LMFDB - Embedded newform 8002.2.a.e.1.14

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:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.17233 q^{3} +1.00000 q^{4} -1.31184 q^{5} +2.17233 q^{6} -2.50290 q^{7} -1.00000 q^{8} +1.71901 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.17233 q^{3} +1.00000 q^{4} -1.31184 q^{5} +2.17233 q^{6} -2.50290 q^{7} -1.00000 q^{8} +1.71901 q^{9} +1.31184 q^{10} -0.100565 q^{11} -2.17233 q^{12} +2.06885 q^{13} +2.50290 q^{14} +2.84976 q^{15} +1.00000 q^{16} -2.01258 q^{17} -1.71901 q^{18} +4.95546 q^{19} -1.31184 q^{20} +5.43713 q^{21} +0.100565 q^{22} +5.18712 q^{23} +2.17233 q^{24} -3.27907 q^{25} -2.06885 q^{26} +2.78273 q^{27} -2.50290 q^{28} +9.97044 q^{29} -2.84976 q^{30} -7.91975 q^{31} -1.00000 q^{32} +0.218460 q^{33} +2.01258 q^{34} +3.28342 q^{35} +1.71901 q^{36} +3.73621 q^{37} -4.95546 q^{38} -4.49422 q^{39} +1.31184 q^{40} +3.49399 q^{41} -5.43713 q^{42} +7.18482 q^{43} -0.100565 q^{44} -2.25507 q^{45} -5.18712 q^{46} -6.40829 q^{47} -2.17233 q^{48} -0.735476 q^{49} +3.27907 q^{50} +4.37198 q^{51} +2.06885 q^{52} -2.04402 q^{53} -2.78273 q^{54} +0.131926 q^{55} +2.50290 q^{56} -10.7649 q^{57} -9.97044 q^{58} -0.710808 q^{59} +2.84976 q^{60} -0.711142 q^{61} +7.91975 q^{62} -4.30252 q^{63} +1.00000 q^{64} -2.71401 q^{65} -0.218460 q^{66} +2.07100 q^{67} -2.01258 q^{68} -11.2681 q^{69} -3.28342 q^{70} -12.5268 q^{71} -1.71901 q^{72} -4.08400 q^{73} -3.73621 q^{74} +7.12321 q^{75} +4.95546 q^{76} +0.251705 q^{77} +4.49422 q^{78} +2.72361 q^{79} -1.31184 q^{80} -11.2020 q^{81} -3.49399 q^{82} +7.12661 q^{83} +5.43713 q^{84} +2.64019 q^{85} -7.18482 q^{86} -21.6591 q^{87} +0.100565 q^{88} -9.67029 q^{89} +2.25507 q^{90} -5.17813 q^{91} +5.18712 q^{92} +17.2043 q^{93} +6.40829 q^{94} -6.50079 q^{95} +2.17233 q^{96} +13.5076 q^{97} +0.735476 q^{98} -0.172872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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
$3$	−2.17233	−1.25419	−0.627097	−	0.778941i	$-0.715757\pi$
$3$	−2.17233	−1.25419	−0.627097	+	0.778941i	$0.715757\pi$
$4$	1.00000	0.500000
$5$	−1.31184	−0.586674	−0.293337	−	0.956009i	$-0.594766\pi$
$5$	−1.31184	−0.586674	−0.293337	+	0.956009i	$0.594766\pi$
$6$	2.17233	0.886849
$7$	−2.50290	−0.946008	−0.473004	−	0.881060i	$-0.656830\pi$
$7$	−2.50290	−0.946008	−0.473004	+	0.881060i	$0.656830\pi$
$8$	−1.00000	−0.353553
$9$	1.71901	0.573003
$10$	1.31184	0.414841
$11$	−0.100565	−0.0303215	−0.0151608	−	0.999885i	$-0.504826\pi$
$11$	−0.100565	−0.0303215	−0.0151608	+	0.999885i	$0.504826\pi$
$12$	−2.17233	−0.627097
$13$	2.06885	0.573796	0.286898	−	0.957961i	$-0.407376\pi$
$13$	2.06885	0.573796	0.286898	+	0.957961i	$0.407376\pi$
$14$	2.50290	0.668929
$15$	2.84976	0.735804
$16$	1.00000	0.250000
$17$	−2.01258	−0.488122	−0.244061	−	0.969760i	$-0.578480\pi$
$17$	−2.01258	−0.488122	−0.244061	+	0.969760i	$0.578480\pi$
$18$	−1.71901	−0.405175
$19$	4.95546	1.13686	0.568430	−	0.822731i	$-0.307551\pi$
$19$	4.95546	1.13686	0.568430	+	0.822731i	$0.307551\pi$
$20$	−1.31184	−0.293337
$21$	5.43713	1.18648
$22$	0.100565	0.0214405
$23$	5.18712	1.08159	0.540795	−	0.841155i	$-0.318124\pi$
$23$	5.18712	1.08159	0.540795	+	0.841155i	$0.318124\pi$
$24$	2.17233	0.443425
$25$	−3.27907	−0.655813
$26$	−2.06885	−0.405735
$27$	2.78273	0.535537
$28$	−2.50290	−0.473004
$29$	9.97044	1.85146	0.925732	−	0.378180i	$-0.123450\pi$
$29$	9.97044	1.85146	0.925732	+	0.378180i	$0.123450\pi$
$30$	−2.84976	−0.520292
$31$	−7.91975	−1.42243	−0.711215	−	0.702975i	$-0.751855\pi$
$31$	−7.91975	−1.42243	−0.711215	+	0.702975i	$0.751855\pi$
$32$	−1.00000	−0.176777
$33$	0.218460	0.0380291
$34$	2.01258	0.345155
$35$	3.28342	0.554999
$36$	1.71901	0.286502
$37$	3.73621	0.614229	0.307114	−	0.951673i	$-0.400637\pi$
$37$	3.73621	0.614229	0.307114	+	0.951673i	$0.400637\pi$
$38$	−4.95546	−0.803882
$39$	−4.49422	−0.719652
$40$	1.31184	0.207421
$41$	3.49399	0.545670	0.272835	−	0.962061i	$-0.412039\pi$
$41$	3.49399	0.545670	0.272835	+	0.962061i	$0.412039\pi$
$42$	−5.43713	−0.838967
$43$	7.18482	1.09568	0.547838	−	0.836585i	$-0.315451\pi$
$43$	7.18482	1.09568	0.547838	+	0.836585i	$0.315451\pi$
$44$	−0.100565	−0.0151608
$45$	−2.25507	−0.336166
$46$	−5.18712	−0.764799
$47$	−6.40829	−0.934745	−0.467372	−	0.884061i	$-0.654799\pi$
$47$	−6.40829	−0.934745	−0.467372	+	0.884061i	$0.654799\pi$
$48$	−2.17233	−0.313549
$49$	−0.735476	−0.105068
$50$	3.27907	0.463730
$51$	4.37198	0.612200
$52$	2.06885	0.286898
$53$	−2.04402	−0.280768	−0.140384	−	0.990097i	$-0.544834\pi$
$53$	−2.04402	−0.280768	−0.140384	+	0.990097i	$0.544834\pi$
$54$	−2.78273	−0.378682
$55$	0.131926	0.0177889
$56$	2.50290	0.334465
$57$	−10.7649	−1.42584
$58$	−9.97044	−1.30918
$59$	−0.710808	−0.0925394	−0.0462697	−	0.998929i	$-0.514733\pi$
$59$	−0.710808	−0.0925394	−0.0462697	+	0.998929i	$0.514733\pi$
$60$	2.84976	0.367902
$61$	−0.711142	−0.0910524	−0.0455262	−	0.998963i	$-0.514496\pi$
$61$	−0.711142	−0.0910524	−0.0455262	+	0.998963i	$0.514496\pi$
$62$	7.91975	1.00581
$63$	−4.30252	−0.542066
$64$	1.00000	0.125000
$65$	−2.71401	−0.336631
$66$	−0.218460	−0.0268906
$67$	2.07100	0.253013	0.126507	−	0.991966i	$-0.459623\pi$
$67$	2.07100	0.253013	0.126507	+	0.991966i	$0.459623\pi$
$68$	−2.01258	−0.244061
$69$	−11.2681	−1.35652
$70$	−3.28342	−0.392444
$71$	−12.5268	−1.48666	−0.743331	−	0.668924i	$-0.766755\pi$
$71$	−12.5268	−1.48666	−0.743331	+	0.668924i	$0.766755\pi$
$72$	−1.71901	−0.202587
$73$	−4.08400	−0.477997	−0.238998	−	0.971020i	$-0.576819\pi$
$73$	−4.08400	−0.477997	−0.238998	+	0.971020i	$0.576819\pi$
$74$	−3.73621	−0.434325
$75$	7.12321	0.822517
$76$	4.95546	0.568430
$77$	0.251705	0.0286844
$78$	4.49422	0.508871
$79$	2.72361	0.306430	0.153215	−	0.988193i	$-0.451037\pi$
$79$	2.72361	0.306430	0.153215	+	0.988193i	$0.451037\pi$
$80$	−1.31184	−0.146669
$81$	−11.2020	−1.24467
$82$	−3.49399	−0.385847
$83$	7.12661	0.782247	0.391124	−	0.920338i	$-0.372087\pi$
$83$	7.12661	0.782247	0.391124	+	0.920338i	$0.372087\pi$
$84$	5.43713	0.593239
$85$	2.64019	0.286369
$86$	−7.18482	−0.774759
$87$	−21.6591	−2.32210
$88$	0.100565	0.0107203
$89$	−9.67029	−1.02505	−0.512524	−	0.858673i	$-0.671290\pi$
$89$	−9.67029	−1.02505	−0.512524	+	0.858673i	$0.671290\pi$
$90$	2.25507	0.237706
$91$	−5.17813	−0.542816
$92$	5.18712	0.540795
$93$	17.2043	1.78400
$94$	6.40829	0.660964
$95$	−6.50079	−0.666967
$96$	2.17233	0.221712
$97$	13.5076	1.37149	0.685746	−	0.727841i	$-0.259476\pi$
$97$	13.5076	1.37149	0.685746	+	0.727841i	$0.259476\pi$
$98$	0.735476	0.0742943
$99$	−0.172872	−0.0173743
$100$	−3.27907	−0.327907
$101$	−8.75991	−0.871644	−0.435822	−	0.900033i	$-0.643542\pi$
$101$	−8.75991	−0.871644	−0.435822	+	0.900033i	$0.643542\pi$
$102$	−4.37198	−0.432891
$103$	10.1373	0.998862	0.499431	−	0.866354i	$-0.333542\pi$
$103$	10.1373	0.998862	0.499431	+	0.866354i	$0.333542\pi$
$104$	−2.06885	−0.202868
$105$	−7.13266	−0.696077
$106$	2.04402	0.198533
$107$	9.92879	0.959853	0.479926	−	0.877309i	$-0.340663\pi$
$107$	9.92879	0.959853	0.479926	+	0.877309i	$0.340663\pi$
$108$	2.78273	0.267768
$109$	−16.1257	−1.54456	−0.772279	−	0.635284i	$-0.780883\pi$
$109$	−16.1257	−1.54456	−0.772279	+	0.635284i	$0.780883\pi$
$110$	−0.131926	−0.0125786
$111$	−8.11627	−0.770362
$112$	−2.50290	−0.236502
$113$	−11.7020	−1.10083	−0.550416	−	0.834891i	$-0.685531\pi$
$113$	−11.7020	−1.10083	−0.550416	+	0.834891i	$0.685531\pi$
$114$	10.7649	1.00822
$115$	−6.80469	−0.634541
$116$	9.97044	0.925732
$117$	3.55638	0.328787
$118$	0.710808	0.0654352
$119$	5.03729	0.461768
$120$	−2.84976	−0.260146
$121$	−10.9899	−0.999081
$122$	0.711142	0.0643838
$123$	−7.59010	−0.684376
$124$	−7.91975	−0.711215
$125$	10.8608	0.971423
$126$	4.30252	0.383299
$127$	−4.84397	−0.429833	−0.214917	−	0.976632i	$-0.568948\pi$
$127$	−4.84397	−0.429833	−0.214917	+	0.976632i	$0.568948\pi$
$128$	−1.00000	−0.0883883
$129$	−15.6078	−1.37419
$130$	2.71401	0.238034
$131$	5.91413	0.516720	0.258360	−	0.966049i	$-0.416818\pi$
$131$	5.91413	0.516720	0.258360	+	0.966049i	$0.416818\pi$
$132$	0.218460	0.0190145
$133$	−12.4030	−1.07548
$134$	−2.07100	−0.178908
$135$	−3.65051	−0.314186
$136$	2.01258	0.172577
$137$	13.2312	1.13041	0.565207	−	0.824949i	$-0.308796\pi$
$137$	13.2312	1.13041	0.565207	+	0.824949i	$0.308796\pi$
$138$	11.2681	0.959207
$139$	−5.31410	−0.450736	−0.225368	−	0.974274i	$-0.572358\pi$
$139$	−5.31410	−0.450736	−0.225368	+	0.974274i	$0.572358\pi$
$140$	3.28342	0.277499
$141$	13.9209	1.17235
$142$	12.5268	1.05123
$143$	−0.208054	−0.0173984
$144$	1.71901	0.143251
$145$	−13.0797	−1.08621
$146$	4.08400	0.337995
$147$	1.59770	0.131776
$148$	3.73621	0.307114
$149$	−4.04539	−0.331411	−0.165706	−	0.986175i	$-0.552990\pi$
$149$	−4.04539	−0.331411	−0.165706	+	0.986175i	$0.552990\pi$
$150$	−7.12321	−0.581607
$151$	3.91908	0.318931	0.159465	−	0.987204i	$-0.449023\pi$
$151$	3.91908	0.318931	0.159465	+	0.987204i	$0.449023\pi$
$152$	−4.95546	−0.401941
$153$	−3.45964	−0.279696
$154$	−0.251705	−0.0202829
$155$	10.3895	0.834503
$156$	−4.49422	−0.359826
$157$	1.29450	0.103312	0.0516560	−	0.998665i	$-0.483550\pi$
$157$	1.29450	0.103312	0.0516560	+	0.998665i	$0.483550\pi$
$158$	−2.72361	−0.216679
$159$	4.44028	0.352137
$160$	1.31184	0.103710
$161$	−12.9829	−1.02319
$162$	11.2020	0.880115
$163$	−5.00829	−0.392280	−0.196140	−	0.980576i	$-0.562841\pi$
$163$	−5.00829	−0.392280	−0.196140	+	0.980576i	$0.562841\pi$
$164$	3.49399	0.272835
$165$	−0.286586	−0.0223107
$166$	−7.12661	−0.553132
$167$	14.5968	1.12953	0.564765	−	0.825252i	$-0.308967\pi$
$167$	14.5968	1.12953	0.564765	+	0.825252i	$0.308967\pi$
$168$	−5.43713	−0.419483
$169$	−8.71986	−0.670758
$170$	−2.64019	−0.202493
$171$	8.51849	0.651425
$172$	7.18482	0.547838
$173$	−18.7254	−1.42367	−0.711833	−	0.702348i	$-0.752135\pi$
$173$	−18.7254	−1.42367	−0.711833	+	0.702348i	$0.752135\pi$
$174$	21.6591	1.64197
$175$	8.20718	0.620405
$176$	−0.100565	−0.00758038
$177$	1.54411	0.116062
$178$	9.67029	0.724819
$179$	16.4101	1.22655	0.613276	−	0.789869i	$-0.289851\pi$
$179$	16.4101	1.22655	0.613276	+	0.789869i	$0.289851\pi$
$180$	−2.25507	−0.168083
$181$	16.1897	1.20337	0.601686	−	0.798732i	$-0.294496\pi$
$181$	16.1897	1.20337	0.601686	+	0.798732i	$0.294496\pi$
$182$	5.17813	0.383829
$183$	1.54483	0.114197
$184$	−5.18712	−0.382400
$185$	−4.90132	−0.360352
$186$	−17.2043	−1.26148
$187$	0.202395	0.0148006
$188$	−6.40829	−0.467372
$189$	−6.96491	−0.506622
$190$	6.50079	0.471617
$191$	−24.9052	−1.80208	−0.901039	−	0.433738i	$-0.857194\pi$
$191$	−24.9052	−1.80208	−0.901039	+	0.433738i	$0.857194\pi$
$192$	−2.17233	−0.156774
$193$	−16.9546	−1.22042	−0.610208	−	0.792241i	$-0.708914\pi$
$193$	−16.9546	−1.22042	−0.610208	+	0.792241i	$0.708914\pi$
$194$	−13.5076	−0.969791
$195$	5.89572	0.422201
$196$	−0.735476	−0.0525340
$197$	19.7851	1.40963	0.704815	−	0.709391i	$-0.251030\pi$
$197$	19.7851	1.40963	0.704815	+	0.709391i	$0.251030\pi$
$198$	0.172872	0.0122855
$199$	−10.1142	−0.716979	−0.358490	−	0.933534i	$-0.616708\pi$
$199$	−10.1142	−0.716979	−0.358490	+	0.933534i	$0.616708\pi$
$200$	3.27907	0.231865
$201$	−4.49890	−0.317328
$202$	8.75991	0.616345
$203$	−24.9550	−1.75150
$204$	4.37198	0.306100
$205$	−4.58357	−0.320131
$206$	−10.1373	−0.706302
$207$	8.91671	0.619754
$208$	2.06885	0.143449
$209$	−0.498346	−0.0344713
$210$	7.13266	0.492200
$211$	−25.2032	−1.73506	−0.867532	−	0.497382i	$-0.834295\pi$
$211$	−25.2032	−1.73506	−0.867532	+	0.497382i	$0.834295\pi$
$212$	−2.04402	−0.140384
$213$	27.2124	1.86456
$214$	−9.92879	−0.678718
$215$	−9.42537	−0.642805
$216$	−2.78273	−0.189341
$217$	19.8224	1.34563
$218$	16.1257	1.09217
$219$	8.87180	0.599501
$220$	0.131926	0.00889443
$221$	−4.16373	−0.280083
$222$	8.11627	0.544728
$223$	14.7802	0.989757	0.494879	−	0.868962i	$-0.335213\pi$
$223$	14.7802	0.989757	0.494879	+	0.868962i	$0.335213\pi$
$224$	2.50290	0.167232
$225$	−5.63675	−0.375783
$226$	11.7020	0.778405
$227$	−10.1598	−0.674330	−0.337165	−	0.941446i	$-0.609468\pi$
$227$	−10.1598	−0.674330	−0.337165	+	0.941446i	$0.609468\pi$
$228$	−10.7649	−0.712922
$229$	19.5203	1.28994	0.644970	−	0.764208i	$-0.276870\pi$
$229$	19.5203	1.28994	0.644970	+	0.764208i	$0.276870\pi$
$230$	6.80469	0.448688
$231$	−0.546785	−0.0359758
$232$	−9.97044	−0.654592
$233$	−9.34433	−0.612168	−0.306084	−	0.952005i	$-0.599019\pi$
$233$	−9.34433	−0.612168	−0.306084	+	0.952005i	$0.599019\pi$
$234$	−3.55638	−0.232488
$235$	8.40667	0.548391
$236$	−0.710808	−0.0462697
$237$	−5.91658	−0.384323
$238$	−5.03729	−0.326519
$239$	20.5513	1.32935	0.664676	−	0.747132i	$-0.268570\pi$
$239$	20.5513	1.32935	0.664676	+	0.747132i	$0.268570\pi$
$240$	2.84976	0.183951
$241$	6.41466	0.413204	0.206602	−	0.978425i	$-0.433759\pi$
$241$	6.41466	0.413204	0.206602	+	0.978425i	$0.433759\pi$
$242$	10.9899	0.706457
$243$	15.9863	1.02552
$244$	−0.711142	−0.0455262
$245$	0.964830	0.0616407
$246$	7.59010	0.483927
$247$	10.2521	0.652326
$248$	7.91975	0.502905
$249$	−15.4813	−0.981090
$250$	−10.8608	−0.686900
$251$	10.7601	0.679170	0.339585	−	0.940575i	$-0.389713\pi$
$251$	10.7601	0.679170	0.339585	+	0.940575i	$0.389713\pi$
$252$	−4.30252	−0.271033
$253$	−0.521643	−0.0327954
$254$	4.84397	0.303938
$255$	−5.73536	−0.359162
$256$	1.00000	0.0625000
$257$	1.29400	0.0807178	0.0403589	−	0.999185i	$-0.487150\pi$
$257$	1.29400	0.0807178	0.0403589	+	0.999185i	$0.487150\pi$
$258$	15.6078	0.971699
$259$	−9.35137	−0.581066
$260$	−2.71401	−0.168316
$261$	17.1393	1.06090
$262$	−5.91413	−0.365376
$263$	−7.04882	−0.434649	−0.217324	−	0.976099i	$-0.569733\pi$
$263$	−7.04882	−0.434649	−0.217324	+	0.976099i	$0.569733\pi$
$264$	−0.218460	−0.0134453
$265$	2.68143	0.164719
$266$	12.4030	0.760479
$267$	21.0070	1.28561
$268$	2.07100	0.126507
$269$	26.9814	1.64509	0.822543	−	0.568702i	$-0.192554\pi$
$269$	26.9814	1.64509	0.822543	+	0.568702i	$0.192554\pi$
$270$	3.65051	0.222163
$271$	−1.38607	−0.0841978	−0.0420989	−	0.999113i	$-0.513404\pi$
$271$	−1.38607	−0.0841978	−0.0420989	+	0.999113i	$0.513404\pi$
$272$	−2.01258	−0.122031
$273$	11.2486	0.680797
$274$	−13.2312	−0.799324
$275$	0.329759	0.0198852
$276$	−11.2681	−0.678262
$277$	−11.3658	−0.682905	−0.341453	−	0.939899i	$-0.610919\pi$
$277$	−11.3658	−0.682905	−0.341453	+	0.939899i	$0.610919\pi$
$278$	5.31410	0.318719
$279$	−13.6141	−0.815057
$280$	−3.28342	−0.196222
$281$	9.12180	0.544161	0.272080	−	0.962275i	$-0.412288\pi$
$281$	9.12180	0.544161	0.272080	+	0.962275i	$0.412288\pi$
$282$	−13.9209	−0.828978
$283$	1.86684	0.110972	0.0554860	−	0.998459i	$-0.482329\pi$
$283$	1.86684	0.110972	0.0554860	+	0.998459i	$0.482329\pi$
$284$	−12.5268	−0.743331
$285$	14.1219	0.836506
$286$	0.208054	0.0123025
$287$	−8.74513	−0.516208
$288$	−1.71901	−0.101294
$289$	−12.9495	−0.761737
$290$	13.0797	0.768064
$291$	−29.3430	−1.72012
$292$	−4.08400	−0.238998
$293$	5.28826	0.308943	0.154472	−	0.987997i	$-0.450632\pi$
$293$	5.28826	0.308943	0.154472	+	0.987997i	$0.450632\pi$
$294$	−1.59770	−0.0931795
$295$	0.932469	0.0542905
$296$	−3.73621	−0.217163
$297$	−0.279845	−0.0162383
$298$	4.04539	0.234343
$299$	10.7314	0.620612
$300$	7.12321	0.411259
$301$	−17.9829	−1.03652
$302$	−3.91908	−0.225518
$303$	19.0294	1.09321
$304$	4.95546	0.284215
$305$	0.932907	0.0534181
$306$	3.45964	0.197775
$307$	27.5283	1.57113	0.785563	−	0.618782i	$-0.212373\pi$
$307$	27.5283	1.57113	0.785563	+	0.618782i	$0.212373\pi$
$308$	0.251705	0.0143422
$309$	−22.0216	−1.25277
$310$	−10.3895	−0.590083
$311$	3.05641	0.173313	0.0866566	−	0.996238i	$-0.472382\pi$
$311$	3.05641	0.173313	0.0866566	+	0.996238i	$0.472382\pi$
$312$	4.49422	0.254435
$313$	−21.5109	−1.21587	−0.607933	−	0.793988i	$-0.708001\pi$
$313$	−21.5109	−1.21587	−0.607933	+	0.793988i	$0.708001\pi$
$314$	−1.29450	−0.0730526
$315$	5.64423	0.318016
$316$	2.72361	0.153215
$317$	−5.45734	−0.306515	−0.153257	−	0.988186i	$-0.548976\pi$
$317$	−5.45734	−0.306515	−0.153257	+	0.988186i	$0.548976\pi$
$318$	−4.44028	−0.248999
$319$	−1.00268	−0.0561392
$320$	−1.31184	−0.0733343
$321$	−21.5686	−1.20384
$322$	12.9829	0.723506
$323$	−9.97326	−0.554927
$324$	−11.2020	−0.622335
$325$	−6.78390	−0.376303
$326$	5.00829	0.277384
$327$	35.0302	1.93718
$328$	−3.49399	−0.192923
$329$	16.0393	0.884276
$330$	0.286586	0.0157760
$331$	−10.4352	−0.573569	−0.286785	−	0.957995i	$-0.592586\pi$
$331$	−10.4352	−0.573569	−0.286785	+	0.957995i	$0.592586\pi$
$332$	7.12661	0.391124
$333$	6.42258	0.351955
$334$	−14.5968	−0.798699
$335$	−2.71683	−0.148437
$336$	5.43713	0.296620
$337$	28.2649	1.53969	0.769844	−	0.638233i	$-0.220334\pi$
$337$	28.2649	1.53969	0.769844	+	0.638233i	$0.220334\pi$
$338$	8.71986	0.474298
$339$	25.4206	1.38066
$340$	2.64019	0.143184
$341$	0.796450	0.0431302
$342$	−8.51849	−0.460627
$343$	19.3611	1.04540
$344$	−7.18482	−0.387380
$345$	14.7820	0.795837
$346$	18.7254	1.00668
$347$	4.29931	0.230799	0.115400	−	0.993319i	$-0.463185\pi$
$347$	4.29931	0.230799	0.115400	+	0.993319i	$0.463185\pi$
$348$	−21.6591	−1.16105
$349$	−15.7538	−0.843283	−0.421642	−	0.906763i	$-0.638546\pi$
$349$	−15.7538	−0.843283	−0.421642	+	0.906763i	$0.638546\pi$
$350$	−8.20718	−0.438692
$351$	5.75706	0.307289
$352$	0.100565	0.00536014
$353$	−32.0369	−1.70515	−0.852577	−	0.522602i	$-0.824961\pi$
$353$	−32.0369	−1.70515	−0.852577	+	0.522602i	$0.824961\pi$
$354$	−1.54411	−0.0820685
$355$	16.4333	0.872187
$356$	−9.67029	−0.512524
$357$	−10.9426	−0.579146
$358$	−16.4101	−0.867303
$359$	−25.5931	−1.35075	−0.675377	−	0.737472i	$-0.736019\pi$
$359$	−25.5931	−1.35075	−0.675377	+	0.737472i	$0.736019\pi$
$360$	2.25507	0.118853
$361$	5.55659	0.292452
$362$	−16.1897	−0.850913
$363$	23.8736	1.25304
$364$	−5.17813	−0.271408
$365$	5.35758	0.280428
$366$	−1.54483	−0.0807497
$367$	−26.2220	−1.36878	−0.684390	−	0.729116i	$-0.739931\pi$
$367$	−26.2220	−1.36878	−0.684390	+	0.729116i	$0.739931\pi$
$368$	5.18712	0.270397
$369$	6.00621	0.312671
$370$	4.90132	0.254808
$371$	5.11598	0.265609
$372$	17.2043	0.892002
$373$	36.7040	1.90046	0.950231	−	0.311546i	$-0.100847\pi$
$373$	36.7040	1.90046	0.950231	+	0.311546i	$0.100847\pi$
$374$	−0.202395	−0.0104656
$375$	−23.5933	−1.21835
$376$	6.40829	0.330482
$377$	20.6274	1.06236
$378$	6.96491	0.358236
$379$	−29.0002	−1.48964	−0.744821	−	0.667265i	$-0.767465\pi$
$379$	−29.0002	−1.48964	−0.744821	+	0.667265i	$0.767465\pi$
$380$	−6.50079	−0.333484
$381$	10.5227	0.539094
$382$	24.9052	1.27426
$383$	25.2690	1.29118	0.645592	−	0.763683i	$-0.276611\pi$
$383$	25.2690	1.29118	0.645592	+	0.763683i	$0.276611\pi$
$384$	2.17233	0.110856
$385$	−0.330197	−0.0168284
$386$	16.9546	0.862964
$387$	12.3508	0.627826
$388$	13.5076	0.685746
$389$	−6.33010	−0.320949	−0.160474	−	0.987040i	$-0.551302\pi$
$389$	−6.33010	−0.320949	−0.160474	+	0.987040i	$0.551302\pi$
$390$	−5.89572	−0.298541
$391$	−10.4395	−0.527948
$392$	0.735476	0.0371471
$393$	−12.8474	−0.648067
$394$	−19.7851	−0.996759
$395$	−3.57296	−0.179775
$396$	−0.172872	−0.00868716
$397$	−13.9127	−0.698256	−0.349128	−	0.937075i	$-0.613522\pi$
$397$	−13.9127	−0.698256	−0.349128	+	0.937075i	$0.613522\pi$
$398$	10.1142	0.506981
$399$	26.9435	1.34886
$400$	−3.27907	−0.163953
$401$	−32.7694	−1.63642	−0.818212	−	0.574916i	$-0.805035\pi$
$401$	−32.7694	−1.63642	−0.818212	+	0.574916i	$0.805035\pi$
$402$	4.49890	0.224385
$403$	−16.3848	−0.816184
$404$	−8.75991	−0.435822
$405$	14.6953	0.730216
$406$	24.9550	1.23850
$407$	−0.375732	−0.0186243
$408$	−4.37198	−0.216445
$409$	−30.9075	−1.52828	−0.764138	−	0.645053i	$-0.776835\pi$
$409$	−30.9075	−1.52828	−0.764138	+	0.645053i	$0.776835\pi$
$410$	4.58357	0.226367
$411$	−28.7424	−1.41776
$412$	10.1373	0.499431
$413$	1.77908	0.0875430
$414$	−8.91671	−0.438232
$415$	−9.34900	−0.458924
$416$	−2.06885	−0.101434
$417$	11.5440	0.565311
$418$	0.498346	0.0243749
$419$	34.5512	1.68794	0.843968	−	0.536394i	$-0.180214\pi$
$419$	34.5512	1.68794	0.843968	+	0.536394i	$0.180214\pi$
$420$	−7.13266	−0.348038
$421$	10.0270	0.488687	0.244344	−	0.969689i	$-0.421428\pi$
$421$	10.0270	0.488687	0.244344	+	0.969689i	$0.421428\pi$
$422$	25.2032	1.22687
$423$	−11.0159	−0.535612
$424$	2.04402	0.0992663
$425$	6.59938	0.320117
$426$	−27.2124	−1.31845
$427$	1.77992	0.0861363
$428$	9.92879	0.479926
$429$	0.451962	0.0218209
$430$	9.42537	0.454532
$431$	12.7690	0.615062	0.307531	−	0.951538i	$-0.400497\pi$
$431$	12.7690	0.615062	0.307531	+	0.951538i	$0.400497\pi$
$432$	2.78273	0.133884
$433$	7.62871	0.366612	0.183306	−	0.983056i	$-0.441320\pi$
$433$	7.62871	0.366612	0.183306	+	0.983056i	$0.441320\pi$
$434$	−19.8224	−0.951504
$435$	28.4133	1.36231
$436$	−16.1257	−0.772279
$437$	25.7046	1.22962
$438$	−8.87180	−0.423911
$439$	−0.892723	−0.0426073	−0.0213037	−	0.999773i	$-0.506782\pi$
$439$	−0.892723	−0.0426073	−0.0213037	+	0.999773i	$0.506782\pi$
$440$	−0.131926	−0.00628931
$441$	−1.26429	−0.0602043
$442$	4.16373	0.198048
$443$	25.6792	1.22005	0.610027	−	0.792380i	$-0.291158\pi$
$443$	25.6792	1.22005	0.610027	+	0.792380i	$0.291158\pi$
$444$	−8.11627	−0.385181
$445$	12.6859	0.601370
$446$	−14.7802	−0.699864
$447$	8.78791	0.415654
$448$	−2.50290	−0.118251
$449$	26.4059	1.24617	0.623087	−	0.782153i	$-0.285878\pi$
$449$	26.4059	1.24617	0.623087	+	0.782153i	$0.285878\pi$
$450$	5.63675	0.265719
$451$	−0.351374	−0.0165455
$452$	−11.7020	−0.550416
$453$	−8.51354	−0.400001
$454$	10.1598	0.476823
$455$	6.79290	0.318456
$456$	10.7649	0.504112
$457$	−16.0306	−0.749880	−0.374940	−	0.927049i	$-0.622337\pi$
$457$	−16.0306	−0.749880	−0.374940	+	0.927049i	$0.622337\pi$
$458$	−19.5203	−0.912126
$459$	−5.60047	−0.261407
$460$	−6.80469	−0.317270
$461$	19.3403	0.900767	0.450383	−	0.892835i	$-0.351287\pi$
$461$	19.3403	0.900767	0.450383	+	0.892835i	$0.351287\pi$
$462$	0.546785	0.0254387
$463$	2.26727	0.105369	0.0526844	−	0.998611i	$-0.483222\pi$
$463$	2.26727	0.105369	0.0526844	+	0.998611i	$0.483222\pi$
$464$	9.97044	0.462866
$465$	−22.5694	−1.04663
$466$	9.34433	0.432868
$467$	24.3815	1.12824	0.564121	−	0.825692i	$-0.309215\pi$
$467$	24.3815	1.12824	0.564121	+	0.825692i	$0.309215\pi$
$468$	3.55638	0.164394
$469$	−5.18352	−0.239353
$470$	−8.40667	−0.387771
$471$	−2.81207	−0.129573
$472$	0.710808	0.0327176
$473$	−0.722542	−0.0332225
$474$	5.91658	0.271758
$475$	−16.2493	−0.745568
$476$	5.03729	0.230884
$477$	−3.51369	−0.160881
$478$	−20.5513	−0.939994
$479$	23.3231	1.06566	0.532831	−	0.846222i	$-0.321128\pi$
$479$	23.3231	1.06566	0.532831	+	0.846222i	$0.321128\pi$
$480$	−2.84976	−0.130073
$481$	7.72966	0.352442
$482$	−6.41466	−0.292180
$483$	28.2030	1.28328
$484$	−10.9899	−0.499540
$485$	−17.7199	−0.804619
$486$	−15.9863	−0.725153
$487$	11.4534	0.519005	0.259503	−	0.965742i	$-0.416441\pi$
$487$	11.4534	0.519005	0.259503	+	0.965742i	$0.416441\pi$
$488$	0.711142	0.0321919
$489$	10.8797	0.491995
$490$	−0.964830	−0.0435866
$491$	−18.5596	−0.837581	−0.418790	−	0.908083i	$-0.637546\pi$
$491$	−18.5596	−0.837581	−0.418790	+	0.908083i	$0.637546\pi$
$492$	−7.59010	−0.342188
$493$	−20.0663	−0.903741
$494$	−10.2521	−0.461264
$495$	0.226782	0.0101931
$496$	−7.91975	−0.355607
$497$	31.3535	1.40640
$498$	15.4813	0.693735
$499$	14.5750	0.652464	0.326232	−	0.945290i	$-0.394221\pi$
$499$	14.5750	0.652464	0.326232	+	0.945290i	$0.394221\pi$
$500$	10.8608	0.485712
$501$	−31.7089	−1.41665
$502$	−10.7601	−0.480246
$503$	35.3826	1.57763	0.788816	−	0.614629i	$-0.210694\pi$
$503$	35.3826	1.57763	0.788816	+	0.614629i	$0.210694\pi$
$504$	4.30252	0.191649
$505$	11.4916	0.511371
$506$	0.521643	0.0231899
$507$	18.9424	0.841261
$508$	−4.84397	−0.214917
$509$	18.7107	0.829337	0.414669	−	0.909972i	$-0.363897\pi$
$509$	18.7107	0.829337	0.414669	+	0.909972i	$0.363897\pi$
$510$	5.73536	0.253966
$511$	10.2219	0.452189
$512$	−1.00000	−0.0441942
$513$	13.7897	0.608831
$514$	−1.29400	−0.0570761
$515$	−13.2986	−0.586007
$516$	−15.6078	−0.687095
$517$	0.644450	0.0283429
$518$	9.35137	0.410875
$519$	40.6777	1.78555
$520$	2.71401	0.119017
$521$	−1.20896	−0.0529655	−0.0264827	−	0.999649i	$-0.508431\pi$
$521$	−1.20896	−0.0529655	−0.0264827	+	0.999649i	$0.508431\pi$
$522$	−17.1393	−0.750166
$523$	13.4025	0.586052	0.293026	−	0.956104i	$-0.405338\pi$
$523$	13.4025	0.586052	0.293026	+	0.956104i	$0.405338\pi$
$524$	5.91413	0.258360
$525$	−17.8287	−0.778108
$526$	7.04882	0.307343
$527$	15.9391	0.694319
$528$	0.218460	0.00950726
$529$	3.90621	0.169835
$530$	−2.68143	−0.116474
$531$	−1.22189	−0.0530254
$532$	−12.4030	−0.537740
$533$	7.22855	0.313103
$534$	−21.0070	−0.909064
$535$	−13.0250	−0.563121
$536$	−2.07100	−0.0894538
$537$	−35.6482	−1.53833
$538$	−26.9814	−1.16325
$539$	0.0739632	0.00318582
$540$	−3.65051	−0.157093
$541$	−41.9329	−1.80284	−0.901418	−	0.432950i	$-0.857472\pi$
$541$	−41.9329	−1.80284	−0.901418	+	0.432950i	$0.857472\pi$
$542$	1.38607	0.0595369
$543$	−35.1694	−1.50926
$544$	2.01258	0.0862886
$545$	21.1543	0.906153
$546$	−11.2486	−0.481396
$547$	−31.9661	−1.36677	−0.683385	−	0.730058i	$-0.739493\pi$
$547$	−31.9661	−1.36677	−0.683385	+	0.730058i	$0.739493\pi$
$548$	13.2312	0.565207
$549$	−1.22246	−0.0521733
$550$	−0.329759	−0.0140610
$551$	49.4081	2.10486
$552$	11.2681	0.479603
$553$	−6.81694	−0.289886
$554$	11.3658	0.482887
$555$	10.6473	0.451952
$556$	−5.31410	−0.225368
$557$	43.1997	1.83043	0.915215	−	0.402967i	$-0.132021\pi$
$557$	43.1997	1.83043	0.915215	+	0.402967i	$0.132021\pi$
$558$	13.6141	0.576332
$559$	14.8643	0.628694
$560$	3.28342	0.138750
$561$	−0.439669	−0.0185628
$562$	−9.12180	−0.384780
$563$	−13.9123	−0.586332	−0.293166	−	0.956062i	$-0.594709\pi$
$563$	−13.9123	−0.586332	−0.293166	+	0.956062i	$0.594709\pi$
$564$	13.9209	0.586176
$565$	15.3512	0.645830
$566$	−1.86684	−0.0784690
$567$	28.0376	1.17747
$568$	12.5268	0.525614
$569$	−11.1738	−0.468430	−0.234215	−	0.972185i	$-0.575252\pi$
$569$	−11.1738	−0.468430	−0.234215	+	0.972185i	$0.575252\pi$
$570$	−14.1219	−0.591499
$571$	−14.9473	−0.625523	−0.312762	−	0.949832i	$-0.601254\pi$
$571$	−14.9473	−0.625523	−0.312762	+	0.949832i	$0.601254\pi$
$572$	−0.208054	−0.00869918
$573$	54.1023	2.26016
$574$	8.74513	0.365015
$575$	−17.0089	−0.709320
$576$	1.71901	0.0716254
$577$	27.2187	1.13313	0.566566	−	0.824017i	$-0.308272\pi$
$577$	27.2187	1.13313	0.566566	+	0.824017i	$0.308272\pi$
$578$	12.9495	0.538629
$579$	36.8309	1.53064
$580$	−13.0797	−0.543103
$581$	−17.8372	−0.740012
$582$	29.3430	1.21631
$583$	0.205557	0.00851330
$584$	4.08400	0.168997
$585$	−4.66541	−0.192891
$586$	−5.28826	−0.218456
$587$	−10.4117	−0.429737	−0.214869	−	0.976643i	$-0.568932\pi$
$587$	−10.4117	−0.429737	−0.214869	+	0.976643i	$0.568932\pi$
$588$	1.59770	0.0658878
$589$	−39.2460	−1.61710
$590$	−0.932469	−0.0383892
$591$	−42.9797	−1.76795
$592$	3.73621	0.153557
$593$	−30.0513	−1.23406	−0.617030	−	0.786940i	$-0.711664\pi$
$593$	−30.0513	−1.23406	−0.617030	+	0.786940i	$0.711664\pi$
$594$	0.279845	0.0114822
$595$	−6.60814	−0.270907
$596$	−4.04539	−0.165706
$597$	21.9714	0.899231
$598$	−10.7314	−0.438839
$599$	12.5523	0.512873	0.256436	−	0.966561i	$-0.417452\pi$
$599$	12.5523	0.512873	0.256436	+	0.966561i	$0.417452\pi$
$600$	−7.12321	−0.290804
$601$	−31.2086	−1.27303	−0.636513	−	0.771266i	$-0.719624\pi$
$601$	−31.2086	−1.27303	−0.636513	+	0.771266i	$0.719624\pi$
$602$	17.9829	0.732929
$603$	3.56008	0.144978
$604$	3.91908	0.159465
$605$	14.4170	0.586135
$606$	−19.0294	−0.773017
$607$	−24.8789	−1.00980	−0.504901	−	0.863177i	$-0.668471\pi$
$607$	−24.8789	−1.00980	−0.504901	+	0.863177i	$0.668471\pi$
$608$	−4.95546	−0.200970
$609$	54.2106	2.19672
$610$	−0.932907	−0.0377723
$611$	−13.2578	−0.536353
$612$	−3.45964	−0.139848
$613$	30.6685	1.23869	0.619345	−	0.785119i	$-0.287398\pi$
$613$	30.6685	1.23869	0.619345	+	0.785119i	$0.287398\pi$
$614$	−27.5283	−1.11095
$615$	9.95703	0.401506
$616$	−0.251705	−0.0101415
$617$	30.5353	1.22930	0.614651	−	0.788799i	$-0.289297\pi$
$617$	30.5353	1.22930	0.614651	+	0.788799i	$0.289297\pi$
$618$	22.0216	0.885840
$619$	44.7812	1.79991	0.899954	−	0.435986i	$-0.143600\pi$
$619$	44.7812	1.79991	0.899954	+	0.435986i	$0.143600\pi$
$620$	10.3895	0.417252
$621$	14.4344	0.579231
$622$	−3.05641	−0.122551
$623$	24.2038	0.969705
$624$	−4.49422	−0.179913
$625$	2.14760	0.0859039
$626$	21.5109	0.859747
$627$	1.08257	0.0432337
$628$	1.29450	0.0516560
$629$	−7.51941	−0.299819
$630$	−5.64423	−0.224871
$631$	−30.4326	−1.21150	−0.605752	−	0.795653i	$-0.707128\pi$
$631$	−30.4326	−1.21150	−0.605752	+	0.795653i	$0.707128\pi$
$632$	−2.72361	−0.108340
$633$	54.7497	2.17611
$634$	5.45734	0.216739
$635$	6.35454	0.252172
$636$	4.44028	0.176069
$637$	−1.52159	−0.0602876
$638$	1.00268	0.0396964
$639$	−21.5338	−0.851862
$640$	1.31184	0.0518552
$641$	33.3018	1.31534	0.657671	−	0.753306i	$-0.271542\pi$
$641$	33.3018	1.31534	0.657671	+	0.753306i	$0.271542\pi$
$642$	21.5686	0.851245
$643$	−27.4330	−1.08185	−0.540926	−	0.841070i	$-0.681926\pi$
$643$	−27.4330	−1.08185	−0.540926	+	0.841070i	$0.681926\pi$
$644$	−12.9829	−0.511596
$645$	20.4750	0.806202
$646$	9.97326	0.392393
$647$	−26.7203	−1.05048	−0.525242	−	0.850953i	$-0.676025\pi$
$647$	−26.7203	−1.05048	−0.525242	+	0.850953i	$0.676025\pi$
$648$	11.2020	0.440057
$649$	0.0714825	0.00280593
$650$	6.78390	0.266086
$651$	−43.0607	−1.68768
$652$	−5.00829	−0.196140
$653$	17.2176	0.673776	0.336888	−	0.941545i	$-0.390626\pi$
$653$	17.2176	0.673776	0.336888	+	0.941545i	$0.390626\pi$
$654$	−35.0302	−1.36979
$655$	−7.75841	−0.303146
$656$	3.49399	0.136418
$657$	−7.02044	−0.273894
$658$	−16.0393	−0.625278
$659$	7.61250	0.296541	0.148270	−	0.988947i	$-0.452629\pi$
$659$	7.61250	0.296541	0.148270	+	0.988947i	$0.452629\pi$
$660$	−0.286586	−0.0111553
$661$	12.9707	0.504502	0.252251	−	0.967662i	$-0.418829\pi$
$661$	12.9707	0.504502	0.252251	+	0.967662i	$0.418829\pi$
$662$	10.4352	0.405575
$663$	9.04498	0.351278
$664$	−7.12661	−0.276566
$665$	16.2708	0.630956
$666$	−6.42258	−0.248870
$667$	51.7179	2.00252
$668$	14.5968	0.564765
$669$	−32.1075	−1.24135
$670$	2.71683	0.104960
$671$	0.0715160	0.00276084
$672$	−5.43713	−0.209742
$673$	39.5644	1.52509	0.762547	−	0.646932i	$-0.223948\pi$
$673$	39.5644	1.52509	0.762547	+	0.646932i	$0.223948\pi$
$674$	−28.2649	−1.08872
$675$	−9.12476	−0.351212
$676$	−8.71986	−0.335379
$677$	16.6832	0.641188	0.320594	−	0.947217i	$-0.396117\pi$
$677$	16.6832	0.641188	0.320594	+	0.947217i	$0.396117\pi$
$678$	−25.4206	−0.976272
$679$	−33.8083	−1.29744
$680$	−2.64019	−0.101247
$681$	22.0704	0.845741
$682$	−0.796450	−0.0304977
$683$	47.6884	1.82475	0.912373	−	0.409360i	$-0.134248\pi$
$683$	47.6884	1.82475	0.912373	+	0.409360i	$0.134248\pi$
$684$	8.51849	0.325712
$685$	−17.3572	−0.663185
$686$	−19.3611	−0.739212
$687$	−42.4046	−1.61784
$688$	7.18482	0.273919
$689$	−4.22877	−0.161103
$690$	−14.7820	−0.562742
$691$	47.1497	1.79366	0.896829	−	0.442377i	$-0.145865\pi$
$691$	47.1497	1.79366	0.896829	+	0.442377i	$0.145865\pi$
$692$	−18.7254	−0.711833
$693$	0.432683	0.0164363
$694$	−4.29931	−0.163200
$695$	6.97127	0.264435
$696$	21.6591	0.820985
$697$	−7.03194	−0.266354
$698$	15.7538	0.596291
$699$	20.2990	0.767777
$700$	8.20718	0.310202
$701$	18.2319	0.688610	0.344305	−	0.938858i	$-0.388115\pi$
$701$	18.2319	0.688610	0.344305	+	0.938858i	$0.388115\pi$
$702$	−5.75706	−0.217286
$703$	18.5146	0.698292
$704$	−0.100565	−0.00379019
$705$	−18.2621	−0.687789
$706$	32.0369	1.20573
$707$	21.9252	0.824582
$708$	1.54411	0.0580312
$709$	−30.6601	−1.15146	−0.575731	−	0.817639i	$-0.695283\pi$
$709$	−30.6601	−1.15146	−0.575731	+	0.817639i	$0.695283\pi$
$710$	−16.4333	−0.616729
$711$	4.68192	0.175586
$712$	9.67029	0.362410
$713$	−41.0807	−1.53848
$714$	10.9426	0.409518
$715$	0.272935	0.0102072
$716$	16.4101	0.613276
$717$	−44.6441	−1.66727
$718$	25.5931	0.955128
$719$	−6.05972	−0.225989	−0.112995	−	0.993596i	$-0.536044\pi$
$719$	−6.05972	−0.225989	−0.112995	+	0.993596i	$0.536044\pi$
$720$	−2.25507	−0.0840416
$721$	−25.3728	−0.944932
$722$	−5.55659	−0.206795
$723$	−13.9347	−0.518239
$724$	16.1897	0.601686
$725$	−32.6937	−1.21421
$726$	−23.8736	−0.886034
$727$	52.9498	1.96380	0.981901	−	0.189397i	$-0.0606534\pi$
$727$	52.9498	1.96380	0.981901	+	0.189397i	$0.0606534\pi$
$728$	5.17813	0.191914
$729$	−1.12140	−0.0415332
$730$	−5.35758	−0.198293
$731$	−14.4600	−0.534823
$732$	1.54483	0.0570987
$733$	−42.0710	−1.55393	−0.776965	−	0.629544i	$-0.783242\pi$
$733$	−42.0710	−1.55393	−0.776965	+	0.629544i	$0.783242\pi$
$734$	26.2220	0.967873
$735$	−2.09593	−0.0773094
$736$	−5.18712	−0.191200
$737$	−0.208271	−0.00767175
$738$	−6.00621	−0.221092
$739$	11.0290	0.405707	0.202853	−	0.979209i	$-0.434979\pi$
$739$	11.0290	0.405707	0.202853	+	0.979209i	$0.434979\pi$
$740$	−4.90132	−0.180176
$741$	−22.2709	−0.818144
$742$	−5.11598	−0.187814
$743$	14.0240	0.514489	0.257244	−	0.966346i	$-0.417185\pi$
$743$	14.0240	0.514489	0.257244	+	0.966346i	$0.417185\pi$
$744$	−17.2043	−0.630740
$745$	5.30692	0.194430
$746$	−36.7040	−1.34383
$747$	12.2507	0.448230
$748$	0.202395	0.00740030
$749$	−24.8508	−0.908029
$750$	23.5933	0.861506
$751$	34.0777	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$751$	34.0777	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$752$	−6.40829	−0.233686
$753$	−23.3744	−0.851811
$754$	−20.6274	−0.751204
$755$	−5.14123	−0.187108
$756$	−6.96491	−0.253311
$757$	−23.6972	−0.861290	−0.430645	−	0.902521i	$-0.641714\pi$
$757$	−23.6972	−0.861290	−0.430645	+	0.902521i	$0.641714\pi$
$758$	29.0002	1.05334
$759$	1.13318	0.0411318
$760$	6.50079	0.235808
$761$	4.04853	0.146759	0.0733795	−	0.997304i	$-0.476622\pi$
$761$	4.04853	0.146759	0.0733795	+	0.997304i	$0.476622\pi$
$762$	−10.5227	−0.381197
$763$	40.3610	1.46116
$764$	−24.9052	−0.901039
$765$	4.53851	0.164090
$766$	−25.2690	−0.913005
$767$	−1.47056	−0.0530987
$768$	−2.17233	−0.0783871
$769$	40.7296	1.46875	0.734374	−	0.678745i	$-0.237476\pi$
$769$	40.7296	1.46875	0.734374	+	0.678745i	$0.237476\pi$
$770$	0.330197	0.0118995
$771$	−2.81100	−0.101236
$772$	−16.9546	−0.610208
$773$	−21.4110	−0.770100	−0.385050	−	0.922896i	$-0.625816\pi$
$773$	−21.4110	−0.770100	−0.385050	+	0.922896i	$0.625816\pi$
$774$	−12.3508	−0.443940
$775$	25.9694	0.932848
$776$	−13.5076	−0.484895
$777$	20.3142	0.728769
$778$	6.33010	0.226945
$779$	17.3143	0.620351
$780$	5.89572	0.211101
$781$	1.25976	0.0450778
$782$	10.4395	0.373315
$783$	27.7451	0.991527
$784$	−0.735476	−0.0262670
$785$	−1.69818	−0.0606105
$786$	12.8474	0.458253
$787$	25.0065	0.891385	0.445693	−	0.895186i	$-0.352957\pi$
$787$	25.0065	0.891385	0.445693	+	0.895186i	$0.352957\pi$
$788$	19.7851	0.704815
$789$	15.3123	0.545134
$790$	3.57296	0.127120
$791$	29.2890	1.04140
$792$	0.172872	0.00614275
$793$	−1.47125	−0.0522455
$794$	13.9127	0.493742
$795$	−5.82495	−0.206590
$796$	−10.1142	−0.358490
$797$	−34.9899	−1.23940	−0.619702	−	0.784837i	$-0.712747\pi$
$797$	−34.9899	−1.23940	−0.619702	+	0.784837i	$0.712747\pi$
$798$	−26.9435	−0.953788
$799$	12.8972	0.456270
$800$	3.27907	0.115932
$801$	−16.6233	−0.587356
$802$	32.7694	1.15713
$803$	0.410708	0.0144936
$804$	−4.49890	−0.158664
$805$	17.0315	0.600281
$806$	16.3848	0.577130
$807$	−58.6125	−2.06326
$808$	8.75991	0.308173
$809$	−29.7270	−1.04515	−0.522573	−	0.852595i	$-0.675028\pi$
$809$	−29.7270	−1.04515	−0.522573	+	0.852595i	$0.675028\pi$
$810$	−14.6953	−0.516341
$811$	21.0565	0.739395	0.369697	−	0.929152i	$-0.379461\pi$
$811$	21.0565	0.739395	0.369697	+	0.929152i	$0.379461\pi$
$812$	−24.9550	−0.875751
$813$	3.01100	0.105600
$814$	0.375732	0.0131694
$815$	6.57010	0.230140
$816$	4.37198	0.153050
$817$	35.6041	1.24563
$818$	30.9075	1.08065
$819$	−8.90126	−0.311035
$820$	−4.58357	−0.160065
$821$	14.8753	0.519153	0.259577	−	0.965723i	$-0.416417\pi$
$821$	14.8753	0.519153	0.259577	+	0.965723i	$0.416417\pi$
$822$	28.7424	1.00251
$823$	37.0263	1.29066	0.645328	−	0.763906i	$-0.276721\pi$
$823$	37.0263	1.29066	0.645328	+	0.763906i	$0.276721\pi$
$824$	−10.1373	−0.353151
$825$	−0.716346	−0.0249400
$826$	−1.77908	−0.0619023
$827$	34.3635	1.19493	0.597467	−	0.801893i	$-0.296174\pi$
$827$	34.3635	1.19493	0.597467	+	0.801893i	$0.296174\pi$
$828$	8.91671	0.309877
$829$	−15.8069	−0.548996	−0.274498	−	0.961588i	$-0.588512\pi$
$829$	−15.8069	−0.548996	−0.274498	+	0.961588i	$0.588512\pi$
$830$	9.34900	0.324509
$831$	24.6903	0.856496
$832$	2.06885	0.0717245
$833$	1.48020	0.0512860
$834$	−11.5440	−0.399735
$835$	−19.1487	−0.662667
$836$	−0.498346	−0.0172357
$837$	−22.0385	−0.761763
$838$	−34.5512	−1.19355
$839$	37.3168	1.28832	0.644159	−	0.764891i	$-0.277207\pi$
$839$	37.3168	1.28832	0.644159	+	0.764891i	$0.277207\pi$
$840$	7.13266	0.246100
$841$	70.4097	2.42792
$842$	−10.0270	−0.345554
$843$	−19.8155	−0.682483
$844$	−25.2032	−0.867532
$845$	11.4391	0.393517
$846$	11.0159	0.378735
$847$	27.5066	0.945139
$848$	−2.04402	−0.0701919
$849$	−4.05538	−0.139180
$850$	−6.59938	−0.226357
$851$	19.3802	0.664343
$852$	27.2124	0.932282
$853$	−39.4222	−1.34979	−0.674895	−	0.737914i	$-0.735811\pi$
$853$	−39.4222	−1.34979	−0.674895	+	0.737914i	$0.735811\pi$
$854$	−1.77992	−0.0609076
$855$	−11.1749	−0.382174
$856$	−9.92879	−0.339359
$857$	−46.8985	−1.60202	−0.801012	−	0.598648i	$-0.795705\pi$
$857$	−46.8985	−1.60202	−0.801012	+	0.598648i	$0.795705\pi$
$858$	−0.451962	−0.0154297
$859$	21.0160	0.717055	0.358528	−	0.933519i	$-0.383279\pi$
$859$	21.0160	0.717055	0.358528	+	0.933519i	$0.383279\pi$
$860$	−9.42537	−0.321402
$861$	18.9973	0.647426
$862$	−12.7690	−0.434914
$863$	1.99957	0.0680661	0.0340331	−	0.999421i	$-0.489165\pi$
$863$	1.99957	0.0680661	0.0340331	+	0.999421i	$0.489165\pi$
$864$	−2.78273	−0.0946704
$865$	24.5648	0.835229
$866$	−7.62871	−0.259234
$867$	28.1306	0.955366
$868$	19.8224	0.672815
$869$	−0.273900	−0.00929143
$870$	−28.4133	−0.963302
$871$	4.28460	0.145178
$872$	16.1257	0.546084
$873$	23.2197	0.785869
$874$	−25.7046	−0.869470
$875$	−27.1836	−0.918975
$876$	8.87180	0.299750
$877$	−29.4135	−0.993224	−0.496612	−	0.867973i	$-0.665423\pi$
$877$	−29.4135	−0.993224	−0.496612	+	0.867973i	$0.665423\pi$
$878$	0.892723	0.0301279
$879$	−11.4878	−0.387475
$880$	0.131926	0.00444721
$881$	6.76250	0.227834	0.113917	−	0.993490i	$-0.463660\pi$
$881$	6.76250	0.227834	0.113917	+	0.993490i	$0.463660\pi$
$882$	1.26429	0.0425709
$883$	−14.9701	−0.503782	−0.251891	−	0.967756i	$-0.581053\pi$
$883$	−14.9701	−0.503782	−0.251891	+	0.967756i	$0.581053\pi$
$884$	−4.16373	−0.140041
$885$	−2.02563	−0.0680908
$886$	−25.6792	−0.862709
$887$	−26.0458	−0.874534	−0.437267	−	0.899332i	$-0.644053\pi$
$887$	−26.0458	−0.874534	−0.437267	+	0.899332i	$0.644053\pi$
$888$	8.11627	0.272364
$889$	12.1240	0.406626
$890$	−12.6859	−0.425233
$891$	1.12653	0.0377403
$892$	14.7802	0.494879
$893$	−31.7560	−1.06267
$894$	−8.78791	−0.293912
$895$	−21.5275	−0.719587
$896$	2.50290	0.0836161
$897$	−23.3121	−0.778368
$898$	−26.4059	−0.881177
$899$	−78.9634	−2.63358
$900$	−5.63675	−0.187892
$901$	4.11375	0.137049
$902$	0.351374	0.0116995
$903$	39.0648	1.29999
$904$	11.7020	0.389203
$905$	−21.2384	−0.705988
$906$	8.51354	0.282843
$907$	38.2589	1.27036	0.635182	−	0.772362i	$-0.280925\pi$
$907$	38.2589	1.27036	0.635182	+	0.772362i	$0.280925\pi$
$908$	−10.1598	−0.337165
$909$	−15.0584	−0.499455
$910$	−6.79290	−0.225183
$911$	17.7130	0.586859	0.293430	−	0.955981i	$-0.405203\pi$
$911$	17.7130	0.586859	0.293430	+	0.955981i	$0.405203\pi$
$912$	−10.7649	−0.356461
$913$	−0.716688	−0.0237189
$914$	16.0306	0.530245
$915$	−2.02658	−0.0669967
$916$	19.5203	0.644970
$917$	−14.8025	−0.488821
$918$	5.60047	0.184843
$919$	−58.4634	−1.92853	−0.964264	−	0.264942i	$-0.914647\pi$
$919$	−58.4634	−1.92853	−0.964264	+	0.264942i	$0.914647\pi$
$920$	6.80469	0.224344
$921$	−59.8006	−1.97050
$922$	−19.3403	−0.636938
$923$	−25.9162	−0.853041
$924$	−0.546785	−0.0179879
$925$	−12.2513	−0.402819
$926$	−2.26727	−0.0745070
$927$	17.4262	0.572351
$928$	−9.97044	−0.327296
$929$	47.1093	1.54561	0.772803	−	0.634646i	$-0.218854\pi$
$929$	47.1093	1.54561	0.772803	+	0.634646i	$0.218854\pi$
$930$	22.5694	0.740078
$931$	−3.64462	−0.119448
$932$	−9.34433	−0.306084
$933$	−6.63953	−0.217368
$934$	−24.3815	−0.797788
$935$	−0.265511	−0.00868313
$936$	−3.55638	−0.116244
$937$	16.6377	0.543530	0.271765	−	0.962364i	$-0.412393\pi$
$937$	16.6377	0.543530	0.271765	+	0.962364i	$0.412393\pi$
$938$	5.18352	0.169248
$939$	46.7287	1.52493
$940$	8.40667	0.274195
$941$	46.3653	1.51146	0.755732	−	0.654881i	$-0.227281\pi$
$941$	46.3653	1.51146	0.755732	+	0.654881i	$0.227281\pi$
$942$	2.81207	0.0916222
$943$	18.1238	0.590191
$944$	−0.710808	−0.0231348
$945$	9.13687	0.297222
$946$	0.722542	0.0234919
$947$	49.7566	1.61687	0.808436	−	0.588585i	$-0.200315\pi$
$947$	49.7566	1.61687	0.808436	+	0.588585i	$0.200315\pi$
$948$	−5.91658	−0.192162
$949$	−8.44920	−0.274273
$950$	16.2493	0.527196
$951$	11.8551	0.384429
$952$	−5.03729	−0.163260
$953$	−53.0218	−1.71754	−0.858772	−	0.512358i	$-0.828772\pi$
$953$	−53.0218	−1.71754	−0.858772	+	0.512358i	$0.828772\pi$
$954$	3.51369	0.113760
$955$	32.6718	1.05723
$956$	20.5513	0.664676
$957$	2.17815	0.0704094
$958$	−23.3231	−0.753536
$959$	−33.1163	−1.06938
$960$	2.84976	0.0919755
$961$	31.7225	1.02331
$962$	−7.72966	−0.249214
$963$	17.0677	0.549999
$964$	6.41466	0.206602
$965$	22.2417	0.715987
$966$	−28.2030	−0.907418
$967$	−31.5421	−1.01433	−0.507163	−	0.861850i	$-0.669306\pi$
$967$	−31.5421	−1.01433	−0.507163	+	0.861850i	$0.669306\pi$
$968$	10.9899	0.353228
$969$	21.6652	0.695986
$970$	17.7199	0.568951
$971$	35.8122	1.14927	0.574634	−	0.818410i	$-0.305144\pi$
$971$	35.8122	1.14927	0.574634	+	0.818410i	$0.305144\pi$
$972$	15.9863	0.512761
$973$	13.3007	0.426400
$974$	−11.4534	−0.366992
$975$	14.7369	0.471957
$976$	−0.711142	−0.0227631
$977$	−0.0185896	−0.000594735 0	−0.000297368	−	1.00000i	$-0.500095\pi$
$977$	−0.0185896	−0.000594735 0	−0.000297368		1.00000i	$0.500095\pi$
$978$	−10.8797	−0.347893
$979$	0.972493	0.0310810
$980$	0.964830	0.0308203
$981$	−27.7202	−0.885037
$982$	18.5596	0.592259
$983$	11.2924	0.360172	0.180086	−	0.983651i	$-0.442362\pi$
$983$	11.2924	0.360172	0.180086	+	0.983651i	$0.442362\pi$
$984$	7.59010	0.241964
$985$	−25.9550	−0.826994
$986$	20.0663	0.639041
$987$	−34.8427	−1.10905
$988$	10.2521	0.326163
$989$	37.2685	1.18507
$990$	−0.226782	−0.00720759
$991$	20.6817	0.656974	0.328487	−	0.944508i	$-0.393461\pi$
$991$	20.6817	0.656974	0.328487	+	0.944508i	$0.393461\pi$
$992$	7.91975	0.251452
$993$	22.6686	0.719367
$994$	−31.3535	−0.994472
$995$	13.2683	0.420633
$996$	−15.4813	−0.490545
$997$	28.7917	0.911842	0.455921	−	0.890020i	$-0.349310\pi$
$997$	28.7917	0.911842	0.455921	+	0.890020i	$0.349310\pi$
$998$	−14.5750	−0.461362
$999$	10.3969	0.328942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.14	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.14	✓	77	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.17233 q^{3} +1.00000 q^{4} -1.31184 q^{5} +2.17233 q^{6} -2.50290 q^{7} -1.00000 q^{8} +1.71901 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.17233 q^{3} +1.00000 q^{4} -1.31184 q^{5} +2.17233 q^{6} -2.50290 q^{7} -1.00000 q^{8} +1.71901 q^{9} +1.31184 q^{10} -0.100565 q^{11} -2.17233 q^{12} +2.06885 q^{13} +2.50290 q^{14} +2.84976 q^{15} +1.00000 q^{16} -2.01258 q^{17} -1.71901 q^{18} +4.95546 q^{19} -1.31184 q^{20} +5.43713 q^{21} +0.100565 q^{22} +5.18712 q^{23} +2.17233 q^{24} -3.27907 q^{25} -2.06885 q^{26} +2.78273 q^{27} -2.50290 q^{28} +9.97044 q^{29} -2.84976 q^{30} -7.91975 q^{31} -1.00000 q^{32} +0.218460 q^{33} +2.01258 q^{34} +3.28342 q^{35} +1.71901 q^{36} +3.73621 q^{37} -4.95546 q^{38} -4.49422 q^{39} +1.31184 q^{40} +3.49399 q^{41} -5.43713 q^{42} +7.18482 q^{43} -0.100565 q^{44} -2.25507 q^{45} -5.18712 q^{46} -6.40829 q^{47} -2.17233 q^{48} -0.735476 q^{49} +3.27907 q^{50} +4.37198 q^{51} +2.06885 q^{52} -2.04402 q^{53} -2.78273 q^{54} +0.131926 q^{55} +2.50290 q^{56} -10.7649 q^{57} -9.97044 q^{58} -0.710808 q^{59} +2.84976 q^{60} -0.711142 q^{61} +7.91975 q^{62} -4.30252 q^{63} +1.00000 q^{64} -2.71401 q^{65} -0.218460 q^{66} +2.07100 q^{67} -2.01258 q^{68} -11.2681 q^{69} -3.28342 q^{70} -12.5268 q^{71} -1.71901 q^{72} -4.08400 q^{73} -3.73621 q^{74} +7.12321 q^{75} +4.95546 q^{76} +0.251705 q^{77} +4.49422 q^{78} +2.72361 q^{79} -1.31184 q^{80} -11.2020 q^{81} -3.49399 q^{82} +7.12661 q^{83} +5.43713 q^{84} +2.64019 q^{85} -7.18482 q^{86} -21.6591 q^{87} +0.100565 q^{88} -9.67029 q^{89} +2.25507 q^{90} -5.17813 q^{91} +5.18712 q^{92} +17.2043 q^{93} +6.40829 q^{94} -6.50079 q^{95} +2.17233 q^{96} +13.5076 q^{97} +0.735476 q^{98} -0.172872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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