LMFDB - Embedded newform 667.2.a.d.1.1

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			1.1
Root			$-2.75586$ 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)

$f(q)$	$=$	$q-2.75586 q^{2} +2.22549 q^{3} +5.59478 q^{4} +3.97063 q^{5} -6.13314 q^{6} +1.71912 q^{7} -9.90674 q^{8} +1.95279 q^{9} +O(q^{10})$	\(q-2.75586 q^{2} +2.22549 q^{3} +5.59478 q^{4} +3.97063 q^{5} -6.13314 q^{6} +1.71912 q^{7} -9.90674 q^{8} +1.95279 q^{9} -10.9425 q^{10} +2.05797 q^{11} +12.4511 q^{12} -3.29445 q^{13} -4.73766 q^{14} +8.83659 q^{15} +16.1120 q^{16} +6.66207 q^{17} -5.38163 q^{18} -5.33022 q^{19} +22.2148 q^{20} +3.82588 q^{21} -5.67149 q^{22} +1.00000 q^{23} -22.0473 q^{24} +10.7659 q^{25} +9.07907 q^{26} -2.33054 q^{27} +9.61810 q^{28} -1.00000 q^{29} -24.3524 q^{30} -7.39507 q^{31} -24.5891 q^{32} +4.57999 q^{33} -18.3598 q^{34} +6.82598 q^{35} +10.9255 q^{36} -0.411484 q^{37} +14.6894 q^{38} -7.33177 q^{39} -39.3360 q^{40} -0.911502 q^{41} -10.5436 q^{42} -8.79049 q^{43} +11.5139 q^{44} +7.75382 q^{45} -2.75586 q^{46} +2.09177 q^{47} +35.8572 q^{48} -4.04463 q^{49} -29.6694 q^{50} +14.8264 q^{51} -18.4318 q^{52} +4.39224 q^{53} +6.42266 q^{54} +8.17145 q^{55} -17.0308 q^{56} -11.8623 q^{57} +2.75586 q^{58} -10.2746 q^{59} +49.4388 q^{60} -3.66225 q^{61} +20.3798 q^{62} +3.35708 q^{63} +35.5402 q^{64} -13.0811 q^{65} -12.6218 q^{66} +6.04116 q^{67} +37.2729 q^{68} +2.22549 q^{69} -18.8115 q^{70} -3.14393 q^{71} -19.3458 q^{72} -9.21024 q^{73} +1.13399 q^{74} +23.9594 q^{75} -29.8215 q^{76} +3.53790 q^{77} +20.2054 q^{78} +15.8406 q^{79} +63.9750 q^{80} -11.0450 q^{81} +2.51198 q^{82} +4.38108 q^{83} +21.4049 q^{84} +26.4526 q^{85} +24.2254 q^{86} -2.22549 q^{87} -20.3878 q^{88} -3.34067 q^{89} -21.3685 q^{90} -5.66356 q^{91} +5.59478 q^{92} -16.4576 q^{93} -5.76464 q^{94} -21.1644 q^{95} -54.7228 q^{96} +10.1055 q^{97} +11.1465 q^{98} +4.01880 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.75586	−1.94869	−0.974345	−	0.225060i	$-0.927742\pi$
$2$	−2.75586	−1.94869	−0.974345	+	0.225060i	$0.927742\pi$
$3$	2.22549	1.28489	0.642443	−	0.766334i	$-0.277921\pi$
$3$	2.22549	1.28489	0.642443	+	0.766334i	$0.277921\pi$
$4$	5.59478	2.79739
$5$	3.97063	1.77572	0.887860	−	0.460113i	$-0.152191\pi$
$5$	3.97063	1.77572	0.887860	+	0.460113i	$0.152191\pi$
$6$	−6.13314	−2.50384
$7$	1.71912	0.649766	0.324883	−	0.945754i	$-0.394675\pi$
$7$	1.71912	0.649766	0.324883	+	0.945754i	$0.394675\pi$
$8$	−9.90674	−3.50256
$9$	1.95279	0.650931
$10$	−10.9425	−3.46033
$11$	2.05797	0.620502	0.310251	−	0.950655i	$-0.399587\pi$
$11$	2.05797	0.620502	0.310251	+	0.950655i	$0.399587\pi$
$12$	12.4511	3.59433
$13$	−3.29445	−0.913717	−0.456859	−	0.889539i	$-0.651026\pi$
$13$	−3.29445	−0.913717	−0.456859	+	0.889539i	$0.651026\pi$
$14$	−4.73766	−1.26619
$15$	8.83659	2.28160
$16$	16.1120	4.02801
$17$	6.66207	1.61579	0.807895	−	0.589327i	$-0.200607\pi$
$17$	6.66207	1.61579	0.807895	+	0.589327i	$0.200607\pi$
$18$	−5.38163	−1.26846
$19$	−5.33022	−1.22284	−0.611419	−	0.791307i	$-0.709401\pi$
$19$	−5.33022	−1.22284	−0.611419	+	0.791307i	$0.709401\pi$
$20$	22.2148	4.96739
$21$	3.82588	0.834874
$22$	−5.67149	−1.20917
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−22.0473	−4.50039
$25$	10.7659	2.15318
$26$	9.07907	1.78055
$27$	−2.33054	−0.448514
$28$	9.61810	1.81765
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−24.3524	−4.44613
$31$	−7.39507	−1.32819	−0.664097	−	0.747647i	$-0.731184\pi$
$31$	−7.39507	−1.32819	−0.664097	+	0.747647i	$0.731184\pi$
$32$	−24.5891	−4.34678
$33$	4.57999	0.797274
$34$	−18.3598	−3.14867
$35$	6.82598	1.15380
$36$	10.9255	1.82091
$37$	−0.411484	−0.0676475	−0.0338237	−	0.999428i	$-0.510768\pi$
$37$	−0.411484	−0.0676475	−0.0338237	+	0.999428i	$0.510768\pi$
$38$	14.6894	2.38293
$39$	−7.33177	−1.17402
$40$	−39.3360	−6.21957
$41$	−0.911502	−0.142353	−0.0711764	−	0.997464i	$-0.522675\pi$
$41$	−0.911502	−0.142353	−0.0711764	+	0.997464i	$0.522675\pi$
$42$	−10.5436	−1.62691
$43$	−8.79049	−1.34054	−0.670269	−	0.742119i	$-0.733821\pi$
$43$	−8.79049	−1.34054	−0.670269	+	0.742119i	$0.733821\pi$
$44$	11.5139	1.73579
$45$	7.75382	1.15587
$46$	−2.75586	−0.406330
$47$	2.09177	0.305117	0.152558	−	0.988294i	$-0.451249\pi$
$47$	2.09177	0.305117	0.152558	+	0.988294i	$0.451249\pi$
$48$	35.8572	5.17553
$49$	−4.04463	−0.577805
$50$	−29.6694	−4.19589
$51$	14.8264	2.07611
$52$	−18.4318	−2.55603
$53$	4.39224	0.603320	0.301660	−	0.953415i	$-0.402459\pi$
$53$	4.39224	0.603320	0.301660	+	0.953415i	$0.402459\pi$
$54$	6.42266	0.874014
$55$	8.17145	1.10184
$56$	−17.0308	−2.27584
$57$	−11.8623	−1.57121
$58$	2.75586	0.361863
$59$	−10.2746	−1.33764	−0.668822	−	0.743422i	$-0.733201\pi$
$59$	−10.2746	−1.33764	−0.668822	+	0.743422i	$0.733201\pi$
$60$	49.4388	6.38252
$61$	−3.66225	−0.468903	−0.234452	−	0.972128i	$-0.575329\pi$
$61$	−3.66225	−0.468903	−0.234452	+	0.972128i	$0.575329\pi$
$62$	20.3798	2.58824
$63$	3.35708	0.422953
$64$	35.5402	4.44252
$65$	−13.0811	−1.62251
$66$	−12.6218	−1.55364
$67$	6.04116	0.738045	0.369022	−	0.929420i	$-0.379693\pi$
$67$	6.04116	0.738045	0.369022	+	0.929420i	$0.379693\pi$
$68$	37.2729	4.52000
$69$	2.22549	0.267917
$70$	−18.8115	−2.24840
$71$	−3.14393	−0.373116	−0.186558	−	0.982444i	$-0.559733\pi$
$71$	−3.14393	−0.373116	−0.186558	+	0.982444i	$0.559733\pi$
$72$	−19.3458	−2.27993
$73$	−9.21024	−1.07798	−0.538989	−	0.842313i	$-0.681193\pi$
$73$	−9.21024	−1.07798	−0.538989	+	0.842313i	$0.681193\pi$
$74$	1.13399	0.131824
$75$	23.9594	2.76659
$76$	−29.8215	−3.42076
$77$	3.53790	0.403181
$78$	20.2054	2.28781
$79$	15.8406	1.78220	0.891101	−	0.453805i	$-0.149934\pi$
$79$	15.8406	1.78220	0.891101	+	0.453805i	$0.149934\pi$
$80$	63.9750	7.15262
$81$	−11.0450	−1.22722
$82$	2.51198	0.277401
$83$	4.38108	0.480887	0.240443	−	0.970663i	$-0.422707\pi$
$83$	4.38108	0.480887	0.240443	+	0.970663i	$0.422707\pi$
$84$	21.4049	2.33547
$85$	26.4526	2.86919
$86$	24.2254	2.61229
$87$	−2.22549	−0.238597
$88$	−20.3878	−2.17335
$89$	−3.34067	−0.354110	−0.177055	−	0.984201i	$-0.556657\pi$
$89$	−3.34067	−0.354110	−0.177055	+	0.984201i	$0.556657\pi$
$90$	−21.3685	−2.25244
$91$	−5.66356	−0.593702
$92$	5.59478	0.583297
$93$	−16.4576	−1.70658
$94$	−5.76464	−0.594577
$95$	−21.1644	−2.17142
$96$	−54.7228	−5.58512
$97$	10.1055	1.02606	0.513031	−	0.858370i	$-0.328523\pi$
$97$	10.1055	1.02606	0.513031	+	0.858370i	$0.328523\pi$
$98$	11.1465	1.12596
$99$	4.01880	0.403904
$100$	60.2330	6.02330
$101$	−10.9988	−1.09442	−0.547209	−	0.836996i	$-0.684310\pi$
$101$	−10.9988	−1.09442	−0.547209	+	0.836996i	$0.684310\pi$
$102$	−40.8594	−4.04569
$103$	2.52417	0.248713	0.124357	−	0.992238i	$-0.460313\pi$
$103$	2.52417	0.248713	0.124357	+	0.992238i	$0.460313\pi$
$104$	32.6373	3.20035
$105$	15.1911	1.48250
$106$	−12.1044	−1.17568
$107$	6.34184	0.613089	0.306545	−	0.951856i	$-0.400827\pi$
$107$	6.34184	0.613089	0.306545	+	0.951856i	$0.400827\pi$
$108$	−13.0389	−1.25467
$109$	−1.94433	−0.186233	−0.0931163	−	0.995655i	$-0.529683\pi$
$109$	−1.94433	−0.186233	−0.0931163	+	0.995655i	$0.529683\pi$
$110$	−22.5194	−2.14714
$111$	−0.915752	−0.0869193
$112$	27.6985	2.61726
$113$	1.34668	0.126685	0.0633427	−	0.997992i	$-0.479824\pi$
$113$	1.34668	0.126685	0.0633427	+	0.997992i	$0.479824\pi$
$114$	32.6910	3.06179
$115$	3.97063	0.370263
$116$	−5.59478	−0.519463
$117$	−6.43339	−0.594767
$118$	28.3155	2.60665
$119$	11.4529	1.04988
$120$	−87.5418	−7.99143
$121$	−6.76475	−0.614977
$122$	10.0927	0.913747
$123$	−2.02854	−0.182907
$124$	−41.3738	−3.71548
$125$	22.8943	2.04773
$126$	−9.25166	−0.824204
$127$	−12.1063	−1.07426	−0.537129	−	0.843500i	$-0.680491\pi$
$127$	−12.1063	−1.07426	−0.537129	+	0.843500i	$0.680491\pi$
$128$	−48.7657	−4.31032
$129$	−19.5631	−1.72244
$130$	36.0496	3.16176
$131$	−5.85661	−0.511694	−0.255847	−	0.966717i	$-0.582354\pi$
$131$	−5.85661	−0.511694	−0.255847	+	0.966717i	$0.582354\pi$
$132$	25.6241	2.23029
$133$	−9.16329	−0.794558
$134$	−16.6486	−1.43822
$135$	−9.25373	−0.796435
$136$	−65.9994	−5.65940
$137$	12.3684	1.05671	0.528353	−	0.849025i	$-0.322810\pi$
$137$	12.3684	1.05671	0.528353	+	0.849025i	$0.322810\pi$
$138$	−6.13314	−0.522088
$139$	14.5699	1.23580	0.617900	−	0.786256i	$-0.287983\pi$
$139$	14.5699	1.23580	0.617900	+	0.786256i	$0.287983\pi$
$140$	38.1899	3.22764
$141$	4.65521	0.392040
$142$	8.66424	0.727087
$143$	−6.77990	−0.566964
$144$	31.4635	2.62196
$145$	−3.97063	−0.329743
$146$	25.3822	2.10064
$147$	−9.00128	−0.742413
$148$	−2.30216	−0.189237
$149$	24.3509	1.99490	0.997451	−	0.0713479i	$-0.0227301\pi$
$149$	24.3509	1.99490	0.997451	+	0.0713479i	$0.0227301\pi$
$150$	−66.0289	−5.39123
$151$	−21.9491	−1.78619	−0.893095	−	0.449868i	$-0.851471\pi$
$151$	−21.9491	−1.78619	−0.893095	+	0.449868i	$0.851471\pi$
$152$	52.8051	4.28306
$153$	13.0097	1.05177
$154$	−9.74997	−0.785675
$155$	−29.3631	−2.35850
$156$	−41.0197	−3.28420
$157$	−0.771320	−0.0615580	−0.0307790	−	0.999526i	$-0.509799\pi$
$157$	−0.771320	−0.0615580	−0.0307790	+	0.999526i	$0.509799\pi$
$158$	−43.6544	−3.47296
$159$	9.77487	0.775198
$160$	−97.6344	−7.71867
$161$	1.71912	0.135485
$162$	30.4385	2.39147
$163$	1.97507	0.154700	0.0773498	−	0.997004i	$-0.475354\pi$
$163$	1.97507	0.154700	0.0773498	+	0.997004i	$0.475354\pi$
$164$	−5.09966	−0.398216
$165$	18.1855	1.41574
$166$	−12.0737	−0.937099
$167$	3.60798	0.279194	0.139597	−	0.990208i	$-0.455419\pi$
$167$	3.60798	0.279194	0.139597	+	0.990208i	$0.455419\pi$
$168$	−37.9019	−2.92420
$169$	−2.14657	−0.165121
$170$	−72.8999	−5.59116
$171$	−10.4088	−0.795983
$172$	−49.1809	−3.75001
$173$	22.0323	1.67509	0.837543	−	0.546371i	$-0.183991\pi$
$173$	22.0323	1.67509	0.837543	+	0.546371i	$0.183991\pi$
$174$	6.13314	0.464952
$175$	18.5079	1.39906
$176$	33.1582	2.49939
$177$	−22.8661	−1.71872
$178$	9.20642	0.690050
$179$	15.9969	1.19566	0.597830	−	0.801623i	$-0.296030\pi$
$179$	15.9969	1.19566	0.597830	+	0.801623i	$0.296030\pi$
$180$	43.3810	3.23343
$181$	18.4448	1.37099	0.685494	−	0.728078i	$-0.259586\pi$
$181$	18.4448	1.37099	0.685494	+	0.728078i	$0.259586\pi$
$182$	15.6080	1.15694
$183$	−8.15030	−0.602487
$184$	−9.90674	−0.730334
$185$	−1.63385	−0.120123
$186$	45.3550	3.32559
$187$	13.7104	1.00260
$188$	11.7030	0.853531
$189$	−4.00648	−0.291429
$190$	58.3261	4.23142
$191$	−10.7558	−0.778266	−0.389133	−	0.921182i	$-0.627225\pi$
$191$	−10.7558	−0.778266	−0.389133	+	0.921182i	$0.627225\pi$
$192$	79.0942	5.70814
$193$	6.20786	0.446852	0.223426	−	0.974721i	$-0.428276\pi$
$193$	6.20786	0.446852	0.223426	+	0.974721i	$0.428276\pi$
$194$	−27.8495	−1.99948
$195$	−29.1117	−2.08474
$196$	−22.6288	−1.61635
$197$	−7.85502	−0.559647	−0.279823	−	0.960051i	$-0.590276\pi$
$197$	−7.85502	−0.559647	−0.279823	+	0.960051i	$0.590276\pi$
$198$	−11.0753	−0.787084
$199$	−12.1554	−0.861675	−0.430837	−	0.902430i	$-0.641782\pi$
$199$	−12.1554	−0.861675	−0.430837	+	0.902430i	$0.641782\pi$
$200$	−106.655	−7.54165
$201$	13.4445	0.948303
$202$	30.3111	2.13268
$203$	−1.71912	−0.120658
$204$	82.9503	5.80768
$205$	−3.61924	−0.252779
$206$	−6.95626	−0.484665
$207$	1.95279	0.135729
$208$	−53.0804	−3.68046
$209$	−10.9695	−0.758773
$210$	−41.8647	−2.88894
$211$	12.1084	0.833578	0.416789	−	0.909003i	$-0.363155\pi$
$211$	12.1084	0.833578	0.416789	+	0.909003i	$0.363155\pi$
$212$	24.5736	1.68772
$213$	−6.99677	−0.479411
$214$	−17.4773	−1.19472
$215$	−34.9038	−2.38042
$216$	23.0881	1.57095
$217$	−12.7130	−0.863014
$218$	5.35830	0.362910
$219$	−20.4973	−1.38508
$220$	45.7175	3.08227
$221$	−21.9479	−1.47638
$222$	2.52369	0.169379
$223$	−7.58420	−0.507876	−0.253938	−	0.967221i	$-0.581726\pi$
$223$	−7.58420	−0.507876	−0.253938	+	0.967221i	$0.581726\pi$
$224$	−42.2716	−2.82439
$225$	21.0236	1.40157
$226$	−3.71128	−0.246870
$227$	8.88335	0.589608	0.294804	−	0.955558i	$-0.404746\pi$
$227$	8.88335	0.589608	0.294804	+	0.955558i	$0.404746\pi$
$228$	−66.3673	−4.39528
$229$	13.5545	0.895707	0.447853	−	0.894107i	$-0.352189\pi$
$229$	13.5545	0.895707	0.447853	+	0.894107i	$0.352189\pi$
$230$	−10.9425	−0.721528
$231$	7.87355	0.518042
$232$	9.90674	0.650409
$233$	−8.48384	−0.555795	−0.277898	−	0.960611i	$-0.589638\pi$
$233$	−8.48384	−0.555795	−0.277898	+	0.960611i	$0.589638\pi$
$234$	17.7295	1.15902
$235$	8.30566	0.541802
$236$	−57.4844	−3.74192
$237$	35.2530	2.28993
$238$	−31.5626	−2.04590
$239$	−13.9812	−0.904368	−0.452184	−	0.891925i	$-0.649355\pi$
$239$	−13.9812	−0.904368	−0.452184	+	0.891925i	$0.649355\pi$
$240$	142.376	9.19030
$241$	8.96116	0.577239	0.288619	−	0.957444i	$-0.406804\pi$
$241$	8.96116	0.577239	0.288619	+	0.957444i	$0.406804\pi$
$242$	18.6427	1.19840
$243$	−17.5888	−1.12832
$244$	−20.4895	−1.31171
$245$	−16.0597	−1.02602
$246$	5.59037	0.356429
$247$	17.5602	1.11733
$248$	73.2610	4.65208
$249$	9.75005	0.617884
$250$	−63.0937	−3.99039
$251$	−0.338546	−0.0213688	−0.0106844	−	0.999943i	$-0.503401\pi$
$251$	−0.338546	−0.0213688	−0.0106844	+	0.999943i	$0.503401\pi$
$252$	18.7822	1.18316
$253$	2.05797	0.129384
$254$	33.3632	2.09339
$255$	58.8700	3.68658
$256$	63.3111	3.95695
$257$	12.6586	0.789622	0.394811	−	0.918762i	$-0.370810\pi$
$257$	12.6586	0.789622	0.394811	+	0.918762i	$0.370810\pi$
$258$	53.9133	3.35650
$259$	−0.707389	−0.0439550
$260$	−73.1858	−4.53879
$261$	−1.95279	−0.120875
$262$	16.1400	0.997133
$263$	21.2595	1.31091	0.655457	−	0.755232i	$-0.272476\pi$
$263$	21.2595	1.31091	0.655457	+	0.755232i	$0.272476\pi$
$264$	−45.3728	−2.79250
$265$	17.4400	1.07133
$266$	25.2528	1.54835
$267$	−7.43461	−0.454991
$268$	33.7990	2.06460
$269$	−1.05807	−0.0645117	−0.0322558	−	0.999480i	$-0.510269\pi$
$269$	−1.05807	−0.0645117	−0.0322558	+	0.999480i	$0.510269\pi$
$270$	25.5020	1.55200
$271$	15.3645	0.933329	0.466664	−	0.884434i	$-0.345456\pi$
$271$	15.3645	0.933329	0.466664	+	0.884434i	$0.345456\pi$
$272$	107.340	6.50842
$273$	−12.6042	−0.762839
$274$	−34.0857	−2.05919
$275$	22.1560	1.33606
$276$	12.4511	0.749469
$277$	−1.28420	−0.0771603	−0.0385802	−	0.999256i	$-0.512283\pi$
$277$	−1.28420	−0.0771603	−0.0385802	+	0.999256i	$0.512283\pi$
$278$	−40.1526	−2.40819
$279$	−14.4410	−0.864562
$280$	−67.6232	−4.04126
$281$	−27.7871	−1.65764	−0.828820	−	0.559515i	$-0.810988\pi$
$281$	−27.7871	−1.65764	−0.828820	+	0.559515i	$0.810988\pi$
$282$	−12.8291	−0.763964
$283$	2.11938	0.125984	0.0629920	−	0.998014i	$-0.479936\pi$
$283$	2.11938	0.125984	0.0629920	+	0.998014i	$0.479936\pi$
$284$	−17.5896	−1.04375
$285$	−47.1010	−2.79002
$286$	18.6845	1.10484
$287$	−1.56698	−0.0924959
$288$	−48.0175	−2.82946
$289$	27.3832	1.61078
$290$	10.9425	0.642567
$291$	22.4898	1.31837
$292$	−51.5293	−3.01553
$293$	18.5649	1.08458	0.542288	−	0.840193i	$-0.317558\pi$
$293$	18.5649	1.08458	0.542288	+	0.840193i	$0.317558\pi$
$294$	24.8063	1.44673
$295$	−40.7968	−2.37528
$296$	4.07646	0.236939
$297$	−4.79620	−0.278304
$298$	−67.1077	−3.88745
$299$	−3.29445	−0.190523
$300$	134.048	7.73925
$301$	−15.1119	−0.871035
$302$	60.4886	3.48073
$303$	−24.4776	−1.40620
$304$	−85.8808	−4.92560
$305$	−14.5415	−0.832641
$306$	−35.8528	−2.04957
$307$	−15.3804	−0.877808	−0.438904	−	0.898534i	$-0.644633\pi$
$307$	−15.3804	−0.877808	−0.438904	+	0.898534i	$0.644633\pi$
$308$	19.7938	1.12786
$309$	5.61750	0.319568
$310$	80.9207	4.59598
$311$	−2.89200	−0.163990	−0.0819950	−	0.996633i	$-0.526129\pi$
$311$	−2.89200	−0.163990	−0.0819950	+	0.996633i	$0.526129\pi$
$312$	72.6339	4.11208
$313$	−4.88430	−0.276077	−0.138039	−	0.990427i	$-0.544080\pi$
$313$	−4.88430	−0.276077	−0.138039	+	0.990427i	$0.544080\pi$
$314$	2.12565	0.119958
$315$	13.3297	0.751046
$316$	88.6245	4.98552
$317$	−25.2420	−1.41773	−0.708866	−	0.705343i	$-0.750793\pi$
$317$	−25.2420	−1.41773	−0.708866	+	0.705343i	$0.750793\pi$
$318$	−26.9382	−1.51062
$319$	−2.05797	−0.115224
$320$	141.117	7.88868
$321$	14.1137	0.787750
$322$	−4.73766	−0.264019
$323$	−35.5103	−1.97585
$324$	−61.7943	−3.43302
$325$	−35.4678	−1.96740
$326$	−5.44303	−0.301462
$327$	−4.32707	−0.239288
$328$	9.03001	0.498599
$329$	3.59601	0.198254
$330$	−50.1167	−2.75883
$331$	−31.1187	−1.71044	−0.855219	−	0.518267i	$-0.826577\pi$
$331$	−31.1187	−1.71044	−0.855219	+	0.518267i	$0.826577\pi$
$332$	24.5112	1.34523
$333$	−0.803543	−0.0440339
$334$	−9.94310	−0.544062
$335$	23.9872	1.31056
$336$	61.6427	3.36288
$337$	27.1461	1.47874	0.739370	−	0.673300i	$-0.235124\pi$
$337$	27.1461	1.47874	0.739370	+	0.673300i	$0.235124\pi$
$338$	5.91564	0.321769
$339$	2.99703	0.162776
$340$	147.997	8.02625
$341$	−15.2188	−0.824147
$342$	28.6853	1.55112
$343$	−18.9870	−1.02520
$344$	87.0851	4.69531
$345$	8.83659	0.475746
$346$	−60.7181	−3.26422
$347$	−25.5084	−1.36936	−0.684682	−	0.728842i	$-0.740059\pi$
$347$	−25.5084	−1.36936	−0.684682	+	0.728842i	$0.740059\pi$
$348$	−12.4511	−0.667450
$349$	5.24931	0.280989	0.140495	−	0.990081i	$-0.455131\pi$
$349$	5.24931	0.280989	0.140495	+	0.990081i	$0.455131\pi$
$350$	−51.0052	−2.72634
$351$	7.67787	0.409815
$352$	−50.6038	−2.69719
$353$	3.78021	0.201200	0.100600	−	0.994927i	$-0.467924\pi$
$353$	3.78021	0.201200	0.100600	+	0.994927i	$0.467924\pi$
$354$	63.0158	3.34925
$355$	−12.4834	−0.662549
$356$	−18.6903	−0.990584
$357$	25.4883	1.34898
$358$	−44.0851	−2.32997
$359$	−30.1937	−1.59356	−0.796781	−	0.604268i	$-0.793466\pi$
$359$	−30.1937	−1.59356	−0.796781	+	0.604268i	$0.793466\pi$
$360$	−76.8151	−4.04851
$361$	9.41130	0.495331
$362$	−50.8312	−2.67163
$363$	−15.0549	−0.790175
$364$	−31.6864	−1.66082
$365$	−36.5705	−1.91419
$366$	22.4611	1.17406
$367$	18.7318	0.977791	0.488896	−	0.872342i	$-0.337400\pi$
$367$	18.7318	0.977791	0.488896	+	0.872342i	$0.337400\pi$
$368$	16.1120	0.839898
$369$	−1.77998	−0.0926618
$370$	4.50267	0.234083
$371$	7.55078	0.392017
$372$	−92.0769	−4.77396
$373$	7.52447	0.389602	0.194801	−	0.980843i	$-0.437594\pi$
$373$	7.52447	0.389602	0.194801	+	0.980843i	$0.437594\pi$
$374$	−37.7839	−1.95376
$375$	50.9510	2.63110
$376$	−20.7226	−1.06869
$377$	3.29445	0.169673
$378$	11.0413	0.567904
$379$	−24.1680	−1.24143	−0.620714	−	0.784037i	$-0.713157\pi$
$379$	−24.1680	−1.24143	−0.620714	+	0.784037i	$0.713157\pi$
$380$	−118.410	−6.07431
$381$	−26.9423	−1.38030
$382$	29.6416	1.51660
$383$	−20.6573	−1.05554	−0.527769	−	0.849388i	$-0.676971\pi$
$383$	−20.6573	−1.05554	−0.527769	+	0.849388i	$0.676971\pi$
$384$	−108.527	−5.53826
$385$	14.0477	0.715937
$386$	−17.1080	−0.870775
$387$	−17.1660	−0.872598
$388$	56.5383	2.87030
$389$	4.49653	0.227983	0.113992	−	0.993482i	$-0.463636\pi$
$389$	4.49653	0.227983	0.113992	+	0.993482i	$0.463636\pi$
$390$	80.2280	4.06250
$391$	6.66207	0.336915
$392$	40.0691	2.02380
$393$	−13.0338	−0.657468
$394$	21.6474	1.09058
$395$	62.8970	3.16469
$396$	22.4843	1.12988
$397$	−6.20320	−0.311330	−0.155665	−	0.987810i	$-0.549752\pi$
$397$	−6.20320	−0.311330	−0.155665	+	0.987810i	$0.549752\pi$
$398$	33.4987	1.67914
$399$	−20.3928	−1.02092
$400$	173.461	8.67305
$401$	−20.4595	−1.02170	−0.510848	−	0.859671i	$-0.670669\pi$
$401$	−20.4595	−1.02170	−0.510848	+	0.859671i	$0.670669\pi$
$402$	−37.0513	−1.84795
$403$	24.3627	1.21359
$404$	−61.5357	−3.06152
$405$	−43.8555	−2.17920
$406$	4.73766	0.235126
$407$	−0.846822	−0.0419754
$408$	−146.881	−7.27168
$409$	7.99251	0.395204	0.197602	−	0.980282i	$-0.436685\pi$
$409$	7.99251	0.395204	0.197602	+	0.980282i	$0.436685\pi$
$410$	9.97413	0.492587
$411$	27.5258	1.35775
$412$	14.1222	0.695749
$413$	−17.6633	−0.869156
$414$	−5.38163	−0.264493
$415$	17.3957	0.853920
$416$	81.0078	3.97173
$417$	32.4251	1.58786
$418$	30.2303	1.47861
$419$	−0.850537	−0.0415514	−0.0207757	−	0.999784i	$-0.506614\pi$
$419$	−0.850537	−0.0415514	−0.0207757	+	0.999784i	$0.506614\pi$
$420$	84.9912	4.14714
$421$	−17.2900	−0.842663	−0.421331	−	0.906907i	$-0.638437\pi$
$421$	−17.2900	−0.842663	−0.421331	+	0.906907i	$0.638437\pi$
$422$	−33.3691	−1.62438
$423$	4.08480	0.198610
$424$	−43.5128	−2.11317
$425$	71.7233	3.47909
$426$	19.2822	0.934224
$427$	−6.29585	−0.304677
$428$	35.4812	1.71505
$429$	−15.0886	−0.728484
$430$	96.1901	4.63870
$431$	−1.79968	−0.0866874	−0.0433437	−	0.999060i	$-0.513801\pi$
$431$	−1.79968	−0.0866874	−0.0433437	+	0.999060i	$0.513801\pi$
$432$	−37.5498	−1.80662
$433$	−1.06711	−0.0512820	−0.0256410	−	0.999671i	$-0.508163\pi$
$433$	−1.06711	−0.0512820	−0.0256410	+	0.999671i	$0.508163\pi$
$434$	35.0353	1.68175
$435$	−8.83659	−0.423682
$436$	−10.8781	−0.520966
$437$	−5.33022	−0.254979
$438$	56.4877	2.69909
$439$	22.5518	1.07634	0.538169	−	0.842837i	$-0.319116\pi$
$439$	22.5518	1.07634	0.538169	+	0.842837i	$0.319116\pi$
$440$	−80.9524	−3.85926
$441$	−7.89833	−0.376111
$442$	60.4854	2.87700
$443$	28.3020	1.34467	0.672333	−	0.740249i	$-0.265292\pi$
$443$	28.3020	1.34467	0.672333	+	0.740249i	$0.265292\pi$
$444$	−5.12343	−0.243147
$445$	−13.2646	−0.628800
$446$	20.9010	0.989692
$447$	54.1926	2.56322
$448$	61.0978	2.88660
$449$	22.2150	1.04839	0.524195	−	0.851598i	$-0.324366\pi$
$449$	22.2150	1.04839	0.524195	+	0.851598i	$0.324366\pi$
$450$	−57.9382	−2.73123
$451$	−1.87585	−0.0883302
$452$	7.53441	0.354389
$453$	−48.8474	−2.29505
$454$	−24.4813	−1.14896
$455$	−22.4879	−1.05425
$456$	117.517	5.50324
$457$	−1.32853	−0.0621462	−0.0310731	−	0.999517i	$-0.509892\pi$
$457$	−1.32853	−0.0621462	−0.0310731	+	0.999517i	$0.509892\pi$
$458$	−37.3544	−1.74545
$459$	−15.5263	−0.724704
$460$	22.2148	1.03577
$461$	−20.9432	−0.975423	−0.487712	−	0.873005i	$-0.662168\pi$
$461$	−20.9432	−0.975423	−0.487712	+	0.873005i	$0.662168\pi$
$462$	−21.6984	−1.00950
$463$	−19.0107	−0.883501	−0.441751	−	0.897138i	$-0.645642\pi$
$463$	−19.0107	−0.883501	−0.441751	+	0.897138i	$0.645642\pi$
$464$	−16.1120	−0.747983
$465$	−65.3472	−3.03040
$466$	23.3803	1.08307
$467$	−12.8807	−0.596048	−0.298024	−	0.954558i	$-0.596327\pi$
$467$	−12.8807	−0.596048	−0.298024	+	0.954558i	$0.596327\pi$
$468$	−35.9934	−1.66380
$469$	10.3855	0.479556
$470$	−22.8893	−1.05580
$471$	−1.71656	−0.0790950
$472$	101.788	4.68518
$473$	−18.0906	−0.831806
$474$	−97.1523	−4.46235
$475$	−57.3848	−2.63299
$476$	64.0764	2.93694
$477$	8.57714	0.392720
$478$	38.5303	1.76233
$479$	8.08127	0.369243	0.184621	−	0.982810i	$-0.440894\pi$
$479$	8.08127	0.369243	0.184621	+	0.982810i	$0.440894\pi$
$480$	−217.284	−9.91761
$481$	1.35561	0.0618107
$482$	−24.6957	−1.12486
$483$	3.82588	0.174083
$484$	−37.8473	−1.72033
$485$	40.1254	1.82200
$486$	48.4724	2.19875
$487$	15.3967	0.697692	0.348846	−	0.937180i	$-0.386574\pi$
$487$	15.3967	0.697692	0.348846	+	0.937180i	$0.386574\pi$
$488$	36.2810	1.64236
$489$	4.39550	0.198771
$490$	44.2585	1.99939
$491$	25.7566	1.16238	0.581190	−	0.813768i	$-0.302587\pi$
$491$	25.7566	1.16238	0.581190	+	0.813768i	$0.302587\pi$
$492$	−11.3492	−0.511662
$493$	−6.66207	−0.300045
$494$	−48.3935	−2.17733
$495$	15.9572	0.717221
$496$	−119.150	−5.34998
$497$	−5.40479	−0.242438
$498$	−26.8698	−1.20406
$499$	−14.5071	−0.649429	−0.324715	−	0.945812i	$-0.605268\pi$
$499$	−14.5071	−0.649429	−0.324715	+	0.945812i	$0.605268\pi$
$500$	128.089	5.72831
$501$	8.02951	0.358732
$502$	0.932987	0.0416412
$503$	−8.10676	−0.361463	−0.180731	−	0.983533i	$-0.557846\pi$
$503$	−8.10676	−0.361463	−0.180731	+	0.983533i	$0.557846\pi$
$504$	−33.2577	−1.48142
$505$	−43.6721	−1.94338
$506$	−5.67149	−0.252129
$507$	−4.77716	−0.212161
$508$	−67.7319	−3.00512
$509$	24.5409	1.08776	0.543878	−	0.839164i	$-0.316955\pi$
$509$	24.5409	1.08776	0.543878	+	0.839164i	$0.316955\pi$
$510$	−162.238	−7.18401
$511$	−15.8335	−0.700433
$512$	−76.9456	−3.40055
$513$	12.4223	0.548459
$514$	−34.8854	−1.53873
$515$	10.0225	0.441646
$516$	−109.451	−4.81833
$517$	4.30481	0.189325
$518$	1.94947	0.0856547
$519$	49.0327	2.15230
$520$	129.591	5.68293
$521$	−42.1003	−1.84445	−0.922225	−	0.386655i	$-0.873631\pi$
$521$	−42.1003	−1.84445	−0.922225	+	0.386655i	$0.873631\pi$
$522$	5.38163	0.235548
$523$	−28.8156	−1.26002	−0.630009	−	0.776587i	$-0.716949\pi$
$523$	−28.8156	−1.26002	−0.630009	+	0.776587i	$0.716949\pi$
$524$	−32.7664	−1.43141
$525$	41.1891	1.79764
$526$	−58.5882	−2.55457
$527$	−49.2665	−2.14608
$528$	73.7931	3.21143
$529$	1.00000	0.0434783
$530$	−48.0622	−2.08769
$531$	−20.0643	−0.870715
$532$	−51.2666	−2.22269
$533$	3.00290	0.130070
$534$	20.4888	0.886636
$535$	25.1811	1.08868
$536$	−59.8482	−2.58505
$537$	35.6008	1.53629
$538$	2.91590	0.125713
$539$	−8.32375	−0.358529
$540$	−51.7726	−2.22794
$541$	19.3793	0.833181	0.416590	−	0.909094i	$-0.363225\pi$
$541$	19.3793	0.833181	0.416590	+	0.909094i	$0.363225\pi$
$542$	−42.3426	−1.81877
$543$	41.0486	1.76156
$544$	−163.815	−7.02349
$545$	−7.72020	−0.330697
$546$	34.7354	1.48654
$547$	−34.2057	−1.46253	−0.731264	−	0.682094i	$-0.761069\pi$
$547$	−34.2057	−1.46253	−0.731264	+	0.682094i	$0.761069\pi$
$548$	69.1987	2.95602
$549$	−7.15162	−0.305224
$550$	−61.0588	−2.60356
$551$	5.33022	0.227075
$552$	−22.0473	−0.938396
$553$	27.2318	1.15801
$554$	3.53909	0.150362
$555$	−3.63611	−0.154344
$556$	81.5153	3.45702
$557$	46.5284	1.97147	0.985736	−	0.168299i	$-0.0538274\pi$
$557$	46.5284	1.97147	0.985736	+	0.168299i	$0.0538274\pi$
$558$	39.7975	1.68476
$559$	28.9599	1.22487
$560$	109.981	4.64753
$561$	30.5122	1.28823
$562$	76.5775	3.23023
$563$	27.5819	1.16244	0.581219	−	0.813747i	$-0.302576\pi$
$563$	27.5819	1.16244	0.581219	+	0.813747i	$0.302576\pi$
$564$	26.0449	1.09669
$565$	5.34719	0.224958
$566$	−5.84072	−0.245504
$567$	−18.9876	−0.797405
$568$	31.1461	1.30686
$569$	−14.9145	−0.625249	−0.312625	−	0.949877i	$-0.601208\pi$
$569$	−14.9145	−0.625249	−0.312625	+	0.949877i	$0.601208\pi$
$570$	129.804	5.43689
$571$	−28.6762	−1.20006	−0.600030	−	0.799978i	$-0.704845\pi$
$571$	−28.6762	−1.20006	−0.600030	+	0.799978i	$0.704845\pi$
$572$	−37.9321	−1.58602
$573$	−23.9370	−0.999982
$574$	4.31838	0.180246
$575$	10.7659	0.448970
$576$	69.4027	2.89178
$577$	28.4626	1.18491	0.592457	−	0.805602i	$-0.298158\pi$
$577$	28.4626	1.18491	0.592457	+	0.805602i	$0.298158\pi$
$578$	−75.4644	−3.13891
$579$	13.8155	0.574153
$580$	−22.2148	−0.922421
$581$	7.53160	0.312464
$582$	−61.9787	−2.56910
$583$	9.03911	0.374362
$584$	91.2435	3.77568
$585$	−25.5446	−1.05614
$586$	−51.1625	−2.11350
$587$	−31.3487	−1.29390	−0.646950	−	0.762532i	$-0.723956\pi$
$587$	−31.3487	−1.29390	−0.646950	+	0.762532i	$0.723956\pi$
$588$	−50.3602	−2.07682
$589$	39.4174	1.62416
$590$	112.431	4.62869
$591$	−17.4812	−0.719082
$592$	−6.62984	−0.272485
$593$	24.2159	0.994426	0.497213	−	0.867628i	$-0.334357\pi$
$593$	24.2159	0.994426	0.497213	+	0.867628i	$0.334357\pi$
$594$	13.2177	0.542328
$595$	45.4752	1.86430
$596$	136.238	5.58053
$597$	−27.0517	−1.10715
$598$	9.07907	0.371271
$599$	13.1963	0.539187	0.269594	−	0.962974i	$-0.413111\pi$
$599$	13.1963	0.539187	0.269594	+	0.962974i	$0.413111\pi$
$600$	−237.360	−9.69016
$601$	−38.2640	−1.56082	−0.780411	−	0.625267i	$-0.784990\pi$
$601$	−38.2640	−1.56082	−0.780411	+	0.625267i	$0.784990\pi$
$602$	41.6463	1.69738
$603$	11.7971	0.480416
$604$	−122.800	−4.99667
$605$	−26.8603	−1.09203
$606$	67.4570	2.74025
$607$	22.7999	0.925418	0.462709	−	0.886510i	$-0.346878\pi$
$607$	22.7999	0.925418	0.462709	+	0.886510i	$0.346878\pi$
$608$	131.066	5.31541
$609$	−3.82588	−0.155032
$610$	40.0743	1.62256
$611$	−6.89125	−0.278790
$612$	72.7862	2.94221
$613$	26.4881	1.06984	0.534922	−	0.844901i	$-0.320341\pi$
$613$	26.4881	1.06984	0.534922	+	0.844901i	$0.320341\pi$
$614$	42.3864	1.71058
$615$	−8.05457	−0.324792
$616$	−35.0490	−1.41217
$617$	−8.11283	−0.326610	−0.163305	−	0.986576i	$-0.552215\pi$
$617$	−8.11283	−0.326610	−0.163305	+	0.986576i	$0.552215\pi$
$618$	−15.4811	−0.622740
$619$	−32.9673	−1.32507	−0.662533	−	0.749032i	$-0.730519\pi$
$619$	−32.9673	−1.32507	−0.662533	+	0.749032i	$0.730519\pi$
$620$	−164.280	−6.59765
$621$	−2.33054	−0.0935215
$622$	7.96995	0.319566
$623$	−5.74300	−0.230088
$624$	−118.130	−4.72898
$625$	37.0754	1.48301
$626$	13.4605	0.537989
$627$	−24.4124	−0.974937
$628$	−4.31537	−0.172202
$629$	−2.74133	−0.109304
$630$	−36.7349	−1.46356
$631$	−13.9221	−0.554230	−0.277115	−	0.960837i	$-0.589378\pi$
$631$	−13.9221	−0.554230	−0.277115	+	0.960837i	$0.589378\pi$
$632$	−156.928	−6.24227
$633$	26.9471	1.07105
$634$	69.5635	2.76272
$635$	−48.0695	−1.90758
$636$	54.6883	2.16853
$637$	13.3249	0.527950
$638$	5.67149	0.224537
$639$	−6.13945	−0.242873
$640$	−193.630	−7.65392
$641$	−39.8891	−1.57552	−0.787762	−	0.615980i	$-0.788760\pi$
$641$	−39.8891	−1.57552	−0.787762	+	0.615980i	$0.788760\pi$
$642$	−38.8954	−1.53508
$643$	−13.7780	−0.543350	−0.271675	−	0.962389i	$-0.587578\pi$
$643$	−13.7780	−0.543350	−0.271675	+	0.962389i	$0.587578\pi$
$644$	9.61810	0.379006
$645$	−77.6780	−3.05857
$646$	97.8617	3.85032
$647$	16.7857	0.659914	0.329957	−	0.943996i	$-0.392966\pi$
$647$	16.7857	0.659914	0.329957	+	0.943996i	$0.392966\pi$
$648$	109.420	4.29841
$649$	−21.1449	−0.830012
$650$	97.7445	3.83385
$651$	−28.2926	−1.10887
$652$	11.0501	0.432756
$653$	42.4136	1.65977	0.829886	−	0.557933i	$-0.188405\pi$
$653$	42.4136	1.65977	0.829886	+	0.557933i	$0.188405\pi$
$654$	11.9248	0.466297
$655$	−23.2544	−0.908626
$656$	−14.6862	−0.573398
$657$	−17.9857	−0.701689
$658$	−9.91010	−0.386336
$659$	28.6127	1.11459	0.557297	−	0.830313i	$-0.311838\pi$
$659$	28.6127	1.11459	0.557297	+	0.830313i	$0.311838\pi$
$660$	101.744	3.96037
$661$	26.9749	1.04920	0.524601	−	0.851349i	$-0.324215\pi$
$661$	26.9749	1.04920	0.524601	+	0.851349i	$0.324215\pi$
$662$	85.7589	3.33311
$663$	−48.8448	−1.89697
$664$	−43.4022	−1.68433
$665$	−36.3840	−1.41091
$666$	2.21445	0.0858083
$667$	−1.00000	−0.0387202
$668$	20.1859	0.781015
$669$	−16.8785	−0.652562
$670$	−66.1055	−2.55388
$671$	−7.53682	−0.290956
$672$	−94.0749	−3.62902
$673$	45.2189	1.74306	0.871531	−	0.490341i	$-0.163128\pi$
$673$	45.2189	1.74306	0.871531	+	0.490341i	$0.163128\pi$
$674$	−74.8108	−2.88161
$675$	−25.0904	−0.965732
$676$	−12.0096	−0.461907
$677$	39.5522	1.52011	0.760057	−	0.649857i	$-0.225171\pi$
$677$	39.5522	1.52011	0.760057	+	0.649857i	$0.225171\pi$
$678$	−8.25940	−0.317200
$679$	17.3726	0.666700
$680$	−262.059	−10.0495
$681$	19.7698	0.757579
$682$	41.9411	1.60601
$683$	−14.8440	−0.567990	−0.283995	−	0.958826i	$-0.591660\pi$
$683$	−14.8440	−0.567990	−0.283995	+	0.958826i	$0.591660\pi$
$684$	−58.2352	−2.22668
$685$	49.1105	1.87641
$686$	52.3257	1.99780
$687$	30.1654	1.15088
$688$	−141.633	−5.39970
$689$	−14.4700	−0.551264
$690$	−24.3524	−0.927081
$691$	21.4738	0.816903	0.408452	−	0.912780i	$-0.366069\pi$
$691$	21.4738	0.816903	0.408452	+	0.912780i	$0.366069\pi$
$692$	123.266	4.68587
$693$	6.90879	0.262443
$694$	70.2977	2.66846
$695$	57.8516	2.19444
$696$	22.0473	0.835701
$697$	−6.07249	−0.230012
$698$	−14.4664	−0.547560
$699$	−18.8807	−0.714133
$700$	103.548	3.91373
$701$	26.7986	1.01217	0.506085	−	0.862484i	$-0.331092\pi$
$701$	26.7986	1.01217	0.506085	+	0.862484i	$0.331092\pi$
$702$	−21.1592	−0.798602
$703$	2.19330	0.0827219
$704$	73.1408	2.75660
$705$	18.4841	0.696153
$706$	−10.4178	−0.392077
$707$	−18.9082	−0.711115
$708$	−127.931	−4.80794
$709$	4.46257	0.167595	0.0837976	−	0.996483i	$-0.473295\pi$
$709$	4.46257	0.167595	0.0837976	+	0.996483i	$0.473295\pi$
$710$	34.4025	1.29110
$711$	30.9333	1.16009
$712$	33.0951	1.24029
$713$	−7.39507	−0.276947
$714$	−70.2422	−2.62875
$715$	−26.9205	−1.00677
$716$	89.4989	3.34473
$717$	−31.1150	−1.16201
$718$	83.2097	3.10536
$719$	45.2228	1.68653	0.843263	−	0.537502i	$-0.180632\pi$
$719$	45.2228	1.68653	0.843263	+	0.537502i	$0.180632\pi$
$720$	124.930	4.65586
$721$	4.33934	0.161605
$722$	−25.9363	−0.965247
$723$	19.9429	0.741686
$724$	103.194	3.83519
$725$	−10.7659	−0.399836
$726$	41.4891	1.53981
$727$	9.52550	0.353281	0.176641	−	0.984275i	$-0.443477\pi$
$727$	9.52550	0.353281	0.176641	+	0.984275i	$0.443477\pi$
$728$	56.1074	2.07948
$729$	−6.00877	−0.222547
$730$	100.783	3.73016
$731$	−58.5629	−2.16603
$732$	−45.5992	−1.68539
$733$	23.4970	0.867883	0.433941	−	0.900941i	$-0.357123\pi$
$733$	23.4970	0.867883	0.433941	+	0.900941i	$0.357123\pi$
$734$	−51.6223	−1.90541
$735$	−35.7408	−1.31832
$736$	−24.5891	−0.906367
$737$	12.4325	0.457959
$738$	4.90537	0.180569
$739$	−21.1678	−0.778672	−0.389336	−	0.921096i	$-0.627295\pi$
$739$	−21.1678	−0.778672	−0.389336	+	0.921096i	$0.627295\pi$
$740$	−9.14104	−0.336031
$741$	39.0800	1.43564
$742$	−20.8089	−0.763919
$743$	−3.57125	−0.131016	−0.0655082	−	0.997852i	$-0.520867\pi$
$743$	−3.57125	−0.131016	−0.0655082	+	0.997852i	$0.520867\pi$
$744$	163.041	5.97739
$745$	96.6884	3.54239
$746$	−20.7364	−0.759214
$747$	8.55535	0.313024
$748$	76.7065	2.80467
$749$	10.9024	0.398364
$750$	−140.414	−5.12720
$751$	13.4685	0.491473	0.245737	−	0.969337i	$-0.420970\pi$
$751$	13.4685	0.491473	0.245737	+	0.969337i	$0.420970\pi$
$752$	33.7027	1.22901
$753$	−0.753430	−0.0274565
$754$	−9.07907	−0.330640
$755$	−87.1517	−3.17177
$756$	−22.4154	−0.815240
$757$	0.558236	0.0202894	0.0101447	−	0.999949i	$-0.496771\pi$
$757$	0.558236	0.0202894	0.0101447	+	0.999949i	$0.496771\pi$
$758$	66.6037	2.41916
$759$	4.57999	0.166243
$760$	209.670	7.60552
$761$	−9.01669	−0.326855	−0.163427	−	0.986555i	$-0.552255\pi$
$761$	−9.01669	−0.326855	−0.163427	+	0.986555i	$0.552255\pi$
$762$	74.2494	2.68977
$763$	−3.34252	−0.121008
$764$	−60.1766	−2.17711
$765$	51.6565	1.86765
$766$	56.9286	2.05692
$767$	33.8494	1.22223
$768$	140.898	5.08422
$769$	−13.7355	−0.495316	−0.247658	−	0.968847i	$-0.579661\pi$
$769$	−13.7355	−0.495316	−0.247658	+	0.968847i	$0.579661\pi$
$770$	−38.7135	−1.39514
$771$	28.1716	1.01457
$772$	34.7316	1.25002
$773$	−22.1739	−0.797541	−0.398771	−	0.917051i	$-0.630563\pi$
$773$	−22.1739	−0.797541	−0.398771	+	0.917051i	$0.630563\pi$
$774$	47.3072	1.70042
$775$	−79.6147	−2.85984
$776$	−100.113	−3.59384
$777$	−1.57429	−0.0564772
$778$	−12.3918	−0.444268
$779$	4.85851	0.174074
$780$	−162.874	−5.83182
$781$	−6.47012	−0.231519
$782$	−18.3598	−0.656544
$783$	2.33054	0.0832869
$784$	−65.1673	−2.32740
$785$	−3.06263	−0.109310
$786$	35.9194	1.28120
$787$	19.9942	0.712717	0.356358	−	0.934349i	$-0.384018\pi$
$787$	19.9942	0.712717	0.356358	+	0.934349i	$0.384018\pi$
$788$	−43.9471	−1.56555
$789$	47.3127	1.68438
$790$	−173.336	−6.16700
$791$	2.31511	0.0823158
$792$	−39.8132	−1.41470
$793$	12.0651	0.428445
$794$	17.0952	0.606685
$795$	38.8124	1.37653
$796$	−68.0069	−2.41044
$797$	1.75791	0.0622684	0.0311342	−	0.999515i	$-0.490088\pi$
$797$	1.75791	0.0622684	0.0311342	+	0.999515i	$0.490088\pi$
$798$	56.1997	1.98945
$799$	13.9355	0.493004
$800$	−264.724	−9.35942
$801$	−6.52363	−0.230501
$802$	56.3835	1.99097
$803$	−18.9544	−0.668888
$804$	75.2192	2.65278
$805$	6.82598	0.240584
$806$	−67.1403	−2.36492
$807$	−2.35472	−0.0828901
$808$	108.962	3.83327
$809$	37.7352	1.32670	0.663349	−	0.748310i	$-0.269134\pi$
$809$	37.7352	1.32670	0.663349	+	0.748310i	$0.269134\pi$
$810$	120.860	4.24658
$811$	6.28749	0.220784	0.110392	−	0.993888i	$-0.464789\pi$
$811$	6.28749	0.220784	0.110392	+	0.993888i	$0.464789\pi$
$812$	−9.61810	−0.337529
$813$	34.1936	1.19922
$814$	2.33373	0.0817971
$815$	7.84229	0.274703
$816$	238.883	8.36258
$817$	46.8553	1.63926
$818$	−22.0263	−0.770131
$819$	−11.0598	−0.386459
$820$	−20.2489	−0.707121
$821$	−3.93426	−0.137307	−0.0686533	−	0.997641i	$-0.521870\pi$
$821$	−3.93426	−0.137307	−0.0686533	+	0.997641i	$0.521870\pi$
$822$	−75.8573	−2.64583
$823$	−46.9572	−1.63682	−0.818412	−	0.574632i	$-0.805145\pi$
$823$	−46.9572	−1.63682	−0.818412	+	0.574632i	$0.805145\pi$
$824$	−25.0062	−0.871134
$825$	49.3078	1.71668
$826$	48.6777	1.69371
$827$	46.5834	1.61986	0.809932	−	0.586524i	$-0.199504\pi$
$827$	46.5834	1.61986	0.809932	+	0.586524i	$0.199504\pi$
$828$	10.9255	0.379686
$829$	30.6097	1.06312	0.531559	−	0.847021i	$-0.321607\pi$
$829$	30.6097	1.06312	0.531559	+	0.847021i	$0.321607\pi$
$830$	−47.9401	−1.66403
$831$	−2.85798	−0.0991422
$832$	−117.086	−4.05921
$833$	−26.9456	−0.933611
$834$	−89.3591	−3.09425
$835$	14.3260	0.495770
$836$	−61.3718	−2.12259
$837$	17.2345	0.595713
$838$	2.34396	0.0809709
$839$	−2.86614	−0.0989500	−0.0494750	−	0.998775i	$-0.515755\pi$
$839$	−2.86614	−0.0989500	−0.0494750	+	0.998775i	$0.515755\pi$
$840$	−150.495	−5.19256
$841$	1.00000	0.0344828
$842$	47.6489	1.64209
$843$	−61.8399	−2.12988
$844$	67.7440	2.33184
$845$	−8.52323	−0.293208
$846$	−11.2572	−0.387029
$847$	−11.6294	−0.399591
$848$	70.7680	2.43018
$849$	4.71665	0.161875
$850$	−197.660	−6.77967
$851$	−0.411484	−0.0141055
$852$	−39.1454	−1.34110
$853$	−15.3699	−0.526256	−0.263128	−	0.964761i	$-0.584754\pi$
$853$	−15.3699	−0.526256	−0.263128	+	0.964761i	$0.584754\pi$
$854$	17.3505	0.593722
$855$	−41.3296	−1.41344
$856$	−62.8270	−2.14738
$857$	−23.8310	−0.814052	−0.407026	−	0.913417i	$-0.633434\pi$
$857$	−23.8310	−0.814052	−0.407026	+	0.913417i	$0.633434\pi$
$858$	41.5821	1.41959
$859$	47.0780	1.60628	0.803140	−	0.595791i	$-0.203161\pi$
$859$	47.0780	1.60628	0.803140	+	0.595791i	$0.203161\pi$
$860$	−195.279	−6.65897
$861$	−3.48729	−0.118847
$862$	4.95967	0.168927
$863$	−37.7132	−1.28377	−0.641886	−	0.766800i	$-0.721848\pi$
$863$	−37.7132	−1.28377	−0.641886	+	0.766800i	$0.721848\pi$
$864$	57.3061	1.94959
$865$	87.4823	2.97449
$866$	2.94080	0.0999326
$867$	60.9410	2.06966
$868$	−71.1265	−2.41419
$869$	32.5994	1.10586
$870$	24.3524	0.825625
$871$	−19.9023	−0.674365
$872$	19.2619	0.652291
$873$	19.7340	0.667896
$874$	14.6894	0.496875
$875$	39.3581	1.33055
$876$	−114.678	−3.87461
$877$	−42.8677	−1.44754	−0.723770	−	0.690041i	$-0.757592\pi$
$877$	−42.8677	−1.44754	−0.723770	+	0.690041i	$0.757592\pi$
$878$	−62.1497	−2.09745
$879$	41.3160	1.39356
$880$	131.659	4.43822
$881$	−10.1139	−0.340747	−0.170374	−	0.985380i	$-0.554497\pi$
$881$	−10.1139	−0.340747	−0.170374	+	0.985380i	$0.554497\pi$
$882$	21.7667	0.732924
$883$	−45.0920	−1.51747	−0.758734	−	0.651401i	$-0.774182\pi$
$883$	−45.0920	−1.51747	−0.758734	+	0.651401i	$0.774182\pi$
$884$	−122.794	−4.13000
$885$	−90.7928	−3.05197
$886$	−77.9963	−2.62034
$887$	−14.7122	−0.493987	−0.246994	−	0.969017i	$-0.579443\pi$
$887$	−14.7122	−0.493987	−0.246994	+	0.969017i	$0.579443\pi$
$888$	9.07211	0.304440
$889$	−20.8121	−0.698015
$890$	36.5553	1.22534
$891$	−22.7303	−0.761493
$892$	−42.4320	−1.42073
$893$	−11.1496	−0.373108
$894$	−149.347	−4.99493
$895$	63.5176	2.12316
$896$	−83.8339	−2.80070
$897$	−7.33177	−0.244801
$898$	−61.2215	−2.04299
$899$	7.39507	0.246639
$900$	117.623	3.92075
$901$	29.2614	0.974839
$902$	5.16958	0.172128
$903$	−33.6313	−1.11918
$904$	−13.3412	−0.443723
$905$	73.2373	2.43449
$906$	134.617	4.47234
$907$	−29.6697	−0.985166	−0.492583	−	0.870266i	$-0.663947\pi$
$907$	−29.6697	−0.985166	−0.492583	+	0.870266i	$0.663947\pi$
$908$	49.7004	1.64937
$909$	−21.4783	−0.712391
$910$	61.9736	2.05440
$911$	26.1653	0.866896	0.433448	−	0.901178i	$-0.357297\pi$
$911$	26.1653	0.866896	0.433448	+	0.901178i	$0.357297\pi$
$912$	−191.127	−6.32884
$913$	9.01616	0.298391
$914$	3.66126	0.121104
$915$	−32.3618	−1.06985
$916$	75.8345	2.50564
$917$	−10.0682	−0.332481
$918$	42.7882	1.41222
$919$	−29.6177	−0.976998	−0.488499	−	0.872565i	$-0.662455\pi$
$919$	−29.6177	−0.976998	−0.488499	+	0.872565i	$0.662455\pi$
$920$	−39.3360	−1.29687
$921$	−34.2290	−1.12788
$922$	57.7167	1.90080
$923$	10.3575	0.340922
$924$	44.0508	1.44917
$925$	−4.43000	−0.145657
$926$	52.3908	1.72167
$927$	4.92918	0.161895
$928$	24.5891	0.807178
$929$	−41.0086	−1.34545	−0.672723	−	0.739894i	$-0.734876\pi$
$929$	−41.0086	−1.34545	−0.672723	+	0.739894i	$0.734876\pi$
$930$	180.088	5.90531
$931$	21.5588	0.706561
$932$	−47.4653	−1.55478
$933$	−6.43610	−0.210709
$934$	35.4974	1.16151
$935$	54.4388	1.78034
$936$	63.7339	2.08321
$937$	6.53949	0.213636	0.106818	−	0.994279i	$-0.465934\pi$
$937$	6.53949	0.213636	0.106818	+	0.994279i	$0.465934\pi$
$938$	−28.6209	−0.934506
$939$	−10.8700	−0.354728
$940$	46.4684	1.51563
$941$	17.9875	0.586377	0.293189	−	0.956055i	$-0.405284\pi$
$941$	17.9875	0.586377	0.293189	+	0.956055i	$0.405284\pi$
$942$	4.73061	0.154132
$943$	−0.911502	−0.0296826
$944$	−165.546	−5.38805
$945$	−15.9083	−0.517496
$946$	49.8552	1.62093
$947$	−46.9505	−1.52569	−0.762844	−	0.646583i	$-0.776197\pi$
$947$	−46.9505	−1.52569	−0.762844	+	0.646583i	$0.776197\pi$
$948$	197.233	6.40582
$949$	30.3427	0.984967
$950$	158.145	5.13089
$951$	−56.1758	−1.82162
$952$	−113.461	−3.67728
$953$	−43.5495	−1.41071	−0.705353	−	0.708856i	$-0.749212\pi$
$953$	−43.5495	−1.41071	−0.705353	+	0.708856i	$0.749212\pi$
$954$	−23.6374	−0.765290
$955$	−42.7075	−1.38198
$956$	−78.2218	−2.52987
$957$	−4.57999	−0.148050
$958$	−22.2709	−0.719540
$959$	21.2628	0.686611
$960$	314.054	10.1361
$961$	23.6870	0.764097
$962$	−3.73589	−0.120450
$963$	12.3843	0.399079
$964$	50.1357	1.61476
$965$	24.6491	0.793484
$966$	−10.5436	−0.339234
$967$	0.684193	0.0220022	0.0110011	−	0.999939i	$-0.496498\pi$
$967$	0.684193	0.0220022	0.0110011	+	0.999939i	$0.496498\pi$
$968$	67.0166	2.15399
$969$	−79.0278	−2.53874
$970$	−110.580	−3.55051
$971$	41.1510	1.32060	0.660299	−	0.751003i	$-0.270429\pi$
$971$	41.1510	1.32060	0.660299	+	0.751003i	$0.270429\pi$
$972$	−98.4057	−3.15636
$973$	25.0473	0.802981
$974$	−42.4313	−1.35959
$975$	−78.9332	−2.52789
$976$	−59.0064	−1.88875
$977$	52.9142	1.69287	0.846437	−	0.532489i	$-0.178743\pi$
$977$	52.9142	1.69287	0.846437	+	0.532489i	$0.178743\pi$
$978$	−12.1134	−0.387344
$979$	−6.87500	−0.219726
$980$	−89.8508	−2.87018
$981$	−3.79687	−0.121225
$982$	−70.9818	−2.26512
$983$	−14.0460	−0.447998	−0.223999	−	0.974589i	$-0.571911\pi$
$983$	−14.0460	−0.447998	−0.223999	+	0.974589i	$0.571911\pi$
$984$	20.0962	0.640643
$985$	−31.1894	−0.993777
$986$	18.3598	0.584694
$987$	8.00286	0.254734
$988$	98.2455	3.12560
$989$	−8.79049	−0.279521
$990$	−43.9758	−1.39764
$991$	−16.9531	−0.538532	−0.269266	−	0.963066i	$-0.586781\pi$
$991$	−16.9531	−0.538532	−0.269266	+	0.963066i	$0.586781\pi$
$992$	181.838	5.77337
$993$	−69.2542	−2.19772
$994$	14.8949	0.472436
$995$	−48.2647	−1.53009
$996$	54.5494	1.72846
$997$	−43.4643	−1.37653	−0.688263	−	0.725461i	$-0.741627\pi$
$997$	−43.4643	−1.37653	−0.688263	+	0.725461i	$0.741627\pi$
$998$	39.9797	1.26554
$999$	0.958981	0.0303408

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.1	✓	16
3.2	odd	2		6003.2.a.q.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.1	✓	16	1.1	even	1	trivial
6003.2.a.q.1.16		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)

\(f(q)\)	\(=\)	\(q-2.75586 q^{2} +2.22549 q^{3} +5.59478 q^{4} +3.97063 q^{5} -6.13314 q^{6} +1.71912 q^{7} -9.90674 q^{8} +1.95279 q^{9} +O(q^{10})\)	\(q-2.75586 q^{2} +2.22549 q^{3} +5.59478 q^{4} +3.97063 q^{5} -6.13314 q^{6} +1.71912 q^{7} -9.90674 q^{8} +1.95279 q^{9} -10.9425 q^{10} +2.05797 q^{11} +12.4511 q^{12} -3.29445 q^{13} -4.73766 q^{14} +8.83659 q^{15} +16.1120 q^{16} +6.66207 q^{17} -5.38163 q^{18} -5.33022 q^{19} +22.2148 q^{20} +3.82588 q^{21} -5.67149 q^{22} +1.00000 q^{23} -22.0473 q^{24} +10.7659 q^{25} +9.07907 q^{26} -2.33054 q^{27} +9.61810 q^{28} -1.00000 q^{29} -24.3524 q^{30} -7.39507 q^{31} -24.5891 q^{32} +4.57999 q^{33} -18.3598 q^{34} +6.82598 q^{35} +10.9255 q^{36} -0.411484 q^{37} +14.6894 q^{38} -7.33177 q^{39} -39.3360 q^{40} -0.911502 q^{41} -10.5436 q^{42} -8.79049 q^{43} +11.5139 q^{44} +7.75382 q^{45} -2.75586 q^{46} +2.09177 q^{47} +35.8572 q^{48} -4.04463 q^{49} -29.6694 q^{50} +14.8264 q^{51} -18.4318 q^{52} +4.39224 q^{53} +6.42266 q^{54} +8.17145 q^{55} -17.0308 q^{56} -11.8623 q^{57} +2.75586 q^{58} -10.2746 q^{59} +49.4388 q^{60} -3.66225 q^{61} +20.3798 q^{62} +3.35708 q^{63} +35.5402 q^{64} -13.0811 q^{65} -12.6218 q^{66} +6.04116 q^{67} +37.2729 q^{68} +2.22549 q^{69} -18.8115 q^{70} -3.14393 q^{71} -19.3458 q^{72} -9.21024 q^{73} +1.13399 q^{74} +23.9594 q^{75} -29.8215 q^{76} +3.53790 q^{77} +20.2054 q^{78} +15.8406 q^{79} +63.9750 q^{80} -11.0450 q^{81} +2.51198 q^{82} +4.38108 q^{83} +21.4049 q^{84} +26.4526 q^{85} +24.2254 q^{86} -2.22549 q^{87} -20.3878 q^{88} -3.34067 q^{89} -21.3685 q^{90} -5.66356 q^{91} +5.59478 q^{92} -16.4576 q^{93} -5.76464 q^{94} -21.1644 q^{95} -54.7228 q^{96} +10.1055 q^{97} +11.1465 q^{98} +4.01880 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 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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