LMFDB - Embedded newform 667.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$5.32602181482$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} + \cdots - 5 $ x^12 - 3x^11 - 13x^10 + 41x^9 + 54x^8 - 188x^7 - 77x^6 + 342x^5 + 13x^4 - 215x^3 + 9x^2 + 37*x - 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.08419$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.08419 q^{2} +1.50990 q^{3} -0.824542 q^{4} +0.786014 q^{5} -1.63701 q^{6} -4.63453 q^{7} +3.06233 q^{8} -0.720207 q^{9} +O(q^{10})$	\(q-1.08419 q^{2} +1.50990 q^{3} -0.824542 q^{4} +0.786014 q^{5} -1.63701 q^{6} -4.63453 q^{7} +3.06233 q^{8} -0.720207 q^{9} -0.852185 q^{10} +4.80440 q^{11} -1.24497 q^{12} -3.44502 q^{13} +5.02469 q^{14} +1.18680 q^{15} -1.67105 q^{16} -1.46070 q^{17} +0.780838 q^{18} -1.81007 q^{19} -0.648102 q^{20} -6.99768 q^{21} -5.20885 q^{22} -1.00000 q^{23} +4.62380 q^{24} -4.38218 q^{25} +3.73504 q^{26} -5.61713 q^{27} +3.82137 q^{28} -1.00000 q^{29} -1.28671 q^{30} -4.86699 q^{31} -4.31293 q^{32} +7.25415 q^{33} +1.58367 q^{34} -3.64281 q^{35} +0.593841 q^{36} -10.3517 q^{37} +1.96245 q^{38} -5.20163 q^{39} +2.40703 q^{40} +9.91091 q^{41} +7.58678 q^{42} -6.59023 q^{43} -3.96143 q^{44} -0.566093 q^{45} +1.08419 q^{46} +2.49788 q^{47} -2.52311 q^{48} +14.4789 q^{49} +4.75110 q^{50} -2.20551 q^{51} +2.84056 q^{52} +1.06830 q^{53} +6.09001 q^{54} +3.77632 q^{55} -14.1925 q^{56} -2.73303 q^{57} +1.08419 q^{58} -8.50982 q^{59} -0.978568 q^{60} +5.33862 q^{61} +5.27672 q^{62} +3.33782 q^{63} +8.01811 q^{64} -2.70783 q^{65} -7.86484 q^{66} -2.04102 q^{67} +1.20441 q^{68} -1.50990 q^{69} +3.94948 q^{70} -7.02707 q^{71} -2.20551 q^{72} -6.41672 q^{73} +11.2232 q^{74} -6.61665 q^{75} +1.49248 q^{76} -22.2661 q^{77} +5.63953 q^{78} -4.87925 q^{79} -1.31347 q^{80} -6.32068 q^{81} -10.7453 q^{82} +1.67762 q^{83} +5.76988 q^{84} -1.14813 q^{85} +7.14503 q^{86} -1.50990 q^{87} +14.7126 q^{88} +14.1259 q^{89} +0.613749 q^{90} +15.9661 q^{91} +0.824542 q^{92} -7.34866 q^{93} -2.70816 q^{94} -1.42274 q^{95} -6.51209 q^{96} -8.39649 q^{97} -15.6978 q^{98} -3.46016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.08419	−0.766635	−0.383317	−	0.923617i	$-0.625218\pi$
$2$	−1.08419	−0.766635	−0.383317	+	0.923617i	$0.625218\pi$
$3$	1.50990	0.871740	0.435870	−	0.900010i	$-0.356441\pi$
$3$	1.50990	0.871740	0.435870	+	0.900010i	$0.356441\pi$
$4$	−0.824542	−0.412271
$5$	0.786014	0.351516	0.175758	−	0.984433i	$-0.443762\pi$
$5$	0.786014	0.351516	0.175758	+	0.984433i	$0.443762\pi$
$6$	−1.63701	−0.668306
$7$	−4.63453	−1.75169	−0.875845	−	0.482593i	$-0.839695\pi$
$7$	−4.63453	−1.75169	−0.875845	+	0.482593i	$0.839695\pi$
$8$	3.06233	1.08270
$9$	−0.720207	−0.240069
$10$	−0.852185	−0.269485
$11$	4.80440	1.44858	0.724290	−	0.689496i	$-0.242168\pi$
$11$	4.80440	1.44858	0.724290	+	0.689496i	$0.242168\pi$
$12$	−1.24497	−0.359393
$13$	−3.44502	−0.955477	−0.477738	−	0.878502i	$-0.658543\pi$
$13$	−3.44502	−0.955477	−0.477738	+	0.878502i	$0.658543\pi$
$14$	5.02469	1.34291
$15$	1.18680	0.306431
$16$	−1.67105	−0.417761
$17$	−1.46070	−0.354272	−0.177136	−	0.984186i	$-0.556683\pi$
$17$	−1.46070	−0.354272	−0.177136	+	0.984186i	$0.556683\pi$
$18$	0.780838	0.184045
$19$	−1.81007	−0.415259	−0.207630	−	0.978208i	$-0.566575\pi$
$19$	−1.81007	−0.415259	−0.207630	+	0.978208i	$0.566575\pi$
$20$	−0.648102	−0.144920
$21$	−6.99768	−1.52702
$22$	−5.20885	−1.11053
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	4.62380	0.943830
$25$	−4.38218	−0.876436
$26$	3.73504	0.732502
$27$	−5.61713	−1.08102
$28$	3.82137	0.722171
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−1.28671	−0.234921
$31$	−4.86699	−0.874137	−0.437069	−	0.899428i	$-0.643983\pi$
$31$	−4.86699	−0.874137	−0.437069	+	0.899428i	$0.643983\pi$
$32$	−4.31293	−0.762426
$33$	7.25415	1.26279
$34$	1.58367	0.271598
$35$	−3.64281	−0.615747
$36$	0.593841	0.0989735
$37$	−10.3517	−1.70182	−0.850908	−	0.525315i	$-0.823947\pi$
$37$	−10.3517	−1.70182	−0.850908	+	0.525315i	$0.823947\pi$
$38$	1.96245	0.318352
$39$	−5.20163	−0.832928
$40$	2.40703	0.380585
$41$	9.91091	1.54782	0.773912	−	0.633293i	$-0.218297\pi$
$41$	9.91091	1.54782	0.773912	+	0.633293i	$0.218297\pi$
$42$	7.58678	1.17067
$43$	−6.59023	−1.00500	−0.502500	−	0.864577i	$-0.667586\pi$
$43$	−6.59023	−1.00500	−0.502500	+	0.864577i	$0.667586\pi$
$44$	−3.96143	−0.597208
$45$	−0.566093	−0.0843881
$46$	1.08419	0.159854
$47$	2.49788	0.364353	0.182177	−	0.983266i	$-0.441686\pi$
$47$	2.49788	0.364353	0.182177	+	0.983266i	$0.441686\pi$
$48$	−2.52311	−0.364179
$49$	14.4789	2.06842
$50$	4.75110	0.671907
$51$	−2.20551	−0.308834
$52$	2.84056	0.393915
$53$	1.06830	0.146742	0.0733709	−	0.997305i	$-0.476624\pi$
$53$	1.06830	0.146742	0.0733709	+	0.997305i	$0.476624\pi$
$54$	6.09001	0.828746
$55$	3.77632	0.509199
$56$	−14.1925	−1.89655
$57$	−2.73303	−0.361998
$58$	1.08419	0.142361
$59$	−8.50982	−1.10788	−0.553942	−	0.832555i	$-0.686877\pi$
$59$	−8.50982	−1.10788	−0.553942	+	0.832555i	$0.686877\pi$
$60$	−0.978568	−0.126333
$61$	5.33862	0.683540	0.341770	−	0.939784i	$-0.388974\pi$
$61$	5.33862	0.683540	0.341770	+	0.939784i	$0.388974\pi$
$62$	5.27672	0.670144
$63$	3.33782	0.420526
$64$	8.01811	1.00226
$65$	−2.70783	−0.335866
$66$	−7.86484	−0.968095
$67$	−2.04102	−0.249350	−0.124675	−	0.992198i	$-0.539789\pi$
$67$	−2.04102	−0.249350	−0.124675	+	0.992198i	$0.539789\pi$
$68$	1.20441	0.146056
$69$	−1.50990	−0.181770
$70$	3.94948	0.472053
$71$	−7.02707	−0.833959	−0.416980	−	0.908916i	$-0.636911\pi$
$71$	−7.02707	−0.833959	−0.416980	+	0.908916i	$0.636911\pi$
$72$	−2.20551	−0.259922
$73$	−6.41672	−0.751020	−0.375510	−	0.926818i	$-0.622532\pi$
$73$	−6.41672	−0.751020	−0.375510	+	0.926818i	$0.622532\pi$
$74$	11.2232	1.30467
$75$	−6.61665	−0.764025
$76$	1.49248	0.171199
$77$	−22.2661	−2.53746
$78$	5.63953	0.638551
$79$	−4.87925	−0.548958	−0.274479	−	0.961593i	$-0.588505\pi$
$79$	−4.87925	−0.548958	−0.274479	+	0.961593i	$0.588505\pi$
$80$	−1.31347	−0.146850
$81$	−6.32068	−0.702298
$82$	−10.7453	−1.18662
$83$	1.67762	0.184143	0.0920715	−	0.995752i	$-0.470651\pi$
$83$	1.67762	0.184143	0.0920715	+	0.995752i	$0.470651\pi$
$84$	5.76988	0.629545
$85$	−1.14813	−0.124532
$86$	7.14503	0.770468
$87$	−1.50990	−0.161878
$88$	14.7126	1.56837
$89$	14.1259	1.49735	0.748673	−	0.662940i	$-0.230692\pi$
$89$	14.1259	1.49735	0.748673	+	0.662940i	$0.230692\pi$
$90$	0.613749	0.0646949
$91$	15.9661	1.67370
$92$	0.824542	0.0859645
$93$	−7.34866	−0.762021
$94$	−2.70816	−0.279326
$95$	−1.42274	−0.145970
$96$	−6.51209	−0.664637
$97$	−8.39649	−0.852535	−0.426267	−	0.904597i	$-0.640172\pi$
$97$	−8.39649	−0.852535	−0.426267	+	0.904597i	$0.640172\pi$
$98$	−15.6978	−1.58572
$99$	−3.46016	−0.347759
$100$	3.61329	0.361329
$101$	−3.68109	−0.366283	−0.183141	−	0.983087i	$-0.558627\pi$
$101$	−3.68109	−0.366283	−0.183141	+	0.983087i	$0.558627\pi$
$102$	2.39118	0.236763
$103$	12.6337	1.24483	0.622417	−	0.782686i	$-0.286151\pi$
$103$	12.6337	1.24483	0.622417	+	0.782686i	$0.286151\pi$
$104$	−10.5498	−1.03449
$105$	−5.50027	−0.536772
$106$	−1.15823	−0.112497
$107$	17.1297	1.65599	0.827997	−	0.560732i	$-0.189480\pi$
$107$	17.1297	1.65599	0.827997	+	0.560732i	$0.189480\pi$
$108$	4.63156	0.445672
$109$	−4.21849	−0.404058	−0.202029	−	0.979380i	$-0.564754\pi$
$109$	−4.21849	−0.404058	−0.202029	+	0.979380i	$0.564754\pi$
$110$	−4.09423	−0.390370
$111$	−15.6301	−1.48354
$112$	7.74452	0.731788
$113$	−12.4166	−1.16806	−0.584028	−	0.811734i	$-0.698524\pi$
$113$	−12.4166	−1.16806	−0.584028	+	0.811734i	$0.698524\pi$
$114$	2.96311	0.277520
$115$	−0.786014	−0.0732962
$116$	0.824542	0.0765568
$117$	2.48113	0.229380
$118$	9.22622	0.849343
$119$	6.76968	0.620575
$120$	3.63437	0.331771
$121$	12.0822	1.09838
$122$	−5.78805	−0.524026
$123$	14.9645	1.34930
$124$	4.01304	0.360382
$125$	−7.37453	−0.659598
$126$	−3.61882	−0.322390
$127$	−1.77286	−0.157316	−0.0786578	−	0.996902i	$-0.525063\pi$
$127$	−1.77286	−0.157316	−0.0786578	+	0.996902i	$0.525063\pi$
$128$	−0.0672536	−0.00594443
$129$	−9.95058	−0.876099
$130$	2.93579	0.257486
$131$	5.37219	0.469370	0.234685	−	0.972071i	$-0.424594\pi$
$131$	5.37219	0.469370	0.234685	+	0.972071i	$0.424594\pi$
$132$	−5.98135	−0.520610
$133$	8.38885	0.727405
$134$	2.21284	0.191160
$135$	−4.41515	−0.379995
$136$	−4.47315	−0.383569
$137$	−15.7630	−1.34672	−0.673361	−	0.739314i	$-0.735150\pi$
$137$	−15.7630	−1.34672	−0.673361	+	0.739314i	$0.735150\pi$
$138$	1.63701	0.139352
$139$	16.2070	1.37466	0.687329	−	0.726346i	$-0.258783\pi$
$139$	16.2070	1.37466	0.687329	+	0.726346i	$0.258783\pi$
$140$	3.00365	0.253855
$141$	3.77154	0.317621
$142$	7.61864	0.639342
$143$	−16.5512	−1.38408
$144$	1.20350	0.100292
$145$	−0.786014	−0.0652749
$146$	6.95691	0.575758
$147$	21.8617	1.80312
$148$	8.53544	0.701609
$149$	−0.767900	−0.0629088	−0.0314544	−	0.999505i	$-0.510014\pi$
$149$	−0.767900	−0.0629088	−0.0314544	+	0.999505i	$0.510014\pi$
$150$	7.17367	0.585728
$151$	3.51621	0.286145	0.143073	−	0.989712i	$-0.454302\pi$
$151$	3.51621	0.286145	0.143073	+	0.989712i	$0.454302\pi$
$152$	−5.54304	−0.449600
$153$	1.05201	0.0850498
$154$	24.1406	1.94531
$155$	−3.82552	−0.307273
$156$	4.28896	0.343392
$157$	13.6276	1.08760	0.543799	−	0.839216i	$-0.316986\pi$
$157$	13.6276	1.08760	0.543799	+	0.839216i	$0.316986\pi$
$158$	5.29001	0.420851
$159$	1.61302	0.127921
$160$	−3.39002	−0.268005
$161$	4.63453	0.365252
$162$	6.85279	0.538406
$163$	24.1685	1.89302	0.946510	−	0.322675i	$-0.104582\pi$
$163$	24.1685	1.89302	0.946510	+	0.322675i	$0.104582\pi$
$164$	−8.17196	−0.638123
$165$	5.70186	0.443889
$166$	−1.81885	−0.141170
$167$	3.00489	0.232526	0.116263	−	0.993218i	$-0.462909\pi$
$167$	3.00489	0.232526	0.116263	+	0.993218i	$0.462909\pi$
$168$	−21.4292	−1.65330
$169$	−1.13183	−0.0870639
$170$	1.24479	0.0954709
$171$	1.30363	0.0996909
$172$	5.43392	0.414333
$173$	−3.14834	−0.239364	−0.119682	−	0.992812i	$-0.538187\pi$
$173$	−3.14834	−0.239364	−0.119682	+	0.992812i	$0.538187\pi$
$174$	1.63701	0.124101
$175$	20.3094	1.53524
$176$	−8.02836	−0.605161
$177$	−12.8490	−0.965787
$178$	−15.3151	−1.14792
$179$	24.8759	1.85931	0.929656	−	0.368430i	$-0.120104\pi$
$179$	24.8759	1.85931	0.929656	+	0.368430i	$0.120104\pi$
$180$	0.466767	0.0347908
$181$	−1.14502	−0.0851086	−0.0425543	−	0.999094i	$-0.513550\pi$
$181$	−1.14502	−0.0851086	−0.0425543	+	0.999094i	$0.513550\pi$
$182$	−17.3102	−1.28312
$183$	8.06077	0.595869
$184$	−3.06233	−0.225758
$185$	−8.13661	−0.598216
$186$	7.96731	0.584192
$187$	−7.01779	−0.513192
$188$	−2.05961	−0.150212
$189$	26.0328	1.89361
$190$	1.54252	0.111906
$191$	−12.7023	−0.919109	−0.459555	−	0.888150i	$-0.651991\pi$
$191$	−12.7023	−0.919109	−0.459555	+	0.888150i	$0.651991\pi$
$192$	12.1065	0.873713
$193$	15.7139	1.13111	0.565555	−	0.824711i	$-0.308662\pi$
$193$	15.7139	1.13111	0.565555	+	0.824711i	$0.308662\pi$
$194$	9.10335	0.653583
$195$	−4.08856	−0.292788
$196$	−11.9385	−0.852748
$197$	5.69145	0.405499	0.202749	−	0.979231i	$-0.435012\pi$
$197$	5.69145	0.405499	0.202749	+	0.979231i	$0.435012\pi$
$198$	3.75145	0.266604
$199$	−26.0226	−1.84469	−0.922347	−	0.386363i	$-0.873731\pi$
$199$	−26.0226	−1.84469	−0.922347	+	0.386363i	$0.873731\pi$
$200$	−13.4197	−0.948914
$201$	−3.08173	−0.217368
$202$	3.99099	0.280805
$203$	4.63453	0.325281
$204$	1.81854	0.127323
$205$	7.79012	0.544085
$206$	−13.6973	−0.954333
$207$	0.720207	0.0500578
$208$	5.75679	0.399161
$209$	−8.69631	−0.601536
$210$	5.96331	0.411508
$211$	5.97054	0.411029	0.205514	−	0.978654i	$-0.434113\pi$
$211$	5.97054	0.411029	0.205514	+	0.978654i	$0.434113\pi$
$212$	−0.880855	−0.0604974
$213$	−10.6102	−0.726996
$214$	−18.5718	−1.26954
$215$	−5.18001	−0.353274
$216$	−17.2015	−1.17041
$217$	22.5562	1.53122
$218$	4.57363	0.309765
$219$	−9.68860	−0.654695
$220$	−3.11374	−0.209928
$221$	5.03215	0.338499
$222$	16.9459	1.13733
$223$	−1.94599	−0.130313	−0.0651565	−	0.997875i	$-0.520755\pi$
$223$	−1.94599	−0.130313	−0.0651565	+	0.997875i	$0.520755\pi$
$224$	19.9884	1.33553
$225$	3.15608	0.210405
$226$	13.4619	0.895472
$227$	14.1896	0.941794	0.470897	−	0.882188i	$-0.343930\pi$
$227$	14.1896	0.941794	0.470897	+	0.882188i	$0.343930\pi$
$228$	2.25350	0.149241
$229$	−17.1122	−1.13081	−0.565405	−	0.824814i	$-0.691280\pi$
$229$	−17.1122	−1.13081	−0.565405	+	0.824814i	$0.691280\pi$
$230$	0.852185	0.0561914
$231$	−33.6196	−2.21201
$232$	−3.06233	−0.201052
$233$	9.79924	0.641970	0.320985	−	0.947084i	$-0.395986\pi$
$233$	9.79924	0.641970	0.320985	+	0.947084i	$0.395986\pi$
$234$	−2.69000	−0.175851
$235$	1.96337	0.128076
$236$	7.01671	0.456749
$237$	−7.36717	−0.478549
$238$	−7.33958	−0.475755
$239$	13.8667	0.896964	0.448482	−	0.893792i	$-0.351965\pi$
$239$	13.8667	0.896964	0.448482	+	0.893792i	$0.351965\pi$
$240$	−1.98320	−0.128015
$241$	−11.2309	−0.723443	−0.361722	−	0.932286i	$-0.617811\pi$
$241$	−11.2309	−0.723443	−0.361722	+	0.932286i	$0.617811\pi$
$242$	−13.0994	−0.842059
$243$	7.30782	0.468797
$244$	−4.40192	−0.281804
$245$	11.3806	0.727082
$246$	−16.2243	−1.03442
$247$	6.23574	0.396771
$248$	−14.9043	−0.946425
$249$	2.53304	0.160525
$250$	7.99535	0.505671
$251$	−7.20786	−0.454956	−0.227478	−	0.973783i	$-0.573048\pi$
$251$	−7.20786	−0.454956	−0.227478	+	0.973783i	$0.573048\pi$
$252$	−2.75218	−0.173371
$253$	−4.80440	−0.302050
$254$	1.92210	0.120604
$255$	−1.73356	−0.108560
$256$	−15.9633	−0.997706
$257$	−22.1065	−1.37897	−0.689483	−	0.724302i	$-0.742162\pi$
$257$	−22.1065	−1.37897	−0.689483	+	0.724302i	$0.742162\pi$
$258$	10.7883	0.671648
$259$	47.9755	2.98105
$260$	2.23272	0.138468
$261$	0.720207	0.0445797
$262$	−5.82444	−0.359835
$263$	8.38486	0.517033	0.258516	−	0.966007i	$-0.416766\pi$
$263$	8.38486	0.517033	0.258516	+	0.966007i	$0.416766\pi$
$264$	22.2146	1.36721
$265$	0.839696	0.0515821
$266$	−9.09506	−0.557654
$267$	21.3287	1.30530
$268$	1.68291	0.102800
$269$	5.76591	0.351554	0.175777	−	0.984430i	$-0.443756\pi$
$269$	5.76591	0.351554	0.175777	+	0.984430i	$0.443756\pi$
$270$	4.78684	0.291318
$271$	−20.2643	−1.23097	−0.615484	−	0.788149i	$-0.711039\pi$
$271$	−20.2643	−1.23097	−0.615484	+	0.788149i	$0.711039\pi$
$272$	2.44090	0.148001
$273$	24.1071	1.45903
$274$	17.0900	1.03244
$275$	−21.0537	−1.26959
$276$	1.24497	0.0749387
$277$	−27.1992	−1.63424	−0.817120	−	0.576468i	$-0.804431\pi$
$277$	−27.1992	−1.63424	−0.817120	+	0.576468i	$0.804431\pi$
$278$	−17.5714	−1.05386
$279$	3.50524	0.209853
$280$	−11.1555	−0.666667
$281$	6.82835	0.407345	0.203673	−	0.979039i	$-0.434712\pi$
$281$	6.82835	0.407345	0.203673	+	0.979039i	$0.434712\pi$
$282$	−4.08905	−0.243500
$283$	−27.8034	−1.65274	−0.826369	−	0.563128i	$-0.809598\pi$
$283$	−27.8034	−1.65274	−0.826369	+	0.563128i	$0.809598\pi$
$284$	5.79411	0.343817
$285$	−2.14820	−0.127248
$286$	17.9446	1.06109
$287$	−45.9325	−2.71131
$288$	3.10620	0.183035
$289$	−14.8663	−0.874491
$290$	0.852185	0.0500420
$291$	−12.6778	−0.743189
$292$	5.29086	0.309624
$293$	−0.0118298	−0.000691103 0	−0.000345552	−	1.00000i	$-0.500110\pi$
$293$	−0.0118298	−0.000691103 0	−0.000345552		1.00000i	$0.500110\pi$
$294$	−23.7021	−1.38234
$295$	−6.68884	−0.389439
$296$	−31.7004	−1.84255
$297$	−26.9869	−1.56594
$298$	0.832545	0.0482281
$299$	3.44502	0.199231
$300$	5.45571	0.314985
$301$	30.5426	1.76045
$302$	−3.81223	−0.219369
$303$	−5.55808	−0.319303
$304$	3.02472	0.173479
$305$	4.19623	0.240275
$306$	−1.14057	−0.0652021
$307$	−0.487792	−0.0278398	−0.0139199	−	0.999903i	$-0.504431\pi$
$307$	−0.487792	−0.0278398	−0.0139199	+	0.999903i	$0.504431\pi$
$308$	18.3594	1.04612
$309$	19.0756	1.08517
$310$	4.14758	0.235567
$311$	33.4115	1.89459	0.947297	−	0.320356i	$-0.103802\pi$
$311$	33.4115	1.89459	0.947297	+	0.320356i	$0.103802\pi$
$312$	−15.9291	−0.901808
$313$	19.5869	1.10712	0.553559	−	0.832810i	$-0.313270\pi$
$313$	19.5869	1.10712	0.553559	+	0.832810i	$0.313270\pi$
$314$	−14.7748	−0.833790
$315$	2.62358	0.147822
$316$	4.02315	0.226320
$317$	−11.5304	−0.647613	−0.323807	−	0.946123i	$-0.604963\pi$
$317$	−11.5304	−0.647613	−0.323807	+	0.946123i	$0.604963\pi$
$318$	−1.74881	−0.0980684
$319$	−4.80440	−0.268994
$320$	6.30235	0.352312
$321$	25.8642	1.44360
$322$	−5.02469	−0.280015
$323$	2.64398	0.147115
$324$	5.21167	0.289537
$325$	15.0967	0.837415
$326$	−26.2031	−1.45125
$327$	−6.36949	−0.352234
$328$	30.3505	1.67582
$329$	−11.5765	−0.638234
$330$	−6.18188	−0.340301
$331$	−31.3361	−1.72239	−0.861193	−	0.508278i	$-0.830282\pi$
$331$	−31.3361	−1.72239	−0.861193	+	0.508278i	$0.830282\pi$
$332$	−1.38327	−0.0759169
$333$	7.45539	0.408553
$334$	−3.25786	−0.178262
$335$	−1.60427	−0.0876506
$336$	11.6934	0.637929
$337$	−13.3519	−0.727323	−0.363661	−	0.931531i	$-0.618473\pi$
$337$	−13.3519	−0.727323	−0.363661	+	0.931531i	$0.618473\pi$
$338$	1.22711	0.0667462
$339$	−18.7478	−1.01824
$340$	0.946684	0.0513411
$341$	−23.3829	−1.26626
$342$	−1.41337	−0.0764265
$343$	−34.6613	−1.87153
$344$	−20.1814	−1.08811
$345$	−1.18680	−0.0638952
$346$	3.41338	0.183505
$347$	8.66047	0.464919	0.232459	−	0.972606i	$-0.425323\pi$
$347$	8.66047	0.464919	0.232459	+	0.972606i	$0.425323\pi$
$348$	1.24497	0.0667377
$349$	−13.0354	−0.697767	−0.348883	−	0.937166i	$-0.613439\pi$
$349$	−13.0354	−0.697767	−0.348883	+	0.937166i	$0.613439\pi$
$350$	−22.0191	−1.17697
$351$	19.3511	1.03289
$352$	−20.7210	−1.10443
$353$	−18.8898	−1.00540	−0.502702	−	0.864460i	$-0.667661\pi$
$353$	−18.8898	−1.00540	−0.502702	+	0.864460i	$0.667661\pi$
$354$	13.9307	0.740406
$355$	−5.52337	−0.293150
$356$	−11.6474	−0.617312
$357$	10.2215	0.540980
$358$	−26.9701	−1.42541
$359$	26.9376	1.42171	0.710856	−	0.703337i	$-0.248308\pi$
$359$	26.9376	1.42171	0.710856	+	0.703337i	$0.248308\pi$
$360$	−1.73356	−0.0913667
$361$	−15.7236	−0.827560
$362$	1.24141	0.0652472
$363$	18.2429	0.957505
$364$	−13.1647	−0.690018
$365$	−5.04363	−0.263996
$366$	−8.73937	−0.456814
$367$	−33.8885	−1.76897	−0.884483	−	0.466572i	$-0.845489\pi$
$367$	−33.8885	−1.76897	−0.884483	+	0.466572i	$0.845489\pi$
$368$	1.67105	0.0871093
$369$	−7.13791	−0.371584
$370$	8.82160	0.458613
$371$	−4.95105	−0.257046
$372$	6.05928	0.314159
$373$	−23.7038	−1.22734	−0.613668	−	0.789564i	$-0.710307\pi$
$373$	−23.7038	−1.22734	−0.613668	+	0.789564i	$0.710307\pi$
$374$	7.60859	0.393431
$375$	−11.1348	−0.574998
$376$	7.64932	0.394484
$377$	3.44502	0.177428
$378$	−28.2244	−1.45171
$379$	−4.50732	−0.231525	−0.115763	−	0.993277i	$-0.536931\pi$
$379$	−4.50732	−0.231525	−0.115763	+	0.993277i	$0.536931\pi$
$380$	1.17311	0.0601794
$381$	−2.67683	−0.137138
$382$	13.7717	0.704621
$383$	14.3548	0.733496	0.366748	−	0.930320i	$-0.380471\pi$
$383$	14.3548	0.733496	0.366748	+	0.930320i	$0.380471\pi$
$384$	−0.101546	−0.00518200
$385$	−17.5015	−0.891959
$386$	−17.0367	−0.867148
$387$	4.74633	0.241269
$388$	6.92326	0.351475
$389$	−34.9730	−1.77320	−0.886601	−	0.462534i	$-0.846940\pi$
$389$	−34.9730	−1.77320	−0.886601	+	0.462534i	$0.846940\pi$
$390$	4.43275	0.224461
$391$	1.46070	0.0738709
$392$	44.3392	2.23947
$393$	8.11145	0.409169
$394$	−6.17058	−0.310870
$395$	−3.83516	−0.192968
$396$	2.85305	0.143371
$397$	17.6680	0.886733	0.443366	−	0.896341i	$-0.353784\pi$
$397$	17.6680	0.886733	0.443366	+	0.896341i	$0.353784\pi$
$398$	28.2133	1.41421
$399$	12.6663	0.634108
$400$	7.32283	0.366141
$401$	−21.8754	−1.09241	−0.546203	−	0.837653i	$-0.683927\pi$
$401$	−21.8754	−1.09241	−0.546203	+	0.837653i	$0.683927\pi$
$402$	3.34117	0.166642
$403$	16.7669	0.835218
$404$	3.03522	0.151008
$405$	−4.96814	−0.246869
$406$	−5.02469	−0.249371
$407$	−49.7338	−2.46522
$408$	−6.75400	−0.334373
$409$	9.81435	0.485288	0.242644	−	0.970115i	$-0.421985\pi$
$409$	9.81435	0.485288	0.242644	+	0.970115i	$0.421985\pi$
$410$	−8.44593	−0.417115
$411$	−23.8005	−1.17399
$412$	−10.4170	−0.513209
$413$	39.4391	1.94067
$414$	−0.780838	−0.0383761
$415$	1.31864	0.0647293
$416$	14.8581	0.728480
$417$	24.4709	1.19834
$418$	9.42841	0.461159
$419$	0.696845	0.0340431	0.0170216	−	0.999855i	$-0.494582\pi$
$419$	0.696845	0.0340431	0.0170216	+	0.999855i	$0.494582\pi$
$420$	4.53521	0.221295
$421$	3.13846	0.152959	0.0764795	−	0.997071i	$-0.475632\pi$
$421$	3.13846	0.152959	0.0764795	+	0.997071i	$0.475632\pi$
$422$	−6.47317	−0.315109
$423$	−1.79899	−0.0874699
$424$	3.27147	0.158877
$425$	6.40106	0.310497
$426$	11.5034	0.557340
$427$	−24.7420	−1.19735
$428$	−14.1242	−0.682719
$429$	−24.9907	−1.20656
$430$	5.61609	0.270832
$431$	37.0873	1.78643	0.893217	−	0.449626i	$-0.148443\pi$
$431$	37.0873	1.78643	0.893217	+	0.449626i	$0.148443\pi$
$432$	9.38649	0.451608
$433$	−20.1836	−0.969960	−0.484980	−	0.874525i	$-0.661173\pi$
$433$	−20.1836	−0.969960	−0.484980	+	0.874525i	$0.661173\pi$
$434$	−24.4551	−1.17388
$435$	−1.18680	−0.0569028
$436$	3.47832	0.166582
$437$	1.81007	0.0865875
$438$	10.5042	0.501912
$439$	−28.5330	−1.36181	−0.680904	−	0.732373i	$-0.738413\pi$
$439$	−28.5330	−1.36181	−0.680904	+	0.732373i	$0.738413\pi$
$440$	11.5643	0.551308
$441$	−10.4278	−0.496562
$442$	−5.45578	−0.259505
$443$	−29.2659	−1.39046	−0.695231	−	0.718786i	$-0.744698\pi$
$443$	−29.2659	−1.39046	−0.695231	+	0.718786i	$0.744698\pi$
$444$	12.8877	0.611621
$445$	11.1032	0.526341
$446$	2.10981	0.0999025
$447$	−1.15945	−0.0548401
$448$	−37.1602	−1.75565
$449$	4.20481	0.198437	0.0992185	−	0.995066i	$-0.468366\pi$
$449$	4.20481	0.198437	0.0992185	+	0.995066i	$0.468366\pi$
$450$	−3.42177	−0.161304
$451$	47.6159	2.24215
$452$	10.2380	0.481556
$453$	5.30912	0.249444
$454$	−15.3841	−0.722012
$455$	12.5496	0.588332
$456$	−8.36942	−0.391934
$457$	20.6073	0.963968	0.481984	−	0.876180i	$-0.339916\pi$
$457$	20.6073	0.963968	0.481984	+	0.876180i	$0.339916\pi$
$458$	18.5529	0.866918
$459$	8.20496	0.382975
$460$	0.648102	0.0302179
$461$	21.3498	0.994359	0.497179	−	0.867648i	$-0.334369\pi$
$461$	21.3498	0.994359	0.497179	+	0.867648i	$0.334369\pi$
$462$	36.4499	1.69580
$463$	−11.0632	−0.514148	−0.257074	−	0.966392i	$-0.582758\pi$
$463$	−11.0632	−0.514148	−0.257074	+	0.966392i	$0.582758\pi$
$464$	1.67105	0.0775764
$465$	−5.77615	−0.267863
$466$	−10.6242	−0.492156
$467$	28.8402	1.33457	0.667283	−	0.744804i	$-0.267457\pi$
$467$	28.8402	1.33457	0.667283	+	0.744804i	$0.267457\pi$
$468$	−2.04579	−0.0945669
$469$	9.45917	0.436784
$470$	−2.12866	−0.0981875
$471$	20.5762	0.948102
$472$	−26.0599	−1.19950
$473$	−31.6621	−1.45582
$474$	7.98738	0.366872
$475$	7.93207	0.363948
$476$	−5.58188	−0.255845
$477$	−0.769394	−0.0352281
$478$	−15.0341	−0.687644
$479$	−38.2372	−1.74710	−0.873550	−	0.486734i	$-0.838188\pi$
$479$	−38.2372	−1.74710	−0.873550	+	0.486734i	$0.838188\pi$
$480$	−5.11859	−0.233631
$481$	35.6620	1.62605
$482$	12.1763	0.554617
$483$	6.99768	0.318405
$484$	−9.96229	−0.452832
$485$	−6.59976	−0.299680
$486$	−7.92303	−0.359396
$487$	35.5068	1.60897	0.804484	−	0.593975i	$-0.202442\pi$
$487$	35.5068	1.60897	0.804484	+	0.593975i	$0.202442\pi$
$488$	16.3486	0.740066
$489$	36.4919	1.65022
$490$	−12.3387	−0.557406
$491$	35.3266	1.59427	0.797135	−	0.603802i	$-0.206348\pi$
$491$	35.3266	1.59427	0.797135	+	0.603802i	$0.206348\pi$
$492$	−12.3388	−0.556278
$493$	1.46070	0.0657867
$494$	−6.76070	−0.304178
$495$	−2.71973	−0.122243
$496$	8.13297	0.365181
$497$	32.5672	1.46084
$498$	−2.74629	−0.123064
$499$	22.0133	0.985449	0.492724	−	0.870185i	$-0.336001\pi$
$499$	22.0133	0.985449	0.492724	+	0.870185i	$0.336001\pi$
$500$	6.08061	0.271933
$501$	4.53708	0.202702
$502$	7.81466	0.348785
$503$	−6.03824	−0.269232	−0.134616	−	0.990898i	$-0.542980\pi$
$503$	−6.03824	−0.269232	−0.134616	+	0.990898i	$0.542980\pi$
$504$	10.2215	0.455302
$505$	−2.89339	−0.128754
$506$	5.20885	0.231562
$507$	−1.70895	−0.0758971
$508$	1.46179	0.0648566
$509$	−10.2485	−0.454258	−0.227129	−	0.973865i	$-0.572934\pi$
$509$	−10.2485	−0.454258	−0.227129	+	0.973865i	$0.572934\pi$
$510$	1.87950	0.0832259
$511$	29.7385	1.31555
$512$	17.4417	0.770821
$513$	10.1674	0.448903
$514$	23.9675	1.05716
$515$	9.93026	0.437579
$516$	8.20467	0.361190
$517$	12.0008	0.527795
$518$	−52.0143	−2.28538
$519$	−4.75367	−0.208663
$520$	−8.29228	−0.363640
$521$	−4.07192	−0.178394	−0.0891971	−	0.996014i	$-0.528430\pi$
$521$	−4.07192	−0.178394	−0.0891971	+	0.996014i	$0.528430\pi$
$522$	−0.780838	−0.0341763
$523$	11.8406	0.517755	0.258878	−	0.965910i	$-0.416647\pi$
$523$	11.8406	0.517755	0.258878	+	0.965910i	$0.416647\pi$
$524$	−4.42959	−0.193508
$525$	30.6651	1.33833
$526$	−9.09075	−0.396375
$527$	7.10923	0.309683
$528$	−12.1220	−0.527543
$529$	1.00000	0.0434783
$530$	−0.910386	−0.0395446
$531$	6.12883	0.265969
$532$	−6.91696	−0.299888
$533$	−34.1433	−1.47891
$534$	−23.1243	−1.00069
$535$	13.4642	0.582109
$536$	−6.25027	−0.269970
$537$	37.5601	1.62084
$538$	−6.25131	−0.269513
$539$	69.5624	2.99626
$540$	3.64047	0.156661
$541$	23.8471	1.02527	0.512634	−	0.858607i	$-0.328670\pi$
$541$	23.8471	1.02527	0.512634	+	0.858607i	$0.328670\pi$
$542$	21.9702	0.943703
$543$	−1.72886	−0.0741926
$544$	6.29991	0.270106
$545$	−3.31579	−0.142033
$546$	−26.1366	−1.11854
$547$	1.89606	0.0810697	0.0405349	−	0.999178i	$-0.487094\pi$
$547$	1.89606	0.0810697	0.0405349	+	0.999178i	$0.487094\pi$
$548$	12.9972	0.555214
$549$	−3.84491	−0.164097
$550$	22.8261	0.973310
$551$	1.81007	0.0771117
$552$	−4.62380	−0.196802
$553$	22.6130	0.961604
$554$	29.4889	1.25287
$555$	−12.2855	−0.521489
$556$	−13.3633	−0.566732
$557$	−37.6779	−1.59646	−0.798231	−	0.602351i	$-0.794231\pi$
$557$	−37.6779	−1.59646	−0.798231	+	0.602351i	$0.794231\pi$
$558$	−3.80033	−0.160881
$559$	22.7035	0.960255
$560$	6.08730	0.257235
$561$	−10.5962	−0.447370
$562$	−7.40319	−0.312285
$563$	−21.4129	−0.902444	−0.451222	−	0.892412i	$-0.649012\pi$
$563$	−21.4129	−0.902444	−0.451222	+	0.892412i	$0.649012\pi$
$564$	−3.10980	−0.130946
$565$	−9.75962	−0.410590
$566$	30.1440	1.26705
$567$	29.2934	1.23021
$568$	−21.5192	−0.902925
$569$	7.76547	0.325545	0.162773	−	0.986664i	$-0.447956\pi$
$569$	7.76547	0.325545	0.162773	+	0.986664i	$0.447956\pi$
$570$	2.32904	0.0975529
$571$	−28.3747	−1.18744	−0.593721	−	0.804671i	$-0.702342\pi$
$571$	−28.3747	−1.18744	−0.593721	+	0.804671i	$0.702342\pi$
$572$	13.6472	0.570618
$573$	−19.1792	−0.801224
$574$	49.7993	2.07858
$575$	4.38218	0.182750
$576$	−5.77470	−0.240612
$577$	−3.14685	−0.131005	−0.0655026	−	0.997852i	$-0.520865\pi$
$577$	−3.14685	−0.131005	−0.0655026	+	0.997852i	$0.520865\pi$
$578$	16.1179	0.670415
$579$	23.7264	0.986033
$580$	0.648102	0.0269110
$581$	−7.77500	−0.322561
$582$	13.7451	0.569754
$583$	5.13252	0.212567
$584$	−19.6501	−0.813127
$585$	1.95020	0.0806309
$586$	0.0128257	0.000529824 0
$587$	27.8440	1.14924	0.574622	−	0.818419i	$-0.305149\pi$
$587$	27.8440	1.14924	0.574622	+	0.818419i	$0.305149\pi$
$588$	−18.0259	−0.743375
$589$	8.80961	0.362994
$590$	7.25194	0.298558
$591$	8.59351	0.353490
$592$	17.2982	0.710953
$593$	2.77521	0.113964	0.0569820	−	0.998375i	$-0.481852\pi$
$593$	2.77521	0.113964	0.0569820	+	0.998375i	$0.481852\pi$
$594$	29.2588	1.20050
$595$	5.32106	0.218142
$596$	0.633166	0.0259355
$597$	−39.2915	−1.60809
$598$	−3.73504	−0.152737
$599$	−23.8140	−0.973012	−0.486506	−	0.873677i	$-0.661729\pi$
$599$	−23.8140	−0.973012	−0.486506	+	0.873677i	$0.661729\pi$
$600$	−20.2623	−0.827207
$601$	20.9662	0.855231	0.427616	−	0.903961i	$-0.359354\pi$
$601$	20.9662	0.855231	0.427616	+	0.903961i	$0.359354\pi$
$602$	−33.1139	−1.34962
$603$	1.46996	0.0598612
$604$	−2.89926	−0.117969
$605$	9.49679	0.386099
$606$	6.02599	0.244789
$607$	−2.59519	−0.105336	−0.0526678	−	0.998612i	$-0.516772\pi$
$607$	−2.59519	−0.105336	−0.0526678	+	0.998612i	$0.516772\pi$
$608$	7.80672	0.316604
$609$	6.99768	0.283560
$610$	−4.54949	−0.184204
$611$	−8.60525	−0.348131
$612$	−0.867425	−0.0350636
$613$	−35.4865	−1.43329	−0.716644	−	0.697439i	$-0.754323\pi$
$613$	−35.4865	−1.43329	−0.716644	+	0.697439i	$0.754323\pi$
$614$	0.528857	0.0213429
$615$	11.7623	0.474301
$616$	−68.1862	−2.74730
$617$	−15.1294	−0.609085	−0.304543	−	0.952499i	$-0.598504\pi$
$617$	−15.1294	−0.609085	−0.304543	+	0.952499i	$0.598504\pi$
$618$	−20.6815	−0.831931
$619$	−28.5271	−1.14660	−0.573301	−	0.819345i	$-0.694338\pi$
$619$	−28.5271	−1.14660	−0.573301	+	0.819345i	$0.694338\pi$
$620$	3.15431	0.126680
$621$	5.61713	0.225408
$622$	−36.2243	−1.45246
$623$	−65.4671	−2.62288
$624$	8.69217	0.347965
$625$	16.1144	0.644577
$626$	−21.2358	−0.848754
$627$	−13.1305	−0.524383
$628$	−11.2365	−0.448385
$629$	15.1208	0.602906
$630$	−2.84444	−0.113325
$631$	19.9685	0.794935	0.397467	−	0.917616i	$-0.369889\pi$
$631$	19.9685	0.794935	0.397467	+	0.917616i	$0.369889\pi$
$632$	−14.9419	−0.594355
$633$	9.01491	0.358310
$634$	12.5011	0.496483
$635$	−1.39349	−0.0552990
$636$	−1.33000	−0.0527380
$637$	−49.8801	−1.97632
$638$	5.20885	0.206221
$639$	5.06094	0.200208
$640$	−0.0528623	−0.00208956
$641$	−22.0041	−0.869111	−0.434556	−	0.900645i	$-0.643095\pi$
$641$	−22.0041	−0.869111	−0.434556	+	0.900645i	$0.643095\pi$
$642$	−28.0415	−1.10671
$643$	−43.6608	−1.72181	−0.860907	−	0.508763i	$-0.830103\pi$
$643$	−43.6608	−1.72181	−0.860907	+	0.508763i	$0.830103\pi$
$644$	−3.82137	−0.150583
$645$	−7.82129	−0.307963
$646$	−2.86656	−0.112783
$647$	−39.8183	−1.56542	−0.782709	−	0.622388i	$-0.786162\pi$
$647$	−39.8183	−1.56542	−0.782709	+	0.622388i	$0.786162\pi$
$648$	−19.3560	−0.760375
$649$	−40.8845	−1.60486
$650$	−16.3676	−0.641991
$651$	34.0576	1.33482
$652$	−19.9279	−0.780437
$653$	−15.2538	−0.596927	−0.298463	−	0.954421i	$-0.596474\pi$
$653$	−15.2538	−0.596927	−0.298463	+	0.954421i	$0.596474\pi$
$654$	6.90571	0.270035
$655$	4.22261	0.164991
$656$	−16.5616	−0.646621
$657$	4.62137	0.180297
$658$	12.5511	0.489292
$659$	2.69443	0.104960	0.0524801	−	0.998622i	$-0.483287\pi$
$659$	2.69443	0.104960	0.0524801	+	0.998622i	$0.483287\pi$
$660$	−4.70143	−0.183003
$661$	19.4470	0.756402	0.378201	−	0.925723i	$-0.376543\pi$
$661$	19.4470	0.756402	0.378201	+	0.925723i	$0.376543\pi$
$662$	33.9741	1.32044
$663$	7.59804	0.295083
$664$	5.13743	0.199371
$665$	6.59375	0.255695
$666$	−8.08303	−0.313211
$667$	1.00000	0.0387202
$668$	−2.47766	−0.0958635
$669$	−2.93825	−0.113599
$670$	1.73933	0.0671960
$671$	25.6488	0.990162
$672$	30.1805	1.16424
$673$	−35.7115	−1.37658	−0.688289	−	0.725436i	$-0.741638\pi$
$673$	−35.7115	−1.37658	−0.688289	+	0.725436i	$0.741638\pi$
$674$	14.4759	0.557591
$675$	24.6153	0.947443
$676$	0.933242	0.0358939
$677$	−21.0987	−0.810890	−0.405445	−	0.914119i	$-0.632883\pi$
$677$	−21.0987	−0.810890	−0.405445	+	0.914119i	$0.632883\pi$
$678$	20.3261	0.780619
$679$	38.9138	1.49338
$680$	−3.51596	−0.134831
$681$	21.4248	0.821000
$682$	25.3515	0.970757
$683$	37.5417	1.43649	0.718247	−	0.695788i	$-0.244945\pi$
$683$	37.5417	1.43649	0.718247	+	0.695788i	$0.244945\pi$
$684$	−1.07490	−0.0410997
$685$	−12.3899	−0.473394
$686$	37.5792	1.43478
$687$	−25.8378	−0.985772
$688$	11.0126	0.419850
$689$	−3.68030	−0.140208
$690$	1.28671	0.0489843
$691$	−16.6961	−0.635148	−0.317574	−	0.948234i	$-0.602868\pi$
$691$	−16.6961	−0.635148	−0.317574	+	0.948234i	$0.602868\pi$
$692$	2.59594	0.0986828
$693$	16.0362	0.609166
$694$	−9.38956	−0.356423
$695$	12.7389	0.483214
$696$	−4.62380	−0.175265
$697$	−14.4769	−0.548351
$698$	14.1327	0.534932
$699$	14.7959	0.559631
$700$	−16.7459	−0.632937
$701$	−13.1653	−0.497248	−0.248624	−	0.968600i	$-0.579978\pi$
$701$	−13.1653	−0.497248	−0.248624	+	0.968600i	$0.579978\pi$
$702$	−20.9802	−0.791848
$703$	18.7374	0.706695
$704$	38.5222	1.45186
$705$	2.96449	0.111649
$706$	20.4801	0.770778
$707$	17.0602	0.641613
$708$	10.5945	0.398166
$709$	38.7350	1.45472	0.727362	−	0.686254i	$-0.240746\pi$
$709$	38.7350	1.45472	0.727362	+	0.686254i	$0.240746\pi$
$710$	5.98836	0.224739
$711$	3.51407	0.131788
$712$	43.2582	1.62117
$713$	4.86699	0.182270
$714$	−11.0820	−0.414734
$715$	−13.0095	−0.486528
$716$	−20.5112	−0.766540
$717$	20.9373	0.781920
$718$	−29.2054	−1.08993
$719$	23.8247	0.888510	0.444255	−	0.895900i	$-0.353468\pi$
$719$	23.8247	0.888510	0.444255	+	0.895900i	$0.353468\pi$
$720$	0.945967	0.0352541
$721$	−58.5513	−2.18056
$722$	17.0473	0.634436
$723$	−16.9575	−0.630654
$724$	0.944117	0.0350878
$725$	4.38218	0.162750
$726$	−19.7787	−0.734056
$727$	−31.4321	−1.16575	−0.582877	−	0.812561i	$-0.698073\pi$
$727$	−31.4321	−1.16575	−0.582877	+	0.812561i	$0.698073\pi$
$728$	48.8933	1.81211
$729$	29.9961	1.11097
$730$	5.46823	0.202388
$731$	9.62636	0.356044
$732$	−6.64645	−0.245660
$733$	−38.3457	−1.41633	−0.708165	−	0.706047i	$-0.750477\pi$
$733$	−38.3457	−1.41633	−0.708165	+	0.706047i	$0.750477\pi$
$734$	36.7414	1.35615
$735$	17.1836	0.633826
$736$	4.31293	0.158977
$737$	−9.80586	−0.361203
$738$	7.73881	0.284870
$739$	34.3034	1.26187	0.630935	−	0.775836i	$-0.282672\pi$
$739$	34.3034	1.26187	0.630935	+	0.775836i	$0.282672\pi$
$740$	6.70898	0.246627
$741$	9.41533	0.345881
$742$	5.36786	0.197060
$743$	10.8086	0.396529	0.198264	−	0.980149i	$-0.436470\pi$
$743$	10.8086	0.396529	0.198264	+	0.980149i	$0.436470\pi$
$744$	−22.5040	−0.825037
$745$	−0.603580	−0.0221135
$746$	25.6993	0.940919
$747$	−1.20824	−0.0442070
$748$	5.78647	0.211574
$749$	−79.3884	−2.90079
$750$	12.0722	0.440813
$751$	−24.6782	−0.900521	−0.450260	−	0.892897i	$-0.648669\pi$
$751$	−24.6782	−0.900521	−0.450260	+	0.892897i	$0.648669\pi$
$752$	−4.17407	−0.152213
$753$	−10.8831	−0.396604
$754$	−3.73504	−0.136022
$755$	2.76379	0.100585
$756$	−21.4651	−0.780680
$757$	32.4734	1.18027	0.590134	−	0.807306i	$-0.299075\pi$
$757$	32.4734	1.18027	0.590134	+	0.807306i	$0.299075\pi$
$758$	4.88677	0.177495
$759$	−7.25415	−0.263309
$760$	−4.35690	−0.158042
$761$	17.9063	0.649104	0.324552	−	0.945868i	$-0.394786\pi$
$761$	17.9063	0.649104	0.324552	+	0.945868i	$0.394786\pi$
$762$	2.90218	0.105135
$763$	19.5507	0.707785
$764$	10.4736	0.378922
$765$	0.826893	0.0298964
$766$	−15.5633	−0.562324
$767$	29.3165	1.05856
$768$	−24.1030	−0.869741
$769$	18.7697	0.676852	0.338426	−	0.940993i	$-0.390106\pi$
$769$	18.7697	0.676852	0.338426	+	0.940993i	$0.390106\pi$
$770$	18.9749	0.683807
$771$	−33.3786	−1.20210
$772$	−12.9567	−0.466324
$773$	−44.3825	−1.59633	−0.798163	−	0.602441i	$-0.794195\pi$
$773$	−44.3825	−1.59633	−0.798163	+	0.602441i	$0.794195\pi$
$774$	−5.14590	−0.184966
$775$	21.3280	0.766126
$776$	−25.7128	−0.923036
$777$	72.4381	2.59870
$778$	37.9172	1.35940
$779$	−17.9395	−0.642748
$780$	3.37119	0.120708
$781$	−33.7608	−1.20806
$782$	−1.58367	−0.0566320
$783$	5.61713	0.200740
$784$	−24.1949	−0.864104
$785$	10.7114	0.382308
$786$	−8.79432	−0.313683
$787$	−29.9582	−1.06790	−0.533948	−	0.845517i	$-0.679292\pi$
$787$	−29.9582	−1.06790	−0.533948	+	0.845517i	$0.679292\pi$
$788$	−4.69284	−0.167175
$789$	12.6603	0.450718
$790$	4.15802	0.147936
$791$	57.5452	2.04607
$792$	−10.5961	−0.376517
$793$	−18.3917	−0.653107
$794$	−19.1554	−0.679800
$795$	1.26786	0.0449662
$796$	21.4567	0.760514
$797$	3.16027	0.111942	0.0559712	−	0.998432i	$-0.482175\pi$
$797$	3.16027	0.111942	0.0559712	+	0.998432i	$0.482175\pi$
$798$	−13.7326	−0.486130
$799$	−3.64866	−0.129080
$800$	18.9000	0.668218
$801$	−10.1736	−0.359466
$802$	23.7170	0.837476
$803$	−30.8285	−1.08791
$804$	2.54102	0.0896147
$805$	3.64281	0.128392
$806$	−18.1784	−0.640307
$807$	8.70594	0.306464
$808$	−11.2727	−0.396573
$809$	−45.7986	−1.61019	−0.805096	−	0.593145i	$-0.797886\pi$
$809$	−45.7986	−1.61019	−0.805096	+	0.593145i	$0.797886\pi$
$810$	5.38639	0.189258
$811$	16.1790	0.568120	0.284060	−	0.958806i	$-0.408318\pi$
$811$	16.1790	0.568120	0.284060	+	0.958806i	$0.408318\pi$
$812$	−3.82137	−0.134104
$813$	−30.5970	−1.07308
$814$	53.9207	1.88992
$815$	18.9967	0.665427
$816$	3.68551	0.129019
$817$	11.9288	0.417336
$818$	−10.6406	−0.372039
$819$	−11.4989	−0.401803
$820$	−6.42328	−0.224311
$821$	−5.87948	−0.205195	−0.102598	−	0.994723i	$-0.532715\pi$
$821$	−5.87948	−0.205195	−0.102598	+	0.994723i	$0.532715\pi$
$822$	25.8041	0.900023
$823$	−38.8583	−1.35452	−0.677258	−	0.735745i	$-0.736832\pi$
$823$	−38.8583	−1.35452	−0.677258	+	0.735745i	$0.736832\pi$
$824$	38.6885	1.34778
$825$	−31.7890	−1.10675
$826$	−42.7592	−1.48778
$827$	22.6489	0.787581	0.393791	−	0.919200i	$-0.371164\pi$
$827$	22.6489	0.787581	0.393791	+	0.919200i	$0.371164\pi$
$828$	−0.593841	−0.0206374
$829$	−2.01054	−0.0698290	−0.0349145	−	0.999390i	$-0.511116\pi$
$829$	−2.01054	−0.0698290	−0.0349145	+	0.999390i	$0.511116\pi$
$830$	−1.42965	−0.0496237
$831$	−41.0680	−1.42463
$832$	−27.6226	−0.957640
$833$	−21.1494	−0.732783
$834$	−26.5310	−0.918692
$835$	2.36189	0.0817365
$836$	7.17047	0.247996
$837$	27.3385	0.944958
$838$	−0.755510	−0.0260986
$839$	7.17708	0.247780	0.123890	−	0.992296i	$-0.460463\pi$
$839$	7.17708	0.247780	0.123890	+	0.992296i	$0.460463\pi$
$840$	−16.8436	−0.581161
$841$	1.00000	0.0344828
$842$	−3.40267	−0.117264
$843$	10.3101	0.355099
$844$	−4.92296	−0.169455
$845$	−0.889635	−0.0306044
$846$	1.95044	0.0670574
$847$	−55.9954	−1.92403
$848$	−1.78517	−0.0613030
$849$	−41.9803	−1.44076
$850$	−6.93994	−0.238038
$851$	10.3517	0.354853
$852$	8.74852	0.299719
$853$	17.2084	0.589204	0.294602	−	0.955620i	$-0.404813\pi$
$853$	17.2084	0.589204	0.294602	+	0.955620i	$0.404813\pi$
$854$	26.8249	0.917930
$855$	1.02467	0.0350429
$856$	52.4569	1.79294
$857$	−35.4590	−1.21126	−0.605629	−	0.795747i	$-0.707078\pi$
$857$	−35.4590	−1.21126	−0.605629	+	0.795747i	$0.707078\pi$
$858$	27.0945	0.924992
$859$	53.2336	1.81631	0.908153	−	0.418638i	$-0.137492\pi$
$859$	53.2336	1.81631	0.908153	+	0.418638i	$0.137492\pi$
$860$	4.27114	0.145645
$861$	−69.3533	−2.36356
$862$	−40.2095	−1.36954
$863$	−24.5153	−0.834509	−0.417255	−	0.908790i	$-0.637008\pi$
$863$	−24.5153	−0.834509	−0.417255	+	0.908790i	$0.637008\pi$
$864$	24.2263	0.824196
$865$	−2.47464	−0.0841402
$866$	21.8827	0.743605
$867$	−22.4467	−0.762329
$868$	−18.5986	−0.631277
$869$	−23.4418	−0.795210
$870$	1.28671	0.0436236
$871$	7.03135	0.238248
$872$	−12.9184	−0.437472
$873$	6.04721	0.204667
$874$	−1.96245	−0.0663810
$875$	34.1775	1.15541
$876$	7.98866	0.269912
$877$	32.3744	1.09320	0.546602	−	0.837392i	$-0.315921\pi$
$877$	32.3744	1.09320	0.546602	+	0.837392i	$0.315921\pi$
$878$	30.9351	1.04401
$879$	−0.0178618	−0.000602463 0
$880$	−6.31041	−0.212724
$881$	8.70671	0.293337	0.146668	−	0.989186i	$-0.453145\pi$
$881$	8.70671	0.293337	0.146668	+	0.989186i	$0.453145\pi$
$882$	11.3057	0.380682
$883$	21.8907	0.736681	0.368341	−	0.929691i	$-0.379926\pi$
$883$	21.8907	0.736681	0.368341	+	0.929691i	$0.379926\pi$
$884$	−4.14922	−0.139553
$885$	−10.0995	−0.339490
$886$	31.7296	1.06598
$887$	−38.4846	−1.29219	−0.646093	−	0.763259i	$-0.723598\pi$
$887$	−38.4846	−1.29219	−0.646093	+	0.763259i	$0.723598\pi$
$888$	−47.8644	−1.60622
$889$	8.21636	0.275568
$890$	−12.0379	−0.403511
$891$	−30.3671	−1.01733
$892$	1.60455	0.0537243
$893$	−4.52134	−0.151301
$894$	1.25706	0.0420423
$895$	19.5528	0.653578
$896$	0.311689	0.0104128
$897$	5.20163	0.173677
$898$	−4.55879	−0.152129
$899$	4.86699	0.162323
$900$	−2.60232	−0.0867440
$901$	−1.56046	−0.0519866
$902$	−51.6245	−1.71891
$903$	46.1163	1.53465
$904$	−38.0237	−1.26465
$905$	−0.900002	−0.0299171
$906$	−5.75607	−0.191233
$907$	−2.29646	−0.0762528	−0.0381264	−	0.999273i	$-0.512139\pi$
$907$	−2.29646	−0.0762528	−0.0381264	+	0.999273i	$0.512139\pi$
$908$	−11.6999	−0.388274
$909$	2.65115	0.0879331
$910$	−13.6060	−0.451036
$911$	51.4864	1.70582	0.852910	−	0.522059i	$-0.174836\pi$
$911$	51.4864	1.70582	0.852910	+	0.522059i	$0.174836\pi$
$912$	4.56701	0.151229
$913$	8.05997	0.266746
$914$	−22.3421	−0.739011
$915$	6.33588	0.209458
$916$	14.1098	0.466200
$917$	−24.8976	−0.822190
$918$	−8.89570	−0.293602
$919$	35.4694	1.17003	0.585014	−	0.811023i	$-0.301089\pi$
$919$	35.4694	1.17003	0.585014	+	0.811023i	$0.301089\pi$
$920$	−2.40703	−0.0793575
$921$	−0.736517	−0.0242690
$922$	−23.1471	−0.762310
$923$	24.2084	0.796829
$924$	27.7208	0.911947
$925$	45.3632	1.49153
$926$	11.9945	0.394164
$927$	−9.09887	−0.298846
$928$	4.31293	0.141579
$929$	−31.5925	−1.03652	−0.518258	−	0.855224i	$-0.673419\pi$
$929$	−31.5925	−1.03652	−0.518258	+	0.855224i	$0.673419\pi$
$930$	6.26242	0.205353
$931$	−26.2079	−0.858929
$932$	−8.07989	−0.264666
$933$	50.4480	1.65159
$934$	−31.2681	−1.02312
$935$	−5.51608	−0.180395
$936$	7.59802	0.248349
$937$	−31.3788	−1.02510	−0.512550	−	0.858657i	$-0.671299\pi$
$937$	−31.3788	−1.02510	−0.512550	+	0.858657i	$0.671299\pi$
$938$	−10.2555	−0.334854
$939$	29.5742	0.965118
$940$	−1.61888	−0.0528020
$941$	−23.7309	−0.773606	−0.386803	−	0.922162i	$-0.626421\pi$
$941$	−23.7309	−0.773606	−0.386803	+	0.922162i	$0.626421\pi$
$942$	−22.3084	−0.726848
$943$	−9.91091	−0.322744
$944$	14.2203	0.462831
$945$	20.4621	0.665634
$946$	34.3275	1.11608
$947$	−36.6882	−1.19221	−0.596103	−	0.802908i	$-0.703285\pi$
$947$	−36.6882	−1.19221	−0.596103	+	0.802908i	$0.703285\pi$
$948$	6.07454	0.197292
$949$	22.1057	0.717583
$950$	−8.59983	−0.279015
$951$	−17.4098	−0.564551
$952$	20.7310	0.671894
$953$	22.0458	0.714133	0.357067	−	0.934079i	$-0.383777\pi$
$953$	22.0458	0.714133	0.357067	+	0.934079i	$0.383777\pi$
$954$	0.834166	0.0270071
$955$	−9.98422	−0.323082
$956$	−11.4337	−0.369792
$957$	−7.25415	−0.234493
$958$	41.4562	1.33939
$959$	73.0540	2.35904
$960$	9.51590	0.307124
$961$	−7.31240	−0.235884
$962$	−38.6642	−1.24658
$963$	−12.3370	−0.397553
$964$	9.26031	0.298255
$965$	12.3513	0.397603
$966$	−7.58678	−0.244101
$967$	35.0782	1.12804	0.564019	−	0.825762i	$-0.309254\pi$
$967$	35.0782	1.12804	0.564019	+	0.825762i	$0.309254\pi$
$968$	36.9997	1.18922
$969$	3.99214	0.128246
$970$	7.15536	0.229745
$971$	33.0765	1.06147	0.530737	−	0.847537i	$-0.321915\pi$
$971$	33.0765	1.06147	0.530737	+	0.847537i	$0.321915\pi$
$972$	−6.02560	−0.193271
$973$	−75.1118	−2.40797
$974$	−38.4960	−1.23349
$975$	22.7945	0.730008
$976$	−8.92108	−0.285557
$977$	47.8887	1.53209	0.766047	−	0.642785i	$-0.222221\pi$
$977$	47.8887	1.53209	0.766047	+	0.642785i	$0.222221\pi$
$978$	−39.5640	−1.26512
$979$	67.8665	2.16902
$980$	−9.38381	−0.299755
$981$	3.03819	0.0970018
$982$	−38.3006	−1.22222
$983$	36.4581	1.16283	0.581416	−	0.813606i	$-0.302499\pi$
$983$	36.4581	1.16283	0.581416	+	0.813606i	$0.302499\pi$
$984$	45.8261	1.46088
$985$	4.47356	0.142539
$986$	−1.58367	−0.0504344
$987$	−17.4794	−0.556374
$988$	−5.14163	−0.163577
$989$	6.59023	0.209557
$990$	2.94869	0.0937157
$991$	−29.1548	−0.926134	−0.463067	−	0.886323i	$-0.653251\pi$
$991$	−29.1548	−0.926134	−0.463067	+	0.886323i	$0.653251\pi$
$992$	20.9910	0.666465
$993$	−47.3143	−1.50147
$994$	−35.3089	−1.11993
$995$	−20.4541	−0.648440
$996$	−2.08860	−0.0661798
$997$	38.3967	1.21604	0.608018	−	0.793923i	$-0.291965\pi$
$997$	38.3967	1.21604	0.608018	+	0.793923i	$0.291965\pi$
$998$	−23.8665	−0.755479
$999$	58.1471	1.83969

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.b.1.5	✓	12
3.2	odd	2		6003.2.a.n.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.b.1.5	✓	12	1.1	even	1	trivial
6003.2.a.n.1.8		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.08419 q^{2} +1.50990 q^{3} -0.824542 q^{4} +0.786014 q^{5} -1.63701 q^{6} -4.63453 q^{7} +3.06233 q^{8} -0.720207 q^{9} +O(q^{10})\)	\(q-1.08419 q^{2} +1.50990 q^{3} -0.824542 q^{4} +0.786014 q^{5} -1.63701 q^{6} -4.63453 q^{7} +3.06233 q^{8} -0.720207 q^{9} -0.852185 q^{10} +4.80440 q^{11} -1.24497 q^{12} -3.44502 q^{13} +5.02469 q^{14} +1.18680 q^{15} -1.67105 q^{16} -1.46070 q^{17} +0.780838 q^{18} -1.81007 q^{19} -0.648102 q^{20} -6.99768 q^{21} -5.20885 q^{22} -1.00000 q^{23} +4.62380 q^{24} -4.38218 q^{25} +3.73504 q^{26} -5.61713 q^{27} +3.82137 q^{28} -1.00000 q^{29} -1.28671 q^{30} -4.86699 q^{31} -4.31293 q^{32} +7.25415 q^{33} +1.58367 q^{34} -3.64281 q^{35} +0.593841 q^{36} -10.3517 q^{37} +1.96245 q^{38} -5.20163 q^{39} +2.40703 q^{40} +9.91091 q^{41} +7.58678 q^{42} -6.59023 q^{43} -3.96143 q^{44} -0.566093 q^{45} +1.08419 q^{46} +2.49788 q^{47} -2.52311 q^{48} +14.4789 q^{49} +4.75110 q^{50} -2.20551 q^{51} +2.84056 q^{52} +1.06830 q^{53} +6.09001 q^{54} +3.77632 q^{55} -14.1925 q^{56} -2.73303 q^{57} +1.08419 q^{58} -8.50982 q^{59} -0.978568 q^{60} +5.33862 q^{61} +5.27672 q^{62} +3.33782 q^{63} +8.01811 q^{64} -2.70783 q^{65} -7.86484 q^{66} -2.04102 q^{67} +1.20441 q^{68} -1.50990 q^{69} +3.94948 q^{70} -7.02707 q^{71} -2.20551 q^{72} -6.41672 q^{73} +11.2232 q^{74} -6.61665 q^{75} +1.49248 q^{76} -22.2661 q^{77} +5.63953 q^{78} -4.87925 q^{79} -1.31347 q^{80} -6.32068 q^{81} -10.7453 q^{82} +1.67762 q^{83} +5.76988 q^{84} -1.14813 q^{85} +7.14503 q^{86} -1.50990 q^{87} +14.7126 q^{88} +14.1259 q^{89} +0.613749 q^{90} +15.9661 q^{91} +0.824542 q^{92} -7.34866 q^{93} -2.70816 q^{94} -1.42274 q^{95} -6.51209 q^{96} -8.39649 q^{97} -15.6978 q^{98} -3.46016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} + 11 q^{4} - 16 q^{5} - 2 q^{6} - 7 q^{7} - 9 q^{8} + 3 q^{9} - 6 q^{11} - 21 q^{12} - 15 q^{13} - 8 q^{14} + 6 q^{15} + 17 q^{16} - 18 q^{17} - 12 q^{18} - 6 q^{19} - 39 q^{20} - q^{21} - 5 q^{22} - 12 q^{23} + 4 q^{24} + 14 q^{25} - 3 q^{26} - 12 q^{27} - 19 q^{28} - 12 q^{29} - 11 q^{30} + 16 q^{31} - 21 q^{32} - 19 q^{33} - 7 q^{34} - 11 q^{35} - 13 q^{36} - q^{37} - 24 q^{38} + 6 q^{39} + 30 q^{40} + 3 q^{41} + 22 q^{42} - 23 q^{43} + 23 q^{44} - 22 q^{45} + 3 q^{46} - 35 q^{47} - 21 q^{48} + 3 q^{49} - 2 q^{50} - 34 q^{51} - 45 q^{53} + 55 q^{54} + 17 q^{55} - 17 q^{56} - 34 q^{57} + 3 q^{58} - 11 q^{59} + 93 q^{60} + 4 q^{61} - 7 q^{62} + q^{63} + 15 q^{64} + 5 q^{65} - 35 q^{66} - 19 q^{67} + q^{68} + 3 q^{69} + 14 q^{70} + 19 q^{71} + 4 q^{72} + 10 q^{73} - 15 q^{74} - 3 q^{75} - 4 q^{76} - 39 q^{77} + 16 q^{78} + 17 q^{79} - 90 q^{80} + 4 q^{81} - 3 q^{82} - 12 q^{83} + 42 q^{84} + 14 q^{85} + 17 q^{86} + 3 q^{87} - 2 q^{88} - 20 q^{89} + 65 q^{90} + 11 q^{91} - 11 q^{92} - 2 q^{93} + 13 q^{94} + 12 q^{95} + 14 q^{96} - 12 q^{97} + 75 q^{98} - 4 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 + 11 * q^4 - 16 * q^5 - 2 * q^6 - 7 * q^7 - 9 * q^8 + 3 * q^9 - 6 * q^11 - 21 * q^12 - 15 * q^13 - 8 * q^14 + 6 * q^15 + 17 * q^16 - 18 * q^17 - 12 * q^18 - 6 * q^19 - 39 * q^20 - q^21 - 5 * q^22 - 12 * q^23 + 4 * q^24 + 14 * q^25 - 3 * q^26 - 12 * q^27 - 19 * q^28 - 12 * q^29 - 11 * q^30 + 16 * q^31 - 21 * q^32 - 19 * q^33 - 7 * q^34 - 11 * q^35 - 13 * q^36 - q^37 - 24 * q^38 + 6 * q^39 + 30 * q^40 + 3 * q^41 + 22 * q^42 - 23 * q^43 + 23 * q^44 - 22 * q^45 + 3 * q^46 - 35 * q^47 - 21 * q^48 + 3 * q^49 - 2 * q^50 - 34 * q^51 - 45 * q^53 + 55 * q^54 + 17 * q^55 - 17 * q^56 - 34 * q^57 + 3 * q^58 - 11 * q^59 + 93 * q^60 + 4 * q^61 - 7 * q^62 + q^63 + 15 * q^64 + 5 * q^65 - 35 * q^66 - 19 * q^67 + q^68 + 3 * q^69 + 14 * q^70 + 19 * q^71 + 4 * q^72 + 10 * q^73 - 15 * q^74 - 3 * q^75 - 4 * q^76 - 39 * q^77 + 16 * q^78 + 17 * q^79 - 90 * q^80 + 4 * q^81 - 3 * q^82 - 12 * q^83 + 42 * q^84 + 14 * q^85 + 17 * q^86 + 3 * q^87 - 2 * q^88 - 20 * q^89 + 65 * q^90 + 11 * q^91 - 11 * q^92 - 2 * q^93 + 13 * q^94 + 12 * q^95 + 14 * q^96 - 12 * q^97 + 75 * q^98 - 4 * q^99

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