LMFDB - Embedded newform 6046.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.79217 q^{3} +1.00000 q^{4} -3.46015 q^{5} -1.79217 q^{6} -4.09544 q^{7} +1.00000 q^{8} +0.211861 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.79217 q^{3} +1.00000 q^{4} -3.46015 q^{5} -1.79217 q^{6} -4.09544 q^{7} +1.00000 q^{8} +0.211861 q^{9} -3.46015 q^{10} +2.31571 q^{11} -1.79217 q^{12} +3.74594 q^{13} -4.09544 q^{14} +6.20117 q^{15} +1.00000 q^{16} -0.0731347 q^{17} +0.211861 q^{18} -0.645030 q^{19} -3.46015 q^{20} +7.33971 q^{21} +2.31571 q^{22} -7.70388 q^{23} -1.79217 q^{24} +6.97265 q^{25} +3.74594 q^{26} +4.99681 q^{27} -4.09544 q^{28} +8.05098 q^{29} +6.20117 q^{30} -4.51474 q^{31} +1.00000 q^{32} -4.15014 q^{33} -0.0731347 q^{34} +14.1708 q^{35} +0.211861 q^{36} +11.2868 q^{37} -0.645030 q^{38} -6.71334 q^{39} -3.46015 q^{40} +7.25263 q^{41} +7.33971 q^{42} -4.95382 q^{43} +2.31571 q^{44} -0.733069 q^{45} -7.70388 q^{46} -4.78951 q^{47} -1.79217 q^{48} +9.77261 q^{49} +6.97265 q^{50} +0.131070 q^{51} +3.74594 q^{52} +3.36670 q^{53} +4.99681 q^{54} -8.01272 q^{55} -4.09544 q^{56} +1.15600 q^{57} +8.05098 q^{58} +6.30513 q^{59} +6.20117 q^{60} -0.451182 q^{61} -4.51474 q^{62} -0.867661 q^{63} +1.00000 q^{64} -12.9615 q^{65} -4.15014 q^{66} -3.12432 q^{67} -0.0731347 q^{68} +13.8066 q^{69} +14.1708 q^{70} -9.19262 q^{71} +0.211861 q^{72} -0.398835 q^{73} +11.2868 q^{74} -12.4962 q^{75} -0.645030 q^{76} -9.48385 q^{77} -6.71334 q^{78} -8.08453 q^{79} -3.46015 q^{80} -9.59070 q^{81} +7.25263 q^{82} +15.3875 q^{83} +7.33971 q^{84} +0.253057 q^{85} -4.95382 q^{86} -14.4287 q^{87} +2.31571 q^{88} -1.55018 q^{89} -0.733069 q^{90} -15.3412 q^{91} -7.70388 q^{92} +8.09117 q^{93} -4.78951 q^{94} +2.23190 q^{95} -1.79217 q^{96} +10.2684 q^{97} +9.77261 q^{98} +0.490608 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.79217	−1.03471	−0.517354	−	0.855772i	$-0.673083\pi$
$3$	−1.79217	−1.03471	−0.517354	+	0.855772i	$0.673083\pi$
$4$	1.00000	0.500000
$5$	−3.46015	−1.54743	−0.773713	−	0.633536i	$-0.781603\pi$
$5$	−3.46015	−1.54743	−0.773713	+	0.633536i	$0.781603\pi$
$6$	−1.79217	−0.731649
$7$	−4.09544	−1.54793	−0.773965	−	0.633228i	$-0.781729\pi$
$7$	−4.09544	−1.54793	−0.773965	+	0.633228i	$0.781729\pi$
$8$	1.00000	0.353553
$9$	0.211861	0.0706202
$10$	−3.46015	−1.09420
$11$	2.31571	0.698214	0.349107	−	0.937083i	$-0.386485\pi$
$11$	2.31571	0.698214	0.349107	+	0.937083i	$0.386485\pi$
$12$	−1.79217	−0.517354
$13$	3.74594	1.03894	0.519468	−	0.854490i	$-0.326130\pi$
$13$	3.74594	1.03894	0.519468	+	0.854490i	$0.326130\pi$
$14$	−4.09544	−1.09455
$15$	6.20117	1.60113
$16$	1.00000	0.250000
$17$	−0.0731347	−0.0177378	−0.00886889	−	0.999961i	$-0.502823\pi$
$17$	−0.0731347	−0.0177378	−0.00886889	+	0.999961i	$0.502823\pi$
$18$	0.211861	0.0499360
$19$	−0.645030	−0.147980	−0.0739900	−	0.997259i	$-0.523573\pi$
$19$	−0.645030	−0.147980	−0.0739900	+	0.997259i	$0.523573\pi$
$20$	−3.46015	−0.773713
$21$	7.33971	1.60166
$22$	2.31571	0.493712
$23$	−7.70388	−1.60637	−0.803186	−	0.595729i	$-0.796863\pi$
$23$	−7.70388	−1.60637	−0.803186	+	0.595729i	$0.796863\pi$
$24$	−1.79217	−0.365824
$25$	6.97265	1.39453
$26$	3.74594	0.734639
$27$	4.99681	0.961637
$28$	−4.09544	−0.773965
$29$	8.05098	1.49503	0.747514	−	0.664246i	$-0.231247\pi$
$29$	8.05098	1.49503	0.747514	+	0.664246i	$0.231247\pi$
$30$	6.20117	1.13217
$31$	−4.51474	−0.810872	−0.405436	−	0.914123i	$-0.632880\pi$
$31$	−4.51474	−0.810872	−0.405436	+	0.914123i	$0.632880\pi$
$32$	1.00000	0.176777
$33$	−4.15014	−0.722447
$34$	−0.0731347	−0.0125425
$35$	14.1708	2.39531
$36$	0.211861	0.0353101
$37$	11.2868	1.85554	0.927771	−	0.373151i	$-0.121723\pi$
$37$	11.2868	1.85554	0.927771	+	0.373151i	$0.121723\pi$
$38$	−0.645030	−0.104638
$39$	−6.71334	−1.07500
$40$	−3.46015	−0.547098
$41$	7.25263	1.13267	0.566336	−	0.824175i	$-0.308361\pi$
$41$	7.25263	1.13267	0.566336	+	0.824175i	$0.308361\pi$
$42$	7.33971	1.13254
$43$	−4.95382	−0.755450	−0.377725	−	0.925918i	$-0.623294\pi$
$43$	−4.95382	−0.755450	−0.377725	+	0.925918i	$0.623294\pi$
$44$	2.31571	0.349107
$45$	−0.733069	−0.109280
$46$	−7.70388	−1.13588
$47$	−4.78951	−0.698622	−0.349311	−	0.937007i	$-0.613584\pi$
$47$	−4.78951	−0.698622	−0.349311	+	0.937007i	$0.613584\pi$
$48$	−1.79217	−0.258677
$49$	9.77261	1.39609
$50$	6.97265	0.986082
$51$	0.131070	0.0183534
$52$	3.74594	0.519468
$53$	3.36670	0.462452	0.231226	−	0.972900i	$-0.425726\pi$
$53$	3.36670	0.462452	0.231226	+	0.972900i	$0.425726\pi$
$54$	4.99681	0.679980
$55$	−8.01272	−1.08043
$56$	−4.09544	−0.547276
$57$	1.15600	0.153116
$58$	8.05098	1.05715
$59$	6.30513	0.820859	0.410429	−	0.911892i	$-0.365379\pi$
$59$	6.30513	0.820859	0.410429	+	0.911892i	$0.365379\pi$
$60$	6.20117	0.800567
$61$	−0.451182	−0.0577680	−0.0288840	−	0.999583i	$-0.509195\pi$
$61$	−0.451182	−0.0577680	−0.0288840	+	0.999583i	$0.509195\pi$
$62$	−4.51474	−0.573373
$63$	−0.867661	−0.109315
$64$	1.00000	0.125000
$65$	−12.9615	−1.60768
$66$	−4.15014	−0.510847
$67$	−3.12432	−0.381696	−0.190848	−	0.981620i	$-0.561124\pi$
$67$	−3.12432	−0.381696	−0.190848	+	0.981620i	$0.561124\pi$
$68$	−0.0731347	−0.00886889
$69$	13.8066	1.66212
$70$	14.1708	1.69374
$71$	−9.19262	−1.09096	−0.545482	−	0.838123i	$-0.683653\pi$
$71$	−9.19262	−1.09096	−0.545482	+	0.838123i	$0.683653\pi$
$72$	0.211861	0.0249680
$73$	−0.398835	−0.0466801	−0.0233401	−	0.999728i	$-0.507430\pi$
$73$	−0.398835	−0.0466801	−0.0233401	+	0.999728i	$0.507430\pi$
$74$	11.2868	1.31207
$75$	−12.4962	−1.44293
$76$	−0.645030	−0.0739900
$77$	−9.48385	−1.08079
$78$	−6.71334	−0.760136
$79$	−8.08453	−0.909581	−0.454790	−	0.890598i	$-0.650286\pi$
$79$	−8.08453	−0.909581	−0.454790	+	0.890598i	$0.650286\pi$
$80$	−3.46015	−0.386857
$81$	−9.59070	−1.06563
$82$	7.25263	0.800919
$83$	15.3875	1.68900	0.844501	−	0.535554i	$-0.179897\pi$
$83$	15.3875	1.68900	0.844501	+	0.535554i	$0.179897\pi$
$84$	7.33971	0.800828
$85$	0.253057	0.0274479
$86$	−4.95382	−0.534184
$87$	−14.4287	−1.54692
$88$	2.31571	0.246856
$89$	−1.55018	−0.164319	−0.0821594	−	0.996619i	$-0.526182\pi$
$89$	−1.55018	−0.164319	−0.0821594	+	0.996619i	$0.526182\pi$
$90$	−0.733069	−0.0772723
$91$	−15.3412	−1.60820
$92$	−7.70388	−0.803186
$93$	8.09117	0.839016
$94$	−4.78951	−0.494000
$95$	2.23190	0.228988
$96$	−1.79217	−0.182912
$97$	10.2684	1.04260	0.521301	−	0.853373i	$-0.325447\pi$
$97$	10.2684	1.04260	0.521301	+	0.853373i	$0.325447\pi$
$98$	9.77261	0.987182
$99$	0.490608	0.0493080
$100$	6.97265	0.697265
$101$	−1.04005	−0.103489	−0.0517445	−	0.998660i	$-0.516478\pi$
$101$	−1.04005	−0.103489	−0.0517445	+	0.998660i	$0.516478\pi$
$102$	0.131070	0.0129778
$103$	15.2501	1.50264	0.751318	−	0.659941i	$-0.229419\pi$
$103$	15.2501	1.50264	0.751318	+	0.659941i	$0.229419\pi$
$104$	3.74594	0.367319
$105$	−25.3965	−2.47844
$106$	3.36670	0.327003
$107$	−4.69643	−0.454021	−0.227011	−	0.973892i	$-0.572895\pi$
$107$	−4.69643	−0.454021	−0.227011	+	0.973892i	$0.572895\pi$
$108$	4.99681	0.480818
$109$	−10.2361	−0.980443	−0.490222	−	0.871598i	$-0.663084\pi$
$109$	−10.2361	−0.980443	−0.490222	+	0.871598i	$0.663084\pi$
$110$	−8.01272	−0.763982
$111$	−20.2279	−1.91994
$112$	−4.09544	−0.386982
$113$	−3.30171	−0.310599	−0.155299	−	0.987867i	$-0.549634\pi$
$113$	−3.30171	−0.310599	−0.155299	+	0.987867i	$0.549634\pi$
$114$	1.15600	0.108269
$115$	26.6566	2.48574
$116$	8.05098	0.747514
$117$	0.793616	0.0733698
$118$	6.30513	0.580435
$119$	0.299519	0.0274568
$120$	6.20117	0.566087
$121$	−5.63748	−0.512498
$122$	−0.451182	−0.0408481
$123$	−12.9979	−1.17198
$124$	−4.51474	−0.405436
$125$	−6.82567	−0.610507
$126$	−0.867661	−0.0772974
$127$	−9.58273	−0.850330	−0.425165	−	0.905116i	$-0.639784\pi$
$127$	−9.58273	−0.850330	−0.425165	+	0.905116i	$0.639784\pi$
$128$	1.00000	0.0883883
$129$	8.87807	0.781670
$130$	−12.9615	−1.13680
$131$	−8.91452	−0.778865	−0.389433	−	0.921055i	$-0.627329\pi$
$131$	−8.91452	−0.778865	−0.389433	+	0.921055i	$0.627329\pi$
$132$	−4.15014	−0.361223
$133$	2.64168	0.229063
$134$	−3.12432	−0.269900
$135$	−17.2897	−1.48806
$136$	−0.0731347	−0.00627125
$137$	−3.04296	−0.259977	−0.129989	−	0.991515i	$-0.541494\pi$
$137$	−3.04296	−0.259977	−0.129989	+	0.991515i	$0.541494\pi$
$138$	13.8066	1.17530
$139$	0.153001	0.0129774	0.00648869	−	0.999979i	$-0.497935\pi$
$139$	0.153001	0.0129774	0.00648869	+	0.999979i	$0.497935\pi$
$140$	14.1708	1.19765
$141$	8.58360	0.722870
$142$	−9.19262	−0.771428
$143$	8.67451	0.725399
$144$	0.211861	0.0176550
$145$	−27.8576	−2.31345
$146$	−0.398835	−0.0330078
$147$	−17.5141	−1.44454
$148$	11.2868	0.927771
$149$	−16.4958	−1.35139	−0.675695	−	0.737181i	$-0.736156\pi$
$149$	−16.4958	−1.35139	−0.675695	+	0.737181i	$0.736156\pi$
$150$	−12.4962	−1.02031
$151$	−9.98568	−0.812623	−0.406311	−	0.913735i	$-0.633185\pi$
$151$	−9.98568	−0.812623	−0.406311	+	0.913735i	$0.633185\pi$
$152$	−0.645030	−0.0523188
$153$	−0.0154944	−0.00125265
$154$	−9.48385	−0.764231
$155$	15.6217	1.25477
$156$	−6.71334	−0.537498
$157$	8.76645	0.699639	0.349819	−	0.936817i	$-0.386243\pi$
$157$	8.76645	0.699639	0.349819	+	0.936817i	$0.386243\pi$
$158$	−8.08453	−0.643171
$159$	−6.03369	−0.478503
$160$	−3.46015	−0.273549
$161$	31.5508	2.48655
$162$	−9.59070	−0.753516
$163$	12.5855	0.985773	0.492887	−	0.870094i	$-0.335942\pi$
$163$	12.5855	0.985773	0.492887	+	0.870094i	$0.335942\pi$
$164$	7.25263	0.566336
$165$	14.3601	1.11793
$166$	15.3875	1.19430
$167$	−5.36582	−0.415220	−0.207610	−	0.978212i	$-0.566568\pi$
$167$	−5.36582	−0.415220	−0.207610	+	0.978212i	$0.566568\pi$
$168$	7.33971	0.566271
$169$	1.03204	0.0793877
$170$	0.253057	0.0194086
$171$	−0.136656	−0.0104504
$172$	−4.95382	−0.377725
$173$	6.55214	0.498150	0.249075	−	0.968484i	$-0.419873\pi$
$173$	6.55214	0.498150	0.249075	+	0.968484i	$0.419873\pi$
$174$	−14.4287	−1.09384
$175$	−28.5561	−2.15863
$176$	2.31571	0.174553
$177$	−11.2999	−0.849349
$178$	−1.55018	−0.116191
$179$	−1.02642	−0.0767186	−0.0383593	−	0.999264i	$-0.512213\pi$
$179$	−1.02642	−0.0767186	−0.0383593	+	0.999264i	$0.512213\pi$
$180$	−0.733069	−0.0546398
$181$	−13.0164	−0.967498	−0.483749	−	0.875207i	$-0.660725\pi$
$181$	−13.0164	−0.967498	−0.483749	+	0.875207i	$0.660725\pi$
$182$	−15.3412	−1.13717
$183$	0.808594	0.0597730
$184$	−7.70388	−0.567938
$185$	−39.0541	−2.87131
$186$	8.09117	0.593274
$187$	−0.169359	−0.0123848
$188$	−4.78951	−0.349311
$189$	−20.4641	−1.48855
$190$	2.23190	0.161919
$191$	−2.14013	−0.154855	−0.0774274	−	0.996998i	$-0.524671\pi$
$191$	−2.14013	−0.154855	−0.0774274	+	0.996998i	$0.524671\pi$
$192$	−1.79217	−0.129338
$193$	−17.3745	−1.25064	−0.625321	−	0.780367i	$-0.715032\pi$
$193$	−17.3745	−1.25064	−0.625321	+	0.780367i	$0.715032\pi$
$194$	10.2684	0.737232
$195$	23.2292	1.66348
$196$	9.77261	0.698043
$197$	−5.46065	−0.389055	−0.194528	−	0.980897i	$-0.562317\pi$
$197$	−5.46065	−0.389055	−0.194528	+	0.980897i	$0.562317\pi$
$198$	0.490608	0.0348660
$199$	−23.8880	−1.69338	−0.846689	−	0.532089i	$-0.821407\pi$
$199$	−23.8880	−1.69338	−0.846689	+	0.532089i	$0.821407\pi$
$200$	6.97265	0.493041
$201$	5.59929	0.394944
$202$	−1.04005	−0.0731778
$203$	−32.9723	−2.31420
$204$	0.131070	0.00917671
$205$	−25.0952	−1.75273
$206$	15.2501	1.06252
$207$	−1.63215	−0.113442
$208$	3.74594	0.259734
$209$	−1.49370	−0.103322
$210$	−25.3965	−1.75252
$211$	17.1566	1.18111	0.590553	−	0.806999i	$-0.298910\pi$
$211$	17.1566	1.18111	0.590553	+	0.806999i	$0.298910\pi$
$212$	3.36670	0.231226
$213$	16.4747	1.12883
$214$	−4.69643	−0.321042
$215$	17.1410	1.16900
$216$	4.99681	0.339990
$217$	18.4899	1.25517
$218$	−10.2361	−0.693278
$219$	0.714779	0.0483003
$220$	−8.01272	−0.540217
$221$	−0.273958	−0.0184284
$222$	−20.2279	−1.35760
$223$	4.97202	0.332951	0.166476	−	0.986046i	$-0.446761\pi$
$223$	4.97202	0.332951	0.166476	+	0.986046i	$0.446761\pi$
$224$	−4.09544	−0.273638
$225$	1.47723	0.0984819
$226$	−3.30171	−0.219627
$227$	−16.7993	−1.11501	−0.557504	−	0.830174i	$-0.688241\pi$
$227$	−16.7993	−1.11501	−0.557504	+	0.830174i	$0.688241\pi$
$228$	1.15600	0.0765580
$229$	18.6284	1.23100	0.615499	−	0.788138i	$-0.288955\pi$
$229$	18.6284	1.23100	0.615499	+	0.788138i	$0.288955\pi$
$230$	26.6566	1.75768
$231$	16.9966	1.11830
$232$	8.05098	0.528573
$233$	−11.7084	−0.767044	−0.383522	−	0.923532i	$-0.625289\pi$
$233$	−11.7084	−0.767044	−0.383522	+	0.923532i	$0.625289\pi$
$234$	0.793616	0.0518803
$235$	16.5724	1.08107
$236$	6.30513	0.410429
$237$	14.4888	0.941150
$238$	0.299519	0.0194149
$239$	−9.30655	−0.601991	−0.300995	−	0.953626i	$-0.597319\pi$
$239$	−9.30655	−0.601991	−0.300995	+	0.953626i	$0.597319\pi$
$240$	6.20117	0.400284
$241$	0.614680	0.0395950	0.0197975	−	0.999804i	$-0.493698\pi$
$241$	0.614680	0.0395950	0.0197975	+	0.999804i	$0.493698\pi$
$242$	−5.63748	−0.362391
$243$	2.19769	0.140982
$244$	−0.451182	−0.0288840
$245$	−33.8147	−2.16034
$246$	−12.9979	−0.828718
$247$	−2.41624	−0.153742
$248$	−4.51474	−0.286687
$249$	−27.5770	−1.74762
$250$	−6.82567	−0.431693
$251$	8.12172	0.512639	0.256319	−	0.966592i	$-0.417490\pi$
$251$	8.12172	0.512639	0.256319	+	0.966592i	$0.417490\pi$
$252$	−0.867661	−0.0546575
$253$	−17.8400	−1.12159
$254$	−9.58273	−0.601274
$255$	−0.453521	−0.0284006
$256$	1.00000	0.0625000
$257$	11.4488	0.714154	0.357077	−	0.934075i	$-0.383773\pi$
$257$	11.4488	0.714154	0.357077	+	0.934075i	$0.383773\pi$
$258$	8.87807	0.552724
$259$	−46.2244	−2.87225
$260$	−12.9615	−0.803839
$261$	1.70568	0.105579
$262$	−8.91452	−0.550741
$263$	−5.87738	−0.362415	−0.181207	−	0.983445i	$-0.558001\pi$
$263$	−5.87738	−0.362415	−0.181207	+	0.983445i	$0.558001\pi$
$264$	−4.15014	−0.255424
$265$	−11.6493	−0.715610
$266$	2.64168	0.161972
$267$	2.77818	0.170022
$268$	−3.12432	−0.190848
$269$	−16.9462	−1.03323	−0.516614	−	0.856218i	$-0.672808\pi$
$269$	−16.9462	−1.03323	−0.516614	+	0.856218i	$0.672808\pi$
$270$	−17.2897	−1.05222
$271$	12.6085	0.765912	0.382956	−	0.923767i	$-0.374906\pi$
$271$	12.6085	0.765912	0.382956	+	0.923767i	$0.374906\pi$
$272$	−0.0731347	−0.00443445
$273$	27.4941	1.66402
$274$	−3.04296	−0.183832
$275$	16.1467	0.973680
$276$	13.8066	0.831062
$277$	8.72048	0.523963	0.261981	−	0.965073i	$-0.415624\pi$
$277$	8.72048	0.523963	0.261981	+	0.965073i	$0.415624\pi$
$278$	0.153001	0.00917640
$279$	−0.956496	−0.0572639
$280$	14.1708	0.846869
$281$	−31.0015	−1.84939	−0.924696	−	0.380705i	$-0.875681\pi$
$281$	−31.0015	−1.84939	−0.924696	+	0.380705i	$0.875681\pi$
$282$	8.58360	0.511146
$283$	25.1716	1.49630	0.748148	−	0.663532i	$-0.230943\pi$
$283$	25.1716	1.49630	0.748148	+	0.663532i	$0.230943\pi$
$284$	−9.19262	−0.545482
$285$	−3.99994	−0.236936
$286$	8.67451	0.512935
$287$	−29.7027	−1.75330
$288$	0.211861	0.0124840
$289$	−16.9947	−0.999685
$290$	−27.8576	−1.63585
$291$	−18.4028	−1.07879
$292$	−0.398835	−0.0233401
$293$	−22.0554	−1.28849	−0.644244	−	0.764820i	$-0.722828\pi$
$293$	−22.0554	−1.28849	−0.644244	+	0.764820i	$0.722828\pi$
$294$	−17.5141	−1.02145
$295$	−21.8167	−1.27022
$296$	11.2868	0.656033
$297$	11.5712	0.671428
$298$	−16.4958	−0.955577
$299$	−28.8583	−1.66892
$300$	−12.4962	−0.721466
$301$	20.2881	1.16938
$302$	−9.98568	−0.574611
$303$	1.86395	0.107081
$304$	−0.645030	−0.0369950
$305$	1.56116	0.0893917
$306$	−0.0154944	−0.000885754 0
$307$	29.4258	1.67942	0.839710	−	0.543036i	$-0.182725\pi$
$307$	29.4258	1.67942	0.839710	+	0.543036i	$0.182725\pi$
$308$	−9.48385	−0.540393
$309$	−27.3307	−1.55479
$310$	15.6217	0.887253
$311$	−13.3058	−0.754502	−0.377251	−	0.926111i	$-0.623131\pi$
$311$	−13.3058	−0.754502	−0.377251	+	0.926111i	$0.623131\pi$
$312$	−6.71334	−0.380068
$313$	−11.3437	−0.641184	−0.320592	−	0.947217i	$-0.603882\pi$
$313$	−11.3437	−0.641184	−0.320592	+	0.947217i	$0.603882\pi$
$314$	8.76645	0.494719
$315$	3.00224	0.169157
$316$	−8.08453	−0.454790
$317$	−9.33495	−0.524303	−0.262152	−	0.965027i	$-0.584432\pi$
$317$	−9.33495	−0.524303	−0.262152	+	0.965027i	$0.584432\pi$
$318$	−6.03369	−0.338352
$319$	18.6437	1.04385
$320$	−3.46015	−0.193428
$321$	8.41679	0.469779
$322$	31.5508	1.75826
$323$	0.0471741	0.00262484
$324$	−9.59070	−0.532816
$325$	26.1191	1.44883
$326$	12.5855	0.697047
$327$	18.3448	1.01447
$328$	7.25263	0.400460
$329$	19.6151	1.08142
$330$	14.3601	0.790499
$331$	−26.7765	−1.47177	−0.735886	−	0.677106i	$-0.763234\pi$
$331$	−26.7765	−1.47177	−0.735886	+	0.677106i	$0.763234\pi$
$332$	15.3875	0.844501
$333$	2.39123	0.131039
$334$	−5.36582	−0.293605
$335$	10.8106	0.590646
$336$	7.33971	0.400414
$337$	29.7599	1.62112	0.810562	−	0.585652i	$-0.199162\pi$
$337$	29.7599	1.62112	0.810562	+	0.585652i	$0.199162\pi$
$338$	1.03204	0.0561356
$339$	5.91721	0.321379
$340$	0.253057	0.0137240
$341$	−10.4548	−0.566162
$342$	−0.136656	−0.00738953
$343$	−11.3550	−0.613115
$344$	−4.95382	−0.267092
$345$	−47.7731	−2.57202
$346$	6.55214	0.352245
$347$	23.0650	1.23819	0.619097	−	0.785315i	$-0.287499\pi$
$347$	23.0650	1.23819	0.619097	+	0.785315i	$0.287499\pi$
$348$	−14.4287	−0.773459
$349$	4.43306	0.237296	0.118648	−	0.992936i	$-0.462144\pi$
$349$	4.43306	0.237296	0.118648	+	0.992936i	$0.462144\pi$
$350$	−28.5561	−1.52639
$351$	18.7177	0.999079
$352$	2.31571	0.123428
$353$	−1.92167	−0.102280	−0.0511402	−	0.998691i	$-0.516286\pi$
$353$	−1.92167	−0.102280	−0.0511402	+	0.998691i	$0.516286\pi$
$354$	−11.2999	−0.600580
$355$	31.8079	1.68819
$356$	−1.55018	−0.0821594
$357$	−0.536787	−0.0284098
$358$	−1.02642	−0.0542482
$359$	23.3212	1.23085	0.615424	−	0.788197i	$-0.288985\pi$
$359$	23.3212	1.23085	0.615424	+	0.788197i	$0.288985\pi$
$360$	−0.733069	−0.0386362
$361$	−18.5839	−0.978102
$362$	−13.0164	−0.684125
$363$	10.1033	0.530286
$364$	−15.3412	−0.804100
$365$	1.38003	0.0722341
$366$	0.808594	0.0422659
$367$	−26.0899	−1.36188	−0.680941	−	0.732338i	$-0.738429\pi$
$367$	−26.0899	−1.36188	−0.680941	+	0.732338i	$0.738429\pi$
$368$	−7.70388	−0.401593
$369$	1.53655	0.0799894
$370$	−39.0541	−2.03033
$371$	−13.7881	−0.715843
$372$	8.09117	0.419508
$373$	15.3260	0.793553	0.396776	−	0.917915i	$-0.370129\pi$
$373$	15.3260	0.793553	0.396776	+	0.917915i	$0.370129\pi$
$374$	−0.169359	−0.00875735
$375$	12.2327	0.631696
$376$	−4.78951	−0.247000
$377$	30.1584	1.55324
$378$	−20.4641	−1.05256
$379$	−6.51998	−0.334909	−0.167454	−	0.985880i	$-0.553555\pi$
$379$	−6.51998	−0.334909	−0.167454	+	0.985880i	$0.553555\pi$
$380$	2.23190	0.114494
$381$	17.1738	0.879843
$382$	−2.14013	−0.109499
$383$	−2.95171	−0.150825	−0.0754127	−	0.997152i	$-0.524027\pi$
$383$	−2.95171	−0.150825	−0.0754127	+	0.997152i	$0.524027\pi$
$384$	−1.79217	−0.0914561
$385$	32.8156	1.67244
$386$	−17.3745	−0.884338
$387$	−1.04952	−0.0533500
$388$	10.2684	0.521301
$389$	1.20844	0.0612703	0.0306352	−	0.999531i	$-0.490247\pi$
$389$	1.20844	0.0612703	0.0306352	+	0.999531i	$0.490247\pi$
$390$	23.2292	1.17626
$391$	0.563422	0.0284935
$392$	9.77261	0.493591
$393$	15.9763	0.805898
$394$	−5.46065	−0.275104
$395$	27.9737	1.40751
$396$	0.490608	0.0246540
$397$	22.7034	1.13945	0.569725	−	0.821836i	$-0.307050\pi$
$397$	22.7034	1.13945	0.569725	+	0.821836i	$0.307050\pi$
$398$	−23.8880	−1.19740
$399$	−4.73433	−0.237013
$400$	6.97265	0.348633
$401$	−1.33772	−0.0668024	−0.0334012	−	0.999442i	$-0.510634\pi$
$401$	−1.33772	−0.0668024	−0.0334012	+	0.999442i	$0.510634\pi$
$402$	5.59929	0.279267
$403$	−16.9119	−0.842444
$404$	−1.04005	−0.0517445
$405$	33.1853	1.64899
$406$	−32.9723	−1.63639
$407$	26.1370	1.29556
$408$	0.131070	0.00648891
$409$	−7.12689	−0.352402	−0.176201	−	0.984354i	$-0.556381\pi$
$409$	−7.12689	−0.352402	−0.176201	+	0.984354i	$0.556381\pi$
$410$	−25.0952	−1.23936
$411$	5.45349	0.269001
$412$	15.2501	0.751318
$413$	−25.8223	−1.27063
$414$	−1.63215	−0.0802157
$415$	−53.2432	−2.61361
$416$	3.74594	0.183660
$417$	−0.274203	−0.0134278
$418$	−1.49370	−0.0730594
$419$	9.35460	0.457002	0.228501	−	0.973544i	$-0.426618\pi$
$419$	9.35460	0.457002	0.228501	+	0.973544i	$0.426618\pi$
$420$	−25.3965	−1.23922
$421$	0.151842	0.00740034	0.00370017	−	0.999993i	$-0.498822\pi$
$421$	0.151842	0.00740034	0.00370017	+	0.999993i	$0.498822\pi$
$422$	17.1566	0.835168
$423$	−1.01471	−0.0493368
$424$	3.36670	0.163501
$425$	−0.509943	−0.0247359
$426$	16.4747	0.798202
$427$	1.84779	0.0894208
$428$	−4.69643	−0.227011
$429$	−15.5462	−0.750576
$430$	17.1410	0.826611
$431$	0.927062	0.0446550	0.0223275	−	0.999751i	$-0.492892\pi$
$431$	0.927062	0.0446550	0.0223275	+	0.999751i	$0.492892\pi$
$432$	4.99681	0.240409
$433$	37.5776	1.80586	0.902932	−	0.429784i	$-0.141410\pi$
$433$	37.5776	1.80586	0.902932	+	0.429784i	$0.141410\pi$
$434$	18.4899	0.887541
$435$	49.9255	2.39374
$436$	−10.2361	−0.490222
$437$	4.96923	0.237711
$438$	0.714779	0.0341535
$439$	−26.6258	−1.27078	−0.635390	−	0.772192i	$-0.719160\pi$
$439$	−26.6258	−1.27078	−0.635390	+	0.772192i	$0.719160\pi$
$440$	−8.01272	−0.381991
$441$	2.07043	0.0985919
$442$	−0.273958	−0.0130309
$443$	9.47396	0.450121	0.225061	−	0.974345i	$-0.427742\pi$
$443$	9.47396	0.450121	0.225061	+	0.974345i	$0.427742\pi$
$444$	−20.2279	−0.959971
$445$	5.36386	0.254271
$446$	4.97202	0.235432
$447$	29.5632	1.39829
$448$	−4.09544	−0.193491
$449$	2.16653	0.102245	0.0511224	−	0.998692i	$-0.483720\pi$
$449$	2.16653	0.102245	0.0511224	+	0.998692i	$0.483720\pi$
$450$	1.47723	0.0696373
$451$	16.7950	0.790846
$452$	−3.30171	−0.155299
$453$	17.8960	0.840827
$454$	−16.7993	−0.788430
$455$	53.0830	2.48857
$456$	1.15600	0.0541347
$457$	10.2078	0.477503	0.238751	−	0.971081i	$-0.423262\pi$
$457$	10.2078	0.477503	0.238751	+	0.971081i	$0.423262\pi$
$458$	18.6284	0.870447
$459$	−0.365440	−0.0170573
$460$	26.6566	1.24287
$461$	13.9442	0.649448	0.324724	−	0.945809i	$-0.394729\pi$
$461$	13.9442	0.649448	0.324724	+	0.945809i	$0.394729\pi$
$462$	16.9966	0.790756
$463$	−3.66848	−0.170489	−0.0852444	−	0.996360i	$-0.527167\pi$
$463$	−3.66848	−0.170489	−0.0852444	+	0.996360i	$0.527167\pi$
$464$	8.05098	0.373757
$465$	−27.9967	−1.29832
$466$	−11.7084	−0.542382
$467$	−10.9951	−0.508792	−0.254396	−	0.967100i	$-0.581877\pi$
$467$	−10.9951	−0.508792	−0.254396	+	0.967100i	$0.581877\pi$
$468$	0.793616	0.0366849
$469$	12.7954	0.590838
$470$	16.5724	0.764430
$471$	−15.7109	−0.723922
$472$	6.30513	0.290217
$473$	−11.4716	−0.527465
$474$	14.4888	0.665494
$475$	−4.49757	−0.206362
$476$	0.299519	0.0137284
$477$	0.713271	0.0326584
$478$	−9.30655	−0.425672
$479$	−30.4069	−1.38933	−0.694664	−	0.719334i	$-0.744447\pi$
$479$	−30.4069	−1.38933	−0.694664	+	0.719334i	$0.744447\pi$
$480$	6.20117	0.283043
$481$	42.2797	1.92779
$482$	0.614680	0.0279979
$483$	−56.5442	−2.57285
$484$	−5.63748	−0.256249
$485$	−35.5304	−1.61335
$486$	2.19769	0.0996894
$487$	21.1047	0.956345	0.478172	−	0.878266i	$-0.341299\pi$
$487$	21.1047	0.956345	0.478172	+	0.878266i	$0.341299\pi$
$488$	−0.451182	−0.0204241
$489$	−22.5553	−1.01999
$490$	−33.8147	−1.52759
$491$	42.6563	1.92505	0.962527	−	0.271186i	$-0.0874160\pi$
$491$	42.6563	1.92505	0.962527	+	0.271186i	$0.0874160\pi$
$492$	−12.9979	−0.585992
$493$	−0.588806	−0.0265185
$494$	−2.41624	−0.108712
$495$	−1.69758	−0.0763005
$496$	−4.51474	−0.202718
$497$	37.6478	1.68873
$498$	−27.5770	−1.23576
$499$	−28.2909	−1.26648	−0.633238	−	0.773957i	$-0.718275\pi$
$499$	−28.2909	−1.26648	−0.633238	+	0.773957i	$0.718275\pi$
$500$	−6.82567	−0.305253
$501$	9.61645	0.429631
$502$	8.12172	0.362490
$503$	12.9442	0.577152	0.288576	−	0.957457i	$-0.406818\pi$
$503$	12.9442	0.577152	0.288576	+	0.957457i	$0.406818\pi$
$504$	−0.867661	−0.0386487
$505$	3.59874	0.160142
$506$	−17.8400	−0.793084
$507$	−1.84959	−0.0821431
$508$	−9.58273	−0.425165
$509$	−31.1259	−1.37963	−0.689817	−	0.723984i	$-0.742309\pi$
$509$	−31.1259	−1.37963	−0.689817	+	0.723984i	$0.742309\pi$
$510$	−0.453521	−0.0200822
$511$	1.63340	0.0722575
$512$	1.00000	0.0441942
$513$	−3.22309	−0.142303
$514$	11.4488	0.504983
$515$	−52.7676	−2.32522
$516$	8.87807	0.390835
$517$	−11.0911	−0.487787
$518$	−46.2244	−2.03099
$519$	−11.7425	−0.515439
$520$	−12.9615	−0.568400
$521$	−3.98189	−0.174450	−0.0872249	−	0.996189i	$-0.527800\pi$
$521$	−3.98189	−0.174450	−0.0872249	+	0.996189i	$0.527800\pi$
$522$	1.70568	0.0746558
$523$	−12.7019	−0.555417	−0.277709	−	0.960665i	$-0.589575\pi$
$523$	−12.7019	−0.555417	−0.277709	+	0.960665i	$0.589575\pi$
$524$	−8.91452	−0.389433
$525$	51.1772	2.23356
$526$	−5.87738	−0.256266
$527$	0.330185	0.0143831
$528$	−4.15014	−0.180612
$529$	36.3498	1.58043
$530$	−11.6493	−0.506013
$531$	1.33581	0.0579692
$532$	2.64168	0.114531
$533$	27.1679	1.17677
$534$	2.77818	0.120224
$535$	16.2504	0.702565
$536$	−3.12432	−0.134950
$537$	1.83952	0.0793813
$538$	−16.9462	−0.730602
$539$	22.6305	0.974767
$540$	−17.2897	−0.744031
$541$	8.62431	0.370788	0.185394	−	0.982664i	$-0.440644\pi$
$541$	8.62431	0.370788	0.185394	+	0.982664i	$0.440644\pi$
$542$	12.6085	0.541581
$543$	23.3275	1.00108
$544$	−0.0731347	−0.00313563
$545$	35.4186	1.51716
$546$	27.4941	1.17664
$547$	−13.7684	−0.588695	−0.294347	−	0.955698i	$-0.595102\pi$
$547$	−13.7684	−0.588695	−0.294347	+	0.955698i	$0.595102\pi$
$548$	−3.04296	−0.129989
$549$	−0.0955877	−0.00407958
$550$	16.1467	0.688496
$551$	−5.19312	−0.221234
$552$	13.8066	0.587650
$553$	33.1097	1.40797
$554$	8.72048	0.370498
$555$	69.9914	2.97097
$556$	0.153001	0.00648869
$557$	28.2612	1.19747	0.598733	−	0.800948i	$-0.295671\pi$
$557$	28.2612	1.19747	0.598733	+	0.800948i	$0.295671\pi$
$558$	−0.956496	−0.0404917
$559$	−18.5567	−0.784864
$560$	14.1708	0.598827
$561$	0.303520	0.0128146
$562$	−31.0015	−1.30772
$563$	10.4480	0.440332	0.220166	−	0.975462i	$-0.429340\pi$
$563$	10.4480	0.440332	0.220166	+	0.975462i	$0.429340\pi$
$564$	8.58360	0.361435
$565$	11.4244	0.480629
$566$	25.1716	1.05804
$567$	39.2781	1.64953
$568$	−9.19262	−0.385714
$569$	1.90526	0.0798725	0.0399362	−	0.999202i	$-0.487285\pi$
$569$	1.90526	0.0798725	0.0399362	+	0.999202i	$0.487285\pi$
$570$	−3.99994	−0.167539
$571$	−6.14894	−0.257325	−0.128663	−	0.991688i	$-0.541068\pi$
$571$	−6.14894	−0.257325	−0.128663	+	0.991688i	$0.541068\pi$
$572$	8.67451	0.362700
$573$	3.83548	0.160229
$574$	−29.7027	−1.23977
$575$	−53.7165	−2.24013
$576$	0.211861	0.00882752
$577$	−14.1566	−0.589349	−0.294674	−	0.955598i	$-0.595211\pi$
$577$	−14.1566	−0.589349	−0.294674	+	0.955598i	$0.595211\pi$
$578$	−16.9947	−0.706884
$579$	31.1380	1.29405
$580$	−27.8576	−1.15672
$581$	−63.0187	−2.61446
$582$	−18.4028	−0.762819
$583$	7.79631	0.322890
$584$	−0.398835	−0.0165039
$585$	−2.74603	−0.113534
$586$	−22.0554	−0.911099
$587$	−17.8568	−0.737028	−0.368514	−	0.929622i	$-0.620133\pi$
$587$	−17.8568	−0.737028	−0.368514	+	0.929622i	$0.620133\pi$
$588$	−17.5141	−0.722271
$589$	2.91214	0.119993
$590$	−21.8167	−0.898180
$591$	9.78640	0.402559
$592$	11.2868	0.463885
$593$	−4.75809	−0.195391	−0.0976957	−	0.995216i	$-0.531147\pi$
$593$	−4.75809	−0.195391	−0.0976957	+	0.995216i	$0.531147\pi$
$594$	11.5712	0.474771
$595$	−1.03638	−0.0424875
$596$	−16.4958	−0.675695
$597$	42.8113	1.75215
$598$	−28.8583	−1.18010
$599$	43.5849	1.78083	0.890416	−	0.455148i	$-0.150414\pi$
$599$	43.5849	1.78083	0.890416	+	0.455148i	$0.150414\pi$
$600$	−12.4962	−0.510153
$601$	−26.2991	−1.07276	−0.536381	−	0.843976i	$-0.680209\pi$
$601$	−26.2991	−1.07276	−0.536381	+	0.843976i	$0.680209\pi$
$602$	20.2881	0.826879
$603$	−0.661919	−0.0269554
$604$	−9.98568	−0.406311
$605$	19.5065	0.793053
$606$	1.86395	0.0757176
$607$	−40.1331	−1.62895	−0.814475	−	0.580198i	$-0.802975\pi$
$607$	−40.1331	−1.62895	−0.814475	+	0.580198i	$0.802975\pi$
$608$	−0.645030	−0.0261594
$609$	59.0918	2.39452
$610$	1.56116	0.0632095
$611$	−17.9412	−0.725824
$612$	−0.0154944	−0.000626323 0
$613$	6.42791	0.259621	0.129810	−	0.991539i	$-0.458563\pi$
$613$	6.42791	0.259621	0.129810	+	0.991539i	$0.458563\pi$
$614$	29.4258	1.18753
$615$	44.9748	1.81356
$616$	−9.48385	−0.382115
$617$	−26.8306	−1.08016	−0.540079	−	0.841614i	$-0.681606\pi$
$617$	−26.8306	−1.08016	−0.540079	+	0.841614i	$0.681606\pi$
$618$	−27.3307	−1.09940
$619$	−10.4094	−0.418388	−0.209194	−	0.977874i	$-0.567084\pi$
$619$	−10.4094	−0.418388	−0.209194	+	0.977874i	$0.567084\pi$
$620$	15.6217	0.627383
$621$	−38.4948	−1.54475
$622$	−13.3058	−0.533513
$623$	6.34867	0.254354
$624$	−6.71334	−0.268749
$625$	−11.2454	−0.449816
$626$	−11.3437	−0.453386
$627$	2.67696	0.106908
$628$	8.76645	0.349819
$629$	−0.825458	−0.0329132
$630$	3.00224	0.119612
$631$	4.55608	0.181375	0.0906873	−	0.995879i	$-0.471094\pi$
$631$	4.55608	0.181375	0.0906873	+	0.995879i	$0.471094\pi$
$632$	−8.08453	−0.321585
$633$	−30.7474	−1.22210
$634$	−9.33495	−0.370738
$635$	33.1577	1.31582
$636$	−6.03369	−0.239251
$637$	36.6076	1.45044
$638$	18.6437	0.738113
$639$	−1.94755	−0.0770440
$640$	−3.46015	−0.136775
$641$	3.76476	0.148699	0.0743495	−	0.997232i	$-0.476312\pi$
$641$	3.76476	0.148699	0.0743495	+	0.997232i	$0.476312\pi$
$642$	8.41679	0.332184
$643$	28.5045	1.12411	0.562055	−	0.827100i	$-0.310011\pi$
$643$	28.5045	1.12411	0.562055	+	0.827100i	$0.310011\pi$
$644$	31.5508	1.24327
$645$	−30.7195	−1.20958
$646$	0.0471741	0.00185604
$647$	−31.2202	−1.22739	−0.613696	−	0.789542i	$-0.710318\pi$
$647$	−31.2202	−1.22739	−0.613696	+	0.789542i	$0.710318\pi$
$648$	−9.59070	−0.376758
$649$	14.6009	0.573135
$650$	26.1191	1.02448
$651$	−33.1369	−1.29874
$652$	12.5855	0.492887
$653$	−46.8825	−1.83465	−0.917326	−	0.398137i	$-0.869657\pi$
$653$	−46.8825	−1.83465	−0.917326	+	0.398137i	$0.869657\pi$
$654$	18.3448	0.717340
$655$	30.8456	1.20524
$656$	7.25263	0.283168
$657$	−0.0844974	−0.00329656
$658$	19.6151	0.764678
$659$	45.4924	1.77213	0.886066	−	0.463559i	$-0.153428\pi$
$659$	45.4924	1.77213	0.886066	+	0.463559i	$0.153428\pi$
$660$	14.3601	0.558967
$661$	15.3429	0.596770	0.298385	−	0.954446i	$-0.403552\pi$
$661$	15.3429	0.596770	0.298385	+	0.954446i	$0.403552\pi$
$662$	−26.7765	−1.04070
$663$	0.490979	0.0190680
$664$	15.3875	0.597152
$665$	−9.14061	−0.354458
$666$	2.39123	0.0926583
$667$	−62.0238	−2.40157
$668$	−5.36582	−0.207610
$669$	−8.91069	−0.344507
$670$	10.8106	0.417650
$671$	−1.04481	−0.0403344
$672$	7.33971	0.283135
$673$	17.6810	0.681552	0.340776	−	0.940144i	$-0.389310\pi$
$673$	17.6810	0.681552	0.340776	+	0.940144i	$0.389310\pi$
$674$	29.7599	1.14631
$675$	34.8410	1.34103
$676$	1.03204	0.0396939
$677$	−5.07843	−0.195180	−0.0975900	−	0.995227i	$-0.531113\pi$
$677$	−5.07843	−0.195180	−0.0975900	+	0.995227i	$0.531113\pi$
$678$	5.91721	0.227249
$679$	−42.0538	−1.61388
$680$	0.253057	0.00970430
$681$	30.1071	1.15371
$682$	−10.4548	−0.400337
$683$	−12.9628	−0.496008	−0.248004	−	0.968759i	$-0.579775\pi$
$683$	−12.9628	−0.496008	−0.248004	+	0.968759i	$0.579775\pi$
$684$	−0.136656	−0.00522518
$685$	10.5291	0.402296
$686$	−11.3550	−0.433537
$687$	−33.3851	−1.27372
$688$	−4.95382	−0.188863
$689$	12.6114	0.480458
$690$	−47.7731	−1.81869
$691$	−2.53476	−0.0964266	−0.0482133	−	0.998837i	$-0.515353\pi$
$691$	−2.53476	−0.0964266	−0.0482133	+	0.998837i	$0.515353\pi$
$692$	6.55214	0.249075
$693$	−2.00925	−0.0763253
$694$	23.0650	0.875535
$695$	−0.529407	−0.0200816
$696$	−14.4287	−0.546918
$697$	−0.530420	−0.0200911
$698$	4.43306	0.167794
$699$	20.9834	0.793666
$700$	−28.5561	−1.07932
$701$	14.9936	0.566300	0.283150	−	0.959076i	$-0.408621\pi$
$701$	14.9936	0.566300	0.283150	+	0.959076i	$0.408621\pi$
$702$	18.7177	0.706455
$703$	−7.28033	−0.274583
$704$	2.31571	0.0872767
$705$	−29.7006	−1.11859
$706$	−1.92167	−0.0723231
$707$	4.25947	0.160194
$708$	−11.2999	−0.424674
$709$	−3.58234	−0.134538	−0.0672689	−	0.997735i	$-0.521429\pi$
$709$	−3.58234	−0.134538	−0.0672689	+	0.997735i	$0.521429\pi$
$710$	31.8079	1.19373
$711$	−1.71279	−0.0642347
$712$	−1.55018	−0.0580955
$713$	34.7811	1.30256
$714$	−0.536787	−0.0200888
$715$	−30.0151	−1.12250
$716$	−1.02642	−0.0383593
$717$	16.6789	0.622885
$718$	23.3212	0.870340
$719$	−14.7557	−0.550295	−0.275148	−	0.961402i	$-0.588727\pi$
$719$	−14.7557	−0.550295	−0.275148	+	0.961402i	$0.588727\pi$
$720$	−0.733069	−0.0273199
$721$	−62.4558	−2.32597
$722$	−18.5839	−0.691623
$723$	−1.10161	−0.0409693
$724$	−13.0164	−0.483749
$725$	56.1366	2.08486
$726$	10.1033	0.374969
$727$	3.90168	0.144705	0.0723527	−	0.997379i	$-0.476949\pi$
$727$	3.90168	0.144705	0.0723527	+	0.997379i	$0.476949\pi$
$728$	−15.3412	−0.568585
$729$	24.8335	0.919758
$730$	1.38003	0.0510772
$731$	0.362296	0.0134000
$732$	0.808594	0.0298865
$733$	23.2111	0.857321	0.428660	−	0.903466i	$-0.358986\pi$
$733$	23.2111	0.857321	0.428660	+	0.903466i	$0.358986\pi$
$734$	−26.0899	−0.962997
$735$	60.6016	2.23532
$736$	−7.70388	−0.283969
$737$	−7.23502	−0.266505
$738$	1.53655	0.0565611
$739$	−50.0882	−1.84252	−0.921262	−	0.388942i	$-0.872841\pi$
$739$	−50.0882	−1.84252	−0.921262	+	0.388942i	$0.872841\pi$
$740$	−39.0541	−1.43566
$741$	4.33030	0.159078
$742$	−13.7881	−0.506177
$743$	−43.4469	−1.59391	−0.796956	−	0.604037i	$-0.793558\pi$
$743$	−43.4469	−1.59391	−0.796956	+	0.604037i	$0.793558\pi$
$744$	8.09117	0.296637
$745$	57.0780	2.09118
$746$	15.3260	0.561126
$747$	3.26001	0.119278
$748$	−0.169359	−0.00619238
$749$	19.2339	0.702793
$750$	12.2327	0.446676
$751$	−1.80517	−0.0658717	−0.0329359	−	0.999457i	$-0.510486\pi$
$751$	−1.80517	−0.0658717	−0.0329359	+	0.999457i	$0.510486\pi$
$752$	−4.78951	−0.174656
$753$	−14.5555	−0.530431
$754$	30.1584	1.09831
$755$	34.5520	1.25747
$756$	−20.4641	−0.744273
$757$	−25.4040	−0.923324	−0.461662	−	0.887056i	$-0.652747\pi$
$757$	−25.4040	−0.923324	−0.461662	+	0.887056i	$0.652747\pi$
$758$	−6.51998	−0.236816
$759$	31.9722	1.16052
$760$	2.23190	0.0809595
$761$	−17.2289	−0.624547	−0.312273	−	0.949992i	$-0.601090\pi$
$761$	−17.2289	−0.624547	−0.312273	+	0.949992i	$0.601090\pi$
$762$	17.1738	0.622143
$763$	41.9214	1.51766
$764$	−2.14013	−0.0774274
$765$	0.0536128	0.00193838
$766$	−2.95171	−0.106650
$767$	23.6186	0.852819
$768$	−1.79217	−0.0646692
$769$	47.3683	1.70815	0.854073	−	0.520153i	$-0.174125\pi$
$769$	47.3683	1.70815	0.854073	+	0.520153i	$0.174125\pi$
$770$	32.8156	1.18259
$771$	−20.5181	−0.738940
$772$	−17.3745	−0.625321
$773$	30.9009	1.11143	0.555715	−	0.831373i	$-0.312445\pi$
$773$	30.9009	1.11143	0.555715	+	0.831373i	$0.312445\pi$
$774$	−1.04952	−0.0377242
$775$	−31.4797	−1.13079
$776$	10.2684	0.368616
$777$	82.8419	2.97194
$778$	1.20844	0.0433247
$779$	−4.67816	−0.167613
$780$	23.2292	0.831738
$781$	−21.2875	−0.761725
$782$	0.563422	0.0201479
$783$	40.2292	1.43767
$784$	9.77261	0.349022
$785$	−30.3332	−1.08264
$786$	15.9763	0.569856
$787$	−34.3815	−1.22557	−0.612784	−	0.790250i	$-0.709951\pi$
$787$	−34.3815	−1.22557	−0.612784	+	0.790250i	$0.709951\pi$
$788$	−5.46065	−0.194528
$789$	10.5332	0.374993
$790$	27.9737	0.995260
$791$	13.5219	0.480785
$792$	0.490608	0.0174330
$793$	−1.69010	−0.0600172
$794$	22.7034	0.805712
$795$	20.8775	0.740448
$796$	−23.8880	−0.846689
$797$	−6.15988	−0.218194	−0.109097	−	0.994031i	$-0.534796\pi$
$797$	−6.15988	−0.218194	−0.109097	+	0.994031i	$0.534796\pi$
$798$	−4.73433	−0.167593
$799$	0.350280	0.0123920
$800$	6.97265	0.246520
$801$	−0.328422	−0.0116042
$802$	−1.33772	−0.0472364
$803$	−0.923587	−0.0325927
$804$	5.59929	0.197472
$805$	−109.170	−3.84775
$806$	−16.9119	−0.595698
$807$	30.3704	1.06909
$808$	−1.04005	−0.0365889
$809$	−50.0461	−1.75953	−0.879764	−	0.475410i	$-0.842300\pi$
$809$	−50.0461	−1.75953	−0.879764	+	0.475410i	$0.842300\pi$
$810$	33.1853	1.16601
$811$	42.4054	1.48905	0.744527	−	0.667592i	$-0.232675\pi$
$811$	42.4054	1.48905	0.744527	+	0.667592i	$0.232675\pi$
$812$	−32.9723	−1.15710
$813$	−22.5965	−0.792495
$814$	26.1370	0.916102
$815$	−43.5478	−1.52541
$816$	0.131070	0.00458835
$817$	3.19536	0.111791
$818$	−7.12689	−0.249186
$819$	−3.25020	−0.113571
$820$	−25.0952	−0.876363
$821$	2.39422	0.0835590	0.0417795	−	0.999127i	$-0.486697\pi$
$821$	2.39422	0.0835590	0.0417795	+	0.999127i	$0.486697\pi$
$822$	5.45349	0.190212
$823$	−30.0391	−1.04710	−0.523548	−	0.851996i	$-0.675392\pi$
$823$	−30.0391	−1.04710	−0.523548	+	0.851996i	$0.675392\pi$
$824$	15.2501	0.531262
$825$	−28.9375	−1.00747
$826$	−25.8223	−0.898472
$827$	−24.3593	−0.847055	−0.423528	−	0.905883i	$-0.639208\pi$
$827$	−24.3593	−0.847055	−0.423528	+	0.905883i	$0.639208\pi$
$828$	−1.63215	−0.0567211
$829$	0.200646	0.00696872	0.00348436	−	0.999994i	$-0.498891\pi$
$829$	0.200646	0.00696872	0.00348436	+	0.999994i	$0.498891\pi$
$830$	−53.2432	−1.84810
$831$	−15.6286	−0.542149
$832$	3.74594	0.129867
$833$	−0.714717	−0.0247635
$834$	−0.274203	−0.00949489
$835$	18.5666	0.642522
$836$	−1.49370	−0.0516608
$837$	−22.5593	−0.779764
$838$	9.35460	0.323149
$839$	−17.1350	−0.591565	−0.295783	−	0.955255i	$-0.595580\pi$
$839$	−17.1350	−0.591565	−0.295783	+	0.955255i	$0.595580\pi$
$840$	−25.3965	−0.876262
$841$	35.8182	1.23511
$842$	0.151842	0.00523283
$843$	55.5598	1.91358
$844$	17.1566	0.590553
$845$	−3.57102	−0.122847
$846$	−1.01471	−0.0348864
$847$	23.0879	0.793311
$848$	3.36670	0.115613
$849$	−45.1117	−1.54823
$850$	−0.509943	−0.0174909
$851$	−86.9523	−2.98069
$852$	16.4747	0.564414
$853$	−40.3545	−1.38171	−0.690856	−	0.722992i	$-0.742766\pi$
$853$	−40.3545	−1.38171	−0.690856	+	0.722992i	$0.742766\pi$
$854$	1.84779	0.0632300
$855$	0.472851	0.0161712
$856$	−4.69643	−0.160521
$857$	−48.1696	−1.64544	−0.822721	−	0.568446i	$-0.807545\pi$
$857$	−48.1696	−1.64544	−0.822721	+	0.568446i	$0.807545\pi$
$858$	−15.5462	−0.530737
$859$	−28.9312	−0.987121	−0.493561	−	0.869711i	$-0.664305\pi$
$859$	−28.9312	−0.987121	−0.493561	+	0.869711i	$0.664305\pi$
$860$	17.1410	0.584502
$861$	53.2322	1.81415
$862$	0.927062	0.0315759
$863$	−38.2248	−1.30119	−0.650594	−	0.759425i	$-0.725480\pi$
$863$	−38.2248	−1.30119	−0.650594	+	0.759425i	$0.725480\pi$
$864$	4.99681	0.169995
$865$	−22.6714	−0.770850
$866$	37.5776	1.27694
$867$	30.4572	1.03438
$868$	18.4899	0.627586
$869$	−18.7214	−0.635082
$870$	49.9255	1.69263
$871$	−11.7035	−0.396558
$872$	−10.2361	−0.346639
$873$	2.17548	0.0736288
$874$	4.96923	0.168087
$875$	27.9541	0.945021
$876$	0.714779	0.0241501
$877$	−5.81597	−0.196391	−0.0981957	−	0.995167i	$-0.531307\pi$
$877$	−5.81597	−0.196391	−0.0981957	+	0.995167i	$0.531307\pi$
$878$	−26.6258	−0.898577
$879$	39.5269	1.33321
$880$	−8.01272	−0.270109
$881$	50.1450	1.68943	0.844714	−	0.535218i	$-0.179771\pi$
$881$	50.1450	1.68943	0.844714	+	0.535218i	$0.179771\pi$
$882$	2.07043	0.0697150
$883$	−40.2283	−1.35379	−0.676895	−	0.736080i	$-0.736675\pi$
$883$	−40.2283	−1.35379	−0.676895	+	0.736080i	$0.736675\pi$
$884$	−0.273958	−0.00921421
$885$	39.0992	1.31431
$886$	9.47396	0.318284
$887$	38.8125	1.30320	0.651598	−	0.758564i	$-0.274099\pi$
$887$	38.8125	1.30320	0.651598	+	0.758564i	$0.274099\pi$
$888$	−20.2279	−0.678802
$889$	39.2455	1.31625
$890$	5.36386	0.179797
$891$	−22.2093	−0.744039
$892$	4.97202	0.166476
$893$	3.08938	0.103382
$894$	29.5632	0.988743
$895$	3.55159	0.118716
$896$	−4.09544	−0.136819
$897$	51.7188	1.72684
$898$	2.16653	0.0722981
$899$	−36.3481	−1.21228
$900$	1.47723	0.0492410
$901$	−0.246223	−0.00820287
$902$	16.7950	0.559213
$903$	−36.3596	−1.20997
$904$	−3.30171	−0.109813
$905$	45.0386	1.49713
$906$	17.8960	0.594555
$907$	−42.1714	−1.40028	−0.700139	−	0.714007i	$-0.746878\pi$
$907$	−42.1714	−1.40028	−0.700139	+	0.714007i	$0.746878\pi$
$908$	−16.7993	−0.557504
$909$	−0.220346	−0.00730841
$910$	53.0830	1.75969
$911$	9.17004	0.303817	0.151909	−	0.988395i	$-0.451458\pi$
$911$	9.17004	0.303817	0.151909	+	0.988395i	$0.451458\pi$
$912$	1.15600	0.0382790
$913$	35.6331	1.17928
$914$	10.2078	0.337645
$915$	−2.79786	−0.0924943
$916$	18.6284	0.615499
$917$	36.5088	1.20563
$918$	−0.365440	−0.0120613
$919$	−48.3492	−1.59489	−0.797446	−	0.603390i	$-0.793816\pi$
$919$	−48.3492	−1.59489	−0.797446	+	0.603390i	$0.793816\pi$
$920$	26.6566	0.878842
$921$	−52.7359	−1.73771
$922$	13.9442	0.459229
$923$	−34.4350	−1.13344
$924$	16.9966	0.559149
$925$	78.6990	2.58761
$926$	−3.66848	−0.120554
$927$	3.23089	0.106116
$928$	8.05098	0.264286
$929$	−37.8594	−1.24213	−0.621064	−	0.783760i	$-0.713299\pi$
$929$	−37.8594	−1.24213	−0.621064	+	0.783760i	$0.713299\pi$
$930$	−27.9967	−0.918048
$931$	−6.30362	−0.206593
$932$	−11.7084	−0.383522
$933$	23.8462	0.780689
$934$	−10.9951	−0.359770
$935$	0.586008	0.0191645
$936$	0.793616	0.0259402
$937$	17.4770	0.570950	0.285475	−	0.958386i	$-0.407849\pi$
$937$	17.4770	0.570950	0.285475	+	0.958386i	$0.407849\pi$
$938$	12.7954	0.417786
$939$	20.3298	0.663439
$940$	16.5724	0.540533
$941$	35.0910	1.14393	0.571966	−	0.820277i	$-0.306181\pi$
$941$	35.0910	1.14393	0.571966	+	0.820277i	$0.306181\pi$
$942$	−15.7109	−0.511890
$943$	−55.8735	−1.81949
$944$	6.30513	0.205215
$945$	70.8090	2.30342
$946$	−11.4716	−0.372974
$947$	−30.3057	−0.984804	−0.492402	−	0.870368i	$-0.663881\pi$
$947$	−30.3057	−0.984804	−0.492402	+	0.870368i	$0.663881\pi$
$948$	14.4888	0.470575
$949$	−1.49401	−0.0484976
$950$	−4.49757	−0.145920
$951$	16.7298	0.542501
$952$	0.299519	0.00970746
$953$	25.3238	0.820318	0.410159	−	0.912014i	$-0.365473\pi$
$953$	25.3238	0.820318	0.410159	+	0.912014i	$0.365473\pi$
$954$	0.713271	0.0230930
$955$	7.40519	0.239626
$956$	−9.30655	−0.300995
$957$	−33.4127	−1.08008
$958$	−30.4069	−0.982404
$959$	12.4622	0.402427
$960$	6.20117	0.200142
$961$	−10.6171	−0.342487
$962$	42.2797	1.36315
$963$	−0.994989	−0.0320631
$964$	0.614680	0.0197975
$965$	60.1184	1.93528
$966$	−56.5442	−1.81928
$967$	−9.04948	−0.291012	−0.145506	−	0.989357i	$-0.546481\pi$
$967$	−9.04948	−0.291012	−0.145506	+	0.989357i	$0.546481\pi$
$968$	−5.63748	−0.181195
$969$	−0.0845438	−0.00271594
$970$	−35.5304	−1.14081
$971$	−12.8897	−0.413651	−0.206825	−	0.978378i	$-0.566313\pi$
$971$	−12.8897	−0.413651	−0.206825	+	0.978378i	$0.566313\pi$
$972$	2.19769	0.0704911
$973$	−0.626606	−0.0200881
$974$	21.1047	0.676238
$975$	−46.8098	−1.49911
$976$	−0.451182	−0.0144420
$977$	−27.9974	−0.895717	−0.447858	−	0.894105i	$-0.647813\pi$
$977$	−27.9974	−0.895717	−0.447858	+	0.894105i	$0.647813\pi$
$978$	−22.5553	−0.721240
$979$	−3.58977	−0.114730
$980$	−33.8147	−1.08017
$981$	−2.16863	−0.0692391
$982$	42.6563	1.36122
$983$	0.792164	0.0252661	0.0126331	−	0.999920i	$-0.495979\pi$
$983$	0.792164	0.0252661	0.0126331	+	0.999920i	$0.495979\pi$
$984$	−12.9979	−0.414359
$985$	18.8947	0.602035
$986$	−0.588806	−0.0187514
$987$	−35.1536	−1.11895
$988$	−2.41624	−0.0768708
$989$	38.1636	1.21353
$990$	−1.69758	−0.0539526
$991$	33.2193	1.05525	0.527623	−	0.849479i	$-0.323083\pi$
$991$	33.2193	1.05525	0.527623	+	0.849479i	$0.323083\pi$
$992$	−4.51474	−0.143343
$993$	47.9880	1.52285
$994$	37.6478	1.19412
$995$	82.6562	2.62038
$996$	−27.5770	−0.873812
$997$	15.9661	0.505651	0.252826	−	0.967512i	$-0.418640\pi$
$997$	15.9661	0.505651	0.252826	+	0.967512i	$0.418640\pi$
$998$	−28.2909	−0.895534
$999$	56.3981	1.78436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.16	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.16	✓	56	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.79217 q^{3} +1.00000 q^{4} -3.46015 q^{5} -1.79217 q^{6} -4.09544 q^{7} +1.00000 q^{8} +0.211861 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.79217 q^{3} +1.00000 q^{4} -3.46015 q^{5} -1.79217 q^{6} -4.09544 q^{7} +1.00000 q^{8} +0.211861 q^{9} -3.46015 q^{10} +2.31571 q^{11} -1.79217 q^{12} +3.74594 q^{13} -4.09544 q^{14} +6.20117 q^{15} +1.00000 q^{16} -0.0731347 q^{17} +0.211861 q^{18} -0.645030 q^{19} -3.46015 q^{20} +7.33971 q^{21} +2.31571 q^{22} -7.70388 q^{23} -1.79217 q^{24} +6.97265 q^{25} +3.74594 q^{26} +4.99681 q^{27} -4.09544 q^{28} +8.05098 q^{29} +6.20117 q^{30} -4.51474 q^{31} +1.00000 q^{32} -4.15014 q^{33} -0.0731347 q^{34} +14.1708 q^{35} +0.211861 q^{36} +11.2868 q^{37} -0.645030 q^{38} -6.71334 q^{39} -3.46015 q^{40} +7.25263 q^{41} +7.33971 q^{42} -4.95382 q^{43} +2.31571 q^{44} -0.733069 q^{45} -7.70388 q^{46} -4.78951 q^{47} -1.79217 q^{48} +9.77261 q^{49} +6.97265 q^{50} +0.131070 q^{51} +3.74594 q^{52} +3.36670 q^{53} +4.99681 q^{54} -8.01272 q^{55} -4.09544 q^{56} +1.15600 q^{57} +8.05098 q^{58} +6.30513 q^{59} +6.20117 q^{60} -0.451182 q^{61} -4.51474 q^{62} -0.867661 q^{63} +1.00000 q^{64} -12.9615 q^{65} -4.15014 q^{66} -3.12432 q^{67} -0.0731347 q^{68} +13.8066 q^{69} +14.1708 q^{70} -9.19262 q^{71} +0.211861 q^{72} -0.398835 q^{73} +11.2868 q^{74} -12.4962 q^{75} -0.645030 q^{76} -9.48385 q^{77} -6.71334 q^{78} -8.08453 q^{79} -3.46015 q^{80} -9.59070 q^{81} +7.25263 q^{82} +15.3875 q^{83} +7.33971 q^{84} +0.253057 q^{85} -4.95382 q^{86} -14.4287 q^{87} +2.31571 q^{88} -1.55018 q^{89} -0.733069 q^{90} -15.3412 q^{91} -7.70388 q^{92} +8.09117 q^{93} -4.78951 q^{94} +2.23190 q^{95} -1.79217 q^{96} +10.2684 q^{97} +9.77261 q^{98} +0.490608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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