LMFDB - Embedded newform 6041.2.a.d.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.15616 q^{2} -2.99968 q^{3} +2.64901 q^{4} -1.14985 q^{5} +6.46779 q^{6} -1.00000 q^{7} -1.39937 q^{8} +5.99811 q^{9} +O(q^{10})$	\(q-2.15616 q^{2} -2.99968 q^{3} +2.64901 q^{4} -1.14985 q^{5} +6.46779 q^{6} -1.00000 q^{7} -1.39937 q^{8} +5.99811 q^{9} +2.47926 q^{10} -3.56048 q^{11} -7.94620 q^{12} +5.35378 q^{13} +2.15616 q^{14} +3.44919 q^{15} -2.28076 q^{16} +2.86945 q^{17} -12.9329 q^{18} +3.40765 q^{19} -3.04597 q^{20} +2.99968 q^{21} +7.67695 q^{22} -3.56649 q^{23} +4.19767 q^{24} -3.67784 q^{25} -11.5436 q^{26} -8.99337 q^{27} -2.64901 q^{28} +6.78374 q^{29} -7.43700 q^{30} -3.56514 q^{31} +7.71642 q^{32} +10.6803 q^{33} -6.18699 q^{34} +1.14985 q^{35} +15.8891 q^{36} -4.12275 q^{37} -7.34744 q^{38} -16.0596 q^{39} +1.60907 q^{40} +5.76111 q^{41} -6.46779 q^{42} -4.18460 q^{43} -9.43175 q^{44} -6.89693 q^{45} +7.68992 q^{46} +4.79867 q^{47} +6.84156 q^{48} +1.00000 q^{49} +7.93000 q^{50} -8.60746 q^{51} +14.1822 q^{52} +0.0998902 q^{53} +19.3911 q^{54} +4.09402 q^{55} +1.39937 q^{56} -10.2219 q^{57} -14.6268 q^{58} -5.81104 q^{59} +9.13695 q^{60} -9.28429 q^{61} +7.68700 q^{62} -5.99811 q^{63} -12.0763 q^{64} -6.15605 q^{65} -23.0284 q^{66} -7.45950 q^{67} +7.60122 q^{68} +10.6984 q^{69} -2.47926 q^{70} -10.8765 q^{71} -8.39357 q^{72} -2.84026 q^{73} +8.88929 q^{74} +11.0324 q^{75} +9.02691 q^{76} +3.56048 q^{77} +34.6271 q^{78} -4.25972 q^{79} +2.62254 q^{80} +8.98297 q^{81} -12.4218 q^{82} +10.3596 q^{83} +7.94620 q^{84} -3.29945 q^{85} +9.02265 q^{86} -20.3491 q^{87} +4.98243 q^{88} -9.38564 q^{89} +14.8709 q^{90} -5.35378 q^{91} -9.44768 q^{92} +10.6943 q^{93} -10.3467 q^{94} -3.91830 q^{95} -23.1468 q^{96} -1.09618 q^{97} -2.15616 q^{98} -21.3561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−2.15616	−1.52463	−0.762316	−	0.647204i	$-0.775938\pi$
$2$	−2.15616	−1.52463	−0.762316	+	0.647204i	$0.775938\pi$
$3$	−2.99968	−1.73187	−0.865934	−	0.500158i	$-0.833275\pi$
$3$	−2.99968	−1.73187	−0.865934	+	0.500158i	$0.833275\pi$
$4$	2.64901	1.32451
$5$	−1.14985	−0.514229	−0.257115	−	0.966381i	$-0.582772\pi$
$5$	−1.14985	−0.514229	−0.257115	+	0.966381i	$0.582772\pi$
$6$	6.46779	2.64046
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.39937	−0.494752
$9$	5.99811	1.99937
$10$	2.47926	0.784011
$11$	−3.56048	−1.07352	−0.536762	−	0.843733i	$-0.680353\pi$
$11$	−3.56048	−1.07352	−0.536762	+	0.843733i	$0.680353\pi$
$12$	−7.94620	−2.29387
$13$	5.35378	1.48487	0.742436	−	0.669917i	$-0.233670\pi$
$13$	5.35378	1.48487	0.742436	+	0.669917i	$0.233670\pi$
$14$	2.15616	0.576257
$15$	3.44919	0.890578
$16$	−2.28076	−0.570190
$17$	2.86945	0.695945	0.347972	−	0.937505i	$-0.386870\pi$
$17$	2.86945	0.695945	0.347972	+	0.937505i	$0.386870\pi$
$18$	−12.9329	−3.04830
$19$	3.40765	0.781769	0.390885	−	0.920440i	$-0.372169\pi$
$19$	3.40765	0.781769	0.390885	+	0.920440i	$0.372169\pi$
$20$	−3.04597	−0.681100
$21$	2.99968	0.654585
$22$	7.67695	1.63673
$23$	−3.56649	−0.743665	−0.371833	−	0.928300i	$-0.621270\pi$
$23$	−3.56649	−0.743665	−0.371833	+	0.928300i	$0.621270\pi$
$24$	4.19767	0.856846
$25$	−3.67784	−0.735568
$26$	−11.5436	−2.26388
$27$	−8.99337	−1.73078
$28$	−2.64901	−0.500616
$29$	6.78374	1.25971	0.629855	−	0.776713i	$-0.283114\pi$
$29$	6.78374	1.25971	0.629855	+	0.776713i	$0.283114\pi$
$30$	−7.43700	−1.35780
$31$	−3.56514	−0.640318	−0.320159	−	0.947364i	$-0.603736\pi$
$31$	−3.56514	−0.640318	−0.320159	+	0.947364i	$0.603736\pi$
$32$	7.71642	1.36408
$33$	10.6803	1.85920
$34$	−6.18699	−1.06106
$35$	1.14985	0.194360
$36$	15.8891	2.64818
$37$	−4.12275	−0.677776	−0.338888	−	0.940827i	$-0.610051\pi$
$37$	−4.12275	−0.677776	−0.338888	+	0.940827i	$0.610051\pi$
$38$	−7.34744	−1.19191
$39$	−16.0596	−2.57160
$40$	1.60907	0.254416
$41$	5.76111	0.899734	0.449867	−	0.893096i	$-0.351471\pi$
$41$	5.76111	0.899734	0.449867	+	0.893096i	$0.351471\pi$
$42$	−6.46779	−0.998002
$43$	−4.18460	−0.638145	−0.319073	−	0.947730i	$-0.603371\pi$
$43$	−4.18460	−0.638145	−0.319073	+	0.947730i	$0.603371\pi$
$44$	−9.43175	−1.42189
$45$	−6.89693	−1.02813
$46$	7.68992	1.13382
$47$	4.79867	0.699958	0.349979	−	0.936757i	$-0.386189\pi$
$47$	4.79867	0.699958	0.349979	+	0.936757i	$0.386189\pi$
$48$	6.84156	0.987495
$49$	1.00000	0.142857
$50$	7.93000	1.12147
$51$	−8.60746	−1.20528
$52$	14.1822	1.96672
$53$	0.0998902	0.0137210	0.00686048	−	0.999976i	$-0.497816\pi$
$53$	0.0998902	0.0137210	0.00686048	+	0.999976i	$0.497816\pi$
$54$	19.3911	2.63880
$55$	4.09402	0.552038
$56$	1.39937	0.186999
$57$	−10.2219	−1.35392
$58$	−14.6268	−1.92059
$59$	−5.81104	−0.756533	−0.378267	−	0.925697i	$-0.623480\pi$
$59$	−5.81104	−0.756533	−0.378267	+	0.925697i	$0.623480\pi$
$60$	9.13695	1.17958
$61$	−9.28429	−1.18873	−0.594366	−	0.804195i	$-0.702597\pi$
$61$	−9.28429	−1.18873	−0.594366	+	0.804195i	$0.702597\pi$
$62$	7.68700	0.976250
$63$	−5.99811	−0.755690
$64$	−12.0763	−1.50954
$65$	−6.15605	−0.763564
$66$	−23.0284	−2.83460
$67$	−7.45950	−0.911323	−0.455662	−	0.890153i	$-0.650597\pi$
$67$	−7.45950	−0.911323	−0.455662	+	0.890153i	$0.650597\pi$
$68$	7.60122	0.921783
$69$	10.6984	1.28793
$70$	−2.47926	−0.296328
$71$	−10.8765	−1.29080	−0.645401	−	0.763844i	$-0.723310\pi$
$71$	−10.8765	−1.29080	−0.645401	+	0.763844i	$0.723310\pi$
$72$	−8.39357	−0.989192
$73$	−2.84026	−0.332428	−0.166214	−	0.986090i	$-0.553154\pi$
$73$	−2.84026	−0.332428	−0.166214	+	0.986090i	$0.553154\pi$
$74$	8.88929	1.03336
$75$	11.0324	1.27391
$76$	9.02691	1.03546
$77$	3.56048	0.405754
$78$	34.6271	3.92075
$79$	−4.25972	−0.479256	−0.239628	−	0.970865i	$-0.577025\pi$
$79$	−4.25972	−0.479256	−0.239628	+	0.970865i	$0.577025\pi$
$80$	2.62254	0.293209
$81$	8.98297	0.998107
$82$	−12.4218	−1.37176
$83$	10.3596	1.13711	0.568555	−	0.822645i	$-0.307503\pi$
$83$	10.3596	1.13711	0.568555	+	0.822645i	$0.307503\pi$
$84$	7.94620	0.867001
$85$	−3.29945	−0.357875
$86$	9.02265	0.972938
$87$	−20.3491	−2.18165
$88$	4.98243	0.531129
$89$	−9.38564	−0.994876	−0.497438	−	0.867500i	$-0.665726\pi$
$89$	−9.38564	−0.994876	−0.497438	+	0.867500i	$0.665726\pi$
$90$	14.8709	1.56753
$91$	−5.35378	−0.561229
$92$	−9.44768	−0.984989
$93$	10.6943	1.10895
$94$	−10.3467	−1.06718
$95$	−3.91830	−0.402009
$96$	−23.1468	−2.36241
$97$	−1.09618	−0.111300	−0.0556500	−	0.998450i	$-0.517723\pi$
$97$	−1.09618	−0.111300	−0.0556500	+	0.998450i	$0.517723\pi$
$98$	−2.15616	−0.217805
$99$	−21.3561	−2.14637
$100$	−9.74264	−0.974264
$101$	17.5895	1.75022	0.875111	−	0.483923i	$-0.160789\pi$
$101$	17.5895	1.75022	0.875111	+	0.483923i	$0.160789\pi$
$102$	18.5590	1.83762
$103$	7.30716	0.719996	0.359998	−	0.932953i	$-0.382777\pi$
$103$	7.30716	0.719996	0.359998	+	0.932953i	$0.382777\pi$
$104$	−7.49192	−0.734643
$105$	−3.44919	−0.336607
$106$	−0.215379	−0.0209194
$107$	11.3051	1.09290	0.546451	−	0.837491i	$-0.315978\pi$
$107$	11.3051	1.09290	0.546451	+	0.837491i	$0.315978\pi$
$108$	−23.8236	−2.29242
$109$	−0.653745	−0.0626174	−0.0313087	−	0.999510i	$-0.509968\pi$
$109$	−0.653745	−0.0626174	−0.0313087	+	0.999510i	$0.509968\pi$
$110$	−8.82735	−0.841655
$111$	12.3669	1.17382
$112$	2.28076	0.215512
$113$	17.8656	1.68066	0.840329	−	0.542076i	$-0.182362\pi$
$113$	17.8656	1.68066	0.840329	+	0.542076i	$0.182362\pi$
$114$	22.0400	2.06423
$115$	4.10094	0.382414
$116$	17.9702	1.66849
$117$	32.1125	2.96881
$118$	12.5295	1.15344
$119$	−2.86945	−0.263042
$120$	−4.82670	−0.440615
$121$	1.67701	0.152455
$122$	20.0184	1.81238
$123$	−17.2815	−1.55822
$124$	−9.44409	−0.848105
$125$	9.97823	0.892480
$126$	12.9329	1.15215
$127$	−7.50304	−0.665787	−0.332894	−	0.942964i	$-0.608025\pi$
$127$	−7.50304	−0.665787	−0.332894	+	0.942964i	$0.608025\pi$
$128$	10.6055	0.937405
$129$	12.5525	1.10518
$130$	13.2734	1.16416
$131$	−10.2069	−0.891783	−0.445891	−	0.895087i	$-0.647113\pi$
$131$	−10.2069	−0.891783	−0.445891	+	0.895087i	$0.647113\pi$
$132$	28.2923	2.46253
$133$	−3.40765	−0.295481
$134$	16.0839	1.38943
$135$	10.3410	0.890016
$136$	−4.01543	−0.344320
$137$	2.80313	0.239487	0.119744	−	0.992805i	$-0.461793\pi$
$137$	2.80313	0.239487	0.119744	+	0.992805i	$0.461793\pi$
$138$	−23.0673	−1.96362
$139$	−7.39376	−0.627131	−0.313565	−	0.949567i	$-0.601523\pi$
$139$	−7.39376	−0.627131	−0.313565	+	0.949567i	$0.601523\pi$
$140$	3.04597	0.257431
$141$	−14.3945	−1.21224
$142$	23.4514	1.96800
$143$	−19.0620	−1.59405
$144$	−13.6802	−1.14002
$145$	−7.80030	−0.647780
$146$	6.12405	0.506830
$147$	−2.99968	−0.247410
$148$	−10.9212	−0.897718
$149$	11.5939	0.949812	0.474906	−	0.880037i	$-0.342482\pi$
$149$	11.5939	0.949812	0.474906	+	0.880037i	$0.342482\pi$
$150$	−23.7875	−1.94224
$151$	4.91307	0.399820	0.199910	−	0.979814i	$-0.435935\pi$
$151$	4.91307	0.399820	0.199910	+	0.979814i	$0.435935\pi$
$152$	−4.76857	−0.386782
$153$	17.2113	1.39145
$154$	−7.67695	−0.618626
$155$	4.09938	0.329270
$156$	−42.5422	−3.40610
$157$	−14.1083	−1.12596	−0.562980	−	0.826470i	$-0.690345\pi$
$157$	−14.1083	−1.12596	−0.562980	+	0.826470i	$0.690345\pi$
$158$	9.18463	0.730690
$159$	−0.299639	−0.0237629
$160$	−8.87274	−0.701451
$161$	3.56649	0.281079
$162$	−19.3687	−1.52175
$163$	11.1495	0.873299	0.436650	−	0.899632i	$-0.356165\pi$
$163$	11.1495	0.873299	0.436650	+	0.899632i	$0.356165\pi$
$164$	15.2612	1.19170
$165$	−12.2808	−0.956057
$166$	−22.3368	−1.73367
$167$	−14.8184	−1.14668	−0.573342	−	0.819316i	$-0.694354\pi$
$167$	−14.8184	−1.14668	−0.573342	+	0.819316i	$0.694354\pi$
$168$	−4.19767	−0.323857
$169$	15.6630	1.20484
$170$	7.11412	0.545628
$171$	20.4395	1.56305
$172$	−11.0851	−0.845227
$173$	−1.42236	−0.108140	−0.0540701	−	0.998537i	$-0.517219\pi$
$173$	−1.42236	−0.108140	−0.0540701	+	0.998537i	$0.517219\pi$
$174$	43.8758	3.32622
$175$	3.67784	0.278019
$176$	8.12060	0.612113
$177$	17.4313	1.31022
$178$	20.2369	1.51682
$179$	−2.89779	−0.216591	−0.108296	−	0.994119i	$-0.534539\pi$
$179$	−2.89779	−0.216591	−0.108296	+	0.994119i	$0.534539\pi$
$180$	−18.2701	−1.36177
$181$	−24.3680	−1.81126	−0.905629	−	0.424070i	$-0.860601\pi$
$181$	−24.3680	−1.81126	−0.905629	+	0.424070i	$0.860601\pi$
$182$	11.5436	0.855668
$183$	27.8499	2.05873
$184$	4.99085	0.367930
$185$	4.74055	0.348532
$186$	−23.0586	−1.69074
$187$	−10.2166	−0.747114
$188$	12.7117	0.927099
$189$	8.99337	0.654172
$190$	8.44846	0.612916
$191$	9.86805	0.714027	0.357013	−	0.934099i	$-0.383795\pi$
$191$	9.86805	0.714027	0.357013	+	0.934099i	$0.383795\pi$
$192$	36.2250	2.61432
$193$	20.0555	1.44363	0.721814	−	0.692087i	$-0.243308\pi$
$193$	20.0555	1.44363	0.721814	+	0.692087i	$0.243308\pi$
$194$	2.36353	0.169692
$195$	18.4662	1.32239
$196$	2.64901	0.189215
$197$	8.78236	0.625717	0.312859	−	0.949800i	$-0.398713\pi$
$197$	8.78236	0.625717	0.312859	+	0.949800i	$0.398713\pi$
$198$	46.0472	3.27243
$199$	14.1320	1.00179	0.500896	−	0.865508i	$-0.333004\pi$
$199$	14.1320	1.00179	0.500896	+	0.865508i	$0.333004\pi$
$200$	5.14666	0.363924
$201$	22.3762	1.57829
$202$	−37.9257	−2.66844
$203$	−6.78374	−0.476125
$204$	−22.8012	−1.59641
$205$	−6.62442	−0.462669
$206$	−15.7554	−1.09773
$207$	−21.3922	−1.48686
$208$	−12.2107	−0.846659
$209$	−12.1329	−0.839249
$210$	7.43700	0.513202
$211$	7.50900	0.516941	0.258471	−	0.966019i	$-0.416781\pi$
$211$	7.50900	0.516941	0.258471	+	0.966019i	$0.416781\pi$
$212$	0.264610	0.0181735
$213$	32.6260	2.23550
$214$	−24.3755	−1.66628
$215$	4.81167	0.328153
$216$	12.5851	0.856305
$217$	3.56514	0.242017
$218$	1.40958	0.0954686
$219$	8.51990	0.575721
$220$	10.8451	0.731177
$221$	15.3624	1.03339
$222$	−26.6651	−1.78964
$223$	20.0953	1.34568	0.672840	−	0.739788i	$-0.265074\pi$
$223$	20.0953	1.34568	0.672840	+	0.739788i	$0.265074\pi$
$224$	−7.71642	−0.515575
$225$	−22.0601	−1.47067
$226$	−38.5211	−2.56239
$227$	−17.1060	−1.13536	−0.567682	−	0.823248i	$-0.692160\pi$
$227$	−17.1060	−1.13536	−0.567682	+	0.823248i	$0.692160\pi$
$228$	−27.0779	−1.79328
$229$	−14.5176	−0.959347	−0.479673	−	0.877447i	$-0.659245\pi$
$229$	−14.5176	−0.959347	−0.479673	+	0.877447i	$0.659245\pi$
$230$	−8.84226	−0.583042
$231$	−10.6803	−0.702713
$232$	−9.49297	−0.623244
$233$	4.90477	0.321322	0.160661	−	0.987010i	$-0.448637\pi$
$233$	4.90477	0.321322	0.160661	+	0.987010i	$0.448637\pi$
$234$	−69.2397	−4.52634
$235$	−5.51776	−0.359939
$236$	−15.3935	−1.00203
$237$	12.7778	0.830009
$238$	6.18699	0.401043
$239$	16.1250	1.04304	0.521520	−	0.853239i	$-0.325365\pi$
$239$	16.1250	1.04304	0.521520	+	0.853239i	$0.325365\pi$
$240$	−7.86678	−0.507799
$241$	−5.05297	−0.325490	−0.162745	−	0.986668i	$-0.552035\pi$
$241$	−5.05297	−0.325490	−0.162745	+	0.986668i	$0.552035\pi$
$242$	−3.61589	−0.232438
$243$	0.0340609	0.00218501
$244$	−24.5942	−1.57448
$245$	−1.14985	−0.0734613
$246$	37.2616	2.37571
$247$	18.2438	1.16083
$248$	4.98895	0.316799
$249$	−31.0754	−1.96932
$250$	−21.5146	−1.36070
$251$	−4.03764	−0.254853	−0.127427	−	0.991848i	$-0.540672\pi$
$251$	−4.03764	−0.254853	−0.127427	+	0.991848i	$0.540672\pi$
$252$	−15.8891	−1.00092
$253$	12.6984	0.798343
$254$	16.1777	1.01508
$255$	9.89730	0.619793
$256$	1.28539	0.0803372
$257$	5.79734	0.361628	0.180814	−	0.983517i	$-0.442127\pi$
$257$	5.79734	0.361628	0.180814	+	0.983517i	$0.442127\pi$
$258$	−27.0651	−1.68500
$259$	4.12275	0.256175
$260$	−16.3075	−1.01135
$261$	40.6896	2.51862
$262$	22.0077	1.35964
$263$	20.7090	1.27697	0.638485	−	0.769634i	$-0.279561\pi$
$263$	20.7090	1.27697	0.638485	+	0.769634i	$0.279561\pi$
$264$	−14.9457	−0.919845
$265$	−0.114859	−0.00705572
$266$	7.34744	0.450500
$267$	28.1540	1.72299
$268$	−19.7603	−1.20705
$269$	9.86173	0.601280	0.300640	−	0.953738i	$-0.402800\pi$
$269$	9.86173	0.601280	0.300640	+	0.953738i	$0.402800\pi$
$270$	−22.2969	−1.35695
$271$	−6.19971	−0.376605	−0.188303	−	0.982111i	$-0.560299\pi$
$271$	−6.19971	−0.376605	−0.188303	+	0.982111i	$0.560299\pi$
$272$	−6.54454	−0.396821
$273$	16.0596	0.971974
$274$	−6.04399	−0.365131
$275$	13.0949	0.789651
$276$	28.3401	1.70587
$277$	11.0201	0.662132	0.331066	−	0.943608i	$-0.392592\pi$
$277$	11.0201	0.662132	0.331066	+	0.943608i	$0.392592\pi$
$278$	15.9421	0.956144
$279$	−21.3841	−1.28023
$280$	−1.60907	−0.0961602
$281$	22.1064	1.31876	0.659378	−	0.751812i	$-0.270820\pi$
$281$	22.1064	1.31876	0.659378	+	0.751812i	$0.270820\pi$
$282$	31.0368	1.84821
$283$	23.4449	1.39365	0.696827	−	0.717240i	$-0.254595\pi$
$283$	23.4449	1.39365	0.696827	+	0.717240i	$0.254595\pi$
$284$	−28.8119	−1.70967
$285$	11.7537	0.696226
$286$	41.1007	2.43034
$287$	−5.76111	−0.340067
$288$	46.2839	2.72731
$289$	−8.76624	−0.515661
$290$	16.8187	0.987626
$291$	3.28819	0.192757
$292$	−7.52389	−0.440303
$293$	−10.5974	−0.619105	−0.309553	−	0.950882i	$-0.600179\pi$
$293$	−10.5974	−0.619105	−0.309553	+	0.950882i	$0.600179\pi$
$294$	6.46779	0.377209
$295$	6.68184	0.389032
$296$	5.76925	0.335331
$297$	32.0207	1.85803
$298$	−24.9983	−1.44811
$299$	−19.0942	−1.10425
$300$	29.2249	1.68730
$301$	4.18460	0.241196
$302$	−10.5934	−0.609579
$303$	−52.7630	−3.03115
$304$	−7.77204	−0.445757
$305$	10.6756	0.611281
$306$	−37.1102	−2.12145
$307$	−1.82457	−0.104134	−0.0520669	−	0.998644i	$-0.516581\pi$
$307$	−1.82457	−0.104134	−0.0520669	+	0.998644i	$0.516581\pi$
$308$	9.43175	0.537424
$309$	−21.9192	−1.24694
$310$	−8.83891	−0.502016
$311$	−1.74052	−0.0986961	−0.0493480	−	0.998782i	$-0.515714\pi$
$311$	−1.74052	−0.0986961	−0.0493480	+	0.998782i	$0.515714\pi$
$312$	22.4734	1.27231
$313$	9.24713	0.522678	0.261339	−	0.965247i	$-0.415836\pi$
$313$	9.24713	0.522678	0.261339	+	0.965247i	$0.415836\pi$
$314$	30.4196	1.71668
$315$	6.89693	0.388598
$316$	−11.2841	−0.634778
$317$	18.6432	1.04711	0.523553	−	0.851993i	$-0.324606\pi$
$317$	18.6432	1.04711	0.523553	+	0.851993i	$0.324606\pi$
$318$	0.646068	0.0362297
$319$	−24.1534	−1.35233
$320$	13.8859	0.776248
$321$	−33.9117	−1.89276
$322$	−7.68992	−0.428542
$323$	9.77810	0.544068
$324$	23.7960	1.32200
$325$	−19.6904	−1.09222
$326$	−24.0401	−1.33146
$327$	1.96103	0.108445
$328$	−8.06192	−0.445145
$329$	−4.79867	−0.264559
$330$	26.4793	1.45764
$331$	15.7367	0.864965	0.432482	−	0.901642i	$-0.357638\pi$
$331$	15.7367	0.864965	0.432482	+	0.901642i	$0.357638\pi$
$332$	27.4426	1.50611
$333$	−24.7287	−1.35512
$334$	31.9509	1.74827
$335$	8.57732	0.468629
$336$	−6.84156	−0.373238
$337$	−6.66697	−0.363173	−0.181587	−	0.983375i	$-0.558123\pi$
$337$	−6.66697	−0.363173	−0.181587	+	0.983375i	$0.558123\pi$
$338$	−33.7718	−1.83694
$339$	−53.5913	−2.91068
$340$	−8.74027	−0.474008
$341$	12.6936	0.687397
$342$	−44.0707	−2.38307
$343$	−1.00000	−0.0539949
$344$	5.85581	0.315724
$345$	−12.3015	−0.662292
$346$	3.06683	0.164874
$347$	−17.4024	−0.934211	−0.467105	−	0.884202i	$-0.654703\pi$
$347$	−17.4024	−0.934211	−0.467105	+	0.884202i	$0.654703\pi$
$348$	−53.9050	−2.88961
$349$	13.7279	0.734838	0.367419	−	0.930056i	$-0.380242\pi$
$349$	13.7279	0.734838	0.367419	+	0.930056i	$0.380242\pi$
$350$	−7.93000	−0.423876
$351$	−48.1485	−2.56998
$352$	−27.4741	−1.46438
$353$	0.314716	0.0167507	0.00837533	−	0.999965i	$-0.497334\pi$
$353$	0.314716	0.0167507	0.00837533	+	0.999965i	$0.497334\pi$
$354$	−37.5846	−1.99760
$355$	12.5063	0.663768
$356$	−24.8627	−1.31772
$357$	8.60746	0.455555
$358$	6.24809	0.330222
$359$	−9.77490	−0.515900	−0.257950	−	0.966158i	$-0.583047\pi$
$359$	−9.77490	−0.515900	−0.257950	+	0.966158i	$0.583047\pi$
$360$	9.65137	0.508672
$361$	−7.38790	−0.388837
$362$	52.5412	2.76150
$363$	−5.03050	−0.264033
$364$	−14.1822	−0.743351
$365$	3.26588	0.170944
$366$	−60.0489	−3.13880
$367$	17.0136	0.888100	0.444050	−	0.896002i	$-0.353541\pi$
$367$	17.0136	0.888100	0.444050	+	0.896002i	$0.353541\pi$
$368$	8.13432	0.424031
$369$	34.5557	1.79890
$370$	−10.2214	−0.531384
$371$	−0.0998902	−0.00518604
$372$	28.3293	1.46881
$373$	−3.47283	−0.179816	−0.0899081	−	0.995950i	$-0.528657\pi$
$373$	−3.47283	−0.179816	−0.0899081	+	0.995950i	$0.528657\pi$
$374$	22.0287	1.13907
$375$	−29.9315	−1.54566
$376$	−6.71512	−0.346306
$377$	36.3187	1.87051
$378$	−19.3911	−0.997372
$379$	1.67537	0.0860581	0.0430290	−	0.999074i	$-0.486299\pi$
$379$	1.67537	0.0860581	0.0430290	+	0.999074i	$0.486299\pi$
$380$	−10.3796	−0.532463
$381$	22.5068	1.15306
$382$	−21.2771	−1.08863
$383$	−6.56338	−0.335373	−0.167687	−	0.985840i	$-0.553630\pi$
$383$	−6.56338	−0.335373	−0.167687	+	0.985840i	$0.553630\pi$
$384$	−31.8132	−1.62346
$385$	−4.09402	−0.208651
$386$	−43.2429	−2.20100
$387$	−25.0997	−1.27589
$388$	−2.90379	−0.147418
$389$	−14.3100	−0.725544	−0.362772	−	0.931878i	$-0.618170\pi$
$389$	−14.3100	−0.725544	−0.362772	+	0.931878i	$0.618170\pi$
$390$	−39.8161	−2.01616
$391$	−10.2339	−0.517550
$392$	−1.39937	−0.0706789
$393$	30.6175	1.54445
$394$	−18.9361	−0.953989
$395$	4.89805	0.246448
$396$	−56.5726	−2.84288
$397$	−7.11389	−0.357036	−0.178518	−	0.983937i	$-0.557130\pi$
$397$	−7.11389	−0.357036	−0.178518	+	0.983937i	$0.557130\pi$
$398$	−30.4708	−1.52736
$399$	10.2219	0.511734
$400$	8.38828	0.419414
$401$	−16.8821	−0.843052	−0.421526	−	0.906816i	$-0.638505\pi$
$401$	−16.8821	−0.843052	−0.421526	+	0.906816i	$0.638505\pi$
$402$	−48.2465	−2.40632
$403$	−19.0870	−0.950790
$404$	46.5948	2.31818
$405$	−10.3291	−0.513256
$406$	14.6268	0.725917
$407$	14.6790	0.727609
$408$	12.0450	0.596317
$409$	−14.7522	−0.729452	−0.364726	−	0.931115i	$-0.618837\pi$
$409$	−14.7522	−0.729452	−0.364726	+	0.931115i	$0.618837\pi$
$410$	14.2833	0.705401
$411$	−8.40850	−0.414761
$412$	19.3568	0.953639
$413$	5.81104	0.285943
$414$	46.1249	2.26692
$415$	−11.9120	−0.584735
$416$	41.3120	2.02549
$417$	22.1790	1.08611
$418$	26.1604	1.27955
$419$	17.9678	0.877783	0.438891	−	0.898540i	$-0.355371\pi$
$419$	17.9678	0.877783	0.438891	+	0.898540i	$0.355371\pi$
$420$	−9.13695	−0.445837
$421$	7.90288	0.385163	0.192581	−	0.981281i	$-0.438314\pi$
$421$	7.90288	0.385163	0.192581	+	0.981281i	$0.438314\pi$
$422$	−16.1906	−0.788146
$423$	28.7830	1.39948
$424$	−0.139783	−0.00678848
$425$	−10.5534	−0.511915
$426$	−70.3468	−3.40831
$427$	9.28429	0.449298
$428$	29.9473	1.44756
$429$	57.1800	2.76068
$430$	−10.3747	−0.500313
$431$	−25.3174	−1.21950	−0.609748	−	0.792595i	$-0.708730\pi$
$431$	−25.3174	−1.21950	−0.609748	+	0.792595i	$0.708730\pi$
$432$	20.5117	0.986871
$433$	−7.99496	−0.384213	−0.192107	−	0.981374i	$-0.561532\pi$
$433$	−7.99496	−0.384213	−0.192107	+	0.981374i	$0.561532\pi$
$434$	−7.68700	−0.368988
$435$	23.3984	1.12187
$436$	−1.73178	−0.0829372
$437$	−12.1534	−0.581375
$438$	−18.3702	−0.877764
$439$	−30.4825	−1.45485	−0.727426	−	0.686186i	$-0.759283\pi$
$439$	−30.4825	−1.45485	−0.727426	+	0.686186i	$0.759283\pi$
$440$	−5.72905	−0.273122
$441$	5.99811	0.285624
$442$	−33.1238	−1.57554
$443$	−6.04886	−0.287390	−0.143695	−	0.989622i	$-0.545898\pi$
$443$	−6.04886	−0.287390	−0.143695	+	0.989622i	$0.545898\pi$
$444$	32.7602	1.55473
$445$	10.7921	0.511594
$446$	−43.3286	−2.05167
$447$	−34.7781	−1.64495
$448$	12.0763	0.570551
$449$	−17.6035	−0.830759	−0.415379	−	0.909648i	$-0.636351\pi$
$449$	−17.6035	−0.830759	−0.415379	+	0.909648i	$0.636351\pi$
$450$	47.5650	2.24224
$451$	−20.5123	−0.965886
$452$	47.3263	2.22604
$453$	−14.7377	−0.692436
$454$	36.8832	1.73101
$455$	6.15605	0.288600
$456$	14.3042	0.669856
$457$	19.4658	0.910573	0.455286	−	0.890345i	$-0.349537\pi$
$457$	19.4658	0.910573	0.455286	+	0.890345i	$0.349537\pi$
$458$	31.3021	1.46265
$459$	−25.8061	−1.20452
$460$	10.8634	0.506510
$461$	−36.7773	−1.71289	−0.856444	−	0.516239i	$-0.827332\pi$
$461$	−36.7773	−1.71289	−0.856444	+	0.516239i	$0.827332\pi$
$462$	23.0284	1.07138
$463$	12.4592	0.579029	0.289515	−	0.957174i	$-0.406506\pi$
$463$	12.4592	0.579029	0.289515	+	0.957174i	$0.406506\pi$
$464$	−15.4721	−0.718274
$465$	−12.2968	−0.570253
$466$	−10.5755	−0.489899
$467$	−36.3580	−1.68245	−0.841224	−	0.540687i	$-0.818164\pi$
$467$	−36.3580	−1.68245	−0.841224	+	0.540687i	$0.818164\pi$
$468$	85.0665	3.93220
$469$	7.45950	0.344448
$470$	11.8972	0.548775
$471$	42.3203	1.95002
$472$	8.13180	0.374296
$473$	14.8992	0.685065
$474$	−27.5510	−1.26546
$475$	−12.5328	−0.575045
$476$	−7.60122	−0.348401
$477$	0.599152	0.0274333
$478$	−34.7681	−1.59025
$479$	−12.4422	−0.568498	−0.284249	−	0.958751i	$-0.591744\pi$
$479$	−12.4422	−0.568498	−0.284249	+	0.958751i	$0.591744\pi$
$480$	26.6154	1.21482
$481$	−22.0723	−1.00641
$482$	10.8950	0.496253
$483$	−10.6984	−0.486792
$484$	4.44242	0.201928
$485$	1.26044	0.0572337
$486$	−0.0734406	−0.00333133
$487$	−35.5074	−1.60900	−0.804498	−	0.593956i	$-0.797565\pi$
$487$	−35.5074	−1.60900	−0.804498	+	0.593956i	$0.797565\pi$
$488$	12.9922	0.588128
$489$	−33.4451	−1.51244
$490$	2.47926	0.112002
$491$	−21.1709	−0.955429	−0.477715	−	0.878515i	$-0.658535\pi$
$491$	−21.1709	−0.955429	−0.477715	+	0.878515i	$0.658535\pi$
$492$	−45.7789	−2.06387
$493$	19.4656	0.876688
$494$	−39.3366	−1.76984
$495$	24.5564	1.10373
$496$	8.13123	0.365103
$497$	10.8765	0.487877
$498$	67.0035	3.00250
$499$	3.21643	0.143987	0.0719935	−	0.997405i	$-0.477064\pi$
$499$	3.21643	0.143987	0.0719935	+	0.997405i	$0.477064\pi$
$500$	26.4324	1.18209
$501$	44.4506	1.98591
$502$	8.70578	0.388558
$503$	−13.2667	−0.591534	−0.295767	−	0.955260i	$-0.595575\pi$
$503$	−13.2667	−0.591534	−0.295767	+	0.955260i	$0.595575\pi$
$504$	8.39357	0.373880
$505$	−20.2253	−0.900015
$506$	−27.3798	−1.21718
$507$	−46.9839	−2.08663
$508$	−19.8756	−0.881839
$509$	−0.0779118	−0.00345338	−0.00172669	−	0.999999i	$-0.500550\pi$
$509$	−0.0779118	−0.00345338	−0.00172669	+	0.999999i	$0.500550\pi$
$510$	−21.3401	−0.944956
$511$	2.84026	0.125646
$512$	−23.9826	−1.05989
$513$	−30.6463	−1.35307
$514$	−12.5000	−0.551351
$515$	−8.40215	−0.370243
$516$	33.2517	1.46382
$517$	−17.0856	−0.751423
$518$	−8.88929	−0.390573
$519$	4.26663	0.187284
$520$	8.61460	0.377775
$521$	−36.1560	−1.58402	−0.792012	−	0.610506i	$-0.790966\pi$
$521$	−36.1560	−1.58402	−0.792012	+	0.610506i	$0.790966\pi$
$522$	−87.7332	−3.83998
$523$	1.13168	0.0494850	0.0247425	−	0.999694i	$-0.492123\pi$
$523$	1.13168	0.0494850	0.0247425	+	0.999694i	$0.492123\pi$
$524$	−27.0382	−1.18117
$525$	−11.0324	−0.481492
$526$	−44.6518	−1.94691
$527$	−10.2300	−0.445626
$528$	−24.3592	−1.06010
$529$	−10.2801	−0.446962
$530$	0.247654	0.0107574
$531$	−34.8552	−1.51259
$532$	−9.02691	−0.391366
$533$	30.8437	1.33599
$534$	−60.7043	−2.62693
$535$	−12.9992	−0.562003
$536$	10.4386	0.450879
$537$	8.69246	0.375107
$538$	−21.2634	−0.916732
$539$	−3.56048	−0.153361
$540$	27.3936	1.17883
$541$	2.38411	0.102501	0.0512505	−	0.998686i	$-0.483679\pi$
$541$	2.38411	0.102501	0.0512505	+	0.998686i	$0.483679\pi$
$542$	13.3675	0.574185
$543$	73.0963	3.13686
$544$	22.1419	0.949326
$545$	0.751710	0.0321997
$546$	−34.6271	−1.48190
$547$	14.5922	0.623917	0.311959	−	0.950096i	$-0.399015\pi$
$547$	14.5922	0.623917	0.311959	+	0.950096i	$0.399015\pi$
$548$	7.42552	0.317203
$549$	−55.6882	−2.37671
$550$	−28.2346	−1.20393
$551$	23.1166	0.984802
$552$	−14.9710	−0.637206
$553$	4.25972	0.181142
$554$	−23.7610	−1.00951
$555$	−14.2202	−0.603612
$556$	−19.5862	−0.830638
$557$	42.5525	1.80301	0.901504	−	0.432771i	$-0.142464\pi$
$557$	42.5525	1.80301	0.901504	+	0.432771i	$0.142464\pi$
$558$	46.1074	1.95188
$559$	−22.4034	−0.947564
$560$	−2.62254	−0.110822
$561$	30.6467	1.29390
$562$	−47.6648	−2.01062
$563$	20.0790	0.846228	0.423114	−	0.906076i	$-0.360937\pi$
$563$	20.0790	0.846228	0.423114	+	0.906076i	$0.360937\pi$
$564$	−38.1312	−1.60561
$565$	−20.5428	−0.864244
$566$	−50.5508	−2.12481
$567$	−8.98297	−0.377249
$568$	15.2202	0.638627
$569$	32.1478	1.34771	0.673854	−	0.738865i	$-0.264638\pi$
$569$	32.1478	1.34771	0.673854	+	0.738865i	$0.264638\pi$
$570$	−25.3427	−1.06149
$571$	−16.8161	−0.703733	−0.351866	−	0.936050i	$-0.614453\pi$
$571$	−16.8161	−0.703733	−0.351866	+	0.936050i	$0.614453\pi$
$572$	−50.4955	−2.11132
$573$	−29.6010	−1.23660
$574$	12.4218	0.518478
$575$	13.1170	0.547016
$576$	−72.4349	−3.01812
$577$	−28.6963	−1.19464	−0.597322	−	0.802002i	$-0.703769\pi$
$577$	−28.6963	−1.19464	−0.597322	+	0.802002i	$0.703769\pi$
$578$	18.9014	0.786194
$579$	−60.1603	−2.50018
$580$	−20.6631	−0.857988
$581$	−10.3596	−0.429787
$582$	−7.08985	−0.293884
$583$	−0.355657	−0.0147298
$584$	3.97458	0.164469
$585$	−36.9247	−1.52665
$586$	22.8496	0.943908
$587$	−13.8380	−0.571155	−0.285578	−	0.958356i	$-0.592185\pi$
$587$	−13.8380	−0.571155	−0.285578	+	0.958356i	$0.592185\pi$
$588$	−7.94620	−0.327696
$589$	−12.1488	−0.500581
$590$	−14.4071	−0.593130
$591$	−26.3443	−1.08366
$592$	9.40300	0.386461
$593$	35.1640	1.44401	0.722006	−	0.691887i	$-0.243220\pi$
$593$	35.1640	1.44401	0.722006	+	0.691887i	$0.243220\pi$
$594$	−69.0417	−2.83281
$595$	3.29945	0.135264
$596$	30.7125	1.25803
$597$	−42.3916	−1.73497
$598$	41.1701	1.68357
$599$	−25.1580	−1.02793	−0.513964	−	0.857812i	$-0.671823\pi$
$599$	−25.1580	−1.02793	−0.513964	+	0.857812i	$0.671823\pi$
$600$	−15.4384	−0.630269
$601$	−37.7509	−1.53989	−0.769946	−	0.638109i	$-0.779717\pi$
$601$	−37.7509	−1.53989	−0.769946	+	0.638109i	$0.779717\pi$
$602$	−9.02265	−0.367736
$603$	−44.7429	−1.82207
$604$	13.0148	0.529564
$605$	−1.92831	−0.0783970
$606$	113.765	4.62140
$607$	−31.4636	−1.27707	−0.638534	−	0.769594i	$-0.720459\pi$
$607$	−31.4636	−1.27707	−0.638534	+	0.769594i	$0.720459\pi$
$608$	26.2949	1.06640
$609$	20.3491	0.824587
$610$	−23.0182	−0.931979
$611$	25.6910	1.03935
$612$	45.5929	1.84298
$613$	26.2869	1.06172	0.530859	−	0.847460i	$-0.321869\pi$
$613$	26.2869	1.06172	0.530859	+	0.847460i	$0.321869\pi$
$614$	3.93407	0.158766
$615$	19.8712	0.801283
$616$	−4.98243	−0.200748
$617$	−29.9368	−1.20521	−0.602605	−	0.798040i	$-0.705870\pi$
$617$	−29.9368	−1.20521	−0.602605	+	0.798040i	$0.705870\pi$
$618$	47.2612	1.90112
$619$	41.1037	1.65210	0.826048	−	0.563600i	$-0.190584\pi$
$619$	41.1037	1.65210	0.826048	+	0.563600i	$0.190584\pi$
$620$	10.8593	0.436120
$621$	32.0748	1.28712
$622$	3.75284	0.150475
$623$	9.38564	0.376028
$624$	36.6282	1.46630
$625$	6.91572	0.276629
$626$	−19.9383	−0.796893
$627$	36.3948	1.45347
$628$	−37.3729	−1.49134
$629$	−11.8300	−0.471694
$630$	−14.8709	−0.592470
$631$	−14.9899	−0.596738	−0.298369	−	0.954451i	$-0.596443\pi$
$631$	−14.9899	−0.596738	−0.298369	+	0.954451i	$0.596443\pi$
$632$	5.96093	0.237113
$633$	−22.5246	−0.895274
$634$	−40.1976	−1.59645
$635$	8.62738	0.342367
$636$	−0.793747	−0.0314741
$637$	5.35378	0.212124
$638$	52.0785	2.06181
$639$	−65.2383	−2.58079
$640$	−12.1948	−0.482041
$641$	−33.0834	−1.30672	−0.653358	−	0.757049i	$-0.726640\pi$
$641$	−33.0834	−1.30672	−0.653358	+	0.757049i	$0.726640\pi$
$642$	73.1188	2.88577
$643$	13.9286	0.549292	0.274646	−	0.961545i	$-0.411439\pi$
$643$	13.9286	0.549292	0.274646	+	0.961545i	$0.411439\pi$
$644$	9.44768	0.372291
$645$	−14.4335	−0.568318
$646$	−21.0831	−0.829504
$647$	−18.2043	−0.715684	−0.357842	−	0.933782i	$-0.616487\pi$
$647$	−18.2043	−0.715684	−0.357842	+	0.933782i	$0.616487\pi$
$648$	−12.5705	−0.493816
$649$	20.6901	0.812157
$650$	42.4555	1.66524
$651$	−10.6943	−0.419142
$652$	29.5352	1.15669
$653$	18.3980	0.719969	0.359985	−	0.932958i	$-0.382782\pi$
$653$	18.3980	0.719969	0.359985	+	0.932958i	$0.382782\pi$
$654$	−4.22829	−0.165339
$655$	11.7364	0.458581
$656$	−13.1397	−0.513019
$657$	−17.0362	−0.664646
$658$	10.3467	0.403356
$659$	−4.02784	−0.156902	−0.0784511	−	0.996918i	$-0.524997\pi$
$659$	−4.02784	−0.156902	−0.0784511	+	0.996918i	$0.524997\pi$
$660$	−32.5319	−1.26630
$661$	4.85946	0.189011	0.0945056	−	0.995524i	$-0.469873\pi$
$661$	4.85946	0.189011	0.0945056	+	0.995524i	$0.469873\pi$
$662$	−33.9307	−1.31875
$663$	−46.0824	−1.78969
$664$	−14.4969	−0.562587
$665$	3.91830	0.151945
$666$	53.3189	2.06607
$667$	−24.1942	−0.936802
$668$	−39.2542	−1.51879
$669$	−60.2795	−2.33054
$670$	−18.4940	−0.714487
$671$	33.0565	1.27613
$672$	23.1468	0.892908
$673$	21.2424	0.818833	0.409416	−	0.912348i	$-0.365732\pi$
$673$	21.2424	0.818833	0.409416	+	0.912348i	$0.365732\pi$
$674$	14.3750	0.553706
$675$	33.0762	1.27310
$676$	41.4914	1.59582
$677$	−12.7725	−0.490886	−0.245443	−	0.969411i	$-0.578933\pi$
$677$	−12.7725	−0.490886	−0.245443	+	0.969411i	$0.578933\pi$
$678$	115.551	4.43772
$679$	1.09618	0.0420675
$680$	4.61715	0.177060
$681$	51.3126	1.96630
$682$	−27.3694	−1.04803
$683$	30.4787	1.16624	0.583118	−	0.812387i	$-0.301832\pi$
$683$	30.4787	1.16624	0.583118	+	0.812387i	$0.301832\pi$
$684$	54.1444	2.07026
$685$	−3.22318	−0.123151
$686$	2.15616	0.0823224
$687$	43.5481	1.66146
$688$	9.54407	0.363864
$689$	0.534790	0.0203739
$690$	26.5240	1.00975
$691$	34.1317	1.29843	0.649216	−	0.760604i	$-0.275097\pi$
$691$	34.1317	1.29843	0.649216	+	0.760604i	$0.275097\pi$
$692$	−3.76785	−0.143232
$693$	21.3561	0.811252
$694$	37.5223	1.42433
$695$	8.50173	0.322489
$696$	28.4759	1.07938
$697$	16.5312	0.626165
$698$	−29.5995	−1.12036
$699$	−14.7128	−0.556488
$700$	9.74264	0.368237
$701$	−35.1770	−1.32862	−0.664309	−	0.747458i	$-0.731274\pi$
$701$	−35.1770	−1.32862	−0.664309	+	0.747458i	$0.731274\pi$
$702$	103.816	3.91828
$703$	−14.0489	−0.529864
$704$	42.9974	1.62052
$705$	16.5515	0.623367
$706$	−0.678578	−0.0255386
$707$	−17.5895	−0.661521
$708$	46.1757	1.73539
$709$	32.4768	1.21969	0.609847	−	0.792519i	$-0.291231\pi$
$709$	32.4768	1.21969	0.609847	+	0.792519i	$0.291231\pi$
$710$	−26.9656	−1.01200
$711$	−25.5503	−0.958210
$712$	13.1340	0.492217
$713$	12.7150	0.476182
$714$	−18.5590	−0.694554
$715$	21.9185	0.819705
$716$	−7.67628	−0.286876
$717$	−48.3700	−1.80641
$718$	21.0762	0.786558
$719$	39.5509	1.47500	0.737500	−	0.675347i	$-0.236006\pi$
$719$	39.5509	1.47500	0.737500	+	0.675347i	$0.236006\pi$
$720$	15.7303	0.586232
$721$	−7.30716	−0.272133
$722$	15.9295	0.592833
$723$	15.1573	0.563706
$724$	−64.5511	−2.39902
$725$	−24.9495	−0.926602
$726$	10.8465	0.402553
$727$	−16.1578	−0.599258	−0.299629	−	0.954056i	$-0.596863\pi$
$727$	−16.1578	−0.599258	−0.299629	+	0.954056i	$0.596863\pi$
$728$	7.49192	0.277669
$729$	−27.0511	−1.00189
$730$	−7.04175	−0.260627
$731$	−12.0075	−0.444114
$732$	73.7748	2.72680
$733$	−14.7196	−0.543680	−0.271840	−	0.962342i	$-0.587632\pi$
$733$	−14.7196	−0.543680	−0.271840	+	0.962342i	$0.587632\pi$
$734$	−36.6839	−1.35403
$735$	3.44919	0.127225
$736$	−27.5206	−1.01442
$737$	26.5594	0.978328
$738$	−74.5076	−2.74266
$739$	−44.9347	−1.65295	−0.826475	−	0.562973i	$-0.809657\pi$
$739$	−44.9347	−1.65295	−0.826475	+	0.562973i	$0.809657\pi$
$740$	12.5578	0.461633
$741$	−54.7257	−2.01040
$742$	0.215379	0.00790681
$743$	−5.93541	−0.217749	−0.108875	−	0.994056i	$-0.534725\pi$
$743$	−5.93541	−0.217749	−0.108875	+	0.994056i	$0.534725\pi$
$744$	−14.9653	−0.548654
$745$	−13.3313	−0.488421
$746$	7.48796	0.274154
$747$	62.1377	2.27350
$748$	−27.0640	−0.989557
$749$	−11.3051	−0.413078
$750$	64.5371	2.35656
$751$	17.0340	0.621581	0.310791	−	0.950478i	$-0.399406\pi$
$751$	17.0340	0.621581	0.310791	+	0.950478i	$0.399406\pi$
$752$	−10.9446	−0.399109
$753$	12.1116	0.441373
$754$	−78.3087	−2.85184
$755$	−5.64931	−0.205599
$756$	23.8236	0.866454
$757$	−18.6065	−0.676266	−0.338133	−	0.941098i	$-0.609795\pi$
$757$	−18.6065	−0.676266	−0.338133	+	0.941098i	$0.609795\pi$
$758$	−3.61236	−0.131207
$759$	−38.0913	−1.38263
$760$	5.48315	0.198895
$761$	5.04787	0.182985	0.0914926	−	0.995806i	$-0.470836\pi$
$761$	5.04787	0.182985	0.0914926	+	0.995806i	$0.470836\pi$
$762$	−48.5281	−1.75799
$763$	0.653745	0.0236672
$764$	26.1406	0.945733
$765$	−19.7904	−0.715524
$766$	14.1517	0.511321
$767$	−31.1110	−1.12335
$768$	−3.85578	−0.139133
$769$	37.7378	1.36086	0.680430	−	0.732813i	$-0.261793\pi$
$769$	37.7378	1.36086	0.680430	+	0.732813i	$0.261793\pi$
$770$	8.82735	0.318116
$771$	−17.3902	−0.626293
$772$	53.1273	1.91209
$773$	−30.4875	−1.09656	−0.548279	−	0.836295i	$-0.684717\pi$
$773$	−30.4875	−1.09656	−0.548279	+	0.836295i	$0.684717\pi$
$774$	54.1188	1.94526
$775$	13.1120	0.470997
$776$	1.53396	0.0550659
$777$	−12.3669	−0.443662
$778$	30.8545	1.10619
$779$	19.6319	0.703384
$780$	48.9172	1.75152
$781$	38.7255	1.38571
$782$	22.0659	0.789074
$783$	−61.0087	−2.18027
$784$	−2.28076	−0.0814557
$785$	16.2224	0.579002
$786$	−66.0162	−2.35472
$787$	17.7001	0.630939	0.315470	−	0.948936i	$-0.397838\pi$
$787$	17.7001	0.630939	0.315470	+	0.948936i	$0.397838\pi$
$788$	23.2646	0.828766
$789$	−62.1204	−2.21154
$790$	−10.5610	−0.375742
$791$	−17.8656	−0.635229
$792$	29.8851	1.06192
$793$	−49.7061	−1.76511
$794$	15.3387	0.544349
$795$	0.344540	0.0122196
$796$	37.4359	1.32688
$797$	38.4933	1.36350	0.681751	−	0.731584i	$-0.261219\pi$
$797$	38.4933	1.36350	0.681751	+	0.731584i	$0.261219\pi$
$798$	−22.0400	−0.780207
$799$	13.7696	0.487132
$800$	−28.3798	−1.00338
$801$	−56.2961	−1.98912
$802$	36.4005	1.28534
$803$	10.1127	0.356869
$804$	59.2747	2.09046
$805$	−4.10094	−0.144539
$806$	41.1545	1.44961
$807$	−29.5821	−1.04134
$808$	−24.6142	−0.865926
$809$	−9.96463	−0.350338	−0.175169	−	0.984538i	$-0.556047\pi$
$809$	−9.96463	−0.350338	−0.175169	+	0.984538i	$0.556047\pi$
$810$	22.2711	0.782527
$811$	−13.7114	−0.481471	−0.240736	−	0.970591i	$-0.577389\pi$
$811$	−13.7114	−0.481471	−0.240736	+	0.970591i	$0.577389\pi$
$812$	−17.9702	−0.630631
$813$	18.5972	0.652231
$814$	−31.6501	−1.10934
$815$	−12.8203	−0.449076
$816$	19.6315	0.687242
$817$	−14.2597	−0.498883
$818$	31.8082	1.11215
$819$	−32.1125	−1.12210
$820$	−17.5482	−0.612808
$821$	−7.23616	−0.252544	−0.126272	−	0.991996i	$-0.540301\pi$
$821$	−7.23616	−0.252544	−0.126272	+	0.991996i	$0.540301\pi$
$822$	18.1300	0.632358
$823$	−46.0607	−1.60558	−0.802788	−	0.596265i	$-0.796651\pi$
$823$	−46.0607	−1.60558	−0.802788	+	0.596265i	$0.796651\pi$
$824$	−10.2254	−0.356220
$825$	−39.2805	−1.36757
$826$	−12.5295	−0.435958
$827$	50.2910	1.74879	0.874395	−	0.485215i	$-0.161259\pi$
$827$	50.2910	1.74879	0.874395	+	0.485215i	$0.161259\pi$
$828$	−56.6682	−1.96936
$829$	27.7602	0.964151	0.482075	−	0.876130i	$-0.339883\pi$
$829$	27.7602	0.964151	0.482075	+	0.876130i	$0.339883\pi$
$830$	25.6840	0.891506
$831$	−33.0568	−1.14673
$832$	−64.6538	−2.24147
$833$	2.86945	0.0994207
$834$	−47.8213	−1.65592
$835$	17.0390	0.589659
$836$	−32.1401	−1.11159
$837$	32.0626	1.10825
$838$	−38.7413	−1.33830
$839$	8.29948	0.286530	0.143265	−	0.989684i	$-0.454240\pi$
$839$	8.29948	0.286530	0.143265	+	0.989684i	$0.454240\pi$
$840$	4.82670	0.166537
$841$	17.0192	0.586868
$842$	−17.0399	−0.587232
$843$	−66.3122	−2.28391
$844$	19.8914	0.684692
$845$	−18.0101	−0.619565
$846$	−62.0606	−2.13369
$847$	−1.67701	−0.0576227
$848$	−0.227826	−0.00782356
$849$	−70.3272	−2.41362
$850$	22.7548	0.780482
$851$	14.7038	0.504038
$852$	86.4267	2.96093
$853$	−12.0553	−0.412765	−0.206383	−	0.978471i	$-0.566169\pi$
$853$	−12.0553	−0.412765	−0.206383	+	0.978471i	$0.566169\pi$
$854$	−20.0184	−0.685015
$855$	−23.5024	−0.803764
$856$	−15.8200	−0.540716
$857$	10.0064	0.341813	0.170907	−	0.985287i	$-0.445330\pi$
$857$	10.0064	0.341813	0.170907	+	0.985287i	$0.445330\pi$
$858$	−123.289	−4.20902
$859$	38.6818	1.31981	0.659903	−	0.751351i	$-0.270597\pi$
$859$	38.6818	1.31981	0.659903	+	0.751351i	$0.270597\pi$
$860$	12.7462	0.434641
$861$	17.2815	0.588952
$862$	54.5883	1.85929
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−69.3966	−2.36092
$865$	1.63550	0.0556088
$866$	17.2384	0.585784
$867$	26.2959	0.893057
$868$	9.44409	0.320553
$869$	15.1666	0.514493
$870$	−50.4507	−1.71044
$871$	−39.9365	−1.35320
$872$	0.914832	0.0309801
$873$	−6.57500	−0.222530
$874$	26.2046	0.886383
$875$	−9.97823	−0.337326
$876$	22.5693	0.762546
$877$	−48.4614	−1.63643	−0.818213	−	0.574915i	$-0.805035\pi$
$877$	−48.4614	−1.63643	−0.818213	+	0.574915i	$0.805035\pi$
$878$	65.7251	2.21811
$879$	31.7888	1.07221
$880$	−9.33749	−0.314767
$881$	18.8785	0.636034	0.318017	−	0.948085i	$-0.396983\pi$
$881$	18.8785	0.636034	0.318017	+	0.948085i	$0.396983\pi$
$882$	−12.9329	−0.435472
$883$	55.9399	1.88253	0.941263	−	0.337674i	$-0.109640\pi$
$883$	55.9399	1.88253	0.941263	+	0.337674i	$0.109640\pi$
$884$	40.6952	1.36873
$885$	−20.0434	−0.673752
$886$	13.0423	0.438164
$887$	−5.31177	−0.178352	−0.0891759	−	0.996016i	$-0.528423\pi$
$887$	−5.31177	−0.178352	−0.0891759	+	0.996016i	$0.528423\pi$
$888$	−17.3059	−0.580749
$889$	7.50304	0.251644
$890$	−23.2694	−0.779993
$891$	−31.9837	−1.07149
$892$	53.2326	1.78236
$893$	16.3522	0.547206
$894$	74.9871	2.50794
$895$	3.33203	0.111377
$896$	−10.6055	−0.354306
$897$	57.2766	1.91241
$898$	37.9558	1.26660
$899$	−24.1850	−0.806614
$900$	−58.4374	−1.94791
$901$	0.286630	0.00954903
$902$	44.2277	1.47262
$903$	−12.5525	−0.417720
$904$	−25.0007	−0.831510
$905$	28.0196	0.931402
$906$	31.7767	1.05571
$907$	−42.3558	−1.40640	−0.703201	−	0.710992i	$-0.748246\pi$
$907$	−42.3558	−1.40640	−0.703201	+	0.710992i	$0.748246\pi$
$908$	−45.3140	−1.50380
$909$	105.504	3.49934
$910$	−13.2734	−0.440009
$911$	56.5777	1.87450	0.937252	−	0.348654i	$-0.113361\pi$
$911$	56.5777	1.87450	0.937252	+	0.348654i	$0.113361\pi$
$912$	23.3137	0.771993
$913$	−36.8850	−1.22072
$914$	−41.9714	−1.38829
$915$	−32.0233	−1.05866
$916$	−38.4572	−1.27066
$917$	10.2069	0.337062
$918$	55.6419	1.83646
$919$	−33.4050	−1.10193	−0.550965	−	0.834528i	$-0.685740\pi$
$919$	−33.4050	−1.10193	−0.550965	+	0.834528i	$0.685740\pi$
$920$	−5.73873	−0.189200
$921$	5.47314	0.180346
$922$	79.2976	2.61153
$923$	−58.2303	−1.91667
$924$	−28.2923	−0.930747
$925$	15.1628	0.498550
$926$	−26.8640	−0.882807
$927$	43.8291	1.43954
$928$	52.3462	1.71835
$929$	−33.7603	−1.10764	−0.553819	−	0.832637i	$-0.686830\pi$
$929$	−33.7603	−1.10764	−0.553819	+	0.832637i	$0.686830\pi$
$930$	26.5139	0.869426
$931$	3.40765	0.111681
$932$	12.9928	0.425593
$933$	5.22102	0.170929
$934$	78.3936	2.56512
$935$	11.7476	0.384188
$936$	−44.9373	−1.46882
$937$	−44.1949	−1.44378	−0.721892	−	0.692006i	$-0.756727\pi$
$937$	−44.1949	−1.44378	−0.721892	+	0.692006i	$0.756727\pi$
$938$	−16.0839	−0.525157
$939$	−27.7385	−0.905210
$940$	−14.6166	−0.476741
$941$	−11.4446	−0.373082	−0.186541	−	0.982447i	$-0.559728\pi$
$941$	−11.4446	−0.373082	−0.186541	+	0.982447i	$0.559728\pi$
$942$	−91.2492	−2.97306
$943$	−20.5469	−0.669101
$944$	13.2536	0.431368
$945$	−10.3410	−0.336394
$946$	−32.1250	−1.04447
$947$	15.9862	0.519482	0.259741	−	0.965678i	$-0.416363\pi$
$947$	15.9862	0.519482	0.259741	+	0.965678i	$0.416363\pi$
$948$	33.8486	1.09935
$949$	−15.2061	−0.493612
$950$	27.0227	0.876732
$951$	−55.9237	−1.81345
$952$	4.01543	0.130141
$953$	−48.7165	−1.57808	−0.789041	−	0.614340i	$-0.789422\pi$
$953$	−48.7165	−1.57808	−0.789041	+	0.614340i	$0.789422\pi$
$954$	−1.29187	−0.0418257
$955$	−11.3468	−0.367174
$956$	42.7154	1.38151
$957$	72.4525	2.34206
$958$	26.8273	0.866750
$959$	−2.80313	−0.0905178
$960$	−41.6534	−1.34436
$961$	−18.2898	−0.589993
$962$	47.5913	1.53441
$963$	67.8090	2.18512
$964$	−13.3854	−0.431114
$965$	−23.0609	−0.742356
$966$	23.0673	0.742179
$967$	14.0015	0.450258	0.225129	−	0.974329i	$-0.427720\pi$
$967$	14.0015	0.450258	0.225129	+	0.974329i	$0.427720\pi$
$968$	−2.34676	−0.0754276
$969$	−29.3312	−0.942255
$970$	−2.71771	−0.0872605
$971$	35.7775	1.14815	0.574077	−	0.818802i	$-0.305361\pi$
$971$	35.7775	1.14815	0.574077	+	0.818802i	$0.305361\pi$
$972$	0.0902276	0.00289405
$973$	7.39376	0.237033
$974$	76.5596	2.45313
$975$	59.0648	1.89159
$976$	21.1753	0.677803
$977$	14.6201	0.467740	0.233870	−	0.972268i	$-0.424861\pi$
$977$	14.6201	0.467740	0.233870	+	0.972268i	$0.424861\pi$
$978$	72.1129	2.30591
$979$	33.4174	1.06802
$980$	−3.04597	−0.0973000
$981$	−3.92123	−0.125195
$982$	45.6478	1.45668
$983$	11.0022	0.350914	0.175457	−	0.984487i	$-0.443860\pi$
$983$	11.0022	0.350914	0.175457	+	0.984487i	$0.443860\pi$
$984$	24.1832	0.770933
$985$	−10.0984	−0.321762
$986$	−41.9710	−1.33663
$987$	14.3945	0.458182
$988$	48.3281	1.53752
$989$	14.9243	0.474567
$990$	−52.9474	−1.68278
$991$	−15.6656	−0.497635	−0.248818	−	0.968550i	$-0.580042\pi$
$991$	−15.6656	−0.497635	−0.248818	+	0.968550i	$0.580042\pi$
$992$	−27.5101	−0.873447
$993$	−47.2050	−1.49801
$994$	−23.4514	−0.743834
$995$	−16.2497	−0.515151
$996$	−82.3191	−2.60838
$997$	−31.2580	−0.989952	−0.494976	−	0.868907i	$-0.664823\pi$
$997$	−31.2580	−0.989952	−0.494976	+	0.868907i	$0.664823\pi$
$998$	−6.93512	−0.219527
$999$	37.0774	1.17308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.13	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.13	✓	101	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.15616 q^{2} -2.99968 q^{3} +2.64901 q^{4} -1.14985 q^{5} +6.46779 q^{6} -1.00000 q^{7} -1.39937 q^{8} +5.99811 q^{9} +O(q^{10})\)	\(q-2.15616 q^{2} -2.99968 q^{3} +2.64901 q^{4} -1.14985 q^{5} +6.46779 q^{6} -1.00000 q^{7} -1.39937 q^{8} +5.99811 q^{9} +2.47926 q^{10} -3.56048 q^{11} -7.94620 q^{12} +5.35378 q^{13} +2.15616 q^{14} +3.44919 q^{15} -2.28076 q^{16} +2.86945 q^{17} -12.9329 q^{18} +3.40765 q^{19} -3.04597 q^{20} +2.99968 q^{21} +7.67695 q^{22} -3.56649 q^{23} +4.19767 q^{24} -3.67784 q^{25} -11.5436 q^{26} -8.99337 q^{27} -2.64901 q^{28} +6.78374 q^{29} -7.43700 q^{30} -3.56514 q^{31} +7.71642 q^{32} +10.6803 q^{33} -6.18699 q^{34} +1.14985 q^{35} +15.8891 q^{36} -4.12275 q^{37} -7.34744 q^{38} -16.0596 q^{39} +1.60907 q^{40} +5.76111 q^{41} -6.46779 q^{42} -4.18460 q^{43} -9.43175 q^{44} -6.89693 q^{45} +7.68992 q^{46} +4.79867 q^{47} +6.84156 q^{48} +1.00000 q^{49} +7.93000 q^{50} -8.60746 q^{51} +14.1822 q^{52} +0.0998902 q^{53} +19.3911 q^{54} +4.09402 q^{55} +1.39937 q^{56} -10.2219 q^{57} -14.6268 q^{58} -5.81104 q^{59} +9.13695 q^{60} -9.28429 q^{61} +7.68700 q^{62} -5.99811 q^{63} -12.0763 q^{64} -6.15605 q^{65} -23.0284 q^{66} -7.45950 q^{67} +7.60122 q^{68} +10.6984 q^{69} -2.47926 q^{70} -10.8765 q^{71} -8.39357 q^{72} -2.84026 q^{73} +8.88929 q^{74} +11.0324 q^{75} +9.02691 q^{76} +3.56048 q^{77} +34.6271 q^{78} -4.25972 q^{79} +2.62254 q^{80} +8.98297 q^{81} -12.4218 q^{82} +10.3596 q^{83} +7.94620 q^{84} -3.29945 q^{85} +9.02265 q^{86} -20.3491 q^{87} +4.98243 q^{88} -9.38564 q^{89} +14.8709 q^{90} -5.35378 q^{91} -9.44768 q^{92} +10.6943 q^{93} -10.3467 q^{94} -3.91830 q^{95} -23.1468 q^{96} -1.09618 q^{97} -2.15616 q^{98} -21.3561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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