LMFDB - Embedded newform 6018.2.a.m.1.3

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:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
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			1.3
Root			$0.311108$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.52543 q^{5} -1.00000 q^{6} -2.59210 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.52543 q^{5} -1.00000 q^{6} -2.59210 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.52543 q^{10} +5.05086 q^{11} +1.00000 q^{12} +3.52543 q^{13} +2.59210 q^{14} +3.52543 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.14764 q^{19} +3.52543 q^{20} -2.59210 q^{21} -5.05086 q^{22} +5.21432 q^{23} -1.00000 q^{24} +7.42864 q^{25} -3.52543 q^{26} +1.00000 q^{27} -2.59210 q^{28} -2.90321 q^{29} -3.52543 q^{30} -2.00000 q^{31} -1.00000 q^{32} +5.05086 q^{33} +1.00000 q^{34} -9.13828 q^{35} +1.00000 q^{36} +9.13828 q^{37} -1.14764 q^{38} +3.52543 q^{39} -3.52543 q^{40} +2.09679 q^{41} +2.59210 q^{42} +6.42864 q^{43} +5.05086 q^{44} +3.52543 q^{45} -5.21432 q^{46} -1.09679 q^{47} +1.00000 q^{48} -0.280996 q^{49} -7.42864 q^{50} -1.00000 q^{51} +3.52543 q^{52} -9.44938 q^{53} -1.00000 q^{54} +17.8064 q^{55} +2.59210 q^{56} +1.14764 q^{57} +2.90321 q^{58} -1.00000 q^{59} +3.52543 q^{60} -2.94914 q^{61} +2.00000 q^{62} -2.59210 q^{63} +1.00000 q^{64} +12.4286 q^{65} -5.05086 q^{66} -5.09679 q^{67} -1.00000 q^{68} +5.21432 q^{69} +9.13828 q^{70} -7.13828 q^{71} -1.00000 q^{72} +7.90321 q^{73} -9.13828 q^{74} +7.42864 q^{75} +1.14764 q^{76} -13.0923 q^{77} -3.52543 q^{78} +7.46520 q^{79} +3.52543 q^{80} +1.00000 q^{81} -2.09679 q^{82} +8.46520 q^{83} -2.59210 q^{84} -3.52543 q^{85} -6.42864 q^{86} -2.90321 q^{87} -5.05086 q^{88} -12.0509 q^{89} -3.52543 q^{90} -9.13828 q^{91} +5.21432 q^{92} -2.00000 q^{93} +1.09679 q^{94} +4.04593 q^{95} -1.00000 q^{96} -9.00000 q^{97} +0.280996 q^{98} +5.05086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{19} + 4 q^{20} - q^{21} - 2 q^{22} + 9 q^{23} - 3 q^{24} + 9 q^{25} - 4 q^{26} + 3 q^{27} - q^{28} - 2 q^{29} - 4 q^{30} - 6 q^{31} - 3 q^{32} + 2 q^{33} + 3 q^{34} + 6 q^{35} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - 4 q^{40} + 13 q^{41} + q^{42} + 6 q^{43} + 2 q^{44} + 4 q^{45} - 9 q^{46} - 10 q^{47} + 3 q^{48} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 4 q^{52} + 5 q^{53} - 3 q^{54} + 40 q^{55} + q^{56} - 3 q^{57} + 2 q^{58} - 3 q^{59} + 4 q^{60} - 22 q^{61} + 6 q^{62} - q^{63} + 3 q^{64} + 24 q^{65} - 2 q^{66} - 22 q^{67} - 3 q^{68} + 9 q^{69} - 6 q^{70} + 12 q^{71} - 3 q^{72} + 17 q^{73} + 6 q^{74} + 9 q^{75} - 3 q^{76} + 14 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 3 q^{81} - 13 q^{82} + 5 q^{83} - q^{84} - 4 q^{85} - 6 q^{86} - 2 q^{87} - 2 q^{88} - 23 q^{89} - 4 q^{90} + 6 q^{91} + 9 q^{92} - 6 q^{93} + 10 q^{94} + 32 q^{95} - 3 q^{96} - 27 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^19 + 4 * q^20 - q^21 - 2 * q^22 + 9 * q^23 - 3 * q^24 + 9 * q^25 - 4 * q^26 + 3 * q^27 - q^28 - 2 * q^29 - 4 * q^30 - 6 * q^31 - 3 * q^32 + 2 * q^33 + 3 * q^34 + 6 * q^35 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - 4 * q^40 + 13 * q^41 + q^42 + 6 * q^43 + 2 * q^44 + 4 * q^45 - 9 * q^46 - 10 * q^47 + 3 * q^48 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 4 * q^52 + 5 * q^53 - 3 * q^54 + 40 * q^55 + q^56 - 3 * q^57 + 2 * q^58 - 3 * q^59 + 4 * q^60 - 22 * q^61 + 6 * q^62 - q^63 + 3 * q^64 + 24 * q^65 - 2 * q^66 - 22 * q^67 - 3 * q^68 + 9 * q^69 - 6 * q^70 + 12 * q^71 - 3 * q^72 + 17 * q^73 + 6 * q^74 + 9 * q^75 - 3 * q^76 + 14 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 3 * q^81 - 13 * q^82 + 5 * q^83 - q^84 - 4 * q^85 - 6 * q^86 - 2 * q^87 - 2 * q^88 - 23 * q^89 - 4 * q^90 + 6 * q^91 + 9 * q^92 - 6 * q^93 + 10 * q^94 + 32 * q^95 - 3 * q^96 - 27 * q^97 - 6 * q^98 + 2 * 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
$5$	3.52543	1.57662	0.788310	−	0.615279i	$-0.210957\pi$
$5$	3.52543	1.57662	0.788310	+	0.615279i	$0.210957\pi$
$6$	−1.00000	−0.408248
$7$	−2.59210	−0.979723	−0.489862	−	0.871800i	$-0.662953\pi$
$7$	−2.59210	−0.979723	−0.489862	+	0.871800i	$0.662953\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.52543	−1.11484
$11$	5.05086	1.52289	0.761445	−	0.648229i	$-0.224490\pi$
$11$	5.05086	1.52289	0.761445	+	0.648229i	$0.224490\pi$
$12$	1.00000	0.288675
$13$	3.52543	0.977778	0.488889	−	0.872346i	$-0.337402\pi$
$13$	3.52543	0.977778	0.488889	+	0.872346i	$0.337402\pi$
$14$	2.59210	0.692769
$15$	3.52543	0.910261
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	1.14764	0.263287	0.131644	−	0.991297i	$-0.457975\pi$
$19$	1.14764	0.263287	0.131644	+	0.991297i	$0.457975\pi$
$20$	3.52543	0.788310
$21$	−2.59210	−0.565643
$22$	−5.05086	−1.07685
$23$	5.21432	1.08726	0.543630	−	0.839325i	$-0.317049\pi$
$23$	5.21432	1.08726	0.543630	+	0.839325i	$0.317049\pi$
$24$	−1.00000	−0.204124
$25$	7.42864	1.48573
$26$	−3.52543	−0.691393
$27$	1.00000	0.192450
$28$	−2.59210	−0.489862
$29$	−2.90321	−0.539113	−0.269556	−	0.962985i	$-0.586877\pi$
$29$	−2.90321	−0.539113	−0.269556	+	0.962985i	$0.586877\pi$
$30$	−3.52543	−0.643652
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	5.05086	0.879241
$34$	1.00000	0.171499
$35$	−9.13828	−1.54465
$36$	1.00000	0.166667
$37$	9.13828	1.50232	0.751162	−	0.660118i	$-0.229494\pi$
$37$	9.13828	1.50232	0.751162	+	0.660118i	$0.229494\pi$
$38$	−1.14764	−0.186172
$39$	3.52543	0.564520
$40$	−3.52543	−0.557419
$41$	2.09679	0.327463	0.163732	−	0.986505i	$-0.447647\pi$
$41$	2.09679	0.327463	0.163732	+	0.986505i	$0.447647\pi$
$42$	2.59210	0.399970
$43$	6.42864	0.980358	0.490179	−	0.871622i	$-0.336931\pi$
$43$	6.42864	0.980358	0.490179	+	0.871622i	$0.336931\pi$
$44$	5.05086	0.761445
$45$	3.52543	0.525540
$46$	−5.21432	−0.768810
$47$	−1.09679	−0.159983	−0.0799915	−	0.996796i	$-0.525489\pi$
$47$	−1.09679	−0.159983	−0.0799915	+	0.996796i	$0.525489\pi$
$48$	1.00000	0.144338
$49$	−0.280996	−0.0401423
$50$	−7.42864	−1.05057
$51$	−1.00000	−0.140028
$52$	3.52543	0.488889
$53$	−9.44938	−1.29797	−0.648986	−	0.760800i	$-0.724807\pi$
$53$	−9.44938	−1.29797	−0.648986	+	0.760800i	$0.724807\pi$
$54$	−1.00000	−0.136083
$55$	17.8064	2.40102
$56$	2.59210	0.346384
$57$	1.14764	0.152009
$58$	2.90321	0.381210
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.52543	0.455131
$61$	−2.94914	−0.377599	−0.188800	−	0.982016i	$-0.560460\pi$
$61$	−2.94914	−0.377599	−0.188800	+	0.982016i	$0.560460\pi$
$62$	2.00000	0.254000
$63$	−2.59210	−0.326574
$64$	1.00000	0.125000
$65$	12.4286	1.54158
$66$	−5.05086	−0.621717
$67$	−5.09679	−0.622672	−0.311336	−	0.950300i	$-0.600776\pi$
$67$	−5.09679	−0.622672	−0.311336	+	0.950300i	$0.600776\pi$
$68$	−1.00000	−0.121268
$69$	5.21432	0.627730
$70$	9.13828	1.09223
$71$	−7.13828	−0.847157	−0.423579	−	0.905859i	$-0.639226\pi$
$71$	−7.13828	−0.847157	−0.423579	+	0.905859i	$0.639226\pi$
$72$	−1.00000	−0.117851
$73$	7.90321	0.925001	0.462500	−	0.886619i	$-0.346952\pi$
$73$	7.90321	0.925001	0.462500	+	0.886619i	$0.346952\pi$
$74$	−9.13828	−1.06230
$75$	7.42864	0.857785
$76$	1.14764	0.131644
$77$	−13.0923	−1.49201
$78$	−3.52543	−0.399176
$79$	7.46520	0.839901	0.419951	−	0.907547i	$-0.362047\pi$
$79$	7.46520	0.839901	0.419951	+	0.907547i	$0.362047\pi$
$80$	3.52543	0.394155
$81$	1.00000	0.111111
$82$	−2.09679	−0.231552
$83$	8.46520	0.929177	0.464588	−	0.885527i	$-0.346202\pi$
$83$	8.46520	0.929177	0.464588	+	0.885527i	$0.346202\pi$
$84$	−2.59210	−0.282822
$85$	−3.52543	−0.382386
$86$	−6.42864	−0.693218
$87$	−2.90321	−0.311257
$88$	−5.05086	−0.538423
$89$	−12.0509	−1.27739	−0.638694	−	0.769461i	$-0.720525\pi$
$89$	−12.0509	−1.27739	−0.638694	+	0.769461i	$0.720525\pi$
$90$	−3.52543	−0.371613
$91$	−9.13828	−0.957952
$92$	5.21432	0.543630
$93$	−2.00000	−0.207390
$94$	1.09679	0.113125
$95$	4.04593	0.415104
$96$	−1.00000	−0.102062
$97$	−9.00000	−0.913812	−0.456906	−	0.889515i	$-0.651042\pi$
$97$	−9.00000	−0.913812	−0.456906	+	0.889515i	$0.651042\pi$
$98$	0.280996	0.0283849
$99$	5.05086	0.507630
$100$	7.42864	0.742864
$101$	6.70964	0.667634	0.333817	−	0.942638i	$-0.391663\pi$
$101$	6.70964	0.667634	0.333817	+	0.942638i	$0.391663\pi$
$102$	1.00000	0.0990148
$103$	3.50961	0.345812	0.172906	−	0.984938i	$-0.444684\pi$
$103$	3.50961	0.345812	0.172906	+	0.984938i	$0.444684\pi$
$104$	−3.52543	−0.345697
$105$	−9.13828	−0.891804
$106$	9.44938	0.917805
$107$	−4.52543	−0.437490	−0.218745	−	0.975782i	$-0.570196\pi$
$107$	−4.52543	−0.437490	−0.218745	+	0.975782i	$0.570196\pi$
$108$	1.00000	0.0962250
$109$	−17.2859	−1.65569	−0.827845	−	0.560956i	$-0.810434\pi$
$109$	−17.2859	−1.65569	−0.827845	+	0.560956i	$0.810434\pi$
$110$	−17.8064	−1.69778
$111$	9.13828	0.867367
$112$	−2.59210	−0.244931
$113$	−14.6494	−1.37810	−0.689050	−	0.724713i	$-0.741972\pi$
$113$	−14.6494	−1.37810	−0.689050	+	0.724713i	$0.741972\pi$
$114$	−1.14764	−0.107487
$115$	18.3827	1.71420
$116$	−2.90321	−0.269556
$117$	3.52543	0.325926
$118$	1.00000	0.0920575
$119$	2.59210	0.237618
$120$	−3.52543	−0.321826
$121$	14.5111	1.31919
$122$	2.94914	0.267003
$123$	2.09679	0.189061
$124$	−2.00000	−0.179605
$125$	8.56199	0.765808
$126$	2.59210	0.230923
$127$	−13.5669	−1.20387	−0.601935	−	0.798545i	$-0.705603\pi$
$127$	−13.5669	−1.20387	−0.601935	+	0.798545i	$0.705603\pi$
$128$	−1.00000	−0.0883883
$129$	6.42864	0.566010
$130$	−12.4286	−1.09006
$131$	17.2716	1.50903	0.754515	−	0.656283i	$-0.227872\pi$
$131$	17.2716	1.50903	0.754515	+	0.656283i	$0.227872\pi$
$132$	5.05086	0.439621
$133$	−2.97481	−0.257949
$134$	5.09679	0.440295
$135$	3.52543	0.303420
$136$	1.00000	0.0857493
$137$	3.91258	0.334274	0.167137	−	0.985934i	$-0.446548\pi$
$137$	3.91258	0.334274	0.167137	+	0.985934i	$0.446548\pi$
$138$	−5.21432	−0.443872
$139$	−0.341219	−0.0289418	−0.0144709	−	0.999895i	$-0.504606\pi$
$139$	−0.341219	−0.0289418	−0.0144709	+	0.999895i	$0.504606\pi$
$140$	−9.13828	−0.772325
$141$	−1.09679	−0.0923662
$142$	7.13828	0.599031
$143$	17.8064	1.48905
$144$	1.00000	0.0833333
$145$	−10.2351	−0.849976
$146$	−7.90321	−0.654074
$147$	−0.280996	−0.0231762
$148$	9.13828	0.751162
$149$	9.28592	0.760732	0.380366	−	0.924836i	$-0.375798\pi$
$149$	9.28592	0.760732	0.380366	+	0.924836i	$0.375798\pi$
$150$	−7.42864	−0.606546
$151$	22.7812	1.85391	0.926955	−	0.375172i	$-0.122416\pi$
$151$	22.7812	1.85391	0.926955	+	0.375172i	$0.122416\pi$
$152$	−1.14764	−0.0930862
$153$	−1.00000	−0.0808452
$154$	13.0923	1.05501
$155$	−7.05086	−0.566338
$156$	3.52543	0.282260
$157$	−1.54125	−0.123005	−0.0615025	−	0.998107i	$-0.519589\pi$
$157$	−1.54125	−0.123005	−0.0615025	+	0.998107i	$0.519589\pi$
$158$	−7.46520	−0.593900
$159$	−9.44938	−0.749385
$160$	−3.52543	−0.278710
$161$	−13.5161	−1.06521
$162$	−1.00000	−0.0785674
$163$	−8.38271	−0.656584	−0.328292	−	0.944576i	$-0.606473\pi$
$163$	−8.38271	−0.656584	−0.328292	+	0.944576i	$0.606473\pi$
$164$	2.09679	0.163732
$165$	17.8064	1.38623
$166$	−8.46520	−0.657027
$167$	22.2766	1.72381	0.861906	−	0.507069i	$-0.169271\pi$
$167$	22.2766	1.72381	0.861906	+	0.507069i	$0.169271\pi$
$168$	2.59210	0.199985
$169$	−0.571361	−0.0439508
$170$	3.52543	0.270388
$171$	1.14764	0.0877625
$172$	6.42864	0.490179
$173$	10.4429	0.793961	0.396981	−	0.917827i	$-0.370058\pi$
$173$	10.4429	0.793961	0.396981	+	0.917827i	$0.370058\pi$
$174$	2.90321	0.220092
$175$	−19.2558	−1.45560
$176$	5.05086	0.380723
$177$	−1.00000	−0.0751646
$178$	12.0509	0.903250
$179$	−20.1526	−1.50627	−0.753137	−	0.657864i	$-0.771460\pi$
$179$	−20.1526	−1.50627	−0.753137	+	0.657864i	$0.771460\pi$
$180$	3.52543	0.262770
$181$	6.57628	0.488811	0.244406	−	0.969673i	$-0.421407\pi$
$181$	6.57628	0.488811	0.244406	+	0.969673i	$0.421407\pi$
$182$	9.13828	0.677374
$183$	−2.94914	−0.218007
$184$	−5.21432	−0.384405
$185$	32.2163	2.36859
$186$	2.00000	0.146647
$187$	−5.05086	−0.369355
$188$	−1.09679	−0.0799915
$189$	−2.59210	−0.188548
$190$	−4.04593	−0.293523
$191$	−0.769859	−0.0557050	−0.0278525	−	0.999612i	$-0.508867\pi$
$191$	−0.769859	−0.0557050	−0.0278525	+	0.999612i	$0.508867\pi$
$192$	1.00000	0.0721688
$193$	−0.861725	−0.0620283	−0.0310142	−	0.999519i	$-0.509874\pi$
$193$	−0.861725	−0.0620283	−0.0310142	+	0.999519i	$0.509874\pi$
$194$	9.00000	0.646162
$195$	12.4286	0.890033
$196$	−0.280996	−0.0200712
$197$	−6.81579	−0.485605	−0.242803	−	0.970076i	$-0.578067\pi$
$197$	−6.81579	−0.485605	−0.242803	+	0.970076i	$0.578067\pi$
$198$	−5.05086	−0.358949
$199$	−8.97481	−0.636207	−0.318104	−	0.948056i	$-0.603046\pi$
$199$	−8.97481	−0.636207	−0.318104	+	0.948056i	$0.603046\pi$
$200$	−7.42864	−0.525284
$201$	−5.09679	−0.359500
$202$	−6.70964	−0.472088
$203$	7.52543	0.528181
$204$	−1.00000	−0.0700140
$205$	7.39207	0.516285
$206$	−3.50961	−0.244526
$207$	5.21432	0.362420
$208$	3.52543	0.244444
$209$	5.79658	0.400958
$210$	9.13828	0.630601
$211$	−9.96836	−0.686250	−0.343125	−	0.939290i	$-0.611485\pi$
$211$	−9.96836	−0.686250	−0.343125	+	0.939290i	$0.611485\pi$
$212$	−9.44938	−0.648986
$213$	−7.13828	−0.489107
$214$	4.52543	0.309352
$215$	22.6637	1.54565
$216$	−1.00000	−0.0680414
$217$	5.18421	0.351927
$218$	17.2859	1.17075
$219$	7.90321	0.534050
$220$	17.8064	1.20051
$221$	−3.52543	−0.237146
$222$	−9.13828	−0.613321
$223$	−6.34122	−0.424639	−0.212320	−	0.977200i	$-0.568102\pi$
$223$	−6.34122	−0.424639	−0.212320	+	0.977200i	$0.568102\pi$
$224$	2.59210	0.173192
$225$	7.42864	0.495243
$226$	14.6494	0.974464
$227$	−18.7511	−1.24456	−0.622278	−	0.782796i	$-0.713793\pi$
$227$	−18.7511	−1.24456	−0.622278	+	0.782796i	$0.713793\pi$
$228$	1.14764	0.0760045
$229$	−0.357041	−0.0235939	−0.0117970	−	0.999930i	$-0.503755\pi$
$229$	−0.357041	−0.0235939	−0.0117970	+	0.999930i	$0.503755\pi$
$230$	−18.3827	−1.21212
$231$	−13.0923	−0.861413
$232$	2.90321	0.190605
$233$	8.75557	0.573596	0.286798	−	0.957991i	$-0.407409\pi$
$233$	8.75557	0.573596	0.286798	+	0.957991i	$0.407409\pi$
$234$	−3.52543	−0.230464
$235$	−3.86665	−0.252232
$236$	−1.00000	−0.0650945
$237$	7.46520	0.484917
$238$	−2.59210	−0.168021
$239$	8.14764	0.527027	0.263514	−	0.964656i	$-0.415119\pi$
$239$	8.14764	0.527027	0.263514	+	0.964656i	$0.415119\pi$
$240$	3.52543	0.227565
$241$	18.6178	1.19928	0.599638	−	0.800271i	$-0.295311\pi$
$241$	18.6178	1.19928	0.599638	+	0.800271i	$0.295311\pi$
$242$	−14.5111	−0.932811
$243$	1.00000	0.0641500
$244$	−2.94914	−0.188800
$245$	−0.990632	−0.0632892
$246$	−2.09679	−0.133686
$247$	4.04593	0.257437
$248$	2.00000	0.127000
$249$	8.46520	0.536461
$250$	−8.56199	−0.541508
$251$	22.1289	1.39676	0.698382	−	0.715725i	$-0.253904\pi$
$251$	22.1289	1.39676	0.698382	+	0.715725i	$0.253904\pi$
$252$	−2.59210	−0.163287
$253$	26.3368	1.65578
$254$	13.5669	0.851264
$255$	−3.52543	−0.220771
$256$	1.00000	0.0625000
$257$	15.5067	0.967281	0.483640	−	0.875267i	$-0.339314\pi$
$257$	15.5067	0.967281	0.483640	+	0.875267i	$0.339314\pi$
$258$	−6.42864	−0.400230
$259$	−23.6874	−1.47186
$260$	12.4286	0.770792
$261$	−2.90321	−0.179704
$262$	−17.2716	−1.06704
$263$	28.5462	1.76023	0.880116	−	0.474758i	$-0.157465\pi$
$263$	28.5462	1.76023	0.880116	+	0.474758i	$0.157465\pi$
$264$	−5.05086	−0.310859
$265$	−33.3131	−2.04641
$266$	2.97481	0.182397
$267$	−12.0509	−0.737500
$268$	−5.09679	−0.311336
$269$	10.6064	0.646683	0.323342	−	0.946282i	$-0.395194\pi$
$269$	10.6064	0.646683	0.323342	+	0.946282i	$0.395194\pi$
$270$	−3.52543	−0.214551
$271$	8.99063	0.546142	0.273071	−	0.961994i	$-0.411961\pi$
$271$	8.99063	0.546142	0.273071	+	0.961994i	$0.411961\pi$
$272$	−1.00000	−0.0606339
$273$	−9.13828	−0.553074
$274$	−3.91258	−0.236368
$275$	37.5210	2.26260
$276$	5.21432	0.313865
$277$	−25.7862	−1.54934	−0.774670	−	0.632366i	$-0.782084\pi$
$277$	−25.7862	−1.54934	−0.774670	+	0.632366i	$0.782084\pi$
$278$	0.341219	0.0204650
$279$	−2.00000	−0.119737
$280$	9.13828	0.546116
$281$	−10.2208	−0.609720	−0.304860	−	0.952397i	$-0.598610\pi$
$281$	−10.2208	−0.609720	−0.304860	+	0.952397i	$0.598610\pi$
$282$	1.09679	0.0653128
$283$	0.00936793	0.000556866 0	0.000278433	−	1.00000i	$-0.499911\pi$
$283$	0.00936793	0.000556866 0	0.000278433		1.00000i	$0.499911\pi$
$284$	−7.13828	−0.423579
$285$	4.04593	0.239660
$286$	−17.8064	−1.05292
$287$	−5.43509	−0.320823
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	10.2351	0.601024
$291$	−9.00000	−0.527589
$292$	7.90321	0.462500
$293$	−6.66815	−0.389557	−0.194779	−	0.980847i	$-0.562399\pi$
$293$	−6.66815	−0.389557	−0.194779	+	0.980847i	$0.562399\pi$
$294$	0.280996	0.0163880
$295$	−3.52543	−0.205258
$296$	−9.13828	−0.531151
$297$	5.05086	0.293080
$298$	−9.28592	−0.537919
$299$	18.3827	1.06310
$300$	7.42864	0.428893
$301$	−16.6637	−0.960480
$302$	−22.7812	−1.31091
$303$	6.70964	0.385459
$304$	1.14764	0.0658219
$305$	−10.3970	−0.595330
$306$	1.00000	0.0571662
$307$	−12.7649	−0.728533	−0.364267	−	0.931295i	$-0.618680\pi$
$307$	−12.7649	−0.728533	−0.364267	+	0.931295i	$0.618680\pi$
$308$	−13.0923	−0.746005
$309$	3.50961	0.199655
$310$	7.05086	0.400462
$311$	−4.76986	−0.270474	−0.135237	−	0.990813i	$-0.543180\pi$
$311$	−4.76986	−0.270474	−0.135237	+	0.990813i	$0.543180\pi$
$312$	−3.52543	−0.199588
$313$	20.2351	1.14375	0.571877	−	0.820340i	$-0.306216\pi$
$313$	20.2351	1.14375	0.571877	+	0.820340i	$0.306216\pi$
$314$	1.54125	0.0869777
$315$	−9.13828	−0.514883
$316$	7.46520	0.419951
$317$	−21.3778	−1.20070	−0.600348	−	0.799739i	$-0.704971\pi$
$317$	−21.3778	−1.20070	−0.600348	+	0.799739i	$0.704971\pi$
$318$	9.44938	0.529895
$319$	−14.6637	−0.821010
$320$	3.52543	0.197077
$321$	−4.52543	−0.252585
$322$	13.5161	0.753221
$323$	−1.14764	−0.0638566
$324$	1.00000	0.0555556
$325$	26.1891	1.45271
$326$	8.38271	0.464275
$327$	−17.2859	−0.955913
$328$	−2.09679	−0.115776
$329$	2.84299	0.156739
$330$	−17.8064	−0.980211
$331$	4.63158	0.254575	0.127287	−	0.991866i	$-0.459373\pi$
$331$	4.63158	0.254575	0.127287	+	0.991866i	$0.459373\pi$
$332$	8.46520	0.464588
$333$	9.13828	0.500774
$334$	−22.2766	−1.21892
$335$	−17.9684	−0.981716
$336$	−2.59210	−0.141411
$337$	−4.33185	−0.235971	−0.117985	−	0.993015i	$-0.537644\pi$
$337$	−4.33185	−0.235971	−0.117985	+	0.993015i	$0.537644\pi$
$338$	0.571361	0.0310779
$339$	−14.6494	−0.795647
$340$	−3.52543	−0.191193
$341$	−10.1017	−0.547038
$342$	−1.14764	−0.0620574
$343$	18.8731	1.01905
$344$	−6.42864	−0.346609
$345$	18.3827	0.989692
$346$	−10.4429	−0.561415
$347$	−9.16992	−0.492267	−0.246133	−	0.969236i	$-0.579160\pi$
$347$	−9.16992	−0.492267	−0.246133	+	0.969236i	$0.579160\pi$
$348$	−2.90321	−0.155628
$349$	14.3941	0.770498	0.385249	−	0.922813i	$-0.374116\pi$
$349$	14.3941	0.770498	0.385249	+	0.922813i	$0.374116\pi$
$350$	19.2558	1.02927
$351$	3.52543	0.188173
$352$	−5.05086	−0.269211
$353$	−23.6780	−1.26025	−0.630126	−	0.776493i	$-0.716997\pi$
$353$	−23.6780	−1.26025	−0.630126	+	0.776493i	$0.716997\pi$
$354$	1.00000	0.0531494
$355$	−25.1655	−1.33564
$356$	−12.0509	−0.638694
$357$	2.59210	0.137189
$358$	20.1526	1.06510
$359$	−1.58274	−0.0835336	−0.0417668	−	0.999127i	$-0.513299\pi$
$359$	−1.58274	−0.0835336	−0.0417668	+	0.999127i	$0.513299\pi$
$360$	−3.52543	−0.185806
$361$	−17.6829	−0.930680
$362$	−6.57628	−0.345642
$363$	14.5111	0.761637
$364$	−9.13828	−0.478976
$365$	27.8622	1.45837
$366$	2.94914	0.154154
$367$	−9.28592	−0.484721	−0.242360	−	0.970186i	$-0.577922\pi$
$367$	−9.28592	−0.484721	−0.242360	+	0.970186i	$0.577922\pi$
$368$	5.21432	0.271815
$369$	2.09679	0.109154
$370$	−32.2163	−1.67485
$371$	24.4938	1.27165
$372$	−2.00000	−0.103695
$373$	−26.8113	−1.38824	−0.694119	−	0.719860i	$-0.744206\pi$
$373$	−26.8113	−1.38824	−0.694119	+	0.719860i	$0.744206\pi$
$374$	5.05086	0.261174
$375$	8.56199	0.442139
$376$	1.09679	0.0565625
$377$	−10.2351	−0.527133
$378$	2.59210	0.133323
$379$	−8.32693	−0.427726	−0.213863	−	0.976864i	$-0.568605\pi$
$379$	−8.32693	−0.427726	−0.213863	+	0.976864i	$0.568605\pi$
$380$	4.04593	0.207552
$381$	−13.5669	−0.695054
$382$	0.769859	0.0393894
$383$	3.68445	0.188266	0.0941332	−	0.995560i	$-0.469992\pi$
$383$	3.68445	0.188266	0.0941332	+	0.995560i	$0.469992\pi$
$384$	−1.00000	−0.0510310
$385$	−46.1561	−2.35233
$386$	0.861725	0.0438606
$387$	6.42864	0.326786
$388$	−9.00000	−0.456906
$389$	−37.9768	−1.92550	−0.962751	−	0.270391i	$-0.912847\pi$
$389$	−37.9768	−1.92550	−0.962751	+	0.270391i	$0.912847\pi$
$390$	−12.4286	−0.629349
$391$	−5.21432	−0.263699
$392$	0.280996	0.0141925
$393$	17.2716	0.871238
$394$	6.81579	0.343375
$395$	26.3180	1.32420
$396$	5.05086	0.253815
$397$	4.74128	0.237958	0.118979	−	0.992897i	$-0.462038\pi$
$397$	4.74128	0.237958	0.118979	+	0.992897i	$0.462038\pi$
$398$	8.97481	0.449867
$399$	−2.97481	−0.148927
$400$	7.42864	0.371432
$401$	−11.4652	−0.572545	−0.286272	−	0.958148i	$-0.592416\pi$
$401$	−11.4652	−0.572545	−0.286272	+	0.958148i	$0.592416\pi$
$402$	5.09679	0.254205
$403$	−7.05086	−0.351228
$404$	6.70964	0.333817
$405$	3.52543	0.175180
$406$	−7.52543	−0.373481
$407$	46.1561	2.28787
$408$	1.00000	0.0495074
$409$	−38.4701	−1.90223	−0.951113	−	0.308844i	$-0.900058\pi$
$409$	−38.4701	−1.90223	−0.951113	+	0.308844i	$0.900058\pi$
$410$	−7.39207	−0.365069
$411$	3.91258	0.192993
$412$	3.50961	0.172906
$413$	2.59210	0.127549
$414$	−5.21432	−0.256270
$415$	29.8435	1.46496
$416$	−3.52543	−0.172848
$417$	−0.341219	−0.0167096
$418$	−5.79658	−0.283520
$419$	16.7382	0.817715	0.408858	−	0.912598i	$-0.365927\pi$
$419$	16.7382	0.817715	0.408858	+	0.912598i	$0.365927\pi$
$420$	−9.13828	−0.445902
$421$	−7.58274	−0.369560	−0.184780	−	0.982780i	$-0.559157\pi$
$421$	−7.58274	−0.369560	−0.184780	+	0.982780i	$0.559157\pi$
$422$	9.96836	0.485252
$423$	−1.09679	−0.0533277
$424$	9.44938	0.458903
$425$	−7.42864	−0.360342
$426$	7.13828	0.345851
$427$	7.64449	0.369943
$428$	−4.52543	−0.218745
$429$	17.8064	0.859702
$430$	−22.6637	−1.09294
$431$	16.3240	0.786300	0.393150	−	0.919474i	$-0.371385\pi$
$431$	16.3240	0.786300	0.393150	+	0.919474i	$0.371385\pi$
$432$	1.00000	0.0481125
$433$	−23.4701	−1.12790	−0.563951	−	0.825808i	$-0.690719\pi$
$433$	−23.4701	−1.12790	−0.563951	+	0.825808i	$0.690719\pi$
$434$	−5.18421	−0.248850
$435$	−10.2351	−0.490734
$436$	−17.2859	−0.827845
$437$	5.98418	0.286262
$438$	−7.90321	−0.377630
$439$	−6.60793	−0.315379	−0.157690	−	0.987489i	$-0.550405\pi$
$439$	−6.60793	−0.315379	−0.157690	+	0.987489i	$0.550405\pi$
$440$	−17.8064	−0.848888
$441$	−0.280996	−0.0133808
$442$	3.52543	0.167687
$443$	17.4572	0.829418	0.414709	−	0.909954i	$-0.363883\pi$
$443$	17.4572	0.829418	0.414709	+	0.909954i	$0.363883\pi$
$444$	9.13828	0.433683
$445$	−42.4844	−2.01395
$446$	6.34122	0.300265
$447$	9.28592	0.439209
$448$	−2.59210	−0.122465
$449$	9.20342	0.434336	0.217168	−	0.976134i	$-0.430318\pi$
$449$	9.20342	0.434336	0.217168	+	0.976134i	$0.430318\pi$
$450$	−7.42864	−0.350189
$451$	10.5906	0.498691
$452$	−14.6494	−0.689050
$453$	22.7812	1.07036
$454$	18.7511	0.880034
$455$	−32.2163	−1.51032
$456$	−1.14764	−0.0537433
$457$	31.8020	1.48763	0.743817	−	0.668383i	$-0.233013\pi$
$457$	31.8020	1.48763	0.743817	+	0.668383i	$0.233013\pi$
$458$	0.357041	0.0166834
$459$	−1.00000	−0.0466760
$460$	18.3827	0.857098
$461$	−0.306662	−0.0142827	−0.00714134	−	0.999975i	$-0.502273\pi$
$461$	−0.306662	−0.0142827	−0.00714134	+	0.999975i	$0.502273\pi$
$462$	13.0923	0.609111
$463$	−12.6178	−0.586397	−0.293199	−	0.956052i	$-0.594720\pi$
$463$	−12.6178	−0.586397	−0.293199	+	0.956052i	$0.594720\pi$
$464$	−2.90321	−0.134778
$465$	−7.05086	−0.326976
$466$	−8.75557	−0.405594
$467$	11.3176	0.523714	0.261857	−	0.965107i	$-0.415665\pi$
$467$	11.3176	0.523714	0.261857	+	0.965107i	$0.415665\pi$
$468$	3.52543	0.162963
$469$	13.2114	0.610046
$470$	3.86665	0.178355
$471$	−1.54125	−0.0710170
$472$	1.00000	0.0460287
$473$	32.4701	1.49298
$474$	−7.46520	−0.342888
$475$	8.52543	0.391173
$476$	2.59210	0.118809
$477$	−9.44938	−0.432658
$478$	−8.14764	−0.372665
$479$	−3.84791	−0.175816	−0.0879078	−	0.996129i	$-0.528018\pi$
$479$	−3.84791	−0.175816	−0.0879078	+	0.996129i	$0.528018\pi$
$480$	−3.52543	−0.160913
$481$	32.2163	1.46894
$482$	−18.6178	−0.848016
$483$	−13.5161	−0.615002
$484$	14.5111	0.659597
$485$	−31.7288	−1.44073
$486$	−1.00000	−0.0453609
$487$	26.5274	1.20207	0.601036	−	0.799222i	$-0.294755\pi$
$487$	26.5274	1.20207	0.601036	+	0.799222i	$0.294755\pi$
$488$	2.94914	0.133502
$489$	−8.38271	−0.379079
$490$	0.990632	0.0447522
$491$	7.85236	0.354372	0.177186	−	0.984177i	$-0.443301\pi$
$491$	7.85236	0.354372	0.177186	+	0.984177i	$0.443301\pi$
$492$	2.09679	0.0945305
$493$	2.90321	0.130754
$494$	−4.04593	−0.182035
$495$	17.8064	0.800339
$496$	−2.00000	−0.0898027
$497$	18.5032	0.829980
$498$	−8.46520	−0.379335
$499$	−18.2208	−0.815674	−0.407837	−	0.913055i	$-0.633717\pi$
$499$	−18.2208	−0.815674	−0.407837	+	0.913055i	$0.633717\pi$
$500$	8.56199	0.382904
$501$	22.2766	0.995243
$502$	−22.1289	−0.987661
$503$	−6.78123	−0.302360	−0.151180	−	0.988506i	$-0.548307\pi$
$503$	−6.78123	−0.302360	−0.151180	+	0.988506i	$0.548307\pi$
$504$	2.59210	0.115461
$505$	23.6543	1.05260
$506$	−26.3368	−1.17081
$507$	−0.571361	−0.0253750
$508$	−13.5669	−0.601935
$509$	−6.42864	−0.284944	−0.142472	−	0.989799i	$-0.545505\pi$
$509$	−6.42864	−0.284944	−0.142472	+	0.989799i	$0.545505\pi$
$510$	3.52543	0.156109
$511$	−20.4859	−0.906245
$512$	−1.00000	−0.0441942
$513$	1.14764	0.0506697
$514$	−15.5067	−0.683971
$515$	12.3729	0.545213
$516$	6.42864	0.283005
$517$	−5.53972	−0.243637
$518$	23.6874	1.04076
$519$	10.4429	0.458394
$520$	−12.4286	−0.545032
$521$	−22.1240	−0.969269	−0.484635	−	0.874717i	$-0.661047\pi$
$521$	−22.1240	−0.969269	−0.484635	+	0.874717i	$0.661047\pi$
$522$	2.90321	0.127070
$523$	19.9496	0.872336	0.436168	−	0.899865i	$-0.356335\pi$
$523$	19.9496	0.872336	0.436168	+	0.899865i	$0.356335\pi$
$524$	17.2716	0.754515
$525$	−19.2558	−0.840392
$526$	−28.5462	−1.24467
$527$	2.00000	0.0871214
$528$	5.05086	0.219810
$529$	4.18913	0.182136
$530$	33.3131	1.44703
$531$	−1.00000	−0.0433963
$532$	−2.97481	−0.128974
$533$	7.39207	0.320186
$534$	12.0509	0.521492
$535$	−15.9541	−0.689754
$536$	5.09679	0.220148
$537$	−20.1526	−0.869647
$538$	−10.6064	−0.457274
$539$	−1.41927	−0.0611324
$540$	3.52543	0.151710
$541$	24.4701	1.05205	0.526026	−	0.850468i	$-0.323681\pi$
$541$	24.4701	1.05205	0.526026	+	0.850468i	$0.323681\pi$
$542$	−8.99063	−0.386181
$543$	6.57628	0.282215
$544$	1.00000	0.0428746
$545$	−60.9403	−2.61039
$546$	9.13828	0.391082
$547$	30.9273	1.32236	0.661179	−	0.750228i	$-0.270056\pi$
$547$	30.9273	1.32236	0.661179	+	0.750228i	$0.270056\pi$
$548$	3.91258	0.167137
$549$	−2.94914	−0.125866
$550$	−37.5210	−1.59990
$551$	−3.33185	−0.141942
$552$	−5.21432	−0.221936
$553$	−19.3506	−0.822871
$554$	25.7862	1.09555
$555$	32.2163	1.36751
$556$	−0.341219	−0.0144709
$557$	−10.1476	−0.429969	−0.214985	−	0.976617i	$-0.568970\pi$
$557$	−10.1476	−0.429969	−0.214985	+	0.976617i	$0.568970\pi$
$558$	2.00000	0.0846668
$559$	22.6637	0.958572
$560$	−9.13828	−0.386163
$561$	−5.05086	−0.213247
$562$	10.2208	0.431137
$563$	0.764937	0.0322382	0.0161191	−	0.999870i	$-0.494869\pi$
$563$	0.764937	0.0322382	0.0161191	+	0.999870i	$0.494869\pi$
$564$	−1.09679	−0.0461831
$565$	−51.6454	−2.17274
$566$	−0.00936793	−0.000393764 0
$567$	−2.59210	−0.108858
$568$	7.13828	0.299515
$569$	35.4286	1.48525	0.742623	−	0.669710i	$-0.233582\pi$
$569$	35.4286	1.48525	0.742623	+	0.669710i	$0.233582\pi$
$570$	−4.04593	−0.169465
$571$	−34.9670	−1.46332	−0.731661	−	0.681669i	$-0.761255\pi$
$571$	−34.9670	−1.46332	−0.731661	+	0.681669i	$0.761255\pi$
$572$	17.8064	0.744524
$573$	−0.769859	−0.0321613
$574$	5.43509	0.226856
$575$	38.7353	1.61537
$576$	1.00000	0.0416667
$577$	12.7841	0.532211	0.266106	−	0.963944i	$-0.414263\pi$
$577$	12.7841	0.532211	0.266106	+	0.963944i	$0.414263\pi$
$578$	−1.00000	−0.0415945
$579$	−0.861725	−0.0358121
$580$	−10.2351	−0.424988
$581$	−21.9427	−0.910336
$582$	9.00000	0.373062
$583$	−47.7275	−1.97667
$584$	−7.90321	−0.327037
$585$	12.4286	0.513861
$586$	6.66815	0.275459
$587$	22.0651	0.910726	0.455363	−	0.890306i	$-0.349509\pi$
$587$	22.0651	0.910726	0.455363	+	0.890306i	$0.349509\pi$
$588$	−0.280996	−0.0115881
$589$	−2.29529	−0.0945756
$590$	3.52543	0.145140
$591$	−6.81579	−0.280364
$592$	9.13828	0.375581
$593$	32.6321	1.34004	0.670019	−	0.742344i	$-0.266286\pi$
$593$	32.6321	1.34004	0.670019	+	0.742344i	$0.266286\pi$
$594$	−5.05086	−0.207239
$595$	9.13828	0.374633
$596$	9.28592	0.380366
$597$	−8.97481	−0.367315
$598$	−18.3827	−0.751725
$599$	−4.10324	−0.167654	−0.0838270	−	0.996480i	$-0.526714\pi$
$599$	−4.10324	−0.167654	−0.0838270	+	0.996480i	$0.526714\pi$
$600$	−7.42864	−0.303273
$601$	−7.23506	−0.295124	−0.147562	−	0.989053i	$-0.547143\pi$
$601$	−7.23506	−0.295124	−0.147562	+	0.989053i	$0.547143\pi$
$602$	16.6637	0.679162
$603$	−5.09679	−0.207557
$604$	22.7812	0.926955
$605$	51.1580	2.07987
$606$	−6.70964	−0.272560
$607$	−40.3022	−1.63582	−0.817908	−	0.575349i	$-0.804866\pi$
$607$	−40.3022	−1.63582	−0.817908	+	0.575349i	$0.804866\pi$
$608$	−1.14764	−0.0465431
$609$	7.52543	0.304946
$610$	10.3970	0.420962
$611$	−3.86665	−0.156428
$612$	−1.00000	−0.0404226
$613$	40.7812	1.64714	0.823569	−	0.567216i	$-0.191979\pi$
$613$	40.7812	1.64714	0.823569	+	0.567216i	$0.191979\pi$
$614$	12.7649	0.515151
$615$	7.39207	0.298077
$616$	13.0923	0.527506
$617$	16.7190	0.673082	0.336541	−	0.941669i	$-0.390743\pi$
$617$	16.7190	0.673082	0.336541	+	0.941669i	$0.390743\pi$
$618$	−3.50961	−0.141177
$619$	5.38223	0.216330	0.108165	−	0.994133i	$-0.465503\pi$
$619$	5.38223	0.216330	0.108165	+	0.994133i	$0.465503\pi$
$620$	−7.05086	−0.283169
$621$	5.21432	0.209243
$622$	4.76986	0.191254
$623$	31.2371	1.25149
$624$	3.52543	0.141130
$625$	−6.95851	−0.278341
$626$	−20.2351	−0.808756
$627$	5.79658	0.231493
$628$	−1.54125	−0.0615025
$629$	−9.13828	−0.364367
$630$	9.13828	0.364078
$631$	−21.9813	−0.875060	−0.437530	−	0.899204i	$-0.644147\pi$
$631$	−21.9813	−0.875060	−0.437530	+	0.899204i	$0.644147\pi$
$632$	−7.46520	−0.296950
$633$	−9.96836	−0.396207
$634$	21.3778	0.849020
$635$	−47.8292	−1.89804
$636$	−9.44938	−0.374692
$637$	−0.990632	−0.0392503
$638$	14.6637	0.580542
$639$	−7.13828	−0.282386
$640$	−3.52543	−0.139355
$641$	−6.06515	−0.239559	−0.119779	−	0.992801i	$-0.538219\pi$
$641$	−6.06515	−0.239559	−0.119779	+	0.992801i	$0.538219\pi$
$642$	4.52543	0.178604
$643$	16.1191	0.635674	0.317837	−	0.948145i	$-0.397044\pi$
$643$	16.1191	0.635674	0.317837	+	0.948145i	$0.397044\pi$
$644$	−13.5161	−0.532607
$645$	22.6637	0.892382
$646$	1.14764	0.0451534
$647$	38.0716	1.49675	0.748374	−	0.663276i	$-0.230835\pi$
$647$	38.0716	1.49675	0.748374	+	0.663276i	$0.230835\pi$
$648$	−1.00000	−0.0392837
$649$	−5.05086	−0.198263
$650$	−26.1891	−1.02722
$651$	5.18421	0.203185
$652$	−8.38271	−0.328292
$653$	38.6450	1.51229	0.756147	−	0.654402i	$-0.227079\pi$
$653$	38.6450	1.51229	0.756147	+	0.654402i	$0.227079\pi$
$654$	17.2859	0.675933
$655$	60.8899	2.37916
$656$	2.09679	0.0818658
$657$	7.90321	0.308334
$658$	−2.84299	−0.110831
$659$	17.7511	0.691486	0.345743	−	0.938329i	$-0.387627\pi$
$659$	17.7511	0.691486	0.345743	+	0.938329i	$0.387627\pi$
$660$	17.8064	0.693114
$661$	36.5620	1.42210	0.711048	−	0.703143i	$-0.248221\pi$
$661$	36.5620	1.42210	0.711048	+	0.703143i	$0.248221\pi$
$662$	−4.63158	−0.180012
$663$	−3.52543	−0.136916
$664$	−8.46520	−0.328514
$665$	−10.4875	−0.406687
$666$	−9.13828	−0.354101
$667$	−15.1383	−0.586156
$668$	22.2766	0.861906
$669$	−6.34122	−0.245166
$670$	17.9684	0.694178
$671$	−14.8957	−0.575042
$672$	2.59210	0.0999926
$673$	−33.7239	−1.29996	−0.649981	−	0.759951i	$-0.725223\pi$
$673$	−33.7239	−1.29996	−0.649981	+	0.759951i	$0.725223\pi$
$674$	4.33185	0.166857
$675$	7.42864	0.285928
$676$	−0.571361	−0.0219754
$677$	48.9545	1.88148	0.940738	−	0.339134i	$-0.110134\pi$
$677$	48.9545	1.88148	0.940738	+	0.339134i	$0.110134\pi$
$678$	14.6494	0.562607
$679$	23.3289	0.895282
$680$	3.52543	0.135194
$681$	−18.7511	−0.718545
$682$	10.1017	0.386814
$683$	35.8751	1.37272	0.686361	−	0.727261i	$-0.259207\pi$
$683$	35.8751	1.37272	0.686361	+	0.727261i	$0.259207\pi$
$684$	1.14764	0.0438812
$685$	13.7935	0.527023
$686$	−18.8731	−0.720578
$687$	−0.357041	−0.0136220
$688$	6.42864	0.245090
$689$	−33.3131	−1.26913
$690$	−18.3827	−0.699818
$691$	45.0469	1.71366	0.856832	−	0.515595i	$-0.172429\pi$
$691$	45.0469	1.71366	0.856832	+	0.515595i	$0.172429\pi$
$692$	10.4429	0.396981
$693$	−13.0923	−0.497337
$694$	9.16992	0.348085
$695$	−1.20294	−0.0456303
$696$	2.90321	0.110046
$697$	−2.09679	−0.0794215
$698$	−14.3941	−0.544824
$699$	8.75557	0.331166
$700$	−19.2558	−0.727801
$701$	−20.6450	−0.779750	−0.389875	−	0.920868i	$-0.627482\pi$
$701$	−20.6450	−0.779750	−0.389875	+	0.920868i	$0.627482\pi$
$702$	−3.52543	−0.133059
$703$	10.4875	0.395543
$704$	5.05086	0.190361
$705$	−3.86665	−0.145626
$706$	23.6780	0.891133
$707$	−17.3921	−0.654096
$708$	−1.00000	−0.0375823
$709$	−27.9956	−1.05140	−0.525698	−	0.850672i	$-0.676196\pi$
$709$	−27.9956	−1.05140	−0.525698	+	0.850672i	$0.676196\pi$
$710$	25.1655	0.944443
$711$	7.46520	0.279967
$712$	12.0509	0.451625
$713$	−10.4286	−0.390556
$714$	−2.59210	−0.0970071
$715$	62.7753	2.34766
$716$	−20.1526	−0.753137
$717$	8.14764	0.304279
$718$	1.58274	0.0590672
$719$	24.6178	0.918088	0.459044	−	0.888414i	$-0.348192\pi$
$719$	24.6178	0.918088	0.459044	+	0.888414i	$0.348192\pi$
$720$	3.52543	0.131385
$721$	−9.09726	−0.338800
$722$	17.6829	0.658090
$723$	18.6178	0.692402
$724$	6.57628	0.244406
$725$	−21.5669	−0.800975
$726$	−14.5111	−0.538559
$727$	−44.8430	−1.66313	−0.831567	−	0.555424i	$-0.812556\pi$
$727$	−44.8430	−1.66313	−0.831567	+	0.555424i	$0.812556\pi$
$728$	9.13828	0.338687
$729$	1.00000	0.0370370
$730$	−27.8622	−1.03123
$731$	−6.42864	−0.237772
$732$	−2.94914	−0.109004
$733$	31.7605	1.17310	0.586550	−	0.809913i	$-0.300486\pi$
$733$	31.7605	1.17310	0.586550	+	0.809913i	$0.300486\pi$
$734$	9.28592	0.342750
$735$	−0.990632	−0.0365400
$736$	−5.21432	−0.192202
$737$	−25.7431	−0.948261
$738$	−2.09679	−0.0771838
$739$	−24.0415	−0.884380	−0.442190	−	0.896921i	$-0.645798\pi$
$739$	−24.0415	−0.884380	−0.442190	+	0.896921i	$0.645798\pi$
$740$	32.2163	1.18430
$741$	4.04593	0.148631
$742$	−24.4938	−0.899195
$743$	51.9081	1.90432	0.952162	−	0.305593i	$-0.0988545\pi$
$743$	51.9081	1.90432	0.952162	+	0.305593i	$0.0988545\pi$
$744$	2.00000	0.0733236
$745$	32.7368	1.19938
$746$	26.8113	0.981633
$747$	8.46520	0.309726
$748$	−5.05086	−0.184678
$749$	11.7304	0.428619
$750$	−8.56199	−0.312640
$751$	−11.1383	−0.406441	−0.203221	−	0.979133i	$-0.565141\pi$
$751$	−11.1383	−0.406441	−0.203221	+	0.979133i	$0.565141\pi$
$752$	−1.09679	−0.0399957
$753$	22.1289	0.806422
$754$	10.2351	0.372739
$755$	80.3136	2.92291
$756$	−2.59210	−0.0942739
$757$	27.4193	0.996570	0.498285	−	0.867013i	$-0.333963\pi$
$757$	27.4193	0.996570	0.498285	+	0.867013i	$0.333963\pi$
$758$	8.32693	0.302448
$759$	26.3368	0.955964
$760$	−4.04593	−0.146761
$761$	−49.8992	−1.80885	−0.904423	−	0.426637i	$-0.859698\pi$
$761$	−49.8992	−1.80885	−0.904423	+	0.426637i	$0.859698\pi$
$762$	13.5669	0.491477
$763$	44.8069	1.62212
$764$	−0.769859	−0.0278525
$765$	−3.52543	−0.127462
$766$	−3.68445	−0.133124
$767$	−3.52543	−0.127296
$768$	1.00000	0.0360844
$769$	0.414349	0.0149418	0.00747091	−	0.999972i	$-0.497622\pi$
$769$	0.414349	0.0149418	0.00747091	+	0.999972i	$0.497622\pi$
$770$	46.1561	1.66335
$771$	15.5067	0.558460
$772$	−0.861725	−0.0310142
$773$	30.7797	1.10707	0.553534	−	0.832826i	$-0.313279\pi$
$773$	30.7797	1.10707	0.553534	+	0.832826i	$0.313279\pi$
$774$	−6.42864	−0.231073
$775$	−14.8573	−0.533689
$776$	9.00000	0.323081
$777$	−23.6874	−0.849779
$778$	37.9768	1.36153
$779$	2.40636	0.0862170
$780$	12.4286	0.445017
$781$	−36.0544	−1.29013
$782$	5.21432	0.186464
$783$	−2.90321	−0.103752
$784$	−0.280996	−0.0100356
$785$	−5.43356	−0.193932
$786$	−17.2716	−0.616059
$787$	6.01874	0.214545	0.107272	−	0.994230i	$-0.465788\pi$
$787$	6.01874	0.214545	0.107272	+	0.994230i	$0.465788\pi$
$788$	−6.81579	−0.242803
$789$	28.5462	1.01627
$790$	−26.3180	−0.936354
$791$	37.9728	1.35016
$792$	−5.05086	−0.179474
$793$	−10.3970	−0.369208
$794$	−4.74128	−0.168262
$795$	−33.3131	−1.18149
$796$	−8.97481	−0.318104
$797$	20.0558	0.710412	0.355206	−	0.934788i	$-0.384411\pi$
$797$	20.0558	0.710412	0.355206	+	0.934788i	$0.384411\pi$
$798$	2.97481	0.105307
$799$	1.09679	0.0388016
$800$	−7.42864	−0.262642
$801$	−12.0509	−0.425796
$802$	11.4652	0.404850
$803$	39.9180	1.40867
$804$	−5.09679	−0.179750
$805$	−47.6499	−1.67944
$806$	7.05086	0.248356
$807$	10.6064	0.373363
$808$	−6.70964	−0.236044
$809$	0.189130	0.00664947	0.00332474	−	0.999994i	$-0.498942\pi$
$809$	0.189130	0.00664947	0.00332474	+	0.999994i	$0.498942\pi$
$810$	−3.52543	−0.123871
$811$	−29.8800	−1.04923	−0.524615	−	0.851340i	$-0.675791\pi$
$811$	−29.8800	−1.04923	−0.524615	+	0.851340i	$0.675791\pi$
$812$	7.52543	0.264091
$813$	8.99063	0.315315
$814$	−46.1561	−1.61777
$815$	−29.5526	−1.03518
$816$	−1.00000	−0.0350070
$817$	7.37778	0.258116
$818$	38.4701	1.34508
$819$	−9.13828	−0.319317
$820$	7.39207	0.258142
$821$	2.75710	0.0962235	0.0481117	−	0.998842i	$-0.484680\pi$
$821$	2.75710	0.0962235	0.0481117	+	0.998842i	$0.484680\pi$
$822$	−3.91258	−0.136467
$823$	12.2065	0.425491	0.212746	−	0.977108i	$-0.431759\pi$
$823$	12.2065	0.425491	0.212746	+	0.977108i	$0.431759\pi$
$824$	−3.50961	−0.122263
$825$	37.5210	1.30631
$826$	−2.59210	−0.0901908
$827$	34.8064	1.21034	0.605169	−	0.796097i	$-0.293106\pi$
$827$	34.8064	1.21034	0.605169	+	0.796097i	$0.293106\pi$
$828$	5.21432	0.181210
$829$	14.1476	0.491368	0.245684	−	0.969350i	$-0.420987\pi$
$829$	14.1476	0.491368	0.245684	+	0.969350i	$0.420987\pi$
$830$	−29.8435	−1.03588
$831$	−25.7862	−0.894512
$832$	3.52543	0.122222
$833$	0.280996	0.00973594
$834$	0.341219	0.0118155
$835$	78.5344	2.71779
$836$	5.79658	0.200479
$837$	−2.00000	−0.0691301
$838$	−16.7382	−0.578212
$839$	−55.6972	−1.92288	−0.961441	−	0.275013i	$-0.911318\pi$
$839$	−55.6972	−1.92288	−0.961441	+	0.275013i	$0.911318\pi$
$840$	9.13828	0.315300
$841$	−20.5714	−0.709357
$842$	7.58274	0.261318
$843$	−10.2208	−0.352022
$844$	−9.96836	−0.343125
$845$	−2.01429	−0.0692937
$846$	1.09679	0.0377084
$847$	−37.6144	−1.29245
$848$	−9.44938	−0.324493
$849$	0.00936793	0.000321507 0
$850$	7.42864	0.254800
$851$	47.6499	1.63342
$852$	−7.13828	−0.244553
$853$	−51.8533	−1.77542	−0.887712	−	0.460400i	$-0.847706\pi$
$853$	−51.8533	−1.77542	−0.887712	+	0.460400i	$0.847706\pi$
$854$	−7.64449	−0.261589
$855$	4.04593	0.138368
$856$	4.52543	0.154676
$857$	10.0874	0.344580	0.172290	−	0.985046i	$-0.444883\pi$
$857$	10.0874	0.344580	0.172290	+	0.985046i	$0.444883\pi$
$858$	−17.8064	−0.607901
$859$	−18.5290	−0.632200	−0.316100	−	0.948726i	$-0.602374\pi$
$859$	−18.5290	−0.632200	−0.316100	+	0.948726i	$0.602374\pi$
$860$	22.6637	0.772826
$861$	−5.43509	−0.185227
$862$	−16.3240	−0.555998
$863$	2.08742	0.0710566	0.0355283	−	0.999369i	$-0.488689\pi$
$863$	2.08742	0.0710566	0.0355283	+	0.999369i	$0.488689\pi$
$864$	−1.00000	−0.0340207
$865$	36.8158	1.25177
$866$	23.4701	0.797547
$867$	1.00000	0.0339618
$868$	5.18421	0.175963
$869$	37.7057	1.27908
$870$	10.2351	0.347001
$871$	−17.9684	−0.608835
$872$	17.2859	0.585375
$873$	−9.00000	−0.304604
$874$	−5.98418	−0.202418
$875$	−22.1936	−0.750280
$876$	7.90321	0.267025
$877$	−45.2099	−1.52663	−0.763314	−	0.646027i	$-0.776429\pi$
$877$	−45.2099	−1.52663	−0.763314	+	0.646027i	$0.776429\pi$
$878$	6.60793	0.223007
$879$	−6.66815	−0.224911
$880$	17.8064	0.600254
$881$	−55.8292	−1.88093	−0.940466	−	0.339887i	$-0.889611\pi$
$881$	−55.8292	−1.88093	−0.940466	+	0.339887i	$0.889611\pi$
$882$	0.280996	0.00946164
$883$	25.8069	0.868471	0.434236	−	0.900799i	$-0.357019\pi$
$883$	25.8069	0.868471	0.434236	+	0.900799i	$0.357019\pi$
$884$	−3.52543	−0.118573
$885$	−3.52543	−0.118506
$886$	−17.4572	−0.586487
$887$	3.67905	0.123530	0.0617652	−	0.998091i	$-0.480327\pi$
$887$	3.67905	0.123530	0.0617652	+	0.998091i	$0.480327\pi$
$888$	−9.13828	−0.306660
$889$	35.1669	1.17946
$890$	42.4844	1.42408
$891$	5.05086	0.169210
$892$	−6.34122	−0.212320
$893$	−1.25872	−0.0421215
$894$	−9.28592	−0.310568
$895$	−71.0464	−2.37482
$896$	2.59210	0.0865961
$897$	18.3827	0.613781
$898$	−9.20342	−0.307122
$899$	5.80642	0.193655
$900$	7.42864	0.247621
$901$	9.44938	0.314805
$902$	−10.5906	−0.352628
$903$	−16.6637	−0.554533
$904$	14.6494	0.487232
$905$	23.1842	0.770669
$906$	−22.7812	−0.756856
$907$	6.44738	0.214082	0.107041	−	0.994255i	$-0.465862\pi$
$907$	6.44738	0.214082	0.107041	+	0.994255i	$0.465862\pi$
$908$	−18.7511	−0.622278
$909$	6.70964	0.222545
$910$	32.2163	1.06796
$911$	−51.2529	−1.69808	−0.849042	−	0.528325i	$-0.822820\pi$
$911$	−51.2529	−1.69808	−0.849042	+	0.528325i	$0.822820\pi$
$912$	1.14764	0.0380023
$913$	42.7565	1.41503
$914$	−31.8020	−1.05192
$915$	−10.3970	−0.343714
$916$	−0.357041	−0.0117970
$917$	−44.7699	−1.47843
$918$	1.00000	0.0330049
$919$	−54.5072	−1.79803	−0.899013	−	0.437922i	$-0.855714\pi$
$919$	−54.5072	−1.79803	−0.899013	+	0.437922i	$0.855714\pi$
$920$	−18.3827	−0.606060
$921$	−12.7649	−0.420619
$922$	0.306662	0.0100994
$923$	−25.1655	−0.828332
$924$	−13.0923	−0.430706
$925$	67.8850	2.23204
$926$	12.6178	0.414646
$927$	3.50961	0.115271
$928$	2.90321	0.0953026
$929$	−26.6035	−0.872832	−0.436416	−	0.899745i	$-0.643752\pi$
$929$	−26.6035	−0.872832	−0.436416	+	0.899745i	$0.643752\pi$
$930$	7.05086	0.231207
$931$	−0.322483	−0.0105690
$932$	8.75557	0.286798
$933$	−4.76986	−0.156158
$934$	−11.3176	−0.370322
$935$	−17.8064	−0.582332
$936$	−3.52543	−0.115232
$937$	−51.1753	−1.67182	−0.835912	−	0.548863i	$-0.815061\pi$
$937$	−51.1753	−1.67182	−0.835912	+	0.548863i	$0.815061\pi$
$938$	−13.2114	−0.431368
$939$	20.2351	0.660346
$940$	−3.86665	−0.126116
$941$	−36.6064	−1.19333	−0.596667	−	0.802489i	$-0.703509\pi$
$941$	−36.6064	−1.19333	−0.596667	+	0.802489i	$0.703509\pi$
$942$	1.54125	0.0502166
$943$	10.9333	0.356038
$944$	−1.00000	−0.0325472
$945$	−9.13828	−0.297268
$946$	−32.4701	−1.05569
$947$	−1.11906	−0.0363647	−0.0181823	−	0.999835i	$-0.505788\pi$
$947$	−1.11906	−0.0363647	−0.0181823	+	0.999835i	$0.505788\pi$
$948$	7.46520	0.242459
$949$	27.8622	0.904445
$950$	−8.52543	−0.276601
$951$	−21.3778	−0.693222
$952$	−2.59210	−0.0840106
$953$	17.8666	0.578757	0.289379	−	0.957215i	$-0.406551\pi$
$953$	17.8666	0.578757	0.289379	+	0.957215i	$0.406551\pi$
$954$	9.44938	0.305935
$955$	−2.71408	−0.0878256
$956$	8.14764	0.263514
$957$	−14.6637	−0.474010
$958$	3.84791	0.124320
$959$	−10.1418	−0.327496
$960$	3.52543	0.113783
$961$	−27.0000	−0.870968
$962$	−32.2163	−1.03870
$963$	−4.52543	−0.145830
$964$	18.6178	0.599638
$965$	−3.03795	−0.0977950
$966$	13.5161	0.434872
$967$	31.6572	1.01803	0.509014	−	0.860758i	$-0.330010\pi$
$967$	31.6572	1.01803	0.509014	+	0.860758i	$0.330010\pi$
$968$	−14.5111	−0.466406
$969$	−1.14764	−0.0368676
$970$	31.7288	1.01875
$971$	−43.4608	−1.39472	−0.697361	−	0.716720i	$-0.745643\pi$
$971$	−43.4608	−1.39472	−0.697361	+	0.716720i	$0.745643\pi$
$972$	1.00000	0.0320750
$973$	0.884476	0.0283550
$974$	−26.5274	−0.849994
$975$	26.1891	0.838723
$976$	−2.94914	−0.0943998
$977$	−53.9407	−1.72572	−0.862858	−	0.505446i	$-0.831328\pi$
$977$	−53.9407	−1.72572	−0.862858	+	0.505446i	$0.831328\pi$
$978$	8.38271	0.268049
$979$	−60.8671	−1.94532
$980$	−0.990632	−0.0316446
$981$	−17.2859	−0.551897
$982$	−7.85236	−0.250579
$983$	−19.6287	−0.626057	−0.313029	−	0.949744i	$-0.601344\pi$
$983$	−19.6287	−0.626057	−0.313029	+	0.949744i	$0.601344\pi$
$984$	−2.09679	−0.0668432
$985$	−24.0286	−0.765614
$986$	−2.90321	−0.0924571
$987$	2.84299	0.0904933
$988$	4.04593	0.128718
$989$	33.5210	1.06591
$990$	−17.8064	−0.565925
$991$	22.0874	0.701630	0.350815	−	0.936445i	$-0.385905\pi$
$991$	22.0874	0.701630	0.350815	+	0.936445i	$0.385905\pi$
$992$	2.00000	0.0635001
$993$	4.63158	0.146979
$994$	−18.5032	−0.586884
$995$	−31.6400	−1.00306
$996$	8.46520	0.268230
$997$	−30.4730	−0.965091	−0.482545	−	0.875871i	$-0.660288\pi$
$997$	−30.4730	−0.965091	−0.482545	+	0.875871i	$0.660288\pi$
$998$	18.2208	0.576768
$999$	9.13828	0.289122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.m.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.m.1.3	✓	3	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.52543 q^{5} -1.00000 q^{6} -2.59210 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.52543 q^{5} -1.00000 q^{6} -2.59210 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.52543 q^{10} +5.05086 q^{11} +1.00000 q^{12} +3.52543 q^{13} +2.59210 q^{14} +3.52543 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +1.14764 q^{19} +3.52543 q^{20} -2.59210 q^{21} -5.05086 q^{22} +5.21432 q^{23} -1.00000 q^{24} +7.42864 q^{25} -3.52543 q^{26} +1.00000 q^{27} -2.59210 q^{28} -2.90321 q^{29} -3.52543 q^{30} -2.00000 q^{31} -1.00000 q^{32} +5.05086 q^{33} +1.00000 q^{34} -9.13828 q^{35} +1.00000 q^{36} +9.13828 q^{37} -1.14764 q^{38} +3.52543 q^{39} -3.52543 q^{40} +2.09679 q^{41} +2.59210 q^{42} +6.42864 q^{43} +5.05086 q^{44} +3.52543 q^{45} -5.21432 q^{46} -1.09679 q^{47} +1.00000 q^{48} -0.280996 q^{49} -7.42864 q^{50} -1.00000 q^{51} +3.52543 q^{52} -9.44938 q^{53} -1.00000 q^{54} +17.8064 q^{55} +2.59210 q^{56} +1.14764 q^{57} +2.90321 q^{58} -1.00000 q^{59} +3.52543 q^{60} -2.94914 q^{61} +2.00000 q^{62} -2.59210 q^{63} +1.00000 q^{64} +12.4286 q^{65} -5.05086 q^{66} -5.09679 q^{67} -1.00000 q^{68} +5.21432 q^{69} +9.13828 q^{70} -7.13828 q^{71} -1.00000 q^{72} +7.90321 q^{73} -9.13828 q^{74} +7.42864 q^{75} +1.14764 q^{76} -13.0923 q^{77} -3.52543 q^{78} +7.46520 q^{79} +3.52543 q^{80} +1.00000 q^{81} -2.09679 q^{82} +8.46520 q^{83} -2.59210 q^{84} -3.52543 q^{85} -6.42864 q^{86} -2.90321 q^{87} -5.05086 q^{88} -12.0509 q^{89} -3.52543 q^{90} -9.13828 q^{91} +5.21432 q^{92} -2.00000 q^{93} +1.09679 q^{94} +4.04593 q^{95} -1.00000 q^{96} -9.00000 q^{97} +0.280996 q^{98} +5.05086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 4 q^{5} - 3 q^{6} - q^{7} - 3 q^{8} + 3 q^{9} - 4 q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 4 q^{15} + 3 q^{16} - 3 q^{17} - 3 q^{18} - 3 q^{19} + 4 q^{20} - q^{21} - 2 q^{22} + 9 q^{23} - 3 q^{24} + 9 q^{25} - 4 q^{26} + 3 q^{27} - q^{28} - 2 q^{29} - 4 q^{30} - 6 q^{31} - 3 q^{32} + 2 q^{33} + 3 q^{34} + 6 q^{35} + 3 q^{36} - 6 q^{37} + 3 q^{38} + 4 q^{39} - 4 q^{40} + 13 q^{41} + q^{42} + 6 q^{43} + 2 q^{44} + 4 q^{45} - 9 q^{46} - 10 q^{47} + 3 q^{48} + 6 q^{49} - 9 q^{50} - 3 q^{51} + 4 q^{52} + 5 q^{53} - 3 q^{54} + 40 q^{55} + q^{56} - 3 q^{57} + 2 q^{58} - 3 q^{59} + 4 q^{60} - 22 q^{61} + 6 q^{62} - q^{63} + 3 q^{64} + 24 q^{65} - 2 q^{66} - 22 q^{67} - 3 q^{68} + 9 q^{69} - 6 q^{70} + 12 q^{71} - 3 q^{72} + 17 q^{73} + 6 q^{74} + 9 q^{75} - 3 q^{76} + 14 q^{77} - 4 q^{78} + 2 q^{79} + 4 q^{80} + 3 q^{81} - 13 q^{82} + 5 q^{83} - q^{84} - 4 q^{85} - 6 q^{86} - 2 q^{87} - 2 q^{88} - 23 q^{89} - 4 q^{90} + 6 q^{91} + 9 q^{92} - 6 q^{93} + 10 q^{94} + 32 q^{95} - 3 q^{96} - 27 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 + 4 * q^5 - 3 * q^6 - q^7 - 3 * q^8 + 3 * q^9 - 4 * q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 4 * q^15 + 3 * q^16 - 3 * q^17 - 3 * q^18 - 3 * q^19 + 4 * q^20 - q^21 - 2 * q^22 + 9 * q^23 - 3 * q^24 + 9 * q^25 - 4 * q^26 + 3 * q^27 - q^28 - 2 * q^29 - 4 * q^30 - 6 * q^31 - 3 * q^32 + 2 * q^33 + 3 * q^34 + 6 * q^35 + 3 * q^36 - 6 * q^37 + 3 * q^38 + 4 * q^39 - 4 * q^40 + 13 * q^41 + q^42 + 6 * q^43 + 2 * q^44 + 4 * q^45 - 9 * q^46 - 10 * q^47 + 3 * q^48 + 6 * q^49 - 9 * q^50 - 3 * q^51 + 4 * q^52 + 5 * q^53 - 3 * q^54 + 40 * q^55 + q^56 - 3 * q^57 + 2 * q^58 - 3 * q^59 + 4 * q^60 - 22 * q^61 + 6 * q^62 - q^63 + 3 * q^64 + 24 * q^65 - 2 * q^66 - 22 * q^67 - 3 * q^68 + 9 * q^69 - 6 * q^70 + 12 * q^71 - 3 * q^72 + 17 * q^73 + 6 * q^74 + 9 * q^75 - 3 * q^76 + 14 * q^77 - 4 * q^78 + 2 * q^79 + 4 * q^80 + 3 * q^81 - 13 * q^82 + 5 * q^83 - q^84 - 4 * q^85 - 6 * q^86 - 2 * q^87 - 2 * q^88 - 23 * q^89 - 4 * q^90 + 6 * q^91 + 9 * q^92 - 6 * q^93 + 10 * q^94 + 32 * q^95 - 3 * q^96 - 27 * q^97 - 6 * q^98 + 2 * q^99

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