LMFDB - Embedded newform 2667.2.a.j.1.5

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:	$7$
Coefficient field:	7.7.118870813.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 $ x^7 - 9x^5 - 3x^4 + 20x^3 + 7x^2 - 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.06168$ 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)

$f(q)$	$=$	$q+0.692358 q^{2} +1.00000 q^{3} -1.52064 q^{4} -2.78145 q^{5} +0.692358 q^{6} +1.00000 q^{7} -2.43754 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.692358 q^{2} +1.00000 q^{3} -1.52064 q^{4} -2.78145 q^{5} +0.692358 q^{6} +1.00000 q^{7} -2.43754 q^{8} +1.00000 q^{9} -1.92576 q^{10} -0.348849 q^{11} -1.52064 q^{12} +2.17757 q^{13} +0.692358 q^{14} -2.78145 q^{15} +1.35363 q^{16} +7.42626 q^{17} +0.692358 q^{18} -0.255629 q^{19} +4.22958 q^{20} +1.00000 q^{21} -0.241529 q^{22} -4.98233 q^{23} -2.43754 q^{24} +2.73644 q^{25} +1.50766 q^{26} +1.00000 q^{27} -1.52064 q^{28} -6.88124 q^{29} -1.92576 q^{30} -10.1038 q^{31} +5.81228 q^{32} -0.348849 q^{33} +5.14163 q^{34} -2.78145 q^{35} -1.52064 q^{36} -1.64279 q^{37} -0.176987 q^{38} +2.17757 q^{39} +6.77989 q^{40} +3.56990 q^{41} +0.692358 q^{42} -9.34628 q^{43} +0.530475 q^{44} -2.78145 q^{45} -3.44956 q^{46} +9.73885 q^{47} +1.35363 q^{48} +1.00000 q^{49} +1.89460 q^{50} +7.42626 q^{51} -3.31130 q^{52} -7.44666 q^{53} +0.692358 q^{54} +0.970306 q^{55} -2.43754 q^{56} -0.255629 q^{57} -4.76428 q^{58} -2.01055 q^{59} +4.22958 q^{60} -7.69549 q^{61} -6.99543 q^{62} +1.00000 q^{63} +1.31692 q^{64} -6.05678 q^{65} -0.241529 q^{66} -6.52951 q^{67} -11.2927 q^{68} -4.98233 q^{69} -1.92576 q^{70} +13.7550 q^{71} -2.43754 q^{72} -9.37124 q^{73} -1.13740 q^{74} +2.73644 q^{75} +0.388720 q^{76} -0.348849 q^{77} +1.50766 q^{78} -5.92206 q^{79} -3.76505 q^{80} +1.00000 q^{81} +2.47165 q^{82} +1.68660 q^{83} -1.52064 q^{84} -20.6557 q^{85} -6.47097 q^{86} -6.88124 q^{87} +0.850335 q^{88} -17.6750 q^{89} -1.92576 q^{90} +2.17757 q^{91} +7.57634 q^{92} -10.1038 q^{93} +6.74277 q^{94} +0.711019 q^{95} +5.81228 q^{96} -0.216772 q^{97} +0.692358 q^{98} -0.348849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * 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 $

$2$	0.692358	0.489571	0.244785	−	0.969577i	$-0.421282\pi$
$2$	0.692358	0.489571	0.244785	+	0.969577i	$0.421282\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.52064	−0.760320
$5$	−2.78145	−1.24390	−0.621950	−	0.783057i	$-0.713659\pi$
$5$	−2.78145	−1.24390	−0.621950	+	0.783057i	$0.713659\pi$
$6$	0.692358	0.282654
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.43754	−0.861801
$9$	1.00000	0.333333
$10$	−1.92576	−0.608977
$11$	−0.348849	−0.105182	−0.0525910	−	0.998616i	$-0.516748\pi$
$11$	−0.348849	−0.105182	−0.0525910	+	0.998616i	$0.516748\pi$
$12$	−1.52064	−0.438971
$13$	2.17757	0.603948	0.301974	−	0.953316i	$-0.402354\pi$
$13$	2.17757	0.603948	0.301974	+	0.953316i	$0.402354\pi$
$14$	0.692358	0.185040
$15$	−2.78145	−0.718166
$16$	1.35363	0.338408
$17$	7.42626	1.80113	0.900567	−	0.434718i	$-0.143152\pi$
$17$	7.42626	1.80113	0.900567	+	0.434718i	$0.143152\pi$
$18$	0.692358	0.163190
$19$	−0.255629	−0.0586454	−0.0293227	−	0.999570i	$-0.509335\pi$
$19$	−0.255629	−0.0586454	−0.0293227	+	0.999570i	$0.509335\pi$
$20$	4.22958	0.945763
$21$	1.00000	0.218218
$22$	−0.241529	−0.0514941
$23$	−4.98233	−1.03889	−0.519444	−	0.854504i	$-0.673861\pi$
$23$	−4.98233	−1.03889	−0.519444	+	0.854504i	$0.673861\pi$
$24$	−2.43754	−0.497561
$25$	2.73644	0.547288
$26$	1.50766	0.295676
$27$	1.00000	0.192450
$28$	−1.52064	−0.287374
$29$	−6.88124	−1.27781	−0.638907	−	0.769284i	$-0.720613\pi$
$29$	−6.88124	−1.27781	−0.638907	+	0.769284i	$0.720613\pi$
$30$	−1.92576	−0.351593
$31$	−10.1038	−1.81469	−0.907346	−	0.420385i	$-0.861895\pi$
$31$	−10.1038	−1.81469	−0.907346	+	0.420385i	$0.861895\pi$
$32$	5.81228	1.02748
$33$	−0.348849	−0.0607269
$34$	5.14163	0.881782
$35$	−2.78145	−0.470150
$36$	−1.52064	−0.253440
$37$	−1.64279	−0.270072	−0.135036	−	0.990841i	$-0.543115\pi$
$37$	−1.64279	−0.270072	−0.135036	+	0.990841i	$0.543115\pi$
$38$	−0.176987	−0.0287111
$39$	2.17757	0.348690
$40$	6.77989	1.07200
$41$	3.56990	0.557525	0.278762	−	0.960360i	$-0.410076\pi$
$41$	3.56990	0.557525	0.278762	+	0.960360i	$0.410076\pi$
$42$	0.692358	0.106833
$43$	−9.34628	−1.42529	−0.712647	−	0.701523i	$-0.752504\pi$
$43$	−9.34628	−1.42529	−0.712647	+	0.701523i	$0.752504\pi$
$44$	0.530475	0.0799721
$45$	−2.78145	−0.414633
$46$	−3.44956	−0.508610
$47$	9.73885	1.42056	0.710279	−	0.703920i	$-0.248569\pi$
$47$	9.73885	1.42056	0.710279	+	0.703920i	$0.248569\pi$
$48$	1.35363	0.195380
$49$	1.00000	0.142857
$50$	1.89460	0.267936
$51$	7.42626	1.03988
$52$	−3.31130	−0.459194
$53$	−7.44666	−1.02288	−0.511439	−	0.859320i	$-0.670887\pi$
$53$	−7.44666	−1.02288	−0.511439	+	0.859320i	$0.670887\pi$
$54$	0.692358	0.0942179
$55$	0.970306	0.130836
$56$	−2.43754	−0.325730
$57$	−0.255629	−0.0338589
$58$	−4.76428	−0.625581
$59$	−2.01055	−0.261752	−0.130876	−	0.991399i	$-0.541779\pi$
$59$	−2.01055	−0.261752	−0.130876	+	0.991399i	$0.541779\pi$
$60$	4.22958	0.546036
$61$	−7.69549	−0.985306	−0.492653	−	0.870226i	$-0.663973\pi$
$61$	−7.69549	−0.985306	−0.492653	+	0.870226i	$0.663973\pi$
$62$	−6.99543	−0.888420
$63$	1.00000	0.125988
$64$	1.31692	0.164615
$65$	−6.05678	−0.751252
$66$	−0.241529	−0.0297301
$67$	−6.52951	−0.797706	−0.398853	−	0.917015i	$-0.630592\pi$
$67$	−6.52951	−0.797706	−0.398853	+	0.917015i	$0.630592\pi$
$68$	−11.2927	−1.36944
$69$	−4.98233	−0.599803
$70$	−1.92576	−0.230172
$71$	13.7550	1.63242	0.816208	−	0.577758i	$-0.196072\pi$
$71$	13.7550	1.63242	0.816208	+	0.577758i	$0.196072\pi$
$72$	−2.43754	−0.287267
$73$	−9.37124	−1.09682	−0.548411	−	0.836209i	$-0.684767\pi$
$73$	−9.37124	−1.09682	−0.548411	+	0.836209i	$0.684767\pi$
$74$	−1.13740	−0.132220
$75$	2.73644	0.315977
$76$	0.388720	0.0445893
$77$	−0.348849	−0.0397551
$78$	1.50766	0.170708
$79$	−5.92206	−0.666283	−0.333142	−	0.942877i	$-0.608109\pi$
$79$	−5.92206	−0.666283	−0.333142	+	0.942877i	$0.608109\pi$
$80$	−3.76505	−0.420945
$81$	1.00000	0.111111
$82$	2.47165	0.272948
$83$	1.68660	0.185128	0.0925642	−	0.995707i	$-0.470494\pi$
$83$	1.68660	0.185128	0.0925642	+	0.995707i	$0.470494\pi$
$84$	−1.52064	−0.165916
$85$	−20.6557	−2.24043
$86$	−6.47097	−0.697783
$87$	−6.88124	−0.737747
$88$	0.850335	0.0906461
$89$	−17.6750	−1.87355	−0.936775	−	0.349932i	$-0.886205\pi$
$89$	−17.6750	−1.87355	−0.936775	+	0.349932i	$0.886205\pi$
$90$	−1.92576	−0.202992
$91$	2.17757	0.228271
$92$	7.57634	0.789888
$93$	−10.1038	−1.04771
$94$	6.74277	0.695464
$95$	0.711019	0.0729490
$96$	5.81228	0.593214
$97$	−0.216772	−0.0220099	−0.0110049	−	0.999939i	$-0.503503\pi$
$97$	−0.216772	−0.0220099	−0.0110049	+	0.999939i	$0.503503\pi$
$98$	0.692358	0.0699387
$99$	−0.348849	−0.0350607
$100$	−4.16114	−0.416114
$101$	−15.6270	−1.55494	−0.777472	−	0.628918i	$-0.783498\pi$
$101$	−15.6270	−1.55494	−0.777472	+	0.628918i	$0.783498\pi$
$102$	5.14163	0.509097
$103$	−2.82388	−0.278245	−0.139122	−	0.990275i	$-0.544428\pi$
$103$	−2.82388	−0.278245	−0.139122	+	0.990275i	$0.544428\pi$
$104$	−5.30791	−0.520484
$105$	−2.78145	−0.271441
$106$	−5.15575	−0.500771
$107$	−13.6505	−1.31964	−0.659820	−	0.751424i	$-0.729367\pi$
$107$	−13.6505	−1.31964	−0.659820	+	0.751424i	$0.729367\pi$
$108$	−1.52064	−0.146324
$109$	−12.4581	−1.19327	−0.596633	−	0.802514i	$-0.703495\pi$
$109$	−12.4581	−1.19327	−0.596633	+	0.802514i	$0.703495\pi$
$110$	0.671799	0.0640535
$111$	−1.64279	−0.155926
$112$	1.35363	0.127906
$113$	17.1295	1.61140	0.805702	−	0.592322i	$-0.201788\pi$
$113$	17.1295	1.61140	0.805702	+	0.592322i	$0.201788\pi$
$114$	−0.176987	−0.0165763
$115$	13.8581	1.29227
$116$	10.4639	0.971549
$117$	2.17757	0.201316
$118$	−1.39202	−0.128146
$119$	7.42626	0.680764
$120$	6.77989	0.618917
$121$	−10.8783	−0.988937
$122$	−5.32803	−0.482377
$123$	3.56990	0.321887
$124$	15.3642	1.37975
$125$	6.29597	0.563128
$126$	0.692358	0.0616801
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	−10.7128	−0.946885
$129$	−9.34628	−0.822894
$130$	−4.19346	−0.367791
$131$	8.33905	0.728587	0.364293	−	0.931284i	$-0.381311\pi$
$131$	8.33905	0.728587	0.364293	+	0.931284i	$0.381311\pi$
$132$	0.530475	0.0461719
$133$	−0.255629	−0.0221659
$134$	−4.52075	−0.390534
$135$	−2.78145	−0.239389
$136$	−18.1018	−1.55222
$137$	20.9573	1.79050	0.895251	−	0.445563i	$-0.146996\pi$
$137$	20.9573	1.79050	0.895251	+	0.445563i	$0.146996\pi$
$138$	−3.44956	−0.293646
$139$	−10.1867	−0.864026	−0.432013	−	0.901867i	$-0.642197\pi$
$139$	−10.1867	−0.864026	−0.432013	+	0.901867i	$0.642197\pi$
$140$	4.22958	0.357465
$141$	9.73885	0.820159
$142$	9.52337	0.799183
$143$	−0.759643	−0.0635245
$144$	1.35363	0.112803
$145$	19.1398	1.58947
$146$	−6.48825	−0.536972
$147$	1.00000	0.0824786
$148$	2.49809	0.205342
$149$	−4.86877	−0.398865	−0.199433	−	0.979912i	$-0.563910\pi$
$149$	−4.86877	−0.398865	−0.199433	+	0.979912i	$0.563910\pi$
$150$	1.89460	0.154693
$151$	−1.93573	−0.157528	−0.0787638	−	0.996893i	$-0.525097\pi$
$151$	−1.93573	−0.157528	−0.0787638	+	0.996893i	$0.525097\pi$
$152$	0.623107	0.0505407
$153$	7.42626	0.600378
$154$	−0.241529	−0.0194629
$155$	28.1031	2.25730
$156$	−3.31130	−0.265116
$157$	4.29270	0.342595	0.171297	−	0.985219i	$-0.445204\pi$
$157$	4.29270	0.342595	0.171297	+	0.985219i	$0.445204\pi$
$158$	−4.10018	−0.326193
$159$	−7.44666	−0.590559
$160$	−16.1665	−1.27808
$161$	−4.98233	−0.392663
$162$	0.692358	0.0543968
$163$	4.96855	0.389167	0.194583	−	0.980886i	$-0.437664\pi$
$163$	4.96855	0.389167	0.194583	+	0.980886i	$0.437664\pi$
$164$	−5.42854	−0.423897
$165$	0.970306	0.0755382
$166$	1.16773	0.0906335
$167$	−14.3188	−1.10802	−0.554012	−	0.832508i	$-0.686904\pi$
$167$	−14.3188	−1.10802	−0.554012	+	0.832508i	$0.686904\pi$
$168$	−2.43754	−0.188061
$169$	−8.25820	−0.635246
$170$	−14.3012	−1.09685
$171$	−0.255629	−0.0195485
$172$	14.2123	1.08368
$173$	−22.2870	−1.69445	−0.847225	−	0.531235i	$-0.821728\pi$
$173$	−22.2870	−1.69445	−0.847225	+	0.531235i	$0.821728\pi$
$174$	−4.76428	−0.361179
$175$	2.73644	0.206855
$176$	−0.472213	−0.0355944
$177$	−2.01055	−0.151122
$178$	−12.2374	−0.917235
$179$	26.5031	1.98093	0.990467	−	0.137748i	$-0.0439863\pi$
$179$	26.5031	1.98093	0.990467	+	0.137748i	$0.0439863\pi$
$180$	4.22958	0.315254
$181$	−6.62020	−0.492076	−0.246038	−	0.969260i	$-0.579129\pi$
$181$	−6.62020	−0.492076	−0.246038	+	0.969260i	$0.579129\pi$
$182$	1.50766	0.111755
$183$	−7.69549	−0.568867
$184$	12.1447	0.895316
$185$	4.56932	0.335943
$186$	−6.99543	−0.512930
$187$	−2.59065	−0.189447
$188$	−14.8093	−1.08008
$189$	1.00000	0.0727393
$190$	0.492279	0.0357137
$191$	9.50979	0.688104	0.344052	−	0.938951i	$-0.388200\pi$
$191$	9.50979	0.688104	0.344052	+	0.938951i	$0.388200\pi$
$192$	1.31692	0.0950403
$193$	18.2187	1.31141	0.655706	−	0.755016i	$-0.272371\pi$
$193$	18.2187	1.31141	0.655706	+	0.755016i	$0.272371\pi$
$194$	−0.150084	−0.0107754
$195$	−6.05678	−0.433735
$196$	−1.52064	−0.108617
$197$	−6.73369	−0.479756	−0.239878	−	0.970803i	$-0.577107\pi$
$197$	−6.73369	−0.479756	−0.239878	+	0.970803i	$0.577107\pi$
$198$	−0.241529	−0.0171647
$199$	19.1877	1.36018	0.680088	−	0.733130i	$-0.261941\pi$
$199$	19.1877	1.36018	0.680088	+	0.733130i	$0.261941\pi$
$200$	−6.67019	−0.471654
$201$	−6.52951	−0.460556
$202$	−10.8195	−0.761255
$203$	−6.88124	−0.482969
$204$	−11.2927	−0.790646
$205$	−9.92948	−0.693505
$206$	−1.95513	−0.136221
$207$	−4.98233	−0.346296
$208$	2.94762	0.204381
$209$	0.0891761	0.00616844
$210$	−1.92576	−0.132890
$211$	3.89333	0.268028	0.134014	−	0.990979i	$-0.457213\pi$
$211$	3.89333	0.268028	0.134014	+	0.990979i	$0.457213\pi$
$212$	11.3237	0.777715
$213$	13.7550	0.942476
$214$	−9.45100	−0.646057
$215$	25.9962	1.77292
$216$	−2.43754	−0.165854
$217$	−10.1038	−0.685889
$218$	−8.62544	−0.584189
$219$	−9.37124	−0.633250
$220$	−1.47549	−0.0994773
$221$	16.1712	1.08779
$222$	−1.13740	−0.0763370
$223$	17.8977	1.19852	0.599258	−	0.800556i	$-0.295462\pi$
$223$	17.8977	1.19852	0.599258	+	0.800556i	$0.295462\pi$
$224$	5.81228	0.388349
$225$	2.73644	0.182429
$226$	11.8597	0.788896
$227$	8.76418	0.581699	0.290850	−	0.956769i	$-0.406062\pi$
$227$	8.76418	0.581699	0.290850	+	0.956769i	$0.406062\pi$
$228$	0.388720	0.0257436
$229$	−20.1983	−1.33474	−0.667371	−	0.744726i	$-0.732580\pi$
$229$	−20.1983	−1.33474	−0.667371	+	0.744726i	$0.732580\pi$
$230$	9.59476	0.632660
$231$	−0.348849	−0.0229526
$232$	16.7733	1.10122
$233$	−29.4789	−1.93122	−0.965612	−	0.259986i	$-0.916282\pi$
$233$	−29.4789	−1.93122	−0.965612	+	0.259986i	$0.916282\pi$
$234$	1.50766	0.0985585
$235$	−27.0881	−1.76703
$236$	3.05733	0.199015
$237$	−5.92206	−0.384679
$238$	5.14163	0.333282
$239$	−22.7548	−1.47188	−0.735941	−	0.677045i	$-0.763260\pi$
$239$	−22.7548	−1.47188	−0.735941	+	0.677045i	$0.763260\pi$
$240$	−3.76505	−0.243033
$241$	12.6179	0.812789	0.406395	−	0.913698i	$-0.366786\pi$
$241$	12.6179	0.812789	0.406395	+	0.913698i	$0.366786\pi$
$242$	−7.53168	−0.484155
$243$	1.00000	0.0641500
$244$	11.7021	0.749148
$245$	−2.78145	−0.177700
$246$	2.47165	0.157586
$247$	−0.556650	−0.0354188
$248$	24.6284	1.56390
$249$	1.68660	0.106884
$250$	4.35906	0.275691
$251$	−17.4819	−1.10345	−0.551725	−	0.834026i	$-0.686030\pi$
$251$	−17.4819	−1.10345	−0.551725	+	0.834026i	$0.686030\pi$
$252$	−1.52064	−0.0957914
$253$	1.73808	0.109272
$254$	−0.692358	−0.0434424
$255$	−20.6557	−1.29351
$256$	−10.0509	−0.628182
$257$	8.26061	0.515283	0.257641	−	0.966241i	$-0.417055\pi$
$257$	8.26061	0.515283	0.257641	+	0.966241i	$0.417055\pi$
$258$	−6.47097	−0.402865
$259$	−1.64279	−0.102078
$260$	9.21019	0.571192
$261$	−6.88124	−0.425938
$262$	5.77361	0.356695
$263$	25.8026	1.59106	0.795530	−	0.605915i	$-0.207193\pi$
$263$	25.8026	1.59106	0.795530	+	0.605915i	$0.207193\pi$
$264$	0.850335	0.0523345
$265$	20.7125	1.27236
$266$	−0.176987	−0.0108518
$267$	−17.6750	−1.08169
$268$	9.92903	0.606512
$269$	−6.10591	−0.372284	−0.186142	−	0.982523i	$-0.559598\pi$
$269$	−6.10591	−0.372284	−0.186142	+	0.982523i	$0.559598\pi$
$270$	−1.92576	−0.117198
$271$	−16.8740	−1.02503	−0.512513	−	0.858680i	$-0.671285\pi$
$271$	−16.8740	−1.02503	−0.512513	+	0.858680i	$0.671285\pi$
$272$	10.0524	0.609517
$273$	2.17757	0.131792
$274$	14.5099	0.876577
$275$	−0.954606	−0.0575649
$276$	7.57634	0.456042
$277$	29.0357	1.74459	0.872293	−	0.488983i	$-0.162632\pi$
$277$	29.0357	1.74459	0.872293	+	0.488983i	$0.162632\pi$
$278$	−7.05285	−0.423002
$279$	−10.1038	−0.604897
$280$	6.77989	0.405176
$281$	3.71119	0.221391	0.110695	−	0.993854i	$-0.464692\pi$
$281$	3.71119	0.221391	0.110695	+	0.993854i	$0.464692\pi$
$282$	6.74277	0.401526
$283$	−10.0392	−0.596770	−0.298385	−	0.954446i	$-0.596448\pi$
$283$	−10.0392	−0.596770	−0.298385	+	0.954446i	$0.596448\pi$
$284$	−20.9164	−1.24116
$285$	0.711019	0.0421171
$286$	−0.525945	−0.0310998
$287$	3.56990	0.210725
$288$	5.81228	0.342492
$289$	38.1494	2.24408
$290$	13.2516	0.778160
$291$	−0.216772	−0.0127074
$292$	14.2503	0.833935
$293$	30.6862	1.79271	0.896355	−	0.443338i	$-0.146206\pi$
$293$	30.6862	1.79271	0.896355	+	0.443338i	$0.146206\pi$
$294$	0.692358	0.0403791
$295$	5.59224	0.325593
$296$	4.00436	0.232749
$297$	−0.348849	−0.0202423
$298$	−3.37093	−0.195273
$299$	−10.8494	−0.627435
$300$	−4.16114	−0.240244
$301$	−9.34628	−0.538711
$302$	−1.34022	−0.0771209
$303$	−15.6270	−0.897747
$304$	−0.346027	−0.0198460
$305$	21.4046	1.22562
$306$	5.14163	0.293927
$307$	−7.58942	−0.433151	−0.216575	−	0.976266i	$-0.569489\pi$
$307$	−7.58942	−0.433151	−0.216575	+	0.976266i	$0.569489\pi$
$308$	0.530475	0.0302266
$309$	−2.82388	−0.160645
$310$	19.4574	1.10511
$311$	−31.5432	−1.78865	−0.894324	−	0.447419i	$-0.852343\pi$
$311$	−31.5432	−1.78865	−0.894324	+	0.447419i	$0.852343\pi$
$312$	−5.30791	−0.300501
$313$	25.5982	1.44689	0.723447	−	0.690379i	$-0.242556\pi$
$313$	25.5982	1.44689	0.723447	+	0.690379i	$0.242556\pi$
$314$	2.97208	0.167724
$315$	−2.78145	−0.156717
$316$	9.00532	0.506589
$317$	20.7732	1.16674	0.583370	−	0.812206i	$-0.301734\pi$
$317$	20.7732	1.16674	0.583370	+	0.812206i	$0.301734\pi$
$318$	−5.15575	−0.289120
$319$	2.40052	0.134403
$320$	−3.66293	−0.204764
$321$	−13.6505	−0.761894
$322$	−3.44956	−0.192236
$323$	−1.89837	−0.105628
$324$	−1.52064	−0.0844800
$325$	5.95878	0.330534
$326$	3.44001	0.190525
$327$	−12.4581	−0.688933
$328$	−8.70178	−0.480476
$329$	9.73885	0.536920
$330$	0.671799	0.0369813
$331$	−3.11825	−0.171394	−0.0856971	−	0.996321i	$-0.527312\pi$
$331$	−3.11825	−0.171394	−0.0856971	+	0.996321i	$0.527312\pi$
$332$	−2.56471	−0.140757
$333$	−1.64279	−0.0900241
$334$	−9.91376	−0.542457
$335$	18.1615	0.992267
$336$	1.35363	0.0738466
$337$	0.0769121	0.00418967	0.00209483	−	0.999998i	$-0.499333\pi$
$337$	0.0769121	0.00418967	0.00209483	+	0.999998i	$0.499333\pi$
$338$	−5.71763	−0.310998
$339$	17.1295	0.930344
$340$	31.4100	1.70344
$341$	3.52470	0.190873
$342$	−0.176987	−0.00957035
$343$	1.00000	0.0539949
$344$	22.7820	1.22832
$345$	13.8581	0.746095
$346$	−15.4306	−0.829553
$347$	−7.04794	−0.378353	−0.189177	−	0.981943i	$-0.560582\pi$
$347$	−7.04794	−0.378353	−0.189177	+	0.981943i	$0.560582\pi$
$348$	10.4639	0.560924
$349$	15.4067	0.824703	0.412351	−	0.911025i	$-0.364708\pi$
$349$	15.4067	0.824703	0.412351	+	0.911025i	$0.364708\pi$
$350$	1.89460	0.101270
$351$	2.17757	0.116230
$352$	−2.02761	−0.108072
$353$	15.3530	0.817157	0.408578	−	0.912723i	$-0.366025\pi$
$353$	15.3530	0.817157	0.408578	+	0.912723i	$0.366025\pi$
$354$	−1.39202	−0.0739851
$355$	−38.2587	−2.03056
$356$	26.8774	1.42450
$357$	7.42626	0.393039
$358$	18.3496	0.969808
$359$	−2.58094	−0.136217	−0.0681084	−	0.997678i	$-0.521696\pi$
$359$	−2.58094	−0.136217	−0.0681084	+	0.997678i	$0.521696\pi$
$360$	6.77989	0.357332
$361$	−18.9347	−0.996561
$362$	−4.58355	−0.240906
$363$	−10.8783	−0.570963
$364$	−3.31130	−0.173559
$365$	26.0656	1.36434
$366$	−5.32803	−0.278501
$367$	22.1135	1.15431	0.577157	−	0.816634i	$-0.304162\pi$
$367$	22.1135	1.15431	0.577157	+	0.816634i	$0.304162\pi$
$368$	−6.74424	−0.351568
$369$	3.56990	0.185842
$370$	3.16360	0.164468
$371$	−7.44666	−0.386612
$372$	15.3642	0.796597
$373$	−16.3558	−0.846873	−0.423436	−	0.905926i	$-0.639176\pi$
$373$	−16.3558	−0.846873	−0.423436	+	0.905926i	$0.639176\pi$
$374$	−1.79365	−0.0927477
$375$	6.29597	0.325122
$376$	−23.7389	−1.22424
$377$	−14.9844	−0.771734
$378$	0.692358	0.0356110
$379$	22.3125	1.14612	0.573059	−	0.819514i	$-0.305757\pi$
$379$	22.3125	1.14612	0.573059	+	0.819514i	$0.305757\pi$
$380$	−1.08120	−0.0554646
$381$	−1.00000	−0.0512316
$382$	6.58418	0.336876
$383$	−18.0582	−0.922729	−0.461365	−	0.887211i	$-0.652640\pi$
$383$	−18.0582	−0.922729	−0.461365	+	0.887211i	$0.652640\pi$
$384$	−10.7128	−0.546685
$385$	0.970306	0.0494514
$386$	12.6139	0.642029
$387$	−9.34628	−0.475098
$388$	0.329632	0.0167346
$389$	−1.96882	−0.0998232	−0.0499116	−	0.998754i	$-0.515894\pi$
$389$	−1.96882	−0.0998232	−0.0499116	+	0.998754i	$0.515894\pi$
$390$	−4.19346	−0.212344
$391$	−37.0001	−1.87118
$392$	−2.43754	−0.123114
$393$	8.33905	0.420650
$394$	−4.66212	−0.234874
$395$	16.4719	0.828790
$396$	0.530475	0.0266574
$397$	−13.1572	−0.660341	−0.330171	−	0.943921i	$-0.607106\pi$
$397$	−13.1572	−0.660341	−0.330171	+	0.943921i	$0.607106\pi$
$398$	13.2847	0.665903
$399$	−0.255629	−0.0127975
$400$	3.70413	0.185206
$401$	−27.6771	−1.38213	−0.691063	−	0.722794i	$-0.742857\pi$
$401$	−27.6771	−1.38213	−0.691063	+	0.722794i	$0.742857\pi$
$402$	−4.52075	−0.225475
$403$	−22.0017	−1.09598
$404$	23.7630	1.18226
$405$	−2.78145	−0.138211
$406$	−4.76428	−0.236447
$407$	0.573085	0.0284068
$408$	−18.1018	−0.896174
$409$	−23.5157	−1.16278	−0.581388	−	0.813626i	$-0.697490\pi$
$409$	−23.5157	−1.16278	−0.581388	+	0.813626i	$0.697490\pi$
$410$	−6.87475	−0.339520
$411$	20.9573	1.03375
$412$	4.29410	0.211555
$413$	−2.01055	−0.0989328
$414$	−3.44956	−0.169537
$415$	−4.69119	−0.230281
$416$	12.6566	0.620542
$417$	−10.1867	−0.498846
$418$	0.0617418	0.00301989
$419$	3.78832	0.185072	0.0925359	−	0.995709i	$-0.470503\pi$
$419$	3.78832	0.185072	0.0925359	+	0.995709i	$0.470503\pi$
$420$	4.22958	0.206382
$421$	−40.3970	−1.96883	−0.984415	−	0.175859i	$-0.943730\pi$
$421$	−40.3970	−1.96883	−0.984415	+	0.175859i	$0.943730\pi$
$422$	2.69558	0.131219
$423$	9.73885	0.473519
$424$	18.1516	0.881518
$425$	20.3215	0.985739
$426$	9.52337	0.461409
$427$	−7.69549	−0.372411
$428$	20.7574	1.00335
$429$	−0.759643	−0.0366759
$430$	17.9986	0.867972
$431$	26.3339	1.26846	0.634230	−	0.773144i	$-0.281317\pi$
$431$	26.3339	1.26846	0.634230	+	0.773144i	$0.281317\pi$
$432$	1.35363	0.0651266
$433$	−6.47692	−0.311261	−0.155631	−	0.987815i	$-0.549741\pi$
$433$	−6.47692	−0.311261	−0.155631	+	0.987815i	$0.549741\pi$
$434$	−6.99543	−0.335791
$435$	19.1398	0.917684
$436$	18.9443	0.907265
$437$	1.27363	0.0609260
$438$	−6.48825	−0.310021
$439$	11.9232	0.569062	0.284531	−	0.958667i	$-0.408162\pi$
$439$	11.9232	0.569062	0.284531	+	0.958667i	$0.408162\pi$
$440$	−2.36516	−0.112755
$441$	1.00000	0.0476190
$442$	11.1962	0.532551
$443$	31.9287	1.51698	0.758490	−	0.651685i	$-0.225938\pi$
$443$	31.9287	1.51698	0.758490	+	0.651685i	$0.225938\pi$
$444$	2.49809	0.118554
$445$	49.1622	2.33051
$446$	12.3916	0.586759
$447$	−4.86877	−0.230285
$448$	1.31692	0.0622185
$449$	31.3379	1.47893	0.739463	−	0.673197i	$-0.235079\pi$
$449$	31.3379	1.47893	0.739463	+	0.673197i	$0.235079\pi$
$450$	1.89460	0.0893121
$451$	−1.24536	−0.0586416
$452$	−26.0477	−1.22518
$453$	−1.93573	−0.0909486
$454$	6.06795	0.284783
$455$	−6.05678	−0.283946
$456$	0.623107	0.0291797
$457$	−17.5797	−0.822344	−0.411172	−	0.911558i	$-0.634880\pi$
$457$	−17.5797	−0.822344	−0.411172	+	0.911558i	$0.634880\pi$
$458$	−13.9844	−0.653450
$459$	7.42626	0.346628
$460$	−21.0732	−0.982542
$461$	−27.4541	−1.27867	−0.639333	−	0.768930i	$-0.720789\pi$
$461$	−27.4541	−1.27867	−0.639333	+	0.768930i	$0.720789\pi$
$462$	−0.241529	−0.0112369
$463$	−18.2297	−0.847207	−0.423604	−	0.905848i	$-0.639235\pi$
$463$	−18.2297	−0.847207	−0.423604	+	0.905848i	$0.639235\pi$
$464$	−9.31466	−0.432422
$465$	28.1031	1.30325
$466$	−20.4099	−0.945471
$467$	−6.72456	−0.311176	−0.155588	−	0.987822i	$-0.549727\pi$
$467$	−6.72456	−0.311176	−0.155588	+	0.987822i	$0.549727\pi$
$468$	−3.31130	−0.153065
$469$	−6.52951	−0.301505
$470$	−18.7546	−0.865087
$471$	4.29270	0.197797
$472$	4.90081	0.225578
$473$	3.26044	0.149915
$474$	−4.10018	−0.188328
$475$	−0.699514	−0.0320959
$476$	−11.2927	−0.517599
$477$	−7.44666	−0.340959
$478$	−15.7544	−0.720591
$479$	19.3112	0.882350	0.441175	−	0.897421i	$-0.354562\pi$
$479$	19.3112	0.882350	0.441175	+	0.897421i	$0.354562\pi$
$480$	−16.1665	−0.737899
$481$	−3.57728	−0.163110
$482$	8.73609	0.397918
$483$	−4.98233	−0.226704
$484$	16.5420	0.751909
$485$	0.602940	0.0273781
$486$	0.692358	0.0314060
$487$	−38.4870	−1.74401	−0.872007	−	0.489494i	$-0.837182\pi$
$487$	−38.4870	−1.74401	−0.872007	+	0.489494i	$0.837182\pi$
$488$	18.7581	0.849138
$489$	4.96855	0.224686
$490$	−1.92576	−0.0869968
$491$	19.8484	0.895746	0.447873	−	0.894097i	$-0.352182\pi$
$491$	19.8484	0.895746	0.447873	+	0.894097i	$0.352182\pi$
$492$	−5.42854	−0.244737
$493$	−51.1019	−2.30151
$494$	−0.385401	−0.0173400
$495$	0.970306	0.0436120
$496$	−13.6768	−0.614105
$497$	13.7550	0.616995
$498$	1.16773	0.0523273
$499$	12.8775	0.576476	0.288238	−	0.957559i	$-0.406931\pi$
$499$	12.8775	0.576476	0.288238	+	0.957559i	$0.406931\pi$
$500$	−9.57391	−0.428158
$501$	−14.3188	−0.639718
$502$	−12.1037	−0.540217
$503$	−35.1228	−1.56605	−0.783024	−	0.621992i	$-0.786324\pi$
$503$	−35.1228	−1.56605	−0.783024	+	0.621992i	$0.786324\pi$
$504$	−2.43754	−0.108577
$505$	43.4656	1.93419
$506$	1.20338	0.0534966
$507$	−8.25820	−0.366760
$508$	1.52064	0.0674675
$509$	−1.90456	−0.0844184	−0.0422092	−	0.999109i	$-0.513440\pi$
$509$	−1.90456	−0.0844184	−0.0422092	+	0.999109i	$0.513440\pi$
$510$	−14.3012	−0.633266
$511$	−9.37124	−0.414559
$512$	14.4667	0.639346
$513$	−0.255629	−0.0112863
$514$	5.71930	0.252267
$515$	7.85446	0.346109
$516$	14.2123	0.625663
$517$	−3.39739	−0.149417
$518$	−1.13740	−0.0499743
$519$	−22.2870	−0.978291
$520$	14.7637	0.647430
$521$	−31.1698	−1.36558	−0.682788	−	0.730617i	$-0.739233\pi$
$521$	−31.1698	−1.36558	−0.682788	+	0.730617i	$0.739233\pi$
$522$	−4.76428	−0.208527
$523$	−16.1856	−0.707748	−0.353874	−	0.935293i	$-0.615136\pi$
$523$	−16.1856	−0.707748	−0.353874	+	0.935293i	$0.615136\pi$
$524$	−12.6807	−0.553959
$525$	2.73644	0.119428
$526$	17.8647	0.778936
$527$	−75.0333	−3.26850
$528$	−0.472213	−0.0205504
$529$	1.82366	0.0792896
$530$	14.3405	0.622909
$531$	−2.01055	−0.0872505
$532$	0.388720	0.0168532
$533$	7.77370	0.336716
$534$	−12.2374	−0.529566
$535$	37.9680	1.64150
$536$	15.9160	0.687464
$537$	26.5031	1.14369
$538$	−4.22748	−0.182259
$539$	−0.348849	−0.0150260
$540$	4.22958	0.182012
$541$	−18.5894	−0.799221	−0.399610	−	0.916685i	$-0.630855\pi$
$541$	−18.5894	−0.799221	−0.399610	+	0.916685i	$0.630855\pi$
$542$	−11.6829	−0.501822
$543$	−6.62020	−0.284100
$544$	43.1635	1.85062
$545$	34.6514	1.48430
$546$	1.50766	0.0645217
$547$	16.3670	0.699802	0.349901	−	0.936787i	$-0.386215\pi$
$547$	16.3670	0.699802	0.349901	+	0.936787i	$0.386215\pi$
$548$	−31.8685	−1.36135
$549$	−7.69549	−0.328435
$550$	−0.660929	−0.0281821
$551$	1.75905	0.0749379
$552$	12.1447	0.516911
$553$	−5.92206	−0.251831
$554$	20.1031	0.854099
$555$	4.56932	0.193957
$556$	15.4903	0.656937
$557$	37.7810	1.60083	0.800417	−	0.599444i	$-0.204612\pi$
$557$	37.7810	1.60083	0.800417	+	0.599444i	$0.204612\pi$
$558$	−6.99543	−0.296140
$559$	−20.3522	−0.860804
$560$	−3.76505	−0.159102
$561$	−2.59065	−0.109377
$562$	2.56947	0.108386
$563$	13.6001	0.573176	0.286588	−	0.958054i	$-0.407479\pi$
$563$	13.6001	0.573176	0.286588	+	0.958054i	$0.407479\pi$
$564$	−14.8093	−0.623584
$565$	−47.6446	−2.00443
$566$	−6.95074	−0.292161
$567$	1.00000	0.0419961
$568$	−33.5284	−1.40682
$569$	9.94802	0.417043	0.208521	−	0.978018i	$-0.433135\pi$
$569$	9.94802	0.417043	0.208521	+	0.978018i	$0.433135\pi$
$570$	0.492279	0.0206193
$571$	8.42532	0.352588	0.176294	−	0.984338i	$-0.443589\pi$
$571$	8.42532	0.352588	0.176294	+	0.984338i	$0.443589\pi$
$572$	1.15514	0.0482990
$573$	9.50979	0.397277
$574$	2.47165	0.103165
$575$	−13.6339	−0.568571
$576$	1.31692	0.0548715
$577$	−20.5668	−0.856206	−0.428103	−	0.903730i	$-0.640818\pi$
$577$	−20.5668	−0.856206	−0.428103	+	0.903730i	$0.640818\pi$
$578$	26.4130	1.09864
$579$	18.2187	0.757145
$580$	−29.1048	−1.20851
$581$	1.68660	0.0699720
$582$	−0.150084	−0.00622117
$583$	2.59776	0.107588
$584$	22.8428	0.945242
$585$	−6.05678	−0.250417
$586$	21.2459	0.877658
$587$	23.2118	0.958053	0.479027	−	0.877800i	$-0.340990\pi$
$587$	23.2118	0.958053	0.479027	+	0.877800i	$0.340990\pi$
$588$	−1.52064	−0.0627102
$589$	2.58282	0.106423
$590$	3.87183	0.159401
$591$	−6.73369	−0.276987
$592$	−2.22373	−0.0913945
$593$	29.0658	1.19359	0.596795	−	0.802393i	$-0.296440\pi$
$593$	29.0658	1.19359	0.596795	+	0.802393i	$0.296440\pi$
$594$	−0.241529	−0.00991004
$595$	−20.6557	−0.846803
$596$	7.40365	0.303265
$597$	19.1877	0.785298
$598$	−7.51164	−0.307174
$599$	−31.7965	−1.29917	−0.649584	−	0.760290i	$-0.725057\pi$
$599$	−31.7965	−1.29917	−0.649584	+	0.760290i	$0.725057\pi$
$600$	−6.67019	−0.272309
$601$	21.6226	0.882004	0.441002	−	0.897506i	$-0.354623\pi$
$601$	21.6226	0.882004	0.441002	+	0.897506i	$0.354623\pi$
$602$	−6.47097	−0.263737
$603$	−6.52951	−0.265902
$604$	2.94355	0.119771
$605$	30.2574	1.23014
$606$	−10.8195	−0.439511
$607$	19.7589	0.801988	0.400994	−	0.916081i	$-0.368665\pi$
$607$	19.7589	0.801988	0.400994	+	0.916081i	$0.368665\pi$
$608$	−1.48579	−0.0602567
$609$	−6.88124	−0.278842
$610$	14.8196	0.600029
$611$	21.2070	0.857944
$612$	−11.2927	−0.456479
$613$	−7.69528	−0.310809	−0.155405	−	0.987851i	$-0.549668\pi$
$613$	−7.69528	−0.310809	−0.155405	+	0.987851i	$0.549668\pi$
$614$	−5.25459	−0.212058
$615$	−9.92948	−0.400395
$616$	0.850335	0.0342610
$617$	−46.4653	−1.87062	−0.935310	−	0.353828i	$-0.884880\pi$
$617$	−46.4653	−1.87062	−0.935310	+	0.353828i	$0.884880\pi$
$618$	−1.95513	−0.0786470
$619$	−9.42955	−0.379006	−0.189503	−	0.981880i	$-0.560688\pi$
$619$	−9.42955	−0.379006	−0.189503	+	0.981880i	$0.560688\pi$
$620$	−42.7347	−1.71627
$621$	−4.98233	−0.199934
$622$	−21.8391	−0.875670
$623$	−17.6750	−0.708135
$624$	2.94762	0.117999
$625$	−31.1941	−1.24776
$626$	17.7231	0.708357
$627$	0.0891761	0.00356135
$628$	−6.52765	−0.260482
$629$	−12.1998	−0.486436
$630$	−1.92576	−0.0767239
$631$	−34.1327	−1.35880	−0.679401	−	0.733768i	$-0.737760\pi$
$631$	−34.1327	−1.35880	−0.679401	+	0.733768i	$0.737760\pi$
$632$	14.4353	0.574204
$633$	3.89333	0.154746
$634$	14.3825	0.571202
$635$	2.78145	0.110378
$636$	11.3237	0.449014
$637$	2.17757	0.0862783
$638$	1.66202	0.0657999
$639$	13.7550	0.544139
$640$	29.7970	1.17783
$641$	35.7111	1.41050	0.705252	−	0.708956i	$-0.250834\pi$
$641$	35.7111	1.41050	0.705252	+	0.708956i	$0.250834\pi$
$642$	−9.45100	−0.373001
$643$	0.292989	0.0115544	0.00577718	−	0.999983i	$-0.498161\pi$
$643$	0.292989	0.0115544	0.00577718	+	0.999983i	$0.498161\pi$
$644$	7.57634	0.298550
$645$	25.9962	1.02360
$646$	−1.31435	−0.0517124
$647$	7.55746	0.297114	0.148557	−	0.988904i	$-0.452537\pi$
$647$	7.55746	0.297114	0.148557	+	0.988904i	$0.452537\pi$
$648$	−2.43754	−0.0957557
$649$	0.701380	0.0275316
$650$	4.12561	0.161820
$651$	−10.1038	−0.395998
$652$	−7.55538	−0.295892
$653$	−43.1190	−1.68738	−0.843688	−	0.536833i	$-0.819620\pi$
$653$	−43.1190	−1.68738	−0.843688	+	0.536833i	$0.819620\pi$
$654$	−8.62544	−0.337281
$655$	−23.1946	−0.906289
$656$	4.83232	0.188671
$657$	−9.37124	−0.365607
$658$	6.74277	0.262861
$659$	−22.2019	−0.864865	−0.432433	−	0.901666i	$-0.642345\pi$
$659$	−22.2019	−0.864865	−0.432433	+	0.901666i	$0.642345\pi$
$660$	−1.47549	−0.0574332
$661$	42.4146	1.64974	0.824868	−	0.565326i	$-0.191249\pi$
$661$	42.4146	1.64974	0.824868	+	0.565326i	$0.191249\pi$
$662$	−2.15894	−0.0839096
$663$	16.1712	0.628037
$664$	−4.11116	−0.159544
$665$	0.711019	0.0275721
$666$	−1.13740	−0.0440732
$667$	34.2847	1.32751
$668$	21.7738	0.842454
$669$	17.8977	0.691964
$670$	12.5742	0.485785
$671$	2.68457	0.103637
$672$	5.81228	0.224214
$673$	−21.3504	−0.822998	−0.411499	−	0.911410i	$-0.634995\pi$
$673$	−21.3504	−0.822998	−0.411499	+	0.911410i	$0.634995\pi$
$674$	0.0532507	0.00205114
$675$	2.73644	0.105326
$676$	12.5578	0.482991
$677$	6.31191	0.242587	0.121293	−	0.992617i	$-0.461296\pi$
$677$	6.31191	0.242587	0.121293	+	0.992617i	$0.461296\pi$
$678$	11.8597	0.455469
$679$	−0.216772	−0.00831895
$680$	50.3493	1.93081
$681$	8.76418	0.335844
$682$	2.44035	0.0934459
$683$	44.6920	1.71009	0.855047	−	0.518551i	$-0.173528\pi$
$683$	44.6920	1.71009	0.855047	+	0.518551i	$0.173528\pi$
$684$	0.388720	0.0148631
$685$	−58.2915	−2.22721
$686$	0.692358	0.0264343
$687$	−20.1983	−0.770613
$688$	−12.6514	−0.482330
$689$	−16.2156	−0.617766
$690$	9.59476	0.365266
$691$	−16.3228	−0.620948	−0.310474	−	0.950582i	$-0.600488\pi$
$691$	−16.3228	−0.620948	−0.310474	+	0.950582i	$0.600488\pi$
$692$	33.8905	1.28832
$693$	−0.348849	−0.0132517
$694$	−4.87970	−0.185231
$695$	28.3338	1.07476
$696$	16.7733	0.635791
$697$	26.5110	1.00418
$698$	10.6670	0.403750
$699$	−29.4789	−1.11499
$700$	−4.16114	−0.157276
$701$	16.1072	0.608360	0.304180	−	0.952615i	$-0.401618\pi$
$701$	16.1072	0.608360	0.304180	+	0.952615i	$0.401618\pi$
$702$	1.50766	0.0569028
$703$	0.419944	0.0158385
$704$	−0.459406	−0.0173145
$705$	−27.0881	−1.02020
$706$	10.6298	0.400056
$707$	−15.6270	−0.587713
$708$	3.05733	0.114901
$709$	18.7118	0.702738	0.351369	−	0.936237i	$-0.385716\pi$
$709$	18.7118	0.702738	0.351369	+	0.936237i	$0.385716\pi$
$710$	−26.4887	−0.994104
$711$	−5.92206	−0.222094
$712$	43.0837	1.61463
$713$	50.3404	1.88526
$714$	5.14163	0.192421
$715$	2.11291	0.0790182
$716$	−40.3017	−1.50615
$717$	−22.7548	−0.849792
$718$	−1.78693	−0.0666878
$719$	2.91001	0.108525	0.0542625	−	0.998527i	$-0.482719\pi$
$719$	2.91001	0.108525	0.0542625	+	0.998527i	$0.482719\pi$
$720$	−3.76505	−0.140315
$721$	−2.82388	−0.105167
$722$	−13.1096	−0.487887
$723$	12.6179	0.469264
$724$	10.0669	0.374135
$725$	−18.8301	−0.699333
$726$	−7.53168	−0.279527
$727$	−31.1593	−1.15563	−0.577817	−	0.816166i	$-0.696095\pi$
$727$	−31.1593	−1.15563	−0.577817	+	0.816166i	$0.696095\pi$
$728$	−5.30791	−0.196724
$729$	1.00000	0.0370370
$730$	18.0467	0.667939
$731$	−69.4079	−2.56715
$732$	11.7021	0.432521
$733$	−35.0113	−1.29317	−0.646586	−	0.762841i	$-0.723804\pi$
$733$	−35.0113	−1.29317	−0.646586	+	0.762841i	$0.723804\pi$
$734$	15.3104	0.565118
$735$	−2.78145	−0.102595
$736$	−28.9587	−1.06743
$737$	2.27782	0.0839044
$738$	2.47165	0.0909826
$739$	−31.9289	−1.17452	−0.587262	−	0.809397i	$-0.699794\pi$
$739$	−31.9289	−1.17452	−0.587262	+	0.809397i	$0.699794\pi$
$740$	−6.94830	−0.255424
$741$	−0.556650	−0.0204490
$742$	−5.15575	−0.189274
$743$	−9.30835	−0.341490	−0.170745	−	0.985315i	$-0.554618\pi$
$743$	−9.30835	−0.341490	−0.170745	+	0.985315i	$0.554618\pi$
$744$	24.6284	0.902920
$745$	13.5422	0.496149
$746$	−11.3241	−0.414604
$747$	1.68660	0.0617095
$748$	3.93944	0.144040
$749$	−13.6505	−0.498777
$750$	4.35906	0.159170
$751$	51.6363	1.88424	0.942118	−	0.335282i	$-0.108832\pi$
$751$	51.6363	1.88424	0.942118	+	0.335282i	$0.108832\pi$
$752$	13.1828	0.480728
$753$	−17.4819	−0.637077
$754$	−10.3745	−0.377819
$755$	5.38413	0.195949
$756$	−1.52064	−0.0553052
$757$	42.6294	1.54939	0.774695	−	0.632335i	$-0.217903\pi$
$757$	42.6294	1.54939	0.774695	+	0.632335i	$0.217903\pi$
$758$	15.4482	0.561106
$759$	1.73808	0.0630885
$760$	−1.73314	−0.0628675
$761$	−31.2012	−1.13104	−0.565520	−	0.824734i	$-0.691325\pi$
$761$	−31.2012	−1.13104	−0.565520	+	0.824734i	$0.691325\pi$
$762$	−0.692358	−0.0250815
$763$	−12.4581	−0.451012
$764$	−14.4610	−0.523180
$765$	−20.6557	−0.746810
$766$	−12.5027	−0.451741
$767$	−4.37811	−0.158084
$768$	−10.0509	−0.362681
$769$	−14.0501	−0.506660	−0.253330	−	0.967380i	$-0.581526\pi$
$769$	−14.0501	−0.506660	−0.253330	+	0.967380i	$0.581526\pi$
$770$	0.671799	0.0242099
$771$	8.26061	0.297499
$772$	−27.7041	−0.997094
$773$	14.5672	0.523945	0.261973	−	0.965075i	$-0.415627\pi$
$773$	14.5672	0.523945	0.261973	+	0.965075i	$0.415627\pi$
$774$	−6.47097	−0.232594
$775$	−27.6484	−0.993159
$776$	0.528391	0.0189681
$777$	−1.64279	−0.0589346
$778$	−1.36313	−0.0488705
$779$	−0.912570	−0.0326962
$780$	9.21019	0.329778
$781$	−4.79842	−0.171701
$782$	−25.6173	−0.916074
$783$	−6.88124	−0.245916
$784$	1.35363	0.0483439
$785$	−11.9399	−0.426153
$786$	5.77361	0.205938
$787$	33.4906	1.19381	0.596905	−	0.802312i	$-0.296397\pi$
$787$	33.4906	1.19381	0.596905	+	0.802312i	$0.296397\pi$
$788$	10.2395	0.364768
$789$	25.8026	0.918599
$790$	11.4044	0.405751
$791$	17.1295	0.609053
$792$	0.850335	0.0302154
$793$	−16.7574	−0.595074
$794$	−9.10949	−0.323284
$795$	20.7125	0.734596
$796$	−29.1775	−1.03417
$797$	18.4316	0.652880	0.326440	−	0.945218i	$-0.394151\pi$
$797$	18.4316	0.652880	0.326440	+	0.945218i	$0.394151\pi$
$798$	−0.176987	−0.00626527
$799$	72.3233	2.55861
$800$	15.9050	0.562325
$801$	−17.6750	−0.624517
$802$	−19.1624	−0.676649
$803$	3.26915	0.115366
$804$	9.92903	0.350170
$805$	13.8581	0.488434
$806$	−15.2330	−0.536560
$807$	−6.10591	−0.214938
$808$	38.0914	1.34005
$809$	9.24970	0.325202	0.162601	−	0.986692i	$-0.448012\pi$
$809$	9.24970	0.325202	0.162601	+	0.986692i	$0.448012\pi$
$810$	−1.92576	−0.0676641
$811$	−43.2167	−1.51755	−0.758773	−	0.651356i	$-0.774201\pi$
$811$	−43.2167	−1.51755	−0.758773	+	0.651356i	$0.774201\pi$
$812$	10.4639	0.367211
$813$	−16.8740	−0.591799
$814$	0.396780	0.0139071
$815$	−13.8198	−0.484085
$816$	10.0524	0.351905
$817$	2.38918	0.0835869
$818$	−16.2813	−0.569261
$819$	2.17757	0.0760903
$820$	15.0992	0.527286
$821$	29.3683	1.02496	0.512481	−	0.858699i	$-0.328727\pi$
$821$	29.3683	1.02496	0.512481	+	0.858699i	$0.328727\pi$
$822$	14.5099	0.506092
$823$	16.4590	0.573726	0.286863	−	0.957972i	$-0.407388\pi$
$823$	16.4590	0.573726	0.286863	+	0.957972i	$0.407388\pi$
$824$	6.88332	0.239792
$825$	−0.954606	−0.0332351
$826$	−1.39202	−0.0484346
$827$	42.9794	1.49454	0.747270	−	0.664521i	$-0.231364\pi$
$827$	42.9794	1.49454	0.747270	+	0.664521i	$0.231364\pi$
$828$	7.57634	0.263296
$829$	8.69707	0.302062	0.151031	−	0.988529i	$-0.451741\pi$
$829$	8.69707	0.302062	0.151031	+	0.988529i	$0.451741\pi$
$830$	−3.24798	−0.112739
$831$	29.0357	1.00724
$832$	2.86768	0.0994188
$833$	7.42626	0.257305
$834$	−7.05285	−0.244220
$835$	39.8271	1.37827
$836$	−0.135605	−0.00468999
$837$	−10.1038	−0.349238
$838$	2.62287	0.0906057
$839$	14.0856	0.486289	0.243144	−	0.969990i	$-0.421821\pi$
$839$	14.0856	0.486289	0.243144	+	0.969990i	$0.421821\pi$
$840$	6.77989	0.233929
$841$	18.3515	0.632811
$842$	−27.9692	−0.963882
$843$	3.71119	0.127820
$844$	−5.92036	−0.203787
$845$	22.9697	0.790183
$846$	6.74277	0.231821
$847$	−10.8783	−0.373783
$848$	−10.0800	−0.346150
$849$	−10.0392	−0.344545
$850$	14.0698	0.482589
$851$	8.18491	0.280575
$852$	−20.9164	−0.716584
$853$	21.4439	0.734225	0.367113	−	0.930176i	$-0.380346\pi$
$853$	21.4439	0.734225	0.367113	+	0.930176i	$0.380346\pi$
$854$	−5.32803	−0.182321
$855$	0.711019	0.0243163
$856$	33.2736	1.13727
$857$	27.2216	0.929873	0.464936	−	0.885344i	$-0.346077\pi$
$857$	27.2216	0.929873	0.464936	+	0.885344i	$0.346077\pi$
$858$	−0.525945	−0.0179555
$859$	−47.7733	−1.63000	−0.815001	−	0.579459i	$-0.803264\pi$
$859$	−47.7733	−1.63000	−0.815001	+	0.579459i	$0.803264\pi$
$860$	−39.5308	−1.34799
$861$	3.56990	0.121662
$862$	18.2325	0.621001
$863$	8.00836	0.272608	0.136304	−	0.990667i	$-0.456478\pi$
$863$	8.00836	0.272608	0.136304	+	0.990667i	$0.456478\pi$
$864$	5.81228	0.197738
$865$	61.9901	2.10773
$866$	−4.48435	−0.152384
$867$	38.1494	1.29562
$868$	15.3642	0.521495
$869$	2.06591	0.0700811
$870$	13.2516	0.449271
$871$	−14.2184	−0.481773
$872$	30.3671	1.02836
$873$	−0.216772	−0.00733662
$874$	0.881808	0.0298276
$875$	6.29597	0.212843
$876$	14.2503	0.481473
$877$	−29.0720	−0.981691	−0.490845	−	0.871247i	$-0.663312\pi$
$877$	−29.0720	−0.981691	−0.490845	+	0.871247i	$0.663312\pi$
$878$	8.25510	0.278596
$879$	30.6862	1.03502
$880$	1.31344	0.0442759
$881$	−34.1165	−1.14941	−0.574707	−	0.818360i	$-0.694884\pi$
$881$	−34.1165	−1.14941	−0.574707	+	0.818360i	$0.694884\pi$
$882$	0.692358	0.0233129
$883$	50.0021	1.68271	0.841353	−	0.540486i	$-0.181760\pi$
$883$	50.0021	1.68271	0.841353	+	0.540486i	$0.181760\pi$
$884$	−24.5906	−0.827070
$885$	5.59224	0.187981
$886$	22.1061	0.742669
$887$	7.91800	0.265861	0.132930	−	0.991125i	$-0.457561\pi$
$887$	7.91800	0.265861	0.132930	+	0.991125i	$0.457561\pi$
$888$	4.00436	0.134378
$889$	−1.00000	−0.0335389
$890$	34.0378	1.14095
$891$	−0.348849	−0.0116869
$892$	−27.2159	−0.911257
$893$	−2.48953	−0.0833091
$894$	−3.37093	−0.112741
$895$	−73.7169	−2.46409
$896$	−10.7128	−0.357889
$897$	−10.8494	−0.362250
$898$	21.6970	0.724039
$899$	69.5266	2.31884
$900$	−4.16114	−0.138705
$901$	−55.3009	−1.84234
$902$	−0.862233	−0.0287092
$903$	−9.34628	−0.311025
$904$	−41.7538	−1.38871
$905$	18.4137	0.612093
$906$	−1.34022	−0.0445258
$907$	11.4971	0.381756	0.190878	−	0.981614i	$-0.438867\pi$
$907$	11.4971	0.381756	0.190878	+	0.981614i	$0.438867\pi$
$908$	−13.3272	−0.442278
$909$	−15.6270	−0.518314
$910$	−4.19346	−0.139012
$911$	15.6924	0.519913	0.259957	−	0.965620i	$-0.416292\pi$
$911$	15.6924	0.519913	0.259957	+	0.965620i	$0.416292\pi$
$912$	−0.346027	−0.0114581
$913$	−0.588370	−0.0194722
$914$	−12.1714	−0.402596
$915$	21.4046	0.707614
$916$	30.7144	1.01483
$917$	8.33905	0.275380
$918$	5.14163	0.169699
$919$	−17.3175	−0.571252	−0.285626	−	0.958341i	$-0.592202\pi$
$919$	−17.3175	−0.571252	−0.285626	+	0.958341i	$0.592202\pi$
$920$	−33.7797	−1.11368
$921$	−7.58942	−0.250080
$922$	−19.0081	−0.625997
$923$	29.9524	0.985895
$924$	0.530475	0.0174513
$925$	−4.49539	−0.147807
$926$	−12.6215	−0.414768
$927$	−2.82388	−0.0927483
$928$	−39.9957	−1.31292
$929$	24.5131	0.804249	0.402125	−	0.915585i	$-0.368272\pi$
$929$	24.5131	0.804249	0.402125	+	0.915585i	$0.368272\pi$
$930$	19.4574	0.638033
$931$	−0.255629	−0.00837791
$932$	44.8268	1.46835
$933$	−31.5432	−1.03268
$934$	−4.65580	−0.152342
$935$	7.20575	0.235653
$936$	−5.30791	−0.173495
$937$	39.1077	1.27759	0.638796	−	0.769376i	$-0.279433\pi$
$937$	39.1077	1.27759	0.638796	+	0.769376i	$0.279433\pi$
$938$	−4.52075	−0.147608
$939$	25.5982	0.835365
$940$	41.1913	1.34351
$941$	−24.8154	−0.808958	−0.404479	−	0.914547i	$-0.632547\pi$
$941$	−24.8154	−0.808958	−0.404479	+	0.914547i	$0.632547\pi$
$942$	2.97208	0.0968357
$943$	−17.7864	−0.579206
$944$	−2.72154	−0.0885787
$945$	−2.78145	−0.0904804
$946$	2.25739	0.0733942
$947$	−7.86086	−0.255444	−0.127722	−	0.991810i	$-0.540766\pi$
$947$	−7.86086	−0.255444	−0.127722	+	0.991810i	$0.540766\pi$
$948$	9.00532	0.292479
$949$	−20.4065	−0.662423
$950$	−0.484314	−0.0157132
$951$	20.7732	0.673618
$952$	−18.1018	−0.586684
$953$	19.4522	0.630119	0.315060	−	0.949072i	$-0.397976\pi$
$953$	19.4522	0.630119	0.315060	+	0.949072i	$0.397976\pi$
$954$	−5.15575	−0.166924
$955$	−26.4510	−0.855933
$956$	34.6018	1.11910
$957$	2.40052	0.0775977
$958$	13.3702	0.431973
$959$	20.9573	0.676746
$960$	−3.66293	−0.118221
$961$	71.0863	2.29311
$962$	−2.47676	−0.0798538
$963$	−13.6505	−0.439880
$964$	−19.1873	−0.617980
$965$	−50.6744	−1.63127
$966$	−3.44956	−0.110988
$967$	−31.4602	−1.01169	−0.505846	−	0.862624i	$-0.668819\pi$
$967$	−31.4602	−1.01169	−0.505846	+	0.862624i	$0.668819\pi$
$968$	26.5163	0.852267
$969$	−1.89837	−0.0609844
$970$	0.417450	0.0134035
$971$	9.05176	0.290485	0.145242	−	0.989396i	$-0.453604\pi$
$971$	9.05176	0.290485	0.145242	+	0.989396i	$0.453604\pi$
$972$	−1.52064	−0.0487746
$973$	−10.1867	−0.326571
$974$	−26.6468	−0.853818
$975$	5.95878	0.190834
$976$	−10.4168	−0.333435
$977$	7.31839	0.234136	0.117068	−	0.993124i	$-0.462650\pi$
$977$	7.31839	0.234136	0.117068	+	0.993124i	$0.462650\pi$
$978$	3.44001	0.110000
$979$	6.16593	0.197064
$980$	4.22958	0.135109
$981$	−12.4581	−0.397756
$982$	13.7422	0.438531
$983$	7.36329	0.234852	0.117426	−	0.993082i	$-0.462536\pi$
$983$	7.36329	0.234852	0.117426	+	0.993082i	$0.462536\pi$
$984$	−8.70178	−0.277403
$985$	18.7294	0.596768
$986$	−35.3808	−1.12675
$987$	9.73885	0.309991
$988$	0.846464	0.0269296
$989$	46.5663	1.48072
$990$	0.671799	0.0213512
$991$	41.9301	1.33195	0.665976	−	0.745973i	$-0.268015\pi$
$991$	41.9301	1.33195	0.665976	+	0.745973i	$0.268015\pi$
$992$	−58.7260	−1.86455
$993$	−3.11825	−0.0989545
$994$	9.52337	0.302063
$995$	−53.3694	−1.69192
$996$	−2.56471	−0.0812660
$997$	42.0879	1.33294	0.666468	−	0.745533i	$-0.267805\pi$
$997$	42.0879	1.33294	0.666468	+	0.745533i	$0.267805\pi$
$998$	8.91583	0.282226
$999$	−1.64279	−0.0519755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.j.1.5	✓	7
3.2	odd	2		8001.2.a.l.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.j.1.5	✓	7	1.1	even	1	trivial
8001.2.a.l.1.3		7	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)

\(f(q)\)	\(=\)	\(q+0.692358 q^{2} +1.00000 q^{3} -1.52064 q^{4} -2.78145 q^{5} +0.692358 q^{6} +1.00000 q^{7} -2.43754 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.692358 q^{2} +1.00000 q^{3} -1.52064 q^{4} -2.78145 q^{5} +0.692358 q^{6} +1.00000 q^{7} -2.43754 q^{8} +1.00000 q^{9} -1.92576 q^{10} -0.348849 q^{11} -1.52064 q^{12} +2.17757 q^{13} +0.692358 q^{14} -2.78145 q^{15} +1.35363 q^{16} +7.42626 q^{17} +0.692358 q^{18} -0.255629 q^{19} +4.22958 q^{20} +1.00000 q^{21} -0.241529 q^{22} -4.98233 q^{23} -2.43754 q^{24} +2.73644 q^{25} +1.50766 q^{26} +1.00000 q^{27} -1.52064 q^{28} -6.88124 q^{29} -1.92576 q^{30} -10.1038 q^{31} +5.81228 q^{32} -0.348849 q^{33} +5.14163 q^{34} -2.78145 q^{35} -1.52064 q^{36} -1.64279 q^{37} -0.176987 q^{38} +2.17757 q^{39} +6.77989 q^{40} +3.56990 q^{41} +0.692358 q^{42} -9.34628 q^{43} +0.530475 q^{44} -2.78145 q^{45} -3.44956 q^{46} +9.73885 q^{47} +1.35363 q^{48} +1.00000 q^{49} +1.89460 q^{50} +7.42626 q^{51} -3.31130 q^{52} -7.44666 q^{53} +0.692358 q^{54} +0.970306 q^{55} -2.43754 q^{56} -0.255629 q^{57} -4.76428 q^{58} -2.01055 q^{59} +4.22958 q^{60} -7.69549 q^{61} -6.99543 q^{62} +1.00000 q^{63} +1.31692 q^{64} -6.05678 q^{65} -0.241529 q^{66} -6.52951 q^{67} -11.2927 q^{68} -4.98233 q^{69} -1.92576 q^{70} +13.7550 q^{71} -2.43754 q^{72} -9.37124 q^{73} -1.13740 q^{74} +2.73644 q^{75} +0.388720 q^{76} -0.348849 q^{77} +1.50766 q^{78} -5.92206 q^{79} -3.76505 q^{80} +1.00000 q^{81} +2.47165 q^{82} +1.68660 q^{83} -1.52064 q^{84} -20.6557 q^{85} -6.47097 q^{86} -6.88124 q^{87} +0.850335 q^{88} -17.6750 q^{89} -1.92576 q^{90} +2.17757 q^{91} +7.57634 q^{92} -10.1038 q^{93} +6.74277 q^{94} +0.711019 q^{95} +5.81228 q^{96} -0.216772 q^{97} +0.692358 q^{98} -0.348849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9} - 3 q^{11} + 4 q^{12} - 23 q^{13} - 2 q^{14} - 8 q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - 9 q^{19} - 9 q^{20} + 7 q^{21} - 19 q^{22} + 12 q^{23} - 9 q^{24} + 3 q^{25} + 18 q^{26} + 7 q^{27} + 4 q^{28} - 9 q^{29} - 33 q^{31} + 10 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 4 q^{36} - 33 q^{37} - 3 q^{38} - 23 q^{39} - 9 q^{40} - 3 q^{41} - 2 q^{42} - 9 q^{43} + 2 q^{44} - 8 q^{45} - 32 q^{46} + 11 q^{47} + 2 q^{48} + 7 q^{49} + 29 q^{50} + 3 q^{51} - 21 q^{52} + q^{53} - 2 q^{54} - 16 q^{55} - 9 q^{56} - 9 q^{57} - 5 q^{58} - 30 q^{59} - 9 q^{60} - 19 q^{61} + 3 q^{62} + 7 q^{63} - 21 q^{64} + 14 q^{65} - 19 q^{66} - 30 q^{67} + 24 q^{68} + 12 q^{69} + 8 q^{71} - 9 q^{72} - 20 q^{73} - 9 q^{74} + 3 q^{75} - 42 q^{76} - 3 q^{77} + 18 q^{78} + 8 q^{79} + 12 q^{80} + 7 q^{81} + 10 q^{82} - 34 q^{83} + 4 q^{84} - 28 q^{85} + 24 q^{86} - 9 q^{87} - q^{88} - 12 q^{89} - 23 q^{91} + 60 q^{92} - 33 q^{93} - 3 q^{94} + 12 q^{95} + 10 q^{96} + 7 q^{97} - 2 q^{98} - 3 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 + 7 * q^3 + 4 * q^4 - 8 * q^5 - 2 * q^6 + 7 * q^7 - 9 * q^8 + 7 * q^9 - 3 * q^11 + 4 * q^12 - 23 * q^13 - 2 * q^14 - 8 * q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - 9 * q^19 - 9 * q^20 + 7 * q^21 - 19 * q^22 + 12 * q^23 - 9 * q^24 + 3 * q^25 + 18 * q^26 + 7 * q^27 + 4 * q^28 - 9 * q^29 - 33 * q^31 + 10 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 4 * q^36 - 33 * q^37 - 3 * q^38 - 23 * q^39 - 9 * q^40 - 3 * q^41 - 2 * q^42 - 9 * q^43 + 2 * q^44 - 8 * q^45 - 32 * q^46 + 11 * q^47 + 2 * q^48 + 7 * q^49 + 29 * q^50 + 3 * q^51 - 21 * q^52 + q^53 - 2 * q^54 - 16 * q^55 - 9 * q^56 - 9 * q^57 - 5 * q^58 - 30 * q^59 - 9 * q^60 - 19 * q^61 + 3 * q^62 + 7 * q^63 - 21 * q^64 + 14 * q^65 - 19 * q^66 - 30 * q^67 + 24 * q^68 + 12 * q^69 + 8 * q^71 - 9 * q^72 - 20 * q^73 - 9 * q^74 + 3 * q^75 - 42 * q^76 - 3 * q^77 + 18 * q^78 + 8 * q^79 + 12 * q^80 + 7 * q^81 + 10 * q^82 - 34 * q^83 + 4 * q^84 - 28 * q^85 + 24 * q^86 - 9 * q^87 - q^88 - 12 * q^89 - 23 * q^91 + 60 * q^92 - 33 * q^93 - 3 * q^94 + 12 * q^95 + 10 * q^96 + 7 * q^97 - 2 * q^98 - 3 * q^99

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