LMFDB - Embedded newform 4730.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.23252.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 2 $ x^4 - x^3 - 6*x^2 + 2
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			1.1
Root			$-1.88474$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.88474 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.88474 q^{6} -2.43697 q^{7} +1.00000 q^{8} +5.32171 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.88474 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.88474 q^{6} -2.43697 q^{7} +1.00000 q^{8} +5.32171 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.88474 q^{12} -1.17642 q^{13} -2.43697 q^{14} -2.88474 q^{15} +1.00000 q^{16} -6.19940 q^{17} +5.32171 q^{18} +6.20645 q^{19} +1.00000 q^{20} +7.03003 q^{21} -1.00000 q^{22} +3.20645 q^{23} -2.88474 q^{24} +1.00000 q^{25} -1.17642 q^{26} -6.69753 q^{27} -2.43697 q^{28} -0.624181 q^{29} -2.88474 q^{30} +5.87395 q^{31} +1.00000 q^{32} +2.88474 q^{33} -6.19940 q^{34} -2.43697 q^{35} +5.32171 q^{36} +1.00705 q^{37} +6.20645 q^{38} +3.39366 q^{39} +1.00000 q^{40} +0.823582 q^{41} +7.03003 q^{42} -1.00000 q^{43} -1.00000 q^{44} +5.32171 q^{45} +3.20645 q^{46} -2.00000 q^{47} -2.88474 q^{48} -1.06116 q^{49} +1.00000 q^{50} +17.8836 q^{51} -1.17642 q^{52} -11.1523 q^{53} -6.69753 q^{54} -1.00000 q^{55} -2.43697 q^{56} -17.9040 q^{57} -0.624181 q^{58} +11.9581 q^{59} -2.88474 q^{60} -5.91851 q^{61} +5.87395 q^{62} -12.9689 q^{63} +1.00000 q^{64} -1.17642 q^{65} +2.88474 q^{66} -15.8428 q^{67} -6.19940 q^{68} -9.24977 q^{69} -2.43697 q^{70} +9.88100 q^{71} +5.32171 q^{72} -1.73944 q^{73} +1.00705 q^{74} -2.88474 q^{75} +6.20645 q^{76} +2.43697 q^{77} +3.39366 q^{78} -12.8377 q^{79} +1.00000 q^{80} +3.35548 q^{81} +0.823582 q^{82} -2.14265 q^{83} +7.03003 q^{84} -6.19940 q^{85} -1.00000 q^{86} +1.80060 q^{87} -1.00000 q^{88} -13.8836 q^{89} +5.32171 q^{90} +2.86690 q^{91} +3.20645 q^{92} -16.9448 q^{93} -2.00000 q^{94} +6.20645 q^{95} -2.88474 q^{96} +15.0638 q^{97} -1.06116 q^{98} -5.32171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9	$ 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} - 3 q^{12} - 9 q^{13} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 3 q^{18} - 2 q^{19} + 4 q^{20} - 3 q^{21} - 4 q^{22} - 14 q^{23} - 3 q^{24} + 4 q^{25} - 9 q^{26} - 3 q^{27} - 8 q^{29} - 3 q^{30} + 4 q^{31} + 4 q^{32} + 3 q^{33} - 15 q^{34} + 3 q^{36} - 13 q^{37} - 2 q^{38} + 2 q^{39} + 4 q^{40} - q^{41} - 3 q^{42} - 4 q^{43} - 4 q^{44} + 3 q^{45} - 14 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{50} + 5 q^{51} - 9 q^{52} - 5 q^{53} - 3 q^{54} - 4 q^{55} - 21 q^{57} - 8 q^{58} + 10 q^{59} - 3 q^{60} - 12 q^{61} + 4 q^{62} - 25 q^{63} + 4 q^{64} - 9 q^{65} + 3 q^{66} - 17 q^{67} - 15 q^{68} - 12 q^{69} + 3 q^{71} + 3 q^{72} - 21 q^{73} - 13 q^{74} - 3 q^{75} - 2 q^{76} + 2 q^{78} - 13 q^{79} + 4 q^{80} - 8 q^{81} - q^{82} - 16 q^{83} - 3 q^{84} - 15 q^{85} - 4 q^{86} + 17 q^{87} - 4 q^{88} + 11 q^{89} + 3 q^{90} + 9 q^{91} - 14 q^{92} + 3 q^{93} - 8 q^{94} - 2 q^{95} - 3 q^{96} + 26 q^{97} - 3 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 - 3 * q^12 - 9 * q^13 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 3 * q^18 - 2 * q^19 + 4 * q^20 - 3 * q^21 - 4 * q^22 - 14 * q^23 - 3 * q^24 + 4 * q^25 - 9 * q^26 - 3 * q^27 - 8 * q^29 - 3 * q^30 + 4 * q^31 + 4 * q^32 + 3 * q^33 - 15 * q^34 + 3 * q^36 - 13 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - q^41 - 3 * q^42 - 4 * q^43 - 4 * q^44 + 3 * q^45 - 14 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^50 + 5 * q^51 - 9 * q^52 - 5 * q^53 - 3 * q^54 - 4 * q^55 - 21 * q^57 - 8 * q^58 + 10 * q^59 - 3 * q^60 - 12 * q^61 + 4 * q^62 - 25 * q^63 + 4 * q^64 - 9 * q^65 + 3 * q^66 - 17 * q^67 - 15 * q^68 - 12 * q^69 + 3 * q^71 + 3 * q^72 - 21 * q^73 - 13 * q^74 - 3 * q^75 - 2 * q^76 + 2 * q^78 - 13 * q^79 + 4 * q^80 - 8 * q^81 - q^82 - 16 * q^83 - 3 * q^84 - 15 * q^85 - 4 * q^86 + 17 * q^87 - 4 * q^88 + 11 * q^89 + 3 * q^90 + 9 * q^91 - 14 * q^92 + 3 * q^93 - 8 * q^94 - 2 * q^95 - 3 * q^96 + 26 * q^97 - 3 * 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
$3$	−2.88474	−1.66550	−0.832752	−	0.553646i	$-0.813236\pi$
$3$	−2.88474	−1.66550	−0.832752	+	0.553646i	$0.813236\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.88474	−1.17769
$7$	−2.43697	−0.921090	−0.460545	−	0.887636i	$-0.652346\pi$
$7$	−2.43697	−0.921090	−0.460545	+	0.887636i	$0.652346\pi$
$8$	1.00000	0.353553
$9$	5.32171	1.77390
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.88474	−0.832752
$13$	−1.17642	−0.326280	−0.163140	−	0.986603i	$-0.552162\pi$
$13$	−1.17642	−0.326280	−0.163140	+	0.986603i	$0.552162\pi$
$14$	−2.43697	−0.651309
$15$	−2.88474	−0.744836
$16$	1.00000	0.250000
$17$	−6.19940	−1.50358	−0.751788	−	0.659405i	$-0.770808\pi$
$17$	−6.19940	−1.50358	−0.751788	+	0.659405i	$0.770808\pi$
$18$	5.32171	1.25434
$19$	6.20645	1.42386	0.711929	−	0.702252i	$-0.247822\pi$
$19$	6.20645	1.42386	0.711929	+	0.702252i	$0.247822\pi$
$20$	1.00000	0.223607
$21$	7.03003	1.53408
$22$	−1.00000	−0.213201
$23$	3.20645	0.668591	0.334296	−	0.942468i	$-0.391502\pi$
$23$	3.20645	0.668591	0.334296	+	0.942468i	$0.391502\pi$
$24$	−2.88474	−0.588845
$25$	1.00000	0.200000
$26$	−1.17642	−0.230715
$27$	−6.69753	−1.28894
$28$	−2.43697	−0.460545
$29$	−0.624181	−0.115908	−0.0579538	−	0.998319i	$-0.518458\pi$
$29$	−0.624181	−0.115908	−0.0579538	+	0.998319i	$0.518458\pi$
$30$	−2.88474	−0.526679
$31$	5.87395	1.05499	0.527496	−	0.849557i	$-0.323131\pi$
$31$	5.87395	1.05499	0.527496	+	0.849557i	$0.323131\pi$
$32$	1.00000	0.176777
$33$	2.88474	0.502168
$34$	−6.19940	−1.06319
$35$	−2.43697	−0.411924
$36$	5.32171	0.886952
$37$	1.00705	0.165558	0.0827789	−	0.996568i	$-0.473620\pi$
$37$	1.00705	0.165558	0.0827789	+	0.996568i	$0.473620\pi$
$38$	6.20645	1.00682
$39$	3.39366	0.543420
$40$	1.00000	0.158114
$41$	0.823582	0.128622	0.0643110	−	0.997930i	$-0.479515\pi$
$41$	0.823582	0.128622	0.0643110	+	0.997930i	$0.479515\pi$
$42$	7.03003	1.08476
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−1.00000	−0.150756
$45$	5.32171	0.793314
$46$	3.20645	0.472765
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	−2.88474	−0.416376
$49$	−1.06116	−0.151594
$50$	1.00000	0.141421
$51$	17.8836	2.50421
$52$	−1.17642	−0.163140
$53$	−11.1523	−1.53189	−0.765946	−	0.642905i	$-0.777729\pi$
$53$	−11.1523	−1.53189	−0.765946	+	0.642905i	$0.777729\pi$
$54$	−6.69753	−0.911419
$55$	−1.00000	−0.134840
$56$	−2.43697	−0.325654
$57$	−17.9040	−2.37144
$58$	−0.624181	−0.0819590
$59$	11.9581	1.55681	0.778405	−	0.627762i	$-0.216029\pi$
$59$	11.9581	1.55681	0.778405	+	0.627762i	$0.216029\pi$
$60$	−2.88474	−0.372418
$61$	−5.91851	−0.757788	−0.378894	−	0.925440i	$-0.623695\pi$
$61$	−5.91851	−0.757788	−0.378894	+	0.925440i	$0.623695\pi$
$62$	5.87395	0.745992
$63$	−12.9689	−1.63392
$64$	1.00000	0.125000
$65$	−1.17642	−0.145917
$66$	2.88474	0.355087
$67$	−15.8428	−1.93551	−0.967755	−	0.251895i	$-0.918946\pi$
$67$	−15.8428	−1.93551	−0.967755	+	0.251895i	$0.918946\pi$
$68$	−6.19940	−0.751788
$69$	−9.24977	−1.11354
$70$	−2.43697	−0.291274
$71$	9.88100	1.17266	0.586329	−	0.810073i	$-0.300572\pi$
$71$	9.88100	1.17266	0.586329	+	0.810073i	$0.300572\pi$
$72$	5.32171	0.627170
$73$	−1.73944	−0.203586	−0.101793	−	0.994806i	$-0.532458\pi$
$73$	−1.73944	−0.203586	−0.101793	+	0.994806i	$0.532458\pi$
$74$	1.00705	0.117067
$75$	−2.88474	−0.333101
$76$	6.20645	0.711929
$77$	2.43697	0.277719
$78$	3.39366	0.384256
$79$	−12.8377	−1.44435	−0.722176	−	0.691709i	$-0.756858\pi$
$79$	−12.8377	−1.44435	−0.722176	+	0.691709i	$0.756858\pi$
$80$	1.00000	0.111803
$81$	3.35548	0.372832
$82$	0.823582	0.0909494
$83$	−2.14265	−0.235186	−0.117593	−	0.993062i	$-0.537518\pi$
$83$	−2.14265	−0.235186	−0.117593	+	0.993062i	$0.537518\pi$
$84$	7.03003	0.767039
$85$	−6.19940	−0.672419
$86$	−1.00000	−0.107833
$87$	1.80060	0.193044
$88$	−1.00000	−0.106600
$89$	−13.8836	−1.47166	−0.735832	−	0.677164i	$-0.763209\pi$
$89$	−13.8836	−1.47166	−0.735832	+	0.677164i	$0.763209\pi$
$90$	5.32171	0.560958
$91$	2.86690	0.300533
$92$	3.20645	0.334296
$93$	−16.9448	−1.75709
$94$	−2.00000	−0.206284
$95$	6.20645	0.636768
$96$	−2.88474	−0.294422
$97$	15.0638	1.52950	0.764749	−	0.644329i	$-0.222863\pi$
$97$	15.0638	1.52950	0.764749	+	0.644329i	$0.222863\pi$
$98$	−1.06116	−0.107193
$99$	−5.32171	−0.534852
$100$	1.00000	0.100000
$101$	1.29168	0.128527	0.0642635	−	0.997933i	$-0.479530\pi$
$101$	1.29168	0.128527	0.0642635	+	0.997933i	$0.479530\pi$
$102$	17.8836	1.77074
$103$	13.2728	1.30780	0.653902	−	0.756580i	$-0.273131\pi$
$103$	13.2728	1.30780	0.653902	+	0.756580i	$0.273131\pi$
$104$	−1.17642	−0.115357
$105$	7.03003	0.686061
$106$	−11.1523	−1.08321
$107$	16.5052	1.59562	0.797808	−	0.602912i	$-0.205993\pi$
$107$	16.5052	1.59562	0.797808	+	0.602912i	$0.205993\pi$
$108$	−6.69753	−0.644470
$109$	−0.165629	−0.0158644	−0.00793218	−	0.999969i	$-0.502525\pi$
$109$	−0.165629	−0.0158644	−0.00793218	+	0.999969i	$0.502525\pi$
$110$	−1.00000	−0.0953463
$111$	−2.90507	−0.275737
$112$	−2.43697	−0.230272
$113$	0.634970	0.0597330	0.0298665	−	0.999554i	$-0.490492\pi$
$113$	0.634970	0.0597330	0.0298665	+	0.999554i	$0.490492\pi$
$114$	−17.9040	−1.67686
$115$	3.20645	0.299003
$116$	−0.624181	−0.0579538
$117$	−6.26056	−0.578789
$118$	11.9581	1.10083
$119$	15.1078	1.38493
$120$	−2.88474	−0.263339
$121$	1.00000	0.0909091
$122$	−5.91851	−0.535837
$123$	−2.37582	−0.214220
$124$	5.87395	0.527496
$125$	1.00000	0.0894427
$126$	−12.9689	−1.15536
$127$	5.22943	0.464037	0.232019	−	0.972711i	$-0.425467\pi$
$127$	5.22943	0.464037	0.232019	+	0.972711i	$0.425467\pi$
$128$	1.00000	0.0883883
$129$	2.88474	0.253987
$130$	−1.17642	−0.103179
$131$	−3.63638	−0.317712	−0.158856	−	0.987302i	$-0.550780\pi$
$131$	−3.63638	−0.317712	−0.158856	+	0.987302i	$0.550780\pi$
$132$	2.88474	0.251084
$133$	−15.1250	−1.31150
$134$	−15.8428	−1.36861
$135$	−6.69753	−0.576432
$136$	−6.19940	−0.531594
$137$	−4.48220	−0.382940	−0.191470	−	0.981498i	$-0.561325\pi$
$137$	−4.48220	−0.382940	−0.191470	+	0.981498i	$0.561325\pi$
$138$	−9.24977	−0.787393
$139$	−9.56069	−0.810927	−0.405464	−	0.914111i	$-0.632890\pi$
$139$	−9.56069	−0.810927	−0.405464	+	0.914111i	$0.632890\pi$
$140$	−2.43697	−0.205962
$141$	5.76948	0.485877
$142$	9.88100	0.829195
$143$	1.17642	0.0983770
$144$	5.32171	0.443476
$145$	−0.624181	−0.0518354
$146$	−1.73944	−0.143957
$147$	3.06116	0.252480
$148$	1.00705	0.0827789
$149$	12.8358	1.05155	0.525774	−	0.850624i	$-0.323776\pi$
$149$	12.8358	1.05155	0.525774	+	0.850624i	$0.323776\pi$
$150$	−2.88474	−0.235538
$151$	−17.3314	−1.41041	−0.705205	−	0.709003i	$-0.749145\pi$
$151$	−17.3314	−1.41041	−0.705205	+	0.709003i	$0.749145\pi$
$152$	6.20645	0.503410
$153$	−32.9914	−2.66720
$154$	2.43697	0.196377
$155$	5.87395	0.471807
$156$	3.39366	0.271710
$157$	−12.7002	−1.01358	−0.506792	−	0.862068i	$-0.669169\pi$
$157$	−12.7002	−1.01358	−0.506792	+	0.862068i	$0.669169\pi$
$158$	−12.8377	−1.02131
$159$	32.1716	2.55137
$160$	1.00000	0.0790569
$161$	−7.81404	−0.615832
$162$	3.35548	0.263632
$163$	−12.1357	−0.950545	−0.475273	−	0.879839i	$-0.657651\pi$
$163$	−12.1357	−0.950545	−0.475273	+	0.879839i	$0.657651\pi$
$164$	0.823582	0.0643110
$165$	2.88474	0.224577
$166$	−2.14265	−0.166302
$167$	−14.0236	−1.08518	−0.542591	−	0.839997i	$-0.682557\pi$
$167$	−14.0236	−1.08518	−0.542591	+	0.839997i	$0.682557\pi$
$168$	7.03003	0.542379
$169$	−11.6160	−0.893542
$170$	−6.19940	−0.475472
$171$	33.0289	2.52579
$172$	−1.00000	−0.0762493
$173$	−4.09228	−0.311130	−0.155565	−	0.987826i	$-0.549720\pi$
$173$	−4.09228	−0.311130	−0.155565	+	0.987826i	$0.549720\pi$
$174$	1.80060	0.136503
$175$	−2.43697	−0.184218
$176$	−1.00000	−0.0753778
$177$	−34.4959	−2.59287
$178$	−13.8836	−1.04062
$179$	−10.2747	−0.767964	−0.383982	−	0.923341i	$-0.625447\pi$
$179$	−10.2747	−0.767964	−0.383982	+	0.923341i	$0.625447\pi$
$180$	5.32171	0.396657
$181$	−20.6650	−1.53602	−0.768009	−	0.640439i	$-0.778752\pi$
$181$	−20.6650	−1.53602	−0.768009	+	0.640439i	$0.778752\pi$
$182$	2.86690	0.212509
$183$	17.0734	1.26210
$184$	3.20645	0.236383
$185$	1.00705	0.0740397
$186$	−16.9448	−1.24245
$187$	6.19940	0.453345
$188$	−2.00000	−0.145865
$189$	16.3217	1.18723
$190$	6.20645	0.450263
$191$	−7.98107	−0.577490	−0.288745	−	0.957406i	$-0.593238\pi$
$191$	−7.98107	−0.577490	−0.288745	+	0.957406i	$0.593238\pi$
$192$	−2.88474	−0.208188
$193$	−7.05161	−0.507586	−0.253793	−	0.967259i	$-0.581678\pi$
$193$	−7.05161	−0.507586	−0.253793	+	0.967259i	$0.581678\pi$
$194$	15.0638	1.08152
$195$	3.39366	0.243025
$196$	−1.06116	−0.0757968
$197$	−23.5014	−1.67441	−0.837204	−	0.546891i	$-0.815811\pi$
$197$	−23.5014	−1.67441	−0.837204	+	0.546891i	$0.815811\pi$
$198$	−5.32171	−0.378198
$199$	−16.9422	−1.20100	−0.600499	−	0.799626i	$-0.705031\pi$
$199$	−16.9422	−1.20100	−0.600499	+	0.799626i	$0.705031\pi$
$200$	1.00000	0.0707107
$201$	45.7024	3.22360
$202$	1.29168	0.0908823
$203$	1.52111	0.106761
$204$	17.8836	1.25211
$205$	0.823582	0.0575215
$206$	13.2728	0.924756
$207$	17.0638	1.18602
$208$	−1.17642	−0.0815699
$209$	−6.20645	−0.429309
$210$	7.03003	0.485118
$211$	−0.176418	−0.0121451	−0.00607255	−	0.999982i	$-0.501933\pi$
$211$	−0.176418	−0.0121451	−0.00607255	+	0.999982i	$0.501933\pi$
$212$	−11.1523	−0.765946
$213$	−28.5041	−1.95307
$214$	16.5052	1.12827
$215$	−1.00000	−0.0681994
$216$	−6.69753	−0.455709
$217$	−14.3147	−0.971743
$218$	−0.165629	−0.0112178
$219$	5.01784	0.339074
$220$	−1.00000	−0.0674200
$221$	7.29309	0.490586
$222$	−2.90507	−0.194976
$223$	−18.4218	−1.23361	−0.616807	−	0.787114i	$-0.711574\pi$
$223$	−18.4218	−1.23361	−0.616807	+	0.787114i	$0.711574\pi$
$224$	−2.43697	−0.162827
$225$	5.32171	0.354781
$226$	0.634970	0.0422376
$227$	21.2868	1.41286	0.706429	−	0.707784i	$-0.250305\pi$
$227$	21.2868	1.41286	0.706429	+	0.707784i	$0.250305\pi$
$228$	−17.9040	−1.18572
$229$	14.8258	0.979716	0.489858	−	0.871802i	$-0.337049\pi$
$229$	14.8258	0.979716	0.489858	+	0.871802i	$0.337049\pi$
$230$	3.20645	0.211427
$231$	−7.03003	−0.462542
$232$	−0.624181	−0.0409795
$233$	−24.6683	−1.61607	−0.808037	−	0.589131i	$-0.799470\pi$
$233$	−24.6683	−1.61607	−0.808037	+	0.589131i	$0.799470\pi$
$234$	−6.26056	−0.409265
$235$	−2.00000	−0.130466
$236$	11.9581	0.778405
$237$	37.0333	2.40557
$238$	15.1078	0.979292
$239$	−12.3688	−0.800069	−0.400035	−	0.916500i	$-0.631002\pi$
$239$	−12.3688	−0.800069	−0.400035	+	0.916500i	$0.631002\pi$
$240$	−2.88474	−0.186209
$241$	−23.9607	−1.54345	−0.771723	−	0.635958i	$-0.780605\pi$
$241$	−23.9607	−1.54345	−0.771723	+	0.635958i	$0.780605\pi$
$242$	1.00000	0.0642824
$243$	10.4129	0.667988
$244$	−5.91851	−0.378894
$245$	−1.06116	−0.0677947
$246$	−2.37582	−0.151477
$247$	−7.30138	−0.464576
$248$	5.87395	0.372996
$249$	6.18097	0.391703
$250$	1.00000	0.0632456
$251$	3.03817	0.191768	0.0958839	−	0.995393i	$-0.469432\pi$
$251$	3.03817	0.191768	0.0958839	+	0.995393i	$0.469432\pi$
$252$	−12.9689	−0.816962
$253$	−3.20645	−0.201588
$254$	5.22943	0.328124
$255$	17.8836	1.11992
$256$	1.00000	0.0625000
$257$	13.3244	0.831151	0.415575	−	0.909559i	$-0.363580\pi$
$257$	13.3244	0.831151	0.415575	+	0.909559i	$0.363580\pi$
$258$	2.88474	0.179596
$259$	−2.45415	−0.152494
$260$	−1.17642	−0.0729583
$261$	−3.32171	−0.205609
$262$	−3.63638	−0.224656
$263$	−4.89802	−0.302025	−0.151013	−	0.988532i	$-0.548253\pi$
$263$	−4.89802	−0.302025	−0.151013	+	0.988532i	$0.548253\pi$
$264$	2.88474	0.177543
$265$	−11.1523	−0.685083
$266$	−15.1250	−0.927371
$267$	40.0507	2.45106
$268$	−15.8428	−0.967755
$269$	−0.264957	−0.0161547	−0.00807734	−	0.999967i	$-0.502571\pi$
$269$	−0.264957	−0.0161547	−0.00807734	+	0.999967i	$0.502571\pi$
$270$	−6.69753	−0.407599
$271$	22.0238	1.33785	0.668925	−	0.743330i	$-0.266755\pi$
$271$	22.0238	1.33785	0.668925	+	0.743330i	$0.266755\pi$
$272$	−6.19940	−0.375894
$273$	−8.27025	−0.500539
$274$	−4.48220	−0.270779
$275$	−1.00000	−0.0603023
$276$	−9.24977	−0.556771
$277$	4.32767	0.260025	0.130012	−	0.991512i	$-0.458498\pi$
$277$	4.32767	0.260025	0.130012	+	0.991512i	$0.458498\pi$
$278$	−9.56069	−0.573412
$279$	31.2595	1.87146
$280$	−2.43697	−0.145637
$281$	−31.0519	−1.85240	−0.926201	−	0.377029i	$-0.876946\pi$
$281$	−31.0519	−1.85240	−0.926201	+	0.377029i	$0.876946\pi$
$282$	5.76948	0.343567
$283$	−2.45041	−0.145662	−0.0728310	−	0.997344i	$-0.523203\pi$
$283$	−2.45041	−0.145662	−0.0728310	+	0.997344i	$0.523203\pi$
$284$	9.88100	0.586329
$285$	−17.9040	−1.06054
$286$	1.17642	0.0695630
$287$	−2.00705	−0.118472
$288$	5.32171	0.313585
$289$	21.4326	1.26074
$290$	−0.624181	−0.0366532
$291$	−43.4551	−2.54738
$292$	−1.73944	−0.101793
$293$	−19.9722	−1.16679	−0.583394	−	0.812189i	$-0.698276\pi$
$293$	−19.9722	−1.16679	−0.583394	+	0.812189i	$0.698276\pi$
$294$	3.06116	0.178530
$295$	11.9581	0.696227
$296$	1.00705	0.0585335
$297$	6.69753	0.388630
$298$	12.8358	0.743557
$299$	−3.77212	−0.218148
$300$	−2.88474	−0.166550
$301$	2.43697	0.140465
$302$	−17.3314	−0.997311
$303$	−3.72616	−0.214062
$304$	6.20645	0.355964
$305$	−5.91851	−0.338893
$306$	−32.9914	−1.88599
$307$	−18.7194	−1.06837	−0.534187	−	0.845366i	$-0.679382\pi$
$307$	−18.7194	−1.06837	−0.534187	+	0.845366i	$0.679382\pi$
$308$	2.43697	0.138860
$309$	−38.2884	−2.17815
$310$	5.87395	0.333618
$311$	−7.97452	−0.452194	−0.226097	−	0.974105i	$-0.572597\pi$
$311$	−7.97452	−0.452194	−0.226097	+	0.974105i	$0.572597\pi$
$312$	3.39366	0.192128
$313$	21.2728	1.20241	0.601203	−	0.799096i	$-0.294688\pi$
$313$	21.2728	1.20241	0.601203	+	0.799096i	$0.294688\pi$
$314$	−12.7002	−0.716713
$315$	−12.9689	−0.730713
$316$	−12.8377	−0.722176
$317$	−14.9021	−0.836984	−0.418492	−	0.908220i	$-0.637441\pi$
$317$	−14.9021	−0.836984	−0.418492	+	0.908220i	$0.637441\pi$
$318$	32.1716	1.80409
$319$	0.624181	0.0349474
$320$	1.00000	0.0559017
$321$	−47.6131	−2.65750
$322$	−7.81404	−0.435459
$323$	−38.4763	−2.14088
$324$	3.35548	0.186416
$325$	−1.17642	−0.0652559
$326$	−12.1357	−0.672137
$327$	0.477796	0.0264222
$328$	0.823582	0.0454747
$329$	4.87395	0.268710
$330$	2.88474	0.158800
$331$	−33.6450	−1.84930	−0.924648	−	0.380823i	$-0.875641\pi$
$331$	−33.6450	−1.84930	−0.924648	+	0.380823i	$0.875641\pi$
$332$	−2.14265	−0.117593
$333$	5.35922	0.293684
$334$	−14.0236	−0.767340
$335$	−15.8428	−0.865586
$336$	7.03003	0.383520
$337$	−6.75354	−0.367889	−0.183944	−	0.982937i	$-0.558887\pi$
$337$	−6.75354	−0.367889	−0.183944	+	0.982937i	$0.558887\pi$
$338$	−11.6160	−0.631829
$339$	−1.83172	−0.0994855
$340$	−6.19940	−0.336210
$341$	−5.87395	−0.318092
$342$	33.0289	1.78600
$343$	19.6448	1.06072
$344$	−1.00000	−0.0539164
$345$	−9.24977	−0.497991
$346$	−4.09228	−0.220002
$347$	−3.83453	−0.205849	−0.102924	−	0.994689i	$-0.532820\pi$
$347$	−3.83453	−0.205849	−0.102924	+	0.994689i	$0.532820\pi$
$348$	1.80060	0.0965222
$349$	25.6309	1.37199	0.685995	−	0.727606i	$-0.259367\pi$
$349$	25.6309	1.37199	0.685995	+	0.727606i	$0.259367\pi$
$350$	−2.43697	−0.130262
$351$	7.87909	0.420555
$352$	−1.00000	−0.0533002
$353$	6.46510	0.344103	0.172051	−	0.985088i	$-0.444960\pi$
$353$	6.46510	0.344103	0.172051	+	0.985088i	$0.444960\pi$
$354$	−34.4959	−1.83344
$355$	9.88100	0.524429
$356$	−13.8836	−0.735832
$357$	−43.5820	−2.30660
$358$	−10.2747	−0.543032
$359$	9.07974	0.479210	0.239605	−	0.970870i	$-0.422982\pi$
$359$	9.07974	0.479210	0.239605	+	0.970870i	$0.422982\pi$
$360$	5.32171	0.280479
$361$	19.5200	1.02737
$362$	−20.6650	−1.08613
$363$	−2.88474	−0.151409
$364$	2.86690	0.150266
$365$	−1.73944	−0.0910466
$366$	17.0734	0.892438
$367$	15.2740	0.797296	0.398648	−	0.917104i	$-0.369480\pi$
$367$	15.2740	0.797296	0.398648	+	0.917104i	$0.369480\pi$
$368$	3.20645	0.167148
$369$	4.38287	0.228163
$370$	1.00705	0.0523540
$371$	27.1780	1.41101
$372$	−16.9448	−0.878547
$373$	−1.00515	−0.0520445	−0.0260222	−	0.999661i	$-0.508284\pi$
$373$	−1.00515	−0.0520445	−0.0260222	+	0.999661i	$0.508284\pi$
$374$	6.19940	0.320563
$375$	−2.88474	−0.148967
$376$	−2.00000	−0.103142
$377$	0.734298	0.0378183
$378$	16.3217	0.839498
$379$	−17.1658	−0.881747	−0.440873	−	0.897569i	$-0.645331\pi$
$379$	−17.1658	−0.881747	−0.440873	+	0.897569i	$0.645331\pi$
$380$	6.20645	0.318384
$381$	−15.0855	−0.772856
$382$	−7.98107	−0.408347
$383$	1.75495	0.0896736	0.0448368	−	0.998994i	$-0.485723\pi$
$383$	1.75495	0.0896736	0.0448368	+	0.998994i	$0.485723\pi$
$384$	−2.88474	−0.147211
$385$	2.43697	0.124200
$386$	−7.05161	−0.358918
$387$	−5.32171	−0.270518
$388$	15.0638	0.764749
$389$	24.8244	1.25865	0.629323	−	0.777144i	$-0.283332\pi$
$389$	24.8244	1.25865	0.629323	+	0.777144i	$0.283332\pi$
$390$	3.39366	0.171844
$391$	−19.8781	−1.00528
$392$	−1.06116	−0.0535964
$393$	10.4900	0.529150
$394$	−23.5014	−1.18399
$395$	−12.8377	−0.645934
$396$	−5.32171	−0.267426
$397$	6.51846	0.327152	0.163576	−	0.986531i	$-0.447697\pi$
$397$	6.51846	0.327152	0.163576	+	0.986531i	$0.447697\pi$
$398$	−16.9422	−0.849233
$399$	43.6315	2.18431
$400$	1.00000	0.0500000
$401$	3.62185	0.180866	0.0904332	−	0.995903i	$-0.471175\pi$
$401$	3.62185	0.180866	0.0904332	+	0.995903i	$0.471175\pi$
$402$	45.7024	2.27943
$403$	−6.91022	−0.344222
$404$	1.29168	0.0642635
$405$	3.35548	0.166735
$406$	1.52111	0.0754916
$407$	−1.00705	−0.0499176
$408$	17.8836	0.885372
$409$	−25.0882	−1.24053	−0.620266	−	0.784392i	$-0.712975\pi$
$409$	−25.0882	−1.24053	−0.620266	+	0.784392i	$0.712975\pi$
$410$	0.823582	0.0406738
$411$	12.9300	0.637788
$412$	13.2728	0.653902
$413$	−29.1416	−1.43396
$414$	17.0638	0.838640
$415$	−2.14265	−0.105178
$416$	−1.17642	−0.0576786
$417$	27.5801	1.35060
$418$	−6.20645	−0.303567
$419$	31.9855	1.56259	0.781296	−	0.624160i	$-0.214559\pi$
$419$	31.9855	1.56259	0.781296	+	0.624160i	$0.214559\pi$
$420$	7.03003	0.343030
$421$	−25.3244	−1.23423	−0.617117	−	0.786871i	$-0.711699\pi$
$421$	−25.3244	−1.23423	−0.617117	+	0.786871i	$0.711699\pi$
$422$	−0.176418	−0.00858788
$423$	−10.6434	−0.517501
$424$	−11.1523	−0.541606
$425$	−6.19940	−0.300715
$426$	−28.5041	−1.38103
$427$	14.4233	0.697990
$428$	16.5052	0.797808
$429$	−3.39366	−0.163847
$430$	−1.00000	−0.0482243
$431$	1.39631	0.0672577	0.0336288	−	0.999434i	$-0.489294\pi$
$431$	1.39631	0.0672577	0.0336288	+	0.999434i	$0.489294\pi$
$432$	−6.69753	−0.322235
$433$	4.09228	0.196662	0.0983312	−	0.995154i	$-0.468650\pi$
$433$	4.09228	0.196662	0.0983312	+	0.995154i	$0.468650\pi$
$434$	−14.3147	−0.687126
$435$	1.80060	0.0863321
$436$	−0.165629	−0.00793218
$437$	19.9007	0.951978
$438$	5.01784	0.239762
$439$	9.08414	0.433562	0.216781	−	0.976220i	$-0.430444\pi$
$439$	9.08414	0.433562	0.216781	+	0.976220i	$0.430444\pi$
$440$	−1.00000	−0.0476731
$441$	−5.64716	−0.268913
$442$	7.29309	0.346897
$443$	18.6248	0.884893	0.442446	−	0.896795i	$-0.354111\pi$
$443$	18.6248	0.884893	0.442446	+	0.896795i	$0.354111\pi$
$444$	−2.90507	−0.137869
$445$	−13.8836	−0.658148
$446$	−18.4218	−0.872297
$447$	−37.0279	−1.75136
$448$	−2.43697	−0.115136
$449$	−2.23052	−0.105265	−0.0526325	−	0.998614i	$-0.516761\pi$
$449$	−2.23052	−0.105265	−0.0526325	+	0.998614i	$0.516761\pi$
$450$	5.32171	0.250868
$451$	−0.823582	−0.0387810
$452$	0.634970	0.0298665
$453$	49.9966	2.34904
$454$	21.2868	0.999041
$455$	2.86690	0.134402
$456$	−17.9040	−0.838431
$457$	6.00596	0.280947	0.140473	−	0.990084i	$-0.455138\pi$
$457$	6.00596	0.280947	0.140473	+	0.990084i	$0.455138\pi$
$458$	14.8258	0.692764
$459$	41.5207	1.93802
$460$	3.20645	0.149502
$461$	15.4570	0.719906	0.359953	−	0.932971i	$-0.382793\pi$
$461$	15.4570	0.719906	0.359953	+	0.932971i	$0.382793\pi$
$462$	−7.03003	−0.327067
$463$	23.2161	1.07895	0.539473	−	0.842003i	$-0.318624\pi$
$463$	23.2161	1.07895	0.539473	+	0.842003i	$0.318624\pi$
$464$	−0.624181	−0.0289769
$465$	−16.9448	−0.785796
$466$	−24.6683	−1.14274
$467$	−33.3766	−1.54449	−0.772243	−	0.635327i	$-0.780865\pi$
$467$	−33.3766	−1.54449	−0.772243	+	0.635327i	$0.780865\pi$
$468$	−6.26056	−0.289394
$469$	38.6086	1.78278
$470$	−2.00000	−0.0922531
$471$	36.6367	1.68813
$472$	11.9581	0.550416
$473$	1.00000	0.0459800
$474$	37.0333	1.70100
$475$	6.20645	0.284771
$476$	15.1078	0.692464
$477$	−59.3496	−2.71743
$478$	−12.3688	−0.565734
$479$	38.5211	1.76007	0.880037	−	0.474905i	$-0.157517\pi$
$479$	38.5211	1.76007	0.880037	+	0.474905i	$0.157517\pi$
$480$	−2.88474	−0.131670
$481$	−1.18471	−0.0540181
$482$	−23.9607	−1.09138
$483$	22.5414	1.02567
$484$	1.00000	0.0454545
$485$	15.0638	0.684012
$486$	10.4129	0.472339
$487$	34.2080	1.55011	0.775056	−	0.631892i	$-0.217721\pi$
$487$	34.2080	1.55011	0.775056	+	0.631892i	$0.217721\pi$
$488$	−5.91851	−0.267918
$489$	35.0085	1.58314
$490$	−1.06116	−0.0479381
$491$	5.49497	0.247985	0.123992	−	0.992283i	$-0.460430\pi$
$491$	5.49497	0.247985	0.123992	+	0.992283i	$0.460430\pi$
$492$	−2.37582	−0.107110
$493$	3.86955	0.174276
$494$	−7.30138	−0.328505
$495$	−5.32171	−0.239193
$496$	5.87395	0.263748
$497$	−24.0797	−1.08012
$498$	6.18097	0.276976
$499$	17.6401	0.789680	0.394840	−	0.918750i	$-0.370800\pi$
$499$	17.6401	0.789680	0.394840	+	0.918750i	$0.370800\pi$
$500$	1.00000	0.0447214
$501$	40.4545	1.80738
$502$	3.03817	0.135600
$503$	−28.8436	−1.28607	−0.643036	−	0.765836i	$-0.722325\pi$
$503$	−28.8436	−1.28607	−0.643036	+	0.765836i	$0.722325\pi$
$504$	−12.9689	−0.577680
$505$	1.29168	0.0574790
$506$	−3.20645	−0.142544
$507$	33.5092	1.48820
$508$	5.22943	0.232019
$509$	−18.6077	−0.824774	−0.412387	−	0.911009i	$-0.635305\pi$
$509$	−18.6077	−0.824774	−0.412387	+	0.911009i	$0.635305\pi$
$510$	17.8836	0.791901
$511$	4.23898	0.187521
$512$	1.00000	0.0441942
$513$	−41.5679	−1.83527
$514$	13.3244	0.587712
$515$	13.2728	0.584867
$516$	2.88474	0.126994
$517$	2.00000	0.0879599
$518$	−2.45415	−0.107829
$519$	11.8052	0.518189
$520$	−1.17642	−0.0515893
$521$	34.4079	1.50744	0.753719	−	0.657197i	$-0.228258\pi$
$521$	34.4079	1.50744	0.753719	+	0.657197i	$0.228258\pi$
$522$	−3.32171	−0.145387
$523$	−39.7687	−1.73896	−0.869482	−	0.493965i	$-0.835547\pi$
$523$	−39.7687	−1.73896	−0.869482	+	0.493965i	$0.835547\pi$
$524$	−3.63638	−0.158856
$525$	7.03003	0.306816
$526$	−4.89802	−0.213564
$527$	−36.4150	−1.58626
$528$	2.88474	0.125542
$529$	−12.7187	−0.552986
$530$	−11.1523	−0.484427
$531$	63.6375	2.76163
$532$	−15.1250	−0.655750
$533$	−0.968877	−0.0419667
$534$	40.0507	1.73316
$535$	16.5052	0.713581
$536$	−15.8428	−0.684306
$537$	29.6397	1.27905
$538$	−0.264957	−0.0114231
$539$	1.06116	0.0457072
$540$	−6.69753	−0.288216
$541$	−27.6301	−1.18791	−0.593956	−	0.804497i	$-0.702435\pi$
$541$	−27.6301	−1.18791	−0.593956	+	0.804497i	$0.702435\pi$
$542$	22.0238	0.946003
$543$	59.6131	2.55824
$544$	−6.19940	−0.265797
$545$	−0.165629	−0.00709476
$546$	−8.27025	−0.353934
$547$	25.3951	1.08581	0.542907	−	0.839793i	$-0.317324\pi$
$547$	25.3951	1.08581	0.542907	+	0.839793i	$0.317324\pi$
$548$	−4.48220	−0.191470
$549$	−31.4966	−1.34424
$550$	−1.00000	−0.0426401
$551$	−3.87395	−0.165036
$552$	−9.24977	−0.393696
$553$	31.2851	1.33038
$554$	4.32767	0.183865
$555$	−2.90507	−0.123313
$556$	−9.56069	−0.405464
$557$	−24.5268	−1.03923	−0.519616	−	0.854400i	$-0.673925\pi$
$557$	−24.5268	−1.03923	−0.519616	+	0.854400i	$0.673925\pi$
$558$	31.2595	1.32332
$559$	1.17642	0.0497572
$560$	−2.43697	−0.102981
$561$	−17.8836	−0.755048
$562$	−31.0519	−1.30985
$563$	15.0250	0.633230	0.316615	−	0.948554i	$-0.397454\pi$
$563$	15.0250	0.633230	0.316615	+	0.948554i	$0.397454\pi$
$564$	5.76948	0.242939
$565$	0.634970	0.0267134
$566$	−2.45041	−0.102999
$567$	−8.17723	−0.343411
$568$	9.88100	0.414597
$569$	11.7689	0.493377	0.246689	−	0.969095i	$-0.420658\pi$
$569$	11.7689	0.493377	0.246689	+	0.969095i	$0.420658\pi$
$570$	−17.9040	−0.749915
$571$	20.7659	0.869025	0.434513	−	0.900666i	$-0.356921\pi$
$571$	20.7659	0.869025	0.434513	+	0.900666i	$0.356921\pi$
$572$	1.17642	0.0491885
$573$	23.0233	0.961812
$574$	−2.00705	−0.0837726
$575$	3.20645	0.133718
$576$	5.32171	0.221738
$577$	41.8164	1.74084	0.870420	−	0.492310i	$-0.163847\pi$
$577$	41.8164	1.74084	0.870420	+	0.492310i	$0.163847\pi$
$578$	21.4326	0.891478
$579$	20.3420	0.845387
$580$	−0.624181	−0.0259177
$581$	5.22157	0.216627
$582$	−43.4551	−1.80127
$583$	11.1523	0.461883
$584$	−1.73944	−0.0719787
$585$	−6.26056	−0.258842
$586$	−19.9722	−0.825043
$587$	23.0097	0.949712	0.474856	−	0.880064i	$-0.342500\pi$
$587$	23.0097	0.949712	0.474856	+	0.880064i	$0.342500\pi$
$588$	3.06116	0.126240
$589$	36.4564	1.50216
$590$	11.9581	0.492307
$591$	67.7955	2.78873
$592$	1.00705	0.0413895
$593$	−7.89362	−0.324152	−0.162076	−	0.986778i	$-0.551819\pi$
$593$	−7.89362	−0.324152	−0.162076	+	0.986778i	$0.551819\pi$
$594$	6.69753	0.274803
$595$	15.1078	0.619359
$596$	12.8358	0.525774
$597$	48.8737	2.00027
$598$	−3.77212	−0.154254
$599$	−24.0938	−0.984447	−0.492224	−	0.870469i	$-0.663816\pi$
$599$	−24.0938	−0.984447	−0.492224	+	0.870469i	$0.663816\pi$
$600$	−2.88474	−0.117769
$601$	−37.4106	−1.52601	−0.763004	−	0.646393i	$-0.776277\pi$
$601$	−37.4106	−1.52601	−0.763004	+	0.646393i	$0.776277\pi$
$602$	2.43697	0.0993237
$603$	−84.3110	−3.43341
$604$	−17.3314	−0.705205
$605$	1.00000	0.0406558
$606$	−3.72616	−0.151365
$607$	−6.59945	−0.267863	−0.133932	−	0.990991i	$-0.542760\pi$
$607$	−6.59945	−0.267863	−0.133932	+	0.990991i	$0.542760\pi$
$608$	6.20645	0.251705
$609$	−4.38801	−0.177811
$610$	−5.91851	−0.239633
$611$	2.35284	0.0951855
$612$	−32.9914	−1.33360
$613$	−24.7613	−1.00010	−0.500050	−	0.865996i	$-0.666685\pi$
$613$	−24.7613	−1.00010	−0.500050	+	0.865996i	$0.666685\pi$
$614$	−18.7194	−0.755454
$615$	−2.37582	−0.0958023
$616$	2.43697	0.0981885
$617$	−14.3059	−0.575935	−0.287968	−	0.957640i	$-0.592980\pi$
$617$	−14.3059	−0.575935	−0.287968	+	0.957640i	$0.592980\pi$
$618$	−38.2884	−1.54019
$619$	−5.23832	−0.210546	−0.105273	−	0.994443i	$-0.533572\pi$
$619$	−5.23832	−0.210546	−0.105273	+	0.994443i	$0.533572\pi$
$620$	5.87395	0.235903
$621$	−21.4753	−0.861774
$622$	−7.97452	−0.319749
$623$	33.8341	1.35553
$624$	3.39366	0.135855
$625$	1.00000	0.0400000
$626$	21.2728	0.850230
$627$	17.9040	0.715016
$628$	−12.7002	−0.506792
$629$	−6.24310	−0.248929
$630$	−12.9689	−0.516692
$631$	−9.80465	−0.390317	−0.195159	−	0.980772i	$-0.562522\pi$
$631$	−9.80465	−0.390317	−0.195159	+	0.980772i	$0.562522\pi$
$632$	−12.8377	−0.510655
$633$	0.508919	0.0202277
$634$	−14.9021	−0.591837
$635$	5.22943	0.207524
$636$	32.1716	1.27569
$637$	1.24836	0.0494619
$638$	0.624181	0.0247116
$639$	52.5838	2.08018
$640$	1.00000	0.0395285
$641$	−21.0557	−0.831649	−0.415824	−	0.909445i	$-0.636507\pi$
$641$	−21.0557	−0.831649	−0.415824	+	0.909445i	$0.636507\pi$
$642$	−47.6131	−1.87914
$643$	−19.8230	−0.781742	−0.390871	−	0.920445i	$-0.627826\pi$
$643$	−19.8230	−0.781742	−0.390871	+	0.920445i	$0.627826\pi$
$644$	−7.81404	−0.307916
$645$	2.88474	0.113586
$646$	−38.4763	−1.51383
$647$	−12.3599	−0.485917	−0.242959	−	0.970037i	$-0.578118\pi$
$647$	−12.3599	−0.485917	−0.242959	+	0.970037i	$0.578118\pi$
$648$	3.35548	0.131816
$649$	−11.9581	−0.469396
$650$	−1.17642	−0.0461429
$651$	41.2941	1.61844
$652$	−12.1357	−0.475273
$653$	39.3335	1.53924	0.769619	−	0.638503i	$-0.220446\pi$
$653$	39.3335	1.53924	0.769619	+	0.638503i	$0.220446\pi$
$654$	0.477796	0.0186833
$655$	−3.63638	−0.142085
$656$	0.823582	0.0321555
$657$	−9.25682	−0.361143
$658$	4.87395	0.190006
$659$	−10.5881	−0.412453	−0.206226	−	0.978504i	$-0.566118\pi$
$659$	−10.5881	−0.412453	−0.206226	+	0.978504i	$0.566118\pi$
$660$	2.88474	0.112288
$661$	37.0832	1.44237	0.721185	−	0.692743i	$-0.243598\pi$
$661$	37.0832	1.44237	0.721185	+	0.692743i	$0.243598\pi$
$662$	−33.6450	−1.30765
$663$	−21.0386	−0.817073
$664$	−2.14265	−0.0831508
$665$	−15.1250	−0.586521
$666$	5.35922	0.207666
$667$	−2.00141	−0.0774947
$668$	−14.0236	−0.542591
$669$	53.1420	2.05459
$670$	−15.8428	−0.612062
$671$	5.91851	0.228482
$672$	7.03003	0.271189
$673$	−18.1734	−0.700534	−0.350267	−	0.936650i	$-0.613909\pi$
$673$	−18.1734	−0.700534	−0.350267	+	0.936650i	$0.613909\pi$
$674$	−6.75354	−0.260137
$675$	−6.69753	−0.257788
$676$	−11.6160	−0.446771
$677$	−34.9304	−1.34249	−0.671243	−	0.741238i	$-0.734239\pi$
$677$	−34.9304	−1.34249	−0.671243	+	0.741238i	$0.734239\pi$
$678$	−1.83172	−0.0703469
$679$	−36.7101	−1.40880
$680$	−6.19940	−0.237736
$681$	−61.4070	−2.35312
$682$	−5.87395	−0.224925
$683$	−6.57663	−0.251648	−0.125824	−	0.992053i	$-0.540157\pi$
$683$	−6.57663	−0.251648	−0.125824	+	0.992053i	$0.540157\pi$
$684$	33.0289	1.26289
$685$	−4.48220	−0.171256
$686$	19.6448	0.750043
$687$	−42.7685	−1.63172
$688$	−1.00000	−0.0381246
$689$	13.1198	0.499825
$690$	−9.24977	−0.352133
$691$	−13.5810	−0.516647	−0.258323	−	0.966059i	$-0.583170\pi$
$691$	−13.5810	−0.516647	−0.258323	+	0.966059i	$0.583170\pi$
$692$	−4.09228	−0.155565
$693$	12.9689	0.492647
$694$	−3.83453	−0.145557
$695$	−9.56069	−0.362658
$696$	1.80060	0.0682515
$697$	−5.10572	−0.193393
$698$	25.6309	0.970143
$699$	71.1616	2.69158
$700$	−2.43697	−0.0921090
$701$	−29.6301	−1.11911	−0.559557	−	0.828792i	$-0.689029\pi$
$701$	−29.6301	−1.11911	−0.559557	+	0.828792i	$0.689029\pi$
$702$	7.87909	0.297377
$703$	6.25020	0.235731
$704$	−1.00000	−0.0376889
$705$	5.76948	0.217291
$706$	6.46510	0.243317
$707$	−3.14779	−0.118385
$708$	−34.4959	−1.29644
$709$	42.6973	1.60353	0.801764	−	0.597640i	$-0.203895\pi$
$709$	42.6973	1.60353	0.801764	+	0.597640i	$0.203895\pi$
$710$	9.88100	0.370827
$711$	−68.3184	−2.56214
$712$	−13.8836	−0.520312
$713$	18.8345	0.705358
$714$	−43.5820	−1.63102
$715$	1.17642	0.0439955
$716$	−10.2747	−0.383982
$717$	35.6807	1.33252
$718$	9.07974	0.338853
$719$	−0.782761	−0.0291921	−0.0145960	−	0.999893i	$-0.504646\pi$
$719$	−0.782761	−0.0291921	−0.0145960	+	0.999893i	$0.504646\pi$
$720$	5.32171	0.198329
$721$	−32.3454	−1.20460
$722$	19.5200	0.726460
$723$	69.1204	2.57062
$724$	−20.6650	−0.768009
$725$	−0.624181	−0.0231815
$726$	−2.88474	−0.107063
$727$	−6.04815	−0.224313	−0.112157	−	0.993691i	$-0.535776\pi$
$727$	−6.04815	−0.224313	−0.112157	+	0.993691i	$0.535776\pi$
$728$	2.86690	0.106254
$729$	−40.1049	−1.48537
$730$	−1.73944	−0.0643797
$731$	6.19940	0.229293
$732$	17.0734	0.631049
$733$	−19.9889	−0.738308	−0.369154	−	0.929368i	$-0.620353\pi$
$733$	−19.9889	−0.738308	−0.369154	+	0.929368i	$0.620353\pi$
$734$	15.2740	0.563773
$735$	3.06116	0.112912
$736$	3.20645	0.118191
$737$	15.8428	0.583578
$738$	4.38287	0.161336
$739$	26.1334	0.961333	0.480667	−	0.876903i	$-0.340395\pi$
$739$	26.1334	0.961333	0.480667	+	0.876903i	$0.340395\pi$
$740$	1.00705	0.0370199
$741$	21.0626	0.773753
$742$	27.1780	0.997735
$743$	−16.6117	−0.609424	−0.304712	−	0.952444i	$-0.598560\pi$
$743$	−16.6117	−0.609424	−0.304712	+	0.952444i	$0.598560\pi$
$744$	−16.9448	−0.621227
$745$	12.8358	0.470266
$746$	−1.00515	−0.0368010
$747$	−11.4025	−0.417197
$748$	6.19940	0.226673
$749$	−40.2227	−1.46971
$750$	−2.88474	−0.105336
$751$	38.9690	1.42200	0.711000	−	0.703192i	$-0.248243\pi$
$751$	38.9690	1.42200	0.711000	+	0.703192i	$0.248243\pi$
$752$	−2.00000	−0.0729325
$753$	−8.76433	−0.319390
$754$	0.734298	0.0267415
$755$	−17.3314	−0.630755
$756$	16.3217	0.593615
$757$	6.58118	0.239197	0.119598	−	0.992822i	$-0.461839\pi$
$757$	6.58118	0.239197	0.119598	+	0.992822i	$0.461839\pi$
$758$	−17.1658	−0.623489
$759$	9.24977	0.335745
$760$	6.20645	0.225132
$761$	−25.3840	−0.920169	−0.460085	−	0.887875i	$-0.652181\pi$
$761$	−25.3840	−0.920169	−0.460085	+	0.887875i	$0.652181\pi$
$762$	−15.0855	−0.546492
$763$	0.403633	0.0146125
$764$	−7.98107	−0.288745
$765$	−32.9914	−1.19281
$766$	1.75495	0.0634088
$767$	−14.0677	−0.507955
$768$	−2.88474	−0.104094
$769$	8.17673	0.294861	0.147430	−	0.989072i	$-0.452900\pi$
$769$	8.17673	0.294861	0.147430	+	0.989072i	$0.452900\pi$
$770$	2.43697	0.0878225
$771$	−38.4373	−1.38429
$772$	−7.05161	−0.253793
$773$	21.7409	0.781966	0.390983	−	0.920398i	$-0.372135\pi$
$773$	21.7409	0.781966	0.390983	+	0.920398i	$0.372135\pi$
$774$	−5.32171	−0.191285
$775$	5.87395	0.210998
$776$	15.0638	0.540759
$777$	7.07959	0.253979
$778$	24.8244	0.889998
$779$	5.11152	0.183139
$780$	3.39366	0.121512
$781$	−9.88100	−0.353570
$782$	−19.8781	−0.710838
$783$	4.18047	0.149398
$784$	−1.06116	−0.0378984
$785$	−12.7002	−0.453289
$786$	10.4900	0.374166
$787$	39.8277	1.41970	0.709852	−	0.704351i	$-0.248762\pi$
$787$	39.8277	1.41970	0.709852	+	0.704351i	$0.248762\pi$
$788$	−23.5014	−0.837204
$789$	14.1295	0.503024
$790$	−12.8377	−0.456744
$791$	−1.54741	−0.0550194
$792$	−5.32171	−0.189099
$793$	6.96264	0.247251
$794$	6.51846	0.231332
$795$	32.1716	1.14101
$796$	−16.9422	−0.600499
$797$	41.9577	1.48622	0.743108	−	0.669171i	$-0.233351\pi$
$797$	41.9577	1.48622	0.743108	+	0.669171i	$0.233351\pi$
$798$	43.6315	1.54454
$799$	12.3988	0.438638
$800$	1.00000	0.0353553
$801$	−73.8848	−2.61059
$802$	3.62185	0.127892
$803$	1.73944	0.0613836
$804$	45.7024	1.61180
$805$	−7.81404	−0.275409
$806$	−6.91022	−0.243402
$807$	0.764330	0.0269057
$808$	1.29168	0.0454411
$809$	43.9637	1.54568	0.772841	−	0.634599i	$-0.218835\pi$
$809$	43.9637	1.54568	0.772841	+	0.634599i	$0.218835\pi$
$810$	3.35548	0.117900
$811$	−14.2423	−0.500114	−0.250057	−	0.968231i	$-0.580449\pi$
$811$	−14.2423	−0.500114	−0.250057	+	0.968231i	$0.580449\pi$
$812$	1.52111	0.0533806
$813$	−63.5329	−2.22820
$814$	−1.00705	−0.0352970
$815$	−12.1357	−0.425097
$816$	17.8836	0.626053
$817$	−6.20645	−0.217136
$818$	−25.0882	−0.877188
$819$	15.2568	0.533116
$820$	0.823582	0.0287607
$821$	12.7581	0.445261	0.222630	−	0.974903i	$-0.428536\pi$
$821$	12.7581	0.445261	0.222630	+	0.974903i	$0.428536\pi$
$822$	12.9300	0.450984
$823$	−26.7720	−0.933212	−0.466606	−	0.884465i	$-0.654523\pi$
$823$	−26.7720	−0.933212	−0.466606	+	0.884465i	$0.654523\pi$
$824$	13.2728	0.462378
$825$	2.88474	0.100434
$826$	−29.1416	−1.01396
$827$	10.9906	0.382181	0.191091	−	0.981572i	$-0.438798\pi$
$827$	10.9906	0.382181	0.191091	+	0.981572i	$0.438798\pi$
$828$	17.0638	0.593008
$829$	35.8988	1.24682	0.623409	−	0.781896i	$-0.285747\pi$
$829$	35.8988	1.24682	0.623409	+	0.781896i	$0.285747\pi$
$830$	−2.14265	−0.0743723
$831$	−12.4842	−0.433072
$832$	−1.17642	−0.0407849
$833$	6.57853	0.227933
$834$	27.5801	0.955020
$835$	−14.0236	−0.485308
$836$	−6.20645	−0.214655
$837$	−39.3410	−1.35982
$838$	31.9855	1.10492
$839$	−19.7598	−0.682185	−0.341092	−	0.940030i	$-0.610797\pi$
$839$	−19.7598	−0.682185	−0.341092	+	0.940030i	$0.610797\pi$
$840$	7.03003	0.242559
$841$	−28.6104	−0.986565
$842$	−25.3244	−0.872735
$843$	89.5767	3.08518
$844$	−0.176418	−0.00607255
$845$	−11.6160	−0.399604
$846$	−10.6434	−0.365928
$847$	−2.43697	−0.0837354
$848$	−11.1523	−0.382973
$849$	7.06880	0.242601
$850$	−6.19940	−0.212638
$851$	3.22905	0.110690
$852$	−28.5041	−0.976534
$853$	−0.167034	−0.00571915	−0.00285957	−	0.999996i	$-0.500910\pi$
$853$	−0.167034	−0.00571915	−0.00285957	+	0.999996i	$0.500910\pi$
$854$	14.4233	0.493554
$855$	33.0289	1.12957
$856$	16.5052	0.564135
$857$	−6.57381	−0.224557	−0.112279	−	0.993677i	$-0.535815\pi$
$857$	−6.57381	−0.224557	−0.112279	+	0.993677i	$0.535815\pi$
$858$	−3.39366	−0.115858
$859$	37.6966	1.28619	0.643096	−	0.765786i	$-0.277650\pi$
$859$	37.6966	1.28619	0.643096	+	0.765786i	$0.277650\pi$
$860$	−1.00000	−0.0340997
$861$	5.78981	0.197316
$862$	1.39631	0.0475584
$863$	−27.8080	−0.946594	−0.473297	−	0.880903i	$-0.656936\pi$
$863$	−27.8080	−0.946594	−0.473297	+	0.880903i	$0.656936\pi$
$864$	−6.69753	−0.227855
$865$	−4.09228	−0.139142
$866$	4.09228	0.139061
$867$	−61.8274	−2.09977
$868$	−14.3147	−0.485871
$869$	12.8377	0.435488
$870$	1.80060	0.0610460
$871$	18.6378	0.631517
$872$	−0.165629	−0.00560890
$873$	80.1652	2.71318
$874$	19.9007	0.673150
$875$	−2.43697	−0.0823848
$876$	5.01784	0.169537
$877$	−26.0689	−0.880283	−0.440141	−	0.897928i	$-0.645072\pi$
$877$	−26.0689	−0.880283	−0.440141	+	0.897928i	$0.645072\pi$
$878$	9.08414	0.306575
$879$	57.6145	1.94329
$880$	−1.00000	−0.0337100
$881$	39.5066	1.33101	0.665505	−	0.746393i	$-0.268216\pi$
$881$	39.5066	1.33101	0.665505	+	0.746393i	$0.268216\pi$
$882$	−5.64716	−0.190150
$883$	23.3366	0.785338	0.392669	−	0.919680i	$-0.371552\pi$
$883$	23.3366	0.785338	0.392669	+	0.919680i	$0.371552\pi$
$884$	7.29309	0.245293
$885$	−34.4959	−1.15957
$886$	18.6248	0.625714
$887$	34.2124	1.14874	0.574370	−	0.818596i	$-0.305247\pi$
$887$	34.2124	1.14874	0.574370	+	0.818596i	$0.305247\pi$
$888$	−2.90507	−0.0974878
$889$	−12.7440	−0.427420
$890$	−13.8836	−0.465381
$891$	−3.35548	−0.112413
$892$	−18.4218	−0.616807
$893$	−12.4129	−0.415382
$894$	−37.0279	−1.23840
$895$	−10.2747	−0.343444
$896$	−2.43697	−0.0814136
$897$	10.8816	0.363326
$898$	−2.23052	−0.0744336
$899$	−3.66641	−0.122282
$900$	5.32171	0.177390
$901$	69.1379	2.30332
$902$	−0.823582	−0.0274223
$903$	−7.03003	−0.233945
$904$	0.634970	0.0211188
$905$	−20.6650	−0.686928
$906$	49.9966	1.66102
$907$	40.0118	1.32857	0.664286	−	0.747479i	$-0.268736\pi$
$907$	40.0118	1.32857	0.664286	+	0.747479i	$0.268736\pi$
$908$	21.2868	0.706429
$909$	6.87395	0.227994
$910$	2.86690	0.0950368
$911$	−53.4395	−1.77053	−0.885265	−	0.465087i	$-0.846023\pi$
$911$	−53.4395	−1.77053	−0.885265	+	0.465087i	$0.846023\pi$
$912$	−17.9040	−0.592860
$913$	2.14265	0.0709112
$914$	6.00596	0.198659
$915$	17.0734	0.564428
$916$	14.8258	0.489858
$917$	8.86175	0.292641
$918$	41.5207	1.37039
$919$	−30.1717	−0.995274	−0.497637	−	0.867385i	$-0.665799\pi$
$919$	−30.1717	−0.995274	−0.497637	+	0.867385i	$0.665799\pi$
$920$	3.20645	0.105714
$921$	54.0006	1.77938
$922$	15.4570	0.509050
$923$	−11.6242	−0.382615
$924$	−7.03003	−0.231271
$925$	1.00705	0.0331116
$926$	23.2161	0.762930
$927$	70.6338	2.31992
$928$	−0.624181	−0.0204897
$929$	−26.6351	−0.873870	−0.436935	−	0.899493i	$-0.643936\pi$
$929$	−26.6351	−0.873870	−0.436935	+	0.899493i	$0.643936\pi$
$930$	−16.9448	−0.555642
$931$	−6.58601	−0.215848
$932$	−24.6683	−0.808037
$933$	23.0044	0.753130
$934$	−33.3766	−1.09212
$935$	6.19940	0.202742
$936$	−6.26056	−0.204633
$937$	−17.8219	−0.582216	−0.291108	−	0.956690i	$-0.594024\pi$
$937$	−17.8219	−0.582216	−0.291108	+	0.956690i	$0.594024\pi$
$938$	38.6086	1.26061
$939$	−61.3663	−2.00261
$940$	−2.00000	−0.0652328
$941$	13.5754	0.442545	0.221272	−	0.975212i	$-0.428979\pi$
$941$	13.5754	0.442545	0.221272	+	0.975212i	$0.428979\pi$
$942$	36.6367	1.19369
$943$	2.64078	0.0859955
$944$	11.9581	0.389203
$945$	16.3217	0.530945
$946$	1.00000	0.0325128
$947$	23.8691	0.775642	0.387821	−	0.921735i	$-0.373228\pi$
$947$	23.8691	0.775642	0.387821	+	0.921735i	$0.373228\pi$
$948$	37.0333	1.20279
$949$	2.04631	0.0664261
$950$	6.20645	0.201364
$951$	42.9886	1.39400
$952$	15.1078	0.489646
$953$	−21.3466	−0.691484	−0.345742	−	0.938330i	$-0.612373\pi$
$953$	−21.3466	−0.691484	−0.345742	+	0.938330i	$0.612373\pi$
$954$	−59.3496	−1.92151
$955$	−7.98107	−0.258261
$956$	−12.3688	−0.400035
$957$	−1.80060	−0.0582051
$958$	38.5211	1.24456
$959$	10.9230	0.352722
$960$	−2.88474	−0.0931045
$961$	3.50328	0.113009
$962$	−1.18471	−0.0381966
$963$	87.8358	2.83047
$964$	−23.9607	−0.771723
$965$	−7.05161	−0.226999
$966$	22.5414	0.725259
$967$	−0.498628	−0.0160348	−0.00801739	−	0.999968i	$-0.502552\pi$
$967$	−0.498628	−0.0160348	−0.00801739	+	0.999968i	$0.502552\pi$
$968$	1.00000	0.0321412
$969$	110.994	3.56564
$970$	15.0638	0.483670
$971$	13.9275	0.446954	0.223477	−	0.974709i	$-0.428259\pi$
$971$	13.9275	0.446954	0.223477	+	0.974709i	$0.428259\pi$
$972$	10.4129	0.333994
$973$	23.2992	0.746937
$974$	34.2080	1.09610
$975$	3.39366	0.108684
$976$	−5.91851	−0.189447
$977$	33.9850	1.08728	0.543639	−	0.839319i	$-0.317046\pi$
$977$	33.9850	1.08728	0.543639	+	0.839319i	$0.317046\pi$
$978$	35.0085	1.11945
$979$	13.8836	0.443723
$980$	−1.06116	−0.0338974
$981$	−0.881429	−0.0281419
$982$	5.49497	0.175352
$983$	−31.3526	−0.999994	−0.499997	−	0.866027i	$-0.666666\pi$
$983$	−31.3526	−0.999994	−0.499997	+	0.866027i	$0.666666\pi$
$984$	−2.37582	−0.0757383
$985$	−23.5014	−0.748818
$986$	3.86955	0.123232
$987$	−14.0601	−0.447537
$988$	−7.30138	−0.232288
$989$	−3.20645	−0.101959
$990$	−5.32171	−0.169135
$991$	−34.1533	−1.08492	−0.542458	−	0.840083i	$-0.682506\pi$
$991$	−34.1533	−1.08492	−0.542458	+	0.840083i	$0.682506\pi$
$992$	5.87395	0.186498
$993$	97.0570	3.08001
$994$	−24.0797	−0.763763
$995$	−16.9422	−0.537102
$996$	6.18097	0.195852
$997$	−42.3507	−1.34126	−0.670629	−	0.741793i	$-0.733976\pi$
$997$	−42.3507	−1.34126	−0.670629	+	0.741793i	$0.733976\pi$
$998$	17.6401	0.558388
$999$	−6.74474	−0.213394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.u.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.u.1.1	✓	4	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.88474 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.88474 q^{6} -2.43697 q^{7} +1.00000 q^{8} +5.32171 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.88474 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.88474 q^{6} -2.43697 q^{7} +1.00000 q^{8} +5.32171 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.88474 q^{12} -1.17642 q^{13} -2.43697 q^{14} -2.88474 q^{15} +1.00000 q^{16} -6.19940 q^{17} +5.32171 q^{18} +6.20645 q^{19} +1.00000 q^{20} +7.03003 q^{21} -1.00000 q^{22} +3.20645 q^{23} -2.88474 q^{24} +1.00000 q^{25} -1.17642 q^{26} -6.69753 q^{27} -2.43697 q^{28} -0.624181 q^{29} -2.88474 q^{30} +5.87395 q^{31} +1.00000 q^{32} +2.88474 q^{33} -6.19940 q^{34} -2.43697 q^{35} +5.32171 q^{36} +1.00705 q^{37} +6.20645 q^{38} +3.39366 q^{39} +1.00000 q^{40} +0.823582 q^{41} +7.03003 q^{42} -1.00000 q^{43} -1.00000 q^{44} +5.32171 q^{45} +3.20645 q^{46} -2.00000 q^{47} -2.88474 q^{48} -1.06116 q^{49} +1.00000 q^{50} +17.8836 q^{51} -1.17642 q^{52} -11.1523 q^{53} -6.69753 q^{54} -1.00000 q^{55} -2.43697 q^{56} -17.9040 q^{57} -0.624181 q^{58} +11.9581 q^{59} -2.88474 q^{60} -5.91851 q^{61} +5.87395 q^{62} -12.9689 q^{63} +1.00000 q^{64} -1.17642 q^{65} +2.88474 q^{66} -15.8428 q^{67} -6.19940 q^{68} -9.24977 q^{69} -2.43697 q^{70} +9.88100 q^{71} +5.32171 q^{72} -1.73944 q^{73} +1.00705 q^{74} -2.88474 q^{75} +6.20645 q^{76} +2.43697 q^{77} +3.39366 q^{78} -12.8377 q^{79} +1.00000 q^{80} +3.35548 q^{81} +0.823582 q^{82} -2.14265 q^{83} +7.03003 q^{84} -6.19940 q^{85} -1.00000 q^{86} +1.80060 q^{87} -1.00000 q^{88} -13.8836 q^{89} +5.32171 q^{90} +2.86690 q^{91} +3.20645 q^{92} -16.9448 q^{93} -2.00000 q^{94} +6.20645 q^{95} -2.88474 q^{96} +15.0638 q^{97} -1.06116 q^{98} -5.32171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9	\( 4 q + 4 q^{2} - 3 q^{3} + 4 q^{4} + 4 q^{5} - 3 q^{6} + 4 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} - 3 q^{12} - 9 q^{13} - 3 q^{15} + 4 q^{16} - 15 q^{17} + 3 q^{18} - 2 q^{19} + 4 q^{20} - 3 q^{21} - 4 q^{22} - 14 q^{23} - 3 q^{24} + 4 q^{25} - 9 q^{26} - 3 q^{27} - 8 q^{29} - 3 q^{30} + 4 q^{31} + 4 q^{32} + 3 q^{33} - 15 q^{34} + 3 q^{36} - 13 q^{37} - 2 q^{38} + 2 q^{39} + 4 q^{40} - q^{41} - 3 q^{42} - 4 q^{43} - 4 q^{44} + 3 q^{45} - 14 q^{46} - 8 q^{47} - 3 q^{48} + 4 q^{50} + 5 q^{51} - 9 q^{52} - 5 q^{53} - 3 q^{54} - 4 q^{55} - 21 q^{57} - 8 q^{58} + 10 q^{59} - 3 q^{60} - 12 q^{61} + 4 q^{62} - 25 q^{63} + 4 q^{64} - 9 q^{65} + 3 q^{66} - 17 q^{67} - 15 q^{68} - 12 q^{69} + 3 q^{71} + 3 q^{72} - 21 q^{73} - 13 q^{74} - 3 q^{75} - 2 q^{76} + 2 q^{78} - 13 q^{79} + 4 q^{80} - 8 q^{81} - q^{82} - 16 q^{83} - 3 q^{84} - 15 q^{85} - 4 q^{86} + 17 q^{87} - 4 q^{88} + 11 q^{89} + 3 q^{90} + 9 q^{91} - 14 q^{92} + 3 q^{93} - 8 q^{94} - 2 q^{95} - 3 q^{96} + 26 q^{97} - 3 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 3 * q^3 + 4 * q^4 + 4 * q^5 - 3 * q^6 + 4 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 - 3 * q^12 - 9 * q^13 - 3 * q^15 + 4 * q^16 - 15 * q^17 + 3 * q^18 - 2 * q^19 + 4 * q^20 - 3 * q^21 - 4 * q^22 - 14 * q^23 - 3 * q^24 + 4 * q^25 - 9 * q^26 - 3 * q^27 - 8 * q^29 - 3 * q^30 + 4 * q^31 + 4 * q^32 + 3 * q^33 - 15 * q^34 + 3 * q^36 - 13 * q^37 - 2 * q^38 + 2 * q^39 + 4 * q^40 - q^41 - 3 * q^42 - 4 * q^43 - 4 * q^44 + 3 * q^45 - 14 * q^46 - 8 * q^47 - 3 * q^48 + 4 * q^50 + 5 * q^51 - 9 * q^52 - 5 * q^53 - 3 * q^54 - 4 * q^55 - 21 * q^57 - 8 * q^58 + 10 * q^59 - 3 * q^60 - 12 * q^61 + 4 * q^62 - 25 * q^63 + 4 * q^64 - 9 * q^65 + 3 * q^66 - 17 * q^67 - 15 * q^68 - 12 * q^69 + 3 * q^71 + 3 * q^72 - 21 * q^73 - 13 * q^74 - 3 * q^75 - 2 * q^76 + 2 * q^78 - 13 * q^79 + 4 * q^80 - 8 * q^81 - q^82 - 16 * q^83 - 3 * q^84 - 15 * q^85 - 4 * q^86 + 17 * q^87 - 4 * q^88 + 11 * q^89 + 3 * q^90 + 9 * q^91 - 14 * q^92 + 3 * q^93 - 8 * q^94 - 2 * q^95 - 3 * q^96 + 26 * q^97 - 3 * q^99

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