LMFDB - Embedded newform 1805.2.a.s.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.30799$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.307988 q^{2} +1.64392 q^{3} -1.90514 q^{4} +1.00000 q^{5} +0.506308 q^{6} +0.0891959 q^{7} -1.20274 q^{8} -0.297533 q^{9} +O(q^{10})$	\(q+0.307988 q^{2} +1.64392 q^{3} -1.90514 q^{4} +1.00000 q^{5} +0.506308 q^{6} +0.0891959 q^{7} -1.20274 q^{8} -0.297533 q^{9} +0.307988 q^{10} -3.36682 q^{11} -3.13190 q^{12} -0.212870 q^{13} +0.0274713 q^{14} +1.64392 q^{15} +3.43986 q^{16} -2.51423 q^{17} -0.0916368 q^{18} -1.90514 q^{20} +0.146631 q^{21} -1.03694 q^{22} -5.96699 q^{23} -1.97720 q^{24} +1.00000 q^{25} -0.0655615 q^{26} -5.42087 q^{27} -0.169931 q^{28} +4.80823 q^{29} +0.506308 q^{30} -8.06815 q^{31} +3.46491 q^{32} -5.53478 q^{33} -0.774354 q^{34} +0.0891959 q^{35} +0.566844 q^{36} -1.84372 q^{37} -0.349941 q^{39} -1.20274 q^{40} +3.01234 q^{41} +0.0451606 q^{42} -2.44787 q^{43} +6.41428 q^{44} -0.297533 q^{45} -1.83776 q^{46} -7.61831 q^{47} +5.65484 q^{48} -6.99204 q^{49} +0.307988 q^{50} -4.13319 q^{51} +0.405548 q^{52} +8.39967 q^{53} -1.66957 q^{54} -3.36682 q^{55} -0.107279 q^{56} +1.48088 q^{58} -10.4354 q^{59} -3.13190 q^{60} -0.988579 q^{61} -2.48490 q^{62} -0.0265388 q^{63} -5.81256 q^{64} -0.212870 q^{65} -1.70465 q^{66} -9.97964 q^{67} +4.78997 q^{68} -9.80923 q^{69} +0.0274713 q^{70} -6.17719 q^{71} +0.357855 q^{72} +15.7450 q^{73} -0.567844 q^{74} +1.64392 q^{75} -0.300307 q^{77} -0.107778 q^{78} +1.02849 q^{79} +3.43986 q^{80} -8.01887 q^{81} +0.927765 q^{82} +17.9388 q^{83} -0.279353 q^{84} -2.51423 q^{85} -0.753916 q^{86} +7.90434 q^{87} +4.04941 q^{88} -0.656354 q^{89} -0.0916368 q^{90} -0.0189871 q^{91} +11.3680 q^{92} -13.2634 q^{93} -2.34635 q^{94} +5.69603 q^{96} -16.8130 q^{97} -2.15347 q^{98} +1.00174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.307988	0.217781	0.108890	−	0.994054i	$-0.465270\pi$
$2$	0.307988	0.217781	0.108890	+	0.994054i	$0.465270\pi$
$3$	1.64392	0.949117	0.474558	−	0.880224i	$-0.342608\pi$
$3$	1.64392	0.949117	0.474558	+	0.880224i	$0.342608\pi$
$4$	−1.90514	−0.952572
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.506308	0.206699
$7$	0.0891959	0.0337129	0.0168564	−	0.999858i	$-0.494634\pi$
$7$	0.0891959	0.0337129	0.0168564	+	0.999858i	$0.494634\pi$
$8$	−1.20274	−0.425232
$9$	−0.297533	−0.0991778
$10$	0.307988	0.0973945
$11$	−3.36682	−1.01513	−0.507567	−	0.861612i	$-0.669455\pi$
$11$	−3.36682	−1.01513	−0.507567	+	0.861612i	$0.669455\pi$
$12$	−3.13190	−0.904101
$13$	−0.212870	−0.0590395	−0.0295198	−	0.999564i	$-0.509398\pi$
$13$	−0.212870	−0.0590395	−0.0295198	+	0.999564i	$0.509398\pi$
$14$	0.0274713	0.00734201
$15$	1.64392	0.424458
$16$	3.43986	0.859964
$17$	−2.51423	−0.609791	−0.304896	−	0.952386i	$-0.598622\pi$
$17$	−2.51423	−0.609791	−0.304896	+	0.952386i	$0.598622\pi$
$18$	−0.0916368	−0.0215990
$19$	0	0
$19$	0	0
$20$	−1.90514	−0.426003
$21$	0.146631	0.0319975
$22$	−1.03694	−0.221077
$23$	−5.96699	−1.24420	−0.622101	−	0.782937i	$-0.713721\pi$
$23$	−5.96699	−1.24420	−0.622101	+	0.782937i	$0.713721\pi$
$24$	−1.97720	−0.403595
$25$	1.00000	0.200000
$26$	−0.0655615	−0.0128577
$27$	−5.42087	−1.04325
$28$	−0.169931	−0.0321139
$29$	4.80823	0.892866	0.446433	−	0.894817i	$-0.352694\pi$
$29$	4.80823	0.892866	0.446433	+	0.894817i	$0.352694\pi$
$30$	0.506308	0.0924387
$31$	−8.06815	−1.44908	−0.724541	−	0.689232i	$-0.757948\pi$
$31$	−8.06815	−1.44908	−0.724541	+	0.689232i	$0.757948\pi$
$32$	3.46491	0.612516
$33$	−5.53478	−0.963481
$34$	−0.774354	−0.132801
$35$	0.0891959	0.0150769
$36$	0.566844	0.0944739
$37$	−1.84372	−0.303106	−0.151553	−	0.988449i	$-0.548427\pi$
$37$	−1.84372	−0.303106	−0.151553	+	0.988449i	$0.548427\pi$
$38$	0	0
$39$	−0.349941	−0.0560354
$40$	−1.20274	−0.190170
$41$	3.01234	0.470448	0.235224	−	0.971941i	$-0.424418\pi$
$41$	3.01234	0.470448	0.235224	+	0.971941i	$0.424418\pi$
$42$	0.0451606	0.00696842
$43$	−2.44787	−0.373297	−0.186648	−	0.982427i	$-0.559763\pi$
$43$	−2.44787	−0.373297	−0.186648	+	0.982427i	$0.559763\pi$
$44$	6.41428	0.966989
$45$	−0.297533	−0.0443537
$46$	−1.83776	−0.270963
$47$	−7.61831	−1.11125	−0.555623	−	0.831435i	$-0.687520\pi$
$47$	−7.61831	−1.11125	−0.555623	+	0.831435i	$0.687520\pi$
$48$	5.65484	0.816206
$49$	−6.99204	−0.998863
$50$	0.307988	0.0435561
$51$	−4.13319	−0.578763
$52$	0.405548	0.0562394
$53$	8.39967	1.15378	0.576891	−	0.816821i	$-0.304266\pi$
$53$	8.39967	1.15378	0.576891	+	0.816821i	$0.304266\pi$
$54$	−1.66957	−0.227199
$55$	−3.36682	−0.453982
$56$	−0.107279	−0.0143358
$57$	0	0
$58$	1.48088	0.194449
$59$	−10.4354	−1.35858	−0.679289	−	0.733871i	$-0.737712\pi$
$59$	−10.4354	−1.35858	−0.679289	+	0.733871i	$0.737712\pi$
$60$	−3.13190	−0.404326
$61$	−0.988579	−0.126575	−0.0632873	−	0.997995i	$-0.520158\pi$
$61$	−0.988579	−0.126575	−0.0632873	+	0.997995i	$0.520158\pi$
$62$	−2.48490	−0.315582
$63$	−0.0265388	−0.00334357
$64$	−5.81256	−0.726570
$65$	−0.212870	−0.0264033
$66$	−1.70465	−0.209828
$67$	−9.97964	−1.21921	−0.609604	−	0.792706i	$-0.708671\pi$
$67$	−9.97964	−1.21921	−0.609604	+	0.792706i	$0.708671\pi$
$68$	4.78997	0.580870
$69$	−9.80923	−1.18089
$70$	0.0274713	0.00328345
$71$	−6.17719	−0.733097	−0.366549	−	0.930399i	$-0.619461\pi$
$71$	−6.17719	−0.733097	−0.366549	+	0.930399i	$0.619461\pi$
$72$	0.357855	0.0421736
$73$	15.7450	1.84281	0.921407	−	0.388600i	$-0.127041\pi$
$73$	15.7450	1.84281	0.921407	+	0.388600i	$0.127041\pi$
$74$	−0.567844	−0.0660106
$75$	1.64392	0.189823
$76$	0	0
$77$	−0.300307	−0.0342231
$78$	−0.107778	−0.0122034
$79$	1.02849	0.115715	0.0578573	−	0.998325i	$-0.481573\pi$
$79$	1.02849	0.115715	0.0578573	+	0.998325i	$0.481573\pi$
$80$	3.43986	0.384588
$81$	−8.01887	−0.890986
$82$	0.927765	0.102455
$83$	17.9388	1.96904	0.984518	−	0.175284i	$-0.0560842\pi$
$83$	17.9388	1.96904	0.984518	+	0.175284i	$0.0560842\pi$
$84$	−0.279353	−0.0304799
$85$	−2.51423	−0.272707
$86$	−0.753916	−0.0812968
$87$	7.90434	0.847434
$88$	4.04941	0.431668
$89$	−0.656354	−0.0695734	−0.0347867	−	0.999395i	$-0.511075\pi$
$89$	−0.656354	−0.0695734	−0.0347867	+	0.999395i	$0.511075\pi$
$90$	−0.0916368	−0.00965937
$91$	−0.0189871	−0.00199039
$92$	11.3680	1.18519
$93$	−13.2634	−1.37535
$94$	−2.34635	−0.242008
$95$	0	0
$96$	5.69603	0.581349
$97$	−16.8130	−1.70711	−0.853553	−	0.521006i	$-0.825557\pi$
$97$	−16.8130	−1.70711	−0.853553	+	0.521006i	$0.825557\pi$
$98$	−2.15347	−0.217533
$99$	1.00174	0.100679
$100$	−1.90514	−0.190514
$101$	3.67973	0.366146	0.183073	−	0.983099i	$-0.441395\pi$
$101$	3.67973	0.366146	0.183073	+	0.983099i	$0.441395\pi$
$102$	−1.27298	−0.126043
$103$	3.53420	0.348235	0.174118	−	0.984725i	$-0.444293\pi$
$103$	3.53420	0.348235	0.174118	+	0.984725i	$0.444293\pi$
$104$	0.256027	0.0251055
$105$	0.146631	0.0143097
$106$	2.58700	0.251272
$107$	1.88660	0.182385	0.0911923	−	0.995833i	$-0.470932\pi$
$107$	1.88660	0.182385	0.0911923	+	0.995833i	$0.470932\pi$
$108$	10.3275	0.993768
$109$	13.1599	1.26049	0.630244	−	0.776397i	$-0.282955\pi$
$109$	13.1599	1.26049	0.630244	+	0.776397i	$0.282955\pi$
$110$	−1.03694	−0.0988685
$111$	−3.03093	−0.287683
$112$	0.306821	0.0289919
$113$	−12.3456	−1.16138	−0.580689	−	0.814125i	$-0.697217\pi$
$113$	−12.3456	−1.16138	−0.580689	+	0.814125i	$0.697217\pi$
$114$	0	0
$115$	−5.96699	−0.556424
$116$	−9.16037	−0.850519
$117$	0.0633359	0.00585541
$118$	−3.21399	−0.295872
$119$	−0.224259	−0.0205578
$120$	−1.97720	−0.180493
$121$	0.335489	0.0304990
$122$	−0.304471	−0.0275655
$123$	4.95204	0.446510
$124$	15.3710	1.38035
$125$	1.00000	0.0894427
$126$	−0.00817363	−0.000728164 0
$127$	−21.2121	−1.88227	−0.941134	−	0.338035i	$-0.890238\pi$
$127$	−21.2121	−1.88227	−0.941134	+	0.338035i	$0.890238\pi$
$128$	−8.72003	−0.770749
$129$	−4.02410	−0.354302
$130$	−0.0655615	−0.00575012
$131$	6.95074	0.607289	0.303645	−	0.952785i	$-0.401796\pi$
$131$	6.95074	0.607289	0.303645	+	0.952785i	$0.401796\pi$
$132$	10.5445	0.917785
$133$	0	0
$134$	−3.07361	−0.265520
$135$	−5.42087	−0.466555
$136$	3.02396	0.259303
$137$	21.0068	1.79474	0.897368	−	0.441283i	$-0.145477\pi$
$137$	21.0068	1.79474	0.897368	+	0.441283i	$0.145477\pi$
$138$	−3.02113	−0.257176
$139$	15.7214	1.33347	0.666736	−	0.745294i	$-0.267691\pi$
$139$	15.7214	1.33347	0.666736	+	0.745294i	$0.267691\pi$
$140$	−0.169931	−0.0143618
$141$	−12.5239	−1.05470
$142$	−1.90250	−0.159654
$143$	0.716695	0.0599331
$144$	−1.02347	−0.0852894
$145$	4.80823	0.399302
$146$	4.84928	0.401329
$147$	−11.4943	−0.948038
$148$	3.51255	0.288730
$149$	−19.5194	−1.59909	−0.799546	−	0.600605i	$-0.794927\pi$
$149$	−19.5194	−1.59909	−0.799546	+	0.600605i	$0.794927\pi$
$150$	0.506308	0.0413398
$151$	−11.2284	−0.913758	−0.456879	−	0.889529i	$-0.651033\pi$
$151$	−11.2284	−0.913758	−0.456879	+	0.889529i	$0.651033\pi$
$152$	0	0
$153$	0.748068	0.0604777
$154$	−0.0924909	−0.00745313
$155$	−8.06815	−0.648049
$156$	0.666687	0.0533777
$157$	4.61281	0.368143	0.184071	−	0.982913i	$-0.441072\pi$
$157$	4.61281	0.368143	0.184071	+	0.982913i	$0.441072\pi$
$158$	0.316764	0.0252004
$159$	13.8084	1.09507
$160$	3.46491	0.273925
$161$	−0.532231	−0.0419456
$162$	−2.46972	−0.194039
$163$	−0.574735	−0.0450167	−0.0225084	−	0.999747i	$-0.507165\pi$
$163$	−0.574735	−0.0450167	−0.0225084	+	0.999747i	$0.507165\pi$
$164$	−5.73894	−0.448136
$165$	−5.53478	−0.430882
$166$	5.52493	0.428818
$167$	−4.12202	−0.318971	−0.159486	−	0.987200i	$-0.550984\pi$
$167$	−4.12202	−0.318971	−0.159486	+	0.987200i	$0.550984\pi$
$168$	−0.176358	−0.0136063
$169$	−12.9547	−0.996514
$170$	−0.774354	−0.0593903
$171$	0	0
$172$	4.66355	0.355592
$173$	6.43458	0.489212	0.244606	−	0.969623i	$-0.421341\pi$
$173$	6.43458	0.489212	0.244606	+	0.969623i	$0.421341\pi$
$174$	2.43444	0.184555
$175$	0.0891959	0.00674258
$176$	−11.5814	−0.872980
$177$	−17.1550	−1.28945
$178$	−0.202149	−0.0151517
$179$	−3.83032	−0.286291	−0.143146	−	0.989702i	$-0.545722\pi$
$179$	−3.83032	−0.286291	−0.143146	+	0.989702i	$0.545722\pi$
$180$	0.566844	0.0422500
$181$	−16.6878	−1.24039	−0.620195	−	0.784447i	$-0.712947\pi$
$181$	−16.6878	−1.24039	−0.620195	+	0.784447i	$0.712947\pi$
$182$	−0.00584781	−0.000433469 0
$183$	−1.62514	−0.120134
$184$	7.17672	0.529075
$185$	−1.84372	−0.135553
$186$	−4.08496	−0.299524
$187$	8.46497	0.619020
$188$	14.5140	1.05854
$189$	−0.483520	−0.0351709
$190$	0	0
$191$	7.92694	0.573573	0.286787	−	0.957994i	$-0.407413\pi$
$191$	7.92694	0.573573	0.286787	+	0.957994i	$0.407413\pi$
$192$	−9.55538	−0.689600
$193$	21.2669	1.53082	0.765412	−	0.643540i	$-0.222535\pi$
$193$	21.2669	1.53082	0.765412	+	0.643540i	$0.222535\pi$
$194$	−5.17822	−0.371775
$195$	−0.349941	−0.0250598
$196$	13.3208	0.951489
$197$	2.88742	0.205720	0.102860	−	0.994696i	$-0.467201\pi$
$197$	2.88742	0.205720	0.102860	+	0.994696i	$0.467201\pi$
$198$	0.308525	0.0219259
$199$	11.6149	0.823355	0.411678	−	0.911330i	$-0.364943\pi$
$199$	11.6149	0.823355	0.411678	+	0.911330i	$0.364943\pi$
$200$	−1.20274	−0.0850464
$201$	−16.4057	−1.15717
$202$	1.13331	0.0797396
$203$	0.428874	0.0301011
$204$	7.87432	0.551313
$205$	3.01234	0.210391
$206$	1.08849	0.0758389
$207$	1.77538	0.123397
$208$	−0.732242	−0.0507719
$209$	0	0
$210$	0.0451606	0.00311637
$211$	23.7001	1.63158	0.815790	−	0.578349i	$-0.196303\pi$
$211$	23.7001	1.63158	0.815790	+	0.578349i	$0.196303\pi$
$212$	−16.0026	−1.09906
$213$	−10.1548	−0.695795
$214$	0.581051	0.0397198
$215$	−2.44787	−0.166943
$216$	6.51989	0.443623
$217$	−0.719646	−0.0488527
$218$	4.05309	0.274510
$219$	25.8835	1.74904
$220$	6.41428	0.432451
$221$	0.535205	0.0360018
$222$	−0.933490	−0.0626517
$223$	8.81587	0.590354	0.295177	−	0.955443i	$-0.404621\pi$
$223$	8.81587	0.590354	0.295177	+	0.955443i	$0.404621\pi$
$224$	0.309056	0.0206497
$225$	−0.297533	−0.0198356
$226$	−3.80231	−0.252926
$227$	1.04512	0.0693671	0.0346835	−	0.999398i	$-0.488958\pi$
$227$	1.04512	0.0693671	0.0346835	+	0.999398i	$0.488958\pi$
$228$	0	0
$229$	−13.4837	−0.891031	−0.445515	−	0.895274i	$-0.646980\pi$
$229$	−13.4837	−0.891031	−0.445515	+	0.895274i	$0.646980\pi$
$230$	−1.83776	−0.121178
$231$	−0.493680	−0.0324817
$232$	−5.78304	−0.379675
$233$	11.2178	0.734905	0.367452	−	0.930042i	$-0.380230\pi$
$233$	11.2178	0.734905	0.367452	+	0.930042i	$0.380230\pi$
$234$	0.0195067	0.00127519
$235$	−7.61831	−0.496964
$236$	19.8810	1.29414
$237$	1.69076	0.109827
$238$	−0.0690692	−0.00447709
$239$	−20.3290	−1.31497	−0.657487	−	0.753466i	$-0.728380\pi$
$239$	−20.3290	−1.31497	−0.657487	+	0.753466i	$0.728380\pi$
$240$	5.65484	0.365019
$241$	3.84452	0.247647	0.123824	−	0.992304i	$-0.460484\pi$
$241$	3.84452	0.247647	0.123824	+	0.992304i	$0.460484\pi$
$242$	0.103327	0.00664209
$243$	3.08025	0.197598
$244$	1.88339	0.120571
$245$	−6.99204	−0.446705
$246$	1.52517	0.0972413
$247$	0	0
$248$	9.70387	0.616197
$249$	29.4899	1.86884
$250$	0.307988	0.0194789
$251$	−7.93776	−0.501027	−0.250513	−	0.968113i	$-0.580599\pi$
$251$	−7.93776	−0.501027	−0.250513	+	0.968113i	$0.580599\pi$
$252$	0.0505601	0.00318499
$253$	20.0898	1.26303
$254$	−6.53307	−0.409921
$255$	−4.13319	−0.258831
$256$	8.93946	0.558716
$257$	−24.2278	−1.51129	−0.755643	−	0.654984i	$-0.772675\pi$
$257$	−24.2278	−1.51129	−0.755643	+	0.654984i	$0.772675\pi$
$258$	−1.23938	−0.0771602
$259$	−0.164452	−0.0102186
$260$	0.405548	0.0251510
$261$	−1.43061	−0.0885525
$262$	2.14075	0.132256
$263$	−12.3772	−0.763212	−0.381606	−	0.924325i	$-0.624629\pi$
$263$	−12.3772	−0.763212	−0.381606	+	0.924325i	$0.624629\pi$
$264$	6.65689	0.409703
$265$	8.39967	0.515987
$266$	0	0
$267$	−1.07899	−0.0660333
$268$	19.0127	1.16138
$269$	24.3788	1.48640	0.743202	−	0.669067i	$-0.233306\pi$
$269$	24.3788	1.48640	0.743202	+	0.669067i	$0.233306\pi$
$270$	−1.66957	−0.101607
$271$	17.4183	1.05809	0.529043	−	0.848595i	$-0.322551\pi$
$271$	17.4183	1.05809	0.529043	+	0.848595i	$0.322551\pi$
$272$	−8.64860	−0.524398
$273$	−0.0312133	−0.00188911
$274$	6.46986	0.390859
$275$	−3.36682	−0.203027
$276$	18.6880	1.12489
$277$	20.7839	1.24879	0.624393	−	0.781110i	$-0.285346\pi$
$277$	20.7839	1.24879	0.624393	+	0.781110i	$0.285346\pi$
$278$	4.84201	0.290404
$279$	2.40054	0.143717
$280$	−0.107279	−0.00641117
$281$	6.00987	0.358519	0.179259	−	0.983802i	$-0.442630\pi$
$281$	6.00987	0.358519	0.179259	+	0.983802i	$0.442630\pi$
$282$	−3.85721	−0.229694
$283$	11.5738	0.687993	0.343997	−	0.938971i	$-0.388219\pi$
$283$	11.5738	0.687993	0.343997	+	0.938971i	$0.388219\pi$
$284$	11.7684	0.698327
$285$	0	0
$286$	0.220734	0.0130523
$287$	0.268688	0.0158602
$288$	−1.03093	−0.0607480
$289$	−10.6786	−0.628155
$290$	1.48088	0.0869602
$291$	−27.6393	−1.62024
$292$	−29.9965	−1.75541
$293$	−17.4693	−1.02057	−0.510284	−	0.860006i	$-0.670460\pi$
$293$	−17.4693	−1.02057	−0.510284	+	0.860006i	$0.670460\pi$
$294$	−3.54012	−0.206464
$295$	−10.4354	−0.607574
$296$	2.21751	0.128890
$297$	18.2511	1.05904
$298$	−6.01175	−0.348251
$299$	1.27019	0.0734571
$300$	−3.13190	−0.180820
$301$	−0.218340	−0.0125849
$302$	−3.45823	−0.198999
$303$	6.04917	0.347516
$304$	0	0
$305$	−0.988579	−0.0566059
$306$	0.230396	0.0131709
$307$	−29.6533	−1.69240	−0.846201	−	0.532863i	$-0.821116\pi$
$307$	−29.6533	−1.69240	−0.846201	+	0.532863i	$0.821116\pi$
$308$	0.572127	0.0326000
$309$	5.80994	0.330516
$310$	−2.48490	−0.141133
$311$	−11.6224	−0.659045	−0.329522	−	0.944148i	$-0.606888\pi$
$311$	−11.6224	−0.659045	−0.329522	+	0.944148i	$0.606888\pi$
$312$	0.420887	0.0238280
$313$	−0.474863	−0.0268409	−0.0134204	−	0.999910i	$-0.504272\pi$
$313$	−0.474863	−0.0268409	−0.0134204	+	0.999910i	$0.504272\pi$
$314$	1.42069	0.0801743
$315$	−0.0265388	−0.00149529
$316$	−1.95943	−0.110226
$317$	20.2283	1.13613	0.568066	−	0.822983i	$-0.307692\pi$
$317$	20.2283	1.13613	0.568066	+	0.822983i	$0.307692\pi$
$318$	4.25281	0.238486
$319$	−16.1885	−0.906379
$320$	−5.81256	−0.324932
$321$	3.10142	0.173104
$322$	−0.163921	−0.00913495
$323$	0	0
$324$	15.2771	0.848728
$325$	−0.212870	−0.0118079
$326$	−0.177012	−0.00980377
$327$	21.6338	1.19635
$328$	−3.62306	−0.200050
$329$	−0.679522	−0.0374633
$330$	−1.70465	−0.0938377
$331$	6.01306	0.330508	0.165254	−	0.986251i	$-0.447156\pi$
$331$	6.01306	0.330508	0.165254	+	0.986251i	$0.447156\pi$
$332$	−34.1759	−1.87565
$333$	0.548568	0.0300614
$334$	−1.26953	−0.0694658
$335$	−9.97964	−0.545246
$336$	0.504389	0.0275167
$337$	8.86733	0.483034	0.241517	−	0.970397i	$-0.422355\pi$
$337$	8.86733	0.483034	0.241517	+	0.970397i	$0.422355\pi$
$338$	−3.98989	−0.217022
$339$	−20.2952	−1.10228
$340$	4.78997	0.259773
$341$	27.1640	1.47101
$342$	0	0
$343$	−1.24803	−0.0673874
$344$	2.94415	0.158738
$345$	−9.80923	−0.528111
$346$	1.98177	0.106541
$347$	19.9712	1.07211	0.536055	−	0.844183i	$-0.319914\pi$
$347$	19.9712	1.07211	0.536055	+	0.844183i	$0.319914\pi$
$348$	−15.0589	−0.807241
$349$	−0.810214	−0.0433698	−0.0216849	−	0.999765i	$-0.506903\pi$
$349$	−0.810214	−0.0433698	−0.0216849	+	0.999765i	$0.506903\pi$
$350$	0.0274713	0.00146840
$351$	1.15394	0.0615928
$352$	−11.6657	−0.621786
$353$	−20.9503	−1.11507	−0.557536	−	0.830153i	$-0.688253\pi$
$353$	−20.9503	−1.11507	−0.557536	+	0.830153i	$0.688253\pi$
$354$	−5.28354	−0.280817
$355$	−6.17719	−0.327851
$356$	1.25045	0.0662736
$357$	−0.368664	−0.0195118
$358$	−1.17969	−0.0623487
$359$	25.7019	1.35649	0.678246	−	0.734835i	$-0.262740\pi$
$359$	25.7019	1.35649	0.678246	+	0.734835i	$0.262740\pi$
$360$	0.357855	0.0188606
$361$	0	0
$362$	−5.13963	−0.270133
$363$	0.551516	0.0289471
$364$	0.0361732	0.00189599
$365$	15.7450	0.824131
$366$	−0.500525	−0.0261629
$367$	−24.2860	−1.26772	−0.633858	−	0.773449i	$-0.718530\pi$
$367$	−24.2860	−1.26772	−0.633858	+	0.773449i	$0.718530\pi$
$368$	−20.5256	−1.06997
$369$	−0.896271	−0.0466580
$370$	−0.567844	−0.0295208
$371$	0.749216	0.0388973
$372$	25.2686	1.31012
$373$	−10.8809	−0.563390	−0.281695	−	0.959504i	$-0.590897\pi$
$373$	−10.8809	−0.563390	−0.281695	+	0.959504i	$0.590897\pi$
$374$	2.60711	0.134811
$375$	1.64392	0.0848916
$376$	9.16284	0.472537
$377$	−1.02353	−0.0527144
$378$	−0.148918	−0.00765954
$379$	−19.3318	−0.993008	−0.496504	−	0.868034i	$-0.665383\pi$
$379$	−19.3318	−0.993008	−0.496504	+	0.868034i	$0.665383\pi$
$380$	0	0
$381$	−34.8709	−1.78649
$382$	2.44140	0.124913
$383$	1.04305	0.0532973	0.0266487	−	0.999645i	$-0.491516\pi$
$383$	1.04305	0.0532973	0.0266487	+	0.999645i	$0.491516\pi$
$384$	−14.3350	−0.731530
$385$	−0.300307	−0.0153050
$386$	6.54995	0.333384
$387$	0.728323	0.0370228
$388$	32.0313	1.62614
$389$	26.6031	1.34883	0.674416	−	0.738352i	$-0.264395\pi$
$389$	26.6031	1.34883	0.674416	+	0.738352i	$0.264395\pi$
$390$	−0.107778	−0.00545753
$391$	15.0024	0.758703
$392$	8.40960	0.424749
$393$	11.4264	0.576388
$394$	0.889293	0.0448019
$395$	1.02849	0.0517491
$396$	−1.90846	−0.0959038
$397$	−3.69756	−0.185575	−0.0927877	−	0.995686i	$-0.529578\pi$
$397$	−3.69756	−0.185575	−0.0927877	+	0.995686i	$0.529578\pi$
$398$	3.57724	0.179311
$399$	0	0
$400$	3.43986	0.171993
$401$	20.2351	1.01049	0.505245	−	0.862976i	$-0.331402\pi$
$401$	20.2351	1.01049	0.505245	+	0.862976i	$0.331402\pi$
$402$	−5.05277	−0.252009
$403$	1.71747	0.0855531
$404$	−7.01040	−0.348781
$405$	−8.01887	−0.398461
$406$	0.132088	0.00655543
$407$	6.20748	0.307693
$408$	4.97115	0.246109
$409$	−12.4768	−0.616939	−0.308470	−	0.951234i	$-0.599817\pi$
$409$	−12.4768	−0.616939	−0.308470	+	0.951234i	$0.599817\pi$
$410$	0.927765	0.0458191
$411$	34.5335	1.70341
$412$	−6.73316	−0.331719
$413$	−0.930798	−0.0458016
$414$	0.546795	0.0268735
$415$	17.9388	0.880580
$416$	−0.737576	−0.0361626
$417$	25.8447	1.26562
$418$	0	0
$419$	28.9962	1.41656	0.708279	−	0.705933i	$-0.249472\pi$
$419$	28.9962	1.41656	0.708279	+	0.705933i	$0.249472\pi$
$420$	−0.279353	−0.0136310
$421$	−14.5960	−0.711368	−0.355684	−	0.934606i	$-0.615752\pi$
$421$	−14.5960	−0.711368	−0.355684	+	0.934606i	$0.615752\pi$
$422$	7.29934	0.355326
$423$	2.26670	0.110211
$424$	−10.1026	−0.490626
$425$	−2.51423	−0.121958
$426$	−3.12756	−0.151531
$427$	−0.0881772	−0.00426720
$428$	−3.59424	−0.173734
$429$	1.17819	0.0568835
$430$	−0.753916	−0.0363570
$431$	−13.5081	−0.650663	−0.325332	−	0.945600i	$-0.605476\pi$
$431$	−13.5081	−0.650663	−0.325332	+	0.945600i	$0.605476\pi$
$432$	−18.6470	−0.897156
$433$	−38.0206	−1.82715	−0.913576	−	0.406668i	$-0.866690\pi$
$433$	−38.0206	−1.82715	−0.913576	+	0.406668i	$0.866690\pi$
$434$	−0.221642	−0.0106392
$435$	7.90434	0.378984
$436$	−25.0714	−1.20070
$437$	0	0
$438$	7.97181	0.380908
$439$	23.7870	1.13529	0.567645	−	0.823273i	$-0.307854\pi$
$439$	23.7870	1.13529	0.567645	+	0.823273i	$0.307854\pi$
$440$	4.04941	0.193048
$441$	2.08037	0.0990651
$442$	0.164837	0.00784049
$443$	−19.2991	−0.916929	−0.458465	−	0.888713i	$-0.651600\pi$
$443$	−19.2991	−0.916929	−0.458465	+	0.888713i	$0.651600\pi$
$444$	5.77435	0.274038
$445$	−0.656354	−0.0311142
$446$	2.71518	0.128568
$447$	−32.0883	−1.51772
$448$	−0.518457	−0.0244948
$449$	26.4136	1.24654	0.623268	−	0.782008i	$-0.285805\pi$
$449$	26.4136	1.24654	0.623268	+	0.782008i	$0.285805\pi$
$450$	−0.0916368	−0.00431980
$451$	−10.1420	−0.477569
$452$	23.5202	1.10630
$453$	−18.4586	−0.867263
$454$	0.321885	0.0151068
$455$	−0.0189871	−0.000890130 0
$456$	0	0
$457$	−38.4641	−1.79927	−0.899637	−	0.436638i	$-0.856169\pi$
$457$	−38.4641	−1.79927	−0.899637	+	0.436638i	$0.856169\pi$
$458$	−4.15283	−0.194049
$459$	13.6293	0.636163
$460$	11.3680	0.530034
$461$	33.9836	1.58277	0.791387	−	0.611315i	$-0.209359\pi$
$461$	33.9836	1.58277	0.791387	+	0.611315i	$0.209359\pi$
$462$	−0.152048	−0.00707389
$463$	−5.39446	−0.250702	−0.125351	−	0.992112i	$-0.540006\pi$
$463$	−5.39446	−0.250702	−0.125351	+	0.992112i	$0.540006\pi$
$464$	16.5396	0.767833
$465$	−13.2634	−0.615074
$466$	3.45496	0.160048
$467$	22.4289	1.03788	0.518942	−	0.854809i	$-0.326326\pi$
$467$	22.4289	1.03788	0.518942	+	0.854809i	$0.326326\pi$
$468$	−0.120664	−0.00557770
$469$	−0.890143	−0.0411030
$470$	−2.34635	−0.108229
$471$	7.58309	0.349410
$472$	12.5511	0.577711
$473$	8.24155	0.378947
$474$	0.520734	0.0239181
$475$	0	0
$476$	0.427246	0.0195828
$477$	−2.49918	−0.114430
$478$	−6.26109	−0.286376
$479$	−28.7406	−1.31319	−0.656597	−	0.754242i	$-0.728005\pi$
$479$	−28.7406	−1.31319	−0.656597	+	0.754242i	$0.728005\pi$
$480$	5.69603	0.259987
$481$	0.392473	0.0178952
$482$	1.18407	0.0539328
$483$	−0.874943	−0.0398113
$484$	−0.639154	−0.0290525
$485$	−16.8130	−0.763441
$486$	0.948682	0.0430331
$487$	34.4441	1.56081	0.780406	−	0.625273i	$-0.215012\pi$
$487$	34.4441	1.56081	0.780406	+	0.625273i	$0.215012\pi$
$488$	1.18900	0.0538236
$489$	−0.944817	−0.0427261
$490$	−2.15347	−0.0972838
$491$	−19.3862	−0.874887	−0.437444	−	0.899246i	$-0.644116\pi$
$491$	−19.3862	−0.874887	−0.437444	+	0.899246i	$0.644116\pi$
$492$	−9.43434	−0.425333
$493$	−12.0890	−0.544462
$494$	0	0
$495$	1.00174	0.0450249
$496$	−27.7533	−1.24616
$497$	−0.550980	−0.0247148
$498$	9.08254	0.406998
$499$	11.2685	0.504445	0.252223	−	0.967669i	$-0.418838\pi$
$499$	11.2685	0.504445	0.252223	+	0.967669i	$0.418838\pi$
$500$	−1.90514	−0.0852006
$501$	−6.77626	−0.302741
$502$	−2.44474	−0.109114
$503$	10.5918	0.472266	0.236133	−	0.971721i	$-0.424120\pi$
$503$	10.5918	0.472266	0.236133	+	0.971721i	$0.424120\pi$
$504$	0.0319192	0.00142179
$505$	3.67973	0.163746
$506$	6.18742	0.275064
$507$	−21.2964	−0.945808
$508$	40.4120	1.79299
$509$	2.17937	0.0965988	0.0482994	−	0.998833i	$-0.484620\pi$
$509$	2.17937	0.0965988	0.0482994	+	0.998833i	$0.484620\pi$
$510$	−1.27298	−0.0563683
$511$	1.40439	0.0621266
$512$	20.1933	0.892426
$513$	0	0
$514$	−7.46186	−0.329129
$515$	3.53420	0.155735
$516$	7.66649	0.337498
$517$	25.6495	1.12806
$518$	−0.0506494	−0.00222541
$519$	10.5779	0.464319
$520$	0.256027	0.0112275
$521$	11.4473	0.501517	0.250759	−	0.968050i	$-0.419320\pi$
$521$	11.4473	0.501517	0.250759	+	0.968050i	$0.419320\pi$
$522$	−0.440611	−0.0192850
$523$	9.75228	0.426437	0.213219	−	0.977004i	$-0.431605\pi$
$523$	9.75228	0.426437	0.213219	+	0.977004i	$0.431605\pi$
$524$	−13.2422	−0.578486
$525$	0.146631	0.00639949
$526$	−3.81204	−0.166213
$527$	20.2852	0.883637
$528$	−19.0388	−0.828560
$529$	12.6049	0.548040
$530$	2.58700	0.112372
$531$	3.10489	0.134741
$532$	0	0
$533$	−0.641237	−0.0277750
$534$	−0.332317	−0.0143808
$535$	1.88660	0.0815649
$536$	12.0029	0.518446
$537$	−6.29673	−0.271724
$538$	7.50840	0.323710
$539$	23.5410	1.01398
$540$	10.3275	0.444427
$541$	22.8160	0.980938	0.490469	−	0.871459i	$-0.336825\pi$
$541$	22.8160	0.980938	0.490469	+	0.871459i	$0.336825\pi$
$542$	5.36463	0.230430
$543$	−27.4333	−1.17728
$544$	−8.71160	−0.373507
$545$	13.1599	0.563707
$546$	−0.00961333	−0.000411412 0
$547$	−30.9172	−1.32192	−0.660962	−	0.750419i	$-0.729852\pi$
$547$	−30.9172	−1.32192	−0.660962	+	0.750419i	$0.729852\pi$
$548$	−40.0210	−1.70961
$549$	0.294135	0.0125534
$550$	−1.03694	−0.0442153
$551$	0	0
$552$	11.7979	0.502154
$553$	0.0917374	0.00390107
$554$	6.40121	0.271961
$555$	−3.03093	−0.128656
$556$	−29.9515	−1.27023
$557$	−9.82887	−0.416463	−0.208231	−	0.978080i	$-0.566771\pi$
$557$	−9.82887	−0.416463	−0.208231	+	0.978080i	$0.566771\pi$
$558$	0.739339	0.0312987
$559$	0.521078	0.0220393
$560$	0.306821	0.0129656
$561$	13.9157	0.587522
$562$	1.85097	0.0780785
$563$	−33.4193	−1.40846	−0.704228	−	0.709974i	$-0.748707\pi$
$563$	−33.4193	−1.40846	−0.704228	+	0.709974i	$0.748707\pi$
$564$	23.8598	1.00468
$565$	−12.3456	−0.519384
$566$	3.56461	0.149832
$567$	−0.715251	−0.0300377
$568$	7.42954	0.311736
$569$	−37.6326	−1.57764	−0.788820	−	0.614624i	$-0.789308\pi$
$569$	−37.6326	−1.57764	−0.788820	+	0.614624i	$0.789308\pi$
$570$	0	0
$571$	−2.75232	−0.115181	−0.0575904	−	0.998340i	$-0.518342\pi$
$571$	−2.75232	−0.115181	−0.0575904	+	0.998340i	$0.518342\pi$
$572$	−1.36541	−0.0570905
$573$	13.0312	0.544388
$574$	0.0827528	0.00345404
$575$	−5.96699	−0.248840
$576$	1.72943	0.0720596
$577$	0.0370999	0.00154449	0.000772245	−	1.00000i	$-0.499754\pi$
$577$	0.0370999	0.00154449	0.000772245		1.00000i	$0.499754\pi$
$578$	−3.28889	−0.136800
$579$	34.9610	1.45293
$580$	−9.16037	−0.380363
$581$	1.60006	0.0663819
$582$	−8.51257	−0.352857
$583$	−28.2802	−1.17125
$584$	−18.9371	−0.783624
$585$	0.0633359	0.00261862
$586$	−5.38035	−0.222260
$587$	−3.60678	−0.148868	−0.0744340	−	0.997226i	$-0.523715\pi$
$587$	−3.60678	−0.148868	−0.0744340	+	0.997226i	$0.523715\pi$
$588$	21.8984	0.903074
$589$	0	0
$590$	−3.21399	−0.132318
$591$	4.74669	0.195253
$592$	−6.34214	−0.260660
$593$	17.8435	0.732744	0.366372	−	0.930469i	$-0.380600\pi$
$593$	17.8435	0.732744	0.366372	+	0.930469i	$0.380600\pi$
$594$	5.62113	0.230638
$595$	−0.224259	−0.00919373
$596$	37.1873	1.52325
$597$	19.0939	0.781460
$598$	0.391204	0.0159975
$599$	21.9448	0.896642	0.448321	−	0.893873i	$-0.352022\pi$
$599$	21.9448	0.896642	0.448321	+	0.893873i	$0.352022\pi$
$600$	−1.97720	−0.0807190
$601$	−10.2808	−0.419362	−0.209681	−	0.977770i	$-0.567243\pi$
$601$	−10.2808	−0.419362	−0.209681	+	0.977770i	$0.567243\pi$
$602$	−0.0672462	−0.00274075
$603$	2.96928	0.120918
$604$	21.3918	0.870420
$605$	0.335489	0.0136396
$606$	1.86307	0.0756822
$607$	−32.2616	−1.30946	−0.654729	−	0.755864i	$-0.727217\pi$
$607$	−32.2616	−1.30946	−0.654729	+	0.755864i	$0.727217\pi$
$608$	0	0
$609$	0.705034	0.0285694
$610$	−0.304471	−0.0123277
$611$	1.62171	0.0656074
$612$	−1.42518	−0.0576094
$613$	−16.3957	−0.662215	−0.331108	−	0.943593i	$-0.607422\pi$
$613$	−16.3957	−0.662215	−0.331108	+	0.943593i	$0.607422\pi$
$614$	−9.13287	−0.368573
$615$	4.95204	0.199685
$616$	0.361190	0.0145528
$617$	−12.7768	−0.514377	−0.257188	−	0.966361i	$-0.582796\pi$
$617$	−12.7768	−0.514377	−0.257188	+	0.966361i	$0.582796\pi$
$618$	1.78939	0.0719799
$619$	4.28207	0.172111	0.0860555	−	0.996290i	$-0.472574\pi$
$619$	4.28207	0.172111	0.0860555	+	0.996290i	$0.472574\pi$
$620$	15.3710	0.617313
$621$	32.3463	1.29801
$622$	−3.57956	−0.143527
$623$	−0.0585441	−0.00234552
$624$	−1.20375	−0.0481884
$625$	1.00000	0.0400000
$626$	−0.146252	−0.00584542
$627$	0	0
$628$	−8.78807	−0.350682
$629$	4.63554	0.184831
$630$	−0.00817363	−0.000325645 0
$631$	−22.7879	−0.907170	−0.453585	−	0.891213i	$-0.649855\pi$
$631$	−22.7879	−0.907170	−0.453585	+	0.891213i	$0.649855\pi$
$632$	−1.23701	−0.0492055
$633$	38.9610	1.54856
$634$	6.23007	0.247428
$635$	−21.2121	−0.841776
$636$	−26.3069	−1.04314
$637$	1.48840	0.0589724
$638$	−4.98585	−0.197392
$639$	1.83792	0.0727069
$640$	−8.72003	−0.344689
$641$	31.3626	1.23875	0.619373	−	0.785097i	$-0.287387\pi$
$641$	31.3626	1.23875	0.619373	+	0.785097i	$0.287387\pi$
$642$	0.955200	0.0376987
$643$	−11.1490	−0.439674	−0.219837	−	0.975537i	$-0.570553\pi$
$643$	−11.1490	−0.439674	−0.219837	+	0.975537i	$0.570553\pi$
$644$	1.01398	0.0399562
$645$	−4.02410	−0.158449
$646$	0	0
$647$	−17.5536	−0.690102	−0.345051	−	0.938584i	$-0.612138\pi$
$647$	−17.5536	−0.690102	−0.345051	+	0.938584i	$0.612138\pi$
$648$	9.64461	0.378876
$649$	35.1342	1.37914
$650$	−0.0655615	−0.00257153
$651$	−1.18304	−0.0463669
$652$	1.09495	0.0428816
$653$	−2.09533	−0.0819966	−0.0409983	−	0.999159i	$-0.513054\pi$
$653$	−2.09533	−0.0819966	−0.0409983	+	0.999159i	$0.513054\pi$
$654$	6.66294	0.260542
$655$	6.95074	0.271588
$656$	10.3620	0.404569
$657$	−4.68466	−0.182766
$658$	−0.209285	−0.00815878
$659$	13.0001	0.506411	0.253205	−	0.967413i	$-0.418515\pi$
$659$	13.0001	0.506411	0.253205	+	0.967413i	$0.418515\pi$
$660$	10.5445	0.410446
$661$	−38.0961	−1.48177	−0.740884	−	0.671633i	$-0.765593\pi$
$661$	−38.0961	−1.48177	−0.740884	+	0.671633i	$0.765593\pi$
$662$	1.85195	0.0719782
$663$	0.879833	0.0341699
$664$	−21.5756	−0.837298
$665$	0	0
$666$	0.168953	0.00654678
$667$	−28.6906	−1.11091
$668$	7.85304	0.303843
$669$	14.4926	0.560315
$670$	−3.07361	−0.118744
$671$	3.32837	0.128490
$672$	0.508063	0.0195989
$673$	−33.9497	−1.30867	−0.654333	−	0.756207i	$-0.727050\pi$
$673$	−33.9497	−1.30867	−0.654333	+	0.756207i	$0.727050\pi$
$674$	2.73103	0.105196
$675$	−5.42087	−0.208650
$676$	24.6805	0.949251
$677$	16.5562	0.636307	0.318153	−	0.948039i	$-0.396937\pi$
$677$	16.5562	0.636307	0.318153	+	0.948039i	$0.396937\pi$
$678$	−6.25068	−0.240056
$679$	−1.49965	−0.0575515
$680$	3.02396	0.115964
$681$	1.71809	0.0658374
$682$	8.36620	0.320358
$683$	−5.33328	−0.204072	−0.102036	−	0.994781i	$-0.532536\pi$
$683$	−5.33328	−0.204072	−0.102036	+	0.994781i	$0.532536\pi$
$684$	0	0
$685$	21.0068	0.802630
$686$	−0.384380	−0.0146757
$687$	−22.1662	−0.845692
$688$	−8.42033	−0.321022
$689$	−1.78804	−0.0681188
$690$	−3.02113	−0.115012
$691$	−14.1302	−0.537538	−0.268769	−	0.963205i	$-0.586617\pi$
$691$	−14.1302	−0.537538	−0.268769	+	0.963205i	$0.586617\pi$
$692$	−12.2588	−0.466009
$693$	0.0893513	0.00339417
$694$	6.15089	0.233485
$695$	15.7214	0.596347
$696$	−9.50685	−0.360356
$697$	−7.57372	−0.286875
$698$	−0.249536	−0.00944510
$699$	18.4412	0.697510
$700$	−0.169931	−0.00642279
$701$	−38.1622	−1.44137	−0.720683	−	0.693265i	$-0.756172\pi$
$701$	−38.1622	−1.44137	−0.720683	+	0.693265i	$0.756172\pi$
$702$	0.355400	0.0134137
$703$	0	0
$704$	19.5699	0.737567
$705$	−12.5239	−0.471677
$706$	−6.45245	−0.242841
$707$	0.328216	0.0123438
$708$	32.6827	1.22829
$709$	33.1675	1.24563	0.622816	−	0.782368i	$-0.285988\pi$
$709$	33.1675	1.24563	0.622816	+	0.782368i	$0.285988\pi$
$710$	−1.90250	−0.0713996
$711$	−0.306011	−0.0114763
$712$	0.789422	0.0295849
$713$	48.1425	1.80295
$714$	−0.113544	−0.00424928
$715$	0.716695	0.0268029
$716$	7.29730	0.272713
$717$	−33.4192	−1.24806
$718$	7.91587	0.295418
$719$	42.3410	1.57905	0.789527	−	0.613716i	$-0.210326\pi$
$719$	42.3410	1.57905	0.789527	+	0.613716i	$0.210326\pi$
$720$	−1.02347	−0.0381426
$721$	0.315236	0.0117400
$722$	0	0
$723$	6.32007	0.235046
$724$	31.7926	1.18156
$725$	4.80823	0.178573
$726$	0.169861	0.00630412
$727$	−4.20162	−0.155829	−0.0779147	−	0.996960i	$-0.524826\pi$
$727$	−4.20162	−0.155829	−0.0779147	+	0.996960i	$0.524826\pi$
$728$	0.0228365	0.000846379 0
$729$	29.1203	1.07853
$730$	4.84928	0.179480
$731$	6.15452	0.227633
$732$	3.09613	0.114436
$733$	16.9357	0.625536	0.312768	−	0.949830i	$-0.398744\pi$
$733$	16.9357	0.625536	0.312768	+	0.949830i	$0.398744\pi$
$734$	−7.47979	−0.276084
$735$	−11.4943	−0.423975
$736$	−20.6751	−0.762094
$737$	33.5997	1.23766
$738$	−0.276041	−0.0101612
$739$	20.8465	0.766852	0.383426	−	0.923572i	$-0.374744\pi$
$739$	20.8465	0.766852	0.383426	+	0.923572i	$0.374744\pi$
$740$	3.51255	0.129124
$741$	0	0
$742$	0.230750	0.00847109
$743$	−45.3499	−1.66373	−0.831863	−	0.554981i	$-0.812726\pi$
$743$	−45.3499	−1.66373	−0.831863	+	0.554981i	$0.812726\pi$
$744$	15.9524	0.584842
$745$	−19.5194	−0.715136
$746$	−3.35118	−0.122695
$747$	−5.33738	−0.195285
$748$	−16.1270	−0.589661
$749$	0.168277	0.00614871
$750$	0.506308	0.0184877
$751$	8.67683	0.316622	0.158311	−	0.987389i	$-0.449395\pi$
$751$	8.67683	0.316622	0.158311	+	0.987389i	$0.449395\pi$
$752$	−26.2059	−0.955631
$753$	−13.0490	−0.475533
$754$	−0.315235	−0.0114802
$755$	−11.2284	−0.408645
$756$	0.921174	0.0335028
$757$	10.0763	0.366229	0.183114	−	0.983092i	$-0.441382\pi$
$757$	10.0763	0.366229	0.183114	+	0.983092i	$0.441382\pi$
$758$	−5.95397	−0.216258
$759$	33.0259	1.19877
$760$	0	0
$761$	4.52014	0.163855	0.0819275	−	0.996638i	$-0.473892\pi$
$761$	4.52014	0.163855	0.0819275	+	0.996638i	$0.473892\pi$
$762$	−10.7398	−0.389063
$763$	1.17381	0.0424947
$764$	−15.1020	−0.546370
$765$	0.748068	0.0270465
$766$	0.321247	0.0116071
$767$	2.22139	0.0802097
$768$	14.6957	0.530287
$769$	−39.5765	−1.42717	−0.713583	−	0.700571i	$-0.752929\pi$
$769$	−39.5765	−1.42717	−0.713583	+	0.700571i	$0.752929\pi$
$770$	−0.0924909	−0.00333314
$771$	−39.8284	−1.43439
$772$	−40.5165	−1.45822
$773$	23.4986	0.845187	0.422593	−	0.906319i	$-0.361120\pi$
$773$	23.4986	0.845187	0.422593	+	0.906319i	$0.361120\pi$
$774$	0.224315	0.00806284
$775$	−8.06815	−0.289816
$776$	20.2217	0.725917
$777$	−0.270346	−0.00969861
$778$	8.19345	0.293749
$779$	0	0
$780$	0.666687	0.0238712
$781$	20.7975	0.744192
$782$	4.62056	0.165231
$783$	−26.0648	−0.931480
$784$	−24.0516	−0.858987
$785$	4.61281	0.164638
$786$	3.51921	0.125526
$787$	−7.52483	−0.268231	−0.134116	−	0.990966i	$-0.542819\pi$
$787$	−7.52483	−0.268231	−0.134116	+	0.990966i	$0.542819\pi$
$788$	−5.50096	−0.195963
$789$	−20.3471	−0.724377
$790$	0.316764	0.0112700
$791$	−1.10118	−0.0391534
$792$	−1.20483	−0.0428119
$793$	0.210439	0.00747290
$794$	−1.13881	−0.0404147
$795$	13.8084	0.489732
$796$	−22.1280	−0.784305
$797$	18.7858	0.665426	0.332713	−	0.943028i	$-0.392036\pi$
$797$	18.7858	0.665426	0.332713	+	0.943028i	$0.392036\pi$
$798$	0	0
$799$	19.1542	0.677627
$800$	3.46491	0.122503
$801$	0.195287	0.00690014
$802$	6.23216	0.220065
$803$	−53.0106	−1.87070
$804$	31.2552	1.10229
$805$	−0.532231	−0.0187587
$806$	0.528960	0.0186318
$807$	40.0768	1.41077
$808$	−4.42575	−0.155697
$809$	−19.4930	−0.685338	−0.342669	−	0.939456i	$-0.611331\pi$
$809$	−19.4930	−0.685338	−0.342669	+	0.939456i	$0.611331\pi$
$810$	−2.46972	−0.0867771
$811$	−15.2060	−0.533954	−0.266977	−	0.963703i	$-0.586025\pi$
$811$	−15.2060	−0.533954	−0.266977	+	0.963703i	$0.586025\pi$
$812$	−0.817067	−0.0286734
$813$	28.6342	1.00425
$814$	1.91183	0.0670096
$815$	−0.574735	−0.0201321
$816$	−14.2176	−0.497715
$817$	0	0
$818$	−3.84272	−0.134357
$819$	0.00564930	0.000197403 0
$820$	−5.73894	−0.200412
$821$	−26.7664	−0.934154	−0.467077	−	0.884217i	$-0.654693\pi$
$821$	−26.7664	−0.934154	−0.467077	+	0.884217i	$0.654693\pi$
$822$	10.6359	0.370970
$823$	27.6484	0.963763	0.481881	−	0.876236i	$-0.339954\pi$
$823$	27.6484	0.963763	0.481881	+	0.876236i	$0.339954\pi$
$824$	−4.25072	−0.148081
$825$	−5.53478	−0.192696
$826$	−0.286675	−0.00997469
$827$	−12.8221	−0.445869	−0.222935	−	0.974833i	$-0.571564\pi$
$827$	−12.8221	−0.445869	−0.222935	+	0.974833i	$0.571564\pi$
$828$	−3.38235	−0.117545
$829$	−45.4531	−1.57865	−0.789326	−	0.613974i	$-0.789570\pi$
$829$	−45.4531	−1.57865	−0.789326	+	0.613974i	$0.789570\pi$
$830$	5.52493	0.191773
$831$	34.1671	1.18524
$832$	1.23732	0.0428963
$833$	17.5796	0.609098
$834$	7.95986	0.275628
$835$	−4.12202	−0.142648
$836$	0	0
$837$	43.7364	1.51175
$838$	8.93049	0.308499
$839$	−23.3132	−0.804859	−0.402430	−	0.915451i	$-0.631834\pi$
$839$	−23.3132	−0.804859	−0.402430	+	0.915451i	$0.631834\pi$
$840$	−0.176358	−0.00608494
$841$	−5.88093	−0.202791
$842$	−4.49541	−0.154922
$843$	9.87974	0.340276
$844$	−45.1520	−1.55420
$845$	−12.9547	−0.445655
$846$	0.698118	0.0240018
$847$	0.0299242	0.00102821
$848$	28.8937	0.992212
$849$	19.0264	0.652986
$850$	−0.774354	−0.0265601
$851$	11.0015	0.377125
$852$	19.3463	0.662794
$853$	−45.7832	−1.56759	−0.783793	−	0.621022i	$-0.786718\pi$
$853$	−45.7832	−1.56759	−0.783793	+	0.621022i	$0.786718\pi$
$854$	−0.0271576	−0.000929312 0
$855$	0	0
$856$	−2.26909	−0.0775558
$857$	−6.44896	−0.220292	−0.110146	−	0.993915i	$-0.535132\pi$
$857$	−6.44896	−0.220292	−0.110146	+	0.993915i	$0.535132\pi$
$858$	0.362868	0.0123881
$859$	−14.5369	−0.495993	−0.247997	−	0.968761i	$-0.579772\pi$
$859$	−14.5369	−0.495993	−0.247997	+	0.968761i	$0.579772\pi$
$860$	4.66355	0.159026
$861$	0.441702	0.0150531
$862$	−4.16034	−0.141702
$863$	4.57136	0.155611	0.0778054	−	0.996969i	$-0.475209\pi$
$863$	4.57136	0.155611	0.0778054	+	0.996969i	$0.475209\pi$
$864$	−18.7829	−0.639006
$865$	6.43458	0.218782
$866$	−11.7099	−0.397918
$867$	−17.5548	−0.596192
$868$	1.37103	0.0465357
$869$	−3.46275	−0.117466
$870$	2.43444	0.0825353
$871$	2.12437	0.0719814
$872$	−15.8279	−0.536000
$873$	5.00244	0.169307
$874$	0	0
$875$	0.0891959	0.00301537
$876$	−49.3118	−1.66609
$877$	−32.9569	−1.11288	−0.556438	−	0.830889i	$-0.687832\pi$
$877$	−32.9569	−1.11288	−0.556438	+	0.830889i	$0.687832\pi$
$878$	7.32611	0.247244
$879$	−28.7181	−0.968639
$880$	−11.5814	−0.390408
$881$	−16.2413	−0.547184	−0.273592	−	0.961846i	$-0.588212\pi$
$881$	−16.2413	−0.547184	−0.273592	+	0.961846i	$0.588212\pi$
$882$	0.640729	0.0215745
$883$	−28.5141	−0.959575	−0.479787	−	0.877385i	$-0.659286\pi$
$883$	−28.5141	−0.959575	−0.479787	+	0.877385i	$0.659286\pi$
$884$	−1.01964	−0.0342943
$885$	−17.1550	−0.576659
$886$	−5.94391	−0.199689
$887$	−38.6352	−1.29724	−0.648622	−	0.761111i	$-0.724654\pi$
$887$	−38.6352	−1.29724	−0.648622	+	0.761111i	$0.724654\pi$
$888$	3.64541	0.122332
$889$	−1.89203	−0.0634567
$890$	−0.202149	−0.00677606
$891$	26.9981	0.904471
$892$	−16.7955	−0.562355
$893$	0	0
$894$	−9.88282	−0.330531
$895$	−3.83032	−0.128033
$896$	−0.777791	−0.0259842
$897$	2.08809	0.0697193
$898$	8.13508	0.271471
$899$	−38.7935	−1.29384
$900$	0.566844	0.0188948
$901$	−21.1187	−0.703566
$902$	−3.12362	−0.104005
$903$	−0.358933	−0.0119446
$904$	14.8486	0.493855
$905$	−16.6878	−0.554720
$906$	−5.68505	−0.188873
$907$	−28.6565	−0.951522	−0.475761	−	0.879575i	$-0.657827\pi$
$907$	−28.6565	−0.951522	−0.475761	+	0.879575i	$0.657827\pi$
$908$	−1.99110	−0.0660771
$909$	−1.09484	−0.0363136
$910$	−0.00584781	−0.000193853 0
$911$	47.5952	1.57690	0.788450	−	0.615099i	$-0.210884\pi$
$911$	47.5952	1.57690	0.788450	+	0.615099i	$0.210884\pi$
$912$	0	0
$913$	−60.3966	−1.99884
$914$	−11.8465	−0.391847
$915$	−1.62514	−0.0537256
$916$	25.6885	0.848770
$917$	0.619978	0.0204735
$918$	4.19768	0.138544
$919$	−27.2196	−0.897891	−0.448945	−	0.893559i	$-0.648200\pi$
$919$	−27.2196	−0.897891	−0.448945	+	0.893559i	$0.648200\pi$
$920$	7.17672	0.236610
$921$	−48.7476	−1.60629
$922$	10.4666	0.344698
$923$	1.31494	0.0432817
$924$	0.940530	0.0309412
$925$	−1.84372	−0.0606212
$926$	−1.66143	−0.0545980
$927$	−1.05154	−0.0345372
$928$	16.6601	0.546894
$929$	−32.2399	−1.05776	−0.528879	−	0.848697i	$-0.677387\pi$
$929$	−32.2399	−1.05776	−0.528879	+	0.848697i	$0.677387\pi$
$930$	−4.08496	−0.133951
$931$	0	0
$932$	−21.3716	−0.700049
$933$	−19.1062	−0.625510
$934$	6.90783	0.226031
$935$	8.46497	0.276834
$936$	−0.0761765	−0.00248991
$937$	18.1725	0.593668	0.296834	−	0.954929i	$-0.404069\pi$
$937$	18.1725	0.593668	0.296834	+	0.954929i	$0.404069\pi$
$938$	−0.274154	−0.00895144
$939$	−0.780637	−0.0254751
$940$	14.5140	0.473394
$941$	−23.5571	−0.767939	−0.383970	−	0.923346i	$-0.625443\pi$
$941$	−23.5571	−0.767939	−0.383970	+	0.923346i	$0.625443\pi$
$942$	2.33550	0.0760948
$943$	−17.9746	−0.585333
$944$	−35.8964	−1.16833
$945$	−0.483520	−0.0157289
$946$	2.53830	0.0825273
$947$	−8.43157	−0.273989	−0.136995	−	0.990572i	$-0.543744\pi$
$947$	−8.43157	−0.273989	−0.136995	+	0.990572i	$0.543744\pi$
$948$	−3.22114	−0.104618
$949$	−3.35164	−0.108799
$950$	0	0
$951$	33.2536	1.07832
$952$	0.269725	0.00874184
$953$	−50.0741	−1.62206	−0.811029	−	0.585005i	$-0.801092\pi$
$953$	−50.0741	−1.62206	−0.811029	+	0.585005i	$0.801092\pi$
$954$	−0.769719	−0.0249206
$955$	7.92694	0.256510
$956$	38.7296	1.25261
$957$	−26.6125	−0.860260
$958$	−8.85178	−0.285988
$959$	1.87372	0.0605057
$960$	−9.55538	−0.308398
$961$	34.0950	1.09984
$962$	0.120877	0.00389723
$963$	−0.561327	−0.0180885
$964$	−7.32436	−0.235902
$965$	21.2669	0.684605
$966$	−0.269472	−0.00867013
$967$	−6.00845	−0.193219	−0.0966094	−	0.995322i	$-0.530800\pi$
$967$	−6.00845	−0.193219	−0.0966094	+	0.995322i	$0.530800\pi$
$968$	−0.403505	−0.0129692
$969$	0	0
$970$	−5.17822	−0.166263
$971$	−35.9725	−1.15441	−0.577206	−	0.816599i	$-0.695857\pi$
$971$	−35.9725	−1.15441	−0.577206	+	0.816599i	$0.695857\pi$
$972$	−5.86832	−0.188227
$973$	1.40228	0.0449552
$974$	10.6084	0.339915
$975$	−0.349941	−0.0112071
$976$	−3.40057	−0.108850
$977$	−33.6347	−1.07607	−0.538035	−	0.842922i	$-0.680833\pi$
$977$	−33.6347	−1.07607	−0.538035	+	0.842922i	$0.680833\pi$
$978$	−0.290993	−0.00930492
$979$	2.20983	0.0706264
$980$	13.3208	0.425519
$981$	−3.91550	−0.125012
$982$	−5.97072	−0.190533
$983$	−45.0395	−1.43654	−0.718268	−	0.695766i	$-0.755065\pi$
$983$	−45.0395	−1.43654	−0.718268	+	0.695766i	$0.755065\pi$
$984$	−5.95601	−0.189871
$985$	2.88742	0.0920010
$986$	−3.72327	−0.118573
$987$	−1.11708	−0.0355570
$988$	0	0
$989$	14.6064	0.464457
$990$	0.308525	0.00980556
$991$	6.12993	0.194724	0.0973619	−	0.995249i	$-0.468960\pi$
$991$	6.12993	0.194724	0.0973619	+	0.995249i	$0.468960\pi$
$992$	−27.9554	−0.887586
$993$	9.88498	0.313690
$994$	−0.169695	−0.00538241
$995$	11.6149	0.368216
$996$	−56.1824	−1.78021
$997$	−44.9173	−1.42255	−0.711273	−	0.702916i	$-0.751881\pi$
$997$	−44.9173	−1.42255	−0.711273	+	0.702916i	$0.751881\pi$
$998$	3.47055	0.109858
$999$	9.99458	0.316214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.s.1.7		9
5.4	even	2		9025.2.a.cf.1.3		9
19.2	odd	18		95.2.k.a.61.3	✓	18
19.10	odd	18		95.2.k.a.81.3	yes	18
19.18	odd	2		1805.2.a.v.1.3		9
57.2	even	18		855.2.bs.c.631.1		18
57.29	even	18		855.2.bs.c.271.1		18
95.2	even	36		475.2.u.b.99.3		36
95.29	odd	18		475.2.l.c.176.1		18
95.48	even	36		475.2.u.b.24.3		36
95.59	odd	18		475.2.l.c.251.1		18
95.67	even	36		475.2.u.b.24.4		36
95.78	even	36		475.2.u.b.99.4		36
95.94	odd	2		9025.2.a.cc.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.61.3	✓	18	19.2	odd	18
95.2.k.a.81.3	yes	18	19.10	odd	18
475.2.l.c.176.1		18	95.29	odd	18
475.2.l.c.251.1		18	95.59	odd	18
475.2.u.b.24.3		36	95.48	even	36
475.2.u.b.24.4		36	95.67	even	36
475.2.u.b.99.3		36	95.2	even	36
475.2.u.b.99.4		36	95.78	even	36
855.2.bs.c.271.1		18	57.29	even	18
855.2.bs.c.631.1		18	57.2	even	18
1805.2.a.s.1.7		9	1.1	even	1	trivial
1805.2.a.v.1.3		9	19.18	odd	2
9025.2.a.cc.1.7		9	95.94	odd	2
9025.2.a.cf.1.3		9	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+0.307988 q^{2} +1.64392 q^{3} -1.90514 q^{4} +1.00000 q^{5} +0.506308 q^{6} +0.0891959 q^{7} -1.20274 q^{8} -0.297533 q^{9} +O(q^{10})\)	\(q+0.307988 q^{2} +1.64392 q^{3} -1.90514 q^{4} +1.00000 q^{5} +0.506308 q^{6} +0.0891959 q^{7} -1.20274 q^{8} -0.297533 q^{9} +0.307988 q^{10} -3.36682 q^{11} -3.13190 q^{12} -0.212870 q^{13} +0.0274713 q^{14} +1.64392 q^{15} +3.43986 q^{16} -2.51423 q^{17} -0.0916368 q^{18} -1.90514 q^{20} +0.146631 q^{21} -1.03694 q^{22} -5.96699 q^{23} -1.97720 q^{24} +1.00000 q^{25} -0.0655615 q^{26} -5.42087 q^{27} -0.169931 q^{28} +4.80823 q^{29} +0.506308 q^{30} -8.06815 q^{31} +3.46491 q^{32} -5.53478 q^{33} -0.774354 q^{34} +0.0891959 q^{35} +0.566844 q^{36} -1.84372 q^{37} -0.349941 q^{39} -1.20274 q^{40} +3.01234 q^{41} +0.0451606 q^{42} -2.44787 q^{43} +6.41428 q^{44} -0.297533 q^{45} -1.83776 q^{46} -7.61831 q^{47} +5.65484 q^{48} -6.99204 q^{49} +0.307988 q^{50} -4.13319 q^{51} +0.405548 q^{52} +8.39967 q^{53} -1.66957 q^{54} -3.36682 q^{55} -0.107279 q^{56} +1.48088 q^{58} -10.4354 q^{59} -3.13190 q^{60} -0.988579 q^{61} -2.48490 q^{62} -0.0265388 q^{63} -5.81256 q^{64} -0.212870 q^{65} -1.70465 q^{66} -9.97964 q^{67} +4.78997 q^{68} -9.80923 q^{69} +0.0274713 q^{70} -6.17719 q^{71} +0.357855 q^{72} +15.7450 q^{73} -0.567844 q^{74} +1.64392 q^{75} -0.300307 q^{77} -0.107778 q^{78} +1.02849 q^{79} +3.43986 q^{80} -8.01887 q^{81} +0.927765 q^{82} +17.9388 q^{83} -0.279353 q^{84} -2.51423 q^{85} -0.753916 q^{86} +7.90434 q^{87} +4.04941 q^{88} -0.656354 q^{89} -0.0916368 q^{90} -0.0189871 q^{91} +11.3680 q^{92} -13.2634 q^{93} -2.34635 q^{94} +5.69603 q^{96} -16.8130 q^{97} -2.15347 q^{98} +1.00174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 9 q^{5} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 18 q^{12} - 9 q^{13} - 9 q^{15} + 12 q^{16} - 9 q^{17} - 24 q^{18} + 6 q^{20} - 12 q^{21} - 24 q^{22} - 12 q^{23} + 3 q^{24} + 9 q^{25} - 3 q^{26} - 24 q^{27} - 15 q^{28} - 9 q^{29} + 12 q^{30} - 18 q^{31} - 3 q^{32} + 9 q^{33} + 24 q^{34} + 18 q^{36} - 18 q^{37} + 18 q^{39} - 6 q^{40} - 6 q^{41} - 12 q^{43} + 48 q^{44} + 6 q^{45} + 9 q^{46} + 15 q^{47} + 21 q^{48} - 9 q^{49} - 6 q^{50} + 6 q^{51} - 33 q^{52} - 15 q^{53} + 63 q^{54} + 6 q^{58} - 21 q^{59} - 18 q^{60} - 12 q^{61} - 36 q^{62} + 21 q^{63} - 36 q^{64} - 9 q^{65} + 3 q^{66} - 60 q^{67} - 51 q^{68} + 15 q^{69} + 18 q^{71} + 27 q^{73} + 27 q^{74} - 9 q^{75} - 30 q^{77} + 6 q^{78} - 15 q^{79} + 12 q^{80} + 33 q^{81} + 24 q^{82} + 48 q^{84} - 9 q^{85} + 39 q^{86} + 15 q^{87} - 27 q^{88} + 39 q^{89} - 24 q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} - 15 q^{94} - 33 q^{96} - 15 q^{97} + 15 q^{98} - 36 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 9 * q^5 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 18 * q^12 - 9 * q^13 - 9 * q^15 + 12 * q^16 - 9 * q^17 - 24 * q^18 + 6 * q^20 - 12 * q^21 - 24 * q^22 - 12 * q^23 + 3 * q^24 + 9 * q^25 - 3 * q^26 - 24 * q^27 - 15 * q^28 - 9 * q^29 + 12 * q^30 - 18 * q^31 - 3 * q^32 + 9 * q^33 + 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 - 6 * q^40 - 6 * q^41 - 12 * q^43 + 48 * q^44 + 6 * q^45 + 9 * q^46 + 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^50 + 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 + 6 * q^58 - 21 * q^59 - 18 * q^60 - 12 * q^61 - 36 * q^62 + 21 * q^63 - 36 * q^64 - 9 * q^65 + 3 * q^66 - 60 * q^67 - 51 * q^68 + 15 * q^69 + 18 * q^71 + 27 * q^73 + 27 * q^74 - 9 * q^75 - 30 * q^77 + 6 * q^78 - 15 * q^79 + 12 * q^80 + 33 * q^81 + 24 * q^82 + 48 * q^84 - 9 * q^85 + 39 * q^86 + 15 * q^87 - 27 * q^88 + 39 * q^89 - 24 * q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 - 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

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