LMFDB - Embedded newform 8018.2.a.f.1.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.24
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.15760 q^{3} +1.00000 q^{4} +0.303099 q^{5} -1.15760 q^{6} +5.16405 q^{7} -1.00000 q^{8} -1.65997 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.15760 q^{3} +1.00000 q^{4} +0.303099 q^{5} -1.15760 q^{6} +5.16405 q^{7} -1.00000 q^{8} -1.65997 q^{9} -0.303099 q^{10} -4.94150 q^{11} +1.15760 q^{12} -0.449094 q^{13} -5.16405 q^{14} +0.350867 q^{15} +1.00000 q^{16} -1.00758 q^{17} +1.65997 q^{18} -1.00000 q^{19} +0.303099 q^{20} +5.97789 q^{21} +4.94150 q^{22} +0.609118 q^{23} -1.15760 q^{24} -4.90813 q^{25} +0.449094 q^{26} -5.39437 q^{27} +5.16405 q^{28} +7.13085 q^{29} -0.350867 q^{30} -10.1274 q^{31} -1.00000 q^{32} -5.72027 q^{33} +1.00758 q^{34} +1.56522 q^{35} -1.65997 q^{36} -6.79167 q^{37} +1.00000 q^{38} -0.519870 q^{39} -0.303099 q^{40} +11.1562 q^{41} -5.97789 q^{42} +1.82657 q^{43} -4.94150 q^{44} -0.503134 q^{45} -0.609118 q^{46} -3.44053 q^{47} +1.15760 q^{48} +19.6674 q^{49} +4.90813 q^{50} -1.16638 q^{51} -0.449094 q^{52} +10.9120 q^{53} +5.39437 q^{54} -1.49776 q^{55} -5.16405 q^{56} -1.15760 q^{57} -7.13085 q^{58} +1.35024 q^{59} +0.350867 q^{60} -11.7976 q^{61} +10.1274 q^{62} -8.57215 q^{63} +1.00000 q^{64} -0.136120 q^{65} +5.72027 q^{66} -4.14880 q^{67} -1.00758 q^{68} +0.705114 q^{69} -1.56522 q^{70} -11.8548 q^{71} +1.65997 q^{72} -11.0565 q^{73} +6.79167 q^{74} -5.68164 q^{75} -1.00000 q^{76} -25.5181 q^{77} +0.519870 q^{78} +15.9006 q^{79} +0.303099 q^{80} -1.26461 q^{81} -11.1562 q^{82} -3.16922 q^{83} +5.97789 q^{84} -0.305397 q^{85} -1.82657 q^{86} +8.25466 q^{87} +4.94150 q^{88} +14.7763 q^{89} +0.503134 q^{90} -2.31914 q^{91} +0.609118 q^{92} -11.7235 q^{93} +3.44053 q^{94} -0.303099 q^{95} -1.15760 q^{96} -17.2188 q^{97} -19.6674 q^{98} +8.20272 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.15760	0.668340	0.334170	−	0.942513i	$-0.391544\pi$
$3$	1.15760	0.668340	0.334170	+	0.942513i	$0.391544\pi$
$4$	1.00000	0.500000
$5$	0.303099	0.135550	0.0677750	−	0.997701i	$-0.478410\pi$
$5$	0.303099	0.135550	0.0677750	+	0.997701i	$0.478410\pi$
$6$	−1.15760	−0.472587
$7$	5.16405	1.95183	0.975914	−	0.218157i	$-0.0700044\pi$
$7$	5.16405	1.95183	0.975914	+	0.218157i	$0.0700044\pi$
$8$	−1.00000	−0.353553
$9$	−1.65997	−0.553322
$10$	−0.303099	−0.0958483
$11$	−4.94150	−1.48992	−0.744959	−	0.667111i	$-0.767531\pi$
$11$	−4.94150	−1.48992	−0.744959	+	0.667111i	$0.767531\pi$
$12$	1.15760	0.334170
$13$	−0.449094	−0.124556	−0.0622781	−	0.998059i	$-0.519837\pi$
$13$	−0.449094	−0.124556	−0.0622781	+	0.998059i	$0.519837\pi$
$14$	−5.16405	−1.38015
$15$	0.350867	0.0905934
$16$	1.00000	0.250000
$17$	−1.00758	−0.244375	−0.122187	−	0.992507i	$-0.538991\pi$
$17$	−1.00758	−0.244375	−0.122187	+	0.992507i	$0.538991\pi$
$18$	1.65997	0.391258
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.303099	0.0677750
$21$	5.97789	1.30448
$22$	4.94150	1.05353
$23$	0.609118	0.127010	0.0635050	−	0.997982i	$-0.479772\pi$
$23$	0.609118	0.127010	0.0635050	+	0.997982i	$0.479772\pi$
$24$	−1.15760	−0.236294
$25$	−4.90813	−0.981626
$26$	0.449094	0.0880745
$27$	−5.39437	−1.03815
$28$	5.16405	0.975914
$29$	7.13085	1.32417	0.662083	−	0.749431i	$-0.269673\pi$
$29$	7.13085	1.32417	0.662083	+	0.749431i	$0.269673\pi$
$30$	−0.350867	−0.0640592
$31$	−10.1274	−1.81894	−0.909471	−	0.415767i	$-0.863513\pi$
$31$	−10.1274	−1.81894	−0.909471	+	0.415767i	$0.863513\pi$
$32$	−1.00000	−0.176777
$33$	−5.72027	−0.995771
$34$	1.00758	0.172799
$35$	1.56522	0.264570
$36$	−1.65997	−0.276661
$37$	−6.79167	−1.11654	−0.558272	−	0.829658i	$-0.688535\pi$
$37$	−6.79167	−1.11654	−0.558272	+	0.829658i	$0.688535\pi$
$38$	1.00000	0.162221
$39$	−0.519870	−0.0832458
$40$	−0.303099	−0.0479242
$41$	11.1562	1.74231	0.871154	−	0.491009i	$-0.163372\pi$
$41$	11.1562	1.74231	0.871154	+	0.491009i	$0.163372\pi$
$42$	−5.97789	−0.922409
$43$	1.82657	0.278549	0.139275	−	0.990254i	$-0.455523\pi$
$43$	1.82657	0.278549	0.139275	+	0.990254i	$0.455523\pi$
$44$	−4.94150	−0.744959
$45$	−0.503134	−0.0750028
$46$	−0.609118	−0.0898096
$47$	−3.44053	−0.501852	−0.250926	−	0.968006i	$-0.580735\pi$
$47$	−3.44053	−0.501852	−0.250926	+	0.968006i	$0.580735\pi$
$48$	1.15760	0.167085
$49$	19.6674	2.80963
$50$	4.90813	0.694115
$51$	−1.16638	−0.163325
$52$	−0.449094	−0.0622781
$53$	10.9120	1.49888	0.749439	−	0.662073i	$-0.230323\pi$
$53$	10.9120	1.49888	0.749439	+	0.662073i	$0.230323\pi$
$54$	5.39437	0.734081
$55$	−1.49776	−0.201958
$56$	−5.16405	−0.690075
$57$	−1.15760	−0.153328
$58$	−7.13085	−0.936327
$59$	1.35024	0.175787	0.0878935	−	0.996130i	$-0.471986\pi$
$59$	1.35024	0.175787	0.0878935	+	0.996130i	$0.471986\pi$
$60$	0.350867	0.0452967
$61$	−11.7976	−1.51053	−0.755267	−	0.655418i	$-0.772493\pi$
$61$	−11.7976	−1.51053	−0.755267	+	0.655418i	$0.772493\pi$
$62$	10.1274	1.28619
$63$	−8.57215	−1.07999
$64$	1.00000	0.125000
$65$	−0.136120	−0.0168836
$66$	5.72027	0.704116
$67$	−4.14880	−0.506857	−0.253428	−	0.967354i	$-0.581558\pi$
$67$	−4.14880	−0.506857	−0.253428	+	0.967354i	$0.581558\pi$
$68$	−1.00758	−0.122187
$69$	0.705114	0.0848858
$70$	−1.56522	−0.187079
$71$	−11.8548	−1.40690	−0.703451	−	0.710744i	$-0.748358\pi$
$71$	−11.8548	−1.40690	−0.703451	+	0.710744i	$0.748358\pi$
$72$	1.65997	0.195629
$73$	−11.0565	−1.29407	−0.647035	−	0.762460i	$-0.723991\pi$
$73$	−11.0565	−1.29407	−0.647035	+	0.762460i	$0.723991\pi$
$74$	6.79167	0.789515
$75$	−5.68164	−0.656060
$76$	−1.00000	−0.114708
$77$	−25.5181	−2.90806
$78$	0.519870	0.0588637
$79$	15.9006	1.78896	0.894480	−	0.447108i	$-0.147546\pi$
$79$	15.9006	1.78896	0.894480	+	0.447108i	$0.147546\pi$
$80$	0.303099	0.0338875
$81$	−1.26461	−0.140512
$82$	−11.1562	−1.23200
$83$	−3.16922	−0.347867	−0.173934	−	0.984757i	$-0.555648\pi$
$83$	−3.16922	−0.347867	−0.173934	+	0.984757i	$0.555648\pi$
$84$	5.97789	0.652242
$85$	−0.305397	−0.0331250
$86$	−1.82657	−0.196964
$87$	8.25466	0.884992
$88$	4.94150	0.526765
$89$	14.7763	1.56629	0.783144	−	0.621840i	$-0.213615\pi$
$89$	14.7763	1.56629	0.783144	+	0.621840i	$0.213615\pi$
$90$	0.503134	0.0530350
$91$	−2.31914	−0.243112
$92$	0.609118	0.0635050
$93$	−11.7235	−1.21567
$94$	3.44053	0.354863
$95$	−0.303099	−0.0310973
$96$	−1.15760	−0.118147
$97$	−17.2188	−1.74830	−0.874151	−	0.485655i	$-0.838581\pi$
$97$	−17.2188	−1.74830	−0.874151	+	0.485655i	$0.838581\pi$
$98$	−19.6674	−1.98671
$99$	8.20272	0.824404
$100$	−4.90813	−0.490813
$101$	−12.9391	−1.28749	−0.643746	−	0.765239i	$-0.722621\pi$
$101$	−12.9391	−1.28749	−0.643746	+	0.765239i	$0.722621\pi$
$102$	1.16638	0.115488
$103$	−6.91709	−0.681561	−0.340780	−	0.940143i	$-0.610691\pi$
$103$	−6.91709	−0.681561	−0.340780	+	0.940143i	$0.610691\pi$
$104$	0.449094	0.0440373
$105$	1.81189	0.176823
$106$	−10.9120	−1.05987
$107$	4.34837	0.420373	0.210186	−	0.977661i	$-0.432593\pi$
$107$	4.34837	0.420373	0.210186	+	0.977661i	$0.432593\pi$
$108$	−5.39437	−0.519073
$109$	12.7279	1.21911	0.609557	−	0.792742i	$-0.291347\pi$
$109$	12.7279	1.21911	0.609557	+	0.792742i	$0.291347\pi$
$110$	1.49776	0.142806
$111$	−7.86202	−0.746230
$112$	5.16405	0.487957
$113$	−2.67899	−0.252018	−0.126009	−	0.992029i	$-0.540217\pi$
$113$	−2.67899	−0.252018	−0.126009	+	0.992029i	$0.540217\pi$
$114$	1.15760	0.108419
$115$	0.184623	0.0172162
$116$	7.13085	0.662083
$117$	0.745481	0.0689197
$118$	−1.35024	−0.124300
$119$	−5.20321	−0.476977
$120$	−0.350867	−0.0320296
$121$	13.4184	1.21985
$122$	11.7976	1.06811
$123$	12.9144	1.16445
$124$	−10.1274	−0.909471
$125$	−3.00315	−0.268609
$126$	8.57215	0.763668
$127$	−12.9511	−1.14922	−0.574612	−	0.818426i	$-0.694847\pi$
$127$	−12.9511	−1.14922	−0.574612	+	0.818426i	$0.694847\pi$
$128$	−1.00000	−0.0883883
$129$	2.11443	0.186166
$130$	0.136120	0.0119385
$131$	−14.2709	−1.24685	−0.623427	−	0.781882i	$-0.714260\pi$
$131$	−14.2709	−1.24685	−0.623427	+	0.781882i	$0.714260\pi$
$132$	−5.72027	−0.497885
$133$	−5.16405	−0.447780
$134$	4.14880	0.358402
$135$	−1.63503	−0.140721
$136$	1.00758	0.0863995
$137$	14.2293	1.21569	0.607846	−	0.794055i	$-0.292034\pi$
$137$	14.2293	1.21569	0.607846	+	0.794055i	$0.292034\pi$
$138$	−0.705114	−0.0600233
$139$	−15.7484	−1.33576	−0.667879	−	0.744270i	$-0.732798\pi$
$139$	−15.7484	−1.33576	−0.667879	+	0.744270i	$0.732798\pi$
$140$	1.56522	0.132285
$141$	−3.98275	−0.335408
$142$	11.8548	0.994829
$143$	2.21920	0.185578
$144$	−1.65997	−0.138331
$145$	2.16135	0.179491
$146$	11.0565	0.915046
$147$	22.7670	1.87779
$148$	−6.79167	−0.558272
$149$	−0.376372	−0.0308336	−0.0154168	−	0.999881i	$-0.504908\pi$
$149$	−0.376372	−0.0308336	−0.0154168	+	0.999881i	$0.504908\pi$
$150$	5.68164	0.463904
$151$	−20.9967	−1.70869	−0.854343	−	0.519710i	$-0.826040\pi$
$151$	−20.9967	−1.70869	−0.854343	+	0.519710i	$0.826040\pi$
$152$	1.00000	0.0811107
$153$	1.67255	0.135218
$154$	25.5181	2.05631
$155$	−3.06962	−0.246558
$156$	−0.519870	−0.0416229
$157$	5.18928	0.414149	0.207075	−	0.978325i	$-0.433606\pi$
$157$	5.18928	0.414149	0.207075	+	0.978325i	$0.433606\pi$
$158$	−15.9006	−1.26499
$159$	12.6317	1.00176
$160$	−0.303099	−0.0239621
$161$	3.14552	0.247902
$162$	1.26461	0.0993571
$163$	−18.1159	−1.41894	−0.709472	−	0.704733i	$-0.751067\pi$
$163$	−18.1159	−1.41894	−0.709472	+	0.704733i	$0.751067\pi$
$164$	11.1562	0.871154
$165$	−1.73381	−0.134977
$166$	3.16922	0.245979
$167$	−15.5999	−1.20716	−0.603579	−	0.797304i	$-0.706259\pi$
$167$	−15.5999	−1.20716	−0.603579	+	0.797304i	$0.706259\pi$
$168$	−5.97789	−0.461205
$169$	−12.7983	−0.984486
$170$	0.305397	0.0234229
$171$	1.65997	0.126941
$172$	1.82657	0.139275
$173$	−2.49692	−0.189837	−0.0949185	−	0.995485i	$-0.530259\pi$
$173$	−2.49692	−0.189837	−0.0949185	+	0.995485i	$0.530259\pi$
$174$	−8.25466	−0.625784
$175$	−25.3458	−1.91596
$176$	−4.94150	−0.372479
$177$	1.56304	0.117485
$178$	−14.7763	−1.10753
$179$	−6.68898	−0.499958	−0.249979	−	0.968251i	$-0.580424\pi$
$179$	−6.68898	−0.499958	−0.249979	+	0.968251i	$0.580424\pi$
$180$	−0.503134	−0.0375014
$181$	−1.84059	−0.136810	−0.0684051	−	0.997658i	$-0.521791\pi$
$181$	−1.84059	−0.136810	−0.0684051	+	0.997658i	$0.521791\pi$
$182$	2.31914	0.171906
$183$	−13.6569	−1.00955
$184$	−0.609118	−0.0449048
$185$	−2.05855	−0.151347
$186$	11.7235	0.859609
$187$	4.97897	0.364098
$188$	−3.44053	−0.250926
$189$	−27.8568	−2.02628
$190$	0.303099	0.0219891
$191$	−21.6034	−1.56317	−0.781585	−	0.623799i	$-0.785588\pi$
$191$	−21.6034	−1.56317	−0.781585	+	0.623799i	$0.785588\pi$
$192$	1.15760	0.0835424
$193$	−4.33318	−0.311909	−0.155955	−	0.987764i	$-0.549845\pi$
$193$	−4.33318	−0.311909	−0.155955	+	0.987764i	$0.549845\pi$
$194$	17.2188	1.23624
$195$	−0.157572	−0.0112840
$196$	19.6674	1.40482
$197$	10.4562	0.744976	0.372488	−	0.928037i	$-0.378505\pi$
$197$	10.4562	0.744976	0.372488	+	0.928037i	$0.378505\pi$
$198$	−8.20272	−0.582942
$199$	0.627596	0.0444891	0.0222445	−	0.999753i	$-0.492919\pi$
$199$	0.627596	0.0444891	0.0222445	+	0.999753i	$0.492919\pi$
$200$	4.90813	0.347057
$201$	−4.80264	−0.338752
$202$	12.9391	0.910395
$203$	36.8241	2.58454
$204$	−1.16638	−0.0816626
$205$	3.38144	0.236170
$206$	6.91709	0.481936
$207$	−1.01112	−0.0702774
$208$	−0.449094	−0.0311391
$209$	4.94150	0.341810
$210$	−1.81189	−0.125033
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	10.9120	0.749439
$213$	−13.7230	−0.940288
$214$	−4.34837	−0.297248
$215$	0.553632	0.0377574
$216$	5.39437	0.367040
$217$	−52.2986	−3.55026
$218$	−12.7279	−0.862044
$219$	−12.7990	−0.864878
$220$	−1.49776	−0.100979
$221$	0.452499	0.0304384
$222$	7.86202	0.527664
$223$	−11.4085	−0.763970	−0.381985	−	0.924168i	$-0.624759\pi$
$223$	−11.4085	−0.763970	−0.381985	+	0.924168i	$0.624759\pi$
$224$	−5.16405	−0.345038
$225$	8.14733	0.543156
$226$	2.67899	0.178204
$227$	−3.16347	−0.209967	−0.104983	−	0.994474i	$-0.533479\pi$
$227$	−3.16347	−0.209967	−0.104983	+	0.994474i	$0.533479\pi$
$228$	−1.15760	−0.0766638
$229$	24.4127	1.61324	0.806619	−	0.591072i	$-0.201295\pi$
$229$	24.4127	1.61324	0.806619	+	0.591072i	$0.201295\pi$
$230$	−0.184623	−0.0121737
$231$	−29.5397	−1.94357
$232$	−7.13085	−0.468163
$233$	−11.1411	−0.729878	−0.364939	−	0.931031i	$-0.618910\pi$
$233$	−11.1411	−0.729878	−0.364939	+	0.931031i	$0.618910\pi$
$234$	−0.745481	−0.0487336
$235$	−1.04282	−0.0680261
$236$	1.35024	0.0878935
$237$	18.4065	1.19563
$238$	5.20321	0.337274
$239$	8.84593	0.572195	0.286098	−	0.958200i	$-0.407642\pi$
$239$	8.84593	0.572195	0.286098	+	0.958200i	$0.407642\pi$
$240$	0.350867	0.0226484
$241$	0.520167	0.0335069	0.0167534	−	0.999860i	$-0.494667\pi$
$241$	0.520167	0.0335069	0.0167534	+	0.999860i	$0.494667\pi$
$242$	−13.4184	−0.862567
$243$	14.7192	0.944237
$244$	−11.7976	−0.755267
$245$	5.96117	0.380845
$246$	−12.9144	−0.823393
$247$	0.449094	0.0285752
$248$	10.1274	0.643093
$249$	−3.66868	−0.232493
$250$	3.00315	0.189936
$251$	−2.84474	−0.179558	−0.0897791	−	0.995962i	$-0.528616\pi$
$251$	−2.84474	−0.179558	−0.0897791	+	0.995962i	$0.528616\pi$
$252$	−8.57215	−0.539995
$253$	−3.00996	−0.189234
$254$	12.9511	0.812624
$255$	−0.353527	−0.0221387
$256$	1.00000	0.0625000
$257$	−21.2453	−1.32525	−0.662624	−	0.748953i	$-0.730557\pi$
$257$	−21.2453	−1.32525	−0.662624	+	0.748953i	$0.730557\pi$
$258$	−2.11443	−0.131639
$259$	−35.0725	−2.17930
$260$	−0.136120	−0.00844180
$261$	−11.8370	−0.732690
$262$	14.2709	0.881659
$263$	7.36934	0.454413	0.227206	−	0.973847i	$-0.427041\pi$
$263$	7.36934	0.454413	0.227206	+	0.973847i	$0.427041\pi$
$264$	5.72027	0.352058
$265$	3.30742	0.203173
$266$	5.16405	0.316628
$267$	17.1051	1.04681
$268$	−4.14880	−0.253428
$269$	15.1125	0.921426	0.460713	−	0.887549i	$-0.347594\pi$
$269$	15.1125	0.921426	0.460713	+	0.887549i	$0.347594\pi$
$270$	1.63503	0.0995046
$271$	8.56246	0.520133	0.260066	−	0.965591i	$-0.416256\pi$
$271$	8.56246	0.520133	0.260066	+	0.965591i	$0.416256\pi$
$272$	−1.00758	−0.0610937
$273$	−2.68464	−0.162482
$274$	−14.2293	−0.859625
$275$	24.2535	1.46254
$276$	0.705114	0.0424429
$277$	−21.7949	−1.30953	−0.654765	−	0.755832i	$-0.727232\pi$
$277$	−21.7949	−1.30953	−0.654765	+	0.755832i	$0.727232\pi$
$278$	15.7484	0.944524
$279$	16.8112	1.00646
$280$	−1.56522	−0.0935397
$281$	−28.0216	−1.67163	−0.835815	−	0.549011i	$-0.815005\pi$
$281$	−28.0216	−1.67163	−0.835815	+	0.549011i	$0.815005\pi$
$282$	3.98275	0.237169
$283$	15.9046	0.945430	0.472715	−	0.881215i	$-0.343274\pi$
$283$	15.9046	0.945430	0.472715	+	0.881215i	$0.343274\pi$
$284$	−11.8548	−0.703451
$285$	−0.350867	−0.0207836
$286$	−2.21920	−0.131224
$287$	57.6113	3.40069
$288$	1.65997	0.0978145
$289$	−15.9848	−0.940281
$290$	−2.16135	−0.126919
$291$	−19.9324	−1.16846
$292$	−11.0565	−0.647035
$293$	−14.8089	−0.865143	−0.432571	−	0.901600i	$-0.642394\pi$
$293$	−14.8089	−0.865143	−0.432571	+	0.901600i	$0.642394\pi$
$294$	−22.7670	−1.32780
$295$	0.409258	0.0238279
$296$	6.79167	0.394758
$297$	26.6563	1.54675
$298$	0.376372	0.0218026
$299$	−0.273551	−0.0158199
$300$	−5.68164	−0.328030
$301$	9.43250	0.543680
$302$	20.9967	1.20822
$303$	−14.9783	−0.860482
$304$	−1.00000	−0.0573539
$305$	−3.57585	−0.204753
$306$	−1.67255	−0.0956135
$307$	−0.811256	−0.0463008	−0.0231504	−	0.999732i	$-0.507370\pi$
$307$	−0.811256	−0.0463008	−0.0231504	+	0.999732i	$0.507370\pi$
$308$	−25.5181	−1.45403
$309$	−8.00721	−0.455514
$310$	3.06962	0.174343
$311$	23.6688	1.34213	0.671067	−	0.741397i	$-0.265836\pi$
$311$	23.6688	1.34213	0.671067	+	0.741397i	$0.265836\pi$
$312$	0.519870	0.0294318
$313$	17.3521	0.980798	0.490399	−	0.871498i	$-0.336851\pi$
$313$	17.3521	0.980798	0.490399	+	0.871498i	$0.336851\pi$
$314$	−5.18928	−0.292848
$315$	−2.59821	−0.146393
$316$	15.9006	0.894480
$317$	27.2009	1.52776	0.763878	−	0.645360i	$-0.223293\pi$
$317$	27.2009	1.52776	0.763878	+	0.645360i	$0.223293\pi$
$318$	−12.6317	−0.708351
$319$	−35.2371	−1.97290
$320$	0.303099	0.0169438
$321$	5.03366	0.280952
$322$	−3.14552	−0.175293
$323$	1.00758	0.0560634
$324$	−1.26461	−0.0702561
$325$	2.20421	0.122268
$326$	18.1159	1.00335
$327$	14.7338	0.814782
$328$	−11.1562	−0.615999
$329$	−17.7670	−0.979529
$330$	1.73381	0.0954430
$331$	13.7328	0.754824	0.377412	−	0.926045i	$-0.376814\pi$
$331$	13.7328	0.754824	0.377412	+	0.926045i	$0.376814\pi$
$332$	−3.16922	−0.173934
$333$	11.2739	0.617808
$334$	15.5999	0.853589
$335$	−1.25750	−0.0687044
$336$	5.97789	0.326121
$337$	−24.7738	−1.34951	−0.674756	−	0.738041i	$-0.735751\pi$
$337$	−24.7738	−1.34951	−0.674756	+	0.738041i	$0.735751\pi$
$338$	12.7983	0.696137
$339$	−3.10119	−0.168434
$340$	−0.305397	−0.0165625
$341$	50.0447	2.71007
$342$	−1.65997	−0.0897607
$343$	65.4152	3.53209
$344$	−1.82657	−0.0984821
$345$	0.213719	0.0115063
$346$	2.49692	0.134235
$347$	−6.65933	−0.357491	−0.178746	−	0.983895i	$-0.557204\pi$
$347$	−6.65933	−0.357491	−0.178746	+	0.983895i	$0.557204\pi$
$348$	8.25466	0.442496
$349$	26.8968	1.43975	0.719877	−	0.694102i	$-0.244198\pi$
$349$	26.8968	1.43975	0.719877	+	0.694102i	$0.244198\pi$
$350$	25.3458	1.35479
$351$	2.42258	0.129308
$352$	4.94150	0.263383
$353$	20.5627	1.09444	0.547220	−	0.836989i	$-0.315686\pi$
$353$	20.5627	1.09444	0.547220	+	0.836989i	$0.315686\pi$
$354$	−1.56304	−0.0830747
$355$	−3.59317	−0.190705
$356$	14.7763	0.783144
$357$	−6.02322	−0.318783
$358$	6.68898	0.353523
$359$	14.0061	0.739212	0.369606	−	0.929189i	$-0.379493\pi$
$359$	14.0061	0.739212	0.369606	+	0.929189i	$0.379493\pi$
$360$	0.503134	0.0265175
$361$	1.00000	0.0526316
$362$	1.84059	0.0967395
$363$	15.5331	0.815276
$364$	−2.31914	−0.121556
$365$	−3.35123	−0.175411
$366$	13.6569	0.713859
$367$	7.85802	0.410185	0.205093	−	0.978743i	$-0.434250\pi$
$367$	7.85802	0.410185	0.205093	+	0.978743i	$0.434250\pi$
$368$	0.609118	0.0317525
$369$	−18.5190	−0.964058
$370$	2.05855	0.107019
$371$	56.3501	2.92555
$372$	−11.7235	−0.607836
$373$	−18.3143	−0.948280	−0.474140	−	0.880449i	$-0.657241\pi$
$373$	−18.3143	−0.948280	−0.474140	+	0.880449i	$0.657241\pi$
$374$	−4.97897	−0.257456
$375$	−3.47643	−0.179522
$376$	3.44053	0.177432
$377$	−3.20242	−0.164933
$378$	27.8568	1.43280
$379$	−28.2657	−1.45191	−0.725956	−	0.687741i	$-0.758602\pi$
$379$	−28.2657	−1.45191	−0.725956	+	0.687741i	$0.758602\pi$
$380$	−0.303099	−0.0155487
$381$	−14.9922	−0.768072
$382$	21.6034	1.10533
$383$	33.1556	1.69417	0.847086	−	0.531457i	$-0.178355\pi$
$383$	33.1556	1.69417	0.847086	+	0.531457i	$0.178355\pi$
$384$	−1.15760	−0.0590734
$385$	−7.73452	−0.394188
$386$	4.33318	0.220553
$387$	−3.03205	−0.154128
$388$	−17.2188	−0.874151
$389$	−12.8267	−0.650338	−0.325169	−	0.945656i	$-0.605421\pi$
$389$	−12.8267	−0.650338	−0.325169	+	0.945656i	$0.605421\pi$
$390$	0.157572	0.00797898
$391$	−0.613737	−0.0310380
$392$	−19.6674	−0.993354
$393$	−16.5200	−0.833322
$394$	−10.4562	−0.526778
$395$	4.81946	0.242494
$396$	8.20272	0.412202
$397$	32.5341	1.63284	0.816419	−	0.577460i	$-0.195956\pi$
$397$	32.5341	1.63284	0.816419	+	0.577460i	$0.195956\pi$
$398$	−0.627596	−0.0314585
$399$	−5.97789	−0.299269
$400$	−4.90813	−0.245407
$401$	−23.1876	−1.15793	−0.578966	−	0.815352i	$-0.696544\pi$
$401$	−23.1876	−1.15793	−0.578966	+	0.815352i	$0.696544\pi$
$402$	4.80264	0.239534
$403$	4.54817	0.226561
$404$	−12.9391	−0.643746
$405$	−0.383302	−0.0190464
$406$	−36.8241	−1.82755
$407$	33.5610	1.66356
$408$	1.16638	0.0577442
$409$	−20.7790	−1.02746	−0.513728	−	0.857953i	$-0.671736\pi$
$409$	−20.7790	−1.02746	−0.513728	+	0.857953i	$0.671736\pi$
$410$	−3.38144	−0.166997
$411$	16.4718	0.812496
$412$	−6.91709	−0.340780
$413$	6.97273	0.343106
$414$	1.01112	0.0496937
$415$	−0.960588	−0.0471534
$416$	0.449094	0.0220186
$417$	−18.2303	−0.892740
$418$	−4.94150	−0.241696
$419$	−11.6983	−0.571498	−0.285749	−	0.958305i	$-0.592242\pi$
$419$	−11.6983	−0.571498	−0.285749	+	0.958305i	$0.592242\pi$
$420$	1.81189	0.0884114
$421$	−35.1593	−1.71356	−0.856780	−	0.515682i	$-0.827539\pi$
$421$	−35.1593	−1.71356	−0.856780	+	0.515682i	$0.827539\pi$
$422$	1.00000	0.0486792
$423$	5.71116	0.277686
$424$	−10.9120	−0.529934
$425$	4.94535	0.239885
$426$	13.7230	0.664884
$427$	−60.9236	−2.94830
$428$	4.34837	0.210186
$429$	2.56894	0.124029
$430$	−0.553632	−0.0266985
$431$	16.3075	0.785506	0.392753	−	0.919644i	$-0.371523\pi$
$431$	16.3075	0.785506	0.392753	+	0.919644i	$0.371523\pi$
$432$	−5.39437	−0.259537
$433$	−30.2235	−1.45245	−0.726223	−	0.687459i	$-0.758726\pi$
$433$	−30.2235	−1.45245	−0.726223	+	0.687459i	$0.758726\pi$
$434$	52.2986	2.51041
$435$	2.50198	0.119961
$436$	12.7279	0.609557
$437$	−0.609118	−0.0291381
$438$	12.7990	0.611561
$439$	25.3149	1.20822	0.604108	−	0.796903i	$-0.293530\pi$
$439$	25.3149	1.20822	0.604108	+	0.796903i	$0.293530\pi$
$440$	1.49776	0.0714030
$441$	−32.6473	−1.55463
$442$	−0.452499	−0.0215232
$443$	16.6978	0.793338	0.396669	−	0.917962i	$-0.370166\pi$
$443$	16.6978	0.793338	0.396669	+	0.917962i	$0.370166\pi$
$444$	−7.86202	−0.373115
$445$	4.47869	0.212310
$446$	11.4085	0.540209
$447$	−0.435688	−0.0206073
$448$	5.16405	0.243978
$449$	−5.38686	−0.254222	−0.127111	−	0.991889i	$-0.540570\pi$
$449$	−5.38686	−0.254222	−0.127111	+	0.991889i	$0.540570\pi$
$450$	−8.14733	−0.384069
$451$	−55.1284	−2.59590
$452$	−2.67899	−0.126009
$453$	−24.3057	−1.14198
$454$	3.16347	0.148469
$455$	−0.702930	−0.0329539
$456$	1.15760	0.0542095
$457$	28.5082	1.33356	0.666779	−	0.745256i	$-0.267673\pi$
$457$	28.5082	1.33356	0.666779	+	0.745256i	$0.267673\pi$
$458$	−24.4127	−1.14073
$459$	5.43527	0.253697
$460$	0.184623	0.00860810
$461$	27.5561	1.28342	0.641708	−	0.766949i	$-0.278226\pi$
$461$	27.5561	1.28342	0.641708	+	0.766949i	$0.278226\pi$
$462$	29.5397	1.37431
$463$	2.21654	0.103011	0.0515057	−	0.998673i	$-0.483598\pi$
$463$	2.21654	0.103011	0.0515057	+	0.998673i	$0.483598\pi$
$464$	7.13085	0.331041
$465$	−3.55338	−0.164784
$466$	11.1411	0.516102
$467$	18.0964	0.837401	0.418701	−	0.908124i	$-0.362486\pi$
$467$	18.0964	0.837401	0.418701	+	0.908124i	$0.362486\pi$
$468$	0.745481	0.0344599
$469$	−21.4246	−0.989297
$470$	1.04282	0.0481017
$471$	6.00710	0.276792
$472$	−1.35024	−0.0621501
$473$	−9.02599	−0.415016
$474$	−18.4065	−0.845440
$475$	4.90813	0.225200
$476$	−5.20321	−0.238489
$477$	−18.1136	−0.829363
$478$	−8.84593	−0.404603
$479$	−4.71277	−0.215332	−0.107666	−	0.994187i	$-0.534338\pi$
$479$	−4.71277	−0.215332	−0.107666	+	0.994187i	$0.534338\pi$
$480$	−0.350867	−0.0160148
$481$	3.05010	0.139072
$482$	−0.520167	−0.0236930
$483$	3.64125	0.165682
$484$	13.4184	0.609927
$485$	−5.21899	−0.236982
$486$	−14.7192	−0.667676
$487$	25.2904	1.14602	0.573010	−	0.819549i	$-0.305776\pi$
$487$	25.2904	1.14602	0.573010	+	0.819549i	$0.305776\pi$
$488$	11.7976	0.534054
$489$	−20.9709	−0.948337
$490$	−5.96117	−0.269298
$491$	−42.4850	−1.91732	−0.958662	−	0.284548i	$-0.908156\pi$
$491$	−42.4850	−1.91732	−0.958662	+	0.284548i	$0.908156\pi$
$492$	12.9144	0.582227
$493$	−7.18492	−0.323593
$494$	−0.449094	−0.0202057
$495$	2.48624	0.111748
$496$	−10.1274	−0.454736
$497$	−61.2186	−2.74603
$498$	3.66868	0.164398
$499$	−2.52549	−0.113057	−0.0565283	−	0.998401i	$-0.518003\pi$
$499$	−2.52549	−0.113057	−0.0565283	+	0.998401i	$0.518003\pi$
$500$	−3.00315	−0.134305
$501$	−18.0584	−0.806791
$502$	2.84474	0.126967
$503$	11.8311	0.527523	0.263762	−	0.964588i	$-0.415037\pi$
$503$	11.8311	0.527523	0.263762	+	0.964588i	$0.415037\pi$
$504$	8.57215	0.381834
$505$	−3.92184	−0.174520
$506$	3.00996	0.133809
$507$	−14.8153	−0.657971
$508$	−12.9511	−0.574612
$509$	−8.30586	−0.368151	−0.184075	−	0.982912i	$-0.558929\pi$
$509$	−8.30586	−0.368151	−0.184075	+	0.982912i	$0.558929\pi$
$510$	0.353527	0.0156545
$511$	−57.0965	−2.52580
$512$	−1.00000	−0.0441942
$513$	5.39437	0.238167
$514$	21.2453	0.937091
$515$	−2.09656	−0.0923856
$516$	2.11443	0.0930828
$517$	17.0013	0.747718
$518$	35.0725	1.54100
$519$	−2.89043	−0.126876
$520$	0.136120	0.00596925
$521$	11.1137	0.486899	0.243450	−	0.969914i	$-0.421721\pi$
$521$	11.1137	0.486899	0.243450	+	0.969914i	$0.421721\pi$
$522$	11.8370	0.518090
$523$	−0.876814	−0.0383404	−0.0191702	−	0.999816i	$-0.506102\pi$
$523$	−0.876814	−0.0383404	−0.0191702	+	0.999816i	$0.506102\pi$
$524$	−14.2709	−0.623427
$525$	−29.3403	−1.28052
$526$	−7.36934	−0.321318
$527$	10.2042	0.444503
$528$	−5.72027	−0.248943
$529$	−22.6290	−0.983868
$530$	−3.30742	−0.143665
$531$	−2.24136	−0.0972668
$532$	−5.16405	−0.223890
$533$	−5.01019	−0.217015
$534$	−17.1051	−0.740208
$535$	1.31799	0.0569815
$536$	4.14880	0.179201
$537$	−7.74315	−0.334141
$538$	−15.1125	−0.651547
$539$	−97.1865	−4.18612
$540$	−1.63503	−0.0703604
$541$	−15.0402	−0.646630	−0.323315	−	0.946291i	$-0.604797\pi$
$541$	−15.0402	−0.646630	−0.323315	+	0.946291i	$0.604797\pi$
$542$	−8.56246	−0.367789
$543$	−2.13067	−0.0914357
$544$	1.00758	0.0431997
$545$	3.85782	0.165251
$546$	2.68464	0.114892
$547$	3.13839	0.134188	0.0670938	−	0.997747i	$-0.478627\pi$
$547$	3.13839	0.134188	0.0670938	+	0.997747i	$0.478627\pi$
$548$	14.2293	0.607846
$549$	19.5837	0.835812
$550$	−24.2535	−1.03417
$551$	−7.13085	−0.303784
$552$	−0.705114	−0.0300117
$553$	82.1116	3.49174
$554$	21.7949	0.925978
$555$	−2.38297	−0.101151
$556$	−15.7484	−0.667879
$557$	26.8813	1.13900	0.569498	−	0.821993i	$-0.307138\pi$
$557$	26.8813	1.13900	0.569498	+	0.821993i	$0.307138\pi$
$558$	−16.8112	−0.711676
$559$	−0.820302	−0.0346951
$560$	1.56522	0.0661426
$561$	5.76364	0.243341
$562$	28.0216	1.18202
$563$	−2.56742	−0.108204	−0.0541020	−	0.998535i	$-0.517230\pi$
$563$	−2.56742	−0.108204	−0.0541020	+	0.998535i	$0.517230\pi$
$564$	−3.98275	−0.167704
$565$	−0.811999	−0.0341611
$566$	−15.9046	−0.668520
$567$	−6.53051	−0.274256
$568$	11.8548	0.497415
$569$	−0.821477	−0.0344381	−0.0172191	−	0.999852i	$-0.505481\pi$
$569$	−0.821477	−0.0344381	−0.0172191	+	0.999852i	$0.505481\pi$
$570$	0.350867	0.0146962
$571$	10.5962	0.443436	0.221718	−	0.975111i	$-0.428834\pi$
$571$	10.5962	0.443436	0.221718	+	0.975111i	$0.428834\pi$
$572$	2.21920	0.0927892
$573$	−25.0081	−1.04473
$574$	−57.6113	−2.40465
$575$	−2.98963	−0.124676
$576$	−1.65997	−0.0691653
$577$	−23.4526	−0.976343	−0.488172	−	0.872748i	$-0.662336\pi$
$577$	−23.4526	−0.976343	−0.488172	+	0.872748i	$0.662336\pi$
$578$	15.9848	0.664879
$579$	−5.01608	−0.208461
$580$	2.16135	0.0897453
$581$	−16.3660	−0.678977
$582$	19.9324	0.826225
$583$	−53.9216	−2.23321
$584$	11.0565	0.457523
$585$	0.225955	0.00934207
$586$	14.8089	0.611748
$587$	−11.9358	−0.492642	−0.246321	−	0.969188i	$-0.579222\pi$
$587$	−11.9358	−0.492642	−0.246321	+	0.969188i	$0.579222\pi$
$588$	22.7670	0.938894
$589$	10.1274	0.417294
$590$	−0.409258	−0.0168489
$591$	12.1041	0.497897
$592$	−6.79167	−0.279136
$593$	12.0152	0.493404	0.246702	−	0.969091i	$-0.420653\pi$
$593$	12.0152	0.493404	0.246702	+	0.969091i	$0.420653\pi$
$594$	−26.6563	−1.09372
$595$	−1.57709	−0.0646543
$596$	−0.376372	−0.0154168
$597$	0.726504	0.0297338
$598$	0.273551	0.0111863
$599$	29.6458	1.21130	0.605648	−	0.795733i	$-0.292914\pi$
$599$	29.6458	1.21130	0.605648	+	0.795733i	$0.292914\pi$
$600$	5.68164	0.231952
$601$	23.3520	0.952549	0.476274	−	0.879297i	$-0.341987\pi$
$601$	23.3520	0.952549	0.476274	+	0.879297i	$0.341987\pi$
$602$	−9.43250	−0.384440
$603$	6.88687	0.280455
$604$	−20.9967	−0.854343
$605$	4.06710	0.165351
$606$	14.9783	0.608453
$607$	−40.1580	−1.62996	−0.814982	−	0.579486i	$-0.803253\pi$
$607$	−40.1580	−1.62996	−0.814982	+	0.579486i	$0.803253\pi$
$608$	1.00000	0.0405554
$609$	42.6275	1.72735
$610$	3.57585	0.144782
$611$	1.54512	0.0625088
$612$	1.67255	0.0676090
$613$	−27.2177	−1.09931	−0.549656	−	0.835391i	$-0.685241\pi$
$613$	−27.2177	−1.09931	−0.549656	+	0.835391i	$0.685241\pi$
$614$	0.811256	0.0327396
$615$	3.91435	0.157842
$616$	25.5181	1.02815
$617$	36.6380	1.47499	0.737494	−	0.675353i	$-0.236009\pi$
$617$	36.6380	1.47499	0.737494	+	0.675353i	$0.236009\pi$
$618$	8.00721	0.322097
$619$	−15.3713	−0.617825	−0.308912	−	0.951091i	$-0.599965\pi$
$619$	−15.3713	−0.617825	−0.308912	+	0.951091i	$0.599965\pi$
$620$	−3.06962	−0.123279
$621$	−3.28581	−0.131855
$622$	−23.6688	−0.949032
$623$	76.3057	3.05712
$624$	−0.519870	−0.0208115
$625$	23.6304	0.945216
$626$	−17.3521	−0.693529
$627$	5.72027	0.228445
$628$	5.18928	0.207075
$629$	6.84316	0.272855
$630$	2.59821	0.103515
$631$	10.1741	0.405023	0.202512	−	0.979280i	$-0.435090\pi$
$631$	10.1741	0.405023	0.202512	+	0.979280i	$0.435090\pi$
$632$	−15.9006	−0.632493
$633$	−1.15760	−0.0460104
$634$	−27.2009	−1.08029
$635$	−3.92547	−0.155777
$636$	12.6317	0.500880
$637$	−8.83251	−0.349957
$638$	35.2371	1.39505
$639$	19.6785	0.778470
$640$	−0.303099	−0.0119810
$641$	−39.8346	−1.57337	−0.786685	−	0.617354i	$-0.788205\pi$
$641$	−39.8346	−1.57337	−0.786685	+	0.617354i	$0.788205\pi$
$642$	−5.03366	−0.198663
$643$	36.6542	1.44550	0.722751	−	0.691109i	$-0.242877\pi$
$643$	36.6542	1.44550	0.722751	+	0.691109i	$0.242877\pi$
$644$	3.14552	0.123951
$645$	0.640883	0.0252347
$646$	−1.00758	−0.0396428
$647$	−35.8076	−1.40774	−0.703872	−	0.710327i	$-0.748547\pi$
$647$	−35.8076	−1.40774	−0.703872	+	0.710327i	$0.748547\pi$
$648$	1.26461	0.0496786
$649$	−6.67223	−0.261908
$650$	−2.20421	−0.0864563
$651$	−60.5408	−2.37278
$652$	−18.1159	−0.709472
$653$	−24.7724	−0.969420	−0.484710	−	0.874675i	$-0.661075\pi$
$653$	−24.7724	−0.969420	−0.484710	+	0.874675i	$0.661075\pi$
$654$	−14.7338	−0.576138
$655$	−4.32549	−0.169011
$656$	11.1562	0.435577
$657$	18.3535	0.716038
$658$	17.7670	0.692632
$659$	−16.2817	−0.634246	−0.317123	−	0.948384i	$-0.602717\pi$
$659$	−16.2817	−0.634246	−0.317123	+	0.948384i	$0.602717\pi$
$660$	−1.73381	−0.0674884
$661$	34.3162	1.33474	0.667372	−	0.744724i	$-0.267419\pi$
$661$	34.3162	1.33474	0.667372	+	0.744724i	$0.267419\pi$
$662$	−13.7328	−0.533741
$663$	0.523812	0.0203432
$664$	3.16922	0.122990
$665$	−1.56522	−0.0606966
$666$	−11.2739	−0.436856
$667$	4.34353	0.168182
$668$	−15.5999	−0.603579
$669$	−13.2065	−0.510591
$670$	1.25750	0.0485814
$671$	58.2980	2.25057
$672$	−5.97789	−0.230602
$673$	16.0016	0.616817	0.308408	−	0.951254i	$-0.400204\pi$
$673$	16.0016	0.616817	0.308408	+	0.951254i	$0.400204\pi$
$674$	24.7738	0.954250
$675$	26.4763	1.01907
$676$	−12.7983	−0.492243
$677$	11.4442	0.439835	0.219918	−	0.975518i	$-0.429421\pi$
$677$	11.4442	0.439835	0.219918	+	0.975518i	$0.429421\pi$
$678$	3.10119	0.119101
$679$	−88.9186	−3.41238
$680$	0.305397	0.0117115
$681$	−3.66203	−0.140329
$682$	−50.0447	−1.91631
$683$	37.7685	1.44517	0.722586	−	0.691281i	$-0.242953\pi$
$683$	37.7685	1.44517	0.722586	+	0.691281i	$0.242953\pi$
$684$	1.65997	0.0634704
$685$	4.31289	0.164787
$686$	−65.4152	−2.49756
$687$	28.2601	1.07819
$688$	1.82657	0.0696374
$689$	−4.90051	−0.186695
$690$	−0.213719	−0.00813616
$691$	2.70709	0.102983	0.0514913	−	0.998673i	$-0.483603\pi$
$691$	2.70709	0.102983	0.0514913	+	0.998673i	$0.483603\pi$
$692$	−2.49692	−0.0949185
$693$	42.3593	1.60910
$694$	6.65933	0.252785
$695$	−4.77331	−0.181062
$696$	−8.25466	−0.312892
$697$	−11.2408	−0.425776
$698$	−26.8968	−1.01806
$699$	−12.8969	−0.487807
$700$	−25.3458	−0.957982
$701$	14.8152	0.559562	0.279781	−	0.960064i	$-0.409738\pi$
$701$	14.8152	0.559562	0.279781	+	0.960064i	$0.409738\pi$
$702$	−2.42258	−0.0914343
$703$	6.79167	0.256153
$704$	−4.94150	−0.186240
$705$	−1.20717	−0.0454645
$706$	−20.5627	−0.773886
$707$	−66.8184	−2.51296
$708$	1.56304	0.0587427
$709$	36.3859	1.36650	0.683251	−	0.730183i	$-0.260565\pi$
$709$	36.3859	1.36650	0.683251	+	0.730183i	$0.260565\pi$
$710$	3.59317	0.134849
$711$	−26.3945	−0.989871
$712$	−14.7763	−0.553766
$713$	−6.16881	−0.231024
$714$	6.02322	0.225413
$715$	0.672636	0.0251552
$716$	−6.68898	−0.249979
$717$	10.2400	0.382421
$718$	−14.0061	−0.522702
$719$	−8.82852	−0.329248	−0.164624	−	0.986356i	$-0.552641\pi$
$719$	−8.82852	−0.329248	−0.164624	+	0.986356i	$0.552641\pi$
$720$	−0.503134	−0.0187507
$721$	−35.7202	−1.33029
$722$	−1.00000	−0.0372161
$723$	0.602144	0.0223940
$724$	−1.84059	−0.0684051
$725$	−34.9991	−1.29984
$726$	−15.5331	−0.576487
$727$	−11.6652	−0.432640	−0.216320	−	0.976323i	$-0.569405\pi$
$727$	−11.6652	−0.432640	−0.216320	+	0.976323i	$0.569405\pi$
$728$	2.31914	0.0859532
$729$	20.8327	0.771583
$730$	3.35123	0.124034
$731$	−1.84042	−0.0680704
$732$	−13.6569	−0.504775
$733$	−40.4914	−1.49558	−0.747792	−	0.663933i	$-0.768886\pi$
$733$	−40.4914	−1.49558	−0.747792	+	0.663933i	$0.768886\pi$
$734$	−7.85802	−0.290045
$735$	6.90064	0.254534
$736$	−0.609118	−0.0224524
$737$	20.5013	0.755174
$738$	18.5190	0.681692
$739$	−2.83381	−0.104243	−0.0521217	−	0.998641i	$-0.516598\pi$
$739$	−2.83381	−0.104243	−0.0521217	+	0.998641i	$0.516598\pi$
$740$	−2.05855	−0.0756737
$741$	0.519870	0.0190979
$742$	−56.3501	−2.06868
$743$	−29.9122	−1.09737	−0.548685	−	0.836029i	$-0.684872\pi$
$743$	−29.9122	−1.09737	−0.548685	+	0.836029i	$0.684872\pi$
$744$	11.7235	0.429805
$745$	−0.114078	−0.00417949
$746$	18.3143	0.670535
$747$	5.26080	0.192483
$748$	4.97897	0.182049
$749$	22.4552	0.820495
$750$	3.47643	0.126941
$751$	23.9433	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$751$	23.9433	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$752$	−3.44053	−0.125463
$753$	−3.29306	−0.120006
$754$	3.20242	0.116625
$755$	−6.36407	−0.231612
$756$	−27.8568	−1.01314
$757$	−36.7070	−1.33414	−0.667069	−	0.744996i	$-0.732451\pi$
$757$	−36.7070	−1.33414	−0.667069	+	0.744996i	$0.732451\pi$
$758$	28.2657	1.02666
$759$	−3.48432	−0.126473
$760$	0.303099	0.0109946
$761$	−5.93997	−0.215324	−0.107662	−	0.994188i	$-0.534336\pi$
$761$	−5.93997	−0.215324	−0.107662	+	0.994188i	$0.534336\pi$
$762$	14.9922	0.543109
$763$	65.7276	2.37950
$764$	−21.6034	−0.781585
$765$	0.506949	0.0183288
$766$	−33.1556	−1.19796
$767$	−0.606387	−0.0218954
$768$	1.15760	0.0417712
$769$	18.3285	0.660942	0.330471	−	0.943816i	$-0.392792\pi$
$769$	18.3285	0.660942	0.330471	+	0.943816i	$0.392792\pi$
$770$	7.73452	0.278733
$771$	−24.5935	−0.885715
$772$	−4.33318	−0.155955
$773$	−36.2186	−1.30269	−0.651347	−	0.758780i	$-0.725796\pi$
$773$	−36.2186	−1.30269	−0.651347	+	0.758780i	$0.725796\pi$
$774$	3.03205	0.108985
$775$	49.7068	1.78552
$776$	17.2188	0.618118
$777$	−40.5999	−1.45651
$778$	12.8267	0.459858
$779$	−11.1562	−0.399713
$780$	−0.157572	−0.00564199
$781$	58.5803	2.09617
$782$	0.613737	0.0219472
$783$	−38.4664	−1.37468
$784$	19.6674	0.702408
$785$	1.57286	0.0561380
$786$	16.5200	0.589247
$787$	−20.9099	−0.745358	−0.372679	−	0.927960i	$-0.621561\pi$
$787$	−20.9099	−0.745358	−0.372679	+	0.927960i	$0.621561\pi$
$788$	10.4562	0.372488
$789$	8.53073	0.303702
$790$	−4.81946	−0.171469
$791$	−13.8344	−0.491896
$792$	−8.20272	−0.291471
$793$	5.29825	0.188146
$794$	−32.5341	−1.15459
$795$	3.82866	0.135789
$796$	0.627596	0.0222445
$797$	33.5131	1.18709	0.593547	−	0.804800i	$-0.297727\pi$
$797$	33.5131	1.18709	0.593547	+	0.804800i	$0.297727\pi$
$798$	5.97789	0.211615
$799$	3.46661	0.122640
$800$	4.90813	0.173529
$801$	−24.5282	−0.866662
$802$	23.1876	0.818781
$803$	54.6358	1.92806
$804$	−4.80264	−0.169376
$805$	0.953403	0.0336031
$806$	−4.54817	−0.160203
$807$	17.4942	0.615825
$808$	12.9391	0.455197
$809$	−17.7748	−0.624929	−0.312464	−	0.949929i	$-0.601155\pi$
$809$	−17.7748	−0.624929	−0.312464	+	0.949929i	$0.601155\pi$
$810$	0.383302	0.0134679
$811$	36.1451	1.26923	0.634614	−	0.772829i	$-0.281159\pi$
$811$	36.1451	1.26923	0.634614	+	0.772829i	$0.281159\pi$
$812$	36.8241	1.29227
$813$	9.91189	0.347625
$814$	−33.5610	−1.17631
$815$	−5.49090	−0.192338
$816$	−1.16638	−0.0408313
$817$	−1.82657	−0.0639036
$818$	20.7790	0.726521
$819$	3.84970	0.134519
$820$	3.38144	0.118085
$821$	50.6803	1.76875	0.884377	−	0.466773i	$-0.154583\pi$
$821$	50.6803	1.76875	0.884377	+	0.466773i	$0.154583\pi$
$822$	−16.4718	−0.574521
$823$	24.4598	0.852616	0.426308	−	0.904578i	$-0.359814\pi$
$823$	24.4598	0.852616	0.426308	+	0.904578i	$0.359814\pi$
$824$	6.91709	0.240968
$825$	28.0758	0.977475
$826$	−6.97273	−0.242612
$827$	−4.35780	−0.151535	−0.0757677	−	0.997125i	$-0.524141\pi$
$827$	−4.35780	−0.151535	−0.0757677	+	0.997125i	$0.524141\pi$
$828$	−1.01112	−0.0351387
$829$	24.4893	0.850550	0.425275	−	0.905064i	$-0.360177\pi$
$829$	24.4893	0.850550	0.425275	+	0.905064i	$0.360177\pi$
$830$	0.960588	0.0333425
$831$	−25.2298	−0.875211
$832$	−0.449094	−0.0155695
$833$	−19.8165	−0.686602
$834$	18.2303	0.631262
$835$	−4.72832	−0.163630
$836$	4.94150	0.170905
$837$	54.6312	1.88833
$838$	11.6983	0.404110
$839$	−48.5981	−1.67779	−0.838896	−	0.544292i	$-0.816798\pi$
$839$	−48.5981	−1.67779	−0.838896	+	0.544292i	$0.816798\pi$
$840$	−1.81189	−0.0625163
$841$	21.8490	0.753415
$842$	35.1593	1.21167
$843$	−32.4378	−1.11722
$844$	−1.00000	−0.0344214
$845$	−3.87916	−0.133447
$846$	−5.71116	−0.196354
$847$	69.2932	2.38094
$848$	10.9120	0.374720
$849$	18.4111	0.631868
$850$	−4.94535	−0.169624
$851$	−4.13693	−0.141812
$852$	−13.7230	−0.470144
$853$	−20.4737	−0.701005	−0.350502	−	0.936562i	$-0.613989\pi$
$853$	−20.4737	−0.701005	−0.350502	+	0.936562i	$0.613989\pi$
$854$	60.9236	2.08476
$855$	0.503134	0.0172068
$856$	−4.34837	−0.148624
$857$	−4.04647	−0.138225	−0.0691124	−	0.997609i	$-0.522017\pi$
$857$	−4.04647	−0.138225	−0.0691124	+	0.997609i	$0.522017\pi$
$858$	−2.56894	−0.0877020
$859$	22.5662	0.769950	0.384975	−	0.922927i	$-0.374210\pi$
$859$	22.5662	0.769950	0.384975	+	0.922927i	$0.374210\pi$
$860$	0.553632	0.0188787
$861$	66.6907	2.27281
$862$	−16.3075	−0.555437
$863$	31.6852	1.07858	0.539288	−	0.842121i	$-0.318693\pi$
$863$	31.6852	1.07858	0.539288	+	0.842121i	$0.318693\pi$
$864$	5.39437	0.183520
$865$	−0.756813	−0.0257324
$866$	30.2235	1.02704
$867$	−18.5039	−0.628427
$868$	−52.2986	−1.77513
$869$	−78.5729	−2.66540
$870$	−2.50198	−0.0848250
$871$	1.86320	0.0631321
$872$	−12.7279	−0.431022
$873$	28.5826	0.967374
$874$	0.609118	0.0206037
$875$	−15.5084	−0.524279
$876$	−12.7990	−0.432439
$877$	37.0035	1.24952	0.624760	−	0.780817i	$-0.285197\pi$
$877$	37.0035	1.24952	0.624760	+	0.780817i	$0.285197\pi$
$878$	−25.3149	−0.854337
$879$	−17.1427	−0.578209
$880$	−1.49776	−0.0504896
$881$	−46.4518	−1.56500	−0.782501	−	0.622649i	$-0.786056\pi$
$881$	−46.4518	−1.56500	−0.782501	+	0.622649i	$0.786056\pi$
$882$	32.6473	1.09929
$883$	−26.4489	−0.890078	−0.445039	−	0.895511i	$-0.646810\pi$
$883$	−26.4489	−0.890078	−0.445039	+	0.895511i	$0.646810\pi$
$884$	0.452499	0.0152192
$885$	0.473756	0.0159251
$886$	−16.6978	−0.560975
$887$	−17.4180	−0.584840	−0.292420	−	0.956290i	$-0.594461\pi$
$887$	−17.4180	−0.584840	−0.292420	+	0.956290i	$0.594461\pi$
$888$	7.86202	0.263832
$889$	−66.8801	−2.24309
$890$	−4.47869	−0.150126
$891$	6.24907	0.209352
$892$	−11.4085	−0.381985
$893$	3.44053	0.115133
$894$	0.435688	0.0145716
$895$	−2.02742	−0.0677693
$896$	−5.16405	−0.172519
$897$	−0.316662	−0.0105731
$898$	5.38686	0.179762
$899$	−72.2173	−2.40858
$900$	8.14733	0.271578
$901$	−10.9947	−0.366288
$902$	55.1284	1.83558
$903$	10.9190	0.363363
$904$	2.67899	0.0891018
$905$	−0.557882	−0.0185446
$906$	24.3057	0.807503
$907$	2.14999	0.0713891	0.0356946	−	0.999363i	$-0.488636\pi$
$907$	2.14999	0.0713891	0.0356946	+	0.999363i	$0.488636\pi$
$908$	−3.16347	−0.104983
$909$	21.4785	0.712398
$910$	0.702930	0.0233019
$911$	−21.0039	−0.695892	−0.347946	−	0.937515i	$-0.613121\pi$
$911$	−21.0039	−0.695892	−0.347946	+	0.937515i	$0.613121\pi$
$912$	−1.15760	−0.0383319
$913$	15.6607	0.518293
$914$	−28.5082	−0.942968
$915$	−4.13940	−0.136844
$916$	24.4127	0.806619
$917$	−73.6956	−2.43364
$918$	−5.43527	−0.179391
$919$	−15.7311	−0.518922	−0.259461	−	0.965754i	$-0.583545\pi$
$919$	−15.7311	−0.518922	−0.259461	+	0.965754i	$0.583545\pi$
$920$	−0.184623	−0.00608685
$921$	−0.939109	−0.0309447
$922$	−27.5561	−0.907513
$923$	5.32390	0.175238
$924$	−29.5397	−0.971786
$925$	33.3344	1.09603
$926$	−2.21654	−0.0728400
$927$	11.4821	0.377123
$928$	−7.13085	−0.234082
$929$	−39.2913	−1.28910	−0.644552	−	0.764560i	$-0.722956\pi$
$929$	−39.2913	−1.28910	−0.644552	+	0.764560i	$0.722956\pi$
$930$	3.55338	0.116520
$931$	−19.6674	−0.644573
$932$	−11.1411	−0.364939
$933$	27.3989	0.897001
$934$	−18.0964	−0.592132
$935$	1.50912	0.0493535
$936$	−0.745481	−0.0243668
$937$	21.2409	0.693911	0.346956	−	0.937882i	$-0.387215\pi$
$937$	21.2409	0.693911	0.346956	+	0.937882i	$0.387215\pi$
$938$	21.4246	0.699538
$939$	20.0867	0.655506
$940$	−1.04282	−0.0340130
$941$	−41.7114	−1.35975	−0.679876	−	0.733327i	$-0.737966\pi$
$941$	−41.7114	−1.35975	−0.679876	+	0.733327i	$0.737966\pi$
$942$	−6.00710	−0.195722
$943$	6.79546	0.221291
$944$	1.35024	0.0439467
$945$	−8.44337	−0.274663
$946$	9.02599	0.293460
$947$	−1.69767	−0.0551668	−0.0275834	−	0.999620i	$-0.508781\pi$
$947$	−1.69767	−0.0551668	−0.0275834	+	0.999620i	$0.508781\pi$
$948$	18.4065	0.597816
$949$	4.96542	0.161184
$950$	−4.90813	−0.159241
$951$	31.4877	1.02106
$952$	5.20321	0.168637
$953$	−39.9751	−1.29492	−0.647460	−	0.762099i	$-0.724169\pi$
$953$	−39.9751	−1.29492	−0.647460	+	0.762099i	$0.724169\pi$
$954$	18.1136	0.586448
$955$	−6.54798	−0.211888
$956$	8.84593	0.286098
$957$	−40.7904	−1.31857
$958$	4.71277	0.152263
$959$	73.4809	2.37282
$960$	0.350867	0.0113242
$961$	71.5651	2.30855
$962$	−3.05010	−0.0983390
$963$	−7.21815	−0.232602
$964$	0.520167	0.0167534
$965$	−1.31338	−0.0422793
$966$	−3.64125	−0.117155
$967$	−55.7526	−1.79288	−0.896441	−	0.443162i	$-0.853856\pi$
$967$	−55.7526	−1.79288	−0.896441	+	0.443162i	$0.853856\pi$
$968$	−13.4184	−0.431283
$969$	1.16638	0.0374694
$970$	5.21899	0.167572
$971$	6.92143	0.222119	0.111060	−	0.993814i	$-0.464576\pi$
$971$	6.92143	0.222119	0.111060	+	0.993814i	$0.464576\pi$
$972$	14.7192	0.472118
$973$	−81.3253	−2.60717
$974$	−25.2904	−0.810358
$975$	2.55159	0.0817163
$976$	−11.7976	−0.377633
$977$	35.7256	1.14296	0.571481	−	0.820615i	$-0.306369\pi$
$977$	35.7256	1.14296	0.571481	+	0.820615i	$0.306369\pi$
$978$	20.9709	0.670575
$979$	−73.0172	−2.33364
$980$	5.96117	0.190423
$981$	−21.1279	−0.674563
$982$	42.4850	1.35575
$983$	21.9883	0.701319	0.350659	−	0.936503i	$-0.385958\pi$
$983$	21.9883	0.701319	0.350659	+	0.936503i	$0.385958\pi$
$984$	−12.9144	−0.411697
$985$	3.16928	0.100982
$986$	7.18492	0.228814
$987$	−20.5671	−0.654658
$988$	0.449094	0.0142876
$989$	1.11260	0.0353785
$990$	−2.48624	−0.0790178
$991$	−4.71730	−0.149850	−0.0749250	−	0.997189i	$-0.523872\pi$
$991$	−4.71730	−0.149850	−0.0749250	+	0.997189i	$0.523872\pi$
$992$	10.1274	0.321547
$993$	15.8971	0.504479
$994$	61.2186	1.94174
$995$	0.190224	0.00603050
$996$	−3.66868	−0.116247
$997$	−1.58930	−0.0503337	−0.0251668	−	0.999683i	$-0.508012\pi$
$997$	−1.58930	−0.0503337	−0.0251668	+	0.999683i	$0.508012\pi$
$998$	2.52549	0.0799431
$999$	36.6368	1.15914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.24	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.24	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.15760 q^{3} +1.00000 q^{4} +0.303099 q^{5} -1.15760 q^{6} +5.16405 q^{7} -1.00000 q^{8} -1.65997 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.15760 q^{3} +1.00000 q^{4} +0.303099 q^{5} -1.15760 q^{6} +5.16405 q^{7} -1.00000 q^{8} -1.65997 q^{9} -0.303099 q^{10} -4.94150 q^{11} +1.15760 q^{12} -0.449094 q^{13} -5.16405 q^{14} +0.350867 q^{15} +1.00000 q^{16} -1.00758 q^{17} +1.65997 q^{18} -1.00000 q^{19} +0.303099 q^{20} +5.97789 q^{21} +4.94150 q^{22} +0.609118 q^{23} -1.15760 q^{24} -4.90813 q^{25} +0.449094 q^{26} -5.39437 q^{27} +5.16405 q^{28} +7.13085 q^{29} -0.350867 q^{30} -10.1274 q^{31} -1.00000 q^{32} -5.72027 q^{33} +1.00758 q^{34} +1.56522 q^{35} -1.65997 q^{36} -6.79167 q^{37} +1.00000 q^{38} -0.519870 q^{39} -0.303099 q^{40} +11.1562 q^{41} -5.97789 q^{42} +1.82657 q^{43} -4.94150 q^{44} -0.503134 q^{45} -0.609118 q^{46} -3.44053 q^{47} +1.15760 q^{48} +19.6674 q^{49} +4.90813 q^{50} -1.16638 q^{51} -0.449094 q^{52} +10.9120 q^{53} +5.39437 q^{54} -1.49776 q^{55} -5.16405 q^{56} -1.15760 q^{57} -7.13085 q^{58} +1.35024 q^{59} +0.350867 q^{60} -11.7976 q^{61} +10.1274 q^{62} -8.57215 q^{63} +1.00000 q^{64} -0.136120 q^{65} +5.72027 q^{66} -4.14880 q^{67} -1.00758 q^{68} +0.705114 q^{69} -1.56522 q^{70} -11.8548 q^{71} +1.65997 q^{72} -11.0565 q^{73} +6.79167 q^{74} -5.68164 q^{75} -1.00000 q^{76} -25.5181 q^{77} +0.519870 q^{78} +15.9006 q^{79} +0.303099 q^{80} -1.26461 q^{81} -11.1562 q^{82} -3.16922 q^{83} +5.97789 q^{84} -0.305397 q^{85} -1.82657 q^{86} +8.25466 q^{87} +4.94150 q^{88} +14.7763 q^{89} +0.503134 q^{90} -2.31914 q^{91} +0.609118 q^{92} -11.7235 q^{93} +3.44053 q^{94} -0.303099 q^{95} -1.15760 q^{96} -17.2188 q^{97} -19.6674 q^{98} +8.20272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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