LMFDB - Embedded newform 4011.2.a.l.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.343679 q^{2} -1.00000 q^{3} -1.88188 q^{4} -1.00728 q^{5} -0.343679 q^{6} +1.00000 q^{7} -1.33412 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.343679 q^{2} -1.00000 q^{3} -1.88188 q^{4} -1.00728 q^{5} -0.343679 q^{6} +1.00000 q^{7} -1.33412 q^{8} +1.00000 q^{9} -0.346179 q^{10} -5.60703 q^{11} +1.88188 q^{12} -6.26985 q^{13} +0.343679 q^{14} +1.00728 q^{15} +3.30526 q^{16} -7.76609 q^{17} +0.343679 q^{18} +5.12428 q^{19} +1.89558 q^{20} -1.00000 q^{21} -1.92702 q^{22} -4.36612 q^{23} +1.33412 q^{24} -3.98540 q^{25} -2.15481 q^{26} -1.00000 q^{27} -1.88188 q^{28} -7.08004 q^{29} +0.346179 q^{30} -0.373326 q^{31} +3.80419 q^{32} +5.60703 q^{33} -2.66904 q^{34} -1.00728 q^{35} -1.88188 q^{36} +4.00585 q^{37} +1.76111 q^{38} +6.26985 q^{39} +1.34383 q^{40} +0.0294115 q^{41} -0.343679 q^{42} +7.31028 q^{43} +10.5518 q^{44} -1.00728 q^{45} -1.50054 q^{46} +3.59574 q^{47} -3.30526 q^{48} +1.00000 q^{49} -1.36970 q^{50} +7.76609 q^{51} +11.7991 q^{52} -9.95882 q^{53} -0.343679 q^{54} +5.64782 q^{55} -1.33412 q^{56} -5.12428 q^{57} -2.43326 q^{58} -9.74289 q^{59} -1.89558 q^{60} -0.441001 q^{61} -0.128304 q^{62} +1.00000 q^{63} -5.30310 q^{64} +6.31546 q^{65} +1.92702 q^{66} +9.96981 q^{67} +14.6149 q^{68} +4.36612 q^{69} -0.346179 q^{70} -5.36055 q^{71} -1.33412 q^{72} -10.6741 q^{73} +1.37672 q^{74} +3.98540 q^{75} -9.64331 q^{76} -5.60703 q^{77} +2.15481 q^{78} -17.6943 q^{79} -3.32931 q^{80} +1.00000 q^{81} +0.0101081 q^{82} +0.590926 q^{83} +1.88188 q^{84} +7.82259 q^{85} +2.51239 q^{86} +7.08004 q^{87} +7.48046 q^{88} +4.00039 q^{89} -0.346179 q^{90} -6.26985 q^{91} +8.21654 q^{92} +0.373326 q^{93} +1.23578 q^{94} -5.16156 q^{95} -3.80419 q^{96} -9.11311 q^{97} +0.343679 q^{98} -5.60703 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.343679	0.243018	0.121509	−	0.992590i	$-0.461227\pi$
$2$	0.343679	0.243018	0.121509	+	0.992590i	$0.461227\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.88188	−0.940942
$5$	−1.00728	−0.450467	−0.225234	−	0.974305i	$-0.572315\pi$
$5$	−1.00728	−0.450467	−0.225234	+	0.974305i	$0.572315\pi$
$6$	−0.343679	−0.140306
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.33412	−0.471683
$9$	1.00000	0.333333
$10$	−0.346179	−0.109472
$11$	−5.60703	−1.69058	−0.845291	−	0.534306i	$-0.820573\pi$
$11$	−5.60703	−1.69058	−0.845291	+	0.534306i	$0.820573\pi$
$12$	1.88188	0.543253
$13$	−6.26985	−1.73894	−0.869471	−	0.493984i	$-0.835540\pi$
$13$	−6.26985	−1.73894	−0.869471	+	0.493984i	$0.835540\pi$
$14$	0.343679	0.0918521
$15$	1.00728	0.260077
$16$	3.30526	0.826315
$17$	−7.76609	−1.88355	−0.941776	−	0.336240i	$-0.890845\pi$
$17$	−7.76609	−1.88355	−0.941776	+	0.336240i	$0.890845\pi$
$18$	0.343679	0.0810059
$19$	5.12428	1.17559	0.587795	−	0.809010i	$-0.299996\pi$
$19$	5.12428	1.17559	0.587795	+	0.809010i	$0.299996\pi$
$20$	1.89558	0.423864
$21$	−1.00000	−0.218218
$22$	−1.92702	−0.410841
$23$	−4.36612	−0.910399	−0.455200	−	0.890389i	$-0.650432\pi$
$23$	−4.36612	−0.910399	−0.455200	+	0.890389i	$0.650432\pi$
$24$	1.33412	0.272327
$25$	−3.98540	−0.797079
$26$	−2.15481	−0.422594
$27$	−1.00000	−0.192450
$28$	−1.88188	−0.355643
$29$	−7.08004	−1.31473	−0.657365	−	0.753572i	$-0.728329\pi$
$29$	−7.08004	−1.31473	−0.657365	+	0.753572i	$0.728329\pi$
$30$	0.346179	0.0632034
$31$	−0.373326	−0.0670514	−0.0335257	−	0.999438i	$-0.510674\pi$
$31$	−0.373326	−0.0670514	−0.0335257	+	0.999438i	$0.510674\pi$
$32$	3.80419	0.672493
$33$	5.60703	0.976058
$34$	−2.66904	−0.457737
$35$	−1.00728	−0.170261
$36$	−1.88188	−0.313647
$37$	4.00585	0.658557	0.329278	−	0.944233i	$-0.393195\pi$
$37$	4.00585	0.658557	0.329278	+	0.944233i	$0.393195\pi$
$38$	1.76111	0.285689
$39$	6.26985	1.00398
$40$	1.34383	0.212478
$41$	0.0294115	0.00459331	0.00229665	−	0.999997i	$-0.499269\pi$
$41$	0.0294115	0.00459331	0.00229665	+	0.999997i	$0.499269\pi$
$42$	−0.343679	−0.0530308
$43$	7.31028	1.11481	0.557404	−	0.830242i	$-0.311798\pi$
$43$	7.31028	1.11481	0.557404	+	0.830242i	$0.311798\pi$
$44$	10.5518	1.59074
$45$	−1.00728	−0.150156
$46$	−1.50054	−0.221243
$47$	3.59574	0.524492	0.262246	−	0.965001i	$-0.415537\pi$
$47$	3.59574	0.524492	0.262246	+	0.965001i	$0.415537\pi$
$48$	−3.30526	−0.477073
$49$	1.00000	0.142857
$50$	−1.36970	−0.193704
$51$	7.76609	1.08747
$52$	11.7991	1.63624
$53$	−9.95882	−1.36795	−0.683974	−	0.729506i	$-0.739750\pi$
$53$	−9.95882	−1.36795	−0.683974	+	0.729506i	$0.739750\pi$
$54$	−0.343679	−0.0467688
$55$	5.64782	0.761552
$56$	−1.33412	−0.178280
$57$	−5.12428	−0.678728
$58$	−2.43326	−0.319503
$59$	−9.74289	−1.26842	−0.634208	−	0.773162i	$-0.718674\pi$
$59$	−9.74289	−1.26842	−0.634208	+	0.773162i	$0.718674\pi$
$60$	−1.89558	−0.244718
$61$	−0.441001	−0.0564644	−0.0282322	−	0.999601i	$-0.508988\pi$
$61$	−0.441001	−0.0564644	−0.0282322	+	0.999601i	$0.508988\pi$
$62$	−0.128304	−0.0162947
$63$	1.00000	0.125988
$64$	−5.30310	−0.662887
$65$	6.31546	0.783337
$66$	1.92702	0.237199
$67$	9.96981	1.21801	0.609003	−	0.793168i	$-0.291570\pi$
$67$	9.96981	1.21801	0.609003	+	0.793168i	$0.291570\pi$
$68$	14.6149	1.77231
$69$	4.36612	0.525619
$70$	−0.346179	−0.0413764
$71$	−5.36055	−0.636180	−0.318090	−	0.948060i	$-0.603041\pi$
$71$	−5.36055	−0.636180	−0.318090	+	0.948060i	$0.603041\pi$
$72$	−1.33412	−0.157228
$73$	−10.6741	−1.24931	−0.624654	−	0.780901i	$-0.714760\pi$
$73$	−10.6741	−1.24931	−0.624654	+	0.780901i	$0.714760\pi$
$74$	1.37672	0.160041
$75$	3.98540	0.460194
$76$	−9.64331	−1.10616
$77$	−5.60703	−0.638980
$78$	2.15481	0.243985
$79$	−17.6943	−1.99076	−0.995380	−	0.0960123i	$-0.969391\pi$
$79$	−17.6943	−1.99076	−0.995380	+	0.0960123i	$0.969391\pi$
$80$	−3.32931	−0.372228
$81$	1.00000	0.111111
$82$	0.0101081	0.00111626
$83$	0.590926	0.0648626	0.0324313	−	0.999474i	$-0.489675\pi$
$83$	0.590926	0.0648626	0.0324313	+	0.999474i	$0.489675\pi$
$84$	1.88188	0.205330
$85$	7.82259	0.848479
$86$	2.51239	0.270918
$87$	7.08004	0.759060
$88$	7.48046	0.797420
$89$	4.00039	0.424041	0.212020	−	0.977265i	$-0.431996\pi$
$89$	4.00039	0.424041	0.212020	+	0.977265i	$0.431996\pi$
$90$	−0.346179	−0.0364905
$91$	−6.26985	−0.657258
$92$	8.21654	0.856633
$93$	0.373326	0.0387122
$94$	1.23578	0.127461
$95$	−5.16156	−0.529565
$96$	−3.80419	−0.388264
$97$	−9.11311	−0.925296	−0.462648	−	0.886542i	$-0.653101\pi$
$97$	−9.11311	−0.925296	−0.462648	+	0.886542i	$0.653101\pi$
$98$	0.343679	0.0347168
$99$	−5.60703	−0.563527
$100$	7.50006	0.750006
$101$	−10.6853	−1.06322	−0.531612	−	0.846988i	$-0.678414\pi$
$101$	−10.6853	−1.06322	−0.531612	+	0.846988i	$0.678414\pi$
$102$	2.66904	0.264274
$103$	8.70376	0.857607	0.428803	−	0.903398i	$-0.358935\pi$
$103$	8.70376	0.857607	0.428803	+	0.903398i	$0.358935\pi$
$104$	8.36474	0.820230
$105$	1.00728	0.0983000
$106$	−3.42264	−0.332436
$107$	−5.39543	−0.521596	−0.260798	−	0.965393i	$-0.583986\pi$
$107$	−5.39543	−0.521596	−0.260798	+	0.965393i	$0.583986\pi$
$108$	1.88188	0.181084
$109$	4.20752	0.403007	0.201504	−	0.979488i	$-0.435417\pi$
$109$	4.20752	0.403007	0.201504	+	0.979488i	$0.435417\pi$
$110$	1.94104	0.185071
$111$	−4.00585	−0.380218
$112$	3.30526	0.312318
$113$	−0.734132	−0.0690613	−0.0345307	−	0.999404i	$-0.510994\pi$
$113$	−0.734132	−0.0690613	−0.0345307	+	0.999404i	$0.510994\pi$
$114$	−1.76111	−0.164943
$115$	4.39789	0.410105
$116$	13.3238	1.23709
$117$	−6.26985	−0.579647
$118$	−3.34843	−0.308248
$119$	−7.76609	−0.711916
$120$	−1.34383	−0.122674
$121$	20.4388	1.85807
$122$	−0.151563	−0.0137219
$123$	−0.0294115	−0.00265195
$124$	0.702557	0.0630915
$125$	9.05077	0.809525
$126$	0.343679	0.0306174
$127$	6.24920	0.554527	0.277263	−	0.960794i	$-0.410573\pi$
$127$	6.24920	0.554527	0.277263	+	0.960794i	$0.410573\pi$
$128$	−9.43095	−0.833586
$129$	−7.31028	−0.643634
$130$	2.17049	0.190365
$131$	20.7496	1.81290	0.906449	−	0.422316i	$-0.138783\pi$
$131$	20.7496	1.81290	0.906449	+	0.422316i	$0.138783\pi$
$132$	−10.5518	−0.918414
$133$	5.12428	0.444332
$134$	3.42641	0.295997
$135$	1.00728	0.0866925
$136$	10.3609	0.888440
$137$	0.968419	0.0827376	0.0413688	−	0.999144i	$-0.486828\pi$
$137$	0.968419	0.0827376	0.0413688	+	0.999144i	$0.486828\pi$
$138$	1.50054	0.127735
$139$	4.51438	0.382905	0.191453	−	0.981502i	$-0.438680\pi$
$139$	4.51438	0.382905	0.191453	+	0.981502i	$0.438680\pi$
$140$	1.89558	0.160205
$141$	−3.59574	−0.302816
$142$	−1.84231	−0.154603
$143$	35.1552	2.93982
$144$	3.30526	0.275438
$145$	7.13155	0.592243
$146$	−3.66846	−0.303604
$147$	−1.00000	−0.0824786
$148$	−7.53854	−0.619664
$149$	14.5089	1.18862	0.594308	−	0.804237i	$-0.297426\pi$
$149$	14.5089	1.18862	0.594308	+	0.804237i	$0.297426\pi$
$150$	1.36970	0.111835
$151$	9.41687	0.766334	0.383167	−	0.923679i	$-0.374833\pi$
$151$	9.41687	0.766334	0.383167	+	0.923679i	$0.374833\pi$
$152$	−6.83642	−0.554507
$153$	−7.76609	−0.627851
$154$	−1.92702	−0.155283
$155$	0.376043	0.0302045
$156$	−11.7991	−0.944686
$157$	4.17171	0.332939	0.166470	−	0.986047i	$-0.446763\pi$
$157$	4.17171	0.332939	0.166470	+	0.986047i	$0.446763\pi$
$158$	−6.08115	−0.483790
$159$	9.95882	0.789786
$160$	−3.83187	−0.302936
$161$	−4.36612	−0.344099
$162$	0.343679	0.0270020
$163$	−24.5646	−1.92405	−0.962023	−	0.272968i	$-0.911995\pi$
$163$	−24.5646	−1.92405	−0.962023	+	0.272968i	$0.911995\pi$
$164$	−0.0553491	−0.00432204
$165$	−5.64782	−0.439682
$166$	0.203089	0.0157628
$167$	21.7126	1.68017	0.840087	−	0.542452i	$-0.182504\pi$
$167$	21.7126	1.68017	0.840087	+	0.542452i	$0.182504\pi$
$168$	1.33412	0.102930
$169$	26.3110	2.02392
$170$	2.68846	0.206195
$171$	5.12428	0.391864
$172$	−13.7571	−1.04897
$173$	−3.73528	−0.283988	−0.141994	−	0.989868i	$-0.545351\pi$
$173$	−3.73528	−0.283988	−0.141994	+	0.989868i	$0.545351\pi$
$174$	2.43326	0.184465
$175$	−3.98540	−0.301268
$176$	−18.5327	−1.39695
$177$	9.74289	0.732320
$178$	1.37485	0.103049
$179$	20.6192	1.54115	0.770575	−	0.637350i	$-0.219969\pi$
$179$	20.6192	1.54115	0.770575	+	0.637350i	$0.219969\pi$
$180$	1.89558	0.141288
$181$	4.98851	0.370793	0.185396	−	0.982664i	$-0.440643\pi$
$181$	4.98851	0.370793	0.185396	+	0.982664i	$0.440643\pi$
$182$	−2.15481	−0.159725
$183$	0.441001	0.0325998
$184$	5.82494	0.429420
$185$	−4.03499	−0.296658
$186$	0.128304	0.00940774
$187$	43.5447	3.18430
$188$	−6.76676	−0.493517
$189$	−1.00000	−0.0727393
$190$	−1.77392	−0.128694
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	5.30310	0.382718
$193$	−21.8794	−1.57491	−0.787457	−	0.616369i	$-0.788603\pi$
$193$	−21.8794	−1.57491	−0.787457	+	0.616369i	$0.788603\pi$
$194$	−3.13198	−0.224863
$195$	−6.31546	−0.452260
$196$	−1.88188	−0.134420
$197$	−12.2753	−0.874580	−0.437290	−	0.899321i	$-0.644062\pi$
$197$	−12.2753	−0.874580	−0.437290	+	0.899321i	$0.644062\pi$
$198$	−1.92702	−0.136947
$199$	5.09317	0.361045	0.180523	−	0.983571i	$-0.442221\pi$
$199$	5.09317	0.361045	0.180523	+	0.983571i	$0.442221\pi$
$200$	5.31700	0.375969
$201$	−9.96981	−0.703216
$202$	−3.67230	−0.258382
$203$	−7.08004	−0.496921
$204$	−14.6149	−1.02325
$205$	−0.0296255	−0.00206913
$206$	2.99130	0.208414
$207$	−4.36612	−0.303466
$208$	−20.7235	−1.43691
$209$	−28.7320	−1.98743
$210$	0.346179	0.0238886
$211$	−16.8360	−1.15904	−0.579521	−	0.814958i	$-0.696760\pi$
$211$	−16.8360	−1.15904	−0.579521	+	0.814958i	$0.696760\pi$
$212$	18.7413	1.28716
$213$	5.36055	0.367299
$214$	−1.85429	−0.126757
$215$	−7.36347	−0.502184
$216$	1.33412	0.0907755
$217$	−0.373326	−0.0253431
$218$	1.44604	0.0979379
$219$	10.6741	0.721289
$220$	−10.6285	−0.716577
$221$	48.6922	3.27539
$222$	−1.37672	−0.0923997
$223$	1.69360	0.113412	0.0567060	−	0.998391i	$-0.481940\pi$
$223$	1.69360	0.113412	0.0567060	+	0.998391i	$0.481940\pi$
$224$	3.80419	0.254178
$225$	−3.98540	−0.265693
$226$	−0.252306	−0.0167831
$227$	−0.625032	−0.0414848	−0.0207424	−	0.999785i	$-0.506603\pi$
$227$	−0.625032	−0.0414848	−0.0207424	+	0.999785i	$0.506603\pi$
$228$	9.64331	0.638644
$229$	12.0486	0.796193	0.398097	−	0.917344i	$-0.369671\pi$
$229$	12.0486	0.796193	0.398097	+	0.917344i	$0.369671\pi$
$230$	1.51146	0.0996628
$231$	5.60703	0.368915
$232$	9.44564	0.620136
$233$	−5.06099	−0.331557	−0.165778	−	0.986163i	$-0.553014\pi$
$233$	−5.06099	−0.331557	−0.165778	+	0.986163i	$0.553014\pi$
$234$	−2.15481	−0.140865
$235$	−3.62190	−0.236267
$236$	18.3350	1.19351
$237$	17.6943	1.14937
$238$	−2.66904	−0.173008
$239$	10.8028	0.698777	0.349388	−	0.936978i	$-0.386389\pi$
$239$	10.8028	0.698777	0.349388	+	0.936978i	$0.386389\pi$
$240$	3.32931	0.214906
$241$	−16.6936	−1.07533	−0.537663	−	0.843160i	$-0.680693\pi$
$241$	−16.6936	−1.07533	−0.537663	+	0.843160i	$0.680693\pi$
$242$	7.02437	0.451544
$243$	−1.00000	−0.0641500
$244$	0.829914	0.0531298
$245$	−1.00728	−0.0643525
$246$	−0.0101081	−0.000644470 0
$247$	−32.1285	−2.04428
$248$	0.498063	0.0316270
$249$	−0.590926	−0.0374484
$250$	3.11056	0.196729
$251$	10.3796	0.655157	0.327578	−	0.944824i	$-0.393767\pi$
$251$	10.3796	0.655157	0.327578	+	0.944824i	$0.393767\pi$
$252$	−1.88188	−0.118548
$253$	24.4810	1.53910
$254$	2.14772	0.134760
$255$	−7.82259	−0.489869
$256$	7.36498	0.460311
$257$	17.2555	1.07637	0.538183	−	0.842828i	$-0.319111\pi$
$257$	17.2555	1.07637	0.538183	+	0.842828i	$0.319111\pi$
$258$	−2.51239	−0.156415
$259$	4.00585	0.248911
$260$	−11.8850	−0.737075
$261$	−7.08004	−0.438243
$262$	7.13119	0.440566
$263$	0.765762	0.0472189	0.0236095	−	0.999721i	$-0.492484\pi$
$263$	0.765762	0.0472189	0.0236095	+	0.999721i	$0.492484\pi$
$264$	−7.48046	−0.460390
$265$	10.0313	0.616216
$266$	1.76111	0.107980
$267$	−4.00039	−0.244820
$268$	−18.7620	−1.14607
$269$	−21.4449	−1.30752	−0.653758	−	0.756704i	$-0.726809\pi$
$269$	−21.4449	−1.30752	−0.653758	+	0.756704i	$0.726809\pi$
$270$	0.346179	0.0210678
$271$	−21.0090	−1.27621	−0.638104	−	0.769950i	$-0.720281\pi$
$271$	−21.0090	−1.27621	−0.638104	+	0.769950i	$0.720281\pi$
$272$	−25.6689	−1.55641
$273$	6.26985	0.379468
$274$	0.332825	0.0201067
$275$	22.3462	1.34753
$276$	−8.21654	−0.494577
$277$	22.2987	1.33980	0.669899	−	0.742452i	$-0.266337\pi$
$277$	22.2987	1.33980	0.669899	+	0.742452i	$0.266337\pi$
$278$	1.55150	0.0930527
$279$	−0.373326	−0.0223505
$280$	1.34383	0.0803091
$281$	−27.2876	−1.62784	−0.813922	−	0.580974i	$-0.802672\pi$
$281$	−27.2876	−1.62784	−0.813922	+	0.580974i	$0.802672\pi$
$282$	−1.23578	−0.0735896
$283$	−5.47201	−0.325277	−0.162639	−	0.986686i	$-0.552000\pi$
$283$	−5.47201	−0.325277	−0.162639	+	0.986686i	$0.552000\pi$
$284$	10.0879	0.598609
$285$	5.16156	0.305745
$286$	12.0821	0.714430
$287$	0.0294115	0.00173611
$288$	3.80419	0.224164
$289$	43.3121	2.54777
$290$	2.45096	0.143926
$291$	9.11311	0.534220
$292$	20.0874	1.17553
$293$	33.7085	1.96927	0.984636	−	0.174618i	$-0.0558690\pi$
$293$	33.7085	1.96927	0.984636	+	0.174618i	$0.0558690\pi$
$294$	−0.343679	−0.0200438
$295$	9.81377	0.571380
$296$	−5.34429	−0.310630
$297$	5.60703	0.325353
$298$	4.98641	0.288855
$299$	27.3749	1.58313
$300$	−7.50006	−0.433016
$301$	7.31028	0.421358
$302$	3.23638	0.186233
$303$	10.6853	0.613853
$304$	16.9371	0.971408
$305$	0.444210	0.0254354
$306$	−2.66904	−0.152579
$307$	14.5446	0.830104	0.415052	−	0.909798i	$-0.363763\pi$
$307$	14.5446	0.830104	0.415052	+	0.909798i	$0.363763\pi$
$308$	10.5518	0.601243
$309$	−8.70376	−0.495140
$310$	0.129238	0.00734022
$311$	12.4063	0.703500	0.351750	−	0.936094i	$-0.385587\pi$
$311$	12.4063	0.703500	0.351750	+	0.936094i	$0.385587\pi$
$312$	−8.36474	−0.473560
$313$	−14.8984	−0.842107	−0.421054	−	0.907036i	$-0.638340\pi$
$313$	−14.8984	−0.842107	−0.421054	+	0.907036i	$0.638340\pi$
$314$	1.43373	0.0809101
$315$	−1.00728	−0.0567535
$316$	33.2986	1.87319
$317$	−24.7759	−1.39156	−0.695778	−	0.718257i	$-0.744940\pi$
$317$	−24.7759	−1.39156	−0.695778	+	0.718257i	$0.744940\pi$
$318$	3.42264	0.191932
$319$	39.6980	2.22266
$320$	5.34168	0.298609
$321$	5.39543	0.301143
$322$	−1.50054	−0.0836221
$323$	−39.7956	−2.21429
$324$	−1.88188	−0.104549
$325$	24.9878	1.38607
$326$	−8.44233	−0.467577
$327$	−4.20752	−0.232676
$328$	−0.0392386	−0.00216659
$329$	3.59574	0.198239
$330$	−1.94104	−0.106851
$331$	−4.77288	−0.262341	−0.131170	−	0.991360i	$-0.541874\pi$
$331$	−4.77288	−0.262341	−0.131170	+	0.991360i	$0.541874\pi$
$332$	−1.11205	−0.0610319
$333$	4.00585	0.219519
$334$	7.46217	0.408312
$335$	−10.0423	−0.548672
$336$	−3.30526	−0.180317
$337$	−4.62355	−0.251861	−0.125930	−	0.992039i	$-0.540192\pi$
$337$	−4.62355	−0.251861	−0.125930	+	0.992039i	$0.540192\pi$
$338$	9.04252	0.491849
$339$	0.734132	0.0398726
$340$	−14.7212	−0.798370
$341$	2.09325	0.113356
$342$	1.76111	0.0952298
$343$	1.00000	0.0539949
$344$	−9.75281	−0.525836
$345$	−4.39789	−0.236774
$346$	−1.28374	−0.0690141
$347$	−22.8285	−1.22550	−0.612750	−	0.790277i	$-0.709937\pi$
$347$	−22.8285	−1.22550	−0.612750	+	0.790277i	$0.709937\pi$
$348$	−13.3238	−0.714232
$349$	21.0552	1.12706	0.563531	−	0.826095i	$-0.309443\pi$
$349$	21.0552	1.12706	0.563531	+	0.826095i	$0.309443\pi$
$350$	−1.36970	−0.0732134
$351$	6.26985	0.334660
$352$	−21.3302	−1.13690
$353$	−1.20346	−0.0640540	−0.0320270	−	0.999487i	$-0.510196\pi$
$353$	−1.20346	−0.0640540	−0.0320270	+	0.999487i	$0.510196\pi$
$354$	3.34843	0.177967
$355$	5.39955	0.286578
$356$	−7.52828	−0.398998
$357$	7.76609	0.411025
$358$	7.08638	0.374527
$359$	−19.4862	−1.02844	−0.514222	−	0.857657i	$-0.671919\pi$
$359$	−19.4862	−1.02844	−0.514222	+	0.857657i	$0.671919\pi$
$360$	1.34383	0.0708260
$361$	7.25826	0.382014
$362$	1.71445	0.0901093
$363$	−20.4388	−1.07276
$364$	11.7991	0.618442
$365$	10.7518	0.562773
$366$	0.151563	0.00792232
$367$	−36.3025	−1.89497	−0.947487	−	0.319795i	$-0.896386\pi$
$367$	−36.3025	−1.89497	−0.947487	+	0.319795i	$0.896386\pi$
$368$	−14.4312	−0.752277
$369$	0.0294115	0.00153110
$370$	−1.38674	−0.0720932
$371$	−9.95882	−0.517036
$372$	−0.702557	−0.0364259
$373$	−3.13305	−0.162223	−0.0811115	−	0.996705i	$-0.525847\pi$
$373$	−3.13305	−0.162223	−0.0811115	+	0.996705i	$0.525847\pi$
$374$	14.9654	0.773841
$375$	−9.05077	−0.467380
$376$	−4.79715	−0.247394
$377$	44.3908	2.28624
$378$	−0.343679	−0.0176769
$379$	−13.0575	−0.670717	−0.335359	−	0.942091i	$-0.608857\pi$
$379$	−13.0575	−0.670717	−0.335359	+	0.942091i	$0.608857\pi$
$380$	9.71347	0.498290
$381$	−6.24920	−0.320156
$382$	−0.343679	−0.0175841
$383$	−21.4701	−1.09707	−0.548536	−	0.836127i	$-0.684815\pi$
$383$	−21.4701	−1.09707	−0.548536	+	0.836127i	$0.684815\pi$
$384$	9.43095	0.481271
$385$	5.64782	0.287840
$386$	−7.51949	−0.382732
$387$	7.31028	0.371603
$388$	17.1498	0.870651
$389$	−6.83250	−0.346422	−0.173211	−	0.984885i	$-0.555414\pi$
$389$	−6.83250	−0.346422	−0.173211	+	0.984885i	$0.555414\pi$
$390$	−2.17049	−0.109907
$391$	33.9077	1.71478
$392$	−1.33412	−0.0673833
$393$	−20.7496	−1.04668
$394$	−4.21877	−0.212538
$395$	17.8230	0.896772
$396$	10.5518	0.530247
$397$	−5.91596	−0.296913	−0.148457	−	0.988919i	$-0.547431\pi$
$397$	−5.91596	−0.296913	−0.148457	+	0.988919i	$0.547431\pi$
$398$	1.75041	0.0877403
$399$	−5.12428	−0.256535
$400$	−13.1728	−0.658638
$401$	8.33031	0.415996	0.207998	−	0.978129i	$-0.433305\pi$
$401$	8.33031	0.415996	0.207998	+	0.978129i	$0.433305\pi$
$402$	−3.42641	−0.170894
$403$	2.34070	0.116599
$404$	20.1084	1.00043
$405$	−1.00728	−0.0500519
$406$	−2.43326	−0.120761
$407$	−22.4609	−1.11334
$408$	−10.3609	−0.512941
$409$	−13.9354	−0.689059	−0.344530	−	0.938775i	$-0.611962\pi$
$409$	−13.9354	−0.689059	−0.344530	+	0.938775i	$0.611962\pi$
$410$	−0.0101817	−0.000502836 0
$411$	−0.968419	−0.0477686
$412$	−16.3795	−0.806959
$413$	−9.74289	−0.479416
$414$	−1.50054	−0.0737477
$415$	−0.595225	−0.0292185
$416$	−23.8517	−1.16943
$417$	−4.51438	−0.221070
$418$	−9.87458	−0.482981
$419$	−4.40960	−0.215423	−0.107711	−	0.994182i	$-0.534352\pi$
$419$	−4.40960	−0.215423	−0.107711	+	0.994182i	$0.534352\pi$
$420$	−1.89558	−0.0924947
$421$	10.7531	0.524073	0.262036	−	0.965058i	$-0.415606\pi$
$421$	10.7531	0.524073	0.262036	+	0.965058i	$0.415606\pi$
$422$	−5.78620	−0.281668
$423$	3.59574	0.174831
$424$	13.2863	0.645239
$425$	30.9509	1.50134
$426$	1.84231	0.0892601
$427$	−0.441001	−0.0213415
$428$	10.1536	0.490791
$429$	−35.1552	−1.69731
$430$	−2.53067	−0.122040
$431$	15.4468	0.744046	0.372023	−	0.928223i	$-0.378664\pi$
$431$	15.4468	0.744046	0.372023	+	0.928223i	$0.378664\pi$
$432$	−3.30526	−0.159024
$433$	−35.2936	−1.69610	−0.848051	−	0.529915i	$-0.822224\pi$
$433$	−35.2936	−1.69610	−0.848051	+	0.529915i	$0.822224\pi$
$434$	−0.128304	−0.00615881
$435$	−7.13155	−0.341932
$436$	−7.91807	−0.379207
$437$	−22.3732	−1.07026
$438$	3.66846	0.175286
$439$	−20.5753	−0.982004	−0.491002	−	0.871158i	$-0.663369\pi$
$439$	−20.5753	−0.982004	−0.491002	+	0.871158i	$0.663369\pi$
$440$	−7.53488	−0.359211
$441$	1.00000	0.0476190
$442$	16.7345	0.795978
$443$	−21.5849	−1.02553	−0.512764	−	0.858530i	$-0.671378\pi$
$443$	−21.5849	−1.02553	−0.512764	+	0.858530i	$0.671378\pi$
$444$	7.53854	0.357763
$445$	−4.02950	−0.191016
$446$	0.582056	0.0275611
$447$	−14.5089	−0.686248
$448$	−5.30310	−0.250548
$449$	10.7382	0.506768	0.253384	−	0.967366i	$-0.418456\pi$
$449$	10.7382	0.506768	0.253384	+	0.967366i	$0.418456\pi$
$450$	−1.36970	−0.0645681
$451$	−0.164911	−0.00776536
$452$	1.38155	0.0649827
$453$	−9.41687	−0.442443
$454$	−0.214810	−0.0100816
$455$	6.31546	0.296073
$456$	6.83642	0.320145
$457$	30.5808	1.43051	0.715254	−	0.698864i	$-0.246311\pi$
$457$	30.5808	1.43051	0.715254	+	0.698864i	$0.246311\pi$
$458$	4.14085	0.193489
$459$	7.76609	0.362490
$460$	−8.27632	−0.385885
$461$	18.6376	0.868040	0.434020	−	0.900903i	$-0.357095\pi$
$461$	18.6376	0.868040	0.434020	+	0.900903i	$0.357095\pi$
$462$	1.92702	0.0896530
$463$	−1.50599	−0.0699895	−0.0349948	−	0.999387i	$-0.511141\pi$
$463$	−1.50599	−0.0699895	−0.0349948	+	0.999387i	$0.511141\pi$
$464$	−23.4014	−1.08638
$465$	−0.376043	−0.0174386
$466$	−1.73936	−0.0805741
$467$	−27.9656	−1.29409	−0.647047	−	0.762450i	$-0.723996\pi$
$467$	−27.9656	−1.29409	−0.647047	+	0.762450i	$0.723996\pi$
$468$	11.7991	0.545415
$469$	9.96981	0.460363
$470$	−1.24477	−0.0574170
$471$	−4.17171	−0.192222
$472$	12.9982	0.598291
$473$	−40.9890	−1.88467
$474$	6.08115	0.279316
$475$	−20.4223	−0.937039
$476$	14.6149	0.669872
$477$	−9.95882	−0.455983
$478$	3.71270	0.169815
$479$	12.1360	0.554507	0.277254	−	0.960797i	$-0.410576\pi$
$479$	12.1360	0.554507	0.277254	+	0.960797i	$0.410576\pi$
$480$	3.83187	0.174900
$481$	−25.1160	−1.14519
$482$	−5.73722	−0.261323
$483$	4.36612	0.198665
$484$	−38.4634	−1.74834
$485$	9.17941	0.416816
$486$	−0.343679	−0.0155896
$487$	9.50591	0.430754	0.215377	−	0.976531i	$-0.430902\pi$
$487$	9.50591	0.430754	0.215377	+	0.976531i	$0.430902\pi$
$488$	0.588350	0.0266333
$489$	24.5646	1.11085
$490$	−0.346179	−0.0156388
$491$	13.4015	0.604801	0.302400	−	0.953181i	$-0.402212\pi$
$491$	13.4015	0.604801	0.302400	+	0.953181i	$0.402212\pi$
$492$	0.0553491	0.00249533
$493$	54.9842	2.47636
$494$	−11.0419	−0.496797
$495$	5.64782	0.253851
$496$	−1.23394	−0.0554056
$497$	−5.36055	−0.240454
$498$	−0.203089	−0.00910063
$499$	−37.3262	−1.67095	−0.835474	−	0.549529i	$-0.814807\pi$
$499$	−37.3262	−1.67095	−0.835474	+	0.549529i	$0.814807\pi$
$500$	−17.0325	−0.761717
$501$	−21.7126	−0.970049
$502$	3.56726	0.159215
$503$	−17.5764	−0.783691	−0.391846	−	0.920031i	$-0.628163\pi$
$503$	−17.5764	−0.783691	−0.391846	+	0.920031i	$0.628163\pi$
$504$	−1.33412	−0.0594265
$505$	10.7630	0.478948
$506$	8.41359	0.374030
$507$	−26.3110	−1.16851
$508$	−11.7603	−0.521778
$509$	−29.4529	−1.30547	−0.652737	−	0.757584i	$-0.726380\pi$
$509$	−29.4529	−1.30547	−0.652737	+	0.757584i	$0.726380\pi$
$510$	−2.68846	−0.119047
$511$	−10.6741	−0.472194
$512$	21.3931	0.945450
$513$	−5.12428	−0.226243
$514$	5.93034	0.261576
$515$	−8.76708	−0.386324
$516$	13.7571	0.605623
$517$	−20.1614	−0.886697
$518$	1.37672	0.0604898
$519$	3.73528	0.163960
$520$	−8.42560	−0.369487
$521$	21.7858	0.954453	0.477227	−	0.878780i	$-0.341642\pi$
$521$	21.7858	0.954453	0.477227	+	0.878780i	$0.341642\pi$
$522$	−2.43326	−0.106501
$523$	2.00366	0.0876141	0.0438070	−	0.999040i	$-0.486051\pi$
$523$	2.00366	0.0876141	0.0438070	+	0.999040i	$0.486051\pi$
$524$	−39.0483	−1.70583
$525$	3.98540	0.173937
$526$	0.263176	0.0114750
$527$	2.89929	0.126295
$528$	18.5327	0.806531
$529$	−3.93698	−0.171173
$530$	3.44754	0.149751
$531$	−9.74289	−0.422805
$532$	−9.64331	−0.418090
$533$	−0.184406	−0.00798750
$534$	−1.37485	−0.0594956
$535$	5.43468	0.234962
$536$	−13.3009	−0.574513
$537$	−20.6192	−0.889783
$538$	−7.37015	−0.317750
$539$	−5.60703	−0.241512
$540$	−1.89558	−0.0815726
$541$	−20.3125	−0.873303	−0.436651	−	0.899631i	$-0.643836\pi$
$541$	−20.3125	−0.873303	−0.436651	+	0.899631i	$0.643836\pi$
$542$	−7.22037	−0.310141
$543$	−4.98851	−0.214077
$544$	−29.5437	−1.26668
$545$	−4.23813	−0.181542
$546$	2.15481	0.0922175
$547$	19.0188	0.813184	0.406592	−	0.913610i	$-0.366717\pi$
$547$	19.0188	0.813184	0.406592	+	0.913610i	$0.366717\pi$
$548$	−1.82245	−0.0778513
$549$	−0.441001	−0.0188215
$550$	7.67993	0.327473
$551$	−36.2801	−1.54558
$552$	−5.82494	−0.247926
$553$	−17.6943	−0.752437
$554$	7.66359	0.325595
$555$	4.03499	0.171276
$556$	−8.49555	−0.360292
$557$	15.4507	0.654669	0.327334	−	0.944909i	$-0.393850\pi$
$557$	15.4507	0.654669	0.327334	+	0.944909i	$0.393850\pi$
$558$	−0.128304	−0.00543156
$559$	−45.8343	−1.93859
$560$	−3.32931	−0.140689
$561$	−43.5447	−1.83846
$562$	−9.37819	−0.395595
$563$	23.0178	0.970085	0.485043	−	0.874491i	$-0.338804\pi$
$563$	23.0178	0.970085	0.485043	+	0.874491i	$0.338804\pi$
$564$	6.76676	0.284932
$565$	0.739473	0.0311099
$566$	−1.88062	−0.0790482
$567$	1.00000	0.0419961
$568$	7.15163	0.300076
$569$	−37.0905	−1.55492	−0.777458	−	0.628935i	$-0.783491\pi$
$569$	−37.0905	−1.55492	−0.777458	+	0.628935i	$0.783491\pi$
$570$	1.77392	0.0743014
$571$	−8.22009	−0.344000	−0.172000	−	0.985097i	$-0.555023\pi$
$571$	−8.22009	−0.344000	−0.172000	+	0.985097i	$0.555023\pi$
$572$	−66.1580	−2.76621
$573$	1.00000	0.0417756
$574$	0.0101081	0.000421905 0
$575$	17.4007	0.725660
$576$	−5.30310	−0.220962
$577$	−9.19757	−0.382900	−0.191450	−	0.981502i	$-0.561319\pi$
$577$	−9.19757	−0.382900	−0.191450	+	0.981502i	$0.561319\pi$
$578$	14.8855	0.619153
$579$	21.8794	0.909277
$580$	−13.4208	−0.557267
$581$	0.590926	0.0245157
$582$	3.13198	0.129825
$583$	55.8394	2.31263
$584$	14.2406	0.589278
$585$	6.31546	0.261112
$586$	11.5849	0.478568
$587$	1.04741	0.0432313	0.0216157	−	0.999766i	$-0.493119\pi$
$587$	1.04741	0.0432313	0.0216157	+	0.999766i	$0.493119\pi$
$588$	1.88188	0.0776076
$589$	−1.91303	−0.0788250
$590$	3.37279	0.138855
$591$	12.2753	0.504939
$592$	13.2404	0.544175
$593$	33.0699	1.35802	0.679010	−	0.734129i	$-0.262409\pi$
$593$	33.0699	1.35802	0.679010	+	0.734129i	$0.262409\pi$
$594$	1.92702	0.0790665
$595$	7.82259	0.320695
$596$	−27.3041	−1.11842
$597$	−5.09317	−0.208449
$598$	9.40818	0.384729
$599$	20.4798	0.836782	0.418391	−	0.908267i	$-0.362594\pi$
$599$	20.4798	0.836782	0.418391	+	0.908267i	$0.362594\pi$
$600$	−5.31700	−0.217066
$601$	26.8813	1.09651	0.548255	−	0.836311i	$-0.315292\pi$
$601$	26.8813	1.09651	0.548255	+	0.836311i	$0.315292\pi$
$602$	2.51239	0.102397
$603$	9.96981	0.406002
$604$	−17.7215	−0.721076
$605$	−20.5875	−0.836999
$606$	3.67230	0.149177
$607$	10.7001	0.434302	0.217151	−	0.976138i	$-0.430324\pi$
$607$	10.7001	0.434302	0.217151	+	0.976138i	$0.430324\pi$
$608$	19.4938	0.790576
$609$	7.08004	0.286898
$610$	0.152666	0.00618125
$611$	−22.5447	−0.912062
$612$	14.6149	0.590771
$613$	−6.82881	−0.275813	−0.137907	−	0.990445i	$-0.544037\pi$
$613$	−6.82881	−0.275813	−0.137907	+	0.990445i	$0.544037\pi$
$614$	4.99867	0.201730
$615$	0.0296255	0.00119462
$616$	7.48046	0.301396
$617$	26.0235	1.04767	0.523834	−	0.851820i	$-0.324501\pi$
$617$	26.0235	1.04767	0.523834	+	0.851820i	$0.324501\pi$
$618$	−2.99130	−0.120328
$619$	24.3309	0.977942	0.488971	−	0.872300i	$-0.337372\pi$
$619$	24.3309	0.977942	0.488971	+	0.872300i	$0.337372\pi$
$620$	−0.707669	−0.0284207
$621$	4.36612	0.175206
$622$	4.26380	0.170963
$623$	4.00039	0.160272
$624$	20.7235	0.829603
$625$	10.8104	0.432415
$626$	−5.12027	−0.204647
$627$	28.7320	1.14744
$628$	−7.85069	−0.313276
$629$	−31.1097	−1.24043
$630$	−0.346179	−0.0137921
$631$	−21.8642	−0.870401	−0.435200	−	0.900334i	$-0.643323\pi$
$631$	−21.8642	−0.870401	−0.435200	+	0.900334i	$0.643323\pi$
$632$	23.6063	0.939009
$633$	16.8360	0.669173
$634$	−8.51497	−0.338173
$635$	−6.29467	−0.249796
$636$	−18.7413	−0.743143
$637$	−6.26985	−0.248420
$638$	13.6434	0.540146
$639$	−5.36055	−0.212060
$640$	9.49956	0.375503
$641$	−27.2142	−1.07489	−0.537447	−	0.843297i	$-0.680611\pi$
$641$	−27.2142	−1.07489	−0.537447	+	0.843297i	$0.680611\pi$
$642$	1.85429	0.0731832
$643$	42.6981	1.68385	0.841925	−	0.539595i	$-0.181422\pi$
$643$	42.6981	1.68385	0.841925	+	0.539595i	$0.181422\pi$
$644$	8.21654	0.323777
$645$	7.36347	0.289936
$646$	−13.6769	−0.538111
$647$	−46.4586	−1.82648	−0.913238	−	0.407426i	$-0.866426\pi$
$647$	−46.4586	−1.82648	−0.913238	+	0.407426i	$0.866426\pi$
$648$	−1.33412	−0.0524093
$649$	54.6286	2.14436
$650$	8.58779	0.336841
$651$	0.373326	0.0146318
$652$	46.2277	1.81042
$653$	−1.73655	−0.0679563	−0.0339782	−	0.999423i	$-0.510818\pi$
$653$	−1.73655	−0.0679563	−0.0339782	+	0.999423i	$0.510818\pi$
$654$	−1.44604	−0.0565445
$655$	−20.9005	−0.816651
$656$	0.0972127	0.00379552
$657$	−10.6741	−0.416436
$658$	1.23578	0.0481757
$659$	0.204522	0.00796706	0.00398353	−	0.999992i	$-0.498732\pi$
$659$	0.204522	0.00796706	0.00398353	+	0.999992i	$0.498732\pi$
$660$	10.6285	0.413716
$661$	28.3633	1.10321	0.551603	−	0.834107i	$-0.314016\pi$
$661$	28.3633	1.10321	0.551603	+	0.834107i	$0.314016\pi$
$662$	−1.64034	−0.0637535
$663$	−48.6922	−1.89105
$664$	−0.788368	−0.0305946
$665$	−5.16156	−0.200157
$666$	1.37672	0.0533470
$667$	30.9123	1.19693
$668$	−40.8607	−1.58095
$669$	−1.69360	−0.0654785
$670$	−3.45134	−0.133337
$671$	2.47271	0.0954578
$672$	−3.80419	−0.146750
$673$	−36.2345	−1.39674	−0.698368	−	0.715739i	$-0.746090\pi$
$673$	−36.2345	−1.39674	−0.698368	+	0.715739i	$0.746090\pi$
$674$	−1.58902	−0.0612066
$675$	3.98540	0.153398
$676$	−49.5142	−1.90439
$677$	−32.5762	−1.25201	−0.626003	−	0.779820i	$-0.715310\pi$
$677$	−32.5762	−1.25201	−0.626003	+	0.779820i	$0.715310\pi$
$678$	0.252306	0.00968974
$679$	−9.11311	−0.349729
$680$	−10.4363	−0.400213
$681$	0.625032	0.0239513
$682$	0.719407	0.0275475
$683$	−46.8132	−1.79126	−0.895628	−	0.444803i	$-0.853274\pi$
$683$	−46.8132	−1.79126	−0.895628	+	0.444803i	$0.853274\pi$
$684$	−9.64331	−0.368721
$685$	−0.975465	−0.0372706
$686$	0.343679	0.0131217
$687$	−12.0486	−0.459682
$688$	24.1624	0.921182
$689$	62.4403	2.37878
$690$	−1.51146	−0.0575403
$691$	−1.82688	−0.0694978	−0.0347489	−	0.999396i	$-0.511063\pi$
$691$	−1.82688	−0.0694978	−0.0347489	+	0.999396i	$0.511063\pi$
$692$	7.02936	0.267216
$693$	−5.60703	−0.212993
$694$	−7.84569	−0.297818
$695$	−4.54723	−0.172486
$696$	−9.44564	−0.358036
$697$	−0.228412	−0.00865174
$698$	7.23625	0.273896
$699$	5.06099	0.191424
$700$	7.50006	0.283475
$701$	−12.7083	−0.479987	−0.239993	−	0.970775i	$-0.577145\pi$
$701$	−12.7083	−0.479987	−0.239993	+	0.970775i	$0.577145\pi$
$702$	2.15481	0.0813282
$703$	20.5271	0.774193
$704$	29.7346	1.12067
$705$	3.62190	0.136409
$706$	−0.413605	−0.0155662
$707$	−10.6853	−0.401861
$708$	−18.3350	−0.689071
$709$	47.1959	1.77248	0.886239	−	0.463228i	$-0.153309\pi$
$709$	47.1959	1.77248	0.886239	+	0.463228i	$0.153309\pi$
$710$	1.85571	0.0696436
$711$	−17.6943	−0.663587
$712$	−5.33701	−0.200013
$713$	1.62999	0.0610436
$714$	2.66904	0.0998863
$715$	−35.4110	−1.32430
$716$	−38.8029	−1.45013
$717$	−10.8028	−0.403439
$718$	−6.69701	−0.249930
$719$	28.5686	1.06543	0.532714	−	0.846295i	$-0.321172\pi$
$719$	28.5686	1.06543	0.532714	+	0.846295i	$0.321172\pi$
$720$	−3.32931	−0.124076
$721$	8.70376	0.324145
$722$	2.49451	0.0928361
$723$	16.6936	0.620840
$724$	−9.38780	−0.348895
$725$	28.2168	1.04794
$726$	−7.02437	−0.260699
$727$	−6.50220	−0.241153	−0.120577	−	0.992704i	$-0.538474\pi$
$727$	−6.50220	−0.241153	−0.120577	+	0.992704i	$0.538474\pi$
$728$	8.36474	0.310018
$729$	1.00000	0.0370370
$730$	3.69515	0.136764
$731$	−56.7723	−2.09980
$732$	−0.829914	−0.0306745
$733$	24.7303	0.913434	0.456717	−	0.889612i	$-0.349025\pi$
$733$	24.7303	0.913434	0.456717	+	0.889612i	$0.349025\pi$
$734$	−12.4764	−0.460512
$735$	1.00728	0.0371539
$736$	−16.6096	−0.612237
$737$	−55.9010	−2.05914
$738$	0.0101081	0.000372085 0
$739$	−12.4841	−0.459235	−0.229617	−	0.973281i	$-0.573748\pi$
$739$	−12.4841	−0.459235	−0.229617	+	0.973281i	$0.573748\pi$
$740$	7.59339	0.279138
$741$	32.1285	1.18027
$742$	−3.42264	−0.125649
$743$	−36.6703	−1.34530	−0.672651	−	0.739960i	$-0.734844\pi$
$743$	−36.6703	−1.34530	−0.672651	+	0.739960i	$0.734844\pi$
$744$	−0.498063	−0.0182599
$745$	−14.6145	−0.535433
$746$	−1.07676	−0.0394231
$747$	0.590926	0.0216209
$748$	−81.9460	−2.99624
$749$	−5.39543	−0.197145
$750$	−3.11056	−0.113582
$751$	−2.11612	−0.0772185	−0.0386092	−	0.999254i	$-0.512293\pi$
$751$	−2.11612	−0.0772185	−0.0386092	+	0.999254i	$0.512293\pi$
$752$	11.8848	0.433396
$753$	−10.3796	−0.378255
$754$	15.2562	0.555597
$755$	−9.48538	−0.345208
$756$	1.88188	0.0684435
$757$	−32.1402	−1.16815	−0.584077	−	0.811698i	$-0.698544\pi$
$757$	−32.1402	−1.16815	−0.584077	+	0.811698i	$0.698544\pi$
$758$	−4.48758	−0.162996
$759$	−24.4810	−0.888603
$760$	6.88616	0.249787
$761$	−12.1749	−0.441341	−0.220671	−	0.975348i	$-0.570825\pi$
$761$	−12.1749	−0.441341	−0.220671	+	0.975348i	$0.570825\pi$
$762$	−2.14772	−0.0778036
$763$	4.20752	0.152322
$764$	1.88188	0.0680842
$765$	7.82259	0.282826
$766$	−7.37883	−0.266608
$767$	61.0864	2.20570
$768$	−7.36498	−0.265761
$769$	−9.48311	−0.341970	−0.170985	−	0.985274i	$-0.554695\pi$
$769$	−9.48311	−0.341970	−0.170985	+	0.985274i	$0.554695\pi$
$770$	1.94104	0.0699501
$771$	−17.2555	−0.621440
$772$	41.1745	1.48190
$773$	−7.86064	−0.282727	−0.141364	−	0.989958i	$-0.545149\pi$
$773$	−7.86064	−0.282727	−0.141364	+	0.989958i	$0.545149\pi$
$774$	2.51239	0.0903060
$775$	1.48785	0.0534453
$776$	12.1580	0.436447
$777$	−4.00585	−0.143709
$778$	−2.34819	−0.0841866
$779$	0.150713	0.00539985
$780$	11.8850	0.425550
$781$	30.0567	1.07551
$782$	11.6534	0.416723
$783$	7.08004	0.253020
$784$	3.30526	0.118045
$785$	−4.20207	−0.149978
$786$	−7.13119	−0.254361
$787$	49.5518	1.76633	0.883165	−	0.469062i	$-0.155408\pi$
$787$	49.5518	1.76633	0.883165	+	0.469062i	$0.155408\pi$
$788$	23.1007	0.822929
$789$	−0.765762	−0.0272619
$790$	6.12539	0.217932
$791$	−0.734132	−0.0261027
$792$	7.48046	0.265807
$793$	2.76501	0.0981884
$794$	−2.03319	−0.0721552
$795$	−10.0313	−0.355773
$796$	−9.58475	−0.339723
$797$	−29.8239	−1.05642	−0.528209	−	0.849115i	$-0.677136\pi$
$797$	−29.8239	−1.05642	−0.528209	+	0.849115i	$0.677136\pi$
$798$	−1.76111	−0.0623425
$799$	−27.9248	−0.987909
$800$	−15.1612	−0.536030
$801$	4.00039	0.141347
$802$	2.86295	0.101094
$803$	59.8500	2.11206
$804$	18.7620	0.661686
$805$	4.39789	0.155005
$806$	0.804449	0.0283355
$807$	21.4449	0.754895
$808$	14.2555	0.501505
$809$	−9.90991	−0.348414	−0.174207	−	0.984709i	$-0.555736\pi$
$809$	−9.90991	−0.348414	−0.174207	+	0.984709i	$0.555736\pi$
$810$	−0.346179	−0.0121635
$811$	−46.7218	−1.64063	−0.820313	−	0.571915i	$-0.806201\pi$
$811$	−46.7218	−1.64063	−0.820313	+	0.571915i	$0.806201\pi$
$812$	13.3238	0.467574
$813$	21.0090	0.736819
$814$	−7.71933	−0.270562
$815$	24.7433	0.866720
$816$	25.6689	0.898592
$817$	37.4599	1.31056
$818$	−4.78929	−0.167454
$819$	−6.26985	−0.219086
$820$	0.0557518	0.00194694
$821$	13.1359	0.458447	0.229224	−	0.973374i	$-0.426381\pi$
$821$	13.1359	0.458447	0.229224	+	0.973374i	$0.426381\pi$
$822$	−0.332825	−0.0116086
$823$	13.3854	0.466585	0.233292	−	0.972407i	$-0.425050\pi$
$823$	13.3854	0.466585	0.233292	+	0.972407i	$0.425050\pi$
$824$	−11.6119	−0.404519
$825$	−22.3462	−0.777996
$826$	−3.34843	−0.116507
$827$	−29.3329	−1.02000	−0.510002	−	0.860173i	$-0.670356\pi$
$827$	−29.3329	−1.02000	−0.510002	+	0.860173i	$0.670356\pi$
$828$	8.21654	0.285544
$829$	48.1109	1.67096	0.835481	−	0.549520i	$-0.185189\pi$
$829$	48.1109	1.67096	0.835481	+	0.549520i	$0.185189\pi$
$830$	−0.204566	−0.00710061
$831$	−22.2987	−0.773533
$832$	33.2496	1.15272
$833$	−7.76609	−0.269079
$834$	−1.55150	−0.0537240
$835$	−21.8706	−0.756863
$836$	54.0703	1.87006
$837$	0.373326	0.0129041
$838$	−1.51549	−0.0523516
$839$	0.297926	0.0102855	0.00514277	−	0.999987i	$-0.498363\pi$
$839$	0.297926	0.0102855	0.00514277	+	0.999987i	$0.498363\pi$
$840$	−1.34383	−0.0463665
$841$	21.1270	0.728516
$842$	3.69560	0.127359
$843$	27.2876	0.939836
$844$	31.6835	1.09059
$845$	−26.5024	−0.911710
$846$	1.23578	0.0424870
$847$	20.4388	0.702284
$848$	−32.9165	−1.13036
$849$	5.47201	0.187799
$850$	10.6372	0.364852
$851$	−17.4900	−0.599550
$852$	−10.0879	−0.345607
$853$	−33.6432	−1.15192	−0.575960	−	0.817478i	$-0.695372\pi$
$853$	−33.6432	−1.15192	−0.575960	+	0.817478i	$0.695372\pi$
$854$	−0.151563	−0.00518637
$855$	−5.16156	−0.176522
$856$	7.19816	0.246028
$857$	29.3909	1.00397	0.501986	−	0.864876i	$-0.332603\pi$
$857$	29.3909	1.00397	0.501986	+	0.864876i	$0.332603\pi$
$858$	−12.0821	−0.412476
$859$	42.3077	1.44352	0.721761	−	0.692143i	$-0.243333\pi$
$859$	42.3077	1.44352	0.721761	+	0.692143i	$0.243333\pi$
$860$	13.8572	0.472527
$861$	−0.0294115	−0.00100234
$862$	5.30874	0.180816
$863$	−30.6992	−1.04501	−0.522506	−	0.852636i	$-0.675003\pi$
$863$	−30.6992	−1.04501	−0.522506	+	0.852636i	$0.675003\pi$
$864$	−3.80419	−0.129421
$865$	3.76245	0.127927
$866$	−12.1297	−0.412183
$867$	−43.3121	−1.47096
$868$	0.702557	0.0238464
$869$	99.2122	3.36554
$870$	−2.45096	−0.0830955
$871$	−62.5092	−2.11804
$872$	−5.61335	−0.190092
$873$	−9.11311	−0.308432
$874$	−7.68921	−0.260091
$875$	9.05077	0.305972
$876$	−20.0874	−0.678691
$877$	−58.4249	−1.97287	−0.986435	−	0.164155i	$-0.947510\pi$
$877$	−58.4249	−1.97287	−0.986435	+	0.164155i	$0.947510\pi$
$878$	−7.07129	−0.238644
$879$	−33.7085	−1.13696
$880$	18.6675	0.629282
$881$	8.01205	0.269933	0.134966	−	0.990850i	$-0.456907\pi$
$881$	8.01205	0.269933	0.134966	+	0.990850i	$0.456907\pi$
$882$	0.343679	0.0115723
$883$	5.43759	0.182989	0.0914947	−	0.995806i	$-0.470836\pi$
$883$	5.43759	0.182989	0.0914947	+	0.995806i	$0.470836\pi$
$884$	−91.6330	−3.08195
$885$	−9.81377	−0.329886
$886$	−7.41826	−0.249221
$887$	32.8194	1.10197	0.550983	−	0.834516i	$-0.314253\pi$
$887$	32.8194	1.10197	0.550983	+	0.834516i	$0.314253\pi$
$888$	5.34429	0.179343
$889$	6.24920	0.209591
$890$	−1.38485	−0.0464204
$891$	−5.60703	−0.187842
$892$	−3.18717	−0.106714
$893$	18.4256	0.616588
$894$	−4.98641	−0.166770
$895$	−20.7692	−0.694237
$896$	−9.43095	−0.315066
$897$	−27.3749	−0.914022
$898$	3.69050	0.123153
$899$	2.64317	0.0881545
$900$	7.50006	0.250002
$901$	77.3410	2.57660
$902$	−0.0566765	−0.00188712
$903$	−7.31028	−0.243271
$904$	0.979421	0.0325751
$905$	−5.02480	−0.167030
$906$	−3.23638	−0.107522
$907$	33.8193	1.12295	0.561476	−	0.827493i	$-0.310234\pi$
$907$	33.8193	1.12295	0.561476	+	0.827493i	$0.310234\pi$
$908$	1.17624	0.0390348
$909$	−10.6853	−0.354408
$910$	2.17049	0.0719511
$911$	−35.0479	−1.16119	−0.580595	−	0.814193i	$-0.697180\pi$
$911$	−35.0479	−1.16119	−0.580595	+	0.814193i	$0.697180\pi$
$912$	−16.9371	−0.560843
$913$	−3.31334	−0.109656
$914$	10.5100	0.347639
$915$	−0.444210	−0.0146851
$916$	−22.6741	−0.749172
$917$	20.7496	0.685211
$918$	2.66904	0.0880915
$919$	−29.6822	−0.979127	−0.489563	−	0.871968i	$-0.662844\pi$
$919$	−29.6822	−0.979127	−0.489563	+	0.871968i	$0.662844\pi$
$920$	−5.86732	−0.193440
$921$	−14.5446	−0.479261
$922$	6.40535	0.210949
$923$	33.6098	1.10628
$924$	−10.5518	−0.347128
$925$	−15.9649	−0.524922
$926$	−0.517579	−0.0170087
$927$	8.70376	0.285869
$928$	−26.9338	−0.884146
$929$	30.1886	0.990456	0.495228	−	0.868763i	$-0.335085\pi$
$929$	30.1886	0.990456	0.495228	+	0.868763i	$0.335085\pi$
$930$	−0.129238	−0.00423788
$931$	5.12428	0.167942
$932$	9.52421	0.311976
$933$	−12.4063	−0.406166
$934$	−9.61119	−0.314488
$935$	−43.8615	−1.43442
$936$	8.36474	0.273410
$937$	51.3495	1.67751	0.838757	−	0.544506i	$-0.183283\pi$
$937$	51.3495	1.67751	0.838757	+	0.544506i	$0.183283\pi$
$938$	3.42641	0.111876
$939$	14.8984	0.486191
$940$	6.81600	0.222313
$941$	−11.3414	−0.369718	−0.184859	−	0.982765i	$-0.559183\pi$
$941$	−11.3414	−0.369718	−0.184859	+	0.982765i	$0.559183\pi$
$942$	−1.43373	−0.0467135
$943$	−0.128414	−0.00418174
$944$	−32.2028	−1.04811
$945$	1.00728	0.0327667
$946$	−14.0870	−0.458009
$947$	8.81635	0.286493	0.143246	−	0.989687i	$-0.454246\pi$
$947$	8.81635	0.286493	0.143246	+	0.989687i	$0.454246\pi$
$948$	−33.2986	−1.08149
$949$	66.9250	2.17248
$950$	−7.01871	−0.227717
$951$	24.7759	0.803415
$952$	10.3609	0.335799
$953$	−10.5304	−0.341113	−0.170557	−	0.985348i	$-0.554557\pi$
$953$	−10.5304	−0.341113	−0.170557	+	0.985348i	$0.554557\pi$
$954$	−3.42264	−0.110812
$955$	1.00728	0.0325947
$956$	−20.3297	−0.657509
$957$	−39.6980	−1.28325
$958$	4.17088	0.134755
$959$	0.968419	0.0312719
$960$	−5.34168	−0.172402
$961$	−30.8606	−0.995504
$962$	−8.63185	−0.278302
$963$	−5.39543	−0.173865
$964$	31.4153	1.01182
$965$	22.0386	0.709448
$966$	1.50054	0.0482792
$967$	−37.6673	−1.21130	−0.605649	−	0.795732i	$-0.707086\pi$
$967$	−37.6673	−1.21130	−0.605649	+	0.795732i	$0.707086\pi$
$968$	−27.2678	−0.876420
$969$	39.7956	1.27842
$970$	3.15477	0.101294
$971$	−9.76647	−0.313421	−0.156710	−	0.987645i	$-0.550089\pi$
$971$	−9.76647	−0.313421	−0.156710	+	0.987645i	$0.550089\pi$
$972$	1.88188	0.0603615
$973$	4.51438	0.144725
$974$	3.26698	0.104681
$975$	−24.9878	−0.800251
$976$	−1.45762	−0.0466574
$977$	−36.1790	−1.15747	−0.578734	−	0.815516i	$-0.696453\pi$
$977$	−36.1790	−1.15747	−0.578734	+	0.815516i	$0.696453\pi$
$978$	8.44233	0.269956
$979$	−22.4303	−0.716876
$980$	1.89558	0.0605520
$981$	4.20752	0.134336
$982$	4.60581	0.146977
$983$	−11.2344	−0.358323	−0.179161	−	0.983820i	$-0.557338\pi$
$983$	−11.2344	−0.358323	−0.179161	+	0.983820i	$0.557338\pi$
$984$	0.0392386	0.00125088
$985$	12.3646	0.393970
$986$	18.8969	0.601800
$987$	−3.59574	−0.114454
$988$	60.4620	1.92355
$989$	−31.9176	−1.01492
$990$	1.94104	0.0616902
$991$	−46.9885	−1.49264	−0.746319	−	0.665588i	$-0.768181\pi$
$991$	−46.9885	−1.49264	−0.746319	+	0.665588i	$0.768181\pi$
$992$	−1.42021	−0.0450916
$993$	4.77288	0.151463
$994$	−1.84231	−0.0584345
$995$	−5.13022	−0.162639
$996$	1.11205	0.0352368
$997$	−11.1462	−0.353003	−0.176502	−	0.984300i	$-0.556478\pi$
$997$	−11.1462	−0.353003	−0.176502	+	0.984300i	$0.556478\pi$
$998$	−12.8282	−0.406070
$999$	−4.00585	−0.126739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.17	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.17	✓	28	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.343679 q^{2} -1.00000 q^{3} -1.88188 q^{4} -1.00728 q^{5} -0.343679 q^{6} +1.00000 q^{7} -1.33412 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.343679 q^{2} -1.00000 q^{3} -1.88188 q^{4} -1.00728 q^{5} -0.343679 q^{6} +1.00000 q^{7} -1.33412 q^{8} +1.00000 q^{9} -0.346179 q^{10} -5.60703 q^{11} +1.88188 q^{12} -6.26985 q^{13} +0.343679 q^{14} +1.00728 q^{15} +3.30526 q^{16} -7.76609 q^{17} +0.343679 q^{18} +5.12428 q^{19} +1.89558 q^{20} -1.00000 q^{21} -1.92702 q^{22} -4.36612 q^{23} +1.33412 q^{24} -3.98540 q^{25} -2.15481 q^{26} -1.00000 q^{27} -1.88188 q^{28} -7.08004 q^{29} +0.346179 q^{30} -0.373326 q^{31} +3.80419 q^{32} +5.60703 q^{33} -2.66904 q^{34} -1.00728 q^{35} -1.88188 q^{36} +4.00585 q^{37} +1.76111 q^{38} +6.26985 q^{39} +1.34383 q^{40} +0.0294115 q^{41} -0.343679 q^{42} +7.31028 q^{43} +10.5518 q^{44} -1.00728 q^{45} -1.50054 q^{46} +3.59574 q^{47} -3.30526 q^{48} +1.00000 q^{49} -1.36970 q^{50} +7.76609 q^{51} +11.7991 q^{52} -9.95882 q^{53} -0.343679 q^{54} +5.64782 q^{55} -1.33412 q^{56} -5.12428 q^{57} -2.43326 q^{58} -9.74289 q^{59} -1.89558 q^{60} -0.441001 q^{61} -0.128304 q^{62} +1.00000 q^{63} -5.30310 q^{64} +6.31546 q^{65} +1.92702 q^{66} +9.96981 q^{67} +14.6149 q^{68} +4.36612 q^{69} -0.346179 q^{70} -5.36055 q^{71} -1.33412 q^{72} -10.6741 q^{73} +1.37672 q^{74} +3.98540 q^{75} -9.64331 q^{76} -5.60703 q^{77} +2.15481 q^{78} -17.6943 q^{79} -3.32931 q^{80} +1.00000 q^{81} +0.0101081 q^{82} +0.590926 q^{83} +1.88188 q^{84} +7.82259 q^{85} +2.51239 q^{86} +7.08004 q^{87} +7.48046 q^{88} +4.00039 q^{89} -0.346179 q^{90} -6.26985 q^{91} +8.21654 q^{92} +0.373326 q^{93} +1.23578 q^{94} -5.16156 q^{95} -3.80419 q^{96} -9.11311 q^{97} +0.343679 q^{98} -5.60703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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