858
$523$			22.3505i			0.977319i	0.872475	+	0.488660i	$0.162514\pi$
$523$			22.3505i			0.977319i	−0.872475	+	0.488660i	$0.837486\pi$
$524$			3.54417i			0.154828i
$525$		0			0
$526$	24.8139			1.08194
$527$	−8.74491	+	36.3996i	−0.380934	+	1.58559i
$528$			4.52181i			0.196786i
$529$	−22.7722			−0.990095
$530$		0			0
$531$	0.842970			0.0365818
$532$	0.619803			0.0268719
$533$	−45.2210			−1.95874
$534$		−	8.61995i		−	0.373022i
$535$		0			0
$536$	11.0379			0.476763
$537$	8.48016			0.365946
$538$	−11.0893			−0.478095
$539$		−	6.65536i		−	0.286666i
$540$		0			0
$541$			1.49693i			0.0643580i	0.999482	+	0.0321790i	$0.0102447\pi$
$541$			1.49693i			0.0643580i	−0.999482	+	0.0321790i	$0.989755\pi$
$542$		−	11.0917i		−	0.476431i
$543$		−	11.2829i		−	0.484194i
$544$	−2.10704	+	8.77030i	−0.0903387	+	0.376023i
$545$		0			0
$546$	−3.43279			−0.146910
$547$	−23.1972			−0.991843			−0.495921	−	0.868367i	$-0.665170\pi$
$547$	−23.1972			−0.991843			−0.495921	+	0.868367i	$0.665170\pi$
$548$		−	5.80607i		−	0.248023i
$549$			4.24945i			0.181362i
$550$		0			0
$551$		−	24.3287i		−	1.03644i
$552$		−	1.18701i		−	0.0505224i
$553$			1.06360i			0.0452288i
$554$		−	37.3952i		−	1.58877i
$555$		0			0
$556$			4.77970i			0.202705i
$557$			44.8334i			1.89965i	0.312777	+	0.949827i	$0.398741\pi$
$557$			44.8334i			1.89965i	−0.312777	+	0.949827i	$0.601259\pi$
$558$	14.0424			0.594462
$559$	−35.1390			−1.48622
$560$		0			0
$561$	0.940575	−	3.91503i	0.0397111	−	0.165292i
$562$			43.6907i			1.84298i
$563$			43.5968i			1.83739i	0.394970	+	0.918694i	$0.370755\pi$
$563$			43.5968i			1.83739i	−0.394970	+	0.918694i	$0.629245\pi$
$564$		−	1.86710i		−	0.0786192i
$565$		0			0
$566$			49.8942i			2.09721i
$567$	−0.429930			−0.0180554
$568$	−21.4323			−0.899278
$569$	−16.0087			−0.671118			−0.335559	−	0.942019i	$-0.608925\pi$
$569$	−16.0087			−0.671118			−0.335559	+	0.942019i	$0.608925\pi$
$570$		0			0
$571$			46.0825i			1.92849i	0.265007	+	0.964246i	$0.414626\pi$
$571$			46.0825i			1.92849i	−0.265007	+	0.964246i	$0.585374\pi$
$572$	−1.97647			−0.0826402
$573$	−3.03667			−0.126859
$574$	5.82448			0.243109
$575$		0			0
$576$	−5.87732			−0.244888
$577$			7.87973i			0.328037i	0.986457	+	0.164019i	$0.0524457\pi$
$577$			7.87973i			0.328037i	−0.986457	+	0.164019i	$0.947554\pi$
$578$	11.9441	−	23.4230i	0.496807	−	0.974270i
$579$	23.9780			0.996492
$580$		0			0
$581$			2.70585i			0.112258i
$582$		−	5.79909i		−	0.240380i
$583$	7.75151			0.321035
$584$			17.5763i			0.727313i
$585$		0			0
$586$	−40.2210			−1.66152
$587$			10.6361i			0.439000i	0.975613	+	0.219500i	$0.0704425\pi$
$587$			10.6361i			0.439000i	−0.975613	+	0.219500i	$0.929557\pi$
$588$	−2.67181			−0.110183
$589$			33.3875i			1.37571i
$590$		0			0
$591$	−8.42347			−0.346495
$592$	35.7536			1.46946
$593$		−	7.79634i		−	0.320157i	−0.987104	−	0.160079i	$-0.948825\pi$
$593$		−	7.79634i		−	0.320157i	0.987104	−	0.160079i	$-0.0511748\pi$
$594$	−1.51036			−0.0619707
$595$		0			0
$596$	−0.994731			−0.0407458
$597$			26.2107i			1.07273i
$598$	3.81104			0.155845
$599$	2.26066			0.0923679			0.0461840	−	0.998933i	$-0.485294\pi$
$599$	2.26066			0.0923679			0.0461840	+	0.998933i	$0.485294\pi$
$600$		0			0
$601$		−	4.72766i		−	0.192845i	−0.995340	−	0.0964226i	$-0.969260\pi$
$601$		−	4.72766i		−	0.192845i	0.995340	−	0.0964226i	$-0.0307400\pi$
$602$	4.52591			0.184462
$603$			4.43839i			0.180745i
$604$	−7.91153			−0.321915
$605$		0			0
$606$			11.9015i			0.483465i
$607$	26.7457			1.08557			0.542786	−	0.839871i	$-0.317369\pi$
$607$	26.7457			1.08557			0.542786	+	0.839871i	$0.317369\pi$
$608$			8.04455i			0.326250i
$609$		−	2.84439i		−	0.115261i
$610$		0			0
$611$	−24.5869			−0.994681
$612$	−1.57170	−	0.377596i	−0.0635320	−	0.0152634i
$613$			2.83165i			0.114369i	0.998364	+	0.0571847i	$0.0182124\pi$
$613$			2.83165i			0.114369i	−0.998364	+	0.0571847i	$0.981788\pi$
$614$	−8.91142			−0.359636
$615$		0			0
$616$	−1.04413			−0.0420690
$617$	8.05591			0.324319			0.162159	−	0.986765i	$-0.448154\pi$
$617$	8.05591			0.324319			0.162159	+	0.986765i	$0.448154\pi$
$618$	−8.76604			−0.352622
$619$			20.4157i			0.820576i	0.911956	+	0.410288i	$0.134572\pi$
$619$			20.4157i			0.820576i	−0.911956	+	0.410288i	$0.865428\pi$
$620$		0			0
$621$	0.477303			0.0191535
$622$	38.6631			1.55025
$623$	2.39617			0.0960007
$624$		−	23.9046i		−	0.956952i
$625$		0			0
$626$		−	5.29745i		−	0.211729i
$627$		−	3.59105i		−	0.143413i
$628$		−	3.16945i		−	0.126475i
$629$	−30.9558	−	7.43706i	−1.23429	−	0.296535i
$630$		0			0
$631$	−20.6328			−0.821378			−0.410689	−	0.911775i	$-0.634712\pi$
$631$	−20.6328			−0.821378			−0.410689	+	0.911775i	$0.634712\pi$
$632$	−6.15232			−0.244726
$633$		−	4.35210i		−	0.172980i
$634$			36.7692i			1.46029i
$635$		0			0
$636$		−	3.11186i		−	0.123393i
$637$			35.1837i			1.39403i
$638$		−	9.99243i		−	0.395604i
$639$		−	8.61804i		−	0.340924i
$640$		0			0
$641$		−	17.5622i		−	0.693667i	−0.937927	−	0.346833i	$-0.887257\pi$
$641$		−	17.5622i		−	0.693667i	0.937927	−	0.346833i	$-0.112743\pi$
$642$			17.3403i			0.684368i
$643$	−2.24211			−0.0884201			−0.0442100	−	0.999022i	$-0.514077\pi$
$643$	−2.24211			−0.0884201			−0.0442100	+	0.999022i	$0.514077\pi$
$644$	−0.0804491			−0.00317014
$645$		0			0
$646$	5.47784	−	22.8008i	0.215523	−	0.897086i
$647$		−	35.5856i		−	1.39902i	−0.714625	−	0.699508i	$-0.753403\pi$
$647$		−	35.5856i		−	1.39902i	0.714625	−	0.699508i	$-0.246597\pi$
$648$		−	2.48691i		−	0.0976950i
$649$			0.823204i			0.0323136i
$650$		0			0
$651$			3.90351i			0.152990i
$652$	−5.80926			−0.227508
$653$	−17.6154			−0.689345			−0.344672	−	0.938723i	$-0.612010\pi$
$653$	−17.6154			−0.689345			−0.344672	+	0.938723i	$0.612010\pi$
$654$	−5.01712			−0.196185
$655$		0			0
$656$			40.5595i			1.58358i
$657$	−7.06754			−0.275731
$658$	3.16680			0.123455
$659$	−8.61882			−0.335742			−0.167871	−	0.985809i	$-0.553689\pi$
$659$	−8.61882			−0.335742			−0.167871	+	0.985809i	$0.553689\pi$
$660$		0			0
$661$	−11.7014			−0.455132			−0.227566	−	0.973763i	$-0.573077\pi$
$661$	−11.7014			−0.455132			−0.227566	+	0.973763i	$0.573077\pi$
$662$		−	14.8070i		−	0.575491i
$663$	−4.97237	+	20.6969i	−0.193111	+	0.803800i
$664$	−15.6518			−0.607409
$665$		0			0
$666$			11.9423i			0.462754i
$667$			3.15781i			0.122271i
$668$	0.719831			0.0278511
$669$		−	3.48378i		−	0.134691i
$670$		0			0
$671$	−4.14981			−0.160202
$672$			0.940530i			0.0362817i
$673$	44.9610			1.73312			0.866560	−	0.499073i	$-0.166326\pi$
$673$	44.9610			1.73312			0.866560	+	0.499073i	$0.166326\pi$
$674$		−	28.1062i		−	1.08261i
$675$		0			0
$676$	5.35213			0.205851
$677$	−2.79937			−0.107589			−0.0537943	−	0.998552i	$-0.517132\pi$
$677$	−2.79937			−0.107589			−0.0537943	+	0.998552i	$0.517132\pi$
$678$		−	25.7930i		−	0.990575i
$679$	1.61203			0.0618641
$680$		0			0
$681$	−1.89538			−0.0726312
$682$			13.7131i			0.525103i
$683$	22.2621			0.851835			0.425917	−	0.904762i	$-0.359951\pi$
$683$	22.2621			0.851835			0.425917	+	0.904762i	$0.359951\pi$
$684$	−1.44164			−0.0551223
$685$		0			0
$686$		−	9.18624i		−	0.350732i
$687$	−8.85340			−0.337778
$688$			31.5167i			1.20156i
$689$	−40.9785			−1.56116
$690$		0			0
$691$			16.1547i			0.614554i	0.951620	+	0.307277i	$0.0994177\pi$
$691$			16.1547i			0.614554i	−0.951620	+	0.307277i	$0.900582\pi$
$692$	−6.47402			−0.246105
$693$		−	0.419849i		−	0.0159487i
$694$			35.9635i			1.36516i
$695$		0			0
$696$	16.4532			0.623658
$697$	8.43672	−	35.1168i	0.319563	−	1.33014i
$698$		−	50.9267i		−	1.92761i
$699$	−26.0340			−0.984695
$700$		0			0
$701$	−29.6175			−1.11864			−0.559319	−	0.828952i	$-0.688937\pi$
$701$	−29.6175			−1.11864			−0.559319	+	0.828952i	$0.688937\pi$
$702$	7.98453			0.301357
$703$	−28.3942			−1.07091
$704$		−	5.73951i		−	0.216316i
$705$		0			0
$706$	10.4569			0.393551
$707$	−3.30838			−0.124424
$708$	0.330477			0.0124201
$709$			4.66171i			0.175074i	0.996161	+	0.0875371i	$0.0278996\pi$
$709$			4.66171i			0.175074i	−0.996161	+	0.0875371i	$0.972100\pi$
$710$		0			0
$711$		−	2.47389i		−	0.0927780i
$712$			13.8605i			0.519446i
$713$		−	4.33363i		−	0.162296i
$714$	0.640443	−	2.66576i	0.0239680	−	0.0997636i
$715$		0			0
$716$	3.32455			0.124244
$717$	−24.0664			−0.898776
$718$		−	39.0053i		−	1.45566i
$719$		−	0.691404i		−	0.0257850i	−0.999917	−	0.0128925i	$-0.995896\pi$
$719$		−	0.691404i		−	0.0257850i	0.999917	−	0.0128925i	$-0.00410393\pi$
$720$		0			0
$721$		−	2.43678i		−	0.0907506i
$722$			8.47180i			0.315288i
$723$			11.2091i			0.416871i
$724$		−	4.42332i		−	0.164392i
$725$		0			0
$726$			15.5379i			0.576665i
$727$		−	26.9835i		−	1.00076i	−0.865806	−	0.500380i	$-0.833193\pi$
$727$		−	26.9835i		−	1.00076i	0.865806	−	0.500380i	$-0.166807\pi$
$728$	5.51979			0.204577
$729$	1.00000			0.0370370
$730$		0			0
$731$	6.55575	−	27.2875i	0.242473	−	1.00926i
$732$			1.66595i			0.0615753i
$733$		−	38.6190i		−	1.42643i	−0.700948	−	0.713213i	$-0.747239\pi$
$733$		−	38.6190i		−	1.42643i	0.700948	−	0.713213i	$-0.252761\pi$
$734$			12.4993i			0.461358i
$735$		0			0
$736$		−	1.04417i		−	0.0384884i
$737$	−4.33431			−0.159656
$738$	−13.5475			−0.498690
$739$	12.7144			0.467705			0.233853	−	0.972272i	$-0.424867\pi$
$739$	12.7144			0.467705			0.233853	+	0.972272i	$0.424867\pi$
$740$		0			0
$741$			18.9842i			0.697401i
$742$	5.27804			0.193763
$743$	−4.75526			−0.174454			−0.0872268	−	0.996188i	$-0.527800\pi$
$743$	−4.75526			−0.174454			−0.0872268	+	0.996188i	$0.527800\pi$
$744$	−22.5796			−0.827809
$745$		0			0
$746$	26.6005			0.973915
$747$		−	6.29370i		−	0.230274i
$748$	0.368742	−	1.53484i	0.0134825	−	0.0561194i
$749$	−4.82027			−0.176129
$750$		0			0
$751$			16.7360i			0.610705i	0.952239	+	0.305352i	$0.0987742\pi$
$751$			16.7360i			0.610705i	−0.952239	+	0.305352i	$0.901226\pi$
$752$			22.0524i			0.804168i
$753$	−28.2730			−1.03033
$754$			52.8252i			1.92378i
$755$		0			0
$756$	−0.168549			−0.00613008
$757$			1.54235i			0.0560578i	0.999607	+	0.0280289i	$0.00892304\pi$
$757$			1.54235i			0.0560578i	−0.999607	+	0.0280289i	$0.991077\pi$
$758$	−0.821906			−0.0298530
$759$			0.466111i			0.0169188i
$760$		0			0
$761$	−30.8203			−1.11723			−0.558617	−	0.829426i	$-0.688668\pi$
$761$	−30.8203			−1.11723			−0.558617	+	0.829426i	$0.688668\pi$
$762$	−15.8153			−0.572928
$763$		−	1.39466i		−	0.0504900i
$764$	−1.19049			−0.0430705
$765$		0			0
$766$	1.35294			0.0488838
$767$		−	4.35189i		−	0.157138i
$768$	−9.07103			−0.327323
$769$	−30.7066			−1.10731			−0.553654	−	0.832747i	$-0.686767\pi$
$769$	−30.7066			−1.10731			−0.553654	+	0.832747i	$0.686767\pi$
$770$		0			0
$771$		−	5.51730i		−	0.198701i
$772$	9.40031			0.338325
$773$		−	7.40148i		−	0.266213i	−0.991102	−	0.133106i	$-0.957505\pi$
$773$		−	7.40148i		−	0.266213i	0.991102	−	0.133106i	$-0.0424952\pi$
$774$	−10.5271			−0.378388
$775$		0			0
$776$			9.32471i			0.334738i
$777$	−3.31971			−0.119094
$778$		−	38.5940i		−	1.38366i
$779$		−	32.2108i		−	1.15407i
$780$		0			0
$781$	8.41596			0.301147
$782$	−0.711012	+	2.95950i	−0.0254257	+	0.105831i
$783$			6.61594i			0.236434i
$784$	31.5568			1.12703
$785$		0			0
$786$	13.9820			0.498722
$787$	3.70140			0.131941			0.0659703	−	0.997822i	$-0.478986\pi$
$787$	3.70140			0.131941			0.0659703	+	0.997822i	$0.478986\pi$
$788$	−3.30233			−0.117640
$789$		−	16.0439i		−	0.571178i
$790$		0			0
$791$	7.16995			0.254934
$792$	2.42859			0.0862963
$793$	21.9381			0.779043
$794$		−	24.3790i		−	0.865180i
$795$		0			0
$796$			10.2756i			0.364210i
$797$		−	34.7651i		−	1.23144i	−0.787963	−	0.615722i	$-0.788864\pi$
$797$		−	34.7651i		−	1.23144i	0.787963	−	0.615722i	$-0.211136\pi$
$798$		−	2.44517i		−	0.0865580i
$799$	4.58709	−	19.0932i	0.162280	−	0.675468i
$800$		0			0
$801$	−5.57341			−0.196927
$802$	−16.6505			−0.587950
$803$		−	6.90181i		−	0.243560i
$804$			1.74002i			0.0613658i
$805$		0			0
$806$		−	72.4947i		−	2.55352i
$807$			7.17003i			0.252397i
$808$		−	19.1371i		−	0.673242i
$809$		−	42.0271i		−	1.47760i	−0.673927	−	0.738798i	$-0.735394\pi$
$809$		−	42.0271i		−	1.47760i	0.673927	−	0.738798i	$-0.264606\pi$
$810$		0			0
$811$		−	35.1420i		−	1.23400i	−0.786962	−	0.617001i	$-0.788347\pi$
$811$		−	35.1420i		−	1.23400i	0.786962	−	0.617001i	$-0.211653\pi$
$812$		−	1.11511i		−	0.0391327i
$813$	−7.17160			−0.251519
$814$	−11.6623			−0.408762
$815$		0			0
$816$	18.5633	+	4.45980i	0.649847	+	0.156124i
$817$		−	25.0294i		−	0.875668i
$818$			15.8670i			0.554777i
$819$			2.21954i			0.0775570i
$820$		0			0
$821$			17.8719i			0.623734i	0.950126	+	0.311867i	$0.100954\pi$
$821$			17.8719i			0.623734i	−0.950126	+	0.311867i	$0.899046\pi$
$822$	−22.9054			−0.798916
$823$	−33.3852			−1.16373			−0.581867	−	0.813284i	$-0.697678\pi$
$823$	−33.3852			−1.16373			−0.581867	+	0.813284i	$0.697678\pi$
$824$	14.0955			0.491038
$825$		0			0
$826$			0.560524i			0.0195031i
$827$	42.7442			1.48636			0.743180	−	0.669091i	$-0.233317\pi$
$827$	42.7442			1.48636			0.743180	+	0.669091i	$0.233317\pi$
$828$	0.187121			0.00650292
$829$	17.0407			0.591848			0.295924	−	0.955212i	$-0.404373\pi$
$829$	17.0407			0.591848			0.295924	+	0.955212i	$0.404373\pi$
$830$		0			0
$831$	−24.1787			−0.838748
$832$			30.3420i			1.05192i
$833$	−27.3222	−	6.56409i	−0.946658	−	0.227432i
$834$	18.8563			0.652940
$835$		0			0
$836$		−	1.40783i		−	0.0486909i
$837$		−	9.07940i		−	0.313830i
$838$	50.0221			1.72799
$839$		−	5.38898i		−	0.186048i	−0.995664	−	0.0930242i	$-0.970347\pi$
$839$		−	5.38898i		−	0.186048i	0.995664	−	0.0930242i	$-0.0296534\pi$
$840$		0			0
$841$	−14.7707			−0.509333
$842$			40.9729i			1.41202i
$843$	28.2491			0.972951
$844$		−	1.70619i		−	0.0587295i
$845$		0			0
$846$	−7.36585			−0.253243
$847$	−4.31923			−0.148410
$848$			36.7543i			1.26215i
$849$	32.2601			1.10716
$850$		0			0
$851$	3.68551			0.126338
$852$		−	3.37861i		−	0.115749i
$853$	44.3831			1.51965			0.759824	−	0.650129i	$-0.225285\pi$
$853$	44.3831			1.51965			0.759824	+	0.650129i	$0.225285\pi$
$854$	−2.82563			−0.0966909
$855$		0			0
$856$		−	27.8826i		−	0.953007i
$857$	21.4348			0.732199			0.366100	−	0.930576i	$-0.380693\pi$
$857$	21.4348			0.732199			0.366100	+	0.930576i	$0.380693\pi$
$858$			7.79731i			0.266196i
$859$	41.7437			1.42428			0.712138	−	0.702039i	$-0.247727\pi$
$859$	41.7437			1.42428			0.712138	+	0.702039i	$0.247727\pi$
$860$		0			0
$861$		−	3.76594i		−	0.128343i
$862$	−24.0890			−0.820475
$863$			13.7962i			0.469627i	0.972040	+	0.234813i	$0.0754479\pi$
$863$			13.7962i			0.469627i	−0.972040	+	0.234813i	$0.924552\pi$
$864$		−	2.18764i		−	0.0744249i
$865$		0			0
$866$	−56.6741			−1.92586
$867$	−15.1446	−	7.72267i	−0.514339	−	0.262276i
$868$			1.53033i			0.0519426i
$869$	2.41588			0.0819530
$870$		0			0
$871$	22.9134			0.776392
$872$	8.06733			0.273194
$873$	−3.74952			−0.126902
$874$			2.71459i			0.0918225i
$875$		0			0
$876$	−2.77075			−0.0936149
$877$	29.2334			0.987141			0.493571	−	0.869706i	$-0.335691\pi$
$877$	29.2334			0.987141			0.493571	+	0.869706i	$0.335691\pi$
$878$	−55.2946			−1.86610
$879$			26.0057i			0.877152i
$880$		0			0
$881$			18.7208i			0.630721i	0.948972	+	0.315360i	$0.102125\pi$
$881$			18.7208i			0.630721i	−0.948972	+	0.315360i	$0.897875\pi$
$882$			10.5405i			0.354916i
$883$			29.4224i			0.990142i	0.868852	+	0.495071i	$0.164858\pi$
$883$			29.4224i			0.990142i	−0.868852	+	0.495071i	$0.835142\pi$
$884$	−1.94936	+	8.11398i	−0.0655642	+	0.272903i
$885$		0			0
$886$	−26.0015			−0.873538
$887$	−43.7003			−1.46731			−0.733656	−	0.679521i	$-0.762188\pi$
$887$	−43.7003			−1.46731			−0.733656	+	0.679521i	$0.762188\pi$
$888$		−	19.2027i		−	0.644401i
$889$		−	4.39634i		−	0.147449i
$890$		0			0
$891$			0.976552i			0.0327157i
$892$		−	1.36578i		−	0.0457296i
$893$		−	17.5132i		−	0.586057i
$894$			3.92428i			0.131248i
$895$		0			0
$896$		−	5.78912i		−	0.193401i
$897$		−	2.46411i		−	0.0822741i
$898$	27.9331			0.932139
$899$	60.0688			2.00341
$900$		0			0
$901$	7.64521	−	31.8222i	0.254699	−	1.06015i
$902$		−	13.2298i		−	0.440505i
$903$		−	2.92632i		−	0.0973818i
$904$			41.4742i			1.37941i
$905$		0			0
$906$			31.2115i			1.03693i
$907$	−53.1209			−1.76385			−0.881926	−	0.471388i	$-0.843753\pi$
$907$	−53.1209			−1.76385			−0.881926	+	0.471388i	$0.843753\pi$
$908$	−0.743063			−0.0246594
$909$	7.69515			0.255232
$910$		0			0
$911$			47.7278i			1.58129i	0.612273	+	0.790647i	$0.290255\pi$
$911$			47.7278i			1.58129i	−0.612273	+	0.790647i	$0.709745\pi$
$912$	17.0272			0.563827
$913$	6.14612			0.203407
$914$	44.7133			1.47899
$915$		0			0
$916$	−3.47088			−0.114681
$917$			3.88672i			0.128351i
$918$	−1.48964	+	6.20045i	−0.0491656	+	0.204645i
$919$	−1.14793			−0.0378667			−0.0189334	−	0.999821i	$-0.506027\pi$
$919$	−1.14793			−0.0378667			−0.0189334	+	0.999821i	$0.506027\pi$
$920$		0			0
$921$			5.76186i			0.189860i
$922$		−	24.5868i		−	0.809723i
$923$	−44.4912			−1.46445
$924$		−	0.164597i		−	0.00541484i
$925$		0			0
$926$	46.0776			1.51420
$927$			5.66786i			0.186157i
$928$	14.4733			0.475108
$929$			27.1035i			0.889237i	0.895720	+	0.444619i	$0.146661\pi$
$929$			27.1035i			0.889237i	−0.895720	+	0.444619i	$0.853339\pi$
$930$		0			0
$931$	−25.0613			−0.821349
$932$	−10.2063			−0.334319
$933$		−	24.9984i		−	0.818412i
$934$	−3.84038			−0.125661
$935$		0			0
$936$	−12.8388			−0.419650
$937$		−	48.1087i		−	1.57164i	−0.618453	−	0.785822i	$-0.712240\pi$
$937$		−	48.1087i		−	1.57164i	0.618453	−	0.785822i	$-0.287760\pi$
$938$	−2.95126			−0.0963619
$939$	−3.42518			−0.111776
$940$		0			0
$941$		−	31.7723i		−	1.03575i	−0.855457	−	0.517873i	$-0.826724\pi$
$941$		−	31.7723i		−	1.03575i	0.855457	−	0.517873i	$-0.173276\pi$
$942$	−12.5037			−0.407392
$943$			4.18090i			0.136149i
$944$	−3.90328			−0.127041
$945$		0			0
$946$		−	10.2802i		−	0.334239i
$947$	34.4567			1.11969			0.559846	−	0.828596i	$-0.310860\pi$
$947$	34.4567			1.11969			0.559846	+	0.828596i	$0.310860\pi$
$948$		−	0.969859i		−	0.0314996i
$949$			36.4866i			1.18440i
$950$		0			0
$951$	23.7739			0.770921
$952$	−1.02981	+	4.28644i	−0.0333762	+	0.138924i
$953$		−	30.1023i		−	0.975110i	−0.873092	−	0.487555i	$-0.837889\pi$
$953$		−	30.1023i		−	0.975110i	0.873092	−	0.487555i	$-0.162111\pi$
$954$	−12.2765			−0.397467
$955$		0			0
$956$	−9.43496			−0.305149
$957$	−6.46081			−0.208848
$958$	−33.0019			−1.06624
$959$		−	6.36723i		−	0.205609i
$960$		0			0
$961$	−51.4355			−1.65921
$962$	61.6528			1.98776
$963$	11.2117			0.361294
$964$			4.39441i			0.141534i
$965$		0			0
$966$			0.317377i			0.0102115i
$967$			33.5567i			1.07911i	0.841951	+	0.539555i	$0.181407\pi$
$967$			33.5567i			1.07911i	−0.841951	+	0.539555i	$0.818593\pi$
$968$		−	24.9843i		−	0.803027i
$969$	−14.7423	−	3.54181i	−0.473592	−	0.113779i
$970$		0			0
$971$	22.5468			0.723561			0.361780	−	0.932263i	$-0.382169\pi$
$971$	22.5468			0.723561			0.361780	+	0.932263i	$0.382169\pi$
$972$	0.392039			0.0125747
$973$			5.24167i			0.168040i
$974$		−	64.0121i		−	2.05108i
$975$		0			0
$976$		−	19.6766i		−	0.629832i
$977$		−	48.7390i		−	1.55930i	−0.626217	−	0.779649i	$-0.715397\pi$
$977$		−	48.7390i		−	1.55930i	0.626217	−	0.779649i	$-0.284603\pi$
$978$			22.9180i			0.732836i
$979$		−	5.44272i		−	0.173950i
$980$		0			0
$981$			3.24392i			0.103570i
$982$			24.0813i			0.768466i
$983$	−27.7107			−0.883836			−0.441918	−	0.897056i	$-0.645702\pi$
$983$	−27.7107			−0.883836			−0.441918	+	0.897056i	$0.645702\pi$
$984$	21.7839			0.694444
$985$		0			0
$986$	−41.0218	−	9.85540i	−1.30640	−	0.313860i
$987$		−	2.04756i		−	0.0651746i
$988$			7.44254i			0.236779i
$989$			3.24876i			0.103305i
$990$		0			0
$991$			44.7839i			1.42261i	0.702884	+	0.711304i	$0.251895\pi$
$991$			44.7839i			1.42261i	−0.702884	+	0.711304i	$0.748105\pi$
$992$	−19.8624			−0.630633
$993$	−9.57377			−0.303814
$994$	5.73047			0.181760
$995$		0			0
$996$		−	2.46737i		−	0.0781817i
$997$	−24.6416			−0.780408			−0.390204	−	0.920728i	$-0.627595\pi$
$997$	−24.6416			−0.780408			−0.390204	+	0.920728i	$0.627595\pi$
$998$	43.8393			1.38771
$999$	7.72152			0.244298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1275.2.d.i.424.4		12
5.2	odd	4		1275.2.g.f.526.10	yes	12
5.3	odd	4		1275.2.g.e.526.3	✓	12
5.4	even	2		1275.2.d.j.424.9		12
17.16	even	2		1275.2.d.j.424.4		12
85.33	odd	4		1275.2.g.e.526.4	yes	12
85.67	odd	4		1275.2.g.f.526.9	yes	12
85.84	even	2	inner	1275.2.d.i.424.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1275.2.d.i.424.4		12	1.1	even	1	trivial
1275.2.d.i.424.9		12	85.84	even	2	inner
1275.2.d.j.424.4		12	17.16	even	2
1275.2.d.j.424.9		12	5.4	even	2
1275.2.g.e.526.3	✓	12	5.3	odd	4
1275.2.g.e.526.4	yes	12	85.33	odd	4
1275.2.g.f.526.9	yes	12	85.67	odd	4
1275.2.g.f.526.10	yes	12	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1275.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.54662i q^{2} -1.00000 q^{3} -0.392039 q^{4} +1.54662i q^{6} -0.429930 q^{7} -2.48691i q^{8} +1.00000 q^{9} +0.976552i q^{11} +0.392039 q^{12} -5.16256i q^{13} +0.664939i q^{14} -4.63038 q^{16} +(4.00903 + 0.963160i) q^{17} -1.54662i q^{18} +3.67728 q^{19} +0.429930 q^{21} +1.51036 q^{22} -0.477303 q^{23} +2.48691i q^{24} -7.98453 q^{26} -1.00000 q^{27} +0.168549 q^{28} -6.61594i q^{29} +9.07940i q^{31} +2.18764i q^{32} -0.976552i q^{33} +(1.48964 - 6.20045i) q^{34} -0.392039 q^{36} -7.72152 q^{37} -5.68736i q^{38} +5.16256i q^{39} -8.75942i q^{41} -0.664939i q^{42} -6.80650i q^{43} -0.382846i q^{44} +0.738207i q^{46} -4.76254i q^{47} +4.63038 q^{48} -6.81516 q^{49} +(-4.00903 - 0.963160i) q^{51} +2.02392i q^{52} -7.93763i q^{53} +1.54662i q^{54} +1.06920i q^{56} -3.67728 q^{57} -10.2324 q^{58} +0.842970 q^{59} +4.24945i q^{61} +14.0424 q^{62} -0.429930 q^{63} -5.87732 q^{64} -1.51036 q^{66} +4.43839i q^{67} +(-1.57170 - 0.377596i) q^{68} +0.477303 q^{69} -8.61804i q^{71} -2.48691i q^{72} -7.06754 q^{73} +11.9423i q^{74} -1.44164 q^{76} -0.419849i q^{77} +7.98453 q^{78} -2.47389i q^{79} +1.00000 q^{81} -13.5475 q^{82} -6.29370i q^{83} -0.168549 q^{84} -10.5271 q^{86} +6.61594i q^{87} +2.42859 q^{88} -5.57341 q^{89} +2.21954i q^{91} +0.187121 q^{92} -9.07940i q^{93} -7.36585 q^{94} -2.18764i q^{96} -3.74952 q^{97} +10.5405i q^{98} +0.976552i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{3} - 16 q^{4} + 12 q^{9} + 16 q^{12} + 32 q^{16} - 6 q^{17} + 4 q^{19} + 12 q^{22} - 16 q^{23} - 36 q^{26} - 12 q^{27} - 36 q^{28} + 24 q^{34} - 16 q^{36} - 4 q^{37} - 32 q^{48} + 16 q^{49}+ \cdots - 16 q^{97}+O(q^{100}) \) 12 * q - 12 * q^3 - 16 * q^4 + 12 * q^9 + 16 * q^12 + 32 * q^16 - 6 * q^17 + 4 * q^19 + 12 * q^22 - 16 * q^23 - 36 * q^26 - 12 * q^27 - 36 * q^28 + 24 * q^34 - 16 * q^36 - 4 * q^37 - 32 * q^48 + 16 * q^49 + 6 * q^51 - 4 * q^57 + 4 * q^58 - 32 * q^59 - 56 * q^62 - 56 * q^64 - 12 * q^66 - 20 * q^68 + 16 * q^69 + 44 * q^73 + 64 * q^76 + 36 * q^78 + 12 * q^81 - 40 * q^82 + 36 * q^84 + 20 * q^86 - 8 * q^88 - 4 * q^89 - 40 * q^94 - 16 * q^97

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