LMFDB - Embedded newform 667.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 $ x^13 - 4x^12 - 11x^11 + 58x^10 + 24x^9 - 298x^8 + 97x^7 + 641x^6 - 402x^5 - 547x^4 + 352x^3 + 219x^2 - 88x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.775068$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.775068 q^{2} +2.46815 q^{3} -1.39927 q^{4} +3.48646 q^{5} +1.91299 q^{6} +0.0624539 q^{7} -2.63467 q^{8} +3.09179 q^{9} +O(q^{10})$	\(q+0.775068 q^{2} +2.46815 q^{3} -1.39927 q^{4} +3.48646 q^{5} +1.91299 q^{6} +0.0624539 q^{7} -2.63467 q^{8} +3.09179 q^{9} +2.70224 q^{10} +3.55627 q^{11} -3.45361 q^{12} -0.927177 q^{13} +0.0484060 q^{14} +8.60513 q^{15} +0.756494 q^{16} -3.32813 q^{17} +2.39634 q^{18} -5.02979 q^{19} -4.87850 q^{20} +0.154146 q^{21} +2.75635 q^{22} -1.00000 q^{23} -6.50276 q^{24} +7.15541 q^{25} -0.718625 q^{26} +0.226543 q^{27} -0.0873898 q^{28} +1.00000 q^{29} +6.66956 q^{30} +4.47664 q^{31} +5.85566 q^{32} +8.77742 q^{33} -2.57953 q^{34} +0.217743 q^{35} -4.32624 q^{36} -1.59284 q^{37} -3.89843 q^{38} -2.28842 q^{39} -9.18566 q^{40} +1.57116 q^{41} +0.119474 q^{42} -2.30580 q^{43} -4.97618 q^{44} +10.7794 q^{45} -0.775068 q^{46} -5.34319 q^{47} +1.86714 q^{48} -6.99610 q^{49} +5.54593 q^{50} -8.21434 q^{51} +1.29737 q^{52} -9.94550 q^{53} +0.175586 q^{54} +12.3988 q^{55} -0.164545 q^{56} -12.4143 q^{57} +0.775068 q^{58} +7.26432 q^{59} -12.0409 q^{60} +9.22630 q^{61} +3.46970 q^{62} +0.193094 q^{63} +3.02555 q^{64} -3.23257 q^{65} +6.80310 q^{66} +14.2216 q^{67} +4.65695 q^{68} -2.46815 q^{69} +0.168766 q^{70} -7.60080 q^{71} -8.14582 q^{72} +6.51425 q^{73} -1.23456 q^{74} +17.6607 q^{75} +7.03803 q^{76} +0.222103 q^{77} -1.77368 q^{78} -15.6281 q^{79} +2.63749 q^{80} -8.71622 q^{81} +1.21776 q^{82} -8.68598 q^{83} -0.215692 q^{84} -11.6034 q^{85} -1.78715 q^{86} +2.46815 q^{87} -9.36957 q^{88} -15.0849 q^{89} +8.35476 q^{90} -0.0579058 q^{91} +1.39927 q^{92} +11.0490 q^{93} -4.14134 q^{94} -17.5362 q^{95} +14.4527 q^{96} +11.7883 q^{97} -5.42245 q^{98} +10.9952 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * 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 $

$2$	0.775068	0.548056	0.274028	−	0.961722i	$-0.411644\pi$
$2$	0.775068	0.548056	0.274028	+	0.961722i	$0.411644\pi$
$3$	2.46815	1.42499	0.712495	−	0.701677i	$-0.247565\pi$
$3$	2.46815	1.42499	0.712495	+	0.701677i	$0.247565\pi$
$4$	−1.39927	−0.699635
$5$	3.48646	1.55919	0.779596	−	0.626282i	$-0.215424\pi$
$5$	3.48646	1.55919	0.779596	+	0.626282i	$0.215424\pi$
$6$	1.91299	0.780974
$7$	0.0624539	0.0236054	0.0118027	−	0.999930i	$-0.496243\pi$
$7$	0.0624539	0.0236054	0.0118027	+	0.999930i	$0.496243\pi$
$8$	−2.63467	−0.931495
$9$	3.09179	1.03060
$10$	2.70224	0.854525
$11$	3.55627	1.07225	0.536127	−	0.844137i	$-0.319887\pi$
$11$	3.55627	1.07225	0.536127	+	0.844137i	$0.319887\pi$
$12$	−3.45361	−0.996972
$13$	−0.927177	−0.257153	−0.128576	−	0.991700i	$-0.541041\pi$
$13$	−0.927177	−0.257153	−0.128576	+	0.991700i	$0.541041\pi$
$14$	0.0484060	0.0129371
$15$	8.60513	2.22183
$16$	0.756494	0.189124
$17$	−3.32813	−0.807190	−0.403595	−	0.914938i	$-0.632240\pi$
$17$	−3.32813	−0.807190	−0.403595	+	0.914938i	$0.632240\pi$
$18$	2.39634	0.564824
$19$	−5.02979	−1.15391	−0.576956	−	0.816775i	$-0.695760\pi$
$19$	−5.02979	−1.15391	−0.576956	+	0.816775i	$0.695760\pi$
$20$	−4.87850	−1.09087
$21$	0.154146	0.0336374
$22$	2.75635	0.587656
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−6.50276	−1.32737
$25$	7.15541	1.43108
$26$	−0.718625	−0.140934
$27$	0.226543	0.0435983
$28$	−0.0873898	−0.0165151
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	6.66956	1.21769
$31$	4.47664	0.804027	0.402014	−	0.915634i	$-0.368310\pi$
$31$	4.47664	0.804027	0.402014	+	0.915634i	$0.368310\pi$
$32$	5.85566	1.03515
$33$	8.77742	1.52795
$34$	−2.57953	−0.442385
$35$	0.217743	0.0368053
$36$	−4.32624	−0.721040
$37$	−1.59284	−0.261861	−0.130930	−	0.991392i	$-0.541796\pi$
$37$	−1.59284	−0.261861	−0.130930	+	0.991392i	$0.541796\pi$
$38$	−3.89843	−0.632408
$39$	−2.28842	−0.366440
$40$	−9.18566	−1.45238
$41$	1.57116	0.245374	0.122687	−	0.992445i	$-0.460849\pi$
$41$	1.57116	0.245374	0.122687	+	0.992445i	$0.460849\pi$
$42$	0.119474	0.0184352
$43$	−2.30580	−0.351631	−0.175815	−	0.984423i	$-0.556256\pi$
$43$	−2.30580	−0.351631	−0.175815	+	0.984423i	$0.556256\pi$
$44$	−4.97618	−0.750187
$45$	10.7794	1.60690
$46$	−0.775068	−0.114278
$47$	−5.34319	−0.779385	−0.389693	−	0.920945i	$-0.627419\pi$
$47$	−5.34319	−0.779385	−0.389693	+	0.920945i	$0.627419\pi$
$48$	1.86714	0.269499
$49$	−6.99610	−0.999443
$50$	5.54593	0.784313
$51$	−8.21434	−1.15024
$52$	1.29737	0.179913
$53$	−9.94550	−1.36612	−0.683060	−	0.730362i	$-0.739351\pi$
$53$	−9.94550	−1.36612	−0.683060	+	0.730362i	$0.739351\pi$
$54$	0.175586	0.0238943
$55$	12.3988	1.67185
$56$	−0.164545	−0.0219883
$57$	−12.4143	−1.64431
$58$	0.775068	0.101771
$59$	7.26432	0.945734	0.472867	−	0.881134i	$-0.343219\pi$
$59$	7.26432	0.945734	0.472867	+	0.881134i	$0.343219\pi$
$60$	−12.0409	−1.55447
$61$	9.22630	1.18131	0.590653	−	0.806925i	$-0.298870\pi$
$61$	9.22630	1.18131	0.590653	+	0.806925i	$0.298870\pi$
$62$	3.46970	0.440652
$63$	0.193094	0.0243276
$64$	3.02555	0.378194
$65$	−3.23257	−0.400950
$66$	6.80310	0.837403
$67$	14.2216	1.73744	0.868720	−	0.495303i	$-0.164943\pi$
$67$	14.2216	1.73744	0.868720	+	0.495303i	$0.164943\pi$
$68$	4.65695	0.564738
$69$	−2.46815	−0.297131
$70$	0.168766	0.0201714
$71$	−7.60080	−0.902049	−0.451024	−	0.892512i	$-0.648941\pi$
$71$	−7.60080	−0.902049	−0.451024	+	0.892512i	$0.648941\pi$
$72$	−8.14582	−0.959994
$73$	6.51425	0.762436	0.381218	−	0.924485i	$-0.375505\pi$
$73$	6.51425	0.762436	0.381218	+	0.924485i	$0.375505\pi$
$74$	−1.23456	−0.143514
$75$	17.6607	2.03928
$76$	7.03803	0.807317
$77$	0.222103	0.0253110
$78$	−1.77368	−0.200829
$79$	−15.6281	−1.75830	−0.879149	−	0.476547i	$-0.841888\pi$
$79$	−15.6281	−1.75830	−0.879149	+	0.476547i	$0.841888\pi$
$80$	2.63749	0.294880
$81$	−8.71622	−0.968468
$82$	1.21776	0.134479
$83$	−8.68598	−0.953410	−0.476705	−	0.879063i	$-0.658169\pi$
$83$	−8.68598	−0.953410	−0.476705	+	0.879063i	$0.658169\pi$
$84$	−0.215692	−0.0235339
$85$	−11.6034	−1.25856
$86$	−1.78715	−0.192713
$87$	2.46815	0.264614
$88$	−9.36957	−0.998800
$89$	−15.0849	−1.59900	−0.799500	−	0.600666i	$-0.794902\pi$
$89$	−15.0849	−1.59900	−0.799500	+	0.600666i	$0.794902\pi$
$90$	8.35476	0.880669
$91$	−0.0579058	−0.00607018
$92$	1.39927	0.145884
$93$	11.0490	1.14573
$94$	−4.14134	−0.427147
$95$	−17.5362	−1.79917
$96$	14.4527	1.47507
$97$	11.7883	1.19692	0.598462	−	0.801151i	$-0.295779\pi$
$97$	11.7883	1.19692	0.598462	+	0.801151i	$0.295779\pi$
$98$	−5.42245	−0.547750
$99$	10.9952	1.10506
$100$	−10.0124	−1.00124
$101$	−2.43366	−0.242159	−0.121079	−	0.992643i	$-0.538636\pi$
$101$	−2.43366	−0.242159	−0.121079	+	0.992643i	$0.538636\pi$
$102$	−6.36667	−0.630394
$103$	7.20441	0.709871	0.354936	−	0.934891i	$-0.384503\pi$
$103$	7.20441	0.709871	0.354936	+	0.934891i	$0.384503\pi$
$104$	2.44280	0.239536
$105$	0.537424	0.0524472
$106$	−7.70844	−0.748710
$107$	−1.19795	−0.115810	−0.0579051	−	0.998322i	$-0.518442\pi$
$107$	−1.19795	−0.115810	−0.0579051	+	0.998322i	$0.518442\pi$
$108$	−0.316995	−0.0305029
$109$	1.74496	0.167137	0.0835684	−	0.996502i	$-0.473368\pi$
$109$	1.74496	0.167137	0.0835684	+	0.996502i	$0.473368\pi$
$110$	9.60990	0.916268
$111$	−3.93137	−0.373149
$112$	0.0472460	0.00446433
$113$	18.5427	1.74435	0.872175	−	0.489195i	$-0.162709\pi$
$113$	18.5427	1.74435	0.872175	+	0.489195i	$0.162709\pi$
$114$	−9.62192	−0.901175
$115$	−3.48646	−0.325114
$116$	−1.39927	−0.129919
$117$	−2.86663	−0.265020
$118$	5.63034	0.518315
$119$	−0.207855	−0.0190540
$120$	−22.6716	−2.06963
$121$	1.64704	0.149731
$122$	7.15101	0.647422
$123$	3.87787	0.349655
$124$	−6.26402	−0.562525
$125$	7.51476	0.672141
$126$	0.149661	0.0133329
$127$	−1.31494	−0.116682	−0.0583412	−	0.998297i	$-0.518581\pi$
$127$	−1.31494	−0.116682	−0.0583412	+	0.998297i	$0.518581\pi$
$128$	−9.36632	−0.827874
$129$	−5.69107	−0.501070
$130$	−2.50546	−0.219743
$131$	−3.07885	−0.269000	−0.134500	−	0.990914i	$-0.542943\pi$
$131$	−3.07885	−0.269000	−0.134500	+	0.990914i	$0.542943\pi$
$132$	−12.2820	−1.06901
$133$	−0.314130	−0.0272385
$134$	11.0227	0.952214
$135$	0.789834	0.0679781
$136$	8.76851	0.751893
$137$	5.56864	0.475761	0.237880	−	0.971294i	$-0.423547\pi$
$137$	5.56864	0.475761	0.237880	+	0.971294i	$0.423547\pi$
$138$	−1.91299	−0.162844
$139$	−12.6474	−1.07273	−0.536367	−	0.843985i	$-0.680204\pi$
$139$	−12.6474	−1.07273	−0.536367	+	0.843985i	$0.680204\pi$
$140$	−0.304681	−0.0257503
$141$	−13.1878	−1.11062
$142$	−5.89114	−0.494373
$143$	−3.29729	−0.275733
$144$	2.33892	0.194910
$145$	3.48646	0.289535
$146$	5.04899	0.417857
$147$	−17.2675	−1.42420
$148$	2.22881	0.183207
$149$	18.4512	1.51158	0.755791	−	0.654813i	$-0.227253\pi$
$149$	18.4512	1.51158	0.755791	+	0.654813i	$0.227253\pi$
$150$	13.6882	1.11764
$151$	−8.10008	−0.659175	−0.329588	−	0.944125i	$-0.606910\pi$
$151$	−8.10008	−0.659175	−0.329588	+	0.944125i	$0.606910\pi$
$152$	13.2518	1.07486
$153$	−10.2899	−0.831886
$154$	0.172145	0.0138718
$155$	15.6076	1.25363
$156$	3.20211	0.256374
$157$	5.60973	0.447706	0.223853	−	0.974623i	$-0.428137\pi$
$157$	5.60973	0.447706	0.223853	+	0.974623i	$0.428137\pi$
$158$	−12.1128	−0.963646
$159$	−24.5470	−1.94671
$160$	20.4155	1.61399
$161$	−0.0624539	−0.00492206
$162$	−6.75566	−0.530775
$163$	1.87570	0.146916	0.0734580	−	0.997298i	$-0.476597\pi$
$163$	1.87570	0.146916	0.0734580	+	0.997298i	$0.476597\pi$
$164$	−2.19848	−0.171672
$165$	30.6021	2.38237
$166$	−6.73223	−0.522522
$167$	−11.4370	−0.885020	−0.442510	−	0.896764i	$-0.645912\pi$
$167$	−11.4370	−0.885020	−0.442510	+	0.896764i	$0.645912\pi$
$168$	−0.406123	−0.0313331
$169$	−12.1403	−0.933873
$170$	−8.99342	−0.689764
$171$	−15.5510	−1.18922
$172$	3.22643	0.246013
$173$	−0.252942	−0.0192308	−0.00961542	−	0.999954i	$-0.503061\pi$
$173$	−0.252942	−0.0192308	−0.00961542	+	0.999954i	$0.503061\pi$
$174$	1.91299	0.145023
$175$	0.446883	0.0337812
$176$	2.69030	0.202789
$177$	17.9295	1.34766
$178$	−11.6919	−0.876341
$179$	−6.75538	−0.504921	−0.252461	−	0.967607i	$-0.581240\pi$
$179$	−6.75538	−0.504921	−0.252461	+	0.967607i	$0.581240\pi$
$180$	−15.0833	−1.12424
$181$	−19.7057	−1.46471	−0.732356	−	0.680922i	$-0.761579\pi$
$181$	−19.7057	−1.46471	−0.732356	+	0.680922i	$0.761579\pi$
$182$	−0.0448809	−0.00332680
$183$	22.7719	1.68335
$184$	2.63467	0.194230
$185$	−5.55337	−0.408292
$186$	8.56375	0.627924
$187$	−11.8357	−0.865513
$188$	7.47657	0.545285
$189$	0.0141485	0.00102915
$190$	−13.5917	−0.986047
$191$	3.34437	0.241990	0.120995	−	0.992653i	$-0.461391\pi$
$191$	3.34437	0.241990	0.120995	+	0.992653i	$0.461391\pi$
$192$	7.46753	0.538922
$193$	−8.02376	−0.577563	−0.288782	−	0.957395i	$-0.593250\pi$
$193$	−8.02376	−0.577563	−0.288782	+	0.957395i	$0.593250\pi$
$194$	9.13676	0.655981
$195$	−7.97847	−0.571350
$196$	9.78943	0.699245
$197$	27.2979	1.94489	0.972447	−	0.233123i	$-0.0748944\pi$
$197$	27.2979	1.94489	0.972447	+	0.233123i	$0.0748944\pi$
$198$	8.52204	0.605635
$199$	12.1839	0.863692	0.431846	−	0.901947i	$-0.357862\pi$
$199$	12.1839	0.863692	0.431846	+	0.901947i	$0.357862\pi$
$200$	−18.8521	−1.33305
$201$	35.1010	2.47583
$202$	−1.88626	−0.132716
$203$	0.0624539	0.00438340
$204$	11.4941	0.804746
$205$	5.47779	0.382585
$206$	5.58391	0.389049
$207$	−3.09179	−0.214894
$208$	−0.701404	−0.0486336
$209$	−17.8873	−1.23729
$210$	0.416540	0.0287440
$211$	4.16412	0.286670	0.143335	−	0.989674i	$-0.454217\pi$
$211$	4.16412	0.286670	0.143335	+	0.989674i	$0.454217\pi$
$212$	13.9164	0.955785
$213$	−18.7599	−1.28541
$214$	−0.928493	−0.0634705
$215$	−8.03907	−0.548260
$216$	−0.596865	−0.0406115
$217$	0.279583	0.0189794
$218$	1.35246	0.0916003
$219$	16.0782	1.08646
$220$	−17.3492	−1.16969
$221$	3.08576	0.207571
$222$	−3.04708	−0.204507
$223$	16.4546	1.10188	0.550942	−	0.834544i	$-0.314269\pi$
$223$	16.4546	1.10188	0.550942	+	0.834544i	$0.314269\pi$
$224$	0.365709	0.0244350
$225$	22.1230	1.47487
$226$	14.3718	0.956001
$227$	−16.9207	−1.12307	−0.561534	−	0.827453i	$-0.689789\pi$
$227$	−16.9207	−1.12307	−0.561534	+	0.827453i	$0.689789\pi$
$228$	17.3709	1.15042
$229$	18.3965	1.21567	0.607837	−	0.794062i	$-0.292037\pi$
$229$	18.3965	1.21567	0.607837	+	0.794062i	$0.292037\pi$
$230$	−2.70224	−0.178181
$231$	0.548184	0.0360679
$232$	−2.63467	−0.172974
$233$	−20.2748	−1.32824	−0.664122	−	0.747624i	$-0.731194\pi$
$233$	−20.2748	−1.32824	−0.664122	+	0.747624i	$0.731194\pi$
$234$	−2.22184	−0.145246
$235$	−18.6288	−1.21521
$236$	−10.1647	−0.661668
$237$	−38.5726	−2.50556
$238$	−0.161102	−0.0104427
$239$	15.2829	0.988571	0.494286	−	0.869300i	$-0.335430\pi$
$239$	15.2829	0.988571	0.494286	+	0.869300i	$0.335430\pi$
$240$	6.50973	0.420201
$241$	−4.39354	−0.283013	−0.141506	−	0.989937i	$-0.545195\pi$
$241$	−4.39354	−0.283013	−0.141506	+	0.989937i	$0.545195\pi$
$242$	1.27656	0.0820607
$243$	−22.1926	−1.42366
$244$	−12.9101	−0.826483
$245$	−24.3916	−1.55832
$246$	3.00561	0.191631
$247$	4.66350	0.296731
$248$	−11.7944	−0.748947
$249$	−21.4383	−1.35860
$250$	5.82445	0.368371
$251$	9.25415	0.584117	0.292058	−	0.956401i	$-0.405660\pi$
$251$	9.25415	0.584117	0.292058	+	0.956401i	$0.405660\pi$
$252$	−0.270191	−0.0170204
$253$	−3.55627	−0.223581
$254$	−1.01917	−0.0639485
$255$	−28.6390	−1.79344
$256$	−13.3106	−0.831915
$257$	−0.576309	−0.0359491	−0.0179746	−	0.999838i	$-0.505722\pi$
$257$	−0.576309	−0.0359491	−0.0179746	+	0.999838i	$0.505722\pi$
$258$	−4.41096	−0.274615
$259$	−0.0994789	−0.00618132
$260$	4.52323	0.280519
$261$	3.09179	0.191377
$262$	−2.38632	−0.147427
$263$	8.16943	0.503749	0.251874	−	0.967760i	$-0.418953\pi$
$263$	8.16943	0.503749	0.251874	+	0.967760i	$0.418953\pi$
$264$	−23.1256	−1.42328
$265$	−34.6746	−2.13004
$266$	−0.243472	−0.0149282
$267$	−37.2319	−2.27856
$268$	−19.8998	−1.21557
$269$	25.1561	1.53380	0.766898	−	0.641769i	$-0.221799\pi$
$269$	25.1561	1.53380	0.766898	+	0.641769i	$0.221799\pi$
$270$	0.612175	0.0372558
$271$	23.1343	1.40531	0.702656	−	0.711530i	$-0.251997\pi$
$271$	23.1343	1.40531	0.702656	+	0.711530i	$0.251997\pi$
$272$	−2.51771	−0.152659
$273$	−0.142920	−0.00864994
$274$	4.31607	0.260743
$275$	25.4466	1.53449
$276$	3.45361	0.207883
$277$	3.39955	0.204259	0.102130	−	0.994771i	$-0.467434\pi$
$277$	3.39955	0.204259	0.102130	+	0.994771i	$0.467434\pi$
$278$	−9.80256	−0.587919
$279$	13.8408	0.828627
$280$	−0.573680	−0.0342840
$281$	28.4141	1.69505	0.847523	−	0.530759i	$-0.178093\pi$
$281$	28.4141	1.69505	0.847523	+	0.530759i	$0.178093\pi$
$282$	−10.2215	−0.608679
$283$	−7.69721	−0.457552	−0.228776	−	0.973479i	$-0.573472\pi$
$283$	−7.69721	−0.457552	−0.228776	+	0.973479i	$0.573472\pi$
$284$	10.6356	0.631105
$285$	−43.2819	−2.56380
$286$	−2.55562	−0.151117
$287$	0.0981251	0.00579214
$288$	18.1045	1.06682
$289$	−5.92355	−0.348444
$290$	2.70224	0.158681
$291$	29.0954	1.70560
$292$	−9.11520	−0.533427
$293$	11.1030	0.648644	0.324322	−	0.945947i	$-0.394864\pi$
$293$	11.1030	0.648644	0.324322	+	0.945947i	$0.394864\pi$
$294$	−13.3835	−0.780539
$295$	25.3268	1.47458
$296$	4.19659	0.243922
$297$	0.805648	0.0467484
$298$	14.3009	0.828431
$299$	0.927177	0.0536200
$300$	−24.7120	−1.42675
$301$	−0.144006	−0.00830037
$302$	−6.27811	−0.361265
$303$	−6.00666	−0.345074
$304$	−3.80500	−0.218232
$305$	32.1671	1.84188
$306$	−7.97535	−0.455920
$307$	−21.5009	−1.22712	−0.613561	−	0.789647i	$-0.710264\pi$
$307$	−21.5009	−1.22712	−0.613561	+	0.789647i	$0.710264\pi$
$308$	−0.310782	−0.0177084
$309$	17.7816	1.01156
$310$	12.0970	0.687061
$311$	25.6647	1.45531	0.727655	−	0.685943i	$-0.240610\pi$
$311$	25.6647	1.45531	0.727655	+	0.685943i	$0.240610\pi$
$312$	6.02921	0.341337
$313$	30.7981	1.74081	0.870406	−	0.492334i	$-0.163856\pi$
$313$	30.7981	1.74081	0.870406	+	0.492334i	$0.163856\pi$
$314$	4.34793	0.245368
$315$	0.673215	0.0379314
$316$	21.8679	1.23017
$317$	−3.16459	−0.177741	−0.0888706	−	0.996043i	$-0.528326\pi$
$317$	−3.16459	−0.177741	−0.0888706	+	0.996043i	$0.528326\pi$
$318$	−19.0256	−1.06690
$319$	3.55627	0.199113
$320$	10.5485	0.589677
$321$	−2.95673	−0.165028
$322$	−0.0484060	−0.00269756
$323$	16.7398	0.931426
$324$	12.1963	0.677574
$325$	−6.63433	−0.368007
$326$	1.45379	0.0805181
$327$	4.30683	0.238168
$328$	−4.13948	−0.228565
$329$	−0.333703	−0.0183977
$330$	23.7187	1.30567
$331$	−4.73849	−0.260451	−0.130226	−	0.991484i	$-0.541570\pi$
$331$	−4.73849	−0.260451	−0.130226	+	0.991484i	$0.541570\pi$
$332$	12.1540	0.667039
$333$	−4.92471	−0.269873
$334$	−8.86444	−0.485040
$335$	49.5829	2.70900
$336$	0.116610	0.00636162
$337$	31.8821	1.73673	0.868364	−	0.495927i	$-0.165172\pi$
$337$	31.8821	1.73673	0.868364	+	0.495927i	$0.165172\pi$
$338$	−9.40959	−0.511814
$339$	45.7662	2.48568
$340$	16.2363	0.880536
$341$	15.9201	0.862122
$342$	−12.0531	−0.651757
$343$	−0.874111	−0.0471976
$344$	6.07501	0.327542
$345$	−8.60513	−0.463284
$346$	−0.196047	−0.0105396
$347$	−2.76211	−0.148278	−0.0741390	−	0.997248i	$-0.523621\pi$
$347$	−2.76211	−0.148278	−0.0741390	+	0.997248i	$0.523621\pi$
$348$	−3.45361	−0.185133
$349$	−21.7242	−1.16287	−0.581435	−	0.813593i	$-0.697508\pi$
$349$	−21.7242	−1.16287	−0.581435	+	0.813593i	$0.697508\pi$
$350$	0.346365	0.0185140
$351$	−0.210046	−0.0112114
$352$	20.8243	1.10994
$353$	33.1855	1.76629	0.883143	−	0.469105i	$-0.155423\pi$
$353$	33.1855	1.76629	0.883143	+	0.469105i	$0.155423\pi$
$354$	13.8966	0.738594
$355$	−26.4999	−1.40647
$356$	21.1079	1.11872
$357$	−0.513017	−0.0271518
$358$	−5.23588	−0.276725
$359$	−9.46450	−0.499517	−0.249759	−	0.968308i	$-0.580351\pi$
$359$	−9.46450	−0.499517	−0.249759	+	0.968308i	$0.580351\pi$
$360$	−28.4001	−1.49682
$361$	6.29875	0.331513
$362$	−15.2732	−0.802744
$363$	4.06514	0.213364
$364$	0.0810258	0.00424691
$365$	22.7117	1.18878
$366$	17.6498	0.922570
$367$	4.00106	0.208853	0.104427	−	0.994533i	$-0.466699\pi$
$367$	4.00106	0.208853	0.104427	+	0.994533i	$0.466699\pi$
$368$	−0.756494	−0.0394350
$369$	4.85769	0.252881
$370$	−4.30424	−0.223767
$371$	−0.621135	−0.0322477
$372$	−15.4606	−0.801593
$373$	−25.2640	−1.30812	−0.654061	−	0.756441i	$-0.726936\pi$
$373$	−25.2640	−1.30812	−0.654061	+	0.756441i	$0.726936\pi$
$374$	−9.17349	−0.474350
$375$	18.5476	0.957794
$376$	14.0775	0.725993
$377$	−0.927177	−0.0477520
$378$	0.0109661	0.000564033 0
$379$	−2.49577	−0.128199	−0.0640995	−	0.997944i	$-0.520418\pi$
$379$	−2.49577	−0.128199	−0.0640995	+	0.997944i	$0.520418\pi$
$380$	24.5378	1.25876
$381$	−3.24549	−0.166271
$382$	2.59212	0.132624
$383$	34.1153	1.74321	0.871606	−	0.490207i	$-0.163079\pi$
$383$	34.1153	1.74321	0.871606	+	0.490207i	$0.163079\pi$
$384$	−23.1175	−1.17971
$385$	0.774353	0.0394647
$386$	−6.21896	−0.316537
$387$	−7.12903	−0.362389
$388$	−16.4951	−0.837410
$389$	−10.5613	−0.535481	−0.267740	−	0.963491i	$-0.586277\pi$
$389$	−10.5613	−0.535481	−0.267740	+	0.963491i	$0.586277\pi$
$390$	−6.18386	−0.313132
$391$	3.32813	0.168311
$392$	18.4324	0.930976
$393$	−7.59908	−0.383323
$394$	21.1577	1.06591
$395$	−54.4867	−2.74153
$396$	−15.3853	−0.773139
$397$	17.5404	0.880325	0.440163	−	0.897918i	$-0.354921\pi$
$397$	17.5404	0.880325	0.440163	+	0.897918i	$0.354921\pi$
$398$	9.44333	0.473352
$399$	−0.775321	−0.0388146
$400$	5.41303	0.270651
$401$	22.2069	1.10896	0.554479	−	0.832198i	$-0.312918\pi$
$401$	22.2069	1.10896	0.554479	+	0.832198i	$0.312918\pi$
$402$	27.2057	1.35690
$403$	−4.15063	−0.206758
$404$	3.40535	0.169423
$405$	−30.3887	−1.51003
$406$	0.0484060	0.00240235
$407$	−5.66456	−0.280782
$408$	21.6420	1.07144
$409$	−17.7893	−0.879627	−0.439813	−	0.898089i	$-0.644955\pi$
$409$	−17.7893	−0.879627	−0.439813	+	0.898089i	$0.644955\pi$
$410$	4.24566	0.209678
$411$	13.7443	0.677954
$412$	−10.0809	−0.496651
$413$	0.453685	0.0223244
$414$	−2.39634	−0.117774
$415$	−30.2833	−1.48655
$416$	−5.42924	−0.266190
$417$	−31.2156	−1.52864
$418$	−13.8638	−0.678103
$419$	19.6622	0.960562	0.480281	−	0.877115i	$-0.340535\pi$
$419$	19.6622	0.960562	0.480281	+	0.877115i	$0.340535\pi$
$420$	−0.752001	−0.0366939
$421$	32.9612	1.60643	0.803216	−	0.595688i	$-0.203121\pi$
$421$	32.9612	1.60643	0.803216	+	0.595688i	$0.203121\pi$
$422$	3.22748	0.157111
$423$	−16.5200	−0.803231
$424$	26.2031	1.27253
$425$	−23.8141	−1.15516
$426$	−14.5402	−0.704477
$427$	0.576218	0.0278852
$428$	1.67626	0.0810249
$429$	−8.13822	−0.392917
$430$	−6.23083	−0.300477
$431$	3.39015	0.163298	0.0816488	−	0.996661i	$-0.473981\pi$
$431$	3.39015	0.163298	0.0816488	+	0.996661i	$0.473981\pi$
$432$	0.171379	0.00824546
$433$	−19.7726	−0.950211	−0.475105	−	0.879929i	$-0.657590\pi$
$433$	−19.7726	−0.950211	−0.475105	+	0.879929i	$0.657590\pi$
$434$	0.216696	0.0104017
$435$	8.60513	0.412584
$436$	−2.44167	−0.116935
$437$	5.02979	0.240607
$438$	12.4617	0.595442
$439$	−17.6369	−0.841762	−0.420881	−	0.907116i	$-0.638279\pi$
$439$	−17.6369	−0.841762	−0.420881	+	0.907116i	$0.638279\pi$
$440$	−32.6667	−1.55732
$441$	−21.6304	−1.03002
$442$	2.39168	0.113760
$443$	−17.5315	−0.832947	−0.416474	−	0.909148i	$-0.636734\pi$
$443$	−17.5315	−0.832947	−0.416474	+	0.909148i	$0.636734\pi$
$444$	5.50104	0.261068
$445$	−52.5930	−2.49315
$446$	12.7535	0.603894
$447$	45.5404	2.15399
$448$	0.188957	0.00892740
$449$	17.3047	0.816660	0.408330	−	0.912834i	$-0.366111\pi$
$449$	17.3047	0.816660	0.408330	+	0.912834i	$0.366111\pi$
$450$	17.1468	0.808310
$451$	5.58747	0.263104
$452$	−25.9462	−1.22041
$453$	−19.9922	−0.939318
$454$	−13.1147	−0.615504
$455$	−0.201886	−0.00946458
$456$	32.7075	1.53167
$457$	35.6007	1.66533	0.832666	−	0.553776i	$-0.186814\pi$
$457$	35.6007	1.66533	0.832666	+	0.553776i	$0.186814\pi$
$458$	14.2585	0.666257
$459$	−0.753965	−0.0351921
$460$	4.87850	0.227461
$461$	28.9928	1.35033	0.675165	−	0.737667i	$-0.264073\pi$
$461$	28.9928	1.35033	0.675165	+	0.737667i	$0.264073\pi$
$462$	0.424880	0.0197672
$463$	14.8195	0.688720	0.344360	−	0.938838i	$-0.388096\pi$
$463$	14.8195	0.688720	0.344360	+	0.938838i	$0.388096\pi$
$464$	0.756494	0.0351194
$465$	38.5220	1.78642
$466$	−15.7143	−0.727952
$467$	21.1430	0.978382	0.489191	−	0.872177i	$-0.337292\pi$
$467$	21.1430	0.978382	0.489191	+	0.872177i	$0.337292\pi$
$468$	4.01119	0.185417
$469$	0.888192	0.0410129
$470$	−14.4386	−0.666004
$471$	13.8457	0.637976
$472$	−19.1391	−0.880946
$473$	−8.20003	−0.377038
$474$	−29.8964	−1.37318
$475$	−35.9902	−1.65134
$476$	0.290845	0.0133308
$477$	−30.7494	−1.40792
$478$	11.8453	0.541792
$479$	−27.3454	−1.24944	−0.624721	−	0.780848i	$-0.714787\pi$
$479$	−27.3454	−1.24944	−0.624721	+	0.780848i	$0.714787\pi$
$480$	50.3887	2.29992
$481$	1.47684	0.0673382
$482$	−3.40529	−0.155107
$483$	−0.154146	−0.00701388
$484$	−2.30465	−0.104757
$485$	41.0996	1.86624
$486$	−17.2008	−0.780243
$487$	−14.2658	−0.646446	−0.323223	−	0.946323i	$-0.604766\pi$
$487$	−14.2658	−0.646446	−0.323223	+	0.946323i	$0.604766\pi$
$488$	−24.3082	−1.10038
$489$	4.62951	0.209354
$490$	−18.9052	−0.854049
$491$	−35.2425	−1.59047	−0.795236	−	0.606300i	$-0.792653\pi$
$491$	−35.2425	−1.59047	−0.795236	+	0.606300i	$0.792653\pi$
$492$	−5.42618	−0.244631
$493$	−3.32813	−0.149891
$494$	3.61453	0.162625
$495$	38.3344	1.72300
$496$	3.38655	0.152061
$497$	−0.474700	−0.0212932
$498$	−16.6162	−0.744588
$499$	1.01926	0.0456283	0.0228142	−	0.999740i	$-0.492737\pi$
$499$	1.01926	0.0456283	0.0228142	+	0.999740i	$0.492737\pi$
$500$	−10.5152	−0.470253
$501$	−28.2282	−1.26114
$502$	7.17259	0.320129
$503$	−13.4878	−0.601392	−0.300696	−	0.953720i	$-0.597219\pi$
$503$	−13.4878	−0.601392	−0.300696	+	0.953720i	$0.597219\pi$
$504$	−0.508738	−0.0226610
$505$	−8.48488	−0.377572
$506$	−2.75635	−0.122535
$507$	−29.9642	−1.33076
$508$	1.83996	0.0816351
$509$	5.55764	0.246338	0.123169	−	0.992386i	$-0.460694\pi$
$509$	5.55764	0.246338	0.123169	+	0.992386i	$0.460694\pi$
$510$	−22.1972	−0.982906
$511$	0.406841	0.0179976
$512$	8.41599	0.371938
$513$	−1.13946	−0.0503086
$514$	−0.446678	−0.0197021
$515$	25.1179	1.10683
$516$	7.96333	0.350566
$517$	−19.0018	−0.835699
$518$	−0.0771029	−0.00338771
$519$	−0.624301	−0.0274038
$520$	8.51673	0.373483
$521$	0.731714	0.0320570	0.0160285	−	0.999872i	$-0.494898\pi$
$521$	0.731714	0.0320570	0.0160285	+	0.999872i	$0.494898\pi$
$522$	2.39634	0.104885
$523$	23.3248	1.01992	0.509960	−	0.860198i	$-0.329660\pi$
$523$	23.3248	1.01992	0.509960	+	0.860198i	$0.329660\pi$
$524$	4.30814	0.188202
$525$	1.10298	0.0481379
$526$	6.33186	0.276082
$527$	−14.8988	−0.649003
$528$	6.64006	0.288972
$529$	1.00000	0.0434783
$530$	−26.8752	−1.16738
$531$	22.4597	0.974669
$532$	0.439552	0.0190570
$533$	−1.45674	−0.0630986
$534$	−28.8573	−1.24878
$535$	−4.17661	−0.180570
$536$	−37.4691	−1.61842
$537$	−16.6733	−0.719507
$538$	19.4977	0.840606
$539$	−24.8800	−1.07166
$540$	−1.10519	−0.0475598
$541$	−27.8806	−1.19868	−0.599341	−	0.800494i	$-0.704571\pi$
$541$	−27.8806	−1.19868	−0.599341	+	0.800494i	$0.704571\pi$
$542$	17.9307	0.770189
$543$	−48.6366	−2.08720
$544$	−19.4884	−0.835559
$545$	6.08373	0.260598
$546$	−0.110773	−0.00474065
$547$	11.0330	0.471736	0.235868	−	0.971785i	$-0.424207\pi$
$547$	11.0330	0.471736	0.235868	+	0.971785i	$0.424207\pi$
$548$	−7.79202	−0.332859
$549$	28.5257	1.21745
$550$	19.7228	0.840984
$551$	−5.02979	−0.214276
$552$	6.50276	0.276776
$553$	−0.976036	−0.0415053
$554$	2.63488	0.111946
$555$	−13.7066	−0.581811
$556$	17.6971	0.750523
$557$	−18.1806	−0.770338	−0.385169	−	0.922846i	$-0.625857\pi$
$557$	−18.1806	−0.770338	−0.385169	+	0.922846i	$0.625857\pi$
$558$	10.7276	0.454134
$559$	2.13788	0.0904228
$560$	0.164721	0.00696075
$561$	−29.2124	−1.23335
$562$	22.0229	0.928980
$563$	6.60912	0.278541	0.139271	−	0.990254i	$-0.455524\pi$
$563$	6.60912	0.278541	0.139271	+	0.990254i	$0.455524\pi$
$564$	18.4533	0.777025
$565$	64.6484	2.71978
$566$	−5.96586	−0.250764
$567$	−0.544362	−0.0228610
$568$	20.0256	0.840254
$569$	−32.1341	−1.34713	−0.673566	−	0.739127i	$-0.735238\pi$
$569$	−32.1341	−1.34713	−0.673566	+	0.739127i	$0.735238\pi$
$570$	−33.5465	−1.40511
$571$	−32.8338	−1.37405	−0.687025	−	0.726633i	$-0.741084\pi$
$571$	−32.8338	−1.37405	−0.687025	+	0.726633i	$0.741084\pi$
$572$	4.61379	0.192912
$573$	8.25443	0.344834
$574$	0.0760536	0.00317442
$575$	−7.15541	−0.298401
$576$	9.35436	0.389765
$577$	−8.09372	−0.336946	−0.168473	−	0.985706i	$-0.553884\pi$
$577$	−8.09372	−0.336946	−0.168473	+	0.985706i	$0.553884\pi$
$578$	−4.59116	−0.190967
$579$	−19.8039	−0.823022
$580$	−4.87850	−0.202569
$581$	−0.542473	−0.0225056
$582$	22.5509	0.934766
$583$	−35.3689	−1.46483
$584$	−17.1629	−0.710205
$585$	−9.99440	−0.413218
$586$	8.60558	0.355493
$587$	6.27695	0.259078	0.129539	−	0.991574i	$-0.458650\pi$
$587$	6.27695	0.259078	0.129539	+	0.991574i	$0.458650\pi$
$588$	24.1618	0.996417
$589$	−22.5165	−0.927777
$590$	19.6300	0.808153
$591$	67.3754	2.77145
$592$	−1.20497	−0.0495241
$593$	−12.9248	−0.530758	−0.265379	−	0.964144i	$-0.585497\pi$
$593$	−12.9248	−0.530758	−0.265379	+	0.964144i	$0.585497\pi$
$594$	0.624432	0.0256208
$595$	−0.724677	−0.0297089
$596$	−25.8182	−1.05756
$597$	30.0717	1.23075
$598$	0.718625	0.0293868
$599$	13.1317	0.536546	0.268273	−	0.963343i	$-0.413547\pi$
$599$	13.1317	0.536546	0.268273	+	0.963343i	$0.413547\pi$
$600$	−46.5299	−1.89958
$601$	2.15214	0.0877877	0.0438938	−	0.999036i	$-0.486024\pi$
$601$	2.15214	0.0877877	0.0438938	+	0.999036i	$0.486024\pi$
$602$	−0.111615	−0.00454907
$603$	43.9700	1.79060
$604$	11.3342	0.461182
$605$	5.74233	0.233459
$606$	−4.65557	−0.189120
$607$	−22.1876	−0.900566	−0.450283	−	0.892886i	$-0.648677\pi$
$607$	−22.1876	−0.900566	−0.450283	+	0.892886i	$0.648677\pi$
$608$	−29.4527	−1.19447
$609$	0.154146	0.00624631
$610$	24.9317	1.00946
$611$	4.95409	0.200421
$612$	14.3983	0.582017
$613$	47.7378	1.92811	0.964057	−	0.265696i	$-0.0856019\pi$
$613$	47.7378	1.92811	0.964057	+	0.265696i	$0.0856019\pi$
$614$	−16.6647	−0.672532
$615$	13.5200	0.545180
$616$	−0.585166	−0.0235770
$617$	−12.8265	−0.516376	−0.258188	−	0.966095i	$-0.583125\pi$
$617$	−12.8265	−0.516376	−0.258188	+	0.966095i	$0.583125\pi$
$618$	13.7819	0.554391
$619$	−42.7985	−1.72022	−0.860108	−	0.510113i	$-0.829604\pi$
$619$	−42.7985	−1.72022	−0.860108	+	0.510113i	$0.829604\pi$
$620$	−21.8393	−0.877086
$621$	−0.226543	−0.00909086
$622$	19.8919	0.797591
$623$	−0.942113	−0.0377450
$624$	−1.73117	−0.0693024
$625$	−9.57713	−0.383085
$626$	23.8706	0.954063
$627$	−44.1485	−1.76312
$628$	−7.84953	−0.313230
$629$	5.30117	0.211371
$630$	0.521788	0.0207885
$631$	−2.68116	−0.106735	−0.0533676	−	0.998575i	$-0.516996\pi$
$631$	−2.68116	−0.106735	−0.0533676	+	0.998575i	$0.516996\pi$
$632$	41.1748	1.63785
$633$	10.2777	0.408502
$634$	−2.45277	−0.0974121
$635$	−4.58450	−0.181931
$636$	34.3479	1.36198
$637$	6.48662	0.257009
$638$	2.75635	0.109125
$639$	−23.5000	−0.929647
$640$	−32.6553	−1.29081
$641$	18.3001	0.722812	0.361406	−	0.932409i	$-0.382297\pi$
$641$	18.3001	0.722812	0.361406	+	0.932409i	$0.382297\pi$
$642$	−2.29166	−0.0904448
$643$	−44.1602	−1.74151	−0.870754	−	0.491719i	$-0.836369\pi$
$643$	−44.1602	−1.74151	−0.870754	+	0.491719i	$0.836369\pi$
$644$	0.0873898	0.00344364
$645$	−19.8417	−0.781265
$646$	12.9745	0.510474
$647$	−46.8890	−1.84340	−0.921699	−	0.387906i	$-0.873199\pi$
$647$	−46.8890	−1.84340	−0.921699	+	0.387906i	$0.873199\pi$
$648$	22.9643	0.902123
$649$	25.8339	1.01407
$650$	−5.14206	−0.201688
$651$	0.690055	0.0270454
$652$	−2.62461	−0.102787
$653$	42.8826	1.67813	0.839063	−	0.544035i	$-0.183104\pi$
$653$	42.8826	1.67813	0.839063	+	0.544035i	$0.183104\pi$
$654$	3.33808	0.130529
$655$	−10.7343	−0.419424
$656$	1.18857	0.0464060
$657$	20.1407	0.785763
$658$	−0.258643	−0.0100829
$659$	−4.08065	−0.158960	−0.0794799	−	0.996836i	$-0.525326\pi$
$659$	−4.08065	−0.158960	−0.0794799	+	0.996836i	$0.525326\pi$
$660$	−42.8206	−1.66679
$661$	−31.6491	−1.23101	−0.615503	−	0.788134i	$-0.711047\pi$
$661$	−31.6491	−1.23101	−0.615503	+	0.788134i	$0.711047\pi$
$662$	−3.67265	−0.142742
$663$	7.61614	0.295787
$664$	22.8846	0.888097
$665$	−1.09520	−0.0424701
$666$	−3.81699	−0.147905
$667$	−1.00000	−0.0387202
$668$	16.0034	0.619191
$669$	40.6126	1.57017
$670$	38.4301	1.48469
$671$	32.8112	1.26666
$672$	0.902627	0.0348196
$673$	2.89214	0.111484	0.0557418	−	0.998445i	$-0.482248\pi$
$673$	2.89214	0.111484	0.0557418	+	0.998445i	$0.482248\pi$
$674$	24.7108	0.951824
$675$	1.62101	0.0623927
$676$	16.9876	0.653370
$677$	−6.83199	−0.262575	−0.131287	−	0.991344i	$-0.541911\pi$
$677$	−6.83199	−0.262575	−0.131287	+	0.991344i	$0.541911\pi$
$678$	35.4719	1.36229
$679$	0.736227	0.0282538
$680$	30.5711	1.17235
$681$	−41.7630	−1.60036
$682$	12.3392	0.472491
$683$	−37.3148	−1.42781	−0.713906	−	0.700241i	$-0.753076\pi$
$683$	−37.3148	−1.42781	−0.713906	+	0.700241i	$0.753076\pi$
$684$	21.7601	0.832017
$685$	19.4148	0.741803
$686$	−0.677496	−0.0258669
$687$	45.4054	1.73232
$688$	−1.74432	−0.0665017
$689$	9.22124	0.351301
$690$	−6.66956	−0.253906
$691$	−26.5406	−1.00965	−0.504826	−	0.863221i	$-0.668443\pi$
$691$	−26.5406	−1.00965	−0.504826	+	0.863221i	$0.668443\pi$
$692$	0.353934	0.0134546
$693$	0.686694	0.0260854
$694$	−2.14082	−0.0812646
$695$	−44.0945	−1.67260
$696$	−6.50276	−0.246487
$697$	−5.22903	−0.198063
$698$	−16.8377	−0.637317
$699$	−50.0413	−1.89273
$700$	−0.625310	−0.0236345
$701$	−15.9071	−0.600804	−0.300402	−	0.953813i	$-0.597121\pi$
$701$	−15.9071	−0.600804	−0.300402	+	0.953813i	$0.597121\pi$
$702$	−0.162800	−0.00614448
$703$	8.01163	0.302164
$704$	10.7597	0.405520
$705$	−45.9789	−1.73166
$706$	25.7210	0.968023
$707$	−0.151992	−0.00571624
$708$	−25.0882	−0.942871
$709$	44.3680	1.66628	0.833138	−	0.553065i	$-0.186542\pi$
$709$	44.3680	1.66628	0.833138	+	0.553065i	$0.186542\pi$
$710$	−20.5392	−0.770823
$711$	−48.3187	−1.81209
$712$	39.7438	1.48946
$713$	−4.47664	−0.167651
$714$	−0.397623	−0.0148807
$715$	−11.4959	−0.429921
$716$	9.45260	0.353260
$717$	37.7207	1.40870
$718$	−7.33563	−0.273763
$719$	−34.4101	−1.28328	−0.641641	−	0.767005i	$-0.721746\pi$
$719$	−34.4101	−1.28328	−0.641641	+	0.767005i	$0.721746\pi$
$720$	8.15455	0.303902
$721$	0.449943	0.0167568
$722$	4.88196	0.181688
$723$	−10.8439	−0.403291
$724$	27.5736	1.02476
$725$	7.15541	0.265745
$726$	3.15076	0.116936
$727$	−8.54732	−0.317003	−0.158501	−	0.987359i	$-0.550666\pi$
$727$	−8.54732	−0.317003	−0.158501	+	0.987359i	$0.550666\pi$
$728$	0.152562	0.00565434
$729$	−28.6261	−1.06023
$730$	17.6031	0.651520
$731$	7.67399	0.283833
$732$	−31.8641	−1.17773
$733$	13.3991	0.494905	0.247453	−	0.968900i	$-0.420407\pi$
$733$	13.3991	0.494905	0.247453	+	0.968900i	$0.420407\pi$
$734$	3.10109	0.114463
$735$	−60.2023	−2.22060
$736$	−5.85566	−0.215843
$737$	50.5757	1.86298
$738$	3.76504	0.138593
$739$	−44.3998	−1.63327	−0.816637	−	0.577152i	$-0.804164\pi$
$739$	−44.3998	−1.63327	−0.816637	+	0.577152i	$0.804164\pi$
$740$	7.77066	0.285655
$741$	11.5102	0.422839
$742$	−0.481422	−0.0176736
$743$	−35.2336	−1.29259	−0.646297	−	0.763086i	$-0.723683\pi$
$743$	−35.2336	−1.29259	−0.646297	+	0.763086i	$0.723683\pi$
$744$	−29.1105	−1.06724
$745$	64.3294	2.35685
$746$	−19.5814	−0.716924
$747$	−26.8552	−0.982580
$748$	16.5614	0.605543
$749$	−0.0748167	−0.00273374
$750$	14.3757	0.524925
$751$	12.5784	0.458994	0.229497	−	0.973309i	$-0.426292\pi$
$751$	12.5784	0.458994	0.229497	+	0.973309i	$0.426292\pi$
$752$	−4.04210	−0.147400
$753$	22.8407	0.832360
$754$	−0.718625	−0.0261708
$755$	−28.2406	−1.02778
$756$	−0.0197976	−0.000720031 0
$757$	−37.9618	−1.37975	−0.689873	−	0.723931i	$-0.742334\pi$
$757$	−37.9618	−1.37975	−0.689873	+	0.723931i	$0.742334\pi$
$758$	−1.93439	−0.0702602
$759$	−8.77742	−0.318600
$760$	46.2019	1.67592
$761$	−15.3541	−0.556584	−0.278292	−	0.960496i	$-0.589768\pi$
$761$	−15.3541	−0.556584	−0.278292	+	0.960496i	$0.589768\pi$
$762$	−2.51547	−0.0911260
$763$	0.108979	0.00394532
$764$	−4.67968	−0.169305
$765$	−35.8752	−1.29707
$766$	26.4417	0.955378
$767$	−6.73531	−0.243198
$768$	−32.8527	−1.18547
$769$	−7.50788	−0.270741	−0.135371	−	0.990795i	$-0.543222\pi$
$769$	−7.50788	−0.270741	−0.135371	+	0.990795i	$0.543222\pi$
$770$	0.600176	0.0216288
$771$	−1.42242	−0.0512271
$772$	11.2274	0.404083
$773$	24.2141	0.870919	0.435459	−	0.900208i	$-0.356586\pi$
$773$	24.2141	0.870919	0.435459	+	0.900208i	$0.356586\pi$
$774$	−5.52549	−0.198610
$775$	32.0322	1.15063
$776$	−31.0583	−1.11493
$777$	−0.245529	−0.00880832
$778$	−8.18575	−0.293473
$779$	−7.90260	−0.283140
$780$	11.1640	0.399737
$781$	−27.0305	−0.967226
$782$	2.57953	0.0922437
$783$	0.226543	0.00809599
$784$	−5.29251	−0.189018
$785$	19.5581	0.698059
$786$	−5.88980	−0.210082
$787$	22.7577	0.811225	0.405613	−	0.914045i	$-0.367058\pi$
$787$	22.7577	0.811225	0.405613	+	0.914045i	$0.367058\pi$
$788$	−38.1971	−1.36072
$789$	20.1634	0.717836
$790$	−42.2309	−1.50251
$791$	1.15806	0.0411760
$792$	−28.9687	−1.02936
$793$	−8.55441	−0.303776
$794$	13.5950	0.482467
$795$	−85.5823	−3.03529
$796$	−17.0485	−0.604269
$797$	−4.06083	−0.143842	−0.0719210	−	0.997410i	$-0.522913\pi$
$797$	−4.06083	−0.143842	−0.0719210	+	0.997410i	$0.522913\pi$
$798$	−0.600926	−0.0212726
$799$	17.7828	0.629112
$800$	41.8997	1.48138
$801$	−46.6394	−1.64792
$802$	17.2118	0.607771
$803$	23.1664	0.817525
$804$	−49.1158	−1.73218
$805$	−0.217743	−0.00767444
$806$	−3.21702	−0.113315
$807$	62.0892	2.18564
$808$	6.41189	0.225570
$809$	48.2669	1.69697	0.848487	−	0.529217i	$-0.177514\pi$
$809$	48.2669	1.69697	0.848487	+	0.529217i	$0.177514\pi$
$810$	−23.5533	−0.827580
$811$	−31.6174	−1.11024	−0.555118	−	0.831771i	$-0.687327\pi$
$811$	−31.6174	−1.11024	−0.555118	+	0.831771i	$0.687327\pi$
$812$	−0.0873898	−0.00306678
$813$	57.0991	2.00255
$814$	−4.39042	−0.153884
$815$	6.53955	0.229070
$816$	−6.21410	−0.217537
$817$	11.5977	0.405751
$818$	−13.7880	−0.482085
$819$	−0.179032	−0.00625590
$820$	−7.66490	−0.267670
$821$	−34.0753	−1.18924	−0.594618	−	0.804009i	$-0.702697\pi$
$821$	−34.0753	−1.18924	−0.594618	+	0.804009i	$0.702697\pi$
$822$	10.6527	0.371557
$823$	48.4018	1.68718	0.843591	−	0.536987i	$-0.180438\pi$
$823$	48.4018	1.68718	0.843591	+	0.536987i	$0.180438\pi$
$824$	−18.9812	−0.661241
$825$	62.8060	2.18663
$826$	0.351637	0.0122350
$827$	−3.72177	−0.129419	−0.0647094	−	0.997904i	$-0.520612\pi$
$827$	−3.72177	−0.129419	−0.0647094	+	0.997904i	$0.520612\pi$
$828$	4.32624	0.150347
$829$	−23.5721	−0.818692	−0.409346	−	0.912379i	$-0.634243\pi$
$829$	−23.5721	−0.818692	−0.409346	+	0.912379i	$0.634243\pi$
$830$	−23.4716	−0.814713
$831$	8.39062	0.291067
$832$	−2.80522	−0.0972535
$833$	23.2839	0.806740
$834$	−24.1942	−0.837778
$835$	−39.8746	−1.37992
$836$	25.0291	0.865650
$837$	1.01415	0.0350542
$838$	15.2395	0.526442
$839$	45.6828	1.57714	0.788572	−	0.614942i	$-0.210821\pi$
$839$	45.6828	1.57714	0.788572	+	0.614942i	$0.210821\pi$
$840$	−1.41593	−0.0488543
$841$	1.00000	0.0344828
$842$	25.5472	0.880414
$843$	70.1305	2.41542
$844$	−5.82673	−0.200564
$845$	−42.3268	−1.45609
$846$	−12.8041	−0.440215
$847$	0.102864	0.00353444
$848$	−7.52371	−0.258365
$849$	−18.9979	−0.652007
$850$	−18.4576	−0.633090
$851$	1.59284	0.0546018
$852$	26.2502	0.899318
$853$	24.4605	0.837510	0.418755	−	0.908099i	$-0.362467\pi$
$853$	24.4605	0.837510	0.418755	+	0.908099i	$0.362467\pi$
$854$	0.446609	0.0152826
$855$	−54.2181	−1.85422
$856$	3.15620	0.107877
$857$	−5.28505	−0.180534	−0.0902670	−	0.995918i	$-0.528772\pi$
$857$	−5.28505	−0.180534	−0.0902670	+	0.995918i	$0.528772\pi$
$858$	−6.30767	−0.215340
$859$	−46.2825	−1.57914	−0.789570	−	0.613661i	$-0.789696\pi$
$859$	−46.2825	−1.57914	−0.789570	+	0.613661i	$0.789696\pi$
$860$	11.2488	0.383582
$861$	0.242188	0.00825374
$862$	2.62759	0.0894962
$863$	33.5105	1.14071	0.570355	−	0.821398i	$-0.306806\pi$
$863$	33.5105	1.14071	0.570355	+	0.821398i	$0.306806\pi$
$864$	1.32656	0.0451305
$865$	−0.881874	−0.0299846
$866$	−15.3251	−0.520769
$867$	−14.6202	−0.496530
$868$	−0.391212	−0.0132786
$869$	−55.5777	−1.88534
$870$	6.66956	0.226119
$871$	−13.1859	−0.446787
$872$	−4.59738	−0.155687
$873$	36.4470	1.23354
$874$	3.89843	0.131866
$875$	0.469326	0.0158661
$876$	−22.4977	−0.760127
$877$	20.1578	0.680680	0.340340	−	0.940302i	$-0.389458\pi$
$877$	20.1578	0.680680	0.340340	+	0.940302i	$0.389458\pi$
$878$	−13.6698	−0.461333
$879$	27.4039	0.924311
$880$	9.37961	0.316187
$881$	−37.7877	−1.27310	−0.636549	−	0.771236i	$-0.719639\pi$
$881$	−37.7877	−1.27310	−0.636549	+	0.771236i	$0.719639\pi$
$882$	−16.7651	−0.564509
$883$	−25.0568	−0.843228	−0.421614	−	0.906775i	$-0.638536\pi$
$883$	−25.0568	−0.843228	−0.421614	+	0.906775i	$0.638536\pi$
$884$	−4.31782	−0.145224
$885$	62.5104	2.10126
$886$	−13.5881	−0.456502
$887$	−54.0378	−1.81441	−0.907206	−	0.420688i	$-0.861789\pi$
$887$	−54.0378	−1.81441	−0.907206	+	0.420688i	$0.861789\pi$
$888$	10.3578	0.347586
$889$	−0.0821234	−0.00275433
$890$	−40.7632	−1.36639
$891$	−30.9972	−1.03844
$892$	−23.0245	−0.770916
$893$	26.8751	0.899342
$894$	35.2969	1.18051
$895$	−23.5524	−0.787269
$896$	−0.584963	−0.0195423
$897$	2.28842	0.0764080
$898$	13.4123	0.447575
$899$	4.47664	0.149304
$900$	−30.9561	−1.03187
$901$	33.0999	1.10272
$902$	4.33067	0.144195
$903$	−0.355429	−0.0118279
$904$	−48.8538	−1.62485
$905$	−68.7031	−2.28377
$906$	−15.4954	−0.514799
$907$	13.0995	0.434961	0.217481	−	0.976065i	$-0.430216\pi$
$907$	13.0995	0.434961	0.217481	+	0.976065i	$0.430216\pi$
$908$	23.6767	0.785738
$909$	−7.52437	−0.249568
$910$	−0.156476	−0.00518712
$911$	−7.72405	−0.255909	−0.127955	−	0.991780i	$-0.540841\pi$
$911$	−7.72405	−0.255909	−0.127955	+	0.991780i	$0.540841\pi$
$912$	−9.39134	−0.310978
$913$	−30.8897	−1.02230
$914$	27.5930	0.912695
$915$	79.3935	2.62467
$916$	−25.7416	−0.850528
$917$	−0.192286	−0.00634985
$918$	−0.584374	−0.0192872
$919$	−9.57286	−0.315779	−0.157890	−	0.987457i	$-0.550469\pi$
$919$	−9.57286	−0.315779	−0.157890	+	0.987457i	$0.550469\pi$
$920$	9.18566	0.302842
$921$	−53.0676	−1.74864
$922$	22.4714	0.740056
$923$	7.04728	0.231964
$924$	−0.767057	−0.0252343
$925$	−11.3974	−0.374745
$926$	11.4861	0.377457
$927$	22.2745	0.731590
$928$	5.85566	0.192222
$929$	16.9036	0.554590	0.277295	−	0.960785i	$-0.410562\pi$
$929$	16.9036	0.554590	0.277295	+	0.960785i	$0.410562\pi$
$930$	29.8572	0.979055
$931$	35.1889	1.15327
$932$	28.3699	0.929286
$933$	63.3444	2.07380
$934$	16.3873	0.536208
$935$	−41.2648	−1.34950
$936$	7.55262	0.246865
$937$	−48.2978	−1.57782	−0.788910	−	0.614509i	$-0.789354\pi$
$937$	−48.2978	−1.57782	−0.788910	+	0.614509i	$0.789354\pi$
$938$	0.688409	0.0224774
$939$	76.0145	2.48064
$940$	26.0668	0.850204
$941$	18.2235	0.594070	0.297035	−	0.954867i	$-0.404002\pi$
$941$	18.2235	0.594070	0.297035	+	0.954867i	$0.404002\pi$
$942$	10.7314	0.349646
$943$	−1.57116	−0.0511640
$944$	5.49542	0.178861
$945$	0.0493282	0.00160465
$946$	−6.35558	−0.206638
$947$	−22.0443	−0.716343	−0.358172	−	0.933656i	$-0.616600\pi$
$947$	−22.0443	−0.716343	−0.358172	+	0.933656i	$0.616600\pi$
$948$	53.9734	1.75297
$949$	−6.03986	−0.196062
$950$	−27.8949	−0.905029
$951$	−7.81070	−0.253279
$952$	0.547628	0.0177487
$953$	−12.7950	−0.414470	−0.207235	−	0.978291i	$-0.566446\pi$
$953$	−12.7950	−0.414470	−0.207235	+	0.978291i	$0.566446\pi$
$954$	−23.8329	−0.771617
$955$	11.6600	0.377310
$956$	−21.3850	−0.691639
$957$	8.77742	0.283734
$958$	−21.1945	−0.684764
$959$	0.347783	0.0112305
$960$	26.0352	0.840284
$961$	−10.9597	−0.353540
$962$	1.14465	0.0369051
$963$	−3.70381	−0.119353
$964$	6.14775	0.198006
$965$	−27.9745	−0.900532
$966$	−0.119474	−0.00384400
$967$	−1.59257	−0.0512136	−0.0256068	−	0.999672i	$-0.508152\pi$
$967$	−1.59257	−0.0512136	−0.0256068	+	0.999672i	$0.508152\pi$
$968$	−4.33939	−0.139473
$969$	41.3164	1.32727
$970$	31.8550	1.02280
$971$	1.41506	0.0454115	0.0227057	−	0.999742i	$-0.492772\pi$
$971$	1.41506	0.0454115	0.0227057	+	0.999742i	$0.492772\pi$
$972$	31.0534	0.996039
$973$	−0.789877	−0.0253223
$974$	−11.0570	−0.354288
$975$	−16.3746	−0.524406
$976$	6.97964	0.223413
$977$	−52.4116	−1.67680	−0.838398	−	0.545058i	$-0.816508\pi$
$977$	−52.4116	−1.67680	−0.838398	+	0.545058i	$0.816508\pi$
$978$	3.58819	0.114738
$979$	−53.6461	−1.71454
$980$	34.1305	1.09026
$981$	5.39504	0.172250
$982$	−27.3154	−0.871668
$983$	26.8515	0.856430	0.428215	−	0.903677i	$-0.359143\pi$
$983$	26.8515	0.856430	0.428215	+	0.903677i	$0.359143\pi$
$984$	−10.2169	−0.325702
$985$	95.1731	3.03247
$986$	−2.57953	−0.0821489
$987$	−0.823631	−0.0262165
$988$	−6.52550	−0.207604
$989$	2.30580	0.0733201
$990$	29.7118	0.944302
$991$	57.7403	1.83418	0.917090	−	0.398679i	$-0.130531\pi$
$991$	57.7403	1.83418	0.917090	+	0.398679i	$0.130531\pi$
$992$	26.2137	0.832285
$993$	−11.6953	−0.371140
$994$	−0.367924	−0.0116699
$995$	42.4786	1.34666
$996$	29.9980	0.950523
$997$	−1.93519	−0.0612882	−0.0306441	−	0.999530i	$-0.509756\pi$
$997$	−1.93519	−0.0612882	−0.0306441	+	0.999530i	$0.509756\pi$
$998$	0.789995	0.0250069
$999$	−0.360846	−0.0114167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.7	✓	13
3.2	odd	2		6003.2.a.o.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.7	✓	13	1.1	even	1	trivial
6003.2.a.o.1.7		13	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+0.775068 q^{2} +2.46815 q^{3} -1.39927 q^{4} +3.48646 q^{5} +1.91299 q^{6} +0.0624539 q^{7} -2.63467 q^{8} +3.09179 q^{9} +O(q^{10})\)	\(q+0.775068 q^{2} +2.46815 q^{3} -1.39927 q^{4} +3.48646 q^{5} +1.91299 q^{6} +0.0624539 q^{7} -2.63467 q^{8} +3.09179 q^{9} +2.70224 q^{10} +3.55627 q^{11} -3.45361 q^{12} -0.927177 q^{13} +0.0484060 q^{14} +8.60513 q^{15} +0.756494 q^{16} -3.32813 q^{17} +2.39634 q^{18} -5.02979 q^{19} -4.87850 q^{20} +0.154146 q^{21} +2.75635 q^{22} -1.00000 q^{23} -6.50276 q^{24} +7.15541 q^{25} -0.718625 q^{26} +0.226543 q^{27} -0.0873898 q^{28} +1.00000 q^{29} +6.66956 q^{30} +4.47664 q^{31} +5.85566 q^{32} +8.77742 q^{33} -2.57953 q^{34} +0.217743 q^{35} -4.32624 q^{36} -1.59284 q^{37} -3.89843 q^{38} -2.28842 q^{39} -9.18566 q^{40} +1.57116 q^{41} +0.119474 q^{42} -2.30580 q^{43} -4.97618 q^{44} +10.7794 q^{45} -0.775068 q^{46} -5.34319 q^{47} +1.86714 q^{48} -6.99610 q^{49} +5.54593 q^{50} -8.21434 q^{51} +1.29737 q^{52} -9.94550 q^{53} +0.175586 q^{54} +12.3988 q^{55} -0.164545 q^{56} -12.4143 q^{57} +0.775068 q^{58} +7.26432 q^{59} -12.0409 q^{60} +9.22630 q^{61} +3.46970 q^{62} +0.193094 q^{63} +3.02555 q^{64} -3.23257 q^{65} +6.80310 q^{66} +14.2216 q^{67} +4.65695 q^{68} -2.46815 q^{69} +0.168766 q^{70} -7.60080 q^{71} -8.14582 q^{72} +6.51425 q^{73} -1.23456 q^{74} +17.6607 q^{75} +7.03803 q^{76} +0.222103 q^{77} -1.77368 q^{78} -15.6281 q^{79} +2.63749 q^{80} -8.71622 q^{81} +1.21776 q^{82} -8.68598 q^{83} -0.215692 q^{84} -11.6034 q^{85} -1.78715 q^{86} +2.46815 q^{87} -9.36957 q^{88} -15.0849 q^{89} +8.35476 q^{90} -0.0579058 q^{91} +1.39927 q^{92} +11.0490 q^{93} -4.14134 q^{94} -17.5362 q^{95} +14.4527 q^{96} +11.7883 q^{97} -5.42245 q^{98} +10.9952 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

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