LMFDB - Embedded newform 731.2.a.f.1.12

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			1.12
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)

$f(q)$	$=$	$q+0.549823 q^{2} +2.96872 q^{3} -1.69769 q^{4} -0.0524046 q^{5} +1.63227 q^{6} -0.375563 q^{7} -2.03308 q^{8} +5.81330 q^{9} +O(q^{10})$	\(q+0.549823 q^{2} +2.96872 q^{3} -1.69769 q^{4} -0.0524046 q^{5} +1.63227 q^{6} -0.375563 q^{7} -2.03308 q^{8} +5.81330 q^{9} -0.0288132 q^{10} +4.73616 q^{11} -5.03998 q^{12} +2.79185 q^{13} -0.206493 q^{14} -0.155574 q^{15} +2.27756 q^{16} -1.00000 q^{17} +3.19628 q^{18} -1.64106 q^{19} +0.0889670 q^{20} -1.11494 q^{21} +2.60405 q^{22} +7.26534 q^{23} -6.03564 q^{24} -4.99725 q^{25} +1.53502 q^{26} +8.35188 q^{27} +0.637591 q^{28} -6.97966 q^{29} -0.0855385 q^{30} +3.09510 q^{31} +5.31841 q^{32} +14.0603 q^{33} -0.549823 q^{34} +0.0196812 q^{35} -9.86920 q^{36} +0.721144 q^{37} -0.902292 q^{38} +8.28822 q^{39} +0.106543 q^{40} -2.68495 q^{41} -0.613020 q^{42} +1.00000 q^{43} -8.04055 q^{44} -0.304643 q^{45} +3.99465 q^{46} +1.05787 q^{47} +6.76142 q^{48} -6.85895 q^{49} -2.74761 q^{50} -2.96872 q^{51} -4.73971 q^{52} +7.14226 q^{53} +4.59206 q^{54} -0.248196 q^{55} +0.763548 q^{56} -4.87184 q^{57} -3.83758 q^{58} -6.60037 q^{59} +0.264118 q^{60} -3.97961 q^{61} +1.70176 q^{62} -2.18326 q^{63} -1.63093 q^{64} -0.146306 q^{65} +7.73069 q^{66} -10.2588 q^{67} +1.69769 q^{68} +21.5687 q^{69} +0.0108212 q^{70} -11.2759 q^{71} -11.8189 q^{72} -3.01959 q^{73} +0.396502 q^{74} -14.8354 q^{75} +2.78602 q^{76} -1.77872 q^{77} +4.55706 q^{78} +9.25480 q^{79} -0.119354 q^{80} +7.35452 q^{81} -1.47625 q^{82} -6.02940 q^{83} +1.89283 q^{84} +0.0524046 q^{85} +0.549823 q^{86} -20.7206 q^{87} -9.62898 q^{88} -8.44739 q^{89} -0.167500 q^{90} -1.04852 q^{91} -12.3343 q^{92} +9.18848 q^{93} +0.581641 q^{94} +0.0859990 q^{95} +15.7889 q^{96} -8.77572 q^{97} -3.77121 q^{98} +27.5327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.549823	0.388784	0.194392	−	0.980924i	$-0.437727\pi$
$2$	0.549823	0.388784	0.194392	+	0.980924i	$0.437727\pi$
$3$	2.96872	1.71399	0.856995	−	0.515324i	$-0.172328\pi$
$3$	2.96872	1.71399	0.856995	+	0.515324i	$0.172328\pi$
$4$	−1.69769	−0.848847
$5$	−0.0524046	−0.0234360	−0.0117180	−	0.999931i	$-0.503730\pi$
$5$	−0.0524046	−0.0234360	−0.0117180	+	0.999931i	$0.503730\pi$
$6$	1.63227	0.666372
$7$	−0.375563	−0.141949	−0.0709747	−	0.997478i	$-0.522611\pi$
$7$	−0.375563	−0.141949	−0.0709747	+	0.997478i	$0.522611\pi$
$8$	−2.03308	−0.718802
$9$	5.81330	1.93777
$10$	−0.0288132	−0.00911155
$11$	4.73616	1.42801	0.714003	−	0.700143i	$-0.246880\pi$
$11$	4.73616	1.42801	0.714003	+	0.700143i	$0.246880\pi$
$12$	−5.03998	−1.45492
$13$	2.79185	0.774320	0.387160	−	0.922012i	$-0.373456\pi$
$13$	2.79185	0.774320	0.387160	+	0.922012i	$0.373456\pi$
$14$	−0.206493	−0.0551876
$15$	−0.155574	−0.0401692
$16$	2.27756	0.569389
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.19628	0.753371
$19$	−1.64106	−0.376485	−0.188242	−	0.982123i	$-0.560279\pi$
$19$	−1.64106	−0.376485	−0.188242	+	0.982123i	$0.560279\pi$
$20$	0.0889670	0.0198936
$21$	−1.11494	−0.243300
$22$	2.60405	0.555185
$23$	7.26534	1.51493	0.757464	−	0.652877i	$-0.226438\pi$
$23$	7.26534	1.51493	0.757464	+	0.652877i	$0.226438\pi$
$24$	−6.03564	−1.23202
$25$	−4.99725	−0.999451
$26$	1.53502	0.301043
$27$	8.35188	1.60732
$28$	0.637591	0.120493
$29$	−6.97966	−1.29609	−0.648045	−	0.761602i	$-0.724413\pi$
$29$	−6.97966	−1.29609	−0.648045	+	0.761602i	$0.724413\pi$
$30$	−0.0855385	−0.0156171
$31$	3.09510	0.555896	0.277948	−	0.960596i	$-0.410346\pi$
$31$	3.09510	0.555896	0.277948	+	0.960596i	$0.410346\pi$
$32$	5.31841	0.940171
$33$	14.0603	2.44759
$34$	−0.549823	−0.0942939
$35$	0.0196812	0.00332673
$36$	−9.86920	−1.64487
$37$	0.721144	0.118555	0.0592777	−	0.998242i	$-0.481120\pi$
$37$	0.721144	0.118555	0.0592777	+	0.998242i	$0.481120\pi$
$38$	−0.902292	−0.146371
$39$	8.28822	1.32718
$40$	0.106543	0.0168459
$41$	−2.68495	−0.419319	−0.209660	−	0.977774i	$-0.567236\pi$
$41$	−2.68495	−0.419319	−0.209660	+	0.977774i	$0.567236\pi$
$42$	−0.613020	−0.0945910
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−8.04055	−1.21216
$45$	−0.304643	−0.0454135
$46$	3.99465	0.588979
$47$	1.05787	0.154306	0.0771530	−	0.997019i	$-0.475417\pi$
$47$	1.05787	0.154306	0.0771530	+	0.997019i	$0.475417\pi$
$48$	6.76142	0.975928
$49$	−6.85895	−0.979850
$50$	−2.74761	−0.388570
$51$	−2.96872	−0.415704
$52$	−4.73971	−0.657280
$53$	7.14226	0.981065	0.490533	−	0.871423i	$-0.336802\pi$
$53$	7.14226	0.981065	0.490533	+	0.871423i	$0.336802\pi$
$54$	4.59206	0.624900
$55$	−0.248196	−0.0334668
$56$	0.763548	0.102033
$57$	−4.87184	−0.645292
$58$	−3.83758	−0.503899
$59$	−6.60037	−0.859294	−0.429647	−	0.902997i	$-0.641362\pi$
$59$	−6.60037	−0.859294	−0.429647	+	0.902997i	$0.641362\pi$
$60$	0.264118	0.0340975
$61$	−3.97961	−0.509537	−0.254769	−	0.967002i	$-0.581999\pi$
$61$	−3.97961	−0.509537	−0.254769	+	0.967002i	$0.581999\pi$
$62$	1.70176	0.216123
$63$	−2.18326	−0.275064
$64$	−1.63093	−0.203866
$65$	−0.146306	−0.0181470
$66$	7.73069	0.951582
$67$	−10.2588	−1.25331	−0.626655	−	0.779296i	$-0.715577\pi$
$67$	−10.2588	−1.25331	−0.626655	+	0.779296i	$0.715577\pi$
$68$	1.69769	0.205876
$69$	21.5687	2.59657
$70$	0.0108212	0.00129338
$71$	−11.2759	−1.33820	−0.669099	−	0.743174i	$-0.733320\pi$
$71$	−11.2759	−1.33820	−0.669099	+	0.743174i	$0.733320\pi$
$72$	−11.8189	−1.39287
$73$	−3.01959	−0.353416	−0.176708	−	0.984263i	$-0.556545\pi$
$73$	−3.01959	−0.353416	−0.176708	+	0.984263i	$0.556545\pi$
$74$	0.396502	0.0460924
$75$	−14.8354	−1.71305
$76$	2.78602	0.319578
$77$	−1.77872	−0.202704
$78$	4.55706	0.515985
$79$	9.25480	1.04125	0.520623	−	0.853786i	$-0.325700\pi$
$79$	9.25480	1.04125	0.520623	+	0.853786i	$0.325700\pi$
$80$	−0.119354	−0.0133442
$81$	7.35452	0.817169
$82$	−1.47625	−0.163025
$83$	−6.02940	−0.661812	−0.330906	−	0.943664i	$-0.607354\pi$
$83$	−6.02940	−0.661812	−0.330906	+	0.943664i	$0.607354\pi$
$84$	1.89283	0.206524
$85$	0.0524046	0.00568407
$86$	0.549823	0.0592889
$87$	−20.7206	−2.22149
$88$	−9.62898	−1.02645
$89$	−8.44739	−0.895422	−0.447711	−	0.894178i	$-0.647761\pi$
$89$	−8.44739	−0.895422	−0.447711	+	0.894178i	$0.647761\pi$
$90$	−0.167500	−0.0176560
$91$	−1.04852	−0.109914
$92$	−12.3343	−1.28594
$93$	9.18848	0.952801
$94$	0.581641	0.0599917
$95$	0.0859990	0.00882331
$96$	15.7889	1.61144
$97$	−8.77572	−0.891039	−0.445520	−	0.895272i	$-0.646981\pi$
$97$	−8.77572	−0.891039	−0.445520	+	0.895272i	$0.646981\pi$
$98$	−3.77121	−0.380950
$99$	27.5327	2.76714
$100$	8.48381	0.848381
$101$	2.42280	0.241077	0.120539	−	0.992709i	$-0.461538\pi$
$101$	2.42280	0.241077	0.120539	+	0.992709i	$0.461538\pi$
$102$	−1.63227	−0.161619
$103$	−14.0700	−1.38636	−0.693180	−	0.720765i	$-0.743791\pi$
$103$	−14.0700	−1.38636	−0.693180	+	0.720765i	$0.743791\pi$
$104$	−5.67605	−0.556583
$105$	0.0584280	0.00570199
$106$	3.92698	0.381422
$107$	14.2614	1.37870	0.689352	−	0.724427i	$-0.257896\pi$
$107$	14.2614	1.37870	0.689352	+	0.724427i	$0.257896\pi$
$108$	−14.1789	−1.36437
$109$	7.67959	0.735572	0.367786	−	0.929911i	$-0.380116\pi$
$109$	7.67959	0.735572	0.367786	+	0.929911i	$0.380116\pi$
$110$	−0.136464	−0.0130113
$111$	2.14087	0.203203
$112$	−0.855365	−0.0808244
$113$	−6.86581	−0.645881	−0.322940	−	0.946419i	$-0.604671\pi$
$113$	−6.86581	−0.645881	−0.322940	+	0.946419i	$0.604671\pi$
$114$	−2.67865	−0.250879
$115$	−0.380737	−0.0355039
$116$	11.8493	1.10018
$117$	16.2299	1.50045
$118$	−3.62903	−0.334080
$119$	0.375563	0.0344278
$120$	0.316295	0.0288737
$121$	11.4312	1.03920
$122$	−2.18808	−0.198100
$123$	−7.97088	−0.718710
$124$	−5.25453	−0.471871
$125$	0.523902	0.0468592
$126$	−1.20040	−0.106941
$127$	12.6851	1.12562	0.562809	−	0.826587i	$-0.309721\pi$
$127$	12.6851	1.12562	0.562809	+	0.826587i	$0.309721\pi$
$128$	−11.5335	−1.01943
$129$	2.96872	0.261381
$130$	−0.0804423	−0.00705526
$131$	15.7989	1.38035	0.690177	−	0.723640i	$-0.257533\pi$
$131$	15.7989	1.38035	0.690177	+	0.723640i	$0.257533\pi$
$132$	−23.8701	−2.07763
$133$	0.616320	0.0534418
$134$	−5.64052	−0.487267
$135$	−0.437677	−0.0376692
$136$	2.03308	0.174335
$137$	−0.0450388	−0.00384793	−0.00192396	−	0.999998i	$-0.500612\pi$
$137$	−0.0450388	−0.00384793	−0.00192396	+	0.999998i	$0.500612\pi$
$138$	11.8590	1.00950
$139$	−11.9173	−1.01081	−0.505407	−	0.862881i	$-0.668658\pi$
$139$	−11.9173	−1.01081	−0.505407	+	0.862881i	$0.668658\pi$
$140$	−0.0334127	−0.00282389
$141$	3.14052	0.264479
$142$	−6.19972	−0.520269
$143$	13.2226	1.10573
$144$	13.2401	1.10334
$145$	0.365766	0.0303752
$146$	−1.66024	−0.137402
$147$	−20.3623	−1.67945
$148$	−1.22428	−0.100635
$149$	−20.1961	−1.65453	−0.827267	−	0.561810i	$-0.810105\pi$
$149$	−20.1961	−1.65453	−0.827267	+	0.561810i	$0.810105\pi$
$150$	−8.15687	−0.666006
$151$	17.4619	1.42103	0.710513	−	0.703684i	$-0.248463\pi$
$151$	17.4619	1.42103	0.710513	+	0.703684i	$0.248463\pi$
$152$	3.33640	0.270618
$153$	−5.81330	−0.469977
$154$	−0.977983	−0.0788081
$155$	−0.162197	−0.0130280
$156$	−14.0709	−1.12657
$157$	−10.3824	−0.828604	−0.414302	−	0.910140i	$-0.635974\pi$
$157$	−10.3824	−0.828604	−0.414302	+	0.910140i	$0.635974\pi$
$158$	5.08850	0.404820
$159$	21.2034	1.68154
$160$	−0.278709	−0.0220339
$161$	−2.72859	−0.215043
$162$	4.04368	0.317702
$163$	13.0362	1.02107	0.510537	−	0.859856i	$-0.329447\pi$
$163$	13.0362	1.02107	0.510537	+	0.859856i	$0.329447\pi$
$164$	4.55823	0.355938
$165$	−0.736825	−0.0573618
$166$	−3.31510	−0.257302
$167$	14.8506	1.14918	0.574588	−	0.818443i	$-0.305162\pi$
$167$	14.8506	1.14918	0.574588	+	0.818443i	$0.305162\pi$
$168$	2.26676	0.174884
$169$	−5.20556	−0.400428
$170$	0.0288132	0.00220988
$171$	−9.53996	−0.729539
$172$	−1.69769	−0.129448
$173$	11.4885	0.873457	0.436729	−	0.899593i	$-0.356137\pi$
$173$	11.4885	0.873457	0.436729	+	0.899593i	$0.356137\pi$
$174$	−11.3927	−0.863678
$175$	1.87678	0.141871
$176$	10.7869	0.813090
$177$	−19.5946	−1.47282
$178$	−4.64457	−0.348125
$179$	−10.0935	−0.754422	−0.377211	−	0.926127i	$-0.623117\pi$
$179$	−10.0935	−0.754422	−0.377211	+	0.926127i	$0.623117\pi$
$180$	0.517191	0.0385492
$181$	2.23393	0.166047	0.0830235	−	0.996548i	$-0.473542\pi$
$181$	2.23393	0.166047	0.0830235	+	0.996548i	$0.473542\pi$
$182$	−0.576498	−0.0427329
$183$	−11.8144	−0.873342
$184$	−14.7710	−1.08893
$185$	−0.0377913	−0.00277847
$186$	5.05204	0.370433
$187$	−4.73616	−0.346342
$188$	−1.79594	−0.130982
$189$	−3.13666	−0.228158
$190$	0.0472842	0.00343036
$191$	−13.4108	−0.970374	−0.485187	−	0.874410i	$-0.661249\pi$
$191$	−13.4108	−0.970374	−0.485187	+	0.874410i	$0.661249\pi$
$192$	−4.84177	−0.349425
$193$	18.1990	1.31000	0.654998	−	0.755631i	$-0.272670\pi$
$193$	18.1990	1.31000	0.654998	+	0.755631i	$0.272670\pi$
$194$	−4.82509	−0.346421
$195$	−0.434341	−0.0311038
$196$	11.6444	0.831743
$197$	12.0875	0.861198	0.430599	−	0.902543i	$-0.358302\pi$
$197$	12.0875	0.861198	0.430599	+	0.902543i	$0.358302\pi$
$198$	15.1381	1.07582
$199$	−6.14049	−0.435287	−0.217644	−	0.976028i	$-0.569837\pi$
$199$	−6.14049	−0.435287	−0.217644	+	0.976028i	$0.569837\pi$
$200$	10.1598	0.718407
$201$	−30.4555	−2.14816
$202$	1.33211	0.0937269
$203$	2.62130	0.183979
$204$	5.03998	0.352869
$205$	0.140704	0.00982719
$206$	−7.73602	−0.538994
$207$	42.2355	2.93557
$208$	6.35860	0.440889
$209$	−7.77231	−0.537622
$210$	0.0321250	0.00221684
$211$	10.0933	0.694853	0.347427	−	0.937707i	$-0.387056\pi$
$211$	10.0933	0.694853	0.347427	+	0.937707i	$0.387056\pi$
$212$	−12.1254	−0.832775
$213$	−33.4748	−2.29366
$214$	7.84126	0.536017
$215$	−0.0524046	−0.00357396
$216$	−16.9800	−1.15534
$217$	−1.16240	−0.0789091
$218$	4.22242	0.285978
$219$	−8.96431	−0.605752
$220$	0.421362	0.0284082
$221$	−2.79185	−0.187800
$222$	1.17710	0.0790019
$223$	−3.13348	−0.209833	−0.104917	−	0.994481i	$-0.533458\pi$
$223$	−3.13348	−0.209833	−0.104917	+	0.994481i	$0.533458\pi$
$224$	−1.99740	−0.133457
$225$	−29.0505	−1.93670
$226$	−3.77498	−0.251108
$227$	−28.7289	−1.90680	−0.953401	−	0.301706i	$-0.902444\pi$
$227$	−28.7289	−1.90680	−0.953401	+	0.301706i	$0.902444\pi$
$228$	8.27090	0.547754
$229$	20.9621	1.38521	0.692606	−	0.721316i	$-0.256463\pi$
$229$	20.9621	1.38521	0.692606	+	0.721316i	$0.256463\pi$
$230$	−0.209338	−0.0138033
$231$	−5.28053	−0.347433
$232$	14.1902	0.931631
$233$	−10.0081	−0.655655	−0.327828	−	0.944738i	$-0.606317\pi$
$233$	−10.0081	−0.655655	−0.327828	+	0.944738i	$0.606317\pi$
$234$	8.92355	0.583351
$235$	−0.0554372	−0.00361632
$236$	11.2054	0.729410
$237$	27.4749	1.78469
$238$	0.206493	0.0133850
$239$	19.6621	1.27184	0.635918	−	0.771756i	$-0.280622\pi$
$239$	19.6621	1.27184	0.635918	+	0.771756i	$0.280622\pi$
$240$	−0.354330	−0.0228719
$241$	10.8298	0.697610	0.348805	−	0.937195i	$-0.386588\pi$
$241$	10.8298	0.697610	0.348805	+	0.937195i	$0.386588\pi$
$242$	6.28513	0.404023
$243$	−3.22216	−0.206701
$244$	6.75616	0.432519
$245$	0.359441	0.0229638
$246$	−4.38257	−0.279423
$247$	−4.58159	−0.291520
$248$	−6.29257	−0.399579
$249$	−17.8996	−1.13434
$250$	0.288053	0.0182181
$251$	−23.6465	−1.49255	−0.746277	−	0.665635i	$-0.768161\pi$
$251$	−23.6465	−1.49255	−0.746277	+	0.665635i	$0.768161\pi$
$252$	3.70650	0.233488
$253$	34.4098	2.16332
$254$	6.97455	0.437622
$255$	0.155574	0.00974245
$256$	−3.07955	−0.192472
$257$	−13.3758	−0.834361	−0.417180	−	0.908824i	$-0.636982\pi$
$257$	−13.3758	−0.834361	−0.417180	+	0.908824i	$0.636982\pi$
$258$	1.63227	0.101621
$259$	−0.270835	−0.0168289
$260$	0.248383	0.0154040
$261$	−40.5748	−2.51152
$262$	8.68659	0.536659
$263$	13.4971	0.832265	0.416133	−	0.909304i	$-0.363385\pi$
$263$	13.4971	0.832265	0.416133	+	0.909304i	$0.363385\pi$
$264$	−28.5857	−1.75933
$265$	−0.374287	−0.0229923
$266$	0.338867	0.0207773
$267$	−25.0779	−1.53475
$268$	17.4163	1.06387
$269$	−6.11303	−0.372718	−0.186359	−	0.982482i	$-0.559669\pi$
$269$	−6.11303	−0.372718	−0.186359	+	0.982482i	$0.559669\pi$
$270$	−0.240645	−0.0146452
$271$	−17.9534	−1.09059	−0.545295	−	0.838244i	$-0.683582\pi$
$271$	−17.9534	−1.09059	−0.545295	+	0.838244i	$0.683582\pi$
$272$	−2.27756	−0.138097
$273$	−3.11275	−0.188392
$274$	−0.0247634	−0.00149601
$275$	−23.6678	−1.42722
$276$	−36.6171	−2.20409
$277$	−20.3876	−1.22497	−0.612486	−	0.790481i	$-0.709830\pi$
$277$	−20.3876	−1.22497	−0.612486	+	0.790481i	$0.709830\pi$
$278$	−6.55242	−0.392988
$279$	17.9927	1.07720
$280$	−0.0400134	−0.00239126
$281$	−7.29584	−0.435233	−0.217617	−	0.976034i	$-0.569828\pi$
$281$	−7.29584	−0.435233	−0.217617	+	0.976034i	$0.569828\pi$
$282$	1.72673	0.102825
$283$	−1.85352	−0.110180	−0.0550901	−	0.998481i	$-0.517545\pi$
$283$	−1.85352	−0.110180	−0.0550901	+	0.998481i	$0.517545\pi$
$284$	19.1430	1.13593
$285$	0.255307	0.0151231
$286$	7.27012	0.429891
$287$	1.00837	0.0595221
$288$	30.9175	1.82183
$289$	1.00000	0.0588235
$290$	0.201107	0.0118094
$291$	−26.0526	−1.52723
$292$	5.12634	0.299996
$293$	−22.9729	−1.34209	−0.671045	−	0.741417i	$-0.734154\pi$
$293$	−22.9729	−1.34209	−0.671045	+	0.741417i	$0.734154\pi$
$294$	−11.1957	−0.652945
$295$	0.345889	0.0201385
$296$	−1.46614	−0.0852178
$297$	39.5558	2.29526
$298$	−11.1043	−0.643255
$299$	20.2837	1.17304
$300$	25.1861	1.45412
$301$	−0.375563	−0.0216471
$302$	9.60094	0.552472
$303$	7.19260	0.413204
$304$	−3.73760	−0.214366
$305$	0.208550	0.0119415
$306$	−3.19628	−0.182719
$307$	22.4184	1.27949	0.639743	−	0.768589i	$-0.279041\pi$
$307$	22.4184	1.27949	0.639743	+	0.768589i	$0.279041\pi$
$308$	3.01973	0.172065
$309$	−41.7699	−2.37621
$310$	−0.0891798	−0.00506507
$311$	24.2988	1.37786	0.688928	−	0.724830i	$-0.258081\pi$
$311$	24.2988	1.37786	0.688928	+	0.724830i	$0.258081\pi$
$312$	−16.8506	−0.953978
$313$	28.5245	1.61230	0.806150	−	0.591711i	$-0.201547\pi$
$313$	28.5245	1.61230	0.806150	+	0.591711i	$0.201547\pi$
$314$	−5.70847	−0.322148
$315$	0.114413	0.00644642
$316$	−15.7118	−0.883859
$317$	−24.2698	−1.36313	−0.681565	−	0.731758i	$-0.738700\pi$
$317$	−24.2698	−1.36313	−0.681565	+	0.731758i	$0.738700\pi$
$318$	11.6581	0.653754
$319$	−33.0568	−1.85082
$320$	0.0854681	0.00477781
$321$	42.3381	2.36308
$322$	−1.50024	−0.0836052
$323$	1.64106	0.0913110
$324$	−12.4857	−0.693651
$325$	−13.9516	−0.773895
$326$	7.16760	0.396977
$327$	22.7986	1.26076
$328$	5.45872	0.301408
$329$	−0.397296	−0.0219036
$330$	−0.405124	−0.0223013
$331$	6.53263	0.359066	0.179533	−	0.983752i	$-0.442541\pi$
$331$	6.53263	0.359066	0.179533	+	0.983752i	$0.442541\pi$
$332$	10.2361	0.561778
$333$	4.19222	0.229732
$334$	8.16521	0.446781
$335$	0.537608	0.0293726
$336$	−2.53934	−0.138532
$337$	21.7870	1.18681	0.593407	−	0.804902i	$-0.297782\pi$
$337$	21.7870	1.18681	0.593407	+	0.804902i	$0.297782\pi$
$338$	−2.86214	−0.155680
$339$	−20.3827	−1.10703
$340$	−0.0889670	−0.00482491
$341$	14.6589	0.793822
$342$	−5.24529	−0.283633
$343$	5.20490	0.281038
$344$	−2.03308	−0.109616
$345$	−1.13030	−0.0608534
$346$	6.31666	0.339586
$347$	−4.26751	−0.229092	−0.114546	−	0.993418i	$-0.536541\pi$
$347$	−4.26751	−0.229092	−0.114546	+	0.993418i	$0.536541\pi$
$348$	35.1773	1.88570
$349$	31.3918	1.68037	0.840183	−	0.542303i	$-0.182447\pi$
$349$	31.3918	1.68037	0.840183	+	0.542303i	$0.182447\pi$
$350$	1.03190	0.0551573
$351$	23.3172	1.24458
$352$	25.1888	1.34257
$353$	12.3599	0.657853	0.328927	−	0.944355i	$-0.393313\pi$
$353$	12.3599	0.657853	0.328927	+	0.944355i	$0.393313\pi$
$354$	−10.7736	−0.572609
$355$	0.590906	0.0313621
$356$	14.3411	0.760076
$357$	1.11494	0.0590089
$358$	−5.54963	−0.293307
$359$	13.9630	0.736938	0.368469	−	0.929640i	$-0.379882\pi$
$359$	13.9630	0.736938	0.368469	+	0.929640i	$0.379882\pi$
$360$	0.619364	0.0326433
$361$	−16.3069	−0.858259
$362$	1.22827	0.0645564
$363$	33.9360	1.78118
$364$	1.78006	0.0933004
$365$	0.158240	0.00828267
$366$	−6.49580	−0.339541
$367$	25.7715	1.34526	0.672631	−	0.739978i	$-0.265164\pi$
$367$	25.7715	1.34526	0.672631	+	0.739978i	$0.265164\pi$
$368$	16.5472	0.862583
$369$	−15.6084	−0.812543
$370$	−0.0207785	−0.00108022
$371$	−2.68237	−0.139262
$372$	−15.5992	−0.808782
$373$	−22.4813	−1.16404	−0.582020	−	0.813175i	$-0.697737\pi$
$373$	−22.4813	−1.16404	−0.582020	+	0.813175i	$0.697737\pi$
$374$	−2.60405	−0.134652
$375$	1.55532	0.0803163
$376$	−2.15073	−0.110915
$377$	−19.4862	−1.00359
$378$	−1.72461	−0.0887041
$379$	27.5025	1.41271	0.706355	−	0.707858i	$-0.250338\pi$
$379$	27.5025	1.41271	0.706355	+	0.707858i	$0.250338\pi$
$380$	−0.146000	−0.00748965
$381$	37.6584	1.92930
$382$	−7.37359	−0.377266
$383$	29.0931	1.48659	0.743294	−	0.668965i	$-0.233262\pi$
$383$	29.0931	1.48659	0.743294	+	0.668965i	$0.233262\pi$
$384$	−34.2398	−1.74729
$385$	0.0932133	0.00475059
$386$	10.0063	0.509305
$387$	5.81330	0.295506
$388$	14.8985	0.756356
$389$	32.6538	1.65561	0.827807	−	0.561013i	$-0.189588\pi$
$389$	32.6538	1.65561	0.827807	+	0.561013i	$0.189588\pi$
$390$	−0.238811	−0.0120926
$391$	−7.26534	−0.367424
$392$	13.9448	0.704318
$393$	46.9024	2.36592
$394$	6.64598	0.334820
$395$	−0.484994	−0.0244027
$396$	−46.7421	−2.34888
$397$	30.9684	1.55426	0.777129	−	0.629341i	$-0.216675\pi$
$397$	30.9684	1.55426	0.777129	+	0.629341i	$0.216675\pi$
$398$	−3.37618	−0.169233
$399$	1.82968	0.0915987
$400$	−11.3815	−0.569076
$401$	−4.28379	−0.213922	−0.106961	−	0.994263i	$-0.534112\pi$
$401$	−4.28379	−0.213922	−0.106961	+	0.994263i	$0.534112\pi$
$402$	−16.7451	−0.835171
$403$	8.64105	0.430442
$404$	−4.11317	−0.204638
$405$	−0.385410	−0.0191512
$406$	1.44125	0.0715281
$407$	3.41545	0.169298
$408$	6.03564	0.298809
$409$	28.8011	1.42412	0.712061	−	0.702117i	$-0.247762\pi$
$409$	28.8011	1.42412	0.712061	+	0.702117i	$0.247762\pi$
$410$	0.0773623	0.00382065
$411$	−0.133708	−0.00659531
$412$	23.8866	1.17681
$413$	2.47885	0.121976
$414$	23.2221	1.14130
$415$	0.315968	0.0155103
$416$	14.8482	0.727993
$417$	−35.3792	−1.73253
$418$	−4.27340	−0.209019
$419$	1.49178	0.0728783	0.0364392	−	0.999336i	$-0.488398\pi$
$419$	1.49178	0.0728783	0.0364392	+	0.999336i	$0.488398\pi$
$420$	−0.0991928	−0.00484011
$421$	22.3746	1.09047	0.545235	−	0.838283i	$-0.316440\pi$
$421$	22.3746	1.09047	0.545235	+	0.838283i	$0.316440\pi$
$422$	5.54954	0.270148
$423$	6.14971	0.299009
$424$	−14.5208	−0.705191
$425$	4.99725	0.242402
$426$	−18.4052	−0.891737
$427$	1.49459	0.0723284
$428$	−24.2115	−1.17031
$429$	39.2543	1.89522
$430$	−0.0288132	−0.00138950
$431$	−30.4334	−1.46593	−0.732963	−	0.680269i	$-0.761863\pi$
$431$	−30.4334	−1.46593	−0.732963	+	0.680269i	$0.761863\pi$
$432$	19.0219	0.915191
$433$	16.8836	0.811374	0.405687	−	0.914012i	$-0.367032\pi$
$433$	16.8836	0.811374	0.405687	+	0.914012i	$0.367032\pi$
$434$	−0.639116	−0.0306786
$435$	1.08586	0.0520628
$436$	−13.0376	−0.624388
$437$	−11.9228	−0.570347
$438$	−4.92878	−0.235506
$439$	−8.44440	−0.403029	−0.201514	−	0.979486i	$-0.564586\pi$
$439$	−8.44440	−0.403029	−0.201514	+	0.979486i	$0.564586\pi$
$440$	0.504602	0.0240560
$441$	−39.8731	−1.89872
$442$	−1.53502	−0.0730137
$443$	25.8535	1.22834	0.614170	−	0.789174i	$-0.289491\pi$
$443$	25.8535	1.22834	0.614170	+	0.789174i	$0.289491\pi$
$444$	−3.63455	−0.172488
$445$	0.442682	0.0209851
$446$	−1.72286	−0.0815798
$447$	−59.9567	−2.83585
$448$	0.612516	0.0289386
$449$	−27.0290	−1.27558	−0.637788	−	0.770212i	$-0.720150\pi$
$449$	−27.0290	−1.27558	−0.637788	+	0.770212i	$0.720150\pi$
$450$	−15.9726	−0.752958
$451$	−12.7164	−0.598790
$452$	11.6560	0.548254
$453$	51.8394	2.43563
$454$	−15.7958	−0.741333
$455$	0.0549470	0.00257595
$456$	9.90484	0.463837
$457$	16.2906	0.762042	0.381021	−	0.924566i	$-0.375573\pi$
$457$	16.2906	0.762042	0.381021	+	0.924566i	$0.375573\pi$
$458$	11.5254	0.538548
$459$	−8.35188	−0.389833
$460$	0.646375	0.0301374
$461$	−27.3744	−1.27495	−0.637476	−	0.770470i	$-0.720021\pi$
$461$	−27.3744	−1.27495	−0.637476	+	0.770470i	$0.720021\pi$
$462$	−2.90336	−0.135076
$463$	−17.4639	−0.811616	−0.405808	−	0.913958i	$-0.633010\pi$
$463$	−17.4639	−0.811616	−0.405808	+	0.913958i	$0.633010\pi$
$464$	−15.8966	−0.737979
$465$	−0.481518	−0.0223299
$466$	−5.50271	−0.254908
$467$	−28.6234	−1.32453	−0.662266	−	0.749269i	$-0.730405\pi$
$467$	−28.6234	−1.32453	−0.662266	+	0.749269i	$0.730405\pi$
$468$	−27.5533	−1.27365
$469$	3.85282	0.177907
$470$	−0.0304806	−0.00140597
$471$	−30.8224	−1.42022
$472$	13.4191	0.617662
$473$	4.73616	0.217769
$474$	15.1063	0.693857
$475$	8.20079	0.376278
$476$	−0.637591	−0.0292239
$477$	41.5201	1.90107
$478$	10.8107	0.494469
$479$	−9.64382	−0.440637	−0.220319	−	0.975428i	$-0.570710\pi$
$479$	−9.64382	−0.440637	−0.220319	+	0.975428i	$0.570710\pi$
$480$	−0.827409	−0.0377659
$481$	2.01333	0.0917998
$482$	5.95449	0.271219
$483$	−8.10041	−0.368582
$484$	−19.4067	−0.882121
$485$	0.459888	0.0208824
$486$	−1.77162	−0.0803622
$487$	−37.8563	−1.71543	−0.857716	−	0.514124i	$-0.828117\pi$
$487$	−37.8563	−1.71543	−0.857716	+	0.514124i	$0.828117\pi$
$488$	8.09086	0.366256
$489$	38.7008	1.75011
$490$	0.197629	0.00892795
$491$	−27.7239	−1.25116	−0.625580	−	0.780160i	$-0.715138\pi$
$491$	−27.7239	−1.25116	−0.625580	+	0.780160i	$0.715138\pi$
$492$	13.5321	0.610075
$493$	6.97966	0.314348
$494$	−2.51907	−0.113338
$495$	−1.44284	−0.0648508
$496$	7.04926	0.316521
$497$	4.23479	0.189956
$498$	−9.84161	−0.441013
$499$	−16.3592	−0.732339	−0.366169	−	0.930548i	$-0.619331\pi$
$499$	−16.3592	−0.732339	−0.366169	+	0.930548i	$0.619331\pi$
$500$	−0.889425	−0.0397763
$501$	44.0873	1.96968
$502$	−13.0014	−0.580281
$503$	−14.6304	−0.652335	−0.326168	−	0.945312i	$-0.605757\pi$
$503$	−14.6304	−0.652335	−0.326168	+	0.945312i	$0.605757\pi$
$504$	4.43873	0.197717
$505$	−0.126966	−0.00564990
$506$	18.9193	0.841065
$507$	−15.4539	−0.686330
$508$	−21.5354	−0.955478
$509$	−25.0169	−1.10886	−0.554428	−	0.832232i	$-0.687063\pi$
$509$	−25.0169	−1.10886	−0.554428	+	0.832232i	$0.687063\pi$
$510$	0.0855385	0.00378771
$511$	1.13404	0.0501672
$512$	21.3739	0.944601
$513$	−13.7059	−0.605132
$514$	−7.35434	−0.324386
$515$	0.737333	0.0324908
$516$	−5.03998	−0.221873
$517$	5.01023	0.220350
$518$	−0.148911	−0.00654278
$519$	34.1062	1.49710
$520$	0.297451	0.0130441
$521$	−32.9085	−1.44175	−0.720874	−	0.693066i	$-0.756259\pi$
$521$	−32.9085	−1.44175	−0.720874	+	0.693066i	$0.756259\pi$
$522$	−22.3090	−0.976437
$523$	0.425110	0.0185888	0.00929439	−	0.999957i	$-0.497041\pi$
$523$	0.425110	0.0185888	0.00929439	+	0.999957i	$0.497041\pi$
$524$	−26.8217	−1.17171
$525$	5.57164	0.243166
$526$	7.42100	0.323571
$527$	−3.09510	−0.134825
$528$	32.0232	1.39363
$529$	29.7851	1.29501
$530$	−0.205792	−0.00893902
$531$	−38.3699	−1.66511
$532$	−1.04632	−0.0453639
$533$	−7.49600	−0.324688
$534$	−13.7884	−0.596684
$535$	−0.747364	−0.0323113
$536$	20.8569	0.900882
$537$	−29.9647	−1.29307
$538$	−3.36108	−0.144907
$539$	−32.4851	−1.39923
$540$	0.743042	0.0319754
$541$	4.88255	0.209917	0.104959	−	0.994477i	$-0.466529\pi$
$541$	4.88255	0.209917	0.104959	+	0.994477i	$0.466529\pi$
$542$	−9.87118	−0.424003
$543$	6.63193	0.284603
$544$	−5.31841	−0.228025
$545$	−0.402446	−0.0172389
$546$	−1.71146	−0.0732437
$547$	−28.9421	−1.23747	−0.618737	−	0.785598i	$-0.712355\pi$
$547$	−28.9421	−1.23747	−0.618737	+	0.785598i	$0.712355\pi$
$548$	0.0764622	0.00326630
$549$	−23.1347	−0.987363
$550$	−13.0131	−0.554880
$551$	11.4540	0.487958
$552$	−43.8509	−1.86642
$553$	−3.47576	−0.147804
$554$	−11.2096	−0.476249
$555$	−0.112192	−0.00476227
$556$	20.2320	0.858028
$557$	1.45054	0.0614613	0.0307307	−	0.999528i	$-0.490217\pi$
$557$	1.45054	0.0614613	0.0307307	+	0.999528i	$0.490217\pi$
$558$	9.89281	0.418796
$559$	2.79185	0.118083
$560$	0.0448250	0.00189420
$561$	−14.0603	−0.593627
$562$	−4.01142	−0.169212
$563$	31.6229	1.33275	0.666374	−	0.745618i	$-0.267846\pi$
$563$	31.6229	1.33275	0.666374	+	0.745618i	$0.267846\pi$
$564$	−5.33164	−0.224502
$565$	0.359800	0.0151369
$566$	−1.01911	−0.0428363
$567$	−2.76208	−0.115997
$568$	22.9247	0.961898
$569$	−9.03657	−0.378833	−0.189416	−	0.981897i	$-0.560660\pi$
$569$	−9.03657	−0.378833	−0.189416	+	0.981897i	$0.560660\pi$
$570$	0.140374	0.00587961
$571$	−14.4400	−0.604297	−0.302148	−	0.953261i	$-0.597704\pi$
$571$	−14.4400	−0.604297	−0.302148	+	0.953261i	$0.597704\pi$
$572$	−22.4480	−0.938599
$573$	−39.8130	−1.66321
$574$	0.554424	0.0231412
$575$	−36.3067	−1.51410
$576$	−9.48107	−0.395044
$577$	13.5385	0.563616	0.281808	−	0.959471i	$-0.409066\pi$
$577$	13.5385	0.563616	0.281808	+	0.959471i	$0.409066\pi$
$578$	0.549823	0.0228696
$579$	54.0278	2.24532
$580$	−0.620959	−0.0257839
$581$	2.26442	0.0939438
$582$	−14.3243	−0.593763
$583$	33.8269	1.40097
$584$	6.13906	0.254036
$585$	−0.850519	−0.0351646
$586$	−12.6310	−0.521782
$587$	35.2270	1.45398	0.726988	−	0.686650i	$-0.240920\pi$
$587$	35.2270	1.45398	0.726988	+	0.686650i	$0.240920\pi$
$588$	34.5690	1.42560
$589$	−5.07924	−0.209286
$590$	0.190178	0.00782950
$591$	35.8844	1.47608
$592$	1.64245	0.0675041
$593$	−27.2400	−1.11861	−0.559306	−	0.828961i	$-0.688932\pi$
$593$	−27.2400	−1.11861	−0.559306	+	0.828961i	$0.688932\pi$
$594$	21.7487	0.892361
$595$	−0.0196812	−0.000806851 0
$596$	34.2869	1.40445
$597$	−18.2294	−0.746079
$598$	11.1525	0.456058
$599$	8.33318	0.340484	0.170242	−	0.985402i	$-0.445545\pi$
$599$	8.33318	0.340484	0.170242	+	0.985402i	$0.445545\pi$
$600$	30.1616	1.23134
$601$	44.0594	1.79722	0.898611	−	0.438747i	$-0.144577\pi$
$601$	44.0594	1.79722	0.898611	+	0.438747i	$0.144577\pi$
$602$	−0.206493	−0.00841603
$603$	−59.6374	−2.42862
$604$	−29.6449	−1.20623
$605$	−0.599046	−0.0243547
$606$	3.95466	0.160647
$607$	29.2244	1.18618	0.593090	−	0.805136i	$-0.297908\pi$
$607$	29.2244	1.18618	0.593090	+	0.805136i	$0.297908\pi$
$608$	−8.72782	−0.353960
$609$	7.78190	0.315338
$610$	0.114666	0.00464267
$611$	2.95341	0.119482
$612$	9.86920	0.398939
$613$	11.8524	0.478715	0.239358	−	0.970931i	$-0.423063\pi$
$613$	11.8524	0.478715	0.239358	+	0.970931i	$0.423063\pi$
$614$	12.3262	0.497444
$615$	0.417710	0.0168437
$616$	3.61628	0.145704
$617$	−4.43703	−0.178628	−0.0893141	−	0.996004i	$-0.528467\pi$
$617$	−4.43703	−0.178628	−0.0893141	+	0.996004i	$0.528467\pi$
$618$	−22.9661	−0.923831
$619$	−10.9800	−0.441324	−0.220662	−	0.975350i	$-0.570822\pi$
$619$	−10.9800	−0.441324	−0.220662	+	0.975350i	$0.570822\pi$
$620$	0.275361	0.0110588
$621$	60.6793	2.43497
$622$	13.3600	0.535688
$623$	3.17253	0.127105
$624$	18.8769	0.755681
$625$	24.9588	0.998353
$626$	15.6834	0.626836
$627$	−23.0738	−0.921480
$628$	17.6261	0.703358
$629$	−0.721144	−0.0287539
$630$	0.0629067	0.00250626
$631$	16.7977	0.668708	0.334354	−	0.942448i	$-0.391482\pi$
$631$	16.7977	0.668708	0.334354	+	0.942448i	$0.391482\pi$
$632$	−18.8157	−0.748450
$633$	29.9642	1.19097
$634$	−13.3441	−0.529962
$635$	−0.664756	−0.0263800
$636$	−35.9969	−1.42737
$637$	−19.1492	−0.758718
$638$	−18.1754	−0.719570
$639$	−65.5499	−2.59311
$640$	0.604410	0.0238914
$641$	32.4857	1.28311	0.641554	−	0.767078i	$-0.278290\pi$
$641$	32.4857	1.28311	0.641554	+	0.767078i	$0.278290\pi$
$642$	23.2785	0.918729
$643$	−10.2149	−0.402836	−0.201418	−	0.979505i	$-0.564555\pi$
$643$	−10.2149	−0.402836	−0.201418	+	0.979505i	$0.564555\pi$
$644$	4.63231	0.182539
$645$	−0.155574	−0.00612574
$646$	0.902292	0.0355002
$647$	−49.3507	−1.94018	−0.970088	−	0.242752i	$-0.921950\pi$
$647$	−49.3507	−1.94018	−0.970088	+	0.242752i	$0.921950\pi$
$648$	−14.9523	−0.587382
$649$	−31.2604	−1.22708
$650$	−7.67091	−0.300878
$651$	−3.45085	−0.135249
$652$	−22.1315	−0.866735
$653$	−12.2979	−0.481253	−0.240626	−	0.970618i	$-0.577353\pi$
$653$	−12.2979	−0.481253	−0.240626	+	0.970618i	$0.577353\pi$
$654$	12.5352	0.490164
$655$	−0.827934	−0.0323500
$656$	−6.11513	−0.238756
$657$	−17.5538	−0.684837
$658$	−0.218443	−0.00851578
$659$	20.8859	0.813599	0.406799	−	0.913518i	$-0.366645\pi$
$659$	20.8859	0.813599	0.406799	+	0.913518i	$0.366645\pi$
$660$	1.25090	0.0486914
$661$	−15.6583	−0.609036	−0.304518	−	0.952507i	$-0.598495\pi$
$661$	−15.6583	−0.609036	−0.304518	+	0.952507i	$0.598495\pi$
$662$	3.59179	0.139599
$663$	−8.28822	−0.321888
$664$	12.2582	0.475712
$665$	−0.0322980	−0.00125246
$666$	2.30498	0.0893162
$667$	−50.7096	−1.96348
$668$	−25.2118	−0.975475
$669$	−9.30243	−0.359653
$670$	0.295589	0.0114196
$671$	−18.8481	−0.727621
$672$	−5.92971	−0.228743
$673$	−12.3241	−0.475060	−0.237530	−	0.971380i	$-0.576338\pi$
$673$	−12.3241	−0.475060	−0.237530	+	0.971380i	$0.576338\pi$
$674$	11.9790	0.461414
$675$	−41.7365	−1.60644
$676$	8.83746	0.339902
$677$	−15.7914	−0.606914	−0.303457	−	0.952845i	$-0.598141\pi$
$677$	−15.7914	−0.606914	−0.303457	+	0.952845i	$0.598141\pi$
$678$	−11.2069	−0.430397
$679$	3.29583	0.126482
$680$	−0.106543	−0.00408572
$681$	−85.2880	−3.26824
$682$	8.05979	0.308625
$683$	−23.7656	−0.909367	−0.454683	−	0.890653i	$-0.650248\pi$
$683$	−23.7656	−0.909367	−0.454683	+	0.890653i	$0.650248\pi$
$684$	16.1959	0.619267
$685$	0.00236024	9.01802e−5 0
$686$	2.86178	0.109263
$687$	62.2305	2.37424
$688$	2.27756	0.0868310
$689$	19.9401	0.759659
$690$	−0.621466	−0.0236588
$691$	−24.9846	−0.950458	−0.475229	−	0.879862i	$-0.657635\pi$
$691$	−24.9846	−0.950458	−0.475229	+	0.879862i	$0.657635\pi$
$692$	−19.5040	−0.741432
$693$	−10.3402	−0.392793
$694$	−2.34637	−0.0890671
$695$	0.624523	0.0236895
$696$	42.1267	1.59681
$697$	2.68495	0.101700
$698$	17.2600	0.653299
$699$	−29.7114	−1.12379
$700$	−3.18620	−0.120427
$701$	45.7888	1.72942	0.864709	−	0.502273i	$-0.167503\pi$
$701$	45.7888	1.72942	0.864709	+	0.502273i	$0.167503\pi$
$702$	12.8203	0.483873
$703$	−1.18344	−0.0446343
$704$	−7.72433	−0.291122
$705$	−0.164577	−0.00619835
$706$	6.79578	0.255763
$707$	−0.909912	−0.0342208
$708$	33.2657	1.25020
$709$	24.2903	0.912240	0.456120	−	0.889918i	$-0.349239\pi$
$709$	24.2903	0.912240	0.456120	+	0.889918i	$0.349239\pi$
$710$	0.324894	0.0121931
$711$	53.8009	2.01769
$712$	17.1742	0.643631
$713$	22.4869	0.842142
$714$	0.613020	0.0229417
$715$	−0.692927	−0.0259140
$716$	17.1356	0.640389
$717$	58.3713	2.17992
$718$	7.67717	0.286510
$719$	−18.7655	−0.699834	−0.349917	−	0.936781i	$-0.613790\pi$
$719$	−18.7655	−0.699834	−0.349917	+	0.936781i	$0.613790\pi$
$720$	−0.693842	−0.0258580
$721$	5.28417	0.196793
$722$	−8.96592	−0.333677
$723$	32.1507	1.19570
$724$	−3.79254	−0.140949
$725$	34.8791	1.29538
$726$	18.6588	0.692492
$727$	32.2605	1.19648	0.598238	−	0.801319i	$-0.295868\pi$
$727$	32.2605	1.19648	0.598238	+	0.801319i	$0.295868\pi$
$728$	2.13171	0.0790065
$729$	−31.6292	−1.17145
$730$	0.0870041	0.00322017
$731$	−1.00000	−0.0369863
$732$	20.0572	0.741334
$733$	−2.59273	−0.0957647	−0.0478823	−	0.998853i	$-0.515247\pi$
$733$	−2.59273	−0.0957647	−0.0478823	+	0.998853i	$0.515247\pi$
$734$	14.1698	0.523016
$735$	1.06708	0.0393598
$736$	38.6400	1.42429
$737$	−48.5873	−1.78973
$738$	−8.58188	−0.315903
$739$	−26.2902	−0.967099	−0.483550	−	0.875317i	$-0.660653\pi$
$739$	−26.2902	−0.967099	−0.483550	+	0.875317i	$0.660653\pi$
$740$	0.0641580	0.00235850
$741$	−13.6015	−0.499662
$742$	−1.47483	−0.0541426
$743$	−18.8943	−0.693165	−0.346582	−	0.938020i	$-0.612658\pi$
$743$	−18.8943	−0.693165	−0.346582	+	0.938020i	$0.612658\pi$
$744$	−18.6809	−0.684875
$745$	1.05837	0.0387757
$746$	−12.3608	−0.452560
$747$	−35.0507	−1.28244
$748$	8.04055	0.293992
$749$	−5.35606	−0.195706
$750$	0.855150	0.0312256
$751$	0.0568192	0.00207336	0.00103668	−	0.999999i	$-0.499670\pi$
$751$	0.0568192	0.00207336	0.00103668	+	0.999999i	$0.499670\pi$
$752$	2.40936	0.0878602
$753$	−70.1999	−2.55823
$754$	−10.7139	−0.390179
$755$	−0.915082	−0.0333032
$756$	5.32508	0.193671
$757$	11.6037	0.421743	0.210872	−	0.977514i	$-0.432370\pi$
$757$	11.6037	0.421743	0.210872	+	0.977514i	$0.432370\pi$
$758$	15.1215	0.549238
$759$	102.153	3.70792
$760$	−0.174843	−0.00634221
$761$	19.4228	0.704076	0.352038	−	0.935986i	$-0.385489\pi$
$761$	19.4228	0.704076	0.352038	+	0.935986i	$0.385489\pi$
$762$	20.7055	0.750080
$763$	−2.88417	−0.104414
$764$	22.7675	0.823700
$765$	0.304643	0.0110144
$766$	15.9961	0.577961
$767$	−18.4272	−0.665369
$768$	−9.14232	−0.329895
$769$	−0.535709	−0.0193182	−0.00965908	−	0.999953i	$-0.503075\pi$
$769$	−0.535709	−0.0193182	−0.00965908	+	0.999953i	$0.503075\pi$
$770$	0.0512508	0.00184695
$771$	−39.7091	−1.43009
$772$	−30.8964	−1.11199
$773$	−20.4874	−0.736881	−0.368440	−	0.929651i	$-0.620108\pi$
$773$	−20.4874	−0.736881	−0.368440	+	0.929651i	$0.620108\pi$
$774$	3.19628	0.114888
$775$	−15.4670	−0.555591
$776$	17.8417	0.640480
$777$	−0.804033	−0.0288445
$778$	17.9538	0.643676
$779$	4.40617	0.157867
$780$	0.737378	0.0264024
$781$	−53.4042	−1.91095
$782$	−3.99465	−0.142848
$783$	−58.2933	−2.08323
$784$	−15.6216	−0.557916
$785$	0.544084	0.0194192
$786$	25.7880	0.919829
$787$	−14.2497	−0.507948	−0.253974	−	0.967211i	$-0.581738\pi$
$787$	−14.2497	−0.507948	−0.253974	+	0.967211i	$0.581738\pi$
$788$	−20.5209	−0.731025
$789$	40.0690	1.42650
$790$	−0.266661	−0.00948737
$791$	2.57854	0.0916824
$792$	−55.9761	−1.98902
$793$	−11.1105	−0.394545
$794$	17.0271	0.604270
$795$	−1.11115	−0.0394086
$796$	10.4247	0.369493
$797$	37.5732	1.33091	0.665456	−	0.746437i	$-0.268237\pi$
$797$	37.5732	1.33091	0.665456	+	0.746437i	$0.268237\pi$
$798$	1.00600	0.0356121
$799$	−1.05787	−0.0374247
$800$	−26.5774	−0.939654
$801$	−49.1072	−1.73512
$802$	−2.35533	−0.0831695
$803$	−14.3012	−0.504680
$804$	51.7041	1.82346
$805$	0.142991	0.00503975
$806$	4.75105	0.167349
$807$	−18.1479	−0.638835
$808$	−4.92573	−0.173287
$809$	36.2013	1.27277	0.636385	−	0.771372i	$-0.280429\pi$
$809$	36.2013	1.27277	0.636385	+	0.771372i	$0.280429\pi$
$810$	−0.211908	−0.00744567
$811$	−27.0112	−0.948492	−0.474246	−	0.880393i	$-0.657279\pi$
$811$	−27.0112	−0.948492	−0.474246	+	0.880393i	$0.657279\pi$
$812$	−4.45016	−0.156170
$813$	−53.2985	−1.86926
$814$	1.87789	0.0658202
$815$	−0.683156	−0.0239299
$816$	−6.76142	−0.236697
$817$	−1.64106	−0.0574134
$818$	15.8355	0.553676
$819$	−6.09533	−0.212988
$820$	−0.238872	−0.00834178
$821$	41.9661	1.46463	0.732313	−	0.680968i	$-0.238441\pi$
$821$	41.9661	1.46463	0.732313	+	0.680968i	$0.238441\pi$
$822$	−0.0735156	−0.00256415
$823$	44.3754	1.54683	0.773414	−	0.633901i	$-0.218547\pi$
$823$	44.3754	1.54683	0.773414	+	0.633901i	$0.218547\pi$
$824$	28.6054	0.996518
$825$	−70.2630	−2.44624
$826$	1.36293	0.0474224
$827$	−4.72801	−0.164409	−0.0822045	−	0.996615i	$-0.526196\pi$
$827$	−4.72801	−0.164409	−0.0822045	+	0.996615i	$0.526196\pi$
$828$	−71.7031	−2.49185
$829$	38.5175	1.33777	0.668884	−	0.743367i	$-0.266772\pi$
$829$	38.5175	1.33777	0.668884	+	0.743367i	$0.266772\pi$
$830$	0.173727	0.00603014
$831$	−60.5251	−2.09959
$832$	−4.55331	−0.157858
$833$	6.85895	0.237649
$834$	−19.4523	−0.673578
$835$	−0.778241	−0.0269321
$836$	13.1950	0.456359
$837$	25.8499	0.893503
$838$	0.820216	0.0283339
$839$	−20.2113	−0.697770	−0.348885	−	0.937165i	$-0.613440\pi$
$839$	−20.2113	−0.697770	−0.348885	+	0.937165i	$0.613440\pi$
$840$	−0.118789	−0.00409860
$841$	19.7156	0.679849
$842$	12.3021	0.423957
$843$	−21.6593	−0.745986
$844$	−17.1354	−0.589824
$845$	0.272795	0.00938445
$846$	3.38125	0.116250
$847$	−4.29313	−0.147514
$848$	16.2669	0.558608
$849$	−5.50258	−0.188848
$850$	2.74761	0.0942421
$851$	5.23936	0.179603
$852$	56.8301	1.94697
$853$	−32.7344	−1.12081	−0.560403	−	0.828220i	$-0.689354\pi$
$853$	−32.7344	−1.12081	−0.560403	+	0.828220i	$0.689354\pi$
$854$	0.821762	0.0281201
$855$	0.499938	0.0170975
$856$	−28.9946	−0.991014
$857$	45.5327	1.55537	0.777684	−	0.628656i	$-0.216394\pi$
$857$	45.5327	1.55537	0.777684	+	0.628656i	$0.216394\pi$
$858$	21.5829	0.736829
$859$	54.3652	1.85492	0.927458	−	0.373927i	$-0.121989\pi$
$859$	54.3652	1.85492	0.927458	+	0.373927i	$0.121989\pi$
$860$	0.0889670	0.00303375
$861$	2.99356	0.102020
$862$	−16.7330	−0.569928
$863$	−12.8907	−0.438804	−0.219402	−	0.975635i	$-0.570411\pi$
$863$	−12.8907	−0.438804	−0.219402	+	0.975635i	$0.570411\pi$
$864$	44.4187	1.51116
$865$	−0.602052	−0.0204704
$866$	9.28300	0.315449
$867$	2.96872	0.100823
$868$	1.97341	0.0669817
$869$	43.8322	1.48691
$870$	0.597029	0.0202412
$871$	−28.6410	−0.970464
$872$	−15.6132	−0.528730
$873$	−51.0158	−1.72662
$874$	−6.55546	−0.221742
$875$	−0.196758	−0.00665163
$876$	15.2187	0.514191
$877$	−18.5358	−0.625909	−0.312955	−	0.949768i	$-0.601319\pi$
$877$	−18.5358	−0.625909	−0.312955	+	0.949768i	$0.601319\pi$
$878$	−4.64292	−0.156691
$879$	−68.2000	−2.30033
$880$	−0.565281	−0.0190556
$881$	56.0305	1.88771	0.943857	−	0.330353i	$-0.107168\pi$
$881$	56.0305	1.88771	0.943857	+	0.330353i	$0.107168\pi$
$882$	−21.9232	−0.738191
$883$	−27.7968	−0.935437	−0.467718	−	0.883878i	$-0.654924\pi$
$883$	−27.7968	−0.935437	−0.467718	+	0.883878i	$0.654924\pi$
$884$	4.73971	0.159414
$885$	1.02685	0.0345171
$886$	14.2149	0.477558
$887$	12.6169	0.423635	0.211817	−	0.977309i	$-0.432062\pi$
$887$	12.6169	0.423635	0.211817	+	0.977309i	$0.432062\pi$
$888$	−4.35257	−0.146063
$889$	−4.76404	−0.159781
$890$	0.243397	0.00815868
$891$	34.8321	1.16692
$892$	5.31969	0.178117
$893$	−1.73603	−0.0580939
$894$	−32.9656	−1.10253
$895$	0.528945	0.0176807
$896$	4.33157	0.144707
$897$	60.2167	2.01058
$898$	−14.8611	−0.495923
$899$	−21.6027	−0.720491
$900$	49.3189	1.64396
$901$	−7.14226	−0.237943
$902$	−6.99175	−0.232800
$903$	−1.11494	−0.0371029
$904$	13.9587	0.464260
$905$	−0.117068	−0.00389149
$906$	28.5025	0.946932
$907$	26.9203	0.893876	0.446938	−	0.894565i	$-0.352515\pi$
$907$	26.9203	0.893876	0.446938	+	0.894565i	$0.352515\pi$
$908$	48.7728	1.61858
$909$	14.0844	0.467151
$910$	0.0302111	0.00100149
$911$	38.8412	1.28687	0.643434	−	0.765502i	$-0.277509\pi$
$911$	38.8412	1.28687	0.643434	+	0.765502i	$0.277509\pi$
$912$	−11.0959	−0.367422
$913$	−28.5562	−0.945072
$914$	8.95695	0.296270
$915$	0.619126	0.0204677
$916$	−35.5872	−1.17583
$917$	−5.93347	−0.195940
$918$	−4.59206	−0.151561
$919$	−29.3528	−0.968261	−0.484130	−	0.874996i	$-0.660864\pi$
$919$	−29.3528	−0.968261	−0.484130	+	0.874996i	$0.660864\pi$
$920$	0.774068	0.0255203
$921$	66.5540	2.19303
$922$	−15.0511	−0.495680
$923$	−31.4805	−1.03619
$924$	8.96473	0.294918
$925$	−3.60374	−0.118490
$926$	−9.60206	−0.315543
$927$	−81.7932	−2.68644
$928$	−37.1207	−1.21855
$929$	−41.2802	−1.35436	−0.677180	−	0.735818i	$-0.736798\pi$
$929$	−41.2802	−1.35436	−0.677180	+	0.735818i	$0.736798\pi$
$930$	−0.264750	−0.00868149
$931$	11.2559	0.368899
$932$	16.9908	0.556551
$933$	72.1362	2.36163
$934$	−15.7378	−0.514956
$935$	0.248196	0.00811689
$936$	−32.9966	−1.07853
$937$	50.0328	1.63450	0.817251	−	0.576282i	$-0.195497\pi$
$937$	50.0328	1.63450	0.817251	+	0.576282i	$0.195497\pi$
$938$	2.11837	0.0691672
$939$	84.6812	2.76347
$940$	0.0941154	0.00306971
$941$	−1.82935	−0.0596352	−0.0298176	−	0.999555i	$-0.509493\pi$
$941$	−1.82935	−0.0596352	−0.0298176	+	0.999555i	$0.509493\pi$
$942$	−16.9468	−0.552158
$943$	−19.5071	−0.635239
$944$	−15.0327	−0.489273
$945$	0.164375	0.00534712
$946$	2.60405	0.0846649
$947$	−59.1804	−1.92310	−0.961552	−	0.274625i	$-0.911446\pi$
$947$	−59.1804	−1.92310	−0.961552	+	0.274625i	$0.911446\pi$
$948$	−46.6440	−1.51493
$949$	−8.43024	−0.273657
$950$	4.50898	0.146291
$951$	−72.0503	−2.33639
$952$	−0.763548	−0.0247467
$953$	25.6458	0.830750	0.415375	−	0.909650i	$-0.363650\pi$
$953$	25.6458	0.830750	0.415375	+	0.909650i	$0.363650\pi$
$954$	22.8287	0.739107
$955$	0.702789	0.0227417
$956$	−33.3803	−1.07959
$957$	−98.1362	−3.17229
$958$	−5.30239	−0.171313
$959$	0.0169149	0.000546211 0
$960$	0.253731	0.00818913
$961$	−21.4204	−0.690980
$962$	1.10697	0.0356903
$963$	82.9058	2.67160
$964$	−18.3857	−0.592164
$965$	−0.953713	−0.0307011
$966$	−4.45380	−0.143299
$967$	−45.4154	−1.46046	−0.730231	−	0.683201i	$-0.760587\pi$
$967$	−45.4154	−1.46046	−0.730231	+	0.683201i	$0.760587\pi$
$968$	−23.2405	−0.746978
$969$	4.87184	0.156506
$970$	0.252857	0.00811875
$971$	−29.8356	−0.957471	−0.478736	−	0.877959i	$-0.658905\pi$
$971$	−29.8356	−0.957471	−0.478736	+	0.877959i	$0.658905\pi$
$972$	5.47024	0.175458
$973$	4.47570	0.143485
$974$	−20.8143	−0.666932
$975$	−41.4184	−1.32645
$976$	−9.06379	−0.290125
$977$	−8.57886	−0.274462	−0.137231	−	0.990539i	$-0.543820\pi$
$977$	−8.57886	−0.274462	−0.137231	+	0.990539i	$0.543820\pi$
$978$	21.2786	0.680414
$979$	−40.0082	−1.27867
$980$	−0.610220	−0.0194928
$981$	44.6437	1.42536
$982$	−15.2432	−0.486431
$983$	1.07028	0.0341366	0.0170683	−	0.999854i	$-0.494567\pi$
$983$	1.07028	0.0341366	0.0170683	+	0.999854i	$0.494567\pi$
$984$	16.2054	0.516610
$985$	−0.633440	−0.0201831
$986$	3.83758	0.122213
$987$	−1.17946	−0.0375426
$988$	7.77815	0.247456
$989$	7.26534	0.231024
$990$	−0.793306	−0.0252129
$991$	8.14153	0.258624	0.129312	−	0.991604i	$-0.458723\pi$
$991$	8.14153	0.258624	0.129312	+	0.991604i	$0.458723\pi$
$992$	16.4610	0.522637
$993$	19.3935	0.615435
$994$	2.32838	0.0738519
$995$	0.321790	0.0102014
$996$	30.3880	0.962882
$997$	10.7518	0.340514	0.170257	−	0.985400i	$-0.445540\pi$
$997$	10.7518	0.340514	0.170257	+	0.985400i	$0.445540\pi$
$998$	−8.99467	−0.284721
$999$	6.02291	0.190557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.12	✓	21
3.2	odd	2		6579.2.a.u.1.10		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.12	✓	21	1.1	even	1	trivial
6579.2.a.u.1.10		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)

\(f(q)\)	\(=\)	\(q+0.549823 q^{2} +2.96872 q^{3} -1.69769 q^{4} -0.0524046 q^{5} +1.63227 q^{6} -0.375563 q^{7} -2.03308 q^{8} +5.81330 q^{9} +O(q^{10})\)	\(q+0.549823 q^{2} +2.96872 q^{3} -1.69769 q^{4} -0.0524046 q^{5} +1.63227 q^{6} -0.375563 q^{7} -2.03308 q^{8} +5.81330 q^{9} -0.0288132 q^{10} +4.73616 q^{11} -5.03998 q^{12} +2.79185 q^{13} -0.206493 q^{14} -0.155574 q^{15} +2.27756 q^{16} -1.00000 q^{17} +3.19628 q^{18} -1.64106 q^{19} +0.0889670 q^{20} -1.11494 q^{21} +2.60405 q^{22} +7.26534 q^{23} -6.03564 q^{24} -4.99725 q^{25} +1.53502 q^{26} +8.35188 q^{27} +0.637591 q^{28} -6.97966 q^{29} -0.0855385 q^{30} +3.09510 q^{31} +5.31841 q^{32} +14.0603 q^{33} -0.549823 q^{34} +0.0196812 q^{35} -9.86920 q^{36} +0.721144 q^{37} -0.902292 q^{38} +8.28822 q^{39} +0.106543 q^{40} -2.68495 q^{41} -0.613020 q^{42} +1.00000 q^{43} -8.04055 q^{44} -0.304643 q^{45} +3.99465 q^{46} +1.05787 q^{47} +6.76142 q^{48} -6.85895 q^{49} -2.74761 q^{50} -2.96872 q^{51} -4.73971 q^{52} +7.14226 q^{53} +4.59206 q^{54} -0.248196 q^{55} +0.763548 q^{56} -4.87184 q^{57} -3.83758 q^{58} -6.60037 q^{59} +0.264118 q^{60} -3.97961 q^{61} +1.70176 q^{62} -2.18326 q^{63} -1.63093 q^{64} -0.146306 q^{65} +7.73069 q^{66} -10.2588 q^{67} +1.69769 q^{68} +21.5687 q^{69} +0.0108212 q^{70} -11.2759 q^{71} -11.8189 q^{72} -3.01959 q^{73} +0.396502 q^{74} -14.8354 q^{75} +2.78602 q^{76} -1.77872 q^{77} +4.55706 q^{78} +9.25480 q^{79} -0.119354 q^{80} +7.35452 q^{81} -1.47625 q^{82} -6.02940 q^{83} +1.89283 q^{84} +0.0524046 q^{85} +0.549823 q^{86} -20.7206 q^{87} -9.62898 q^{88} -8.44739 q^{89} -0.167500 q^{90} -1.04852 q^{91} -12.3343 q^{92} +9.18848 q^{93} +0.581641 q^{94} +0.0859990 q^{95} +15.7889 q^{96} -8.77572 q^{97} -3.77121 q^{98} +27.5327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 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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