LMFDB - Embedded newform 6045.2.a.w.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2695680219$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 15 x^{9} + 29 x^{8} + 81 x^{7} - 151 x^{6} - 192 x^{5} + 345 x^{4} + 199 x^{3} + \cdots + 118 $ x^11 - 2x^10 - 15x^9 + 29x^8 + 81x^7 - 151x^6 - 192x^5 + 345x^4 + 199x^3 - 344x^2 - 70x + 118
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$2.49644$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.49644 q^{2} -1.00000 q^{3} +4.23221 q^{4} -1.00000 q^{5} -2.49644 q^{6} -0.699311 q^{7} +5.57257 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.49644 q^{2} -1.00000 q^{3} +4.23221 q^{4} -1.00000 q^{5} -2.49644 q^{6} -0.699311 q^{7} +5.57257 q^{8} +1.00000 q^{9} -2.49644 q^{10} +0.185093 q^{11} -4.23221 q^{12} -1.00000 q^{13} -1.74579 q^{14} +1.00000 q^{15} +5.44717 q^{16} -5.75767 q^{17} +2.49644 q^{18} +2.01828 q^{19} -4.23221 q^{20} +0.699311 q^{21} +0.462073 q^{22} -4.09296 q^{23} -5.57257 q^{24} +1.00000 q^{25} -2.49644 q^{26} -1.00000 q^{27} -2.95963 q^{28} -2.18369 q^{29} +2.49644 q^{30} -1.00000 q^{31} +2.45339 q^{32} -0.185093 q^{33} -14.3737 q^{34} +0.699311 q^{35} +4.23221 q^{36} +2.05917 q^{37} +5.03851 q^{38} +1.00000 q^{39} -5.57257 q^{40} -11.3754 q^{41} +1.74579 q^{42} +2.02188 q^{43} +0.783351 q^{44} -1.00000 q^{45} -10.2178 q^{46} +0.316572 q^{47} -5.44717 q^{48} -6.51096 q^{49} +2.49644 q^{50} +5.75767 q^{51} -4.23221 q^{52} +7.62292 q^{53} -2.49644 q^{54} -0.185093 q^{55} -3.89696 q^{56} -2.01828 q^{57} -5.45145 q^{58} +6.78378 q^{59} +4.23221 q^{60} -8.55605 q^{61} -2.49644 q^{62} -0.699311 q^{63} -4.76961 q^{64} +1.00000 q^{65} -0.462073 q^{66} +0.160637 q^{67} -24.3676 q^{68} +4.09296 q^{69} +1.74579 q^{70} +3.09495 q^{71} +5.57257 q^{72} -12.1688 q^{73} +5.14060 q^{74} -1.00000 q^{75} +8.54178 q^{76} -0.129437 q^{77} +2.49644 q^{78} -9.40498 q^{79} -5.44717 q^{80} +1.00000 q^{81} -28.3980 q^{82} +3.65363 q^{83} +2.95963 q^{84} +5.75767 q^{85} +5.04750 q^{86} +2.18369 q^{87} +1.03144 q^{88} -5.43025 q^{89} -2.49644 q^{90} +0.699311 q^{91} -17.3223 q^{92} +1.00000 q^{93} +0.790302 q^{94} -2.01828 q^{95} -2.45339 q^{96} -18.3788 q^{97} -16.2542 q^{98} +0.185093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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 $

$2$	2.49644	1.76525	0.882625	−	0.470079i	$-0.155774\pi$
$2$	2.49644	1.76525	0.882625	+	0.470079i	$0.155774\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.23221	2.11610
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.49644	−1.01917
$7$	−0.699311	−0.264315	−0.132157	−	0.991229i	$-0.542190\pi$
$7$	−0.699311	−0.264315	−0.132157	+	0.991229i	$0.542190\pi$
$8$	5.57257	1.97020
$9$	1.00000	0.333333
$10$	−2.49644	−0.789443
$11$	0.185093	0.0558076	0.0279038	−	0.999611i	$-0.491117\pi$
$11$	0.185093	0.0558076	0.0279038	+	0.999611i	$0.491117\pi$
$12$	−4.23221	−1.22173
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.74579	−0.466582
$15$	1.00000	0.258199
$16$	5.44717	1.36179
$17$	−5.75767	−1.39644	−0.698219	−	0.715884i	$-0.746024\pi$
$17$	−5.75767	−1.39644	−0.698219	+	0.715884i	$0.746024\pi$
$18$	2.49644	0.588416
$19$	2.01828	0.463025	0.231513	−	0.972832i	$-0.425633\pi$
$19$	2.01828	0.463025	0.231513	+	0.972832i	$0.425633\pi$
$20$	−4.23221	−0.946351
$21$	0.699311	0.152602
$22$	0.462073	0.0985142
$23$	−4.09296	−0.853442	−0.426721	−	0.904383i	$-0.640331\pi$
$23$	−4.09296	−0.853442	−0.426721	+	0.904383i	$0.640331\pi$
$24$	−5.57257	−1.13750
$25$	1.00000	0.200000
$26$	−2.49644	−0.489592
$27$	−1.00000	−0.192450
$28$	−2.95963	−0.559318
$29$	−2.18369	−0.405501	−0.202751	−	0.979230i	$-0.564988\pi$
$29$	−2.18369	−0.405501	−0.202751	+	0.979230i	$0.564988\pi$
$30$	2.49644	0.455785
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	2.45339	0.433702
$33$	−0.185093	−0.0322205
$34$	−14.3737	−2.46506
$35$	0.699311	0.118205
$36$	4.23221	0.705368
$37$	2.05917	0.338526	0.169263	−	0.985571i	$-0.445861\pi$
$37$	2.05917	0.338526	0.169263	+	0.985571i	$0.445861\pi$
$38$	5.03851	0.817355
$39$	1.00000	0.160128
$40$	−5.57257	−0.881101
$41$	−11.3754	−1.77654	−0.888271	−	0.459320i	$-0.848093\pi$
$41$	−11.3754	−1.77654	−0.888271	+	0.459320i	$0.848093\pi$
$42$	1.74579	0.269381
$43$	2.02188	0.308334	0.154167	−	0.988045i	$-0.450731\pi$
$43$	2.02188	0.308334	0.154167	+	0.988045i	$0.450731\pi$
$44$	0.783351	0.118095
$45$	−1.00000	−0.149071
$46$	−10.2178	−1.50654
$47$	0.316572	0.0461768	0.0230884	−	0.999733i	$-0.492650\pi$
$47$	0.316572	0.0461768	0.0230884	+	0.999733i	$0.492650\pi$
$48$	−5.44717	−0.786232
$49$	−6.51096	−0.930138
$50$	2.49644	0.353050
$51$	5.75767	0.806234
$52$	−4.23221	−0.586902
$53$	7.62292	1.04709	0.523545	−	0.851998i	$-0.324609\pi$
$53$	7.62292	1.04709	0.523545	+	0.851998i	$0.324609\pi$
$54$	−2.49644	−0.339722
$55$	−0.185093	−0.0249579
$56$	−3.89696	−0.520754
$57$	−2.01828	−0.267328
$58$	−5.45145	−0.715811
$59$	6.78378	0.883173	0.441586	−	0.897219i	$-0.354416\pi$
$59$	6.78378	0.883173	0.441586	+	0.897219i	$0.354416\pi$
$60$	4.23221	0.546376
$61$	−8.55605	−1.09549	−0.547745	−	0.836645i	$-0.684514\pi$
$61$	−8.55605	−1.09549	−0.547745	+	0.836645i	$0.684514\pi$
$62$	−2.49644	−0.317048
$63$	−0.699311	−0.0881050
$64$	−4.76961	−0.596201
$65$	1.00000	0.124035
$66$	−0.462073	−0.0568772
$67$	0.160637	0.0196250	0.00981249	−	0.999952i	$-0.496877\pi$
$67$	0.160637	0.0196250	0.00981249	+	0.999952i	$0.496877\pi$
$68$	−24.3676	−2.95501
$69$	4.09296	0.492735
$70$	1.74579	0.208662
$71$	3.09495	0.367303	0.183651	−	0.982991i	$-0.441208\pi$
$71$	3.09495	0.367303	0.183651	+	0.982991i	$0.441208\pi$
$72$	5.57257	0.656734
$73$	−12.1688	−1.42425	−0.712124	−	0.702054i	$-0.752266\pi$
$73$	−12.1688	−1.42425	−0.712124	+	0.702054i	$0.752266\pi$
$74$	5.14060	0.597582
$75$	−1.00000	−0.115470
$76$	8.54178	0.979810
$77$	−0.129437	−0.0147508
$78$	2.49644	0.282666
$79$	−9.40498	−1.05814	−0.529071	−	0.848577i	$-0.677460\pi$
$79$	−9.40498	−1.05814	−0.529071	+	0.848577i	$0.677460\pi$
$80$	−5.44717	−0.609012
$81$	1.00000	0.111111
$82$	−28.3980	−3.13604
$83$	3.65363	0.401038	0.200519	−	0.979690i	$-0.435737\pi$
$83$	3.65363	0.401038	0.200519	+	0.979690i	$0.435737\pi$
$84$	2.95963	0.322922
$85$	5.75767	0.624507
$86$	5.04750	0.544286
$87$	2.18369	0.234116
$88$	1.03144	0.109952
$89$	−5.43025	−0.575605	−0.287803	−	0.957690i	$-0.592925\pi$
$89$	−5.43025	−0.575605	−0.287803	+	0.957690i	$0.592925\pi$
$90$	−2.49644	−0.263148
$91$	0.699311	0.0733078
$92$	−17.3223	−1.80597
$93$	1.00000	0.103695
$94$	0.790302	0.0815135
$95$	−2.01828	−0.207071
$96$	−2.45339	−0.250398
$97$	−18.3788	−1.86609	−0.933045	−	0.359761i	$-0.882858\pi$
$97$	−18.3788	−1.86609	−0.933045	+	0.359761i	$0.882858\pi$
$98$	−16.2542	−1.64192
$99$	0.185093	0.0186025
$100$	4.23221	0.423221
$101$	16.8211	1.67376	0.836881	−	0.547385i	$-0.184377\pi$
$101$	16.8211	1.67376	0.836881	+	0.547385i	$0.184377\pi$
$102$	14.3737	1.42320
$103$	0.0437836	0.00431413	0.00215706	−	0.999998i	$-0.499313\pi$
$103$	0.0437836	0.00431413	0.00215706	+	0.999998i	$0.499313\pi$
$104$	−5.57257	−0.546436
$105$	−0.699311	−0.0682458
$106$	19.0302	1.84837
$107$	10.9090	1.05462	0.527308	−	0.849674i	$-0.323202\pi$
$107$	10.9090	1.05462	0.527308	+	0.849674i	$0.323202\pi$
$108$	−4.23221	−0.407244
$109$	−13.7050	−1.31270	−0.656352	−	0.754455i	$-0.727901\pi$
$109$	−13.7050	−1.31270	−0.656352	+	0.754455i	$0.727901\pi$
$110$	−0.462073	−0.0440569
$111$	−2.05917	−0.195448
$112$	−3.80927	−0.359942
$113$	−2.63432	−0.247816	−0.123908	−	0.992294i	$-0.539543\pi$
$113$	−2.63432	−0.247816	−0.123908	+	0.992294i	$0.539543\pi$
$114$	−5.03851	−0.471900
$115$	4.09296	0.381671
$116$	−9.24183	−0.858083
$117$	−1.00000	−0.0924500
$118$	16.9353	1.55902
$119$	4.02640	0.369100
$120$	5.57257	0.508704
$121$	−10.9657	−0.996886
$122$	−21.3597	−1.93381
$123$	11.3754	1.02569
$124$	−4.23221	−0.380064
$125$	−1.00000	−0.0894427
$126$	−1.74579	−0.155527
$127$	5.07536	0.450365	0.225183	−	0.974317i	$-0.427702\pi$
$127$	5.07536	0.450365	0.225183	+	0.974317i	$0.427702\pi$
$128$	−16.8138	−1.48615
$129$	−2.02188	−0.178017
$130$	2.49644	0.218952
$131$	10.4071	0.909269	0.454635	−	0.890678i	$-0.349770\pi$
$131$	10.4071	0.909269	0.454635	+	0.890678i	$0.349770\pi$
$132$	−0.783351	−0.0681820
$133$	−1.41141	−0.122384
$134$	0.401021	0.0346430
$135$	1.00000	0.0860663
$136$	−32.0850	−2.75127
$137$	8.85627	0.756642	0.378321	−	0.925674i	$-0.376502\pi$
$137$	8.85627	0.756642	0.378321	+	0.925674i	$0.376502\pi$
$138$	10.2178	0.869800
$139$	−22.6333	−1.91973	−0.959864	−	0.280466i	$-0.909511\pi$
$139$	−22.6333	−1.91973	−0.959864	+	0.280466i	$0.909511\pi$
$140$	2.95963	0.250135
$141$	−0.316572	−0.0266602
$142$	7.72634	0.648380
$143$	−0.185093	−0.0154782
$144$	5.44717	0.453931
$145$	2.18369	0.181346
$146$	−30.3786	−2.51415
$147$	6.51096	0.537015
$148$	8.71485	0.716356
$149$	0.237528	0.0194590	0.00972951	−	0.999953i	$-0.496903\pi$
$149$	0.237528	0.0194590	0.00972951	+	0.999953i	$0.496903\pi$
$150$	−2.49644	−0.203833
$151$	−3.08757	−0.251263	−0.125631	−	0.992077i	$-0.540096\pi$
$151$	−3.08757	−0.251263	−0.125631	+	0.992077i	$0.540096\pi$
$152$	11.2470	0.912253
$153$	−5.75767	−0.465480
$154$	−0.323133	−0.0260388
$155$	1.00000	0.0803219
$156$	4.23221	0.338848
$157$	10.1842	0.812786	0.406393	−	0.913698i	$-0.366786\pi$
$157$	10.1842	0.812786	0.406393	+	0.913698i	$0.366786\pi$
$158$	−23.4790	−1.86789
$159$	−7.62292	−0.604537
$160$	−2.45339	−0.193957
$161$	2.86226	0.225577
$162$	2.49644	0.196139
$163$	19.8544	1.55512	0.777558	−	0.628811i	$-0.216458\pi$
$163$	19.8544	1.55512	0.777558	+	0.628811i	$0.216458\pi$
$164$	−48.1431	−3.75935
$165$	0.185093	0.0144094
$166$	9.12108	0.707933
$167$	−9.93383	−0.768703	−0.384351	−	0.923187i	$-0.625575\pi$
$167$	−9.93383	−0.768703	−0.384351	+	0.923187i	$0.625575\pi$
$168$	3.89696	0.300657
$169$	1.00000	0.0769231
$170$	14.3737	1.10241
$171$	2.01828	0.154342
$172$	8.55703	0.652467
$173$	15.9527	1.21286	0.606430	−	0.795137i	$-0.292601\pi$
$173$	15.9527	1.21286	0.606430	+	0.795137i	$0.292601\pi$
$174$	5.45145	0.413273
$175$	−0.699311	−0.0528630
$176$	1.00823	0.0759983
$177$	−6.78378	−0.509900
$178$	−13.5563	−1.01609
$179$	2.20047	0.164471	0.0822354	−	0.996613i	$-0.473794\pi$
$179$	2.20047	0.164471	0.0822354	+	0.996613i	$0.473794\pi$
$180$	−4.23221	−0.315450
$181$	−3.79834	−0.282328	−0.141164	−	0.989986i	$-0.545085\pi$
$181$	−3.79834	−0.282328	−0.141164	+	0.989986i	$0.545085\pi$
$182$	1.74579	0.129406
$183$	8.55605	0.632482
$184$	−22.8083	−1.68145
$185$	−2.05917	−0.151393
$186$	2.49644	0.183048
$187$	−1.06570	−0.0779318
$188$	1.33980	0.0977148
$189$	0.699311	0.0508674
$190$	−5.03851	−0.365532
$191$	−19.6088	−1.41884	−0.709421	−	0.704785i	$-0.751043\pi$
$191$	−19.6088	−1.41884	−0.709421	+	0.704785i	$0.751043\pi$
$192$	4.76961	0.344217
$193$	14.6160	1.05208	0.526041	−	0.850459i	$-0.323676\pi$
$193$	14.6160	1.05208	0.526041	+	0.850459i	$0.323676\pi$
$194$	−45.8817	−3.29411
$195$	−1.00000	−0.0716115
$196$	−27.5558	−1.96827
$197$	−10.3671	−0.738623	−0.369312	−	0.929306i	$-0.620407\pi$
$197$	−10.3671	−0.738623	−0.369312	+	0.929306i	$0.620407\pi$
$198$	0.462073	0.0328381
$199$	−24.1171	−1.70962	−0.854809	−	0.518943i	$-0.826326\pi$
$199$	−24.1171	−1.70962	−0.854809	+	0.518943i	$0.826326\pi$
$200$	5.57257	0.394040
$201$	−0.160637	−0.0113305
$202$	41.9928	2.95461
$203$	1.52708	0.107180
$204$	24.3676	1.70608
$205$	11.3754	0.794494
$206$	0.109303	0.00761551
$207$	−4.09296	−0.284481
$208$	−5.44717	−0.377693
$209$	0.373569	0.0258403
$210$	−1.74579	−0.120471
$211$	−7.79430	−0.536582	−0.268291	−	0.963338i	$-0.586459\pi$
$211$	−7.79430	−0.536582	−0.268291	+	0.963338i	$0.586459\pi$
$212$	32.2618	2.21575
$213$	−3.09495	−0.212062
$214$	27.2337	1.86166
$215$	−2.02188	−0.137891
$216$	−5.57257	−0.379166
$217$	0.699311	0.0474724
$218$	−34.2138	−2.31725
$219$	12.1688	0.822290
$220$	−0.783351	−0.0528135
$221$	5.75767	0.387302
$222$	−5.14060	−0.345014
$223$	−8.37182	−0.560619	−0.280309	−	0.959910i	$-0.590437\pi$
$223$	−8.37182	−0.560619	−0.280309	+	0.959910i	$0.590437\pi$
$224$	−1.71568	−0.114634
$225$	1.00000	0.0666667
$226$	−6.57642	−0.437457
$227$	0.0214715	0.00142511	0.000712557	−	1.00000i	$-0.499773\pi$
$227$	0.0214715	0.00142511	0.000712557		1.00000i	$0.499773\pi$
$228$	−8.54178	−0.565693
$229$	21.4483	1.41734	0.708671	−	0.705539i	$-0.249295\pi$
$229$	21.4483	1.41734	0.708671	+	0.705539i	$0.249295\pi$
$230$	10.2178	0.673744
$231$	0.129437	0.00851636
$232$	−12.1688	−0.798919
$233$	−15.9366	−1.04404	−0.522021	−	0.852933i	$-0.674822\pi$
$233$	−15.9366	−1.04404	−0.522021	+	0.852933i	$0.674822\pi$
$234$	−2.49644	−0.163197
$235$	−0.316572	−0.0206509
$236$	28.7104	1.86889
$237$	9.40498	0.610919
$238$	10.0517	0.651553
$239$	−12.7693	−0.825974	−0.412987	−	0.910737i	$-0.635515\pi$
$239$	−12.7693	−0.825974	−0.412987	+	0.910737i	$0.635515\pi$
$240$	5.44717	0.351613
$241$	13.5772	0.874583	0.437291	−	0.899320i	$-0.355938\pi$
$241$	13.5772	0.874583	0.437291	+	0.899320i	$0.355938\pi$
$242$	−27.3753	−1.75975
$243$	−1.00000	−0.0641500
$244$	−36.2110	−2.31817
$245$	6.51096	0.415970
$246$	28.3980	1.81059
$247$	−2.01828	−0.128420
$248$	−5.57257	−0.353859
$249$	−3.65363	−0.231540
$250$	−2.49644	−0.157889
$251$	−25.1041	−1.58456	−0.792279	−	0.610159i	$-0.791106\pi$
$251$	−25.1041	−1.58456	−0.792279	+	0.610159i	$0.791106\pi$
$252$	−2.95963	−0.186439
$253$	−0.757577	−0.0476285
$254$	12.6703	0.795007
$255$	−5.75767	−0.360559
$256$	−32.4355	−2.02722
$257$	28.3742	1.76994	0.884968	−	0.465651i	$-0.154180\pi$
$257$	28.3742	1.76994	0.884968	+	0.465651i	$0.154180\pi$
$258$	−5.04750	−0.314244
$259$	−1.44000	−0.0894774
$260$	4.23221	0.262470
$261$	−2.18369	−0.135167
$262$	25.9806	1.60509
$263$	10.0719	0.621057	0.310528	−	0.950564i	$-0.399494\pi$
$263$	10.0719	0.621057	0.310528	+	0.950564i	$0.399494\pi$
$264$	−1.03144	−0.0634809
$265$	−7.62292	−0.468273
$266$	−3.52349	−0.216039
$267$	5.43025	0.332326
$268$	0.679851	0.0415285
$269$	−16.0270	−0.977186	−0.488593	−	0.872512i	$-0.662490\pi$
$269$	−16.0270	−0.977186	−0.488593	+	0.872512i	$0.662490\pi$
$270$	2.49644	0.151928
$271$	−11.7667	−0.714775	−0.357388	−	0.933956i	$-0.616333\pi$
$271$	−11.7667	−0.714775	−0.357388	+	0.933956i	$0.616333\pi$
$272$	−31.3630	−1.90166
$273$	−0.699311	−0.0423243
$274$	22.1091	1.33566
$275$	0.185093	0.0111615
$276$	17.3223	1.04268
$277$	12.9275	0.776737	0.388369	−	0.921504i	$-0.373039\pi$
$277$	12.9275	0.776737	0.388369	+	0.921504i	$0.373039\pi$
$278$	−56.5026	−3.38880
$279$	−1.00000	−0.0598684
$280$	3.89696	0.232888
$281$	8.87439	0.529402	0.264701	−	0.964331i	$-0.414727\pi$
$281$	8.87439	0.529402	0.264701	+	0.964331i	$0.414727\pi$
$282$	−0.790302	−0.0470618
$283$	−17.7209	−1.05340	−0.526700	−	0.850052i	$-0.676571\pi$
$283$	−17.7209	−1.05340	−0.526700	+	0.850052i	$0.676571\pi$
$284$	13.0985	0.777250
$285$	2.01828	0.119553
$286$	−0.462073	−0.0273229
$287$	7.95496	0.469567
$288$	2.45339	0.144567
$289$	16.1507	0.950042
$290$	5.45145	0.320120
$291$	18.3788	1.07739
$292$	−51.5008	−3.01386
$293$	−18.3289	−1.07079	−0.535393	−	0.844603i	$-0.679836\pi$
$293$	−18.3289	−1.07079	−0.535393	+	0.844603i	$0.679836\pi$
$294$	16.2542	0.947966
$295$	−6.78378	−0.394967
$296$	11.4749	0.666964
$297$	−0.185093	−0.0107402
$298$	0.592973	0.0343500
$299$	4.09296	0.236702
$300$	−4.23221	−0.244347
$301$	−1.41393	−0.0814973
$302$	−7.70792	−0.443541
$303$	−16.8211	−0.966347
$304$	10.9939	0.630544
$305$	8.55605	0.489918
$306$	−14.3737	−0.821688
$307$	25.8822	1.47718	0.738588	−	0.674157i	$-0.235493\pi$
$307$	25.8822	1.47718	0.738588	+	0.674157i	$0.235493\pi$
$308$	−0.547806	−0.0312142
$309$	−0.0437836	−0.00249076
$310$	2.49644	0.141788
$311$	2.57903	0.146243	0.0731216	−	0.997323i	$-0.476704\pi$
$311$	2.57903	0.146243	0.0731216	+	0.997323i	$0.476704\pi$
$312$	5.57257	0.315485
$313$	5.90981	0.334042	0.167021	−	0.985953i	$-0.446585\pi$
$313$	5.90981	0.334042	0.167021	+	0.985953i	$0.446585\pi$
$314$	25.4242	1.43477
$315$	0.699311	0.0394017
$316$	−39.8038	−2.23914
$317$	5.80302	0.325930	0.162965	−	0.986632i	$-0.447894\pi$
$317$	5.80302	0.325930	0.162965	+	0.986632i	$0.447894\pi$
$318$	−19.0302	−1.06716
$319$	−0.404185	−0.0226300
$320$	4.76961	0.266629
$321$	−10.9090	−0.608882
$322$	7.14545	0.398200
$323$	−11.6206	−0.646586
$324$	4.23221	0.235123
$325$	−1.00000	−0.0554700
$326$	49.5653	2.74517
$327$	13.7050	0.757890
$328$	−63.3904	−3.50015
$329$	−0.221382	−0.0122052
$330$	0.462073	0.0254363
$331$	4.68731	0.257638	0.128819	−	0.991668i	$-0.458881\pi$
$331$	4.68731	0.257638	0.128819	+	0.991668i	$0.458881\pi$
$332$	15.4629	0.848639
$333$	2.05917	0.112842
$334$	−24.7992	−1.35695
$335$	−0.160637	−0.00877656
$336$	3.80927	0.207813
$337$	26.6748	1.45307	0.726536	−	0.687129i	$-0.241129\pi$
$337$	26.6748	1.45307	0.726536	+	0.687129i	$0.241129\pi$
$338$	2.49644	0.135788
$339$	2.63432	0.143077
$340$	24.3676	1.32152
$341$	−0.185093	−0.0100233
$342$	5.03851	0.272452
$343$	9.44837	0.510164
$344$	11.2671	0.607480
$345$	−4.09296	−0.220358
$346$	39.8249	2.14100
$347$	22.8504	1.22668	0.613338	−	0.789821i	$-0.289826\pi$
$347$	22.8504	1.22668	0.613338	+	0.789821i	$0.289826\pi$
$348$	9.24183	0.495414
$349$	−15.0668	−0.806507	−0.403253	−	0.915088i	$-0.632121\pi$
$349$	−15.0668	−0.806507	−0.403253	+	0.915088i	$0.632121\pi$
$350$	−1.74579	−0.0933163
$351$	1.00000	0.0533761
$352$	0.454104	0.0242038
$353$	17.4283	0.927615	0.463807	−	0.885936i	$-0.346483\pi$
$353$	17.4283	0.927615	0.463807	+	0.885936i	$0.346483\pi$
$354$	−16.9353	−0.900100
$355$	−3.09495	−0.164263
$356$	−22.9819	−1.21804
$357$	−4.02640	−0.213100
$358$	5.49334	0.290332
$359$	7.48246	0.394909	0.197455	−	0.980312i	$-0.436733\pi$
$359$	7.48246	0.394909	0.197455	+	0.980312i	$0.436733\pi$
$360$	−5.57257	−0.293700
$361$	−14.9265	−0.785608
$362$	−9.48232	−0.498380
$363$	10.9657	0.575552
$364$	2.95963	0.155127
$365$	12.1688	0.636943
$366$	21.3597	1.11649
$367$	2.23468	0.116649	0.0583247	−	0.998298i	$-0.481424\pi$
$367$	2.23468	0.116649	0.0583247	+	0.998298i	$0.481424\pi$
$368$	−22.2951	−1.16221
$369$	−11.3754	−0.592181
$370$	−5.14060	−0.267247
$371$	−5.33080	−0.276761
$372$	4.23221	0.219430
$373$	10.6215	0.549959	0.274980	−	0.961450i	$-0.411329\pi$
$373$	10.6215	0.549959	0.274980	+	0.961450i	$0.411329\pi$
$374$	−2.66046	−0.137569
$375$	1.00000	0.0516398
$376$	1.76412	0.0909775
$377$	2.18369	0.112466
$378$	1.74579	0.0897937
$379$	23.5664	1.21053	0.605263	−	0.796025i	$-0.293068\pi$
$379$	23.5664	1.21053	0.605263	+	0.796025i	$0.293068\pi$
$380$	−8.54178	−0.438184
$381$	−5.07536	−0.260018
$382$	−48.9521	−2.50461
$383$	−8.70911	−0.445015	−0.222507	−	0.974931i	$-0.571424\pi$
$383$	−8.70911	−0.445015	−0.222507	+	0.974931i	$0.571424\pi$
$384$	16.8138	0.858027
$385$	0.129437	0.00659674
$386$	36.4880	1.85719
$387$	2.02188	0.102778
$388$	−77.7831	−3.94884
$389$	20.0233	1.01522	0.507610	−	0.861587i	$-0.330529\pi$
$389$	20.0233	1.01522	0.507610	+	0.861587i	$0.330529\pi$
$390$	−2.49644	−0.126412
$391$	23.5659	1.19178
$392$	−36.2828	−1.83256
$393$	−10.4071	−0.524967
$394$	−25.8808	−1.30385
$395$	9.40498	0.473216
$396$	0.783351	0.0393649
$397$	16.6560	0.835940	0.417970	−	0.908461i	$-0.362742\pi$
$397$	16.6560	0.835940	0.417970	+	0.908461i	$0.362742\pi$
$398$	−60.2069	−3.01790
$399$	1.41141	0.0706587
$400$	5.44717	0.272359
$401$	−22.6120	−1.12919	−0.564595	−	0.825368i	$-0.690968\pi$
$401$	−22.6120	−1.12919	−0.564595	+	0.825368i	$0.690968\pi$
$402$	−0.401021	−0.0200011
$403$	1.00000	0.0498135
$404$	71.1904	3.54185
$405$	−1.00000	−0.0496904
$406$	3.81226	0.189199
$407$	0.381138	0.0188923
$408$	32.0850	1.58844
$409$	−16.8812	−0.834721	−0.417361	−	0.908741i	$-0.637045\pi$
$409$	−16.8812	−0.834721	−0.417361	+	0.908741i	$0.637045\pi$
$410$	28.3980	1.40248
$411$	−8.85627	−0.436847
$412$	0.185301	0.00912914
$413$	−4.74397	−0.233436
$414$	−10.2178	−0.502179
$415$	−3.65363	−0.179350
$416$	−2.45339	−0.120287
$417$	22.6333	1.10836
$418$	0.932592	0.0456146
$419$	−5.69686	−0.278310	−0.139155	−	0.990271i	$-0.544439\pi$
$419$	−5.69686	−0.278310	−0.139155	+	0.990271i	$0.544439\pi$
$420$	−2.95963	−0.144415
$421$	−27.7723	−1.35354	−0.676769	−	0.736196i	$-0.736620\pi$
$421$	−27.7723	−1.35354	−0.676769	+	0.736196i	$0.736620\pi$
$422$	−19.4580	−0.947201
$423$	0.316572	0.0153923
$424$	42.4793	2.06298
$425$	−5.75767	−0.279288
$426$	−7.72634	−0.374343
$427$	5.98335	0.289554
$428$	46.1693	2.23168
$429$	0.185093	0.00893636
$430$	−5.04750	−0.243412
$431$	22.1442	1.06665	0.533323	−	0.845911i	$-0.320943\pi$
$431$	22.1442	1.06665	0.533323	+	0.845911i	$0.320943\pi$
$432$	−5.44717	−0.262077
$433$	3.53079	0.169679	0.0848394	−	0.996395i	$-0.472962\pi$
$433$	3.53079	0.169679	0.0848394	+	0.996395i	$0.472962\pi$
$434$	1.74579	0.0838005
$435$	−2.18369	−0.104700
$436$	−58.0025	−2.77782
$437$	−8.26074	−0.395165
$438$	30.3786	1.45155
$439$	27.9630	1.33460	0.667301	−	0.744788i	$-0.267449\pi$
$439$	27.9630	1.33460	0.667301	+	0.744788i	$0.267449\pi$
$440$	−1.03144	−0.0491721
$441$	−6.51096	−0.310046
$442$	14.3737	0.683685
$443$	0.328349	0.0156003	0.00780016	−	0.999970i	$-0.497517\pi$
$443$	0.328349	0.0156003	0.00780016	+	0.999970i	$0.497517\pi$
$444$	−8.71485	−0.413588
$445$	5.43025	0.257418
$446$	−20.8997	−0.989632
$447$	−0.237528	−0.0112347
$448$	3.33544	0.157585
$449$	18.8502	0.889595	0.444797	−	0.895631i	$-0.353276\pi$
$449$	18.8502	0.889595	0.444797	+	0.895631i	$0.353276\pi$
$450$	2.49644	0.117683
$451$	−2.10551	−0.0991445
$452$	−11.1490	−0.524405
$453$	3.08757	0.145067
$454$	0.0536023	0.00251568
$455$	−0.699311	−0.0327842
$456$	−11.2470	−0.526690
$457$	−12.8965	−0.603274	−0.301637	−	0.953423i	$-0.597533\pi$
$457$	−12.8965	−0.603274	−0.301637	+	0.953423i	$0.597533\pi$
$458$	53.5443	2.50196
$459$	5.75767	0.268745
$460$	17.3223	0.807655
$461$	−8.47098	−0.394533	−0.197267	−	0.980350i	$-0.563206\pi$
$461$	−8.47098	−0.394533	−0.197267	+	0.980350i	$0.563206\pi$
$462$	0.323133	0.0150335
$463$	−16.9948	−0.789813	−0.394907	−	0.918721i	$-0.629223\pi$
$463$	−16.9948	−0.789813	−0.394907	+	0.918721i	$0.629223\pi$
$464$	−11.8949	−0.552209
$465$	−1.00000	−0.0463739
$466$	−39.7848	−1.84299
$467$	−13.9268	−0.644458	−0.322229	−	0.946662i	$-0.604432\pi$
$467$	−13.9268	−0.644458	−0.322229	+	0.946662i	$0.604432\pi$
$468$	−4.23221	−0.195634
$469$	−0.112336	−0.00518717
$470$	−0.790302	−0.0364539
$471$	−10.1842	−0.469262
$472$	37.8031	1.74003
$473$	0.374236	0.0172074
$474$	23.4790	1.07842
$475$	2.01828	0.0926050
$476$	17.0406	0.781053
$477$	7.62292	0.349030
$478$	−31.8777	−1.45805
$479$	−5.51573	−0.252020	−0.126010	−	0.992029i	$-0.540217\pi$
$479$	−5.51573	−0.252020	−0.126010	+	0.992029i	$0.540217\pi$
$480$	2.45339	0.111981
$481$	−2.05917	−0.0938902
$482$	33.8946	1.54386
$483$	−2.86226	−0.130237
$484$	−46.4093	−2.10951
$485$	18.3788	0.834540
$486$	−2.49644	−0.113241
$487$	−28.5422	−1.29337	−0.646686	−	0.762757i	$-0.723845\pi$
$487$	−28.5422	−1.29337	−0.646686	+	0.762757i	$0.723845\pi$
$488$	−47.6792	−2.15834
$489$	−19.8544	−0.897847
$490$	16.2542	0.734291
$491$	29.7270	1.34156	0.670781	−	0.741655i	$-0.265959\pi$
$491$	29.7270	1.34156	0.670781	+	0.741655i	$0.265959\pi$
$492$	48.1431	2.17046
$493$	12.5730	0.566258
$494$	−5.03851	−0.226693
$495$	−0.185093	−0.00831930
$496$	−5.44717	−0.244585
$497$	−2.16433	−0.0970835
$498$	−9.12108	−0.408725
$499$	−6.72031	−0.300842	−0.150421	−	0.988622i	$-0.548063\pi$
$499$	−6.72031	−0.300842	−0.150421	+	0.988622i	$0.548063\pi$
$500$	−4.23221	−0.189270
$501$	9.93383	0.443811
$502$	−62.6709	−2.79714
$503$	8.99380	0.401014	0.200507	−	0.979692i	$-0.435741\pi$
$503$	8.99380	0.401014	0.200507	+	0.979692i	$0.435741\pi$
$504$	−3.89696	−0.173585
$505$	−16.8211	−0.748529
$506$	−1.89125	−0.0840761
$507$	−1.00000	−0.0444116
$508$	21.4800	0.953019
$509$	31.8002	1.40952	0.704758	−	0.709447i	$-0.251055\pi$
$509$	31.8002	1.40952	0.704758	+	0.709447i	$0.251055\pi$
$510$	−14.3737	−0.636476
$511$	8.50976	0.376450
$512$	−47.3455	−2.09240
$513$	−2.01828	−0.0891092
$514$	70.8346	3.12438
$515$	−0.0437836	−0.00192934
$516$	−8.55703	−0.376702
$517$	0.0585952	0.00257701
$518$	−3.59488	−0.157950
$519$	−15.9527	−0.700244
$520$	5.57257	0.244373
$521$	29.4648	1.29088	0.645438	−	0.763812i	$-0.276675\pi$
$521$	29.4648	1.29088	0.645438	+	0.763812i	$0.276675\pi$
$522$	−5.45145	−0.238604
$523$	−24.9443	−1.09074	−0.545369	−	0.838196i	$-0.683611\pi$
$523$	−24.9443	−1.09074	−0.545369	+	0.838196i	$0.683611\pi$
$524$	44.0448	1.92411
$525$	0.699311	0.0305205
$526$	25.1438	1.09632
$527$	5.75767	0.250808
$528$	−1.00823	−0.0438777
$529$	−6.24766	−0.271637
$530$	−19.0302	−0.826618
$531$	6.78378	0.294391
$532$	−5.97337	−0.258978
$533$	11.3754	0.492724
$534$	13.5563	0.586638
$535$	−10.9090	−0.471638
$536$	0.895163	0.0386652
$537$	−2.20047	−0.0949573
$538$	−40.0106	−1.72498
$539$	−1.20513	−0.0519087
$540$	4.23221	0.182125
$541$	−34.8464	−1.49817	−0.749083	−	0.662477i	$-0.769505\pi$
$541$	−34.8464	−1.49817	−0.749083	+	0.662477i	$0.769505\pi$
$542$	−29.3748	−1.26176
$543$	3.79834	0.163002
$544$	−14.1258	−0.605638
$545$	13.7050	0.587059
$546$	−1.74579	−0.0747128
$547$	22.9740	0.982299	0.491149	−	0.871075i	$-0.336577\pi$
$547$	22.9740	0.982299	0.491149	+	0.871075i	$0.336577\pi$
$548$	37.4816	1.60113
$549$	−8.55605	−0.365163
$550$	0.462073	0.0197028
$551$	−4.40730	−0.187757
$552$	22.8083	0.970787
$553$	6.57701	0.279683
$554$	32.2727	1.37114
$555$	2.05917	0.0874070
$556$	−95.7887	−4.06234
$557$	−8.87404	−0.376005	−0.188003	−	0.982169i	$-0.560201\pi$
$557$	−8.87404	−0.376005	−0.188003	+	0.982169i	$0.560201\pi$
$558$	−2.49644	−0.105683
$559$	−2.02188	−0.0855165
$560$	3.80927	0.160971
$561$	1.06570	0.0449940
$562$	22.1544	0.934526
$563$	−43.0687	−1.81513	−0.907565	−	0.419912i	$-0.862061\pi$
$563$	−43.0687	−1.81513	−0.907565	+	0.419912i	$0.862061\pi$
$564$	−1.33980	−0.0564157
$565$	2.63432	0.110827
$566$	−44.2392	−1.85951
$567$	−0.699311	−0.0293683
$568$	17.2468	0.723660
$569$	46.5134	1.94994	0.974972	−	0.222329i	$-0.0713659\pi$
$569$	46.5134	1.94994	0.974972	+	0.222329i	$0.0713659\pi$
$570$	5.03851	0.211040
$571$	28.5468	1.19464	0.597322	−	0.802001i	$-0.296231\pi$
$571$	28.5468	1.19464	0.597322	+	0.802001i	$0.296231\pi$
$572$	−0.783351	−0.0327535
$573$	19.6088	0.819169
$574$	19.8591	0.828902
$575$	−4.09296	−0.170688
$576$	−4.76961	−0.198734
$577$	31.1325	1.29606	0.648032	−	0.761613i	$-0.275592\pi$
$577$	31.1325	1.29606	0.648032	+	0.761613i	$0.275592\pi$
$578$	40.3193	1.67706
$579$	−14.6160	−0.607420
$580$	9.24183	0.383746
$581$	−2.55503	−0.106000
$582$	45.8817	1.90186
$583$	1.41095	0.0584355
$584$	−67.8114	−2.80605
$585$	1.00000	0.0413449
$586$	−45.7570	−1.89020
$587$	−26.0522	−1.07529	−0.537644	−	0.843172i	$-0.680686\pi$
$587$	−26.0522	−1.07529	−0.537644	+	0.843172i	$0.680686\pi$
$588$	27.5558	1.13638
$589$	−2.01828	−0.0831618
$590$	−16.9353	−0.697215
$591$	10.3671	0.426444
$592$	11.2167	0.461002
$593$	2.49422	0.102425	0.0512127	−	0.998688i	$-0.483691\pi$
$593$	2.49422	0.102425	0.0512127	+	0.998688i	$0.483691\pi$
$594$	−0.462073	−0.0189591
$595$	−4.02640	−0.165066
$596$	1.00527	0.0411773
$597$	24.1171	0.987048
$598$	10.2178	0.417838
$599$	−38.3426	−1.56663	−0.783317	−	0.621622i	$-0.786474\pi$
$599$	−38.3426	−1.56663	−0.783317	+	0.621622i	$0.786474\pi$
$600$	−5.57257	−0.227499
$601$	−23.6406	−0.964319	−0.482159	−	0.876084i	$-0.660147\pi$
$601$	−23.6406	−0.964319	−0.482159	+	0.876084i	$0.660147\pi$
$602$	−3.52978	−0.143863
$603$	0.160637	0.00654166
$604$	−13.0672	−0.531698
$605$	10.9657	0.445821
$606$	−41.9928	−1.70584
$607$	6.16830	0.250364	0.125182	−	0.992134i	$-0.460049\pi$
$607$	6.16830	0.250364	0.125182	+	0.992134i	$0.460049\pi$
$608$	4.95162	0.200815
$609$	−1.52708	−0.0618804
$610$	21.3597	0.864828
$611$	−0.316572	−0.0128071
$612$	−24.3676	−0.985003
$613$	4.23954	0.171234	0.0856168	−	0.996328i	$-0.472714\pi$
$613$	4.23954	0.171234	0.0856168	+	0.996328i	$0.472714\pi$
$614$	64.6134	2.60758
$615$	−11.3754	−0.458701
$616$	−0.721300	−0.0290620
$617$	41.5943	1.67453	0.837263	−	0.546801i	$-0.184155\pi$
$617$	41.5943	1.67453	0.837263	+	0.546801i	$0.184155\pi$
$618$	−0.109303	−0.00439682
$619$	−1.06982	−0.0429996	−0.0214998	−	0.999769i	$-0.506844\pi$
$619$	−1.06982	−0.0429996	−0.0214998	+	0.999769i	$0.506844\pi$
$620$	4.23221	0.169970
$621$	4.09296	0.164245
$622$	6.43838	0.258156
$623$	3.79743	0.152141
$624$	5.44717	0.218061
$625$	1.00000	0.0400000
$626$	14.7535	0.589668
$627$	−0.373569	−0.0149189
$628$	43.1016	1.71994
$629$	−11.8560	−0.472731
$630$	1.74579	0.0695539
$631$	−8.03693	−0.319945	−0.159973	−	0.987121i	$-0.551141\pi$
$631$	−8.03693	−0.319945	−0.159973	+	0.987121i	$0.551141\pi$
$632$	−52.4099	−2.08475
$633$	7.79430	0.309796
$634$	14.4869	0.575348
$635$	−5.07536	−0.201409
$636$	−32.2618	−1.27926
$637$	6.51096	0.257974
$638$	−1.00902	−0.0399476
$639$	3.09495	0.122434
$640$	16.8138	0.664625
$641$	27.9586	1.10430	0.552149	−	0.833745i	$-0.313808\pi$
$641$	27.9586	1.10430	0.552149	+	0.833745i	$0.313808\pi$
$642$	−27.2337	−1.07483
$643$	12.6786	0.499994	0.249997	−	0.968247i	$-0.419570\pi$
$643$	12.6786	0.499994	0.249997	+	0.968247i	$0.419570\pi$
$644$	12.1137	0.477345
$645$	2.02188	0.0796115
$646$	−29.0101	−1.14139
$647$	36.3253	1.42809	0.714047	−	0.700098i	$-0.246860\pi$
$647$	36.3253	1.42809	0.714047	+	0.700098i	$0.246860\pi$
$648$	5.57257	0.218911
$649$	1.25563	0.0492877
$650$	−2.49644	−0.0979184
$651$	−0.699311	−0.0274082
$652$	84.0280	3.29079
$653$	−24.1932	−0.946755	−0.473377	−	0.880860i	$-0.656965\pi$
$653$	−24.1932	−0.946755	−0.473377	+	0.880860i	$0.656965\pi$
$654$	34.2138	1.33786
$655$	−10.4071	−0.406637
$656$	−61.9639	−2.41928
$657$	−12.1688	−0.474749
$658$	−0.552668	−0.0215452
$659$	42.9601	1.67349	0.836743	−	0.547595i	$-0.184457\pi$
$659$	42.9601	1.67349	0.836743	+	0.547595i	$0.184457\pi$
$660$	0.783351	0.0304919
$661$	−44.6677	−1.73737	−0.868687	−	0.495361i	$-0.835036\pi$
$661$	−44.6677	−1.73737	−0.868687	+	0.495361i	$0.835036\pi$
$662$	11.7016	0.454795
$663$	−5.75767	−0.223609
$664$	20.3601	0.790127
$665$	1.41141	0.0547320
$666$	5.14060	0.199194
$667$	8.93776	0.346072
$668$	−42.0420	−1.62666
$669$	8.37182	0.323673
$670$	−0.401021	−0.0154928
$671$	−1.58366	−0.0611366
$672$	1.71568	0.0661839
$673$	−33.8569	−1.30509	−0.652543	−	0.757752i	$-0.726298\pi$
$673$	−33.8569	−1.30509	−0.652543	+	0.757752i	$0.726298\pi$
$674$	66.5921	2.56503
$675$	−1.00000	−0.0384900
$676$	4.23221	0.162777
$677$	−6.39930	−0.245945	−0.122973	−	0.992410i	$-0.539243\pi$
$677$	−6.39930	−0.245945	−0.122973	+	0.992410i	$0.539243\pi$
$678$	6.57642	0.252566
$679$	12.8525	0.493235
$680$	32.0850	1.23040
$681$	−0.0214715	−0.000822790 0
$682$	−0.462073	−0.0176937
$683$	−12.1429	−0.464634	−0.232317	−	0.972640i	$-0.574631\pi$
$683$	−12.1429	−0.464634	−0.232317	+	0.972640i	$0.574631\pi$
$684$	8.54178	0.326603
$685$	−8.85627	−0.338381
$686$	23.5873	0.900567
$687$	−21.4483	−0.818303
$688$	11.0135	0.419887
$689$	−7.62292	−0.290410
$690$	−10.2178	−0.388986
$691$	33.0101	1.25576	0.627881	−	0.778309i	$-0.283922\pi$
$691$	33.0101	1.25576	0.627881	+	0.778309i	$0.283922\pi$
$692$	67.5150	2.56654
$693$	−0.129437	−0.00491692
$694$	57.0447	2.16539
$695$	22.6333	0.858528
$696$	12.1688	0.461256
$697$	65.4959	2.48083
$698$	−37.6133	−1.42369
$699$	15.9366	0.602778
$700$	−2.95963	−0.111864
$701$	32.6020	1.23136	0.615680	−	0.787996i	$-0.288881\pi$
$701$	32.6020	1.23136	0.615680	+	0.787996i	$0.288881\pi$
$702$	2.49644	0.0942220
$703$	4.15599	0.156746
$704$	−0.882820	−0.0332725
$705$	0.316572	0.0119228
$706$	43.5087	1.63747
$707$	−11.7632	−0.442400
$708$	−28.7104	−1.07900
$709$	4.61183	0.173201	0.0866004	−	0.996243i	$-0.472400\pi$
$709$	4.61183	0.173201	0.0866004	+	0.996243i	$0.472400\pi$
$710$	−7.72634	−0.289965
$711$	−9.40498	−0.352714
$712$	−30.2605	−1.13406
$713$	4.09296	0.153283
$714$	−10.0517	−0.376174
$715$	0.185093	0.00692208
$716$	9.31284	0.348037
$717$	12.7693	0.476877
$718$	18.6795	0.697113
$719$	17.6816	0.659412	0.329706	−	0.944084i	$-0.393050\pi$
$719$	17.6816	0.659412	0.329706	+	0.944084i	$0.393050\pi$
$720$	−5.44717	−0.203004
$721$	−0.0306184	−0.00114029
$722$	−37.2632	−1.38679
$723$	−13.5772	−0.504941
$724$	−16.0754	−0.597436
$725$	−2.18369	−0.0811002
$726$	27.3753	1.01599
$727$	46.0406	1.70755	0.853775	−	0.520642i	$-0.174307\pi$
$727$	46.0406	1.70755	0.853775	+	0.520642i	$0.174307\pi$
$728$	3.89696	0.144431
$729$	1.00000	0.0370370
$730$	30.3786	1.12436
$731$	−11.6413	−0.430570
$732$	36.2110	1.33840
$733$	−2.18990	−0.0808859	−0.0404430	−	0.999182i	$-0.512877\pi$
$733$	−2.18990	−0.0808859	−0.0404430	+	0.999182i	$0.512877\pi$
$734$	5.57874	0.205915
$735$	−6.51096	−0.240161
$736$	−10.0416	−0.370139
$737$	0.0297328	0.00109522
$738$	−28.3980	−1.04535
$739$	−13.4909	−0.496271	−0.248135	−	0.968725i	$-0.579818\pi$
$739$	−13.4909	−0.496271	−0.248135	+	0.968725i	$0.579818\pi$
$740$	−8.71485	−0.320364
$741$	2.01828	0.0741434
$742$	−13.3080	−0.488553
$743$	27.6186	1.01323	0.506615	−	0.862172i	$-0.330897\pi$
$743$	27.6186	1.01323	0.506615	+	0.862172i	$0.330897\pi$
$744$	5.57257	0.204300
$745$	−0.237528	−0.00870233
$746$	26.5159	0.970815
$747$	3.65363	0.133679
$748$	−4.51027	−0.164912
$749$	−7.62881	−0.278751
$750$	2.49644	0.0911571
$751$	4.72392	0.172378	0.0861891	−	0.996279i	$-0.472531\pi$
$751$	4.72392	0.172378	0.0861891	+	0.996279i	$0.472531\pi$
$752$	1.72442	0.0628832
$753$	25.1041	0.914845
$754$	5.45145	0.198530
$755$	3.08757	0.112368
$756$	2.95963	0.107641
$757$	9.00919	0.327445	0.163722	−	0.986506i	$-0.447650\pi$
$757$	9.00919	0.327445	0.163722	+	0.986506i	$0.447650\pi$
$758$	58.8322	2.13688
$759$	0.757577	0.0274983
$760$	−11.2470	−0.407972
$761$	−22.9728	−0.832763	−0.416381	−	0.909190i	$-0.636702\pi$
$761$	−22.9728	−0.832763	−0.416381	+	0.909190i	$0.636702\pi$
$762$	−12.6703	−0.458997
$763$	9.58408	0.346967
$764$	−82.9885	−3.00242
$765$	5.75767	0.208169
$766$	−21.7418	−0.785562
$767$	−6.78378	−0.244948
$768$	32.4355	1.17041
$769$	19.5406	0.704651	0.352325	−	0.935878i	$-0.385391\pi$
$769$	19.5406	0.704651	0.352325	+	0.935878i	$0.385391\pi$
$770$	0.323133	0.0116449
$771$	−28.3742	−1.02187
$772$	61.8580	2.22632
$773$	−52.2502	−1.87931	−0.939654	−	0.342127i	$-0.888853\pi$
$773$	−52.2502	−1.87931	−0.939654	+	0.342127i	$0.888853\pi$
$774$	5.04750	0.181429
$775$	−1.00000	−0.0359211
$776$	−102.417	−3.67657
$777$	1.44000	0.0516598
$778$	49.9869	1.79212
$779$	−22.9588	−0.822584
$780$	−4.23221	−0.151537
$781$	0.572852	0.0204983
$782$	58.8309	2.10379
$783$	2.18369	0.0780387
$784$	−35.4663	−1.26665
$785$	−10.1842	−0.363489
$786$	−25.9806	−0.926697
$787$	−21.8192	−0.777772	−0.388886	−	0.921286i	$-0.627140\pi$
$787$	−21.8192	−0.777772	−0.388886	+	0.921286i	$0.627140\pi$
$788$	−43.8756	−1.56300
$789$	−10.0719	−0.358567
$790$	23.4790	0.835344
$791$	1.84221	0.0655015
$792$	1.03144	0.0366507
$793$	8.55605	0.303834
$794$	41.5806	1.47564
$795$	7.62292	0.270357
$796$	−102.069	−3.61773
$797$	37.9359	1.34376	0.671879	−	0.740661i	$-0.265487\pi$
$797$	37.9359	1.34376	0.671879	+	0.740661i	$0.265487\pi$
$798$	3.52349	0.124730
$799$	−1.82271	−0.0644830
$800$	2.45339	0.0867403
$801$	−5.43025	−0.191868
$802$	−56.4495	−1.99330
$803$	−2.25235	−0.0794838
$804$	−0.679851	−0.0239765
$805$	−2.86226	−0.100881
$806$	2.49644	0.0879333
$807$	16.0270	0.564179
$808$	93.7368	3.29765
$809$	−36.9161	−1.29790	−0.648950	−	0.760831i	$-0.724792\pi$
$809$	−36.9161	−1.29790	−0.648950	+	0.760831i	$0.724792\pi$
$810$	−2.49644	−0.0877159
$811$	−18.2065	−0.639317	−0.319659	−	0.947533i	$-0.603568\pi$
$811$	−18.2065	−0.639317	−0.319659	+	0.947533i	$0.603568\pi$
$812$	6.46292	0.226804
$813$	11.7667	0.412676
$814$	0.951487	0.0333496
$815$	−19.8544	−0.695469
$816$	31.3630	1.09792
$817$	4.08072	0.142766
$818$	−42.1429	−1.47349
$819$	0.699311	0.0244359
$820$	48.1431	1.68123
$821$	25.5127	0.890399	0.445199	−	0.895432i	$-0.353133\pi$
$821$	25.5127	0.890399	0.445199	+	0.895432i	$0.353133\pi$
$822$	−22.1091	−0.771144
$823$	−11.4349	−0.398597	−0.199298	−	0.979939i	$-0.563866\pi$
$823$	−11.4349	−0.398597	−0.199298	+	0.979939i	$0.563866\pi$
$824$	0.243987	0.00849970
$825$	−0.185093	−0.00644410
$826$	−11.8430	−0.412072
$827$	−22.6936	−0.789135	−0.394567	−	0.918867i	$-0.629106\pi$
$827$	−22.6936	−0.789135	−0.394567	+	0.918867i	$0.629106\pi$
$828$	−17.3223	−0.601990
$829$	25.5653	0.887918	0.443959	−	0.896047i	$-0.353574\pi$
$829$	25.5653	0.887918	0.443959	+	0.896047i	$0.353574\pi$
$830$	−9.12108	−0.316597
$831$	−12.9275	−0.448450
$832$	4.76961	0.165357
$833$	37.4879	1.29888
$834$	56.5026	1.95652
$835$	9.93383	0.343774
$836$	1.58102	0.0546808
$837$	1.00000	0.0345651
$838$	−14.2219	−0.491286
$839$	31.2288	1.07814	0.539069	−	0.842262i	$-0.318776\pi$
$839$	31.2288	1.07814	0.539069	+	0.842262i	$0.318776\pi$
$840$	−3.89696	−0.134458
$841$	−24.2315	−0.835569
$842$	−69.3318	−2.38933
$843$	−8.87439	−0.305650
$844$	−32.9871	−1.13546
$845$	−1.00000	−0.0344010
$846$	0.790302	0.0271712
$847$	7.66847	0.263492
$848$	41.5234	1.42592
$849$	17.7209	0.608180
$850$	−14.3737	−0.493013
$851$	−8.42811	−0.288912
$852$	−13.0985	−0.448746
$853$	35.4275	1.21302	0.606508	−	0.795077i	$-0.292570\pi$
$853$	35.4275	1.21302	0.606508	+	0.795077i	$0.292570\pi$
$854$	14.9371	0.511136
$855$	−2.01828	−0.0690237
$856$	60.7913	2.07781
$857$	12.7689	0.436178	0.218089	−	0.975929i	$-0.430018\pi$
$857$	12.7689	0.436178	0.218089	+	0.975929i	$0.430018\pi$
$858$	0.462073	0.0157749
$859$	−26.0342	−0.888275	−0.444137	−	0.895959i	$-0.646490\pi$
$859$	−26.0342	−0.888275	−0.444137	+	0.895959i	$0.646490\pi$
$860$	−8.55703	−0.291792
$861$	−7.95496	−0.271104
$862$	55.2816	1.88290
$863$	38.5861	1.31349	0.656744	−	0.754114i	$-0.271933\pi$
$863$	38.5861	1.31349	0.656744	+	0.754114i	$0.271933\pi$
$864$	−2.45339	−0.0834659
$865$	−15.9527	−0.542407
$866$	8.81439	0.299525
$867$	−16.1507	−0.548507
$868$	2.95963	0.100456
$869$	−1.74079	−0.0590523
$870$	−5.45145	−0.184822
$871$	−0.160637	−0.00544299
$872$	−76.3722	−2.58629
$873$	−18.3788	−0.622030
$874$	−20.6224	−0.697565
$875$	0.699311	0.0236410
$876$	51.5008	1.74005
$877$	18.5010	0.624735	0.312368	−	0.949961i	$-0.398878\pi$
$877$	18.5010	0.624735	0.312368	+	0.949961i	$0.398878\pi$
$878$	69.8080	2.35591
$879$	18.3289	0.618218
$880$	−1.00823	−0.0339875
$881$	7.76275	0.261534	0.130767	−	0.991413i	$-0.458256\pi$
$881$	7.76275	0.261534	0.130767	+	0.991413i	$0.458256\pi$
$882$	−16.2542	−0.547308
$883$	−18.4634	−0.621343	−0.310672	−	0.950517i	$-0.600554\pi$
$883$	−18.4634	−0.621343	−0.310672	+	0.950517i	$0.600554\pi$
$884$	24.3676	0.819572
$885$	6.78378	0.228034
$886$	0.819703	0.0275385
$887$	−45.8879	−1.54077	−0.770383	−	0.637582i	$-0.779935\pi$
$887$	−45.8879	−1.54077	−0.770383	+	0.637582i	$0.779935\pi$
$888$	−11.4749	−0.385072
$889$	−3.54926	−0.119038
$890$	13.5563	0.454408
$891$	0.185093	0.00620084
$892$	−35.4313	−1.18633
$893$	0.638931	0.0213810
$894$	−0.592973	−0.0198320
$895$	−2.20047	−0.0735536
$896$	11.7581	0.392810
$897$	−4.09296	−0.136660
$898$	47.0583	1.57036
$899$	2.18369	0.0728302
$900$	4.23221	0.141074
$901$	−43.8902	−1.46220
$902$	−5.25627	−0.175015
$903$	1.41393	0.0470525
$904$	−14.6799	−0.488248
$905$	3.79834	0.126261
$906$	7.70792	0.256079
$907$	−25.9416	−0.861378	−0.430689	−	0.902500i	$-0.641729\pi$
$907$	−25.9416	−0.861378	−0.430689	+	0.902500i	$0.641729\pi$
$908$	0.0908719	0.00301569
$909$	16.8211	0.557920
$910$	−1.74579	−0.0578723
$911$	−26.0450	−0.862910	−0.431455	−	0.902134i	$-0.642000\pi$
$911$	−26.0450	−0.862910	−0.431455	+	0.902134i	$0.642000\pi$
$912$	−10.9939	−0.364045
$913$	0.676261	0.0223810
$914$	−32.1954	−1.06493
$915$	−8.55605	−0.282854
$916$	90.7736	2.99924
$917$	−7.27778	−0.240333
$918$	14.3737	0.474402
$919$	51.7883	1.70834	0.854170	−	0.519994i	$-0.174066\pi$
$919$	51.7883	1.70834	0.854170	+	0.519994i	$0.174066\pi$
$920$	22.8083	0.751968
$921$	−25.8822	−0.852848
$922$	−21.1473	−0.696449
$923$	−3.09495	−0.101871
$924$	0.547806	0.0180215
$925$	2.05917	0.0677052
$926$	−42.4264	−1.39422
$927$	0.0437836	0.00143804
$928$	−5.35744	−0.175867
$929$	−7.83874	−0.257181	−0.128590	−	0.991698i	$-0.541045\pi$
$929$	−7.83874	−0.257181	−0.128590	+	0.991698i	$0.541045\pi$
$930$	−2.49644	−0.0818615
$931$	−13.1409	−0.430677
$932$	−67.4471	−2.20930
$933$	−2.57903	−0.0844335
$934$	−34.7675	−1.13763
$935$	1.06570	0.0348522
$936$	−5.57257	−0.182145
$937$	−52.1638	−1.70412	−0.852059	−	0.523446i	$-0.824646\pi$
$937$	−52.1638	−1.70412	−0.852059	+	0.523446i	$0.824646\pi$
$938$	−0.280439	−0.00915665
$939$	−5.90981	−0.192859
$940$	−1.33980	−0.0436994
$941$	6.51608	0.212418	0.106209	−	0.994344i	$-0.466129\pi$
$941$	6.51608	0.212418	0.106209	+	0.994344i	$0.466129\pi$
$942$	−25.4242	−0.828365
$943$	46.5592	1.51617
$944$	36.9524	1.20270
$945$	−0.699311	−0.0227486
$946$	0.934256	0.0303753
$947$	3.68145	0.119631	0.0598156	−	0.998209i	$-0.480949\pi$
$947$	3.68145	0.119631	0.0598156	+	0.998209i	$0.480949\pi$
$948$	39.8038	1.29277
$949$	12.1688	0.395015
$950$	5.03851	0.163471
$951$	−5.80302	−0.188176
$952$	22.4374	0.727201
$953$	32.6588	1.05792	0.528961	−	0.848646i	$-0.322582\pi$
$953$	32.6588	1.05792	0.528961	+	0.848646i	$0.322582\pi$
$954$	19.0302	0.616124
$955$	19.6088	0.634525
$956$	−54.0421	−1.74785
$957$	0.404185	0.0130655
$958$	−13.7697	−0.444878
$959$	−6.19329	−0.199992
$960$	−4.76961	−0.153939
$961$	1.00000	0.0322581
$962$	−5.14060	−0.165740
$963$	10.9090	0.351538
$964$	57.4614	1.85071
$965$	−14.6160	−0.470506
$966$	−7.14545	−0.229901
$967$	18.7051	0.601517	0.300758	−	0.953700i	$-0.402760\pi$
$967$	18.7051	0.601517	0.300758	+	0.953700i	$0.402760\pi$
$968$	−61.1074	−1.96407
$969$	11.6206	0.373307
$970$	45.8817	1.47317
$971$	−0.540281	−0.0173385	−0.00866923	−	0.999962i	$-0.502760\pi$
$971$	−0.540281	−0.0173385	−0.00866923	+	0.999962i	$0.502760\pi$
$972$	−4.23221	−0.135748
$973$	15.8277	0.507413
$974$	−71.2539	−2.28312
$975$	1.00000	0.0320256
$976$	−46.6063	−1.49183
$977$	−26.7210	−0.854879	−0.427440	−	0.904044i	$-0.640584\pi$
$977$	−26.7210	−0.854879	−0.427440	+	0.904044i	$0.640584\pi$
$978$	−49.5653	−1.58492
$979$	−1.00510	−0.0321231
$980$	27.5558	0.880236
$981$	−13.7050	−0.437568
$982$	74.2117	2.36819
$983$	−21.4666	−0.684677	−0.342339	−	0.939577i	$-0.611219\pi$
$983$	−21.4666	−0.684677	−0.342339	+	0.939577i	$0.611219\pi$
$984$	63.3904	2.02081
$985$	10.3671	0.330322
$986$	31.3876	0.999586
$987$	0.221382	0.00704668
$988$	−8.54178	−0.271750
$989$	−8.27549	−0.263145
$990$	−0.462073	−0.0146856
$991$	−39.8654	−1.26637	−0.633183	−	0.774002i	$-0.718252\pi$
$991$	−39.8654	−1.26637	−0.633183	+	0.774002i	$0.718252\pi$
$992$	−2.45339	−0.0778951
$993$	−4.68731	−0.148747
$994$	−5.40312	−0.171377
$995$	24.1171	0.764564
$996$	−15.4629	−0.489962
$997$	42.9913	1.36155	0.680774	−	0.732494i	$-0.261644\pi$
$997$	42.9913	1.36155	0.680774	+	0.732494i	$0.261644\pi$
$998$	−16.7768	−0.531062
$999$	−2.05917	−0.0651493

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.w.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.w.1.11	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+2.49644 q^{2} -1.00000 q^{3} +4.23221 q^{4} -1.00000 q^{5} -2.49644 q^{6} -0.699311 q^{7} +5.57257 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.49644 q^{2} -1.00000 q^{3} +4.23221 q^{4} -1.00000 q^{5} -2.49644 q^{6} -0.699311 q^{7} +5.57257 q^{8} +1.00000 q^{9} -2.49644 q^{10} +0.185093 q^{11} -4.23221 q^{12} -1.00000 q^{13} -1.74579 q^{14} +1.00000 q^{15} +5.44717 q^{16} -5.75767 q^{17} +2.49644 q^{18} +2.01828 q^{19} -4.23221 q^{20} +0.699311 q^{21} +0.462073 q^{22} -4.09296 q^{23} -5.57257 q^{24} +1.00000 q^{25} -2.49644 q^{26} -1.00000 q^{27} -2.95963 q^{28} -2.18369 q^{29} +2.49644 q^{30} -1.00000 q^{31} +2.45339 q^{32} -0.185093 q^{33} -14.3737 q^{34} +0.699311 q^{35} +4.23221 q^{36} +2.05917 q^{37} +5.03851 q^{38} +1.00000 q^{39} -5.57257 q^{40} -11.3754 q^{41} +1.74579 q^{42} +2.02188 q^{43} +0.783351 q^{44} -1.00000 q^{45} -10.2178 q^{46} +0.316572 q^{47} -5.44717 q^{48} -6.51096 q^{49} +2.49644 q^{50} +5.75767 q^{51} -4.23221 q^{52} +7.62292 q^{53} -2.49644 q^{54} -0.185093 q^{55} -3.89696 q^{56} -2.01828 q^{57} -5.45145 q^{58} +6.78378 q^{59} +4.23221 q^{60} -8.55605 q^{61} -2.49644 q^{62} -0.699311 q^{63} -4.76961 q^{64} +1.00000 q^{65} -0.462073 q^{66} +0.160637 q^{67} -24.3676 q^{68} +4.09296 q^{69} +1.74579 q^{70} +3.09495 q^{71} +5.57257 q^{72} -12.1688 q^{73} +5.14060 q^{74} -1.00000 q^{75} +8.54178 q^{76} -0.129437 q^{77} +2.49644 q^{78} -9.40498 q^{79} -5.44717 q^{80} +1.00000 q^{81} -28.3980 q^{82} +3.65363 q^{83} +2.95963 q^{84} +5.75767 q^{85} +5.04750 q^{86} +2.18369 q^{87} +1.03144 q^{88} -5.43025 q^{89} -2.49644 q^{90} +0.699311 q^{91} -17.3223 q^{92} +1.00000 q^{93} +0.790302 q^{94} -2.01828 q^{95} -2.45339 q^{96} -18.3788 q^{97} -16.2542 q^{98} +0.185093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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