LMFDB - Embedded newform 6045.2.a.w.1.10

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			1.10
Root			$2.41951$ 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)

$f(q)$	$=$	$q+2.41951 q^{2} -1.00000 q^{3} +3.85401 q^{4} -1.00000 q^{5} -2.41951 q^{6} +1.95823 q^{7} +4.48578 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.41951 q^{2} -1.00000 q^{3} +3.85401 q^{4} -1.00000 q^{5} -2.41951 q^{6} +1.95823 q^{7} +4.48578 q^{8} +1.00000 q^{9} -2.41951 q^{10} -4.98736 q^{11} -3.85401 q^{12} -1.00000 q^{13} +4.73794 q^{14} +1.00000 q^{15} +3.14535 q^{16} +0.501580 q^{17} +2.41951 q^{18} -5.42639 q^{19} -3.85401 q^{20} -1.95823 q^{21} -12.0669 q^{22} +3.81151 q^{23} -4.48578 q^{24} +1.00000 q^{25} -2.41951 q^{26} -1.00000 q^{27} +7.54701 q^{28} -2.52132 q^{29} +2.41951 q^{30} -1.00000 q^{31} -1.36136 q^{32} +4.98736 q^{33} +1.21357 q^{34} -1.95823 q^{35} +3.85401 q^{36} -6.95072 q^{37} -13.1292 q^{38} +1.00000 q^{39} -4.48578 q^{40} +9.13206 q^{41} -4.73794 q^{42} +1.64422 q^{43} -19.2213 q^{44} -1.00000 q^{45} +9.22198 q^{46} -8.17075 q^{47} -3.14535 q^{48} -3.16535 q^{49} +2.41951 q^{50} -0.501580 q^{51} -3.85401 q^{52} -3.24881 q^{53} -2.41951 q^{54} +4.98736 q^{55} +8.78416 q^{56} +5.42639 q^{57} -6.10035 q^{58} +2.12934 q^{59} +3.85401 q^{60} -6.92486 q^{61} -2.41951 q^{62} +1.95823 q^{63} -9.58452 q^{64} +1.00000 q^{65} +12.0669 q^{66} -7.22598 q^{67} +1.93309 q^{68} -3.81151 q^{69} -4.73794 q^{70} -0.733327 q^{71} +4.48578 q^{72} -5.16672 q^{73} -16.8173 q^{74} -1.00000 q^{75} -20.9133 q^{76} -9.76637 q^{77} +2.41951 q^{78} -2.17614 q^{79} -3.14535 q^{80} +1.00000 q^{81} +22.0951 q^{82} -6.55104 q^{83} -7.54701 q^{84} -0.501580 q^{85} +3.97819 q^{86} +2.52132 q^{87} -22.3722 q^{88} -5.01394 q^{89} -2.41951 q^{90} -1.95823 q^{91} +14.6896 q^{92} +1.00000 q^{93} -19.7692 q^{94} +5.42639 q^{95} +1.36136 q^{96} +11.7894 q^{97} -7.65859 q^{98} -4.98736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.41951	1.71085	0.855424	−	0.517928i	$-0.173296\pi$
$2$	2.41951	1.71085	0.855424	+	0.517928i	$0.173296\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.85401	1.92700
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.41951	−0.987759
$7$	1.95823	0.740140	0.370070	−	0.929004i	$-0.379334\pi$
$7$	1.95823	0.740140	0.370070	+	0.929004i	$0.379334\pi$
$8$	4.48578	1.58596
$9$	1.00000	0.333333
$10$	−2.41951	−0.765115
$11$	−4.98736	−1.50374	−0.751872	−	0.659309i	$-0.770849\pi$
$11$	−4.98736	−1.50374	−0.751872	+	0.659309i	$0.770849\pi$
$12$	−3.85401	−1.11256
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.73794	1.26627
$15$	1.00000	0.258199
$16$	3.14535	0.786338
$17$	0.501580	0.121651	0.0608255	−	0.998148i	$-0.480627\pi$
$17$	0.501580	0.121651	0.0608255	+	0.998148i	$0.480627\pi$
$18$	2.41951	0.570283
$19$	−5.42639	−1.24490	−0.622449	−	0.782660i	$-0.713862\pi$
$19$	−5.42639	−1.24490	−0.622449	+	0.782660i	$0.713862\pi$
$20$	−3.85401	−0.861782
$21$	−1.95823	−0.427320
$22$	−12.0669	−2.57268
$23$	3.81151	0.794755	0.397378	−	0.917655i	$-0.369920\pi$
$23$	3.81151	0.794755	0.397378	+	0.917655i	$0.369920\pi$
$24$	−4.48578	−0.915656
$25$	1.00000	0.200000
$26$	−2.41951	−0.474504
$27$	−1.00000	−0.192450
$28$	7.54701	1.42625
$29$	−2.52132	−0.468198	−0.234099	−	0.972213i	$-0.575214\pi$
$29$	−2.52132	−0.468198	−0.234099	+	0.972213i	$0.575214\pi$
$30$	2.41951	0.441739
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.36136	−0.240657
$33$	4.98736	0.868188
$34$	1.21357	0.208126
$35$	−1.95823	−0.331000
$36$	3.85401	0.642334
$37$	−6.95072	−1.14269	−0.571345	−	0.820710i	$-0.693578\pi$
$37$	−6.95072	−1.14269	−0.571345	+	0.820710i	$0.693578\pi$
$38$	−13.1292	−2.12983
$39$	1.00000	0.160128
$40$	−4.48578	−0.709264
$41$	9.13206	1.42619	0.713094	−	0.701068i	$-0.247293\pi$
$41$	9.13206	1.42619	0.713094	+	0.701068i	$0.247293\pi$
$42$	−4.73794	−0.731079
$43$	1.64422	0.250741	0.125370	−	0.992110i	$-0.459988\pi$
$43$	1.64422	0.250741	0.125370	+	0.992110i	$0.459988\pi$
$44$	−19.2213	−2.89772
$45$	−1.00000	−0.149071
$46$	9.22198	1.35971
$47$	−8.17075	−1.19183	−0.595913	−	0.803049i	$-0.703210\pi$
$47$	−8.17075	−1.19183	−0.595913	+	0.803049i	$0.703210\pi$
$48$	−3.14535	−0.453992
$49$	−3.16535	−0.452193
$50$	2.41951	0.342170
$51$	−0.501580	−0.0702352
$52$	−3.85401	−0.534455
$53$	−3.24881	−0.446259	−0.223129	−	0.974789i	$-0.571627\pi$
$53$	−3.24881	−0.446259	−0.223129	+	0.974789i	$0.571627\pi$
$54$	−2.41951	−0.329253
$55$	4.98736	0.672495
$56$	8.78416	1.17383
$57$	5.42639	0.718743
$58$	−6.10035	−0.801016
$59$	2.12934	0.277216	0.138608	−	0.990347i	$-0.455737\pi$
$59$	2.12934	0.277216	0.138608	+	0.990347i	$0.455737\pi$
$60$	3.85401	0.497550
$61$	−6.92486	−0.886638	−0.443319	−	0.896364i	$-0.646199\pi$
$61$	−6.92486	−0.886638	−0.443319	+	0.896364i	$0.646199\pi$
$62$	−2.41951	−0.307277
$63$	1.95823	0.246713
$64$	−9.58452	−1.19807
$65$	1.00000	0.124035
$66$	12.0669	1.48534
$67$	−7.22598	−0.882793	−0.441397	−	0.897312i	$-0.645517\pi$
$67$	−7.22598	−0.882793	−0.441397	+	0.897312i	$0.645517\pi$
$68$	1.93309	0.234422
$69$	−3.81151	−0.458852
$70$	−4.73794	−0.566292
$71$	−0.733327	−0.0870299	−0.0435149	−	0.999053i	$-0.513856\pi$
$71$	−0.733327	−0.0870299	−0.0435149	+	0.999053i	$0.513856\pi$
$72$	4.48578	0.528654
$73$	−5.16672	−0.604719	−0.302359	−	0.953194i	$-0.597774\pi$
$73$	−5.16672	−0.604719	−0.302359	+	0.953194i	$0.597774\pi$
$74$	−16.8173	−1.95497
$75$	−1.00000	−0.115470
$76$	−20.9133	−2.39892
$77$	−9.76637	−1.11298
$78$	2.41951	0.273955
$79$	−2.17614	−0.244835	−0.122417	−	0.992479i	$-0.539065\pi$
$79$	−2.17614	−0.244835	−0.122417	+	0.992479i	$0.539065\pi$
$80$	−3.14535	−0.351661
$81$	1.00000	0.111111
$82$	22.0951	2.43999
$83$	−6.55104	−0.719070	−0.359535	−	0.933132i	$-0.617065\pi$
$83$	−6.55104	−0.719070	−0.359535	+	0.933132i	$0.617065\pi$
$84$	−7.54701	−0.823447
$85$	−0.501580	−0.0544039
$86$	3.97819	0.428979
$87$	2.52132	0.270314
$88$	−22.3722	−2.38488
$89$	−5.01394	−0.531476	−0.265738	−	0.964045i	$-0.585616\pi$
$89$	−5.01394	−0.531476	−0.265738	+	0.964045i	$0.585616\pi$
$90$	−2.41951	−0.255038
$91$	−1.95823	−0.205278
$92$	14.6896	1.53150
$93$	1.00000	0.103695
$94$	−19.7692	−2.03904
$95$	5.42639	0.556736
$96$	1.36136	0.138943
$97$	11.7894	1.19704	0.598519	−	0.801109i	$-0.295756\pi$
$97$	11.7894	1.19704	0.598519	+	0.801109i	$0.295756\pi$
$98$	−7.65859	−0.773635
$99$	−4.98736	−0.501248
$100$	3.85401	0.385401
$101$	−6.40747	−0.637567	−0.318783	−	0.947828i	$-0.603274\pi$
$101$	−6.40747	−0.637567	−0.318783	+	0.947828i	$0.603274\pi$
$102$	−1.21357	−0.120162
$103$	−3.36259	−0.331326	−0.165663	−	0.986182i	$-0.552976\pi$
$103$	−3.36259	−0.331326	−0.165663	+	0.986182i	$0.552976\pi$
$104$	−4.48578	−0.439867
$105$	1.95823	0.191103
$106$	−7.86052	−0.763481
$107$	−8.85861	−0.856394	−0.428197	−	0.903685i	$-0.640851\pi$
$107$	−8.85861	−0.856394	−0.428197	+	0.903685i	$0.640851\pi$
$108$	−3.85401	−0.370852
$109$	13.3440	1.27812	0.639061	−	0.769156i	$-0.279323\pi$
$109$	13.3440	1.27812	0.639061	+	0.769156i	$0.279323\pi$
$110$	12.0669	1.15054
$111$	6.95072	0.659733
$112$	6.15931	0.582000
$113$	2.18635	0.205675	0.102837	−	0.994698i	$-0.467208\pi$
$113$	2.18635	0.205675	0.102837	+	0.994698i	$0.467208\pi$
$114$	13.1292	1.22966
$115$	−3.81151	−0.355425
$116$	−9.71719	−0.902219
$117$	−1.00000	−0.0924500
$118$	5.15195	0.474275
$119$	0.982206	0.0900386
$120$	4.48578	0.409494
$121$	13.8737	1.26125
$122$	−16.7547	−1.51690
$123$	−9.13206	−0.823410
$124$	−3.85401	−0.346100
$125$	−1.00000	−0.0894427
$126$	4.73794	0.422089
$127$	14.4864	1.28546	0.642731	−	0.766092i	$-0.277801\pi$
$127$	14.4864	1.28546	0.642731	+	0.766092i	$0.277801\pi$
$128$	−20.4671	−1.80905
$129$	−1.64422	−0.144765
$130$	2.41951	0.212205
$131$	6.75438	0.590133	0.295067	−	0.955477i	$-0.404658\pi$
$131$	6.75438	0.590133	0.295067	+	0.955477i	$0.404658\pi$
$132$	19.2213	1.67300
$133$	−10.6261	−0.921399
$134$	−17.4833	−1.51033
$135$	1.00000	0.0860663
$136$	2.24997	0.192934
$137$	−14.1498	−1.20890	−0.604448	−	0.796644i	$-0.706606\pi$
$137$	−14.1498	−1.20890	−0.604448	+	0.796644i	$0.706606\pi$
$138$	−9.22198	−0.785027
$139$	−14.3358	−1.21595	−0.607975	−	0.793956i	$-0.708018\pi$
$139$	−14.3358	−1.21595	−0.607975	+	0.793956i	$0.708018\pi$
$140$	−7.54701	−0.637839
$141$	8.17075	0.688102
$142$	−1.77429	−0.148895
$143$	4.98736	0.417064
$144$	3.14535	0.262113
$145$	2.52132	0.209384
$146$	−12.5009	−1.03458
$147$	3.16535	0.261074
$148$	−26.7881	−2.20197
$149$	20.9355	1.71510	0.857551	−	0.514399i	$-0.171985\pi$
$149$	20.9355	1.71510	0.857551	+	0.514399i	$0.171985\pi$
$150$	−2.41951	−0.197552
$151$	−0.513113	−0.0417565	−0.0208783	−	0.999782i	$-0.506646\pi$
$151$	−0.513113	−0.0417565	−0.0208783	+	0.999782i	$0.506646\pi$
$152$	−24.3416	−1.97436
$153$	0.501580	0.0405503
$154$	−23.6298	−1.90414
$155$	1.00000	0.0803219
$156$	3.85401	0.308567
$157$	5.31106	0.423869	0.211934	−	0.977284i	$-0.432024\pi$
$157$	5.31106	0.423869	0.211934	+	0.977284i	$0.432024\pi$
$158$	−5.26518	−0.418875
$159$	3.24881	0.257648
$160$	1.36136	0.107625
$161$	7.46380	0.588230
$162$	2.41951	0.190094
$163$	−7.99503	−0.626219	−0.313109	−	0.949717i	$-0.601371\pi$
$163$	−7.99503	−0.626219	−0.313109	+	0.949717i	$0.601371\pi$
$164$	35.1950	2.74827
$165$	−4.98736	−0.388265
$166$	−15.8503	−1.23022
$167$	13.8823	1.07425	0.537123	−	0.843504i	$-0.319511\pi$
$167$	13.8823	1.07425	0.537123	+	0.843504i	$0.319511\pi$
$168$	−8.78416	−0.677713
$169$	1.00000	0.0769231
$170$	−1.21357	−0.0930769
$171$	−5.42639	−0.414966
$172$	6.33682	0.483178
$173$	−18.8233	−1.43111	−0.715554	−	0.698558i	$-0.753826\pi$
$173$	−18.8233	−1.43111	−0.715554	+	0.698558i	$0.753826\pi$
$174$	6.10035	0.462467
$175$	1.95823	0.148028
$176$	−15.6870	−1.18245
$177$	−2.12934	−0.160051
$178$	−12.1313	−0.909276
$179$	10.7464	0.803225	0.401612	−	0.915810i	$-0.368450\pi$
$179$	10.7464	0.803225	0.401612	+	0.915810i	$0.368450\pi$
$180$	−3.85401	−0.287261
$181$	−6.32219	−0.469925	−0.234962	−	0.972004i	$-0.575497\pi$
$181$	−6.32219	−0.469925	−0.234962	+	0.972004i	$0.575497\pi$
$182$	−4.73794	−0.351199
$183$	6.92486	0.511901
$184$	17.0976	1.26045
$185$	6.95072	0.511027
$186$	2.41951	0.177407
$187$	−2.50156	−0.182932
$188$	−31.4901	−2.29665
$189$	−1.95823	−0.142440
$190$	13.1292	0.952491
$191$	10.1191	0.732190	0.366095	−	0.930578i	$-0.380695\pi$
$191$	10.1191	0.732190	0.366095	+	0.930578i	$0.380695\pi$
$192$	9.58452	0.691703
$193$	−2.43654	−0.175386	−0.0876932	−	0.996148i	$-0.527950\pi$
$193$	−2.43654	−0.175386	−0.0876932	+	0.996148i	$0.527950\pi$
$194$	28.5246	2.04795
$195$	−1.00000	−0.0716115
$196$	−12.1993	−0.871378
$197$	15.8225	1.12730	0.563652	−	0.826013i	$-0.309396\pi$
$197$	15.8225	1.12730	0.563652	+	0.826013i	$0.309396\pi$
$198$	−12.0669	−0.857560
$199$	−15.1127	−1.07131	−0.535655	−	0.844437i	$-0.679935\pi$
$199$	−15.1127	−1.07131	−0.535655	+	0.844437i	$0.679935\pi$
$200$	4.48578	0.317192
$201$	7.22598	0.509681
$202$	−15.5029	−1.09078
$203$	−4.93732	−0.346532
$204$	−1.93309	−0.135343
$205$	−9.13206	−0.637811
$206$	−8.13581	−0.566849
$207$	3.81151	0.264918
$208$	−3.14535	−0.218091
$209$	27.0633	1.87201
$210$	4.73794	0.326949
$211$	12.5209	0.861977	0.430989	−	0.902357i	$-0.358165\pi$
$211$	12.5209	0.861977	0.430989	+	0.902357i	$0.358165\pi$
$212$	−12.5209	−0.859942
$213$	0.733327	0.0502467
$214$	−21.4335	−1.46516
$215$	−1.64422	−0.112135
$216$	−4.48578	−0.305219
$217$	−1.95823	−0.132933
$218$	32.2859	2.18667
$219$	5.16672	0.349135
$220$	19.2213	1.29590
$221$	−0.501580	−0.0337399
$222$	16.8173	1.12870
$223$	−17.2541	−1.15542	−0.577711	−	0.816242i	$-0.696054\pi$
$223$	−17.2541	−1.15542	−0.577711	+	0.816242i	$0.696054\pi$
$224$	−2.66585	−0.178120
$225$	1.00000	0.0666667
$226$	5.28989	0.351878
$227$	−6.00736	−0.398722	−0.199361	−	0.979926i	$-0.563887\pi$
$227$	−6.00736	−0.398722	−0.199361	+	0.979926i	$0.563887\pi$
$228$	20.9133	1.38502
$229$	−2.94853	−0.194844	−0.0974222	−	0.995243i	$-0.531060\pi$
$229$	−2.94853	−0.194844	−0.0974222	+	0.995243i	$0.531060\pi$
$230$	−9.22198	−0.608079
$231$	9.76637	0.642580
$232$	−11.3101	−0.742544
$233$	−1.83791	−0.120405	−0.0602027	−	0.998186i	$-0.519175\pi$
$233$	−1.83791	−0.120405	−0.0602027	+	0.998186i	$0.519175\pi$
$234$	−2.41951	−0.158168
$235$	8.17075	0.533001
$236$	8.20649	0.534197
$237$	2.17614	0.141356
$238$	2.37645	0.154042
$239$	−7.91169	−0.511765	−0.255882	−	0.966708i	$-0.582366\pi$
$239$	−7.91169	−0.511765	−0.255882	+	0.966708i	$0.582366\pi$
$240$	3.14535	0.203032
$241$	−6.54282	−0.421460	−0.210730	−	0.977544i	$-0.567584\pi$
$241$	−6.54282	−0.421460	−0.210730	+	0.977544i	$0.567584\pi$
$242$	33.5676	2.15781
$243$	−1.00000	−0.0641500
$244$	−26.6885	−1.70855
$245$	3.16535	0.202227
$246$	−22.0951	−1.40873
$247$	5.42639	0.345273
$248$	−4.48578	−0.284847
$249$	6.55104	0.415155
$250$	−2.41951	−0.153023
$251$	−11.0997	−0.700608	−0.350304	−	0.936636i	$-0.613922\pi$
$251$	−11.0997	−0.700608	−0.350304	+	0.936636i	$0.613922\pi$
$252$	7.54701	0.475417
$253$	−19.0094	−1.19511
$254$	35.0500	2.19923
$255$	0.501580	0.0314101
$256$	−30.3512	−1.89695
$257$	3.18213	0.198496	0.0992478	−	0.995063i	$-0.468356\pi$
$257$	3.18213	0.198496	0.0992478	+	0.995063i	$0.468356\pi$
$258$	−3.97819	−0.247671
$259$	−13.6111	−0.845751
$260$	3.85401	0.239015
$261$	−2.52132	−0.156066
$262$	16.3423	1.00963
$263$	−19.1204	−1.17902	−0.589508	−	0.807762i	$-0.700679\pi$
$263$	−19.1204	−1.17902	−0.589508	+	0.807762i	$0.700679\pi$
$264$	22.3722	1.37691
$265$	3.24881	0.199573
$266$	−25.7099	−1.57637
$267$	5.01394	0.306848
$268$	−27.8490	−1.70115
$269$	−13.6510	−0.832318	−0.416159	−	0.909292i	$-0.636624\pi$
$269$	−13.6510	−0.832318	−0.416159	+	0.909292i	$0.636624\pi$
$270$	2.41951	0.147246
$271$	7.37202	0.447819	0.223909	−	0.974610i	$-0.428118\pi$
$271$	7.37202	0.447819	0.223909	+	0.974610i	$0.428118\pi$
$272$	1.57764	0.0956587
$273$	1.95823	0.118517
$274$	−34.2354	−2.06824
$275$	−4.98736	−0.300749
$276$	−14.6896	−0.884210
$277$	−17.6793	−1.06225	−0.531125	−	0.847294i	$-0.678230\pi$
$277$	−17.6793	−1.06225	−0.531125	+	0.847294i	$0.678230\pi$
$278$	−34.6857	−2.08031
$279$	−1.00000	−0.0598684
$280$	−8.78416	−0.524954
$281$	14.9685	0.892948	0.446474	−	0.894796i	$-0.352679\pi$
$281$	14.9685	0.892948	0.446474	+	0.894796i	$0.352679\pi$
$282$	19.7692	1.17724
$283$	−3.79941	−0.225851	−0.112926	−	0.993603i	$-0.536022\pi$
$283$	−3.79941	−0.225851	−0.112926	+	0.993603i	$0.536022\pi$
$284$	−2.82625	−0.167707
$285$	−5.42639	−0.321432
$286$	12.0669	0.713533
$287$	17.8826	1.05558
$288$	−1.36136	−0.0802190
$289$	−16.7484	−0.985201
$290$	6.10035	0.358225
$291$	−11.7894	−0.691110
$292$	−19.9126	−1.16530
$293$	21.2921	1.24390	0.621948	−	0.783059i	$-0.286342\pi$
$293$	21.2921	1.24390	0.621948	+	0.783059i	$0.286342\pi$
$294$	7.65859	0.446658
$295$	−2.12934	−0.123975
$296$	−31.1794	−1.81226
$297$	4.98736	0.289396
$298$	50.6535	2.93428
$299$	−3.81151	−0.220425
$300$	−3.85401	−0.222511
$301$	3.21975	0.185583
$302$	−1.24148	−0.0714391
$303$	6.40747	0.368099
$304$	−17.0679	−0.978911
$305$	6.92486	0.396517
$306$	1.21357	0.0693754
$307$	−7.60563	−0.434076	−0.217038	−	0.976163i	$-0.569640\pi$
$307$	−7.60563	−0.434076	−0.217038	+	0.976163i	$0.569640\pi$
$308$	−37.6396	−2.14472
$309$	3.36259	0.191291
$310$	2.41951	0.137419
$311$	−5.59454	−0.317238	−0.158619	−	0.987340i	$-0.550704\pi$
$311$	−5.59454	−0.317238	−0.158619	+	0.987340i	$0.550704\pi$
$312$	4.48578	0.253957
$313$	10.9292	0.617754	0.308877	−	0.951102i	$-0.400047\pi$
$313$	10.9292	0.617754	0.308877	+	0.951102i	$0.400047\pi$
$314$	12.8501	0.725175
$315$	−1.95823	−0.110333
$316$	−8.38686	−0.471798
$317$	6.44115	0.361771	0.180885	−	0.983504i	$-0.442104\pi$
$317$	6.44115	0.361771	0.180885	+	0.983504i	$0.442104\pi$
$318$	7.86052	0.440796
$319$	12.5747	0.704050
$320$	9.58452	0.535791
$321$	8.85861	0.494440
$322$	18.0587	1.00637
$323$	−2.72177	−0.151443
$324$	3.85401	0.214111
$325$	−1.00000	−0.0554700
$326$	−19.3440	−1.07137
$327$	−13.3440	−0.737925
$328$	40.9644	2.26188
$329$	−16.0002	−0.882118
$330$	−12.0669	−0.664263
$331$	−7.38292	−0.405802	−0.202901	−	0.979199i	$-0.565037\pi$
$331$	−7.38292	−0.405802	−0.202901	+	0.979199i	$0.565037\pi$
$332$	−25.2477	−1.38565
$333$	−6.95072	−0.380897
$334$	33.5884	1.83787
$335$	7.22598	0.394797
$336$	−6.15931	−0.336018
$337$	−7.59507	−0.413730	−0.206865	−	0.978370i	$-0.566326\pi$
$337$	−7.59507	−0.413730	−0.206865	+	0.978370i	$0.566326\pi$
$338$	2.41951	0.131604
$339$	−2.18635	−0.118746
$340$	−1.93309	−0.104837
$341$	4.98736	0.270081
$342$	−13.1292	−0.709945
$343$	−19.9061	−1.07483
$344$	7.37559	0.397665
$345$	3.81151	0.205205
$346$	−45.5430	−2.44841
$347$	12.0675	0.647819	0.323909	−	0.946088i	$-0.395003\pi$
$347$	12.0675	0.647819	0.323909	+	0.946088i	$0.395003\pi$
$348$	9.71719	0.520896
$349$	9.62522	0.515226	0.257613	−	0.966248i	$-0.417064\pi$
$349$	9.62522	0.515226	0.257613	+	0.966248i	$0.417064\pi$
$350$	4.73794	0.253253
$351$	1.00000	0.0533761
$352$	6.78959	0.361887
$353$	8.20400	0.436655	0.218328	−	0.975876i	$-0.429940\pi$
$353$	8.20400	0.436655	0.218328	+	0.975876i	$0.429940\pi$
$354$	−5.15195	−0.273823
$355$	0.733327	0.0389209
$356$	−19.3238	−1.02416
$357$	−0.982206	−0.0519838
$358$	26.0010	1.37420
$359$	12.2807	0.648153	0.324076	−	0.946031i	$-0.394946\pi$
$359$	12.2807	0.648153	0.324076	+	0.946031i	$0.394946\pi$
$360$	−4.48578	−0.236421
$361$	10.4457	0.549773
$362$	−15.2966	−0.803970
$363$	−13.8737	−0.728182
$364$	−7.54701	−0.395571
$365$	5.16672	0.270439
$366$	16.7547	0.875785
$367$	1.62272	0.0847052	0.0423526	−	0.999103i	$-0.486515\pi$
$367$	1.62272	0.0847052	0.0423526	+	0.999103i	$0.486515\pi$
$368$	11.9885	0.624946
$369$	9.13206	0.475396
$370$	16.8173	0.874290
$371$	−6.36191	−0.330294
$372$	3.85401	0.199821
$373$	−12.3031	−0.637032	−0.318516	−	0.947918i	$-0.603184\pi$
$373$	−12.3031	−0.637032	−0.318516	+	0.947918i	$0.603184\pi$
$374$	−6.05253	−0.312969
$375$	1.00000	0.0516398
$376$	−36.6522	−1.89019
$377$	2.52132	0.129855
$378$	−4.73794	−0.243693
$379$	6.66410	0.342312	0.171156	−	0.985244i	$-0.445250\pi$
$379$	6.66410	0.342312	0.171156	+	0.985244i	$0.445250\pi$
$380$	20.9133	1.07283
$381$	−14.4864	−0.742162
$382$	24.4831	1.25267
$383$	6.65979	0.340299	0.170150	−	0.985418i	$-0.445575\pi$
$383$	6.65979	0.340299	0.170150	+	0.985418i	$0.445575\pi$
$384$	20.4671	1.04446
$385$	9.76637	0.497740
$386$	−5.89523	−0.300059
$387$	1.64422	0.0835802
$388$	45.4366	2.30669
$389$	−6.13036	−0.310822	−0.155411	−	0.987850i	$-0.549670\pi$
$389$	−6.13036	−0.310822	−0.155411	+	0.987850i	$0.549670\pi$
$390$	−2.41951	−0.122516
$391$	1.91178	0.0966827
$392$	−14.1991	−0.717162
$393$	−6.75438	−0.340714
$394$	38.2825	1.92865
$395$	2.17614	0.109494
$396$	−19.2213	−0.965907
$397$	−3.25693	−0.163461	−0.0817304	−	0.996654i	$-0.526045\pi$
$397$	−3.25693	−0.163461	−0.0817304	+	0.996654i	$0.526045\pi$
$398$	−36.5653	−1.83285
$399$	10.6261	0.531970
$400$	3.14535	0.157268
$401$	35.6827	1.78191	0.890955	−	0.454091i	$-0.150036\pi$
$401$	35.6827	1.78191	0.890955	+	0.454091i	$0.150036\pi$
$402$	17.4833	0.871987
$403$	1.00000	0.0498135
$404$	−24.6944	−1.22859
$405$	−1.00000	−0.0496904
$406$	−11.9459	−0.592863
$407$	34.6657	1.71832
$408$	−2.24997	−0.111390
$409$	−14.1735	−0.700833	−0.350417	−	0.936594i	$-0.613960\pi$
$409$	−14.1735	−0.700833	−0.350417	+	0.936594i	$0.613960\pi$
$410$	−22.0951	−1.09120
$411$	14.1498	0.697957
$412$	−12.9595	−0.638467
$413$	4.16973	0.205179
$414$	9.22198	0.453235
$415$	6.55104	0.321578
$416$	1.36136	0.0667462
$417$	14.3358	0.702030
$418$	65.4799	3.20273
$419$	20.0322	0.978638	0.489319	−	0.872105i	$-0.337245\pi$
$419$	20.0322	0.978638	0.489319	+	0.872105i	$0.337245\pi$
$420$	7.54701	0.368256
$421$	17.9141	0.873081	0.436541	−	0.899685i	$-0.356204\pi$
$421$	17.9141	0.873081	0.436541	+	0.899685i	$0.356204\pi$
$422$	30.2945	1.47471
$423$	−8.17075	−0.397276
$424$	−14.5735	−0.707749
$425$	0.501580	0.0243302
$426$	1.77429	0.0859645
$427$	−13.5604	−0.656236
$428$	−34.1411	−1.65027
$429$	−4.98736	−0.240792
$430$	−3.97819	−0.191845
$431$	30.6761	1.47762	0.738809	−	0.673915i	$-0.235389\pi$
$431$	30.6761	1.47762	0.738809	+	0.673915i	$0.235389\pi$
$432$	−3.14535	−0.151331
$433$	−8.66706	−0.416512	−0.208256	−	0.978074i	$-0.566779\pi$
$433$	−8.66706	−0.416512	−0.208256	+	0.978074i	$0.566779\pi$
$434$	−4.73794	−0.227428
$435$	−2.52132	−0.120888
$436$	51.4278	2.46295
$437$	−20.6827	−0.989390
$438$	12.5009	0.597317
$439$	−24.6913	−1.17845	−0.589225	−	0.807969i	$-0.700567\pi$
$439$	−24.6913	−1.17845	−0.589225	+	0.807969i	$0.700567\pi$
$440$	22.3722	1.06655
$441$	−3.16535	−0.150731
$442$	−1.21357	−0.0577238
$443$	34.4263	1.63564	0.817822	−	0.575471i	$-0.195181\pi$
$443$	34.4263	1.63564	0.817822	+	0.575471i	$0.195181\pi$
$444$	26.7881	1.27131
$445$	5.01394	0.237683
$446$	−41.7464	−1.97675
$447$	−20.9355	−0.990215
$448$	−18.7687	−0.886736
$449$	1.52692	0.0720600	0.0360300	−	0.999351i	$-0.488529\pi$
$449$	1.52692	0.0720600	0.0360300	+	0.999351i	$0.488529\pi$
$450$	2.41951	0.114057
$451$	−45.5448	−2.14462
$452$	8.42621	0.396336
$453$	0.513113	0.0241081
$454$	−14.5348	−0.682153
$455$	1.95823	0.0918030
$456$	24.3416	1.13990
$457$	39.8581	1.86448	0.932241	−	0.361837i	$-0.117850\pi$
$457$	39.8581	1.86448	0.932241	+	0.361837i	$0.117850\pi$
$458$	−7.13399	−0.333349
$459$	−0.501580	−0.0234117
$460$	−14.6896	−0.684906
$461$	34.3433	1.59953	0.799764	−	0.600314i	$-0.204958\pi$
$461$	34.3433	1.59953	0.799764	+	0.600314i	$0.204958\pi$
$462$	23.6298	1.09936
$463$	−19.4941	−0.905968	−0.452984	−	0.891519i	$-0.649640\pi$
$463$	−19.4941	−0.905968	−0.452984	+	0.891519i	$0.649640\pi$
$464$	−7.93044	−0.368162
$465$	−1.00000	−0.0463739
$466$	−4.44683	−0.205995
$467$	−1.25662	−0.0581494	−0.0290747	−	0.999577i	$-0.509256\pi$
$467$	−1.25662	−0.0581494	−0.0290747	+	0.999577i	$0.509256\pi$
$468$	−3.85401	−0.178152
$469$	−14.1501	−0.653390
$470$	19.7692	0.911884
$471$	−5.31106	−0.244721
$472$	9.55175	0.439655
$473$	−8.20029	−0.377050
$474$	5.26518	0.241838
$475$	−5.42639	−0.248980
$476$	3.78543	0.173505
$477$	−3.24881	−0.148753
$478$	−19.1424	−0.875552
$479$	19.8826	0.908460	0.454230	−	0.890884i	$-0.349914\pi$
$479$	19.8826	0.908460	0.454230	+	0.890884i	$0.349914\pi$
$480$	−1.36136	−0.0621373
$481$	6.95072	0.316925
$482$	−15.8304	−0.721054
$483$	−7.46380	−0.339615
$484$	53.4695	2.43043
$485$	−11.7894	−0.535331
$486$	−2.41951	−0.109751
$487$	28.2117	1.27839	0.639197	−	0.769043i	$-0.279267\pi$
$487$	28.2117	1.27839	0.639197	+	0.769043i	$0.279267\pi$
$488$	−31.0634	−1.40617
$489$	7.99503	0.361548
$490$	7.65859	0.345980
$491$	−37.6364	−1.69851	−0.849253	−	0.527987i	$-0.822947\pi$
$491$	−37.6364	−1.69851	−0.849253	+	0.527987i	$0.822947\pi$
$492$	−35.1950	−1.58671
$493$	−1.26464	−0.0569567
$494$	13.1292	0.590710
$495$	4.98736	0.224165
$496$	−3.14535	−0.141230
$497$	−1.43602	−0.0644142
$498$	15.8503	0.710267
$499$	−37.3348	−1.67133	−0.835667	−	0.549236i	$-0.814919\pi$
$499$	−37.3348	−1.67133	−0.835667	+	0.549236i	$0.814919\pi$
$500$	−3.85401	−0.172356
$501$	−13.8823	−0.620217
$502$	−26.8558	−1.19863
$503$	−11.6288	−0.518501	−0.259251	−	0.965810i	$-0.583476\pi$
$503$	−11.6288	−0.518501	−0.259251	+	0.965810i	$0.583476\pi$
$504$	8.78416	0.391278
$505$	6.40747	0.285128
$506$	−45.9933	−2.04465
$507$	−1.00000	−0.0444116
$508$	55.8308	2.47709
$509$	−20.7380	−0.919197	−0.459599	−	0.888127i	$-0.652007\pi$
$509$	−20.7380	−0.919197	−0.459599	+	0.888127i	$0.652007\pi$
$510$	1.21357	0.0537380
$511$	−10.1176	−0.447576
$512$	−32.5007	−1.43634
$513$	5.42639	0.239581
$514$	7.69917	0.339596
$515$	3.36259	0.148174
$516$	−6.33682	−0.278963
$517$	40.7505	1.79220
$518$	−32.9321	−1.44695
$519$	18.8233	0.826250
$520$	4.48578	0.196714
$521$	14.9327	0.654214	0.327107	−	0.944987i	$-0.393926\pi$
$521$	14.9327	0.654214	0.327107	+	0.944987i	$0.393926\pi$
$522$	−6.10035	−0.267005
$523$	−8.42154	−0.368248	−0.184124	−	0.982903i	$-0.558945\pi$
$523$	−8.42154	−0.368248	−0.184124	+	0.982903i	$0.558945\pi$
$524$	26.0314	1.13719
$525$	−1.95823	−0.0854640
$526$	−46.2620	−2.01712
$527$	−0.501580	−0.0218491
$528$	15.6870	0.682689
$529$	−8.47237	−0.368364
$530$	7.86052	0.341439
$531$	2.12934	0.0924055
$532$	−40.9530	−1.77554
$533$	−9.13206	−0.395553
$534$	12.1313	0.524971
$535$	8.85861	0.382991
$536$	−32.4141	−1.40008
$537$	−10.7464	−0.463742
$538$	−33.0288	−1.42397
$539$	15.7868	0.679984
$540$	3.85401	0.165850
$541$	12.2140	0.525121	0.262561	−	0.964916i	$-0.415433\pi$
$541$	12.2140	0.525121	0.262561	+	0.964916i	$0.415433\pi$
$542$	17.8367	0.766150
$543$	6.32219	0.271311
$544$	−0.682831	−0.0292761
$545$	−13.3440	−0.571594
$546$	4.73794	0.202765
$547$	−31.0867	−1.32917	−0.664585	−	0.747213i	$-0.731392\pi$
$547$	−31.0867	−1.32917	−0.664585	+	0.747213i	$0.731392\pi$
$548$	−54.5333	−2.32955
$549$	−6.92486	−0.295546
$550$	−12.0669	−0.514536
$551$	13.6817	0.582859
$552$	−17.0976	−0.727722
$553$	−4.26137	−0.181212
$554$	−42.7753	−1.81735
$555$	−6.95072	−0.295041
$556$	−55.2504	−2.34314
$557$	17.2884	0.732534	0.366267	−	0.930510i	$-0.380636\pi$
$557$	17.2884	0.732534	0.366267	+	0.930510i	$0.380636\pi$
$558$	−2.41951	−0.102426
$559$	−1.64422	−0.0695429
$560$	−6.15931	−0.260278
$561$	2.50156	0.105616
$562$	36.2165	1.52770
$563$	−0.545982	−0.0230104	−0.0115052	−	0.999934i	$-0.503662\pi$
$563$	−0.545982	−0.0230104	−0.0115052	+	0.999934i	$0.503662\pi$
$564$	31.4901	1.32597
$565$	−2.18635	−0.0919805
$566$	−9.19269	−0.386398
$567$	1.95823	0.0822377
$568$	−3.28954	−0.138026
$569$	24.4281	1.02408	0.512040	−	0.858962i	$-0.328890\pi$
$569$	24.4281	1.02408	0.512040	+	0.858962i	$0.328890\pi$
$570$	−13.1292	−0.549921
$571$	9.59296	0.401453	0.200727	−	0.979647i	$-0.435670\pi$
$571$	9.59296	0.401453	0.200727	+	0.979647i	$0.435670\pi$
$572$	19.2213	0.803683
$573$	−10.1191	−0.422730
$574$	43.2671	1.80593
$575$	3.81151	0.158951
$576$	−9.58452	−0.399355
$577$	30.3381	1.26299	0.631496	−	0.775379i	$-0.282441\pi$
$577$	30.3381	1.26299	0.631496	+	0.775379i	$0.282441\pi$
$578$	−40.5229	−1.68553
$579$	2.43654	0.101259
$580$	9.71719	0.403484
$581$	−12.8284	−0.532212
$582$	−28.5246	−1.18238
$583$	16.2030	0.671059
$584$	−23.1768	−0.959061
$585$	1.00000	0.0413449
$586$	51.5163	2.12812
$587$	−27.2941	−1.12655	−0.563275	−	0.826270i	$-0.690459\pi$
$587$	−27.2941	−1.12655	−0.563275	+	0.826270i	$0.690459\pi$
$588$	12.1993	0.503090
$589$	5.42639	0.223590
$590$	−5.15195	−0.212102
$591$	−15.8225	−0.650849
$592$	−21.8624	−0.898541
$593$	−41.7638	−1.71503	−0.857517	−	0.514456i	$-0.827994\pi$
$593$	−41.7638	−1.71503	−0.857517	+	0.514456i	$0.827994\pi$
$594$	12.0669	0.495112
$595$	−0.982206	−0.0402665
$596$	80.6855	3.30501
$597$	15.1127	0.618522
$598$	−9.22198	−0.377115
$599$	6.99235	0.285700	0.142850	−	0.989744i	$-0.454373\pi$
$599$	6.99235	0.285700	0.142850	+	0.989744i	$0.454373\pi$
$600$	−4.48578	−0.183131
$601$	−27.5502	−1.12379	−0.561897	−	0.827207i	$-0.689928\pi$
$601$	−27.5502	−1.12379	−0.561897	+	0.827207i	$0.689928\pi$
$602$	7.79019	0.317505
$603$	−7.22598	−0.294264
$604$	−1.97754	−0.0804650
$605$	−13.8737	−0.564048
$606$	15.5029	0.629762
$607$	−23.9454	−0.971915	−0.485958	−	0.873982i	$-0.661529\pi$
$607$	−23.9454	−0.971915	−0.485958	+	0.873982i	$0.661529\pi$
$608$	7.38727	0.299594
$609$	4.93732	0.200070
$610$	16.7547	0.678380
$611$	8.17075	0.330553
$612$	1.93309	0.0781406
$613$	33.9889	1.37280	0.686399	−	0.727225i	$-0.259190\pi$
$613$	33.9889	1.37280	0.686399	+	0.727225i	$0.259190\pi$
$614$	−18.4019	−0.742639
$615$	9.13206	0.368240
$616$	−43.8098	−1.76515
$617$	18.3946	0.740538	0.370269	−	0.928925i	$-0.379265\pi$
$617$	18.3946	0.740538	0.370269	+	0.928925i	$0.379265\pi$
$618$	8.13581	0.327270
$619$	−1.51206	−0.0607747	−0.0303874	−	0.999538i	$-0.509674\pi$
$619$	−1.51206	−0.0607747	−0.0303874	+	0.999538i	$0.509674\pi$
$620$	3.85401	0.154781
$621$	−3.81151	−0.152951
$622$	−13.5360	−0.542745
$623$	−9.81842	−0.393367
$624$	3.14535	0.125915
$625$	1.00000	0.0400000
$626$	26.4432	1.05688
$627$	−27.0633	−1.08081
$628$	20.4689	0.816797
$629$	−3.48634	−0.139009
$630$	−4.73794	−0.188764
$631$	−16.2265	−0.645968	−0.322984	−	0.946404i	$-0.604686\pi$
$631$	−16.2265	−0.645968	−0.322984	+	0.946404i	$0.604686\pi$
$632$	−9.76168	−0.388299
$633$	−12.5209	−0.497663
$634$	15.5844	0.618935
$635$	−14.4864	−0.574876
$636$	12.5209	0.496488
$637$	3.16535	0.125416
$638$	30.4246	1.20452
$639$	−0.733327	−0.0290100
$640$	20.4671	0.809033
$641$	−6.22082	−0.245708	−0.122854	−	0.992425i	$-0.539205\pi$
$641$	−6.22082	−0.245708	−0.122854	+	0.992425i	$0.539205\pi$
$642$	21.4335	0.845911
$643$	35.1182	1.38493	0.692463	−	0.721453i	$-0.256526\pi$
$643$	35.1182	1.38493	0.692463	+	0.721453i	$0.256526\pi$
$644$	28.7655	1.13352
$645$	1.64422	0.0647410
$646$	−6.58533	−0.259096
$647$	32.8884	1.29298	0.646488	−	0.762924i	$-0.276237\pi$
$647$	32.8884	1.29298	0.646488	+	0.762924i	$0.276237\pi$
$648$	4.48578	0.176218
$649$	−10.6198	−0.416863
$650$	−2.41951	−0.0949008
$651$	1.95823	0.0767489
$652$	−30.8129	−1.20673
$653$	18.8111	0.736134	0.368067	−	0.929799i	$-0.380020\pi$
$653$	18.8111	0.736134	0.368067	+	0.929799i	$0.380020\pi$
$654$	−32.2859	−1.26248
$655$	−6.75438	−0.263916
$656$	28.7235	1.12147
$657$	−5.16672	−0.201573
$658$	−38.7125	−1.50917
$659$	11.0804	0.431629	0.215815	−	0.976434i	$-0.430759\pi$
$659$	11.0804	0.431629	0.215815	+	0.976434i	$0.430759\pi$
$660$	−19.2213	−0.748188
$661$	4.32723	0.168310	0.0841548	−	0.996453i	$-0.473181\pi$
$661$	4.32723	0.168310	0.0841548	+	0.996453i	$0.473181\pi$
$662$	−17.8630	−0.694266
$663$	0.501580	0.0194797
$664$	−29.3865	−1.14042
$665$	10.6261	0.412062
$666$	−16.8173	−0.651657
$667$	−9.61005	−0.372103
$668$	53.5026	2.07008
$669$	17.2541	0.667083
$670$	17.4833	0.675438
$671$	34.5368	1.33328
$672$	2.66585	0.102837
$673$	−19.0973	−0.736148	−0.368074	−	0.929796i	$-0.619983\pi$
$673$	−19.0973	−0.736148	−0.368074	+	0.929796i	$0.619983\pi$
$674$	−18.3763	−0.707829
$675$	−1.00000	−0.0384900
$676$	3.85401	0.148231
$677$	−23.8311	−0.915905	−0.457952	−	0.888977i	$-0.651417\pi$
$677$	−23.8311	−0.915905	−0.457952	+	0.888977i	$0.651417\pi$
$678$	−5.28989	−0.203157
$679$	23.0864	0.885975
$680$	−2.24997	−0.0862826
$681$	6.00736	0.230202
$682$	12.0669	0.462067
$683$	44.6705	1.70927	0.854634	−	0.519231i	$-0.173781\pi$
$683$	44.6705	1.70927	0.854634	+	0.519231i	$0.173781\pi$
$684$	−20.9133	−0.799641
$685$	14.1498	0.540635
$686$	−48.1628	−1.83886
$687$	2.94853	0.112494
$688$	5.17164	0.197167
$689$	3.24881	0.123770
$690$	9.22198	0.351075
$691$	2.49083	0.0947557	0.0473778	−	0.998877i	$-0.484914\pi$
$691$	2.49083	0.0947557	0.0473778	+	0.998877i	$0.484914\pi$
$692$	−72.5450	−2.75775
$693$	−9.76637	−0.370994
$694$	29.1974	1.10832
$695$	14.3358	0.543790
$696$	11.3101	0.428708
$697$	4.58045	0.173497
$698$	23.2883	0.881474
$699$	1.83791	0.0695161
$700$	7.54701	0.285250
$701$	2.33027	0.0880130	0.0440065	−	0.999031i	$-0.485988\pi$
$701$	2.33027	0.0880130	0.0440065	+	0.999031i	$0.485988\pi$
$702$	2.41951	0.0913183
$703$	37.7173	1.42253
$704$	47.8014	1.80158
$705$	−8.17075	−0.307728
$706$	19.8496	0.747051
$707$	−12.5473	−0.471888
$708$	−8.20649	−0.308419
$709$	−17.4768	−0.656356	−0.328178	−	0.944616i	$-0.606435\pi$
$709$	−17.4768	−0.656356	−0.328178	+	0.944616i	$0.606435\pi$
$710$	1.77429	0.0665878
$711$	−2.17614	−0.0816116
$712$	−22.4914	−0.842901
$713$	−3.81151	−0.142742
$714$	−2.37645	−0.0889365
$715$	−4.98736	−0.186517
$716$	41.4167	1.54782
$717$	7.91169	0.295468
$718$	29.7133	1.10889
$719$	−19.1201	−0.713061	−0.356531	−	0.934284i	$-0.616040\pi$
$719$	−19.1201	−0.713061	−0.356531	+	0.934284i	$0.616040\pi$
$720$	−3.14535	−0.117220
$721$	−6.58471	−0.245228
$722$	25.2734	0.940579
$723$	6.54282	0.243330
$724$	−24.3658	−0.905546
$725$	−2.52132	−0.0936396
$726$	−33.5676	−1.24581
$727$	19.3277	0.716823	0.358412	−	0.933564i	$-0.383318\pi$
$727$	19.3277	0.716823	0.358412	+	0.933564i	$0.383318\pi$
$728$	−8.78416	−0.325563
$729$	1.00000	0.0370370
$730$	12.5009	0.462679
$731$	0.824705	0.0305028
$732$	26.6885	0.986434
$733$	18.6517	0.688915	0.344457	−	0.938802i	$-0.388063\pi$
$733$	18.6517	0.688915	0.344457	+	0.938802i	$0.388063\pi$
$734$	3.92617	0.144918
$735$	−3.16535	−0.116756
$736$	−5.18885	−0.191263
$737$	36.0385	1.32750
$738$	22.0951	0.813331
$739$	−24.8441	−0.913905	−0.456952	−	0.889491i	$-0.651059\pi$
$739$	−24.8441	−0.913905	−0.456952	+	0.889491i	$0.651059\pi$
$740$	26.7881	0.984750
$741$	−5.42639	−0.199343
$742$	−15.3927	−0.565083
$743$	23.4434	0.860055	0.430027	−	0.902816i	$-0.358504\pi$
$743$	23.4434	0.860055	0.430027	+	0.902816i	$0.358504\pi$
$744$	4.48578	0.164457
$745$	−20.9355	−0.767017
$746$	−29.7675	−1.08986
$747$	−6.55104	−0.239690
$748$	−9.64101	−0.352510
$749$	−17.3472	−0.633851
$750$	2.41951	0.0883478
$751$	−8.23670	−0.300561	−0.150281	−	0.988643i	$-0.548018\pi$
$751$	−8.23670	−0.300561	−0.150281	+	0.988643i	$0.548018\pi$
$752$	−25.6999	−0.937179
$753$	11.0997	0.404496
$754$	6.10035	0.222162
$755$	0.513113	0.0186741
$756$	−7.54701	−0.274482
$757$	17.9401	0.652043	0.326022	−	0.945362i	$-0.394292\pi$
$757$	17.9401	0.652043	0.326022	+	0.945362i	$0.394292\pi$
$758$	16.1238	0.585643
$759$	19.0094	0.689997
$760$	24.3416	0.882962
$761$	12.4138	0.449999	0.224999	−	0.974359i	$-0.427762\pi$
$761$	12.4138	0.449999	0.224999	+	0.974359i	$0.427762\pi$
$762$	−35.0500	−1.26973
$763$	26.1305	0.945989
$764$	38.9989	1.41093
$765$	−0.501580	−0.0181346
$766$	16.1134	0.582201
$767$	−2.12934	−0.0768860
$768$	30.3512	1.09520
$769$	53.0486	1.91298	0.956491	−	0.291763i	$-0.0942417\pi$
$769$	53.0486	1.91298	0.956491	+	0.291763i	$0.0942417\pi$
$770$	23.6298	0.851558
$771$	−3.18213	−0.114602
$772$	−9.39046	−0.337970
$773$	−1.77657	−0.0638986	−0.0319493	−	0.999489i	$-0.510172\pi$
$773$	−1.77657	−0.0638986	−0.0319493	+	0.999489i	$0.510172\pi$
$774$	3.97819	0.142993
$775$	−1.00000	−0.0359211
$776$	52.8849	1.89846
$777$	13.6111	0.488294
$778$	−14.8324	−0.531769
$779$	−49.5541	−1.77546
$780$	−3.85401	−0.137996
$781$	3.65736	0.130871
$782$	4.62555	0.165409
$783$	2.52132	0.0901047
$784$	−9.95615	−0.355577
$785$	−5.31106	−0.189560
$786$	−16.3423	−0.582909
$787$	22.9342	0.817517	0.408759	−	0.912642i	$-0.365962\pi$
$787$	22.9342	0.817517	0.408759	+	0.912642i	$0.365962\pi$
$788$	60.9799	2.17232
$789$	19.1204	0.680706
$790$	5.26518	0.187327
$791$	4.28137	0.152228
$792$	−22.3722	−0.794961
$793$	6.92486	0.245909
$794$	−7.88017	−0.279657
$795$	−3.24881	−0.115224
$796$	−58.2444	−2.06442
$797$	24.9099	0.882356	0.441178	−	0.897420i	$-0.354561\pi$
$797$	24.9099	0.882356	0.441178	+	0.897420i	$0.354561\pi$
$798$	25.7099	0.910120
$799$	−4.09828	−0.144987
$800$	−1.36136	−0.0481314
$801$	−5.01394	−0.177159
$802$	86.3345	3.04858
$803$	25.7683	0.909343
$804$	27.8490	0.982157
$805$	−7.46380	−0.263064
$806$	2.41951	0.0852234
$807$	13.6510	0.480539
$808$	−28.7425	−1.01116
$809$	−23.4822	−0.825589	−0.412795	−	0.910824i	$-0.635447\pi$
$809$	−23.4822	−0.825589	−0.412795	+	0.910824i	$0.635447\pi$
$810$	−2.41951	−0.0850128
$811$	−11.1841	−0.392726	−0.196363	−	0.980531i	$-0.562913\pi$
$811$	−11.1841	−0.392726	−0.196363	+	0.980531i	$0.562913\pi$
$812$	−19.0284	−0.667768
$813$	−7.37202	−0.258548
$814$	83.8739	2.93978
$815$	7.99503	0.280054
$816$	−1.57764	−0.0552286
$817$	−8.92216	−0.312147
$818$	−34.2928	−1.19902
$819$	−1.95823	−0.0684259
$820$	−35.1950	−1.22906
$821$	−7.49894	−0.261715	−0.130857	−	0.991401i	$-0.541773\pi$
$821$	−7.49894	−0.261715	−0.130857	+	0.991401i	$0.541773\pi$
$822$	34.2354	1.19410
$823$	−8.26923	−0.288247	−0.144124	−	0.989560i	$-0.546036\pi$
$823$	−8.26923	−0.288247	−0.144124	+	0.989560i	$0.546036\pi$
$824$	−15.0838	−0.525471
$825$	4.98736	0.173638
$826$	10.0887	0.351030
$827$	30.3502	1.05538	0.527690	−	0.849437i	$-0.323058\pi$
$827$	30.3502	1.05538	0.527690	+	0.849437i	$0.323058\pi$
$828$	14.6896	0.510499
$829$	−9.47447	−0.329062	−0.164531	−	0.986372i	$-0.552611\pi$
$829$	−9.47447	−0.329062	−0.164531	+	0.986372i	$0.552611\pi$
$830$	15.8503	0.550171
$831$	17.6793	0.613290
$832$	9.58452	0.332284
$833$	−1.58768	−0.0550097
$834$	34.6857	1.20107
$835$	−13.8823	−0.480418
$836$	104.302	3.60737
$837$	1.00000	0.0345651
$838$	48.4681	1.67430
$839$	4.37303	0.150974	0.0754868	−	0.997147i	$-0.475949\pi$
$839$	4.37303	0.150974	0.0754868	+	0.997147i	$0.475949\pi$
$840$	8.78416	0.303082
$841$	−22.6429	−0.780791
$842$	43.3433	1.49371
$843$	−14.9685	−0.515544
$844$	48.2558	1.66103
$845$	−1.00000	−0.0344010
$846$	−19.7692	−0.679678
$847$	27.1679	0.933500
$848$	−10.2187	−0.350910
$849$	3.79941	0.130395
$850$	1.21357	0.0416253
$851$	−26.4927	−0.908160
$852$	2.82625	0.0968256
$853$	−30.4034	−1.04099	−0.520496	−	0.853864i	$-0.674253\pi$
$853$	−30.4034	−1.04099	−0.520496	+	0.853864i	$0.674253\pi$
$854$	−32.8096	−1.12272
$855$	5.42639	0.185579
$856$	−39.7378	−1.35821
$857$	−28.9968	−0.990511	−0.495255	−	0.868747i	$-0.664926\pi$
$857$	−28.9968	−0.990511	−0.495255	+	0.868747i	$0.664926\pi$
$858$	−12.0669	−0.411958
$859$	36.3463	1.24012	0.620059	−	0.784555i	$-0.287109\pi$
$859$	36.3463	1.24012	0.620059	+	0.784555i	$0.287109\pi$
$860$	−6.33682	−0.216084
$861$	−17.8826	−0.609438
$862$	74.2211	2.52798
$863$	5.33980	0.181769	0.0908844	−	0.995861i	$-0.471031\pi$
$863$	5.33980	0.181769	0.0908844	+	0.995861i	$0.471031\pi$
$864$	1.36136	0.0463144
$865$	18.8233	0.640011
$866$	−20.9700	−0.712589
$867$	16.7484	0.568806
$868$	−7.54701	−0.256162
$869$	10.8532	0.368169
$870$	−6.10035	−0.206821
$871$	7.22598	0.244843
$872$	59.8582	2.02705
$873$	11.7894	0.399012
$874$	−50.0420	−1.69270
$875$	−1.95823	−0.0662001
$876$	19.9126	0.672784
$877$	−0.600956	−0.0202929	−0.0101464	−	0.999949i	$-0.503230\pi$
$877$	−0.600956	−0.0202929	−0.0101464	+	0.999949i	$0.503230\pi$
$878$	−59.7406	−2.01615
$879$	−21.2921	−0.718163
$880$	15.6870	0.528808
$881$	−16.2684	−0.548095	−0.274048	−	0.961716i	$-0.588363\pi$
$881$	−16.2684	−0.548095	−0.274048	+	0.961716i	$0.588363\pi$
$882$	−7.65859	−0.257878
$883$	43.5823	1.46666	0.733330	−	0.679873i	$-0.237965\pi$
$883$	43.5823	1.46666	0.733330	+	0.679873i	$0.237965\pi$
$884$	−1.93309	−0.0650169
$885$	2.12934	0.0715770
$886$	83.2947	2.79834
$887$	−14.7740	−0.496062	−0.248031	−	0.968752i	$-0.579784\pi$
$887$	−14.7740	−0.496062	−0.248031	+	0.968752i	$0.579784\pi$
$888$	31.1794	1.04631
$889$	28.3677	0.951421
$890$	12.1313	0.406640
$891$	−4.98736	−0.167083
$892$	−66.4975	−2.22650
$893$	44.3377	1.48370
$894$	−50.6535	−1.69411
$895$	−10.7464	−0.359213
$896$	−40.0792	−1.33895
$897$	3.81151	0.127263
$898$	3.69440	0.123284
$899$	2.52132	0.0840908
$900$	3.85401	0.128467
$901$	−1.62954	−0.0542878
$902$	−110.196	−3.66913
$903$	−3.21975	−0.107146
$904$	9.80749	0.326192
$905$	6.32219	0.210157
$906$	1.24148	0.0412454
$907$	22.9476	0.761964	0.380982	−	0.924582i	$-0.375586\pi$
$907$	22.9476	0.761964	0.380982	+	0.924582i	$0.375586\pi$
$908$	−23.1524	−0.768339
$909$	−6.40747	−0.212522
$910$	4.73794	0.157061
$911$	−33.8240	−1.12064	−0.560320	−	0.828276i	$-0.689322\pi$
$911$	−33.8240	−1.12064	−0.560320	+	0.828276i	$0.689322\pi$
$912$	17.0679	0.565175
$913$	32.6724	1.08130
$914$	96.4369	3.18985
$915$	−6.92486	−0.228929
$916$	−11.3637	−0.375466
$917$	13.2266	0.436781
$918$	−1.21357	−0.0400539
$919$	21.1193	0.696662	0.348331	−	0.937372i	$-0.386749\pi$
$919$	21.1193	0.696662	0.348331	+	0.937372i	$0.386749\pi$
$920$	−17.0976	−0.563691
$921$	7.60563	0.250614
$922$	83.0939	2.73655
$923$	0.733327	0.0241377
$924$	37.6396	1.23825
$925$	−6.95072	−0.228538
$926$	−47.1661	−1.54997
$927$	−3.36259	−0.110442
$928$	3.43243	0.112675
$929$	5.51376	0.180901	0.0904503	−	0.995901i	$-0.471169\pi$
$929$	5.51376	0.180901	0.0904503	+	0.995901i	$0.471169\pi$
$930$	−2.41951	−0.0793387
$931$	17.1764	0.562935
$932$	−7.08331	−0.232022
$933$	5.59454	0.183157
$934$	−3.04040	−0.0994849
$935$	2.50156	0.0818096
$936$	−4.48578	−0.146622
$937$	13.0539	0.426451	0.213226	−	0.977003i	$-0.431603\pi$
$937$	13.0539	0.426451	0.213226	+	0.977003i	$0.431603\pi$
$938$	−34.2362	−1.11785
$939$	−10.9292	−0.356660
$940$	31.4901	1.02709
$941$	−48.3383	−1.57578	−0.787892	−	0.615813i	$-0.788828\pi$
$941$	−48.3383	−1.57578	−0.787892	+	0.615813i	$0.788828\pi$
$942$	−12.8501	−0.418680
$943$	34.8070	1.13347
$944$	6.69752	0.217986
$945$	1.95823	0.0637011
$946$	−19.8407	−0.645075
$947$	−17.3771	−0.564680	−0.282340	−	0.959314i	$-0.591111\pi$
$947$	−17.3771	−0.564680	−0.282340	+	0.959314i	$0.591111\pi$
$948$	8.38686	0.272392
$949$	5.16672	0.167719
$950$	−13.1292	−0.425967
$951$	−6.44115	−0.208869
$952$	4.40596	0.142798
$953$	38.1611	1.23616	0.618080	−	0.786115i	$-0.287911\pi$
$953$	38.1611	1.23616	0.618080	+	0.786115i	$0.287911\pi$
$954$	−7.86052	−0.254494
$955$	−10.1191	−0.327445
$956$	−30.4917	−0.986173
$957$	−12.5747	−0.406483
$958$	48.1061	1.55424
$959$	−27.7084	−0.894752
$960$	−9.58452	−0.309339
$961$	1.00000	0.0322581
$962$	16.8173	0.542211
$963$	−8.85861	−0.285465
$964$	−25.2161	−0.812155
$965$	2.43654	0.0784352
$966$	−18.0587	−0.581029
$967$	−16.8834	−0.542934	−0.271467	−	0.962448i	$-0.587509\pi$
$967$	−16.8834	−0.542934	−0.271467	+	0.962448i	$0.587509\pi$
$968$	62.2345	2.00029
$969$	2.72177	0.0874357
$970$	−28.5246	−0.915871
$971$	−47.3587	−1.51981	−0.759906	−	0.650033i	$-0.774755\pi$
$971$	−47.3587	−1.51981	−0.759906	+	0.650033i	$0.774755\pi$
$972$	−3.85401	−0.123617
$973$	−28.0728	−0.899973
$974$	68.2583	2.18714
$975$	1.00000	0.0320256
$976$	−21.7811	−0.697197
$977$	−20.6473	−0.660566	−0.330283	−	0.943882i	$-0.607144\pi$
$977$	−20.6473	−0.660566	−0.330283	+	0.943882i	$0.607144\pi$
$978$	19.3440	0.618553
$979$	25.0063	0.799205
$980$	12.1993	0.389692
$981$	13.3440	0.426041
$982$	−91.0614	−2.90589
$983$	−22.2935	−0.711053	−0.355527	−	0.934666i	$-0.615698\pi$
$983$	−22.2935	−0.711053	−0.355527	+	0.934666i	$0.615698\pi$
$984$	−40.9644	−1.30590
$985$	−15.8225	−0.504145
$986$	−3.05981	−0.0974443
$987$	16.0002	0.509291
$988$	20.9133	0.665342
$989$	6.26695	0.199277
$990$	12.0669	0.383512
$991$	−40.9399	−1.30050	−0.650250	−	0.759721i	$-0.725336\pi$
$991$	−40.9399	−1.30050	−0.650250	+	0.759721i	$0.725336\pi$
$992$	1.36136	0.0432233
$993$	7.38292	0.234290
$994$	−3.47445	−0.110203
$995$	15.1127	0.479105
$996$	25.2477	0.800005
$997$	−32.9009	−1.04198	−0.520991	−	0.853562i	$-0.674438\pi$
$997$	−32.9009	−1.04198	−0.520991	+	0.853562i	$0.674438\pi$
$998$	−90.3317	−2.85940
$999$	6.95072	0.219911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.w.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.w.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+2.41951 q^{2} -1.00000 q^{3} +3.85401 q^{4} -1.00000 q^{5} -2.41951 q^{6} +1.95823 q^{7} +4.48578 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.41951 q^{2} -1.00000 q^{3} +3.85401 q^{4} -1.00000 q^{5} -2.41951 q^{6} +1.95823 q^{7} +4.48578 q^{8} +1.00000 q^{9} -2.41951 q^{10} -4.98736 q^{11} -3.85401 q^{12} -1.00000 q^{13} +4.73794 q^{14} +1.00000 q^{15} +3.14535 q^{16} +0.501580 q^{17} +2.41951 q^{18} -5.42639 q^{19} -3.85401 q^{20} -1.95823 q^{21} -12.0669 q^{22} +3.81151 q^{23} -4.48578 q^{24} +1.00000 q^{25} -2.41951 q^{26} -1.00000 q^{27} +7.54701 q^{28} -2.52132 q^{29} +2.41951 q^{30} -1.00000 q^{31} -1.36136 q^{32} +4.98736 q^{33} +1.21357 q^{34} -1.95823 q^{35} +3.85401 q^{36} -6.95072 q^{37} -13.1292 q^{38} +1.00000 q^{39} -4.48578 q^{40} +9.13206 q^{41} -4.73794 q^{42} +1.64422 q^{43} -19.2213 q^{44} -1.00000 q^{45} +9.22198 q^{46} -8.17075 q^{47} -3.14535 q^{48} -3.16535 q^{49} +2.41951 q^{50} -0.501580 q^{51} -3.85401 q^{52} -3.24881 q^{53} -2.41951 q^{54} +4.98736 q^{55} +8.78416 q^{56} +5.42639 q^{57} -6.10035 q^{58} +2.12934 q^{59} +3.85401 q^{60} -6.92486 q^{61} -2.41951 q^{62} +1.95823 q^{63} -9.58452 q^{64} +1.00000 q^{65} +12.0669 q^{66} -7.22598 q^{67} +1.93309 q^{68} -3.81151 q^{69} -4.73794 q^{70} -0.733327 q^{71} +4.48578 q^{72} -5.16672 q^{73} -16.8173 q^{74} -1.00000 q^{75} -20.9133 q^{76} -9.76637 q^{77} +2.41951 q^{78} -2.17614 q^{79} -3.14535 q^{80} +1.00000 q^{81} +22.0951 q^{82} -6.55104 q^{83} -7.54701 q^{84} -0.501580 q^{85} +3.97819 q^{86} +2.52132 q^{87} -22.3722 q^{88} -5.01394 q^{89} -2.41951 q^{90} -1.95823 q^{91} +14.6896 q^{92} +1.00000 q^{93} -19.7692 q^{94} +5.42639 q^{95} +1.36136 q^{96} +11.7894 q^{97} -7.65859 q^{98} -4.98736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 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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