LMFDB - Embedded newform 1815.2.a.u.1.4

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:	$\Q(\zeta_{15})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + 4x + 1 $ x^4 - x^3 - 4x^2 + 4x + 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			1.4
Root			$1.33826$ 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)

$f(q)$	$=$	$q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} +1.00000 q^{5} -1.82709 q^{6} +1.74724 q^{7} -1.20906 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} +1.00000 q^{5} -1.82709 q^{6} +1.74724 q^{7} -1.20906 q^{8} +1.00000 q^{9} +1.82709 q^{10} -1.33826 q^{12} -5.35772 q^{13} +3.19236 q^{14} -1.00000 q^{15} -4.88558 q^{16} +7.33070 q^{17} +1.82709 q^{18} +6.01478 q^{19} +1.33826 q^{20} -1.74724 q^{21} +8.35772 q^{23} +1.20906 q^{24} +1.00000 q^{25} -9.78903 q^{26} -1.00000 q^{27} +2.33826 q^{28} +5.53818 q^{29} -1.82709 q^{30} -0.0213642 q^{31} -6.50828 q^{32} +13.3939 q^{34} +1.74724 q^{35} +1.33826 q^{36} -1.12165 q^{37} +10.9896 q^{38} +5.35772 q^{39} -1.20906 q^{40} -3.65983 q^{41} -3.19236 q^{42} -1.96950 q^{43} +1.00000 q^{45} +15.2703 q^{46} +3.81953 q^{47} +4.88558 q^{48} -3.94716 q^{49} +1.82709 q^{50} -7.33070 q^{51} -7.17002 q^{52} +1.67088 q^{53} -1.82709 q^{54} -2.11251 q^{56} -6.01478 q^{57} +10.1188 q^{58} +5.66332 q^{59} -1.33826 q^{60} +9.27977 q^{61} -0.0390343 q^{62} +1.74724 q^{63} -2.12007 q^{64} -5.35772 q^{65} +0.350489 q^{67} +9.81040 q^{68} -8.35772 q^{69} +3.19236 q^{70} +4.53818 q^{71} -1.20906 q^{72} +10.1395 q^{73} -2.04935 q^{74} -1.00000 q^{75} +8.04935 q^{76} +9.78903 q^{78} +2.56401 q^{79} -4.88558 q^{80} +1.00000 q^{81} -6.68684 q^{82} -16.0805 q^{83} -2.33826 q^{84} +7.33070 q^{85} -3.59845 q^{86} -5.53818 q^{87} -14.5062 q^{89} +1.82709 q^{90} -9.36121 q^{91} +11.1848 q^{92} +0.0213642 q^{93} +6.97864 q^{94} +6.01478 q^{95} +6.50828 q^{96} -1.89972 q^{97} -7.21182 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 4 q^{3} + q^{4} + 4 q^{5} - q^{6} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 - 4 * q^3 + q^4 + 4 * q^5 - q^6 - 3 * q^8 + 4 * q^9	$ 4 q + q^{2} - 4 q^{3} + q^{4} + 4 q^{5} - q^{6} - 3 q^{8} + 4 q^{9} + q^{10} - q^{12} + 7 q^{13} - 5 q^{14} - 4 q^{15} - 9 q^{16} + 8 q^{17} + q^{18} + 11 q^{19} + q^{20} + 5 q^{23} + 3 q^{24} + 4 q^{25} - 12 q^{26} - 4 q^{27} + 5 q^{28} + 17 q^{29} - q^{30} - 5 q^{31} + 17 q^{34} + q^{36} + 15 q^{37} - q^{38} - 7 q^{39} - 3 q^{40} + 10 q^{41} + 5 q^{42} - 4 q^{43} + 4 q^{45} + 15 q^{46} - 8 q^{47} + 9 q^{48} - 8 q^{49} + q^{50} - 8 q^{51} - 7 q^{52} + 10 q^{53} - q^{54} + 10 q^{56} - 11 q^{57} - 7 q^{58} + 9 q^{59} - q^{60} + 37 q^{61} - 20 q^{62} - 7 q^{64} + 7 q^{65} + 3 q^{67} + 17 q^{68} - 5 q^{69} - 5 q^{70} + 13 q^{71} - 3 q^{72} + 15 q^{73} - 5 q^{74} - 4 q^{75} + 29 q^{76} + 12 q^{78} + 20 q^{79} - 9 q^{80} + 4 q^{81} + 5 q^{82} - 17 q^{83} - 5 q^{84} + 8 q^{85} + 34 q^{86} - 17 q^{87} - 24 q^{89} + q^{90} - 20 q^{91} + 10 q^{92} + 5 q^{93} + 23 q^{94} + 11 q^{95} - 32 q^{97} + 13 q^{98}+O(q^{100}) $ 4 * q + q^2 - 4 * q^3 + q^4 + 4 * q^5 - q^6 - 3 * q^8 + 4 * q^9 + q^10 - q^12 + 7 * q^13 - 5 * q^14 - 4 * q^15 - 9 * q^16 + 8 * q^17 + q^18 + 11 * q^19 + q^20 + 5 * q^23 + 3 * q^24 + 4 * q^25 - 12 * q^26 - 4 * q^27 + 5 * q^28 + 17 * q^29 - q^30 - 5 * q^31 + 17 * q^34 + q^36 + 15 * q^37 - q^38 - 7 * q^39 - 3 * q^40 + 10 * q^41 + 5 * q^42 - 4 * q^43 + 4 * q^45 + 15 * q^46 - 8 * q^47 + 9 * q^48 - 8 * q^49 + q^50 - 8 * q^51 - 7 * q^52 + 10 * q^53 - q^54 + 10 * q^56 - 11 * q^57 - 7 * q^58 + 9 * q^59 - q^60 + 37 * q^61 - 20 * q^62 - 7 * q^64 + 7 * q^65 + 3 * q^67 + 17 * q^68 - 5 * q^69 - 5 * q^70 + 13 * q^71 - 3 * q^72 + 15 * q^73 - 5 * q^74 - 4 * q^75 + 29 * q^76 + 12 * q^78 + 20 * q^79 - 9 * q^80 + 4 * q^81 + 5 * q^82 - 17 * q^83 - 5 * q^84 + 8 * q^85 + 34 * q^86 - 17 * q^87 - 24 * q^89 + q^90 - 20 * q^91 + 10 * q^92 + 5 * q^93 + 23 * q^94 + 11 * q^95 - 32 * q^97 + 13 * 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 $

$2$	1.82709	1.29195	0.645974	−	0.763359i	$-0.276451\pi$
$2$	1.82709	1.29195	0.645974	+	0.763359i	$0.276451\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.33826	0.669131
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.82709	−0.745907
$7$	1.74724	0.660394	0.330197	−	0.943912i	$-0.392885\pi$
$7$	1.74724	0.660394	0.330197	+	0.943912i	$0.392885\pi$
$8$	−1.20906	−0.427466
$9$	1.00000	0.333333
$10$	1.82709	0.577777
$11$	0	0
$11$	0	0
$12$	−1.33826	−0.386323
$13$	−5.35772	−1.48596	−0.742981	−	0.669312i	$-0.766589\pi$
$13$	−5.35772	−1.48596	−0.742981	+	0.669312i	$0.766589\pi$
$14$	3.19236	0.853195
$15$	−1.00000	−0.258199
$16$	−4.88558	−1.22139
$17$	7.33070	1.77796	0.888978	−	0.457949i	$-0.151416\pi$
$17$	7.33070	1.77796	0.888978	+	0.457949i	$0.151416\pi$
$18$	1.82709	0.430649
$19$	6.01478	1.37989	0.689943	−	0.723864i	$-0.257636\pi$
$19$	6.01478	1.37989	0.689943	+	0.723864i	$0.257636\pi$
$20$	1.33826	0.299244
$21$	−1.74724	−0.381279
$22$	0	0
$23$	8.35772	1.74270	0.871352	−	0.490658i	$-0.163244\pi$
$23$	8.35772	1.74270	0.871352	+	0.490658i	$0.163244\pi$
$24$	1.20906	0.246798
$25$	1.00000	0.200000
$26$	−9.78903	−1.91979
$27$	−1.00000	−0.192450
$28$	2.33826	0.441890
$29$	5.53818	1.02841	0.514207	−	0.857666i	$-0.328086\pi$
$29$	5.53818	1.02841	0.514207	+	0.857666i	$0.328086\pi$
$30$	−1.82709	−0.333580
$31$	−0.0213642	−0.00383712	−0.00191856	−	0.999998i	$-0.500611\pi$
$31$	−0.0213642	−0.00383712	−0.00191856	+	0.999998i	$0.500611\pi$
$32$	−6.50828	−1.15051
$33$	0	0
$34$	13.3939	2.29703
$35$	1.74724	0.295337
$36$	1.33826	0.223044
$37$	−1.12165	−0.184398	−0.0921988	−	0.995741i	$-0.529390\pi$
$37$	−1.12165	−0.184398	−0.0921988	+	0.995741i	$0.529390\pi$
$38$	10.9896	1.78274
$39$	5.35772	0.857921
$40$	−1.20906	−0.191169
$41$	−3.65983	−0.571569	−0.285785	−	0.958294i	$-0.592254\pi$
$41$	−3.65983	−0.571569	−0.285785	+	0.958294i	$0.592254\pi$
$42$	−3.19236	−0.492592
$43$	−1.96950	−0.300346	−0.150173	−	0.988660i	$-0.547983\pi$
$43$	−1.96950	−0.300346	−0.150173	+	0.988660i	$0.547983\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	15.2703	2.25148
$47$	3.81953	0.557136	0.278568	−	0.960416i	$-0.410140\pi$
$47$	3.81953	0.557136	0.278568	+	0.960416i	$0.410140\pi$
$48$	4.88558	0.705173
$49$	−3.94716	−0.563880
$50$	1.82709	0.258390
$51$	−7.33070	−1.02650
$52$	−7.17002	−0.994303
$53$	1.67088	0.229512	0.114756	−	0.993394i	$-0.463391\pi$
$53$	1.67088	0.229512	0.114756	+	0.993394i	$0.463391\pi$
$54$	−1.82709	−0.248636
$55$	0	0
$56$	−2.11251	−0.282296
$57$	−6.01478	−0.796678
$58$	10.1188	1.32866
$59$	5.66332	0.737301	0.368651	−	0.929568i	$-0.379820\pi$
$59$	5.66332	0.737301	0.368651	+	0.929568i	$0.379820\pi$
$60$	−1.33826	−0.172769
$61$	9.27977	1.18815	0.594077	−	0.804408i	$-0.297518\pi$
$61$	9.27977	1.18815	0.594077	+	0.804408i	$0.297518\pi$
$62$	−0.0390343	−0.00495737
$63$	1.74724	0.220131
$64$	−2.12007	−0.265008
$65$	−5.35772	−0.664543
$66$	0	0
$67$	0.350489	0.0428190	0.0214095	−	0.999771i	$-0.493185\pi$
$67$	0.350489	0.0428190	0.0214095	+	0.999771i	$0.493185\pi$
$68$	9.81040	1.18969
$69$	−8.35772	−1.00615
$70$	3.19236	0.381560
$71$	4.53818	0.538583	0.269292	−	0.963059i	$-0.413210\pi$
$71$	4.53818	0.538583	0.269292	+	0.963059i	$0.413210\pi$
$72$	−1.20906	−0.142489
$73$	10.1395	1.18674	0.593371	−	0.804929i	$-0.297797\pi$
$73$	10.1395	1.18674	0.593371	+	0.804929i	$0.297797\pi$
$74$	−2.04935	−0.238232
$75$	−1.00000	−0.115470
$76$	8.04935	0.923324
$77$	0	0
$78$	9.78903	1.10839
$79$	2.56401	0.288474	0.144237	−	0.989543i	$-0.453927\pi$
$79$	2.56401	0.288474	0.144237	+	0.989543i	$0.453927\pi$
$80$	−4.88558	−0.546224
$81$	1.00000	0.111111
$82$	−6.68684	−0.738438
$83$	−16.0805	−1.76506	−0.882532	−	0.470252i	$-0.844163\pi$
$83$	−16.0805	−1.76506	−0.882532	+	0.470252i	$0.844163\pi$
$84$	−2.33826	−0.255125
$85$	7.33070	0.795127
$86$	−3.59845	−0.388031
$87$	−5.53818	−0.593755
$88$	0	0
$89$	−14.5062	−1.53765	−0.768825	−	0.639459i	$-0.779159\pi$
$89$	−14.5062	−1.53765	−0.768825	+	0.639459i	$0.779159\pi$
$90$	1.82709	0.192592
$91$	−9.36121	−0.981321
$92$	11.1848	1.16610
$93$	0.0213642	0.00221536
$94$	6.97864	0.719791
$95$	6.01478	0.617104
$96$	6.50828	0.664249
$97$	−1.89972	−0.192887	−0.0964435	−	0.995338i	$-0.530747\pi$
$97$	−1.89972	−0.192887	−0.0964435	+	0.995338i	$0.530747\pi$
$98$	−7.21182	−0.728504
$99$	0	0
$100$	1.33826	0.133826
$101$	6.71011	0.667681	0.333841	−	0.942630i	$-0.391655\pi$
$101$	6.71011	0.667681	0.333841	+	0.942630i	$0.391655\pi$
$102$	−13.3939	−1.32619
$103$	−4.24678	−0.418448	−0.209224	−	0.977868i	$-0.567094\pi$
$103$	−4.24678	−0.418448	−0.209224	+	0.977868i	$0.567094\pi$
$104$	6.47778	0.635199
$105$	−1.74724	−0.170513
$106$	3.05284	0.296518
$107$	−15.7230	−1.52000	−0.759999	−	0.649924i	$-0.774801\pi$
$107$	−15.7230	−1.52000	−0.759999	+	0.649924i	$0.774801\pi$
$108$	−1.33826	−0.128774
$109$	4.23895	0.406018	0.203009	−	0.979177i	$-0.434928\pi$
$109$	4.23895	0.406018	0.203009	+	0.979177i	$0.434928\pi$
$110$	0	0
$111$	1.12165	0.106462
$112$	−8.53627	−0.806602
$113$	−7.19643	−0.676983	−0.338492	−	0.940969i	$-0.609917\pi$
$113$	−7.19643	−0.676983	−0.338492	+	0.940969i	$0.609917\pi$
$114$	−10.9896	−1.02927
$115$	8.35772	0.779361
$116$	7.41153	0.688144
$117$	−5.35772	−0.495321
$118$	10.3474	0.952555
$119$	12.8085	1.17415
$120$	1.20906	0.110371
$121$	0	0
$122$	16.9550	1.53503
$123$	3.65983	0.329996
$124$	−0.0285909	−0.00256754
$125$	1.00000	0.0894427
$126$	3.19236	0.284398
$127$	12.6870	1.12579	0.562897	−	0.826527i	$-0.309687\pi$
$127$	12.6870	1.12579	0.562897	+	0.826527i	$0.309687\pi$
$128$	9.14301	0.808136
$129$	1.96950	0.173405
$130$	−9.78903	−0.858555
$131$	−0.970102	−0.0847582	−0.0423791	−	0.999102i	$-0.513494\pi$
$131$	−0.970102	−0.0847582	−0.0423791	+	0.999102i	$0.513494\pi$
$132$	0	0
$133$	10.5093	0.911268
$134$	0.640375	0.0553199
$135$	−1.00000	−0.0860663
$136$	−8.86324	−0.760016
$137$	4.22035	0.360569	0.180284	−	0.983615i	$-0.442298\pi$
$137$	4.22035	0.360569	0.180284	+	0.983615i	$0.442298\pi$
$138$	−15.2703	−1.29989
$139$	8.84846	0.750516	0.375258	−	0.926920i	$-0.377554\pi$
$139$	8.84846	0.750516	0.375258	+	0.926920i	$0.377554\pi$
$140$	2.33826	0.197619
$141$	−3.81953	−0.321663
$142$	8.29167	0.695821
$143$	0	0
$144$	−4.88558	−0.407132
$145$	5.53818	0.459921
$146$	18.5258	1.53321
$147$	3.94716	0.325556
$148$	−1.50106	−0.123386
$149$	9.55357	0.782659	0.391329	−	0.920251i	$-0.372015\pi$
$149$	9.55357	0.782659	0.391329	+	0.920251i	$0.372015\pi$
$150$	−1.82709	−0.149181
$151$	−6.75158	−0.549436	−0.274718	−	0.961525i	$-0.588584\pi$
$151$	−6.75158	−0.549436	−0.274718	+	0.961525i	$0.588584\pi$
$152$	−7.27222	−0.589855
$153$	7.33070	0.592652
$154$	0	0
$155$	−0.0213642	−0.00171601
$156$	7.17002	0.574061
$157$	−12.6604	−1.01041	−0.505206	−	0.862999i	$-0.668584\pi$
$157$	−12.6604	−1.01041	−0.505206	+	0.862999i	$0.668584\pi$
$158$	4.68468	0.372693
$159$	−1.67088	−0.132509
$160$	−6.50828	−0.514525
$161$	14.6029	1.15087
$162$	1.82709	0.143550
$163$	−23.4058	−1.83328	−0.916640	−	0.399713i	$-0.869110\pi$
$163$	−23.4058	−1.83328	−0.916640	+	0.399713i	$0.869110\pi$
$164$	−4.89781	−0.382454
$165$	0	0
$166$	−29.3805	−2.28037
$167$	3.05191	0.236164	0.118082	−	0.993004i	$-0.462325\pi$
$167$	3.05191	0.236164	0.118082	+	0.993004i	$0.462325\pi$
$168$	2.11251	0.162984
$169$	15.7051	1.20809
$170$	13.3939	1.02726
$171$	6.01478	0.459962
$172$	−2.63570	−0.200971
$173$	16.0074	1.21702	0.608511	−	0.793545i	$-0.291767\pi$
$173$	16.0074	1.21702	0.608511	+	0.793545i	$0.291767\pi$
$174$	−10.1188	−0.767101
$175$	1.74724	0.132079
$176$	0	0
$177$	−5.66332	−0.425681
$178$	−26.5041	−1.98657
$179$	−19.2991	−1.44248	−0.721241	−	0.692684i	$-0.756428\pi$
$179$	−19.2991	−1.44248	−0.721241	+	0.692684i	$0.756428\pi$
$180$	1.33826	0.0997481
$181$	−12.1911	−0.906154	−0.453077	−	0.891471i	$-0.649674\pi$
$181$	−12.1911	−0.906154	−0.453077	+	0.891471i	$0.649674\pi$
$182$	−17.1038	−1.26782
$183$	−9.27977	−0.685981
$184$	−10.1050	−0.744947
$185$	−1.12165	−0.0824652
$186$	0.0390343	0.00286214
$187$	0	0
$188$	5.11153	0.372797
$189$	−1.74724	−0.127093
$190$	10.9896	0.797266
$191$	−13.4244	−0.971353	−0.485676	−	0.874139i	$-0.661427\pi$
$191$	−13.4244	−0.971353	−0.485676	+	0.874139i	$0.661427\pi$
$192$	2.12007	0.153003
$193$	7.57782	0.545463	0.272732	−	0.962090i	$-0.412073\pi$
$193$	7.57782	0.545463	0.272732	+	0.962090i	$0.412073\pi$
$194$	−3.47096	−0.249200
$195$	5.35772	0.383674
$196$	−5.28233	−0.377309
$197$	−6.89118	−0.490976	−0.245488	−	0.969400i	$-0.578948\pi$
$197$	−6.89118	−0.490976	−0.245488	+	0.969400i	$0.578948\pi$
$198$	0	0
$199$	0.639398	0.0453257	0.0226629	−	0.999743i	$-0.492786\pi$
$199$	0.639398	0.0453257	0.0226629	+	0.999743i	$0.492786\pi$
$200$	−1.20906	−0.0854932
$201$	−0.350489	−0.0247216
$202$	12.2600	0.862610
$203$	9.67652	0.679159
$204$	−9.81040	−0.686865
$205$	−3.65983	−0.255614
$206$	−7.75926	−0.540613
$207$	8.35772	0.580901
$208$	26.1755	1.81495
$209$	0	0
$210$	−3.19236	−0.220294
$211$	−3.82149	−0.263082	−0.131541	−	0.991311i	$-0.541992\pi$
$211$	−3.82149	−0.263082	−0.131541	+	0.991311i	$0.541992\pi$
$212$	2.23607	0.153574
$213$	−4.53818	−0.310951
$214$	−28.7273	−1.96376
$215$	−1.96950	−0.134319
$216$	1.20906	0.0822659
$217$	−0.0373284	−0.00253401
$218$	7.74496	0.524555
$219$	−10.1395	−0.685165
$220$	0	0
$221$	−39.2758	−2.64198
$222$	2.04935	0.137543
$223$	−26.7201	−1.78931	−0.894657	−	0.446755i	$-0.852580\pi$
$223$	−26.7201	−1.78931	−0.894657	+	0.446755i	$0.852580\pi$
$224$	−11.3715	−0.759792
$225$	1.00000	0.0666667
$226$	−13.1485	−0.874627
$227$	12.2373	0.812219	0.406110	−	0.913824i	$-0.366885\pi$
$227$	12.2373	0.812219	0.406110	+	0.913824i	$0.366885\pi$
$228$	−8.04935	−0.533081
$229$	−6.68664	−0.441865	−0.220933	−	0.975289i	$-0.570910\pi$
$229$	−6.68664	−0.441865	−0.220933	+	0.975289i	$0.570910\pi$
$230$	15.2703	1.00689
$231$	0	0
$232$	−6.69598	−0.439612
$233$	−6.51742	−0.426970	−0.213485	−	0.976946i	$-0.568482\pi$
$233$	−6.51742	−0.426970	−0.213485	+	0.976946i	$0.568482\pi$
$234$	−9.78903	−0.639929
$235$	3.81953	0.249159
$236$	7.57900	0.493351
$237$	−2.56401	−0.166550
$238$	23.4023	1.51694
$239$	−10.8419	−0.701303	−0.350651	−	0.936506i	$-0.614040\pi$
$239$	−10.8419	−0.701303	−0.350651	+	0.936506i	$0.614040\pi$
$240$	4.88558	0.315363
$241$	27.1803	1.75084	0.875420	−	0.483363i	$-0.160585\pi$
$241$	27.1803	1.75084	0.875420	+	0.483363i	$0.160585\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	12.4188	0.795030
$245$	−3.94716	−0.252175
$246$	6.68684	0.426337
$247$	−32.2255	−2.05046
$248$	0.0258305	0.00164024
$249$	16.0805	1.01906
$250$	1.82709	0.115555
$251$	5.54443	0.349961	0.174981	−	0.984572i	$-0.444014\pi$
$251$	5.54443	0.349961	0.174981	+	0.984572i	$0.444014\pi$
$252$	2.33826	0.147297
$253$	0	0
$254$	23.1804	1.45447
$255$	−7.33070	−0.459067
$256$	20.9452	1.30908
$257$	−18.9439	−1.18169	−0.590845	−	0.806785i	$-0.701206\pi$
$257$	−18.9439	−1.18169	−0.590845	+	0.806785i	$0.701206\pi$
$258$	3.59845	0.224030
$259$	−1.95979	−0.121775
$260$	−7.17002	−0.444666
$261$	5.53818	0.342805
$262$	−1.77247	−0.109503
$263$	3.20873	0.197859	0.0989293	−	0.995094i	$-0.468458\pi$
$263$	3.20873	0.197859	0.0989293	+	0.995094i	$0.468458\pi$
$264$	0	0
$265$	1.67088	0.102641
$266$	19.2014	1.17731
$267$	14.5062	0.887763
$268$	0.469045	0.0286515
$269$	−3.24423	−0.197804	−0.0989020	−	0.995097i	$-0.531533\pi$
$269$	−3.24423	−0.197804	−0.0989020	+	0.995097i	$0.531533\pi$
$270$	−1.82709	−0.111193
$271$	−2.02977	−0.123300	−0.0616499	−	0.998098i	$-0.519636\pi$
$271$	−2.02977	−0.123300	−0.0616499	+	0.998098i	$0.519636\pi$
$272$	−35.8147	−2.17159
$273$	9.36121	0.566566
$274$	7.71096	0.465836
$275$	0	0
$276$	−11.1848	−0.673246
$277$	11.3166	0.679947	0.339973	−	0.940435i	$-0.389582\pi$
$277$	11.3166	0.679947	0.339973	+	0.940435i	$0.389582\pi$
$278$	16.1669	0.969628
$279$	−0.0213642	−0.00127904
$280$	−2.11251	−0.126247
$281$	−10.3177	−0.615503	−0.307751	−	0.951467i	$-0.599576\pi$
$281$	−10.3177	−0.615503	−0.307751	+	0.951467i	$0.599576\pi$
$282$	−6.97864	−0.415572
$283$	−2.10589	−0.125182	−0.0625910	−	0.998039i	$-0.519936\pi$
$283$	−2.10589	−0.125182	−0.0625910	+	0.998039i	$0.519936\pi$
$284$	6.07327	0.360382
$285$	−6.01478	−0.356285
$286$	0	0
$287$	−6.39459	−0.377461
$288$	−6.50828	−0.383504
$289$	36.7392	2.16113
$290$	10.1188	0.594194
$291$	1.89972	0.111363
$292$	13.5693	0.794085
$293$	−23.3755	−1.36561	−0.682805	−	0.730601i	$-0.739240\pi$
$293$	−23.3755	−1.36561	−0.682805	+	0.730601i	$0.739240\pi$
$294$	7.21182	0.420602
$295$	5.66332	0.329731
$296$	1.35614	0.0788238
$297$	0	0
$298$	17.4552	1.01115
$299$	−44.7783	−2.58959
$300$	−1.33826	−0.0772645
$301$	−3.44118	−0.198347
$302$	−12.3357	−0.709843
$303$	−6.71011	−0.385486
$304$	−29.3857	−1.68539
$305$	9.27977	0.531358
$306$	13.3939	0.765676
$307$	−32.0518	−1.82929	−0.914646	−	0.404256i	$-0.867531\pi$
$307$	−32.0518	−1.82929	−0.914646	+	0.404256i	$0.867531\pi$
$308$	0	0
$309$	4.24678	0.241591
$310$	−0.0390343	−0.00221700
$311$	1.63433	0.0926743	0.0463371	−	0.998926i	$-0.485245\pi$
$311$	1.63433	0.0926743	0.0463371	+	0.998926i	$0.485245\pi$
$312$	−6.47778	−0.366732
$313$	30.4130	1.71904	0.859522	−	0.511099i	$-0.170761\pi$
$313$	30.4130	1.71904	0.859522	+	0.511099i	$0.170761\pi$
$314$	−23.1318	−1.30540
$315$	1.74724	0.0984457
$316$	3.43132	0.193027
$317$	−29.4340	−1.65318	−0.826590	−	0.562805i	$-0.809722\pi$
$317$	−29.4340	−1.65318	−0.826590	+	0.562805i	$0.809722\pi$
$318$	−3.05284	−0.171195
$319$	0	0
$320$	−2.12007	−0.118515
$321$	15.7230	0.877572
$322$	26.6809	1.48687
$323$	44.0926	2.45338
$324$	1.33826	0.0743478
$325$	−5.35772	−0.297193
$326$	−42.7645	−2.36850
$327$	−4.23895	−0.234415
$328$	4.42494	0.244327
$329$	6.67364	0.367929
$330$	0	0
$331$	−22.7902	−1.25266	−0.626332	−	0.779557i	$-0.715444\pi$
$331$	−22.7902	−1.25266	−0.626332	+	0.779557i	$0.715444\pi$
$332$	−21.5199	−1.18106
$333$	−1.12165	−0.0614659
$334$	5.57611	0.305111
$335$	0.350489	0.0191492
$336$	8.53627	0.465692
$337$	−14.4901	−0.789325	−0.394662	−	0.918826i	$-0.629138\pi$
$337$	−14.4901	−0.789325	−0.394662	+	0.918826i	$0.629138\pi$
$338$	28.6947	1.56078
$339$	7.19643	0.390856
$340$	9.81040	0.532043
$341$	0	0
$342$	10.9896	0.594247
$343$	−19.1273	−1.03278
$344$	2.38124	0.128388
$345$	−8.35772	−0.449964
$346$	29.2470	1.57233
$347$	4.38728	0.235522	0.117761	−	0.993042i	$-0.462428\pi$
$347$	4.38728	0.235522	0.117761	+	0.993042i	$0.462428\pi$
$348$	−7.41153	−0.397300
$349$	14.4061	0.771140	0.385570	−	0.922679i	$-0.374005\pi$
$349$	14.4061	0.771140	0.385570	+	0.922679i	$0.374005\pi$
$350$	3.19236	0.170639
$351$	5.35772	0.285974
$352$	0	0
$353$	−6.01065	−0.319914	−0.159957	−	0.987124i	$-0.551136\pi$
$353$	−6.01065	−0.319914	−0.159957	+	0.987124i	$0.551136\pi$
$354$	−10.3474	−0.549958
$355$	4.53818	0.240862
$356$	−19.4130	−1.02889
$357$	−12.8085	−0.677897
$358$	−35.2612	−1.86361
$359$	−2.45715	−0.129683	−0.0648417	−	0.997896i	$-0.520654\pi$
$359$	−2.45715	−0.129683	−0.0648417	+	0.997896i	$0.520654\pi$
$360$	−1.20906	−0.0637229
$361$	17.1776	0.904085
$362$	−22.2742	−1.17070
$363$	0	0
$364$	−12.5277	−0.656632
$365$	10.1395	0.530727
$366$	−16.9550	−0.886251
$367$	1.47990	0.0772500	0.0386250	−	0.999254i	$-0.487702\pi$
$367$	1.47990	0.0772500	0.0386250	+	0.999254i	$0.487702\pi$
$368$	−40.8323	−2.12853
$369$	−3.65983	−0.190523
$370$	−2.04935	−0.106541
$371$	2.91942	0.151569
$372$	0.0285909	0.00148237
$373$	−24.3331	−1.25992	−0.629961	−	0.776627i	$-0.716929\pi$
$373$	−24.3331	−1.25992	−0.629961	+	0.776627i	$0.716929\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−4.61803	−0.238157
$377$	−29.6720	−1.52819
$378$	−3.19236	−0.164197
$379$	15.9311	0.818328	0.409164	−	0.912461i	$-0.365820\pi$
$379$	15.9311	0.818328	0.409164	+	0.912461i	$0.365820\pi$
$380$	8.04935	0.412923
$381$	−12.6870	−0.649977
$382$	−24.5275	−1.25494
$383$	−3.91994	−0.200300	−0.100150	−	0.994972i	$-0.531932\pi$
$383$	−3.91994	−0.200300	−0.100150	+	0.994972i	$0.531932\pi$
$384$	−9.14301	−0.466577
$385$	0	0
$386$	13.8454	0.704710
$387$	−1.96950	−0.100115
$388$	−2.54232	−0.129067
$389$	−35.2910	−1.78933	−0.894663	−	0.446742i	$-0.852584\pi$
$389$	−35.2910	−1.78933	−0.894663	+	0.446742i	$0.852584\pi$
$390$	9.78903	0.495687
$391$	61.2679	3.09845
$392$	4.77234	0.241040
$393$	0.970102	0.0489352
$394$	−12.5908	−0.634316
$395$	2.56401	0.129009
$396$	0	0
$397$	23.2231	1.16553	0.582767	−	0.812639i	$-0.301970\pi$
$397$	23.2231	1.16553	0.582767	+	0.812639i	$0.301970\pi$
$398$	1.16824	0.0585585
$399$	−10.5093	−0.526121
$400$	−4.88558	−0.244279
$401$	5.69460	0.284375	0.142187	−	0.989840i	$-0.454586\pi$
$401$	5.69460	0.284375	0.142187	+	0.989840i	$0.454586\pi$
$402$	−0.640375	−0.0319390
$403$	0.114463	0.00570182
$404$	8.97989	0.446766
$405$	1.00000	0.0496904
$406$	17.6799	0.877438
$407$	0	0
$408$	8.86324	0.438796
$409$	25.4530	1.25857	0.629284	−	0.777176i	$-0.283348\pi$
$409$	25.4530	1.25857	0.629284	+	0.777176i	$0.283348\pi$
$410$	−6.68684	−0.330239
$411$	−4.22035	−0.208175
$412$	−5.68331	−0.279996
$413$	9.89517	0.486909
$414$	15.2703	0.750495
$415$	−16.0805	−0.789361
$416$	34.8695	1.70962
$417$	−8.84846	−0.433311
$418$	0	0
$419$	−13.4850	−0.658786	−0.329393	−	0.944193i	$-0.606844\pi$
$419$	−13.4850	−0.658786	−0.329393	+	0.944193i	$0.606844\pi$
$420$	−2.33826	−0.114095
$421$	2.94967	0.143758	0.0718791	−	0.997413i	$-0.477100\pi$
$421$	2.94967	0.143758	0.0718791	+	0.997413i	$0.477100\pi$
$422$	−6.98220	−0.339888
$423$	3.81953	0.185712
$424$	−2.02018	−0.0981088
$425$	7.33070	0.355591
$426$	−8.29167	−0.401733
$427$	16.2140	0.784649
$428$	−21.0415	−1.01708
$429$	0	0
$430$	−3.59845	−0.173533
$431$	11.5227	0.555031	0.277515	−	0.960721i	$-0.410489\pi$
$431$	11.5227	0.555031	0.277515	+	0.960721i	$0.410489\pi$
$432$	4.88558	0.235058
$433$	11.1638	0.536500	0.268250	−	0.963349i	$-0.413555\pi$
$433$	11.1638	0.536500	0.268250	+	0.963349i	$0.413555\pi$
$434$	−0.0682023	−0.00327382
$435$	−5.53818	−0.265535
$436$	5.67283	0.271679
$437$	50.2698	2.40473
$438$	−18.5258	−0.885198
$439$	0.993624	0.0474231	0.0237115	−	0.999719i	$-0.492452\pi$
$439$	0.993624	0.0474231	0.0237115	+	0.999719i	$0.492452\pi$
$440$	0	0
$441$	−3.94716	−0.187960
$442$	−71.7605	−3.41330
$443$	−10.9825	−0.521796	−0.260898	−	0.965366i	$-0.584019\pi$
$443$	−10.9825	−0.521796	−0.260898	+	0.965366i	$0.584019\pi$
$444$	1.50106	0.0712370
$445$	−14.5062	−0.687658
$446$	−48.8201	−2.31170
$447$	−9.55357	−0.451868
$448$	−3.70426	−0.175010
$449$	29.0203	1.36955	0.684776	−	0.728753i	$-0.259900\pi$
$449$	29.0203	1.36955	0.684776	+	0.728753i	$0.259900\pi$
$450$	1.82709	0.0861299
$451$	0	0
$452$	−9.63070	−0.452990
$453$	6.75158	0.317217
$454$	22.3587	1.04935
$455$	−9.36121	−0.438860
$456$	7.27222	0.340553
$457$	−3.55670	−0.166375	−0.0831877	−	0.996534i	$-0.526510\pi$
$457$	−3.55670	−0.166375	−0.0831877	+	0.996534i	$0.526510\pi$
$458$	−12.2171	−0.570867
$459$	−7.33070	−0.342168
$460$	11.1848	0.521494
$461$	25.1829	1.17288	0.586441	−	0.809992i	$-0.300528\pi$
$461$	25.1829	1.17288	0.586441	+	0.809992i	$0.300528\pi$
$462$	0	0
$463$	−17.8743	−0.830690	−0.415345	−	0.909664i	$-0.636339\pi$
$463$	−17.8743	−0.830690	−0.415345	+	0.909664i	$0.636339\pi$
$464$	−27.0572	−1.25610
$465$	0.0213642	0.000990741 0
$466$	−11.9079	−0.551624
$467$	−25.2252	−1.16728	−0.583642	−	0.812011i	$-0.698373\pi$
$467$	−25.2252	−1.16728	−0.583642	+	0.812011i	$0.698373\pi$
$468$	−7.17002	−0.331434
$469$	0.612387	0.0282774
$470$	6.97864	0.321900
$471$	12.6604	0.583362
$472$	−6.84727	−0.315171
$473$	0	0
$474$	−4.68468	−0.215175
$475$	6.01478	0.275977
$476$	17.1411	0.785661
$477$	1.67088	0.0765041
$478$	−19.8091	−0.906047
$479$	−5.23574	−0.239227	−0.119613	−	0.992821i	$-0.538166\pi$
$479$	−5.23574	−0.239227	−0.119613	+	0.992821i	$0.538166\pi$
$480$	6.50828	0.297061
$481$	6.00947	0.274008
$482$	49.6610	2.26199
$483$	−14.6029	−0.664456
$484$	0	0
$485$	−1.89972	−0.0862617
$486$	−1.82709	−0.0828785
$487$	9.04508	0.409872	0.204936	−	0.978775i	$-0.434301\pi$
$487$	9.04508	0.409872	0.204936	+	0.978775i	$0.434301\pi$
$488$	−11.2198	−0.507895
$489$	23.4058	1.05845
$490$	−7.21182	−0.325797
$491$	−34.8112	−1.57101	−0.785505	−	0.618856i	$-0.787597\pi$
$491$	−34.8112	−1.57101	−0.785505	+	0.618856i	$0.787597\pi$
$492$	4.89781	0.220810
$493$	40.5988	1.82848
$494$	−58.8789	−2.64909
$495$	0	0
$496$	0.104377	0.00468664
$497$	7.92928	0.355677
$498$	29.3805	1.31657
$499$	19.5992	0.877380	0.438690	−	0.898638i	$-0.355443\pi$
$499$	19.5992	0.877380	0.438690	+	0.898638i	$0.355443\pi$
$500$	1.33826	0.0598489
$501$	−3.05191	−0.136349
$502$	10.1302	0.452132
$503$	18.4160	0.821129	0.410564	−	0.911832i	$-0.365332\pi$
$503$	18.4160	0.821129	0.410564	+	0.911832i	$0.365332\pi$
$504$	−2.11251	−0.0940987
$505$	6.71011	0.298596
$506$	0	0
$507$	−15.7051	−0.697489
$508$	16.9786	0.753303
$509$	1.23838	0.0548901	0.0274451	−	0.999623i	$-0.491263\pi$
$509$	1.23838	0.0548901	0.0274451	+	0.999623i	$0.491263\pi$
$510$	−13.3939	−0.593090
$511$	17.7162	0.783717
$512$	19.9828	0.883126
$513$	−6.01478	−0.265559
$514$	−34.6123	−1.52668
$515$	−4.24678	−0.187136
$516$	2.63570	0.116030
$517$	0	0
$518$	−3.58071	−0.157327
$519$	−16.0074	−0.702648
$520$	6.47778	0.284070
$521$	33.1850	1.45386	0.726931	−	0.686711i	$-0.240946\pi$
$521$	33.1850	1.45386	0.726931	+	0.686711i	$0.240946\pi$
$522$	10.1188	0.442886
$523$	13.1508	0.575046	0.287523	−	0.957774i	$-0.407168\pi$
$523$	13.1508	0.575046	0.287523	+	0.957774i	$0.407168\pi$
$524$	−1.29825	−0.0567143
$525$	−1.74724	−0.0762557
$526$	5.86264	0.255623
$527$	−0.156615	−0.00682224
$528$	0	0
$529$	46.8514	2.03702
$530$	3.05284	0.132607
$531$	5.66332	0.245767
$532$	14.0641	0.609758
$533$	19.6083	0.849331
$534$	26.5041	1.14694
$535$	−15.7230	−0.679764
$536$	−0.423761	−0.0183037
$537$	19.2991	0.832818
$538$	−5.92750	−0.255553
$539$	0	0
$540$	−1.33826	−0.0575896
$541$	32.6519	1.40381	0.701907	−	0.712269i	$-0.252332\pi$
$541$	32.6519	1.40381	0.701907	+	0.712269i	$0.252332\pi$
$542$	−3.70858	−0.159297
$543$	12.1911	0.523168
$544$	−47.7103	−2.04556
$545$	4.23895	0.181577
$546$	17.1038	0.731974
$547$	27.7048	1.18457	0.592285	−	0.805728i	$-0.298226\pi$
$547$	27.7048	1.18457	0.592285	+	0.805728i	$0.298226\pi$
$548$	5.64793	0.241268
$549$	9.27977	0.396051
$550$	0	0
$551$	33.3110	1.41909
$552$	10.1050	0.430095
$553$	4.47994	0.190506
$554$	20.6764	0.878456
$555$	1.12165	0.0476113
$556$	11.8415	0.502193
$557$	−23.4252	−0.992558	−0.496279	−	0.868163i	$-0.665301\pi$
$557$	−23.4252	−0.992558	−0.496279	+	0.868163i	$0.665301\pi$
$558$	−0.0390343	−0.00165246
$559$	10.5520	0.446303
$560$	−8.53627	−0.360723
$561$	0	0
$562$	−18.8514	−0.795198
$563$	22.0856	0.930796	0.465398	−	0.885101i	$-0.345911\pi$
$563$	22.0856	0.930796	0.465398	+	0.885101i	$0.345911\pi$
$564$	−5.11153	−0.215234
$565$	−7.19643	−0.302756
$566$	−3.84765	−0.161729
$567$	1.74724	0.0733771
$568$	−5.48692	−0.230226
$569$	−13.7351	−0.575805	−0.287902	−	0.957660i	$-0.592958\pi$
$569$	−13.7351	−0.575805	−0.287902	+	0.957660i	$0.592958\pi$
$570$	−10.9896	−0.460302
$571$	−26.5201	−1.10983	−0.554915	−	0.831907i	$-0.687249\pi$
$571$	−26.5201	−1.10983	−0.554915	+	0.831907i	$0.687249\pi$
$572$	0	0
$573$	13.4244	0.560811
$574$	−11.6835	−0.487660
$575$	8.35772	0.348541
$576$	−2.12007	−0.0883361
$577$	5.68765	0.236780	0.118390	−	0.992967i	$-0.462227\pi$
$577$	5.68765	0.236780	0.118390	+	0.992967i	$0.462227\pi$
$578$	67.1259	2.79207
$579$	−7.57782	−0.314923
$580$	7.41153	0.307747
$581$	−28.0965	−1.16564
$582$	3.47096	0.143876
$583$	0	0
$584$	−12.2593	−0.507292
$585$	−5.35772	−0.221514
$586$	−42.7091	−1.76430
$587$	13.5460	0.559104	0.279552	−	0.960131i	$-0.409814\pi$
$587$	13.5460	0.559104	0.279552	+	0.960131i	$0.409814\pi$
$588$	5.28233	0.217840
$589$	−0.128501	−0.00529479
$590$	10.3474	0.425996
$591$	6.89118	0.283465
$592$	5.47990	0.225222
$593$	21.1786	0.869702	0.434851	−	0.900502i	$-0.356801\pi$
$593$	21.1786	0.869702	0.434851	+	0.900502i	$0.356801\pi$
$594$	0	0
$595$	12.8085	0.525097
$596$	12.7852	0.523701
$597$	−0.639398	−0.0261688
$598$	−81.8140	−3.34562
$599$	−33.8404	−1.38268	−0.691341	−	0.722528i	$-0.742980\pi$
$599$	−33.8404	−1.38268	−0.691341	+	0.722528i	$0.742980\pi$
$600$	1.20906	0.0493595
$601$	29.3177	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$601$	29.3177	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$602$	−6.28736	−0.256254
$603$	0.350489	0.0142730
$604$	−9.03538	−0.367644
$605$	0	0
$606$	−12.2600	−0.498028
$607$	7.17486	0.291219	0.145609	−	0.989342i	$-0.453486\pi$
$607$	7.17486	0.291219	0.145609	+	0.989342i	$0.453486\pi$
$608$	−39.1459	−1.58758
$609$	−9.67652	−0.392112
$610$	16.9550	0.686487
$611$	−20.4640	−0.827884
$612$	9.81040	0.396562
$613$	−27.5044	−1.11089	−0.555447	−	0.831552i	$-0.687453\pi$
$613$	−27.5044	−1.11089	−0.555447	+	0.831552i	$0.687453\pi$
$614$	−58.5615	−2.36335
$615$	3.65983	0.147579
$616$	0	0
$617$	24.0712	0.969068	0.484534	−	0.874772i	$-0.338989\pi$
$617$	24.0712	0.969068	0.484534	+	0.874772i	$0.338989\pi$
$618$	7.75926	0.312123
$619$	26.9729	1.08413	0.542067	−	0.840335i	$-0.317642\pi$
$619$	26.9729	1.08413	0.542067	+	0.840335i	$0.317642\pi$
$620$	−0.0285909	−0.00114824
$621$	−8.35772	−0.335384
$622$	2.98607	0.119730
$623$	−25.3457	−1.01546
$624$	−26.1755	−1.04786
$625$	1.00000	0.0400000
$626$	55.5673	2.22092
$627$	0	0
$628$	−16.9430	−0.676098
$629$	−8.22246	−0.327851
$630$	3.19236	0.127187
$631$	9.73627	0.387595	0.193797	−	0.981042i	$-0.437920\pi$
$631$	9.73627	0.387595	0.193797	+	0.981042i	$0.437920\pi$
$632$	−3.10004	−0.123313
$633$	3.82149	0.151890
$634$	−53.7786	−2.13582
$635$	12.6870	0.503470
$636$	−2.23607	−0.0886659
$637$	21.1478	0.837904
$638$	0	0
$639$	4.53818	0.179528
$640$	9.14301	0.361409
$641$	25.1165	0.992040	0.496020	−	0.868311i	$-0.334794\pi$
$641$	25.1165	0.992040	0.496020	+	0.868311i	$0.334794\pi$
$642$	28.7273	1.13378
$643$	−26.9257	−1.06185	−0.530924	−	0.847420i	$-0.678155\pi$
$643$	−26.9257	−1.06185	−0.530924	+	0.847420i	$0.678155\pi$
$644$	19.5425	0.770083
$645$	1.96950	0.0775489
$646$	80.5612	3.16964
$647$	−26.8011	−1.05366	−0.526829	−	0.849971i	$-0.676619\pi$
$647$	−26.8011	−1.05366	−0.526829	+	0.849971i	$0.676619\pi$
$648$	−1.20906	−0.0474962
$649$	0	0
$650$	−9.78903	−0.383957
$651$	0.0373284	0.00146301
$652$	−31.3230	−1.22670
$653$	28.7633	1.12559	0.562797	−	0.826595i	$-0.309725\pi$
$653$	28.7633	1.12559	0.562797	+	0.826595i	$0.309725\pi$
$654$	−7.74496	−0.302852
$655$	−0.970102	−0.0379050
$656$	17.8804	0.698112
$657$	10.1395	0.395580
$658$	12.1933	0.475346
$659$	36.5327	1.42311	0.711556	−	0.702629i	$-0.247991\pi$
$659$	36.5327	1.42311	0.711556	+	0.702629i	$0.247991\pi$
$660$	0	0
$661$	−35.7750	−1.39149	−0.695743	−	0.718291i	$-0.744925\pi$
$661$	−35.7750	−1.39149	−0.695743	+	0.718291i	$0.744925\pi$
$662$	−41.6398	−1.61838
$663$	39.2758	1.52535
$664$	19.4422	0.754505
$665$	10.5093	0.407532
$666$	−2.04935	−0.0794108
$667$	46.2865	1.79222
$668$	4.08425	0.158024
$669$	26.7201	1.03306
$670$	0.640375	0.0247398
$671$	0	0
$672$	11.3715	0.438666
$673$	−11.2915	−0.435254	−0.217627	−	0.976032i	$-0.569832\pi$
$673$	−11.2915	−0.435254	−0.217627	+	0.976032i	$0.569832\pi$
$674$	−26.4747	−1.01977
$675$	−1.00000	−0.0384900
$676$	21.0175	0.808367
$677$	−43.8574	−1.68558	−0.842788	−	0.538246i	$-0.819087\pi$
$677$	−43.8574	−1.68558	−0.842788	+	0.538246i	$0.819087\pi$
$678$	13.1485	0.504966
$679$	−3.31926	−0.127381
$680$	−8.86324	−0.339890
$681$	−12.2373	−0.468935
$682$	0	0
$683$	−18.5355	−0.709241	−0.354620	−	0.935010i	$-0.615390\pi$
$683$	−18.5355	−0.709241	−0.354620	+	0.935010i	$0.615390\pi$
$684$	8.04935	0.307775
$685$	4.22035	0.161251
$686$	−34.9473	−1.33429
$687$	6.68664	0.255111
$688$	9.62214	0.366841
$689$	−8.95208	−0.341047
$690$	−15.2703	−0.581331
$691$	−28.2055	−1.07299	−0.536494	−	0.843904i	$-0.680251\pi$
$691$	−28.2055	−1.07299	−0.536494	+	0.843904i	$0.680251\pi$
$692$	21.4221	0.814347
$693$	0	0
$694$	8.01596	0.304282
$695$	8.84846	0.335641
$696$	6.69598	0.253810
$697$	−26.8291	−1.01623
$698$	26.3212	0.996274
$699$	6.51742	0.246511
$700$	2.33826	0.0883780
$701$	0.315386	0.0119120	0.00595599	−	0.999982i	$-0.498104\pi$
$701$	0.315386	0.0119120	0.00595599	+	0.999982i	$0.498104\pi$
$702$	9.78903	0.369463
$703$	−6.74647	−0.254448
$704$	0	0
$705$	−3.81953	−0.143852
$706$	−10.9820	−0.413313
$707$	11.7242	0.440933
$708$	−7.57900	−0.284836
$709$	39.0246	1.46560	0.732800	−	0.680444i	$-0.238213\pi$
$709$	39.0246	1.46560	0.732800	+	0.680444i	$0.238213\pi$
$710$	8.29167	0.311181
$711$	2.56401	0.0961580
$712$	17.5388	0.657294
$713$	−0.178556	−0.00668697
$714$	−23.4023	−0.875808
$715$	0	0
$716$	−25.8272	−0.965209
$717$	10.8419	0.404897
$718$	−4.48943	−0.167544
$719$	28.4691	1.06172	0.530859	−	0.847460i	$-0.321869\pi$
$719$	28.4691	1.06172	0.530859	+	0.847460i	$0.321869\pi$
$720$	−4.88558	−0.182075
$721$	−7.42014	−0.276341
$722$	31.3851	1.16803
$723$	−27.1803	−1.01085
$724$	−16.3148	−0.606335
$725$	5.53818	0.205683
$726$	0	0
$727$	45.8400	1.70011	0.850057	−	0.526691i	$-0.176568\pi$
$727$	45.8400	1.70011	0.850057	+	0.526691i	$0.176568\pi$
$728$	11.3182	0.419482
$729$	1.00000	0.0370370
$730$	18.5258	0.685672
$731$	−14.4378	−0.534002
$732$	−12.4188	−0.459011
$733$	37.9681	1.40239	0.701193	−	0.712972i	$-0.252651\pi$
$733$	37.9681	1.40239	0.701193	+	0.712972i	$0.252651\pi$
$734$	2.70391	0.0998030
$735$	3.94716	0.145593
$736$	−54.3944	−2.00500
$737$	0	0
$738$	−6.68684	−0.246146
$739$	21.1226	0.777008	0.388504	−	0.921447i	$-0.372992\pi$
$739$	21.1226	0.777008	0.388504	+	0.921447i	$0.372992\pi$
$740$	−1.50106	−0.0551800
$741$	32.2255	1.18383
$742$	5.33404	0.195819
$743$	7.98035	0.292771	0.146385	−	0.989228i	$-0.453236\pi$
$743$	7.98035	0.292771	0.146385	+	0.989228i	$0.453236\pi$
$744$	−0.0258305	−0.000946993 0
$745$	9.55357	0.350016
$746$	−44.4588	−1.62775
$747$	−16.0805	−0.588355
$748$	0	0
$749$	−27.4718	−1.00380
$750$	−1.82709	−0.0667159
$751$	−9.62482	−0.351215	−0.175607	−	0.984460i	$-0.556189\pi$
$751$	−9.62482	−0.351215	−0.175607	+	0.984460i	$0.556189\pi$
$752$	−18.6606	−0.680483
$753$	−5.54443	−0.202050
$754$	−54.2134	−1.97434
$755$	−6.75158	−0.245715
$756$	−2.33826	−0.0850417
$757$	−46.6153	−1.69426	−0.847130	−	0.531385i	$-0.821672\pi$
$757$	−46.6153	−1.69426	−0.847130	+	0.531385i	$0.821672\pi$
$758$	29.1076	1.05724
$759$	0	0
$760$	−7.27222	−0.263791
$761$	−21.9943	−0.797293	−0.398646	−	0.917105i	$-0.630520\pi$
$761$	−21.9943	−0.797293	−0.398646	+	0.917105i	$0.630520\pi$
$762$	−23.1804	−0.839737
$763$	7.40646	0.268132
$764$	−17.9653	−0.649962
$765$	7.33070	0.265042
$766$	−7.16209	−0.258777
$767$	−30.3424	−1.09560
$768$	−20.9452	−0.755797
$769$	48.0330	1.73211	0.866057	−	0.499946i	$-0.166647\pi$
$769$	48.0330	1.73211	0.866057	+	0.499946i	$0.166647\pi$
$770$	0	0
$771$	18.9439	0.682249
$772$	10.1411	0.364986
$773$	−17.0851	−0.614509	−0.307255	−	0.951627i	$-0.599410\pi$
$773$	−17.0851	−0.614509	−0.307255	+	0.951627i	$0.599410\pi$
$774$	−3.59845	−0.129344
$775$	−0.0213642	−0.000767425 0
$776$	2.29687	0.0824527
$777$	1.95979	0.0703069
$778$	−64.4799	−2.31172
$779$	−22.0131	−0.788700
$780$	7.17002	0.256728
$781$	0	0
$782$	111.942	4.00304
$783$	−5.53818	−0.197918
$784$	19.2842	0.688720
$785$	−12.6604	−0.451870
$786$	1.77247	0.0632217
$787$	−22.4918	−0.801746	−0.400873	−	0.916134i	$-0.631293\pi$
$787$	−22.4918	−0.801746	−0.400873	+	0.916134i	$0.631293\pi$
$788$	−9.22220	−0.328527
$789$	−3.20873	−0.114234
$790$	4.68468	0.166674
$791$	−12.5739	−0.447076
$792$	0	0
$793$	−49.7184	−1.76555
$794$	42.4307	1.50581
$795$	−1.67088	−0.0592598
$796$	0.855682	0.0303288
$797$	−3.41778	−0.121064	−0.0605321	−	0.998166i	$-0.519280\pi$
$797$	−3.41778	−0.121064	−0.0605321	+	0.998166i	$0.519280\pi$
$798$	−19.2014	−0.679721
$799$	27.9999	0.990564
$800$	−6.50828	−0.230103
$801$	−14.5062	−0.512550
$802$	10.4046	0.367398
$803$	0	0
$804$	−0.469045	−0.0165420
$805$	14.6029	0.514685
$806$	0.209135	0.00736646
$807$	3.24423	0.114202
$808$	−8.11291	−0.285411
$809$	−10.1185	−0.355748	−0.177874	−	0.984053i	$-0.556922\pi$
$809$	−10.1185	−0.355748	−0.177874	+	0.984053i	$0.556922\pi$
$810$	1.82709	0.0641974
$811$	25.3749	0.891034	0.445517	−	0.895273i	$-0.353020\pi$
$811$	25.3749	0.891034	0.445517	+	0.895273i	$0.353020\pi$
$812$	12.9497	0.454446
$813$	2.02977	0.0711872
$814$	0	0
$815$	−23.4058	−0.819868
$816$	35.8147	1.25377
$817$	−11.8461	−0.414443
$818$	46.5049	1.62600
$819$	−9.36121	−0.327107
$820$	−4.89781	−0.171039
$821$	1.49915	0.0523206	0.0261603	−	0.999658i	$-0.491672\pi$
$821$	1.49915	0.0523206	0.0261603	+	0.999658i	$0.491672\pi$
$822$	−7.71096	−0.268951
$823$	−19.1246	−0.666641	−0.333320	−	0.942814i	$-0.608169\pi$
$823$	−19.1246	−0.666641	−0.333320	+	0.942814i	$0.608169\pi$
$824$	5.13460	0.178872
$825$	0	0
$826$	18.0794	0.629062
$827$	−16.6305	−0.578298	−0.289149	−	0.957284i	$-0.593372\pi$
$827$	−16.6305	−0.578298	−0.289149	+	0.957284i	$0.593372\pi$
$828$	11.1848	0.388699
$829$	25.6955	0.892442	0.446221	−	0.894923i	$-0.352769\pi$
$829$	25.6955	0.892442	0.446221	+	0.894923i	$0.352769\pi$
$830$	−29.3805	−1.01981
$831$	−11.3166	−0.392567
$832$	11.3587	0.393793
$833$	−28.9355	−1.00255
$834$	−16.1669	−0.559815
$835$	3.05191	0.105616
$836$	0	0
$837$	0.0213642	0.000738455 0
$838$	−24.6383	−0.851117
$839$	−28.3971	−0.980376	−0.490188	−	0.871617i	$-0.663072\pi$
$839$	−28.3971	−0.980376	−0.490188	+	0.871617i	$0.663072\pi$
$840$	2.11251	0.0728885
$841$	1.67145	0.0576363
$842$	5.38932	0.185728
$843$	10.3177	0.355361
$844$	−5.11415	−0.176036
$845$	15.7051	0.540272
$846$	6.97864	0.239930
$847$	0	0
$848$	−8.16320	−0.280325
$849$	2.10589	0.0722739
$850$	13.3939	0.459406
$851$	−9.37441	−0.321351
$852$	−6.07327	−0.208067
$853$	15.1072	0.517260	0.258630	−	0.965976i	$-0.416729\pi$
$853$	15.1072	0.517260	0.258630	+	0.965976i	$0.416729\pi$
$854$	29.6244	1.01373
$855$	6.01478	0.205701
$856$	19.0100	0.649748
$857$	2.37040	0.0809713	0.0404856	−	0.999180i	$-0.487109\pi$
$857$	2.37040	0.0809713	0.0404856	+	0.999180i	$0.487109\pi$
$858$	0	0
$859$	45.0423	1.53682	0.768411	−	0.639956i	$-0.221048\pi$
$859$	45.0423	1.53682	0.768411	+	0.639956i	$0.221048\pi$
$860$	−2.63570	−0.0898768
$861$	6.39459	0.217927
$862$	21.0531	0.717071
$863$	−25.0210	−0.851724	−0.425862	−	0.904788i	$-0.640029\pi$
$863$	−25.0210	−0.851724	−0.425862	+	0.904788i	$0.640029\pi$
$864$	6.50828	0.221416
$865$	16.0074	0.544269
$866$	20.3974	0.693130
$867$	−36.7392	−1.24773
$868$	−0.0499551	−0.00169559
$869$	0	0
$870$	−10.1188	−0.343058
$871$	−1.87782	−0.0636274
$872$	−5.12514	−0.173559
$873$	−1.89972	−0.0642957
$874$	91.8476	3.10679
$875$	1.74724	0.0590674
$876$	−13.5693	−0.458465
$877$	−48.8755	−1.65041	−0.825203	−	0.564836i	$-0.808940\pi$
$877$	−48.8755	−1.65041	−0.825203	+	0.564836i	$0.808940\pi$
$878$	1.81544	0.0612682
$879$	23.3755	0.788435
$880$	0	0
$881$	44.5530	1.50103	0.750515	−	0.660853i	$-0.229805\pi$
$881$	44.5530	1.50103	0.750515	+	0.660853i	$0.229805\pi$
$882$	−7.21182	−0.242835
$883$	−44.0547	−1.48256	−0.741279	−	0.671197i	$-0.765780\pi$
$883$	−44.0547	−1.48256	−0.741279	+	0.671197i	$0.765780\pi$
$884$	−52.5613	−1.76783
$885$	−5.66332	−0.190370
$886$	−20.0661	−0.674133
$887$	−12.1293	−0.407261	−0.203631	−	0.979048i	$-0.565274\pi$
$887$	−12.1293	−0.407261	−0.203631	+	0.979048i	$0.565274\pi$
$888$	−1.35614	−0.0455089
$889$	22.1673	0.743467
$890$	−26.5041	−0.888419
$891$	0	0
$892$	−35.7585	−1.19728
$893$	22.9737	0.768785
$894$	−17.4552	−0.583790
$895$	−19.2991	−0.645098
$896$	15.9750	0.533688
$897$	44.7783	1.49510
$898$	53.0227	1.76939
$899$	−0.118319	−0.00394615
$900$	1.33826	0.0446087
$901$	12.2487	0.408063
$902$	0	0
$903$	3.44118	0.114515
$904$	8.70089	0.289387
$905$	−12.1911	−0.405244
$906$	12.3357	0.409828
$907$	32.8672	1.09134	0.545670	−	0.838000i	$-0.316275\pi$
$907$	32.8672	1.09134	0.545670	+	0.838000i	$0.316275\pi$
$908$	16.3767	0.543481
$909$	6.71011	0.222560
$910$	−17.1038	−0.566985
$911$	−46.7054	−1.54742	−0.773710	−	0.633540i	$-0.781601\pi$
$911$	−46.7054	−1.54742	−0.773710	+	0.633540i	$0.781601\pi$
$912$	29.3857	0.973058
$913$	0	0
$914$	−6.49842	−0.214949
$915$	−9.27977	−0.306780
$916$	−8.94847	−0.295666
$917$	−1.69500	−0.0559738
$918$	−13.3939	−0.442063
$919$	7.33826	0.242067	0.121033	−	0.992648i	$-0.461379\pi$
$919$	7.33826	0.242067	0.121033	+	0.992648i	$0.461379\pi$
$920$	−10.1050	−0.333150
$921$	32.0518	1.05614
$922$	46.0114	1.51530
$923$	−24.3143	−0.800314
$924$	0	0
$925$	−1.12165	−0.0368795
$926$	−32.6580	−1.07321
$927$	−4.24678	−0.139483
$928$	−36.0441	−1.18320
$929$	12.7285	0.417609	0.208804	−	0.977957i	$-0.433043\pi$
$929$	12.7285	0.417609	0.208804	+	0.977957i	$0.433043\pi$
$930$	0.0390343	0.00127999
$931$	−23.7413	−0.778090
$932$	−8.72201	−0.285699
$933$	−1.63433	−0.0535055
$934$	−46.0888	−1.50807
$935$	0	0
$936$	6.47778	0.211733
$937$	19.2533	0.628979	0.314490	−	0.949261i	$-0.398167\pi$
$937$	19.2533	0.628979	0.314490	+	0.949261i	$0.398167\pi$
$938$	1.11889	0.0365330
$939$	−30.4130	−0.992490
$940$	5.11153	0.166720
$941$	−41.2694	−1.34535	−0.672673	−	0.739940i	$-0.734854\pi$
$941$	−41.2694	−1.34535	−0.672673	+	0.739940i	$0.734854\pi$
$942$	23.1318	0.753673
$943$	−30.5878	−0.996076
$944$	−27.6686	−0.900536
$945$	−1.74724	−0.0568377
$946$	0	0
$947$	−50.3012	−1.63457	−0.817285	−	0.576233i	$-0.804522\pi$
$947$	−50.3012	−1.63457	−0.817285	+	0.576233i	$0.804522\pi$
$948$	−3.43132	−0.111444
$949$	−54.3247	−1.76345
$950$	10.9896	0.356548
$951$	29.4340	0.954464
$952$	−15.4862	−0.501910
$953$	−9.02580	−0.292374	−0.146187	−	0.989257i	$-0.546700\pi$
$953$	−9.02580	−0.292374	−0.146187	+	0.989257i	$0.546700\pi$
$954$	3.05284	0.0988394
$955$	−13.4244	−0.434402
$956$	−14.5093	−0.469263
$957$	0	0
$958$	−9.56617	−0.309069
$959$	7.37396	0.238118
$960$	2.12007	0.0684249
$961$	−30.9995	−0.999985
$962$	10.9798	0.354004
$963$	−15.7230	−0.506666
$964$	36.3744	1.17154
$965$	7.57782	0.243939
$966$	−26.6809	−0.858443
$967$	−30.2503	−0.972785	−0.486392	−	0.873740i	$-0.661687\pi$
$967$	−30.2503	−0.972785	−0.486392	+	0.873740i	$0.661687\pi$
$968$	0	0
$969$	−44.0926	−1.41646
$970$	−3.47096	−0.111446
$971$	12.8285	0.411686	0.205843	−	0.978585i	$-0.434006\pi$
$971$	12.8285	0.411686	0.205843	+	0.978585i	$0.434006\pi$
$972$	−1.33826	−0.0429247
$973$	15.4604	0.495636
$974$	16.5262	0.529533
$975$	5.35772	0.171584
$976$	−45.3371	−1.45120
$977$	−13.1592	−0.420999	−0.210500	−	0.977594i	$-0.567509\pi$
$977$	−13.1592	−0.420999	−0.210500	+	0.977594i	$0.567509\pi$
$978$	42.7645	1.36746
$979$	0	0
$980$	−5.28233	−0.168738
$981$	4.23895	0.135339
$982$	−63.6033	−2.02966
$983$	22.4369	0.715627	0.357813	−	0.933793i	$-0.383522\pi$
$983$	22.4369	0.715627	0.357813	+	0.933793i	$0.383522\pi$
$984$	−4.42494	−0.141062
$985$	−6.89118	−0.219571
$986$	74.1776	2.36230
$987$	−6.67364	−0.212424
$988$	−43.1261	−1.37203
$989$	−16.4605	−0.523414
$990$	0	0
$991$	22.9146	0.727907	0.363953	−	0.931417i	$-0.381427\pi$
$991$	22.9146	0.727907	0.363953	+	0.931417i	$0.381427\pi$
$992$	0.139044	0.00441466
$993$	22.7902	0.723226
$994$	14.4875	0.459516
$995$	0.639398	0.0202703
$996$	21.5199	0.681884
$997$	−16.8394	−0.533309	−0.266654	−	0.963792i	$-0.585918\pi$
$997$	−16.8394	−0.533309	−0.266654	+	0.963792i	$0.585918\pi$
$998$	35.8095	1.13353
$999$	1.12165	0.0354874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.u.1.4		4
3.2	odd	2		5445.2.a.bj.1.1		4
5.4	even	2		9075.2.a.co.1.1		4
11.3	even	5		165.2.m.c.31.2	yes	8
11.4	even	5		165.2.m.c.16.2	✓	8
11.10	odd	2		1815.2.a.q.1.1		4
33.14	odd	10		495.2.n.c.361.1		8
33.26	odd	10		495.2.n.c.181.1		8
33.32	even	2		5445.2.a.bq.1.4		4
55.3	odd	20		825.2.bx.e.724.1		16
55.4	even	10		825.2.n.j.676.1		8
55.14	even	10		825.2.n.j.526.1		8
55.37	odd	20		825.2.bx.e.49.1		16
55.47	odd	20		825.2.bx.e.724.4		16
55.48	odd	20		825.2.bx.e.49.4		16
55.54	odd	2		9075.2.a.df.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.c.16.2	✓	8	11.4	even	5
165.2.m.c.31.2	yes	8	11.3	even	5
495.2.n.c.181.1		8	33.26	odd	10
495.2.n.c.361.1		8	33.14	odd	10
825.2.n.j.526.1		8	55.14	even	10
825.2.n.j.676.1		8	55.4	even	10
825.2.bx.e.49.1		16	55.37	odd	20
825.2.bx.e.49.4		16	55.48	odd	20
825.2.bx.e.724.1		16	55.3	odd	20
825.2.bx.e.724.4		16	55.47	odd	20
1815.2.a.q.1.1		4	11.10	odd	2
1815.2.a.u.1.4		4	1.1	even	1	trivial
5445.2.a.bj.1.1		4	3.2	odd	2
5445.2.a.bq.1.4		4	33.32	even	2
9075.2.a.co.1.1		4	5.4	even	2
9075.2.a.df.1.4		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)

\(f(q)\)	\(=\)	\(q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} +1.00000 q^{5} -1.82709 q^{6} +1.74724 q^{7} -1.20906 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.82709 q^{2} -1.00000 q^{3} +1.33826 q^{4} +1.00000 q^{5} -1.82709 q^{6} +1.74724 q^{7} -1.20906 q^{8} +1.00000 q^{9} +1.82709 q^{10} -1.33826 q^{12} -5.35772 q^{13} +3.19236 q^{14} -1.00000 q^{15} -4.88558 q^{16} +7.33070 q^{17} +1.82709 q^{18} +6.01478 q^{19} +1.33826 q^{20} -1.74724 q^{21} +8.35772 q^{23} +1.20906 q^{24} +1.00000 q^{25} -9.78903 q^{26} -1.00000 q^{27} +2.33826 q^{28} +5.53818 q^{29} -1.82709 q^{30} -0.0213642 q^{31} -6.50828 q^{32} +13.3939 q^{34} +1.74724 q^{35} +1.33826 q^{36} -1.12165 q^{37} +10.9896 q^{38} +5.35772 q^{39} -1.20906 q^{40} -3.65983 q^{41} -3.19236 q^{42} -1.96950 q^{43} +1.00000 q^{45} +15.2703 q^{46} +3.81953 q^{47} +4.88558 q^{48} -3.94716 q^{49} +1.82709 q^{50} -7.33070 q^{51} -7.17002 q^{52} +1.67088 q^{53} -1.82709 q^{54} -2.11251 q^{56} -6.01478 q^{57} +10.1188 q^{58} +5.66332 q^{59} -1.33826 q^{60} +9.27977 q^{61} -0.0390343 q^{62} +1.74724 q^{63} -2.12007 q^{64} -5.35772 q^{65} +0.350489 q^{67} +9.81040 q^{68} -8.35772 q^{69} +3.19236 q^{70} +4.53818 q^{71} -1.20906 q^{72} +10.1395 q^{73} -2.04935 q^{74} -1.00000 q^{75} +8.04935 q^{76} +9.78903 q^{78} +2.56401 q^{79} -4.88558 q^{80} +1.00000 q^{81} -6.68684 q^{82} -16.0805 q^{83} -2.33826 q^{84} +7.33070 q^{85} -3.59845 q^{86} -5.53818 q^{87} -14.5062 q^{89} +1.82709 q^{90} -9.36121 q^{91} +11.1848 q^{92} +0.0213642 q^{93} +6.97864 q^{94} +6.01478 q^{95} +6.50828 q^{96} -1.89972 q^{97} -7.21182 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 4 q^{3} + q^{4} + 4 q^{5} - q^{6} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 - 4 * q^3 + q^4 + 4 * q^5 - q^6 - 3 * q^8 + 4 * q^9	\( 4 q + q^{2} - 4 q^{3} + q^{4} + 4 q^{5} - q^{6} - 3 q^{8} + 4 q^{9} + q^{10} - q^{12} + 7 q^{13} - 5 q^{14} - 4 q^{15} - 9 q^{16} + 8 q^{17} + q^{18} + 11 q^{19} + q^{20} + 5 q^{23} + 3 q^{24} + 4 q^{25} - 12 q^{26} - 4 q^{27} + 5 q^{28} + 17 q^{29} - q^{30} - 5 q^{31} + 17 q^{34} + q^{36} + 15 q^{37} - q^{38} - 7 q^{39} - 3 q^{40} + 10 q^{41} + 5 q^{42} - 4 q^{43} + 4 q^{45} + 15 q^{46} - 8 q^{47} + 9 q^{48} - 8 q^{49} + q^{50} - 8 q^{51} - 7 q^{52} + 10 q^{53} - q^{54} + 10 q^{56} - 11 q^{57} - 7 q^{58} + 9 q^{59} - q^{60} + 37 q^{61} - 20 q^{62} - 7 q^{64} + 7 q^{65} + 3 q^{67} + 17 q^{68} - 5 q^{69} - 5 q^{70} + 13 q^{71} - 3 q^{72} + 15 q^{73} - 5 q^{74} - 4 q^{75} + 29 q^{76} + 12 q^{78} + 20 q^{79} - 9 q^{80} + 4 q^{81} + 5 q^{82} - 17 q^{83} - 5 q^{84} + 8 q^{85} + 34 q^{86} - 17 q^{87} - 24 q^{89} + q^{90} - 20 q^{91} + 10 q^{92} + 5 q^{93} + 23 q^{94} + 11 q^{95} - 32 q^{97} + 13 q^{98}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 + q^4 + 4 * q^5 - q^6 - 3 * q^8 + 4 * q^9 + q^10 - q^12 + 7 * q^13 - 5 * q^14 - 4 * q^15 - 9 * q^16 + 8 * q^17 + q^18 + 11 * q^19 + q^20 + 5 * q^23 + 3 * q^24 + 4 * q^25 - 12 * q^26 - 4 * q^27 + 5 * q^28 + 17 * q^29 - q^30 - 5 * q^31 + 17 * q^34 + q^36 + 15 * q^37 - q^38 - 7 * q^39 - 3 * q^40 + 10 * q^41 + 5 * q^42 - 4 * q^43 + 4 * q^45 + 15 * q^46 - 8 * q^47 + 9 * q^48 - 8 * q^49 + q^50 - 8 * q^51 - 7 * q^52 + 10 * q^53 - q^54 + 10 * q^56 - 11 * q^57 - 7 * q^58 + 9 * q^59 - q^60 + 37 * q^61 - 20 * q^62 - 7 * q^64 + 7 * q^65 + 3 * q^67 + 17 * q^68 - 5 * q^69 - 5 * q^70 + 13 * q^71 - 3 * q^72 + 15 * q^73 - 5 * q^74 - 4 * q^75 + 29 * q^76 + 12 * q^78 + 20 * q^79 - 9 * q^80 + 4 * q^81 + 5 * q^82 - 17 * q^83 - 5 * q^84 + 8 * q^85 + 34 * q^86 - 17 * q^87 - 24 * q^89 + q^90 - 20 * q^91 + 10 * q^92 + 5 * q^93 + 23 * q^94 + 11 * q^95 - 32 * q^97 + 13 * q^98

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