LMFDB - Embedded newform 1849.2.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.16300$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16300 q^{2} -2.91800 q^{3} +2.67858 q^{4} +2.73005 q^{5} +6.31164 q^{6} -2.02167 q^{7} -1.46776 q^{8} +5.51474 q^{9} +O(q^{10})$	\(q-2.16300 q^{2} -2.91800 q^{3} +2.67858 q^{4} +2.73005 q^{5} +6.31164 q^{6} -2.02167 q^{7} -1.46776 q^{8} +5.51474 q^{9} -5.90511 q^{10} -0.826851 q^{11} -7.81609 q^{12} +3.16156 q^{13} +4.37288 q^{14} -7.96631 q^{15} -2.18238 q^{16} +3.41419 q^{17} -11.9284 q^{18} -2.96222 q^{19} +7.31266 q^{20} +5.89924 q^{21} +1.78848 q^{22} -1.22412 q^{23} +4.28293 q^{24} +2.45320 q^{25} -6.83845 q^{26} -7.33801 q^{27} -5.41520 q^{28} -8.47865 q^{29} +17.2311 q^{30} -5.33928 q^{31} +7.65602 q^{32} +2.41275 q^{33} -7.38490 q^{34} -5.51927 q^{35} +14.7716 q^{36} +3.46435 q^{37} +6.40728 q^{38} -9.22543 q^{39} -4.00706 q^{40} -6.88771 q^{41} -12.7601 q^{42} -2.21478 q^{44} +15.0555 q^{45} +2.64778 q^{46} +3.75228 q^{47} +6.36820 q^{48} -2.91285 q^{49} -5.30627 q^{50} -9.96261 q^{51} +8.46847 q^{52} +8.87019 q^{53} +15.8721 q^{54} -2.25735 q^{55} +2.96733 q^{56} +8.64376 q^{57} +18.3393 q^{58} +2.84701 q^{59} -21.3384 q^{60} +7.67381 q^{61} +11.5489 q^{62} -11.1490 q^{63} -12.1952 q^{64} +8.63122 q^{65} -5.21879 q^{66} -10.3109 q^{67} +9.14517 q^{68} +3.57199 q^{69} +11.9382 q^{70} +12.1231 q^{71} -8.09431 q^{72} +12.4579 q^{73} -7.49339 q^{74} -7.15844 q^{75} -7.93452 q^{76} +1.67162 q^{77} +19.9546 q^{78} +4.68574 q^{79} -5.95803 q^{80} +4.86812 q^{81} +14.8981 q^{82} -4.77345 q^{83} +15.8016 q^{84} +9.32092 q^{85} +24.7407 q^{87} +1.21362 q^{88} -2.06599 q^{89} -32.5651 q^{90} -6.39162 q^{91} -3.27891 q^{92} +15.5800 q^{93} -8.11619 q^{94} -8.08702 q^{95} -22.3403 q^{96} -12.0498 q^{97} +6.30050 q^{98} -4.55987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * 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 $

$2$	−2.16300	−1.52947	−0.764737	−	0.644343i	$-0.777131\pi$
$2$	−2.16300	−1.52947	−0.764737	+	0.644343i	$0.777131\pi$
$3$	−2.91800	−1.68471	−0.842355	−	0.538924i	$-0.818831\pi$
$3$	−2.91800	−1.68471	−0.842355	+	0.538924i	$0.818831\pi$
$4$	2.67858	1.33929
$5$	2.73005	1.22092	0.610459	−	0.792048i	$-0.290985\pi$
$5$	2.73005	1.22092	0.610459	+	0.792048i	$0.290985\pi$
$6$	6.31164	2.57672
$7$	−2.02167	−0.764119	−0.382060	−	0.924138i	$-0.624785\pi$
$7$	−2.02167	−0.764119	−0.382060	+	0.924138i	$0.624785\pi$
$8$	−1.46776	−0.518932
$9$	5.51474	1.83825
$10$	−5.90511	−1.86736
$11$	−0.826851	−0.249305	−0.124653	−	0.992200i	$-0.539782\pi$
$11$	−0.826851	−0.249305	−0.124653	+	0.992200i	$0.539782\pi$
$12$	−7.81609	−2.25631
$13$	3.16156	0.876858	0.438429	−	0.898766i	$-0.355535\pi$
$13$	3.16156	0.876858	0.438429	+	0.898766i	$0.355535\pi$
$14$	4.37288	1.16870
$15$	−7.96631	−2.05689
$16$	−2.18238	−0.545596
$17$	3.41419	0.828063	0.414031	−	0.910263i	$-0.364120\pi$
$17$	3.41419	0.828063	0.414031	+	0.910263i	$0.364120\pi$
$18$	−11.9284	−2.81155
$19$	−2.96222	−0.679579	−0.339790	−	0.940501i	$-0.610356\pi$
$19$	−2.96222	−0.679579	−0.339790	+	0.940501i	$0.610356\pi$
$20$	7.31266	1.63516
$21$	5.89924	1.28732
$22$	1.78848	0.381305
$23$	−1.22412	−0.255247	−0.127624	−	0.991823i	$-0.540735\pi$
$23$	−1.22412	−0.255247	−0.127624	+	0.991823i	$0.540735\pi$
$24$	4.28293	0.874249
$25$	2.45320	0.490640
$26$	−6.83845	−1.34113
$27$	−7.33801	−1.41220
$28$	−5.41520	−1.02338
$29$	−8.47865	−1.57444	−0.787222	−	0.616669i	$-0.788482\pi$
$29$	−8.47865	−1.57444	−0.787222	+	0.616669i	$0.788482\pi$
$30$	17.2311	3.14596
$31$	−5.33928	−0.958962	−0.479481	−	0.877552i	$-0.659175\pi$
$31$	−5.33928	−0.958962	−0.479481	+	0.877552i	$0.659175\pi$
$32$	7.65602	1.35341
$33$	2.41275	0.420007
$34$	−7.38490	−1.26650
$35$	−5.51927	−0.932927
$36$	14.7716	2.46194
$37$	3.46435	0.569536	0.284768	−	0.958597i	$-0.408084\pi$
$37$	3.46435	0.569536	0.284768	+	0.958597i	$0.408084\pi$
$38$	6.40728	1.03940
$39$	−9.22543	−1.47725
$40$	−4.00706	−0.633573
$41$	−6.88771	−1.07568	−0.537840	−	0.843047i	$-0.680759\pi$
$41$	−6.88771	−1.07568	−0.537840	+	0.843047i	$0.680759\pi$
$42$	−12.7601	−1.96892
$43$	0	0
$43$	0	0
$44$	−2.21478	−0.333891
$45$	15.0555	2.24435
$46$	2.64778	0.390394
$47$	3.75228	0.547326	0.273663	−	0.961826i	$-0.411765\pi$
$47$	3.75228	0.547326	0.273663	+	0.961826i	$0.411765\pi$
$48$	6.36820	0.919171
$49$	−2.91285	−0.416121
$50$	−5.30627	−0.750420
$51$	−9.96261	−1.39504
$52$	8.46847	1.17436
$53$	8.87019	1.21841	0.609207	−	0.793011i	$-0.291488\pi$
$53$	8.87019	1.21841	0.609207	+	0.793011i	$0.291488\pi$
$54$	15.8721	2.15992
$55$	−2.25735	−0.304381
$56$	2.96733	0.396526
$57$	8.64376	1.14489
$58$	18.3393	2.40807
$59$	2.84701	0.370649	0.185325	−	0.982677i	$-0.440666\pi$
$59$	2.84701	0.370649	0.185325	+	0.982677i	$0.440666\pi$
$60$	−21.3384	−2.75477
$61$	7.67381	0.982531	0.491265	−	0.871010i	$-0.336535\pi$
$61$	7.67381	0.982531	0.491265	+	0.871010i	$0.336535\pi$
$62$	11.5489	1.46671
$63$	−11.1490	−1.40464
$64$	−12.1952	−1.52440
$65$	8.63122	1.07057
$66$	−5.21879	−0.642389
$67$	−10.3109	−1.25967	−0.629837	−	0.776728i	$-0.716878\pi$
$67$	−10.3109	−1.25967	−0.629837	+	0.776728i	$0.716878\pi$
$68$	9.14517	1.10901
$69$	3.57199	0.430017
$70$	11.9382	1.42689
$71$	12.1231	1.43875	0.719374	−	0.694623i	$-0.244429\pi$
$71$	12.1231	1.43875	0.719374	+	0.694623i	$0.244429\pi$
$72$	−8.09431	−0.953924
$73$	12.4579	1.45809	0.729045	−	0.684466i	$-0.239965\pi$
$73$	12.4579	1.45809	0.729045	+	0.684466i	$0.239965\pi$
$74$	−7.49339	−0.871089
$75$	−7.15844	−0.826585
$76$	−7.93452	−0.910152
$77$	1.67162	0.190499
$78$	19.9546	2.25941
$79$	4.68574	0.527187	0.263593	−	0.964634i	$-0.415092\pi$
$79$	4.68574	0.527187	0.263593	+	0.964634i	$0.415092\pi$
$80$	−5.95803	−0.666128
$81$	4.86812	0.540902
$82$	14.8981	1.64522
$83$	−4.77345	−0.523955	−0.261977	−	0.965074i	$-0.584375\pi$
$83$	−4.77345	−0.523955	−0.261977	+	0.965074i	$0.584375\pi$
$84$	15.8016	1.72409
$85$	9.32092	1.01100
$86$	0	0
$87$	24.7407	2.65248
$88$	1.21362	0.129372
$89$	−2.06599	−0.218995	−0.109497	−	0.993987i	$-0.534924\pi$
$89$	−2.06599	−0.218995	−0.109497	+	0.993987i	$0.534924\pi$
$90$	−32.5651	−3.43267
$91$	−6.39162	−0.670024
$92$	−3.27891	−0.341850
$93$	15.5800	1.61557
$94$	−8.11619	−0.837121
$95$	−8.08702	−0.829710
$96$	−22.3403	−2.28010
$97$	−12.0498	−1.22348	−0.611738	−	0.791060i	$-0.709529\pi$
$97$	−12.0498	−1.22348	−0.611738	+	0.791060i	$0.709529\pi$
$98$	6.30050	0.636447
$99$	−4.55987	−0.458284
$100$	6.57108	0.657108
$101$	2.54866	0.253602	0.126801	−	0.991928i	$-0.459529\pi$
$101$	2.54866	0.253602	0.126801	+	0.991928i	$0.459529\pi$
$102$	21.5491	2.13368
$103$	7.86468	0.774930	0.387465	−	0.921884i	$-0.373351\pi$
$103$	7.86468	0.774930	0.387465	+	0.921884i	$0.373351\pi$
$104$	−4.64040	−0.455029
$105$	16.1052	1.57171
$106$	−19.1862	−1.86353
$107$	−8.38671	−0.810774	−0.405387	−	0.914145i	$-0.632863\pi$
$107$	−8.38671	−0.810774	−0.405387	+	0.914145i	$0.632863\pi$
$108$	−19.6554	−1.89134
$109$	−5.67245	−0.543322	−0.271661	−	0.962393i	$-0.587573\pi$
$109$	−5.67245	−0.543322	−0.271661	+	0.962393i	$0.587573\pi$
$110$	4.88265	0.465542
$111$	−10.1090	−0.959502
$112$	4.41206	0.416900
$113$	−17.9462	−1.68824	−0.844120	−	0.536154i	$-0.819877\pi$
$113$	−17.9462	−1.68824	−0.844120	+	0.536154i	$0.819877\pi$
$114$	−18.6965	−1.75108
$115$	−3.34192	−0.311636
$116$	−22.7107	−2.10863
$117$	17.4351	1.61188
$118$	−6.15809	−0.566898
$119$	−6.90237	−0.632739
$120$	11.6926	1.06739
$121$	−10.3163	−0.937847
$122$	−16.5985	−1.50275
$123$	20.0984	1.81221
$124$	−14.3017	−1.28433
$125$	−6.95291	−0.621887
$126$	24.1153	2.14836
$127$	19.5909	1.73841	0.869205	−	0.494451i	$-0.164631\pi$
$127$	19.5909	1.73841	0.869205	+	0.494451i	$0.164631\pi$
$128$	11.0662	0.978126
$129$	0	0
$130$	−18.6693	−1.63741
$131$	−12.1265	−1.05950	−0.529750	−	0.848154i	$-0.677714\pi$
$131$	−12.1265	−1.05950	−0.529750	+	0.848154i	$0.677714\pi$
$132$	6.46275	0.562510
$133$	5.98863	0.519280
$134$	22.3024	1.92664
$135$	−20.0332	−1.72418
$136$	−5.01121	−0.429708
$137$	5.96441	0.509574	0.254787	−	0.966997i	$-0.417995\pi$
$137$	5.96441	0.509574	0.254787	+	0.966997i	$0.417995\pi$
$138$	−7.72623	−0.657700
$139$	3.10904	0.263705	0.131852	−	0.991269i	$-0.457907\pi$
$139$	3.10904	0.263705	0.131852	+	0.991269i	$0.457907\pi$
$140$	−14.7838	−1.24946
$141$	−10.9492	−0.922086
$142$	−26.2223	−2.20053
$143$	−2.61414	−0.218605
$144$	−12.0353	−1.00294
$145$	−23.1472	−1.92227
$146$	−26.9465	−2.23011
$147$	8.49970	0.701044
$148$	9.27952	0.762772
$149$	−1.61086	−0.131967	−0.0659834	−	0.997821i	$-0.521018\pi$
$149$	−1.61086	−0.131967	−0.0659834	+	0.997821i	$0.521018\pi$
$150$	15.4837	1.26424
$151$	−4.43166	−0.360643	−0.180322	−	0.983608i	$-0.557714\pi$
$151$	−4.43166	−0.360643	−0.180322	+	0.983608i	$0.557714\pi$
$152$	4.34782	0.352655
$153$	18.8284	1.52218
$154$	−3.61572	−0.291363
$155$	−14.5765	−1.17081
$156$	−24.7110	−1.97846
$157$	3.64796	0.291139	0.145569	−	0.989348i	$-0.453499\pi$
$157$	3.64796	0.291139	0.145569	+	0.989348i	$0.453499\pi$
$158$	−10.1353	−0.806318
$159$	−25.8832	−2.05267
$160$	20.9014	1.65240
$161$	2.47477	0.195039
$162$	−10.5297	−0.827295
$163$	7.70520	0.603518	0.301759	−	0.953384i	$-0.402426\pi$
$163$	7.70520	0.603518	0.301759	+	0.953384i	$0.402426\pi$
$164$	−18.4493	−1.44064
$165$	6.58695	0.512793
$166$	10.3250	0.801374
$167$	−4.92138	−0.380828	−0.190414	−	0.981704i	$-0.560983\pi$
$167$	−4.92138	−0.380828	−0.190414	+	0.981704i	$0.560983\pi$
$168$	−8.65867	−0.668031
$169$	−3.00457	−0.231121
$170$	−20.1612	−1.54629
$171$	−16.3359	−1.24923
$172$	0	0
$173$	−21.5624	−1.63936	−0.819680	−	0.572821i	$-0.805849\pi$
$173$	−21.5624	−1.63936	−0.819680	+	0.572821i	$0.805849\pi$
$174$	−53.5142	−4.05690
$175$	−4.95956	−0.374907
$176$	1.80451	0.136020
$177$	−8.30758	−0.624436
$178$	4.46875	0.334947
$179$	−16.8050	−1.25606	−0.628031	−	0.778188i	$-0.716139\pi$
$179$	−16.8050	−1.25606	−0.628031	+	0.778188i	$0.716139\pi$
$180$	40.3274	3.00583
$181$	0.805682	0.0598859	0.0299429	−	0.999552i	$-0.490467\pi$
$181$	0.805682	0.0598859	0.0299429	+	0.999552i	$0.490467\pi$
$182$	13.8251	1.02478
$183$	−22.3922	−1.65528
$184$	1.79672	0.132456
$185$	9.45786	0.695356
$186$	−33.6996	−2.47098
$187$	−2.82303	−0.206440
$188$	10.0508	0.733027
$189$	14.8350	1.07909
$190$	17.4922	1.26902
$191$	−11.5729	−0.837386	−0.418693	−	0.908128i	$-0.637512\pi$
$191$	−11.5729	−0.837386	−0.418693	+	0.908128i	$0.637512\pi$
$192$	35.5857	2.56817
$193$	−5.87067	−0.422580	−0.211290	−	0.977423i	$-0.567766\pi$
$193$	−5.87067	−0.422580	−0.211290	+	0.977423i	$0.567766\pi$
$194$	26.0638	1.87127
$195$	−25.1859	−1.80360
$196$	−7.80229	−0.557306
$197$	5.51455	0.392895	0.196448	−	0.980514i	$-0.437059\pi$
$197$	5.51455	0.392895	0.196448	+	0.980514i	$0.437059\pi$
$198$	9.86300	0.700933
$199$	19.6548	1.39329	0.696647	−	0.717415i	$-0.254675\pi$
$199$	19.6548	1.39329	0.696647	+	0.717415i	$0.254675\pi$
$200$	−3.60071	−0.254608
$201$	30.0871	2.12218
$202$	−5.51277	−0.387877
$203$	17.1410	1.20306
$204$	−26.6856	−1.86837
$205$	−18.8038	−1.31332
$206$	−17.0113	−1.18523
$207$	−6.75072	−0.469207
$208$	−6.89973	−0.478410
$209$	2.44931	0.169423
$210$	−34.8357	−2.40389
$211$	17.4167	1.19902	0.599508	−	0.800369i	$-0.295363\pi$
$211$	17.4167	1.19902	0.599508	+	0.800369i	$0.295363\pi$
$212$	23.7595	1.63181
$213$	−35.3752	−2.42387
$214$	18.1405	1.24006
$215$	0	0
$216$	10.7704	0.732835
$217$	10.7943	0.732762
$218$	12.2695	0.830997
$219$	−36.3522	−2.45646
$220$	−6.04648	−0.407654
$221$	10.7942	0.726093
$222$	21.8657	1.46753
$223$	−15.1079	−1.01170	−0.505849	−	0.862622i	$-0.668821\pi$
$223$	−15.1079	−1.01170	−0.505849	+	0.862622i	$0.668821\pi$
$224$	−15.4779	−1.03416
$225$	13.5287	0.901916
$226$	38.8178	2.58212
$227$	−12.5396	−0.832285	−0.416142	−	0.909300i	$-0.636618\pi$
$227$	−12.5396	−0.832285	−0.416142	+	0.909300i	$0.636618\pi$
$228$	23.1530	1.53334
$229$	20.3566	1.34520	0.672600	−	0.740006i	$-0.265177\pi$
$229$	20.3566	1.34520	0.672600	+	0.740006i	$0.265177\pi$
$230$	7.22858	0.476639
$231$	−4.87779	−0.320935
$232$	12.4446	0.817029
$233$	−29.5281	−1.93445	−0.967225	−	0.253920i	$-0.918280\pi$
$233$	−29.5281	−1.93445	−0.967225	+	0.253920i	$0.918280\pi$
$234$	−37.7123	−2.46533
$235$	10.2439	0.668240
$236$	7.62593	0.496406
$237$	−13.6730	−0.888157
$238$	14.9298	0.967757
$239$	−24.1069	−1.55934	−0.779672	−	0.626188i	$-0.784614\pi$
$239$	−24.1069	−1.55934	−0.779672	+	0.626188i	$0.784614\pi$
$240$	17.3855	1.12223
$241$	−5.93359	−0.382216	−0.191108	−	0.981569i	$-0.561208\pi$
$241$	−5.93359	−0.382216	−0.191108	+	0.981569i	$0.561208\pi$
$242$	22.3142	1.43441
$243$	7.80885	0.500938
$244$	20.5549	1.31589
$245$	−7.95224	−0.508050
$246$	−43.4728	−2.77172
$247$	−9.36521	−0.595894
$248$	7.83678	0.497636
$249$	13.9289	0.882711
$250$	15.0392	0.951159
$251$	−14.3848	−0.907963	−0.453982	−	0.891011i	$-0.649997\pi$
$251$	−14.3848	−0.907963	−0.453982	+	0.891011i	$0.649997\pi$
$252$	−29.8634	−1.88122
$253$	1.01217	0.0636344
$254$	−42.3751	−2.65885
$255$	−27.1985	−1.70323
$256$	0.454161	0.0283850
$257$	−18.1706	−1.13345	−0.566724	−	0.823908i	$-0.691789\pi$
$257$	−18.1706	−1.13345	−0.566724	+	0.823908i	$0.691789\pi$
$258$	0	0
$259$	−7.00377	−0.435193
$260$	23.1194	1.43380
$261$	−46.7575	−2.89422
$262$	26.2297	1.62048
$263$	−15.8533	−0.977555	−0.488777	−	0.872409i	$-0.662557\pi$
$263$	−15.8533	−0.977555	−0.488777	+	0.872409i	$0.662557\pi$
$264$	−3.54134	−0.217955
$265$	24.2161	1.48758
$266$	−12.9534	−0.794224
$267$	6.02857	0.368943
$268$	−27.6184	−1.68706
$269$	10.5719	0.644580	0.322290	−	0.946641i	$-0.395547\pi$
$269$	10.5719	0.644580	0.322290	+	0.946641i	$0.395547\pi$
$270$	43.3318	2.63709
$271$	−1.77571	−0.107867	−0.0539335	−	0.998545i	$-0.517176\pi$
$271$	−1.77571	−0.107867	−0.0539335	+	0.998545i	$0.517176\pi$
$272$	−7.45107	−0.451788
$273$	18.6508	1.12880
$274$	−12.9010	−0.779380
$275$	−2.02843	−0.122319
$276$	9.56785	0.575917
$277$	1.86826	0.112253	0.0561264	−	0.998424i	$-0.482125\pi$
$277$	1.86826	0.112253	0.0561264	+	0.998424i	$0.482125\pi$
$278$	−6.72485	−0.403330
$279$	−29.4447	−1.76281
$280$	8.10096	0.484125
$281$	−5.44886	−0.325051	−0.162526	−	0.986704i	$-0.551964\pi$
$281$	−5.44886	−0.325051	−0.162526	+	0.986704i	$0.551964\pi$
$282$	23.6831	1.41031
$283$	9.47163	0.563030	0.281515	−	0.959557i	$-0.409163\pi$
$283$	9.47163	0.563030	0.281515	+	0.959557i	$0.409163\pi$
$284$	32.4727	1.92690
$285$	23.5979	1.39782
$286$	5.65438	0.334351
$287$	13.9247	0.821948
$288$	42.2209	2.48789
$289$	−5.34331	−0.314312
$290$	50.0674	2.94006
$291$	35.1615	2.06120
$292$	33.3695	1.95280
$293$	9.56215	0.558627	0.279313	−	0.960200i	$-0.409893\pi$
$293$	9.56215	0.558627	0.279313	+	0.960200i	$0.409893\pi$
$294$	−18.3849	−1.07223
$295$	7.77249	0.452532
$296$	−5.08483	−0.295550
$297$	6.06744	0.352069
$298$	3.48429	0.201840
$299$	−3.87013	−0.223816
$300$	−19.1744	−1.10704
$301$	0	0
$302$	9.58569	0.551594
$303$	−7.43701	−0.427245
$304$	6.46470	0.370776
$305$	20.9499	1.19959
$306$	−40.7258	−2.32814
$307$	−17.9247	−1.02302	−0.511508	−	0.859278i	$-0.670913\pi$
$307$	−17.9247	−1.02302	−0.511508	+	0.859278i	$0.670913\pi$
$308$	4.47756	0.255133
$309$	−22.9492	−1.30553
$310$	31.5290	1.79073
$311$	12.4690	0.707050	0.353525	−	0.935425i	$-0.384983\pi$
$311$	12.4690	0.707050	0.353525	+	0.935425i	$0.384983\pi$
$312$	13.5407	0.766592
$313$	26.1868	1.48017	0.740084	−	0.672515i	$-0.234786\pi$
$313$	26.1868	1.48017	0.740084	+	0.672515i	$0.234786\pi$
$314$	−7.89054	−0.445289
$315$	−30.4373	−1.71495
$316$	12.5511	0.706055
$317$	9.05037	0.508319	0.254160	−	0.967162i	$-0.418201\pi$
$317$	9.05037	0.508319	0.254160	+	0.967162i	$0.418201\pi$
$318$	55.9855	3.13951
$319$	7.01058	0.392517
$320$	−33.2936	−1.86117
$321$	24.4724	1.36592
$322$	−5.35294	−0.298307
$323$	−10.1136	−0.562734
$324$	13.0396	0.724423
$325$	7.75592	0.430221
$326$	−16.6664	−0.923064
$327$	16.5522	0.915340
$328$	10.1095	0.558204
$329$	−7.58587	−0.418223
$330$	−14.2476	−0.784304
$331$	−3.49505	−0.192105	−0.0960526	−	0.995376i	$-0.530622\pi$
$331$	−3.49505	−0.192105	−0.0960526	+	0.995376i	$0.530622\pi$
$332$	−12.7861	−0.701726
$333$	19.1050	1.04695
$334$	10.6450	0.582466
$335$	−28.1492	−1.53796
$336$	−12.8744	−0.702356
$337$	5.20069	0.283300	0.141650	−	0.989917i	$-0.454759\pi$
$337$	5.20069	0.283300	0.141650	+	0.989917i	$0.454759\pi$
$338$	6.49888	0.353493
$339$	52.3672	2.84419
$340$	24.9668	1.35401
$341$	4.41479	0.239074
$342$	35.3345	1.91067
$343$	20.0405	1.08209
$344$	0	0
$345$	9.75174	0.525016
$346$	46.6395	2.50736
$347$	7.67327	0.411923	0.205961	−	0.978560i	$-0.433968\pi$
$347$	7.67327	0.411923	0.205961	+	0.978560i	$0.433968\pi$
$348$	66.2699	3.55244
$349$	−26.4292	−1.41472	−0.707362	−	0.706851i	$-0.750115\pi$
$349$	−26.4292	−1.41472	−0.707362	+	0.706851i	$0.750115\pi$
$350$	10.7275	0.573411
$351$	−23.1995	−1.23830
$352$	−6.33039	−0.337411
$353$	−9.96735	−0.530508	−0.265254	−	0.964179i	$-0.585456\pi$
$353$	−9.96735	−0.530508	−0.265254	+	0.964179i	$0.585456\pi$
$354$	17.9693	0.955058
$355$	33.0967	1.75659
$356$	−5.53392	−0.293297
$357$	20.1411	1.06598
$358$	36.3492	1.92111
$359$	−1.41395	−0.0746256	−0.0373128	−	0.999304i	$-0.511880\pi$
$359$	−1.41395	−0.0746256	−0.0373128	+	0.999304i	$0.511880\pi$
$360$	−22.0979	−1.16466
$361$	−10.2253	−0.538172
$362$	−1.74269	−0.0915939
$363$	30.1030	1.58000
$364$	−17.1204	−0.897355
$365$	34.0108	1.78021
$366$	48.4344	2.53170
$367$	28.3427	1.47948	0.739739	−	0.672893i	$-0.234949\pi$
$367$	28.3427	1.47948	0.739739	+	0.672893i	$0.234949\pi$
$368$	2.67151	0.139262
$369$	−37.9839	−1.97736
$370$	−20.4574	−1.06353
$371$	−17.9326	−0.931014
$372$	41.7323	2.16372
$373$	−23.5640	−1.22010	−0.610048	−	0.792365i	$-0.708850\pi$
$373$	−23.5640	−1.22010	−0.610048	+	0.792365i	$0.708850\pi$
$374$	6.10621	0.315745
$375$	20.2886	1.04770
$376$	−5.50745	−0.284025
$377$	−26.8057	−1.38056
$378$	−32.0882	−1.65044
$379$	−2.27631	−0.116926	−0.0584631	−	0.998290i	$-0.518620\pi$
$379$	−2.27631	−0.116926	−0.0584631	+	0.998290i	$0.518620\pi$
$380$	−21.6617	−1.11122
$381$	−57.1663	−2.92872
$382$	25.0322	1.28076
$383$	−19.5958	−1.00130	−0.500649	−	0.865650i	$-0.666905\pi$
$383$	−19.5958	−1.00130	−0.500649	+	0.865650i	$0.666905\pi$
$384$	−32.2913	−1.64786
$385$	4.56362	0.232583
$386$	12.6983	0.646325
$387$	0	0
$388$	−32.2764	−1.63859
$389$	0.720884	0.0365503	0.0182751	−	0.999833i	$-0.494183\pi$
$389$	0.720884	0.0365503	0.0182751	+	0.999833i	$0.494183\pi$
$390$	54.4772	2.75856
$391$	−4.17939	−0.211361
$392$	4.27537	0.215939
$393$	35.3852	1.78495
$394$	−11.9280	−0.600923
$395$	12.7923	0.643652
$396$	−12.2140	−0.613774
$397$	−8.39383	−0.421274	−0.210637	−	0.977564i	$-0.567554\pi$
$397$	−8.39383	−0.421274	−0.210637	+	0.977564i	$0.567554\pi$
$398$	−42.5134	−2.13100
$399$	−17.4748	−0.874835
$400$	−5.35382	−0.267691
$401$	28.5811	1.42727	0.713636	−	0.700517i	$-0.247047\pi$
$401$	28.5811	1.42727	0.713636	+	0.700517i	$0.247047\pi$
$402$	−65.0785	−3.24582
$403$	−16.8804	−0.840874
$404$	6.82679	0.339646
$405$	13.2902	0.660397
$406$	−37.0761	−1.84005
$407$	−2.86450	−0.141988
$408$	14.6227	0.723933
$409$	−10.6121	−0.524736	−0.262368	−	0.964968i	$-0.584503\pi$
$409$	−10.6121	−0.524736	−0.262368	+	0.964968i	$0.584503\pi$
$410$	40.6727	2.00868
$411$	−17.4042	−0.858485
$412$	21.0661	1.03785
$413$	−5.75572	−0.283220
$414$	14.6018	0.717640
$415$	−13.0318	−0.639705
$416$	24.2049	1.18674
$417$	−9.07217	−0.444266
$418$	−5.29787	−0.259127
$419$	−19.1972	−0.937843	−0.468921	−	0.883240i	$-0.655357\pi$
$419$	−19.1972	−0.937843	−0.468921	+	0.883240i	$0.655357\pi$
$420$	43.1391	2.10497
$421$	−29.8935	−1.45692	−0.728459	−	0.685089i	$-0.759763\pi$
$421$	−29.8935	−1.45692	−0.728459	+	0.685089i	$0.759763\pi$
$422$	−37.6724	−1.83386
$423$	20.6928	1.00612
$424$	−13.0193	−0.632274
$425$	8.37568	0.406280
$426$	76.5167	3.70725
$427$	−15.5139	−0.750771
$428$	−22.4644	−1.08586
$429$	7.62806	0.368286
$430$	0	0
$431$	20.3418	0.979832	0.489916	−	0.871770i	$-0.337028\pi$
$431$	20.3418	0.979832	0.489916	+	0.871770i	$0.337028\pi$
$432$	16.0144	0.770491
$433$	−27.5912	−1.32595	−0.662973	−	0.748643i	$-0.730706\pi$
$433$	−27.5912	−1.32595	−0.662973	+	0.748643i	$0.730706\pi$
$434$	−23.3480	−1.12074
$435$	67.5435	3.23846
$436$	−15.1941	−0.727665
$437$	3.62612	0.173461
$438$	78.6300	3.75709
$439$	−25.6843	−1.22585	−0.612923	−	0.790142i	$-0.710007\pi$
$439$	−25.6843	−1.22585	−0.612923	+	0.790142i	$0.710007\pi$
$440$	3.31325	0.157953
$441$	−16.0636	−0.764934
$442$	−23.3478	−1.11054
$443$	0.278534	0.0132335	0.00661677	−	0.999978i	$-0.497894\pi$
$443$	0.278534	0.0132335	0.00661677	+	0.999978i	$0.497894\pi$
$444$	−27.0777	−1.28505
$445$	−5.64027	−0.267375
$446$	32.6784	1.54737
$447$	4.70049	0.222326
$448$	24.6547	1.16483
$449$	13.5226	0.638172	0.319086	−	0.947726i	$-0.396624\pi$
$449$	13.5226	0.638172	0.319086	+	0.947726i	$0.396624\pi$
$450$	−29.2627	−1.37946
$451$	5.69511	0.268172
$452$	−48.0704	−2.26104
$453$	12.9316	0.607579
$454$	27.1232	1.27296
$455$	−17.4495	−0.818044
$456$	−12.6870	−0.594121
$457$	−17.1975	−0.804465	−0.402232	−	0.915538i	$-0.631766\pi$
$457$	−17.1975	−0.804465	−0.402232	+	0.915538i	$0.631766\pi$
$458$	−44.0313	−2.05745
$459$	−25.0534	−1.16939
$460$	−8.95159	−0.417370
$461$	−3.25011	−0.151373	−0.0756863	−	0.997132i	$-0.524115\pi$
$461$	−3.25011	−0.151373	−0.0756863	+	0.997132i	$0.524115\pi$
$462$	10.5507	0.490862
$463$	34.1291	1.58611	0.793057	−	0.609147i	$-0.208488\pi$
$463$	34.1291	1.58611	0.793057	+	0.609147i	$0.208488\pi$
$464$	18.5037	0.859011
$465$	42.5343	1.97248
$466$	63.8693	2.95869
$467$	−34.6760	−1.60462	−0.802308	−	0.596910i	$-0.796395\pi$
$467$	−34.6760	−1.60462	−0.802308	+	0.596910i	$0.796395\pi$
$468$	46.7014	2.15877
$469$	20.8452	0.962541
$470$	−22.1576	−1.02206
$471$	−10.6448	−0.490484
$472$	−4.17873	−0.192342
$473$	0	0
$474$	29.5747	1.35841
$475$	−7.26691	−0.333428
$476$	−18.4885	−0.847419
$477$	48.9168	2.23975
$478$	52.1432	2.38497
$479$	7.72387	0.352913	0.176456	−	0.984308i	$-0.443537\pi$
$479$	7.72387	0.352913	0.176456	+	0.984308i	$0.443537\pi$
$480$	−60.9902	−2.78381
$481$	10.9527	0.499402
$482$	12.8344	0.584590
$483$	−7.22139	−0.328585
$484$	−27.6330	−1.25605
$485$	−32.8967	−1.49376
$486$	−16.8906	−0.766171
$487$	−23.0800	−1.04585	−0.522927	−	0.852377i	$-0.675160\pi$
$487$	−23.0800	−1.04585	−0.522927	+	0.852377i	$0.675160\pi$
$488$	−11.2633	−0.509866
$489$	−22.4838	−1.01675
$490$	17.2007	0.777049
$491$	−9.86268	−0.445097	−0.222548	−	0.974922i	$-0.571438\pi$
$491$	−9.86268	−0.445097	−0.222548	+	0.974922i	$0.571438\pi$
$492$	53.8350	2.42707
$493$	−28.9477	−1.30374
$494$	20.2570	0.911404
$495$	−12.4487	−0.559527
$496$	11.6524	0.523206
$497$	−24.5089	−1.09938
$498$	−30.1283	−1.35008
$499$	−41.3470	−1.85094	−0.925472	−	0.378815i	$-0.876332\pi$
$499$	−41.3470	−1.85094	−0.925472	+	0.378815i	$0.876332\pi$
$500$	−18.6239	−0.832886
$501$	14.3606	0.641585
$502$	31.1144	1.38870
$503$	13.8269	0.616510	0.308255	−	0.951304i	$-0.400255\pi$
$503$	13.8269	0.616510	0.308255	+	0.951304i	$0.400255\pi$
$504$	16.3640	0.728912
$505$	6.95799	0.309627
$506$	−2.18932	−0.0973272
$507$	8.76733	0.389371
$508$	52.4757	2.32823
$509$	−24.2177	−1.07343	−0.536716	−	0.843763i	$-0.680335\pi$
$509$	−24.2177	−1.07343	−0.536716	+	0.843763i	$0.680335\pi$
$510$	58.8304	2.60505
$511$	−25.1858	−1.11415
$512$	−23.1148	−1.02154
$513$	21.7368	0.959702
$514$	39.3029	1.73358
$515$	21.4710	0.946125
$516$	0	0
$517$	−3.10258	−0.136451
$518$	15.1492	0.665616
$519$	62.9192	2.76185
$520$	−12.6686	−0.555553
$521$	6.01881	0.263689	0.131844	−	0.991270i	$-0.457910\pi$
$521$	6.01881	0.263689	0.131844	+	0.991270i	$0.457910\pi$
$522$	101.137	4.42663
$523$	37.0092	1.61830	0.809149	−	0.587604i	$-0.199929\pi$
$523$	37.0092	1.61830	0.809149	+	0.587604i	$0.199929\pi$
$524$	−32.4818	−1.41898
$525$	14.4720	0.631610
$526$	34.2907	1.49514
$527$	−18.2293	−0.794081
$528$	−5.26556	−0.229154
$529$	−21.5015	−0.934849
$530$	−52.3795	−2.27522
$531$	15.7005	0.681344
$532$	16.0410	0.695465
$533$	−21.7759	−0.943218
$534$	−13.0398	−0.564288
$535$	−22.8962	−0.989888
$536$	15.1339	0.653684
$537$	49.0369	2.11610
$538$	−22.8670	−0.985867
$539$	2.40849	0.103741
$540$	−53.6604	−2.30917
$541$	−3.39478	−0.145953	−0.0729764	−	0.997334i	$-0.523250\pi$
$541$	−3.39478	−0.145953	−0.0729764	+	0.997334i	$0.523250\pi$
$542$	3.84087	0.164980
$543$	−2.35098	−0.100890
$544$	26.1391	1.12070
$545$	−15.4861	−0.663352
$546$	−40.3416	−1.72646
$547$	−25.5700	−1.09330	−0.546648	−	0.837362i	$-0.684096\pi$
$547$	−25.5700	−1.09330	−0.546648	+	0.837362i	$0.684096\pi$
$548$	15.9761	0.682467
$549$	42.3190	1.80613
$550$	4.38750	0.187084
$551$	25.1156	1.06996
$552$	−5.24283	−0.223150
$553$	−9.47302	−0.402834
$554$	−4.04105	−0.171688
$555$	−27.5981	−1.17147
$556$	8.32779	0.353177
$557$	20.9938	0.889536	0.444768	−	0.895646i	$-0.353286\pi$
$557$	20.9938	0.889536	0.444768	+	0.895646i	$0.353286\pi$
$558$	63.6890	2.69617
$559$	0	0
$560$	12.0452	0.509001
$561$	8.23760	0.347792
$562$	11.7859	0.497157
$563$	−27.0621	−1.14053	−0.570266	−	0.821460i	$-0.693160\pi$
$563$	−27.0621	−1.14053	−0.570266	+	0.821460i	$0.693160\pi$
$564$	−29.3282	−1.23494
$565$	−48.9942	−2.06120
$566$	−20.4871	−0.861139
$567$	−9.84173	−0.413314
$568$	−17.7938	−0.746612
$569$	−27.5093	−1.15325	−0.576625	−	0.817009i	$-0.695631\pi$
$569$	−27.5093	−1.15325	−0.576625	+	0.817009i	$0.695631\pi$
$570$	−51.0424	−2.13793
$571$	34.3456	1.43732	0.718659	−	0.695363i	$-0.244756\pi$
$571$	34.3456	1.43732	0.718659	+	0.695363i	$0.244756\pi$
$572$	−7.00216	−0.292775
$573$	33.7698	1.41075
$574$	−30.1191	−1.25715
$575$	−3.00302	−0.125234
$576$	−67.2534	−2.80223
$577$	−0.542179	−0.0225712	−0.0112856	−	0.999936i	$-0.503592\pi$
$577$	−0.542179	−0.0225712	−0.0112856	+	0.999936i	$0.503592\pi$
$578$	11.5576	0.480732
$579$	17.1306	0.711925
$580$	−62.0014	−2.57447
$581$	9.65035	0.400364
$582$	−76.0543	−3.15255
$583$	−7.33433	−0.303757
$584$	−18.2852	−0.756649
$585$	47.5989	1.96797
$586$	−20.6829	−0.854404
$587$	−9.83168	−0.405797	−0.202899	−	0.979200i	$-0.565036\pi$
$587$	−9.83168	−0.405797	−0.202899	+	0.979200i	$0.565036\pi$
$588$	22.7671	0.938899
$589$	15.8161	0.651691
$590$	−16.8119	−0.692136
$591$	−16.0915	−0.661914
$592$	−7.56054	−0.310736
$593$	28.9125	1.18729	0.593647	−	0.804726i	$-0.297688\pi$
$593$	28.9125	1.18729	0.593647	+	0.804726i	$0.297688\pi$
$594$	−13.1239	−0.538480
$595$	−18.8438	−0.772522
$596$	−4.31481	−0.176741
$597$	−57.3528	−2.34729
$598$	8.37110	0.342320
$599$	−1.92300	−0.0785715	−0.0392857	−	0.999228i	$-0.512508\pi$
$599$	−1.92300	−0.0785715	−0.0392857	+	0.999228i	$0.512508\pi$
$600$	10.5069	0.428941
$601$	−45.9528	−1.87446	−0.937228	−	0.348718i	$-0.886617\pi$
$601$	−45.9528	−1.87446	−0.937228	+	0.348718i	$0.886617\pi$
$602$	0	0
$603$	−56.8617	−2.31559
$604$	−11.8705	−0.483005
$605$	−28.1641	−1.14503
$606$	16.0863	0.653460
$607$	−29.5757	−1.20044	−0.600221	−	0.799834i	$-0.704921\pi$
$607$	−29.5757	−1.20044	−0.600221	+	0.799834i	$0.704921\pi$
$608$	−22.6788	−0.919747
$609$	−50.0175	−2.02681
$610$	−45.3147	−1.83474
$611$	11.8630	0.479927
$612$	50.4332	2.03864
$613$	−2.94272	−0.118855	−0.0594277	−	0.998233i	$-0.518928\pi$
$613$	−2.94272	−0.118855	−0.0594277	+	0.998233i	$0.518928\pi$
$614$	38.7712	1.56468
$615$	54.8696	2.21256
$616$	−2.45354	−0.0988559
$617$	−9.28871	−0.373950	−0.186975	−	0.982365i	$-0.559868\pi$
$617$	−9.28871	−0.373950	−0.186975	+	0.982365i	$0.559868\pi$
$618$	49.6391	1.99678
$619$	39.4859	1.58707	0.793536	−	0.608523i	$-0.208238\pi$
$619$	39.4859	1.58707	0.793536	+	0.608523i	$0.208238\pi$
$620$	−39.0443	−1.56806
$621$	8.98263	0.360460
$622$	−26.9704	−1.08141
$623$	4.17676	0.167338
$624$	20.1334	0.805982
$625$	−31.2478	−1.24991
$626$	−56.6422	−2.26388
$627$	−7.14710	−0.285428
$628$	9.77133	0.389919
$629$	11.8279	0.471611
$630$	65.8360	2.62297
$631$	−21.9182	−0.872551	−0.436276	−	0.899813i	$-0.643703\pi$
$631$	−21.9182	−0.872551	−0.436276	+	0.899813i	$0.643703\pi$
$632$	−6.87754	−0.273574
$633$	−50.8220	−2.01999
$634$	−19.5760	−0.777461
$635$	53.4842	2.12246
$636$	−69.3302	−2.74912
$637$	−9.20914	−0.364879
$638$	−15.1639	−0.600344
$639$	66.8557	2.64477
$640$	30.2114	1.19421
$641$	23.1923	0.916042	0.458021	−	0.888941i	$-0.348558\pi$
$641$	23.1923	0.916042	0.458021	+	0.888941i	$0.348558\pi$
$642$	−52.9339	−2.08913
$643$	20.3786	0.803653	0.401827	−	0.915716i	$-0.368375\pi$
$643$	20.3786	0.803653	0.401827	+	0.915716i	$0.368375\pi$
$644$	6.62887	0.261214
$645$	0	0
$646$	21.8757	0.860687
$647$	0.841638	0.0330882	0.0165441	−	0.999863i	$-0.494734\pi$
$647$	0.841638	0.0330882	0.0165441	+	0.999863i	$0.494734\pi$
$648$	−7.14523	−0.280691
$649$	−2.35406	−0.0924047
$650$	−16.7761	−0.658012
$651$	−31.4977	−1.23449
$652$	20.6390	0.808284
$653$	40.1908	1.57279	0.786393	−	0.617726i	$-0.211946\pi$
$653$	40.1908	1.57279	0.786393	+	0.617726i	$0.211946\pi$
$654$	−35.8025	−1.39999
$655$	−33.1061	−1.29356
$656$	15.0316	0.586887
$657$	68.7022	2.68033
$658$	16.4083	0.639660
$659$	−20.5442	−0.800287	−0.400144	−	0.916452i	$-0.631040\pi$
$659$	−20.5442	−0.800287	−0.400144	+	0.916452i	$0.631040\pi$
$660$	17.6436	0.686778
$661$	19.2341	0.748120	0.374060	−	0.927404i	$-0.377965\pi$
$661$	19.2341	0.748120	0.374060	+	0.927404i	$0.377965\pi$
$662$	7.55979	0.293820
$663$	−31.4974	−1.22326
$664$	7.00628	0.271897
$665$	16.3493	0.633998
$666$	−41.3241	−1.60128
$667$	10.3789	0.401873
$668$	−13.1823	−0.510039
$669$	44.0848	1.70442
$670$	60.8868	2.35226
$671$	−6.34510	−0.244950
$672$	45.1647	1.74227
$673$	−11.8018	−0.454927	−0.227463	−	0.973787i	$-0.573043\pi$
$673$	−11.8018	−0.454927	−0.227463	+	0.973787i	$0.573043\pi$
$674$	−11.2491	−0.433299
$675$	−18.0016	−0.692882
$676$	−8.04796	−0.309537
$677$	−8.15632	−0.313473	−0.156736	−	0.987640i	$-0.550097\pi$
$677$	−8.15632	−0.313473	−0.156736	+	0.987640i	$0.550097\pi$
$678$	−113.270	−4.35012
$679$	24.3608	0.934882
$680$	−13.6809	−0.524638
$681$	36.5907	1.40216
$682$	−9.54920	−0.365658
$683$	−5.87345	−0.224742	−0.112371	−	0.993666i	$-0.535844\pi$
$683$	−5.87345	−0.224742	−0.112371	+	0.993666i	$0.535844\pi$
$684$	−43.7568	−1.67308
$685$	16.2832	0.622148
$686$	−43.3477	−1.65502
$687$	−59.4005	−2.26627
$688$	0	0
$689$	28.0436	1.06838
$690$	−21.0930	−0.802998
$691$	36.9131	1.40424	0.702120	−	0.712058i	$-0.252237\pi$
$691$	36.9131	1.40424	0.702120	+	0.712058i	$0.252237\pi$
$692$	−57.7566	−2.19558
$693$	9.21855	0.350184
$694$	−16.5973	−0.630025
$695$	8.48784	0.321962
$696$	−36.3134	−1.37646
$697$	−23.5160	−0.890730
$698$	57.1665	2.16378
$699$	86.1631	3.25899
$700$	−13.2845	−0.502109
$701$	−13.9784	−0.527958	−0.263979	−	0.964528i	$-0.585035\pi$
$701$	−13.9784	−0.527958	−0.263979	+	0.964528i	$0.585035\pi$
$702$	50.1806	1.89394
$703$	−10.2622	−0.387045
$704$	10.0836	0.380041
$705$	−29.8918	−1.12579
$706$	21.5594	0.811398
$707$	−5.15256	−0.193782
$708$	−22.2525	−0.836300
$709$	29.8483	1.12098	0.560488	−	0.828162i	$-0.310613\pi$
$709$	29.8483	1.12098	0.560488	+	0.828162i	$0.310613\pi$
$710$	−71.5883	−2.68666
$711$	25.8406	0.969099
$712$	3.03238	0.113643
$713$	6.53593	0.244773
$714$	−43.5653	−1.63039
$715$	−7.13674	−0.266899
$716$	−45.0134	−1.68223
$717$	70.3439	2.62704
$718$	3.05838	0.114138
$719$	9.37016	0.349448	0.174724	−	0.984617i	$-0.444097\pi$
$719$	9.37016	0.349448	0.174724	+	0.984617i	$0.444097\pi$
$720$	−32.8570	−1.22451
$721$	−15.8998	−0.592139
$722$	22.1173	0.823120
$723$	17.3142	0.643923
$724$	2.15808	0.0802044
$725$	−20.7998	−0.772485
$726$	−65.1129	−2.41657
$727$	−51.9324	−1.92607	−0.963033	−	0.269384i	$-0.913180\pi$
$727$	−51.9324	−1.92607	−0.963033	+	0.269384i	$0.913180\pi$
$728$	9.38137	0.347697
$729$	−37.3906	−1.38484
$730$	−73.5654	−2.72278
$731$	0	0
$732$	−59.9792	−2.21689
$733$	−16.1241	−0.595556	−0.297778	−	0.954635i	$-0.596246\pi$
$733$	−16.1241	−0.595556	−0.297778	+	0.954635i	$0.596246\pi$
$734$	−61.3054	−2.26282
$735$	23.2047	0.855917
$736$	−9.37191	−0.345453
$737$	8.52556	0.314043
$738$	82.1593	3.02432
$739$	13.3390	0.490684	0.245342	−	0.969437i	$-0.421100\pi$
$739$	13.3390	0.490684	0.245342	+	0.969437i	$0.421100\pi$
$740$	25.3336	0.931282
$741$	27.3277	1.00391
$742$	38.7882	1.42396
$743$	3.56395	0.130749	0.0653743	−	0.997861i	$-0.479176\pi$
$743$	3.56395	0.130749	0.0653743	+	0.997861i	$0.479176\pi$
$744$	−22.8677	−0.838372
$745$	−4.39773	−0.161121
$746$	50.9689	1.86610
$747$	−26.3243	−0.963157
$748$	−7.56169	−0.276483
$749$	16.9552	0.619528
$750$	−43.8843	−1.60243
$751$	−0.739168	−0.0269726	−0.0134863	−	0.999909i	$-0.504293\pi$
$751$	−0.739168	−0.0269726	−0.0134863	+	0.999909i	$0.504293\pi$
$752$	−8.18891	−0.298619
$753$	41.9750	1.52965
$754$	57.9808	2.11154
$755$	−12.0987	−0.440316
$756$	39.7368	1.44521
$757$	5.68386	0.206584	0.103292	−	0.994651i	$-0.467062\pi$
$757$	5.68386	0.206584	0.103292	+	0.994651i	$0.467062\pi$
$758$	4.92366	0.178835
$759$	−2.95351	−0.107206
$760$	11.8698	0.430563
$761$	−25.0484	−0.908005	−0.454002	−	0.891000i	$-0.650004\pi$
$761$	−25.0484	−0.908005	−0.454002	+	0.891000i	$0.650004\pi$
$762$	123.651	4.47939
$763$	11.4678	0.415163
$764$	−30.9989	−1.12150
$765$	51.4025	1.85846
$766$	42.3857	1.53146
$767$	9.00098	0.325007
$768$	−1.32524	−0.0478206
$769$	27.0154	0.974201	0.487101	−	0.873346i	$-0.338054\pi$
$769$	27.0154	0.974201	0.487101	+	0.873346i	$0.338054\pi$
$770$	−9.87111	−0.355730
$771$	53.0217	1.90953
$772$	−15.7250	−0.565957
$773$	31.0614	1.11720	0.558600	−	0.829437i	$-0.311339\pi$
$773$	31.0614	1.11720	0.558600	+	0.829437i	$0.311339\pi$
$774$	0	0
$775$	−13.0983	−0.470505
$776$	17.6863	0.634901
$777$	20.4370	0.733174
$778$	−1.55927	−0.0559026
$779$	20.4029	0.731010
$780$	−67.4624	−2.41554
$781$	−10.0240	−0.358687
$782$	9.04002	0.323271
$783$	62.2164	2.22343
$784$	6.35696	0.227034
$785$	9.95913	0.355456
$786$	−76.5383	−2.73003
$787$	−11.3351	−0.404053	−0.202027	−	0.979380i	$-0.564753\pi$
$787$	−11.3351	−0.404053	−0.202027	+	0.979380i	$0.564753\pi$
$788$	14.7711	0.526200
$789$	46.2599	1.64690
$790$	−27.6698	−0.984448
$791$	36.2814	1.29002
$792$	6.69279	0.237818
$793$	24.2612	0.861540
$794$	18.1559	0.644327
$795$	−70.6627	−2.50615
$796$	52.6469	1.86602
$797$	−10.8112	−0.382953	−0.191476	−	0.981497i	$-0.561328\pi$
$797$	−10.8112	−0.382953	−0.191476	+	0.981497i	$0.561328\pi$
$798$	37.7981	1.33804
$799$	12.8110	0.453220
$800$	18.7817	0.664035
$801$	−11.3934	−0.402566
$802$	−61.8210	−2.18297
$803$	−10.3009	−0.363509
$804$	80.5907	2.84221
$805$	6.75626	0.238127
$806$	36.5124	1.28609
$807$	−30.8488	−1.08593
$808$	−3.74083	−0.131602
$809$	−38.8970	−1.36755	−0.683774	−	0.729694i	$-0.739662\pi$
$809$	−38.8970	−1.36755	−0.683774	+	0.729694i	$0.739662\pi$
$810$	−28.7468	−1.01006
$811$	4.79058	0.168220	0.0841100	−	0.996456i	$-0.473195\pi$
$811$	4.79058	0.168220	0.0841100	+	0.996456i	$0.473195\pi$
$812$	45.9135	1.61125
$813$	5.18154	0.181724
$814$	6.19592	0.217167
$815$	21.0356	0.736845
$816$	21.7422	0.761131
$817$	0	0
$818$	22.9540	0.802569
$819$	−35.2481	−1.23167
$820$	−50.3675	−1.75891
$821$	−52.4361	−1.83003	−0.915015	−	0.403419i	$-0.867822\pi$
$821$	−52.4361	−1.83003	−0.915015	+	0.403419i	$0.867822\pi$
$822$	37.6453	1.31303
$823$	−9.37266	−0.326710	−0.163355	−	0.986567i	$-0.552232\pi$
$823$	−9.37266	−0.326710	−0.163355	+	0.986567i	$0.552232\pi$
$824$	−11.5435	−0.402136
$825$	5.91896	0.206072
$826$	12.4496	0.433178
$827$	−47.1684	−1.64020	−0.820102	−	0.572217i	$-0.806083\pi$
$827$	−47.1684	−1.64020	−0.820102	+	0.572217i	$0.806083\pi$
$828$	−18.0823	−0.628403
$829$	6.64448	0.230772	0.115386	−	0.993321i	$-0.463189\pi$
$829$	6.64448	0.230772	0.115386	+	0.993321i	$0.463189\pi$
$830$	28.1878	0.978412
$831$	−5.45158	−0.189113
$832$	−38.5558	−1.33668
$833$	−9.94502	−0.344575
$834$	19.6231	0.679493
$835$	−13.4356	−0.464960
$836$	6.56067	0.226906
$837$	39.1797	1.35425
$838$	41.5235	1.43440
$839$	−23.2683	−0.803310	−0.401655	−	0.915791i	$-0.631565\pi$
$839$	−23.2683	−0.803310	−0.401655	+	0.915791i	$0.631565\pi$
$840$	−23.6386	−0.815610
$841$	42.8874	1.47888
$842$	64.6596	2.22832
$843$	15.8998	0.547617
$844$	46.6520	1.60583
$845$	−8.20263	−0.282179
$846$	−44.7586	−1.53883
$847$	20.8562	0.716627
$848$	−19.3582	−0.664762
$849$	−27.6382	−0.948542
$850$	−18.1166	−0.621395
$851$	−4.24079	−0.145372
$852$	−94.7553	−3.24626
$853$	45.3378	1.55234	0.776168	−	0.630527i	$-0.217161\pi$
$853$	45.3378	1.55234	0.776168	+	0.630527i	$0.217161\pi$
$854$	33.5566	1.14828
$855$	−44.5978	−1.52521
$856$	12.3097	0.420736
$857$	29.1071	0.994278	0.497139	−	0.867671i	$-0.334384\pi$
$857$	29.1071	0.994278	0.497139	+	0.867671i	$0.334384\pi$
$858$	−16.4995	−0.563284
$859$	34.6694	1.18290	0.591452	−	0.806340i	$-0.298555\pi$
$859$	34.6694	1.18290	0.591452	+	0.806340i	$0.298555\pi$
$860$	0	0
$861$	−40.6322	−1.38474
$862$	−43.9994	−1.49863
$863$	−10.4786	−0.356696	−0.178348	−	0.983967i	$-0.557075\pi$
$863$	−10.4786	−0.356696	−0.178348	+	0.983967i	$0.557075\pi$
$864$	−56.1799	−1.91128
$865$	−58.8666	−2.00152
$866$	59.6797	2.02800
$867$	15.5918	0.529525
$868$	28.9132	0.981379
$869$	−3.87441	−0.131430
$870$	−146.097	−4.95314
$871$	−32.5984	−1.10455
$872$	8.32580	0.281947
$873$	−66.4517	−2.24905
$874$	−7.84330	−0.265304
$875$	14.0565	0.475196
$876$	−97.3722	−3.28990
$877$	−11.3896	−0.384598	−0.192299	−	0.981336i	$-0.561594\pi$
$877$	−11.3896	−0.384598	−0.192299	+	0.981336i	$0.561594\pi$
$878$	55.5553	1.87490
$879$	−27.9024	−0.941124
$880$	4.92640	0.166069
$881$	5.66099	0.190723	0.0953617	−	0.995443i	$-0.469599\pi$
$881$	5.66099	0.190723	0.0953617	+	0.995443i	$0.469599\pi$
$882$	34.7456	1.16995
$883$	−15.5884	−0.524592	−0.262296	−	0.964988i	$-0.584480\pi$
$883$	−15.5884	−0.524592	−0.262296	+	0.964988i	$0.584480\pi$
$884$	28.9129	0.972448
$885$	−22.6802	−0.762385
$886$	−0.602469	−0.0202403
$887$	−15.4577	−0.519017	−0.259509	−	0.965741i	$-0.583561\pi$
$887$	−15.4577	−0.519017	−0.259509	+	0.965741i	$0.583561\pi$
$888$	14.8376	0.497916
$889$	−39.6063	−1.32835
$890$	12.1999	0.408942
$891$	−4.02521	−0.134850
$892$	−40.4676	−1.35496
$893$	−11.1151	−0.371952
$894$	−10.1672	−0.340041
$895$	−45.8785	−1.53355
$896$	−22.3723	−0.747405
$897$	11.2931	0.377064
$898$	−29.2494	−0.976066
$899$	45.2698	1.50983
$900$	36.2378	1.20793
$901$	30.2845	1.00892
$902$	−12.3185	−0.410163
$903$	0	0
$904$	26.3408	0.876081
$905$	2.19956	0.0731157
$906$	−27.9711	−0.929276
$907$	48.7422	1.61846	0.809229	−	0.587493i	$-0.199885\pi$
$907$	48.7422	1.61846	0.809229	+	0.587493i	$0.199885\pi$
$908$	−33.5883	−1.11467
$909$	14.0552	0.466182
$910$	37.7432	1.25118
$911$	−13.0406	−0.432053	−0.216026	−	0.976388i	$-0.569310\pi$
$911$	−13.0406	−0.432053	−0.216026	+	0.976388i	$0.569310\pi$
$912$	−18.8640	−0.624649
$913$	3.94694	0.130625
$914$	37.1982	1.23041
$915$	−61.1319	−2.02096
$916$	54.5266	1.80161
$917$	24.5158	0.809584
$918$	54.1905	1.78855
$919$	21.7099	0.716144	0.358072	−	0.933694i	$-0.383434\pi$
$919$	21.7099	0.716144	0.358072	+	0.933694i	$0.383434\pi$
$920$	4.90514	0.161718
$921$	52.3043	1.72349
$922$	7.02999	0.231520
$923$	38.3279	1.26158
$924$	−13.0655	−0.429825
$925$	8.49874	0.279437
$926$	−73.8213	−2.42592
$927$	43.3716	1.42451
$928$	−64.9127	−2.13086
$929$	−32.2585	−1.05837	−0.529184	−	0.848507i	$-0.677502\pi$
$929$	−32.2585	−1.05837	−0.529184	+	0.848507i	$0.677502\pi$
$930$	−92.0018	−3.01686
$931$	8.62850	0.282788
$932$	−79.0933	−2.59079
$933$	−36.3845	−1.19117
$934$	75.0043	2.45422
$935$	−7.70702	−0.252047
$936$	−25.5906	−0.836455
$937$	−11.0411	−0.360697	−0.180348	−	0.983603i	$-0.557723\pi$
$937$	−11.0411	−0.360697	−0.180348	+	0.983603i	$0.557723\pi$
$938$	−45.0881	−1.47218
$939$	−76.4132	−2.49365
$940$	27.4391	0.894966
$941$	−33.3907	−1.08851	−0.544253	−	0.838921i	$-0.683187\pi$
$941$	−33.3907	−1.08851	−0.544253	+	0.838921i	$0.683187\pi$
$942$	23.0246	0.750182
$943$	8.43140	0.274564
$944$	−6.21327	−0.202225
$945$	40.5005	1.31748
$946$	0	0
$947$	14.9637	0.486256	0.243128	−	0.969994i	$-0.421827\pi$
$947$	14.9637	0.486256	0.243128	+	0.969994i	$0.421827\pi$
$948$	−36.6242	−1.18950
$949$	39.3864	1.27854
$950$	15.7183	0.509970
$951$	−26.4090	−0.856370
$952$	10.1310	0.328348
$953$	20.6748	0.669723	0.334862	−	0.942267i	$-0.391310\pi$
$953$	20.6748	0.669723	0.334862	+	0.942267i	$0.391310\pi$
$954$	−105.807	−3.42563
$955$	−31.5946	−1.02238
$956$	−64.5721	−2.08841
$957$	−20.4569	−0.661277
$958$	−16.7067	−0.539770
$959$	−12.0581	−0.389376
$960$	97.1508	3.13553
$961$	−2.49212	−0.0803911
$962$	−23.6908	−0.763821
$963$	−46.2505	−1.49040
$964$	−15.8936	−0.511898
$965$	−16.0273	−0.515936
$966$	15.6199	0.502561
$967$	−10.9347	−0.351636	−0.175818	−	0.984423i	$-0.556257\pi$
$967$	−10.9347	−0.351636	−0.175818	+	0.984423i	$0.556257\pi$
$968$	15.1419	0.486678
$969$	29.5114	0.948044
$970$	71.1557	2.28467
$971$	−21.6086	−0.693452	−0.346726	−	0.937966i	$-0.612707\pi$
$971$	−21.6086	−0.693452	−0.346726	+	0.937966i	$0.612707\pi$
$972$	20.9166	0.670900
$973$	−6.28544	−0.201502
$974$	49.9221	1.59961
$975$	−22.6318	−0.724798
$976$	−16.7472	−0.536065
$977$	1.60268	0.0512742	0.0256371	−	0.999671i	$-0.491839\pi$
$977$	1.60268	0.0512742	0.0256371	+	0.999671i	$0.491839\pi$
$978$	48.6325	1.55509
$979$	1.70827	0.0545965
$980$	−21.3007	−0.680425
$981$	−31.2821	−0.998760
$982$	21.3330	0.680763
$983$	−1.02445	−0.0326750	−0.0163375	−	0.999867i	$-0.505201\pi$
$983$	−1.02445	−0.0326750	−0.0163375	+	0.999867i	$0.505201\pi$
$984$	−29.4996	−0.940412
$985$	15.0550	0.479693
$986$	62.6139	1.99403
$987$	22.1356	0.704584
$988$	−25.0854	−0.798074
$989$	0	0
$990$	26.9265	0.855782
$991$	14.6234	0.464528	0.232264	−	0.972653i	$-0.425387\pi$
$991$	14.6234	0.464528	0.232264	+	0.972653i	$0.425387\pi$
$992$	−40.8776	−1.29787
$993$	10.1986	0.323641
$994$	53.0128	1.68146
$995$	53.6587	1.70110
$996$	37.3097	1.18220
$997$	3.51760	0.111403	0.0557017	−	0.998447i	$-0.482260\pi$
$997$	3.51760	0.111403	0.0557017	+	0.998447i	$0.482260\pi$
$998$	89.4336	2.83097
$999$	−25.4214	−0.804299

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.4		18
43.17	even	21		43.2.g.a.31.3	yes	36
43.38	even	21		43.2.g.a.25.3	✓	36
43.42	odd	2		1849.2.a.o.1.15		18
129.17	odd	42		387.2.y.c.289.1		36
129.38	odd	42		387.2.y.c.154.1		36
172.103	odd	42		688.2.bg.c.289.3		36
172.167	odd	42		688.2.bg.c.369.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.25.3	✓	36	43.38	even	21
43.2.g.a.31.3	yes	36	43.17	even	21
387.2.y.c.154.1		36	129.38	odd	42
387.2.y.c.289.1		36	129.17	odd	42
688.2.bg.c.289.3		36	172.103	odd	42
688.2.bg.c.369.3		36	172.167	odd	42
1849.2.a.n.1.4		18	1.1	even	1	trivial
1849.2.a.o.1.15		18	43.42	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-2.16300 q^{2} -2.91800 q^{3} +2.67858 q^{4} +2.73005 q^{5} +6.31164 q^{6} -2.02167 q^{7} -1.46776 q^{8} +5.51474 q^{9} +O(q^{10})\)	\(q-2.16300 q^{2} -2.91800 q^{3} +2.67858 q^{4} +2.73005 q^{5} +6.31164 q^{6} -2.02167 q^{7} -1.46776 q^{8} +5.51474 q^{9} -5.90511 q^{10} -0.826851 q^{11} -7.81609 q^{12} +3.16156 q^{13} +4.37288 q^{14} -7.96631 q^{15} -2.18238 q^{16} +3.41419 q^{17} -11.9284 q^{18} -2.96222 q^{19} +7.31266 q^{20} +5.89924 q^{21} +1.78848 q^{22} -1.22412 q^{23} +4.28293 q^{24} +2.45320 q^{25} -6.83845 q^{26} -7.33801 q^{27} -5.41520 q^{28} -8.47865 q^{29} +17.2311 q^{30} -5.33928 q^{31} +7.65602 q^{32} +2.41275 q^{33} -7.38490 q^{34} -5.51927 q^{35} +14.7716 q^{36} +3.46435 q^{37} +6.40728 q^{38} -9.22543 q^{39} -4.00706 q^{40} -6.88771 q^{41} -12.7601 q^{42} -2.21478 q^{44} +15.0555 q^{45} +2.64778 q^{46} +3.75228 q^{47} +6.36820 q^{48} -2.91285 q^{49} -5.30627 q^{50} -9.96261 q^{51} +8.46847 q^{52} +8.87019 q^{53} +15.8721 q^{54} -2.25735 q^{55} +2.96733 q^{56} +8.64376 q^{57} +18.3393 q^{58} +2.84701 q^{59} -21.3384 q^{60} +7.67381 q^{61} +11.5489 q^{62} -11.1490 q^{63} -12.1952 q^{64} +8.63122 q^{65} -5.21879 q^{66} -10.3109 q^{67} +9.14517 q^{68} +3.57199 q^{69} +11.9382 q^{70} +12.1231 q^{71} -8.09431 q^{72} +12.4579 q^{73} -7.49339 q^{74} -7.15844 q^{75} -7.93452 q^{76} +1.67162 q^{77} +19.9546 q^{78} +4.68574 q^{79} -5.95803 q^{80} +4.86812 q^{81} +14.8981 q^{82} -4.77345 q^{83} +15.8016 q^{84} +9.32092 q^{85} +24.7407 q^{87} +1.21362 q^{88} -2.06599 q^{89} -32.5651 q^{90} -6.39162 q^{91} -3.27891 q^{92} +15.5800 q^{93} -8.11619 q^{94} -8.08702 q^{95} -22.3403 q^{96} -12.0498 q^{97} +6.30050 q^{98} -4.55987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

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