LMFDB - Embedded newform 2014.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.4
Root			$-0.303994$ of defining polynomial
Character	$\chi$	$=$	2014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.303994 q^{3} +1.00000 q^{4} +0.384085 q^{5} -0.303994 q^{6} +3.38802 q^{7} -1.00000 q^{8} -2.90759 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.303994 q^{3} +1.00000 q^{4} +0.384085 q^{5} -0.303994 q^{6} +3.38802 q^{7} -1.00000 q^{8} -2.90759 q^{9} -0.384085 q^{10} -4.48372 q^{11} +0.303994 q^{12} +4.53640 q^{13} -3.38802 q^{14} +0.116759 q^{15} +1.00000 q^{16} -3.64195 q^{17} +2.90759 q^{18} -1.00000 q^{19} +0.384085 q^{20} +1.02994 q^{21} +4.48372 q^{22} -6.29729 q^{23} -0.303994 q^{24} -4.85248 q^{25} -4.53640 q^{26} -1.79587 q^{27} +3.38802 q^{28} -4.93019 q^{29} -0.116759 q^{30} +3.40194 q^{31} -1.00000 q^{32} -1.36302 q^{33} +3.64195 q^{34} +1.30129 q^{35} -2.90759 q^{36} -1.43648 q^{37} +1.00000 q^{38} +1.37904 q^{39} -0.384085 q^{40} -2.89212 q^{41} -1.02994 q^{42} +1.09635 q^{43} -4.48372 q^{44} -1.11676 q^{45} +6.29729 q^{46} -3.58030 q^{47} +0.303994 q^{48} +4.47867 q^{49} +4.85248 q^{50} -1.10713 q^{51} +4.53640 q^{52} -1.00000 q^{53} +1.79587 q^{54} -1.72213 q^{55} -3.38802 q^{56} -0.303994 q^{57} +4.93019 q^{58} -8.65878 q^{59} +0.116759 q^{60} +0.670002 q^{61} -3.40194 q^{62} -9.85096 q^{63} +1.00000 q^{64} +1.74236 q^{65} +1.36302 q^{66} -9.02195 q^{67} -3.64195 q^{68} -1.91434 q^{69} -1.30129 q^{70} +2.48700 q^{71} +2.90759 q^{72} -0.918095 q^{73} +1.43648 q^{74} -1.47513 q^{75} -1.00000 q^{76} -15.1909 q^{77} -1.37904 q^{78} +7.94533 q^{79} +0.384085 q^{80} +8.17683 q^{81} +2.89212 q^{82} +4.26709 q^{83} +1.02994 q^{84} -1.39882 q^{85} -1.09635 q^{86} -1.49875 q^{87} +4.48372 q^{88} +14.8010 q^{89} +1.11676 q^{90} +15.3694 q^{91} -6.29729 q^{92} +1.03417 q^{93} +3.58030 q^{94} -0.384085 q^{95} -0.303994 q^{96} -3.38043 q^{97} -4.47867 q^{98} +13.0368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 5 q^{13} + q^{15} + 8 q^{16} - 9 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} - 9 q^{21} + 6 q^{22} - q^{23} - 9 q^{25} + 5 q^{26} - 3 q^{27} - 23 q^{29} - q^{30} - 6 q^{31} - 8 q^{32} - 6 q^{33} + 9 q^{34} - 7 q^{35} + 2 q^{36} + q^{37} + 8 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} + 9 q^{42} + 9 q^{43} - 6 q^{44} - 9 q^{45} + q^{46} - 13 q^{47} - 8 q^{49} + 9 q^{50} - 24 q^{51} - 5 q^{52} - 8 q^{53} + 3 q^{54} - 11 q^{55} + 23 q^{58} - 9 q^{59} + q^{60} + 6 q^{62} - 18 q^{63} + 8 q^{64} - 26 q^{65} + 6 q^{66} + 9 q^{67} - 9 q^{68} - 22 q^{69} + 7 q^{70} - 31 q^{71} - 2 q^{72} + 5 q^{73} - q^{74} - q^{75} - 8 q^{76} - 4 q^{77} + 5 q^{78} + 19 q^{79} + q^{80} - 24 q^{81} + 3 q^{82} + 11 q^{83} - 9 q^{84} + 19 q^{85} - 9 q^{86} - 22 q^{87} + 6 q^{88} - 41 q^{89} + 9 q^{90} + 18 q^{91} - q^{92} + 3 q^{93} + 13 q^{94} - q^{95} - 24 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 5 * q^13 + q^15 + 8 * q^16 - 9 * q^17 - 2 * q^18 - 8 * q^19 + q^20 - 9 * q^21 + 6 * q^22 - q^23 - 9 * q^25 + 5 * q^26 - 3 * q^27 - 23 * q^29 - q^30 - 6 * q^31 - 8 * q^32 - 6 * q^33 + 9 * q^34 - 7 * q^35 + 2 * q^36 + q^37 + 8 * q^38 - 5 * q^39 - q^40 - 3 * q^41 + 9 * q^42 + 9 * q^43 - 6 * q^44 - 9 * q^45 + q^46 - 13 * q^47 - 8 * q^49 + 9 * q^50 - 24 * q^51 - 5 * q^52 - 8 * q^53 + 3 * q^54 - 11 * q^55 + 23 * q^58 - 9 * q^59 + q^60 + 6 * q^62 - 18 * q^63 + 8 * q^64 - 26 * q^65 + 6 * q^66 + 9 * q^67 - 9 * q^68 - 22 * q^69 + 7 * q^70 - 31 * q^71 - 2 * q^72 + 5 * q^73 - q^74 - q^75 - 8 * q^76 - 4 * q^77 + 5 * q^78 + 19 * q^79 + q^80 - 24 * q^81 + 3 * q^82 + 11 * q^83 - 9 * q^84 + 19 * q^85 - 9 * q^86 - 22 * q^87 + 6 * q^88 - 41 * q^89 + 9 * q^90 + 18 * q^91 - q^92 + 3 * q^93 + 13 * q^94 - q^95 - 24 * q^97 + 8 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.303994	0.175511	0.0877556	−	0.996142i	$-0.472031\pi$
$3$	0.303994	0.175511	0.0877556	+	0.996142i	$0.472031\pi$
$4$	1.00000	0.500000
$5$	0.384085	0.171768	0.0858839	−	0.996305i	$-0.472629\pi$
$5$	0.384085	0.171768	0.0858839	+	0.996305i	$0.472629\pi$
$6$	−0.303994	−0.124105
$7$	3.38802	1.28055	0.640275	−	0.768145i	$-0.278820\pi$
$7$	3.38802	1.28055	0.640275	+	0.768145i	$0.278820\pi$
$8$	−1.00000	−0.353553
$9$	−2.90759	−0.969196
$10$	−0.384085	−0.121458
$11$	−4.48372	−1.35189	−0.675946	−	0.736951i	$-0.736265\pi$
$11$	−4.48372	−1.35189	−0.675946	+	0.736951i	$0.736265\pi$
$12$	0.303994	0.0877556
$13$	4.53640	1.25817	0.629086	−	0.777336i	$-0.283429\pi$
$13$	4.53640	1.25817	0.629086	+	0.777336i	$0.283429\pi$
$14$	−3.38802	−0.905486
$15$	0.116759	0.0301472
$16$	1.00000	0.250000
$17$	−3.64195	−0.883302	−0.441651	−	0.897187i	$-0.645607\pi$
$17$	−3.64195	−0.883302	−0.441651	+	0.897187i	$0.645607\pi$
$18$	2.90759	0.685325
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.384085	0.0858839
$21$	1.02994	0.224751
$22$	4.48372	0.955932
$23$	−6.29729	−1.31308	−0.656538	−	0.754293i	$-0.727980\pi$
$23$	−6.29729	−1.31308	−0.656538	+	0.754293i	$0.727980\pi$
$24$	−0.303994	−0.0620526
$25$	−4.85248	−0.970496
$26$	−4.53640	−0.889662
$27$	−1.79587	−0.345616
$28$	3.38802	0.640275
$29$	−4.93019	−0.915513	−0.457757	−	0.889078i	$-0.651347\pi$
$29$	−4.93019	−0.915513	−0.457757	+	0.889078i	$0.651347\pi$
$30$	−0.116759	−0.0213173
$31$	3.40194	0.611007	0.305503	−	0.952191i	$-0.401175\pi$
$31$	3.40194	0.611007	0.305503	+	0.952191i	$0.401175\pi$
$32$	−1.00000	−0.176777
$33$	−1.36302	−0.237272
$34$	3.64195	0.624589
$35$	1.30129	0.219957
$36$	−2.90759	−0.484598
$37$	−1.43648	−0.236157	−0.118078	−	0.993004i	$-0.537673\pi$
$37$	−1.43648	−0.236157	−0.118078	+	0.993004i	$0.537673\pi$
$38$	1.00000	0.162221
$39$	1.37904	0.220823
$40$	−0.384085	−0.0607291
$41$	−2.89212	−0.451673	−0.225837	−	0.974165i	$-0.572512\pi$
$41$	−2.89212	−0.451673	−0.225837	+	0.974165i	$0.572512\pi$
$42$	−1.02994	−0.158923
$43$	1.09635	0.167191	0.0835957	−	0.996500i	$-0.473360\pi$
$43$	1.09635	0.167191	0.0835957	+	0.996500i	$0.473360\pi$
$44$	−4.48372	−0.675946
$45$	−1.11676	−0.166477
$46$	6.29729	0.928485
$47$	−3.58030	−0.522240	−0.261120	−	0.965306i	$-0.584092\pi$
$47$	−3.58030	−0.522240	−0.261120	+	0.965306i	$0.584092\pi$
$48$	0.303994	0.0438778
$49$	4.47867	0.639811
$50$	4.85248	0.686244
$51$	−1.10713	−0.155029
$52$	4.53640	0.629086
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.79587	0.244387
$55$	−1.72213	−0.232212
$56$	−3.38802	−0.452743
$57$	−0.303994	−0.0402650
$58$	4.93019	0.647366
$59$	−8.65878	−1.12728	−0.563638	−	0.826022i	$-0.690599\pi$
$59$	−8.65878	−1.12728	−0.563638	+	0.826022i	$0.690599\pi$
$60$	0.116759	0.0150736
$61$	0.670002	0.0857850	0.0428925	−	0.999080i	$-0.486343\pi$
$61$	0.670002	0.0857850	0.0428925	+	0.999080i	$0.486343\pi$
$62$	−3.40194	−0.432047
$63$	−9.85096	−1.24110
$64$	1.00000	0.125000
$65$	1.74236	0.216113
$66$	1.36302	0.167777
$67$	−9.02195	−1.10221	−0.551104	−	0.834437i	$-0.685793\pi$
$67$	−9.02195	−1.10221	−0.551104	+	0.834437i	$0.685793\pi$
$68$	−3.64195	−0.441651
$69$	−1.91434	−0.230460
$70$	−1.30129	−0.155533
$71$	2.48700	0.295153	0.147577	−	0.989051i	$-0.452853\pi$
$71$	2.48700	0.295153	0.147577	+	0.989051i	$0.452853\pi$
$72$	2.90759	0.342662
$73$	−0.918095	−0.107455	−0.0537275	−	0.998556i	$-0.517110\pi$
$73$	−0.918095	−0.107455	−0.0537275	+	0.998556i	$0.517110\pi$
$74$	1.43648	0.166988
$75$	−1.47513	−0.170333
$76$	−1.00000	−0.114708
$77$	−15.1909	−1.73117
$78$	−1.37904	−0.156146
$79$	7.94533	0.893919	0.446959	−	0.894554i	$-0.352507\pi$
$79$	7.94533	0.893919	0.446959	+	0.894554i	$0.352507\pi$
$80$	0.384085	0.0429420
$81$	8.17683	0.908536
$82$	2.89212	0.319381
$83$	4.26709	0.468374	0.234187	−	0.972192i	$-0.424757\pi$
$83$	4.26709	0.468374	0.234187	+	0.972192i	$0.424757\pi$
$84$	1.02994	0.112375
$85$	−1.39882	−0.151723
$86$	−1.09635	−0.118222
$87$	−1.49875	−0.160683
$88$	4.48372	0.477966
$89$	14.8010	1.56891	0.784453	−	0.620188i	$-0.212944\pi$
$89$	14.8010	1.56891	0.784453	+	0.620188i	$0.212944\pi$
$90$	1.11676	0.117717
$91$	15.3694	1.61115
$92$	−6.29729	−0.656538
$93$	1.03417	0.107238
$94$	3.58030	0.369280
$95$	−0.384085	−0.0394062
$96$	−0.303994	−0.0310263
$97$	−3.38043	−0.343231	−0.171615	−	0.985164i	$-0.554899\pi$
$97$	−3.38043	−0.343231	−0.171615	+	0.985164i	$0.554899\pi$
$98$	−4.47867	−0.452414
$99$	13.0368	1.31025
$100$	−4.85248	−0.485248
$101$	−0.160326	−0.0159530	−0.00797650	−	0.999968i	$-0.502539\pi$
$101$	−0.160326	−0.0159530	−0.00797650	+	0.999968i	$0.502539\pi$
$102$	1.10713	0.109622
$103$	−13.5627	−1.33637	−0.668185	−	0.743996i	$-0.732928\pi$
$103$	−13.5627	−1.33637	−0.668185	+	0.743996i	$0.732928\pi$
$104$	−4.53640	−0.444831
$105$	0.395583	0.0386050
$106$	1.00000	0.0971286
$107$	11.8314	1.14378	0.571892	−	0.820329i	$-0.306210\pi$
$107$	11.8314	1.14378	0.571892	+	0.820329i	$0.306210\pi$
$108$	−1.79587	−0.172808
$109$	−7.61613	−0.729493	−0.364747	−	0.931107i	$-0.618844\pi$
$109$	−7.61613	−0.729493	−0.364747	+	0.931107i	$0.618844\pi$
$110$	1.72213	0.164198
$111$	−0.436683	−0.0414481
$112$	3.38802	0.320138
$113$	0.560216	0.0527007	0.0263504	−	0.999653i	$-0.491611\pi$
$113$	0.560216	0.0527007	0.0263504	+	0.999653i	$0.491611\pi$
$114$	0.303994	0.0284717
$115$	−2.41869	−0.225544
$116$	−4.93019	−0.457757
$117$	−13.1900	−1.21942
$118$	8.65878	0.797105
$119$	−12.3390	−1.13111
$120$	−0.116759	−0.0106586
$121$	9.10373	0.827612
$122$	−0.670002	−0.0606592
$123$	−0.879187	−0.0792736
$124$	3.40194	0.305503
$125$	−3.78419	−0.338468
$126$	9.85096	0.877593
$127$	−7.76997	−0.689473	−0.344737	−	0.938699i	$-0.612032\pi$
$127$	−7.76997	−0.689473	−0.344737	+	0.938699i	$0.612032\pi$
$128$	−1.00000	−0.0883883
$129$	0.333283	0.0293439
$130$	−1.74236	−0.152815
$131$	13.9348	1.21749	0.608745	−	0.793366i	$-0.291673\pi$
$131$	13.9348	1.21749	0.608745	+	0.793366i	$0.291673\pi$
$132$	−1.36302	−0.118636
$133$	−3.38802	−0.293779
$134$	9.02195	0.779378
$135$	−0.689767	−0.0593657
$136$	3.64195	0.312295
$137$	−15.9508	−1.36277	−0.681383	−	0.731927i	$-0.738621\pi$
$137$	−15.9508	−1.36277	−0.681383	+	0.731927i	$0.738621\pi$
$138$	1.91434	0.162959
$139$	9.24743	0.784357	0.392178	−	0.919889i	$-0.371722\pi$
$139$	9.24743	0.784357	0.392178	+	0.919889i	$0.371722\pi$
$140$	1.30129	0.109979
$141$	−1.08839	−0.0916590
$142$	−2.48700	−0.208705
$143$	−20.3400	−1.70091
$144$	−2.90759	−0.242299
$145$	−1.89361	−0.157256
$146$	0.918095	0.0759821
$147$	1.36149	0.112294
$148$	−1.43648	−0.118078
$149$	2.89296	0.237000	0.118500	−	0.992954i	$-0.462191\pi$
$149$	2.89296	0.237000	0.118500	+	0.992954i	$0.462191\pi$
$150$	1.47513	0.120443
$151$	−2.50618	−0.203950	−0.101975	−	0.994787i	$-0.532516\pi$
$151$	−2.50618	−0.203950	−0.101975	+	0.994787i	$0.532516\pi$
$152$	1.00000	0.0811107
$153$	10.5893	0.856093
$154$	15.1909	1.22412
$155$	1.30663	0.104951
$156$	1.37904	0.110412
$157$	−5.07548	−0.405068	−0.202534	−	0.979275i	$-0.564918\pi$
$157$	−5.07548	−0.405068	−0.202534	+	0.979275i	$0.564918\pi$
$158$	−7.94533	−0.632096
$159$	−0.303994	−0.0241083
$160$	−0.384085	−0.0303646
$161$	−21.3354	−1.68146
$162$	−8.17683	−0.642432
$163$	−19.1933	−1.50334	−0.751669	−	0.659540i	$-0.770751\pi$
$163$	−19.1933	−1.50334	−0.751669	+	0.659540i	$0.770751\pi$
$164$	−2.89212	−0.225837
$165$	−0.523517	−0.0407557
$166$	−4.26709	−0.331191
$167$	9.80611	0.758820	0.379410	−	0.925229i	$-0.376127\pi$
$167$	9.80611	0.758820	0.379410	+	0.925229i	$0.376127\pi$
$168$	−1.02994	−0.0794615
$169$	7.57896	0.582997
$170$	1.39882	0.107284
$171$	2.90759	0.222349
$172$	1.09635	0.0835957
$173$	−10.4921	−0.797697	−0.398849	−	0.917017i	$-0.630590\pi$
$173$	−10.4921	−0.797697	−0.398849	+	0.917017i	$0.630590\pi$
$174$	1.49875	0.113620
$175$	−16.4403	−1.24277
$176$	−4.48372	−0.337973
$177$	−2.63222	−0.197850
$178$	−14.8010	−1.10938
$179$	−6.33829	−0.473746	−0.236873	−	0.971541i	$-0.576122\pi$
$179$	−6.33829	−0.473746	−0.236873	+	0.971541i	$0.576122\pi$
$180$	−1.11676	−0.0832383
$181$	−19.9662	−1.48408	−0.742039	−	0.670356i	$-0.766141\pi$
$181$	−19.9662	−1.48408	−0.742039	+	0.670356i	$0.766141\pi$
$182$	−15.3694	−1.13926
$183$	0.203677	0.0150562
$184$	6.29729	0.464243
$185$	−0.551732	−0.0405641
$186$	−1.03417	−0.0758291
$187$	16.3295	1.19413
$188$	−3.58030	−0.261120
$189$	−6.08445	−0.442579
$190$	0.384085	0.0278644
$191$	−1.02363	−0.0740676	−0.0370338	−	0.999314i	$-0.511791\pi$
$191$	−1.02363	−0.0740676	−0.0370338	+	0.999314i	$0.511791\pi$
$192$	0.303994	0.0219389
$193$	9.88425	0.711484	0.355742	−	0.934584i	$-0.384228\pi$
$193$	9.88425	0.711484	0.355742	+	0.934584i	$0.384228\pi$
$194$	3.38043	0.242701
$195$	0.529668	0.0379303
$196$	4.47867	0.319905
$197$	3.92018	0.279301	0.139651	−	0.990201i	$-0.455402\pi$
$197$	3.92018	0.279301	0.139651	+	0.990201i	$0.455402\pi$
$198$	−13.0368	−0.926485
$199$	−22.0238	−1.56122	−0.780612	−	0.625016i	$-0.785092\pi$
$199$	−22.0238	−1.56122	−0.780612	+	0.625016i	$0.785092\pi$
$200$	4.85248	0.343122
$201$	−2.74262	−0.193450
$202$	0.160326	0.0112805
$203$	−16.7036	−1.17236
$204$	−1.10713	−0.0775147
$205$	−1.11082	−0.0775829
$206$	13.5627	0.944956
$207$	18.3099	1.27263
$208$	4.53640	0.314543
$209$	4.48372	0.310145
$210$	−0.395583	−0.0272978
$211$	−15.6298	−1.07600	−0.537999	−	0.842945i	$-0.680820\pi$
$211$	−15.6298	−1.07600	−0.537999	+	0.842945i	$0.680820\pi$
$212$	−1.00000	−0.0686803
$213$	0.756035	0.0518026
$214$	−11.8314	−0.808777
$215$	0.421090	0.0287181
$216$	1.79587	0.122194
$217$	11.5258	0.782425
$218$	7.61613	0.515829
$219$	−0.279096	−0.0188595
$220$	−1.72213	−0.116106
$221$	−16.5214	−1.11135
$222$	0.436683	0.0293082
$223$	22.6635	1.51766	0.758831	−	0.651287i	$-0.225771\pi$
$223$	22.6635	1.51766	0.758831	+	0.651287i	$0.225771\pi$
$224$	−3.38802	−0.226372
$225$	14.1090	0.940601
$226$	−0.560216	−0.0372650
$227$	−22.2342	−1.47573	−0.737867	−	0.674946i	$-0.764167\pi$
$227$	−22.2342	−1.47573	−0.737867	+	0.674946i	$0.764167\pi$
$228$	−0.303994	−0.0201325
$229$	−15.0724	−0.996011	−0.498005	−	0.867174i	$-0.665934\pi$
$229$	−15.0724	−0.996011	−0.498005	+	0.867174i	$0.665934\pi$
$230$	2.41869	0.159484
$231$	−4.61795	−0.303839
$232$	4.93019	0.323683
$233$	18.1633	1.18992	0.594958	−	0.803757i	$-0.297169\pi$
$233$	18.1633	1.18992	0.594958	+	0.803757i	$0.297169\pi$
$234$	13.1900	0.862257
$235$	−1.37514	−0.0897041
$236$	−8.65878	−0.563638
$237$	2.41533	0.156893
$238$	12.3390	0.799818
$239$	−4.45072	−0.287893	−0.143947	−	0.989585i	$-0.545979\pi$
$239$	−4.45072	−0.287893	−0.143947	+	0.989585i	$0.545979\pi$
$240$	0.116759	0.00753679
$241$	2.01272	0.129651	0.0648253	−	0.997897i	$-0.479351\pi$
$241$	2.01272	0.129651	0.0648253	+	0.997897i	$0.479351\pi$
$242$	−9.10373	−0.585210
$243$	7.87333	0.505074
$244$	0.670002	0.0428925
$245$	1.72019	0.109899
$246$	0.879187	0.0560549
$247$	−4.53640	−0.288644
$248$	−3.40194	−0.216023
$249$	1.29717	0.0822049
$250$	3.78419	0.239333
$251$	0.872969	0.0551013	0.0275507	−	0.999620i	$-0.491229\pi$
$251$	0.872969	0.0551013	0.0275507	+	0.999620i	$0.491229\pi$
$252$	−9.85096	−0.620552
$253$	28.2353	1.77514
$254$	7.76997	0.487531
$255$	−0.425232	−0.0266291
$256$	1.00000	0.0625000
$257$	−0.0632412	−0.00394488	−0.00197244	−	0.999998i	$-0.500628\pi$
$257$	−0.0632412	−0.00394488	−0.00197244	+	0.999998i	$0.500628\pi$
$258$	−0.333283	−0.0207493
$259$	−4.86684	−0.302411
$260$	1.74236	0.108057
$261$	14.3350	0.887312
$262$	−13.9348	−0.860896
$263$	21.7087	1.33862	0.669309	−	0.742984i	$-0.266590\pi$
$263$	21.7087	1.33862	0.669309	+	0.742984i	$0.266590\pi$
$264$	1.36302	0.0838884
$265$	−0.384085	−0.0235941
$266$	3.38802	0.207733
$267$	4.49943	0.275361
$268$	−9.02195	−0.551104
$269$	−1.82032	−0.110987	−0.0554933	−	0.998459i	$-0.517673\pi$
$269$	−1.82032	−0.110987	−0.0554933	+	0.998459i	$0.517673\pi$
$270$	0.689767	0.0419779
$271$	−27.4840	−1.66953	−0.834766	−	0.550604i	$-0.814397\pi$
$271$	−27.4840	−1.66953	−0.834766	+	0.550604i	$0.814397\pi$
$272$	−3.64195	−0.220826
$273$	4.67222	0.282775
$274$	15.9508	0.963621
$275$	21.7572	1.31201
$276$	−1.91434	−0.115230
$277$	−16.9734	−1.01983	−0.509917	−	0.860224i	$-0.670324\pi$
$277$	−16.9734	−1.01983	−0.509917	+	0.860224i	$0.670324\pi$
$278$	−9.24743	−0.554624
$279$	−9.89144	−0.592185
$280$	−1.30129	−0.0777667
$281$	10.9749	0.654707	0.327353	−	0.944902i	$-0.393843\pi$
$281$	10.9749	0.654707	0.327353	+	0.944902i	$0.393843\pi$
$282$	1.08839	0.0648127
$283$	−4.85924	−0.288852	−0.144426	−	0.989516i	$-0.546134\pi$
$283$	−4.85924	−0.288852	−0.144426	+	0.989516i	$0.546134\pi$
$284$	2.48700	0.147577
$285$	−0.116759	−0.00691623
$286$	20.3400	1.20273
$287$	−9.79855	−0.578390
$288$	2.90759	0.171331
$289$	−3.73621	−0.219777
$290$	1.89361	0.111197
$291$	−1.02763	−0.0602409
$292$	−0.918095	−0.0537275
$293$	−2.46006	−0.143718	−0.0718590	−	0.997415i	$-0.522893\pi$
$293$	−2.46006	−0.143718	−0.0718590	+	0.997415i	$0.522893\pi$
$294$	−1.36149	−0.0794038
$295$	−3.32570	−0.193630
$296$	1.43648	0.0834940
$297$	8.05219	0.467235
$298$	−2.89296	−0.167585
$299$	−28.5671	−1.65208
$300$	−1.47513	−0.0851664
$301$	3.71445	0.214097
$302$	2.50618	0.144214
$303$	−0.0487381	−0.00279993
$304$	−1.00000	−0.0573539
$305$	0.257338	0.0147351
$306$	−10.5893	−0.605349
$307$	1.68947	0.0964232	0.0482116	−	0.998837i	$-0.484648\pi$
$307$	1.68947	0.0964232	0.0482116	+	0.998837i	$0.484648\pi$
$308$	−15.1909	−0.865583
$309$	−4.12297	−0.234548
$310$	−1.30663	−0.0742118
$311$	32.2269	1.82742	0.913709	−	0.406370i	$-0.133205\pi$
$311$	32.2269	1.82742	0.913709	+	0.406370i	$0.133205\pi$
$312$	−1.37904	−0.0780728
$313$	−6.28785	−0.355411	−0.177705	−	0.984084i	$-0.556867\pi$
$313$	−6.28785	−0.355411	−0.177705	+	0.984084i	$0.556867\pi$
$314$	5.07548	0.286426
$315$	−3.78360	−0.213182
$316$	7.94533	0.446959
$317$	−0.296601	−0.0166588	−0.00832939	−	0.999965i	$-0.502651\pi$
$317$	−0.296601	−0.0166588	−0.00832939	+	0.999965i	$0.502651\pi$
$318$	0.303994	0.0170471
$319$	22.1056	1.23767
$320$	0.384085	0.0214710
$321$	3.59667	0.200747
$322$	21.3354	1.18897
$323$	3.64195	0.202643
$324$	8.17683	0.454268
$325$	−22.0128	−1.22105
$326$	19.1933	1.06302
$327$	−2.31526	−0.128034
$328$	2.89212	0.159691
$329$	−12.1301	−0.668755
$330$	0.523517	0.0288186
$331$	14.3942	0.791177	0.395589	−	0.918428i	$-0.370541\pi$
$331$	14.3942	0.791177	0.395589	+	0.918428i	$0.370541\pi$
$332$	4.26709	0.234187
$333$	4.17671	0.228882
$334$	−9.80611	−0.536567
$335$	−3.46519	−0.189324
$336$	1.02994	0.0561877
$337$	−9.84034	−0.536038	−0.268019	−	0.963414i	$-0.586369\pi$
$337$	−9.84034	−0.536038	−0.268019	+	0.963414i	$0.586369\pi$
$338$	−7.57896	−0.412241
$339$	0.170302	0.00924956
$340$	−1.39882	−0.0758615
$341$	−15.2533	−0.826015
$342$	−2.90759	−0.157224
$343$	−8.54230	−0.461241
$344$	−1.09635	−0.0591111
$345$	−0.735269	−0.0395855
$346$	10.4921	0.564057
$347$	23.2078	1.24586	0.622929	−	0.782278i	$-0.285943\pi$
$347$	23.2078	1.24586	0.622929	+	0.782278i	$0.285943\pi$
$348$	−1.49875	−0.0803414
$349$	27.6937	1.48241	0.741206	−	0.671278i	$-0.234254\pi$
$349$	27.6937	1.48241	0.741206	+	0.671278i	$0.234254\pi$
$350$	16.4403	0.878771
$351$	−8.14680	−0.434844
$352$	4.48372	0.238983
$353$	2.84918	0.151647	0.0758234	−	0.997121i	$-0.475841\pi$
$353$	2.84918	0.151647	0.0758234	+	0.997121i	$0.475841\pi$
$354$	2.63222	0.139901
$355$	0.955220	0.0506978
$356$	14.8010	0.784453
$357$	−3.75098	−0.198523
$358$	6.33829	0.334989
$359$	21.5298	1.13630	0.568150	−	0.822925i	$-0.307660\pi$
$359$	21.5298	1.13630	0.568150	+	0.822925i	$0.307660\pi$
$360$	1.11676	0.0588584
$361$	1.00000	0.0526316
$362$	19.9662	1.04940
$363$	2.76748	0.145255
$364$	15.3694	0.805577
$365$	−0.352626	−0.0184573
$366$	−0.203677	−0.0106464
$367$	−0.916610	−0.0478466	−0.0239233	−	0.999714i	$-0.507616\pi$
$367$	−0.916610	−0.0478466	−0.0239233	+	0.999714i	$0.507616\pi$
$368$	−6.29729	−0.328269
$369$	8.40909	0.437760
$370$	0.551732	0.0286832
$371$	−3.38802	−0.175897
$372$	1.03417	0.0536192
$373$	−1.41740	−0.0733899	−0.0366950	−	0.999327i	$-0.511683\pi$
$373$	−1.41740	−0.0733899	−0.0366950	+	0.999327i	$0.511683\pi$
$374$	−16.3295	−0.844377
$375$	−1.15037	−0.0594049
$376$	3.58030	0.184640
$377$	−22.3653	−1.15187
$378$	6.08445	0.312950
$379$	34.6668	1.78072	0.890358	−	0.455261i	$-0.150454\pi$
$379$	34.6668	1.78072	0.890358	+	0.455261i	$0.150454\pi$
$380$	−0.384085	−0.0197031
$381$	−2.36202	−0.121010
$382$	1.02363	0.0523737
$383$	−9.64813	−0.492996	−0.246498	−	0.969143i	$-0.579280\pi$
$383$	−9.64813	−0.492996	−0.246498	+	0.969143i	$0.579280\pi$
$384$	−0.303994	−0.0155131
$385$	−5.83460	−0.297359
$386$	−9.88425	−0.503095
$387$	−3.18773	−0.162041
$388$	−3.38043	−0.171615
$389$	24.6671	1.25067	0.625336	−	0.780356i	$-0.284962\pi$
$389$	24.6671	1.25067	0.625336	+	0.780356i	$0.284962\pi$
$390$	−0.529668	−0.0268208
$391$	22.9344	1.15984
$392$	−4.47867	−0.226207
$393$	4.23610	0.213683
$394$	−3.92018	−0.197496
$395$	3.05168	0.153547
$396$	13.0368	0.655124
$397$	16.2621	0.816173	0.408087	−	0.912943i	$-0.366196\pi$
$397$	16.2621	0.816173	0.408087	+	0.912943i	$0.366196\pi$
$398$	22.0238	1.10395
$399$	−1.02994	−0.0515614
$400$	−4.85248	−0.242624
$401$	−33.8562	−1.69070	−0.845348	−	0.534216i	$-0.820607\pi$
$401$	−33.8562	−1.69070	−0.845348	+	0.534216i	$0.820607\pi$
$402$	2.74262	0.136790
$403$	15.4326	0.768752
$404$	−0.160326	−0.00797650
$405$	3.14059	0.156057
$406$	16.7036	0.828985
$407$	6.44079	0.319258
$408$	1.10713	0.0548112
$409$	−30.8689	−1.52637	−0.763185	−	0.646180i	$-0.776366\pi$
$409$	−30.8689	−1.52637	−0.763185	+	0.646180i	$0.776366\pi$
$410$	1.11082	0.0548594
$411$	−4.84894	−0.239181
$412$	−13.5627	−0.668185
$413$	−29.3361	−1.44354
$414$	−18.3099	−0.899884
$415$	1.63892	0.0804517
$416$	−4.53640	−0.222415
$417$	2.81116	0.137663
$418$	−4.48372	−0.219306
$419$	−5.19704	−0.253892	−0.126946	−	0.991910i	$-0.540518\pi$
$419$	−5.19704	−0.253892	−0.126946	+	0.991910i	$0.540518\pi$
$420$	0.395583	0.0193025
$421$	−5.12367	−0.249712	−0.124856	−	0.992175i	$-0.539847\pi$
$421$	−5.12367	−0.249712	−0.124856	+	0.992175i	$0.539847\pi$
$422$	15.6298	0.760846
$423$	10.4100	0.506153
$424$	1.00000	0.0485643
$425$	17.6725	0.857241
$426$	−0.756035	−0.0366300
$427$	2.26998	0.109852
$428$	11.8314	0.571892
$429$	−6.18323	−0.298529
$430$	−0.421090	−0.0203068
$431$	−22.6014	−1.08867	−0.544335	−	0.838868i	$-0.683218\pi$
$431$	−22.6014	−1.08867	−0.544335	+	0.838868i	$0.683218\pi$
$432$	−1.79587	−0.0864039
$433$	−36.7670	−1.76691	−0.883455	−	0.468516i	$-0.844789\pi$
$433$	−36.7670	−1.76691	−0.883455	+	0.468516i	$0.844789\pi$
$434$	−11.5258	−0.553258
$435$	−0.575646	−0.0276001
$436$	−7.61613	−0.364747
$437$	6.29729	0.301240
$438$	0.279096	0.0133357
$439$	16.2577	0.775939	0.387969	−	0.921672i	$-0.373177\pi$
$439$	16.2577	0.775939	0.387969	+	0.921672i	$0.373177\pi$
$440$	1.72213	0.0820992
$441$	−13.0221	−0.620102
$442$	16.5214	0.785841
$443$	34.0140	1.61606	0.808028	−	0.589144i	$-0.200535\pi$
$443$	34.0140	1.61606	0.808028	+	0.589144i	$0.200535\pi$
$444$	−0.436683	−0.0207241
$445$	5.68485	0.269488
$446$	−22.6635	−1.07315
$447$	0.879443	0.0415962
$448$	3.38802	0.160069
$449$	−8.76025	−0.413422	−0.206711	−	0.978402i	$-0.566276\pi$
$449$	−8.76025	−0.413422	−0.206711	+	0.978402i	$0.566276\pi$
$450$	−14.1090	−0.665105
$451$	12.9674	0.610613
$452$	0.560216	0.0263504
$453$	−0.761864	−0.0357955
$454$	22.2342	1.04350
$455$	5.90316	0.276744
$456$	0.303994	0.0142358
$457$	22.2255	1.03966	0.519832	−	0.854269i	$-0.325995\pi$
$457$	22.2255	1.03966	0.519832	+	0.854269i	$0.325995\pi$
$458$	15.0724	0.704286
$459$	6.54048	0.305283
$460$	−2.41869	−0.112772
$461$	−1.83780	−0.0855948	−0.0427974	−	0.999084i	$-0.513627\pi$
$461$	−1.83780	−0.0855948	−0.0427974	+	0.999084i	$0.513627\pi$
$462$	4.61795	0.214847
$463$	8.03904	0.373606	0.186803	−	0.982397i	$-0.440187\pi$
$463$	8.03904	0.373606	0.186803	+	0.982397i	$0.440187\pi$
$464$	−4.93019	−0.228878
$465$	0.397209	0.0184201
$466$	−18.1633	−0.841398
$467$	38.5539	1.78406	0.892030	−	0.451976i	$-0.149281\pi$
$467$	38.5539	1.78406	0.892030	+	0.451976i	$0.149281\pi$
$468$	−13.1900	−0.609708
$469$	−30.5666	−1.41143
$470$	1.37514	0.0634304
$471$	−1.54292	−0.0710939
$472$	8.65878	0.398552
$473$	−4.91571	−0.226025
$474$	−2.41533	−0.110940
$475$	4.85248	0.222647
$476$	−12.3390	−0.565557
$477$	2.90759	0.133129
$478$	4.45072	0.203571
$479$	−25.9575	−1.18603	−0.593014	−	0.805192i	$-0.702062\pi$
$479$	−25.9575	−1.18603	−0.593014	+	0.805192i	$0.702062\pi$
$480$	−0.116759	−0.00532932
$481$	−6.51647	−0.297126
$482$	−2.01272	−0.0916769
$483$	−6.48582	−0.295115
$484$	9.10373	0.413806
$485$	−1.29837	−0.0589560
$486$	−7.87333	−0.357141
$487$	−39.5542	−1.79237	−0.896185	−	0.443680i	$-0.853673\pi$
$487$	−39.5542	−1.79237	−0.896185	+	0.443680i	$0.853673\pi$
$488$	−0.670002	−0.0303296
$489$	−5.83466	−0.263853
$490$	−1.72019	−0.0777102
$491$	31.0685	1.40210	0.701051	−	0.713111i	$-0.252715\pi$
$491$	31.0685	1.40210	0.701051	+	0.713111i	$0.252715\pi$
$492$	−0.879187	−0.0396368
$493$	17.9555	0.808675
$494$	4.53640	0.204102
$495$	5.00724	0.225058
$496$	3.40194	0.152752
$497$	8.42602	0.377959
$498$	−1.29717	−0.0581277
$499$	26.4803	1.18542	0.592710	−	0.805416i	$-0.298058\pi$
$499$	26.4803	1.18542	0.592710	+	0.805416i	$0.298058\pi$
$500$	−3.78419	−0.169234
$501$	2.98100	0.133181
$502$	−0.872969	−0.0389625
$503$	11.2652	0.502289	0.251145	−	0.967950i	$-0.419193\pi$
$503$	11.2652	0.502289	0.251145	+	0.967950i	$0.419193\pi$
$504$	9.85096	0.438797
$505$	−0.0615786	−0.00274021
$506$	−28.2353	−1.25521
$507$	2.30396	0.102322
$508$	−7.76997	−0.344737
$509$	−5.87629	−0.260462	−0.130231	−	0.991484i	$-0.541572\pi$
$509$	−5.87629	−0.260462	−0.130231	+	0.991484i	$0.541572\pi$
$510$	0.425232	0.0188296
$511$	−3.11052	−0.137601
$512$	−1.00000	−0.0441942
$513$	1.79587	0.0792897
$514$	0.0632412	0.00278945
$515$	−5.20921	−0.229545
$516$	0.333283	0.0146720
$517$	16.0530	0.706012
$518$	4.86684	0.213837
$519$	−3.18953	−0.140005
$520$	−1.74236	−0.0764077
$521$	−3.35816	−0.147124	−0.0735619	−	0.997291i	$-0.523437\pi$
$521$	−3.35816	−0.147124	−0.0735619	+	0.997291i	$0.523437\pi$
$522$	−14.3350	−0.627424
$523$	21.2041	0.927190	0.463595	−	0.886047i	$-0.346559\pi$
$523$	21.2041	0.927190	0.463595	+	0.886047i	$0.346559\pi$
$524$	13.9348	0.608745
$525$	−4.99775	−0.218120
$526$	−21.7087	−0.946545
$527$	−12.3897	−0.539704
$528$	−1.36302	−0.0593180
$529$	16.6559	0.724170
$530$	0.384085	0.0166836
$531$	25.1761	1.09255
$532$	−3.38802	−0.146889
$533$	−13.1198	−0.568282
$534$	−4.49943	−0.194709
$535$	4.54425	0.196465
$536$	9.02195	0.389689
$537$	−1.92680	−0.0831476
$538$	1.82032	0.0784794
$539$	−20.0811	−0.864955
$540$	−0.689767	−0.0296828
$541$	11.2870	0.485265	0.242633	−	0.970118i	$-0.421989\pi$
$541$	11.2870	0.485265	0.242633	+	0.970118i	$0.421989\pi$
$542$	27.4840	1.18054
$543$	−6.06962	−0.260472
$544$	3.64195	0.156147
$545$	−2.92524	−0.125303
$546$	−4.67222	−0.199952
$547$	28.3777	1.21334	0.606671	−	0.794953i	$-0.292504\pi$
$547$	28.3777	1.21334	0.606671	+	0.794953i	$0.292504\pi$
$548$	−15.9508	−0.681383
$549$	−1.94809	−0.0831425
$550$	−21.7572	−0.927728
$551$	4.93019	0.210033
$552$	1.91434	0.0814797
$553$	26.9189	1.14471
$554$	16.9734	0.721131
$555$	−0.167723	−0.00711945
$556$	9.24743	0.392178
$557$	20.0351	0.848914	0.424457	−	0.905448i	$-0.360465\pi$
$557$	20.0351	0.848914	0.424457	+	0.905448i	$0.360465\pi$
$558$	9.89144	0.418738
$559$	4.97347	0.210355
$560$	1.30129	0.0549894
$561$	4.96407	0.209583
$562$	−10.9749	−0.462948
$563$	32.0588	1.35112	0.675558	−	0.737307i	$-0.263903\pi$
$563$	32.0588	1.35112	0.675558	+	0.737307i	$0.263903\pi$
$564$	−1.08839	−0.0458295
$565$	0.215170	0.00905229
$566$	4.85924	0.204249
$567$	27.7033	1.16343
$568$	−2.48700	−0.104352
$569$	20.0237	0.839438	0.419719	−	0.907654i	$-0.362129\pi$
$569$	20.0237	0.839438	0.419719	+	0.907654i	$0.362129\pi$
$570$	0.116759	0.00489052
$571$	43.4210	1.81711	0.908556	−	0.417764i	$-0.137186\pi$
$571$	43.4210	1.81711	0.908556	+	0.417764i	$0.137186\pi$
$572$	−20.3400	−0.850456
$573$	−0.311179	−0.0129997
$574$	9.79855	0.408984
$575$	30.5575	1.27434
$576$	−2.90759	−0.121149
$577$	−8.26511	−0.344081	−0.172041	−	0.985090i	$-0.555036\pi$
$577$	−8.26511	−0.344081	−0.172041	+	0.985090i	$0.555036\pi$
$578$	3.73621	0.155406
$579$	3.00475	0.124873
$580$	−1.89361	−0.0786279
$581$	14.4570	0.599777
$582$	1.02763	0.0425967
$583$	4.48372	0.185697
$584$	0.918095	0.0379910
$585$	−5.06607	−0.209456
$586$	2.46006	0.101624
$587$	−11.3026	−0.466509	−0.233255	−	0.972416i	$-0.574938\pi$
$587$	−11.3026	−0.466509	−0.233255	+	0.972416i	$0.574938\pi$
$588$	1.36149	0.0561469
$589$	−3.40194	−0.140175
$590$	3.32570	0.136917
$591$	1.19171	0.0490205
$592$	−1.43648	−0.0590392
$593$	−42.1694	−1.73169	−0.865845	−	0.500312i	$-0.833219\pi$
$593$	−42.1694	−1.73169	−0.865845	+	0.500312i	$0.833219\pi$
$594$	−8.05219	−0.330385
$595$	−4.73922	−0.194289
$596$	2.89296	0.118500
$597$	−6.69510	−0.274012
$598$	28.5671	1.16819
$599$	−23.9930	−0.980329	−0.490164	−	0.871630i	$-0.663063\pi$
$599$	−23.9930	−0.980329	−0.490164	+	0.871630i	$0.663063\pi$
$600$	1.47513	0.0602217
$601$	28.8075	1.17508	0.587540	−	0.809195i	$-0.300096\pi$
$601$	28.8075	1.17508	0.587540	+	0.809195i	$0.300096\pi$
$602$	−3.71445	−0.151389
$603$	26.2321	1.06825
$604$	−2.50618	−0.101975
$605$	3.49660	0.142157
$606$	0.0487381	0.00197985
$607$	−13.5167	−0.548626	−0.274313	−	0.961640i	$-0.588450\pi$
$607$	−13.5167	−0.548626	−0.274313	+	0.961640i	$0.588450\pi$
$608$	1.00000	0.0405554
$609$	−5.07779	−0.205762
$610$	−0.257338	−0.0104193
$611$	−16.2417	−0.657068
$612$	10.5893	0.428047
$613$	44.7446	1.80722	0.903610	−	0.428357i	$-0.140907\pi$
$613$	44.7446	1.80722	0.903610	+	0.428357i	$0.140907\pi$
$614$	−1.68947	−0.0681815
$615$	−0.337682	−0.0136167
$616$	15.1909	0.612060
$617$	−25.6217	−1.03149	−0.515745	−	0.856742i	$-0.672485\pi$
$617$	−25.6217	−1.03149	−0.515745	+	0.856742i	$0.672485\pi$
$618$	4.12297	0.165850
$619$	−8.51468	−0.342234	−0.171117	−	0.985251i	$-0.554738\pi$
$619$	−8.51468	−0.342234	−0.171117	+	0.985251i	$0.554738\pi$
$620$	1.30663	0.0524757
$621$	11.3091	0.453820
$622$	−32.2269	−1.29218
$623$	50.1462	2.00906
$624$	1.37904	0.0552058
$625$	22.8089	0.912358
$626$	6.28785	0.251313
$627$	1.36302	0.0544340
$628$	−5.07548	−0.202534
$629$	5.23160	0.208598
$630$	3.78360	0.150742
$631$	40.4901	1.61189	0.805944	−	0.591992i	$-0.201658\pi$
$631$	40.4901	1.61189	0.805944	+	0.591992i	$0.201658\pi$
$632$	−7.94533	−0.316048
$633$	−4.75136	−0.188850
$634$	0.296601	0.0117795
$635$	−2.98432	−0.118429
$636$	−0.303994	−0.0120542
$637$	20.3171	0.804992
$638$	−22.1056	−0.875168
$639$	−7.23118	−0.286061
$640$	−0.384085	−0.0151823
$641$	−5.77238	−0.227995	−0.113998	−	0.993481i	$-0.536366\pi$
$641$	−5.77238	−0.227995	−0.113998	+	0.993481i	$0.536366\pi$
$642$	−3.59667	−0.141949
$643$	−10.4535	−0.412244	−0.206122	−	0.978526i	$-0.566084\pi$
$643$	−10.4535	−0.412244	−0.206122	+	0.978526i	$0.566084\pi$
$644$	−21.3354	−0.840731
$645$	0.128009	0.00504035
$646$	−3.64195	−0.143291
$647$	33.8522	1.33087	0.665434	−	0.746457i	$-0.268247\pi$
$647$	33.8522	1.33087	0.665434	+	0.746457i	$0.268247\pi$
$648$	−8.17683	−0.321216
$649$	38.8235	1.52396
$650$	22.0128	0.863413
$651$	3.50379	0.137324
$652$	−19.1933	−0.751669
$653$	16.4777	0.644822	0.322411	−	0.946600i	$-0.395507\pi$
$653$	16.4777	0.644822	0.322411	+	0.946600i	$0.395507\pi$
$654$	2.31526	0.0905338
$655$	5.35215	0.209126
$656$	−2.89212	−0.112918
$657$	2.66944	0.104145
$658$	12.1301	0.472881
$659$	−28.4628	−1.10875	−0.554377	−	0.832265i	$-0.687044\pi$
$659$	−28.4628	−1.10875	−0.554377	+	0.832265i	$0.687044\pi$
$660$	−0.523517	−0.0203779
$661$	−47.8875	−1.86261	−0.931305	−	0.364242i	$-0.881328\pi$
$661$	−47.8875	−1.86261	−0.931305	+	0.364242i	$0.881328\pi$
$662$	−14.3942	−0.559447
$663$	−5.02239	−0.195054
$664$	−4.26709	−0.165595
$665$	−1.30129	−0.0504617
$666$	−4.17671	−0.161844
$667$	31.0468	1.20214
$668$	9.80611	0.379410
$669$	6.88958	0.266367
$670$	3.46519	0.133872
$671$	−3.00410	−0.115972
$672$	−1.02994	−0.0397307
$673$	−1.60440	−0.0618449	−0.0309225	−	0.999522i	$-0.509844\pi$
$673$	−1.60440	−0.0618449	−0.0309225	+	0.999522i	$0.509844\pi$
$674$	9.84034	0.379036
$675$	8.71443	0.335419
$676$	7.57896	0.291498
$677$	13.7696	0.529209	0.264604	−	0.964357i	$-0.414759\pi$
$677$	13.7696	0.529209	0.264604	+	0.964357i	$0.414759\pi$
$678$	−0.170302	−0.00654043
$679$	−11.4530	−0.439525
$680$	1.39882	0.0536422
$681$	−6.75906	−0.259008
$682$	15.2533	0.584081
$683$	−17.3868	−0.665287	−0.332644	−	0.943053i	$-0.607941\pi$
$683$	−17.3868	−0.665287	−0.332644	+	0.943053i	$0.607941\pi$
$684$	2.90759	0.111174
$685$	−6.12644	−0.234079
$686$	8.54230	0.326147
$687$	−4.58192	−0.174811
$688$	1.09635	0.0417978
$689$	−4.53640	−0.172823
$690$	0.735269	0.0279912
$691$	−1.31572	−0.0500525	−0.0250262	−	0.999687i	$-0.507967\pi$
$691$	−1.31572	−0.0500525	−0.0250262	+	0.999687i	$0.507967\pi$
$692$	−10.4921	−0.398849
$693$	44.1689	1.67784
$694$	−23.2078	−0.880955
$695$	3.55179	0.134727
$696$	1.49875	0.0568099
$697$	10.5329	0.398964
$698$	−27.6937	−1.04822
$699$	5.52154	0.208844
$700$	−16.4403	−0.621385
$701$	−48.0212	−1.81374	−0.906868	−	0.421415i	$-0.861534\pi$
$701$	−48.0212	−1.81374	−0.906868	+	0.421415i	$0.861534\pi$
$702$	8.14680	0.307481
$703$	1.43648	0.0541780
$704$	−4.48372	−0.168987
$705$	−0.418034	−0.0157441
$706$	−2.84918	−0.107230
$707$	−0.543187	−0.0204286
$708$	−2.63222	−0.0989248
$709$	−40.2088	−1.51007	−0.755036	−	0.655684i	$-0.772381\pi$
$709$	−40.2088	−1.51007	−0.755036	+	0.655684i	$0.772381\pi$
$710$	−0.955220	−0.0358488
$711$	−23.1017	−0.866382
$712$	−14.8010	−0.554692
$713$	−21.4230	−0.802299
$714$	3.75098	0.140377
$715$	−7.81226	−0.292162
$716$	−6.33829	−0.236873
$717$	−1.35299	−0.0505285
$718$	−21.5298	−0.803485
$719$	−8.11948	−0.302806	−0.151403	−	0.988472i	$-0.548379\pi$
$719$	−8.11948	−0.302806	−0.151403	+	0.988472i	$0.548379\pi$
$720$	−1.11676	−0.0416192
$721$	−45.9506	−1.71129
$722$	−1.00000	−0.0372161
$723$	0.611855	0.0227551
$724$	−19.9662	−0.742039
$725$	23.9236	0.888502
$726$	−2.76748	−0.102711
$727$	13.2089	0.489892	0.244946	−	0.969537i	$-0.421230\pi$
$727$	13.2089	0.489892	0.244946	+	0.969537i	$0.421230\pi$
$728$	−15.3694	−0.569629
$729$	−22.1370	−0.819890
$730$	0.352626	0.0130513
$731$	−3.99284	−0.147681
$732$	0.203677	0.00752811
$733$	−15.5249	−0.573424	−0.286712	−	0.958017i	$-0.592562\pi$
$733$	−15.5249	−0.573424	−0.286712	+	0.958017i	$0.592562\pi$
$734$	0.916610	0.0338327
$735$	0.522928	0.0192885
$736$	6.29729	0.232121
$737$	40.4519	1.49006
$738$	−8.40909	−0.309543
$739$	13.8630	0.509958	0.254979	−	0.966947i	$-0.417931\pi$
$739$	13.8630	0.509958	0.254979	+	0.966947i	$0.417931\pi$
$740$	−0.551732	−0.0202821
$741$	−1.37904	−0.0506603
$742$	3.38802	0.124378
$743$	27.3576	1.00365	0.501826	−	0.864969i	$-0.332662\pi$
$743$	27.3576	1.00365	0.501826	+	0.864969i	$0.332662\pi$
$744$	−1.03417	−0.0379145
$745$	1.11114	0.0407091
$746$	1.41740	0.0518945
$747$	−12.4069	−0.453947
$748$	16.3295	0.597065
$749$	40.0850	1.46467
$750$	1.15037	0.0420056
$751$	16.2051	0.591333	0.295666	−	0.955291i	$-0.404458\pi$
$751$	16.2051	0.591333	0.295666	+	0.955291i	$0.404458\pi$
$752$	−3.58030	−0.130560
$753$	0.265378	0.00967090
$754$	22.3653	0.814497
$755$	−0.962585	−0.0350321
$756$	−6.08445	−0.221289
$757$	−44.2607	−1.60868	−0.804340	−	0.594169i	$-0.797481\pi$
$757$	−44.2607	−1.60868	−0.804340	+	0.594169i	$0.797481\pi$
$758$	−34.6668	−1.25916
$759$	8.58336	0.311556
$760$	0.384085	0.0139322
$761$	−48.3147	−1.75141	−0.875703	−	0.482851i	$-0.839601\pi$
$761$	−48.3147	−1.75141	−0.875703	+	0.482851i	$0.839601\pi$
$762$	2.36202	0.0855671
$763$	−25.8036	−0.934153
$764$	−1.02363	−0.0370338
$765$	4.06718	0.147049
$766$	9.64813	0.348601
$767$	−39.2797	−1.41831
$768$	0.303994	0.0109694
$769$	30.2092	1.08937	0.544686	−	0.838640i	$-0.316649\pi$
$769$	30.2092	1.08937	0.544686	+	0.838640i	$0.316649\pi$
$770$	5.83460	0.210264
$771$	−0.0192250	−0.000692370 0
$772$	9.88425	0.355742
$773$	−24.5543	−0.883156	−0.441578	−	0.897223i	$-0.645581\pi$
$773$	−24.5543	−0.883156	−0.441578	+	0.897223i	$0.645581\pi$
$774$	3.18773	0.114580
$775$	−16.5078	−0.592979
$776$	3.38043	0.121350
$777$	−1.47949	−0.0530764
$778$	−24.6671	−0.884359
$779$	2.89212	0.103621
$780$	0.529668	0.0189652
$781$	−11.1510	−0.399015
$782$	−22.9344	−0.820133
$783$	8.85399	0.316416
$784$	4.47867	0.159953
$785$	−1.94942	−0.0695776
$786$	−4.23610	−0.151097
$787$	53.1506	1.89461	0.947307	−	0.320328i	$-0.103793\pi$
$787$	53.1506	1.89461	0.947307	+	0.320328i	$0.103793\pi$
$788$	3.92018	0.139651
$789$	6.59933	0.234942
$790$	−3.05168	−0.108574
$791$	1.89802	0.0674859
$792$	−13.0368	−0.463243
$793$	3.03940	0.107932
$794$	−16.2621	−0.577122
$795$	−0.116759	−0.00414103
$796$	−22.0238	−0.780612
$797$	−39.2798	−1.39136	−0.695681	−	0.718351i	$-0.744897\pi$
$797$	−39.2798	−1.39136	−0.695681	+	0.718351i	$0.744897\pi$
$798$	1.02994	0.0364594
$799$	13.0393	0.461296
$800$	4.85248	0.171561
$801$	−43.0353	−1.52058
$802$	33.8562	1.19550
$803$	4.11648	0.145267
$804$	−2.74262	−0.0967248
$805$	−8.19458	−0.288821
$806$	−15.4326	−0.543589
$807$	−0.553365	−0.0194794
$808$	0.160326	0.00564024
$809$	−39.6367	−1.39355	−0.696776	−	0.717289i	$-0.745383\pi$
$809$	−39.6367	−1.39355	−0.696776	+	0.717289i	$0.745383\pi$
$810$	−3.14059	−0.110349
$811$	−51.8796	−1.82174	−0.910870	−	0.412692i	$-0.864588\pi$
$811$	−51.8796	−1.82174	−0.910870	+	0.412692i	$0.864588\pi$
$812$	−16.7036	−0.586181
$813$	−8.35497	−0.293022
$814$	−6.44079	−0.225750
$815$	−7.37187	−0.258225
$816$	−1.10713	−0.0387574
$817$	−1.09635	−0.0383563
$818$	30.8689	1.07931
$819$	−44.6879	−1.56152
$820$	−1.11082	−0.0387914
$821$	27.2446	0.950843	0.475422	−	0.879758i	$-0.342296\pi$
$821$	27.2446	0.950843	0.475422	+	0.879758i	$0.342296\pi$
$822$	4.84894	0.169126
$823$	−12.2016	−0.425321	−0.212661	−	0.977126i	$-0.568213\pi$
$823$	−12.2016	−0.425321	−0.212661	+	0.977126i	$0.568213\pi$
$824$	13.5627	0.472478
$825$	6.61405	0.230272
$826$	29.3361	1.02073
$827$	−2.34959	−0.0817032	−0.0408516	−	0.999165i	$-0.513007\pi$
$827$	−2.34959	−0.0817032	−0.0408516	+	0.999165i	$0.513007\pi$
$828$	18.3099	0.636314
$829$	−12.5136	−0.434614	−0.217307	−	0.976103i	$-0.569727\pi$
$829$	−12.5136	−0.434614	−0.217307	+	0.976103i	$0.569727\pi$
$830$	−1.63892	−0.0568879
$831$	−5.15982	−0.178992
$832$	4.53640	0.157271
$833$	−16.3111	−0.565146
$834$	−2.81116	−0.0973427
$835$	3.76638	0.130341
$836$	4.48372	0.155073
$837$	−6.10945	−0.211174
$838$	5.19704	0.179529
$839$	25.9278	0.895128	0.447564	−	0.894252i	$-0.352292\pi$
$839$	25.9278	0.895128	0.447564	+	0.894252i	$0.352292\pi$
$840$	−0.395583	−0.0136489
$841$	−4.69323	−0.161836
$842$	5.12367	0.176573
$843$	3.33630	0.114908
$844$	−15.6298	−0.537999
$845$	2.91096	0.100140
$846$	−10.4100	−0.357904
$847$	30.8436	1.05980
$848$	−1.00000	−0.0343401
$849$	−1.47718	−0.0506967
$850$	−17.6725	−0.606161
$851$	9.04597	0.310092
$852$	0.756035	0.0259013
$853$	27.4988	0.941541	0.470771	−	0.882256i	$-0.343976\pi$
$853$	27.4988	0.941541	0.470771	+	0.882256i	$0.343976\pi$
$854$	−2.26998	−0.0776771
$855$	1.11676	0.0381924
$856$	−11.8314	−0.404388
$857$	−28.9902	−0.990288	−0.495144	−	0.868811i	$-0.664885\pi$
$857$	−28.9902	−0.990288	−0.495144	+	0.868811i	$0.664885\pi$
$858$	6.18323	0.211092
$859$	7.06969	0.241215	0.120607	−	0.992700i	$-0.461516\pi$
$859$	7.06969	0.241215	0.120607	+	0.992700i	$0.461516\pi$
$860$	0.421090	0.0143591
$861$	−2.97870	−0.101514
$862$	22.6014	0.769807
$863$	31.8377	1.08377	0.541884	−	0.840453i	$-0.317711\pi$
$863$	31.8377	1.08377	0.541884	+	0.840453i	$0.317711\pi$
$864$	1.79587	0.0610968
$865$	−4.02984	−0.137019
$866$	36.7670	1.24939
$867$	−1.13578	−0.0385733
$868$	11.5258	0.391213
$869$	−35.6246	−1.20848
$870$	0.575646	0.0195162
$871$	−40.9272	−1.38677
$872$	7.61613	0.257915
$873$	9.82891	0.332658
$874$	−6.29729	−0.213009
$875$	−12.8209	−0.433425
$876$	−0.279096	−0.00942977
$877$	29.6006	0.999541	0.499770	−	0.866158i	$-0.333418\pi$
$877$	29.6006	0.999541	0.499770	+	0.866158i	$0.333418\pi$
$878$	−16.2577	−0.548671
$879$	−0.747842	−0.0252241
$880$	−1.72213	−0.0580529
$881$	−13.4876	−0.454410	−0.227205	−	0.973847i	$-0.572959\pi$
$881$	−13.4876	−0.454410	−0.227205	+	0.973847i	$0.572959\pi$
$882$	13.0221	0.438478
$883$	−27.5873	−0.928387	−0.464193	−	0.885734i	$-0.653656\pi$
$883$	−27.5873	−0.928387	−0.464193	+	0.885734i	$0.653656\pi$
$884$	−16.5214	−0.555673
$885$	−1.01099	−0.0339842
$886$	−34.0140	−1.14272
$887$	−41.6510	−1.39850	−0.699251	−	0.714876i	$-0.746483\pi$
$887$	−41.6510	−1.39850	−0.699251	+	0.714876i	$0.746483\pi$
$888$	0.436683	0.0146541
$889$	−26.3248	−0.882905
$890$	−5.68485	−0.190557
$891$	−36.6626	−1.22824
$892$	22.6635	0.758831
$893$	3.58030	0.119810
$894$	−0.879443	−0.0294130
$895$	−2.43444	−0.0813743
$896$	−3.38802	−0.113186
$897$	−8.68422	−0.289958
$898$	8.76025	0.292333
$899$	−16.7722	−0.559385
$900$	14.1090	0.470300
$901$	3.64195	0.121331
$902$	−12.9674	−0.431769
$903$	1.12917	0.0375764
$904$	−0.560216	−0.0186325
$905$	−7.66872	−0.254917
$906$	0.761864	0.0253112
$907$	2.15380	0.0715158	0.0357579	−	0.999360i	$-0.488615\pi$
$907$	2.15380	0.0715158	0.0357579	+	0.999360i	$0.488615\pi$
$908$	−22.2342	−0.737867
$909$	0.466161	0.0154616
$910$	−5.90316	−0.195688
$911$	−12.0412	−0.398944	−0.199472	−	0.979904i	$-0.563923\pi$
$911$	−12.0412	−0.398944	−0.199472	+	0.979904i	$0.563923\pi$
$912$	−0.303994	−0.0100663
$913$	−19.1324	−0.633192
$914$	−22.2255	−0.735153
$915$	0.0782291	0.00258617
$916$	−15.0724	−0.498005
$917$	47.2114	1.55906
$918$	−6.54048	−0.215868
$919$	−7.22170	−0.238222	−0.119111	−	0.992881i	$-0.538004\pi$
$919$	−7.22170	−0.238222	−0.119111	+	0.992881i	$0.538004\pi$
$920$	2.41869	0.0797420
$921$	0.513589	0.0169233
$922$	1.83780	0.0605247
$923$	11.2821	0.371353
$924$	−4.61795	−0.151919
$925$	6.97051	0.229189
$926$	−8.03904	−0.264179
$927$	39.4346	1.29520
$928$	4.93019	0.161841
$929$	−38.9714	−1.27861	−0.639305	−	0.768953i	$-0.720778\pi$
$929$	−38.9714	−1.27861	−0.639305	+	0.768953i	$0.720778\pi$
$930$	−0.397209	−0.0130250
$931$	−4.47867	−0.146783
$932$	18.1633	0.594958
$933$	9.79678	0.320732
$934$	−38.5539	−1.26152
$935$	6.27190	0.205113
$936$	13.1900	0.431128
$937$	−24.3269	−0.794724	−0.397362	−	0.917662i	$-0.630074\pi$
$937$	−24.3269	−0.794724	−0.397362	+	0.917662i	$0.630074\pi$
$938$	30.5666	0.998033
$939$	−1.91147	−0.0623785
$940$	−1.37514	−0.0448520
$941$	16.7992	0.547637	0.273818	−	0.961781i	$-0.411713\pi$
$941$	16.7992	0.547637	0.273818	+	0.961781i	$0.411713\pi$
$942$	1.54292	0.0502710
$943$	18.2125	0.593081
$944$	−8.65878	−0.281819
$945$	−2.33694	−0.0760208
$946$	4.91571	0.159824
$947$	−10.6341	−0.345563	−0.172781	−	0.984960i	$-0.555275\pi$
$947$	−10.6341	−0.345563	−0.172781	+	0.984960i	$0.555275\pi$
$948$	2.41533	0.0784464
$949$	−4.16485	−0.135197
$950$	−4.85248	−0.157435
$951$	−0.0901650	−0.00292380
$952$	12.3390	0.399909
$953$	−1.95516	−0.0633339	−0.0316670	−	0.999498i	$-0.510082\pi$
$953$	−1.95516	−0.0633339	−0.0316670	+	0.999498i	$0.510082\pi$
$954$	−2.90759	−0.0941366
$955$	−0.393162	−0.0127224
$956$	−4.45072	−0.143947
$957$	6.71997	0.217226
$958$	25.9575	0.838649
$959$	−54.0415	−1.74509
$960$	0.116759	0.00376840
$961$	−19.4268	−0.626671
$962$	6.51647	0.210100
$963$	−34.4008	−1.10855
$964$	2.01272	0.0648253
$965$	3.79639	0.122210
$966$	6.48582	0.208678
$967$	24.3867	0.784222	0.392111	−	0.919918i	$-0.371745\pi$
$967$	24.3867	0.784222	0.392111	+	0.919918i	$0.371745\pi$
$968$	−9.10373	−0.292605
$969$	1.10713	0.0355662
$970$	1.29837	0.0416882
$971$	38.7021	1.24201	0.621004	−	0.783807i	$-0.286725\pi$
$971$	38.7021	1.24201	0.621004	+	0.783807i	$0.286725\pi$
$972$	7.87333	0.252537
$973$	31.3305	1.00441
$974$	39.5542	1.26740
$975$	−6.69176	−0.214308
$976$	0.670002	0.0214463
$977$	−25.5693	−0.818033	−0.409016	−	0.912527i	$-0.634128\pi$
$977$	−25.5693	−0.818033	−0.409016	+	0.912527i	$0.634128\pi$
$978$	5.83466	0.186572
$979$	−66.3637	−2.12099
$980$	1.72019	0.0549494
$981$	22.1446	0.707022
$982$	−31.0685	−0.991436
$983$	19.0296	0.606950	0.303475	−	0.952839i	$-0.401853\pi$
$983$	19.0296	0.606950	0.303475	+	0.952839i	$0.401853\pi$
$984$	0.879187	0.0280275
$985$	1.50568	0.0479750
$986$	−17.9555	−0.571820
$987$	−3.68749	−0.117374
$988$	−4.53640	−0.144322
$989$	−6.90402	−0.219535
$990$	−5.00724	−0.159140
$991$	3.01187	0.0956753	0.0478376	−	0.998855i	$-0.484767\pi$
$991$	3.01187	0.0956753	0.0478376	+	0.998855i	$0.484767\pi$
$992$	−3.40194	−0.108012
$993$	4.37576	0.138860
$994$	−8.42602	−0.267257
$995$	−8.45899	−0.268168
$996$	1.29717	0.0411025
$997$	−5.09277	−0.161290	−0.0806448	−	0.996743i	$-0.525698\pi$
$997$	−5.09277	−0.161290	−0.0806448	+	0.996743i	$0.525698\pi$
$998$	−26.4803	−0.838218
$999$	2.57974	0.0816195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2014.2.a.g.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2014.2.a.g.1.4	✓	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.303994 q^{3} +1.00000 q^{4} +0.384085 q^{5} -0.303994 q^{6} +3.38802 q^{7} -1.00000 q^{8} -2.90759 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.303994 q^{3} +1.00000 q^{4} +0.384085 q^{5} -0.303994 q^{6} +3.38802 q^{7} -1.00000 q^{8} -2.90759 q^{9} -0.384085 q^{10} -4.48372 q^{11} +0.303994 q^{12} +4.53640 q^{13} -3.38802 q^{14} +0.116759 q^{15} +1.00000 q^{16} -3.64195 q^{17} +2.90759 q^{18} -1.00000 q^{19} +0.384085 q^{20} +1.02994 q^{21} +4.48372 q^{22} -6.29729 q^{23} -0.303994 q^{24} -4.85248 q^{25} -4.53640 q^{26} -1.79587 q^{27} +3.38802 q^{28} -4.93019 q^{29} -0.116759 q^{30} +3.40194 q^{31} -1.00000 q^{32} -1.36302 q^{33} +3.64195 q^{34} +1.30129 q^{35} -2.90759 q^{36} -1.43648 q^{37} +1.00000 q^{38} +1.37904 q^{39} -0.384085 q^{40} -2.89212 q^{41} -1.02994 q^{42} +1.09635 q^{43} -4.48372 q^{44} -1.11676 q^{45} +6.29729 q^{46} -3.58030 q^{47} +0.303994 q^{48} +4.47867 q^{49} +4.85248 q^{50} -1.10713 q^{51} +4.53640 q^{52} -1.00000 q^{53} +1.79587 q^{54} -1.72213 q^{55} -3.38802 q^{56} -0.303994 q^{57} +4.93019 q^{58} -8.65878 q^{59} +0.116759 q^{60} +0.670002 q^{61} -3.40194 q^{62} -9.85096 q^{63} +1.00000 q^{64} +1.74236 q^{65} +1.36302 q^{66} -9.02195 q^{67} -3.64195 q^{68} -1.91434 q^{69} -1.30129 q^{70} +2.48700 q^{71} +2.90759 q^{72} -0.918095 q^{73} +1.43648 q^{74} -1.47513 q^{75} -1.00000 q^{76} -15.1909 q^{77} -1.37904 q^{78} +7.94533 q^{79} +0.384085 q^{80} +8.17683 q^{81} +2.89212 q^{82} +4.26709 q^{83} +1.02994 q^{84} -1.39882 q^{85} -1.09635 q^{86} -1.49875 q^{87} +4.48372 q^{88} +14.8010 q^{89} +1.11676 q^{90} +15.3694 q^{91} -6.29729 q^{92} +1.03417 q^{93} +3.58030 q^{94} -0.384085 q^{95} -0.303994 q^{96} -3.38043 q^{97} -4.47867 q^{98} +13.0368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + q^{5} - 8 q^{8} + 2 q^{9} - q^{10} - 6 q^{11} - 5 q^{13} + q^{15} + 8 q^{16} - 9 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} - 9 q^{21} + 6 q^{22} - q^{23} - 9 q^{25} + 5 q^{26} - 3 q^{27} - 23 q^{29} - q^{30} - 6 q^{31} - 8 q^{32} - 6 q^{33} + 9 q^{34} - 7 q^{35} + 2 q^{36} + q^{37} + 8 q^{38} - 5 q^{39} - q^{40} - 3 q^{41} + 9 q^{42} + 9 q^{43} - 6 q^{44} - 9 q^{45} + q^{46} - 13 q^{47} - 8 q^{49} + 9 q^{50} - 24 q^{51} - 5 q^{52} - 8 q^{53} + 3 q^{54} - 11 q^{55} + 23 q^{58} - 9 q^{59} + q^{60} + 6 q^{62} - 18 q^{63} + 8 q^{64} - 26 q^{65} + 6 q^{66} + 9 q^{67} - 9 q^{68} - 22 q^{69} + 7 q^{70} - 31 q^{71} - 2 q^{72} + 5 q^{73} - q^{74} - q^{75} - 8 q^{76} - 4 q^{77} + 5 q^{78} + 19 q^{79} + q^{80} - 24 q^{81} + 3 q^{82} + 11 q^{83} - 9 q^{84} + 19 q^{85} - 9 q^{86} - 22 q^{87} + 6 q^{88} - 41 q^{89} + 9 q^{90} + 18 q^{91} - q^{92} + 3 q^{93} + 13 q^{94} - q^{95} - 24 q^{97} + 8 q^{98} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + q^5 - 8 * q^8 + 2 * q^9 - q^10 - 6 * q^11 - 5 * q^13 + q^15 + 8 * q^16 - 9 * q^17 - 2 * q^18 - 8 * q^19 + q^20 - 9 * q^21 + 6 * q^22 - q^23 - 9 * q^25 + 5 * q^26 - 3 * q^27 - 23 * q^29 - q^30 - 6 * q^31 - 8 * q^32 - 6 * q^33 + 9 * q^34 - 7 * q^35 + 2 * q^36 + q^37 + 8 * q^38 - 5 * q^39 - q^40 - 3 * q^41 + 9 * q^42 + 9 * q^43 - 6 * q^44 - 9 * q^45 + q^46 - 13 * q^47 - 8 * q^49 + 9 * q^50 - 24 * q^51 - 5 * q^52 - 8 * q^53 + 3 * q^54 - 11 * q^55 + 23 * q^58 - 9 * q^59 + q^60 + 6 * q^62 - 18 * q^63 + 8 * q^64 - 26 * q^65 + 6 * q^66 + 9 * q^67 - 9 * q^68 - 22 * q^69 + 7 * q^70 - 31 * q^71 - 2 * q^72 + 5 * q^73 - q^74 - q^75 - 8 * q^76 - 4 * q^77 + 5 * q^78 + 19 * q^79 + q^80 - 24 * q^81 + 3 * q^82 + 11 * q^83 - 9 * q^84 + 19 * q^85 - 9 * q^86 - 22 * q^87 + 6 * q^88 - 41 * q^89 + 9 * q^90 + 18 * q^91 - q^92 + 3 * q^93 + 13 * q^94 - q^95 - 24 * q^97 + 8 * q^98 - 4 * q^99

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