LMFDB - Embedded newform 619.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.262115 q^{2} -0.800074 q^{3} -1.93130 q^{4} -2.40890 q^{5} -0.209711 q^{6} +1.00913 q^{7} -1.03045 q^{8} -2.35988 q^{9} +O(q^{10})$	\(q+0.262115 q^{2} -0.800074 q^{3} -1.93130 q^{4} -2.40890 q^{5} -0.209711 q^{6} +1.00913 q^{7} -1.03045 q^{8} -2.35988 q^{9} -0.631409 q^{10} +2.12041 q^{11} +1.54518 q^{12} -0.383666 q^{13} +0.264508 q^{14} +1.92730 q^{15} +3.59249 q^{16} +3.95666 q^{17} -0.618560 q^{18} +3.69738 q^{19} +4.65230 q^{20} -0.807379 q^{21} +0.555792 q^{22} +4.85826 q^{23} +0.824438 q^{24} +0.802803 q^{25} -0.100565 q^{26} +4.28830 q^{27} -1.94893 q^{28} -3.08630 q^{29} +0.505174 q^{30} +0.275136 q^{31} +3.00255 q^{32} -1.69649 q^{33} +1.03710 q^{34} -2.43089 q^{35} +4.55763 q^{36} -3.06862 q^{37} +0.969139 q^{38} +0.306961 q^{39} +2.48226 q^{40} +2.32888 q^{41} -0.211626 q^{42} +8.80051 q^{43} -4.09514 q^{44} +5.68472 q^{45} +1.27342 q^{46} +1.90425 q^{47} -2.87426 q^{48} -5.98166 q^{49} +0.210427 q^{50} -3.16563 q^{51} +0.740973 q^{52} +8.51466 q^{53} +1.12403 q^{54} -5.10786 q^{55} -1.03986 q^{56} -2.95818 q^{57} -0.808965 q^{58} +0.748989 q^{59} -3.72218 q^{60} +8.47450 q^{61} +0.0721173 q^{62} -2.38143 q^{63} -6.39798 q^{64} +0.924214 q^{65} -0.444674 q^{66} -7.23066 q^{67} -7.64149 q^{68} -3.88697 q^{69} -0.637174 q^{70} +13.5055 q^{71} +2.43174 q^{72} -3.23037 q^{73} -0.804330 q^{74} -0.642302 q^{75} -7.14074 q^{76} +2.13977 q^{77} +0.0804592 q^{78} -5.96598 q^{79} -8.65396 q^{80} +3.64868 q^{81} +0.610433 q^{82} +2.05758 q^{83} +1.55929 q^{84} -9.53121 q^{85} +2.30674 q^{86} +2.46927 q^{87} -2.18498 q^{88} -6.75369 q^{89} +1.49005 q^{90} -0.387169 q^{91} -9.38273 q^{92} -0.220129 q^{93} +0.499131 q^{94} -8.90663 q^{95} -2.40226 q^{96} +1.61662 q^{97} -1.56788 q^{98} -5.00392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * 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 $

$2$	0.262115	0.185343	0.0926717	−	0.995697i	$-0.470459\pi$
$2$	0.262115	0.185343	0.0926717	+	0.995697i	$0.470459\pi$
$3$	−0.800074	−0.461923	−0.230962	−	0.972963i	$-0.574187\pi$
$3$	−0.800074	−0.461923	−0.230962	+	0.972963i	$0.574187\pi$
$4$	−1.93130	−0.965648
$5$	−2.40890	−1.07729	−0.538647	−	0.842532i	$-0.681064\pi$
$5$	−2.40890	−1.07729	−0.538647	+	0.842532i	$0.681064\pi$
$6$	−0.209711	−0.0856143
$7$	1.00913	0.381415	0.190708	−	0.981647i	$-0.438922\pi$
$7$	1.00913	0.381415	0.190708	+	0.981647i	$0.438922\pi$
$8$	−1.03045	−0.364320
$9$	−2.35988	−0.786627
$10$	−0.631409	−0.199669
$11$	2.12041	0.639328	0.319664	−	0.947531i	$-0.396430\pi$
$11$	2.12041	0.639328	0.319664	+	0.947531i	$0.396430\pi$
$12$	1.54518	0.446055
$13$	−0.383666	−0.106410	−0.0532049	−	0.998584i	$-0.516944\pi$
$13$	−0.383666	−0.106410	−0.0532049	+	0.998584i	$0.516944\pi$
$14$	0.264508	0.0706928
$15$	1.92730	0.497627
$16$	3.59249	0.898124
$17$	3.95666	0.959632	0.479816	−	0.877369i	$-0.340703\pi$
$17$	3.95666	0.959632	0.479816	+	0.877369i	$0.340703\pi$
$18$	−0.618560	−0.145796
$19$	3.69738	0.848238	0.424119	−	0.905607i	$-0.360584\pi$
$19$	3.69738	0.848238	0.424119	+	0.905607i	$0.360584\pi$
$20$	4.65230	1.04029
$21$	−0.807379	−0.176185
$22$	0.555792	0.118495
$23$	4.85826	1.01302	0.506508	−	0.862235i	$-0.330936\pi$
$23$	4.85826	1.01302	0.506508	+	0.862235i	$0.330936\pi$
$24$	0.824438	0.168288
$25$	0.802803	0.160561
$26$	−0.100565	−0.0197224
$27$	4.28830	0.825284
$28$	−1.94893	−0.368313
$29$	−3.08630	−0.573111	−0.286555	−	0.958064i	$-0.592510\pi$
$29$	−3.08630	−0.573111	−0.286555	+	0.958064i	$0.592510\pi$
$30$	0.505174	0.0922317
$31$	0.275136	0.0494159	0.0247079	−	0.999695i	$-0.492134\pi$
$31$	0.275136	0.0494159	0.0247079	+	0.999695i	$0.492134\pi$
$32$	3.00255	0.530781
$33$	−1.69649	−0.295320
$34$	1.03710	0.177861
$35$	−2.43089	−0.410896
$36$	4.55763	0.759605
$37$	−3.06862	−0.504477	−0.252239	−	0.967665i	$-0.581167\pi$
$37$	−3.06862	−0.504477	−0.252239	+	0.967665i	$0.581167\pi$
$38$	0.969139	0.157215
$39$	0.306961	0.0491532
$40$	2.48226	0.392479
$41$	2.32888	0.363709	0.181855	−	0.983325i	$-0.441790\pi$
$41$	2.32888	0.363709	0.181855	+	0.983325i	$0.441790\pi$
$42$	−0.211626	−0.0326546
$43$	8.80051	1.34206	0.671032	−	0.741428i	$-0.265851\pi$
$43$	8.80051	1.34206	0.671032	+	0.741428i	$0.265851\pi$
$44$	−4.09514	−0.617366
$45$	5.68472	0.847428
$46$	1.27342	0.187756
$47$	1.90425	0.277763	0.138881	−	0.990309i	$-0.455649\pi$
$47$	1.90425	0.277763	0.138881	+	0.990309i	$0.455649\pi$
$48$	−2.87426	−0.414864
$49$	−5.98166	−0.854522
$50$	0.210427	0.0297589
$51$	−3.16563	−0.443276
$52$	0.740973	0.102754
$53$	8.51466	1.16958	0.584789	−	0.811185i	$-0.301177\pi$
$53$	8.51466	1.16958	0.584789	+	0.811185i	$0.301177\pi$
$54$	1.12403	0.152961
$55$	−5.10786	−0.688744
$56$	−1.03986	−0.138957
$57$	−2.95818	−0.391820
$58$	−0.808965	−0.106222
$59$	0.748989	0.0975101	0.0487550	−	0.998811i	$-0.484475\pi$
$59$	0.748989	0.0975101	0.0487550	+	0.998811i	$0.484475\pi$
$60$	−3.72218	−0.480532
$61$	8.47450	1.08505	0.542524	−	0.840040i	$-0.317469\pi$
$61$	8.47450	1.08505	0.542524	+	0.840040i	$0.317469\pi$
$62$	0.0721173	0.00915890
$63$	−2.38143	−0.300032
$64$	−6.39798	−0.799747
$65$	0.924214	0.114635
$66$	−0.444674	−0.0547356
$67$	−7.23066	−0.883366	−0.441683	−	0.897171i	$-0.645618\pi$
$67$	−7.23066	−0.883366	−0.441683	+	0.897171i	$0.645618\pi$
$68$	−7.64149	−0.926667
$69$	−3.88697	−0.467936
$70$	−0.637174	−0.0761569
$71$	13.5055	1.60281	0.801404	−	0.598123i	$-0.204087\pi$
$71$	13.5055	1.60281	0.801404	+	0.598123i	$0.204087\pi$
$72$	2.43174	0.286584
$73$	−3.23037	−0.378087	−0.189043	−	0.981969i	$-0.560539\pi$
$73$	−3.23037	−0.378087	−0.189043	+	0.981969i	$0.560539\pi$
$74$	−0.804330	−0.0935015
$75$	−0.642302	−0.0741667
$76$	−7.14074	−0.819099
$77$	2.13977	0.243849
$78$	0.0804592	0.00911021
$79$	−5.96598	−0.671226	−0.335613	−	0.942000i	$-0.608943\pi$
$79$	−5.96598	−0.671226	−0.335613	+	0.942000i	$0.608943\pi$
$80$	−8.65396	−0.967543
$81$	3.64868	0.405409
$82$	0.610433	0.0674111
$83$	2.05758	0.225849	0.112924	−	0.993604i	$-0.463978\pi$
$83$	2.05758	0.225849	0.112924	+	0.993604i	$0.463978\pi$
$84$	1.55929	0.170132
$85$	−9.53121	−1.03381
$86$	2.30674	0.248743
$87$	2.46927	0.264733
$88$	−2.18498	−0.232920
$89$	−6.75369	−0.715890	−0.357945	−	0.933743i	$-0.616522\pi$
$89$	−6.75369	−0.715890	−0.357945	+	0.933743i	$0.616522\pi$
$90$	1.49005	0.157065
$91$	−0.387169	−0.0405863
$92$	−9.38273	−0.978217
$93$	−0.220129	−0.0228263
$94$	0.499131	0.0514815
$95$	−8.90663	−0.913801
$96$	−2.40226	−0.245180
$97$	1.61662	0.164143	0.0820717	−	0.996626i	$-0.473846\pi$
$97$	1.61662	0.164143	0.0820717	+	0.996626i	$0.473846\pi$
$98$	−1.56788	−0.158380
$99$	−5.00392	−0.502913
$100$	−1.55045	−0.155045
$101$	10.1205	1.00703	0.503514	−	0.863987i	$-0.332040\pi$
$101$	10.1205	1.00703	0.503514	+	0.863987i	$0.332040\pi$
$102$	−0.829758	−0.0821583
$103$	−6.95922	−0.685712	−0.342856	−	0.939388i	$-0.611394\pi$
$103$	−6.95922	−0.685712	−0.342856	+	0.939388i	$0.611394\pi$
$104$	0.395349	0.0387672
$105$	1.94490	0.189802
$106$	2.23182	0.216774
$107$	0.297802	0.0287896	0.0143948	−	0.999896i	$-0.495418\pi$
$107$	0.297802	0.0287896	0.0143948	+	0.999896i	$0.495418\pi$
$108$	−8.28198	−0.796934
$109$	14.4679	1.38577	0.692885	−	0.721049i	$-0.256340\pi$
$109$	14.4679	1.38577	0.692885	+	0.721049i	$0.256340\pi$
$110$	−1.33885	−0.127654
$111$	2.45512	0.233030
$112$	3.62529	0.342558
$113$	−9.51734	−0.895316	−0.447658	−	0.894205i	$-0.647742\pi$
$113$	−9.51734	−0.895316	−0.447658	+	0.894205i	$0.647742\pi$
$114$	−0.775383	−0.0726213
$115$	−11.7031	−1.09132
$116$	5.96055	0.553423
$117$	0.905407	0.0837049
$118$	0.196321	0.0180728
$119$	3.99279	0.366018
$120$	−1.98599	−0.181295
$121$	−6.50386	−0.591260
$122$	2.22129	0.201106
$123$	−1.86327	−0.168006
$124$	−0.531369	−0.0477183
$125$	10.1106	0.904322
$126$	−0.624208	−0.0556089
$127$	9.24816	0.820642	0.410321	−	0.911941i	$-0.365417\pi$
$127$	9.24816	0.820642	0.410321	+	0.911941i	$0.365417\pi$
$128$	−7.68211	−0.679009
$129$	−7.04106	−0.619930
$130$	0.242250	0.0212468
$131$	−5.64071	−0.492831	−0.246416	−	0.969164i	$-0.579253\pi$
$131$	−5.64071	−0.492831	−0.246416	+	0.969164i	$0.579253\pi$
$132$	3.27642	0.285175
$133$	3.73114	0.323531
$134$	−1.89526	−0.163726
$135$	−10.3301	−0.889073
$136$	−4.07715	−0.349613
$137$	12.1718	1.03991	0.519955	−	0.854194i	$-0.325949\pi$
$137$	12.1718	1.03991	0.519955	+	0.854194i	$0.325949\pi$
$138$	−1.01883	−0.0867288
$139$	3.67807	0.311970	0.155985	−	0.987759i	$-0.450145\pi$
$139$	3.67807	0.311970	0.155985	+	0.987759i	$0.450145\pi$
$140$	4.69478	0.396781
$141$	−1.52354	−0.128305
$142$	3.54000	0.297070
$143$	−0.813530	−0.0680308
$144$	−8.47786	−0.706488
$145$	7.43458	0.617408
$146$	−0.846730	−0.0700758
$147$	4.78577	0.394724
$148$	5.92640	0.487147
$149$	−3.21754	−0.263591	−0.131796	−	0.991277i	$-0.542074\pi$
$149$	−3.21754	−0.263591	−0.131796	+	0.991277i	$0.542074\pi$
$150$	−0.168357	−0.0137463
$151$	8.66435	0.705094	0.352547	−	0.935794i	$-0.385316\pi$
$151$	8.66435	0.705094	0.352547	+	0.935794i	$0.385316\pi$
$152$	−3.80997	−0.309030
$153$	−9.33726	−0.754873
$154$	0.560866	0.0451959
$155$	−0.662775	−0.0532354
$156$	−0.592833	−0.0474646
$157$	18.5287	1.47875	0.739375	−	0.673294i	$-0.235121\pi$
$157$	18.5287	1.47875	0.739375	+	0.673294i	$0.235121\pi$
$158$	−1.56377	−0.124407
$159$	−6.81236	−0.540255
$160$	−7.23285	−0.571807
$161$	4.90261	0.386380
$162$	0.956375	0.0751399
$163$	9.98299	0.781928	0.390964	−	0.920406i	$-0.372142\pi$
$163$	9.98299	0.781928	0.390964	+	0.920406i	$0.372142\pi$
$164$	−4.49775	−0.351215
$165$	4.08667	0.318147
$166$	0.539322	0.0418595
$167$	2.79958	0.216638	0.108319	−	0.994116i	$-0.465453\pi$
$167$	2.79958	0.216638	0.108319	+	0.994116i	$0.465453\pi$
$168$	0.831965	0.0641875
$169$	−12.8528	−0.988677
$170$	−2.49827	−0.191609
$171$	−8.72538	−0.667247
$172$	−16.9964	−1.29596
$173$	8.63473	0.656486	0.328243	−	0.944593i	$-0.393544\pi$
$173$	8.63473	0.656486	0.328243	+	0.944593i	$0.393544\pi$
$174$	0.647232	0.0490665
$175$	0.810133	0.0612403
$176$	7.61756	0.574196
$177$	−0.599247	−0.0450421
$178$	−1.77024	−0.132685
$179$	16.2997	1.21830	0.609150	−	0.793055i	$-0.291511\pi$
$179$	16.2997	1.21830	0.609150	+	0.793055i	$0.291511\pi$
$180$	−10.9789	−0.818317
$181$	−21.9972	−1.63504	−0.817518	−	0.575903i	$-0.804651\pi$
$181$	−21.9972	−1.63504	−0.817518	+	0.575903i	$0.804651\pi$
$182$	−0.101483	−0.00752241
$183$	−6.78023	−0.501209
$184$	−5.00620	−0.369062
$185$	7.39199	0.543470
$186$	−0.0576992	−0.00423071
$187$	8.38976	0.613520
$188$	−3.67766	−0.268221
$189$	4.32746	0.314776
$190$	−2.33456	−0.169367
$191$	8.79300	0.636239	0.318120	−	0.948051i	$-0.396949\pi$
$191$	8.79300	0.636239	0.318120	+	0.948051i	$0.396949\pi$
$192$	5.11885	0.369422
$193$	1.50460	0.108304	0.0541518	−	0.998533i	$-0.482755\pi$
$193$	1.50460	0.108304	0.0541518	+	0.998533i	$0.482755\pi$
$194$	0.423742	0.0304229
$195$	−0.739439	−0.0529524
$196$	11.5523	0.825168
$197$	−3.97952	−0.283529	−0.141765	−	0.989900i	$-0.545278\pi$
$197$	−3.97952	−0.283529	−0.141765	+	0.989900i	$0.545278\pi$
$198$	−1.31160	−0.0932115
$199$	−22.6337	−1.60446	−0.802230	−	0.597016i	$-0.796353\pi$
$199$	−22.6337	−1.60446	−0.802230	+	0.597016i	$0.796353\pi$
$200$	−0.827250	−0.0584954
$201$	5.78506	0.408047
$202$	2.65274	0.186646
$203$	−3.11447	−0.218593
$204$	6.11376	0.428049
$205$	−5.61003	−0.391822
$206$	−1.82412	−0.127092
$207$	−11.4649	−0.796866
$208$	−1.37832	−0.0955692
$209$	7.83997	0.542302
$210$	0.509786	0.0351786
$211$	2.96100	0.203844	0.101922	−	0.994792i	$-0.467501\pi$
$211$	2.96100	0.203844	0.101922	+	0.994792i	$0.467501\pi$
$212$	−16.4443	−1.12940
$213$	−10.8054	−0.740374
$214$	0.0780583	0.00533595
$215$	−21.1995	−1.44580
$216$	−4.41889	−0.300667
$217$	0.277648	0.0188480
$218$	3.79224	0.256843
$219$	2.58454	0.174647
$220$	9.86479	0.665084
$221$	−1.51804	−0.102114
$222$	0.643524	0.0431905
$223$	−12.0183	−0.804806	−0.402403	−	0.915463i	$-0.631825\pi$
$223$	−12.0183	−0.804806	−0.402403	+	0.915463i	$0.631825\pi$
$224$	3.02996	0.202448
$225$	−1.89452	−0.126301
$226$	−2.49464	−0.165941
$227$	−4.40039	−0.292064	−0.146032	−	0.989280i	$-0.546650\pi$
$227$	−4.40039	−0.292064	−0.146032	+	0.989280i	$0.546650\pi$
$228$	5.71312	0.378361
$229$	15.6483	1.03407	0.517034	−	0.855965i	$-0.327036\pi$
$229$	15.6483	1.03407	0.517034	+	0.855965i	$0.327036\pi$
$230$	−3.06755	−0.202268
$231$	−1.71198	−0.112640
$232$	3.18028	0.208796
$233$	−9.00072	−0.589657	−0.294828	−	0.955550i	$-0.595262\pi$
$233$	−9.00072	−0.589657	−0.294828	+	0.955550i	$0.595262\pi$
$234$	0.237321	0.0155141
$235$	−4.58714	−0.299232
$236$	−1.44652	−0.0941604
$237$	4.77323	0.310055
$238$	1.04657	0.0678391
$239$	12.6679	0.819422	0.409711	−	0.912215i	$-0.365630\pi$
$239$	12.6679	0.819422	0.409711	+	0.912215i	$0.365630\pi$
$240$	6.92381	0.446930
$241$	14.8688	0.957781	0.478891	−	0.877875i	$-0.341039\pi$
$241$	14.8688	0.957781	0.478891	+	0.877875i	$0.341039\pi$
$242$	−1.70476	−0.109586
$243$	−15.7841	−1.01255
$244$	−16.3668	−1.04777
$245$	14.4092	0.920571
$246$	−0.488392	−0.0311387
$247$	−1.41856	−0.0902608
$248$	−0.283514	−0.0180032
$249$	−1.64621	−0.104325
$250$	2.65015	0.167610
$251$	−3.77537	−0.238299	−0.119150	−	0.992876i	$-0.538017\pi$
$251$	−3.77537	−0.238299	−0.119150	+	0.992876i	$0.538017\pi$
$252$	4.59924	0.289725
$253$	10.3015	0.647650
$254$	2.42408	0.152100
$255$	7.62568	0.477538
$256$	10.7824	0.673897
$257$	14.4687	0.902532	0.451266	−	0.892389i	$-0.350973\pi$
$257$	14.4687	0.902532	0.451266	+	0.892389i	$0.350973\pi$
$258$	−1.84557	−0.114900
$259$	−3.09663	−0.192415
$260$	−1.78493	−0.110697
$261$	7.28329	0.450825
$262$	−1.47851	−0.0913429
$263$	24.7739	1.52763	0.763813	−	0.645438i	$-0.223325\pi$
$263$	24.7739	1.52763	0.763813	+	0.645438i	$0.223325\pi$
$264$	1.74815	0.107591
$265$	−20.5110	−1.25998
$266$	0.977988	0.0599643
$267$	5.40345	0.330686
$268$	13.9645	0.853020
$269$	19.4958	1.18868	0.594339	−	0.804215i	$-0.297414\pi$
$269$	19.4958	1.18868	0.594339	+	0.804215i	$0.297414\pi$
$270$	−2.70767	−0.164784
$271$	−21.4412	−1.30246	−0.651229	−	0.758881i	$-0.725746\pi$
$271$	−21.4412	−1.30246	−0.651229	+	0.758881i	$0.725746\pi$
$272$	14.2143	0.861868
$273$	0.309764	0.0187478
$274$	3.19042	0.192740
$275$	1.70227	0.102651
$276$	7.50688	0.451861
$277$	15.9152	0.956250	0.478125	−	0.878292i	$-0.341317\pi$
$277$	15.9152	0.956250	0.478125	+	0.878292i	$0.341317\pi$
$278$	0.964077	0.0578215
$279$	−0.649288	−0.0388719
$280$	2.50492	0.149698
$281$	29.9031	1.78387	0.891934	−	0.452166i	$-0.149349\pi$
$281$	29.9031	1.78387	0.891934	+	0.452166i	$0.149349\pi$
$282$	−0.399342	−0.0237805
$283$	−3.34136	−0.198623	−0.0993116	−	0.995056i	$-0.531664\pi$
$283$	−3.34136	−0.198623	−0.0993116	+	0.995056i	$0.531664\pi$
$284$	−26.0831	−1.54775
$285$	7.12596	0.422106
$286$	−0.213238	−0.0126091
$287$	2.35014	0.138724
$288$	−7.08566	−0.417527
$289$	−1.34480	−0.0791060
$290$	1.94872	0.114433
$291$	−1.29342	−0.0758216
$292$	6.23881	0.365099
$293$	4.26459	0.249140	0.124570	−	0.992211i	$-0.460245\pi$
$293$	4.26459	0.249140	0.124570	+	0.992211i	$0.460245\pi$
$294$	1.25442	0.0731594
$295$	−1.80424	−0.105047
$296$	3.16206	0.183791
$297$	9.09296	0.527627
$298$	−0.843366	−0.0488549
$299$	−1.86395	−0.107795
$300$	1.24048	0.0716189
$301$	8.88086	0.511884
$302$	2.27106	0.130685
$303$	−8.09716	−0.465169
$304$	13.2828	0.761822
$305$	−20.4142	−1.16892
$306$	−2.44744	−0.139911
$307$	−14.3903	−0.821298	−0.410649	−	0.911793i	$-0.634698\pi$
$307$	−14.3903	−0.821298	−0.410649	+	0.911793i	$0.634698\pi$
$308$	−4.13253	−0.235473
$309$	5.56789	0.316746
$310$	−0.173723	−0.00986682
$311$	−10.1113	−0.573358	−0.286679	−	0.958027i	$-0.592551\pi$
$311$	−10.1113	−0.573358	−0.286679	+	0.958027i	$0.592551\pi$
$312$	−0.316309	−0.0179075
$313$	1.93265	0.109240	0.0546199	−	0.998507i	$-0.482605\pi$
$313$	1.93265	0.109240	0.0546199	+	0.998507i	$0.482605\pi$
$314$	4.85664	0.274076
$315$	5.73662	0.323222
$316$	11.5221	0.648168
$317$	−3.41079	−0.191569	−0.0957845	−	0.995402i	$-0.530536\pi$
$317$	−3.41079	−0.191569	−0.0957845	+	0.995402i	$0.530536\pi$
$318$	−1.78562	−0.100133
$319$	−6.54422	−0.366406
$320$	15.4121	0.861562
$321$	−0.238263	−0.0132986
$322$	1.28505	0.0716130
$323$	14.6293	0.813996
$324$	−7.04669	−0.391483
$325$	−0.308009	−0.0170852
$326$	2.61669	0.144925
$327$	−11.5754	−0.640119
$328$	−2.39979	−0.132506
$329$	1.92163	0.105943
$330$	1.07118	0.0589663
$331$	−5.01276	−0.275526	−0.137763	−	0.990465i	$-0.543991\pi$
$331$	−5.01276	−0.275526	−0.137763	+	0.990465i	$0.543991\pi$
$332$	−3.97379	−0.218090
$333$	7.24157	0.396835
$334$	0.733813	0.0401525
$335$	17.4179	0.951644
$336$	−2.90050	−0.158235
$337$	10.5267	0.573423	0.286712	−	0.958017i	$-0.407438\pi$
$337$	10.5267	0.573423	0.286712	+	0.958017i	$0.407438\pi$
$338$	−3.36891	−0.183245
$339$	7.61457	0.413567
$340$	18.4076	0.998292
$341$	0.583401	0.0315930
$342$	−2.28705	−0.123670
$343$	−13.1002	−0.707343
$344$	−9.06850	−0.488941
$345$	9.36332	0.504104
$346$	2.26329	0.121675
$347$	−33.0916	−1.77645	−0.888226	−	0.459407i	$-0.848062\pi$
$347$	−33.0916	−1.77645	−0.888226	+	0.459407i	$0.848062\pi$
$348$	−4.76888	−0.255639
$349$	−16.5572	−0.886285	−0.443142	−	0.896451i	$-0.646136\pi$
$349$	−16.5572	−0.886285	−0.443142	+	0.896451i	$0.646136\pi$
$350$	0.212348	0.0113505
$351$	−1.64528	−0.0878184
$352$	6.36664	0.339343
$353$	−6.01295	−0.320037	−0.160019	−	0.987114i	$-0.551155\pi$
$353$	−6.01295	−0.320037	−0.160019	+	0.987114i	$0.551155\pi$
$354$	−0.157072	−0.00834826
$355$	−32.5334	−1.72669
$356$	13.0434	0.691297
$357$	−3.19453	−0.169072
$358$	4.27241	0.225804
$359$	−8.74423	−0.461503	−0.230751	−	0.973013i	$-0.574118\pi$
$359$	−8.74423	−0.461503	−0.230751	+	0.973013i	$0.574118\pi$
$360$	−5.85783	−0.308735
$361$	−5.32937	−0.280493
$362$	−5.76579	−0.303043
$363$	5.20357	0.273117
$364$	0.747738	0.0391921
$365$	7.78165	0.407310
$366$	−1.77720	−0.0928957
$367$	6.83596	0.356834	0.178417	−	0.983955i	$-0.442902\pi$
$367$	6.83596	0.356834	0.178417	+	0.983955i	$0.442902\pi$
$368$	17.4533	0.909814
$369$	−5.49587	−0.286104
$370$	1.93755	0.100729
$371$	8.59240	0.446095
$372$	0.425135	0.0220422
$373$	−22.7402	−1.17744	−0.588721	−	0.808336i	$-0.700368\pi$
$373$	−22.7402	−1.17744	−0.588721	+	0.808336i	$0.700368\pi$
$374$	2.19908	0.113712
$375$	−8.08925	−0.417727
$376$	−1.96223	−0.101194
$377$	1.18411	0.0609846
$378$	1.13429	0.0583416
$379$	30.0357	1.54283	0.771415	−	0.636333i	$-0.219549\pi$
$379$	30.0357	1.54283	0.771415	+	0.636333i	$0.219549\pi$
$380$	17.2013	0.882410
$381$	−7.39921	−0.379073
$382$	2.30478	0.117923
$383$	1.26648	0.0647139	0.0323569	−	0.999476i	$-0.489699\pi$
$383$	1.26648	0.0647139	0.0323569	+	0.999476i	$0.489699\pi$
$384$	6.14625	0.313650
$385$	−5.15450	−0.262697
$386$	0.394379	0.0200734
$387$	−20.7681	−1.05570
$388$	−3.12218	−0.158505
$389$	36.1037	1.83053	0.915265	−	0.402852i	$-0.131981\pi$
$389$	36.1037	1.83053	0.915265	+	0.402852i	$0.131981\pi$
$390$	−0.193818	−0.00981437
$391$	19.2225	0.972123
$392$	6.16381	0.311319
$393$	4.51299	0.227650
$394$	−1.04309	−0.0525503
$395$	14.3715	0.723107
$396$	9.66405	0.485637
$397$	−23.5430	−1.18159	−0.590796	−	0.806821i	$-0.701186\pi$
$397$	−23.5430	−1.18159	−0.590796	+	0.806821i	$0.701186\pi$
$398$	−5.93263	−0.297376
$399$	−2.98519	−0.149446
$400$	2.88407	0.144203
$401$	28.8556	1.44098	0.720490	−	0.693466i	$-0.243917\pi$
$401$	28.8556	1.44098	0.720490	+	0.693466i	$0.243917\pi$
$402$	1.51635	0.0756288
$403$	−0.105560	−0.00525834
$404$	−19.5457	−0.972435
$405$	−8.78932	−0.436745
$406$	−0.816351	−0.0405148
$407$	−6.50673	−0.322526
$408$	3.26202	0.161494
$409$	−4.19880	−0.207617	−0.103809	−	0.994597i	$-0.533103\pi$
$409$	−4.19880	−0.207617	−0.103809	+	0.994597i	$0.533103\pi$
$410$	−1.47047	−0.0726215
$411$	−9.73837	−0.480358
$412$	13.4403	0.662156
$413$	0.755827	0.0371918
$414$	−3.00513	−0.147694
$415$	−4.95650	−0.243305
$416$	−1.15198	−0.0564803
$417$	−2.94273	−0.144106
$418$	2.05497	0.100512
$419$	20.9705	1.02448	0.512239	−	0.858843i	$-0.328816\pi$
$419$	20.9705	1.02448	0.512239	+	0.858843i	$0.328816\pi$
$420$	−3.75617	−0.183282
$421$	12.9690	0.632072	0.316036	−	0.948747i	$-0.397648\pi$
$421$	12.9690	0.632072	0.316036	+	0.948747i	$0.397648\pi$
$422$	0.776122	0.0377810
$423$	−4.49379	−0.218496
$424$	−8.77395	−0.426101
$425$	3.17642	0.154079
$426$	−2.83226	−0.137223
$427$	8.55187	0.413854
$428$	−0.575143	−0.0278006
$429$	0.650884	0.0314250
$430$	−5.55672	−0.267969
$431$	−9.27696	−0.446855	−0.223428	−	0.974721i	$-0.571725\pi$
$431$	−9.27696	−0.446855	−0.223428	+	0.974721i	$0.571725\pi$
$432$	15.4057	0.741207
$433$	−6.06108	−0.291277	−0.145638	−	0.989338i	$-0.546524\pi$
$433$	−6.06108	−0.291277	−0.145638	+	0.989338i	$0.546524\pi$
$434$	0.0727757	0.00349335
$435$	−5.94822	−0.285195
$436$	−27.9417	−1.33816
$437$	17.9628	0.859279
$438$	0.677446	0.0323696
$439$	8.23653	0.393108	0.196554	−	0.980493i	$-0.437025\pi$
$439$	8.23653	0.393108	0.196554	+	0.980493i	$0.437025\pi$
$440$	5.26340	0.250923
$441$	14.1160	0.672190
$442$	−0.397901	−0.0189262
$443$	10.7693	0.511664	0.255832	−	0.966721i	$-0.417651\pi$
$443$	10.7693	0.511664	0.255832	+	0.966721i	$0.417651\pi$
$444$	−4.74156	−0.225025
$445$	16.2690	0.771223
$446$	−3.15018	−0.149165
$447$	2.57427	0.121759
$448$	−6.45639	−0.305036
$449$	22.1975	1.04757	0.523783	−	0.851852i	$-0.324520\pi$
$449$	22.1975	1.04757	0.523783	+	0.851852i	$0.324520\pi$
$450$	−0.496582	−0.0234091
$451$	4.93817	0.232530
$452$	18.3808	0.864560
$453$	−6.93212	−0.325699
$454$	−1.15341	−0.0541321
$455$	0.932652	0.0437234
$456$	3.04826	0.142748
$457$	−14.2708	−0.667558	−0.333779	−	0.942651i	$-0.608324\pi$
$457$	−14.2708	−0.667558	−0.333779	+	0.942651i	$0.608324\pi$
$458$	4.10165	0.191657
$459$	16.9674	0.791969
$460$	22.6021	1.05383
$461$	−7.11632	−0.331440	−0.165720	−	0.986173i	$-0.552995\pi$
$461$	−7.11632	−0.331440	−0.165720	+	0.986173i	$0.552995\pi$
$462$	−0.448734	−0.0208770
$463$	−34.0230	−1.58118	−0.790592	−	0.612343i	$-0.790227\pi$
$463$	−34.0230	−1.58118	−0.790592	+	0.612343i	$0.790227\pi$
$464$	−11.0875	−0.514724
$465$	0.530269	0.0245907
$466$	−2.35922	−0.109289
$467$	−34.8259	−1.61155	−0.805776	−	0.592220i	$-0.798252\pi$
$467$	−34.8259	−1.61155	−0.805776	+	0.592220i	$0.798252\pi$
$468$	−1.74861	−0.0808294
$469$	−7.29668	−0.336929
$470$	−1.20236	−0.0554607
$471$	−14.8243	−0.683068
$472$	−0.771797	−0.0355248
$473$	18.6607	0.858019
$474$	1.25114	0.0574665
$475$	2.96827	0.136194
$476$	−7.71126	−0.353445
$477$	−20.0936	−0.920023
$478$	3.32046	0.151874
$479$	4.37495	0.199896	0.0999482	−	0.994993i	$-0.468132\pi$
$479$	4.37495	0.199896	0.0999482	+	0.994993i	$0.468132\pi$
$480$	5.78681	0.264131
$481$	1.17732	0.0536813
$482$	3.89733	0.177518
$483$	−3.92245	−0.178478
$484$	12.5609	0.570949
$485$	−3.89429	−0.176831
$486$	−4.13726	−0.187670
$487$	−17.8840	−0.810403	−0.405201	−	0.914228i	$-0.632799\pi$
$487$	−17.8840	−0.810403	−0.405201	+	0.914228i	$0.632799\pi$
$488$	−8.73256	−0.395304
$489$	−7.98713	−0.361191
$490$	3.77687	0.170622
$491$	−20.4968	−0.925009	−0.462504	−	0.886617i	$-0.653049\pi$
$491$	−20.4968	−0.925009	−0.462504	+	0.886617i	$0.653049\pi$
$492$	3.59853	0.162234
$493$	−12.2114	−0.549976
$494$	−0.371826	−0.0167292
$495$	12.0539	0.541784
$496$	0.988425	0.0443816
$497$	13.6288	0.611336
$498$	−0.431498	−0.0193359
$499$	−36.1253	−1.61719	−0.808596	−	0.588364i	$-0.799772\pi$
$499$	−36.1253	−1.61719	−0.808596	+	0.588364i	$0.799772\pi$
$500$	−19.5266	−0.873257
$501$	−2.23987	−0.100070
$502$	−0.989582	−0.0441672
$503$	−35.1350	−1.56659	−0.783297	−	0.621648i	$-0.786464\pi$
$503$	−35.1350	−1.56659	−0.783297	+	0.621648i	$0.786464\pi$
$504$	2.45395	0.109307
$505$	−24.3793	−1.08486
$506$	2.70018	0.120038
$507$	10.2832	0.456693
$508$	−17.8609	−0.792451
$509$	11.1424	0.493876	0.246938	−	0.969031i	$-0.420576\pi$
$509$	11.1424	0.493876	0.246938	+	0.969031i	$0.420576\pi$
$510$	1.99880	0.0885086
$511$	−3.25987	−0.144208
$512$	18.1904	0.803911
$513$	15.8555	0.700037
$514$	3.79246	0.167278
$515$	16.7641	0.738713
$516$	13.5984	0.598635
$517$	4.03778	0.177582
$518$	−0.811674	−0.0356629
$519$	−6.90842	−0.303246
$520$	−0.952358	−0.0417636
$521$	20.1245	0.881671	0.440836	−	0.897588i	$-0.354682\pi$
$521$	20.1245	0.881671	0.440836	+	0.897588i	$0.354682\pi$
$522$	1.90906	0.0835573
$523$	6.00331	0.262506	0.131253	−	0.991349i	$-0.458100\pi$
$523$	6.00331	0.262506	0.131253	+	0.991349i	$0.458100\pi$
$524$	10.8939	0.475901
$525$	−0.648167	−0.0282883
$526$	6.49362	0.283135
$527$	1.08862	0.0474211
$528$	−6.09462	−0.265234
$529$	0.602666	0.0262029
$530$	−5.37624	−0.233529
$531$	−1.76753	−0.0767041
$532$	−7.20593	−0.312417
$533$	−0.893511	−0.0387023
$534$	1.41633	0.0612904
$535$	−0.717375	−0.0310148
$536$	7.45085	0.321828
$537$	−13.0410	−0.562761
$538$	5.11013	0.220314
$539$	−12.6836	−0.546320
$540$	19.9505	0.858531
$541$	−15.8329	−0.680709	−0.340354	−	0.940297i	$-0.610547\pi$
$541$	−15.8329	−0.680709	−0.340354	+	0.940297i	$0.610547\pi$
$542$	−5.62005	−0.241402
$543$	17.5994	0.755261
$544$	11.8801	0.509354
$545$	−34.8516	−1.49288
$546$	0.0811938	0.00347477
$547$	7.50332	0.320819	0.160409	−	0.987051i	$-0.448719\pi$
$547$	7.50332	0.320819	0.160409	+	0.987051i	$0.448719\pi$
$548$	−23.5074	−1.00419
$549$	−19.9988	−0.853529
$550$	0.446191	0.0190257
$551$	−11.4112	−0.486134
$552$	4.00533	0.170478
$553$	−6.02045	−0.256016
$554$	4.17161	0.177235
$555$	−5.91414	−0.251041
$556$	−7.10343	−0.301253
$557$	24.0444	1.01879	0.509397	−	0.860531i	$-0.329868\pi$
$557$	24.0444	1.01879	0.509397	+	0.860531i	$0.329868\pi$
$558$	−0.170188	−0.00720464
$559$	−3.37646	−0.142809
$560$	−8.73298	−0.369036
$561$	−6.71243	−0.283399
$562$	7.83804	0.330628
$563$	−31.5911	−1.33141	−0.665703	−	0.746217i	$-0.731868\pi$
$563$	−31.5911	−1.33141	−0.665703	+	0.746217i	$0.731868\pi$
$564$	2.94240	0.123897
$565$	22.9263	0.964517
$566$	−0.875820	−0.0368135
$567$	3.68200	0.154629
$568$	−13.9168	−0.583935
$569$	−21.5037	−0.901484	−0.450742	−	0.892654i	$-0.648840\pi$
$569$	−21.5037	−0.901484	−0.450742	+	0.892654i	$0.648840\pi$
$570$	1.86782	0.0782344
$571$	41.1731	1.72304	0.861519	−	0.507725i	$-0.169513\pi$
$571$	41.1731	1.72304	0.861519	+	0.507725i	$0.169513\pi$
$572$	1.57117	0.0656938
$573$	−7.03505	−0.293894
$574$	0.616007	0.0257116
$575$	3.90023	0.162651
$576$	15.0985	0.629103
$577$	−38.3133	−1.59500	−0.797501	−	0.603317i	$-0.793845\pi$
$577$	−38.3133	−1.59500	−0.797501	+	0.603317i	$0.793845\pi$
$578$	−0.352493	−0.0146618
$579$	−1.20379	−0.0500279
$580$	−14.3584	−0.596199
$581$	2.07636	0.0861421
$582$	−0.339025	−0.0140530
$583$	18.0546	0.747744
$584$	3.32874	0.137744
$585$	−2.18103	−0.0901747
$586$	1.11781	0.0461764
$587$	−22.0197	−0.908849	−0.454425	−	0.890785i	$-0.650155\pi$
$587$	−22.0197	−0.908849	−0.454425	+	0.890785i	$0.650155\pi$
$588$	−9.24273	−0.381164
$589$	1.01728	0.0419164
$590$	−0.472918	−0.0194697
$591$	3.18391	0.130969
$592$	−11.0240	−0.453083
$593$	−22.4640	−0.922487	−0.461244	−	0.887274i	$-0.652597\pi$
$593$	−22.4640	−0.922487	−0.461244	+	0.887274i	$0.652597\pi$
$594$	2.38340	0.0977922
$595$	−9.61824	−0.394309
$596$	6.21403	0.254536
$597$	18.1086	0.741137
$598$	−0.488569	−0.0199791
$599$	20.1519	0.823385	0.411692	−	0.911323i	$-0.364938\pi$
$599$	20.1519	0.823385	0.411692	+	0.911323i	$0.364938\pi$
$600$	0.661861	0.0270204
$601$	−38.0446	−1.55187	−0.775936	−	0.630812i	$-0.782722\pi$
$601$	−38.0446	−1.55187	−0.775936	+	0.630812i	$0.782722\pi$
$602$	2.32781	0.0948743
$603$	17.0635	0.694879
$604$	−16.7334	−0.680873
$605$	15.6671	0.636960
$606$	−2.12239	−0.0862160
$607$	−2.91732	−0.118410	−0.0592051	−	0.998246i	$-0.518857\pi$
$607$	−2.91732	−0.118410	−0.0592051	+	0.998246i	$0.518857\pi$
$608$	11.1016	0.450228
$609$	2.49181	0.100973
$610$	−5.35088	−0.216651
$611$	−0.730595	−0.0295567
$612$	18.0330	0.728941
$613$	2.06332	0.0833368	0.0416684	−	0.999131i	$-0.486733\pi$
$613$	2.06332	0.0833368	0.0416684	+	0.999131i	$0.486733\pi$
$614$	−3.77192	−0.152222
$615$	4.48844	0.180991
$616$	−2.20493	−0.0888392
$617$	−17.5993	−0.708519	−0.354260	−	0.935147i	$-0.615267\pi$
$617$	−17.5993	−0.708519	−0.354260	+	0.935147i	$0.615267\pi$
$618$	1.45943	0.0587068
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	1.28002	0.0514066
$621$	20.8337	0.836027
$622$	−2.65032	−0.106268
$623$	−6.81535	−0.273051
$624$	1.10276	0.0441456
$625$	−28.3695	−1.13478
$626$	0.506577	0.0202469
$627$	−6.27256	−0.250502
$628$	−35.7844	−1.42795
$629$	−12.1415	−0.484113
$630$	1.50366	0.0599071
$631$	−10.2646	−0.408627	−0.204314	−	0.978906i	$-0.565496\pi$
$631$	−10.2646	−0.408627	−0.204314	+	0.978906i	$0.565496\pi$
$632$	6.14766	0.244541
$633$	−2.36902	−0.0941600
$634$	−0.894019	−0.0355060
$635$	−22.2779	−0.884072
$636$	13.1567	0.521696
$637$	2.29496	0.0909296
$638$	−1.71534	−0.0679109
$639$	−31.8714	−1.26081
$640$	18.5054	0.731491
$641$	−0.596268	−0.0235512	−0.0117756	−	0.999931i	$-0.503748\pi$
$641$	−0.596268	−0.0235512	−0.0117756	+	0.999931i	$0.503748\pi$
$642$	−0.0624524	−0.00246480
$643$	−11.2477	−0.443564	−0.221782	−	0.975096i	$-0.571187\pi$
$643$	−11.2477	−0.443564	−0.221782	+	0.975096i	$0.571187\pi$
$644$	−9.46840	−0.373107
$645$	16.9612	0.667847
$646$	3.83456	0.150869
$647$	21.3388	0.838915	0.419458	−	0.907775i	$-0.362220\pi$
$647$	21.3388	0.838915	0.419458	+	0.907775i	$0.362220\pi$
$648$	−3.75979	−0.147699
$649$	1.58816	0.0623409
$650$	−0.0807337	−0.00316663
$651$	−0.222139	−0.00870631
$652$	−19.2801	−0.755068
$653$	−28.2196	−1.10432	−0.552159	−	0.833739i	$-0.686196\pi$
$653$	−28.2196	−1.10432	−0.552159	+	0.833739i	$0.686196\pi$
$654$	−3.03407	−0.118642
$655$	13.5879	0.530924
$656$	8.36647	0.326656
$657$	7.62330	0.297413
$658$	0.503689	0.0196358
$659$	4.65272	0.181244	0.0906221	−	0.995885i	$-0.471114\pi$
$659$	4.65272	0.181244	0.0906221	+	0.995885i	$0.471114\pi$
$660$	−7.89256	−0.307218
$661$	12.1011	0.470677	0.235339	−	0.971913i	$-0.424380\pi$
$661$	12.1011	0.470677	0.235339	+	0.971913i	$0.424380\pi$
$662$	−1.31392	−0.0510670
$663$	1.21454	0.0471689
$664$	−2.12023	−0.0822811
$665$	−8.98795	−0.348538
$666$	1.89812	0.0735508
$667$	−14.9940	−0.580571
$668$	−5.40682	−0.209196
$669$	9.61554	0.371758
$670$	4.56550	0.176381
$671$	17.9694	0.693702
$672$	−2.42420	−0.0935154
$673$	−26.9341	−1.03823	−0.519116	−	0.854704i	$-0.673739\pi$
$673$	−26.9341	−1.03823	−0.519116	+	0.854704i	$0.673739\pi$
$674$	2.75919	0.106280
$675$	3.44266	0.132508
$676$	24.8226	0.954714
$677$	−34.9794	−1.34437	−0.672183	−	0.740385i	$-0.734643\pi$
$677$	−34.9794	−1.34437	−0.672183	+	0.740385i	$0.734643\pi$
$678$	1.99589	0.0766519
$679$	1.63138	0.0626068
$680$	9.82145	0.376636
$681$	3.52064	0.134911
$682$	0.152918	0.00585554
$683$	−19.9925	−0.764993	−0.382496	−	0.923957i	$-0.624936\pi$
$683$	−19.9925	−0.764993	−0.382496	+	0.923957i	$0.624936\pi$
$684$	16.8513	0.644325
$685$	−29.3207	−1.12029
$686$	−3.43375	−0.131101
$687$	−12.5198	−0.477660
$688$	31.6158	1.20534
$689$	−3.26679	−0.124455
$690$	2.45427	0.0934323
$691$	17.5169	0.666375	0.333187	−	0.942861i	$-0.391876\pi$
$691$	17.5169	0.666375	0.333187	+	0.942861i	$0.391876\pi$
$692$	−16.6762	−0.633934
$693$	−5.04960	−0.191819
$694$	−8.67381	−0.329253
$695$	−8.86010	−0.336083
$696$	−2.54446	−0.0964475
$697$	9.21458	0.349027
$698$	−4.33988	−0.164267
$699$	7.20124	0.272376
$700$	−1.56461	−0.0591366
$701$	38.9945	1.47280	0.736401	−	0.676545i	$-0.236523\pi$
$701$	38.9945	1.47280	0.736401	+	0.676545i	$0.236523\pi$
$702$	−0.431252	−0.0162765
$703$	−11.3458	−0.427917
$704$	−13.5663	−0.511301
$705$	3.67005	0.138222
$706$	−1.57609	−0.0593168
$707$	10.2129	0.384096
$708$	1.15732	0.0434948
$709$	37.2995	1.40081	0.700406	−	0.713745i	$-0.253002\pi$
$709$	37.2995	1.40081	0.700406	+	0.713745i	$0.253002\pi$
$710$	−8.52750	−0.320031
$711$	14.0790	0.528004
$712$	6.95935	0.260813
$713$	1.33668	0.0500591
$714$	−0.837334	−0.0313364
$715$	1.95971	0.0732891
$716$	−31.4796	−1.17645
$717$	−10.1353	−0.378510
$718$	−2.29199	−0.0855365
$719$	1.18695	0.0442658	0.0221329	−	0.999755i	$-0.492954\pi$
$719$	1.18695	0.0442658	0.0221329	+	0.999755i	$0.492954\pi$
$720$	20.4223	0.761095
$721$	−7.02276	−0.261541
$722$	−1.39691	−0.0519875
$723$	−11.8961	−0.442421
$724$	42.4830	1.57887
$725$	−2.47769	−0.0920191
$726$	1.36393	0.0506203
$727$	−15.7890	−0.585583	−0.292792	−	0.956176i	$-0.594584\pi$
$727$	−15.7890	−0.585583	−0.292792	+	0.956176i	$0.594584\pi$
$728$	0.398959	0.0147864
$729$	1.68242	0.0623117
$730$	2.03969	0.0754922
$731$	34.8207	1.28789
$732$	13.0946	0.483991
$733$	−20.1850	−0.745549	−0.372775	−	0.927922i	$-0.621594\pi$
$733$	−20.1850	−0.745549	−0.372775	+	0.927922i	$0.621594\pi$
$734$	1.79181	0.0661368
$735$	−11.5284	−0.425233
$736$	14.5872	0.537690
$737$	−15.3320	−0.564760
$738$	−1.44055	−0.0530274
$739$	20.5447	0.755749	0.377874	−	0.925857i	$-0.376655\pi$
$739$	20.5447	0.755749	0.377874	+	0.925857i	$0.376655\pi$
$740$	−14.2761	−0.524801
$741$	1.13495	0.0416936
$742$	2.25220	0.0826808
$743$	−50.2502	−1.84350	−0.921750	−	0.387784i	$-0.873241\pi$
$743$	−50.2502	−1.84350	−0.921750	+	0.387784i	$0.873241\pi$
$744$	0.226832	0.00831608
$745$	7.75074	0.283965
$746$	−5.96055	−0.218231
$747$	−4.85564	−0.177659
$748$	−16.2031	−0.592444
$749$	0.300521	0.0109808
$750$	−2.12031	−0.0774230
$751$	41.5373	1.51572	0.757859	−	0.652418i	$-0.226245\pi$
$751$	41.5373	1.51572	0.757859	+	0.652418i	$0.226245\pi$
$752$	6.84099	0.249465
$753$	3.02058	0.110076
$754$	0.310372	0.0113031
$755$	−20.8715	−0.759593
$756$	−8.35760	−0.303963
$757$	31.5365	1.14621	0.573107	−	0.819481i	$-0.305738\pi$
$757$	31.5365	1.14621	0.573107	+	0.819481i	$0.305738\pi$
$758$	7.87280	0.285953
$759$	−8.24196	−0.299164
$760$	9.17785	0.332916
$761$	−11.6535	−0.422439	−0.211220	−	0.977439i	$-0.567743\pi$
$761$	−11.6535	−0.422439	−0.211220	+	0.977439i	$0.567743\pi$
$762$	−1.93945	−0.0702587
$763$	14.5999	0.528554
$764$	−16.9819	−0.614383
$765$	22.4925	0.813219
$766$	0.331962	0.0119943
$767$	−0.287362	−0.0103760
$768$	−8.62668	−0.311289
$769$	−12.1474	−0.438045	−0.219022	−	0.975720i	$-0.570287\pi$
$769$	−12.1474	−0.438045	−0.219022	+	0.975720i	$0.570287\pi$
$770$	−1.35107	−0.0486892
$771$	−11.5760	−0.416900
$772$	−2.90583	−0.104583
$773$	40.7959	1.46733	0.733664	−	0.679513i	$-0.237809\pi$
$773$	40.7959	1.46733	0.733664	+	0.679513i	$0.237809\pi$
$774$	−5.44364	−0.195668
$775$	0.220880	0.00793425
$776$	−1.66585	−0.0598007
$777$	2.47754	0.0888811
$778$	9.46332	0.339277
$779$	8.61074	0.308512
$780$	1.42808	0.0511333
$781$	28.6372	1.02472
$782$	5.03851	0.180177
$783$	−13.2350	−0.472979
$784$	−21.4891	−0.767467
$785$	−44.6337	−1.59305
$786$	1.18292	0.0421934
$787$	19.2173	0.685024	0.342512	−	0.939513i	$-0.388722\pi$
$787$	19.2173	0.685024	0.342512	+	0.939513i	$0.388722\pi$
$788$	7.68564	0.273789
$789$	−19.8210	−0.705645
$790$	3.76698	0.134023
$791$	−9.60423	−0.341487
$792$	5.15630	0.183221
$793$	−3.25138	−0.115460
$794$	−6.17098	−0.219000
$795$	16.4103	0.582013
$796$	43.7123	1.54934
$797$	24.5973	0.871281	0.435641	−	0.900121i	$-0.356522\pi$
$797$	24.5973	0.871281	0.435641	+	0.900121i	$0.356522\pi$
$798$	−0.782463	−0.0276989
$799$	7.53446	0.266550
$800$	2.41046	0.0852225
$801$	15.9379	0.563138
$802$	7.56348	0.267076
$803$	−6.84972	−0.241721
$804$	−11.1727	−0.394030
$805$	−11.8099	−0.416245
$806$	−0.0276690	−0.000974597 0
$807$	−15.5981	−0.549078
$808$	−10.4287	−0.366880
$809$	−7.85945	−0.276323	−0.138162	−	0.990410i	$-0.544119\pi$
$809$	−7.85945	−0.276323	−0.138162	+	0.990410i	$0.544119\pi$
$810$	−2.30381	−0.0809477
$811$	−3.90177	−0.137010	−0.0685048	−	0.997651i	$-0.521823\pi$
$811$	−3.90177	−0.137010	−0.0685048	+	0.997651i	$0.521823\pi$
$812$	6.01497	0.211084
$813$	17.1545	0.601636
$814$	−1.70551	−0.0597781
$815$	−24.0480	−0.842366
$816$	−11.3725	−0.398117
$817$	32.5388	1.13839
$818$	−1.10057	−0.0384805
$819$	0.913673	0.0319263
$820$	10.8346	0.378362
$821$	−35.8129	−1.24988	−0.624940	−	0.780673i	$-0.714877\pi$
$821$	−35.8129	−1.24988	−0.624940	+	0.780673i	$0.714877\pi$
$822$	−2.55257	−0.0890312
$823$	17.2606	0.601666	0.300833	−	0.953677i	$-0.402735\pi$
$823$	17.2606	0.601666	0.300833	+	0.953677i	$0.402735\pi$
$824$	7.17114	0.249818
$825$	−1.36194	−0.0474168
$826$	0.198114	0.00689326
$827$	21.7249	0.755450	0.377725	−	0.925918i	$-0.376706\pi$
$827$	21.7249	0.755450	0.377725	+	0.925918i	$0.376706\pi$
$828$	22.1421	0.769492
$829$	19.5563	0.679218	0.339609	−	0.940567i	$-0.389705\pi$
$829$	19.5563	0.679218	0.339609	+	0.940567i	$0.389705\pi$
$830$	−1.29917	−0.0450950
$831$	−12.7333	−0.441714
$832$	2.45469	0.0851009
$833$	−23.6674	−0.820027
$834$	−0.771333	−0.0267091
$835$	−6.74392	−0.233383
$836$	−15.1413	−0.523673
$837$	1.17987	0.0407821
$838$	5.49669	0.189880
$839$	−4.74068	−0.163667	−0.0818333	−	0.996646i	$-0.526078\pi$
$839$	−4.74068	−0.163667	−0.0818333	+	0.996646i	$0.526078\pi$
$840$	−2.00412	−0.0691487
$841$	−19.4748	−0.671544
$842$	3.39938	0.117150
$843$	−23.9247	−0.824009
$844$	−5.71856	−0.196841
$845$	30.9611	1.06509
$846$	−1.17789	−0.0404967
$847$	−6.56324	−0.225516
$848$	30.5889	1.05043
$849$	2.67333	0.0917486
$850$	0.832589	0.0285576
$851$	−14.9081	−0.511044
$852$	20.8684	0.714941
$853$	20.3318	0.696147	0.348073	−	0.937467i	$-0.386836\pi$
$853$	20.3318	0.696147	0.348073	+	0.937467i	$0.386836\pi$
$854$	2.24157	0.0767051
$855$	21.0186	0.718820
$856$	−0.306870	−0.0104886
$857$	−36.5460	−1.24839	−0.624194	−	0.781269i	$-0.714573\pi$
$857$	−36.5460	−1.24839	−0.624194	+	0.781269i	$0.714573\pi$
$858$	0.170607	0.00582441
$859$	49.2965	1.68197	0.840987	−	0.541056i	$-0.181975\pi$
$859$	49.2965	1.68197	0.840987	+	0.541056i	$0.181975\pi$
$860$	40.9426	1.39613
$861$	−1.88029	−0.0640800
$862$	−2.43163	−0.0828217
$863$	23.9058	0.813763	0.406881	−	0.913481i	$-0.366616\pi$
$863$	23.9058	0.813763	0.406881	+	0.913481i	$0.366616\pi$
$864$	12.8758	0.438045
$865$	−20.8002	−0.707228
$866$	−1.58870	−0.0539862
$867$	1.07594	0.0365409
$868$	−0.536220	−0.0182005
$869$	−12.6503	−0.429133
$870$	−1.55912	−0.0528590
$871$	2.77416	0.0939988
$872$	−14.9084	−0.504863
$873$	−3.81504	−0.129120
$874$	4.70833	0.159262
$875$	10.2029	0.344922
$876$	−4.99151	−0.168647
$877$	43.0857	1.45490	0.727451	−	0.686160i	$-0.240705\pi$
$877$	43.0857	1.45490	0.727451	+	0.686160i	$0.240705\pi$
$878$	2.15892	0.0728600
$879$	−3.41199	−0.115083
$880$	−18.3500	−0.618577
$881$	11.7673	0.396451	0.198225	−	0.980156i	$-0.436482\pi$
$881$	11.7673	0.396451	0.198225	+	0.980156i	$0.436482\pi$
$882$	3.70002	0.124586
$883$	24.4742	0.823623	0.411811	−	0.911269i	$-0.364896\pi$
$883$	24.4742	0.823623	0.411811	+	0.911269i	$0.364896\pi$
$884$	2.93178	0.0986065
$885$	1.44353	0.0485236
$886$	2.82279	0.0948334
$887$	−13.6220	−0.457381	−0.228691	−	0.973499i	$-0.573444\pi$
$887$	−13.6220	−0.457381	−0.228691	+	0.973499i	$0.573444\pi$
$888$	−2.52988	−0.0848973
$889$	9.33260	0.313005
$890$	4.26434	0.142941
$891$	7.73671	0.259190
$892$	23.2109	0.777159
$893$	7.04073	0.235609
$894$	0.674756	0.0225672
$895$	−39.2645	−1.31247
$896$	−7.75224	−0.258984
$897$	1.49130	0.0497930
$898$	5.81831	0.194159
$899$	−0.849151	−0.0283208
$900$	3.65888	0.121963
$901$	33.6897	1.12237
$902$	1.29437	0.0430978
$903$	−7.10534	−0.236451
$904$	9.80715	0.326181
$905$	52.9890	1.76141
$906$	−1.81701	−0.0603662
$907$	41.7337	1.38574	0.692872	−	0.721061i	$-0.256345\pi$
$907$	41.7337	1.38574	0.692872	+	0.721061i	$0.256345\pi$
$908$	8.49846	0.282031
$909$	−23.8832	−0.792156
$910$	0.244462	0.00810384
$911$	7.64253	0.253208	0.126604	−	0.991953i	$-0.459592\pi$
$911$	7.64253	0.253208	0.126604	+	0.991953i	$0.459592\pi$
$912$	−10.6272	−0.351903
$913$	4.36291	0.144391
$914$	−3.74058	−0.123727
$915$	16.3329	0.539949
$916$	−30.2215	−0.998545
$917$	−5.69221	−0.187973
$918$	4.44740	0.146786
$919$	4.45650	0.147006	0.0735032	−	0.997295i	$-0.476582\pi$
$919$	4.45650	0.147006	0.0735032	+	0.997295i	$0.476582\pi$
$920$	12.0594	0.397588
$921$	11.5133	0.379377
$922$	−1.86529	−0.0614302
$923$	−5.18160	−0.170555
$924$	3.30633	0.108770
$925$	−2.46350	−0.0809992
$926$	−8.91795	−0.293062
$927$	16.4229	0.539400
$928$	−9.26676	−0.304196
$929$	29.8968	0.980881	0.490440	−	0.871475i	$-0.336836\pi$
$929$	29.8968	0.980881	0.490440	+	0.871475i	$0.336836\pi$
$930$	0.138992	0.00455771
$931$	−22.1165	−0.724838
$932$	17.3830	0.569401
$933$	8.08978	0.264847
$934$	−9.12840	−0.298690
$935$	−20.2101	−0.660941
$936$	−0.932978	−0.0304953
$937$	−39.2012	−1.28065	−0.640323	−	0.768106i	$-0.721200\pi$
$937$	−39.2012	−1.28065	−0.640323	+	0.768106i	$0.721200\pi$
$938$	−1.91257	−0.0624476
$939$	−1.54626	−0.0504604
$940$	8.85912	0.288953
$941$	−20.1105	−0.655584	−0.327792	−	0.944750i	$-0.606305\pi$
$941$	−20.1105	−0.655584	−0.327792	+	0.944750i	$0.606305\pi$
$942$	−3.88568	−0.126602
$943$	11.3143	0.368444
$944$	2.69074	0.0875761
$945$	−10.4244	−0.339106
$946$	4.89125	0.159028
$947$	−56.7523	−1.84420	−0.922102	−	0.386948i	$-0.873529\pi$
$947$	−56.7523	−1.84420	−0.922102	+	0.386948i	$0.873529\pi$
$948$	−9.21852	−0.299404
$949$	1.23939	0.0402321
$950$	0.778028	0.0252426
$951$	2.72888	0.0884902
$952$	−4.11438	−0.133348
$953$	49.6844	1.60943	0.804717	−	0.593658i	$-0.202317\pi$
$953$	49.6844	1.60943	0.804717	+	0.593658i	$0.202317\pi$
$954$	−5.26683	−0.170520
$955$	−21.1815	−0.685416
$956$	−24.4656	−0.791273
$957$	5.23586	0.169251
$958$	1.14674	0.0370495
$959$	12.2830	0.396637
$960$	−12.3308	−0.397975
$961$	−30.9243	−0.997558
$962$	0.308594	0.00994948
$963$	−0.702777	−0.0226467
$964$	−28.7160	−0.924880
$965$	−3.62444	−0.116675
$966$	−1.02813	−0.0330797
$967$	−0.945457	−0.0304039	−0.0152019	−	0.999884i	$-0.504839\pi$
$967$	−0.945457	−0.0304039	−0.0152019	+	0.999884i	$0.504839\pi$
$968$	6.70191	0.215408
$969$	−11.7045	−0.376004
$970$	−1.02075	−0.0327744
$971$	6.60315	0.211905	0.105953	−	0.994371i	$-0.466211\pi$
$971$	6.60315	0.211905	0.105953	+	0.994371i	$0.466211\pi$
$972$	30.4838	0.977769
$973$	3.71165	0.118990
$974$	−4.68767	−0.150203
$975$	0.246430	0.00789206
$976$	30.4446	0.974508
$977$	−1.77714	−0.0568558	−0.0284279	−	0.999596i	$-0.509050\pi$
$977$	−1.77714	−0.0568558	−0.0284279	+	0.999596i	$0.509050\pi$
$978$	−2.09355	−0.0669443
$979$	−14.3206	−0.457688
$980$	−27.8285	−0.888948
$981$	−34.1424	−1.09008
$982$	−5.37253	−0.171444
$983$	50.3861	1.60707	0.803534	−	0.595259i	$-0.202950\pi$
$983$	50.3861	1.60707	0.803534	+	0.595259i	$0.202950\pi$
$984$	1.92001	0.0612078
$985$	9.58628	0.305444
$986$	−3.20080	−0.101934
$987$	−1.53745	−0.0489375
$988$	2.73966	0.0871602
$989$	42.7551	1.35953
$990$	3.15952	0.100416
$991$	38.9186	1.23629	0.618144	−	0.786065i	$-0.287885\pi$
$991$	38.9186	1.23629	0.618144	+	0.786065i	$0.287885\pi$
$992$	0.826110	0.0262290
$993$	4.01058	0.127272
$994$	3.57232	0.113307
$995$	54.5223	1.72847
$996$	3.17933	0.100741
$997$	59.0463	1.87002	0.935008	−	0.354627i	$-0.115392\pi$
$997$	59.0463	1.87002	0.935008	+	0.354627i	$0.115392\pi$
$998$	−9.46899	−0.299736
$999$	−13.1592	−0.416337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.15	✓	30
3.2	odd	2		5571.2.a.g.1.16		30
4.3	odd	2		9904.2.a.n.1.19		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.15	✓	30	1.1	even	1	trivial
5571.2.a.g.1.16		30	3.2	odd	2
9904.2.a.n.1.19		30	4.3	odd	2

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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q+0.262115 q^{2} -0.800074 q^{3} -1.93130 q^{4} -2.40890 q^{5} -0.209711 q^{6} +1.00913 q^{7} -1.03045 q^{8} -2.35988 q^{9} +O(q^{10})\)	\(q+0.262115 q^{2} -0.800074 q^{3} -1.93130 q^{4} -2.40890 q^{5} -0.209711 q^{6} +1.00913 q^{7} -1.03045 q^{8} -2.35988 q^{9} -0.631409 q^{10} +2.12041 q^{11} +1.54518 q^{12} -0.383666 q^{13} +0.264508 q^{14} +1.92730 q^{15} +3.59249 q^{16} +3.95666 q^{17} -0.618560 q^{18} +3.69738 q^{19} +4.65230 q^{20} -0.807379 q^{21} +0.555792 q^{22} +4.85826 q^{23} +0.824438 q^{24} +0.802803 q^{25} -0.100565 q^{26} +4.28830 q^{27} -1.94893 q^{28} -3.08630 q^{29} +0.505174 q^{30} +0.275136 q^{31} +3.00255 q^{32} -1.69649 q^{33} +1.03710 q^{34} -2.43089 q^{35} +4.55763 q^{36} -3.06862 q^{37} +0.969139 q^{38} +0.306961 q^{39} +2.48226 q^{40} +2.32888 q^{41} -0.211626 q^{42} +8.80051 q^{43} -4.09514 q^{44} +5.68472 q^{45} +1.27342 q^{46} +1.90425 q^{47} -2.87426 q^{48} -5.98166 q^{49} +0.210427 q^{50} -3.16563 q^{51} +0.740973 q^{52} +8.51466 q^{53} +1.12403 q^{54} -5.10786 q^{55} -1.03986 q^{56} -2.95818 q^{57} -0.808965 q^{58} +0.748989 q^{59} -3.72218 q^{60} +8.47450 q^{61} +0.0721173 q^{62} -2.38143 q^{63} -6.39798 q^{64} +0.924214 q^{65} -0.444674 q^{66} -7.23066 q^{67} -7.64149 q^{68} -3.88697 q^{69} -0.637174 q^{70} +13.5055 q^{71} +2.43174 q^{72} -3.23037 q^{73} -0.804330 q^{74} -0.642302 q^{75} -7.14074 q^{76} +2.13977 q^{77} +0.0804592 q^{78} -5.96598 q^{79} -8.65396 q^{80} +3.64868 q^{81} +0.610433 q^{82} +2.05758 q^{83} +1.55929 q^{84} -9.53121 q^{85} +2.30674 q^{86} +2.46927 q^{87} -2.18498 q^{88} -6.75369 q^{89} +1.49005 q^{90} -0.387169 q^{91} -9.38273 q^{92} -0.220129 q^{93} +0.499131 q^{94} -8.90663 q^{95} -2.40226 q^{96} +1.61662 q^{97} -1.56788 q^{98} -5.00392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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