LMFDB - Embedded newform 667.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.10
Root			$1.46878$ 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)

$f(q)$	$=$	$q+1.46878 q^{2} -2.50203 q^{3} +0.157302 q^{4} +4.31834 q^{5} -3.67492 q^{6} +1.97692 q^{7} -2.70651 q^{8} +3.26016 q^{9} +O(q^{10})$	\(q+1.46878 q^{2} -2.50203 q^{3} +0.157302 q^{4} +4.31834 q^{5} -3.67492 q^{6} +1.97692 q^{7} -2.70651 q^{8} +3.26016 q^{9} +6.34267 q^{10} +1.83320 q^{11} -0.393574 q^{12} -3.87390 q^{13} +2.90366 q^{14} -10.8046 q^{15} -4.28986 q^{16} +4.20465 q^{17} +4.78844 q^{18} +5.07651 q^{19} +0.679284 q^{20} -4.94633 q^{21} +2.69255 q^{22} -1.00000 q^{23} +6.77177 q^{24} +13.6481 q^{25} -5.68989 q^{26} -0.650924 q^{27} +0.310974 q^{28} +1.00000 q^{29} -15.8696 q^{30} -5.47778 q^{31} -0.887822 q^{32} -4.58671 q^{33} +6.17568 q^{34} +8.53703 q^{35} +0.512829 q^{36} +9.06579 q^{37} +7.45626 q^{38} +9.69261 q^{39} -11.6876 q^{40} +10.5865 q^{41} -7.26504 q^{42} +4.73958 q^{43} +0.288365 q^{44} +14.0785 q^{45} -1.46878 q^{46} -6.05915 q^{47} +10.7334 q^{48} -3.09177 q^{49} +20.0459 q^{50} -10.5202 q^{51} -0.609372 q^{52} +2.15287 q^{53} -0.956062 q^{54} +7.91636 q^{55} -5.35057 q^{56} -12.7016 q^{57} +1.46878 q^{58} -13.0731 q^{59} -1.69959 q^{60} -11.1000 q^{61} -8.04563 q^{62} +6.44509 q^{63} +7.27571 q^{64} -16.7288 q^{65} -6.73685 q^{66} -9.49675 q^{67} +0.661399 q^{68} +2.50203 q^{69} +12.5390 q^{70} -8.07109 q^{71} -8.82365 q^{72} +16.6448 q^{73} +13.3156 q^{74} -34.1479 q^{75} +0.798545 q^{76} +3.62409 q^{77} +14.2363 q^{78} -2.02071 q^{79} -18.5251 q^{80} -8.15184 q^{81} +15.5491 q^{82} -6.08722 q^{83} -0.778067 q^{84} +18.1571 q^{85} +6.96138 q^{86} -2.50203 q^{87} -4.96156 q^{88} -2.99601 q^{89} +20.6781 q^{90} -7.65840 q^{91} -0.157302 q^{92} +13.7056 q^{93} -8.89953 q^{94} +21.9221 q^{95} +2.22136 q^{96} -2.79853 q^{97} -4.54112 q^{98} +5.97651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.46878	1.03858	0.519291	−	0.854598i	$-0.326196\pi$
$2$	1.46878	1.03858	0.519291	+	0.854598i	$0.326196\pi$
$3$	−2.50203	−1.44455	−0.722274	−	0.691607i	$-0.756903\pi$
$3$	−2.50203	−1.44455	−0.722274	+	0.691607i	$0.756903\pi$
$4$	0.157302	0.0786510
$5$	4.31834	1.93122	0.965610	−	0.259994i	$-0.0837207\pi$
$5$	4.31834	1.93122	0.965610	+	0.259994i	$0.0837207\pi$
$6$	−3.67492	−1.50028
$7$	1.97692	0.747207	0.373604	−	0.927588i	$-0.378122\pi$
$7$	1.97692	0.747207	0.373604	+	0.927588i	$0.378122\pi$
$8$	−2.70651	−0.956896
$9$	3.26016	1.08672
$10$	6.34267	2.00573
$11$	1.83320	0.552729	0.276365	−	0.961053i	$-0.410870\pi$
$11$	1.83320	0.552729	0.276365	+	0.961053i	$0.410870\pi$
$12$	−0.393574	−0.113615
$13$	−3.87390	−1.07443	−0.537213	−	0.843447i	$-0.680523\pi$
$13$	−3.87390	−1.07443	−0.537213	+	0.843447i	$0.680523\pi$
$14$	2.90366	0.776035
$15$	−10.8046	−2.78974
$16$	−4.28986	−1.07247
$17$	4.20465	1.01978	0.509888	−	0.860241i	$-0.329687\pi$
$17$	4.20465	1.01978	0.509888	+	0.860241i	$0.329687\pi$
$18$	4.78844	1.12865
$19$	5.07651	1.16463	0.582316	−	0.812963i	$-0.302147\pi$
$19$	5.07651	1.16463	0.582316	+	0.812963i	$0.302147\pi$
$20$	0.679284	0.151892
$21$	−4.94633	−1.07938
$22$	2.69255	0.574054
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	6.77177	1.38228
$25$	13.6481	2.72961
$26$	−5.68989	−1.11588
$27$	−0.650924	−0.125270
$28$	0.310974	0.0587686
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−15.8696	−2.89737
$31$	−5.47778	−0.983838	−0.491919	−	0.870641i	$-0.663704\pi$
$31$	−5.47778	−0.983838	−0.491919	+	0.870641i	$0.663704\pi$
$32$	−0.887822	−0.156946
$33$	−4.58671	−0.798444
$34$	6.17568	1.05912
$35$	8.53703	1.44302
$36$	0.512829	0.0854716
$37$	9.06579	1.49041	0.745203	−	0.666838i	$-0.232353\pi$
$37$	9.06579	1.49041	0.745203	+	0.666838i	$0.232353\pi$
$38$	7.45626	1.20956
$39$	9.69261	1.55206
$40$	−11.6876	−1.84798
$41$	10.5865	1.65333	0.826664	−	0.562696i	$-0.190236\pi$
$41$	10.5865	1.65333	0.826664	+	0.562696i	$0.190236\pi$
$42$	−7.26504	−1.12102
$43$	4.73958	0.722779	0.361389	−	0.932415i	$-0.382303\pi$
$43$	4.73958	0.722779	0.361389	+	0.932415i	$0.382303\pi$
$44$	0.288365	0.0434727
$45$	14.0785	2.09869
$46$	−1.46878	−0.216559
$47$	−6.05915	−0.883817	−0.441909	−	0.897060i	$-0.645698\pi$
$47$	−6.05915	−0.883817	−0.441909	+	0.897060i	$0.645698\pi$
$48$	10.7334	1.54923
$49$	−3.09177	−0.441681
$50$	20.0459	2.83492
$51$	−10.5202	−1.47312
$52$	−0.609372	−0.0845047
$53$	2.15287	0.295719	0.147859	−	0.989008i	$-0.452762\pi$
$53$	2.15287	0.295719	0.147859	+	0.989008i	$0.452762\pi$
$54$	−0.956062	−0.130104
$55$	7.91636	1.06744
$56$	−5.35057	−0.714999
$57$	−12.7016	−1.68237
$58$	1.46878	0.192860
$59$	−13.0731	−1.70198	−0.850988	−	0.525185i	$-0.823996\pi$
$59$	−13.0731	−1.70198	−0.850988	+	0.525185i	$0.823996\pi$
$60$	−1.69959	−0.219416
$61$	−11.1000	−1.42121	−0.710607	−	0.703590i	$-0.751579\pi$
$61$	−11.1000	−1.42121	−0.710607	+	0.703590i	$0.751579\pi$
$62$	−8.04563	−1.02180
$63$	6.44509	0.812005
$64$	7.27571	0.909464
$65$	−16.7288	−2.07495
$66$	−6.73685	−0.829249
$67$	−9.49675	−1.16021	−0.580106	−	0.814541i	$-0.696989\pi$
$67$	−9.49675	−1.16021	−0.580106	+	0.814541i	$0.696989\pi$
$68$	0.661399	0.0802064
$69$	2.50203	0.301209
$70$	12.5390	1.49870
$71$	−8.07109	−0.957863	−0.478931	−	0.877852i	$-0.658976\pi$
$71$	−8.07109	−0.957863	−0.478931	+	0.877852i	$0.658976\pi$
$72$	−8.82365	−1.03988
$73$	16.6448	1.94812	0.974062	−	0.226279i	$-0.0726563\pi$
$73$	16.6448	1.94812	0.974062	+	0.226279i	$0.0726563\pi$
$74$	13.3156	1.54791
$75$	−34.1479	−3.94306
$76$	0.798545	0.0915994
$77$	3.62409	0.413003
$78$	14.2363	1.61194
$79$	−2.02071	−0.227347	−0.113674	−	0.993518i	$-0.536262\pi$
$79$	−2.02071	−0.227347	−0.113674	+	0.993518i	$0.536262\pi$
$80$	−18.5251	−2.07117
$81$	−8.15184	−0.905760
$82$	15.5491	1.71712
$83$	−6.08722	−0.668160	−0.334080	−	0.942545i	$-0.608426\pi$
$83$	−6.08722	−0.668160	−0.334080	+	0.942545i	$0.608426\pi$
$84$	−0.778067	−0.0848941
$85$	18.1571	1.96941
$86$	6.96138	0.750664
$87$	−2.50203	−0.268246
$88$	−4.96156	−0.528904
$89$	−2.99601	−0.317576	−0.158788	−	0.987313i	$-0.550759\pi$
$89$	−2.99601	−0.317576	−0.158788	+	0.987313i	$0.550759\pi$
$90$	20.6781	2.17967
$91$	−7.65840	−0.802819
$92$	−0.157302	−0.0163999
$93$	13.7056	1.42120
$94$	−8.89953	−0.917916
$95$	21.9221	2.24916
$96$	2.22136	0.226716
$97$	−2.79853	−0.284148	−0.142074	−	0.989856i	$-0.545377\pi$
$97$	−2.79853	−0.284148	−0.142074	+	0.989856i	$0.545377\pi$
$98$	−4.54112	−0.458722
$99$	5.97651	0.600662
$100$	2.14687	0.214687
$101$	1.46716	0.145988	0.0729939	−	0.997332i	$-0.476745\pi$
$101$	1.46716	0.145988	0.0729939	+	0.997332i	$0.476745\pi$
$102$	−15.4517	−1.52995
$103$	−2.23140	−0.219866	−0.109933	−	0.993939i	$-0.535064\pi$
$103$	−2.23140	−0.219866	−0.109933	+	0.993939i	$0.535064\pi$
$104$	10.4847	1.02811
$105$	−21.3599	−2.08451
$106$	3.16208	0.307128
$107$	6.98440	0.675208	0.337604	−	0.941288i	$-0.390384\pi$
$107$	6.98440	0.675208	0.337604	+	0.941288i	$0.390384\pi$
$108$	−0.102392	−0.00985265
$109$	−0.478672	−0.0458485	−0.0229242	−	0.999737i	$-0.507298\pi$
$109$	−0.478672	−0.0458485	−0.0229242	+	0.999737i	$0.507298\pi$
$110$	11.6274	1.10863
$111$	−22.6829	−2.15296
$112$	−8.48073	−0.801354
$113$	−19.1178	−1.79845	−0.899227	−	0.437482i	$-0.855870\pi$
$113$	−19.1178	−1.79845	−0.899227	+	0.437482i	$0.855870\pi$
$114$	−18.6558	−1.74727
$115$	−4.31834	−0.402687
$116$	0.157302	0.0146051
$117$	−12.6295	−1.16760
$118$	−19.2015	−1.76764
$119$	8.31227	0.761984
$120$	29.2428	2.66949
$121$	−7.63939	−0.694490
$122$	−16.3035	−1.47605
$123$	−26.4877	−2.38831
$124$	−0.861665	−0.0773798
$125$	37.3453	3.34026
$126$	9.46639	0.843333
$127$	7.04182	0.624860	0.312430	−	0.949941i	$-0.398857\pi$
$127$	7.04182	0.624860	0.312430	+	0.949941i	$0.398857\pi$
$128$	12.4620	1.10150
$129$	−11.8586	−1.04409
$130$	−24.5709	−2.15501
$131$	−10.0499	−0.878062	−0.439031	−	0.898472i	$-0.644678\pi$
$131$	−10.0499	−0.878062	−0.439031	+	0.898472i	$0.644678\pi$
$132$	−0.721499	−0.0627984
$133$	10.0359	0.870221
$134$	−13.9486	−1.20498
$135$	−2.81091	−0.241925
$136$	−11.3799	−0.975820
$137$	−5.22983	−0.446814	−0.223407	−	0.974725i	$-0.571718\pi$
$137$	−5.22983	−0.446814	−0.223407	+	0.974725i	$0.571718\pi$
$138$	3.67492	0.312830
$139$	6.50655	0.551879	0.275939	−	0.961175i	$-0.411011\pi$
$139$	6.50655	0.551879	0.275939	+	0.961175i	$0.411011\pi$
$140$	1.34289	0.113495
$141$	15.1602	1.27672
$142$	−11.8546	−0.994818
$143$	−7.10161	−0.593867
$144$	−13.9856	−1.16547
$145$	4.31834	0.358619
$146$	24.4475	2.02329
$147$	7.73570	0.638030
$148$	1.42607	0.117222
$149$	−12.7045	−1.04080	−0.520398	−	0.853924i	$-0.674216\pi$
$149$	−12.7045	−1.04080	−0.520398	+	0.853924i	$0.674216\pi$
$150$	−50.1556	−4.09518
$151$	−8.10479	−0.659558	−0.329779	−	0.944058i	$-0.606974\pi$
$151$	−8.10479	−0.659558	−0.329779	+	0.944058i	$0.606974\pi$
$152$	−13.7396	−1.11443
$153$	13.7078	1.10821
$154$	5.32297	0.428938
$155$	−23.6549	−1.90001
$156$	1.52467	0.122071
$157$	2.66910	0.213017	0.106509	−	0.994312i	$-0.466033\pi$
$157$	2.66910	0.213017	0.106509	+	0.994312i	$0.466033\pi$
$158$	−2.96796	−0.236119
$159$	−5.38654	−0.427180
$160$	−3.83392	−0.303098
$161$	−1.97692	−0.155803
$162$	−11.9732	−0.940706
$163$	−0.170762	−0.0133751	−0.00668755	−	0.999978i	$-0.502129\pi$
$163$	−0.170762	−0.0133751	−0.00668755	+	0.999978i	$0.502129\pi$
$164$	1.66527	0.130036
$165$	−19.8070	−1.54197
$166$	−8.94077	−0.693938
$167$	7.64267	0.591407	0.295704	−	0.955280i	$-0.404446\pi$
$167$	7.64267	0.591407	0.295704	+	0.955280i	$0.404446\pi$
$168$	13.3873	1.03285
$169$	2.00708	0.154391
$170$	26.6687	2.04540
$171$	16.5502	1.26563
$172$	0.745545	0.0568473
$173$	−9.05474	−0.688419	−0.344209	−	0.938893i	$-0.611853\pi$
$173$	−9.05474	−0.688419	−0.344209	+	0.938893i	$0.611853\pi$
$174$	−3.67492	−0.278595
$175$	26.9812	2.03959
$176$	−7.86415	−0.592783
$177$	32.7094	2.45859
$178$	−4.40047	−0.329829
$179$	−13.8782	−1.03730	−0.518651	−	0.854986i	$-0.673566\pi$
$179$	−13.8782	−1.03730	−0.518651	+	0.854986i	$0.673566\pi$
$180$	2.21457	0.165064
$181$	18.4738	1.37314	0.686572	−	0.727061i	$-0.259114\pi$
$181$	18.4738	1.37314	0.686572	+	0.727061i	$0.259114\pi$
$182$	−11.2485	−0.833792
$183$	27.7726	2.05301
$184$	2.70651	0.199527
$185$	39.1491	2.87830
$186$	20.1304	1.47603
$187$	7.70794	0.563660
$188$	−0.953116	−0.0695131
$189$	−1.28683	−0.0936030
$190$	32.1986	2.33594
$191$	−19.2748	−1.39467	−0.697337	−	0.716743i	$-0.745632\pi$
$191$	−19.2748	−1.39467	−0.697337	+	0.716743i	$0.745632\pi$
$192$	−18.2040	−1.31376
$193$	−2.64644	−0.190495	−0.0952474	−	0.995454i	$-0.530364\pi$
$193$	−2.64644	−0.190495	−0.0952474	+	0.995454i	$0.530364\pi$
$194$	−4.11041	−0.295110
$195$	41.8560	2.99737
$196$	−0.486342	−0.0347387
$197$	19.0630	1.35818	0.679091	−	0.734054i	$-0.262374\pi$
$197$	19.0630	1.35818	0.679091	+	0.734054i	$0.262374\pi$
$198$	8.77815	0.623836
$199$	11.2745	0.799225	0.399613	−	0.916684i	$-0.369145\pi$
$199$	11.2745	0.799225	0.399613	+	0.916684i	$0.369145\pi$
$200$	−36.9386	−2.61195
$201$	23.7612	1.67598
$202$	2.15493	0.151620
$203$	1.97692	0.138753
$204$	−1.65484	−0.115862
$205$	45.7160	3.19294
$206$	−3.27743	−0.228349
$207$	−3.26016	−0.226597
$208$	16.6185	1.15228
$209$	9.30624	0.643726
$210$	−31.3729	−2.16494
$211$	−6.25288	−0.430466	−0.215233	−	0.976563i	$-0.569051\pi$
$211$	−6.25288	−0.430466	−0.215233	+	0.976563i	$0.569051\pi$
$212$	0.338650	0.0232586
$213$	20.1941	1.38368
$214$	10.2585	0.701258
$215$	20.4671	1.39585
$216$	1.76173	0.119871
$217$	−10.8292	−0.735131
$218$	−0.703062	−0.0476174
$219$	−41.6458	−2.81416
$220$	1.24526	0.0839554
$221$	−16.2884	−1.09567
$222$	−33.3161	−2.23603
$223$	−18.9022	−1.26578	−0.632891	−	0.774241i	$-0.718132\pi$
$223$	−18.9022	−1.26578	−0.632891	+	0.774241i	$0.718132\pi$
$224$	−1.75516	−0.117271
$225$	44.4948	2.96632
$226$	−28.0798	−1.86784
$227$	10.8786	0.722036	0.361018	−	0.932559i	$-0.382429\pi$
$227$	10.8786	0.722036	0.361018	+	0.932559i	$0.382429\pi$
$228$	−1.99799	−0.132320
$229$	−17.1411	−1.13271	−0.566357	−	0.824160i	$-0.691648\pi$
$229$	−17.1411	−1.13271	−0.566357	+	0.824160i	$0.691648\pi$
$230$	−6.34267	−0.418223
$231$	−9.06758	−0.596603
$232$	−2.70651	−0.177691
$233$	−4.32390	−0.283268	−0.141634	−	0.989919i	$-0.545236\pi$
$233$	−4.32390	−0.283268	−0.141634	+	0.989919i	$0.545236\pi$
$234$	−18.5499	−1.21265
$235$	−26.1654	−1.70685
$236$	−2.05643	−0.133862
$237$	5.05587	0.328414
$238$	12.2089	0.791383
$239$	8.89820	0.575577	0.287788	−	0.957694i	$-0.407080\pi$
$239$	8.89820	0.575577	0.287788	+	0.957694i	$0.407080\pi$
$240$	46.3503	2.99190
$241$	−4.59323	−0.295876	−0.147938	−	0.988997i	$-0.547264\pi$
$241$	−4.59323	−0.295876	−0.147938	+	0.988997i	$0.547264\pi$
$242$	−11.2206	−0.721285
$243$	22.3489	1.43368
$244$	−1.74606	−0.111780
$245$	−13.3513	−0.852984
$246$	−38.9044	−2.48046
$247$	−19.6659	−1.25131
$248$	14.8257	0.941430
$249$	15.2304	0.965189
$250$	54.8518	3.46913
$251$	19.9458	1.25897	0.629484	−	0.777013i	$-0.283266\pi$
$251$	19.9458	1.25897	0.629484	+	0.777013i	$0.283266\pi$
$252$	1.01383	0.0638650
$253$	−1.83320	−0.115252
$254$	10.3429	0.648968
$255$	−45.4296	−2.84491
$256$	3.75251	0.234532
$257$	−23.1679	−1.44518	−0.722588	−	0.691279i	$-0.757048\pi$
$257$	−23.1679	−1.44518	−0.722588	+	0.691279i	$0.757048\pi$
$258$	−17.4176	−1.08437
$259$	17.9224	1.11364
$260$	−2.63147	−0.163197
$261$	3.26016	0.201799
$262$	−14.7610	−0.911939
$263$	0.500370	0.0308542	0.0154271	−	0.999881i	$-0.495089\pi$
$263$	0.500370	0.0308542	0.0154271	+	0.999881i	$0.495089\pi$
$264$	12.4140	0.764028
$265$	9.29681	0.571098
$266$	14.7405	0.903795
$267$	7.49611	0.458755
$268$	−1.49386	−0.0912519
$269$	6.17017	0.376202	0.188101	−	0.982150i	$-0.439767\pi$
$269$	6.17017	0.376202	0.188101	+	0.982150i	$0.439767\pi$
$270$	−4.12860	−0.251259
$271$	16.3328	0.992146	0.496073	−	0.868281i	$-0.334775\pi$
$271$	16.3328	0.992146	0.496073	+	0.868281i	$0.334775\pi$
$272$	−18.0373	−1.09367
$273$	19.1616	1.15971
$274$	−7.68144	−0.464053
$275$	25.0196	1.50874
$276$	0.393574	0.0236904
$277$	−1.81971	−0.109336	−0.0546679	−	0.998505i	$-0.517410\pi$
$277$	−1.81971	−0.109336	−0.0546679	+	0.998505i	$0.517410\pi$
$278$	9.55667	0.573171
$279$	−17.8584	−1.06916
$280$	−23.1056	−1.38082
$281$	1.22881	0.0733047	0.0366523	−	0.999328i	$-0.488331\pi$
$281$	1.22881	0.0733047	0.0366523	+	0.999328i	$0.488331\pi$
$282$	22.2669	1.32597
$283$	17.8740	1.06250	0.531249	−	0.847216i	$-0.321723\pi$
$283$	17.8740	1.06250	0.531249	+	0.847216i	$0.321723\pi$
$284$	−1.26960	−0.0753369
$285$	−54.8498	−3.24902
$286$	−10.4307	−0.616779
$287$	20.9286	1.23538
$288$	−2.89444	−0.170557
$289$	0.679044	0.0399438
$290$	6.34267	0.372455
$291$	7.00200	0.410465
$292$	2.61826	0.153222
$293$	21.6627	1.26555	0.632775	−	0.774335i	$-0.281916\pi$
$293$	21.6627	1.26555	0.632775	+	0.774335i	$0.281916\pi$
$294$	11.3620	0.662646
$295$	−56.4542	−3.28689
$296$	−24.5366	−1.42616
$297$	−1.19327	−0.0692407
$298$	−18.6601	−1.08095
$299$	3.87390	0.224033
$300$	−5.37153	−0.310125
$301$	9.36979	0.540066
$302$	−11.9041	−0.685005
$303$	−3.67088	−0.210886
$304$	−21.7775	−1.24903
$305$	−47.9337	−2.74468
$306$	20.1337	1.15097
$307$	−19.9586	−1.13910	−0.569548	−	0.821958i	$-0.692882\pi$
$307$	−19.9586	−1.13910	−0.569548	+	0.821958i	$0.692882\pi$
$308$	0.570077	0.0324831
$309$	5.58303	0.317608
$310$	−34.7438	−1.97331
$311$	30.1721	1.71090	0.855452	−	0.517882i	$-0.173279\pi$
$311$	30.1721	1.71090	0.855452	+	0.517882i	$0.173279\pi$
$312$	−26.2331	−1.48516
$313$	7.10502	0.401600	0.200800	−	0.979632i	$-0.435646\pi$
$313$	7.10502	0.401600	0.200800	+	0.979632i	$0.435646\pi$
$314$	3.92031	0.221236
$315$	27.8321	1.56816
$316$	−0.317861	−0.0178811
$317$	21.9769	1.23435	0.617173	−	0.786828i	$-0.288278\pi$
$317$	21.9769	1.23435	0.617173	+	0.786828i	$0.288278\pi$
$318$	−7.91161	−0.443661
$319$	1.83320	0.102639
$320$	31.4190	1.75637
$321$	−17.4752	−0.975370
$322$	−2.90366	−0.161815
$323$	21.3449	1.18766
$324$	−1.28230	−0.0712389
$325$	−52.8712	−2.93277
$326$	−0.250811	−0.0138911
$327$	1.19765	0.0662303
$328$	−28.6524	−1.58206
$329$	−11.9785	−0.660395
$330$	−29.0920	−1.60146
$331$	−27.6093	−1.51754	−0.758771	−	0.651357i	$-0.774200\pi$
$331$	−27.6093	−1.51754	−0.758771	+	0.651357i	$0.774200\pi$
$332$	−0.957533	−0.0525514
$333$	29.5559	1.61965
$334$	11.2254	0.614224
$335$	−41.0102	−2.24063
$336$	21.2190	1.15759
$337$	4.74384	0.258414	0.129207	−	0.991618i	$-0.458757\pi$
$337$	4.74384	0.258414	0.129207	+	0.991618i	$0.458757\pi$
$338$	2.94795	0.160347
$339$	47.8334	2.59795
$340$	2.85615	0.154896
$341$	−10.0418	−0.543796
$342$	24.3086	1.31446
$343$	−19.9507	−1.07723
$344$	−12.8277	−0.691624
$345$	10.8046	0.581701
$346$	−13.2994	−0.714979
$347$	−1.82991	−0.0982348	−0.0491174	−	0.998793i	$-0.515641\pi$
$347$	−1.82991	−0.0982348	−0.0491174	+	0.998793i	$0.515641\pi$
$348$	−0.393574	−0.0210978
$349$	−4.01236	−0.214777	−0.107388	−	0.994217i	$-0.534249\pi$
$349$	−4.01236	−0.214777	−0.107388	+	0.994217i	$0.534249\pi$
$350$	39.6293	2.11828
$351$	2.52161	0.134594
$352$	−1.62755	−0.0867488
$353$	−29.1168	−1.54973	−0.774865	−	0.632126i	$-0.782182\pi$
$353$	−29.1168	−1.54973	−0.774865	+	0.632126i	$0.782182\pi$
$354$	48.0427	2.55344
$355$	−34.8537	−1.84984
$356$	−0.471278	−0.0249777
$357$	−20.7975	−1.10072
$358$	−20.3839	−1.07732
$359$	−8.79160	−0.464003	−0.232002	−	0.972715i	$-0.574527\pi$
$359$	−8.79160	−0.464003	−0.232002	+	0.972715i	$0.574527\pi$
$360$	−38.1035	−2.00823
$361$	6.77096	0.356366
$362$	27.1338	1.42612
$363$	19.1140	1.00322
$364$	−1.20468	−0.0631425
$365$	71.8778	3.76226
$366$	40.7917	2.13222
$367$	10.8159	0.564583	0.282292	−	0.959329i	$-0.408905\pi$
$367$	10.8159	0.564583	0.282292	+	0.959329i	$0.408905\pi$
$368$	4.28986	0.223624
$369$	34.5136	1.79670
$370$	57.5013	2.98935
$371$	4.25605	0.220963
$372$	2.15591	0.111779
$373$	−0.0211051	−0.00109278	−0.000546391	−	1.00000i	$-0.500174\pi$
$373$	−0.0211051	−0.00109278	−0.000546391		1.00000i	$0.500174\pi$
$374$	11.3212	0.585407
$375$	−93.4390	−4.82517
$376$	16.3991	0.845721
$377$	−3.87390	−0.199516
$378$	−1.89006	−0.0972143
$379$	−28.6833	−1.47336	−0.736681	−	0.676240i	$-0.763608\pi$
$379$	−28.6833	−1.47336	−0.736681	+	0.676240i	$0.763608\pi$
$380$	3.44839	0.176899
$381$	−17.6189	−0.902641
$382$	−28.3103	−1.44848
$383$	−10.9234	−0.558160	−0.279080	−	0.960268i	$-0.590030\pi$
$383$	−10.9234	−0.558160	−0.279080	+	0.960268i	$0.590030\pi$
$384$	−31.1804	−1.59117
$385$	15.6501	0.797600
$386$	−3.88703	−0.197844
$387$	15.4518	0.785458
$388$	−0.440214	−0.0223485
$389$	7.22681	0.366414	0.183207	−	0.983074i	$-0.441352\pi$
$389$	7.22681	0.366414	0.183207	+	0.983074i	$0.441352\pi$
$390$	61.4771	3.11301
$391$	−4.20465	−0.212638
$392$	8.36790	0.422643
$393$	25.1451	1.26840
$394$	27.9993	1.41058
$395$	−8.72610	−0.439058
$396$	0.940117	0.0472426
$397$	−7.14485	−0.358590	−0.179295	−	0.983795i	$-0.557382\pi$
$397$	−7.14485	−0.358590	−0.179295	+	0.983795i	$0.557382\pi$
$398$	16.5596	0.830060
$399$	−25.1101	−1.25708
$400$	−58.5483	−2.92741
$401$	15.8074	0.789386	0.394693	−	0.918813i	$-0.370851\pi$
$401$	15.8074	0.789386	0.394693	+	0.918813i	$0.370851\pi$
$402$	34.8998	1.74064
$403$	21.2203	1.05706
$404$	0.230787	0.0114821
$405$	−35.2024	−1.74922
$406$	2.90366	0.144106
$407$	16.6194	0.823791
$408$	28.4729	1.40962
$409$	19.7351	0.975839	0.487920	−	0.872889i	$-0.337756\pi$
$409$	19.7351	0.975839	0.487920	+	0.872889i	$0.337756\pi$
$410$	67.1465	3.31613
$411$	13.0852	0.645445
$412$	−0.351004	−0.0172927
$413$	−25.8446	−1.27173
$414$	−4.78844	−0.235339
$415$	−26.2867	−1.29036
$416$	3.43933	0.168627
$417$	−16.2796	−0.797215
$418$	13.6688	0.668562
$419$	9.62363	0.470145	0.235073	−	0.971978i	$-0.424467\pi$
$419$	9.62363	0.470145	0.235073	+	0.971978i	$0.424467\pi$
$420$	−3.35996	−0.163949
$421$	−34.0713	−1.66054	−0.830268	−	0.557365i	$-0.811812\pi$
$421$	−34.0713	−1.66054	−0.830268	+	0.557365i	$0.811812\pi$
$422$	−9.18408	−0.447074
$423$	−19.7538	−0.960461
$424$	−5.82675	−0.282972
$425$	57.3853	2.78359
$426$	29.6606	1.43706
$427$	−21.9439	−1.06194
$428$	1.09866	0.0531058
$429$	17.7685	0.857869
$430$	30.0616	1.44970
$431$	5.47912	0.263920	0.131960	−	0.991255i	$-0.457873\pi$
$431$	5.47912	0.263920	0.131960	+	0.991255i	$0.457873\pi$
$432$	2.79237	0.134348
$433$	−21.6270	−1.03933	−0.519664	−	0.854371i	$-0.673943\pi$
$433$	−21.6270	−1.03933	−0.519664	+	0.854371i	$0.673943\pi$
$434$	−15.9056	−0.763493
$435$	−10.8046	−0.518042
$436$	−0.0752961	−0.00360603
$437$	−5.07651	−0.242842
$438$	−61.1683	−2.92273
$439$	−15.5504	−0.742178	−0.371089	−	0.928597i	$-0.621016\pi$
$439$	−15.5504	−0.742178	−0.371089	+	0.928597i	$0.621016\pi$
$440$	−21.4257	−1.02143
$441$	−10.0797	−0.479984
$442$	−23.9240	−1.13795
$443$	41.6611	1.97938	0.989690	−	0.143225i	$-0.0457472\pi$
$443$	41.6611	1.97938	0.989690	+	0.143225i	$0.0457472\pi$
$444$	−3.56806	−0.169333
$445$	−12.9378	−0.613310
$446$	−27.7630	−1.31462
$447$	31.7871	1.50348
$448$	14.3835	0.679558
$449$	−25.8510	−1.21998	−0.609992	−	0.792408i	$-0.708827\pi$
$449$	−25.8510	−1.21998	−0.609992	+	0.792408i	$0.708827\pi$
$450$	65.3529	3.08077
$451$	19.4071	0.913843
$452$	−3.00727	−0.141450
$453$	20.2784	0.952764
$454$	15.9782	0.749893
$455$	−33.0716	−1.55042
$456$	34.3770	1.60985
$457$	−14.4237	−0.674713	−0.337357	−	0.941377i	$-0.609533\pi$
$457$	−14.4237	−0.674713	−0.337357	+	0.941377i	$0.609533\pi$
$458$	−25.1764	−1.17642
$459$	−2.73691	−0.127748
$460$	−0.679284	−0.0316718
$461$	−12.6609	−0.589676	−0.294838	−	0.955547i	$-0.595266\pi$
$461$	−12.6609	−0.589676	−0.294838	+	0.955547i	$0.595266\pi$
$462$	−13.3182	−0.619621
$463$	−0.406547	−0.0188938	−0.00944691	−	0.999955i	$-0.503007\pi$
$463$	−0.406547	−0.0188938	−0.00944691	+	0.999955i	$0.503007\pi$
$464$	−4.28986	−0.199152
$465$	59.1853	2.74465
$466$	−6.35084	−0.294197
$467$	1.68222	0.0778439	0.0389220	−	0.999242i	$-0.487608\pi$
$467$	1.68222	0.0778439	0.0389220	+	0.999242i	$0.487608\pi$
$468$	−1.98665	−0.0918329
$469$	−18.7744	−0.866919
$470$	−38.4312	−1.77270
$471$	−6.67817	−0.307714
$472$	35.3825	1.62861
$473$	8.68857	0.399501
$474$	7.42594	0.341085
$475$	69.2845	3.17899
$476$	1.30754	0.0599308
$477$	7.01868	0.321363
$478$	13.0695	0.597783
$479$	25.4029	1.16069	0.580343	−	0.814372i	$-0.302918\pi$
$479$	25.4029	1.16069	0.580343	+	0.814372i	$0.302918\pi$
$480$	9.59258	0.437839
$481$	−35.1199	−1.60133
$482$	−6.74642	−0.307291
$483$	4.94633	0.225066
$484$	−1.20169	−0.0546224
$485$	−12.0850	−0.548751
$486$	32.8256	1.48900
$487$	34.2968	1.55414	0.777069	−	0.629415i	$-0.216706\pi$
$487$	34.2968	1.55414	0.777069	+	0.629415i	$0.216706\pi$
$488$	30.0423	1.35995
$489$	0.427251	0.0193210
$490$	−19.6101	−0.885893
$491$	28.8727	1.30300	0.651502	−	0.758647i	$-0.274139\pi$
$491$	28.8727	1.30300	0.651502	+	0.758647i	$0.274139\pi$
$492$	−4.16656	−0.187843
$493$	4.20465	0.189368
$494$	−28.8848	−1.29959
$495$	25.8086	1.16001
$496$	23.4989	1.05513
$497$	−15.9559	−0.715722
$498$	22.3701	1.00243
$499$	−1.97330	−0.0883371	−0.0441685	−	0.999024i	$-0.514064\pi$
$499$	−1.97330	−0.0883371	−0.0441685	+	0.999024i	$0.514064\pi$
$500$	5.87448	0.262715
$501$	−19.1222	−0.854316
$502$	29.2959	1.30754
$503$	24.9289	1.11152	0.555762	−	0.831342i	$-0.312427\pi$
$503$	24.9289	1.11152	0.555762	+	0.831342i	$0.312427\pi$
$504$	−17.4437	−0.777004
$505$	6.33569	0.281935
$506$	−2.69255	−0.119699
$507$	−5.02177	−0.223025
$508$	1.10769	0.0491459
$509$	37.1015	1.64449	0.822247	−	0.569131i	$-0.192720\pi$
$509$	37.1015	1.64449	0.822247	+	0.569131i	$0.192720\pi$
$510$	−66.7259	−2.95467
$511$	32.9055	1.45565
$512$	−19.4125	−0.857918
$513$	−3.30443	−0.145894
$514$	−34.0285	−1.50093
$515$	−9.63594	−0.424610
$516$	−1.86538	−0.0821186
$517$	−11.1076	−0.488512
$518$	26.3239	1.15661
$519$	22.6552	0.994454
$520$	45.2767	1.98551
$521$	26.5629	1.16374	0.581870	−	0.813282i	$-0.302321\pi$
$521$	26.5629	1.16374	0.581870	+	0.813282i	$0.302321\pi$
$522$	4.78844	0.209584
$523$	−23.3634	−1.02161	−0.510806	−	0.859696i	$-0.670653\pi$
$523$	−23.3634	−1.02161	−0.510806	+	0.859696i	$0.670653\pi$
$524$	−1.58087	−0.0690604
$525$	−67.5078	−2.94628
$526$	0.734932	0.0320445
$527$	−23.0321	−1.00329
$528$	19.6764	0.856303
$529$	1.00000	0.0434783
$530$	13.6549	0.593132
$531$	−42.6205	−1.84957
$532$	1.57866	0.0684438
$533$	−41.0109	−1.77638
$534$	11.0101	0.476454
$535$	30.1610	1.30397
$536$	25.7031	1.11020
$537$	34.7236	1.49843
$538$	9.06259	0.390716
$539$	−5.66782	−0.244130
$540$	−0.442162	−0.0190276
$541$	2.48754	0.106948	0.0534738	−	0.998569i	$-0.482971\pi$
$541$	2.48754	0.106948	0.0534738	+	0.998569i	$0.482971\pi$
$542$	23.9892	1.03042
$543$	−46.2220	−1.98357
$544$	−3.73298	−0.160050
$545$	−2.06707	−0.0885435
$546$	28.1440	1.20445
$547$	−3.69422	−0.157953	−0.0789767	−	0.996876i	$-0.525165\pi$
$547$	−3.69422	−0.157953	−0.0789767	+	0.996876i	$0.525165\pi$
$548$	−0.822662	−0.0351424
$549$	−36.1879	−1.54446
$550$	36.7481	1.56695
$551$	5.07651	0.216267
$552$	−6.77177	−0.288226
$553$	−3.99478	−0.169875
$554$	−2.67275	−0.113554
$555$	−97.9524	−4.15785
$556$	1.02349	0.0434058
$557$	−30.6634	−1.29925	−0.649626	−	0.760254i	$-0.725074\pi$
$557$	−30.6634	−1.29925	−0.649626	+	0.760254i	$0.725074\pi$
$558$	−26.2300	−1.11041
$559$	−18.3606	−0.776572
$560$	−36.6227	−1.54759
$561$	−19.2855	−0.814234
$562$	1.80485	0.0761328
$563$	15.8280	0.667070	0.333535	−	0.942738i	$-0.391758\pi$
$563$	15.8280	0.667070	0.333535	+	0.942738i	$0.391758\pi$
$564$	2.38472	0.100415
$565$	−82.5573	−3.47321
$566$	26.2529	1.10349
$567$	−16.1156	−0.676791
$568$	21.8445	0.916575
$569$	−25.2392	−1.05808	−0.529042	−	0.848596i	$-0.677448\pi$
$569$	−25.2392	−1.05808	−0.529042	+	0.848596i	$0.677448\pi$
$570$	−80.5620	−3.37437
$571$	40.6814	1.70247	0.851233	−	0.524789i	$-0.175856\pi$
$571$	40.6814	1.70247	0.851233	+	0.524789i	$0.175856\pi$
$572$	−1.11710	−0.0467082
$573$	48.2261	2.01467
$574$	30.7395	1.28304
$575$	−13.6481	−0.569163
$576$	23.7200	0.988332
$577$	−29.9842	−1.24826	−0.624128	−	0.781322i	$-0.714546\pi$
$577$	−29.9842	−1.24826	−0.624128	+	0.781322i	$0.714546\pi$
$578$	0.997363	0.0414848
$579$	6.62147	0.275179
$580$	0.679284	0.0282057
$581$	−12.0340	−0.499254
$582$	10.2844	0.426301
$583$	3.94662	0.163452
$584$	−45.0493	−1.86415
$585$	−54.5386	−2.25489
$586$	31.8177	1.31438
$587$	37.9283	1.56547	0.782734	−	0.622356i	$-0.213824\pi$
$587$	37.9283	1.56547	0.782734	+	0.622356i	$0.213824\pi$
$588$	1.21684	0.0501817
$589$	−27.8080	−1.14581
$590$	−82.9185	−3.41370
$591$	−47.6962	−1.96196
$592$	−38.8910	−1.59841
$593$	17.6162	0.723410	0.361705	−	0.932293i	$-0.382195\pi$
$593$	17.6162	0.723410	0.361705	+	0.932293i	$0.382195\pi$
$594$	−1.75265	−0.0719121
$595$	35.8952	1.47156
$596$	−1.99845	−0.0818596
$597$	−28.2090	−1.15452
$598$	5.68989	0.232677
$599$	−11.9876	−0.489799	−0.244900	−	0.969548i	$-0.578755\pi$
$599$	−11.9876	−0.489799	−0.244900	+	0.969548i	$0.578755\pi$
$600$	92.4215	3.77309
$601$	36.1976	1.47653	0.738266	−	0.674510i	$-0.235645\pi$
$601$	36.1976	1.47653	0.738266	+	0.674510i	$0.235645\pi$
$602$	13.7621	0.560902
$603$	−30.9609	−1.26083
$604$	−1.27490	−0.0518749
$605$	−32.9895	−1.34121
$606$	−5.39170	−0.219023
$607$	9.60236	0.389748	0.194874	−	0.980828i	$-0.437570\pi$
$607$	9.60236	0.389748	0.194874	+	0.980828i	$0.437570\pi$
$608$	−4.50704	−0.182785
$609$	−4.94633	−0.200435
$610$	−70.4039	−2.85057
$611$	23.4725	0.949596
$612$	2.15627	0.0871619
$613$	10.5423	0.425799	0.212900	−	0.977074i	$-0.431709\pi$
$613$	10.5423	0.425799	0.212900	+	0.977074i	$0.431709\pi$
$614$	−29.3147	−1.18304
$615$	−114.383	−4.61236
$616$	−9.80864	−0.395201
$617$	−44.5861	−1.79497	−0.897484	−	0.441048i	$-0.854607\pi$
$617$	−44.5861	−1.79497	−0.897484	+	0.441048i	$0.854607\pi$
$618$	8.20022	0.329861
$619$	−7.87917	−0.316690	−0.158345	−	0.987384i	$-0.550616\pi$
$619$	−7.87917	−0.316690	−0.158345	+	0.987384i	$0.550616\pi$
$620$	−3.72096	−0.149438
$621$	0.650924	0.0261207
$622$	44.3161	1.77691
$623$	−5.92289	−0.237295
$624$	−41.5799	−1.66453
$625$	93.0292	3.72117
$626$	10.4357	0.417094
$627$	−23.2845	−0.929893
$628$	0.419855	0.0167540
$629$	38.1184	1.51988
$630$	40.8791	1.62866
$631$	−30.3776	−1.20931	−0.604657	−	0.796486i	$-0.706690\pi$
$631$	−30.3776	−1.20931	−0.604657	+	0.796486i	$0.706690\pi$
$632$	5.46906	0.217548
$633$	15.6449	0.621829
$634$	32.2791	1.28197
$635$	30.4090	1.20674
$636$	−0.847313	−0.0335981
$637$	11.9772	0.474554
$638$	2.69255	0.106599
$639$	−26.3130	−1.04093
$640$	53.8153	2.12724
$641$	−13.3578	−0.527600	−0.263800	−	0.964577i	$-0.584976\pi$
$641$	−13.3578	−0.527600	−0.263800	+	0.964577i	$0.584976\pi$
$642$	−25.6671	−1.01300
$643$	12.3603	0.487443	0.243722	−	0.969845i	$-0.421632\pi$
$643$	12.3603	0.487443	0.243722	+	0.969845i	$0.421632\pi$
$644$	−0.310974	−0.0122541
$645$	−51.2093	−2.01637
$646$	31.3509	1.23349
$647$	37.8303	1.48726	0.743632	−	0.668589i	$-0.233102\pi$
$647$	37.8303	1.48726	0.743632	+	0.668589i	$0.233102\pi$
$648$	22.0630	0.866718
$649$	−23.9656	−0.940732
$650$	−77.6559	−3.04591
$651$	27.0949	1.06193
$652$	−0.0268612	−0.00105196
$653$	34.8560	1.36402	0.682011	−	0.731342i	$-0.261106\pi$
$653$	34.8560	1.36402	0.682011	+	0.731342i	$0.261106\pi$
$654$	1.75908	0.0687856
$655$	−43.3988	−1.69573
$656$	−45.4145	−1.77314
$657$	54.2646	2.11707
$658$	−17.5937	−0.685873
$659$	−20.4878	−0.798090	−0.399045	−	0.916931i	$-0.630658\pi$
$659$	−20.4878	−0.798090	−0.399045	+	0.916931i	$0.630658\pi$
$660$	−3.11568	−0.121278
$661$	27.2935	1.06160	0.530798	−	0.847498i	$-0.321892\pi$
$661$	27.2935	1.06160	0.530798	+	0.847498i	$0.321892\pi$
$662$	−40.5518	−1.57609
$663$	40.7540	1.58275
$664$	16.4751	0.639359
$665$	43.3383	1.68059
$666$	43.4110	1.68214
$667$	−1.00000	−0.0387202
$668$	1.20221	0.0465148
$669$	47.2938	1.82848
$670$	−60.2348	−2.32707
$671$	−20.3485	−0.785546
$672$	4.39146	0.169404
$673$	−9.50307	−0.366316	−0.183158	−	0.983083i	$-0.558632\pi$
$673$	−9.50307	−0.366316	−0.183158	+	0.983083i	$0.558632\pi$
$674$	6.96764	0.268383
$675$	−8.88386	−0.341940
$676$	0.315717	0.0121430
$677$	17.6511	0.678388	0.339194	−	0.940717i	$-0.389846\pi$
$677$	17.6511	0.678388	0.339194	+	0.940717i	$0.389846\pi$
$678$	70.2565	2.69819
$679$	−5.53248	−0.212317
$680$	−49.1423	−1.88452
$681$	−27.2185	−1.04302
$682$	−14.7492	−0.564776
$683$	6.40203	0.244967	0.122483	−	0.992471i	$-0.460914\pi$
$683$	6.40203	0.244967	0.122483	+	0.992471i	$0.460914\pi$
$684$	2.60338	0.0995429
$685$	−22.5842	−0.862897
$686$	−29.3031	−1.11880
$687$	42.8875	1.63626
$688$	−20.3321	−0.775155
$689$	−8.33998	−0.317728
$690$	15.8696	0.604144
$691$	−50.4784	−1.92029	−0.960144	−	0.279507i	$-0.909829\pi$
$691$	−50.4784	−1.92029	−0.960144	+	0.279507i	$0.909829\pi$
$692$	−1.42433	−0.0541448
$693$	11.8151	0.448819
$694$	−2.68773	−0.102025
$695$	28.0975	1.06580
$696$	6.77177	0.256683
$697$	44.5123	1.68603
$698$	−5.89325	−0.223063
$699$	10.8185	0.409194
$700$	4.24419	0.160415
$701$	−26.8061	−1.01245	−0.506227	−	0.862400i	$-0.668960\pi$
$701$	−26.8061	−1.01245	−0.506227	+	0.862400i	$0.668960\pi$
$702$	3.70369	0.139787
$703$	46.0226	1.73577
$704$	13.3378	0.502687
$705$	65.4668	2.46562
$706$	−42.7660	−1.60952
$707$	2.90046	0.109083
$708$	5.14525	0.193370
$709$	−21.5712	−0.810122	−0.405061	−	0.914290i	$-0.632750\pi$
$709$	−21.5712	−0.810122	−0.405061	+	0.914290i	$0.632750\pi$
$710$	−51.1923	−1.92121
$711$	−6.58782	−0.247063
$712$	8.10873	0.303888
$713$	5.47778	0.205144
$714$	−30.5469	−1.14319
$715$	−30.6672	−1.14689
$716$	−2.18306	−0.0815848
$717$	−22.2636	−0.831448
$718$	−12.9129	−0.481905
$719$	20.2309	0.754486	0.377243	−	0.926114i	$-0.376872\pi$
$719$	20.2309	0.754486	0.377243	+	0.926114i	$0.376872\pi$
$720$	−60.3947	−2.25078
$721$	−4.41131	−0.164286
$722$	9.94503	0.370116
$723$	11.4924	0.427407
$724$	2.90596	0.107999
$725$	13.6481	0.506876
$726$	28.0742	1.04193
$727$	−9.12267	−0.338341	−0.169171	−	0.985587i	$-0.554109\pi$
$727$	−9.12267	−0.338341	−0.169171	+	0.985587i	$0.554109\pi$
$728$	20.7275	0.768214
$729$	−31.4622	−1.16527
$730$	105.572	3.90741
$731$	19.9282	0.737073
$732$	4.36869	0.161471
$733$	−3.48854	−0.128852	−0.0644262	−	0.997922i	$-0.520522\pi$
$733$	−3.48854	−0.128852	−0.0644262	+	0.997922i	$0.520522\pi$
$734$	15.8861	0.586365
$735$	33.4054	1.23218
$736$	0.887822	0.0327256
$737$	−17.4094	−0.641284
$738$	50.6927	1.86602
$739$	−16.9510	−0.623552	−0.311776	−	0.950156i	$-0.600924\pi$
$739$	−16.9510	−0.623552	−0.311776	+	0.950156i	$0.600924\pi$
$740$	6.15824	0.226381
$741$	49.2046	1.80758
$742$	6.25119	0.229488
$743$	−35.5481	−1.30413	−0.652067	−	0.758162i	$-0.726098\pi$
$743$	−35.5481	−1.30413	−0.652067	+	0.758162i	$0.726098\pi$
$744$	−37.0943	−1.35994
$745$	−54.8625	−2.01001
$746$	−0.0309987	−0.00113494
$747$	−19.8453	−0.726102
$748$	1.21247	0.0443324
$749$	13.8076	0.504520
$750$	−137.241	−5.01133
$751$	7.34241	0.267929	0.133964	−	0.990986i	$-0.457229\pi$
$751$	7.34241	0.267929	0.133964	+	0.990986i	$0.457229\pi$
$752$	25.9929	0.947863
$753$	−49.9050	−1.81864
$754$	−5.68989	−0.207213
$755$	−34.9992	−1.27375
$756$	−0.202421	−0.00736197
$757$	30.4932	1.10830	0.554148	−	0.832418i	$-0.313044\pi$
$757$	30.4932	1.10830	0.554148	+	0.832418i	$0.313044\pi$
$758$	−42.1293	−1.53021
$759$	4.58671	0.166487
$760$	−59.3324	−2.15221
$761$	−48.3414	−1.75237	−0.876187	−	0.481972i	$-0.839921\pi$
$761$	−48.3414	−1.75237	−0.876187	+	0.481972i	$0.839921\pi$
$762$	−25.8781	−0.937466
$763$	−0.946299	−0.0342583
$764$	−3.03196	−0.109693
$765$	59.1950	2.14020
$766$	−16.0440	−0.579695
$767$	50.6439	1.82865
$768$	−9.38889	−0.338792
$769$	−32.9910	−1.18969	−0.594843	−	0.803842i	$-0.702786\pi$
$769$	−32.9910	−1.18969	−0.594843	+	0.803842i	$0.702786\pi$
$770$	22.9864	0.828373
$771$	57.9669	2.08763
$772$	−0.416290	−0.0149826
$773$	27.2251	0.979218	0.489609	−	0.871942i	$-0.337140\pi$
$773$	27.2251	0.979218	0.489609	+	0.871942i	$0.337140\pi$
$774$	22.6952	0.815762
$775$	−74.7610	−2.68550
$776$	7.57425	0.271900
$777$	−44.8423	−1.60871
$778$	10.6146	0.380551
$779$	53.7423	1.92552
$780$	6.58403	0.235746
$781$	−14.7959	−0.529439
$782$	−6.17568	−0.220842
$783$	−0.650924	−0.0232621
$784$	13.2633	0.473688
$785$	11.5261	0.411384
$786$	36.9325	1.31734
$787$	−17.4869	−0.623341	−0.311671	−	0.950190i	$-0.600889\pi$
$787$	−17.4869	−0.623341	−0.311671	+	0.950190i	$0.600889\pi$
$788$	2.99865	0.106822
$789$	−1.25194	−0.0445703
$790$	−12.8167	−0.455997
$791$	−37.7945	−1.34382
$792$	−16.1755	−0.574771
$793$	43.0004	1.52699
$794$	−10.4942	−0.372424
$795$	−23.2609	−0.824979
$796$	1.77349	0.0628599
$797$	46.5153	1.64766	0.823829	−	0.566838i	$-0.191834\pi$
$797$	46.5153	1.64766	0.823829	+	0.566838i	$0.191834\pi$
$798$	−36.8811	−1.30558
$799$	−25.4766	−0.901296
$800$	−12.1170	−0.428402
$801$	−9.76747	−0.345117
$802$	23.2176	0.819841
$803$	30.5132	1.07679
$804$	3.73768	0.131818
$805$	−8.53703	−0.300891
$806$	31.1679	1.09784
$807$	−15.4380	−0.543442
$808$	−3.97088	−0.139695
$809$	−43.0308	−1.51288	−0.756441	−	0.654062i	$-0.773064\pi$
$809$	−43.0308	−1.51288	−0.756441	+	0.654062i	$0.773064\pi$
$810$	−51.7045	−1.81671
$811$	13.3752	0.469667	0.234834	−	0.972036i	$-0.424545\pi$
$811$	13.3752	0.469667	0.234834	+	0.972036i	$0.424545\pi$
$812$	0.310974	0.0109131
$813$	−40.8651	−1.43320
$814$	24.4101	0.855574
$815$	−0.737407	−0.0258303
$816$	45.1300	1.57987
$817$	24.0605	0.841771
$818$	28.9865	1.01349
$819$	−24.9676	−0.872439
$820$	7.19121	0.251128
$821$	−37.0332	−1.29247	−0.646235	−	0.763139i	$-0.723657\pi$
$821$	−37.0332	−1.29247	−0.646235	+	0.763139i	$0.723657\pi$
$822$	19.2192	0.670347
$823$	20.7639	0.723786	0.361893	−	0.932220i	$-0.382131\pi$
$823$	20.7639	0.723786	0.361893	+	0.932220i	$0.382131\pi$
$824$	6.03931	0.210389
$825$	−62.5997	−2.17944
$826$	−37.9599	−1.32079
$827$	35.9493	1.25008	0.625040	−	0.780593i	$-0.285083\pi$
$827$	35.9493	1.25008	0.625040	+	0.780593i	$0.285083\pi$
$828$	−0.512829	−0.0178221
$829$	−38.3647	−1.33246	−0.666231	−	0.745745i	$-0.732094\pi$
$829$	−38.3647	−1.33246	−0.666231	+	0.745745i	$0.732094\pi$
$830$	−38.6093	−1.34015
$831$	4.55297	0.157941
$832$	−28.1853	−0.977151
$833$	−12.9998	−0.450416
$834$	−23.9111	−0.827973
$835$	33.0036	1.14214
$836$	1.46389	0.0506297
$837$	3.56562	0.123246
$838$	14.1350	0.488284
$839$	34.1180	1.17789	0.588943	−	0.808175i	$-0.299544\pi$
$839$	34.1180	1.17789	0.588943	+	0.808175i	$0.299544\pi$
$840$	57.8108	1.99466
$841$	1.00000	0.0344828
$842$	−50.0431	−1.72460
$843$	−3.07452	−0.105892
$844$	−0.983591	−0.0338566
$845$	8.66724	0.298162
$846$	−29.0139	−0.997517
$847$	−15.1025	−0.518928
$848$	−9.23549	−0.317148
$849$	−44.7212	−1.53483
$850$	84.2861	2.89099
$851$	−9.06579	−0.310771
$852$	3.17658	0.108828
$853$	17.8613	0.611560	0.305780	−	0.952102i	$-0.401083\pi$
$853$	17.8613	0.611560	0.305780	+	0.952102i	$0.401083\pi$
$854$	−32.2307	−1.10291
$855$	71.4695	2.44421
$856$	−18.9034	−0.646103
$857$	−40.9341	−1.39828	−0.699142	−	0.714983i	$-0.746434\pi$
$857$	−40.9341	−1.39828	−0.699142	+	0.714983i	$0.746434\pi$
$858$	26.0979	0.890967
$859$	−4.71520	−0.160881	−0.0804403	−	0.996759i	$-0.525633\pi$
$859$	−4.71520	−0.160881	−0.0804403	+	0.996759i	$0.525633\pi$
$860$	3.21952	0.109785
$861$	−52.3641	−1.78456
$862$	8.04759	0.274102
$863$	25.6983	0.874779	0.437389	−	0.899272i	$-0.355903\pi$
$863$	25.6983	0.874779	0.437389	+	0.899272i	$0.355903\pi$
$864$	0.577905	0.0196607
$865$	−39.1014	−1.32949
$866$	−31.7652	−1.07943
$867$	−1.69899	−0.0577007
$868$	−1.70345	−0.0578188
$869$	−3.70435	−0.125661
$870$	−15.8696	−0.538029
$871$	36.7894	1.24656
$872$	1.29553	0.0438722
$873$	−9.12365	−0.308789
$874$	−7.45626	−0.252212
$875$	73.8288	2.49587
$876$	−6.55096	−0.221337
$877$	46.7316	1.57801	0.789007	−	0.614385i	$-0.210596\pi$
$877$	46.7316	1.57801	0.789007	+	0.614385i	$0.210596\pi$
$878$	−22.8400	−0.770812
$879$	−54.2008	−1.82815
$880$	−33.9601	−1.14479
$881$	12.0024	0.404372	0.202186	−	0.979347i	$-0.435196\pi$
$881$	12.0024	0.404372	0.202186	+	0.979347i	$0.435196\pi$
$882$	−14.8048	−0.498502
$883$	19.3283	0.650448	0.325224	−	0.945637i	$-0.394560\pi$
$883$	19.3283	0.650448	0.325224	+	0.945637i	$0.394560\pi$
$884$	−2.56219	−0.0861758
$885$	141.250	4.74807
$886$	61.1909	2.05575
$887$	4.73456	0.158971	0.0794855	−	0.996836i	$-0.474672\pi$
$887$	4.73456	0.158971	0.0794855	+	0.996836i	$0.474672\pi$
$888$	61.3914	2.06016
$889$	13.9211	0.466900
$890$	−19.0027	−0.636972
$891$	−14.9439	−0.500640
$892$	−2.97335	−0.0995550
$893$	−30.7593	−1.02932
$894$	46.6881	1.56149
$895$	−59.9306	−2.00326
$896$	24.6365	0.823047
$897$	−9.69261	−0.323627
$898$	−37.9693	−1.26705
$899$	−5.47778	−0.182694
$900$	6.99913	0.233304
$901$	9.05204	0.301567
$902$	28.5046	0.949100
$903$	−23.4435	−0.780151
$904$	51.7426	1.72093
$905$	79.7760	2.65185
$906$	29.7845	0.989523
$907$	46.6197	1.54798	0.773992	−	0.633196i	$-0.218257\pi$
$907$	46.6197	1.54798	0.773992	+	0.633196i	$0.218257\pi$
$908$	1.71122	0.0567889
$909$	4.78317	0.158648
$910$	−48.5747	−1.61024
$911$	33.8874	1.12274	0.561371	−	0.827565i	$-0.310274\pi$
$911$	33.8874	1.12274	0.561371	+	0.827565i	$0.310274\pi$
$912$	54.4880	1.80428
$913$	−11.1591	−0.369311
$914$	−21.1852	−0.700745
$915$	119.932	3.96482
$916$	−2.69632	−0.0890891
$917$	−19.8678	−0.656094
$918$	−4.01990	−0.132677
$919$	−15.9739	−0.526931	−0.263465	−	0.964669i	$-0.584865\pi$
$919$	−15.9739	−0.526931	−0.263465	+	0.964669i	$0.584865\pi$
$920$	11.6876	0.385330
$921$	49.9370	1.64548
$922$	−18.5960	−0.612426
$923$	31.2666	1.02915
$924$	−1.42635	−0.0469234
$925$	123.730	4.06823
$926$	−0.597126	−0.0196228
$927$	−7.27472	−0.238933
$928$	−0.887822	−0.0291442
$929$	−6.83071	−0.224108	−0.112054	−	0.993702i	$-0.535743\pi$
$929$	−6.83071	−0.224108	−0.112054	+	0.993702i	$0.535743\pi$
$930$	86.9299	2.85055
$931$	−15.6954	−0.514396
$932$	−0.680158	−0.0222793
$933$	−75.4916	−2.47148
$934$	2.47081	0.0808473
$935$	33.2855	1.08855
$936$	34.1819	1.11727
$937$	4.13943	0.135229	0.0676146	−	0.997712i	$-0.478461\pi$
$937$	4.13943	0.135229	0.0676146	+	0.997712i	$0.478461\pi$
$938$	−27.5753	−0.900366
$939$	−17.7770	−0.580130
$940$	−4.11588	−0.134245
$941$	−33.2797	−1.08489	−0.542444	−	0.840092i	$-0.682501\pi$
$941$	−33.2797	−1.08489	−0.542444	+	0.840092i	$0.682501\pi$
$942$	−9.80874	−0.319586
$943$	−10.5865	−0.344743
$944$	56.0819	1.82531
$945$	−5.55696	−0.180768
$946$	12.7616	0.414914
$947$	−54.7802	−1.78012	−0.890058	−	0.455847i	$-0.849336\pi$
$947$	−54.7802	−1.78012	−0.890058	+	0.455847i	$0.849336\pi$
$948$	0.795298	0.0258301
$949$	−64.4802	−2.09312
$950$	101.763	3.30164
$951$	−54.9869	−1.78307
$952$	−22.4972	−0.729140
$953$	−11.2383	−0.364045	−0.182023	−	0.983294i	$-0.558264\pi$
$953$	−11.2383	−0.364045	−0.182023	+	0.983294i	$0.558264\pi$
$954$	10.3089	0.333762
$955$	−83.2351	−2.69342
$956$	1.39970	0.0452697
$957$	−4.58671	−0.148267
$958$	37.3111	1.20547
$959$	−10.3390	−0.333863
$960$	−78.6113	−2.53717
$961$	−0.993945	−0.0320627
$962$	−51.5833	−1.66311
$963$	22.7703	0.733761
$964$	−0.722524	−0.0232709
$965$	−11.4282	−0.367888
$966$	7.26504	0.233749
$967$	−40.6294	−1.30655	−0.653276	−	0.757120i	$-0.726606\pi$
$967$	−40.6294	−1.30655	−0.653276	+	0.757120i	$0.726606\pi$
$968$	20.6761	0.664555
$969$	−53.4057	−1.71564
$970$	−17.7502	−0.569923
$971$	−13.1817	−0.423022	−0.211511	−	0.977376i	$-0.567838\pi$
$971$	−13.1817	−0.423022	−0.211511	+	0.977376i	$0.567838\pi$
$972$	3.51553	0.112761
$973$	12.8630	0.412368
$974$	50.3744	1.61410
$975$	132.285	4.23652
$976$	47.6176	1.52420
$977$	−1.55708	−0.0498154	−0.0249077	−	0.999690i	$-0.507929\pi$
$977$	−1.55708	−0.0498154	−0.0249077	+	0.999690i	$0.507929\pi$
$978$	0.627536	0.0200664
$979$	−5.49227	−0.175534
$980$	−2.10019	−0.0670880
$981$	−1.56055	−0.0498244
$982$	42.4075	1.35328
$983$	−37.0826	−1.18275	−0.591376	−	0.806396i	$-0.701415\pi$
$983$	−37.0826	−1.18275	−0.591376	+	0.806396i	$0.701415\pi$
$984$	71.6891	2.28537
$985$	82.3205	2.62295
$986$	6.17568	0.196674
$987$	29.9705	0.953972
$988$	−3.09348	−0.0984168
$989$	−4.73958	−0.150710
$990$	37.9070	1.20476
$991$	26.3834	0.838096	0.419048	−	0.907964i	$-0.362364\pi$
$991$	26.3834	0.838096	0.419048	+	0.907964i	$0.362364\pi$
$992$	4.86329	0.154410
$993$	69.0792	2.19216
$994$	−23.4357	−0.743335
$995$	48.6869	1.54348
$996$	2.39578	0.0759131
$997$	−25.1891	−0.797747	−0.398873	−	0.917006i	$-0.630599\pi$
$997$	−25.1891	−0.797747	−0.398873	+	0.917006i	$0.630599\pi$
$998$	−2.89834	−0.0917452
$999$	−5.90114	−0.186704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.10	✓	13
3.2	odd	2		6003.2.a.o.1.4		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.10	✓	13	1.1	even	1	trivial
6003.2.a.o.1.4		13	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+1.46878 q^{2} -2.50203 q^{3} +0.157302 q^{4} +4.31834 q^{5} -3.67492 q^{6} +1.97692 q^{7} -2.70651 q^{8} +3.26016 q^{9} +O(q^{10})\)	\(q+1.46878 q^{2} -2.50203 q^{3} +0.157302 q^{4} +4.31834 q^{5} -3.67492 q^{6} +1.97692 q^{7} -2.70651 q^{8} +3.26016 q^{9} +6.34267 q^{10} +1.83320 q^{11} -0.393574 q^{12} -3.87390 q^{13} +2.90366 q^{14} -10.8046 q^{15} -4.28986 q^{16} +4.20465 q^{17} +4.78844 q^{18} +5.07651 q^{19} +0.679284 q^{20} -4.94633 q^{21} +2.69255 q^{22} -1.00000 q^{23} +6.77177 q^{24} +13.6481 q^{25} -5.68989 q^{26} -0.650924 q^{27} +0.310974 q^{28} +1.00000 q^{29} -15.8696 q^{30} -5.47778 q^{31} -0.887822 q^{32} -4.58671 q^{33} +6.17568 q^{34} +8.53703 q^{35} +0.512829 q^{36} +9.06579 q^{37} +7.45626 q^{38} +9.69261 q^{39} -11.6876 q^{40} +10.5865 q^{41} -7.26504 q^{42} +4.73958 q^{43} +0.288365 q^{44} +14.0785 q^{45} -1.46878 q^{46} -6.05915 q^{47} +10.7334 q^{48} -3.09177 q^{49} +20.0459 q^{50} -10.5202 q^{51} -0.609372 q^{52} +2.15287 q^{53} -0.956062 q^{54} +7.91636 q^{55} -5.35057 q^{56} -12.7016 q^{57} +1.46878 q^{58} -13.0731 q^{59} -1.69959 q^{60} -11.1000 q^{61} -8.04563 q^{62} +6.44509 q^{63} +7.27571 q^{64} -16.7288 q^{65} -6.73685 q^{66} -9.49675 q^{67} +0.661399 q^{68} +2.50203 q^{69} +12.5390 q^{70} -8.07109 q^{71} -8.82365 q^{72} +16.6448 q^{73} +13.3156 q^{74} -34.1479 q^{75} +0.798545 q^{76} +3.62409 q^{77} +14.2363 q^{78} -2.02071 q^{79} -18.5251 q^{80} -8.15184 q^{81} +15.5491 q^{82} -6.08722 q^{83} -0.778067 q^{84} +18.1571 q^{85} +6.96138 q^{86} -2.50203 q^{87} -4.96156 q^{88} -2.99601 q^{89} +20.6781 q^{90} -7.65840 q^{91} -0.157302 q^{92} +13.7056 q^{93} -8.89953 q^{94} +21.9221 q^{95} +2.22136 q^{96} -2.79853 q^{97} -4.54112 q^{98} +5.97651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

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