LMFDB - Embedded newform 4334.2.a.g.1.7

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			1.7
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.44389 q^{3} +1.00000 q^{4} -0.880270 q^{5} -1.44389 q^{6} -5.04870 q^{7} +1.00000 q^{8} -0.915168 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.44389 q^{3} +1.00000 q^{4} -0.880270 q^{5} -1.44389 q^{6} -5.04870 q^{7} +1.00000 q^{8} -0.915168 q^{9} -0.880270 q^{10} +1.00000 q^{11} -1.44389 q^{12} +1.58937 q^{13} -5.04870 q^{14} +1.27102 q^{15} +1.00000 q^{16} -3.33984 q^{17} -0.915168 q^{18} -2.18701 q^{19} -0.880270 q^{20} +7.28978 q^{21} +1.00000 q^{22} +0.594770 q^{23} -1.44389 q^{24} -4.22513 q^{25} +1.58937 q^{26} +5.65309 q^{27} -5.04870 q^{28} +6.81432 q^{29} +1.27102 q^{30} -8.51050 q^{31} +1.00000 q^{32} -1.44389 q^{33} -3.33984 q^{34} +4.44421 q^{35} -0.915168 q^{36} -11.5469 q^{37} -2.18701 q^{38} -2.29489 q^{39} -0.880270 q^{40} -0.0999763 q^{41} +7.28978 q^{42} -7.64379 q^{43} +1.00000 q^{44} +0.805595 q^{45} +0.594770 q^{46} +10.6610 q^{47} -1.44389 q^{48} +18.4893 q^{49} -4.22513 q^{50} +4.82237 q^{51} +1.58937 q^{52} -8.79832 q^{53} +5.65309 q^{54} -0.880270 q^{55} -5.04870 q^{56} +3.15781 q^{57} +6.81432 q^{58} +12.2524 q^{59} +1.27102 q^{60} -6.41861 q^{61} -8.51050 q^{62} +4.62041 q^{63} +1.00000 q^{64} -1.39908 q^{65} -1.44389 q^{66} +2.66780 q^{67} -3.33984 q^{68} -0.858786 q^{69} +4.44421 q^{70} +8.78579 q^{71} -0.915168 q^{72} +0.0781045 q^{73} -11.5469 q^{74} +6.10064 q^{75} -2.18701 q^{76} -5.04870 q^{77} -2.29489 q^{78} -0.149095 q^{79} -0.880270 q^{80} -5.41696 q^{81} -0.0999763 q^{82} +6.73880 q^{83} +7.28978 q^{84} +2.93996 q^{85} -7.64379 q^{86} -9.83915 q^{87} +1.00000 q^{88} -13.1212 q^{89} +0.805595 q^{90} -8.02427 q^{91} +0.594770 q^{92} +12.2883 q^{93} +10.6610 q^{94} +1.92516 q^{95} -1.44389 q^{96} +7.38017 q^{97} +18.4893 q^{98} -0.915168 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.44389	−0.833633	−0.416816	−	0.908991i	$-0.636854\pi$
$3$	−1.44389	−0.833633	−0.416816	+	0.908991i	$0.636854\pi$
$4$	1.00000	0.500000
$5$	−0.880270	−0.393669	−0.196834	−	0.980437i	$-0.563066\pi$
$5$	−0.880270	−0.393669	−0.196834	+	0.980437i	$0.563066\pi$
$6$	−1.44389	−0.589467
$7$	−5.04870	−1.90823	−0.954114	−	0.299444i	$-0.903199\pi$
$7$	−5.04870	−1.90823	−0.954114	+	0.299444i	$0.903199\pi$
$8$	1.00000	0.353553
$9$	−0.915168	−0.305056
$10$	−0.880270	−0.278366
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.44389	−0.416816
$13$	1.58937	0.440813	0.220407	−	0.975408i	$-0.429262\pi$
$13$	1.58937	0.440813	0.220407	+	0.975408i	$0.429262\pi$
$14$	−5.04870	−1.34932
$15$	1.27102	0.328175
$16$	1.00000	0.250000
$17$	−3.33984	−0.810029	−0.405015	−	0.914310i	$-0.632734\pi$
$17$	−3.33984	−0.810029	−0.405015	+	0.914310i	$0.632734\pi$
$18$	−0.915168	−0.215707
$19$	−2.18701	−0.501734	−0.250867	−	0.968022i	$-0.580716\pi$
$19$	−2.18701	−0.501734	−0.250867	+	0.968022i	$0.580716\pi$
$20$	−0.880270	−0.196834
$21$	7.28978	1.59076
$22$	1.00000	0.213201
$23$	0.594770	0.124018	0.0620091	−	0.998076i	$-0.480249\pi$
$23$	0.594770	0.124018	0.0620091	+	0.998076i	$0.480249\pi$
$24$	−1.44389	−0.294734
$25$	−4.22513	−0.845025
$26$	1.58937	0.311702
$27$	5.65309	1.08794
$28$	−5.04870	−0.954114
$29$	6.81432	1.26539	0.632693	−	0.774402i	$-0.281949\pi$
$29$	6.81432	1.26539	0.632693	+	0.774402i	$0.281949\pi$
$30$	1.27102	0.232055
$31$	−8.51050	−1.52853	−0.764265	−	0.644902i	$-0.776898\pi$
$31$	−8.51050	−1.52853	−0.764265	+	0.644902i	$0.776898\pi$
$32$	1.00000	0.176777
$33$	−1.44389	−0.251350
$34$	−3.33984	−0.572777
$35$	4.44421	0.751209
$36$	−0.915168	−0.152528
$37$	−11.5469	−1.89830	−0.949151	−	0.314822i	$-0.898055\pi$
$37$	−11.5469	−1.89830	−0.949151	+	0.314822i	$0.898055\pi$
$38$	−2.18701	−0.354780
$39$	−2.29489	−0.367476
$40$	−0.880270	−0.139183
$41$	−0.0999763	−0.0156137	−0.00780684	−	0.999970i	$-0.502485\pi$
$41$	−0.0999763	−0.0156137	−0.00780684	+	0.999970i	$0.502485\pi$
$42$	7.28978	1.12484
$43$	−7.64379	−1.16567	−0.582833	−	0.812592i	$-0.698056\pi$
$43$	−7.64379	−1.16567	−0.582833	+	0.812592i	$0.698056\pi$
$44$	1.00000	0.150756
$45$	0.805595	0.120091
$46$	0.594770	0.0876941
$47$	10.6610	1.55507	0.777533	−	0.628842i	$-0.216471\pi$
$47$	10.6610	1.55507	0.777533	+	0.628842i	$0.216471\pi$
$48$	−1.44389	−0.208408
$49$	18.4893	2.64133
$50$	−4.22513	−0.597523
$51$	4.82237	0.675267
$52$	1.58937	0.220407
$53$	−8.79832	−1.20854	−0.604271	−	0.796779i	$-0.706536\pi$
$53$	−8.79832	−1.20854	−0.604271	+	0.796779i	$0.706536\pi$
$54$	5.65309	0.769288
$55$	−0.880270	−0.118696
$56$	−5.04870	−0.674660
$57$	3.15781	0.418262
$58$	6.81432	0.894764
$59$	12.2524	1.59512	0.797562	−	0.603237i	$-0.206123\pi$
$59$	12.2524	1.59512	0.797562	+	0.603237i	$0.206123\pi$
$60$	1.27102	0.164088
$61$	−6.41861	−0.821819	−0.410909	−	0.911676i	$-0.634789\pi$
$61$	−6.41861	−0.821819	−0.410909	+	0.911676i	$0.634789\pi$
$62$	−8.51050	−1.08083
$63$	4.62041	0.582117
$64$	1.00000	0.125000
$65$	−1.39908	−0.173534
$66$	−1.44389	−0.177731
$67$	2.66780	0.325923	0.162962	−	0.986632i	$-0.447895\pi$
$67$	2.66780	0.325923	0.162962	+	0.986632i	$0.447895\pi$
$68$	−3.33984	−0.405015
$69$	−0.858786	−0.103386
$70$	4.44421	0.531185
$71$	8.78579	1.04268	0.521341	−	0.853349i	$-0.325432\pi$
$71$	8.78579	1.04268	0.521341	+	0.853349i	$0.325432\pi$
$72$	−0.915168	−0.107854
$73$	0.0781045	0.00914144	0.00457072	−	0.999990i	$-0.498545\pi$
$73$	0.0781045	0.00914144	0.00457072	+	0.999990i	$0.498545\pi$
$74$	−11.5469	−1.34230
$75$	6.10064	0.704441
$76$	−2.18701	−0.250867
$77$	−5.04870	−0.575352
$78$	−2.29489	−0.259845
$79$	−0.149095	−0.0167745	−0.00838724	−	0.999965i	$-0.502670\pi$
$79$	−0.149095	−0.0167745	−0.00838724	+	0.999965i	$0.502670\pi$
$80$	−0.880270	−0.0984171
$81$	−5.41696	−0.601885
$82$	−0.0999763	−0.0110405
$83$	6.73880	0.739680	0.369840	−	0.929096i	$-0.379413\pi$
$83$	6.73880	0.739680	0.369840	+	0.929096i	$0.379413\pi$
$84$	7.28978	0.795381
$85$	2.93996	0.318883
$86$	−7.64379	−0.824251
$87$	−9.83915	−1.05487
$88$	1.00000	0.106600
$89$	−13.1212	−1.39084	−0.695421	−	0.718602i	$-0.744782\pi$
$89$	−13.1212	−1.39084	−0.695421	+	0.718602i	$0.744782\pi$
$90$	0.805595	0.0849172
$91$	−8.02427	−0.841172
$92$	0.594770	0.0620091
$93$	12.2883	1.27423
$94$	10.6610	1.09960
$95$	1.92516	0.197517
$96$	−1.44389	−0.147367
$97$	7.38017	0.749342	0.374671	−	0.927158i	$-0.377756\pi$
$97$	7.38017	0.749342	0.374671	+	0.927158i	$0.377756\pi$
$98$	18.4893	1.86770
$99$	−0.915168	−0.0919779
$100$	−4.22513	−0.422513
$101$	10.4210	1.03692	0.518462	−	0.855101i	$-0.326505\pi$
$101$	10.4210	1.03692	0.518462	+	0.855101i	$0.326505\pi$
$102$	4.82237	0.477486
$103$	−1.04881	−0.103342	−0.0516710	−	0.998664i	$-0.516455\pi$
$103$	−1.04881	−0.103342	−0.0516710	+	0.998664i	$0.516455\pi$
$104$	1.58937	0.155851
$105$	−6.41698	−0.626233
$106$	−8.79832	−0.854568
$107$	14.8629	1.43685	0.718425	−	0.695604i	$-0.244863\pi$
$107$	14.8629	1.43685	0.718425	+	0.695604i	$0.244863\pi$
$108$	5.65309	0.543969
$109$	9.52282	0.912121	0.456060	−	0.889949i	$-0.349260\pi$
$109$	9.52282	0.912121	0.456060	+	0.889949i	$0.349260\pi$
$110$	−0.880270	−0.0839304
$111$	16.6725	1.58249
$112$	−5.04870	−0.477057
$113$	17.4354	1.64018	0.820091	−	0.572233i	$-0.193923\pi$
$113$	17.4354	1.64018	0.820091	+	0.572233i	$0.193923\pi$
$114$	3.15781	0.295756
$115$	−0.523558	−0.0488221
$116$	6.81432	0.632693
$117$	−1.45455	−0.134473
$118$	12.2524	1.12792
$119$	16.8618	1.54572
$120$	1.27102	0.116027
$121$	1.00000	0.0909091
$122$	−6.41861	−0.581114
$123$	0.144355	0.0130161
$124$	−8.51050	−0.764265
$125$	8.12060	0.726328
$126$	4.62041	0.411619
$127$	14.9631	1.32776	0.663882	−	0.747838i	$-0.268908\pi$
$127$	14.9631	1.32776	0.663882	+	0.747838i	$0.268908\pi$
$128$	1.00000	0.0883883
$129$	11.0368	0.971738
$130$	−1.39908	−0.122707
$131$	19.4126	1.69609	0.848043	−	0.529928i	$-0.177781\pi$
$131$	19.4126	1.69609	0.848043	+	0.529928i	$0.177781\pi$
$132$	−1.44389	−0.125675
$133$	11.0415	0.957424
$134$	2.66780	0.230463
$135$	−4.97624	−0.428287
$136$	−3.33984	−0.286389
$137$	−4.81891	−0.411707	−0.205854	−	0.978583i	$-0.565997\pi$
$137$	−4.81891	−0.411707	−0.205854	+	0.978583i	$0.565997\pi$
$138$	−0.858786	−0.0731047
$139$	−16.7243	−1.41854	−0.709269	−	0.704938i	$-0.750975\pi$
$139$	−16.7243	−1.41854	−0.709269	+	0.704938i	$0.750975\pi$
$140$	4.44421	0.375605
$141$	−15.3933	−1.29635
$142$	8.78579	0.737287
$143$	1.58937	0.132910
$144$	−0.915168	−0.0762640
$145$	−5.99844	−0.498143
$146$	0.0781045	0.00646397
$147$	−26.6966	−2.20190
$148$	−11.5469	−0.949151
$149$	−14.6284	−1.19840	−0.599201	−	0.800599i	$-0.704515\pi$
$149$	−14.6284	−1.19840	−0.599201	+	0.800599i	$0.704515\pi$
$150$	6.10064	0.498115
$151$	22.0137	1.79145	0.895725	−	0.444608i	$-0.146657\pi$
$151$	22.0137	1.79145	0.895725	+	0.444608i	$0.146657\pi$
$152$	−2.18701	−0.177390
$153$	3.05651	0.247104
$154$	−5.04870	−0.406835
$155$	7.49153	0.601734
$156$	−2.29489	−0.183738
$157$	−6.74428	−0.538252	−0.269126	−	0.963105i	$-0.586735\pi$
$157$	−6.74428	−0.538252	−0.269126	+	0.963105i	$0.586735\pi$
$158$	−0.149095	−0.0118614
$159$	12.7038	1.00748
$160$	−0.880270	−0.0695914
$161$	−3.00282	−0.236655
$162$	−5.41696	−0.425597
$163$	−7.86399	−0.615955	−0.307977	−	0.951394i	$-0.599652\pi$
$163$	−7.86399	−0.615955	−0.307977	+	0.951394i	$0.599652\pi$
$164$	−0.0999763	−0.00780684
$165$	1.27102	0.0989485
$166$	6.73880	0.523032
$167$	12.2190	0.945534	0.472767	−	0.881187i	$-0.343255\pi$
$167$	12.2190	0.945534	0.472767	+	0.881187i	$0.343255\pi$
$168$	7.28978	0.562419
$169$	−10.4739	−0.805684
$170$	2.93996	0.225484
$171$	2.00148	0.153057
$172$	−7.64379	−0.582833
$173$	−2.73513	−0.207948	−0.103974	−	0.994580i	$-0.533156\pi$
$173$	−2.73513	−0.207948	−0.103974	+	0.994580i	$0.533156\pi$
$174$	−9.83915	−0.745904
$175$	21.3314	1.61250
$176$	1.00000	0.0753778
$177$	−17.6911	−1.32975
$178$	−13.1212	−0.983474
$179$	9.45338	0.706579	0.353289	−	0.935514i	$-0.385063\pi$
$179$	9.45338	0.706579	0.353289	+	0.935514i	$0.385063\pi$
$180$	0.805595	0.0600455
$181$	19.1365	1.42240	0.711202	−	0.702988i	$-0.248151\pi$
$181$	19.1365	1.42240	0.711202	+	0.702988i	$0.248151\pi$
$182$	−8.02427	−0.594798
$183$	9.26780	0.685095
$184$	0.594770	0.0438471
$185$	10.1644	0.747301
$186$	12.2883	0.901019
$187$	−3.33984	−0.244233
$188$	10.6610	0.777533
$189$	−28.5407	−2.07603
$190$	1.92516	0.139666
$191$	17.2098	1.24526	0.622628	−	0.782518i	$-0.286065\pi$
$191$	17.2098	1.24526	0.622628	+	0.782518i	$0.286065\pi$
$192$	−1.44389	−0.104204
$193$	−6.91213	−0.497546	−0.248773	−	0.968562i	$-0.580027\pi$
$193$	−6.91213	−0.497546	−0.248773	+	0.968562i	$0.580027\pi$
$194$	7.38017	0.529865
$195$	2.02012	0.144664
$196$	18.4893	1.32067
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−0.915168	−0.0650382
$199$	−5.37847	−0.381269	−0.190635	−	0.981661i	$-0.561055\pi$
$199$	−5.37847	−0.381269	−0.190635	+	0.981661i	$0.561055\pi$
$200$	−4.22513	−0.298761
$201$	−3.85202	−0.271700
$202$	10.4210	0.733216
$203$	−34.4034	−2.41465
$204$	4.82237	0.337634
$205$	0.0880061	0.00614661
$206$	−1.04881	−0.0730738
$207$	−0.544315	−0.0378325
$208$	1.58937	0.110203
$209$	−2.18701	−0.151279
$210$	−6.41698	−0.442813
$211$	−26.6202	−1.83261	−0.916305	−	0.400480i	$-0.868843\pi$
$211$	−26.6202	−1.83261	−0.916305	+	0.400480i	$0.868843\pi$
$212$	−8.79832	−0.604271
$213$	−12.6858	−0.869214
$214$	14.8629	1.01601
$215$	6.72859	0.458886
$216$	5.65309	0.384644
$217$	42.9669	2.91678
$218$	9.52282	0.644967
$219$	−0.112775	−0.00762061
$220$	−0.880270	−0.0593478
$221$	−5.30825	−0.357072
$222$	16.6725	1.11899
$223$	−15.6479	−1.04786	−0.523930	−	0.851761i	$-0.675535\pi$
$223$	−15.6479	−1.04786	−0.523930	+	0.851761i	$0.675535\pi$
$224$	−5.04870	−0.337330
$225$	3.86670	0.257780
$226$	17.4354	1.15978
$227$	−13.3236	−0.884317	−0.442158	−	0.896937i	$-0.645787\pi$
$227$	−13.3236	−0.884317	−0.442158	+	0.896937i	$0.645787\pi$
$228$	3.15781	0.209131
$229$	14.7794	0.976648	0.488324	−	0.872663i	$-0.337609\pi$
$229$	14.7794	0.976648	0.488324	+	0.872663i	$0.337609\pi$
$230$	−0.523558	−0.0345224
$231$	7.28978	0.479633
$232$	6.81432	0.447382
$233$	−13.5300	−0.886380	−0.443190	−	0.896428i	$-0.646153\pi$
$233$	−13.5300	−0.886380	−0.443190	+	0.896428i	$0.646153\pi$
$234$	−1.45455	−0.0950866
$235$	−9.38455	−0.612180
$236$	12.2524	0.797562
$237$	0.215277	0.0139838
$238$	16.8618	1.09299
$239$	−3.32174	−0.214866	−0.107433	−	0.994212i	$-0.534263\pi$
$239$	−3.32174	−0.214866	−0.107433	+	0.994212i	$0.534263\pi$
$240$	1.27102	0.0820438
$241$	−1.44506	−0.0930846	−0.0465423	−	0.998916i	$-0.514820\pi$
$241$	−1.44506	−0.0930846	−0.0465423	+	0.998916i	$0.514820\pi$
$242$	1.00000	0.0642824
$243$	−9.13775	−0.586187
$244$	−6.41861	−0.410909
$245$	−16.2756	−1.03981
$246$	0.144355	0.00920375
$247$	−3.47598	−0.221171
$248$	−8.51050	−0.540417
$249$	−9.73012	−0.616621
$250$	8.12060	0.513592
$251$	−0.391010	−0.0246803	−0.0123402	−	0.999924i	$-0.503928\pi$
$251$	−0.391010	−0.0246803	−0.0123402	+	0.999924i	$0.503928\pi$
$252$	4.62041	0.291058
$253$	0.594770	0.0373929
$254$	14.9631	0.938870
$255$	−4.24499	−0.265831
$256$	1.00000	0.0625000
$257$	−23.9484	−1.49386	−0.746931	−	0.664902i	$-0.768473\pi$
$257$	−23.9484	−1.49386	−0.746931	+	0.664902i	$0.768473\pi$
$258$	11.0368	0.687123
$259$	58.2969	3.62239
$260$	−1.39908	−0.0867671
$261$	−6.23625	−0.386014
$262$	19.4126	1.19931
$263$	3.06283	0.188862	0.0944312	−	0.995531i	$-0.469897\pi$
$263$	3.06283	0.188862	0.0944312	+	0.995531i	$0.469897\pi$
$264$	−1.44389	−0.0888656
$265$	7.74489	0.475765
$266$	11.0415	0.677001
$267$	18.9456	1.15945
$268$	2.66780	0.162962
$269$	23.6940	1.44465	0.722325	−	0.691553i	$-0.243073\pi$
$269$	23.6940	1.44465	0.722325	+	0.691553i	$0.243073\pi$
$270$	−4.97624	−0.302845
$271$	29.5632	1.79584	0.897919	−	0.440160i	$-0.145078\pi$
$271$	29.5632	1.79584	0.897919	+	0.440160i	$0.145078\pi$
$272$	−3.33984	−0.202507
$273$	11.5862	0.701228
$274$	−4.81891	−0.291121
$275$	−4.22513	−0.254785
$276$	−0.858786	−0.0516928
$277$	−31.3643	−1.88450	−0.942250	−	0.334910i	$-0.891294\pi$
$277$	−31.3643	−1.88450	−0.942250	+	0.334910i	$0.891294\pi$
$278$	−16.7243	−1.00306
$279$	7.78854	0.466288
$280$	4.44421	0.265593
$281$	6.32290	0.377193	0.188596	−	0.982055i	$-0.439606\pi$
$281$	6.32290	0.377193	0.188596	+	0.982055i	$0.439606\pi$
$282$	−15.3933	−0.916661
$283$	−12.5026	−0.743203	−0.371601	−	0.928392i	$-0.621191\pi$
$283$	−12.5026	−0.743203	−0.371601	+	0.928392i	$0.621191\pi$
$284$	8.78579	0.521341
$285$	−2.77973	−0.164657
$286$	1.58937	0.0939817
$287$	0.504750	0.0297944
$288$	−0.915168	−0.0539268
$289$	−5.84549	−0.343852
$290$	−5.99844	−0.352240
$291$	−10.6562	−0.624676
$292$	0.0781045	0.00457072
$293$	−19.6350	−1.14709	−0.573543	−	0.819175i	$-0.694432\pi$
$293$	−19.6350	−1.14709	−0.573543	+	0.819175i	$0.694432\pi$
$294$	−26.6966	−1.55698
$295$	−10.7854	−0.627950
$296$	−11.5469	−0.671151
$297$	5.65309	0.328026
$298$	−14.6284	−0.847398
$299$	0.945313	0.0546689
$300$	6.10064	0.352220
$301$	38.5912	2.22436
$302$	22.0137	1.26675
$303$	−15.0468	−0.864414
$304$	−2.18701	−0.125434
$305$	5.65011	0.323524
$306$	3.05651	0.174729
$307$	19.4170	1.10819	0.554094	−	0.832454i	$-0.313065\pi$
$307$	19.4170	1.10819	0.554094	+	0.832454i	$0.313065\pi$
$308$	−5.04870	−0.287676
$309$	1.51437	0.0861493
$310$	7.49153	0.425491
$311$	−9.47098	−0.537050	−0.268525	−	0.963273i	$-0.586536\pi$
$311$	−9.47098	−0.537050	−0.268525	+	0.963273i	$0.586536\pi$
$312$	−2.29489	−0.129923
$313$	14.4608	0.817374	0.408687	−	0.912675i	$-0.365987\pi$
$313$	14.4608	0.817374	0.408687	+	0.912675i	$0.365987\pi$
$314$	−6.74428	−0.380602
$315$	−4.06720	−0.229161
$316$	−0.149095	−0.00838724
$317$	15.6786	0.880600	0.440300	−	0.897851i	$-0.354872\pi$
$317$	15.6786	0.880600	0.440300	+	0.897851i	$0.354872\pi$
$318$	12.7038	0.712396
$319$	6.81432	0.381528
$320$	−0.880270	−0.0492086
$321$	−21.4604	−1.19781
$322$	−3.00282	−0.167340
$323$	7.30426	0.406420
$324$	−5.41696	−0.300942
$325$	−6.71531	−0.372498
$326$	−7.86399	−0.435546
$327$	−13.7499	−0.760374
$328$	−0.0999763	−0.00552027
$329$	−53.8241	−2.96742
$330$	1.27102	0.0699672
$331$	−16.6573	−0.915567	−0.457784	−	0.889064i	$-0.651357\pi$
$331$	−16.6573	−0.915567	−0.457784	+	0.889064i	$0.651357\pi$
$332$	6.73880	0.369840
$333$	10.5674	0.579088
$334$	12.2190	0.668594
$335$	−2.34838	−0.128306
$336$	7.28978	0.397690
$337$	32.3648	1.76303	0.881513	−	0.472160i	$-0.156526\pi$
$337$	32.3648	1.76303	0.881513	+	0.472160i	$0.156526\pi$
$338$	−10.4739	−0.569704
$339$	−25.1748	−1.36731
$340$	2.93996	0.159442
$341$	−8.51050	−0.460869
$342$	2.00148	0.108228
$343$	−58.0061	−3.13204
$344$	−7.64379	−0.412125
$345$	0.755963	0.0406997
$346$	−2.73513	−0.147042
$347$	−19.4041	−1.04167	−0.520835	−	0.853658i	$-0.674379\pi$
$347$	−19.4041	−1.04167	−0.520835	+	0.853658i	$0.674379\pi$
$348$	−9.83915	−0.527434
$349$	9.64496	0.516283	0.258141	−	0.966107i	$-0.416890\pi$
$349$	9.64496	0.516283	0.258141	+	0.966107i	$0.416890\pi$
$350$	21.3314	1.14021
$351$	8.98488	0.479577
$352$	1.00000	0.0533002
$353$	21.6340	1.15146	0.575731	−	0.817639i	$-0.304718\pi$
$353$	21.6340	1.15146	0.575731	+	0.817639i	$0.304718\pi$
$354$	−17.6911	−0.940273
$355$	−7.73387	−0.410471
$356$	−13.1212	−0.695421
$357$	−24.3467	−1.28856
$358$	9.45338	0.499627
$359$	3.30685	0.174529	0.0872645	−	0.996185i	$-0.472187\pi$
$359$	3.30685	0.174529	0.0872645	+	0.996185i	$0.472187\pi$
$360$	0.805595	0.0424586
$361$	−14.2170	−0.748263
$362$	19.1365	1.00579
$363$	−1.44389	−0.0757848
$364$	−8.02427	−0.420586
$365$	−0.0687530	−0.00359870
$366$	9.26780	0.484436
$367$	6.97451	0.364067	0.182033	−	0.983292i	$-0.441732\pi$
$367$	6.97451	0.364067	0.182033	+	0.983292i	$0.441732\pi$
$368$	0.594770	0.0310046
$369$	0.0914952	0.00476305
$370$	10.1644	0.528422
$371$	44.4200	2.30617
$372$	12.2883	0.637117
$373$	−27.4676	−1.42222	−0.711108	−	0.703083i	$-0.751806\pi$
$373$	−27.4676	−1.42222	−0.711108	+	0.703083i	$0.751806\pi$
$374$	−3.33984	−0.172699
$375$	−11.7253	−0.605491
$376$	10.6610	0.549799
$377$	10.8305	0.557799
$378$	−28.5407	−1.46798
$379$	−1.24602	−0.0640040	−0.0320020	−	0.999488i	$-0.510188\pi$
$379$	−1.24602	−0.0640040	−0.0320020	+	0.999488i	$0.510188\pi$
$380$	1.92516	0.0987585
$381$	−21.6052	−1.10687
$382$	17.2098	0.880528
$383$	−15.2911	−0.781340	−0.390670	−	0.920531i	$-0.627757\pi$
$383$	−15.2911	−0.781340	−0.390670	+	0.920531i	$0.627757\pi$
$384$	−1.44389	−0.0736834
$385$	4.44421	0.226498
$386$	−6.91213	−0.351818
$387$	6.99535	0.355594
$388$	7.38017	0.374671
$389$	12.1854	0.617823	0.308912	−	0.951091i	$-0.400035\pi$
$389$	12.1854	0.617823	0.308912	+	0.951091i	$0.400035\pi$
$390$	2.02012	0.102293
$391$	−1.98644	−0.100458
$392$	18.4893	0.933852
$393$	−28.0297	−1.41391
$394$	1.00000	0.0503793
$395$	0.131244	0.00660359
$396$	−0.915168	−0.0459889
$397$	−33.6081	−1.68674	−0.843372	−	0.537330i	$-0.819433\pi$
$397$	−33.6081	−1.68674	−0.843372	+	0.537330i	$0.819433\pi$
$398$	−5.37847	−0.269598
$399$	−15.9428	−0.798140
$400$	−4.22513	−0.211256
$401$	−27.5483	−1.37570	−0.687849	−	0.725854i	$-0.741445\pi$
$401$	−27.5483	−1.37570	−0.687849	+	0.725854i	$0.741445\pi$
$402$	−3.85202	−0.192121
$403$	−13.5264	−0.673796
$404$	10.4210	0.518462
$405$	4.76839	0.236943
$406$	−34.4034	−1.70741
$407$	−11.5469	−0.572359
$408$	4.82237	0.238743
$409$	24.6144	1.21710	0.608552	−	0.793514i	$-0.291751\pi$
$409$	24.6144	1.21710	0.608552	+	0.793514i	$0.291751\pi$
$410$	0.0880061	0.00434631
$411$	6.95800	0.343213
$412$	−1.04881	−0.0516710
$413$	−61.8585	−3.04386
$414$	−0.544315	−0.0267516
$415$	−5.93196	−0.291189
$416$	1.58937	0.0779255
$417$	24.1481	1.18254
$418$	−2.18701	−0.106970
$419$	16.9172	0.826459	0.413230	−	0.910627i	$-0.364401\pi$
$419$	16.9172	0.826459	0.413230	+	0.910627i	$0.364401\pi$
$420$	−6.41698	−0.313116
$421$	19.7096	0.960588	0.480294	−	0.877107i	$-0.340530\pi$
$421$	19.7096	0.960588	0.480294	+	0.877107i	$0.340530\pi$
$422$	−26.6202	−1.29585
$423$	−9.75660	−0.474382
$424$	−8.79832	−0.427284
$425$	14.1112	0.684495
$426$	−12.6858	−0.614627
$427$	32.4056	1.56822
$428$	14.8629	0.718425
$429$	−2.29489	−0.110798
$430$	6.72859	0.324482
$431$	−18.7848	−0.904834	−0.452417	−	0.891807i	$-0.649438\pi$
$431$	−18.7848	−0.904834	−0.452417	+	0.891807i	$0.649438\pi$
$432$	5.65309	0.271984
$433$	8.72681	0.419384	0.209692	−	0.977768i	$-0.432754\pi$
$433$	8.72681	0.419384	0.209692	+	0.977768i	$0.432754\pi$
$434$	42.9669	2.06248
$435$	8.66111	0.415268
$436$	9.52282	0.456060
$437$	−1.30077	−0.0622242
$438$	−0.112775	−0.00538858
$439$	7.05658	0.336792	0.168396	−	0.985719i	$-0.446141\pi$
$439$	7.05658	0.336792	0.168396	+	0.985719i	$0.446141\pi$
$440$	−0.880270	−0.0419652
$441$	−16.9209	−0.805755
$442$	−5.30825	−0.252488
$443$	25.2265	1.19855	0.599275	−	0.800543i	$-0.295456\pi$
$443$	25.2265	1.19855	0.599275	+	0.800543i	$0.295456\pi$
$444$	16.6725	0.791243
$445$	11.5502	0.547531
$446$	−15.6479	−0.740949
$447$	21.1218	0.999028
$448$	−5.04870	−0.238528
$449$	13.3348	0.629306	0.314653	−	0.949207i	$-0.398112\pi$
$449$	13.3348	0.629306	0.314653	+	0.949207i	$0.398112\pi$
$450$	3.86670	0.182278
$451$	−0.0999763	−0.00470770
$452$	17.4354	0.820091
$453$	−31.7855	−1.49341
$454$	−13.3236	−0.625306
$455$	7.06352	0.331143
$456$	3.15781	0.147878
$457$	−15.9201	−0.744709	−0.372354	−	0.928091i	$-0.621449\pi$
$457$	−15.9201	−0.744709	−0.372354	+	0.928091i	$0.621449\pi$
$458$	14.7794	0.690594
$459$	−18.8804	−0.881262
$460$	−0.523558	−0.0244110
$461$	12.5893	0.586342	0.293171	−	0.956060i	$-0.405290\pi$
$461$	12.5893	0.586342	0.293171	+	0.956060i	$0.405290\pi$
$462$	7.28978	0.339151
$463$	33.6257	1.56272	0.781360	−	0.624080i	$-0.214526\pi$
$463$	33.6257	1.56272	0.781360	+	0.624080i	$0.214526\pi$
$464$	6.81432	0.316347
$465$	−10.8170	−0.501626
$466$	−13.5300	−0.626765
$467$	25.4854	1.17932	0.589662	−	0.807650i	$-0.299261\pi$
$467$	25.4854	1.17932	0.589662	+	0.807650i	$0.299261\pi$
$468$	−1.45455	−0.0672364
$469$	−13.4689	−0.621936
$470$	−9.38455	−0.432877
$471$	9.73803	0.448705
$472$	12.2524	0.563961
$473$	−7.64379	−0.351462
$474$	0.215277	0.00988802
$475$	9.24039	0.423978
$476$	16.8618	0.772860
$477$	8.05195	0.368673
$478$	−3.32174	−0.151933
$479$	22.4360	1.02513	0.512563	−	0.858649i	$-0.328696\pi$
$479$	22.4360	1.02513	0.512563	+	0.858649i	$0.328696\pi$
$480$	1.27102	0.0580137
$481$	−18.3524	−0.836796
$482$	−1.44506	−0.0658208
$483$	4.33575	0.197283
$484$	1.00000	0.0454545
$485$	−6.49654	−0.294993
$486$	−9.13775	−0.414497
$487$	21.2895	0.964721	0.482361	−	0.875973i	$-0.339779\pi$
$487$	21.2895	0.964721	0.482361	+	0.875973i	$0.339779\pi$
$488$	−6.41861	−0.290557
$489$	11.3548	0.513480
$490$	−16.2756	−0.735256
$491$	−22.0437	−0.994820	−0.497410	−	0.867516i	$-0.665716\pi$
$491$	−22.0437	−0.994820	−0.497410	+	0.867516i	$0.665716\pi$
$492$	0.144355	0.00650804
$493$	−22.7587	−1.02500
$494$	−3.47598	−0.156392
$495$	0.805595	0.0362088
$496$	−8.51050	−0.382133
$497$	−44.3568	−1.98967
$498$	−9.73012	−0.436017
$499$	−34.1956	−1.53081	−0.765404	−	0.643550i	$-0.777461\pi$
$499$	−34.1956	−1.53081	−0.765404	+	0.643550i	$0.777461\pi$
$500$	8.12060	0.363164
$501$	−17.6429	−0.788228
$502$	−0.391010	−0.0174516
$503$	−4.99014	−0.222499	−0.111250	−	0.993792i	$-0.535485\pi$
$503$	−4.99014	−0.222499	−0.111250	+	0.993792i	$0.535485\pi$
$504$	4.62041	0.205809
$505$	−9.17325	−0.408204
$506$	0.594770	0.0264408
$507$	15.1232	0.671645
$508$	14.9631	0.663882
$509$	8.12393	0.360087	0.180043	−	0.983659i	$-0.442376\pi$
$509$	8.12393	0.360087	0.180043	+	0.983659i	$0.442376\pi$
$510$	−4.24499	−0.187971
$511$	−0.394326	−0.0174439
$512$	1.00000	0.0441942
$513$	−12.3634	−0.545856
$514$	−23.9484	−1.05632
$515$	0.923232	0.0406825
$516$	11.0368	0.485869
$517$	10.6610	0.468870
$518$	58.2969	2.56142
$519$	3.94924	0.173353
$520$	−1.39908	−0.0613536
$521$	36.4451	1.59669	0.798343	−	0.602202i	$-0.205710\pi$
$521$	36.4451	1.59669	0.798343	+	0.602202i	$0.205710\pi$
$522$	−6.23625	−0.272953
$523$	5.87211	0.256770	0.128385	−	0.991724i	$-0.459021\pi$
$523$	5.87211	0.256770	0.128385	+	0.991724i	$0.459021\pi$
$524$	19.4126	0.848043
$525$	−30.8003	−1.34423
$526$	3.06283	0.133546
$527$	28.4237	1.23815
$528$	−1.44389	−0.0628374
$529$	−22.6462	−0.984619
$530$	7.74489	0.336417
$531$	−11.2130	−0.486602
$532$	11.0415	0.478712
$533$	−0.158900	−0.00688271
$534$	18.9456	0.819856
$535$	−13.0834	−0.565643
$536$	2.66780	0.115231
$537$	−13.6497	−0.589027
$538$	23.6940	1.02152
$539$	18.4893	0.796392
$540$	−4.97624	−0.214143
$541$	−18.6061	−0.799939	−0.399969	−	0.916528i	$-0.630979\pi$
$541$	−18.6061	−0.799939	−0.399969	+	0.916528i	$0.630979\pi$
$542$	29.5632	1.26985
$543$	−27.6311	−1.18576
$544$	−3.33984	−0.143194
$545$	−8.38265	−0.359073
$546$	11.5862	0.495843
$547$	10.7066	0.457780	0.228890	−	0.973452i	$-0.426490\pi$
$547$	10.7066	0.457780	0.228890	+	0.973452i	$0.426490\pi$
$548$	−4.81891	−0.205854
$549$	5.87411	0.250701
$550$	−4.22513	−0.180160
$551$	−14.9030	−0.634888
$552$	−0.858786	−0.0365524
$553$	0.752735	0.0320095
$554$	−31.3643	−1.33254
$555$	−14.6763	−0.622975
$556$	−16.7243	−0.709269
$557$	−16.9689	−0.718994	−0.359497	−	0.933146i	$-0.617052\pi$
$557$	−16.9689	−0.718994	−0.359497	+	0.933146i	$0.617052\pi$
$558$	7.78854	0.329715
$559$	−12.1488	−0.513841
$560$	4.44421	0.187802
$561$	4.82237	0.203601
$562$	6.32290	0.266715
$563$	−1.21078	−0.0510285	−0.0255142	−	0.999674i	$-0.508122\pi$
$563$	−1.21078	−0.0510285	−0.0255142	+	0.999674i	$0.508122\pi$
$564$	−15.3933	−0.648177
$565$	−15.3478	−0.645688
$566$	−12.5026	−0.525524
$567$	27.3486	1.14853
$568$	8.78579	0.368644
$569$	8.01404	0.335966	0.167983	−	0.985790i	$-0.446275\pi$
$569$	8.01404	0.335966	0.167983	+	0.985790i	$0.446275\pi$
$570$	−2.77973	−0.116430
$571$	−4.48484	−0.187685	−0.0938424	−	0.995587i	$-0.529915\pi$
$571$	−4.48484	−0.187685	−0.0938424	+	0.995587i	$0.529915\pi$
$572$	1.58937	0.0664551
$573$	−24.8491	−1.03809
$574$	0.504750	0.0210679
$575$	−2.51298	−0.104799
$576$	−0.915168	−0.0381320
$577$	−7.35900	−0.306359	−0.153180	−	0.988198i	$-0.548951\pi$
$577$	−7.35900	−0.306359	−0.153180	+	0.988198i	$0.548951\pi$
$578$	−5.84549	−0.243140
$579$	9.98038	0.414771
$580$	−5.99844	−0.249071
$581$	−34.0222	−1.41148
$582$	−10.6562	−0.441713
$583$	−8.79832	−0.364389
$584$	0.0781045	0.00323199
$585$	1.28039	0.0529377
$586$	−19.6350	−0.811113
$587$	32.9009	1.35797	0.678983	−	0.734154i	$-0.262421\pi$
$587$	32.9009	1.35797	0.678983	+	0.734154i	$0.262421\pi$
$588$	−26.6966	−1.10095
$589$	18.6125	0.766916
$590$	−10.7854	−0.444028
$591$	−1.44389	−0.0593939
$592$	−11.5469	−0.474575
$593$	23.3548	0.959067	0.479534	−	0.877524i	$-0.340806\pi$
$593$	23.3548	0.959067	0.479534	+	0.877524i	$0.340806\pi$
$594$	5.65309	0.231949
$595$	−14.8429	−0.608502
$596$	−14.6284	−0.599201
$597$	7.76594	0.317839
$598$	0.945313	0.0386567
$599$	−25.0587	−1.02387	−0.511936	−	0.859024i	$-0.671071\pi$
$599$	−25.0587	−1.02387	−0.511936	+	0.859024i	$0.671071\pi$
$600$	6.10064	0.249057
$601$	0.112766	0.00459984	0.00229992	−	0.999997i	$-0.499268\pi$
$601$	0.112766	0.00459984	0.00229992	+	0.999997i	$0.499268\pi$
$602$	38.5912	1.57286
$603$	−2.44148	−0.0994249
$604$	22.0137	0.895725
$605$	−0.880270	−0.0357881
$606$	−15.0468	−0.611233
$607$	−24.0781	−0.977300	−0.488650	−	0.872480i	$-0.662511\pi$
$607$	−24.0781	−0.977300	−0.488650	+	0.872480i	$0.662511\pi$
$608$	−2.18701	−0.0886950
$609$	49.6749	2.01293
$610$	5.65011	0.228766
$611$	16.9443	0.685493
$612$	3.05651	0.123552
$613$	−25.2776	−1.02095	−0.510477	−	0.859892i	$-0.670531\pi$
$613$	−25.2776	−1.02095	−0.510477	+	0.859892i	$0.670531\pi$
$614$	19.4170	0.783607
$615$	−0.127072	−0.00512402
$616$	−5.04870	−0.203418
$617$	12.3561	0.497438	0.248719	−	0.968576i	$-0.419991\pi$
$617$	12.3561	0.497438	0.248719	+	0.968576i	$0.419991\pi$
$618$	1.51437	0.0609167
$619$	3.51032	0.141091	0.0705457	−	0.997509i	$-0.477526\pi$
$619$	3.51032	0.141091	0.0705457	+	0.997509i	$0.477526\pi$
$620$	7.49153	0.300867
$621$	3.36229	0.134924
$622$	−9.47098	−0.379752
$623$	66.2448	2.65404
$624$	−2.29489	−0.0918691
$625$	13.9773	0.559092
$626$	14.4608	0.577971
$627$	3.15781	0.126111
$628$	−6.74428	−0.269126
$629$	38.5648	1.53768
$630$	−4.06720	−0.162041
$631$	36.0566	1.43539	0.717696	−	0.696357i	$-0.245197\pi$
$631$	36.0566	1.43539	0.717696	+	0.696357i	$0.245197\pi$
$632$	−0.149095	−0.00593068
$633$	38.4368	1.52772
$634$	15.6786	0.622678
$635$	−13.1716	−0.522699
$636$	12.7038	0.503740
$637$	29.3865	1.16433
$638$	6.81432	0.269781
$639$	−8.04048	−0.318076
$640$	−0.880270	−0.0347957
$641$	−1.98377	−0.0783543	−0.0391772	−	0.999232i	$-0.512474\pi$
$641$	−1.98377	−0.0783543	−0.0391772	+	0.999232i	$0.512474\pi$
$642$	−21.4604	−0.846976
$643$	−11.8958	−0.469125	−0.234563	−	0.972101i	$-0.575366\pi$
$643$	−11.8958	−0.469125	−0.234563	+	0.972101i	$0.575366\pi$
$644$	−3.00282	−0.118327
$645$	−9.71538	−0.382543
$646$	7.30426	0.287382
$647$	7.20476	0.283248	0.141624	−	0.989920i	$-0.454768\pi$
$647$	7.20476	0.283248	0.141624	+	0.989920i	$0.454768\pi$
$648$	−5.41696	−0.212798
$649$	12.2524	0.480948
$650$	−6.71531	−0.263396
$651$	−62.0397	−2.43153
$652$	−7.86399	−0.307977
$653$	23.9709	0.938055	0.469028	−	0.883184i	$-0.344604\pi$
$653$	23.9709	0.938055	0.469028	+	0.883184i	$0.344604\pi$
$654$	−13.7499	−0.537666
$655$	−17.0883	−0.667695
$656$	−0.0999763	−0.00390342
$657$	−0.0714788	−0.00278865
$658$	−53.8241	−2.09828
$659$	−2.27960	−0.0888005	−0.0444002	−	0.999014i	$-0.514138\pi$
$659$	−2.27960	−0.0888005	−0.0444002	+	0.999014i	$0.514138\pi$
$660$	1.27102	0.0494743
$661$	1.65178	0.0642467	0.0321233	−	0.999484i	$-0.489773\pi$
$661$	1.65178	0.0642467	0.0321233	+	0.999484i	$0.489773\pi$
$662$	−16.6573	−0.647404
$663$	7.66456	0.297667
$664$	6.73880	0.261516
$665$	−9.71954	−0.376908
$666$	10.5674	0.409477
$667$	4.05295	0.156931
$668$	12.2190	0.472767
$669$	22.5939	0.873531
$670$	−2.34838	−0.0907259
$671$	−6.41861	−0.247788
$672$	7.28978	0.281210
$673$	−4.04331	−0.155858	−0.0779291	−	0.996959i	$-0.524831\pi$
$673$	−4.04331	−0.155858	−0.0779291	+	0.996959i	$0.524831\pi$
$674$	32.3648	1.24665
$675$	−23.8850	−0.919335
$676$	−10.4739	−0.402842
$677$	−14.1594	−0.544190	−0.272095	−	0.962270i	$-0.587717\pi$
$677$	−14.1594	−0.544190	−0.272095	+	0.962270i	$0.587717\pi$
$678$	−25.1748	−0.966834
$679$	−37.2602	−1.42992
$680$	2.93996	0.112742
$681$	19.2378	0.737195
$682$	−8.51050	−0.325884
$683$	10.3207	0.394911	0.197456	−	0.980312i	$-0.436732\pi$
$683$	10.3207	0.394911	0.197456	+	0.980312i	$0.436732\pi$
$684$	2.00148	0.0765286
$685$	4.24194	0.162076
$686$	−58.0061	−2.21468
$687$	−21.3398	−0.814166
$688$	−7.64379	−0.291417
$689$	−13.9838	−0.532741
$690$	0.755963	0.0287790
$691$	−15.7126	−0.597735	−0.298867	−	0.954295i	$-0.596609\pi$
$691$	−15.7126	−0.597735	−0.298867	+	0.954295i	$0.596609\pi$
$692$	−2.73513	−0.103974
$693$	4.62041	0.175515
$694$	−19.4041	−0.736571
$695$	14.7219	0.558434
$696$	−9.83915	−0.372952
$697$	0.333905	0.0126475
$698$	9.64496	0.365067
$699$	19.5359	0.738915
$700$	21.3314	0.806250
$701$	21.1227	0.797793	0.398897	−	0.916996i	$-0.369393\pi$
$701$	21.1227	0.797793	0.398897	+	0.916996i	$0.369393\pi$
$702$	8.98488	0.339112
$703$	25.2532	0.952443
$704$	1.00000	0.0376889
$705$	13.5503	0.510334
$706$	21.6340	0.814206
$707$	−52.6122	−1.97869
$708$	−17.6911	−0.664874
$709$	−41.6743	−1.56511	−0.782555	−	0.622582i	$-0.786084\pi$
$709$	−41.6743	−1.56511	−0.782555	+	0.622582i	$0.786084\pi$
$710$	−7.73387	−0.290247
$711$	0.136447	0.00511716
$712$	−13.1212	−0.491737
$713$	−5.06179	−0.189566
$714$	−24.3467	−0.911152
$715$	−1.39908	−0.0523226
$716$	9.45338	0.353289
$717$	4.79624	0.179119
$718$	3.30685	0.123411
$719$	20.7487	0.773794	0.386897	−	0.922123i	$-0.373547\pi$
$719$	20.7487	0.773794	0.386897	+	0.922123i	$0.373547\pi$
$720$	0.805595	0.0300228
$721$	5.29510	0.197200
$722$	−14.2170	−0.529102
$723$	2.08652	0.0775984
$724$	19.1365	0.711202
$725$	−28.7913	−1.06928
$726$	−1.44389	−0.0535880
$727$	25.4430	0.943629	0.471815	−	0.881698i	$-0.343599\pi$
$727$	25.4430	0.943629	0.471815	+	0.881698i	$0.343599\pi$
$728$	−8.02427	−0.297399
$729$	29.4448	1.09055
$730$	−0.0687530	−0.00254466
$731$	25.5290	0.944224
$732$	9.26780	0.342548
$733$	−23.4763	−0.867117	−0.433558	−	0.901125i	$-0.642742\pi$
$733$	−23.4763	−0.867117	−0.433558	+	0.901125i	$0.642742\pi$
$734$	6.97451	0.257434
$735$	23.5002	0.866820
$736$	0.594770	0.0219235
$737$	2.66780	0.0982696
$738$	0.0914952	0.00336798
$739$	52.5932	1.93467	0.967337	−	0.253495i	$-0.0815803\pi$
$739$	52.5932	1.93467	0.967337	+	0.253495i	$0.0815803\pi$
$740$	10.1644	0.373651
$741$	5.01894	0.184376
$742$	44.4200	1.63071
$743$	13.1888	0.483851	0.241925	−	0.970295i	$-0.422221\pi$
$743$	13.1888	0.483851	0.241925	+	0.970295i	$0.422221\pi$
$744$	12.2883	0.450510
$745$	12.8769	0.471773
$746$	−27.4676	−1.00566
$747$	−6.16714	−0.225644
$748$	−3.33984	−0.122117
$749$	−75.0382	−2.74184
$750$	−11.7253	−0.428147
$751$	39.8951	1.45579	0.727896	−	0.685687i	$-0.240498\pi$
$751$	39.8951	1.45579	0.727896	+	0.685687i	$0.240498\pi$
$752$	10.6610	0.388766
$753$	0.564577	0.0205743
$754$	10.8305	0.394424
$755$	−19.3780	−0.705238
$756$	−28.5407	−1.03802
$757$	−50.5984	−1.83903	−0.919516	−	0.393053i	$-0.871419\pi$
$757$	−50.5984	−1.83903	−0.919516	+	0.393053i	$0.871419\pi$
$758$	−1.24602	−0.0452577
$759$	−0.858786	−0.0311720
$760$	1.92516	0.0698328
$761$	1.70332	0.0617452	0.0308726	−	0.999523i	$-0.490171\pi$
$761$	1.70332	0.0617452	0.0308726	+	0.999523i	$0.490171\pi$
$762$	−21.6052	−0.782673
$763$	−48.0778	−1.74053
$764$	17.2098	0.622628
$765$	−2.69056	−0.0972773
$766$	−15.2911	−0.552491
$767$	19.4736	0.703151
$768$	−1.44389	−0.0521021
$769$	1.96422	0.0708315	0.0354158	−	0.999373i	$-0.488724\pi$
$769$	1.96422	0.0708315	0.0354158	+	0.999373i	$0.488724\pi$
$770$	4.44421	0.160158
$771$	34.5790	1.24533
$772$	−6.91213	−0.248773
$773$	54.9197	1.97532	0.987662	−	0.156600i	$-0.0500535\pi$
$773$	54.9197	1.97532	0.987662	+	0.156600i	$0.0500535\pi$
$774$	6.99535	0.251443
$775$	35.9579	1.29165
$776$	7.38017	0.264933
$777$	−84.1745	−3.01974
$778$	12.1854	0.436867
$779$	0.218649	0.00783392
$780$	2.02012	0.0723319
$781$	8.78579	0.314380
$782$	−1.98644	−0.0710348
$783$	38.5219	1.37666
$784$	18.4893	0.660333
$785$	5.93678	0.211893
$786$	−28.0297	−0.999787
$787$	3.14000	0.111929	0.0559645	−	0.998433i	$-0.482177\pi$
$787$	3.14000	0.111929	0.0559645	+	0.998433i	$0.482177\pi$
$788$	1.00000	0.0356235
$789$	−4.42241	−0.157442
$790$	0.131244	0.00466944
$791$	−88.0259	−3.12984
$792$	−0.915168	−0.0325191
$793$	−10.2016	−0.362269
$794$	−33.6081	−1.19271
$795$	−11.1828	−0.396613
$796$	−5.37847	−0.190635
$797$	1.27330	0.0451025	0.0225512	−	0.999746i	$-0.492821\pi$
$797$	1.27330	0.0451025	0.0225512	+	0.999746i	$0.492821\pi$
$798$	−15.9428	−0.564370
$799$	−35.6060	−1.25965
$800$	−4.22513	−0.149381
$801$	12.0081	0.424285
$802$	−27.5483	−0.972765
$803$	0.0781045	0.00275625
$804$	−3.85202	−0.135850
$805$	2.64329	0.0931636
$806$	−13.5264	−0.476446
$807$	−34.2117	−1.20431
$808$	10.4210	0.366608
$809$	−37.2702	−1.31035	−0.655175	−	0.755477i	$-0.727405\pi$
$809$	−37.2702	−1.31035	−0.655175	+	0.755477i	$0.727405\pi$
$810$	4.76839	0.167544
$811$	13.0739	0.459088	0.229544	−	0.973298i	$-0.426277\pi$
$811$	13.0739	0.459088	0.229544	+	0.973298i	$0.426277\pi$
$812$	−34.4034	−1.20732
$813$	−42.6862	−1.49707
$814$	−11.5469	−0.404719
$815$	6.92243	0.242482
$816$	4.82237	0.168817
$817$	16.7170	0.584855
$818$	24.6144	0.860622
$819$	7.34356	0.256605
$820$	0.0880061	0.00307331
$821$	49.8139	1.73852	0.869258	−	0.494358i	$-0.164597\pi$
$821$	49.8139	1.73852	0.869258	+	0.494358i	$0.164597\pi$
$822$	6.95800	0.242688
$823$	−35.1735	−1.22607	−0.613035	−	0.790055i	$-0.710052\pi$
$823$	−35.1735	−1.22607	−0.613035	+	0.790055i	$0.710052\pi$
$824$	−1.04881	−0.0365369
$825$	6.10064	0.212397
$826$	−61.8585	−2.15233
$827$	−18.6216	−0.647538	−0.323769	−	0.946136i	$-0.604950\pi$
$827$	−18.6216	−0.647538	−0.323769	+	0.946136i	$0.604950\pi$
$828$	−0.544315	−0.0189163
$829$	−27.3746	−0.950760	−0.475380	−	0.879780i	$-0.657689\pi$
$829$	−27.3746	−0.950760	−0.475380	+	0.879780i	$0.657689\pi$
$830$	−5.93196	−0.205901
$831$	45.2868	1.57098
$832$	1.58937	0.0551016
$833$	−61.7513	−2.13956
$834$	24.1481	0.836182
$835$	−10.7560	−0.372227
$836$	−2.18701	−0.0756393
$837$	−48.1106	−1.66295
$838$	16.9172	0.584395
$839$	−40.6758	−1.40428	−0.702142	−	0.712037i	$-0.747773\pi$
$839$	−40.6758	−1.40428	−0.702142	+	0.712037i	$0.747773\pi$
$840$	−6.41698	−0.221407
$841$	17.4349	0.601204
$842$	19.7096	0.679238
$843$	−9.12960	−0.314440
$844$	−26.6202	−0.916305
$845$	9.21985	0.317172
$846$	−9.75660	−0.335439
$847$	−5.04870	−0.173475
$848$	−8.79832	−0.302136
$849$	18.0524	0.619558
$850$	14.1112	0.484011
$851$	−6.86776	−0.235424
$852$	−12.6858	−0.434607
$853$	−12.7417	−0.436268	−0.218134	−	0.975919i	$-0.569997\pi$
$853$	−12.7417	−0.436268	−0.218134	+	0.975919i	$0.569997\pi$
$854$	32.4056	1.10890
$855$	−1.76184	−0.0602538
$856$	14.8629	0.508003
$857$	33.1562	1.13260	0.566298	−	0.824201i	$-0.308375\pi$
$857$	33.1562	1.13260	0.566298	+	0.824201i	$0.308375\pi$
$858$	−2.29489	−0.0783462
$859$	44.5782	1.52099	0.760495	−	0.649344i	$-0.224956\pi$
$859$	44.5782	1.52099	0.760495	+	0.649344i	$0.224956\pi$
$860$	6.72859	0.229443
$861$	−0.728806	−0.0248376
$862$	−18.7848	−0.639814
$863$	−8.41725	−0.286527	−0.143263	−	0.989685i	$-0.545760\pi$
$863$	−8.41725	−0.286527	−0.143263	+	0.989685i	$0.545760\pi$
$864$	5.65309	0.192322
$865$	2.40765	0.0818627
$866$	8.72681	0.296549
$867$	8.44027	0.286647
$868$	42.9669	1.45839
$869$	−0.149095	−0.00505770
$870$	8.66111	0.293639
$871$	4.24013	0.143671
$872$	9.52282	0.322483
$873$	−6.75410	−0.228592
$874$	−1.30077	−0.0439992
$875$	−40.9984	−1.38600
$876$	−0.112775	−0.00381030
$877$	7.74519	0.261536	0.130768	−	0.991413i	$-0.458256\pi$
$877$	7.74519	0.261536	0.130768	+	0.991413i	$0.458256\pi$
$878$	7.05658	0.238148
$879$	28.3508	0.956249
$880$	−0.880270	−0.0296739
$881$	−6.95411	−0.234290	−0.117145	−	0.993115i	$-0.537374\pi$
$881$	−6.95411	−0.234290	−0.117145	+	0.993115i	$0.537374\pi$
$882$	−16.9209	−0.569755
$883$	−24.5937	−0.827645	−0.413822	−	0.910358i	$-0.635807\pi$
$883$	−24.5937	−0.827645	−0.413822	+	0.910358i	$0.635807\pi$
$884$	−5.30825	−0.178536
$885$	15.5730	0.523480
$886$	25.2265	0.847502
$887$	18.5173	0.621750	0.310875	−	0.950451i	$-0.399378\pi$
$887$	18.5173	0.621750	0.310875	+	0.950451i	$0.399378\pi$
$888$	16.6725	0.559493
$889$	−75.5443	−2.53367
$890$	11.5502	0.387163
$891$	−5.41696	−0.181475
$892$	−15.6479	−0.523930
$893$	−23.3157	−0.780230
$894$	21.1218	0.706419
$895$	−8.32152	−0.278158
$896$	−5.04870	−0.168665
$897$	−1.36493	−0.0455738
$898$	13.3348	0.444986
$899$	−57.9932	−1.93418
$900$	3.86670	0.128890
$901$	29.3850	0.978955
$902$	−0.0999763	−0.00332885
$903$	−55.7216	−1.85430
$904$	17.4354	0.579892
$905$	−16.8453	−0.559956
$906$	−31.7855	−1.05600
$907$	32.3280	1.07343	0.536716	−	0.843763i	$-0.319665\pi$
$907$	32.3280	1.07343	0.536716	+	0.843763i	$0.319665\pi$
$908$	−13.3236	−0.442158
$909$	−9.53693	−0.316320
$910$	7.06352	0.234153
$911$	−37.4263	−1.23999	−0.619995	−	0.784606i	$-0.712865\pi$
$911$	−37.4263	−1.23999	−0.619995	+	0.784606i	$0.712865\pi$
$912$	3.15781	0.104566
$913$	6.73880	0.223022
$914$	−15.9201	−0.526589
$915$	−8.15816	−0.269700
$916$	14.7794	0.488324
$917$	−98.0082	−3.23652
$918$	−18.8804	−0.623146
$919$	21.7349	0.716969	0.358485	−	0.933536i	$-0.383294\pi$
$919$	21.7349	0.716969	0.358485	+	0.933536i	$0.383294\pi$
$920$	−0.523558	−0.0172612
$921$	−28.0361	−0.923821
$922$	12.5893	0.414606
$923$	13.9639	0.459628
$924$	7.28978	0.239816
$925$	48.7872	1.60411
$926$	33.6257	1.10501
$927$	0.959834	0.0315251
$928$	6.81432	0.223691
$929$	−44.4884	−1.45962	−0.729808	−	0.683652i	$-0.760391\pi$
$929$	−44.4884	−1.45962	−0.729808	+	0.683652i	$0.760391\pi$
$930$	−10.8170	−0.354703
$931$	−40.4363	−1.32525
$932$	−13.5300	−0.443190
$933$	13.6751	0.447703
$934$	25.4854	0.833907
$935$	2.93996	0.0961469
$936$	−1.45455	−0.0475433
$937$	14.8066	0.483709	0.241855	−	0.970313i	$-0.422244\pi$
$937$	14.8066	0.483709	0.241855	+	0.970313i	$0.422244\pi$
$938$	−13.4689	−0.439775
$939$	−20.8799	−0.681390
$940$	−9.38455	−0.306090
$941$	42.8294	1.39620	0.698100	−	0.716000i	$-0.254029\pi$
$941$	42.8294	1.39620	0.698100	+	0.716000i	$0.254029\pi$
$942$	9.73803	0.317282
$943$	−0.0594630	−0.00193638
$944$	12.2524	0.398781
$945$	25.1235	0.817269
$946$	−7.64379	−0.248521
$947$	−16.3276	−0.530577	−0.265288	−	0.964169i	$-0.585467\pi$
$947$	−16.3276	−0.530577	−0.265288	+	0.964169i	$0.585467\pi$
$948$	0.215277	0.00699188
$949$	0.124137	0.00402967
$950$	9.24039	0.299798
$951$	−22.6383	−0.734097
$952$	16.8618	0.546495
$953$	−59.9891	−1.94324	−0.971619	−	0.236550i	$-0.923983\pi$
$953$	−59.9891	−1.94324	−0.971619	+	0.236550i	$0.923983\pi$
$954$	8.05195	0.260691
$955$	−15.1492	−0.490218
$956$	−3.32174	−0.107433
$957$	−9.83915	−0.318055
$958$	22.4360	0.724874
$959$	24.3292	0.785631
$960$	1.27102	0.0410219
$961$	41.4286	1.33641
$962$	−18.3524	−0.591704
$963$	−13.6021	−0.438320
$964$	−1.44506	−0.0465423
$965$	6.08454	0.195868
$966$	4.33575	0.139500
$967$	25.8926	0.832650	0.416325	−	0.909216i	$-0.363318\pi$
$967$	25.8926	0.832650	0.416325	+	0.909216i	$0.363318\pi$
$968$	1.00000	0.0321412
$969$	−10.5466	−0.338805
$970$	−6.49654	−0.208591
$971$	50.5802	1.62320	0.811598	−	0.584216i	$-0.198598\pi$
$971$	50.5802	1.62320	0.811598	+	0.584216i	$0.198598\pi$
$972$	−9.13775	−0.293093
$973$	84.4360	2.70689
$974$	21.2895	0.682161
$975$	9.69619	0.310527
$976$	−6.41861	−0.205455
$977$	−1.71948	−0.0550112	−0.0275056	−	0.999622i	$-0.508756\pi$
$977$	−1.71948	−0.0550112	−0.0275056	+	0.999622i	$0.508756\pi$
$978$	11.3548	0.363085
$979$	−13.1212	−0.419355
$980$	−16.2756	−0.519905
$981$	−8.71498	−0.278248
$982$	−22.0437	−0.703444
$983$	−25.5480	−0.814856	−0.407428	−	0.913237i	$-0.633574\pi$
$983$	−25.5480	−0.814856	−0.407428	+	0.913237i	$0.633574\pi$
$984$	0.144355	0.00460188
$985$	−0.880270	−0.0280477
$986$	−22.7587	−0.724785
$987$	77.7163	2.47374
$988$	−3.47598	−0.110586
$989$	−4.54630	−0.144564
$990$	0.805595	0.0256035
$991$	−8.90881	−0.282998	−0.141499	−	0.989938i	$-0.545192\pi$
$991$	−8.90881	−0.282998	−0.141499	+	0.989938i	$0.545192\pi$
$992$	−8.51050	−0.270209
$993$	24.0514	0.763247
$994$	−44.3568	−1.40691
$995$	4.73450	0.150094
$996$	−9.73012	−0.308311
$997$	−47.9767	−1.51944	−0.759718	−	0.650253i	$-0.774663\pi$
$997$	−47.9767	−1.51944	−0.759718	+	0.650253i	$0.774663\pi$
$998$	−34.1956	−1.08244
$999$	−65.2758	−2.06523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.g.1.7	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.g.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.44389 q^{3} +1.00000 q^{4} -0.880270 q^{5} -1.44389 q^{6} -5.04870 q^{7} +1.00000 q^{8} -0.915168 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.44389 q^{3} +1.00000 q^{4} -0.880270 q^{5} -1.44389 q^{6} -5.04870 q^{7} +1.00000 q^{8} -0.915168 q^{9} -0.880270 q^{10} +1.00000 q^{11} -1.44389 q^{12} +1.58937 q^{13} -5.04870 q^{14} +1.27102 q^{15} +1.00000 q^{16} -3.33984 q^{17} -0.915168 q^{18} -2.18701 q^{19} -0.880270 q^{20} +7.28978 q^{21} +1.00000 q^{22} +0.594770 q^{23} -1.44389 q^{24} -4.22513 q^{25} +1.58937 q^{26} +5.65309 q^{27} -5.04870 q^{28} +6.81432 q^{29} +1.27102 q^{30} -8.51050 q^{31} +1.00000 q^{32} -1.44389 q^{33} -3.33984 q^{34} +4.44421 q^{35} -0.915168 q^{36} -11.5469 q^{37} -2.18701 q^{38} -2.29489 q^{39} -0.880270 q^{40} -0.0999763 q^{41} +7.28978 q^{42} -7.64379 q^{43} +1.00000 q^{44} +0.805595 q^{45} +0.594770 q^{46} +10.6610 q^{47} -1.44389 q^{48} +18.4893 q^{49} -4.22513 q^{50} +4.82237 q^{51} +1.58937 q^{52} -8.79832 q^{53} +5.65309 q^{54} -0.880270 q^{55} -5.04870 q^{56} +3.15781 q^{57} +6.81432 q^{58} +12.2524 q^{59} +1.27102 q^{60} -6.41861 q^{61} -8.51050 q^{62} +4.62041 q^{63} +1.00000 q^{64} -1.39908 q^{65} -1.44389 q^{66} +2.66780 q^{67} -3.33984 q^{68} -0.858786 q^{69} +4.44421 q^{70} +8.78579 q^{71} -0.915168 q^{72} +0.0781045 q^{73} -11.5469 q^{74} +6.10064 q^{75} -2.18701 q^{76} -5.04870 q^{77} -2.29489 q^{78} -0.149095 q^{79} -0.880270 q^{80} -5.41696 q^{81} -0.0999763 q^{82} +6.73880 q^{83} +7.28978 q^{84} +2.93996 q^{85} -7.64379 q^{86} -9.83915 q^{87} +1.00000 q^{88} -13.1212 q^{89} +0.805595 q^{90} -8.02427 q^{91} +0.594770 q^{92} +12.2883 q^{93} +10.6610 q^{94} +1.92516 q^{95} -1.44389 q^{96} +7.38017 q^{97} +18.4893 q^{98} -0.915168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 26 q^{2} + 12 q^{3} + 26 q^{4} + 13 q^{5} + 12 q^{6} + 13 q^{7} + 26 q^{8} + 38 q^{9}+O(q^{10}) \) 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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