LMFDB - Embedded newform 2667.2.a.o.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
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} - 5 x^{15} - 13 x^{14} + 98 x^{13} + 9 x^{12} - 712 x^{11} + 565 x^{10} + 2282 x^{9} - 3082 x^{8} + \cdots + 4 $ x^16 - 5x^15 - 13x^14 + 98x^13 + 9x^12 - 712x^11 + 565x^10 + 2282x^9 - 3082x^8 - 2747x^7 + 5821x^6 - 158x^5 - 3341x^4 + 1002x^3 + 416x^2 - 148*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.415886$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.415886 q^{2} -1.00000 q^{3} -1.82704 q^{4} -0.233776 q^{5} +0.415886 q^{6} -1.00000 q^{7} +1.59161 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.415886 q^{2} -1.00000 q^{3} -1.82704 q^{4} -0.233776 q^{5} +0.415886 q^{6} -1.00000 q^{7} +1.59161 q^{8} +1.00000 q^{9} +0.0972242 q^{10} +2.55512 q^{11} +1.82704 q^{12} +1.50814 q^{13} +0.415886 q^{14} +0.233776 q^{15} +2.99215 q^{16} +0.262289 q^{17} -0.415886 q^{18} +0.541081 q^{19} +0.427118 q^{20} +1.00000 q^{21} -1.06264 q^{22} -3.11874 q^{23} -1.59161 q^{24} -4.94535 q^{25} -0.627215 q^{26} -1.00000 q^{27} +1.82704 q^{28} -2.23156 q^{29} -0.0972242 q^{30} +8.80983 q^{31} -4.42762 q^{32} -2.55512 q^{33} -0.109083 q^{34} +0.233776 q^{35} -1.82704 q^{36} -9.13854 q^{37} -0.225028 q^{38} -1.50814 q^{39} -0.372081 q^{40} -7.98771 q^{41} -0.415886 q^{42} -2.63460 q^{43} -4.66830 q^{44} -0.233776 q^{45} +1.29704 q^{46} +5.48952 q^{47} -2.99215 q^{48} +1.00000 q^{49} +2.05670 q^{50} -0.262289 q^{51} -2.75543 q^{52} +6.41058 q^{53} +0.415886 q^{54} -0.597325 q^{55} -1.59161 q^{56} -0.541081 q^{57} +0.928077 q^{58} +0.296590 q^{59} -0.427118 q^{60} -6.94324 q^{61} -3.66389 q^{62} -1.00000 q^{63} -4.14291 q^{64} -0.352567 q^{65} +1.06264 q^{66} +11.7484 q^{67} -0.479213 q^{68} +3.11874 q^{69} -0.0972242 q^{70} +2.31407 q^{71} +1.59161 q^{72} +9.14504 q^{73} +3.80059 q^{74} +4.94535 q^{75} -0.988575 q^{76} -2.55512 q^{77} +0.627215 q^{78} +3.82656 q^{79} -0.699492 q^{80} +1.00000 q^{81} +3.32198 q^{82} -2.11859 q^{83} -1.82704 q^{84} -0.0613169 q^{85} +1.09569 q^{86} +2.23156 q^{87} +4.06676 q^{88} -15.5991 q^{89} +0.0972242 q^{90} -1.50814 q^{91} +5.69806 q^{92} -8.80983 q^{93} -2.28302 q^{94} -0.126492 q^{95} +4.42762 q^{96} +16.3042 q^{97} -0.415886 q^{98} +2.55512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19} - q^{20} + 16 q^{21} + q^{22} + 13 q^{23} - 6 q^{24} + 33 q^{25} + 8 q^{26} - 16 q^{27} - 19 q^{28} + 24 q^{29} + 12 q^{30} - 42 q^{31} + 42 q^{32} - 11 q^{33} + 9 q^{34} + q^{35} + 19 q^{36} + 40 q^{37} + 38 q^{38} - 18 q^{39} - 61 q^{40} + 9 q^{41} + 5 q^{42} + 7 q^{43} + 3 q^{44} - q^{45} + 24 q^{46} + 31 q^{47} - 25 q^{48} + 16 q^{49} + 6 q^{50} + 5 q^{51} + 52 q^{52} + 66 q^{53} - 5 q^{54} - 36 q^{55} - 6 q^{56} + 11 q^{57} + 19 q^{58} - 7 q^{59} + q^{60} + 6 q^{61} + 52 q^{62} - 16 q^{63} + 10 q^{64} + 51 q^{65} - q^{66} + 16 q^{67} + 14 q^{68} - 13 q^{69} + 12 q^{70} + 46 q^{71} + 6 q^{72} + 39 q^{73} + 72 q^{74} - 33 q^{75} + 24 q^{76} - 11 q^{77} - 8 q^{78} + 4 q^{79} - 2 q^{80} + 16 q^{81} - 18 q^{82} + 15 q^{83} + 19 q^{84} - 4 q^{85} + 14 q^{86} - 24 q^{87} + 58 q^{88} - q^{89} - 12 q^{90} - 18 q^{91} + 26 q^{92} + 42 q^{93} + 5 q^{94} + 44 q^{95} - 42 q^{96} + 41 q^{97} + 5 q^{98} + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.415886	−0.294076	−0.147038	−	0.989131i	$-0.546974\pi$
$2$	−0.415886	−0.294076	−0.147038	+	0.989131i	$0.546974\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.82704	−0.913519
$5$	−0.233776	−0.104548	−0.0522739	−	0.998633i	$-0.516647\pi$
$5$	−0.233776	−0.104548	−0.0522739	+	0.998633i	$0.516647\pi$
$6$	0.415886	0.169785
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.59161	0.562720
$9$	1.00000	0.333333
$10$	0.0972242	0.0307450
$11$	2.55512	0.770397	0.385198	−	0.922834i	$-0.374133\pi$
$11$	2.55512	0.770397	0.385198	+	0.922834i	$0.374133\pi$
$12$	1.82704	0.527421
$13$	1.50814	0.418283	0.209142	−	0.977885i	$-0.432933\pi$
$13$	1.50814	0.418283	0.209142	+	0.977885i	$0.432933\pi$
$14$	0.415886	0.111150
$15$	0.233776	0.0603607
$16$	2.99215	0.748037
$17$	0.262289	0.0636145	0.0318073	−	0.999494i	$-0.489874\pi$
$17$	0.262289	0.0636145	0.0318073	+	0.999494i	$0.489874\pi$
$18$	−0.415886	−0.0980253
$19$	0.541081	0.124132	0.0620662	−	0.998072i	$-0.480231\pi$
$19$	0.541081	0.124132	0.0620662	+	0.998072i	$0.480231\pi$
$20$	0.427118	0.0955064
$21$	1.00000	0.218218
$22$	−1.06264	−0.226555
$23$	−3.11874	−0.650303	−0.325151	−	0.945662i	$-0.605415\pi$
$23$	−3.11874	−0.650303	−0.325151	+	0.945662i	$0.605415\pi$
$24$	−1.59161	−0.324887
$25$	−4.94535	−0.989070
$26$	−0.627215	−0.123007
$27$	−1.00000	−0.192450
$28$	1.82704	0.345278
$29$	−2.23156	−0.414391	−0.207196	−	0.978300i	$-0.566434\pi$
$29$	−2.23156	−0.414391	−0.207196	+	0.978300i	$0.566434\pi$
$30$	−0.0972242	−0.0177506
$31$	8.80983	1.58229	0.791146	−	0.611627i	$-0.209485\pi$
$31$	8.80983	1.58229	0.791146	+	0.611627i	$0.209485\pi$
$32$	−4.42762	−0.782700
$33$	−2.55512	−0.444789
$34$	−0.109083	−0.0187075
$35$	0.233776	0.0395153
$36$	−1.82704	−0.304506
$37$	−9.13854	−1.50237	−0.751183	−	0.660094i	$-0.770517\pi$
$37$	−9.13854	−1.50237	−0.751183	+	0.660094i	$0.770517\pi$
$38$	−0.225028	−0.0365044
$39$	−1.50814	−0.241496
$40$	−0.372081	−0.0588311
$41$	−7.98771	−1.24747	−0.623735	−	0.781636i	$-0.714386\pi$
$41$	−7.98771	−1.24747	−0.623735	+	0.781636i	$0.714386\pi$
$42$	−0.415886	−0.0641726
$43$	−2.63460	−0.401773	−0.200886	−	0.979615i	$-0.564382\pi$
$43$	−2.63460	−0.401773	−0.200886	+	0.979615i	$0.564382\pi$
$44$	−4.66830	−0.703772
$45$	−0.233776	−0.0348492
$46$	1.29704	0.191238
$47$	5.48952	0.800729	0.400365	−	0.916356i	$-0.368883\pi$
$47$	5.48952	0.800729	0.400365	+	0.916356i	$0.368883\pi$
$48$	−2.99215	−0.431879
$49$	1.00000	0.142857
$50$	2.05670	0.290862
$51$	−0.262289	−0.0367279
$52$	−2.75543	−0.382110
$53$	6.41058	0.880561	0.440280	−	0.897860i	$-0.354879\pi$
$53$	6.41058	0.880561	0.440280	+	0.897860i	$0.354879\pi$
$54$	0.415886	0.0565949
$55$	−0.597325	−0.0805433
$56$	−1.59161	−0.212688
$57$	−0.541081	−0.0716679
$58$	0.928077	0.121862
$59$	0.296590	0.0386127	0.0193064	−	0.999814i	$-0.493854\pi$
$59$	0.296590	0.0386127	0.0193064	+	0.999814i	$0.493854\pi$
$60$	−0.427118	−0.0551406
$61$	−6.94324	−0.888990	−0.444495	−	0.895781i	$-0.646617\pi$
$61$	−6.94324	−0.888990	−0.444495	+	0.895781i	$0.646617\pi$
$62$	−3.66389	−0.465314
$63$	−1.00000	−0.125988
$64$	−4.14291	−0.517864
$65$	−0.352567	−0.0437305
$66$	1.06264	0.130802
$67$	11.7484	1.43530	0.717649	−	0.696405i	$-0.245218\pi$
$67$	11.7484	1.43530	0.717649	+	0.696405i	$0.245218\pi$
$68$	−0.479213	−0.0581131
$69$	3.11874	0.375452
$70$	−0.0972242	−0.0116205
$71$	2.31407	0.274630	0.137315	−	0.990527i	$-0.456153\pi$
$71$	2.31407	0.274630	0.137315	+	0.990527i	$0.456153\pi$
$72$	1.59161	0.187573
$73$	9.14504	1.07035	0.535173	−	0.844743i	$-0.320246\pi$
$73$	9.14504	1.07035	0.535173	+	0.844743i	$0.320246\pi$
$74$	3.80059	0.441810
$75$	4.94535	0.571040
$76$	−0.988575	−0.113397
$77$	−2.55512	−0.291183
$78$	0.627215	0.0710181
$79$	3.82656	0.430522	0.215261	−	0.976557i	$-0.430940\pi$
$79$	3.82656	0.430522	0.215261	+	0.976557i	$0.430940\pi$
$80$	−0.699492	−0.0782056
$81$	1.00000	0.111111
$82$	3.32198	0.366851
$83$	−2.11859	−0.232546	−0.116273	−	0.993217i	$-0.537095\pi$
$83$	−2.11859	−0.232546	−0.116273	+	0.993217i	$0.537095\pi$
$84$	−1.82704	−0.199346
$85$	−0.0613169	−0.00665075
$86$	1.09569	0.118152
$87$	2.23156	0.239249
$88$	4.06676	0.433518
$89$	−15.5991	−1.65350	−0.826750	−	0.562569i	$-0.809813\pi$
$89$	−15.5991	−1.65350	−0.826750	+	0.562569i	$0.809813\pi$
$90$	0.0972242	0.0102483
$91$	−1.50814	−0.158096
$92$	5.69806	0.594064
$93$	−8.80983	−0.913537
$94$	−2.28302	−0.235475
$95$	−0.126492	−0.0129778
$96$	4.42762	0.451892
$97$	16.3042	1.65544	0.827722	−	0.561138i	$-0.189636\pi$
$97$	16.3042	1.65544	0.827722	+	0.561138i	$0.189636\pi$
$98$	−0.415886	−0.0420109
$99$	2.55512	0.256799
$100$	9.03534	0.903534
$101$	5.23614	0.521016	0.260508	−	0.965472i	$-0.416110\pi$
$101$	5.23614	0.521016	0.260508	+	0.965472i	$0.416110\pi$
$102$	0.109083	0.0108008
$103$	−6.04580	−0.595710	−0.297855	−	0.954611i	$-0.596271\pi$
$103$	−6.04580	−0.595710	−0.297855	+	0.954611i	$0.596271\pi$
$104$	2.40038	0.235376
$105$	−0.233776	−0.0228142
$106$	−2.66607	−0.258952
$107$	0.930174	0.0899233	0.0449617	−	0.998989i	$-0.485683\pi$
$107$	0.930174	0.0899233	0.0449617	+	0.998989i	$0.485683\pi$
$108$	1.82704	0.175807
$109$	14.5050	1.38933	0.694665	−	0.719333i	$-0.255552\pi$
$109$	14.5050	1.38933	0.694665	+	0.719333i	$0.255552\pi$
$110$	0.248419	0.0236858
$111$	9.13854	0.867392
$112$	−2.99215	−0.282731
$113$	20.2664	1.90650	0.953250	−	0.302184i	$-0.0977155\pi$
$113$	20.2664	1.90650	0.953250	+	0.302184i	$0.0977155\pi$
$114$	0.225028	0.0210758
$115$	0.729087	0.0679877
$116$	4.07715	0.378554
$117$	1.50814	0.139428
$118$	−0.123348	−0.0113551
$119$	−0.262289	−0.0240440
$120$	0.372081	0.0339662
$121$	−4.47137	−0.406489
$122$	2.88760	0.261431
$123$	7.98771	0.720227
$124$	−16.0959	−1.44545
$125$	2.32498	0.207953
$126$	0.415886	0.0370501
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	10.5782	0.934991
$129$	2.63460	0.231964
$130$	0.146628	0.0128601
$131$	13.3874	1.16966	0.584832	−	0.811154i	$-0.301160\pi$
$131$	13.3874	1.16966	0.584832	+	0.811154i	$0.301160\pi$
$132$	4.66830	0.406323
$133$	−0.541081	−0.0469176
$134$	−4.88600	−0.422087
$135$	0.233776	0.0201202
$136$	0.417463	0.0357972
$137$	19.7793	1.68986	0.844930	−	0.534878i	$-0.179642\pi$
$137$	19.7793	1.68986	0.844930	+	0.534878i	$0.179642\pi$
$138$	−1.29704	−0.110412
$139$	−19.1936	−1.62798	−0.813992	−	0.580876i	$-0.802710\pi$
$139$	−19.1936	−1.62798	−0.813992	+	0.580876i	$0.802710\pi$
$140$	−0.427118	−0.0360980
$141$	−5.48952	−0.462301
$142$	−0.962391	−0.0807621
$143$	3.85348	0.322244
$144$	2.99215	0.249346
$145$	0.521686	0.0433237
$146$	−3.80329	−0.314763
$147$	−1.00000	−0.0824786
$148$	16.6965	1.37244
$149$	19.2699	1.57865	0.789324	−	0.613977i	$-0.210431\pi$
$149$	19.2699	1.57865	0.789324	+	0.613977i	$0.210431\pi$
$150$	−2.05670	−0.167929
$151$	−9.79088	−0.796770	−0.398385	−	0.917218i	$-0.630429\pi$
$151$	−9.79088	−0.796770	−0.398385	+	0.917218i	$0.630429\pi$
$152$	0.861191	0.0698518
$153$	0.262289	0.0212048
$154$	1.06264	0.0856298
$155$	−2.05953	−0.165425
$156$	2.75543	0.220611
$157$	7.92860	0.632772	0.316386	−	0.948631i	$-0.397531\pi$
$157$	7.92860	0.632772	0.316386	+	0.948631i	$0.397531\pi$
$158$	−1.59142	−0.126606
$159$	−6.41058	−0.508392
$160$	1.03507	0.0818295
$161$	3.11874	0.245791
$162$	−0.415886	−0.0326751
$163$	−4.12383	−0.323003	−0.161502	−	0.986872i	$-0.551634\pi$
$163$	−4.12383	−0.323003	−0.161502	+	0.986872i	$0.551634\pi$
$164$	14.5939	1.13959
$165$	0.597325	0.0465017
$166$	0.881093	0.0683861
$167$	−13.3468	−1.03281	−0.516405	−	0.856345i	$-0.672730\pi$
$167$	−13.3468	−1.03281	−0.516405	+	0.856345i	$0.672730\pi$
$168$	1.59161	0.122796
$169$	−10.7255	−0.825039
$170$	0.0255009	0.00195583
$171$	0.541081	0.0413775
$172$	4.81352	0.367027
$173$	11.2737	0.857121	0.428561	−	0.903513i	$-0.359021\pi$
$173$	11.2737	0.857121	0.428561	+	0.903513i	$0.359021\pi$
$174$	−0.928077	−0.0703573
$175$	4.94535	0.373833
$176$	7.64529	0.576285
$177$	−0.296590	−0.0222931
$178$	6.48745	0.486255
$179$	−19.0428	−1.42333	−0.711663	−	0.702521i	$-0.752058\pi$
$179$	−19.0428	−1.42333	−0.711663	+	0.702521i	$0.752058\pi$
$180$	0.427118	0.0318355
$181$	11.6032	0.862456	0.431228	−	0.902243i	$-0.358080\pi$
$181$	11.6032	0.862456	0.431228	+	0.902243i	$0.358080\pi$
$182$	0.627215	0.0464923
$183$	6.94324	0.513259
$184$	−4.96383	−0.365938
$185$	2.13637	0.157069
$186$	3.66389	0.268649
$187$	0.670180	0.0490084
$188$	−10.0296	−0.731482
$189$	1.00000	0.0727393
$190$	0.0526061	0.00381645
$191$	18.7637	1.35769	0.678846	−	0.734281i	$-0.262481\pi$
$191$	18.7637	1.35769	0.678846	+	0.734281i	$0.262481\pi$
$192$	4.14291	0.298989
$193$	−0.321177	−0.0231188	−0.0115594	−	0.999933i	$-0.503680\pi$
$193$	−0.321177	−0.0231188	−0.0115594	+	0.999933i	$0.503680\pi$
$194$	−6.78071	−0.486826
$195$	0.352567	0.0252478
$196$	−1.82704	−0.130503
$197$	15.8224	1.12730	0.563648	−	0.826015i	$-0.309397\pi$
$197$	15.8224	1.12730	0.563648	+	0.826015i	$0.309397\pi$
$198$	−1.06264	−0.0755184
$199$	−23.0558	−1.63438	−0.817192	−	0.576365i	$-0.804471\pi$
$199$	−23.0558	−1.63438	−0.817192	+	0.576365i	$0.804471\pi$
$200$	−7.87108	−0.556569
$201$	−11.7484	−0.828669
$202$	−2.17764	−0.153218
$203$	2.23156	0.156625
$204$	0.479213	0.0335516
$205$	1.86733	0.130420
$206$	2.51436	0.175184
$207$	−3.11874	−0.216768
$208$	4.51258	0.312891
$209$	1.38252	0.0956312
$210$	0.0972242	0.00670910
$211$	17.7515	1.22206	0.611031	−	0.791607i	$-0.290755\pi$
$211$	17.7515	1.22206	0.611031	+	0.791607i	$0.290755\pi$
$212$	−11.7124	−0.804409
$213$	−2.31407	−0.158558
$214$	−0.386847	−0.0264443
$215$	0.615906	0.0420044
$216$	−1.59161	−0.108296
$217$	−8.80983	−0.598050
$218$	−6.03245	−0.408569
$219$	−9.14504	−0.617964
$220$	1.09134	0.0735778
$221$	0.395569	0.0266089
$222$	−3.80059	−0.255079
$223$	−8.62336	−0.577463	−0.288731	−	0.957410i	$-0.593233\pi$
$223$	−8.62336	−0.577463	−0.288731	+	0.957410i	$0.593233\pi$
$224$	4.42762	0.295833
$225$	−4.94535	−0.329690
$226$	−8.42850	−0.560656
$227$	−5.68235	−0.377151	−0.188575	−	0.982059i	$-0.560387\pi$
$227$	−5.68235	−0.377151	−0.188575	+	0.982059i	$0.560387\pi$
$228$	0.988575	0.0654700
$229$	−9.61432	−0.635332	−0.317666	−	0.948203i	$-0.602899\pi$
$229$	−9.61432	−0.635332	−0.317666	+	0.948203i	$0.602899\pi$
$230$	−0.303217	−0.0199935
$231$	2.55512	0.168114
$232$	−3.55179	−0.233186
$233$	11.3140	0.741208	0.370604	−	0.928791i	$-0.379151\pi$
$233$	11.3140	0.741208	0.370604	+	0.928791i	$0.379151\pi$
$234$	−0.627215	−0.0410023
$235$	−1.28332	−0.0837144
$236$	−0.541882	−0.0352735
$237$	−3.82656	−0.248562
$238$	0.109083	0.00707077
$239$	11.3788	0.736033	0.368016	−	0.929819i	$-0.380037\pi$
$239$	11.3788	0.736033	0.368016	+	0.929819i	$0.380037\pi$
$240$	0.699492	0.0451520
$241$	29.3396	1.88993	0.944965	−	0.327171i	$-0.106095\pi$
$241$	29.3396	1.88993	0.944965	+	0.327171i	$0.106095\pi$
$242$	1.85958	0.119539
$243$	−1.00000	−0.0641500
$244$	12.6856	0.812110
$245$	−0.233776	−0.0149354
$246$	−3.32198	−0.211802
$247$	0.816026	0.0519225
$248$	14.0218	0.890388
$249$	2.11859	0.134260
$250$	−0.966928	−0.0611539
$251$	20.2496	1.27814	0.639072	−	0.769147i	$-0.279318\pi$
$251$	20.2496	1.27814	0.639072	+	0.769147i	$0.279318\pi$
$252$	1.82704	0.115093
$253$	−7.96875	−0.500991
$254$	−0.415886	−0.0260950
$255$	0.0613169	0.00383981
$256$	3.88649	0.242905
$257$	17.2732	1.07747	0.538737	−	0.842474i	$-0.318902\pi$
$257$	17.2732	1.07747	0.538737	+	0.842474i	$0.318902\pi$
$258$	−1.09569	−0.0682149
$259$	9.13854	0.567841
$260$	0.644153	0.0399487
$261$	−2.23156	−0.138130
$262$	−5.56764	−0.343970
$263$	0.909253	0.0560670	0.0280335	−	0.999607i	$-0.491075\pi$
$263$	0.909253	0.0560670	0.0280335	+	0.999607i	$0.491075\pi$
$264$	−4.06676	−0.250292
$265$	−1.49864	−0.0920606
$266$	0.225028	0.0137974
$267$	15.5991	0.954649
$268$	−21.4648	−1.31117
$269$	18.4398	1.12429	0.562146	−	0.827038i	$-0.309976\pi$
$269$	18.4398	1.12429	0.562146	+	0.827038i	$0.309976\pi$
$270$	−0.0972242	−0.00591687
$271$	−22.6557	−1.37624	−0.688118	−	0.725599i	$-0.741563\pi$
$271$	−22.6557	−1.37624	−0.688118	+	0.725599i	$0.741563\pi$
$272$	0.784808	0.0475860
$273$	1.50814	0.0912768
$274$	−8.22594	−0.496947
$275$	−12.6359	−0.761976
$276$	−5.69806	−0.342983
$277$	26.7313	1.60613	0.803063	−	0.595894i	$-0.203202\pi$
$277$	26.7313	1.60613	0.803063	+	0.595894i	$0.203202\pi$
$278$	7.98237	0.478751
$279$	8.80983	0.527431
$280$	0.372081	0.0222361
$281$	29.5348	1.76190	0.880948	−	0.473213i	$-0.156906\pi$
$281$	29.5348	1.76190	0.880948	+	0.473213i	$0.156906\pi$
$282$	2.28302	0.135952
$283$	31.5045	1.87275	0.936375	−	0.351002i	$-0.114159\pi$
$283$	31.5045	1.87275	0.936375	+	0.351002i	$0.114159\pi$
$284$	−4.22790	−0.250880
$285$	0.126492	0.00749272
$286$	−1.60261	−0.0947642
$287$	7.98771	0.471500
$288$	−4.42762	−0.260900
$289$	−16.9312	−0.995953
$290$	−0.216962	−0.0127404
$291$	−16.3042	−0.955771
$292$	−16.7083	−0.977781
$293$	−13.5309	−0.790486	−0.395243	−	0.918577i	$-0.629340\pi$
$293$	−13.5309	−0.790486	−0.395243	+	0.918577i	$0.629340\pi$
$294$	0.415886	0.0242550
$295$	−0.0693356	−0.00403688
$296$	−14.5450	−0.845412
$297$	−2.55512	−0.148263
$298$	−8.01407	−0.464242
$299$	−4.70350	−0.272011
$300$	−9.03534	−0.521656
$301$	2.63460	0.151856
$302$	4.07189	0.234311
$303$	−5.23614	−0.300809
$304$	1.61899	0.0928556
$305$	1.62316	0.0929419
$306$	−0.109083	−0.00623583
$307$	−18.7542	−1.07036	−0.535179	−	0.844739i	$-0.679756\pi$
$307$	−18.7542	−1.07036	−0.535179	+	0.844739i	$0.679756\pi$
$308$	4.66830	0.266001
$309$	6.04580	0.343934
$310$	0.856528	0.0486475
$311$	−9.23956	−0.523927	−0.261964	−	0.965078i	$-0.584370\pi$
$311$	−9.23956	−0.523927	−0.261964	+	0.965078i	$0.584370\pi$
$312$	−2.40038	−0.135895
$313$	19.3735	1.09505	0.547527	−	0.836788i	$-0.315569\pi$
$313$	19.3735	1.09505	0.547527	+	0.836788i	$0.315569\pi$
$314$	−3.29740	−0.186083
$315$	0.233776	0.0131718
$316$	−6.99128	−0.393290
$317$	−34.6176	−1.94432	−0.972159	−	0.234323i	$-0.924713\pi$
$317$	−34.6176	−1.94432	−0.972159	+	0.234323i	$0.924713\pi$
$318$	2.66607	0.149506
$319$	−5.70191	−0.319246
$320$	0.968512	0.0541415
$321$	−0.930174	−0.0519172
$322$	−1.29704	−0.0722813
$323$	0.141920	0.00789662
$324$	−1.82704	−0.101502
$325$	−7.45828	−0.413711
$326$	1.71504	0.0949875
$327$	−14.5050	−0.802130
$328$	−12.7133	−0.701977
$329$	−5.48952	−0.302647
$330$	−0.248419	−0.0136750
$331$	−21.2380	−1.16734	−0.583672	−	0.811990i	$-0.698385\pi$
$331$	−21.2380	−1.16734	−0.583672	+	0.811990i	$0.698385\pi$
$332$	3.87075	0.212435
$333$	−9.13854	−0.500789
$334$	5.55077	0.303724
$335$	−2.74650	−0.150057
$336$	2.99215	0.163235
$337$	−19.4542	−1.05974	−0.529868	−	0.848080i	$-0.677759\pi$
$337$	−19.4542	−1.05974	−0.529868	+	0.848080i	$0.677759\pi$
$338$	4.46059	0.242624
$339$	−20.2664	−1.10072
$340$	0.112028	0.00607559
$341$	22.5102	1.21899
$342$	−0.225028	−0.0121681
$343$	−1.00000	−0.0539949
$344$	−4.19326	−0.226086
$345$	−0.729087	−0.0392527
$346$	−4.68857	−0.252059
$347$	1.01218	0.0543368	0.0271684	−	0.999631i	$-0.491351\pi$
$347$	1.01218	0.0543368	0.0271684	+	0.999631i	$0.491351\pi$
$348$	−4.07715	−0.218558
$349$	−10.2536	−0.548862	−0.274431	−	0.961607i	$-0.588489\pi$
$349$	−10.2536	−0.548862	−0.274431	+	0.961607i	$0.588489\pi$
$350$	−2.05670	−0.109935
$351$	−1.50814	−0.0804986
$352$	−11.3131	−0.602989
$353$	0.637692	0.0339409	0.0169705	−	0.999856i	$-0.494598\pi$
$353$	0.637692	0.0339409	0.0169705	+	0.999856i	$0.494598\pi$
$354$	0.123348	0.00655586
$355$	−0.540974	−0.0287119
$356$	28.5001	1.51050
$357$	0.262289	0.0138818
$358$	7.91964	0.418566
$359$	5.89606	0.311182	0.155591	−	0.987822i	$-0.450272\pi$
$359$	5.89606	0.311182	0.155591	+	0.987822i	$0.450272\pi$
$360$	−0.372081	−0.0196104
$361$	−18.7072	−0.984591
$362$	−4.82560	−0.253628
$363$	4.47137	0.234686
$364$	2.75543	0.144424
$365$	−2.13789	−0.111902
$366$	−2.88760	−0.150937
$367$	20.2487	1.05698	0.528488	−	0.848941i	$-0.322759\pi$
$367$	20.2487	1.05698	0.528488	+	0.848941i	$0.322759\pi$
$368$	−9.33174	−0.486450
$369$	−7.98771	−0.415824
$370$	−0.888487	−0.0461902
$371$	−6.41058	−0.332821
$372$	16.0959	0.834534
$373$	1.45351	0.0752599	0.0376300	−	0.999292i	$-0.488019\pi$
$373$	1.45351	0.0752599	0.0376300	+	0.999292i	$0.488019\pi$
$374$	−0.278719	−0.0144122
$375$	−2.32498	−0.120062
$376$	8.73719	0.450586
$377$	−3.36551	−0.173333
$378$	−0.415886	−0.0213909
$379$	6.90345	0.354606	0.177303	−	0.984156i	$-0.443263\pi$
$379$	6.90345	0.354606	0.177303	+	0.984156i	$0.443263\pi$
$380$	0.231105	0.0118554
$381$	−1.00000	−0.0512316
$382$	−7.80355	−0.399264
$383$	34.0654	1.74066	0.870332	−	0.492466i	$-0.163905\pi$
$383$	34.0654	1.74066	0.870332	+	0.492466i	$0.163905\pi$
$384$	−10.5782	−0.539817
$385$	0.597325	0.0304425
$386$	0.133573	0.00679869
$387$	−2.63460	−0.133924
$388$	−29.7885	−1.51228
$389$	30.8976	1.56657	0.783284	−	0.621664i	$-0.213543\pi$
$389$	30.8976	1.56657	0.783284	+	0.621664i	$0.213543\pi$
$390$	−0.146628	−0.00742478
$391$	−0.818013	−0.0413687
$392$	1.59161	0.0803886
$393$	−13.3874	−0.675306
$394$	−6.58030	−0.331511
$395$	−0.894558	−0.0450101
$396$	−4.66830	−0.234591
$397$	−3.47389	−0.174350	−0.0871749	−	0.996193i	$-0.527784\pi$
$397$	−3.47389	−0.174350	−0.0871749	+	0.996193i	$0.527784\pi$
$398$	9.58860	0.480633
$399$	0.541081	0.0270879
$400$	−14.7972	−0.739861
$401$	17.7552	0.886650	0.443325	−	0.896361i	$-0.353799\pi$
$401$	17.7552	0.886650	0.443325	+	0.896361i	$0.353799\pi$
$402$	4.88600	0.243692
$403$	13.2865	0.661846
$404$	−9.56663	−0.475958
$405$	−0.233776	−0.0116164
$406$	−0.928077	−0.0460597
$407$	−23.3500	−1.15742
$408$	−0.417463	−0.0206675
$409$	34.1586	1.68904	0.844518	−	0.535527i	$-0.179887\pi$
$409$	34.1586	1.68904	0.844518	+	0.535527i	$0.179887\pi$
$410$	−0.776598	−0.0383535
$411$	−19.7793	−0.975641
$412$	11.0459	0.544193
$413$	−0.296590	−0.0145942
$414$	1.29704	0.0637461
$415$	0.495276	0.0243121
$416$	−6.67747	−0.327390
$417$	19.1936	0.939917
$418$	−0.574973	−0.0281228
$419$	−24.8237	−1.21272	−0.606358	−	0.795192i	$-0.707370\pi$
$419$	−24.8237	−1.21272	−0.606358	+	0.795192i	$0.707370\pi$
$420$	0.427118	0.0208412
$421$	28.5585	1.39185	0.695927	−	0.718112i	$-0.254994\pi$
$421$	28.5585	1.39185	0.695927	+	0.718112i	$0.254994\pi$
$422$	−7.38259	−0.359379
$423$	5.48952	0.266910
$424$	10.2032	0.495509
$425$	−1.29711	−0.0629192
$426$	0.962391	0.0466280
$427$	6.94324	0.336007
$428$	−1.69946	−0.0821467
$429$	−3.85348	−0.186048
$430$	−0.256147	−0.0123525
$431$	5.59470	0.269487	0.134744	−	0.990880i	$-0.456979\pi$
$431$	5.59470	0.269487	0.134744	+	0.990880i	$0.456979\pi$
$432$	−2.99215	−0.143960
$433$	−18.4625	−0.887252	−0.443626	−	0.896212i	$-0.646308\pi$
$433$	−18.4625	−0.887252	−0.443626	+	0.896212i	$0.646308\pi$
$434$	3.66389	0.175872
$435$	−0.521686	−0.0250129
$436$	−26.5013	−1.26918
$437$	−1.68749	−0.0807236
$438$	3.80329	0.181728
$439$	−32.1653	−1.53516	−0.767582	−	0.640950i	$-0.778540\pi$
$439$	−32.1653	−1.53516	−0.767582	+	0.640950i	$0.778540\pi$
$440$	−0.950710	−0.0453233
$441$	1.00000	0.0476190
$442$	−0.164512	−0.00782503
$443$	37.7878	1.79535	0.897675	−	0.440658i	$-0.145255\pi$
$443$	37.7878	1.79535	0.897675	+	0.440658i	$0.145255\pi$
$444$	−16.6965	−0.792379
$445$	3.64669	0.172870
$446$	3.58634	0.169818
$447$	−19.2699	−0.911433
$448$	4.14291	0.195734
$449$	22.6568	1.06924	0.534620	−	0.845092i	$-0.320455\pi$
$449$	22.6568	1.06924	0.534620	+	0.845092i	$0.320455\pi$
$450$	2.05670	0.0969539
$451$	−20.4095	−0.961047
$452$	−37.0274	−1.74162
$453$	9.79088	0.460016
$454$	2.36321	0.110911
$455$	0.352567	0.0165286
$456$	−0.861191	−0.0403290
$457$	33.4798	1.56612	0.783059	−	0.621947i	$-0.213658\pi$
$457$	33.4798	1.56612	0.783059	+	0.621947i	$0.213658\pi$
$458$	3.99846	0.186836
$459$	−0.262289	−0.0122426
$460$	−1.33207	−0.0621081
$461$	−18.3167	−0.853092	−0.426546	−	0.904466i	$-0.640270\pi$
$461$	−18.3167	−0.853092	−0.426546	+	0.904466i	$0.640270\pi$
$462$	−1.06264	−0.0494384
$463$	−12.6537	−0.588065	−0.294033	−	0.955795i	$-0.594997\pi$
$463$	−12.6537	−0.588065	−0.294033	+	0.955795i	$0.594997\pi$
$464$	−6.67717	−0.309980
$465$	2.05953	0.0955082
$466$	−4.70536	−0.217971
$467$	−32.6838	−1.51243	−0.756213	−	0.654325i	$-0.772953\pi$
$467$	−32.6838	−1.51243	−0.756213	+	0.654325i	$0.772953\pi$
$468$	−2.75543	−0.127370
$469$	−11.7484	−0.542491
$470$	0.533714	0.0246184
$471$	−7.92860	−0.365331
$472$	0.472057	0.0217282
$473$	−6.73171	−0.309524
$474$	1.59142	0.0730961
$475$	−2.67583	−0.122776
$476$	0.479213	0.0219647
$477$	6.41058	0.293520
$478$	−4.73228	−0.216450
$479$	19.5405	0.892829	0.446415	−	0.894826i	$-0.352701\pi$
$479$	19.5405	0.892829	0.446415	+	0.894826i	$0.352701\pi$
$480$	−1.03507	−0.0472443
$481$	−13.7822	−0.628415
$482$	−12.2019	−0.555783
$483$	−3.11874	−0.141908
$484$	8.16937	0.371335
$485$	−3.81154	−0.173073
$486$	0.415886	0.0188650
$487$	12.0567	0.546340	0.273170	−	0.961966i	$-0.411928\pi$
$487$	12.0567	0.546340	0.273170	+	0.961966i	$0.411928\pi$
$488$	−11.0509	−0.500253
$489$	4.12383	0.186486
$490$	0.0972242	0.00439214
$491$	16.5951	0.748928	0.374464	−	0.927241i	$-0.377827\pi$
$491$	16.5951	0.748928	0.374464	+	0.927241i	$0.377827\pi$
$492$	−14.5939	−0.657942
$493$	−0.585316	−0.0263613
$494$	−0.339374	−0.0152692
$495$	−0.597325	−0.0268478
$496$	26.3603	1.18361
$497$	−2.31407	−0.103800
$498$	−0.881093	−0.0394827
$499$	−11.0152	−0.493106	−0.246553	−	0.969129i	$-0.579298\pi$
$499$	−11.0152	−0.493106	−0.246553	+	0.969129i	$0.579298\pi$
$500$	−4.24783	−0.189969
$501$	13.3468	0.596293
$502$	−8.42154	−0.375872
$503$	33.2843	1.48407	0.742037	−	0.670359i	$-0.233860\pi$
$503$	33.2843	1.48407	0.742037	+	0.670359i	$0.233860\pi$
$504$	−1.59161	−0.0708961
$505$	−1.22408	−0.0544710
$506$	3.31409	0.147329
$507$	10.7255	0.476337
$508$	−1.82704	−0.0810617
$509$	−20.6251	−0.914191	−0.457096	−	0.889418i	$-0.651110\pi$
$509$	−20.6251	−0.914191	−0.457096	+	0.889418i	$0.651110\pi$
$510$	−0.0255009	−0.00112920
$511$	−9.14504	−0.404553
$512$	−22.7728	−1.00642
$513$	−0.541081	−0.0238893
$514$	−7.18369	−0.316859
$515$	1.41336	0.0622802
$516$	−4.81352	−0.211903
$517$	14.0264	0.616879
$518$	−3.80059	−0.166988
$519$	−11.2737	−0.494859
$520$	−0.561150	−0.0246081
$521$	−14.3461	−0.628515	−0.314258	−	0.949338i	$-0.601756\pi$
$521$	−14.3461	−0.628515	−0.314258	+	0.949338i	$0.601756\pi$
$522$	0.928077	0.0406208
$523$	−27.0993	−1.18497	−0.592484	−	0.805582i	$-0.701853\pi$
$523$	−27.0993	−1.18497	−0.592484	+	0.805582i	$0.701853\pi$
$524$	−24.4593	−1.06851
$525$	−4.94535	−0.215833
$526$	−0.378146	−0.0164879
$527$	2.31072	0.100657
$528$	−7.64529	−0.332718
$529$	−13.2734	−0.577106
$530$	0.623263	0.0270728
$531$	0.296590	0.0128709
$532$	0.988575	0.0428602
$533$	−12.0466	−0.521796
$534$	−6.48745	−0.280739
$535$	−0.217452	−0.00940128
$536$	18.6989	0.807671
$537$	19.0428	0.821758
$538$	−7.66884	−0.330627
$539$	2.55512	0.110057
$540$	−0.427118	−0.0183802
$541$	−7.68896	−0.330574	−0.165287	−	0.986245i	$-0.552855\pi$
$541$	−7.68896	−0.330574	−0.165287	+	0.986245i	$0.552855\pi$
$542$	9.42219	0.404718
$543$	−11.6032	−0.497939
$544$	−1.16132	−0.0497911
$545$	−3.39093	−0.145251
$546$	−0.627215	−0.0268423
$547$	1.35436	0.0579084	0.0289542	−	0.999581i	$-0.490782\pi$
$547$	1.35436	0.0579084	0.0289542	+	0.999581i	$0.490782\pi$
$548$	−36.1375	−1.54372
$549$	−6.94324	−0.296330
$550$	5.25512	0.224079
$551$	−1.20746	−0.0514394
$552$	4.96383	0.211275
$553$	−3.82656	−0.162722
$554$	−11.1172	−0.472323
$555$	−2.13637	−0.0906839
$556$	35.0675	1.48719
$557$	2.07592	0.0879594	0.0439797	−	0.999032i	$-0.485996\pi$
$557$	2.07592	0.0879594	0.0439797	+	0.999032i	$0.485996\pi$
$558$	−3.66389	−0.155105
$559$	−3.97335	−0.168055
$560$	0.699492	0.0295589
$561$	−0.670180	−0.0282950
$562$	−12.2831	−0.518131
$563$	32.5774	1.37297	0.686486	−	0.727143i	$-0.259152\pi$
$563$	32.5774	1.37297	0.686486	+	0.727143i	$0.259152\pi$
$564$	10.0296	0.422321
$565$	−4.73779	−0.199320
$566$	−13.1023	−0.550731
$567$	−1.00000	−0.0419961
$568$	3.68311	0.154540
$569$	28.1702	1.18095	0.590477	−	0.807054i	$-0.298940\pi$
$569$	28.1702	1.18095	0.590477	+	0.807054i	$0.298940\pi$
$570$	−0.0526061	−0.00220343
$571$	20.9774	0.877876	0.438938	−	0.898517i	$-0.355355\pi$
$571$	20.9774	0.877876	0.438938	+	0.898517i	$0.355355\pi$
$572$	−7.04045	−0.294376
$573$	−18.7637	−0.783863
$574$	−3.32198	−0.138657
$575$	15.4233	0.643195
$576$	−4.14291	−0.172621
$577$	−22.7704	−0.947943	−0.473972	−	0.880540i	$-0.657180\pi$
$577$	−22.7704	−0.947943	−0.473972	+	0.880540i	$0.657180\pi$
$578$	7.04145	0.292886
$579$	0.321177	0.0133477
$580$	−0.953140	−0.0395770
$581$	2.11859	0.0878940
$582$	6.78071	0.281069
$583$	16.3798	0.678381
$584$	14.5554	0.602305
$585$	−0.352567	−0.0145768
$586$	5.62733	0.232463
$587$	−27.4915	−1.13469	−0.567347	−	0.823479i	$-0.692030\pi$
$587$	−27.4915	−1.13469	−0.567347	+	0.823479i	$0.692030\pi$
$588$	1.82704	0.0753458
$589$	4.76683	0.196414
$590$	0.0288357	0.00118715
$591$	−15.8224	−0.650845
$592$	−27.3439	−1.12383
$593$	−5.82344	−0.239140	−0.119570	−	0.992826i	$-0.538152\pi$
$593$	−5.82344	−0.239140	−0.119570	+	0.992826i	$0.538152\pi$
$594$	1.06264	0.0436006
$595$	0.0613169	0.00251375
$596$	−35.2068	−1.44213
$597$	23.0558	0.943613
$598$	1.95612	0.0799918
$599$	−33.8888	−1.38466	−0.692328	−	0.721582i	$-0.743415\pi$
$599$	−33.8888	−1.38466	−0.692328	+	0.721582i	$0.743415\pi$
$600$	7.87108	0.321335
$601$	−16.2335	−0.662179	−0.331090	−	0.943599i	$-0.607416\pi$
$601$	−16.2335	−0.662179	−0.331090	+	0.943599i	$0.607416\pi$
$602$	−1.09569	−0.0446571
$603$	11.7484	0.478433
$604$	17.8883	0.727865
$605$	1.04530	0.0424975
$606$	2.17764	0.0884606
$607$	−16.0952	−0.653283	−0.326642	−	0.945148i	$-0.605917\pi$
$607$	−16.0952	−0.653283	−0.326642	+	0.945148i	$0.605917\pi$
$608$	−2.39570	−0.0971584
$609$	−2.23156	−0.0904276
$610$	−0.675050	−0.0273320
$611$	8.27897	0.334931
$612$	−0.479213	−0.0193710
$613$	−42.7403	−1.72627	−0.863133	−	0.504976i	$-0.831501\pi$
$613$	−42.7403	−1.72627	−0.863133	+	0.504976i	$0.831501\pi$
$614$	7.79960	0.314766
$615$	−1.86733	−0.0752982
$616$	−4.06676	−0.163854
$617$	15.1918	0.611599	0.305799	−	0.952096i	$-0.401076\pi$
$617$	15.1918	0.611599	0.305799	+	0.952096i	$0.401076\pi$
$618$	−2.51436	−0.101143
$619$	−22.9392	−0.922005	−0.461003	−	0.887399i	$-0.652510\pi$
$619$	−22.9392	−0.922005	−0.461003	+	0.887399i	$0.652510\pi$
$620$	3.76283	0.151119
$621$	3.11874	0.125151
$622$	3.84261	0.154074
$623$	15.5991	0.624964
$624$	−4.51258	−0.180648
$625$	24.1832	0.967329
$626$	−8.05717	−0.322029
$627$	−1.38252	−0.0552127
$628$	−14.4859	−0.578049
$629$	−2.39694	−0.0955723
$630$	−0.0972242	−0.00387350
$631$	7.21212	0.287110	0.143555	−	0.989642i	$-0.454147\pi$
$631$	7.21212	0.287110	0.143555	+	0.989642i	$0.454147\pi$
$632$	6.09041	0.242263
$633$	−17.7515	−0.705558
$634$	14.3970	0.571777
$635$	−0.233776	−0.00927711
$636$	11.7124	0.464426
$637$	1.50814	0.0597547
$638$	2.37135	0.0938825
$639$	2.31407	0.0915433
$640$	−2.47293	−0.0977512
$641$	4.74405	0.187379	0.0936893	−	0.995601i	$-0.470134\pi$
$641$	4.74405	0.187379	0.0936893	+	0.995601i	$0.470134\pi$
$642$	0.386847	0.0152676
$643$	21.8862	0.863107	0.431554	−	0.902087i	$-0.357966\pi$
$643$	21.8862	0.863107	0.431554	+	0.902087i	$0.357966\pi$
$644$	−5.69806	−0.224535
$645$	−0.615906	−0.0242513
$646$	−0.0590224	−0.00232221
$647$	30.4209	1.19597	0.597984	−	0.801508i	$-0.295969\pi$
$647$	30.4209	1.19597	0.597984	+	0.801508i	$0.295969\pi$
$648$	1.59161	0.0625244
$649$	0.757823	0.0297471
$650$	3.10180	0.121662
$651$	8.80983	0.345285
$652$	7.53439	0.295070
$653$	−26.1136	−1.02190	−0.510952	−	0.859609i	$-0.670707\pi$
$653$	−26.1136	−1.02190	−0.510952	+	0.859609i	$0.670707\pi$
$654$	6.03245	0.235887
$655$	−3.12965	−0.122286
$656$	−23.9004	−0.933154
$657$	9.14504	0.356782
$658$	2.28302	0.0890013
$659$	34.7355	1.35310	0.676552	−	0.736395i	$-0.263473\pi$
$659$	34.7355	1.35310	0.676552	+	0.736395i	$0.263473\pi$
$660$	−1.09134	−0.0424802
$661$	19.5074	0.758751	0.379375	−	0.925243i	$-0.376139\pi$
$661$	19.5074	0.758751	0.379375	+	0.925243i	$0.376139\pi$
$662$	8.83257	0.343288
$663$	−0.395569	−0.0153626
$664$	−3.37198	−0.130858
$665$	0.126492	0.00490513
$666$	3.80059	0.147270
$667$	6.95967	0.269480
$668$	24.3852	0.943491
$669$	8.62336	0.333398
$670$	1.14223	0.0441282
$671$	−17.7408	−0.684875
$672$	−4.42762	−0.170799
$673$	5.79306	0.223306	0.111653	−	0.993747i	$-0.464386\pi$
$673$	5.79306	0.223306	0.111653	+	0.993747i	$0.464386\pi$
$674$	8.09073	0.311643
$675$	4.94535	0.190347
$676$	19.5959	0.753689
$677$	−27.0216	−1.03852	−0.519261	−	0.854616i	$-0.673793\pi$
$677$	−27.0216	−1.03852	−0.519261	+	0.854616i	$0.673793\pi$
$678$	8.42850	0.323695
$679$	−16.3042	−0.625699
$680$	−0.0975928	−0.00374251
$681$	5.68235	0.217748
$682$	−9.36166	−0.358477
$683$	−20.5033	−0.784537	−0.392268	−	0.919851i	$-0.628310\pi$
$683$	−20.5033	−0.784537	−0.392268	+	0.919851i	$0.628310\pi$
$684$	−0.988575	−0.0377991
$685$	−4.62392	−0.176671
$686$	0.415886	0.0158786
$687$	9.61432	0.366809
$688$	−7.88311	−0.300541
$689$	9.66805	0.368324
$690$	0.303217	0.0115433
$691$	0.801681	0.0304974	0.0152487	−	0.999884i	$-0.495146\pi$
$691$	0.801681	0.0304974	0.0152487	+	0.999884i	$0.495146\pi$
$692$	−20.5974	−0.782997
$693$	−2.55512	−0.0970609
$694$	−0.420953	−0.0159792
$695$	4.48701	0.170202
$696$	3.55179	0.134630
$697$	−2.09509	−0.0793572
$698$	4.26433	0.161407
$699$	−11.3140	−0.427937
$700$	−9.03534	−0.341504
$701$	−10.8290	−0.409005	−0.204503	−	0.978866i	$-0.565558\pi$
$701$	−10.8290	−0.409005	−0.204503	+	0.978866i	$0.565558\pi$
$702$	0.627215	0.0236727
$703$	−4.94469	−0.186492
$704$	−10.5856	−0.398961
$705$	1.28332	0.0483325
$706$	−0.265207	−0.00998121
$707$	−5.23614	−0.196925
$708$	0.541882	0.0203652
$709$	25.9381	0.974125	0.487062	−	0.873367i	$-0.338068\pi$
$709$	25.9381	0.974125	0.487062	+	0.873367i	$0.338068\pi$
$710$	0.224984	0.00844349
$711$	3.82656	0.143507
$712$	−24.8277	−0.930458
$713$	−27.4756	−1.02897
$714$	−0.109083	−0.00408231
$715$	−0.900850	−0.0336899
$716$	34.7920	1.30024
$717$	−11.3788	−0.424949
$718$	−2.45209	−0.0915112
$719$	34.7457	1.29580	0.647898	−	0.761727i	$-0.275648\pi$
$719$	34.7457	1.29580	0.647898	+	0.761727i	$0.275648\pi$
$720$	−0.699492	−0.0260685
$721$	6.04580	0.225157
$722$	7.78008	0.289545
$723$	−29.3396	−1.09115
$724$	−21.1994	−0.787870
$725$	11.0359	0.409862
$726$	−1.85958	−0.0690156
$727$	−0.970577	−0.0359967	−0.0179984	−	0.999838i	$-0.505729\pi$
$727$	−0.970577	−0.0359967	−0.0179984	+	0.999838i	$0.505729\pi$
$728$	−2.40038	−0.0889639
$729$	1.00000	0.0370370
$730$	0.889118	0.0329078
$731$	−0.691028	−0.0255586
$732$	−12.6856	−0.468872
$733$	31.8418	1.17610	0.588051	−	0.808824i	$-0.299895\pi$
$733$	31.8418	1.17610	0.588051	+	0.808824i	$0.299895\pi$
$734$	−8.42117	−0.310831
$735$	0.233776	0.00862295
$736$	13.8086	0.508992
$737$	30.0186	1.10575
$738$	3.32198	0.122284
$739$	−15.4180	−0.567160	−0.283580	−	0.958949i	$-0.591522\pi$
$739$	−15.4180	−0.567160	−0.283580	+	0.958949i	$0.591522\pi$
$740$	−3.90323	−0.143486
$741$	−0.816026	−0.0299775
$742$	2.66607	0.0978745
$743$	29.0370	1.06526	0.532632	−	0.846347i	$-0.321203\pi$
$743$	29.0370	1.06526	0.532632	+	0.846347i	$0.321203\pi$
$744$	−14.0218	−0.514066
$745$	−4.50483	−0.165044
$746$	−0.604495	−0.0221321
$747$	−2.11859	−0.0775152
$748$	−1.22444	−0.0447701
$749$	−0.930174	−0.0339878
$750$	0.966928	0.0353072
$751$	−28.2756	−1.03179	−0.515896	−	0.856651i	$-0.672541\pi$
$751$	−28.2756	−1.03179	−0.515896	+	0.856651i	$0.672541\pi$
$752$	16.4255	0.598975
$753$	−20.2496	−0.737937
$754$	1.39967	0.0509730
$755$	2.28887	0.0833005
$756$	−1.82704	−0.0664488
$757$	45.8305	1.66574	0.832868	−	0.553471i	$-0.186697\pi$
$757$	45.8305	1.66574	0.832868	+	0.553471i	$0.186697\pi$
$758$	−2.87105	−0.104281
$759$	7.96875	0.289247
$760$	−0.201326	−0.00730285
$761$	−18.3092	−0.663708	−0.331854	−	0.943331i	$-0.607674\pi$
$761$	−18.3092	−0.663708	−0.331854	+	0.943331i	$0.607674\pi$
$762$	0.415886	0.0150660
$763$	−14.5050	−0.525118
$764$	−34.2819	−1.24028
$765$	−0.0613169	−0.00221692
$766$	−14.1674	−0.511887
$767$	0.447300	0.0161511
$768$	−3.88649	−0.140241
$769$	33.1824	1.19659	0.598294	−	0.801277i	$-0.295846\pi$
$769$	33.1824	1.19659	0.598294	+	0.801277i	$0.295846\pi$
$770$	−0.248419	−0.00895240
$771$	−17.2732	−0.622080
$772$	0.586803	0.0211195
$773$	−12.1762	−0.437946	−0.218973	−	0.975731i	$-0.570271\pi$
$773$	−12.1762	−0.437946	−0.218973	+	0.975731i	$0.570271\pi$
$774$	1.09569	0.0393839
$775$	−43.5677	−1.56500
$776$	25.9500	0.931552
$777$	−9.13854	−0.327843
$778$	−12.8499	−0.460690
$779$	−4.32200	−0.154852
$780$	−0.644153	−0.0230644
$781$	5.91273	0.211574
$782$	0.340200	0.0121655
$783$	2.23156	0.0797496
$784$	2.99215	0.106862
$785$	−1.85352	−0.0661548
$786$	5.56764	0.198591
$787$	−15.3085	−0.545690	−0.272845	−	0.962058i	$-0.587965\pi$
$787$	−15.3085	−0.545690	−0.272845	+	0.962058i	$0.587965\pi$
$788$	−28.9081	−1.02981
$789$	−0.909253	−0.0323703
$790$	0.372034	0.0132364
$791$	−20.2664	−0.720589
$792$	4.06676	0.144506
$793$	−10.4714	−0.371850
$794$	1.44474	0.0512721
$795$	1.49864	0.0531512
$796$	42.1239	1.49304
$797$	55.5963	1.96932	0.984662	−	0.174474i	$-0.0558225\pi$
$797$	55.5963	1.96932	0.984662	+	0.174474i	$0.0558225\pi$
$798$	−0.225028	−0.00796590
$799$	1.43984	0.0509380
$800$	21.8961	0.774145
$801$	−15.5991	−0.551167
$802$	−7.38413	−0.260743
$803$	23.3666	0.824591
$804$	21.4648	0.757006
$805$	−0.729087	−0.0256969
$806$	−5.52566	−0.194633
$807$	−18.4398	−0.649110
$808$	8.33391	0.293186
$809$	−28.7363	−1.01032	−0.505158	−	0.863027i	$-0.668566\pi$
$809$	−28.7363	−1.01032	−0.505158	+	0.863027i	$0.668566\pi$
$810$	0.0972242	0.00341611
$811$	−27.0970	−0.951504	−0.475752	−	0.879579i	$-0.657824\pi$
$811$	−27.0970	−0.951504	−0.475752	+	0.879579i	$0.657824\pi$
$812$	−4.07715	−0.143080
$813$	22.6557	0.794570
$814$	9.71096	0.340369
$815$	0.964051	0.0337693
$816$	−0.784808	−0.0274738
$817$	−1.42553	−0.0498730
$818$	−14.2061	−0.496705
$819$	−1.50814	−0.0526987
$820$	−3.41169	−0.119141
$821$	−8.53361	−0.297825	−0.148913	−	0.988850i	$-0.547577\pi$
$821$	−8.53361	−0.297825	−0.148913	+	0.988850i	$0.547577\pi$
$822$	8.22594	0.286912
$823$	19.1860	0.668782	0.334391	−	0.942434i	$-0.391469\pi$
$823$	19.1860	0.668782	0.334391	+	0.942434i	$0.391469\pi$
$824$	−9.62257	−0.335218
$825$	12.6359	0.439927
$826$	0.123348	0.00429182
$827$	19.5848	0.681032	0.340516	−	0.940239i	$-0.389398\pi$
$827$	19.5848	0.681032	0.340516	+	0.940239i	$0.389398\pi$
$828$	5.69806	0.198021
$829$	10.2487	0.355954	0.177977	−	0.984035i	$-0.443045\pi$
$829$	10.2487	0.355954	0.177977	+	0.984035i	$0.443045\pi$
$830$	−0.205978	−0.00714961
$831$	−26.7313	−0.927297
$832$	−6.24809	−0.216614
$833$	0.262289	0.00908779
$834$	−7.98237	−0.276407
$835$	3.12017	0.107978
$836$	−2.52593	−0.0873610
$837$	−8.80983	−0.304512
$838$	10.3238	0.356630
$839$	−6.85135	−0.236535	−0.118267	−	0.992982i	$-0.537734\pi$
$839$	−6.85135	−0.236535	−0.118267	+	0.992982i	$0.537734\pi$
$840$	−0.372081	−0.0128380
$841$	−24.0201	−0.828280
$842$	−11.8771	−0.409311
$843$	−29.5348	−1.01723
$844$	−32.4326	−1.11638
$845$	2.50737	0.0862560
$846$	−2.28302	−0.0784917
$847$	4.47137	0.153638
$848$	19.1814	0.658692
$849$	−31.5045	−1.08123
$850$	0.539451	0.0185030
$851$	28.5008	0.976993
$852$	4.22790	0.144846
$853$	−35.2516	−1.20699	−0.603496	−	0.797366i	$-0.706226\pi$
$853$	−35.2516	−1.20699	−0.603496	+	0.797366i	$0.706226\pi$
$854$	−2.88760	−0.0988115
$855$	−0.126492	−0.00432592
$856$	1.48048	0.0506016
$857$	−47.7812	−1.63217	−0.816087	−	0.577929i	$-0.803861\pi$
$857$	−47.7812	−1.63217	−0.816087	+	0.577929i	$0.803861\pi$
$858$	1.60261	0.0547121
$859$	−8.64937	−0.295113	−0.147556	−	0.989054i	$-0.547141\pi$
$859$	−8.64937	−0.295113	−0.147556	+	0.989054i	$0.547141\pi$
$860$	−1.12528	−0.0383719
$861$	−7.98771	−0.272220
$862$	−2.32676	−0.0792497
$863$	37.8764	1.28933	0.644664	−	0.764466i	$-0.276997\pi$
$863$	37.8764	1.28933	0.644664	+	0.764466i	$0.276997\pi$
$864$	4.42762	0.150631
$865$	−2.63551	−0.0896101
$866$	7.67831	0.260919
$867$	16.9312	0.575014
$868$	16.0959	0.546331
$869$	9.77732	0.331673
$870$	0.216962	0.00735570
$871$	17.7183	0.600361
$872$	23.0864	0.781804
$873$	16.3042	0.551815
$874$	0.701804	0.0237389
$875$	−2.32498	−0.0785987
$876$	16.7083	0.564522
$877$	−19.8055	−0.668785	−0.334393	−	0.942434i	$-0.608531\pi$
$877$	−19.8055	−0.668785	−0.334393	+	0.942434i	$0.608531\pi$
$878$	13.3771	0.451455
$879$	13.5309	0.456387
$880$	−1.78728	−0.0602493
$881$	−24.5225	−0.826183	−0.413091	−	0.910690i	$-0.635551\pi$
$881$	−24.5225	−0.826183	−0.413091	+	0.910690i	$0.635551\pi$
$882$	−0.415886	−0.0140036
$883$	16.5522	0.557027	0.278513	−	0.960432i	$-0.410158\pi$
$883$	16.5522	0.557027	0.278513	+	0.960432i	$0.410158\pi$
$884$	−0.722720	−0.0243077
$885$	0.0693356	0.00233069
$886$	−15.7154	−0.527969
$887$	−5.01125	−0.168261	−0.0841307	−	0.996455i	$-0.526811\pi$
$887$	−5.01125	−0.168261	−0.0841307	+	0.996455i	$0.526811\pi$
$888$	14.5450	0.488099
$889$	−1.00000	−0.0335389
$890$	−1.51661	−0.0508368
$891$	2.55512	0.0855997
$892$	15.7552	0.527523
$893$	2.97027	0.0993964
$894$	8.01407	0.268031
$895$	4.45175	0.148806
$896$	−10.5782	−0.353393
$897$	4.70350	0.157045
$898$	−9.42266	−0.314438
$899$	−19.6597	−0.655688
$900$	9.03534	0.301178
$901$	1.68143	0.0560164
$902$	8.48804	0.282621
$903$	−2.63460	−0.0876740
$904$	32.2562	1.07283
$905$	−2.71254	−0.0901678
$906$	−4.07189	−0.135280
$907$	−2.46395	−0.0818140	−0.0409070	−	0.999163i	$-0.513025\pi$
$907$	−2.46395	−0.0818140	−0.0409070	+	0.999163i	$0.513025\pi$
$908$	10.3819	0.344535
$909$	5.23614	0.173672
$910$	−0.146628	−0.00486066
$911$	50.1497	1.66153	0.830766	−	0.556622i	$-0.187903\pi$
$911$	50.1497	1.66153	0.830766	+	0.556622i	$0.187903\pi$
$912$	−1.61899	−0.0536102
$913$	−5.41325	−0.179153
$914$	−13.9238	−0.460558
$915$	−1.62316	−0.0536600
$916$	17.5657	0.580388
$917$	−13.3874	−0.442091
$918$	0.109083	0.00360026
$919$	−35.3629	−1.16651	−0.583257	−	0.812288i	$-0.698222\pi$
$919$	−35.3629	−1.16651	−0.583257	+	0.812288i	$0.698222\pi$
$920$	1.16042	0.0382580
$921$	18.7542	0.617971
$922$	7.61765	0.250874
$923$	3.48995	0.114873
$924$	−4.66830	−0.153576
$925$	45.1933	1.48595
$926$	5.26248	0.172936
$927$	−6.04580	−0.198570
$928$	9.88052	0.324344
$929$	−47.8519	−1.56997	−0.784984	−	0.619516i	$-0.787329\pi$
$929$	−47.8519	−1.56997	−0.784984	+	0.619516i	$0.787329\pi$
$930$	−0.856528	−0.0280867
$931$	0.541081	0.0177332
$932$	−20.6712	−0.677108
$933$	9.23956	0.302490
$934$	13.5927	0.444768
$935$	−0.156672	−0.00512372
$936$	2.40038	0.0784587
$937$	−25.5485	−0.834632	−0.417316	−	0.908761i	$-0.637029\pi$
$937$	−25.5485	−0.834632	−0.417316	+	0.908761i	$0.637029\pi$
$938$	4.88600	0.159534
$939$	−19.3735	−0.632230
$940$	2.34467	0.0764747
$941$	14.6471	0.477482	0.238741	−	0.971083i	$-0.423265\pi$
$941$	14.6471	0.477482	0.238741	+	0.971083i	$0.423265\pi$
$942$	3.29740	0.107435
$943$	24.9116	0.811234
$944$	0.887441	0.0288838
$945$	−0.233776	−0.00760473
$946$	2.79963	0.0910237
$947$	−37.3948	−1.21517	−0.607584	−	0.794256i	$-0.707861\pi$
$947$	−37.3948	−1.21517	−0.607584	+	0.794256i	$0.707861\pi$
$948$	6.99128	0.227066
$949$	13.7920	0.447707
$950$	1.11284	0.0361054
$951$	34.6176	1.12255
$952$	−0.417463	−0.0135301
$953$	−13.2720	−0.429921	−0.214961	−	0.976623i	$-0.568962\pi$
$953$	−13.2720	−0.429921	−0.214961	+	0.976623i	$0.568962\pi$
$954$	−2.66607	−0.0863172
$955$	−4.38649	−0.141944
$956$	−20.7895	−0.672380
$957$	5.70191	0.184317
$958$	−8.12663	−0.262560
$959$	−19.7793	−0.638707
$960$	−0.968512	−0.0312586
$961$	46.6131	1.50365
$962$	5.73183	0.184802
$963$	0.930174	0.0299744
$964$	−53.6046	−1.72649
$965$	0.0750834	0.00241702
$966$	1.29704	0.0417316
$967$	11.2385	0.361406	0.180703	−	0.983538i	$-0.442163\pi$
$967$	11.2385	0.361406	0.180703	+	0.983538i	$0.442163\pi$
$968$	−7.11670	−0.228739
$969$	−0.141920	−0.00455912
$970$	1.58517	0.0508966
$971$	−38.5997	−1.23872	−0.619361	−	0.785106i	$-0.712608\pi$
$971$	−38.5997	−1.23872	−0.619361	+	0.785106i	$0.712608\pi$
$972$	1.82704	0.0586023
$973$	19.1936	0.615320
$974$	−5.01421	−0.160666
$975$	7.45828	0.238856
$976$	−20.7752	−0.664998
$977$	55.3476	1.77073	0.885363	−	0.464900i	$-0.153910\pi$
$977$	55.3476	1.77073	0.885363	+	0.464900i	$0.153910\pi$
$978$	−1.71504	−0.0548410
$979$	−39.8575	−1.27385
$980$	0.427118	0.0136438
$981$	14.5050	0.463110
$982$	−6.90169	−0.220242
$983$	−22.5714	−0.719916	−0.359958	−	0.932969i	$-0.617209\pi$
$983$	−22.5714	−0.719916	−0.359958	+	0.932969i	$0.617209\pi$
$984$	12.7133	0.405286
$985$	−3.69889	−0.117856
$986$	0.243425	0.00775222
$987$	5.48952	0.174733
$988$	−1.49091	−0.0474322
$989$	8.21664	0.261274
$990$	0.248419	0.00789528
$991$	−13.6847	−0.434709	−0.217354	−	0.976093i	$-0.569743\pi$
$991$	−13.6847	−0.434709	−0.217354	+	0.976093i	$0.569743\pi$
$992$	−39.0066	−1.23846
$993$	21.2380	0.673966
$994$	0.962391	0.0305252
$995$	5.38990	0.170871
$996$	−3.87075	−0.122649
$997$	−12.8075	−0.405617	−0.202808	−	0.979218i	$-0.565007\pi$
$997$	−12.8075	−0.405617	−0.202808	+	0.979218i	$0.565007\pi$
$998$	4.58105	0.145011
$999$	9.13854	0.289131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.o.1.6	✓	16
3.2	odd	2		8001.2.a.r.1.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.o.1.6	✓	16	1.1	even	1	trivial
8001.2.a.r.1.11		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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.415886 q^{2} -1.00000 q^{3} -1.82704 q^{4} -0.233776 q^{5} +0.415886 q^{6} -1.00000 q^{7} +1.59161 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.415886 q^{2} -1.00000 q^{3} -1.82704 q^{4} -0.233776 q^{5} +0.415886 q^{6} -1.00000 q^{7} +1.59161 q^{8} +1.00000 q^{9} +0.0972242 q^{10} +2.55512 q^{11} +1.82704 q^{12} +1.50814 q^{13} +0.415886 q^{14} +0.233776 q^{15} +2.99215 q^{16} +0.262289 q^{17} -0.415886 q^{18} +0.541081 q^{19} +0.427118 q^{20} +1.00000 q^{21} -1.06264 q^{22} -3.11874 q^{23} -1.59161 q^{24} -4.94535 q^{25} -0.627215 q^{26} -1.00000 q^{27} +1.82704 q^{28} -2.23156 q^{29} -0.0972242 q^{30} +8.80983 q^{31} -4.42762 q^{32} -2.55512 q^{33} -0.109083 q^{34} +0.233776 q^{35} -1.82704 q^{36} -9.13854 q^{37} -0.225028 q^{38} -1.50814 q^{39} -0.372081 q^{40} -7.98771 q^{41} -0.415886 q^{42} -2.63460 q^{43} -4.66830 q^{44} -0.233776 q^{45} +1.29704 q^{46} +5.48952 q^{47} -2.99215 q^{48} +1.00000 q^{49} +2.05670 q^{50} -0.262289 q^{51} -2.75543 q^{52} +6.41058 q^{53} +0.415886 q^{54} -0.597325 q^{55} -1.59161 q^{56} -0.541081 q^{57} +0.928077 q^{58} +0.296590 q^{59} -0.427118 q^{60} -6.94324 q^{61} -3.66389 q^{62} -1.00000 q^{63} -4.14291 q^{64} -0.352567 q^{65} +1.06264 q^{66} +11.7484 q^{67} -0.479213 q^{68} +3.11874 q^{69} -0.0972242 q^{70} +2.31407 q^{71} +1.59161 q^{72} +9.14504 q^{73} +3.80059 q^{74} +4.94535 q^{75} -0.988575 q^{76} -2.55512 q^{77} +0.627215 q^{78} +3.82656 q^{79} -0.699492 q^{80} +1.00000 q^{81} +3.32198 q^{82} -2.11859 q^{83} -1.82704 q^{84} -0.0613169 q^{85} +1.09569 q^{86} +2.23156 q^{87} +4.06676 q^{88} -15.5991 q^{89} +0.0972242 q^{90} -1.50814 q^{91} +5.69806 q^{92} -8.80983 q^{93} -2.28302 q^{94} -0.126492 q^{95} +4.42762 q^{96} +16.3042 q^{97} -0.415886 q^{98} +2.55512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9	\( 16 q + 5 q^{2} - 16 q^{3} + 19 q^{4} - q^{5} - 5 q^{6} - 16 q^{7} + 6 q^{8} + 16 q^{9} - 12 q^{10} + 11 q^{11} - 19 q^{12} + 18 q^{13} - 5 q^{14} + q^{15} + 25 q^{16} - 5 q^{17} + 5 q^{18} - 11 q^{19} - q^{20} + 16 q^{21} + q^{22} + 13 q^{23} - 6 q^{24} + 33 q^{25} + 8 q^{26} - 16 q^{27} - 19 q^{28} + 24 q^{29} + 12 q^{30} - 42 q^{31} + 42 q^{32} - 11 q^{33} + 9 q^{34} + q^{35} + 19 q^{36} + 40 q^{37} + 38 q^{38} - 18 q^{39} - 61 q^{40} + 9 q^{41} + 5 q^{42} + 7 q^{43} + 3 q^{44} - q^{45} + 24 q^{46} + 31 q^{47} - 25 q^{48} + 16 q^{49} + 6 q^{50} + 5 q^{51} + 52 q^{52} + 66 q^{53} - 5 q^{54} - 36 q^{55} - 6 q^{56} + 11 q^{57} + 19 q^{58} - 7 q^{59} + q^{60} + 6 q^{61} + 52 q^{62} - 16 q^{63} + 10 q^{64} + 51 q^{65} - q^{66} + 16 q^{67} + 14 q^{68} - 13 q^{69} + 12 q^{70} + 46 q^{71} + 6 q^{72} + 39 q^{73} + 72 q^{74} - 33 q^{75} + 24 q^{76} - 11 q^{77} - 8 q^{78} + 4 q^{79} - 2 q^{80} + 16 q^{81} - 18 q^{82} + 15 q^{83} + 19 q^{84} - 4 q^{85} + 14 q^{86} - 24 q^{87} + 58 q^{88} - q^{89} - 12 q^{90} - 18 q^{91} + 26 q^{92} + 42 q^{93} + 5 q^{94} + 44 q^{95} - 42 q^{96} + 41 q^{97} + 5 q^{98} + 11 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 16 * q^3 + 19 * q^4 - q^5 - 5 * q^6 - 16 * q^7 + 6 * q^8 + 16 * q^9 - 12 * q^10 + 11 * q^11 - 19 * q^12 + 18 * q^13 - 5 * q^14 + q^15 + 25 * q^16 - 5 * q^17 + 5 * q^18 - 11 * q^19 - q^20 + 16 * q^21 + q^22 + 13 * q^23 - 6 * q^24 + 33 * q^25 + 8 * q^26 - 16 * q^27 - 19 * q^28 + 24 * q^29 + 12 * q^30 - 42 * q^31 + 42 * q^32 - 11 * q^33 + 9 * q^34 + q^35 + 19 * q^36 + 40 * q^37 + 38 * q^38 - 18 * q^39 - 61 * q^40 + 9 * q^41 + 5 * q^42 + 7 * q^43 + 3 * q^44 - q^45 + 24 * q^46 + 31 * q^47 - 25 * q^48 + 16 * q^49 + 6 * q^50 + 5 * q^51 + 52 * q^52 + 66 * q^53 - 5 * q^54 - 36 * q^55 - 6 * q^56 + 11 * q^57 + 19 * q^58 - 7 * q^59 + q^60 + 6 * q^61 + 52 * q^62 - 16 * q^63 + 10 * q^64 + 51 * q^65 - q^66 + 16 * q^67 + 14 * q^68 - 13 * q^69 + 12 * q^70 + 46 * q^71 + 6 * q^72 + 39 * q^73 + 72 * q^74 - 33 * q^75 + 24 * q^76 - 11 * q^77 - 8 * q^78 + 4 * q^79 - 2 * q^80 + 16 * q^81 - 18 * q^82 + 15 * q^83 + 19 * q^84 - 4 * q^85 + 14 * q^86 - 24 * q^87 + 58 * q^88 - q^89 - 12 * q^90 - 18 * q^91 + 26 * q^92 + 42 * q^93 + 5 * q^94 + 44 * q^95 - 42 * q^96 + 41 * q^97 + 5 * q^98 + 11 * q^99

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