LMFDB - Embedded newform 6014.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.39762 q^{3} +1.00000 q^{4} +2.43962 q^{5} +3.39762 q^{6} +3.88412 q^{7} -1.00000 q^{8} +8.54381 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.39762 q^{3} +1.00000 q^{4} +2.43962 q^{5} +3.39762 q^{6} +3.88412 q^{7} -1.00000 q^{8} +8.54381 q^{9} -2.43962 q^{10} +2.19121 q^{11} -3.39762 q^{12} -1.08829 q^{13} -3.88412 q^{14} -8.28888 q^{15} +1.00000 q^{16} +5.44373 q^{17} -8.54381 q^{18} -4.77734 q^{19} +2.43962 q^{20} -13.1967 q^{21} -2.19121 q^{22} +6.65829 q^{23} +3.39762 q^{24} +0.951722 q^{25} +1.08829 q^{26} -18.8358 q^{27} +3.88412 q^{28} -0.0887226 q^{29} +8.28888 q^{30} -1.00000 q^{31} -1.00000 q^{32} -7.44488 q^{33} -5.44373 q^{34} +9.47575 q^{35} +8.54381 q^{36} +3.40974 q^{37} +4.77734 q^{38} +3.69760 q^{39} -2.43962 q^{40} +1.24593 q^{41} +13.1967 q^{42} +4.57991 q^{43} +2.19121 q^{44} +20.8436 q^{45} -6.65829 q^{46} +0.727937 q^{47} -3.39762 q^{48} +8.08635 q^{49} -0.951722 q^{50} -18.4957 q^{51} -1.08829 q^{52} -3.57010 q^{53} +18.8358 q^{54} +5.34570 q^{55} -3.88412 q^{56} +16.2316 q^{57} +0.0887226 q^{58} +4.93197 q^{59} -8.28888 q^{60} +6.57529 q^{61} +1.00000 q^{62} +33.1851 q^{63} +1.00000 q^{64} -2.65501 q^{65} +7.44488 q^{66} -9.48904 q^{67} +5.44373 q^{68} -22.6223 q^{69} -9.47575 q^{70} -0.918311 q^{71} -8.54381 q^{72} +0.773732 q^{73} -3.40974 q^{74} -3.23359 q^{75} -4.77734 q^{76} +8.51090 q^{77} -3.69760 q^{78} +16.9404 q^{79} +2.43962 q^{80} +38.3653 q^{81} -1.24593 q^{82} +5.29098 q^{83} -13.1967 q^{84} +13.2806 q^{85} -4.57991 q^{86} +0.301446 q^{87} -2.19121 q^{88} +16.0635 q^{89} -20.8436 q^{90} -4.22705 q^{91} +6.65829 q^{92} +3.39762 q^{93} -0.727937 q^{94} -11.6549 q^{95} +3.39762 q^{96} +1.00000 q^{97} -8.08635 q^{98} +18.7213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * 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
$3$	−3.39762	−1.96162	−0.980808	−	0.194976i	$-0.937537\pi$
$3$	−3.39762	−1.96162	−0.980808	+	0.194976i	$0.937537\pi$
$4$	1.00000	0.500000
$5$	2.43962	1.09103	0.545515	−	0.838101i	$-0.316334\pi$
$5$	2.43962	1.09103	0.545515	+	0.838101i	$0.316334\pi$
$6$	3.39762	1.38707
$7$	3.88412	1.46806	0.734029	−	0.679118i	$-0.237638\pi$
$7$	3.88412	1.46806	0.734029	+	0.679118i	$0.237638\pi$
$8$	−1.00000	−0.353553
$9$	8.54381	2.84794
$10$	−2.43962	−0.771474
$11$	2.19121	0.660674	0.330337	−	0.943863i	$-0.392838\pi$
$11$	2.19121	0.660674	0.330337	+	0.943863i	$0.392838\pi$
$12$	−3.39762	−0.980808
$13$	−1.08829	−0.301837	−0.150919	−	0.988546i	$-0.548223\pi$
$13$	−1.08829	−0.301837	−0.150919	+	0.988546i	$0.548223\pi$
$14$	−3.88412	−1.03807
$15$	−8.28888	−2.14018
$16$	1.00000	0.250000
$17$	5.44373	1.32030	0.660150	−	0.751134i	$-0.270493\pi$
$17$	5.44373	1.32030	0.660150	+	0.751134i	$0.270493\pi$
$18$	−8.54381	−2.01380
$19$	−4.77734	−1.09600	−0.547999	−	0.836479i	$-0.684610\pi$
$19$	−4.77734	−1.09600	−0.547999	+	0.836479i	$0.684610\pi$
$20$	2.43962	0.545515
$21$	−13.1967	−2.87977
$22$	−2.19121	−0.467167
$23$	6.65829	1.38835	0.694175	−	0.719807i	$-0.255770\pi$
$23$	6.65829	1.38835	0.694175	+	0.719807i	$0.255770\pi$
$24$	3.39762	0.693536
$25$	0.951722	0.190344
$26$	1.08829	0.213431
$27$	−18.8358	−3.62494
$28$	3.88412	0.734029
$29$	−0.0887226	−0.0164754	−0.00823769	−	0.999966i	$-0.502622\pi$
$29$	−0.0887226	−0.0164754	−0.00823769	+	0.999966i	$0.502622\pi$
$30$	8.28888	1.51334
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−7.44488	−1.29599
$34$	−5.44373	−0.933593
$35$	9.47575	1.60169
$36$	8.54381	1.42397
$37$	3.40974	0.560557	0.280279	−	0.959919i	$-0.409573\pi$
$37$	3.40974	0.560557	0.280279	+	0.959919i	$0.409573\pi$
$38$	4.77734	0.774987
$39$	3.69760	0.592089
$40$	−2.43962	−0.385737
$41$	1.24593	0.194582	0.0972911	−	0.995256i	$-0.468982\pi$
$41$	1.24593	0.194582	0.0972911	+	0.995256i	$0.468982\pi$
$42$	13.1967	2.03630
$43$	4.57991	0.698430	0.349215	−	0.937043i	$-0.386448\pi$
$43$	4.57991	0.698430	0.349215	+	0.937043i	$0.386448\pi$
$44$	2.19121	0.330337
$45$	20.8436	3.10718
$46$	−6.65829	−0.981711
$47$	0.727937	0.106180	0.0530902	−	0.998590i	$-0.483093\pi$
$47$	0.727937	0.106180	0.0530902	+	0.998590i	$0.483093\pi$
$48$	−3.39762	−0.490404
$49$	8.08635	1.15519
$50$	−0.951722	−0.134594
$51$	−18.4957	−2.58992
$52$	−1.08829	−0.150919
$53$	−3.57010	−0.490390	−0.245195	−	0.969474i	$-0.578852\pi$
$53$	−3.57010	−0.490390	−0.245195	+	0.969474i	$0.578852\pi$
$54$	18.8358	2.56322
$55$	5.34570	0.720814
$56$	−3.88412	−0.519037
$57$	16.2316	2.14993
$58$	0.0887226	0.0116499
$59$	4.93197	0.642087	0.321044	−	0.947064i	$-0.395966\pi$
$59$	4.93197	0.642087	0.321044	+	0.947064i	$0.395966\pi$
$60$	−8.28888	−1.07009
$61$	6.57529	0.841880	0.420940	−	0.907088i	$-0.361700\pi$
$61$	6.57529	0.841880	0.420940	+	0.907088i	$0.361700\pi$
$62$	1.00000	0.127000
$63$	33.1851	4.18094
$64$	1.00000	0.125000
$65$	−2.65501	−0.329313
$66$	7.44488	0.916402
$67$	−9.48904	−1.15927	−0.579635	−	0.814876i	$-0.696805\pi$
$67$	−9.48904	−1.15927	−0.579635	+	0.814876i	$0.696805\pi$
$68$	5.44373	0.660150
$69$	−22.6223	−2.72341
$70$	−9.47575	−1.13257
$71$	−0.918311	−0.108983	−0.0544917	−	0.998514i	$-0.517354\pi$
$71$	−0.918311	−0.108983	−0.0544917	+	0.998514i	$0.517354\pi$
$72$	−8.54381	−1.00690
$73$	0.773732	0.0905585	0.0452793	−	0.998974i	$-0.485582\pi$
$73$	0.773732	0.0905585	0.0452793	+	0.998974i	$0.485582\pi$
$74$	−3.40974	−0.396374
$75$	−3.23359	−0.373382
$76$	−4.77734	−0.547999
$77$	8.51090	0.969907
$78$	−3.69760	−0.418670
$79$	16.9404	1.90594	0.952969	−	0.303067i	$-0.0980105\pi$
$79$	16.9404	1.90594	0.952969	+	0.303067i	$0.0980105\pi$
$80$	2.43962	0.272757
$81$	38.3653	4.26281
$82$	−1.24593	−0.137590
$83$	5.29098	0.580761	0.290380	−	0.956911i	$-0.406218\pi$
$83$	5.29098	0.580761	0.290380	+	0.956911i	$0.406218\pi$
$84$	−13.1967	−1.43988
$85$	13.2806	1.44048
$86$	−4.57991	−0.493865
$87$	0.301446	0.0323184
$88$	−2.19121	−0.233583
$89$	16.0635	1.70273	0.851365	−	0.524574i	$-0.175775\pi$
$89$	16.0635	1.70273	0.851365	+	0.524574i	$0.175775\pi$
$90$	−20.8436	−2.19711
$91$	−4.22705	−0.443115
$92$	6.65829	0.694175
$93$	3.39762	0.352317
$94$	−0.727937	−0.0750809
$95$	−11.6549	−1.19577
$96$	3.39762	0.346768
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−8.08635	−0.816845
$99$	18.7213	1.88156
$100$	0.951722	0.0951722
$101$	15.3738	1.52975	0.764873	−	0.644181i	$-0.222802\pi$
$101$	15.3738	1.52975	0.764873	+	0.644181i	$0.222802\pi$
$102$	18.4957	1.83135
$103$	6.54327	0.644727	0.322364	−	0.946616i	$-0.395523\pi$
$103$	6.54327	0.644727	0.322364	+	0.946616i	$0.395523\pi$
$104$	1.08829	0.106716
$105$	−32.1950	−3.14191
$106$	3.57010	0.346758
$107$	−13.9417	−1.34779	−0.673896	−	0.738826i	$-0.735381\pi$
$107$	−13.9417	−1.34779	−0.673896	+	0.738826i	$0.735381\pi$
$108$	−18.8358	−1.81247
$109$	−0.623212	−0.0596929	−0.0298464	−	0.999554i	$-0.509502\pi$
$109$	−0.623212	−0.0596929	−0.0298464	+	0.999554i	$0.509502\pi$
$110$	−5.34570	−0.509693
$111$	−11.5850	−1.09960
$112$	3.88412	0.367014
$113$	7.46100	0.701871	0.350936	−	0.936400i	$-0.385864\pi$
$113$	7.46100	0.701871	0.350936	+	0.936400i	$0.385864\pi$
$114$	−16.2316	−1.52023
$115$	16.2437	1.51473
$116$	−0.0887226	−0.00823769
$117$	−9.29815	−0.859614
$118$	−4.93197	−0.454024
$119$	21.1441	1.93828
$120$	8.28888	0.756668
$121$	−6.19861	−0.563510
$122$	−6.57529	−0.595299
$123$	−4.23321	−0.381695
$124$	−1.00000	−0.0898027
$125$	−9.87624	−0.883358
$126$	−33.1851	−2.95637
$127$	−12.5580	−1.11434	−0.557170	−	0.830398i	$-0.688113\pi$
$127$	−12.5580	−1.11434	−0.557170	+	0.830398i	$0.688113\pi$
$128$	−1.00000	−0.0883883
$129$	−15.5608	−1.37005
$130$	2.65501	0.232860
$131$	−9.17902	−0.801975	−0.400987	−	0.916084i	$-0.631333\pi$
$131$	−9.17902	−0.801975	−0.400987	+	0.916084i	$0.631333\pi$
$132$	−7.44488	−0.647994
$133$	−18.5558	−1.60899
$134$	9.48904	0.819728
$135$	−45.9520	−3.95492
$136$	−5.44373	−0.466796
$137$	−2.70080	−0.230745	−0.115372	−	0.993322i	$-0.536806\pi$
$137$	−2.70080	−0.230745	−0.115372	+	0.993322i	$0.536806\pi$
$138$	22.6223	1.92574
$139$	−16.9343	−1.43635	−0.718176	−	0.695862i	$-0.755023\pi$
$139$	−16.9343	−1.43635	−0.718176	+	0.695862i	$0.755023\pi$
$140$	9.47575	0.800847
$141$	−2.47325	−0.208285
$142$	0.918311	0.0770629
$143$	−2.38467	−0.199416
$144$	8.54381	0.711984
$145$	−0.216449	−0.0179751
$146$	−0.773732	−0.0640345
$147$	−27.4743	−2.26605
$148$	3.40974	0.280279
$149$	−6.42045	−0.525984	−0.262992	−	0.964798i	$-0.584709\pi$
$149$	−6.42045	−0.525984	−0.262992	+	0.964798i	$0.584709\pi$
$150$	3.23359	0.264021
$151$	−9.57614	−0.779296	−0.389648	−	0.920964i	$-0.627403\pi$
$151$	−9.57614	−0.779296	−0.389648	+	0.920964i	$0.627403\pi$
$152$	4.77734	0.387494
$153$	46.5102	3.76013
$154$	−8.51090	−0.685828
$155$	−2.43962	−0.195955
$156$	3.69760	0.296045
$157$	12.8398	1.02473	0.512364	−	0.858768i	$-0.328770\pi$
$157$	12.8398	1.02473	0.512364	+	0.858768i	$0.328770\pi$
$158$	−16.9404	−1.34770
$159$	12.1298	0.961958
$160$	−2.43962	−0.192869
$161$	25.8616	2.03818
$162$	−38.3653	−3.01426
$163$	−20.1142	−1.57546	−0.787731	−	0.616019i	$-0.788744\pi$
$163$	−20.1142	−1.57546	−0.787731	+	0.616019i	$0.788744\pi$
$164$	1.24593	0.0972911
$165$	−18.1627	−1.41396
$166$	−5.29098	−0.410660
$167$	−25.0213	−1.93620	−0.968102	−	0.250558i	$-0.919386\pi$
$167$	−25.0213	−1.93620	−0.968102	+	0.250558i	$0.919386\pi$
$168$	13.1967	1.01815
$169$	−11.8156	−0.908894
$170$	−13.2806	−1.01858
$171$	−40.8167	−3.12133
$172$	4.57991	0.349215
$173$	−2.05355	−0.156129	−0.0780643	−	0.996948i	$-0.524874\pi$
$173$	−2.05355	−0.156129	−0.0780643	+	0.996948i	$0.524874\pi$
$174$	−0.301446	−0.0228525
$175$	3.69660	0.279436
$176$	2.19121	0.165168
$177$	−16.7569	−1.25953
$178$	−16.0635	−1.20401
$179$	13.4604	1.00608	0.503038	−	0.864264i	$-0.332216\pi$
$179$	13.4604	1.00608	0.503038	+	0.864264i	$0.332216\pi$
$180$	20.8436	1.55359
$181$	25.4480	1.89153	0.945766	−	0.324849i	$-0.105313\pi$
$181$	25.4480	1.89153	0.945766	+	0.324849i	$0.105313\pi$
$182$	4.22705	0.313329
$183$	−22.3403	−1.65145
$184$	−6.65829	−0.490856
$185$	8.31845	0.611584
$186$	−3.39762	−0.249125
$187$	11.9283	0.872287
$188$	0.727937	0.0530902
$189$	−73.1602	−5.32162
$190$	11.6549	0.845534
$191$	16.4753	1.19211	0.596055	−	0.802943i	$-0.296734\pi$
$191$	16.4753	1.19211	0.596055	+	0.802943i	$0.296734\pi$
$192$	−3.39762	−0.245202
$193$	14.6100	1.05165	0.525826	−	0.850592i	$-0.323756\pi$
$193$	14.6100	1.05165	0.525826	+	0.850592i	$0.323756\pi$
$194$	−1.00000	−0.0717958
$195$	9.02071	0.645986
$196$	8.08635	0.577597
$197$	2.00053	0.142532	0.0712658	−	0.997457i	$-0.477296\pi$
$197$	2.00053	0.142532	0.0712658	+	0.997457i	$0.477296\pi$
$198$	−18.7213	−1.33046
$199$	−7.01560	−0.497323	−0.248661	−	0.968590i	$-0.579991\pi$
$199$	−7.01560	−0.497323	−0.248661	+	0.968590i	$0.579991\pi$
$200$	−0.951722	−0.0672969
$201$	32.2401	2.27404
$202$	−15.3738	−1.08169
$203$	−0.344609	−0.0241868
$204$	−18.4957	−1.29496
$205$	3.03960	0.212295
$206$	−6.54327	−0.455891
$207$	56.8872	3.95393
$208$	−1.08829	−0.0754594
$209$	−10.4681	−0.724097
$210$	32.1950	2.22166
$211$	−21.9492	−1.51105	−0.755524	−	0.655121i	$-0.772618\pi$
$211$	−21.9492	−1.51105	−0.755524	+	0.655121i	$0.772618\pi$
$212$	−3.57010	−0.245195
$213$	3.12007	0.213784
$214$	13.9417	0.953033
$215$	11.1732	0.762008
$216$	18.8358	1.28161
$217$	−3.88412	−0.263671
$218$	0.623212	0.0422092
$219$	−2.62885	−0.177641
$220$	5.34570	0.360407
$221$	−5.92436	−0.398516
$222$	11.5850	0.777534
$223$	25.5122	1.70843	0.854213	−	0.519924i	$-0.174040\pi$
$223$	25.5122	1.70843	0.854213	+	0.519924i	$0.174040\pi$
$224$	−3.88412	−0.259518
$225$	8.13133	0.542089
$226$	−7.46100	−0.496298
$227$	−17.5172	−1.16265	−0.581327	−	0.813670i	$-0.697466\pi$
$227$	−17.5172	−1.16265	−0.581327	+	0.813670i	$0.697466\pi$
$228$	16.2316	1.07496
$229$	6.80429	0.449640	0.224820	−	0.974400i	$-0.427821\pi$
$229$	6.80429	0.449640	0.224820	+	0.974400i	$0.427821\pi$
$230$	−16.2437	−1.07108
$231$	−28.9168	−1.90259
$232$	0.0887226	0.00582493
$233$	−30.4665	−1.99593	−0.997963	−	0.0637906i	$-0.979681\pi$
$233$	−30.4665	−1.99593	−0.997963	+	0.0637906i	$0.979681\pi$
$234$	9.29815	0.607839
$235$	1.77589	0.115846
$236$	4.93197	0.321044
$237$	−57.5569	−3.73872
$238$	−21.1441	−1.37057
$239$	22.7908	1.47421	0.737107	−	0.675776i	$-0.236191\pi$
$239$	22.7908	1.47421	0.737107	+	0.675776i	$0.236191\pi$
$240$	−8.28888	−0.535045
$241$	−6.61805	−0.426306	−0.213153	−	0.977019i	$-0.568373\pi$
$241$	−6.61805	−0.426306	−0.213153	+	0.977019i	$0.568373\pi$
$242$	6.19861	0.398462
$243$	−73.8433	−4.73705
$244$	6.57529	0.420940
$245$	19.7276	1.26035
$246$	4.23321	0.269899
$247$	5.19914	0.330813
$248$	1.00000	0.0635001
$249$	−17.9767	−1.13923
$250$	9.87624	0.624628
$251$	−18.8430	−1.18936	−0.594679	−	0.803963i	$-0.702721\pi$
$251$	−18.8430	−1.18936	−0.594679	+	0.803963i	$0.702721\pi$
$252$	33.1851	2.09047
$253$	14.5897	0.917246
$254$	12.5580	0.787958
$255$	−45.1225	−2.82568
$256$	1.00000	0.0625000
$257$	−10.4789	−0.653655	−0.326827	−	0.945084i	$-0.605980\pi$
$257$	−10.4789	−0.653655	−0.326827	+	0.945084i	$0.605980\pi$
$258$	15.5608	0.968773
$259$	13.2438	0.822931
$260$	−2.65501	−0.164657
$261$	−0.758029	−0.0469208
$262$	9.17902	0.567082
$263$	−5.18551	−0.319752	−0.159876	−	0.987137i	$-0.551109\pi$
$263$	−5.18551	−0.319752	−0.159876	+	0.987137i	$0.551109\pi$
$264$	7.44488	0.458201
$265$	−8.70966	−0.535030
$266$	18.5558	1.13773
$267$	−54.5777	−3.34010
$268$	−9.48904	−0.579635
$269$	31.4464	1.91732	0.958661	−	0.284551i	$-0.0918445\pi$
$269$	31.4464	1.91732	0.958661	+	0.284551i	$0.0918445\pi$
$270$	45.9520	2.79655
$271$	−11.3523	−0.689601	−0.344800	−	0.938676i	$-0.612053\pi$
$271$	−11.3523	−0.689601	−0.344800	+	0.938676i	$0.612053\pi$
$272$	5.44373	0.330075
$273$	14.3619	0.869221
$274$	2.70080	0.163161
$275$	2.08542	0.125755
$276$	−22.6223	−1.36170
$277$	14.8216	0.890542	0.445271	−	0.895396i	$-0.353107\pi$
$277$	14.8216	0.890542	0.445271	+	0.895396i	$0.353107\pi$
$278$	16.9343	1.01565
$279$	−8.54381	−0.511505
$280$	−9.47575	−0.566284
$281$	−4.66534	−0.278311	−0.139155	−	0.990271i	$-0.544439\pi$
$281$	−4.66534	−0.278311	−0.139155	+	0.990271i	$0.544439\pi$
$282$	2.47325	0.147280
$283$	29.8815	1.77627	0.888134	−	0.459584i	$-0.152002\pi$
$283$	29.8815	1.77627	0.888134	+	0.459584i	$0.152002\pi$
$284$	−0.918311	−0.0544917
$285$	39.5988	2.34563
$286$	2.38467	0.141008
$287$	4.83935	0.285658
$288$	−8.54381	−0.503449
$289$	12.6342	0.743190
$290$	0.216449	0.0127103
$291$	−3.39762	−0.199172
$292$	0.773732	0.0452793
$293$	15.4856	0.904680	0.452340	−	0.891846i	$-0.350589\pi$
$293$	15.4856	0.904680	0.452340	+	0.891846i	$0.350589\pi$
$294$	27.4743	1.60234
$295$	12.0321	0.700536
$296$	−3.40974	−0.198187
$297$	−41.2730	−2.39490
$298$	6.42045	0.371927
$299$	−7.24615	−0.419056
$300$	−3.23359	−0.186691
$301$	17.7889	1.02534
$302$	9.57614	0.551045
$303$	−52.2342	−3.00077
$304$	−4.77734	−0.273999
$305$	16.0412	0.918516
$306$	−46.5102	−2.65881
$307$	21.7411	1.24083	0.620416	−	0.784273i	$-0.286964\pi$
$307$	21.7411	1.24083	0.620416	+	0.784273i	$0.286964\pi$
$308$	8.51090	0.484954
$309$	−22.2315	−1.26471
$310$	2.43962	0.138561
$311$	30.4273	1.72538	0.862688	−	0.505737i	$-0.168780\pi$
$311$	30.4273	1.72538	0.862688	+	0.505737i	$0.168780\pi$
$312$	−3.69760	−0.209335
$313$	20.5267	1.16024	0.580119	−	0.814531i	$-0.303006\pi$
$313$	20.5267	1.16024	0.580119	+	0.814531i	$0.303006\pi$
$314$	−12.8398	−0.724593
$315$	80.9590	4.56152
$316$	16.9404	0.952969
$317$	9.93064	0.557761	0.278880	−	0.960326i	$-0.410037\pi$
$317$	9.93064	0.557761	0.278880	+	0.960326i	$0.410037\pi$
$318$	−12.1298	−0.680207
$319$	−0.194410	−0.0108848
$320$	2.43962	0.136379
$321$	47.3685	2.64385
$322$	−25.8616	−1.44121
$323$	−26.0066	−1.44704
$324$	38.3653	2.13140
$325$	−1.03575	−0.0574530
$326$	20.1142	1.11402
$327$	2.11744	0.117094
$328$	−1.24593	−0.0687952
$329$	2.82739	0.155879
$330$	18.1627	0.999821
$331$	12.2562	0.673662	0.336831	−	0.941565i	$-0.390645\pi$
$331$	12.2562	0.673662	0.336831	+	0.941565i	$0.390645\pi$
$332$	5.29098	0.290380
$333$	29.1322	1.59643
$334$	25.0213	1.36910
$335$	−23.1496	−1.26480
$336$	−13.1967	−0.719941
$337$	5.55263	0.302471	0.151236	−	0.988498i	$-0.451675\pi$
$337$	5.55263	0.302471	0.151236	+	0.988498i	$0.451675\pi$
$338$	11.8156	0.642685
$339$	−25.3496	−1.37680
$340$	13.2806	0.720242
$341$	−2.19121	−0.118660
$342$	40.8167	2.20712
$343$	4.21953	0.227833
$344$	−4.57991	−0.246932
$345$	−55.1898	−2.97132
$346$	2.05355	0.110400
$347$	−20.1956	−1.08416	−0.542079	−	0.840328i	$-0.682363\pi$
$347$	−20.1956	−1.08416	−0.542079	+	0.840328i	$0.682363\pi$
$348$	0.301446	0.0161592
$349$	−4.37382	−0.234125	−0.117063	−	0.993125i	$-0.537348\pi$
$349$	−4.37382	−0.234125	−0.117063	+	0.993125i	$0.537348\pi$
$350$	−3.69660	−0.197591
$351$	20.4988	1.09414
$352$	−2.19121	−0.116792
$353$	−10.3571	−0.551251	−0.275626	−	0.961265i	$-0.588885\pi$
$353$	−10.3571	−0.551251	−0.275626	+	0.961265i	$0.588885\pi$
$354$	16.7569	0.890621
$355$	−2.24033	−0.118904
$356$	16.0635	0.851365
$357$	−71.8395	−3.80215
$358$	−13.4604	−0.711403
$359$	−26.7964	−1.41426	−0.707130	−	0.707084i	$-0.750010\pi$
$359$	−26.7964	−1.41426	−0.707130	+	0.707084i	$0.750010\pi$
$360$	−20.8436	−1.09855
$361$	3.82301	0.201211
$362$	−25.4480	−1.33752
$363$	21.0605	1.10539
$364$	−4.22705	−0.221557
$365$	1.88761	0.0988020
$366$	22.3403	1.16775
$367$	6.53339	0.341040	0.170520	−	0.985354i	$-0.445455\pi$
$367$	6.53339	0.341040	0.170520	+	0.985354i	$0.445455\pi$
$368$	6.65829	0.347087
$369$	10.6450	0.554158
$370$	−8.31845	−0.432456
$371$	−13.8667	−0.719921
$372$	3.39762	0.176158
$373$	−14.6639	−0.759268	−0.379634	−	0.925137i	$-0.623950\pi$
$373$	−14.6639	−0.759268	−0.379634	+	0.925137i	$0.623950\pi$
$374$	−11.9283	−0.616800
$375$	33.5557	1.73281
$376$	−0.727937	−0.0375405
$377$	0.0965560	0.00497289
$378$	73.1602	3.76296
$379$	15.5152	0.796960	0.398480	−	0.917177i	$-0.369538\pi$
$379$	15.5152	0.796960	0.398480	+	0.917177i	$0.369538\pi$
$380$	−11.6549	−0.597883
$381$	42.6672	2.18591
$382$	−16.4753	−0.842950
$383$	−35.8197	−1.83030	−0.915152	−	0.403109i	$-0.867929\pi$
$383$	−35.8197	−1.83030	−0.915152	+	0.403109i	$0.867929\pi$
$384$	3.39762	0.173384
$385$	20.7633	1.05820
$386$	−14.6100	−0.743630
$387$	39.1299	1.98909
$388$	1.00000	0.0507673
$389$	−24.2419	−1.22911	−0.614556	−	0.788874i	$-0.710665\pi$
$389$	−24.2419	−1.22911	−0.614556	+	0.788874i	$0.710665\pi$
$390$	−9.02071	−0.456781
$391$	36.2459	1.83304
$392$	−8.08635	−0.408423
$393$	31.1868	1.57317
$394$	−2.00053	−0.100785
$395$	41.3279	2.07943
$396$	18.7213	0.940778
$397$	−7.90653	−0.396817	−0.198409	−	0.980119i	$-0.563577\pi$
$397$	−7.90653	−0.396817	−0.198409	+	0.980119i	$0.563577\pi$
$398$	7.01560	0.351660
$399$	63.0454	3.15622
$400$	0.951722	0.0475861
$401$	−3.48707	−0.174136	−0.0870679	−	0.996202i	$-0.527750\pi$
$401$	−3.48707	−0.174136	−0.0870679	+	0.996202i	$0.527750\pi$
$402$	−32.2401	−1.60799
$403$	1.08829	0.0542116
$404$	15.3738	0.764873
$405$	93.5965	4.65085
$406$	0.344609	0.0171027
$407$	7.47144	0.370346
$408$	18.4957	0.915675
$409$	10.3257	0.510571	0.255286	−	0.966866i	$-0.417830\pi$
$409$	10.3257	0.510571	0.255286	+	0.966866i	$0.417830\pi$
$410$	−3.03960	−0.150115
$411$	9.17629	0.452633
$412$	6.54327	0.322364
$413$	19.1563	0.942621
$414$	−56.8872	−2.79585
$415$	12.9080	0.633627
$416$	1.08829	0.0533578
$417$	57.5364	2.81757
$418$	10.4681	0.512014
$419$	−30.6049	−1.49515	−0.747573	−	0.664179i	$-0.768781\pi$
$419$	−30.6049	−1.49515	−0.747573	+	0.664179i	$0.768781\pi$
$420$	−32.1950	−1.57095
$421$	−34.9285	−1.70231	−0.851156	−	0.524913i	$-0.824098\pi$
$421$	−34.9285	−1.70231	−0.851156	+	0.524913i	$0.824098\pi$
$422$	21.9492	1.06847
$423$	6.21935	0.302395
$424$	3.57010	0.173379
$425$	5.18092	0.251311
$426$	−3.12007	−0.151168
$427$	25.5392	1.23593
$428$	−13.9417	−0.673896
$429$	8.10220	0.391178
$430$	−11.1732	−0.538821
$431$	5.22414	0.251638	0.125819	−	0.992053i	$-0.459844\pi$
$431$	5.22414	0.251638	0.125819	+	0.992053i	$0.459844\pi$
$432$	−18.8358	−0.906236
$433$	6.83062	0.328259	0.164129	−	0.986439i	$-0.447519\pi$
$433$	6.83062	0.328259	0.164129	+	0.986439i	$0.447519\pi$
$434$	3.88412	0.186444
$435$	0.735411	0.0352603
$436$	−0.623212	−0.0298464
$437$	−31.8089	−1.52163
$438$	2.62885	0.125611
$439$	15.6047	0.744772	0.372386	−	0.928078i	$-0.378540\pi$
$439$	15.6047	0.744772	0.372386	+	0.928078i	$0.378540\pi$
$440$	−5.34570	−0.254846
$441$	69.0883	3.28992
$442$	5.92436	0.281793
$443$	−17.1517	−0.814901	−0.407451	−	0.913227i	$-0.633582\pi$
$443$	−17.1517	−0.814901	−0.407451	+	0.913227i	$0.633582\pi$
$444$	−11.5850	−0.549799
$445$	39.1888	1.85773
$446$	−25.5122	−1.20804
$447$	21.8142	1.03178
$448$	3.88412	0.183507
$449$	7.00184	0.330437	0.165219	−	0.986257i	$-0.447167\pi$
$449$	7.00184	0.330437	0.165219	+	0.986257i	$0.447167\pi$
$450$	−8.13133	−0.383315
$451$	2.73010	0.128555
$452$	7.46100	0.350936
$453$	32.5361	1.52868
$454$	17.5172	0.822121
$455$	−10.3124	−0.483451
$456$	−16.2316	−0.760114
$457$	3.48425	0.162986	0.0814931	−	0.996674i	$-0.474031\pi$
$457$	3.48425	0.162986	0.0814931	+	0.996674i	$0.474031\pi$
$458$	−6.80429	−0.317944
$459$	−102.537	−4.78601
$460$	16.2437	0.757365
$461$	11.1447	0.519060	0.259530	−	0.965735i	$-0.416432\pi$
$461$	11.1447	0.519060	0.259530	+	0.965735i	$0.416432\pi$
$462$	28.9168	1.34533
$463$	8.75372	0.406820	0.203410	−	0.979094i	$-0.434798\pi$
$463$	8.75372	0.406820	0.203410	+	0.979094i	$0.434798\pi$
$464$	−0.0887226	−0.00411884
$465$	8.28888	0.384388
$466$	30.4665	1.41133
$467$	0.280338	0.0129725	0.00648625	−	0.999979i	$-0.497935\pi$
$467$	0.280338	0.0129725	0.00648625	+	0.999979i	$0.497935\pi$
$468$	−9.29815	−0.429807
$469$	−36.8565	−1.70188
$470$	−1.77589	−0.0819155
$471$	−43.6248	−2.01012
$472$	−4.93197	−0.227012
$473$	10.0355	0.461434
$474$	57.5569	2.64367
$475$	−4.54670	−0.208617
$476$	21.1441	0.969138
$477$	−30.5022	−1.39660
$478$	−22.7908	−1.04243
$479$	15.7247	0.718482	0.359241	−	0.933245i	$-0.383036\pi$
$479$	15.7247	0.718482	0.359241	+	0.933245i	$0.383036\pi$
$480$	8.28888	0.378334
$481$	−3.71079	−0.169197
$482$	6.61805	0.301444
$483$	−87.8677	−3.99812
$484$	−6.19861	−0.281755
$485$	2.43962	0.110777
$486$	73.8433	3.34960
$487$	−11.3248	−0.513177	−0.256589	−	0.966521i	$-0.582599\pi$
$487$	−11.3248	−0.513177	−0.256589	+	0.966521i	$0.582599\pi$
$488$	−6.57529	−0.297650
$489$	68.3402	3.09045
$490$	−19.7276	−0.891202
$491$	3.39414	0.153176	0.0765878	−	0.997063i	$-0.475597\pi$
$491$	3.39414	0.153176	0.0765878	+	0.997063i	$0.475597\pi$
$492$	−4.23321	−0.190848
$493$	−0.482982	−0.0217524
$494$	−5.19914	−0.233920
$495$	45.6727	2.05283
$496$	−1.00000	−0.0449013
$497$	−3.56683	−0.159994
$498$	17.9767	0.805557
$499$	−13.2838	−0.594663	−0.297332	−	0.954774i	$-0.596097\pi$
$499$	−13.2838	−0.594663	−0.297332	+	0.954774i	$0.596097\pi$
$500$	−9.87624	−0.441679
$501$	85.0127	3.79809
$502$	18.8430	0.841003
$503$	−15.1566	−0.675798	−0.337899	−	0.941182i	$-0.609716\pi$
$503$	−15.1566	−0.675798	−0.337899	+	0.941182i	$0.609716\pi$
$504$	−33.1851	−1.47818
$505$	37.5061	1.66900
$506$	−14.5897	−0.648591
$507$	40.1450	1.78290
$508$	−12.5580	−0.557170
$509$	28.7079	1.27245	0.636227	−	0.771502i	$-0.280494\pi$
$509$	28.7079	1.27245	0.636227	+	0.771502i	$0.280494\pi$
$510$	45.1225	1.99806
$511$	3.00527	0.132945
$512$	−1.00000	−0.0441942
$513$	89.9849	3.97293
$514$	10.4789	0.462204
$515$	15.9631	0.703416
$516$	−15.5608	−0.685026
$517$	1.59506	0.0701506
$518$	−13.2438	−0.581900
$519$	6.97718	0.306264
$520$	2.65501	0.116430
$521$	0.488745	0.0214123	0.0107062	−	0.999943i	$-0.496592\pi$
$521$	0.488745	0.0214123	0.0107062	+	0.999943i	$0.496592\pi$
$522$	0.758029	0.0331780
$523$	6.80225	0.297442	0.148721	−	0.988879i	$-0.452484\pi$
$523$	6.80225	0.297442	0.148721	+	0.988879i	$0.452484\pi$
$524$	−9.17902	−0.400987
$525$	−12.5596	−0.548147
$526$	5.18551	0.226099
$527$	−5.44373	−0.237133
$528$	−7.44488	−0.323997
$529$	21.3328	0.927513
$530$	8.70966	0.378323
$531$	42.1378	1.82862
$532$	−18.5558	−0.804494
$533$	−1.35594	−0.0587322
$534$	54.5777	2.36181
$535$	−34.0123	−1.47048
$536$	9.48904	0.409864
$537$	−45.7332	−1.97353
$538$	−31.4464	−1.35575
$539$	17.7189	0.763206
$540$	−45.9520	−1.97746
$541$	−2.70857	−0.116451	−0.0582253	−	0.998303i	$-0.518544\pi$
$541$	−2.70857	−0.116451	−0.0582253	+	0.998303i	$0.518544\pi$
$542$	11.3523	0.487621
$543$	−86.4625	−3.71046
$544$	−5.44373	−0.233398
$545$	−1.52040	−0.0651266
$546$	−14.3619	−0.614632
$547$	−15.5036	−0.662887	−0.331443	−	0.943475i	$-0.607536\pi$
$547$	−15.5036	−0.662887	−0.331443	+	0.943475i	$0.607536\pi$
$548$	−2.70080	−0.115372
$549$	56.1781	2.39762
$550$	−2.08542	−0.0889226
$551$	0.423858	0.0180570
$552$	22.6223	0.962870
$553$	65.7983	2.79803
$554$	−14.8216	−0.629709
$555$	−28.2629	−1.19969
$556$	−16.9343	−0.718176
$557$	−30.6231	−1.29754	−0.648772	−	0.760983i	$-0.724717\pi$
$557$	−30.6231	−1.29754	−0.648772	+	0.760983i	$0.724717\pi$
$558$	8.54381	0.361688
$559$	−4.98428	−0.210812
$560$	9.47575	0.400423
$561$	−40.5280	−1.71109
$562$	4.66534	0.196795
$563$	9.84255	0.414814	0.207407	−	0.978255i	$-0.433498\pi$
$563$	9.84255	0.414814	0.207407	+	0.978255i	$0.433498\pi$
$564$	−2.47325	−0.104143
$565$	18.2020	0.765762
$566$	−29.8815	−1.25601
$567$	149.015	6.25805
$568$	0.918311	0.0385315
$569$	−13.1496	−0.551262	−0.275631	−	0.961264i	$-0.588887\pi$
$569$	−13.1496	−0.551262	−0.275631	+	0.961264i	$0.588887\pi$
$570$	−39.5988	−1.65861
$571$	9.48790	0.397056	0.198528	−	0.980095i	$-0.436384\pi$
$571$	9.48790	0.397056	0.198528	+	0.980095i	$0.436384\pi$
$572$	−2.38467	−0.0997080
$573$	−55.9768	−2.33846
$574$	−4.83935	−0.201991
$575$	6.33684	0.264264
$576$	8.54381	0.355992
$577$	−29.2831	−1.21907	−0.609536	−	0.792758i	$-0.708644\pi$
$577$	−29.2831	−1.21907	−0.609536	+	0.792758i	$0.708644\pi$
$578$	−12.6342	−0.525515
$579$	−49.6392	−2.06294
$580$	−0.216449	−0.00898756
$581$	20.5508	0.852590
$582$	3.39762	0.140836
$583$	−7.82282	−0.323988
$584$	−0.773732	−0.0320173
$585$	−22.6839	−0.937864
$586$	−15.4856	−0.639705
$587$	26.1874	1.08087	0.540434	−	0.841386i	$-0.318260\pi$
$587$	26.1874	1.08087	0.540434	+	0.841386i	$0.318260\pi$
$588$	−27.4743	−1.13302
$589$	4.77734	0.196847
$590$	−12.0321	−0.495354
$591$	−6.79703	−0.279592
$592$	3.40974	0.140139
$593$	−20.8815	−0.857502	−0.428751	−	0.903423i	$-0.641046\pi$
$593$	−20.8815	−0.857502	−0.428751	+	0.903423i	$0.641046\pi$
$594$	41.2730	1.69345
$595$	51.5834	2.11471
$596$	−6.42045	−0.262992
$597$	23.8363	0.975556
$598$	7.24615	0.296317
$599$	2.31216	0.0944724	0.0472362	−	0.998884i	$-0.484959\pi$
$599$	2.31216	0.0944724	0.0472362	+	0.998884i	$0.484959\pi$
$600$	3.23359	0.132011
$601$	25.6122	1.04474	0.522371	−	0.852718i	$-0.325048\pi$
$601$	25.6122	1.04474	0.522371	+	0.852718i	$0.325048\pi$
$602$	−17.7889	−0.725022
$603$	−81.0725	−3.30153
$604$	−9.57614	−0.389648
$605$	−15.1222	−0.614806
$606$	52.2342	2.12187
$607$	23.2472	0.943576	0.471788	−	0.881712i	$-0.343609\pi$
$607$	23.2472	0.943576	0.471788	+	0.881712i	$0.343609\pi$
$608$	4.77734	0.193747
$609$	1.17085	0.0474452
$610$	−16.0412	−0.649489
$611$	−0.792206	−0.0320492
$612$	46.5102	1.88006
$613$	−15.7838	−0.637501	−0.318750	−	0.947839i	$-0.603263\pi$
$613$	−15.7838	−0.637501	−0.318750	+	0.947839i	$0.603263\pi$
$614$	−21.7411	−0.877401
$615$	−10.3274	−0.416441
$616$	−8.51090	−0.342914
$617$	−39.6356	−1.59567	−0.797835	−	0.602876i	$-0.794022\pi$
$617$	−39.6356	−1.59567	−0.797835	+	0.602876i	$0.794022\pi$
$618$	22.2315	0.894283
$619$	44.2777	1.77967	0.889836	−	0.456280i	$-0.150818\pi$
$619$	44.2777	1.77967	0.889836	+	0.456280i	$0.150818\pi$
$620$	−2.43962	−0.0979773
$621$	−125.414	−5.03269
$622$	−30.4273	−1.22002
$623$	62.3926	2.49971
$624$	3.69760	0.148022
$625$	−28.8528	−1.15411
$626$	−20.5267	−0.820413
$627$	35.5668	1.42040
$628$	12.8398	0.512364
$629$	18.5617	0.740104
$630$	−80.9590	−3.22548
$631$	−25.5011	−1.01518	−0.507591	−	0.861598i	$-0.669464\pi$
$631$	−25.5011	−1.01518	−0.507591	+	0.861598i	$0.669464\pi$
$632$	−16.9404	−0.673851
$633$	74.5752	2.96410
$634$	−9.93064	−0.394396
$635$	−30.6366	−1.21578
$636$	12.1298	0.480979
$637$	−8.80030	−0.348681
$638$	0.194410	0.00769675
$639$	−7.84588	−0.310378
$640$	−2.43962	−0.0964343
$641$	29.0078	1.14574	0.572869	−	0.819647i	$-0.305830\pi$
$641$	29.0078	1.14574	0.572869	+	0.819647i	$0.305830\pi$
$642$	−47.3685	−1.86949
$643$	−40.6013	−1.60116	−0.800579	−	0.599228i	$-0.795474\pi$
$643$	−40.6013	−1.60116	−0.800579	+	0.599228i	$0.795474\pi$
$644$	25.8616	1.01909
$645$	−37.9624	−1.49477
$646$	26.0066	1.02322
$647$	−16.5335	−0.649999	−0.325000	−	0.945714i	$-0.605364\pi$
$647$	−16.5335	−0.649999	−0.325000	+	0.945714i	$0.605364\pi$
$648$	−38.3653	−1.50713
$649$	10.8070	0.424210
$650$	1.03575	0.0406254
$651$	13.1967	0.517221
$652$	−20.1142	−0.787731
$653$	−33.4411	−1.30865	−0.654325	−	0.756214i	$-0.727047\pi$
$653$	−33.4411	−1.30865	−0.654325	+	0.756214i	$0.727047\pi$
$654$	−2.11744	−0.0827983
$655$	−22.3933	−0.874977
$656$	1.24593	0.0486455
$657$	6.61062	0.257905
$658$	−2.82739	−0.110223
$659$	18.3164	0.713507	0.356754	−	0.934199i	$-0.383884\pi$
$659$	18.3164	0.713507	0.356754	+	0.934199i	$0.383884\pi$
$660$	−18.1627	−0.706980
$661$	44.2159	1.71980	0.859899	−	0.510465i	$-0.170527\pi$
$661$	44.2159	1.71980	0.859899	+	0.510465i	$0.170527\pi$
$662$	−12.2562	−0.476351
$663$	20.1287	0.781735
$664$	−5.29098	−0.205330
$665$	−45.2689	−1.75545
$666$	−29.1322	−1.12885
$667$	−0.590741	−0.0228736
$668$	−25.0213	−0.968102
$669$	−86.6808	−3.35127
$670$	23.1496	0.894347
$671$	14.4078	0.556208
$672$	13.1967	0.509075
$673$	−5.66777	−0.218477	−0.109238	−	0.994016i	$-0.534841\pi$
$673$	−5.66777	−0.218477	−0.109238	+	0.994016i	$0.534841\pi$
$674$	−5.55263	−0.213879
$675$	−17.9264	−0.689987
$676$	−11.8156	−0.454447
$677$	−7.65976	−0.294389	−0.147194	−	0.989108i	$-0.547024\pi$
$677$	−7.65976	−0.294389	−0.147194	+	0.989108i	$0.547024\pi$
$678$	25.3496	0.973546
$679$	3.88412	0.149059
$680$	−13.2806	−0.509288
$681$	59.5166	2.28068
$682$	2.19121	0.0839056
$683$	−35.8236	−1.37075	−0.685377	−	0.728188i	$-0.740363\pi$
$683$	−35.8236	−1.37075	−0.685377	+	0.728188i	$0.740363\pi$
$684$	−40.8167	−1.56067
$685$	−6.58891	−0.251749
$686$	−4.21953	−0.161102
$687$	−23.1184	−0.882022
$688$	4.57991	0.174608
$689$	3.88530	0.148018
$690$	55.1898	2.10104
$691$	−12.6923	−0.482839	−0.241420	−	0.970421i	$-0.577613\pi$
$691$	−12.6923	−0.482839	−0.241420	+	0.970421i	$0.577613\pi$
$692$	−2.05355	−0.0780643
$693$	72.7155	2.76223
$694$	20.1956	0.766615
$695$	−41.3133	−1.56710
$696$	−0.301446	−0.0114263
$697$	6.78253	0.256907
$698$	4.37382	0.165551
$699$	103.514	3.91524
$700$	3.69660	0.139718
$701$	29.6974	1.12166	0.560828	−	0.827932i	$-0.310483\pi$
$701$	29.6974	1.12166	0.560828	+	0.827932i	$0.310483\pi$
$702$	−20.4988	−0.773676
$703$	−16.2895	−0.614370
$704$	2.19121	0.0825842
$705$	−6.03378	−0.227245
$706$	10.3571	0.389793
$707$	59.7135	2.24576
$708$	−16.7569	−0.629764
$709$	−3.31667	−0.124560	−0.0622800	−	0.998059i	$-0.519837\pi$
$709$	−3.31667	−0.124560	−0.0622800	+	0.998059i	$0.519837\pi$
$710$	2.24033	0.0840779
$711$	144.735	5.42799
$712$	−16.0635	−0.602006
$713$	−6.65829	−0.249355
$714$	71.8395	2.68853
$715$	−5.81767	−0.217569
$716$	13.4604	0.503038
$717$	−77.4344	−2.89184
$718$	26.7964	1.00003
$719$	2.65765	0.0991136	0.0495568	−	0.998771i	$-0.484219\pi$
$719$	2.65765	0.0991136	0.0495568	+	0.998771i	$0.484219\pi$
$720$	20.8436	0.776795
$721$	25.4148	0.946497
$722$	−3.82301	−0.142278
$723$	22.4856	0.836249
$724$	25.4480	0.945766
$725$	−0.0844392	−0.00313599
$726$	−21.0605	−0.781629
$727$	13.4290	0.498056	0.249028	−	0.968496i	$-0.419889\pi$
$727$	13.4290	0.498056	0.249028	+	0.968496i	$0.419889\pi$
$728$	4.22705	0.156665
$729$	135.795	5.02946
$730$	−1.88761	−0.0698636
$731$	24.9318	0.922137
$732$	−22.3403	−0.825723
$733$	0.149951	0.00553858	0.00276929	−	0.999996i	$-0.499119\pi$
$733$	0.149951	0.00553858	0.00276929	+	0.999996i	$0.499119\pi$
$734$	−6.53339	−0.241152
$735$	−67.0268	−2.47232
$736$	−6.65829	−0.245428
$737$	−20.7924	−0.765899
$738$	−10.6450	−0.391849
$739$	23.6327	0.869344	0.434672	−	0.900589i	$-0.356864\pi$
$739$	23.6327	0.869344	0.434672	+	0.900589i	$0.356864\pi$
$740$	8.31845	0.305792
$741$	−17.6647	−0.648928
$742$	13.8667	0.509061
$743$	−22.0970	−0.810662	−0.405331	−	0.914170i	$-0.632844\pi$
$743$	−22.0970	−0.810662	−0.405331	+	0.914170i	$0.632844\pi$
$744$	−3.39762	−0.124563
$745$	−15.6634	−0.573863
$746$	14.6639	0.536883
$747$	45.2052	1.65397
$748$	11.9283	0.436143
$749$	−54.1511	−1.97864
$750$	−33.5557	−1.22528
$751$	42.0652	1.53498	0.767491	−	0.641060i	$-0.221505\pi$
$751$	42.0652	1.53498	0.767491	+	0.641060i	$0.221505\pi$
$752$	0.727937	0.0265451
$753$	64.0212	2.33306
$754$	−0.0965560	−0.00351636
$755$	−23.3621	−0.850234
$756$	−73.1602	−2.66081
$757$	−24.2448	−0.881194	−0.440597	−	0.897705i	$-0.645233\pi$
$757$	−24.2448	−0.881194	−0.440597	+	0.897705i	$0.645233\pi$
$758$	−15.5152	−0.563536
$759$	−49.5702	−1.79928
$760$	11.6549	0.422767
$761$	5.48475	0.198822	0.0994111	−	0.995046i	$-0.468304\pi$
$761$	5.48475	0.198822	0.0994111	+	0.995046i	$0.468304\pi$
$762$	−42.6672	−1.54567
$763$	−2.42063	−0.0876326
$764$	16.4753	0.596055
$765$	113.467	4.10241
$766$	35.8197	1.29422
$767$	−5.36741	−0.193806
$768$	−3.39762	−0.122601
$769$	−0.454240	−0.0163803	−0.00819015	−	0.999966i	$-0.502607\pi$
$769$	−0.454240	−0.0163803	−0.00819015	+	0.999966i	$0.502607\pi$
$770$	−20.7633	−0.748258
$771$	35.6032	1.28222
$772$	14.6100	0.525826
$773$	−19.2896	−0.693799	−0.346900	−	0.937902i	$-0.612766\pi$
$773$	−19.2896	−0.693799	−0.346900	+	0.937902i	$0.612766\pi$
$774$	−39.1299	−1.40650
$775$	−0.951722	−0.0341868
$776$	−1.00000	−0.0358979
$777$	−44.9974	−1.61427
$778$	24.2419	0.869113
$779$	−5.95225	−0.213262
$780$	9.02071	0.322993
$781$	−2.01221	−0.0720025
$782$	−36.2459	−1.29615
$783$	1.67116	0.0597223
$784$	8.08635	0.288798
$785$	31.3242	1.11801
$786$	−31.1868	−1.11240
$787$	16.5251	0.589056	0.294528	−	0.955643i	$-0.404838\pi$
$787$	16.5251	0.589056	0.294528	+	0.955643i	$0.404838\pi$
$788$	2.00053	0.0712658
$789$	17.6184	0.627231
$790$	−41.3279	−1.47038
$791$	28.9794	1.03039
$792$	−18.7213	−0.665231
$793$	−7.15583	−0.254111
$794$	7.90653	0.280592
$795$	29.5921	1.04952
$796$	−7.01560	−0.248661
$797$	−23.9103	−0.846947	−0.423473	−	0.905909i	$-0.639189\pi$
$797$	−23.9103	−0.846947	−0.423473	+	0.905909i	$0.639189\pi$
$798$	−63.0454	−2.23178
$799$	3.96269	0.140190
$800$	−0.951722	−0.0336484
$801$	137.244	4.84927
$802$	3.48707	0.123133
$803$	1.69541	0.0598296
$804$	32.2401	1.13702
$805$	63.0923	2.22371
$806$	−1.08829	−0.0383334
$807$	−106.843	−3.76105
$808$	−15.3738	−0.540847
$809$	−4.40251	−0.154784	−0.0773919	−	0.997001i	$-0.524659\pi$
$809$	−4.40251	−0.154784	−0.0773919	+	0.997001i	$0.524659\pi$
$810$	−93.5965	−3.28865
$811$	40.9375	1.43751	0.718755	−	0.695263i	$-0.244712\pi$
$811$	40.9375	1.43751	0.718755	+	0.695263i	$0.244712\pi$
$812$	−0.344609	−0.0120934
$813$	38.5706	1.35273
$814$	−7.47144	−0.261874
$815$	−49.0708	−1.71888
$816$	−18.4957	−0.647480
$817$	−21.8798	−0.765478
$818$	−10.3257	−0.361029
$819$	−36.1151	−1.26196
$820$	3.03960	0.106147
$821$	36.0673	1.25876	0.629379	−	0.777098i	$-0.283309\pi$
$821$	36.0673	1.25876	0.629379	+	0.777098i	$0.283309\pi$
$822$	−9.17629	−0.320060
$823$	−11.1300	−0.387969	−0.193985	−	0.981005i	$-0.562141\pi$
$823$	−11.1300	−0.387969	−0.193985	+	0.981005i	$0.562141\pi$
$824$	−6.54327	−0.227945
$825$	−7.08546	−0.246684
$826$	−19.1563	−0.666534
$827$	6.44282	0.224039	0.112019	−	0.993706i	$-0.464268\pi$
$827$	6.44282	0.224039	0.112019	+	0.993706i	$0.464268\pi$
$828$	56.8872	1.97697
$829$	−33.0228	−1.14693	−0.573465	−	0.819230i	$-0.694401\pi$
$829$	−33.0228	−1.14693	−0.573465	+	0.819230i	$0.694401\pi$
$830$	−12.9080	−0.448042
$831$	−50.3581	−1.74690
$832$	−1.08829	−0.0377297
$833$	44.0200	1.52520
$834$	−57.5364	−1.99232
$835$	−61.0422	−2.11245
$836$	−10.4681	−0.362048
$837$	18.8358	0.651059
$838$	30.6049	1.05723
$839$	6.31742	0.218102	0.109051	−	0.994036i	$-0.465219\pi$
$839$	6.31742	0.218102	0.109051	+	0.994036i	$0.465219\pi$
$840$	32.1950	1.11083
$841$	−28.9921	−0.999729
$842$	34.9285	1.20372
$843$	15.8510	0.545939
$844$	−21.9492	−0.755524
$845$	−28.8256	−0.991630
$846$	−6.21935	−0.213826
$847$	−24.0761	−0.827266
$848$	−3.57010	−0.122598
$849$	−101.526	−3.48436
$850$	−5.18092	−0.177704
$851$	22.7030	0.778249
$852$	3.12007	0.106892
$853$	−41.5535	−1.42276	−0.711382	−	0.702805i	$-0.751931\pi$
$853$	−41.5535	−1.42276	−0.711382	+	0.702805i	$0.751931\pi$
$854$	−25.5392	−0.873934
$855$	−99.5771	−3.40546
$856$	13.9417	0.476517
$857$	26.1934	0.894749	0.447375	−	0.894347i	$-0.352359\pi$
$857$	26.1934	0.894749	0.447375	+	0.894347i	$0.352359\pi$
$858$	−8.10220	−0.276604
$859$	−17.1867	−0.586403	−0.293202	−	0.956051i	$-0.594721\pi$
$859$	−17.1867	−0.586403	−0.293202	+	0.956051i	$0.594721\pi$
$860$	11.1732	0.381004
$861$	−16.4423	−0.560351
$862$	−5.22414	−0.177935
$863$	16.9404	0.576658	0.288329	−	0.957531i	$-0.406900\pi$
$863$	16.9404	0.576658	0.288329	+	0.957531i	$0.406900\pi$
$864$	18.8358	0.640805
$865$	−5.00988	−0.170341
$866$	−6.83062	−0.232114
$867$	−42.9263	−1.45785
$868$	−3.88412	−0.131835
$869$	37.1198	1.25920
$870$	−0.735411	−0.0249328
$871$	10.3268	0.349911
$872$	0.623212	0.0211046
$873$	8.54381	0.289164
$874$	31.8089	1.07595
$875$	−38.3605	−1.29682
$876$	−2.62885	−0.0888205
$877$	31.4407	1.06168	0.530839	−	0.847472i	$-0.321877\pi$
$877$	31.4407	1.06168	0.530839	+	0.847472i	$0.321877\pi$
$878$	−15.6047	−0.526633
$879$	−52.6142	−1.77463
$880$	5.34570	0.180204
$881$	−15.9682	−0.537982	−0.268991	−	0.963143i	$-0.586690\pi$
$881$	−15.9682	−0.537982	−0.268991	+	0.963143i	$0.586690\pi$
$882$	−69.0883	−2.32632
$883$	45.9252	1.54550	0.772752	−	0.634708i	$-0.218879\pi$
$883$	45.9252	1.54550	0.772752	+	0.634708i	$0.218879\pi$
$884$	−5.92436	−0.199258
$885$	−40.8805	−1.37418
$886$	17.1517	0.576222
$887$	−38.7248	−1.30025	−0.650126	−	0.759827i	$-0.725284\pi$
$887$	−38.7248	−1.30025	−0.650126	+	0.759827i	$0.725284\pi$
$888$	11.5850	0.388767
$889$	−48.7767	−1.63592
$890$	−39.1888	−1.31361
$891$	84.0662	2.81632
$892$	25.5122	0.854213
$893$	−3.47760	−0.116374
$894$	−21.8142	−0.729577
$895$	32.8381	1.09766
$896$	−3.88412	−0.129759
$897$	24.6197	0.822026
$898$	−7.00184	−0.233654
$899$	0.0887226	0.00295907
$900$	8.13133	0.271044
$901$	−19.4346	−0.647462
$902$	−2.73010	−0.0909023
$903$	−60.4399	−2.01132
$904$	−7.46100	−0.248149
$905$	62.0832	2.06372
$906$	−32.5361	−1.08094
$907$	−14.4050	−0.478310	−0.239155	−	0.970981i	$-0.576870\pi$
$907$	−14.4050	−0.478310	−0.239155	+	0.970981i	$0.576870\pi$
$908$	−17.5172	−0.581327
$909$	131.350	4.35662
$910$	10.3124	0.341852
$911$	22.7864	0.754946	0.377473	−	0.926020i	$-0.376793\pi$
$911$	22.7864	0.754946	0.377473	+	0.926020i	$0.376793\pi$
$912$	16.2316	0.537482
$913$	11.5936	0.383693
$914$	−3.48425	−0.115249
$915$	−54.5018	−1.80178
$916$	6.80429	0.224820
$917$	−35.6524	−1.17734
$918$	102.537	3.38422
$919$	3.91262	0.129065	0.0645326	−	0.997916i	$-0.479444\pi$
$919$	3.91262	0.129065	0.0645326	+	0.997916i	$0.479444\pi$
$920$	−16.2437	−0.535538
$921$	−73.8681	−2.43404
$922$	−11.1447	−0.367031
$923$	0.999389	0.0328953
$924$	−28.9168	−0.951293
$925$	3.24512	0.106699
$926$	−8.75372	−0.287665
$927$	55.9044	1.83614
$928$	0.0887226	0.00291246
$929$	−21.8850	−0.718023	−0.359012	−	0.933333i	$-0.616886\pi$
$929$	−21.8850	−0.718023	−0.359012	+	0.933333i	$0.616886\pi$
$930$	−8.28888	−0.271803
$931$	−38.6313	−1.26609
$932$	−30.4665	−0.997963
$933$	−103.380	−3.38452
$934$	−0.280338	−0.00917294
$935$	29.1006	0.951690
$936$	9.29815	0.303919
$937$	54.4210	1.77786	0.888929	−	0.458045i	$-0.151450\pi$
$937$	54.4210	1.77786	0.888929	+	0.458045i	$0.151450\pi$
$938$	36.8565	1.20341
$939$	−69.7420	−2.27594
$940$	1.77589	0.0579230
$941$	23.1553	0.754840	0.377420	−	0.926042i	$-0.376811\pi$
$941$	23.1553	0.754840	0.377420	+	0.926042i	$0.376811\pi$
$942$	43.6248	1.42137
$943$	8.29578	0.270148
$944$	4.93197	0.160522
$945$	−178.483	−5.80605
$946$	−10.0355	−0.326283
$947$	18.9431	0.615568	0.307784	−	0.951456i	$-0.400413\pi$
$947$	18.9431	0.615568	0.307784	+	0.951456i	$0.400413\pi$
$948$	−57.5569	−1.86936
$949$	−0.842046	−0.0273340
$950$	4.54670	0.147514
$951$	−33.7405	−1.09411
$952$	−21.1441	−0.685284
$953$	31.6044	1.02377	0.511883	−	0.859055i	$-0.328948\pi$
$953$	31.6044	1.02377	0.511883	+	0.859055i	$0.328948\pi$
$954$	30.5022	0.987546
$955$	40.1934	1.30063
$956$	22.7908	0.737107
$957$	0.660530	0.0213519
$958$	−15.7247	−0.508043
$959$	−10.4902	−0.338747
$960$	−8.28888	−0.267522
$961$	1.00000	0.0322581
$962$	3.71079	0.119641
$963$	−119.115	−3.83843
$964$	−6.61805	−0.213153
$965$	35.6428	1.14738
$966$	87.8677	2.82710
$967$	−14.8062	−0.476135	−0.238067	−	0.971249i	$-0.576514\pi$
$967$	−14.8062	−0.476135	−0.238067	+	0.971249i	$0.576514\pi$
$968$	6.19861	0.199231
$969$	88.3604	2.83855
$970$	−2.43962	−0.0783313
$971$	4.92523	0.158058	0.0790291	−	0.996872i	$-0.474818\pi$
$971$	4.92523	0.158058	0.0790291	+	0.996872i	$0.474818\pi$
$972$	−73.8433	−2.36852
$973$	−65.7749	−2.10865
$974$	11.3248	0.362871
$975$	3.51908	0.112701
$976$	6.57529	0.210470
$977$	−34.7023	−1.11022	−0.555112	−	0.831775i	$-0.687325\pi$
$977$	−34.7023	−1.11022	−0.555112	+	0.831775i	$0.687325\pi$
$978$	−68.3402	−2.18528
$979$	35.1985	1.12495
$980$	19.7276	0.630175
$981$	−5.32460	−0.170001
$982$	−3.39414	−0.108311
$983$	−7.72017	−0.246235	−0.123118	−	0.992392i	$-0.539289\pi$
$983$	−7.72017	−0.246235	−0.123118	+	0.992392i	$0.539289\pi$
$984$	4.23321	0.134950
$985$	4.88052	0.155506
$986$	0.482982	0.0153813
$987$	−9.60639	−0.305775
$988$	5.19914	0.165407
$989$	30.4944	0.969665
$990$	−45.6727	−1.45157
$991$	37.3382	1.18609	0.593044	−	0.805170i	$-0.297926\pi$
$991$	37.3382	1.18609	0.593044	+	0.805170i	$0.297926\pi$
$992$	1.00000	0.0317500
$993$	−41.6419	−1.32147
$994$	3.56683	0.113133
$995$	−17.1154	−0.542594
$996$	−17.9767	−0.569615
$997$	22.4794	0.711929	0.355965	−	0.934499i	$-0.384152\pi$
$997$	22.4794	0.711929	0.355965	+	0.934499i	$0.384152\pi$
$998$	13.2838	0.420490
$999$	−64.2250	−2.03199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.1	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.39762 q^{3} +1.00000 q^{4} +2.43962 q^{5} +3.39762 q^{6} +3.88412 q^{7} -1.00000 q^{8} +8.54381 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.39762 q^{3} +1.00000 q^{4} +2.43962 q^{5} +3.39762 q^{6} +3.88412 q^{7} -1.00000 q^{8} +8.54381 q^{9} -2.43962 q^{10} +2.19121 q^{11} -3.39762 q^{12} -1.08829 q^{13} -3.88412 q^{14} -8.28888 q^{15} +1.00000 q^{16} +5.44373 q^{17} -8.54381 q^{18} -4.77734 q^{19} +2.43962 q^{20} -13.1967 q^{21} -2.19121 q^{22} +6.65829 q^{23} +3.39762 q^{24} +0.951722 q^{25} +1.08829 q^{26} -18.8358 q^{27} +3.88412 q^{28} -0.0887226 q^{29} +8.28888 q^{30} -1.00000 q^{31} -1.00000 q^{32} -7.44488 q^{33} -5.44373 q^{34} +9.47575 q^{35} +8.54381 q^{36} +3.40974 q^{37} +4.77734 q^{38} +3.69760 q^{39} -2.43962 q^{40} +1.24593 q^{41} +13.1967 q^{42} +4.57991 q^{43} +2.19121 q^{44} +20.8436 q^{45} -6.65829 q^{46} +0.727937 q^{47} -3.39762 q^{48} +8.08635 q^{49} -0.951722 q^{50} -18.4957 q^{51} -1.08829 q^{52} -3.57010 q^{53} +18.8358 q^{54} +5.34570 q^{55} -3.88412 q^{56} +16.2316 q^{57} +0.0887226 q^{58} +4.93197 q^{59} -8.28888 q^{60} +6.57529 q^{61} +1.00000 q^{62} +33.1851 q^{63} +1.00000 q^{64} -2.65501 q^{65} +7.44488 q^{66} -9.48904 q^{67} +5.44373 q^{68} -22.6223 q^{69} -9.47575 q^{70} -0.918311 q^{71} -8.54381 q^{72} +0.773732 q^{73} -3.40974 q^{74} -3.23359 q^{75} -4.77734 q^{76} +8.51090 q^{77} -3.69760 q^{78} +16.9404 q^{79} +2.43962 q^{80} +38.3653 q^{81} -1.24593 q^{82} +5.29098 q^{83} -13.1967 q^{84} +13.2806 q^{85} -4.57991 q^{86} +0.301446 q^{87} -2.19121 q^{88} +16.0635 q^{89} -20.8436 q^{90} -4.22705 q^{91} +6.65829 q^{92} +3.39762 q^{93} -0.727937 q^{94} -11.6549 q^{95} +3.39762 q^{96} +1.00000 q^{97} -8.08635 q^{98} +18.7213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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