LMFDB - Embedded newform 975.2.h.e.649.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(649,975)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("975.649");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.h (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.2
Root			$2.56155i$ of defining polynomial
Character	$\chi$	$=$	975.649
Dual form			975.2.h.e.649.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.56155 q^{2} +1.00000i q^{3} +4.56155 q^{4} -2.56155i q^{6} -3.56155 q^{7} -6.56155 q^{8} -1.00000 q^{9} +5.56155i q^{11} +4.56155i q^{12} +(3.56155 - 0.561553i) q^{13} +9.12311 q^{14} +7.68466 q^{16} +0.438447i q^{17} +2.56155 q^{18} -1.12311i q^{19} -3.56155i q^{21} -14.2462i q^{22} +5.56155i q^{23} -6.56155i q^{24} +(-9.12311 + 1.43845i) q^{26} -1.00000i q^{27} -16.2462 q^{28} -8.24621 q^{29} -6.00000i q^{31} -6.56155 q^{32} -5.56155 q^{33} -1.12311i q^{34} -4.56155 q^{36} +5.56155 q^{37} +2.87689i q^{38} +(0.561553 + 3.56155i) q^{39} -0.438447i q^{41} +9.12311i q^{42} +7.12311i q^{43} +25.3693i q^{44} -14.2462i q^{46} -4.00000 q^{47} +7.68466i q^{48} +5.68466 q^{49} -0.438447 q^{51} +(16.2462 - 2.56155i) q^{52} -9.80776i q^{53} +2.56155i q^{54} +23.3693 q^{56} +1.12311 q^{57} +21.1231 q^{58} -4.00000i q^{59} -8.43845 q^{61} +15.3693i q^{62} +3.56155 q^{63} +1.43845 q^{64} +14.2462 q^{66} +2.87689 q^{67} +2.00000i q^{68} -5.56155 q^{69} +8.68466i q^{71} +6.56155 q^{72} -11.1231 q^{73} -14.2462 q^{74} -5.12311i q^{76} -19.8078i q^{77} +(-1.43845 - 9.12311i) q^{78} +5.56155 q^{79} +1.00000 q^{81} +1.12311i q^{82} -13.3693 q^{83} -16.2462i q^{84} -18.2462i q^{86} -8.24621i q^{87} -36.4924i q^{88} -1.31534i q^{89} +(-12.6847 + 2.00000i) q^{91} +25.3693i q^{92} +6.00000 q^{93} +10.2462 q^{94} -6.56155i q^{96} -14.9309 q^{97} -14.5616 q^{98} -5.56155i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 10 q^{4} - 6 q^{7} - 18 q^{8} - 4 q^{9} + 6 q^{13} + 20 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{26} - 32 q^{28} - 18 q^{32} - 14 q^{33} - 10 q^{36} + 14 q^{37} - 6 q^{39} - 16 q^{47} - 2 q^{49}+ \cdots - 50 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 10 * q^4 - 6 * q^7 - 18 * q^8 - 4 * q^9 + 6 * q^13 + 20 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^26 - 32 * q^28 - 18 * q^32 - 14 * q^33 - 10 * q^36 + 14 * q^37 - 6 * q^39 - 16 * q^47 - 2 * q^49 - 10 * q^51 + 32 * q^52 + 44 * q^56 - 12 * q^57 + 68 * q^58 - 42 * q^61 + 6 * q^63 + 14 * q^64 + 24 * q^66 + 28 * q^67 - 14 * q^69 + 18 * q^72 - 28 * q^73 - 24 * q^74 - 14 * q^78 + 14 * q^79 + 4 * q^81 - 4 * q^83 - 26 * q^91 + 24 * q^93 + 8 * q^94 - 2 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−2.56155			−1.81129			−0.905646	−	0.424035i	$-0.860613\pi$
$2$	−2.56155			−1.81129			−0.905646	+	0.424035i	$0.860613\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	4.56155			2.28078
$5$		0			0
$5$		0			0
$6$		−	2.56155i		−	1.04575i
$7$	−3.56155			−1.34614			−0.673070	−	0.739579i	$-0.735025\pi$
$7$	−3.56155			−1.34614			−0.673070	+	0.739579i	$0.735025\pi$
$8$	−6.56155			−2.31986
$9$	−1.00000			−0.333333
$10$		0			0
$11$			5.56155i			1.67687i	0.545001	+	0.838436i	$0.316529\pi$
$11$			5.56155i			1.67687i	−0.545001	+	0.838436i	$0.683471\pi$
$12$			4.56155i			1.31681i
$13$	3.56155	−	0.561553i	0.987797	−	0.155747i
$13$	3.56155	−	0.561553i	0.987797	−	0.155747i
$14$	9.12311			2.43825
$15$		0			0
$16$	7.68466			1.92116
$17$			0.438447i			0.106339i	0.998586	+	0.0531695i	$0.0169324\pi$
$17$			0.438447i			0.106339i	−0.998586	+	0.0531695i	$0.983068\pi$
$18$	2.56155			0.603764
$19$		−	1.12311i		−	0.257658i	−0.991667	−	0.128829i	$-0.958878\pi$
$19$		−	1.12311i		−	0.257658i	0.991667	−	0.128829i	$-0.0411218\pi$
$20$		0			0
$21$		−	3.56155i		−	0.777195i
$22$		−	14.2462i		−	3.03730i
$23$			5.56155i			1.15966i	0.814736	+	0.579832i	$0.196882\pi$
$23$			5.56155i			1.15966i	−0.814736	+	0.579832i	$0.803118\pi$
$24$		−	6.56155i		−	1.33937i
$25$		0			0
$26$	−9.12311	+	1.43845i	−1.78919	+	0.282103i
$27$		−	1.00000i		−	0.192450i
$28$	−16.2462			−3.07025
$29$	−8.24621			−1.53128			−0.765641	−	0.643268i	$-0.777578\pi$
$29$	−8.24621			−1.53128			−0.765641	+	0.643268i	$0.777578\pi$
$30$		0			0
$31$		−	6.00000i		−	1.07763i	−0.842424	−	0.538816i	$-0.818872\pi$
$31$		−	6.00000i		−	1.07763i	0.842424	−	0.538816i	$-0.181128\pi$
$32$	−6.56155			−1.15993
$33$	−5.56155			−0.968142
$34$		−	1.12311i		−	0.192611i
$35$		0			0
$36$	−4.56155			−0.760259
$37$	5.56155			0.914314			0.457157	−	0.889386i	$-0.348868\pi$
$37$	5.56155			0.914314			0.457157	+	0.889386i	$0.348868\pi$
$38$			2.87689i			0.466694i
$39$	0.561553	+	3.56155i	0.0899204	+	0.570305i
$40$		0			0
$41$		−	0.438447i		−	0.0684739i	−0.999414	−	0.0342370i	$-0.989100\pi$
$41$		−	0.438447i		−	0.0684739i	0.999414	−	0.0342370i	$-0.0109001\pi$
$42$			9.12311i			1.40773i
$43$			7.12311i			1.08626i	0.839648	+	0.543132i	$0.182762\pi$
$43$			7.12311i			1.08626i	−0.839648	+	0.543132i	$0.817238\pi$
$44$			25.3693i			3.82457i
$45$		0			0
$46$		−	14.2462i		−	2.10049i
$47$	−4.00000			−0.583460			−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000			−0.583460			−0.291730	+	0.956501i	$0.594231\pi$
$48$			7.68466i			1.10918i
$49$	5.68466			0.812094
$50$		0			0
$51$	−0.438447			−0.0613949
$52$	16.2462	−	2.56155i	2.25294	−	0.355223i
$53$		−	9.80776i		−	1.34720i	−0.739096	−	0.673600i	$-0.764747\pi$
$53$		−	9.80776i		−	1.34720i	0.739096	−	0.673600i	$-0.235253\pi$
$54$			2.56155i			0.348583i
$55$		0			0
$56$	23.3693			3.12286
$57$	1.12311			0.148759
$58$	21.1231			2.77360
$59$		−	4.00000i		−	0.520756i	−0.965507	−	0.260378i	$-0.916153\pi$
$59$		−	4.00000i		−	0.520756i	0.965507	−	0.260378i	$-0.0838471\pi$
$60$		0			0
$61$	−8.43845			−1.08043			−0.540216	−	0.841526i	$-0.681658\pi$
$61$	−8.43845			−1.08043			−0.540216	+	0.841526i	$0.681658\pi$
$62$			15.3693i			1.95191i
$63$	3.56155			0.448713
$64$	1.43845			0.179806
$65$		0			0
$66$	14.2462			1.75359
$67$	2.87689			0.351469			0.175734	−	0.984438i	$-0.443770\pi$
$67$	2.87689			0.351469			0.175734	+	0.984438i	$0.443770\pi$
$68$			2.00000i			0.242536i
$69$	−5.56155			−0.669532
$70$		0			0
$71$			8.68466i			1.03068i	0.856986	+	0.515340i	$0.172334\pi$
$71$			8.68466i			1.03068i	−0.856986	+	0.515340i	$0.827666\pi$
$72$	6.56155			0.773286
$73$	−11.1231			−1.30186			−0.650931	−	0.759137i	$-0.725621\pi$
$73$	−11.1231			−1.30186			−0.650931	+	0.759137i	$0.725621\pi$
$74$	−14.2462			−1.65609
$75$		0			0
$76$		−	5.12311i		−	0.587661i
$77$		−	19.8078i		−	2.25730i
$78$	−1.43845	−	9.12311i	−0.162872	−	1.03299i
$79$	5.56155			0.625724			0.312862	−	0.949799i	$-0.398712\pi$
$79$	5.56155			0.625724			0.312862	+	0.949799i	$0.398712\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$			1.12311i			0.124026i
$83$	−13.3693			−1.46747			−0.733737	−	0.679434i	$-0.762225\pi$
$83$	−13.3693			−1.46747			−0.733737	+	0.679434i	$0.762225\pi$
$84$		−	16.2462i		−	1.77261i
$85$		0			0
$86$		−	18.2462i		−	1.96754i
$87$		−	8.24621i		−	0.884087i
$88$		−	36.4924i		−	3.89011i
$89$		−	1.31534i		−	0.139426i	−0.997567	−	0.0697130i	$-0.977792\pi$
$89$		−	1.31534i		−	0.139426i	0.997567	−	0.0697130i	$-0.0222083\pi$
$90$		0			0
$91$	−12.6847	+	2.00000i	−1.32971	+	0.209657i
$92$			25.3693i			2.64493i
$93$	6.00000			0.622171
$94$	10.2462			1.05682
$95$		0			0
$96$		−	6.56155i		−	0.669686i
$97$	−14.9309			−1.51600			−0.758000	−	0.652254i	$-0.773823\pi$
$97$	−14.9309			−1.51600			−0.758000	+	0.652254i	$0.773823\pi$
$98$	−14.5616			−1.47094
$99$		−	5.56155i		−	0.558957i
$100$		0			0
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$	1.12311			0.111204
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$	−23.3693	+	3.68466i	−2.29155	+	0.361310i
$105$		0			0
$106$			25.1231i			2.44017i
$107$		−	0.684658i		−	0.0661884i	−0.999452	−	0.0330942i	$-0.989464\pi$
$107$		−	0.684658i		−	0.0661884i	0.999452	−	0.0330942i	$-0.0105361\pi$
$108$		−	4.56155i		−	0.438936i
$109$		−	4.87689i		−	0.467122i	−0.972342	−	0.233561i	$-0.924962\pi$
$109$		−	4.87689i		−	0.467122i	0.972342	−	0.233561i	$-0.0750378\pi$
$110$		0			0
$111$			5.56155i			0.527879i
$112$	−27.3693			−2.58616
$113$		−	20.2462i		−	1.90460i	−0.305158	−	0.952302i	$-0.598709\pi$
$113$		−	20.2462i		−	1.90460i	0.305158	−	0.952302i	$-0.401291\pi$
$114$	−2.87689			−0.269446
$115$		0			0
$116$	−37.6155			−3.49251
$117$	−3.56155	+	0.561553i	−0.329266	+	0.0519156i
$118$			10.2462i			0.943240i
$119$		−	1.56155i		−	0.143147i
$120$		0			0
$121$	−19.9309			−1.81190
$122$	21.6155			1.95698
$123$	0.438447			0.0395335
$124$		−	27.3693i		−	2.45784i
$125$		0			0
$126$	−9.12311			−0.812751
$127$		−	17.3693i		−	1.54128i	−0.637272	−	0.770639i	$-0.719937\pi$
$127$		−	17.3693i		−	1.54128i	0.637272	−	0.770639i	$-0.280063\pi$
$128$	9.43845			0.834249
$129$	−7.12311			−0.627154
$130$		0			0
$131$	−2.24621			−0.196252			−0.0981262	−	0.995174i	$-0.531285\pi$
$131$	−2.24621			−0.196252			−0.0981262	+	0.995174i	$0.531285\pi$
$132$	−25.3693			−2.20812
$133$			4.00000i			0.346844i
$134$	−7.36932			−0.636612
$135$		0			0
$136$		−	2.87689i		−	0.246692i
$137$	−0.246211			−0.0210352			−0.0105176	−	0.999945i	$-0.503348\pi$
$137$	−0.246211			−0.0210352			−0.0105176	+	0.999945i	$0.503348\pi$
$138$	14.2462			1.21272
$139$	−17.5616			−1.48955			−0.744776	−	0.667315i	$-0.767444\pi$
$139$	−17.5616			−1.48955			−0.744776	+	0.667315i	$0.767444\pi$
$140$		0			0
$141$		−	4.00000i		−	0.336861i
$142$		−	22.2462i		−	1.86686i
$143$	3.12311	+	19.8078i	0.261167	+	1.65641i
$144$	−7.68466			−0.640388
$145$		0			0
$146$	28.4924			2.35805
$147$			5.68466i			0.468863i
$148$	25.3693			2.08535
$149$		−	12.9309i		−	1.05934i	−0.848204	−	0.529669i	$-0.822316\pi$
$149$		−	12.9309i		−	1.05934i	0.848204	−	0.529669i	$-0.177684\pi$
$150$		0			0
$151$			0.246211i			0.0200364i	0.999950	+	0.0100182i	$0.00318894\pi$
$151$			0.246211i			0.0200364i	−0.999950	+	0.0100182i	$0.996811\pi$
$152$			7.36932i			0.597731i
$153$		−	0.438447i		−	0.0354464i
$154$			50.7386i			4.08864i
$155$		0			0
$156$	2.56155	+	16.2462i	0.205088	+	1.30074i
$157$			13.1231i			1.04734i	0.851922	+	0.523669i	$0.175437\pi$
$157$			13.1231i			1.04734i	−0.851922	+	0.523669i	$0.824563\pi$
$158$	−14.2462			−1.13337
$159$	9.80776			0.777806
$160$		0			0
$161$		−	19.8078i		−	1.56107i
$162$	−2.56155			−0.201255
$163$	3.56155			0.278962			0.139481	−	0.990225i	$-0.455457\pi$
$163$	3.56155			0.278962			0.139481	+	0.990225i	$0.455457\pi$
$164$		−	2.00000i		−	0.156174i
$165$		0			0
$166$	34.2462			2.65802
$167$	2.24621			0.173817			0.0869085	−	0.996216i	$-0.472301\pi$
$167$	2.24621			0.173817			0.0869085	+	0.996216i	$0.472301\pi$
$168$			23.3693i			1.80298i
$169$	12.3693	−	4.00000i	0.951486	−	0.307692i
$170$		0			0
$171$			1.12311i			0.0858860i
$172$			32.4924i			2.47752i
$173$		−	12.2462i		−	0.931062i	−0.885032	−	0.465531i	$-0.845863\pi$
$173$		−	12.2462i		−	0.931062i	0.885032	−	0.465531i	$-0.154137\pi$
$174$			21.1231i			1.60134i
$175$		0			0
$176$			42.7386i			3.22155i
$177$	4.00000			0.300658
$178$			3.36932i			0.252541i
$179$	−2.24621			−0.167890			−0.0839449	−	0.996470i	$-0.526752\pi$
$179$	−2.24621			−0.167890			−0.0839449	+	0.996470i	$0.526752\pi$
$180$		0			0
$181$	−7.56155			−0.562046			−0.281023	−	0.959701i	$-0.590674\pi$
$181$	−7.56155			−0.562046			−0.281023	+	0.959701i	$0.590674\pi$
$182$	32.4924	−	5.12311i	2.40850	−	0.379750i
$183$		−	8.43845i		−	0.623788i
$184$		−	36.4924i		−	2.69026i
$185$		0			0
$186$	−15.3693			−1.12693
$187$	−2.43845			−0.178317
$188$	−18.2462			−1.33074
$189$			3.56155i			0.259065i
$190$		0			0
$191$	5.75379			0.416330			0.208165	−	0.978094i	$-0.433251\pi$
$191$	5.75379			0.416330			0.208165	+	0.978094i	$0.433251\pi$
$192$			1.43845i			0.103811i
$193$	2.93087			0.210969			0.105484	−	0.994421i	$-0.466361\pi$
$193$	2.93087			0.210969			0.105484	+	0.994421i	$0.466361\pi$
$194$	38.2462			2.74592
$195$		0			0
$196$	25.9309			1.85220
$197$	−12.2462			−0.872506			−0.436253	−	0.899824i	$-0.643695\pi$
$197$	−12.2462			−0.872506			−0.436253	+	0.899824i	$0.643695\pi$
$198$			14.2462i			1.01243i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$			2.87689i			0.202920i
$202$	5.12311			0.360460
$203$	29.3693			2.06132
$204$	−2.00000			−0.140028
$205$		0			0
$206$		0			0
$207$		−	5.56155i		−	0.386555i
$208$	27.3693	−	4.31534i	1.89772	−	0.299215i
$209$	6.24621			0.432059
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		−	44.7386i		−	3.07266i
$213$	−8.68466			−0.595063
$214$			1.75379i			0.119887i
$215$		0			0
$216$			6.56155i			0.446457i
$217$			21.3693i			1.45064i
$218$			12.4924i			0.846094i
$219$		−	11.1231i		−	0.751630i
$220$		0			0
$221$	0.246211	+	1.56155i	0.0165620	+	0.105041i
$222$		−	14.2462i		−	0.956143i
$223$	−2.87689			−0.192651			−0.0963255	−	0.995350i	$-0.530709\pi$
$223$	−2.87689			−0.192651			−0.0963255	+	0.995350i	$0.530709\pi$
$224$	23.3693			1.56143
$225$		0			0
$226$			51.8617i			3.44979i
$227$	−26.7386			−1.77471			−0.887353	−	0.461091i	$-0.847458\pi$
$227$	−26.7386			−1.77471			−0.887353	+	0.461091i	$0.847458\pi$
$228$	5.12311			0.339286
$229$			19.1231i			1.26369i	0.775095	+	0.631845i	$0.217702\pi$
$229$			19.1231i			1.26369i	−0.775095	+	0.631845i	$0.782298\pi$
$230$		0			0
$231$	19.8078			1.30326
$232$	54.1080			3.55236
$233$			22.6847i			1.48612i	0.669224	+	0.743061i	$0.266627\pi$
$233$			22.6847i			1.48612i	−0.669224	+	0.743061i	$0.733373\pi$
$234$	9.12311	−	1.43845i	0.596396	−	0.0940342i
$235$		0			0
$236$		−	18.2462i		−	1.18773i
$237$			5.56155i			0.361262i
$238$			4.00000i			0.259281i
$239$			13.5616i			0.877224i	0.898677	+	0.438612i	$0.144530\pi$
$239$			13.5616i			0.877224i	−0.898677	+	0.438612i	$0.855470\pi$
$240$		0			0
$241$		−	19.6155i		−	1.26355i	−0.775153	−	0.631774i	$-0.782327\pi$
$241$		−	19.6155i		−	1.26355i	0.775153	−	0.631774i	$-0.217673\pi$
$242$	51.0540			3.28187
$243$			1.00000i			0.0641500i
$244$	−38.4924			−2.46422
$245$		0			0
$246$	−1.12311			−0.0716066
$247$	−0.630683	−	4.00000i	−0.0401294	−	0.254514i
$248$			39.3693i			2.49995i
$249$		−	13.3693i		−	0.847246i
$250$		0			0
$251$	−1.36932			−0.0864305			−0.0432153	−	0.999066i	$-0.513760\pi$
$251$	−1.36932			−0.0864305			−0.0432153	+	0.999066i	$0.513760\pi$
$252$	16.2462			1.02342
$253$	−30.9309			−1.94461
$254$			44.4924i			2.79170i
$255$		0			0
$256$	−27.0540			−1.69087
$257$			2.00000i			0.124757i	0.998053	+	0.0623783i	$0.0198685\pi$
$257$			2.00000i			0.124757i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$	18.2462			1.13596
$259$	−19.8078			−1.23079
$260$		0			0
$261$	8.24621			0.510428
$262$	5.75379			0.355470
$263$		−	26.2462i		−	1.61841i	−0.587526	−	0.809205i	$-0.699898\pi$
$263$		−	26.2462i		−	1.61841i	0.587526	−	0.809205i	$-0.300102\pi$
$264$	36.4924			2.24595
$265$		0			0
$266$		−	10.2462i		−	0.628236i
$267$	1.31534			0.0804976
$268$	13.1231			0.801621
$269$	13.6155			0.830153			0.415077	−	0.909786i	$-0.363755\pi$
$269$	13.6155			0.830153			0.415077	+	0.909786i	$0.363755\pi$
$270$		0			0
$271$			28.2462i			1.71584i	0.513787	+	0.857918i	$0.328242\pi$
$271$			28.2462i			1.71584i	−0.513787	+	0.857918i	$0.671758\pi$
$272$			3.36932i			0.204295i
$273$	−2.00000	−	12.6847i	−0.121046	−	0.767710i
$274$	0.630683			0.0381010
$275$		0			0
$276$	−25.3693			−1.52705
$277$		−	2.87689i		−	0.172856i	−0.996258	−	0.0864279i	$-0.972455\pi$
$277$		−	2.87689i		−	0.172856i	0.996258	−	0.0864279i	$-0.0275452\pi$
$278$	44.9848			2.69801
$279$			6.00000i			0.359211i
$280$		0			0
$281$			22.0000i			1.31241i	0.754583	+	0.656205i	$0.227839\pi$
$281$			22.0000i			1.31241i	−0.754583	+	0.656205i	$0.772161\pi$
$282$			10.2462i			0.610153i
$283$			25.8617i			1.53732i	0.639657	+	0.768660i	$0.279076\pi$
$283$			25.8617i			1.53732i	−0.639657	+	0.768660i	$0.720924\pi$
$284$			39.6155i			2.35075i
$285$		0			0
$286$	−8.00000	−	50.7386i	−0.473050	−	3.00024i
$287$			1.56155i			0.0921755i
$288$	6.56155			0.386643
$289$	16.8078			0.988692
$290$		0			0
$291$		−	14.9309i		−	0.875263i
$292$	−50.7386			−2.96925
$293$	−8.24621			−0.481749			−0.240874	−	0.970556i	$-0.577434\pi$
$293$	−8.24621			−0.481749			−0.240874	+	0.970556i	$0.577434\pi$
$294$		−	14.5616i		−	0.849247i
$295$		0			0
$296$	−36.4924			−2.12108
$297$	5.56155			0.322714
$298$			33.1231i			1.91877i
$299$	3.12311	+	19.8078i	0.180614	+	1.14551i
$300$		0			0
$301$		−	25.3693i		−	1.46226i
$302$		−	0.630683i		−	0.0362917i
$303$		−	2.00000i		−	0.114897i
$304$		−	8.63068i		−	0.495004i
$305$		0			0
$306$			1.12311i			0.0642037i
$307$	−3.06913			−0.175165			−0.0875823	−	0.996157i	$-0.527914\pi$
$307$	−3.06913			−0.175165			−0.0875823	+	0.996157i	$0.527914\pi$
$308$		−	90.3542i		−	5.14841i
$309$		0			0
$310$		0			0
$311$	15.1231			0.857553			0.428776	−	0.903411i	$-0.358945\pi$
$311$	15.1231			0.857553			0.428776	+	0.903411i	$0.358945\pi$
$312$	−3.68466	−	23.3693i	−0.208603	−	1.32303i
$313$			17.1231i			0.967855i	0.875108	+	0.483928i	$0.160790\pi$
$313$			17.1231i			0.967855i	−0.875108	+	0.483928i	$0.839210\pi$
$314$		−	33.6155i		−	1.89703i
$315$		0			0
$316$	25.3693			1.42714
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	−25.1231			−1.40883
$319$		−	45.8617i		−	2.56776i
$320$		0			0
$321$	0.684658			0.0382139
$322$			50.7386i			2.82755i
$323$	0.492423			0.0273991
$324$	4.56155			0.253420
$325$		0			0
$326$	−9.12311			−0.505282
$327$	4.87689			0.269693
$328$			2.87689i			0.158850i
$329$	14.2462			0.785419
$330$		0			0
$331$			9.61553i			0.528517i	0.964452	+	0.264259i	$0.0851272\pi$
$331$			9.61553i			0.528517i	−0.964452	+	0.264259i	$0.914873\pi$
$332$	−60.9848			−3.34698
$333$	−5.56155			−0.304771
$334$	−5.75379			−0.314833
$335$		0			0
$336$		−	27.3693i		−	1.49312i
$337$			26.0000i			1.41631i	0.706057	+	0.708155i	$0.250472\pi$
$337$			26.0000i			1.41631i	−0.706057	+	0.708155i	$0.749528\pi$
$338$	−31.6847	+	10.2462i	−1.72342	+	0.557320i
$339$	20.2462			1.09962
$340$		0			0
$341$	33.3693			1.80705
$342$		−	2.87689i		−	0.155565i
$343$	4.68466			0.252948
$344$		−	46.7386i		−	2.51998i
$345$		0			0
$346$			31.3693i			1.68642i
$347$		−	10.9309i		−	0.586800i	−0.955990	−	0.293400i	$-0.905213\pi$
$347$		−	10.9309i		−	0.586800i	0.955990	−	0.293400i	$-0.0947867\pi$
$348$		−	37.6155i		−	2.01640i
$349$		−	8.87689i		−	0.475169i	−0.971367	−	0.237585i	$-0.923644\pi$
$349$		−	8.87689i		−	0.475169i	0.971367	−	0.237585i	$-0.0763557\pi$
$350$		0			0
$351$	−0.561553	−	3.56155i	−0.0299735	−	0.190102i
$352$		−	36.4924i		−	1.94505i
$353$	18.8769			1.00472			0.502358	−	0.864660i	$-0.332466\pi$
$353$	18.8769			1.00472			0.502358	+	0.864660i	$0.332466\pi$
$354$	−10.2462			−0.544580
$355$		0			0
$356$		−	6.00000i		−	0.317999i
$357$	1.56155			0.0826461
$358$	5.75379			0.304097
$359$		−	26.2462i		−	1.38522i	−0.721311	−	0.692611i	$-0.756460\pi$
$359$		−	26.2462i		−	1.38522i	0.721311	−	0.692611i	$-0.243540\pi$
$360$		0			0
$361$	17.7386			0.933612
$362$	19.3693			1.01803
$363$		−	19.9309i		−	1.04610i
$364$	−57.8617	+	9.12311i	−3.03278	+	0.478181i
$365$		0			0
$366$			21.6155i			1.12986i
$367$			11.1231i			0.580621i	0.956932	+	0.290311i	$0.0937587\pi$
$367$			11.1231i			0.580621i	−0.956932	+	0.290311i	$0.906241\pi$
$368$			42.7386i			2.22791i
$369$			0.438447i			0.0228246i
$370$		0			0
$371$			34.9309i			1.81352i
$372$	27.3693			1.41903
$373$			33.6155i			1.74055i	0.492570	+	0.870273i	$0.336058\pi$
$373$			33.6155i			1.74055i	−0.492570	+	0.870273i	$0.663942\pi$
$374$	6.24621			0.322984
$375$		0			0
$376$	26.2462			1.35354
$377$	−29.3693	+	4.63068i	−1.51260	+	0.238492i
$378$		−	9.12311i		−	0.469242i
$379$			3.75379i			0.192819i	0.995342	+	0.0964096i	$0.0307359\pi$
$379$			3.75379i			0.192819i	−0.995342	+	0.0964096i	$0.969264\pi$
$380$		0			0
$381$	17.3693			0.889857
$382$	−14.7386			−0.754094
$383$	−5.36932			−0.274359			−0.137180	−	0.990546i	$-0.543804\pi$
$383$	−5.36932			−0.274359			−0.137180	+	0.990546i	$0.543804\pi$
$384$			9.43845i			0.481654i
$385$		0			0
$386$	−7.50758			−0.382126
$387$		−	7.12311i		−	0.362088i
$388$	−68.1080			−3.45766
$389$	−12.7386			−0.645874			−0.322937	−	0.946420i	$-0.604670\pi$
$389$	−12.7386			−0.645874			−0.322937	+	0.946420i	$0.604670\pi$
$390$		0			0
$391$	−2.43845			−0.123318
$392$	−37.3002			−1.88394
$393$		−	2.24621i		−	0.113306i
$394$	31.3693			1.58036
$395$		0			0
$396$		−	25.3693i		−	1.27486i
$397$	24.3002			1.21959			0.609796	−	0.792559i	$-0.291251\pi$
$397$	24.3002			1.21959			0.609796	+	0.792559i	$0.291251\pi$
$398$	−20.4924			−1.02719
$399$	−4.00000			−0.200250
$400$		0			0
$401$			6.49242i			0.324216i	0.986773	+	0.162108i	$0.0518293\pi$
$401$			6.49242i			0.324216i	−0.986773	+	0.162108i	$0.948171\pi$
$402$		−	7.36932i		−	0.367548i
$403$	−3.36932	−	21.3693i	−0.167838	−	1.06448i
$404$	−9.12311			−0.453891
$405$		0			0
$406$	−75.2311			−3.73365
$407$			30.9309i			1.53319i
$408$	2.87689			0.142427
$409$		−	12.0000i		−	0.593362i	−0.954977	−	0.296681i	$-0.904120\pi$
$409$		−	12.0000i		−	0.593362i	0.954977	−	0.296681i	$-0.0958798\pi$
$410$		0			0
$411$		−	0.246211i		−	0.0121447i
$412$		0			0
$413$			14.2462i			0.701010i
$414$			14.2462i			0.700163i
$415$		0			0
$416$	−23.3693	+	3.68466i	−1.14578	+	0.180655i
$417$		−	17.5616i		−	0.859993i
$418$	−16.0000			−0.782586
$419$	−27.6155			−1.34911			−0.674553	−	0.738226i	$-0.735664\pi$
$419$	−27.6155			−1.34911			−0.674553	+	0.738226i	$0.735664\pi$
$420$		0			0
$421$		−	25.3693i		−	1.23642i	−0.786011	−	0.618212i	$-0.787857\pi$
$421$		−	25.3693i		−	1.23642i	0.786011	−	0.618212i	$-0.212143\pi$
$422$	−10.2462			−0.498778
$423$	4.00000			0.194487
$424$			64.3542i			3.12531i
$425$		0			0
$426$	22.2462			1.07783
$427$	30.0540			1.45441
$428$		−	3.12311i		−	0.150961i
$429$	−19.8078	+	3.12311i	−0.956328	+	0.150785i
$430$		0			0
$431$			30.7386i			1.48063i	0.672261	+	0.740314i	$0.265323\pi$
$431$			30.7386i			1.48063i	−0.672261	+	0.740314i	$0.734677\pi$
$432$		−	7.68466i		−	0.369728i
$433$		−	20.7386i		−	0.996635i	−0.866995	−	0.498318i	$-0.833951\pi$
$433$		−	20.7386i		−	0.996635i	0.866995	−	0.498318i	$-0.166049\pi$
$434$		−	54.7386i		−	2.62754i
$435$		0			0
$436$		−	22.2462i		−	1.06540i
$437$	6.24621			0.298797
$438$			28.4924i			1.36142i
$439$	−12.1922			−0.581904			−0.290952	−	0.956738i	$-0.593972\pi$
$439$	−12.1922			−0.581904			−0.290952	+	0.956738i	$0.593972\pi$
$440$		0			0
$441$	−5.68466			−0.270698
$442$	−0.630683	−	4.00000i	−0.0299985	−	0.190261i
$443$		−	5.56155i		−	0.264237i	−0.991234	−	0.132119i	$-0.957822\pi$
$443$		−	5.56155i		−	0.264237i	0.991234	−	0.132119i	$-0.0421780\pi$
$444$			25.3693i			1.20397i
$445$		0			0
$446$	7.36932			0.348947
$447$	12.9309			0.611609
$448$	−5.12311			−0.242044
$449$			3.56155i			0.168080i	0.996462	+	0.0840400i	$0.0267824\pi$
$449$			3.56155i			0.168080i	−0.996462	+	0.0840400i	$0.973218\pi$
$450$		0			0
$451$	2.43845			0.114822
$452$		−	92.3542i		−	4.34397i
$453$	−0.246211			−0.0115680
$454$	68.4924			3.21451
$455$		0			0
$456$	−7.36932			−0.345100
$457$	−26.4384			−1.23674			−0.618369	−	0.785888i	$-0.712206\pi$
$457$	−26.4384			−1.23674			−0.618369	+	0.785888i	$0.712206\pi$
$458$		−	48.9848i		−	2.28891i
$459$	0.438447			0.0204650
$460$		0			0
$461$		−	19.1771i		−	0.893166i	−0.894742	−	0.446583i	$-0.852641\pi$
$461$		−	19.1771i		−	0.893166i	0.894742	−	0.446583i	$-0.147359\pi$
$462$	−50.7386			−2.36057
$463$	41.8078			1.94297			0.971486	−	0.237098i	$-0.0761962\pi$
$463$	41.8078			1.94297			0.971486	+	0.237098i	$0.0761962\pi$
$464$	−63.3693			−2.94185
$465$		0			0
$466$		−	58.1080i		−	2.69180i
$467$			26.9309i			1.24621i	0.782137	+	0.623106i	$0.214129\pi$
$467$			26.9309i			1.24621i	−0.782137	+	0.623106i	$0.785871\pi$
$468$	−16.2462	+	2.56155i	−0.750981	+	0.118408i
$469$	−10.2462			−0.473126
$470$		0			0
$471$	−13.1231			−0.604681
$472$			26.2462i			1.20808i
$473$	−39.6155			−1.82152
$474$		−	14.2462i		−	0.654350i
$475$		0			0
$476$		−	7.12311i		−	0.326487i
$477$			9.80776i			0.449067i
$478$		−	34.7386i		−	1.58891i
$479$			18.0540i			0.824907i	0.910979	+	0.412454i	$0.135328\pi$
$479$			18.0540i			0.824907i	−0.910979	+	0.412454i	$0.864672\pi$
$480$		0			0
$481$	19.8078	−	3.12311i	0.903156	−	0.142401i
$482$			50.2462i			2.28865i
$483$	19.8078			0.901284
$484$	−90.9157			−4.13253
$485$		0			0
$486$		−	2.56155i		−	0.116194i
$487$	−4.05398			−0.183703			−0.0918516	−	0.995773i	$-0.529279\pi$
$487$	−4.05398			−0.183703			−0.0918516	+	0.995773i	$0.529279\pi$
$488$	55.3693			2.50645
$489$			3.56155i			0.161059i
$490$		0			0
$491$	−36.4924			−1.64688			−0.823440	−	0.567403i	$-0.807948\pi$
$491$	−36.4924			−1.64688			−0.823440	+	0.567403i	$0.807948\pi$
$492$	2.00000			0.0901670
$493$		−	3.61553i		−	0.162835i
$494$	1.61553	+	10.2462i	0.0726860	+	0.460999i
$495$		0			0
$496$		−	46.1080i		−	2.07031i
$497$		−	30.9309i		−	1.38744i
$498$			34.2462i			1.53461i
$499$		−	0.630683i		−	0.0282333i	−0.999900	−	0.0141166i	$-0.995506\pi$
$499$		−	0.630683i		−	0.0282333i	0.999900	−	0.0141166i	$-0.00449361\pi$
$500$		0			0
$501$			2.24621i			0.100353i
$502$	3.50758			0.156551
$503$		−	7.50758i		−	0.334746i	−0.985894	−	0.167373i	$-0.946472\pi$
$503$		−	7.50758i		−	0.334746i	0.985894	−	0.167373i	$-0.0535285\pi$
$504$	−23.3693			−1.04095
$505$		0			0
$506$	79.2311			3.52225
$507$	4.00000	+	12.3693i	0.177646	+	0.549341i
$508$		−	79.2311i		−	3.51531i
$509$			7.06913i			0.313334i	0.987652	+	0.156667i	$0.0500749\pi$
$509$			7.06913i			0.313334i	−0.987652	+	0.156667i	$0.949925\pi$
$510$		0			0
$511$	39.6155			1.75249
$512$	50.4233			2.22842
$513$	−1.12311			−0.0495863
$514$		−	5.12311i		−	0.225971i
$515$		0			0
$516$	−32.4924			−1.43040
$517$		−	22.2462i		−	0.978387i
$518$	50.7386			2.22933
$519$	12.2462			0.537549
$520$		0			0
$521$	−43.3693			−1.90004			−0.950022	−	0.312183i	$-0.898940\pi$
$521$	−43.3693			−1.90004			−0.950022	+	0.312183i	$0.898940\pi$
$522$	−21.1231			−0.924533
$523$			27.6155i			1.20754i	0.797158	+	0.603771i	$0.206336\pi$
$523$			27.6155i			1.20754i	−0.797158	+	0.603771i	$0.793664\pi$
$524$	−10.2462			−0.447608
$525$		0			0
$526$			67.2311i			2.93141i
$527$	2.63068			0.114594
$528$	−42.7386			−1.85996
$529$	−7.93087			−0.344820
$530$		0			0
$531$			4.00000i			0.173585i
$532$			18.2462i			0.791074i
$533$	−0.246211	−	1.56155i	−0.0106646	−	0.0676384i
$534$	−3.36932			−0.145805
$535$		0			0
$536$	−18.8769			−0.815358
$537$		−	2.24621i		−	0.0969312i
$538$	−34.8769			−1.50365
$539$			31.6155i			1.36178i
$540$		0			0
$541$			4.49242i			0.193144i	0.995326	+	0.0965722i	$0.0307879\pi$
$541$			4.49242i			0.193144i	−0.995326	+	0.0965722i	$0.969212\pi$
$542$		−	72.3542i		−	3.10788i
$543$		−	7.56155i		−	0.324497i
$544$		−	2.87689i		−	0.123346i
$545$		0			0
$546$	5.12311	+	32.4924i	0.219249	+	1.39055i
$547$		−	4.38447i		−	0.187466i	−0.995597	−	0.0937332i	$-0.970120\pi$
$547$		−	4.38447i		−	0.187466i	0.995597	−	0.0937332i	$-0.0298801\pi$
$548$	−1.12311			−0.0479767
$549$	8.43845			0.360144
$550$		0			0
$551$			9.26137i			0.394547i
$552$	36.4924			1.55322
$553$	−19.8078			−0.842312
$554$			7.36932i			0.313092i
$555$		0			0
$556$	−80.1080			−3.39733
$557$	6.49242			0.275093			0.137546	−	0.990495i	$-0.456078\pi$
$557$	6.49242			0.275093			0.137546	+	0.990495i	$0.456078\pi$
$558$		−	15.3693i		−	0.650635i
$559$	4.00000	+	25.3693i	0.169182	+	1.07301i
$560$		0			0
$561$		−	2.43845i		−	0.102951i
$562$		−	56.3542i		−	2.37716i
$563$		−	13.1771i		−	0.555348i	−0.960675	−	0.277674i	$-0.910437\pi$
$563$		−	13.1771i		−	0.555348i	0.960675	−	0.277674i	$-0.0895635\pi$
$564$		−	18.2462i		−	0.768304i
$565$		0			0
$566$		−	66.2462i		−	2.78454i
$567$	−3.56155			−0.149571
$568$		−	56.9848i		−	2.39103i
$569$	10.4924			0.439865			0.219933	−	0.975515i	$-0.429416\pi$
$569$	10.4924			0.439865			0.219933	+	0.975515i	$0.429416\pi$
$570$		0			0
$571$	3.31534			0.138743			0.0693714	−	0.997591i	$-0.477901\pi$
$571$	3.31534			0.138743			0.0693714	+	0.997591i	$0.477901\pi$
$572$	14.2462	+	90.3542i	0.595664	+	3.77790i
$573$			5.75379i			0.240368i
$574$		−	4.00000i		−	0.166957i
$575$		0			0
$576$	−1.43845			−0.0599353
$577$	−15.4233			−0.642080			−0.321040	−	0.947066i	$-0.604032\pi$
$577$	−15.4233			−0.642080			−0.321040	+	0.947066i	$0.604032\pi$
$578$	−43.0540			−1.79081
$579$			2.93087i			0.121803i
$580$		0			0
$581$	47.6155			1.97542
$582$			38.2462i			1.58536i
$583$	54.5464			2.25908
$584$	72.9848			3.02013
$585$		0			0
$586$	21.1231			0.872587
$587$	7.12311			0.294002			0.147001	−	0.989136i	$-0.453038\pi$
$587$	7.12311			0.294002			0.147001	+	0.989136i	$0.453038\pi$
$588$			25.9309i			1.06937i
$589$	−6.73863			−0.277661
$590$		0			0
$591$		−	12.2462i		−	0.503742i
$592$	42.7386			1.75655
$593$	−13.5076			−0.554690			−0.277345	−	0.960770i	$-0.589454\pi$
$593$	−13.5076			−0.554690			−0.277345	+	0.960770i	$0.589454\pi$
$594$	−14.2462			−0.584529
$595$		0			0
$596$		−	58.9848i		−	2.41611i
$597$			8.00000i			0.327418i
$598$	−8.00000	−	50.7386i	−0.327144	−	2.07486i
$599$	−6.24621			−0.255213			−0.127607	−	0.991825i	$-0.540730\pi$
$599$	−6.24621			−0.255213			−0.127607	+	0.991825i	$0.540730\pi$
$600$		0			0
$601$	4.93087			0.201134			0.100567	−	0.994930i	$-0.467934\pi$
$601$	4.93087			0.201134			0.100567	+	0.994930i	$0.467934\pi$
$602$			64.9848i			2.64858i
$603$	−2.87689			−0.117156
$604$			1.12311i			0.0456985i
$605$		0			0
$606$			5.12311i			0.208112i
$607$			46.2462i			1.87708i	0.345176	+	0.938538i	$0.387819\pi$
$607$			46.2462i			1.87708i	−0.345176	+	0.938538i	$0.612181\pi$
$608$			7.36932i			0.298865i
$609$			29.3693i			1.19010i
$610$		0			0
$611$	−14.2462	+	2.24621i	−0.576340	+	0.0908720i
$612$		−	2.00000i		−	0.0808452i
$613$	−3.80776			−0.153794			−0.0768971	−	0.997039i	$-0.524501\pi$
$613$	−3.80776			−0.153794			−0.0768971	+	0.997039i	$0.524501\pi$
$614$	7.86174			0.317274
$615$		0			0
$616$			129.970i			5.23663i
$617$	16.2462			0.654048			0.327024	−	0.945016i	$-0.393954\pi$
$617$	16.2462			0.654048			0.327024	+	0.945016i	$0.393954\pi$
$618$		0			0
$619$			30.0000i			1.20580i	0.797816	+	0.602901i	$0.205989\pi$
$619$			30.0000i			1.20580i	−0.797816	+	0.602901i	$0.794011\pi$
$620$		0			0
$621$	5.56155			0.223177
$622$	−38.7386			−1.55328
$623$			4.68466i			0.187687i
$624$	4.31534	+	27.3693i	0.172752	+	1.09565i
$625$		0			0
$626$		−	43.8617i		−	1.75307i
$627$			6.24621i			0.249450i
$628$			59.8617i			2.38874i
$629$			2.43845i			0.0972273i
$630$		0			0
$631$		−	38.9848i		−	1.55196i	−0.630756	−	0.775981i	$-0.717255\pi$
$631$		−	38.9848i		−	1.55196i	0.630756	−	0.775981i	$-0.282745\pi$
$632$	−36.4924			−1.45159
$633$			4.00000i			0.158986i
$634$	15.3693			0.610394
$635$		0			0
$636$	44.7386			1.77400
$637$	20.2462	−	3.19224i	0.802184	−	0.126481i
$638$			117.477i			4.65097i
$639$		−	8.68466i		−	0.343560i
$640$		0			0
$641$	2.87689			0.113630			0.0568152	−	0.998385i	$-0.481905\pi$
$641$	2.87689			0.113630			0.0568152	+	0.998385i	$0.481905\pi$
$642$	−1.75379			−0.0692165
$643$	−19.5616			−0.771432			−0.385716	−	0.922617i	$-0.626046\pi$
$643$	−19.5616			−0.771432			−0.385716	+	0.922617i	$0.626046\pi$
$644$		−	90.3542i		−	3.56045i
$645$		0			0
$646$	−1.26137			−0.0496278
$647$			26.5464i			1.04365i	0.853054	+	0.521823i	$0.174748\pi$
$647$			26.5464i			1.04365i	−0.853054	+	0.521823i	$0.825252\pi$
$648$	−6.56155			−0.257762
$649$	22.2462			0.873240
$650$		0			0
$651$	−21.3693			−0.837530
$652$	16.2462			0.636251
$653$			16.7386i			0.655033i	0.944845	+	0.327517i	$0.106212\pi$
$653$			16.7386i			0.655033i	−0.944845	+	0.327517i	$0.893788\pi$
$654$	−12.4924			−0.488492
$655$		0			0
$656$		−	3.36932i		−	0.131550i
$657$	11.1231			0.433954
$658$	−36.4924			−1.42262
$659$	39.6155			1.54320			0.771601	−	0.636107i	$-0.219456\pi$
$659$	39.6155			1.54320			0.771601	+	0.636107i	$0.219456\pi$
$660$		0			0
$661$			32.4924i			1.26381i	0.775046	+	0.631904i	$0.217726\pi$
$661$			32.4924i			1.26381i	−0.775046	+	0.631904i	$0.782274\pi$
$662$		−	24.6307i		−	0.957299i
$663$	−1.56155	+	0.246211i	−0.0606457	+	0.00956205i
$664$	87.7235			3.40433
$665$		0			0
$666$	14.2462			0.552029
$667$		−	45.8617i		−	1.77577i
$668$	10.2462			0.396438
$669$		−	2.87689i		−	0.111227i
$670$		0			0
$671$		−	46.9309i		−	1.81175i
$672$			23.3693i			0.901491i
$673$		−	34.1080i		−	1.31476i	−0.753557	−	0.657382i	$-0.771664\pi$
$673$		−	34.1080i		−	1.31476i	0.753557	−	0.657382i	$-0.228336\pi$
$674$		−	66.6004i		−	2.56535i
$675$		0			0
$676$	56.4233	−	18.2462i	2.17013	−	0.701777i
$677$		−	37.4233i		−	1.43829i	−0.694858	−	0.719147i	$-0.744533\pi$
$677$		−	37.4233i		−	1.43829i	0.694858	−	0.719147i	$-0.255467\pi$
$678$	−51.8617			−1.99174
$679$	53.1771			2.04075
$680$		0			0
$681$		−	26.7386i		−	1.02463i
$682$	−85.4773			−3.27309
$683$	−19.1231			−0.731725			−0.365863	−	0.930669i	$-0.619226\pi$
$683$	−19.1231			−0.731725			−0.365863	+	0.930669i	$0.619226\pi$
$684$			5.12311i			0.195887i
$685$		0			0
$686$	−12.0000			−0.458162
$687$	−19.1231			−0.729592
$688$			54.7386i			2.08689i
$689$	−5.50758	−	34.9309i	−0.209822	−	1.33076i
$690$		0			0
$691$			18.0000i			0.684752i	0.939563	+	0.342376i	$0.111232\pi$
$691$			18.0000i			0.684752i	−0.939563	+	0.342376i	$0.888768\pi$
$692$		−	55.8617i		−	2.12354i
$693$			19.8078i			0.752435i
$694$			28.0000i			1.06287i
$695$		0			0
$696$			54.1080i			2.05096i
$697$	0.192236			0.00728146
$698$			22.7386i			0.860670i
$699$	−22.6847			−0.858013
$700$		0			0
$701$	19.3693			0.731569			0.365785	−	0.930700i	$-0.380801\pi$
$701$	19.3693			0.731569			0.365785	+	0.930700i	$0.380801\pi$
$702$	1.43845	+	9.12311i	0.0542907	+	0.344329i
$703$		−	6.24621i		−	0.235580i
$704$			8.00000i			0.301511i
$705$		0			0
$706$	−48.3542			−1.81983
$707$	7.12311			0.267892
$708$	18.2462			0.685735
$709$			48.0000i			1.80268i	0.433114	+	0.901339i	$0.357415\pi$
$709$			48.0000i			1.80268i	−0.433114	+	0.901339i	$0.642585\pi$
$710$		0			0
$711$	−5.56155			−0.208575
$712$			8.63068i			0.323449i
$713$	33.3693			1.24969
$714$	−4.00000			−0.149696
$715$		0			0
$716$	−10.2462			−0.382919
$717$	−13.5616			−0.506465
$718$			67.2311i			2.50904i
$719$	−7.12311			−0.265647			−0.132824	−	0.991140i	$-0.542404\pi$
$719$	−7.12311			−0.265647			−0.132824	+	0.991140i	$0.542404\pi$
$720$		0			0
$721$		0			0
$722$	−45.4384			−1.69104
$723$	19.6155			0.729509
$724$	−34.4924			−1.28190
$725$		0			0
$726$			51.0540i			1.89479i
$727$		−	6.63068i		−	0.245918i	−0.992412	−	0.122959i	$-0.960762\pi$
$727$		−	6.63068i		−	0.245918i	0.992412	−	0.122959i	$-0.0392384\pi$
$728$	83.2311	−	13.1231i	3.08475	−	0.486375i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−3.12311			−0.115512
$732$		−	38.4924i		−	1.42272i
$733$	−25.1771			−0.929937			−0.464968	−	0.885327i	$-0.653934\pi$
$733$	−25.1771			−0.929937			−0.464968	+	0.885327i	$0.653934\pi$
$734$		−	28.4924i		−	1.05167i
$735$		0			0
$736$		−	36.4924i		−	1.34513i
$737$			16.0000i			0.589368i
$738$		−	1.12311i		−	0.0413421i
$739$		−	36.7386i		−	1.35145i	−0.737153	−	0.675726i	$-0.763830\pi$
$739$		−	36.7386i		−	1.35145i	0.737153	−	0.675726i	$-0.236170\pi$
$740$		0			0
$741$	4.00000	−	0.630683i	0.146944	−	0.0231687i
$742$		−	89.4773i		−	3.28481i
$743$	24.9848			0.916605			0.458303	−	0.888796i	$-0.348458\pi$
$743$	24.9848			0.916605			0.458303	+	0.888796i	$0.348458\pi$
$744$	−39.3693			−1.44335
$745$		0			0
$746$		−	86.1080i		−	3.15264i
$747$	13.3693			0.489158
$748$	−11.1231			−0.406701
$749$			2.43845i			0.0890989i
$750$		0			0
$751$	−48.3002			−1.76250			−0.881249	−	0.472652i	$-0.843297\pi$
$751$	−48.3002			−1.76250			−0.881249	+	0.472652i	$0.843297\pi$
$752$	−30.7386			−1.12092
$753$		−	1.36932i		−	0.0499007i
$754$	75.2311	−	11.8617i	2.73975	−	0.431979i
$755$		0			0
$756$			16.2462i			0.590869i
$757$		−	14.8769i		−	0.540710i	−0.962761	−	0.270355i	$-0.912859\pi$
$757$		−	14.8769i		−	0.540710i	0.962761	−	0.270355i	$-0.0871411\pi$
$758$		−	9.61553i		−	0.349252i
$759$		−	30.9309i		−	1.12272i
$760$		0			0
$761$		−	0.246211i		−	0.00892515i	−0.999990	−	0.00446258i	$-0.998580\pi$
$761$		−	0.246211i		−	0.00892515i	0.999990	−	0.00446258i	$-0.00142049\pi$
$762$	−44.4924			−1.61179
$763$			17.3693i			0.628811i
$764$	26.2462			0.949555
$765$		0			0
$766$	13.7538			0.496945
$767$	−2.24621	−	14.2462i	−0.0811060	−	0.514401i
$768$		−	27.0540i		−	0.976226i
$769$			8.00000i			0.288487i	0.989542	+	0.144244i	$0.0460749\pi$
$769$			8.00000i			0.288487i	−0.989542	+	0.144244i	$0.953925\pi$
$770$		0			0
$771$	−2.00000			−0.0720282
$772$	13.3693			0.481172
$773$	22.4924			0.808996			0.404498	−	0.914539i	$-0.367446\pi$
$773$	22.4924			0.808996			0.404498	+	0.914539i	$0.367446\pi$
$774$			18.2462i			0.655847i
$775$		0			0
$776$	97.9697			3.51691
$777$		−	19.8078i		−	0.710600i
$778$	32.6307			1.16987
$779$	−0.492423			−0.0176429
$780$		0			0
$781$	−48.3002			−1.72832
$782$	6.24621			0.223364
$783$			8.24621i			0.294696i
$784$	43.6847			1.56017
$785$		0			0
$786$			5.75379i			0.205231i
$787$	−6.87689			−0.245135			−0.122567	−	0.992460i	$-0.539113\pi$
$787$	−6.87689			−0.245135			−0.122567	+	0.992460i	$0.539113\pi$
$788$	−55.8617			−1.98999
$789$	26.2462			0.934390
$790$		0			0
$791$			72.1080i			2.56386i
$792$			36.4924i			1.29670i
$793$	−30.0540	+	4.73863i	−1.06725	+	0.168274i
$794$	−62.2462			−2.20904
$795$		0			0
$796$	36.4924			1.29344
$797$			15.5616i			0.551218i	0.961270	+	0.275609i	$0.0888796\pi$
$797$			15.5616i			0.551218i	−0.961270	+	0.275609i	$0.911120\pi$
$798$	10.2462			0.362712
$799$		−	1.75379i		−	0.0620446i
$800$		0			0
$801$			1.31534i			0.0464753i
$802$		−	16.6307i		−	0.587250i
$803$		−	61.8617i		−	2.18305i
$804$			13.1231i			0.462816i
$805$		0			0
$806$	8.63068	+	54.7386i	0.304003	+	1.92809i
$807$			13.6155i			0.479289i
$808$	13.1231			0.461669
$809$	6.87689			0.241779			0.120889	−	0.992666i	$-0.461425\pi$
$809$	6.87689			0.241779			0.120889	+	0.992666i	$0.461425\pi$
$810$		0			0
$811$			2.49242i			0.0875208i	0.999042	+	0.0437604i	$0.0139338\pi$
$811$			2.49242i			0.0875208i	−0.999042	+	0.0437604i	$0.986066\pi$
$812$	133.970			4.70141
$813$	−28.2462			−0.990638
$814$		−	79.2311i		−	2.77705i
$815$		0			0
$816$	−3.36932			−0.117950
$817$	8.00000			0.279885
$818$			30.7386i			1.07475i
$819$	12.6847	−	2.00000i	0.443238	−	0.0698857i
$820$		0			0
$821$			8.05398i			0.281086i	0.990075	+	0.140543i	$0.0448848\pi$
$821$			8.05398i			0.281086i	−0.990075	+	0.140543i	$0.955115\pi$
$822$			0.630683i			0.0219976i
$823$			15.6155i			0.544323i	0.962252	+	0.272162i	$0.0877385\pi$
$823$			15.6155i			0.544323i	−0.962252	+	0.272162i	$0.912261\pi$
$824$		0			0
$825$		0			0
$826$		−	36.4924i		−	1.26973i
$827$	34.7386			1.20798			0.603990	−	0.796992i	$-0.293577\pi$
$827$	34.7386			1.20798			0.603990	+	0.796992i	$0.293577\pi$
$828$		−	25.3693i		−	0.881645i
$829$	−36.7386			−1.27599			−0.637993	−	0.770042i	$-0.720235\pi$
$829$	−36.7386			−1.27599			−0.637993	+	0.770042i	$0.720235\pi$
$830$		0			0
$831$	2.87689			0.0997984
$832$	5.12311	−	0.807764i	0.177612	−	0.0280042i
$833$			2.49242i			0.0863573i
$834$			44.9848i			1.55770i
$835$		0			0
$836$	28.4924			0.985431
$837$	−6.00000			−0.207390
$838$	70.7386			2.44363
$839$		−	7.31534i		−	0.252554i	−0.991995	−	0.126277i	$-0.959697\pi$
$839$		−	7.31534i		−	0.252554i	0.991995	−	0.126277i	$-0.0403028\pi$
$840$		0			0
$841$	39.0000			1.34483
$842$			64.9848i			2.23953i
$843$	−22.0000			−0.757720
$844$	18.2462			0.628060
$845$		0			0
$846$	−10.2462			−0.352272
$847$	70.9848			2.43907
$848$		−	75.3693i		−	2.58819i
$849$	−25.8617			−0.887573
$850$		0			0
$851$			30.9309i			1.06030i
$852$	−39.6155			−1.35721
$853$	−22.9309			−0.785138			−0.392569	−	0.919723i	$-0.628414\pi$
$853$	−22.9309			−0.785138			−0.392569	+	0.919723i	$0.628414\pi$
$854$	−76.9848			−2.63437
$855$		0			0
$856$			4.49242i			0.153548i
$857$			7.56155i			0.258298i	0.991625	+	0.129149i	$0.0412245\pi$
$857$			7.56155i			0.258298i	−0.991625	+	0.129149i	$0.958775\pi$
$858$	50.7386	−	8.00000i	1.73219	−	0.273115i
$859$	−26.5464			−0.905751			−0.452876	−	0.891574i	$-0.649602\pi$
$859$	−26.5464			−0.905751			−0.452876	+	0.891574i	$0.649602\pi$
$860$		0			0
$861$	−1.56155			−0.0532176
$862$		−	78.7386i		−	2.68185i
$863$	−13.3693			−0.455097			−0.227548	−	0.973767i	$-0.573071\pi$
$863$	−13.3693			−0.455097			−0.227548	+	0.973767i	$0.573071\pi$
$864$			6.56155i			0.223229i
$865$		0			0
$866$			53.1231i			1.80520i
$867$			16.8078i			0.570822i
$868$			97.4773i			3.30859i
$869$			30.9309i			1.04926i
$870$		0			0
$871$	10.2462	−	1.61553i	0.347180	−	0.0547401i
$872$			32.0000i			1.08366i
$873$	14.9309			0.505333
$874$	−16.0000			−0.541208
$875$		0			0
$876$		−	50.7386i		−	1.71430i
$877$	27.1231			0.915882			0.457941	−	0.888983i	$-0.348587\pi$
$877$	27.1231			0.915882			0.457941	+	0.888983i	$0.348587\pi$
$878$	31.2311			1.05400
$879$		−	8.24621i		−	0.278138i
$880$		0			0
$881$	−47.3693			−1.59591			−0.797956	−	0.602715i	$-0.794086\pi$
$881$	−47.3693			−1.59591			−0.797956	+	0.602715i	$0.794086\pi$
$882$	14.5616			0.490313
$883$			8.49242i			0.285793i	0.989738	+	0.142896i	$0.0456416\pi$
$883$			8.49242i			0.285793i	−0.989738	+	0.142896i	$0.954358\pi$
$884$	1.12311	+	7.12311i	0.0377741	+	0.239576i
$885$		0			0
$886$			14.2462i			0.478611i
$887$		−	7.31534i		−	0.245625i	−0.992430	−	0.122813i	$-0.960809\pi$
$887$		−	7.31534i		−	0.245625i	0.992430	−	0.122813i	$-0.0391914\pi$
$888$		−	36.4924i		−	1.22461i
$889$			61.8617i			2.07478i
$890$		0			0
$891$			5.56155i			0.186319i
$892$	−13.1231			−0.439394
$893$			4.49242i			0.150333i
$894$	−33.1231			−1.10780
$895$		0			0
$896$	−33.6155			−1.12302
$897$	−19.8078	+	3.12311i	−0.661362	+	0.104277i
$898$		−	9.12311i		−	0.304442i
$899$			49.4773i			1.65016i
$900$		0			0
$901$	4.30019			0.143260
$902$	−6.24621			−0.207976
$903$	25.3693			0.844238
$904$			132.847i			4.41841i
$905$		0			0
$906$	0.630683			0.0209530
$907$			14.7386i			0.489388i	0.969600	+	0.244694i	$0.0786876\pi$
$907$			14.7386i			0.489388i	−0.969600	+	0.244694i	$0.921312\pi$
$908$	−121.970			−4.04771
$909$	2.00000			0.0663358
$910$		0			0
$911$	21.3693			0.707997			0.353999	−	0.935246i	$-0.384822\pi$
$911$	21.3693			0.707997			0.353999	+	0.935246i	$0.384822\pi$
$912$	8.63068			0.285790
$913$		−	74.3542i		−	2.46076i
$914$	67.7235			2.24009
$915$		0			0
$916$			87.2311i			2.88220i
$917$	8.00000			0.264183
$918$	−1.12311			−0.0370680
$919$	44.7926			1.47757			0.738786	−	0.673940i	$-0.235399\pi$
$919$	44.7926			1.47757			0.738786	+	0.673940i	$0.235399\pi$
$920$		0			0
$921$		−	3.06913i		−	0.101131i
$922$			49.1231i			1.61778i
$923$	4.87689	+	30.9309i	0.160525	+	1.01810i
$924$	90.3542			2.97243
$925$		0			0
$926$	−107.093			−3.51929
$927$		0			0
$928$	54.1080			1.77618
$929$		−	34.6847i		−	1.13797i	−0.822349	−	0.568983i	$-0.807337\pi$
$929$		−	34.6847i		−	1.13797i	0.822349	−	0.568983i	$-0.192663\pi$
$930$		0			0
$931$		−	6.38447i		−	0.209243i
$932$			103.477i			3.38951i
$933$			15.1231i			0.495108i
$934$		−	68.9848i		−	2.25725i
$935$		0			0
$936$	23.3693	−	3.68466i	0.763850	−	0.120437i
$937$			6.49242i			0.212098i	0.994361	+	0.106049i	$0.0338201\pi$
$937$			6.49242i			0.212098i	−0.994361	+	0.106049i	$0.966180\pi$
$938$	26.2462			0.856969
$939$	−17.1231			−0.558791
$940$		0			0
$941$		−	9.31534i		−	0.303671i	−0.988406	−	0.151836i	$-0.951482\pi$
$941$		−	9.31534i		−	0.303671i	0.988406	−	0.151836i	$-0.0485185\pi$
$942$	33.6155			1.09525
$943$	2.43845			0.0794068
$944$		−	30.7386i		−	1.00046i
$945$		0			0
$946$	101.477			3.29931
$947$	15.5076			0.503929			0.251964	−	0.967737i	$-0.418923\pi$
$947$	15.5076			0.503929			0.251964	+	0.967737i	$0.418923\pi$
$948$			25.3693i			0.823957i
$949$	−39.6155	+	6.24621i	−1.28597	+	0.202761i
$950$		0			0
$951$		−	6.00000i		−	0.194563i
$952$			10.2462i			0.332082i
$953$			21.3153i			0.690472i	0.938516	+	0.345236i	$0.112201\pi$
$953$			21.3153i			0.690472i	−0.938516	+	0.345236i	$0.887799\pi$
$954$		−	25.1231i		−	0.813391i
$955$		0			0
$956$			61.8617i			2.00075i
$957$	45.8617			1.48250
$958$		−	46.2462i		−	1.49415i
$959$	0.876894			0.0283164
$960$		0			0
$961$	−5.00000			−0.161290
$962$	−50.7386	+	8.00000i	−1.63588	+	0.257930i
$963$			0.684658i			0.0220628i
$964$		−	89.4773i		−	2.88187i
$965$		0			0
$966$	−50.7386			−1.63249
$967$	−38.1080			−1.22547			−0.612735	−	0.790289i	$-0.709931\pi$
$967$	−38.1080			−1.22547			−0.612735	+	0.790289i	$0.709931\pi$
$968$	130.777			4.20335
$969$			0.492423i			0.0158189i
$970$		0			0
$971$	20.8769			0.669971			0.334986	−	0.942223i	$-0.391269\pi$
$971$	20.8769			0.669971			0.334986	+	0.942223i	$0.391269\pi$
$972$			4.56155i			0.146312i
$973$	62.5464			2.00515
$974$	10.3845			0.332740
$975$		0			0
$976$	−64.8466			−2.07569
$977$	−27.3693			−0.875622			−0.437811	−	0.899067i	$-0.644246\pi$
$977$	−27.3693			−0.875622			−0.437811	+	0.899067i	$0.644246\pi$
$978$		−	9.12311i		−	0.291725i
$979$	7.31534			0.233799
$980$		0			0
$981$			4.87689i			0.155707i
$982$	93.4773			2.98298
$983$	42.7386			1.36315			0.681575	−	0.731748i	$-0.261295\pi$
$983$	42.7386			1.36315			0.681575	+	0.731748i	$0.261295\pi$
$984$	−2.87689			−0.0917120
$985$		0			0
$986$			9.26137i			0.294942i
$987$			14.2462i			0.453462i
$988$	−2.87689	−	18.2462i	−0.0915262	−	0.580489i
$989$	−39.6155			−1.25970
$990$		0			0
$991$	−39.9157			−1.26796			−0.633982	−	0.773348i	$-0.718581\pi$
$991$	−39.9157			−1.26796			−0.633982	+	0.773348i	$0.718581\pi$
$992$			39.3693i			1.24998i
$993$	−9.61553			−0.305140
$994$			79.2311i			2.51306i
$995$		0			0
$996$		−	60.9848i		−	1.93238i
$997$		−	42.1080i		−	1.33357i	−0.745249	−	0.666786i	$-0.767669\pi$
$997$		−	42.1080i		−	1.33357i	0.745249	−	0.666786i	$-0.232331\pi$
$998$			1.61553i			0.0511386i
$999$		−	5.56155i		−	0.175960i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.h.e.649.2		4
5.2	odd	4		195.2.b.c.181.1	✓	4
5.3	odd	4		975.2.b.f.376.4		4
5.4	even	2		975.2.h.g.649.3		4
13.12	even	2		975.2.h.g.649.4		4
15.2	even	4		585.2.b.e.181.4		4
20.7	even	4		3120.2.g.n.961.2		4
65.12	odd	4		195.2.b.c.181.4	yes	4
65.38	odd	4		975.2.b.f.376.1		4
65.47	even	4		2535.2.a.q.1.2		2
65.57	even	4		2535.2.a.p.1.1		2
65.64	even	2	inner	975.2.h.e.649.1		4
195.47	odd	4		7605.2.a.bc.1.1		2
195.77	even	4		585.2.b.e.181.1		4
195.122	odd	4		7605.2.a.bh.1.2		2
260.207	even	4		3120.2.g.n.961.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.b.c.181.1	✓	4	5.2	odd	4
195.2.b.c.181.4	yes	4	65.12	odd	4
585.2.b.e.181.1		4	195.77	even	4
585.2.b.e.181.4		4	15.2	even	4
975.2.b.f.376.1		4	65.38	odd	4
975.2.b.f.376.4		4	5.3	odd	4
975.2.h.e.649.1		4	65.64	even	2	inner
975.2.h.e.649.2		4	1.1	even	1	trivial
975.2.h.g.649.3		4	5.4	even	2
975.2.h.g.649.4		4	13.12	even	2
2535.2.a.p.1.1		2	65.57	even	4
2535.2.a.q.1.2		2	65.47	even	4
3120.2.g.n.961.2		4	20.7	even	4
3120.2.g.n.961.3		4	260.207	even	4
7605.2.a.bc.1.1		2	195.47	odd	4
7605.2.a.bh.1.2		2	195.122	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.56155 q^{2} +1.00000i q^{3} +4.56155 q^{4} -2.56155i q^{6} -3.56155 q^{7} -6.56155 q^{8} -1.00000 q^{9} +5.56155i q^{11} +4.56155i q^{12} +(3.56155 - 0.561553i) q^{13} +9.12311 q^{14} +7.68466 q^{16} +0.438447i q^{17} +2.56155 q^{18} -1.12311i q^{19} -3.56155i q^{21} -14.2462i q^{22} +5.56155i q^{23} -6.56155i q^{24} +(-9.12311 + 1.43845i) q^{26} -1.00000i q^{27} -16.2462 q^{28} -8.24621 q^{29} -6.00000i q^{31} -6.56155 q^{32} -5.56155 q^{33} -1.12311i q^{34} -4.56155 q^{36} +5.56155 q^{37} +2.87689i q^{38} +(0.561553 + 3.56155i) q^{39} -0.438447i q^{41} +9.12311i q^{42} +7.12311i q^{43} +25.3693i q^{44} -14.2462i q^{46} -4.00000 q^{47} +7.68466i q^{48} +5.68466 q^{49} -0.438447 q^{51} +(16.2462 - 2.56155i) q^{52} -9.80776i q^{53} +2.56155i q^{54} +23.3693 q^{56} +1.12311 q^{57} +21.1231 q^{58} -4.00000i q^{59} -8.43845 q^{61} +15.3693i q^{62} +3.56155 q^{63} +1.43845 q^{64} +14.2462 q^{66} +2.87689 q^{67} +2.00000i q^{68} -5.56155 q^{69} +8.68466i q^{71} +6.56155 q^{72} -11.1231 q^{73} -14.2462 q^{74} -5.12311i q^{76} -19.8078i q^{77} +(-1.43845 - 9.12311i) q^{78} +5.56155 q^{79} +1.00000 q^{81} +1.12311i q^{82} -13.3693 q^{83} -16.2462i q^{84} -18.2462i q^{86} -8.24621i q^{87} -36.4924i q^{88} -1.31534i q^{89} +(-12.6847 + 2.00000i) q^{91} +25.3693i q^{92} +6.00000 q^{93} +10.2462 q^{94} -6.56155i q^{96} -14.9309 q^{97} -14.5616 q^{98} -5.56155i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 10 q^{4} - 6 q^{7} - 18 q^{8} - 4 q^{9} + 6 q^{13} + 20 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{26} - 32 q^{28} - 18 q^{32} - 14 q^{33} - 10 q^{36} + 14 q^{37} - 6 q^{39} - 16 q^{47} - 2 q^{49}+ \cdots - 50 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 10 * q^4 - 6 * q^7 - 18 * q^8 - 4 * q^9 + 6 * q^13 + 20 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^26 - 32 * q^28 - 18 * q^32 - 14 * q^33 - 10 * q^36 + 14 * q^37 - 6 * q^39 - 16 * q^47 - 2 * q^49 - 10 * q^51 + 32 * q^52 + 44 * q^56 - 12 * q^57 + 68 * q^58 - 42 * q^61 + 6 * q^63 + 14 * q^64 + 24 * q^66 + 28 * q^67 - 14 * q^69 + 18 * q^72 - 28 * q^73 - 24 * q^74 - 14 * q^78 + 14 * q^79 + 4 * q^81 - 4 * q^83 - 26 * q^91 + 24 * q^93 + 8 * q^94 - 2 * q^97 - 50 * q^98

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