LMFDB - Embedded newform 731.2.a.d.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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 9x^{6} + 9x^{5} + 21x^{4} - 21x^{3} - 8x^{2} + 7x - 1 $ x^8 - x^7 - 9x^6 + 9x^5 + 21x^4 - 21x^3 - 8x^2 + 7x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.31200$ of defining polynomial
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)

$f(q)$	$=$	$q-2.31200 q^{2} -1.95532 q^{3} +3.34533 q^{4} +1.83479 q^{5} +4.52069 q^{6} +0.437329 q^{7} -3.11039 q^{8} +0.823276 q^{9} +O(q^{10})$	\(q-2.31200 q^{2} -1.95532 q^{3} +3.34533 q^{4} +1.83479 q^{5} +4.52069 q^{6} +0.437329 q^{7} -3.11039 q^{8} +0.823276 q^{9} -4.24203 q^{10} -2.43560 q^{11} -6.54119 q^{12} -1.79840 q^{13} -1.01110 q^{14} -3.58760 q^{15} +0.500565 q^{16} +1.00000 q^{17} -1.90341 q^{18} -1.69071 q^{19} +6.13797 q^{20} -0.855118 q^{21} +5.63109 q^{22} +9.21615 q^{23} +6.08182 q^{24} -1.63355 q^{25} +4.15789 q^{26} +4.25619 q^{27} +1.46301 q^{28} -3.04732 q^{29} +8.29452 q^{30} -0.112112 q^{31} +5.06348 q^{32} +4.76237 q^{33} -2.31200 q^{34} +0.802407 q^{35} +2.75413 q^{36} -5.70394 q^{37} +3.90891 q^{38} +3.51644 q^{39} -5.70692 q^{40} -3.89073 q^{41} +1.97703 q^{42} +1.00000 q^{43} -8.14787 q^{44} +1.51054 q^{45} -21.3077 q^{46} +8.80502 q^{47} -0.978765 q^{48} -6.80874 q^{49} +3.77675 q^{50} -1.95532 q^{51} -6.01623 q^{52} -9.54770 q^{53} -9.84030 q^{54} -4.46881 q^{55} -1.36027 q^{56} +3.30587 q^{57} +7.04540 q^{58} +0.163476 q^{59} -12.0017 q^{60} -7.05431 q^{61} +0.259202 q^{62} +0.360043 q^{63} -12.7079 q^{64} -3.29968 q^{65} -11.0106 q^{66} -1.42971 q^{67} +3.34533 q^{68} -18.0205 q^{69} -1.85516 q^{70} +0.618350 q^{71} -2.56071 q^{72} +2.13881 q^{73} +13.1875 q^{74} +3.19410 q^{75} -5.65597 q^{76} -1.06516 q^{77} -8.13001 q^{78} +2.88966 q^{79} +0.918432 q^{80} -10.7920 q^{81} +8.99536 q^{82} -13.6770 q^{83} -2.86065 q^{84} +1.83479 q^{85} -2.31200 q^{86} +5.95849 q^{87} +7.57566 q^{88} -6.29577 q^{89} -3.49236 q^{90} -0.786492 q^{91} +30.8311 q^{92} +0.219215 q^{93} -20.3572 q^{94} -3.10209 q^{95} -9.90073 q^{96} -16.3955 q^{97} +15.7418 q^{98} -2.00517 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * 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 $

$2$	−2.31200	−1.63483	−0.817414	−	0.576050i	$-0.804593\pi$
$2$	−2.31200	−1.63483	−0.817414	+	0.576050i	$0.804593\pi$
$3$	−1.95532	−1.12890	−0.564452	−	0.825466i	$-0.690913\pi$
$3$	−1.95532	−1.12890	−0.564452	+	0.825466i	$0.690913\pi$
$4$	3.34533	1.67266
$5$	1.83479	0.820543	0.410272	−	0.911963i	$-0.365434\pi$
$5$	1.83479	0.820543	0.410272	+	0.911963i	$0.365434\pi$
$6$	4.52069	1.84557
$7$	0.437329	0.165295	0.0826474	−	0.996579i	$-0.473662\pi$
$7$	0.437329	0.165295	0.0826474	+	0.996579i	$0.473662\pi$
$8$	−3.11039	−1.09969
$9$	0.823276	0.274425
$10$	−4.24203	−1.34145
$11$	−2.43560	−0.734360	−0.367180	−	0.930150i	$-0.619677\pi$
$11$	−2.43560	−0.734360	−0.367180	+	0.930150i	$0.619677\pi$
$12$	−6.54119	−1.88828
$13$	−1.79840	−0.498786	−0.249393	−	0.968402i	$-0.580231\pi$
$13$	−1.79840	−0.498786	−0.249393	+	0.968402i	$0.580231\pi$
$14$	−1.01110	−0.270229
$15$	−3.58760	−0.926315
$16$	0.500565	0.125141
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.90341	−0.448638
$19$	−1.69071	−0.387874	−0.193937	−	0.981014i	$-0.562126\pi$
$19$	−1.69071	−0.387874	−0.193937	+	0.981014i	$0.562126\pi$
$20$	6.13797	1.37249
$21$	−0.855118	−0.186602
$22$	5.63109	1.20055
$23$	9.21615	1.92170	0.960850	−	0.277068i	$-0.0893627\pi$
$23$	9.21615	1.92170	0.960850	+	0.277068i	$0.0893627\pi$
$24$	6.08182	1.24145
$25$	−1.63355	−0.326709
$26$	4.15789	0.815429
$27$	4.25619	0.819105
$28$	1.46301	0.276483
$29$	−3.04732	−0.565873	−0.282937	−	0.959139i	$-0.591309\pi$
$29$	−3.04732	−0.565873	−0.282937	+	0.959139i	$0.591309\pi$
$30$	8.29452	1.51437
$31$	−0.112112	−0.0201359	−0.0100680	−	0.999949i	$-0.503205\pi$
$31$	−0.112112	−0.0201359	−0.0100680	+	0.999949i	$0.503205\pi$
$32$	5.06348	0.895106
$33$	4.76237	0.829022
$34$	−2.31200	−0.396504
$35$	0.802407	0.135632
$36$	2.75413	0.459021
$37$	−5.70394	−0.937723	−0.468861	−	0.883272i	$-0.655336\pi$
$37$	−5.70394	−0.937723	−0.468861	+	0.883272i	$0.655336\pi$
$38$	3.90891	0.634108
$39$	3.51644	0.563082
$40$	−5.70692	−0.902343
$41$	−3.89073	−0.607631	−0.303815	−	0.952731i	$-0.598261\pi$
$41$	−3.89073	−0.607631	−0.303815	+	0.952731i	$0.598261\pi$
$42$	1.97703	0.305062
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−8.14787	−1.22834
$45$	1.51054	0.225178
$46$	−21.3077	−3.14165
$47$	8.80502	1.28434	0.642172	−	0.766560i	$-0.278033\pi$
$47$	8.80502	1.28434	0.642172	+	0.766560i	$0.278033\pi$
$48$	−0.978765	−0.141273
$49$	−6.80874	−0.972678
$50$	3.77675	0.534113
$51$	−1.95532	−0.273800
$52$	−6.01623	−0.834301
$53$	−9.54770	−1.31148	−0.655739	−	0.754988i	$-0.727643\pi$
$53$	−9.54770	−1.31148	−0.655739	+	0.754988i	$0.727643\pi$
$54$	−9.84030	−1.33910
$55$	−4.46881	−0.602574
$56$	−1.36027	−0.181773
$57$	3.30587	0.437873
$58$	7.04540	0.925106
$59$	0.163476	0.0212828	0.0106414	−	0.999943i	$-0.496613\pi$
$59$	0.163476	0.0212828	0.0106414	+	0.999943i	$0.496613\pi$
$60$	−12.0017	−1.54941
$61$	−7.05431	−0.903212	−0.451606	−	0.892217i	$-0.649149\pi$
$61$	−7.05431	−0.903212	−0.451606	+	0.892217i	$0.649149\pi$
$62$	0.259202	0.0329187
$63$	0.360043	0.0453611
$64$	−12.7079	−1.58849
$65$	−3.29968	−0.409275
$66$	−11.0106	−1.35531
$67$	−1.42971	−0.174667	−0.0873333	−	0.996179i	$-0.527835\pi$
$67$	−1.42971	−0.174667	−0.0873333	+	0.996179i	$0.527835\pi$
$68$	3.34533	0.405681
$69$	−18.0205	−2.16942
$70$	−1.85516	−0.221734
$71$	0.618350	0.0733847	0.0366923	−	0.999327i	$-0.488318\pi$
$71$	0.618350	0.0733847	0.0366923	+	0.999327i	$0.488318\pi$
$72$	−2.56071	−0.301783
$73$	2.13881	0.250329	0.125164	−	0.992136i	$-0.460054\pi$
$73$	2.13881	0.250329	0.125164	+	0.992136i	$0.460054\pi$
$74$	13.1875	1.53302
$75$	3.19410	0.368823
$76$	−5.65597	−0.648784
$77$	−1.06516	−0.121386
$78$	−8.13001	−0.920542
$79$	2.88966	0.325112	0.162556	−	0.986699i	$-0.448026\pi$
$79$	2.88966	0.325112	0.162556	+	0.986699i	$0.448026\pi$
$80$	0.918432	0.102684
$81$	−10.7920	−1.19912
$82$	8.99536	0.993372
$83$	−13.6770	−1.50125	−0.750623	−	0.660731i	$-0.770247\pi$
$83$	−13.6770	−1.50125	−0.750623	+	0.660731i	$0.770247\pi$
$84$	−2.86065	−0.312123
$85$	1.83479	0.199011
$86$	−2.31200	−0.249309
$87$	5.95849	0.638817
$88$	7.57566	0.807568
$89$	−6.29577	−0.667350	−0.333675	−	0.942688i	$-0.608289\pi$
$89$	−6.29577	−0.667350	−0.333675	+	0.942688i	$0.608289\pi$
$90$	−3.49236	−0.368127
$91$	−0.786492	−0.0824468
$92$	30.8311	3.21436
$93$	0.219215	0.0227315
$94$	−20.3572	−2.09968
$95$	−3.10209	−0.318268
$96$	−9.90073	−1.01049
$97$	−16.3955	−1.66471	−0.832357	−	0.554240i	$-0.813009\pi$
$97$	−16.3955	−1.66471	−0.832357	+	0.554240i	$0.813009\pi$
$98$	15.7418	1.59016
$99$	−2.00517	−0.201527
$100$	−5.46475	−0.546475
$101$	−3.23929	−0.322322	−0.161161	−	0.986928i	$-0.551524\pi$
$101$	−3.23929	−0.322322	−0.161161	+	0.986928i	$0.551524\pi$
$102$	4.52069	0.447615
$103$	−4.41243	−0.434770	−0.217385	−	0.976086i	$-0.569753\pi$
$103$	−4.41243	−0.434770	−0.217385	+	0.976086i	$0.569753\pi$
$104$	5.59373	0.548510
$105$	−1.56896	−0.153115
$106$	22.0743	2.14404
$107$	−7.49271	−0.724347	−0.362174	−	0.932111i	$-0.617965\pi$
$107$	−7.49271	−0.724347	−0.362174	+	0.932111i	$0.617965\pi$
$108$	14.2384	1.37009
$109$	−3.14886	−0.301606	−0.150803	−	0.988564i	$-0.548186\pi$
$109$	−3.14886	−0.301606	−0.150803	+	0.988564i	$0.548186\pi$
$110$	10.3319	0.985104
$111$	11.1530	1.05860
$112$	0.218912	0.0206852
$113$	11.5106	1.08282	0.541411	−	0.840758i	$-0.317890\pi$
$113$	11.5106	1.08282	0.541411	+	0.840758i	$0.317890\pi$
$114$	−7.64316	−0.715848
$115$	16.9097	1.57684
$116$	−10.1943	−0.946516
$117$	−1.48058	−0.136879
$118$	−0.377956	−0.0347937
$119$	0.437329	0.0400899
$120$	11.1589	1.01866
$121$	−5.06788	−0.460716
$122$	16.3095	1.47660
$123$	7.60763	0.685957
$124$	−0.375051	−0.0336806
$125$	−12.1712	−1.08862
$126$	−0.832417	−0.0741576
$127$	−3.84650	−0.341321	−0.170661	−	0.985330i	$-0.554590\pi$
$127$	−3.84650	−0.341321	−0.170661	+	0.985330i	$0.554590\pi$
$128$	19.2536	1.70180
$129$	−1.95532	−0.172156
$130$	7.62885	0.669095
$131$	0.843969	0.0737379	0.0368690	−	0.999320i	$-0.488262\pi$
$131$	0.843969	0.0737379	0.0368690	+	0.999320i	$0.488262\pi$
$132$	15.9317	1.38668
$133$	−0.739395	−0.0641137
$134$	3.30548	0.285550
$135$	7.80922	0.672110
$136$	−3.11039	−0.266714
$137$	12.7529	1.08955	0.544775	−	0.838582i	$-0.316615\pi$
$137$	12.7529	1.08955	0.544775	+	0.838582i	$0.316615\pi$
$138$	41.6634	3.54662
$139$	−14.1480	−1.20002	−0.600009	−	0.799993i	$-0.704836\pi$
$139$	−14.1480	−1.20002	−0.600009	+	0.799993i	$0.704836\pi$
$140$	2.68432	0.226866
$141$	−17.2166	−1.44990
$142$	−1.42962	−0.119971
$143$	4.38017	0.366288
$144$	0.412103	0.0343419
$145$	−5.59119	−0.464323
$146$	−4.94492	−0.409245
$147$	13.3133	1.09806
$148$	−19.0816	−1.56849
$149$	19.1855	1.57174	0.785869	−	0.618392i	$-0.212216\pi$
$149$	19.1855	1.57174	0.785869	+	0.618392i	$0.212216\pi$
$150$	−7.38476	−0.602963
$151$	−17.1448	−1.39522	−0.697611	−	0.716477i	$-0.745754\pi$
$151$	−17.1448	−1.39522	−0.697611	+	0.716477i	$0.745754\pi$
$152$	5.25876	0.426542
$153$	0.823276	0.0665579
$154$	2.46264	0.198445
$155$	−0.205702	−0.0165224
$156$	11.7637	0.941846
$157$	7.85333	0.626764	0.313382	−	0.949627i	$-0.398538\pi$
$157$	7.85333	0.626764	0.313382	+	0.949627i	$0.398538\pi$
$158$	−6.68089	−0.531503
$159$	18.6688	1.48053
$160$	9.29043	0.734473
$161$	4.03049	0.317647
$162$	24.9512	1.96035
$163$	2.48869	0.194930	0.0974648	−	0.995239i	$-0.468927\pi$
$163$	2.48869	0.194930	0.0974648	+	0.995239i	$0.468927\pi$
$164$	−13.0158	−1.01636
$165$	8.73794	0.680248
$166$	31.6212	2.45428
$167$	−16.8622	−1.30484	−0.652418	−	0.757860i	$-0.726245\pi$
$167$	−16.8622	−1.30484	−0.652418	+	0.757860i	$0.726245\pi$
$168$	2.65976	0.205205
$169$	−9.76576	−0.751213
$170$	−4.24203	−0.325349
$171$	−1.39192	−0.106443
$172$	3.34533	0.255079
$173$	−12.2909	−0.934463	−0.467232	−	0.884135i	$-0.654749\pi$
$173$	−12.2909	−0.934463	−0.467232	+	0.884135i	$0.654749\pi$
$174$	−13.7760	−1.04436
$175$	−0.714397	−0.0540034
$176$	−1.21917	−0.0918987
$177$	−0.319648	−0.0240262
$178$	14.5558	1.09100
$179$	−12.7514	−0.953083	−0.476541	−	0.879152i	$-0.658110\pi$
$179$	−12.7514	−0.953083	−0.476541	+	0.879152i	$0.658110\pi$
$180$	5.05325	0.376647
$181$	7.17412	0.533248	0.266624	−	0.963801i	$-0.414092\pi$
$181$	7.17412	0.533248	0.266624	+	0.963801i	$0.414092\pi$
$182$	1.81837	0.134786
$183$	13.7934	1.01964
$184$	−28.6659	−2.11328
$185$	−10.4655	−0.769442
$186$	−0.506824	−0.0371621
$187$	−2.43560	−0.178108
$188$	29.4557	2.14828
$189$	1.86136	0.135394
$190$	7.17202	0.520313
$191$	13.7593	0.995588	0.497794	−	0.867295i	$-0.334143\pi$
$191$	13.7593	0.995588	0.497794	+	0.867295i	$0.334143\pi$
$192$	24.8480	1.79325
$193$	−16.9837	−1.22251	−0.611255	−	0.791434i	$-0.709335\pi$
$193$	−16.9837	−1.22251	−0.611255	+	0.791434i	$0.709335\pi$
$194$	37.9064	2.72152
$195$	6.45194	0.462033
$196$	−22.7775	−1.62696
$197$	4.29619	0.306091	0.153046	−	0.988219i	$-0.451092\pi$
$197$	4.29619	0.306091	0.153046	+	0.988219i	$0.451092\pi$
$198$	4.63594	0.329462
$199$	−2.14436	−0.152009	−0.0760047	−	0.997107i	$-0.524216\pi$
$199$	−2.14436	−0.152009	−0.0760047	+	0.997107i	$0.524216\pi$
$200$	5.08097	0.359279
$201$	2.79554	0.197182
$202$	7.48923	0.526941
$203$	−1.33268	−0.0935360
$204$	−6.54119	−0.457975
$205$	−7.13868	−0.498587
$206$	10.2015	0.710774
$207$	7.58744	0.527363
$208$	−0.900215	−0.0624187
$209$	4.11787	0.284839
$210$	3.62744	0.250317
$211$	−9.81433	−0.675646	−0.337823	−	0.941210i	$-0.609691\pi$
$211$	−9.81433	−0.675646	−0.337823	+	0.941210i	$0.609691\pi$
$212$	−31.9402	−2.19366
$213$	−1.20907	−0.0828443
$214$	17.3231	1.18418
$215$	1.83479	0.125132
$216$	−13.2384	−0.900762
$217$	−0.0490298	−0.00332836
$218$	7.28015	0.493074
$219$	−4.18206	−0.282597
$220$	−14.9496	−1.00790
$221$	−1.79840	−0.120973
$222$	−25.7858	−1.73063
$223$	6.79311	0.454900	0.227450	−	0.973790i	$-0.426961\pi$
$223$	6.79311	0.454900	0.227450	+	0.973790i	$0.426961\pi$
$224$	2.21441	0.147956
$225$	−1.34486	−0.0896573
$226$	−26.6124	−1.77023
$227$	4.28478	0.284391	0.142196	−	0.989839i	$-0.454584\pi$
$227$	4.28478	0.284391	0.142196	+	0.989839i	$0.454584\pi$
$228$	11.0592	0.732415
$229$	17.8638	1.18048	0.590238	−	0.807229i	$-0.299034\pi$
$229$	17.8638	1.18048	0.590238	+	0.807229i	$0.299034\pi$
$230$	−39.0952	−2.57786
$231$	2.08272	0.137033
$232$	9.47837	0.622285
$233$	−27.1507	−1.77870	−0.889350	−	0.457227i	$-0.848843\pi$
$233$	−27.1507	−1.77870	−0.889350	+	0.457227i	$0.848843\pi$
$234$	3.42309	0.223774
$235$	16.1554	1.05386
$236$	0.546881	0.0355989
$237$	−5.65021	−0.367021
$238$	−1.01110	−0.0655401
$239$	−9.94962	−0.643588	−0.321794	−	0.946810i	$-0.604286\pi$
$239$	−9.94962	−0.643588	−0.321794	+	0.946810i	$0.604286\pi$
$240$	−1.79583	−0.115920
$241$	17.5554	1.13085	0.565423	−	0.824801i	$-0.308713\pi$
$241$	17.5554	1.13085	0.565423	+	0.824801i	$0.308713\pi$
$242$	11.7169	0.753192
$243$	8.33332	0.534583
$244$	−23.5990	−1.51077
$245$	−12.4926	−0.798124
$246$	−17.5888	−1.12142
$247$	3.04056	0.193466
$248$	0.348712	0.0221433
$249$	26.7429	1.69476
$250$	28.1397	1.77971
$251$	−14.3387	−0.905053	−0.452527	−	0.891751i	$-0.649477\pi$
$251$	−14.3387	−0.905053	−0.452527	+	0.891751i	$0.649477\pi$
$252$	1.20446	0.0758739
$253$	−22.4468	−1.41122
$254$	8.89309	0.558002
$255$	−3.58760	−0.224664
$256$	−19.0985	−1.19366
$257$	19.2105	1.19832	0.599158	−	0.800631i	$-0.295502\pi$
$257$	19.2105	1.19832	0.599158	+	0.800631i	$0.295502\pi$
$258$	4.52069	0.281446
$259$	−2.49450	−0.155001
$260$	−11.0385	−0.684580
$261$	−2.50879	−0.155290
$262$	−1.95125	−0.120549
$263$	7.20907	0.444530	0.222265	−	0.974986i	$-0.428655\pi$
$263$	7.20907	0.444530	0.222265	+	0.974986i	$0.428655\pi$
$264$	−14.8128	−0.911667
$265$	−17.5180	−1.07612
$266$	1.70948	0.104815
$267$	12.3102	0.753375
$268$	−4.78284	−0.292159
$269$	−0.761074	−0.0464035	−0.0232017	−	0.999731i	$-0.507386\pi$
$269$	−0.761074	−0.0464035	−0.0232017	+	0.999731i	$0.507386\pi$
$270$	−18.0549	−1.09879
$271$	−5.03731	−0.305995	−0.152997	−	0.988227i	$-0.548893\pi$
$271$	−5.03731	−0.305995	−0.152997	+	0.988227i	$0.548893\pi$
$272$	0.500565	0.0303512
$273$	1.53784	0.0930745
$274$	−29.4846	−1.78123
$275$	3.97866	0.239922
$276$	−60.2846	−3.62871
$277$	16.8951	1.01513	0.507565	−	0.861613i	$-0.330546\pi$
$277$	16.8951	1.01513	0.507565	+	0.861613i	$0.330546\pi$
$278$	32.7101	1.96182
$279$	−0.0922991	−0.00552580
$280$	−2.49580	−0.149153
$281$	13.9710	0.833441	0.416720	−	0.909035i	$-0.363179\pi$
$281$	13.9710	0.833441	0.416720	+	0.909035i	$0.363179\pi$
$282$	39.8048	2.37034
$283$	−10.7373	−0.638267	−0.319134	−	0.947710i	$-0.603392\pi$
$283$	−10.7373	−0.638267	−0.319134	+	0.947710i	$0.603392\pi$
$284$	2.06859	0.122748
$285$	6.06558	0.359294
$286$	−10.1269	−0.598818
$287$	−1.70153	−0.100438
$288$	4.16864	0.245640
$289$	1.00000	0.0588235
$290$	12.9268	0.759089
$291$	32.0585	1.87930
$292$	7.15502	0.418716
$293$	14.2422	0.832037	0.416019	−	0.909356i	$-0.363425\pi$
$293$	14.2422	0.832037	0.416019	+	0.909356i	$0.363425\pi$
$294$	−30.7802	−1.79514
$295$	0.299944	0.0174634
$296$	17.7415	1.03120
$297$	−10.3664	−0.601517
$298$	−44.3569	−2.56952
$299$	−16.5743	−0.958517
$300$	10.6853	0.616918
$301$	0.437329	0.0252072
$302$	39.6387	2.28095
$303$	6.33385	0.363870
$304$	−0.846308	−0.0485391
$305$	−12.9432	−0.741125
$306$	−1.90341	−0.108811
$307$	4.05981	0.231706	0.115853	−	0.993266i	$-0.463040\pi$
$307$	4.05981	0.231706	0.115853	+	0.993266i	$0.463040\pi$
$308$	−3.56330	−0.203038
$309$	8.62772	0.490814
$310$	0.475582	0.0270112
$311$	9.71312	0.550780	0.275390	−	0.961333i	$-0.411193\pi$
$311$	9.71312	0.550780	0.275390	+	0.961333i	$0.411193\pi$
$312$	−10.9375	−0.619216
$313$	−4.81716	−0.272282	−0.136141	−	0.990689i	$-0.543470\pi$
$313$	−4.81716	−0.272282	−0.136141	+	0.990689i	$0.543470\pi$
$314$	−18.1569	−1.02465
$315$	0.660603	0.0372207
$316$	9.66686	0.543804
$317$	−18.5919	−1.04423	−0.522113	−	0.852876i	$-0.674856\pi$
$317$	−18.5919	−1.04423	−0.522113	+	0.852876i	$0.674856\pi$
$318$	−43.1622	−2.42042
$319$	7.42204	0.415554
$320$	−23.3163	−1.30342
$321$	14.6506	0.817719
$322$	−9.31848	−0.519299
$323$	−1.69071	−0.0940734
$324$	−36.1029	−2.00572
$325$	2.93777	0.162958
$326$	−5.75385	−0.318676
$327$	6.15702	0.340484
$328$	12.1017	0.668206
$329$	3.85069	0.212296
$330$	−20.2021	−1.11209
$331$	−6.02079	−0.330933	−0.165466	−	0.986215i	$-0.552913\pi$
$331$	−6.02079	−0.330933	−0.165466	+	0.986215i	$0.552913\pi$
$332$	−45.7541	−2.51108
$333$	−4.69592	−0.257335
$334$	38.9853	2.13318
$335$	−2.62321	−0.143322
$336$	−0.428042	−0.0233516
$337$	6.91931	0.376919	0.188459	−	0.982081i	$-0.439651\pi$
$337$	6.91931	0.376919	0.188459	+	0.982081i	$0.439651\pi$
$338$	22.5784	1.22810
$339$	−22.5068	−1.22240
$340$	6.13797	0.332878
$341$	0.273059	0.0147870
$342$	3.21811	0.174015
$343$	−6.03897	−0.326074
$344$	−3.11039	−0.167701
$345$	−33.0639	−1.78010
$346$	28.4166	1.52769
$347$	−17.4606	−0.937337	−0.468668	−	0.883374i	$-0.655266\pi$
$347$	−17.4606	−0.937337	−0.468668	+	0.883374i	$0.655266\pi$
$348$	19.9331	1.06853
$349$	−24.6273	−1.31827	−0.659135	−	0.752025i	$-0.729077\pi$
$349$	−24.6273	−1.31827	−0.659135	+	0.752025i	$0.729077\pi$
$350$	1.65168	0.0882862
$351$	−7.65433	−0.408558
$352$	−12.3326	−0.657330
$353$	−12.4791	−0.664194	−0.332097	−	0.943245i	$-0.607756\pi$
$353$	−12.4791	−0.664194	−0.332097	+	0.943245i	$0.607756\pi$
$354$	0.739025	0.0392787
$355$	1.13454	0.0602153
$356$	−21.0614	−1.11625
$357$	−0.855118	−0.0452577
$358$	29.4812	1.55813
$359$	25.1138	1.32546	0.662729	−	0.748860i	$-0.269398\pi$
$359$	25.1138	1.32546	0.662729	+	0.748860i	$0.269398\pi$
$360$	−4.69837	−0.247626
$361$	−16.1415	−0.849553
$362$	−16.5866	−0.871770
$363$	9.90932	0.520104
$364$	−2.63107	−0.137906
$365$	3.92427	0.205406
$366$	−31.8904	−1.66694
$367$	11.5734	0.604127	0.302063	−	0.953288i	$-0.402325\pi$
$367$	11.5734	0.604127	0.302063	+	0.953288i	$0.402325\pi$
$368$	4.61328	0.240484
$369$	−3.20315	−0.166749
$370$	24.1963	1.25791
$371$	−4.17549	−0.216781
$372$	0.733345	0.0380222
$373$	7.90179	0.409139	0.204570	−	0.978852i	$-0.434421\pi$
$373$	7.90179	0.409139	0.204570	+	0.978852i	$0.434421\pi$
$374$	5.63109	0.291177
$375$	23.7985	1.22895
$376$	−27.3871	−1.41238
$377$	5.48030	0.282250
$378$	−4.30345	−0.221346
$379$	18.1592	0.932775	0.466388	−	0.884580i	$-0.345555\pi$
$379$	18.1592	0.932775	0.466388	+	0.884580i	$0.345555\pi$
$380$	−10.3775	−0.532355
$381$	7.52113	0.385319
$382$	−31.8115	−1.62762
$383$	22.9306	1.17170	0.585850	−	0.810419i	$-0.300761\pi$
$383$	22.9306	1.17170	0.585850	+	0.810419i	$0.300761\pi$
$384$	−37.6470	−1.92117
$385$	−1.95434	−0.0996023
$386$	39.2661	1.99859
$387$	0.823276	0.0418495
$388$	−54.8484	−2.78451
$389$	12.7923	0.648593	0.324297	−	0.945955i	$-0.394872\pi$
$389$	12.7923	0.648593	0.324297	+	0.945955i	$0.394872\pi$
$390$	−14.9169	−0.755344
$391$	9.21615	0.466081
$392$	21.1779	1.06964
$393$	−1.65023	−0.0832431
$394$	−9.93278	−0.500406
$395$	5.30192	0.266769
$396$	−6.70794	−0.337087
$397$	31.4720	1.57953	0.789766	−	0.613408i	$-0.210202\pi$
$397$	31.4720	1.57953	0.789766	+	0.613408i	$0.210202\pi$
$398$	4.95775	0.248509
$399$	1.44575	0.0723782
$400$	−0.817696	−0.0408848
$401$	−32.7399	−1.63495	−0.817475	−	0.575964i	$-0.804627\pi$
$401$	−32.7399	−1.63495	−0.817475	+	0.575964i	$0.804627\pi$
$402$	−6.46327	−0.322359
$403$	0.201622	0.0100435
$404$	−10.8365	−0.539136
$405$	−19.8011	−0.983926
$406$	3.08116	0.152915
$407$	13.8925	0.688625
$408$	6.08182	0.301095
$409$	24.3863	1.20582	0.602911	−	0.797808i	$-0.294007\pi$
$409$	24.3863	1.20582	0.602911	+	0.797808i	$0.294007\pi$
$410$	16.5046	0.815104
$411$	−24.9359	−1.23000
$412$	−14.7610	−0.727224
$413$	0.0714928	0.00351793
$414$	−17.5421	−0.862149
$415$	−25.0944	−1.23184
$416$	−9.10616	−0.446466
$417$	27.6639	1.35471
$418$	−9.52051	−0.465663
$419$	7.02392	0.343141	0.171571	−	0.985172i	$-0.445116\pi$
$419$	7.02392	0.343141	0.171571	+	0.985172i	$0.445116\pi$
$420$	−5.24870	−0.256110
$421$	−29.5711	−1.44121	−0.720603	−	0.693348i	$-0.756135\pi$
$421$	−29.5711	−1.44121	−0.720603	+	0.693348i	$0.756135\pi$
$422$	22.6907	1.10457
$423$	7.24897	0.352457
$424$	29.6971	1.44222
$425$	−1.63355	−0.0792386
$426$	2.79537	0.135436
$427$	−3.08506	−0.149296
$428$	−25.0656	−1.21159
$429$	−8.56463	−0.413504
$430$	−4.24203	−0.204569
$431$	8.73218	0.420614	0.210307	−	0.977635i	$-0.432554\pi$
$431$	8.73218	0.420614	0.210307	+	0.977635i	$0.432554\pi$
$432$	2.13050	0.102504
$433$	11.0124	0.529222	0.264611	−	0.964355i	$-0.414756\pi$
$433$	11.0124	0.529222	0.264611	+	0.964355i	$0.414756\pi$
$434$	0.113357	0.00544130
$435$	10.9326	0.524177
$436$	−10.5340	−0.504485
$437$	−15.5818	−0.745379
$438$	9.66891	0.461998
$439$	36.4259	1.73851	0.869256	−	0.494363i	$-0.164599\pi$
$439$	36.4259	1.73851	0.869256	+	0.494363i	$0.164599\pi$
$440$	13.8997	0.662644
$441$	−5.60547	−0.266927
$442$	4.15789	0.197771
$443$	18.7022	0.888570	0.444285	−	0.895885i	$-0.353458\pi$
$443$	18.7022	0.888570	0.444285	+	0.895885i	$0.353458\pi$
$444$	37.3106	1.77068
$445$	−11.5514	−0.547590
$446$	−15.7057	−0.743684
$447$	−37.5138	−1.77434
$448$	−5.55753	−0.262569
$449$	−29.3520	−1.38520	−0.692602	−	0.721320i	$-0.743536\pi$
$449$	−29.3520	−1.38520	−0.692602	+	0.721320i	$0.743536\pi$
$450$	3.10931	0.146574
$451$	9.47625	0.446219
$452$	38.5066	1.81120
$453$	33.5235	1.57507
$454$	−9.90640	−0.464931
$455$	−1.44305	−0.0676511
$456$	−10.2826	−0.481525
$457$	36.3996	1.70270	0.851351	−	0.524596i	$-0.175784\pi$
$457$	36.3996	1.70270	0.851351	+	0.524596i	$0.175784\pi$
$458$	−41.3011	−1.92987
$459$	4.25619	0.198662
$460$	56.5685	2.63752
$461$	16.0704	0.748473	0.374236	−	0.927333i	$-0.377905\pi$
$461$	16.0704	0.748473	0.374236	+	0.927333i	$0.377905\pi$
$462$	−4.81525	−0.224026
$463$	−35.5400	−1.65168	−0.825842	−	0.563902i	$-0.809299\pi$
$463$	−35.5400	−1.65168	−0.825842	+	0.563902i	$0.809299\pi$
$464$	−1.52538	−0.0708141
$465$	0.402213	0.0186522
$466$	62.7723	2.90787
$467$	−11.3404	−0.524773	−0.262387	−	0.964963i	$-0.584510\pi$
$467$	−11.3404	−0.524773	−0.262387	+	0.964963i	$0.584510\pi$
$468$	−4.95302	−0.228953
$469$	−0.625253	−0.0288715
$470$	−37.3512	−1.72288
$471$	−15.3558	−0.707557
$472$	−0.508475	−0.0234045
$473$	−2.43560	−0.111989
$474$	13.0633	0.600016
$475$	2.76185	0.126722
$476$	1.46301	0.0670569
$477$	−7.86039	−0.359903
$478$	23.0035	1.05216
$479$	21.7694	0.994671	0.497336	−	0.867558i	$-0.334312\pi$
$479$	21.7694	0.994671	0.497336	+	0.867558i	$0.334312\pi$
$480$	−18.1658	−0.829150
$481$	10.2580	0.467723
$482$	−40.5881	−1.84874
$483$	−7.88090	−0.358593
$484$	−16.9537	−0.770623
$485$	−30.0824	−1.36597
$486$	−19.2666	−0.873951
$487$	40.6474	1.84191	0.920955	−	0.389669i	$-0.127411\pi$
$487$	40.6474	1.84191	0.920955	+	0.389669i	$0.127411\pi$
$488$	21.9417	0.993254
$489$	−4.86619	−0.220057
$490$	28.8829	1.30480
$491$	21.3910	0.965361	0.482680	−	0.875797i	$-0.339663\pi$
$491$	21.3910	0.965361	0.482680	+	0.875797i	$0.339663\pi$
$492$	25.4500	1.14738
$493$	−3.04732	−0.137244
$494$	−7.02977	−0.316284
$495$	−3.67906	−0.165361
$496$	−0.0561193	−0.00251983
$497$	0.270423	0.0121301
$498$	−61.8295	−2.77065
$499$	14.5636	0.651957	0.325978	−	0.945377i	$-0.394306\pi$
$499$	14.5636	0.651957	0.325978	+	0.945377i	$0.394306\pi$
$500$	−40.7165	−1.82090
$501$	32.9710	1.47303
$502$	33.1511	1.47961
$503$	−23.5001	−1.04782	−0.523910	−	0.851774i	$-0.675527\pi$
$503$	−23.5001	−1.04782	−0.523910	+	0.851774i	$0.675527\pi$
$504$	−1.11987	−0.0498832
$505$	−5.94342	−0.264479
$506$	51.8970	2.30710
$507$	19.0952	0.848047
$508$	−12.8678	−0.570916
$509$	5.72376	0.253701	0.126851	−	0.991922i	$-0.459513\pi$
$509$	5.72376	0.253701	0.126851	+	0.991922i	$0.459513\pi$
$510$	8.29452	0.367288
$511$	0.935364	0.0413781
$512$	5.64851	0.249631
$513$	−7.19597	−0.317710
$514$	−44.4146	−1.95904
$515$	−8.09589	−0.356747
$516$	−6.54119	−0.287960
$517$	−21.4455	−0.943171
$518$	5.76728	0.253400
$519$	24.0327	1.05492
$520$	10.2633	0.450076
$521$	−35.8683	−1.57142	−0.785709	−	0.618596i	$-0.787702\pi$
$521$	−35.8683	−1.57142	−0.785709	+	0.618596i	$0.787702\pi$
$522$	5.80030	0.253872
$523$	−10.2933	−0.450094	−0.225047	−	0.974348i	$-0.572254\pi$
$523$	−10.2933	−0.450094	−0.225047	+	0.974348i	$0.572254\pi$
$524$	2.82335	0.123339
$525$	1.39688	0.0609646
$526$	−16.6673	−0.726730
$527$	−0.112112	−0.00488367
$528$	2.38388	0.103745
$529$	61.9375	2.69293
$530$	40.5016	1.75928
$531$	0.134586	0.00584053
$532$	−2.47352	−0.107241
$533$	6.99709	0.303078
$534$	−28.4612	−1.23164
$535$	−13.7475	−0.594358
$536$	4.44696	0.192079
$537$	24.9330	1.07594
$538$	1.75960	0.0758618
$539$	16.5833	0.714295
$540$	26.1244	1.12422
$541$	−40.5577	−1.74371	−0.871857	−	0.489761i	$-0.837084\pi$
$541$	−40.5577	−1.74371	−0.871857	+	0.489761i	$0.837084\pi$
$542$	11.6462	0.500249
$543$	−14.0277	−0.601987
$544$	5.06348	0.217095
$545$	−5.77749	−0.247481
$546$	−3.55549	−0.152161
$547$	−17.1998	−0.735409	−0.367705	−	0.929943i	$-0.619856\pi$
$547$	−17.1998	−0.735409	−0.367705	+	0.929943i	$0.619856\pi$
$548$	42.6625	1.82245
$549$	−5.80765	−0.247864
$550$	−9.19864	−0.392231
$551$	5.15212	0.219488
$552$	56.0509	2.38569
$553$	1.26373	0.0537394
$554$	−39.0615	−1.65956
$555$	20.4635	0.868626
$556$	−47.3297	−2.00723
$557$	−28.7839	−1.21961	−0.609807	−	0.792550i	$-0.708753\pi$
$557$	−28.7839	−1.21961	−0.609807	+	0.792550i	$0.708753\pi$
$558$	0.213395	0.00903374
$559$	−1.79840	−0.0760641
$560$	0.401657	0.0169731
$561$	4.76237	0.201067
$562$	−32.3009	−1.36253
$563$	−14.3813	−0.606098	−0.303049	−	0.952975i	$-0.598005\pi$
$563$	−14.3813	−0.606098	−0.303049	+	0.952975i	$0.598005\pi$
$564$	−57.5953	−2.42520
$565$	21.1194	0.888502
$566$	24.8246	1.04346
$567$	−4.71968	−0.198208
$568$	−1.92331	−0.0807005
$569$	−0.487321	−0.0204295	−0.0102148	−	0.999948i	$-0.503252\pi$
$569$	−0.487321	−0.0204295	−0.0102148	+	0.999948i	$0.503252\pi$
$570$	−14.0236	−0.587384
$571$	13.3318	0.557918	0.278959	−	0.960303i	$-0.410011\pi$
$571$	13.3318	0.557918	0.278959	+	0.960303i	$0.410011\pi$
$572$	14.6531	0.612677
$573$	−26.9038	−1.12392
$574$	3.93393	0.164199
$575$	−15.0550	−0.627837
$576$	−10.4621	−0.435921
$577$	39.1839	1.63125	0.815623	−	0.578584i	$-0.196394\pi$
$577$	39.1839	1.63125	0.815623	+	0.578584i	$0.196394\pi$
$578$	−2.31200	−0.0961664
$579$	33.2085	1.38010
$580$	−18.7044	−0.776657
$581$	−5.98135	−0.248148
$582$	−74.1192	−3.07234
$583$	23.2543	0.963096
$584$	−6.65255	−0.275284
$585$	−2.71655	−0.112315
$586$	−32.9279	−1.36024
$587$	−18.6708	−0.770626	−0.385313	−	0.922786i	$-0.625906\pi$
$587$	−18.6708	−0.770626	−0.385313	+	0.922786i	$0.625906\pi$
$588$	44.5373	1.83669
$589$	0.189548	0.00781020
$590$	−0.693470	−0.0285497
$591$	−8.40043	−0.345548
$592$	−2.85520	−0.117348
$593$	−18.8558	−0.774314	−0.387157	−	0.922014i	$-0.626543\pi$
$593$	−18.8558	−0.774314	−0.387157	+	0.922014i	$0.626543\pi$
$594$	23.9670	0.983377
$595$	0.802407	0.0328955
$596$	64.1819	2.62899
$597$	4.19290	0.171604
$598$	38.3197	1.56701
$599$	41.4409	1.69323	0.846615	−	0.532205i	$-0.178637\pi$
$599$	41.4409	1.69323	0.846615	+	0.532205i	$0.178637\pi$
$600$	−9.93493	−0.405592
$601$	−34.8317	−1.42081	−0.710407	−	0.703791i	$-0.751489\pi$
$601$	−34.8317	−1.42081	−0.710407	+	0.703791i	$0.751489\pi$
$602$	−1.01110	−0.0412095
$603$	−1.17704	−0.0479330
$604$	−57.3549	−2.33374
$605$	−9.29849	−0.378037
$606$	−14.6438	−0.594866
$607$	19.1968	0.779173	0.389586	−	0.920990i	$-0.372618\pi$
$607$	19.1968	0.779173	0.389586	+	0.920990i	$0.372618\pi$
$608$	−8.56086	−0.347189
$609$	2.60582	0.105593
$610$	29.9246	1.21161
$611$	−15.8349	−0.640613
$612$	2.75413	0.111329
$613$	30.7075	1.24026	0.620132	−	0.784498i	$-0.287079\pi$
$613$	30.7075	1.24026	0.620132	+	0.784498i	$0.287079\pi$
$614$	−9.38628	−0.378799
$615$	13.9584	0.562857
$616$	3.31306	0.133487
$617$	20.4017	0.821343	0.410672	−	0.911783i	$-0.365294\pi$
$617$	20.4017	0.821343	0.410672	+	0.911783i	$0.365294\pi$
$618$	−19.9473	−0.802396
$619$	−14.4498	−0.580785	−0.290393	−	0.956908i	$-0.593786\pi$
$619$	−14.4498	−0.580785	−0.290393	+	0.956908i	$0.593786\pi$
$620$	−0.688140	−0.0276364
$621$	39.2257	1.57407
$622$	−22.4567	−0.900432
$623$	−2.75332	−0.110310
$624$	1.76021	0.0704648
$625$	−14.1638	−0.566552
$626$	11.1373	0.445134
$627$	−8.05176	−0.321556
$628$	26.2720	1.04837
$629$	−5.70394	−0.227431
$630$	−1.52731	−0.0608495
$631$	−24.8728	−0.990169	−0.495084	−	0.868845i	$-0.664863\pi$
$631$	−24.8728	−0.990169	−0.495084	+	0.868845i	$0.664863\pi$
$632$	−8.98798	−0.357523
$633$	19.1902	0.762740
$634$	42.9845	1.70713
$635$	−7.05751	−0.280069
$636$	62.4533	2.47643
$637$	12.2448	0.485158
$638$	−17.1597	−0.679360
$639$	0.509073	0.0201386
$640$	35.3264	1.39640
$641$	−2.22438	−0.0878578	−0.0439289	−	0.999035i	$-0.513988\pi$
$641$	−2.22438	−0.0878578	−0.0439289	+	0.999035i	$0.513988\pi$
$642$	−33.8722	−1.33683
$643$	−1.77734	−0.0700913	−0.0350457	−	0.999386i	$-0.511158\pi$
$643$	−1.77734	−0.0700913	−0.0350457	+	0.999386i	$0.511158\pi$
$644$	13.4833	0.531317
$645$	−3.58760	−0.141262
$646$	3.90891	0.153794
$647$	30.3732	1.19409	0.597047	−	0.802206i	$-0.296341\pi$
$647$	30.3732	1.19409	0.597047	+	0.802206i	$0.296341\pi$
$648$	33.5675	1.31866
$649$	−0.398161	−0.0156292
$650$	−6.79210	−0.266408
$651$	0.0958690	0.00375740
$652$	8.32550	0.326052
$653$	11.2373	0.439751	0.219875	−	0.975528i	$-0.429435\pi$
$653$	11.2373	0.439751	0.219875	+	0.975528i	$0.429435\pi$
$654$	−14.2350	−0.556633
$655$	1.54851	0.0605051
$656$	−1.94757	−0.0760397
$657$	1.76083	0.0686966
$658$	−8.90279	−0.347067
$659$	−1.87406	−0.0730029	−0.0365014	−	0.999334i	$-0.511621\pi$
$659$	−1.87406	−0.0730029	−0.0365014	+	0.999334i	$0.511621\pi$
$660$	29.2313	1.13783
$661$	−13.0923	−0.509232	−0.254616	−	0.967042i	$-0.581949\pi$
$661$	−13.0923	−0.509232	−0.254616	+	0.967042i	$0.581949\pi$
$662$	13.9200	0.541018
$663$	3.51644	0.136567
$664$	42.5409	1.65091
$665$	−1.35663	−0.0526080
$666$	10.8569	0.420698
$667$	−28.0846	−1.08744
$668$	−56.4095	−2.18255
$669$	−13.2827	−0.513539
$670$	6.06486	0.234306
$671$	17.1815	0.663283
$672$	−4.32988	−0.167029
$673$	21.9737	0.847022	0.423511	−	0.905891i	$-0.360797\pi$
$673$	21.9737	0.847022	0.423511	+	0.905891i	$0.360797\pi$
$674$	−15.9974	−0.616198
$675$	−6.95268	−0.267609
$676$	−32.6697	−1.25653
$677$	14.0111	0.538492	0.269246	−	0.963071i	$-0.413226\pi$
$677$	14.0111	0.538492	0.269246	+	0.963071i	$0.413226\pi$
$678$	52.0357	1.99842
$679$	−7.17025	−0.275169
$680$	−5.70692	−0.218850
$681$	−8.37812	−0.321050
$682$	−0.631312	−0.0241742
$683$	−30.9027	−1.18246	−0.591229	−	0.806504i	$-0.701357\pi$
$683$	−30.9027	−1.18246	−0.591229	+	0.806504i	$0.701357\pi$
$684$	−4.65642	−0.178043
$685$	23.3988	0.894023
$686$	13.9621	0.533074
$687$	−34.9295	−1.33264
$688$	0.500565	0.0190839
$689$	17.1706	0.654147
$690$	76.4436	2.91016
$691$	10.4564	0.397782	0.198891	−	0.980022i	$-0.436266\pi$
$691$	10.4564	0.397782	0.198891	+	0.980022i	$0.436266\pi$
$692$	−41.1172	−1.56304
$693$	−0.876918	−0.0333114
$694$	40.3690	1.53238
$695$	−25.9586	−0.984666
$696$	−18.5332	−0.702501
$697$	−3.89073	−0.147372
$698$	56.9382	2.15514
$699$	53.0883	2.00798
$700$	−2.38989	−0.0903295
$701$	30.2736	1.14342	0.571709	−	0.820456i	$-0.306281\pi$
$701$	30.2736	1.14342	0.571709	+	0.820456i	$0.306281\pi$
$702$	17.6968	0.667922
$703$	9.64369	0.363719
$704$	30.9513	1.16652
$705$	−31.5889	−1.18971
$706$	28.8516	1.08584
$707$	−1.41664	−0.0532781
$708$	−1.06933	−0.0401878
$709$	21.7248	0.815892	0.407946	−	0.913006i	$-0.366245\pi$
$709$	21.7248	0.815892	0.407946	+	0.913006i	$0.366245\pi$
$710$	−2.62306	−0.0984417
$711$	2.37899	0.0892190
$712$	19.5823	0.733879
$713$	−1.03324	−0.0386952
$714$	1.97703	0.0739885
$715$	8.03669	0.300555
$716$	−42.6576	−1.59419
$717$	19.4547	0.726549
$718$	−58.0631	−2.16690
$719$	26.3694	0.983414	0.491707	−	0.870761i	$-0.336373\pi$
$719$	26.3694	0.983414	0.491707	+	0.870761i	$0.336373\pi$
$720$	0.756123	0.0281790
$721$	−1.92969	−0.0718652
$722$	37.3191	1.38887
$723$	−34.3265	−1.27662
$724$	23.9998	0.891946
$725$	4.97794	0.184876
$726$	−22.9103	−0.850281
$727$	42.5572	1.57836	0.789180	−	0.614162i	$-0.210506\pi$
$727$	42.5572	1.57836	0.789180	+	0.614162i	$0.210506\pi$
$728$	2.44630	0.0906659
$729$	16.0818	0.595623
$730$	−9.07290	−0.335803
$731$	1.00000	0.0369863
$732$	46.1436	1.70552
$733$	16.8260	0.621482	0.310741	−	0.950495i	$-0.399423\pi$
$733$	16.8260	0.621482	0.310741	+	0.950495i	$0.399423\pi$
$734$	−26.7577	−0.987644
$735$	24.4271	0.901006
$736$	46.6658	1.72013
$737$	3.48219	0.128268
$738$	7.40567	0.272606
$739$	−9.93051	−0.365300	−0.182650	−	0.983178i	$-0.558467\pi$
$739$	−9.93051	−0.365300	−0.182650	+	0.983178i	$0.558467\pi$
$740$	−35.0107	−1.28702
$741$	−5.94527	−0.218405
$742$	9.65372	0.354399
$743$	−42.4908	−1.55884	−0.779419	−	0.626503i	$-0.784485\pi$
$743$	−42.4908	−1.55884	−0.779419	+	0.626503i	$0.784485\pi$
$744$	−0.681844	−0.0249976
$745$	35.2014	1.28968
$746$	−18.2689	−0.668872
$747$	−11.2599	−0.411980
$748$	−8.14787	−0.297915
$749$	−3.27678	−0.119731
$750$	−55.0221	−2.00912
$751$	−28.3471	−1.03440	−0.517201	−	0.855864i	$-0.673026\pi$
$751$	−28.3471	−1.03440	−0.517201	+	0.855864i	$0.673026\pi$
$752$	4.40749	0.160725
$753$	28.0368	1.02172
$754$	−12.6704	−0.461430
$755$	−31.4571	−1.14484
$756$	6.22685	0.226468
$757$	40.8559	1.48493	0.742467	−	0.669883i	$-0.233656\pi$
$757$	40.8559	1.48493	0.742467	+	0.669883i	$0.233656\pi$
$758$	−41.9840	−1.52493
$759$	43.8907	1.59313
$760$	9.64872	0.349996
$761$	−44.6173	−1.61738	−0.808688	−	0.588238i	$-0.799822\pi$
$761$	−44.6173	−1.61738	−0.808688	+	0.588238i	$0.799822\pi$
$762$	−17.3888	−0.629931
$763$	−1.37709	−0.0498539
$764$	46.0294	1.66529
$765$	1.51054	0.0546136
$766$	−53.0155	−1.91553
$767$	−0.293995	−0.0106155
$768$	37.3438	1.34753
$769$	−45.9951	−1.65863	−0.829313	−	0.558785i	$-0.811268\pi$
$769$	−45.9951	−1.65863	−0.829313	+	0.558785i	$0.811268\pi$
$770$	4.51843	0.162833
$771$	−37.5626	−1.35279
$772$	−56.8159	−2.04485
$773$	−12.1436	−0.436773	−0.218387	−	0.975862i	$-0.570079\pi$
$773$	−12.1436	−0.436773	−0.218387	+	0.975862i	$0.570079\pi$
$774$	−1.90341	−0.0684167
$775$	0.183140	0.00657858
$776$	50.9966	1.83067
$777$	4.87755	0.174981
$778$	−29.5757	−1.06034
$779$	6.57809	0.235684
$780$	21.5838	0.772825
$781$	−1.50605	−0.0538908
$782$	−21.3077	−0.761962
$783$	−12.9700	−0.463509
$784$	−3.40822	−0.121722
$785$	14.4092	0.514287
$786$	3.81532	0.136088
$787$	40.9029	1.45803	0.729016	−	0.684497i	$-0.239978\pi$
$787$	40.9029	1.45803	0.729016	+	0.684497i	$0.239978\pi$
$788$	14.3722	0.511988
$789$	−14.0960	−0.501832
$790$	−12.2580	−0.436121
$791$	5.03390	0.178985
$792$	6.23686	0.221617
$793$	12.6865	0.450510
$794$	−72.7631	−2.58227
$795$	34.2534	1.21484
$796$	−7.17358	−0.254261
$797$	33.4623	1.18529	0.592647	−	0.805462i	$-0.298083\pi$
$797$	33.4623	1.18529	0.592647	+	0.805462i	$0.298083\pi$
$798$	−3.34258	−0.118326
$799$	8.80502	0.311499
$800$	−8.27143	−0.292439
$801$	−5.18316	−0.183138
$802$	75.6944	2.67286
$803$	−5.20928	−0.183831
$804$	9.35199	0.329819
$805$	7.39511	0.260643
$806$	−0.466149	−0.0164194
$807$	1.48814	0.0523851
$808$	10.0755	0.354454
$809$	−21.2341	−0.746550	−0.373275	−	0.927721i	$-0.621765\pi$
$809$	−21.2341	−0.746550	−0.373275	+	0.927721i	$0.621765\pi$
$810$	45.7802	1.60855
$811$	−25.5476	−0.897099	−0.448549	−	0.893758i	$-0.648059\pi$
$811$	−25.5476	−0.897099	−0.448549	+	0.893758i	$0.648059\pi$
$812$	−4.45826	−0.156454
$813$	9.84956	0.345439
$814$	−32.1194	−1.12578
$815$	4.56623	0.159948
$816$	−0.978765	−0.0342636
$817$	−1.69071	−0.0591503
$818$	−56.3809	−1.97131
$819$	−0.647500	−0.0226255
$820$	−23.8812	−0.833969
$821$	11.6000	0.404841	0.202421	−	0.979299i	$-0.435119\pi$
$821$	11.6000	0.404841	0.202421	+	0.979299i	$0.435119\pi$
$822$	57.6517	2.01084
$823$	−34.5005	−1.20261	−0.601305	−	0.799019i	$-0.705352\pi$
$823$	−34.5005	−1.20261	−0.601305	+	0.799019i	$0.705352\pi$
$824$	13.7244	0.478112
$825$	−7.77955	−0.270849
$826$	−0.165291	−0.00575121
$827$	−7.41205	−0.257742	−0.128871	−	0.991661i	$-0.541135\pi$
$827$	−7.41205	−0.257742	−0.128871	+	0.991661i	$0.541135\pi$
$828$	25.3825	0.882102
$829$	−52.3403	−1.81785	−0.908927	−	0.416956i	$-0.863097\pi$
$829$	−52.3403	−1.81785	−0.908927	+	0.416956i	$0.863097\pi$
$830$	58.0182	2.01384
$831$	−33.0354	−1.14599
$832$	22.8538	0.792314
$833$	−6.80874	−0.235909
$834$	−63.9588	−2.21471
$835$	−30.9386	−1.07067
$836$	13.7756	0.476441
$837$	−0.477170	−0.0164934
$838$	−16.2393	−0.560977
$839$	−22.8959	−0.790455	−0.395227	−	0.918583i	$-0.629334\pi$
$839$	−22.8959	−0.790455	−0.395227	+	0.918583i	$0.629334\pi$
$840$	4.88009	0.168379
$841$	−19.7138	−0.679787
$842$	68.3682	2.35612
$843$	−27.3178	−0.940875
$844$	−32.8322	−1.13013
$845$	−17.9181	−0.616402
$846$	−16.7596	−0.576206
$847$	−2.21633	−0.0761540
$848$	−4.77925	−0.164120
$849$	20.9949	0.720543
$850$	3.77675	0.129542
$851$	−52.5684	−1.80202
$852$	−4.04475	−0.138571
$853$	−44.2263	−1.51428	−0.757140	−	0.653252i	$-0.773404\pi$
$853$	−44.2263	−1.51428	−0.757140	+	0.653252i	$0.773404\pi$
$854$	7.13264	0.244074
$855$	−2.55388	−0.0873407
$856$	23.3053	0.796558
$857$	−19.0317	−0.650111	−0.325056	−	0.945695i	$-0.605383\pi$
$857$	−19.0317	−0.650111	−0.325056	+	0.945695i	$0.605383\pi$
$858$	19.8014	0.676009
$859$	−6.19840	−0.211487	−0.105743	−	0.994393i	$-0.533722\pi$
$859$	−6.19840	−0.211487	−0.105743	+	0.994393i	$0.533722\pi$
$860$	6.13797	0.209303
$861$	3.32704	0.113385
$862$	−20.1888	−0.687632
$863$	27.0847	0.921973	0.460986	−	0.887407i	$-0.347496\pi$
$863$	27.0847	0.921973	0.460986	+	0.887407i	$0.347496\pi$
$864$	21.5512	0.733185
$865$	−22.5513	−0.766767
$866$	−25.4606	−0.865188
$867$	−1.95532	−0.0664061
$868$	−0.164021	−0.00556723
$869$	−7.03804	−0.238749
$870$	−25.2761	−0.856939
$871$	2.57118	0.0871213
$872$	9.79419	0.331673
$873$	−13.4980	−0.456840
$874$	36.0251	1.21857
$875$	−5.32280	−0.179944
$876$	−13.9904	−0.472690
$877$	−21.2759	−0.718435	−0.359217	−	0.933254i	$-0.616956\pi$
$877$	−21.2759	−0.718435	−0.359217	+	0.933254i	$0.616956\pi$
$878$	−84.2165	−2.84217
$879$	−27.8480	−0.939291
$880$	−2.23693	−0.0754068
$881$	−12.4698	−0.420118	−0.210059	−	0.977689i	$-0.567366\pi$
$881$	−12.4698	−0.420118	−0.210059	+	0.977689i	$0.567366\pi$
$882$	12.9598	0.436380
$883$	−49.0567	−1.65089	−0.825445	−	0.564483i	$-0.809076\pi$
$883$	−49.0567	−1.65089	−0.825445	+	0.564483i	$0.809076\pi$
$884$	−6.01623	−0.202348
$885$	−0.586487	−0.0197145
$886$	−43.2395	−1.45266
$887$	−29.5400	−0.991856	−0.495928	−	0.868364i	$-0.665172\pi$
$887$	−29.5400	−0.991856	−0.495928	+	0.868364i	$0.665172\pi$
$888$	−34.6903	−1.16413
$889$	−1.68219	−0.0564187
$890$	26.7068	0.895215
$891$	26.2851	0.880582
$892$	22.7252	0.760896
$893$	−14.8867	−0.498165
$894$	86.7318	2.90075
$895$	−23.3961	−0.782046
$896$	8.42017	0.281298
$897$	32.4081	1.08207
$898$	67.8616	2.26457
$899$	0.341641	0.0113944
$900$	−4.49900	−0.149967
$901$	−9.54770	−0.318080
$902$	−21.9091	−0.729492
$903$	−0.855118	−0.0284566
$904$	−35.8024	−1.19077
$905$	13.1630	0.437553
$906$	−77.5063	−2.57497
$907$	−32.9094	−1.09274	−0.546369	−	0.837545i	$-0.683990\pi$
$907$	−32.9094	−1.09274	−0.546369	+	0.837545i	$0.683990\pi$
$908$	14.3340	0.475691
$909$	−2.66683	−0.0884532
$910$	3.33632	0.110598
$911$	−29.3342	−0.971885	−0.485943	−	0.873991i	$-0.661524\pi$
$911$	−29.3342	−0.971885	−0.485943	+	0.873991i	$0.661524\pi$
$912$	1.65480	0.0547960
$913$	33.3116	1.10245
$914$	−84.1558	−2.78363
$915$	25.3081	0.836659
$916$	59.7604	1.97454
$917$	0.369092	0.0121885
$918$	−9.84030	−0.324778
$919$	25.9023	0.854438	0.427219	−	0.904148i	$-0.359493\pi$
$919$	25.9023	0.854438	0.427219	+	0.904148i	$0.359493\pi$
$920$	−52.5959	−1.73403
$921$	−7.93824	−0.261574
$922$	−37.1547	−1.22362
$923$	−1.11204	−0.0366032
$924$	6.96739	0.229210
$925$	9.31765	0.306363
$926$	82.1683	2.70022
$927$	−3.63265	−0.119312
$928$	−15.4301	−0.506517
$929$	55.7964	1.83062	0.915311	−	0.402748i	$-0.131945\pi$
$929$	55.7964	1.83062	0.915311	+	0.402748i	$0.131945\pi$
$930$	−0.929915	−0.0304931
$931$	11.5116	0.377277
$932$	−90.8279	−2.97517
$933$	−18.9923	−0.621778
$934$	26.2191	0.857914
$935$	−4.46881	−0.146146
$936$	4.60518	0.150525
$937$	−36.2791	−1.18519	−0.592593	−	0.805502i	$-0.701896\pi$
$937$	−36.2791	−1.18519	−0.592593	+	0.805502i	$0.701896\pi$
$938$	1.44558	0.0472000
$939$	9.41909	0.307380
$940$	54.0450	1.76275
$941$	−59.8854	−1.95221	−0.976104	−	0.217303i	$-0.930274\pi$
$941$	−59.8854	−1.95221	−0.976104	+	0.217303i	$0.930274\pi$
$942$	35.5025	1.15673
$943$	−35.8576	−1.16768
$944$	0.0818304	0.00266335
$945$	3.41520	0.111096
$946$	5.63109	0.183082
$947$	23.5074	0.763888	0.381944	−	0.924185i	$-0.375255\pi$
$947$	23.5074	0.763888	0.381944	+	0.924185i	$0.375255\pi$
$948$	−18.9018	−0.613902
$949$	−3.84643	−0.124860
$950$	−6.38538	−0.207169
$951$	36.3532	1.17883
$952$	−1.36027	−0.0440865
$953$	−25.5864	−0.828825	−0.414412	−	0.910089i	$-0.636013\pi$
$953$	−25.5864	−0.828825	−0.414412	+	0.910089i	$0.636013\pi$
$954$	18.1732	0.588379
$955$	25.2454	0.816923
$956$	−33.2848	−1.07651
$957$	−14.5125	−0.469121
$958$	−50.3309	−1.62612
$959$	5.57720	0.180097
$960$	45.5908	1.47144
$961$	−30.9874	−0.999595
$962$	−23.7164	−0.764646
$963$	−6.16856	−0.198779
$964$	58.7287	1.89152
$965$	−31.1614	−1.00312
$966$	18.2206	0.586239
$967$	40.7452	1.31028	0.655139	−	0.755508i	$-0.272610\pi$
$967$	40.7452	1.31028	0.655139	+	0.755508i	$0.272610\pi$
$968$	15.7631	0.506645
$969$	3.30587	0.106200
$970$	69.5503	2.23313
$971$	−3.50173	−0.112376	−0.0561879	−	0.998420i	$-0.517895\pi$
$971$	−3.50173	−0.112376	−0.0561879	+	0.998420i	$0.517895\pi$
$972$	27.8777	0.894178
$973$	−6.18733	−0.198357
$974$	−93.9767	−3.01121
$975$	−5.74427	−0.183964
$976$	−3.53114	−0.113029
$977$	−18.0494	−0.577452	−0.288726	−	0.957412i	$-0.593232\pi$
$977$	−18.0494	−0.577452	−0.288726	+	0.957412i	$0.593232\pi$
$978$	11.2506	0.359755
$979$	15.3339	0.490075
$980$	−41.7919	−1.33499
$981$	−2.59238	−0.0827683
$982$	−49.4558	−1.57820
$983$	27.7142	0.883947	0.441973	−	0.897028i	$-0.354279\pi$
$983$	27.7142	0.883947	0.441973	+	0.897028i	$0.354279\pi$
$984$	−23.6627	−0.754340
$985$	7.88261	0.251161
$986$	7.04540	0.224371
$987$	−7.52934	−0.239661
$988$	10.1717	0.323604
$989$	9.21615	0.293057
$990$	8.50597	0.270338
$991$	12.0142	0.381644	0.190822	−	0.981625i	$-0.438885\pi$
$991$	12.0142	0.381644	0.190822	+	0.981625i	$0.438885\pi$
$992$	−0.567677	−0.0180238
$993$	11.7726	0.373591
$994$	−0.625216	−0.0198307
$995$	−3.93444	−0.124730
$996$	89.4638	2.83477
$997$	8.25231	0.261353	0.130677	−	0.991425i	$-0.458285\pi$
$997$	8.25231	0.261353	0.130677	+	0.991425i	$0.458285\pi$
$998$	−33.6710	−1.06584
$999$	−24.2771	−0.768093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.d.1.1	✓	8
3.2	odd	2		6579.2.a.k.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.d.1.1	✓	8	1.1	even	1	trivial
6579.2.a.k.1.8		8	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)

\(f(q)\)	\(=\)	\(q-2.31200 q^{2} -1.95532 q^{3} +3.34533 q^{4} +1.83479 q^{5} +4.52069 q^{6} +0.437329 q^{7} -3.11039 q^{8} +0.823276 q^{9} +O(q^{10})\)	\(q-2.31200 q^{2} -1.95532 q^{3} +3.34533 q^{4} +1.83479 q^{5} +4.52069 q^{6} +0.437329 q^{7} -3.11039 q^{8} +0.823276 q^{9} -4.24203 q^{10} -2.43560 q^{11} -6.54119 q^{12} -1.79840 q^{13} -1.01110 q^{14} -3.58760 q^{15} +0.500565 q^{16} +1.00000 q^{17} -1.90341 q^{18} -1.69071 q^{19} +6.13797 q^{20} -0.855118 q^{21} +5.63109 q^{22} +9.21615 q^{23} +6.08182 q^{24} -1.63355 q^{25} +4.15789 q^{26} +4.25619 q^{27} +1.46301 q^{28} -3.04732 q^{29} +8.29452 q^{30} -0.112112 q^{31} +5.06348 q^{32} +4.76237 q^{33} -2.31200 q^{34} +0.802407 q^{35} +2.75413 q^{36} -5.70394 q^{37} +3.90891 q^{38} +3.51644 q^{39} -5.70692 q^{40} -3.89073 q^{41} +1.97703 q^{42} +1.00000 q^{43} -8.14787 q^{44} +1.51054 q^{45} -21.3077 q^{46} +8.80502 q^{47} -0.978765 q^{48} -6.80874 q^{49} +3.77675 q^{50} -1.95532 q^{51} -6.01623 q^{52} -9.54770 q^{53} -9.84030 q^{54} -4.46881 q^{55} -1.36027 q^{56} +3.30587 q^{57} +7.04540 q^{58} +0.163476 q^{59} -12.0017 q^{60} -7.05431 q^{61} +0.259202 q^{62} +0.360043 q^{63} -12.7079 q^{64} -3.29968 q^{65} -11.0106 q^{66} -1.42971 q^{67} +3.34533 q^{68} -18.0205 q^{69} -1.85516 q^{70} +0.618350 q^{71} -2.56071 q^{72} +2.13881 q^{73} +13.1875 q^{74} +3.19410 q^{75} -5.65597 q^{76} -1.06516 q^{77} -8.13001 q^{78} +2.88966 q^{79} +0.918432 q^{80} -10.7920 q^{81} +8.99536 q^{82} -13.6770 q^{83} -2.86065 q^{84} +1.83479 q^{85} -2.31200 q^{86} +5.95849 q^{87} +7.57566 q^{88} -6.29577 q^{89} -3.49236 q^{90} -0.786492 q^{91} +30.8311 q^{92} +0.219215 q^{93} -20.3572 q^{94} -3.10209 q^{95} -9.90073 q^{96} -16.3955 q^{97} +15.7418 q^{98} -2.00517 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * q^99

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