LMFDB - Embedded newform 465.2.a.d.1.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
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			1.1
Root			$-1.73205$ 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)

$f(q)$	$=$	$q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.26795 q^{7} +1.73205 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.26795 q^{7} +1.73205 q^{8} +1.00000 q^{9} +1.73205 q^{10} +5.46410 q^{11} -1.00000 q^{12} -4.73205 q^{13} +2.19615 q^{14} +1.00000 q^{15} -5.00000 q^{16} +5.46410 q^{17} -1.73205 q^{18} -1.46410 q^{19} -1.00000 q^{20} +1.26795 q^{21} -9.46410 q^{22} -7.46410 q^{23} -1.73205 q^{24} +1.00000 q^{25} +8.19615 q^{26} -1.00000 q^{27} -1.26795 q^{28} -2.73205 q^{29} -1.73205 q^{30} -1.00000 q^{31} +5.19615 q^{32} -5.46410 q^{33} -9.46410 q^{34} +1.26795 q^{35} +1.00000 q^{36} -3.26795 q^{37} +2.53590 q^{38} +4.73205 q^{39} -1.73205 q^{40} -3.46410 q^{41} -2.19615 q^{42} -4.00000 q^{43} +5.46410 q^{44} -1.00000 q^{45} +12.9282 q^{46} -6.00000 q^{47} +5.00000 q^{48} -5.39230 q^{49} -1.73205 q^{50} -5.46410 q^{51} -4.73205 q^{52} -8.39230 q^{53} +1.73205 q^{54} -5.46410 q^{55} -2.19615 q^{56} +1.46410 q^{57} +4.73205 q^{58} -1.80385 q^{59} +1.00000 q^{60} +10.3923 q^{61} +1.73205 q^{62} -1.26795 q^{63} +1.00000 q^{64} +4.73205 q^{65} +9.46410 q^{66} +0.196152 q^{67} +5.46410 q^{68} +7.46410 q^{69} -2.19615 q^{70} -14.1962 q^{71} +1.73205 q^{72} -11.6603 q^{73} +5.66025 q^{74} -1.00000 q^{75} -1.46410 q^{76} -6.92820 q^{77} -8.19615 q^{78} -10.0000 q^{79} +5.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +8.53590 q^{83} +1.26795 q^{84} -5.46410 q^{85} +6.92820 q^{86} +2.73205 q^{87} +9.46410 q^{88} +10.7321 q^{89} +1.73205 q^{90} +6.00000 q^{91} -7.46410 q^{92} +1.00000 q^{93} +10.3923 q^{94} +1.46410 q^{95} -5.19615 q^{96} -2.00000 q^{97} +9.33975 q^{98} +5.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} - 2 q^{5} - 6 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^4 - 2 * q^5 - 6 * q^7 + 2 * q^9	$ 2 q - 2 q^{3} + 2 q^{4} - 2 q^{5} - 6 q^{7} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 6 q^{13} - 6 q^{14} + 2 q^{15} - 10 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} + 6 q^{21} - 12 q^{22} - 8 q^{23} + 2 q^{25} + 6 q^{26} - 2 q^{27} - 6 q^{28} - 2 q^{29} - 2 q^{31} - 4 q^{33} - 12 q^{34} + 6 q^{35} + 2 q^{36} - 10 q^{37} + 12 q^{38} + 6 q^{39} + 6 q^{42} - 8 q^{43} + 4 q^{44} - 2 q^{45} + 12 q^{46} - 12 q^{47} + 10 q^{48} + 10 q^{49} - 4 q^{51} - 6 q^{52} + 4 q^{53} - 4 q^{55} + 6 q^{56} - 4 q^{57} + 6 q^{58} - 14 q^{59} + 2 q^{60} - 6 q^{63} + 2 q^{64} + 6 q^{65} + 12 q^{66} - 10 q^{67} + 4 q^{68} + 8 q^{69} + 6 q^{70} - 18 q^{71} - 6 q^{73} - 6 q^{74} - 2 q^{75} + 4 q^{76} - 6 q^{78} - 20 q^{79} + 10 q^{80} + 2 q^{81} + 12 q^{82} + 24 q^{83} + 6 q^{84} - 4 q^{85} + 2 q^{87} + 12 q^{88} + 18 q^{89} + 12 q^{91} - 8 q^{92} + 2 q^{93} - 4 q^{95} - 4 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 - 2 * q^5 - 6 * q^7 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 6 * q^13 - 6 * q^14 + 2 * q^15 - 10 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 + 6 * q^21 - 12 * q^22 - 8 * q^23 + 2 * q^25 + 6 * q^26 - 2 * q^27 - 6 * q^28 - 2 * q^29 - 2 * q^31 - 4 * q^33 - 12 * q^34 + 6 * q^35 + 2 * q^36 - 10 * q^37 + 12 * q^38 + 6 * q^39 + 6 * q^42 - 8 * q^43 + 4 * q^44 - 2 * q^45 + 12 * q^46 - 12 * q^47 + 10 * q^48 + 10 * q^49 - 4 * q^51 - 6 * q^52 + 4 * q^53 - 4 * q^55 + 6 * q^56 - 4 * q^57 + 6 * q^58 - 14 * q^59 + 2 * q^60 - 6 * q^63 + 2 * q^64 + 6 * q^65 + 12 * q^66 - 10 * q^67 + 4 * q^68 + 8 * q^69 + 6 * q^70 - 18 * q^71 - 6 * q^73 - 6 * q^74 - 2 * q^75 + 4 * q^76 - 6 * q^78 - 20 * q^79 + 10 * q^80 + 2 * q^81 + 12 * q^82 + 24 * q^83 + 6 * q^84 - 4 * q^85 + 2 * q^87 + 12 * q^88 + 18 * q^89 + 12 * q^91 - 8 * q^92 + 2 * q^93 - 4 * q^95 - 4 * q^97 + 36 * q^98 + 4 * 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 $

$2$	−1.73205	−1.22474	−0.612372	−	0.790569i	$-0.709785\pi$
$2$	−1.73205	−1.22474	−0.612372	+	0.790569i	$0.709785\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.73205	0.707107
$7$	−1.26795	−0.479240	−0.239620	−	0.970867i	$-0.577023\pi$
$7$	−1.26795	−0.479240	−0.239620	+	0.970867i	$0.577023\pi$
$8$	1.73205	0.612372
$9$	1.00000	0.333333
$10$	1.73205	0.547723
$11$	5.46410	1.64749	0.823744	−	0.566961i	$-0.191881\pi$
$11$	5.46410	1.64749	0.823744	+	0.566961i	$0.191881\pi$
$12$	−1.00000	−0.288675
$13$	−4.73205	−1.31243	−0.656217	−	0.754572i	$-0.727845\pi$
$13$	−4.73205	−1.31243	−0.656217	+	0.754572i	$0.727845\pi$
$14$	2.19615	0.586946
$15$	1.00000	0.258199
$16$	−5.00000	−1.25000
$17$	5.46410	1.32524	0.662620	−	0.748956i	$-0.269445\pi$
$17$	5.46410	1.32524	0.662620	+	0.748956i	$0.269445\pi$
$18$	−1.73205	−0.408248
$19$	−1.46410	−0.335888	−0.167944	−	0.985797i	$-0.553713\pi$
$19$	−1.46410	−0.335888	−0.167944	+	0.985797i	$0.553713\pi$
$20$	−1.00000	−0.223607
$21$	1.26795	0.276689
$22$	−9.46410	−2.01775
$23$	−7.46410	−1.55637	−0.778186	−	0.628033i	$-0.783860\pi$
$23$	−7.46410	−1.55637	−0.778186	+	0.628033i	$0.783860\pi$
$24$	−1.73205	−0.353553
$25$	1.00000	0.200000
$26$	8.19615	1.60740
$27$	−1.00000	−0.192450
$28$	−1.26795	−0.239620
$29$	−2.73205	−0.507329	−0.253665	−	0.967292i	$-0.581636\pi$
$29$	−2.73205	−0.507329	−0.253665	+	0.967292i	$0.581636\pi$
$30$	−1.73205	−0.316228
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	5.19615	0.918559
$33$	−5.46410	−0.951178
$34$	−9.46410	−1.62308
$35$	1.26795	0.214323
$36$	1.00000	0.166667
$37$	−3.26795	−0.537248	−0.268624	−	0.963245i	$-0.586569\pi$
$37$	−3.26795	−0.537248	−0.268624	+	0.963245i	$0.586569\pi$
$38$	2.53590	0.411377
$39$	4.73205	0.757735
$40$	−1.73205	−0.273861
$41$	−3.46410	−0.541002	−0.270501	−	0.962720i	$-0.587189\pi$
$41$	−3.46410	−0.541002	−0.270501	+	0.962720i	$0.587189\pi$
$42$	−2.19615	−0.338874
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	5.46410	0.823744
$45$	−1.00000	−0.149071
$46$	12.9282	1.90616
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	5.00000	0.721688
$49$	−5.39230	−0.770329
$50$	−1.73205	−0.244949
$51$	−5.46410	−0.765127
$52$	−4.73205	−0.656217
$53$	−8.39230	−1.15277	−0.576386	−	0.817178i	$-0.695537\pi$
$53$	−8.39230	−1.15277	−0.576386	+	0.817178i	$0.695537\pi$
$54$	1.73205	0.235702
$55$	−5.46410	−0.736779
$56$	−2.19615	−0.293473
$57$	1.46410	0.193925
$58$	4.73205	0.621349
$59$	−1.80385	−0.234841	−0.117420	−	0.993082i	$-0.537463\pi$
$59$	−1.80385	−0.234841	−0.117420	+	0.993082i	$0.537463\pi$
$60$	1.00000	0.129099
$61$	10.3923	1.33060	0.665299	−	0.746577i	$-0.268304\pi$
$61$	10.3923	1.33060	0.665299	+	0.746577i	$0.268304\pi$
$62$	1.73205	0.219971
$63$	−1.26795	−0.159747
$64$	1.00000	0.125000
$65$	4.73205	0.586939
$66$	9.46410	1.16495
$67$	0.196152	0.0239638	0.0119819	−	0.999928i	$-0.496186\pi$
$67$	0.196152	0.0239638	0.0119819	+	0.999928i	$0.496186\pi$
$68$	5.46410	0.662620
$69$	7.46410	0.898572
$70$	−2.19615	−0.262490
$71$	−14.1962	−1.68477	−0.842387	−	0.538874i	$-0.818850\pi$
$71$	−14.1962	−1.68477	−0.842387	+	0.538874i	$0.818850\pi$
$72$	1.73205	0.204124
$73$	−11.6603	−1.36473	−0.682365	−	0.731012i	$-0.739048\pi$
$73$	−11.6603	−1.36473	−0.682365	+	0.731012i	$0.739048\pi$
$74$	5.66025	0.657991
$75$	−1.00000	−0.115470
$76$	−1.46410	−0.167944
$77$	−6.92820	−0.789542
$78$	−8.19615	−0.928032
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	5.00000	0.559017
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	8.53590	0.936937	0.468468	−	0.883480i	$-0.344806\pi$
$83$	8.53590	0.936937	0.468468	+	0.883480i	$0.344806\pi$
$84$	1.26795	0.138345
$85$	−5.46410	−0.592665
$86$	6.92820	0.747087
$87$	2.73205	0.292907
$88$	9.46410	1.00888
$89$	10.7321	1.13760	0.568798	−	0.822478i	$-0.307409\pi$
$89$	10.7321	1.13760	0.568798	+	0.822478i	$0.307409\pi$
$90$	1.73205	0.182574
$91$	6.00000	0.628971
$92$	−7.46410	−0.778186
$93$	1.00000	0.103695
$94$	10.3923	1.07188
$95$	1.46410	0.150214
$96$	−5.19615	−0.530330
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	9.33975	0.943457
$99$	5.46410	0.549163
$100$	1.00000	0.100000
$101$	11.4641	1.14072	0.570360	−	0.821395i	$-0.306804\pi$
$101$	11.4641	1.14072	0.570360	+	0.821395i	$0.306804\pi$
$102$	9.46410	0.937086
$103$	6.73205	0.663329	0.331664	−	0.943397i	$-0.392390\pi$
$103$	6.73205	0.663329	0.331664	+	0.943397i	$0.392390\pi$
$104$	−8.19615	−0.803699
$105$	−1.26795	−0.123739
$106$	14.5359	1.41185
$107$	11.8564	1.14620	0.573101	−	0.819485i	$-0.305740\pi$
$107$	11.8564	1.14620	0.573101	+	0.819485i	$0.305740\pi$
$108$	−1.00000	−0.0962250
$109$	−9.46410	−0.906497	−0.453248	−	0.891384i	$-0.649735\pi$
$109$	−9.46410	−0.906497	−0.453248	+	0.891384i	$0.649735\pi$
$110$	9.46410	0.902367
$111$	3.26795	0.310180
$112$	6.33975	0.599050
$113$	8.92820	0.839895	0.419947	−	0.907548i	$-0.362049\pi$
$113$	8.92820	0.839895	0.419947	+	0.907548i	$0.362049\pi$
$114$	−2.53590	−0.237509
$115$	7.46410	0.696031
$116$	−2.73205	−0.253665
$117$	−4.73205	−0.437478
$118$	3.12436	0.287620
$119$	−6.92820	−0.635107
$120$	1.73205	0.158114
$121$	18.8564	1.71422
$122$	−18.0000	−1.62964
$123$	3.46410	0.312348
$124$	−1.00000	−0.0898027
$125$	−1.00000	−0.0894427
$126$	2.19615	0.195649
$127$	−17.4641	−1.54969	−0.774844	−	0.632152i	$-0.782172\pi$
$127$	−17.4641	−1.54969	−0.774844	+	0.632152i	$0.782172\pi$
$128$	−12.1244	−1.07165
$129$	4.00000	0.352180
$130$	−8.19615	−0.718850
$131$	3.26795	0.285522	0.142761	−	0.989757i	$-0.454402\pi$
$131$	3.26795	0.285522	0.142761	+	0.989757i	$0.454402\pi$
$132$	−5.46410	−0.475589
$133$	1.85641	0.160971
$134$	−0.339746	−0.0293496
$135$	1.00000	0.0860663
$136$	9.46410	0.811540
$137$	5.07180	0.433313	0.216656	−	0.976248i	$-0.430485\pi$
$137$	5.07180	0.433313	0.216656	+	0.976248i	$0.430485\pi$
$138$	−12.9282	−1.10052
$139$	−17.8564	−1.51456	−0.757280	−	0.653090i	$-0.773472\pi$
$139$	−17.8564	−1.51456	−0.757280	+	0.653090i	$0.773472\pi$
$140$	1.26795	0.107161
$141$	6.00000	0.505291
$142$	24.5885	2.06342
$143$	−25.8564	−2.16222
$144$	−5.00000	−0.416667
$145$	2.73205	0.226884
$146$	20.1962	1.67145
$147$	5.39230	0.444750
$148$	−3.26795	−0.268624
$149$	−13.3205	−1.09126	−0.545629	−	0.838027i	$-0.683709\pi$
$149$	−13.3205	−1.09126	−0.545629	+	0.838027i	$0.683709\pi$
$150$	1.73205	0.141421
$151$	−7.07180	−0.575495	−0.287747	−	0.957706i	$-0.592906\pi$
$151$	−7.07180	−0.575495	−0.287747	+	0.957706i	$0.592906\pi$
$152$	−2.53590	−0.205689
$153$	5.46410	0.441746
$154$	12.0000	0.966988
$155$	1.00000	0.0803219
$156$	4.73205	0.378867
$157$	0.928203	0.0740787	0.0370393	−	0.999314i	$-0.488207\pi$
$157$	0.928203	0.0740787	0.0370393	+	0.999314i	$0.488207\pi$
$158$	17.3205	1.37795
$159$	8.39230	0.665553
$160$	−5.19615	−0.410792
$161$	9.46410	0.745876
$162$	−1.73205	−0.136083
$163$	−3.80385	−0.297940	−0.148970	−	0.988842i	$-0.547596\pi$
$163$	−3.80385	−0.297940	−0.148970	+	0.988842i	$0.547596\pi$
$164$	−3.46410	−0.270501
$165$	5.46410	0.425380
$166$	−14.7846	−1.14751
$167$	−13.8564	−1.07224	−0.536120	−	0.844141i	$-0.680111\pi$
$167$	−13.8564	−1.07224	−0.536120	+	0.844141i	$0.680111\pi$
$168$	2.19615	0.169437
$169$	9.39230	0.722485
$170$	9.46410	0.725863
$171$	−1.46410	−0.111963
$172$	−4.00000	−0.304997
$173$	18.7846	1.42817	0.714084	−	0.700060i	$-0.246844\pi$
$173$	18.7846	1.42817	0.714084	+	0.700060i	$0.246844\pi$
$174$	−4.73205	−0.358736
$175$	−1.26795	−0.0958479
$176$	−27.3205	−2.05936
$177$	1.80385	0.135585
$178$	−18.5885	−1.39326
$179$	−22.9282	−1.71373	−0.856867	−	0.515537i	$-0.827592\pi$
$179$	−22.9282	−1.71373	−0.856867	+	0.515537i	$0.827592\pi$
$180$	−1.00000	−0.0745356
$181$	10.3923	0.772454	0.386227	−	0.922404i	$-0.373778\pi$
$181$	10.3923	0.772454	0.386227	+	0.922404i	$0.373778\pi$
$182$	−10.3923	−0.770329
$183$	−10.3923	−0.768221
$184$	−12.9282	−0.953080
$185$	3.26795	0.240264
$186$	−1.73205	−0.127000
$187$	29.8564	2.18332
$188$	−6.00000	−0.437595
$189$	1.26795	0.0922297
$190$	−2.53590	−0.183973
$191$	−22.1962	−1.60606	−0.803029	−	0.595940i	$-0.796779\pi$
$191$	−22.1962	−1.60606	−0.803029	+	0.595940i	$0.796779\pi$
$192$	−1.00000	−0.0721688
$193$	3.85641	0.277590	0.138795	−	0.990321i	$-0.455677\pi$
$193$	3.85641	0.277590	0.138795	+	0.990321i	$0.455677\pi$
$194$	3.46410	0.248708
$195$	−4.73205	−0.338869
$196$	−5.39230	−0.385165
$197$	26.9282	1.91856	0.959278	−	0.282465i	$-0.0911522\pi$
$197$	26.9282	1.91856	0.959278	+	0.282465i	$0.0911522\pi$
$198$	−9.46410	−0.672584
$199$	3.07180	0.217754	0.108877	−	0.994055i	$-0.465275\pi$
$199$	3.07180	0.217754	0.108877	+	0.994055i	$0.465275\pi$
$200$	1.73205	0.122474
$201$	−0.196152	−0.0138355
$202$	−19.8564	−1.39709
$203$	3.46410	0.243132
$204$	−5.46410	−0.382564
$205$	3.46410	0.241943
$206$	−11.6603	−0.812408
$207$	−7.46410	−0.518791
$208$	23.6603	1.64054
$209$	−8.00000	−0.553372
$210$	2.19615	0.151549
$211$	−27.3205	−1.88082	−0.940411	−	0.340041i	$-0.889559\pi$
$211$	−27.3205	−1.88082	−0.940411	+	0.340041i	$0.889559\pi$
$212$	−8.39230	−0.576386
$213$	14.1962	0.972704
$214$	−20.5359	−1.40381
$215$	4.00000	0.272798
$216$	−1.73205	−0.117851
$217$	1.26795	0.0860740
$218$	16.3923	1.11023
$219$	11.6603	0.787927
$220$	−5.46410	−0.368390
$221$	−25.8564	−1.73929
$222$	−5.66025	−0.379891
$223$	20.3923	1.36557	0.682785	−	0.730619i	$-0.260769\pi$
$223$	20.3923	1.36557	0.682785	+	0.730619i	$0.260769\pi$
$224$	−6.58846	−0.440210
$225$	1.00000	0.0666667
$226$	−15.4641	−1.02866
$227$	−21.3205	−1.41509	−0.707546	−	0.706667i	$-0.750198\pi$
$227$	−21.3205	−1.41509	−0.707546	+	0.706667i	$0.750198\pi$
$228$	1.46410	0.0969625
$229$	−22.7846	−1.50565	−0.752825	−	0.658221i	$-0.771309\pi$
$229$	−22.7846	−1.50565	−0.752825	+	0.658221i	$0.771309\pi$
$230$	−12.9282	−0.852460
$231$	6.92820	0.455842
$232$	−4.73205	−0.310674
$233$	−2.92820	−0.191833	−0.0959165	−	0.995389i	$-0.530578\pi$
$233$	−2.92820	−0.191833	−0.0959165	+	0.995389i	$0.530578\pi$
$234$	8.19615	0.535799
$235$	6.00000	0.391397
$236$	−1.80385	−0.117420
$237$	10.0000	0.649570
$238$	12.0000	0.777844
$239$	13.8564	0.896296	0.448148	−	0.893959i	$-0.352084\pi$
$239$	13.8564	0.896296	0.448148	+	0.893959i	$0.352084\pi$
$240$	−5.00000	−0.322749
$241$	−3.85641	−0.248413	−0.124206	−	0.992256i	$-0.539639\pi$
$241$	−3.85641	−0.248413	−0.124206	+	0.992256i	$0.539639\pi$
$242$	−32.6603	−2.09948
$243$	−1.00000	−0.0641500
$244$	10.3923	0.665299
$245$	5.39230	0.344502
$246$	−6.00000	−0.382546
$247$	6.92820	0.440831
$248$	−1.73205	−0.109985
$249$	−8.53590	−0.540941
$250$	1.73205	0.109545
$251$	−10.9282	−0.689782	−0.344891	−	0.938643i	$-0.612084\pi$
$251$	−10.9282	−0.689782	−0.344891	+	0.938643i	$0.612084\pi$
$252$	−1.26795	−0.0798733
$253$	−40.7846	−2.56411
$254$	30.2487	1.89797
$255$	5.46410	0.342175
$256$	19.0000	1.18750
$257$	17.8564	1.11385	0.556926	−	0.830562i	$-0.311981\pi$
$257$	17.8564	1.11385	0.556926	+	0.830562i	$0.311981\pi$
$258$	−6.92820	−0.431331
$259$	4.14359	0.257470
$260$	4.73205	0.293469
$261$	−2.73205	−0.169110
$262$	−5.66025	−0.349692
$263$	−30.9282	−1.90711	−0.953557	−	0.301212i	$-0.902609\pi$
$263$	−30.9282	−1.90711	−0.953557	+	0.301212i	$0.902609\pi$
$264$	−9.46410	−0.582475
$265$	8.39230	0.515535
$266$	−3.21539	−0.197148
$267$	−10.7321	−0.656791
$268$	0.196152	0.0119819
$269$	20.1962	1.23138	0.615691	−	0.787988i	$-0.288877\pi$
$269$	20.1962	1.23138	0.615691	+	0.787988i	$0.288877\pi$
$270$	−1.73205	−0.105409
$271$	24.7846	1.50556	0.752779	−	0.658273i	$-0.228713\pi$
$271$	24.7846	1.50556	0.752779	+	0.658273i	$0.228713\pi$
$272$	−27.3205	−1.65655
$273$	−6.00000	−0.363137
$274$	−8.78461	−0.530698
$275$	5.46410	0.329498
$276$	7.46410	0.449286
$277$	9.12436	0.548229	0.274115	−	0.961697i	$-0.411615\pi$
$277$	9.12436	0.548229	0.274115	+	0.961697i	$0.411615\pi$
$278$	30.9282	1.85495
$279$	−1.00000	−0.0598684
$280$	2.19615	0.131245
$281$	−23.4641	−1.39975	−0.699875	−	0.714265i	$-0.746761\pi$
$281$	−23.4641	−1.39975	−0.699875	+	0.714265i	$0.746761\pi$
$282$	−10.3923	−0.618853
$283$	10.7321	0.637954	0.318977	−	0.947762i	$-0.396661\pi$
$283$	10.7321	0.637954	0.318977	+	0.947762i	$0.396661\pi$
$284$	−14.1962	−0.842387
$285$	−1.46410	−0.0867259
$286$	44.7846	2.64817
$287$	4.39230	0.259270
$288$	5.19615	0.306186
$289$	12.8564	0.756259
$290$	−4.73205	−0.277876
$291$	2.00000	0.117242
$292$	−11.6603	−0.682365
$293$	18.9282	1.10580	0.552899	−	0.833248i	$-0.313522\pi$
$293$	18.9282	1.10580	0.552899	+	0.833248i	$0.313522\pi$
$294$	−9.33975	−0.544705
$295$	1.80385	0.105024
$296$	−5.66025	−0.328996
$297$	−5.46410	−0.317059
$298$	23.0718	1.33651
$299$	35.3205	2.04264
$300$	−1.00000	−0.0577350
$301$	5.07180	0.292334
$302$	12.2487	0.704834
$303$	−11.4641	−0.658595
$304$	7.32051	0.419860
$305$	−10.3923	−0.595062
$306$	−9.46410	−0.541027
$307$	−4.58846	−0.261877	−0.130939	−	0.991390i	$-0.541799\pi$
$307$	−4.58846	−0.261877	−0.130939	+	0.991390i	$0.541799\pi$
$308$	−6.92820	−0.394771
$309$	−6.73205	−0.382973
$310$	−1.73205	−0.0983739
$311$	−3.66025	−0.207554	−0.103777	−	0.994601i	$-0.533093\pi$
$311$	−3.66025	−0.207554	−0.103777	+	0.994601i	$0.533093\pi$
$312$	8.19615	0.464016
$313$	−4.33975	−0.245297	−0.122648	−	0.992450i	$-0.539139\pi$
$313$	−4.33975	−0.245297	−0.122648	+	0.992450i	$0.539139\pi$
$314$	−1.60770	−0.0907275
$315$	1.26795	0.0714408
$316$	−10.0000	−0.562544
$317$	−9.07180	−0.509523	−0.254761	−	0.967004i	$-0.581997\pi$
$317$	−9.07180	−0.509523	−0.254761	+	0.967004i	$0.581997\pi$
$318$	−14.5359	−0.815133
$319$	−14.9282	−0.835819
$320$	−1.00000	−0.0559017
$321$	−11.8564	−0.661760
$322$	−16.3923	−0.913507
$323$	−8.00000	−0.445132
$324$	1.00000	0.0555556
$325$	−4.73205	−0.262487
$326$	6.58846	0.364901
$327$	9.46410	0.523366
$328$	−6.00000	−0.331295
$329$	7.60770	0.419426
$330$	−9.46410	−0.520982
$331$	11.0718	0.608561	0.304280	−	0.952582i	$-0.401584\pi$
$331$	11.0718	0.608561	0.304280	+	0.952582i	$0.401584\pi$
$332$	8.53590	0.468468
$333$	−3.26795	−0.179083
$334$	24.0000	1.31322
$335$	−0.196152	−0.0107170
$336$	−6.33975	−0.345861
$337$	−20.0526	−1.09233	−0.546166	−	0.837677i	$-0.683913\pi$
$337$	−20.0526	−1.09233	−0.546166	+	0.837677i	$0.683913\pi$
$338$	−16.2679	−0.884860
$339$	−8.92820	−0.484913
$340$	−5.46410	−0.296333
$341$	−5.46410	−0.295898
$342$	2.53590	0.137126
$343$	15.7128	0.848412
$344$	−6.92820	−0.373544
$345$	−7.46410	−0.401854
$346$	−32.5359	−1.74914
$347$	28.7846	1.54524	0.772619	−	0.634869i	$-0.218946\pi$
$347$	28.7846	1.54524	0.772619	+	0.634869i	$0.218946\pi$
$348$	2.73205	0.146453
$349$	13.4641	0.720717	0.360358	−	0.932814i	$-0.382654\pi$
$349$	13.4641	0.720717	0.360358	+	0.932814i	$0.382654\pi$
$350$	2.19615	0.117389
$351$	4.73205	0.252578
$352$	28.3923	1.51331
$353$	16.3923	0.872474	0.436237	−	0.899832i	$-0.356311\pi$
$353$	16.3923	0.872474	0.436237	+	0.899832i	$0.356311\pi$
$354$	−3.12436	−0.166058
$355$	14.1962	0.753454
$356$	10.7321	0.568798
$357$	6.92820	0.366679
$358$	39.7128	2.09889
$359$	15.6603	0.826517	0.413258	−	0.910614i	$-0.364391\pi$
$359$	15.6603	0.826517	0.413258	+	0.910614i	$0.364391\pi$
$360$	−1.73205	−0.0912871
$361$	−16.8564	−0.887179
$362$	−18.0000	−0.946059
$363$	−18.8564	−0.989705
$364$	6.00000	0.314485
$365$	11.6603	0.610326
$366$	18.0000	0.940875
$367$	5.85641	0.305702	0.152851	−	0.988249i	$-0.451155\pi$
$367$	5.85641	0.305702	0.152851	+	0.988249i	$0.451155\pi$
$368$	37.3205	1.94547
$369$	−3.46410	−0.180334
$370$	−5.66025	−0.294263
$371$	10.6410	0.552454
$372$	1.00000	0.0518476
$373$	5.60770	0.290355	0.145178	−	0.989406i	$-0.453625\pi$
$373$	5.60770	0.290355	0.145178	+	0.989406i	$0.453625\pi$
$374$	−51.7128	−2.67401
$375$	1.00000	0.0516398
$376$	−10.3923	−0.535942
$377$	12.9282	0.665836
$378$	−2.19615	−0.112958
$379$	11.6077	0.596247	0.298124	−	0.954527i	$-0.403639\pi$
$379$	11.6077	0.596247	0.298124	+	0.954527i	$0.403639\pi$
$380$	1.46410	0.0751068
$381$	17.4641	0.894713
$382$	38.4449	1.96701
$383$	21.3205	1.08943	0.544714	−	0.838622i	$-0.316638\pi$
$383$	21.3205	1.08943	0.544714	+	0.838622i	$0.316638\pi$
$384$	12.1244	0.618718
$385$	6.92820	0.353094
$386$	−6.67949	−0.339977
$387$	−4.00000	−0.203331
$388$	−2.00000	−0.101535
$389$	29.6603	1.50383	0.751917	−	0.659257i	$-0.229129\pi$
$389$	29.6603	1.50383	0.751917	+	0.659257i	$0.229129\pi$
$390$	8.19615	0.415028
$391$	−40.7846	−2.06257
$392$	−9.33975	−0.471728
$393$	−3.26795	−0.164846
$394$	−46.6410	−2.34974
$395$	10.0000	0.503155
$396$	5.46410	0.274581
$397$	−3.85641	−0.193547	−0.0967737	−	0.995306i	$-0.530852\pi$
$397$	−3.85641	−0.193547	−0.0967737	+	0.995306i	$0.530852\pi$
$398$	−5.32051	−0.266693
$399$	−1.85641	−0.0929366
$400$	−5.00000	−0.250000
$401$	−35.5167	−1.77362	−0.886809	−	0.462137i	$-0.847083\pi$
$401$	−35.5167	−1.77362	−0.886809	+	0.462137i	$0.847083\pi$
$402$	0.339746	0.0169450
$403$	4.73205	0.235720
$404$	11.4641	0.570360
$405$	−1.00000	−0.0496904
$406$	−6.00000	−0.297775
$407$	−17.8564	−0.885109
$408$	−9.46410	−0.468543
$409$	17.3205	0.856444	0.428222	−	0.903674i	$-0.359140\pi$
$409$	17.3205	0.856444	0.428222	+	0.903674i	$0.359140\pi$
$410$	−6.00000	−0.296319
$411$	−5.07180	−0.250173
$412$	6.73205	0.331664
$413$	2.28719	0.112545
$414$	12.9282	0.635387
$415$	−8.53590	−0.419011
$416$	−24.5885	−1.20555
$417$	17.8564	0.874432
$418$	13.8564	0.677739
$419$	−2.87564	−0.140484	−0.0702422	−	0.997530i	$-0.522377\pi$
$419$	−2.87564	−0.140484	−0.0702422	+	0.997530i	$0.522377\pi$
$420$	−1.26795	−0.0618696
$421$	19.3205	0.941624	0.470812	−	0.882234i	$-0.343961\pi$
$421$	19.3205	0.941624	0.470812	+	0.882234i	$0.343961\pi$
$422$	47.3205	2.30353
$423$	−6.00000	−0.291730
$424$	−14.5359	−0.705926
$425$	5.46410	0.265048
$426$	−24.5885	−1.19131
$427$	−13.1769	−0.637676
$428$	11.8564	0.573101
$429$	25.8564	1.24836
$430$	−6.92820	−0.334108
$431$	33.1244	1.59554	0.797772	−	0.602959i	$-0.206012\pi$
$431$	33.1244	1.59554	0.797772	+	0.602959i	$0.206012\pi$
$432$	5.00000	0.240563
$433$	−29.5167	−1.41848	−0.709240	−	0.704967i	$-0.750962\pi$
$433$	−29.5167	−1.41848	−0.709240	+	0.704967i	$0.750962\pi$
$434$	−2.19615	−0.105419
$435$	−2.73205	−0.130992
$436$	−9.46410	−0.453248
$437$	10.9282	0.522767
$438$	−20.1962	−0.965009
$439$	19.7128	0.940841	0.470421	−	0.882442i	$-0.344102\pi$
$439$	19.7128	0.940841	0.470421	+	0.882442i	$0.344102\pi$
$440$	−9.46410	−0.451183
$441$	−5.39230	−0.256776
$442$	44.7846	2.13019
$443$	9.60770	0.456475	0.228238	−	0.973605i	$-0.426704\pi$
$443$	9.60770	0.456475	0.228238	+	0.973605i	$0.426704\pi$
$444$	3.26795	0.155090
$445$	−10.7321	−0.508748
$446$	−35.3205	−1.67247
$447$	13.3205	0.630038
$448$	−1.26795	−0.0599050
$449$	37.2679	1.75878	0.879392	−	0.476099i	$-0.157950\pi$
$449$	37.2679	1.75878	0.879392	+	0.476099i	$0.157950\pi$
$450$	−1.73205	−0.0816497
$451$	−18.9282	−0.891294
$452$	8.92820	0.419947
$453$	7.07180	0.332262
$454$	36.9282	1.73313
$455$	−6.00000	−0.281284
$456$	2.53590	0.118754
$457$	1.41154	0.0660292	0.0330146	−	0.999455i	$-0.489489\pi$
$457$	1.41154	0.0660292	0.0330146	+	0.999455i	$0.489489\pi$
$458$	39.4641	1.84404
$459$	−5.46410	−0.255042
$460$	7.46410	0.348016
$461$	2.73205	0.127244	0.0636221	−	0.997974i	$-0.479735\pi$
$461$	2.73205	0.127244	0.0636221	+	0.997974i	$0.479735\pi$
$462$	−12.0000	−0.558291
$463$	−15.7128	−0.730236	−0.365118	−	0.930961i	$-0.618971\pi$
$463$	−15.7128	−0.730236	−0.365118	+	0.930961i	$0.618971\pi$
$464$	13.6603	0.634161
$465$	−1.00000	−0.0463739
$466$	5.07180	0.234946
$467$	2.00000	0.0925490	0.0462745	−	0.998929i	$-0.485265\pi$
$467$	2.00000	0.0925490	0.0462745	+	0.998929i	$0.485265\pi$
$468$	−4.73205	−0.218739
$469$	−0.248711	−0.0114844
$470$	−10.3923	−0.479361
$471$	−0.928203	−0.0427693
$472$	−3.12436	−0.143810
$473$	−21.8564	−1.00496
$474$	−17.3205	−0.795557
$475$	−1.46410	−0.0671776
$476$	−6.92820	−0.317554
$477$	−8.39230	−0.384257
$478$	−24.0000	−1.09773
$479$	−38.1962	−1.74523	−0.872613	−	0.488412i	$-0.837576\pi$
$479$	−38.1962	−1.74523	−0.872613	+	0.488412i	$0.837576\pi$
$480$	5.19615	0.237171
$481$	15.4641	0.705102
$482$	6.67949	0.304243
$483$	−9.46410	−0.430632
$484$	18.8564	0.857109
$485$	2.00000	0.0908153
$486$	1.73205	0.0785674
$487$	17.4641	0.791374	0.395687	−	0.918385i	$-0.370507\pi$
$487$	17.4641	0.791374	0.395687	+	0.918385i	$0.370507\pi$
$488$	18.0000	0.814822
$489$	3.80385	0.172016
$490$	−9.33975	−0.421927
$491$	3.60770	0.162813	0.0814065	−	0.996681i	$-0.474059\pi$
$491$	3.60770	0.162813	0.0814065	+	0.996681i	$0.474059\pi$
$492$	3.46410	0.156174
$493$	−14.9282	−0.672332
$494$	−12.0000	−0.539906
$495$	−5.46410	−0.245593
$496$	5.00000	0.224507
$497$	18.0000	0.807410
$498$	14.7846	0.662514
$499$	−1.07180	−0.0479802	−0.0239901	−	0.999712i	$-0.507637\pi$
$499$	−1.07180	−0.0479802	−0.0239901	+	0.999712i	$0.507637\pi$
$500$	−1.00000	−0.0447214
$501$	13.8564	0.619059
$502$	18.9282	0.844807
$503$	15.8564	0.707002	0.353501	−	0.935434i	$-0.384991\pi$
$503$	15.8564	0.707002	0.353501	+	0.935434i	$0.384991\pi$
$504$	−2.19615	−0.0978244
$505$	−11.4641	−0.510146
$506$	70.6410	3.14038
$507$	−9.39230	−0.417127
$508$	−17.4641	−0.774844
$509$	13.2679	0.588092	0.294046	−	0.955791i	$-0.404998\pi$
$509$	13.2679	0.588092	0.294046	+	0.955791i	$0.404998\pi$
$510$	−9.46410	−0.419077
$511$	14.7846	0.654033
$512$	−8.66025	−0.382733
$513$	1.46410	0.0646417
$514$	−30.9282	−1.36418
$515$	−6.73205	−0.296650
$516$	4.00000	0.176090
$517$	−32.7846	−1.44187
$518$	−7.17691	−0.315336
$519$	−18.7846	−0.824553
$520$	8.19615	0.359425
$521$	−13.3205	−0.583582	−0.291791	−	0.956482i	$-0.594251\pi$
$521$	−13.3205	−0.583582	−0.291791	+	0.956482i	$0.594251\pi$
$522$	4.73205	0.207116
$523$	−32.3923	−1.41642	−0.708208	−	0.706004i	$-0.750496\pi$
$523$	−32.3923	−1.41642	−0.708208	+	0.706004i	$0.750496\pi$
$524$	3.26795	0.142761
$525$	1.26795	0.0553378
$526$	53.5692	2.33573
$527$	−5.46410	−0.238020
$528$	27.3205	1.18897
$529$	32.7128	1.42230
$530$	−14.5359	−0.631399
$531$	−1.80385	−0.0782803
$532$	1.85641	0.0804854
$533$	16.3923	0.710030
$534$	18.5885	0.804401
$535$	−11.8564	−0.512597
$536$	0.339746	0.0146748
$537$	22.9282	0.989425
$538$	−34.9808	−1.50813
$539$	−29.4641	−1.26911
$540$	1.00000	0.0430331
$541$	−13.4641	−0.578867	−0.289433	−	0.957198i	$-0.593467\pi$
$541$	−13.4641	−0.578867	−0.289433	+	0.957198i	$0.593467\pi$
$542$	−42.9282	−1.84392
$543$	−10.3923	−0.445976
$544$	28.3923	1.21731
$545$	9.46410	0.405398
$546$	10.3923	0.444750
$547$	−23.8038	−1.01778	−0.508890	−	0.860832i	$-0.669944\pi$
$547$	−23.8038	−1.01778	−0.508890	+	0.860832i	$0.669944\pi$
$548$	5.07180	0.216656
$549$	10.3923	0.443533
$550$	−9.46410	−0.403551
$551$	4.00000	0.170406
$552$	12.9282	0.550261
$553$	12.6795	0.539187
$554$	−15.8038	−0.671441
$555$	−3.26795	−0.138717
$556$	−17.8564	−0.757280
$557$	−2.53590	−0.107449	−0.0537247	−	0.998556i	$-0.517109\pi$
$557$	−2.53590	−0.107449	−0.0537247	+	0.998556i	$0.517109\pi$
$558$	1.73205	0.0733236
$559$	18.9282	0.800578
$560$	−6.33975	−0.267903
$561$	−29.8564	−1.26054
$562$	40.6410	1.71434
$563$	−28.6410	−1.20707	−0.603537	−	0.797335i	$-0.706243\pi$
$563$	−28.6410	−1.20707	−0.603537	+	0.797335i	$0.706243\pi$
$564$	6.00000	0.252646
$565$	−8.92820	−0.375612
$566$	−18.5885	−0.781331
$567$	−1.26795	−0.0532489
$568$	−24.5885	−1.03171
$569$	−25.2679	−1.05929	−0.529644	−	0.848220i	$-0.677674\pi$
$569$	−25.2679	−1.05929	−0.529644	+	0.848220i	$0.677674\pi$
$570$	2.53590	0.106217
$571$	31.7128	1.32714	0.663570	−	0.748114i	$-0.269041\pi$
$571$	31.7128	1.32714	0.663570	+	0.748114i	$0.269041\pi$
$572$	−25.8564	−1.08111
$573$	22.1962	0.927258
$574$	−7.60770	−0.317539
$575$	−7.46410	−0.311275
$576$	1.00000	0.0416667
$577$	−29.3205	−1.22063	−0.610314	−	0.792159i	$-0.708957\pi$
$577$	−29.3205	−1.22063	−0.610314	+	0.792159i	$0.708957\pi$
$578$	−22.2679	−0.926225
$579$	−3.85641	−0.160267
$580$	2.73205	0.113442
$581$	−10.8231	−0.449017
$582$	−3.46410	−0.143592
$583$	−45.8564	−1.89918
$584$	−20.1962	−0.835723
$585$	4.73205	0.195646
$586$	−32.7846	−1.35432
$587$	−2.92820	−0.120860	−0.0604299	−	0.998172i	$-0.519247\pi$
$587$	−2.92820	−0.120860	−0.0604299	+	0.998172i	$0.519247\pi$
$588$	5.39230	0.222375
$589$	1.46410	0.0603273
$590$	−3.12436	−0.128628
$591$	−26.9282	−1.10768
$592$	16.3397	0.671559
$593$	−22.0000	−0.903432	−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000	−0.903432	−0.451716	+	0.892162i	$0.649188\pi$
$594$	9.46410	0.388317
$595$	6.92820	0.284029
$596$	−13.3205	−0.545629
$597$	−3.07180	−0.125720
$598$	−61.1769	−2.50171
$599$	−31.3731	−1.28187	−0.640934	−	0.767596i	$-0.721453\pi$
$599$	−31.3731	−1.28187	−0.640934	+	0.767596i	$0.721453\pi$
$600$	−1.73205	−0.0707107
$601$	−2.67949	−0.109299	−0.0546494	−	0.998506i	$-0.517404\pi$
$601$	−2.67949	−0.109299	−0.0546494	+	0.998506i	$0.517404\pi$
$602$	−8.78461	−0.358034
$603$	0.196152	0.00798794
$604$	−7.07180	−0.287747
$605$	−18.8564	−0.766622
$606$	19.8564	0.806611
$607$	−39.1244	−1.58801	−0.794004	−	0.607912i	$-0.792007\pi$
$607$	−39.1244	−1.58801	−0.794004	+	0.607912i	$0.792007\pi$
$608$	−7.60770	−0.308533
$609$	−3.46410	−0.140372
$610$	18.0000	0.728799
$611$	28.3923	1.14863
$612$	5.46410	0.220873
$613$	48.4449	1.95667	0.978335	−	0.207029i	$-0.0663794\pi$
$613$	48.4449	1.95667	0.978335	+	0.207029i	$0.0663794\pi$
$614$	7.94744	0.320733
$615$	−3.46410	−0.139686
$616$	−12.0000	−0.483494
$617$	6.78461	0.273138	0.136569	−	0.990631i	$-0.456392\pi$
$617$	6.78461	0.273138	0.136569	+	0.990631i	$0.456392\pi$
$618$	11.6603	0.469044
$619$	−11.8564	−0.476549	−0.238275	−	0.971198i	$-0.576582\pi$
$619$	−11.8564	−0.476549	−0.238275	+	0.971198i	$0.576582\pi$
$620$	1.00000	0.0401610
$621$	7.46410	0.299524
$622$	6.33975	0.254201
$623$	−13.6077	−0.545181
$624$	−23.6603	−0.947168
$625$	1.00000	0.0400000
$626$	7.51666	0.300426
$627$	8.00000	0.319489
$628$	0.928203	0.0370393
$629$	−17.8564	−0.711982
$630$	−2.19615	−0.0874968
$631$	−10.9282	−0.435045	−0.217522	−	0.976055i	$-0.569798\pi$
$631$	−10.9282	−0.435045	−0.217522	+	0.976055i	$0.569798\pi$
$632$	−17.3205	−0.688973
$633$	27.3205	1.08589
$634$	15.7128	0.624036
$635$	17.4641	0.693042
$636$	8.39230	0.332777
$637$	25.5167	1.01101
$638$	25.8564	1.02366
$639$	−14.1962	−0.561591
$640$	12.1244	0.479257
$641$	−4.48334	−0.177081	−0.0885406	−	0.996073i	$-0.528220\pi$
$641$	−4.48334	−0.177081	−0.0885406	+	0.996073i	$0.528220\pi$
$642$	20.5359	0.810487
$643$	−2.24871	−0.0886805	−0.0443403	−	0.999016i	$-0.514119\pi$
$643$	−2.24871	−0.0886805	−0.0443403	+	0.999016i	$0.514119\pi$
$644$	9.46410	0.372938
$645$	−4.00000	−0.157500
$646$	13.8564	0.545173
$647$	44.7846	1.76066	0.880332	−	0.474357i	$-0.157320\pi$
$647$	44.7846	1.76066	0.880332	+	0.474357i	$0.157320\pi$
$648$	1.73205	0.0680414
$649$	−9.85641	−0.386898
$650$	8.19615	0.321480
$651$	−1.26795	−0.0496948
$652$	−3.80385	−0.148970
$653$	1.85641	0.0726468	0.0363234	−	0.999340i	$-0.488435\pi$
$653$	1.85641	0.0726468	0.0363234	+	0.999340i	$0.488435\pi$
$654$	−16.3923	−0.640990
$655$	−3.26795	−0.127689
$656$	17.3205	0.676252
$657$	−11.6603	−0.454910
$658$	−13.1769	−0.513690
$659$	−14.8756	−0.579473	−0.289736	−	0.957106i	$-0.593568\pi$
$659$	−14.8756	−0.579473	−0.289736	+	0.957106i	$0.593568\pi$
$660$	5.46410	0.212690
$661$	24.6410	0.958424	0.479212	−	0.877699i	$-0.340922\pi$
$661$	24.6410	0.958424	0.479212	+	0.877699i	$0.340922\pi$
$662$	−19.1769	−0.745332
$663$	25.8564	1.00418
$664$	14.7846	0.573754
$665$	−1.85641	−0.0719884
$666$	5.66025	0.219330
$667$	20.3923	0.789593
$668$	−13.8564	−0.536120
$669$	−20.3923	−0.788412
$670$	0.339746	0.0131255
$671$	56.7846	2.19215
$672$	6.58846	0.254155
$673$	−12.7321	−0.490784	−0.245392	−	0.969424i	$-0.578917\pi$
$673$	−12.7321	−0.490784	−0.245392	+	0.969424i	$0.578917\pi$
$674$	34.7321	1.33783
$675$	−1.00000	−0.0384900
$676$	9.39230	0.361242
$677$	7.60770	0.292387	0.146194	−	0.989256i	$-0.453298\pi$
$677$	7.60770	0.292387	0.146194	+	0.989256i	$0.453298\pi$
$678$	15.4641	0.593895
$679$	2.53590	0.0973188
$680$	−9.46410	−0.362932
$681$	21.3205	0.817004
$682$	9.46410	0.362399
$683$	43.1769	1.65212	0.826059	−	0.563583i	$-0.190578\pi$
$683$	43.1769	1.65212	0.826059	+	0.563583i	$0.190578\pi$
$684$	−1.46410	−0.0559813
$685$	−5.07180	−0.193783
$686$	−27.2154	−1.03909
$687$	22.7846	0.869287
$688$	20.0000	0.762493
$689$	39.7128	1.51294
$690$	12.9282	0.492168
$691$	16.0000	0.608669	0.304334	−	0.952565i	$-0.401566\pi$
$691$	16.0000	0.608669	0.304334	+	0.952565i	$0.401566\pi$
$692$	18.7846	0.714084
$693$	−6.92820	−0.263181
$694$	−49.8564	−1.89252
$695$	17.8564	0.677332
$696$	4.73205	0.179368
$697$	−18.9282	−0.716957
$698$	−23.3205	−0.882694
$699$	2.92820	0.110755
$700$	−1.26795	−0.0479240
$701$	−34.7846	−1.31380	−0.656898	−	0.753979i	$-0.728132\pi$
$701$	−34.7846	−1.31380	−0.656898	+	0.753979i	$0.728132\pi$
$702$	−8.19615	−0.309344
$703$	4.78461	0.180455
$704$	5.46410	0.205936
$705$	−6.00000	−0.225973
$706$	−28.3923	−1.06856
$707$	−14.5359	−0.546679
$708$	1.80385	0.0677927
$709$	19.0718	0.716256	0.358128	−	0.933672i	$-0.383415\pi$
$709$	19.0718	0.716256	0.358128	+	0.933672i	$0.383415\pi$
$710$	−24.5885	−0.922788
$711$	−10.0000	−0.375029
$712$	18.5885	0.696632
$713$	7.46410	0.279533
$714$	−12.0000	−0.449089
$715$	25.8564	0.966975
$716$	−22.9282	−0.856867
$717$	−13.8564	−0.517477
$718$	−27.1244	−1.01227
$719$	−2.53590	−0.0945731	−0.0472865	−	0.998881i	$-0.515057\pi$
$719$	−2.53590	−0.0945731	−0.0472865	+	0.998881i	$0.515057\pi$
$720$	5.00000	0.186339
$721$	−8.53590	−0.317893
$722$	29.1962	1.08657
$723$	3.85641	0.143421
$724$	10.3923	0.386227
$725$	−2.73205	−0.101466
$726$	32.6603	1.21214
$727$	−27.5167	−1.02054	−0.510268	−	0.860015i	$-0.670454\pi$
$727$	−27.5167	−1.02054	−0.510268	+	0.860015i	$0.670454\pi$
$728$	10.3923	0.385164
$729$	1.00000	0.0370370
$730$	−20.1962	−0.747493
$731$	−21.8564	−0.808388
$732$	−10.3923	−0.384111
$733$	−4.92820	−0.182027	−0.0910137	−	0.995850i	$-0.529011\pi$
$733$	−4.92820	−0.182027	−0.0910137	+	0.995850i	$0.529011\pi$
$734$	−10.1436	−0.374407
$735$	−5.39230	−0.198898
$736$	−38.7846	−1.42962
$737$	1.07180	0.0394801
$738$	6.00000	0.220863
$739$	43.5692	1.60272	0.801360	−	0.598183i	$-0.204110\pi$
$739$	43.5692	1.60272	0.801360	+	0.598183i	$0.204110\pi$
$740$	3.26795	0.120132
$741$	−6.92820	−0.254514
$742$	−18.4308	−0.676615
$743$	−48.4974	−1.77920	−0.889599	−	0.456743i	$-0.849016\pi$
$743$	−48.4974	−1.77920	−0.889599	+	0.456743i	$0.849016\pi$
$744$	1.73205	0.0635001
$745$	13.3205	0.488026
$746$	−9.71281	−0.355611
$747$	8.53590	0.312312
$748$	29.8564	1.09166
$749$	−15.0333	−0.549306
$750$	−1.73205	−0.0632456
$751$	32.7846	1.19633	0.598164	−	0.801374i	$-0.295897\pi$
$751$	32.7846	1.19633	0.598164	+	0.801374i	$0.295897\pi$
$752$	30.0000	1.09399
$753$	10.9282	0.398246
$754$	−22.3923	−0.815480
$755$	7.07180	0.257369
$756$	1.26795	0.0461149
$757$	19.2679	0.700306	0.350153	−	0.936693i	$-0.386130\pi$
$757$	19.2679	0.700306	0.350153	+	0.936693i	$0.386130\pi$
$758$	−20.1051	−0.730251
$759$	40.7846	1.48039
$760$	2.53590	0.0919867
$761$	−14.3397	−0.519815	−0.259908	−	0.965633i	$-0.583692\pi$
$761$	−14.3397	−0.519815	−0.259908	+	0.965633i	$0.583692\pi$
$762$	−30.2487	−1.09580
$763$	12.0000	0.434429
$764$	−22.1962	−0.803029
$765$	−5.46410	−0.197555
$766$	−36.9282	−1.33427
$767$	8.53590	0.308213
$768$	−19.0000	−0.685603
$769$	−15.6077	−0.562828	−0.281414	−	0.959586i	$-0.590803\pi$
$769$	−15.6077	−0.562828	−0.281414	+	0.959586i	$0.590803\pi$
$770$	−12.0000	−0.432450
$771$	−17.8564	−0.643083
$772$	3.85641	0.138795
$773$	45.1769	1.62490	0.812450	−	0.583030i	$-0.198133\pi$
$773$	45.1769	1.62490	0.812450	+	0.583030i	$0.198133\pi$
$774$	6.92820	0.249029
$775$	−1.00000	−0.0359211
$776$	−3.46410	−0.124354
$777$	−4.14359	−0.148651
$778$	−51.3731	−1.84181
$779$	5.07180	0.181716
$780$	−4.73205	−0.169435
$781$	−77.5692	−2.77564
$782$	70.6410	2.52612
$783$	2.73205	0.0976355
$784$	26.9615	0.962912
$785$	−0.928203	−0.0331290
$786$	5.66025	0.201895
$787$	−46.5359	−1.65883	−0.829413	−	0.558636i	$-0.811325\pi$
$787$	−46.5359	−1.65883	−0.829413	+	0.558636i	$0.811325\pi$
$788$	26.9282	0.959278
$789$	30.9282	1.10107
$790$	−17.3205	−0.616236
$791$	−11.3205	−0.402511
$792$	9.46410	0.336292
$793$	−49.1769	−1.74632
$794$	6.67949	0.237046
$795$	−8.39230	−0.297644
$796$	3.07180	0.108877
$797$	25.8564	0.915881	0.457940	−	0.888983i	$-0.348587\pi$
$797$	25.8564	0.915881	0.457940	+	0.888983i	$0.348587\pi$
$798$	3.21539	0.113824
$799$	−32.7846	−1.15984
$800$	5.19615	0.183712
$801$	10.7321	0.379198
$802$	61.5167	2.17223
$803$	−63.7128	−2.24838
$804$	−0.196152	−0.00691776
$805$	−9.46410	−0.333566
$806$	−8.19615	−0.288697
$807$	−20.1962	−0.710938
$808$	19.8564	0.698546
$809$	50.8372	1.78734	0.893670	−	0.448725i	$-0.148122\pi$
$809$	50.8372	1.78734	0.893670	+	0.448725i	$0.148122\pi$
$810$	1.73205	0.0608581
$811$	18.2487	0.640799	0.320399	−	0.947283i	$-0.396183\pi$
$811$	18.2487	0.640799	0.320399	+	0.947283i	$0.396183\pi$
$812$	3.46410	0.121566
$813$	−24.7846	−0.869234
$814$	30.9282	1.08403
$815$	3.80385	0.133243
$816$	27.3205	0.956409
$817$	5.85641	0.204890
$818$	−30.0000	−1.04893
$819$	6.00000	0.209657
$820$	3.46410	0.120972
$821$	−7.12436	−0.248642	−0.124321	−	0.992242i	$-0.539675\pi$
$821$	−7.12436	−0.248642	−0.124321	+	0.992242i	$0.539675\pi$
$822$	8.78461	0.306398
$823$	31.7128	1.10544	0.552720	−	0.833367i	$-0.313590\pi$
$823$	31.7128	1.10544	0.552720	+	0.833367i	$0.313590\pi$
$824$	11.6603	0.406204
$825$	−5.46410	−0.190236
$826$	−3.96152	−0.137839
$827$	42.1051	1.46414	0.732069	−	0.681230i	$-0.238555\pi$
$827$	42.1051	1.46414	0.732069	+	0.681230i	$0.238555\pi$
$828$	−7.46410	−0.259395
$829$	22.1051	0.767742	0.383871	−	0.923387i	$-0.374591\pi$
$829$	22.1051	0.767742	0.383871	+	0.923387i	$0.374591\pi$
$830$	14.7846	0.513181
$831$	−9.12436	−0.316520
$832$	−4.73205	−0.164054
$833$	−29.4641	−1.02087
$834$	−30.9282	−1.07096
$835$	13.8564	0.479521
$836$	−8.00000	−0.276686
$837$	1.00000	0.0345651
$838$	4.98076	0.172058
$839$	−13.4115	−0.463018	−0.231509	−	0.972833i	$-0.574366\pi$
$839$	−13.4115	−0.463018	−0.231509	+	0.972833i	$0.574366\pi$
$840$	−2.19615	−0.0757745
$841$	−21.5359	−0.742617
$842$	−33.4641	−1.15325
$843$	23.4641	0.808147
$844$	−27.3205	−0.940411
$845$	−9.39230	−0.323105
$846$	10.3923	0.357295
$847$	−23.9090	−0.821522
$848$	41.9615	1.44096
$849$	−10.7321	−0.368323
$850$	−9.46410	−0.324616
$851$	24.3923	0.836157
$852$	14.1962	0.486352
$853$	3.75129	0.128442	0.0642208	−	0.997936i	$-0.479544\pi$
$853$	3.75129	0.128442	0.0642208	+	0.997936i	$0.479544\pi$
$854$	22.8231	0.780990
$855$	1.46410	0.0500712
$856$	20.5359	0.701903
$857$	−45.7128	−1.56152	−0.780760	−	0.624831i	$-0.785168\pi$
$857$	−45.7128	−1.56152	−0.780760	+	0.624831i	$0.785168\pi$
$858$	−44.7846	−1.52892
$859$	−15.7128	−0.536114	−0.268057	−	0.963403i	$-0.586382\pi$
$859$	−15.7128	−0.536114	−0.268057	+	0.963403i	$0.586382\pi$
$860$	4.00000	0.136399
$861$	−4.39230	−0.149689
$862$	−57.3731	−1.95413
$863$	−27.7128	−0.943355	−0.471678	−	0.881771i	$-0.656351\pi$
$863$	−27.7128	−0.943355	−0.471678	+	0.881771i	$0.656351\pi$
$864$	−5.19615	−0.176777
$865$	−18.7846	−0.638696
$866$	51.1244	1.73728
$867$	−12.8564	−0.436626
$868$	1.26795	0.0430370
$869$	−54.6410	−1.85357
$870$	4.73205	0.160432
$871$	−0.928203	−0.0314510
$872$	−16.3923	−0.555113
$873$	−2.00000	−0.0676897
$874$	−18.9282	−0.640256
$875$	1.26795	0.0428645
$876$	11.6603	0.393963
$877$	42.1051	1.42179	0.710894	−	0.703299i	$-0.248290\pi$
$877$	42.1051	1.42179	0.710894	+	0.703299i	$0.248290\pi$
$878$	−34.1436	−1.15229
$879$	−18.9282	−0.638432
$880$	27.3205	0.920974
$881$	−30.8372	−1.03893	−0.519465	−	0.854492i	$-0.673869\pi$
$881$	−30.8372	−1.03893	−0.519465	+	0.854492i	$0.673869\pi$
$882$	9.33975	0.314486
$883$	15.3205	0.515576	0.257788	−	0.966201i	$-0.417006\pi$
$883$	15.3205	0.515576	0.257788	+	0.966201i	$0.417006\pi$
$884$	−25.8564	−0.869645
$885$	−1.80385	−0.0606357
$886$	−16.6410	−0.559066
$887$	−8.53590	−0.286607	−0.143304	−	0.989679i	$-0.545773\pi$
$887$	−8.53590	−0.286607	−0.143304	+	0.989679i	$0.545773\pi$
$888$	5.66025	0.189946
$889$	22.1436	0.742672
$890$	18.5885	0.623087
$891$	5.46410	0.183054
$892$	20.3923	0.682785
$893$	8.78461	0.293966
$894$	−23.0718	−0.771636
$895$	22.9282	0.766405
$896$	15.3731	0.513578
$897$	−35.3205	−1.17932
$898$	−64.5500	−2.15406
$899$	2.73205	0.0911190
$900$	1.00000	0.0333333
$901$	−45.8564	−1.52770
$902$	32.7846	1.09161
$903$	−5.07180	−0.168779
$904$	15.4641	0.514328
$905$	−10.3923	−0.345452
$906$	−12.2487	−0.406936
$907$	17.2679	0.573373	0.286686	−	0.958024i	$-0.407446\pi$
$907$	17.2679	0.573373	0.286686	+	0.958024i	$0.407446\pi$
$908$	−21.3205	−0.707546
$909$	11.4641	0.380240
$910$	10.3923	0.344502
$911$	−2.53590	−0.0840181	−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590	−0.0840181	−0.0420090	+	0.999117i	$0.513376\pi$
$912$	−7.32051	−0.242406
$913$	46.6410	1.54359
$914$	−2.44486	−0.0808689
$915$	10.3923	0.343559
$916$	−22.7846	−0.752825
$917$	−4.14359	−0.136834
$918$	9.46410	0.312362
$919$	−17.4641	−0.576088	−0.288044	−	0.957617i	$-0.593005\pi$
$919$	−17.4641	−0.576088	−0.288044	+	0.957617i	$0.593005\pi$
$920$	12.9282	0.426230
$921$	4.58846	0.151195
$922$	−4.73205	−0.155842
$923$	67.1769	2.21116
$924$	6.92820	0.227921
$925$	−3.26795	−0.107450
$926$	27.2154	0.894353
$927$	6.73205	0.221110
$928$	−14.1962	−0.466012
$929$	−39.8038	−1.30592	−0.652961	−	0.757392i	$-0.726473\pi$
$929$	−39.8038	−1.30592	−0.652961	+	0.757392i	$0.726473\pi$
$930$	1.73205	0.0567962
$931$	7.89488	0.258744
$932$	−2.92820	−0.0959165
$933$	3.66025	0.119831
$934$	−3.46410	−0.113349
$935$	−29.8564	−0.976409
$936$	−8.19615	−0.267900
$937$	−27.8564	−0.910029	−0.455015	−	0.890484i	$-0.650366\pi$
$937$	−27.8564	−0.910029	−0.455015	+	0.890484i	$0.650366\pi$
$938$	0.430781	0.0140655
$939$	4.33975	0.141622
$940$	6.00000	0.195698
$941$	24.5885	0.801561	0.400780	−	0.916174i	$-0.368739\pi$
$941$	24.5885	0.801561	0.400780	+	0.916174i	$0.368739\pi$
$942$	1.60770	0.0523815
$943$	25.8564	0.842000
$944$	9.01924	0.293551
$945$	−1.26795	−0.0412464
$946$	37.8564	1.23082
$947$	−39.1769	−1.27308	−0.636539	−	0.771244i	$-0.719635\pi$
$947$	−39.1769	−1.27308	−0.636539	+	0.771244i	$0.719635\pi$
$948$	10.0000	0.324785
$949$	55.1769	1.79112
$950$	2.53590	0.0822754
$951$	9.07180	0.294173
$952$	−12.0000	−0.388922
$953$	−3.21539	−0.104157	−0.0520784	−	0.998643i	$-0.516585\pi$
$953$	−3.21539	−0.104157	−0.0520784	+	0.998643i	$0.516585\pi$
$954$	14.5359	0.470617
$955$	22.1962	0.718251
$956$	13.8564	0.448148
$957$	14.9282	0.482560
$958$	66.1577	2.13746
$959$	−6.43078	−0.207661
$960$	1.00000	0.0322749
$961$	1.00000	0.0322581
$962$	−26.7846	−0.863570
$963$	11.8564	0.382067
$964$	−3.85641	−0.124206
$965$	−3.85641	−0.124142
$966$	16.3923	0.527414
$967$	−55.3205	−1.77899	−0.889494	−	0.456947i	$-0.848943\pi$
$967$	−55.3205	−1.77899	−0.889494	+	0.456947i	$0.848943\pi$
$968$	32.6603	1.04974
$969$	8.00000	0.256997
$970$	−3.46410	−0.111226
$971$	38.1962	1.22577	0.612886	−	0.790171i	$-0.290008\pi$
$971$	38.1962	1.22577	0.612886	+	0.790171i	$0.290008\pi$
$972$	−1.00000	−0.0320750
$973$	22.6410	0.725838
$974$	−30.2487	−0.969231
$975$	4.73205	0.151547
$976$	−51.9615	−1.66325
$977$	−7.07180	−0.226247	−0.113123	−	0.993581i	$-0.536086\pi$
$977$	−7.07180	−0.226247	−0.113123	+	0.993581i	$0.536086\pi$
$978$	−6.58846	−0.210676
$979$	58.6410	1.87418
$980$	5.39230	0.172251
$981$	−9.46410	−0.302166
$982$	−6.24871	−0.199404
$983$	37.5692	1.19827	0.599136	−	0.800647i	$-0.295511\pi$
$983$	37.5692	1.19827	0.599136	+	0.800647i	$0.295511\pi$
$984$	6.00000	0.191273
$985$	−26.9282	−0.858004
$986$	25.8564	0.823436
$987$	−7.60770	−0.242156
$988$	6.92820	0.220416
$989$	29.8564	0.949378
$990$	9.46410	0.300789
$991$	45.8564	1.45668	0.728338	−	0.685218i	$-0.240293\pi$
$991$	45.8564	1.45668	0.728338	+	0.685218i	$0.240293\pi$
$992$	−5.19615	−0.164978
$993$	−11.0718	−0.351353
$994$	−31.1769	−0.988872
$995$	−3.07180	−0.0973825
$996$	−8.53590	−0.270470
$997$	−50.3923	−1.59594	−0.797970	−	0.602697i	$-0.794093\pi$
$997$	−50.3923	−1.59594	−0.797970	+	0.602697i	$0.794093\pi$
$998$	1.85641	0.0587635
$999$	3.26795	0.103393

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.a.d.1.1	✓	2
3.2	odd	2		1395.2.a.f.1.2		2
4.3	odd	2		7440.2.a.bk.1.1		2
5.2	odd	4		2325.2.c.j.1024.2		4
5.3	odd	4		2325.2.c.j.1024.3		4
5.4	even	2		2325.2.a.m.1.2		2
15.14	odd	2		6975.2.a.v.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.a.d.1.1	✓	2	1.1	even	1	trivial
1395.2.a.f.1.2		2	3.2	odd	2
2325.2.a.m.1.2		2	5.4	even	2
2325.2.c.j.1024.2		4	5.2	odd	4
2325.2.c.j.1024.3		4	5.3	odd	4
6975.2.a.v.1.1		2	15.14	odd	2
7440.2.a.bk.1.1		2	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)

\(f(q)\)	\(=\)	\(q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.26795 q^{7} +1.73205 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.73205 q^{6} -1.26795 q^{7} +1.73205 q^{8} +1.00000 q^{9} +1.73205 q^{10} +5.46410 q^{11} -1.00000 q^{12} -4.73205 q^{13} +2.19615 q^{14} +1.00000 q^{15} -5.00000 q^{16} +5.46410 q^{17} -1.73205 q^{18} -1.46410 q^{19} -1.00000 q^{20} +1.26795 q^{21} -9.46410 q^{22} -7.46410 q^{23} -1.73205 q^{24} +1.00000 q^{25} +8.19615 q^{26} -1.00000 q^{27} -1.26795 q^{28} -2.73205 q^{29} -1.73205 q^{30} -1.00000 q^{31} +5.19615 q^{32} -5.46410 q^{33} -9.46410 q^{34} +1.26795 q^{35} +1.00000 q^{36} -3.26795 q^{37} +2.53590 q^{38} +4.73205 q^{39} -1.73205 q^{40} -3.46410 q^{41} -2.19615 q^{42} -4.00000 q^{43} +5.46410 q^{44} -1.00000 q^{45} +12.9282 q^{46} -6.00000 q^{47} +5.00000 q^{48} -5.39230 q^{49} -1.73205 q^{50} -5.46410 q^{51} -4.73205 q^{52} -8.39230 q^{53} +1.73205 q^{54} -5.46410 q^{55} -2.19615 q^{56} +1.46410 q^{57} +4.73205 q^{58} -1.80385 q^{59} +1.00000 q^{60} +10.3923 q^{61} +1.73205 q^{62} -1.26795 q^{63} +1.00000 q^{64} +4.73205 q^{65} +9.46410 q^{66} +0.196152 q^{67} +5.46410 q^{68} +7.46410 q^{69} -2.19615 q^{70} -14.1962 q^{71} +1.73205 q^{72} -11.6603 q^{73} +5.66025 q^{74} -1.00000 q^{75} -1.46410 q^{76} -6.92820 q^{77} -8.19615 q^{78} -10.0000 q^{79} +5.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} +8.53590 q^{83} +1.26795 q^{84} -5.46410 q^{85} +6.92820 q^{86} +2.73205 q^{87} +9.46410 q^{88} +10.7321 q^{89} +1.73205 q^{90} +6.00000 q^{91} -7.46410 q^{92} +1.00000 q^{93} +10.3923 q^{94} +1.46410 q^{95} -5.19615 q^{96} -2.00000 q^{97} +9.33975 q^{98} +5.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} - 2 q^{5} - 6 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^4 - 2 * q^5 - 6 * q^7 + 2 * q^9	\( 2 q - 2 q^{3} + 2 q^{4} - 2 q^{5} - 6 q^{7} + 2 q^{9} + 4 q^{11} - 2 q^{12} - 6 q^{13} - 6 q^{14} + 2 q^{15} - 10 q^{16} + 4 q^{17} + 4 q^{19} - 2 q^{20} + 6 q^{21} - 12 q^{22} - 8 q^{23} + 2 q^{25} + 6 q^{26} - 2 q^{27} - 6 q^{28} - 2 q^{29} - 2 q^{31} - 4 q^{33} - 12 q^{34} + 6 q^{35} + 2 q^{36} - 10 q^{37} + 12 q^{38} + 6 q^{39} + 6 q^{42} - 8 q^{43} + 4 q^{44} - 2 q^{45} + 12 q^{46} - 12 q^{47} + 10 q^{48} + 10 q^{49} - 4 q^{51} - 6 q^{52} + 4 q^{53} - 4 q^{55} + 6 q^{56} - 4 q^{57} + 6 q^{58} - 14 q^{59} + 2 q^{60} - 6 q^{63} + 2 q^{64} + 6 q^{65} + 12 q^{66} - 10 q^{67} + 4 q^{68} + 8 q^{69} + 6 q^{70} - 18 q^{71} - 6 q^{73} - 6 q^{74} - 2 q^{75} + 4 q^{76} - 6 q^{78} - 20 q^{79} + 10 q^{80} + 2 q^{81} + 12 q^{82} + 24 q^{83} + 6 q^{84} - 4 q^{85} + 2 q^{87} + 12 q^{88} + 18 q^{89} + 12 q^{91} - 8 q^{92} + 2 q^{93} - 4 q^{95} - 4 q^{97} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 - 2 * q^5 - 6 * q^7 + 2 * q^9 + 4 * q^11 - 2 * q^12 - 6 * q^13 - 6 * q^14 + 2 * q^15 - 10 * q^16 + 4 * q^17 + 4 * q^19 - 2 * q^20 + 6 * q^21 - 12 * q^22 - 8 * q^23 + 2 * q^25 + 6 * q^26 - 2 * q^27 - 6 * q^28 - 2 * q^29 - 2 * q^31 - 4 * q^33 - 12 * q^34 + 6 * q^35 + 2 * q^36 - 10 * q^37 + 12 * q^38 + 6 * q^39 + 6 * q^42 - 8 * q^43 + 4 * q^44 - 2 * q^45 + 12 * q^46 - 12 * q^47 + 10 * q^48 + 10 * q^49 - 4 * q^51 - 6 * q^52 + 4 * q^53 - 4 * q^55 + 6 * q^56 - 4 * q^57 + 6 * q^58 - 14 * q^59 + 2 * q^60 - 6 * q^63 + 2 * q^64 + 6 * q^65 + 12 * q^66 - 10 * q^67 + 4 * q^68 + 8 * q^69 + 6 * q^70 - 18 * q^71 - 6 * q^73 - 6 * q^74 - 2 * q^75 + 4 * q^76 - 6 * q^78 - 20 * q^79 + 10 * q^80 + 2 * q^81 + 12 * q^82 + 24 * q^83 + 6 * q^84 - 4 * q^85 + 2 * q^87 + 12 * q^88 + 18 * q^89 + 12 * q^91 - 8 * q^92 + 2 * q^93 - 4 * q^95 - 4 * q^97 + 36 * q^98 + 4 * q^99

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