LMFDB - Embedded newform 8041.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70684 q^{2} -0.791084 q^{3} +5.32698 q^{4} +2.18902 q^{5} +2.14134 q^{6} +2.25606 q^{7} -9.00562 q^{8} -2.37419 q^{9} +O(q^{10})$	\(q-2.70684 q^{2} -0.791084 q^{3} +5.32698 q^{4} +2.18902 q^{5} +2.14134 q^{6} +2.25606 q^{7} -9.00562 q^{8} -2.37419 q^{9} -5.92532 q^{10} +1.00000 q^{11} -4.21409 q^{12} +5.45597 q^{13} -6.10679 q^{14} -1.73170 q^{15} +13.7228 q^{16} -1.00000 q^{17} +6.42654 q^{18} -4.03682 q^{19} +11.6609 q^{20} -1.78473 q^{21} -2.70684 q^{22} -8.10653 q^{23} +7.12420 q^{24} -0.208196 q^{25} -14.7684 q^{26} +4.25143 q^{27} +12.0180 q^{28} +0.580123 q^{29} +4.68743 q^{30} +6.61000 q^{31} -19.1342 q^{32} -0.791084 q^{33} +2.70684 q^{34} +4.93856 q^{35} -12.6473 q^{36} +4.56964 q^{37} +10.9270 q^{38} -4.31613 q^{39} -19.7135 q^{40} -9.98067 q^{41} +4.83099 q^{42} +1.00000 q^{43} +5.32698 q^{44} -5.19714 q^{45} +21.9431 q^{46} -7.35867 q^{47} -10.8559 q^{48} -1.91019 q^{49} +0.563554 q^{50} +0.791084 q^{51} +29.0639 q^{52} -4.80700 q^{53} -11.5080 q^{54} +2.18902 q^{55} -20.3172 q^{56} +3.19346 q^{57} -1.57030 q^{58} +3.88412 q^{59} -9.22473 q^{60} -6.26730 q^{61} -17.8922 q^{62} -5.35631 q^{63} +24.3476 q^{64} +11.9432 q^{65} +2.14134 q^{66} +9.18605 q^{67} -5.32698 q^{68} +6.41295 q^{69} -13.3679 q^{70} -6.50612 q^{71} +21.3810 q^{72} -9.77844 q^{73} -12.3693 q^{74} +0.164701 q^{75} -21.5041 q^{76} +2.25606 q^{77} +11.6831 q^{78} +14.6523 q^{79} +30.0395 q^{80} +3.75932 q^{81} +27.0161 q^{82} +9.04577 q^{83} -9.50725 q^{84} -2.18902 q^{85} -2.70684 q^{86} -0.458926 q^{87} -9.00562 q^{88} +2.84526 q^{89} +14.0678 q^{90} +12.3090 q^{91} -43.1834 q^{92} -5.22906 q^{93} +19.9187 q^{94} -8.83667 q^{95} +15.1368 q^{96} -14.3801 q^{97} +5.17059 q^{98} -2.37419 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * 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 $

$2$	−2.70684	−1.91403	−0.957013	−	0.290046i	$-0.906329\pi$
$2$	−2.70684	−1.91403	−0.957013	+	0.290046i	$0.906329\pi$
$3$	−0.791084	−0.456733	−0.228366	−	0.973575i	$-0.573338\pi$
$3$	−0.791084	−0.456733	−0.228366	+	0.973575i	$0.573338\pi$
$4$	5.32698	2.66349
$5$	2.18902	0.978959	0.489480	−	0.872015i	$-0.337187\pi$
$5$	2.18902	0.978959	0.489480	+	0.872015i	$0.337187\pi$
$6$	2.14134	0.874198
$7$	2.25606	0.852711	0.426355	−	0.904556i	$-0.359797\pi$
$7$	2.25606	0.852711	0.426355	+	0.904556i	$0.359797\pi$
$8$	−9.00562	−3.18397
$9$	−2.37419	−0.791395
$10$	−5.92532	−1.87375
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.21409	−1.21650
$13$	5.45597	1.51321	0.756607	−	0.653870i	$-0.226856\pi$
$13$	5.45597	1.51321	0.756607	+	0.653870i	$0.226856\pi$
$14$	−6.10679	−1.63211
$15$	−1.73170	−0.447123
$16$	13.7228	3.43070
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	6.42654	1.51475
$19$	−4.03682	−0.926109	−0.463054	−	0.886330i	$-0.653247\pi$
$19$	−4.03682	−0.926109	−0.463054	+	0.886330i	$0.653247\pi$
$20$	11.6609	2.60745
$21$	−1.78473	−0.389461
$22$	−2.70684	−0.577100
$23$	−8.10653	−1.69033	−0.845164	−	0.534507i	$-0.820497\pi$
$23$	−8.10653	−1.69033	−0.845164	+	0.534507i	$0.820497\pi$
$24$	7.12420	1.45422
$25$	−0.208196	−0.0416393
$26$	−14.7684	−2.89633
$27$	4.25143	0.818189
$28$	12.0180	2.27119
$29$	0.580123	0.107726	0.0538631	−	0.998548i	$-0.482847\pi$
$29$	0.580123	0.107726	0.0538631	+	0.998548i	$0.482847\pi$
$30$	4.68743	0.855804
$31$	6.61000	1.18719	0.593595	−	0.804764i	$-0.297708\pi$
$31$	6.61000	1.18719	0.593595	+	0.804764i	$0.297708\pi$
$32$	−19.1342	−3.38248
$33$	−0.791084	−0.137710
$34$	2.70684	0.464219
$35$	4.93856	0.834769
$36$	−12.6473	−2.10788
$37$	4.56964	0.751244	0.375622	−	0.926773i	$-0.377429\pi$
$37$	4.56964	0.751244	0.375622	+	0.926773i	$0.377429\pi$
$38$	10.9270	1.77260
$39$	−4.31613	−0.691134
$40$	−19.7135	−3.11697
$41$	−9.98067	−1.55872	−0.779360	−	0.626577i	$-0.784455\pi$
$41$	−9.98067	−1.55872	−0.779360	+	0.626577i	$0.784455\pi$
$42$	4.83099	0.745438
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	5.32698	0.803073
$45$	−5.19714	−0.774744
$46$	21.9431	3.23533
$47$	−7.35867	−1.07337	−0.536686	−	0.843782i	$-0.680324\pi$
$47$	−7.35867	−1.07337	−0.536686	+	0.843782i	$0.680324\pi$
$48$	−10.8559	−1.56691
$49$	−1.91019	−0.272885
$50$	0.563554	0.0796986
$51$	0.791084	0.110774
$52$	29.0639	4.03043
$53$	−4.80700	−0.660292	−0.330146	−	0.943930i	$-0.607098\pi$
$53$	−4.80700	−0.660292	−0.330146	+	0.943930i	$0.607098\pi$
$54$	−11.5080	−1.56603
$55$	2.18902	0.295167
$56$	−20.3172	−2.71500
$57$	3.19346	0.422984
$58$	−1.57030	−0.206191
$59$	3.88412	0.505670	0.252835	−	0.967509i	$-0.418637\pi$
$59$	3.88412	0.505670	0.252835	+	0.967509i	$0.418637\pi$
$60$	−9.22473	−1.19091
$61$	−6.26730	−0.802445	−0.401223	−	0.915981i	$-0.631415\pi$
$61$	−6.26730	−0.802445	−0.401223	+	0.915981i	$0.631415\pi$
$62$	−17.8922	−2.27231
$63$	−5.35631	−0.674831
$64$	24.3476	3.04345
$65$	11.9432	1.48137
$66$	2.14134	0.263581
$67$	9.18605	1.12225	0.561127	−	0.827729i	$-0.310368\pi$
$67$	9.18605	1.12225	0.561127	+	0.827729i	$0.310368\pi$
$68$	−5.32698	−0.645992
$69$	6.41295	0.772028
$70$	−13.3679	−1.59777
$71$	−6.50612	−0.772134	−0.386067	−	0.922471i	$-0.626167\pi$
$71$	−6.50612	−0.772134	−0.386067	+	0.922471i	$0.626167\pi$
$72$	21.3810	2.51978
$73$	−9.77844	−1.14448	−0.572240	−	0.820086i	$-0.693925\pi$
$73$	−9.77844	−1.14448	−0.572240	+	0.820086i	$0.693925\pi$
$74$	−12.3693	−1.43790
$75$	0.164701	0.0190180
$76$	−21.5041	−2.46668
$77$	2.25606	0.257102
$78$	11.6831	1.32285
$79$	14.6523	1.64851	0.824257	−	0.566216i	$-0.191593\pi$
$79$	14.6523	1.64851	0.824257	+	0.566216i	$0.191593\pi$
$80$	30.0395	3.35851
$81$	3.75932	0.417702
$82$	27.0161	2.98343
$83$	9.04577	0.992902	0.496451	−	0.868065i	$-0.334636\pi$
$83$	9.04577	0.992902	0.496451	+	0.868065i	$0.334636\pi$
$84$	−9.50725	−1.03733
$85$	−2.18902	−0.237432
$86$	−2.70684	−0.291886
$87$	−0.458926	−0.0492020
$88$	−9.00562	−0.960002
$89$	2.84526	0.301597	0.150799	−	0.988565i	$-0.451815\pi$
$89$	2.84526	0.301597	0.150799	+	0.988565i	$0.451815\pi$
$90$	14.0678	1.48288
$91$	12.3090	1.29033
$92$	−43.1834	−4.50218
$93$	−5.22906	−0.542229
$94$	19.9187	2.05446
$95$	−8.83667	−0.906623
$96$	15.1368	1.54489
$97$	−14.3801	−1.46008	−0.730038	−	0.683407i	$-0.760497\pi$
$97$	−14.3801	−1.46008	−0.730038	+	0.683407i	$0.760497\pi$
$98$	5.17059	0.522308
$99$	−2.37419	−0.238615
$100$	−1.10906	−0.110906
$101$	13.6557	1.35879	0.679395	−	0.733773i	$-0.262242\pi$
$101$	13.6557	1.35879	0.679395	+	0.733773i	$0.262242\pi$
$102$	−2.14134	−0.212024
$103$	0.324963	0.0320195	0.0160098	−	0.999872i	$-0.494904\pi$
$103$	0.324963	0.0320195	0.0160098	+	0.999872i	$0.494904\pi$
$104$	−49.1344	−4.81802
$105$	−3.90682	−0.381266
$106$	13.0118	1.26381
$107$	−19.1933	−1.85548	−0.927742	−	0.373223i	$-0.878253\pi$
$107$	−19.1933	−1.85548	−0.927742	+	0.373223i	$0.878253\pi$
$108$	22.6473	2.17924
$109$	0.429283	0.0411179	0.0205590	−	0.999789i	$-0.493455\pi$
$109$	0.429283	0.0411179	0.0205590	+	0.999789i	$0.493455\pi$
$110$	−5.92532	−0.564958
$111$	−3.61497	−0.343118
$112$	30.9595	2.92539
$113$	5.04892	0.474963	0.237481	−	0.971392i	$-0.423678\pi$
$113$	5.04892	0.474963	0.237481	+	0.971392i	$0.423678\pi$
$114$	−8.64419	−0.809602
$115$	−17.7453	−1.65476
$116$	3.09031	0.286928
$117$	−12.9535	−1.19755
$118$	−10.5137	−0.967865
$119$	−2.25606	−0.206813
$120$	15.5950	1.42362
$121$	1.00000	0.0909091
$122$	16.9646	1.53590
$123$	7.89555	0.711918
$124$	35.2113	3.16207
$125$	−11.4008	−1.01972
$126$	14.4987	1.29164
$127$	−1.01867	−0.0903924	−0.0451962	−	0.998978i	$-0.514391\pi$
$127$	−1.01867	−0.0903924	−0.0451962	+	0.998978i	$0.514391\pi$
$128$	−27.6367	−2.44276
$129$	−0.791084	−0.0696511
$130$	−32.3284	−2.83539
$131$	1.86596	0.163030	0.0815148	−	0.996672i	$-0.474024\pi$
$131$	1.86596	0.163030	0.0815148	+	0.996672i	$0.474024\pi$
$132$	−4.21409	−0.366790
$133$	−9.10730	−0.789703
$134$	−24.8652	−2.14802
$135$	9.30647	0.800973
$136$	9.00562	0.772225
$137$	−5.33865	−0.456112	−0.228056	−	0.973648i	$-0.573237\pi$
$137$	−5.33865	−0.456112	−0.228056	+	0.973648i	$0.573237\pi$
$138$	−17.3588	−1.47768
$139$	−18.0239	−1.52877	−0.764383	−	0.644762i	$-0.776956\pi$
$139$	−18.0239	−1.52877	−0.764383	+	0.644762i	$0.776956\pi$
$140$	26.3076	2.22340
$141$	5.82132	0.490244
$142$	17.6110	1.47788
$143$	5.45597	0.456251
$144$	−32.5805	−2.71504
$145$	1.26990	0.105459
$146$	26.4687	2.19056
$147$	1.51112	0.124635
$148$	24.3424	2.00093
$149$	6.08325	0.498359	0.249179	−	0.968457i	$-0.419839\pi$
$149$	6.08325	0.498359	0.249179	+	0.968457i	$0.419839\pi$
$150$	−0.445819	−0.0364009
$151$	−9.95081	−0.809786	−0.404893	−	0.914364i	$-0.632691\pi$
$151$	−9.95081	−0.809786	−0.404893	+	0.914364i	$0.632691\pi$
$152$	36.3540	2.94870
$153$	2.37419	0.191942
$154$	−6.10679	−0.492100
$155$	14.4694	1.16221
$156$	−22.9920	−1.84083
$157$	−12.6703	−1.01120	−0.505599	−	0.862769i	$-0.668728\pi$
$157$	−12.6703	−1.01120	−0.505599	+	0.862769i	$0.668728\pi$
$158$	−39.6615	−3.15530
$159$	3.80274	0.301577
$160$	−41.8851	−3.31131
$161$	−18.2888	−1.44136
$162$	−10.1759	−0.799492
$163$	−8.74083	−0.684634	−0.342317	−	0.939584i	$-0.611212\pi$
$163$	−8.74083	−0.684634	−0.342317	+	0.939584i	$0.611212\pi$
$164$	−53.1669	−4.15164
$165$	−1.73170	−0.134813
$166$	−24.4855	−1.90044
$167$	13.2007	1.02150	0.510751	−	0.859729i	$-0.329367\pi$
$167$	13.2007	1.02150	0.510751	+	0.859729i	$0.329367\pi$
$168$	16.0726	1.24003
$169$	16.7676	1.28982
$170$	5.92532	0.454452
$171$	9.58415	0.732918
$172$	5.32698	0.406179
$173$	19.2601	1.46432	0.732161	−	0.681132i	$-0.238512\pi$
$173$	19.2601	1.46432	0.732161	+	0.681132i	$0.238512\pi$
$174$	1.24224	0.0941740
$175$	−0.469703	−0.0355062
$176$	13.7228	1.03439
$177$	−3.07267	−0.230956
$178$	−7.70167	−0.577265
$179$	−16.1798	−1.20934	−0.604668	−	0.796478i	$-0.706694\pi$
$179$	−16.1798	−1.20934	−0.604668	+	0.796478i	$0.706694\pi$
$180$	−27.6851	−2.06352
$181$	−19.0164	−1.41348	−0.706739	−	0.707474i	$-0.749835\pi$
$181$	−19.0164	−1.41348	−0.706739	+	0.707474i	$0.749835\pi$
$182$	−33.3185	−2.46973
$183$	4.95796	0.366503
$184$	73.0043	5.38195
$185$	10.0030	0.735437
$186$	14.1542	1.03784
$187$	−1.00000	−0.0731272
$188$	−39.1995	−2.85892
$189$	9.59149	0.697678
$190$	23.9194	1.73530
$191$	−20.6628	−1.49511	−0.747553	−	0.664202i	$-0.768771\pi$
$191$	−20.6628	−1.49511	−0.747553	+	0.664202i	$0.768771\pi$
$192$	−19.2610	−1.39004
$193$	−23.5308	−1.69379	−0.846893	−	0.531763i	$-0.821530\pi$
$193$	−23.5308	−1.69379	−0.846893	+	0.531763i	$0.821530\pi$
$194$	38.9246	2.79462
$195$	−9.44809	−0.676592
$196$	−10.1756	−0.726826
$197$	−22.8391	−1.62722	−0.813608	−	0.581414i	$-0.802500\pi$
$197$	−22.8391	−1.62722	−0.813608	+	0.581414i	$0.802500\pi$
$198$	6.42654	0.456714
$199$	−25.4303	−1.80271	−0.901353	−	0.433086i	$-0.857425\pi$
$199$	−25.4303	−1.80271	−0.901353	+	0.433086i	$0.857425\pi$
$200$	1.87494	0.132578
$201$	−7.26694	−0.512570
$202$	−36.9637	−2.60076
$203$	1.30879	0.0918592
$204$	4.21409	0.295046
$205$	−21.8479	−1.52592
$206$	−0.879622	−0.0612862
$207$	19.2464	1.33772
$208$	74.8712	5.19138
$209$	−4.03682	−0.279232
$210$	10.5751	0.729753
$211$	−20.9285	−1.44078	−0.720390	−	0.693569i	$-0.756037\pi$
$211$	−20.9285	−1.44078	−0.720390	+	0.693569i	$0.756037\pi$
$212$	−25.6068	−1.75868
$213$	5.14689	0.352659
$214$	51.9531	3.55144
$215$	2.18902	0.149290
$216$	−38.2868	−2.60509
$217$	14.9125	1.01233
$218$	−1.16200	−0.0787007
$219$	7.73557	0.522722
$220$	11.6609	0.786176
$221$	−5.45597	−0.367008
$222$	9.78515	0.656736
$223$	4.85315	0.324991	0.162496	−	0.986709i	$-0.448046\pi$
$223$	4.85315	0.324991	0.162496	+	0.986709i	$0.448046\pi$
$224$	−43.1679	−2.88428
$225$	0.494297	0.0329531
$226$	−13.6666	−0.909090
$227$	10.3273	0.685446	0.342723	−	0.939437i	$-0.388651\pi$
$227$	10.3273	0.685446	0.342723	+	0.939437i	$0.388651\pi$
$228$	17.0115	1.12662
$229$	20.5314	1.35675	0.678376	−	0.734715i	$-0.262684\pi$
$229$	20.5314	1.35675	0.678376	+	0.734715i	$0.262684\pi$
$230$	48.0338	3.16726
$231$	−1.78473	−0.117427
$232$	−5.22437	−0.342996
$233$	17.8095	1.16674	0.583368	−	0.812208i	$-0.301734\pi$
$233$	17.8095	1.16674	0.583368	+	0.812208i	$0.301734\pi$
$234$	35.0630	2.29214
$235$	−16.1083	−1.05079
$236$	20.6907	1.34685
$237$	−11.5912	−0.752930
$238$	6.10679	0.395845
$239$	−27.7981	−1.79811	−0.899054	−	0.437837i	$-0.855745\pi$
$239$	−27.7981	−1.79811	−0.899054	+	0.437837i	$0.855745\pi$
$240$	−23.7637	−1.53394
$241$	21.7616	1.40179	0.700893	−	0.713266i	$-0.252785\pi$
$241$	21.7616	1.40179	0.700893	+	0.713266i	$0.252785\pi$
$242$	−2.70684	−0.174002
$243$	−15.7282	−1.00897
$244$	−33.3858	−2.13731
$245$	−4.18145	−0.267143
$246$	−21.3720	−1.36263
$247$	−22.0247	−1.40140
$248$	−59.5271	−3.77997
$249$	−7.15597	−0.453491
$250$	30.8603	1.95177
$251$	−24.7339	−1.56119	−0.780594	−	0.625038i	$-0.785083\pi$
$251$	−24.7339	−1.56119	−0.780594	+	0.625038i	$0.785083\pi$
$252$	−28.5330	−1.79741
$253$	−8.10653	−0.509653
$254$	2.75738	0.173013
$255$	1.73170	0.108443
$256$	26.1129	1.63206
$257$	8.07245	0.503546	0.251773	−	0.967786i	$-0.418986\pi$
$257$	8.07245	0.503546	0.251773	+	0.967786i	$0.418986\pi$
$258$	2.14134	0.133314
$259$	10.3094	0.640594
$260$	63.6214	3.94563
$261$	−1.37732	−0.0852540
$262$	−5.05085	−0.312043
$263$	16.0890	0.992089	0.496045	−	0.868297i	$-0.334785\pi$
$263$	16.0890	0.992089	0.496045	+	0.868297i	$0.334785\pi$
$264$	7.12420	0.438464
$265$	−10.5226	−0.646399
$266$	24.6520	1.51151
$267$	−2.25084	−0.137749
$268$	48.9340	2.98912
$269$	−14.5622	−0.887874	−0.443937	−	0.896058i	$-0.646419\pi$
$269$	−14.5622	−0.887874	−0.443937	+	0.896058i	$0.646419\pi$
$270$	−25.1911	−1.53308
$271$	26.5261	1.61135	0.805673	−	0.592360i	$-0.201804\pi$
$271$	26.5261	1.61135	0.805673	+	0.592360i	$0.201804\pi$
$272$	−13.7228	−0.832067
$273$	−9.73745	−0.589337
$274$	14.4509	0.873009
$275$	−0.208196	−0.0125547
$276$	34.1617	2.05629
$277$	4.76863	0.286519	0.143260	−	0.989685i	$-0.454242\pi$
$277$	4.76863	0.286519	0.143260	+	0.989685i	$0.454242\pi$
$278$	48.7878	2.92610
$279$	−15.6934	−0.939537
$280$	−44.4748	−2.65788
$281$	22.6142	1.34905	0.674524	−	0.738252i	$-0.264349\pi$
$281$	22.6142	1.34905	0.674524	+	0.738252i	$0.264349\pi$
$282$	−15.7574	−0.938339
$283$	−2.44830	−0.145536	−0.0727681	−	0.997349i	$-0.523183\pi$
$283$	−2.44830	−0.145536	−0.0727681	+	0.997349i	$0.523183\pi$
$284$	−34.6580	−2.05657
$285$	6.99055	0.414084
$286$	−14.7684	−0.873276
$287$	−22.5170	−1.32914
$288$	45.4281	2.67688
$289$	1.00000	0.0588235
$290$	−3.43742	−0.201852
$291$	11.3758	0.666864
$292$	−52.0896	−3.04831
$293$	−15.1451	−0.884788	−0.442394	−	0.896821i	$-0.645871\pi$
$293$	−15.1451	−0.884788	−0.442394	+	0.896821i	$0.645871\pi$
$294$	−4.09037	−0.238555
$295$	8.50242	0.495030
$296$	−41.1524	−2.39194
$297$	4.25143	0.246693
$298$	−16.4664	−0.953872
$299$	−44.2290	−2.55783
$300$	0.877359	0.0506543
$301$	2.25606	0.130037
$302$	26.9353	1.54995
$303$	−10.8028	−0.620604
$304$	−55.3964	−3.17720
$305$	−13.7192	−0.785561
$306$	−6.42654	−0.367381
$307$	−12.8979	−0.736123	−0.368061	−	0.929802i	$-0.619978\pi$
$307$	−12.8979	−0.736123	−0.368061	+	0.929802i	$0.619978\pi$
$308$	12.0180	0.684789
$309$	−0.257073	−0.0146244
$310$	−39.1664	−2.22450
$311$	−19.8324	−1.12459	−0.562297	−	0.826935i	$-0.690082\pi$
$311$	−19.8324	−1.12459	−0.562297	+	0.826935i	$0.690082\pi$
$312$	38.8694	2.20055
$313$	14.5481	0.822307	0.411154	−	0.911566i	$-0.365126\pi$
$313$	14.5481	0.822307	0.411154	+	0.911566i	$0.365126\pi$
$314$	34.2964	1.93546
$315$	−11.7251	−0.660632
$316$	78.0526	4.39080
$317$	4.57893	0.257178	0.128589	−	0.991698i	$-0.458955\pi$
$317$	4.57893	0.257178	0.128589	+	0.991698i	$0.458955\pi$
$318$	−10.2934	−0.577226
$319$	0.580123	0.0324807
$320$	53.2973	2.97941
$321$	15.1835	0.847460
$322$	49.5049	2.75880
$323$	4.03682	0.224614
$324$	20.0258	1.11255
$325$	−1.13591	−0.0630091
$326$	23.6600	1.31041
$327$	−0.339599	−0.0187799
$328$	89.8821	4.96291
$329$	−16.6016	−0.915275
$330$	4.68743	0.258035
$331$	−9.00062	−0.494719	−0.247359	−	0.968924i	$-0.579563\pi$
$331$	−9.00062	−0.494719	−0.247359	+	0.968924i	$0.579563\pi$
$332$	48.1867	2.64459
$333$	−10.8492	−0.594531
$334$	−35.7323	−1.95518
$335$	20.1084	1.09864
$336$	−24.4915	−1.33612
$337$	17.1354	0.933426	0.466713	−	0.884409i	$-0.345438\pi$
$337$	17.1354	0.933426	0.466713	+	0.884409i	$0.345438\pi$
$338$	−45.3872	−2.46874
$339$	−3.99412	−0.216931
$340$	−11.6609	−0.632399
$341$	6.61000	0.357951
$342$	−25.9428	−1.40282
$343$	−20.1019	−1.08540
$344$	−9.00562	−0.485550
$345$	14.0381	0.755784
$346$	−52.1341	−2.80275
$347$	31.2194	1.67595	0.837973	−	0.545712i	$-0.183741\pi$
$347$	31.2194	1.67595	0.837973	+	0.545712i	$0.183741\pi$
$348$	−2.44469	−0.131049
$349$	19.5441	1.04617	0.523086	−	0.852280i	$-0.324781\pi$
$349$	19.5441	1.04617	0.523086	+	0.852280i	$0.324781\pi$
$350$	1.27141	0.0679598
$351$	23.1957	1.23809
$352$	−19.1342	−1.01986
$353$	−0.733096	−0.0390188	−0.0195094	−	0.999810i	$-0.506210\pi$
$353$	−0.733096	−0.0390188	−0.0195094	+	0.999810i	$0.506210\pi$
$354$	8.31722	0.442055
$355$	−14.2420	−0.755888
$356$	15.1567	0.803302
$357$	1.78473	0.0944581
$358$	43.7962	2.31470
$359$	25.7612	1.35962	0.679812	−	0.733386i	$-0.262061\pi$
$359$	25.7612	1.35962	0.679812	+	0.733386i	$0.262061\pi$
$360$	46.8034	2.46676
$361$	−2.70412	−0.142322
$362$	51.4744	2.70543
$363$	−0.791084	−0.0415212
$364$	65.5698	3.43679
$365$	−21.4052	−1.12040
$366$	−13.4204	−0.701496
$367$	8.49071	0.443211	0.221606	−	0.975136i	$-0.428870\pi$
$367$	8.49071	0.443211	0.221606	+	0.975136i	$0.428870\pi$
$368$	−111.244	−5.79901
$369$	23.6960	1.23356
$370$	−27.0766	−1.40765
$371$	−10.8449	−0.563038
$372$	−27.8551	−1.44422
$373$	16.0570	0.831399	0.415699	−	0.909502i	$-0.363537\pi$
$373$	16.0570	0.831399	0.415699	+	0.909502i	$0.363537\pi$
$374$	2.70684	0.139967
$375$	9.01902	0.465740
$376$	66.2693	3.41758
$377$	3.16513	0.163013
$378$	−25.9626	−1.33537
$379$	−13.7806	−0.707861	−0.353931	−	0.935272i	$-0.615155\pi$
$379$	−13.7806	−0.707861	−0.353931	+	0.935272i	$0.615155\pi$
$380$	−47.0728	−2.41478
$381$	0.805854	0.0412851
$382$	55.9308	2.86167
$383$	−2.28479	−0.116747	−0.0583737	−	0.998295i	$-0.518591\pi$
$383$	−2.28479	−0.116747	−0.0583737	+	0.998295i	$0.518591\pi$
$384$	21.8629	1.11569
$385$	4.93856	0.251692
$386$	63.6942	3.24195
$387$	−2.37419	−0.120687
$388$	−76.6024	−3.88890
$389$	−23.2091	−1.17675	−0.588374	−	0.808589i	$-0.700232\pi$
$389$	−23.2091	−1.17675	−0.588374	+	0.808589i	$0.700232\pi$
$390$	25.5745	1.29501
$391$	8.10653	0.409965
$392$	17.2025	0.868855
$393$	−1.47613	−0.0744609
$394$	61.8217	3.11453
$395$	32.0742	1.61383
$396$	−12.6473	−0.635548
$397$	29.9966	1.50549	0.752743	−	0.658314i	$-0.228730\pi$
$397$	29.9966	1.50549	0.752743	+	0.658314i	$0.228730\pi$
$398$	68.8357	3.45042
$399$	7.20464	0.360683
$400$	−2.85704	−0.142852
$401$	−8.81318	−0.440109	−0.220055	−	0.975488i	$-0.570624\pi$
$401$	−8.81318	−0.440109	−0.220055	+	0.975488i	$0.570624\pi$
$402$	19.6704	0.981073
$403$	36.0639	1.79647
$404$	72.7436	3.61913
$405$	8.22921	0.408913
$406$	−3.54269	−0.175821
$407$	4.56964	0.226509
$408$	−7.12420	−0.352701
$409$	11.3334	0.560402	0.280201	−	0.959941i	$-0.409599\pi$
$409$	11.3334	0.560402	0.280201	+	0.959941i	$0.409599\pi$
$410$	59.1387	2.92065
$411$	4.22332	0.208321
$412$	1.73107	0.0852838
$413$	8.76281	0.431190
$414$	−52.0969	−2.56043
$415$	19.8014	0.972011
$416$	−104.396	−5.11841
$417$	14.2584	0.698237
$418$	10.9270	0.534458
$419$	13.0044	0.635307	0.317654	−	0.948207i	$-0.397105\pi$
$419$	13.0044	0.635307	0.317654	+	0.948207i	$0.397105\pi$
$420$	−20.8115	−1.01550
$421$	−8.10785	−0.395153	−0.197576	−	0.980288i	$-0.563307\pi$
$421$	−8.10785	−0.395153	−0.197576	+	0.980288i	$0.563307\pi$
$422$	56.6502	2.75769
$423$	17.4708	0.849461
$424$	43.2900	2.10235
$425$	0.208196	0.0100990
$426$	−13.9318	−0.674998
$427$	−14.1394	−0.684254
$428$	−102.242	−4.94207
$429$	−4.31613	−0.208385
$430$	−5.92532	−0.285745
$431$	−31.0152	−1.49395	−0.746975	−	0.664852i	$-0.768494\pi$
$431$	−31.0152	−1.49395	−0.746975	+	0.664852i	$0.768494\pi$
$432$	58.3416	2.80696
$433$	−12.4246	−0.597090	−0.298545	−	0.954396i	$-0.596501\pi$
$433$	−12.4246	−0.597090	−0.298545	+	0.954396i	$0.596501\pi$
$434$	−40.3659	−1.93762
$435$	−1.00460	−0.0481668
$436$	2.28679	0.109517
$437$	32.7246	1.56543
$438$	−20.9390	−1.00050
$439$	22.2632	1.06257	0.531283	−	0.847195i	$-0.321710\pi$
$439$	22.2632	1.06257	0.531283	+	0.847195i	$0.321710\pi$
$440$	−19.7135	−0.939803
$441$	4.53515	0.215960
$442$	14.7684	0.702463
$443$	16.3199	0.775384	0.387692	−	0.921789i	$-0.373272\pi$
$443$	16.3199	0.775384	0.387692	+	0.921789i	$0.373272\pi$
$444$	−19.2569	−0.913891
$445$	6.22833	0.295251
$446$	−13.1367	−0.622041
$447$	−4.81236	−0.227617
$448$	54.9296	2.59518
$449$	−1.27059	−0.0599630	−0.0299815	−	0.999550i	$-0.509545\pi$
$449$	−1.27059	−0.0599630	−0.0299815	+	0.999550i	$0.509545\pi$
$450$	−1.33798	−0.0630731
$451$	−9.98067	−0.469972
$452$	26.8955	1.26506
$453$	7.87193	0.369856
$454$	−27.9543	−1.31196
$455$	26.9446	1.26318
$456$	−28.7591	−1.34677
$457$	35.7567	1.67263	0.836313	−	0.548252i	$-0.184707\pi$
$457$	35.7567	1.67263	0.836313	+	0.548252i	$0.184707\pi$
$458$	−55.5752	−2.59686
$459$	−4.25143	−0.198440
$460$	−94.5292	−4.40745
$461$	−29.3523	−1.36707	−0.683537	−	0.729916i	$-0.739559\pi$
$461$	−29.3523	−1.36707	−0.683537	+	0.729916i	$0.739559\pi$
$462$	4.83099	0.224758
$463$	27.0690	1.25800	0.629002	−	0.777403i	$-0.283464\pi$
$463$	27.0690	1.25800	0.629002	+	0.777403i	$0.283464\pi$
$464$	7.96091	0.369576
$465$	−11.4465	−0.530820
$466$	−48.2074	−2.23316
$467$	27.5845	1.27646	0.638230	−	0.769845i	$-0.279667\pi$
$467$	27.5845	1.27646	0.638230	+	0.769845i	$0.279667\pi$
$468$	−69.0030	−3.18967
$469$	20.7243	0.956958
$470$	43.6025	2.01123
$471$	10.0233	0.461847
$472$	−34.9789	−1.61004
$473$	1.00000	0.0459800
$474$	31.3756	1.44113
$475$	0.840450	0.0385625
$476$	−12.0180	−0.550844
$477$	11.4127	0.522552
$478$	75.2450	3.44163
$479$	−7.33182	−0.334999	−0.167500	−	0.985872i	$-0.553569\pi$
$479$	−7.33182	−0.334999	−0.167500	+	0.985872i	$0.553569\pi$
$480$	33.1346	1.51238
$481$	24.9318	1.13679
$482$	−58.9051	−2.68305
$483$	14.4680	0.658317
$484$	5.32698	0.242136
$485$	−31.4783	−1.42935
$486$	42.5738	1.93119
$487$	0.912270	0.0413389	0.0206695	−	0.999786i	$-0.493420\pi$
$487$	0.912270	0.0413389	0.0206695	+	0.999786i	$0.493420\pi$
$488$	56.4409	2.55496
$489$	6.91473	0.312695
$490$	11.3185	0.511318
$491$	−32.5051	−1.46694	−0.733468	−	0.679724i	$-0.762100\pi$
$491$	−32.5051	−1.46694	−0.733468	+	0.679724i	$0.762100\pi$
$492$	42.0595	1.89619
$493$	−0.580123	−0.0261274
$494$	59.6175	2.68232
$495$	−5.19714	−0.233594
$496$	90.7076	4.07289
$497$	−14.6782	−0.658407
$498$	19.3701	0.867993
$499$	7.22334	0.323361	0.161681	−	0.986843i	$-0.448309\pi$
$499$	7.22334	0.323361	0.161681	+	0.986843i	$0.448309\pi$
$500$	−60.7321	−2.71602
$501$	−10.4429	−0.466554
$502$	66.9507	2.98815
$503$	18.5971	0.829203	0.414601	−	0.910003i	$-0.363921\pi$
$503$	18.5971	0.829203	0.414601	+	0.910003i	$0.363921\pi$
$504$	48.2368	2.14864
$505$	29.8925	1.33020
$506$	21.9431	0.975489
$507$	−13.2646	−0.589101
$508$	−5.42644	−0.240759
$509$	−16.4432	−0.728831	−0.364415	−	0.931236i	$-0.618731\pi$
$509$	−16.4432	−0.728831	−0.364415	+	0.931236i	$0.618731\pi$
$510$	−4.68743	−0.207563
$511$	−22.0608	−0.975911
$512$	−15.4101	−0.681035
$513$	−17.1623	−0.757732
$514$	−21.8508	−0.963799
$515$	0.711350	0.0313458
$516$	−4.21409	−0.185515
$517$	−7.35867	−0.323634
$518$	−27.9058	−1.22611
$519$	−15.2364	−0.668803
$520$	−107.556	−4.71665
$521$	−31.8170	−1.39393	−0.696963	−	0.717107i	$-0.745466\pi$
$521$	−31.8170	−1.39393	−0.696963	+	0.717107i	$0.745466\pi$
$522$	3.72818	0.163178
$523$	−21.2818	−0.930587	−0.465293	−	0.885157i	$-0.654051\pi$
$523$	−21.2818	−0.930587	−0.465293	+	0.885157i	$0.654051\pi$
$524$	9.93993	0.434228
$525$	0.371575	0.0162169
$526$	−43.5503	−1.89888
$527$	−6.61000	−0.287936
$528$	−10.8559	−0.472442
$529$	42.7158	1.85721
$530$	28.4830	1.23722
$531$	−9.22163	−0.400185
$532$	−48.5144	−2.10337
$533$	−54.4542	−2.35868
$534$	6.09267	0.263656
$535$	−42.0144	−1.81644
$536$	−82.7260	−3.57322
$537$	12.7996	0.552343
$538$	39.4176	1.69941
$539$	−1.91019	−0.0822778
$540$	49.5754	2.13339
$541$	−18.2271	−0.783642	−0.391821	−	0.920041i	$-0.628155\pi$
$541$	−18.2271	−0.783642	−0.391821	+	0.920041i	$0.628155\pi$
$542$	−71.8019	−3.08416
$543$	15.0436	0.645582
$544$	19.1342	0.820372
$545$	0.939710	0.0402527
$546$	26.3577	1.12801
$547$	0.769577	0.0329047	0.0164524	−	0.999865i	$-0.494763\pi$
$547$	0.769577	0.0329047	0.0164524	+	0.999865i	$0.494763\pi$
$548$	−28.4389	−1.21485
$549$	14.8797	0.635051
$550$	0.563554	0.0240300
$551$	−2.34185	−0.0997661
$552$	−57.7525	−2.45811
$553$	33.0565	1.40571
$554$	−12.9079	−0.548405
$555$	−7.91324	−0.335898
$556$	−96.0130	−4.07186
$557$	26.8096	1.13596	0.567980	−	0.823042i	$-0.307725\pi$
$557$	26.8096	1.13596	0.567980	+	0.823042i	$0.307725\pi$
$558$	42.4794	1.79830
$559$	5.45597	0.230763
$560$	67.7708	2.86384
$561$	0.791084	0.0333996
$562$	−61.2130	−2.58211
$563$	−29.8271	−1.25706	−0.628531	−	0.777785i	$-0.716343\pi$
$563$	−29.8271	−1.25706	−0.628531	+	0.777785i	$0.716343\pi$
$564$	31.0101	1.30576
$565$	11.0522	0.464969
$566$	6.62715	0.278560
$567$	8.48124	0.356179
$568$	58.5916	2.45845
$569$	−25.3489	−1.06268	−0.531341	−	0.847158i	$-0.678312\pi$
$569$	−25.3489	−1.06268	−0.531341	+	0.847158i	$0.678312\pi$
$570$	−18.9223	−0.792568
$571$	−8.88670	−0.371897	−0.185948	−	0.982559i	$-0.559536\pi$
$571$	−8.88670	−0.371897	−0.185948	+	0.982559i	$0.559536\pi$
$572$	29.0639	1.21522
$573$	16.3460	0.682864
$574$	60.9499	2.54400
$575$	1.68775	0.0703840
$576$	−57.8057	−2.40857
$577$	−5.19465	−0.216256	−0.108128	−	0.994137i	$-0.534486\pi$
$577$	−5.19465	−0.216256	−0.108128	+	0.994137i	$0.534486\pi$
$578$	−2.70684	−0.112590
$579$	18.6149	0.773608
$580$	6.76474	0.280891
$581$	20.4078	0.846658
$582$	−30.7926	−1.27639
$583$	−4.80700	−0.199085
$584$	88.0609	3.64399
$585$	−28.3554	−1.17235
$586$	40.9954	1.69351
$587$	0.948903	0.0391654	0.0195827	−	0.999808i	$-0.493766\pi$
$587$	0.948903	0.0391654	0.0195827	+	0.999808i	$0.493766\pi$
$588$	8.04973	0.331965
$589$	−26.6833	−1.09947
$590$	−23.0147	−0.947500
$591$	18.0676	0.743203
$592$	62.7082	2.57729
$593$	−23.0696	−0.947354	−0.473677	−	0.880699i	$-0.657074\pi$
$593$	−23.0696	−0.947354	−0.473677	+	0.880699i	$0.657074\pi$
$594$	−11.5080	−0.472177
$595$	−4.93856	−0.202461
$596$	32.4054	1.32738
$597$	20.1175	0.823354
$598$	119.721	4.89575
$599$	−45.3661	−1.85361	−0.926805	−	0.375543i	$-0.877456\pi$
$599$	−45.3661	−1.85361	−0.926805	+	0.375543i	$0.877456\pi$
$600$	−1.48323	−0.0605527
$601$	35.5034	1.44821	0.724106	−	0.689689i	$-0.242253\pi$
$601$	35.5034	1.44821	0.724106	+	0.689689i	$0.242253\pi$
$602$	−6.10679	−0.248894
$603$	−21.8094	−0.888147
$604$	−53.0078	−2.15686
$605$	2.18902	0.0889963
$606$	29.2414	1.18785
$607$	−28.2565	−1.14690	−0.573448	−	0.819242i	$-0.694395\pi$
$607$	−28.2565	−1.14690	−0.573448	+	0.819242i	$0.694395\pi$
$608$	77.2412	3.13254
$609$	−1.03537	−0.0419551
$610$	37.1358	1.50358
$611$	−40.1487	−1.62424
$612$	12.6473	0.511235
$613$	−28.4963	−1.15096	−0.575478	−	0.817817i	$-0.695184\pi$
$613$	−28.4963	−1.15096	−0.575478	+	0.817817i	$0.695184\pi$
$614$	34.9126	1.40896
$615$	17.2835	0.696939
$616$	−20.3172	−0.818604
$617$	44.1608	1.77785	0.888924	−	0.458054i	$-0.151453\pi$
$617$	44.1608	1.77785	0.888924	+	0.458054i	$0.151453\pi$
$618$	0.695855	0.0279914
$619$	−40.7414	−1.63754	−0.818768	−	0.574124i	$-0.805343\pi$
$619$	−40.7414	−1.63754	−0.818768	+	0.574124i	$0.805343\pi$
$620$	77.0783	3.09554
$621$	−34.4644	−1.38301
$622$	53.6833	2.15250
$623$	6.41908	0.257175
$624$	−59.2294	−2.37107
$625$	−23.9157	−0.956627
$626$	−39.3794	−1.57392
$627$	3.19346	0.127535
$628$	−67.4944	−2.69332
$629$	−4.56964	−0.182203
$630$	31.7379	1.26447
$631$	−2.02146	−0.0804731	−0.0402365	−	0.999190i	$-0.512811\pi$
$631$	−2.02146	−0.0804731	−0.0402365	+	0.999190i	$0.512811\pi$
$632$	−131.953	−5.24881
$633$	16.5562	0.658051
$634$	−12.3944	−0.492245
$635$	−2.22989	−0.0884904
$636$	20.2571	0.803248
$637$	−10.4220	−0.412933
$638$	−1.57030	−0.0621688
$639$	15.4467	0.611063
$640$	−60.4972	−2.39136
$641$	−11.5899	−0.457772	−0.228886	−	0.973453i	$-0.573508\pi$
$641$	−11.5899	−0.457772	−0.228886	+	0.973453i	$0.573508\pi$
$642$	−41.0993	−1.62206
$643$	−26.9766	−1.06385	−0.531927	−	0.846790i	$-0.678532\pi$
$643$	−26.9766	−1.06385	−0.531927	+	0.846790i	$0.678532\pi$
$644$	−97.4243	−3.83905
$645$	−1.73170	−0.0681856
$646$	−10.9270	−0.429918
$647$	44.8832	1.76454	0.882270	−	0.470744i	$-0.156014\pi$
$647$	44.8832	1.76454	0.882270	+	0.470744i	$0.156014\pi$
$648$	−33.8550	−1.32995
$649$	3.88412	0.152465
$650$	3.07473	0.120601
$651$	−11.7971	−0.462364
$652$	−46.5623	−1.82352
$653$	−0.658733	−0.0257782	−0.0128891	−	0.999917i	$-0.504103\pi$
$653$	−0.658733	−0.0257782	−0.0128891	+	0.999917i	$0.504103\pi$
$654$	0.919241	0.0359452
$655$	4.08462	0.159599
$656$	−136.963	−5.34750
$657$	23.2158	0.905736
$658$	44.9379	1.75186
$659$	15.5219	0.604647	0.302324	−	0.953205i	$-0.402238\pi$
$659$	15.5219	0.604647	0.302324	+	0.953205i	$0.402238\pi$
$660$	−9.22473	−0.359072
$661$	−8.73195	−0.339634	−0.169817	−	0.985476i	$-0.554318\pi$
$661$	−8.73195	−0.339634	−0.169817	+	0.985476i	$0.554318\pi$
$662$	24.3632	0.946905
$663$	4.31613	0.167625
$664$	−81.4627	−3.16137
$665$	−19.9360	−0.773087
$666$	29.3670	1.13795
$667$	−4.70278	−0.182093
$668$	70.3201	2.72076
$669$	−3.83925	−0.148434
$670$	−54.4303	−2.10283
$671$	−6.26730	−0.241946
$672$	34.1494	1.31734
$673$	24.8313	0.957177	0.478589	−	0.878039i	$-0.341149\pi$
$673$	24.8313	0.957177	0.478589	+	0.878039i	$0.341149\pi$
$674$	−46.3829	−1.78660
$675$	−0.885133	−0.0340688
$676$	89.3208	3.43541
$677$	5.46489	0.210033	0.105016	−	0.994470i	$-0.466510\pi$
$677$	5.46489	0.210033	0.105016	+	0.994470i	$0.466510\pi$
$678$	10.8114	0.415211
$679$	−32.4423	−1.24502
$680$	19.7135	0.755977
$681$	−8.16975	−0.313066
$682$	−17.8922	−0.685128
$683$	−26.7602	−1.02395	−0.511976	−	0.859000i	$-0.671086\pi$
$683$	−26.7602	−1.02395	−0.511976	+	0.859000i	$0.671086\pi$
$684$	51.0546	1.95212
$685$	−11.6864	−0.446515
$686$	54.4127	2.07749
$687$	−16.2420	−0.619673
$688$	13.7228	0.523177
$689$	−26.2268	−0.999162
$690$	−37.9988	−1.44659
$691$	7.79582	0.296567	0.148284	−	0.988945i	$-0.452625\pi$
$691$	7.79582	0.296567	0.148284	+	0.988945i	$0.452625\pi$
$692$	102.598	3.90021
$693$	−5.35631	−0.203469
$694$	−84.5060	−3.20780
$695$	−39.4546	−1.49660
$696$	4.13291	0.156658
$697$	9.98067	0.378045
$698$	−52.9028	−2.00240
$699$	−14.0888	−0.532887
$700$	−2.50210	−0.0945706
$701$	19.4179	0.733406	0.366703	−	0.930338i	$-0.380487\pi$
$701$	19.4179	0.733406	0.366703	+	0.930338i	$0.380487\pi$
$702$	−62.7870	−2.36974
$703$	−18.4468	−0.695734
$704$	24.3476	0.917635
$705$	12.7430	0.479929
$706$	1.98437	0.0746829
$707$	30.8080	1.15865
$708$	−16.3681	−0.615149
$709$	37.7397	1.41734	0.708672	−	0.705538i	$-0.249295\pi$
$709$	37.7397	1.41734	0.708672	+	0.705538i	$0.249295\pi$
$710$	38.5509	1.44679
$711$	−34.7873	−1.30463
$712$	−25.6233	−0.960275
$713$	−53.5841	−2.00674
$714$	−4.83099	−0.180795
$715$	11.9432	0.446651
$716$	−86.1896	−3.22106
$717$	21.9906	0.821255
$718$	−69.7315	−2.60236
$719$	−10.4059	−0.388076	−0.194038	−	0.980994i	$-0.562159\pi$
$719$	−10.4059	−0.388076	−0.194038	+	0.980994i	$0.562159\pi$
$720$	−71.3193	−2.65791
$721$	0.733136	0.0273034
$722$	7.31962	0.272408
$723$	−17.2152	−0.640242
$724$	−101.300	−3.76479
$725$	−0.120779	−0.00448564
$726$	2.14134	0.0794725
$727$	−53.2530	−1.97504	−0.987522	−	0.157480i	$-0.949663\pi$
$727$	−53.2530	−1.97504	−0.987522	+	0.157480i	$0.949663\pi$
$728$	−110.850	−4.10838
$729$	1.16441	0.0431264
$730$	57.9405	2.14447
$731$	−1.00000	−0.0369863
$732$	26.4110	0.976178
$733$	23.7987	0.879026	0.439513	−	0.898236i	$-0.355151\pi$
$733$	23.7987	0.879026	0.439513	+	0.898236i	$0.355151\pi$
$734$	−22.9830	−0.848318
$735$	3.30788	0.122013
$736$	155.112	5.71750
$737$	9.18605	0.338373
$738$	−64.1412	−2.36107
$739$	−25.8061	−0.949293	−0.474647	−	0.880176i	$-0.657424\pi$
$739$	−25.8061	−0.949293	−0.474647	+	0.880176i	$0.657424\pi$
$740$	53.2860	1.95883
$741$	17.4234	0.640066
$742$	29.3553	1.07767
$743$	43.4841	1.59528	0.797639	−	0.603135i	$-0.206082\pi$
$743$	43.4841	1.59528	0.797639	+	0.603135i	$0.206082\pi$
$744$	47.0909	1.72644
$745$	13.3163	0.487873
$746$	−43.4637	−1.59132
$747$	−21.4763	−0.785778
$748$	−5.32698	−0.194774
$749$	−43.3012	−1.58219
$750$	−24.4131	−0.891439
$751$	−33.3259	−1.21608	−0.608040	−	0.793906i	$-0.708044\pi$
$751$	−33.3259	−1.21608	−0.608040	+	0.793906i	$0.708044\pi$
$752$	−100.981	−3.68242
$753$	19.5666	0.713046
$754$	−8.56751	−0.312010
$755$	−21.7825	−0.792747
$756$	51.0937	1.85826
$757$	−9.75698	−0.354624	−0.177312	−	0.984155i	$-0.556740\pi$
$757$	−9.75698	−0.354624	−0.177312	+	0.984155i	$0.556740\pi$
$758$	37.3019	1.35486
$759$	6.41295	0.232775
$760$	79.5796	2.88666
$761$	36.4054	1.31969	0.659847	−	0.751400i	$-0.270621\pi$
$761$	36.4054	1.31969	0.659847	+	0.751400i	$0.270621\pi$
$762$	−2.18132	−0.0790208
$763$	0.968489	0.0350617
$764$	−110.070	−3.98220
$765$	5.19714	0.187903
$766$	6.18456	0.223457
$767$	21.1917	0.765186
$768$	−20.6575	−0.745413
$769$	−17.7668	−0.640687	−0.320344	−	0.947301i	$-0.603798\pi$
$769$	−17.7668	−0.640687	−0.320344	+	0.947301i	$0.603798\pi$
$770$	−13.3679	−0.481745
$771$	−6.38599	−0.229986
$772$	−125.348	−4.51139
$773$	−18.1326	−0.652183	−0.326091	−	0.945338i	$-0.605732\pi$
$773$	−18.1326	−0.652183	−0.326091	+	0.945338i	$0.605732\pi$
$774$	6.42654	0.230997
$775$	−1.37618	−0.0494337
$776$	129.501	4.64883
$777$	−8.15559	−0.292580
$778$	62.8233	2.25233
$779$	40.2901	1.44354
$780$	−50.3298	−1.80210
$781$	−6.50612	−0.232807
$782$	−21.9431	−0.784683
$783$	2.46635	0.0881403
$784$	−26.2132	−0.936185
$785$	−27.7355	−0.989921
$786$	3.99565	0.142520
$787$	−13.6094	−0.485123	−0.242561	−	0.970136i	$-0.577988\pi$
$787$	−13.6094	−0.485123	−0.242561	+	0.970136i	$0.577988\pi$
$788$	−121.663	−4.33408
$789$	−12.7277	−0.453120
$790$	−86.8197	−3.08891
$791$	11.3907	0.405006
$792$	21.3810	0.759741
$793$	−34.1942	−1.21427
$794$	−81.1960	−2.88154
$795$	8.32427	0.295231
$796$	−135.467	−4.80149
$797$	22.4215	0.794211	0.397106	−	0.917773i	$-0.370015\pi$
$797$	22.4215	0.794211	0.397106	+	0.917773i	$0.370015\pi$
$798$	−19.5018	−0.690357
$799$	7.35867	0.260331
$800$	3.98367	0.140844
$801$	−6.75518	−0.238683
$802$	23.8559	0.842380
$803$	−9.77844	−0.345074
$804$	−38.7109	−1.36523
$805$	−40.0346	−1.41103
$806$	−97.6193	−3.43849
$807$	11.5199	0.405521
$808$	−122.978	−4.32634
$809$	−26.3982	−0.928110	−0.464055	−	0.885806i	$-0.653606\pi$
$809$	−26.3982	−0.928110	−0.464055	+	0.885806i	$0.653606\pi$
$810$	−22.2752	−0.782670
$811$	30.7406	1.07945	0.539724	−	0.841842i	$-0.318528\pi$
$811$	30.7406	1.07945	0.539724	+	0.841842i	$0.318528\pi$
$812$	6.97192	0.244666
$813$	−20.9844	−0.735955
$814$	−12.3693	−0.433543
$815$	−19.1338	−0.670229
$816$	10.8559	0.380032
$817$	−4.03682	−0.141230
$818$	−30.6778	−1.07262
$819$	−29.2238	−1.02116
$820$	−116.383	−4.06428
$821$	−31.9325	−1.11445	−0.557226	−	0.830361i	$-0.688134\pi$
$821$	−31.9325	−1.11445	−0.557226	+	0.830361i	$0.688134\pi$
$822$	−11.4319	−0.398732
$823$	−24.0372	−0.837884	−0.418942	−	0.908013i	$-0.637599\pi$
$823$	−24.0372	−0.837884	−0.418942	+	0.908013i	$0.637599\pi$
$824$	−2.92649	−0.101949
$825$	0.164701	0.00573415
$826$	−23.7195	−0.825308
$827$	10.8434	0.377062	0.188531	−	0.982067i	$-0.439627\pi$
$827$	10.8434	0.377062	0.188531	+	0.982067i	$0.439627\pi$
$828$	102.525	3.56300
$829$	32.1501	1.11662	0.558310	−	0.829633i	$-0.311450\pi$
$829$	32.1501	1.11662	0.558310	+	0.829633i	$0.311450\pi$
$830$	−53.5991	−1.86045
$831$	−3.77239	−0.130863
$832$	132.840	4.60539
$833$	1.91019	0.0661842
$834$	−38.5952	−1.33644
$835$	28.8966	1.00001
$836$	−21.5041	−0.743733
$837$	28.1020	0.971346
$838$	−35.2009	−1.21599
$839$	33.8156	1.16745	0.583723	−	0.811953i	$-0.301595\pi$
$839$	33.8156	1.16745	0.583723	+	0.811953i	$0.301595\pi$
$840$	35.1833	1.21394
$841$	−28.6635	−0.988395
$842$	21.9467	0.756332
$843$	−17.8897	−0.616155
$844$	−111.486	−3.83751
$845$	36.7046	1.26268
$846$	−47.2908	−1.62589
$847$	2.25606	0.0775191
$848$	−65.9654	−2.26526
$849$	1.93681	0.0664712
$850$	−0.563554	−0.0193297
$851$	−37.0439	−1.26985
$852$	27.4174	0.939305
$853$	−13.5176	−0.462834	−0.231417	−	0.972855i	$-0.574336\pi$
$853$	−13.5176	−0.462834	−0.231417	+	0.972855i	$0.574336\pi$
$854$	38.2731	1.30968
$855$	20.9799	0.717497
$856$	172.847	5.90780
$857$	9.77004	0.333738	0.166869	−	0.985979i	$-0.446634\pi$
$857$	9.77004	0.333738	0.166869	+	0.985979i	$0.446634\pi$
$858$	11.6831	0.398854
$859$	26.3253	0.898207	0.449104	−	0.893480i	$-0.351743\pi$
$859$	26.3253	0.898207	0.449104	+	0.893480i	$0.351743\pi$
$860$	11.6609	0.397632
$861$	17.8128	0.607060
$862$	83.9532	2.85946
$863$	−7.05194	−0.240051	−0.120025	−	0.992771i	$-0.538298\pi$
$863$	−7.05194	−0.240051	−0.120025	+	0.992771i	$0.538298\pi$
$864$	−81.3477	−2.76751
$865$	42.1608	1.43351
$866$	33.6315	1.14285
$867$	−0.791084	−0.0268666
$868$	79.4389	2.69633
$869$	14.6523	0.497046
$870$	2.71929	0.0921924
$871$	50.1188	1.69821
$872$	−3.86596	−0.130918
$873$	34.1410	1.15550
$874$	−88.5802	−2.99627
$875$	−25.7210	−0.869528
$876$	41.2073	1.39226
$877$	−32.4168	−1.09464	−0.547319	−	0.836924i	$-0.684352\pi$
$877$	−32.4168	−1.09464	−0.547319	+	0.836924i	$0.684352\pi$
$878$	−60.2630	−2.03378
$879$	11.9811	0.404111
$880$	30.0395	1.01263
$881$	5.05060	0.170159	0.0850795	−	0.996374i	$-0.472886\pi$
$881$	5.05060	0.170159	0.0850795	+	0.996374i	$0.472886\pi$
$882$	−12.2759	−0.413352
$883$	29.3402	0.987378	0.493689	−	0.869639i	$-0.335648\pi$
$883$	29.3402	0.987378	0.493689	+	0.869639i	$0.335648\pi$
$884$	−29.0639	−0.977524
$885$	−6.72613	−0.226096
$886$	−44.1755	−1.48410
$887$	31.1929	1.04735	0.523677	−	0.851917i	$-0.324560\pi$
$887$	31.1929	1.04735	0.523677	+	0.851917i	$0.324560\pi$
$888$	32.5550	1.09248
$889$	−2.29818	−0.0770785
$890$	−16.8591	−0.565119
$891$	3.75932	0.125942
$892$	25.8527	0.865612
$893$	29.7056	0.994059
$894$	13.0263	0.435664
$895$	−35.4179	−1.18389
$896$	−62.3500	−2.08297
$897$	34.9888	1.16824
$898$	3.43930	0.114771
$899$	3.83461	0.127891
$900$	2.63311	0.0877704
$901$	4.80700	0.160144
$902$	27.0161	0.899537
$903$	−1.78473	−0.0593922
$904$	−45.4686	−1.51226
$905$	−41.6273	−1.38374
$906$	−21.3081	−0.707913
$907$	−49.4831	−1.64306	−0.821529	−	0.570167i	$-0.806879\pi$
$907$	−49.4831	−1.64306	−0.821529	+	0.570167i	$0.806879\pi$
$908$	55.0133	1.82568
$909$	−32.4211	−1.07534
$910$	−72.9348	−2.41776
$911$	−38.9033	−1.28892	−0.644461	−	0.764637i	$-0.722918\pi$
$911$	−38.9033	−1.28892	−0.644461	+	0.764637i	$0.722918\pi$
$912$	43.8232	1.45113
$913$	9.04577	0.299371
$914$	−96.7876	−3.20145
$915$	10.8531	0.358791
$916$	109.370	3.61370
$917$	4.20972	0.139017
$918$	11.5080	0.379819
$919$	−9.94640	−0.328102	−0.164051	−	0.986452i	$-0.552456\pi$
$919$	−9.94640	−0.328102	−0.164051	+	0.986452i	$0.552456\pi$
$920$	159.808	5.26871
$921$	10.2033	0.336211
$922$	79.4520	2.61661
$923$	−35.4972	−1.16840
$924$	−9.50725	−0.312766
$925$	−0.951382	−0.0312812
$926$	−73.2716	−2.40785
$927$	−0.771522	−0.0253401
$928$	−11.1002	−0.364381
$929$	19.6978	0.646265	0.323132	−	0.946354i	$-0.395264\pi$
$929$	19.6978	0.646265	0.323132	+	0.946354i	$0.395264\pi$
$930$	30.9839	1.01600
$931$	7.71109	0.252721
$932$	94.8707	3.10759
$933$	15.6891	0.513639
$934$	−74.6670	−2.44318
$935$	−2.18902	−0.0715886
$936$	116.654	3.81296
$937$	8.98016	0.293369	0.146685	−	0.989183i	$-0.453140\pi$
$937$	8.98016	0.293369	0.146685	+	0.989183i	$0.453140\pi$
$938$	−56.0973	−1.83164
$939$	−11.5088	−0.375575
$940$	−85.8084	−2.79876
$941$	23.6063	0.769542	0.384771	−	0.923012i	$-0.374280\pi$
$941$	23.6063	0.769542	0.384771	+	0.923012i	$0.374280\pi$
$942$	−27.1313	−0.883987
$943$	80.9086	2.63475
$944$	53.3010	1.73480
$945$	20.9960	0.682998
$946$	−2.70684	−0.0880070
$947$	25.5141	0.829097	0.414549	−	0.910027i	$-0.363939\pi$
$947$	25.5141	0.829097	0.414549	+	0.910027i	$0.363939\pi$
$948$	−61.7462	−2.00542
$949$	−53.3509	−1.73184
$950$	−2.27496	−0.0738096
$951$	−3.62232	−0.117462
$952$	20.3172	0.658485
$953$	−45.0656	−1.45982	−0.729910	−	0.683544i	$-0.760438\pi$
$953$	−45.0656	−1.45982	−0.729910	+	0.683544i	$0.760438\pi$
$954$	−30.8924	−1.00018
$955$	−45.2312	−1.46365
$956$	−148.080	−4.78925
$957$	−0.458926	−0.0148350
$958$	19.8461	0.641197
$959$	−12.0443	−0.388931
$960$	−42.1627	−1.36079
$961$	12.6920	0.409421
$962$	−67.4864	−2.17585
$963$	45.5684	1.46842
$964$	115.924	3.73365
$965$	−51.5094	−1.65815
$966$	−39.1626	−1.26003
$967$	−9.08442	−0.292135	−0.146068	−	0.989275i	$-0.546662\pi$
$967$	−9.08442	−0.292135	−0.146068	+	0.989275i	$0.546662\pi$
$968$	−9.00562	−0.289451
$969$	−3.19346	−0.102589
$970$	85.2066	2.73582
$971$	−24.9446	−0.800510	−0.400255	−	0.916404i	$-0.631078\pi$
$971$	−24.9446	−0.800510	−0.400255	+	0.916404i	$0.631078\pi$
$972$	−83.7841	−2.68738
$973$	−40.6630	−1.30360
$974$	−2.46937	−0.0791237
$975$	0.898603	0.0287783
$976$	−86.0049	−2.75295
$977$	11.6774	0.373592	0.186796	−	0.982399i	$-0.440190\pi$
$977$	11.6774	0.373592	0.186796	+	0.982399i	$0.440190\pi$
$978$	−18.7171	−0.598506
$979$	2.84526	0.0909350
$980$	−22.2745	−0.711533
$981$	−1.01920	−0.0325405
$982$	87.9862	2.80775
$983$	−51.0411	−1.62796	−0.813979	−	0.580894i	$-0.802703\pi$
$983$	−51.0411	−1.62796	−0.813979	+	0.580894i	$0.802703\pi$
$984$	−71.1043	−2.26672
$985$	−49.9952	−1.59298
$986$	1.57030	0.0500086
$987$	13.1333	0.418036
$988$	−117.325	−3.73262
$989$	−8.10653	−0.257773
$990$	14.0678	0.447105
$991$	−53.7303	−1.70680	−0.853399	−	0.521258i	$-0.825463\pi$
$991$	−53.7303	−1.70680	−0.853399	+	0.521258i	$0.825463\pi$
$992$	−126.477	−4.01565
$993$	7.12025	0.225954
$994$	39.7315	1.26021
$995$	−55.6674	−1.76477
$996$	−38.1197	−1.20787
$997$	31.8351	1.00823	0.504114	−	0.863637i	$-0.331819\pi$
$997$	31.8351	1.00823	0.504114	+	0.863637i	$0.331819\pi$
$998$	−19.5524	−0.618922
$999$	19.4275	0.614659

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.2	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.2	✓	62	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70684 q^{2} -0.791084 q^{3} +5.32698 q^{4} +2.18902 q^{5} +2.14134 q^{6} +2.25606 q^{7} -9.00562 q^{8} -2.37419 q^{9} +O(q^{10})\)	\(q-2.70684 q^{2} -0.791084 q^{3} +5.32698 q^{4} +2.18902 q^{5} +2.14134 q^{6} +2.25606 q^{7} -9.00562 q^{8} -2.37419 q^{9} -5.92532 q^{10} +1.00000 q^{11} -4.21409 q^{12} +5.45597 q^{13} -6.10679 q^{14} -1.73170 q^{15} +13.7228 q^{16} -1.00000 q^{17} +6.42654 q^{18} -4.03682 q^{19} +11.6609 q^{20} -1.78473 q^{21} -2.70684 q^{22} -8.10653 q^{23} +7.12420 q^{24} -0.208196 q^{25} -14.7684 q^{26} +4.25143 q^{27} +12.0180 q^{28} +0.580123 q^{29} +4.68743 q^{30} +6.61000 q^{31} -19.1342 q^{32} -0.791084 q^{33} +2.70684 q^{34} +4.93856 q^{35} -12.6473 q^{36} +4.56964 q^{37} +10.9270 q^{38} -4.31613 q^{39} -19.7135 q^{40} -9.98067 q^{41} +4.83099 q^{42} +1.00000 q^{43} +5.32698 q^{44} -5.19714 q^{45} +21.9431 q^{46} -7.35867 q^{47} -10.8559 q^{48} -1.91019 q^{49} +0.563554 q^{50} +0.791084 q^{51} +29.0639 q^{52} -4.80700 q^{53} -11.5080 q^{54} +2.18902 q^{55} -20.3172 q^{56} +3.19346 q^{57} -1.57030 q^{58} +3.88412 q^{59} -9.22473 q^{60} -6.26730 q^{61} -17.8922 q^{62} -5.35631 q^{63} +24.3476 q^{64} +11.9432 q^{65} +2.14134 q^{66} +9.18605 q^{67} -5.32698 q^{68} +6.41295 q^{69} -13.3679 q^{70} -6.50612 q^{71} +21.3810 q^{72} -9.77844 q^{73} -12.3693 q^{74} +0.164701 q^{75} -21.5041 q^{76} +2.25606 q^{77} +11.6831 q^{78} +14.6523 q^{79} +30.0395 q^{80} +3.75932 q^{81} +27.0161 q^{82} +9.04577 q^{83} -9.50725 q^{84} -2.18902 q^{85} -2.70684 q^{86} -0.458926 q^{87} -9.00562 q^{88} +2.84526 q^{89} +14.0678 q^{90} +12.3090 q^{91} -43.1834 q^{92} -5.22906 q^{93} +19.9187 q^{94} -8.83667 q^{95} +15.1368 q^{96} -14.3801 q^{97} +5.17059 q^{98} -2.37419 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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