LMFDB - Embedded newform 1815.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1815.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.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:	$14.4928479669$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.477260$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.47726 q^{2} +1.00000 q^{3} +0.182297 q^{4} +1.00000 q^{5} +1.47726 q^{6} +2.29496 q^{7} -2.68522 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.47726 q^{2} +1.00000 q^{3} +0.182297 q^{4} +1.00000 q^{5} +1.47726 q^{6} +2.29496 q^{7} -2.68522 q^{8} +1.00000 q^{9} +1.47726 q^{10} +0.182297 q^{12} +2.14077 q^{13} +3.39026 q^{14} +1.00000 q^{15} -4.33136 q^{16} -0.544446 q^{17} +1.47726 q^{18} +2.18230 q^{19} +0.182297 q^{20} +2.29496 q^{21} +2.03908 q^{23} -2.68522 q^{24} +1.00000 q^{25} +3.16248 q^{26} +1.00000 q^{27} +0.418365 q^{28} +9.94544 q^{29} +1.47726 q^{30} +6.77143 q^{31} -1.02811 q^{32} -0.804288 q^{34} +2.29496 q^{35} +0.182297 q^{36} -8.81959 q^{37} +3.22382 q^{38} +2.14077 q^{39} -2.68522 q^{40} +1.82283 q^{41} +3.39026 q^{42} +0.620713 q^{43} +1.00000 q^{45} +3.01225 q^{46} -0.378009 q^{47} -4.33136 q^{48} -1.73315 q^{49} +1.47726 q^{50} -0.544446 q^{51} +0.390257 q^{52} +11.5931 q^{53} +1.47726 q^{54} -6.16248 q^{56} +2.18230 q^{57} +14.6920 q^{58} -8.07792 q^{59} +0.182297 q^{60} -8.72595 q^{61} +10.0032 q^{62} +2.29496 q^{63} +7.14394 q^{64} +2.14077 q^{65} -9.75802 q^{67} -0.0992509 q^{68} +2.03908 q^{69} +3.39026 q^{70} -14.9968 q^{71} -2.68522 q^{72} -7.85844 q^{73} -13.0288 q^{74} +1.00000 q^{75} +0.397826 q^{76} +3.16248 q^{78} +9.22454 q^{79} -4.33136 q^{80} +1.00000 q^{81} +2.69279 q^{82} +9.45232 q^{83} +0.418365 q^{84} -0.544446 q^{85} +0.916954 q^{86} +9.94544 q^{87} +0.583290 q^{89} +1.47726 q^{90} +4.91300 q^{91} +0.371718 q^{92} +6.77143 q^{93} -0.558418 q^{94} +2.18230 q^{95} -1.02811 q^{96} -5.37801 q^{97} -2.56031 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 4 q^{3} + q^{4} + 4 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 4 * q^3 + q^4 + 4 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 4 * q^9	$ 4 q + 3 q^{2} + 4 q^{3} + q^{4} + 4 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 4 q^{9} + 3 q^{10} + q^{12} + 7 q^{13} + 3 q^{14} + 4 q^{15} - q^{16} + 10 q^{17} + 3 q^{18} + 9 q^{19} + q^{20} + 6 q^{21} - 3 q^{23} + 3 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} - 7 q^{28} + 15 q^{29} + 3 q^{30} - 13 q^{31} - 6 q^{32} - 3 q^{34} + 6 q^{35} + q^{36} - 3 q^{37} + 15 q^{38} + 7 q^{39} + 3 q^{40} + 22 q^{41} + 3 q^{42} + 4 q^{45} + q^{46} - 2 q^{47} - q^{48} - 12 q^{49} + 3 q^{50} + 10 q^{51} - 9 q^{52} + 10 q^{53} + 3 q^{54} - 8 q^{56} + 9 q^{57} + 39 q^{58} - 21 q^{59} + q^{60} + 11 q^{61} + 10 q^{62} + 6 q^{63} - 3 q^{64} + 7 q^{65} + q^{67} + 3 q^{68} - 3 q^{69} + 3 q^{70} - 13 q^{71} + 3 q^{72} + q^{73} - 11 q^{74} + 4 q^{75} + 19 q^{76} - 4 q^{78} - 4 q^{79} - q^{80} + 4 q^{81} + 25 q^{82} + 3 q^{83} - 7 q^{84} + 10 q^{85} + 15 q^{87} - 10 q^{89} + 3 q^{90} + 12 q^{91} - 24 q^{92} - 13 q^{93} - 35 q^{94} + 9 q^{95} - 6 q^{96} - 22 q^{97} - 11 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 + 4 * q^3 + q^4 + 4 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 4 * q^9 + 3 * q^10 + q^12 + 7 * q^13 + 3 * q^14 + 4 * q^15 - q^16 + 10 * q^17 + 3 * q^18 + 9 * q^19 + q^20 + 6 * q^21 - 3 * q^23 + 3 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 - 7 * q^28 + 15 * q^29 + 3 * q^30 - 13 * q^31 - 6 * q^32 - 3 * q^34 + 6 * q^35 + q^36 - 3 * q^37 + 15 * q^38 + 7 * q^39 + 3 * q^40 + 22 * q^41 + 3 * q^42 + 4 * q^45 + q^46 - 2 * q^47 - q^48 - 12 * q^49 + 3 * q^50 + 10 * q^51 - 9 * q^52 + 10 * q^53 + 3 * q^54 - 8 * q^56 + 9 * q^57 + 39 * q^58 - 21 * q^59 + q^60 + 11 * q^61 + 10 * q^62 + 6 * q^63 - 3 * q^64 + 7 * q^65 + q^67 + 3 * q^68 - 3 * q^69 + 3 * q^70 - 13 * q^71 + 3 * q^72 + q^73 - 11 * q^74 + 4 * q^75 + 19 * q^76 - 4 * q^78 - 4 * q^79 - q^80 + 4 * q^81 + 25 * q^82 + 3 * q^83 - 7 * q^84 + 10 * q^85 + 15 * q^87 - 10 * q^89 + 3 * q^90 + 12 * q^91 - 24 * q^92 - 13 * q^93 - 35 * q^94 + 9 * q^95 - 6 * q^96 - 22 * q^97 - 11 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.47726	1.04458	0.522290	−	0.852768i	$-0.325078\pi$
$2$	1.47726	1.04458	0.522290	+	0.852768i	$0.325078\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.182297	0.0911485
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.47726	0.603089
$7$	2.29496	0.867414	0.433707	−	0.901054i	$-0.357205\pi$
$7$	2.29496	0.867414	0.433707	+	0.901054i	$0.357205\pi$
$8$	−2.68522	−0.949369
$9$	1.00000	0.333333
$10$	1.47726	0.467151
$11$	0	0
$11$	0	0
$12$	0.182297	0.0526246
$13$	2.14077	0.593744	0.296872	−	0.954917i	$-0.404057\pi$
$13$	2.14077	0.593744	0.296872	+	0.954917i	$0.404057\pi$
$14$	3.39026	0.906084
$15$	1.00000	0.258199
$16$	−4.33136	−1.08284
$17$	−0.544446	−0.132048	−0.0660238	−	0.997818i	$-0.521031\pi$
$17$	−0.544446	−0.132048	−0.0660238	+	0.997818i	$0.521031\pi$
$18$	1.47726	0.348194
$19$	2.18230	0.500653	0.250327	−	0.968161i	$-0.419462\pi$
$19$	2.18230	0.500653	0.250327	+	0.968161i	$0.419462\pi$
$20$	0.182297	0.0407629
$21$	2.29496	0.500802
$22$	0	0
$23$	2.03908	0.425177	0.212589	−	0.977142i	$-0.431811\pi$
$23$	2.03908	0.425177	0.212589	+	0.977142i	$0.431811\pi$
$24$	−2.68522	−0.548118
$25$	1.00000	0.200000
$26$	3.16248	0.620213
$27$	1.00000	0.192450
$28$	0.418365	0.0790636
$29$	9.94544	1.84682	0.923411	−	0.383813i	$-0.125389\pi$
$29$	9.94544	1.84682	0.923411	+	0.383813i	$0.125389\pi$
$30$	1.47726	0.269710
$31$	6.77143	1.21619	0.608093	−	0.793866i	$-0.291935\pi$
$31$	6.77143	1.21619	0.608093	+	0.793866i	$0.291935\pi$
$32$	−1.02811	−0.181746
$33$	0	0
$34$	−0.804288	−0.137934
$35$	2.29496	0.387920
$36$	0.182297	0.0303828
$37$	−8.81959	−1.44993	−0.724966	−	0.688785i	$-0.758145\pi$
$37$	−8.81959	−1.44993	−0.724966	+	0.688785i	$0.758145\pi$
$38$	3.22382	0.522973
$39$	2.14077	0.342798
$40$	−2.68522	−0.424571
$41$	1.82283	0.284678	0.142339	−	0.989818i	$-0.454538\pi$
$41$	1.82283	0.284678	0.142339	+	0.989818i	$0.454538\pi$
$42$	3.39026	0.523128
$43$	0.620713	0.0946578	0.0473289	−	0.998879i	$-0.484929\pi$
$43$	0.620713	0.0946578	0.0473289	+	0.998879i	$0.484929\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	3.01225	0.444132
$47$	−0.378009	−0.0551383	−0.0275691	−	0.999620i	$-0.508777\pi$
$47$	−0.378009	−0.0551383	−0.0275691	+	0.999620i	$0.508777\pi$
$48$	−4.33136	−0.625178
$49$	−1.73315	−0.247592
$50$	1.47726	0.208916
$51$	−0.544446	−0.0762377
$52$	0.390257	0.0541189
$53$	11.5931	1.59243	0.796217	−	0.605011i	$-0.206831\pi$
$53$	11.5931	1.59243	0.796217	+	0.605011i	$0.206831\pi$
$54$	1.47726	0.201030
$55$	0	0
$56$	−6.16248	−0.823496
$57$	2.18230	0.289052
$58$	14.6920	1.92915
$59$	−8.07792	−1.05166	−0.525828	−	0.850591i	$-0.676244\pi$
$59$	−8.07792	−1.05166	−0.525828	+	0.850591i	$0.676244\pi$
$60$	0.182297	0.0235345
$61$	−8.72595	−1.11724	−0.558622	−	0.829422i	$-0.688670\pi$
$61$	−8.72595	−1.11724	−0.558622	+	0.829422i	$0.688670\pi$
$62$	10.0032	1.27040
$63$	2.29496	0.289138
$64$	7.14394	0.892993
$65$	2.14077	0.265530
$66$	0	0
$67$	−9.75802	−1.19213	−0.596066	−	0.802936i	$-0.703270\pi$
$67$	−9.75802	−1.19213	−0.596066	+	0.802936i	$0.703270\pi$
$68$	−0.0992509	−0.0120359
$69$	2.03908	0.245476
$70$	3.39026	0.405213
$71$	−14.9968	−1.77979	−0.889894	−	0.456167i	$-0.849222\pi$
$71$	−14.9968	−1.77979	−0.889894	+	0.456167i	$0.849222\pi$
$72$	−2.68522	−0.316456
$73$	−7.85844	−0.919760	−0.459880	−	0.887981i	$-0.652108\pi$
$73$	−7.85844	−0.919760	−0.459880	+	0.887981i	$0.652108\pi$
$74$	−13.0288	−1.51457
$75$	1.00000	0.115470
$76$	0.397826	0.0456338
$77$	0	0
$78$	3.16248	0.358080
$79$	9.22454	1.03784	0.518921	−	0.854822i	$-0.326334\pi$
$79$	9.22454	1.03784	0.518921	+	0.854822i	$0.326334\pi$
$80$	−4.33136	−0.484261
$81$	1.00000	0.111111
$82$	2.69279	0.297369
$83$	9.45232	1.03753	0.518763	−	0.854918i	$-0.326393\pi$
$83$	9.45232	1.03753	0.518763	+	0.854918i	$0.326393\pi$
$84$	0.418365	0.0456474
$85$	−0.544446	−0.0590534
$86$	0.916954	0.0988777
$87$	9.94544	1.06626
$88$	0	0
$89$	0.583290	0.0618287	0.0309143	−	0.999522i	$-0.490158\pi$
$89$	0.583290	0.0618287	0.0309143	+	0.999522i	$0.490158\pi$
$90$	1.47726	0.155717
$91$	4.91300	0.515022
$92$	0.371718	0.0387543
$93$	6.77143	0.702165
$94$	−0.558418	−0.0575964
$95$	2.18230	0.223899
$96$	−1.02811	−0.104931
$97$	−5.37801	−0.546054	−0.273027	−	0.962006i	$-0.588025\pi$
$97$	−5.37801	−0.546054	−0.273027	+	0.962006i	$0.588025\pi$
$98$	−2.56031	−0.258630
$99$	0	0
$100$	0.182297	0.0182297
$101$	19.5291	1.94322	0.971608	−	0.236598i	$-0.0760323\pi$
$101$	19.5291	1.94322	0.971608	+	0.236598i	$0.0760323\pi$
$102$	−0.804288	−0.0796364
$103$	13.0062	1.28154	0.640771	−	0.767732i	$-0.278615\pi$
$103$	13.0062	1.28154	0.640771	+	0.767732i	$0.278615\pi$
$104$	−5.74845	−0.563682
$105$	2.29496	0.223965
$106$	17.1260	1.66343
$107$	−1.97355	−0.190790	−0.0953950	−	0.995439i	$-0.530411\pi$
$107$	−1.97355	−0.190790	−0.0953950	+	0.995439i	$0.530411\pi$
$108$	0.182297	0.0175415
$109$	−10.6212	−1.01733	−0.508663	−	0.860966i	$-0.669860\pi$
$109$	−10.6212	−1.01733	−0.508663	+	0.860966i	$0.669860\pi$
$110$	0	0
$111$	−8.81959	−0.837119
$112$	−9.94032	−0.939271
$113$	−16.8956	−1.58940	−0.794700	−	0.607002i	$-0.792372\pi$
$113$	−16.8956	−1.58940	−0.794700	+	0.607002i	$0.792372\pi$
$114$	3.22382	0.301938
$115$	2.03908	0.190145
$116$	1.81302	0.168335
$117$	2.14077	0.197915
$118$	−11.9332	−1.09854
$119$	−1.24948	−0.114540
$120$	−2.68522	−0.245126
$121$	0	0
$122$	−12.8905	−1.16705
$123$	1.82283	0.164359
$124$	1.23441	0.110854
$125$	1.00000	0.0894427
$126$	3.39026	0.302028
$127$	−4.13248	−0.366699	−0.183349	−	0.983048i	$-0.558694\pi$
$127$	−4.13248	−0.366699	−0.183349	+	0.983048i	$0.558694\pi$
$128$	12.6097	1.11455
$129$	0.620713	0.0546507
$130$	3.16248	0.277368
$131$	0.436527	0.0381395	0.0190698	−	0.999818i	$-0.493930\pi$
$131$	0.436527	0.0381395	0.0190698	+	0.999818i	$0.493930\pi$
$132$	0	0
$133$	5.00829	0.434274
$134$	−14.4151	−1.24528
$135$	1.00000	0.0860663
$136$	1.46196	0.125362
$137$	−7.86789	−0.672200	−0.336100	−	0.941826i	$-0.609108\pi$
$137$	−7.86789	−0.672200	−0.336100	+	0.941826i	$0.609108\pi$
$138$	3.01225	0.256420
$139$	−17.6431	−1.49647	−0.748236	−	0.663433i	$-0.769099\pi$
$139$	−17.6431	−1.49647	−0.748236	+	0.663433i	$0.769099\pi$
$140$	0.418365	0.0353583
$141$	−0.378009	−0.0318341
$142$	−22.1541	−1.85913
$143$	0	0
$144$	−4.33136	−0.360947
$145$	9.94544	0.825924
$146$	−11.6090	−0.960764
$147$	−1.73315	−0.142947
$148$	−1.60779	−0.132159
$149$	10.9601	0.897889	0.448945	−	0.893560i	$-0.351800\pi$
$149$	10.9601	0.897889	0.448945	+	0.893560i	$0.351800\pi$
$150$	1.47726	0.120618
$151$	20.0324	1.63021	0.815106	−	0.579312i	$-0.196679\pi$
$151$	20.0324	1.63021	0.815106	+	0.579312i	$0.196679\pi$
$152$	−5.85995	−0.475304
$153$	−0.544446	−0.0440158
$154$	0	0
$155$	6.77143	0.543895
$156$	0.390257	0.0312456
$157$	9.15468	0.730623	0.365311	−	0.930885i	$-0.380963\pi$
$157$	9.15468	0.730623	0.365311	+	0.930885i	$0.380963\pi$
$158$	13.6270	1.08411
$159$	11.5931	0.919392
$160$	−1.02811	−0.0812791
$161$	4.67961	0.368805
$162$	1.47726	0.116065
$163$	−11.3321	−0.887597	−0.443799	−	0.896127i	$-0.646369\pi$
$163$	−11.3321	−0.887597	−0.443799	+	0.896127i	$0.646369\pi$
$164$	0.332296	0.0259480
$165$	0	0
$166$	13.9635	1.08378
$167$	−15.1001	−1.16848	−0.584241	−	0.811580i	$-0.698608\pi$
$167$	−15.1001	−1.16848	−0.584241	+	0.811580i	$0.698608\pi$
$168$	−6.16248	−0.475446
$169$	−8.41709	−0.647468
$170$	−0.804288	−0.0616861
$171$	2.18230	0.166884
$172$	0.113154	0.00862792
$173$	−18.2641	−1.38859	−0.694297	−	0.719688i	$-0.744285\pi$
$173$	−18.2641	−1.38859	−0.694297	+	0.719688i	$0.744285\pi$
$174$	14.6920	1.11380
$175$	2.29496	0.173483
$176$	0	0
$177$	−8.07792	−0.607174
$178$	0.861672	0.0645850
$179$	−0.525419	−0.0392716	−0.0196358	−	0.999807i	$-0.506251\pi$
$179$	−0.525419	−0.0392716	−0.0196358	+	0.999807i	$0.506251\pi$
$180$	0.182297	0.0135876
$181$	−17.7106	−1.31642	−0.658211	−	0.752833i	$-0.728687\pi$
$181$	−17.7106	−1.31642	−0.658211	+	0.752833i	$0.728687\pi$
$182$	7.25777	0.537982
$183$	−8.72595	−0.645041
$184$	−5.47537	−0.403650
$185$	−8.81959	−0.648429
$186$	10.0032	0.733468
$187$	0	0
$188$	−0.0689100	−0.00502578
$189$	2.29496	0.166934
$190$	3.22382	0.233880
$191$	−16.5519	−1.19766	−0.598828	−	0.800877i	$-0.704367\pi$
$191$	−16.5519	−1.19766	−0.598828	+	0.800877i	$0.704367\pi$
$192$	7.14394	0.515570
$193$	24.5032	1.76378	0.881891	−	0.471454i	$-0.156271\pi$
$193$	24.5032	1.76378	0.881891	+	0.471454i	$0.156271\pi$
$194$	−7.94472	−0.570397
$195$	2.14077	0.153304
$196$	−0.315947	−0.0225677
$197$	7.50877	0.534978	0.267489	−	0.963561i	$-0.413806\pi$
$197$	7.50877	0.534978	0.267489	+	0.963561i	$0.413806\pi$
$198$	0	0
$199$	−20.0956	−1.42454	−0.712270	−	0.701906i	$-0.752333\pi$
$199$	−20.0956	−1.42454	−0.712270	+	0.701906i	$0.752333\pi$
$200$	−2.68522	−0.189874
$201$	−9.75802	−0.688278
$202$	28.8495	2.02985
$203$	22.8244	1.60196
$204$	−0.0992509	−0.00694895
$205$	1.82283	0.127312
$206$	19.2136	1.33867
$207$	2.03908	0.141726
$208$	−9.27247	−0.642930
$209$	0	0
$210$	3.39026	0.233950
$211$	−5.41860	−0.373032	−0.186516	−	0.982452i	$-0.559720\pi$
$211$	−5.41860	−0.373032	−0.186516	+	0.982452i	$0.559720\pi$
$212$	2.11339	0.145148
$213$	−14.9968	−1.02756
$214$	−2.91544	−0.199296
$215$	0.620713	0.0423322
$216$	−2.68522	−0.182706
$217$	15.5402	1.05494
$218$	−15.6903	−1.06268
$219$	−7.85844	−0.531024
$220$	0	0
$221$	−1.16554	−0.0784024
$222$	−13.0288	−0.874438
$223$	15.7074	1.05185	0.525923	−	0.850532i	$-0.323720\pi$
$223$	15.7074	1.05185	0.525923	+	0.850532i	$0.323720\pi$
$224$	−2.35947	−0.157649
$225$	1.00000	0.0666667
$226$	−24.9591	−1.66026
$227$	1.47141	0.0976612	0.0488306	−	0.998807i	$-0.484451\pi$
$227$	1.47141	0.0976612	0.0488306	+	0.998807i	$0.484451\pi$
$228$	0.397826	0.0263467
$229$	−15.9751	−1.05566	−0.527831	−	0.849350i	$-0.676994\pi$
$229$	−15.9751	−1.05566	−0.527831	+	0.849350i	$0.676994\pi$
$230$	3.01225	0.198622
$231$	0	0
$232$	−26.7057	−1.75331
$233$	25.6382	1.67961	0.839806	−	0.542887i	$-0.182669\pi$
$233$	25.6382	1.67961	0.839806	+	0.542887i	$0.182669\pi$
$234$	3.16248	0.206738
$235$	−0.378009	−0.0246586
$236$	−1.47258	−0.0958569
$237$	9.22454	0.599198
$238$	−1.84581	−0.119646
$239$	4.18206	0.270515	0.135258	−	0.990810i	$-0.456814\pi$
$239$	4.18206	0.270515	0.135258	+	0.990810i	$0.456814\pi$
$240$	−4.33136	−0.279588
$241$	3.29180	0.212043	0.106022	−	0.994364i	$-0.466189\pi$
$241$	3.29180	0.212043	0.106022	+	0.994364i	$0.466189\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−1.59072	−0.101835
$245$	−1.73315	−0.110727
$246$	2.69279	0.171686
$247$	4.67180	0.297260
$248$	−18.1828	−1.15461
$249$	9.45232	0.599016
$250$	1.47726	0.0934301
$251$	−9.36459	−0.591088	−0.295544	−	0.955329i	$-0.595501\pi$
$251$	−9.36459	−0.591088	−0.295544	+	0.955329i	$0.595501\pi$
$252$	0.418365	0.0263545
$253$	0	0
$254$	−6.10475	−0.383046
$255$	−0.544446	−0.0340945
$256$	4.33989	0.271243
$257$	−12.5714	−0.784182	−0.392091	−	0.919927i	$-0.628248\pi$
$257$	−12.5714	−0.784182	−0.392091	+	0.919927i	$0.628248\pi$
$258$	0.916954	0.0570870
$259$	−20.2406	−1.25769
$260$	0.390257	0.0242027
$261$	9.94544	0.615607
$262$	0.644864	0.0398398
$263$	−4.82946	−0.297797	−0.148899	−	0.988852i	$-0.547573\pi$
$263$	−4.82946	−0.297797	−0.148899	+	0.988852i	$0.547573\pi$
$264$	0	0
$265$	11.5931	0.712158
$266$	7.39855	0.453634
$267$	0.583290	0.0356968
$268$	−1.77886	−0.108661
$269$	−5.22929	−0.318835	−0.159418	−	0.987211i	$-0.550962\pi$
$269$	−5.22929	−0.318835	−0.159418	+	0.987211i	$0.550962\pi$
$270$	1.47726	0.0899032
$271$	−30.3311	−1.84248	−0.921240	−	0.388994i	$-0.872823\pi$
$271$	−30.3311	−1.84248	−0.921240	+	0.388994i	$0.872823\pi$
$272$	2.35819	0.142986
$273$	4.91300	0.297348
$274$	−11.6229	−0.702167
$275$	0	0
$276$	0.371718	0.0223748
$277$	−15.9694	−0.959511	−0.479756	−	0.877402i	$-0.659275\pi$
$277$	−15.9694	−0.959511	−0.479756	+	0.877402i	$0.659275\pi$
$278$	−26.0635	−1.56319
$279$	6.77143	0.405395
$280$	−6.16248	−0.368279
$281$	1.39067	0.0829604	0.0414802	−	0.999139i	$-0.486793\pi$
$281$	1.39067	0.0829604	0.0414802	+	0.999139i	$0.486793\pi$
$282$	−0.558418	−0.0332533
$283$	−5.87453	−0.349205	−0.174602	−	0.984639i	$-0.555864\pi$
$283$	−5.87453	−0.349205	−0.174602	+	0.984639i	$0.555864\pi$
$284$	−2.73387	−0.162225
$285$	2.18230	0.129268
$286$	0	0
$287$	4.18332	0.246934
$288$	−1.02811	−0.0605819
$289$	−16.7036	−0.982563
$290$	14.6920	0.862744
$291$	−5.37801	−0.315264
$292$	−1.43257	−0.0838348
$293$	−19.9745	−1.16692	−0.583461	−	0.812141i	$-0.698302\pi$
$293$	−19.9745	−1.16692	−0.583461	+	0.812141i	$0.698302\pi$
$294$	−2.56031	−0.149320
$295$	−8.07792	−0.470315
$296$	23.6825	1.37652
$297$	0	0
$298$	16.1910	0.937917
$299$	4.36520	0.252446
$300$	0.182297	0.0105249
$301$	1.42451	0.0821075
$302$	29.5930	1.70289
$303$	19.5291	1.12192
$304$	−9.45232	−0.542128
$305$	−8.72595	−0.499647
$306$	−0.804288	−0.0459781
$307$	−19.4372	−1.10934	−0.554671	−	0.832070i	$-0.687156\pi$
$307$	−19.4372	−1.10934	−0.554671	+	0.832070i	$0.687156\pi$
$308$	0	0
$309$	13.0062	0.739898
$310$	10.0032	0.568142
$311$	6.02182	0.341466	0.170733	−	0.985317i	$-0.445386\pi$
$311$	6.02182	0.341466	0.170733	+	0.985317i	$0.445386\pi$
$312$	−5.74845	−0.325442
$313$	−5.10833	−0.288740	−0.144370	−	0.989524i	$-0.546116\pi$
$313$	−5.10833	−0.288740	−0.144370	+	0.989524i	$0.546116\pi$
$314$	13.5238	0.763194
$315$	2.29496	0.129307
$316$	1.68161	0.0945978
$317$	13.6788	0.768279	0.384139	−	0.923275i	$-0.374498\pi$
$317$	13.6788	0.768279	0.384139	+	0.923275i	$0.374498\pi$
$318$	17.1260	0.960379
$319$	0	0
$320$	7.14394	0.399358
$321$	−1.97355	−0.110153
$322$	6.91300	0.385246
$323$	−1.18814	−0.0661100
$324$	0.182297	0.0101276
$325$	2.14077	0.118749
$326$	−16.7404	−0.927167
$327$	−10.6212	−0.587354
$328$	−4.89469	−0.270264
$329$	−0.867517	−0.0478278
$330$	0	0
$331$	11.4695	0.630418	0.315209	−	0.949022i	$-0.397925\pi$
$331$	11.4695	0.630418	0.315209	+	0.949022i	$0.397925\pi$
$332$	1.72313	0.0945691
$333$	−8.81959	−0.483311
$334$	−22.3068	−1.22057
$335$	−9.75802	−0.533137
$336$	−9.94032	−0.542289
$337$	−3.76404	−0.205041	−0.102520	−	0.994731i	$-0.532691\pi$
$337$	−3.76404	−0.205041	−0.102520	+	0.994731i	$0.532691\pi$
$338$	−12.4342	−0.676333
$339$	−16.8956	−0.917641
$340$	−0.0992509	−0.00538264
$341$	0	0
$342$	3.22382	0.174324
$343$	−20.0422	−1.08218
$344$	−1.66675	−0.0898651
$345$	2.03908	0.109780
$346$	−26.9808	−1.45050
$347$	0.395980	0.0212573	0.0106287	−	0.999944i	$-0.496617\pi$
$347$	0.395980	0.0212573	0.0106287	+	0.999944i	$0.496617\pi$
$348$	1.81302	0.0971883
$349$	13.1708	0.705015	0.352508	−	0.935809i	$-0.385329\pi$
$349$	13.1708	0.705015	0.352508	+	0.935809i	$0.385329\pi$
$350$	3.39026	0.181217
$351$	2.14077	0.114266
$352$	0	0
$353$	11.3853	0.605977	0.302989	−	0.952994i	$-0.402016\pi$
$353$	11.3853	0.605977	0.302989	+	0.952994i	$0.402016\pi$
$354$	−11.9332	−0.634242
$355$	−14.9968	−0.795946
$356$	0.106332	0.00563559
$357$	−1.24948	−0.0661296
$358$	−0.776180	−0.0410224
$359$	14.3682	0.758326	0.379163	−	0.925330i	$-0.376212\pi$
$359$	14.3682	0.758326	0.379163	+	0.925330i	$0.376212\pi$
$360$	−2.68522	−0.141524
$361$	−14.2376	−0.749346
$362$	−26.1632	−1.37511
$363$	0	0
$364$	0.895625	0.0469435
$365$	−7.85844	−0.411329
$366$	−12.8905	−0.673797
$367$	−26.2640	−1.37097	−0.685485	−	0.728087i	$-0.740410\pi$
$367$	−26.2640	−1.37097	−0.685485	+	0.728087i	$0.740410\pi$
$368$	−8.83198	−0.460399
$369$	1.82283	0.0948926
$370$	−13.0288	−0.677337
$371$	26.6057	1.38130
$372$	1.23441	0.0640013
$373$	−21.8951	−1.13368	−0.566842	−	0.823827i	$-0.691835\pi$
$373$	−21.8951	−1.13368	−0.566842	+	0.823827i	$0.691835\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	1.01504	0.0523466
$377$	21.2909	1.09654
$378$	3.39026	0.174376
$379$	25.5596	1.31291	0.656455	−	0.754365i	$-0.272055\pi$
$379$	25.5596	1.31291	0.656455	+	0.754365i	$0.272055\pi$
$380$	0.397826	0.0204081
$381$	−4.13248	−0.211714
$382$	−24.4515	−1.25105
$383$	19.0519	0.973508	0.486754	−	0.873539i	$-0.338181\pi$
$383$	19.0519	0.973508	0.486754	+	0.873539i	$0.338181\pi$
$384$	12.6097	0.643485
$385$	0	0
$386$	36.1976	1.84241
$387$	0.620713	0.0315526
$388$	−0.980395	−0.0497720
$389$	16.3925	0.831134	0.415567	−	0.909563i	$-0.363583\pi$
$389$	16.3925	0.831134	0.415567	+	0.909563i	$0.363583\pi$
$390$	3.16248	0.160138
$391$	−1.11017	−0.0561436
$392$	4.65388	0.235056
$393$	0.436527	0.0220199
$394$	11.0924	0.558827
$395$	9.22454	0.464137
$396$	0	0
$397$	30.9826	1.55497	0.777485	−	0.628901i	$-0.216495\pi$
$397$	30.9826	1.55497	0.777485	+	0.628901i	$0.216495\pi$
$398$	−29.6864	−1.48805
$399$	5.00829	0.250728
$400$	−4.33136	−0.216568
$401$	−6.36611	−0.317908	−0.158954	−	0.987286i	$-0.550812\pi$
$401$	−6.36611	−0.317908	−0.158954	+	0.987286i	$0.550812\pi$
$402$	−14.4151	−0.718961
$403$	14.4961	0.722103
$404$	3.56009	0.177121
$405$	1.00000	0.0496904
$406$	33.7176	1.67338
$407$	0	0
$408$	1.46196	0.0723776
$409$	6.26874	0.309969	0.154985	−	0.987917i	$-0.450467\pi$
$409$	6.26874	0.309969	0.154985	+	0.987917i	$0.450467\pi$
$410$	2.69279	0.132987
$411$	−7.86789	−0.388095
$412$	2.37100	0.116811
$413$	−18.5385	−0.912222
$414$	3.01225	0.148044
$415$	9.45232	0.463996
$416$	−2.20095	−0.107910
$417$	−17.6431	−0.863988
$418$	0	0
$419$	3.90332	0.190689	0.0953447	−	0.995444i	$-0.469605\pi$
$419$	3.90332	0.190689	0.0953447	+	0.995444i	$0.469605\pi$
$420$	0.418365	0.0204141
$421$	17.3715	0.846637	0.423318	−	0.905981i	$-0.360865\pi$
$421$	17.3715	0.846637	0.423318	+	0.905981i	$0.360865\pi$
$422$	−8.00468	−0.389662
$423$	−0.378009	−0.0183794
$424$	−31.1300	−1.51181
$425$	−0.544446	−0.0264095
$426$	−22.1541	−1.07337
$427$	−20.0257	−0.969113
$428$	−0.359772	−0.0173902
$429$	0	0
$430$	0.916954	0.0442194
$431$	7.03651	0.338937	0.169468	−	0.985536i	$-0.445795\pi$
$431$	7.03651	0.338937	0.169468	+	0.985536i	$0.445795\pi$
$432$	−4.33136	−0.208393
$433$	2.75229	0.132267	0.0661334	−	0.997811i	$-0.478934\pi$
$433$	2.75229	0.132267	0.0661334	+	0.997811i	$0.478934\pi$
$434$	22.9569	1.10197
$435$	9.94544	0.476847
$436$	−1.93621	−0.0927278
$437$	4.44987	0.212866
$438$	−11.6090	−0.554697
$439$	2.73703	0.130631	0.0653157	−	0.997865i	$-0.479195\pi$
$439$	2.73703	0.130631	0.0653157	+	0.997865i	$0.479195\pi$
$440$	0	0
$441$	−1.73315	−0.0825307
$442$	−1.72180	−0.0818976
$443$	11.1042	0.527576	0.263788	−	0.964581i	$-0.415028\pi$
$443$	11.1042	0.527576	0.263788	+	0.964581i	$0.415028\pi$
$444$	−1.60779	−0.0763021
$445$	0.583290	0.0276506
$446$	23.2039	1.09874
$447$	10.9601	0.518396
$448$	16.3951	0.774595
$449$	14.8268	0.699722	0.349861	−	0.936802i	$-0.386229\pi$
$449$	14.8268	0.699722	0.349861	+	0.936802i	$0.386229\pi$
$450$	1.47726	0.0696387
$451$	0	0
$452$	−3.08001	−0.144872
$453$	20.0324	0.941203
$454$	2.17366	0.102015
$455$	4.91300	0.230325
$456$	−5.85995	−0.274417
$457$	−29.1825	−1.36510	−0.682549	−	0.730840i	$-0.739129\pi$
$457$	−29.1825	−1.36510	−0.682549	+	0.730840i	$0.739129\pi$
$458$	−23.5993	−1.10272
$459$	−0.544446	−0.0254126
$460$	0.371718	0.0173314
$461$	31.1798	1.45219	0.726094	−	0.687595i	$-0.241334\pi$
$461$	31.1798	1.45219	0.726094	+	0.687595i	$0.241334\pi$
$462$	0	0
$463$	41.1642	1.91306	0.956531	−	0.291631i	$-0.0941978\pi$
$463$	41.1642	1.91306	0.956531	+	0.291631i	$0.0941978\pi$
$464$	−43.0773	−1.99981
$465$	6.77143	0.314018
$466$	37.8742	1.75449
$467$	38.7766	1.79437	0.897184	−	0.441656i	$-0.145609\pi$
$467$	38.7766	1.79437	0.897184	+	0.441656i	$0.145609\pi$
$468$	0.390257	0.0180396
$469$	−22.3943	−1.03407
$470$	−0.558418	−0.0257579
$471$	9.15468	0.421825
$472$	21.6910	0.998409
$473$	0	0
$474$	13.6270	0.625911
$475$	2.18230	0.100131
$476$	−0.227777	−0.0104401
$477$	11.5931	0.530811
$478$	6.17800	0.282575
$479$	−16.6876	−0.762476	−0.381238	−	0.924477i	$-0.624502\pi$
$479$	−16.6876	−0.762476	−0.381238	+	0.924477i	$0.624502\pi$
$480$	−1.02811	−0.0469265
$481$	−18.8808	−0.860888
$482$	4.86284	0.221496
$483$	4.67961	0.212930
$484$	0	0
$485$	−5.37801	−0.244203
$486$	1.47726	0.0670099
$487$	2.51193	0.113827	0.0569133	−	0.998379i	$-0.481874\pi$
$487$	2.51193	0.113827	0.0569133	+	0.998379i	$0.481874\pi$
$488$	23.4311	1.06068
$489$	−11.3321	−0.512455
$490$	−2.56031	−0.115663
$491$	7.55865	0.341117	0.170559	−	0.985348i	$-0.445443\pi$
$491$	7.55865	0.341117	0.170559	+	0.985348i	$0.445443\pi$
$492$	0.332296	0.0149811
$493$	−5.41475	−0.243868
$494$	6.90147	0.310512
$495$	0	0
$496$	−29.3295	−1.31693
$497$	−34.4170	−1.54381
$498$	13.9635	0.625721
$499$	16.7964	0.751911	0.375955	−	0.926638i	$-0.377315\pi$
$499$	16.7964	0.751911	0.375955	+	0.926638i	$0.377315\pi$
$500$	0.182297	0.00815257
$501$	−15.1001	−0.674623
$502$	−13.8339	−0.617439
$503$	−7.63258	−0.340320	−0.170160	−	0.985416i	$-0.554428\pi$
$503$	−7.63258	−0.340320	−0.170160	+	0.985416i	$0.554428\pi$
$504$	−6.16248	−0.274499
$505$	19.5291	0.869032
$506$	0	0
$507$	−8.41709	−0.373816
$508$	−0.753340	−0.0334240
$509$	32.9039	1.45844	0.729219	−	0.684280i	$-0.239883\pi$
$509$	32.9039	1.45844	0.729219	+	0.684280i	$0.239883\pi$
$510$	−0.804288	−0.0356145
$511$	−18.0348	−0.797813
$512$	−18.8082	−0.831213
$513$	2.18230	0.0963508
$514$	−18.5712	−0.819141
$515$	13.0062	0.573123
$516$	0.113154	0.00498133
$517$	0	0
$518$	−29.9007	−1.31376
$519$	−18.2641	−0.801705
$520$	−5.74845	−0.252086
$521$	0.797954	0.0349590	0.0174795	−	0.999847i	$-0.494436\pi$
$521$	0.797954	0.0349590	0.0174795	+	0.999847i	$0.494436\pi$
$522$	14.6920	0.643051
$523$	−4.30514	−0.188251	−0.0941254	−	0.995560i	$-0.530005\pi$
$523$	−4.30514	−0.188251	−0.0941254	+	0.995560i	$0.530005\pi$
$524$	0.0795776	0.00347636
$525$	2.29496	0.100160
$526$	−7.13437	−0.311073
$527$	−3.68668	−0.160594
$528$	0	0
$529$	−18.8422	−0.819224
$530$	17.1260	0.743906
$531$	−8.07792	−0.350552
$532$	0.912997	0.0395834
$533$	3.90226	0.169026
$534$	0.861672	0.0372882
$535$	−1.97355	−0.0853239
$536$	26.2024	1.13177
$537$	−0.525419	−0.0226735
$538$	−7.72502	−0.333049
$539$	0	0
$540$	0.182297	0.00784482
$541$	22.7081	0.976299	0.488149	−	0.872760i	$-0.337672\pi$
$541$	22.7081	0.976299	0.488149	+	0.872760i	$0.337672\pi$
$542$	−44.8069	−1.92462
$543$	−17.7106	−0.760037
$544$	0.559749	0.0239990
$545$	−10.6212	−0.454962
$546$	7.25777	0.310604
$547$	−32.1551	−1.37485	−0.687425	−	0.726255i	$-0.741259\pi$
$547$	−32.1551	−1.37485	−0.687425	+	0.726255i	$0.741259\pi$
$548$	−1.43429	−0.0612700
$549$	−8.72595	−0.372415
$550$	0	0
$551$	21.7039	0.924617
$552$	−5.47537	−0.233047
$553$	21.1700	0.900239
$554$	−23.5910	−1.00229
$555$	−8.81959	−0.374371
$556$	−3.21629	−0.136401
$557$	−37.7151	−1.59804	−0.799021	−	0.601303i	$-0.794648\pi$
$557$	−37.7151	−1.59804	−0.799021	+	0.601303i	$0.794648\pi$
$558$	10.0032	0.423468
$559$	1.32881	0.0562025
$560$	−9.94032	−0.420055
$561$	0	0
$562$	2.05438	0.0866588
$563$	−21.9871	−0.926645	−0.463322	−	0.886190i	$-0.653343\pi$
$563$	−21.9871	−0.926645	−0.463322	+	0.886190i	$0.653343\pi$
$564$	−0.0689100	−0.00290163
$565$	−16.8956	−0.710801
$566$	−8.67821	−0.364772
$567$	2.29496	0.0963794
$568$	40.2696	1.68968
$569$	20.4804	0.858584	0.429292	−	0.903166i	$-0.358763\pi$
$569$	20.4804	0.858584	0.429292	+	0.903166i	$0.358763\pi$
$570$	3.22382	0.135031
$571$	−17.4373	−0.729728	−0.364864	−	0.931061i	$-0.618884\pi$
$571$	−17.4373	−0.729728	−0.364864	+	0.931061i	$0.618884\pi$
$572$	0	0
$573$	−16.5519	−0.691467
$574$	6.17985	0.257942
$575$	2.03908	0.0850354
$576$	7.14394	0.297664
$577$	−33.2349	−1.38359	−0.691793	−	0.722096i	$-0.743179\pi$
$577$	−33.2349	−1.38359	−0.691793	+	0.722096i	$0.743179\pi$
$578$	−24.6755	−1.02637
$579$	24.5032	1.01832
$580$	1.81302	0.0752818
$581$	21.6927	0.899966
$582$	−7.94472	−0.329319
$583$	0	0
$584$	21.1016	0.873192
$585$	2.14077	0.0885101
$586$	−29.5075	−1.21894
$587$	−42.7954	−1.76635	−0.883177	−	0.469040i	$-0.844600\pi$
$587$	−42.7954	−1.76635	−0.883177	+	0.469040i	$0.844600\pi$
$588$	−0.315947	−0.0130294
$589$	14.7773	0.608887
$590$	−11.9332	−0.491282
$591$	7.50877	0.308869
$592$	38.2008	1.57004
$593$	42.6570	1.75171	0.875857	−	0.482570i	$-0.160297\pi$
$593$	42.6570	1.75171	0.875857	+	0.482570i	$0.160297\pi$
$594$	0	0
$595$	−1.24948	−0.0512238
$596$	1.99800	0.0818413
$597$	−20.0956	−0.822458
$598$	6.44854	0.263700
$599$	28.3204	1.15714	0.578570	−	0.815633i	$-0.303611\pi$
$599$	28.3204	1.15714	0.578570	+	0.815633i	$0.303611\pi$
$600$	−2.68522	−0.109624
$601$	7.65458	0.312237	0.156118	−	0.987738i	$-0.450102\pi$
$601$	7.65458	0.312237	0.156118	+	0.987738i	$0.450102\pi$
$602$	2.10437	0.0857679
$603$	−9.75802	−0.397377
$604$	3.65184	0.148591
$605$	0	0
$606$	28.8495	1.17193
$607$	−11.5986	−0.470771	−0.235386	−	0.971902i	$-0.575635\pi$
$607$	−11.5986	−0.470771	−0.235386	+	0.971902i	$0.575635\pi$
$608$	−2.24364	−0.0909915
$609$	22.8244	0.924892
$610$	−12.8905	−0.521921
$611$	−0.809232	−0.0327380
$612$	−0.0992509	−0.00401198
$613$	32.1077	1.29682	0.648410	−	0.761292i	$-0.275434\pi$
$613$	32.1077	1.29682	0.648410	+	0.761292i	$0.275434\pi$
$614$	−28.7139	−1.15880
$615$	1.82283	0.0735035
$616$	0	0
$617$	−18.7392	−0.754414	−0.377207	−	0.926129i	$-0.623115\pi$
$617$	−18.7392	−0.754414	−0.377207	+	0.926129i	$0.623115\pi$
$618$	19.2136	0.772883
$619$	−39.0600	−1.56995	−0.784977	−	0.619525i	$-0.787325\pi$
$619$	−39.0600	−1.56995	−0.784977	+	0.619525i	$0.787325\pi$
$620$	1.23441	0.0495752
$621$	2.03908	0.0818254
$622$	8.89579	0.356689
$623$	1.33863	0.0536311
$624$	−9.27247	−0.371196
$625$	1.00000	0.0400000
$626$	−7.54633	−0.301612
$627$	0	0
$628$	1.66887	0.0665952
$629$	4.80179	0.191460
$630$	3.39026	0.135071
$631$	45.0561	1.79366	0.896828	−	0.442380i	$-0.145866\pi$
$631$	45.0561	1.79366	0.896828	+	0.442380i	$0.145866\pi$
$632$	−24.7699	−0.985295
$633$	−5.41860	−0.215370
$634$	20.2072	0.802529
$635$	−4.13248	−0.163993
$636$	2.11339	0.0838013
$637$	−3.71027	−0.147006
$638$	0	0
$639$	−14.9968	−0.593263
$640$	12.6097	0.498441
$641$	25.8928	1.02270	0.511351	−	0.859372i	$-0.329145\pi$
$641$	25.8928	1.02270	0.511351	+	0.859372i	$0.329145\pi$
$642$	−2.91544	−0.115063
$643$	30.6381	1.20825	0.604125	−	0.796890i	$-0.293523\pi$
$643$	30.6381	1.20825	0.604125	+	0.796890i	$0.293523\pi$
$644$	0.853079	0.0336160
$645$	0.620713	0.0244405
$646$	−1.75520	−0.0690572
$647$	−15.1084	−0.593972	−0.296986	−	0.954882i	$-0.595981\pi$
$647$	−15.1084	−0.593972	−0.296986	+	0.954882i	$0.595981\pi$
$648$	−2.68522	−0.105485
$649$	0	0
$650$	3.16248	0.124043
$651$	15.5402	0.609068
$652$	−2.06581	−0.0809032
$653$	−5.23528	−0.204872	−0.102436	−	0.994740i	$-0.532664\pi$
$653$	−5.23528	−0.204872	−0.102436	+	0.994740i	$0.532664\pi$
$654$	−15.6903	−0.613538
$655$	0.436527	0.0170565
$656$	−7.89532	−0.308261
$657$	−7.85844	−0.306587
$658$	−1.28155	−0.0499599
$659$	−14.9207	−0.581229	−0.290615	−	0.956840i	$-0.593860\pi$
$659$	−14.9207	−0.581229	−0.290615	+	0.956840i	$0.593860\pi$
$660$	0	0
$661$	45.7403	1.77909	0.889545	−	0.456847i	$-0.151021\pi$
$661$	45.7403	1.77909	0.889545	+	0.456847i	$0.151021\pi$
$662$	16.9434	0.658523
$663$	−1.16554	−0.0452656
$664$	−25.3816	−0.984995
$665$	5.00829	0.194213
$666$	−13.0288	−0.504857
$667$	20.2795	0.785226
$668$	−2.75271	−0.106505
$669$	15.7074	0.607284
$670$	−14.4151	−0.556905
$671$	0	0
$672$	−2.35947	−0.0910185
$673$	−21.1087	−0.813680	−0.406840	−	0.913500i	$-0.633369\pi$
$673$	−21.1087	−0.813680	−0.406840	+	0.913500i	$0.633369\pi$
$674$	−5.56047	−0.214181
$675$	1.00000	0.0384900
$676$	−1.53441	−0.0590158
$677$	44.0695	1.69373	0.846863	−	0.531810i	$-0.178488\pi$
$677$	44.0695	1.69373	0.846863	+	0.531810i	$0.178488\pi$
$678$	−24.9591	−0.958550
$679$	−12.3423	−0.473655
$680$	1.46196	0.0560635
$681$	1.47141	0.0563847
$682$	0	0
$683$	−42.5318	−1.62743	−0.813717	−	0.581261i	$-0.802560\pi$
$683$	−42.5318	−1.62743	−0.813717	+	0.581261i	$0.802560\pi$
$684$	0.397826	0.0152113
$685$	−7.86789	−0.300617
$686$	−29.6076	−1.13042
$687$	−15.9751	−0.609487
$688$	−2.68853	−0.102499
$689$	24.8182	0.945498
$690$	3.01225	0.114674
$691$	−5.74570	−0.218577	−0.109288	−	0.994010i	$-0.534857\pi$
$691$	−5.74570	−0.218577	−0.109288	+	0.994010i	$0.534857\pi$
$692$	−3.32949	−0.126568
$693$	0	0
$694$	0.584966	0.0222050
$695$	−17.6431	−0.669242
$696$	−26.7057	−1.01228
$697$	−0.992430	−0.0375910
$698$	19.4567	0.736445
$699$	25.6382	0.969724
$700$	0.418365	0.0158127
$701$	1.21594	0.0459255	0.0229628	−	0.999736i	$-0.492690\pi$
$701$	1.21594	0.0459255	0.0229628	+	0.999736i	$0.492690\pi$
$702$	3.16248	0.119360
$703$	−19.2470	−0.725913
$704$	0	0
$705$	−0.378009	−0.0142366
$706$	16.8190	0.632992
$707$	44.8185	1.68557
$708$	−1.47258	−0.0553430
$709$	−26.4100	−0.991850	−0.495925	−	0.868365i	$-0.665171\pi$
$709$	−26.4100	−0.991850	−0.495925	+	0.868365i	$0.665171\pi$
$710$	−22.1541	−0.831429
$711$	9.22454	0.345947
$712$	−1.56626	−0.0586982
$713$	13.8075	0.517094
$714$	−1.84581	−0.0690777
$715$	0	0
$716$	−0.0957823	−0.00357955
$717$	4.18206	0.156182
$718$	21.2256	0.792133
$719$	49.4435	1.84393	0.921967	−	0.387269i	$-0.126582\pi$
$719$	49.4435	1.84393	0.921967	+	0.387269i	$0.126582\pi$
$720$	−4.33136	−0.161420
$721$	29.8488	1.11163
$722$	−21.0326	−0.782753
$723$	3.29180	0.122423
$724$	−3.22860	−0.119990
$725$	9.94544	0.369364
$726$	0	0
$727$	−39.2447	−1.45551	−0.727753	−	0.685839i	$-0.759435\pi$
$727$	−39.2447	−1.45551	−0.727753	+	0.685839i	$0.759435\pi$
$728$	−13.1925	−0.488946
$729$	1.00000	0.0370370
$730$	−11.6090	−0.429667
$731$	−0.337944	−0.0124993
$732$	−1.59072	−0.0587946
$733$	−5.19920	−0.192037	−0.0960185	−	0.995380i	$-0.530611\pi$
$733$	−5.19920	−0.192037	−0.0960185	+	0.995380i	$0.530611\pi$
$734$	−38.7988	−1.43209
$735$	−1.73315	−0.0639280
$736$	−2.09639	−0.0772740
$737$	0	0
$738$	2.69279	0.0991229
$739$	−29.0090	−1.06711	−0.533557	−	0.845764i	$-0.679145\pi$
$739$	−29.0090	−1.06711	−0.533557	+	0.845764i	$0.679145\pi$
$740$	−1.60779	−0.0591034
$741$	4.67180	0.171623
$742$	39.3036	1.44288
$743$	−8.50677	−0.312083	−0.156042	−	0.987750i	$-0.549873\pi$
$743$	−8.50677	−0.312083	−0.156042	+	0.987750i	$0.549873\pi$
$744$	−18.1828	−0.666613
$745$	10.9601	0.401548
$746$	−32.3447	−1.18422
$747$	9.45232	0.345842
$748$	0	0
$749$	−4.52922	−0.165494
$750$	1.47726	0.0539419
$751$	−35.1051	−1.28100	−0.640502	−	0.767957i	$-0.721274\pi$
$751$	−35.1051	−1.28100	−0.640502	+	0.767957i	$0.721274\pi$
$752$	1.63729	0.0597060
$753$	−9.36459	−0.341265
$754$	31.4522	1.14542
$755$	20.0324	0.729053
$756$	0.418365	0.0152158
$757$	−7.18316	−0.261076	−0.130538	−	0.991443i	$-0.541671\pi$
$757$	−7.18316	−0.261076	−0.130538	+	0.991443i	$0.541671\pi$
$758$	37.7582	1.37144
$759$	0	0
$760$	−5.85995	−0.212563
$761$	43.3866	1.57276	0.786382	−	0.617741i	$-0.211952\pi$
$761$	43.3866	1.57276	0.786382	+	0.617741i	$0.211952\pi$
$762$	−6.10475	−0.221152
$763$	−24.3753	−0.882444
$764$	−3.01737	−0.109165
$765$	−0.544446	−0.0196845
$766$	28.1447	1.01691
$767$	−17.2930	−0.624414
$768$	4.33989	0.156602
$769$	19.6548	0.708771	0.354385	−	0.935099i	$-0.384690\pi$
$769$	19.6548	0.708771	0.354385	+	0.935099i	$0.384690\pi$
$770$	0	0
$771$	−12.5714	−0.452747
$772$	4.46687	0.160766
$773$	−24.4359	−0.878899	−0.439450	−	0.898267i	$-0.644826\pi$
$773$	−24.4359	−0.878899	−0.439450	+	0.898267i	$0.644826\pi$
$774$	0.916954	0.0329592
$775$	6.77143	0.243237
$776$	14.4411	0.518407
$777$	−20.2406	−0.726129
$778$	24.2160	0.868186
$779$	3.97795	0.142525
$780$	0.390257	0.0139734
$781$	0	0
$782$	−1.64001	−0.0586465
$783$	9.94544	0.355421
$784$	7.50688	0.268103
$785$	9.15468	0.326744
$786$	0.644864	0.0230015
$787$	34.1432	1.21707	0.608536	−	0.793526i	$-0.291757\pi$
$787$	34.1432	1.21707	0.608536	+	0.793526i	$0.291757\pi$
$788$	1.36883	0.0487624
$789$	−4.82946	−0.171933
$790$	13.6270	0.484829
$791$	−38.7747	−1.37867
$792$	0	0
$793$	−18.6803	−0.663357
$794$	45.7693	1.62429
$795$	11.5931	0.411165
$796$	−3.66337	−0.129845
$797$	−3.04303	−0.107790	−0.0538949	−	0.998547i	$-0.517164\pi$
$797$	−3.04303	−0.107790	−0.0538949	+	0.998547i	$0.517164\pi$
$798$	7.39855	0.261906
$799$	0.205805	0.00728087
$800$	−1.02811	−0.0363491
$801$	0.583290	0.0206096
$802$	−9.40439	−0.332081
$803$	0	0
$804$	−1.77886	−0.0627355
$805$	4.67961	0.164934
$806$	21.4145	0.754294
$807$	−5.22929	−0.184080
$808$	−52.4399	−1.84483
$809$	11.1011	0.390294	0.195147	−	0.980774i	$-0.437482\pi$
$809$	11.1011	0.390294	0.195147	+	0.980774i	$0.437482\pi$
$810$	1.47726	0.0519056
$811$	−41.3262	−1.45116	−0.725579	−	0.688139i	$-0.758428\pi$
$811$	−41.3262	−1.45116	−0.725579	+	0.688139i	$0.758428\pi$
$812$	4.16082	0.146016
$813$	−30.3311	−1.06376
$814$	0	0
$815$	−11.3321	−0.396946
$816$	2.35819	0.0825532
$817$	1.35458	0.0473907
$818$	9.26056	0.323788
$819$	4.91300	0.171674
$820$	0.332296	0.0116043
$821$	−8.17883	−0.285443	−0.142722	−	0.989763i	$-0.545585\pi$
$821$	−8.17883	−0.285443	−0.142722	+	0.989763i	$0.545585\pi$
$822$	−11.6229	−0.405396
$823$	13.1973	0.460029	0.230014	−	0.973187i	$-0.426123\pi$
$823$	13.1973	0.460029	0.230014	+	0.973187i	$0.426123\pi$
$824$	−34.9246	−1.21665
$825$	0	0
$826$	−27.3862	−0.952889
$827$	30.7370	1.06883	0.534415	−	0.845222i	$-0.320532\pi$
$827$	30.7370	1.06883	0.534415	+	0.845222i	$0.320532\pi$
$828$	0.371718	0.0129181
$829$	3.68790	0.128086	0.0640430	−	0.997947i	$-0.479601\pi$
$829$	3.68790	0.128086	0.0640430	+	0.997947i	$0.479601\pi$
$830$	13.9635	0.484681
$831$	−15.9694	−0.553974
$832$	15.2936	0.530209
$833$	0.943604	0.0326939
$834$	−26.0635	−0.902505
$835$	−15.1001	−0.522561
$836$	0	0
$837$	6.77143	0.234055
$838$	5.76621	0.199191
$839$	43.5517	1.50357	0.751786	−	0.659407i	$-0.229192\pi$
$839$	43.5517	1.50357	0.751786	+	0.659407i	$0.229192\pi$
$840$	−6.16248	−0.212626
$841$	69.9118	2.41075
$842$	25.6623	0.884381
$843$	1.39067	0.0478972
$844$	−0.987795	−0.0340013
$845$	−8.41709	−0.289557
$846$	−0.558418	−0.0191988
$847$	0	0
$848$	−50.2139	−1.72435
$849$	−5.87453	−0.201613
$850$	−0.804288	−0.0275869
$851$	−17.9838	−0.616478
$852$	−2.73387	−0.0936607
$853$	30.3434	1.03894	0.519469	−	0.854489i	$-0.326130\pi$
$853$	30.3434	1.03894	0.519469	+	0.854489i	$0.326130\pi$
$854$	−29.5832	−1.01232
$855$	2.18230	0.0746330
$856$	5.29941	0.181130
$857$	−12.5402	−0.428365	−0.214182	−	0.976794i	$-0.568709\pi$
$857$	−12.5402	−0.428365	−0.214182	+	0.976794i	$0.568709\pi$
$858$	0	0
$859$	−8.67783	−0.296084	−0.148042	−	0.988981i	$-0.547297\pi$
$859$	−8.67783	−0.296084	−0.148042	+	0.988981i	$0.547297\pi$
$860$	0.113154	0.00385852
$861$	4.18332	0.142567
$862$	10.3948	0.354047
$863$	−38.3918	−1.30687	−0.653437	−	0.756981i	$-0.726673\pi$
$863$	−38.3918	−1.30687	−0.653437	+	0.756981i	$0.726673\pi$
$864$	−1.02811	−0.0349770
$865$	−18.2641	−0.620998
$866$	4.06585	0.138163
$867$	−16.7036	−0.567283
$868$	2.83293	0.0961559
$869$	0	0
$870$	14.6920	0.498105
$871$	−20.8897	−0.707821
$872$	28.5203	0.965818
$873$	−5.37801	−0.182018
$874$	6.57362	0.222356
$875$	2.29496	0.0775839
$876$	−1.43257	−0.0484021
$877$	−31.2898	−1.05658	−0.528291	−	0.849064i	$-0.677167\pi$
$877$	−31.2898	−1.05658	−0.528291	+	0.849064i	$0.677167\pi$
$878$	4.04331	0.136455
$879$	−19.9745	−0.673723
$880$	0	0
$881$	49.2703	1.65996	0.829979	−	0.557795i	$-0.188353\pi$
$881$	49.2703	1.65996	0.829979	+	0.557795i	$0.188353\pi$
$882$	−2.56031	−0.0862100
$883$	28.1861	0.948539	0.474270	−	0.880380i	$-0.342712\pi$
$883$	28.1861	0.948539	0.474270	+	0.880380i	$0.342712\pi$
$884$	−0.212474	−0.00714626
$885$	−8.07792	−0.271536
$886$	16.4038	0.551096
$887$	25.4943	0.856016	0.428008	−	0.903775i	$-0.359216\pi$
$887$	25.4943	0.856016	0.428008	+	0.903775i	$0.359216\pi$
$888$	23.6825	0.794734
$889$	−9.48390	−0.318080
$890$	0.861672	0.0288833
$891$	0	0
$892$	2.86342	0.0958743
$893$	−0.824928	−0.0276052
$894$	16.1910	0.541507
$895$	−0.525419	−0.0175628
$896$	28.9387	0.966775
$897$	4.36520	0.145750
$898$	21.9031	0.730916
$899$	67.3449	2.24608
$900$	0.182297	0.00607657
$901$	−6.31181	−0.210277
$902$	0	0
$903$	1.42451	0.0474048
$904$	45.3683	1.50893
$905$	−17.7106	−0.588722
$906$	29.5930	0.983162
$907$	2.48054	0.0823649	0.0411825	−	0.999152i	$-0.486888\pi$
$907$	2.48054	0.0823649	0.0411825	+	0.999152i	$0.486888\pi$
$908$	0.268235	0.00890168
$909$	19.5291	0.647738
$910$	7.25777	0.240593
$911$	2.71559	0.0899716	0.0449858	−	0.998988i	$-0.485676\pi$
$911$	2.71559	0.0899716	0.0449858	+	0.998988i	$0.485676\pi$
$912$	−9.45232	−0.312998
$913$	0	0
$914$	−43.1101	−1.42595
$915$	−8.72595	−0.288471
$916$	−2.91221	−0.0962220
$917$	1.00181	0.0330828
$918$	−0.804288	−0.0265455
$919$	−3.23900	−0.106845	−0.0534224	−	0.998572i	$-0.517013\pi$
$919$	−3.23900	−0.106845	−0.0534224	+	0.998572i	$0.517013\pi$
$920$	−5.47537	−0.180518
$921$	−19.4372	−0.640479
$922$	46.0607	1.51693
$923$	−32.1047	−1.05674
$924$	0	0
$925$	−8.81959	−0.289986
$926$	60.8102	1.99835
$927$	13.0062	0.427180
$928$	−10.2250	−0.335652
$929$	7.18207	0.235636	0.117818	−	0.993035i	$-0.462410\pi$
$929$	7.18207	0.235636	0.117818	+	0.993035i	$0.462410\pi$
$930$	10.0032	0.328017
$931$	−3.78224	−0.123958
$932$	4.67376	0.153094
$933$	6.02182	0.197145
$934$	57.2832	1.87436
$935$	0	0
$936$	−5.74845	−0.187894
$937$	−20.3127	−0.663586	−0.331793	−	0.943352i	$-0.607654\pi$
$937$	−20.3127	−0.663586	−0.331793	+	0.943352i	$0.607654\pi$
$938$	−33.0822	−1.08017
$939$	−5.10833	−0.166704
$940$	−0.0689100	−0.00224760
$941$	25.4246	0.828818	0.414409	−	0.910091i	$-0.363988\pi$
$941$	25.4246	0.828818	0.414409	+	0.910091i	$0.363988\pi$
$942$	13.5238	0.440630
$943$	3.71689	0.121038
$944$	34.9884	1.13878
$945$	2.29496	0.0746551
$946$	0	0
$947$	−4.55536	−0.148029	−0.0740147	−	0.997257i	$-0.523581\pi$
$947$	−4.55536	−0.148029	−0.0740147	+	0.997257i	$0.523581\pi$
$948$	1.68161	0.0546161
$949$	−16.8231	−0.546102
$950$	3.22382	0.104595
$951$	13.6788	0.443566
$952$	3.35514	0.108741
$953$	41.5855	1.34709	0.673543	−	0.739148i	$-0.264772\pi$
$953$	41.5855	1.34709	0.673543	+	0.739148i	$0.264772\pi$
$954$	17.1260	0.554475
$955$	−16.5519	−0.535608
$956$	0.762378	0.0246571
$957$	0	0
$958$	−24.6519	−0.796467
$959$	−18.0565	−0.583076
$960$	7.14394	0.230570
$961$	14.8523	0.479107
$962$	−27.8918	−0.899267
$963$	−1.97355	−0.0635967
$964$	0.600085	0.0193274
$965$	24.5032	0.788787
$966$	6.91300	0.222422
$967$	16.2161	0.521476	0.260738	−	0.965410i	$-0.416034\pi$
$967$	16.2161	0.521476	0.260738	+	0.965410i	$0.416034\pi$
$968$	0	0
$969$	−1.18814	−0.0381686
$970$	−7.94472	−0.255090
$971$	−13.4705	−0.432290	−0.216145	−	0.976361i	$-0.569348\pi$
$971$	−13.4705	−0.432290	−0.216145	+	0.976361i	$0.569348\pi$
$972$	0.182297	0.00584718
$973$	−40.4904	−1.29806
$974$	3.71078	0.118901
$975$	2.14077	0.0685596
$976$	37.7953	1.20980
$977$	−14.5400	−0.465177	−0.232588	−	0.972575i	$-0.574719\pi$
$977$	−14.5400	−0.465177	−0.232588	+	0.972575i	$0.574719\pi$
$978$	−16.7404	−0.535300
$979$	0	0
$980$	−0.315947	−0.0100926
$981$	−10.6212	−0.339109
$982$	11.1661	0.356324
$983$	−24.5938	−0.784422	−0.392211	−	0.919875i	$-0.628290\pi$
$983$	−24.5938	−0.784422	−0.392211	+	0.919875i	$0.628290\pi$
$984$	−4.89469	−0.156037
$985$	7.50877	0.239249
$986$	−7.99900	−0.254740
$987$	−0.867517	−0.0276134
$988$	0.851656	0.0270948
$989$	1.26568	0.0402463
$990$	0	0
$991$	4.43775	0.140970	0.0704848	−	0.997513i	$-0.477545\pi$
$991$	4.43775	0.140970	0.0704848	+	0.997513i	$0.477545\pi$
$992$	−6.96177	−0.221036
$993$	11.4695	0.363972
$994$	−50.8429	−1.61264
$995$	−20.0956	−0.637073
$996$	1.72313	0.0545995
$997$	−0.0104705	−0.000331605 0	−0.000165802	−	1.00000i	$-0.500053\pi$
$997$	−0.0104705	−0.000331605 0	−0.000165802		1.00000i	$0.500053\pi$
$998$	24.8127	0.785431
$999$	−8.81959	−0.279040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.w.1.3		4
3.2	odd	2		5445.2.a.bf.1.2		4
5.4	even	2		9075.2.a.cm.1.2		4
11.7	odd	10		165.2.m.d.16.1	✓	8
11.8	odd	10		165.2.m.d.31.1	yes	8
11.10	odd	2		1815.2.a.p.1.2		4
33.8	even	10		495.2.n.a.361.2		8
33.29	even	10		495.2.n.a.181.2		8
33.32	even	2		5445.2.a.bt.1.3		4
55.7	even	20		825.2.bx.f.49.4		16
55.8	even	20		825.2.bx.f.724.4		16
55.18	even	20		825.2.bx.f.49.1		16
55.19	odd	10		825.2.n.g.526.2		8
55.29	odd	10		825.2.n.g.676.2		8
55.52	even	20		825.2.bx.f.724.1		16
55.54	odd	2		9075.2.a.di.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.16.1	✓	8	11.7	odd	10
165.2.m.d.31.1	yes	8	11.8	odd	10
495.2.n.a.181.2		8	33.29	even	10
495.2.n.a.361.2		8	33.8	even	10
825.2.n.g.526.2		8	55.19	odd	10
825.2.n.g.676.2		8	55.29	odd	10
825.2.bx.f.49.1		16	55.18	even	20
825.2.bx.f.49.4		16	55.7	even	20
825.2.bx.f.724.1		16	55.52	even	20
825.2.bx.f.724.4		16	55.8	even	20
1815.2.a.p.1.2		4	11.10	odd	2
1815.2.a.w.1.3		4	1.1	even	1	trivial
5445.2.a.bf.1.2		4	3.2	odd	2
5445.2.a.bt.1.3		4	33.32	even	2
9075.2.a.cm.1.2		4	5.4	even	2
9075.2.a.di.1.3		4	55.54	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q+1.47726 q^{2} +1.00000 q^{3} +0.182297 q^{4} +1.00000 q^{5} +1.47726 q^{6} +2.29496 q^{7} -2.68522 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.47726 q^{2} +1.00000 q^{3} +0.182297 q^{4} +1.00000 q^{5} +1.47726 q^{6} +2.29496 q^{7} -2.68522 q^{8} +1.00000 q^{9} +1.47726 q^{10} +0.182297 q^{12} +2.14077 q^{13} +3.39026 q^{14} +1.00000 q^{15} -4.33136 q^{16} -0.544446 q^{17} +1.47726 q^{18} +2.18230 q^{19} +0.182297 q^{20} +2.29496 q^{21} +2.03908 q^{23} -2.68522 q^{24} +1.00000 q^{25} +3.16248 q^{26} +1.00000 q^{27} +0.418365 q^{28} +9.94544 q^{29} +1.47726 q^{30} +6.77143 q^{31} -1.02811 q^{32} -0.804288 q^{34} +2.29496 q^{35} +0.182297 q^{36} -8.81959 q^{37} +3.22382 q^{38} +2.14077 q^{39} -2.68522 q^{40} +1.82283 q^{41} +3.39026 q^{42} +0.620713 q^{43} +1.00000 q^{45} +3.01225 q^{46} -0.378009 q^{47} -4.33136 q^{48} -1.73315 q^{49} +1.47726 q^{50} -0.544446 q^{51} +0.390257 q^{52} +11.5931 q^{53} +1.47726 q^{54} -6.16248 q^{56} +2.18230 q^{57} +14.6920 q^{58} -8.07792 q^{59} +0.182297 q^{60} -8.72595 q^{61} +10.0032 q^{62} +2.29496 q^{63} +7.14394 q^{64} +2.14077 q^{65} -9.75802 q^{67} -0.0992509 q^{68} +2.03908 q^{69} +3.39026 q^{70} -14.9968 q^{71} -2.68522 q^{72} -7.85844 q^{73} -13.0288 q^{74} +1.00000 q^{75} +0.397826 q^{76} +3.16248 q^{78} +9.22454 q^{79} -4.33136 q^{80} +1.00000 q^{81} +2.69279 q^{82} +9.45232 q^{83} +0.418365 q^{84} -0.544446 q^{85} +0.916954 q^{86} +9.94544 q^{87} +0.583290 q^{89} +1.47726 q^{90} +4.91300 q^{91} +0.371718 q^{92} +6.77143 q^{93} -0.558418 q^{94} +2.18230 q^{95} -1.02811 q^{96} -5.37801 q^{97} -2.56031 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 4 q^{3} + q^{4} + 4 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 4 * q^3 + q^4 + 4 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q + 3 q^{2} + 4 q^{3} + q^{4} + 4 q^{5} + 3 q^{6} + 6 q^{7} + 3 q^{8} + 4 q^{9} + 3 q^{10} + q^{12} + 7 q^{13} + 3 q^{14} + 4 q^{15} - q^{16} + 10 q^{17} + 3 q^{18} + 9 q^{19} + q^{20} + 6 q^{21} - 3 q^{23} + 3 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} - 7 q^{28} + 15 q^{29} + 3 q^{30} - 13 q^{31} - 6 q^{32} - 3 q^{34} + 6 q^{35} + q^{36} - 3 q^{37} + 15 q^{38} + 7 q^{39} + 3 q^{40} + 22 q^{41} + 3 q^{42} + 4 q^{45} + q^{46} - 2 q^{47} - q^{48} - 12 q^{49} + 3 q^{50} + 10 q^{51} - 9 q^{52} + 10 q^{53} + 3 q^{54} - 8 q^{56} + 9 q^{57} + 39 q^{58} - 21 q^{59} + q^{60} + 11 q^{61} + 10 q^{62} + 6 q^{63} - 3 q^{64} + 7 q^{65} + q^{67} + 3 q^{68} - 3 q^{69} + 3 q^{70} - 13 q^{71} + 3 q^{72} + q^{73} - 11 q^{74} + 4 q^{75} + 19 q^{76} - 4 q^{78} - 4 q^{79} - q^{80} + 4 q^{81} + 25 q^{82} + 3 q^{83} - 7 q^{84} + 10 q^{85} + 15 q^{87} - 10 q^{89} + 3 q^{90} + 12 q^{91} - 24 q^{92} - 13 q^{93} - 35 q^{94} + 9 q^{95} - 6 q^{96} - 22 q^{97} - 11 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 + 4 * q^3 + q^4 + 4 * q^5 + 3 * q^6 + 6 * q^7 + 3 * q^8 + 4 * q^9 + 3 * q^10 + q^12 + 7 * q^13 + 3 * q^14 + 4 * q^15 - q^16 + 10 * q^17 + 3 * q^18 + 9 * q^19 + q^20 + 6 * q^21 - 3 * q^23 + 3 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 - 7 * q^28 + 15 * q^29 + 3 * q^30 - 13 * q^31 - 6 * q^32 - 3 * q^34 + 6 * q^35 + q^36 - 3 * q^37 + 15 * q^38 + 7 * q^39 + 3 * q^40 + 22 * q^41 + 3 * q^42 + 4 * q^45 + q^46 - 2 * q^47 - q^48 - 12 * q^49 + 3 * q^50 + 10 * q^51 - 9 * q^52 + 10 * q^53 + 3 * q^54 - 8 * q^56 + 9 * q^57 + 39 * q^58 - 21 * q^59 + q^60 + 11 * q^61 + 10 * q^62 + 6 * q^63 - 3 * q^64 + 7 * q^65 + q^67 + 3 * q^68 - 3 * q^69 + 3 * q^70 - 13 * q^71 + 3 * q^72 + q^73 - 11 * q^74 + 4 * q^75 + 19 * q^76 - 4 * q^78 - 4 * q^79 - q^80 + 4 * q^81 + 25 * q^82 + 3 * q^83 - 7 * q^84 + 10 * q^85 + 15 * q^87 - 10 * q^89 + 3 * q^90 + 12 * q^91 - 24 * q^92 - 13 * q^93 - 35 * q^94 + 9 * q^95 - 6 * q^96 - 22 * q^97 - 11 * q^98

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