LMFDB - Embedded newform 1275.2.g.e.526.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1275,2,Mod(526,1275)] 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, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1275.526"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1275 = 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1275.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,16,0,0,0,0,-12,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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			526.3
Root			$-1.54662i$ of defining polynomial
Character	$\chi$	$=$	1275.526
Dual form			1275.2.g.e.526.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.54662 q^{2} -1.00000i q^{3} +0.392039 q^{4} +1.54662i q^{6} +0.429930i q^{7} +2.48691 q^{8} -1.00000 q^{9} +0.976552i q^{11} -0.392039i q^{12} +5.16256 q^{13} -0.664939i q^{14} -4.63038 q^{16} +(0.963160 - 4.00903i) q^{17} +1.54662 q^{18} -3.67728 q^{19} +0.429930 q^{21} -1.51036i q^{22} -0.477303i q^{23} -2.48691i q^{24} -7.98453 q^{26} +1.00000i q^{27} +0.168549i q^{28} +6.61594i q^{29} +9.07940i q^{31} +2.18764 q^{32} +0.976552 q^{33} +(-1.48964 + 6.20045i) q^{34} -0.392039 q^{36} +7.72152i q^{37} +5.68736 q^{38} -5.16256i q^{39} -8.75942i q^{41} -0.664939 q^{42} +6.80650 q^{43} +0.382846i q^{44} +0.738207i q^{46} -4.76254 q^{47} +4.63038i q^{48} +6.81516 q^{49} +(-4.00903 - 0.963160i) q^{51} +2.02392 q^{52} +7.93763 q^{53} -1.54662i q^{54} +1.06920i q^{56} +3.67728i q^{57} -10.2324i q^{58} -0.842970 q^{59} +4.24945i q^{61} -14.0424i q^{62} -0.429930i q^{63} +5.87732 q^{64} -1.51036 q^{66} +4.43839 q^{67} +(0.377596 - 1.57170i) q^{68} -0.477303 q^{69} -8.61804i q^{71} -2.48691 q^{72} -7.06754i q^{73} -11.9423i q^{74} -1.44164 q^{76} -0.419849 q^{77} +7.98453i q^{78} +2.47389i q^{79} +1.00000 q^{81} +13.5475i q^{82} +6.29370 q^{83} +0.168549 q^{84} -10.5271 q^{86} +6.61594 q^{87} +2.42859i q^{88} +5.57341 q^{89} +2.21954i q^{91} -0.187121i q^{92} +9.07940 q^{93} +7.36585 q^{94} -2.18764i q^{96} +3.74952i q^{97} -10.5405 q^{98} -0.976552i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{4} - 12 q^{9} - 4 q^{13} + 32 q^{16} + 10 q^{17} - 4 q^{19} - 36 q^{26} - 20 q^{32} - 12 q^{33} - 24 q^{34} - 16 q^{36} - 44 q^{38} + 28 q^{42} + 28 q^{43} - 16 q^{47} - 16 q^{49} + 6 q^{51}+ \cdots - 8 q^{98}+O(q^{100}) $ 12 * q + 16 * q^4 - 12 * q^9 - 4 * q^13 + 32 * q^16 + 10 * q^17 - 4 * q^19 - 36 * q^26 - 20 * q^32 - 12 * q^33 - 24 * q^34 - 16 * q^36 - 44 * q^38 + 28 * q^42 + 28 * q^43 - 16 * q^47 - 16 * q^49 + 6 * q^51 + 16 * q^52 - 12 * q^53 + 32 * q^59 + 56 * q^64 - 12 * q^66 - 20 * q^67 + 56 * q^68 - 16 * q^69 + 64 * q^76 - 72 * q^77 + 12 * q^81 - 44 * q^83 - 36 * q^84 + 20 * q^86 + 32 * q^87 + 4 * q^89 + 8 * q^93 + 40 * q^94 - 8 * q^98

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 $

$2$	−1.54662			−1.09363			−0.546813	−	0.837255i	$-0.684159\pi$
$2$	−1.54662			−1.09363			−0.546813	+	0.837255i	$0.684159\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.392039			0.196019
$5$		0			0
$5$		0			0
$6$			1.54662i			0.631406i
$7$			0.429930i			0.162498i	0.996694	+	0.0812491i	$0.0258909\pi$
$7$			0.429930i			0.162498i	−0.996694	+	0.0812491i	$0.974109\pi$
$8$	2.48691			0.879255
$9$	−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	$0.952967\pi$
$12$		−	0.392039i		−	0.113172i
$13$	5.16256			1.43184			0.715919	−	0.698184i	$-0.246008\pi$
$13$	5.16256			1.43184			0.715919	+	0.698184i	$0.246008\pi$
$14$		−	0.664939i		−	0.177712i
$15$		0			0
$16$	−4.63038			−1.15760
$17$	0.963160	−	4.00903i	0.233601	−	0.972333i
$17$	0.963160	−	4.00903i	0.233601	−	0.972333i
$18$	1.54662			0.364542
$19$	−3.67728			−0.843626			−0.421813	−	0.906683i	$-0.638606\pi$
$19$	−3.67728			−0.843626			−0.421813	+	0.906683i	$0.638606\pi$
$20$		0			0
$21$	0.429930			0.0938184
$22$		−	1.51036i		−	0.322009i
$23$		−	0.477303i		−	0.0995246i	−0.998761	−	0.0497623i	$-0.984154\pi$
$23$		−	0.477303i		−	0.0995246i	0.998761	−	0.0497623i	$-0.0158464\pi$
$24$		−	2.48691i		−	0.507638i
$25$		0			0
$26$	−7.98453			−1.56590
$27$			1.00000i			0.192450i
$28$			0.168549i			0.0318528i
$29$			6.61594i			1.22855i	0.789092	+	0.614275i	$0.210551\pi$
$29$			6.61594i			1.22855i	−0.789092	+	0.614275i	$0.789449\pi$
$30$		0			0
$31$			9.07940i			1.63071i	0.578962	+	0.815354i	$0.303458\pi$
$31$			9.07940i			1.63071i	−0.578962	+	0.815354i	$0.696542\pi$
$32$	2.18764			0.386723
$33$	0.976552			0.169996
$34$	−1.48964	+	6.20045i	−0.255472	+	1.06337i
$35$		0			0
$36$	−0.392039			−0.0653398
$37$			7.72152i			1.26941i	0.772754	+	0.634705i	$0.218879\pi$
$37$			7.72152i			1.26941i	−0.772754	+	0.634705i	$0.781121\pi$
$38$	5.68736			0.922612
$39$		−	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	$-0.239759\pi$
$42$	−0.664939			−0.102602
$43$	6.80650			1.03798			0.518991	−	0.854780i	$-0.326308\pi$
$43$	6.80650			1.03798			0.518991	+	0.854780i	$0.326308\pi$
$44$			0.382846i			0.0577162i
$45$		0			0
$46$			0.738207i			0.108843i
$47$	−4.76254			−0.694688			−0.347344	−	0.937738i	$-0.612916\pi$
$47$	−4.76254			−0.694688			−0.347344	+	0.937738i	$0.612916\pi$
$48$			4.63038i			0.668338i
$49$	6.81516			0.973594
$50$		0			0
$51$	−4.00903	−	0.963160i	−0.561377	−	0.134869i
$52$	2.02392			0.280668
$53$	7.93763			1.09032			0.545159	−	0.838333i	$-0.316469\pi$
$53$	7.93763			1.09032			0.545159	+	0.838333i	$0.316469\pi$
$54$		−	1.54662i		−	0.210469i
$55$		0			0
$56$			1.06920i			0.142877i
$57$			3.67728i			0.487068i
$58$		−	10.2324i		−	1.34357i
$59$	−0.842970			−0.109745			−0.0548727	−	0.998493i	$-0.517475\pi$
$59$	−0.842970			−0.109745			−0.0548727	+	0.998493i	$0.517475\pi$
$60$		0			0
$61$			4.24945i			0.544087i	0.962285	+	0.272043i	$0.0876994\pi$
$61$			4.24945i			0.544087i	−0.962285	+	0.272043i	$0.912301\pi$
$62$		−	14.0424i		−	1.78339i
$63$		−	0.429930i		−	0.0541661i
$64$	5.87732			0.734665
$65$		0			0
$66$	−1.51036			−0.185912
$67$	4.43839			0.542235			0.271118	−	0.962546i	$-0.412607\pi$
$67$	4.43839			0.542235			0.271118	+	0.962546i	$0.412607\pi$
$68$	0.377596	−	1.57170i	0.0457902	−	0.190596i
$69$	−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	$-0.170868\pi$
$72$	−2.48691			−0.293085
$73$		−	7.06754i		−	0.827192i	−0.910460	−	0.413596i	$-0.864273\pi$
$73$		−	7.06754i		−	0.827192i	0.910460	−	0.413596i	$-0.135727\pi$
$74$		−	11.9423i		−	1.38826i
$75$		0			0
$76$	−1.44164			−0.165367
$77$	−0.419849			−0.0478462
$78$			7.98453i			0.904070i
$79$			2.47389i			0.278334i	0.990269	+	0.139167i	$0.0444425\pi$
$79$			2.47389i			0.278334i	−0.990269	+	0.139167i	$0.955558\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$			13.5475i			1.49607i
$83$	6.29370			0.690823			0.345411	−	0.938451i	$-0.387739\pi$
$83$	6.29370			0.690823			0.345411	+	0.938451i	$0.387739\pi$
$84$	0.168549			0.0183902
$85$		0			0
$86$	−10.5271			−1.13516
$87$	6.61594			0.709303
$88$			2.42859i			0.258889i
$89$	5.57341			0.590780			0.295390	−	0.955377i	$-0.404550\pi$
$89$	5.57341			0.590780			0.295390	+	0.955377i	$0.404550\pi$
$90$		0			0
$91$			2.21954i			0.232671i
$92$		−	0.187121i		−	0.0195087i
$93$	9.07940			0.941490
$94$	7.36585			0.759730
$95$		0			0
$96$		−	2.18764i		−	0.223275i
$97$			3.74952i			0.380706i	0.981716	+	0.190353i	$0.0609633\pi$
$97$			3.74952i			0.380706i	−0.981716	+	0.190353i	$0.939037\pi$
$98$	−10.5405			−1.06475
$99$		−	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	$0.374943\pi$
$102$	6.20045	+	1.48964i	0.613936	+	0.147497i
$103$	−5.66786			−0.558471			−0.279236	−	0.960223i	$-0.590081\pi$
$103$	−5.66786			−0.558471			−0.279236	+	0.960223i	$0.590081\pi$
$104$	12.8388			1.25895
$105$		0			0
$106$	−12.2765			−1.19240
$107$		−	11.2117i		−	1.08388i	−0.840417	−	0.541940i	$-0.817690\pi$
$107$		−	11.2117i		−	1.08388i	0.840417	−	0.541940i	$-0.182310\pi$
$108$			0.392039i			0.0377240i
$109$		−	3.24392i		−	0.310711i	−0.987859	−	0.155356i	$-0.950348\pi$
$109$		−	3.24392i		−	0.310711i	0.987859	−	0.155356i	$-0.0496523\pi$
$110$		0			0
$111$	7.72152			0.732895
$112$		−	1.99074i		−	0.188107i
$113$		−	16.6770i		−	1.56884i	−0.620229	−	0.784421i	$-0.712960\pi$
$113$		−	16.6770i		−	1.56884i	0.620229	−	0.784421i	$-0.287040\pi$
$114$		−	5.68736i		−	0.532670i
$115$		0			0
$116$			2.59371i			0.240820i
$117$	−5.16256			−0.477279
$118$	1.30376			0.120020
$119$	1.72360	+	0.414091i	0.158002	+	0.0379597i
$120$		0			0
$121$	10.0463			0.913304
$122$		−	6.57229i		−	0.595028i
$123$	−8.75942			−0.789810
$124$			3.55948i			0.319650i
$125$		0			0
$126$			0.664939i			0.0592375i
$127$	10.2257			0.907385			0.453693	−	0.891158i	$-0.350106\pi$
$127$	10.2257			0.907385			0.453693	+	0.891158i	$0.350106\pi$
$128$	−13.4653			−1.19017
$129$		−	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	$-0.129231\pi$
$132$	0.382846			0.0333225
$133$		−	1.58097i		−	0.137088i
$134$	−6.86450			−0.593003
$135$		0			0
$136$	2.39529	−	9.97009i	0.205394	−	0.854928i
$137$	14.8099			1.26530			0.632649	−	0.774439i	$-0.281968\pi$
$137$	14.8099			1.26530			0.632649	+	0.774439i	$0.281968\pi$
$138$	0.738207			0.0628404
$139$			12.1919i			1.03410i	0.855954	+	0.517052i	$0.172971\pi$
$139$			12.1919i			1.03410i	−0.855954	+	0.517052i	$0.827029\pi$
$140$		0			0
$141$			4.76254i			0.401079i
$142$			13.3289i			1.11853i
$143$			5.04151i			0.421592i
$144$	4.63038			0.385865
$145$		0			0
$146$			10.9308i			0.904640i
$147$		−	6.81516i		−	0.562105i
$148$			3.02714i			0.248829i
$149$	−2.53733			−0.207866			−0.103933	−	0.994584i	$-0.533143\pi$
$149$	−2.53733			−0.207866			−0.103933	+	0.994584i	$0.533143\pi$
$150$		0			0
$151$	20.1805			1.64226			0.821131	−	0.570739i	$-0.193343\pi$
$151$	20.1805			1.64226			0.821131	+	0.570739i	$0.193343\pi$
$152$	−9.14506			−0.741762
$153$	−0.963160	+	4.00903i	−0.0778669	+	0.324111i
$154$	0.649347			0.0523259
$155$		0			0
$156$		−	2.02392i		−	0.162044i
$157$	8.08452			0.645215			0.322607	−	0.946533i	$-0.395441\pi$
$157$	8.08452			0.645215			0.322607	+	0.946533i	$0.395441\pi$
$158$		−	3.82617i		−	0.304393i
$159$		−	7.93763i		−	0.629495i
$160$		0			0
$161$	0.205207			0.0161726
$162$	−1.54662			−0.121514
$163$			14.8181i			1.16064i	0.814388	+	0.580321i	$0.197073\pi$
$163$			14.8181i			1.16064i	−0.814388	+	0.580321i	$0.802927\pi$
$164$		−	3.43403i		−	0.268153i
$165$		0			0
$166$	−9.73397			−0.755502
$167$			1.83612i			0.142083i	0.997473	+	0.0710417i	$0.0226323\pi$
$167$			1.83612i			0.142083i	−0.997473	+	0.0710417i	$0.977368\pi$
$168$	1.06920			0.0824903
$169$	13.6520			1.05016
$170$		0			0
$171$	3.67728			0.281209
$172$	2.66841			0.203465
$173$			16.5137i			1.25551i	0.778409	+	0.627757i	$0.216027\pi$
$173$			16.5137i			1.25551i	−0.778409	+	0.627757i	$0.783973\pi$
$174$	−10.2324			−0.775713
$175$		0			0
$176$		−	4.52181i		−	0.340844i
$177$			0.842970i			0.0633615i
$178$	−8.61995			−0.646093
$179$	8.48016			0.633837			0.316919	−	0.948453i	$-0.397352\pi$
$179$	8.48016			0.633837			0.316919	+	0.948453i	$0.397352\pi$
$180$		0			0
$181$			11.2829i			0.838649i	0.907836	+	0.419325i	$0.137733\pi$
$181$			11.2829i			0.838649i	−0.907836	+	0.419325i	$0.862267\pi$
$182$		−	3.43279i		−	0.254455i
$183$	4.24945			0.314129
$184$		−	1.18701i		−	0.0875074i
$185$		0			0
$186$	−14.0424			−1.02964
$187$	3.91503	+	0.940575i	0.286295	+	0.0687817i
$188$	−1.86710			−0.136172
$189$	−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	$0.464959\pi$
$192$		−	5.87732i		−	0.424159i
$193$		−	23.9780i		−	1.72598i	−0.505225	−	0.862988i	$-0.668591\pi$
$193$		−	23.9780i		−	1.72598i	0.505225	−	0.862988i	$-0.331409\pi$
$194$		−	5.79909i		−	0.416351i
$195$		0			0
$196$	2.67181			0.190843
$197$		−	8.42347i		−	0.600147i	−0.953916	−	0.300074i	$-0.902989\pi$
$197$		−	8.42347i		−	0.600147i	0.953916	−	0.300074i	$-0.0970112\pi$
$198$			1.51036i			0.107336i
$199$			26.2107i			1.85803i	0.370042	+	0.929015i	$0.379343\pi$
$199$			26.2107i			1.85803i	−0.370042	+	0.929015i	$0.620657\pi$
$200$		0			0
$201$		−	4.43839i		−	0.313060i
$202$	−11.9015			−0.837386
$203$	−2.84439			−0.199637
$204$	−1.57170	−	0.377596i	−0.110041	−	0.0264370i
$205$		0			0
$206$	8.76604			0.610759
$207$			0.477303i			0.0331749i
$208$	−23.9046			−1.65749
$209$		−	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	$0.952135\pi$
$212$	3.11186			0.213723
$213$	−8.61804			−0.590499
$214$			17.3403i			1.18536i
$215$		0			0
$216$			2.48691i			0.169213i
$217$	−3.90351			−0.264987
$218$			5.01712i			0.339802i
$219$	−7.06754			−0.477580
$220$		0			0
$221$	4.97237	−	20.6969i	0.334478	−	1.39222i
$222$	−11.9423			−0.801513
$223$	−3.48378			−0.233291			−0.116646	−	0.993174i	$-0.537214\pi$
$223$	−3.48378			−0.233291			−0.116646	+	0.993174i	$0.537214\pi$
$224$			0.940530i			0.0628418i
$225$		0			0
$226$			25.7930i			1.71573i
$227$		−	1.89538i		−	0.125801i	−0.998020	−	0.0629004i	$-0.979965\pi$
$227$		−	1.89538i		−	0.125801i	0.998020	−	0.0629004i	$-0.0200351\pi$
$228$			1.44164i			0.0954747i
$229$	−8.85340			−0.585049			−0.292524	−	0.956258i	$-0.594495\pi$
$229$	−8.85340			−0.585049			−0.292524	+	0.956258i	$0.594495\pi$
$230$		0			0
$231$			0.419849i			0.0276240i
$232$			16.4532i			1.08021i
$233$			26.0340i			1.70554i	0.522285	+	0.852771i	$0.325080\pi$
$233$			26.0340i			1.70554i	−0.522285	+	0.852771i	$0.674920\pi$
$234$	7.98453			0.521965
$235$		0			0
$236$	−0.330477			−0.0215122
$237$	2.47389			0.160696
$238$	−2.66576	−	0.640443i	−0.172796	−	0.0415137i
$239$	−24.0664			−1.55673			−0.778363	−	0.627815i	$-0.783950\pi$
$239$	−24.0664			−1.55673			−0.778363	+	0.627815i	$0.783950\pi$
$240$		0			0
$241$		−	11.2091i		−	0.722042i	−0.932558	−	0.361021i	$-0.882428\pi$
$241$		−	11.2091i		−	0.722042i	0.932558	−	0.361021i	$-0.117572\pi$
$242$	−15.5379			−0.998814
$243$		−	1.00000i		−	0.0641500i
$244$			1.66595i			0.106652i
$245$		0			0
$246$	13.5475			0.863757
$247$	−18.9842			−1.20793
$248$			22.5796i			1.43381i
$249$		−	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	$0.149098\pi$
$252$		−	0.168549i		−	0.0106176i
$253$	0.466111			0.0293042
$254$	−15.8153			−0.992341
$255$		0			0
$256$	9.07103			0.566939
$257$	5.51730			0.344159			0.172080	−	0.985083i	$-0.444951\pi$
$257$	5.51730			0.344159			0.172080	+	0.985083i	$0.444951\pi$
$258$			10.5271i			0.655387i
$259$	−3.31971			−0.206277
$260$		0			0
$261$		−	6.61594i		−	0.409516i
$262$			13.9820i			0.863812i
$263$	−16.0439			−0.989310			−0.494655	−	0.869089i	$-0.664706\pi$
$263$	−16.0439			−0.989310			−0.494655	+	0.869089i	$0.664706\pi$
$264$	2.42859			0.149470
$265$		0			0
$266$			2.44517i			0.149923i
$267$		−	5.57341i		−	0.341087i
$268$	1.74002			0.106289
$269$			7.17003i			0.437165i	0.975819	+	0.218582i	$0.0701432\pi$
$269$			7.17003i			0.437165i	−0.975819	+	0.218582i	$0.929857\pi$
$270$		0			0
$271$	7.17160			0.435643			0.217822	−	0.975989i	$-0.430105\pi$
$271$	7.17160			0.435643			0.217822	+	0.975989i	$0.430105\pi$
$272$	−4.45980	+	18.5633i	−0.270415	+	1.12557i
$273$	2.21954			0.134333
$274$	−22.9054			−1.38376
$275$		0			0
$276$	−0.187121			−0.0112634
$277$		−	24.1787i		−	1.45275i	−0.687296	−	0.726377i	$-0.741203\pi$
$277$		−	24.1787i		−	1.45275i	0.687296	−	0.726377i	$-0.258797\pi$
$278$		−	18.8563i		−	1.13092i
$279$		−	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	$0.818976\pi$
$282$		−	7.36585i		−	0.438630i
$283$		−	32.2601i		−	1.91766i	−0.283973	−	0.958832i	$-0.591653\pi$
$283$		−	32.2601i		−	1.91766i	0.283973	−	0.958832i	$-0.408347\pi$
$284$		−	3.37861i		−	0.200483i
$285$		0			0
$286$		−	7.79731i		−	0.461064i
$287$	3.76594			0.222296
$288$	−2.18764			−0.128908
$289$	−15.1446	−	7.72267i	−0.890862	−	0.454275i
$290$		0			0
$291$	3.74952			0.219801
$292$		−	2.77075i		−	0.162146i
$293$	26.0057			1.51927			0.759636	−	0.650349i	$-0.225377\pi$
$293$	26.0057			1.51927			0.759636	+	0.650349i	$0.225377\pi$
$294$			10.5405i			0.614733i
$295$		0			0
$296$			19.2027i			1.11614i
$297$	−0.976552			−0.0566653
$298$	3.92428			0.227328
$299$		−	2.46411i		−	0.142503i
$300$		0			0
$301$			2.92632i			0.168670i
$302$	−31.2115			−1.79602
$303$		−	7.69515i		−	0.442075i
$304$	17.0272			0.976578
$305$		0			0
$306$	1.48964	−	6.20045i	0.0851573	−	0.354456i
$307$	−5.76186			−0.328847			−0.164423	−	0.986390i	$-0.552576\pi$
$307$	−5.76186			−0.328847			−0.164423	+	0.986390i	$0.552576\pi$
$308$	−0.164597			−0.00937879
$309$			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	$0.749252\pi$
$312$		−	12.8388i		−	0.726855i
$313$			3.42518i			0.193602i	0.995304	+	0.0968012i	$0.0308611\pi$
$313$			3.42518i			0.193602i	−0.995304	+	0.0968012i	$0.969139\pi$
$314$	−12.5037			−0.705624
$315$		0			0
$316$			0.969859i			0.0545588i
$317$			23.7739i			1.33527i	0.744487	+	0.667637i	$0.232694\pi$
$317$			23.7739i			1.33527i	−0.744487	+	0.667637i	$0.767306\pi$
$318$			12.2765i			0.688433i
$319$	−6.46081			−0.361736
$320$		0			0
$321$	−11.2117			−0.625779
$322$	−0.317377			−0.0176868
$323$	−3.54181	+	14.7423i	−0.197071	+	0.820285i
$324$	0.392039			0.0217799
$325$		0			0
$326$		−	22.9180i		−	1.26931i
$327$	−3.24392			−0.179389
$328$		−	21.7839i		−	1.20281i
$329$		−	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	$0.415251\pi$
$332$	2.46737			0.135415
$333$		−	7.72152i		−	0.423137i
$334$		−	2.83979i		−	0.155386i
$335$		0			0
$336$	−1.99074			−0.108604
$337$		−	18.1726i		−	0.989927i	−0.868914	−	0.494963i	$-0.835181\pi$
$337$		−	18.1726i		−	0.989927i	0.868914	−	0.494963i	$-0.164819\pi$
$338$	−21.1146			−1.14848
$339$	−16.6770			−0.905771
$340$		0			0
$341$	−8.86650			−0.480148
$342$	−5.68736			−0.307537
$343$			5.93955i			0.320706i
$344$	16.9271			0.912650
$345$		0			0
$346$		−	25.5405i		−	1.37306i
$347$			23.2530i			1.24828i	0.781311	+	0.624142i	$0.214551\pi$
$347$			23.2530i			1.24828i	−0.781311	+	0.624142i	$0.785449\pi$
$348$	2.59371			0.139037
$349$	−32.9277			−1.76258			−0.881290	−	0.472575i	$-0.843324\pi$
$349$	−32.9277			−1.76258			−0.881290	+	0.472575i	$0.843324\pi$
$350$		0			0
$351$			5.16256i			0.275557i
$352$			2.13634i			0.113867i
$353$	−6.76112			−0.359858			−0.179929	−	0.983680i	$-0.557587\pi$
$353$	−6.76112			−0.359858			−0.179929	+	0.983680i	$0.557587\pi$
$354$		−	1.30376i		−	0.0692939i
$355$		0			0
$356$	2.18499			0.115804
$357$	0.414091	−	1.72360i	0.0219160	−	0.0912227i
$358$	−13.1156			−0.693181
$359$	−25.2197			−1.33104			−0.665521	−	0.746379i	$-0.731791\pi$
$359$	−25.2197			−1.33104			−0.665521	+	0.746379i	$0.731791\pi$
$360$		0			0
$361$	−5.47761			−0.288295
$362$		−	17.4503i		−	0.917169i
$363$		−	10.0463i		−	0.527296i
$364$			0.870146i			0.0456080i
$365$		0			0
$366$	−6.57229			−0.343539
$367$			8.08168i			0.421860i	0.977501	+	0.210930i	$0.0676493\pi$
$367$			8.08168i			0.421860i	−0.977501	+	0.210930i	$0.932351\pi$
$368$			2.21010i			0.115209i
$369$			8.75942i			0.455997i
$370$		0			0
$371$			3.41263i			0.177175i
$372$	3.55948			0.184550
$373$	−17.1991			−0.890537			−0.445268	−	0.895397i	$-0.646892\pi$
$373$	−17.1991			−0.890537			−0.445268	+	0.895397i	$0.646892\pi$
$374$	−6.05506	−	1.45471i	−0.313100	−	0.0752215i
$375$		0			0
$376$	−11.8440			−0.610808
$377$			34.1552i			1.75908i
$378$	0.664939			0.0342008
$379$			0.531420i			0.0272972i	0.999907	+	0.0136486i	$0.00434462\pi$
$379$			0.531420i			0.0272972i	−0.999907	+	0.0136486i	$0.995655\pi$
$380$		0			0
$381$		−	10.2257i		−	0.523879i
$382$	−4.69658			−0.240298
$383$	−0.874772			−0.0446988			−0.0223494	−	0.999750i	$-0.507115\pi$
$383$	−0.874772			−0.0446988			−0.0223494	+	0.999750i	$0.507115\pi$
$384$			13.4653i			0.687146i
$385$		0			0
$386$			37.0849i			1.88757i
$387$	−6.80650			−0.345994
$388$			1.46996i			0.0746258i
$389$	−24.9537			−1.26520			−0.632602	−	0.774477i	$-0.718013\pi$
$389$	−24.9537			−1.26520			−0.632602	+	0.774477i	$0.718013\pi$
$390$		0			0
$391$	−1.91352	−	0.459719i	−0.0967710	−	0.0232490i
$392$	16.9487			0.856037
$393$	−9.04036			−0.456026
$394$			13.0279i			0.656337i
$395$		0			0
$396$		−	0.382846i		−	0.0192387i
$397$		−	15.7628i		−	0.791111i	−0.918442	−	0.395555i	$-0.870552\pi$
$397$		−	15.7628i		−	0.791111i	0.918442	−	0.395555i	$-0.129448\pi$
$398$		−	40.5381i		−	2.03199i
$399$	−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	$-0.0866295\pi$
$402$			6.86450i			0.342370i
$403$			46.8730i			2.33491i
$404$	3.01680			0.150091
$405$		0			0
$406$	4.39920			0.218328
$407$	−7.54047			−0.373767
$408$	−9.97009	−	2.39529i	−0.493593	−	0.118585i
$409$	10.2591			0.507282			0.253641	−	0.967298i	$-0.418372\pi$
$409$	10.2591			0.507282			0.253641	+	0.967298i	$0.418372\pi$
$410$		0			0
$411$		−	14.8099i		−	0.730520i
$412$	−2.22202			−0.109471
$413$		−	0.362418i		−	0.0178334i
$414$		−	0.738207i		−	0.0362809i
$415$		0			0
$416$	11.2938			0.553724
$417$	12.1919			0.597041
$418$			5.55400i			0.271655i
$419$		−	32.3428i		−	1.58005i	−0.613074	−	0.790026i	$-0.710067\pi$
$419$		−	32.3428i		−	1.58005i	0.613074	−	0.790026i	$-0.289933\pi$
$420$		0			0
$421$	−26.4919			−1.29114			−0.645568	−	0.763703i	$-0.723379\pi$
$421$	−26.4919			−1.29114			−0.645568	+	0.763703i	$0.723379\pi$
$422$		−	6.73104i		−	0.327662i
$423$	4.76254			0.231563
$424$	19.7402			0.958667
$425$		0			0
$426$	13.3289			0.645785
$427$	−1.82697			−0.0884131
$428$		−	4.39544i		−	0.212462i
$429$	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	$-0.122397\pi$
$432$		−	4.63038i		−	0.222779i
$433$	36.6438			1.76099			0.880494	−	0.474057i	$-0.157211\pi$
$433$	36.6438			1.76099			0.880494	+	0.474057i	$0.157211\pi$
$434$	6.03725			0.289797
$435$		0			0
$436$		−	1.27174i		−	0.0609054i
$437$			1.75518i			0.0839615i
$438$	10.9308			0.522294
$439$			35.7519i			1.70634i	0.521630	+	0.853172i	$0.325324\pi$
$439$			35.7519i			1.70634i	−0.521630	+	0.853172i	$0.674676\pi$
$440$		0			0
$441$	−6.81516			−0.324531
$442$	−7.69038	+	32.0102i	−0.365794	+	1.52257i
$443$	16.8118			0.798753			0.399377	−	0.916787i	$-0.369227\pi$
$443$	16.8118			0.798753			0.399377	+	0.916787i	$0.369227\pi$
$444$	3.02714			0.143662
$445$		0			0
$446$	5.38809			0.255133
$447$			2.53733i			0.120011i
$448$			2.52684i			0.119382i
$449$		−	18.0607i		−	0.852337i	−0.904644	−	0.426169i	$-0.859863\pi$
$449$		−	18.0607i		−	0.852337i	0.904644	−	0.426169i	$-0.140137\pi$
$450$		0			0
$451$	8.55402			0.402793
$452$		−	6.53804i		−	0.307523i
$453$		−	20.1805i		−	0.948161i
$454$			2.93144i			0.137579i
$455$		0			0
$456$			9.14506i			0.428256i
$457$	28.9103			1.35237			0.676184	−	0.736733i	$-0.263632\pi$
$457$	28.9103			1.35237			0.676184	+	0.736733i	$0.263632\pi$
$458$	13.6929			0.639825
$459$	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	$0.379289\pi$
$462$		−	0.649347i		−	0.0302104i
$463$	−29.7924			−1.38457			−0.692285	−	0.721624i	$-0.743396\pi$
$463$	−29.7924			−1.38457			−0.692285	+	0.721624i	$0.743396\pi$
$464$		−	30.6343i		−	1.42216i
$465$		0			0
$466$		−	40.2647i		−	1.86523i
$467$	−2.48308			−0.114903			−0.0574516	−	0.998348i	$-0.518297\pi$
$467$	−2.48308			−0.114903			−0.0574516	+	0.998348i	$0.518297\pi$
$468$	−2.02392			−0.0935560
$469$			1.90819i			0.0881122i
$470$		0			0
$471$		−	8.08452i		−	0.372515i
$472$	−2.09639			−0.0964941
$473$			6.64690i			0.305625i
$474$	−3.82617			−0.175742
$475$		0			0
$476$	0.675719	+	0.162340i	0.0309715	+	0.00744083i
$477$	−7.93763			−0.363439
$478$	37.2216			1.70248
$479$			21.3380i			0.974960i	0.873134	+	0.487480i	$0.162084\pi$
$479$			21.3380i			0.974960i	−0.873134	+	0.487480i	$0.837916\pi$
$480$		0			0
$481$			39.8629i			1.81759i
$482$			17.3363i			0.789645i
$483$		−	0.205207i		−	0.00933724i
$484$	3.93856			0.179025
$485$		0			0
$486$			1.54662i			0.0701562i
$487$		−	41.3883i		−	1.87548i	−0.347333	−	0.937742i	$-0.612913\pi$
$487$		−	41.3883i		−	1.87548i	0.347333	−	0.937742i	$-0.387087\pi$
$488$			10.5680i			0.478391i
$489$	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	$0.614273\pi$
$492$	−3.43403			−0.154818
$493$	26.5235	+	6.37221i	1.19456	+	0.286990i
$494$	29.3614			1.32103
$495$		0			0
$496$		−	42.0411i		−	1.88770i
$497$	3.70515			0.166199
$498$			9.73397i			0.436190i
$499$		−	28.3452i		−	1.26891i	−0.772961	−	0.634453i	$-0.781225\pi$
$499$		−	28.3452i		−	1.26891i	0.772961	−	0.634453i	$-0.218775\pi$
$500$		0			0
$501$	1.83612			0.0820319
$502$	−43.7277			−1.95166
$503$			28.3949i			1.26606i	0.774125	+	0.633032i	$0.218190\pi$
$503$			28.3949i			1.26606i	−0.774125	+	0.633032i	$0.781810\pi$
$504$		−	1.06920i		−	0.0476258i
$505$		0			0
$506$	−0.720898			−0.0320478
$507$		−	13.6520i		−	0.606309i
$508$	4.00888			0.177865
$509$	15.6779			0.694909			0.347454	−	0.937697i	$-0.387046\pi$
$509$	15.6779			0.694909			0.347454	+	0.937697i	$0.387046\pi$
$510$		0			0
$511$	3.03854			0.134417
$512$	12.9011			0.570153
$513$		−	3.67728i		−	0.162356i
$514$	−8.53317			−0.376382
$515$		0			0
$516$		−	2.66841i		−	0.117470i
$517$		−	4.65087i		−	0.204545i
$518$	5.13434			0.225590
$519$	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	$0.834159\pi$
$522$			10.2324i			0.447858i
$523$	−22.3505			−0.977319			−0.488660	−	0.872475i	$-0.662514\pi$
$523$	−22.3505			−0.977319			−0.488660	+	0.872475i	$0.662514\pi$
$524$		−	3.54417i		−	0.154828i
$525$		0			0
$526$	24.8139			1.08194
$527$	36.3996	+	8.74491i	1.58559	+	0.380934i
$528$	−4.52181			−0.196786
$529$	22.7722			0.990095
$530$		0			0
$531$	0.842970			0.0365818
$532$		−	0.619803i		−	0.0268719i
$533$		−	45.2210i		−	1.95874i
$534$			8.61995i			0.373022i
$535$		0			0
$536$	11.0379			0.476763
$537$		−	8.48016i		−	0.365946i
$538$		−	11.0893i		−	0.478095i
$539$			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	$0.989755\pi$
$542$	−11.0917			−0.476431
$543$	11.2829			0.484194
$544$	2.10704	−	8.77030i	0.0903387	−	0.376023i
$545$		0			0
$546$	−3.43279			−0.146910
$547$			23.1972i			0.991843i	0.868367	+	0.495921i	$0.165170\pi$
$547$			23.1972i			0.991843i	−0.868367	+	0.495921i	$0.834830\pi$
$548$	5.80607			0.248023
$549$		−	4.24945i		−	0.181362i
$550$		0			0
$551$		−	24.3287i		−	1.03644i
$552$	−1.18701			−0.0505224
$553$	−1.06360			−0.0452288
$554$			37.3952i			1.58877i
$555$		0			0
$556$			4.77970i			0.202705i
$557$	44.8334			1.89965			0.949827	−	0.312777i	$-0.101259\pi$
$557$	44.8334			1.89965			0.949827	+	0.312777i	$0.101259\pi$
$558$			14.0424i			0.594462i
$559$	35.1390			1.48622
$560$		0			0
$561$	0.940575	−	3.91503i	0.0397111	−	0.165292i
$562$	43.6907			1.84298
$563$	−43.5968			−1.83739			−0.918694	−	0.394970i	$-0.870755\pi$
$563$	−43.5968			−1.83739			−0.918694	+	0.394970i	$0.870755\pi$
$564$			1.86710i			0.0786192i
$565$		0			0
$566$			49.8942i			2.09721i
$567$			0.429930i			0.0180554i
$568$		−	21.4323i		−	0.899278i
$569$	16.0087			0.671118			0.335559	−	0.942019i	$-0.391075\pi$
$569$	16.0087			0.671118			0.335559	+	0.942019i	$0.391075\pi$
$570$		0			0
$571$			46.0825i			1.92849i	0.265007	+	0.964246i	$0.414626\pi$
$571$			46.0825i			1.92849i	−0.265007	+	0.964246i	$0.585374\pi$
$572$			1.97647i			0.0826402i
$573$		−	3.03667i		−	0.126859i
$574$	−5.82448			−0.243109
$575$		0			0
$576$	−5.87732			−0.244888
$577$	7.87973			0.328037			0.164019	−	0.986457i	$-0.447554\pi$
$577$	7.87973			0.328037			0.164019	+	0.986457i	$0.447554\pi$
$578$	23.4230	+	11.9441i	0.974270	+	0.496807i
$579$	−23.9780			−0.996492
$580$		0			0
$581$			2.70585i			0.112258i
$582$	−5.79909			−0.240380
$583$			7.75151i			0.321035i
$584$		−	17.5763i		−	0.727313i
$585$		0			0
$586$	−40.2210			−1.66152
$587$	10.6361			0.439000			0.219500	−	0.975613i	$-0.429557\pi$
$587$	10.6361			0.439000			0.219500	+	0.975613i	$0.429557\pi$
$588$		−	2.67181i		−	0.110183i
$589$		−	33.3875i		−	1.37571i
$590$		0			0
$591$	−8.42347			−0.346495
$592$		−	35.7536i		−	1.46946i
$593$	7.79634			0.320157			0.160079	−	0.987104i	$-0.448825\pi$
$593$	7.79634			0.320157			0.160079	+	0.987104i	$0.448825\pi$
$594$	1.51036			0.0619707
$595$		0			0
$596$	−0.994731			−0.0407458
$597$	26.2107			1.07273
$598$			3.81104i			0.155845i
$599$	−2.26066			−0.0923679			−0.0461840	−	0.998933i	$-0.514706\pi$
$599$	−2.26066			−0.0923679			−0.0461840	+	0.998933i	$0.514706\pi$
$600$		0			0
$601$		−	4.72766i		−	0.192845i	−0.995340	−	0.0964226i	$-0.969260\pi$
$601$		−	4.72766i		−	0.192845i	0.995340	−	0.0964226i	$-0.0307400\pi$
$602$		−	4.52591i		−	0.184462i
$603$	−4.43839			−0.180745
$604$	7.91153			0.321915
$605$		0			0
$606$			11.9015i			0.483465i
$607$		−	26.7457i		−	1.08557i	−0.839871	−	0.542786i	$-0.817369\pi$
$607$		−	26.7457i		−	1.08557i	0.839871	−	0.542786i	$-0.182631\pi$
$608$	−8.04455			−0.326250
$609$			2.84439i			0.115261i
$610$		0			0
$611$	−24.5869			−0.994681
$612$	−0.377596	+	1.57170i	−0.0152634	+	0.0635320i
$613$	−2.83165			−0.114369			−0.0571847	−	0.998364i	$-0.518212\pi$
$613$	−2.83165			−0.114369			−0.0571847	+	0.998364i	$0.518212\pi$
$614$	8.91142			0.359636
$615$		0			0
$616$	−1.04413			−0.0420690
$617$		−	8.05591i		−	0.324319i	−0.986765	−	0.162159i	$-0.948154\pi$
$617$		−	8.05591i		−	0.324319i	0.986765	−	0.162159i	$-0.0518459\pi$
$618$		−	8.76604i		−	0.352622i
$619$		−	20.4157i		−	0.820576i	−0.911956	−	0.410288i	$-0.865428\pi$
$619$		−	20.4157i		−	0.820576i	0.911956	−	0.410288i	$-0.134572\pi$
$620$		0			0
$621$	0.477303			0.0191535
$622$		−	38.6631i		−	1.55025i
$623$			2.39617i			0.0960007i
$624$			23.9046i			0.956952i
$625$		0			0
$626$		−	5.29745i		−	0.211729i
$627$	−3.59105			−0.143413
$628$	3.16945			0.126475
$629$	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	$0.634712\pi$
$632$			6.15232i			0.244726i
$633$	4.35210			0.172980
$634$		−	36.7692i		−	1.46029i
$635$		0			0
$636$		−	3.11186i		−	0.123393i
$637$	35.1837			1.39403
$638$	9.99243			0.395604
$639$			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	$-0.112743\pi$
$642$	17.3403			0.684368
$643$		−	2.24211i		−	0.0884201i	−0.999022	−	0.0442100i	$-0.985923\pi$
$643$		−	2.24211i		−	0.0884201i	0.999022	−	0.0442100i	$-0.0140771\pi$
$644$	0.0804491			0.00317014
$645$		0			0
$646$	5.47784	−	22.8008i	0.215523	−	0.897086i
$647$	−35.5856			−1.39902			−0.699508	−	0.714625i	$-0.746597\pi$
$647$	−35.5856			−1.39902			−0.699508	+	0.714625i	$0.746597\pi$
$648$	2.48691			0.0976950
$649$		−	0.823204i		−	0.0323136i
$650$		0			0
$651$			3.90351i			0.152990i
$652$			5.80926i			0.227508i
$653$		−	17.6154i		−	0.689345i	−0.938723	−	0.344672i	$-0.887990\pi$
$653$		−	17.6154i		−	0.689345i	0.938723	−	0.344672i	$-0.112010\pi$
$654$	5.01712			0.196185
$655$		0			0
$656$			40.5595i			1.58358i
$657$			7.06754i			0.275731i
$658$			3.16680i			0.123455i
$659$	8.61882			0.335742			0.167871	−	0.985809i	$-0.446311\pi$
$659$	8.61882			0.335742			0.167871	+	0.985809i	$0.446311\pi$
$660$		0			0
$661$	−11.7014			−0.455132			−0.227566	−	0.973763i	$-0.573077\pi$
$661$	−11.7014			−0.455132			−0.227566	+	0.973763i	$0.573077\pi$
$662$	−14.8070			−0.575491
$663$	−20.6969	−	4.97237i	−0.803800	−	0.193111i
$664$	15.6518			0.607409
$665$		0			0
$666$			11.9423i			0.462754i
$667$	3.15781			0.122271
$668$			0.719831i			0.0278511i
$669$			3.48378i			0.134691i
$670$		0			0
$671$	−4.14981			−0.160202
$672$	0.940530			0.0362817
$673$			44.9610i			1.73312i	0.499073	+	0.866560i	$0.333674\pi$
$673$			44.9610i			1.73312i	−0.499073	+	0.866560i	$0.666326\pi$
$674$			28.1062i			1.08261i
$675$		0			0
$676$	5.35213			0.205851
$677$			2.79937i			0.107589i	0.998552	+	0.0537943i	$0.0171315\pi$
$677$			2.79937i			0.107589i	−0.998552	+	0.0537943i	$0.982868\pi$
$678$	25.7930			0.990575
$679$	−1.61203			−0.0618641
$680$		0			0
$681$	−1.89538			−0.0726312
$682$	13.7131			0.525103
$683$			22.2621i			0.851835i	0.904762	+	0.425917i	$0.140049\pi$
$683$			22.2621i			0.851835i	−0.904762	+	0.425917i	$0.859951\pi$
$684$	1.44164			0.0551223
$685$		0			0
$686$		−	9.18624i		−	0.350732i
$687$			8.85340i			0.337778i
$688$	−31.5167			−1.20156
$689$	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	$0.900582\pi$
$692$			6.47402i			0.246105i
$693$	0.419849			0.0159487
$694$		−	35.9635i		−	1.36516i
$695$		0			0
$696$	16.4532			0.623658
$697$	−35.1168	−	8.43672i	−1.33014	−	0.319563i
$698$	50.9267			1.92761
$699$	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	$0.688937\pi$
$702$		−	7.98453i		−	0.301357i
$703$		−	28.3942i		−	1.07091i
$704$			5.73951i			0.216316i
$705$		0			0
$706$	10.4569			0.393551
$707$			3.30838i			0.124424i
$708$			0.330477i			0.0124201i
$709$		−	4.66171i		−	0.175074i	−0.996161	−	0.0875371i	$-0.972100\pi$
$709$		−	4.66171i		−	0.175074i	0.996161	−	0.0875371i	$-0.0278996\pi$
$710$		0			0
$711$		−	2.47389i		−	0.0927780i
$712$	13.8605			0.519446
$713$	4.33363			0.162296
$714$	−0.640443	+	2.66576i	−0.0239680	+	0.0997636i
$715$		0			0
$716$	3.32455			0.124244
$717$			24.0664i			0.898776i
$718$	39.0053			1.45566
$719$			0.691404i			0.0257850i	0.999917	+	0.0128925i	$0.00410393\pi$
$719$			0.691404i			0.0257850i	−0.999917	+	0.0128925i	$0.995896\pi$
$720$		0			0
$721$		−	2.43678i		−	0.0907506i
$722$	8.47180			0.315288
$723$	−11.2091			−0.416871
$724$			4.42332i			0.164392i
$725$		0			0
$726$			15.5379i			0.576665i
$727$	−26.9835			−1.00076			−0.500380	−	0.865806i	$-0.666807\pi$
$727$	−26.9835			−1.00076			−0.500380	+	0.865806i	$0.666807\pi$
$728$			5.51979i			0.204577i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	6.55575	−	27.2875i	0.242473	−	1.00926i
$732$	1.66595			0.0615753
$733$	38.6190			1.42643			0.713213	−	0.700948i	$-0.247239\pi$
$733$	38.6190			1.42643			0.713213	+	0.700948i	$0.247239\pi$
$734$		−	12.4993i		−	0.461358i
$735$		0			0
$736$		−	1.04417i		−	0.0384884i
$737$			4.33431i			0.159656i
$738$		−	13.5475i		−	0.498690i
$739$	−12.7144			−0.467705			−0.233853	−	0.972272i	$-0.575133\pi$
$739$	−12.7144			−0.467705			−0.233853	+	0.972272i	$0.575133\pi$
$740$		0			0
$741$			18.9842i			0.697401i
$742$		−	5.27804i		−	0.193763i
$743$		−	4.75526i		−	0.174454i	−0.996188	−	0.0872268i	$-0.972200\pi$
$743$		−	4.75526i		−	0.174454i	0.996188	−	0.0872268i	$-0.0278005\pi$
$744$	22.5796			0.827809
$745$		0			0
$746$	26.6005			0.973915
$747$	−6.29370			−0.230274
$748$	1.53484	+	0.368742i	0.0561194	+	0.0134825i
$749$	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	$0.901226\pi$
$752$	22.0524			0.804168
$753$		−	28.2730i		−	1.03033i
$754$		−	52.8252i		−	1.92378i
$755$		0			0
$756$	−0.168549			−0.00613008
$757$	1.54235			0.0560578			0.0280289	−	0.999607i	$-0.491077\pi$
$757$	1.54235			0.0560578			0.0280289	+	0.999607i	$0.491077\pi$
$758$		−	0.821906i		−	0.0298530i
$759$		−	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	$0.688668\pi$
$762$			15.8153i			0.572928i
$763$	1.39466			0.0504900
$764$	1.19049			0.0430705
$765$		0			0
$766$	1.35294			0.0488838
$767$	−4.35189			−0.157138
$768$		−	9.07103i		−	0.327323i
$769$	30.7066			1.10731			0.553654	−	0.832747i	$-0.313233\pi$
$769$	30.7066			1.10731			0.553654	+	0.832747i	$0.313233\pi$
$770$		0			0
$771$		−	5.51730i		−	0.198701i
$772$		−	9.40031i		−	0.338325i
$773$	7.40148			0.266213			0.133106	−	0.991102i	$-0.457505\pi$
$773$	7.40148			0.266213			0.133106	+	0.991102i	$0.457505\pi$
$774$	10.5271			0.378388
$775$		0			0
$776$			9.32471i			0.334738i
$777$			3.31971i			0.119094i
$778$	38.5940			1.38366
$779$			32.2108i			1.15407i
$780$		0			0
$781$	8.41596			0.301147
$782$	2.95950	+	0.711012i	0.105831	+	0.0254257i
$783$	−6.61594			−0.236434
$784$	−31.5568			−1.12703
$785$		0			0
$786$	13.9820			0.498722
$787$		−	3.70140i		−	0.131941i	−0.997822	−	0.0659703i	$-0.978986\pi$
$787$		−	3.70140i		−	0.131941i	0.997822	−	0.0659703i	$-0.0210143\pi$
$788$		−	3.30233i		−	0.117640i
$789$			16.0439i			0.571178i
$790$		0			0
$791$	7.16995			0.254934
$792$		−	2.42859i		−	0.0862963i
$793$			21.9381i			0.779043i
$794$			24.3790i			0.865180i
$795$		0			0
$796$			10.2756i			0.364210i
$797$	−34.7651			−1.23144			−0.615722	−	0.787963i	$-0.711136\pi$
$797$	−34.7651			−1.23144			−0.615722	+	0.787963i	$0.711136\pi$
$798$	2.44517			0.0865580
$799$	−4.58709	+	19.0932i	−0.162280	+	0.675468i
$800$		0			0
$801$	−5.57341			−0.196927
$802$			16.6505i			0.587950i
$803$	6.90181			0.243560
$804$		−	1.74002i		−	0.0613658i
$805$		0			0
$806$		−	72.4947i		−	2.55352i
$807$	7.17003			0.252397
$808$	19.1371			0.673242
$809$			42.0271i			1.47760i	0.673927	+	0.738798i	$0.264606\pi$
$809$			42.0271i			1.47760i	−0.673927	+	0.738798i	$0.735394\pi$
$810$		0			0
$811$		−	35.1420i		−	1.23400i	−0.786962	−	0.617001i	$-0.788347\pi$
$811$		−	35.1420i		−	1.23400i	0.786962	−	0.617001i	$-0.211653\pi$
$812$	−1.11511			−0.0391327
$813$		−	7.17160i		−	0.251519i
$814$	11.6623			0.408762
$815$		0			0
$816$	18.5633	+	4.45980i	0.649847	+	0.156124i
$817$	−25.0294			−0.875668
$818$	−15.8670			−0.554777
$819$		−	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	$0.899046\pi$
$822$			22.9054i			0.798916i
$823$		−	33.3852i		−	1.16373i	−0.813284	−	0.581867i	$-0.802322\pi$
$823$		−	33.3852i		−	1.16373i	0.813284	−	0.581867i	$-0.197678\pi$
$824$	−14.0955			−0.491038
$825$		0			0
$826$			0.560524i			0.0195031i
$827$		−	42.7442i		−	1.48636i	−0.669091	−	0.743180i	$-0.733317\pi$
$827$		−	42.7442i		−	1.48636i	0.669091	−	0.743180i	$-0.266683\pi$
$828$			0.187121i			0.00650292i
$829$	−17.0407			−0.591848			−0.295924	−	0.955212i	$-0.595627\pi$
$829$	−17.0407			−0.591848			−0.295924	+	0.955212i	$0.595627\pi$
$830$		0			0
$831$	−24.1787			−0.838748
$832$	30.3420			1.05192
$833$	6.56409	−	27.3222i	0.227432	−	0.946658i
$834$	−18.8563			−0.652940
$835$		0			0
$836$		−	1.40783i		−	0.0486909i
$837$	−9.07940			−0.313830
$838$			50.0221i			1.72799i
$839$			5.38898i			0.186048i	0.995664	+	0.0930242i	$0.0296534\pi$
$839$			5.38898i			0.186048i	−0.995664	+	0.0930242i	$0.970347\pi$
$840$		0			0
$841$	−14.7707			−0.509333
$842$	40.9729			1.41202
$843$			28.2491i			0.972951i
$844$			1.70619i			0.0587295i
$845$		0			0
$846$	−7.36585			−0.253243
$847$			4.31923i			0.148410i
$848$	−36.7543			−1.26215
$849$	−32.2601			−1.10716
$850$		0			0
$851$	3.68551			0.126338
$852$	−3.37861			−0.115749
$853$			44.3831i			1.51965i	0.650129	+	0.759824i	$0.274715\pi$
$853$			44.3831i			1.51965i	−0.650129	+	0.759824i	$0.725285\pi$
$854$	2.82563			0.0966909
$855$		0			0
$856$		−	27.8826i		−	0.953007i
$857$		−	21.4348i		−	0.732199i	−0.930576	−	0.366100i	$-0.880693\pi$
$857$		−	21.4348i		−	0.732199i	0.930576	−	0.366100i	$-0.119307\pi$
$858$	−7.79731			−0.266196
$859$	−41.7437			−1.42428			−0.712138	−	0.702039i	$-0.752273\pi$
$859$	−41.7437			−1.42428			−0.712138	+	0.702039i	$0.752273\pi$
$860$		0			0
$861$		−	3.76594i		−	0.128343i
$862$			24.0890i			0.820475i
$863$	−13.7962			−0.469627			−0.234813	−	0.972040i	$-0.575448\pi$
$863$	−13.7962			−0.469627			−0.234813	+	0.972040i	$0.575448\pi$
$864$			2.18764i			0.0744249i
$865$		0			0
$866$	−56.6741			−1.92586
$867$	−7.72267	+	15.1446i	−0.262276	+	0.514339i
$868$	−1.53033			−0.0519426
$869$	−2.41588			−0.0819530
$870$		0			0
$871$	22.9134			0.776392
$872$		−	8.06733i		−	0.273194i
$873$		−	3.74952i		−	0.126902i
$874$		−	2.71459i		−	0.0918225i
$875$		0			0
$876$	−2.77075			−0.0936149
$877$		−	29.2334i		−	0.987141i	−0.869706	−	0.493571i	$-0.835691\pi$
$877$		−	29.2334i		−	0.987141i	0.869706	−	0.493571i	$-0.164309\pi$
$878$		−	55.2946i		−	1.86610i
$879$		−	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	$0.897875\pi$
$882$	10.5405			0.354916
$883$	−29.4224			−0.990142			−0.495071	−	0.868852i	$-0.664858\pi$
$883$	−29.4224			−0.990142			−0.495071	+	0.868852i	$0.664858\pi$
$884$	1.94936	−	8.11398i	0.0655642	−	0.272903i
$885$		0			0
$886$	−26.0015			−0.873538
$887$			43.7003i			1.46731i	0.679521	+	0.733656i	$0.262188\pi$
$887$			43.7003i			1.46731i	−0.679521	+	0.733656i	$0.737812\pi$
$888$	19.2027			0.644401
$889$			4.39634i			0.147449i
$890$		0			0
$891$			0.976552i			0.0327157i
$892$	−1.36578			−0.0457296
$893$	17.5132			0.586057
$894$		−	3.92428i		−	0.131248i
$895$		0			0
$896$		−	5.78912i		−	0.193401i
$897$	−2.46411			−0.0822741
$898$			27.9331i			0.932139i
$899$	−60.0688			−2.00341
$900$		0			0
$901$	7.64521	−	31.8222i	0.254699	−	1.06015i
$902$	−13.2298			−0.440505
$903$	2.92632			0.0973818
$904$		−	41.4742i		−	1.37941i
$905$		0			0
$906$			31.2115i			1.03693i
$907$			53.1209i			1.76385i	0.471388	+	0.881926i	$0.343753\pi$
$907$			53.1209i			1.76385i	−0.471388	+	0.881926i	$0.656247\pi$
$908$		−	0.743063i		−	0.0246594i
$909$	−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	$0.709745\pi$
$912$		−	17.0272i		−	0.563827i
$913$			6.14612i			0.203407i
$914$	−44.7133			−1.47899
$915$		0			0
$916$	−3.47088			−0.114681
$917$	3.88672			0.128351
$918$	−6.20045	−	1.48964i	−0.204645	−	0.0491656i
$919$	1.14793			0.0378667			0.0189334	−	0.999821i	$-0.493973\pi$
$919$	1.14793			0.0378667			0.0189334	+	0.999821i	$0.493973\pi$
$920$		0			0
$921$			5.76186i			0.189860i
$922$	−24.5868			−0.809723
$923$		−	44.4912i		−	1.46445i
$924$			0.164597i			0.00541484i
$925$		0			0
$926$	46.0776			1.51420
$927$	5.66786			0.186157
$928$			14.4733i			0.475108i
$929$		−	27.1035i		−	0.889237i	−0.895720	−	0.444619i	$-0.853339\pi$
$929$		−	27.1035i		−	0.889237i	0.895720	−	0.444619i	$-0.146661\pi$
$930$		0			0
$931$	−25.0613			−0.821349
$932$			10.2063i			0.334319i
$933$	24.9984			0.818412
$934$	3.84038			0.125661
$935$		0			0
$936$	−12.8388			−0.419650
$937$	−48.1087			−1.57164			−0.785822	−	0.618453i	$-0.787760\pi$
$937$	−48.1087			−1.57164			−0.785822	+	0.618453i	$0.787760\pi$
$938$		−	2.95126i		−	0.0963619i
$939$	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	$-0.173276\pi$
$942$			12.5037i			0.407392i
$943$	−4.18090			−0.136149
$944$	3.90328			0.127041
$945$		0			0
$946$		−	10.2802i		−	0.334239i
$947$		−	34.4567i		−	1.11969i	−0.828596	−	0.559846i	$-0.810860\pi$
$947$		−	34.4567i		−	1.11969i	0.828596	−	0.559846i	$-0.189140\pi$
$948$	0.969859			0.0314996
$949$		−	36.4866i		−	1.18440i
$950$		0			0
$951$	23.7739			0.770921
$952$	4.28644	+	1.02981i	0.138924	+	0.0333762i
$953$	30.1023			0.975110			0.487555	−	0.873092i	$-0.337889\pi$
$953$	30.1023			0.975110			0.487555	+	0.873092i	$0.337889\pi$
$954$	12.2765			0.397467
$955$		0			0
$956$	−9.43496			−0.305149
$957$			6.46081i			0.208848i
$958$		−	33.0019i		−	1.06624i
$959$			6.36723i			0.205609i
$960$		0			0
$961$	−51.4355			−1.65921
$962$		−	61.6528i		−	1.98776i
$963$			11.2117i			0.361294i
$964$		−	4.39441i		−	0.141534i
$965$		0			0
$966$			0.317377i			0.0102115i
$967$	33.5567			1.07911			0.539555	−	0.841951i	$-0.318593\pi$
$967$	33.5567			1.07911			0.539555	+	0.841951i	$0.318593\pi$
$968$	24.9843			0.803027
$969$	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	$0.382169\pi$
$972$		−	0.392039i		−	0.0125747i
$973$	−5.24167			−0.168040
$974$			64.0121i			2.05108i
$975$		0			0
$976$		−	19.6766i		−	0.629832i
$977$	−48.7390			−1.55930			−0.779649	−	0.626217i	$-0.784603\pi$
$977$	−48.7390			−1.55930			−0.779649	+	0.626217i	$0.784603\pi$
$978$	−22.9180			−0.732836
$979$			5.44272i			0.173950i
$980$		0			0
$981$			3.24392i			0.103570i
$982$	24.0813			0.768466
$983$		−	27.7107i		−	0.883836i	−0.897056	−	0.441918i	$-0.854298\pi$
$983$		−	27.7107i		−	0.883836i	0.897056	−	0.441918i	$-0.145702\pi$
$984$	−21.7839			−0.694444
$985$		0			0
$986$	−41.0218	−	9.85540i	−1.30640	−	0.313860i
$987$	−2.04756			−0.0651746
$988$	−7.44254			−0.236779
$989$		−	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	$0.748105\pi$
$992$			19.8624i			0.630633i
$993$		−	9.57377i		−	0.303814i
$994$	−5.73047			−0.181760
$995$		0			0
$996$		−	2.46737i		−	0.0781817i
$997$			24.6416i			0.780408i	0.920728	+	0.390204i	$0.127595\pi$
$997$			24.6416i			0.780408i	−0.920728	+	0.390204i	$0.872405\pi$
$998$			43.8393i			1.38771i
$999$	−7.72152			−0.244298

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1275.2.d.i.424.4		12	5.2	odd	4
1275.2.d.i.424.9		12	85.33	odd	4
1275.2.d.j.424.4		12	85.67	odd	4
1275.2.d.j.424.9		12	5.3	odd	4
1275.2.g.e.526.3	✓	12	1.1	even	1	trivial
1275.2.g.e.526.4	yes	12	17.16	even	2	inner
1275.2.g.f.526.9	yes	12	85.84	even	2
1275.2.g.f.526.10	yes	12	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:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1275.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.54662 q^{2} -1.00000i q^{3} +0.392039 q^{4} +1.54662i q^{6} +0.429930i q^{7} +2.48691 q^{8} -1.00000 q^{9} +0.976552i q^{11} -0.392039i q^{12} +5.16256 q^{13} -0.664939i q^{14} -4.63038 q^{16} +(0.963160 - 4.00903i) q^{17} +1.54662 q^{18} -3.67728 q^{19} +0.429930 q^{21} -1.51036i q^{22} -0.477303i q^{23} -2.48691i q^{24} -7.98453 q^{26} +1.00000i q^{27} +0.168549i q^{28} +6.61594i q^{29} +9.07940i q^{31} +2.18764 q^{32} +0.976552 q^{33} +(-1.48964 + 6.20045i) q^{34} -0.392039 q^{36} +7.72152i q^{37} +5.68736 q^{38} -5.16256i q^{39} -8.75942i q^{41} -0.664939 q^{42} +6.80650 q^{43} +0.382846i q^{44} +0.738207i q^{46} -4.76254 q^{47} +4.63038i q^{48} +6.81516 q^{49} +(-4.00903 - 0.963160i) q^{51} +2.02392 q^{52} +7.93763 q^{53} -1.54662i q^{54} +1.06920i q^{56} +3.67728i q^{57} -10.2324i q^{58} -0.842970 q^{59} +4.24945i q^{61} -14.0424i q^{62} -0.429930i q^{63} +5.87732 q^{64} -1.51036 q^{66} +4.43839 q^{67} +(0.377596 - 1.57170i) q^{68} -0.477303 q^{69} -8.61804i q^{71} -2.48691 q^{72} -7.06754i q^{73} -11.9423i q^{74} -1.44164 q^{76} -0.419849 q^{77} +7.98453i q^{78} +2.47389i q^{79} +1.00000 q^{81} +13.5475i q^{82} +6.29370 q^{83} +0.168549 q^{84} -10.5271 q^{86} +6.61594 q^{87} +2.42859i q^{88} +5.57341 q^{89} +2.21954i q^{91} -0.187121i q^{92} +9.07940 q^{93} +7.36585 q^{94} -2.18764i q^{96} +3.74952i q^{97} -10.5405 q^{98} -0.976552i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{4} - 12 q^{9} - 4 q^{13} + 32 q^{16} + 10 q^{17} - 4 q^{19} - 36 q^{26} - 20 q^{32} - 12 q^{33} - 24 q^{34} - 16 q^{36} - 44 q^{38} + 28 q^{42} + 28 q^{43} - 16 q^{47} - 16 q^{49} + 6 q^{51}+ \cdots - 8 q^{98}+O(q^{100}) \) 12 * q + 16 * q^4 - 12 * q^9 - 4 * q^13 + 32 * q^16 + 10 * q^17 - 4 * q^19 - 36 * q^26 - 20 * q^32 - 12 * q^33 - 24 * q^34 - 16 * q^36 - 44 * q^38 + 28 * q^42 + 28 * q^43 - 16 * q^47 - 16 * q^49 + 6 * q^51 + 16 * q^52 - 12 * q^53 + 32 * q^59 + 56 * q^64 - 12 * q^66 - 20 * q^67 + 56 * q^68 - 16 * q^69 + 64 * q^76 - 72 * q^77 + 12 * q^81 - 44 * q^83 - 36 * q^84 + 20 * q^86 + 32 * q^87 + 4 * q^89 + 8 * q^93 + 40 * q^94 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more