LMFDB - Embedded newform 4034.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.523973 q^{3} +1.00000 q^{4} +1.37573 q^{5} -0.523973 q^{6} -3.92552 q^{7} +1.00000 q^{8} -2.72545 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.523973 q^{3} +1.00000 q^{4} +1.37573 q^{5} -0.523973 q^{6} -3.92552 q^{7} +1.00000 q^{8} -2.72545 q^{9} +1.37573 q^{10} +1.18179 q^{11} -0.523973 q^{12} +5.13369 q^{13} -3.92552 q^{14} -0.720847 q^{15} +1.00000 q^{16} -3.19750 q^{17} -2.72545 q^{18} -6.02426 q^{19} +1.37573 q^{20} +2.05687 q^{21} +1.18179 q^{22} +8.56991 q^{23} -0.523973 q^{24} -3.10736 q^{25} +5.13369 q^{26} +2.99998 q^{27} -3.92552 q^{28} -4.87522 q^{29} -0.720847 q^{30} +5.99164 q^{31} +1.00000 q^{32} -0.619228 q^{33} -3.19750 q^{34} -5.40047 q^{35} -2.72545 q^{36} -5.74989 q^{37} -6.02426 q^{38} -2.68991 q^{39} +1.37573 q^{40} -0.0599683 q^{41} +2.05687 q^{42} -9.15869 q^{43} +1.18179 q^{44} -3.74949 q^{45} +8.56991 q^{46} +5.61143 q^{47} -0.523973 q^{48} +8.40972 q^{49} -3.10736 q^{50} +1.67541 q^{51} +5.13369 q^{52} -12.3956 q^{53} +2.99998 q^{54} +1.62583 q^{55} -3.92552 q^{56} +3.15655 q^{57} -4.87522 q^{58} -4.93905 q^{59} -0.720847 q^{60} -7.66203 q^{61} +5.99164 q^{62} +10.6988 q^{63} +1.00000 q^{64} +7.06258 q^{65} -0.619228 q^{66} -6.06824 q^{67} -3.19750 q^{68} -4.49040 q^{69} -5.40047 q^{70} -14.2196 q^{71} -2.72545 q^{72} +5.27470 q^{73} -5.74989 q^{74} +1.62817 q^{75} -6.02426 q^{76} -4.63916 q^{77} -2.68991 q^{78} +11.0761 q^{79} +1.37573 q^{80} +6.60444 q^{81} -0.0599683 q^{82} -6.40447 q^{83} +2.05687 q^{84} -4.39891 q^{85} -9.15869 q^{86} +2.55449 q^{87} +1.18179 q^{88} +6.10024 q^{89} -3.74949 q^{90} -20.1524 q^{91} +8.56991 q^{92} -3.13946 q^{93} +5.61143 q^{94} -8.28777 q^{95} -0.523973 q^{96} +7.36178 q^{97} +8.40972 q^{98} -3.22092 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * 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
$3$	−0.523973	−0.302516	−0.151258	−	0.988494i	$-0.548332\pi$
$3$	−0.523973	−0.302516	−0.151258	+	0.988494i	$0.548332\pi$
$4$	1.00000	0.500000
$5$	1.37573	0.615246	0.307623	−	0.951508i	$-0.400466\pi$
$5$	1.37573	0.615246	0.307623	+	0.951508i	$0.400466\pi$
$6$	−0.523973	−0.213911
$7$	−3.92552	−1.48371	−0.741854	−	0.670562i	$-0.766053\pi$
$7$	−3.92552	−1.48371	−0.741854	+	0.670562i	$0.766053\pi$
$8$	1.00000	0.353553
$9$	−2.72545	−0.908484
$10$	1.37573	0.435045
$11$	1.18179	0.356324	0.178162	−	0.984001i	$-0.442985\pi$
$11$	1.18179	0.356324	0.178162	+	0.984001i	$0.442985\pi$
$12$	−0.523973	−0.151258
$13$	5.13369	1.42383	0.711914	−	0.702266i	$-0.247828\pi$
$13$	5.13369	1.42383	0.711914	+	0.702266i	$0.247828\pi$
$14$	−3.92552	−1.04914
$15$	−0.720847	−0.186122
$16$	1.00000	0.250000
$17$	−3.19750	−0.775508	−0.387754	−	0.921763i	$-0.626749\pi$
$17$	−3.19750	−0.775508	−0.387754	+	0.921763i	$0.626749\pi$
$18$	−2.72545	−0.642395
$19$	−6.02426	−1.38206	−0.691030	−	0.722826i	$-0.742843\pi$
$19$	−6.02426	−1.38206	−0.691030	+	0.722826i	$0.742843\pi$
$20$	1.37573	0.307623
$21$	2.05687	0.448845
$22$	1.18179	0.251959
$23$	8.56991	1.78695	0.893475	−	0.449113i	$-0.148260\pi$
$23$	8.56991	1.78695	0.893475	+	0.449113i	$0.148260\pi$
$24$	−0.523973	−0.106956
$25$	−3.10736	−0.621472
$26$	5.13369	1.00680
$27$	2.99998	0.577347
$28$	−3.92552	−0.741854
$29$	−4.87522	−0.905306	−0.452653	−	0.891687i	$-0.649522\pi$
$29$	−4.87522	−0.905306	−0.452653	+	0.891687i	$0.649522\pi$
$30$	−0.720847	−0.131608
$31$	5.99164	1.07613	0.538065	−	0.842903i	$-0.319155\pi$
$31$	5.99164	1.07613	0.538065	+	0.842903i	$0.319155\pi$
$32$	1.00000	0.176777
$33$	−0.619228	−0.107794
$34$	−3.19750	−0.548367
$35$	−5.40047	−0.912845
$36$	−2.72545	−0.454242
$37$	−5.74989	−0.945276	−0.472638	−	0.881257i	$-0.656698\pi$
$37$	−5.74989	−0.945276	−0.472638	+	0.881257i	$0.656698\pi$
$38$	−6.02426	−0.977264
$39$	−2.68991	−0.430731
$40$	1.37573	0.217522
$41$	−0.0599683	−0.00936547	−0.00468274	−	0.999989i	$-0.501491\pi$
$41$	−0.0599683	−0.00936547	−0.00468274	+	0.999989i	$0.501491\pi$
$42$	2.05687	0.317382
$43$	−9.15869	−1.39669	−0.698344	−	0.715762i	$-0.746079\pi$
$43$	−9.15869	−1.39669	−0.698344	+	0.715762i	$0.746079\pi$
$44$	1.18179	0.178162
$45$	−3.74949	−0.558941
$46$	8.56991	1.26356
$47$	5.61143	0.818511	0.409256	−	0.912420i	$-0.365788\pi$
$47$	5.61143	0.818511	0.409256	+	0.912420i	$0.365788\pi$
$48$	−0.523973	−0.0756290
$49$	8.40972	1.20139
$50$	−3.10736	−0.439447
$51$	1.67541	0.234604
$52$	5.13369	0.711914
$53$	−12.3956	−1.70267	−0.851334	−	0.524624i	$-0.824206\pi$
$53$	−12.3956	−1.70267	−0.851334	+	0.524624i	$0.824206\pi$
$54$	2.99998	0.408246
$55$	1.62583	0.219227
$56$	−3.92552	−0.524570
$57$	3.15655	0.418095
$58$	−4.87522	−0.640148
$59$	−4.93905	−0.643009	−0.321505	−	0.946908i	$-0.604189\pi$
$59$	−4.93905	−0.643009	−0.321505	+	0.946908i	$0.604189\pi$
$60$	−0.720847	−0.0930609
$61$	−7.66203	−0.981023	−0.490511	−	0.871435i	$-0.663190\pi$
$61$	−7.66203	−0.981023	−0.490511	+	0.871435i	$0.663190\pi$
$62$	5.99164	0.760939
$63$	10.6988	1.34792
$64$	1.00000	0.125000
$65$	7.06258	0.876005
$66$	−0.619228	−0.0762217
$67$	−6.06824	−0.741353	−0.370677	−	0.928762i	$-0.620874\pi$
$67$	−6.06824	−0.741353	−0.370677	+	0.928762i	$0.620874\pi$
$68$	−3.19750	−0.387754
$69$	−4.49040	−0.540581
$70$	−5.40047	−0.645479
$71$	−14.2196	−1.68756	−0.843778	−	0.536692i	$-0.819674\pi$
$71$	−14.2196	−1.68756	−0.843778	+	0.536692i	$0.819674\pi$
$72$	−2.72545	−0.321198
$73$	5.27470	0.617357	0.308678	−	0.951166i	$-0.400113\pi$
$73$	5.27470	0.617357	0.308678	+	0.951166i	$0.400113\pi$
$74$	−5.74989	−0.668411
$75$	1.62817	0.188005
$76$	−6.02426	−0.691030
$77$	−4.63916	−0.528681
$78$	−2.68991	−0.304573
$79$	11.0761	1.24615	0.623077	−	0.782160i	$-0.285882\pi$
$79$	11.0761	1.24615	0.623077	+	0.782160i	$0.285882\pi$
$80$	1.37573	0.153812
$81$	6.60444	0.733827
$82$	−0.0599683	−0.00662239
$83$	−6.40447	−0.702982	−0.351491	−	0.936191i	$-0.614325\pi$
$83$	−6.40447	−0.702982	−0.351491	+	0.936191i	$0.614325\pi$
$84$	2.05687	0.224423
$85$	−4.39891	−0.477128
$86$	−9.15869	−0.987607
$87$	2.55449	0.273870
$88$	1.18179	0.125980
$89$	6.10024	0.646624	0.323312	−	0.946292i	$-0.395204\pi$
$89$	6.10024	0.646624	0.323312	+	0.946292i	$0.395204\pi$
$90$	−3.74949	−0.395231
$91$	−20.1524	−2.11255
$92$	8.56991	0.893475
$93$	−3.13946	−0.325547
$94$	5.61143	0.578775
$95$	−8.28777	−0.850307
$96$	−0.523973	−0.0534778
$97$	7.36178	0.747476	0.373738	−	0.927534i	$-0.378076\pi$
$97$	7.36178	0.747476	0.373738	+	0.927534i	$0.378076\pi$
$98$	8.40972	0.849510
$99$	−3.22092	−0.323715
$100$	−3.10736	−0.310736
$101$	−10.8327	−1.07790	−0.538948	−	0.842339i	$-0.681178\pi$
$101$	−10.8327	−1.07790	−0.538948	+	0.842339i	$0.681178\pi$
$102$	1.67541	0.165890
$103$	−16.1688	−1.59315	−0.796577	−	0.604537i	$-0.793358\pi$
$103$	−16.1688	−1.59315	−0.796577	+	0.604537i	$0.793358\pi$
$104$	5.13369	0.503399
$105$	2.82970	0.276150
$106$	−12.3956	−1.20397
$107$	−15.2351	−1.47284	−0.736418	−	0.676527i	$-0.763484\pi$
$107$	−15.2351	−1.47284	−0.736418	+	0.676527i	$0.763484\pi$
$108$	2.99998	0.288674
$109$	−6.19609	−0.593478	−0.296739	−	0.954959i	$-0.595899\pi$
$109$	−6.19609	−0.593478	−0.296739	+	0.954959i	$0.595899\pi$
$110$	1.62583	0.155017
$111$	3.01279	0.285961
$112$	−3.92552	−0.370927
$113$	1.07314	0.100952	0.0504761	−	0.998725i	$-0.483926\pi$
$113$	1.07314	0.100952	0.0504761	+	0.998725i	$0.483926\pi$
$114$	3.15655	0.295638
$115$	11.7899	1.09941
$116$	−4.87522	−0.452653
$117$	−13.9916	−1.29353
$118$	−4.93905	−0.454676
$119$	12.5519	1.15063
$120$	−0.720847	−0.0658040
$121$	−9.60336	−0.873033
$122$	−7.66203	−0.693688
$123$	0.0314218	0.00283321
$124$	5.99164	0.538065
$125$	−11.1536	−0.997605
$126$	10.6988	0.953127
$127$	−16.6872	−1.48075	−0.740374	−	0.672195i	$-0.765352\pi$
$127$	−16.6872	−1.48075	−0.740374	+	0.672195i	$0.765352\pi$
$128$	1.00000	0.0883883
$129$	4.79891	0.422521
$130$	7.06258	0.619429
$131$	8.06049	0.704248	0.352124	−	0.935953i	$-0.385460\pi$
$131$	8.06049	0.704248	0.352124	+	0.935953i	$0.385460\pi$
$132$	−0.619228	−0.0538969
$133$	23.6484	2.05057
$134$	−6.06824	−0.524216
$135$	4.12717	0.355211
$136$	−3.19750	−0.274184
$137$	−17.9832	−1.53641	−0.768206	−	0.640203i	$-0.778850\pi$
$137$	−17.9832	−1.53641	−0.768206	+	0.640203i	$0.778850\pi$
$138$	−4.49040	−0.382249
$139$	10.3067	0.874203	0.437101	−	0.899412i	$-0.356005\pi$
$139$	10.3067	0.874203	0.437101	+	0.899412i	$0.356005\pi$
$140$	−5.40047	−0.456423
$141$	−2.94024	−0.247613
$142$	−14.2196	−1.19328
$143$	6.06696	0.507345
$144$	−2.72545	−0.227121
$145$	−6.70700	−0.556986
$146$	5.27470	0.436537
$147$	−4.40647	−0.363439
$148$	−5.74989	−0.472638
$149$	4.71743	0.386467	0.193234	−	0.981153i	$-0.438103\pi$
$149$	4.71743	0.386467	0.193234	+	0.981153i	$0.438103\pi$
$150$	1.62817	0.132940
$151$	3.85978	0.314105	0.157052	−	0.987590i	$-0.449801\pi$
$151$	3.85978	0.314105	0.157052	+	0.987590i	$0.449801\pi$
$152$	−6.02426	−0.488632
$153$	8.71464	0.704537
$154$	−4.63916	−0.373834
$155$	8.24289	0.662085
$156$	−2.68991	−0.215366
$157$	8.43344	0.673062	0.336531	−	0.941672i	$-0.390746\pi$
$157$	8.43344	0.673062	0.336531	+	0.941672i	$0.390746\pi$
$158$	11.0761	0.881164
$159$	6.49497	0.515084
$160$	1.37573	0.108761
$161$	−33.6414	−2.65131
$162$	6.60444	0.518894
$163$	16.9204	1.32530	0.662652	−	0.748927i	$-0.269431\pi$
$163$	16.9204	1.32530	0.662652	+	0.748927i	$0.269431\pi$
$164$	−0.0599683	−0.00468274
$165$	−0.851892	−0.0663197
$166$	−6.40447	−0.497083
$167$	9.33795	0.722592	0.361296	−	0.932451i	$-0.382334\pi$
$167$	9.33795	0.722592	0.361296	+	0.932451i	$0.382334\pi$
$168$	2.05687	0.158691
$169$	13.3547	1.02729
$170$	−4.39891	−0.337381
$171$	16.4188	1.25558
$172$	−9.15869	−0.698344
$173$	−16.9923	−1.29190	−0.645950	−	0.763380i	$-0.723538\pi$
$173$	−16.9923	−1.29190	−0.645950	+	0.763380i	$0.723538\pi$
$174$	2.55449	0.193655
$175$	12.1980	0.922083
$176$	1.18179	0.0890810
$177$	2.58793	0.194521
$178$	6.10024	0.457232
$179$	9.10508	0.680546	0.340273	−	0.940327i	$-0.389481\pi$
$179$	9.10508	0.680546	0.340273	+	0.940327i	$0.389481\pi$
$180$	−3.74949	−0.279471
$181$	−21.4554	−1.59477	−0.797385	−	0.603471i	$-0.793784\pi$
$181$	−21.4554	−1.59477	−0.797385	+	0.603471i	$0.793784\pi$
$182$	−20.1524	−1.49380
$183$	4.01470	0.296775
$184$	8.56991	0.631782
$185$	−7.91030	−0.581577
$186$	−3.13946	−0.230196
$187$	−3.77879	−0.276332
$188$	5.61143	0.409256
$189$	−11.7765	−0.856614
$190$	−8.28777	−0.601258
$191$	18.9455	1.37085	0.685426	−	0.728142i	$-0.259616\pi$
$191$	18.9455	1.37085	0.685426	+	0.728142i	$0.259616\pi$
$192$	−0.523973	−0.0378145
$193$	17.5704	1.26475	0.632374	−	0.774664i	$-0.282081\pi$
$193$	17.5704	1.26475	0.632374	+	0.774664i	$0.282081\pi$
$194$	7.36178	0.528545
$195$	−3.70060	−0.265006
$196$	8.40972	0.600694
$197$	−13.2054	−0.940844	−0.470422	−	0.882442i	$-0.655898\pi$
$197$	−13.2054	−0.940844	−0.470422	+	0.882442i	$0.655898\pi$
$198$	−3.22092	−0.228901
$199$	19.8396	1.40639	0.703195	−	0.710997i	$-0.251756\pi$
$199$	19.8396	1.40639	0.703195	+	0.710997i	$0.251756\pi$
$200$	−3.10736	−0.219724
$201$	3.17959	0.224271
$202$	−10.8327	−0.762188
$203$	19.1378	1.34321
$204$	1.67541	0.117302
$205$	−0.0825003	−0.00576207
$206$	−16.1688	−1.12653
$207$	−23.3569	−1.62342
$208$	5.13369	0.355957
$209$	−7.11943	−0.492461
$210$	2.82970	0.195268
$211$	0.690640	0.0475456	0.0237728	−	0.999717i	$-0.492432\pi$
$211$	0.690640	0.0475456	0.0237728	+	0.999717i	$0.492432\pi$
$212$	−12.3956	−0.851334
$213$	7.45069	0.510513
$214$	−15.2351	−1.04145
$215$	−12.5999	−0.859307
$216$	2.99998	0.204123
$217$	−23.5203	−1.59666
$218$	−6.19609	−0.419652
$219$	−2.76380	−0.186760
$220$	1.62583	0.109614
$221$	−16.4150	−1.10419
$222$	3.01279	0.202205
$223$	−3.47860	−0.232944	−0.116472	−	0.993194i	$-0.537159\pi$
$223$	−3.47860	−0.232944	−0.116472	+	0.993194i	$0.537159\pi$
$224$	−3.92552	−0.262285
$225$	8.46896	0.564598
$226$	1.07314	0.0713839
$227$	24.8143	1.64698	0.823492	−	0.567328i	$-0.192023\pi$
$227$	24.8143	1.64698	0.823492	+	0.567328i	$0.192023\pi$
$228$	3.15655	0.209048
$229$	−23.5415	−1.55566	−0.777832	−	0.628472i	$-0.783681\pi$
$229$	−23.5415	−1.55566	−0.777832	+	0.628472i	$0.783681\pi$
$230$	11.7899	0.777403
$231$	2.43079	0.159935
$232$	−4.87522	−0.320074
$233$	18.9626	1.24228	0.621142	−	0.783698i	$-0.286669\pi$
$233$	18.9626	1.24228	0.621142	+	0.783698i	$0.286669\pi$
$234$	−13.9916	−0.914661
$235$	7.71983	0.503586
$236$	−4.93905	−0.321505
$237$	−5.80356	−0.376982
$238$	12.5519	0.813616
$239$	−5.86052	−0.379086	−0.189543	−	0.981872i	$-0.560701\pi$
$239$	−5.86052	−0.379086	−0.189543	+	0.981872i	$0.560701\pi$
$240$	−0.720847	−0.0465305
$241$	−26.8667	−1.73064	−0.865319	−	0.501222i	$-0.832884\pi$
$241$	−26.8667	−1.73064	−0.865319	+	0.501222i	$0.832884\pi$
$242$	−9.60336	−0.617328
$243$	−12.4605	−0.799342
$244$	−7.66203	−0.490511
$245$	11.5695	0.739150
$246$	0.0314218	0.00200338
$247$	−30.9267	−1.96782
$248$	5.99164	0.380469
$249$	3.35577	0.212663
$250$	−11.1536	−0.705413
$251$	−21.9948	−1.38830	−0.694149	−	0.719831i	$-0.744219\pi$
$251$	−21.9948	−1.38830	−0.694149	+	0.719831i	$0.744219\pi$
$252$	10.6988	0.673962
$253$	10.1279	0.636734
$254$	−16.6872	−1.04705
$255$	2.30491	0.144339
$256$	1.00000	0.0625000
$257$	−17.5043	−1.09189	−0.545945	−	0.837821i	$-0.683829\pi$
$257$	−17.5043	−1.09189	−0.545945	+	0.837821i	$0.683829\pi$
$258$	4.79891	0.298767
$259$	22.5713	1.40251
$260$	7.06258	0.438003
$261$	13.2872	0.822456
$262$	8.06049	0.497979
$263$	−9.89436	−0.610113	−0.305056	−	0.952334i	$-0.598675\pi$
$263$	−9.89436	−0.610113	−0.305056	+	0.952334i	$0.598675\pi$
$264$	−0.619228	−0.0381109
$265$	−17.0530	−1.04756
$266$	23.6484	1.44997
$267$	−3.19636	−0.195614
$268$	−6.06824	−0.370677
$269$	18.7236	1.14160	0.570798	−	0.821091i	$-0.306634\pi$
$269$	18.7236	1.14160	0.570798	+	0.821091i	$0.306634\pi$
$270$	4.12717	0.251172
$271$	29.2208	1.77503	0.887517	−	0.460774i	$-0.152428\pi$
$271$	29.2208	1.77503	0.887517	+	0.460774i	$0.152428\pi$
$272$	−3.19750	−0.193877
$273$	10.5593	0.639079
$274$	−17.9832	−1.08641
$275$	−3.67226	−0.221446
$276$	−4.49040	−0.270291
$277$	1.79245	0.107698	0.0538489	−	0.998549i	$-0.482851\pi$
$277$	1.79245	0.107698	0.0538489	+	0.998549i	$0.482851\pi$
$278$	10.3067	0.618155
$279$	−16.3299	−0.977647
$280$	−5.40047	−0.322740
$281$	31.5434	1.88172	0.940861	−	0.338793i	$-0.110019\pi$
$281$	31.5434	1.88172	0.940861	+	0.338793i	$0.110019\pi$
$282$	−2.94024	−0.175089
$283$	13.1519	0.781801	0.390901	−	0.920433i	$-0.372164\pi$
$283$	13.1519	0.781801	0.390901	+	0.920433i	$0.372164\pi$
$284$	−14.2196	−0.843778
$285$	4.34257	0.257232
$286$	6.06696	0.358747
$287$	0.235407	0.0138956
$288$	−2.72545	−0.160599
$289$	−6.77598	−0.398587
$290$	−6.70700	−0.393849
$291$	−3.85738	−0.226124
$292$	5.27470	0.308678
$293$	−14.1628	−0.827402	−0.413701	−	0.910413i	$-0.635764\pi$
$293$	−14.1628	−0.827402	−0.413701	+	0.910413i	$0.635764\pi$
$294$	−4.40647	−0.256990
$295$	−6.79481	−0.395609
$296$	−5.74989	−0.334205
$297$	3.54536	0.205723
$298$	4.71743	0.273273
$299$	43.9952	2.54431
$300$	1.62817	0.0940027
$301$	35.9527	2.07228
$302$	3.85978	0.222106
$303$	5.67606	0.326081
$304$	−6.02426	−0.345515
$305$	−10.5409	−0.603571
$306$	8.71464	0.498183
$307$	23.5037	1.34143	0.670714	−	0.741716i	$-0.265988\pi$
$307$	23.5037	1.34143	0.670714	+	0.741716i	$0.265988\pi$
$308$	−4.63916	−0.264340
$309$	8.47199	0.481955
$310$	8.24289	0.468165
$311$	5.78880	0.328253	0.164126	−	0.986439i	$-0.447519\pi$
$311$	5.78880	0.328253	0.164126	+	0.986439i	$0.447519\pi$
$312$	−2.68991	−0.152286
$313$	9.91048	0.560174	0.280087	−	0.959975i	$-0.409637\pi$
$313$	9.91048	0.560174	0.280087	+	0.959975i	$0.409637\pi$
$314$	8.43344	0.475926
$315$	14.7187	0.829306
$316$	11.0761	0.623077
$317$	−17.8757	−1.00400	−0.502000	−	0.864868i	$-0.667402\pi$
$317$	−17.8757	−1.00400	−0.502000	+	0.864868i	$0.667402\pi$
$318$	6.49497	0.364220
$319$	−5.76151	−0.322582
$320$	1.37573	0.0769058
$321$	7.98280	0.445557
$322$	−33.6414	−1.87476
$323$	19.2626	1.07180
$324$	6.60444	0.366914
$325$	−15.9522	−0.884870
$326$	16.9204	0.937132
$327$	3.24659	0.179537
$328$	−0.0599683	−0.00331119
$329$	−22.0278	−1.21443
$330$	−0.851892	−0.0468951
$331$	−30.1233	−1.65572	−0.827862	−	0.560931i	$-0.810443\pi$
$331$	−30.1233	−1.65572	−0.827862	+	0.560931i	$0.810443\pi$
$332$	−6.40447	−0.351491
$333$	15.6710	0.858768
$334$	9.33795	0.510950
$335$	−8.34827	−0.456115
$336$	2.05687	0.112211
$337$	30.2872	1.64985	0.824925	−	0.565243i	$-0.191218\pi$
$337$	30.2872	1.64985	0.824925	+	0.565243i	$0.191218\pi$
$338$	13.3547	0.726402
$339$	−0.562294	−0.0305396
$340$	−4.39891	−0.238564
$341$	7.08088	0.383451
$342$	16.4188	0.887829
$343$	−5.53389	−0.298802
$344$	−9.15869	−0.493804
$345$	−6.17759	−0.332591
$346$	−16.9923	−0.913511
$347$	23.7309	1.27394	0.636971	−	0.770888i	$-0.280187\pi$
$347$	23.7309	1.27394	0.636971	+	0.770888i	$0.280187\pi$
$348$	2.55449	0.136935
$349$	−9.72527	−0.520582	−0.260291	−	0.965530i	$-0.583818\pi$
$349$	−9.72527	−0.520582	−0.260291	+	0.965530i	$0.583818\pi$
$350$	12.1980	0.652011
$351$	15.4010	0.822043
$352$	1.18179	0.0629898
$353$	21.5995	1.14962	0.574812	−	0.818286i	$-0.305075\pi$
$353$	21.5995	1.14962	0.574812	+	0.818286i	$0.305075\pi$
$354$	2.58793	0.137547
$355$	−19.5624	−1.03826
$356$	6.10024	0.323312
$357$	−6.57684	−0.348083
$358$	9.10508	0.481218
$359$	−0.0920868	−0.00486015	−0.00243008	−	0.999997i	$-0.500774\pi$
$359$	−0.0920868	−0.00486015	−0.00243008	+	0.999997i	$0.500774\pi$
$360$	−3.74949	−0.197616
$361$	17.2917	0.910090
$362$	−21.4554	−1.12767
$363$	5.03191	0.264107
$364$	−20.1524	−1.05627
$365$	7.25657	0.379826
$366$	4.01470	0.209852
$367$	8.73122	0.455766	0.227883	−	0.973689i	$-0.426820\pi$
$367$	8.73122	0.455766	0.227883	+	0.973689i	$0.426820\pi$
$368$	8.56991	0.446738
$369$	0.163441	0.00850838
$370$	−7.91030	−0.411237
$371$	48.6592	2.52626
$372$	−3.13946	−0.162773
$373$	−1.37705	−0.0713008	−0.0356504	−	0.999364i	$-0.511350\pi$
$373$	−1.37705	−0.0713008	−0.0356504	+	0.999364i	$0.511350\pi$
$374$	−3.77879	−0.195396
$375$	5.84417	0.301791
$376$	5.61143	0.289387
$377$	−25.0279	−1.28900
$378$	−11.7765	−0.605718
$379$	−21.8176	−1.12069	−0.560347	−	0.828258i	$-0.689332\pi$
$379$	−21.8176	−1.12069	−0.560347	+	0.828258i	$0.689332\pi$
$380$	−8.28777	−0.425154
$381$	8.74364	0.447950
$382$	18.9455	0.969339
$383$	−30.2201	−1.54417	−0.772087	−	0.635516i	$-0.780787\pi$
$383$	−30.2201	−1.54417	−0.772087	+	0.635516i	$0.780787\pi$
$384$	−0.523973	−0.0267389
$385$	−6.38224	−0.325269
$386$	17.5704	0.894311
$387$	24.9616	1.26887
$388$	7.36178	0.373738
$389$	19.0026	0.963472	0.481736	−	0.876316i	$-0.340006\pi$
$389$	19.0026	0.963472	0.481736	+	0.876316i	$0.340006\pi$
$390$	−3.70060	−0.187387
$391$	−27.4023	−1.38579
$392$	8.40972	0.424755
$393$	−4.22348	−0.213046
$394$	−13.2054	−0.665277
$395$	15.2377	0.766691
$396$	−3.22092	−0.161857
$397$	−16.9366	−0.850026	−0.425013	−	0.905187i	$-0.639730\pi$
$397$	−16.9366	−0.850026	−0.425013	+	0.905187i	$0.639730\pi$
$398$	19.8396	0.994467
$399$	−12.3911	−0.620331
$400$	−3.10736	−0.155368
$401$	−15.1390	−0.756007	−0.378004	−	0.925804i	$-0.623389\pi$
$401$	−15.1390	−0.756007	−0.378004	+	0.925804i	$0.623389\pi$
$402$	3.17959	0.158584
$403$	30.7592	1.53222
$404$	−10.8327	−0.538948
$405$	9.08595	0.451484
$406$	19.1378	0.949793
$407$	−6.79518	−0.336825
$408$	1.67541	0.0829449
$409$	3.67768	0.181850	0.0909248	−	0.995858i	$-0.471018\pi$
$409$	3.67768	0.181850	0.0909248	+	0.995858i	$0.471018\pi$
$410$	−0.0825003	−0.00407440
$411$	9.42273	0.464789
$412$	−16.1688	−0.796577
$413$	19.3883	0.954037
$414$	−23.3569	−1.14793
$415$	−8.81084	−0.432507
$416$	5.13369	0.251700
$417$	−5.40043	−0.264460
$418$	−7.11943	−0.348223
$419$	15.3659	0.750674	0.375337	−	0.926888i	$-0.377527\pi$
$419$	15.3659	0.750674	0.375337	+	0.926888i	$0.377527\pi$
$420$	2.82970	0.138075
$421$	−10.5228	−0.512852	−0.256426	−	0.966564i	$-0.582545\pi$
$421$	−10.5228	−0.512852	−0.256426	+	0.966564i	$0.582545\pi$
$422$	0.690640	0.0336198
$423$	−15.2937	−0.743605
$424$	−12.3956	−0.601984
$425$	9.93579	0.481957
$426$	7.45069	0.360987
$427$	30.0775	1.45555
$428$	−15.2351	−0.736418
$429$	−3.17892	−0.153480
$430$	−12.5999	−0.607622
$431$	−18.6853	−0.900037	−0.450018	−	0.893019i	$-0.648583\pi$
$431$	−18.6853	−0.900037	−0.450018	+	0.893019i	$0.648583\pi$
$432$	2.99998	0.144337
$433$	1.60828	0.0772889	0.0386444	−	0.999253i	$-0.487696\pi$
$433$	1.60828	0.0772889	0.0386444	+	0.999253i	$0.487696\pi$
$434$	−23.5203	−1.12901
$435$	3.51429	0.168497
$436$	−6.19609	−0.296739
$437$	−51.6274	−2.46967
$438$	−2.76380	−0.132059
$439$	19.6362	0.937183	0.468591	−	0.883415i	$-0.344762\pi$
$439$	19.6362	0.937183	0.468591	+	0.883415i	$0.344762\pi$
$440$	1.62583	0.0775085
$441$	−22.9203	−1.09144
$442$	−16.4150	−0.780781
$443$	0.618634	0.0293922	0.0146961	−	0.999892i	$-0.495322\pi$
$443$	0.618634	0.0293922	0.0146961	+	0.999892i	$0.495322\pi$
$444$	3.01279	0.142981
$445$	8.39230	0.397833
$446$	−3.47860	−0.164717
$447$	−2.47181	−0.116912
$448$	−3.92552	−0.185463
$449$	−16.2897	−0.768757	−0.384378	−	0.923176i	$-0.625584\pi$
$449$	−16.2897	−0.768757	−0.384378	+	0.923176i	$0.625584\pi$
$450$	8.46896	0.399231
$451$	−0.0708701	−0.00333714
$452$	1.07314	0.0504761
$453$	−2.02242	−0.0950217
$454$	24.8143	1.16459
$455$	−27.7243	−1.29974
$456$	3.15655	0.147819
$457$	−30.3988	−1.42200	−0.710998	−	0.703194i	$-0.751756\pi$
$457$	−30.3988	−1.42200	−0.710998	+	0.703194i	$0.751756\pi$
$458$	−23.5415	−1.10002
$459$	−9.59245	−0.447737
$460$	11.7899	0.549707
$461$	6.59391	0.307109	0.153555	−	0.988140i	$-0.450928\pi$
$461$	6.59391	0.307109	0.153555	+	0.988140i	$0.450928\pi$
$462$	2.43079	0.113091
$463$	9.88876	0.459570	0.229785	−	0.973241i	$-0.426198\pi$
$463$	9.88876	0.459570	0.229785	+	0.973241i	$0.426198\pi$
$464$	−4.87522	−0.226327
$465$	−4.31905	−0.200291
$466$	18.9626	0.878427
$467$	−41.2671	−1.90961	−0.954806	−	0.297230i	$-0.903937\pi$
$467$	−41.2671	−1.90961	−0.954806	+	0.297230i	$0.903937\pi$
$468$	−13.9916	−0.646763
$469$	23.8210	1.09995
$470$	7.71983	0.356089
$471$	−4.41890	−0.203612
$472$	−4.93905	−0.227338
$473$	−10.8237	−0.497674
$474$	−5.80356	−0.266566
$475$	18.7195	0.858912
$476$	12.5519	0.575314
$477$	33.7836	1.54685
$478$	−5.86052	−0.268054
$479$	−2.05627	−0.0939533	−0.0469767	−	0.998896i	$-0.514959\pi$
$479$	−2.05627	−0.0939533	−0.0469767	+	0.998896i	$0.514959\pi$
$480$	−0.720847	−0.0329020
$481$	−29.5181	−1.34591
$482$	−26.8667	−1.22375
$483$	17.6272	0.802065
$484$	−9.60336	−0.436517
$485$	10.1278	0.459882
$486$	−12.4605	−0.565220
$487$	−23.1104	−1.04723	−0.523617	−	0.851954i	$-0.675418\pi$
$487$	−23.1104	−1.04723	−0.523617	+	0.851954i	$0.675418\pi$
$488$	−7.66203	−0.346844
$489$	−8.86582	−0.400926
$490$	11.5695	0.522658
$491$	−19.5102	−0.880485	−0.440242	−	0.897879i	$-0.645107\pi$
$491$	−19.5102	−0.880485	−0.440242	+	0.897879i	$0.645107\pi$
$492$	0.0314218	0.00141660
$493$	15.5885	0.702072
$494$	−30.9267	−1.39146
$495$	−4.43113	−0.199164
$496$	5.99164	0.269033
$497$	55.8194	2.50384
$498$	3.35577	0.150376
$499$	38.6397	1.72975	0.864875	−	0.501988i	$-0.167398\pi$
$499$	38.6397	1.72975	0.864875	+	0.501988i	$0.167398\pi$
$500$	−11.1536	−0.498802
$501$	−4.89284	−0.218596
$502$	−21.9948	−0.981675
$503$	36.5846	1.63123	0.815613	−	0.578597i	$-0.196400\pi$
$503$	36.5846	1.63123	0.815613	+	0.578597i	$0.196400\pi$
$504$	10.6988	0.476563
$505$	−14.9029	−0.663171
$506$	10.1279	0.450239
$507$	−6.99753	−0.310771
$508$	−16.6872	−0.740374
$509$	−40.3607	−1.78896	−0.894478	−	0.447111i	$-0.852453\pi$
$509$	−40.3607	−1.78896	−0.894478	+	0.447111i	$0.852453\pi$
$510$	2.30491	0.102063
$511$	−20.7059	−0.915977
$512$	1.00000	0.0441942
$513$	−18.0727	−0.797928
$514$	−17.5043	−0.772082
$515$	−22.2439	−0.980182
$516$	4.79891	0.211260
$517$	6.63155	0.291655
$518$	22.5713	0.991726
$519$	8.90350	0.390820
$520$	7.06258	0.309715
$521$	−33.6224	−1.47302	−0.736511	−	0.676425i	$-0.763528\pi$
$521$	−33.6224	−1.47302	−0.736511	+	0.676425i	$0.763528\pi$
$522$	13.2872	0.581564
$523$	19.3936	0.848024	0.424012	−	0.905657i	$-0.360621\pi$
$523$	19.3936	0.848024	0.424012	+	0.905657i	$0.360621\pi$
$524$	8.06049	0.352124
$525$	−6.39143	−0.278945
$526$	−9.89436	−0.431415
$527$	−19.1583	−0.834548
$528$	−0.619228	−0.0269485
$529$	50.4434	2.19319
$530$	−17.0530	−0.740737
$531$	13.4611	0.584163
$532$	23.6484	1.02529
$533$	−0.307858	−0.0133348
$534$	−3.19636	−0.138320
$535$	−20.9595	−0.906157
$536$	−6.06824	−0.262108
$537$	−4.77082	−0.205876
$538$	18.7236	0.807230
$539$	9.93855	0.428084
$540$	4.12717	0.177605
$541$	45.8977	1.97329	0.986647	−	0.162872i	$-0.0520758\pi$
$541$	45.8977	1.97329	0.986647	+	0.162872i	$0.0520758\pi$
$542$	29.2208	1.25514
$543$	11.2421	0.482444
$544$	−3.19750	−0.137092
$545$	−8.52416	−0.365135
$546$	10.5593	0.451897
$547$	−18.6835	−0.798850	−0.399425	−	0.916766i	$-0.630790\pi$
$547$	−18.6835	−0.798850	−0.399425	+	0.916766i	$0.630790\pi$
$548$	−17.9832	−0.768206
$549$	20.8825	0.891244
$550$	−3.67226	−0.156586
$551$	29.3696	1.25119
$552$	−4.49040	−0.191124
$553$	−43.4793	−1.84893
$554$	1.79245	0.0761539
$555$	4.14479	0.175936
$556$	10.3067	0.437101
$557$	−2.04224	−0.0865327	−0.0432663	−	0.999064i	$-0.513776\pi$
$557$	−2.04224	−0.0865327	−0.0432663	+	0.999064i	$0.513776\pi$
$558$	−16.3299	−0.691301
$559$	−47.0179	−1.98864
$560$	−5.40047	−0.228211
$561$	1.97998	0.0835950
$562$	31.5434	1.33058
$563$	1.25388	0.0528448	0.0264224	−	0.999651i	$-0.491589\pi$
$563$	1.25388	0.0528448	0.0264224	+	0.999651i	$0.491589\pi$
$564$	−2.94024	−0.123806
$565$	1.47635	0.0621104
$566$	13.1519	0.552817
$567$	−25.9259	−1.08879
$568$	−14.2196	−0.596641
$569$	11.0833	0.464638	0.232319	−	0.972640i	$-0.425369\pi$
$569$	11.0833	0.464638	0.232319	+	0.972640i	$0.425369\pi$
$570$	4.34257	0.181890
$571$	−17.7799	−0.744066	−0.372033	−	0.928219i	$-0.621339\pi$
$571$	−17.7799	−0.744066	−0.372033	+	0.928219i	$0.621339\pi$
$572$	6.06696	0.253672
$573$	−9.92696	−0.414705
$574$	0.235407	0.00982569
$575$	−26.6298	−1.11054
$576$	−2.72545	−0.113561
$577$	37.8430	1.57543	0.787713	−	0.616042i	$-0.211265\pi$
$577$	37.8430	1.57543	0.787713	+	0.616042i	$0.211265\pi$
$578$	−6.77598	−0.281844
$579$	−9.20644	−0.382606
$580$	−6.70700	−0.278493
$581$	25.1409	1.04302
$582$	−3.85738	−0.159893
$583$	−14.6491	−0.606702
$584$	5.27470	0.218269
$585$	−19.2487	−0.795837
$586$	−14.1628	−0.585062
$587$	22.7196	0.937739	0.468869	−	0.883268i	$-0.344662\pi$
$587$	22.7196	0.937739	0.468869	+	0.883268i	$0.344662\pi$
$588$	−4.40647	−0.181720
$589$	−36.0952	−1.48728
$590$	−6.79481	−0.279738
$591$	6.91926	0.284620
$592$	−5.74989	−0.236319
$593$	−18.7757	−0.771025	−0.385512	−	0.922703i	$-0.625975\pi$
$593$	−18.7757	−0.771025	−0.385512	+	0.922703i	$0.625975\pi$
$594$	3.54536	0.145468
$595$	17.2680	0.707919
$596$	4.71743	0.193234
$597$	−10.3954	−0.425455
$598$	43.9952	1.79910
$599$	9.63651	0.393737	0.196868	−	0.980430i	$-0.436923\pi$
$599$	9.63651	0.393737	0.196868	+	0.980430i	$0.436923\pi$
$600$	1.62817	0.0664699
$601$	0.573332	0.0233867	0.0116934	−	0.999932i	$-0.496278\pi$
$601$	0.573332	0.0233867	0.0116934	+	0.999932i	$0.496278\pi$
$602$	35.9527	1.46532
$603$	16.5387	0.673507
$604$	3.85978	0.157052
$605$	−13.2117	−0.537130
$606$	5.67606	0.230574
$607$	0.862575	0.0350108	0.0175054	−	0.999847i	$-0.494428\pi$
$607$	0.862575	0.0350108	0.0175054	+	0.999847i	$0.494428\pi$
$608$	−6.02426	−0.244316
$609$	−10.0277	−0.406343
$610$	−10.5409	−0.426789
$611$	28.8073	1.16542
$612$	8.71464	0.352268
$613$	−22.9008	−0.924956	−0.462478	−	0.886631i	$-0.653040\pi$
$613$	−22.9008	−0.924956	−0.462478	+	0.886631i	$0.653040\pi$
$614$	23.5037	0.948532
$615$	0.0432280	0.00174312
$616$	−4.63916	−0.186917
$617$	−9.95055	−0.400594	−0.200297	−	0.979735i	$-0.564191\pi$
$617$	−9.95055	−0.400594	−0.200297	+	0.979735i	$0.564191\pi$
$618$	8.47199	0.340794
$619$	7.45304	0.299563	0.149782	−	0.988719i	$-0.452143\pi$
$619$	7.45304	0.299563	0.149782	+	0.988719i	$0.452143\pi$
$620$	8.24289	0.331042
$621$	25.7096	1.03169
$622$	5.78880	0.232110
$623$	−23.9466	−0.959402
$624$	−2.68991	−0.107683
$625$	0.192495	0.00769980
$626$	9.91048	0.396103
$627$	3.73039	0.148978
$628$	8.43344	0.336531
$629$	18.3853	0.733069
$630$	14.7187	0.586408
$631$	24.3886	0.970896	0.485448	−	0.874265i	$-0.338656\pi$
$631$	24.3886	0.970896	0.485448	+	0.874265i	$0.338656\pi$
$632$	11.0761	0.440582
$633$	−0.361877	−0.0143833
$634$	−17.8757	−0.709935
$635$	−22.9571	−0.911025
$636$	6.49497	0.257542
$637$	43.1729	1.71057
$638$	−5.76151	−0.228100
$639$	38.7548	1.53312
$640$	1.37573	0.0543806
$641$	−8.16222	−0.322388	−0.161194	−	0.986923i	$-0.551535\pi$
$641$	−8.16222	−0.322388	−0.161194	+	0.986923i	$0.551535\pi$
$642$	7.98280	0.315056
$643$	−12.8671	−0.507431	−0.253715	−	0.967279i	$-0.581653\pi$
$643$	−12.8671	−0.507431	−0.253715	+	0.967279i	$0.581653\pi$
$644$	−33.6414	−1.32566
$645$	6.60202	0.259954
$646$	19.2626	0.757876
$647$	11.3268	0.445302	0.222651	−	0.974898i	$-0.428529\pi$
$647$	11.3268	0.445302	0.222651	+	0.974898i	$0.428529\pi$
$648$	6.60444	0.259447
$649$	−5.83693	−0.229120
$650$	−15.9522	−0.625697
$651$	12.3240	0.483016
$652$	16.9204	0.662652
$653$	−41.3271	−1.61725	−0.808626	−	0.588323i	$-0.799789\pi$
$653$	−41.3271	−1.61725	−0.808626	+	0.588323i	$0.799789\pi$
$654$	3.24659	0.126952
$655$	11.0891	0.433286
$656$	−0.0599683	−0.00234137
$657$	−14.3759	−0.560859
$658$	−22.0278	−0.858733
$659$	28.9178	1.12648	0.563239	−	0.826294i	$-0.309555\pi$
$659$	28.9178	1.12648	0.563239	+	0.826294i	$0.309555\pi$
$660$	−0.851892	−0.0331599
$661$	−0.780612	−0.0303623	−0.0151811	−	0.999885i	$-0.504832\pi$
$661$	−0.780612	−0.0303623	−0.0151811	+	0.999885i	$0.504832\pi$
$662$	−30.1233	−1.17077
$663$	8.60101	0.334035
$664$	−6.40447	−0.248542
$665$	32.5338	1.26161
$666$	15.6710	0.607240
$667$	−41.7802	−1.61774
$668$	9.33795	0.361296
$669$	1.82269	0.0704694
$670$	−8.34827	−0.322522
$671$	−9.05494	−0.349562
$672$	2.05687	0.0793454
$673$	29.1547	1.12383	0.561915	−	0.827195i	$-0.310065\pi$
$673$	29.1547	1.12383	0.561915	+	0.827195i	$0.310065\pi$
$674$	30.2872	1.16662
$675$	−9.32203	−0.358805
$676$	13.3547	0.513644
$677$	−30.3074	−1.16481	−0.582405	−	0.812899i	$-0.697888\pi$
$677$	−30.3074	−1.16481	−0.582405	+	0.812899i	$0.697888\pi$
$678$	−0.562294	−0.0215948
$679$	−28.8988	−1.10904
$680$	−4.39891	−0.168690
$681$	−13.0020	−0.498239
$682$	7.08088	0.271141
$683$	−32.1451	−1.23000	−0.614999	−	0.788528i	$-0.710844\pi$
$683$	−32.1451	−1.23000	−0.614999	+	0.788528i	$0.710844\pi$
$684$	16.4188	0.627790
$685$	−24.7401	−0.945271
$686$	−5.53389	−0.211285
$687$	12.3351	0.470613
$688$	−9.15869	−0.349172
$689$	−63.6352	−2.42431
$690$	−6.17759	−0.235177
$691$	−21.5871	−0.821210	−0.410605	−	0.911813i	$-0.634683\pi$
$691$	−21.5871	−0.821210	−0.410605	+	0.911813i	$0.634683\pi$
$692$	−16.9923	−0.645950
$693$	12.6438	0.480298
$694$	23.7309	0.900813
$695$	14.1793	0.537850
$696$	2.55449	0.0968276
$697$	0.191749	0.00726300
$698$	−9.72527	−0.368107
$699$	−9.93591	−0.375811
$700$	12.1980	0.461042
$701$	41.9905	1.58596	0.792979	−	0.609248i	$-0.208529\pi$
$701$	41.9905	1.58596	0.792979	+	0.609248i	$0.208529\pi$
$702$	15.4010	0.581272
$703$	34.6388	1.30643
$704$	1.18179	0.0445405
$705$	−4.04498	−0.152343
$706$	21.5995	0.812906
$707$	42.5241	1.59928
$708$	2.58793	0.0972603
$709$	25.4593	0.956146	0.478073	−	0.878320i	$-0.341336\pi$
$709$	25.4593	0.956146	0.478073	+	0.878320i	$0.341336\pi$
$710$	−19.5624	−0.734162
$711$	−30.1873	−1.13211
$712$	6.10024	0.228616
$713$	51.3478	1.92299
$714$	−6.57684	−0.246132
$715$	8.34651	0.312142
$716$	9.10508	0.340273
$717$	3.07076	0.114679
$718$	−0.0920868	−0.00343665
$719$	−15.2987	−0.570546	−0.285273	−	0.958446i	$-0.592084\pi$
$719$	−15.2987	−0.570546	−0.285273	+	0.958446i	$0.592084\pi$
$720$	−3.74949	−0.139735
$721$	63.4708	2.36378
$722$	17.2917	0.643531
$723$	14.0774	0.523546
$724$	−21.4554	−0.797385
$725$	15.1491	0.562623
$726$	5.03191	0.186752
$727$	−19.9955	−0.741590	−0.370795	−	0.928715i	$-0.620915\pi$
$727$	−19.9955	−0.741590	−0.370795	+	0.928715i	$0.620915\pi$
$728$	−20.1524	−0.746898
$729$	−13.2844	−0.492013
$730$	7.25657	0.268578
$731$	29.2849	1.08314
$732$	4.01470	0.148388
$733$	30.5698	1.12912	0.564561	−	0.825391i	$-0.309045\pi$
$733$	30.5698	1.12912	0.564561	+	0.825391i	$0.309045\pi$
$734$	8.73122	0.322275
$735$	−6.06212	−0.223605
$736$	8.56991	0.315891
$737$	−7.17140	−0.264162
$738$	0.163441	0.00601634
$739$	47.8204	1.75910	0.879552	−	0.475803i	$-0.157843\pi$
$739$	47.8204	1.75910	0.879552	+	0.475803i	$0.157843\pi$
$740$	−7.91030	−0.290789
$741$	16.2047	0.595296
$742$	48.6592	1.78634
$743$	50.2238	1.84253	0.921266	−	0.388934i	$-0.127157\pi$
$743$	50.2238	1.84253	0.921266	+	0.388934i	$0.127157\pi$
$744$	−3.13946	−0.115098
$745$	6.48992	0.237772
$746$	−1.37705	−0.0504173
$747$	17.4551	0.638648
$748$	−3.77879	−0.138166
$749$	59.8058	2.18526
$750$	5.84417	0.213399
$751$	20.1877	0.736661	0.368330	−	0.929695i	$-0.379930\pi$
$751$	20.1877	0.736661	0.368330	+	0.929695i	$0.379930\pi$
$752$	5.61143	0.204628
$753$	11.5247	0.419983
$754$	−25.0279	−0.911461
$755$	5.31003	0.193252
$756$	−11.7765	−0.428307
$757$	25.7782	0.936926	0.468463	−	0.883483i	$-0.344808\pi$
$757$	25.7782	0.936926	0.468463	+	0.883483i	$0.344808\pi$
$758$	−21.8176	−0.792451
$759$	−5.30673	−0.192622
$760$	−8.28777	−0.300629
$761$	12.3840	0.448918	0.224459	−	0.974483i	$-0.427938\pi$
$761$	12.3840	0.448918	0.224459	+	0.974483i	$0.427938\pi$
$762$	8.74364	0.316749
$763$	24.3229	0.880548
$764$	18.9455	0.685426
$765$	11.9890	0.433464
$766$	−30.2201	−1.09190
$767$	−25.3555	−0.915535
$768$	−0.523973	−0.0189073
$769$	46.5310	1.67795	0.838975	−	0.544169i	$-0.183155\pi$
$769$	46.5310	1.67795	0.838975	+	0.544169i	$0.183155\pi$
$770$	−6.38224	−0.230000
$771$	9.17179	0.330314
$772$	17.5704	0.632374
$773$	−36.4440	−1.31080	−0.655401	−	0.755281i	$-0.727500\pi$
$773$	−36.4440	−1.31080	−0.655401	+	0.755281i	$0.727500\pi$
$774$	24.9616	0.897225
$775$	−18.6182	−0.668785
$776$	7.36178	0.264273
$777$	−11.8268	−0.424283
$778$	19.0026	0.681278
$779$	0.361265	0.0129436
$780$	−3.70060	−0.132503
$781$	−16.8046	−0.601317
$782$	−27.4023	−0.979905
$783$	−14.6256	−0.522676
$784$	8.40972	0.300347
$785$	11.6022	0.414099
$786$	−4.22348	−0.150647
$787$	−12.1300	−0.432389	−0.216195	−	0.976350i	$-0.569365\pi$
$787$	−12.1300	−0.432389	−0.216195	+	0.976350i	$0.569365\pi$
$788$	−13.2054	−0.470422
$789$	5.18438	0.184569
$790$	15.2377	0.542133
$791$	−4.21262	−0.149783
$792$	−3.22092	−0.114450
$793$	−39.3345	−1.39681
$794$	−16.9366	−0.601059
$795$	8.93534	0.316904
$796$	19.8396	0.703195
$797$	52.8468	1.87193	0.935964	−	0.352094i	$-0.114530\pi$
$797$	52.8468	1.87193	0.935964	+	0.352094i	$0.114530\pi$
$798$	−12.3911	−0.438641
$799$	−17.9426	−0.634762
$800$	−3.10736	−0.109862
$801$	−16.6259	−0.587448
$802$	−15.1390	−0.534578
$803$	6.23360	0.219979
$804$	3.17959	0.112136
$805$	−46.2815	−1.63121
$806$	30.7592	1.08345
$807$	−9.81064	−0.345351
$808$	−10.8327	−0.381094
$809$	10.3156	0.362676	0.181338	−	0.983421i	$-0.441957\pi$
$809$	10.3156	0.362676	0.181338	+	0.983421i	$0.441957\pi$
$810$	9.08595	0.319248
$811$	−38.7492	−1.36067	−0.680335	−	0.732901i	$-0.738166\pi$
$811$	−38.7492	−1.36067	−0.680335	+	0.732901i	$0.738166\pi$
$812$	19.1378	0.671605
$813$	−15.3109	−0.536977
$814$	−6.79518	−0.238171
$815$	23.2779	0.815389
$816$	1.67541	0.0586509
$817$	55.1743	1.93031
$818$	3.67768	0.128587
$819$	54.9244	1.91921
$820$	−0.0825003	−0.00288104
$821$	12.6607	0.441861	0.220930	−	0.975290i	$-0.429091\pi$
$821$	12.6607	0.441861	0.220930	+	0.975290i	$0.429091\pi$
$822$	9.42273	0.328656
$823$	48.7038	1.69771	0.848853	−	0.528629i	$-0.177294\pi$
$823$	48.7038	1.69771	0.848853	+	0.528629i	$0.177294\pi$
$824$	−16.1688	−0.563265
$825$	1.92417	0.0669908
$826$	19.3883	0.674606
$827$	−27.8261	−0.967609	−0.483804	−	0.875176i	$-0.660745\pi$
$827$	−27.8261	−0.967609	−0.483804	+	0.875176i	$0.660745\pi$
$828$	−23.3569	−0.811708
$829$	0.338334	0.0117508	0.00587541	−	0.999983i	$-0.498130\pi$
$829$	0.338334	0.0117508	0.00587541	+	0.999983i	$0.498130\pi$
$830$	−8.81084	−0.305829
$831$	−0.939195	−0.0325803
$832$	5.13369	0.177979
$833$	−26.8901	−0.931687
$834$	−5.40043	−0.187002
$835$	12.8465	0.444572
$836$	−7.11943	−0.246231
$837$	17.9748	0.621301
$838$	15.3659	0.530807
$839$	21.6572	0.747690	0.373845	−	0.927491i	$-0.378039\pi$
$839$	21.6572	0.747690	0.373845	+	0.927491i	$0.378039\pi$
$840$	2.82970	0.0976339
$841$	−5.23221	−0.180421
$842$	−10.5228	−0.362641
$843$	−16.5279	−0.569251
$844$	0.690640	0.0237728
$845$	18.3725	0.632035
$846$	−15.2937	−0.525808
$847$	37.6982	1.29533
$848$	−12.3956	−0.425667
$849$	−6.89126	−0.236507
$850$	9.93579	0.340795
$851$	−49.2760	−1.68916
$852$	7.45069	0.255256
$853$	33.3756	1.14276	0.571379	−	0.820686i	$-0.306409\pi$
$853$	33.3756	1.14276	0.571379	+	0.820686i	$0.306409\pi$
$854$	30.0775	1.02923
$855$	22.5879	0.772490
$856$	−15.2351	−0.520726
$857$	5.55383	0.189715	0.0948576	−	0.995491i	$-0.469760\pi$
$857$	5.55383	0.189715	0.0948576	+	0.995491i	$0.469760\pi$
$858$	−3.17892	−0.108527
$859$	−38.1688	−1.30230	−0.651152	−	0.758948i	$-0.725714\pi$
$859$	−38.1688	−1.30230	−0.651152	+	0.758948i	$0.725714\pi$
$860$	−12.5999	−0.429653
$861$	−0.123347	−0.00420365
$862$	−18.6853	−0.636422
$863$	34.5111	1.17477	0.587386	−	0.809307i	$-0.300157\pi$
$863$	34.5111	1.17477	0.587386	+	0.809307i	$0.300157\pi$
$864$	2.99998	0.102062
$865$	−23.3768	−0.794836
$866$	1.60828	0.0546515
$867$	3.55043	0.120579
$868$	−23.5203	−0.798331
$869$	13.0896	0.444035
$870$	3.51429	0.119146
$871$	−31.1524	−1.05556
$872$	−6.19609	−0.209826
$873$	−20.0642	−0.679070
$874$	−51.6274	−1.74632
$875$	43.7835	1.48015
$876$	−2.76380	−0.0933802
$877$	−23.7032	−0.800400	−0.400200	−	0.916428i	$-0.631059\pi$
$877$	−23.7032	−0.800400	−0.400200	+	0.916428i	$0.631059\pi$
$878$	19.6362	0.662688
$879$	7.42095	0.250303
$880$	1.62583	0.0548068
$881$	−32.8079	−1.10533	−0.552664	−	0.833404i	$-0.686389\pi$
$881$	−32.8079	−1.10533	−0.552664	+	0.833404i	$0.686389\pi$
$882$	−22.9203	−0.771766
$883$	−20.4107	−0.686874	−0.343437	−	0.939176i	$-0.611591\pi$
$883$	−20.4107	−0.686874	−0.343437	+	0.939176i	$0.611591\pi$
$884$	−16.4150	−0.552095
$885$	3.56030	0.119678
$886$	0.618634	0.0207834
$887$	29.1242	0.977895	0.488947	−	0.872313i	$-0.337381\pi$
$887$	29.1242	0.977895	0.488947	+	0.872313i	$0.337381\pi$
$888$	3.01279	0.101103
$889$	65.5059	2.19700
$890$	8.39230	0.281311
$891$	7.80509	0.261480
$892$	−3.47860	−0.116472
$893$	−33.8047	−1.13123
$894$	−2.47181	−0.0826696
$895$	12.5262	0.418703
$896$	−3.92552	−0.131142
$897$	−23.0523	−0.769695
$898$	−16.2897	−0.543593
$899$	−29.2106	−0.974227
$900$	8.46896	0.282299
$901$	39.6350	1.32043
$902$	−0.0708701	−0.00235972
$903$	−18.8382	−0.626897
$904$	1.07314	0.0356920
$905$	−29.5169	−0.981176
$906$	−2.02242	−0.0671905
$907$	−20.0163	−0.664631	−0.332315	−	0.943168i	$-0.607830\pi$
$907$	−20.0163	−0.664631	−0.332315	+	0.943168i	$0.607830\pi$
$908$	24.8143	0.823492
$909$	29.5241	0.979251
$910$	−27.7243	−0.919052
$911$	−18.3670	−0.608527	−0.304263	−	0.952588i	$-0.598410\pi$
$911$	−18.3670	−0.608527	−0.304263	+	0.952588i	$0.598410\pi$
$912$	3.15655	0.104524
$913$	−7.56877	−0.250490
$914$	−30.3988	−1.00550
$915$	5.52315	0.182590
$916$	−23.5415	−0.777832
$917$	−31.6416	−1.04490
$918$	−9.59245	−0.316598
$919$	−44.2420	−1.45941	−0.729705	−	0.683762i	$-0.760343\pi$
$919$	−44.2420	−1.45941	−0.729705	+	0.683762i	$0.760343\pi$
$920$	11.7899	0.388702
$921$	−12.3153	−0.405803
$922$	6.59391	0.217159
$923$	−72.9990	−2.40279
$924$	2.43079	0.0799673
$925$	17.8670	0.587462
$926$	9.88876	0.324965
$927$	44.0672	1.44736
$928$	−4.87522	−0.160037
$929$	−18.4562	−0.605528	−0.302764	−	0.953066i	$-0.597909\pi$
$929$	−18.4562	−0.605528	−0.302764	+	0.953066i	$0.597909\pi$
$930$	−4.31905	−0.141627
$931$	−50.6623	−1.66039
$932$	18.9626	0.621142
$933$	−3.03318	−0.0993018
$934$	−41.2671	−1.35030
$935$	−5.19860	−0.170012
$936$	−13.9916	−0.457330
$937$	−11.3125	−0.369563	−0.184781	−	0.982780i	$-0.559158\pi$
$937$	−11.3125	−0.369563	−0.184781	+	0.982780i	$0.559158\pi$
$938$	23.8210	0.777783
$939$	−5.19283	−0.169462
$940$	7.71983	0.251793
$941$	−31.4517	−1.02529	−0.512647	−	0.858599i	$-0.671335\pi$
$941$	−31.4517	−1.02529	−0.512647	+	0.858599i	$0.671335\pi$
$942$	−4.41890	−0.143975
$943$	−0.513923	−0.0167356
$944$	−4.93905	−0.160752
$945$	−16.2013	−0.527029
$946$	−10.8237	−0.351908
$947$	54.1876	1.76086	0.880430	−	0.474176i	$-0.157254\pi$
$947$	54.1876	1.76086	0.880430	+	0.474176i	$0.157254\pi$
$948$	−5.80356	−0.188491
$949$	27.0786	0.879010
$950$	18.7195	0.607342
$951$	9.36640	0.303726
$952$	12.5519	0.406808
$953$	33.5415	1.08651	0.543257	−	0.839566i	$-0.317191\pi$
$953$	33.5415	1.08651	0.543257	+	0.839566i	$0.317191\pi$
$954$	33.7836	1.09379
$955$	26.0640	0.843411
$956$	−5.86052	−0.189543
$957$	3.01888	0.0975864
$958$	−2.05627	−0.0664350
$959$	70.5936	2.27958
$960$	−0.720847	−0.0232652
$961$	4.89974	0.158056
$962$	−29.5181	−0.951702
$963$	41.5226	1.33805
$964$	−26.8667	−0.865319
$965$	24.1722	0.778131
$966$	17.6272	0.567145
$967$	28.1976	0.906772	0.453386	−	0.891314i	$-0.350216\pi$
$967$	28.1976	0.906772	0.453386	+	0.891314i	$0.350216\pi$
$968$	−9.60336	−0.308664
$969$	−10.0931	−0.324236
$970$	10.1278	0.325185
$971$	10.6521	0.341841	0.170921	−	0.985285i	$-0.445326\pi$
$971$	10.6521	0.341841	0.170921	+	0.985285i	$0.445326\pi$
$972$	−12.4605	−0.399671
$973$	−40.4592	−1.29706
$974$	−23.1104	−0.740506
$975$	8.35853	0.267687
$976$	−7.66203	−0.245256
$977$	8.23702	0.263526	0.131763	−	0.991281i	$-0.457936\pi$
$977$	8.23702	0.263526	0.131763	+	0.991281i	$0.457936\pi$
$978$	−8.86582	−0.283498
$979$	7.20923	0.230408
$980$	11.5695	0.369575
$981$	16.8872	0.539165
$982$	−19.5102	−0.622597
$983$	2.32403	0.0741251	0.0370625	−	0.999313i	$-0.488200\pi$
$983$	2.32403	0.0741251	0.0370625	+	0.999313i	$0.488200\pi$
$984$	0.0314218	0.00100169
$985$	−18.1671	−0.578851
$986$	15.5885	0.496440
$987$	11.5420	0.367385
$988$	−30.9267	−0.983908
$989$	−78.4892	−2.49581
$990$	−4.43113	−0.140830
$991$	12.7185	0.404017	0.202009	−	0.979384i	$-0.435253\pi$
$991$	12.7185	0.404017	0.202009	+	0.979384i	$0.435253\pi$
$992$	5.99164	0.190235
$993$	15.7838	0.500883
$994$	55.8194	1.77048
$995$	27.2939	0.865276
$996$	3.35577	0.106332
$997$	39.3939	1.24762	0.623808	−	0.781577i	$-0.285585\pi$
$997$	39.3939	1.24762	0.623808	+	0.781577i	$0.285585\pi$
$998$	38.6397	1.22312
$999$	−17.2496	−0.545752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.15	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.15	✓	33	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.523973 q^{3} +1.00000 q^{4} +1.37573 q^{5} -0.523973 q^{6} -3.92552 q^{7} +1.00000 q^{8} -2.72545 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.523973 q^{3} +1.00000 q^{4} +1.37573 q^{5} -0.523973 q^{6} -3.92552 q^{7} +1.00000 q^{8} -2.72545 q^{9} +1.37573 q^{10} +1.18179 q^{11} -0.523973 q^{12} +5.13369 q^{13} -3.92552 q^{14} -0.720847 q^{15} +1.00000 q^{16} -3.19750 q^{17} -2.72545 q^{18} -6.02426 q^{19} +1.37573 q^{20} +2.05687 q^{21} +1.18179 q^{22} +8.56991 q^{23} -0.523973 q^{24} -3.10736 q^{25} +5.13369 q^{26} +2.99998 q^{27} -3.92552 q^{28} -4.87522 q^{29} -0.720847 q^{30} +5.99164 q^{31} +1.00000 q^{32} -0.619228 q^{33} -3.19750 q^{34} -5.40047 q^{35} -2.72545 q^{36} -5.74989 q^{37} -6.02426 q^{38} -2.68991 q^{39} +1.37573 q^{40} -0.0599683 q^{41} +2.05687 q^{42} -9.15869 q^{43} +1.18179 q^{44} -3.74949 q^{45} +8.56991 q^{46} +5.61143 q^{47} -0.523973 q^{48} +8.40972 q^{49} -3.10736 q^{50} +1.67541 q^{51} +5.13369 q^{52} -12.3956 q^{53} +2.99998 q^{54} +1.62583 q^{55} -3.92552 q^{56} +3.15655 q^{57} -4.87522 q^{58} -4.93905 q^{59} -0.720847 q^{60} -7.66203 q^{61} +5.99164 q^{62} +10.6988 q^{63} +1.00000 q^{64} +7.06258 q^{65} -0.619228 q^{66} -6.06824 q^{67} -3.19750 q^{68} -4.49040 q^{69} -5.40047 q^{70} -14.2196 q^{71} -2.72545 q^{72} +5.27470 q^{73} -5.74989 q^{74} +1.62817 q^{75} -6.02426 q^{76} -4.63916 q^{77} -2.68991 q^{78} +11.0761 q^{79} +1.37573 q^{80} +6.60444 q^{81} -0.0599683 q^{82} -6.40447 q^{83} +2.05687 q^{84} -4.39891 q^{85} -9.15869 q^{86} +2.55449 q^{87} +1.18179 q^{88} +6.10024 q^{89} -3.74949 q^{90} -20.1524 q^{91} +8.56991 q^{92} -3.13946 q^{93} +5.61143 q^{94} -8.28777 q^{95} -0.523973 q^{96} +7.36178 q^{97} +8.40972 q^{98} -3.22092 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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