LMFDB - Embedded newform 6018.2.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 16x^{7} + 37x^{6} + 97x^{5} - 72x^{4} - 182x^{3} + 24x^{2} + 70x - 19 $ x^9 - 4x^8 - 16x^7 + 37x^6 + 97x^5 - 72x^4 - 182x^3 + 24x^2 + 70x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.443000$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03963 q^{5} +1.00000 q^{6} -4.77480 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03963 q^{5} +1.00000 q^{6} -4.77480 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.03963 q^{10} -2.24639 q^{11} -1.00000 q^{12} -5.97798 q^{13} +4.77480 q^{14} +2.03963 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +3.41029 q^{19} -2.03963 q^{20} +4.77480 q^{21} +2.24639 q^{22} -2.81366 q^{23} +1.00000 q^{24} -0.839893 q^{25} +5.97798 q^{26} -1.00000 q^{27} -4.77480 q^{28} +6.33268 q^{29} -2.03963 q^{30} +5.89965 q^{31} -1.00000 q^{32} +2.24639 q^{33} -1.00000 q^{34} +9.73885 q^{35} +1.00000 q^{36} +8.31348 q^{37} -3.41029 q^{38} +5.97798 q^{39} +2.03963 q^{40} +4.30463 q^{41} -4.77480 q^{42} +0.956651 q^{43} -2.24639 q^{44} -2.03963 q^{45} +2.81366 q^{46} -5.52929 q^{47} -1.00000 q^{48} +15.7987 q^{49} +0.839893 q^{50} -1.00000 q^{51} -5.97798 q^{52} +4.45423 q^{53} +1.00000 q^{54} +4.58182 q^{55} +4.77480 q^{56} -3.41029 q^{57} -6.33268 q^{58} +1.00000 q^{59} +2.03963 q^{60} -4.50283 q^{61} -5.89965 q^{62} -4.77480 q^{63} +1.00000 q^{64} +12.1929 q^{65} -2.24639 q^{66} -1.84562 q^{67} +1.00000 q^{68} +2.81366 q^{69} -9.73885 q^{70} -1.53649 q^{71} -1.00000 q^{72} +13.3357 q^{73} -8.31348 q^{74} +0.839893 q^{75} +3.41029 q^{76} +10.7261 q^{77} -5.97798 q^{78} -0.881718 q^{79} -2.03963 q^{80} +1.00000 q^{81} -4.30463 q^{82} -8.48862 q^{83} +4.77480 q^{84} -2.03963 q^{85} -0.956651 q^{86} -6.33268 q^{87} +2.24639 q^{88} +8.40538 q^{89} +2.03963 q^{90} +28.5437 q^{91} -2.81366 q^{92} -5.89965 q^{93} +5.52929 q^{94} -6.95575 q^{95} +1.00000 q^{96} -13.1187 q^{97} -15.7987 q^{98} -2.24639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.03963	−0.912152	−0.456076	−	0.889941i	$-0.650746\pi$
$5$	−2.03963	−0.912152	−0.456076	+	0.889941i	$0.650746\pi$
$6$	1.00000	0.408248
$7$	−4.77480	−1.80470	−0.902352	−	0.430999i	$-0.858161\pi$
$7$	−4.77480	−1.80470	−0.902352	+	0.430999i	$0.858161\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.03963	0.644989
$11$	−2.24639	−0.677313	−0.338656	−	0.940910i	$-0.609972\pi$
$11$	−2.24639	−0.677313	−0.338656	+	0.940910i	$0.609972\pi$
$12$	−1.00000	−0.288675
$13$	−5.97798	−1.65799	−0.828996	−	0.559254i	$-0.811088\pi$
$13$	−5.97798	−1.65799	−0.828996	+	0.559254i	$0.811088\pi$
$14$	4.77480	1.27612
$15$	2.03963	0.526631
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.00000	−0.235702
$19$	3.41029	0.782375	0.391188	−	0.920311i	$-0.372064\pi$
$19$	3.41029	0.782375	0.391188	+	0.920311i	$0.372064\pi$
$20$	−2.03963	−0.456076
$21$	4.77480	1.04195
$22$	2.24639	0.478933
$23$	−2.81366	−0.586689	−0.293344	−	0.956007i	$-0.594768\pi$
$23$	−2.81366	−0.586689	−0.293344	+	0.956007i	$0.594768\pi$
$24$	1.00000	0.204124
$25$	−0.839893	−0.167979
$26$	5.97798	1.17238
$27$	−1.00000	−0.192450
$28$	−4.77480	−0.902352
$29$	6.33268	1.17595	0.587974	−	0.808880i	$-0.299926\pi$
$29$	6.33268	1.17595	0.587974	+	0.808880i	$0.299926\pi$
$30$	−2.03963	−0.372385
$31$	5.89965	1.05961	0.529804	−	0.848120i	$-0.322265\pi$
$31$	5.89965	1.05961	0.529804	+	0.848120i	$0.322265\pi$
$32$	−1.00000	−0.176777
$33$	2.24639	0.391047
$34$	−1.00000	−0.171499
$35$	9.73885	1.64617
$36$	1.00000	0.166667
$37$	8.31348	1.36673	0.683363	−	0.730078i	$-0.260516\pi$
$37$	8.31348	1.36673	0.683363	+	0.730078i	$0.260516\pi$
$38$	−3.41029	−0.553223
$39$	5.97798	0.957243
$40$	2.03963	0.322494
$41$	4.30463	0.672270	0.336135	−	0.941814i	$-0.390880\pi$
$41$	4.30463	0.672270	0.336135	+	0.941814i	$0.390880\pi$
$42$	−4.77480	−0.736768
$43$	0.956651	0.145888	0.0729439	−	0.997336i	$-0.476761\pi$
$43$	0.956651	0.145888	0.0729439	+	0.997336i	$0.476761\pi$
$44$	−2.24639	−0.338656
$45$	−2.03963	−0.304051
$46$	2.81366	0.414851
$47$	−5.52929	−0.806529	−0.403265	−	0.915083i	$-0.632125\pi$
$47$	−5.52929	−0.806529	−0.403265	+	0.915083i	$0.632125\pi$
$48$	−1.00000	−0.144338
$49$	15.7987	2.25696
$50$	0.839893	0.118779
$51$	−1.00000	−0.140028
$52$	−5.97798	−0.828996
$53$	4.45423	0.611835	0.305918	−	0.952058i	$-0.401037\pi$
$53$	4.45423	0.611835	0.305918	+	0.952058i	$0.401037\pi$
$54$	1.00000	0.136083
$55$	4.58182	0.617812
$56$	4.77480	0.638060
$57$	−3.41029	−0.451704
$58$	−6.33268	−0.831521
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	2.03963	0.263316
$61$	−4.50283	−0.576529	−0.288264	−	0.957551i	$-0.593078\pi$
$61$	−4.50283	−0.576529	−0.288264	+	0.957551i	$0.593078\pi$
$62$	−5.89965	−0.749257
$63$	−4.77480	−0.601568
$64$	1.00000	0.125000
$65$	12.1929	1.51234
$66$	−2.24639	−0.276512
$67$	−1.84562	−0.225478	−0.112739	−	0.993625i	$-0.535962\pi$
$67$	−1.84562	−0.225478	−0.112739	+	0.993625i	$0.535962\pi$
$68$	1.00000	0.121268
$69$	2.81366	0.338725
$70$	−9.73885	−1.16401
$71$	−1.53649	−0.182348	−0.0911741	−	0.995835i	$-0.529062\pi$
$71$	−1.53649	−0.182348	−0.0911741	+	0.995835i	$0.529062\pi$
$72$	−1.00000	−0.117851
$73$	13.3357	1.56083	0.780415	−	0.625262i	$-0.215008\pi$
$73$	13.3357	1.56083	0.780415	+	0.625262i	$0.215008\pi$
$74$	−8.31348	−0.966422
$75$	0.839893	0.0969825
$76$	3.41029	0.391188
$77$	10.7261	1.22235
$78$	−5.97798	−0.676873
$79$	−0.881718	−0.0992010	−0.0496005	−	0.998769i	$-0.515795\pi$
$79$	−0.881718	−0.0992010	−0.0496005	+	0.998769i	$0.515795\pi$
$80$	−2.03963	−0.228038
$81$	1.00000	0.111111
$82$	−4.30463	−0.475367
$83$	−8.48862	−0.931747	−0.465874	−	0.884851i	$-0.654260\pi$
$83$	−8.48862	−0.931747	−0.465874	+	0.884851i	$0.654260\pi$
$84$	4.77480	0.520973
$85$	−2.03963	−0.221229
$86$	−0.956651	−0.103158
$87$	−6.33268	−0.678934
$88$	2.24639	0.239466
$89$	8.40538	0.890968	0.445484	−	0.895290i	$-0.353032\pi$
$89$	8.40538	0.890968	0.445484	+	0.895290i	$0.353032\pi$
$90$	2.03963	0.214996
$91$	28.5437	2.99219
$92$	−2.81366	−0.293344
$93$	−5.89965	−0.611765
$94$	5.52929	0.570302
$95$	−6.95575	−0.713645
$96$	1.00000	0.102062
$97$	−13.1187	−1.33200	−0.665999	−	0.745953i	$-0.731994\pi$
$97$	−13.1187	−1.33200	−0.665999	+	0.745953i	$0.731994\pi$
$98$	−15.7987	−1.59591
$99$	−2.24639	−0.225771
$100$	−0.839893	−0.0839893
$101$	−5.61774	−0.558986	−0.279493	−	0.960148i	$-0.590166\pi$
$101$	−5.61774	−0.558986	−0.279493	+	0.960148i	$0.590166\pi$
$102$	1.00000	0.0990148
$103$	−2.16480	−0.213304	−0.106652	−	0.994296i	$-0.534013\pi$
$103$	−2.16480	−0.213304	−0.106652	+	0.994296i	$0.534013\pi$
$104$	5.97798	0.586189
$105$	−9.73885	−0.950414
$106$	−4.45423	−0.432633
$107$	8.01120	0.774472	0.387236	−	0.921981i	$-0.373430\pi$
$107$	8.01120	0.774472	0.387236	+	0.921981i	$0.373430\pi$
$108$	−1.00000	−0.0962250
$109$	−9.41641	−0.901929	−0.450964	−	0.892542i	$-0.648920\pi$
$109$	−9.41641	−0.901929	−0.450964	+	0.892542i	$0.648920\pi$
$110$	−4.58182	−0.436859
$111$	−8.31348	−0.789080
$112$	−4.77480	−0.451176
$113$	5.10591	0.480324	0.240162	−	0.970733i	$-0.422799\pi$
$113$	5.10591	0.480324	0.240162	+	0.970733i	$0.422799\pi$
$114$	3.41029	0.319403
$115$	5.73884	0.535149
$116$	6.33268	0.587974
$117$	−5.97798	−0.552664
$118$	−1.00000	−0.0920575
$119$	−4.77480	−0.437705
$120$	−2.03963	−0.186192
$121$	−5.95372	−0.541247
$122$	4.50283	0.407668
$123$	−4.30463	−0.388135
$124$	5.89965	0.529804
$125$	11.9112	1.06537
$126$	4.77480	0.425373
$127$	−15.1762	−1.34667	−0.673335	−	0.739337i	$-0.735139\pi$
$127$	−15.1762	−1.34667	−0.673335	+	0.739337i	$0.735139\pi$
$128$	−1.00000	−0.0883883
$129$	−0.956651	−0.0842284
$130$	−12.1929	−1.06939
$131$	19.5584	1.70882	0.854411	−	0.519597i	$-0.173918\pi$
$131$	19.5584	1.70882	0.854411	+	0.519597i	$0.173918\pi$
$132$	2.24639	0.195523
$133$	−16.2835	−1.41196
$134$	1.84562	0.159437
$135$	2.03963	0.175544
$136$	−1.00000	−0.0857493
$137$	1.78007	0.152082	0.0760409	−	0.997105i	$-0.475772\pi$
$137$	1.78007	0.152082	0.0760409	+	0.997105i	$0.475772\pi$
$138$	−2.81366	−0.239515
$139$	−2.75252	−0.233466	−0.116733	−	0.993163i	$-0.537242\pi$
$139$	−2.75252	−0.233466	−0.116733	+	0.993163i	$0.537242\pi$
$140$	9.73885	0.823083
$141$	5.52929	0.465650
$142$	1.53649	0.128940
$143$	13.4289	1.12298
$144$	1.00000	0.0833333
$145$	−12.9163	−1.07264
$146$	−13.3357	−1.10367
$147$	−15.7987	−1.30306
$148$	8.31348	0.683363
$149$	9.67029	0.792221	0.396110	−	0.918203i	$-0.370360\pi$
$149$	9.67029	0.792221	0.396110	+	0.918203i	$0.370360\pi$
$150$	−0.839893	−0.0685770
$151$	−10.0421	−0.817218	−0.408609	−	0.912710i	$-0.633986\pi$
$151$	−10.0421	−0.817218	−0.408609	+	0.912710i	$0.633986\pi$
$152$	−3.41029	−0.276611
$153$	1.00000	0.0808452
$154$	−10.7261	−0.864332
$155$	−12.0331	−0.966524
$156$	5.97798	0.478621
$157$	−8.03183	−0.641010	−0.320505	−	0.947247i	$-0.603853\pi$
$157$	−8.03183	−0.641010	−0.320505	+	0.947247i	$0.603853\pi$
$158$	0.881718	0.0701457
$159$	−4.45423	−0.353243
$160$	2.03963	0.161247
$161$	13.4347	1.05880
$162$	−1.00000	−0.0785674
$163$	−1.70157	−0.133277	−0.0666386	−	0.997777i	$-0.521227\pi$
$163$	−1.70157	−0.133277	−0.0666386	+	0.997777i	$0.521227\pi$
$164$	4.30463	0.336135
$165$	−4.58182	−0.356694
$166$	8.48862	0.658845
$167$	17.7713	1.37518	0.687591	−	0.726098i	$-0.258668\pi$
$167$	17.7713	1.37518	0.687591	+	0.726098i	$0.258668\pi$
$168$	−4.77480	−0.368384
$169$	22.7362	1.74894
$170$	2.03963	0.156433
$171$	3.41029	0.260792
$172$	0.956651	0.0729439
$173$	−16.1834	−1.23040	−0.615201	−	0.788370i	$-0.710925\pi$
$173$	−16.1834	−1.23040	−0.615201	+	0.788370i	$0.710925\pi$
$174$	6.33268	0.480079
$175$	4.01032	0.303152
$176$	−2.24639	−0.169328
$177$	−1.00000	−0.0751646
$178$	−8.40538	−0.630010
$179$	17.3959	1.30023	0.650116	−	0.759835i	$-0.274720\pi$
$179$	17.3959	1.30023	0.650116	+	0.759835i	$0.274720\pi$
$180$	−2.03963	−0.152025
$181$	−7.59452	−0.564496	−0.282248	−	0.959341i	$-0.591080\pi$
$181$	−7.59452	−0.564496	−0.282248	+	0.959341i	$0.591080\pi$
$182$	−28.5437	−2.11580
$183$	4.50283	0.332859
$184$	2.81366	0.207426
$185$	−16.9564	−1.24666
$186$	5.89965	0.432584
$187$	−2.24639	−0.164273
$188$	−5.52929	−0.403265
$189$	4.77480	0.347316
$190$	6.95575	0.504623
$191$	−19.1427	−1.38512	−0.692558	−	0.721362i	$-0.743516\pi$
$191$	−19.1427	−1.38512	−0.692558	+	0.721362i	$0.743516\pi$
$192$	−1.00000	−0.0721688
$193$	−7.18234	−0.516996	−0.258498	−	0.966012i	$-0.583228\pi$
$193$	−7.18234	−0.516996	−0.258498	+	0.966012i	$0.583228\pi$
$194$	13.1187	0.941864
$195$	−12.1929	−0.873151
$196$	15.7987	1.12848
$197$	−19.4747	−1.38751	−0.693756	−	0.720210i	$-0.744045\pi$
$197$	−19.4747	−1.38751	−0.693756	+	0.720210i	$0.744045\pi$
$198$	2.24639	0.159644
$199$	5.40165	0.382913	0.191456	−	0.981501i	$-0.438679\pi$
$199$	5.40165	0.382913	0.191456	+	0.981501i	$0.438679\pi$
$200$	0.839893	0.0593894
$201$	1.84562	0.130180
$202$	5.61774	0.395263
$203$	−30.2373	−2.12224
$204$	−1.00000	−0.0700140
$205$	−8.77986	−0.613212
$206$	2.16480	0.150829
$207$	−2.81366	−0.195563
$208$	−5.97798	−0.414498
$209$	−7.66086	−0.529913
$210$	9.73885	0.672044
$211$	−18.2308	−1.25506	−0.627529	−	0.778593i	$-0.715934\pi$
$211$	−18.2308	−1.25506	−0.627529	+	0.778593i	$0.715934\pi$
$212$	4.45423	0.305918
$213$	1.53649	0.105279
$214$	−8.01120	−0.547634
$215$	−1.95122	−0.133072
$216$	1.00000	0.0680414
$217$	−28.1697	−1.91228
$218$	9.41641	0.637760
$219$	−13.3357	−0.901146
$220$	4.58182	0.308906
$221$	−5.97798	−0.402122
$222$	8.31348	0.557964
$223$	21.5560	1.44350	0.721749	−	0.692155i	$-0.243338\pi$
$223$	21.5560	1.44350	0.721749	+	0.692155i	$0.243338\pi$
$224$	4.77480	0.319030
$225$	−0.839893	−0.0559929
$226$	−5.10591	−0.339640
$227$	22.2084	1.47403	0.737013	−	0.675879i	$-0.236236\pi$
$227$	22.2084	1.47403	0.737013	+	0.675879i	$0.236236\pi$
$228$	−3.41029	−0.225852
$229$	−13.1028	−0.865858	−0.432929	−	0.901428i	$-0.642520\pi$
$229$	−13.1028	−0.865858	−0.432929	+	0.901428i	$0.642520\pi$
$230$	−5.73884	−0.378408
$231$	−10.7261	−0.705724
$232$	−6.33268	−0.415761
$233$	18.3882	1.20465	0.602325	−	0.798251i	$-0.294241\pi$
$233$	18.3882	1.20465	0.602325	+	0.798251i	$0.294241\pi$
$234$	5.97798	0.390793
$235$	11.2777	0.735677
$236$	1.00000	0.0650945
$237$	0.881718	0.0572737
$238$	4.77480	0.309504
$239$	10.2032	0.659988	0.329994	−	0.943983i	$-0.392953\pi$
$239$	10.2032	0.659988	0.329994	+	0.943983i	$0.392953\pi$
$240$	2.03963	0.131658
$241$	8.82257	0.568312	0.284156	−	0.958778i	$-0.408287\pi$
$241$	8.82257	0.568312	0.284156	+	0.958778i	$0.408287\pi$
$242$	5.95372	0.382720
$243$	−1.00000	−0.0641500
$244$	−4.50283	−0.288264
$245$	−32.2236	−2.05869
$246$	4.30463	0.274453
$247$	−20.3867	−1.29717
$248$	−5.89965	−0.374628
$249$	8.48862	0.537945
$250$	−11.9112	−0.753333
$251$	8.75667	0.552716	0.276358	−	0.961055i	$-0.410872\pi$
$251$	8.75667	0.552716	0.276358	+	0.961055i	$0.410872\pi$
$252$	−4.77480	−0.300784
$253$	6.32058	0.397372
$254$	15.1762	0.952240
$255$	2.03963	0.127727
$256$	1.00000	0.0625000
$257$	−2.98524	−0.186214	−0.0931071	−	0.995656i	$-0.529680\pi$
$257$	−2.98524	−0.186214	−0.0931071	+	0.995656i	$0.529680\pi$
$258$	0.956651	0.0595585
$259$	−39.6952	−2.46654
$260$	12.1929	0.756171
$261$	6.33268	0.391983
$262$	−19.5584	−1.20832
$263$	−8.46139	−0.521752	−0.260876	−	0.965372i	$-0.584011\pi$
$263$	−8.46139	−0.521752	−0.260876	+	0.965372i	$0.584011\pi$
$264$	−2.24639	−0.138256
$265$	−9.08500	−0.558087
$266$	16.2835	0.998404
$267$	−8.40538	−0.514401
$268$	−1.84562	−0.112739
$269$	10.1193	0.616982	0.308491	−	0.951227i	$-0.400176\pi$
$269$	10.1193	0.616982	0.308491	+	0.951227i	$0.400176\pi$
$270$	−2.03963	−0.124128
$271$	−30.4861	−1.85190	−0.925949	−	0.377648i	$-0.876733\pi$
$271$	−30.4861	−1.85190	−0.925949	+	0.377648i	$0.876733\pi$
$272$	1.00000	0.0606339
$273$	−28.5437	−1.72754
$274$	−1.78007	−0.107538
$275$	1.88673	0.113774
$276$	2.81366	0.169362
$277$	23.9036	1.43623	0.718115	−	0.695924i	$-0.245005\pi$
$277$	23.9036	1.43623	0.718115	+	0.695924i	$0.245005\pi$
$278$	2.75252	0.165085
$279$	5.89965	0.353203
$280$	−9.73885	−0.582007
$281$	12.8959	0.769302	0.384651	−	0.923062i	$-0.374322\pi$
$281$	12.8959	0.769302	0.384651	+	0.923062i	$0.374322\pi$
$282$	−5.52929	−0.329264
$283$	−10.4364	−0.620379	−0.310189	−	0.950675i	$-0.600392\pi$
$283$	−10.4364	−0.620379	−0.310189	+	0.950675i	$0.600392\pi$
$284$	−1.53649	−0.0911741
$285$	6.95575	0.412023
$286$	−13.4289	−0.794067
$287$	−20.5537	−1.21325
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	12.9163	0.758474
$291$	13.1187	0.769029
$292$	13.3357	0.780415
$293$	5.94212	0.347142	0.173571	−	0.984821i	$-0.444469\pi$
$293$	5.94212	0.347142	0.173571	+	0.984821i	$0.444469\pi$
$294$	15.7987	0.921400
$295$	−2.03963	−0.118752
$296$	−8.31348	−0.483211
$297$	2.24639	0.130349
$298$	−9.67029	−0.560185
$299$	16.8200	0.972725
$300$	0.839893	0.0484912
$301$	−4.56782	−0.263285
$302$	10.0421	0.577860
$303$	5.61774	0.322731
$304$	3.41029	0.195594
$305$	9.18414	0.525882
$306$	−1.00000	−0.0571662
$307$	8.03112	0.458360	0.229180	−	0.973384i	$-0.426396\pi$
$307$	8.03112	0.458360	0.229180	+	0.973384i	$0.426396\pi$
$308$	10.7261	0.611175
$309$	2.16480	0.123151
$310$	12.0331	0.683436
$311$	12.4090	0.703652	0.351826	−	0.936065i	$-0.385561\pi$
$311$	12.4090	0.703652	0.351826	+	0.936065i	$0.385561\pi$
$312$	−5.97798	−0.338436
$313$	18.1266	1.02457	0.512287	−	0.858814i	$-0.328798\pi$
$313$	18.1266	1.02457	0.512287	+	0.858814i	$0.328798\pi$
$314$	8.03183	0.453262
$315$	9.73885	0.548722
$316$	−0.881718	−0.0496005
$317$	4.59866	0.258286	0.129143	−	0.991626i	$-0.458777\pi$
$317$	4.59866	0.258286	0.129143	+	0.991626i	$0.458777\pi$
$318$	4.45423	0.249781
$319$	−14.2257	−0.796485
$320$	−2.03963	−0.114019
$321$	−8.01120	−0.447141
$322$	−13.4347	−0.748685
$323$	3.41029	0.189754
$324$	1.00000	0.0555556
$325$	5.02086	0.278507
$326$	1.70157	0.0942413
$327$	9.41641	0.520729
$328$	−4.30463	−0.237683
$329$	26.4012	1.45555
$330$	4.58182	0.252221
$331$	−11.1763	−0.614305	−0.307152	−	0.951660i	$-0.599376\pi$
$331$	−11.1763	−0.614305	−0.307152	+	0.951660i	$0.599376\pi$
$332$	−8.48862	−0.465874
$333$	8.31348	0.455576
$334$	−17.7713	−0.972401
$335$	3.76438	0.205670
$336$	4.77480	0.260487
$337$	−22.8761	−1.24614	−0.623071	−	0.782165i	$-0.714115\pi$
$337$	−22.8761	−1.24614	−0.623071	+	0.782165i	$0.714115\pi$
$338$	−22.7362	−1.23669
$339$	−5.10591	−0.277315
$340$	−2.03963	−0.110615
$341$	−13.2529	−0.717687
$342$	−3.41029	−0.184408
$343$	−42.0121	−2.26844
$344$	−0.956651	−0.0515792
$345$	−5.73884	−0.308969
$346$	16.1834	0.870026
$347$	−17.7217	−0.951351	−0.475675	−	0.879621i	$-0.657796\pi$
$347$	−17.7217	−0.951351	−0.475675	+	0.879621i	$0.657796\pi$
$348$	−6.33268	−0.339467
$349$	−9.98566	−0.534520	−0.267260	−	0.963624i	$-0.586118\pi$
$349$	−9.98566	−0.534520	−0.267260	+	0.963624i	$0.586118\pi$
$350$	−4.01032	−0.214361
$351$	5.97798	0.319081
$352$	2.24639	0.119733
$353$	1.06858	0.0568749	0.0284375	−	0.999596i	$-0.490947\pi$
$353$	1.06858	0.0568749	0.0284375	+	0.999596i	$0.490947\pi$
$354$	1.00000	0.0531494
$355$	3.13388	0.166329
$356$	8.40538	0.445484
$357$	4.77480	0.252709
$358$	−17.3959	−0.919403
$359$	−4.63166	−0.244449	−0.122225	−	0.992502i	$-0.539003\pi$
$359$	−4.63166	−0.244449	−0.122225	+	0.992502i	$0.539003\pi$
$360$	2.03963	0.107498
$361$	−7.36990	−0.387889
$362$	7.59452	0.399159
$363$	5.95372	0.312489
$364$	28.5437	1.49609
$365$	−27.2000	−1.42371
$366$	−4.50283	−0.235367
$367$	12.7138	0.663656	0.331828	−	0.943340i	$-0.392335\pi$
$367$	12.7138	0.663656	0.331828	+	0.943340i	$0.392335\pi$
$368$	−2.81366	−0.146672
$369$	4.30463	0.224090
$370$	16.9564	0.881524
$371$	−21.2680	−1.10418
$372$	−5.89965	−0.305883
$373$	31.2142	1.61621	0.808106	−	0.589037i	$-0.200493\pi$
$373$	31.2142	1.61621	0.808106	+	0.589037i	$0.200493\pi$
$374$	2.24639	0.116158
$375$	−11.9112	−0.615094
$376$	5.52929	0.285151
$377$	−37.8566	−1.94971
$378$	−4.77480	−0.245589
$379$	−13.6167	−0.699443	−0.349722	−	0.936854i	$-0.613724\pi$
$379$	−13.6167	−0.699443	−0.349722	+	0.936854i	$0.613724\pi$
$380$	−6.95575	−0.356823
$381$	15.1762	0.777500
$382$	19.1427	0.979425
$383$	20.3418	1.03942	0.519709	−	0.854343i	$-0.326040\pi$
$383$	20.3418	1.03942	0.519709	+	0.854343i	$0.326040\pi$
$384$	1.00000	0.0510310
$385$	−21.8773	−1.11497
$386$	7.18234	0.365571
$387$	0.956651	0.0486293
$388$	−13.1187	−0.665999
$389$	4.72827	0.239733	0.119866	−	0.992790i	$-0.461753\pi$
$389$	4.72827	0.239733	0.119866	+	0.992790i	$0.461753\pi$
$390$	12.1929	0.617411
$391$	−2.81366	−0.142293
$392$	−15.7987	−0.797956
$393$	−19.5584	−0.986589
$394$	19.4747	0.981119
$395$	1.79838	0.0904864
$396$	−2.24639	−0.112885
$397$	26.6546	1.33776	0.668879	−	0.743371i	$-0.266774\pi$
$397$	26.6546	1.33776	0.668879	+	0.743371i	$0.266774\pi$
$398$	−5.40165	−0.270760
$399$	16.2835	0.815193
$400$	−0.839893	−0.0419946
$401$	28.6420	1.43031	0.715157	−	0.698964i	$-0.246355\pi$
$401$	28.6420	1.43031	0.715157	+	0.698964i	$0.246355\pi$
$402$	−1.84562	−0.0920510
$403$	−35.2680	−1.75682
$404$	−5.61774	−0.279493
$405$	−2.03963	−0.101350
$406$	30.2373	1.50065
$407$	−18.6753	−0.925702
$408$	1.00000	0.0495074
$409$	6.63408	0.328034	0.164017	−	0.986457i	$-0.447555\pi$
$409$	6.63408	0.328034	0.164017	+	0.986457i	$0.447555\pi$
$410$	8.77986	0.433607
$411$	−1.78007	−0.0878044
$412$	−2.16480	−0.106652
$413$	−4.77480	−0.234953
$414$	2.81366	0.138284
$415$	17.3137	0.849895
$416$	5.97798	0.293094
$417$	2.75252	0.134792
$418$	7.66086	0.374705
$419$	5.91056	0.288750	0.144375	−	0.989523i	$-0.453883\pi$
$419$	5.91056	0.288750	0.144375	+	0.989523i	$0.453883\pi$
$420$	−9.73885	−0.475207
$421$	15.3770	0.749427	0.374714	−	0.927141i	$-0.377741\pi$
$421$	15.3770	0.749427	0.374714	+	0.927141i	$0.377741\pi$
$422$	18.2308	0.887460
$423$	−5.52929	−0.268843
$424$	−4.45423	−0.216316
$425$	−0.839893	−0.0407408
$426$	−1.53649	−0.0744433
$427$	21.5001	1.04046
$428$	8.01120	0.387236
$429$	−13.4289	−0.648353
$430$	1.95122	0.0940961
$431$	−8.92502	−0.429903	−0.214951	−	0.976625i	$-0.568959\pi$
$431$	−8.92502	−0.429903	−0.214951	+	0.976625i	$0.568959\pi$
$432$	−1.00000	−0.0481125
$433$	3.37474	0.162180	0.0810899	−	0.996707i	$-0.474160\pi$
$433$	3.37474	0.162180	0.0810899	+	0.996707i	$0.474160\pi$
$434$	28.1697	1.35219
$435$	12.9163	0.619291
$436$	−9.41641	−0.450964
$437$	−9.59541	−0.459011
$438$	13.3357	0.637206
$439$	−23.9987	−1.14539	−0.572697	−	0.819767i	$-0.694103\pi$
$439$	−23.9987	−1.14539	−0.572697	+	0.819767i	$0.694103\pi$
$440$	−4.58182	−0.218430
$441$	15.7987	0.752320
$442$	5.97798	0.284343
$443$	−18.5822	−0.882867	−0.441433	−	0.897294i	$-0.645530\pi$
$443$	−18.5822	−0.882867	−0.441433	+	0.897294i	$0.645530\pi$
$444$	−8.31348	−0.394540
$445$	−17.1439	−0.812698
$446$	−21.5560	−1.02071
$447$	−9.67029	−0.457389
$448$	−4.77480	−0.225588
$449$	26.9064	1.26979	0.634896	−	0.772597i	$-0.281043\pi$
$449$	26.9064	1.26979	0.634896	+	0.772597i	$0.281043\pi$
$450$	0.839893	0.0395929
$451$	−9.66988	−0.455337
$452$	5.10591	0.240162
$453$	10.0421	0.471821
$454$	−22.2084	−1.04229
$455$	−58.2186	−2.72933
$456$	3.41029	0.159702
$457$	−17.9618	−0.840220	−0.420110	−	0.907473i	$-0.638008\pi$
$457$	−17.9618	−0.840220	−0.420110	+	0.907473i	$0.638008\pi$
$458$	13.1028	0.612254
$459$	−1.00000	−0.0466760
$460$	5.73884	0.267575
$461$	26.4859	1.23357	0.616785	−	0.787132i	$-0.288435\pi$
$461$	26.4859	1.23357	0.616785	+	0.787132i	$0.288435\pi$
$462$	10.7261	0.499022
$463$	−23.0996	−1.07353	−0.536766	−	0.843731i	$-0.680354\pi$
$463$	−23.0996	−1.07353	−0.536766	+	0.843731i	$0.680354\pi$
$464$	6.33268	0.293987
$465$	12.0331	0.558023
$466$	−18.3882	−0.851816
$467$	−26.5868	−1.23029	−0.615144	−	0.788415i	$-0.710902\pi$
$467$	−26.5868	−1.23029	−0.615144	+	0.788415i	$0.710902\pi$
$468$	−5.97798	−0.276332
$469$	8.81245	0.406921
$470$	−11.2777	−0.520202
$471$	8.03183	0.370087
$472$	−1.00000	−0.0460287
$473$	−2.14901	−0.0988117
$474$	−0.881718	−0.0404986
$475$	−2.86428	−0.131422
$476$	−4.77480	−0.218853
$477$	4.45423	0.203945
$478$	−10.2032	−0.466682
$479$	−2.76877	−0.126508	−0.0632541	−	0.997997i	$-0.520148\pi$
$479$	−2.76877	−0.126508	−0.0632541	+	0.997997i	$0.520148\pi$
$480$	−2.03963	−0.0930961
$481$	−49.6978	−2.26602
$482$	−8.82257	−0.401857
$483$	−13.4347	−0.611298
$484$	−5.95372	−0.270624
$485$	26.7573	1.21498
$486$	1.00000	0.0453609
$487$	−20.2658	−0.918330	−0.459165	−	0.888351i	$-0.651851\pi$
$487$	−20.2658	−0.918330	−0.459165	+	0.888351i	$0.651851\pi$
$488$	4.50283	0.203834
$489$	1.70157	0.0769477
$490$	32.2236	1.45571
$491$	16.7011	0.753709	0.376855	−	0.926272i	$-0.377006\pi$
$491$	16.7011	0.753709	0.376855	+	0.926272i	$0.377006\pi$
$492$	−4.30463	−0.194068
$493$	6.33268	0.285209
$494$	20.3867	0.917239
$495$	4.58182	0.205937
$496$	5.89965	0.264902
$497$	7.33645	0.329085
$498$	−8.48862	−0.380384
$499$	38.6142	1.72861	0.864305	−	0.502969i	$-0.167759\pi$
$499$	38.6142	1.72861	0.864305	+	0.502969i	$0.167759\pi$
$500$	11.9112	0.532687
$501$	−17.7713	−0.793962
$502$	−8.75667	−0.390829
$503$	−6.50646	−0.290109	−0.145054	−	0.989424i	$-0.546336\pi$
$503$	−6.50646	−0.290109	−0.145054	+	0.989424i	$0.546336\pi$
$504$	4.77480	0.212687
$505$	11.4581	0.509881
$506$	−6.32058	−0.280984
$507$	−22.7362	−1.00975
$508$	−15.1762	−0.673335
$509$	−15.5959	−0.691278	−0.345639	−	0.938368i	$-0.612338\pi$
$509$	−15.5959	−0.691278	−0.345639	+	0.938368i	$0.612338\pi$
$510$	−2.03963	−0.0903165
$511$	−63.6755	−2.81684
$512$	−1.00000	−0.0441942
$513$	−3.41029	−0.150568
$514$	2.98524	0.131673
$515$	4.41539	0.194565
$516$	−0.956651	−0.0421142
$517$	12.4209	0.546273
$518$	39.6952	1.74411
$519$	16.1834	0.710373
$520$	−12.1929	−0.534693
$521$	−40.6509	−1.78095	−0.890475	−	0.455032i	$-0.849628\pi$
$521$	−40.6509	−1.78095	−0.890475	+	0.455032i	$0.849628\pi$
$522$	−6.33268	−0.277174
$523$	−23.1680	−1.01307	−0.506533	−	0.862221i	$-0.669073\pi$
$523$	−23.1680	−1.01307	−0.506533	+	0.862221i	$0.669073\pi$
$524$	19.5584	0.854411
$525$	−4.01032	−0.175025
$526$	8.46139	0.368934
$527$	5.89965	0.256993
$528$	2.24639	0.0977617
$529$	−15.0833	−0.655796
$530$	9.08500	0.394627
$531$	1.00000	0.0433963
$532$	−16.2835	−0.705978
$533$	−25.7330	−1.11462
$534$	8.40538	0.363736
$535$	−16.3399	−0.706436
$536$	1.84562	0.0797185
$537$	−17.3959	−0.750690
$538$	−10.1193	−0.436272
$539$	−35.4901	−1.52867
$540$	2.03963	0.0877719
$541$	−4.33742	−0.186480	−0.0932401	−	0.995644i	$-0.529722\pi$
$541$	−4.33742	−0.186480	−0.0932401	+	0.995644i	$0.529722\pi$
$542$	30.4861	1.30949
$543$	7.59452	0.325912
$544$	−1.00000	−0.0428746
$545$	19.2060	0.822696
$546$	28.5437	1.22156
$547$	−14.9103	−0.637520	−0.318760	−	0.947836i	$-0.603266\pi$
$547$	−14.9103	−0.637520	−0.318760	+	0.947836i	$0.603266\pi$
$548$	1.78007	0.0760409
$549$	−4.50283	−0.192176
$550$	−1.88673	−0.0804504
$551$	21.5963	0.920033
$552$	−2.81366	−0.119757
$553$	4.21003	0.179029
$554$	−23.9036	−1.01557
$555$	16.9564	0.719761
$556$	−2.75252	−0.116733
$557$	−17.2505	−0.730927	−0.365463	−	0.930826i	$-0.619089\pi$
$557$	−17.2505	−0.730927	−0.365463	+	0.930826i	$0.619089\pi$
$558$	−5.89965	−0.249752
$559$	−5.71884	−0.241881
$560$	9.73885	0.411541
$561$	2.24639	0.0948428
$562$	−12.8959	−0.543979
$563$	25.7395	1.08479	0.542395	−	0.840124i	$-0.317518\pi$
$563$	25.7395	1.08479	0.542395	+	0.840124i	$0.317518\pi$
$564$	5.52929	0.232825
$565$	−10.4142	−0.438128
$566$	10.4364	0.438674
$567$	−4.77480	−0.200523
$568$	1.53649	0.0644698
$569$	−25.4569	−1.06721	−0.533603	−	0.845735i	$-0.679162\pi$
$569$	−25.4569	−1.06721	−0.533603	+	0.845735i	$0.679162\pi$
$570$	−6.95575	−0.291344
$571$	−31.4734	−1.31712	−0.658560	−	0.752528i	$-0.728834\pi$
$571$	−31.4734	−1.31712	−0.658560	+	0.752528i	$0.728834\pi$
$572$	13.4289	0.561490
$573$	19.1427	0.799697
$574$	20.5537	0.857896
$575$	2.36317	0.0985511
$576$	1.00000	0.0416667
$577$	4.08392	0.170016	0.0850080	−	0.996380i	$-0.472908\pi$
$577$	4.08392	0.170016	0.0850080	+	0.996380i	$0.472908\pi$
$578$	−1.00000	−0.0415945
$579$	7.18234	0.298488
$580$	−12.9163	−0.536322
$581$	40.5315	1.68153
$582$	−13.1187	−0.543786
$583$	−10.0059	−0.414404
$584$	−13.3357	−0.551837
$585$	12.1929	0.504114
$586$	−5.94212	−0.245467
$587$	−35.6087	−1.46973	−0.734864	−	0.678215i	$-0.762754\pi$
$587$	−35.6087	−1.46973	−0.734864	+	0.678215i	$0.762754\pi$
$588$	−15.7987	−0.651528
$589$	20.1195	0.829012
$590$	2.03963	0.0839704
$591$	19.4747	0.801080
$592$	8.31348	0.341682
$593$	16.8503	0.691960	0.345980	−	0.938242i	$-0.387546\pi$
$593$	16.8503	0.691960	0.345980	+	0.938242i	$0.387546\pi$
$594$	−2.24639	−0.0921706
$595$	9.73885	0.399254
$596$	9.67029	0.396110
$597$	−5.40165	−0.221075
$598$	−16.8200	−0.687821
$599$	−15.7268	−0.642578	−0.321289	−	0.946981i	$-0.604116\pi$
$599$	−15.7268	−0.642578	−0.321289	+	0.946981i	$0.604116\pi$
$600$	−0.839893	−0.0342885
$601$	32.9603	1.34448	0.672239	−	0.740335i	$-0.265333\pi$
$601$	32.9603	1.34448	0.672239	+	0.740335i	$0.265333\pi$
$602$	4.56782	0.186170
$603$	−1.84562	−0.0751593
$604$	−10.0421	−0.408609
$605$	12.1434	0.493700
$606$	−5.61774	−0.228205
$607$	−10.7745	−0.437322	−0.218661	−	0.975801i	$-0.570169\pi$
$607$	−10.7745	−0.437322	−0.218661	+	0.975801i	$0.570169\pi$
$608$	−3.41029	−0.138306
$609$	30.2373	1.22528
$610$	−9.18414	−0.371855
$611$	33.0539	1.33722
$612$	1.00000	0.0404226
$613$	28.6063	1.15540	0.577699	−	0.816250i	$-0.303951\pi$
$613$	28.6063	1.15540	0.577699	+	0.816250i	$0.303951\pi$
$614$	−8.03112	−0.324110
$615$	8.77986	0.354038
$616$	−10.7261	−0.432166
$617$	−16.0651	−0.646757	−0.323378	−	0.946270i	$-0.604819\pi$
$617$	−16.0651	−0.646757	−0.323378	+	0.946270i	$0.604819\pi$
$618$	−2.16480	−0.0870809
$619$	41.9214	1.68496	0.842482	−	0.538725i	$-0.181094\pi$
$619$	41.9214	1.68496	0.842482	+	0.538725i	$0.181094\pi$
$620$	−12.0331	−0.483262
$621$	2.81366	0.112908
$622$	−12.4090	−0.497557
$623$	−40.1340	−1.60793
$624$	5.97798	0.239311
$625$	−20.0951	−0.803805
$626$	−18.1266	−0.724483
$627$	7.66086	0.305945
$628$	−8.03183	−0.320505
$629$	8.31348	0.331480
$630$	−9.73885	−0.388005
$631$	31.1487	1.24001	0.620006	−	0.784597i	$-0.287130\pi$
$631$	31.1487	1.24001	0.620006	+	0.784597i	$0.287130\pi$
$632$	0.881718	0.0350729
$633$	18.2308	0.724608
$634$	−4.59866	−0.182636
$635$	30.9539	1.22837
$636$	−4.45423	−0.176622
$637$	−94.4444	−3.74202
$638$	14.2257	0.563200
$639$	−1.53649	−0.0607827
$640$	2.03963	0.0806236
$641$	−3.81298	−0.150603	−0.0753017	−	0.997161i	$-0.523992\pi$
$641$	−3.81298	−0.150603	−0.0753017	+	0.997161i	$0.523992\pi$
$642$	8.01120	0.316177
$643$	20.8584	0.822575	0.411288	−	0.911506i	$-0.365079\pi$
$643$	20.8584	0.822575	0.411288	+	0.911506i	$0.365079\pi$
$644$	13.4347	0.529400
$645$	1.95122	0.0768291
$646$	−3.41029	−0.134176
$647$	−3.46042	−0.136043	−0.0680215	−	0.997684i	$-0.521669\pi$
$647$	−3.46042	−0.136043	−0.0680215	+	0.997684i	$0.521669\pi$
$648$	−1.00000	−0.0392837
$649$	−2.24639	−0.0881786
$650$	−5.02086	−0.196934
$651$	28.1697	1.10406
$652$	−1.70157	−0.0666386
$653$	−27.1345	−1.06186	−0.530928	−	0.847417i	$-0.678157\pi$
$653$	−27.1345	−1.06186	−0.530928	+	0.847417i	$0.678157\pi$
$654$	−9.41641	−0.368211
$655$	−39.8919	−1.55871
$656$	4.30463	0.168067
$657$	13.3357	0.520277
$658$	−26.4012	−1.02923
$659$	−30.7129	−1.19641	−0.598203	−	0.801344i	$-0.704118\pi$
$659$	−30.7129	−1.19641	−0.598203	+	0.801344i	$0.704118\pi$
$660$	−4.58182	−0.178347
$661$	−22.9951	−0.894406	−0.447203	−	0.894433i	$-0.647580\pi$
$661$	−22.9951	−0.894406	−0.447203	+	0.894433i	$0.647580\pi$
$662$	11.1763	0.434379
$663$	5.97798	0.232165
$664$	8.48862	0.329422
$665$	33.2123	1.28792
$666$	−8.31348	−0.322141
$667$	−17.8180	−0.689916
$668$	17.7713	0.687591
$669$	−21.5560	−0.833404
$670$	−3.76438	−0.145431
$671$	10.1151	0.390490
$672$	−4.77480	−0.184192
$673$	−38.7922	−1.49533	−0.747665	−	0.664077i	$-0.768825\pi$
$673$	−38.7922	−1.49533	−0.747665	+	0.664077i	$0.768825\pi$
$674$	22.8761	0.881155
$675$	0.839893	0.0323275
$676$	22.7362	0.874470
$677$	41.0629	1.57818	0.789088	−	0.614280i	$-0.210554\pi$
$677$	41.0629	1.57818	0.789088	+	0.614280i	$0.210554\pi$
$678$	5.10591	0.196091
$679$	62.6390	2.40386
$680$	2.03963	0.0782164
$681$	−22.2084	−0.851029
$682$	13.2529	0.507481
$683$	7.84007	0.299992	0.149996	−	0.988687i	$-0.452074\pi$
$683$	7.84007	0.299992	0.149996	+	0.988687i	$0.452074\pi$
$684$	3.41029	0.130396
$685$	−3.63069	−0.138722
$686$	42.0121	1.60403
$687$	13.1028	0.499903
$688$	0.956651	0.0364720
$689$	−26.6273	−1.01442
$690$	5.73884	0.218474
$691$	−6.86813	−0.261276	−0.130638	−	0.991430i	$-0.541703\pi$
$691$	−6.86813	−0.261276	−0.130638	+	0.991430i	$0.541703\pi$
$692$	−16.1834	−0.615201
$693$	10.7261	0.407450
$694$	17.7217	0.672706
$695$	5.61414	0.212956
$696$	6.33268	0.240040
$697$	4.30463	0.163049
$698$	9.98566	0.377963
$699$	−18.3882	−0.695505
$700$	4.01032	0.151576
$701$	−25.5637	−0.965529	−0.482764	−	0.875750i	$-0.660367\pi$
$701$	−25.5637	−0.965529	−0.482764	+	0.875750i	$0.660367\pi$
$702$	−5.97798	−0.225624
$703$	28.3514	1.06929
$704$	−2.24639	−0.0846641
$705$	−11.2777	−0.424743
$706$	−1.06858	−0.0402167
$707$	26.8236	1.00881
$708$	−1.00000	−0.0375823
$709$	28.3231	1.06370	0.531849	−	0.846839i	$-0.321497\pi$
$709$	28.3231	1.06370	0.531849	+	0.846839i	$0.321497\pi$
$710$	−3.13388	−0.117613
$711$	−0.881718	−0.0330670
$712$	−8.40538	−0.315005
$713$	−16.5996	−0.621660
$714$	−4.77480	−0.178692
$715$	−27.3900	−1.02433
$716$	17.3959	0.650116
$717$	−10.2032	−0.381044
$718$	4.63166	0.172852
$719$	−5.30148	−0.197712	−0.0988560	−	0.995102i	$-0.531518\pi$
$719$	−5.30148	−0.197712	−0.0988560	+	0.995102i	$0.531518\pi$
$720$	−2.03963	−0.0760127
$721$	10.3365	0.384950
$722$	7.36990	0.274279
$723$	−8.82257	−0.328115
$724$	−7.59452	−0.282248
$725$	−5.31877	−0.197534
$726$	−5.95372	−0.220963
$727$	41.2471	1.52977	0.764884	−	0.644168i	$-0.222796\pi$
$727$	41.2471	1.52977	0.764884	+	0.644168i	$0.222796\pi$
$728$	−28.5437	−1.05790
$729$	1.00000	0.0370370
$730$	27.2000	1.00672
$731$	0.956651	0.0353830
$732$	4.50283	0.166430
$733$	−4.69704	−0.173489	−0.0867446	−	0.996231i	$-0.527646\pi$
$733$	−4.69704	−0.173489	−0.0867446	+	0.996231i	$0.527646\pi$
$734$	−12.7138	−0.469276
$735$	32.2236	1.18859
$736$	2.81366	0.103713
$737$	4.14598	0.152719
$738$	−4.30463	−0.158456
$739$	−37.0979	−1.36467	−0.682334	−	0.731041i	$-0.739035\pi$
$739$	−37.0979	−1.36467	−0.682334	+	0.731041i	$0.739035\pi$
$740$	−16.9564	−0.623331
$741$	20.3867	0.748923
$742$	21.2680	0.780775
$743$	−28.3643	−1.04058	−0.520292	−	0.853988i	$-0.674177\pi$
$743$	−28.3643	−1.04058	−0.520292	+	0.853988i	$0.674177\pi$
$744$	5.89965	0.216292
$745$	−19.7238	−0.722626
$746$	−31.2142	−1.14283
$747$	−8.48862	−0.310582
$748$	−2.24639	−0.0821363
$749$	−38.2519	−1.39769
$750$	11.9112	0.434937
$751$	−33.3720	−1.21776	−0.608880	−	0.793262i	$-0.708381\pi$
$751$	−33.3720	−1.21776	−0.608880	+	0.793262i	$0.708381\pi$
$752$	−5.52929	−0.201632
$753$	−8.75667	−0.319111
$754$	37.8566	1.37866
$755$	20.4823	0.745427
$756$	4.77480	0.173658
$757$	32.1478	1.16843	0.584217	−	0.811598i	$-0.301402\pi$
$757$	32.1478	1.16843	0.584217	+	0.811598i	$0.301402\pi$
$758$	13.6167	0.494581
$759$	−6.32058	−0.229423
$760$	6.95575	0.252312
$761$	−36.5613	−1.32534	−0.662672	−	0.748909i	$-0.730578\pi$
$761$	−36.5613	−1.32534	−0.662672	+	0.748909i	$0.730578\pi$
$762$	−15.1762	−0.549776
$763$	44.9615	1.62772
$764$	−19.1427	−0.692558
$765$	−2.03963	−0.0737431
$766$	−20.3418	−0.734980
$767$	−5.97798	−0.215852
$768$	−1.00000	−0.0360844
$769$	12.4542	0.449111	0.224556	−	0.974461i	$-0.427907\pi$
$769$	12.4542	0.449111	0.224556	+	0.974461i	$0.427907\pi$
$770$	21.8773	0.788402
$771$	2.98524	0.107511
$772$	−7.18234	−0.258498
$773$	23.4438	0.843215	0.421607	−	0.906778i	$-0.361466\pi$
$773$	23.4438	0.843215	0.421607	+	0.906778i	$0.361466\pi$
$774$	−0.956651	−0.0343861
$775$	−4.95508	−0.177992
$776$	13.1187	0.470932
$777$	39.6952	1.42406
$778$	−4.72827	−0.169517
$779$	14.6800	0.525967
$780$	−12.1929	−0.436575
$781$	3.45157	0.123507
$782$	2.81366	0.100616
$783$	−6.33268	−0.226311
$784$	15.7987	0.564240
$785$	16.3820	0.584698
$786$	19.5584	0.697624
$787$	−38.1512	−1.35994	−0.679971	−	0.733239i	$-0.738008\pi$
$787$	−38.1512	−1.35994	−0.679971	+	0.733239i	$0.738008\pi$
$788$	−19.4747	−0.693756
$789$	8.46139	0.301233
$790$	−1.79838	−0.0639836
$791$	−24.3797	−0.866843
$792$	2.24639	0.0798221
$793$	26.9178	0.955881
$794$	−26.6546	−0.945938
$795$	9.08500	0.322212
$796$	5.40165	0.191456
$797$	−10.2016	−0.361358	−0.180679	−	0.983542i	$-0.557829\pi$
$797$	−10.2016	−0.361358	−0.180679	+	0.983542i	$0.557829\pi$
$798$	−16.2835	−0.576429
$799$	−5.52929	−0.195612
$800$	0.839893	0.0296947
$801$	8.40538	0.296989
$802$	−28.6420	−1.01139
$803$	−29.9573	−1.05717
$804$	1.84562	0.0650899
$805$	−27.4018	−0.965786
$806$	35.2680	1.24226
$807$	−10.1193	−0.356215
$808$	5.61774	0.197632
$809$	−10.2814	−0.361474	−0.180737	−	0.983532i	$-0.557848\pi$
$809$	−10.2814	−0.361474	−0.180737	+	0.983532i	$0.557848\pi$
$810$	2.03963	0.0716654
$811$	30.0874	1.05651	0.528255	−	0.849086i	$-0.322847\pi$
$811$	30.0874	1.05651	0.528255	+	0.849086i	$0.322847\pi$
$812$	−30.2373	−1.06112
$813$	30.4861	1.06919
$814$	18.6753	0.654570
$815$	3.47058	0.121569
$816$	−1.00000	−0.0350070
$817$	3.26246	0.114139
$818$	−6.63408	−0.231955
$819$	28.5437	0.997396
$820$	−8.77986	−0.306606
$821$	38.0389	1.32757	0.663783	−	0.747925i	$-0.268950\pi$
$821$	38.0389	1.32757	0.663783	+	0.747925i	$0.268950\pi$
$822$	1.78007	0.0620871
$823$	−12.1982	−0.425204	−0.212602	−	0.977139i	$-0.568194\pi$
$823$	−12.1982	−0.425204	−0.212602	+	0.977139i	$0.568194\pi$
$824$	2.16480	0.0754143
$825$	−1.88673	−0.0656875
$826$	4.77480	0.166137
$827$	20.7953	0.723125	0.361562	−	0.932348i	$-0.382243\pi$
$827$	20.7953	0.723125	0.361562	+	0.932348i	$0.382243\pi$
$828$	−2.81366	−0.0977814
$829$	−39.9285	−1.38677	−0.693387	−	0.720566i	$-0.743882\pi$
$829$	−39.9285	−1.38677	−0.693387	+	0.720566i	$0.743882\pi$
$830$	−17.3137	−0.600967
$831$	−23.9036	−0.829208
$832$	−5.97798	−0.207249
$833$	15.7987	0.547393
$834$	−2.75252	−0.0953120
$835$	−36.2469	−1.25438
$836$	−7.66086	−0.264956
$837$	−5.89965	−0.203922
$838$	−5.91056	−0.204177
$839$	−4.75270	−0.164082	−0.0820408	−	0.996629i	$-0.526144\pi$
$839$	−4.75270	−0.164082	−0.0820408	+	0.996629i	$0.526144\pi$
$840$	9.73885	0.336022
$841$	11.1028	0.382856
$842$	−15.3770	−0.529925
$843$	−12.8959	−0.444157
$844$	−18.2308	−0.627529
$845$	−46.3736	−1.59530
$846$	5.52929	0.190101
$847$	28.4278	0.976792
$848$	4.45423	0.152959
$849$	10.4364	0.358176
$850$	0.839893	0.0288081
$851$	−23.3913	−0.801843
$852$	1.53649	0.0526394
$853$	−6.26279	−0.214434	−0.107217	−	0.994236i	$-0.534194\pi$
$853$	−6.26279	−0.214434	−0.107217	+	0.994236i	$0.534194\pi$
$854$	−21.5001	−0.735720
$855$	−6.95575	−0.237882
$856$	−8.01120	−0.273817
$857$	−0.370878	−0.0126690	−0.00633448	−	0.999980i	$-0.502016\pi$
$857$	−0.370878	−0.0126690	−0.00633448	+	0.999980i	$0.502016\pi$
$858$	13.4289	0.458455
$859$	−26.5833	−0.907011	−0.453505	−	0.891254i	$-0.649827\pi$
$859$	−26.5833	−0.907011	−0.453505	+	0.891254i	$0.649827\pi$
$860$	−1.95122	−0.0665360
$861$	20.5537	0.700469
$862$	8.92502	0.303987
$863$	−43.9162	−1.49492	−0.747462	−	0.664305i	$-0.768728\pi$
$863$	−43.9162	−1.49492	−0.747462	+	0.664305i	$0.768728\pi$
$864$	1.00000	0.0340207
$865$	33.0082	1.12231
$866$	−3.37474	−0.114678
$867$	−1.00000	−0.0339618
$868$	−28.1697	−0.956141
$869$	1.98068	0.0671901
$870$	−12.9163	−0.437905
$871$	11.0331	0.373841
$872$	9.41641	0.318880
$873$	−13.1187	−0.443999
$874$	9.59541	0.324569
$875$	−56.8738	−1.92269
$876$	−13.3357	−0.450573
$877$	56.9719	1.92381	0.961903	−	0.273392i	$-0.0881455\pi$
$877$	56.9719	1.92381	0.961903	+	0.273392i	$0.0881455\pi$
$878$	23.9987	0.809916
$879$	−5.94212	−0.200423
$880$	4.58182	0.154453
$881$	−13.6163	−0.458745	−0.229373	−	0.973339i	$-0.573667\pi$
$881$	−13.6163	−0.458745	−0.229373	+	0.973339i	$0.573667\pi$
$882$	−15.7987	−0.531971
$883$	0.285056	0.00959291	0.00479646	−	0.999988i	$-0.498473\pi$
$883$	0.285056	0.00959291	0.00479646	+	0.999988i	$0.498473\pi$
$884$	−5.97798	−0.201061
$885$	2.03963	0.0685615
$886$	18.5822	0.624281
$887$	33.5304	1.12584	0.562921	−	0.826511i	$-0.309678\pi$
$887$	33.5304	1.12584	0.562921	+	0.826511i	$0.309678\pi$
$888$	8.31348	0.278982
$889$	72.4633	2.43034
$890$	17.1439	0.574665
$891$	−2.24639	−0.0752570
$892$	21.5560	0.721749
$893$	−18.8565	−0.631008
$894$	9.67029	0.323423
$895$	−35.4813	−1.18601
$896$	4.77480	0.159515
$897$	−16.8200	−0.561603
$898$	−26.9064	−0.897879
$899$	37.3606	1.24605
$900$	−0.839893	−0.0279964
$901$	4.45423	0.148392
$902$	9.66988	0.321972
$903$	4.56782	0.152007
$904$	−5.10591	−0.169820
$905$	15.4900	0.514906
$906$	−10.0421	−0.333628
$907$	0.832720	0.0276500	0.0138250	−	0.999904i	$-0.495599\pi$
$907$	0.832720	0.0276500	0.0138250	+	0.999904i	$0.495599\pi$
$908$	22.2084	0.737013
$909$	−5.61774	−0.186329
$910$	58.2186	1.92993
$911$	−39.8186	−1.31925	−0.659625	−	0.751595i	$-0.729285\pi$
$911$	−39.8186	−1.31925	−0.659625	+	0.751595i	$0.729285\pi$
$912$	−3.41029	−0.112926
$913$	19.0688	0.631085
$914$	17.9618	0.594125
$915$	−9.18414	−0.303618
$916$	−13.1028	−0.432929
$917$	−93.3873	−3.08392
$918$	1.00000	0.0330049
$919$	−34.2948	−1.13128	−0.565640	−	0.824652i	$-0.691371\pi$
$919$	−34.2948	−1.13128	−0.565640	+	0.824652i	$0.691371\pi$
$920$	−5.73884	−0.189204
$921$	−8.03112	−0.264634
$922$	−26.4859	−0.872266
$923$	9.18512	0.302332
$924$	−10.7261	−0.352862
$925$	−6.98243	−0.229581
$926$	23.0996	0.759101
$927$	−2.16480	−0.0711013
$928$	−6.33268	−0.207880
$929$	0.0809881	0.00265713	0.00132857	−	0.999999i	$-0.499577\pi$
$929$	0.0809881	0.00265713	0.00132857	+	0.999999i	$0.499577\pi$
$930$	−12.0331	−0.394582
$931$	53.8783	1.76579
$932$	18.3882	0.602325
$933$	−12.4090	−0.406254
$934$	26.5868	0.869945
$935$	4.58182	0.149842
$936$	5.97798	0.195396
$937$	−37.2632	−1.21734	−0.608668	−	0.793425i	$-0.708296\pi$
$937$	−37.2632	−1.21734	−0.608668	+	0.793425i	$0.708296\pi$
$938$	−8.81245	−0.287737
$939$	−18.1266	−0.591538
$940$	11.2777	0.367839
$941$	1.79643	0.0585620	0.0292810	−	0.999571i	$-0.490678\pi$
$941$	1.79643	0.0585620	0.0292810	+	0.999571i	$0.490678\pi$
$942$	−8.03183	−0.261691
$943$	−12.1118	−0.394413
$944$	1.00000	0.0325472
$945$	−9.73885	−0.316805
$946$	2.14901	0.0698705
$947$	−42.4780	−1.38035	−0.690174	−	0.723643i	$-0.742466\pi$
$947$	−42.4780	−1.38035	−0.690174	+	0.723643i	$0.742466\pi$
$948$	0.881718	0.0286369
$949$	−79.7207	−2.58784
$950$	2.86428	0.0929296
$951$	−4.59866	−0.149122
$952$	4.77480	0.154752
$953$	39.6346	1.28389	0.641946	−	0.766750i	$-0.278127\pi$
$953$	39.6346	1.28389	0.641946	+	0.766750i	$0.278127\pi$
$954$	−4.45423	−0.144211
$955$	39.0441	1.26344
$956$	10.2032	0.329994
$957$	14.2257	0.459851
$958$	2.76877	0.0894548
$959$	−8.49948	−0.274463
$960$	2.03963	0.0658289
$961$	3.80590	0.122771
$962$	49.6978	1.60232
$963$	8.01120	0.258157
$964$	8.82257	0.284156
$965$	14.6493	0.471579
$966$	13.4347	0.432253
$967$	28.6103	0.920047	0.460023	−	0.887907i	$-0.347841\pi$
$967$	28.6103	0.920047	0.460023	+	0.887907i	$0.347841\pi$
$968$	5.95372	0.191360
$969$	−3.41029	−0.109554
$970$	−26.7573	−0.859124
$971$	20.2687	0.650455	0.325228	−	0.945636i	$-0.394559\pi$
$971$	20.2687	0.650455	0.325228	+	0.945636i	$0.394559\pi$
$972$	−1.00000	−0.0320750
$973$	13.1427	0.421337
$974$	20.2658	0.649357
$975$	−5.02086	−0.160796
$976$	−4.50283	−0.144132
$977$	41.3102	1.32163	0.660815	−	0.750549i	$-0.270211\pi$
$977$	41.3102	1.32163	0.660815	+	0.750549i	$0.270211\pi$
$978$	−1.70157	−0.0544102
$979$	−18.8818	−0.603464
$980$	−32.2236	−1.02935
$981$	−9.41641	−0.300643
$982$	−16.7011	−0.532953
$983$	−30.2531	−0.964925	−0.482462	−	0.875917i	$-0.660257\pi$
$983$	−30.2531	−0.964925	−0.482462	+	0.875917i	$0.660257\pi$
$984$	4.30463	0.137226
$985$	39.7212	1.26562
$986$	−6.33268	−0.201674
$987$	−26.4012	−0.840361
$988$	−20.3867	−0.648586
$989$	−2.69169	−0.0855908
$990$	−4.58182	−0.145620
$991$	−56.6517	−1.79960	−0.899800	−	0.436303i	$-0.856288\pi$
$991$	−56.6517	−1.79960	−0.899800	+	0.436303i	$0.856288\pi$
$992$	−5.89965	−0.187314
$993$	11.1763	0.354669
$994$	−7.33645	−0.232698
$995$	−11.0174	−0.349275
$996$	8.48862	0.268972
$997$	41.0510	1.30010	0.650049	−	0.759892i	$-0.274748\pi$
$997$	41.0510	1.30010	0.650049	+	0.759892i	$0.274748\pi$
$998$	−38.6142	−1.22231
$999$	−8.31348	−0.263027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.u.1.2	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.u.1.2	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03963 q^{5} +1.00000 q^{6} -4.77480 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.03963 q^{5} +1.00000 q^{6} -4.77480 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.03963 q^{10} -2.24639 q^{11} -1.00000 q^{12} -5.97798 q^{13} +4.77480 q^{14} +2.03963 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +3.41029 q^{19} -2.03963 q^{20} +4.77480 q^{21} +2.24639 q^{22} -2.81366 q^{23} +1.00000 q^{24} -0.839893 q^{25} +5.97798 q^{26} -1.00000 q^{27} -4.77480 q^{28} +6.33268 q^{29} -2.03963 q^{30} +5.89965 q^{31} -1.00000 q^{32} +2.24639 q^{33} -1.00000 q^{34} +9.73885 q^{35} +1.00000 q^{36} +8.31348 q^{37} -3.41029 q^{38} +5.97798 q^{39} +2.03963 q^{40} +4.30463 q^{41} -4.77480 q^{42} +0.956651 q^{43} -2.24639 q^{44} -2.03963 q^{45} +2.81366 q^{46} -5.52929 q^{47} -1.00000 q^{48} +15.7987 q^{49} +0.839893 q^{50} -1.00000 q^{51} -5.97798 q^{52} +4.45423 q^{53} +1.00000 q^{54} +4.58182 q^{55} +4.77480 q^{56} -3.41029 q^{57} -6.33268 q^{58} +1.00000 q^{59} +2.03963 q^{60} -4.50283 q^{61} -5.89965 q^{62} -4.77480 q^{63} +1.00000 q^{64} +12.1929 q^{65} -2.24639 q^{66} -1.84562 q^{67} +1.00000 q^{68} +2.81366 q^{69} -9.73885 q^{70} -1.53649 q^{71} -1.00000 q^{72} +13.3357 q^{73} -8.31348 q^{74} +0.839893 q^{75} +3.41029 q^{76} +10.7261 q^{77} -5.97798 q^{78} -0.881718 q^{79} -2.03963 q^{80} +1.00000 q^{81} -4.30463 q^{82} -8.48862 q^{83} +4.77480 q^{84} -2.03963 q^{85} -0.956651 q^{86} -6.33268 q^{87} +2.24639 q^{88} +8.40538 q^{89} +2.03963 q^{90} +28.5437 q^{91} -2.81366 q^{92} -5.89965 q^{93} +5.52929 q^{94} -6.95575 q^{95} +1.00000 q^{96} -13.1187 q^{97} -15.7987 q^{98} -2.24639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9	\( 9 q - 9 q^{2} - 9 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} - 5 q^{7} - 9 q^{8} + 9 q^{9} - 2 q^{10} - q^{11} - 9 q^{12} - 4 q^{13} + 5 q^{14} - 2 q^{15} + 9 q^{16} + 9 q^{17} - 9 q^{18} - 7 q^{19} + 2 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 9 q^{24} + 5 q^{25} + 4 q^{26} - 9 q^{27} - 5 q^{28} + 6 q^{29} + 2 q^{30} - 17 q^{31} - 9 q^{32} + q^{33} - 9 q^{34} + 10 q^{35} + 9 q^{36} + 2 q^{37} + 7 q^{38} + 4 q^{39} - 2 q^{40} + 14 q^{41} - 5 q^{42} - 27 q^{43} - q^{44} + 2 q^{45} + 8 q^{46} - 18 q^{47} - 9 q^{48} + 18 q^{49} - 5 q^{50} - 9 q^{51} - 4 q^{52} + 4 q^{53} + 9 q^{54} - 27 q^{55} + 5 q^{56} + 7 q^{57} - 6 q^{58} + 9 q^{59} - 2 q^{60} + 5 q^{61} + 17 q^{62} - 5 q^{63} + 9 q^{64} + 2 q^{65} - q^{66} - 22 q^{67} + 9 q^{68} + 8 q^{69} - 10 q^{70} + 16 q^{71} - 9 q^{72} - 12 q^{73} - 2 q^{74} - 5 q^{75} - 7 q^{76} + 6 q^{77} - 4 q^{78} - 9 q^{79} + 2 q^{80} + 9 q^{81} - 14 q^{82} + 10 q^{83} + 5 q^{84} + 2 q^{85} + 27 q^{86} - 6 q^{87} + q^{88} + 15 q^{89} - 2 q^{90} + 3 q^{91} - 8 q^{92} + 17 q^{93} + 18 q^{94} - 9 q^{95} + 9 q^{96} - 33 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 9 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 - 5 * q^7 - 9 * q^8 + 9 * q^9 - 2 * q^10 - q^11 - 9 * q^12 - 4 * q^13 + 5 * q^14 - 2 * q^15 + 9 * q^16 + 9 * q^17 - 9 * q^18 - 7 * q^19 + 2 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 9 * q^24 + 5 * q^25 + 4 * q^26 - 9 * q^27 - 5 * q^28 + 6 * q^29 + 2 * q^30 - 17 * q^31 - 9 * q^32 + q^33 - 9 * q^34 + 10 * q^35 + 9 * q^36 + 2 * q^37 + 7 * q^38 + 4 * q^39 - 2 * q^40 + 14 * q^41 - 5 * q^42 - 27 * q^43 - q^44 + 2 * q^45 + 8 * q^46 - 18 * q^47 - 9 * q^48 + 18 * q^49 - 5 * q^50 - 9 * q^51 - 4 * q^52 + 4 * q^53 + 9 * q^54 - 27 * q^55 + 5 * q^56 + 7 * q^57 - 6 * q^58 + 9 * q^59 - 2 * q^60 + 5 * q^61 + 17 * q^62 - 5 * q^63 + 9 * q^64 + 2 * q^65 - q^66 - 22 * q^67 + 9 * q^68 + 8 * q^69 - 10 * q^70 + 16 * q^71 - 9 * q^72 - 12 * q^73 - 2 * q^74 - 5 * q^75 - 7 * q^76 + 6 * q^77 - 4 * q^78 - 9 * q^79 + 2 * q^80 + 9 * q^81 - 14 * q^82 + 10 * q^83 + 5 * q^84 + 2 * q^85 + 27 * q^86 - 6 * q^87 + q^88 + 15 * q^89 - 2 * q^90 + 3 * q^91 - 8 * q^92 + 17 * q^93 + 18 * q^94 - 9 * q^95 + 9 * q^96 - 33 * q^97 - 18 * q^98 - q^99

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