LMFDB - Embedded newform 731.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79909 q^{2} -2.92541 q^{3} +5.83488 q^{4} -1.76305 q^{5} +8.18847 q^{6} -2.49895 q^{7} -10.7342 q^{8} +5.55801 q^{9} +O(q^{10})$	\(q-2.79909 q^{2} -2.92541 q^{3} +5.83488 q^{4} -1.76305 q^{5} +8.18847 q^{6} -2.49895 q^{7} -10.7342 q^{8} +5.55801 q^{9} +4.93492 q^{10} -4.10421 q^{11} -17.0694 q^{12} +1.48217 q^{13} +6.99478 q^{14} +5.15763 q^{15} +18.3761 q^{16} -1.00000 q^{17} -15.5573 q^{18} -6.14564 q^{19} -10.2872 q^{20} +7.31046 q^{21} +11.4880 q^{22} -8.11725 q^{23} +31.4018 q^{24} -1.89167 q^{25} -4.14873 q^{26} -7.48321 q^{27} -14.5811 q^{28} -0.180793 q^{29} -14.4366 q^{30} -10.2498 q^{31} -29.9679 q^{32} +12.0065 q^{33} +2.79909 q^{34} +4.40577 q^{35} +32.4303 q^{36} -3.36465 q^{37} +17.2022 q^{38} -4.33596 q^{39} +18.9248 q^{40} -7.82987 q^{41} -20.4626 q^{42} +1.00000 q^{43} -23.9476 q^{44} -9.79903 q^{45} +22.7209 q^{46} -2.06136 q^{47} -53.7575 q^{48} -0.755233 q^{49} +5.29493 q^{50} +2.92541 q^{51} +8.64830 q^{52} -1.11427 q^{53} +20.9462 q^{54} +7.23591 q^{55} +26.8242 q^{56} +17.9785 q^{57} +0.506055 q^{58} +6.80606 q^{59} +30.0942 q^{60} +10.0964 q^{61} +28.6902 q^{62} -13.8892 q^{63} +47.1305 q^{64} -2.61314 q^{65} -33.6072 q^{66} -1.24263 q^{67} -5.83488 q^{68} +23.7463 q^{69} -12.3321 q^{70} +4.62011 q^{71} -59.6605 q^{72} -7.09458 q^{73} +9.41793 q^{74} +5.53389 q^{75} -35.8591 q^{76} +10.2562 q^{77} +12.1367 q^{78} +1.98308 q^{79} -32.3979 q^{80} +5.21742 q^{81} +21.9165 q^{82} +0.0602651 q^{83} +42.6556 q^{84} +1.76305 q^{85} -2.79909 q^{86} +0.528893 q^{87} +44.0552 q^{88} +2.85872 q^{89} +27.4283 q^{90} -3.70388 q^{91} -47.3632 q^{92} +29.9850 q^{93} +5.76992 q^{94} +10.8350 q^{95} +87.6682 q^{96} -0.205429 q^{97} +2.11396 q^{98} -22.8112 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.79909	−1.97925	−0.989626	−	0.143666i	$-0.954111\pi$
$2$	−2.79909	−1.97925	−0.989626	+	0.143666i	$0.954111\pi$
$3$	−2.92541	−1.68898	−0.844492	−	0.535568i	$-0.820098\pi$
$3$	−2.92541	−1.68898	−0.844492	+	0.535568i	$0.820098\pi$
$4$	5.83488	2.91744
$5$	−1.76305	−0.788459	−0.394229	−	0.919012i	$-0.628988\pi$
$5$	−1.76305	−0.788459	−0.394229	+	0.919012i	$0.628988\pi$
$6$	8.18847	3.34293
$7$	−2.49895	−0.944516	−0.472258	−	0.881460i	$-0.656561\pi$
$7$	−2.49895	−0.944516	−0.472258	+	0.881460i	$0.656561\pi$
$8$	−10.7342	−3.79510
$9$	5.55801	1.85267
$10$	4.93492	1.56056
$11$	−4.10421	−1.23747	−0.618733	−	0.785601i	$-0.712354\pi$
$11$	−4.10421	−1.23747	−0.618733	+	0.785601i	$0.712354\pi$
$12$	−17.0694	−4.92751
$13$	1.48217	0.411081	0.205540	−	0.978649i	$-0.434105\pi$
$13$	1.48217	0.411081	0.205540	+	0.978649i	$0.434105\pi$
$14$	6.99478	1.86943
$15$	5.15763	1.33169
$16$	18.3761	4.59402
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−15.5573	−3.66690
$19$	−6.14564	−1.40991	−0.704953	−	0.709254i	$-0.749032\pi$
$19$	−6.14564	−1.40991	−0.704953	+	0.709254i	$0.749032\pi$
$20$	−10.2872	−2.30028
$21$	7.31046	1.59527
$22$	11.4880	2.44926
$23$	−8.11725	−1.69256	−0.846282	−	0.532736i	$-0.821164\pi$
$23$	−8.11725	−1.69256	−0.846282	+	0.532736i	$0.821164\pi$
$24$	31.4018	6.40986
$25$	−1.89167	−0.378333
$26$	−4.14873	−0.813632
$27$	−7.48321	−1.44014
$28$	−14.5811	−2.75557
$29$	−0.180793	−0.0335724	−0.0167862	−	0.999859i	$-0.505343\pi$
$29$	−0.180793	−0.0335724	−0.0167862	+	0.999859i	$0.505343\pi$
$30$	−14.4366	−2.63576
$31$	−10.2498	−1.84093	−0.920464	−	0.390829i	$-0.872189\pi$
$31$	−10.2498	−1.84093	−0.920464	+	0.390829i	$0.872189\pi$
$32$	−29.9679	−5.29762
$33$	12.0065	2.09006
$34$	2.79909	0.480039
$35$	4.40577	0.744711
$36$	32.4303	5.40505
$37$	−3.36465	−0.553144	−0.276572	−	0.960993i	$-0.589198\pi$
$37$	−3.36465	−0.553144	−0.276572	+	0.960993i	$0.589198\pi$
$38$	17.2022	2.79056
$39$	−4.33596	−0.694309
$40$	18.9248	2.99228
$41$	−7.82987	−1.22282	−0.611410	−	0.791314i	$-0.709398\pi$
$41$	−7.82987	−1.22282	−0.611410	+	0.791314i	$0.709398\pi$
$42$	−20.4626	−3.15745
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−23.9476	−3.61023
$45$	−9.79903	−1.46075
$46$	22.7209	3.35001
$47$	−2.06136	−0.300680	−0.150340	−	0.988634i	$-0.548037\pi$
$47$	−2.06136	−0.300680	−0.150340	+	0.988634i	$0.548037\pi$
$48$	−53.7575	−7.75922
$49$	−0.755233	−0.107890
$50$	5.29493	0.748817
$51$	2.92541	0.409639
$52$	8.64830	1.19930
$53$	−1.11427	−0.153056	−0.0765282	−	0.997067i	$-0.524384\pi$
$53$	−1.11427	−0.153056	−0.0765282	+	0.997067i	$0.524384\pi$
$54$	20.9462	2.85041
$55$	7.23591	0.975690
$56$	26.8242	3.58453
$57$	17.9785	2.38131
$58$	0.506055	0.0664483
$59$	6.80606	0.886073	0.443036	−	0.896504i	$-0.353901\pi$
$59$	6.80606	0.886073	0.443036	+	0.896504i	$0.353901\pi$
$60$	30.0942	3.88514
$61$	10.0964	1.29271	0.646353	−	0.763039i	$-0.276293\pi$
$61$	10.0964	1.29271	0.646353	+	0.763039i	$0.276293\pi$
$62$	28.6902	3.64366
$63$	−13.8892	−1.74987
$64$	47.1305	5.89131
$65$	−2.61314	−0.324120
$66$	−33.6072	−4.13676
$67$	−1.24263	−0.151812	−0.0759060	−	0.997115i	$-0.524185\pi$
$67$	−1.24263	−0.151812	−0.0759060	+	0.997115i	$0.524185\pi$
$68$	−5.83488	−0.707583
$69$	23.7463	2.85871
$70$	−12.3321	−1.47397
$71$	4.62011	0.548306	0.274153	−	0.961686i	$-0.411603\pi$
$71$	4.62011	0.548306	0.274153	+	0.961686i	$0.411603\pi$
$72$	−59.6605	−7.03106
$73$	−7.09458	−0.830358	−0.415179	−	0.909740i	$-0.636281\pi$
$73$	−7.09458	−0.830358	−0.415179	+	0.909740i	$0.636281\pi$
$74$	9.41793	1.09481
$75$	5.53389	0.638999
$76$	−35.8591	−4.11332
$77$	10.2562	1.16881
$78$	12.1367	1.37421
$79$	1.98308	0.223114	0.111557	−	0.993758i	$-0.464416\pi$
$79$	1.98308	0.223114	0.111557	+	0.993758i	$0.464416\pi$
$80$	−32.3979	−3.62219
$81$	5.21742	0.579714
$82$	21.9165	2.42027
$83$	0.0602651	0.00661495	0.00330748	−	0.999995i	$-0.498947\pi$
$83$	0.0602651	0.00661495	0.00330748	+	0.999995i	$0.498947\pi$
$84$	42.6556	4.65411
$85$	1.76305	0.191229
$86$	−2.79909	−0.301833
$87$	0.528893	0.0567033
$88$	44.0552	4.69630
$89$	2.85872	0.303023	0.151512	−	0.988455i	$-0.451586\pi$
$89$	2.85872	0.303023	0.151512	+	0.988455i	$0.451586\pi$
$90$	27.4283	2.89120
$91$	−3.70388	−0.388272
$92$	−47.3632	−4.93795
$93$	29.9850	3.10930
$94$	5.76992	0.595122
$95$	10.8350	1.11165
$96$	87.6682	8.94760
$97$	−0.205429	−0.0208582	−0.0104291	−	0.999946i	$-0.503320\pi$
$97$	−0.205429	−0.0208582	−0.0104291	+	0.999946i	$0.503320\pi$
$98$	2.11396	0.213542
$99$	−22.8112	−2.29261
$100$	−11.0376	−1.10376
$101$	−7.29500	−0.725880	−0.362940	−	0.931813i	$-0.618227\pi$
$101$	−7.29500	−0.725880	−0.362940	+	0.931813i	$0.618227\pi$
$102$	−8.18847	−0.810779
$103$	−1.53761	−0.151505	−0.0757527	−	0.997127i	$-0.524136\pi$
$103$	−1.53761	−0.151505	−0.0757527	+	0.997127i	$0.524136\pi$
$104$	−15.9099	−1.56009
$105$	−12.8887	−1.25781
$106$	3.11893	0.302937
$107$	15.8359	1.53092	0.765458	−	0.643486i	$-0.222513\pi$
$107$	15.8359	1.53092	0.765458	+	0.643486i	$0.222513\pi$
$108$	−43.6636	−4.20154
$109$	−2.99456	−0.286827	−0.143413	−	0.989663i	$-0.545808\pi$
$109$	−2.99456	−0.286827	−0.143413	+	0.989663i	$0.545808\pi$
$110$	−20.2539	−1.93114
$111$	9.84296	0.934252
$112$	−45.9209	−4.33912
$113$	−7.78428	−0.732283	−0.366142	−	0.930559i	$-0.619321\pi$
$113$	−7.78428	−0.732283	−0.366142	+	0.930559i	$0.619321\pi$
$114$	−50.3233	−4.71321
$115$	14.3111	1.33452
$116$	−1.05491	−0.0979455
$117$	8.23792	0.761596
$118$	−19.0507	−1.75376
$119$	2.49895	0.229079
$120$	−55.3628	−5.05391
$121$	5.84453	0.531321
$122$	−28.2606	−2.55859
$123$	22.9056	2.06533
$124$	−59.8066	−5.37079
$125$	12.1503	1.08676
$126$	38.8771	3.46344
$127$	8.95669	0.794778	0.397389	−	0.917650i	$-0.369916\pi$
$127$	8.95669	0.794778	0.397389	+	0.917650i	$0.369916\pi$
$128$	−71.9865	−6.36277
$129$	−2.92541	−0.257568
$130$	7.31440	0.641515
$131$	0.153437	0.0134059	0.00670294	−	0.999978i	$-0.497866\pi$
$131$	0.153437	0.0134059	0.00670294	+	0.999978i	$0.497866\pi$
$132$	70.0564	6.09763
$133$	15.3577	1.33168
$134$	3.47824	0.300474
$135$	13.1933	1.13549
$136$	10.7342	0.920446
$137$	−6.94062	−0.592977	−0.296489	−	0.955036i	$-0.595816\pi$
$137$	−6.94062	−0.592977	−0.296489	+	0.955036i	$0.595816\pi$
$138$	−66.4678	−5.65812
$139$	−6.17320	−0.523604	−0.261802	−	0.965122i	$-0.584317\pi$
$139$	−6.17320	−0.523604	−0.261802	+	0.965122i	$0.584317\pi$
$140$	25.7072	2.17265
$141$	6.03032	0.507844
$142$	−12.9321	−1.08524
$143$	−6.08314	−0.508698
$144$	102.134	8.51119
$145$	0.318747	0.0264705
$146$	19.8583	1.64349
$147$	2.20936	0.182225
$148$	−19.6323	−1.61377
$149$	3.82745	0.313557	0.156779	−	0.987634i	$-0.449889\pi$
$149$	3.82745	0.313557	0.156779	+	0.987634i	$0.449889\pi$
$150$	−15.4898	−1.26474
$151$	−19.0530	−1.55051	−0.775254	−	0.631649i	$-0.782378\pi$
$151$	−19.0530	−1.55051	−0.775254	+	0.631649i	$0.782378\pi$
$152$	65.9682	5.35073
$153$	−5.55801	−0.449338
$154$	−28.7081	−2.31336
$155$	18.0710	1.45149
$156$	−25.2998	−2.02560
$157$	−11.8610	−0.946614	−0.473307	−	0.880897i	$-0.656940\pi$
$157$	−11.8610	−0.946614	−0.473307	+	0.880897i	$0.656940\pi$
$158$	−5.55081	−0.441599
$159$	3.25969	0.258510
$160$	52.8347	4.17695
$161$	20.2846	1.59865
$162$	−14.6040	−1.14740
$163$	9.84798	0.771353	0.385677	−	0.922634i	$-0.373968\pi$
$163$	9.84798	0.771353	0.385677	+	0.922634i	$0.373968\pi$
$164$	−45.6864	−3.56751
$165$	−21.1680	−1.64793
$166$	−0.168687	−0.0130927
$167$	7.32981	0.567198	0.283599	−	0.958943i	$-0.408472\pi$
$167$	7.32981	0.567198	0.283599	+	0.958943i	$0.408472\pi$
$168$	−78.4716	−6.05421
$169$	−10.8032	−0.831013
$170$	−4.93492	−0.378491
$171$	−34.1575	−2.61209
$172$	5.83488	0.444905
$173$	−7.12678	−0.541839	−0.270919	−	0.962602i	$-0.587328\pi$
$173$	−7.12678	−0.541839	−0.270919	+	0.962602i	$0.587328\pi$
$174$	−1.48042	−0.112230
$175$	4.72718	0.357341
$176$	−75.4192	−5.68494
$177$	−19.9105	−1.49656
$178$	−8.00179	−0.599760
$179$	8.86645	0.662710	0.331355	−	0.943506i	$-0.392494\pi$
$179$	8.86645	0.662710	0.331355	+	0.943506i	$0.392494\pi$
$180$	−57.1762	−4.26166
$181$	5.14560	0.382470	0.191235	−	0.981544i	$-0.438751\pi$
$181$	5.14560	0.382470	0.191235	+	0.981544i	$0.438751\pi$
$182$	10.3675	0.768488
$183$	−29.5359	−2.18336
$184$	87.1318	6.42344
$185$	5.93203	0.436131
$186$	−83.9305	−6.15408
$187$	4.10421	0.300130
$188$	−12.0278	−0.877216
$189$	18.7002	1.36024
$190$	−30.3282	−2.20024
$191$	−24.6075	−1.78054	−0.890269	−	0.455436i	$-0.849483\pi$
$191$	−24.6075	−1.78054	−0.890269	+	0.455436i	$0.849483\pi$
$192$	−137.876	−9.95033
$193$	21.4616	1.54484	0.772420	−	0.635112i	$-0.219046\pi$
$193$	21.4616	1.54484	0.772420	+	0.635112i	$0.219046\pi$
$194$	0.575014	0.0412836
$195$	7.64450	0.547434
$196$	−4.40669	−0.314764
$197$	10.1520	0.723299	0.361650	−	0.932314i	$-0.382214\pi$
$197$	10.1520	0.723299	0.361650	+	0.932314i	$0.382214\pi$
$198$	63.8506	4.53766
$199$	−4.90566	−0.347753	−0.173876	−	0.984767i	$-0.555629\pi$
$199$	−4.90566	−0.347753	−0.173876	+	0.984767i	$0.555629\pi$
$200$	20.3054	1.43581
$201$	3.63521	0.256408
$202$	20.4193	1.43670
$203$	0.451793	0.0317097
$204$	17.0694	1.19510
$205$	13.8044	0.964144
$206$	4.30390	0.299867
$207$	−45.1157	−3.13576
$208$	27.2365	1.88851
$209$	25.2230	1.74471
$210$	36.0765	2.48952
$211$	16.3793	1.12760	0.563800	−	0.825911i	$-0.309339\pi$
$211$	16.3793	1.12760	0.563800	+	0.825911i	$0.309339\pi$
$212$	−6.50162	−0.446533
$213$	−13.5157	−0.926081
$214$	−44.3261	−3.03007
$215$	−1.76305	−0.120239
$216$	80.3260	5.46549
$217$	25.6139	1.73878
$218$	8.38203	0.567703
$219$	20.7545	1.40246
$220$	42.2207	2.84652
$221$	−1.48217	−0.0997017
$222$	−27.5513	−1.84912
$223$	−7.80833	−0.522885	−0.261442	−	0.965219i	$-0.584198\pi$
$223$	−7.80833	−0.522885	−0.261442	+	0.965219i	$0.584198\pi$
$224$	74.8883	5.00368
$225$	−10.5139	−0.700926
$226$	21.7889	1.44937
$227$	−8.93398	−0.592969	−0.296484	−	0.955038i	$-0.595814\pi$
$227$	−8.93398	−0.592969	−0.296484	+	0.955038i	$0.595814\pi$
$228$	104.902	6.94733
$229$	−19.5834	−1.29411	−0.647053	−	0.762445i	$-0.723999\pi$
$229$	−19.5834	−1.29411	−0.647053	+	0.762445i	$0.723999\pi$
$230$	−40.0580	−2.64134
$231$	−30.0036	−1.97409
$232$	1.94066	0.127411
$233$	−4.48955	−0.294120	−0.147060	−	0.989128i	$-0.546981\pi$
$233$	−4.48955	−0.294120	−0.147060	+	0.989128i	$0.546981\pi$
$234$	−23.0586	−1.50739
$235$	3.63427	0.237074
$236$	39.7125	2.58506
$237$	−5.80132	−0.376836
$238$	−6.99478	−0.453404
$239$	13.7189	0.887400	0.443700	−	0.896175i	$-0.353665\pi$
$239$	13.7189	0.887400	0.443700	+	0.896175i	$0.353665\pi$
$240$	94.7769	6.11783
$241$	3.85292	0.248188	0.124094	−	0.992270i	$-0.460398\pi$
$241$	3.85292	0.248188	0.124094	+	0.992270i	$0.460398\pi$
$242$	−16.3594	−1.05162
$243$	7.18655	0.461018
$244$	58.9110	3.77139
$245$	1.33151	0.0850671
$246$	−64.1146	−4.08780
$247$	−9.10889	−0.579585
$248$	110.023	6.98650
$249$	−0.176300	−0.0111726
$250$	−34.0098	−2.15097
$251$	−22.3925	−1.41340	−0.706700	−	0.707514i	$-0.749817\pi$
$251$	−22.3925	−1.41340	−0.706700	+	0.707514i	$0.749817\pi$
$252$	−81.0418	−5.10515
$253$	33.3149	2.09449
$254$	−25.0706	−1.57307
$255$	−5.15763	−0.322983
$256$	107.235	6.70222
$257$	−1.86193	−0.116144	−0.0580720	−	0.998312i	$-0.518495\pi$
$257$	−1.86193	−0.116144	−0.0580720	+	0.998312i	$0.518495\pi$
$258$	8.18847	0.509792
$259$	8.40809	0.522453
$260$	−15.2474	−0.945601
$261$	−1.00485	−0.0621986
$262$	−0.429484	−0.0265336
$263$	21.5085	1.32627	0.663136	−	0.748499i	$-0.269225\pi$
$263$	21.5085	1.32627	0.663136	+	0.748499i	$0.269225\pi$
$264$	−128.879	−7.93198
$265$	1.96451	0.120679
$266$	−42.9874	−2.63573
$267$	−8.36291	−0.511802
$268$	−7.25062	−0.442902
$269$	−25.6016	−1.56096	−0.780478	−	0.625183i	$-0.785024\pi$
$269$	−25.6016	−1.56096	−0.780478	+	0.625183i	$0.785024\pi$
$270$	−36.9291	−2.24743
$271$	−20.1655	−1.22497	−0.612483	−	0.790484i	$-0.709829\pi$
$271$	−20.1655	−1.22497	−0.612483	+	0.790484i	$0.709829\pi$
$272$	−18.3761	−1.11421
$273$	10.8354	0.655785
$274$	19.4274	1.17365
$275$	7.76379	0.468174
$276$	138.557	8.34013
$277$	30.5209	1.83383	0.916913	−	0.399088i	$-0.130673\pi$
$277$	30.5209	1.83383	0.916913	+	0.399088i	$0.130673\pi$
$278$	17.2793	1.03634
$279$	−56.9687	−3.41063
$280$	−47.2922	−2.82625
$281$	−7.34187	−0.437979	−0.218989	−	0.975727i	$-0.570276\pi$
$281$	−7.34187	−0.437979	−0.218989	+	0.975727i	$0.570276\pi$
$282$	−16.8794	−1.00515
$283$	−15.9561	−0.948493	−0.474247	−	0.880392i	$-0.657280\pi$
$283$	−15.9561	−0.948493	−0.474247	+	0.880392i	$0.657280\pi$
$284$	26.9578	1.59965
$285$	−31.6969	−1.87756
$286$	17.0272	1.00684
$287$	19.5665	1.15497
$288$	−166.562	−9.81474
$289$	1.00000	0.0588235
$290$	−0.892199	−0.0523917
$291$	0.600965	0.0352292
$292$	−41.3960	−2.42252
$293$	17.3894	1.01590	0.507949	−	0.861387i	$-0.330404\pi$
$293$	17.3894	1.01590	0.507949	+	0.861387i	$0.330404\pi$
$294$	−6.18420	−0.360670
$295$	−11.9994	−0.698632
$296$	36.1166	2.09924
$297$	30.7127	1.78213
$298$	−10.7134	−0.620609
$299$	−12.0312	−0.695780
$300$	32.2896	1.86424
$301$	−2.49895	−0.144037
$302$	53.3309	3.06885
$303$	21.3409	1.22600
$304$	−112.933	−6.47713
$305$	−17.8003	−1.01924
$306$	15.5573	0.889354
$307$	−10.2527	−0.585152	−0.292576	−	0.956242i	$-0.594512\pi$
$307$	−10.2527	−0.585152	−0.292576	+	0.956242i	$0.594512\pi$
$308$	59.8439	3.40992
$309$	4.49814	0.255890
$310$	−50.5822	−2.87287
$311$	−19.9181	−1.12945	−0.564725	−	0.825279i	$-0.691018\pi$
$311$	−19.9181	−1.12945	−0.564725	+	0.825279i	$0.691018\pi$
$312$	46.5428	2.63497
$313$	−32.0096	−1.80929	−0.904646	−	0.426164i	$-0.859865\pi$
$313$	−32.0096	−1.80929	−0.904646	+	0.426164i	$0.859865\pi$
$314$	33.2001	1.87359
$315$	24.4873	1.37970
$316$	11.5710	0.650922
$317$	15.4924	0.870141	0.435071	−	0.900396i	$-0.356723\pi$
$317$	15.4924	0.870141	0.435071	+	0.900396i	$0.356723\pi$
$318$	−9.12414	−0.511656
$319$	0.742012	0.0415447
$320$	−83.0933	−4.64505
$321$	−46.3265	−2.58569
$322$	−56.7784	−3.16414
$323$	6.14564	0.341952
$324$	30.4430	1.69128
$325$	−2.80377	−0.155525
$326$	−27.5653	−1.52670
$327$	8.76030	0.484446
$328$	84.0471	4.64072
$329$	5.15124	0.283997
$330$	59.2510	3.26166
$331$	5.15998	0.283618	0.141809	−	0.989894i	$-0.454708\pi$
$331$	5.15998	0.283618	0.141809	+	0.989894i	$0.454708\pi$
$332$	0.351639	0.0192987
$333$	−18.7007	−1.02479
$334$	−20.5168	−1.12263
$335$	2.19082	0.119697
$336$	134.337	7.32871
$337$	5.25873	0.286461	0.143231	−	0.989689i	$-0.454251\pi$
$337$	5.25873	0.286461	0.143231	+	0.989689i	$0.454251\pi$
$338$	30.2390	1.64478
$339$	22.7722	1.23682
$340$	10.2872	0.557900
$341$	42.0675	2.27808
$342$	95.6098	5.16998
$343$	19.3800	1.04642
$344$	−10.7342	−0.578747
$345$	−41.8658	−2.25398
$346$	19.9485	1.07244
$347$	−34.3977	−1.84656	−0.923282	−	0.384123i	$-0.874504\pi$
$347$	−34.3977	−1.84656	−0.923282	+	0.384123i	$0.874504\pi$
$348$	3.08603	0.165428
$349$	−35.8474	−1.91887	−0.959435	−	0.281930i	$-0.909025\pi$
$349$	−35.8474	−1.91887	−0.959435	+	0.281930i	$0.909025\pi$
$350$	−13.2318	−0.707269
$351$	−11.0914	−0.592016
$352$	122.994	6.55562
$353$	13.9521	0.742595	0.371297	−	0.928514i	$-0.378913\pi$
$353$	13.9521	0.742595	0.371297	+	0.928514i	$0.378913\pi$
$354$	55.7311	2.96208
$355$	−8.14547	−0.432317
$356$	16.6803	0.884053
$357$	−7.31046	−0.386910
$358$	−24.8180	−1.31167
$359$	29.9674	1.58162	0.790808	−	0.612064i	$-0.209660\pi$
$359$	29.9674	1.58162	0.790808	+	0.612064i	$0.209660\pi$
$360$	105.184	5.54370
$361$	18.7689	0.987835
$362$	−14.4030	−0.757004
$363$	−17.0976	−0.897394
$364$	−21.6117	−1.13276
$365$	12.5081	0.654703
$366$	82.6736	4.32142
$367$	−5.67181	−0.296066	−0.148033	−	0.988982i	$-0.547294\pi$
$367$	−5.67181	−0.296066	−0.148033	+	0.988982i	$0.547294\pi$
$368$	−149.163	−7.77566
$369$	−43.5185	−2.26548
$370$	−16.6043	−0.863214
$371$	2.78450	0.144564
$372$	174.959	9.07119
$373$	−10.8704	−0.562845	−0.281423	−	0.959584i	$-0.590806\pi$
$373$	−10.8704	−0.562845	−0.281423	+	0.959584i	$0.590806\pi$
$374$	−11.4880	−0.594032
$375$	−35.5447	−1.83552
$376$	22.1270	1.14111
$377$	−0.267966	−0.0138010
$378$	−52.3435	−2.69226
$379$	6.20247	0.318600	0.159300	−	0.987230i	$-0.449076\pi$
$379$	6.20247	0.318600	0.159300	+	0.987230i	$0.449076\pi$
$380$	63.2212	3.24318
$381$	−26.2020	−1.34237
$382$	68.8785	3.52413
$383$	20.5724	1.05120	0.525601	−	0.850731i	$-0.323840\pi$
$383$	20.5724	1.05120	0.525601	+	0.850731i	$0.323840\pi$
$384$	210.590	10.7466
$385$	−18.0822	−0.921555
$386$	−60.0728	−3.05763
$387$	5.55801	0.282529
$388$	−1.19866	−0.0608525
$389$	−16.3417	−0.828556	−0.414278	−	0.910150i	$-0.635966\pi$
$389$	−16.3417	−0.828556	−0.414278	+	0.910150i	$0.635966\pi$
$390$	−21.3976	−1.08351
$391$	8.11725	0.410507
$392$	8.10679	0.409455
$393$	−0.448867	−0.0226423
$394$	−28.4163	−1.43159
$395$	−3.49626	−0.175916
$396$	−133.101	−6.68856
$397$	−3.37459	−0.169366	−0.0846830	−	0.996408i	$-0.526988\pi$
$397$	−3.37459	−0.169366	−0.0846830	+	0.996408i	$0.526988\pi$
$398$	13.7314	0.688290
$399$	−44.9274	−2.24918
$400$	−34.7614	−1.73807
$401$	−26.2616	−1.31144	−0.655722	−	0.755002i	$-0.727636\pi$
$401$	−26.2616	−1.31144	−0.655722	+	0.755002i	$0.727636\pi$
$402$	−10.1753	−0.507496
$403$	−15.1920	−0.756769
$404$	−42.5655	−2.11771
$405$	−9.19856	−0.457080
$406$	−1.26461	−0.0627615
$407$	13.8092	0.684497
$408$	−31.4018	−1.55462
$409$	−27.0254	−1.33632	−0.668161	−	0.744017i	$-0.732918\pi$
$409$	−27.0254	−1.33632	−0.668161	+	0.744017i	$0.732918\pi$
$410$	−38.6398	−1.90828
$411$	20.3041	1.00153
$412$	−8.97178	−0.442008
$413$	−17.0080	−0.836910
$414$	126.283	6.20646
$415$	−0.106250	−0.00521562
$416$	−44.4175	−2.17775
$417$	18.0591	0.884359
$418$	−70.6013	−3.45322
$419$	3.87762	0.189434	0.0947171	−	0.995504i	$-0.469805\pi$
$419$	3.87762	0.189434	0.0947171	+	0.995504i	$0.469805\pi$
$420$	−75.2039	−3.66957
$421$	36.5722	1.78242	0.891210	−	0.453590i	$-0.149857\pi$
$421$	36.5722	1.78242	0.891210	+	0.453590i	$0.149857\pi$
$422$	−45.8472	−2.23181
$423$	−11.4571	−0.557061
$424$	11.9607	0.580864
$425$	1.89167	0.0917592
$426$	37.8316	1.83295
$427$	−25.2303	−1.22098
$428$	92.4006	4.46635
$429$	17.7957	0.859183
$430$	4.93492	0.237983
$431$	13.9297	0.670970	0.335485	−	0.942045i	$-0.391100\pi$
$431$	13.9297	0.670970	0.335485	+	0.942045i	$0.391100\pi$
$432$	−137.512	−6.61605
$433$	14.8440	0.713358	0.356679	−	0.934227i	$-0.383909\pi$
$433$	14.8440	0.713358	0.356679	+	0.934227i	$0.383909\pi$
$434$	−71.6955	−3.44149
$435$	−0.932464	−0.0447082
$436$	−17.4729	−0.836800
$437$	49.8857	2.38636
$438$	−58.0937	−2.77583
$439$	11.5089	0.549292	0.274646	−	0.961545i	$-0.411439\pi$
$439$	11.5089	0.549292	0.274646	+	0.961545i	$0.411439\pi$
$440$	−77.6714	−3.70284
$441$	−4.19759	−0.199885
$442$	4.14873	0.197335
$443$	−5.29553	−0.251598	−0.125799	−	0.992056i	$-0.540149\pi$
$443$	−5.29553	−0.251598	−0.125799	+	0.992056i	$0.540149\pi$
$444$	57.4325	2.72562
$445$	−5.04005	−0.238921
$446$	21.8562	1.03492
$447$	−11.1969	−0.529593
$448$	−117.777	−5.56443
$449$	27.6975	1.30713	0.653564	−	0.756871i	$-0.273273\pi$
$449$	27.6975	1.30713	0.653564	+	0.756871i	$0.273273\pi$
$450$	29.4293	1.38731
$451$	32.1354	1.51320
$452$	−45.4203	−2.13639
$453$	55.7377	2.61879
$454$	25.0070	1.17364
$455$	6.53011	0.306136
$456$	−192.984	−9.03730
$457$	−30.7721	−1.43946	−0.719729	−	0.694255i	$-0.755734\pi$
$457$	−30.7721	−1.43946	−0.719729	+	0.694255i	$0.755734\pi$
$458$	54.8156	2.56136
$459$	7.48321	0.349286
$460$	83.5035	3.89337
$461$	30.1367	1.40360	0.701802	−	0.712372i	$-0.252379\pi$
$461$	30.1367	1.40360	0.701802	+	0.712372i	$0.252379\pi$
$462$	83.9828	3.90723
$463$	−20.4218	−0.949084	−0.474542	−	0.880233i	$-0.657386\pi$
$463$	−20.4218	−0.949084	−0.474542	+	0.880233i	$0.657386\pi$
$464$	−3.32226	−0.154232
$465$	−52.8649	−2.45155
$466$	12.5666	0.582138
$467$	1.96232	0.0908054	0.0454027	−	0.998969i	$-0.485543\pi$
$467$	1.96232	0.0908054	0.0454027	+	0.998969i	$0.485543\pi$
$468$	48.0673	2.22191
$469$	3.10529	0.143389
$470$	−10.1726	−0.469229
$471$	34.6984	1.59882
$472$	−73.0573	−3.36273
$473$	−4.10421	−0.188712
$474$	16.2384	0.745854
$475$	11.6255	0.533414
$476$	14.5811	0.668323
$477$	−6.19311	−0.283563
$478$	−38.4003	−1.75639
$479$	−24.5932	−1.12369	−0.561846	−	0.827242i	$-0.689909\pi$
$479$	−24.5932	−1.12369	−0.561846	+	0.827242i	$0.689909\pi$
$480$	−154.563	−7.05481
$481$	−4.98698	−0.227387
$482$	−10.7846	−0.491227
$483$	−59.3408	−2.70010
$484$	34.1022	1.55010
$485$	0.362182	0.0164458
$486$	−20.1158	−0.912470
$487$	8.48941	0.384692	0.192346	−	0.981327i	$-0.438390\pi$
$487$	8.48941	0.384692	0.192346	+	0.981327i	$0.438390\pi$
$488$	−108.376	−4.90594
$489$	−28.8093	−1.30280
$490$	−3.72701	−0.168369
$491$	39.4692	1.78122	0.890609	−	0.454769i	$-0.150278\pi$
$491$	39.4692	1.78122	0.890609	+	0.454769i	$0.150278\pi$
$492$	133.651	6.02546
$493$	0.180793	0.00814251
$494$	25.4966	1.14714
$495$	40.2173	1.80763
$496$	−188.352	−8.45725
$497$	−11.5454	−0.517884
$498$	0.493478	0.0221133
$499$	−43.4130	−1.94343	−0.971716	−	0.236152i	$-0.924114\pi$
$499$	−43.4130	−1.94343	−0.971716	+	0.236152i	$0.924114\pi$
$500$	70.8957	3.17055
$501$	−21.4427	−0.957988
$502$	62.6784	2.79747
$503$	−12.5309	−0.558726	−0.279363	−	0.960186i	$-0.590123\pi$
$503$	−12.5309	−0.558726	−0.279363	+	0.960186i	$0.590123\pi$
$504$	149.089	6.64095
$505$	12.8614	0.572326
$506$	−93.2512	−4.14552
$507$	31.6037	1.40357
$508$	52.2612	2.31872
$509$	3.19880	0.141784	0.0708921	−	0.997484i	$-0.477415\pi$
$509$	3.19880	0.141784	0.0708921	+	0.997484i	$0.477415\pi$
$510$	14.4366	0.639266
$511$	17.7290	0.784286
$512$	−156.188	−6.90261
$513$	45.9891	2.03047
$514$	5.21170	0.229878
$515$	2.71088	0.119456
$516$	−17.0694	−0.751438
$517$	8.46025	0.372081
$518$	−23.5350	−1.03407
$519$	20.8487	0.915158
$520$	28.0498	1.23007
$521$	−0.142833	−0.00625761	−0.00312880	−	0.999995i	$-0.500996\pi$
$521$	−0.142833	−0.00625761	−0.00312880	+	0.999995i	$0.500996\pi$
$522$	2.81266	0.123107
$523$	7.47430	0.326828	0.163414	−	0.986558i	$-0.447749\pi$
$523$	7.47430	0.326828	0.163414	+	0.986558i	$0.447749\pi$
$524$	0.895289	0.0391109
$525$	−13.8289	−0.603544
$526$	−60.2042	−2.62503
$527$	10.2498	0.446490
$528$	220.632	9.60177
$529$	42.8897	1.86477
$530$	−5.49882	−0.238853
$531$	37.8281	1.64160
$532$	89.6101	3.88509
$533$	−11.6052	−0.502678
$534$	23.4085	1.01299
$535$	−27.9195	−1.20706
$536$	13.3386	0.576141
$537$	−25.9380	−1.11931
$538$	71.6611	3.08953
$539$	3.09963	0.133511
$540$	76.9811	3.31274
$541$	3.90076	0.167707	0.0838533	−	0.996478i	$-0.473277\pi$
$541$	3.90076	0.167707	0.0838533	+	0.996478i	$0.473277\pi$
$542$	56.4449	2.42452
$543$	−15.0530	−0.645986
$544$	29.9679	1.28486
$545$	5.27955	0.226151
$546$	−30.3291	−1.29796
$547$	−31.6317	−1.35247	−0.676237	−	0.736684i	$-0.736390\pi$
$547$	−31.6317	−1.35247	−0.676237	+	0.736684i	$0.736390\pi$
$548$	−40.4977	−1.72998
$549$	56.1156	2.39496
$550$	−21.7315	−0.926635
$551$	1.11109	0.0473340
$552$	−254.896	−10.8491
$553$	−4.95562	−0.210735
$554$	−85.4307	−3.62960
$555$	−17.3536	−0.736619
$556$	−36.0199	−1.52758
$557$	−42.5392	−1.80244	−0.901221	−	0.433359i	$-0.857328\pi$
$557$	−42.5392	−1.80244	−0.901221	+	0.433359i	$0.857328\pi$
$558$	159.460	6.75049
$559$	1.48217	0.0626892
$560$	80.9607	3.42122
$561$	−12.0065	−0.506914
$562$	20.5505	0.866871
$563$	13.0204	0.548744	0.274372	−	0.961624i	$-0.411530\pi$
$563$	13.0204	0.548744	0.274372	+	0.961624i	$0.411530\pi$
$564$	35.1862	1.48161
$565$	13.7240	0.577375
$566$	44.6626	1.87731
$567$	−13.0381	−0.547549
$568$	−49.5930	−2.08088
$569$	11.0915	0.464981	0.232490	−	0.972599i	$-0.425313\pi$
$569$	11.0915	0.464981	0.232490	+	0.972599i	$0.425313\pi$
$570$	88.7224	3.71617
$571$	10.8543	0.454238	0.227119	−	0.973867i	$-0.427069\pi$
$571$	10.8543	0.454238	0.227119	+	0.973867i	$0.427069\pi$
$572$	−35.4944	−1.48410
$573$	71.9870	3.00730
$574$	−54.7683	−2.28598
$575$	15.3551	0.640353
$576$	261.952	10.9146
$577$	11.7088	0.487444	0.243722	−	0.969845i	$-0.421631\pi$
$577$	11.7088	0.487444	0.243722	+	0.969845i	$0.421631\pi$
$578$	−2.79909	−0.116427
$579$	−62.7839	−2.60921
$580$	1.85985	0.0772260
$581$	−0.150600	−0.00624792
$582$	−1.68215	−0.0697274
$583$	4.57319	0.189402
$584$	76.1544	3.15129
$585$	−14.5238	−0.600487
$586$	−48.6744	−2.01072
$587$	−20.6722	−0.853235	−0.426618	−	0.904432i	$-0.640295\pi$
$587$	−20.6722	−0.853235	−0.426618	+	0.904432i	$0.640295\pi$
$588$	12.8914	0.531631
$589$	62.9919	2.59553
$590$	33.5873	1.38277
$591$	−29.6987	−1.22164
$592$	−61.8289	−2.54115
$593$	−5.13239	−0.210762	−0.105381	−	0.994432i	$-0.533606\pi$
$593$	−5.13239	−0.210762	−0.105381	+	0.994432i	$0.533606\pi$
$594$	−85.9674	−3.52729
$595$	−4.40577	−0.180619
$596$	22.3327	0.914784
$597$	14.3510	0.587349
$598$	33.6762	1.37712
$599$	−20.0160	−0.817830	−0.408915	−	0.912573i	$-0.634093\pi$
$599$	−20.0160	−0.817830	−0.408915	+	0.912573i	$0.634093\pi$
$600$	−59.4017	−2.42506
$601$	28.8157	1.17542	0.587709	−	0.809072i	$-0.300030\pi$
$601$	28.8157	1.17542	0.587709	+	0.809072i	$0.300030\pi$
$602$	6.99478	0.285086
$603$	−6.90657	−0.281257
$604$	−111.172	−4.52352
$605$	−10.3042	−0.418925
$606$	−59.7349	−2.42656
$607$	−40.3645	−1.63834	−0.819172	−	0.573549i	$-0.805566\pi$
$607$	−40.3645	−1.63834	−0.819172	+	0.573549i	$0.805566\pi$
$608$	184.172	7.46915
$609$	−1.32168	−0.0535572
$610$	49.8247	2.01734
$611$	−3.05529	−0.123604
$612$	−32.4303	−1.31092
$613$	−5.16934	−0.208788	−0.104394	−	0.994536i	$-0.533290\pi$
$613$	−5.16934	−0.208788	−0.104394	+	0.994536i	$0.533290\pi$
$614$	28.6982	1.15816
$615$	−40.3836	−1.62842
$616$	−110.092	−4.43573
$617$	−11.0287	−0.444000	−0.222000	−	0.975047i	$-0.571259\pi$
$617$	−11.0287	−0.444000	−0.222000	+	0.975047i	$0.571259\pi$
$618$	−12.5907	−0.506471
$619$	−43.2930	−1.74009	−0.870046	−	0.492971i	$-0.835911\pi$
$619$	−43.2930	−1.74009	−0.870046	+	0.492971i	$0.835911\pi$
$620$	105.442	4.23465
$621$	60.7431	2.43754
$622$	55.7523	2.23546
$623$	−7.14380	−0.286210
$624$	−79.6778	−3.18967
$625$	−11.9633	−0.478531
$626$	89.5977	3.58105
$627$	−73.7875	−2.94679
$628$	−69.2078	−2.76169
$629$	3.36465	0.134157
$630$	−68.5421	−2.73078
$631$	−18.5232	−0.737395	−0.368698	−	0.929549i	$-0.620196\pi$
$631$	−18.5232	−0.737395	−0.368698	+	0.929549i	$0.620196\pi$
$632$	−21.2867	−0.846739
$633$	−47.9162	−1.90450
$634$	−43.3646	−1.72223
$635$	−15.7911	−0.626650
$636$	19.0199	0.754187
$637$	−1.11938	−0.0443516
$638$	−2.07696	−0.0822275
$639$	25.6786	1.01583
$640$	126.916	5.01678
$641$	15.5445	0.613972	0.306986	−	0.951714i	$-0.400679\pi$
$641$	15.5445	0.613972	0.306986	+	0.951714i	$0.400679\pi$
$642$	129.672	5.11774
$643$	39.0833	1.54130	0.770648	−	0.637262i	$-0.219933\pi$
$643$	39.0833	1.54130	0.770648	+	0.637262i	$0.219933\pi$
$644$	118.358	4.66397
$645$	5.15763	0.203081
$646$	−17.2022	−0.676810
$647$	10.1575	0.399332	0.199666	−	0.979864i	$-0.436014\pi$
$647$	10.1575	0.399332	0.199666	+	0.979864i	$0.436014\pi$
$648$	−56.0046	−2.20007
$649$	−27.9335	−1.09648
$650$	7.84800	0.307824
$651$	−74.9311	−2.93678
$652$	57.4618	2.25038
$653$	−26.7778	−1.04790	−0.523948	−	0.851750i	$-0.675541\pi$
$653$	−26.7778	−1.04790	−0.523948	+	0.851750i	$0.675541\pi$
$654$	−24.5208	−0.958841
$655$	−0.270517	−0.0105700
$656$	−143.882	−5.61766
$657$	−39.4317	−1.53838
$658$	−14.4188	−0.562102
$659$	−10.0753	−0.392478	−0.196239	−	0.980556i	$-0.562873\pi$
$659$	−10.0753	−0.392478	−0.196239	+	0.980556i	$0.562873\pi$
$660$	−123.513	−4.80773
$661$	23.6691	0.920619	0.460310	−	0.887758i	$-0.347738\pi$
$661$	23.6691	0.920619	0.460310	+	0.887758i	$0.347738\pi$
$662$	−14.4432	−0.561352
$663$	4.33596	0.168395
$664$	−0.646895	−0.0251044
$665$	−27.0763	−1.04997
$666$	52.3449	2.02832
$667$	1.46754	0.0568235
$668$	42.7685	1.65476
$669$	22.8425	0.883144
$670$	−6.13230	−0.236911
$671$	−41.4375	−1.59968
$672$	−219.079	−8.45115
$673$	−15.6868	−0.604683	−0.302342	−	0.953200i	$-0.597768\pi$
$673$	−15.6868	−0.604683	−0.302342	+	0.953200i	$0.597768\pi$
$674$	−14.7196	−0.566979
$675$	14.1557	0.544854
$676$	−63.0352	−2.42443
$677$	−35.0901	−1.34862	−0.674312	−	0.738447i	$-0.735560\pi$
$677$	−35.0901	−1.34862	−0.674312	+	0.738447i	$0.735560\pi$
$678$	−63.7413	−2.44797
$679$	0.513358	0.0197009
$680$	−18.9248	−0.725734
$681$	26.1355	1.00152
$682$	−117.751	−4.50890
$683$	−0.0415023	−0.00158804	−0.000794022	−	1.00000i	$-0.500253\pi$
$683$	−0.0415023	−0.00158804	−0.000794022		1.00000i	$0.500253\pi$
$684$	−199.305	−7.62061
$685$	12.2366	0.467538
$686$	−54.2462	−2.07113
$687$	57.2894	2.18573
$688$	18.3761	0.700581
$689$	−1.65154	−0.0629185
$690$	117.186	4.46119
$691$	43.3951	1.65083	0.825414	−	0.564528i	$-0.190942\pi$
$691$	43.3951	1.65083	0.825414	+	0.564528i	$0.190942\pi$
$692$	−41.5839	−1.58078
$693$	57.0042	2.16541
$694$	96.2820	3.65482
$695$	10.8836	0.412840
$696$	−5.67722	−0.215195
$697$	7.82987	0.296578
$698$	100.340	3.79793
$699$	13.1337	0.496764
$700$	27.5825	1.04252
$701$	39.7549	1.50152	0.750760	−	0.660575i	$-0.229687\pi$
$701$	39.7549	1.50152	0.750760	+	0.660575i	$0.229687\pi$
$702$	31.0458	1.17175
$703$	20.6779	0.779882
$704$	−193.433	−7.29029
$705$	−10.6317	−0.400414
$706$	−39.0531	−1.46978
$707$	18.2299	0.685605
$708$	−116.175	−4.36613
$709$	−32.7206	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$709$	−32.7206	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$710$	22.7999	0.855664
$711$	11.0220	0.413356
$712$	−30.6859	−1.15000
$713$	83.2006	3.11589
$714$	20.4626	0.765793
$715$	10.7249	0.401087
$716$	51.7347	1.93342
$717$	−40.1333	−1.49881
$718$	−83.8812	−3.13042
$719$	9.03931	0.337109	0.168555	−	0.985692i	$-0.446090\pi$
$719$	9.03931	0.337109	0.168555	+	0.985692i	$0.446090\pi$
$720$	−180.068	−6.71072
$721$	3.84242	0.143099
$722$	−52.5357	−1.95518
$723$	−11.2713	−0.419186
$724$	30.0240	1.11583
$725$	0.342000	0.0127016
$726$	47.8578	1.77617
$727$	11.9628	0.443677	0.221838	−	0.975083i	$-0.428794\pi$
$727$	11.9628	0.443677	0.221838	+	0.975083i	$0.428794\pi$
$728$	39.7580	1.47353
$729$	−36.6759	−1.35837
$730$	−35.0112	−1.29582
$731$	−1.00000	−0.0369863
$732$	−172.339	−6.36982
$733$	−33.0612	−1.22114	−0.610571	−	0.791961i	$-0.709060\pi$
$733$	−33.0612	−1.22114	−0.610571	+	0.791961i	$0.709060\pi$
$734$	15.8759	0.585989
$735$	−3.89521	−0.143677
$736$	243.257	8.96656
$737$	5.10003	0.187862
$738$	121.812	4.48396
$739$	−14.7115	−0.541173	−0.270586	−	0.962696i	$-0.587218\pi$
$739$	−14.7115	−0.541173	−0.270586	+	0.962696i	$0.587218\pi$
$740$	34.6127	1.27239
$741$	26.6472	0.978910
$742$	−7.79406	−0.286129
$743$	11.4737	0.420928	0.210464	−	0.977602i	$-0.432503\pi$
$743$	11.4737	0.420928	0.210464	+	0.977602i	$0.432503\pi$
$744$	−321.863	−11.8001
$745$	−6.74798	−0.247227
$746$	30.4270	1.11401
$747$	0.334954	0.0122553
$748$	23.9476	0.875610
$749$	−39.5732	−1.44597
$750$	99.4926	3.63295
$751$	−21.9586	−0.801281	−0.400641	−	0.916235i	$-0.631212\pi$
$751$	−21.9586	−0.801281	−0.400641	+	0.916235i	$0.631212\pi$
$752$	−37.8797	−1.38133
$753$	65.5071	2.38721
$754$	0.750061	0.0273156
$755$	33.5913	1.22251
$756$	109.113	3.96842
$757$	−14.6539	−0.532605	−0.266303	−	0.963889i	$-0.585802\pi$
$757$	−14.6539	−0.532605	−0.266303	+	0.963889i	$0.585802\pi$
$758$	−17.3613	−0.630589
$759$	−97.4596	−3.53756
$760$	−116.305	−4.21883
$761$	−44.8064	−1.62423	−0.812115	−	0.583498i	$-0.801684\pi$
$761$	−44.8064	−1.62423	−0.812115	+	0.583498i	$0.801684\pi$
$762$	73.3416	2.65689
$763$	7.48326	0.270912
$764$	−143.582	−5.19461
$765$	9.79903	0.354285
$766$	−57.5840	−2.08060
$767$	10.0877	0.364247
$768$	−313.707	−11.3199
$769$	10.4174	0.375660	0.187830	−	0.982202i	$-0.439855\pi$
$769$	10.4174	0.375660	0.187830	+	0.982202i	$0.439855\pi$
$770$	50.6137	1.82399
$771$	5.44690	0.196165
$772$	125.226	4.50698
$773$	16.3584	0.588372	0.294186	−	0.955748i	$-0.404952\pi$
$773$	16.3584	0.588372	0.294186	+	0.955748i	$0.404952\pi$
$774$	−15.5573	−0.559197
$775$	19.3893	0.696484
$776$	2.20511	0.0791589
$777$	−24.5971	−0.882416
$778$	45.7418	1.63992
$779$	48.1196	1.72406
$780$	44.6047	1.59710
$781$	−18.9619	−0.678510
$782$	−22.7209	−0.812497
$783$	1.35291	0.0483492
$784$	−13.8782	−0.495650
$785$	20.9116	0.746366
$786$	1.25642	0.0448149
$787$	3.78407	0.134887	0.0674437	−	0.997723i	$-0.478516\pi$
$787$	3.78407	0.134887	0.0674437	+	0.997723i	$0.478516\pi$
$788$	59.2356	2.11018
$789$	−62.9212	−2.24005
$790$	9.78634	0.348182
$791$	19.4525	0.691653
$792$	244.859	8.70070
$793$	14.9645	0.531406
$794$	9.44577	0.335218
$795$	−5.74698	−0.203824
$796$	−28.6239	−1.01455
$797$	−46.5292	−1.64815	−0.824075	−	0.566480i	$-0.808305\pi$
$797$	−46.5292	−1.64815	−0.824075	+	0.566480i	$0.808305\pi$
$798$	125.756	4.45170
$799$	2.06136	0.0729257
$800$	56.6892	2.00426
$801$	15.8888	0.561402
$802$	73.5086	2.59568
$803$	29.1177	1.02754
$804$	21.2110	0.748055
$805$	−35.7628	−1.26047
$806$	42.5238	1.49784
$807$	74.8951	2.63643
$808$	78.3057	2.75479
$809$	12.1022	0.425491	0.212746	−	0.977108i	$-0.431759\pi$
$809$	12.1022	0.425491	0.212746	+	0.977108i	$0.431759\pi$
$810$	25.7476	0.904677
$811$	12.9420	0.454456	0.227228	−	0.973842i	$-0.427034\pi$
$811$	12.9420	0.454456	0.227228	+	0.973842i	$0.427034\pi$
$812$	2.63616	0.0925111
$813$	58.9923	2.06895
$814$	−38.6532	−1.35479
$815$	−17.3624	−0.608180
$816$	53.7575	1.88189
$817$	−6.14564	−0.215009
$818$	75.6465	2.64492
$819$	−20.5862	−0.719339
$820$	80.5472	2.81283
$821$	40.9210	1.42815	0.714077	−	0.700067i	$-0.246847\pi$
$821$	40.9210	1.42815	0.714077	+	0.700067i	$0.246847\pi$
$822$	−56.8330	−1.98228
$823$	46.2657	1.61272	0.806360	−	0.591425i	$-0.201434\pi$
$823$	46.2657	1.61272	0.806360	+	0.591425i	$0.201434\pi$
$824$	16.5050	0.574977
$825$	−22.7122	−0.790739
$826$	47.6069	1.65646
$827$	−19.0327	−0.661831	−0.330916	−	0.943660i	$-0.607358\pi$
$827$	−19.0327	−0.661831	−0.330916	+	0.943660i	$0.607358\pi$
$828$	−263.245	−9.14839
$829$	−7.28093	−0.252877	−0.126439	−	0.991974i	$-0.540355\pi$
$829$	−7.28093	−0.252877	−0.126439	+	0.991974i	$0.540355\pi$
$830$	0.297403	0.0103230
$831$	−89.2862	−3.09730
$832$	69.8555	2.42180
$833$	0.755233	0.0261673
$834$	−50.5490	−1.75037
$835$	−12.9228	−0.447212
$836$	147.173	5.09009
$837$	76.7018	2.65120
$838$	−10.8538	−0.374938
$839$	−10.8108	−0.373230	−0.186615	−	0.982433i	$-0.559752\pi$
$839$	−10.8108	−0.373230	−0.186615	+	0.982433i	$0.559752\pi$
$840$	138.349	4.77350
$841$	−28.9673	−0.998873
$842$	−102.369	−3.52786
$843$	21.4779	0.739740
$844$	95.5715	3.28971
$845$	19.0465	0.655219
$846$	32.0693	1.10256
$847$	−14.6052	−0.501841
$848$	−20.4758	−0.703143
$849$	46.6782	1.60199
$850$	−5.29493	−0.181615
$851$	27.3117	0.936232
$852$	−78.8625	−2.70178
$853$	23.0218	0.788252	0.394126	−	0.919056i	$-0.371047\pi$
$853$	23.0218	0.788252	0.394126	+	0.919056i	$0.371047\pi$
$854$	70.6218	2.41663
$855$	60.2213	2.05952
$856$	−169.985	−5.80997
$857$	−38.9588	−1.33081	−0.665404	−	0.746484i	$-0.731741\pi$
$857$	−38.9588	−1.33081	−0.665404	+	0.746484i	$0.731741\pi$
$858$	−49.8116	−1.70054
$859$	−41.9700	−1.43200	−0.715998	−	0.698102i	$-0.754028\pi$
$859$	−41.9700	−1.43200	−0.715998	+	0.698102i	$0.754028\pi$
$860$	−10.2872	−0.350790
$861$	−57.2399	−1.95073
$862$	−38.9904	−1.32802
$863$	0.817594	0.0278312	0.0139156	−	0.999903i	$-0.495570\pi$
$863$	0.817594	0.0278312	0.0139156	+	0.999903i	$0.495570\pi$
$864$	224.256	7.62934
$865$	12.5648	0.427218
$866$	−41.5497	−1.41192
$867$	−2.92541	−0.0993520
$868$	149.454	5.07280
$869$	−8.13898	−0.276096
$870$	2.61005	0.0884888
$871$	−1.84180	−0.0624069
$872$	32.1441	1.08854
$873$	−1.14178	−0.0386433
$874$	−139.634	−4.72320
$875$	−30.3631	−1.02646
$876$	121.100	4.09160
$877$	−28.1066	−0.949094	−0.474547	−	0.880230i	$-0.657388\pi$
$877$	−28.1066	−0.949094	−0.474547	+	0.880230i	$0.657388\pi$
$878$	−32.2145	−1.08719
$879$	−50.8710	−1.71584
$880$	132.968	4.48234
$881$	0.0643241	0.00216713	0.00108357	−	0.999999i	$-0.499655\pi$
$881$	0.0643241	0.00216713	0.00108357	+	0.999999i	$0.499655\pi$
$882$	11.7494	0.395623
$883$	−13.3305	−0.448606	−0.224303	−	0.974519i	$-0.572011\pi$
$883$	−13.3305	−0.448606	−0.224303	+	0.974519i	$0.572011\pi$
$884$	−8.64830	−0.290874
$885$	35.1031	1.17998
$886$	14.8226	0.497976
$887$	−40.3565	−1.35504	−0.677520	−	0.735504i	$-0.736945\pi$
$887$	−40.3565	−1.35504	−0.677520	+	0.735504i	$0.736945\pi$
$888$	−105.656	−3.54558
$889$	−22.3824	−0.750680
$890$	14.1075	0.472886
$891$	−21.4134	−0.717376
$892$	−45.5607	−1.52548
$893$	12.6684	0.423931
$894$	31.3410	1.04820
$895$	−15.6320	−0.522519
$896$	179.891	6.00974
$897$	35.1960	1.17516
$898$	−77.5278	−2.58714
$899$	1.85310	0.0618044
$900$	−61.3473	−2.04491
$901$	1.11427	0.0371216
$902$	−89.9498	−2.99500
$903$	7.31046	0.243277
$904$	83.5577	2.77909
$905$	−9.07194	−0.301562
$906$	−156.015	−5.18324
$907$	−29.7155	−0.986687	−0.493343	−	0.869835i	$-0.664225\pi$
$907$	−29.7155	−0.986687	−0.493343	+	0.869835i	$0.664225\pi$
$908$	−52.1287	−1.72995
$909$	−40.5457	−1.34482
$910$	−18.2783	−0.605921
$911$	6.36206	0.210785	0.105392	−	0.994431i	$-0.466390\pi$
$911$	6.36206	0.210785	0.105392	+	0.994431i	$0.466390\pi$
$912$	330.374	10.9398
$913$	−0.247340	−0.00818578
$914$	86.1337	2.84905
$915$	52.0733	1.72149
$916$	−114.267	−3.77548
$917$	−0.383433	−0.0126621
$918$	−20.9462	−0.691326
$919$	37.9434	1.25164	0.625819	−	0.779969i	$-0.284765\pi$
$919$	37.9434	1.25164	0.625819	+	0.779969i	$0.284765\pi$
$920$	−153.618	−5.06462
$921$	29.9933	0.988313
$922$	−84.3551	−2.77809
$923$	6.84780	0.225398
$924$	−175.068	−5.75930
$925$	6.36478	0.209273
$926$	57.1625	1.87848
$927$	−8.54605	−0.280689
$928$	5.41798	0.177854
$929$	54.2110	1.77860	0.889302	−	0.457320i	$-0.151191\pi$
$929$	54.2110	1.77860	0.889302	+	0.457320i	$0.151191\pi$
$930$	147.973	4.85224
$931$	4.64139	0.152115
$932$	−26.1960	−0.858077
$933$	58.2684	1.90762
$934$	−5.49271	−0.179727
$935$	−7.23591	−0.236640
$936$	−88.4272	−2.89033
$937$	26.5369	0.866923	0.433462	−	0.901172i	$-0.357292\pi$
$937$	26.5369	0.866923	0.433462	+	0.901172i	$0.357292\pi$
$938$	−8.69196	−0.283803
$939$	93.6412	3.05587
$940$	21.2056	0.691649
$941$	40.6994	1.32676	0.663382	−	0.748281i	$-0.269121\pi$
$941$	40.6994	1.32676	0.663382	+	0.748281i	$0.269121\pi$
$942$	−97.1237	−3.16446
$943$	63.5570	2.06970
$944$	125.069	4.07063
$945$	−32.9693	−1.07249
$946$	11.4880	0.373508
$947$	−40.7234	−1.32333	−0.661667	−	0.749798i	$-0.730151\pi$
$947$	−40.7234	−1.32333	−0.661667	+	0.749798i	$0.730151\pi$
$948$	−33.8500	−1.09940
$949$	−10.5154	−0.341344
$950$	−32.5407	−1.05576
$951$	−45.3217	−1.46966
$952$	−26.8242	−0.869376
$953$	−40.6130	−1.31558	−0.657792	−	0.753199i	$-0.728510\pi$
$953$	−40.6130	−1.31558	−0.657792	+	0.753199i	$0.728510\pi$
$954$	17.3350	0.561242
$955$	43.3842	1.40388
$956$	80.0480	2.58894
$957$	−2.17069	−0.0701684
$958$	68.8385	2.22407
$959$	17.3443	0.560076
$960$	243.082	7.84542
$961$	74.0594	2.38901
$962$	13.9590	0.450056
$963$	88.0161	2.83628
$964$	22.4813	0.724074
$965$	−37.8378	−1.21804
$966$	166.100	5.34418
$967$	−29.2342	−0.940108	−0.470054	−	0.882638i	$-0.655766\pi$
$967$	−29.2342	−0.940108	−0.470054	+	0.882638i	$0.655766\pi$
$968$	−62.7362	−2.01642
$969$	−17.9785	−0.577552
$970$	−1.01378	−0.0325504
$971$	16.2860	0.522643	0.261322	−	0.965252i	$-0.415842\pi$
$971$	16.2860	0.522643	0.261322	+	0.965252i	$0.415842\pi$
$972$	41.9327	1.34499
$973$	15.4265	0.494552
$974$	−23.7626	−0.761403
$975$	8.20218	0.262680
$976$	185.531	5.93871
$977$	−32.2088	−1.03045	−0.515225	−	0.857055i	$-0.672292\pi$
$977$	−32.2088	−1.03045	−0.515225	+	0.857055i	$0.672292\pi$
$978$	80.6398	2.57858
$979$	−11.7328	−0.374981
$980$	7.76921	0.248178
$981$	−16.6438	−0.531395
$982$	−110.478	−3.52548
$983$	16.4266	0.523927	0.261964	−	0.965078i	$-0.415630\pi$
$983$	16.4266	0.523927	0.261964	+	0.965078i	$0.415630\pi$
$984$	−245.872	−7.83811
$985$	−17.8984	−0.570291
$986$	−0.506055	−0.0161161
$987$	−15.0695	−0.479667
$988$	−53.1493	−1.69090
$989$	−8.11725	−0.258114
$990$	−112.572	−3.57776
$991$	24.5815	0.780858	0.390429	−	0.920633i	$-0.372327\pi$
$991$	24.5815	0.780858	0.390429	+	0.920633i	$0.372327\pi$
$992$	307.166	9.75253
$993$	−15.0951	−0.479027
$994$	32.3167	1.02502
$995$	8.64890	0.274189
$996$	−1.02869	−0.0325952
$997$	7.25753	0.229848	0.114924	−	0.993374i	$-0.463337\pi$
$997$	7.25753	0.229848	0.114924	+	0.993374i	$0.463337\pi$
$998$	121.517	3.84654
$999$	25.1784	0.796608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.1	✓	21
3.2	odd	2		6579.2.a.u.1.21		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.1	✓	21	1.1	even	1	trivial
6579.2.a.u.1.21		21	3.2	odd	2

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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79909 q^{2} -2.92541 q^{3} +5.83488 q^{4} -1.76305 q^{5} +8.18847 q^{6} -2.49895 q^{7} -10.7342 q^{8} +5.55801 q^{9} +O(q^{10})\)	\(q-2.79909 q^{2} -2.92541 q^{3} +5.83488 q^{4} -1.76305 q^{5} +8.18847 q^{6} -2.49895 q^{7} -10.7342 q^{8} +5.55801 q^{9} +4.93492 q^{10} -4.10421 q^{11} -17.0694 q^{12} +1.48217 q^{13} +6.99478 q^{14} +5.15763 q^{15} +18.3761 q^{16} -1.00000 q^{17} -15.5573 q^{18} -6.14564 q^{19} -10.2872 q^{20} +7.31046 q^{21} +11.4880 q^{22} -8.11725 q^{23} +31.4018 q^{24} -1.89167 q^{25} -4.14873 q^{26} -7.48321 q^{27} -14.5811 q^{28} -0.180793 q^{29} -14.4366 q^{30} -10.2498 q^{31} -29.9679 q^{32} +12.0065 q^{33} +2.79909 q^{34} +4.40577 q^{35} +32.4303 q^{36} -3.36465 q^{37} +17.2022 q^{38} -4.33596 q^{39} +18.9248 q^{40} -7.82987 q^{41} -20.4626 q^{42} +1.00000 q^{43} -23.9476 q^{44} -9.79903 q^{45} +22.7209 q^{46} -2.06136 q^{47} -53.7575 q^{48} -0.755233 q^{49} +5.29493 q^{50} +2.92541 q^{51} +8.64830 q^{52} -1.11427 q^{53} +20.9462 q^{54} +7.23591 q^{55} +26.8242 q^{56} +17.9785 q^{57} +0.506055 q^{58} +6.80606 q^{59} +30.0942 q^{60} +10.0964 q^{61} +28.6902 q^{62} -13.8892 q^{63} +47.1305 q^{64} -2.61314 q^{65} -33.6072 q^{66} -1.24263 q^{67} -5.83488 q^{68} +23.7463 q^{69} -12.3321 q^{70} +4.62011 q^{71} -59.6605 q^{72} -7.09458 q^{73} +9.41793 q^{74} +5.53389 q^{75} -35.8591 q^{76} +10.2562 q^{77} +12.1367 q^{78} +1.98308 q^{79} -32.3979 q^{80} +5.21742 q^{81} +21.9165 q^{82} +0.0602651 q^{83} +42.6556 q^{84} +1.76305 q^{85} -2.79909 q^{86} +0.528893 q^{87} +44.0552 q^{88} +2.85872 q^{89} +27.4283 q^{90} -3.70388 q^{91} -47.3632 q^{92} +29.9850 q^{93} +5.76992 q^{94} +10.8350 q^{95} +87.6682 q^{96} -0.205429 q^{97} +2.11396 q^{98} -22.8112 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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