LMFDB - Embedded newform 8002.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.73719 q^{3} +1.00000 q^{4} -4.28393 q^{5} -2.73719 q^{6} +2.06732 q^{7} +1.00000 q^{8} +4.49223 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.73719 q^{3} +1.00000 q^{4} -4.28393 q^{5} -2.73719 q^{6} +2.06732 q^{7} +1.00000 q^{8} +4.49223 q^{9} -4.28393 q^{10} -4.65115 q^{11} -2.73719 q^{12} -7.04120 q^{13} +2.06732 q^{14} +11.7259 q^{15} +1.00000 q^{16} +3.79446 q^{17} +4.49223 q^{18} -1.74040 q^{19} -4.28393 q^{20} -5.65865 q^{21} -4.65115 q^{22} -0.612761 q^{23} -2.73719 q^{24} +13.3520 q^{25} -7.04120 q^{26} -4.08451 q^{27} +2.06732 q^{28} +7.92947 q^{29} +11.7259 q^{30} +1.07513 q^{31} +1.00000 q^{32} +12.7311 q^{33} +3.79446 q^{34} -8.85624 q^{35} +4.49223 q^{36} +2.44096 q^{37} -1.74040 q^{38} +19.2731 q^{39} -4.28393 q^{40} -8.48552 q^{41} -5.65865 q^{42} +8.97146 q^{43} -4.65115 q^{44} -19.2444 q^{45} -0.612761 q^{46} +1.99611 q^{47} -2.73719 q^{48} -2.72620 q^{49} +13.3520 q^{50} -10.3862 q^{51} -7.04120 q^{52} +7.08196 q^{53} -4.08451 q^{54} +19.9252 q^{55} +2.06732 q^{56} +4.76381 q^{57} +7.92947 q^{58} +7.17783 q^{59} +11.7259 q^{60} -10.7917 q^{61} +1.07513 q^{62} +9.28686 q^{63} +1.00000 q^{64} +30.1640 q^{65} +12.7311 q^{66} -10.0032 q^{67} +3.79446 q^{68} +1.67725 q^{69} -8.85624 q^{70} -9.46462 q^{71} +4.49223 q^{72} +16.3706 q^{73} +2.44096 q^{74} -36.5471 q^{75} -1.74040 q^{76} -9.61542 q^{77} +19.2731 q^{78} +8.98411 q^{79} -4.28393 q^{80} -2.29658 q^{81} -8.48552 q^{82} +8.10098 q^{83} -5.65865 q^{84} -16.2552 q^{85} +8.97146 q^{86} -21.7045 q^{87} -4.65115 q^{88} -12.0925 q^{89} -19.2444 q^{90} -14.5564 q^{91} -0.612761 q^{92} -2.94283 q^{93} +1.99611 q^{94} +7.45576 q^{95} -2.73719 q^{96} -8.55655 q^{97} -2.72620 q^{98} -20.8940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.73719	−1.58032	−0.790160	−	0.612901i	$-0.790002\pi$
$3$	−2.73719	−1.58032	−0.790160	+	0.612901i	$0.790002\pi$
$4$	1.00000	0.500000
$5$	−4.28393	−1.91583	−0.957916	−	0.287050i	$-0.907325\pi$
$5$	−4.28393	−1.91583	−0.957916	+	0.287050i	$0.907325\pi$
$6$	−2.73719	−1.11745
$7$	2.06732	0.781373	0.390686	−	0.920524i	$-0.372238\pi$
$7$	2.06732	0.781373	0.390686	+	0.920524i	$0.372238\pi$
$8$	1.00000	0.353553
$9$	4.49223	1.49741
$10$	−4.28393	−1.35470
$11$	−4.65115	−1.40238	−0.701188	−	0.712977i	$-0.747347\pi$
$11$	−4.65115	−1.40238	−0.701188	+	0.712977i	$0.747347\pi$
$12$	−2.73719	−0.790160
$13$	−7.04120	−1.95288	−0.976439	−	0.215793i	$-0.930766\pi$
$13$	−7.04120	−1.95288	−0.976439	+	0.215793i	$0.930766\pi$
$14$	2.06732	0.552514
$15$	11.7259	3.02762
$16$	1.00000	0.250000
$17$	3.79446	0.920291	0.460146	−	0.887843i	$-0.347797\pi$
$17$	3.79446	0.920291	0.460146	+	0.887843i	$0.347797\pi$
$18$	4.49223	1.05883
$19$	−1.74040	−0.399275	−0.199638	−	0.979870i	$-0.563977\pi$
$19$	−1.74040	−0.399275	−0.199638	+	0.979870i	$0.563977\pi$
$20$	−4.28393	−0.957916
$21$	−5.65865	−1.23482
$22$	−4.65115	−0.991629
$23$	−0.612761	−0.127770	−0.0638848	−	0.997957i	$-0.520349\pi$
$23$	−0.612761	−0.127770	−0.0638848	+	0.997957i	$0.520349\pi$
$24$	−2.73719	−0.558727
$25$	13.3520	2.67041
$26$	−7.04120	−1.38089
$27$	−4.08451	−0.786064
$28$	2.06732	0.390686
$29$	7.92947	1.47247	0.736233	−	0.676728i	$-0.236603\pi$
$29$	7.92947	1.47247	0.736233	+	0.676728i	$0.236603\pi$
$30$	11.7259	2.14085
$31$	1.07513	0.193098	0.0965492	−	0.995328i	$-0.469219\pi$
$31$	1.07513	0.193098	0.0965492	+	0.995328i	$0.469219\pi$
$32$	1.00000	0.176777
$33$	12.7311	2.21620
$34$	3.79446	0.650744
$35$	−8.85624	−1.49698
$36$	4.49223	0.748704
$37$	2.44096	0.401292	0.200646	−	0.979664i	$-0.435696\pi$
$37$	2.44096	0.401292	0.200646	+	0.979664i	$0.435696\pi$
$38$	−1.74040	−0.282330
$39$	19.2731	3.08617
$40$	−4.28393	−0.677349
$41$	−8.48552	−1.32522	−0.662608	−	0.748967i	$-0.730550\pi$
$41$	−8.48552	−1.32522	−0.662608	+	0.748967i	$0.730550\pi$
$42$	−5.65865	−0.873149
$43$	8.97146	1.36814	0.684068	−	0.729419i	$-0.260209\pi$
$43$	8.97146	1.36814	0.684068	+	0.729419i	$0.260209\pi$
$44$	−4.65115	−0.701188
$45$	−19.2444	−2.86878
$46$	−0.612761	−0.0903467
$47$	1.99611	0.291163	0.145581	−	0.989346i	$-0.453495\pi$
$47$	1.99611	0.291163	0.145581	+	0.989346i	$0.453495\pi$
$48$	−2.73719	−0.395080
$49$	−2.72620	−0.389456
$50$	13.3520	1.88826
$51$	−10.3862	−1.45435
$52$	−7.04120	−0.976439
$53$	7.08196	0.972783	0.486391	−	0.873741i	$-0.338313\pi$
$53$	7.08196	0.972783	0.486391	+	0.873741i	$0.338313\pi$
$54$	−4.08451	−0.555832
$55$	19.9252	2.68672
$56$	2.06732	0.276257
$57$	4.76381	0.630983
$58$	7.92947	1.04119
$59$	7.17783	0.934474	0.467237	−	0.884132i	$-0.345249\pi$
$59$	7.17783	0.934474	0.467237	+	0.884132i	$0.345249\pi$
$60$	11.7259	1.51381
$61$	−10.7917	−1.38174	−0.690868	−	0.722981i	$-0.742771\pi$
$61$	−10.7917	−1.38174	−0.690868	+	0.722981i	$0.742771\pi$
$62$	1.07513	0.136541
$63$	9.28686	1.17003
$64$	1.00000	0.125000
$65$	30.1640	3.74139
$66$	12.7311	1.56709
$67$	−10.0032	−1.22209	−0.611045	−	0.791596i	$-0.709251\pi$
$67$	−10.0032	−1.22209	−0.611045	+	0.791596i	$0.709251\pi$
$68$	3.79446	0.460146
$69$	1.67725	0.201917
$70$	−8.85624	−1.05852
$71$	−9.46462	−1.12324	−0.561622	−	0.827394i	$-0.689822\pi$
$71$	−9.46462	−1.12324	−0.561622	+	0.827394i	$0.689822\pi$
$72$	4.49223	0.529414
$73$	16.3706	1.91603	0.958017	−	0.286711i	$-0.0925619\pi$
$73$	16.3706	1.91603	0.958017	+	0.286711i	$0.0925619\pi$
$74$	2.44096	0.283756
$75$	−36.5471	−4.22010
$76$	−1.74040	−0.199638
$77$	−9.61542	−1.09578
$78$	19.2731	2.18225
$79$	8.98411	1.01079	0.505396	−	0.862888i	$-0.331347\pi$
$79$	8.98411	1.01079	0.505396	+	0.862888i	$0.331347\pi$
$80$	−4.28393	−0.478958
$81$	−2.29658	−0.255176
$82$	−8.48552	−0.937069
$83$	8.10098	0.889199	0.444599	−	0.895730i	$-0.353346\pi$
$83$	8.10098	0.889199	0.444599	+	0.895730i	$0.353346\pi$
$84$	−5.65865	−0.617409
$85$	−16.2552	−1.76312
$86$	8.97146	0.967418
$87$	−21.7045	−2.32697
$88$	−4.65115	−0.495815
$89$	−12.0925	−1.28180	−0.640901	−	0.767624i	$-0.721439\pi$
$89$	−12.0925	−1.28180	−0.640901	+	0.767624i	$0.721439\pi$
$90$	−19.2444	−2.02854
$91$	−14.5564	−1.52593
$92$	−0.612761	−0.0638848
$93$	−2.94283	−0.305157
$94$	1.99611	0.205883
$95$	7.45576	0.764944
$96$	−2.73719	−0.279364
$97$	−8.55655	−0.868786	−0.434393	−	0.900723i	$-0.643037\pi$
$97$	−8.55655	−0.868786	−0.434393	+	0.900723i	$0.643037\pi$
$98$	−2.72620	−0.275387
$99$	−20.8940	−2.09993
$100$	13.3520	1.33520
$101$	−0.356227	−0.0354459	−0.0177229	−	0.999843i	$-0.505642\pi$
$101$	−0.356227	−0.0354459	−0.0177229	+	0.999843i	$0.505642\pi$
$102$	−10.3862	−1.02838
$103$	7.99950	0.788214	0.394107	−	0.919065i	$-0.371054\pi$
$103$	7.99950	0.788214	0.394107	+	0.919065i	$0.371054\pi$
$104$	−7.04120	−0.690447
$105$	24.2412	2.36570
$106$	7.08196	0.687861
$107$	−5.24711	−0.507257	−0.253629	−	0.967302i	$-0.581624\pi$
$107$	−5.24711	−0.507257	−0.253629	+	0.967302i	$0.581624\pi$
$108$	−4.08451	−0.393032
$109$	13.6531	1.30773	0.653863	−	0.756613i	$-0.273147\pi$
$109$	13.6531	1.30773	0.653863	+	0.756613i	$0.273147\pi$
$110$	19.9252	1.89979
$111$	−6.68139	−0.634169
$112$	2.06732	0.195343
$113$	7.99975	0.752553	0.376277	−	0.926507i	$-0.377204\pi$
$113$	7.99975	0.752553	0.376277	+	0.926507i	$0.377204\pi$
$114$	4.76381	0.446172
$115$	2.62502	0.244785
$116$	7.92947	0.736233
$117$	−31.6307	−2.92426
$118$	7.17783	0.660773
$119$	7.84435	0.719091
$120$	11.7259	1.07043
$121$	10.6332	0.966658
$122$	−10.7917	−0.977035
$123$	23.2265	2.09426
$124$	1.07513	0.0965492
$125$	−35.7796	−3.20022
$126$	9.28686	0.827339
$127$	20.9325	1.85746	0.928729	−	0.370760i	$-0.120903\pi$
$127$	20.9325	1.85746	0.928729	+	0.370760i	$0.120903\pi$
$128$	1.00000	0.0883883
$129$	−24.5566	−2.16209
$130$	30.1640	2.64556
$131$	7.61448	0.665280	0.332640	−	0.943054i	$-0.392061\pi$
$131$	7.61448	0.665280	0.332640	+	0.943054i	$0.392061\pi$
$132$	12.7311	1.10810
$133$	−3.59796	−0.311983
$134$	−10.0032	−0.864148
$135$	17.4978	1.50597
$136$	3.79446	0.325372
$137$	17.2028	1.46973	0.734866	−	0.678212i	$-0.237245\pi$
$137$	17.2028	1.46973	0.734866	+	0.678212i	$0.237245\pi$
$138$	1.67725	0.142777
$139$	−0.705096	−0.0598055	−0.0299027	−	0.999553i	$-0.509520\pi$
$139$	−0.705096	−0.0598055	−0.0299027	+	0.999553i	$0.509520\pi$
$140$	−8.85624	−0.748489
$141$	−5.46375	−0.460130
$142$	−9.46462	−0.794253
$143$	32.7497	2.73867
$144$	4.49223	0.374352
$145$	−33.9693	−2.82100
$146$	16.3706	1.35484
$147$	7.46212	0.615465
$148$	2.44096	0.200646
$149$	−10.5970	−0.868138	−0.434069	−	0.900880i	$-0.642923\pi$
$149$	−10.5970	−0.868138	−0.434069	+	0.900880i	$0.642923\pi$
$150$	−36.5471	−2.98406
$151$	−12.8896	−1.04894	−0.524470	−	0.851429i	$-0.675737\pi$
$151$	−12.8896	−1.04894	−0.524470	+	0.851429i	$0.675737\pi$
$152$	−1.74040	−0.141165
$153$	17.0456	1.37805
$154$	−9.61542	−0.774832
$155$	−4.60576	−0.369944
$156$	19.2731	1.54309
$157$	1.86205	0.148608	0.0743040	−	0.997236i	$-0.476326\pi$
$157$	1.86205	0.148608	0.0743040	+	0.997236i	$0.476326\pi$
$158$	8.98411	0.714737
$159$	−19.3847	−1.53731
$160$	−4.28393	−0.338674
$161$	−1.26677	−0.0998356
$162$	−2.29658	−0.180437
$163$	4.99759	0.391441	0.195721	−	0.980660i	$-0.437295\pi$
$163$	4.99759	0.391441	0.195721	+	0.980660i	$0.437295\pi$
$164$	−8.48552	−0.662608
$165$	−54.5392	−4.24587
$166$	8.10098	0.628758
$167$	−4.50548	−0.348645	−0.174322	−	0.984689i	$-0.555774\pi$
$167$	−4.50548	−0.348645	−0.174322	+	0.984689i	$0.555774\pi$
$168$	−5.65865	−0.436574
$169$	36.5785	2.81373
$170$	−16.2552	−1.24672
$171$	−7.81828	−0.597879
$172$	8.97146	0.684068
$173$	2.21520	0.168419	0.0842094	−	0.996448i	$-0.473164\pi$
$173$	2.21520	0.168419	0.0842094	+	0.996448i	$0.473164\pi$
$174$	−21.7045	−1.64541
$175$	27.6029	2.08659
$176$	−4.65115	−0.350594
$177$	−19.6471	−1.47677
$178$	−12.0925	−0.906370
$179$	−5.07565	−0.379372	−0.189686	−	0.981845i	$-0.560747\pi$
$179$	−5.07565	−0.379372	−0.189686	+	0.981845i	$0.560747\pi$
$180$	−19.2444	−1.43439
$181$	5.48808	0.407926	0.203963	−	0.978979i	$-0.434618\pi$
$181$	5.48808	0.407926	0.203963	+	0.978979i	$0.434618\pi$
$182$	−14.5564	−1.07899
$183$	29.5390	2.18358
$184$	−0.612761	−0.0451733
$185$	−10.4569	−0.768808
$186$	−2.94283	−0.215779
$187$	−17.6486	−1.29059
$188$	1.99611	0.145581
$189$	−8.44398	−0.614209
$190$	7.45576	0.540897
$191$	−13.8102	−0.999269	−0.499634	−	0.866236i	$-0.666532\pi$
$191$	−13.8102	−0.999269	−0.499634	+	0.866236i	$0.666532\pi$
$192$	−2.73719	−0.197540
$193$	−5.47424	−0.394045	−0.197022	−	0.980399i	$-0.563127\pi$
$193$	−5.47424	−0.394045	−0.197022	+	0.980399i	$0.563127\pi$
$194$	−8.55655	−0.614324
$195$	−82.5647	−5.91258
$196$	−2.72620	−0.194728
$197$	−15.8978	−1.13267	−0.566335	−	0.824175i	$-0.691639\pi$
$197$	−15.8978	−1.13267	−0.566335	+	0.824175i	$0.691639\pi$
$198$	−20.8940	−1.48487
$199$	−3.90842	−0.277060	−0.138530	−	0.990358i	$-0.544238\pi$
$199$	−3.90842	−0.277060	−0.138530	+	0.990358i	$0.544238\pi$
$200$	13.3520	0.944132
$201$	27.3808	1.93129
$202$	−0.356227	−0.0250640
$203$	16.3927	1.15055
$204$	−10.3862	−0.727177
$205$	36.3513	2.53889
$206$	7.99950	0.557351
$207$	−2.75266	−0.191323
$208$	−7.04120	−0.488220
$209$	8.09488	0.559934
$210$	24.2412	1.67281
$211$	−27.9217	−1.92221	−0.961104	−	0.276188i	$-0.910929\pi$
$211$	−27.9217	−1.92221	−0.961104	+	0.276188i	$0.910929\pi$
$212$	7.08196	0.486391
$213$	25.9065	1.77508
$214$	−5.24711	−0.358685
$215$	−38.4331	−2.62112
$216$	−4.08451	−0.277916
$217$	2.22263	0.150882
$218$	13.6531	0.924702
$219$	−44.8095	−3.02795
$220$	19.9252	1.34336
$221$	−26.7176	−1.79722
$222$	−6.68139	−0.448425
$223$	−20.1877	−1.35187	−0.675935	−	0.736961i	$-0.736260\pi$
$223$	−20.1877	−1.35187	−0.675935	+	0.736961i	$0.736260\pi$
$224$	2.06732	0.138129
$225$	59.9804	3.99869
$226$	7.99975	0.532135
$227$	−24.2855	−1.61189	−0.805944	−	0.591991i	$-0.798342\pi$
$227$	−24.2855	−1.61189	−0.805944	+	0.591991i	$0.798342\pi$
$228$	4.76381	0.315491
$229$	27.1669	1.79524	0.897619	−	0.440772i	$-0.145295\pi$
$229$	27.1669	1.79524	0.897619	+	0.440772i	$0.145295\pi$
$230$	2.62502	0.173089
$231$	26.3193	1.73168
$232$	7.92947	0.520595
$233$	−25.7002	−1.68367	−0.841837	−	0.539731i	$-0.818526\pi$
$233$	−25.7002	−1.68367	−0.841837	+	0.539731i	$0.818526\pi$
$234$	−31.6307	−2.06776
$235$	−8.55120	−0.557819
$236$	7.17783	0.467237
$237$	−24.5912	−1.59737
$238$	7.84435	0.508474
$239$	−6.99025	−0.452161	−0.226081	−	0.974109i	$-0.572591\pi$
$239$	−6.99025	−0.452161	−0.226081	+	0.974109i	$0.572591\pi$
$240$	11.7259	0.756906
$241$	−1.08519	−0.0699031	−0.0349516	−	0.999389i	$-0.511128\pi$
$241$	−1.08519	−0.0699031	−0.0349516	+	0.999389i	$0.511128\pi$
$242$	10.6332	0.683530
$243$	18.5397	1.18932
$244$	−10.7917	−0.690868
$245$	11.6788	0.746133
$246$	23.2265	1.48087
$247$	12.2545	0.779736
$248$	1.07513	0.0682706
$249$	−22.1740	−1.40522
$250$	−35.7796	−2.26290
$251$	0.470311	0.0296857	0.0148429	−	0.999890i	$-0.495275\pi$
$251$	0.470311	0.0296857	0.0148429	+	0.999890i	$0.495275\pi$
$252$	9.28686	0.585017
$253$	2.85005	0.179181
$254$	20.9325	1.31342
$255$	44.4936	2.78630
$256$	1.00000	0.0625000
$257$	−13.7274	−0.856289	−0.428144	−	0.903710i	$-0.640833\pi$
$257$	−13.7274	−0.856289	−0.428144	+	0.903710i	$0.640833\pi$
$258$	−24.5566	−1.52883
$259$	5.04625	0.313559
$260$	30.1640	1.87069
$261$	35.6210	2.20488
$262$	7.61448	0.470424
$263$	−5.75753	−0.355024	−0.177512	−	0.984119i	$-0.556805\pi$
$263$	−5.75753	−0.355024	−0.177512	+	0.984119i	$0.556805\pi$
$264$	12.7311	0.783546
$265$	−30.3386	−1.86369
$266$	−3.59796	−0.220605
$267$	33.0995	2.02565
$268$	−10.0032	−0.611045
$269$	10.0363	0.611923	0.305962	−	0.952044i	$-0.401022\pi$
$269$	10.0363	0.611923	0.305962	+	0.952044i	$0.401022\pi$
$270$	17.4978	1.06488
$271$	12.2574	0.744583	0.372292	−	0.928116i	$-0.378572\pi$
$271$	12.2574	0.744583	0.372292	+	0.928116i	$0.378572\pi$
$272$	3.79446	0.230073
$273$	39.8437	2.41145
$274$	17.2028	1.03926
$275$	−62.1024	−3.74492
$276$	1.67725	0.100958
$277$	29.6381	1.78078	0.890389	−	0.455200i	$-0.150432\pi$
$277$	29.6381	1.78078	0.890389	+	0.455200i	$0.150432\pi$
$278$	−0.705096	−0.0422888
$279$	4.82971	0.289147
$280$	−8.85624	−0.529262
$281$	13.4393	0.801719	0.400860	−	0.916139i	$-0.368712\pi$
$281$	13.4393	0.801719	0.400860	+	0.916139i	$0.368712\pi$
$282$	−5.46375	−0.325361
$283$	−14.2486	−0.846994	−0.423497	−	0.905897i	$-0.639198\pi$
$283$	−14.2486	−0.846994	−0.423497	+	0.905897i	$0.639198\pi$
$284$	−9.46462	−0.561622
$285$	−20.4078	−1.20886
$286$	32.7497	1.93653
$287$	−17.5423	−1.03549
$288$	4.49223	0.264707
$289$	−2.60209	−0.153064
$290$	−33.9693	−1.99475
$291$	23.4209	1.37296
$292$	16.3706	0.958017
$293$	−22.8332	−1.33393	−0.666966	−	0.745088i	$-0.732407\pi$
$293$	−22.8332	−1.33393	−0.666966	+	0.745088i	$0.732407\pi$
$294$	7.46212	0.435200
$295$	−30.7493	−1.79030
$296$	2.44096	0.141878
$297$	18.9977	1.10236
$298$	−10.5970	−0.613866
$299$	4.31457	0.249518
$300$	−36.5471	−2.11005
$301$	18.5469	1.06902
$302$	−12.8896	−0.741713
$303$	0.975061	0.0560158
$304$	−1.74040	−0.0998189
$305$	46.2309	2.64717
$306$	17.0456	0.974430
$307$	19.7499	1.12718	0.563592	−	0.826053i	$-0.309419\pi$
$307$	19.7499	1.12718	0.563592	+	0.826053i	$0.309419\pi$
$308$	−9.61542	−0.547889
$309$	−21.8962	−1.24563
$310$	−4.60576	−0.261590
$311$	9.57097	0.542720	0.271360	−	0.962478i	$-0.412527\pi$
$311$	9.57097	0.542720	0.271360	+	0.962478i	$0.412527\pi$
$312$	19.2731	1.09113
$313$	−11.9806	−0.677182	−0.338591	−	0.940934i	$-0.609950\pi$
$313$	−11.9806	−0.677182	−0.338591	+	0.940934i	$0.609950\pi$
$314$	1.86205	0.105082
$315$	−39.7842	−2.24159
$316$	8.98411	0.505396
$317$	−20.3207	−1.14132	−0.570662	−	0.821185i	$-0.693314\pi$
$317$	−20.3207	−1.14132	−0.570662	+	0.821185i	$0.693314\pi$
$318$	−19.3847	−1.08704
$319$	−36.8812	−2.06495
$320$	−4.28393	−0.239479
$321$	14.3624	0.801629
$322$	−1.26677	−0.0705944
$323$	−6.60388	−0.367450
$324$	−2.29658	−0.127588
$325$	−94.0145	−5.21498
$326$	4.99759	0.276791
$327$	−37.3711	−2.06662
$328$	−8.48552	−0.468534
$329$	4.12660	0.227507
$330$	−54.5392	−3.00228
$331$	2.75256	0.151294	0.0756471	−	0.997135i	$-0.475898\pi$
$331$	2.75256	0.151294	0.0756471	+	0.997135i	$0.475898\pi$
$332$	8.10098	0.444599
$333$	10.9654	0.600898
$334$	−4.50548	−0.246529
$335$	42.8532	2.34132
$336$	−5.65865	−0.308705
$337$	13.5761	0.739537	0.369768	−	0.929124i	$-0.379437\pi$
$337$	13.5761	0.739537	0.369768	+	0.929124i	$0.379437\pi$
$338$	36.5785	1.98961
$339$	−21.8969	−1.18927
$340$	−16.2552	−0.881561
$341$	−5.00058	−0.270797
$342$	−7.81828	−0.422764
$343$	−20.1071	−1.08568
$344$	8.97146	0.483709
$345$	−7.18520	−0.386838
$346$	2.21520	0.119090
$347$	−24.8795	−1.33560	−0.667800	−	0.744341i	$-0.732764\pi$
$347$	−24.8795	−1.33560	−0.667800	+	0.744341i	$0.732764\pi$
$348$	−21.7045	−1.16348
$349$	−8.01230	−0.428889	−0.214444	−	0.976736i	$-0.568794\pi$
$349$	−8.01230	−0.428889	−0.214444	+	0.976736i	$0.568794\pi$
$350$	27.6029	1.47544
$351$	28.7599	1.53509
$352$	−4.65115	−0.247907
$353$	6.37884	0.339511	0.169756	−	0.985486i	$-0.445702\pi$
$353$	6.37884	0.339511	0.169756	+	0.985486i	$0.445702\pi$
$354$	−19.6471	−1.04423
$355$	40.5457	2.15194
$356$	−12.0925	−0.640901
$357$	−21.4715	−1.13639
$358$	−5.07565	−0.268257
$359$	26.0215	1.37336	0.686680	−	0.726960i	$-0.259067\pi$
$359$	26.0215	1.37336	0.686680	+	0.726960i	$0.259067\pi$
$360$	−19.2444	−1.01427
$361$	−15.9710	−0.840579
$362$	5.48808	0.288447
$363$	−29.1052	−1.52763
$364$	−14.5564	−0.762963
$365$	−70.1305	−3.67080
$366$	29.5390	1.54403
$367$	−31.1860	−1.62790	−0.813949	−	0.580937i	$-0.802686\pi$
$367$	−31.1860	−1.62790	−0.813949	+	0.580937i	$0.802686\pi$
$368$	−0.612761	−0.0319424
$369$	−38.1189	−1.98439
$370$	−10.4569	−0.543629
$371$	14.6407	0.760106
$372$	−2.94283	−0.152579
$373$	−15.1527	−0.784576	−0.392288	−	0.919842i	$-0.628316\pi$
$373$	−15.1527	−0.784576	−0.392288	+	0.919842i	$0.628316\pi$
$374$	−17.6486	−0.912588
$375$	97.9356	5.05737
$376$	1.99611	0.102942
$377$	−55.8330	−2.87555
$378$	−8.44398	−0.434312
$379$	28.0140	1.43898	0.719492	−	0.694501i	$-0.244375\pi$
$379$	28.0140	1.43898	0.719492	+	0.694501i	$0.244375\pi$
$380$	7.45576	0.382472
$381$	−57.2962	−2.93538
$382$	−13.8102	−0.706590
$383$	−30.4461	−1.55572	−0.777860	−	0.628437i	$-0.783695\pi$
$383$	−30.4461	−1.55572	−0.777860	+	0.628437i	$0.783695\pi$
$384$	−2.73719	−0.139682
$385$	41.1918	2.09933
$386$	−5.47424	−0.278632
$387$	40.3018	2.04866
$388$	−8.55655	−0.434393
$389$	−12.7784	−0.647892	−0.323946	−	0.946076i	$-0.605010\pi$
$389$	−12.7784	−0.647892	−0.323946	+	0.946076i	$0.605010\pi$
$390$	−82.5647	−4.18083
$391$	−2.32510	−0.117585
$392$	−2.72620	−0.137694
$393$	−20.8423	−1.05135
$394$	−15.8978	−0.800918
$395$	−38.4873	−1.93650
$396$	−20.8940	−1.04996
$397$	19.7669	0.992072	0.496036	−	0.868302i	$-0.334788\pi$
$397$	19.7669	0.992072	0.496036	+	0.868302i	$0.334788\pi$
$398$	−3.90842	−0.195911
$399$	9.84832	0.493033
$400$	13.3520	0.667602
$401$	−1.35492	−0.0676617	−0.0338308	−	0.999428i	$-0.510771\pi$
$401$	−1.35492	−0.0676617	−0.0338308	+	0.999428i	$0.510771\pi$
$402$	27.3808	1.36563
$403$	−7.57018	−0.377098
$404$	−0.356227	−0.0177229
$405$	9.83840	0.488874
$406$	16.3927	0.813558
$407$	−11.3533	−0.562762
$408$	−10.3862	−0.514192
$409$	15.1138	0.747330	0.373665	−	0.927564i	$-0.378101\pi$
$409$	15.1138	0.747330	0.373665	+	0.927564i	$0.378101\pi$
$410$	36.3513	1.79527
$411$	−47.0873	−2.32265
$412$	7.99950	0.394107
$413$	14.8389	0.730173
$414$	−2.75266	−0.135286
$415$	−34.7040	−1.70355
$416$	−7.04120	−0.345223
$417$	1.92998	0.0945117
$418$	8.09488	0.395933
$419$	−0.572505	−0.0279687	−0.0139843	−	0.999902i	$-0.504452\pi$
$419$	−0.572505	−0.0279687	−0.0139843	+	0.999902i	$0.504452\pi$
$420$	24.2412	1.18285
$421$	−17.7182	−0.863532	−0.431766	−	0.901986i	$-0.642109\pi$
$421$	−17.7182	−0.863532	−0.431766	+	0.901986i	$0.642109\pi$
$422$	−27.9217	−1.35921
$423$	8.96699	0.435990
$424$	7.08196	0.343931
$425$	50.6638	2.45755
$426$	25.9065	1.25517
$427$	−22.3099	−1.07965
$428$	−5.24711	−0.253629
$429$	−89.6423	−4.32797
$430$	−38.4331	−1.85341
$431$	10.7600	0.518291	0.259146	−	0.965838i	$-0.416559\pi$
$431$	10.7600	0.518291	0.259146	+	0.965838i	$0.416559\pi$
$432$	−4.08451	−0.196516
$433$	−28.4859	−1.36895	−0.684474	−	0.729038i	$-0.739968\pi$
$433$	−28.4859	−1.36895	−0.684474	+	0.729038i	$0.739968\pi$
$434$	2.22263	0.106690
$435$	92.9805	4.45807
$436$	13.6531	0.653863
$437$	1.06645	0.0510152
$438$	−44.8095	−2.14108
$439$	7.51679	0.358757	0.179378	−	0.983780i	$-0.442591\pi$
$439$	7.51679	0.358757	0.179378	+	0.983780i	$0.442591\pi$
$440$	19.9252	0.949897
$441$	−12.2467	−0.583175
$442$	−26.7176	−1.27082
$443$	−12.5262	−0.595138	−0.297569	−	0.954700i	$-0.596176\pi$
$443$	−12.5262	−0.595138	−0.297569	+	0.954700i	$0.596176\pi$
$444$	−6.68139	−0.317085
$445$	51.8034	2.45571
$446$	−20.1877	−0.955916
$447$	29.0060	1.37194
$448$	2.06732	0.0976716
$449$	−0.194462	−0.00917723	−0.00458862	−	0.999989i	$-0.501461\pi$
$449$	−0.194462	−0.00917723	−0.00458862	+	0.999989i	$0.501461\pi$
$450$	59.9804	2.82750
$451$	39.4675	1.85845
$452$	7.99975	0.376277
$453$	35.2813	1.65766
$454$	−24.2855	−1.13978
$455$	62.3586	2.92342
$456$	4.76381	0.223086
$457$	28.1871	1.31854	0.659268	−	0.751908i	$-0.270866\pi$
$457$	28.1871	1.31854	0.659268	+	0.751908i	$0.270866\pi$
$458$	27.1669	1.26942
$459$	−15.4985	−0.723408
$460$	2.62502	0.122392
$461$	−4.75490	−0.221458	−0.110729	−	0.993851i	$-0.535319\pi$
$461$	−4.75490	−0.221458	−0.110729	+	0.993851i	$0.535319\pi$
$462$	26.3193	1.22448
$463$	−26.9723	−1.25351	−0.626755	−	0.779216i	$-0.715617\pi$
$463$	−26.9723	−1.25351	−0.626755	+	0.779216i	$0.715617\pi$
$464$	7.92947	0.368117
$465$	12.6069	0.584629
$466$	−25.7002	−1.19054
$467$	−0.677155	−0.0313350	−0.0156675	−	0.999877i	$-0.504987\pi$
$467$	−0.677155	−0.0313350	−0.0156675	+	0.999877i	$0.504987\pi$
$468$	−31.6307	−1.46213
$469$	−20.6799	−0.954908
$470$	−8.55120	−0.394438
$471$	−5.09680	−0.234848
$472$	7.17783	0.330387
$473$	−41.7277	−1.91864
$474$	−24.5912	−1.12951
$475$	−23.2379	−1.06623
$476$	7.84435	0.359545
$477$	31.8138	1.45665
$478$	−6.99025	−0.319726
$479$	34.6760	1.58439	0.792194	−	0.610270i	$-0.208939\pi$
$479$	34.6760	1.58439	0.792194	+	0.610270i	$0.208939\pi$
$480$	11.7259	0.535213
$481$	−17.1873	−0.783674
$482$	−1.08519	−0.0494290
$483$	3.46740	0.157772
$484$	10.6332	0.483329
$485$	36.6556	1.66445
$486$	18.5397	0.840979
$487$	17.8032	0.806740	0.403370	−	0.915037i	$-0.367839\pi$
$487$	17.8032	0.806740	0.403370	+	0.915037i	$0.367839\pi$
$488$	−10.7917	−0.488517
$489$	−13.6794	−0.618602
$490$	11.6788	0.527596
$491$	4.05148	0.182841	0.0914205	−	0.995812i	$-0.470859\pi$
$491$	4.05148	0.182841	0.0914205	+	0.995812i	$0.470859\pi$
$492$	23.2265	1.04713
$493$	30.0881	1.35510
$494$	12.2545	0.551357
$495$	89.5086	4.02311
$496$	1.07513	0.0482746
$497$	−19.5664	−0.877672
$498$	−22.1740	−0.993639
$499$	−11.5589	−0.517446	−0.258723	−	0.965952i	$-0.583302\pi$
$499$	−11.5589	−0.517446	−0.258723	+	0.965952i	$0.583302\pi$
$500$	−35.7796	−1.60011
$501$	12.3324	0.550970
$502$	0.470311	0.0209910
$503$	−12.7786	−0.569768	−0.284884	−	0.958562i	$-0.591955\pi$
$503$	−12.7786	−0.569768	−0.284884	+	0.958562i	$0.591955\pi$
$504$	9.28686	0.413670
$505$	1.52605	0.0679083
$506$	2.85005	0.126700
$507$	−100.123	−4.44660
$508$	20.9325	0.928729
$509$	9.43871	0.418363	0.209182	−	0.977877i	$-0.432920\pi$
$509$	9.43871	0.418363	0.209182	+	0.977877i	$0.432920\pi$
$510$	44.4936	1.97021
$511$	33.8432	1.49714
$512$	1.00000	0.0441942
$513$	7.10869	0.313856
$514$	−13.7274	−0.605488
$515$	−34.2693	−1.51008
$516$	−24.5566	−1.08105
$517$	−9.28423	−0.408320
$518$	5.04625	0.221719
$519$	−6.06344	−0.266155
$520$	30.1640	1.32278
$521$	−6.72953	−0.294826	−0.147413	−	0.989075i	$-0.547095\pi$
$521$	−6.72953	−0.294826	−0.147413	+	0.989075i	$0.547095\pi$
$522$	35.6210	1.55909
$523$	41.7310	1.82477	0.912384	−	0.409336i	$-0.134240\pi$
$523$	41.7310	1.82477	0.912384	+	0.409336i	$0.134240\pi$
$524$	7.61448	0.332640
$525$	−75.5545	−3.29747
$526$	−5.75753	−0.251040
$527$	4.07952	0.177707
$528$	12.7311	0.554050
$529$	−22.6245	−0.983675
$530$	−30.3386	−1.31783
$531$	32.2445	1.39929
$532$	−3.59796	−0.155992
$533$	59.7483	2.58798
$534$	33.0995	1.43235
$535$	22.4783	0.971820
$536$	−10.0032	−0.432074
$537$	13.8930	0.599529
$538$	10.0363	0.432695
$539$	12.6800	0.546164
$540$	17.4978	0.752983
$541$	−19.2831	−0.829047	−0.414523	−	0.910039i	$-0.636052\pi$
$541$	−19.2831	−0.829047	−0.414523	+	0.910039i	$0.636052\pi$
$542$	12.2574	0.526500
$543$	−15.0219	−0.644653
$544$	3.79446	0.162686
$545$	−58.4887	−2.50538
$546$	39.8437	1.70515
$547$	−12.8816	−0.550778	−0.275389	−	0.961333i	$-0.588807\pi$
$547$	−12.8816	−0.550778	−0.275389	+	0.961333i	$0.588807\pi$
$548$	17.2028	0.734866
$549$	−48.4788	−2.06902
$550$	−62.1024	−2.64806
$551$	−13.8005	−0.587920
$552$	1.67725	0.0713883
$553$	18.5730	0.789805
$554$	29.6381	1.25920
$555$	28.6226	1.21496
$556$	−0.705096	−0.0299027
$557$	−15.9809	−0.677131	−0.338566	−	0.940943i	$-0.609942\pi$
$557$	−15.9809	−0.677131	−0.338566	+	0.940943i	$0.609942\pi$
$558$	4.82971	0.204458
$559$	−63.1699	−2.67180
$560$	−8.85624	−0.374245
$561$	48.3077	2.03955
$562$	13.4393	0.566901
$563$	24.3742	1.02725	0.513625	−	0.858015i	$-0.328302\pi$
$563$	24.3742	1.02725	0.513625	+	0.858015i	$0.328302\pi$
$564$	−5.46375	−0.230065
$565$	−34.2704	−1.44176
$566$	−14.2486	−0.598915
$567$	−4.74777	−0.199388
$568$	−9.46462	−0.397127
$569$	29.4925	1.23639	0.618195	−	0.786025i	$-0.287864\pi$
$569$	29.4925	1.23639	0.618195	+	0.786025i	$0.287864\pi$
$570$	−20.4078	−0.854790
$571$	−15.4754	−0.647626	−0.323813	−	0.946121i	$-0.604965\pi$
$571$	−15.4754	−0.647626	−0.323813	+	0.946121i	$0.604965\pi$
$572$	32.7497	1.36933
$573$	37.8011	1.57916
$574$	−17.5423	−0.732200
$575$	−8.18161	−0.341197
$576$	4.49223	0.187176
$577$	−20.4856	−0.852827	−0.426413	−	0.904528i	$-0.640223\pi$
$577$	−20.4856	−0.852827	−0.426413	+	0.904528i	$0.640223\pi$
$578$	−2.60209	−0.108233
$579$	14.9841	0.622716
$580$	−33.9693	−1.41050
$581$	16.7473	0.694796
$582$	23.4209	0.970829
$583$	−32.9393	−1.36421
$584$	16.3706	0.677420
$585$	135.504	5.60238
$586$	−22.8332	−0.943232
$587$	19.7002	0.813113	0.406556	−	0.913626i	$-0.366729\pi$
$587$	19.7002	0.813113	0.406556	+	0.913626i	$0.366729\pi$
$588$	7.46212	0.307733
$589$	−1.87115	−0.0770994
$590$	−30.7493	−1.26593
$591$	43.5153	1.78998
$592$	2.44096	0.100323
$593$	−40.3808	−1.65824	−0.829121	−	0.559069i	$-0.811159\pi$
$593$	−40.3808	−1.65824	−0.829121	+	0.559069i	$0.811159\pi$
$594$	18.9977	0.779485
$595$	−33.6046	−1.37766
$596$	−10.5970	−0.434069
$597$	10.6981	0.437844
$598$	4.31457	0.176436
$599$	32.1171	1.31227	0.656135	−	0.754644i	$-0.272190\pi$
$599$	32.1171	1.31227	0.656135	+	0.754644i	$0.272190\pi$
$600$	−36.5471	−1.49203
$601$	31.2226	1.27360	0.636799	−	0.771030i	$-0.280258\pi$
$601$	31.2226	1.27360	0.636799	+	0.771030i	$0.280258\pi$
$602$	18.5469	0.755914
$603$	−44.9368	−1.82997
$604$	−12.8896	−0.524470
$605$	−45.5520	−1.85195
$606$	0.975061	0.0396092
$607$	−9.88634	−0.401274	−0.200637	−	0.979666i	$-0.564301\pi$
$607$	−9.88634	−0.401274	−0.200637	+	0.979666i	$0.564301\pi$
$608$	−1.74040	−0.0705826
$609$	−44.8701	−1.81823
$610$	46.2309	1.87183
$611$	−14.0550	−0.568606
$612$	17.0456	0.689026
$613$	−2.67726	−0.108134	−0.0540668	−	0.998537i	$-0.517218\pi$
$613$	−2.67726	−0.108134	−0.0540668	+	0.998537i	$0.517218\pi$
$614$	19.7499	0.797040
$615$	−99.5007	−4.01225
$616$	−9.61542	−0.387416
$617$	−34.1745	−1.37581	−0.687907	−	0.725799i	$-0.741470\pi$
$617$	−34.1745	−1.37581	−0.687907	+	0.725799i	$0.741470\pi$
$618$	−21.8962	−0.880793
$619$	14.2245	0.571729	0.285865	−	0.958270i	$-0.407719\pi$
$619$	14.2245	0.571729	0.285865	+	0.958270i	$0.407719\pi$
$620$	−4.60576	−0.184972
$621$	2.50283	0.100435
$622$	9.57097	0.383761
$623$	−24.9990	−1.00156
$624$	19.2731	0.771543
$625$	86.5169	3.46067
$626$	−11.9806	−0.478840
$627$	−22.1572	−0.884875
$628$	1.86205	0.0743040
$629$	9.26213	0.369305
$630$	−39.7842	−1.58504
$631$	−21.0628	−0.838499	−0.419249	−	0.907871i	$-0.637707\pi$
$631$	−21.0628	−0.838499	−0.419249	+	0.907871i	$0.637707\pi$
$632$	8.98411	0.357369
$633$	76.4270	3.03770
$634$	−20.3207	−0.807039
$635$	−89.6733	−3.55858
$636$	−19.3847	−0.768653
$637$	19.1957	0.760561
$638$	−36.8812	−1.46014
$639$	−42.5172	−1.68195
$640$	−4.28393	−0.169337
$641$	−1.38934	−0.0548756	−0.0274378	−	0.999624i	$-0.508735\pi$
$641$	−1.38934	−0.0548756	−0.0274378	+	0.999624i	$0.508735\pi$
$642$	14.3624	0.566837
$643$	−19.7197	−0.777668	−0.388834	−	0.921308i	$-0.627122\pi$
$643$	−19.7197	−0.777668	−0.388834	+	0.921308i	$0.627122\pi$
$644$	−1.26677	−0.0499178
$645$	105.199	4.14220
$646$	−6.60388	−0.259826
$647$	1.27750	0.0502236	0.0251118	−	0.999685i	$-0.492006\pi$
$647$	1.27750	0.0502236	0.0251118	+	0.999685i	$0.492006\pi$
$648$	−2.29658	−0.0902183
$649$	−33.3852	−1.31048
$650$	−94.0145	−3.68755
$651$	−6.08376	−0.238441
$652$	4.99759	0.195721
$653$	−44.5950	−1.74514	−0.872569	−	0.488491i	$-0.837548\pi$
$653$	−44.5950	−1.74514	−0.872569	+	0.488491i	$0.837548\pi$
$654$	−37.3711	−1.46132
$655$	−32.6199	−1.27456
$656$	−8.48552	−0.331304
$657$	73.5405	2.86909
$658$	4.12660	0.160872
$659$	28.5111	1.11063	0.555317	−	0.831638i	$-0.312597\pi$
$659$	28.5111	1.11063	0.555317	+	0.831638i	$0.312597\pi$
$660$	−54.5392	−2.12293
$661$	−24.8512	−0.966599	−0.483299	−	0.875455i	$-0.660562\pi$
$661$	−24.8512	−0.966599	−0.483299	+	0.875455i	$0.660562\pi$
$662$	2.75256	0.106981
$663$	73.1311	2.84018
$664$	8.10098	0.314379
$665$	15.4134	0.597707
$666$	10.9654	0.424899
$667$	−4.85887	−0.188136
$668$	−4.50548	−0.174322
$669$	55.2577	2.13639
$670$	42.8532	1.65556
$671$	50.1939	1.93771
$672$	−5.65865	−0.218287
$673$	−24.0020	−0.925210	−0.462605	−	0.886565i	$-0.653085\pi$
$673$	−24.0020	−0.925210	−0.462605	+	0.886565i	$0.653085\pi$
$674$	13.5761	0.522932
$675$	−54.5366	−2.09911
$676$	36.5785	1.40687
$677$	−9.69296	−0.372531	−0.186265	−	0.982499i	$-0.559638\pi$
$677$	−9.69296	−0.372531	−0.186265	+	0.982499i	$0.559638\pi$
$678$	−21.8969	−0.840944
$679$	−17.6891	−0.678846
$680$	−16.2552	−0.623358
$681$	66.4742	2.54730
$682$	−5.00058	−0.191482
$683$	−16.7310	−0.640193	−0.320097	−	0.947385i	$-0.603715\pi$
$683$	−16.7310	−0.640193	−0.320097	+	0.947385i	$0.603715\pi$
$684$	−7.81828	−0.298939
$685$	−73.6955	−2.81576
$686$	−20.1071	−0.767694
$687$	−74.3610	−2.83705
$688$	8.97146	0.342034
$689$	−49.8655	−1.89973
$690$	−7.18520	−0.273536
$691$	0.679125	0.0258351	0.0129176	−	0.999917i	$-0.495888\pi$
$691$	0.679125	0.0258351	0.0129176	+	0.999917i	$0.495888\pi$
$692$	2.21520	0.0842094
$693$	−43.1946	−1.64083
$694$	−24.8795	−0.944411
$695$	3.02058	0.114577
$696$	−21.7045	−0.822707
$697$	−32.1979	−1.21958
$698$	−8.01230	−0.303270
$699$	70.3464	2.66074
$700$	27.6029	1.04329
$701$	−17.4003	−0.657202	−0.328601	−	0.944469i	$-0.606577\pi$
$701$	−17.4003	−0.657202	−0.328601	+	0.944469i	$0.606577\pi$
$702$	28.7599	1.08547
$703$	−4.24826	−0.160226
$704$	−4.65115	−0.175297
$705$	23.4063	0.881532
$706$	6.37884	0.240071
$707$	−0.736434	−0.0276964
$708$	−19.6471	−0.738384
$709$	−51.7250	−1.94257	−0.971287	−	0.237911i	$-0.923537\pi$
$709$	−51.7250	−1.94257	−0.971287	+	0.237911i	$0.923537\pi$
$710$	40.5457	1.52165
$711$	40.3586	1.51357
$712$	−12.0925	−0.453185
$713$	−0.658796	−0.0246721
$714$	−21.4715	−0.803551
$715$	−140.297	−5.24683
$716$	−5.07565	−0.189686
$717$	19.1337	0.714559
$718$	26.0215	0.971112
$719$	−24.0634	−0.897412	−0.448706	−	0.893679i	$-0.648115\pi$
$719$	−24.0634	−0.897412	−0.448706	+	0.893679i	$0.648115\pi$
$720$	−19.2444	−0.717196
$721$	16.5375	0.615889
$722$	−15.9710	−0.594379
$723$	2.97037	0.110469
$724$	5.48808	0.203963
$725$	105.875	3.93209
$726$	−29.1052	−1.08020
$727$	23.8542	0.884704	0.442352	−	0.896841i	$-0.354144\pi$
$727$	23.8542	0.884704	0.442352	+	0.896841i	$0.354144\pi$
$728$	−14.5564	−0.539496
$729$	−43.8571	−1.62434
$730$	−70.1305	−2.59565
$731$	34.0418	1.25908
$732$	29.5390	1.09179
$733$	32.5574	1.20254	0.601268	−	0.799048i	$-0.294663\pi$
$733$	32.5574	1.20254	0.601268	+	0.799048i	$0.294663\pi$
$734$	−31.1860	−1.15110
$735$	−31.9672	−1.17913
$736$	−0.612761	−0.0225867
$737$	46.5266	1.71383
$738$	−38.1189	−1.40317
$739$	−3.57997	−0.131691	−0.0658456	−	0.997830i	$-0.520974\pi$
$739$	−3.57997	−0.131691	−0.0658456	+	0.997830i	$0.520974\pi$
$740$	−10.4569	−0.384404
$741$	−33.5430	−1.23223
$742$	14.6407	0.537476
$743$	22.4272	0.822775	0.411388	−	0.911460i	$-0.365044\pi$
$743$	22.4272	0.822775	0.411388	+	0.911460i	$0.365044\pi$
$744$	−2.94283	−0.107889
$745$	45.3967	1.66321
$746$	−15.1527	−0.554779
$747$	36.3915	1.33149
$748$	−17.6486	−0.645297
$749$	−10.8474	−0.396357
$750$	97.9356	3.57610
$751$	25.1674	0.918371	0.459186	−	0.888340i	$-0.348141\pi$
$751$	25.1674	0.918371	0.459186	+	0.888340i	$0.348141\pi$
$752$	1.99611	0.0727907
$753$	−1.28733	−0.0469129
$754$	−55.8330	−2.03332
$755$	55.2181	2.00959
$756$	−8.44398	−0.307105
$757$	−34.9213	−1.26924	−0.634618	−	0.772826i	$-0.718843\pi$
$757$	−34.9213	−1.26924	−0.634618	+	0.772826i	$0.718843\pi$
$758$	28.0140	1.01752
$759$	−7.80113	−0.283163
$760$	7.45576	0.270449
$761$	−27.0027	−0.978847	−0.489423	−	0.872046i	$-0.662793\pi$
$761$	−27.0027	−0.978847	−0.489423	+	0.872046i	$0.662793\pi$
$762$	−57.2962	−2.07562
$763$	28.2252	1.02182
$764$	−13.8102	−0.499634
$765$	−73.0220	−2.64012
$766$	−30.4461	−1.10006
$767$	−50.5406	−1.82491
$768$	−2.73719	−0.0987699
$769$	37.4667	1.35108	0.675542	−	0.737321i	$-0.263910\pi$
$769$	37.4667	1.35108	0.675542	+	0.737321i	$0.263910\pi$
$770$	41.1918	1.48445
$771$	37.5744	1.35321
$772$	−5.47424	−0.197022
$773$	−18.1944	−0.654407	−0.327204	−	0.944954i	$-0.606106\pi$
$773$	−18.1944	−0.654407	−0.327204	+	0.944954i	$0.606106\pi$
$774$	40.3018	1.44862
$775$	14.3551	0.515652
$776$	−8.55655	−0.307162
$777$	−13.8126	−0.495523
$778$	−12.7784	−0.458129
$779$	14.7682	0.529126
$780$	−82.5647	−2.95629
$781$	44.0214	1.57521
$782$	−2.32510	−0.0831453
$783$	−32.3880	−1.15745
$784$	−2.72620	−0.0973641
$785$	−7.97690	−0.284708
$786$	−20.8423	−0.743420
$787$	−6.29325	−0.224330	−0.112165	−	0.993690i	$-0.535779\pi$
$787$	−6.29325	−0.224330	−0.112165	+	0.993690i	$0.535779\pi$
$788$	−15.8978	−0.566335
$789$	15.7595	0.561052
$790$	−38.4873	−1.36932
$791$	16.5380	0.588025
$792$	−20.8940	−0.742437
$793$	75.9866	2.69836
$794$	19.7669	0.701501
$795$	83.0427	2.94522
$796$	−3.90842	−0.138530
$797$	41.3364	1.46421	0.732105	−	0.681191i	$-0.238538\pi$
$797$	41.3364	1.46421	0.732105	+	0.681191i	$0.238538\pi$
$798$	9.84832	0.348627
$799$	7.57417	0.267955
$800$	13.3520	0.472066
$801$	−54.3222	−1.91938
$802$	−1.35492	−0.0478440
$803$	−76.1422	−2.68700
$804$	27.3808	0.965646
$805$	5.42676	0.191268
$806$	−7.57018	−0.266648
$807$	−27.4712	−0.967034
$808$	−0.356227	−0.0125320
$809$	−4.05082	−0.142419	−0.0712096	−	0.997461i	$-0.522686\pi$
$809$	−4.05082	−0.142419	−0.0712096	+	0.997461i	$0.522686\pi$
$810$	9.83840	0.345686
$811$	4.21213	0.147908	0.0739540	−	0.997262i	$-0.476438\pi$
$811$	4.21213	0.147908	0.0739540	+	0.997262i	$0.476438\pi$
$812$	16.3927	0.575273
$813$	−33.5508	−1.17668
$814$	−11.3533	−0.397933
$815$	−21.4093	−0.749936
$816$	−10.3862	−0.363588
$817$	−15.6139	−0.546263
$818$	15.1138	0.528442
$819$	−65.3907	−2.28494
$820$	36.3513	1.26944
$821$	21.1500	0.738142	0.369071	−	0.929401i	$-0.379676\pi$
$821$	21.1500	0.738142	0.369071	+	0.929401i	$0.379676\pi$
$822$	−47.0873	−1.64236
$823$	32.6668	1.13869	0.569347	−	0.822097i	$-0.307196\pi$
$823$	32.6668	1.13869	0.569347	+	0.822097i	$0.307196\pi$
$824$	7.99950	0.278676
$825$	169.986	5.91816
$826$	14.8389	0.516310
$827$	−4.48374	−0.155915	−0.0779574	−	0.996957i	$-0.524840\pi$
$827$	−4.48374	−0.155915	−0.0779574	+	0.996957i	$0.524840\pi$
$828$	−2.75266	−0.0956616
$829$	25.9655	0.901819	0.450910	−	0.892570i	$-0.351100\pi$
$829$	25.9655	0.901819	0.450910	+	0.892570i	$0.351100\pi$
$830$	−34.7040	−1.20459
$831$	−81.1251	−2.81420
$832$	−7.04120	−0.244110
$833$	−10.3444	−0.358413
$834$	1.92998	0.0668299
$835$	19.3012	0.667945
$836$	8.09488	0.279967
$837$	−4.39137	−0.151788
$838$	−0.572505	−0.0197769
$839$	24.9040	0.859782	0.429891	−	0.902881i	$-0.358552\pi$
$839$	24.9040	0.859782	0.429891	+	0.902881i	$0.358552\pi$
$840$	24.2412	0.836403
$841$	33.8765	1.16816
$842$	−17.7182	−0.610609
$843$	−36.7859	−1.26697
$844$	−27.9217	−0.961104
$845$	−156.700	−5.39064
$846$	8.96699	0.308291
$847$	21.9823	0.755320
$848$	7.08196	0.243196
$849$	39.0013	1.33852
$850$	50.6638	1.73775
$851$	−1.49573	−0.0512729
$852$	25.9065	0.887542
$853$	46.6597	1.59760	0.798799	−	0.601598i	$-0.205469\pi$
$853$	46.6597	1.59760	0.798799	+	0.601598i	$0.205469\pi$
$854$	−22.3099	−0.763429
$855$	33.4929	1.14543
$856$	−5.24711	−0.179343
$857$	24.3353	0.831278	0.415639	−	0.909530i	$-0.363558\pi$
$857$	24.3353	0.831278	0.415639	+	0.909530i	$0.363558\pi$
$858$	−89.6423	−3.06034
$859$	42.6621	1.45561	0.727806	−	0.685783i	$-0.240540\pi$
$859$	42.6621	1.45561	0.727806	+	0.685783i	$0.240540\pi$
$860$	−38.4331	−1.31056
$861$	48.0166	1.63640
$862$	10.7600	0.366487
$863$	−7.06902	−0.240632	−0.120316	−	0.992736i	$-0.538391\pi$
$863$	−7.06902	−0.240632	−0.120316	+	0.992736i	$0.538391\pi$
$864$	−4.08451	−0.138958
$865$	−9.48977	−0.322662
$866$	−28.4859	−0.967992
$867$	7.12242	0.241890
$868$	2.22263	0.0754409
$869$	−41.7865	−1.41751
$870$	92.9805	3.15233
$871$	70.4348	2.38659
$872$	13.6531	0.462351
$873$	−38.4380	−1.30093
$874$	1.06645	0.0360732
$875$	−73.9677	−2.50057
$876$	−44.8095	−1.51397
$877$	51.1578	1.72748	0.863739	−	0.503940i	$-0.168117\pi$
$877$	51.1578	1.72748	0.863739	+	0.503940i	$0.168117\pi$
$878$	7.51679	0.253679
$879$	62.4990	2.10804
$880$	19.9252	0.671679
$881$	−45.8500	−1.54473	−0.772363	−	0.635182i	$-0.780925\pi$
$881$	−45.8500	−1.54473	−0.772363	+	0.635182i	$0.780925\pi$
$882$	−12.2467	−0.412367
$883$	51.9155	1.74710	0.873548	−	0.486738i	$-0.161813\pi$
$883$	51.9155	1.74710	0.873548	+	0.486738i	$0.161813\pi$
$884$	−26.7176	−0.898608
$885$	84.1668	2.82924
$886$	−12.5262	−0.420826
$887$	26.8011	0.899895	0.449947	−	0.893055i	$-0.351443\pi$
$887$	26.8011	0.899895	0.449947	+	0.893055i	$0.351443\pi$
$888$	−6.68139	−0.224213
$889$	43.2741	1.45137
$890$	51.8034	1.73645
$891$	10.6818	0.357853
$892$	−20.1877	−0.675935
$893$	−3.47404	−0.116254
$894$	29.0060	0.970105
$895$	21.7437	0.726813
$896$	2.06732	0.0690643
$897$	−11.8098	−0.394319
$898$	−0.194462	−0.00648928
$899$	8.52518	0.284331
$900$	59.9804	1.99935
$901$	26.8722	0.895243
$902$	39.4675	1.31412
$903$	−50.7664	−1.68940
$904$	7.99975	0.266068
$905$	−23.5105	−0.781517
$906$	35.2813	1.17214
$907$	30.3717	1.00847	0.504237	−	0.863565i	$-0.331774\pi$
$907$	30.3717	1.00847	0.504237	+	0.863565i	$0.331774\pi$
$908$	−24.2855	−0.805944
$909$	−1.60025	−0.0530770
$910$	62.3586	2.06717
$911$	56.9981	1.88843	0.944216	−	0.329328i	$-0.106822\pi$
$911$	56.9981	1.88843	0.944216	+	0.329328i	$0.106822\pi$
$912$	4.76381	0.157746
$913$	−37.6789	−1.24699
$914$	28.1871	0.932345
$915$	−126.543	−4.18338
$916$	27.1669	0.897619
$917$	15.7415	0.519832
$918$	−15.4985	−0.511527
$919$	57.5064	1.89696	0.948480	−	0.316836i	$-0.102621\pi$
$919$	57.5064	1.89696	0.948480	+	0.316836i	$0.102621\pi$
$920$	2.62502	0.0865445
$921$	−54.0592	−1.78131
$922$	−4.75490	−0.156594
$923$	66.6423	2.19356
$924$	26.3193	0.865840
$925$	32.5919	1.07161
$926$	−26.9723	−0.886365
$927$	35.9355	1.18028
$928$	7.92947	0.260298
$929$	−10.9728	−0.360006	−0.180003	−	0.983666i	$-0.557611\pi$
$929$	−10.9728	−0.360006	−0.180003	+	0.983666i	$0.557611\pi$
$930$	12.6069	0.413395
$931$	4.74467	0.155500
$932$	−25.7002	−0.841837
$933$	−26.1976	−0.857670
$934$	−0.677155	−0.0221572
$935$	75.6054	2.47256
$936$	−31.6307	−1.03388
$937$	10.2475	0.334770	0.167385	−	0.985892i	$-0.446468\pi$
$937$	10.2475	0.334770	0.167385	+	0.985892i	$0.446468\pi$
$938$	−20.6799	−0.675222
$939$	32.7932	1.07016
$940$	−8.55120	−0.278910
$941$	22.6313	0.737759	0.368879	−	0.929477i	$-0.379742\pi$
$941$	22.6313	0.737759	0.368879	+	0.929477i	$0.379742\pi$
$942$	−5.09680	−0.166063
$943$	5.19959	0.169322
$944$	7.17783	0.233619
$945$	36.1734	1.17672
$946$	−41.7277	−1.35668
$947$	32.7523	1.06431	0.532154	−	0.846648i	$-0.321383\pi$
$947$	32.7523	1.06431	0.532154	+	0.846648i	$0.321383\pi$
$948$	−24.5912	−0.798686
$949$	−115.269	−3.74178
$950$	−23.2379	−0.753938
$951$	55.6217	1.80366
$952$	7.84435	0.254237
$953$	−55.2141	−1.78856	−0.894281	−	0.447507i	$-0.852312\pi$
$953$	−55.2141	−1.78856	−0.894281	+	0.447507i	$0.852312\pi$
$954$	31.8138	1.03001
$955$	59.1618	1.91443
$956$	−6.99025	−0.226081
$957$	100.951	3.26328
$958$	34.6760	1.12033
$959$	35.5636	1.14841
$960$	11.7259	0.378453
$961$	−29.8441	−0.962713
$962$	−17.1873	−0.554141
$963$	−23.5712	−0.759572
$964$	−1.08519	−0.0349516
$965$	23.4513	0.754923
$966$	3.46740	0.111562
$967$	0.0328189	0.00105538	0.000527692	−	1.00000i	$-0.499832\pi$
$967$	0.0328189	0.00105538	0.000527692		1.00000i	$0.499832\pi$
$968$	10.6332	0.341765
$969$	18.0761	0.580688
$970$	36.6556	1.17694
$971$	−12.3380	−0.395945	−0.197972	−	0.980208i	$-0.563436\pi$
$971$	−12.3380	−0.395945	−0.197972	+	0.980208i	$0.563436\pi$
$972$	18.5397	0.594662
$973$	−1.45766	−0.0467304
$974$	17.8032	0.570451
$975$	257.336	8.24134
$976$	−10.7917	−0.345434
$977$	−47.8317	−1.53027	−0.765136	−	0.643869i	$-0.777328\pi$
$977$	−47.8317	−1.53027	−0.765136	+	0.643869i	$0.777328\pi$
$978$	−13.6794	−0.437418
$979$	56.2440	1.79757
$980$	11.6788	0.373066
$981$	61.3326	1.95820
$982$	4.05148	0.129288
$983$	−48.0491	−1.53253	−0.766265	−	0.642525i	$-0.777887\pi$
$983$	−48.0491	−1.53253	−0.766265	+	0.642525i	$0.777887\pi$
$984$	23.2265	0.740434
$985$	68.1049	2.17000
$986$	30.0881	0.958199
$987$	−11.2953	−0.359533
$988$	12.2545	0.389868
$989$	−5.49736	−0.174806
$990$	89.5086	2.84477
$991$	−23.7365	−0.754014	−0.377007	−	0.926210i	$-0.623047\pi$
$991$	−23.7365	−0.754014	−0.377007	+	0.926210i	$0.623047\pi$
$992$	1.07513	0.0341353
$993$	−7.53428	−0.239093
$994$	−19.5664	−0.620608
$995$	16.7434	0.530801
$996$	−22.1740	−0.702609
$997$	−38.6008	−1.22250	−0.611250	−	0.791437i	$-0.709333\pi$
$997$	−38.6008	−1.22250	−0.611250	+	0.791437i	$0.709333\pi$
$998$	−11.5589	−0.365889
$999$	−9.97014	−0.315441

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.10	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.10	✓	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.73719 q^{3} +1.00000 q^{4} -4.28393 q^{5} -2.73719 q^{6} +2.06732 q^{7} +1.00000 q^{8} +4.49223 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.73719 q^{3} +1.00000 q^{4} -4.28393 q^{5} -2.73719 q^{6} +2.06732 q^{7} +1.00000 q^{8} +4.49223 q^{9} -4.28393 q^{10} -4.65115 q^{11} -2.73719 q^{12} -7.04120 q^{13} +2.06732 q^{14} +11.7259 q^{15} +1.00000 q^{16} +3.79446 q^{17} +4.49223 q^{18} -1.74040 q^{19} -4.28393 q^{20} -5.65865 q^{21} -4.65115 q^{22} -0.612761 q^{23} -2.73719 q^{24} +13.3520 q^{25} -7.04120 q^{26} -4.08451 q^{27} +2.06732 q^{28} +7.92947 q^{29} +11.7259 q^{30} +1.07513 q^{31} +1.00000 q^{32} +12.7311 q^{33} +3.79446 q^{34} -8.85624 q^{35} +4.49223 q^{36} +2.44096 q^{37} -1.74040 q^{38} +19.2731 q^{39} -4.28393 q^{40} -8.48552 q^{41} -5.65865 q^{42} +8.97146 q^{43} -4.65115 q^{44} -19.2444 q^{45} -0.612761 q^{46} +1.99611 q^{47} -2.73719 q^{48} -2.72620 q^{49} +13.3520 q^{50} -10.3862 q^{51} -7.04120 q^{52} +7.08196 q^{53} -4.08451 q^{54} +19.9252 q^{55} +2.06732 q^{56} +4.76381 q^{57} +7.92947 q^{58} +7.17783 q^{59} +11.7259 q^{60} -10.7917 q^{61} +1.07513 q^{62} +9.28686 q^{63} +1.00000 q^{64} +30.1640 q^{65} +12.7311 q^{66} -10.0032 q^{67} +3.79446 q^{68} +1.67725 q^{69} -8.85624 q^{70} -9.46462 q^{71} +4.49223 q^{72} +16.3706 q^{73} +2.44096 q^{74} -36.5471 q^{75} -1.74040 q^{76} -9.61542 q^{77} +19.2731 q^{78} +8.98411 q^{79} -4.28393 q^{80} -2.29658 q^{81} -8.48552 q^{82} +8.10098 q^{83} -5.65865 q^{84} -16.2552 q^{85} +8.97146 q^{86} -21.7045 q^{87} -4.65115 q^{88} -12.0925 q^{89} -19.2444 q^{90} -14.5564 q^{91} -0.612761 q^{92} -2.94283 q^{93} +1.99611 q^{94} +7.45576 q^{95} -2.73719 q^{96} -8.55655 q^{97} -2.72620 q^{98} -20.8940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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