LMFDB - Embedded newform 1334.2.a.i.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
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} - 22x^{6} + 151x^{4} - 332x^{2} + 6 $ x^8 - 22x^6 + 151x^4 - 332*x^2 + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.39983$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} +2.39983 q^{5} +2.90642 q^{6} -1.21390 q^{7} +1.00000 q^{8} +5.44730 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} +2.39983 q^{5} +2.90642 q^{6} -1.21390 q^{7} +1.00000 q^{8} +5.44730 q^{9} +2.39983 q^{10} -0.228073 q^{11} +2.90642 q^{12} -3.89899 q^{13} -1.21390 q^{14} +6.97492 q^{15} +1.00000 q^{16} -2.80131 q^{17} +5.44730 q^{18} +3.76221 q^{19} +2.39983 q^{20} -3.52812 q^{21} -0.228073 q^{22} -1.00000 q^{23} +2.90642 q^{24} +0.759171 q^{25} -3.89899 q^{26} +7.11290 q^{27} -1.21390 q^{28} -1.00000 q^{29} +6.97492 q^{30} -8.36223 q^{31} +1.00000 q^{32} -0.662876 q^{33} -2.80131 q^{34} -2.91316 q^{35} +5.44730 q^{36} +2.31052 q^{37} +3.76221 q^{38} -11.3321 q^{39} +2.39983 q^{40} +10.2798 q^{41} -3.52812 q^{42} +4.84303 q^{43} -0.228073 q^{44} +13.0726 q^{45} -1.00000 q^{46} -8.84058 q^{47} +2.90642 q^{48} -5.52644 q^{49} +0.759171 q^{50} -8.14180 q^{51} -3.89899 q^{52} +0.959699 q^{53} +7.11290 q^{54} -0.547335 q^{55} -1.21390 q^{56} +10.9346 q^{57} -1.00000 q^{58} +4.21049 q^{59} +6.97492 q^{60} -9.37309 q^{61} -8.36223 q^{62} -6.61250 q^{63} +1.00000 q^{64} -9.35691 q^{65} -0.662876 q^{66} +0.137501 q^{67} -2.80131 q^{68} -2.90642 q^{69} -2.91316 q^{70} -9.67581 q^{71} +5.44730 q^{72} +3.53877 q^{73} +2.31052 q^{74} +2.20647 q^{75} +3.76221 q^{76} +0.276858 q^{77} -11.3321 q^{78} +6.03471 q^{79} +2.39983 q^{80} +4.33119 q^{81} +10.2798 q^{82} +13.4228 q^{83} -3.52812 q^{84} -6.72267 q^{85} +4.84303 q^{86} -2.90642 q^{87} -0.228073 q^{88} -5.43542 q^{89} +13.0726 q^{90} +4.73300 q^{91} -1.00000 q^{92} -24.3042 q^{93} -8.84058 q^{94} +9.02866 q^{95} +2.90642 q^{96} -11.3899 q^{97} -5.52644 q^{98} -1.24238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

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
$3$	2.90642	1.67802	0.839012	−	0.544112i	$-0.183133\pi$
$3$	2.90642	1.67802	0.839012	+	0.544112i	$0.183133\pi$
$4$	1.00000	0.500000
$5$	2.39983	1.07324	0.536618	−	0.843825i	$-0.319702\pi$
$5$	2.39983	1.07324	0.536618	+	0.843825i	$0.319702\pi$
$6$	2.90642	1.18654
$7$	−1.21390	−0.458813	−0.229406	−	0.973331i	$-0.573678\pi$
$7$	−1.21390	−0.458813	−0.229406	+	0.973331i	$0.573678\pi$
$8$	1.00000	0.353553
$9$	5.44730	1.81577
$10$	2.39983	0.758892
$11$	−0.228073	−0.0687665	−0.0343832	−	0.999409i	$-0.510947\pi$
$11$	−0.228073	−0.0687665	−0.0343832	+	0.999409i	$0.510947\pi$
$12$	2.90642	0.839012
$13$	−3.89899	−1.08139	−0.540693	−	0.841220i	$-0.681838\pi$
$13$	−3.89899	−1.08139	−0.540693	+	0.841220i	$0.681838\pi$
$14$	−1.21390	−0.324430
$15$	6.97492	1.80092
$16$	1.00000	0.250000
$17$	−2.80131	−0.679418	−0.339709	−	0.940531i	$-0.610329\pi$
$17$	−2.80131	−0.679418	−0.339709	+	0.940531i	$0.610329\pi$
$18$	5.44730	1.28394
$19$	3.76221	0.863111	0.431555	−	0.902086i	$-0.357965\pi$
$19$	3.76221	0.863111	0.431555	+	0.902086i	$0.357965\pi$
$20$	2.39983	0.536618
$21$	−3.52812	−0.769899
$22$	−0.228073	−0.0486252
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.90642	0.593271
$25$	0.759171	0.151834
$26$	−3.89899	−0.764655
$27$	7.11290	1.36888
$28$	−1.21390	−0.229406
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	6.97492	1.27344
$31$	−8.36223	−1.50190	−0.750951	−	0.660358i	$-0.770404\pi$
$31$	−8.36223	−1.50190	−0.750951	+	0.660358i	$0.770404\pi$
$32$	1.00000	0.176777
$33$	−0.662876	−0.115392
$34$	−2.80131	−0.480421
$35$	−2.91316	−0.492414
$36$	5.44730	0.907884
$37$	2.31052	0.379848	0.189924	−	0.981799i	$-0.439176\pi$
$37$	2.31052	0.379848	0.189924	+	0.981799i	$0.439176\pi$
$38$	3.76221	0.610312
$39$	−11.3321	−1.81459
$40$	2.39983	0.379446
$41$	10.2798	1.60543	0.802716	−	0.596361i	$-0.203387\pi$
$41$	10.2798	1.60543	0.802716	+	0.596361i	$0.203387\pi$
$42$	−3.52812	−0.544401
$43$	4.84303	0.738556	0.369278	−	0.929319i	$-0.379605\pi$
$43$	4.84303	0.738556	0.369278	+	0.929319i	$0.379605\pi$
$44$	−0.228073	−0.0343832
$45$	13.0726	1.94875
$46$	−1.00000	−0.147442
$47$	−8.84058	−1.28953	−0.644765	−	0.764381i	$-0.723045\pi$
$47$	−8.84058	−1.28953	−0.644765	+	0.764381i	$0.723045\pi$
$48$	2.90642	0.419506
$49$	−5.52644	−0.789491
$50$	0.759171	0.107363
$51$	−8.14180	−1.14008
$52$	−3.89899	−0.540693
$53$	0.959699	0.131825	0.0659124	−	0.997825i	$-0.479004\pi$
$53$	0.959699	0.131825	0.0659124	+	0.997825i	$0.479004\pi$
$54$	7.11290	0.967943
$55$	−0.547335	−0.0738026
$56$	−1.21390	−0.162215
$57$	10.9346	1.44832
$58$	−1.00000	−0.131306
$59$	4.21049	0.548159	0.274080	−	0.961707i	$-0.411627\pi$
$59$	4.21049	0.548159	0.274080	+	0.961707i	$0.411627\pi$
$60$	6.97492	0.900458
$61$	−9.37309	−1.20010	−0.600050	−	0.799962i	$-0.704853\pi$
$61$	−9.37309	−1.20010	−0.600050	+	0.799962i	$0.704853\pi$
$62$	−8.36223	−1.06200
$63$	−6.61250	−0.833097
$64$	1.00000	0.125000
$65$	−9.35691	−1.16058
$66$	−0.662876	−0.0815944
$67$	0.137501	0.0167984	0.00839920	−	0.999965i	$-0.497326\pi$
$67$	0.137501	0.0167984	0.00839920	+	0.999965i	$0.497326\pi$
$68$	−2.80131	−0.339709
$69$	−2.90642	−0.349892
$70$	−2.91316	−0.348189
$71$	−9.67581	−1.14831	−0.574154	−	0.818747i	$-0.694669\pi$
$71$	−9.67581	−1.14831	−0.574154	+	0.818747i	$0.694669\pi$
$72$	5.44730	0.641971
$73$	3.53877	0.414182	0.207091	−	0.978322i	$-0.433600\pi$
$73$	3.53877	0.414182	0.207091	+	0.978322i	$0.433600\pi$
$74$	2.31052	0.268593
$75$	2.20647	0.254781
$76$	3.76221	0.431555
$77$	0.276858	0.0315509
$78$	−11.3321	−1.28311
$79$	6.03471	0.678958	0.339479	−	0.940614i	$-0.389749\pi$
$79$	6.03471	0.678958	0.339479	+	0.940614i	$0.389749\pi$
$80$	2.39983	0.268309
$81$	4.33119	0.481243
$82$	10.2798	1.13521
$83$	13.4228	1.47335	0.736674	−	0.676248i	$-0.236395\pi$
$83$	13.4228	1.47335	0.736674	+	0.676248i	$0.236395\pi$
$84$	−3.52812	−0.384950
$85$	−6.72267	−0.729175
$86$	4.84303	0.522238
$87$	−2.90642	−0.311601
$88$	−0.228073	−0.0243126
$89$	−5.43542	−0.576154	−0.288077	−	0.957607i	$-0.593016\pi$
$89$	−5.43542	−0.576154	−0.288077	+	0.957607i	$0.593016\pi$
$90$	13.0726	1.37797
$91$	4.73300	0.496154
$92$	−1.00000	−0.104257
$93$	−24.3042	−2.52023
$94$	−8.84058	−0.911836
$95$	9.02866	0.926321
$96$	2.90642	0.296636
$97$	−11.3899	−1.15647	−0.578237	−	0.815869i	$-0.696259\pi$
$97$	−11.3899	−1.15647	−0.578237	+	0.815869i	$0.696259\pi$
$98$	−5.52644	−0.558254
$99$	−1.24238	−0.124864
$100$	0.759171	0.0759171
$101$	13.0288	1.29641	0.648207	−	0.761464i	$-0.275519\pi$
$101$	13.0288	1.29641	0.648207	+	0.761464i	$0.275519\pi$
$102$	−8.14180	−0.806159
$103$	8.58321	0.845729	0.422864	−	0.906193i	$-0.361025\pi$
$103$	8.58321	0.845729	0.422864	+	0.906193i	$0.361025\pi$
$104$	−3.89899	−0.382328
$105$	−8.46688	−0.826283
$106$	0.959699	0.0932142
$107$	−0.440155	−0.0425513	−0.0212757	−	0.999774i	$-0.506773\pi$
$107$	−0.440155	−0.0425513	−0.0212757	+	0.999774i	$0.506773\pi$
$108$	7.11290	0.684439
$109$	2.30120	0.220415	0.110207	−	0.993909i	$-0.464848\pi$
$109$	2.30120	0.220415	0.110207	+	0.993909i	$0.464848\pi$
$110$	−0.547335	−0.0521863
$111$	6.71536	0.637394
$112$	−1.21390	−0.114703
$113$	−1.43115	−0.134631	−0.0673157	−	0.997732i	$-0.521443\pi$
$113$	−1.43115	−0.134631	−0.0673157	+	0.997732i	$0.521443\pi$
$114$	10.9346	1.02412
$115$	−2.39983	−0.223785
$116$	−1.00000	−0.0928477
$117$	−21.2390	−1.96355
$118$	4.21049	0.387607
$119$	3.40053	0.311726
$120$	6.97492	0.636720
$121$	−10.9480	−0.995271
$122$	−9.37309	−0.848599
$123$	29.8774	2.69396
$124$	−8.36223	−0.750951
$125$	−10.1773	−0.910282
$126$	−6.61250	−0.589089
$127$	3.06588	0.272053	0.136026	−	0.990705i	$-0.456567\pi$
$127$	3.06588	0.272053	0.136026	+	0.990705i	$0.456567\pi$
$128$	1.00000	0.0883883
$129$	14.0759	1.23931
$130$	−9.35691	−0.820655
$131$	−9.00809	−0.787041	−0.393520	−	0.919316i	$-0.628743\pi$
$131$	−9.00809	−0.787041	−0.393520	+	0.919316i	$0.628743\pi$
$132$	−0.662876	−0.0576959
$133$	−4.56697	−0.396006
$134$	0.137501	0.0118783
$135$	17.0697	1.46913
$136$	−2.80131	−0.240211
$137$	7.06358	0.603482	0.301741	−	0.953390i	$-0.402432\pi$
$137$	7.06358	0.603482	0.301741	+	0.953390i	$0.402432\pi$
$138$	−2.90642	−0.247411
$139$	5.51747	0.467986	0.233993	−	0.972238i	$-0.424821\pi$
$139$	5.51747	0.467986	0.233993	+	0.972238i	$0.424821\pi$
$140$	−2.91316	−0.246207
$141$	−25.6945	−2.16386
$142$	−9.67581	−0.811976
$143$	0.889253	0.0743631
$144$	5.44730	0.453942
$145$	−2.39983	−0.199295
$146$	3.53877	0.292871
$147$	−16.0622	−1.32479
$148$	2.31052	0.189924
$149$	17.2169	1.41047	0.705234	−	0.708975i	$-0.250842\pi$
$149$	17.2169	1.41047	0.705234	+	0.708975i	$0.250842\pi$
$150$	2.20647	0.180158
$151$	−9.38004	−0.763337	−0.381668	−	0.924299i	$-0.624650\pi$
$151$	−9.38004	−0.763337	−0.381668	+	0.924299i	$0.624650\pi$
$152$	3.76221	0.305156
$153$	−15.2596	−1.23366
$154$	0.276858	0.0223099
$155$	−20.0679	−1.61189
$156$	−11.3321	−0.907296
$157$	8.10749	0.647049	0.323524	−	0.946220i	$-0.395132\pi$
$157$	8.10749	0.647049	0.323524	+	0.946220i	$0.395132\pi$
$158$	6.03471	0.480096
$159$	2.78929	0.221205
$160$	2.39983	0.189723
$161$	1.21390	0.0956691
$162$	4.33119	0.340290
$163$	−13.9940	−1.09610	−0.548048	−	0.836447i	$-0.684629\pi$
$163$	−13.9940	−1.09610	−0.548048	+	0.836447i	$0.684629\pi$
$164$	10.2798	0.802716
$165$	−1.59079	−0.123843
$166$	13.4228	1.04181
$167$	6.27277	0.485402	0.242701	−	0.970101i	$-0.421967\pi$
$167$	6.27277	0.485402	0.242701	+	0.970101i	$0.421967\pi$
$168$	−3.52812	−0.272200
$169$	2.20214	0.169395
$170$	−6.72267	−0.515605
$171$	20.4939	1.56721
$172$	4.84303	0.369278
$173$	12.1369	0.922754	0.461377	−	0.887204i	$-0.347356\pi$
$173$	12.1369	0.922754	0.461377	+	0.887204i	$0.347356\pi$
$174$	−2.90642	−0.220335
$175$	−0.921561	−0.0696634
$176$	−0.228073	−0.0171916
$177$	12.2375	0.919824
$178$	−5.43542	−0.407402
$179$	9.11727	0.681457	0.340728	−	0.940162i	$-0.389326\pi$
$179$	9.11727	0.681457	0.340728	+	0.940162i	$0.389326\pi$
$180$	13.0726	0.974373
$181$	1.92008	0.142718	0.0713591	−	0.997451i	$-0.477266\pi$
$181$	1.92008	0.142718	0.0713591	+	0.997451i	$0.477266\pi$
$182$	4.73300	0.350834
$183$	−27.2422	−2.01380
$184$	−1.00000	−0.0737210
$185$	5.54486	0.407666
$186$	−24.3042	−1.78207
$187$	0.638903	0.0467212
$188$	−8.84058	−0.644765
$189$	−8.63438	−0.628058
$190$	9.02866	0.655008
$191$	21.9672	1.58949	0.794745	−	0.606944i	$-0.207605\pi$
$191$	21.9672	1.58949	0.794745	+	0.606944i	$0.207605\pi$
$192$	2.90642	0.209753
$193$	−15.5036	−1.11597	−0.557987	−	0.829850i	$-0.688426\pi$
$193$	−15.5036	−1.11597	−0.557987	+	0.829850i	$0.688426\pi$
$194$	−11.3899	−0.817750
$195$	−27.1951	−1.94748
$196$	−5.52644	−0.394745
$197$	−18.8565	−1.34347	−0.671736	−	0.740791i	$-0.734451\pi$
$197$	−18.8565	−1.34347	−0.671736	+	0.740791i	$0.734451\pi$
$198$	−1.24238	−0.0882921
$199$	11.6924	0.828850	0.414425	−	0.910084i	$-0.363983\pi$
$199$	11.6924	0.828850	0.414425	+	0.910084i	$0.363983\pi$
$200$	0.759171	0.0536815
$201$	0.399636	0.0281881
$202$	13.0288	0.916703
$203$	1.21390	0.0851994
$204$	−8.14180	−0.570040
$205$	24.6697	1.72301
$206$	8.58321	0.598021
$207$	−5.44730	−0.378614
$208$	−3.89899	−0.270346
$209$	−0.858058	−0.0593531
$210$	−8.46688	−0.584270
$211$	5.72006	0.393785	0.196893	−	0.980425i	$-0.436915\pi$
$211$	5.72006	0.393785	0.196893	+	0.980425i	$0.436915\pi$
$212$	0.959699	0.0659124
$213$	−28.1220	−1.92689
$214$	−0.440155	−0.0300883
$215$	11.6224	0.792644
$216$	7.11290	0.483971
$217$	10.1510	0.689091
$218$	2.30120	0.155857
$219$	10.2852	0.695007
$220$	−0.547335	−0.0369013
$221$	10.9223	0.734713
$222$	6.71536	0.450705
$223$	5.26766	0.352749	0.176374	−	0.984323i	$-0.443563\pi$
$223$	5.26766	0.352749	0.176374	+	0.984323i	$0.443563\pi$
$224$	−1.21390	−0.0811074
$225$	4.13543	0.275695
$226$	−1.43115	−0.0951987
$227$	2.09519	0.139063	0.0695313	−	0.997580i	$-0.477850\pi$
$227$	2.09519	0.139063	0.0695313	+	0.997580i	$0.477850\pi$
$228$	10.9346	0.724161
$229$	19.0358	1.25792	0.628960	−	0.777438i	$-0.283481\pi$
$229$	19.0358	1.25792	0.628960	+	0.777438i	$0.283481\pi$
$230$	−2.39983	−0.158240
$231$	0.804668	0.0529433
$232$	−1.00000	−0.0656532
$233$	16.9533	1.11064	0.555322	−	0.831635i	$-0.312595\pi$
$233$	16.9533	1.11064	0.555322	+	0.831635i	$0.312595\pi$
$234$	−21.2390	−1.38844
$235$	−21.2159	−1.38397
$236$	4.21049	0.274080
$237$	17.5394	1.13931
$238$	3.40053	0.220423
$239$	−3.04320	−0.196848	−0.0984242	−	0.995145i	$-0.531380\pi$
$239$	−3.04320	−0.196848	−0.0984242	+	0.995145i	$0.531380\pi$
$240$	6.97492	0.450229
$241$	29.0376	1.87047	0.935237	−	0.354022i	$-0.115186\pi$
$241$	29.0376	1.87047	0.935237	+	0.354022i	$0.115186\pi$
$242$	−10.9480	−0.703763
$243$	−8.75041	−0.561339
$244$	−9.37309	−0.600050
$245$	−13.2625	−0.847310
$246$	29.8774	1.90491
$247$	−14.6688	−0.933356
$248$	−8.36223	−0.531002
$249$	39.0125	2.47231
$250$	−10.1773	−0.643666
$251$	17.2780	1.09058	0.545289	−	0.838248i	$-0.316420\pi$
$251$	17.2780	1.09058	0.545289	+	0.838248i	$0.316420\pi$
$252$	−6.61250	−0.416549
$253$	0.228073	0.0143388
$254$	3.06588	0.192370
$255$	−19.5389	−1.22357
$256$	1.00000	0.0625000
$257$	0.0287847	0.00179554	0.000897769	−	1.00000i	$-0.499714\pi$
$257$	0.0287847	0.00179554	0.000897769		1.00000i	$0.499714\pi$
$258$	14.0759	0.876328
$259$	−2.80475	−0.174279
$260$	−9.35691	−0.580291
$261$	−5.44730	−0.337180
$262$	−9.00809	−0.556522
$263$	−27.6922	−1.70758	−0.853788	−	0.520621i	$-0.825700\pi$
$263$	−27.6922	−1.70758	−0.853788	+	0.520621i	$0.825700\pi$
$264$	−0.662876	−0.0407972
$265$	2.30311	0.141479
$266$	−4.56697	−0.280019
$267$	−15.7976	−0.966800
$268$	0.137501	0.00839920
$269$	−20.7330	−1.26412	−0.632058	−	0.774921i	$-0.717789\pi$
$269$	−20.7330	−1.26412	−0.632058	+	0.774921i	$0.717789\pi$
$270$	17.0697	1.03883
$271$	−6.30991	−0.383300	−0.191650	−	0.981463i	$-0.561384\pi$
$271$	−6.30991	−0.383300	−0.191650	+	0.981463i	$0.561384\pi$
$272$	−2.80131	−0.169855
$273$	13.7561	0.832558
$274$	7.06358	0.426726
$275$	−0.173146	−0.0104411
$276$	−2.90642	−0.174946
$277$	3.41065	0.204926	0.102463	−	0.994737i	$-0.467328\pi$
$277$	3.41065	0.204926	0.102463	+	0.994737i	$0.467328\pi$
$278$	5.51747	0.330916
$279$	−45.5516	−2.72710
$280$	−2.91316	−0.174095
$281$	−2.91553	−0.173926	−0.0869628	−	0.996212i	$-0.527716\pi$
$281$	−2.91553	−0.173926	−0.0869628	+	0.996212i	$0.527716\pi$
$282$	−25.6945	−1.53008
$283$	0.174831	0.0103926	0.00519632	−	0.999986i	$-0.498346\pi$
$283$	0.174831	0.0103926	0.00519632	+	0.999986i	$0.498346\pi$
$284$	−9.67581	−0.574154
$285$	26.2411	1.55439
$286$	0.889253	0.0525827
$287$	−12.4787	−0.736593
$288$	5.44730	0.320985
$289$	−9.15265	−0.538391
$290$	−2.39983	−0.140923
$291$	−33.1040	−1.94059
$292$	3.53877	0.207091
$293$	−32.1365	−1.87743	−0.938717	−	0.344688i	$-0.887985\pi$
$293$	−32.1365	−1.87743	−0.938717	+	0.344688i	$0.887985\pi$
$294$	−16.0622	−0.936765
$295$	10.1044	0.588304
$296$	2.31052	0.134296
$297$	−1.62226	−0.0941329
$298$	17.2169	0.997351
$299$	3.89899	0.225485
$300$	2.20647	0.127391
$301$	−5.87898	−0.338859
$302$	−9.38004	−0.539761
$303$	37.8672	2.17542
$304$	3.76221	0.215778
$305$	−22.4938	−1.28799
$306$	−15.2596	−0.872333
$307$	29.5108	1.68427	0.842136	−	0.539265i	$-0.181298\pi$
$307$	29.5108	1.68427	0.842136	+	0.539265i	$0.181298\pi$
$308$	0.276858	0.0157755
$309$	24.9464	1.41915
$310$	−20.0679	−1.13978
$311$	−20.2530	−1.14844	−0.574220	−	0.818701i	$-0.694695\pi$
$311$	−20.2530	−1.14844	−0.574220	+	0.818701i	$0.694695\pi$
$312$	−11.3321	−0.641555
$313$	−24.3439	−1.37600	−0.688000	−	0.725711i	$-0.741511\pi$
$313$	−24.3439	−1.37600	−0.688000	+	0.725711i	$0.741511\pi$
$314$	8.10749	0.457532
$315$	−15.8689	−0.894109
$316$	6.03471	0.339479
$317$	−0.721552	−0.0405264	−0.0202632	−	0.999795i	$-0.506450\pi$
$317$	−0.721552	−0.0405264	−0.0202632	+	0.999795i	$0.506450\pi$
$318$	2.78929	0.156416
$319$	0.228073	0.0127696
$320$	2.39983	0.134154
$321$	−1.27928	−0.0714022
$322$	1.21390	0.0676482
$323$	−10.5391	−0.586413
$324$	4.33119	0.240622
$325$	−2.96000	−0.164191
$326$	−13.9940	−0.775057
$327$	6.68826	0.369862
$328$	10.2798	0.567606
$329$	10.7316	0.591653
$330$	−1.59079	−0.0875700
$331$	3.78872	0.208247	0.104123	−	0.994564i	$-0.466796\pi$
$331$	3.78872	0.208247	0.104123	+	0.994564i	$0.466796\pi$
$332$	13.4228	0.736674
$333$	12.5861	0.689715
$334$	6.27277	0.343231
$335$	0.329978	0.0180286
$336$	−3.52812	−0.192475
$337$	−12.7500	−0.694538	−0.347269	−	0.937765i	$-0.612891\pi$
$337$	−12.7500	−0.694538	−0.347269	+	0.937765i	$0.612891\pi$
$338$	2.20214	0.119781
$339$	−4.15953	−0.225915
$340$	−6.72267	−0.364588
$341$	1.90720	0.103280
$342$	20.4939	1.10818
$343$	15.2059	0.821041
$344$	4.84303	0.261119
$345$	−6.97492	−0.375517
$346$	12.1369	0.652485
$347$	25.2003	1.35282	0.676412	−	0.736523i	$-0.263534\pi$
$347$	25.2003	1.35282	0.676412	+	0.736523i	$0.263534\pi$
$348$	−2.90642	−0.155801
$349$	−12.4313	−0.665431	−0.332716	−	0.943027i	$-0.607965\pi$
$349$	−12.4313	−0.665431	−0.332716	+	0.943027i	$0.607965\pi$
$350$	−0.921561	−0.0492595
$351$	−27.7331	−1.48028
$352$	−0.228073	−0.0121563
$353$	−10.6857	−0.568742	−0.284371	−	0.958714i	$-0.591785\pi$
$353$	−10.6857	−0.568742	−0.284371	+	0.958714i	$0.591785\pi$
$354$	12.2375	0.650414
$355$	−23.2203	−1.23240
$356$	−5.43542	−0.288077
$357$	9.88337	0.523083
$358$	9.11727	0.481863
$359$	−8.20929	−0.433270	−0.216635	−	0.976253i	$-0.569508\pi$
$359$	−8.20929	−0.433270	−0.216635	+	0.976253i	$0.569508\pi$
$360$	13.0726	0.688986
$361$	−4.84575	−0.255039
$362$	1.92008	0.100917
$363$	−31.8195	−1.67009
$364$	4.73300	0.248077
$365$	8.49244	0.444514
$366$	−27.2422	−1.42397
$367$	20.4646	1.06825	0.534123	−	0.845407i	$-0.320642\pi$
$367$	20.4646	1.06825	0.534123	+	0.845407i	$0.320642\pi$
$368$	−1.00000	−0.0521286
$369$	55.9971	2.91509
$370$	5.54486	0.288263
$371$	−1.16498	−0.0604829
$372$	−24.3042	−1.26011
$373$	−27.6958	−1.43403	−0.717017	−	0.697056i	$-0.754493\pi$
$373$	−27.6958	−1.43403	−0.717017	+	0.697056i	$0.754493\pi$
$374$	0.638903	0.0330369
$375$	−29.5794	−1.52748
$376$	−8.84058	−0.455918
$377$	3.89899	0.200808
$378$	−8.63438	−0.444104
$379$	16.6795	0.856769	0.428384	−	0.903597i	$-0.359083\pi$
$379$	16.6795	0.856769	0.428384	+	0.903597i	$0.359083\pi$
$380$	9.02866	0.463161
$381$	8.91074	0.456511
$382$	21.9672	1.12394
$383$	19.4203	0.992329	0.496165	−	0.868228i	$-0.334741\pi$
$383$	19.4203	0.992329	0.496165	+	0.868228i	$0.334741\pi$
$384$	2.90642	0.148318
$385$	0.664412	0.0338616
$386$	−15.5036	−0.789113
$387$	26.3815	1.34105
$388$	−11.3899	−0.578237
$389$	1.94874	0.0988053	0.0494026	−	0.998779i	$-0.484268\pi$
$389$	1.94874	0.0988053	0.0494026	+	0.998779i	$0.484268\pi$
$390$	−27.1951	−1.37708
$391$	2.80131	0.141668
$392$	−5.52644	−0.279127
$393$	−26.1813	−1.32067
$394$	−18.8565	−0.949978
$395$	14.4823	0.728682
$396$	−1.24238	−0.0624320
$397$	−5.66356	−0.284246	−0.142123	−	0.989849i	$-0.545393\pi$
$397$	−5.66356	−0.284246	−0.142123	+	0.989849i	$0.545393\pi$
$398$	11.6924	0.586085
$399$	−13.2735	−0.664508
$400$	0.759171	0.0379585
$401$	7.13741	0.356425	0.178213	−	0.983992i	$-0.442969\pi$
$401$	7.13741	0.356425	0.178213	+	0.983992i	$0.442969\pi$
$402$	0.399636	0.0199320
$403$	32.6043	1.62413
$404$	13.0288	0.648207
$405$	10.3941	0.516487
$406$	1.21390	0.0602451
$407$	−0.526967	−0.0261208
$408$	−8.14180	−0.403079
$409$	30.5112	1.50868	0.754342	−	0.656482i	$-0.227956\pi$
$409$	30.5112	1.50868	0.754342	+	0.656482i	$0.227956\pi$
$410$	24.6697	1.21835
$411$	20.5298	1.01266
$412$	8.58321	0.422864
$413$	−5.11113	−0.251502
$414$	−5.44730	−0.267720
$415$	32.2125	1.58125
$416$	−3.89899	−0.191164
$417$	16.0361	0.785292
$418$	−0.858058	−0.0419690
$419$	−11.8680	−0.579789	−0.289894	−	0.957059i	$-0.593620\pi$
$419$	−11.8680	−0.579789	−0.289894	+	0.957059i	$0.593620\pi$
$420$	−8.46688	−0.413141
$421$	28.3444	1.38142	0.690710	−	0.723132i	$-0.257298\pi$
$421$	28.3444	1.38142	0.690710	+	0.723132i	$0.257298\pi$
$422$	5.72006	0.278448
$423$	−48.1573	−2.34149
$424$	0.959699	0.0466071
$425$	−2.12667	−0.103159
$426$	−28.1220	−1.36252
$427$	11.3780	0.550621
$428$	−0.440155	−0.0212757
$429$	2.58455	0.124783
$430$	11.6224	0.560484
$431$	−32.8400	−1.58185	−0.790924	−	0.611914i	$-0.790400\pi$
$431$	−32.8400	−1.58185	−0.790924	+	0.611914i	$0.790400\pi$
$432$	7.11290	0.342219
$433$	−26.3759	−1.26755	−0.633773	−	0.773519i	$-0.718494\pi$
$433$	−26.3759	−1.26755	−0.633773	+	0.773519i	$0.718494\pi$
$434$	10.1510	0.487261
$435$	−6.97492	−0.334422
$436$	2.30120	0.110207
$437$	−3.76221	−0.179971
$438$	10.2852	0.491444
$439$	20.8847	0.996771	0.498385	−	0.866956i	$-0.333926\pi$
$439$	20.8847	0.996771	0.498385	+	0.866956i	$0.333926\pi$
$440$	−0.547335	−0.0260932
$441$	−30.1042	−1.43353
$442$	10.9223	0.519521
$443$	8.47680	0.402745	0.201372	−	0.979515i	$-0.435460\pi$
$443$	8.47680	0.402745	0.201372	+	0.979515i	$0.435460\pi$
$444$	6.71536	0.318697
$445$	−13.0441	−0.618349
$446$	5.26766	0.249431
$447$	50.0398	2.36680
$448$	−1.21390	−0.0573516
$449$	−19.9828	−0.943047	−0.471524	−	0.881853i	$-0.656296\pi$
$449$	−19.9828	−0.943047	−0.471524	+	0.881853i	$0.656296\pi$
$450$	4.13543	0.194946
$451$	−2.34454	−0.110400
$452$	−1.43115	−0.0673157
$453$	−27.2624	−1.28090
$454$	2.09519	0.0983321
$455$	11.3584	0.532490
$456$	10.9346	0.512059
$457$	−3.71704	−0.173876	−0.0869380	−	0.996214i	$-0.527708\pi$
$457$	−3.71704	−0.173876	−0.0869380	+	0.996214i	$0.527708\pi$
$458$	19.0358	0.889483
$459$	−19.9254	−0.930040
$460$	−2.39983	−0.111893
$461$	7.62411	0.355090	0.177545	−	0.984113i	$-0.443184\pi$
$461$	7.62411	0.355090	0.177545	+	0.984113i	$0.443184\pi$
$462$	0.804668	0.0374365
$463$	−33.6549	−1.56408	−0.782038	−	0.623230i	$-0.785820\pi$
$463$	−33.6549	−1.56408	−0.782038	+	0.623230i	$0.785820\pi$
$464$	−1.00000	−0.0464238
$465$	−58.3259	−2.70480
$466$	16.9533	0.785344
$467$	−14.6329	−0.677130	−0.338565	−	0.940943i	$-0.609942\pi$
$467$	−14.6329	−0.677130	−0.338565	+	0.940943i	$0.609942\pi$
$468$	−21.2390	−0.981773
$469$	−0.166913	−0.00770732
$470$	−21.2159	−0.978614
$471$	23.5638	1.08576
$472$	4.21049	0.193803
$473$	−1.10456	−0.0507879
$474$	17.5394	0.805613
$475$	2.85616	0.131050
$476$	3.40053	0.155863
$477$	5.22777	0.239363
$478$	−3.04320	−0.139193
$479$	−36.4649	−1.66612	−0.833061	−	0.553181i	$-0.813414\pi$
$479$	−36.4649	−1.66612	−0.833061	+	0.553181i	$0.813414\pi$
$480$	6.97492	0.318360
$481$	−9.00871	−0.410762
$482$	29.0376	1.32262
$483$	3.52812	0.160535
$484$	−10.9480	−0.497636
$485$	−27.3339	−1.24117
$486$	−8.75041	−0.396927
$487$	−36.8018	−1.66765	−0.833823	−	0.552031i	$-0.813853\pi$
$487$	−36.8018	−1.66765	−0.833823	+	0.552031i	$0.813853\pi$
$488$	−9.37309	−0.424300
$489$	−40.6726	−1.83928
$490$	−13.2625	−0.599138
$491$	17.7024	0.798899	0.399450	−	0.916755i	$-0.369201\pi$
$491$	17.7024	0.798899	0.399450	+	0.916755i	$0.369201\pi$
$492$	29.8774	1.34698
$493$	2.80131	0.126165
$494$	−14.6688	−0.659982
$495$	−2.98150	−0.134008
$496$	−8.36223	−0.375475
$497$	11.7455	0.526858
$498$	39.0125	1.74819
$499$	32.6786	1.46290	0.731448	−	0.681897i	$-0.238845\pi$
$499$	32.6786	1.46290	0.731448	+	0.681897i	$0.238845\pi$
$500$	−10.1773	−0.455141
$501$	18.2313	0.814516
$502$	17.2780	0.771156
$503$	−30.3165	−1.35174	−0.675872	−	0.737019i	$-0.736233\pi$
$503$	−30.3165	−1.35174	−0.675872	+	0.737019i	$0.736233\pi$
$504$	−6.61250	−0.294544
$505$	31.2669	1.39136
$506$	0.228073	0.0101391
$507$	6.40036	0.284250
$508$	3.06588	0.136026
$509$	−26.7763	−1.18684	−0.593420	−	0.804893i	$-0.702223\pi$
$509$	−26.7763	−1.18684	−0.593420	+	0.804893i	$0.702223\pi$
$510$	−19.5389	−0.865198
$511$	−4.29573	−0.190032
$512$	1.00000	0.0441942
$513$	26.7602	1.18149
$514$	0.0287847	0.00126964
$515$	20.5982	0.907666
$516$	14.0759	0.619657
$517$	2.01629	0.0886765
$518$	−2.80475	−0.123234
$519$	35.2751	1.54840
$520$	−9.35691	−0.410328
$521$	−15.8340	−0.693698	−0.346849	−	0.937921i	$-0.612748\pi$
$521$	−15.8340	−0.693698	−0.346849	+	0.937921i	$0.612748\pi$
$522$	−5.44730	−0.238422
$523$	−7.84106	−0.342866	−0.171433	−	0.985196i	$-0.554840\pi$
$523$	−7.84106	−0.342866	−0.171433	+	0.985196i	$0.554840\pi$
$524$	−9.00809	−0.393520
$525$	−2.67845	−0.116897
$526$	−27.6922	−1.20744
$527$	23.4252	1.02042
$528$	−0.662876	−0.0288480
$529$	1.00000	0.0434783
$530$	2.30311	0.100041
$531$	22.9358	0.995329
$532$	−4.56697	−0.198003
$533$	−40.0808	−1.73609
$534$	−15.7976	−0.683631
$535$	−1.05629	−0.0456676
$536$	0.137501	0.00593913
$537$	26.4987	1.14350
$538$	−20.7330	−0.893864
$539$	1.26043	0.0542905
$540$	17.0697	0.734564
$541$	25.5277	1.09752	0.548760	−	0.835980i	$-0.315100\pi$
$541$	25.5277	1.09752	0.548760	+	0.835980i	$0.315100\pi$
$542$	−6.30991	−0.271034
$543$	5.58056	0.239485
$544$	−2.80131	−0.120105
$545$	5.52248	0.236557
$546$	13.7561	0.588707
$547$	29.7677	1.27277	0.636387	−	0.771370i	$-0.280428\pi$
$547$	29.7677	1.27277	0.636387	+	0.771370i	$0.280428\pi$
$548$	7.06358	0.301741
$549$	−51.0580	−2.17910
$550$	−0.173146	−0.00738297
$551$	−3.76221	−0.160276
$552$	−2.90642	−0.123706
$553$	−7.32556	−0.311514
$554$	3.41065	0.144905
$555$	16.1157	0.684073
$556$	5.51747	0.233993
$557$	−18.2264	−0.772277	−0.386139	−	0.922441i	$-0.626191\pi$
$557$	−18.2264	−0.772277	−0.386139	+	0.922441i	$0.626191\pi$
$558$	−45.5516	−1.92835
$559$	−18.8829	−0.798664
$560$	−2.91316	−0.123104
$561$	1.85692	0.0783993
$562$	−2.91553	−0.122984
$563$	11.4242	0.481472	0.240736	−	0.970591i	$-0.422611\pi$
$563$	11.4242	0.481472	0.240736	+	0.970591i	$0.422611\pi$
$564$	−25.6945	−1.08193
$565$	−3.43451	−0.144491
$566$	0.174831	0.00734871
$567$	−5.25765	−0.220801
$568$	−9.67581	−0.405988
$569$	34.4982	1.44624	0.723120	−	0.690722i	$-0.242707\pi$
$569$	34.4982	1.44624	0.723120	+	0.690722i	$0.242707\pi$
$570$	26.2411	1.09912
$571$	32.0116	1.33964	0.669821	−	0.742522i	$-0.266371\pi$
$571$	32.0116	1.33964	0.669821	+	0.742522i	$0.266371\pi$
$572$	0.889253	0.0371816
$573$	63.8460	2.66720
$574$	−12.4787	−0.520850
$575$	−0.759171	−0.0316596
$576$	5.44730	0.226971
$577$	21.3376	0.888294	0.444147	−	0.895954i	$-0.353507\pi$
$577$	21.3376	0.888294	0.444147	+	0.895954i	$0.353507\pi$
$578$	−9.15265	−0.380700
$579$	−45.0601	−1.87263
$580$	−2.39983	−0.0996474
$581$	−16.2940	−0.675991
$582$	−33.1040	−1.37221
$583$	−0.218881	−0.00906513
$584$	3.53877	0.146435
$585$	−50.9699	−2.10735
$586$	−32.1365	−1.32755
$587$	−1.84343	−0.0760866	−0.0380433	−	0.999276i	$-0.512112\pi$
$587$	−1.84343	−0.0760866	−0.0380433	+	0.999276i	$0.512112\pi$
$588$	−16.0622	−0.662393
$589$	−31.4605	−1.29631
$590$	10.1044	0.415994
$591$	−54.8051	−2.25438
$592$	2.31052	0.0949619
$593$	−19.6732	−0.807883	−0.403941	−	0.914785i	$-0.632360\pi$
$593$	−19.6732	−0.807883	−0.403941	+	0.914785i	$0.632360\pi$
$594$	−1.62226	−0.0665620
$595$	8.16067	0.334555
$596$	17.2169	0.705234
$597$	33.9830	1.39083
$598$	3.89899	0.159442
$599$	23.3423	0.953739	0.476870	−	0.878974i	$-0.341771\pi$
$599$	23.3423	0.953739	0.476870	+	0.878974i	$0.341771\pi$
$600$	2.20647	0.0900789
$601$	14.5959	0.595379	0.297689	−	0.954663i	$-0.403784\pi$
$601$	14.5959	0.595379	0.297689	+	0.954663i	$0.403784\pi$
$602$	−5.87898	−0.239609
$603$	0.749009	0.0305020
$604$	−9.38004	−0.381668
$605$	−26.2733	−1.06816
$606$	37.8672	1.53825
$607$	21.9695	0.891716	0.445858	−	0.895104i	$-0.352899\pi$
$607$	21.9695	0.891716	0.445858	+	0.895104i	$0.352899\pi$
$608$	3.76221	0.152578
$609$	3.52812	0.142967
$610$	−22.4938	−0.910747
$611$	34.4693	1.39448
$612$	−15.2596	−0.616832
$613$	28.5212	1.15196	0.575979	−	0.817464i	$-0.304621\pi$
$613$	28.5212	1.15196	0.575979	+	0.817464i	$0.304621\pi$
$614$	29.5108	1.19096
$615$	71.7006	2.89125
$616$	0.276858	0.0111549
$617$	−11.7707	−0.473870	−0.236935	−	0.971525i	$-0.576143\pi$
$617$	−11.7707	−0.473870	−0.236935	+	0.971525i	$0.576143\pi$
$618$	24.9464	1.00349
$619$	38.5678	1.55017	0.775086	−	0.631856i	$-0.217706\pi$
$619$	38.5678	1.55017	0.775086	+	0.631856i	$0.217706\pi$
$620$	−20.0679	−0.805947
$621$	−7.11290	−0.285431
$622$	−20.2530	−0.812070
$623$	6.59808	0.264347
$624$	−11.3321	−0.453648
$625$	−28.2195	−1.12878
$626$	−24.3439	−0.972979
$627$	−2.49388	−0.0995960
$628$	8.10749	0.323524
$629$	−6.47250	−0.258075
$630$	−15.8689	−0.632231
$631$	0.591492	0.0235469	0.0117735	−	0.999931i	$-0.496252\pi$
$631$	0.591492	0.0235469	0.0117735	+	0.999931i	$0.496252\pi$
$632$	6.03471	0.240048
$633$	16.6249	0.660781
$634$	−0.721552	−0.0286565
$635$	7.35758	0.291977
$636$	2.78929	0.110603
$637$	21.5475	0.853744
$638$	0.228073	0.00902948
$639$	−52.7071	−2.08506
$640$	2.39983	0.0948615
$641$	−5.65467	−0.223346	−0.111673	−	0.993745i	$-0.535621\pi$
$641$	−5.65467	−0.223346	−0.111673	+	0.993745i	$0.535621\pi$
$642$	−1.27928	−0.0504890
$643$	34.8691	1.37510	0.687551	−	0.726136i	$-0.258686\pi$
$643$	34.8691	1.37510	0.687551	+	0.726136i	$0.258686\pi$
$644$	1.21390	0.0478345
$645$	33.7797	1.33008
$646$	−10.5391	−0.414657
$647$	41.4483	1.62950	0.814750	−	0.579813i	$-0.196874\pi$
$647$	41.4483	1.62950	0.814750	+	0.579813i	$0.196874\pi$
$648$	4.33119	0.170145
$649$	−0.960297	−0.0376950
$650$	−2.96000	−0.116101
$651$	29.5030	1.15631
$652$	−13.9940	−0.548048
$653$	32.6558	1.27792	0.638960	−	0.769240i	$-0.279365\pi$
$653$	32.6558	1.27792	0.638960	+	0.769240i	$0.279365\pi$
$654$	6.68826	0.261532
$655$	−21.6179	−0.844680
$656$	10.2798	0.401358
$657$	19.2767	0.752058
$658$	10.7316	0.418362
$659$	9.45123	0.368168	0.184084	−	0.982911i	$-0.441068\pi$
$659$	9.45123	0.368168	0.184084	+	0.982911i	$0.441068\pi$
$660$	−1.59079	−0.0619213
$661$	20.7758	0.808084	0.404042	−	0.914740i	$-0.367605\pi$
$661$	20.7758	0.808084	0.404042	+	0.914740i	$0.367605\pi$
$662$	3.78872	0.147253
$663$	31.7448	1.23287
$664$	13.4228	0.520907
$665$	−10.9599	−0.425008
$666$	12.5861	0.487702
$667$	1.00000	0.0387202
$668$	6.27277	0.242701
$669$	15.3101	0.591921
$670$	0.329978	0.0127482
$671$	2.13774	0.0825267
$672$	−3.52812	−0.136100
$673$	−45.8402	−1.76701	−0.883505	−	0.468422i	$-0.844823\pi$
$673$	−45.8402	−1.76701	−0.883505	+	0.468422i	$0.844823\pi$
$674$	−12.7500	−0.491113
$675$	5.39990	0.207842
$676$	2.20214	0.0846977
$677$	−29.6538	−1.13969	−0.569844	−	0.821753i	$-0.692996\pi$
$677$	−29.6538	−1.13969	−0.569844	+	0.821753i	$0.692996\pi$
$678$	−4.15953	−0.159746
$679$	13.8263	0.530605
$680$	−6.72267	−0.257802
$681$	6.08951	0.233351
$682$	1.90720	0.0730303
$683$	45.3525	1.73536	0.867682	−	0.497119i	$-0.165609\pi$
$683$	45.3525	1.73536	0.867682	+	0.497119i	$0.165609\pi$
$684$	20.4939	0.783604
$685$	16.9514	0.647678
$686$	15.2059	0.580564
$687$	55.3260	2.11082
$688$	4.84303	0.184639
$689$	−3.74186	−0.142554
$690$	−6.97492	−0.265531
$691$	−2.83849	−0.107981	−0.0539907	−	0.998541i	$-0.517194\pi$
$691$	−2.83849	−0.107981	−0.0539907	+	0.998541i	$0.517194\pi$
$692$	12.1369	0.461377
$693$	1.50813	0.0572892
$694$	25.2003	0.956591
$695$	13.2410	0.502259
$696$	−2.90642	−0.110168
$697$	−28.7969	−1.09076
$698$	−12.4313	−0.470531
$699$	49.2733	1.86369
$700$	−0.921561	−0.0348317
$701$	45.4560	1.71685	0.858425	−	0.512938i	$-0.171443\pi$
$701$	45.4560	1.71685	0.858425	+	0.512938i	$0.171443\pi$
$702$	−27.7331	−1.04672
$703$	8.69268	0.327851
$704$	−0.228073	−0.00859581
$705$	−61.6623	−2.32234
$706$	−10.6857	−0.402161
$707$	−15.8157	−0.594811
$708$	12.2375	0.459912
$709$	−0.764527	−0.0287124	−0.0143562	−	0.999897i	$-0.504570\pi$
$709$	−0.764527	−0.0287124	−0.0143562	+	0.999897i	$0.504570\pi$
$710$	−23.2203	−0.871441
$711$	32.8729	1.23283
$712$	−5.43542	−0.203701
$713$	8.36223	0.313168
$714$	9.88337	0.369876
$715$	2.13405	0.0798091
$716$	9.11727	0.340728
$717$	−8.84484	−0.330317
$718$	−8.20929	−0.306368
$719$	−14.1451	−0.527524	−0.263762	−	0.964588i	$-0.584963\pi$
$719$	−14.1451	−0.527524	−0.263762	+	0.964588i	$0.584963\pi$
$720$	13.0726	0.487186
$721$	−10.4192	−0.388031
$722$	−4.84575	−0.180340
$723$	84.3955	3.13870
$724$	1.92008	0.0713591
$725$	−0.759171	−0.0281949
$726$	−31.8195	−1.18093
$727$	33.7309	1.25101	0.625504	−	0.780221i	$-0.284893\pi$
$727$	33.7309	1.25101	0.625504	+	0.780221i	$0.284893\pi$
$728$	4.73300	0.175417
$729$	−38.4260	−1.42318
$730$	8.49244	0.314319
$731$	−13.5668	−0.501788
$732$	−27.2422	−1.00690
$733$	10.3459	0.382136	0.191068	−	0.981577i	$-0.438805\pi$
$733$	10.3459	0.382136	0.191068	+	0.981577i	$0.438805\pi$
$734$	20.4646	0.755363
$735$	−38.5464	−1.42181
$736$	−1.00000	−0.0368605
$737$	−0.0313602	−0.00115517
$738$	55.9971	2.06128
$739$	24.3973	0.897469	0.448735	−	0.893665i	$-0.351875\pi$
$739$	24.3973	0.897469	0.448735	+	0.893665i	$0.351875\pi$
$740$	5.54486	0.203833
$741$	−42.6339	−1.56619
$742$	−1.16498	−0.0427679
$743$	2.74784	0.100808	0.0504042	−	0.998729i	$-0.483949\pi$
$743$	2.74784	0.100808	0.0504042	+	0.998729i	$0.483949\pi$
$744$	−24.3042	−0.891035
$745$	41.3177	1.51376
$746$	−27.6958	−1.01401
$747$	73.1182	2.67526
$748$	0.638903	0.0233606
$749$	0.534306	0.0195231
$750$	−29.5794	−1.08009
$751$	−8.49080	−0.309834	−0.154917	−	0.987928i	$-0.549511\pi$
$751$	−8.49080	−0.309834	−0.154917	+	0.987928i	$0.549511\pi$
$752$	−8.84058	−0.322383
$753$	50.2173	1.83002
$754$	3.89899	0.141993
$755$	−22.5105	−0.819240
$756$	−8.63438	−0.314029
$757$	7.24026	0.263152	0.131576	−	0.991306i	$-0.457996\pi$
$757$	7.24026	0.263152	0.131576	+	0.991306i	$0.457996\pi$
$758$	16.6795	0.605827
$759$	0.662876	0.0240609
$760$	9.02866	0.327504
$761$	−38.5559	−1.39765	−0.698824	−	0.715293i	$-0.746293\pi$
$761$	−38.5559	−1.39765	−0.698824	+	0.715293i	$0.746293\pi$
$762$	8.91074	0.322802
$763$	−2.79344	−0.101129
$764$	21.9672	0.794745
$765$	−36.6204	−1.32401
$766$	19.4203	0.701683
$767$	−16.4167	−0.592771
$768$	2.90642	0.104877
$769$	32.1266	1.15852	0.579258	−	0.815145i	$-0.303343\pi$
$769$	32.1266	1.15852	0.579258	+	0.815145i	$0.303343\pi$
$770$	0.664412	0.0239438
$771$	0.0836604	0.00301296
$772$	−15.5036	−0.557987
$773$	28.1615	1.01290	0.506449	−	0.862270i	$-0.330958\pi$
$773$	28.1615	1.01290	0.506449	+	0.862270i	$0.330958\pi$
$774$	26.3815	0.948262
$775$	−6.34836	−0.228040
$776$	−11.3899	−0.408875
$777$	−8.15180	−0.292444
$778$	1.94874	0.0698659
$779$	38.6747	1.38567
$780$	−27.1951	−0.973742
$781$	2.20679	0.0789651
$782$	2.80131	0.100175
$783$	−7.11290	−0.254194
$784$	−5.52644	−0.197373
$785$	19.4566	0.694435
$786$	−26.1813	−0.933858
$787$	34.1563	1.21754	0.608771	−	0.793346i	$-0.291663\pi$
$787$	34.1563	1.21754	0.608771	+	0.793346i	$0.291663\pi$
$788$	−18.8565	−0.671736
$789$	−80.4853	−2.86535
$790$	14.4823	0.515256
$791$	1.73728	0.0617706
$792$	−1.24238	−0.0441461
$793$	36.5456	1.29777
$794$	−5.66356	−0.200992
$795$	6.69382	0.237405
$796$	11.6924	0.414425
$797$	12.4989	0.442735	0.221368	−	0.975190i	$-0.428948\pi$
$797$	12.4989	0.442735	0.221368	+	0.975190i	$0.428948\pi$
$798$	−13.2735	−0.469878
$799$	24.7652	0.876130
$800$	0.759171	0.0268407
$801$	−29.6084	−1.04616
$802$	7.13741	0.252031
$803$	−0.807097	−0.0284818
$804$	0.399636	0.0140941
$805$	2.91316	0.102675
$806$	32.6043	1.14844
$807$	−60.2590	−2.12122
$808$	13.0288	0.458352
$809$	−41.7361	−1.46736	−0.733681	−	0.679494i	$-0.762199\pi$
$809$	−41.7361	−1.46736	−0.733681	+	0.679494i	$0.762199\pi$
$810$	10.3941	0.365212
$811$	12.1872	0.427952	0.213976	−	0.976839i	$-0.431359\pi$
$811$	12.1872	0.427952	0.213976	+	0.976839i	$0.431359\pi$
$812$	1.21390	0.0425997
$813$	−18.3393	−0.643187
$814$	−0.526967	−0.0184702
$815$	−33.5832	−1.17637
$816$	−8.14180	−0.285020
$817$	18.2205	0.637455
$818$	30.5112	1.06680
$819$	25.7821	0.900899
$820$	24.6697	0.861503
$821$	−21.8964	−0.764190	−0.382095	−	0.924123i	$-0.624797\pi$
$821$	−21.8964	−0.764190	−0.382095	+	0.924123i	$0.624797\pi$
$822$	20.5298	0.716057
$823$	5.60951	0.195535	0.0977677	−	0.995209i	$-0.468830\pi$
$823$	5.60951	0.195535	0.0977677	+	0.995209i	$0.468830\pi$
$824$	8.58321	0.299010
$825$	−0.503236	−0.0175204
$826$	−5.11113	−0.177839
$827$	−17.0381	−0.592473	−0.296237	−	0.955115i	$-0.595732\pi$
$827$	−17.0381	−0.592473	−0.296237	+	0.955115i	$0.595732\pi$
$828$	−5.44730	−0.189307
$829$	−35.2498	−1.22427	−0.612137	−	0.790751i	$-0.709690\pi$
$829$	−35.2498	−1.22427	−0.612137	+	0.790751i	$0.709690\pi$
$830$	32.2125	1.11811
$831$	9.91281	0.343871
$832$	−3.89899	−0.135173
$833$	15.4813	0.536394
$834$	16.0361	0.555285
$835$	15.0536	0.520950
$836$	−0.858058	−0.0296766
$837$	−59.4797	−2.05592
$838$	−11.8680	−0.409973
$839$	−22.4501	−0.775062	−0.387531	−	0.921857i	$-0.626672\pi$
$839$	−22.4501	−0.775062	−0.387531	+	0.921857i	$0.626672\pi$
$840$	−8.46688	−0.292135
$841$	1.00000	0.0344828
$842$	28.3444	0.976811
$843$	−8.47376	−0.291852
$844$	5.72006	0.196893
$845$	5.28476	0.181801
$846$	−48.1573	−1.65568
$847$	13.2898	0.456643
$848$	0.959699	0.0329562
$849$	0.508134	0.0174391
$850$	−2.12667	−0.0729443
$851$	−2.31052	−0.0792037
$852$	−28.1220	−0.963444
$853$	−12.1494	−0.415988	−0.207994	−	0.978130i	$-0.566693\pi$
$853$	−12.1494	−0.415988	−0.207994	+	0.978130i	$0.566693\pi$
$854$	11.3780	0.389348
$855$	49.1818	1.68198
$856$	−0.440155	−0.0150442
$857$	19.5154	0.666634	0.333317	−	0.942815i	$-0.391832\pi$
$857$	19.5154	0.666634	0.333317	+	0.942815i	$0.391832\pi$
$858$	2.58455	0.0882350
$859$	21.4967	0.733460	0.366730	−	0.930327i	$-0.380477\pi$
$859$	21.4967	0.733460	0.366730	+	0.930327i	$0.380477\pi$
$860$	11.6224	0.396322
$861$	−36.2683	−1.23602
$862$	−32.8400	−1.11854
$863$	−32.5207	−1.10702	−0.553508	−	0.832844i	$-0.686711\pi$
$863$	−32.5207	−1.10702	−0.553508	+	0.832844i	$0.686711\pi$
$864$	7.11290	0.241986
$865$	29.1265	0.990332
$866$	−26.3759	−0.896290
$867$	−26.6015	−0.903434
$868$	10.1510	0.344546
$869$	−1.37635	−0.0466895
$870$	−6.97492	−0.236472
$871$	−0.536115	−0.0181656
$872$	2.30120	0.0779284
$873$	−62.0445	−2.09989
$874$	−3.76221	−0.127259
$875$	12.3542	0.417649
$876$	10.2852	0.347504
$877$	42.5773	1.43773	0.718866	−	0.695149i	$-0.244662\pi$
$877$	42.5773	1.43773	0.718866	+	0.695149i	$0.244662\pi$
$878$	20.8847	0.704824
$879$	−93.4023	−3.15038
$880$	−0.547335	−0.0184507
$881$	1.71752	0.0578646	0.0289323	−	0.999581i	$-0.490789\pi$
$881$	1.71752	0.0578646	0.0289323	+	0.999581i	$0.490789\pi$
$882$	−30.1042	−1.01366
$883$	−40.2835	−1.35565	−0.677824	−	0.735225i	$-0.737077\pi$
$883$	−40.2835	−1.35565	−0.677824	+	0.735225i	$0.737077\pi$
$884$	10.9223	0.367357
$885$	29.3678	0.987188
$886$	8.47680	0.284784
$887$	−19.2623	−0.646765	−0.323383	−	0.946268i	$-0.604820\pi$
$887$	−19.2623	−0.646765	−0.323383	+	0.946268i	$0.604820\pi$
$888$	6.71536	0.225353
$889$	−3.72168	−0.124821
$890$	−13.0441	−0.437238
$891$	−0.987826	−0.0330934
$892$	5.26766	0.176374
$893$	−33.2601	−1.11301
$894$	50.0398	1.67358
$895$	21.8799	0.731364
$896$	−1.21390	−0.0405537
$897$	11.3321	0.378369
$898$	−19.9828	−0.666835
$899$	8.36223	0.278896
$900$	4.13543	0.137848
$901$	−2.68842	−0.0895642
$902$	−2.34454	−0.0780645
$903$	−17.0868	−0.568613
$904$	−1.43115	−0.0475994
$905$	4.60785	0.153170
$906$	−27.2624	−0.905732
$907$	−52.1027	−1.73004	−0.865021	−	0.501736i	$-0.832695\pi$
$907$	−52.1027	−1.73004	−0.865021	+	0.501736i	$0.832695\pi$
$908$	2.09519	0.0695313
$909$	70.9718	2.35399
$910$	11.3584	0.376527
$911$	−43.0466	−1.42620	−0.713099	−	0.701063i	$-0.752709\pi$
$911$	−43.0466	−1.42620	−0.713099	+	0.701063i	$0.752709\pi$
$912$	10.9346	0.362080
$913$	−3.06138	−0.101317
$914$	−3.71704	−0.122949
$915$	−65.3765	−2.16128
$916$	19.0358	0.628960
$917$	10.9350	0.361104
$918$	−19.9254	−0.657638
$919$	40.7303	1.34357	0.671784	−	0.740747i	$-0.265528\pi$
$919$	40.7303	1.34357	0.671784	+	0.740747i	$0.265528\pi$
$920$	−2.39983	−0.0791200
$921$	85.7710	2.82625
$922$	7.62411	0.251087
$923$	37.7259	1.24176
$924$	0.804668	0.0264716
$925$	1.75408	0.0576738
$926$	−33.6549	−1.10597
$927$	46.7553	1.53565
$928$	−1.00000	−0.0328266
$929$	−33.5964	−1.10226	−0.551132	−	0.834418i	$-0.685804\pi$
$929$	−33.5964	−1.10226	−0.551132	+	0.834418i	$0.685804\pi$
$930$	−58.3259	−1.91258
$931$	−20.7916	−0.681418
$932$	16.9533	0.555322
$933$	−58.8637	−1.92711
$934$	−14.6329	−0.478803
$935$	1.53326	0.0501428
$936$	−21.2390	−0.694218
$937$	−30.3701	−0.992147	−0.496073	−	0.868281i	$-0.665225\pi$
$937$	−30.3701	−0.992147	−0.496073	+	0.868281i	$0.665225\pi$
$938$	−0.166913	−0.00544990
$939$	−70.7538	−2.30896
$940$	−21.2159	−0.691985
$941$	40.9172	1.33386	0.666931	−	0.745119i	$-0.267607\pi$
$941$	40.9172	1.33386	0.666931	+	0.745119i	$0.267607\pi$
$942$	23.5638	0.767751
$943$	−10.2798	−0.334756
$944$	4.21049	0.137040
$945$	−20.7210	−0.674055
$946$	−1.10456	−0.0359124
$947$	52.3051	1.69969	0.849844	−	0.527035i	$-0.176696\pi$
$947$	52.3051	1.69969	0.849844	+	0.527035i	$0.176696\pi$
$948$	17.5394	0.569654
$949$	−13.7976	−0.447890
$950$	2.85616	0.0926662
$951$	−2.09714	−0.0680043
$952$	3.40053	0.110212
$953$	51.5179	1.66883	0.834415	−	0.551137i	$-0.185806\pi$
$953$	51.5179	1.66883	0.834415	+	0.551137i	$0.185806\pi$
$954$	5.22777	0.169255
$955$	52.7175	1.70590
$956$	−3.04320	−0.0984242
$957$	0.662876	0.0214277
$958$	−36.4649	−1.17813
$959$	−8.57451	−0.276885
$960$	6.97492	0.225114
$961$	38.9269	1.25571
$962$	−9.00871	−0.290453
$963$	−2.39765	−0.0772633
$964$	29.0376	0.935237
$965$	−37.2060	−1.19770
$966$	3.52812	0.113515
$967$	40.8527	1.31373	0.656867	−	0.754007i	$-0.271881\pi$
$967$	40.8527	1.31373	0.656867	+	0.754007i	$0.271881\pi$
$968$	−10.9480	−0.351881
$969$	−30.6312	−0.984016
$970$	−27.3339	−0.877639
$971$	14.4409	0.463431	0.231716	−	0.972784i	$-0.425566\pi$
$971$	14.4409	0.463431	0.231716	+	0.972784i	$0.425566\pi$
$972$	−8.75041	−0.280670
$973$	−6.69768	−0.214718
$974$	−36.8018	−1.17920
$975$	−8.60302	−0.275517
$976$	−9.37309	−0.300025
$977$	1.38720	0.0443805	0.0221902	−	0.999754i	$-0.492936\pi$
$977$	1.38720	0.0443805	0.0221902	+	0.999754i	$0.492936\pi$
$978$	−40.6726	−1.30057
$979$	1.23967	0.0396201
$980$	−13.2625	−0.423655
$981$	12.5353	0.400222
$982$	17.7024	0.564907
$983$	−14.7402	−0.470141	−0.235070	−	0.971978i	$-0.575532\pi$
$983$	−14.7402	−0.470141	−0.235070	+	0.971978i	$0.575532\pi$
$984$	29.8774	0.952457
$985$	−45.2524	−1.44186
$986$	2.80131	0.0892120
$987$	31.1906	0.992808
$988$	−14.6688	−0.466678
$989$	−4.84303	−0.153999
$990$	−2.98150	−0.0947582
$991$	15.8368	0.503072	0.251536	−	0.967848i	$-0.419064\pi$
$991$	15.8368	0.503072	0.251536	+	0.967848i	$0.419064\pi$
$992$	−8.36223	−0.265501
$993$	11.0116	0.349443
$994$	11.7455	0.372545
$995$	28.0596	0.889551
$996$	39.0125	1.23616
$997$	−51.3569	−1.62649	−0.813245	−	0.581921i	$-0.802301\pi$
$997$	−51.3569	−1.62649	−0.813245	+	0.581921i	$0.802301\pi$
$998$	32.6786	1.03442
$999$	16.4345	0.519965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.i.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.i.1.8	✓	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} +2.39983 q^{5} +2.90642 q^{6} -1.21390 q^{7} +1.00000 q^{8} +5.44730 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.90642 q^{3} +1.00000 q^{4} +2.39983 q^{5} +2.90642 q^{6} -1.21390 q^{7} +1.00000 q^{8} +5.44730 q^{9} +2.39983 q^{10} -0.228073 q^{11} +2.90642 q^{12} -3.89899 q^{13} -1.21390 q^{14} +6.97492 q^{15} +1.00000 q^{16} -2.80131 q^{17} +5.44730 q^{18} +3.76221 q^{19} +2.39983 q^{20} -3.52812 q^{21} -0.228073 q^{22} -1.00000 q^{23} +2.90642 q^{24} +0.759171 q^{25} -3.89899 q^{26} +7.11290 q^{27} -1.21390 q^{28} -1.00000 q^{29} +6.97492 q^{30} -8.36223 q^{31} +1.00000 q^{32} -0.662876 q^{33} -2.80131 q^{34} -2.91316 q^{35} +5.44730 q^{36} +2.31052 q^{37} +3.76221 q^{38} -11.3321 q^{39} +2.39983 q^{40} +10.2798 q^{41} -3.52812 q^{42} +4.84303 q^{43} -0.228073 q^{44} +13.0726 q^{45} -1.00000 q^{46} -8.84058 q^{47} +2.90642 q^{48} -5.52644 q^{49} +0.759171 q^{50} -8.14180 q^{51} -3.89899 q^{52} +0.959699 q^{53} +7.11290 q^{54} -0.547335 q^{55} -1.21390 q^{56} +10.9346 q^{57} -1.00000 q^{58} +4.21049 q^{59} +6.97492 q^{60} -9.37309 q^{61} -8.36223 q^{62} -6.61250 q^{63} +1.00000 q^{64} -9.35691 q^{65} -0.662876 q^{66} +0.137501 q^{67} -2.80131 q^{68} -2.90642 q^{69} -2.91316 q^{70} -9.67581 q^{71} +5.44730 q^{72} +3.53877 q^{73} +2.31052 q^{74} +2.20647 q^{75} +3.76221 q^{76} +0.276858 q^{77} -11.3321 q^{78} +6.03471 q^{79} +2.39983 q^{80} +4.33119 q^{81} +10.2798 q^{82} +13.4228 q^{83} -3.52812 q^{84} -6.72267 q^{85} +4.84303 q^{86} -2.90642 q^{87} -0.228073 q^{88} -5.43542 q^{89} +13.0726 q^{90} +4.73300 q^{91} -1.00000 q^{92} -24.3042 q^{93} -8.84058 q^{94} +9.02866 q^{95} +2.90642 q^{96} -11.3899 q^{97} -5.52644 q^{98} -1.24238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 4 q^{6} + 8 q^{7} + 8 q^{8} + 12 q^{9} + 8 q^{11} + 4 q^{12} + 4 q^{13} + 8 q^{14} + 8 q^{16} + 8 q^{17} + 12 q^{18} + 16 q^{19} - 4 q^{21} + 8 q^{22} - 8 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{26} + 4 q^{27} + 8 q^{28} - 8 q^{29} + 8 q^{31} + 8 q^{32} + 12 q^{33} + 8 q^{34} + 4 q^{35} + 12 q^{36} + 8 q^{37} + 16 q^{38} - 16 q^{39} + 8 q^{41} - 4 q^{42} + 32 q^{43} + 8 q^{44} - 8 q^{46} + 16 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{52} + 4 q^{54} + 8 q^{56} + 8 q^{57} - 8 q^{58} - 4 q^{59} + 8 q^{61} + 8 q^{62} + 24 q^{63} + 8 q^{64} - 4 q^{65} + 12 q^{66} + 20 q^{67} + 8 q^{68} - 4 q^{69} + 4 q^{70} - 24 q^{71} + 12 q^{72} - 4 q^{73} + 8 q^{74} - 16 q^{75} + 16 q^{76} - 16 q^{77} - 16 q^{78} + 4 q^{79} - 8 q^{81} + 8 q^{82} - 4 q^{83} - 4 q^{84} - 44 q^{85} + 32 q^{86} - 4 q^{87} + 8 q^{88} + 20 q^{89} - 8 q^{92} - 4 q^{93} + 16 q^{94} - 8 q^{95} + 4 q^{96} + 4 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 4 * q^6 + 8 * q^7 + 8 * q^8 + 12 * q^9 + 8 * q^11 + 4 * q^12 + 4 * q^13 + 8 * q^14 + 8 * q^16 + 8 * q^17 + 12 * q^18 + 16 * q^19 - 4 * q^21 + 8 * q^22 - 8 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^26 + 4 * q^27 + 8 * q^28 - 8 * q^29 + 8 * q^31 + 8 * q^32 + 12 * q^33 + 8 * q^34 + 4 * q^35 + 12 * q^36 + 8 * q^37 + 16 * q^38 - 16 * q^39 + 8 * q^41 - 4 * q^42 + 32 * q^43 + 8 * q^44 - 8 * q^46 + 16 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^52 + 4 * q^54 + 8 * q^56 + 8 * q^57 - 8 * q^58 - 4 * q^59 + 8 * q^61 + 8 * q^62 + 24 * q^63 + 8 * q^64 - 4 * q^65 + 12 * q^66 + 20 * q^67 + 8 * q^68 - 4 * q^69 + 4 * q^70 - 24 * q^71 + 12 * q^72 - 4 * q^73 + 8 * q^74 - 16 * q^75 + 16 * q^76 - 16 * q^77 - 16 * q^78 + 4 * q^79 - 8 * q^81 + 8 * q^82 - 4 * q^83 - 4 * q^84 - 44 * q^85 + 32 * q^86 - 4 * q^87 + 8 * q^88 + 20 * q^89 - 8 * q^92 - 4 * q^93 + 16 * q^94 - 8 * q^95 + 4 * q^96 + 4 * q^97 + 4 * q^98

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