LMFDB - Embedded newform 8041.2.a.g.1.14

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:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-2.02215 q^{2} +2.02595 q^{3} +2.08909 q^{4} -3.90857 q^{5} -4.09678 q^{6} -0.616656 q^{7} -0.180153 q^{8} +1.10448 q^{9} +O(q^{10})$	\(q-2.02215 q^{2} +2.02595 q^{3} +2.08909 q^{4} -3.90857 q^{5} -4.09678 q^{6} -0.616656 q^{7} -0.180153 q^{8} +1.10448 q^{9} +7.90371 q^{10} -1.00000 q^{11} +4.23240 q^{12} +3.49708 q^{13} +1.24697 q^{14} -7.91857 q^{15} -3.81388 q^{16} +1.00000 q^{17} -2.23343 q^{18} -1.94885 q^{19} -8.16535 q^{20} -1.24932 q^{21} +2.02215 q^{22} +3.59332 q^{23} -0.364982 q^{24} +10.2769 q^{25} -7.07163 q^{26} -3.84023 q^{27} -1.28825 q^{28} -6.45369 q^{29} +16.0125 q^{30} +1.16394 q^{31} +8.07255 q^{32} -2.02595 q^{33} -2.02215 q^{34} +2.41024 q^{35} +2.30736 q^{36} -0.868718 q^{37} +3.94087 q^{38} +7.08492 q^{39} +0.704142 q^{40} +4.28511 q^{41} +2.52630 q^{42} +1.00000 q^{43} -2.08909 q^{44} -4.31694 q^{45} -7.26622 q^{46} -8.11901 q^{47} -7.72674 q^{48} -6.61973 q^{49} -20.7815 q^{50} +2.02595 q^{51} +7.30572 q^{52} +5.73888 q^{53} +7.76552 q^{54} +3.90857 q^{55} +0.111093 q^{56} -3.94828 q^{57} +13.0503 q^{58} -2.86909 q^{59} -16.5426 q^{60} +11.5842 q^{61} -2.35365 q^{62} -0.681085 q^{63} -8.69614 q^{64} -13.6686 q^{65} +4.09678 q^{66} +11.3423 q^{67} +2.08909 q^{68} +7.27988 q^{69} -4.87387 q^{70} +11.2718 q^{71} -0.198976 q^{72} +4.37038 q^{73} +1.75668 q^{74} +20.8205 q^{75} -4.07132 q^{76} +0.616656 q^{77} -14.3268 q^{78} +6.90937 q^{79} +14.9068 q^{80} -11.0936 q^{81} -8.66514 q^{82} -5.62609 q^{83} -2.60993 q^{84} -3.90857 q^{85} -2.02215 q^{86} -13.0749 q^{87} +0.180153 q^{88} -11.1870 q^{89} +8.72950 q^{90} -2.15650 q^{91} +7.50676 q^{92} +2.35808 q^{93} +16.4179 q^{94} +7.61722 q^{95} +16.3546 q^{96} -2.05879 q^{97} +13.3861 q^{98} -1.10448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * 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 $

$2$	−2.02215	−1.42988	−0.714938	−	0.699188i	$-0.753545\pi$
$2$	−2.02215	−1.42988	−0.714938	+	0.699188i	$0.753545\pi$
$3$	2.02595	1.16968	0.584842	−	0.811147i	$-0.301157\pi$
$3$	2.02595	1.16968	0.584842	+	0.811147i	$0.301157\pi$
$4$	2.08909	1.04455
$5$	−3.90857	−1.74797	−0.873983	−	0.485957i	$-0.838471\pi$
$5$	−3.90857	−1.74797	−0.873983	+	0.485957i	$0.838471\pi$
$6$	−4.09678	−1.67250
$7$	−0.616656	−0.233074	−0.116537	−	0.993186i	$-0.537179\pi$
$7$	−0.616656	−0.233074	−0.116537	+	0.993186i	$0.537179\pi$
$8$	−0.180153	−0.0636938
$9$	1.10448	0.368160
$10$	7.90371	2.49937
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.23240	1.22179
$13$	3.49708	0.969917	0.484958	−	0.874537i	$-0.338835\pi$
$13$	3.49708	0.969917	0.484958	+	0.874537i	$0.338835\pi$
$14$	1.24697	0.333267
$15$	−7.91857	−2.04457
$16$	−3.81388	−0.953471
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.23343	−0.526424
$19$	−1.94885	−0.447097	−0.223548	−	0.974693i	$-0.571764\pi$
$19$	−1.94885	−0.447097	−0.223548	+	0.974693i	$0.571764\pi$
$20$	−8.16535	−1.82583
$21$	−1.24932	−0.272623
$22$	2.02215	0.431124
$23$	3.59332	0.749258	0.374629	−	0.927175i	$-0.377770\pi$
$23$	3.59332	0.749258	0.374629	+	0.927175i	$0.377770\pi$
$24$	−0.364982	−0.0745016
$25$	10.2769	2.05538
$26$	−7.07163	−1.38686
$27$	−3.84023	−0.739053
$28$	−1.28825	−0.243456
$29$	−6.45369	−1.19842	−0.599210	−	0.800592i	$-0.704519\pi$
$29$	−6.45369	−1.19842	−0.599210	+	0.800592i	$0.704519\pi$
$30$	16.0125	2.92348
$31$	1.16394	0.209049	0.104525	−	0.994522i	$-0.466668\pi$
$31$	1.16394	0.209049	0.104525	+	0.994522i	$0.466668\pi$
$32$	8.07255	1.42704
$33$	−2.02595	−0.352673
$34$	−2.02215	−0.346796
$35$	2.41024	0.407406
$36$	2.30736	0.384560
$37$	−0.868718	−0.142816	−0.0714081	−	0.997447i	$-0.522749\pi$
$37$	−0.868718	−0.142816	−0.0714081	+	0.997447i	$0.522749\pi$
$38$	3.94087	0.639293
$39$	7.08492	1.13450
$40$	0.704142	0.111335
$41$	4.28511	0.669222	0.334611	−	0.942356i	$-0.391395\pi$
$41$	4.28511	0.669222	0.334611	+	0.942356i	$0.391395\pi$
$42$	2.52630	0.389817
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−2.08909	−0.314942
$45$	−4.31694	−0.643531
$46$	−7.26622	−1.07135
$47$	−8.11901	−1.18428	−0.592140	−	0.805835i	$-0.701717\pi$
$47$	−8.11901	−1.18428	−0.592140	+	0.805835i	$0.701717\pi$
$48$	−7.72674	−1.11526
$49$	−6.61973	−0.945676
$50$	−20.7815	−2.93894
$51$	2.02595	0.283690
$52$	7.30572	1.01312
$53$	5.73888	0.788296	0.394148	−	0.919047i	$-0.371040\pi$
$53$	5.73888	0.788296	0.394148	+	0.919047i	$0.371040\pi$
$54$	7.76552	1.05675
$55$	3.90857	0.527031
$56$	0.111093	0.0148454
$57$	−3.94828	−0.522962
$58$	13.0503	1.71359
$59$	−2.86909	−0.373524	−0.186762	−	0.982405i	$-0.559799\pi$
$59$	−2.86909	−0.373524	−0.186762	+	0.982405i	$0.559799\pi$
$60$	−16.5426	−2.13564
$61$	11.5842	1.48321	0.741605	−	0.670837i	$-0.234065\pi$
$61$	11.5842	1.48321	0.741605	+	0.670837i	$0.234065\pi$
$62$	−2.35365	−0.298914
$63$	−0.681085	−0.0858087
$64$	−8.69614	−1.08702
$65$	−13.6686	−1.69538
$66$	4.09678	0.504279
$67$	11.3423	1.38568	0.692841	−	0.721090i	$-0.256359\pi$
$67$	11.3423	1.38568	0.692841	+	0.721090i	$0.256359\pi$
$68$	2.08909	0.253339
$69$	7.27988	0.876395
$70$	−4.87387	−0.582539
$71$	11.2718	1.33771	0.668857	−	0.743391i	$-0.266784\pi$
$71$	11.2718	1.33771	0.668857	+	0.743391i	$0.266784\pi$
$72$	−0.198976	−0.0234495
$73$	4.37038	0.511515	0.255757	−	0.966741i	$-0.417675\pi$
$73$	4.37038	0.511515	0.255757	+	0.966741i	$0.417675\pi$
$74$	1.75668	0.204210
$75$	20.8205	2.40415
$76$	−4.07132	−0.467013
$77$	0.616656	0.0702745
$78$	−14.3268	−1.62219
$79$	6.90937	0.777365	0.388683	−	0.921372i	$-0.372930\pi$
$79$	6.90937	0.777365	0.388683	+	0.921372i	$0.372930\pi$
$80$	14.9068	1.66663
$81$	−11.0936	−1.23262
$82$	−8.66514	−0.956905
$83$	−5.62609	−0.617544	−0.308772	−	0.951136i	$-0.599918\pi$
$83$	−5.62609	−0.617544	−0.308772	+	0.951136i	$0.599918\pi$
$84$	−2.60993	−0.284767
$85$	−3.90857	−0.423944
$86$	−2.02215	−0.218054
$87$	−13.0749	−1.40177
$88$	0.180153	0.0192044
$89$	−11.1870	−1.18582	−0.592909	−	0.805270i	$-0.702021\pi$
$89$	−11.1870	−1.18582	−0.592909	+	0.805270i	$0.702021\pi$
$90$	8.72950	0.920170
$91$	−2.15650	−0.226063
$92$	7.50676	0.782634
$93$	2.35808	0.244521
$94$	16.4179	1.69337
$95$	7.61722	0.781510
$96$	16.3546	1.66918
$97$	−2.05879	−0.209039	−0.104519	−	0.994523i	$-0.533330\pi$
$97$	−2.05879	−0.209039	−0.104519	+	0.994523i	$0.533330\pi$
$98$	13.3861	1.35220
$99$	−1.10448	−0.111005
$100$	21.4694	2.14694
$101$	−7.19940	−0.716367	−0.358184	−	0.933651i	$-0.616604\pi$
$101$	−7.19940	−0.716367	−0.358184	+	0.933651i	$0.616604\pi$
$102$	−4.09678	−0.405641
$103$	−16.1720	−1.59348	−0.796739	−	0.604324i	$-0.793443\pi$
$103$	−16.1720	−1.59348	−0.796739	+	0.604324i	$0.793443\pi$
$104$	−0.630011	−0.0617777
$105$	4.88304	0.476536
$106$	−11.6049	−1.12717
$107$	−12.9163	−1.24867	−0.624334	−	0.781157i	$-0.714630\pi$
$107$	−12.9163	−1.24867	−0.624334	+	0.781157i	$0.714630\pi$
$108$	−8.02259	−0.771974
$109$	1.47785	0.141552	0.0707761	−	0.997492i	$-0.477452\pi$
$109$	1.47785	0.141552	0.0707761	+	0.997492i	$0.477452\pi$
$110$	−7.90371	−0.753589
$111$	−1.75998	−0.167050
$112$	2.35186	0.222229
$113$	0.190850	0.0179537	0.00897685	−	0.999960i	$-0.497143\pi$
$113$	0.190850	0.0179537	0.00897685	+	0.999960i	$0.497143\pi$
$114$	7.98401	0.747771
$115$	−14.0447	−1.30968
$116$	−13.4823	−1.25180
$117$	3.86246	0.357085
$118$	5.80173	0.534093
$119$	−0.616656	−0.0565288
$120$	1.42656	0.130226
$121$	1.00000	0.0909091
$122$	−23.4251	−2.12081
$123$	8.68143	0.782779
$124$	2.43157	0.218361
$125$	−20.6252	−1.84477
$126$	1.37726	0.122696
$127$	14.5894	1.29460	0.647299	−	0.762236i	$-0.275899\pi$
$127$	14.5894	1.29460	0.647299	+	0.762236i	$0.275899\pi$
$128$	1.43980	0.127261
$129$	2.02595	0.178375
$130$	27.6399	2.42418
$131$	10.7120	0.935913	0.467957	−	0.883751i	$-0.344990\pi$
$131$	10.7120	0.935913	0.467957	+	0.883751i	$0.344990\pi$
$132$	−4.23240	−0.368383
$133$	1.20177	0.104207
$134$	−22.9358	−1.98135
$135$	15.0098	1.29184
$136$	−0.180153	−0.0154480
$137$	6.42922	0.549286	0.274643	−	0.961546i	$-0.411440\pi$
$137$	6.42922	0.549286	0.274643	+	0.961546i	$0.411440\pi$
$138$	−14.7210	−1.25314
$139$	−1.29245	−0.109624	−0.0548120	−	0.998497i	$-0.517456\pi$
$139$	−1.29245	−0.109624	−0.0548120	+	0.998497i	$0.517456\pi$
$140$	5.03522	0.425553
$141$	−16.4487	−1.38523
$142$	−22.7932	−1.91276
$143$	−3.49708	−0.292441
$144$	−4.21236	−0.351030
$145$	25.2247	2.09480
$146$	−8.83757	−0.731403
$147$	−13.4113	−1.10614
$148$	−1.81483	−0.149178
$149$	11.6166	0.951666	0.475833	−	0.879536i	$-0.342147\pi$
$149$	11.6166	0.951666	0.475833	+	0.879536i	$0.342147\pi$
$150$	−42.1022	−3.43763
$151$	7.29036	0.593281	0.296641	−	0.954989i	$-0.404134\pi$
$151$	7.29036	0.593281	0.296641	+	0.954989i	$0.404134\pi$
$152$	0.351092	0.0284773
$153$	1.10448	0.0892920
$154$	−1.24697	−0.100484
$155$	−4.54933	−0.365411
$156$	14.8010	1.18503
$157$	21.7884	1.73890	0.869452	−	0.494017i	$-0.164472\pi$
$157$	21.7884	1.73890	0.869452	+	0.494017i	$0.164472\pi$
$158$	−13.9718	−1.11154
$159$	11.6267	0.922057
$160$	−31.5521	−2.49441
$161$	−2.21584	−0.174633
$162$	22.4329	1.76249
$163$	−8.97580	−0.703039	−0.351519	−	0.936181i	$-0.614335\pi$
$163$	−8.97580	−0.703039	−0.351519	+	0.936181i	$0.614335\pi$
$164$	8.95199	0.699033
$165$	7.91857	0.616460
$166$	11.3768	0.883011
$167$	−8.84965	−0.684807	−0.342403	−	0.939553i	$-0.611241\pi$
$167$	−8.84965	−0.684807	−0.342403	+	0.939553i	$0.611241\pi$
$168$	0.225068	0.0173644
$169$	−0.770401	−0.0592616
$170$	7.90371	0.606187
$171$	−2.15247	−0.164603
$172$	2.08909	0.159292
$173$	7.78391	0.591800	0.295900	−	0.955219i	$-0.404381\pi$
$173$	7.78391	0.591800	0.295900	+	0.955219i	$0.404381\pi$
$174$	26.4393	2.00436
$175$	−6.33732	−0.479057
$176$	3.81388	0.287482
$177$	−5.81264	−0.436905
$178$	22.6218	1.69557
$179$	11.0255	0.824083	0.412041	−	0.911165i	$-0.364816\pi$
$179$	11.0255	0.824083	0.412041	+	0.911165i	$0.364816\pi$
$180$	−9.01848	−0.672197
$181$	−23.2986	−1.73177	−0.865887	−	0.500239i	$-0.833245\pi$
$181$	−23.2986	−1.73177	−0.865887	+	0.500239i	$0.833245\pi$
$182$	4.36076	0.323241
$183$	23.4691	1.73489
$184$	−0.647348	−0.0477231
$185$	3.39544	0.249638
$186$	−4.76839	−0.349635
$187$	−1.00000	−0.0731272
$188$	−16.9614	−1.23703
$189$	2.36810	0.172254
$190$	−15.4032	−1.11746
$191$	−12.3276	−0.891992	−0.445996	−	0.895035i	$-0.647150\pi$
$191$	−12.3276	−0.891992	−0.445996	+	0.895035i	$0.647150\pi$
$192$	−17.6180	−1.27147
$193$	−1.20220	−0.0865360	−0.0432680	−	0.999064i	$-0.513777\pi$
$193$	−1.20220	−0.0865360	−0.0432680	+	0.999064i	$0.513777\pi$
$194$	4.16319	0.298899
$195$	−27.6919	−1.98306
$196$	−13.8292	−0.987802
$197$	−4.53617	−0.323189	−0.161594	−	0.986857i	$-0.551664\pi$
$197$	−4.53617	−0.323189	−0.161594	+	0.986857i	$0.551664\pi$
$198$	2.23343	0.158723
$199$	12.4139	0.879997	0.439999	−	0.897998i	$-0.354979\pi$
$199$	12.4139	0.879997	0.439999	+	0.897998i	$0.354979\pi$
$200$	−1.85142	−0.130915
$201$	22.9789	1.62081
$202$	14.5583	1.02432
$203$	3.97971	0.279321
$204$	4.23240	0.296327
$205$	−16.7487	−1.16978
$206$	32.7023	2.27848
$207$	3.96875	0.275847
$208$	−13.3375	−0.924787
$209$	1.94885	0.134805
$210$	−9.87423	−0.681387
$211$	25.1602	1.73210	0.866051	−	0.499956i	$-0.166651\pi$
$211$	25.1602	1.73210	0.866051	+	0.499956i	$0.166651\pi$
$212$	11.9890	0.823411
$213$	22.8361	1.56470
$214$	26.1188	1.78544
$215$	−3.90857	−0.266562
$216$	0.691830	0.0470731
$217$	−0.717749	−0.0487240
$218$	−2.98843	−0.202402
$219$	8.85419	0.598311
$220$	8.16535	0.550508
$221$	3.49708	0.235239
$222$	3.55894	0.238861
$223$	0.799018	0.0535062	0.0267531	−	0.999642i	$-0.491483\pi$
$223$	0.799018	0.0535062	0.0267531	+	0.999642i	$0.491483\pi$
$224$	−4.97799	−0.332606
$225$	11.3507	0.756710
$226$	−0.385928	−0.0256715
$227$	−21.3790	−1.41897	−0.709486	−	0.704719i	$-0.751073\pi$
$227$	−21.3790	−1.41897	−0.709486	+	0.704719i	$0.751073\pi$
$228$	−8.24831	−0.546257
$229$	−4.65134	−0.307369	−0.153685	−	0.988120i	$-0.549114\pi$
$229$	−4.65134	−0.307369	−0.153685	+	0.988120i	$0.549114\pi$
$230$	28.4005	1.87268
$231$	1.24932	0.0821990
$232$	1.16265	0.0763319
$233$	−20.3553	−1.33352	−0.666760	−	0.745272i	$-0.732319\pi$
$233$	−20.3553	−1.33352	−0.666760	+	0.745272i	$0.732319\pi$
$234$	−7.81048	−0.510587
$235$	31.7337	2.07008
$236$	−5.99379	−0.390162
$237$	13.9981	0.909271
$238$	1.24697	0.0808292
$239$	−28.7116	−1.85720	−0.928599	−	0.371084i	$-0.878986\pi$
$239$	−28.7116	−1.85720	−0.928599	+	0.371084i	$0.878986\pi$
$240$	30.2005	1.94943
$241$	8.80483	0.567169	0.283584	−	0.958947i	$-0.408476\pi$
$241$	8.80483	0.567169	0.283584	+	0.958947i	$0.408476\pi$
$242$	−2.02215	−0.129989
$243$	−10.9543	−0.702721
$244$	24.2005	1.54928
$245$	25.8737	1.65301
$246$	−17.5552	−1.11928
$247$	−6.81529	−0.433647
$248$	−0.209687	−0.0133151
$249$	−11.3982	−0.722331
$250$	41.7072	2.63779
$251$	12.3337	0.778496	0.389248	−	0.921133i	$-0.372735\pi$
$251$	12.3337	0.778496	0.389248	+	0.921133i	$0.372735\pi$
$252$	−1.42285	−0.0896310
$253$	−3.59332	−0.225910
$254$	−29.5019	−1.85111
$255$	−7.91857	−0.495880
$256$	14.4808	0.905050
$257$	27.5418	1.71801	0.859005	−	0.511967i	$-0.171083\pi$
$257$	27.5418	1.71801	0.859005	+	0.511967i	$0.171083\pi$
$258$	−4.09678	−0.255054
$259$	0.535700	0.0332868
$260$	−28.5549	−1.77090
$261$	−7.12798	−0.441211
$262$	−21.6613	−1.33824
$263$	−17.6915	−1.09090	−0.545452	−	0.838142i	$-0.683642\pi$
$263$	−17.6915	−1.09090	−0.545452	+	0.838142i	$0.683642\pi$
$264$	0.364982	0.0224631
$265$	−22.4308	−1.37791
$266$	−2.43016	−0.149003
$267$	−22.6643	−1.38703
$268$	23.6951	1.44741
$269$	−4.71397	−0.287416	−0.143708	−	0.989620i	$-0.545903\pi$
$269$	−4.71397	−0.287416	−0.143708	+	0.989620i	$0.545903\pi$
$270$	−30.3521	−1.84717
$271$	−23.0375	−1.39943	−0.699715	−	0.714422i	$-0.746690\pi$
$271$	−23.0375	−1.39943	−0.699715	+	0.714422i	$0.746690\pi$
$272$	−3.81388	−0.231251
$273$	−4.36896	−0.264422
$274$	−13.0009	−0.785410
$275$	−10.2769	−0.619721
$276$	15.2083	0.915434
$277$	−20.7722	−1.24808	−0.624041	−	0.781392i	$-0.714510\pi$
$277$	−20.7722	−1.24808	−0.624041	+	0.781392i	$0.714510\pi$
$278$	2.61352	0.156749
$279$	1.28555	0.0769636
$280$	−0.434213	−0.0259492
$281$	11.6394	0.694349	0.347174	−	0.937801i	$-0.387141\pi$
$281$	11.6394	0.694349	0.347174	+	0.937801i	$0.387141\pi$
$282$	33.2618	1.98071
$283$	13.8878	0.825544	0.412772	−	0.910834i	$-0.364561\pi$
$283$	13.8878	0.825544	0.412772	+	0.910834i	$0.364561\pi$
$284$	23.5477	1.39730
$285$	15.4321	0.914120
$286$	7.07163	0.418154
$287$	−2.64244	−0.155978
$288$	8.91598	0.525379
$289$	1.00000	0.0588235
$290$	−51.0081	−2.99530
$291$	−4.17101	−0.244509
$292$	9.13013	0.534300
$293$	−9.65732	−0.564187	−0.282093	−	0.959387i	$-0.591029\pi$
$293$	−9.65732	−0.564187	−0.282093	+	0.959387i	$0.591029\pi$
$294$	27.1196	1.58165
$295$	11.2140	0.652906
$296$	0.156502	0.00909651
$297$	3.84023	0.222833
$298$	−23.4904	−1.36076
$299$	12.5661	0.726718
$300$	43.4960	2.51124
$301$	−0.616656	−0.0355435
$302$	−14.7422	−0.848318
$303$	−14.5856	−0.837923
$304$	7.43269	0.426294
$305$	−45.2778	−2.59260
$306$	−2.23343	−0.127676
$307$	−24.5011	−1.39835	−0.699175	−	0.714951i	$-0.746449\pi$
$307$	−24.5011	−1.39835	−0.699175	+	0.714951i	$0.746449\pi$
$308$	1.28825	0.0734049
$309$	−32.7638	−1.86387
$310$	9.19942	0.522492
$311$	18.1724	1.03046	0.515230	−	0.857052i	$-0.327707\pi$
$311$	18.1724	1.03046	0.515230	+	0.857052i	$0.327707\pi$
$312$	−1.27637	−0.0722604
$313$	21.0156	1.18787	0.593937	−	0.804512i	$-0.297573\pi$
$313$	21.0156	1.18787	0.593937	+	0.804512i	$0.297573\pi$
$314$	−44.0594	−2.48642
$315$	2.66207	0.149991
$316$	14.4343	0.811993
$317$	−23.1003	−1.29744	−0.648720	−	0.761027i	$-0.724695\pi$
$317$	−23.1003	−1.29744	−0.648720	+	0.761027i	$0.724695\pi$
$318$	−23.5109	−1.31843
$319$	6.45369	0.361337
$320$	33.9895	1.90007
$321$	−26.1679	−1.46055
$322$	4.48076	0.249703
$323$	−1.94885	−0.108437
$324$	−23.1755	−1.28753
$325$	35.9392	1.99355
$326$	18.1504	1.00526
$327$	2.99405	0.165571
$328$	−0.771978	−0.0426253
$329$	5.00664	0.276025
$330$	−16.0125	−0.881461
$331$	−7.67137	−0.421656	−0.210828	−	0.977523i	$-0.567616\pi$
$331$	−7.67137	−0.421656	−0.210828	+	0.977523i	$0.567616\pi$
$332$	−11.7534	−0.645052
$333$	−0.959482	−0.0525793
$334$	17.8953	0.979189
$335$	−44.3322	−2.42212
$336$	4.76475	0.259938
$337$	−12.8868	−0.701987	−0.350994	−	0.936378i	$-0.614156\pi$
$337$	−12.8868	−0.701987	−0.350994	+	0.936378i	$0.614156\pi$
$338$	1.55787	0.0847367
$339$	0.386654	0.0210001
$340$	−8.16535	−0.442828
$341$	−1.16394	−0.0630307
$342$	4.35261	0.235362
$343$	8.39870	0.453487
$344$	−0.180153	−0.00971322
$345$	−28.4539	−1.53191
$346$	−15.7402	−0.846200
$347$	−17.2251	−0.924690	−0.462345	−	0.886700i	$-0.652992\pi$
$347$	−17.2251	−0.924690	−0.462345	+	0.886700i	$0.652992\pi$
$348$	−27.3146	−1.46421
$349$	3.75398	0.200946	0.100473	−	0.994940i	$-0.467964\pi$
$349$	3.75398	0.200946	0.100473	+	0.994940i	$0.467964\pi$
$350$	12.8150	0.684991
$351$	−13.4296	−0.716820
$352$	−8.07255	−0.430268
$353$	−4.01624	−0.213763	−0.106881	−	0.994272i	$-0.534087\pi$
$353$	−4.01624	−0.213763	−0.106881	+	0.994272i	$0.534087\pi$
$354$	11.7540	0.624719
$355$	−44.0565	−2.33828
$356$	−23.3706	−1.23864
$357$	−1.24932	−0.0661208
$358$	−22.2952	−1.17834
$359$	−25.4201	−1.34162	−0.670810	−	0.741630i	$-0.734053\pi$
$359$	−25.4201	−1.34162	−0.670810	+	0.741630i	$0.734053\pi$
$360$	0.777711	0.0409890
$361$	−15.2020	−0.800104
$362$	47.1134	2.47622
$363$	2.02595	0.106335
$364$	−4.50512	−0.236133
$365$	−17.0819	−0.894110
$366$	−47.4581	−2.48067
$367$	−22.7531	−1.18770	−0.593850	−	0.804576i	$-0.702393\pi$
$367$	−22.7531	−1.18770	−0.593850	+	0.804576i	$0.702393\pi$
$368$	−13.7045	−0.714396
$369$	4.73283	0.246381
$370$	−6.86609	−0.356951
$371$	−3.53892	−0.183732
$372$	4.92624	0.255414
$373$	−23.2096	−1.20175	−0.600874	−	0.799344i	$-0.705181\pi$
$373$	−23.2096	−1.20175	−0.600874	+	0.799344i	$0.705181\pi$
$374$	2.02215	0.104563
$375$	−41.7856	−2.15780
$376$	1.46267	0.0754313
$377$	−22.5691	−1.16237
$378$	−4.78866	−0.246302
$379$	−2.90409	−0.149173	−0.0745865	−	0.997215i	$-0.523764\pi$
$379$	−2.90409	−0.149173	−0.0745865	+	0.997215i	$0.523764\pi$
$380$	15.9131	0.816322
$381$	29.5574	1.51427
$382$	24.9282	1.27544
$383$	−37.0210	−1.89169	−0.945843	−	0.324625i	$-0.894762\pi$
$383$	−37.0210	−1.89169	−0.945843	+	0.324625i	$0.894762\pi$
$384$	2.91696	0.148855
$385$	−2.41024	−0.122837
$386$	2.43102	0.123736
$387$	1.10448	0.0561439
$388$	−4.30100	−0.218350
$389$	−5.87758	−0.298005	−0.149002	−	0.988837i	$-0.547606\pi$
$389$	−5.87758	−0.298005	−0.149002	+	0.988837i	$0.547606\pi$
$390$	55.9972	2.83553
$391$	3.59332	0.181722
$392$	1.19257	0.0602337
$393$	21.7020	1.09472
$394$	9.17282	0.462120
$395$	−27.0058	−1.35881
$396$	−2.30736	−0.115949
$397$	−9.10055	−0.456744	−0.228372	−	0.973574i	$-0.573340\pi$
$397$	−9.10055	−0.456744	−0.228372	+	0.973574i	$0.573340\pi$
$398$	−25.1027	−1.25829
$399$	2.43473	0.121889
$400$	−39.1949	−1.95975
$401$	−20.0744	−1.00247	−0.501234	−	0.865312i	$-0.667120\pi$
$401$	−20.0744	−1.00247	−0.501234	+	0.865312i	$0.667120\pi$
$402$	−46.4669	−2.31756
$403$	4.07038	0.202760
$404$	−15.0402	−0.748278
$405$	43.3600	2.15457
$406$	−8.04757	−0.399394
$407$	0.868718	0.0430607
$408$	−0.364982	−0.0180693
$409$	19.7634	0.977239	0.488620	−	0.872497i	$-0.337501\pi$
$409$	19.7634	0.977239	0.488620	+	0.872497i	$0.337501\pi$
$410$	33.8683	1.67264
$411$	13.0253	0.642491
$412$	−33.7848	−1.66446
$413$	1.76924	0.0870587
$414$	−8.02540	−0.394427
$415$	21.9900	1.07945
$416$	28.2304	1.38411
$417$	−2.61844	−0.128225
$418$	−3.94087	−0.192754
$419$	−34.8150	−1.70082	−0.850411	−	0.526119i	$-0.823647\pi$
$419$	−34.8150	−1.70082	−0.850411	+	0.526119i	$0.823647\pi$
$420$	10.2011	0.497763
$421$	13.4050	0.653318	0.326659	−	0.945142i	$-0.394077\pi$
$421$	13.4050	0.653318	0.326659	+	0.945142i	$0.394077\pi$
$422$	−50.8777	−2.47669
$423$	−8.96730	−0.436005
$424$	−1.03388	−0.0502096
$425$	10.2769	0.498503
$426$	−46.1780	−2.23733
$427$	−7.14350	−0.345698
$428$	−26.9834	−1.30429
$429$	−7.08492	−0.342063
$430$	7.90371	0.381151
$431$	−30.1712	−1.45329	−0.726647	−	0.687011i	$-0.758923\pi$
$431$	−30.1712	−1.45329	−0.726647	+	0.687011i	$0.758923\pi$
$432$	14.6462	0.704665
$433$	31.0713	1.49319	0.746595	−	0.665278i	$-0.231687\pi$
$433$	31.0713	1.49319	0.746595	+	0.665278i	$0.231687\pi$
$434$	1.45140	0.0696692
$435$	51.1040	2.45025
$436$	3.08736	0.147858
$437$	−7.00283	−0.334991
$438$	−17.9045	−0.855510
$439$	−0.322716	−0.0154024	−0.00770121	−	0.999970i	$-0.502451\pi$
$439$	−0.322716	−0.0154024	−0.00770121	+	0.999970i	$0.502451\pi$
$440$	−0.704142	−0.0335686
$441$	−7.31137	−0.348161
$442$	−7.07163	−0.336363
$443$	12.1698	0.578203	0.289101	−	0.957298i	$-0.406643\pi$
$443$	12.1698	0.578203	0.289101	+	0.957298i	$0.406643\pi$
$444$	−3.67676	−0.174491
$445$	43.7251	2.07277
$446$	−1.61573	−0.0765073
$447$	23.5346	1.11315
$448$	5.36253	0.253356
$449$	4.18739	0.197615	0.0988076	−	0.995107i	$-0.468497\pi$
$449$	4.18739	0.197615	0.0988076	+	0.995107i	$0.468497\pi$
$450$	−22.9527	−1.08200
$451$	−4.28511	−0.201778
$452$	0.398704	0.0187534
$453$	14.7699	0.693951
$454$	43.2315	2.02896
$455$	8.42883	0.395149
$456$	0.711295	0.0333095
$457$	−7.48258	−0.350020	−0.175010	−	0.984567i	$-0.555996\pi$
$457$	−7.48258	−0.350020	−0.175010	+	0.984567i	$0.555996\pi$
$458$	9.40571	0.439500
$459$	−3.84023	−0.179247
$460$	−29.3407	−1.36802
$461$	9.06496	0.422197	0.211099	−	0.977465i	$-0.432296\pi$
$461$	9.06496	0.422197	0.211099	+	0.977465i	$0.432296\pi$
$462$	−2.52630	−0.117534
$463$	5.22220	0.242696	0.121348	−	0.992610i	$-0.461278\pi$
$463$	5.22220	0.242696	0.121348	+	0.992610i	$0.461278\pi$
$464$	24.6136	1.14266
$465$	−9.21672	−0.427415
$466$	41.1615	1.90677
$467$	1.32197	0.0611737	0.0305869	−	0.999532i	$-0.490262\pi$
$467$	1.32197	0.0611737	0.0305869	+	0.999532i	$0.490262\pi$
$468$	8.06903	0.372991
$469$	−6.99430	−0.322967
$470$	−64.1703	−2.95996
$471$	44.1423	2.03397
$472$	0.516876	0.0237912
$473$	−1.00000	−0.0459800
$474$	−28.3062	−1.30015
$475$	−20.0282	−0.918955
$476$	−1.28825	−0.0590469
$477$	6.33849	0.290219
$478$	58.0592	2.65556
$479$	−18.3500	−0.838431	−0.419216	−	0.907887i	$-0.637695\pi$
$479$	−18.3500	−0.838431	−0.419216	+	0.907887i	$0.637695\pi$
$480$	−63.9231	−2.91768
$481$	−3.03798	−0.138520
$482$	−17.8047	−0.810981
$483$	−4.48919	−0.204265
$484$	2.08909	0.0949586
$485$	8.04693	0.365392
$486$	22.1513	1.00480
$487$	−5.42957	−0.246037	−0.123019	−	0.992404i	$-0.539258\pi$
$487$	−5.42957	−0.246037	−0.123019	+	0.992404i	$0.539258\pi$
$488$	−2.08694	−0.0944713
$489$	−18.1845	−0.822333
$490$	−52.3205	−2.36360
$491$	−8.75286	−0.395011	−0.197506	−	0.980302i	$-0.563284\pi$
$491$	−8.75286	−0.395011	−0.197506	+	0.980302i	$0.563284\pi$
$492$	18.1363	0.817647
$493$	−6.45369	−0.290660
$494$	13.7815	0.620061
$495$	4.31694	0.194032
$496$	−4.43912	−0.199322
$497$	−6.95081	−0.311786
$498$	23.0489	1.03284
$499$	27.6112	1.23605	0.618024	−	0.786160i	$-0.287934\pi$
$499$	27.6112	1.23605	0.618024	+	0.786160i	$0.287934\pi$
$500$	−43.0878	−1.92695
$501$	−17.9290	−0.801007
$502$	−24.9406	−1.11315
$503$	−33.8389	−1.50880	−0.754401	−	0.656414i	$-0.772072\pi$
$503$	−33.8389	−1.50880	−0.754401	+	0.656414i	$0.772072\pi$
$504$	0.122700	0.00546548
$505$	28.1394	1.25218
$506$	7.26622	0.323023
$507$	−1.56080	−0.0693173
$508$	30.4785	1.35227
$509$	−18.4703	−0.818680	−0.409340	−	0.912382i	$-0.634241\pi$
$509$	−18.4703	−0.818680	−0.409340	+	0.912382i	$0.634241\pi$
$510$	16.0125	0.709047
$511$	−2.69503	−0.119221
$512$	−32.1619	−1.42137
$513$	7.48404	0.330428
$514$	−55.6936	−2.45654
$515$	63.2095	2.78534
$516$	4.23240	0.186321
$517$	8.11901	0.357074
$518$	−1.08327	−0.0475960
$519$	15.7698	0.692219
$520$	2.46244	0.107985
$521$	29.2264	1.28043	0.640216	−	0.768195i	$-0.278845\pi$
$521$	29.2264	1.28043	0.640216	+	0.768195i	$0.278845\pi$
$522$	14.4138	0.630876
$523$	16.1581	0.706545	0.353272	−	0.935520i	$-0.385069\pi$
$523$	16.1581	0.706545	0.353272	+	0.935520i	$0.385069\pi$
$524$	22.3784	0.977603
$525$	−12.8391	−0.560345
$526$	35.7748	1.55986
$527$	1.16394	0.0507019
$528$	7.72674	0.336263
$529$	−10.0881	−0.438612
$530$	45.3585	1.97025
$531$	−3.16886	−0.137517
$532$	2.51061	0.108849
$533$	14.9854	0.649090
$534$	45.8306	1.98328
$535$	50.4844	2.18263
$536$	−2.04335	−0.0882594
$537$	22.3371	0.963916
$538$	9.53236	0.410969
$539$	6.61973	0.285132
$540$	31.3568	1.34938
$541$	−29.6948	−1.27668	−0.638339	−	0.769755i	$-0.720378\pi$
$541$	−29.6948	−1.27668	−0.638339	+	0.769755i	$0.720378\pi$
$542$	46.5853	2.00101
$543$	−47.2019	−2.02563
$544$	8.07255	0.346108
$545$	−5.77627	−0.247428
$546$	8.83470	0.378090
$547$	−46.3890	−1.98345	−0.991724	−	0.128387i	$-0.959020\pi$
$547$	−46.3890	−1.98345	−0.991724	+	0.128387i	$0.959020\pi$
$548$	13.4312	0.573754
$549$	12.7946	0.546059
$550$	20.7815	0.886124
$551$	12.5773	0.535810
$552$	−1.31150	−0.0558210
$553$	−4.26071	−0.181184
$554$	42.0045	1.78460
$555$	6.87900	0.291997
$556$	−2.70004	−0.114507
$557$	4.41040	0.186875	0.0934373	−	0.995625i	$-0.470215\pi$
$557$	4.41040	0.186875	0.0934373	+	0.995625i	$0.470215\pi$
$558$	−2.59957	−0.110048
$559$	3.49708	0.147911
$560$	−9.19239	−0.388449
$561$	−2.02595	−0.0855358
$562$	−23.5366	−0.992832
$563$	11.8063	0.497576	0.248788	−	0.968558i	$-0.419968\pi$
$563$	11.8063	0.497576	0.248788	+	0.968558i	$0.419968\pi$
$564$	−34.3629	−1.44694
$565$	−0.745952	−0.0313824
$566$	−28.0832	−1.18043
$567$	6.84092	0.287292
$568$	−2.03065	−0.0852041
$569$	32.2082	1.35024	0.675119	−	0.737709i	$-0.264092\pi$
$569$	32.2082	1.35024	0.675119	+	0.737709i	$0.264092\pi$
$570$	−31.2060	−1.30708
$571$	−12.6367	−0.528829	−0.264415	−	0.964409i	$-0.585179\pi$
$571$	−12.6367	−0.528829	−0.264415	+	0.964409i	$0.585179\pi$
$572$	−7.30572	−0.305468
$573$	−24.9751	−1.04335
$574$	5.34342	0.223030
$575$	36.9282	1.54001
$576$	−9.60472	−0.400197
$577$	22.2664	0.926962	0.463481	−	0.886107i	$-0.346600\pi$
$577$	22.2664	0.926962	0.463481	+	0.886107i	$0.346600\pi$
$578$	−2.02215	−0.0841103
$579$	−2.43559	−0.101220
$580$	52.6966	2.18811
$581$	3.46937	0.143934
$582$	8.43441	0.349618
$583$	−5.73888	−0.237680
$584$	−0.787339	−0.0325803
$585$	−15.0967	−0.624172
$586$	19.5286	0.806717
$587$	−24.2252	−0.999882	−0.499941	−	0.866060i	$-0.666645\pi$
$587$	−24.2252	−0.999882	−0.499941	+	0.866060i	$0.666645\pi$
$588$	−28.0173	−1.15542
$589$	−2.26834	−0.0934653
$590$	−22.6765	−0.933575
$591$	−9.19007	−0.378029
$592$	3.31319	0.136171
$593$	−6.21644	−0.255279	−0.127639	−	0.991821i	$-0.540740\pi$
$593$	−6.21644	−0.255279	−0.127639	+	0.991821i	$0.540740\pi$
$594$	−7.76552	−0.318623
$595$	2.41024	0.0988104
$596$	24.2681	0.994058
$597$	25.1499	1.02932
$598$	−25.4106	−1.03912
$599$	33.8019	1.38111	0.690553	−	0.723282i	$-0.257367\pi$
$599$	33.8019	1.38111	0.690553	+	0.723282i	$0.257367\pi$
$600$	−3.75089	−0.153129
$601$	−11.4599	−0.467460	−0.233730	−	0.972301i	$-0.575093\pi$
$601$	−11.4599	−0.467460	−0.233730	+	0.972301i	$0.575093\pi$
$602$	1.24697	0.0508228
$603$	12.5274	0.510153
$604$	15.2302	0.619709
$605$	−3.90857	−0.158906
$606$	29.4943	1.19813
$607$	−39.3802	−1.59839	−0.799197	−	0.601070i	$-0.794741\pi$
$607$	−39.3802	−1.59839	−0.799197	+	0.601070i	$0.794741\pi$
$608$	−15.7322	−0.638025
$609$	8.06270	0.326717
$610$	91.5585	3.70710
$611$	−28.3929	−1.14865
$612$	2.30736	0.0932695
$613$	−29.4621	−1.18996	−0.594982	−	0.803739i	$-0.702841\pi$
$613$	−29.4621	−1.18996	−0.594982	+	0.803739i	$0.702841\pi$
$614$	49.5448	1.99947
$615$	−33.9320	−1.36827
$616$	−0.111093	−0.00447605
$617$	−2.64954	−0.106667	−0.0533333	−	0.998577i	$-0.516985\pi$
$617$	−2.64954	−0.106667	−0.0533333	+	0.998577i	$0.516985\pi$
$618$	66.2532	2.66510
$619$	−28.6501	−1.15155	−0.575773	−	0.817610i	$-0.695299\pi$
$619$	−28.6501	−1.15155	−0.575773	+	0.817610i	$0.695299\pi$
$620$	−9.50395	−0.381688
$621$	−13.7992	−0.553741
$622$	−36.7472	−1.47343
$623$	6.89852	0.276383
$624$	−27.0211	−1.08171
$625$	29.2303	1.16921
$626$	−42.4967	−1.69851
$627$	3.94828	0.157679
$628$	45.5180	1.81636
$629$	−0.868718	−0.0346380
$630$	−5.38310	−0.214468
$631$	−20.9029	−0.832132	−0.416066	−	0.909334i	$-0.636592\pi$
$631$	−20.9029	−0.832132	−0.416066	+	0.909334i	$0.636592\pi$
$632$	−1.24475	−0.0495134
$633$	50.9734	2.02601
$634$	46.7122	1.85518
$635$	−57.0236	−2.26291
$636$	24.2892	0.963130
$637$	−23.1498	−0.917227
$638$	−13.0503	−0.516667
$639$	12.4495	0.492493
$640$	−5.62754	−0.222448
$641$	−22.8407	−0.902155	−0.451078	−	0.892485i	$-0.648960\pi$
$641$	−22.8407	−0.902155	−0.451078	+	0.892485i	$0.648960\pi$
$642$	52.9153	2.08840
$643$	33.6497	1.32702	0.663508	−	0.748169i	$-0.269067\pi$
$643$	33.6497	1.32702	0.663508	+	0.748169i	$0.269067\pi$
$644$	−4.62909	−0.182412
$645$	−7.91857	−0.311793
$646$	3.94087	0.155051
$647$	−27.6381	−1.08657	−0.543283	−	0.839549i	$-0.682819\pi$
$647$	−27.6381	−1.08657	−0.543283	+	0.839549i	$0.682819\pi$
$648$	1.99854	0.0785102
$649$	2.86909	0.112622
$650$	−72.6745	−2.85053
$651$	−1.45412	−0.0569916
$652$	−18.7513	−0.734356
$653$	36.8604	1.44246	0.721230	−	0.692695i	$-0.243577\pi$
$653$	36.8604	1.44246	0.721230	+	0.692695i	$0.243577\pi$
$654$	−6.05441	−0.236746
$655$	−41.8687	−1.63594
$656$	−16.3429	−0.638084
$657$	4.82701	0.188319
$658$	−10.1242	−0.394682
$659$	30.2407	1.17801	0.589005	−	0.808129i	$-0.299520\pi$
$659$	30.2407	1.17801	0.589005	+	0.808129i	$0.299520\pi$
$660$	16.5426	0.643920
$661$	−19.1948	−0.746592	−0.373296	−	0.927712i	$-0.621772\pi$
$661$	−19.1948	−0.746592	−0.373296	+	0.927712i	$0.621772\pi$
$662$	15.5126	0.602916
$663$	7.08492	0.275156
$664$	1.01356	0.0393337
$665$	−4.69720	−0.182150
$666$	1.94022	0.0751818
$667$	−23.1901	−0.897926
$668$	−18.4877	−0.715312
$669$	1.61877	0.0625854
$670$	89.6463	3.46334
$671$	−11.5842	−0.447205
$672$	−10.0852	−0.389044
$673$	−22.7730	−0.877833	−0.438917	−	0.898528i	$-0.644638\pi$
$673$	−22.7730	−0.877833	−0.438917	+	0.898528i	$0.644638\pi$
$674$	26.0590	1.00375
$675$	−39.4657	−1.51904
$676$	−1.60944	−0.0619014
$677$	15.4848	0.595129	0.297564	−	0.954702i	$-0.403826\pi$
$677$	15.4848	0.595129	0.297564	+	0.954702i	$0.403826\pi$
$678$	−0.781872	−0.0300276
$679$	1.26957	0.0487215
$680$	0.704142	0.0270026
$681$	−43.3128	−1.65975
$682$	2.35365	0.0901261
$683$	−24.2280	−0.927057	−0.463529	−	0.886082i	$-0.653417\pi$
$683$	−24.2280	−0.927057	−0.463529	+	0.886082i	$0.653417\pi$
$684$	−4.49670	−0.171936
$685$	−25.1291	−0.960132
$686$	−16.9834	−0.648430
$687$	−9.42339	−0.359525
$688$	−3.81388	−0.145403
$689$	20.0694	0.764582
$690$	57.5381	2.19044
$691$	25.4006	0.966285	0.483142	−	0.875542i	$-0.339495\pi$
$691$	25.4006	0.966285	0.483142	+	0.875542i	$0.339495\pi$
$692$	16.2613	0.618162
$693$	0.681085	0.0258723
$694$	34.8317	1.32219
$695$	5.05162	0.191619
$696$	2.35548	0.0892842
$697$	4.28511	0.162310
$698$	−7.59110	−0.287328
$699$	−41.2389	−1.55980
$700$	−13.2392	−0.500396
$701$	−27.4028	−1.03499	−0.517495	−	0.855686i	$-0.673136\pi$
$701$	−27.4028	−1.03499	−0.517495	+	0.855686i	$0.673136\pi$
$702$	27.1567	1.02496
$703$	1.69300	0.0638527
$704$	8.69614	0.327748
$705$	64.2910	2.42134
$706$	8.12144	0.305654
$707$	4.43956	0.166967
$708$	−12.1431	−0.456367
$709$	−38.8487	−1.45899	−0.729496	−	0.683985i	$-0.760245\pi$
$709$	−38.8487	−1.45899	−0.729496	+	0.683985i	$0.760245\pi$
$710$	89.0888	3.34344
$711$	7.63127	0.286195
$712$	2.01537	0.0755293
$713$	4.18239	0.156632
$714$	2.52630	0.0945446
$715$	13.6686	0.511176
$716$	23.0332	0.860792
$717$	−58.1683	−2.17234
$718$	51.4032	1.91835
$719$	21.2829	0.793720	0.396860	−	0.917879i	$-0.370100\pi$
$719$	21.2829	0.793720	0.396860	+	0.917879i	$0.370100\pi$
$720$	16.4643	0.613588
$721$	9.97259	0.371399
$722$	30.7407	1.14405
$723$	17.8382	0.663408
$724$	−48.6730	−1.80892
$725$	−66.3240	−2.46321
$726$	−4.09678	−0.152046
$727$	19.9248	0.738970	0.369485	−	0.929237i	$-0.379534\pi$
$727$	19.9248	0.738970	0.369485	+	0.929237i	$0.379534\pi$
$728$	0.388501	0.0143988
$729$	11.0877	0.410657
$730$	34.5423	1.27847
$731$	1.00000	0.0369863
$732$	49.0291	1.81217
$733$	38.8664	1.43556	0.717782	−	0.696268i	$-0.245157\pi$
$733$	38.8664	1.43556	0.717782	+	0.696268i	$0.245157\pi$
$734$	46.0101	1.69826
$735$	52.4188	1.93350
$736$	29.0072	1.06922
$737$	−11.3423	−0.417799
$738$	−9.57048	−0.352294
$739$	51.2332	1.88465	0.942323	−	0.334706i	$-0.108637\pi$
$739$	51.2332	1.88465	0.942323	+	0.334706i	$0.108637\pi$
$740$	7.09338	0.260758
$741$	−13.8075	−0.507230
$742$	7.15622	0.262713
$743$	−34.8354	−1.27799	−0.638994	−	0.769212i	$-0.720649\pi$
$743$	−34.8354	−1.27799	−0.638994	+	0.769212i	$0.720649\pi$
$744$	−0.424816	−0.0155745
$745$	−45.4041	−1.66348
$746$	46.9333	1.71835
$747$	−6.21391	−0.227355
$748$	−2.08909	−0.0763847
$749$	7.96494	0.291032
$750$	84.4967	3.08538
$751$	38.7739	1.41488	0.707440	−	0.706773i	$-0.249850\pi$
$751$	38.7739	1.41488	0.707440	+	0.706773i	$0.249850\pi$
$752$	30.9650	1.12918
$753$	24.9875	0.910594
$754$	45.6381	1.66204
$755$	−28.4949	−1.03703
$756$	4.94718	0.179927
$757$	18.5025	0.672484	0.336242	−	0.941776i	$-0.390844\pi$
$757$	18.5025	0.672484	0.336242	+	0.941776i	$0.390844\pi$
$758$	5.87251	0.213299
$759$	−7.27988	−0.264243
$760$	−1.37227	−0.0497774
$761$	−11.6430	−0.422059	−0.211029	−	0.977480i	$-0.567682\pi$
$761$	−11.6430	−0.422059	−0.211029	+	0.977480i	$0.567682\pi$
$762$	−59.7694	−2.16522
$763$	−0.911324	−0.0329922
$764$	−25.7534	−0.931726
$765$	−4.31694	−0.156079
$766$	74.8620	2.70488
$767$	−10.0335	−0.362287
$768$	29.3374	1.05862
$769$	−32.0730	−1.15658	−0.578292	−	0.815830i	$-0.696280\pi$
$769$	−32.0730	−1.15658	−0.578292	+	0.815830i	$0.696280\pi$
$770$	4.87387	0.175642
$771$	55.7984	2.00953
$772$	−2.51150	−0.0903907
$773$	22.0240	0.792147	0.396073	−	0.918219i	$-0.370373\pi$
$773$	22.0240	0.792147	0.396073	+	0.918219i	$0.370373\pi$
$774$	−2.23343	−0.0802788
$775$	11.9617	0.429676
$776$	0.370898	0.0133145
$777$	1.08530	0.0389350
$778$	11.8853	0.426110
$779$	−8.35105	−0.299207
$780$	−57.8509	−2.07139
$781$	−11.2718	−0.403336
$782$	−7.26622	−0.259840
$783$	24.7837	0.885695
$784$	25.2469	0.901675
$785$	−85.1615	−3.03954
$786$	−43.8848	−1.56532
$787$	−29.1493	−1.03906	−0.519531	−	0.854452i	$-0.673893\pi$
$787$	−29.1493	−1.03906	−0.519531	+	0.854452i	$0.673893\pi$
$788$	−9.47647	−0.337585
$789$	−35.8421	−1.27601
$790$	54.6097	1.94293
$791$	−0.117689	−0.00418454
$792$	0.198976	0.00707030
$793$	40.5111	1.43859
$794$	18.4027	0.653087
$795$	−45.4438	−1.61172
$796$	25.9337	0.919197
$797$	−22.4102	−0.793811	−0.396905	−	0.917859i	$-0.629916\pi$
$797$	−22.4102	−0.793811	−0.396905	+	0.917859i	$0.629916\pi$
$798$	−4.92339	−0.174286
$799$	−8.11901	−0.287230
$800$	82.9609	2.93311
$801$	−12.3558	−0.436571
$802$	40.5934	1.43340
$803$	−4.37038	−0.154228
$804$	48.0051	1.69301
$805$	8.66077	0.305252
$806$	−8.23093	−0.289922
$807$	−9.55028	−0.336186
$808$	1.29700	0.0456282
$809$	−31.9802	−1.12436	−0.562182	−	0.827013i	$-0.690038\pi$
$809$	−31.9802	−1.12436	−0.562182	+	0.827013i	$0.690038\pi$
$810$	−87.6803	−3.08077
$811$	39.7649	1.39634	0.698168	−	0.715934i	$-0.253999\pi$
$811$	39.7649	1.39634	0.698168	+	0.715934i	$0.253999\pi$
$812$	8.31397	0.291763
$813$	−46.6729	−1.63689
$814$	−1.75668	−0.0615715
$815$	35.0825	1.22889
$816$	−7.72674	−0.270490
$817$	−1.94885	−0.0681816
$818$	−39.9646	−1.39733
$819$	−2.38181	−0.0832273
$820$	−34.9895	−1.22189
$821$	−16.8400	−0.587720	−0.293860	−	0.955849i	$-0.594940\pi$
$821$	−16.8400	−0.587720	−0.293860	+	0.955849i	$0.594940\pi$
$822$	−26.3391	−0.918682
$823$	23.7160	0.826688	0.413344	−	0.910575i	$-0.364361\pi$
$823$	23.7160	0.826688	0.413344	+	0.910575i	$0.364361\pi$
$824$	2.91345	0.101495
$825$	−20.8205	−0.724878
$826$	−3.57767	−0.124483
$827$	−34.6843	−1.20609	−0.603046	−	0.797707i	$-0.706046\pi$
$827$	−34.6843	−1.20609	−0.603046	+	0.797707i	$0.706046\pi$
$828$	8.29107	0.288135
$829$	−7.58080	−0.263292	−0.131646	−	0.991297i	$-0.542026\pi$
$829$	−7.58080	−0.263292	−0.131646	+	0.991297i	$0.542026\pi$
$830$	−44.4670	−1.54347
$831$	−42.0835	−1.45986
$832$	−30.4111	−1.05432
$833$	−6.61973	−0.229360
$834$	5.29487	0.183346
$835$	34.5895	1.19702
$836$	4.07132	0.140810
$837$	−4.46979	−0.154498
$838$	70.4011	2.43197
$839$	36.7771	1.26969	0.634844	−	0.772640i	$-0.281064\pi$
$839$	36.7771	1.26969	0.634844	+	0.772640i	$0.281064\pi$
$840$	−0.879696	−0.0303524
$841$	12.6501	0.436210
$842$	−27.1068	−0.934163
$843$	23.5809	0.812168
$844$	52.5620	1.80926
$845$	3.01116	0.103587
$846$	18.1332	0.623433
$847$	−0.616656	−0.0211886
$848$	−21.8874	−0.751617
$849$	28.1360	0.965626
$850$	−20.7815	−0.712798
$851$	−3.12158	−0.107006
$852$	47.7066	1.63440
$853$	18.4854	0.632929	0.316464	−	0.948604i	$-0.397504\pi$
$853$	18.4854	0.632929	0.316464	+	0.948604i	$0.397504\pi$
$854$	14.4452	0.494305
$855$	8.41307	0.287721
$856$	2.32692	0.0795325
$857$	20.1190	0.687253	0.343627	−	0.939106i	$-0.388345\pi$
$857$	20.1190	0.687253	0.343627	+	0.939106i	$0.388345\pi$
$858$	14.3268	0.489108
$859$	12.5145	0.426988	0.213494	−	0.976944i	$-0.431516\pi$
$859$	12.5145	0.426988	0.213494	+	0.976944i	$0.431516\pi$
$860$	−8.16535	−0.278436
$861$	−5.35346	−0.182445
$862$	61.0107	2.07803
$863$	−32.5646	−1.10851	−0.554256	−	0.832346i	$-0.686997\pi$
$863$	−32.5646	−1.10851	−0.554256	+	0.832346i	$0.686997\pi$
$864$	−31.0005	−1.05466
$865$	−30.4240	−1.03445
$866$	−62.8308	−2.13508
$867$	2.02595	0.0688049
$868$	−1.49944	−0.0508944
$869$	−6.90937	−0.234384
$870$	−103.340	−3.50355
$871$	39.6650	1.34400
$872$	−0.266239	−0.00901600
$873$	−2.27390	−0.0769597
$874$	14.1608	0.478996
$875$	12.7186	0.429969
$876$	18.4972	0.624962
$877$	−51.2538	−1.73072	−0.865358	−	0.501154i	$-0.832909\pi$
$877$	−51.2538	−1.73072	−0.865358	+	0.501154i	$0.832909\pi$
$878$	0.652581	0.0220235
$879$	−19.5653	−0.659920
$880$	−14.9068	−0.502509
$881$	−12.1003	−0.407671	−0.203836	−	0.979005i	$-0.565341\pi$
$881$	−12.1003	−0.407671	−0.203836	+	0.979005i	$0.565341\pi$
$882$	14.7847	0.497826
$883$	−32.1222	−1.08100	−0.540499	−	0.841345i	$-0.681765\pi$
$883$	−32.1222	−1.08100	−0.540499	+	0.841345i	$0.681765\pi$
$884$	7.30572	0.245718
$885$	22.7191	0.763694
$886$	−24.6091	−0.826758
$887$	−25.5468	−0.857779	−0.428889	−	0.903357i	$-0.641095\pi$
$887$	−25.5468	−0.857779	−0.428889	+	0.903357i	$0.641095\pi$
$888$	0.317066	0.0106400
$889$	−8.99663	−0.301737
$890$	−88.4187	−2.96380
$891$	11.0936	0.371648
$892$	1.66922	0.0558897
$893$	15.8227	0.529488
$894$	−47.5905	−1.59166
$895$	−43.0938	−1.44047
$896$	−0.887860	−0.0296613
$897$	25.4584	0.850030
$898$	−8.46753	−0.282565
$899$	−7.51168	−0.250529
$900$	23.7125	0.790418
$901$	5.73888	0.191190
$902$	8.66514	0.288518
$903$	−1.24932	−0.0415746
$904$	−0.0343823	−0.00114354
$905$	91.0644	3.02708
$906$	−29.8670	−0.992264
$907$	18.3973	0.610872	0.305436	−	0.952213i	$-0.401198\pi$
$907$	18.3973	0.610872	0.305436	+	0.952213i	$0.401198\pi$
$908$	−44.6626	−1.48218
$909$	−7.95160	−0.263738
$910$	−17.0443	−0.565015
$911$	−28.5891	−0.947197	−0.473599	−	0.880741i	$-0.657045\pi$
$911$	−28.5891	−0.947197	−0.473599	+	0.880741i	$0.657045\pi$
$912$	15.0583	0.498629
$913$	5.62609	0.186197
$914$	15.1309	0.500486
$915$	−91.7306	−3.03252
$916$	−9.71707	−0.321061
$917$	−6.60563	−0.218137
$918$	7.76552	0.256300
$919$	−35.3462	−1.16596	−0.582982	−	0.812485i	$-0.698114\pi$
$919$	−35.3462	−1.16596	−0.582982	+	0.812485i	$0.698114\pi$
$920$	2.53020	0.0834183
$921$	−49.6380	−1.63563
$922$	−18.3307	−0.603690
$923$	39.4183	1.29747
$924$	2.60993	0.0858605
$925$	−8.92773	−0.293542
$926$	−10.5601	−0.347025
$927$	−17.8617	−0.586655
$928$	−52.0977	−1.71019
$929$	6.33066	0.207702	0.103851	−	0.994593i	$-0.466883\pi$
$929$	6.33066	0.207702	0.103851	+	0.994593i	$0.466883\pi$
$930$	18.6376	0.611150
$931$	12.9009	0.422809
$932$	−42.5241	−1.39292
$933$	36.8163	1.20531
$934$	−2.67323	−0.0874708
$935$	3.90857	0.127824
$936$	−0.695836	−0.0227441
$937$	22.7343	0.742697	0.371348	−	0.928494i	$-0.378896\pi$
$937$	22.7343	0.742697	0.371348	+	0.928494i	$0.378896\pi$
$938$	14.1435	0.461802
$939$	42.5766	1.38944
$940$	66.2946	2.16229
$941$	40.9500	1.33493	0.667465	−	0.744641i	$-0.267379\pi$
$941$	40.9500	1.33493	0.667465	+	0.744641i	$0.267379\pi$
$942$	−89.2623	−2.90832
$943$	15.3978	0.501420
$944$	10.9424	0.356144
$945$	−9.25589	−0.301094
$946$	2.02215	0.0657458
$947$	28.7063	0.932831	0.466415	−	0.884566i	$-0.345545\pi$
$947$	28.7063	0.932831	0.466415	+	0.884566i	$0.345545\pi$
$948$	29.2432	0.949775
$949$	15.2836	0.496127
$950$	40.4999	1.31399
$951$	−46.8000	−1.51760
$952$	0.111093	0.00360054
$953$	−12.0592	−0.390635	−0.195318	−	0.980740i	$-0.562574\pi$
$953$	−12.0592	−0.390635	−0.195318	+	0.980740i	$0.562574\pi$
$954$	−12.8174	−0.414978
$955$	48.1832	1.55917
$956$	−59.9811	−1.93993
$957$	13.0749	0.422650
$958$	37.1064	1.19885
$959$	−3.96462	−0.128024
$960$	68.8610	2.22248
$961$	−29.6453	−0.956298
$962$	6.14325	0.198066
$963$	−14.2658	−0.459710
$964$	18.3941	0.592433
$965$	4.69887	0.151262
$966$	9.07781	0.292074
$967$	−28.5200	−0.917141	−0.458570	−	0.888658i	$-0.651638\pi$
$967$	−28.5200	−0.917141	−0.458570	+	0.888658i	$0.651638\pi$
$968$	−0.180153	−0.00579035
$969$	−3.94828	−0.126837
$970$	−16.2721	−0.522466
$971$	30.9750	0.994036	0.497018	−	0.867740i	$-0.334428\pi$
$971$	30.9750	0.994036	0.497018	+	0.867740i	$0.334428\pi$
$972$	−22.8846	−0.734024
$973$	0.796996	0.0255505
$974$	10.9794	0.351803
$975$	72.8111	2.33182
$976$	−44.1809	−1.41420
$977$	−45.8483	−1.46682	−0.733408	−	0.679789i	$-0.762072\pi$
$977$	−45.8483	−1.46682	−0.733408	+	0.679789i	$0.762072\pi$
$978$	36.7719	1.17583
$979$	11.1870	0.357537
$980$	54.0525	1.72664
$981$	1.63225	0.0521139
$982$	17.6996	0.564817
$983$	40.6723	1.29724	0.648622	−	0.761111i	$-0.275346\pi$
$983$	40.6723	1.29724	0.648622	+	0.761111i	$0.275346\pi$
$984$	−1.56399	−0.0498582
$985$	17.7299	0.564923
$986$	13.0503	0.415607
$987$	10.1432	0.322862
$988$	−14.2378	−0.452964
$989$	3.59332	0.114261
$990$	−8.72950	−0.277442
$991$	5.32483	0.169149	0.0845745	−	0.996417i	$-0.473047\pi$
$991$	5.32483	0.169149	0.0845745	+	0.996417i	$0.473047\pi$
$992$	9.39594	0.298321
$993$	−15.5418	−0.493205
$994$	14.0556	0.445816
$995$	−48.5205	−1.53820
$996$	−23.8119	−0.754507
$997$	−8.92479	−0.282651	−0.141326	−	0.989963i	$-0.545136\pi$
$997$	−8.92479	−0.282651	−0.141326	+	0.989963i	$0.545136\pi$
$998$	−55.8340	−1.76739
$999$	3.33608	0.105549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.14	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.14	✓	69	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)

\(f(q)\)	\(=\)	\(q-2.02215 q^{2} +2.02595 q^{3} +2.08909 q^{4} -3.90857 q^{5} -4.09678 q^{6} -0.616656 q^{7} -0.180153 q^{8} +1.10448 q^{9} +O(q^{10})\)	\(q-2.02215 q^{2} +2.02595 q^{3} +2.08909 q^{4} -3.90857 q^{5} -4.09678 q^{6} -0.616656 q^{7} -0.180153 q^{8} +1.10448 q^{9} +7.90371 q^{10} -1.00000 q^{11} +4.23240 q^{12} +3.49708 q^{13} +1.24697 q^{14} -7.91857 q^{15} -3.81388 q^{16} +1.00000 q^{17} -2.23343 q^{18} -1.94885 q^{19} -8.16535 q^{20} -1.24932 q^{21} +2.02215 q^{22} +3.59332 q^{23} -0.364982 q^{24} +10.2769 q^{25} -7.07163 q^{26} -3.84023 q^{27} -1.28825 q^{28} -6.45369 q^{29} +16.0125 q^{30} +1.16394 q^{31} +8.07255 q^{32} -2.02595 q^{33} -2.02215 q^{34} +2.41024 q^{35} +2.30736 q^{36} -0.868718 q^{37} +3.94087 q^{38} +7.08492 q^{39} +0.704142 q^{40} +4.28511 q^{41} +2.52630 q^{42} +1.00000 q^{43} -2.08909 q^{44} -4.31694 q^{45} -7.26622 q^{46} -8.11901 q^{47} -7.72674 q^{48} -6.61973 q^{49} -20.7815 q^{50} +2.02595 q^{51} +7.30572 q^{52} +5.73888 q^{53} +7.76552 q^{54} +3.90857 q^{55} +0.111093 q^{56} -3.94828 q^{57} +13.0503 q^{58} -2.86909 q^{59} -16.5426 q^{60} +11.5842 q^{61} -2.35365 q^{62} -0.681085 q^{63} -8.69614 q^{64} -13.6686 q^{65} +4.09678 q^{66} +11.3423 q^{67} +2.08909 q^{68} +7.27988 q^{69} -4.87387 q^{70} +11.2718 q^{71} -0.198976 q^{72} +4.37038 q^{73} +1.75668 q^{74} +20.8205 q^{75} -4.07132 q^{76} +0.616656 q^{77} -14.3268 q^{78} +6.90937 q^{79} +14.9068 q^{80} -11.0936 q^{81} -8.66514 q^{82} -5.62609 q^{83} -2.60993 q^{84} -3.90857 q^{85} -2.02215 q^{86} -13.0749 q^{87} +0.180153 q^{88} -11.1870 q^{89} +8.72950 q^{90} -2.15650 q^{91} +7.50676 q^{92} +2.35808 q^{93} +16.4179 q^{94} +7.61722 q^{95} +16.3546 q^{96} -2.05879 q^{97} +13.3861 q^{98} -1.10448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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