LMFDB - Embedded newform 2667.2.a.p.1.18

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:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 11 x^{16} + 123 x^{15} - 35 x^{14} - 982 x^{13} + 988 x^{12} + 3872 x^{11} + \cdots + 16 $ x^18 - 6x^17 - 11x^16 + 123x^15 - 35x^14 - 982x^13 + 988x^12 + 3872x^11 - 5421x^10 - 7882x^9 + 13376x^8 + 7948x^7 - 15795x^6 - 3858x^5 + 8199x^4 + 1453x^3 - 1610x^2 - 380*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-2.55461$ 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)

$f(q)$	$=$	$q+2.55461 q^{2} -1.00000 q^{3} +4.52602 q^{4} -2.12871 q^{5} -2.55461 q^{6} +1.00000 q^{7} +6.45298 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.55461 q^{2} -1.00000 q^{3} +4.52602 q^{4} -2.12871 q^{5} -2.55461 q^{6} +1.00000 q^{7} +6.45298 q^{8} +1.00000 q^{9} -5.43801 q^{10} -4.13995 q^{11} -4.52602 q^{12} -4.75071 q^{13} +2.55461 q^{14} +2.12871 q^{15} +7.43278 q^{16} -1.32611 q^{17} +2.55461 q^{18} -5.03962 q^{19} -9.63456 q^{20} -1.00000 q^{21} -10.5759 q^{22} +0.634865 q^{23} -6.45298 q^{24} -0.468604 q^{25} -12.1362 q^{26} -1.00000 q^{27} +4.52602 q^{28} -6.95445 q^{29} +5.43801 q^{30} -3.31737 q^{31} +6.08189 q^{32} +4.13995 q^{33} -3.38770 q^{34} -2.12871 q^{35} +4.52602 q^{36} +7.32426 q^{37} -12.8742 q^{38} +4.75071 q^{39} -13.7365 q^{40} +4.92704 q^{41} -2.55461 q^{42} -0.118376 q^{43} -18.7375 q^{44} -2.12871 q^{45} +1.62183 q^{46} +10.6971 q^{47} -7.43278 q^{48} +1.00000 q^{49} -1.19710 q^{50} +1.32611 q^{51} -21.5018 q^{52} +4.29353 q^{53} -2.55461 q^{54} +8.81274 q^{55} +6.45298 q^{56} +5.03962 q^{57} -17.7659 q^{58} -9.53007 q^{59} +9.63456 q^{60} -9.70203 q^{61} -8.47457 q^{62} +1.00000 q^{63} +0.671262 q^{64} +10.1129 q^{65} +10.5759 q^{66} +2.95734 q^{67} -6.00202 q^{68} -0.634865 q^{69} -5.43801 q^{70} +1.45245 q^{71} +6.45298 q^{72} +7.08465 q^{73} +18.7106 q^{74} +0.468604 q^{75} -22.8094 q^{76} -4.13995 q^{77} +12.1362 q^{78} +5.36766 q^{79} -15.8222 q^{80} +1.00000 q^{81} +12.5867 q^{82} -10.4852 q^{83} -4.52602 q^{84} +2.82291 q^{85} -0.302403 q^{86} +6.95445 q^{87} -26.7150 q^{88} -3.15112 q^{89} -5.43801 q^{90} -4.75071 q^{91} +2.87341 q^{92} +3.31737 q^{93} +27.3270 q^{94} +10.7279 q^{95} -6.08189 q^{96} -16.7425 q^{97} +2.55461 q^{98} -4.13995 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19} - 21 q^{20} - 18 q^{21} + 5 q^{22} - 14 q^{23} + 21 q^{24} + 28 q^{25} - 8 q^{26} - 18 q^{27} + 22 q^{28} - 17 q^{29} + 4 q^{30} + 5 q^{31} - 53 q^{32} + 9 q^{33} - 19 q^{34} - 10 q^{35} + 22 q^{36} - 15 q^{37} - 22 q^{38} + 25 q^{39} - q^{40} - 17 q^{41} + 6 q^{42} + q^{43} - 33 q^{44} - 10 q^{45} + 10 q^{46} - 31 q^{47} - 34 q^{48} + 18 q^{49} - 35 q^{50} + 17 q^{51} - 70 q^{52} - 35 q^{53} + 6 q^{54} + 4 q^{55} - 21 q^{56} + 5 q^{57} + 3 q^{58} - 46 q^{59} + 21 q^{60} - 5 q^{61} - 10 q^{62} + 18 q^{63} + 63 q^{64} - 12 q^{65} - 5 q^{66} + 6 q^{67} - 56 q^{68} + 14 q^{69} - 4 q^{70} - 22 q^{71} - 21 q^{72} - 16 q^{73} + 18 q^{74} - 28 q^{75} + 32 q^{76} - 9 q^{77} + 8 q^{78} + 46 q^{79} - 30 q^{80} + 18 q^{81} - 12 q^{82} - 46 q^{83} - 22 q^{84} + 4 q^{85} + 18 q^{86} + 17 q^{87} + 30 q^{88} - 42 q^{89} - 4 q^{90} - 25 q^{91} - 48 q^{92} - 5 q^{93} + 3 q^{94} - 2 q^{95} + 53 q^{96} - 35 q^{97} - 6 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.55461	1.80638	0.903190	−	0.429241i	$-0.141219\pi$
$2$	2.55461	1.80638	0.903190	+	0.429241i	$0.141219\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.52602	2.26301
$5$	−2.12871	−0.951987	−0.475993	−	0.879449i	$-0.657911\pi$
$5$	−2.12871	−0.951987	−0.475993	+	0.879449i	$0.657911\pi$
$6$	−2.55461	−1.04291
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	6.45298	2.28147
$9$	1.00000	0.333333
$10$	−5.43801	−1.71965
$11$	−4.13995	−1.24824	−0.624121	−	0.781328i	$-0.714543\pi$
$11$	−4.13995	−1.24824	−0.624121	+	0.781328i	$0.714543\pi$
$12$	−4.52602	−1.30655
$13$	−4.75071	−1.31761	−0.658805	−	0.752313i	$-0.728938\pi$
$13$	−4.75071	−1.31761	−0.658805	+	0.752313i	$0.728938\pi$
$14$	2.55461	0.682747
$15$	2.12871	0.549630
$16$	7.43278	1.85820
$17$	−1.32611	−0.321630	−0.160815	−	0.986985i	$-0.551412\pi$
$17$	−1.32611	−0.321630	−0.160815	+	0.986985i	$0.551412\pi$
$18$	2.55461	0.602127
$19$	−5.03962	−1.15617	−0.578083	−	0.815978i	$-0.696199\pi$
$19$	−5.03962	−1.15617	−0.578083	+	0.815978i	$0.696199\pi$
$20$	−9.63456	−2.15435
$21$	−1.00000	−0.218218
$22$	−10.5759	−2.25480
$23$	0.634865	0.132378	0.0661892	−	0.997807i	$-0.478916\pi$
$23$	0.634865	0.132378	0.0661892	+	0.997807i	$0.478916\pi$
$24$	−6.45298	−1.31721
$25$	−0.468604	−0.0937208
$26$	−12.1362	−2.38011
$27$	−1.00000	−0.192450
$28$	4.52602	0.855336
$29$	−6.95445	−1.29141	−0.645705	−	0.763587i	$-0.723436\pi$
$29$	−6.95445	−1.29141	−0.645705	+	0.763587i	$0.723436\pi$
$30$	5.43801	0.992840
$31$	−3.31737	−0.595817	−0.297908	−	0.954594i	$-0.596289\pi$
$31$	−3.31737	−0.595817	−0.297908	+	0.954594i	$0.596289\pi$
$32$	6.08189	1.07514
$33$	4.13995	0.720673
$34$	−3.38770	−0.580986
$35$	−2.12871	−0.359817
$36$	4.52602	0.754336
$37$	7.32426	1.20410	0.602051	−	0.798458i	$-0.294350\pi$
$37$	7.32426	1.20410	0.602051	+	0.798458i	$0.294350\pi$
$38$	−12.8742	−2.08848
$39$	4.75071	0.760723
$40$	−13.7365	−2.17193
$41$	4.92704	0.769475	0.384737	−	0.923026i	$-0.374292\pi$
$41$	4.92704	0.769475	0.384737	+	0.923026i	$0.374292\pi$
$42$	−2.55461	−0.394184
$43$	−0.118376	−0.0180521	−0.00902606	−	0.999959i	$-0.502873\pi$
$43$	−0.118376	−0.0180521	−0.00902606	+	0.999959i	$0.502873\pi$
$44$	−18.7375	−2.82478
$45$	−2.12871	−0.317329
$46$	1.62183	0.239126
$47$	10.6971	1.56034	0.780169	−	0.625568i	$-0.215133\pi$
$47$	10.6971	1.56034	0.780169	+	0.625568i	$0.215133\pi$
$48$	−7.43278	−1.07283
$49$	1.00000	0.142857
$50$	−1.19710	−0.169295
$51$	1.32611	0.185693
$52$	−21.5018	−2.98176
$53$	4.29353	0.589762	0.294881	−	0.955534i	$-0.404720\pi$
$53$	4.29353	0.589762	0.294881	+	0.955534i	$0.404720\pi$
$54$	−2.55461	−0.347638
$55$	8.81274	1.18831
$56$	6.45298	0.862315
$57$	5.03962	0.667513
$58$	−17.7659	−2.33278
$59$	−9.53007	−1.24071	−0.620355	−	0.784321i	$-0.713011\pi$
$59$	−9.53007	−1.24071	−0.620355	+	0.784321i	$0.713011\pi$
$60$	9.63456	1.24382
$61$	−9.70203	−1.24222	−0.621109	−	0.783724i	$-0.713318\pi$
$61$	−9.70203	−1.24222	−0.621109	+	0.783724i	$0.713318\pi$
$62$	−8.47457	−1.07627
$63$	1.00000	0.125988
$64$	0.671262	0.0839078
$65$	10.1129	1.25435
$66$	10.5759	1.30181
$67$	2.95734	0.361297	0.180648	−	0.983548i	$-0.442180\pi$
$67$	2.95734	0.361297	0.180648	+	0.983548i	$0.442180\pi$
$68$	−6.00202	−0.727851
$69$	−0.634865	−0.0764288
$70$	−5.43801	−0.649967
$71$	1.45245	0.172375	0.0861873	−	0.996279i	$-0.472532\pi$
$71$	1.45245	0.172375	0.0861873	+	0.996279i	$0.472532\pi$
$72$	6.45298	0.760490
$73$	7.08465	0.829195	0.414598	−	0.910005i	$-0.363922\pi$
$73$	7.08465	0.829195	0.414598	+	0.910005i	$0.363922\pi$
$74$	18.7106	2.17506
$75$	0.468604	0.0541097
$76$	−22.8094	−2.61641
$77$	−4.13995	−0.471791
$78$	12.1362	1.37415
$79$	5.36766	0.603909	0.301954	−	0.953322i	$-0.402361\pi$
$79$	5.36766	0.603909	0.301954	+	0.953322i	$0.402361\pi$
$80$	−15.8222	−1.76898
$81$	1.00000	0.111111
$82$	12.5867	1.38996
$83$	−10.4852	−1.15090	−0.575451	−	0.817836i	$-0.695174\pi$
$83$	−10.4852	−1.15090	−0.575451	+	0.817836i	$0.695174\pi$
$84$	−4.52602	−0.493829
$85$	2.82291	0.306188
$86$	−0.302403	−0.0326090
$87$	6.95445	0.745595
$88$	−26.7150	−2.84783
$89$	−3.15112	−0.334018	−0.167009	−	0.985955i	$-0.553411\pi$
$89$	−3.15112	−0.334018	−0.167009	+	0.985955i	$0.553411\pi$
$90$	−5.43801	−0.573217
$91$	−4.75071	−0.498010
$92$	2.87341	0.299574
$93$	3.31737	0.343995
$94$	27.3270	2.81856
$95$	10.7279	1.10066
$96$	−6.08189	−0.620730
$97$	−16.7425	−1.69994	−0.849970	−	0.526831i	$-0.823380\pi$
$97$	−16.7425	−1.69994	−0.849970	+	0.526831i	$0.823380\pi$
$98$	2.55461	0.258054
$99$	−4.13995	−0.416081
$100$	−2.12091	−0.212091
$101$	−18.6303	−1.85378	−0.926891	−	0.375331i	$-0.877529\pi$
$101$	−18.6303	−1.85378	−0.926891	+	0.375331i	$0.877529\pi$
$102$	3.38770	0.335432
$103$	7.48405	0.737426	0.368713	−	0.929543i	$-0.379799\pi$
$103$	7.48405	0.737426	0.368713	+	0.929543i	$0.379799\pi$
$104$	−30.6562	−3.00609
$105$	2.12871	0.207741
$106$	10.9683	1.06533
$107$	−11.2137	−1.08407	−0.542035	−	0.840356i	$-0.682346\pi$
$107$	−11.2137	−1.08407	−0.542035	+	0.840356i	$0.682346\pi$
$108$	−4.52602	−0.435516
$109$	3.85001	0.368765	0.184382	−	0.982855i	$-0.440972\pi$
$109$	3.85001	0.368765	0.184382	+	0.982855i	$0.440972\pi$
$110$	22.5131	2.14654
$111$	−7.32426	−0.695188
$112$	7.43278	0.702332
$113$	4.76521	0.448273	0.224137	−	0.974558i	$-0.428044\pi$
$113$	4.76521	0.448273	0.224137	+	0.974558i	$0.428044\pi$
$114$	12.8742	1.20578
$115$	−1.35144	−0.126023
$116$	−31.4759	−2.92247
$117$	−4.75071	−0.439204
$118$	−24.3456	−2.24119
$119$	−1.32611	−0.121565
$120$	13.7365	1.25396
$121$	6.13918	0.558107
$122$	−24.7849	−2.24392
$123$	−4.92704	−0.444256
$124$	−15.0145	−1.34834
$125$	11.6411	1.04121
$126$	2.55461	0.227582
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−10.4490	−0.923567
$129$	0.118376	0.0104224
$130$	25.8344	2.26583
$131$	−11.0346	−0.964098	−0.482049	−	0.876144i	$-0.660107\pi$
$131$	−11.0346	−0.964098	−0.482049	+	0.876144i	$0.660107\pi$
$132$	18.7375	1.63089
$133$	−5.03962	−0.436990
$134$	7.55485	0.652639
$135$	2.12871	0.183210
$136$	−8.55738	−0.733790
$137$	−10.6933	−0.913589	−0.456794	−	0.889572i	$-0.651003\pi$
$137$	−10.6933	−0.913589	−0.456794	+	0.889572i	$0.651003\pi$
$138$	−1.62183	−0.138059
$139$	−3.73393	−0.316708	−0.158354	−	0.987382i	$-0.550619\pi$
$139$	−3.73393	−0.316708	−0.158354	+	0.987382i	$0.550619\pi$
$140$	−9.63456	−0.814269
$141$	−10.6971	−0.900862
$142$	3.71045	0.311374
$143$	19.6677	1.64470
$144$	7.43278	0.619399
$145$	14.8040	1.22940
$146$	18.0985	1.49784
$147$	−1.00000	−0.0824786
$148$	33.1497	2.72489
$149$	−11.4885	−0.941174	−0.470587	−	0.882354i	$-0.655958\pi$
$149$	−11.4885	−0.941174	−0.470587	+	0.882354i	$0.655958\pi$
$150$	1.19710	0.0977427
$151$	12.9894	1.05707	0.528533	−	0.848913i	$-0.322742\pi$
$151$	12.9894	1.05707	0.528533	+	0.848913i	$0.322742\pi$
$152$	−32.5205	−2.63776
$153$	−1.32611	−0.107210
$154$	−10.5759	−0.852234
$155$	7.06171	0.567210
$156$	21.5018	1.72152
$157$	12.6471	1.00934	0.504672	−	0.863311i	$-0.331613\pi$
$157$	12.6471	1.00934	0.504672	+	0.863311i	$0.331613\pi$
$158$	13.7123	1.09089
$159$	−4.29353	−0.340499
$160$	−12.9466	−1.02352
$161$	0.634865	0.0500344
$162$	2.55461	0.200709
$163$	6.11310	0.478815	0.239407	−	0.970919i	$-0.423047\pi$
$163$	6.11310	0.478815	0.239407	+	0.970919i	$0.423047\pi$
$164$	22.2999	1.74133
$165$	−8.81274	−0.686071
$166$	−26.7856	−2.07897
$167$	18.3586	1.42063	0.710314	−	0.703885i	$-0.248553\pi$
$167$	18.3586	1.42063	0.710314	+	0.703885i	$0.248553\pi$
$168$	−6.45298	−0.497858
$169$	9.56928	0.736098
$170$	7.21143	0.553091
$171$	−5.03962	−0.385389
$172$	−0.535770	−0.0408521
$173$	18.7445	1.42512	0.712558	−	0.701613i	$-0.247536\pi$
$173$	18.7445	1.42512	0.712558	+	0.701613i	$0.247536\pi$
$174$	17.7659	1.34683
$175$	−0.468604	−0.0354231
$176$	−30.7713	−2.31948
$177$	9.53007	0.716324
$178$	−8.04987	−0.603363
$179$	2.99701	0.224007	0.112004	−	0.993708i	$-0.464273\pi$
$179$	2.99701	0.224007	0.112004	+	0.993708i	$0.464273\pi$
$180$	−9.63456	−0.718118
$181$	24.4052	1.81402	0.907012	−	0.421105i	$-0.138358\pi$
$181$	24.4052	1.81402	0.907012	+	0.421105i	$0.138358\pi$
$182$	−12.1362	−0.899595
$183$	9.70203	0.717195
$184$	4.09677	0.302018
$185$	−15.5912	−1.14629
$186$	8.47457	0.621386
$187$	5.49005	0.401472
$188$	48.4154	3.53106
$189$	−1.00000	−0.0727393
$190$	27.4055	1.98820
$191$	−15.5134	−1.12251	−0.561254	−	0.827643i	$-0.689681\pi$
$191$	−15.5134	−1.12251	−0.561254	+	0.827643i	$0.689681\pi$
$192$	−0.671262	−0.0484442
$193$	23.3101	1.67789	0.838947	−	0.544213i	$-0.183172\pi$
$193$	23.3101	1.67789	0.838947	+	0.544213i	$0.183172\pi$
$194$	−42.7704	−3.07074
$195$	−10.1129	−0.724198
$196$	4.52602	0.323287
$197$	−22.0204	−1.56889	−0.784444	−	0.620200i	$-0.787051\pi$
$197$	−22.0204	−1.56889	−0.784444	+	0.620200i	$0.787051\pi$
$198$	−10.5759	−0.751599
$199$	−1.90444	−0.135002	−0.0675011	−	0.997719i	$-0.521503\pi$
$199$	−1.90444	−0.135002	−0.0675011	+	0.997719i	$0.521503\pi$
$200$	−3.02389	−0.213821
$201$	−2.95734	−0.208595
$202$	−47.5930	−3.34863
$203$	−6.95445	−0.488107
$204$	6.00202	0.420225
$205$	−10.4882	−0.732530
$206$	19.1188	1.33207
$207$	0.634865	0.0441262
$208$	−35.3110	−2.44838
$209$	20.8637	1.44318
$210$	5.43801	0.375258
$211$	14.5624	1.00252	0.501260	−	0.865297i	$-0.332870\pi$
$211$	14.5624	1.00252	0.501260	+	0.865297i	$0.332870\pi$
$212$	19.4326	1.33464
$213$	−1.45245	−0.0995206
$214$	−28.6466	−1.95824
$215$	0.251987	0.0171854
$216$	−6.45298	−0.439069
$217$	−3.31737	−0.225198
$218$	9.83527	0.666129
$219$	−7.08465	−0.478736
$220$	39.8866	2.68915
$221$	6.29999	0.423783
$222$	−18.7106	−1.25577
$223$	2.83408	0.189784	0.0948919	−	0.995488i	$-0.469749\pi$
$223$	2.83408	0.189784	0.0948919	+	0.995488i	$0.469749\pi$
$224$	6.08189	0.406363
$225$	−0.468604	−0.0312403
$226$	12.1732	0.809751
$227$	1.45824	0.0967865	0.0483933	−	0.998828i	$-0.484590\pi$
$227$	1.45824	0.0967865	0.0483933	+	0.998828i	$0.484590\pi$
$228$	22.8094	1.51059
$229$	21.1581	1.39817	0.699084	−	0.715040i	$-0.253591\pi$
$229$	21.1581	1.39817	0.699084	+	0.715040i	$0.253591\pi$
$230$	−3.45240	−0.227645
$231$	4.13995	0.272389
$232$	−44.8769	−2.94631
$233$	−9.49469	−0.622018	−0.311009	−	0.950407i	$-0.600667\pi$
$233$	−9.49469	−0.622018	−0.311009	+	0.950407i	$0.600667\pi$
$234$	−12.1362	−0.793368
$235$	−22.7711	−1.48542
$236$	−43.1332	−2.80774
$237$	−5.36766	−0.348667
$238$	−3.38770	−0.219592
$239$	−25.7367	−1.66477	−0.832384	−	0.554199i	$-0.813025\pi$
$239$	−25.7367	−1.66477	−0.832384	+	0.554199i	$0.813025\pi$
$240$	15.8222	1.02132
$241$	16.7397	1.07830	0.539149	−	0.842211i	$-0.318746\pi$
$241$	16.7397	1.07830	0.539149	+	0.842211i	$0.318746\pi$
$242$	15.6832	1.00815
$243$	−1.00000	−0.0641500
$244$	−43.9115	−2.81115
$245$	−2.12871	−0.135998
$246$	−12.5867	−0.802496
$247$	23.9418	1.52338
$248$	−21.4069	−1.35934
$249$	10.4852	0.664474
$250$	29.7383	1.88082
$251$	−5.36016	−0.338330	−0.169165	−	0.985588i	$-0.554107\pi$
$251$	−5.36016	−0.338330	−0.169165	+	0.985588i	$0.554107\pi$
$252$	4.52602	0.285112
$253$	−2.62831	−0.165240
$254$	2.55461	0.160290
$255$	−2.82291	−0.176778
$256$	−28.0355	−1.75222
$257$	13.1565	0.820678	0.410339	−	0.911933i	$-0.365410\pi$
$257$	13.1565	0.820678	0.410339	+	0.911933i	$0.365410\pi$
$258$	0.302403	0.0188268
$259$	7.32426	0.455108
$260$	45.7710	2.83860
$261$	−6.95445	−0.430470
$262$	−28.1891	−1.74153
$263$	−15.6935	−0.967702	−0.483851	−	0.875150i	$-0.660762\pi$
$263$	−15.6935	−0.967702	−0.483851	+	0.875150i	$0.660762\pi$
$264$	26.7150	1.64419
$265$	−9.13968	−0.561446
$266$	−12.8742	−0.789370
$267$	3.15112	0.192845
$268$	13.3850	0.817618
$269$	−28.0155	−1.70813	−0.854067	−	0.520163i	$-0.825871\pi$
$269$	−28.0155	−1.70813	−0.854067	+	0.520163i	$0.825871\pi$
$270$	5.43801	0.330947
$271$	−19.4489	−1.18143	−0.590717	−	0.806879i	$-0.701155\pi$
$271$	−19.4489	−1.18143	−0.590717	+	0.806879i	$0.701155\pi$
$272$	−9.85672	−0.597652
$273$	4.75071	0.287526
$274$	−27.3171	−1.65029
$275$	1.94000	0.116986
$276$	−2.87341	−0.172959
$277$	−15.0931	−0.906858	−0.453429	−	0.891292i	$-0.649799\pi$
$277$	−15.0931	−0.906858	−0.453429	+	0.891292i	$0.649799\pi$
$278$	−9.53872	−0.572094
$279$	−3.31737	−0.198606
$280$	−13.7365	−0.820913
$281$	−15.7060	−0.936943	−0.468471	−	0.883479i	$-0.655195\pi$
$281$	−15.7060	−0.936943	−0.468471	+	0.883479i	$0.655195\pi$
$282$	−27.3270	−1.62730
$283$	29.8370	1.77363	0.886813	−	0.462129i	$-0.152914\pi$
$283$	29.8370	1.77363	0.886813	+	0.462129i	$0.152914\pi$
$284$	6.57383	0.390085
$285$	−10.7279	−0.635464
$286$	50.2433	2.97095
$287$	4.92704	0.290834
$288$	6.08189	0.358379
$289$	−15.2414	−0.896554
$290$	37.8184	2.22077
$291$	16.7425	0.981461
$292$	32.0652	1.87648
$293$	17.2017	1.00493	0.502467	−	0.864596i	$-0.332426\pi$
$293$	17.2017	1.00493	0.502467	+	0.864596i	$0.332426\pi$
$294$	−2.55461	−0.148988
$295$	20.2867	1.18114
$296$	47.2633	2.74712
$297$	4.13995	0.240224
$298$	−29.3486	−1.70012
$299$	−3.01606	−0.174423
$300$	2.12091	0.122451
$301$	−0.118376	−0.00682306
$302$	33.1829	1.90946
$303$	18.6303	1.07028
$304$	−37.4584	−2.14838
$305$	20.6528	1.18258
$306$	−3.38770	−0.193662
$307$	−13.9522	−0.796294	−0.398147	−	0.917322i	$-0.630347\pi$
$307$	−13.9522	−0.796294	−0.398147	+	0.917322i	$0.630347\pi$
$308$	−18.7375	−1.06767
$309$	−7.48405	−0.425753
$310$	18.0399	1.02460
$311$	4.04310	0.229263	0.114632	−	0.993408i	$-0.463431\pi$
$311$	4.04310	0.229263	0.114632	+	0.993408i	$0.463431\pi$
$312$	30.6562	1.73557
$313$	3.51810	0.198855	0.0994274	−	0.995045i	$-0.468299\pi$
$313$	3.51810	0.198855	0.0994274	+	0.995045i	$0.468299\pi$
$314$	32.3082	1.82326
$315$	−2.12871	−0.119939
$316$	24.2941	1.36665
$317$	−11.1408	−0.625731	−0.312865	−	0.949797i	$-0.601289\pi$
$317$	−11.1408	−0.625731	−0.312865	+	0.949797i	$0.601289\pi$
$318$	−10.9683	−0.615071
$319$	28.7911	1.61199
$320$	−1.42892	−0.0798791
$321$	11.2137	0.625889
$322$	1.62183	0.0903811
$323$	6.68311	0.371858
$324$	4.52602	0.251445
$325$	2.22620	0.123487
$326$	15.6166	0.864921
$327$	−3.85001	−0.212906
$328$	31.7941	1.75553
$329$	10.6971	0.589753
$330$	−22.5131	−1.23930
$331$	24.8759	1.36730	0.683650	−	0.729810i	$-0.260391\pi$
$331$	24.8759	1.36730	0.683650	+	0.729810i	$0.260391\pi$
$332$	−47.4563	−2.60450
$333$	7.32426	0.401367
$334$	46.8989	2.56619
$335$	−6.29532	−0.343950
$336$	−7.43278	−0.405492
$337$	−26.4887	−1.44293	−0.721465	−	0.692451i	$-0.756531\pi$
$337$	−26.4887	−1.44293	−0.721465	+	0.692451i	$0.756531\pi$
$338$	24.4457	1.32967
$339$	−4.76521	−0.258811
$340$	12.7765	0.692905
$341$	13.7337	0.743723
$342$	−12.8742	−0.696159
$343$	1.00000	0.0539949
$344$	−0.763875	−0.0411854
$345$	1.35144	0.0727592
$346$	47.8848	2.57430
$347$	22.3607	1.20039	0.600193	−	0.799855i	$-0.295090\pi$
$347$	22.3607	1.20039	0.600193	+	0.799855i	$0.295090\pi$
$348$	31.4759	1.68729
$349$	6.65405	0.356183	0.178092	−	0.984014i	$-0.443008\pi$
$349$	6.65405	0.356183	0.178092	+	0.984014i	$0.443008\pi$
$350$	−1.19710	−0.0639876
$351$	4.75071	0.253574
$352$	−25.1787	−1.34203
$353$	5.95514	0.316960	0.158480	−	0.987362i	$-0.449341\pi$
$353$	5.95514	0.316960	0.158480	+	0.987362i	$0.449341\pi$
$354$	24.3456	1.29395
$355$	−3.09185	−0.164098
$356$	−14.2620	−0.755885
$357$	1.32611	0.0701854
$358$	7.65618	0.404642
$359$	−2.04929	−0.108158	−0.0540788	−	0.998537i	$-0.517222\pi$
$359$	−2.04929	−0.108158	−0.0540788	+	0.998537i	$0.517222\pi$
$360$	−13.7365	−0.723977
$361$	6.39772	0.336722
$362$	62.3457	3.27682
$363$	−6.13918	−0.322223
$364$	−21.5018	−1.12700
$365$	−15.0811	−0.789383
$366$	24.7849	1.29553
$367$	−17.1828	−0.896936	−0.448468	−	0.893799i	$-0.648030\pi$
$367$	−17.1828	−0.896936	−0.448468	+	0.893799i	$0.648030\pi$
$368$	4.71881	0.245985
$369$	4.92704	0.256492
$370$	−39.8294	−2.07063
$371$	4.29353	0.222909
$372$	15.0145	0.778463
$373$	13.0837	0.677449	0.338725	−	0.940886i	$-0.390005\pi$
$373$	13.0837	0.677449	0.338725	+	0.940886i	$0.390005\pi$
$374$	14.0249	0.725211
$375$	−11.6411	−0.601142
$376$	69.0284	3.55987
$377$	33.0386	1.70157
$378$	−2.55461	−0.131395
$379$	−20.7955	−1.06819	−0.534096	−	0.845424i	$-0.679348\pi$
$379$	−20.7955	−1.06819	−0.534096	+	0.845424i	$0.679348\pi$
$380$	48.5545	2.49079
$381$	−1.00000	−0.0512316
$382$	−39.6306	−2.02768
$383$	6.61047	0.337779	0.168890	−	0.985635i	$-0.445982\pi$
$383$	6.61047	0.337779	0.168890	+	0.985635i	$0.445982\pi$
$384$	10.4490	0.533221
$385$	8.81274	0.449139
$386$	59.5480	3.03091
$387$	−0.118376	−0.00601737
$388$	−75.7767	−3.84698
$389$	7.82979	0.396986	0.198493	−	0.980102i	$-0.436395\pi$
$389$	7.82979	0.396986	0.198493	+	0.980102i	$0.436395\pi$
$390$	−25.8344	−1.30818
$391$	−0.841904	−0.0425769
$392$	6.45298	0.325924
$393$	11.0346	0.556622
$394$	−56.2534	−2.83401
$395$	−11.4262	−0.574913
$396$	−18.7375	−0.941593
$397$	−23.8727	−1.19814	−0.599068	−	0.800698i	$-0.704462\pi$
$397$	−23.8727	−1.19814	−0.599068	+	0.800698i	$0.704462\pi$
$398$	−4.86509	−0.243865
$399$	5.03962	0.252296
$400$	−3.48303	−0.174152
$401$	19.4992	0.973741	0.486871	−	0.873474i	$-0.338138\pi$
$401$	19.4992	0.973741	0.486871	+	0.873474i	$0.338138\pi$
$402$	−7.55485	−0.376802
$403$	15.7599	0.785055
$404$	−84.3209	−4.19512
$405$	−2.12871	−0.105776
$406$	−17.7659	−0.881706
$407$	−30.3221	−1.50301
$408$	8.55738	0.423654
$409$	−26.3931	−1.30505	−0.652526	−	0.757766i	$-0.726291\pi$
$409$	−26.3931	−1.30505	−0.652526	+	0.757766i	$0.726291\pi$
$410$	−26.7933	−1.32323
$411$	10.6933	0.527461
$412$	33.8729	1.66880
$413$	−9.53007	−0.468944
$414$	1.62183	0.0797086
$415$	22.3200	1.09564
$416$	−28.8933	−1.41661
$417$	3.73393	0.182851
$418$	53.2987	2.60692
$419$	−21.2813	−1.03966	−0.519831	−	0.854269i	$-0.674005\pi$
$419$	−21.2813	−1.03966	−0.519831	+	0.854269i	$0.674005\pi$
$420$	9.63456	0.470119
$421$	7.10895	0.346469	0.173235	−	0.984881i	$-0.444578\pi$
$421$	7.10895	0.346469	0.173235	+	0.984881i	$0.444578\pi$
$422$	37.2013	1.81093
$423$	10.6971	0.520113
$424$	27.7061	1.34553
$425$	0.621422	0.0301434
$426$	−3.71045	−0.179772
$427$	−9.70203	−0.469514
$428$	−50.7535	−2.45326
$429$	−19.6677	−0.949566
$430$	0.643728	0.0310433
$431$	22.4856	1.08309	0.541546	−	0.840671i	$-0.317839\pi$
$431$	22.4856	1.08309	0.541546	+	0.840671i	$0.317839\pi$
$432$	−7.43278	−0.357610
$433$	−24.4030	−1.17273	−0.586367	−	0.810046i	$-0.699442\pi$
$433$	−24.4030	−1.17273	−0.586367	+	0.810046i	$0.699442\pi$
$434$	−8.47457	−0.406792
$435$	−14.8040	−0.709797
$436$	17.4252	0.834517
$437$	−3.19947	−0.153052
$438$	−18.0985	−0.864779
$439$	−8.99162	−0.429147	−0.214573	−	0.976708i	$-0.568836\pi$
$439$	−8.99162	−0.429147	−0.214573	+	0.976708i	$0.568836\pi$
$440$	56.8684	2.71109
$441$	1.00000	0.0476190
$442$	16.0940	0.765513
$443$	3.16638	0.150439	0.0752196	−	0.997167i	$-0.476034\pi$
$443$	3.16638	0.150439	0.0752196	+	0.997167i	$0.476034\pi$
$444$	−33.1497	−1.57322
$445$	6.70781	0.317981
$446$	7.23995	0.342822
$447$	11.4885	0.543387
$448$	0.671262	0.0317142
$449$	−3.58210	−0.169050	−0.0845248	−	0.996421i	$-0.526937\pi$
$449$	−3.58210	−0.169050	−0.0845248	+	0.996421i	$0.526937\pi$
$450$	−1.19710	−0.0564318
$451$	−20.3977	−0.960490
$452$	21.5674	1.01445
$453$	−12.9894	−0.610297
$454$	3.72522	0.174833
$455$	10.1129	0.474099
$456$	32.5205	1.52291
$457$	−12.8800	−0.602500	−0.301250	−	0.953545i	$-0.597404\pi$
$457$	−12.8800	−0.602500	−0.301250	+	0.953545i	$0.597404\pi$
$458$	54.0507	2.52562
$459$	1.32611	0.0618977
$460$	−6.11665	−0.285190
$461$	−17.0189	−0.792648	−0.396324	−	0.918111i	$-0.629714\pi$
$461$	−17.0189	−0.792648	−0.396324	+	0.918111i	$0.629714\pi$
$462$	10.5759	0.492037
$463$	−26.4544	−1.22944	−0.614721	−	0.788745i	$-0.710731\pi$
$463$	−26.4544	−1.22944	−0.614721	+	0.788745i	$0.710731\pi$
$464$	−51.6909	−2.39969
$465$	−7.06171	−0.327479
$466$	−24.2552	−1.12360
$467$	22.8012	1.05511	0.527557	−	0.849520i	$-0.323108\pi$
$467$	22.8012	1.05511	0.527557	+	0.849520i	$0.323108\pi$
$468$	−21.5018	−0.993921
$469$	2.95734	0.136557
$470$	−58.1712	−2.68324
$471$	−12.6471	−0.582745
$472$	−61.4973	−2.83064
$473$	0.490069	0.0225334
$474$	−13.7123	−0.629825
$475$	2.36158	0.108357
$476$	−6.00202	−0.275102
$477$	4.29353	0.196587
$478$	−65.7471	−3.00720
$479$	−10.8867	−0.497424	−0.248712	−	0.968578i	$-0.580007\pi$
$479$	−10.8867	−0.497424	−0.248712	+	0.968578i	$0.580007\pi$
$480$	12.9466	0.590927
$481$	−34.7955	−1.58654
$482$	42.7633	1.94781
$483$	−0.634865	−0.0288874
$484$	27.7860	1.26300
$485$	35.6398	1.61832
$486$	−2.55461	−0.115879
$487$	−17.0508	−0.772645	−0.386323	−	0.922364i	$-0.626255\pi$
$487$	−17.0508	−0.772645	−0.386323	+	0.922364i	$0.626255\pi$
$488$	−62.6070	−2.83408
$489$	−6.11310	−0.276444
$490$	−5.43801	−0.245664
$491$	−27.2143	−1.22817	−0.614083	−	0.789241i	$-0.710474\pi$
$491$	−27.2143	−1.22817	−0.614083	+	0.789241i	$0.710474\pi$
$492$	−22.2999	−1.00536
$493$	9.22240	0.415356
$494$	61.1618	2.75180
$495$	8.81274	0.396103
$496$	−24.6573	−1.10714
$497$	1.45245	0.0651515
$498$	26.7856	1.20029
$499$	3.74789	0.167779	0.0838893	−	0.996475i	$-0.473266\pi$
$499$	3.74789	0.167779	0.0838893	+	0.996475i	$0.473266\pi$
$500$	52.6876	2.35626
$501$	−18.3586	−0.820200
$502$	−13.6931	−0.611152
$503$	−3.01178	−0.134289	−0.0671443	−	0.997743i	$-0.521389\pi$
$503$	−3.01178	−0.134289	−0.0671443	+	0.997743i	$0.521389\pi$
$504$	6.45298	0.287438
$505$	39.6584	1.76478
$506$	−6.71429	−0.298487
$507$	−9.56928	−0.424987
$508$	4.52602	0.200809
$509$	22.0551	0.977576	0.488788	−	0.872402i	$-0.337439\pi$
$509$	22.0551	0.977576	0.488788	+	0.872402i	$0.337439\pi$
$510$	−7.21143	−0.319327
$511$	7.08465	0.313406
$512$	−50.7218	−2.24161
$513$	5.03962	0.222504
$514$	33.6096	1.48246
$515$	−15.9314	−0.702020
$516$	0.535770	0.0235860
$517$	−44.2856	−1.94768
$518$	18.7106	0.822097
$519$	−18.7445	−0.822791
$520$	65.2582	2.86176
$521$	3.30328	0.144719	0.0723596	−	0.997379i	$-0.476947\pi$
$521$	3.30328	0.144719	0.0723596	+	0.997379i	$0.476947\pi$
$522$	−17.7659	−0.777592
$523$	29.4263	1.28672	0.643362	−	0.765562i	$-0.277539\pi$
$523$	29.4263	1.28672	0.643362	+	0.765562i	$0.277539\pi$
$524$	−49.9428	−2.18176
$525$	0.468604	0.0204515
$526$	−40.0907	−1.74804
$527$	4.39921	0.191633
$528$	30.7713	1.33915
$529$	−22.5969	−0.982476
$530$	−23.3483	−1.01418
$531$	−9.53007	−0.413570
$532$	−22.8094	−0.988912
$533$	−23.4070	−1.01387
$534$	8.04987	0.348352
$535$	23.8707	1.03202
$536$	19.0837	0.824288
$537$	−2.99701	−0.129331
$538$	−71.5686	−3.08554
$539$	−4.13995	−0.178320
$540$	9.63456	0.414606
$541$	27.5971	1.18649	0.593246	−	0.805021i	$-0.297846\pi$
$541$	27.5971	1.18649	0.593246	+	0.805021i	$0.297846\pi$
$542$	−49.6842	−2.13412
$543$	−24.4052	−1.04733
$544$	−8.06528	−0.345796
$545$	−8.19556	−0.351059
$546$	12.1362	0.519382
$547$	−1.48013	−0.0632860	−0.0316430	−	0.999499i	$-0.510074\pi$
$547$	−1.48013	−0.0632860	−0.0316430	+	0.999499i	$0.510074\pi$
$548$	−48.3980	−2.06746
$549$	−9.70203	−0.414073
$550$	4.95593	0.211321
$551$	35.0478	1.49308
$552$	−4.09677	−0.174370
$553$	5.36766	0.228256
$554$	−38.5570	−1.63813
$555$	15.5912	0.661810
$556$	−16.8998	−0.716712
$557$	−38.4105	−1.62751	−0.813753	−	0.581211i	$-0.802579\pi$
$557$	−38.4105	−1.62751	−0.813753	+	0.581211i	$0.802579\pi$
$558$	−8.47457	−0.358757
$559$	0.562369	0.0237857
$560$	−15.8222	−0.668611
$561$	−5.49005	−0.231790
$562$	−40.1227	−1.69247
$563$	43.0432	1.81406	0.907028	−	0.421070i	$-0.138345\pi$
$563$	43.0432	1.81406	0.907028	+	0.421070i	$0.138345\pi$
$564$	−48.4154	−2.03866
$565$	−10.1437	−0.426750
$566$	76.2218	3.20384
$567$	1.00000	0.0419961
$568$	9.37265	0.393268
$569$	−1.66577	−0.0698327	−0.0349163	−	0.999390i	$-0.511116\pi$
$569$	−1.66577	−0.0698327	−0.0349163	+	0.999390i	$0.511116\pi$
$570$	−27.4055	−1.14789
$571$	33.4302	1.39901	0.699505	−	0.714627i	$-0.253404\pi$
$571$	33.4302	1.39901	0.699505	+	0.714627i	$0.253404\pi$
$572$	89.0164	3.72196
$573$	15.5134	0.648081
$574$	12.5867	0.525357
$575$	−0.297500	−0.0124066
$576$	0.671262	0.0279693
$577$	−11.3687	−0.473286	−0.236643	−	0.971597i	$-0.576047\pi$
$577$	−11.3687	−0.473286	−0.236643	+	0.971597i	$0.576047\pi$
$578$	−38.9358	−1.61952
$579$	−23.3101	−0.968733
$580$	67.0031	2.78215
$581$	−10.4852	−0.435000
$582$	42.7704	1.77289
$583$	−17.7750	−0.736165
$584$	45.7171	1.89179
$585$	10.1129	0.418116
$586$	43.9436	1.81529
$587$	−29.5488	−1.21961	−0.609805	−	0.792551i	$-0.708752\pi$
$587$	−29.5488	−1.21961	−0.609805	+	0.792551i	$0.708752\pi$
$588$	−4.52602	−0.186650
$589$	16.7183	0.688864
$590$	51.8246	2.13359
$591$	22.0204	0.905797
$592$	54.4397	2.23746
$593$	−22.9545	−0.942628	−0.471314	−	0.881966i	$-0.656220\pi$
$593$	−22.9545	−0.942628	−0.471314	+	0.881966i	$0.656220\pi$
$594$	10.5759	0.433936
$595$	2.82291	0.115728
$596$	−51.9971	−2.12988
$597$	1.90444	0.0779435
$598$	−7.70485	−0.315075
$599$	39.1632	1.60016	0.800082	−	0.599890i	$-0.204789\pi$
$599$	39.1632	1.60016	0.800082	+	0.599890i	$0.204789\pi$
$600$	3.02389	0.123450
$601$	−16.5220	−0.673947	−0.336973	−	0.941514i	$-0.609403\pi$
$601$	−16.5220	−0.673947	−0.336973	+	0.941514i	$0.609403\pi$
$602$	−0.302403	−0.0123250
$603$	2.95734	0.120432
$604$	58.7904	2.39215
$605$	−13.0685	−0.531311
$606$	47.5930	1.93333
$607$	5.46104	0.221657	0.110828	−	0.993840i	$-0.464650\pi$
$607$	5.46104	0.221657	0.110828	+	0.993840i	$0.464650\pi$
$608$	−30.6504	−1.24304
$609$	6.95445	0.281809
$610$	52.7597	2.13618
$611$	−50.8191	−2.05592
$612$	−6.00202	−0.242617
$613$	−22.0546	−0.890779	−0.445389	−	0.895337i	$-0.646935\pi$
$613$	−22.0546	−0.890779	−0.445389	+	0.895337i	$0.646935\pi$
$614$	−35.6424	−1.43841
$615$	10.4882	0.422926
$616$	−26.7150	−1.07638
$617$	−42.7536	−1.72119	−0.860597	−	0.509287i	$-0.829909\pi$
$617$	−42.7536	−1.72119	−0.860597	+	0.509287i	$0.829909\pi$
$618$	−19.1188	−0.769071
$619$	43.8372	1.76197	0.880983	−	0.473147i	$-0.156882\pi$
$619$	43.8372	1.76197	0.880983	+	0.473147i	$0.156882\pi$
$620$	31.9614	1.28360
$621$	−0.634865	−0.0254763
$622$	10.3285	0.414137
$623$	−3.15112	−0.126247
$624$	35.3110	1.41357
$625$	−22.4374	−0.897496
$626$	8.98736	0.359207
$627$	−20.8637	−0.833218
$628$	57.2408	2.28415
$629$	−9.71281	−0.387275
$630$	−5.43801	−0.216656
$631$	−12.7391	−0.507135	−0.253568	−	0.967318i	$-0.581604\pi$
$631$	−12.7391	−0.507135	−0.253568	+	0.967318i	$0.581604\pi$
$632$	34.6374	1.37780
$633$	−14.5624	−0.578805
$634$	−28.4604	−1.13031
$635$	−2.12871	−0.0844752
$636$	−19.4326	−0.770552
$637$	−4.75071	−0.188230
$638$	73.5499	2.91187
$639$	1.45245	0.0574582
$640$	22.2428	0.879223
$641$	6.94532	0.274323	0.137162	−	0.990549i	$-0.456202\pi$
$641$	6.94532	0.274323	0.137162	+	0.990549i	$0.456202\pi$
$642$	28.6466	1.13059
$643$	−38.9483	−1.53597	−0.767986	−	0.640467i	$-0.778741\pi$
$643$	−38.9483	−1.53597	−0.767986	+	0.640467i	$0.778741\pi$
$644$	2.87341	0.113228
$645$	−0.251987	−0.00992198
$646$	17.0727	0.671717
$647$	−24.7855	−0.974417	−0.487209	−	0.873286i	$-0.661985\pi$
$647$	−24.7855	−0.974417	−0.487209	+	0.873286i	$0.661985\pi$
$648$	6.45298	0.253497
$649$	39.4540	1.54871
$650$	5.68707	0.223065
$651$	3.31737	0.130018
$652$	27.6680	1.08356
$653$	−23.6675	−0.926182	−0.463091	−	0.886311i	$-0.653260\pi$
$653$	−23.6675	−0.926182	−0.463091	+	0.886311i	$0.653260\pi$
$654$	−9.83527	−0.384590
$655$	23.4895	0.917809
$656$	36.6216	1.42983
$657$	7.08465	0.276398
$658$	27.3270	1.06532
$659$	13.2866	0.517572	0.258786	−	0.965935i	$-0.416678\pi$
$659$	13.2866	0.517572	0.258786	+	0.965935i	$0.416678\pi$
$660$	−39.8866	−1.55258
$661$	−22.0055	−0.855915	−0.427958	−	0.903799i	$-0.640767\pi$
$661$	−22.0055	−0.855915	−0.427958	+	0.903799i	$0.640767\pi$
$662$	63.5480	2.46986
$663$	−6.29999	−0.244671
$664$	−67.6609	−2.62575
$665$	10.7279	0.416009
$666$	18.7106	0.725021
$667$	−4.41514	−0.170955
$668$	83.0912	3.21489
$669$	−2.83408	−0.109572
$670$	−16.0821	−0.621304
$671$	40.1659	1.55059
$672$	−6.08189	−0.234614
$673$	24.1513	0.930964	0.465482	−	0.885057i	$-0.345881\pi$
$673$	24.1513	0.930964	0.465482	+	0.885057i	$0.345881\pi$
$674$	−67.6681	−2.60648
$675$	0.468604	0.0180366
$676$	43.3107	1.66580
$677$	−19.8265	−0.761993	−0.380996	−	0.924577i	$-0.624419\pi$
$677$	−19.8265	−0.761993	−0.380996	+	0.924577i	$0.624419\pi$
$678$	−12.1732	−0.467510
$679$	−16.7425	−0.642517
$680$	18.2162	0.698558
$681$	−1.45824	−0.0558797
$682$	35.0843	1.34345
$683$	11.5130	0.440533	0.220267	−	0.975440i	$-0.429307\pi$
$683$	11.5130	0.440533	0.220267	+	0.975440i	$0.429307\pi$
$684$	−22.8094	−0.872138
$685$	22.7629	0.869725
$686$	2.55461	0.0975353
$687$	−21.1581	−0.807232
$688$	−0.879861	−0.0335444
$689$	−20.3973	−0.777077
$690$	3.45240	0.131431
$691$	8.79146	0.334443	0.167222	−	0.985919i	$-0.446520\pi$
$691$	8.79146	0.334443	0.167222	+	0.985919i	$0.446520\pi$
$692$	84.8378	3.22505
$693$	−4.13995	−0.157264
$694$	57.1229	2.16835
$695$	7.94844	0.301502
$696$	44.8769	1.70105
$697$	−6.53382	−0.247486
$698$	16.9985	0.643402
$699$	9.49469	0.359122
$700$	−2.12091	−0.0801628
$701$	−7.46770	−0.282051	−0.141026	−	0.990006i	$-0.545040\pi$
$701$	−7.46770	−0.282051	−0.141026	+	0.990006i	$0.545040\pi$
$702$	12.1362	0.458052
$703$	−36.9115	−1.39214
$704$	−2.77899	−0.104737
$705$	22.7711	0.857609
$706$	15.2130	0.572550
$707$	−18.6303	−0.700664
$708$	43.1332	1.62105
$709$	30.0859	1.12990	0.564950	−	0.825125i	$-0.308895\pi$
$709$	30.0859	1.12990	0.564950	+	0.825125i	$0.308895\pi$
$710$	−7.89846	−0.296424
$711$	5.36766	0.201303
$712$	−20.3341	−0.762052
$713$	−2.10608	−0.0788733
$714$	3.38770	0.126782
$715$	−41.8668	−1.56573
$716$	13.5645	0.506930
$717$	25.7367	0.961155
$718$	−5.23514	−0.195374
$719$	−12.0466	−0.449261	−0.224631	−	0.974444i	$-0.572118\pi$
$719$	−12.0466	−0.449261	−0.224631	+	0.974444i	$0.572118\pi$
$720$	−15.8222	−0.589659
$721$	7.48405	0.278721
$722$	16.3437	0.608248
$723$	−16.7397	−0.622555
$724$	110.458	4.10515
$725$	3.25888	0.121032
$726$	−15.6832	−0.582057
$727$	12.0016	0.445115	0.222557	−	0.974920i	$-0.428560\pi$
$727$	12.0016	0.445115	0.222557	+	0.974920i	$0.428560\pi$
$728$	−30.6562	−1.13620
$729$	1.00000	0.0370370
$730$	−38.5264	−1.42593
$731$	0.156980	0.00580610
$732$	43.9115	1.62302
$733$	−2.59393	−0.0958090	−0.0479045	−	0.998852i	$-0.515254\pi$
$733$	−2.59393	−0.0958090	−0.0479045	+	0.998852i	$0.515254\pi$
$734$	−43.8954	−1.62021
$735$	2.12871	0.0785186
$736$	3.86118	0.142325
$737$	−12.2432	−0.450986
$738$	12.5867	0.463321
$739$	−7.97887	−0.293508	−0.146754	−	0.989173i	$-0.546883\pi$
$739$	−7.97887	−0.293508	−0.146754	+	0.989173i	$0.546883\pi$
$740$	−70.5661	−2.59406
$741$	−23.9418	−0.879523
$742$	10.9683	0.402658
$743$	−4.32447	−0.158650	−0.0793248	−	0.996849i	$-0.525276\pi$
$743$	−4.32447	−0.158650	−0.0793248	+	0.996849i	$0.525276\pi$
$744$	21.4069	0.784815
$745$	24.4557	0.895986
$746$	33.4238	1.22373
$747$	−10.4852	−0.383634
$748$	24.8480	0.908534
$749$	−11.2137	−0.409740
$750$	−29.7383	−1.08589
$751$	2.34648	0.0856244	0.0428122	−	0.999083i	$-0.486368\pi$
$751$	2.34648	0.0856244	0.0428122	+	0.999083i	$0.486368\pi$
$752$	79.5095	2.89941
$753$	5.36016	0.195335
$754$	84.4006	3.07369
$755$	−27.6507	−1.00631
$756$	−4.52602	−0.164610
$757$	−26.4656	−0.961909	−0.480954	−	0.876746i	$-0.659710\pi$
$757$	−26.4656	−0.961909	−0.480954	+	0.876746i	$0.659710\pi$
$758$	−53.1243	−1.92956
$759$	2.62831	0.0954015
$760$	69.2267	2.51111
$761$	−40.6849	−1.47483	−0.737414	−	0.675441i	$-0.763953\pi$
$761$	−40.6849	−1.47483	−0.737414	+	0.675441i	$0.763953\pi$
$762$	−2.55461	−0.0925436
$763$	3.85001	0.139380
$764$	−70.2138	−2.54025
$765$	2.82291	0.102063
$766$	16.8871	0.610157
$767$	45.2746	1.63477
$768$	28.0355	1.01164
$769$	−9.94961	−0.358792	−0.179396	−	0.983777i	$-0.557414\pi$
$769$	−9.94961	−0.358792	−0.179396	+	0.983777i	$0.557414\pi$
$770$	22.5131	0.811315
$771$	−13.1565	−0.473818
$772$	105.502	3.79709
$773$	31.8949	1.14718	0.573590	−	0.819142i	$-0.305550\pi$
$773$	31.8949	1.14718	0.573590	+	0.819142i	$0.305550\pi$
$774$	−0.302403	−0.0108697
$775$	1.55453	0.0558404
$776$	−108.039	−3.87837
$777$	−7.32426	−0.262756
$778$	20.0020	0.717108
$779$	−24.8304	−0.889641
$780$	−45.7710	−1.63887
$781$	−6.01309	−0.215165
$782$	−2.15073	−0.0769100
$783$	6.95445	0.248532
$784$	7.43278	0.265457
$785$	−26.9219	−0.960883
$786$	28.1891	1.00547
$787$	−38.6972	−1.37941	−0.689703	−	0.724093i	$-0.742259\pi$
$787$	−38.6972	−1.37941	−0.689703	+	0.724093i	$0.742259\pi$
$788$	−99.6646	−3.55040
$789$	15.6935	0.558703
$790$	−29.1894	−1.03851
$791$	4.76521	0.169431
$792$	−26.7150	−0.949276
$793$	46.0916	1.63676
$794$	−60.9854	−2.16429
$795$	9.13968	0.324151
$796$	−8.61952	−0.305511
$797$	−9.68211	−0.342958	−0.171479	−	0.985188i	$-0.554855\pi$
$797$	−9.68211	−0.342958	−0.171479	+	0.985188i	$0.554855\pi$
$798$	12.8742	0.455743
$799$	−14.1856	−0.501852
$800$	−2.85000	−0.100763
$801$	−3.15112	−0.111339
$802$	49.8127	1.75895
$803$	−29.3301	−1.03504
$804$	−13.3850	−0.472052
$805$	−1.35144	−0.0476321
$806$	40.2603	1.41811
$807$	28.0155	0.986192
$808$	−120.221	−4.22935
$809$	−25.8293	−0.908111	−0.454056	−	0.890973i	$-0.650023\pi$
$809$	−25.8293	−0.908111	−0.454056	+	0.890973i	$0.650023\pi$
$810$	−5.43801	−0.191072
$811$	20.7060	0.727087	0.363544	−	0.931577i	$-0.381567\pi$
$811$	20.7060	0.727087	0.363544	+	0.931577i	$0.381567\pi$
$812$	−31.4759	−1.10459
$813$	19.4489	0.682102
$814$	−77.4610	−2.71501
$815$	−13.0130	−0.455825
$816$	9.85672	0.345054
$817$	0.596568	0.0208713
$818$	−67.4239	−2.35742
$819$	−4.75071	−0.166003
$820$	−47.4699	−1.65772
$821$	−36.0955	−1.25974	−0.629871	−	0.776700i	$-0.716892\pi$
$821$	−36.0955	−1.25974	−0.629871	+	0.776700i	$0.716892\pi$
$822$	27.3171	0.952795
$823$	45.5252	1.58691	0.793455	−	0.608629i	$-0.208280\pi$
$823$	45.5252	1.58691	0.793455	+	0.608629i	$0.208280\pi$
$824$	48.2944	1.68242
$825$	−1.94000	−0.0675420
$826$	−24.3456	−0.847091
$827$	19.6678	0.683916	0.341958	−	0.939715i	$-0.388910\pi$
$827$	19.6678	0.683916	0.341958	+	0.939715i	$0.388910\pi$
$828$	2.87341	0.0998578
$829$	−46.1390	−1.60247	−0.801237	−	0.598347i	$-0.795825\pi$
$829$	−46.1390	−1.60247	−0.801237	+	0.598347i	$0.795825\pi$
$830$	57.0187	1.97915
$831$	15.0931	0.523575
$832$	−3.18897	−0.110558
$833$	−1.32611	−0.0459471
$834$	9.53872	0.330299
$835$	−39.0800	−1.35242
$836$	94.4296	3.26592
$837$	3.31737	0.114665
$838$	−54.3654	−1.87802
$839$	−45.6364	−1.57554	−0.787772	−	0.615966i	$-0.788766\pi$
$839$	−45.6364	−1.57554	−0.787772	+	0.615966i	$0.788766\pi$
$840$	13.7365	0.473954
$841$	19.3644	0.667737
$842$	18.1606	0.625855
$843$	15.7060	0.540944
$844$	65.9098	2.26871
$845$	−20.3702	−0.700756
$846$	27.3270	0.939521
$847$	6.13918	0.210945
$848$	31.9129	1.09589
$849$	−29.8370	−1.02400
$850$	1.58749	0.0544504
$851$	4.64992	0.159397
$852$	−6.57383	−0.225216
$853$	14.5096	0.496799	0.248400	−	0.968658i	$-0.420095\pi$
$853$	14.5096	0.496799	0.248400	+	0.968658i	$0.420095\pi$
$854$	−24.7849	−0.848121
$855$	10.7279	0.366885
$856$	−72.3618	−2.47328
$857$	3.03303	0.103606	0.0518031	−	0.998657i	$-0.483503\pi$
$857$	3.03303	0.103606	0.0518031	+	0.998657i	$0.483503\pi$
$858$	−50.2433	−1.71528
$859$	54.2596	1.85131	0.925657	−	0.378365i	$-0.123513\pi$
$859$	54.2596	1.85131	0.925657	+	0.378365i	$0.123513\pi$
$860$	1.14050	0.0388906
$861$	−4.92704	−0.167913
$862$	57.4418	1.95648
$863$	−48.8955	−1.66442	−0.832211	−	0.554460i	$-0.812925\pi$
$863$	−48.8955	−1.66442	−0.832211	+	0.554460i	$0.812925\pi$
$864$	−6.08189	−0.206910
$865$	−39.9015	−1.35669
$866$	−62.3401	−2.11840
$867$	15.2414	0.517626
$868$	−15.0145	−0.509624
$869$	−22.2218	−0.753824
$870$	−37.8184	−1.28216
$871$	−14.0495	−0.476049
$872$	24.8440	0.841326
$873$	−16.7425	−0.566647
$874$	−8.17340	−0.276469
$875$	11.6411	0.393540
$876$	−32.0652	−1.08338
$877$	−25.9003	−0.874590	−0.437295	−	0.899318i	$-0.644063\pi$
$877$	−25.9003	−0.874590	−0.437295	+	0.899318i	$0.644063\pi$
$878$	−22.9701	−0.775202
$879$	−17.2017	−0.580199
$880$	65.5032	2.20811
$881$	−1.06900	−0.0360156	−0.0180078	−	0.999838i	$-0.505732\pi$
$881$	−1.06900	−0.0360156	−0.0180078	+	0.999838i	$0.505732\pi$
$882$	2.55461	0.0860181
$883$	−29.3081	−0.986295	−0.493147	−	0.869946i	$-0.664154\pi$
$883$	−29.3081	−0.986295	−0.493147	+	0.869946i	$0.664154\pi$
$884$	28.5139	0.959025
$885$	−20.2867	−0.681931
$886$	8.08885	0.271750
$887$	−40.0423	−1.34449	−0.672244	−	0.740330i	$-0.734669\pi$
$887$	−40.0423	−1.34449	−0.672244	+	0.740330i	$0.734669\pi$
$888$	−47.2633	−1.58605
$889$	1.00000	0.0335389
$890$	17.1358	0.574394
$891$	−4.13995	−0.138694
$892$	12.8271	0.429482
$893$	−53.9095	−1.80401
$894$	29.3486	0.981564
$895$	−6.37976	−0.213252
$896$	−10.4490	−0.349075
$897$	3.01606	0.100703
$898$	−9.15085	−0.305368
$899$	23.0705	0.769443
$900$	−2.12091	−0.0706969
$901$	−5.69372	−0.189685
$902$	−52.1081	−1.73501
$903$	0.118376	0.00393930
$904$	30.7498	1.02272
$905$	−51.9515	−1.72693
$906$	−33.1829	−1.10243
$907$	25.5478	0.848302	0.424151	−	0.905592i	$-0.360573\pi$
$907$	25.5478	0.848302	0.424151	+	0.905592i	$0.360573\pi$
$908$	6.60000	0.219029
$909$	−18.6303	−0.617927
$910$	25.8344	0.856403
$911$	29.3845	0.973553	0.486777	−	0.873526i	$-0.338173\pi$
$911$	29.3845	0.973553	0.486777	+	0.873526i	$0.338173\pi$
$912$	37.4584	1.24037
$913$	43.4083	1.43660
$914$	−32.9033	−1.08834
$915$	−20.6528	−0.682760
$916$	95.7619	3.16406
$917$	−11.0346	−0.364395
$918$	3.38770	0.111811
$919$	−10.8678	−0.358494	−0.179247	−	0.983804i	$-0.557366\pi$
$919$	−10.8678	−0.358494	−0.179247	+	0.983804i	$0.557366\pi$
$920$	−8.72082	−0.287517
$921$	13.9522	0.459741
$922$	−43.4766	−1.43182
$923$	−6.90020	−0.227123
$924$	18.7375	0.616418
$925$	−3.43218	−0.112849
$926$	−67.5807	−2.22084
$927$	7.48405	0.245809
$928$	−42.2962	−1.38844
$929$	4.66688	0.153115	0.0765577	−	0.997065i	$-0.475607\pi$
$929$	4.66688	0.153115	0.0765577	+	0.997065i	$0.475607\pi$
$930$	−18.0399	−0.591551
$931$	−5.03962	−0.165167
$932$	−42.9731	−1.40763
$933$	−4.04310	−0.132365
$934$	58.2481	1.90594
$935$	−11.6867	−0.382196
$936$	−30.6562	−1.00203
$937$	−14.0249	−0.458175	−0.229088	−	0.973406i	$-0.573574\pi$
$937$	−14.0249	−0.458175	−0.229088	+	0.973406i	$0.573574\pi$
$938$	7.55485	0.246674
$939$	−3.51810	−0.114809
$940$	−103.062	−3.36152
$941$	46.2542	1.50784	0.753921	−	0.656965i	$-0.228160\pi$
$941$	46.2542	1.50784	0.753921	+	0.656965i	$0.228160\pi$
$942$	−32.3082	−1.05266
$943$	3.12801	0.101862
$944$	−70.8350	−2.30548
$945$	2.12871	0.0692469
$946$	1.25193	0.0407039
$947$	5.19190	0.168714	0.0843571	−	0.996436i	$-0.473116\pi$
$947$	5.19190	0.168714	0.0843571	+	0.996436i	$0.473116\pi$
$948$	−24.2941	−0.789036
$949$	−33.6571	−1.09256
$950$	6.03291	0.195734
$951$	11.1408	0.361266
$952$	−8.55738	−0.277346
$953$	−31.0054	−1.00436	−0.502181	−	0.864762i	$-0.667469\pi$
$953$	−31.0054	−1.00436	−0.502181	+	0.864762i	$0.667469\pi$
$954$	10.9683	0.355111
$955$	33.0235	1.06861
$956$	−116.485	−3.76738
$957$	−28.7911	−0.930683
$958$	−27.8111	−0.898536
$959$	−10.6933	−0.345304
$960$	1.42892	0.0461182
$961$	−19.9951	−0.645002
$962$	−88.8887	−2.86589
$963$	−11.2137	−0.361357
$964$	75.7640	2.44020
$965$	−49.6203	−1.59733
$966$	−1.62183	−0.0521815
$967$	6.06932	0.195176	0.0975881	−	0.995227i	$-0.468887\pi$
$967$	6.06932	0.195176	0.0975881	+	0.995227i	$0.468887\pi$
$968$	39.6159	1.27330
$969$	−6.68311	−0.214692
$970$	91.0458	2.92330
$971$	−8.98673	−0.288398	−0.144199	−	0.989549i	$-0.546061\pi$
$971$	−8.98673	−0.288398	−0.144199	+	0.989549i	$0.546061\pi$
$972$	−4.52602	−0.145172
$973$	−3.73393	−0.119704
$974$	−43.5581	−1.39569
$975$	−2.22620	−0.0712955
$976$	−72.1131	−2.30828
$977$	55.0884	1.76243	0.881217	−	0.472711i	$-0.156725\pi$
$977$	55.0884	1.76243	0.881217	+	0.472711i	$0.156725\pi$
$978$	−15.6166	−0.499362
$979$	13.0455	0.416935
$980$	−9.63456	−0.307765
$981$	3.85001	0.122922
$982$	−69.5219	−2.21853
$983$	59.7557	1.90591	0.952956	−	0.303109i	$-0.0980246\pi$
$983$	59.7557	1.90591	0.952956	+	0.303109i	$0.0980246\pi$
$984$	−31.7941	−1.01356
$985$	46.8750	1.49356
$986$	23.5596	0.750291
$987$	−10.6971	−0.340494
$988$	108.361	3.44742
$989$	−0.0751526	−0.00238971
$990$	22.5131	0.715513
$991$	−0.373535	−0.0118657	−0.00593286	−	0.999982i	$-0.501888\pi$
$991$	−0.373535	−0.0118657	−0.00593286	+	0.999982i	$0.501888\pi$
$992$	−20.1759	−0.640584
$993$	−24.8759	−0.789411
$994$	3.71045	0.117688
$995$	4.05399	0.128520
$996$	47.4563	1.50371
$997$	38.3145	1.21343	0.606716	−	0.794919i	$-0.292487\pi$
$997$	38.3145	1.21343	0.606716	+	0.794919i	$0.292487\pi$
$998$	9.57439	0.303072
$999$	−7.32426	−0.231729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.p.1.18	✓	18
3.2	odd	2		8001.2.a.u.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.p.1.18	✓	18	1.1	even	1	trivial
8001.2.a.u.1.1		18	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)

\(f(q)\)	\(=\)	\(q+2.55461 q^{2} -1.00000 q^{3} +4.52602 q^{4} -2.12871 q^{5} -2.55461 q^{6} +1.00000 q^{7} +6.45298 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.55461 q^{2} -1.00000 q^{3} +4.52602 q^{4} -2.12871 q^{5} -2.55461 q^{6} +1.00000 q^{7} +6.45298 q^{8} +1.00000 q^{9} -5.43801 q^{10} -4.13995 q^{11} -4.52602 q^{12} -4.75071 q^{13} +2.55461 q^{14} +2.12871 q^{15} +7.43278 q^{16} -1.32611 q^{17} +2.55461 q^{18} -5.03962 q^{19} -9.63456 q^{20} -1.00000 q^{21} -10.5759 q^{22} +0.634865 q^{23} -6.45298 q^{24} -0.468604 q^{25} -12.1362 q^{26} -1.00000 q^{27} +4.52602 q^{28} -6.95445 q^{29} +5.43801 q^{30} -3.31737 q^{31} +6.08189 q^{32} +4.13995 q^{33} -3.38770 q^{34} -2.12871 q^{35} +4.52602 q^{36} +7.32426 q^{37} -12.8742 q^{38} +4.75071 q^{39} -13.7365 q^{40} +4.92704 q^{41} -2.55461 q^{42} -0.118376 q^{43} -18.7375 q^{44} -2.12871 q^{45} +1.62183 q^{46} +10.6971 q^{47} -7.43278 q^{48} +1.00000 q^{49} -1.19710 q^{50} +1.32611 q^{51} -21.5018 q^{52} +4.29353 q^{53} -2.55461 q^{54} +8.81274 q^{55} +6.45298 q^{56} +5.03962 q^{57} -17.7659 q^{58} -9.53007 q^{59} +9.63456 q^{60} -9.70203 q^{61} -8.47457 q^{62} +1.00000 q^{63} +0.671262 q^{64} +10.1129 q^{65} +10.5759 q^{66} +2.95734 q^{67} -6.00202 q^{68} -0.634865 q^{69} -5.43801 q^{70} +1.45245 q^{71} +6.45298 q^{72} +7.08465 q^{73} +18.7106 q^{74} +0.468604 q^{75} -22.8094 q^{76} -4.13995 q^{77} +12.1362 q^{78} +5.36766 q^{79} -15.8222 q^{80} +1.00000 q^{81} +12.5867 q^{82} -10.4852 q^{83} -4.52602 q^{84} +2.82291 q^{85} -0.302403 q^{86} +6.95445 q^{87} -26.7150 q^{88} -3.15112 q^{89} -5.43801 q^{90} -4.75071 q^{91} +2.87341 q^{92} +3.31737 q^{93} +27.3270 q^{94} +10.7279 q^{95} -6.08189 q^{96} -16.7425 q^{97} +2.55461 q^{98} -4.13995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} - 18 q^{3} + 22 q^{4} - 10 q^{5} + 6 q^{6} + 18 q^{7} - 21 q^{8} + 18 q^{9} - 4 q^{10} - 9 q^{11} - 22 q^{12} - 25 q^{13} - 6 q^{14} + 10 q^{15} + 34 q^{16} - 17 q^{17} - 6 q^{18} - 5 q^{19} - 21 q^{20} - 18 q^{21} + 5 q^{22} - 14 q^{23} + 21 q^{24} + 28 q^{25} - 8 q^{26} - 18 q^{27} + 22 q^{28} - 17 q^{29} + 4 q^{30} + 5 q^{31} - 53 q^{32} + 9 q^{33} - 19 q^{34} - 10 q^{35} + 22 q^{36} - 15 q^{37} - 22 q^{38} + 25 q^{39} - q^{40} - 17 q^{41} + 6 q^{42} + q^{43} - 33 q^{44} - 10 q^{45} + 10 q^{46} - 31 q^{47} - 34 q^{48} + 18 q^{49} - 35 q^{50} + 17 q^{51} - 70 q^{52} - 35 q^{53} + 6 q^{54} + 4 q^{55} - 21 q^{56} + 5 q^{57} + 3 q^{58} - 46 q^{59} + 21 q^{60} - 5 q^{61} - 10 q^{62} + 18 q^{63} + 63 q^{64} - 12 q^{65} - 5 q^{66} + 6 q^{67} - 56 q^{68} + 14 q^{69} - 4 q^{70} - 22 q^{71} - 21 q^{72} - 16 q^{73} + 18 q^{74} - 28 q^{75} + 32 q^{76} - 9 q^{77} + 8 q^{78} + 46 q^{79} - 30 q^{80} + 18 q^{81} - 12 q^{82} - 46 q^{83} - 22 q^{84} + 4 q^{85} + 18 q^{86} + 17 q^{87} + 30 q^{88} - 42 q^{89} - 4 q^{90} - 25 q^{91} - 48 q^{92} - 5 q^{93} + 3 q^{94} - 2 q^{95} + 53 q^{96} - 35 q^{97} - 6 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 18 * q^3 + 22 * q^4 - 10 * q^5 + 6 * q^6 + 18 * q^7 - 21 * q^8 + 18 * q^9 - 4 * q^10 - 9 * q^11 - 22 * q^12 - 25 * q^13 - 6 * q^14 + 10 * q^15 + 34 * q^16 - 17 * q^17 - 6 * q^18 - 5 * q^19 - 21 * q^20 - 18 * q^21 + 5 * q^22 - 14 * q^23 + 21 * q^24 + 28 * q^25 - 8 * q^26 - 18 * q^27 + 22 * q^28 - 17 * q^29 + 4 * q^30 + 5 * q^31 - 53 * q^32 + 9 * q^33 - 19 * q^34 - 10 * q^35 + 22 * q^36 - 15 * q^37 - 22 * q^38 + 25 * q^39 - q^40 - 17 * q^41 + 6 * q^42 + q^43 - 33 * q^44 - 10 * q^45 + 10 * q^46 - 31 * q^47 - 34 * q^48 + 18 * q^49 - 35 * q^50 + 17 * q^51 - 70 * q^52 - 35 * q^53 + 6 * q^54 + 4 * q^55 - 21 * q^56 + 5 * q^57 + 3 * q^58 - 46 * q^59 + 21 * q^60 - 5 * q^61 - 10 * q^62 + 18 * q^63 + 63 * q^64 - 12 * q^65 - 5 * q^66 + 6 * q^67 - 56 * q^68 + 14 * q^69 - 4 * q^70 - 22 * q^71 - 21 * q^72 - 16 * q^73 + 18 * q^74 - 28 * q^75 + 32 * q^76 - 9 * q^77 + 8 * q^78 + 46 * q^79 - 30 * q^80 + 18 * q^81 - 12 * q^82 - 46 * q^83 - 22 * q^84 + 4 * q^85 + 18 * q^86 + 17 * q^87 + 30 * q^88 - 42 * q^89 - 4 * q^90 - 25 * q^91 - 48 * q^92 - 5 * q^93 + 3 * q^94 - 2 * q^95 + 53 * q^96 - 35 * q^97 - 6 * q^98 - 9 * q^99

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