LMFDB - Embedded newform 483.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.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:	$3.85677441763$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 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			$2.30278$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} -0.697224 q^{5} -2.30278 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} -0.697224 q^{5} -2.30278 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +1.60555 q^{10} -5.00000 q^{11} +3.30278 q^{12} +2.30278 q^{13} +2.30278 q^{14} -0.697224 q^{15} +0.302776 q^{16} -5.60555 q^{17} -2.30278 q^{18} -1.60555 q^{19} -2.30278 q^{20} -1.00000 q^{21} +11.5139 q^{22} +1.00000 q^{23} -3.00000 q^{24} -4.51388 q^{25} -5.30278 q^{26} +1.00000 q^{27} -3.30278 q^{28} +6.21110 q^{29} +1.60555 q^{30} +3.00000 q^{31} +5.30278 q^{32} -5.00000 q^{33} +12.9083 q^{34} +0.697224 q^{35} +3.30278 q^{36} -9.00000 q^{37} +3.69722 q^{38} +2.30278 q^{39} +2.09167 q^{40} -12.2111 q^{41} +2.30278 q^{42} +5.51388 q^{43} -16.5139 q^{44} -0.697224 q^{45} -2.30278 q^{46} -8.60555 q^{47} +0.302776 q^{48} +1.00000 q^{49} +10.3944 q^{50} -5.60555 q^{51} +7.60555 q^{52} -12.5139 q^{53} -2.30278 q^{54} +3.48612 q^{55} +3.00000 q^{56} -1.60555 q^{57} -14.3028 q^{58} +3.90833 q^{59} -2.30278 q^{60} -1.09167 q^{61} -6.90833 q^{62} -1.00000 q^{63} -12.8167 q^{64} -1.60555 q^{65} +11.5139 q^{66} -11.9083 q^{67} -18.5139 q^{68} +1.00000 q^{69} -1.60555 q^{70} +0.908327 q^{71} -3.00000 q^{72} -2.21110 q^{73} +20.7250 q^{74} -4.51388 q^{75} -5.30278 q^{76} +5.00000 q^{77} -5.30278 q^{78} -1.00000 q^{79} -0.211103 q^{80} +1.00000 q^{81} +28.1194 q^{82} +5.60555 q^{83} -3.30278 q^{84} +3.90833 q^{85} -12.6972 q^{86} +6.21110 q^{87} +15.0000 q^{88} +10.9083 q^{89} +1.60555 q^{90} -2.30278 q^{91} +3.30278 q^{92} +3.00000 q^{93} +19.8167 q^{94} +1.11943 q^{95} +5.30278 q^{96} -17.6056 q^{97} -2.30278 q^{98} -5.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} - 10 q^{11} + 3 q^{12} + q^{13} + q^{14} - 5 q^{15} - 3 q^{16} - 4 q^{17} - q^{18} + 4 q^{19} - q^{20} - 2 q^{21} + 5 q^{22} + 2 q^{23} - 6 q^{24} + 9 q^{25} - 7 q^{26} + 2 q^{27} - 3 q^{28} - 2 q^{29} - 4 q^{30} + 6 q^{31} + 7 q^{32} - 10 q^{33} + 15 q^{34} + 5 q^{35} + 3 q^{36} - 18 q^{37} + 11 q^{38} + q^{39} + 15 q^{40} - 10 q^{41} + q^{42} - 7 q^{43} - 15 q^{44} - 5 q^{45} - q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} + 28 q^{50} - 4 q^{51} + 8 q^{52} - 7 q^{53} - q^{54} + 25 q^{55} + 6 q^{56} + 4 q^{57} - 25 q^{58} - 3 q^{59} - q^{60} - 13 q^{61} - 3 q^{62} - 2 q^{63} - 4 q^{64} + 4 q^{65} + 5 q^{66} - 13 q^{67} - 19 q^{68} + 2 q^{69} + 4 q^{70} - 9 q^{71} - 6 q^{72} + 10 q^{73} + 9 q^{74} + 9 q^{75} - 7 q^{76} + 10 q^{77} - 7 q^{78} - 2 q^{79} + 14 q^{80} + 2 q^{81} + 31 q^{82} + 4 q^{83} - 3 q^{84} - 3 q^{85} - 29 q^{86} - 2 q^{87} + 30 q^{88} + 11 q^{89} - 4 q^{90} - q^{91} + 3 q^{92} + 6 q^{93} + 18 q^{94} - 23 q^{95} + 7 q^{96} - 28 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 - 4 * q^10 - 10 * q^11 + 3 * q^12 + q^13 + q^14 - 5 * q^15 - 3 * q^16 - 4 * q^17 - q^18 + 4 * q^19 - q^20 - 2 * q^21 + 5 * q^22 + 2 * q^23 - 6 * q^24 + 9 * q^25 - 7 * q^26 + 2 * q^27 - 3 * q^28 - 2 * q^29 - 4 * q^30 + 6 * q^31 + 7 * q^32 - 10 * q^33 + 15 * q^34 + 5 * q^35 + 3 * q^36 - 18 * q^37 + 11 * q^38 + q^39 + 15 * q^40 - 10 * q^41 + q^42 - 7 * q^43 - 15 * q^44 - 5 * q^45 - q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 + 28 * q^50 - 4 * q^51 + 8 * q^52 - 7 * q^53 - q^54 + 25 * q^55 + 6 * q^56 + 4 * q^57 - 25 * q^58 - 3 * q^59 - q^60 - 13 * q^61 - 3 * q^62 - 2 * q^63 - 4 * q^64 + 4 * q^65 + 5 * q^66 - 13 * q^67 - 19 * q^68 + 2 * q^69 + 4 * q^70 - 9 * q^71 - 6 * q^72 + 10 * q^73 + 9 * q^74 + 9 * q^75 - 7 * q^76 + 10 * q^77 - 7 * q^78 - 2 * q^79 + 14 * q^80 + 2 * q^81 + 31 * q^82 + 4 * q^83 - 3 * q^84 - 3 * q^85 - 29 * q^86 - 2 * q^87 + 30 * q^88 + 11 * q^89 - 4 * q^90 - q^91 + 3 * q^92 + 6 * q^93 + 18 * q^94 - 23 * q^95 + 7 * q^96 - 28 * q^97 - q^98 - 10 * 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 $

$2$	−2.30278	−1.62831	−0.814154	−	0.580649i	$-0.802799\pi$
$2$	−2.30278	−1.62831	−0.814154	+	0.580649i	$0.802799\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.30278	1.65139
$5$	−0.697224	−0.311808	−0.155904	−	0.987772i	$-0.549829\pi$
$5$	−0.697224	−0.311808	−0.155904	+	0.987772i	$0.549829\pi$
$6$	−2.30278	−0.940104
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	1.60555	0.507720
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	3.30278	0.953429
$13$	2.30278	0.638675	0.319338	−	0.947641i	$-0.396540\pi$
$13$	2.30278	0.638675	0.319338	+	0.947641i	$0.396540\pi$
$14$	2.30278	0.615443
$15$	−0.697224	−0.180023
$16$	0.302776	0.0756939
$17$	−5.60555	−1.35955	−0.679773	−	0.733423i	$-0.737922\pi$
$17$	−5.60555	−1.35955	−0.679773	+	0.733423i	$0.737922\pi$
$18$	−2.30278	−0.542769
$19$	−1.60555	−0.368339	−0.184169	−	0.982895i	$-0.558959\pi$
$19$	−1.60555	−0.368339	−0.184169	+	0.982895i	$0.558959\pi$
$20$	−2.30278	−0.514916
$21$	−1.00000	−0.218218
$22$	11.5139	2.45477
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−3.00000	−0.612372
$25$	−4.51388	−0.902776
$26$	−5.30278	−1.03996
$27$	1.00000	0.192450
$28$	−3.30278	−0.624166
$29$	6.21110	1.15337	0.576686	−	0.816966i	$-0.304345\pi$
$29$	6.21110	1.15337	0.576686	+	0.816966i	$0.304345\pi$
$30$	1.60555	0.293132
$31$	3.00000	0.538816	0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000	0.538816	0.269408	+	0.963026i	$0.413172\pi$
$32$	5.30278	0.937407
$33$	−5.00000	−0.870388
$34$	12.9083	2.21376
$35$	0.697224	0.117852
$36$	3.30278	0.550463
$37$	−9.00000	−1.47959	−0.739795	−	0.672832i	$-0.765078\pi$
$37$	−9.00000	−1.47959	−0.739795	+	0.672832i	$0.765078\pi$
$38$	3.69722	0.599769
$39$	2.30278	0.368739
$40$	2.09167	0.330723
$41$	−12.2111	−1.90705	−0.953527	−	0.301308i	$-0.902577\pi$
$41$	−12.2111	−1.90705	−0.953527	+	0.301308i	$0.902577\pi$
$42$	2.30278	0.355326
$43$	5.51388	0.840859	0.420429	−	0.907325i	$-0.361879\pi$
$43$	5.51388	0.840859	0.420429	+	0.907325i	$0.361879\pi$
$44$	−16.5139	−2.48956
$45$	−0.697224	−0.103936
$46$	−2.30278	−0.339526
$47$	−8.60555	−1.25525	−0.627624	−	0.778516i	$-0.715973\pi$
$47$	−8.60555	−1.25525	−0.627624	+	0.778516i	$0.715973\pi$
$48$	0.302776	0.0437019
$49$	1.00000	0.142857
$50$	10.3944	1.47000
$51$	−5.60555	−0.784934
$52$	7.60555	1.05470
$53$	−12.5139	−1.71891	−0.859457	−	0.511209i	$-0.829198\pi$
$53$	−12.5139	−1.71891	−0.859457	+	0.511209i	$0.829198\pi$
$54$	−2.30278	−0.313368
$55$	3.48612	0.470069
$56$	3.00000	0.400892
$57$	−1.60555	−0.212660
$58$	−14.3028	−1.87805
$59$	3.90833	0.508821	0.254410	−	0.967096i	$-0.418119\pi$
$59$	3.90833	0.508821	0.254410	+	0.967096i	$0.418119\pi$
$60$	−2.30278	−0.297287
$61$	−1.09167	−0.139774	−0.0698872	−	0.997555i	$-0.522264\pi$
$61$	−1.09167	−0.139774	−0.0698872	+	0.997555i	$0.522264\pi$
$62$	−6.90833	−0.877358
$63$	−1.00000	−0.125988
$64$	−12.8167	−1.60208
$65$	−1.60555	−0.199144
$66$	11.5139	1.41726
$67$	−11.9083	−1.45483	−0.727417	−	0.686196i	$-0.759279\pi$
$67$	−11.9083	−1.45483	−0.727417	+	0.686196i	$0.759279\pi$
$68$	−18.5139	−2.24514
$69$	1.00000	0.120386
$70$	−1.60555	−0.191900
$71$	0.908327	0.107799	0.0538993	−	0.998546i	$-0.482835\pi$
$71$	0.908327	0.107799	0.0538993	+	0.998546i	$0.482835\pi$
$72$	−3.00000	−0.353553
$73$	−2.21110	−0.258790	−0.129395	−	0.991593i	$-0.541304\pi$
$73$	−2.21110	−0.258790	−0.129395	+	0.991593i	$0.541304\pi$
$74$	20.7250	2.40923
$75$	−4.51388	−0.521218
$76$	−5.30278	−0.608270
$77$	5.00000	0.569803
$78$	−5.30278	−0.600421
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	−0.211103	−0.0236020
$81$	1.00000	0.111111
$82$	28.1194	3.10527
$83$	5.60555	0.615289	0.307645	−	0.951501i	$-0.400459\pi$
$83$	5.60555	0.615289	0.307645	+	0.951501i	$0.400459\pi$
$84$	−3.30278	−0.360362
$85$	3.90833	0.423918
$86$	−12.6972	−1.36918
$87$	6.21110	0.665900
$88$	15.0000	1.59901
$89$	10.9083	1.15628	0.578140	−	0.815937i	$-0.303779\pi$
$89$	10.9083	1.15628	0.578140	+	0.815937i	$0.303779\pi$
$90$	1.60555	0.169240
$91$	−2.30278	−0.241396
$92$	3.30278	0.344338
$93$	3.00000	0.311086
$94$	19.8167	2.04393
$95$	1.11943	0.114851
$96$	5.30278	0.541212
$97$	−17.6056	−1.78757	−0.893786	−	0.448493i	$-0.851961\pi$
$97$	−17.6056	−1.78757	−0.893786	+	0.448493i	$0.851961\pi$
$98$	−2.30278	−0.232615
$99$	−5.00000	−0.502519
$100$	−14.9083	−1.49083
$101$	9.30278	0.925661	0.462830	−	0.886447i	$-0.346834\pi$
$101$	9.30278	0.925661	0.462830	+	0.886447i	$0.346834\pi$
$102$	12.9083	1.27811
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−6.90833	−0.677417
$105$	0.697224	0.0680421
$106$	28.8167	2.79892
$107$	7.51388	0.726394	0.363197	−	0.931712i	$-0.381685\pi$
$107$	7.51388	0.726394	0.363197	+	0.931712i	$0.381685\pi$
$108$	3.30278	0.317810
$109$	−3.90833	−0.374350	−0.187175	−	0.982327i	$-0.559933\pi$
$109$	−3.90833	−0.374350	−0.187175	+	0.982327i	$0.559933\pi$
$110$	−8.02776	−0.765417
$111$	−9.00000	−0.854242
$112$	−0.302776	−0.0286096
$113$	5.30278	0.498843	0.249422	−	0.968395i	$-0.419760\pi$
$113$	5.30278	0.498843	0.249422	+	0.968395i	$0.419760\pi$
$114$	3.69722	0.346277
$115$	−0.697224	−0.0650165
$116$	20.5139	1.90467
$117$	2.30278	0.212892
$118$	−9.00000	−0.828517
$119$	5.60555	0.513860
$120$	2.09167	0.190943
$121$	14.0000	1.27273
$122$	2.51388	0.227596
$123$	−12.2111	−1.10104
$124$	9.90833	0.889794
$125$	6.63331	0.593301
$126$	2.30278	0.205148
$127$	1.69722	0.150604	0.0753022	−	0.997161i	$-0.476008\pi$
$127$	1.69722	0.150604	0.0753022	+	0.997161i	$0.476008\pi$
$128$	18.9083	1.67128
$129$	5.51388	0.485470
$130$	3.69722	0.324268
$131$	10.3944	0.908167	0.454084	−	0.890959i	$-0.349967\pi$
$131$	10.3944	0.908167	0.454084	+	0.890959i	$0.349967\pi$
$132$	−16.5139	−1.43735
$133$	1.60555	0.139219
$134$	27.4222	2.36892
$135$	−0.697224	−0.0600075
$136$	16.8167	1.44202
$137$	16.8167	1.43674	0.718372	−	0.695659i	$-0.244888\pi$
$137$	16.8167	1.43674	0.718372	+	0.695659i	$0.244888\pi$
$138$	−2.30278	−0.196025
$139$	15.9083	1.34933	0.674663	−	0.738126i	$-0.264289\pi$
$139$	15.9083	1.34933	0.674663	+	0.738126i	$0.264289\pi$
$140$	2.30278	0.194620
$141$	−8.60555	−0.724718
$142$	−2.09167	−0.175529
$143$	−11.5139	−0.962839
$144$	0.302776	0.0252313
$145$	−4.33053	−0.359631
$146$	5.09167	0.421390
$147$	1.00000	0.0824786
$148$	−29.7250	−2.44338
$149$	8.60555	0.704994	0.352497	−	0.935813i	$-0.385333\pi$
$149$	8.60555	0.704994	0.352497	+	0.935813i	$0.385333\pi$
$150$	10.3944	0.848703
$151$	16.6056	1.35134	0.675670	−	0.737204i	$-0.263854\pi$
$151$	16.6056	1.35134	0.675670	+	0.737204i	$0.263854\pi$
$152$	4.81665	0.390682
$153$	−5.60555	−0.453182
$154$	−11.5139	−0.927815
$155$	−2.09167	−0.168007
$156$	7.60555	0.608931
$157$	−3.81665	−0.304602	−0.152301	−	0.988334i	$-0.548668\pi$
$157$	−3.81665	−0.304602	−0.152301	+	0.988334i	$0.548668\pi$
$158$	2.30278	0.183199
$159$	−12.5139	−0.992415
$160$	−3.69722	−0.292291
$161$	−1.00000	−0.0788110
$162$	−2.30278	−0.180923
$163$	−13.7250	−1.07502	−0.537512	−	0.843256i	$-0.680636\pi$
$163$	−13.7250	−1.07502	−0.537512	+	0.843256i	$0.680636\pi$
$164$	−40.3305	−3.14929
$165$	3.48612	0.271394
$166$	−12.9083	−1.00188
$167$	2.81665	0.217959	0.108980	−	0.994044i	$-0.465242\pi$
$167$	2.81665	0.217959	0.108980	+	0.994044i	$0.465242\pi$
$168$	3.00000	0.231455
$169$	−7.69722	−0.592094
$170$	−9.00000	−0.690268
$171$	−1.60555	−0.122780
$172$	18.2111	1.38858
$173$	−18.2111	−1.38456	−0.692282	−	0.721627i	$-0.743395\pi$
$173$	−18.2111	−1.38456	−0.692282	+	0.721627i	$0.743395\pi$
$174$	−14.3028	−1.08429
$175$	4.51388	0.341217
$176$	−1.51388	−0.114113
$177$	3.90833	0.293768
$178$	−25.1194	−1.88278
$179$	−2.69722	−0.201600	−0.100800	−	0.994907i	$-0.532140\pi$
$179$	−2.69722	−0.201600	−0.100800	+	0.994907i	$0.532140\pi$
$180$	−2.30278	−0.171639
$181$	−6.81665	−0.506678	−0.253339	−	0.967378i	$-0.581529\pi$
$181$	−6.81665	−0.506678	−0.253339	+	0.967378i	$0.581529\pi$
$182$	5.30278	0.393068
$183$	−1.09167	−0.0806988
$184$	−3.00000	−0.221163
$185$	6.27502	0.461349
$186$	−6.90833	−0.506543
$187$	28.0278	2.04959
$188$	−28.4222	−2.07290
$189$	−1.00000	−0.0727393
$190$	−2.57779	−0.187013
$191$	−4.60555	−0.333246	−0.166623	−	0.986021i	$-0.553286\pi$
$191$	−4.60555	−0.333246	−0.166623	+	0.986021i	$0.553286\pi$
$192$	−12.8167	−0.924962
$193$	9.02776	0.649832	0.324916	−	0.945743i	$-0.394664\pi$
$193$	9.02776	0.649832	0.324916	+	0.945743i	$0.394664\pi$
$194$	40.5416	2.91072
$195$	−1.60555	−0.114976
$196$	3.30278	0.235913
$197$	−7.09167	−0.505261	−0.252630	−	0.967563i	$-0.581296\pi$
$197$	−7.09167	−0.505261	−0.252630	+	0.967563i	$0.581296\pi$
$198$	11.5139	0.818256
$199$	12.5139	0.887085	0.443543	−	0.896253i	$-0.353721\pi$
$199$	12.5139	0.887085	0.443543	+	0.896253i	$0.353721\pi$
$200$	13.5416	0.957538
$201$	−11.9083	−0.839949
$202$	−21.4222	−1.50726
$203$	−6.21110	−0.435934
$204$	−18.5139	−1.29623
$205$	8.51388	0.594635
$206$	9.21110	0.641768
$207$	1.00000	0.0695048
$208$	0.697224	0.0483438
$209$	8.02776	0.555292
$210$	−1.60555	−0.110794
$211$	−27.4222	−1.88782	−0.943911	−	0.330199i	$-0.892884\pi$
$211$	−27.4222	−1.88782	−0.943911	+	0.330199i	$0.892884\pi$
$212$	−41.3305	−2.83859
$213$	0.908327	0.0622375
$214$	−17.3028	−1.18279
$215$	−3.84441	−0.262187
$216$	−3.00000	−0.204124
$217$	−3.00000	−0.203653
$218$	9.00000	0.609557
$219$	−2.21110	−0.149412
$220$	11.5139	0.776266
$221$	−12.9083	−0.868308
$222$	20.7250	1.39097
$223$	19.9083	1.33316	0.666580	−	0.745433i	$-0.267757\pi$
$223$	19.9083	1.33316	0.666580	+	0.745433i	$0.267757\pi$
$224$	−5.30278	−0.354307
$225$	−4.51388	−0.300925
$226$	−12.2111	−0.812270
$227$	−20.3305	−1.34938	−0.674692	−	0.738099i	$-0.735724\pi$
$227$	−20.3305	−1.34938	−0.674692	+	0.738099i	$0.735724\pi$
$228$	−5.30278	−0.351185
$229$	2.51388	0.166122	0.0830609	−	0.996544i	$-0.473530\pi$
$229$	2.51388	0.166122	0.0830609	+	0.996544i	$0.473530\pi$
$230$	1.60555	0.105867
$231$	5.00000	0.328976
$232$	−18.6333	−1.22334
$233$	−14.3305	−0.938824	−0.469412	−	0.882979i	$-0.655534\pi$
$233$	−14.3305	−0.938824	−0.469412	+	0.882979i	$0.655534\pi$
$234$	−5.30278	−0.346653
$235$	6.00000	0.391397
$236$	12.9083	0.840261
$237$	−1.00000	−0.0649570
$238$	−12.9083	−0.836723
$239$	−14.0917	−0.911515	−0.455757	−	0.890104i	$-0.650631\pi$
$239$	−14.0917	−0.911515	−0.455757	+	0.890104i	$0.650631\pi$
$240$	−0.211103	−0.0136266
$241$	12.0278	0.774776	0.387388	−	0.921917i	$-0.373377\pi$
$241$	12.0278	0.774776	0.387388	+	0.921917i	$0.373377\pi$
$242$	−32.2389	−2.07239
$243$	1.00000	0.0641500
$244$	−3.60555	−0.230822
$245$	−0.697224	−0.0445440
$246$	28.1194	1.79283
$247$	−3.69722	−0.235249
$248$	−9.00000	−0.571501
$249$	5.60555	0.355237
$250$	−15.2750	−0.966077
$251$	23.8167	1.50329	0.751647	−	0.659566i	$-0.229260\pi$
$251$	23.8167	1.50329	0.751647	+	0.659566i	$0.229260\pi$
$252$	−3.30278	−0.208055
$253$	−5.00000	−0.314347
$254$	−3.90833	−0.245230
$255$	3.90833	0.244749
$256$	−17.9083	−1.11927
$257$	27.0278	1.68595	0.842973	−	0.537957i	$-0.180804\pi$
$257$	27.0278	1.68595	0.842973	+	0.537957i	$0.180804\pi$
$258$	−12.6972	−0.790495
$259$	9.00000	0.559233
$260$	−5.30278	−0.328864
$261$	6.21110	0.384458
$262$	−23.9361	−1.47878
$263$	10.3944	0.640949	0.320475	−	0.947257i	$-0.396158\pi$
$263$	10.3944	0.640949	0.320475	+	0.947257i	$0.396158\pi$
$264$	15.0000	0.923186
$265$	8.72498	0.535971
$266$	−3.69722	−0.226691
$267$	10.9083	0.667579
$268$	−39.3305	−2.40249
$269$	0.908327	0.0553817	0.0276908	−	0.999617i	$-0.491185\pi$
$269$	0.908327	0.0553817	0.0276908	+	0.999617i	$0.491185\pi$
$270$	1.60555	0.0977107
$271$	3.60555	0.219022	0.109511	−	0.993986i	$-0.465072\pi$
$271$	3.60555	0.219022	0.109511	+	0.993986i	$0.465072\pi$
$272$	−1.69722	−0.102909
$273$	−2.30278	−0.139370
$274$	−38.7250	−2.33946
$275$	22.5694	1.36099
$276$	3.30278	0.198804
$277$	−12.3028	−0.739202	−0.369601	−	0.929191i	$-0.620506\pi$
$277$	−12.3028	−0.739202	−0.369601	+	0.929191i	$0.620506\pi$
$278$	−36.6333	−2.19712
$279$	3.00000	0.179605
$280$	−2.09167	−0.125001
$281$	27.8167	1.65940	0.829701	−	0.558208i	$-0.188511\pi$
$281$	27.8167	1.65940	0.829701	+	0.558208i	$0.188511\pi$
$282$	19.8167	1.18006
$283$	17.3028	1.02854	0.514272	−	0.857627i	$-0.328062\pi$
$283$	17.3028	1.02854	0.514272	+	0.857627i	$0.328062\pi$
$284$	3.00000	0.178017
$285$	1.11943	0.0663093
$286$	26.5139	1.56780
$287$	12.2111	0.720799
$288$	5.30278	0.312469
$289$	14.4222	0.848365
$290$	9.97224	0.585590
$291$	−17.6056	−1.03206
$292$	−7.30278	−0.427363
$293$	−24.8444	−1.45143	−0.725713	−	0.687998i	$-0.758490\pi$
$293$	−24.8444	−1.45143	−0.725713	+	0.687998i	$0.758490\pi$
$294$	−2.30278	−0.134301
$295$	−2.72498	−0.158655
$296$	27.0000	1.56934
$297$	−5.00000	−0.290129
$298$	−19.8167	−1.14795
$299$	2.30278	0.133173
$300$	−14.9083	−0.860733
$301$	−5.51388	−0.317815
$302$	−38.2389	−2.20040
$303$	9.30278	0.534430
$304$	−0.486122	−0.0278810
$305$	0.761141	0.0435828
$306$	12.9083	0.737920
$307$	18.2111	1.03936	0.519681	−	0.854360i	$-0.326051\pi$
$307$	18.2111	1.03936	0.519681	+	0.854360i	$0.326051\pi$
$308$	16.5139	0.940966
$309$	−4.00000	−0.227552
$310$	4.81665	0.273568
$311$	−9.51388	−0.539483	−0.269741	−	0.962933i	$-0.586938\pi$
$311$	−9.51388	−0.539483	−0.269741	+	0.962933i	$0.586938\pi$
$312$	−6.90833	−0.391107
$313$	1.21110	0.0684556	0.0342278	−	0.999414i	$-0.489103\pi$
$313$	1.21110	0.0684556	0.0342278	+	0.999414i	$0.489103\pi$
$314$	8.78890	0.495986
$315$	0.697224	0.0392841
$316$	−3.30278	−0.185796
$317$	−30.5139	−1.71383	−0.856915	−	0.515458i	$-0.827622\pi$
$317$	−30.5139	−1.71383	−0.856915	+	0.515458i	$0.827622\pi$
$318$	28.8167	1.61596
$319$	−31.0555	−1.73877
$320$	8.93608	0.499542
$321$	7.51388	0.419384
$322$	2.30278	0.128329
$323$	9.00000	0.500773
$324$	3.30278	0.183488
$325$	−10.3944	−0.576580
$326$	31.6056	1.75047
$327$	−3.90833	−0.216131
$328$	36.6333	2.02274
$329$	8.60555	0.474439
$330$	−8.02776	−0.441913
$331$	17.6333	0.969214	0.484607	−	0.874732i	$-0.338963\pi$
$331$	17.6333	0.969214	0.484607	+	0.874732i	$0.338963\pi$
$332$	18.5139	1.01608
$333$	−9.00000	−0.493197
$334$	−6.48612	−0.354905
$335$	8.30278	0.453629
$336$	−0.302776	−0.0165178
$337$	−15.6972	−0.855082	−0.427541	−	0.903996i	$-0.640620\pi$
$337$	−15.6972	−0.855082	−0.427541	+	0.903996i	$0.640620\pi$
$338$	17.7250	0.964112
$339$	5.30278	0.288007
$340$	12.9083	0.700052
$341$	−15.0000	−0.812296
$342$	3.69722	0.199923
$343$	−1.00000	−0.0539949
$344$	−16.5416	−0.891865
$345$	−0.697224	−0.0375373
$346$	41.9361	2.25450
$347$	14.6333	0.785557	0.392779	−	0.919633i	$-0.371514\pi$
$347$	14.6333	0.785557	0.392779	+	0.919633i	$0.371514\pi$
$348$	20.5139	1.09966
$349$	−10.0917	−0.540195	−0.270097	−	0.962833i	$-0.587056\pi$
$349$	−10.0917	−0.540195	−0.270097	+	0.962833i	$0.587056\pi$
$350$	−10.3944	−0.555607
$351$	2.30278	0.122913
$352$	−26.5139	−1.41319
$353$	−11.0000	−0.585471	−0.292735	−	0.956193i	$-0.594566\pi$
$353$	−11.0000	−0.585471	−0.292735	+	0.956193i	$0.594566\pi$
$354$	−9.00000	−0.478345
$355$	−0.633308	−0.0336125
$356$	36.0278	1.90947
$357$	5.60555	0.296677
$358$	6.21110	0.328267
$359$	−35.5416	−1.87582	−0.937908	−	0.346884i	$-0.887240\pi$
$359$	−35.5416	−1.87582	−0.937908	+	0.346884i	$0.887240\pi$
$360$	2.09167	0.110241
$361$	−16.4222	−0.864327
$362$	15.6972	0.825028
$363$	14.0000	0.734809
$364$	−7.60555	−0.398639
$365$	1.54163	0.0806928
$366$	2.51388	0.131403
$367$	21.5139	1.12302	0.561508	−	0.827472i	$-0.310222\pi$
$367$	21.5139	1.12302	0.561508	+	0.827472i	$0.310222\pi$
$368$	0.302776	0.0157833
$369$	−12.2111	−0.635685
$370$	−14.4500	−0.751218
$371$	12.5139	0.649688
$372$	9.90833	0.513723
$373$	16.2111	0.839379	0.419690	−	0.907668i	$-0.362139\pi$
$373$	16.2111	0.839379	0.419690	+	0.907668i	$0.362139\pi$
$374$	−64.5416	−3.33737
$375$	6.63331	0.342543
$376$	25.8167	1.33139
$377$	14.3028	0.736630
$378$	2.30278	0.118442
$379$	−22.4222	−1.15175	−0.575876	−	0.817537i	$-0.695339\pi$
$379$	−22.4222	−1.15175	−0.575876	+	0.817537i	$0.695339\pi$
$380$	3.69722	0.189664
$381$	1.69722	0.0869514
$382$	10.6056	0.542627
$383$	4.81665	0.246120	0.123060	−	0.992399i	$-0.460729\pi$
$383$	4.81665	0.246120	0.123060	+	0.992399i	$0.460729\pi$
$384$	18.9083	0.964912
$385$	−3.48612	−0.177669
$386$	−20.7889	−1.05813
$387$	5.51388	0.280286
$388$	−58.1472	−2.95198
$389$	−36.6333	−1.85738	−0.928691	−	0.370854i	$-0.879065\pi$
$389$	−36.6333	−1.85738	−0.928691	+	0.370854i	$0.879065\pi$
$390$	3.69722	0.187216
$391$	−5.60555	−0.283485
$392$	−3.00000	−0.151523
$393$	10.3944	0.524331
$394$	16.3305	0.822720
$395$	0.697224	0.0350812
$396$	−16.5139	−0.829854
$397$	−27.3944	−1.37489	−0.687444	−	0.726237i	$-0.741267\pi$
$397$	−27.3944	−1.37489	−0.687444	+	0.726237i	$0.741267\pi$
$398$	−28.8167	−1.44445
$399$	1.60555	0.0803781
$400$	−1.36669	−0.0683346
$401$	−13.4222	−0.670273	−0.335136	−	0.942170i	$-0.608782\pi$
$401$	−13.4222	−0.670273	−0.335136	+	0.942170i	$0.608782\pi$
$402$	27.4222	1.36770
$403$	6.90833	0.344128
$404$	30.7250	1.52862
$405$	−0.697224	−0.0346454
$406$	14.3028	0.709835
$407$	45.0000	2.23057
$408$	16.8167	0.832548
$409$	24.0278	1.18810	0.594048	−	0.804430i	$-0.297529\pi$
$409$	24.0278	1.18810	0.594048	+	0.804430i	$0.297529\pi$
$410$	−19.6056	−0.968249
$411$	16.8167	0.829504
$412$	−13.2111	−0.650864
$413$	−3.90833	−0.192316
$414$	−2.30278	−0.113175
$415$	−3.90833	−0.191852
$416$	12.2111	0.598699
$417$	15.9083	0.779034
$418$	−18.4861	−0.904186
$419$	15.1194	0.738632	0.369316	−	0.929304i	$-0.379592\pi$
$419$	15.1194	0.738632	0.369316	+	0.929304i	$0.379592\pi$
$420$	2.30278	0.112364
$421$	9.69722	0.472614	0.236307	−	0.971678i	$-0.424063\pi$
$421$	9.69722	0.472614	0.236307	+	0.971678i	$0.424063\pi$
$422$	63.1472	3.07396
$423$	−8.60555	−0.418416
$424$	37.5416	1.82318
$425$	25.3028	1.22736
$426$	−2.09167	−0.101342
$427$	1.09167	0.0528298
$428$	24.8167	1.19956
$429$	−11.5139	−0.555895
$430$	8.85281	0.426921
$431$	−8.72498	−0.420268	−0.210134	−	0.977673i	$-0.567390\pi$
$431$	−8.72498	−0.420268	−0.210134	+	0.977673i	$0.567390\pi$
$432$	0.302776	0.0145673
$433$	−21.0278	−1.01053	−0.505265	−	0.862964i	$-0.668605\pi$
$433$	−21.0278	−1.01053	−0.505265	+	0.862964i	$0.668605\pi$
$434$	6.90833	0.331610
$435$	−4.33053	−0.207633
$436$	−12.9083	−0.618197
$437$	−1.60555	−0.0768039
$438$	5.09167	0.243290
$439$	20.2111	0.964623	0.482312	−	0.876000i	$-0.339797\pi$
$439$	20.2111	0.964623	0.482312	+	0.876000i	$0.339797\pi$
$440$	−10.4584	−0.498583
$441$	1.00000	0.0476190
$442$	29.7250	1.41387
$443$	−32.8444	−1.56049	−0.780243	−	0.625477i	$-0.784904\pi$
$443$	−32.8444	−1.56049	−0.780243	+	0.625477i	$0.784904\pi$
$444$	−29.7250	−1.41069
$445$	−7.60555	−0.360538
$446$	−45.8444	−2.17080
$447$	8.60555	0.407029
$448$	12.8167	0.605530
$449$	−35.7250	−1.68597	−0.842983	−	0.537940i	$-0.819203\pi$
$449$	−35.7250	−1.68597	−0.842983	+	0.537940i	$0.819203\pi$
$450$	10.3944	0.489999
$451$	61.0555	2.87499
$452$	17.5139	0.823784
$453$	16.6056	0.780197
$454$	46.8167	2.19721
$455$	1.60555	0.0752694
$456$	4.81665	0.225560
$457$	−10.8806	−0.508972	−0.254486	−	0.967077i	$-0.581906\pi$
$457$	−10.8806	−0.508972	−0.254486	+	0.967077i	$0.581906\pi$
$458$	−5.78890	−0.270497
$459$	−5.60555	−0.261645
$460$	−2.30278	−0.107367
$461$	7.72498	0.359788	0.179894	−	0.983686i	$-0.442424\pi$
$461$	7.72498	0.359788	0.179894	+	0.983686i	$0.442424\pi$
$462$	−11.5139	−0.535674
$463$	−18.8167	−0.874484	−0.437242	−	0.899344i	$-0.644045\pi$
$463$	−18.8167	−0.874484	−0.437242	+	0.899344i	$0.644045\pi$
$464$	1.88057	0.0873033
$465$	−2.09167	−0.0969990
$466$	33.0000	1.52870
$467$	23.6056	1.09233	0.546167	−	0.837676i	$-0.316086\pi$
$467$	23.6056	1.09233	0.546167	+	0.837676i	$0.316086\pi$
$468$	7.60555	0.351567
$469$	11.9083	0.549875
$470$	−13.8167	−0.637315
$471$	−3.81665	−0.175862
$472$	−11.7250	−0.539686
$473$	−27.5694	−1.26764
$474$	2.30278	0.105770
$475$	7.24726	0.332527
$476$	18.5139	0.848582
$477$	−12.5139	−0.572971
$478$	32.4500	1.48423
$479$	−18.2111	−0.832087	−0.416043	−	0.909345i	$-0.636584\pi$
$479$	−18.2111	−0.832087	−0.416043	+	0.909345i	$0.636584\pi$
$480$	−3.69722	−0.168754
$481$	−20.7250	−0.944978
$482$	−27.6972	−1.26157
$483$	−1.00000	−0.0455016
$484$	46.2389	2.10177
$485$	12.2750	0.557380
$486$	−2.30278	−0.104456
$487$	−0.816654	−0.0370061	−0.0185031	−	0.999829i	$-0.505890\pi$
$487$	−0.816654	−0.0370061	−0.0185031	+	0.999829i	$0.505890\pi$
$488$	3.27502	0.148253
$489$	−13.7250	−0.620665
$490$	1.60555	0.0725314
$491$	−17.9361	−0.809444	−0.404722	−	0.914440i	$-0.632632\pi$
$491$	−17.9361	−0.809444	−0.404722	+	0.914440i	$0.632632\pi$
$492$	−40.3305	−1.81824
$493$	−34.8167	−1.56806
$494$	8.51388	0.383057
$495$	3.48612	0.156690
$496$	0.908327	0.0407851
$497$	−0.908327	−0.0407440
$498$	−12.9083	−0.578436
$499$	31.9083	1.42841	0.714206	−	0.699935i	$-0.246788\pi$
$499$	31.9083	1.42841	0.714206	+	0.699935i	$0.246788\pi$
$500$	21.9083	0.979770
$501$	2.81665	0.125839
$502$	−54.8444	−2.44783
$503$	17.7250	0.790318	0.395159	−	0.918613i	$-0.370690\pi$
$503$	17.7250	0.790318	0.395159	+	0.918613i	$0.370690\pi$
$504$	3.00000	0.133631
$505$	−6.48612	−0.288629
$506$	11.5139	0.511854
$507$	−7.69722	−0.341846
$508$	5.60555	0.248706
$509$	−33.4500	−1.48264	−0.741322	−	0.671150i	$-0.765801\pi$
$509$	−33.4500	−1.48264	−0.741322	+	0.671150i	$0.765801\pi$
$510$	−9.00000	−0.398527
$511$	2.21110	0.0978134
$512$	3.42221	0.151242
$513$	−1.60555	−0.0708868
$514$	−62.2389	−2.74524
$515$	2.78890	0.122894
$516$	18.2111	0.801699
$517$	43.0278	1.89236
$518$	−20.7250	−0.910603
$519$	−18.2111	−0.799379
$520$	4.81665	0.211224
$521$	21.6333	0.947772	0.473886	−	0.880586i	$-0.342851\pi$
$521$	21.6333	0.947772	0.473886	+	0.880586i	$0.342851\pi$
$522$	−14.3028	−0.626015
$523$	−0.422205	−0.0184617	−0.00923087	−	0.999957i	$-0.502938\pi$
$523$	−0.422205	−0.0184617	−0.00923087	+	0.999957i	$0.502938\pi$
$524$	34.3305	1.49974
$525$	4.51388	0.197002
$526$	−23.9361	−1.04366
$527$	−16.8167	−0.732545
$528$	−1.51388	−0.0658831
$529$	1.00000	0.0434783
$530$	−20.0917	−0.872727
$531$	3.90833	0.169607
$532$	5.30278	0.229904
$533$	−28.1194	−1.21799
$534$	−25.1194	−1.08702
$535$	−5.23886	−0.226496
$536$	35.7250	1.54308
$537$	−2.69722	−0.116394
$538$	−2.09167	−0.0901784
$539$	−5.00000	−0.215365
$540$	−2.30278	−0.0990957
$541$	−5.81665	−0.250077	−0.125039	−	0.992152i	$-0.539906\pi$
$541$	−5.81665	−0.250077	−0.125039	+	0.992152i	$0.539906\pi$
$542$	−8.30278	−0.356635
$543$	−6.81665	−0.292531
$544$	−29.7250	−1.27445
$545$	2.72498	0.116725
$546$	5.30278	0.226938
$547$	−7.72498	−0.330296	−0.165148	−	0.986269i	$-0.552810\pi$
$547$	−7.72498	−0.330296	−0.165148	+	0.986269i	$0.552810\pi$
$548$	55.5416	2.37262
$549$	−1.09167	−0.0465915
$550$	−51.9722	−2.21610
$551$	−9.97224	−0.424832
$552$	−3.00000	−0.127688
$553$	1.00000	0.0425243
$554$	28.3305	1.20365
$555$	6.27502	0.266360
$556$	52.5416	2.22826
$557$	5.02776	0.213033	0.106516	−	0.994311i	$-0.466030\pi$
$557$	5.02776	0.213033	0.106516	+	0.994311i	$0.466030\pi$
$558$	−6.90833	−0.292453
$559$	12.6972	0.537035
$560$	0.211103	0.00892071
$561$	28.0278	1.18333
$562$	−64.0555	−2.70202
$563$	−43.3305	−1.82616	−0.913082	−	0.407776i	$-0.866305\pi$
$563$	−43.3305	−1.82616	−0.913082	+	0.407776i	$0.866305\pi$
$564$	−28.4222	−1.19679
$565$	−3.69722	−0.155543
$566$	−39.8444	−1.67479
$567$	−1.00000	−0.0419961
$568$	−2.72498	−0.114338
$569$	10.7889	0.452294	0.226147	−	0.974093i	$-0.427387\pi$
$569$	10.7889	0.452294	0.226147	+	0.974093i	$0.427387\pi$
$570$	−2.57779	−0.107972
$571$	10.2111	0.427321	0.213661	−	0.976908i	$-0.431461\pi$
$571$	10.2111	0.427321	0.213661	+	0.976908i	$0.431461\pi$
$572$	−38.0278	−1.59002
$573$	−4.60555	−0.192400
$574$	−28.1194	−1.17368
$575$	−4.51388	−0.188242
$576$	−12.8167	−0.534027
$577$	−36.4222	−1.51628	−0.758138	−	0.652094i	$-0.773891\pi$
$577$	−36.4222	−1.51628	−0.758138	+	0.652094i	$0.773891\pi$
$578$	−33.2111	−1.38140
$579$	9.02776	0.375181
$580$	−14.3028	−0.593890
$581$	−5.60555	−0.232557
$582$	40.5416	1.68050
$583$	62.5694	2.59136
$584$	6.63331	0.274488
$585$	−1.60555	−0.0663814
$586$	57.2111	2.36337
$587$	−39.1472	−1.61578	−0.807889	−	0.589335i	$-0.799390\pi$
$587$	−39.1472	−1.61578	−0.807889	+	0.589335i	$0.799390\pi$
$588$	3.30278	0.136204
$589$	−4.81665	−0.198467
$590$	6.27502	0.258338
$591$	−7.09167	−0.291712
$592$	−2.72498	−0.111996
$593$	37.0278	1.52055	0.760274	−	0.649603i	$-0.225065\pi$
$593$	37.0278	1.52055	0.760274	+	0.649603i	$0.225065\pi$
$594$	11.5139	0.472420
$595$	−3.90833	−0.160226
$596$	28.4222	1.16422
$597$	12.5139	0.512159
$598$	−5.30278	−0.216847
$599$	−39.5139	−1.61449	−0.807247	−	0.590214i	$-0.799043\pi$
$599$	−39.5139	−1.61449	−0.807247	+	0.590214i	$0.799043\pi$
$600$	13.5416	0.552835
$601$	40.9361	1.66982	0.834909	−	0.550388i	$-0.185520\pi$
$601$	40.9361	1.66982	0.834909	+	0.550388i	$0.185520\pi$
$602$	12.6972	0.517500
$603$	−11.9083	−0.484945
$604$	54.8444	2.23159
$605$	−9.76114	−0.396847
$606$	−21.4222	−0.870218
$607$	−24.4861	−0.993861	−0.496931	−	0.867790i	$-0.665540\pi$
$607$	−24.4861	−0.993861	−0.496931	+	0.867790i	$0.665540\pi$
$608$	−8.51388	−0.345283
$609$	−6.21110	−0.251687
$610$	−1.75274	−0.0709663
$611$	−19.8167	−0.801696
$612$	−18.5139	−0.748379
$613$	2.81665	0.113764	0.0568818	−	0.998381i	$-0.481884\pi$
$613$	2.81665	0.113764	0.0568818	+	0.998381i	$0.481884\pi$
$614$	−41.9361	−1.69240
$615$	8.51388	0.343313
$616$	−15.0000	−0.604367
$617$	14.7250	0.592805	0.296403	−	0.955063i	$-0.404213\pi$
$617$	14.7250	0.592805	0.296403	+	0.955063i	$0.404213\pi$
$618$	9.21110	0.370525
$619$	9.88057	0.397134	0.198567	−	0.980087i	$-0.436371\pi$
$619$	9.88057	0.397134	0.198567	+	0.980087i	$0.436371\pi$
$620$	−6.90833	−0.277445
$621$	1.00000	0.0401286
$622$	21.9083	0.878444
$623$	−10.9083	−0.437033
$624$	0.697224	0.0279113
$625$	17.9445	0.717779
$626$	−2.78890	−0.111467
$627$	8.02776	0.320598
$628$	−12.6056	−0.503016
$629$	50.4500	2.01157
$630$	−1.60555	−0.0639667
$631$	−11.9722	−0.476607	−0.238304	−	0.971191i	$-0.576591\pi$
$631$	−11.9722	−0.476607	−0.238304	+	0.971191i	$0.576591\pi$
$632$	3.00000	0.119334
$633$	−27.4222	−1.08993
$634$	70.2666	2.79064
$635$	−1.18335	−0.0469597
$636$	−41.3305	−1.63886
$637$	2.30278	0.0912393
$638$	71.5139	2.83126
$639$	0.908327	0.0359329
$640$	−13.1833	−0.521118
$641$	−10.5416	−0.416370	−0.208185	−	0.978090i	$-0.566756\pi$
$641$	−10.5416	−0.416370	−0.208185	+	0.978090i	$0.566756\pi$
$642$	−17.3028	−0.682886
$643$	43.5694	1.71821	0.859105	−	0.511800i	$-0.171021\pi$
$643$	43.5694	1.71821	0.859105	+	0.511800i	$0.171021\pi$
$644$	−3.30278	−0.130148
$645$	−3.84441	−0.151374
$646$	−20.7250	−0.815413
$647$	16.3305	0.642019	0.321010	−	0.947076i	$-0.395978\pi$
$647$	16.3305	0.642019	0.321010	+	0.947076i	$0.395978\pi$
$648$	−3.00000	−0.117851
$649$	−19.5416	−0.767076
$650$	23.9361	0.938850
$651$	−3.00000	−0.117579
$652$	−45.3305	−1.77528
$653$	30.5139	1.19410	0.597050	−	0.802204i	$-0.296339\pi$
$653$	30.5139	1.19410	0.597050	+	0.802204i	$0.296339\pi$
$654$	9.00000	0.351928
$655$	−7.24726	−0.283174
$656$	−3.69722	−0.144352
$657$	−2.21110	−0.0862633
$658$	−19.8167	−0.772534
$659$	42.6333	1.66076	0.830379	−	0.557199i	$-0.188124\pi$
$659$	42.6333	1.66076	0.830379	+	0.557199i	$0.188124\pi$
$660$	11.5139	0.448177
$661$	20.8167	0.809674	0.404837	−	0.914389i	$-0.367328\pi$
$661$	20.8167	0.809674	0.404837	+	0.914389i	$0.367328\pi$
$662$	−40.6056	−1.57818
$663$	−12.9083	−0.501318
$664$	−16.8167	−0.652613
$665$	−1.11943	−0.0434096
$666$	20.7250	0.803077
$667$	6.21110	0.240495
$668$	9.30278	0.359935
$669$	19.9083	0.769700
$670$	−19.1194	−0.738648
$671$	5.45837	0.210718
$672$	−5.30278	−0.204559
$673$	−26.6333	−1.02664	−0.513319	−	0.858198i	$-0.671584\pi$
$673$	−26.6333	−1.02664	−0.513319	+	0.858198i	$0.671584\pi$
$674$	36.1472	1.39234
$675$	−4.51388	−0.173739
$676$	−25.4222	−0.977777
$677$	37.1472	1.42768	0.713841	−	0.700308i	$-0.246954\pi$
$677$	37.1472	1.42768	0.713841	+	0.700308i	$0.246954\pi$
$678$	−12.2111	−0.468965
$679$	17.6056	0.675639
$680$	−11.7250	−0.449632
$681$	−20.3305	−0.779068
$682$	34.5416	1.32267
$683$	−1.42221	−0.0544192	−0.0272096	−	0.999630i	$-0.508662\pi$
$683$	−1.42221	−0.0544192	−0.0272096	+	0.999630i	$0.508662\pi$
$684$	−5.30278	−0.202757
$685$	−11.7250	−0.447988
$686$	2.30278	0.0879204
$687$	2.51388	0.0959104
$688$	1.66947	0.0636479
$689$	−28.8167	−1.09783
$690$	1.60555	0.0611223
$691$	−31.5139	−1.19884	−0.599422	−	0.800433i	$-0.704603\pi$
$691$	−31.5139	−1.19884	−0.599422	+	0.800433i	$0.704603\pi$
$692$	−60.1472	−2.28645
$693$	5.00000	0.189934
$694$	−33.6972	−1.27913
$695$	−11.0917	−0.420731
$696$	−18.6333	−0.706294
$697$	68.4500	2.59273
$698$	23.2389	0.879604
$699$	−14.3305	−0.542031
$700$	14.9083	0.563482
$701$	−25.5416	−0.964694	−0.482347	−	0.875980i	$-0.660216\pi$
$701$	−25.5416	−0.964694	−0.482347	+	0.875980i	$0.660216\pi$
$702$	−5.30278	−0.200140
$703$	14.4500	0.544991
$704$	64.0833	2.41523
$705$	6.00000	0.225973
$706$	25.3305	0.953327
$707$	−9.30278	−0.349867
$708$	12.9083	0.485125
$709$	−47.3305	−1.77754	−0.888768	−	0.458358i	$-0.848438\pi$
$709$	−47.3305	−1.77754	−0.888768	+	0.458358i	$0.848438\pi$
$710$	1.45837	0.0547315
$711$	−1.00000	−0.0375029
$712$	−32.7250	−1.22642
$713$	3.00000	0.112351
$714$	−12.9083	−0.483082
$715$	8.02776	0.300221
$716$	−8.90833	−0.332920
$717$	−14.0917	−0.526263
$718$	81.8444	3.05441
$719$	14.2111	0.529985	0.264992	−	0.964251i	$-0.414631\pi$
$719$	14.2111	0.529985	0.264992	+	0.964251i	$0.414631\pi$
$720$	−0.211103	−0.00786733
$721$	4.00000	0.148968
$722$	37.8167	1.40739
$723$	12.0278	0.447317
$724$	−22.5139	−0.836722
$725$	−28.0362	−1.04124
$726$	−32.2389	−1.19650
$727$	−46.8722	−1.73839	−0.869196	−	0.494467i	$-0.835363\pi$
$727$	−46.8722	−1.73839	−0.869196	+	0.494467i	$0.835363\pi$
$728$	6.90833	0.256040
$729$	1.00000	0.0370370
$730$	−3.55004	−0.131393
$731$	−30.9083	−1.14319
$732$	−3.60555	−0.133265
$733$	−26.6056	−0.982698	−0.491349	−	0.870963i	$-0.663496\pi$
$733$	−26.6056	−0.982698	−0.491349	+	0.870963i	$0.663496\pi$
$734$	−49.5416	−1.82862
$735$	−0.697224	−0.0257175
$736$	5.30278	0.195463
$737$	59.5416	2.19324
$738$	28.1194	1.03509
$739$	−43.4222	−1.59731	−0.798656	−	0.601788i	$-0.794455\pi$
$739$	−43.4222	−1.59731	−0.798656	+	0.601788i	$0.794455\pi$
$740$	20.7250	0.761865
$741$	−3.69722	−0.135821
$742$	−28.8167	−1.05789
$743$	30.5139	1.11945	0.559723	−	0.828680i	$-0.310908\pi$
$743$	30.5139	1.11945	0.559723	+	0.828680i	$0.310908\pi$
$744$	−9.00000	−0.329956
$745$	−6.00000	−0.219823
$746$	−37.3305	−1.36677
$747$	5.60555	0.205096
$748$	92.5694	3.38467
$749$	−7.51388	−0.274551
$750$	−15.2750	−0.557765
$751$	8.69722	0.317366	0.158683	−	0.987330i	$-0.449275\pi$
$751$	8.69722	0.317366	0.158683	+	0.987330i	$0.449275\pi$
$752$	−2.60555	−0.0950147
$753$	23.8167	0.867927
$754$	−32.9361	−1.19946
$755$	−11.5778	−0.421359
$756$	−3.30278	−0.120121
$757$	−3.36669	−0.122365	−0.0611823	−	0.998127i	$-0.519487\pi$
$757$	−3.36669	−0.122365	−0.0611823	+	0.998127i	$0.519487\pi$
$758$	51.6333	1.87541
$759$	−5.00000	−0.181489
$760$	−3.35829	−0.121818
$761$	12.0000	0.435000	0.217500	−	0.976060i	$-0.430210\pi$
$761$	12.0000	0.435000	0.217500	+	0.976060i	$0.430210\pi$
$762$	−3.90833	−0.141584
$763$	3.90833	0.141491
$764$	−15.2111	−0.550318
$765$	3.90833	0.141306
$766$	−11.0917	−0.400758
$767$	9.00000	0.324971
$768$	−17.9083	−0.646211
$769$	−27.4500	−0.989871	−0.494935	−	0.868930i	$-0.664808\pi$
$769$	−27.4500	−0.989871	−0.494935	+	0.868930i	$0.664808\pi$
$770$	8.02776	0.289300
$771$	27.0278	0.973381
$772$	29.8167	1.07312
$773$	31.8444	1.14536	0.572682	−	0.819778i	$-0.305903\pi$
$773$	31.8444	1.14536	0.572682	+	0.819778i	$0.305903\pi$
$774$	−12.6972	−0.456392
$775$	−13.5416	−0.486430
$776$	52.8167	1.89601
$777$	9.00000	0.322873
$778$	84.3583	3.02439
$779$	19.6056	0.702442
$780$	−5.30278	−0.189870
$781$	−4.54163	−0.162512
$782$	12.9083	0.461601
$783$	6.21110	0.221967
$784$	0.302776	0.0108134
$785$	2.66106	0.0949774
$786$	−23.9361	−0.853772
$787$	32.1472	1.14592	0.572962	−	0.819582i	$-0.305794\pi$
$787$	32.1472	1.14592	0.572962	+	0.819582i	$0.305794\pi$
$788$	−23.4222	−0.834382
$789$	10.3944	0.370052
$790$	−1.60555	−0.0571230
$791$	−5.30278	−0.188545
$792$	15.0000	0.533002
$793$	−2.51388	−0.0892704
$794$	63.0833	2.23874
$795$	8.72498	0.309443
$796$	41.3305	1.46492
$797$	−39.0278	−1.38243	−0.691217	−	0.722647i	$-0.742925\pi$
$797$	−39.0278	−1.38243	−0.691217	+	0.722647i	$0.742925\pi$
$798$	−3.69722	−0.130880
$799$	48.2389	1.70657
$800$	−23.9361	−0.846268
$801$	10.9083	0.385427
$802$	30.9083	1.09141
$803$	11.0555	0.390141
$804$	−39.3305	−1.38708
$805$	0.697224	0.0245739
$806$	−15.9083	−0.560347
$807$	0.908327	0.0319746
$808$	−27.9083	−0.981812
$809$	25.9361	0.911864	0.455932	−	0.890015i	$-0.349306\pi$
$809$	25.9361	0.911864	0.455932	+	0.890015i	$0.349306\pi$
$810$	1.60555	0.0564133
$811$	−10.3944	−0.364998	−0.182499	−	0.983206i	$-0.558419\pi$
$811$	−10.3944	−0.364998	−0.182499	+	0.983206i	$0.558419\pi$
$812$	−20.5139	−0.719896
$813$	3.60555	0.126452
$814$	−103.625	−3.63205
$815$	9.56939	0.335201
$816$	−1.69722	−0.0594147
$817$	−8.85281	−0.309721
$818$	−55.3305	−1.93459
$819$	−2.30278	−0.0804655
$820$	28.1194	0.981973
$821$	−19.3944	−0.676871	−0.338435	−	0.940990i	$-0.609898\pi$
$821$	−19.3944	−0.676871	−0.338435	+	0.940990i	$0.609898\pi$
$822$	−38.7250	−1.35069
$823$	6.51388	0.227060	0.113530	−	0.993535i	$-0.463784\pi$
$823$	6.51388	0.227060	0.113530	+	0.993535i	$0.463784\pi$
$824$	12.0000	0.418040
$825$	22.5694	0.785765
$826$	9.00000	0.313150
$827$	−9.90833	−0.344546	−0.172273	−	0.985049i	$-0.555111\pi$
$827$	−9.90833	−0.344546	−0.172273	+	0.985049i	$0.555111\pi$
$828$	3.30278	0.114779
$829$	−30.4500	−1.05757	−0.528785	−	0.848756i	$-0.677352\pi$
$829$	−30.4500	−1.05757	−0.528785	+	0.848756i	$0.677352\pi$
$830$	9.00000	0.312395
$831$	−12.3028	−0.426779
$832$	−29.5139	−1.02321
$833$	−5.60555	−0.194221
$834$	−36.6333	−1.26851
$835$	−1.96384	−0.0679615
$836$	26.5139	0.917002
$837$	3.00000	0.103695
$838$	−34.8167	−1.20272
$839$	38.3028	1.32236	0.661179	−	0.750228i	$-0.270056\pi$
$839$	38.3028	1.32236	0.661179	+	0.750228i	$0.270056\pi$
$840$	−2.09167	−0.0721696
$841$	9.57779	0.330269
$842$	−22.3305	−0.769561
$843$	27.8167	0.958056
$844$	−90.5694	−3.11753
$845$	5.36669	0.184620
$846$	19.8167	0.681311
$847$	−14.0000	−0.481046
$848$	−3.78890	−0.130111
$849$	17.3028	0.593830
$850$	−58.2666	−1.99853
$851$	−9.00000	−0.308516
$852$	3.00000	0.102778
$853$	−58.2389	−1.99406	−0.997030	−	0.0770106i	$-0.975462\pi$
$853$	−58.2389	−1.99406	−0.997030	+	0.0770106i	$0.975462\pi$
$854$	−2.51388	−0.0860231
$855$	1.11943	0.0382837
$856$	−22.5416	−0.770457
$857$	−50.2389	−1.71613	−0.858063	−	0.513544i	$-0.828332\pi$
$857$	−50.2389	−1.71613	−0.858063	+	0.513544i	$0.828332\pi$
$858$	26.5139	0.905169
$859$	43.2111	1.47434	0.737172	−	0.675705i	$-0.236161\pi$
$859$	43.2111	1.47434	0.737172	+	0.675705i	$0.236161\pi$
$860$	−12.6972	−0.432972
$861$	12.2111	0.416153
$862$	20.0917	0.684325
$863$	−5.76114	−0.196112	−0.0980558	−	0.995181i	$-0.531262\pi$
$863$	−5.76114	−0.196112	−0.0980558	+	0.995181i	$0.531262\pi$
$864$	5.30278	0.180404
$865$	12.6972	0.431719
$866$	48.4222	1.64545
$867$	14.4222	0.489804
$868$	−9.90833	−0.336311
$869$	5.00000	0.169613
$870$	9.97224	0.338091
$871$	−27.4222	−0.929166
$872$	11.7250	0.397058
$873$	−17.6056	−0.595858
$874$	3.69722	0.125060
$875$	−6.63331	−0.224247
$876$	−7.30278	−0.246738
$877$	−14.7889	−0.499386	−0.249693	−	0.968325i	$-0.580330\pi$
$877$	−14.7889	−0.499386	−0.249693	+	0.968325i	$0.580330\pi$
$878$	−46.5416	−1.57070
$879$	−24.8444	−0.837981
$880$	1.05551	0.0355813
$881$	−43.8167	−1.47622	−0.738110	−	0.674680i	$-0.764282\pi$
$881$	−43.8167	−1.47622	−0.738110	+	0.674680i	$0.764282\pi$
$882$	−2.30278	−0.0775385
$883$	−18.4861	−0.622108	−0.311054	−	0.950392i	$-0.600682\pi$
$883$	−18.4861	−0.622108	−0.311054	+	0.950392i	$0.600682\pi$
$884$	−42.6333	−1.43391
$885$	−2.72498	−0.0915992
$886$	75.6333	2.54095
$887$	−11.9361	−0.400774	−0.200387	−	0.979717i	$-0.564220\pi$
$887$	−11.9361	−0.400774	−0.200387	+	0.979717i	$0.564220\pi$
$888$	27.0000	0.906061
$889$	−1.69722	−0.0569231
$890$	17.5139	0.587067
$891$	−5.00000	−0.167506
$892$	65.7527	2.20156
$893$	13.8167	0.462357
$894$	−19.8167	−0.662768
$895$	1.88057	0.0628605
$896$	−18.9083	−0.631683
$897$	2.30278	0.0768874
$898$	82.2666	2.74527
$899$	18.6333	0.621456
$900$	−14.9083	−0.496944
$901$	70.1472	2.33694
$902$	−140.597	−4.68137
$903$	−5.51388	−0.183490
$904$	−15.9083	−0.529103
$905$	4.75274	0.157986
$906$	−38.2389	−1.27040
$907$	−8.14719	−0.270523	−0.135261	−	0.990810i	$-0.543187\pi$
$907$	−8.14719	−0.270523	−0.135261	+	0.990810i	$0.543187\pi$
$908$	−67.1472	−2.22836
$909$	9.30278	0.308554
$910$	−3.69722	−0.122562
$911$	−24.2389	−0.803069	−0.401535	−	0.915844i	$-0.631523\pi$
$911$	−24.2389	−0.803069	−0.401535	+	0.915844i	$0.631523\pi$
$912$	−0.486122	−0.0160971
$913$	−28.0278	−0.927583
$914$	25.0555	0.828763
$915$	0.761141	0.0251625
$916$	8.30278	0.274331
$917$	−10.3944	−0.343255
$918$	12.9083	0.426038
$919$	−10.3944	−0.342881	−0.171441	−	0.985194i	$-0.554842\pi$
$919$	−10.3944	−0.342881	−0.171441	+	0.985194i	$0.554842\pi$
$920$	2.09167	0.0689604
$921$	18.2111	0.600076
$922$	−17.7889	−0.585846
$923$	2.09167	0.0688483
$924$	16.5139	0.543267
$925$	40.6249	1.33574
$926$	43.3305	1.42393
$927$	−4.00000	−0.131377
$928$	32.9361	1.08118
$929$	40.3305	1.32320	0.661601	−	0.749856i	$-0.269877\pi$
$929$	40.3305	1.32320	0.661601	+	0.749856i	$0.269877\pi$
$930$	4.81665	0.157944
$931$	−1.60555	−0.0526198
$932$	−47.3305	−1.55036
$933$	−9.51388	−0.311470
$934$	−54.3583	−1.77866
$935$	−19.5416	−0.639080
$936$	−6.90833	−0.225806
$937$	−4.57779	−0.149550	−0.0747750	−	0.997200i	$-0.523824\pi$
$937$	−4.57779	−0.149550	−0.0747750	+	0.997200i	$0.523824\pi$
$938$	−27.4222	−0.895367
$939$	1.21110	0.0395228
$940$	19.8167	0.646348
$941$	−0.844410	−0.0275270	−0.0137635	−	0.999905i	$-0.504381\pi$
$941$	−0.844410	−0.0275270	−0.0137635	+	0.999905i	$0.504381\pi$
$942$	8.78890	0.286358
$943$	−12.2111	−0.397648
$944$	1.18335	0.0385146
$945$	0.697224	0.0226807
$946$	63.4861	2.06411
$947$	−13.6333	−0.443023	−0.221511	−	0.975158i	$-0.571099\pi$
$947$	−13.6333	−0.443023	−0.221511	+	0.975158i	$0.571099\pi$
$948$	−3.30278	−0.107269
$949$	−5.09167	−0.165283
$950$	−16.6888	−0.541457
$951$	−30.5139	−0.989480
$952$	−16.8167	−0.545031
$953$	−51.3305	−1.66276	−0.831380	−	0.555705i	$-0.812448\pi$
$953$	−51.3305	−1.66276	−0.831380	+	0.555705i	$0.812448\pi$
$954$	28.8167	0.932974
$955$	3.21110	0.103909
$956$	−46.5416	−1.50526
$957$	−31.0555	−1.00388
$958$	41.9361	1.35489
$959$	−16.8167	−0.543038
$960$	8.93608	0.288411
$961$	−22.0000	−0.709677
$962$	47.7250	1.53872
$963$	7.51388	0.242131
$964$	39.7250	1.27946
$965$	−6.29437	−0.202623
$966$	2.30278	0.0740906
$967$	41.2666	1.32704	0.663522	−	0.748156i	$-0.269061\pi$
$967$	41.2666	1.32704	0.663522	+	0.748156i	$0.269061\pi$
$968$	−42.0000	−1.34993
$969$	9.00000	0.289122
$970$	−28.2666	−0.907586
$971$	−35.0917	−1.12615	−0.563073	−	0.826407i	$-0.690381\pi$
$971$	−35.0917	−1.12615	−0.563073	+	0.826407i	$0.690381\pi$
$972$	3.30278	0.105937
$973$	−15.9083	−0.509998
$974$	1.88057	0.0602574
$975$	−10.3944	−0.332889
$976$	−0.330532	−0.0105801
$977$	31.1472	0.996487	0.498243	−	0.867037i	$-0.333979\pi$
$977$	31.1472	0.996487	0.498243	+	0.867037i	$0.333979\pi$
$978$	31.6056	1.01063
$979$	−54.5416	−1.74316
$980$	−2.30278	−0.0735595
$981$	−3.90833	−0.124783
$982$	41.3028	1.31802
$983$	−22.8167	−0.727738	−0.363869	−	0.931450i	$-0.618544\pi$
$983$	−22.8167	−0.727738	−0.363869	+	0.931450i	$0.618544\pi$
$984$	36.6333	1.16783
$985$	4.94449	0.157544
$986$	80.1749	2.55329
$987$	8.60555	0.273918
$988$	−12.2111	−0.388487
$989$	5.51388	0.175331
$990$	−8.02776	−0.255139
$991$	35.5139	1.12814	0.564068	−	0.825729i	$-0.309236\pi$
$991$	35.5139	1.12814	0.564068	+	0.825729i	$0.309236\pi$
$992$	15.9083	0.505090
$993$	17.6333	0.559576
$994$	2.09167	0.0663438
$995$	−8.72498	−0.276600
$996$	18.5139	0.586635
$997$	−0.0277564	−0.000879053 0	−0.000439527	−	1.00000i	$-0.500140\pi$
$997$	−0.0277564	−0.000879053 0	−0.000439527		1.00000i	$0.500140\pi$
$998$	−73.4777	−2.32590
$999$	−9.00000	−0.284747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.f.1.1	✓	2
3.2	odd	2		1449.2.a.j.1.2		2
4.3	odd	2		7728.2.a.x.1.2		2
7.6	odd	2		3381.2.a.p.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.f.1.1	✓	2	1.1	even	1	trivial
1449.2.a.j.1.2		2	3.2	odd	2
3381.2.a.p.1.1		2	7.6	odd	2
7728.2.a.x.1.2		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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} -0.697224 q^{5} -2.30278 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} -0.697224 q^{5} -2.30278 q^{6} -1.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} +1.60555 q^{10} -5.00000 q^{11} +3.30278 q^{12} +2.30278 q^{13} +2.30278 q^{14} -0.697224 q^{15} +0.302776 q^{16} -5.60555 q^{17} -2.30278 q^{18} -1.60555 q^{19} -2.30278 q^{20} -1.00000 q^{21} +11.5139 q^{22} +1.00000 q^{23} -3.00000 q^{24} -4.51388 q^{25} -5.30278 q^{26} +1.00000 q^{27} -3.30278 q^{28} +6.21110 q^{29} +1.60555 q^{30} +3.00000 q^{31} +5.30278 q^{32} -5.00000 q^{33} +12.9083 q^{34} +0.697224 q^{35} +3.30278 q^{36} -9.00000 q^{37} +3.69722 q^{38} +2.30278 q^{39} +2.09167 q^{40} -12.2111 q^{41} +2.30278 q^{42} +5.51388 q^{43} -16.5139 q^{44} -0.697224 q^{45} -2.30278 q^{46} -8.60555 q^{47} +0.302776 q^{48} +1.00000 q^{49} +10.3944 q^{50} -5.60555 q^{51} +7.60555 q^{52} -12.5139 q^{53} -2.30278 q^{54} +3.48612 q^{55} +3.00000 q^{56} -1.60555 q^{57} -14.3028 q^{58} +3.90833 q^{59} -2.30278 q^{60} -1.09167 q^{61} -6.90833 q^{62} -1.00000 q^{63} -12.8167 q^{64} -1.60555 q^{65} +11.5139 q^{66} -11.9083 q^{67} -18.5139 q^{68} +1.00000 q^{69} -1.60555 q^{70} +0.908327 q^{71} -3.00000 q^{72} -2.21110 q^{73} +20.7250 q^{74} -4.51388 q^{75} -5.30278 q^{76} +5.00000 q^{77} -5.30278 q^{78} -1.00000 q^{79} -0.211103 q^{80} +1.00000 q^{81} +28.1194 q^{82} +5.60555 q^{83} -3.30278 q^{84} +3.90833 q^{85} -12.6972 q^{86} +6.21110 q^{87} +15.0000 q^{88} +10.9083 q^{89} +1.60555 q^{90} -2.30278 q^{91} +3.30278 q^{92} +3.00000 q^{93} +19.8167 q^{94} +1.11943 q^{95} +5.30278 q^{96} -17.6056 q^{97} -2.30278 q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} - 10 q^{11} + 3 q^{12} + q^{13} + q^{14} - 5 q^{15} - 3 q^{16} - 4 q^{17} - q^{18} + 4 q^{19} - q^{20} - 2 q^{21} + 5 q^{22} + 2 q^{23} - 6 q^{24} + 9 q^{25} - 7 q^{26} + 2 q^{27} - 3 q^{28} - 2 q^{29} - 4 q^{30} + 6 q^{31} + 7 q^{32} - 10 q^{33} + 15 q^{34} + 5 q^{35} + 3 q^{36} - 18 q^{37} + 11 q^{38} + q^{39} + 15 q^{40} - 10 q^{41} + q^{42} - 7 q^{43} - 15 q^{44} - 5 q^{45} - q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} + 28 q^{50} - 4 q^{51} + 8 q^{52} - 7 q^{53} - q^{54} + 25 q^{55} + 6 q^{56} + 4 q^{57} - 25 q^{58} - 3 q^{59} - q^{60} - 13 q^{61} - 3 q^{62} - 2 q^{63} - 4 q^{64} + 4 q^{65} + 5 q^{66} - 13 q^{67} - 19 q^{68} + 2 q^{69} + 4 q^{70} - 9 q^{71} - 6 q^{72} + 10 q^{73} + 9 q^{74} + 9 q^{75} - 7 q^{76} + 10 q^{77} - 7 q^{78} - 2 q^{79} + 14 q^{80} + 2 q^{81} + 31 q^{82} + 4 q^{83} - 3 q^{84} - 3 q^{85} - 29 q^{86} - 2 q^{87} + 30 q^{88} + 11 q^{89} - 4 q^{90} - q^{91} + 3 q^{92} + 6 q^{93} + 18 q^{94} - 23 q^{95} + 7 q^{96} - 28 q^{97} - q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 - 4 * q^10 - 10 * q^11 + 3 * q^12 + q^13 + q^14 - 5 * q^15 - 3 * q^16 - 4 * q^17 - q^18 + 4 * q^19 - q^20 - 2 * q^21 + 5 * q^22 + 2 * q^23 - 6 * q^24 + 9 * q^25 - 7 * q^26 + 2 * q^27 - 3 * q^28 - 2 * q^29 - 4 * q^30 + 6 * q^31 + 7 * q^32 - 10 * q^33 + 15 * q^34 + 5 * q^35 + 3 * q^36 - 18 * q^37 + 11 * q^38 + q^39 + 15 * q^40 - 10 * q^41 + q^42 - 7 * q^43 - 15 * q^44 - 5 * q^45 - q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 + 28 * q^50 - 4 * q^51 + 8 * q^52 - 7 * q^53 - q^54 + 25 * q^55 + 6 * q^56 + 4 * q^57 - 25 * q^58 - 3 * q^59 - q^60 - 13 * q^61 - 3 * q^62 - 2 * q^63 - 4 * q^64 + 4 * q^65 + 5 * q^66 - 13 * q^67 - 19 * q^68 + 2 * q^69 + 4 * q^70 - 9 * q^71 - 6 * q^72 + 10 * q^73 + 9 * q^74 + 9 * q^75 - 7 * q^76 + 10 * q^77 - 7 * q^78 - 2 * q^79 + 14 * q^80 + 2 * q^81 + 31 * q^82 + 4 * q^83 - 3 * q^84 - 3 * q^85 - 29 * q^86 - 2 * q^87 + 30 * q^88 + 11 * q^89 - 4 * q^90 - q^91 + 3 * q^92 + 6 * q^93 + 18 * q^94 - 23 * q^95 + 7 * q^96 - 28 * q^97 - q^98 - 10 * q^99

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