LMFDB - Embedded newform 6015.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.75959 q^{2} +1.00000 q^{3} +1.09616 q^{4} +1.00000 q^{5} +1.75959 q^{6} -3.35674 q^{7} -1.59039 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.75959 q^{2} +1.00000 q^{3} +1.09616 q^{4} +1.00000 q^{5} +1.75959 q^{6} -3.35674 q^{7} -1.59039 q^{8} +1.00000 q^{9} +1.75959 q^{10} +4.95225 q^{11} +1.09616 q^{12} -4.38406 q^{13} -5.90648 q^{14} +1.00000 q^{15} -4.99075 q^{16} +0.849391 q^{17} +1.75959 q^{18} -6.37888 q^{19} +1.09616 q^{20} -3.35674 q^{21} +8.71393 q^{22} +2.99710 q^{23} -1.59039 q^{24} +1.00000 q^{25} -7.71414 q^{26} +1.00000 q^{27} -3.67952 q^{28} -1.30517 q^{29} +1.75959 q^{30} -4.99787 q^{31} -5.60090 q^{32} +4.95225 q^{33} +1.49458 q^{34} -3.35674 q^{35} +1.09616 q^{36} -2.12259 q^{37} -11.2242 q^{38} -4.38406 q^{39} -1.59039 q^{40} -10.2937 q^{41} -5.90648 q^{42} +3.14413 q^{43} +5.42845 q^{44} +1.00000 q^{45} +5.27368 q^{46} +7.47563 q^{47} -4.99075 q^{48} +4.26769 q^{49} +1.75959 q^{50} +0.849391 q^{51} -4.80562 q^{52} -7.02259 q^{53} +1.75959 q^{54} +4.95225 q^{55} +5.33853 q^{56} -6.37888 q^{57} -2.29656 q^{58} -4.59750 q^{59} +1.09616 q^{60} -3.05543 q^{61} -8.79421 q^{62} -3.35674 q^{63} +0.126218 q^{64} -4.38406 q^{65} +8.71393 q^{66} +3.08944 q^{67} +0.931067 q^{68} +2.99710 q^{69} -5.90648 q^{70} -5.13986 q^{71} -1.59039 q^{72} -7.08685 q^{73} -3.73489 q^{74} +1.00000 q^{75} -6.99226 q^{76} -16.6234 q^{77} -7.71414 q^{78} -6.02311 q^{79} -4.99075 q^{80} +1.00000 q^{81} -18.1127 q^{82} -12.2499 q^{83} -3.67952 q^{84} +0.849391 q^{85} +5.53237 q^{86} -1.30517 q^{87} -7.87601 q^{88} -0.595361 q^{89} +1.75959 q^{90} +14.7161 q^{91} +3.28530 q^{92} -4.99787 q^{93} +13.1540 q^{94} -6.37888 q^{95} -5.60090 q^{96} +11.2610 q^{97} +7.50939 q^{98} +4.95225 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * 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 $

$2$	1.75959	1.24422	0.622109	−	0.782931i	$-0.286276\pi$
$2$	1.75959	1.24422	0.622109	+	0.782931i	$0.286276\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.09616	0.548079
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.75959	0.718350
$7$	−3.35674	−1.26873	−0.634364	−	0.773035i	$-0.718738\pi$
$7$	−3.35674	−1.26873	−0.634364	+	0.773035i	$0.718738\pi$
$8$	−1.59039	−0.562288
$9$	1.00000	0.333333
$10$	1.75959	0.556431
$11$	4.95225	1.49316	0.746579	−	0.665296i	$-0.231695\pi$
$11$	4.95225	1.49316	0.746579	+	0.665296i	$0.231695\pi$
$12$	1.09616	0.316434
$13$	−4.38406	−1.21592	−0.607959	−	0.793968i	$-0.708012\pi$
$13$	−4.38406	−1.21592	−0.607959	+	0.793968i	$0.708012\pi$
$14$	−5.90648	−1.57857
$15$	1.00000	0.258199
$16$	−4.99075	−1.24769
$17$	0.849391	0.206007	0.103004	−	0.994681i	$-0.467155\pi$
$17$	0.849391	0.206007	0.103004	+	0.994681i	$0.467155\pi$
$18$	1.75959	0.414739
$19$	−6.37888	−1.46341	−0.731707	−	0.681619i	$-0.761276\pi$
$19$	−6.37888	−1.46341	−0.731707	+	0.681619i	$0.761276\pi$
$20$	1.09616	0.245108
$21$	−3.35674	−0.732500
$22$	8.71393	1.85782
$23$	2.99710	0.624939	0.312470	−	0.949928i	$-0.398844\pi$
$23$	2.99710	0.624939	0.312470	+	0.949928i	$0.398844\pi$
$24$	−1.59039	−0.324637
$25$	1.00000	0.200000
$26$	−7.71414	−1.51287
$27$	1.00000	0.192450
$28$	−3.67952	−0.695363
$29$	−1.30517	−0.242363	−0.121182	−	0.992630i	$-0.538668\pi$
$29$	−1.30517	−0.242363	−0.121182	+	0.992630i	$0.538668\pi$
$30$	1.75959	0.321256
$31$	−4.99787	−0.897645	−0.448822	−	0.893621i	$-0.648156\pi$
$31$	−4.99787	−0.897645	−0.448822	+	0.893621i	$0.648156\pi$
$32$	−5.60090	−0.990109
$33$	4.95225	0.862076
$34$	1.49458	0.256318
$35$	−3.35674	−0.567392
$36$	1.09616	0.182693
$37$	−2.12259	−0.348952	−0.174476	−	0.984661i	$-0.555823\pi$
$37$	−2.12259	−0.348952	−0.174476	+	0.984661i	$0.555823\pi$
$38$	−11.2242	−1.82081
$39$	−4.38406	−0.702011
$40$	−1.59039	−0.251463
$41$	−10.2937	−1.60760	−0.803802	−	0.594896i	$-0.797193\pi$
$41$	−10.2937	−1.60760	−0.803802	+	0.594896i	$0.797193\pi$
$42$	−5.90648	−0.911390
$43$	3.14413	0.479475	0.239737	−	0.970838i	$-0.422939\pi$
$43$	3.14413	0.479475	0.239737	+	0.970838i	$0.422939\pi$
$44$	5.42845	0.818369
$45$	1.00000	0.149071
$46$	5.27368	0.777561
$47$	7.47563	1.09043	0.545216	−	0.838295i	$-0.316448\pi$
$47$	7.47563	1.09043	0.545216	+	0.838295i	$0.316448\pi$
$48$	−4.99075	−0.720353
$49$	4.26769	0.609670
$50$	1.75959	0.248844
$51$	0.849391	0.118938
$52$	−4.80562	−0.666420
$53$	−7.02259	−0.964627	−0.482313	−	0.875999i	$-0.660203\pi$
$53$	−7.02259	−0.964627	−0.482313	+	0.875999i	$0.660203\pi$
$54$	1.75959	0.239450
$55$	4.95225	0.667761
$56$	5.33853	0.713391
$57$	−6.37888	−0.844903
$58$	−2.29656	−0.301553
$59$	−4.59750	−0.598544	−0.299272	−	0.954168i	$-0.596744\pi$
$59$	−4.59750	−0.598544	−0.299272	+	0.954168i	$0.596744\pi$
$60$	1.09616	0.141513
$61$	−3.05543	−0.391207	−0.195604	−	0.980683i	$-0.562667\pi$
$61$	−3.05543	−0.391207	−0.195604	+	0.980683i	$0.562667\pi$
$62$	−8.79421	−1.11687
$63$	−3.35674	−0.422909
$64$	0.126218	0.0157772
$65$	−4.38406	−0.543775
$66$	8.71393	1.07261
$67$	3.08944	0.377435	0.188718	−	0.982031i	$-0.439567\pi$
$67$	3.08944	0.377435	0.188718	+	0.982031i	$0.439567\pi$
$68$	0.931067	0.112908
$69$	2.99710	0.360809
$70$	−5.90648	−0.705960
$71$	−5.13986	−0.609989	−0.304995	−	0.952354i	$-0.598655\pi$
$71$	−5.13986	−0.609989	−0.304995	+	0.952354i	$0.598655\pi$
$72$	−1.59039	−0.187429
$73$	−7.08685	−0.829453	−0.414726	−	0.909946i	$-0.636123\pi$
$73$	−7.08685	−0.829453	−0.414726	+	0.909946i	$0.636123\pi$
$74$	−3.73489	−0.434172
$75$	1.00000	0.115470
$76$	−6.99226	−0.802067
$77$	−16.6234	−1.89441
$78$	−7.71414	−0.873455
$79$	−6.02311	−0.677652	−0.338826	−	0.940849i	$-0.610030\pi$
$79$	−6.02311	−0.677652	−0.338826	+	0.940849i	$0.610030\pi$
$80$	−4.99075	−0.557983
$81$	1.00000	0.111111
$82$	−18.1127	−2.00021
$83$	−12.2499	−1.34460	−0.672299	−	0.740280i	$-0.734693\pi$
$83$	−12.2499	−1.34460	−0.672299	+	0.740280i	$0.734693\pi$
$84$	−3.67952	−0.401468
$85$	0.849391	0.0921294
$86$	5.53237	0.596571
$87$	−1.30517	−0.139929
$88$	−7.87601	−0.839586
$89$	−0.595361	−0.0631081	−0.0315541	−	0.999502i	$-0.510046\pi$
$89$	−0.595361	−0.0631081	−0.0315541	+	0.999502i	$0.510046\pi$
$90$	1.75959	0.185477
$91$	14.7161	1.54267
$92$	3.28530	0.342516
$93$	−4.99787	−0.518255
$94$	13.1540	1.35674
$95$	−6.37888	−0.654459
$96$	−5.60090	−0.571639
$97$	11.2610	1.14339	0.571693	−	0.820468i	$-0.306287\pi$
$97$	11.2610	1.14339	0.571693	+	0.820468i	$0.306287\pi$
$98$	7.50939	0.758563
$99$	4.95225	0.497720
$100$	1.09616	0.109616
$101$	1.63679	0.162867	0.0814334	−	0.996679i	$-0.474050\pi$
$101$	1.63679	0.162867	0.0814334	+	0.996679i	$0.474050\pi$
$102$	1.49458	0.147985
$103$	−9.87624	−0.973135	−0.486567	−	0.873643i	$-0.661751\pi$
$103$	−9.87624	−0.973135	−0.486567	+	0.873643i	$0.661751\pi$
$104$	6.97236	0.683697
$105$	−3.35674	−0.327584
$106$	−12.3569	−1.20021
$107$	−8.65347	−0.836562	−0.418281	−	0.908318i	$-0.637367\pi$
$107$	−8.65347	−0.836562	−0.418281	+	0.908318i	$0.637367\pi$
$108$	1.09616	0.105478
$109$	17.2482	1.65208	0.826040	−	0.563611i	$-0.190588\pi$
$109$	17.2482	1.65208	0.826040	+	0.563611i	$0.190588\pi$
$110$	8.71393	0.830840
$111$	−2.12259	−0.201467
$112$	16.7527	1.58298
$113$	−11.1133	−1.04545	−0.522724	−	0.852502i	$-0.675084\pi$
$113$	−11.1133	−1.04545	−0.522724	+	0.852502i	$0.675084\pi$
$114$	−11.2242	−1.05124
$115$	2.99710	0.279481
$116$	−1.43067	−0.132834
$117$	−4.38406	−0.405306
$118$	−8.08972	−0.744719
$119$	−2.85118	−0.261367
$120$	−1.59039	−0.145182
$121$	13.5248	1.22952
$122$	−5.37630	−0.486747
$123$	−10.2937	−0.928151
$124$	−5.47846	−0.491980
$125$	1.00000	0.0894427
$126$	−5.90648	−0.526191
$127$	15.3129	1.35880	0.679399	−	0.733769i	$-0.262240\pi$
$127$	15.3129	1.35880	0.679399	+	0.733769i	$0.262240\pi$
$128$	11.4239	1.00974
$129$	3.14413	0.276825
$130$	−7.71414	−0.676575
$131$	−14.3635	−1.25494	−0.627470	−	0.778640i	$-0.715910\pi$
$131$	−14.3635	−1.25494	−0.627470	+	0.778640i	$0.715910\pi$
$132$	5.42845	0.472486
$133$	21.4122	1.85667
$134$	5.43615	0.469612
$135$	1.00000	0.0860663
$136$	−1.35086	−0.115836
$137$	9.06424	0.774411	0.387205	−	0.921994i	$-0.373440\pi$
$137$	9.06424	0.774411	0.387205	+	0.921994i	$0.373440\pi$
$138$	5.27368	0.448925
$139$	−4.08375	−0.346380	−0.173190	−	0.984888i	$-0.555407\pi$
$139$	−4.08375	−0.346380	−0.173190	+	0.984888i	$0.555407\pi$
$140$	−3.67952	−0.310976
$141$	7.47563	0.629562
$142$	−9.04405	−0.758960
$143$	−21.7109	−1.81556
$144$	−4.99075	−0.415896
$145$	−1.30517	−0.108388
$146$	−12.4699	−1.03202
$147$	4.26769	0.351993
$148$	−2.32670	−0.191253
$149$	−3.86068	−0.316279	−0.158140	−	0.987417i	$-0.550550\pi$
$149$	−3.86068	−0.316279	−0.158140	+	0.987417i	$0.550550\pi$
$150$	1.75959	0.143670
$151$	−8.07009	−0.656735	−0.328367	−	0.944550i	$-0.606498\pi$
$151$	−8.07009	−0.656735	−0.328367	+	0.944550i	$0.606498\pi$
$152$	10.1449	0.822861
$153$	0.849391	0.0686692
$154$	−29.2504	−2.35706
$155$	−4.99787	−0.401439
$156$	−4.80562	−0.384758
$157$	−3.07807	−0.245657	−0.122828	−	0.992428i	$-0.539196\pi$
$157$	−3.07807	−0.245657	−0.122828	+	0.992428i	$0.539196\pi$
$158$	−10.5982	−0.843147
$159$	−7.02259	−0.556928
$160$	−5.60090	−0.442790
$161$	−10.0605	−0.792878
$162$	1.75959	0.138246
$163$	−23.3432	−1.82838	−0.914189	−	0.405288i	$-0.867171\pi$
$163$	−23.3432	−1.82838	−0.914189	+	0.405288i	$0.867171\pi$
$164$	−11.2835	−0.881095
$165$	4.95225	0.385532
$166$	−21.5548	−1.67297
$167$	−22.6290	−1.75109	−0.875543	−	0.483140i	$-0.839496\pi$
$167$	−22.6290	−1.75109	−0.875543	+	0.483140i	$0.839496\pi$
$168$	5.33853	0.411876
$169$	6.21995	0.478458
$170$	1.49458	0.114629
$171$	−6.37888	−0.487805
$172$	3.44646	0.262790
$173$	5.24607	0.398851	0.199425	−	0.979913i	$-0.436092\pi$
$173$	5.24607	0.398851	0.199425	+	0.979913i	$0.436092\pi$
$174$	−2.29656	−0.174102
$175$	−3.35674	−0.253746
$176$	−24.7154	−1.86300
$177$	−4.59750	−0.345570
$178$	−1.04759	−0.0785203
$179$	16.6567	1.24498	0.622490	−	0.782628i	$-0.286121\pi$
$179$	16.6567	1.24498	0.622490	+	0.782628i	$0.286121\pi$
$180$	1.09616	0.0817028
$181$	20.8795	1.55196	0.775979	−	0.630758i	$-0.217256\pi$
$181$	20.8795	1.55196	0.775979	+	0.630758i	$0.217256\pi$
$182$	25.8944	1.91942
$183$	−3.05543	−0.225864
$184$	−4.76657	−0.351396
$185$	−2.12259	−0.156056
$186$	−8.79421	−0.644823
$187$	4.20639	0.307602
$188$	8.19447	0.597643
$189$	−3.35674	−0.244167
$190$	−11.2242	−0.814290
$191$	13.3616	0.966813	0.483407	−	0.875396i	$-0.339399\pi$
$191$	13.3616	0.966813	0.483407	+	0.875396i	$0.339399\pi$
$192$	0.126218	0.00910899
$193$	13.1335	0.945367	0.472684	−	0.881232i	$-0.343285\pi$
$193$	13.1335	0.945367	0.472684	+	0.881232i	$0.343285\pi$
$194$	19.8148	1.42262
$195$	−4.38406	−0.313949
$196$	4.67806	0.334147
$197$	11.9245	0.849588	0.424794	−	0.905290i	$-0.360347\pi$
$197$	11.9245	0.849588	0.424794	+	0.905290i	$0.360347\pi$
$198$	8.71393	0.619272
$199$	20.3274	1.44097	0.720487	−	0.693469i	$-0.243918\pi$
$199$	20.3274	1.44097	0.720487	+	0.693469i	$0.243918\pi$
$200$	−1.59039	−0.112458
$201$	3.08944	0.217912
$202$	2.88008	0.202642
$203$	4.38110	0.307493
$204$	0.931067	0.0651877
$205$	−10.2937	−0.718943
$206$	−17.3781	−1.21079
$207$	2.99710	0.208313
$208$	21.8797	1.51709
$209$	−31.5898	−2.18511
$210$	−5.90648	−0.407586
$211$	−18.8373	−1.29681	−0.648406	−	0.761295i	$-0.724564\pi$
$211$	−18.8373	−1.29681	−0.648406	+	0.761295i	$0.724564\pi$
$212$	−7.69787	−0.528692
$213$	−5.13986	−0.352177
$214$	−15.2266	−1.04087
$215$	3.14413	0.214428
$216$	−1.59039	−0.108212
$217$	16.7766	1.13887
$218$	30.3498	2.05555
$219$	−7.08685	−0.478885
$220$	5.42845	0.365986
$221$	−3.72378	−0.250488
$222$	−3.73489	−0.250669
$223$	5.85769	0.392260	0.196130	−	0.980578i	$-0.437163\pi$
$223$	5.85769	0.392260	0.196130	+	0.980578i	$0.437163\pi$
$224$	18.8008	1.25618
$225$	1.00000	0.0666667
$226$	−19.5548	−1.30077
$227$	−8.71484	−0.578424	−0.289212	−	0.957265i	$-0.593393\pi$
$227$	−8.71484	−0.578424	−0.289212	+	0.957265i	$0.593393\pi$
$228$	−6.99226	−0.463074
$229$	−4.88901	−0.323075	−0.161538	−	0.986867i	$-0.551645\pi$
$229$	−4.88901	−0.323075	−0.161538	+	0.986867i	$0.551645\pi$
$230$	5.27368	0.347736
$231$	−16.6234	−1.09374
$232$	2.07573	0.136278
$233$	8.53241	0.558977	0.279488	−	0.960149i	$-0.409835\pi$
$233$	8.53241	0.558977	0.279488	+	0.960149i	$0.409835\pi$
$234$	−7.71414	−0.504289
$235$	7.47563	0.487656
$236$	−5.03959	−0.328050
$237$	−6.02311	−0.391243
$238$	−5.01691	−0.325198
$239$	17.3772	1.12404	0.562020	−	0.827124i	$-0.310025\pi$
$239$	17.3772	1.12404	0.562020	+	0.827124i	$0.310025\pi$
$240$	−4.99075	−0.322152
$241$	−23.6004	−1.52024	−0.760119	−	0.649784i	$-0.774859\pi$
$241$	−23.6004	−1.52024	−0.760119	+	0.649784i	$0.774859\pi$
$242$	23.7980	1.52980
$243$	1.00000	0.0641500
$244$	−3.34923	−0.214413
$245$	4.26769	0.272653
$246$	−18.1127	−1.15482
$247$	27.9653	1.77939
$248$	7.94857	0.504735
$249$	−12.2499	−0.776304
$250$	1.75959	0.111286
$251$	8.11121	0.511975	0.255988	−	0.966680i	$-0.417599\pi$
$251$	8.11121	0.511975	0.255988	+	0.966680i	$0.417599\pi$
$252$	−3.67952	−0.231788
$253$	14.8424	0.933134
$254$	26.9444	1.69064
$255$	0.849391	0.0531909
$256$	19.8489	1.24056
$257$	3.01003	0.187760	0.0938802	−	0.995584i	$-0.470073\pi$
$257$	3.01003	0.187760	0.0938802	+	0.995584i	$0.470073\pi$
$258$	5.53237	0.344430
$259$	7.12498	0.442725
$260$	−4.80562	−0.298032
$261$	−1.30517	−0.0807878
$262$	−25.2738	−1.56142
$263$	−0.688617	−0.0424620	−0.0212310	−	0.999775i	$-0.506759\pi$
$263$	−0.688617	−0.0424620	−0.0212310	+	0.999775i	$0.506759\pi$
$264$	−7.87601	−0.484735
$265$	−7.02259	−0.431394
$266$	37.6767	2.31011
$267$	−0.595361	−0.0364355
$268$	3.38652	0.206864
$269$	−6.44208	−0.392781	−0.196390	−	0.980526i	$-0.562922\pi$
$269$	−6.44208	−0.392781	−0.196390	+	0.980526i	$0.562922\pi$
$270$	1.75959	0.107085
$271$	16.1138	0.978844	0.489422	−	0.872047i	$-0.337208\pi$
$271$	16.1138	0.978844	0.489422	+	0.872047i	$0.337208\pi$
$272$	−4.23910	−0.257033
$273$	14.7161	0.890661
$274$	15.9494	0.963536
$275$	4.95225	0.298632
$276$	3.28530	0.197752
$277$	−0.248610	−0.0149375	−0.00746876	−	0.999972i	$-0.502377\pi$
$277$	−0.248610	−0.0149375	−0.00746876	+	0.999972i	$0.502377\pi$
$278$	−7.18573	−0.430972
$279$	−4.99787	−0.299215
$280$	5.33853	0.319038
$281$	−12.5940	−0.751293	−0.375646	−	0.926763i	$-0.622579\pi$
$281$	−12.5940	−0.751293	−0.375646	+	0.926763i	$0.622579\pi$
$282$	13.1540	0.783312
$283$	−17.3123	−1.02911	−0.514556	−	0.857457i	$-0.672043\pi$
$283$	−17.3123	−1.02911	−0.514556	+	0.857457i	$0.672043\pi$
$284$	−5.63410	−0.334322
$285$	−6.37888	−0.377852
$286$	−38.2023	−2.25895
$287$	34.5532	2.03961
$288$	−5.60090	−0.330036
$289$	−16.2785	−0.957561
$290$	−2.29656	−0.134859
$291$	11.2610	0.660134
$292$	−7.76831	−0.454606
$293$	11.6298	0.679419	0.339709	−	0.940530i	$-0.389671\pi$
$293$	11.6298	0.679419	0.339709	+	0.940530i	$0.389671\pi$
$294$	7.50939	0.437956
$295$	−4.59750	−0.267677
$296$	3.37575	0.196211
$297$	4.95225	0.287359
$298$	−6.79322	−0.393521
$299$	−13.1395	−0.759875
$300$	1.09616	0.0632867
$301$	−10.5540	−0.608323
$302$	−14.2001	−0.817121
$303$	1.63679	0.0940312
$304$	31.8354	1.82589
$305$	−3.05543	−0.174953
$306$	1.49458	0.0854394
$307$	25.3710	1.44800	0.724000	−	0.689800i	$-0.242302\pi$
$307$	25.3710	1.44800	0.724000	+	0.689800i	$0.242302\pi$
$308$	−18.2219	−1.03829
$309$	−9.87624	−0.561840
$310$	−8.79421	−0.499478
$311$	−2.58007	−0.146303	−0.0731513	−	0.997321i	$-0.523306\pi$
$311$	−2.58007	−0.146303	−0.0731513	+	0.997321i	$0.523306\pi$
$312$	6.97236	0.394732
$313$	−21.0686	−1.19087	−0.595433	−	0.803405i	$-0.703019\pi$
$313$	−21.0686	−1.19087	−0.595433	+	0.803405i	$0.703019\pi$
$314$	−5.41614	−0.305651
$315$	−3.35674	−0.189131
$316$	−6.60228	−0.371407
$317$	−10.2164	−0.573808	−0.286904	−	0.957959i	$-0.592626\pi$
$317$	−10.2164	−0.573808	−0.286904	+	0.957959i	$0.592626\pi$
$318$	−12.3569	−0.692940
$319$	−6.46351	−0.361887
$320$	0.126218	0.00705579
$321$	−8.65347	−0.482990
$322$	−17.7023	−0.986513
$323$	−5.41816	−0.301474
$324$	1.09616	0.0608977
$325$	−4.38406	−0.243184
$326$	−41.0744	−2.27490
$327$	17.2482	0.953829
$328$	16.3710	0.903937
$329$	−25.0937	−1.38346
$330$	8.71393	0.479686
$331$	−18.6564	−1.02545	−0.512724	−	0.858554i	$-0.671364\pi$
$331$	−18.6564	−1.02545	−0.512724	+	0.858554i	$0.671364\pi$
$332$	−13.4278	−0.736946
$333$	−2.12259	−0.116317
$334$	−39.8178	−2.17873
$335$	3.08944	0.168794
$336$	16.7527	0.913932
$337$	3.64179	0.198381	0.0991906	−	0.995068i	$-0.468375\pi$
$337$	3.64179	0.198381	0.0991906	+	0.995068i	$0.468375\pi$
$338$	10.9446	0.595306
$339$	−11.1133	−0.603590
$340$	0.931067	0.0504942
$341$	−24.7507	−1.34033
$342$	−11.2242	−0.606936
$343$	9.17165	0.495222
$344$	−5.00039	−0.269603
$345$	2.99710	0.161359
$346$	9.23093	0.496258
$347$	−6.40205	−0.343680	−0.171840	−	0.985125i	$-0.554971\pi$
$347$	−6.40205	−0.343680	−0.171840	+	0.985125i	$0.554971\pi$
$348$	−1.43067	−0.0766919
$349$	−0.931859	−0.0498813	−0.0249406	−	0.999689i	$-0.507940\pi$
$349$	−0.931859	−0.0498813	−0.0249406	+	0.999689i	$0.507940\pi$
$350$	−5.90648	−0.315715
$351$	−4.38406	−0.234004
$352$	−27.7370	−1.47839
$353$	11.1209	0.591907	0.295954	−	0.955202i	$-0.404363\pi$
$353$	11.1209	0.591907	0.295954	+	0.955202i	$0.404363\pi$
$354$	−8.08972	−0.429964
$355$	−5.13986	−0.272795
$356$	−0.652610	−0.0345882
$357$	−2.85118	−0.150901
$358$	29.3090	1.54903
$359$	22.5556	1.19044	0.595221	−	0.803562i	$-0.297065\pi$
$359$	22.5556	1.19044	0.595221	+	0.803562i	$0.297065\pi$
$360$	−1.59039	−0.0838210
$361$	21.6901	1.14158
$362$	36.7393	1.93098
$363$	13.5248	0.709866
$364$	16.1312	0.845505
$365$	−7.08685	−0.370943
$366$	−5.37630	−0.281024
$367$	−5.91993	−0.309018	−0.154509	−	0.987991i	$-0.549380\pi$
$367$	−5.91993	−0.309018	−0.154509	+	0.987991i	$0.549380\pi$
$368$	−14.9578	−0.779730
$369$	−10.2937	−0.535868
$370$	−3.73489	−0.194168
$371$	23.5730	1.22385
$372$	−5.47846	−0.284045
$373$	14.6425	0.758160	0.379080	−	0.925364i	$-0.376240\pi$
$373$	14.6425	0.758160	0.379080	+	0.925364i	$0.376240\pi$
$374$	7.40153	0.382724
$375$	1.00000	0.0516398
$376$	−11.8892	−0.613137
$377$	5.72192	0.294694
$378$	−5.90648	−0.303797
$379$	−23.1099	−1.18708	−0.593539	−	0.804806i	$-0.702270\pi$
$379$	−23.1099	−1.18708	−0.593539	+	0.804806i	$0.702270\pi$
$380$	−6.99226	−0.358695
$381$	15.3129	0.784503
$382$	23.5110	1.20293
$383$	−4.43883	−0.226813	−0.113407	−	0.993549i	$-0.536176\pi$
$383$	−4.43883	−0.226813	−0.113407	+	0.993549i	$0.536176\pi$
$384$	11.4239	0.582973
$385$	−16.6234	−0.847207
$386$	23.1095	1.17624
$387$	3.14413	0.159825
$388$	12.3439	0.626666
$389$	−8.23943	−0.417755	−0.208878	−	0.977942i	$-0.566981\pi$
$389$	−8.23943	−0.417755	−0.208878	+	0.977942i	$0.566981\pi$
$390$	−7.71414	−0.390621
$391$	2.54571	0.128742
$392$	−6.78730	−0.342810
$393$	−14.3635	−0.724540
$394$	20.9823	1.05707
$395$	−6.02311	−0.303055
$396$	5.42845	0.272790
$397$	22.7152	1.14005	0.570023	−	0.821629i	$-0.306934\pi$
$397$	22.7152	1.14005	0.570023	+	0.821629i	$0.306934\pi$
$398$	35.7680	1.79289
$399$	21.4122	1.07195
$400$	−4.99075	−0.249538
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	5.43615	0.271131
$403$	21.9110	1.09146
$404$	1.79418	0.0892639
$405$	1.00000	0.0496904
$406$	7.70895	0.382589
$407$	−10.5116	−0.521040
$408$	−1.35086	−0.0668777
$409$	−25.9834	−1.28480	−0.642399	−	0.766370i	$-0.722061\pi$
$409$	−25.9834	−1.28480	−0.642399	+	0.766370i	$0.722061\pi$
$410$	−18.1127	−0.894522
$411$	9.06424	0.447106
$412$	−10.8259	−0.533355
$413$	15.4326	0.759389
$414$	5.27368	0.259187
$415$	−12.2499	−0.601322
$416$	24.5547	1.20389
$417$	−4.08375	−0.199982
$418$	−55.5851	−2.71875
$419$	26.4324	1.29131	0.645653	−	0.763631i	$-0.276585\pi$
$419$	26.4324	1.29131	0.645653	+	0.763631i	$0.276585\pi$
$420$	−3.67952	−0.179542
$421$	32.4661	1.58230	0.791150	−	0.611622i	$-0.209483\pi$
$421$	32.4661	1.58230	0.791150	+	0.611622i	$0.209483\pi$
$422$	−33.1459	−1.61352
$423$	7.47563	0.363478
$424$	11.1687	0.542398
$425$	0.849391	0.0412015
$426$	−9.04405	−0.438186
$427$	10.2563	0.496336
$428$	−9.48557	−0.458502
$429$	−21.7109	−1.04821
$430$	5.53237	0.266795
$431$	−9.26996	−0.446518	−0.223259	−	0.974759i	$-0.571670\pi$
$431$	−9.26996	−0.446518	−0.223259	+	0.974759i	$0.571670\pi$
$432$	−4.99075	−0.240118
$433$	−30.6826	−1.47451	−0.737256	−	0.675613i	$-0.763879\pi$
$433$	−30.6826	−1.47451	−0.737256	+	0.675613i	$0.763879\pi$
$434$	29.5199	1.41700
$435$	−1.30517	−0.0625780
$436$	18.9068	0.905471
$437$	−19.1182	−0.914545
$438$	−12.4699	−0.595837
$439$	−36.6334	−1.74842	−0.874208	−	0.485551i	$-0.838619\pi$
$439$	−36.6334	−1.74842	−0.874208	+	0.485551i	$0.838619\pi$
$440$	−7.87601	−0.375474
$441$	4.26769	0.203223
$442$	−6.55232	−0.311662
$443$	33.0316	1.56938	0.784689	−	0.619890i	$-0.212823\pi$
$443$	33.0316	1.56938	0.784689	+	0.619890i	$0.212823\pi$
$444$	−2.32670	−0.110420
$445$	−0.595361	−0.0282228
$446$	10.3071	0.488057
$447$	−3.86068	−0.182604
$448$	−0.423680	−0.0200170
$449$	−30.0656	−1.41889	−0.709443	−	0.704763i	$-0.751053\pi$
$449$	−30.0656	−1.41889	−0.709443	+	0.704763i	$0.751053\pi$
$450$	1.75959	0.0829479
$451$	−50.9769	−2.40041
$452$	−12.1819	−0.572989
$453$	−8.07009	−0.379166
$454$	−15.3345	−0.719686
$455$	14.7161	0.689903
$456$	10.1449	0.475079
$457$	37.9816	1.77670	0.888352	−	0.459164i	$-0.151851\pi$
$457$	37.9816	1.77670	0.888352	+	0.459164i	$0.151851\pi$
$458$	−8.60266	−0.401976
$459$	0.849391	0.0396462
$460$	3.28530	0.153178
$461$	−6.29420	−0.293150	−0.146575	−	0.989200i	$-0.546825\pi$
$461$	−6.29420	−0.293150	−0.146575	+	0.989200i	$0.546825\pi$
$462$	−29.2504	−1.36085
$463$	32.2871	1.50051	0.750254	−	0.661149i	$-0.229931\pi$
$463$	32.2871	1.50051	0.750254	+	0.661149i	$0.229931\pi$
$464$	6.51377	0.302394
$465$	−4.99787	−0.231771
$466$	15.0136	0.695489
$467$	12.8324	0.593811	0.296905	−	0.954907i	$-0.404045\pi$
$467$	12.8324	0.593811	0.296905	+	0.954907i	$0.404045\pi$
$468$	−4.80562	−0.222140
$469$	−10.3704	−0.478863
$470$	13.1540	0.606751
$471$	−3.07807	−0.141830
$472$	7.31183	0.336554
$473$	15.5705	0.715932
$474$	−10.5982	−0.486791
$475$	−6.37888	−0.292683
$476$	−3.12535	−0.143250
$477$	−7.02259	−0.321542
$478$	30.5768	1.39855
$479$	5.75546	0.262973	0.131487	−	0.991318i	$-0.458025\pi$
$479$	5.75546	0.262973	0.131487	+	0.991318i	$0.458025\pi$
$480$	−5.60090	−0.255645
$481$	9.30556	0.424297
$482$	−41.5271	−1.89151
$483$	−10.0605	−0.457768
$484$	14.8253	0.673876
$485$	11.2610	0.511338
$486$	1.75959	0.0798166
$487$	20.8412	0.944406	0.472203	−	0.881490i	$-0.343459\pi$
$487$	20.8412	0.944406	0.472203	+	0.881490i	$0.343459\pi$
$488$	4.85932	0.219971
$489$	−23.3432	−1.05561
$490$	7.50939	0.339240
$491$	−8.83975	−0.398932	−0.199466	−	0.979905i	$-0.563921\pi$
$491$	−8.83975	−0.398932	−0.199466	+	0.979905i	$0.563921\pi$
$492$	−11.2835	−0.508700
$493$	−1.10860	−0.0499287
$494$	49.2076	2.21395
$495$	4.95225	0.222587
$496$	24.9432	1.11998
$497$	17.2532	0.773910
$498$	−21.5548	−0.965892
$499$	20.2538	0.906685	0.453342	−	0.891336i	$-0.350231\pi$
$499$	20.2538	0.906685	0.453342	+	0.891336i	$0.350231\pi$
$500$	1.09616	0.0490217
$501$	−22.6290	−1.01099
$502$	14.2724	0.637009
$503$	11.2268	0.500580	0.250290	−	0.968171i	$-0.419474\pi$
$503$	11.2268	0.500580	0.250290	+	0.968171i	$0.419474\pi$
$504$	5.33853	0.237797
$505$	1.63679	0.0728363
$506$	26.1165	1.16102
$507$	6.21995	0.276238
$508$	16.7853	0.744729
$509$	−1.37659	−0.0610164	−0.0305082	−	0.999535i	$-0.509713\pi$
$509$	−1.37659	−0.0610164	−0.0305082	+	0.999535i	$0.509713\pi$
$510$	1.49458	0.0661811
$511$	23.7887	1.05235
$512$	12.0782	0.533787
$513$	−6.37888	−0.281634
$514$	5.29642	0.233615
$515$	−9.87624	−0.435199
$516$	3.44646	0.151722
$517$	37.0212	1.62819
$518$	12.5370	0.550846
$519$	5.24607	0.230277
$520$	6.97236	0.305758
$521$	26.1304	1.14479	0.572396	−	0.819977i	$-0.306014\pi$
$521$	26.1304	1.14479	0.572396	+	0.819977i	$0.306014\pi$
$522$	−2.29656	−0.100518
$523$	5.20859	0.227756	0.113878	−	0.993495i	$-0.463673\pi$
$523$	5.20859	0.227756	0.113878	+	0.993495i	$0.463673\pi$
$524$	−15.7446	−0.687807
$525$	−3.35674	−0.146500
$526$	−1.21168	−0.0528320
$527$	−4.24515	−0.184922
$528$	−24.7154	−1.07560
$529$	−14.0174	−0.609451
$530$	−12.3569	−0.536749
$531$	−4.59750	−0.199515
$532$	23.4712	1.01760
$533$	45.1281	1.95472
$534$	−1.04759	−0.0453337
$535$	−8.65347	−0.374122
$536$	−4.91342	−0.212227
$537$	16.6567	0.718790
$538$	−11.3354	−0.488705
$539$	21.1347	0.910334
$540$	1.09616	0.0471711
$541$	18.5599	0.797954	0.398977	−	0.916961i	$-0.369365\pi$
$541$	18.5599	0.797954	0.398977	+	0.916961i	$0.369365\pi$
$542$	28.3537	1.21790
$543$	20.8795	0.896024
$544$	−4.75735	−0.203970
$545$	17.2482	0.738833
$546$	25.8944	1.10818
$547$	−8.31162	−0.355379	−0.177690	−	0.984087i	$-0.556862\pi$
$547$	−8.31162	−0.355379	−0.177690	+	0.984087i	$0.556862\pi$
$548$	9.93585	0.424438
$549$	−3.05543	−0.130402
$550$	8.71393	0.371563
$551$	8.32550	0.354678
$552$	−4.76657	−0.202879
$553$	20.2180	0.859756
$554$	−0.437452	−0.0185855
$555$	−2.12259	−0.0900990
$556$	−4.47644	−0.189843
$557$	16.0754	0.681137	0.340569	−	0.940220i	$-0.389380\pi$
$557$	16.0754	0.681137	0.340569	+	0.940220i	$0.389380\pi$
$558$	−8.79421	−0.372289
$559$	−13.7840	−0.583002
$560$	16.7527	0.707929
$561$	4.20639	0.177594
$562$	−22.1602	−0.934772
$563$	−35.4305	−1.49322	−0.746608	−	0.665264i	$-0.768319\pi$
$563$	−35.4305	−1.49322	−0.746608	+	0.665264i	$0.768319\pi$
$564$	8.19447	0.345050
$565$	−11.1133	−0.467539
$566$	−30.4626	−1.28044
$567$	−3.35674	−0.140970
$568$	8.17439	0.342990
$569$	−26.9838	−1.13122	−0.565611	−	0.824672i	$-0.691360\pi$
$569$	−26.9838	−1.13122	−0.565611	+	0.824672i	$0.691360\pi$
$570$	−11.2242	−0.470130
$571$	9.84879	0.412159	0.206080	−	0.978535i	$-0.433929\pi$
$571$	9.84879	0.412159	0.206080	+	0.978535i	$0.433929\pi$
$572$	−23.7986	−0.995070
$573$	13.3616	0.558190
$574$	60.7995	2.53772
$575$	2.99710	0.124988
$576$	0.126218	0.00525908
$577$	33.8200	1.40794	0.703972	−	0.710227i	$-0.251408\pi$
$577$	33.8200	1.40794	0.703972	+	0.710227i	$0.251408\pi$
$578$	−28.6436	−1.19141
$579$	13.1335	0.545808
$580$	−1.43067	−0.0594053
$581$	41.1196	1.70593
$582$	19.8148	0.821351
$583$	−34.7776	−1.44034
$584$	11.2709	0.466392
$585$	−4.38406	−0.181258
$586$	20.4636	0.845345
$587$	−3.50938	−0.144848	−0.0724238	−	0.997374i	$-0.523073\pi$
$587$	−3.50938	−0.144848	−0.0724238	+	0.997374i	$0.523073\pi$
$588$	4.67806	0.192920
$589$	31.8808	1.31363
$590$	−8.08972	−0.333049
$591$	11.9245	0.490510
$592$	10.5933	0.435383
$593$	−14.5624	−0.598008	−0.299004	−	0.954252i	$-0.596654\pi$
$593$	−14.5624	−0.598008	−0.299004	+	0.954252i	$0.596654\pi$
$594$	8.71393	0.357537
$595$	−2.85118	−0.116887
$596$	−4.23192	−0.173346
$597$	20.3274	0.831946
$598$	−23.1201	−0.945451
$599$	−7.82413	−0.319685	−0.159843	−	0.987142i	$-0.551099\pi$
$599$	−7.82413	−0.319685	−0.159843	+	0.987142i	$0.551099\pi$
$600$	−1.59039	−0.0649274
$601$	−45.2213	−1.84462	−0.922309	−	0.386454i	$-0.873700\pi$
$601$	−45.2213	−1.84462	−0.922309	+	0.386454i	$0.873700\pi$
$602$	−18.5707	−0.756886
$603$	3.08944	0.125812
$604$	−8.84610	−0.359943
$605$	13.5248	0.549859
$606$	2.88008	0.116995
$607$	−39.1517	−1.58912	−0.794559	−	0.607187i	$-0.792298\pi$
$607$	−39.1517	−1.58912	−0.794559	+	0.607187i	$0.792298\pi$
$608$	35.7274	1.44894
$609$	4.38110	0.177531
$610$	−5.37630	−0.217680
$611$	−32.7736	−1.32588
$612$	0.931067	0.0376361
$613$	19.0599	0.769823	0.384912	−	0.922953i	$-0.374232\pi$
$613$	19.0599	0.769823	0.384912	+	0.922953i	$0.374232\pi$
$614$	44.6426	1.80163
$615$	−10.2937	−0.415082
$616$	26.4377	1.06521
$617$	−29.3591	−1.18195	−0.590977	−	0.806688i	$-0.701258\pi$
$617$	−29.3591	−1.18195	−0.590977	+	0.806688i	$0.701258\pi$
$618$	−17.3781	−0.699051
$619$	45.7756	1.83988	0.919939	−	0.392061i	$-0.128238\pi$
$619$	45.7756	1.83988	0.919939	+	0.392061i	$0.128238\pi$
$620$	−5.47846	−0.220020
$621$	2.99710	0.120270
$622$	−4.53987	−0.182032
$623$	1.99847	0.0800670
$624$	21.8797	0.875891
$625$	1.00000	0.0400000
$626$	−37.0721	−1.48170
$627$	−31.5898	−1.26157
$628$	−3.37405	−0.134639
$629$	−1.80291	−0.0718867
$630$	−5.90648	−0.235320
$631$	12.7663	0.508217	0.254109	−	0.967176i	$-0.418218\pi$
$631$	12.7663	0.508217	0.254109	+	0.967176i	$0.418218\pi$
$632$	9.57909	0.381036
$633$	−18.8373	−0.748715
$634$	−17.9766	−0.713942
$635$	15.3129	0.607673
$636$	−7.69787	−0.305240
$637$	−18.7098	−0.741309
$638$	−11.3731	−0.450266
$639$	−5.13986	−0.203330
$640$	11.4239	0.451569
$641$	28.4129	1.12224	0.561121	−	0.827734i	$-0.310370\pi$
$641$	28.4129	1.12224	0.561121	+	0.827734i	$0.310370\pi$
$642$	−15.2266	−0.600944
$643$	−6.36410	−0.250976	−0.125488	−	0.992095i	$-0.540050\pi$
$643$	−6.36410	−0.250976	−0.125488	+	0.992095i	$0.540050\pi$
$644$	−11.0279	−0.434560
$645$	3.14413	0.123800
$646$	−9.53374	−0.375100
$647$	−26.5268	−1.04288	−0.521438	−	0.853289i	$-0.674604\pi$
$647$	−26.5268	−1.04288	−0.521438	+	0.853289i	$0.674604\pi$
$648$	−1.59039	−0.0624765
$649$	−22.7680	−0.893721
$650$	−7.71414	−0.302574
$651$	16.7766	0.657525
$652$	−25.5878	−1.00210
$653$	−29.3862	−1.14997	−0.574985	−	0.818164i	$-0.694992\pi$
$653$	−29.3862	−1.14997	−0.574985	+	0.818164i	$0.694992\pi$
$654$	30.3498	1.18677
$655$	−14.3635	−0.561227
$656$	51.3733	2.00579
$657$	−7.08685	−0.276484
$658$	−44.1547	−1.72133
$659$	37.9426	1.47803	0.739017	−	0.673686i	$-0.235290\pi$
$659$	37.9426	1.47803	0.739017	+	0.673686i	$0.235290\pi$
$660$	5.42845	0.211302
$661$	26.3199	1.02373	0.511863	−	0.859067i	$-0.328956\pi$
$661$	26.3199	1.02373	0.511863	+	0.859067i	$0.328956\pi$
$662$	−32.8276	−1.27588
$663$	−3.72378	−0.144619
$664$	19.4821	0.756051
$665$	21.4122	0.830330
$666$	−3.73489	−0.144724
$667$	−3.91172	−0.151462
$668$	−24.8050	−0.959734
$669$	5.85769	0.226471
$670$	5.43615	0.210017
$671$	−15.1312	−0.584135
$672$	18.8008	0.725255
$673$	31.5012	1.21428	0.607141	−	0.794594i	$-0.292316\pi$
$673$	31.5012	1.21428	0.607141	+	0.794594i	$0.292316\pi$
$674$	6.40807	0.246829
$675$	1.00000	0.0384900
$676$	6.81805	0.262233
$677$	−9.99150	−0.384004	−0.192002	−	0.981394i	$-0.561498\pi$
$677$	−9.99150	−0.384004	−0.192002	+	0.981394i	$0.561498\pi$
$678$	−19.5548	−0.750998
$679$	−37.8004	−1.45065
$680$	−1.35086	−0.0518032
$681$	−8.71484	−0.333953
$682$	−43.5511	−1.66766
$683$	27.3571	1.04679	0.523395	−	0.852090i	$-0.324665\pi$
$683$	27.3571	1.04679	0.523395	+	0.852090i	$0.324665\pi$
$684$	−6.99226	−0.267356
$685$	9.06424	0.346327
$686$	16.1383	0.616165
$687$	−4.88901	−0.186527
$688$	−15.6916	−0.598235
$689$	30.7874	1.17291
$690$	5.27368	0.200765
$691$	9.22704	0.351013	0.175507	−	0.984478i	$-0.443844\pi$
$691$	9.22704	0.351013	0.175507	+	0.984478i	$0.443844\pi$
$692$	5.75052	0.218602
$693$	−16.6234	−0.631471
$694$	−11.2650	−0.427613
$695$	−4.08375	−0.154906
$696$	2.07573	0.0786802
$697$	−8.74337	−0.331179
$698$	−1.63969	−0.0620632
$699$	8.53241	0.322725
$700$	−3.67952	−0.139073
$701$	−17.4525	−0.659173	−0.329587	−	0.944125i	$-0.606909\pi$
$701$	−17.4525	−0.659173	−0.329587	+	0.944125i	$0.606909\pi$
$702$	−7.71414	−0.291152
$703$	13.5397	0.510661
$704$	0.625062	0.0235579
$705$	7.47563	0.281548
$706$	19.5683	0.736462
$707$	−5.49428	−0.206634
$708$	−5.03959	−0.189399
$709$	−29.3026	−1.10048	−0.550242	−	0.835006i	$-0.685464\pi$
$709$	−29.3026	−1.10048	−0.550242	+	0.835006i	$0.685464\pi$
$710$	−9.04405	−0.339417
$711$	−6.02311	−0.225884
$712$	0.946857	0.0354850
$713$	−14.9792	−0.560974
$714$	−5.01691	−0.187753
$715$	−21.7109	−0.811943
$716$	18.2584	0.682348
$717$	17.3772	0.648964
$718$	39.6887	1.48117
$719$	28.7225	1.07117	0.535584	−	0.844482i	$-0.320092\pi$
$719$	28.7225	1.07117	0.535584	+	0.844482i	$0.320092\pi$
$720$	−4.99075	−0.185994
$721$	33.1520	1.23464
$722$	38.1656	1.42038
$723$	−23.6004	−0.877709
$724$	22.8872	0.850596
$725$	−1.30517	−0.0484727
$726$	23.7980	0.883228
$727$	26.1852	0.971155	0.485578	−	0.874194i	$-0.338609\pi$
$727$	26.1852	0.971155	0.485578	+	0.874194i	$0.338609\pi$
$728$	−23.4044	−0.867425
$729$	1.00000	0.0370370
$730$	−12.4699	−0.461534
$731$	2.67059	0.0987754
$732$	−3.34923	−0.123791
$733$	14.1373	0.522175	0.261087	−	0.965315i	$-0.415919\pi$
$733$	14.1373	0.522175	0.261087	+	0.965315i	$0.415919\pi$
$734$	−10.4167	−0.384486
$735$	4.26769	0.157416
$736$	−16.7865	−0.618758
$737$	15.2997	0.563571
$738$	−18.1127	−0.666737
$739$	−39.4809	−1.45233	−0.726164	−	0.687521i	$-0.758699\pi$
$739$	−39.4809	−1.45233	−0.726164	+	0.687521i	$0.758699\pi$
$740$	−2.32670	−0.0855310
$741$	27.9653	1.02733
$742$	41.4788	1.52274
$743$	−24.7792	−0.909060	−0.454530	−	0.890732i	$-0.650193\pi$
$743$	−24.7792	−0.909060	−0.454530	+	0.890732i	$0.650193\pi$
$744$	7.94857	0.291409
$745$	−3.86068	−0.141444
$746$	25.7648	0.943317
$747$	−12.2499	−0.448199
$748$	4.61087	0.168590
$749$	29.0474	1.06137
$750$	1.75959	0.0642512
$751$	15.5023	0.565687	0.282844	−	0.959166i	$-0.408722\pi$
$751$	15.5023	0.565687	0.282844	+	0.959166i	$0.408722\pi$
$752$	−37.3090	−1.36052
$753$	8.11121	0.295589
$754$	10.0682	0.366664
$755$	−8.07009	−0.293701
$756$	−3.67952	−0.133823
$757$	−16.8632	−0.612902	−0.306451	−	0.951886i	$-0.599142\pi$
$757$	−16.8632	−0.612902	−0.306451	+	0.951886i	$0.599142\pi$
$758$	−40.6640	−1.47698
$759$	14.8424	0.538745
$760$	10.1449	0.367994
$761$	−43.4175	−1.57388	−0.786941	−	0.617028i	$-0.788337\pi$
$761$	−43.4175	−1.57388	−0.786941	+	0.617028i	$0.788337\pi$
$762$	26.9444	0.976093
$763$	−57.8978	−2.09604
$764$	14.6465	0.529890
$765$	0.849391	0.0307098
$766$	−7.81052	−0.282205
$767$	20.1557	0.727781
$768$	19.8489	0.716237
$769$	−9.59669	−0.346066	−0.173033	−	0.984916i	$-0.555357\pi$
$769$	−9.59669	−0.346066	−0.173033	+	0.984916i	$0.555357\pi$
$770$	−29.2504	−1.05411
$771$	3.01003	0.108404
$772$	14.3964	0.518136
$773$	−40.4001	−1.45309	−0.726546	−	0.687118i	$-0.758876\pi$
$773$	−40.4001	−1.45309	−0.726546	+	0.687118i	$0.758876\pi$
$774$	5.53237	0.198857
$775$	−4.99787	−0.179529
$776$	−17.9095	−0.642912
$777$	7.12498	0.255607
$778$	−14.4980	−0.519779
$779$	65.6622	2.35259
$780$	−4.80562	−0.172069
$781$	−25.4539	−0.910811
$782$	4.47941	0.160183
$783$	−1.30517	−0.0466429
$784$	−21.2990	−0.760678
$785$	−3.07807	−0.109861
$786$	−25.2738	−0.901486
$787$	26.3469	0.939164	0.469582	−	0.882889i	$-0.344405\pi$
$787$	26.3469	0.939164	0.469582	+	0.882889i	$0.344405\pi$
$788$	13.0712	0.465641
$789$	−0.688617	−0.0245154
$790$	−10.5982	−0.377067
$791$	37.3043	1.32639
$792$	−7.87601	−0.279862
$793$	13.3952	0.475676
$794$	39.9695	1.41847
$795$	−7.02259	−0.249066
$796$	22.2821	0.789767
$797$	3.23637	0.114638	0.0573191	−	0.998356i	$-0.481745\pi$
$797$	3.23637	0.114638	0.0573191	+	0.998356i	$0.481745\pi$
$798$	37.6767	1.33374
$799$	6.34973	0.224637
$800$	−5.60090	−0.198022
$801$	−0.595361	−0.0210360
$802$	−1.75959	−0.0621333
$803$	−35.0958	−1.23850
$804$	3.38652	0.119433
$805$	−10.0605	−0.354586
$806$	38.5543	1.35802
$807$	−6.44208	−0.226772
$808$	−2.60314	−0.0915781
$809$	3.29380	0.115804	0.0579019	−	0.998322i	$-0.481559\pi$
$809$	3.29380	0.115804	0.0579019	+	0.998322i	$0.481559\pi$
$810$	1.75959	0.0618257
$811$	−7.00172	−0.245864	−0.122932	−	0.992415i	$-0.539230\pi$
$811$	−7.00172	−0.245864	−0.122932	+	0.992415i	$0.539230\pi$
$812$	4.80238	0.168531
$813$	16.1138	0.565136
$814$	−18.4961	−0.648288
$815$	−23.3432	−0.817675
$816$	−4.23910	−0.148398
$817$	−20.0560	−0.701670
$818$	−45.7202	−1.59857
$819$	14.7161	0.514223
$820$	−11.2835	−0.394038
$821$	19.5290	0.681565	0.340783	−	0.940142i	$-0.389308\pi$
$821$	19.5290	0.681565	0.340783	+	0.940142i	$0.389308\pi$
$822$	15.9494	0.556298
$823$	19.8692	0.692595	0.346298	−	0.938125i	$-0.387439\pi$
$823$	19.8692	0.692595	0.346298	+	0.938125i	$0.387439\pi$
$824$	15.7071	0.547182
$825$	4.95225	0.172415
$826$	27.1551	0.944846
$827$	51.5350	1.79205	0.896024	−	0.444006i	$-0.146443\pi$
$827$	51.5350	1.79205	0.896024	+	0.444006i	$0.146443\pi$
$828$	3.28530	0.114172
$829$	−56.5105	−1.96269	−0.981346	−	0.192250i	$-0.938421\pi$
$829$	−56.5105	−1.96269	−0.981346	+	0.192250i	$0.938421\pi$
$830$	−21.5548	−0.748176
$831$	−0.248610	−0.00862418
$832$	−0.553346	−0.0191838
$833$	3.62494	0.125597
$834$	−7.18573	−0.248822
$835$	−22.6290	−0.783110
$836$	−34.6274	−1.19761
$837$	−4.99787	−0.172752
$838$	46.5102	1.60667
$839$	−33.5603	−1.15863	−0.579315	−	0.815104i	$-0.696680\pi$
$839$	−33.5603	−1.15863	−0.579315	+	0.815104i	$0.696680\pi$
$840$	5.33853	0.184197
$841$	−27.2965	−0.941260
$842$	57.1270	1.96873
$843$	−12.5940	−0.433759
$844$	−20.6486	−0.710756
$845$	6.21995	0.213973
$846$	13.1540	0.452245
$847$	−45.3991	−1.55993
$848$	35.0480	1.20355
$849$	−17.3123	−0.594158
$850$	1.49458	0.0512637
$851$	−6.36163	−0.218074
$852$	−5.63410	−0.193021
$853$	−17.7858	−0.608974	−0.304487	−	0.952516i	$-0.598485\pi$
$853$	−17.7858	−0.608974	−0.304487	+	0.952516i	$0.598485\pi$
$854$	18.0468	0.617550
$855$	−6.37888	−0.218153
$856$	13.7624	0.470389
$857$	−15.2756	−0.521805	−0.260903	−	0.965365i	$-0.584020\pi$
$857$	−15.2756	−0.521805	−0.260903	+	0.965365i	$0.584020\pi$
$858$	−38.2023	−1.30421
$859$	7.45984	0.254527	0.127263	−	0.991869i	$-0.459381\pi$
$859$	7.45984	0.254527	0.127263	+	0.991869i	$0.459381\pi$
$860$	3.44646	0.117523
$861$	34.5532	1.17757
$862$	−16.3113	−0.555566
$863$	−18.3875	−0.625918	−0.312959	−	0.949767i	$-0.601320\pi$
$863$	−18.3875	−0.625918	−0.312959	+	0.949767i	$0.601320\pi$
$864$	−5.60090	−0.190546
$865$	5.24607	0.178372
$866$	−53.9888	−1.83462
$867$	−16.2785	−0.552848
$868$	18.3898	0.624189
$869$	−29.8279	−1.01184
$870$	−2.29656	−0.0778606
$871$	−13.5443	−0.458931
$872$	−27.4314	−0.928946
$873$	11.2610	0.381129
$874$	−33.6401	−1.13789
$875$	−3.35674	−0.113478
$876$	−7.76831	−0.262467
$877$	22.3675	0.755296	0.377648	−	0.925949i	$-0.376733\pi$
$877$	22.3675	0.755296	0.377648	+	0.925949i	$0.376733\pi$
$878$	−64.4598	−2.17541
$879$	11.6298	0.392263
$880$	−24.7154	−0.833158
$881$	−42.7174	−1.43919	−0.719593	−	0.694396i	$-0.755672\pi$
$881$	−42.7174	−1.43919	−0.719593	+	0.694396i	$0.755672\pi$
$882$	7.50939	0.252854
$883$	11.4598	0.385651	0.192826	−	0.981233i	$-0.438235\pi$
$883$	11.4598	0.385651	0.192826	+	0.981233i	$0.438235\pi$
$884$	−4.08185	−0.137287
$885$	−4.59750	−0.154543
$886$	58.1221	1.95265
$887$	34.9615	1.17389	0.586947	−	0.809625i	$-0.300330\pi$
$887$	34.9615	1.17389	0.586947	+	0.809625i	$0.300330\pi$
$888$	3.37575	0.113283
$889$	−51.4014	−1.72395
$890$	−1.04759	−0.0351153
$891$	4.95225	0.165907
$892$	6.42095	0.214989
$893$	−47.6861	−1.59575
$894$	−6.79322	−0.227199
$895$	16.6567	0.556772
$896$	−38.3470	−1.28108
$897$	−13.1395	−0.438714
$898$	−52.9032	−1.76540
$899$	6.52306	0.217556
$900$	1.09616	0.0365386
$901$	−5.96492	−0.198720
$902$	−89.6985	−2.98663
$903$	−10.5540	−0.351215
$904$	17.6744	0.587843
$905$	20.8795	0.694057
$906$	−14.2001	−0.471765
$907$	−39.7068	−1.31844	−0.659221	−	0.751949i	$-0.729114\pi$
$907$	−39.7068	−1.31844	−0.659221	+	0.751949i	$0.729114\pi$
$908$	−9.55284	−0.317022
$909$	1.63679	0.0542890
$910$	25.8944	0.858390
$911$	−16.9110	−0.560288	−0.280144	−	0.959958i	$-0.590382\pi$
$911$	−16.9110	−0.560288	−0.280144	+	0.959958i	$0.590382\pi$
$912$	31.8354	1.05418
$913$	−60.6644	−2.00770
$914$	66.8320	2.21061
$915$	−3.05543	−0.101009
$916$	−5.35913	−0.177071
$917$	48.2144	1.59218
$918$	1.49458	0.0493285
$919$	−27.6026	−0.910524	−0.455262	−	0.890357i	$-0.650454\pi$
$919$	−27.6026	−0.910524	−0.455262	+	0.890357i	$0.650454\pi$
$920$	−4.76657	−0.157149
$921$	25.3710	0.836003
$922$	−11.0752	−0.364743
$923$	22.5334	0.741697
$924$	−18.2219	−0.599456
$925$	−2.12259	−0.0697904
$926$	56.8121	1.86696
$927$	−9.87624	−0.324378
$928$	7.31011	0.239966
$929$	−12.7329	−0.417752	−0.208876	−	0.977942i	$-0.566981\pi$
$929$	−12.7329	−0.417752	−0.208876	+	0.977942i	$0.566981\pi$
$930$	−8.79421	−0.288374
$931$	−27.2231	−0.892200
$932$	9.35287	0.306364
$933$	−2.58007	−0.0844678
$934$	22.5797	0.738830
$935$	4.20639	0.137564
$936$	6.97236	0.227899
$937$	−38.5165	−1.25828	−0.629139	−	0.777293i	$-0.716592\pi$
$937$	−38.5165	−1.25828	−0.629139	+	0.777293i	$0.716592\pi$
$938$	−18.2477	−0.595810
$939$	−21.0686	−0.687547
$940$	8.19447	0.267274
$941$	−13.9224	−0.453858	−0.226929	−	0.973911i	$-0.572869\pi$
$941$	−13.9224	−0.453858	−0.226929	+	0.973911i	$0.572869\pi$
$942$	−5.41614	−0.176467
$943$	−30.8513	−1.00466
$944$	22.9450	0.746796
$945$	−3.35674	−0.109195
$946$	27.3977	0.890775
$947$	41.1701	1.33785	0.668924	−	0.743330i	$-0.266755\pi$
$947$	41.1701	1.33785	0.668924	+	0.743330i	$0.266755\pi$
$948$	−6.60228	−0.214432
$949$	31.0691	1.00855
$950$	−11.2242	−0.364161
$951$	−10.2164	−0.331288
$952$	4.53449	0.146964
$953$	−30.1801	−0.977630	−0.488815	−	0.872387i	$-0.662571\pi$
$953$	−30.1801	−0.977630	−0.488815	+	0.872387i	$0.662571\pi$
$954$	−12.3569	−0.400069
$955$	13.3616	0.432372
$956$	19.0482	0.616062
$957$	−6.46351	−0.208936
$958$	10.1272	0.327196
$959$	−30.4263	−0.982516
$960$	0.126218	0.00407366
$961$	−6.02125	−0.194234
$962$	16.3740	0.527918
$963$	−8.65347	−0.278854
$964$	−25.8698	−0.833210
$965$	13.1335	0.422781
$966$	−17.7023	−0.569564
$967$	44.5867	1.43381	0.716906	−	0.697169i	$-0.245557\pi$
$967$	44.5867	1.43381	0.716906	+	0.697169i	$0.245557\pi$
$968$	−21.5096	−0.691346
$969$	−5.41816	−0.174056
$970$	19.8148	0.636216
$971$	−32.9145	−1.05628	−0.528138	−	0.849159i	$-0.677109\pi$
$971$	−32.9145	−1.05628	−0.528138	+	0.849159i	$0.677109\pi$
$972$	1.09616	0.0351593
$973$	13.7081	0.439461
$974$	36.6720	1.17505
$975$	−4.38406	−0.140402
$976$	15.2489	0.488105
$977$	−33.2133	−1.06259	−0.531293	−	0.847188i	$-0.678294\pi$
$977$	−33.2133	−1.06259	−0.531293	+	0.847188i	$0.678294\pi$
$978$	−41.0744	−1.31341
$979$	−2.94837	−0.0942305
$980$	4.67806	0.149435
$981$	17.2482	0.550694
$982$	−15.5543	−0.496359
$983$	13.1865	0.420585	0.210293	−	0.977638i	$-0.432558\pi$
$983$	13.1865	0.420585	0.210293	+	0.977638i	$0.432558\pi$
$984$	16.3710	0.521888
$985$	11.9245	0.379947
$986$	−1.95068	−0.0621222
$987$	−25.0937	−0.798742
$988$	30.6545	0.975248
$989$	9.42327	0.299643
$990$	8.71393	0.276947
$991$	−59.5940	−1.89307	−0.946533	−	0.322608i	$-0.895441\pi$
$991$	−59.5940	−1.89307	−0.946533	+	0.322608i	$0.895441\pi$
$992$	27.9926	0.888766
$993$	−18.6564	−0.592042
$994$	30.3585	0.962913
$995$	20.3274	0.644423
$996$	−13.4278	−0.425476
$997$	−1.03569	−0.0328006	−0.0164003	−	0.999866i	$-0.505221\pi$
$997$	−1.03569	−0.0328006	−0.0164003	+	0.999866i	$0.505221\pi$
$998$	35.6384	1.12811
$999$	−2.12259	−0.0671558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.20	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.20	✓	23	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.75959 q^{2} +1.00000 q^{3} +1.09616 q^{4} +1.00000 q^{5} +1.75959 q^{6} -3.35674 q^{7} -1.59039 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.75959 q^{2} +1.00000 q^{3} +1.09616 q^{4} +1.00000 q^{5} +1.75959 q^{6} -3.35674 q^{7} -1.59039 q^{8} +1.00000 q^{9} +1.75959 q^{10} +4.95225 q^{11} +1.09616 q^{12} -4.38406 q^{13} -5.90648 q^{14} +1.00000 q^{15} -4.99075 q^{16} +0.849391 q^{17} +1.75959 q^{18} -6.37888 q^{19} +1.09616 q^{20} -3.35674 q^{21} +8.71393 q^{22} +2.99710 q^{23} -1.59039 q^{24} +1.00000 q^{25} -7.71414 q^{26} +1.00000 q^{27} -3.67952 q^{28} -1.30517 q^{29} +1.75959 q^{30} -4.99787 q^{31} -5.60090 q^{32} +4.95225 q^{33} +1.49458 q^{34} -3.35674 q^{35} +1.09616 q^{36} -2.12259 q^{37} -11.2242 q^{38} -4.38406 q^{39} -1.59039 q^{40} -10.2937 q^{41} -5.90648 q^{42} +3.14413 q^{43} +5.42845 q^{44} +1.00000 q^{45} +5.27368 q^{46} +7.47563 q^{47} -4.99075 q^{48} +4.26769 q^{49} +1.75959 q^{50} +0.849391 q^{51} -4.80562 q^{52} -7.02259 q^{53} +1.75959 q^{54} +4.95225 q^{55} +5.33853 q^{56} -6.37888 q^{57} -2.29656 q^{58} -4.59750 q^{59} +1.09616 q^{60} -3.05543 q^{61} -8.79421 q^{62} -3.35674 q^{63} +0.126218 q^{64} -4.38406 q^{65} +8.71393 q^{66} +3.08944 q^{67} +0.931067 q^{68} +2.99710 q^{69} -5.90648 q^{70} -5.13986 q^{71} -1.59039 q^{72} -7.08685 q^{73} -3.73489 q^{74} +1.00000 q^{75} -6.99226 q^{76} -16.6234 q^{77} -7.71414 q^{78} -6.02311 q^{79} -4.99075 q^{80} +1.00000 q^{81} -18.1127 q^{82} -12.2499 q^{83} -3.67952 q^{84} +0.849391 q^{85} +5.53237 q^{86} -1.30517 q^{87} -7.87601 q^{88} -0.595361 q^{89} +1.75959 q^{90} +14.7161 q^{91} +3.28530 q^{92} -4.99787 q^{93} +13.1540 q^{94} -6.37888 q^{95} -5.60090 q^{96} +11.2610 q^{97} +7.50939 q^{98} +4.95225 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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