LMFDB - Embedded newform 465.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(1,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, 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("465.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.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:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	465.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} +1.00000 q^{5} +2.17009 q^{6} -1.17009 q^{7} +1.53919 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} +1.00000 q^{5} +2.17009 q^{6} -1.17009 q^{7} +1.53919 q^{8} +1.00000 q^{9} +2.17009 q^{10} +2.00000 q^{11} +2.70928 q^{12} +0.0917087 q^{13} -2.53919 q^{14} +1.00000 q^{15} -2.07838 q^{16} -6.04945 q^{17} +2.17009 q^{18} +2.70928 q^{20} -1.17009 q^{21} +4.34017 q^{22} -1.70928 q^{23} +1.53919 q^{24} +1.00000 q^{25} +0.199016 q^{26} +1.00000 q^{27} -3.17009 q^{28} +7.95774 q^{29} +2.17009 q^{30} +1.00000 q^{31} -7.58864 q^{32} +2.00000 q^{33} -13.1278 q^{34} -1.17009 q^{35} +2.70928 q^{36} -3.35350 q^{37} +0.0917087 q^{39} +1.53919 q^{40} -4.68035 q^{41} -2.53919 q^{42} -0.738205 q^{43} +5.41855 q^{44} +1.00000 q^{45} -3.70928 q^{46} -9.12783 q^{47} -2.07838 q^{48} -5.63090 q^{49} +2.17009 q^{50} -6.04945 q^{51} +0.248464 q^{52} +4.97107 q^{53} +2.17009 q^{54} +2.00000 q^{55} -1.80098 q^{56} +17.2690 q^{58} +11.0361 q^{59} +2.70928 q^{60} -3.26180 q^{61} +2.17009 q^{62} -1.17009 q^{63} -12.3112 q^{64} +0.0917087 q^{65} +4.34017 q^{66} +3.85043 q^{67} -16.3896 q^{68} -1.70928 q^{69} -2.53919 q^{70} -1.21953 q^{71} +1.53919 q^{72} +7.66701 q^{73} -7.27739 q^{74} +1.00000 q^{75} -2.34017 q^{77} +0.199016 q^{78} +3.52586 q^{79} -2.07838 q^{80} +1.00000 q^{81} -10.1568 q^{82} +12.5464 q^{83} -3.17009 q^{84} -6.04945 q^{85} -1.60197 q^{86} +7.95774 q^{87} +3.07838 q^{88} -5.77432 q^{89} +2.17009 q^{90} -0.107307 q^{91} -4.63090 q^{92} +1.00000 q^{93} -19.8082 q^{94} -7.58864 q^{96} -12.0000 q^{97} -12.2195 q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + q^{4} + 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + q^4 + 3 * q^5 + q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + q^{4} + 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} + 6 q^{11} + q^{12} - 2 q^{13} - 6 q^{14} + 3 q^{15} - 3 q^{16} + q^{18} + q^{20} + 2 q^{21} + 2 q^{22} + 2 q^{23} + 3 q^{24} + 3 q^{25} + 10 q^{26} + 3 q^{27} - 4 q^{28} + 8 q^{29} + q^{30} + 3 q^{31} - 3 q^{32} + 6 q^{33} - 18 q^{34} + 2 q^{35} + q^{36} - 2 q^{39} + 3 q^{40} + 8 q^{41} - 6 q^{42} - 10 q^{43} + 2 q^{44} + 3 q^{45} - 4 q^{46} - 6 q^{47} - 3 q^{48} - 13 q^{49} + q^{50} - 8 q^{52} + q^{54} + 6 q^{55} + 4 q^{56} + 10 q^{58} + 14 q^{59} + q^{60} - 2 q^{61} + q^{62} + 2 q^{63} - 11 q^{64} - 2 q^{65} + 2 q^{66} - 16 q^{67} - 20 q^{68} + 2 q^{69} - 6 q^{70} + 20 q^{71} + 3 q^{72} - 28 q^{74} + 3 q^{75} + 4 q^{77} + 10 q^{78} + 8 q^{79} - 3 q^{80} + 3 q^{81} - 24 q^{82} + 2 q^{83} - 4 q^{84} + 14 q^{86} + 8 q^{87} + 6 q^{88} - 6 q^{89} + q^{90} - 12 q^{91} - 10 q^{92} + 3 q^{93} - 16 q^{94} - 3 q^{96} - 36 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + q^4 + 3 * q^5 + q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9 + q^10 + 6 * q^11 + q^12 - 2 * q^13 - 6 * q^14 + 3 * q^15 - 3 * q^16 + q^18 + q^20 + 2 * q^21 + 2 * q^22 + 2 * q^23 + 3 * q^24 + 3 * q^25 + 10 * q^26 + 3 * q^27 - 4 * q^28 + 8 * q^29 + q^30 + 3 * q^31 - 3 * q^32 + 6 * q^33 - 18 * q^34 + 2 * q^35 + q^36 - 2 * q^39 + 3 * q^40 + 8 * q^41 - 6 * q^42 - 10 * q^43 + 2 * q^44 + 3 * q^45 - 4 * q^46 - 6 * q^47 - 3 * q^48 - 13 * q^49 + q^50 - 8 * q^52 + q^54 + 6 * q^55 + 4 * q^56 + 10 * q^58 + 14 * q^59 + q^60 - 2 * q^61 + q^62 + 2 * q^63 - 11 * q^64 - 2 * q^65 + 2 * q^66 - 16 * q^67 - 20 * q^68 + 2 * q^69 - 6 * q^70 + 20 * q^71 + 3 * q^72 - 28 * q^74 + 3 * q^75 + 4 * q^77 + 10 * q^78 + 8 * q^79 - 3 * q^80 + 3 * q^81 - 24 * q^82 + 2 * q^83 - 4 * q^84 + 14 * q^86 + 8 * q^87 + 6 * q^88 - 6 * q^89 + q^90 - 12 * q^91 - 10 * q^92 + 3 * q^93 - 16 * q^94 - 3 * q^96 - 36 * q^97 - 13 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.17009	1.53448	0.767241	−	0.641358i	$-0.221629\pi$
$2$	2.17009	1.53448	0.767241	+	0.641358i	$0.221629\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.70928	1.35464
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.17009	0.885934
$7$	−1.17009	−0.442251	−0.221126	−	0.975245i	$-0.570973\pi$
$7$	−1.17009	−0.442251	−0.221126	+	0.975245i	$0.570973\pi$
$8$	1.53919	0.544185
$9$	1.00000	0.333333
$10$	2.17009	0.686242
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	2.70928	0.782100
$13$	0.0917087	0.0254354	0.0127177	−	0.999919i	$-0.495952\pi$
$13$	0.0917087	0.0254354	0.0127177	+	0.999919i	$0.495952\pi$
$14$	−2.53919	−0.678627
$15$	1.00000	0.258199
$16$	−2.07838	−0.519594
$17$	−6.04945	−1.46721	−0.733603	−	0.679578i	$-0.762163\pi$
$17$	−6.04945	−1.46721	−0.733603	+	0.679578i	$0.762163\pi$
$18$	2.17009	0.511494
$19$	0	0		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	2.70928	0.605812
$21$	−1.17009	−0.255334
$22$	4.34017	0.925328
$23$	−1.70928	−0.356409	−0.178204	−	0.983994i	$-0.557029\pi$
$23$	−1.70928	−0.356409	−0.178204	+	0.983994i	$0.557029\pi$
$24$	1.53919	0.314186
$25$	1.00000	0.200000
$26$	0.199016	0.0390302
$27$	1.00000	0.192450
$28$	−3.17009	−0.599090
$29$	7.95774	1.47772	0.738858	−	0.673862i	$-0.235366\pi$
$29$	7.95774	1.47772	0.738858	+	0.673862i	$0.235366\pi$
$30$	2.17009	0.396202
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−7.58864	−1.34149
$33$	2.00000	0.348155
$34$	−13.1278	−2.25140
$35$	−1.17009	−0.197781
$36$	2.70928	0.451546
$37$	−3.35350	−0.551313	−0.275656	−	0.961256i	$-0.588895\pi$
$37$	−3.35350	−0.551313	−0.275656	+	0.961256i	$0.588895\pi$
$38$	0	0
$39$	0.0917087	0.0146852
$40$	1.53919	0.243367
$41$	−4.68035	−0.730947	−0.365474	−	0.930822i	$-0.619093\pi$
$41$	−4.68035	−0.730947	−0.365474	+	0.930822i	$0.619093\pi$
$42$	−2.53919	−0.391805
$43$	−0.738205	−0.112575	−0.0562876	−	0.998415i	$-0.517926\pi$
$43$	−0.738205	−0.112575	−0.0562876	+	0.998415i	$0.517926\pi$
$44$	5.41855	0.816877
$45$	1.00000	0.149071
$46$	−3.70928	−0.546903
$47$	−9.12783	−1.33143	−0.665715	−	0.746206i	$-0.731873\pi$
$47$	−9.12783	−1.33143	−0.665715	+	0.746206i	$0.731873\pi$
$48$	−2.07838	−0.299988
$49$	−5.63090	−0.804414
$50$	2.17009	0.306897
$51$	−6.04945	−0.847092
$52$	0.248464	0.0344558
$53$	4.97107	0.682829	0.341415	−	0.939913i	$-0.389094\pi$
$53$	4.97107	0.682829	0.341415	+	0.939913i	$0.389094\pi$
$54$	2.17009	0.295311
$55$	2.00000	0.269680
$56$	−1.80098	−0.240667
$57$	0	0
$58$	17.2690	2.26753
$59$	11.0361	1.43678	0.718390	−	0.695641i	$-0.244879\pi$
$59$	11.0361	1.43678	0.718390	+	0.695641i	$0.244879\pi$
$60$	2.70928	0.349766
$61$	−3.26180	−0.417630	−0.208815	−	0.977955i	$-0.566961\pi$
$61$	−3.26180	−0.417630	−0.208815	+	0.977955i	$0.566961\pi$
$62$	2.17009	0.275601
$63$	−1.17009	−0.147417
$64$	−12.3112	−1.53891
$65$	0.0917087	0.0113751
$66$	4.34017	0.534238
$67$	3.85043	0.470405	0.235203	−	0.971946i	$-0.424425\pi$
$67$	3.85043	0.470405	0.235203	+	0.971946i	$0.424425\pi$
$68$	−16.3896	−1.98753
$69$	−1.70928	−0.205773
$70$	−2.53919	−0.303491
$71$	−1.21953	−0.144732	−0.0723661	−	0.997378i	$-0.523055\pi$
$71$	−1.21953	−0.144732	−0.0723661	+	0.997378i	$0.523055\pi$
$72$	1.53919	0.181395
$73$	7.66701	0.897356	0.448678	−	0.893693i	$-0.351895\pi$
$73$	7.66701	0.897356	0.448678	+	0.893693i	$0.351895\pi$
$74$	−7.27739	−0.845980
$75$	1.00000	0.115470
$76$	0	0
$77$	−2.34017	−0.266687
$78$	0.199016	0.0225341
$79$	3.52586	0.396690	0.198345	−	0.980132i	$-0.436443\pi$
$79$	3.52586	0.396690	0.198345	+	0.980132i	$0.436443\pi$
$80$	−2.07838	−0.232370
$81$	1.00000	0.111111
$82$	−10.1568	−1.12163
$83$	12.5464	1.37714	0.688572	−	0.725168i	$-0.258238\pi$
$83$	12.5464	1.37714	0.688572	+	0.725168i	$0.258238\pi$
$84$	−3.17009	−0.345885
$85$	−6.04945	−0.656155
$86$	−1.60197	−0.172745
$87$	7.95774	0.853159
$88$	3.07838	0.328156
$89$	−5.77432	−0.612077	−0.306038	−	0.952019i	$-0.599004\pi$
$89$	−5.77432	−0.612077	−0.306038	+	0.952019i	$0.599004\pi$
$90$	2.17009	0.228747
$91$	−0.107307	−0.0112488
$92$	−4.63090	−0.482804
$93$	1.00000	0.103695
$94$	−19.8082	−2.04306
$95$	0	0
$96$	−7.58864	−0.774512
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−12.2195	−1.23436
$99$	2.00000	0.201008
$100$	2.70928	0.270928
$101$	13.9421	1.38729	0.693647	−	0.720315i	$-0.256003\pi$
$101$	13.9421	1.38729	0.693647	+	0.720315i	$0.256003\pi$
$102$	−13.1278	−1.29985
$103$	6.77205	0.667270	0.333635	−	0.942702i	$-0.391725\pi$
$103$	6.77205	0.667270	0.333635	+	0.942702i	$0.391725\pi$
$104$	0.141157	0.0138416
$105$	−1.17009	−0.114189
$106$	10.7877	1.04779
$107$	0.630898	0.0609912	0.0304956	−	0.999535i	$-0.490291\pi$
$107$	0.630898	0.0609912	0.0304956	+	0.999535i	$0.490291\pi$
$108$	2.70928	0.260700
$109$	−11.8660	−1.13656	−0.568280	−	0.822835i	$-0.692391\pi$
$109$	−11.8660	−1.13656	−0.568280	+	0.822835i	$0.692391\pi$
$110$	4.34017	0.413819
$111$	−3.35350	−0.318301
$112$	2.43188	0.229791
$113$	3.75872	0.353591	0.176795	−	0.984248i	$-0.443427\pi$
$113$	3.75872	0.353591	0.176795	+	0.984248i	$0.443427\pi$
$114$	0	0
$115$	−1.70928	−0.159391
$116$	21.5597	2.00177
$117$	0.0917087	0.00847848
$118$	23.9493	2.20471
$119$	7.07838	0.648874
$120$	1.53919	0.140508
$121$	−7.00000	−0.636364
$122$	−7.07838	−0.640846
$123$	−4.68035	−0.422013
$124$	2.70928	0.243300
$125$	1.00000	0.0894427
$126$	−2.53919	−0.226209
$127$	−4.18342	−0.371218	−0.185609	−	0.982624i	$-0.559426\pi$
$127$	−4.18342	−0.371218	−0.185609	+	0.982624i	$0.559426\pi$
$128$	−11.5392	−1.01993
$129$	−0.738205	−0.0649953
$130$	0.199016	0.0174548
$131$	−0.695944	−0.0608049	−0.0304025	−	0.999538i	$-0.509679\pi$
$131$	−0.695944	−0.0608049	−0.0304025	+	0.999538i	$0.509679\pi$
$132$	5.41855	0.471624
$133$	0	0
$134$	8.35577	0.721829
$135$	1.00000	0.0860663
$136$	−9.31124	−0.798433
$137$	8.20620	0.701103	0.350552	−	0.936543i	$-0.385994\pi$
$137$	8.20620	0.701103	0.350552	+	0.936543i	$0.385994\pi$
$138$	−3.70928	−0.315754
$139$	−4.49693	−0.381424	−0.190712	−	0.981646i	$-0.561080\pi$
$139$	−4.49693	−0.381424	−0.190712	+	0.981646i	$0.561080\pi$
$140$	−3.17009	−0.267921
$141$	−9.12783	−0.768702
$142$	−2.64650	−0.222089
$143$	0.183417	0.0153381
$144$	−2.07838	−0.173198
$145$	7.95774	0.660854
$146$	16.6381	1.37698
$147$	−5.63090	−0.464429
$148$	−9.08557	−0.746829
$149$	13.3607	1.09455	0.547275	−	0.836953i	$-0.315665\pi$
$149$	13.3607	1.09455	0.547275	+	0.836953i	$0.315665\pi$
$150$	2.17009	0.177187
$151$	13.8660	1.12840	0.564201	−	0.825638i	$-0.309184\pi$
$151$	13.8660	1.12840	0.564201	+	0.825638i	$0.309184\pi$
$152$	0	0
$153$	−6.04945	−0.489069
$154$	−5.07838	−0.409227
$155$	1.00000	0.0803219
$156$	0.248464	0.0198931
$157$	−20.0989	−1.60407	−0.802033	−	0.597279i	$-0.796248\pi$
$157$	−20.0989	−1.60407	−0.802033	+	0.597279i	$0.796248\pi$
$158$	7.65142	0.608714
$159$	4.97107	0.394232
$160$	−7.58864	−0.599934
$161$	2.00000	0.157622
$162$	2.17009	0.170498
$163$	4.06505	0.318399	0.159200	−	0.987246i	$-0.449109\pi$
$163$	4.06505	0.318399	0.159200	+	0.987246i	$0.449109\pi$
$164$	−12.6803	−0.990169
$165$	2.00000	0.155700
$166$	27.2267	2.11320
$167$	3.91548	0.302989	0.151494	−	0.988458i	$-0.451591\pi$
$167$	3.91548	0.302989	0.151494	+	0.988458i	$0.451591\pi$
$168$	−1.80098	−0.138949
$169$	−12.9916	−0.999353
$170$	−13.1278	−1.00686
$171$	0	0
$172$	−2.00000	−0.152499
$173$	16.0722	1.22195	0.610975	−	0.791650i	$-0.290778\pi$
$173$	16.0722	1.22195	0.610975	+	0.791650i	$0.290778\pi$
$174$	17.2690	1.30916
$175$	−1.17009	−0.0884502
$176$	−4.15676	−0.313327
$177$	11.0361	0.829525
$178$	−12.5308	−0.939222
$179$	21.9421	1.64003	0.820016	−	0.572340i	$-0.193964\pi$
$179$	21.9421	1.64003	0.820016	+	0.572340i	$0.193964\pi$
$180$	2.70928	0.201937
$181$	3.94214	0.293017	0.146509	−	0.989209i	$-0.453196\pi$
$181$	3.94214	0.293017	0.146509	+	0.989209i	$0.453196\pi$
$182$	−0.232866	−0.0172612
$183$	−3.26180	−0.241119
$184$	−2.63090	−0.193952
$185$	−3.35350	−0.246555
$186$	2.17009	0.159118
$187$	−12.0989	−0.884759
$188$	−24.7298	−1.80361
$189$	−1.17009	−0.0851113
$190$	0	0
$191$	23.3184	1.68726	0.843631	−	0.536923i	$-0.180413\pi$
$191$	23.3184	1.68726	0.843631	+	0.536923i	$0.180413\pi$
$192$	−12.3112	−0.888487
$193$	−10.2557	−0.738218	−0.369109	−	0.929386i	$-0.620337\pi$
$193$	−10.2557	−0.738218	−0.369109	+	0.929386i	$0.620337\pi$
$194$	−26.0410	−1.86964
$195$	0.0917087	0.00656740
$196$	−15.2557	−1.08969
$197$	23.9916	1.70933	0.854665	−	0.519180i	$-0.173763\pi$
$197$	23.9916	1.70933	0.854665	+	0.519180i	$0.173763\pi$
$198$	4.34017	0.308443
$199$	−16.1217	−1.14284	−0.571418	−	0.820659i	$-0.693606\pi$
$199$	−16.1217	−1.14284	−0.571418	+	0.820659i	$0.693606\pi$
$200$	1.53919	0.108837
$201$	3.85043	0.271589
$202$	30.2557	2.12878
$203$	−9.31124	−0.653521
$204$	−16.3896	−1.14750
$205$	−4.68035	−0.326890
$206$	14.6959	1.02391
$207$	−1.70928	−0.118803
$208$	−0.190605	−0.0132161
$209$	0	0
$210$	−2.53919	−0.175221
$211$	18.4391	1.26940	0.634699	−	0.772759i	$-0.281124\pi$
$211$	18.4391	1.26940	0.634699	+	0.772759i	$0.281124\pi$
$212$	13.4680	0.924986
$213$	−1.21953	−0.0835611
$214$	1.36910	0.0935899
$215$	−0.738205	−0.0503451
$216$	1.53919	0.104729
$217$	−1.17009	−0.0794306
$218$	−25.7503	−1.74403
$219$	7.66701	0.518089
$220$	5.41855	0.365319
$221$	−0.554787	−0.0373190
$222$	−7.27739	−0.488427
$223$	−15.2762	−1.02297	−0.511484	−	0.859293i	$-0.670904\pi$
$223$	−15.2762	−1.02297	−0.511484	+	0.859293i	$0.670904\pi$
$224$	8.87936	0.593277
$225$	1.00000	0.0666667
$226$	8.15676	0.542579
$227$	−19.7815	−1.31294	−0.656472	−	0.754350i	$-0.727952\pi$
$227$	−19.7815	−1.31294	−0.656472	+	0.754350i	$0.727952\pi$
$228$	0	0
$229$	25.4329	1.68066	0.840328	−	0.542079i	$-0.182363\pi$
$229$	25.4329	1.68066	0.840328	+	0.542079i	$0.182363\pi$
$230$	−3.70928	−0.244582
$231$	−2.34017	−0.153972
$232$	12.2485	0.804151
$233$	−16.2062	−1.06170	−0.530852	−	0.847465i	$-0.678128\pi$
$233$	−16.2062	−1.06170	−0.530852	+	0.847465i	$0.678128\pi$
$234$	0.199016	0.0130101
$235$	−9.12783	−0.595434
$236$	29.8999	1.94632
$237$	3.52586	0.229029
$238$	15.3607	0.995686
$239$	19.7587	1.27809	0.639043	−	0.769171i	$-0.279331\pi$
$239$	19.7587	1.27809	0.639043	+	0.769171i	$0.279331\pi$
$240$	−2.07838	−0.134159
$241$	−8.65368	−0.557433	−0.278716	−	0.960373i	$-0.589909\pi$
$241$	−8.65368	−0.557433	−0.278716	+	0.960373i	$0.589909\pi$
$242$	−15.1906	−0.976489
$243$	1.00000	0.0641500
$244$	−8.83710	−0.565737
$245$	−5.63090	−0.359745
$246$	−10.1568	−0.647571
$247$	0	0
$248$	1.53919	0.0977386
$249$	12.5464	0.795094
$250$	2.17009	0.137248
$251$	−18.9360	−1.19523	−0.597615	−	0.801783i	$-0.703885\pi$
$251$	−18.9360	−1.19523	−0.597615	+	0.801783i	$0.703885\pi$
$252$	−3.17009	−0.199697
$253$	−3.41855	−0.214922
$254$	−9.07838	−0.569628
$255$	−6.04945	−0.378831
$256$	−0.418551	−0.0261594
$257$	−13.1012	−0.817228	−0.408614	−	0.912707i	$-0.633988\pi$
$257$	−13.1012	−0.817228	−0.408614	+	0.912707i	$0.633988\pi$
$258$	−1.60197	−0.0997342
$259$	3.92389	0.243819
$260$	0.248464	0.0154091
$261$	7.95774	0.492572
$262$	−1.51026	−0.0933041
$263$	8.49693	0.523943	0.261972	−	0.965076i	$-0.415627\pi$
$263$	8.49693	0.523943	0.261972	+	0.965076i	$0.415627\pi$
$264$	3.07838	0.189461
$265$	4.97107	0.305370
$266$	0	0
$267$	−5.77432	−0.353383
$268$	10.4319	0.637229
$269$	21.8010	1.32923	0.664615	−	0.747186i	$-0.268596\pi$
$269$	21.8010	1.32923	0.664615	+	0.747186i	$0.268596\pi$
$270$	2.17009	0.132067
$271$	10.3402	0.628121	0.314060	−	0.949403i	$-0.398311\pi$
$271$	10.3402	0.628121	0.314060	+	0.949403i	$0.398311\pi$
$272$	12.5730	0.762352
$273$	−0.107307	−0.00649452
$274$	17.8082	1.07583
$275$	2.00000	0.120605
$276$	−4.63090	−0.278747
$277$	−0.646496	−0.0388442	−0.0194221	−	0.999811i	$-0.506183\pi$
$277$	−0.646496	−0.0388442	−0.0194221	+	0.999811i	$0.506183\pi$
$278$	−9.75872	−0.585289
$279$	1.00000	0.0598684
$280$	−1.80098	−0.107629
$281$	−17.3874	−1.03724	−0.518621	−	0.855004i	$-0.673555\pi$
$281$	−17.3874	−1.03724	−0.518621	+	0.855004i	$0.673555\pi$
$282$	−19.8082	−1.17956
$283$	2.92881	0.174100	0.0870498	−	0.996204i	$-0.472256\pi$
$283$	2.92881	0.174100	0.0870498	+	0.996204i	$0.472256\pi$
$284$	−3.30406	−0.196060
$285$	0	0
$286$	0.398032	0.0235361
$287$	5.47641	0.323262
$288$	−7.58864	−0.447165
$289$	19.5958	1.15270
$290$	17.2690	1.01407
$291$	−12.0000	−0.703452
$292$	20.7721	1.21559
$293$	−31.9916	−1.86897	−0.934484	−	0.356004i	$-0.884139\pi$
$293$	−31.9916	−1.86897	−0.934484	+	0.356004i	$0.884139\pi$
$294$	−12.2195	−0.712658
$295$	11.0361	0.642548
$296$	−5.16168	−0.300016
$297$	2.00000	0.116052
$298$	28.9939	1.67957
$299$	−0.156755	−0.00906540
$300$	2.70928	0.156420
$301$	0.863763	0.0497865
$302$	30.0905	1.73151
$303$	13.9421	0.800955
$304$	0	0
$305$	−3.26180	−0.186770
$306$	−13.1278	−0.750468
$307$	−5.66701	−0.323434	−0.161717	−	0.986837i	$-0.551703\pi$
$307$	−5.66701	−0.323434	−0.161717	+	0.986837i	$0.551703\pi$
$308$	−6.34017	−0.361265
$309$	6.77205	0.385249
$310$	2.17009	0.123253
$311$	−16.2401	−0.920889	−0.460444	−	0.887689i	$-0.652310\pi$
$311$	−16.2401	−0.920889	−0.460444	+	0.887689i	$0.652310\pi$
$312$	0.141157	0.00799145
$313$	7.42574	0.419728	0.209864	−	0.977731i	$-0.432698\pi$
$313$	7.42574	0.419728	0.209864	+	0.977731i	$0.432698\pi$
$314$	−43.6163	−2.46141
$315$	−1.17009	−0.0659269
$316$	9.55252	0.537371
$317$	−13.2534	−0.744384	−0.372192	−	0.928156i	$-0.621394\pi$
$317$	−13.2534	−0.744384	−0.372192	+	0.928156i	$0.621394\pi$
$318$	10.7877	0.604942
$319$	15.9155	0.891096
$320$	−12.3112	−0.688219
$321$	0.630898	0.0352133
$322$	4.34017	0.241868
$323$	0	0
$324$	2.70928	0.150515
$325$	0.0917087	0.00508709
$326$	8.82150	0.488578
$327$	−11.8660	−0.656193
$328$	−7.20394	−0.397771
$329$	10.6803	0.588827
$330$	4.34017	0.238919
$331$	3.62475	0.199235	0.0996173	−	0.995026i	$-0.468238\pi$
$331$	3.62475	0.199235	0.0996173	+	0.995026i	$0.468238\pi$
$332$	33.9916	1.86553
$333$	−3.35350	−0.183771
$334$	8.49693	0.464931
$335$	3.85043	0.210372
$336$	2.43188	0.132670
$337$	13.3268	0.725959	0.362980	−	0.931797i	$-0.381759\pi$
$337$	13.3268	0.725959	0.362980	+	0.931797i	$0.381759\pi$
$338$	−28.1929	−1.53349
$339$	3.75872	0.204146
$340$	−16.3896	−0.888852
$341$	2.00000	0.108306
$342$	0	0
$343$	14.7792	0.798004
$344$	−1.13624	−0.0612618
$345$	−1.70928	−0.0920243
$346$	34.8781	1.87506
$347$	16.2290	0.871218	0.435609	−	0.900136i	$-0.356533\pi$
$347$	16.2290	0.871218	0.435609	+	0.900136i	$0.356533\pi$
$348$	21.5597	1.15572
$349$	2.38962	0.127913	0.0639567	−	0.997953i	$-0.479628\pi$
$349$	2.38962	0.127913	0.0639567	+	0.997953i	$0.479628\pi$
$350$	−2.53919	−0.135725
$351$	0.0917087	0.00489505
$352$	−15.1773	−0.808951
$353$	−36.2062	−1.92706	−0.963531	−	0.267597i	$-0.913770\pi$
$353$	−36.2062	−1.92706	−0.963531	+	0.267597i	$0.913770\pi$
$354$	23.9493	1.27289
$355$	−1.21953	−0.0647262
$356$	−15.6442	−0.829142
$357$	7.07838	0.374627
$358$	47.6163	2.51660
$359$	0.382433	0.0201841	0.0100920	−	0.999949i	$-0.496788\pi$
$359$	0.382433	0.0201841	0.0100920	+	0.999949i	$0.496788\pi$
$360$	1.53919	0.0811224
$361$	−19.0000	−1.00000
$362$	8.55479	0.449630
$363$	−7.00000	−0.367405
$364$	−0.290725	−0.0152381
$365$	7.66701	0.401310
$366$	−7.07838	−0.369993
$367$	−7.63317	−0.398448	−0.199224	−	0.979954i	$-0.563842\pi$
$367$	−7.63317	−0.398448	−0.199224	+	0.979954i	$0.563842\pi$
$368$	3.55252	0.185188
$369$	−4.68035	−0.243649
$370$	−7.27739	−0.378334
$371$	−5.81658	−0.301982
$372$	2.70928	0.140469
$373$	−17.5486	−0.908634	−0.454317	−	0.890840i	$-0.650117\pi$
$373$	−17.5486	−0.908634	−0.454317	+	0.890840i	$0.650117\pi$
$374$	−26.2557	−1.35765
$375$	1.00000	0.0516398
$376$	−14.0494	−0.724545
$377$	0.729794	0.0375863
$378$	−2.53919	−0.130602
$379$	7.68649	0.394828	0.197414	−	0.980320i	$-0.436746\pi$
$379$	7.68649	0.394828	0.197414	+	0.980320i	$0.436746\pi$
$380$	0	0
$381$	−4.18342	−0.214323
$382$	50.6030	2.58908
$383$	−5.92389	−0.302697	−0.151348	−	0.988480i	$-0.548362\pi$
$383$	−5.92389	−0.302697	−0.151348	+	0.988480i	$0.548362\pi$
$384$	−11.5392	−0.588857
$385$	−2.34017	−0.119266
$386$	−22.2557	−1.13278
$387$	−0.738205	−0.0375251
$388$	−32.5113	−1.65051
$389$	−28.7636	−1.45837	−0.729187	−	0.684314i	$-0.760102\pi$
$389$	−28.7636	−1.45837	−0.729187	+	0.684314i	$0.760102\pi$
$390$	0.199016	0.0100776
$391$	10.3402	0.522925
$392$	−8.66701	−0.437750
$393$	−0.695944	−0.0351057
$394$	52.0638	2.62294
$395$	3.52586	0.177405
$396$	5.41855	0.272292
$397$	9.41855	0.472704	0.236352	−	0.971668i	$-0.424048\pi$
$397$	9.41855	0.472704	0.236352	+	0.971668i	$0.424048\pi$
$398$	−34.9854	−1.75366
$399$	0	0
$400$	−2.07838	−0.103919
$401$	13.9721	0.697734	0.348867	−	0.937172i	$-0.386566\pi$
$401$	13.9721	0.697734	0.348867	+	0.937172i	$0.386566\pi$
$402$	8.35577	0.416748
$403$	0.0917087	0.00456834
$404$	37.7731	1.87928
$405$	1.00000	0.0496904
$406$	−20.2062	−1.00282
$407$	−6.70701	−0.332454
$408$	−9.31124	−0.460975
$409$	4.73820	0.234289	0.117145	−	0.993115i	$-0.462626\pi$
$409$	4.73820	0.234289	0.117145	+	0.993115i	$0.462626\pi$
$410$	−10.1568	−0.501606
$411$	8.20620	0.404782
$412$	18.3474	0.903910
$413$	−12.9132	−0.635418
$414$	−3.70928	−0.182301
$415$	12.5464	0.615877
$416$	−0.695944	−0.0341215
$417$	−4.49693	−0.220216
$418$	0	0
$419$	30.3123	1.48085	0.740426	−	0.672138i	$-0.234624\pi$
$419$	30.3123	1.48085	0.740426	+	0.672138i	$0.234624\pi$
$420$	−3.17009	−0.154684
$421$	−33.9916	−1.65665	−0.828324	−	0.560249i	$-0.810706\pi$
$421$	−33.9916	−1.65665	−0.828324	+	0.560249i	$0.810706\pi$
$422$	40.0144	1.94787
$423$	−9.12783	−0.443810
$424$	7.65142	0.371586
$425$	−6.04945	−0.293441
$426$	−2.64650	−0.128223
$427$	3.81658	0.184697
$428$	1.70928	0.0826209
$429$	0.183417	0.00885548
$430$	−1.60197	−0.0772538
$431$	16.6381	0.801428	0.400714	−	0.916203i	$-0.368762\pi$
$431$	16.6381	0.801428	0.400714	+	0.916203i	$0.368762\pi$
$432$	−2.07838	−0.0999960
$433$	−32.8976	−1.58096	−0.790479	−	0.612489i	$-0.790168\pi$
$433$	−32.8976	−1.58096	−0.790479	+	0.612489i	$0.790168\pi$
$434$	−2.53919	−0.121885
$435$	7.95774	0.381544
$436$	−32.1483	−1.53963
$437$	0	0
$438$	16.6381	0.794998
$439$	−28.5113	−1.36077	−0.680385	−	0.732855i	$-0.738187\pi$
$439$	−28.5113	−1.36077	−0.680385	+	0.732855i	$0.738187\pi$
$440$	3.07838	0.146756
$441$	−5.63090	−0.268138
$442$	−1.20394	−0.0572654
$443$	−20.0494	−0.952578	−0.476289	−	0.879289i	$-0.658018\pi$
$443$	−20.0494	−0.952578	−0.476289	+	0.879289i	$0.658018\pi$
$444$	−9.08557	−0.431182
$445$	−5.77432	−0.273729
$446$	−33.1506	−1.56973
$447$	13.3607	0.631939
$448$	14.4052	0.680583
$449$	−31.7308	−1.49747	−0.748735	−	0.662869i	$-0.769339\pi$
$449$	−31.7308	−1.49747	−0.748735	+	0.662869i	$0.769339\pi$
$450$	2.17009	0.102299
$451$	−9.36069	−0.440778
$452$	10.1834	0.478988
$453$	13.8660	0.651483
$454$	−42.9276	−2.01469
$455$	−0.107307	−0.00503064
$456$	0	0
$457$	−38.7864	−1.81435	−0.907176	−	0.420751i	$-0.861767\pi$
$457$	−38.7864	−1.81435	−0.907176	+	0.420751i	$0.861767\pi$
$458$	55.1917	2.57894
$459$	−6.04945	−0.282364
$460$	−4.63090	−0.215917
$461$	−0.324575	−0.0151169	−0.00755847	−	0.999971i	$-0.502406\pi$
$461$	−0.324575	−0.0151169	−0.00755847	+	0.999971i	$0.502406\pi$
$462$	−5.07838	−0.236268
$463$	16.8371	0.782486	0.391243	−	0.920287i	$-0.372045\pi$
$463$	16.8371	0.782486	0.391243	+	0.920287i	$0.372045\pi$
$464$	−16.5392	−0.767813
$465$	1.00000	0.0463739
$466$	−35.1689	−1.62917
$467$	−31.0700	−1.43775	−0.718873	−	0.695141i	$-0.755342\pi$
$467$	−31.0700	−1.43775	−0.718873	+	0.695141i	$0.755342\pi$
$468$	0.248464	0.0114853
$469$	−4.50534	−0.208037
$470$	−19.8082	−0.913683
$471$	−20.0989	−0.926108
$472$	16.9867	0.781875
$473$	−1.47641	−0.0678854
$474$	7.65142	0.351441
$475$	0	0
$476$	19.1773	0.878989
$477$	4.97107	0.227610
$478$	42.8781	1.96120
$479$	−30.3123	−1.38500	−0.692502	−	0.721416i	$-0.743492\pi$
$479$	−30.3123	−1.38500	−0.692502	+	0.721416i	$0.743492\pi$
$480$	−7.58864	−0.346372
$481$	−0.307546	−0.0140229
$482$	−18.7792	−0.855371
$483$	2.00000	0.0910032
$484$	−18.9649	−0.862042
$485$	−12.0000	−0.544892
$486$	2.17009	0.0984371
$487$	5.92777	0.268613	0.134306	−	0.990940i	$-0.457119\pi$
$487$	5.92777	0.268613	0.134306	+	0.990940i	$0.457119\pi$
$488$	−5.02052	−0.227268
$489$	4.06505	0.183828
$490$	−12.2195	−0.552022
$491$	−11.1194	−0.501812	−0.250906	−	0.968011i	$-0.580729\pi$
$491$	−11.1194	−0.501812	−0.250906	+	0.968011i	$0.580729\pi$
$492$	−12.6803	−0.571674
$493$	−48.1399	−2.16811
$494$	0	0
$495$	2.00000	0.0898933
$496$	−2.07838	−0.0933219
$497$	1.42696	0.0640080
$498$	27.2267	1.22006
$499$	−0.482553	−0.0216020	−0.0108010	−	0.999942i	$-0.503438\pi$
$499$	−0.482553	−0.0216020	−0.0108010	+	0.999942i	$0.503438\pi$
$500$	2.70928	0.121162
$501$	3.91548	0.174931
$502$	−41.0928	−1.83406
$503$	28.1795	1.25646	0.628232	−	0.778026i	$-0.283779\pi$
$503$	28.1795	1.25646	0.628232	+	0.778026i	$0.283779\pi$
$504$	−1.80098	−0.0802222
$505$	13.9421	0.620417
$506$	−7.41855	−0.329795
$507$	−12.9916	−0.576977
$508$	−11.3340	−0.502866
$509$	−30.8359	−1.36678	−0.683388	−	0.730055i	$-0.739494\pi$
$509$	−30.8359	−1.36678	−0.683388	+	0.730055i	$0.739494\pi$
$510$	−13.1278	−0.581310
$511$	−8.97107	−0.396857
$512$	22.1701	0.979789
$513$	0	0
$514$	−28.4307	−1.25402
$515$	6.77205	0.298412
$516$	−2.00000	−0.0880451
$517$	−18.2557	−0.802883
$518$	8.51518	0.374136
$519$	16.0722	0.705493
$520$	0.141157	0.00619015
$521$	−29.0472	−1.27258	−0.636290	−	0.771450i	$-0.719532\pi$
$521$	−29.0472	−1.27258	−0.636290	+	0.771450i	$0.719532\pi$
$522$	17.2690	0.755843
$523$	16.5958	0.725685	0.362842	−	0.931851i	$-0.381806\pi$
$523$	16.5958	0.725685	0.362842	+	0.931851i	$0.381806\pi$
$524$	−1.88550	−0.0823687
$525$	−1.17009	−0.0510668
$526$	18.4391	0.803982
$527$	−6.04945	−0.263518
$528$	−4.15676	−0.180900
$529$	−20.0784	−0.872973
$530$	10.7877	0.468586
$531$	11.0361	0.478927
$532$	0	0
$533$	−0.429229	−0.0185920
$534$	−12.5308	−0.542260
$535$	0.630898	0.0272761
$536$	5.92654	0.255988
$537$	21.9421	0.946873
$538$	47.3100	2.03968
$539$	−11.2618	−0.485080
$540$	2.70928	0.116589
$541$	−11.6370	−0.500315	−0.250158	−	0.968205i	$-0.580482\pi$
$541$	−11.6370	−0.500315	−0.250158	+	0.968205i	$0.580482\pi$
$542$	22.4391	0.963841
$543$	3.94214	0.169173
$544$	45.9071	1.96825
$545$	−11.8660	−0.508285
$546$	−0.232866	−0.00996574
$547$	−12.9821	−0.555076	−0.277538	−	0.960715i	$-0.589518\pi$
$547$	−12.9821	−0.555076	−0.277538	+	0.960715i	$0.589518\pi$
$548$	22.2329	0.949741
$549$	−3.26180	−0.139210
$550$	4.34017	0.185066
$551$	0	0
$552$	−2.63090	−0.111978
$553$	−4.12556	−0.175437
$554$	−1.40295	−0.0596057
$555$	−3.35350	−0.142348
$556$	−12.1834	−0.516692
$557$	45.9337	1.94627	0.973137	−	0.230225i	$-0.0739464\pi$
$557$	45.9337	1.94627	0.973137	+	0.230225i	$0.0739464\pi$
$558$	2.17009	0.0918671
$559$	−0.0676998	−0.00286340
$560$	2.43188	0.102766
$561$	−12.0989	−0.510816
$562$	−37.7321	−1.59163
$563$	−20.2017	−0.851399	−0.425699	−	0.904865i	$-0.639972\pi$
$563$	−20.2017	−0.851399	−0.425699	+	0.904865i	$0.639972\pi$
$564$	−24.7298	−1.04131
$565$	3.75872	0.158131
$566$	6.35577	0.267153
$567$	−1.17009	−0.0491390
$568$	−1.87709	−0.0787611
$569$	21.1883	0.888261	0.444131	−	0.895962i	$-0.353513\pi$
$569$	21.1883	0.888261	0.444131	+	0.895962i	$0.353513\pi$
$570$	0	0
$571$	0.299135	0.0125184	0.00625921	−	0.999980i	$-0.498008\pi$
$571$	0.299135	0.0125184	0.00625921	+	0.999980i	$0.498008\pi$
$572$	0.496928	0.0207776
$573$	23.3184	0.974141
$574$	11.8843	0.496040
$575$	−1.70928	−0.0712817
$576$	−12.3112	−0.512968
$577$	19.7009	0.820158	0.410079	−	0.912050i	$-0.365501\pi$
$577$	19.7009	0.820158	0.410079	+	0.912050i	$0.365501\pi$
$578$	42.5246	1.76879
$579$	−10.2557	−0.426210
$580$	21.5597	0.895218
$581$	−14.6803	−0.609043
$582$	−26.0410	−1.07944
$583$	9.94214	0.411761
$584$	11.8010	0.488328
$585$	0.0917087	0.00379169
$586$	−69.4245	−2.86790
$587$	−13.6598	−0.563801	−0.281901	−	0.959444i	$-0.590965\pi$
$587$	−13.6598	−0.563801	−0.281901	+	0.959444i	$0.590965\pi$
$588$	−15.2557	−0.629132
$589$	0	0
$590$	23.9493	0.985978
$591$	23.9916	0.986882
$592$	6.96985	0.286459
$593$	36.4846	1.49824	0.749122	−	0.662432i	$-0.230476\pi$
$593$	36.4846	1.49824	0.749122	+	0.662432i	$0.230476\pi$
$594$	4.34017	0.178079
$595$	7.07838	0.290185
$596$	36.1978	1.48272
$597$	−16.1217	−0.659817
$598$	−0.340173	−0.0139107
$599$	37.1038	1.51602	0.758010	−	0.652242i	$-0.226172\pi$
$599$	37.1038	1.51602	0.758010	+	0.652242i	$0.226172\pi$
$600$	1.53919	0.0628371
$601$	−26.8638	−1.09580	−0.547898	−	0.836545i	$-0.684572\pi$
$601$	−26.8638	−1.09580	−0.547898	+	0.836545i	$0.684572\pi$
$602$	1.87444	0.0763965
$603$	3.85043	0.156802
$604$	37.5669	1.52858
$605$	−7.00000	−0.284590
$606$	30.2557	1.22905
$607$	6.88777	0.279566	0.139783	−	0.990182i	$-0.455359\pi$
$607$	6.88777	0.279566	0.139783	+	0.990182i	$0.455359\pi$
$608$	0	0
$609$	−9.31124	−0.377311
$610$	−7.07838	−0.286595
$611$	−0.837101	−0.0338655
$612$	−16.3896	−0.662511
$613$	28.4729	1.15001	0.575005	−	0.818150i	$-0.305000\pi$
$613$	28.4729	1.15001	0.575005	+	0.818150i	$0.305000\pi$
$614$	−12.2979	−0.496303
$615$	−4.68035	−0.188730
$616$	−3.60197	−0.145127
$617$	5.20394	0.209503	0.104751	−	0.994498i	$-0.466595\pi$
$617$	5.20394	0.209503	0.104751	+	0.994498i	$0.466595\pi$
$618$	14.6959	0.591158
$619$	14.0494	0.564695	0.282348	−	0.959312i	$-0.408887\pi$
$619$	14.0494	0.564695	0.282348	+	0.959312i	$0.408887\pi$
$620$	2.70928	0.108807
$621$	−1.70928	−0.0685909
$622$	−35.2423	−1.41309
$623$	6.75646	0.270692
$624$	−0.190605	−0.00763032
$625$	1.00000	0.0400000
$626$	16.1145	0.644065
$627$	0	0
$628$	−54.4534	−2.17293
$629$	20.2868	0.808890
$630$	−2.53919	−0.101164
$631$	−3.15061	−0.125424	−0.0627120	−	0.998032i	$-0.519975\pi$
$631$	−3.15061	−0.125424	−0.0627120	+	0.998032i	$0.519975\pi$
$632$	5.42696	0.215873
$633$	18.4391	0.732887
$634$	−28.7610	−1.14224
$635$	−4.18342	−0.166014
$636$	13.4680	0.534041
$637$	−0.516403	−0.0204606
$638$	34.5380	1.36737
$639$	−1.21953	−0.0482441
$640$	−11.5392	−0.456126
$641$	4.19448	0.165672	0.0828360	−	0.996563i	$-0.473602\pi$
$641$	4.19448	0.165672	0.0828360	+	0.996563i	$0.473602\pi$
$642$	1.36910	0.0540342
$643$	−38.0722	−1.50142	−0.750711	−	0.660631i	$-0.770289\pi$
$643$	−38.0722	−1.50142	−0.750711	+	0.660631i	$0.770289\pi$
$644$	5.41855	0.213521
$645$	−0.738205	−0.0290668
$646$	0	0
$647$	−5.20847	−0.204766	−0.102383	−	0.994745i	$-0.532647\pi$
$647$	−5.20847	−0.204766	−0.102383	+	0.994745i	$0.532647\pi$
$648$	1.53919	0.0604650
$649$	22.0722	0.866411
$650$	0.199016	0.00780605
$651$	−1.17009	−0.0458593
$652$	11.0133	0.431315
$653$	25.6658	1.00438	0.502190	−	0.864757i	$-0.332528\pi$
$653$	25.6658	1.00438	0.502190	+	0.864757i	$0.332528\pi$
$654$	−25.7503	−1.00692
$655$	−0.695944	−0.0271928
$656$	9.72753	0.379796
$657$	7.66701	0.299119
$658$	23.1773	0.903544
$659$	−11.9721	−0.466367	−0.233184	−	0.972433i	$-0.574914\pi$
$659$	−11.9721	−0.466367	−0.233184	+	0.972433i	$0.574914\pi$
$660$	5.41855	0.210917
$661$	36.9504	1.43720	0.718601	−	0.695422i	$-0.244783\pi$
$661$	36.9504	1.43720	0.718601	+	0.695422i	$0.244783\pi$
$662$	7.86603	0.305722
$663$	−0.554787	−0.0215462
$664$	19.3112	0.749422
$665$	0	0
$666$	−7.27739	−0.281993
$667$	−13.6020	−0.526670
$668$	10.6081	0.410440
$669$	−15.2762	−0.590611
$670$	8.35577	0.322812
$671$	−6.52359	−0.251840
$672$	8.87936	0.342529
$673$	−20.8853	−0.805070	−0.402535	−	0.915405i	$-0.631871\pi$
$673$	−20.8853	−0.805070	−0.402535	+	0.915405i	$0.631871\pi$
$674$	28.9204	1.11397
$675$	1.00000	0.0384900
$676$	−35.1978	−1.35376
$677$	−31.1110	−1.19569	−0.597847	−	0.801611i	$-0.703977\pi$
$677$	−31.1110	−1.19569	−0.597847	+	0.801611i	$0.703977\pi$
$678$	8.15676	0.313258
$679$	14.0410	0.538846
$680$	−9.31124	−0.357070
$681$	−19.7815	−0.758029
$682$	4.34017	0.166194
$683$	27.1545	1.03904	0.519519	−	0.854459i	$-0.326111\pi$
$683$	27.1545	1.03904	0.519519	+	0.854459i	$0.326111\pi$
$684$	0	0
$685$	8.20620	0.313543
$686$	32.0722	1.22452
$687$	25.4329	0.970327
$688$	1.53427	0.0584934
$689$	0.455891	0.0173680
$690$	−3.70928	−0.141210
$691$	42.3234	1.61006	0.805028	−	0.593237i	$-0.202150\pi$
$691$	42.3234	1.61006	0.805028	+	0.593237i	$0.202150\pi$
$692$	43.5441	1.65530
$693$	−2.34017	−0.0888958
$694$	35.2183	1.33687
$695$	−4.49693	−0.170578
$696$	12.2485	0.464277
$697$	28.3135	1.07245
$698$	5.18568	0.196281
$699$	−16.2062	−0.612975
$700$	−3.17009	−0.119818
$701$	−8.69472	−0.328395	−0.164198	−	0.986427i	$-0.552503\pi$
$701$	−8.69472	−0.328395	−0.164198	+	0.986427i	$0.552503\pi$
$702$	0.199016	0.00751137
$703$	0	0
$704$	−24.6225	−0.927995
$705$	−9.12783	−0.343774
$706$	−78.5706	−2.95704
$707$	−16.3135	−0.613533
$708$	29.8999	1.12371
$709$	−31.3074	−1.17577	−0.587886	−	0.808943i	$-0.700040\pi$
$709$	−31.3074	−1.17577	−0.587886	+	0.808943i	$0.700040\pi$
$710$	−2.64650	−0.0993212
$711$	3.52586	0.132230
$712$	−8.88777	−0.333083
$713$	−1.70928	−0.0640129
$714$	15.3607	0.574859
$715$	0.183417	0.00685942
$716$	59.4473	2.22165
$717$	19.7587	0.737903
$718$	0.829914	0.0309721
$719$	20.5236	0.765401	0.382700	−	0.923873i	$-0.374994\pi$
$719$	20.5236	0.765401	0.382700	+	0.923873i	$0.374994\pi$
$720$	−2.07838	−0.0774566
$721$	−7.92389	−0.295101
$722$	−41.2316	−1.53448
$723$	−8.65368	−0.321834
$724$	10.6803	0.396932
$725$	7.95774	0.295543
$726$	−15.1906	−0.563776
$727$	31.7971	1.17929	0.589645	−	0.807663i	$-0.299268\pi$
$727$	31.7971	1.17929	0.589645	+	0.807663i	$0.299268\pi$
$728$	−0.165166	−0.00612146
$729$	1.00000	0.0370370
$730$	16.6381	0.615803
$731$	4.46573	0.165171
$732$	−8.83710	−0.326629
$733$	10.1978	0.376664	0.188332	−	0.982105i	$-0.439692\pi$
$733$	10.1978	0.376664	0.188332	+	0.982105i	$0.439692\pi$
$734$	−16.5646	−0.611412
$735$	−5.63090	−0.207699
$736$	12.9711	0.478120
$737$	7.70086	0.283665
$738$	−10.1568	−0.373875
$739$	41.3835	1.52232	0.761158	−	0.648567i	$-0.224631\pi$
$739$	41.3835	1.52232	0.761158	+	0.648567i	$0.224631\pi$
$740$	−9.08557	−0.333992
$741$	0	0
$742$	−12.6225	−0.463386
$743$	−23.8987	−0.876757	−0.438378	−	0.898791i	$-0.644447\pi$
$743$	−23.8987	−0.876757	−0.438378	+	0.898791i	$0.644447\pi$
$744$	1.53919	0.0564294
$745$	13.3607	0.489498
$746$	−38.0821	−1.39428
$747$	12.5464	0.459048
$748$	−32.7792	−1.19853
$749$	−0.738205	−0.0269734
$750$	2.17009	0.0792404
$751$	51.6475	1.88465	0.942323	−	0.334706i	$-0.108637\pi$
$751$	51.6475	1.88465	0.942323	+	0.334706i	$0.108637\pi$
$752$	18.9711	0.691804
$753$	−18.9360	−0.690066
$754$	1.58372	0.0576756
$755$	13.8660	0.504637
$756$	−3.17009	−0.115295
$757$	−0.687534	−0.0249888	−0.0124944	−	0.999922i	$-0.503977\pi$
$757$	−0.687534	−0.0249888	−0.0124944	+	0.999922i	$0.503977\pi$
$758$	16.6803	0.605857
$759$	−3.41855	−0.124086
$760$	0	0
$761$	−32.1555	−1.16564	−0.582819	−	0.812602i	$-0.698050\pi$
$761$	−32.1555	−1.16564	−0.582819	+	0.812602i	$0.698050\pi$
$762$	−9.07838	−0.328875
$763$	13.8843	0.502645
$764$	63.1761	2.28563
$765$	−6.04945	−0.218718
$766$	−12.8554	−0.464483
$767$	1.01211	0.0365451
$768$	−0.418551	−0.0151031
$769$	−34.2206	−1.23403	−0.617013	−	0.786953i	$-0.711657\pi$
$769$	−34.2206	−1.23403	−0.617013	+	0.786953i	$0.711657\pi$
$770$	−5.07838	−0.183012
$771$	−13.1012	−0.471827
$772$	−27.7854	−1.00002
$773$	9.20781	0.331182	0.165591	−	0.986195i	$-0.447047\pi$
$773$	9.20781	0.331182	0.165591	+	0.986195i	$0.447047\pi$
$774$	−1.60197	−0.0575816
$775$	1.00000	0.0359211
$776$	−18.4703	−0.663044
$777$	3.92389	0.140769
$778$	−62.4196	−2.23785
$779$	0	0
$780$	0.248464	0.00889645
$781$	−2.43907	−0.0872768
$782$	22.4391	0.802419
$783$	7.95774	0.284386
$784$	11.7031	0.417969
$785$	−20.0989	−0.717360
$786$	−1.51026	−0.0538692
$787$	−35.4908	−1.26511	−0.632555	−	0.774515i	$-0.717994\pi$
$787$	−35.4908	−1.26511	−0.632555	+	0.774515i	$0.717994\pi$
$788$	64.9998	2.31552
$789$	8.49693	0.302499
$790$	7.65142	0.272225
$791$	−4.39803	−0.156376
$792$	3.07838	0.109385
$793$	−0.299135	−0.0106226
$794$	20.4391	0.725355
$795$	4.97107	0.176306
$796$	−43.6781	−1.54813
$797$	6.89884	0.244369	0.122185	−	0.992507i	$-0.461010\pi$
$797$	6.89884	0.244369	0.122185	+	0.992507i	$0.461010\pi$
$798$	0	0
$799$	55.2183	1.95348
$800$	−7.58864	−0.268299
$801$	−5.77432	−0.204026
$802$	30.3207	1.07066
$803$	15.3340	0.541126
$804$	10.4319	0.367904
$805$	2.00000	0.0704907
$806$	0.199016	0.00701004
$807$	21.8010	0.767431
$808$	21.4596	0.754946
$809$	56.2278	1.97686	0.988432	−	0.151668i	$-0.0484644\pi$
$809$	56.2278	1.97686	0.988432	+	0.151668i	$0.0484644\pi$
$810$	2.17009	0.0762491
$811$	34.7070	1.21873	0.609364	−	0.792891i	$-0.291425\pi$
$811$	34.7070	1.21873	0.609364	+	0.792891i	$0.291425\pi$
$812$	−25.2267	−0.885284
$813$	10.3402	0.362646
$814$	−14.5548	−0.510145
$815$	4.06505	0.142392
$816$	12.5730	0.440144
$817$	0	0
$818$	10.2823	0.359513
$819$	−0.107307	−0.00374962
$820$	−12.6803	−0.442817
$821$	31.2651	1.09116	0.545580	−	0.838059i	$-0.316309\pi$
$821$	31.2651	1.09116	0.545580	+	0.838059i	$0.316309\pi$
$822$	17.8082	0.621131
$823$	−44.5523	−1.55300	−0.776499	−	0.630119i	$-0.783006\pi$
$823$	−44.5523	−1.55300	−0.776499	+	0.630119i	$0.783006\pi$
$824$	10.4235	0.363119
$825$	2.00000	0.0696311
$826$	−28.0228	−0.975037
$827$	−2.97107	−0.103314	−0.0516571	−	0.998665i	$-0.516450\pi$
$827$	−2.97107	−0.103314	−0.0516571	+	0.998665i	$0.516450\pi$
$828$	−4.63090	−0.160935
$829$	−30.2823	−1.05175	−0.525874	−	0.850562i	$-0.676262\pi$
$829$	−30.2823	−1.05175	−0.525874	+	0.850562i	$0.676262\pi$
$830$	27.2267	0.945053
$831$	−0.646496	−0.0224267
$832$	−1.12905	−0.0391427
$833$	34.0638	1.18024
$834$	−9.75872	−0.337917
$835$	3.91548	0.135501
$836$	0	0
$837$	1.00000	0.0345651
$838$	65.7803	2.27234
$839$	−47.8687	−1.65261	−0.826305	−	0.563223i	$-0.809561\pi$
$839$	−47.8687	−1.65261	−0.826305	+	0.563223i	$0.809561\pi$
$840$	−1.80098	−0.0621399
$841$	34.3256	1.18364
$842$	−73.7647	−2.54210
$843$	−17.3874	−0.598852
$844$	49.9565	1.71957
$845$	−12.9916	−0.446924
$846$	−19.8082	−0.681019
$847$	8.19061	0.281433
$848$	−10.3318	−0.354794
$849$	2.92881	0.100517
$850$	−13.1278	−0.450281
$851$	5.73206	0.196493
$852$	−3.30406	−0.113195
$853$	−47.8531	−1.63846	−0.819229	−	0.573466i	$-0.805598\pi$
$853$	−47.8531	−1.63846	−0.819229	+	0.573466i	$0.805598\pi$
$854$	8.28231	0.283415
$855$	0	0
$856$	0.971071	0.0331905
$857$	3.13170	0.106977	0.0534884	−	0.998568i	$-0.482966\pi$
$857$	3.13170	0.106977	0.0534884	+	0.998568i	$0.482966\pi$
$858$	0.398032	0.0135886
$859$	−18.4703	−0.630197	−0.315099	−	0.949059i	$-0.602038\pi$
$859$	−18.4703	−0.630197	−0.315099	+	0.949059i	$0.602038\pi$
$860$	−2.00000	−0.0681994
$861$	5.47641	0.186636
$862$	36.1061	1.22978
$863$	−47.9130	−1.63098	−0.815489	−	0.578772i	$-0.803532\pi$
$863$	−47.9130	−1.63098	−0.815489	+	0.578772i	$0.803532\pi$
$864$	−7.58864	−0.258171
$865$	16.0722	0.546472
$866$	−71.3907	−2.42595
$867$	19.5958	0.665509
$868$	−3.17009	−0.107600
$869$	7.05172	0.239213
$870$	17.2690	0.585473
$871$	0.353118	0.0119650
$872$	−18.2641	−0.618499
$873$	−12.0000	−0.406138
$874$	0	0
$875$	−1.17009	−0.0395561
$876$	20.7721	0.701823
$877$	44.8104	1.51314	0.756571	−	0.653912i	$-0.226873\pi$
$877$	44.8104	1.51314	0.756571	+	0.653912i	$0.226873\pi$
$878$	−61.8720	−2.08808
$879$	−31.9916	−1.07905
$880$	−4.15676	−0.140124
$881$	−24.4501	−0.823746	−0.411873	−	0.911241i	$-0.635125\pi$
$881$	−24.4501	−0.823746	−0.411873	+	0.911241i	$0.635125\pi$
$882$	−12.2195	−0.411453
$883$	39.8043	1.33952	0.669761	−	0.742577i	$-0.266397\pi$
$883$	39.8043	1.33952	0.669761	+	0.742577i	$0.266397\pi$
$884$	−1.50307	−0.0505538
$885$	11.0361	0.370975
$886$	−43.5090	−1.46171
$887$	16.9588	0.569420	0.284710	−	0.958614i	$-0.408103\pi$
$887$	16.9588	0.569420	0.284710	+	0.958614i	$0.408103\pi$
$888$	−5.16168	−0.173215
$889$	4.89496	0.164172
$890$	−12.5308	−0.420033
$891$	2.00000	0.0670025
$892$	−41.3874	−1.38575
$893$	0	0
$894$	28.9939	0.969700
$895$	21.9421	0.733445
$896$	13.5018	0.451065
$897$	−0.156755	−0.00523391
$898$	−68.8587	−2.29784
$899$	7.95774	0.265405
$900$	2.70928	0.0903092
$901$	−30.0722	−1.00185
$902$	−20.3135	−0.676366
$903$	0.863763	0.0287442
$904$	5.78539	0.192419
$905$	3.94214	0.131041
$906$	30.0905	0.999689
$907$	−3.72487	−0.123682	−0.0618412	−	0.998086i	$-0.519697\pi$
$907$	−3.72487	−0.123682	−0.0618412	+	0.998086i	$0.519697\pi$
$908$	−53.5936	−1.77856
$909$	13.9421	0.462432
$910$	−0.232866	−0.00771943
$911$	−56.5523	−1.87366	−0.936831	−	0.349781i	$-0.886256\pi$
$911$	−56.5523	−1.87366	−0.936831	+	0.349781i	$0.886256\pi$
$912$	0	0
$913$	25.0928	0.830449
$914$	−84.1699	−2.78409
$915$	−3.26180	−0.107832
$916$	68.9048	2.27668
$917$	0.814315	0.0268911
$918$	−13.1278	−0.433283
$919$	−40.9770	−1.35171	−0.675854	−	0.737036i	$-0.736225\pi$
$919$	−40.9770	−1.35171	−0.675854	+	0.737036i	$0.736225\pi$
$920$	−2.63090	−0.0867381
$921$	−5.66701	−0.186734
$922$	−0.704355	−0.0231967
$923$	−0.111842	−0.00368132
$924$	−6.34017	−0.208576
$925$	−3.35350	−0.110263
$926$	36.5380	1.20071
$927$	6.77205	0.222423
$928$	−60.3884	−1.98235
$929$	40.2713	1.32126	0.660628	−	0.750713i	$-0.270290\pi$
$929$	40.2713	1.32126	0.660628	+	0.750713i	$0.270290\pi$
$930$	2.17009	0.0711599
$931$	0	0
$932$	−43.9071	−1.43822
$933$	−16.2401	−0.531675
$934$	−67.4245	−2.20620
$935$	−12.0989	−0.395676
$936$	0.141157	0.00461386
$937$	−28.9405	−0.945446	−0.472723	−	0.881211i	$-0.656729\pi$
$937$	−28.9405	−0.945446	−0.472723	+	0.881211i	$0.656729\pi$
$938$	−9.77698	−0.319230
$939$	7.42574	0.242330
$940$	−24.7298	−0.806597
$941$	45.7431	1.49118	0.745592	−	0.666403i	$-0.232167\pi$
$941$	45.7431	1.49118	0.745592	+	0.666403i	$0.232167\pi$
$942$	−43.6163	−1.42110
$943$	8.00000	0.260516
$944$	−22.9372	−0.746543
$945$	−1.17009	−0.0380629
$946$	−3.20394	−0.104169
$947$	−57.7093	−1.87530	−0.937650	−	0.347582i	$-0.887003\pi$
$947$	−57.7093	−1.87530	−0.937650	+	0.347582i	$0.887003\pi$
$948$	9.55252	0.310251
$949$	0.703132	0.0228246
$950$	0	0
$951$	−13.2534	−0.429770
$952$	10.8950	0.353108
$953$	−3.89269	−0.126097	−0.0630483	−	0.998010i	$-0.520082\pi$
$953$	−3.89269	−0.126097	−0.0630483	+	0.998010i	$0.520082\pi$
$954$	10.7877	0.349263
$955$	23.3184	0.754567
$956$	53.5318	1.73134
$957$	15.9155	0.514474
$958$	−65.7803	−2.12526
$959$	−9.60197	−0.310064
$960$	−12.3112	−0.397344
$961$	1.00000	0.0322581
$962$	−0.667401	−0.0215179
$963$	0.630898	0.0203304
$964$	−23.4452	−0.755119
$965$	−10.2557	−0.330141
$966$	4.34017	0.139643
$967$	23.1317	0.743865	0.371933	−	0.928260i	$-0.378695\pi$
$967$	23.1317	0.743865	0.371933	+	0.928260i	$0.378695\pi$
$968$	−10.7743	−0.346300
$969$	0	0
$970$	−26.0410	−0.836127
$971$	−3.51414	−0.112774	−0.0563870	−	0.998409i	$-0.517958\pi$
$971$	−3.51414	−0.112774	−0.0563870	+	0.998409i	$0.517958\pi$
$972$	2.70928	0.0869000
$973$	5.26180	0.168685
$974$	12.8638	0.412182
$975$	0.0917087	0.00293703
$976$	6.77924	0.216998
$977$	37.5174	1.20029	0.600145	−	0.799891i	$-0.295110\pi$
$977$	37.5174	1.20029	0.600145	+	0.799891i	$0.295110\pi$
$978$	8.82150	0.282081
$979$	−11.5486	−0.369096
$980$	−15.2557	−0.487324
$981$	−11.8660	−0.378853
$982$	−24.1301	−0.770022
$983$	56.2434	1.79388	0.896942	−	0.442147i	$-0.145783\pi$
$983$	56.2434	1.79388	0.896942	+	0.442147i	$0.145783\pi$
$984$	−7.20394	−0.229653
$985$	23.9916	0.764436
$986$	−104.468	−3.32693
$987$	10.6803	0.339959
$988$	0	0
$989$	1.26180	0.0401228
$990$	4.34017	0.137940
$991$	61.4284	1.95134	0.975669	−	0.219251i	$-0.0703612\pi$
$991$	61.4284	1.95134	0.975669	+	0.219251i	$0.0703612\pi$
$992$	−7.58864	−0.240939
$993$	3.62475	0.115028
$994$	3.09663	0.0982191
$995$	−16.1217	−0.511092
$996$	33.9916	1.07706
$997$	49.6307	1.57182	0.785910	−	0.618340i	$-0.212195\pi$
$997$	49.6307	1.57182	0.785910	+	0.618340i	$0.212195\pi$
$998$	−1.04718	−0.0331479
$999$	−3.35350	−0.106100

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.a.f.1.3	✓	3
3.2	odd	2		1395.2.a.i.1.1		3
4.3	odd	2		7440.2.a.bp.1.3		3
5.2	odd	4		2325.2.c.o.1024.6		6
5.3	odd	4		2325.2.c.o.1024.1		6
5.4	even	2		2325.2.a.q.1.1		3
15.14	odd	2		6975.2.a.be.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.a.f.1.3	✓	3	1.1	even	1	trivial
1395.2.a.i.1.1		3	3.2	odd	2
2325.2.a.q.1.1		3	5.4	even	2
2325.2.c.o.1024.1		6	5.3	odd	4
2325.2.c.o.1024.6		6	5.2	odd	4
6975.2.a.be.1.3		3	15.14	odd	2
7440.2.a.bp.1.3		3	4.3	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.a (trivial)

\(f(q)\)	\(=\)	\(q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} +1.00000 q^{5} +2.17009 q^{6} -1.17009 q^{7} +1.53919 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} +1.00000 q^{5} +2.17009 q^{6} -1.17009 q^{7} +1.53919 q^{8} +1.00000 q^{9} +2.17009 q^{10} +2.00000 q^{11} +2.70928 q^{12} +0.0917087 q^{13} -2.53919 q^{14} +1.00000 q^{15} -2.07838 q^{16} -6.04945 q^{17} +2.17009 q^{18} +2.70928 q^{20} -1.17009 q^{21} +4.34017 q^{22} -1.70928 q^{23} +1.53919 q^{24} +1.00000 q^{25} +0.199016 q^{26} +1.00000 q^{27} -3.17009 q^{28} +7.95774 q^{29} +2.17009 q^{30} +1.00000 q^{31} -7.58864 q^{32} +2.00000 q^{33} -13.1278 q^{34} -1.17009 q^{35} +2.70928 q^{36} -3.35350 q^{37} +0.0917087 q^{39} +1.53919 q^{40} -4.68035 q^{41} -2.53919 q^{42} -0.738205 q^{43} +5.41855 q^{44} +1.00000 q^{45} -3.70928 q^{46} -9.12783 q^{47} -2.07838 q^{48} -5.63090 q^{49} +2.17009 q^{50} -6.04945 q^{51} +0.248464 q^{52} +4.97107 q^{53} +2.17009 q^{54} +2.00000 q^{55} -1.80098 q^{56} +17.2690 q^{58} +11.0361 q^{59} +2.70928 q^{60} -3.26180 q^{61} +2.17009 q^{62} -1.17009 q^{63} -12.3112 q^{64} +0.0917087 q^{65} +4.34017 q^{66} +3.85043 q^{67} -16.3896 q^{68} -1.70928 q^{69} -2.53919 q^{70} -1.21953 q^{71} +1.53919 q^{72} +7.66701 q^{73} -7.27739 q^{74} +1.00000 q^{75} -2.34017 q^{77} +0.199016 q^{78} +3.52586 q^{79} -2.07838 q^{80} +1.00000 q^{81} -10.1568 q^{82} +12.5464 q^{83} -3.17009 q^{84} -6.04945 q^{85} -1.60197 q^{86} +7.95774 q^{87} +3.07838 q^{88} -5.77432 q^{89} +2.17009 q^{90} -0.107307 q^{91} -4.63090 q^{92} +1.00000 q^{93} -19.8082 q^{94} -7.58864 q^{96} -12.0000 q^{97} -12.2195 q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + q^{4} + 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + q^4 + 3 * q^5 + q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + q^{4} + 3 q^{5} + q^{6} + 2 q^{7} + 3 q^{8} + 3 q^{9} + q^{10} + 6 q^{11} + q^{12} - 2 q^{13} - 6 q^{14} + 3 q^{15} - 3 q^{16} + q^{18} + q^{20} + 2 q^{21} + 2 q^{22} + 2 q^{23} + 3 q^{24} + 3 q^{25} + 10 q^{26} + 3 q^{27} - 4 q^{28} + 8 q^{29} + q^{30} + 3 q^{31} - 3 q^{32} + 6 q^{33} - 18 q^{34} + 2 q^{35} + q^{36} - 2 q^{39} + 3 q^{40} + 8 q^{41} - 6 q^{42} - 10 q^{43} + 2 q^{44} + 3 q^{45} - 4 q^{46} - 6 q^{47} - 3 q^{48} - 13 q^{49} + q^{50} - 8 q^{52} + q^{54} + 6 q^{55} + 4 q^{56} + 10 q^{58} + 14 q^{59} + q^{60} - 2 q^{61} + q^{62} + 2 q^{63} - 11 q^{64} - 2 q^{65} + 2 q^{66} - 16 q^{67} - 20 q^{68} + 2 q^{69} - 6 q^{70} + 20 q^{71} + 3 q^{72} - 28 q^{74} + 3 q^{75} + 4 q^{77} + 10 q^{78} + 8 q^{79} - 3 q^{80} + 3 q^{81} - 24 q^{82} + 2 q^{83} - 4 q^{84} + 14 q^{86} + 8 q^{87} + 6 q^{88} - 6 q^{89} + q^{90} - 12 q^{91} - 10 q^{92} + 3 q^{93} - 16 q^{94} - 3 q^{96} - 36 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + q^4 + 3 * q^5 + q^6 + 2 * q^7 + 3 * q^8 + 3 * q^9 + q^10 + 6 * q^11 + q^12 - 2 * q^13 - 6 * q^14 + 3 * q^15 - 3 * q^16 + q^18 + q^20 + 2 * q^21 + 2 * q^22 + 2 * q^23 + 3 * q^24 + 3 * q^25 + 10 * q^26 + 3 * q^27 - 4 * q^28 + 8 * q^29 + q^30 + 3 * q^31 - 3 * q^32 + 6 * q^33 - 18 * q^34 + 2 * q^35 + q^36 - 2 * q^39 + 3 * q^40 + 8 * q^41 - 6 * q^42 - 10 * q^43 + 2 * q^44 + 3 * q^45 - 4 * q^46 - 6 * q^47 - 3 * q^48 - 13 * q^49 + q^50 - 8 * q^52 + q^54 + 6 * q^55 + 4 * q^56 + 10 * q^58 + 14 * q^59 + q^60 - 2 * q^61 + q^62 + 2 * q^63 - 11 * q^64 - 2 * q^65 + 2 * q^66 - 16 * q^67 - 20 * q^68 + 2 * q^69 - 6 * q^70 + 20 * q^71 + 3 * q^72 - 28 * q^74 + 3 * q^75 + 4 * q^77 + 10 * q^78 + 8 * q^79 - 3 * q^80 + 3 * q^81 - 24 * q^82 + 2 * q^83 - 4 * q^84 + 14 * q^86 + 8 * q^87 + 6 * q^88 - 6 * q^89 + q^90 - 12 * q^91 - 10 * q^92 + 3 * q^93 - 16 * q^94 - 3 * q^96 - 36 * q^97 - 13 * q^98 + 6 * q^99

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