LMFDB - Embedded newform 1014.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*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			1.1
Root			$1.80194$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15883 q^{5} +1.00000 q^{6} -4.69202 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15883 q^{5} +1.00000 q^{6} -4.69202 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.15883 q^{10} +0.137063 q^{11} -1.00000 q^{12} +4.69202 q^{14} +3.15883 q^{15} +1.00000 q^{16} -5.60388 q^{17} -1.00000 q^{18} -4.98792 q^{19} -3.15883 q^{20} +4.69202 q^{21} -0.137063 q^{22} -6.09783 q^{23} +1.00000 q^{24} +4.97823 q^{25} -1.00000 q^{27} -4.69202 q^{28} -0.850855 q^{29} -3.15883 q^{30} +6.23490 q^{31} -1.00000 q^{32} -0.137063 q^{33} +5.60388 q^{34} +14.8213 q^{35} +1.00000 q^{36} +11.7017 q^{37} +4.98792 q^{38} +3.15883 q^{40} -4.27413 q^{41} -4.69202 q^{42} -2.09783 q^{43} +0.137063 q^{44} -3.15883 q^{45} +6.09783 q^{46} +4.98792 q^{47} -1.00000 q^{48} +15.0151 q^{49} -4.97823 q^{50} +5.60388 q^{51} -1.82908 q^{53} +1.00000 q^{54} -0.432960 q^{55} +4.69202 q^{56} +4.98792 q^{57} +0.850855 q^{58} -5.89977 q^{59} +3.15883 q^{60} +4.39612 q^{61} -6.23490 q^{62} -4.69202 q^{63} +1.00000 q^{64} +0.137063 q^{66} -4.71379 q^{67} -5.60388 q^{68} +6.09783 q^{69} -14.8213 q^{70} -0.0978347 q^{71} -1.00000 q^{72} -2.32304 q^{73} -11.7017 q^{74} -4.97823 q^{75} -4.98792 q^{76} -0.643104 q^{77} +14.5157 q^{79} -3.15883 q^{80} +1.00000 q^{81} +4.27413 q^{82} -9.85623 q^{83} +4.69202 q^{84} +17.7017 q^{85} +2.09783 q^{86} +0.850855 q^{87} -0.137063 q^{88} +17.0858 q^{89} +3.15883 q^{90} -6.09783 q^{92} -6.23490 q^{93} -4.98792 q^{94} +15.7560 q^{95} +1.00000 q^{96} +2.12737 q^{97} -15.0151 q^{98} +0.137063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} - 9 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 - 9 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} - 9 q^{7} - 3 q^{8} + 3 q^{9} + q^{10} - 5 q^{11} - 3 q^{12} + 9 q^{14} + q^{15} + 3 q^{16} - 8 q^{17} - 3 q^{18} + 4 q^{19} - q^{20} + 9 q^{21} + 5 q^{22} + 3 q^{24} + 18 q^{25} - 3 q^{27} - 9 q^{28} + 11 q^{29} - q^{30} - 5 q^{31} - 3 q^{32} + 5 q^{33} + 8 q^{34} - 4 q^{35} + 3 q^{36} + 8 q^{37} - 4 q^{38} + q^{40} - 2 q^{41} - 9 q^{42} + 12 q^{43} - 5 q^{44} - q^{45} - 4 q^{47} - 3 q^{48} + 20 q^{49} - 18 q^{50} + 8 q^{51} + 5 q^{53} + 3 q^{54} + 18 q^{55} + 9 q^{56} - 4 q^{57} - 11 q^{58} + 5 q^{59} + q^{60} + 22 q^{61} + 5 q^{62} - 9 q^{63} + 3 q^{64} - 5 q^{66} - 6 q^{67} - 8 q^{68} + 4 q^{70} + 18 q^{71} - 3 q^{72} + 13 q^{73} - 8 q^{74} - 18 q^{75} + 4 q^{76} - 6 q^{77} + 31 q^{79} - q^{80} + 3 q^{81} + 2 q^{82} - 13 q^{83} + 9 q^{84} + 26 q^{85} - 12 q^{86} - 11 q^{87} + 5 q^{88} + 14 q^{89} + q^{90} + 5 q^{93} + 4 q^{94} + 8 q^{95} + 3 q^{96} + 23 q^{97} - 20 q^{98} - 5 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 - 9 * q^7 - 3 * q^8 + 3 * q^9 + q^10 - 5 * q^11 - 3 * q^12 + 9 * q^14 + q^15 + 3 * q^16 - 8 * q^17 - 3 * q^18 + 4 * q^19 - q^20 + 9 * q^21 + 5 * q^22 + 3 * q^24 + 18 * q^25 - 3 * q^27 - 9 * q^28 + 11 * q^29 - q^30 - 5 * q^31 - 3 * q^32 + 5 * q^33 + 8 * q^34 - 4 * q^35 + 3 * q^36 + 8 * q^37 - 4 * q^38 + q^40 - 2 * q^41 - 9 * q^42 + 12 * q^43 - 5 * q^44 - q^45 - 4 * q^47 - 3 * q^48 + 20 * q^49 - 18 * q^50 + 8 * q^51 + 5 * q^53 + 3 * q^54 + 18 * q^55 + 9 * q^56 - 4 * q^57 - 11 * q^58 + 5 * q^59 + q^60 + 22 * q^61 + 5 * q^62 - 9 * q^63 + 3 * q^64 - 5 * q^66 - 6 * q^67 - 8 * q^68 + 4 * q^70 + 18 * q^71 - 3 * q^72 + 13 * q^73 - 8 * q^74 - 18 * q^75 + 4 * q^76 - 6 * q^77 + 31 * q^79 - q^80 + 3 * q^81 + 2 * q^82 - 13 * q^83 + 9 * q^84 + 26 * q^85 - 12 * q^86 - 11 * q^87 + 5 * q^88 + 14 * q^89 + q^90 + 5 * q^93 + 4 * q^94 + 8 * q^95 + 3 * q^96 + 23 * q^97 - 20 * q^98 - 5 * 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
$5$	−3.15883	−1.41267	−0.706337	−	0.707876i	$-0.749654\pi$
$5$	−3.15883	−1.41267	−0.706337	+	0.707876i	$0.749654\pi$
$6$	1.00000	0.408248
$7$	−4.69202	−1.77342	−0.886709	−	0.462329i	$-0.847014\pi$
$7$	−4.69202	−1.77342	−0.886709	+	0.462329i	$0.847014\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.15883	0.998911
$11$	0.137063	0.0413262	0.0206631	−	0.999786i	$-0.493422\pi$
$11$	0.137063	0.0413262	0.0206631	+	0.999786i	$0.493422\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	4.69202	1.25400
$15$	3.15883	0.815607
$16$	1.00000	0.250000
$17$	−5.60388	−1.35914	−0.679570	−	0.733611i	$-0.737833\pi$
$17$	−5.60388	−1.35914	−0.679570	+	0.733611i	$0.737833\pi$
$18$	−1.00000	−0.235702
$19$	−4.98792	−1.14431	−0.572153	−	0.820147i	$-0.693892\pi$
$19$	−4.98792	−1.14431	−0.572153	+	0.820147i	$0.693892\pi$
$20$	−3.15883	−0.706337
$21$	4.69202	1.02388
$22$	−0.137063	−0.0292220
$23$	−6.09783	−1.27149	−0.635743	−	0.771901i	$-0.719306\pi$
$23$	−6.09783	−1.27149	−0.635743	+	0.771901i	$0.719306\pi$
$24$	1.00000	0.204124
$25$	4.97823	0.995646
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−4.69202	−0.886709
$29$	−0.850855	−0.158000	−0.0789999	−	0.996875i	$-0.525173\pi$
$29$	−0.850855	−0.158000	−0.0789999	+	0.996875i	$0.525173\pi$
$30$	−3.15883	−0.576721
$31$	6.23490	1.11982	0.559910	−	0.828553i	$-0.310836\pi$
$31$	6.23490	1.11982	0.559910	+	0.828553i	$0.310836\pi$
$32$	−1.00000	−0.176777
$33$	−0.137063	−0.0238597
$34$	5.60388	0.961057
$35$	14.8213	2.50526
$36$	1.00000	0.166667
$37$	11.7017	1.92375	0.961875	−	0.273491i	$-0.0881783\pi$
$37$	11.7017	1.92375	0.961875	+	0.273491i	$0.0881783\pi$
$38$	4.98792	0.809147
$39$	0	0
$40$	3.15883	0.499455
$41$	−4.27413	−0.667506	−0.333753	−	0.942660i	$-0.608315\pi$
$41$	−4.27413	−0.667506	−0.333753	+	0.942660i	$0.608315\pi$
$42$	−4.69202	−0.723995
$43$	−2.09783	−0.319917	−0.159958	−	0.987124i	$-0.551136\pi$
$43$	−2.09783	−0.319917	−0.159958	+	0.987124i	$0.551136\pi$
$44$	0.137063	0.0206631
$45$	−3.15883	−0.470891
$46$	6.09783	0.899077
$47$	4.98792	0.727563	0.363781	−	0.931484i	$-0.381486\pi$
$47$	4.98792	0.727563	0.363781	+	0.931484i	$0.381486\pi$
$48$	−1.00000	−0.144338
$49$	15.0151	2.14501
$50$	−4.97823	−0.704028
$51$	5.60388	0.784700
$52$	0	0
$53$	−1.82908	−0.251244	−0.125622	−	0.992078i	$-0.540093\pi$
$53$	−1.82908	−0.251244	−0.125622	+	0.992078i	$0.540093\pi$
$54$	1.00000	0.136083
$55$	−0.432960	−0.0583804
$56$	4.69202	0.626998
$57$	4.98792	0.660666
$58$	0.850855	0.111723
$59$	−5.89977	−0.768085	−0.384042	−	0.923315i	$-0.625468\pi$
$59$	−5.89977	−0.768085	−0.384042	+	0.923315i	$0.625468\pi$
$60$	3.15883	0.407804
$61$	4.39612	0.562866	0.281433	−	0.959581i	$-0.409190\pi$
$61$	4.39612	0.562866	0.281433	+	0.959581i	$0.409190\pi$
$62$	−6.23490	−0.791833
$63$	−4.69202	−0.591139
$64$	1.00000	0.125000
$65$	0	0
$66$	0.137063	0.0168713
$67$	−4.71379	−0.575881	−0.287941	−	0.957648i	$-0.592971\pi$
$67$	−4.71379	−0.575881	−0.287941	+	0.957648i	$0.592971\pi$
$68$	−5.60388	−0.679570
$69$	6.09783	0.734093
$70$	−14.8213	−1.77149
$71$	−0.0978347	−0.0116108	−0.00580542	−	0.999983i	$-0.501848\pi$
$71$	−0.0978347	−0.0116108	−0.00580542	+	0.999983i	$0.501848\pi$
$72$	−1.00000	−0.117851
$73$	−2.32304	−0.271892	−0.135946	−	0.990716i	$-0.543407\pi$
$73$	−2.32304	−0.271892	−0.135946	+	0.990716i	$0.543407\pi$
$74$	−11.7017	−1.36030
$75$	−4.97823	−0.574836
$76$	−4.98792	−0.572153
$77$	−0.643104	−0.0732885
$78$	0	0
$79$	14.5157	1.63315	0.816574	−	0.577241i	$-0.195871\pi$
$79$	14.5157	1.63315	0.816574	+	0.577241i	$0.195871\pi$
$80$	−3.15883	−0.353168
$81$	1.00000	0.111111
$82$	4.27413	0.471998
$83$	−9.85623	−1.08186	−0.540931	−	0.841067i	$-0.681928\pi$
$83$	−9.85623	−1.08186	−0.540931	+	0.841067i	$0.681928\pi$
$84$	4.69202	0.511942
$85$	17.7017	1.92002
$86$	2.09783	0.226215
$87$	0.850855	0.0912212
$88$	−0.137063	−0.0146110
$89$	17.0858	1.81109	0.905543	−	0.424254i	$-0.139464\pi$
$89$	17.0858	1.81109	0.905543	+	0.424254i	$0.139464\pi$
$90$	3.15883	0.332970
$91$	0	0
$92$	−6.09783	−0.635743
$93$	−6.23490	−0.646529
$94$	−4.98792	−0.514465
$95$	15.7560	1.61653
$96$	1.00000	0.102062
$97$	2.12737	0.216002	0.108001	−	0.994151i	$-0.465555\pi$
$97$	2.12737	0.216002	0.108001	+	0.994151i	$0.465555\pi$
$98$	−15.0151	−1.51675
$99$	0.137063	0.0137754
$100$	4.97823	0.497823
$101$	−9.18598	−0.914039	−0.457020	−	0.889457i	$-0.651083\pi$
$101$	−9.18598	−0.914039	−0.457020	+	0.889457i	$0.651083\pi$
$102$	−5.60388	−0.554866
$103$	0.225209	0.0221905	0.0110953	−	0.999938i	$-0.496468\pi$
$103$	0.225209	0.0221905	0.0110953	+	0.999938i	$0.496468\pi$
$104$	0	0
$105$	−14.8213	−1.44641
$106$	1.82908	0.177656
$107$	11.2838	1.09085	0.545424	−	0.838160i	$-0.316369\pi$
$107$	11.2838	1.09085	0.545424	+	0.838160i	$0.316369\pi$
$108$	−1.00000	−0.0962250
$109$	−0.195669	−0.0187417	−0.00937086	−	0.999956i	$-0.502983\pi$
$109$	−0.195669	−0.0187417	−0.00937086	+	0.999956i	$0.502983\pi$
$110$	0.432960	0.0412811
$111$	−11.7017	−1.11068
$112$	−4.69202	−0.443354
$113$	−0.439665	−0.0413602	−0.0206801	−	0.999786i	$-0.506583\pi$
$113$	−0.439665	−0.0413602	−0.0206801	+	0.999786i	$0.506583\pi$
$114$	−4.98792	−0.467161
$115$	19.2620	1.79619
$116$	−0.850855	−0.0789999
$117$	0	0
$118$	5.89977	0.543118
$119$	26.2935	2.41032
$120$	−3.15883	−0.288361
$121$	−10.9812	−0.998292
$122$	−4.39612	−0.398006
$123$	4.27413	0.385385
$124$	6.23490	0.559910
$125$	0.0687686	0.00615085
$126$	4.69202	0.417998
$127$	−7.87263	−0.698583	−0.349291	−	0.937014i	$-0.613578\pi$
$127$	−7.87263	−0.698583	−0.349291	+	0.937014i	$0.613578\pi$
$128$	−1.00000	−0.0883883
$129$	2.09783	0.184704
$130$	0	0
$131$	−0.621334	−0.0542862	−0.0271431	−	0.999632i	$-0.508641\pi$
$131$	−0.621334	−0.0542862	−0.0271431	+	0.999632i	$0.508641\pi$
$132$	−0.137063	−0.0119298
$133$	23.4034	2.02933
$134$	4.71379	0.407210
$135$	3.15883	0.271869
$136$	5.60388	0.480528
$137$	4.00000	0.341743	0.170872	−	0.985293i	$-0.445342\pi$
$137$	4.00000	0.341743	0.170872	+	0.985293i	$0.445342\pi$
$138$	−6.09783	−0.519082
$139$	−13.6582	−1.15847	−0.579235	−	0.815160i	$-0.696649\pi$
$139$	−13.6582	−1.15847	−0.579235	+	0.815160i	$0.696649\pi$
$140$	14.8213	1.25263
$141$	−4.98792	−0.420059
$142$	0.0978347	0.00821010
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.68771	0.223202
$146$	2.32304	0.192256
$147$	−15.0151	−1.23842
$148$	11.7017	0.961875
$149$	16.0586	1.31557	0.657786	−	0.753205i	$-0.271493\pi$
$149$	16.0586	1.31557	0.657786	+	0.753205i	$0.271493\pi$
$150$	4.97823	0.406471
$151$	−21.8823	−1.78076	−0.890379	−	0.455221i	$-0.849560\pi$
$151$	−21.8823	−1.78076	−0.890379	+	0.455221i	$0.849560\pi$
$152$	4.98792	0.404574
$153$	−5.60388	−0.453046
$154$	0.643104	0.0518228
$155$	−19.6950	−1.58194
$156$	0	0
$157$	−7.90217	−0.630661	−0.315331	−	0.948982i	$-0.602115\pi$
$157$	−7.90217	−0.630661	−0.315331	+	0.948982i	$0.602115\pi$
$158$	−14.5157	−1.15481
$159$	1.82908	0.145056
$160$	3.15883	0.249728
$161$	28.6112	2.25488
$162$	−1.00000	−0.0785674
$163$	8.01938	0.628126	0.314063	−	0.949402i	$-0.398310\pi$
$163$	8.01938	0.628126	0.314063	+	0.949402i	$0.398310\pi$
$164$	−4.27413	−0.333753
$165$	0.432960	0.0337059
$166$	9.85623	0.764992
$167$	−17.0858	−1.32214	−0.661068	−	0.750326i	$-0.729896\pi$
$167$	−17.0858	−1.32214	−0.661068	+	0.750326i	$0.729896\pi$
$168$	−4.69202	−0.361997
$169$	0	0
$170$	−17.7017	−1.35766
$171$	−4.98792	−0.381436
$172$	−2.09783	−0.159958
$173$	−15.3448	−1.16664	−0.583322	−	0.812241i	$-0.698248\pi$
$173$	−15.3448	−1.16664	−0.583322	+	0.812241i	$0.698248\pi$
$174$	−0.850855	−0.0645032
$175$	−23.3580	−1.76570
$176$	0.137063	0.0103315
$177$	5.89977	0.443454
$178$	−17.0858	−1.28063
$179$	0.523499	0.0391282	0.0195641	−	0.999809i	$-0.493772\pi$
$179$	0.523499	0.0391282	0.0195641	+	0.999809i	$0.493772\pi$
$180$	−3.15883	−0.235446
$181$	8.89008	0.660795	0.330397	−	0.943842i	$-0.392817\pi$
$181$	8.89008	0.660795	0.330397	+	0.943842i	$0.392817\pi$
$182$	0	0
$183$	−4.39612	−0.324971
$184$	6.09783	0.449538
$185$	−36.9638	−2.71763
$186$	6.23490	0.457165
$187$	−0.768086	−0.0561680
$188$	4.98792	0.363781
$189$	4.69202	0.341294
$190$	−15.7560	−1.14306
$191$	−7.03146	−0.508779	−0.254389	−	0.967102i	$-0.581874\pi$
$191$	−7.03146	−0.508779	−0.254389	+	0.967102i	$0.581874\pi$
$192$	−1.00000	−0.0721688
$193$	−17.7560	−1.27811	−0.639053	−	0.769163i	$-0.720673\pi$
$193$	−17.7560	−1.27811	−0.639053	+	0.769163i	$0.720673\pi$
$194$	−2.12737	−0.152737
$195$	0	0
$196$	15.0151	1.07250
$197$	18.6571	1.32926	0.664632	−	0.747171i	$-0.268588\pi$
$197$	18.6571	1.32926	0.664632	+	0.747171i	$0.268588\pi$
$198$	−0.137063	−0.00974067
$199$	7.66248	0.543179	0.271589	−	0.962413i	$-0.412451\pi$
$199$	7.66248	0.543179	0.271589	+	0.962413i	$0.412451\pi$
$200$	−4.97823	−0.352014
$201$	4.71379	0.332485
$202$	9.18598	0.646323
$203$	3.99223	0.280200
$204$	5.60388	0.392350
$205$	13.5013	0.942969
$206$	−0.225209	−0.0156911
$207$	−6.09783	−0.423829
$208$	0	0
$209$	−0.683661	−0.0472898
$210$	14.8213	1.02277
$211$	11.1642	0.768576	0.384288	−	0.923213i	$-0.374447\pi$
$211$	11.1642	0.768576	0.384288	+	0.923213i	$0.374447\pi$
$212$	−1.82908	−0.125622
$213$	0.0978347	0.00670352
$214$	−11.2838	−0.771346
$215$	6.62671	0.451938
$216$	1.00000	0.0680414
$217$	−29.2543	−1.98591
$218$	0.195669	0.0132524
$219$	2.32304	0.156977
$220$	−0.432960	−0.0291902
$221$	0	0
$222$	11.7017	0.785367
$223$	−24.6353	−1.64970	−0.824852	−	0.565349i	$-0.808742\pi$
$223$	−24.6353	−1.64970	−0.824852	+	0.565349i	$0.808742\pi$
$224$	4.69202	0.313499
$225$	4.97823	0.331882
$226$	0.439665	0.0292461
$227$	7.47650	0.496233	0.248116	−	0.968730i	$-0.420188\pi$
$227$	7.47650	0.496233	0.248116	+	0.968730i	$0.420188\pi$
$228$	4.98792	0.330333
$229$	19.2271	1.27056	0.635282	−	0.772280i	$-0.280884\pi$
$229$	19.2271	1.27056	0.635282	+	0.772280i	$0.280884\pi$
$230$	−19.2620	−1.27010
$231$	0.643104	0.0423131
$232$	0.850855	0.0558614
$233$	3.70171	0.242507	0.121254	−	0.992622i	$-0.461309\pi$
$233$	3.70171	0.242507	0.121254	+	0.992622i	$0.461309\pi$
$234$	0	0
$235$	−15.7560	−1.02781
$236$	−5.89977	−0.384042
$237$	−14.5157	−0.942898
$238$	−26.2935	−1.70435
$239$	−8.51334	−0.550682	−0.275341	−	0.961347i	$-0.588791\pi$
$239$	−8.51334	−0.550682	−0.275341	+	0.961347i	$0.588791\pi$
$240$	3.15883	0.203902
$241$	−17.4330	−1.12296	−0.561478	−	0.827492i	$-0.689767\pi$
$241$	−17.4330	−1.12296	−0.561478	+	0.827492i	$0.689767\pi$
$242$	10.9812	0.705899
$243$	−1.00000	−0.0641500
$244$	4.39612	0.281433
$245$	−47.4301	−3.03020
$246$	−4.27413	−0.272508
$247$	0	0
$248$	−6.23490	−0.395916
$249$	9.85623	0.624613
$250$	−0.0687686	−0.00434931
$251$	−3.48427	−0.219925	−0.109963	−	0.993936i	$-0.535073\pi$
$251$	−3.48427	−0.219925	−0.109963	+	0.993936i	$0.535073\pi$
$252$	−4.69202	−0.295570
$253$	−0.835790	−0.0525456
$254$	7.87263	0.493972
$255$	−17.7017	−1.10852
$256$	1.00000	0.0625000
$257$	−13.6039	−0.848586	−0.424293	−	0.905525i	$-0.639477\pi$
$257$	−13.6039	−0.848586	−0.424293	+	0.905525i	$0.639477\pi$
$258$	−2.09783	−0.130605
$259$	−54.9047	−3.41161
$260$	0	0
$261$	−0.850855	−0.0526666
$262$	0.621334	0.0383861
$263$	11.4577	0.706513	0.353256	−	0.935527i	$-0.385074\pi$
$263$	11.4577	0.706513	0.353256	+	0.935527i	$0.385074\pi$
$264$	0.137063	0.00843567
$265$	5.77777	0.354926
$266$	−23.4034	−1.43496
$267$	−17.0858	−1.04563
$268$	−4.71379	−0.287941
$269$	22.3666	1.36371	0.681857	−	0.731485i	$-0.261172\pi$
$269$	22.3666	1.36371	0.681857	+	0.731485i	$0.261172\pi$
$270$	−3.15883	−0.192240
$271$	3.87263	0.235245	0.117623	−	0.993058i	$-0.462473\pi$
$271$	3.87263	0.235245	0.117623	+	0.993058i	$0.462473\pi$
$272$	−5.60388	−0.339785
$273$	0	0
$274$	−4.00000	−0.241649
$275$	0.682333	0.0411462
$276$	6.09783	0.367047
$277$	28.7090	1.72496	0.862478	−	0.506094i	$-0.168911\pi$
$277$	28.7090	1.72496	0.862478	+	0.506094i	$0.168911\pi$
$278$	13.6582	0.819163
$279$	6.23490	0.373274
$280$	−14.8213	−0.885743
$281$	−29.0858	−1.73511	−0.867555	−	0.497341i	$-0.834310\pi$
$281$	−29.0858	−1.73511	−0.867555	+	0.497341i	$0.834310\pi$
$282$	4.98792	0.297026
$283$	13.7560	0.817710	0.408855	−	0.912599i	$-0.365928\pi$
$283$	13.7560	0.817710	0.408855	+	0.912599i	$0.365928\pi$
$284$	−0.0978347	−0.00580542
$285$	−15.7560	−0.933305
$286$	0	0
$287$	20.0543	1.18377
$288$	−1.00000	−0.0589256
$289$	14.4034	0.847260
$290$	−2.68771	−0.157828
$291$	−2.12737	−0.124709
$292$	−2.32304	−0.135946
$293$	27.7362	1.62036	0.810182	−	0.586179i	$-0.199368\pi$
$293$	27.7362	1.62036	0.810182	+	0.586179i	$0.199368\pi$
$294$	15.0151	0.875696
$295$	18.6364	1.08505
$296$	−11.7017	−0.680148
$297$	−0.137063	−0.00795322
$298$	−16.0586	−0.930250
$299$	0	0
$300$	−4.97823	−0.287418
$301$	9.84309	0.567346
$302$	21.8823	1.25919
$303$	9.18598	0.527721
$304$	−4.98792	−0.286077
$305$	−13.8866	−0.795146
$306$	5.60388	0.320352
$307$	−12.4590	−0.711075	−0.355538	−	0.934662i	$-0.615702\pi$
$307$	−12.4590	−0.711075	−0.355538	+	0.934662i	$0.615702\pi$
$308$	−0.643104	−0.0366443
$309$	−0.225209	−0.0128117
$310$	19.6950	1.11860
$311$	−6.09783	−0.345776	−0.172888	−	0.984941i	$-0.555310\pi$
$311$	−6.09783	−0.345776	−0.172888	+	0.984941i	$0.555310\pi$
$312$	0	0
$313$	−12.7385	−0.720025	−0.360013	−	0.932947i	$-0.617228\pi$
$313$	−12.7385	−0.720025	−0.360013	+	0.932947i	$0.617228\pi$
$314$	7.90217	0.445945
$315$	14.8213	0.835087
$316$	14.5157	0.816574
$317$	14.8140	0.832038	0.416019	−	0.909356i	$-0.363425\pi$
$317$	14.8140	0.832038	0.416019	+	0.909356i	$0.363425\pi$
$318$	−1.82908	−0.102570
$319$	−0.116621	−0.00652952
$320$	−3.15883	−0.176584
$321$	−11.2838	−0.629801
$322$	−28.6112	−1.59444
$323$	27.9517	1.55527
$324$	1.00000	0.0555556
$325$	0	0
$326$	−8.01938	−0.444152
$327$	0.195669	0.0108205
$328$	4.27413	0.235999
$329$	−23.4034	−1.29027
$330$	−0.432960	−0.0238337
$331$	7.70171	0.423324	0.211662	−	0.977343i	$-0.432112\pi$
$331$	7.70171	0.423324	0.211662	+	0.977343i	$0.432112\pi$
$332$	−9.85623	−0.540931
$333$	11.7017	0.641250
$334$	17.0858	0.934891
$335$	14.8901	0.813532
$336$	4.69202	0.255971
$337$	26.5961	1.44878	0.724391	−	0.689389i	$-0.242121\pi$
$337$	26.5961	1.44878	0.724391	+	0.689389i	$0.242121\pi$
$338$	0	0
$339$	0.439665	0.0238793
$340$	17.7017	0.960010
$341$	0.854576	0.0462779
$342$	4.98792	0.269716
$343$	−37.6069	−2.03058
$344$	2.09783	0.113108
$345$	−19.2620	−1.03703
$346$	15.3448	0.824942
$347$	0.911854	0.0489509	0.0244754	−	0.999700i	$-0.492208\pi$
$347$	0.911854	0.0489509	0.0244754	+	0.999700i	$0.492208\pi$
$348$	0.850855	0.0456106
$349$	−17.7211	−0.948588	−0.474294	−	0.880366i	$-0.657297\pi$
$349$	−17.7211	−0.948588	−0.474294	+	0.880366i	$0.657297\pi$
$350$	23.3580	1.24854
$351$	0	0
$352$	−0.137063	−0.00730550
$353$	−26.4349	−1.40699	−0.703493	−	0.710702i	$-0.748378\pi$
$353$	−26.4349	−1.40699	−0.703493	+	0.710702i	$0.748378\pi$
$354$	−5.89977	−0.313569
$355$	0.309043	0.0164023
$356$	17.0858	0.905543
$357$	−26.2935	−1.39160
$358$	−0.523499	−0.0276678
$359$	7.76941	0.410054	0.205027	−	0.978756i	$-0.434272\pi$
$359$	7.76941	0.410054	0.205027	+	0.978756i	$0.434272\pi$
$360$	3.15883	0.166485
$361$	5.87933	0.309438
$362$	−8.89008	−0.467252
$363$	10.9812	0.576364
$364$	0	0
$365$	7.33811	0.384094
$366$	4.39612	0.229789
$367$	−13.3274	−0.695682	−0.347841	−	0.937553i	$-0.613085\pi$
$367$	−13.3274	−0.695682	−0.347841	+	0.937553i	$0.613085\pi$
$368$	−6.09783	−0.317872
$369$	−4.27413	−0.222502
$370$	36.9638	1.92165
$371$	8.58211	0.445561
$372$	−6.23490	−0.323264
$373$	6.70304	0.347070	0.173535	−	0.984828i	$-0.444481\pi$
$373$	6.70304	0.347070	0.173535	+	0.984828i	$0.444481\pi$
$374$	0.768086	0.0397168
$375$	−0.0687686	−0.00355120
$376$	−4.98792	−0.257232
$377$	0	0
$378$	−4.69202	−0.241332
$379$	2.41550	0.124076	0.0620380	−	0.998074i	$-0.480240\pi$
$379$	2.41550	0.124076	0.0620380	+	0.998074i	$0.480240\pi$
$380$	15.7560	0.808266
$381$	7.87263	0.403327
$382$	7.03146	0.359761
$383$	10.0978	0.515975	0.257988	−	0.966148i	$-0.416941\pi$
$383$	10.0978	0.515975	0.257988	+	0.966148i	$0.416941\pi$
$384$	1.00000	0.0510310
$385$	2.03146	0.103533
$386$	17.7560	0.903757
$387$	−2.09783	−0.106639
$388$	2.12737	0.108001
$389$	25.1336	1.27432	0.637162	−	0.770730i	$-0.280108\pi$
$389$	25.1336	1.27432	0.637162	+	0.770730i	$0.280108\pi$
$390$	0	0
$391$	34.1715	1.72813
$392$	−15.0151	−0.758375
$393$	0.621334	0.0313421
$394$	−18.6571	−0.939931
$395$	−45.8528	−2.30710
$396$	0.137063	0.00688769
$397$	20.8358	1.04572	0.522859	−	0.852419i	$-0.324865\pi$
$397$	20.8358	1.04572	0.522859	+	0.852419i	$0.324865\pi$
$398$	−7.66248	−0.384085
$399$	−23.4034	−1.17164
$400$	4.97823	0.248911
$401$	−5.95646	−0.297451	−0.148726	−	0.988878i	$-0.547517\pi$
$401$	−5.95646	−0.297451	−0.148726	+	0.988878i	$0.547517\pi$
$402$	−4.71379	−0.235103
$403$	0	0
$404$	−9.18598	−0.457020
$405$	−3.15883	−0.156964
$406$	−3.99223	−0.198131
$407$	1.60388	0.0795012
$408$	−5.60388	−0.277433
$409$	−1.80194	−0.0891001	−0.0445500	−	0.999007i	$-0.514185\pi$
$409$	−1.80194	−0.0891001	−0.0445500	+	0.999007i	$0.514185\pi$
$410$	−13.5013	−0.666779
$411$	−4.00000	−0.197305
$412$	0.225209	0.0110953
$413$	27.6819	1.36214
$414$	6.09783	0.299692
$415$	31.1342	1.52832
$416$	0	0
$417$	13.6582	0.668843
$418$	0.683661	0.0334389
$419$	−28.4499	−1.38987	−0.694935	−	0.719072i	$-0.744567\pi$
$419$	−28.4499	−1.38987	−0.694935	+	0.719072i	$0.744567\pi$
$420$	−14.8213	−0.723206
$421$	13.9323	0.679019	0.339509	−	0.940603i	$-0.389739\pi$
$421$	13.9323	0.679019	0.339509	+	0.940603i	$0.389739\pi$
$422$	−11.1642	−0.543465
$423$	4.98792	0.242521
$424$	1.82908	0.0888282
$425$	−27.8974	−1.35322
$426$	−0.0978347	−0.00474011
$427$	−20.6267	−0.998196
$428$	11.2838	0.545424
$429$	0	0
$430$	−6.62671	−0.319568
$431$	−15.9022	−0.765980	−0.382990	−	0.923752i	$-0.625106\pi$
$431$	−15.9022	−0.765980	−0.382990	+	0.923752i	$0.625106\pi$
$432$	−1.00000	−0.0481125
$433$	4.77718	0.229577	0.114788	−	0.993390i	$-0.463381\pi$
$433$	4.77718	0.229577	0.114788	+	0.993390i	$0.463381\pi$
$434$	29.2543	1.40425
$435$	−2.68771	−0.128866
$436$	−0.195669	−0.00937086
$437$	30.4155	1.45497
$438$	−2.32304	−0.110999
$439$	−33.6316	−1.60515	−0.802575	−	0.596552i	$-0.796537\pi$
$439$	−33.6316	−1.60515	−0.802575	+	0.596552i	$0.796537\pi$
$440$	0.432960	0.0206406
$441$	15.0151	0.715003
$442$	0	0
$443$	−35.3749	−1.68071	−0.840357	−	0.542033i	$-0.817655\pi$
$443$	−35.3749	−1.68071	−0.840357	+	0.542033i	$0.817655\pi$
$444$	−11.7017	−0.555339
$445$	−53.9711	−2.55847
$446$	24.6353	1.16652
$447$	−16.0586	−0.759546
$448$	−4.69202	−0.221677
$449$	18.0629	0.852442	0.426221	−	0.904619i	$-0.359845\pi$
$449$	18.0629	0.852442	0.426221	+	0.904619i	$0.359845\pi$
$450$	−4.97823	−0.234676
$451$	−0.585826	−0.0275855
$452$	−0.439665	−0.0206801
$453$	21.8823	1.02812
$454$	−7.47650	−0.350890
$455$	0	0
$456$	−4.98792	−0.233581
$457$	15.4668	0.723507	0.361753	−	0.932274i	$-0.382178\pi$
$457$	15.4668	0.723507	0.361753	+	0.932274i	$0.382178\pi$
$458$	−19.2271	−0.898425
$459$	5.60388	0.261567
$460$	19.2620	0.898097
$461$	18.8092	0.876033	0.438017	−	0.898967i	$-0.355681\pi$
$461$	18.8092	0.876033	0.438017	+	0.898967i	$0.355681\pi$
$462$	−0.643104	−0.0299199
$463$	15.8431	0.736291	0.368145	−	0.929768i	$-0.379993\pi$
$463$	15.8431	0.736291	0.368145	+	0.929768i	$0.379993\pi$
$464$	−0.850855	−0.0395000
$465$	19.6950	0.913334
$466$	−3.70171	−0.171478
$467$	22.0006	1.01807	0.509033	−	0.860747i	$-0.330003\pi$
$467$	22.0006	1.01807	0.509033	+	0.860747i	$0.330003\pi$
$468$	0	0
$469$	22.1172	1.02128
$470$	15.7560	0.726770
$471$	7.90217	0.364113
$472$	5.89977	0.271559
$473$	−0.287536	−0.0132209
$474$	14.5157	0.666730
$475$	−24.8310	−1.13932
$476$	26.2935	1.20516
$477$	−1.82908	−0.0837480
$478$	8.51334	0.389391
$479$	21.3491	0.975466	0.487733	−	0.872993i	$-0.337824\pi$
$479$	21.3491	0.975466	0.487733	+	0.872993i	$0.337824\pi$
$480$	−3.15883	−0.144180
$481$	0	0
$482$	17.4330	0.794050
$483$	−28.6112	−1.30185
$484$	−10.9812	−0.499146
$485$	−6.72002	−0.305141
$486$	1.00000	0.0453609
$487$	31.6394	1.43372	0.716859	−	0.697219i	$-0.245579\pi$
$487$	31.6394	1.43372	0.716859	+	0.697219i	$0.245579\pi$
$488$	−4.39612	−0.199003
$489$	−8.01938	−0.362649
$490$	47.4301	2.14267
$491$	−1.39911	−0.0631409	−0.0315704	−	0.999502i	$-0.510051\pi$
$491$	−1.39911	−0.0631409	−0.0315704	+	0.999502i	$0.510051\pi$
$492$	4.27413	0.192693
$493$	4.76809	0.214744
$494$	0	0
$495$	−0.432960	−0.0194601
$496$	6.23490	0.279955
$497$	0.459042	0.0205909
$498$	−9.85623	−0.441668
$499$	0	0		−	1.00000i	$-0.5\pi$
$499$	0	0			1.00000i	$0.5\pi$
$500$	0.0687686	0.00307543
$501$	17.0858	0.763335
$502$	3.48427	0.155511
$503$	−18.3827	−0.819645	−0.409822	−	0.912165i	$-0.634409\pi$
$503$	−18.3827	−0.819645	−0.409822	+	0.912165i	$0.634409\pi$
$504$	4.69202	0.208999
$505$	29.0170	1.29124
$506$	0.835790	0.0371554
$507$	0	0
$508$	−7.87263	−0.349291
$509$	−0.132751	−0.00588411	−0.00294205	−	0.999996i	$-0.500936\pi$
$509$	−0.132751	−0.00588411	−0.00294205	+	0.999996i	$0.500936\pi$
$510$	17.7017	0.783845
$511$	10.8998	0.482178
$512$	−1.00000	−0.0441942
$513$	4.98792	0.220222
$514$	13.6039	0.600041
$515$	−0.711399	−0.0313480
$516$	2.09783	0.0923520
$517$	0.683661	0.0300674
$518$	54.9047	2.41237
$519$	15.3448	0.673563
$520$	0	0
$521$	37.0508	1.62323	0.811613	−	0.584195i	$-0.198590\pi$
$521$	37.0508	1.62323	0.811613	+	0.584195i	$0.198590\pi$
$522$	0.850855	0.0372409
$523$	−3.15346	−0.137891	−0.0689455	−	0.997620i	$-0.521963\pi$
$523$	−3.15346	−0.137891	−0.0689455	+	0.997620i	$0.521963\pi$
$524$	−0.621334	−0.0271431
$525$	23.3580	1.01942
$526$	−11.4577	−0.499580
$527$	−34.9396	−1.52199
$528$	−0.137063	−0.00596492
$529$	14.1836	0.616678
$530$	−5.77777	−0.250970
$531$	−5.89977	−0.256028
$532$	23.4034	1.01467
$533$	0	0
$534$	17.0858	0.739373
$535$	−35.6437	−1.54101
$536$	4.71379	0.203605
$537$	−0.523499	−0.0225907
$538$	−22.3666	−0.964292
$539$	2.05802	0.0886450
$540$	3.15883	0.135935
$541$	4.07846	0.175347	0.0876733	−	0.996149i	$-0.472057\pi$
$541$	4.07846	0.175347	0.0876733	+	0.996149i	$0.472057\pi$
$542$	−3.87263	−0.166344
$543$	−8.89008	−0.381510
$544$	5.60388	0.240264
$545$	0.618087	0.0264759
$546$	0	0
$547$	−23.0508	−0.985583	−0.492791	−	0.870148i	$-0.664023\pi$
$547$	−23.0508	−0.985583	−0.492791	+	0.870148i	$0.664023\pi$
$548$	4.00000	0.170872
$549$	4.39612	0.187622
$550$	−0.682333	−0.0290948
$551$	4.24400	0.180800
$552$	−6.09783	−0.259541
$553$	−68.1081	−2.89625
$554$	−28.7090	−1.21973
$555$	36.9638	1.56902
$556$	−13.6582	−0.579235
$557$	20.4155	0.865033	0.432516	−	0.901626i	$-0.357626\pi$
$557$	20.4155	0.865033	0.432516	+	0.901626i	$0.357626\pi$
$558$	−6.23490	−0.263944
$559$	0	0
$560$	14.8213	0.626315
$561$	0.768086	0.0324286
$562$	29.0858	1.22691
$563$	21.5609	0.908685	0.454342	−	0.890827i	$-0.349874\pi$
$563$	21.5609	0.908685	0.454342	+	0.890827i	$0.349874\pi$
$564$	−4.98792	−0.210029
$565$	1.38883	0.0584285
$566$	−13.7560	−0.578208
$567$	−4.69202	−0.197046
$568$	0.0978347	0.00410505
$569$	8.98792	0.376793	0.188397	−	0.982093i	$-0.439671\pi$
$569$	8.98792	0.376793	0.188397	+	0.982093i	$0.439671\pi$
$570$	15.7560	0.659946
$571$	13.5603	0.567482	0.283741	−	0.958901i	$-0.408424\pi$
$571$	13.5603	0.567482	0.283741	+	0.958901i	$0.408424\pi$
$572$	0	0
$573$	7.03146	0.293743
$574$	−20.0543	−0.837050
$575$	−30.3564	−1.26595
$576$	1.00000	0.0416667
$577$	16.2825	0.677849	0.338924	−	0.940814i	$-0.389937\pi$
$577$	16.2825	0.677849	0.338924	+	0.940814i	$0.389937\pi$
$578$	−14.4034	−0.599103
$579$	17.7560	0.737914
$580$	2.68771	0.111601
$581$	46.2457	1.91859
$582$	2.12737	0.0881825
$583$	−0.250700	−0.0103830
$584$	2.32304	0.0961282
$585$	0	0
$586$	−27.7362	−1.14577
$587$	47.5706	1.96345	0.981725	−	0.190307i	$-0.0609482\pi$
$587$	47.5706	1.96345	0.981725	+	0.190307i	$0.0609482\pi$
$588$	−15.0151	−0.619211
$589$	−31.0992	−1.28142
$590$	−18.6364	−0.767248
$591$	−18.6571	−0.767451
$592$	11.7017	0.480937
$593$	31.0267	1.27411	0.637056	−	0.770817i	$-0.280152\pi$
$593$	31.0267	1.27411	0.637056	+	0.770817i	$0.280152\pi$
$594$	0.137063	0.00562378
$595$	−83.0568	−3.40500
$596$	16.0586	0.657786
$597$	−7.66248	−0.313604
$598$	0	0
$599$	22.3263	0.912228	0.456114	−	0.889921i	$-0.349241\pi$
$599$	22.3263	0.912228	0.456114	+	0.889921i	$0.349241\pi$
$600$	4.97823	0.203235
$601$	−8.18060	−0.333694	−0.166847	−	0.985983i	$-0.553359\pi$
$601$	−8.18060	−0.333694	−0.166847	+	0.985983i	$0.553359\pi$
$602$	−9.84309	−0.401174
$603$	−4.71379	−0.191960
$604$	−21.8823	−0.890379
$605$	34.6878	1.41026
$606$	−9.18598	−0.373155
$607$	3.30798	0.134267	0.0671334	−	0.997744i	$-0.478615\pi$
$607$	3.30798	0.134267	0.0671334	+	0.997744i	$0.478615\pi$
$608$	4.98792	0.202287
$609$	−3.99223	−0.161773
$610$	13.8866	0.562253
$611$	0	0
$612$	−5.60388	−0.226523
$613$	−10.8853	−0.439653	−0.219827	−	0.975539i	$-0.570549\pi$
$613$	−10.8853	−0.439653	−0.219827	+	0.975539i	$0.570549\pi$
$614$	12.4590	0.502806
$615$	−13.5013	−0.544423
$616$	0.643104	0.0259114
$617$	−34.5676	−1.39164	−0.695820	−	0.718216i	$-0.744959\pi$
$617$	−34.5676	−1.39164	−0.695820	+	0.718216i	$0.744959\pi$
$618$	0.225209	0.00905925
$619$	2.86592	0.115191	0.0575955	−	0.998340i	$-0.481657\pi$
$619$	2.86592	0.115191	0.0575955	+	0.998340i	$0.481657\pi$
$620$	−19.6950	−0.790970
$621$	6.09783	0.244698
$622$	6.09783	0.244501
$623$	−80.1667	−3.21181
$624$	0	0
$625$	−25.1084	−1.00434
$626$	12.7385	0.509135
$627$	0.683661	0.0273028
$628$	−7.90217	−0.315331
$629$	−65.5749	−2.61464
$630$	−14.8213	−0.590495
$631$	−42.6631	−1.69839	−0.849195	−	0.528079i	$-0.822912\pi$
$631$	−42.6631	−1.69839	−0.849195	+	0.528079i	$0.822912\pi$
$632$	−14.5157	−0.577405
$633$	−11.1642	−0.443738
$634$	−14.8140	−0.588340
$635$	24.8683	0.986869
$636$	1.82908	0.0725279
$637$	0	0
$638$	0.116621	0.00461707
$639$	−0.0978347	−0.00387028
$640$	3.15883	0.124864
$641$	41.3927	1.63491	0.817456	−	0.575991i	$-0.195384\pi$
$641$	41.3927	1.63491	0.817456	+	0.575991i	$0.195384\pi$
$642$	11.2838	0.445337
$643$	13.7125	0.540767	0.270383	−	0.962753i	$-0.412850\pi$
$643$	13.7125	0.540767	0.270383	+	0.962753i	$0.412850\pi$
$644$	28.6112	1.12744
$645$	−6.62671	−0.260926
$646$	−27.9517	−1.09974
$647$	18.0086	0.707992	0.353996	−	0.935247i	$-0.384823\pi$
$647$	18.0086	0.707992	0.353996	+	0.935247i	$0.384823\pi$
$648$	−1.00000	−0.0392837
$649$	−0.808643	−0.0317420
$650$	0	0
$651$	29.2543	1.14657
$652$	8.01938	0.314063
$653$	46.5652	1.82224	0.911119	−	0.412143i	$-0.135220\pi$
$653$	46.5652	1.82224	0.911119	+	0.412143i	$0.135220\pi$
$654$	−0.195669	−0.00765128
$655$	1.96269	0.0766887
$656$	−4.27413	−0.166877
$657$	−2.32304	−0.0906306
$658$	23.4034	0.912360
$659$	13.8562	0.539762	0.269881	−	0.962894i	$-0.413016\pi$
$659$	13.8562	0.539762	0.269881	+	0.962894i	$0.413016\pi$
$660$	0.432960	0.0168530
$661$	−43.1051	−1.67660	−0.838298	−	0.545213i	$-0.816449\pi$
$661$	−43.1051	−1.67660	−0.838298	+	0.545213i	$0.816449\pi$
$662$	−7.70171	−0.299335
$663$	0	0
$664$	9.85623	0.382496
$665$	−73.9275	−2.86679
$666$	−11.7017	−0.453432
$667$	5.18837	0.200895
$668$	−17.0858	−0.661068
$669$	24.6353	0.952457
$670$	−14.8901	−0.575254
$671$	0.602548	0.0232611
$672$	−4.69202	−0.180999
$673$	30.7415	1.18500	0.592499	−	0.805571i	$-0.298141\pi$
$673$	30.7415	1.18500	0.592499	+	0.805571i	$0.298141\pi$
$674$	−26.5961	−1.02444
$675$	−4.97823	−0.191612
$676$	0	0
$677$	16.5894	0.637582	0.318791	−	0.947825i	$-0.396723\pi$
$677$	16.5894	0.637582	0.318791	+	0.947825i	$0.396723\pi$
$678$	−0.439665	−0.0168852
$679$	−9.98169	−0.383062
$680$	−17.7017	−0.678830
$681$	−7.47650	−0.286500
$682$	−0.854576	−0.0327234
$683$	−34.9885	−1.33880	−0.669399	−	0.742903i	$-0.733448\pi$
$683$	−34.9885	−1.33880	−0.669399	+	0.742903i	$0.733448\pi$
$684$	−4.98792	−0.190718
$685$	−12.6353	−0.482771
$686$	37.6069	1.43584
$687$	−19.2271	−0.733561
$688$	−2.09783	−0.0799792
$689$	0	0
$690$	19.2620	0.733294
$691$	14.0871	0.535898	0.267949	−	0.963433i	$-0.413654\pi$
$691$	14.0871	0.535898	0.267949	+	0.963433i	$0.413654\pi$
$692$	−15.3448	−0.583322
$693$	−0.643104	−0.0244295
$694$	−0.911854	−0.0346135
$695$	43.1439	1.63654
$696$	−0.850855	−0.0322516
$697$	23.9517	0.907234
$698$	17.7211	0.670753
$699$	−3.70171	−0.140012
$700$	−23.3580	−0.882848
$701$	48.6112	1.83602	0.918009	−	0.396559i	$-0.129796\pi$
$701$	48.6112	1.83602	0.918009	+	0.396559i	$0.129796\pi$
$702$	0	0
$703$	−58.3672	−2.20136
$704$	0.137063	0.00516577
$705$	15.7560	0.593405
$706$	26.4349	0.994890
$707$	43.1008	1.62097
$708$	5.89977	0.221727
$709$	17.2862	0.649197	0.324599	−	0.945852i	$-0.394771\pi$
$709$	17.2862	0.649197	0.324599	+	0.945852i	$0.394771\pi$
$710$	−0.309043	−0.0115982
$711$	14.5157	0.544382
$712$	−17.0858	−0.640316
$713$	−38.0194	−1.42384
$714$	26.2935	0.984010
$715$	0	0
$716$	0.523499	0.0195641
$717$	8.51334	0.317936
$718$	−7.76941	−0.289952
$719$	29.1207	1.08602	0.543009	−	0.839727i	$-0.317285\pi$
$719$	29.1207	1.08602	0.543009	+	0.839727i	$0.317285\pi$
$720$	−3.15883	−0.117723
$721$	−1.05669	−0.0393531
$722$	−5.87933	−0.218806
$723$	17.4330	0.648339
$724$	8.89008	0.330397
$725$	−4.23575	−0.157312
$726$	−10.9812	−0.407551
$727$	45.5666	1.68997	0.844985	−	0.534790i	$-0.179609\pi$
$727$	45.5666	1.68997	0.844985	+	0.534790i	$0.179609\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−7.33811	−0.271596
$731$	11.7560	0.434812
$732$	−4.39612	−0.162485
$733$	−21.7995	−0.805185	−0.402592	−	0.915379i	$-0.631891\pi$
$733$	−21.7995	−0.805185	−0.402592	+	0.915379i	$0.631891\pi$
$734$	13.3274	0.491922
$735$	47.4301	1.74949
$736$	6.09783	0.224769
$737$	−0.646088	−0.0237990
$738$	4.27413	0.157333
$739$	−41.5663	−1.52904	−0.764521	−	0.644599i	$-0.777024\pi$
$739$	−41.5663	−1.52904	−0.764521	+	0.644599i	$0.777024\pi$
$740$	−36.9638	−1.35881
$741$	0	0
$742$	−8.58211	−0.315059
$743$	28.8224	1.05739	0.528695	−	0.848812i	$-0.322681\pi$
$743$	28.8224	1.05739	0.528695	+	0.848812i	$0.322681\pi$
$744$	6.23490	0.228582
$745$	−50.7265	−1.85847
$746$	−6.70304	−0.245416
$747$	−9.85623	−0.360621
$748$	−0.768086	−0.0280840
$749$	−52.9439	−1.93453
$750$	0.0687686	0.00251108
$751$	16.6203	0.606482	0.303241	−	0.952914i	$-0.401931\pi$
$751$	16.6203	0.606482	0.303241	+	0.952914i	$0.401931\pi$
$752$	4.98792	0.181891
$753$	3.48427	0.126974
$754$	0	0
$755$	69.1226	2.51563
$756$	4.69202	0.170647
$757$	−40.3913	−1.46805	−0.734024	−	0.679123i	$-0.762360\pi$
$757$	−40.3913	−1.46805	−0.734024	+	0.679123i	$0.762360\pi$
$758$	−2.41550	−0.0877350
$759$	0.835790	0.0303372
$760$	−15.7560	−0.571530
$761$	−3.29483	−0.119438	−0.0597188	−	0.998215i	$-0.519020\pi$
$761$	−3.29483	−0.119438	−0.0597188	+	0.998215i	$0.519020\pi$
$762$	−7.87263	−0.285195
$763$	0.918085	0.0332369
$764$	−7.03146	−0.254389
$765$	17.7017	0.640007
$766$	−10.0978	−0.364850
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−2.35258	−0.0848363	−0.0424182	−	0.999100i	$-0.513506\pi$
$769$	−2.35258	−0.0848363	−0.0424182	+	0.999100i	$0.513506\pi$
$770$	−2.03146	−0.0732087
$771$	13.6039	0.489932
$772$	−17.7560	−0.639053
$773$	−20.3937	−0.733512	−0.366756	−	0.930317i	$-0.619532\pi$
$773$	−20.3937	−0.733512	−0.366756	+	0.930317i	$0.619532\pi$
$774$	2.09783	0.0754051
$775$	31.0388	1.11494
$776$	−2.12737	−0.0763683
$777$	54.9047	1.96969
$778$	−25.1336	−0.901083
$779$	21.3190	0.763832
$780$	0	0
$781$	−0.0134095	−0.000479831 0
$782$	−34.1715	−1.22197
$783$	0.850855	0.0304071
$784$	15.0151	0.536252
$785$	24.9616	0.890919
$786$	−0.621334	−0.0221622
$787$	19.6775	0.701429	0.350714	−	0.936482i	$-0.385939\pi$
$787$	19.6775	0.701429	0.350714	+	0.936482i	$0.385939\pi$
$788$	18.6571	0.664632
$789$	−11.4577	−0.407905
$790$	45.8528	1.63137
$791$	2.06292	0.0733489
$792$	−0.137063	−0.00487033
$793$	0	0
$794$	−20.8358	−0.739435
$795$	−5.77777	−0.204917
$796$	7.66248	0.271589
$797$	−45.8689	−1.62476	−0.812380	−	0.583128i	$-0.801828\pi$
$797$	−45.8689	−1.62476	−0.812380	+	0.583128i	$0.801828\pi$
$798$	23.4034	0.828472
$799$	−27.9517	−0.988859
$800$	−4.97823	−0.176007
$801$	17.0858	0.603695
$802$	5.95646	0.210330
$803$	−0.318404	−0.0112362
$804$	4.71379	0.166243
$805$	−90.3779	−3.18540
$806$	0	0
$807$	−22.3666	−0.787341
$808$	9.18598	0.323162
$809$	38.1414	1.34098	0.670490	−	0.741919i	$-0.266084\pi$
$809$	38.1414	1.34098	0.670490	+	0.741919i	$0.266084\pi$
$810$	3.15883	0.110990
$811$	46.6983	1.63980	0.819899	−	0.572509i	$-0.194030\pi$
$811$	46.6983	1.63980	0.819899	+	0.572509i	$0.194030\pi$
$812$	3.99223	0.140100
$813$	−3.87263	−0.135819
$814$	−1.60388	−0.0562158
$815$	−25.3319	−0.887337
$816$	5.60388	0.196175
$817$	10.4638	0.366083
$818$	1.80194	0.0630033
$819$	0	0
$820$	13.5013	0.471484
$821$	32.6950	1.14106	0.570532	−	0.821276i	$-0.306737\pi$
$821$	32.6950	1.14106	0.570532	+	0.821276i	$0.306737\pi$
$822$	4.00000	0.139516
$823$	−21.6799	−0.755715	−0.377858	−	0.925864i	$-0.623339\pi$
$823$	−21.6799	−0.755715	−0.377858	+	0.925864i	$0.623339\pi$
$824$	−0.225209	−0.00784554
$825$	−0.682333	−0.0237558
$826$	−27.6819	−0.963175
$827$	−13.9172	−0.483950	−0.241975	−	0.970283i	$-0.577795\pi$
$827$	−13.9172	−0.483950	−0.241975	+	0.970283i	$0.577795\pi$
$828$	−6.09783	−0.211914
$829$	−16.4047	−0.569760	−0.284880	−	0.958563i	$-0.591954\pi$
$829$	−16.4047	−0.569760	−0.284880	+	0.958563i	$0.591954\pi$
$830$	−31.1342	−1.08068
$831$	−28.7090	−0.995904
$832$	0	0
$833$	−84.1426	−2.91537
$834$	−13.6582	−0.472944
$835$	53.9711	1.86775
$836$	−0.683661	−0.0236449
$837$	−6.23490	−0.215510
$838$	28.4499	0.982787
$839$	11.6146	0.400982	0.200491	−	0.979696i	$-0.435746\pi$
$839$	11.6146	0.400982	0.200491	+	0.979696i	$0.435746\pi$
$840$	14.8213	0.511384
$841$	−28.2760	−0.975036
$842$	−13.9323	−0.480139
$843$	29.0858	1.00177
$844$	11.1642	0.384288
$845$	0	0
$846$	−4.98792	−0.171488
$847$	51.5241	1.77039
$848$	−1.82908	−0.0628110
$849$	−13.7560	−0.472105
$850$	27.8974	0.956872
$851$	−71.3551	−2.44602
$852$	0.0978347	0.00335176
$853$	26.2983	0.900436	0.450218	−	0.892919i	$-0.351346\pi$
$853$	26.2983	0.900436	0.450218	+	0.892919i	$0.351346\pi$
$854$	20.6267	0.705832
$855$	15.7560	0.538844
$856$	−11.2838	−0.385673
$857$	−48.6305	−1.66119	−0.830594	−	0.556879i	$-0.811999\pi$
$857$	−48.6305	−1.66119	−0.830594	+	0.556879i	$0.811999\pi$
$858$	0	0
$859$	33.6185	1.14705	0.573524	−	0.819189i	$-0.305576\pi$
$859$	33.6185	1.14705	0.573524	+	0.819189i	$0.305576\pi$
$860$	6.62671	0.225969
$861$	−20.0543	−0.683449
$862$	15.9022	0.541630
$863$	−5.78879	−0.197053	−0.0985264	−	0.995134i	$-0.531413\pi$
$863$	−5.78879	−0.197053	−0.0985264	+	0.995134i	$0.531413\pi$
$864$	1.00000	0.0340207
$865$	48.4717	1.64809
$866$	−4.77718	−0.162335
$867$	−14.4034	−0.489166
$868$	−29.2543	−0.992955
$869$	1.98957	0.0674917
$870$	2.68771	0.0911219
$871$	0	0
$872$	0.195669	0.00662620
$873$	2.12737	0.0720007
$874$	−30.4155	−1.02882
$875$	−0.322664	−0.0109080
$876$	2.32304	0.0784884
$877$	9.50604	0.320996	0.160498	−	0.987036i	$-0.448690\pi$
$877$	9.50604	0.320996	0.160498	+	0.987036i	$0.448690\pi$
$878$	33.6316	1.13501
$879$	−27.7362	−0.935517
$880$	−0.432960	−0.0145951
$881$	−46.7875	−1.57631	−0.788155	−	0.615477i	$-0.788963\pi$
$881$	−46.7875	−1.57631	−0.788155	+	0.615477i	$0.788963\pi$
$882$	−15.0151	−0.505584
$883$	3.03146	0.102017	0.0510084	−	0.998698i	$-0.483756\pi$
$883$	3.03146	0.102017	0.0510084	+	0.998698i	$0.483756\pi$
$884$	0	0
$885$	−18.6364	−0.626456
$886$	35.3749	1.18844
$887$	37.0180	1.24294	0.621472	−	0.783436i	$-0.286535\pi$
$887$	37.0180	1.24294	0.621472	+	0.783436i	$0.286535\pi$
$888$	11.7017	0.392684
$889$	36.9385	1.23888
$890$	53.9711	1.80911
$891$	0.137063	0.00459179
$892$	−24.6353	−0.824852
$893$	−24.8793	−0.832555
$894$	16.0586	0.537080
$895$	−1.65365	−0.0552753
$896$	4.69202	0.156749
$897$	0	0
$898$	−18.0629	−0.602767
$899$	−5.30499	−0.176931
$900$	4.97823	0.165941
$901$	10.2500	0.341476
$902$	0.585826	0.0195059
$903$	−9.84309	−0.327557
$904$	0.439665	0.0146230
$905$	−28.0823	−0.933487
$906$	−21.8823	−0.726991
$907$	19.0965	0.634089	0.317045	−	0.948411i	$-0.397310\pi$
$907$	19.0965	0.634089	0.317045	+	0.948411i	$0.397310\pi$
$908$	7.47650	0.248116
$909$	−9.18598	−0.304680
$910$	0	0
$911$	−31.3142	−1.03749	−0.518743	−	0.854930i	$-0.673600\pi$
$911$	−31.3142	−1.03749	−0.518743	+	0.854930i	$0.673600\pi$
$912$	4.98792	0.165166
$913$	−1.35093	−0.0447092
$914$	−15.4668	−0.511597
$915$	13.8866	0.459078
$916$	19.2271	0.635282
$917$	2.91531	0.0962721
$918$	−5.60388	−0.184955
$919$	30.3967	1.00270	0.501348	−	0.865246i	$-0.332838\pi$
$919$	30.3967	1.00270	0.501348	+	0.865246i	$0.332838\pi$
$920$	−19.2620	−0.635051
$921$	12.4590	0.410539
$922$	−18.8092	−0.619449
$923$	0	0
$924$	0.643104	0.0211566
$925$	58.2538	1.91537
$926$	−15.8431	−0.520636
$927$	0.225209	0.00739685
$928$	0.850855	0.0279307
$929$	−40.5810	−1.33142	−0.665710	−	0.746210i	$-0.731871\pi$
$929$	−40.5810	−1.33142	−0.665710	+	0.746210i	$0.731871\pi$
$930$	−19.6950	−0.645825
$931$	−74.8939	−2.45455
$932$	3.70171	0.121254
$933$	6.09783	0.199634
$934$	−22.0006	−0.719881
$935$	2.42626	0.0793470
$936$	0	0
$937$	−18.7047	−0.611056	−0.305528	−	0.952183i	$-0.598833\pi$
$937$	−18.7047	−0.611056	−0.305528	+	0.952183i	$0.598833\pi$
$938$	−22.1172	−0.722153
$939$	12.7385	0.415707
$940$	−15.7560	−0.513904
$941$	−4.04998	−0.132026	−0.0660128	−	0.997819i	$-0.521028\pi$
$941$	−4.04998	−0.132026	−0.0660128	+	0.997819i	$0.521028\pi$
$942$	−7.90217	−0.257466
$943$	26.0629	0.848725
$944$	−5.89977	−0.192021
$945$	−14.8213	−0.482137
$946$	0.287536	0.00934861
$947$	11.5356	0.374856	0.187428	−	0.982278i	$-0.439985\pi$
$947$	11.5356	0.374856	0.187428	+	0.982278i	$0.439985\pi$
$948$	−14.5157	−0.471449
$949$	0	0
$950$	24.8310	0.805624
$951$	−14.8140	−0.480377
$952$	−26.2935	−0.852177
$953$	−9.57109	−0.310038	−0.155019	−	0.987911i	$-0.549544\pi$
$953$	−9.57109	−0.310038	−0.155019	+	0.987911i	$0.549544\pi$
$954$	1.82908	0.0592188
$955$	22.2112	0.718738
$956$	−8.51334	−0.275341
$957$	0.116621	0.00376982
$958$	−21.3491	−0.689759
$959$	−18.7681	−0.606053
$960$	3.15883	0.101951
$961$	7.87395	0.253998
$962$	0	0
$963$	11.2838	0.363616
$964$	−17.4330	−0.561478
$965$	56.0883	1.80555
$966$	28.6112	0.920549
$967$	−61.2073	−1.96829	−0.984147	−	0.177357i	$-0.943245\pi$
$967$	−61.2073	−1.96829	−0.984147	+	0.177357i	$0.943245\pi$
$968$	10.9812	0.352950
$969$	−27.9517	−0.897937
$970$	6.72002	0.215767
$971$	−28.8595	−0.926145	−0.463072	−	0.886320i	$-0.653253\pi$
$971$	−28.8595	−0.926145	−0.463072	+	0.886320i	$0.653253\pi$
$972$	−1.00000	−0.0320750
$973$	64.0844	2.05445
$974$	−31.6394	−1.01379
$975$	0	0
$976$	4.39612	0.140717
$977$	−46.6305	−1.49184	−0.745922	−	0.666034i	$-0.767991\pi$
$977$	−46.6305	−1.49184	−0.745922	+	0.666034i	$0.767991\pi$
$978$	8.01938	0.256431
$979$	2.34183	0.0748452
$980$	−47.4301	−1.51510
$981$	−0.195669	−0.00624724
$982$	1.39911	0.0446473
$983$	−55.6883	−1.77618	−0.888090	−	0.459669i	$-0.847968\pi$
$983$	−55.6883	−1.77618	−0.888090	+	0.459669i	$0.847968\pi$
$984$	−4.27413	−0.136254
$985$	−58.9347	−1.87782
$986$	−4.76809	−0.151847
$987$	23.4034	0.744939
$988$	0	0
$989$	12.7922	0.406770
$990$	0.432960	0.0137604
$991$	−9.32172	−0.296114	−0.148057	−	0.988979i	$-0.547302\pi$
$991$	−9.32172	−0.296114	−0.148057	+	0.988979i	$0.547302\pi$
$992$	−6.23490	−0.197958
$993$	−7.70171	−0.244406
$994$	−0.459042	−0.0145599
$995$	−24.2045	−0.767334
$996$	9.85623	0.312307
$997$	46.0253	1.45764	0.728819	−	0.684707i	$-0.240070\pi$
$997$	46.0253	1.45764	0.728819	+	0.684707i	$0.240070\pi$
$998$	0	0
$999$	−11.7017	−0.370226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.a.l.1.1	✓	3
3.2	odd	2		3042.2.a.bh.1.3		3
4.3	odd	2		8112.2.a.cj.1.1		3
13.2	odd	12		1014.2.i.h.823.3		12
13.3	even	3		1014.2.e.n.529.1		6
13.4	even	6		1014.2.e.l.991.3		6
13.5	odd	4		1014.2.b.f.337.6		6
13.6	odd	12		1014.2.i.h.361.6		12
13.7	odd	12		1014.2.i.h.361.1		12
13.8	odd	4		1014.2.b.f.337.1		6
13.9	even	3		1014.2.e.n.991.1		6
13.10	even	6		1014.2.e.l.529.3		6
13.11	odd	12		1014.2.i.h.823.4		12
13.12	even	2		1014.2.a.n.1.3	yes	3
39.5	even	4		3042.2.b.o.1351.1		6
39.8	even	4		3042.2.b.o.1351.6		6
39.38	odd	2		3042.2.a.ba.1.1		3
52.51	odd	2		8112.2.a.cm.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.1	✓	3	1.1	even	1	trivial
1014.2.a.n.1.3	yes	3	13.12	even	2
1014.2.b.f.337.1		6	13.8	odd	4
1014.2.b.f.337.6		6	13.5	odd	4
1014.2.e.l.529.3		6	13.10	even	6
1014.2.e.l.991.3		6	13.4	even	6
1014.2.e.n.529.1		6	13.3	even	3
1014.2.e.n.991.1		6	13.9	even	3
1014.2.i.h.361.1		12	13.7	odd	12
1014.2.i.h.361.6		12	13.6	odd	12
1014.2.i.h.823.3		12	13.2	odd	12
1014.2.i.h.823.4		12	13.11	odd	12
3042.2.a.ba.1.1		3	39.38	odd	2
3042.2.a.bh.1.3		3	3.2	odd	2
3042.2.b.o.1351.1		6	39.5	even	4
3042.2.b.o.1351.6		6	39.8	even	4
8112.2.a.cj.1.1		3	4.3	odd	2
8112.2.a.cm.1.3		3	52.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15883 q^{5} +1.00000 q^{6} -4.69202 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15883 q^{5} +1.00000 q^{6} -4.69202 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.15883 q^{10} +0.137063 q^{11} -1.00000 q^{12} +4.69202 q^{14} +3.15883 q^{15} +1.00000 q^{16} -5.60388 q^{17} -1.00000 q^{18} -4.98792 q^{19} -3.15883 q^{20} +4.69202 q^{21} -0.137063 q^{22} -6.09783 q^{23} +1.00000 q^{24} +4.97823 q^{25} -1.00000 q^{27} -4.69202 q^{28} -0.850855 q^{29} -3.15883 q^{30} +6.23490 q^{31} -1.00000 q^{32} -0.137063 q^{33} +5.60388 q^{34} +14.8213 q^{35} +1.00000 q^{36} +11.7017 q^{37} +4.98792 q^{38} +3.15883 q^{40} -4.27413 q^{41} -4.69202 q^{42} -2.09783 q^{43} +0.137063 q^{44} -3.15883 q^{45} +6.09783 q^{46} +4.98792 q^{47} -1.00000 q^{48} +15.0151 q^{49} -4.97823 q^{50} +5.60388 q^{51} -1.82908 q^{53} +1.00000 q^{54} -0.432960 q^{55} +4.69202 q^{56} +4.98792 q^{57} +0.850855 q^{58} -5.89977 q^{59} +3.15883 q^{60} +4.39612 q^{61} -6.23490 q^{62} -4.69202 q^{63} +1.00000 q^{64} +0.137063 q^{66} -4.71379 q^{67} -5.60388 q^{68} +6.09783 q^{69} -14.8213 q^{70} -0.0978347 q^{71} -1.00000 q^{72} -2.32304 q^{73} -11.7017 q^{74} -4.97823 q^{75} -4.98792 q^{76} -0.643104 q^{77} +14.5157 q^{79} -3.15883 q^{80} +1.00000 q^{81} +4.27413 q^{82} -9.85623 q^{83} +4.69202 q^{84} +17.7017 q^{85} +2.09783 q^{86} +0.850855 q^{87} -0.137063 q^{88} +17.0858 q^{89} +3.15883 q^{90} -6.09783 q^{92} -6.23490 q^{93} -4.98792 q^{94} +15.7560 q^{95} +1.00000 q^{96} +2.12737 q^{97} -15.0151 q^{98} +0.137063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} - 9 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 - 9 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - q^{5} + 3 q^{6} - 9 q^{7} - 3 q^{8} + 3 q^{9} + q^{10} - 5 q^{11} - 3 q^{12} + 9 q^{14} + q^{15} + 3 q^{16} - 8 q^{17} - 3 q^{18} + 4 q^{19} - q^{20} + 9 q^{21} + 5 q^{22} + 3 q^{24} + 18 q^{25} - 3 q^{27} - 9 q^{28} + 11 q^{29} - q^{30} - 5 q^{31} - 3 q^{32} + 5 q^{33} + 8 q^{34} - 4 q^{35} + 3 q^{36} + 8 q^{37} - 4 q^{38} + q^{40} - 2 q^{41} - 9 q^{42} + 12 q^{43} - 5 q^{44} - q^{45} - 4 q^{47} - 3 q^{48} + 20 q^{49} - 18 q^{50} + 8 q^{51} + 5 q^{53} + 3 q^{54} + 18 q^{55} + 9 q^{56} - 4 q^{57} - 11 q^{58} + 5 q^{59} + q^{60} + 22 q^{61} + 5 q^{62} - 9 q^{63} + 3 q^{64} - 5 q^{66} - 6 q^{67} - 8 q^{68} + 4 q^{70} + 18 q^{71} - 3 q^{72} + 13 q^{73} - 8 q^{74} - 18 q^{75} + 4 q^{76} - 6 q^{77} + 31 q^{79} - q^{80} + 3 q^{81} + 2 q^{82} - 13 q^{83} + 9 q^{84} + 26 q^{85} - 12 q^{86} - 11 q^{87} + 5 q^{88} + 14 q^{89} + q^{90} + 5 q^{93} + 4 q^{94} + 8 q^{95} + 3 q^{96} + 23 q^{97} - 20 q^{98} - 5 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - q^5 + 3 * q^6 - 9 * q^7 - 3 * q^8 + 3 * q^9 + q^10 - 5 * q^11 - 3 * q^12 + 9 * q^14 + q^15 + 3 * q^16 - 8 * q^17 - 3 * q^18 + 4 * q^19 - q^20 + 9 * q^21 + 5 * q^22 + 3 * q^24 + 18 * q^25 - 3 * q^27 - 9 * q^28 + 11 * q^29 - q^30 - 5 * q^31 - 3 * q^32 + 5 * q^33 + 8 * q^34 - 4 * q^35 + 3 * q^36 + 8 * q^37 - 4 * q^38 + q^40 - 2 * q^41 - 9 * q^42 + 12 * q^43 - 5 * q^44 - q^45 - 4 * q^47 - 3 * q^48 + 20 * q^49 - 18 * q^50 + 8 * q^51 + 5 * q^53 + 3 * q^54 + 18 * q^55 + 9 * q^56 - 4 * q^57 - 11 * q^58 + 5 * q^59 + q^60 + 22 * q^61 + 5 * q^62 - 9 * q^63 + 3 * q^64 - 5 * q^66 - 6 * q^67 - 8 * q^68 + 4 * q^70 + 18 * q^71 - 3 * q^72 + 13 * q^73 - 8 * q^74 - 18 * q^75 + 4 * q^76 - 6 * q^77 + 31 * q^79 - q^80 + 3 * q^81 + 2 * q^82 - 13 * q^83 + 9 * q^84 + 26 * q^85 - 12 * q^86 - 11 * q^87 + 5 * q^88 + 14 * q^89 + q^90 + 5 * q^93 + 4 * q^94 + 8 * q^95 + 3 * q^96 + 23 * q^97 - 20 * q^98 - 5 * q^99

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