LMFDB - Embedded newform 1014.2.a.n.1.3

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			1.3
Root			$0.445042$ 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	$-0.250346\pi$
$5$	3.15883	1.41267	0.706337	+	0.707876i	$0.250346\pi$
$6$	−1.00000	−0.408248
$7$	4.69202	1.77342	0.886709	−	0.462329i	$-0.152986\pi$
$7$	4.69202	1.77342	0.886709	+	0.462329i	$0.152986\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.15883	0.998911
$11$	−0.137063	−0.0413262	−0.0206631	−	0.999786i	$-0.506578\pi$
$11$	−0.137063	−0.0413262	−0.0206631	+	0.999786i	$0.506578\pi$
$12$	−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	$-0.306108\pi$
$19$	4.98792	1.14431	0.572153	+	0.820147i	$0.306108\pi$
$20$	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	$-0.689164\pi$
$31$	−6.23490	−1.11982	−0.559910	+	0.828553i	$0.689164\pi$
$32$	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	$-0.911822\pi$
$37$	−11.7017	−1.92375	−0.961875	+	0.273491i	$0.911822\pi$
$38$	4.98792	0.809147
$39$	0	0
$40$	3.15883	0.499455
$41$	4.27413	0.667506	0.333753	−	0.942660i	$-0.391685\pi$
$41$	4.27413	0.667506	0.333753	+	0.942660i	$0.391685\pi$
$42$	−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	$-0.618514\pi$
$47$	−4.98792	−0.727563	−0.363781	+	0.931484i	$0.618514\pi$
$48$	−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	$-0.374532\pi$
$59$	5.89977	0.768085	0.384042	+	0.923315i	$0.374532\pi$
$60$	−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	$-0.407029\pi$
$67$	4.71379	0.575881	0.287941	+	0.957648i	$0.407029\pi$
$68$	−5.60388	−0.679570
$69$	6.09783	0.734093
$70$	14.8213	1.77149
$71$	0.0978347	0.0116108	0.00580542	−	0.999983i	$-0.498152\pi$
$71$	0.0978347	0.0116108	0.00580542	+	0.999983i	$0.498152\pi$
$72$	1.00000	0.117851
$73$	2.32304	0.271892	0.135946	−	0.990716i	$-0.456593\pi$
$73$	2.32304	0.271892	0.135946	+	0.990716i	$0.456593\pi$
$74$	−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	$-0.318072\pi$
$83$	9.85623	1.08186	0.540931	+	0.841067i	$0.318072\pi$
$84$	−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	$-0.860536\pi$
$89$	−17.0858	−1.81109	−0.905543	+	0.424254i	$0.860536\pi$
$90$	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	$-0.534445\pi$
$97$	−2.12737	−0.216002	−0.108001	+	0.994151i	$0.534445\pi$
$98$	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	$-0.497017\pi$
$109$	0.195669	0.0187417	0.00937086	+	0.999956i	$0.497017\pi$
$110$	−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	$-0.554658\pi$
$137$	−4.00000	−0.341743	−0.170872	+	0.985293i	$0.554658\pi$
$138$	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	$-0.728507\pi$
$149$	−16.0586	−1.31557	−0.657786	+	0.753205i	$0.728507\pi$
$150$	−4.97823	−0.406471
$151$	21.8823	1.78076	0.890379	−	0.455221i	$-0.150440\pi$
$151$	21.8823	1.78076	0.890379	+	0.455221i	$0.150440\pi$
$152$	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	$-0.601690\pi$
$163$	−8.01938	−0.628126	−0.314063	+	0.949402i	$0.601690\pi$
$164$	4.27413	0.333753
$165$	0.432960	0.0337059
$166$	9.85623	0.764992
$167$	17.0858	1.32214	0.661068	−	0.750326i	$-0.270104\pi$
$167$	17.0858	1.32214	0.661068	+	0.750326i	$0.270104\pi$
$168$	−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	$-0.279327\pi$
$193$	17.7560	1.27811	0.639053	+	0.769163i	$0.279327\pi$
$194$	−2.12737	−0.152737
$195$	0	0
$196$	15.0151	1.07250
$197$	−18.6571	−1.32926	−0.664632	−	0.747171i	$-0.731412\pi$
$197$	−18.6571	−1.32926	−0.664632	+	0.747171i	$0.731412\pi$
$198$	−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	$-0.191258\pi$
$223$	24.6353	1.64970	0.824852	+	0.565349i	$0.191258\pi$
$224$	4.69202	0.313499
$225$	4.97823	0.331882
$226$	−0.439665	−0.0292461
$227$	−7.47650	−0.496233	−0.248116	−	0.968730i	$-0.579812\pi$
$227$	−7.47650	−0.496233	−0.248116	+	0.968730i	$0.579812\pi$
$228$	−4.98792	−0.330333
$229$	−19.2271	−1.27056	−0.635282	−	0.772280i	$-0.719116\pi$
$229$	−19.2271	−1.27056	−0.635282	+	0.772280i	$0.719116\pi$
$230$	−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	$-0.411209\pi$
$239$	8.51334	0.550682	0.275341	+	0.961347i	$0.411209\pi$
$240$	−3.15883	−0.203902
$241$	17.4330	1.12296	0.561478	−	0.827492i	$-0.310233\pi$
$241$	17.4330	1.12296	0.561478	+	0.827492i	$0.310233\pi$
$242$	−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	$-0.537527\pi$
$271$	−3.87263	−0.235245	−0.117623	+	0.993058i	$0.537527\pi$
$272$	−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	$-0.165690\pi$
$281$	29.0858	1.73511	0.867555	+	0.497341i	$0.165690\pi$
$282$	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	$-0.800632\pi$
$293$	−27.7362	−1.62036	−0.810182	+	0.586179i	$0.800632\pi$
$294$	−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	$-0.384298\pi$
$307$	12.4590	0.711075	0.355538	+	0.934662i	$0.384298\pi$
$308$	−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	$-0.636575\pi$
$317$	−14.8140	−0.832038	−0.416019	+	0.909356i	$0.636575\pi$
$318$	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	$-0.567888\pi$
$331$	−7.70171	−0.423324	−0.211662	+	0.977343i	$0.567888\pi$
$332$	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	$-0.342703\pi$
$349$	17.7211	0.948588	0.474294	+	0.880366i	$0.342703\pi$
$350$	23.3580	1.24854
$351$	0	0
$352$	−0.137063	−0.00730550
$353$	26.4349	1.40699	0.703493	−	0.710702i	$-0.251622\pi$
$353$	26.4349	1.40699	0.703493	+	0.710702i	$0.251622\pi$
$354$	−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	$-0.565728\pi$
$359$	−7.76941	−0.410054	−0.205027	+	0.978756i	$0.565728\pi$
$360$	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	$-0.519760\pi$
$379$	−2.41550	−0.124076	−0.0620380	+	0.998074i	$0.519760\pi$
$380$	15.7560	0.808266
$381$	7.87263	0.403327
$382$	−7.03146	−0.359761
$383$	−10.0978	−0.515975	−0.257988	−	0.966148i	$-0.583059\pi$
$383$	−10.0978	−0.515975	−0.257988	+	0.966148i	$0.583059\pi$
$384$	−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	$-0.675135\pi$
$397$	−20.8358	−1.04572	−0.522859	+	0.852419i	$0.675135\pi$
$398$	7.66248	0.384085
$399$	−23.4034	−1.17164
$400$	4.97823	0.248911
$401$	5.95646	0.297451	0.148726	−	0.988878i	$-0.452483\pi$
$401$	5.95646	0.297451	0.148726	+	0.988878i	$0.452483\pi$
$402$	−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	$-0.485815\pi$
$409$	1.80194	0.0891001	0.0445500	+	0.999007i	$0.485815\pi$
$410$	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	$-0.610261\pi$
$421$	−13.9323	−0.679019	−0.339509	+	0.940603i	$0.610261\pi$
$422$	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	$-0.374894\pi$
$431$	15.9022	0.765980	0.382990	+	0.923752i	$0.374894\pi$
$432$	−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	$-0.640155\pi$
$449$	−18.0629	−0.852442	−0.426221	+	0.904619i	$0.640155\pi$
$450$	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	$-0.617822\pi$
$457$	−15.4668	−0.723507	−0.361753	+	0.932274i	$0.617822\pi$
$458$	−19.2271	−0.898425
$459$	5.60388	0.261567
$460$	−19.2620	−0.898097
$461$	−18.8092	−0.876033	−0.438017	−	0.898967i	$-0.644319\pi$
$461$	−18.8092	−0.876033	−0.438017	+	0.898967i	$0.644319\pi$
$462$	0.643104	0.0299199
$463$	−15.8431	−0.736291	−0.368145	−	0.929768i	$-0.620007\pi$
$463$	−15.8431	−0.736291	−0.368145	+	0.929768i	$0.620007\pi$
$464$	−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	$-0.662176\pi$
$479$	−21.3491	−0.975466	−0.487733	+	0.872993i	$0.662176\pi$
$480$	−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	$-0.754421\pi$
$487$	−31.6394	−1.43372	−0.716859	+	0.697219i	$0.754421\pi$
$488$	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	$-0.499064\pi$
$509$	0.132751	0.00588411	0.00294205	+	0.999996i	$0.499064\pi$
$510$	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	$-0.527943\pi$
$541$	−4.07846	−0.175347	−0.0876733	+	0.996149i	$0.527943\pi$
$542$	−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	$-0.642374\pi$
$557$	−20.4155	−0.865033	−0.432516	+	0.901626i	$0.642374\pi$
$558$	−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	$-0.610063\pi$
$577$	−16.2825	−0.677849	−0.338924	+	0.940814i	$0.610063\pi$
$578$	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	$-0.939052\pi$
$587$	−47.5706	−1.96345	−0.981725	+	0.190307i	$0.939052\pi$
$588$	−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	$-0.719848\pi$
$593$	−31.0267	−1.27411	−0.637056	+	0.770817i	$0.719848\pi$
$594$	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	$-0.429451\pi$
$613$	10.8853	0.439653	0.219827	+	0.975539i	$0.429451\pi$
$614$	12.4590	0.502806
$615$	−13.5013	−0.544423
$616$	−0.643104	−0.0259114
$617$	34.5676	1.39164	0.695820	−	0.718216i	$-0.255041\pi$
$617$	34.5676	1.39164	0.695820	+	0.718216i	$0.255041\pi$
$618$	−0.225209	−0.00905925
$619$	−2.86592	−0.115191	−0.0575955	−	0.998340i	$-0.518343\pi$
$619$	−2.86592	−0.115191	−0.0575955	+	0.998340i	$0.518343\pi$
$620$	−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	$-0.177088\pi$
$631$	42.6631	1.69839	0.849195	+	0.528079i	$0.177088\pi$
$632$	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	$-0.587150\pi$
$643$	−13.7125	−0.540767	−0.270383	+	0.962753i	$0.587150\pi$
$644$	−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	$-0.183551\pi$
$661$	43.1051	1.67660	0.838298	+	0.545213i	$0.183551\pi$
$662$	−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	$-0.266552\pi$
$683$	34.9885	1.33880	0.669399	+	0.742903i	$0.266552\pi$
$684$	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	$-0.586346\pi$
$691$	−14.0871	−0.535898	−0.267949	+	0.963433i	$0.586346\pi$
$692$	−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	$-0.605229\pi$
$709$	−17.2862	−0.649197	−0.324599	+	0.945852i	$0.605229\pi$
$710$	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	$-0.368109\pi$
$733$	21.7995	0.805185	0.402592	+	0.915379i	$0.368109\pi$
$734$	−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	$-0.222976\pi$
$739$	41.5663	1.52904	0.764521	+	0.644599i	$0.222976\pi$
$740$	−36.9638	−1.35881
$741$	0	0
$742$	−8.58211	−0.315059
$743$	−28.8224	−1.05739	−0.528695	−	0.848812i	$-0.677319\pi$
$743$	−28.8224	−1.05739	−0.528695	+	0.848812i	$0.677319\pi$
$744$	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	$-0.480980\pi$
$761$	3.29483	0.119438	0.0597188	+	0.998215i	$0.480980\pi$
$762$	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	$-0.486494\pi$
$769$	2.35258	0.0848363	0.0424182	+	0.999100i	$0.486494\pi$
$770$	−2.03146	−0.0732087
$771$	13.6039	0.489932
$772$	17.7560	0.639053
$773$	20.3937	0.733512	0.366756	−	0.930317i	$-0.380468\pi$
$773$	20.3937	0.733512	0.366756	+	0.930317i	$0.380468\pi$
$774$	−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	$-0.614061\pi$
$787$	−19.6775	−0.701429	−0.350714	+	0.936482i	$0.614061\pi$
$788$	−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	$-0.805970\pi$
$811$	−46.6983	−1.63980	−0.819899	+	0.572509i	$0.805970\pi$
$812$	−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	$-0.693263\pi$
$821$	−32.6950	−1.14106	−0.570532	+	0.821276i	$0.693263\pi$
$822$	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	$-0.422205\pi$
$827$	13.9172	0.483950	0.241975	+	0.970283i	$0.422205\pi$
$828$	−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	$-0.564254\pi$
$839$	−11.6146	−0.400982	−0.200491	+	0.979696i	$0.564254\pi$
$840$	−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	$-0.648654\pi$
$853$	−26.2983	−0.900436	−0.450218	+	0.892919i	$0.648654\pi$
$854$	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	$-0.468587\pi$
$863$	5.78879	0.197053	0.0985264	+	0.995134i	$0.468587\pi$
$864$	−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	$-0.551310\pi$
$877$	−9.50604	−0.320996	−0.160498	+	0.987036i	$0.551310\pi$
$878$	−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	$-0.268129\pi$
$929$	40.5810	1.33142	0.665710	+	0.746210i	$0.268129\pi$
$930$	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	$-0.478972\pi$
$941$	4.04998	0.132026	0.0660128	+	0.997819i	$0.478972\pi$
$942$	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	$-0.560015\pi$
$947$	−11.5356	−0.374856	−0.187428	+	0.982278i	$0.560015\pi$
$948$	−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	$-0.0567546\pi$
$967$	61.2073	1.96829	0.984147	+	0.177357i	$0.0567546\pi$
$968$	−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	$-0.232009\pi$
$977$	46.6305	1.49184	0.745922	+	0.666034i	$0.232009\pi$
$978$	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	$-0.152032\pi$
$983$	55.6883	1.77618	0.888090	+	0.459669i	$0.152032\pi$
$984$	−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.n.1.3	yes	3
3.2	odd	2		3042.2.a.ba.1.1		3
4.3	odd	2		8112.2.a.cm.1.3		3
13.2	odd	12		1014.2.i.h.823.4		12
13.3	even	3		1014.2.e.l.529.3		6
13.4	even	6		1014.2.e.n.991.1		6
13.5	odd	4		1014.2.b.f.337.1		6
13.6	odd	12		1014.2.i.h.361.1		12
13.7	odd	12		1014.2.i.h.361.6		12
13.8	odd	4		1014.2.b.f.337.6		6
13.9	even	3		1014.2.e.l.991.3		6
13.10	even	6		1014.2.e.n.529.1		6
13.11	odd	12		1014.2.i.h.823.3		12
13.12	even	2		1014.2.a.l.1.1	✓	3
39.5	even	4		3042.2.b.o.1351.6		6
39.8	even	4		3042.2.b.o.1351.1		6
39.38	odd	2		3042.2.a.bh.1.3		3
52.51	odd	2		8112.2.a.cj.1.1		3

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