LMFDB - Embedded newform 4334.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.89563 q^{3} +1.00000 q^{4} -0.0366624 q^{5} -2.89563 q^{6} -1.61517 q^{7} +1.00000 q^{8} +5.38466 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.89563 q^{3} +1.00000 q^{4} -0.0366624 q^{5} -2.89563 q^{6} -1.61517 q^{7} +1.00000 q^{8} +5.38466 q^{9} -0.0366624 q^{10} +1.00000 q^{11} -2.89563 q^{12} -5.29026 q^{13} -1.61517 q^{14} +0.106161 q^{15} +1.00000 q^{16} +5.19356 q^{17} +5.38466 q^{18} +3.33946 q^{19} -0.0366624 q^{20} +4.67694 q^{21} +1.00000 q^{22} +0.572013 q^{23} -2.89563 q^{24} -4.99866 q^{25} -5.29026 q^{26} -6.90508 q^{27} -1.61517 q^{28} -2.41166 q^{29} +0.106161 q^{30} -1.42180 q^{31} +1.00000 q^{32} -2.89563 q^{33} +5.19356 q^{34} +0.0592162 q^{35} +5.38466 q^{36} -0.842186 q^{37} +3.33946 q^{38} +15.3186 q^{39} -0.0366624 q^{40} -2.39910 q^{41} +4.67694 q^{42} -7.42820 q^{43} +1.00000 q^{44} -0.197415 q^{45} +0.572013 q^{46} +0.875128 q^{47} -2.89563 q^{48} -4.39121 q^{49} -4.99866 q^{50} -15.0386 q^{51} -5.29026 q^{52} +3.44347 q^{53} -6.90508 q^{54} -0.0366624 q^{55} -1.61517 q^{56} -9.66983 q^{57} -2.41166 q^{58} +14.4156 q^{59} +0.106161 q^{60} +9.81506 q^{61} -1.42180 q^{62} -8.69716 q^{63} +1.00000 q^{64} +0.193954 q^{65} -2.89563 q^{66} -7.16080 q^{67} +5.19356 q^{68} -1.65634 q^{69} +0.0592162 q^{70} +3.51474 q^{71} +5.38466 q^{72} -7.13783 q^{73} -0.842186 q^{74} +14.4742 q^{75} +3.33946 q^{76} -1.61517 q^{77} +15.3186 q^{78} +7.52662 q^{79} -0.0366624 q^{80} +3.84055 q^{81} -2.39910 q^{82} +8.26670 q^{83} +4.67694 q^{84} -0.190408 q^{85} -7.42820 q^{86} +6.98327 q^{87} +1.00000 q^{88} +0.838636 q^{89} -0.197415 q^{90} +8.54469 q^{91} +0.572013 q^{92} +4.11701 q^{93} +0.875128 q^{94} -0.122433 q^{95} -2.89563 q^{96} -15.4349 q^{97} -4.39121 q^{98} +5.38466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) $ 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * 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
$3$	−2.89563	−1.67179	−0.835896	−	0.548889i	$-0.815051\pi$
$3$	−2.89563	−1.67179	−0.835896	+	0.548889i	$0.815051\pi$
$4$	1.00000	0.500000
$5$	−0.0366624	−0.0163959	−0.00819797	−	0.999966i	$-0.502610\pi$
$5$	−0.0366624	−0.0163959	−0.00819797	+	0.999966i	$0.502610\pi$
$6$	−2.89563	−1.18213
$7$	−1.61517	−0.610479	−0.305239	−	0.952276i	$-0.598736\pi$
$7$	−1.61517	−0.610479	−0.305239	+	0.952276i	$0.598736\pi$
$8$	1.00000	0.353553
$9$	5.38466	1.79489
$10$	−0.0366624	−0.0115937
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.89563	−0.835896
$13$	−5.29026	−1.46725	−0.733626	−	0.679553i	$-0.762174\pi$
$13$	−5.29026	−1.46725	−0.733626	+	0.679553i	$0.762174\pi$
$14$	−1.61517	−0.431674
$15$	0.106161	0.0274106
$16$	1.00000	0.250000
$17$	5.19356	1.25962	0.629811	−	0.776748i	$-0.283132\pi$
$17$	5.19356	1.25962	0.629811	+	0.776748i	$0.283132\pi$
$18$	5.38466	1.26918
$19$	3.33946	0.766125	0.383062	−	0.923722i	$-0.374869\pi$
$19$	3.33946	0.766125	0.383062	+	0.923722i	$0.374869\pi$
$20$	−0.0366624	−0.00819797
$21$	4.67694	1.02059
$22$	1.00000	0.213201
$23$	0.572013	0.119273	0.0596365	−	0.998220i	$-0.481006\pi$
$23$	0.572013	0.119273	0.0596365	+	0.998220i	$0.481006\pi$
$24$	−2.89563	−0.591067
$25$	−4.99866	−0.999731
$26$	−5.29026	−1.03750
$27$	−6.90508	−1.32888
$28$	−1.61517	−0.305239
$29$	−2.41166	−0.447834	−0.223917	−	0.974608i	$-0.571884\pi$
$29$	−2.41166	−0.447834	−0.223917	+	0.974608i	$0.571884\pi$
$30$	0.106161	0.0193822
$31$	−1.42180	−0.255363	−0.127682	−	0.991815i	$-0.540754\pi$
$31$	−1.42180	−0.255363	−0.127682	+	0.991815i	$0.540754\pi$
$32$	1.00000	0.176777
$33$	−2.89563	−0.504064
$34$	5.19356	0.890687
$35$	0.0592162	0.0100094
$36$	5.38466	0.897443
$37$	−0.842186	−0.138455	−0.0692273	−	0.997601i	$-0.522053\pi$
$37$	−0.842186	−0.138455	−0.0692273	+	0.997601i	$0.522053\pi$
$38$	3.33946	0.541732
$39$	15.3186	2.45294
$40$	−0.0366624	−0.00579684
$41$	−2.39910	−0.374676	−0.187338	−	0.982296i	$-0.559986\pi$
$41$	−2.39910	−0.374676	−0.187338	+	0.982296i	$0.559986\pi$
$42$	4.67694	0.721668
$43$	−7.42820	−1.13279	−0.566395	−	0.824134i	$-0.691662\pi$
$43$	−7.42820	−1.13279	−0.566395	+	0.824134i	$0.691662\pi$
$44$	1.00000	0.150756
$45$	−0.197415	−0.0294288
$46$	0.572013	0.0843388
$47$	0.875128	0.127650	0.0638252	−	0.997961i	$-0.479670\pi$
$47$	0.875128	0.127650	0.0638252	+	0.997961i	$0.479670\pi$
$48$	−2.89563	−0.417948
$49$	−4.39121	−0.627316
$50$	−4.99866	−0.706917
$51$	−15.0386	−2.10583
$52$	−5.29026	−0.733626
$53$	3.44347	0.472998	0.236499	−	0.971632i	$-0.424000\pi$
$53$	3.44347	0.472998	0.236499	+	0.971632i	$0.424000\pi$
$54$	−6.90508	−0.939662
$55$	−0.0366624	−0.00494356
$56$	−1.61517	−0.215837
$57$	−9.66983	−1.28080
$58$	−2.41166	−0.316666
$59$	14.4156	1.87675	0.938374	−	0.345621i	$-0.112332\pi$
$59$	14.4156	1.87675	0.938374	+	0.345621i	$0.112332\pi$
$60$	0.106161	0.0137053
$61$	9.81506	1.25669	0.628345	−	0.777935i	$-0.283733\pi$
$61$	9.81506	1.25669	0.628345	+	0.777935i	$0.283733\pi$
$62$	−1.42180	−0.180569
$63$	−8.69716	−1.09574
$64$	1.00000	0.125000
$65$	0.193954	0.0240570
$66$	−2.89563	−0.356427
$67$	−7.16080	−0.874831	−0.437415	−	0.899260i	$-0.644106\pi$
$67$	−7.16080	−0.874831	−0.437415	+	0.899260i	$0.644106\pi$
$68$	5.19356	0.629811
$69$	−1.65634	−0.199400
$70$	0.0592162	0.00707769
$71$	3.51474	0.417123	0.208561	−	0.978009i	$-0.433122\pi$
$71$	3.51474	0.417123	0.208561	+	0.978009i	$0.433122\pi$
$72$	5.38466	0.634588
$73$	−7.13783	−0.835420	−0.417710	−	0.908580i	$-0.637167\pi$
$73$	−7.13783	−0.835420	−0.417710	+	0.908580i	$0.637167\pi$
$74$	−0.842186	−0.0979021
$75$	14.4742	1.67134
$76$	3.33946	0.383062
$77$	−1.61517	−0.184066
$78$	15.3186	1.73449
$79$	7.52662	0.846811	0.423406	−	0.905940i	$-0.360835\pi$
$79$	7.52662	0.846811	0.423406	+	0.905940i	$0.360835\pi$
$80$	−0.0366624	−0.00409898
$81$	3.84055	0.426728
$82$	−2.39910	−0.264936
$83$	8.26670	0.907388	0.453694	−	0.891158i	$-0.350106\pi$
$83$	8.26670	0.907388	0.453694	+	0.891158i	$0.350106\pi$
$84$	4.67694	0.510296
$85$	−0.190408	−0.0206527
$86$	−7.42820	−0.801003
$87$	6.98327	0.748685
$88$	1.00000	0.106600
$89$	0.838636	0.0888952	0.0444476	−	0.999012i	$-0.485847\pi$
$89$	0.838636	0.0888952	0.0444476	+	0.999012i	$0.485847\pi$
$90$	−0.197415	−0.0208093
$91$	8.54469	0.895726
$92$	0.572013	0.0596365
$93$	4.11701	0.426914
$94$	0.875128	0.0902625
$95$	−0.122433	−0.0125613
$96$	−2.89563	−0.295534
$97$	−15.4349	−1.56718	−0.783589	−	0.621279i	$-0.786613\pi$
$97$	−15.4349	−1.56718	−0.783589	+	0.621279i	$0.786613\pi$
$98$	−4.39121	−0.443579
$99$	5.38466	0.541178
$100$	−4.99866	−0.499866
$101$	−1.72819	−0.171962	−0.0859808	−	0.996297i	$-0.527402\pi$
$101$	−1.72819	−0.171962	−0.0859808	+	0.996297i	$0.527402\pi$
$102$	−15.0386	−1.48904
$103$	13.9823	1.37771	0.688857	−	0.724897i	$-0.258113\pi$
$103$	13.9823	1.37771	0.688857	+	0.724897i	$0.258113\pi$
$104$	−5.29026	−0.518752
$105$	−0.171468	−0.0167336
$106$	3.44347	0.334460
$107$	13.3440	1.29001	0.645006	−	0.764177i	$-0.276855\pi$
$107$	13.3440	1.29001	0.645006	+	0.764177i	$0.276855\pi$
$108$	−6.90508	−0.664441
$109$	−7.52588	−0.720848	−0.360424	−	0.932789i	$-0.617368\pi$
$109$	−7.52588	−0.720848	−0.360424	+	0.932789i	$0.617368\pi$
$110$	−0.0366624	−0.00349562
$111$	2.43866	0.231467
$112$	−1.61517	−0.152620
$113$	−3.02798	−0.284848	−0.142424	−	0.989806i	$-0.545490\pi$
$113$	−3.02798	−0.284848	−0.142424	+	0.989806i	$0.545490\pi$
$114$	−9.66983	−0.905663
$115$	−0.0209714	−0.00195559
$116$	−2.41166	−0.223917
$117$	−28.4862	−2.63355
$118$	14.4156	1.32706
$119$	−8.38850	−0.768972
$120$	0.106161	0.00969110
$121$	1.00000	0.0909091
$122$	9.81506	0.888614
$123$	6.94688	0.626379
$124$	−1.42180	−0.127682
$125$	0.366575	0.0327875
$126$	−8.69716	−0.774805
$127$	−5.87694	−0.521494	−0.260747	−	0.965407i	$-0.583969\pi$
$127$	−5.87694	−0.521494	−0.260747	+	0.965407i	$0.583969\pi$
$128$	1.00000	0.0883883
$129$	21.5093	1.89379
$130$	0.193954	0.0170109
$131$	7.33099	0.640512	0.320256	−	0.947331i	$-0.396231\pi$
$131$	7.33099	0.640512	0.320256	+	0.947331i	$0.396231\pi$
$132$	−2.89563	−0.252032
$133$	−5.39381	−0.467703
$134$	−7.16080	−0.618599
$135$	0.253157	0.0217883
$136$	5.19356	0.445344
$137$	17.1480	1.46505	0.732525	−	0.680740i	$-0.238342\pi$
$137$	17.1480	1.46505	0.732525	+	0.680740i	$0.238342\pi$
$138$	−1.65634	−0.140997
$139$	19.8532	1.68393	0.841965	−	0.539532i	$-0.181399\pi$
$139$	19.8532	1.68393	0.841965	+	0.539532i	$0.181399\pi$
$140$	0.0592162	0.00500468
$141$	−2.53404	−0.213405
$142$	3.51474	0.294950
$143$	−5.29026	−0.442393
$144$	5.38466	0.448721
$145$	0.0884173	0.00734265
$146$	−7.13783	−0.590731
$147$	12.7153	1.04874
$148$	−0.842186	−0.0692273
$149$	9.93640	0.814022	0.407011	−	0.913423i	$-0.366571\pi$
$149$	9.93640	0.814022	0.407011	+	0.913423i	$0.366571\pi$
$150$	14.4742	1.18182
$151$	6.77066	0.550988	0.275494	−	0.961303i	$-0.411159\pi$
$151$	6.77066	0.550988	0.275494	+	0.961303i	$0.411159\pi$
$152$	3.33946	0.270866
$153$	27.9655	2.26088
$154$	−1.61517	−0.130154
$155$	0.0521267	0.00418692
$156$	15.3186	1.22647
$157$	11.3126	0.902840	0.451420	−	0.892312i	$-0.350918\pi$
$157$	11.3126	0.902840	0.451420	+	0.892312i	$0.350918\pi$
$158$	7.52662	0.598786
$159$	−9.97102	−0.790753
$160$	−0.0366624	−0.00289842
$161$	−0.923902	−0.0728136
$162$	3.84055	0.301742
$163$	2.31205	0.181093	0.0905467	−	0.995892i	$-0.471139\pi$
$163$	2.31205	0.181093	0.0905467	+	0.995892i	$0.471139\pi$
$164$	−2.39910	−0.187338
$165$	0.106161	0.00826460
$166$	8.26670	0.641620
$167$	−2.96046	−0.229087	−0.114544	−	0.993418i	$-0.536541\pi$
$167$	−2.96046	−0.229087	−0.114544	+	0.993418i	$0.536541\pi$
$168$	4.67694	0.360834
$169$	14.9868	1.15283
$170$	−0.190408	−0.0146036
$171$	17.9819	1.37511
$172$	−7.42820	−0.566395
$173$	24.3336	1.85005	0.925024	−	0.379907i	$-0.124044\pi$
$173$	24.3336	1.85005	0.925024	+	0.379907i	$0.124044\pi$
$174$	6.98327	0.529400
$175$	8.07370	0.610314
$176$	1.00000	0.0753778
$177$	−41.7421	−3.13753
$178$	0.838636	0.0628584
$179$	3.84606	0.287468	0.143734	−	0.989616i	$-0.454089\pi$
$179$	3.84606	0.287468	0.143734	+	0.989616i	$0.454089\pi$
$180$	−0.197415	−0.0147144
$181$	−2.33731	−0.173731	−0.0868653	−	0.996220i	$-0.527685\pi$
$181$	−2.33731	−0.173731	−0.0868653	+	0.996220i	$0.527685\pi$
$182$	8.54469	0.633374
$183$	−28.4208	−2.10092
$184$	0.572013	0.0421694
$185$	0.0308766	0.00227009
$186$	4.11701	0.301874
$187$	5.19356	0.379790
$188$	0.875128	0.0638252
$189$	11.1529	0.811254
$190$	−0.122433	−0.00888220
$191$	5.58866	0.404381	0.202191	−	0.979346i	$-0.435194\pi$
$191$	5.58866	0.404381	0.202191	+	0.979346i	$0.435194\pi$
$192$	−2.89563	−0.208974
$193$	−6.60397	−0.475364	−0.237682	−	0.971343i	$-0.576388\pi$
$193$	−6.60397	−0.475364	−0.237682	+	0.971343i	$0.576388\pi$
$194$	−15.4349	−1.10816
$195$	−0.561617	−0.0402182
$196$	−4.39121	−0.313658
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	5.38466	0.382671
$199$	−4.61305	−0.327010	−0.163505	−	0.986542i	$-0.552280\pi$
$199$	−4.61305	−0.327010	−0.163505	+	0.986542i	$0.552280\pi$
$200$	−4.99866	−0.353458
$201$	20.7350	1.46253
$202$	−1.72819	−0.121595
$203$	3.89525	0.273393
$204$	−15.0386	−1.05291
$205$	0.0879566	0.00614316
$206$	13.9823	0.974191
$207$	3.08010	0.214081
$208$	−5.29026	−0.366813
$209$	3.33946	0.230995
$210$	−0.171468	−0.0118324
$211$	2.40573	0.165618	0.0828088	−	0.996565i	$-0.473611\pi$
$211$	2.40573	0.165618	0.0828088	+	0.996565i	$0.473611\pi$
$212$	3.44347	0.236499
$213$	−10.1774	−0.697342
$214$	13.3440	0.912177
$215$	0.272336	0.0185731
$216$	−6.90508	−0.469831
$217$	2.29646	0.155894
$218$	−7.52588	−0.509717
$219$	20.6685	1.39665
$220$	−0.0366624	−0.00247178
$221$	−27.4752	−1.84818
$222$	2.43866	0.163672
$223$	−13.8656	−0.928507	−0.464254	−	0.885702i	$-0.653677\pi$
$223$	−13.8656	−0.928507	−0.464254	+	0.885702i	$0.653677\pi$
$224$	−1.61517	−0.107918
$225$	−26.9160	−1.79440
$226$	−3.02798	−0.201418
$227$	4.11905	0.273391	0.136695	−	0.990613i	$-0.456352\pi$
$227$	4.11905	0.273391	0.136695	+	0.990613i	$0.456352\pi$
$228$	−9.66983	−0.640400
$229$	12.2887	0.812063	0.406031	−	0.913859i	$-0.366912\pi$
$229$	12.2887	0.812063	0.406031	+	0.913859i	$0.366912\pi$
$230$	−0.0209714	−0.00138281
$231$	4.67694	0.307720
$232$	−2.41166	−0.158333
$233$	1.52642	0.0999992	0.0499996	−	0.998749i	$-0.484078\pi$
$233$	1.52642	0.0999992	0.0499996	+	0.998749i	$0.484078\pi$
$234$	−28.4862	−1.86220
$235$	−0.0320843	−0.00209295
$236$	14.4156	0.938374
$237$	−21.7943	−1.41569
$238$	−8.38850	−0.543746
$239$	5.03728	0.325835	0.162917	−	0.986640i	$-0.447910\pi$
$239$	5.03728	0.325835	0.162917	+	0.986640i	$0.447910\pi$
$240$	0.106161	0.00685264
$241$	4.89207	0.315126	0.157563	−	0.987509i	$-0.449636\pi$
$241$	4.89207	0.315126	0.157563	+	0.987509i	$0.449636\pi$
$242$	1.00000	0.0642824
$243$	9.59441	0.615482
$244$	9.81506	0.628345
$245$	0.160992	0.0102854
$246$	6.94688	0.442917
$247$	−17.6666	−1.12410
$248$	−1.42180	−0.0902845
$249$	−23.9373	−1.51696
$250$	0.366575	0.0231842
$251$	−6.91693	−0.436593	−0.218296	−	0.975882i	$-0.570050\pi$
$251$	−6.91693	−0.436593	−0.218296	+	0.975882i	$0.570050\pi$
$252$	−8.69716	−0.547870
$253$	0.572013	0.0359622
$254$	−5.87694	−0.368752
$255$	0.551351	0.0345270
$256$	1.00000	0.0625000
$257$	9.31154	0.580838	0.290419	−	0.956900i	$-0.406205\pi$
$257$	9.31154	0.580838	0.290419	+	0.956900i	$0.406205\pi$
$258$	21.5093	1.33911
$259$	1.36028	0.0845235
$260$	0.193954	0.0120285
$261$	−12.9860	−0.803811
$262$	7.33099	0.452910
$263$	0.386298	0.0238201	0.0119101	−	0.999929i	$-0.496209\pi$
$263$	0.386298	0.0238201	0.0119101	+	0.999929i	$0.496209\pi$
$264$	−2.89563	−0.178214
$265$	−0.126246	−0.00775524
$266$	−5.39381	−0.330716
$267$	−2.42838	−0.148614
$268$	−7.16080	−0.437415
$269$	23.2522	1.41771	0.708857	−	0.705352i	$-0.249211\pi$
$269$	23.2522	1.41771	0.708857	+	0.705352i	$0.249211\pi$
$270$	0.253157	0.0154066
$271$	10.0629	0.611275	0.305638	−	0.952148i	$-0.401130\pi$
$271$	10.0629	0.611275	0.305638	+	0.952148i	$0.401130\pi$
$272$	5.19356	0.314906
$273$	−24.7422	−1.49747
$274$	17.1480	1.03595
$275$	−4.99866	−0.301430
$276$	−1.65634	−0.0996998
$277$	−12.1137	−0.727840	−0.363920	−	0.931430i	$-0.618562\pi$
$277$	−12.1137	−0.727840	−0.363920	+	0.931430i	$0.618562\pi$
$278$	19.8532	1.19072
$279$	−7.65591	−0.458348
$280$	0.0592162	0.00353884
$281$	6.98928	0.416946	0.208473	−	0.978028i	$-0.433151\pi$
$281$	6.98928	0.416946	0.208473	+	0.978028i	$0.433151\pi$
$282$	−2.53404	−0.150900
$283$	5.16924	0.307279	0.153640	−	0.988127i	$-0.450900\pi$
$283$	5.16924	0.307279	0.153640	+	0.988127i	$0.450900\pi$
$284$	3.51474	0.208561
$285$	0.354519	0.0209999
$286$	−5.29026	−0.312819
$287$	3.87496	0.228731
$288$	5.38466	0.317294
$289$	9.97302	0.586648
$290$	0.0884173	0.00519204
$291$	44.6938	2.62000
$292$	−7.13783	−0.417710
$293$	22.7328	1.32806	0.664031	−	0.747705i	$-0.268844\pi$
$293$	22.7328	1.32806	0.664031	+	0.747705i	$0.268844\pi$
$294$	12.7153	0.741572
$295$	−0.528510	−0.0307710
$296$	−0.842186	−0.0489511
$297$	−6.90508	−0.400673
$298$	9.93640	0.575600
$299$	−3.02610	−0.175004
$300$	14.4742	0.835671
$301$	11.9978	0.691544
$302$	6.77066	0.389608
$303$	5.00420	0.287484
$304$	3.33946	0.191531
$305$	−0.359844	−0.0206046
$306$	27.9655	1.59868
$307$	−18.1973	−1.03857	−0.519287	−	0.854600i	$-0.673803\pi$
$307$	−18.1973	−1.03857	−0.519287	+	0.854600i	$0.673803\pi$
$308$	−1.61517	−0.0920331
$309$	−40.4874	−2.30325
$310$	0.0521267	0.00296060
$311$	30.2834	1.71722	0.858608	−	0.512633i	$-0.171330\pi$
$311$	30.2834	1.71722	0.858608	+	0.512633i	$0.171330\pi$
$312$	15.3186	0.867245
$313$	24.4982	1.38472	0.692359	−	0.721553i	$-0.256572\pi$
$313$	24.4982	1.38472	0.692359	+	0.721553i	$0.256572\pi$
$314$	11.3126	0.638404
$315$	0.318859	0.0179657
$316$	7.52662	0.423406
$317$	−17.6290	−0.990141	−0.495071	−	0.868853i	$-0.664858\pi$
$317$	−17.6290	−0.990141	−0.495071	+	0.868853i	$0.664858\pi$
$318$	−9.97102	−0.559147
$319$	−2.41166	−0.135027
$320$	−0.0366624	−0.00204949
$321$	−38.6392	−2.15663
$322$	−0.923902	−0.0514870
$323$	17.3437	0.965028
$324$	3.84055	0.213364
$325$	26.4442	1.46686
$326$	2.31205	0.128052
$327$	21.7921	1.20511
$328$	−2.39910	−0.132468
$329$	−1.41348	−0.0779279
$330$	0.106161	0.00584395
$331$	30.7727	1.69142	0.845709	−	0.533644i	$-0.179178\pi$
$331$	30.7727	1.69142	0.845709	+	0.533644i	$0.179178\pi$
$332$	8.26670	0.453694
$333$	−4.53488	−0.248510
$334$	−2.96046	−0.161989
$335$	0.262532	0.0143437
$336$	4.67694	0.255148
$337$	−32.4580	−1.76810	−0.884050	−	0.467393i	$-0.845193\pi$
$337$	−32.4580	−1.76810	−0.884050	+	0.467393i	$0.845193\pi$
$338$	14.9868	0.815175
$339$	8.76789	0.476207
$340$	−0.190408	−0.0103263
$341$	−1.42180	−0.0769949
$342$	17.9819	0.972347
$343$	18.3988	0.993441
$344$	−7.42820	−0.400501
$345$	0.0607253	0.00326934
$346$	24.3336	1.30818
$347$	24.4645	1.31332	0.656662	−	0.754185i	$-0.271968\pi$
$347$	24.4645	1.31332	0.656662	+	0.754185i	$0.271968\pi$
$348$	6.98327	0.374342
$349$	8.60226	0.460469	0.230234	−	0.973135i	$-0.426051\pi$
$349$	8.60226	0.460469	0.230234	+	0.973135i	$0.426051\pi$
$350$	8.07370	0.431557
$351$	36.5296	1.94981
$352$	1.00000	0.0533002
$353$	2.62078	0.139490	0.0697450	−	0.997565i	$-0.477781\pi$
$353$	2.62078	0.139490	0.0697450	+	0.997565i	$0.477781\pi$
$354$	−41.7421	−2.21857
$355$	−0.128859	−0.00683911
$356$	0.838636	0.0444476
$357$	24.2900	1.28556
$358$	3.84606	0.203271
$359$	4.22527	0.223001	0.111501	−	0.993764i	$-0.464434\pi$
$359$	4.22527	0.223001	0.111501	+	0.993764i	$0.464434\pi$
$360$	−0.197415	−0.0104047
$361$	−7.84800	−0.413053
$362$	−2.33731	−0.122846
$363$	−2.89563	−0.151981
$364$	8.54469	0.447863
$365$	0.261690	0.0136975
$366$	−28.4208	−1.48558
$367$	8.20572	0.428335	0.214167	−	0.976797i	$-0.431296\pi$
$367$	8.20572	0.428335	0.214167	+	0.976797i	$0.431296\pi$
$368$	0.572013	0.0298183
$369$	−12.9183	−0.672500
$370$	0.0308766	0.00160520
$371$	−5.56181	−0.288755
$372$	4.11701	0.213457
$373$	0.348008	0.0180192	0.00900958	−	0.999959i	$-0.497132\pi$
$373$	0.348008	0.0180192	0.00900958	+	0.999959i	$0.497132\pi$
$374$	5.19356	0.268552
$375$	−1.06146	−0.0548138
$376$	0.875128	0.0451313
$377$	12.7583	0.657086
$378$	11.1529	0.573643
$379$	11.8772	0.610092	0.305046	−	0.952338i	$-0.401328\pi$
$379$	11.8772	0.610092	0.305046	+	0.952338i	$0.401328\pi$
$380$	−0.122433	−0.00628067
$381$	17.0174	0.871830
$382$	5.58866	0.285941
$383$	19.0506	0.973442	0.486721	−	0.873558i	$-0.338193\pi$
$383$	19.0506	0.973442	0.486721	+	0.873558i	$0.338193\pi$
$384$	−2.89563	−0.147767
$385$	0.0592162	0.00301794
$386$	−6.60397	−0.336133
$387$	−39.9983	−2.03323
$388$	−15.4349	−0.783589
$389$	28.6196	1.45107	0.725536	−	0.688184i	$-0.241592\pi$
$389$	28.6196	1.45107	0.725536	+	0.688184i	$0.241592\pi$
$390$	−0.561617	−0.0284386
$391$	2.97078	0.150239
$392$	−4.39121	−0.221790
$393$	−21.2278	−1.07080
$394$	1.00000	0.0503793
$395$	−0.275944	−0.0138843
$396$	5.38466	0.270589
$397$	−1.28345	−0.0644144	−0.0322072	−	0.999481i	$-0.510254\pi$
$397$	−1.28345	−0.0644144	−0.0322072	+	0.999481i	$0.510254\pi$
$398$	−4.61305	−0.231231
$399$	15.6185	0.781901
$400$	−4.99866	−0.249933
$401$	−14.9172	−0.744930	−0.372465	−	0.928046i	$-0.621487\pi$
$401$	−14.9172	−0.744930	−0.372465	+	0.928046i	$0.621487\pi$
$402$	20.7350	1.03417
$403$	7.52169	0.374682
$404$	−1.72819	−0.0859808
$405$	−0.140804	−0.00699661
$406$	3.89525	0.193318
$407$	−0.842186	−0.0417456
$408$	−15.0386	−0.744522
$409$	−2.96334	−0.146528	−0.0732639	−	0.997313i	$-0.523342\pi$
$409$	−2.96334	−0.146528	−0.0732639	+	0.997313i	$0.523342\pi$
$410$	0.0879566	0.00434387
$411$	−49.6541	−2.44926
$412$	13.9823	0.688857
$413$	−23.2837	−1.14571
$414$	3.08010	0.151378
$415$	−0.303077	−0.0148775
$416$	−5.29026	−0.259376
$417$	−57.4876	−2.81518
$418$	3.33946	0.163338
$419$	21.5083	1.05075	0.525374	−	0.850872i	$-0.323926\pi$
$419$	21.5083	1.05075	0.525374	+	0.850872i	$0.323926\pi$
$420$	−0.171468	−0.00836678
$421$	−16.5191	−0.805093	−0.402547	−	0.915400i	$-0.631875\pi$
$421$	−16.5191	−0.805093	−0.402547	+	0.915400i	$0.631875\pi$
$422$	2.40573	0.117109
$423$	4.71226	0.229118
$424$	3.44347	0.167230
$425$	−25.9608	−1.25928
$426$	−10.1774	−0.493095
$427$	−15.8530	−0.767182
$428$	13.3440	0.645006
$429$	15.3186	0.739589
$430$	0.272336	0.0131332
$431$	−6.31712	−0.304285	−0.152143	−	0.988359i	$-0.548617\pi$
$431$	−6.31712	−0.304285	−0.152143	+	0.988359i	$0.548617\pi$
$432$	−6.90508	−0.332221
$433$	−24.2002	−1.16299	−0.581493	−	0.813552i	$-0.697531\pi$
$433$	−24.2002	−1.16299	−0.581493	+	0.813552i	$0.697531\pi$
$434$	2.29646	0.110234
$435$	−0.256023	−0.0122754
$436$	−7.52588	−0.360424
$437$	1.91022	0.0913781
$438$	20.6685	0.987579
$439$	−29.4634	−1.40621	−0.703106	−	0.711085i	$-0.748204\pi$
$439$	−29.4634	−1.40621	−0.703106	+	0.711085i	$0.748204\pi$
$440$	−0.0366624	−0.00174781
$441$	−23.6452	−1.12596
$442$	−27.4752	−1.30686
$443$	−37.7199	−1.79213	−0.896063	−	0.443926i	$-0.853585\pi$
$443$	−37.7199	−1.79213	−0.896063	+	0.443926i	$0.853585\pi$
$444$	2.43866	0.115734
$445$	−0.0307464	−0.00145752
$446$	−13.8656	−0.656554
$447$	−28.7721	−1.36087
$448$	−1.61517	−0.0763098
$449$	8.56605	0.404257	0.202129	−	0.979359i	$-0.435214\pi$
$449$	8.56605	0.404257	0.202129	+	0.979359i	$0.435214\pi$
$450$	−26.9160	−1.26883
$451$	−2.39910	−0.112969
$452$	−3.02798	−0.142424
$453$	−19.6053	−0.921138
$454$	4.11905	0.193317
$455$	−0.313269	−0.0146863
$456$	−9.66983	−0.452831
$457$	0.625876	0.0292772	0.0146386	−	0.999893i	$-0.495340\pi$
$457$	0.625876	0.0292772	0.0146386	+	0.999893i	$0.495340\pi$
$458$	12.2887	0.574215
$459$	−35.8619	−1.67389
$460$	−0.0209714	−0.000977796 0
$461$	−28.2529	−1.31587	−0.657934	−	0.753076i	$-0.728569\pi$
$461$	−28.2529	−1.31587	−0.657934	+	0.753076i	$0.728569\pi$
$462$	4.67694	0.217591
$463$	12.6730	0.588965	0.294482	−	0.955657i	$-0.404853\pi$
$463$	12.6730	0.588965	0.294482	+	0.955657i	$0.404853\pi$
$464$	−2.41166	−0.111958
$465$	−0.150939	−0.00699965
$466$	1.52642	0.0707101
$467$	10.6000	0.490510	0.245255	−	0.969459i	$-0.421128\pi$
$467$	10.6000	0.490510	0.245255	+	0.969459i	$0.421128\pi$
$468$	−28.4862	−1.31678
$469$	11.5659	0.534065
$470$	−0.0320843	−0.00147994
$471$	−32.7569	−1.50936
$472$	14.4156	0.663531
$473$	−7.42820	−0.341549
$474$	−21.7943	−1.00105
$475$	−16.6928	−0.765919
$476$	−8.38850	−0.384486
$477$	18.5419	0.848976
$478$	5.03728	0.230400
$479$	−28.0236	−1.28043	−0.640217	−	0.768194i	$-0.721155\pi$
$479$	−28.0236	−1.28043	−0.640217	+	0.768194i	$0.721155\pi$
$480$	0.106161	0.00484555
$481$	4.45538	0.203148
$482$	4.89207	0.222828
$483$	2.67527	0.121729
$484$	1.00000	0.0454545
$485$	0.565882	0.0256954
$486$	9.59441	0.435211
$487$	23.3827	1.05957	0.529786	−	0.848131i	$-0.322272\pi$
$487$	23.3827	1.05957	0.529786	+	0.848131i	$0.322272\pi$
$488$	9.81506	0.444307
$489$	−6.69482	−0.302750
$490$	0.160992	0.00727290
$491$	−13.1661	−0.594179	−0.297089	−	0.954850i	$-0.596016\pi$
$491$	−13.1661	−0.594179	−0.297089	+	0.954850i	$0.596016\pi$
$492$	6.94688	0.313190
$493$	−12.5251	−0.564102
$494$	−17.6666	−0.794858
$495$	−0.197415	−0.00887312
$496$	−1.42180	−0.0638408
$497$	−5.67691	−0.254644
$498$	−23.9373	−1.07265
$499$	−10.4879	−0.469505	−0.234752	−	0.972055i	$-0.575428\pi$
$499$	−10.4879	−0.469505	−0.234752	+	0.972055i	$0.575428\pi$
$500$	0.366575	0.0163937
$501$	8.57239	0.382986
$502$	−6.91693	−0.308718
$503$	−10.9274	−0.487228	−0.243614	−	0.969872i	$-0.578333\pi$
$503$	−10.9274	−0.487228	−0.243614	+	0.969872i	$0.578333\pi$
$504$	−8.69716	−0.387402
$505$	0.0633597	0.00281947
$506$	0.572013	0.0254291
$507$	−43.3962	−1.92729
$508$	−5.87694	−0.260747
$509$	9.84201	0.436239	0.218120	−	0.975922i	$-0.430008\pi$
$509$	9.84201	0.436239	0.218120	+	0.975922i	$0.430008\pi$
$510$	0.551351	0.0244143
$511$	11.5288	0.510006
$512$	1.00000	0.0441942
$513$	−23.0592	−1.01809
$514$	9.31154	0.410714
$515$	−0.512624	−0.0225889
$516$	21.5093	0.946893
$517$	0.875128	0.0384881
$518$	1.36028	0.0597671
$519$	−70.4610	−3.09290
$520$	0.193954	0.00850543
$521$	−5.35989	−0.234821	−0.117410	−	0.993083i	$-0.537459\pi$
$521$	−5.35989	−0.234821	−0.117410	+	0.993083i	$0.537459\pi$
$522$	−12.9860	−0.568380
$523$	−16.9819	−0.742566	−0.371283	−	0.928520i	$-0.621082\pi$
$523$	−16.9819	−0.742566	−0.371283	+	0.928520i	$0.621082\pi$
$524$	7.33099	0.320256
$525$	−23.3784	−1.02032
$526$	0.386298	0.0168434
$527$	−7.38421	−0.321661
$528$	−2.89563	−0.126016
$529$	−22.6728	−0.985774
$530$	−0.126246	−0.00548378
$531$	77.6229	3.36855
$532$	−5.39381	−0.233851
$533$	12.6918	0.549744
$534$	−2.42838	−0.105086
$535$	−0.489223	−0.0211510
$536$	−7.16080	−0.309299
$537$	−11.1368	−0.480587
$538$	23.2522	1.00248
$539$	−4.39121	−0.189143
$540$	0.253157	0.0108941
$541$	15.3932	0.661807	0.330904	−	0.943665i	$-0.392647\pi$
$541$	15.3932	0.661807	0.330904	+	0.943665i	$0.392647\pi$
$542$	10.0629	0.432237
$543$	6.76797	0.290441
$544$	5.19356	0.222672
$545$	0.275917	0.0118190
$546$	−24.7422	−1.05887
$547$	−13.2079	−0.564727	−0.282363	−	0.959307i	$-0.591118\pi$
$547$	−13.2079	−0.564727	−0.282363	+	0.959307i	$0.591118\pi$
$548$	17.1480	0.732525
$549$	52.8507	2.25561
$550$	−4.99866	−0.213143
$551$	−8.05364	−0.343097
$552$	−1.65634	−0.0704984
$553$	−12.1568	−0.516960
$554$	−12.1137	−0.514660
$555$	−0.0894070	−0.00379512
$556$	19.8532	0.841965
$557$	2.70452	0.114594	0.0572971	−	0.998357i	$-0.481752\pi$
$557$	2.70452	0.114594	0.0572971	+	0.998357i	$0.481752\pi$
$558$	−7.65591	−0.324101
$559$	39.2970	1.66209
$560$	0.0592162	0.00250234
$561$	−15.0386	−0.634930
$562$	6.98928	0.294825
$563$	2.09240	0.0881841	0.0440920	−	0.999027i	$-0.485961\pi$
$563$	2.09240	0.0881841	0.0440920	+	0.999027i	$0.485961\pi$
$564$	−2.53404	−0.106702
$565$	0.111013	0.00467035
$566$	5.16924	0.217279
$567$	−6.20317	−0.260508
$568$	3.51474	0.147475
$569$	−23.7478	−0.995560	−0.497780	−	0.867303i	$-0.665851\pi$
$569$	−23.7478	−0.995560	−0.497780	+	0.867303i	$0.665851\pi$
$570$	0.354519	0.0148492
$571$	9.62203	0.402669	0.201335	−	0.979523i	$-0.435472\pi$
$571$	9.62203	0.402669	0.201335	+	0.979523i	$0.435472\pi$
$572$	−5.29026	−0.221197
$573$	−16.1827	−0.676041
$574$	3.87496	0.161738
$575$	−2.85930	−0.119241
$576$	5.38466	0.224361
$577$	30.1099	1.25349	0.626747	−	0.779223i	$-0.284386\pi$
$577$	30.1099	1.25349	0.626747	+	0.779223i	$0.284386\pi$
$578$	9.97302	0.414823
$579$	19.1226	0.794709
$580$	0.0884173	0.00367133
$581$	−13.3522	−0.553941
$582$	44.6938	1.85262
$583$	3.44347	0.142614
$584$	−7.13783	−0.295365
$585$	1.04437	0.0431795
$586$	22.7328	0.939082
$587$	8.37427	0.345643	0.172822	−	0.984953i	$-0.444712\pi$
$587$	8.37427	0.345643	0.172822	+	0.984953i	$0.444712\pi$
$588$	12.7153	0.524371
$589$	−4.74805	−0.195640
$590$	−0.528510	−0.0217584
$591$	−2.89563	−0.119110
$592$	−0.842186	−0.0346136
$593$	1.76067	0.0723021	0.0361510	−	0.999346i	$-0.488490\pi$
$593$	1.76067	0.0723021	0.0361510	+	0.999346i	$0.488490\pi$
$594$	−6.90508	−0.283319
$595$	0.307543	0.0126080
$596$	9.93640	0.407011
$597$	13.3577	0.546693
$598$	−3.02610	−0.123746
$599$	26.0304	1.06357	0.531787	−	0.846878i	$-0.321521\pi$
$599$	26.0304	1.06357	0.531787	+	0.846878i	$0.321521\pi$
$600$	14.4742	0.590909
$601$	−31.9254	−1.30226	−0.651132	−	0.758964i	$-0.725706\pi$
$601$	−31.9254	−1.30226	−0.651132	+	0.758964i	$0.725706\pi$
$602$	11.9978	0.488995
$603$	−38.5584	−1.57022
$604$	6.77066	0.275494
$605$	−0.0366624	−0.00149054
$606$	5.00420	0.203282
$607$	−5.85008	−0.237447	−0.118724	−	0.992927i	$-0.537880\pi$
$607$	−5.85008	−0.237447	−0.118724	+	0.992927i	$0.537880\pi$
$608$	3.33946	0.135433
$609$	−11.2792	−0.457056
$610$	−0.359844	−0.0145697
$611$	−4.62965	−0.187296
$612$	27.9655	1.13044
$613$	27.0319	1.09181	0.545904	−	0.837848i	$-0.316186\pi$
$613$	27.0319	1.09181	0.545904	+	0.837848i	$0.316186\pi$
$614$	−18.1973	−0.734383
$615$	−0.254690	−0.0102701
$616$	−1.61517	−0.0650772
$617$	−41.6444	−1.67654	−0.838270	−	0.545256i	$-0.816432\pi$
$617$	−41.6444	−1.67654	−0.838270	+	0.545256i	$0.816432\pi$
$618$	−40.4874	−1.62864
$619$	−15.9041	−0.639238	−0.319619	−	0.947546i	$-0.603555\pi$
$619$	−15.9041	−0.639238	−0.319619	+	0.947546i	$0.603555\pi$
$620$	0.0521267	0.00209346
$621$	−3.94980	−0.158500
$622$	30.2834	1.21426
$623$	−1.35454	−0.0542686
$624$	15.3186	0.613235
$625$	24.9798	0.999194
$626$	24.4982	0.979143
$627$	−9.66983	−0.386176
$628$	11.3126	0.451420
$629$	−4.37394	−0.174400
$630$	0.318859	0.0127036
$631$	−26.1083	−1.03935	−0.519677	−	0.854363i	$-0.673948\pi$
$631$	−26.1083	−1.03935	−0.519677	+	0.854363i	$0.673948\pi$
$632$	7.52662	0.299393
$633$	−6.96611	−0.276878
$634$	−17.6290	−0.700136
$635$	0.215463	0.00855039
$636$	−9.97102	−0.395377
$637$	23.2306	0.920431
$638$	−2.41166	−0.0954785
$639$	18.9256	0.748687
$640$	−0.0366624	−0.00144921
$641$	−20.9622	−0.827956	−0.413978	−	0.910287i	$-0.635861\pi$
$641$	−20.9622	−0.827956	−0.413978	+	0.910287i	$0.635861\pi$
$642$	−38.6392	−1.52497
$643$	−12.6330	−0.498196	−0.249098	−	0.968478i	$-0.580134\pi$
$643$	−12.6330	−0.498196	−0.249098	+	0.968478i	$0.580134\pi$
$644$	−0.923902	−0.0364068
$645$	−0.788582	−0.0310504
$646$	17.3437	0.682378
$647$	−23.8514	−0.937695	−0.468847	−	0.883279i	$-0.655331\pi$
$647$	−23.8514	−0.937695	−0.468847	+	0.883279i	$0.655331\pi$
$648$	3.84055	0.150871
$649$	14.4156	0.565861
$650$	26.4442	1.03723
$651$	−6.64969	−0.260622
$652$	2.31205	0.0905467
$653$	−31.7342	−1.24186	−0.620928	−	0.783868i	$-0.713244\pi$
$653$	−31.7342	−1.24186	−0.620928	+	0.783868i	$0.713244\pi$
$654$	21.7921	0.852140
$655$	−0.268772	−0.0105018
$656$	−2.39910	−0.0936689
$657$	−38.4348	−1.49948
$658$	−1.41348	−0.0551033
$659$	21.8250	0.850183	0.425091	−	0.905150i	$-0.360242\pi$
$659$	21.8250	0.850183	0.425091	+	0.905150i	$0.360242\pi$
$660$	0.106161	0.00413230
$661$	−20.2998	−0.789573	−0.394786	−	0.918773i	$-0.629181\pi$
$661$	−20.2998	−0.789573	−0.394786	+	0.918773i	$0.629181\pi$
$662$	30.7727	1.19601
$663$	79.5580	3.08978
$664$	8.26670	0.320810
$665$	0.197750	0.00766842
$666$	−4.53488	−0.175723
$667$	−1.37950	−0.0534145
$668$	−2.96046	−0.114544
$669$	40.1495	1.55227
$670$	0.262532	0.0101425
$671$	9.81506	0.378906
$672$	4.67694	0.180417
$673$	−50.7141	−1.95489	−0.977443	−	0.211201i	$-0.932262\pi$
$673$	−50.7141	−1.95489	−0.977443	+	0.211201i	$0.932262\pi$
$674$	−32.4580	−1.25023
$675$	34.5161	1.32853
$676$	14.9868	0.576415
$677$	−29.3035	−1.12623	−0.563113	−	0.826380i	$-0.690397\pi$
$677$	−29.3035	−1.12623	−0.563113	+	0.826380i	$0.690397\pi$
$678$	8.76789	0.336729
$679$	24.9301	0.956729
$680$	−0.190408	−0.00730182
$681$	−11.9272	−0.457053
$682$	−1.42180	−0.0544436
$683$	−8.99206	−0.344072	−0.172036	−	0.985091i	$-0.555034\pi$
$683$	−8.99206	−0.344072	−0.172036	+	0.985091i	$0.555034\pi$
$684$	17.9819	0.687553
$685$	−0.628686	−0.0240209
$686$	18.3988	0.702469
$687$	−35.5836	−1.35760
$688$	−7.42820	−0.283197
$689$	−18.2169	−0.694007
$690$	0.0607253	0.00231177
$691$	13.5705	0.516246	0.258123	−	0.966112i	$-0.416896\pi$
$691$	13.5705	0.516246	0.258123	+	0.966112i	$0.416896\pi$
$692$	24.3336	0.925024
$693$	−8.69716	−0.330378
$694$	24.4645	0.928661
$695$	−0.727868	−0.0276096
$696$	6.98327	0.264700
$697$	−12.4598	−0.471950
$698$	8.60226	0.325600
$699$	−4.41995	−0.167178
$700$	8.07370	0.305157
$701$	7.48301	0.282629	0.141315	−	0.989965i	$-0.454867\pi$
$701$	7.48301	0.282629	0.141315	+	0.989965i	$0.454867\pi$
$702$	36.5296	1.37872
$703$	−2.81245	−0.106073
$704$	1.00000	0.0376889
$705$	0.0929042	0.00349897
$706$	2.62078	0.0986343
$707$	2.79133	0.104979
$708$	−41.7421	−1.56877
$709$	20.3907	0.765790	0.382895	−	0.923792i	$-0.374927\pi$
$709$	20.3907	0.765790	0.382895	+	0.923792i	$0.374927\pi$
$710$	−0.128859	−0.00483598
$711$	40.5283	1.51993
$712$	0.838636	0.0314292
$713$	−0.813290	−0.0304579
$714$	24.2900	0.909029
$715$	0.193954	0.00725345
$716$	3.84606	0.143734
$717$	−14.5861	−0.544728
$718$	4.22527	0.157686
$719$	−17.9624	−0.669883	−0.334942	−	0.942239i	$-0.608717\pi$
$719$	−17.9624	−0.669883	−0.334942	+	0.942239i	$0.608717\pi$
$720$	−0.197415	−0.00735720
$721$	−22.5838	−0.841065
$722$	−7.84800	−0.292072
$723$	−14.1656	−0.526825
$724$	−2.33731	−0.0868653
$725$	12.0551	0.447714
$726$	−2.89563	−0.107467
$727$	−3.39121	−0.125773	−0.0628865	−	0.998021i	$-0.520031\pi$
$727$	−3.39121	−0.125773	−0.0628865	+	0.998021i	$0.520031\pi$
$728$	8.54469	0.316687
$729$	−39.3035	−1.45569
$730$	0.261690	0.00968558
$731$	−38.5787	−1.42689
$732$	−28.4208	−1.05046
$733$	50.4963	1.86512	0.932561	−	0.361012i	$-0.117569\pi$
$733$	50.4963	1.86512	0.932561	+	0.361012i	$0.117569\pi$
$734$	8.20572	0.302879
$735$	−0.466174	−0.0171951
$736$	0.572013	0.0210847
$737$	−7.16080	−0.263771
$738$	−12.9183	−0.475529
$739$	−24.5047	−0.901420	−0.450710	−	0.892670i	$-0.648829\pi$
$739$	−24.5047	−0.901420	−0.450710	+	0.892670i	$0.648829\pi$
$740$	0.0308766	0.00113505
$741$	51.1559	1.87926
$742$	−5.56181	−0.204181
$743$	48.7234	1.78749	0.893744	−	0.448578i	$-0.148069\pi$
$743$	48.7234	1.78749	0.893744	+	0.448578i	$0.148069\pi$
$744$	4.11701	0.150937
$745$	−0.364292	−0.0133466
$746$	0.348008	0.0127415
$747$	44.5133	1.62866
$748$	5.19356	0.189895
$749$	−21.5529	−0.787525
$750$	−1.06146	−0.0387592
$751$	44.9632	1.64073	0.820365	−	0.571841i	$-0.193770\pi$
$751$	44.9632	1.64073	0.820365	+	0.571841i	$0.193770\pi$
$752$	0.875128	0.0319126
$753$	20.0289	0.729892
$754$	12.7583	0.464630
$755$	−0.248229	−0.00903397
$756$	11.1529	0.405627
$757$	−23.4905	−0.853778	−0.426889	−	0.904304i	$-0.640390\pi$
$757$	−23.4905	−0.853778	−0.426889	+	0.904304i	$0.640390\pi$
$758$	11.8772	0.431400
$759$	−1.65634	−0.0601213
$760$	−0.122433	−0.00444110
$761$	12.3760	0.448630	0.224315	−	0.974517i	$-0.427985\pi$
$761$	12.3760	0.448630	0.224315	+	0.974517i	$0.427985\pi$
$762$	17.0174	0.616477
$763$	12.1556	0.440062
$764$	5.58866	0.202191
$765$	−1.02528	−0.0370692
$766$	19.0506	0.688327
$767$	−76.2621	−2.75366
$768$	−2.89563	−0.104487
$769$	51.5327	1.85832	0.929158	−	0.369683i	$-0.120534\pi$
$769$	51.5327	1.85832	0.929158	+	0.369683i	$0.120534\pi$
$770$	0.0592162	0.00213400
$771$	−26.9627	−0.971040
$772$	−6.60397	−0.237682
$773$	41.6902	1.49949	0.749745	−	0.661727i	$-0.230176\pi$
$773$	41.6902	1.49949	0.749745	+	0.661727i	$0.230176\pi$
$774$	−39.9983	−1.43771
$775$	7.10710	0.255294
$776$	−15.4349	−0.554081
$777$	−3.93886	−0.141306
$778$	28.6196	1.02606
$779$	−8.01168	−0.287048
$780$	−0.561617	−0.0201091
$781$	3.51474	0.125767
$782$	2.97078	0.106235
$783$	16.6527	0.595119
$784$	−4.39121	−0.156829
$785$	−0.414745	−0.0148029
$786$	−21.2278	−0.757171
$787$	1.91633	0.0683097	0.0341548	−	0.999417i	$-0.489126\pi$
$787$	1.91633	0.0683097	0.0341548	+	0.999417i	$0.489126\pi$
$788$	1.00000	0.0356235
$789$	−1.11857	−0.0398223
$790$	−0.275944	−0.00981765
$791$	4.89071	0.173894
$792$	5.38466	0.191335
$793$	−51.9242	−1.84388
$794$	−1.28345	−0.0455479
$795$	0.365562	0.0129651
$796$	−4.61305	−0.163505
$797$	−11.6510	−0.412700	−0.206350	−	0.978478i	$-0.566159\pi$
$797$	−11.6510	−0.412700	−0.206350	+	0.978478i	$0.566159\pi$
$798$	15.6185	0.552888
$799$	4.54502	0.160791
$800$	−4.99866	−0.176729
$801$	4.51577	0.159557
$802$	−14.9172	−0.526745
$803$	−7.13783	−0.251889
$804$	20.7350	0.731267
$805$	0.0338725	0.00119385
$806$	7.52169	0.264940
$807$	−67.3298	−2.37012
$808$	−1.72819	−0.0607976
$809$	−5.97783	−0.210169	−0.105085	−	0.994463i	$-0.533511\pi$
$809$	−5.97783	−0.210169	−0.105085	+	0.994463i	$0.533511\pi$
$810$	−0.140804	−0.00494735
$811$	−4.03267	−0.141606	−0.0708030	−	0.997490i	$-0.522556\pi$
$811$	−4.03267	−0.141606	−0.0708030	+	0.997490i	$0.522556\pi$
$812$	3.89525	0.136697
$813$	−29.1383	−1.02192
$814$	−0.842186	−0.0295186
$815$	−0.0847652	−0.00296920
$816$	−15.0386	−0.526456
$817$	−24.8062	−0.867858
$818$	−2.96334	−0.103611
$819$	46.0102	1.60773
$820$	0.0879566	0.00307158
$821$	−27.2170	−0.949878	−0.474939	−	0.880019i	$-0.657530\pi$
$821$	−27.2170	−0.949878	−0.474939	+	0.880019i	$0.657530\pi$
$822$	−49.6541	−1.73189
$823$	40.4059	1.40846	0.704231	−	0.709971i	$-0.251292\pi$
$823$	40.4059	1.40846	0.704231	+	0.709971i	$0.251292\pi$
$824$	13.9823	0.487095
$825$	14.4742	0.503928
$826$	−23.2837	−0.810143
$827$	1.58072	0.0549669	0.0274834	−	0.999622i	$-0.491251\pi$
$827$	1.58072	0.0549669	0.0274834	+	0.999622i	$0.491251\pi$
$828$	3.08010	0.107041
$829$	−49.9262	−1.73401	−0.867005	−	0.498300i	$-0.833958\pi$
$829$	−49.9262	−1.73401	−0.867005	+	0.498300i	$0.833958\pi$
$830$	−0.303077	−0.0105200
$831$	35.0767	1.21680
$832$	−5.29026	−0.183407
$833$	−22.8060	−0.790181
$834$	−57.4876	−1.99063
$835$	0.108538	0.00375610
$836$	3.33946	0.115498
$837$	9.81765	0.339348
$838$	21.5083	0.742990
$839$	2.42289	0.0836475	0.0418237	−	0.999125i	$-0.486683\pi$
$839$	2.42289	0.0836475	0.0418237	+	0.999125i	$0.486683\pi$
$840$	−0.171468	−0.00591621
$841$	−23.1839	−0.799445
$842$	−16.5191	−0.569287
$843$	−20.2383	−0.697046
$844$	2.40573	0.0828088
$845$	−0.549452	−0.0189017
$846$	4.71226	0.162011
$847$	−1.61517	−0.0554981
$848$	3.44347	0.118249
$849$	−14.9682	−0.513707
$850$	−25.9608	−0.890448
$851$	−0.481742	−0.0165139
$852$	−10.1774	−0.348671
$853$	16.4093	0.561843	0.280922	−	0.959731i	$-0.409360\pi$
$853$	16.4093	0.561843	0.280922	+	0.959731i	$0.409360\pi$
$854$	−15.8530	−0.542480
$855$	−0.659258	−0.0225462
$856$	13.3440	0.456088
$857$	−4.28926	−0.146518	−0.0732591	−	0.997313i	$-0.523340\pi$
$857$	−4.28926	−0.146518	−0.0732591	+	0.997313i	$0.523340\pi$
$858$	15.3186	0.522969
$859$	40.9490	1.39716	0.698580	−	0.715532i	$-0.253815\pi$
$859$	40.9490	1.39716	0.698580	+	0.715532i	$0.253815\pi$
$860$	0.272336	0.00928657
$861$	−11.2204	−0.382391
$862$	−6.31712	−0.215162
$863$	20.4362	0.695655	0.347827	−	0.937559i	$-0.386919\pi$
$863$	20.4362	0.695655	0.347827	+	0.937559i	$0.386919\pi$
$864$	−6.90508	−0.234915
$865$	−0.892128	−0.0303333
$866$	−24.2002	−0.822355
$867$	−28.8781	−0.980753
$868$	2.29646	0.0779469
$869$	7.52662	0.255323
$870$	−0.256023	−0.00868001
$871$	37.8824	1.28360
$872$	−7.52588	−0.254858
$873$	−83.1117	−2.81291
$874$	1.91022	0.0646140
$875$	−0.592082	−0.0200160
$876$	20.6685	0.698324
$877$	35.5128	1.19918	0.599591	−	0.800307i	$-0.295330\pi$
$877$	35.5128	1.19918	0.599591	+	0.800307i	$0.295330\pi$
$878$	−29.4634	−0.994342
$879$	−65.8256	−2.22024
$880$	−0.0366624	−0.00123589
$881$	−15.5156	−0.522734	−0.261367	−	0.965239i	$-0.584173\pi$
$881$	−15.5156	−0.522734	−0.261367	+	0.965239i	$0.584173\pi$
$882$	−23.6452	−0.796174
$883$	−16.5083	−0.555549	−0.277775	−	0.960646i	$-0.589597\pi$
$883$	−16.5083	−0.555549	−0.277775	+	0.960646i	$0.589597\pi$
$884$	−27.4752	−0.924092
$885$	1.53037	0.0514428
$886$	−37.7199	−1.26722
$887$	−37.1030	−1.24580	−0.622899	−	0.782302i	$-0.714045\pi$
$887$	−37.1030	−1.24580	−0.622899	+	0.782302i	$0.714045\pi$
$888$	2.43866	0.0818360
$889$	9.49229	0.318361
$890$	−0.0307464	−0.00103062
$891$	3.84055	0.128663
$892$	−13.8656	−0.464254
$893$	2.92245	0.0977962
$894$	−28.7721	−0.962283
$895$	−0.141006	−0.00471331
$896$	−1.61517	−0.0539592
$897$	8.76245	0.292570
$898$	8.56605	0.285853
$899$	3.42890	0.114360
$900$	−26.9160	−0.897201
$901$	17.8839	0.595798
$902$	−2.39910	−0.0798811
$903$	−34.7412	−1.15612
$904$	−3.02798	−0.100709
$905$	0.0856913	0.00284847
$906$	−19.6053	−0.651343
$907$	−53.2182	−1.76708	−0.883541	−	0.468354i	$-0.844847\pi$
$907$	−53.2182	−1.76708	−0.883541	+	0.468354i	$0.844847\pi$
$908$	4.11905	0.136695
$909$	−9.30572	−0.308651
$910$	−0.313269	−0.0103848
$911$	12.9156	0.427914	0.213957	−	0.976843i	$-0.431365\pi$
$911$	12.9156	0.427914	0.213957	+	0.976843i	$0.431365\pi$
$912$	−9.66983	−0.320200
$913$	8.26670	0.273588
$914$	0.625876	0.0207021
$915$	1.04197	0.0344466
$916$	12.2887	0.406031
$917$	−11.8408	−0.391019
$918$	−35.8619	−1.18362
$919$	14.7941	0.488013	0.244007	−	0.969774i	$-0.421538\pi$
$919$	14.7941	0.488013	0.244007	+	0.969774i	$0.421538\pi$
$920$	−0.0209714	−0.000691406 0
$921$	52.6926	1.73628
$922$	−28.2529	−0.930459
$923$	−18.5939	−0.612024
$924$	4.67694	0.153860
$925$	4.20980	0.138417
$926$	12.6730	0.416461
$927$	75.2897	2.47284
$928$	−2.41166	−0.0791666
$929$	18.5529	0.608699	0.304350	−	0.952560i	$-0.401561\pi$
$929$	18.5529	0.608699	0.304350	+	0.952560i	$0.401561\pi$
$930$	−0.150939	−0.00494950
$931$	−14.6643	−0.480602
$932$	1.52642	0.0499996
$933$	−87.6895	−2.87083
$934$	10.6000	0.346843
$935$	−0.190408	−0.00622702
$936$	−28.4862	−0.931101
$937$	10.6963	0.349432	0.174716	−	0.984619i	$-0.444099\pi$
$937$	10.6963	0.349432	0.174716	+	0.984619i	$0.444099\pi$
$938$	11.5659	0.377641
$939$	−70.9375	−2.31496
$940$	−0.0320843	−0.00104647
$941$	6.87782	0.224211	0.112105	−	0.993696i	$-0.464241\pi$
$941$	6.87782	0.224211	0.112105	+	0.993696i	$0.464241\pi$
$942$	−32.7569	−1.06728
$943$	−1.37231	−0.0446887
$944$	14.4156	0.469187
$945$	−0.408892	−0.0133013
$946$	−7.42820	−0.241511
$947$	−17.2634	−0.560985	−0.280493	−	0.959856i	$-0.590498\pi$
$947$	−17.2634	−0.560985	−0.280493	+	0.959856i	$0.590498\pi$
$948$	−21.7943	−0.707846
$949$	37.7609	1.22577
$950$	−16.6928	−0.541587
$951$	51.0469	1.65531
$952$	−8.38850	−0.271873
$953$	16.6963	0.540845	0.270422	−	0.962742i	$-0.412837\pi$
$953$	16.6963	0.540845	0.270422	+	0.962742i	$0.412837\pi$
$954$	18.5419	0.600317
$955$	−0.204894	−0.00663021
$956$	5.03728	0.162917
$957$	6.98327	0.225737
$958$	−28.0236	−0.905403
$959$	−27.6970	−0.894382
$960$	0.106161	0.00342632
$961$	−28.9785	−0.934790
$962$	4.45538	0.143647
$963$	71.8528	2.31543
$964$	4.89207	0.157563
$965$	0.242117	0.00779404
$966$	2.67527	0.0860755
$967$	4.37674	0.140746	0.0703732	−	0.997521i	$-0.477581\pi$
$967$	4.37674	0.140746	0.0703732	+	0.997521i	$0.477581\pi$
$968$	1.00000	0.0321412
$969$	−50.2208	−1.61333
$970$	0.565882	0.0181694
$971$	59.4267	1.90709	0.953546	−	0.301247i	$-0.0974030\pi$
$971$	59.4267	1.90709	0.953546	+	0.301247i	$0.0974030\pi$
$972$	9.59441	0.307741
$973$	−32.0665	−1.02800
$974$	23.3827	0.749230
$975$	−76.5724	−2.45228
$976$	9.81506	0.314172
$977$	32.0308	1.02476	0.512379	−	0.858760i	$-0.328764\pi$
$977$	32.0308	1.02476	0.512379	+	0.858760i	$0.328764\pi$
$978$	−6.69482	−0.214077
$979$	0.838636	0.0268029
$980$	0.160992	0.00514271
$981$	−40.5243	−1.29384
$982$	−13.1661	−0.420148
$983$	0.702886	0.0224186	0.0112093	−	0.999937i	$-0.496432\pi$
$983$	0.702886	0.0224186	0.0112093	+	0.999937i	$0.496432\pi$
$984$	6.94688	0.221459
$985$	−0.0366624	−0.00116816
$986$	−12.5251	−0.398880
$987$	4.09292	0.130279
$988$	−17.6666	−0.562049
$989$	−4.24903	−0.135111
$990$	−0.197415	−0.00627425
$991$	−1.68218	−0.0534363	−0.0267182	−	0.999643i	$-0.508506\pi$
$991$	−1.68218	−0.0534363	−0.0267182	+	0.999643i	$0.508506\pi$
$992$	−1.42180	−0.0451423
$993$	−89.1062	−2.82770
$994$	−5.67691	−0.180061
$995$	0.169125	0.00536164
$996$	−23.9373	−0.758481
$997$	−35.6689	−1.12965	−0.564823	−	0.825212i	$-0.691055\pi$
$997$	−35.6689	−1.12965	−0.564823	+	0.825212i	$0.691055\pi$
$998$	−10.4879	−0.331990
$999$	5.81536	0.183990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.2	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.2	✓	26	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.89563 q^{3} +1.00000 q^{4} -0.0366624 q^{5} -2.89563 q^{6} -1.61517 q^{7} +1.00000 q^{8} +5.38466 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.89563 q^{3} +1.00000 q^{4} -0.0366624 q^{5} -2.89563 q^{6} -1.61517 q^{7} +1.00000 q^{8} +5.38466 q^{9} -0.0366624 q^{10} +1.00000 q^{11} -2.89563 q^{12} -5.29026 q^{13} -1.61517 q^{14} +0.106161 q^{15} +1.00000 q^{16} +5.19356 q^{17} +5.38466 q^{18} +3.33946 q^{19} -0.0366624 q^{20} +4.67694 q^{21} +1.00000 q^{22} +0.572013 q^{23} -2.89563 q^{24} -4.99866 q^{25} -5.29026 q^{26} -6.90508 q^{27} -1.61517 q^{28} -2.41166 q^{29} +0.106161 q^{30} -1.42180 q^{31} +1.00000 q^{32} -2.89563 q^{33} +5.19356 q^{34} +0.0592162 q^{35} +5.38466 q^{36} -0.842186 q^{37} +3.33946 q^{38} +15.3186 q^{39} -0.0366624 q^{40} -2.39910 q^{41} +4.67694 q^{42} -7.42820 q^{43} +1.00000 q^{44} -0.197415 q^{45} +0.572013 q^{46} +0.875128 q^{47} -2.89563 q^{48} -4.39121 q^{49} -4.99866 q^{50} -15.0386 q^{51} -5.29026 q^{52} +3.44347 q^{53} -6.90508 q^{54} -0.0366624 q^{55} -1.61517 q^{56} -9.66983 q^{57} -2.41166 q^{58} +14.4156 q^{59} +0.106161 q^{60} +9.81506 q^{61} -1.42180 q^{62} -8.69716 q^{63} +1.00000 q^{64} +0.193954 q^{65} -2.89563 q^{66} -7.16080 q^{67} +5.19356 q^{68} -1.65634 q^{69} +0.0592162 q^{70} +3.51474 q^{71} +5.38466 q^{72} -7.13783 q^{73} -0.842186 q^{74} +14.4742 q^{75} +3.33946 q^{76} -1.61517 q^{77} +15.3186 q^{78} +7.52662 q^{79} -0.0366624 q^{80} +3.84055 q^{81} -2.39910 q^{82} +8.26670 q^{83} +4.67694 q^{84} -0.190408 q^{85} -7.42820 q^{86} +6.98327 q^{87} +1.00000 q^{88} +0.838636 q^{89} -0.197415 q^{90} +8.54469 q^{91} +0.572013 q^{92} +4.11701 q^{93} +0.875128 q^{94} -0.122433 q^{95} -2.89563 q^{96} -15.4349 q^{97} -4.39121 q^{98} +5.38466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9} + 13 q^{10} + 26 q^{11} + 12 q^{12} + 24 q^{13} + 13 q^{14} + 12 q^{15} + 26 q^{16} + q^{17} + 38 q^{18} + 24 q^{19} + 13 q^{20} + 5 q^{21} + 26 q^{22} + 19 q^{23} + 12 q^{24} + 35 q^{25} + 24 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 12 q^{30} + 34 q^{31} + 26 q^{32} + 12 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} + 15 q^{37} + 24 q^{38} + 3 q^{39} + 13 q^{40} - 9 q^{41} + 5 q^{42} + 6 q^{43} + 26 q^{44} + 22 q^{45} + 19 q^{46} + 34 q^{47} + 12 q^{48} + 53 q^{49} + 35 q^{50} - 2 q^{51} + 24 q^{52} + 6 q^{53} + 39 q^{54} + 13 q^{55} + 13 q^{56} - 16 q^{57} + 5 q^{58} + 50 q^{59} + 12 q^{60} + 26 q^{61} + 34 q^{62} + 2 q^{63} + 26 q^{64} - 5 q^{65} + 12 q^{66} + 18 q^{67} + q^{68} + 15 q^{69} + 14 q^{70} + 23 q^{71} + 38 q^{72} + 37 q^{73} + 15 q^{74} + 18 q^{75} + 24 q^{76} + 13 q^{77} + 3 q^{78} + 10 q^{79} + 13 q^{80} + 50 q^{81} - 9 q^{82} + 7 q^{83} + 5 q^{84} - 7 q^{85} + 6 q^{86} + 16 q^{87} + 26 q^{88} + 3 q^{89} + 22 q^{90} + 31 q^{91} + 19 q^{92} + 52 q^{93} + 34 q^{94} + 9 q^{95} + 12 q^{96} - 9 q^{97} + 53 q^{98} + 38 q^{99}+O(q^{100}) \) 26 * q + 26 * q^2 + 12 * q^3 + 26 * q^4 + 13 * q^5 + 12 * q^6 + 13 * q^7 + 26 * q^8 + 38 * q^9 + 13 * q^10 + 26 * q^11 + 12 * q^12 + 24 * q^13 + 13 * q^14 + 12 * q^15 + 26 * q^16 + q^17 + 38 * q^18 + 24 * q^19 + 13 * q^20 + 5 * q^21 + 26 * q^22 + 19 * q^23 + 12 * q^24 + 35 * q^25 + 24 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 12 * q^30 + 34 * q^31 + 26 * q^32 + 12 * q^33 + q^34 + 14 * q^35 + 38 * q^36 + 15 * q^37 + 24 * q^38 + 3 * q^39 + 13 * q^40 - 9 * q^41 + 5 * q^42 + 6 * q^43 + 26 * q^44 + 22 * q^45 + 19 * q^46 + 34 * q^47 + 12 * q^48 + 53 * q^49 + 35 * q^50 - 2 * q^51 + 24 * q^52 + 6 * q^53 + 39 * q^54 + 13 * q^55 + 13 * q^56 - 16 * q^57 + 5 * q^58 + 50 * q^59 + 12 * q^60 + 26 * q^61 + 34 * q^62 + 2 * q^63 + 26 * q^64 - 5 * q^65 + 12 * q^66 + 18 * q^67 + q^68 + 15 * q^69 + 14 * q^70 + 23 * q^71 + 38 * q^72 + 37 * q^73 + 15 * q^74 + 18 * q^75 + 24 * q^76 + 13 * q^77 + 3 * q^78 + 10 * q^79 + 13 * q^80 + 50 * q^81 - 9 * q^82 + 7 * q^83 + 5 * q^84 - 7 * q^85 + 6 * q^86 + 16 * q^87 + 26 * q^88 + 3 * q^89 + 22 * q^90 + 31 * q^91 + 19 * q^92 + 52 * q^93 + 34 * q^94 + 9 * q^95 + 12 * q^96 - 9 * q^97 + 53 * q^98 + 38 * q^99

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