LMFDB - Embedded newform 2014.2.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2014,2,Mod(1,2014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2014 = 2 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2014.a (trivial)

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:	yes
Analytic conductor:	$16.0818709671$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 13x^{6} - x^{5} + 50x^{4} + 21x^{3} - 61x^{2} - 52x - 10 $ x^8 - 13x^6 - x^5 + 50x^4 + 21x^3 - 61x^2 - 52*x - 10
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.89675$ of defining polynomial
Character	$\chi$	$=$	2014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.89675 q^{3} +1.00000 q^{4} +0.769767 q^{5} +1.89675 q^{6} -3.09528 q^{7} -1.00000 q^{8} +0.597654 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.89675 q^{3} +1.00000 q^{4} +0.769767 q^{5} +1.89675 q^{6} -3.09528 q^{7} -1.00000 q^{8} +0.597654 q^{9} -0.769767 q^{10} +1.83830 q^{11} -1.89675 q^{12} -3.26285 q^{13} +3.09528 q^{14} -1.46005 q^{15} +1.00000 q^{16} +6.40596 q^{17} -0.597654 q^{18} -1.00000 q^{19} +0.769767 q^{20} +5.87096 q^{21} -1.83830 q^{22} +8.27142 q^{23} +1.89675 q^{24} -4.40746 q^{25} +3.26285 q^{26} +4.55665 q^{27} -3.09528 q^{28} -1.27654 q^{29} +1.46005 q^{30} -0.926332 q^{31} -1.00000 q^{32} -3.48680 q^{33} -6.40596 q^{34} -2.38264 q^{35} +0.597654 q^{36} +2.72124 q^{37} +1.00000 q^{38} +6.18881 q^{39} -0.769767 q^{40} -11.0480 q^{41} -5.87096 q^{42} -2.26739 q^{43} +1.83830 q^{44} +0.460054 q^{45} -8.27142 q^{46} +7.95102 q^{47} -1.89675 q^{48} +2.58074 q^{49} +4.40746 q^{50} -12.1505 q^{51} -3.26285 q^{52} -1.00000 q^{53} -4.55665 q^{54} +1.41506 q^{55} +3.09528 q^{56} +1.89675 q^{57} +1.27654 q^{58} +5.37584 q^{59} -1.46005 q^{60} -8.83926 q^{61} +0.926332 q^{62} -1.84990 q^{63} +1.00000 q^{64} -2.51164 q^{65} +3.48680 q^{66} +7.90659 q^{67} +6.40596 q^{68} -15.6888 q^{69} +2.38264 q^{70} -9.37689 q^{71} -0.597654 q^{72} -1.96318 q^{73} -2.72124 q^{74} +8.35984 q^{75} -1.00000 q^{76} -5.69006 q^{77} -6.18881 q^{78} +12.3482 q^{79} +0.769767 q^{80} -10.4358 q^{81} +11.0480 q^{82} +10.2731 q^{83} +5.87096 q^{84} +4.93110 q^{85} +2.26739 q^{86} +2.42127 q^{87} -1.83830 q^{88} -2.33879 q^{89} -0.460054 q^{90} +10.0994 q^{91} +8.27142 q^{92} +1.75702 q^{93} -7.95102 q^{94} -0.769767 q^{95} +1.89675 q^{96} -0.871774 q^{97} -2.58074 q^{98} +1.09867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 5 q^{13} + q^{15} + 8 q^{16} - 9 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} - 9 q^{21} + 6 q^{22} - q^{23} - 9 q^{25} + 5 q^{26} - 3 q^{27} - 23 q^{29} - q^{30} - 6 q^{31} - 8 q^{32} - 6 q^{33} + 9 q^{34} - 7 q^{35} + 2 q^{36} + q^{37} + 8 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} + 9 q^{42} + 9 q^{43} - 6 q^{44} - 9 q^{45} + q^{46} - 13 q^{47} - 8 q^{49} + 9 q^{50} - 24 q^{51} - 5 q^{52} - 8 q^{53} + 3 q^{54} - 11 q^{55} + 23 q^{58} - 9 q^{59} + q^{60} + 6 q^{62} - 18 q^{63} + 8 q^{64} - 26 q^{65} + 6 q^{66} + 9 q^{67} - 9 q^{68} - 22 q^{69} + 7 q^{70} - 31 q^{71} - 2 q^{72} + 5 q^{73} - q^{74} - q^{75} - 8 q^{76} - 4 q^{77} + 5 q^{78} + 19 q^{79} + q^{80} - 24 q^{81} + 3 q^{82} + 11 q^{83} - 9 q^{84} + 19 q^{85} - 9 q^{86} - 22 q^{87} + 6 q^{88} - 41 q^{89} + 9 q^{90} + 18 q^{91} - q^{92} + 3 q^{93} + 13 q^{94} - q^{95} - 24 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 5 * q^13 + q^15 + 8 * q^16 - 9 * q^17 - 2 * q^18 - 8 * q^19 + q^20 - 9 * q^21 + 6 * q^22 - q^23 - 9 * q^25 + 5 * q^26 - 3 * q^27 - 23 * q^29 - q^30 - 6 * q^31 - 8 * q^32 - 6 * q^33 + 9 * q^34 - 7 * q^35 + 2 * q^36 + q^37 + 8 * q^38 - 5 * q^39 - q^40 - 3 * q^41 + 9 * q^42 + 9 * q^43 - 6 * q^44 - 9 * q^45 + q^46 - 13 * q^47 - 8 * q^49 + 9 * q^50 - 24 * q^51 - 5 * q^52 - 8 * q^53 + 3 * q^54 - 11 * q^55 + 23 * q^58 - 9 * q^59 + q^60 + 6 * q^62 - 18 * q^63 + 8 * q^64 - 26 * q^65 + 6 * q^66 + 9 * q^67 - 9 * q^68 - 22 * q^69 + 7 * q^70 - 31 * q^71 - 2 * q^72 + 5 * q^73 - q^74 - q^75 - 8 * q^76 - 4 * q^77 + 5 * q^78 + 19 * q^79 + q^80 - 24 * q^81 + 3 * q^82 + 11 * q^83 - 9 * q^84 + 19 * q^85 - 9 * q^86 - 22 * q^87 + 6 * q^88 - 41 * q^89 + 9 * q^90 + 18 * q^91 - q^92 + 3 * q^93 + 13 * q^94 - q^95 - 24 * q^97 + 8 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.89675	−1.09509	−0.547544	−	0.836777i	$-0.684437\pi$
$3$	−1.89675	−1.09509	−0.547544	+	0.836777i	$0.684437\pi$
$4$	1.00000	0.500000
$5$	0.769767	0.344250	0.172125	−	0.985075i	$-0.444937\pi$
$5$	0.769767	0.344250	0.172125	+	0.985075i	$0.444937\pi$
$6$	1.89675	0.774344
$7$	−3.09528	−1.16991	−0.584953	−	0.811068i	$-0.698887\pi$
$7$	−3.09528	−1.16991	−0.584953	+	0.811068i	$0.698887\pi$
$8$	−1.00000	−0.353553
$9$	0.597654	0.199218
$10$	−0.769767	−0.243422
$11$	1.83830	0.554269	0.277134	−	0.960831i	$-0.410615\pi$
$11$	1.83830	0.554269	0.277134	+	0.960831i	$0.410615\pi$
$12$	−1.89675	−0.547544
$13$	−3.26285	−0.904953	−0.452477	−	0.891776i	$-0.649459\pi$
$13$	−3.26285	−0.904953	−0.452477	+	0.891776i	$0.649459\pi$
$14$	3.09528	0.827248
$15$	−1.46005	−0.376984
$16$	1.00000	0.250000
$17$	6.40596	1.55367	0.776837	−	0.629702i	$-0.216823\pi$
$17$	6.40596	1.55367	0.776837	+	0.629702i	$0.216823\pi$
$18$	−0.597654	−0.140868
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.769767	0.172125
$21$	5.87096	1.28115
$22$	−1.83830	−0.391927
$23$	8.27142	1.72471	0.862355	−	0.506304i	$-0.168989\pi$
$23$	8.27142	1.72471	0.862355	+	0.506304i	$0.168989\pi$
$24$	1.89675	0.387172
$25$	−4.40746	−0.881492
$26$	3.26285	0.639898
$27$	4.55665	0.876927
$28$	−3.09528	−0.584953
$29$	−1.27654	−0.237047	−0.118523	−	0.992951i	$-0.537816\pi$
$29$	−1.27654	−0.237047	−0.118523	+	0.992951i	$0.537816\pi$
$30$	1.46005	0.266568
$31$	−0.926332	−0.166374	−0.0831871	−	0.996534i	$-0.526510\pi$
$31$	−0.926332	−0.166374	−0.0831871	+	0.996534i	$0.526510\pi$
$32$	−1.00000	−0.176777
$33$	−3.48680	−0.606973
$34$	−6.40596	−1.09861
$35$	−2.38264	−0.402740
$36$	0.597654	0.0996089
$37$	2.72124	0.447369	0.223685	−	0.974662i	$-0.428191\pi$
$37$	2.72124	0.447369	0.223685	+	0.974662i	$0.428191\pi$
$38$	1.00000	0.162221
$39$	6.18881	0.991003
$40$	−0.769767	−0.121711
$41$	−11.0480	−1.72541	−0.862707	−	0.505703i	$-0.831233\pi$
$41$	−11.0480	−1.72541	−0.862707	+	0.505703i	$0.831233\pi$
$42$	−5.87096	−0.905909
$43$	−2.26739	−0.345774	−0.172887	−	0.984942i	$-0.555310\pi$
$43$	−2.26739	−0.345774	−0.172887	+	0.984942i	$0.555310\pi$
$44$	1.83830	0.277134
$45$	0.460054	0.0685808
$46$	−8.27142	−1.21955
$47$	7.95102	1.15978	0.579888	−	0.814696i	$-0.303096\pi$
$47$	7.95102	1.15978	0.579888	+	0.814696i	$0.303096\pi$
$48$	−1.89675	−0.273772
$49$	2.58074	0.368678
$50$	4.40746	0.623309
$51$	−12.1505	−1.70141
$52$	−3.26285	−0.452477
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−4.55665	−0.620081
$55$	1.41506	0.190807
$56$	3.09528	0.413624
$57$	1.89675	0.251230
$58$	1.27654	0.167618
$59$	5.37584	0.699875	0.349937	−	0.936773i	$-0.386203\pi$
$59$	5.37584	0.699875	0.349937	+	0.936773i	$0.386203\pi$
$60$	−1.46005	−0.188492
$61$	−8.83926	−1.13175	−0.565876	−	0.824491i	$-0.691462\pi$
$61$	−8.83926	−1.13175	−0.565876	+	0.824491i	$0.691462\pi$
$62$	0.926332	0.117644
$63$	−1.84990	−0.233066
$64$	1.00000	0.125000
$65$	−2.51164	−0.311530
$66$	3.48680	0.429195
$67$	7.90659	0.965943	0.482972	−	0.875636i	$-0.339557\pi$
$67$	7.90659	0.965943	0.482972	+	0.875636i	$0.339557\pi$
$68$	6.40596	0.776837
$69$	−15.6888	−1.88871
$70$	2.38264	0.284780
$71$	−9.37689	−1.11283	−0.556416	−	0.830904i	$-0.687824\pi$
$71$	−9.37689	−1.11283	−0.556416	+	0.830904i	$0.687824\pi$
$72$	−0.597654	−0.0704342
$73$	−1.96318	−0.229773	−0.114886	−	0.993379i	$-0.536650\pi$
$73$	−1.96318	−0.229773	−0.114886	+	0.993379i	$0.536650\pi$
$74$	−2.72124	−0.316338
$75$	8.35984	0.965311
$76$	−1.00000	−0.114708
$77$	−5.69006	−0.648442
$78$	−6.18881	−0.700745
$79$	12.3482	1.38929	0.694643	−	0.719355i	$-0.255562\pi$
$79$	12.3482	1.38929	0.694643	+	0.719355i	$0.255562\pi$
$80$	0.769767	0.0860626
$81$	−10.4358	−1.15953
$82$	11.0480	1.22005
$83$	10.2731	1.12761	0.563807	−	0.825906i	$-0.309336\pi$
$83$	10.2731	1.12761	0.563807	+	0.825906i	$0.309336\pi$
$84$	5.87096	0.640575
$85$	4.93110	0.534852
$86$	2.26739	0.244499
$87$	2.42127	0.259587
$88$	−1.83830	−0.195964
$89$	−2.33879	−0.247912	−0.123956	−	0.992288i	$-0.539558\pi$
$89$	−2.33879	−0.247912	−0.123956	+	0.992288i	$0.539558\pi$
$90$	−0.460054	−0.0484940
$91$	10.0994	1.05871
$92$	8.27142	0.862355
$93$	1.75702	0.182194
$94$	−7.95102	−0.820085
$95$	−0.769767	−0.0789764
$96$	1.89675	0.193586
$97$	−0.871774	−0.0885152	−0.0442576	−	0.999020i	$-0.514092\pi$
$97$	−0.871774	−0.0885152	−0.0442576	+	0.999020i	$0.514092\pi$
$98$	−2.58074	−0.260695
$99$	1.09867	0.110420
$100$	−4.40746	−0.440746
$101$	0.836675	0.0832523	0.0416261	−	0.999133i	$-0.486746\pi$
$101$	0.836675	0.0832523	0.0416261	+	0.999133i	$0.486746\pi$
$102$	12.1505	1.20308
$103$	−18.1103	−1.78446	−0.892230	−	0.451582i	$-0.850860\pi$
$103$	−18.1103	−1.78446	−0.892230	+	0.451582i	$0.850860\pi$
$104$	3.26285	0.319949
$105$	4.51927	0.441036
$106$	1.00000	0.0971286
$107$	−17.0130	−1.64471	−0.822355	−	0.568974i	$-0.807340\pi$
$107$	−17.0130	−1.64471	−0.822355	+	0.568974i	$0.807340\pi$
$108$	4.55665	0.438463
$109$	−8.99448	−0.861515	−0.430758	−	0.902468i	$-0.641754\pi$
$109$	−8.99448	−0.861515	−0.430758	+	0.902468i	$0.641754\pi$
$110$	−1.41506	−0.134921
$111$	−5.16151	−0.489909
$112$	−3.09528	−0.292476
$113$	4.20839	0.395892	0.197946	−	0.980213i	$-0.436573\pi$
$113$	4.20839	0.395892	0.197946	+	0.980213i	$0.436573\pi$
$114$	−1.89675	−0.177647
$115$	6.36706	0.593732
$116$	−1.27654	−0.118523
$117$	−1.95006	−0.180283
$118$	−5.37584	−0.494886
$119$	−19.8282	−1.81765
$120$	1.46005	0.133284
$121$	−7.62064	−0.692786
$122$	8.83926	0.800269
$123$	20.9554	1.88948
$124$	−0.926332	−0.0831871
$125$	−7.24155	−0.647704
$126$	1.84990	0.164803
$127$	−16.4622	−1.46078	−0.730391	−	0.683029i	$-0.760662\pi$
$127$	−16.4622	−1.46078	−0.730391	+	0.683029i	$0.760662\pi$
$128$	−1.00000	−0.0883883
$129$	4.30067	0.378653
$130$	2.51164	0.220285
$131$	3.14329	0.274630	0.137315	−	0.990527i	$-0.456153\pi$
$131$	3.14329	0.274630	0.137315	+	0.990527i	$0.456153\pi$
$132$	−3.48680	−0.303487
$133$	3.09528	0.268395
$134$	−7.90659	−0.683025
$135$	3.50756	0.301882
$136$	−6.40596	−0.549307
$137$	−14.9893	−1.28062	−0.640312	−	0.768115i	$-0.721195\pi$
$137$	−14.9893	−1.28062	−0.640312	+	0.768115i	$0.721195\pi$
$138$	15.6888	1.33552
$139$	2.19740	0.186381	0.0931904	−	0.995648i	$-0.470293\pi$
$139$	2.19740	0.186381	0.0931904	+	0.995648i	$0.470293\pi$
$140$	−2.38264	−0.201370
$141$	−15.0811	−1.27006
$142$	9.37689	0.786891
$143$	−5.99811	−0.501587
$144$	0.597654	0.0498045
$145$	−0.982636	−0.0816035
$146$	1.96318	0.162474
$147$	−4.89502	−0.403735
$148$	2.72124	0.223685
$149$	−16.9961	−1.39237	−0.696185	−	0.717862i	$-0.745121\pi$
$149$	−16.9961	−1.39237	−0.696185	+	0.717862i	$0.745121\pi$
$150$	−8.35984	−0.682578
$151$	13.2003	1.07422	0.537111	−	0.843511i	$-0.319515\pi$
$151$	13.2003	1.07422	0.537111	+	0.843511i	$0.319515\pi$
$152$	1.00000	0.0811107
$153$	3.82855	0.309520
$154$	5.69006	0.458518
$155$	−0.713060	−0.0572744
$156$	6.18881	0.495502
$157$	1.97717	0.157795	0.0788977	−	0.996883i	$-0.474860\pi$
$157$	1.97717	0.157795	0.0788977	+	0.996883i	$0.474860\pi$
$158$	−12.3482	−0.982374
$159$	1.89675	0.150422
$160$	−0.769767	−0.0608554
$161$	−25.6023	−2.01775
$162$	10.4358	0.819912
$163$	4.73254	0.370681	0.185341	−	0.982674i	$-0.440661\pi$
$163$	4.73254	0.370681	0.185341	+	0.982674i	$0.440661\pi$
$164$	−11.0480	−0.862707
$165$	−2.68402	−0.208951
$166$	−10.2731	−0.797344
$167$	−22.4859	−1.74001	−0.870006	−	0.493041i	$-0.835885\pi$
$167$	−22.4859	−1.74001	−0.870006	+	0.493041i	$0.835885\pi$
$168$	−5.87096	−0.452955
$169$	−2.35378	−0.181060
$170$	−4.93110	−0.378198
$171$	−0.597654	−0.0457037
$172$	−2.26739	−0.172887
$173$	18.1796	1.38217	0.691086	−	0.722773i	$-0.257133\pi$
$173$	18.1796	1.38217	0.691086	+	0.722773i	$0.257133\pi$
$174$	−2.42127	−0.183556
$175$	13.6423	1.03126
$176$	1.83830	0.138567
$177$	−10.1966	−0.766425
$178$	2.33879	0.175300
$179$	−15.4575	−1.15535	−0.577675	−	0.816267i	$-0.696040\pi$
$179$	−15.4575	−1.15535	−0.577675	+	0.816267i	$0.696040\pi$
$180$	0.460054	0.0342904
$181$	−0.553017	−0.0411054	−0.0205527	−	0.999789i	$-0.506543\pi$
$181$	−0.553017	−0.0411054	−0.0205527	+	0.999789i	$0.506543\pi$
$182$	−10.0994	−0.748620
$183$	16.7658	1.23937
$184$	−8.27142	−0.609777
$185$	2.09472	0.154007
$186$	−1.75702	−0.128831
$187$	11.7761	0.861153
$188$	7.95102	0.579888
$189$	−14.1041	−1.02592
$190$	0.769767	0.0558448
$191$	−17.0430	−1.23319	−0.616593	−	0.787282i	$-0.711488\pi$
$191$	−17.0430	−1.23319	−0.616593	+	0.787282i	$0.711488\pi$
$192$	−1.89675	−0.136886
$193$	5.77870	0.415960	0.207980	−	0.978133i	$-0.433311\pi$
$193$	5.77870	0.415960	0.207980	+	0.978133i	$0.433311\pi$
$194$	0.871774	0.0625897
$195$	4.76394	0.341153
$196$	2.58074	0.184339
$197$	5.82415	0.414953	0.207477	−	0.978240i	$-0.433475\pi$
$197$	5.82415	0.414953	0.207477	+	0.978240i	$0.433475\pi$
$198$	−1.09867	−0.0780789
$199$	14.8747	1.05444	0.527220	−	0.849729i	$-0.323235\pi$
$199$	14.8747	1.05444	0.527220	+	0.849729i	$0.323235\pi$
$200$	4.40746	0.311654
$201$	−14.9968	−1.05779
$202$	−0.836675	−0.0588683
$203$	3.95124	0.277322
$204$	−12.1505	−0.850705
$205$	−8.50442	−0.593974
$206$	18.1103	1.26180
$207$	4.94344	0.343593
$208$	−3.26285	−0.226238
$209$	−1.83830	−0.127158
$210$	−4.51927	−0.311859
$211$	−26.6685	−1.83593	−0.917967	−	0.396656i	$-0.870171\pi$
$211$	−26.6685	−1.83593	−0.917967	+	0.396656i	$0.870171\pi$
$212$	−1.00000	−0.0686803
$213$	17.7856	1.21865
$214$	17.0130	1.16299
$215$	−1.74536	−0.119033
$216$	−4.55665	−0.310040
$217$	2.86726	0.194642
$218$	8.99448	0.609183
$219$	3.72365	0.251621
$220$	1.41506	0.0954036
$221$	−20.9017	−1.40600
$222$	5.16151	0.346418
$223$	23.9350	1.60281	0.801404	−	0.598124i	$-0.204087\pi$
$223$	23.9350	1.60281	0.801404	+	0.598124i	$0.204087\pi$
$224$	3.09528	0.206812
$225$	−2.63413	−0.175609
$226$	−4.20839	−0.279938
$227$	−19.6014	−1.30099	−0.650495	−	0.759510i	$-0.725439\pi$
$227$	−19.6014	−1.30099	−0.650495	+	0.759510i	$0.725439\pi$
$228$	1.89675	0.125615
$229$	−28.0247	−1.85193	−0.925963	−	0.377615i	$-0.876744\pi$
$229$	−28.0247	−1.85193	−0.925963	+	0.377615i	$0.876744\pi$
$230$	−6.36706	−0.419832
$231$	10.7926	0.710101
$232$	1.27654	0.0838088
$233$	−1.01879	−0.0667432	−0.0333716	−	0.999443i	$-0.510624\pi$
$233$	−1.01879	−0.0667432	−0.0333716	+	0.999443i	$0.510624\pi$
$234$	1.95006	0.127479
$235$	6.12043	0.399253
$236$	5.37584	0.349937
$237$	−23.4215	−1.52139
$238$	19.8282	1.28527
$239$	−10.1920	−0.659263	−0.329631	−	0.944110i	$-0.606924\pi$
$239$	−10.1920	−0.659263	−0.329631	+	0.944110i	$0.606924\pi$
$240$	−1.46005	−0.0942461
$241$	−28.0611	−1.80758	−0.903789	−	0.427979i	$-0.859226\pi$
$241$	−28.0611	−1.80758	−0.903789	+	0.427979i	$0.859226\pi$
$242$	7.62064	0.489874
$243$	6.12409	0.392861
$244$	−8.83926	−0.565876
$245$	1.98657	0.126917
$246$	−20.9554	−1.33607
$247$	3.26285	0.207610
$248$	0.926332	0.0588222
$249$	−19.4854	−1.23484
$250$	7.24155	0.457996
$251$	−7.44248	−0.469765	−0.234883	−	0.972024i	$-0.575471\pi$
$251$	−7.44248	−0.469765	−0.234883	+	0.972024i	$0.575471\pi$
$252$	−1.84990	−0.116533
$253$	15.2054	0.955953
$254$	16.4622	1.03293
$255$	−9.35305	−0.585711
$256$	1.00000	0.0625000
$257$	19.6476	1.22558	0.612791	−	0.790245i	$-0.290047\pi$
$257$	19.6476	1.22558	0.612791	+	0.790245i	$0.290047\pi$
$258$	−4.30067	−0.267748
$259$	−8.42299	−0.523379
$260$	−2.51164	−0.155765
$261$	−0.762927	−0.0472240
$262$	−3.14329	−0.194193
$263$	2.28439	0.140862	0.0704308	−	0.997517i	$-0.477563\pi$
$263$	2.28439	0.140862	0.0704308	+	0.997517i	$0.477563\pi$
$264$	3.48680	0.214597
$265$	−0.769767	−0.0472864
$266$	−3.09528	−0.189784
$267$	4.43610	0.271485
$268$	7.90659	0.482972
$269$	12.0806	0.736565	0.368283	−	0.929714i	$-0.379946\pi$
$269$	12.0806	0.736565	0.368283	+	0.929714i	$0.379946\pi$
$270$	−3.50756	−0.213463
$271$	2.00269	0.121655	0.0608274	−	0.998148i	$-0.480626\pi$
$271$	2.00269	0.121655	0.0608274	+	0.998148i	$0.480626\pi$
$272$	6.40596	0.388418
$273$	−19.1561	−1.15938
$274$	14.9893	0.905538
$275$	−8.10224	−0.488584
$276$	−15.6888	−0.944354
$277$	20.8587	1.25328	0.626639	−	0.779310i	$-0.284430\pi$
$277$	20.8587	1.25328	0.626639	+	0.779310i	$0.284430\pi$
$278$	−2.19740	−0.131791
$279$	−0.553626	−0.0331447
$280$	2.38264	0.142390
$281$	−6.26455	−0.373712	−0.186856	−	0.982387i	$-0.559830\pi$
$281$	−6.26455	−0.373712	−0.186856	+	0.982387i	$0.559830\pi$
$282$	15.0811	0.898065
$283$	−18.6646	−1.10950	−0.554749	−	0.832018i	$-0.687186\pi$
$283$	−18.6646	−1.10950	−0.554749	+	0.832018i	$0.687186\pi$
$284$	−9.37689	−0.556416
$285$	1.46005	0.0864861
$286$	5.99811	0.354676
$287$	34.1968	2.01857
$288$	−0.597654	−0.0352171
$289$	24.0363	1.41390
$290$	0.982636	0.0577024
$291$	1.65354	0.0969320
$292$	−1.96318	−0.114886
$293$	−16.1880	−0.945714	−0.472857	−	0.881139i	$-0.656777\pi$
$293$	−16.1880	−0.945714	−0.472857	+	0.881139i	$0.656777\pi$
$294$	4.89502	0.285483
$295$	4.13814	0.240932
$296$	−2.72124	−0.158169
$297$	8.37649	0.486053
$298$	16.9961	0.984555
$299$	−26.9884	−1.56078
$300$	8.35984	0.482656
$301$	7.01820	0.404523
$302$	−13.2003	−0.759590
$303$	−1.58696	−0.0911686
$304$	−1.00000	−0.0573539
$305$	−6.80417	−0.389606
$306$	−3.82855	−0.218863
$307$	−3.17923	−0.181448	−0.0907242	−	0.995876i	$-0.528918\pi$
$307$	−3.17923	−0.181448	−0.0907242	+	0.995876i	$0.528918\pi$
$308$	−5.69006	−0.324221
$309$	34.3507	1.95414
$310$	0.713060	0.0404991
$311$	−0.343759	−0.0194928	−0.00974640	−	0.999953i	$-0.503102\pi$
$311$	−0.343759	−0.0194928	−0.00974640	+	0.999953i	$0.503102\pi$
$312$	−6.18881	−0.350373
$313$	0.759779	0.0429453	0.0214726	−	0.999769i	$-0.493165\pi$
$313$	0.759779	0.0429453	0.0214726	+	0.999769i	$0.493165\pi$
$314$	−1.97717	−0.111578
$315$	−1.42399	−0.0802330
$316$	12.3482	0.694643
$317$	−18.2471	−1.02486	−0.512430	−	0.858729i	$-0.671254\pi$
$317$	−18.2471	−1.02486	−0.512430	+	0.858729i	$0.671254\pi$
$318$	−1.89675	−0.106364
$319$	−2.34666	−0.131388
$320$	0.769767	0.0430313
$321$	32.2694	1.80110
$322$	25.6023	1.42676
$323$	−6.40596	−0.356437
$324$	−10.4358	−0.579765
$325$	14.3809	0.797709
$326$	−4.73254	−0.262111
$327$	17.0603	0.943435
$328$	11.0480	0.610026
$329$	−24.6106	−1.35683
$330$	2.68402	0.147750
$331$	12.7348	0.699966	0.349983	−	0.936756i	$-0.386187\pi$
$331$	12.7348	0.699966	0.349983	+	0.936756i	$0.386187\pi$
$332$	10.2731	0.563807
$333$	1.62636	0.0891239
$334$	22.4859	1.23037
$335$	6.08623	0.332526
$336$	5.87096	0.320287
$337$	−21.4721	−1.16966	−0.584830	−	0.811156i	$-0.698839\pi$
$337$	−21.4721	−1.16966	−0.584830	+	0.811156i	$0.698839\pi$
$338$	2.35378	0.128029
$339$	−7.98225	−0.433536
$340$	4.93110	0.267426
$341$	−1.70288	−0.0922160
$342$	0.597654	0.0323174
$343$	13.6788	0.738587
$344$	2.26739	0.122250
$345$	−12.0767	−0.650188
$346$	−18.1796	−0.977343
$347$	−4.53353	−0.243372	−0.121686	−	0.992569i	$-0.538830\pi$
$347$	−4.53353	−0.243372	−0.121686	+	0.992569i	$0.538830\pi$
$348$	2.42127	0.129794
$349$	16.4734	0.881802	0.440901	−	0.897556i	$-0.354659\pi$
$349$	16.4734	0.881802	0.440901	+	0.897556i	$0.354659\pi$
$350$	−13.6423	−0.729212
$351$	−14.8677	−0.793578
$352$	−1.83830	−0.0979818
$353$	24.4482	1.30125	0.650624	−	0.759400i	$-0.274507\pi$
$353$	24.4482	1.30125	0.650624	+	0.759400i	$0.274507\pi$
$354$	10.1966	0.541944
$355$	−7.21802	−0.383093
$356$	−2.33879	−0.123956
$357$	37.6091	1.99049
$358$	15.4575	0.816956
$359$	4.47464	0.236162	0.118081	−	0.993004i	$-0.462326\pi$
$359$	4.47464	0.236162	0.118081	+	0.993004i	$0.462326\pi$
$360$	−0.460054	−0.0242470
$361$	1.00000	0.0526316
$362$	0.553017	0.0290659
$363$	14.4544	0.758662
$364$	10.0994	0.529355
$365$	−1.51119	−0.0790992
$366$	−16.7658	−0.876365
$367$	−32.3194	−1.68706	−0.843530	−	0.537082i	$-0.819527\pi$
$367$	−32.3194	−1.68706	−0.843530	+	0.537082i	$0.819527\pi$
$368$	8.27142	0.431177
$369$	−6.60291	−0.343734
$370$	−2.09472	−0.108899
$371$	3.09528	0.160699
$372$	1.75702	0.0910972
$373$	−4.95941	−0.256789	−0.128394	−	0.991723i	$-0.540982\pi$
$373$	−4.95941	−0.256789	−0.128394	+	0.991723i	$0.540982\pi$
$374$	−11.7761	−0.608927
$375$	13.7354	0.709293
$376$	−7.95102	−0.410042
$377$	4.16515	0.214516
$378$	14.1041	0.725436
$379$	5.18325	0.266246	0.133123	−	0.991100i	$-0.457500\pi$
$379$	5.18325	0.266246	0.133123	+	0.991100i	$0.457500\pi$
$380$	−0.769767	−0.0394882
$381$	31.2246	1.59968
$382$	17.0430	0.871995
$383$	32.1469	1.64263	0.821314	−	0.570476i	$-0.193241\pi$
$383$	32.1469	1.64263	0.821314	+	0.570476i	$0.193241\pi$
$384$	1.89675	0.0967930
$385$	−4.38002	−0.223226
$386$	−5.77870	−0.294128
$387$	−1.35511	−0.0688843
$388$	−0.871774	−0.0442576
$389$	−15.2048	−0.770913	−0.385457	−	0.922726i	$-0.625956\pi$
$389$	−15.2048	−0.770913	−0.385457	+	0.922726i	$0.625956\pi$
$390$	−4.76394	−0.241232
$391$	52.9864	2.67964
$392$	−2.58074	−0.130347
$393$	−5.96202	−0.300744
$394$	−5.82415	−0.293416
$395$	9.50527	0.478262
$396$	1.09867	0.0552101
$397$	23.0737	1.15804	0.579018	−	0.815314i	$-0.303436\pi$
$397$	23.0737	1.15804	0.579018	+	0.815314i	$0.303436\pi$
$398$	−14.8747	−0.745601
$399$	−5.87096	−0.293916
$400$	−4.40746	−0.220373
$401$	17.9364	0.895703	0.447851	−	0.894108i	$-0.352189\pi$
$401$	17.9364	0.895703	0.447851	+	0.894108i	$0.352189\pi$
$402$	14.9968	0.747973
$403$	3.02249	0.150561
$404$	0.836675	0.0416261
$405$	−8.03311	−0.399169
$406$	−3.95124	−0.196097
$407$	5.00246	0.247963
$408$	12.1505	0.601539
$409$	−13.3161	−0.658439	−0.329220	−	0.944253i	$-0.606786\pi$
$409$	−13.3161	−0.658439	−0.329220	+	0.944253i	$0.606786\pi$
$410$	8.50442	0.420003
$411$	28.4310	1.40240
$412$	−18.1103	−0.892230
$413$	−16.6397	−0.818787
$414$	−4.94344	−0.242957
$415$	7.90786	0.388182
$416$	3.26285	0.159975
$417$	−4.16791	−0.204103
$418$	1.83830	0.0899143
$419$	−18.3834	−0.898089	−0.449045	−	0.893509i	$-0.648236\pi$
$419$	−18.3834	−0.898089	−0.449045	+	0.893509i	$0.648236\pi$
$420$	4.51927	0.220518
$421$	7.99267	0.389539	0.194769	−	0.980849i	$-0.437604\pi$
$421$	7.99267	0.389539	0.194769	+	0.980849i	$0.437604\pi$
$422$	26.6685	1.29820
$423$	4.75196	0.231048
$424$	1.00000	0.0485643
$425$	−28.2340	−1.36955
$426$	−17.7856	−0.861715
$427$	27.3600	1.32404
$428$	−17.0130	−0.822355
$429$	11.3769	0.549282
$430$	1.74536	0.0841689
$431$	23.0123	1.10846	0.554231	−	0.832363i	$-0.313012\pi$
$431$	23.0123	1.10846	0.554231	+	0.832363i	$0.313012\pi$
$432$	4.55665	0.219232
$433$	−22.0581	−1.06004	−0.530022	−	0.847984i	$-0.677816\pi$
$433$	−22.0581	−1.06004	−0.530022	+	0.847984i	$0.677816\pi$
$434$	−2.86726	−0.137633
$435$	1.86381	0.0893630
$436$	−8.99448	−0.430758
$437$	−8.27142	−0.395676
$438$	−3.72365	−0.177923
$439$	20.4428	0.975680	0.487840	−	0.872933i	$-0.337785\pi$
$439$	20.4428	0.975680	0.487840	+	0.872933i	$0.337785\pi$
$440$	−1.41506	−0.0674605
$441$	1.54239	0.0734472
$442$	20.9017	0.994193
$443$	24.5281	1.16537	0.582683	−	0.812700i	$-0.302003\pi$
$443$	24.5281	1.16537	0.582683	+	0.812700i	$0.302003\pi$
$444$	−5.16151	−0.244954
$445$	−1.80033	−0.0853436
$446$	−23.9350	−1.13336
$447$	32.2372	1.52477
$448$	−3.09528	−0.146238
$449$	7.69215	0.363015	0.181508	−	0.983390i	$-0.441902\pi$
$449$	7.69215	0.363015	0.181508	+	0.983390i	$0.441902\pi$
$450$	2.63413	0.124174
$451$	−20.3096	−0.956344
$452$	4.20839	0.197946
$453$	−25.0376	−1.17637
$454$	19.6014	0.919939
$455$	7.77422	0.364461
$456$	−1.89675	−0.0888234
$457$	−13.6734	−0.639616	−0.319808	−	0.947482i	$-0.603618\pi$
$457$	−13.6734	−0.639616	−0.319808	+	0.947482i	$0.603618\pi$
$458$	28.0247	1.30951
$459$	29.1897	1.36246
$460$	6.36706	0.296866
$461$	38.4771	1.79206	0.896028	−	0.443998i	$-0.146440\pi$
$461$	38.4771	1.79206	0.896028	+	0.443998i	$0.146440\pi$
$462$	−10.7926	−0.502117
$463$	23.9371	1.11245	0.556226	−	0.831031i	$-0.312249\pi$
$463$	23.9371	1.11245	0.556226	+	0.831031i	$0.312249\pi$
$464$	−1.27654	−0.0592617
$465$	1.35250	0.0627205
$466$	1.01879	0.0471945
$467$	1.17385	0.0543192	0.0271596	−	0.999631i	$-0.491354\pi$
$467$	1.17385	0.0543192	0.0271596	+	0.999631i	$0.491354\pi$
$468$	−1.95006	−0.0901414
$469$	−24.4731	−1.13006
$470$	−6.12043	−0.282314
$471$	−3.75020	−0.172800
$472$	−5.37584	−0.247443
$473$	−4.16815	−0.191652
$474$	23.4215	1.07579
$475$	4.40746	0.202228
$476$	−19.8282	−0.908825
$477$	−0.597654	−0.0273647
$478$	10.1920	0.466169
$479$	0.245438	0.0112144	0.00560718	−	0.999984i	$-0.498215\pi$
$479$	0.245438	0.0112144	0.00560718	+	0.999984i	$0.498215\pi$
$480$	1.46005	0.0666420
$481$	−8.87901	−0.404848
$482$	28.0611	1.27815
$483$	48.5612	2.20961
$484$	−7.62064	−0.346393
$485$	−0.671063	−0.0304714
$486$	−6.12409	−0.277794
$487$	−38.3274	−1.73678	−0.868391	−	0.495881i	$-0.834845\pi$
$487$	−38.3274	−1.73678	−0.868391	+	0.495881i	$0.834845\pi$
$488$	8.83926	0.400134
$489$	−8.97644	−0.405929
$490$	−1.98657	−0.0897442
$491$	32.5302	1.46807	0.734034	−	0.679112i	$-0.237635\pi$
$491$	32.5302	1.46807	0.734034	+	0.679112i	$0.237635\pi$
$492$	20.9554	0.944741
$493$	−8.17745	−0.368294
$494$	−3.26285	−0.146803
$495$	0.845718	0.0380122
$496$	−0.926332	−0.0415935
$497$	29.0241	1.30191
$498$	19.4854	0.873162
$499$	2.54420	0.113894	0.0569470	−	0.998377i	$-0.481863\pi$
$499$	2.54420	0.113894	0.0569470	+	0.998377i	$0.481863\pi$
$500$	−7.24155	−0.323852
$501$	42.6501	1.90547
$502$	7.44248	0.332174
$503$	−8.39460	−0.374297	−0.187148	−	0.982332i	$-0.559924\pi$
$503$	−8.39460	−0.374297	−0.187148	+	0.982332i	$0.559924\pi$
$504$	1.84990	0.0824013
$505$	0.644045	0.0286596
$506$	−15.2054	−0.675961
$507$	4.46453	0.198277
$508$	−16.4622	−0.730391
$509$	2.16366	0.0959025	0.0479512	−	0.998850i	$-0.484731\pi$
$509$	2.16366	0.0959025	0.0479512	+	0.998850i	$0.484731\pi$
$510$	9.35305	0.414160
$511$	6.07658	0.268812
$512$	−1.00000	−0.0441942
$513$	−4.55665	−0.201181
$514$	−19.6476	−0.866618
$515$	−13.9407	−0.614301
$516$	4.30067	0.189326
$517$	14.6164	0.642827
$518$	8.42299	0.370085
$519$	−34.4822	−1.51360
$520$	2.51164	0.110143
$521$	−36.6282	−1.60471	−0.802354	−	0.596848i	$-0.796419\pi$
$521$	−36.6282	−1.60471	−0.802354	+	0.596848i	$0.796419\pi$
$522$	0.762927	0.0333924
$523$	−32.6988	−1.42982	−0.714909	−	0.699218i	$-0.753532\pi$
$523$	−32.6988	−1.42982	−0.714909	+	0.699218i	$0.753532\pi$
$524$	3.14329	0.137315
$525$	−25.8760	−1.12932
$526$	−2.28439	−0.0996042
$527$	−5.93405	−0.258491
$528$	−3.48680	−0.151743
$529$	45.4163	1.97462
$530$	0.769767	0.0334365
$531$	3.21289	0.139428
$532$	3.09528	0.134197
$533$	36.0482	1.56142
$534$	−4.43610	−0.191969
$535$	−13.0961	−0.566192
$536$	−7.90659	−0.341512
$537$	29.3190	1.26521
$538$	−12.0806	−0.520830
$539$	4.74419	0.204347
$540$	3.50756	0.150941
$541$	−19.1315	−0.822526	−0.411263	−	0.911517i	$-0.634912\pi$
$541$	−19.1315	−0.822526	−0.411263	+	0.911517i	$0.634912\pi$
$542$	−2.00269	−0.0860229
$543$	1.04893	0.0450141
$544$	−6.40596	−0.274653
$545$	−6.92365	−0.296577
$546$	19.1561	0.819805
$547$	−12.2269	−0.522783	−0.261392	−	0.965233i	$-0.584181\pi$
$547$	−12.2269	−0.522783	−0.261392	+	0.965233i	$0.584181\pi$
$548$	−14.9893	−0.640312
$549$	−5.28282	−0.225465
$550$	8.10224	0.345481
$551$	1.27654	0.0543823
$552$	15.6888	0.667759
$553$	−38.2212	−1.62533
$554$	−20.8587	−0.886201
$555$	−3.97316	−0.168651
$556$	2.19740	0.0931904
$557$	−18.5061	−0.784129	−0.392064	−	0.919938i	$-0.628239\pi$
$557$	−18.5061	−0.784129	−0.392064	+	0.919938i	$0.628239\pi$
$558$	0.553626	0.0234369
$559$	7.39817	0.312909
$560$	−2.38264	−0.100685
$561$	−22.3363	−0.943038
$562$	6.26455	0.264254
$563$	7.62592	0.321394	0.160697	−	0.987004i	$-0.448626\pi$
$563$	7.62592	0.321394	0.160697	+	0.987004i	$0.448626\pi$
$564$	−15.0811	−0.635028
$565$	3.23948	0.136286
$566$	18.6646	0.784533
$567$	32.3016	1.35654
$568$	9.37689	0.393446
$569$	1.68972	0.0708368	0.0354184	−	0.999373i	$-0.488724\pi$
$569$	1.68972	0.0708368	0.0354184	+	0.999373i	$0.488724\pi$
$570$	−1.46005	−0.0611549
$571$	4.41219	0.184644	0.0923222	−	0.995729i	$-0.470571\pi$
$571$	4.41219	0.184644	0.0923222	+	0.995729i	$0.470571\pi$
$572$	−5.99811	−0.250794
$573$	32.3262	1.35045
$574$	−34.1968	−1.42735
$575$	−36.4559	−1.52032
$576$	0.597654	0.0249022
$577$	22.5672	0.939486	0.469743	−	0.882803i	$-0.344347\pi$
$577$	22.5672	0.939486	0.469743	+	0.882803i	$0.344347\pi$
$578$	−24.0363	−0.999779
$579$	−10.9607	−0.455513
$580$	−0.982636	−0.0408017
$581$	−31.7980	−1.31920
$582$	−1.65354	−0.0685412
$583$	−1.83830	−0.0761347
$584$	1.96318	0.0812369
$585$	−1.50109	−0.0620624
$586$	16.1880	0.668721
$587$	31.1269	1.28474	0.642372	−	0.766393i	$-0.277950\pi$
$587$	31.1269	1.28474	0.642372	+	0.766393i	$0.277950\pi$
$588$	−4.89502	−0.201867
$589$	0.926332	0.0381689
$590$	−4.13814	−0.170365
$591$	−11.0469	−0.454411
$592$	2.72124	0.111842
$593$	−35.8927	−1.47394	−0.736969	−	0.675927i	$-0.763744\pi$
$593$	−35.8927	−1.47394	−0.736969	+	0.675927i	$0.763744\pi$
$594$	−8.37649	−0.343692
$595$	−15.2631	−0.625727
$596$	−16.9961	−0.696185
$597$	−28.2136	−1.15470
$598$	26.9884	1.10364
$599$	−14.5377	−0.593995	−0.296997	−	0.954878i	$-0.595985\pi$
$599$	−14.5377	−0.593995	−0.296997	+	0.954878i	$0.595985\pi$
$600$	−8.35984	−0.341289
$601$	−11.8332	−0.482684	−0.241342	−	0.970440i	$-0.577588\pi$
$601$	−11.8332	−0.482684	−0.241342	+	0.970440i	$0.577588\pi$
$602$	−7.01820	−0.286041
$603$	4.72540	0.192433
$604$	13.2003	0.537111
$605$	−5.86612	−0.238492
$606$	1.58696	0.0644659
$607$	−21.7743	−0.883791	−0.441896	−	0.897067i	$-0.645694\pi$
$607$	−21.7743	−0.883791	−0.441896	+	0.897067i	$0.645694\pi$
$608$	1.00000	0.0405554
$609$	−7.49450	−0.303693
$610$	6.80417	0.275493
$611$	−25.9430	−1.04954
$612$	3.82855	0.154760
$613$	1.23580	0.0499134	0.0249567	−	0.999689i	$-0.492055\pi$
$613$	1.23580	0.0499134	0.0249567	+	0.999689i	$0.492055\pi$
$614$	3.17923	0.128303
$615$	16.1307	0.650454
$616$	5.69006	0.229259
$617$	−9.70662	−0.390774	−0.195387	−	0.980726i	$-0.562596\pi$
$617$	−9.70662	−0.390774	−0.195387	+	0.980726i	$0.562596\pi$
$618$	−34.3507	−1.38179
$619$	2.27081	0.0912716	0.0456358	−	0.998958i	$-0.485469\pi$
$619$	2.27081	0.0912716	0.0456358	+	0.998958i	$0.485469\pi$
$620$	−0.713060	−0.0286372
$621$	37.6899	1.51244
$622$	0.343759	0.0137835
$623$	7.23921	0.290033
$624$	6.18881	0.247751
$625$	16.4630	0.658520
$626$	−0.759779	−0.0303669
$627$	3.48680	0.139249
$628$	1.97717	0.0788977
$629$	17.4322	0.695065
$630$	1.42399	0.0567333
$631$	−22.3787	−0.890880	−0.445440	−	0.895312i	$-0.646953\pi$
$631$	−22.3787	−0.890880	−0.445440	+	0.895312i	$0.646953\pi$
$632$	−12.3482	−0.491187
$633$	50.5834	2.01051
$634$	18.2471	0.724685
$635$	−12.6720	−0.502875
$636$	1.89675	0.0752110
$637$	−8.42059	−0.333636
$638$	2.34666	0.0929052
$639$	−5.60413	−0.221696
$640$	−0.769767	−0.0304277
$641$	16.8191	0.664314	0.332157	−	0.943224i	$-0.392224\pi$
$641$	16.8191	0.664314	0.332157	+	0.943224i	$0.392224\pi$
$642$	−32.2694	−1.27357
$643$	−11.3862	−0.449027	−0.224514	−	0.974471i	$-0.572079\pi$
$643$	−11.3862	−0.449027	−0.224514	+	0.974471i	$0.572079\pi$
$644$	−25.6023	−1.00887
$645$	3.31051	0.130351
$646$	6.40596	0.252039
$647$	−46.0160	−1.80907	−0.904537	−	0.426395i	$-0.859784\pi$
$647$	−46.0160	−1.80907	−0.904537	+	0.426395i	$0.859784\pi$
$648$	10.4358	0.409956
$649$	9.88242	0.387919
$650$	−14.3809	−0.564065
$651$	−5.43846	−0.213150
$652$	4.73254	0.185341
$653$	−4.90053	−0.191772	−0.0958862	−	0.995392i	$-0.530568\pi$
$653$	−4.90053	−0.191772	−0.0958862	+	0.995392i	$0.530568\pi$
$654$	−17.0603	−0.667109
$655$	2.41960	0.0945415
$656$	−11.0480	−0.431354
$657$	−1.17330	−0.0457748
$658$	24.6106	0.959421
$659$	1.46527	0.0570787	0.0285394	−	0.999593i	$-0.490914\pi$
$659$	1.46527	0.0570787	0.0285394	+	0.999593i	$0.490914\pi$
$660$	−2.68402	−0.104475
$661$	46.2857	1.80031	0.900153	−	0.435573i	$-0.143454\pi$
$661$	46.2857	1.80031	0.900153	+	0.435573i	$0.143454\pi$
$662$	−12.7348	−0.494951
$663$	39.6453	1.53970
$664$	−10.2731	−0.398672
$665$	2.38264	0.0923949
$666$	−1.62636	−0.0630201
$667$	−10.5588	−0.408837
$668$	−22.4859	−0.870006
$669$	−45.3987	−1.75522
$670$	−6.08623	−0.235132
$671$	−16.2492	−0.627295
$672$	−5.87096	−0.226477
$673$	−34.8207	−1.34224	−0.671119	−	0.741349i	$-0.734186\pi$
$673$	−34.8207	−1.34224	−0.671119	+	0.741349i	$0.734186\pi$
$674$	21.4721	0.827074
$675$	−20.0832	−0.773004
$676$	−2.35378	−0.0905300
$677$	8.14971	0.313219	0.156609	−	0.987661i	$-0.449944\pi$
$677$	8.14971	0.313219	0.156609	+	0.987661i	$0.449944\pi$
$678$	7.98225	0.306557
$679$	2.69838	0.103554
$680$	−4.93110	−0.189099
$681$	37.1789	1.42470
$682$	1.70288	0.0652066
$683$	16.4173	0.628192	0.314096	−	0.949391i	$-0.398299\pi$
$683$	16.4173	0.628192	0.314096	+	0.949391i	$0.398299\pi$
$684$	−0.597654	−0.0228519
$685$	−11.5383	−0.440855
$686$	−13.6788	−0.522260
$687$	53.1558	2.02802
$688$	−2.26739	−0.0864435
$689$	3.26285	0.124305
$690$	12.0767	0.459753
$691$	24.4397	0.929731	0.464866	−	0.885381i	$-0.346103\pi$
$691$	24.4397	0.929731	0.464866	+	0.885381i	$0.346103\pi$
$692$	18.1796	0.691086
$693$	−3.40068	−0.129181
$694$	4.53353	0.172090
$695$	1.69148	0.0641616
$696$	−2.42127	−0.0917780
$697$	−70.7733	−2.68073
$698$	−16.4734	−0.623528
$699$	1.93239	0.0730896
$700$	13.6423	0.515631
$701$	5.80787	0.219360	0.109680	−	0.993967i	$-0.465017\pi$
$701$	5.80787	0.219360	0.109680	+	0.993967i	$0.465017\pi$
$702$	14.8677	0.561144
$703$	−2.72124	−0.102634
$704$	1.83830	0.0692836
$705$	−11.6089	−0.437217
$706$	−24.4482	−0.920121
$707$	−2.58974	−0.0973973
$708$	−10.1966	−0.383212
$709$	−36.9507	−1.38771	−0.693857	−	0.720113i	$-0.744090\pi$
$709$	−36.9507	−1.38771	−0.693857	+	0.720113i	$0.744090\pi$
$710$	7.21802	0.270887
$711$	7.37997	0.276771
$712$	2.33879	0.0876500
$713$	−7.66208	−0.286947
$714$	−37.6091	−1.40749
$715$	−4.61715	−0.172672
$716$	−15.4575	−0.577675
$717$	19.3316	0.721951
$718$	−4.47464	−0.166992
$719$	−41.1510	−1.53467	−0.767336	−	0.641245i	$-0.778418\pi$
$719$	−41.1510	−1.53467	−0.767336	+	0.641245i	$0.778418\pi$
$720$	0.460054	0.0171452
$721$	56.0564	2.08765
$722$	−1.00000	−0.0372161
$723$	53.2249	1.97946
$724$	−0.553017	−0.0205527
$725$	5.62628	0.208955
$726$	−14.4544	−0.536455
$727$	1.23245	0.0457092	0.0228546	−	0.999739i	$-0.492725\pi$
$727$	1.23245	0.0457092	0.0228546	+	0.999739i	$0.492725\pi$
$728$	−10.0994	−0.374310
$729$	19.6915	0.729313
$730$	1.51119	0.0559316
$731$	−14.5248	−0.537220
$732$	16.7658	0.619684
$733$	6.34643	0.234411	0.117205	−	0.993108i	$-0.462606\pi$
$733$	6.34643	0.234411	0.117205	+	0.993108i	$0.462606\pi$
$734$	32.3194	1.19293
$735$	−3.76803	−0.138986
$736$	−8.27142	−0.304888
$737$	14.5347	0.535392
$738$	6.60291	0.243056
$739$	7.32416	0.269424	0.134712	−	0.990885i	$-0.456989\pi$
$739$	7.32416	0.269424	0.134712	+	0.990885i	$0.456989\pi$
$740$	2.09472	0.0770035
$741$	−6.18881	−0.227352
$742$	−3.09528	−0.113631
$743$	−46.2642	−1.69727	−0.848635	−	0.528979i	$-0.822575\pi$
$743$	−46.2642	−1.69727	−0.848635	+	0.528979i	$0.822575\pi$
$744$	−1.75702	−0.0644154
$745$	−13.0830	−0.479324
$746$	4.95941	0.181577
$747$	6.13973	0.224641
$748$	11.7761	0.430577
$749$	52.6600	1.92416
$750$	−13.7354	−0.501546
$751$	14.4334	0.526683	0.263342	−	0.964703i	$-0.415175\pi$
$751$	14.4334	0.526683	0.263342	+	0.964703i	$0.415175\pi$
$752$	7.95102	0.289944
$753$	14.1165	0.514434
$754$	−4.16515	−0.151686
$755$	10.1611	0.369801
$756$	−14.1041	−0.512961
$757$	32.3541	1.17593	0.587965	−	0.808886i	$-0.299929\pi$
$757$	32.3541	1.17593	0.587965	+	0.808886i	$0.299929\pi$
$758$	−5.18325	−0.188264
$759$	−28.8407	−1.04685
$760$	0.769767	0.0279224
$761$	−53.1481	−1.92662	−0.963308	−	0.268399i	$-0.913506\pi$
$761$	−53.1481	−1.92662	−0.963308	+	0.268399i	$0.913506\pi$
$762$	−31.2246	−1.13115
$763$	27.8404	1.00789
$764$	−17.0430	−0.616593
$765$	2.94709	0.106552
$766$	−32.1469	−1.16151
$767$	−17.5406	−0.633354
$768$	−1.89675	−0.0684430
$769$	33.0079	1.19030	0.595148	−	0.803616i	$-0.297093\pi$
$769$	33.0079	1.19030	0.595148	+	0.803616i	$0.297093\pi$
$770$	4.38002	0.157845
$771$	−37.2665	−1.34212
$772$	5.77870	0.207980
$773$	−27.9433	−1.00505	−0.502525	−	0.864563i	$-0.667595\pi$
$773$	−27.9433	−1.00505	−0.502525	+	0.864563i	$0.667595\pi$
$774$	1.35511	0.0487086
$775$	4.08277	0.146657
$776$	0.871774	0.0312949
$777$	15.9763	0.573146
$778$	15.2048	0.545118
$779$	11.0480	0.395837
$780$	4.76394	0.170577
$781$	−17.2376	−0.616808
$782$	−52.9864	−1.89479
$783$	−5.81673	−0.207873
$784$	2.58074	0.0921694
$785$	1.52196	0.0543211
$786$	5.96202	0.212658
$787$	34.1341	1.21675	0.608374	−	0.793650i	$-0.291822\pi$
$787$	34.1341	1.21675	0.608374	+	0.793650i	$0.291822\pi$
$788$	5.82415	0.207477
$789$	−4.33292	−0.154256
$790$	−9.50527	−0.338182
$791$	−13.0261	−0.463156
$792$	−1.09867	−0.0390395
$793$	28.8412	1.02418
$794$	−23.0737	−0.818856
$795$	1.46005	0.0517828
$796$	14.8747	0.527220
$797$	21.4008	0.758057	0.379028	−	0.925385i	$-0.376258\pi$
$797$	21.4008	0.758057	0.379028	+	0.925385i	$0.376258\pi$
$798$	5.87096	0.207830
$799$	50.9339	1.80191
$800$	4.40746	0.155827
$801$	−1.39779	−0.0493884
$802$	−17.9364	−0.633357
$803$	−3.60891	−0.127356
$804$	−14.9968	−0.528896
$805$	−19.7078	−0.694610
$806$	−3.02249	−0.106463
$807$	−22.9138	−0.806604
$808$	−0.836675	−0.0294341
$809$	−35.9072	−1.26243	−0.631214	−	0.775608i	$-0.717443\pi$
$809$	−35.9072	−1.26243	−0.631214	+	0.775608i	$0.717443\pi$
$810$	8.03311	0.282255
$811$	40.8580	1.43472	0.717359	−	0.696704i	$-0.245351\pi$
$811$	40.8580	1.43472	0.717359	+	0.696704i	$0.245351\pi$
$812$	3.95124	0.138661
$813$	−3.79860	−0.133223
$814$	−5.00246	−0.175336
$815$	3.64296	0.127607
$816$	−12.1505	−0.425352
$817$	2.26739	0.0793260
$818$	13.3161	0.465587
$819$	6.03597	0.210914
$820$	−8.50442	−0.296987
$821$	41.2515	1.43969	0.719843	−	0.694137i	$-0.244214\pi$
$821$	41.2515	1.43969	0.719843	+	0.694137i	$0.244214\pi$
$822$	−28.4310	−0.991643
$823$	48.5795	1.69338	0.846688	−	0.532090i	$-0.178593\pi$
$823$	48.5795	1.69338	0.846688	+	0.532090i	$0.178593\pi$
$824$	18.1103	0.630902
$825$	15.3679	0.535042
$826$	16.6397	0.578970
$827$	53.1926	1.84969	0.924843	−	0.380348i	$-0.124196\pi$
$827$	53.1926	1.84969	0.924843	+	0.380348i	$0.124196\pi$
$828$	4.94344	0.171797
$829$	−15.3689	−0.533784	−0.266892	−	0.963727i	$-0.585997\pi$
$829$	−15.3689	−0.533784	−0.266892	+	0.963727i	$0.585997\pi$
$830$	−7.90786	−0.274486
$831$	−39.5637	−1.37245
$832$	−3.26285	−0.113119
$833$	16.5321	0.572805
$834$	4.16791	0.144323
$835$	−17.3089	−0.599000
$836$	−1.83830	−0.0635790
$837$	−4.22097	−0.145898
$838$	18.3834	0.635045
$839$	47.1411	1.62749	0.813745	−	0.581222i	$-0.197425\pi$
$839$	47.1411	1.62749	0.813745	+	0.581222i	$0.197425\pi$
$840$	−4.51927	−0.155930
$841$	−27.3705	−0.943809
$842$	−7.99267	−0.275446
$843$	11.8823	0.409247
$844$	−26.6685	−0.917967
$845$	−1.81186	−0.0623300
$846$	−4.75196	−0.163376
$847$	23.5880	0.810494
$848$	−1.00000	−0.0343401
$849$	35.4021	1.21500
$850$	28.2340	0.968418
$851$	22.5085	0.771582
$852$	17.7856	0.609325
$853$	51.9667	1.77931	0.889653	−	0.456637i	$-0.150946\pi$
$853$	51.9667	1.77931	0.889653	+	0.456637i	$0.150946\pi$
$854$	−27.3600	−0.936239
$855$	−0.460054	−0.0157335
$856$	17.0130	0.581493
$857$	−7.48910	−0.255823	−0.127911	−	0.991786i	$-0.540827\pi$
$857$	−7.48910	−0.255823	−0.127911	+	0.991786i	$0.540827\pi$
$858$	−11.3769	−0.388401
$859$	−49.5260	−1.68981	−0.844903	−	0.534919i	$-0.820342\pi$
$859$	−49.5260	−1.68981	−0.844903	+	0.534919i	$0.820342\pi$
$860$	−1.74536	−0.0595164
$861$	−64.8627	−2.21051
$862$	−23.0123	−0.783801
$863$	18.1370	0.617389	0.308695	−	0.951161i	$-0.400108\pi$
$863$	18.1370	0.617389	0.308695	+	0.951161i	$0.400108\pi$
$864$	−4.55665	−0.155020
$865$	13.9941	0.475813
$866$	22.0581	0.749565
$867$	−45.5908	−1.54835
$868$	2.86726	0.0973210
$869$	22.6998	0.770038
$870$	−1.86381	−0.0631892
$871$	−25.7980	−0.874133
$872$	8.99448	0.304592
$873$	−0.521019	−0.0176338
$874$	8.27142	0.279785
$875$	22.4146	0.757752
$876$	3.72365	0.125811
$877$	16.4349	0.554966	0.277483	−	0.960731i	$-0.410500\pi$
$877$	16.4349	0.554966	0.277483	+	0.960731i	$0.410500\pi$
$878$	−20.4428	−0.689910
$879$	30.7046	1.03564
$880$	1.41506	0.0477018
$881$	−19.2995	−0.650218	−0.325109	−	0.945677i	$-0.605401\pi$
$881$	−19.2995	−0.650218	−0.325109	+	0.945677i	$0.605401\pi$
$882$	−1.54239	−0.0519350
$883$	−23.4243	−0.788292	−0.394146	−	0.919048i	$-0.628960\pi$
$883$	−23.4243	−0.788292	−0.394146	+	0.919048i	$0.628960\pi$
$884$	−20.9017	−0.703001
$885$	−7.84902	−0.263842
$886$	−24.5281	−0.824038
$887$	−23.7266	−0.796662	−0.398331	−	0.917242i	$-0.630411\pi$
$887$	−23.7266	−0.796662	−0.398331	+	0.917242i	$0.630411\pi$
$888$	5.16151	0.173209
$889$	50.9550	1.70898
$890$	1.80033	0.0603470
$891$	−19.1841	−0.642692
$892$	23.9350	0.801404
$893$	−7.95102	−0.266071
$894$	−32.2372	−1.07817
$895$	−11.8987	−0.397730
$896$	3.09528	0.103406
$897$	51.1903	1.70919
$898$	−7.69215	−0.256690
$899$	1.18250	0.0394385
$900$	−2.63413	−0.0878045
$901$	−6.40596	−0.213413
$902$	20.3096	0.676237
$903$	−13.3118	−0.442988
$904$	−4.20839	−0.139969
$905$	−0.425694	−0.0141506
$906$	25.0376	0.831818
$907$	−15.7831	−0.524069	−0.262034	−	0.965059i	$-0.584393\pi$
$907$	−15.7831	−0.524069	−0.262034	+	0.965059i	$0.584393\pi$
$908$	−19.6014	−0.650495
$909$	0.500042	0.0165853
$910$	−7.77422	−0.257713
$911$	−45.4681	−1.50643	−0.753213	−	0.657777i	$-0.771497\pi$
$911$	−45.4681	−1.50643	−0.753213	+	0.657777i	$0.771497\pi$
$912$	1.89675	0.0628076
$913$	18.8850	0.625002
$914$	13.6734	0.452277
$915$	12.9058	0.426652
$916$	−28.0247	−0.925963
$917$	−9.72934	−0.321291
$918$	−29.1897	−0.963403
$919$	−3.86113	−0.127367	−0.0636835	−	0.997970i	$-0.520285\pi$
$919$	−3.86113	−0.127367	−0.0636835	+	0.997970i	$0.520285\pi$
$920$	−6.36706	−0.209916
$921$	6.03021	0.198702
$922$	−38.4771	−1.26717
$923$	30.5954	1.00706
$924$	10.7926	0.355051
$925$	−11.9938	−0.394352
$926$	−23.9371	−0.786622
$927$	−10.8237	−0.355496
$928$	1.27654	0.0419044
$929$	7.69504	0.252466	0.126233	−	0.992001i	$-0.459711\pi$
$929$	7.69504	0.252466	0.126233	+	0.992001i	$0.459711\pi$
$930$	−1.35250	−0.0443501
$931$	−2.58074	−0.0845805
$932$	−1.01879	−0.0333716
$933$	0.652025	0.0213463
$934$	−1.17385	−0.0384095
$935$	9.06484	0.296452
$936$	1.95006	0.0637396
$937$	10.0142	0.327150	0.163575	−	0.986531i	$-0.447697\pi$
$937$	10.0142	0.327150	0.163575	+	0.986531i	$0.447697\pi$
$938$	24.4731	0.799074
$939$	−1.44111	−0.0470288
$940$	6.12043	0.199626
$941$	−38.1562	−1.24385	−0.621927	−	0.783075i	$-0.713650\pi$
$941$	−38.1562	−1.24385	−0.621927	+	0.783075i	$0.713650\pi$
$942$	3.75020	0.122188
$943$	−91.3830	−2.97584
$944$	5.37584	0.174969
$945$	−10.8569	−0.353174
$946$	4.16815	0.135518
$947$	−25.9539	−0.843389	−0.421694	−	0.906738i	$-0.638564\pi$
$947$	−25.9539	−0.843389	−0.421694	+	0.906738i	$0.638564\pi$
$948$	−23.4215	−0.760695
$949$	6.40556	0.207933
$950$	−4.40746	−0.142997
$951$	34.6102	1.12231
$952$	19.8282	0.642636
$953$	−43.1050	−1.39631	−0.698154	−	0.715948i	$-0.745995\pi$
$953$	−43.1050	−1.39631	−0.698154	+	0.715948i	$0.745995\pi$
$954$	0.597654	0.0193498
$955$	−13.1191	−0.424525
$956$	−10.1920	−0.329631
$957$	4.45103	0.143881
$958$	−0.245438	−0.00792975
$959$	46.3961	1.49821
$960$	−1.46005	−0.0471230
$961$	−30.1419	−0.972320
$962$	8.87901	0.286271
$963$	−10.1679	−0.327656
$964$	−28.0611	−0.903789
$965$	4.44825	0.143194
$966$	−48.5612	−1.56243
$967$	−43.1579	−1.38786	−0.693932	−	0.720040i	$-0.744123\pi$
$967$	−43.1579	−1.38786	−0.693932	+	0.720040i	$0.744123\pi$
$968$	7.62064	0.244937
$969$	12.1505	0.390330
$970$	0.671063	0.0215465
$971$	−44.6380	−1.43250	−0.716252	−	0.697842i	$-0.754144\pi$
$971$	−44.6380	−1.43250	−0.716252	+	0.697842i	$0.754144\pi$
$972$	6.12409	0.196430
$973$	−6.80155	−0.218048
$974$	38.3274	1.22809
$975$	−27.2769	−0.873561
$976$	−8.83926	−0.282938
$977$	−49.8361	−1.59440	−0.797199	−	0.603717i	$-0.793686\pi$
$977$	−49.8361	−1.59440	−0.797199	+	0.603717i	$0.793686\pi$
$978$	8.97644	0.287035
$979$	−4.29941	−0.137410
$980$	1.98657	0.0634587
$981$	−5.37558	−0.171629
$982$	−32.5302	−1.03808
$983$	−8.11202	−0.258733	−0.129367	−	0.991597i	$-0.541294\pi$
$983$	−8.11202	−0.258733	−0.129367	+	0.991597i	$0.541294\pi$
$984$	−20.9554	−0.668033
$985$	4.48324	0.142848
$986$	8.17745	0.260423
$987$	46.6801	1.48584
$988$	3.26285	0.103805
$989$	−18.7545	−0.596360
$990$	−0.845718	−0.0268787
$991$	−38.8369	−1.23369	−0.616847	−	0.787083i	$-0.711590\pi$
$991$	−38.8369	−1.23369	−0.616847	+	0.787083i	$0.711590\pi$
$992$	0.926332	0.0294111
$993$	−24.1547	−0.766525
$994$	−29.0241	−0.920588
$995$	11.4500	0.362991
$996$	−19.4854	−0.617419
$997$	−44.5012	−1.40937	−0.704683	−	0.709522i	$-0.748911\pi$
$997$	−44.5012	−1.40937	−0.704683	+	0.709522i	$0.748911\pi$
$998$	−2.54420	−0.0805352
$999$	12.3997	0.392310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2014.2.a.g.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2014.2.a.g.1.3	✓	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2014 = 2 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.89675 q^{3} +1.00000 q^{4} +0.769767 q^{5} +1.89675 q^{6} -3.09528 q^{7} -1.00000 q^{8} +0.597654 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.89675 q^{3} +1.00000 q^{4} +0.769767 q^{5} +1.89675 q^{6} -3.09528 q^{7} -1.00000 q^{8} +0.597654 q^{9} -0.769767 q^{10} +1.83830 q^{11} -1.89675 q^{12} -3.26285 q^{13} +3.09528 q^{14} -1.46005 q^{15} +1.00000 q^{16} +6.40596 q^{17} -0.597654 q^{18} -1.00000 q^{19} +0.769767 q^{20} +5.87096 q^{21} -1.83830 q^{22} +8.27142 q^{23} +1.89675 q^{24} -4.40746 q^{25} +3.26285 q^{26} +4.55665 q^{27} -3.09528 q^{28} -1.27654 q^{29} +1.46005 q^{30} -0.926332 q^{31} -1.00000 q^{32} -3.48680 q^{33} -6.40596 q^{34} -2.38264 q^{35} +0.597654 q^{36} +2.72124 q^{37} +1.00000 q^{38} +6.18881 q^{39} -0.769767 q^{40} -11.0480 q^{41} -5.87096 q^{42} -2.26739 q^{43} +1.83830 q^{44} +0.460054 q^{45} -8.27142 q^{46} +7.95102 q^{47} -1.89675 q^{48} +2.58074 q^{49} +4.40746 q^{50} -12.1505 q^{51} -3.26285 q^{52} -1.00000 q^{53} -4.55665 q^{54} +1.41506 q^{55} +3.09528 q^{56} +1.89675 q^{57} +1.27654 q^{58} +5.37584 q^{59} -1.46005 q^{60} -8.83926 q^{61} +0.926332 q^{62} -1.84990 q^{63} +1.00000 q^{64} -2.51164 q^{65} +3.48680 q^{66} +7.90659 q^{67} +6.40596 q^{68} -15.6888 q^{69} +2.38264 q^{70} -9.37689 q^{71} -0.597654 q^{72} -1.96318 q^{73} -2.72124 q^{74} +8.35984 q^{75} -1.00000 q^{76} -5.69006 q^{77} -6.18881 q^{78} +12.3482 q^{79} +0.769767 q^{80} -10.4358 q^{81} +11.0480 q^{82} +10.2731 q^{83} +5.87096 q^{84} +4.93110 q^{85} +2.26739 q^{86} +2.42127 q^{87} -1.83830 q^{88} -2.33879 q^{89} -0.460054 q^{90} +10.0994 q^{91} +8.27142 q^{92} +1.75702 q^{93} -7.95102 q^{94} -0.769767 q^{95} +1.89675 q^{96} -0.871774 q^{97} -2.58074 q^{98} +1.09867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 5 q^{13} + q^{15} + 8 q^{16} - 9 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} - 9 q^{21} + 6 q^{22} - q^{23} - 9 q^{25} + 5 q^{26} - 3 q^{27} - 23 q^{29} - q^{30} - 6 q^{31} - 8 q^{32} - 6 q^{33} + 9 q^{34} - 7 q^{35} + 2 q^{36} + q^{37} + 8 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} + 9 q^{42} + 9 q^{43} - 6 q^{44} - 9 q^{45} + q^{46} - 13 q^{47} - 8 q^{49} + 9 q^{50} - 24 q^{51} - 5 q^{52} - 8 q^{53} + 3 q^{54} - 11 q^{55} + 23 q^{58} - 9 q^{59} + q^{60} + 6 q^{62} - 18 q^{63} + 8 q^{64} - 26 q^{65} + 6 q^{66} + 9 q^{67} - 9 q^{68} - 22 q^{69} + 7 q^{70} - 31 q^{71} - 2 q^{72} + 5 q^{73} - q^{74} - q^{75} - 8 q^{76} - 4 q^{77} + 5 q^{78} + 19 q^{79} + q^{80} - 24 q^{81} + 3 q^{82} + 11 q^{83} - 9 q^{84} + 19 q^{85} - 9 q^{86} - 22 q^{87} + 6 q^{88} - 41 q^{89} + 9 q^{90} + 18 q^{91} - q^{92} + 3 q^{93} + 13 q^{94} - q^{95} - 24 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 5 * q^13 + q^15 + 8 * q^16 - 9 * q^17 - 2 * q^18 - 8 * q^19 + q^20 - 9 * q^21 + 6 * q^22 - q^23 - 9 * q^25 + 5 * q^26 - 3 * q^27 - 23 * q^29 - q^30 - 6 * q^31 - 8 * q^32 - 6 * q^33 + 9 * q^34 - 7 * q^35 + 2 * q^36 + q^37 + 8 * q^38 - 5 * q^39 - q^40 - 3 * q^41 + 9 * q^42 + 9 * q^43 - 6 * q^44 - 9 * q^45 + q^46 - 13 * q^47 - 8 * q^49 + 9 * q^50 - 24 * q^51 - 5 * q^52 - 8 * q^53 + 3 * q^54 - 11 * q^55 + 23 * q^58 - 9 * q^59 + q^60 + 6 * q^62 - 18 * q^63 + 8 * q^64 - 26 * q^65 + 6 * q^66 + 9 * q^67 - 9 * q^68 - 22 * q^69 + 7 * q^70 - 31 * q^71 - 2 * q^72 + 5 * q^73 - q^74 - q^75 - 8 * q^76 - 4 * q^77 + 5 * q^78 + 19 * q^79 + q^80 - 24 * q^81 + 3 * q^82 + 11 * q^83 - 9 * q^84 + 19 * q^85 - 9 * q^86 - 22 * q^87 + 6 * q^88 - 41 * q^89 + 9 * q^90 + 18 * q^91 - q^92 + 3 * q^93 + 13 * q^94 - q^95 - 24 * q^97 + 8 * q^98 - 4 * q^99

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