LMFDB - Embedded newform 2667.2.a.j.1.2

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			1.2
Root			$-1.14753$ 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)

$f(q)$	$=$	$q-2.15625 q^{2} +1.00000 q^{3} +2.64943 q^{4} -0.239094 q^{5} -2.15625 q^{6} +1.00000 q^{7} -1.40032 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.15625 q^{2} +1.00000 q^{3} +2.64943 q^{4} -0.239094 q^{5} -2.15625 q^{6} +1.00000 q^{7} -1.40032 q^{8} +1.00000 q^{9} +0.515547 q^{10} -3.99784 q^{11} +2.64943 q^{12} -1.61682 q^{13} -2.15625 q^{14} -0.239094 q^{15} -2.27940 q^{16} +4.61421 q^{17} -2.15625 q^{18} -4.17289 q^{19} -0.633462 q^{20} +1.00000 q^{21} +8.62035 q^{22} +5.22408 q^{23} -1.40032 q^{24} -4.94283 q^{25} +3.48627 q^{26} +1.00000 q^{27} +2.64943 q^{28} +9.10130 q^{29} +0.515547 q^{30} -6.57815 q^{31} +7.71560 q^{32} -3.99784 q^{33} -9.94939 q^{34} -0.239094 q^{35} +2.64943 q^{36} -0.353708 q^{37} +8.99781 q^{38} -1.61682 q^{39} +0.334809 q^{40} -7.72038 q^{41} -2.15625 q^{42} -7.33166 q^{43} -10.5920 q^{44} -0.239094 q^{45} -11.2644 q^{46} +3.52396 q^{47} -2.27940 q^{48} +1.00000 q^{49} +10.6580 q^{50} +4.61421 q^{51} -4.28365 q^{52} -0.655025 q^{53} -2.15625 q^{54} +0.955860 q^{55} -1.40032 q^{56} -4.17289 q^{57} -19.6247 q^{58} -11.8415 q^{59} -0.633462 q^{60} -7.05891 q^{61} +14.1842 q^{62} +1.00000 q^{63} -12.0780 q^{64} +0.386572 q^{65} +8.62035 q^{66} -0.167504 q^{67} +12.2250 q^{68} +5.22408 q^{69} +0.515547 q^{70} +6.98566 q^{71} -1.40032 q^{72} -2.79662 q^{73} +0.762683 q^{74} -4.94283 q^{75} -11.0558 q^{76} -3.99784 q^{77} +3.48627 q^{78} +14.2526 q^{79} +0.544990 q^{80} +1.00000 q^{81} +16.6471 q^{82} -6.75526 q^{83} +2.64943 q^{84} -1.10323 q^{85} +15.8089 q^{86} +9.10130 q^{87} +5.59827 q^{88} -11.9943 q^{89} +0.515547 q^{90} -1.61682 q^{91} +13.8408 q^{92} -6.57815 q^{93} -7.59856 q^{94} +0.997714 q^{95} +7.71560 q^{96} -1.79091 q^{97} -2.15625 q^{98} -3.99784 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.15625	−1.52470	−0.762350	−	0.647164i	$-0.775955\pi$
$2$	−2.15625	−1.52470	−0.762350	+	0.647164i	$0.775955\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.64943	1.32471
$5$	−0.239094	−0.106926	−0.0534631	−	0.998570i	$-0.517026\pi$
$5$	−0.239094	−0.106926	−0.0534631	+	0.998570i	$0.517026\pi$
$6$	−2.15625	−0.880286
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.40032	−0.495090
$9$	1.00000	0.333333
$10$	0.515547	0.163030
$11$	−3.99784	−1.20539	−0.602697	−	0.797970i	$-0.705907\pi$
$11$	−3.99784	−1.20539	−0.602697	+	0.797970i	$0.705907\pi$
$12$	2.64943	0.764823
$13$	−1.61682	−0.448425	−0.224213	−	0.974540i	$-0.571981\pi$
$13$	−1.61682	−0.448425	−0.224213	+	0.974540i	$0.571981\pi$
$14$	−2.15625	−0.576283
$15$	−0.239094	−0.0617338
$16$	−2.27940	−0.569849
$17$	4.61421	1.11911	0.559555	−	0.828793i	$-0.310972\pi$
$17$	4.61421	1.11911	0.559555	+	0.828793i	$0.310972\pi$
$18$	−2.15625	−0.508234
$19$	−4.17289	−0.957328	−0.478664	−	0.877998i	$-0.658879\pi$
$19$	−4.17289	−0.957328	−0.478664	+	0.877998i	$0.658879\pi$
$20$	−0.633462	−0.141646
$21$	1.00000	0.218218
$22$	8.62035	1.83786
$23$	5.22408	1.08930	0.544648	−	0.838665i	$-0.316663\pi$
$23$	5.22408	1.08930	0.544648	+	0.838665i	$0.316663\pi$
$24$	−1.40032	−0.285840
$25$	−4.94283	−0.988567
$26$	3.48627	0.683714
$27$	1.00000	0.192450
$28$	2.64943	0.500694
$29$	9.10130	1.69007	0.845035	−	0.534712i	$-0.179580\pi$
$29$	9.10130	1.69007	0.845035	+	0.534712i	$0.179580\pi$
$30$	0.515547	0.0941256
$31$	−6.57815	−1.18147	−0.590736	−	0.806865i	$-0.701162\pi$
$31$	−6.57815	−1.18147	−0.590736	+	0.806865i	$0.701162\pi$
$32$	7.71560	1.36394
$33$	−3.99784	−0.695934
$34$	−9.94939	−1.70631
$35$	−0.239094	−0.0404143
$36$	2.64943	0.441571
$37$	−0.353708	−0.0581492	−0.0290746	−	0.999577i	$-0.509256\pi$
$37$	−0.353708	−0.0581492	−0.0290746	+	0.999577i	$0.509256\pi$
$38$	8.99781	1.45964
$39$	−1.61682	−0.258898
$40$	0.334809	0.0529380
$41$	−7.72038	−1.20572	−0.602860	−	0.797847i	$-0.705972\pi$
$41$	−7.72038	−1.20572	−0.602860	+	0.797847i	$0.705972\pi$
$42$	−2.15625	−0.332717
$43$	−7.33166	−1.11807	−0.559034	−	0.829145i	$-0.688828\pi$
$43$	−7.33166	−1.11807	−0.559034	+	0.829145i	$0.688828\pi$
$44$	−10.5920	−1.59680
$45$	−0.239094	−0.0356420
$46$	−11.2644	−1.66085
$47$	3.52396	0.514023	0.257011	−	0.966408i	$-0.417262\pi$
$47$	3.52396	0.514023	0.257011	+	0.966408i	$0.417262\pi$
$48$	−2.27940	−0.329003
$49$	1.00000	0.142857
$50$	10.6580	1.50727
$51$	4.61421	0.646118
$52$	−4.28365	−0.594035
$53$	−0.655025	−0.0899745	−0.0449873	−	0.998988i	$-0.514325\pi$
$53$	−0.655025	−0.0899745	−0.0449873	+	0.998988i	$0.514325\pi$
$54$	−2.15625	−0.293429
$55$	0.955860	0.128888
$56$	−1.40032	−0.187126
$57$	−4.17289	−0.552713
$58$	−19.6247	−2.57685
$59$	−11.8415	−1.54163	−0.770814	−	0.637060i	$-0.780150\pi$
$59$	−11.8415	−1.54163	−0.770814	+	0.637060i	$0.780150\pi$
$60$	−0.633462	−0.0817796
$61$	−7.05891	−0.903801	−0.451901	−	0.892068i	$-0.649254\pi$
$61$	−7.05891	−0.903801	−0.451901	+	0.892068i	$0.649254\pi$
$62$	14.1842	1.80139
$63$	1.00000	0.125988
$64$	−12.0780	−1.50975
$65$	0.386572	0.0479484
$66$	8.62035	1.06109
$67$	−0.167504	−0.0204638	−0.0102319	−	0.999948i	$-0.503257\pi$
$67$	−0.167504	−0.0204638	−0.0102319	+	0.999948i	$0.503257\pi$
$68$	12.2250	1.48250
$69$	5.22408	0.628905
$70$	0.515547	0.0616197
$71$	6.98566	0.829045	0.414523	−	0.910039i	$-0.363949\pi$
$71$	6.98566	0.829045	0.414523	+	0.910039i	$0.363949\pi$
$72$	−1.40032	−0.165030
$73$	−2.79662	−0.327320	−0.163660	−	0.986517i	$-0.552330\pi$
$73$	−2.79662	−0.327320	−0.163660	+	0.986517i	$0.552330\pi$
$74$	0.762683	0.0886601
$75$	−4.94283	−0.570749
$76$	−11.0558	−1.26818
$77$	−3.99784	−0.455596
$78$	3.48627	0.394743
$79$	14.2526	1.60354	0.801770	−	0.597633i	$-0.203892\pi$
$79$	14.2526	1.60354	0.801770	+	0.597633i	$0.203892\pi$
$80$	0.544990	0.0609317
$81$	1.00000	0.111111
$82$	16.6471	1.83836
$83$	−6.75526	−0.741486	−0.370743	−	0.928735i	$-0.620897\pi$
$83$	−6.75526	−0.741486	−0.370743	+	0.928735i	$0.620897\pi$
$84$	2.64943	0.289076
$85$	−1.10323	−0.119662
$86$	15.8089	1.70472
$87$	9.10130	0.975762
$88$	5.59827	0.596778
$89$	−11.9943	−1.27140	−0.635698	−	0.771938i	$-0.719288\pi$
$89$	−11.9943	−1.27140	−0.635698	+	0.771938i	$0.719288\pi$
$90$	0.515547	0.0543434
$91$	−1.61682	−0.169489
$92$	13.8408	1.44300
$93$	−6.57815	−0.682123
$94$	−7.59856	−0.783731
$95$	0.997714	0.102363
$96$	7.71560	0.787471
$97$	−1.79091	−0.181840	−0.0909199	−	0.995858i	$-0.528981\pi$
$97$	−1.79091	−0.181840	−0.0909199	+	0.995858i	$0.528981\pi$
$98$	−2.15625	−0.217814
$99$	−3.99784	−0.401798
$100$	−13.0957	−1.30957
$101$	−11.0925	−1.10375	−0.551873	−	0.833928i	$-0.686087\pi$
$101$	−11.0925	−1.10375	−0.551873	+	0.833928i	$0.686087\pi$
$102$	−9.94939	−0.985137
$103$	14.5981	1.43839	0.719197	−	0.694806i	$-0.244510\pi$
$103$	14.5981	1.43839	0.719197	+	0.694806i	$0.244510\pi$
$104$	2.26407	0.222011
$105$	−0.239094	−0.0233332
$106$	1.41240	0.137184
$107$	10.6926	1.03369	0.516845	−	0.856079i	$-0.327106\pi$
$107$	10.6926	1.03369	0.516845	+	0.856079i	$0.327106\pi$
$108$	2.64943	0.254941
$109$	−19.1750	−1.83664	−0.918318	−	0.395844i	$-0.870452\pi$
$109$	−19.1750	−1.83664	−0.918318	+	0.395844i	$0.870452\pi$
$110$	−2.06107	−0.196516
$111$	−0.353708	−0.0335725
$112$	−2.27940	−0.215383
$113$	−13.9603	−1.31327	−0.656636	−	0.754208i	$-0.728021\pi$
$113$	−13.9603	−1.31327	−0.656636	+	0.754208i	$0.728021\pi$
$114$	8.99781	0.842722
$115$	−1.24905	−0.116474
$116$	24.1132	2.23886
$117$	−1.61682	−0.149475
$118$	25.5332	2.35052
$119$	4.61421	0.422984
$120$	0.334809	0.0305638
$121$	4.98272	0.452974
$122$	15.2208	1.37803
$123$	−7.72038	−0.696123
$124$	−17.4283	−1.56511
$125$	2.37727	0.212630
$126$	−2.15625	−0.192094
$127$	−1.00000	−0.0887357
$127$	−1.00000	−0.0887357
$128$	10.6120	0.937978
$129$	−7.33166	−0.645516
$130$	−0.833547	−0.0731069
$131$	−1.23738	−0.108111	−0.0540553	−	0.998538i	$-0.517215\pi$
$131$	−1.23738	−0.108111	−0.0540553	+	0.998538i	$0.517215\pi$
$132$	−10.5920	−0.921913
$133$	−4.17289	−0.361836
$134$	0.361180	0.0312012
$135$	−0.239094	−0.0205779
$136$	−6.46139	−0.554059
$137$	−5.10054	−0.435769	−0.217884	−	0.975975i	$-0.569916\pi$
$137$	−5.10054	−0.435769	−0.217884	+	0.975975i	$0.569916\pi$
$138$	−11.2644	−0.958892
$139$	12.5215	1.06206	0.531032	−	0.847352i	$-0.321805\pi$
$139$	12.5215	1.06206	0.531032	+	0.847352i	$0.321805\pi$
$140$	−0.633462	−0.0535373
$141$	3.52396	0.296771
$142$	−15.0628	−1.26405
$143$	6.46379	0.540529
$144$	−2.27940	−0.189950
$145$	−2.17607	−0.180713
$146$	6.03022	0.499065
$147$	1.00000	0.0824786
$148$	−0.937122	−0.0770310
$149$	9.58767	0.785452	0.392726	−	0.919655i	$-0.371532\pi$
$149$	9.58767	0.785452	0.392726	+	0.919655i	$0.371532\pi$
$150$	10.6580	0.870222
$151$	−17.1326	−1.39423	−0.697117	−	0.716957i	$-0.745534\pi$
$151$	−17.1326	−1.39423	−0.697117	+	0.716957i	$0.745534\pi$
$152$	5.84341	0.473963
$153$	4.61421	0.373036
$154$	8.62035	0.694648
$155$	1.57280	0.126330
$156$	−4.28365	−0.342966
$157$	7.98480	0.637257	0.318628	−	0.947880i	$-0.396778\pi$
$157$	7.98480	0.637257	0.318628	+	0.947880i	$0.396778\pi$
$158$	−30.7322	−2.44492
$159$	−0.655025	−0.0519468
$160$	−1.84476	−0.145841
$161$	5.22408	0.411715
$162$	−2.15625	−0.169411
$163$	5.01915	0.393130	0.196565	−	0.980491i	$-0.437021\pi$
$163$	5.01915	0.393130	0.196565	+	0.980491i	$0.437021\pi$
$164$	−20.4546	−1.59723
$165$	0.955860	0.0744136
$166$	14.5661	1.13055
$167$	7.58516	0.586958	0.293479	−	0.955966i	$-0.405187\pi$
$167$	7.58516	0.586958	0.293479	+	0.955966i	$0.405187\pi$
$168$	−1.40032	−0.108037
$169$	−10.3859	−0.798915
$170$	2.37884	0.182449
$171$	−4.17289	−0.319109
$172$	−19.4247	−1.48112
$173$	−4.01343	−0.305135	−0.152568	−	0.988293i	$-0.548754\pi$
$173$	−4.01343	−0.305135	−0.152568	+	0.988293i	$0.548754\pi$
$174$	−19.6247	−1.48775
$175$	−4.94283	−0.373643
$176$	9.11266	0.686893
$177$	−11.8415	−0.890059
$178$	25.8628	1.93850
$179$	−24.8302	−1.85590	−0.927948	−	0.372711i	$-0.878428\pi$
$179$	−24.8302	−1.85590	−0.927948	+	0.372711i	$0.878428\pi$
$180$	−0.633462	−0.0472155
$181$	7.31346	0.543606	0.271803	−	0.962353i	$-0.412380\pi$
$181$	7.31346	0.543606	0.271803	+	0.962353i	$0.412380\pi$
$182$	3.48627	0.258420
$183$	−7.05891	−0.521810
$184$	−7.31540	−0.539299
$185$	0.0845694	0.00621767
$186$	14.1842	1.04003
$187$	−18.4469	−1.34897
$188$	9.33648	0.680933
$189$	1.00000	0.0727393
$190$	−2.15132	−0.156073
$191$	−12.4008	−0.897293	−0.448646	−	0.893709i	$-0.648094\pi$
$191$	−12.4008	−0.897293	−0.448646	+	0.893709i	$0.648094\pi$
$192$	−12.0780	−0.871654
$193$	16.0448	1.15493	0.577465	−	0.816415i	$-0.304042\pi$
$193$	16.0448	1.15493	0.577465	+	0.816415i	$0.304042\pi$
$194$	3.86166	0.277251
$195$	0.386572	0.0276830
$196$	2.64943	0.189245
$197$	12.1872	0.868304	0.434152	−	0.900840i	$-0.357048\pi$
$197$	12.1872	0.868304	0.434152	+	0.900840i	$0.357048\pi$
$198$	8.62035	0.612622
$199$	13.7816	0.976950	0.488475	−	0.872578i	$-0.337553\pi$
$199$	13.7816	0.976950	0.488475	+	0.872578i	$0.337553\pi$
$200$	6.92157	0.489429
$201$	−0.167504	−0.0118148
$202$	23.9183	1.68288
$203$	9.10130	0.638786
$204$	12.2250	0.855921
$205$	1.84590	0.128923
$206$	−31.4772	−2.19312
$207$	5.22408	0.363098
$208$	3.68537	0.255535
$209$	16.6826	1.15396
$210$	0.515547	0.0355761
$211$	−12.3776	−0.852111	−0.426056	−	0.904697i	$-0.640097\pi$
$211$	−12.3776	−0.852111	−0.426056	+	0.904697i	$0.640097\pi$
$212$	−1.73544	−0.119190
$213$	6.98566	0.478649
$214$	−23.0559	−1.57607
$215$	1.75296	0.119551
$216$	−1.40032	−0.0952800
$217$	−6.57815	−0.446554
$218$	41.3462	2.80032
$219$	−2.79662	−0.188978
$220$	2.53248	0.170740
$221$	−7.46034	−0.501837
$222$	0.762683	0.0511879
$223$	−16.9298	−1.13370	−0.566852	−	0.823819i	$-0.691839\pi$
$223$	−16.9298	−1.13370	−0.566852	+	0.823819i	$0.691839\pi$
$224$	7.71560	0.515520
$225$	−4.94283	−0.329522
$226$	30.1019	2.00235
$227$	−14.4225	−0.957256	−0.478628	−	0.878018i	$-0.658866\pi$
$227$	−14.4225	−0.957256	−0.478628	+	0.878018i	$0.658866\pi$
$228$	−11.0558	−0.732186
$229$	−16.4164	−1.08483	−0.542414	−	0.840111i	$-0.682490\pi$
$229$	−16.4164	−1.08483	−0.542414	+	0.840111i	$0.682490\pi$
$230$	2.69326	0.177588
$231$	−3.99784	−0.263039
$232$	−12.7448	−0.836736
$233$	−7.64997	−0.501167	−0.250583	−	0.968095i	$-0.580622\pi$
$233$	−7.64997	−0.501167	−0.250583	+	0.968095i	$0.580622\pi$
$234$	3.48627	0.227905
$235$	−0.842559	−0.0549625
$236$	−31.3731	−2.04221
$237$	14.2526	0.925804
$238$	−9.94939	−0.644923
$239$	8.03695	0.519867	0.259933	−	0.965627i	$-0.416299\pi$
$239$	8.03695	0.519867	0.259933	+	0.965627i	$0.416299\pi$
$240$	0.544990	0.0351790
$241$	−22.8036	−1.46891	−0.734456	−	0.678657i	$-0.762562\pi$
$241$	−22.8036	−1.46891	−0.734456	+	0.678657i	$0.762562\pi$
$242$	−10.7440	−0.690650
$243$	1.00000	0.0641500
$244$	−18.7021	−1.19728
$245$	−0.239094	−0.0152752
$246$	16.6471	1.06138
$247$	6.74682	0.429290
$248$	9.21155	0.584934
$249$	−6.75526	−0.428097
$250$	−5.12600	−0.324197
$251$	−2.22670	−0.140548	−0.0702739	−	0.997528i	$-0.522387\pi$
$251$	−2.22670	−0.140548	−0.0702739	+	0.997528i	$0.522387\pi$
$252$	2.64943	0.166898
$253$	−20.8850	−1.31303
$254$	2.15625	0.135295
$255$	−1.10323	−0.0690869
$256$	1.27383	0.0796142
$257$	12.7786	0.797110	0.398555	−	0.917144i	$-0.369512\pi$
$257$	12.7786	0.797110	0.398555	+	0.917144i	$0.369512\pi$
$258$	15.8089	0.984219
$259$	−0.353708	−0.0219783
$260$	1.02419	0.0635178
$261$	9.10130	0.563356
$262$	2.66811	0.164836
$263$	1.91222	0.117912	0.0589562	−	0.998261i	$-0.481223\pi$
$263$	1.91222	0.117912	0.0589562	+	0.998261i	$0.481223\pi$
$264$	5.59827	0.344550
$265$	0.156612	0.00962063
$266$	8.99781	0.551691
$267$	−11.9943	−0.734041
$268$	−0.443788	−0.0271087
$269$	7.78586	0.474712	0.237356	−	0.971423i	$-0.423719\pi$
$269$	7.78586	0.474712	0.237356	+	0.971423i	$0.423719\pi$
$270$	0.515547	0.0313752
$271$	−10.3228	−0.627064	−0.313532	−	0.949578i	$-0.601512\pi$
$271$	−10.3228	−0.627064	−0.313532	+	0.949578i	$0.601512\pi$
$272$	−10.5176	−0.637723
$273$	−1.61682	−0.0978544
$274$	10.9981	0.664417
$275$	19.7607	1.19161
$276$	13.8408	0.833118
$277$	−13.1278	−0.788776	−0.394388	−	0.918944i	$-0.629043\pi$
$277$	−13.1278	−0.788776	−0.394388	+	0.918944i	$0.629043\pi$
$278$	−26.9996	−1.61933
$279$	−6.57815	−0.393824
$280$	0.334809	0.0200087
$281$	18.1404	1.08216	0.541081	−	0.840970i	$-0.318015\pi$
$281$	18.1404	1.08216	0.541081	+	0.840970i	$0.318015\pi$
$282$	−7.59856	−0.452487
$283$	−19.1287	−1.13708	−0.568542	−	0.822655i	$-0.692492\pi$
$283$	−19.1287	−1.13708	−0.568542	+	0.822655i	$0.692492\pi$
$284$	18.5080	1.09825
$285$	0.997714	0.0590995
$286$	−13.9376	−0.824145
$287$	−7.72038	−0.455720
$288$	7.71560	0.454646
$289$	4.29089	0.252406
$290$	4.69215	0.275533
$291$	−1.79091	−0.104985
$292$	−7.40944	−0.433604
$293$	−26.6893	−1.55921	−0.779603	−	0.626274i	$-0.784579\pi$
$293$	−26.6893	−1.55921	−0.779603	+	0.626274i	$0.784579\pi$
$294$	−2.15625	−0.125755
$295$	2.83122	0.164840
$296$	0.495306	0.0287891
$297$	−3.99784	−0.231978
$298$	−20.6734	−1.19758
$299$	−8.44639	−0.488468
$300$	−13.0957	−0.756079
$301$	−7.33166	−0.422590
$302$	36.9423	2.12579
$303$	−11.0925	−0.637249
$304$	9.51168	0.545532
$305$	1.68774	0.0966400
$306$	−9.94939	−0.568769
$307$	9.45867	0.539835	0.269917	−	0.962883i	$-0.413004\pi$
$307$	9.45867	0.539835	0.269917	+	0.962883i	$0.413004\pi$
$308$	−10.5920	−0.603534
$309$	14.5981	0.830458
$310$	−3.39135	−0.192616
$311$	1.98631	0.112633	0.0563167	−	0.998413i	$-0.482064\pi$
$311$	1.98631	0.112633	0.0563167	+	0.998413i	$0.482064\pi$
$312$	2.26407	0.128178
$313$	−20.0441	−1.13296	−0.566480	−	0.824075i	$-0.691695\pi$
$313$	−20.0441	−1.13296	−0.566480	+	0.824075i	$0.691695\pi$
$314$	−17.2173	−0.971626
$315$	−0.239094	−0.0134714
$316$	37.7611	2.12423
$317$	−27.2490	−1.53046	−0.765228	−	0.643760i	$-0.777374\pi$
$317$	−27.2490	−1.53046	−0.765228	+	0.643760i	$0.777374\pi$
$318$	1.41240	0.0792034
$319$	−36.3855	−2.03720
$320$	2.88778	0.161432
$321$	10.6926	0.596801
$322$	−11.2644	−0.627742
$323$	−19.2546	−1.07135
$324$	2.64943	0.147190
$325$	7.99168	0.443298
$326$	−10.8226	−0.599406
$327$	−19.1750	−1.06038
$328$	10.8110	0.596940
$329$	3.52396	0.194282
$330$	−2.06107	−0.113458
$331$	34.0423	1.87113	0.935567	−	0.353150i	$-0.114889\pi$
$331$	34.0423	1.87113	0.935567	+	0.353150i	$0.114889\pi$
$332$	−17.8976	−0.982256
$333$	−0.353708	−0.0193831
$334$	−16.3555	−0.894935
$335$	0.0400491	0.00218812
$336$	−2.27940	−0.124351
$337$	−13.1131	−0.714318	−0.357159	−	0.934044i	$-0.616255\pi$
$337$	−13.1131	−0.714318	−0.357159	+	0.934044i	$0.616255\pi$
$338$	22.3946	1.21811
$339$	−13.9603	−0.758218
$340$	−2.92292	−0.158518
$341$	26.2984	1.42414
$342$	8.99781	0.486546
$343$	1.00000	0.0539949
$344$	10.2667	0.553543
$345$	−1.24905	−0.0672464
$346$	8.65396	0.465240
$347$	−8.22380	−0.441477	−0.220738	−	0.975333i	$-0.570847\pi$
$347$	−8.22380	−0.441477	−0.220738	+	0.975333i	$0.570847\pi$
$348$	24.1132	1.29260
$349$	−22.6433	−1.21207	−0.606035	−	0.795438i	$-0.707241\pi$
$349$	−22.6433	−1.21207	−0.606035	+	0.795438i	$0.707241\pi$
$350$	10.6580	0.569694
$351$	−1.61682	−0.0862995
$352$	−30.8457	−1.64408
$353$	−22.9217	−1.22000	−0.610000	−	0.792401i	$-0.708831\pi$
$353$	−22.9217	−1.22000	−0.610000	+	0.792401i	$0.708831\pi$
$354$	25.5332	1.35707
$355$	−1.67023	−0.0886466
$356$	−31.7781	−1.68423
$357$	4.61421	0.244210
$358$	53.5402	2.82969
$359$	22.9728	1.21246	0.606230	−	0.795289i	$-0.292681\pi$
$359$	22.9728	1.21246	0.606230	+	0.795289i	$0.292681\pi$
$360$	0.334809	0.0176460
$361$	−1.58696	−0.0835240
$362$	−15.7697	−0.828836
$363$	4.98272	0.261525
$364$	−4.28365	−0.224524
$365$	0.668655	0.0349990
$366$	15.2208	0.795604
$367$	−2.80411	−0.146373	−0.0731866	−	0.997318i	$-0.523317\pi$
$367$	−2.80411	−0.146373	−0.0731866	+	0.997318i	$0.523317\pi$
$368$	−11.9077	−0.620734
$369$	−7.72038	−0.401907
$370$	−0.182353	−0.00948008
$371$	−0.655025	−0.0340072
$372$	−17.4283	−0.903617
$373$	−35.2417	−1.82475	−0.912374	−	0.409358i	$-0.865753\pi$
$373$	−35.2417	−1.82475	−0.912374	+	0.409358i	$0.865753\pi$
$374$	39.7761	2.05677
$375$	2.37727	0.122762
$376$	−4.93469	−0.254487
$377$	−14.7152	−0.757870
$378$	−2.15625	−0.110906
$379$	−8.26039	−0.424308	−0.212154	−	0.977236i	$-0.568048\pi$
$379$	−8.26039	−0.424308	−0.212154	+	0.977236i	$0.568048\pi$
$380$	2.64337	0.135602
$381$	−1.00000	−0.0512316
$382$	26.7393	1.36810
$383$	−6.69505	−0.342101	−0.171050	−	0.985262i	$-0.554716\pi$
$383$	−6.69505	−0.342101	−0.171050	+	0.985262i	$0.554716\pi$
$384$	10.6120	0.541542
$385$	0.955860	0.0487151
$386$	−34.5966	−1.76092
$387$	−7.33166	−0.372689
$388$	−4.74489	−0.240885
$389$	−13.4050	−0.679658	−0.339829	−	0.940487i	$-0.610369\pi$
$389$	−13.4050	−0.679658	−0.339829	+	0.940487i	$0.610369\pi$
$390$	−0.833547	−0.0422083
$391$	24.1050	1.21904
$392$	−1.40032	−0.0707271
$393$	−1.23738	−0.0624176
$394$	−26.2787	−1.32390
$395$	−3.40771	−0.171460
$396$	−10.5920	−0.532267
$397$	1.27937	0.0642097	0.0321048	−	0.999485i	$-0.489779\pi$
$397$	1.27937	0.0642097	0.0321048	+	0.999485i	$0.489779\pi$
$398$	−29.7165	−1.48956
$399$	−4.17289	−0.208906
$400$	11.2667	0.563334
$401$	−25.8637	−1.29157	−0.645785	−	0.763519i	$-0.723470\pi$
$401$	−25.8637	−1.29157	−0.645785	+	0.763519i	$0.723470\pi$
$402$	0.361180	0.0180140
$403$	10.6357	0.529802
$404$	−29.3888	−1.46215
$405$	−0.239094	−0.0118807
$406$	−19.6247	−0.973958
$407$	1.41407	0.0700927
$408$	−6.46139	−0.319886
$409$	−8.40634	−0.415667	−0.207833	−	0.978164i	$-0.566641\pi$
$409$	−8.40634	−0.415667	−0.207833	+	0.978164i	$0.566641\pi$
$410$	−3.98022	−0.196569
$411$	−5.10054	−0.251591
$412$	38.6766	1.90546
$413$	−11.8415	−0.582681
$414$	−11.2644	−0.553616
$415$	1.61514	0.0792843
$416$	−12.4747	−0.611625
$417$	12.5215	0.613183
$418$	−35.9718	−1.75944
$419$	12.0193	0.587183	0.293592	−	0.955931i	$-0.405149\pi$
$419$	12.0193	0.587183	0.293592	+	0.955931i	$0.405149\pi$
$420$	−0.633462	−0.0309098
$421$	27.5197	1.34123	0.670614	−	0.741807i	$-0.266031\pi$
$421$	27.5197	1.34123	0.670614	+	0.741807i	$0.266031\pi$
$422$	26.6893	1.29922
$423$	3.52396	0.171341
$424$	0.917247	0.0445455
$425$	−22.8073	−1.10631
$426$	−15.0628	−0.729797
$427$	−7.05891	−0.341605
$428$	28.3292	1.36934
$429$	6.46379	0.312075
$430$	−3.77981	−0.182279
$431$	35.4733	1.70869	0.854345	−	0.519707i	$-0.173959\pi$
$431$	35.4733	1.70869	0.854345	+	0.519707i	$0.173959\pi$
$432$	−2.27940	−0.109668
$433$	26.5237	1.27465	0.637323	−	0.770597i	$-0.280042\pi$
$433$	26.5237	1.27465	0.637323	+	0.770597i	$0.280042\pi$
$434$	14.1842	0.680862
$435$	−2.17607	−0.104334
$436$	−50.8028	−2.43301
$437$	−21.7995	−1.04281
$438$	6.03022	0.288135
$439$	−32.6301	−1.55735	−0.778674	−	0.627428i	$-0.784108\pi$
$439$	−32.6301	−1.55735	−0.778674	+	0.627428i	$0.784108\pi$
$440$	−1.33851	−0.0638111
$441$	1.00000	0.0476190
$442$	16.0864	0.765151
$443$	16.0947	0.764681	0.382340	−	0.924022i	$-0.375118\pi$
$443$	16.0947	0.764681	0.382340	+	0.924022i	$0.375118\pi$
$444$	−0.937122	−0.0444739
$445$	2.86777	0.135945
$446$	36.5050	1.72856
$447$	9.58767	0.453481
$448$	−12.0780	−0.570632
$449$	33.1478	1.56434	0.782171	−	0.623064i	$-0.214112\pi$
$449$	33.1478	1.56434	0.782171	+	0.623064i	$0.214112\pi$
$450$	10.6580	0.502423
$451$	30.8648	1.45337
$452$	−36.9867	−1.73971
$453$	−17.1326	−0.804962
$454$	31.0986	1.45953
$455$	0.386572	0.0181228
$456$	5.84341	0.273643
$457$	−20.7795	−0.972026	−0.486013	−	0.873952i	$-0.661549\pi$
$457$	−20.7795	−0.972026	−0.486013	+	0.873952i	$0.661549\pi$
$458$	35.3980	1.65404
$459$	4.61421	0.215373
$460$	−3.30925	−0.154295
$461$	26.0027	1.21106	0.605532	−	0.795821i	$-0.292960\pi$
$461$	26.0027	1.21106	0.605532	+	0.795821i	$0.292960\pi$
$462$	8.62035	0.401055
$463$	1.40695	0.0653867	0.0326934	−	0.999465i	$-0.489592\pi$
$463$	1.40695	0.0653867	0.0326934	+	0.999465i	$0.489592\pi$
$464$	−20.7455	−0.963084
$465$	1.57280	0.0729367
$466$	16.4953	0.764129
$467$	−4.52880	−0.209568	−0.104784	−	0.994495i	$-0.533415\pi$
$467$	−4.52880	−0.209568	−0.104784	+	0.994495i	$0.533415\pi$
$468$	−4.28365	−0.198012
$469$	−0.167504	−0.00773460
$470$	1.81677	0.0838013
$471$	7.98480	0.367920
$472$	16.5819	0.763244
$473$	29.3108	1.34771
$474$	−30.7322	−1.41157
$475$	20.6259	0.946382
$476$	12.2250	0.560332
$477$	−0.655025	−0.0299915
$478$	−17.3297	−0.792641
$479$	1.74794	0.0798653	0.0399327	−	0.999202i	$-0.487286\pi$
$479$	1.74794	0.0798653	0.0399327	+	0.999202i	$0.487286\pi$
$480$	−1.84476	−0.0842012
$481$	0.571882	0.0260756
$482$	49.1704	2.23965
$483$	5.22408	0.237704
$484$	13.2013	0.600061
$485$	0.428197	0.0194434
$486$	−2.15625	−0.0978096
$487$	−25.2382	−1.14365	−0.571827	−	0.820375i	$-0.693765\pi$
$487$	−25.2382	−1.14365	−0.571827	+	0.820375i	$0.693765\pi$
$488$	9.88477	0.447463
$489$	5.01915	0.226974
$490$	0.515547	0.0232900
$491$	−27.1705	−1.22619	−0.613093	−	0.790010i	$-0.710075\pi$
$491$	−27.1705	−1.22619	−0.613093	+	0.790010i	$0.710075\pi$
$492$	−20.4546	−0.922163
$493$	41.9953	1.89137
$494$	−14.5478	−0.654539
$495$	0.955860	0.0429627
$496$	14.9942	0.673260
$497$	6.98566	0.313350
$498$	14.5661	0.652720
$499$	−18.9409	−0.847909	−0.423955	−	0.905683i	$-0.639358\pi$
$499$	−18.9409	−0.847909	−0.423955	+	0.905683i	$0.639358\pi$
$500$	6.29841	0.281673
$501$	7.58516	0.338880
$502$	4.80132	0.214293
$503$	−2.52810	−0.112722	−0.0563611	−	0.998410i	$-0.517950\pi$
$503$	−2.52810	−0.112722	−0.0563611	+	0.998410i	$0.517950\pi$
$504$	−1.40032	−0.0623754
$505$	2.65216	0.118019
$506$	45.0334	2.00198
$507$	−10.3859	−0.461254
$508$	−2.64943	−0.117549
$509$	34.9093	1.54733	0.773663	−	0.633598i	$-0.218422\pi$
$509$	34.9093	1.54733	0.773663	+	0.633598i	$0.218422\pi$
$510$	2.37884	0.105337
$511$	−2.79662	−0.123715
$512$	−23.9707	−1.05937
$513$	−4.17289	−0.184238
$514$	−27.5540	−1.21535
$515$	−3.49032	−0.153802
$516$	−19.4247	−0.855124
$517$	−14.0882	−0.619600
$518$	0.762683	0.0335104
$519$	−4.01343	−0.176170
$520$	−0.541327	−0.0237387
$521$	8.56576	0.375273	0.187636	−	0.982239i	$-0.439917\pi$
$521$	8.56576	0.375273	0.187636	+	0.982239i	$0.439917\pi$
$522$	−19.6247	−0.858950
$523$	2.00260	0.0875675	0.0437838	−	0.999041i	$-0.486059\pi$
$523$	2.00260	0.0875675	0.0437838	+	0.999041i	$0.486059\pi$
$524$	−3.27835	−0.143215
$525$	−4.94283	−0.215723
$526$	−4.12322	−0.179781
$527$	−30.3530	−1.32220
$528$	9.11266	0.396578
$529$	4.29098	0.186564
$530$	−0.337696	−0.0146686
$531$	−11.8415	−0.513876
$532$	−11.0558	−0.479328
$533$	12.4825	0.540676
$534$	25.8628	1.11919
$535$	−2.55653	−0.110528
$536$	0.234559	0.0101314
$537$	−24.8302	−1.07150
$538$	−16.7883	−0.723794
$539$	−3.99784	−0.172199
$540$	−0.633462	−0.0272599
$541$	−14.8542	−0.638632	−0.319316	−	0.947648i	$-0.603453\pi$
$541$	−14.8542	−0.638632	−0.319316	+	0.947648i	$0.603453\pi$
$542$	22.2585	0.956085
$543$	7.31346	0.313851
$544$	35.6014	1.52640
$545$	4.58464	0.196384
$546$	3.48627	0.149199
$547$	9.86356	0.421735	0.210868	−	0.977515i	$-0.432371\pi$
$547$	9.86356	0.421735	0.210868	+	0.977515i	$0.432371\pi$
$548$	−13.5135	−0.577268
$549$	−7.05891	−0.301267
$550$	−42.6090	−1.81685
$551$	−37.9788	−1.61795
$552$	−7.31540	−0.311364
$553$	14.2526	0.606081
$554$	28.3069	1.20265
$555$	0.0845694	0.00358977
$556$	33.1749	1.40693
$557$	−1.50087	−0.0635939	−0.0317970	−	0.999494i	$-0.510123\pi$
$557$	−1.50087	−0.0635939	−0.0317970	+	0.999494i	$0.510123\pi$
$558$	14.1842	0.600463
$559$	11.8540	0.501370
$560$	0.544990	0.0230300
$561$	−18.4469	−0.778827
$562$	−39.1152	−1.64997
$563$	40.5430	1.70868	0.854341	−	0.519713i	$-0.173961\pi$
$563$	40.5430	1.70868	0.854341	+	0.519713i	$0.173961\pi$
$564$	9.33648	0.393137
$565$	3.33782	0.140423
$566$	41.2463	1.73371
$567$	1.00000	0.0419961
$568$	−9.78219	−0.410452
$569$	3.51593	0.147396	0.0736978	−	0.997281i	$-0.476520\pi$
$569$	3.51593	0.147396	0.0736978	+	0.997281i	$0.476520\pi$
$570$	−2.15132	−0.0901090
$571$	−39.7252	−1.66245	−0.831224	−	0.555937i	$-0.812359\pi$
$571$	−39.7252	−1.66245	−0.831224	+	0.555937i	$0.812359\pi$
$572$	17.1253	0.716046
$573$	−12.4008	−0.518052
$574$	16.6471	0.694836
$575$	−25.8217	−1.07684
$576$	−12.0780	−0.503250
$577$	34.1969	1.42364	0.711818	−	0.702364i	$-0.247872\pi$
$577$	34.1969	1.42364	0.711818	+	0.702364i	$0.247872\pi$
$578$	−9.25225	−0.384843
$579$	16.0448	0.666799
$580$	−5.76533	−0.239392
$581$	−6.75526	−0.280256
$582$	3.86166	0.160071
$583$	2.61868	0.108455
$584$	3.91618	0.162053
$585$	0.386572	0.0159828
$586$	57.5489	2.37732
$587$	−14.5520	−0.600625	−0.300313	−	0.953841i	$-0.597091\pi$
$587$	−14.5520	−0.600625	−0.300313	+	0.953841i	$0.597091\pi$
$588$	2.64943	0.109260
$589$	27.4499	1.13105
$590$	−6.10483	−0.251332
$591$	12.1872	0.501315
$592$	0.806240	0.0331363
$593$	−22.6700	−0.930947	−0.465473	−	0.885062i	$-0.654116\pi$
$593$	−22.6700	−0.930947	−0.465473	+	0.885062i	$0.654116\pi$
$594$	8.62035	0.353697
$595$	−1.10323	−0.0452280
$596$	25.4018	1.04050
$597$	13.7816	0.564042
$598$	18.2126	0.744767
$599$	19.5665	0.799466	0.399733	−	0.916632i	$-0.369103\pi$
$599$	19.5665	0.799466	0.399733	+	0.916632i	$0.369103\pi$
$600$	6.92157	0.282572
$601$	7.31719	0.298475	0.149237	−	0.988801i	$-0.452318\pi$
$601$	7.31719	0.298475	0.149237	+	0.988801i	$0.452318\pi$
$602$	15.8089	0.644323
$603$	−0.167504	−0.00682127
$604$	−45.3917	−1.84696
$605$	−1.19134	−0.0484348
$606$	23.9183	0.971613
$607$	25.1482	1.02074	0.510368	−	0.859956i	$-0.329509\pi$
$607$	25.1482	1.02074	0.510368	+	0.859956i	$0.329509\pi$
$608$	−32.1964	−1.30574
$609$	9.10130	0.368803
$610$	−3.63920	−0.147347
$611$	−5.69762	−0.230501
$612$	12.2250	0.494166
$613$	40.8861	1.65137	0.825686	−	0.564129i	$-0.190788\pi$
$613$	40.8861	1.65137	0.825686	+	0.564129i	$0.190788\pi$
$614$	−20.3953	−0.823087
$615$	1.84590	0.0744338
$616$	5.59827	0.225561
$617$	23.3040	0.938185	0.469092	−	0.883149i	$-0.344581\pi$
$617$	23.3040	0.938185	0.469092	+	0.883149i	$0.344581\pi$
$618$	−31.4772	−1.26620
$619$	36.2218	1.45588	0.727939	−	0.685642i	$-0.240478\pi$
$619$	36.2218	1.45588	0.727939	+	0.685642i	$0.240478\pi$
$620$	4.16701	0.167351
$621$	5.22408	0.209635
$622$	−4.28299	−0.171732
$623$	−11.9943	−0.480543
$624$	3.68537	0.147533
$625$	24.1458	0.965831
$626$	43.2202	1.72743
$627$	16.6826	0.666237
$628$	21.1551	0.844182
$629$	−1.63208	−0.0650753
$630$	0.515547	0.0205399
$631$	44.1474	1.75748	0.878741	−	0.477299i	$-0.158384\pi$
$631$	44.1474	1.75748	0.878741	+	0.477299i	$0.158384\pi$
$632$	−19.9582	−0.793896
$633$	−12.3776	−0.491967
$634$	58.7557	2.33349
$635$	0.239094	0.00948816
$636$	−1.73544	−0.0688146
$637$	−1.61682	−0.0640608
$638$	78.4564	3.10612
$639$	6.98566	0.276348
$640$	−2.53727	−0.100294
$641$	20.5976	0.813557	0.406779	−	0.913527i	$-0.366652\pi$
$641$	20.5976	0.813557	0.406779	+	0.913527i	$0.366652\pi$
$642$	−23.0559	−0.909943
$643$	−3.13591	−0.123668	−0.0618342	−	0.998086i	$-0.519695\pi$
$643$	−3.13591	−0.123668	−0.0618342	+	0.998086i	$0.519695\pi$
$644$	13.8408	0.545404
$645$	1.75296	0.0690226
$646$	41.5178	1.63349
$647$	6.98764	0.274712	0.137356	−	0.990522i	$-0.456139\pi$
$647$	6.98764	0.274712	0.137356	+	0.990522i	$0.456139\pi$
$648$	−1.40032	−0.0550100
$649$	47.3403	1.85827
$650$	−17.2321	−0.675897
$651$	−6.57815	−0.257818
$652$	13.2979	0.520784
$653$	18.7511	0.733786	0.366893	−	0.930263i	$-0.380422\pi$
$653$	18.7511	0.733786	0.366893	+	0.930263i	$0.380422\pi$
$654$	41.3462	1.61677
$655$	0.295851	0.0115598
$656$	17.5978	0.687079
$657$	−2.79662	−0.109107
$658$	−7.59856	−0.296223
$659$	28.0273	1.09179	0.545895	−	0.837854i	$-0.316190\pi$
$659$	28.0273	1.09179	0.545895	+	0.837854i	$0.316190\pi$
$660$	2.53248	0.0985766
$661$	−46.8900	−1.82381	−0.911905	−	0.410401i	$-0.865389\pi$
$661$	−46.8900	−1.82381	−0.911905	+	0.410401i	$0.865389\pi$
$662$	−73.4038	−2.85292
$663$	−7.46034	−0.289736
$664$	9.45956	0.367102
$665$	0.997714	0.0386897
$666$	0.762683	0.0295534
$667$	47.5459	1.84098
$668$	20.0963	0.777550
$669$	−16.9298	−0.654545
$670$	−0.0863560	−0.00333622
$671$	28.2204	1.08944
$672$	7.71560	0.297636
$673$	30.2264	1.16514	0.582571	−	0.812780i	$-0.302047\pi$
$673$	30.2264	1.16514	0.582571	+	0.812780i	$0.302047\pi$
$674$	28.2752	1.08912
$675$	−4.94283	−0.190250
$676$	−27.5166	−1.05833
$677$	−4.66520	−0.179298	−0.0896491	−	0.995973i	$-0.528575\pi$
$677$	−4.66520	−0.179298	−0.0896491	+	0.995973i	$0.528575\pi$
$678$	30.1019	1.15606
$679$	−1.79091	−0.0687290
$680$	1.54488	0.0592434
$681$	−14.4225	−0.552672
$682$	−56.7060	−2.17138
$683$	−34.8003	−1.33160	−0.665798	−	0.746132i	$-0.731909\pi$
$683$	−34.8003	−1.33160	−0.665798	+	0.746132i	$0.731909\pi$
$684$	−11.0558	−0.422728
$685$	1.21951	0.0465951
$686$	−2.15625	−0.0823261
$687$	−16.4164	−0.626326
$688$	16.7118	0.637130
$689$	1.05906	0.0403469
$690$	2.69326	0.102531
$691$	36.6726	1.39509	0.697546	−	0.716540i	$-0.254275\pi$
$691$	36.6726	1.39509	0.697546	+	0.716540i	$0.254275\pi$
$692$	−10.6333	−0.404216
$693$	−3.99784	−0.151865
$694$	17.7326	0.673120
$695$	−2.99383	−0.113562
$696$	−12.7448	−0.483090
$697$	−35.6234	−1.34933
$698$	48.8247	1.84804
$699$	−7.64997	−0.289349
$700$	−13.0957	−0.494970
$701$	−11.0457	−0.417192	−0.208596	−	0.978002i	$-0.566889\pi$
$701$	−11.0457	−0.417192	−0.208596	+	0.978002i	$0.566889\pi$
$702$	3.48627	0.131581
$703$	1.47598	0.0556678
$704$	48.2859	1.81984
$705$	−0.842559	−0.0317326
$706$	49.4250	1.86014
$707$	−11.0925	−0.417177
$708$	−31.3731	−1.17907
$709$	−7.73369	−0.290445	−0.145222	−	0.989399i	$-0.546390\pi$
$709$	−7.73369	−0.290445	−0.145222	+	0.989399i	$0.546390\pi$
$710$	3.60144	0.135160
$711$	14.2526	0.534513
$712$	16.7960	0.629455
$713$	−34.3648	−1.28697
$714$	−9.94939	−0.372347
$715$	−1.54545	−0.0577967
$716$	−65.7857	−2.45853
$717$	8.03695	0.300145
$718$	−49.5353	−1.84864
$719$	−50.9775	−1.90114	−0.950571	−	0.310509i	$-0.899501\pi$
$719$	−50.9775	−1.90114	−0.950571	+	0.310509i	$0.899501\pi$
$720$	0.544990	0.0203106
$721$	14.5981	0.543662
$722$	3.42188	0.127349
$723$	−22.8036	−0.848076
$724$	19.3765	0.720121
$725$	−44.9862	−1.67075
$726$	−10.7440	−0.398747
$727$	−6.89848	−0.255850	−0.127925	−	0.991784i	$-0.540832\pi$
$727$	−6.89848	−0.255850	−0.127925	+	0.991784i	$0.540832\pi$
$728$	2.26407	0.0839122
$729$	1.00000	0.0370370
$730$	−1.44179	−0.0533630
$731$	−33.8298	−1.25124
$732$	−18.7021	−0.691248
$733$	6.77021	0.250063	0.125032	−	0.992153i	$-0.460097\pi$
$733$	6.77021	0.250063	0.125032	+	0.992153i	$0.460097\pi$
$734$	6.04636	0.223175
$735$	−0.239094	−0.00881912
$736$	40.3069	1.48573
$737$	0.669652	0.0246670
$738$	16.6471	0.612788
$739$	10.2163	0.375814	0.187907	−	0.982187i	$-0.439830\pi$
$739$	10.2163	0.375814	0.187907	+	0.982187i	$0.439830\pi$
$740$	0.224060	0.00823662
$741$	6.74682	0.247851
$742$	1.41240	0.0518508
$743$	3.12087	0.114493	0.0572467	−	0.998360i	$-0.481768\pi$
$743$	3.12087	0.114493	0.0572467	+	0.998360i	$0.481768\pi$
$744$	9.21155	0.337712
$745$	−2.29235	−0.0839854
$746$	75.9901	2.78219
$747$	−6.75526	−0.247162
$748$	−48.8736	−1.78699
$749$	10.6926	0.390698
$750$	−5.12600	−0.187175
$751$	17.9651	0.655557	0.327778	−	0.944755i	$-0.393700\pi$
$751$	17.9651	0.655557	0.327778	+	0.944755i	$0.393700\pi$
$752$	−8.03251	−0.292916
$753$	−2.22670	−0.0811454
$754$	31.7296	1.15552
$755$	4.09631	0.149080
$756$	2.64943	0.0963587
$757$	−41.8801	−1.52216	−0.761080	−	0.648658i	$-0.775330\pi$
$757$	−41.8801	−1.52216	−0.761080	+	0.648658i	$0.775330\pi$
$758$	17.8115	0.646942
$759$	−20.8850	−0.758078
$760$	−1.39712	−0.0506790
$761$	47.4903	1.72152	0.860761	−	0.509010i	$-0.169988\pi$
$761$	47.4903	1.72152	0.860761	+	0.509010i	$0.169988\pi$
$762$	2.15625	0.0781128
$763$	−19.1750	−0.694183
$764$	−32.8551	−1.18866
$765$	−1.10323	−0.0398873
$766$	14.4362	0.521602
$767$	19.1455	0.691305
$768$	1.27383	0.0459653
$769$	44.5562	1.60674	0.803369	−	0.595481i	$-0.203039\pi$
$769$	44.5562	1.60674	0.803369	+	0.595481i	$0.203039\pi$
$770$	−2.06107	−0.0742760
$771$	12.7786	0.460212
$772$	42.5095	1.52995
$773$	28.7248	1.03316	0.516580	−	0.856239i	$-0.327205\pi$
$773$	28.7248	1.03316	0.516580	+	0.856239i	$0.327205\pi$
$774$	15.8089	0.568239
$775$	32.5147	1.16796
$776$	2.50786	0.0900270
$777$	−0.353708	−0.0126892
$778$	28.9045	1.03628
$779$	32.2163	1.15427
$780$	1.02419	0.0366720
$781$	−27.9275	−0.999326
$782$	−51.9764	−1.85867
$783$	9.10130	0.325254
$784$	−2.27940	−0.0814070
$785$	−1.90912	−0.0681394
$786$	2.66811	0.0951682
$787$	−6.88490	−0.245420	−0.122710	−	0.992443i	$-0.539159\pi$
$787$	−6.88490	−0.245420	−0.122710	+	0.992443i	$0.539159\pi$
$788$	32.2891	1.15025
$789$	1.91222	0.0680767
$790$	7.34788	0.261426
$791$	−13.9603	−0.496370
$792$	5.59827	0.198926
$793$	11.4130	0.405287
$794$	−2.75864	−0.0979006
$795$	0.156612	0.00555447
$796$	36.5132	1.29418
$797$	19.8500	0.703123	0.351562	−	0.936165i	$-0.385651\pi$
$797$	19.8500	0.703123	0.351562	+	0.936165i	$0.385651\pi$
$798$	8.99781	0.318519
$799$	16.2603	0.575248
$800$	−38.1370	−1.34834
$801$	−11.9943	−0.423799
$802$	55.7686	1.96926
$803$	11.1804	0.394549
$804$	−0.443788	−0.0156512
$805$	−1.24905	−0.0440231
$806$	−22.9332	−0.807789
$807$	7.78586	0.274075
$808$	15.5331	0.546454
$809$	−18.8305	−0.662046	−0.331023	−	0.943623i	$-0.607394\pi$
$809$	−18.8305	−0.662046	−0.331023	+	0.943623i	$0.607394\pi$
$810$	0.515547	0.0181145
$811$	−47.7100	−1.67533	−0.837663	−	0.546188i	$-0.816078\pi$
$811$	−47.7100	−1.67533	−0.837663	+	0.546188i	$0.816078\pi$
$812$	24.1132	0.846208
$813$	−10.3228	−0.362036
$814$	−3.04908	−0.106870
$815$	−1.20005	−0.0420359
$816$	−10.5176	−0.368190
$817$	30.5942	1.07036
$818$	18.1262	0.633768
$819$	−1.61682	−0.0564963
$820$	4.89057	0.170786
$821$	25.1137	0.876475	0.438238	−	0.898859i	$-0.355603\pi$
$821$	25.1137	0.876475	0.438238	+	0.898859i	$0.355603\pi$
$822$	10.9981	0.383601
$823$	43.0088	1.49919	0.749597	−	0.661895i	$-0.230247\pi$
$823$	43.0088	1.49919	0.749597	+	0.661895i	$0.230247\pi$
$824$	−20.4421	−0.712134
$825$	19.7607	0.687978
$826$	25.5332	0.888413
$827$	13.8440	0.481403	0.240701	−	0.970599i	$-0.422623\pi$
$827$	13.8440	0.481403	0.240701	+	0.970599i	$0.422623\pi$
$828$	13.8408	0.481001
$829$	12.5853	0.437105	0.218553	−	0.975825i	$-0.429867\pi$
$829$	12.5853	0.437105	0.218553	+	0.975825i	$0.429867\pi$
$830$	−3.48266	−0.120885
$831$	−13.1278	−0.455400
$832$	19.5280	0.677010
$833$	4.61421	0.159873
$834$	−26.9996	−0.934920
$835$	−1.81357	−0.0627611
$836$	44.1992	1.52866
$837$	−6.57815	−0.227374
$838$	−25.9167	−0.895279
$839$	−4.46813	−0.154257	−0.0771284	−	0.997021i	$-0.524575\pi$
$839$	−4.46813	−0.154257	−0.0771284	+	0.997021i	$0.524575\pi$
$840$	0.334809	0.0115520
$841$	53.8337	1.85633
$842$	−59.3394	−2.04497
$843$	18.1404	0.624787
$844$	−32.7936	−1.12880
$845$	2.48320	0.0854248
$846$	−7.59856	−0.261244
$847$	4.98272	0.171208
$848$	1.49306	0.0512719
$849$	−19.1287	−0.656495
$850$	49.1782	1.68680
$851$	−1.84780	−0.0633416
$852$	18.5080	0.634073
$853$	−20.9580	−0.717589	−0.358795	−	0.933416i	$-0.616812\pi$
$853$	−20.9580	−0.717589	−0.358795	+	0.933416i	$0.616812\pi$
$854$	15.2208	0.520845
$855$	0.997714	0.0341211
$856$	−14.9731	−0.511769
$857$	−3.36198	−0.114843	−0.0574216	−	0.998350i	$-0.518288\pi$
$857$	−3.36198	−0.114843	−0.0574216	+	0.998350i	$0.518288\pi$
$858$	−13.9376	−0.475820
$859$	31.0025	1.05779	0.528895	−	0.848687i	$-0.322607\pi$
$859$	31.0025	1.05779	0.528895	+	0.848687i	$0.322607\pi$
$860$	4.64432	0.158370
$861$	−7.72038	−0.263110
$862$	−76.4894	−2.60524
$863$	8.87723	0.302185	0.151092	−	0.988520i	$-0.451721\pi$
$863$	8.87723	0.302185	0.151092	+	0.988520i	$0.451721\pi$
$864$	7.71560	0.262490
$865$	0.959586	0.0326269
$866$	−57.1917	−1.94345
$867$	4.29089	0.145726
$868$	−17.4283	−0.591556
$869$	−56.9795	−1.93290
$870$	4.69215	0.159079
$871$	0.270823	0.00917650
$872$	26.8513	0.909299
$873$	−1.79091	−0.0606133
$874$	47.0053	1.58998
$875$	2.37727	0.0803665
$876$	−7.40944	−0.250342
$877$	−19.3103	−0.652061	−0.326030	−	0.945359i	$-0.605711\pi$
$877$	−19.3103	−0.652061	−0.326030	+	0.945359i	$0.605711\pi$
$878$	70.3587	2.37449
$879$	−26.6893	−0.900208
$880$	−2.17878	−0.0734468
$881$	3.30078	0.111206	0.0556030	−	0.998453i	$-0.482292\pi$
$881$	3.30078	0.111206	0.0556030	+	0.998453i	$0.482292\pi$
$882$	−2.15625	−0.0726048
$883$	51.9315	1.74764	0.873818	−	0.486253i	$-0.161637\pi$
$883$	51.9315	1.74764	0.873818	+	0.486253i	$0.161637\pi$
$884$	−19.7656	−0.664790
$885$	2.83122	0.0951706
$886$	−34.7042	−1.16591
$887$	9.29948	0.312246	0.156123	−	0.987738i	$-0.450100\pi$
$887$	9.29948	0.312246	0.156123	+	0.987738i	$0.450100\pi$
$888$	0.495306	0.0166214
$889$	−1.00000	−0.0335389
$890$	−6.18364	−0.207276
$891$	−3.99784	−0.133933
$892$	−44.8543	−1.50183
$893$	−14.7051	−0.492088
$894$	−20.6734	−0.691423
$895$	5.93675	0.198444
$896$	10.6120	0.354522
$897$	−8.44639	−0.282017
$898$	−71.4750	−2.38515
$899$	−59.8698	−1.99677
$900$	−13.0957	−0.436522
$901$	−3.02242	−0.100691
$902$	−66.5524	−2.21595
$903$	−7.33166	−0.243982
$904$	19.5489	0.650187
$905$	−1.74861	−0.0581256
$906$	36.9423	1.22733
$907$	−31.2600	−1.03797	−0.518985	−	0.854783i	$-0.673690\pi$
$907$	−31.2600	−1.03797	−0.518985	+	0.854783i	$0.673690\pi$
$908$	−38.2114	−1.26809
$909$	−11.0925	−0.367916
$910$	−0.833547	−0.0276318
$911$	−30.7338	−1.01826	−0.509128	−	0.860691i	$-0.670032\pi$
$911$	−30.7338	−1.01826	−0.509128	+	0.860691i	$0.670032\pi$
$912$	9.51168	0.314963
$913$	27.0065	0.893783
$914$	44.8059	1.48205
$915$	1.68774	0.0557951
$916$	−43.4941	−1.43709
$917$	−1.23738	−0.0408619
$918$	−9.94939	−0.328379
$919$	7.17530	0.236691	0.118346	−	0.992972i	$-0.462241\pi$
$919$	7.17530	0.236691	0.118346	+	0.992972i	$0.462241\pi$
$920$	1.74907	0.0576651
$921$	9.45867	0.311674
$922$	−56.0683	−1.84651
$923$	−11.2946	−0.371765
$924$	−10.5920	−0.348450
$925$	1.74832	0.0574844
$926$	−3.03375	−0.0996952
$927$	14.5981	0.479465
$928$	70.2220	2.30515
$929$	23.3488	0.766051	0.383025	−	0.923738i	$-0.374882\pi$
$929$	23.3488	0.766051	0.383025	+	0.923738i	$0.374882\pi$
$930$	−3.39135	−0.111207
$931$	−4.17289	−0.136761
$932$	−20.2680	−0.663902
$933$	1.98631	0.0650289
$934$	9.76524	0.319529
$935$	4.41053	0.144240
$936$	2.26407	0.0740036
$937$	−54.8510	−1.79191	−0.895953	−	0.444150i	$-0.853506\pi$
$937$	−54.8510	−1.79191	−0.895953	+	0.444150i	$0.853506\pi$
$938$	0.361180	0.0117929
$939$	−20.0441	−0.654115
$940$	−2.23230	−0.0728095
$941$	−2.79391	−0.0910788	−0.0455394	−	0.998963i	$-0.514501\pi$
$941$	−2.79391	−0.0910788	−0.0455394	+	0.998963i	$0.514501\pi$
$942$	−17.2173	−0.560969
$943$	−40.3319	−1.31339
$944$	26.9914	0.878495
$945$	−0.239094	−0.00777773
$946$	−63.2014	−2.05486
$947$	6.53039	0.212209	0.106105	−	0.994355i	$-0.466162\pi$
$947$	6.53039	0.212209	0.106105	+	0.994355i	$0.466162\pi$
$948$	37.7611	1.22642
$949$	4.52163	0.146778
$950$	−44.4747	−1.44295
$951$	−27.2490	−0.883609
$952$	−6.46139	−0.209415
$953$	19.4446	0.629873	0.314937	−	0.949113i	$-0.398017\pi$
$953$	19.4446	0.629873	0.314937	+	0.949113i	$0.398017\pi$
$954$	1.41240	0.0457281
$955$	2.96497	0.0959440
$956$	21.2933	0.688674
$957$	−36.3855	−1.17618
$958$	−3.76899	−0.121771
$959$	−5.10054	−0.164705
$960$	2.88778	0.0932026
$961$	12.2721	0.395874
$962$	−1.23312	−0.0397574
$963$	10.6926	0.344563
$964$	−60.4165	−1.94589
$965$	−3.83622	−0.123492
$966$	−11.2644	−0.362427
$967$	−4.67554	−0.150355	−0.0751777	−	0.997170i	$-0.523952\pi$
$967$	−4.67554	−0.150355	−0.0751777	+	0.997170i	$0.523952\pi$
$968$	−6.97742	−0.224263
$969$	−19.2546	−0.618547
$970$	−0.923301	−0.0296454
$971$	4.75185	0.152494	0.0762470	−	0.997089i	$-0.475706\pi$
$971$	4.75185	0.152494	0.0762470	+	0.997089i	$0.475706\pi$
$972$	2.64943	0.0849804
$973$	12.5215	0.401422
$974$	54.4200	1.74373
$975$	7.99168	0.255938
$976$	16.0901	0.515030
$977$	−37.3562	−1.19513	−0.597565	−	0.801821i	$-0.703865\pi$
$977$	−37.3562	−1.19513	−0.597565	+	0.801821i	$0.703865\pi$
$978$	−10.8226	−0.346067
$979$	47.9514	1.53253
$980$	−0.633462	−0.0202352
$981$	−19.1750	−0.612212
$982$	58.5864	1.86957
$983$	45.4192	1.44865	0.724324	−	0.689459i	$-0.242152\pi$
$983$	45.4192	1.44865	0.724324	+	0.689459i	$0.242152\pi$
$984$	10.8110	0.344643
$985$	−2.91389	−0.0928444
$986$	−90.5524	−2.88378
$987$	3.52396	0.112169
$988$	17.8752	0.568686
$989$	−38.3011	−1.21791
$990$	−2.06107	−0.0655053
$991$	−8.11368	−0.257739	−0.128870	−	0.991662i	$-0.541135\pi$
$991$	−8.11368	−0.257739	−0.128870	+	0.991662i	$0.541135\pi$
$992$	−50.7544	−1.61145
$993$	34.0423	1.08030
$994$	−15.0628	−0.477764
$995$	−3.29509	−0.104461
$996$	−17.8976	−0.567106
$997$	−33.0431	−1.04648	−0.523242	−	0.852184i	$-0.675278\pi$
$997$	−33.0431	−1.04648	−0.523242	+	0.852184i	$0.675278\pi$
$998$	40.8413	1.29281
$999$	−0.353708	−0.0111908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.j.1.2	✓	7
3.2	odd	2		8001.2.a.l.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.j.1.2	✓	7	1.1	even	1	trivial
8001.2.a.l.1.6		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)

\(f(q)\)	\(=\)	\(q-2.15625 q^{2} +1.00000 q^{3} +2.64943 q^{4} -0.239094 q^{5} -2.15625 q^{6} +1.00000 q^{7} -1.40032 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.15625 q^{2} +1.00000 q^{3} +2.64943 q^{4} -0.239094 q^{5} -2.15625 q^{6} +1.00000 q^{7} -1.40032 q^{8} +1.00000 q^{9} +0.515547 q^{10} -3.99784 q^{11} +2.64943 q^{12} -1.61682 q^{13} -2.15625 q^{14} -0.239094 q^{15} -2.27940 q^{16} +4.61421 q^{17} -2.15625 q^{18} -4.17289 q^{19} -0.633462 q^{20} +1.00000 q^{21} +8.62035 q^{22} +5.22408 q^{23} -1.40032 q^{24} -4.94283 q^{25} +3.48627 q^{26} +1.00000 q^{27} +2.64943 q^{28} +9.10130 q^{29} +0.515547 q^{30} -6.57815 q^{31} +7.71560 q^{32} -3.99784 q^{33} -9.94939 q^{34} -0.239094 q^{35} +2.64943 q^{36} -0.353708 q^{37} +8.99781 q^{38} -1.61682 q^{39} +0.334809 q^{40} -7.72038 q^{41} -2.15625 q^{42} -7.33166 q^{43} -10.5920 q^{44} -0.239094 q^{45} -11.2644 q^{46} +3.52396 q^{47} -2.27940 q^{48} +1.00000 q^{49} +10.6580 q^{50} +4.61421 q^{51} -4.28365 q^{52} -0.655025 q^{53} -2.15625 q^{54} +0.955860 q^{55} -1.40032 q^{56} -4.17289 q^{57} -19.6247 q^{58} -11.8415 q^{59} -0.633462 q^{60} -7.05891 q^{61} +14.1842 q^{62} +1.00000 q^{63} -12.0780 q^{64} +0.386572 q^{65} +8.62035 q^{66} -0.167504 q^{67} +12.2250 q^{68} +5.22408 q^{69} +0.515547 q^{70} +6.98566 q^{71} -1.40032 q^{72} -2.79662 q^{73} +0.762683 q^{74} -4.94283 q^{75} -11.0558 q^{76} -3.99784 q^{77} +3.48627 q^{78} +14.2526 q^{79} +0.544990 q^{80} +1.00000 q^{81} +16.6471 q^{82} -6.75526 q^{83} +2.64943 q^{84} -1.10323 q^{85} +15.8089 q^{86} +9.10130 q^{87} +5.59827 q^{88} -11.9943 q^{89} +0.515547 q^{90} -1.61682 q^{91} +13.8408 q^{92} -6.57815 q^{93} -7.59856 q^{94} +0.997714 q^{95} +7.71560 q^{96} -1.79091 q^{97} -2.15625 q^{98} -3.99784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} + 7 q^{3} + 4 q^{4} - 8 q^{5} - 2 q^{6} + 7 q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 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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