LMFDB - Embedded newform 667.2.a.d.1.2

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.42429$ 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)

$f(q)$	$=$	$q-2.42429 q^{2} -1.02036 q^{3} +3.87720 q^{4} -0.275174 q^{5} +2.47365 q^{6} -5.16310 q^{7} -4.55089 q^{8} -1.95887 q^{9} +O(q^{10})$	\(q-2.42429 q^{2} -1.02036 q^{3} +3.87720 q^{4} -0.275174 q^{5} +2.47365 q^{6} -5.16310 q^{7} -4.55089 q^{8} -1.95887 q^{9} +0.667103 q^{10} -4.59700 q^{11} -3.95614 q^{12} +2.58445 q^{13} +12.5169 q^{14} +0.280777 q^{15} +3.27829 q^{16} +6.77779 q^{17} +4.74887 q^{18} -7.93422 q^{19} -1.06691 q^{20} +5.26822 q^{21} +11.1445 q^{22} +1.00000 q^{23} +4.64355 q^{24} -4.92428 q^{25} -6.26548 q^{26} +5.05983 q^{27} -20.0184 q^{28} -1.00000 q^{29} -0.680686 q^{30} -1.54451 q^{31} +1.15424 q^{32} +4.69059 q^{33} -16.4314 q^{34} +1.42075 q^{35} -7.59492 q^{36} -1.24464 q^{37} +19.2349 q^{38} -2.63707 q^{39} +1.25229 q^{40} -1.39786 q^{41} -12.7717 q^{42} -0.777148 q^{43} -17.8235 q^{44} +0.539029 q^{45} -2.42429 q^{46} -5.57928 q^{47} -3.34504 q^{48} +19.6576 q^{49} +11.9379 q^{50} -6.91579 q^{51} +10.0205 q^{52} +11.5021 q^{53} -12.2665 q^{54} +1.26498 q^{55} +23.4967 q^{56} +8.09576 q^{57} +2.42429 q^{58} +7.31928 q^{59} +1.08863 q^{60} +1.28650 q^{61} +3.74434 q^{62} +10.1138 q^{63} -9.35480 q^{64} -0.711175 q^{65} -11.3714 q^{66} +10.1934 q^{67} +26.2789 q^{68} -1.02036 q^{69} -3.44432 q^{70} +4.16451 q^{71} +8.91458 q^{72} -10.2878 q^{73} +3.01736 q^{74} +5.02454 q^{75} -30.7626 q^{76} +23.7348 q^{77} +6.39304 q^{78} -1.19088 q^{79} -0.902101 q^{80} +0.713751 q^{81} +3.38881 q^{82} -5.53442 q^{83} +20.4260 q^{84} -1.86507 q^{85} +1.88404 q^{86} +1.02036 q^{87} +20.9204 q^{88} +13.4423 q^{89} -1.30677 q^{90} -13.3438 q^{91} +3.87720 q^{92} +1.57596 q^{93} +13.5258 q^{94} +2.18329 q^{95} -1.17774 q^{96} +3.41413 q^{97} -47.6559 q^{98} +9.00490 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * 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 $

$2$	−2.42429	−1.71423	−0.857117	−	0.515121i	$-0.827747\pi$
$2$	−2.42429	−1.71423	−0.857117	+	0.515121i	$0.827747\pi$
$3$	−1.02036	−0.589105	−0.294553	−	0.955635i	$-0.595171\pi$
$3$	−1.02036	−0.589105	−0.294553	+	0.955635i	$0.595171\pi$
$4$	3.87720	1.93860
$5$	−0.275174	−0.123062	−0.0615308	−	0.998105i	$-0.519598\pi$
$5$	−0.275174	−0.123062	−0.0615308	+	0.998105i	$0.519598\pi$
$6$	2.47365	1.00986
$7$	−5.16310	−1.95147	−0.975735	−	0.218956i	$-0.929735\pi$
$7$	−5.16310	−1.95147	−0.975735	+	0.218956i	$0.929735\pi$
$8$	−4.55089	−1.60898
$9$	−1.95887	−0.652955
$10$	0.667103	0.210957
$11$	−4.59700	−1.38605	−0.693024	−	0.720915i	$-0.743722\pi$
$11$	−4.59700	−1.38605	−0.693024	+	0.720915i	$0.743722\pi$
$12$	−3.95614	−1.14204
$13$	2.58445	0.716799	0.358399	−	0.933568i	$-0.383323\pi$
$13$	2.58445	0.716799	0.358399	+	0.933568i	$0.383323\pi$
$14$	12.5169	3.34528
$15$	0.280777	0.0724963
$16$	3.27829	0.819573
$17$	6.77779	1.64386	0.821928	−	0.569591i	$-0.192899\pi$
$17$	6.77779	1.64386	0.821928	+	0.569591i	$0.192899\pi$
$18$	4.74887	1.11932
$19$	−7.93422	−1.82024	−0.910118	−	0.414350i	$-0.864009\pi$
$19$	−7.93422	−1.82024	−0.910118	+	0.414350i	$0.864009\pi$
$20$	−1.06691	−0.238567
$21$	5.26822	1.14962
$22$	11.1445	2.37601
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	4.64355	0.947860
$25$	−4.92428	−0.984856
$26$	−6.26548	−1.22876
$27$	5.05983	0.973764
$28$	−20.0184	−3.78312
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.680686	−0.124276
$31$	−1.54451	−0.277402	−0.138701	−	0.990334i	$-0.544293\pi$
$31$	−1.54451	−0.277402	−0.138701	+	0.990334i	$0.544293\pi$
$32$	1.15424	0.204043
$33$	4.69059	0.816528
$34$	−16.4314	−2.81796
$35$	1.42075	0.240151
$36$	−7.59492	−1.26582
$37$	−1.24464	−0.204617	−0.102308	−	0.994753i	$-0.532623\pi$
$37$	−1.24464	−0.204617	−0.102308	+	0.994753i	$0.532623\pi$
$38$	19.2349	3.12031
$39$	−2.63707	−0.422270
$40$	1.25229	0.198004
$41$	−1.39786	−0.218308	−0.109154	−	0.994025i	$-0.534814\pi$
$41$	−1.39786	−0.218308	−0.109154	+	0.994025i	$0.534814\pi$
$42$	−12.7717	−1.97072
$43$	−0.777148	−0.118514	−0.0592570	−	0.998243i	$-0.518873\pi$
$43$	−0.777148	−0.118514	−0.0592570	+	0.998243i	$0.518873\pi$
$44$	−17.8235	−2.68699
$45$	0.539029	0.0803538
$46$	−2.42429	−0.357443
$47$	−5.57928	−0.813822	−0.406911	−	0.913468i	$-0.633394\pi$
$47$	−5.57928	−0.813822	−0.406911	+	0.913468i	$0.633394\pi$
$48$	−3.34504	−0.482814
$49$	19.6576	2.80823
$50$	11.9379	1.68827
$51$	−6.91579	−0.968404
$52$	10.0205	1.38959
$53$	11.5021	1.57994	0.789970	−	0.613145i	$-0.210096\pi$
$53$	11.5021	1.57994	0.789970	+	0.613145i	$0.210096\pi$
$54$	−12.2665	−1.66926
$55$	1.26498	0.170569
$56$	23.4967	3.13988
$57$	8.09576	1.07231
$58$	2.42429	0.318325
$59$	7.31928	0.952889	0.476444	−	0.879205i	$-0.341925\pi$
$59$	7.31928	0.952889	0.476444	+	0.879205i	$0.341925\pi$
$60$	1.08863	0.140541
$61$	1.28650	0.164719	0.0823596	−	0.996603i	$-0.473754\pi$
$61$	1.28650	0.164719	0.0823596	+	0.996603i	$0.473754\pi$
$62$	3.74434	0.475532
$63$	10.1138	1.27422
$64$	−9.35480	−1.16935
$65$	−0.711175	−0.0882105
$66$	−11.3714	−1.39972
$67$	10.1934	1.24533	0.622663	−	0.782490i	$-0.286051\pi$
$67$	10.1934	1.24533	0.622663	+	0.782490i	$0.286051\pi$
$68$	26.2789	3.18678
$69$	−1.02036	−0.122837
$70$	−3.44432	−0.411675
$71$	4.16451	0.494236	0.247118	−	0.968985i	$-0.420516\pi$
$71$	4.16451	0.494236	0.247118	+	0.968985i	$0.420516\pi$
$72$	8.91458	1.05059
$73$	−10.2878	−1.20409	−0.602046	−	0.798462i	$-0.705648\pi$
$73$	−10.2878	−1.20409	−0.602046	+	0.798462i	$0.705648\pi$
$74$	3.01736	0.350761
$75$	5.02454	0.580184
$76$	−30.7626	−3.52871
$77$	23.7348	2.70483
$78$	6.39304	0.723870
$79$	−1.19088	−0.133985	−0.0669923	−	0.997753i	$-0.521340\pi$
$79$	−1.19088	−0.133985	−0.0669923	+	0.997753i	$0.521340\pi$
$80$	−0.902101	−0.100858
$81$	0.713751	0.0793056
$82$	3.38881	0.374232
$83$	−5.53442	−0.607482	−0.303741	−	0.952755i	$-0.598236\pi$
$83$	−5.53442	−0.607482	−0.303741	+	0.952755i	$0.598236\pi$
$84$	20.4260	2.22866
$85$	−1.86507	−0.202296
$86$	1.88404	0.203161
$87$	1.02036	0.109394
$88$	20.9204	2.23013
$89$	13.4423	1.42488	0.712441	−	0.701732i	$-0.247590\pi$
$89$	13.4423	1.42488	0.712441	+	0.701732i	$0.247590\pi$
$90$	−1.30677	−0.137745
$91$	−13.3438	−1.39881
$92$	3.87720	0.404226
$93$	1.57596	0.163419
$94$	13.5258	1.39508
$95$	2.18329	0.224001
$96$	−1.17774	−0.120203
$97$	3.41413	0.346652	0.173326	−	0.984865i	$-0.444549\pi$
$97$	3.41413	0.346652	0.173326	+	0.984865i	$0.444549\pi$
$98$	−47.6559	−4.81397
$99$	9.00490	0.905027
$100$	−19.0924	−1.90924
$101$	−6.22013	−0.618926	−0.309463	−	0.950912i	$-0.600149\pi$
$101$	−6.22013	−0.618926	−0.309463	+	0.950912i	$0.600149\pi$
$102$	16.7659	1.66007
$103$	−5.78182	−0.569699	−0.284850	−	0.958572i	$-0.591944\pi$
$103$	−5.78182	−0.569699	−0.284850	+	0.958572i	$0.591944\pi$
$104$	−11.7616	−1.15332
$105$	−1.44968	−0.141474
$106$	−27.8846	−2.70839
$107$	18.4577	1.78437	0.892185	−	0.451670i	$-0.149171\pi$
$107$	18.4577	1.78437	0.892185	+	0.451670i	$0.149171\pi$
$108$	19.6180	1.88774
$109$	−0.772038	−0.0739478	−0.0369739	−	0.999316i	$-0.511772\pi$
$109$	−0.772038	−0.0739478	−0.0369739	+	0.999316i	$0.511772\pi$
$110$	−3.06667	−0.292396
$111$	1.26998	0.120541
$112$	−16.9261	−1.59937
$113$	−12.7996	−1.20408	−0.602041	−	0.798465i	$-0.705646\pi$
$113$	−12.7996	−1.20408	−0.602041	+	0.798465i	$0.705646\pi$
$114$	−19.6265	−1.83819
$115$	−0.275174	−0.0256601
$116$	−3.87720	−0.359989
$117$	−5.06260	−0.468037
$118$	−17.7441	−1.63347
$119$	−34.9944	−3.20793
$120$	−1.27778	−0.116645
$121$	10.1324	0.921127
$122$	−3.11885	−0.282367
$123$	1.42632	0.128607
$124$	−5.98837	−0.537772
$125$	2.73091	0.244260
$126$	−24.5189	−2.18432
$127$	15.1484	1.34420	0.672102	−	0.740458i	$-0.265392\pi$
$127$	15.1484	1.34420	0.672102	+	0.740458i	$0.265392\pi$
$128$	20.3703	1.80050
$129$	0.792971	0.0698172
$130$	1.72410	0.151213
$131$	−3.96670	−0.346572	−0.173286	−	0.984872i	$-0.555438\pi$
$131$	−3.96670	−0.346572	−0.173286	+	0.984872i	$0.555438\pi$
$132$	18.1864	1.58292
$133$	40.9652	3.55213
$134$	−24.7119	−2.13478
$135$	−1.39233	−0.119833
$136$	−30.8450	−2.64494
$137$	8.86496	0.757385	0.378692	−	0.925523i	$-0.376374\pi$
$137$	8.86496	0.757385	0.378692	+	0.925523i	$0.376374\pi$
$138$	2.47365	0.210571
$139$	17.1764	1.45689	0.728443	−	0.685106i	$-0.240244\pi$
$139$	17.1764	1.45689	0.728443	+	0.685106i	$0.240244\pi$
$140$	5.50855	0.465557
$141$	5.69287	0.479426
$142$	−10.0960	−0.847237
$143$	−11.8807	−0.993517
$144$	−6.42173	−0.535144
$145$	0.275174	0.0228520
$146$	24.9406	2.06410
$147$	−20.0579	−1.65434
$148$	−4.82570	−0.396670
$149$	−19.2755	−1.57911	−0.789557	−	0.613677i	$-0.789690\pi$
$149$	−19.2755	−1.57911	−0.789557	+	0.613677i	$0.789690\pi$
$150$	−12.1810	−0.994571
$151$	5.14403	0.418615	0.209307	−	0.977850i	$-0.432879\pi$
$151$	5.14403	0.418615	0.209307	+	0.977850i	$0.432879\pi$
$152$	36.1078	2.92873
$153$	−13.2768	−1.07336
$154$	−57.5401	−4.63671
$155$	0.425009	0.0341376
$156$	−10.2245	−0.818613
$157$	−17.4758	−1.39472	−0.697360	−	0.716721i	$-0.745642\pi$
$157$	−17.4758	−1.39472	−0.697360	+	0.716721i	$0.745642\pi$
$158$	2.88704	0.229681
$159$	−11.7363	−0.930751
$160$	−0.317617	−0.0251098
$161$	−5.16310	−0.406909
$162$	−1.73034	−0.135948
$163$	−11.5511	−0.904750	−0.452375	−	0.891828i	$-0.649423\pi$
$163$	−11.5511	−0.904750	−0.452375	+	0.891828i	$0.649423\pi$
$164$	−5.41977	−0.423213
$165$	−1.29073	−0.100483
$166$	13.4171	1.04137
$167$	16.8806	1.30626	0.653128	−	0.757247i	$-0.273456\pi$
$167$	16.8806	1.30626	0.653128	+	0.757247i	$0.273456\pi$
$168$	−23.9751	−1.84972
$169$	−6.32059	−0.486200
$170$	4.52149	0.346782
$171$	15.5421	1.18853
$172$	−3.01316	−0.229751
$173$	−2.08494	−0.158515	−0.0792574	−	0.996854i	$-0.525255\pi$
$173$	−2.08494	−0.158515	−0.0792574	+	0.996854i	$0.525255\pi$
$174$	−2.47365	−0.187527
$175$	25.4246	1.92192
$176$	−15.0703	−1.13597
$177$	−7.46830	−0.561352
$178$	−32.5881	−2.44258
$179$	8.87412	0.663283	0.331641	−	0.943406i	$-0.392398\pi$
$179$	8.87412	0.663283	0.331641	+	0.943406i	$0.392398\pi$
$180$	2.08993	0.155774
$181$	−21.0114	−1.56176	−0.780881	−	0.624680i	$-0.785229\pi$
$181$	−21.0114	−1.56176	−0.780881	+	0.624680i	$0.785229\pi$
$182$	32.3493	2.39789
$183$	−1.31269	−0.0970369
$184$	−4.55089	−0.335496
$185$	0.342492	0.0251805
$186$	−3.82058	−0.280138
$187$	−31.1575	−2.27846
$188$	−21.6320	−1.57768
$189$	−26.1244	−1.90027
$190$	−5.29295	−0.383991
$191$	−9.11834	−0.659780	−0.329890	−	0.944019i	$-0.607012\pi$
$191$	−9.11834	−0.659780	−0.329890	+	0.944019i	$0.607012\pi$
$192$	9.54526	0.688870
$193$	−1.41977	−0.102197	−0.0510987	−	0.998694i	$-0.516272\pi$
$193$	−1.41977	−0.102197	−0.0510987	+	0.998694i	$0.516272\pi$
$194$	−8.27684	−0.594243
$195$	0.725655	0.0519652
$196$	76.2166	5.44404
$197$	−2.98927	−0.212977	−0.106488	−	0.994314i	$-0.533961\pi$
$197$	−2.98927	−0.212977	−0.106488	+	0.994314i	$0.533961\pi$
$198$	−21.8305	−1.55143
$199$	14.2526	1.01034	0.505170	−	0.863020i	$-0.331430\pi$
$199$	14.2526	1.01034	0.505170	+	0.863020i	$0.331430\pi$
$200$	22.4098	1.58462
$201$	−10.4010	−0.733628
$202$	15.0794	1.06098
$203$	5.16310	0.362379
$204$	−26.8139	−1.87735
$205$	0.384654	0.0268654
$206$	14.0168	0.976598
$207$	−1.95887	−0.136151
$208$	8.47259	0.587469
$209$	36.4736	2.52293
$210$	3.51445	0.242520
$211$	−4.99505	−0.343874	−0.171937	−	0.985108i	$-0.555002\pi$
$211$	−4.99505	−0.343874	−0.171937	+	0.985108i	$0.555002\pi$
$212$	44.5961	3.06287
$213$	−4.24930	−0.291157
$214$	−44.7468	−3.05883
$215$	0.213851	0.0145845
$216$	−23.0267	−1.56677
$217$	7.97446	0.541341
$218$	1.87165	0.126764
$219$	10.4972	0.709337
$220$	4.90457	0.330666
$221$	17.5169	1.17831
$222$	−3.07880	−0.206635
$223$	17.0823	1.14391	0.571956	−	0.820284i	$-0.306185\pi$
$223$	17.0823	1.14391	0.571956	+	0.820284i	$0.306185\pi$
$224$	−5.95945	−0.398183
$225$	9.64600	0.643067
$226$	31.0299	2.06408
$227$	−5.65703	−0.375471	−0.187735	−	0.982220i	$-0.560115\pi$
$227$	−5.65703	−0.375471	−0.187735	+	0.982220i	$0.560115\pi$
$228$	31.3889	2.07878
$229$	−13.6271	−0.900503	−0.450251	−	0.892902i	$-0.648666\pi$
$229$	−13.6271	−0.900503	−0.450251	+	0.892902i	$0.648666\pi$
$230$	0.667103	0.0439875
$231$	−24.2180	−1.59343
$232$	4.55089	0.298781
$233$	−8.31854	−0.544965	−0.272483	−	0.962161i	$-0.587845\pi$
$233$	−8.31854	−0.544965	−0.272483	+	0.962161i	$0.587845\pi$
$234$	12.2732	0.802326
$235$	1.53527	0.100150
$236$	28.3783	1.84727
$237$	1.21513	0.0789310
$238$	84.8368	5.49915
$239$	10.6654	0.689886	0.344943	−	0.938624i	$-0.387898\pi$
$239$	10.6654	0.689886	0.344943	+	0.938624i	$0.387898\pi$
$240$	0.920468	0.0594159
$241$	−19.2982	−1.24311	−0.621554	−	0.783371i	$-0.713498\pi$
$241$	−19.2982	−1.24311	−0.621554	+	0.783371i	$0.713498\pi$
$242$	−24.5639	−1.57903
$243$	−15.9078	−1.02048
$244$	4.98801	0.319325
$245$	−5.40927	−0.345586
$246$	−3.45781	−0.220462
$247$	−20.5056	−1.30474
$248$	7.02889	0.446335
$249$	5.64710	0.357870
$250$	−6.62052	−0.418718
$251$	7.91467	0.499570	0.249785	−	0.968301i	$-0.419640\pi$
$251$	7.91467	0.499570	0.249785	+	0.968301i	$0.419640\pi$
$252$	39.2133	2.47021
$253$	−4.59700	−0.289011
$254$	−36.7242	−2.30428
$255$	1.90305	0.119173
$256$	−30.6740	−1.91712
$257$	5.60389	0.349561	0.174781	−	0.984607i	$-0.444078\pi$
$257$	5.60389	0.349561	0.174781	+	0.984607i	$0.444078\pi$
$258$	−1.92239	−0.119683
$259$	6.42618	0.399304
$260$	−2.75737	−0.171005
$261$	1.95887	0.121251
$262$	9.61644	0.594106
$263$	−18.0911	−1.11555	−0.557774	−	0.829993i	$-0.688344\pi$
$263$	−18.0911	−1.11555	−0.557774	+	0.829993i	$0.688344\pi$
$264$	−21.3464	−1.31378
$265$	−3.16509	−0.194430
$266$	−99.3117	−6.08919
$267$	−13.7160	−0.839405
$268$	39.5220	2.41419
$269$	8.37348	0.510540	0.255270	−	0.966870i	$-0.417836\pi$
$269$	8.37348	0.510540	0.255270	+	0.966870i	$0.417836\pi$
$270$	3.37543	0.205422
$271$	2.69125	0.163482	0.0817408	−	0.996654i	$-0.473952\pi$
$271$	2.69125	0.163482	0.0817408	+	0.996654i	$0.473952\pi$
$272$	22.2196	1.34726
$273$	13.6155	0.824047
$274$	−21.4913	−1.29834
$275$	22.6369	1.36506
$276$	−3.95614	−0.238132
$277$	32.6291	1.96049	0.980247	−	0.197776i	$-0.0633718\pi$
$277$	32.6291	1.96049	0.980247	+	0.197776i	$0.0633718\pi$
$278$	−41.6408	−2.49745
$279$	3.02549	0.181131
$280$	−6.46569	−0.386399
$281$	−21.2594	−1.26823	−0.634114	−	0.773239i	$-0.718635\pi$
$281$	−21.2594	−1.26823	−0.634114	+	0.773239i	$0.718635\pi$
$282$	−13.8012	−0.821850
$283$	−6.43670	−0.382622	−0.191311	−	0.981529i	$-0.561274\pi$
$283$	−6.43670	−0.382622	−0.191311	+	0.981529i	$0.561274\pi$
$284$	16.1466	0.958127
$285$	−2.22775	−0.131960
$286$	28.8024	1.70312
$287$	7.21727	0.426022
$288$	−2.26100	−0.133231
$289$	28.9385	1.70226
$290$	−0.667103	−0.0391737
$291$	−3.48364	−0.204214
$292$	−39.8877	−2.33425
$293$	−7.42249	−0.433627	−0.216813	−	0.976213i	$-0.569566\pi$
$293$	−7.42249	−0.433627	−0.216813	+	0.976213i	$0.569566\pi$
$294$	48.6261	2.83593
$295$	−2.01408	−0.117264
$296$	5.66420	0.329225
$297$	−23.2600	−1.34968
$298$	46.7296	2.70697
$299$	2.58445	0.149463
$300$	19.4811	1.12474
$301$	4.01250	0.231276
$302$	−12.4706	−0.717604
$303$	6.34677	0.364612
$304$	−26.0107	−1.49181
$305$	−0.354011	−0.0202706
$306$	32.1868	1.84000
$307$	0.106672	0.00608808	0.00304404	−	0.999995i	$-0.499031\pi$
$307$	0.106672	0.00608808	0.00304404	+	0.999995i	$0.499031\pi$
$308$	92.0245	5.24358
$309$	5.89953	0.335613
$310$	−1.03035	−0.0585198
$311$	−16.3006	−0.924324	−0.462162	−	0.886796i	$-0.652926\pi$
$311$	−16.3006	−0.924324	−0.462162	+	0.886796i	$0.652926\pi$
$312$	12.0010	0.679425
$313$	1.55399	0.0878366	0.0439183	−	0.999035i	$-0.486016\pi$
$313$	1.55399	0.0878366	0.0439183	+	0.999035i	$0.486016\pi$
$314$	42.3664	2.39088
$315$	−2.78306	−0.156808
$316$	−4.61728	−0.259743
$317$	32.8913	1.84736	0.923679	−	0.383166i	$-0.125166\pi$
$317$	32.8913	1.84736	0.923679	+	0.383166i	$0.125166\pi$
$318$	28.4523	1.59553
$319$	4.59700	0.257383
$320$	2.57420	0.143902
$321$	−18.8335	−1.05118
$322$	12.5169	0.697538
$323$	−53.7765	−2.99220
$324$	2.76736	0.153742
$325$	−12.7266	−0.705943
$326$	28.0032	1.55095
$327$	0.787756	0.0435630
$328$	6.36149	0.351254
$329$	28.8064	1.58815
$330$	3.12911	0.172252
$331$	21.5227	1.18299	0.591496	−	0.806308i	$-0.298537\pi$
$331$	21.5227	1.18299	0.591496	+	0.806308i	$0.298537\pi$
$332$	−21.4581	−1.17766
$333$	2.43807	0.133606
$334$	−40.9234	−2.23923
$335$	−2.80497	−0.153252
$336$	17.2708	0.942197
$337$	−30.3271	−1.65202	−0.826012	−	0.563653i	$-0.809396\pi$
$337$	−30.3271	−1.65202	−0.826012	+	0.563653i	$0.809396\pi$
$338$	15.3230	0.833460
$339$	13.0602	0.709331
$340$	−7.23127	−0.392171
$341$	7.10011	0.384492
$342$	−37.6786	−2.03742
$343$	−65.3526	−3.52871
$344$	3.53672	0.190687
$345$	0.280777	0.0151165
$346$	5.05450	0.271732
$347$	1.44730	0.0776953	0.0388476	−	0.999245i	$-0.487631\pi$
$347$	1.44730	0.0776953	0.0388476	+	0.999245i	$0.487631\pi$
$348$	3.95614	0.212071
$349$	−0.963889	−0.0515958	−0.0257979	−	0.999667i	$-0.508213\pi$
$349$	−0.963889	−0.0515958	−0.0257979	+	0.999667i	$0.508213\pi$
$350$	−61.6366	−3.29462
$351$	13.0769	0.697993
$352$	−5.30604	−0.282813
$353$	19.4579	1.03564	0.517821	−	0.855489i	$-0.326743\pi$
$353$	19.4579	1.03564	0.517821	+	0.855489i	$0.326743\pi$
$354$	18.1053	0.962288
$355$	−1.14597	−0.0608215
$356$	52.1186	2.76228
$357$	35.7069	1.88981
$358$	−21.5135	−1.13702
$359$	−22.4871	−1.18682	−0.593411	−	0.804900i	$-0.702219\pi$
$359$	−22.4871	−1.18682	−0.593411	+	0.804900i	$0.702219\pi$
$360$	−2.45306	−0.129288
$361$	43.9519	2.31326
$362$	50.9377	2.67723
$363$	−10.3387	−0.542641
$364$	−51.7366	−2.71174
$365$	2.83093	0.148178
$366$	3.18235	0.166344
$367$	−22.9126	−1.19603	−0.598014	−	0.801486i	$-0.704043\pi$
$367$	−22.9126	−1.19603	−0.598014	+	0.801486i	$0.704043\pi$
$368$	3.27829	0.170893
$369$	2.73821	0.142546
$370$	−0.830301	−0.0431653
$371$	−59.3867	−3.08321
$372$	6.11030	0.316804
$373$	3.09309	0.160154	0.0800770	−	0.996789i	$-0.474483\pi$
$373$	3.09309	0.160154	0.0800770	+	0.996789i	$0.474483\pi$
$374$	75.5349	3.90582
$375$	−2.78651	−0.143895
$376$	25.3907	1.30942
$377$	−2.58445	−0.133106
$378$	63.3333	3.25751
$379$	31.6064	1.62351	0.811756	−	0.583996i	$-0.198512\pi$
$379$	31.6064	1.62351	0.811756	+	0.583996i	$0.198512\pi$
$380$	8.46507	0.434249
$381$	−15.4568	−0.791878
$382$	22.1055	1.13102
$383$	14.6954	0.750898	0.375449	−	0.926843i	$-0.377489\pi$
$383$	14.6954	0.750898	0.375449	+	0.926843i	$0.377489\pi$
$384$	−20.7850	−1.06068
$385$	−6.53120	−0.332861
$386$	3.44195	0.175191
$387$	1.52233	0.0773843
$388$	13.2373	0.672020
$389$	20.4520	1.03696	0.518478	−	0.855091i	$-0.326499\pi$
$389$	20.4520	1.03696	0.518478	+	0.855091i	$0.326499\pi$
$390$	−1.75920	−0.0890806
$391$	6.77779	0.342768
$392$	−89.4597	−4.51840
$393$	4.04746	0.204167
$394$	7.24687	0.365092
$395$	0.327700	0.0164884
$396$	34.9138	1.75449
$397$	1.93448	0.0970887	0.0485443	−	0.998821i	$-0.484542\pi$
$397$	1.93448	0.0970887	0.0485443	+	0.998821i	$0.484542\pi$
$398$	−34.5525	−1.73196
$399$	−41.7993	−2.09258
$400$	−16.1432	−0.807161
$401$	−4.44527	−0.221986	−0.110993	−	0.993821i	$-0.535403\pi$
$401$	−4.44527	−0.221986	−0.110993	+	0.993821i	$0.535403\pi$
$402$	25.2150	1.25761
$403$	−3.99171	−0.198841
$404$	−24.1167	−1.19985
$405$	−0.196406	−0.00975949
$406$	−12.5169	−0.621202
$407$	5.72159	0.283609
$408$	31.4730	1.55814
$409$	7.40105	0.365958	0.182979	−	0.983117i	$-0.441426\pi$
$409$	7.40105	0.365958	0.182979	+	0.983117i	$0.441426\pi$
$410$	−0.932514	−0.0460536
$411$	−9.04545	−0.446179
$412$	−22.4173	−1.10442
$413$	−37.7902	−1.85953
$414$	4.74887	0.233394
$415$	1.52293	0.0747577
$416$	2.98308	0.146257
$417$	−17.5262	−0.858260
$418$	−88.4228	−4.32490
$419$	−39.3381	−1.92179	−0.960896	−	0.276910i	$-0.910690\pi$
$419$	−39.3381	−1.92179	−0.960896	+	0.276910i	$0.910690\pi$
$420$	−5.62070	−0.274262
$421$	34.1384	1.66380	0.831901	−	0.554924i	$-0.187253\pi$
$421$	34.1384	1.66380	0.831901	+	0.554924i	$0.187253\pi$
$422$	12.1095	0.589480
$423$	10.9291	0.531389
$424$	−52.3450	−2.54210
$425$	−33.3757	−1.61896
$426$	10.3015	0.499111
$427$	−6.64232	−0.321444
$428$	71.5641	3.45918
$429$	12.1226	0.585286
$430$	−0.518438	−0.0250013
$431$	19.7955	0.953518	0.476759	−	0.879034i	$-0.341811\pi$
$431$	19.7955	0.953518	0.476759	+	0.879034i	$0.341811\pi$
$432$	16.5876	0.798070
$433$	34.2150	1.64427	0.822134	−	0.569294i	$-0.192783\pi$
$433$	34.2150	1.64427	0.822134	+	0.569294i	$0.192783\pi$
$434$	−19.3324	−0.927986
$435$	−0.280777	−0.0134622
$436$	−2.99335	−0.143355
$437$	−7.93422	−0.379545
$438$	−25.4484	−1.21597
$439$	−9.25190	−0.441569	−0.220784	−	0.975323i	$-0.570862\pi$
$439$	−9.25190	−0.441569	−0.220784	+	0.975323i	$0.570862\pi$
$440$	−5.75676	−0.274443
$441$	−38.5067	−1.83365
$442$	−42.4661	−2.01991
$443$	−6.68002	−0.317377	−0.158689	−	0.987329i	$-0.550727\pi$
$443$	−6.68002	−0.317377	−0.158689	+	0.987329i	$0.550727\pi$
$444$	4.92396	0.233681
$445$	−3.69898	−0.175348
$446$	−41.4124	−1.96093
$447$	19.6680	0.930264
$448$	48.2998	2.28195
$449$	−5.68296	−0.268195	−0.134098	−	0.990968i	$-0.542814\pi$
$449$	−5.68296	−0.268195	−0.134098	+	0.990968i	$0.542814\pi$
$450$	−23.3847	−1.10237
$451$	6.42594	0.302586
$452$	−49.6265	−2.33424
$453$	−5.24876	−0.246608
$454$	13.7143	0.643645
$455$	3.67187	0.172140
$456$	−36.8429	−1.72533
$457$	−18.4227	−0.861776	−0.430888	−	0.902405i	$-0.641800\pi$
$457$	−18.4227	−0.861776	−0.430888	+	0.902405i	$0.641800\pi$
$458$	33.0361	1.54367
$459$	34.2945	1.60073
$460$	−1.06691	−0.0497448
$461$	29.4473	1.37150	0.685749	−	0.727838i	$-0.259475\pi$
$461$	29.4473	1.37150	0.685749	+	0.727838i	$0.259475\pi$
$462$	58.7116	2.73151
$463$	32.0658	1.49022	0.745111	−	0.666941i	$-0.232397\pi$
$463$	32.0658	1.49022	0.745111	+	0.666941i	$0.232397\pi$
$464$	−3.27829	−0.152191
$465$	−0.433662	−0.0201106
$466$	20.1666	0.934199
$467$	14.1343	0.654059	0.327029	−	0.945014i	$-0.393952\pi$
$467$	14.1343	0.654059	0.327029	+	0.945014i	$0.393952\pi$
$468$	−19.6287	−0.907338
$469$	−52.6298	−2.43022
$470$	−3.72196	−0.171681
$471$	17.8316	0.821636
$472$	−33.3092	−1.53318
$473$	3.57255	0.164266
$474$	−2.94582	−0.135306
$475$	39.0703	1.79267
$476$	−135.680	−6.21890
$477$	−22.5312	−1.03163
$478$	−25.8560	−1.18263
$479$	8.84879	0.404312	0.202156	−	0.979353i	$-0.435205\pi$
$479$	8.84879	0.404312	0.202156	+	0.979353i	$0.435205\pi$
$480$	0.324084	0.0147923
$481$	−3.21670	−0.146669
$482$	46.7846	2.13098
$483$	5.26822	0.239712
$484$	39.2854	1.78570
$485$	−0.939479	−0.0426596
$486$	38.5651	1.74935
$487$	6.30353	0.285640	0.142820	−	0.989749i	$-0.454383\pi$
$487$	6.30353	0.285640	0.142820	+	0.989749i	$0.454383\pi$
$488$	−5.85471	−0.265030
$489$	11.7863	0.532993
$490$	13.1137	0.592415
$491$	−22.2801	−1.00549	−0.502743	−	0.864436i	$-0.667676\pi$
$491$	−22.2801	−1.00549	−0.502743	+	0.864436i	$0.667676\pi$
$492$	5.53012	0.249317
$493$	−6.77779	−0.305256
$494$	49.7117	2.23663
$495$	−2.47792	−0.111374
$496$	−5.06335	−0.227351
$497$	−21.5018	−0.964487
$498$	−13.6902	−0.613474
$499$	−5.66457	−0.253581	−0.126791	−	0.991930i	$-0.540468\pi$
$499$	−5.66457	−0.253581	−0.126791	+	0.991930i	$0.540468\pi$
$500$	10.5883	0.473522
$501$	−17.2242	−0.769523
$502$	−19.1875	−0.856380
$503$	25.2240	1.12468	0.562340	−	0.826906i	$-0.309901\pi$
$503$	25.2240	1.12468	0.562340	+	0.826906i	$0.309901\pi$
$504$	−46.0269	−2.05020
$505$	1.71162	0.0761660
$506$	11.1445	0.495432
$507$	6.44928	0.286423
$508$	58.7335	2.60588
$509$	1.51350	0.0670847	0.0335423	−	0.999437i	$-0.489321\pi$
$509$	1.51350	0.0670847	0.0335423	+	0.999437i	$0.489321\pi$
$510$	−4.61355	−0.204291
$511$	53.1168	2.34975
$512$	33.6222	1.48591
$513$	−40.1458	−1.77248
$514$	−13.5855	−0.599230
$515$	1.59101	0.0701081
$516$	3.07451	0.135348
$517$	25.6479	1.12800
$518$	−15.5790	−0.684500
$519$	2.12739	0.0933819
$520$	3.23648	0.141929
$521$	3.07057	0.134524	0.0672621	−	0.997735i	$-0.478574\pi$
$521$	3.07057	0.134524	0.0672621	+	0.997735i	$0.478574\pi$
$522$	−4.74887	−0.207852
$523$	−8.05915	−0.352402	−0.176201	−	0.984354i	$-0.556381\pi$
$523$	−8.05915	−0.352402	−0.176201	+	0.984354i	$0.556381\pi$
$524$	−15.3797	−0.671865
$525$	−25.9422	−1.13221
$526$	43.8583	1.91231
$527$	−10.4684	−0.456009
$528$	15.3771	0.669204
$529$	1.00000	0.0434783
$530$	7.67312	0.333299
$531$	−14.3375	−0.622194
$532$	158.830	6.88617
$533$	−3.61269	−0.156483
$534$	33.2516	1.43894
$535$	−5.07908	−0.219588
$536$	−46.3892	−2.00371
$537$	−9.05479	−0.390743
$538$	−20.2998	−0.875186
$539$	−90.3661	−3.89234
$540$	−5.39836	−0.232308
$541$	43.7791	1.88221	0.941106	−	0.338112i	$-0.109788\pi$
$541$	43.7791	1.88221	0.941106	+	0.338112i	$0.109788\pi$
$542$	−6.52437	−0.280246
$543$	21.4391	0.920042
$544$	7.82319	0.335417
$545$	0.212445	0.00910014
$546$	−33.0079	−1.41261
$547$	−1.38785	−0.0593402	−0.0296701	−	0.999560i	$-0.509446\pi$
$547$	−1.38785	−0.0593402	−0.0296701	+	0.999560i	$0.509446\pi$
$548$	34.3713	1.46827
$549$	−2.52008	−0.107554
$550$	−54.8785	−2.34003
$551$	7.93422	0.338009
$552$	4.64355	0.197642
$553$	6.14864	0.261467
$554$	−79.1026	−3.36075
$555$	−0.349465	−0.0148340
$556$	66.5965	2.82432
$557$	22.8042	0.966246	0.483123	−	0.875552i	$-0.339502\pi$
$557$	22.8042	0.966246	0.483123	+	0.875552i	$0.339502\pi$
$558$	−7.33467	−0.310501
$559$	−2.00850	−0.0849507
$560$	4.65764	0.196821
$561$	31.7919	1.34225
$562$	51.5390	2.17404
$563$	−7.80360	−0.328883	−0.164441	−	0.986387i	$-0.552582\pi$
$563$	−7.80360	−0.328883	−0.164441	+	0.986387i	$0.552582\pi$
$564$	22.0724	0.929417
$565$	3.52211	0.148176
$566$	15.6045	0.655904
$567$	−3.68517	−0.154763
$568$	−18.9522	−0.795217
$569$	−37.1514	−1.55747	−0.778733	−	0.627356i	$-0.784137\pi$
$569$	−37.1514	−1.55747	−0.778733	+	0.627356i	$0.784137\pi$
$570$	5.40071	0.226211
$571$	−22.6811	−0.949174	−0.474587	−	0.880209i	$-0.657403\pi$
$571$	−22.6811	−0.949174	−0.474587	+	0.880209i	$0.657403\pi$
$572$	−46.0640	−1.92603
$573$	9.30399	0.388680
$574$	−17.4968	−0.730302
$575$	−4.92428	−0.205357
$576$	18.3248	0.763533
$577$	−19.6189	−0.816747	−0.408374	−	0.912815i	$-0.633904\pi$
$577$	−19.6189	−0.816747	−0.408374	+	0.912815i	$0.633904\pi$
$578$	−70.1553	−2.91808
$579$	1.44868	0.0602051
$580$	1.06691	0.0443009
$581$	28.5748	1.18548
$582$	8.44536	0.350071
$583$	−52.8753	−2.18987
$584$	46.8185	1.93736
$585$	1.39310	0.0575975
$586$	17.9943	0.743338
$587$	15.7582	0.650411	0.325206	−	0.945643i	$-0.394566\pi$
$587$	15.7582	0.650411	0.325206	+	0.945643i	$0.394566\pi$
$588$	−77.7684	−3.20711
$589$	12.2545	0.504937
$590$	4.88271	0.201018
$591$	3.05013	0.125466
$592$	−4.08028	−0.167698
$593$	−7.35744	−0.302134	−0.151067	−	0.988524i	$-0.548271\pi$
$593$	−7.35744	−0.302134	−0.151067	+	0.988524i	$0.548271\pi$
$594$	56.3891	2.31367
$595$	9.62957	0.394774
$596$	−74.7352	−3.06127
$597$	−14.5428	−0.595197
$598$	−6.26548	−0.256214
$599$	27.0050	1.10340	0.551698	−	0.834044i	$-0.313980\pi$
$599$	27.0050	1.10340	0.551698	+	0.834044i	$0.313980\pi$
$600$	−22.8661	−0.933505
$601$	−23.4245	−0.955504	−0.477752	−	0.878495i	$-0.658548\pi$
$601$	−23.4245	−0.955504	−0.477752	+	0.878495i	$0.658548\pi$
$602$	−9.72747	−0.396462
$603$	−19.9676	−0.813143
$604$	19.9444	0.811527
$605$	−2.78818	−0.113355
$606$	−15.3864	−0.625031
$607$	19.8139	0.804222	0.402111	−	0.915591i	$-0.368277\pi$
$607$	19.8139	0.804222	0.402111	+	0.915591i	$0.368277\pi$
$608$	−9.15799	−0.371405
$609$	−5.26822	−0.213479
$610$	0.858227	0.0347486
$611$	−14.4194	−0.583346
$612$	−51.4768	−2.08082
$613$	7.88252	0.318372	0.159186	−	0.987249i	$-0.449113\pi$
$613$	7.88252	0.318372	0.159186	+	0.987249i	$0.449113\pi$
$614$	−0.258604	−0.0104364
$615$	−0.392485	−0.0158265
$616$	−108.014	−4.35202
$617$	−37.4119	−1.50615	−0.753073	−	0.657937i	$-0.771429\pi$
$617$	−37.4119	−1.50615	−0.753073	+	0.657937i	$0.771429\pi$
$618$	−14.3022	−0.575319
$619$	−14.5529	−0.584931	−0.292465	−	0.956276i	$-0.594476\pi$
$619$	−14.5529	−0.584931	−0.292465	+	0.956276i	$0.594476\pi$
$620$	1.64785	0.0661791
$621$	5.05983	0.203044
$622$	39.5175	1.58451
$623$	−69.4040	−2.78061
$624$	−8.64509	−0.346081
$625$	23.8699	0.954797
$626$	−3.76733	−0.150573
$627$	−37.2162	−1.48627
$628$	−67.7571	−2.70380
$629$	−8.43588	−0.336361
$630$	6.74697	0.268806
$631$	−21.1886	−0.843504	−0.421752	−	0.906711i	$-0.638585\pi$
$631$	−21.1886	−0.843504	−0.421752	+	0.906711i	$0.638585\pi$
$632$	5.41956	0.215579
$633$	5.09675	0.202578
$634$	−79.7382	−3.16681
$635$	−4.16845	−0.165420
$636$	−45.5041	−1.80436
$637$	50.8042	2.01294
$638$	−11.1445	−0.441214
$639$	−8.15771	−0.322714
$640$	−5.60538	−0.221572
$641$	25.4677	1.00591	0.502957	−	0.864312i	$-0.332245\pi$
$641$	25.4677	1.00591	0.502957	+	0.864312i	$0.332245\pi$
$642$	45.6579	1.80197
$643$	36.2517	1.42963	0.714814	−	0.699314i	$-0.246511\pi$
$643$	36.2517	1.42963	0.714814	+	0.699314i	$0.246511\pi$
$644$	−20.0184	−0.788835
$645$	−0.218205	−0.00859182
$646$	130.370	5.12934
$647$	40.3128	1.58486	0.792430	−	0.609963i	$-0.208816\pi$
$647$	40.3128	1.58486	0.792430	+	0.609963i	$0.208816\pi$
$648$	−3.24820	−0.127601
$649$	−33.6467	−1.32075
$650$	30.8530	1.21015
$651$	−8.13682	−0.318907
$652$	−44.7858	−1.75395
$653$	28.4754	1.11433	0.557164	−	0.830402i	$-0.311889\pi$
$653$	28.4754	1.11433	0.557164	+	0.830402i	$0.311889\pi$
$654$	−1.90975	−0.0746773
$655$	1.09153	0.0426497
$656$	−4.58258	−0.178920
$657$	20.1523	0.786218
$658$	−69.8352	−2.72246
$659$	−4.69239	−0.182790	−0.0913948	−	0.995815i	$-0.529133\pi$
$659$	−4.69239	−0.182790	−0.0913948	+	0.995815i	$0.529133\pi$
$660$	−5.00442	−0.194797
$661$	18.8296	0.732386	0.366193	−	0.930539i	$-0.380661\pi$
$661$	18.8296	0.732386	0.366193	+	0.930539i	$0.380661\pi$
$662$	−52.1773	−2.02793
$663$	−17.8735	−0.694151
$664$	25.1865	0.977427
$665$	−11.2726	−0.437132
$666$	−5.91061	−0.229031
$667$	−1.00000	−0.0387202
$668$	65.4493	2.53231
$669$	−17.4300	−0.673885
$670$	6.80008	0.262710
$671$	−5.91403	−0.228309
$672$	6.08079	0.234572
$673$	−15.9078	−0.613201	−0.306600	−	0.951838i	$-0.599192\pi$
$673$	−15.9078	−0.613201	−0.306600	+	0.951838i	$0.599192\pi$
$674$	73.5219	2.83196
$675$	−24.9160	−0.959017
$676$	−24.5062	−0.942547
$677$	30.7038	1.18004	0.590022	−	0.807387i	$-0.299119\pi$
$677$	30.7038	1.18004	0.590022	+	0.807387i	$0.299119\pi$
$678$	−31.6617	−1.21596
$679$	−17.6275	−0.676481
$680$	8.48775	0.325490
$681$	5.77221	0.221192
$682$	−17.2127	−0.659110
$683$	−12.1098	−0.463369	−0.231685	−	0.972791i	$-0.574424\pi$
$683$	−12.1098	−0.463369	−0.231685	+	0.972791i	$0.574424\pi$
$684$	60.2598	2.30409
$685$	−2.43941	−0.0932051
$686$	158.434	6.04904
$687$	13.9045	0.530491
$688$	−2.54772	−0.0971308
$689$	29.7268	1.13250
$690$	−0.680686	−0.0259133
$691$	37.0959	1.41119	0.705597	−	0.708613i	$-0.250679\pi$
$691$	37.0959	1.41119	0.705597	+	0.708613i	$0.250679\pi$
$692$	−8.08372	−0.307297
$693$	−46.4932	−1.76613
$694$	−3.50869	−0.133188
$695$	−4.72652	−0.179287
$696$	−4.64355	−0.176013
$697$	−9.47438	−0.358868
$698$	2.33675	0.0884473
$699$	8.48790	0.321042
$700$	98.5761	3.72583
$701$	10.9045	0.411858	0.205929	−	0.978567i	$-0.433978\pi$
$701$	10.9045	0.411858	0.205929	+	0.978567i	$0.433978\pi$
$702$	−31.7022	−1.19652
$703$	9.87522	0.372451
$704$	43.0040	1.62077
$705$	−1.56653	−0.0589990
$706$	−47.1718	−1.77533
$707$	32.1151	1.20781
$708$	−28.9561	−1.08824
$709$	12.3176	0.462598	0.231299	−	0.972883i	$-0.425702\pi$
$709$	12.3176	0.462598	0.231299	+	0.972883i	$0.425702\pi$
$710$	2.77816	0.104262
$711$	2.33277	0.0874859
$712$	−61.1745	−2.29261
$713$	−1.54451	−0.0578423
$714$	−86.5641	−3.23958
$715$	3.26927	0.122264
$716$	34.4067	1.28584
$717$	−10.8825	−0.406415
$718$	54.5152	2.03449
$719$	0.321584	0.0119931	0.00599654	−	0.999982i	$-0.498091\pi$
$719$	0.321584	0.0119931	0.00599654	+	0.999982i	$0.498091\pi$
$720$	1.76709	0.0658557
$721$	29.8521	1.11175
$722$	−106.552	−3.96547
$723$	19.6911	0.732321
$724$	−81.4653	−3.02763
$725$	4.92428	0.182883
$726$	25.0640	0.930214
$727$	17.3701	0.644223	0.322111	−	0.946702i	$-0.395607\pi$
$727$	17.3701	0.644223	0.322111	+	0.946702i	$0.395607\pi$
$728$	60.7262	2.25066
$729$	14.0904	0.521867
$730$	−6.86300	−0.254011
$731$	−5.26735	−0.194820
$732$	−5.08957	−0.188116
$733$	12.0450	0.444894	0.222447	−	0.974945i	$-0.428596\pi$
$733$	12.0450	0.444894	0.222447	+	0.974945i	$0.428596\pi$
$734$	55.5469	2.05027
$735$	5.51941	0.203586
$736$	1.15424	0.0425458
$737$	−46.8592	−1.72608
$738$	−6.63823	−0.244357
$739$	−16.8201	−0.618737	−0.309368	−	0.950942i	$-0.600118\pi$
$739$	−16.8201	−0.618737	−0.309368	+	0.950942i	$0.600118\pi$
$740$	1.32791	0.0488149
$741$	20.9231	0.768630
$742$	143.971	5.28534
$743$	−17.4044	−0.638505	−0.319253	−	0.947670i	$-0.603432\pi$
$743$	−17.4044	−0.638505	−0.319253	+	0.947670i	$0.603432\pi$
$744$	−7.17200	−0.262938
$745$	5.30413	0.194328
$746$	−7.49856	−0.274542
$747$	10.8412	0.396658
$748$	−120.804	−4.41703
$749$	−95.2988	−3.48214
$750$	6.75531	0.246669
$751$	−0.100736	−0.00367590	−0.00183795	−	0.999998i	$-0.500585\pi$
$751$	−0.100736	−0.00367590	−0.00183795	+	0.999998i	$0.500585\pi$
$752$	−18.2905	−0.666986
$753$	−8.07581	−0.294299
$754$	6.26548	0.228175
$755$	−1.41550	−0.0515155
$756$	−101.290	−3.68387
$757$	34.1198	1.24010	0.620052	−	0.784561i	$-0.287111\pi$
$757$	34.1198	1.24010	0.620052	+	0.784561i	$0.287111\pi$
$758$	−76.6232	−2.78308
$759$	4.69059	0.170258
$760$	−9.93593	−0.360414
$761$	23.5537	0.853822	0.426911	−	0.904294i	$-0.359602\pi$
$761$	23.5537	0.853822	0.426911	+	0.904294i	$0.359602\pi$
$762$	37.4719	1.35746
$763$	3.98611	0.144307
$764$	−35.3536	−1.27905
$765$	3.65343	0.132090
$766$	−35.6259	−1.28722
$767$	18.9163	0.683029
$768$	31.2985	1.12939
$769$	9.02730	0.325533	0.162766	−	0.986665i	$-0.447958\pi$
$769$	9.02730	0.325533	0.162766	+	0.986665i	$0.447958\pi$
$770$	15.8335	0.570602
$771$	−5.71799	−0.205928
$772$	−5.50475	−0.198120
$773$	53.4367	1.92198	0.960992	−	0.276577i	$-0.0892000\pi$
$773$	53.4367	1.92198	0.960992	+	0.276577i	$0.0892000\pi$
$774$	−3.69057	−0.132655
$775$	7.60559	0.273201
$776$	−15.5373	−0.557757
$777$	−6.55702	−0.235232
$778$	−49.5816	−1.77759
$779$	11.0909	0.397373
$780$	2.81351	0.100740
$781$	−19.1442	−0.685035
$782$	−16.4314	−0.587584
$783$	−5.05983	−0.180823
$784$	64.4434	2.30155
$785$	4.80889	0.171636
$786$	−9.81223	−0.349991
$787$	47.7500	1.70210	0.851052	−	0.525081i	$-0.175965\pi$
$787$	47.7500	1.70210	0.851052	+	0.525081i	$0.175965\pi$
$788$	−11.5900	−0.412877
$789$	18.4595	0.657175
$790$	−0.794440	−0.0282649
$791$	66.0855	2.34973
$792$	−40.9803	−1.45617
$793$	3.32489	0.118070
$794$	−4.68974	−0.166433
$795$	3.22954	0.114540
$796$	55.2602	1.95865
$797$	6.00759	0.212800	0.106400	−	0.994323i	$-0.466068\pi$
$797$	6.00759	0.212800	0.106400	+	0.994323i	$0.466068\pi$
$798$	101.334	3.58717
$799$	−37.8152	−1.33781
$800$	−5.68380	−0.200953
$801$	−26.3317	−0.930384
$802$	10.7767	0.380537
$803$	47.2928	1.66893
$804$	−40.3267	−1.42221
$805$	1.42075	0.0500750
$806$	9.67709	0.340861
$807$	−8.54397	−0.300762
$808$	28.3071	0.995840
$809$	33.4712	1.17678	0.588392	−	0.808576i	$-0.299761\pi$
$809$	33.4712	1.17678	0.588392	+	0.808576i	$0.299761\pi$
$810$	0.476146	0.0167300
$811$	12.2370	0.429700	0.214850	−	0.976647i	$-0.431074\pi$
$811$	12.2370	0.429700	0.214850	+	0.976647i	$0.431074\pi$
$812$	20.0184	0.702508
$813$	−2.74604	−0.0963078
$814$	−13.8708	−0.486172
$815$	3.17856	0.111340
$816$	−22.6720	−0.793677
$817$	6.16607	0.215723
$818$	−17.9423	−0.627339
$819$	26.1387	0.913361
$820$	1.49138	0.0520813
$821$	−13.9476	−0.486774	−0.243387	−	0.969929i	$-0.578258\pi$
$821$	−13.9476	−0.486774	−0.243387	+	0.969929i	$0.578258\pi$
$822$	21.9288	0.764856
$823$	2.34522	0.0817493	0.0408746	−	0.999164i	$-0.486986\pi$
$823$	2.34522	0.0817493	0.0408746	+	0.999164i	$0.486986\pi$
$824$	26.3124	0.916636
$825$	−23.0978	−0.804162
$826$	91.6145	3.18768
$827$	14.5485	0.505901	0.252950	−	0.967479i	$-0.418599\pi$
$827$	14.5485	0.505901	0.252950	+	0.967479i	$0.418599\pi$
$828$	−7.59492	−0.263942
$829$	−14.6227	−0.507866	−0.253933	−	0.967222i	$-0.581724\pi$
$829$	−14.6227	−0.507866	−0.253933	+	0.967222i	$0.581724\pi$
$830$	−3.69203	−0.128152
$831$	−33.2935	−1.15494
$832$	−24.1770	−0.838188
$833$	133.235	4.61633
$834$	42.4886	1.47126
$835$	−4.64510	−0.160750
$836$	141.416	4.89096
$837$	−7.81495	−0.270124
$838$	95.3671	3.29440
$839$	7.29576	0.251878	0.125939	−	0.992038i	$-0.459806\pi$
$839$	7.29576	0.251878	0.125939	+	0.992038i	$0.459806\pi$
$840$	6.59733	0.227630
$841$	1.00000	0.0344828
$842$	−82.7615	−2.85215
$843$	21.6922	0.747120
$844$	−19.3668	−0.666634
$845$	1.73926	0.0598325
$846$	−26.4953	−0.910926
$847$	−52.3146	−1.79755
$848$	37.7074	1.29488
$849$	6.56775	0.225405
$850$	80.9126	2.77528
$851$	−1.24464	−0.0426656
$852$	−16.4754	−0.564437
$853$	0.430558	0.0147420	0.00737101	−	0.999973i	$-0.497654\pi$
$853$	0.430558	0.0147420	0.00737101	+	0.999973i	$0.497654\pi$
$854$	16.1029	0.551031
$855$	−4.27678	−0.146263
$856$	−83.9988	−2.87102
$857$	14.3303	0.489513	0.244756	−	0.969585i	$-0.421292\pi$
$857$	14.3303	0.489513	0.244756	+	0.969585i	$0.421292\pi$
$858$	−29.3888	−1.00332
$859$	−28.5387	−0.973730	−0.486865	−	0.873477i	$-0.661860\pi$
$859$	−28.5387	−0.973730	−0.486865	+	0.873477i	$0.661860\pi$
$860$	0.829144	0.0282736
$861$	−7.36422	−0.250972
$862$	−47.9902	−1.63455
$863$	3.69031	0.125620	0.0628098	−	0.998026i	$-0.479994\pi$
$863$	3.69031	0.125620	0.0628098	+	0.998026i	$0.479994\pi$
$864$	5.84025	0.198689
$865$	0.573721	0.0195071
$866$	−82.9472	−2.81866
$867$	−29.5276	−1.00281
$868$	30.9186	1.04945
$869$	5.47448	0.185709
$870$	0.680686	0.0230774
$871$	26.3445	0.892649
$872$	3.51346	0.118981
$873$	−6.68781	−0.226348
$874$	19.2349	0.650630
$875$	−14.0999	−0.476665
$876$	40.6998	1.37512
$877$	−15.6342	−0.527928	−0.263964	−	0.964532i	$-0.585030\pi$
$877$	−15.6342	−0.527928	−0.263964	+	0.964532i	$0.585030\pi$
$878$	22.4293	0.756953
$879$	7.57361	0.255452
$880$	4.14696	0.139794
$881$	39.8258	1.34176	0.670882	−	0.741564i	$-0.265916\pi$
$881$	39.8258	1.34176	0.670882	+	0.741564i	$0.265916\pi$
$882$	93.3514	3.14331
$883$	6.23215	0.209729	0.104864	−	0.994487i	$-0.466559\pi$
$883$	6.23215	0.209729	0.104864	+	0.994487i	$0.466559\pi$
$884$	67.9165	2.28428
$885$	2.05508	0.0690809
$886$	16.1943	0.544059
$887$	1.08225	0.0363383	0.0181691	−	0.999835i	$-0.494216\pi$
$887$	1.08225	0.0363383	0.0181691	+	0.999835i	$0.494216\pi$
$888$	−5.77952	−0.193948
$889$	−78.2128	−2.62317
$890$	8.96741	0.300588
$891$	−3.28111	−0.109921
$892$	66.2313	2.21759
$893$	44.2672	1.48135
$894$	−47.6810	−1.59469
$895$	−2.44193	−0.0816247
$896$	−105.174	−3.51361
$897$	−2.63707	−0.0880493
$898$	13.7772	0.459750
$899$	1.54451	0.0515123
$900$	37.3995	1.24665
$901$	77.9591	2.59720
$902$	−15.5784	−0.518703
$903$	−4.09419	−0.136246
$904$	58.2494	1.93735
$905$	5.78179	0.192193
$906$	12.7245	0.422744
$907$	27.9237	0.927192	0.463596	−	0.886047i	$-0.346559\pi$
$907$	27.9237	0.927192	0.463596	+	0.886047i	$0.346559\pi$
$908$	−21.9335	−0.727888
$909$	12.1844	0.404131
$910$	−8.90170	−0.295088
$911$	−6.32742	−0.209637	−0.104818	−	0.994491i	$-0.533426\pi$
$911$	−6.32742	−0.209637	−0.104818	+	0.994491i	$0.533426\pi$
$912$	26.5403	0.878836
$913$	25.4417	0.841998
$914$	44.6620	1.47729
$915$	0.361219	0.0119415
$916$	−52.8349	−1.74572
$917$	20.4805	0.676324
$918$	−83.1399	−2.74402
$919$	−0.729760	−0.0240726	−0.0120363	−	0.999928i	$-0.503831\pi$
$919$	−0.729760	−0.0240726	−0.0120363	+	0.999928i	$0.503831\pi$
$920$	1.25229	0.0412867
$921$	−0.108844	−0.00358652
$922$	−71.3889	−2.35107
$923$	10.7630	0.354268
$924$	−93.8981	−3.08902
$925$	6.12893	0.201518
$926$	−77.7368	−2.55459
$927$	11.3258	0.371988
$928$	−1.15424	−0.0378898
$929$	−16.4689	−0.540327	−0.270164	−	0.962814i	$-0.587078\pi$
$929$	−16.4689	−0.540327	−0.270164	+	0.962814i	$0.587078\pi$
$930$	1.05132	0.0344743
$931$	−155.968	−5.11164
$932$	−32.2526	−1.05647
$933$	16.6325	0.544524
$934$	−34.2658	−1.12121
$935$	8.57374	0.280391
$936$	23.0393	0.753064
$937$	−14.5792	−0.476283	−0.238142	−	0.971230i	$-0.576538\pi$
$937$	−14.5792	−0.476283	−0.238142	+	0.971230i	$0.576538\pi$
$938$	127.590	4.16596
$939$	−1.58563	−0.0517450
$940$	5.95257	0.194151
$941$	−48.4759	−1.58027	−0.790134	−	0.612934i	$-0.789989\pi$
$941$	−48.4759	−1.58027	−0.790134	+	0.612934i	$0.789989\pi$
$942$	−43.2290	−1.40848
$943$	−1.39786	−0.0455204
$944$	23.9947	0.780961
$945$	7.18877	0.233851
$946$	−8.66091	−0.281591
$947$	−18.1893	−0.591074	−0.295537	−	0.955331i	$-0.595499\pi$
$947$	−18.1893	−0.591074	−0.295537	+	0.955331i	$0.595499\pi$
$948$	4.71129	0.153016
$949$	−26.5883	−0.863091
$950$	−94.7180	−3.07306
$951$	−33.5610	−1.08829
$952$	159.256	5.16151
$953$	−18.1827	−0.588995	−0.294497	−	0.955652i	$-0.595152\pi$
$953$	−18.1827	−0.588995	−0.294497	+	0.955652i	$0.595152\pi$
$954$	54.6221	1.76846
$955$	2.50913	0.0811936
$956$	41.3518	1.33741
$957$	−4.69059	−0.151625
$958$	−21.4521	−0.693085
$959$	−45.7707	−1.47801
$960$	−2.62661	−0.0847735
$961$	−28.6145	−0.923048
$962$	7.79824	0.251425
$963$	−36.1561	−1.16511
$964$	−74.8231	−2.40989
$965$	0.390685	0.0125766
$966$	−12.7717	−0.410923
$967$	−19.0895	−0.613876	−0.306938	−	0.951729i	$-0.599304\pi$
$967$	−19.0895	−0.613876	−0.306938	+	0.951729i	$0.599304\pi$
$968$	−46.1114	−1.48208
$969$	54.8714	1.76272
$970$	2.27757	0.0731285
$971$	30.5549	0.980554	0.490277	−	0.871567i	$-0.336896\pi$
$971$	30.5549	0.980554	0.490277	+	0.871567i	$0.336896\pi$
$972$	−61.6776	−1.97831
$973$	−88.6837	−2.84307
$974$	−15.2816	−0.489655
$975$	12.9857	0.415875
$976$	4.21751	0.134999
$977$	33.4036	1.06868	0.534338	−	0.845271i	$-0.320561\pi$
$977$	33.4036	1.06868	0.534338	+	0.845271i	$0.320561\pi$
$978$	−28.5733	−0.913675
$979$	−61.7943	−1.97495
$980$	−20.9728	−0.669953
$981$	1.51232	0.0482846
$982$	54.0135	1.72364
$983$	17.9500	0.572517	0.286259	−	0.958152i	$-0.407588\pi$
$983$	17.9500	0.572517	0.286259	+	0.958152i	$0.407588\pi$
$984$	−6.49101	−0.206926
$985$	0.822570	0.0262093
$986$	16.4314	0.523281
$987$	−29.3929	−0.935586
$988$	−79.5045	−2.52937
$989$	−0.777148	−0.0247119
$990$	6.00720	0.190921
$991$	−42.9973	−1.36586	−0.682928	−	0.730486i	$-0.739294\pi$
$991$	−42.9973	−1.36586	−0.682928	+	0.730486i	$0.739294\pi$
$992$	−1.78273	−0.0566018
$993$	−21.9609	−0.696907
$994$	52.1266	1.65336
$995$	−3.92195	−0.124334
$996$	21.8950	0.693768
$997$	−7.34146	−0.232506	−0.116253	−	0.993220i	$-0.537088\pi$
$997$	−7.34146	−0.232506	−0.116253	+	0.993220i	$0.537088\pi$
$998$	13.7326	0.434698
$999$	−6.29764	−0.199249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.2	✓	16
3.2	odd	2		6003.2.a.q.1.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.2	✓	16	1.1	even	1	trivial
6003.2.a.q.1.15		16	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)

\(f(q)\)	\(=\)	\(q-2.42429 q^{2} -1.02036 q^{3} +3.87720 q^{4} -0.275174 q^{5} +2.47365 q^{6} -5.16310 q^{7} -4.55089 q^{8} -1.95887 q^{9} +O(q^{10})\)	\(q-2.42429 q^{2} -1.02036 q^{3} +3.87720 q^{4} -0.275174 q^{5} +2.47365 q^{6} -5.16310 q^{7} -4.55089 q^{8} -1.95887 q^{9} +0.667103 q^{10} -4.59700 q^{11} -3.95614 q^{12} +2.58445 q^{13} +12.5169 q^{14} +0.280777 q^{15} +3.27829 q^{16} +6.77779 q^{17} +4.74887 q^{18} -7.93422 q^{19} -1.06691 q^{20} +5.26822 q^{21} +11.1445 q^{22} +1.00000 q^{23} +4.64355 q^{24} -4.92428 q^{25} -6.26548 q^{26} +5.05983 q^{27} -20.0184 q^{28} -1.00000 q^{29} -0.680686 q^{30} -1.54451 q^{31} +1.15424 q^{32} +4.69059 q^{33} -16.4314 q^{34} +1.42075 q^{35} -7.59492 q^{36} -1.24464 q^{37} +19.2349 q^{38} -2.63707 q^{39} +1.25229 q^{40} -1.39786 q^{41} -12.7717 q^{42} -0.777148 q^{43} -17.8235 q^{44} +0.539029 q^{45} -2.42429 q^{46} -5.57928 q^{47} -3.34504 q^{48} +19.6576 q^{49} +11.9379 q^{50} -6.91579 q^{51} +10.0205 q^{52} +11.5021 q^{53} -12.2665 q^{54} +1.26498 q^{55} +23.4967 q^{56} +8.09576 q^{57} +2.42429 q^{58} +7.31928 q^{59} +1.08863 q^{60} +1.28650 q^{61} +3.74434 q^{62} +10.1138 q^{63} -9.35480 q^{64} -0.711175 q^{65} -11.3714 q^{66} +10.1934 q^{67} +26.2789 q^{68} -1.02036 q^{69} -3.44432 q^{70} +4.16451 q^{71} +8.91458 q^{72} -10.2878 q^{73} +3.01736 q^{74} +5.02454 q^{75} -30.7626 q^{76} +23.7348 q^{77} +6.39304 q^{78} -1.19088 q^{79} -0.902101 q^{80} +0.713751 q^{81} +3.38881 q^{82} -5.53442 q^{83} +20.4260 q^{84} -1.86507 q^{85} +1.88404 q^{86} +1.02036 q^{87} +20.9204 q^{88} +13.4423 q^{89} -1.30677 q^{90} -13.3438 q^{91} +3.87720 q^{92} +1.57596 q^{93} +13.5258 q^{94} +2.18329 q^{95} -1.17774 q^{96} +3.41413 q^{97} -47.6559 q^{98} +9.00490 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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