LMFDB - Embedded newform 483.2.a.c.1.2

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:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-0.381966 q^{2} +1.00000 q^{3} -1.85410 q^{4} -1.38197 q^{5} -0.381966 q^{6} +1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.381966 q^{2} +1.00000 q^{3} -1.85410 q^{4} -1.38197 q^{5} -0.381966 q^{6} +1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} +0.527864 q^{10} -5.47214 q^{11} -1.85410 q^{12} -2.38197 q^{13} -0.381966 q^{14} -1.38197 q^{15} +3.14590 q^{16} -1.00000 q^{17} -0.381966 q^{18} -3.00000 q^{19} +2.56231 q^{20} +1.00000 q^{21} +2.09017 q^{22} -1.00000 q^{23} +1.47214 q^{24} -3.09017 q^{25} +0.909830 q^{26} +1.00000 q^{27} -1.85410 q^{28} -7.47214 q^{29} +0.527864 q^{30} -3.76393 q^{31} -4.14590 q^{32} -5.47214 q^{33} +0.381966 q^{34} -1.38197 q^{35} -1.85410 q^{36} +1.47214 q^{37} +1.14590 q^{38} -2.38197 q^{39} -2.03444 q^{40} -4.70820 q^{41} -0.381966 q^{42} +8.09017 q^{43} +10.1459 q^{44} -1.38197 q^{45} +0.381966 q^{46} +1.70820 q^{47} +3.14590 q^{48} +1.00000 q^{49} +1.18034 q^{50} -1.00000 q^{51} +4.41641 q^{52} -3.38197 q^{53} -0.381966 q^{54} +7.56231 q^{55} +1.47214 q^{56} -3.00000 q^{57} +2.85410 q^{58} -6.14590 q^{59} +2.56231 q^{60} +13.7984 q^{61} +1.43769 q^{62} +1.00000 q^{63} -4.70820 q^{64} +3.29180 q^{65} +2.09017 q^{66} +4.14590 q^{67} +1.85410 q^{68} -1.00000 q^{69} +0.527864 q^{70} -3.90983 q^{71} +1.47214 q^{72} +2.70820 q^{73} -0.562306 q^{74} -3.09017 q^{75} +5.56231 q^{76} -5.47214 q^{77} +0.909830 q^{78} +0.527864 q^{79} -4.34752 q^{80} +1.00000 q^{81} +1.79837 q^{82} -3.00000 q^{83} -1.85410 q^{84} +1.38197 q^{85} -3.09017 q^{86} -7.47214 q^{87} -8.05573 q^{88} +3.14590 q^{89} +0.527864 q^{90} -2.38197 q^{91} +1.85410 q^{92} -3.76393 q^{93} -0.652476 q^{94} +4.14590 q^{95} -4.14590 q^{96} +5.00000 q^{97} -0.381966 q^{98} -5.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - 3 * q^6 + 2 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} - 7 q^{13} - 3 q^{14} - 5 q^{15} + 13 q^{16} - 2 q^{17} - 3 q^{18} - 6 q^{19} - 15 q^{20} + 2 q^{21} - 7 q^{22} - 2 q^{23} - 6 q^{24} + 5 q^{25} + 13 q^{26} + 2 q^{27} + 3 q^{28} - 6 q^{29} + 10 q^{30} - 12 q^{31} - 15 q^{32} - 2 q^{33} + 3 q^{34} - 5 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 7 q^{39} + 25 q^{40} + 4 q^{41} - 3 q^{42} + 5 q^{43} + 27 q^{44} - 5 q^{45} + 3 q^{46} - 10 q^{47} + 13 q^{48} + 2 q^{49} - 20 q^{50} - 2 q^{51} - 18 q^{52} - 9 q^{53} - 3 q^{54} - 5 q^{55} - 6 q^{56} - 6 q^{57} - q^{58} - 19 q^{59} - 15 q^{60} + 3 q^{61} + 23 q^{62} + 2 q^{63} + 4 q^{64} + 20 q^{65} - 7 q^{66} + 15 q^{67} - 3 q^{68} - 2 q^{69} + 10 q^{70} - 19 q^{71} - 6 q^{72} - 8 q^{73} + 19 q^{74} + 5 q^{75} - 9 q^{76} - 2 q^{77} + 13 q^{78} + 10 q^{79} - 40 q^{80} + 2 q^{81} - 21 q^{82} - 6 q^{83} + 3 q^{84} + 5 q^{85} + 5 q^{86} - 6 q^{87} - 34 q^{88} + 13 q^{89} + 10 q^{90} - 7 q^{91} - 3 q^{92} - 12 q^{93} + 30 q^{94} + 15 q^{95} - 15 q^{96} + 10 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - 3 * q^6 + 2 * q^7 - 6 * q^8 + 2 * q^9 + 10 * q^10 - 2 * q^11 + 3 * q^12 - 7 * q^13 - 3 * q^14 - 5 * q^15 + 13 * q^16 - 2 * q^17 - 3 * q^18 - 6 * q^19 - 15 * q^20 + 2 * q^21 - 7 * q^22 - 2 * q^23 - 6 * q^24 + 5 * q^25 + 13 * q^26 + 2 * q^27 + 3 * q^28 - 6 * q^29 + 10 * q^30 - 12 * q^31 - 15 * q^32 - 2 * q^33 + 3 * q^34 - 5 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 7 * q^39 + 25 * q^40 + 4 * q^41 - 3 * q^42 + 5 * q^43 + 27 * q^44 - 5 * q^45 + 3 * q^46 - 10 * q^47 + 13 * q^48 + 2 * q^49 - 20 * q^50 - 2 * q^51 - 18 * q^52 - 9 * q^53 - 3 * q^54 - 5 * q^55 - 6 * q^56 - 6 * q^57 - q^58 - 19 * q^59 - 15 * q^60 + 3 * q^61 + 23 * q^62 + 2 * q^63 + 4 * q^64 + 20 * q^65 - 7 * q^66 + 15 * q^67 - 3 * q^68 - 2 * q^69 + 10 * q^70 - 19 * q^71 - 6 * q^72 - 8 * q^73 + 19 * q^74 + 5 * q^75 - 9 * q^76 - 2 * q^77 + 13 * q^78 + 10 * q^79 - 40 * q^80 + 2 * q^81 - 21 * q^82 - 6 * q^83 + 3 * q^84 + 5 * q^85 + 5 * q^86 - 6 * q^87 - 34 * q^88 + 13 * q^89 + 10 * q^90 - 7 * q^91 - 3 * q^92 - 12 * q^93 + 30 * q^94 + 15 * q^95 - 15 * q^96 + 10 * q^97 - 3 * q^98 - 2 * 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 $

$2$	−0.381966	−0.270091	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−0.381966	−0.270091	−0.135045	+	0.990839i	$0.543118\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.85410	−0.927051
$5$	−1.38197	−0.618034	−0.309017	−	0.951057i	$-0.600000\pi$
$5$	−1.38197	−0.618034	−0.309017	+	0.951057i	$0.600000\pi$
$6$	−0.381966	−0.155937
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.47214	0.520479
$9$	1.00000	0.333333
$10$	0.527864	0.166925
$11$	−5.47214	−1.64991	−0.824956	−	0.565198i	$-0.808800\pi$
$11$	−5.47214	−1.64991	−0.824956	+	0.565198i	$0.808800\pi$
$12$	−1.85410	−0.535233
$13$	−2.38197	−0.660639	−0.330319	−	0.943869i	$-0.607156\pi$
$13$	−2.38197	−0.660639	−0.330319	+	0.943869i	$0.607156\pi$
$14$	−0.381966	−0.102085
$15$	−1.38197	−0.356822
$16$	3.14590	0.786475
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	−0.381966	−0.0900303
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	2.56231	0.572949
$21$	1.00000	0.218218
$22$	2.09017	0.445626
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.47214	0.300498
$25$	−3.09017	−0.618034
$26$	0.909830	0.178432
$27$	1.00000	0.192450
$28$	−1.85410	−0.350392
$29$	−7.47214	−1.38754	−0.693770	−	0.720196i	$-0.744052\pi$
$29$	−7.47214	−1.38754	−0.693770	+	0.720196i	$0.744052\pi$
$30$	0.527864	0.0963743
$31$	−3.76393	−0.676022	−0.338011	−	0.941142i	$-0.609754\pi$
$31$	−3.76393	−0.676022	−0.338011	+	0.941142i	$0.609754\pi$
$32$	−4.14590	−0.732898
$33$	−5.47214	−0.952577
$34$	0.381966	0.0655066
$35$	−1.38197	−0.233595
$36$	−1.85410	−0.309017
$37$	1.47214	0.242018	0.121009	−	0.992651i	$-0.461387\pi$
$37$	1.47214	0.242018	0.121009	+	0.992651i	$0.461387\pi$
$38$	1.14590	0.185889
$39$	−2.38197	−0.381420
$40$	−2.03444	−0.321674
$41$	−4.70820	−0.735298	−0.367649	−	0.929965i	$-0.619837\pi$
$41$	−4.70820	−0.735298	−0.367649	+	0.929965i	$0.619837\pi$
$42$	−0.381966	−0.0589386
$43$	8.09017	1.23374	0.616870	−	0.787065i	$-0.288401\pi$
$43$	8.09017	1.23374	0.616870	+	0.787065i	$0.288401\pi$
$44$	10.1459	1.52955
$45$	−1.38197	−0.206011
$46$	0.381966	0.0563178
$47$	1.70820	0.249167	0.124584	−	0.992209i	$-0.460241\pi$
$47$	1.70820	0.249167	0.124584	+	0.992209i	$0.460241\pi$
$48$	3.14590	0.454071
$49$	1.00000	0.142857
$50$	1.18034	0.166925
$51$	−1.00000	−0.140028
$52$	4.41641	0.612446
$53$	−3.38197	−0.464549	−0.232274	−	0.972650i	$-0.574617\pi$
$53$	−3.38197	−0.464549	−0.232274	+	0.972650i	$0.574617\pi$
$54$	−0.381966	−0.0519790
$55$	7.56231	1.01970
$56$	1.47214	0.196722
$57$	−3.00000	−0.397360
$58$	2.85410	0.374762
$59$	−6.14590	−0.800128	−0.400064	−	0.916487i	$-0.631012\pi$
$59$	−6.14590	−0.800128	−0.400064	+	0.916487i	$0.631012\pi$
$60$	2.56231	0.330792
$61$	13.7984	1.76670	0.883350	−	0.468713i	$-0.155282\pi$
$61$	13.7984	1.76670	0.883350	+	0.468713i	$0.155282\pi$
$62$	1.43769	0.182587
$63$	1.00000	0.125988
$64$	−4.70820	−0.588525
$65$	3.29180	0.408297
$66$	2.09017	0.257282
$67$	4.14590	0.506502	0.253251	−	0.967401i	$-0.418500\pi$
$67$	4.14590	0.506502	0.253251	+	0.967401i	$0.418500\pi$
$68$	1.85410	0.224843
$69$	−1.00000	−0.120386
$70$	0.527864	0.0630918
$71$	−3.90983	−0.464011	−0.232006	−	0.972714i	$-0.574529\pi$
$71$	−3.90983	−0.464011	−0.232006	+	0.972714i	$0.574529\pi$
$72$	1.47214	0.173493
$73$	2.70820	0.316971	0.158486	−	0.987361i	$-0.449339\pi$
$73$	2.70820	0.316971	0.158486	+	0.987361i	$0.449339\pi$
$74$	−0.562306	−0.0653667
$75$	−3.09017	−0.356822
$76$	5.56231	0.638040
$77$	−5.47214	−0.623608
$78$	0.909830	0.103018
$79$	0.527864	0.0593893	0.0296947	−	0.999559i	$-0.490547\pi$
$79$	0.527864	0.0593893	0.0296947	+	0.999559i	$0.490547\pi$
$80$	−4.34752	−0.486068
$81$	1.00000	0.111111
$82$	1.79837	0.198597
$83$	−3.00000	−0.329293	−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000	−0.329293	−0.164646	+	0.986353i	$0.552648\pi$
$84$	−1.85410	−0.202299
$85$	1.38197	0.149895
$86$	−3.09017	−0.333222
$87$	−7.47214	−0.801097
$88$	−8.05573	−0.858743
$89$	3.14590	0.333465	0.166732	−	0.986002i	$-0.446678\pi$
$89$	3.14590	0.333465	0.166732	+	0.986002i	$0.446678\pi$
$90$	0.527864	0.0556418
$91$	−2.38197	−0.249698
$92$	1.85410	0.193303
$93$	−3.76393	−0.390302
$94$	−0.652476	−0.0672977
$95$	4.14590	0.425360
$96$	−4.14590	−0.423139
$97$	5.00000	0.507673	0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000	0.507673	0.253837	+	0.967247i	$0.418307\pi$
$98$	−0.381966	−0.0385844
$99$	−5.47214	−0.549970
$100$	5.72949	0.572949
$101$	−1.85410	−0.184490	−0.0922450	−	0.995736i	$-0.529404\pi$
$101$	−1.85410	−0.184490	−0.0922450	+	0.995736i	$0.529404\pi$
$102$	0.381966	0.0378203
$103$	−4.94427	−0.487174	−0.243587	−	0.969879i	$-0.578324\pi$
$103$	−4.94427	−0.487174	−0.243587	+	0.969879i	$0.578324\pi$
$104$	−3.50658	−0.343848
$105$	−1.38197	−0.134866
$106$	1.29180	0.125470
$107$	11.7984	1.14059	0.570296	−	0.821439i	$-0.306829\pi$
$107$	11.7984	1.14059	0.570296	+	0.821439i	$0.306829\pi$
$108$	−1.85410	−0.178411
$109$	−6.32624	−0.605944	−0.302972	−	0.953000i	$-0.597979\pi$
$109$	−6.32624	−0.605944	−0.302972	+	0.953000i	$0.597979\pi$
$110$	−2.88854	−0.275412
$111$	1.47214	0.139729
$112$	3.14590	0.297259
$113$	6.32624	0.595122	0.297561	−	0.954703i	$-0.403827\pi$
$113$	6.32624	0.595122	0.297561	+	0.954703i	$0.403827\pi$
$114$	1.14590	0.107323
$115$	1.38197	0.128869
$116$	13.8541	1.28632
$117$	−2.38197	−0.220213
$118$	2.34752	0.216107
$119$	−1.00000	−0.0916698
$120$	−2.03444	−0.185718
$121$	18.9443	1.72221
$122$	−5.27051	−0.477170
$123$	−4.70820	−0.424524
$124$	6.97871	0.626707
$125$	11.1803	1.00000
$126$	−0.381966	−0.0340282
$127$	18.8541	1.67303	0.836516	−	0.547943i	$-0.184589\pi$
$127$	18.8541	1.67303	0.836516	+	0.547943i	$0.184589\pi$
$128$	10.0902	0.891853
$129$	8.09017	0.712300
$130$	−1.25735	−0.110277
$131$	−17.9443	−1.56780	−0.783899	−	0.620888i	$-0.786772\pi$
$131$	−17.9443	−1.56780	−0.783899	+	0.620888i	$0.786772\pi$
$132$	10.1459	0.883087
$133$	−3.00000	−0.260133
$134$	−1.58359	−0.136802
$135$	−1.38197	−0.118941
$136$	−1.47214	−0.126235
$137$	9.18034	0.784329	0.392165	−	0.919895i	$-0.371726\pi$
$137$	9.18034	0.784329	0.392165	+	0.919895i	$0.371726\pi$
$138$	0.381966	0.0325151
$139$	−16.3262	−1.38477	−0.692387	−	0.721527i	$-0.743441\pi$
$139$	−16.3262	−1.38477	−0.692387	+	0.721527i	$0.743441\pi$
$140$	2.56231	0.216554
$141$	1.70820	0.143857
$142$	1.49342	0.125325
$143$	13.0344	1.08999
$144$	3.14590	0.262158
$145$	10.3262	0.857547
$146$	−1.03444	−0.0856110
$147$	1.00000	0.0824786
$148$	−2.72949	−0.224363
$149$	−16.1803	−1.32555	−0.662773	−	0.748821i	$-0.730620\pi$
$149$	−16.1803	−1.32555	−0.662773	+	0.748821i	$0.730620\pi$
$150$	1.18034	0.0963743
$151$	0.763932	0.0621679	0.0310840	−	0.999517i	$-0.490104\pi$
$151$	0.763932	0.0621679	0.0310840	+	0.999517i	$0.490104\pi$
$152$	−4.41641	−0.358218
$153$	−1.00000	−0.0808452
$154$	2.09017	0.168431
$155$	5.20163	0.417805
$156$	4.41641	0.353596
$157$	−20.6525	−1.64825	−0.824124	−	0.566410i	$-0.808332\pi$
$157$	−20.6525	−1.64825	−0.824124	+	0.566410i	$0.808332\pi$
$158$	−0.201626	−0.0160405
$159$	−3.38197	−0.268207
$160$	5.72949	0.452956
$161$	−1.00000	−0.0788110
$162$	−0.381966	−0.0300101
$163$	2.79837	0.219186	0.109593	−	0.993977i	$-0.465045\pi$
$163$	2.79837	0.219186	0.109593	+	0.993977i	$0.465045\pi$
$164$	8.72949	0.681659
$165$	7.56231	0.588725
$166$	1.14590	0.0889389
$167$	14.5279	1.12420	0.562100	−	0.827069i	$-0.309994\pi$
$167$	14.5279	1.12420	0.562100	+	0.827069i	$0.309994\pi$
$168$	1.47214	0.113578
$169$	−7.32624	−0.563557
$170$	−0.527864	−0.0404853
$171$	−3.00000	−0.229416
$172$	−15.0000	−1.14374
$173$	−9.18034	−0.697968	−0.348984	−	0.937129i	$-0.613473\pi$
$173$	−9.18034	−0.697968	−0.348984	+	0.937129i	$0.613473\pi$
$174$	2.85410	0.216369
$175$	−3.09017	−0.233595
$176$	−17.2148	−1.29761
$177$	−6.14590	−0.461954
$178$	−1.20163	−0.0900657
$179$	7.85410	0.587043	0.293522	−	0.955952i	$-0.405173\pi$
$179$	7.85410	0.587043	0.293522	+	0.955952i	$0.405173\pi$
$180$	2.56231	0.190983
$181$	7.47214	0.555399	0.277700	−	0.960668i	$-0.410428\pi$
$181$	7.47214	0.555399	0.277700	+	0.960668i	$0.410428\pi$
$182$	0.909830	0.0674411
$183$	13.7984	1.02001
$184$	−1.47214	−0.108527
$185$	−2.03444	−0.149575
$186$	1.43769	0.105417
$187$	5.47214	0.400162
$188$	−3.16718	−0.230991
$189$	1.00000	0.0727393
$190$	−1.58359	−0.114886
$191$	6.29180	0.455258	0.227629	−	0.973748i	$-0.426903\pi$
$191$	6.29180	0.455258	0.227629	+	0.973748i	$0.426903\pi$
$192$	−4.70820	−0.339785
$193$	−14.1803	−1.02072	−0.510362	−	0.859960i	$-0.670488\pi$
$193$	−14.1803	−1.02072	−0.510362	+	0.859960i	$0.670488\pi$
$194$	−1.90983	−0.137118
$195$	3.29180	0.235730
$196$	−1.85410	−0.132436
$197$	−12.8541	−0.915817	−0.457908	−	0.888999i	$-0.651401\pi$
$197$	−12.8541	−0.915817	−0.457908	+	0.888999i	$0.651401\pi$
$198$	2.09017	0.148542
$199$	−18.0344	−1.27843	−0.639214	−	0.769029i	$-0.720740\pi$
$199$	−18.0344	−1.27843	−0.639214	+	0.769029i	$0.720740\pi$
$200$	−4.54915	−0.321674
$201$	4.14590	0.292429
$202$	0.708204	0.0498291
$203$	−7.47214	−0.524441
$204$	1.85410	0.129813
$205$	6.50658	0.454439
$206$	1.88854	0.131581
$207$	−1.00000	−0.0695048
$208$	−7.49342	−0.519575
$209$	16.4164	1.13555
$210$	0.527864	0.0364261
$211$	26.4164	1.81858	0.909290	−	0.416163i	$-0.136625\pi$
$211$	26.4164	1.81858	0.909290	+	0.416163i	$0.136625\pi$
$212$	6.27051	0.430660
$213$	−3.90983	−0.267897
$214$	−4.50658	−0.308063
$215$	−11.1803	−0.762493
$216$	1.47214	0.100166
$217$	−3.76393	−0.255512
$218$	2.41641	0.163660
$219$	2.70820	0.183003
$220$	−14.0213	−0.945315
$221$	2.38197	0.160228
$222$	−0.562306	−0.0377395
$223$	−20.3262	−1.36115	−0.680573	−	0.732680i	$-0.738269\pi$
$223$	−20.3262	−1.36115	−0.680573	+	0.732680i	$0.738269\pi$
$224$	−4.14590	−0.277009
$225$	−3.09017	−0.206011
$226$	−2.41641	−0.160737
$227$	−8.79837	−0.583969	−0.291984	−	0.956423i	$-0.594316\pi$
$227$	−8.79837	−0.583969	−0.291984	+	0.956423i	$0.594316\pi$
$228$	5.56231	0.368373
$229$	−21.5623	−1.42488	−0.712439	−	0.701734i	$-0.752409\pi$
$229$	−21.5623	−1.42488	−0.712439	+	0.701734i	$0.752409\pi$
$230$	−0.527864	−0.0348063
$231$	−5.47214	−0.360040
$232$	−11.0000	−0.722185
$233$	19.2705	1.26245	0.631227	−	0.775599i	$-0.282552\pi$
$233$	19.2705	1.26245	0.631227	+	0.775599i	$0.282552\pi$
$234$	0.909830	0.0594775
$235$	−2.36068	−0.153994
$236$	11.3951	0.741759
$237$	0.527864	0.0342885
$238$	0.381966	0.0247592
$239$	−17.8541	−1.15489	−0.577443	−	0.816431i	$-0.695949\pi$
$239$	−17.8541	−1.15489	−0.577443	+	0.816431i	$0.695949\pi$
$240$	−4.34752	−0.280631
$241$	−20.4164	−1.31514	−0.657568	−	0.753395i	$-0.728415\pi$
$241$	−20.4164	−1.31514	−0.657568	+	0.753395i	$0.728415\pi$
$242$	−7.23607	−0.465152
$243$	1.00000	0.0641500
$244$	−25.5836	−1.63782
$245$	−1.38197	−0.0882906
$246$	1.79837	0.114660
$247$	7.14590	0.454683
$248$	−5.54102	−0.351855
$249$	−3.00000	−0.190117
$250$	−4.27051	−0.270091
$251$	1.23607	0.0780199	0.0390100	−	0.999239i	$-0.487580\pi$
$251$	1.23607	0.0780199	0.0390100	+	0.999239i	$0.487580\pi$
$252$	−1.85410	−0.116797
$253$	5.47214	0.344030
$254$	−7.20163	−0.451870
$255$	1.38197	0.0865421
$256$	5.56231	0.347644
$257$	−31.5967	−1.97095	−0.985475	−	0.169818i	$-0.945682\pi$
$257$	−31.5967	−1.97095	−0.985475	+	0.169818i	$0.945682\pi$
$258$	−3.09017	−0.192386
$259$	1.47214	0.0914741
$260$	−6.10333	−0.378512
$261$	−7.47214	−0.462514
$262$	6.85410	0.423448
$263$	23.6525	1.45847	0.729237	−	0.684261i	$-0.239875\pi$
$263$	23.6525	1.45847	0.729237	+	0.684261i	$0.239875\pi$
$264$	−8.05573	−0.495796
$265$	4.67376	0.287107
$266$	1.14590	0.0702595
$267$	3.14590	0.192526
$268$	−7.68692	−0.469553
$269$	−14.2705	−0.870088	−0.435044	−	0.900409i	$-0.643267\pi$
$269$	−14.2705	−0.870088	−0.435044	+	0.900409i	$0.643267\pi$
$270$	0.527864	0.0321248
$271$	31.8328	1.93371	0.966853	−	0.255334i	$-0.0821854\pi$
$271$	31.8328	1.93371	0.966853	+	0.255334i	$0.0821854\pi$
$272$	−3.14590	−0.190748
$273$	−2.38197	−0.144163
$274$	−3.50658	−0.211840
$275$	16.9098	1.01970
$276$	1.85410	0.111604
$277$	−19.1459	−1.15037	−0.575183	−	0.818025i	$-0.695069\pi$
$277$	−19.1459	−1.15037	−0.575183	+	0.818025i	$0.695069\pi$
$278$	6.23607	0.374015
$279$	−3.76393	−0.225341
$280$	−2.03444	−0.121581
$281$	27.7082	1.65293	0.826466	−	0.562986i	$-0.190348\pi$
$281$	27.7082	1.65293	0.826466	+	0.562986i	$0.190348\pi$
$282$	−0.652476	−0.0388544
$283$	−27.0902	−1.61034	−0.805172	−	0.593042i	$-0.797927\pi$
$283$	−27.0902	−1.61034	−0.805172	+	0.593042i	$0.797927\pi$
$284$	7.24922	0.430162
$285$	4.14590	0.245582
$286$	−4.97871	−0.294398
$287$	−4.70820	−0.277916
$288$	−4.14590	−0.244299
$289$	−16.0000	−0.941176
$290$	−3.94427	−0.231616
$291$	5.00000	0.293105
$292$	−5.02129	−0.293849
$293$	3.41641	0.199589	0.0997943	−	0.995008i	$-0.468182\pi$
$293$	3.41641	0.199589	0.0997943	+	0.995008i	$0.468182\pi$
$294$	−0.381966	−0.0222767
$295$	8.49342	0.494506
$296$	2.16718	0.125965
$297$	−5.47214	−0.317526
$298$	6.18034	0.358017
$299$	2.38197	0.137753
$300$	5.72949	0.330792
$301$	8.09017	0.466310
$302$	−0.291796	−0.0167910
$303$	−1.85410	−0.106515
$304$	−9.43769	−0.541289
$305$	−19.0689	−1.09188
$306$	0.381966	0.0218355
$307$	−22.7082	−1.29603	−0.648013	−	0.761629i	$-0.724400\pi$
$307$	−22.7082	−1.29603	−0.648013	+	0.761629i	$0.724400\pi$
$308$	10.1459	0.578116
$309$	−4.94427	−0.281270
$310$	−1.98684	−0.112845
$311$	21.5066	1.21953	0.609763	−	0.792584i	$-0.291265\pi$
$311$	21.5066	1.21953	0.609763	+	0.792584i	$0.291265\pi$
$312$	−3.50658	−0.198521
$313$	−2.47214	−0.139733	−0.0698667	−	0.997556i	$-0.522257\pi$
$313$	−2.47214	−0.139733	−0.0698667	+	0.997556i	$0.522257\pi$
$314$	7.88854	0.445176
$315$	−1.38197	−0.0778650
$316$	−0.978714	−0.0550570
$317$	−24.7984	−1.39282	−0.696408	−	0.717646i	$-0.745219\pi$
$317$	−24.7984	−1.39282	−0.696408	+	0.717646i	$0.745219\pi$
$318$	1.29180	0.0724403
$319$	40.8885	2.28932
$320$	6.50658	0.363729
$321$	11.7984	0.658521
$322$	0.381966	0.0212861
$323$	3.00000	0.166924
$324$	−1.85410	−0.103006
$325$	7.36068	0.408297
$326$	−1.06888	−0.0592000
$327$	−6.32624	−0.349842
$328$	−6.93112	−0.382707
$329$	1.70820	0.0941763
$330$	−2.88854	−0.159009
$331$	18.9443	1.04127	0.520636	−	0.853779i	$-0.325695\pi$
$331$	18.9443	1.04127	0.520636	+	0.853779i	$0.325695\pi$
$332$	5.56231	0.305271
$333$	1.47214	0.0806726
$334$	−5.54915	−0.303636
$335$	−5.72949	−0.313035
$336$	3.14590	0.171623
$337$	12.6738	0.690384	0.345192	−	0.938532i	$-0.387814\pi$
$337$	12.6738	0.690384	0.345192	+	0.938532i	$0.387814\pi$
$338$	2.79837	0.152211
$339$	6.32624	0.343594
$340$	−2.56231	−0.138961
$341$	20.5967	1.11538
$342$	1.14590	0.0619631
$343$	1.00000	0.0539949
$344$	11.9098	0.642135
$345$	1.38197	0.0744025
$346$	3.50658	0.188515
$347$	−6.41641	−0.344451	−0.172225	−	0.985058i	$-0.555096\pi$
$347$	−6.41641	−0.344451	−0.172225	+	0.985058i	$0.555096\pi$
$348$	13.8541	0.742658
$349$	−36.2148	−1.93853	−0.969266	−	0.246013i	$-0.920879\pi$
$349$	−36.2148	−1.93853	−0.969266	+	0.246013i	$0.920879\pi$
$350$	1.18034	0.0630918
$351$	−2.38197	−0.127140
$352$	22.6869	1.20922
$353$	11.6525	0.620199	0.310099	−	0.950704i	$-0.399638\pi$
$353$	11.6525	0.620199	0.310099	+	0.950704i	$0.399638\pi$
$354$	2.34752	0.124770
$355$	5.40325	0.286775
$356$	−5.83282	−0.309139
$357$	−1.00000	−0.0529256
$358$	−3.00000	−0.158555
$359$	−16.5066	−0.871184	−0.435592	−	0.900144i	$-0.643461\pi$
$359$	−16.5066	−0.871184	−0.435592	+	0.900144i	$0.643461\pi$
$360$	−2.03444	−0.107225
$361$	−10.0000	−0.526316
$362$	−2.85410	−0.150008
$363$	18.9443	0.994316
$364$	4.41641	0.231483
$365$	−3.74265	−0.195899
$366$	−5.27051	−0.275494
$367$	24.5623	1.28214	0.641071	−	0.767482i	$-0.278490\pi$
$367$	24.5623	1.28214	0.641071	+	0.767482i	$0.278490\pi$
$368$	−3.14590	−0.163991
$369$	−4.70820	−0.245099
$370$	0.777088	0.0403989
$371$	−3.38197	−0.175583
$372$	6.97871	0.361829
$373$	−12.0557	−0.624222	−0.312111	−	0.950046i	$-0.601036\pi$
$373$	−12.0557	−0.624222	−0.312111	+	0.950046i	$0.601036\pi$
$374$	−2.09017	−0.108080
$375$	11.1803	0.577350
$376$	2.51471	0.129686
$377$	17.7984	0.916663
$378$	−0.381966	−0.0196462
$379$	32.3607	1.66226	0.831128	−	0.556081i	$-0.187696\pi$
$379$	32.3607	1.66226	0.831128	+	0.556081i	$0.187696\pi$
$380$	−7.68692	−0.394331
$381$	18.8541	0.965925
$382$	−2.40325	−0.122961
$383$	−27.4721	−1.40376	−0.701880	−	0.712295i	$-0.747656\pi$
$383$	−27.4721	−1.40376	−0.701880	+	0.712295i	$0.747656\pi$
$384$	10.0902	0.514912
$385$	7.56231	0.385411
$386$	5.41641	0.275688
$387$	8.09017	0.411246
$388$	−9.27051	−0.470639
$389$	8.41641	0.426729	0.213364	−	0.976973i	$-0.431558\pi$
$389$	8.41641	0.426729	0.213364	+	0.976973i	$0.431558\pi$
$390$	−1.25735	−0.0636686
$391$	1.00000	0.0505722
$392$	1.47214	0.0743541
$393$	−17.9443	−0.905169
$394$	4.90983	0.247354
$395$	−0.729490	−0.0367046
$396$	10.1459	0.509851
$397$	−29.7082	−1.49101	−0.745506	−	0.666499i	$-0.767792\pi$
$397$	−29.7082	−1.49101	−0.745506	+	0.666499i	$0.767792\pi$
$398$	6.88854	0.345292
$399$	−3.00000	−0.150188
$400$	−9.72136	−0.486068
$401$	−5.58359	−0.278831	−0.139416	−	0.990234i	$-0.544522\pi$
$401$	−5.58359	−0.278831	−0.139416	+	0.990234i	$0.544522\pi$
$402$	−1.58359	−0.0789824
$403$	8.96556	0.446606
$404$	3.43769	0.171032
$405$	−1.38197	−0.0686704
$406$	2.85410	0.141647
$407$	−8.05573	−0.399308
$408$	−1.47214	−0.0728816
$409$	22.4164	1.10842	0.554210	−	0.832377i	$-0.313020\pi$
$409$	22.4164	1.10842	0.554210	+	0.832377i	$0.313020\pi$
$410$	−2.48529	−0.122740
$411$	9.18034	0.452833
$412$	9.16718	0.451635
$413$	−6.14590	−0.302420
$414$	0.381966	0.0187726
$415$	4.14590	0.203514
$416$	9.87539	0.484181
$417$	−16.3262	−0.799499
$418$	−6.27051	−0.306701
$419$	15.2705	0.746013	0.373007	−	0.927829i	$-0.378327\pi$
$419$	15.2705	0.746013	0.373007	+	0.927829i	$0.378327\pi$
$420$	2.56231	0.125028
$421$	−15.6180	−0.761176	−0.380588	−	0.924745i	$-0.624278\pi$
$421$	−15.6180	−0.761176	−0.380588	+	0.924745i	$0.624278\pi$
$422$	−10.0902	−0.491182
$423$	1.70820	0.0830557
$424$	−4.97871	−0.241788
$425$	3.09017	0.149895
$426$	1.49342	0.0723565
$427$	13.7984	0.667750
$428$	−21.8754	−1.05739
$429$	13.0344	0.629309
$430$	4.27051	0.205942
$431$	−32.1591	−1.54905	−0.774524	−	0.632545i	$-0.782010\pi$
$431$	−32.1591	−1.54905	−0.774524	+	0.632545i	$0.782010\pi$
$432$	3.14590	0.151357
$433$	−14.1803	−0.681464	−0.340732	−	0.940161i	$-0.610675\pi$
$433$	−14.1803	−0.681464	−0.340732	+	0.940161i	$0.610675\pi$
$434$	1.43769	0.0690115
$435$	10.3262	0.495105
$436$	11.7295	0.561741
$437$	3.00000	0.143509
$438$	−1.03444	−0.0494275
$439$	−3.18034	−0.151789	−0.0758947	−	0.997116i	$-0.524181\pi$
$439$	−3.18034	−0.151789	−0.0758947	+	0.997116i	$0.524181\pi$
$440$	11.1327	0.530733
$441$	1.00000	0.0476190
$442$	−0.909830	−0.0432762
$443$	4.58359	0.217773	0.108887	−	0.994054i	$-0.465271\pi$
$443$	4.58359	0.217773	0.108887	+	0.994054i	$0.465271\pi$
$444$	−2.72949	−0.129536
$445$	−4.34752	−0.206092
$446$	7.76393	0.367633
$447$	−16.1803	−0.765304
$448$	−4.70820	−0.222442
$449$	36.5066	1.72285	0.861426	−	0.507883i	$-0.169572\pi$
$449$	36.5066	1.72285	0.861426	+	0.507883i	$0.169572\pi$
$450$	1.18034	0.0556418
$451$	25.7639	1.21318
$452$	−11.7295	−0.551709
$453$	0.763932	0.0358927
$454$	3.36068	0.157725
$455$	3.29180	0.154322
$456$	−4.41641	−0.206817
$457$	18.9098	0.884565	0.442282	−	0.896876i	$-0.354169\pi$
$457$	18.9098	0.884565	0.442282	+	0.896876i	$0.354169\pi$
$458$	8.23607	0.384846
$459$	−1.00000	−0.0466760
$460$	−2.56231	−0.119468
$461$	0.618034	0.0287847	0.0143924	−	0.999896i	$-0.495419\pi$
$461$	0.618034	0.0287847	0.0143924	+	0.999896i	$0.495419\pi$
$462$	2.09017	0.0972435
$463$	37.6525	1.74986	0.874929	−	0.484250i	$-0.160908\pi$
$463$	37.6525	1.74986	0.874929	+	0.484250i	$0.160908\pi$
$464$	−23.5066	−1.09127
$465$	5.20163	0.241220
$466$	−7.36068	−0.340977
$467$	38.7771	1.79439	0.897195	−	0.441635i	$-0.145601\pi$
$467$	38.7771	1.79439	0.897195	+	0.441635i	$0.145601\pi$
$468$	4.41641	0.204149
$469$	4.14590	0.191440
$470$	0.901699	0.0415923
$471$	−20.6525	−0.951616
$472$	−9.04760	−0.416449
$473$	−44.2705	−2.03556
$474$	−0.201626	−0.00926099
$475$	9.27051	0.425360
$476$	1.85410	0.0849826
$477$	−3.38197	−0.154850
$478$	6.81966	0.311924
$479$	18.2361	0.833227	0.416614	−	0.909084i	$-0.363217\pi$
$479$	18.2361	0.833227	0.416614	+	0.909084i	$0.363217\pi$
$480$	5.72949	0.261514
$481$	−3.50658	−0.159886
$482$	7.79837	0.355206
$483$	−1.00000	−0.0455016
$484$	−35.1246	−1.59657
$485$	−6.90983	−0.313759
$486$	−0.381966	−0.0173263
$487$	−12.7082	−0.575864	−0.287932	−	0.957651i	$-0.592968\pi$
$487$	−12.7082	−0.575864	−0.287932	+	0.957651i	$0.592968\pi$
$488$	20.3131	0.919530
$489$	2.79837	0.126547
$490$	0.527864	0.0238465
$491$	15.9787	0.721109	0.360555	−	0.932738i	$-0.382587\pi$
$491$	15.9787	0.721109	0.360555	+	0.932738i	$0.382587\pi$
$492$	8.72949	0.393556
$493$	7.47214	0.336528
$494$	−2.72949	−0.122806
$495$	7.56231	0.339900
$496$	−11.8409	−0.531674
$497$	−3.90983	−0.175380
$498$	1.14590	0.0513489
$499$	−10.0344	−0.449203	−0.224602	−	0.974451i	$-0.572108\pi$
$499$	−10.0344	−0.449203	−0.224602	+	0.974451i	$0.572108\pi$
$500$	−20.7295	−0.927051
$501$	14.5279	0.649057
$502$	−0.472136	−0.0210725
$503$	−37.7426	−1.68286	−0.841431	−	0.540365i	$-0.818286\pi$
$503$	−37.7426	−1.68286	−0.841431	+	0.540365i	$0.818286\pi$
$504$	1.47214	0.0655741
$505$	2.56231	0.114021
$506$	−2.09017	−0.0929194
$507$	−7.32624	−0.325370
$508$	−34.9574	−1.55099
$509$	8.18034	0.362587	0.181294	−	0.983429i	$-0.441972\pi$
$509$	8.18034	0.362587	0.181294	+	0.983429i	$0.441972\pi$
$510$	−0.527864	−0.0233742
$511$	2.70820	0.119804
$512$	−22.3050	−0.985749
$513$	−3.00000	−0.132453
$514$	12.0689	0.532336
$515$	6.83282	0.301090
$516$	−15.0000	−0.660338
$517$	−9.34752	−0.411104
$518$	−0.562306	−0.0247063
$519$	−9.18034	−0.402972
$520$	4.84597	0.212510
$521$	33.4164	1.46400	0.732000	−	0.681305i	$-0.238587\pi$
$521$	33.4164	1.46400	0.732000	+	0.681305i	$0.238587\pi$
$522$	2.85410	0.124921
$523$	−14.3607	−0.627949	−0.313974	−	0.949431i	$-0.601661\pi$
$523$	−14.3607	−0.627949	−0.313974	+	0.949431i	$0.601661\pi$
$524$	33.2705	1.45343
$525$	−3.09017	−0.134866
$526$	−9.03444	−0.393920
$527$	3.76393	0.163959
$528$	−17.2148	−0.749177
$529$	1.00000	0.0434783
$530$	−1.78522	−0.0775449
$531$	−6.14590	−0.266709
$532$	5.56231	0.241157
$533$	11.2148	0.485766
$534$	−1.20163	−0.0519994
$535$	−16.3050	−0.704925
$536$	6.10333	0.263624
$537$	7.85410	0.338930
$538$	5.45085	0.235003
$539$	−5.47214	−0.235702
$540$	2.56231	0.110264
$541$	−38.6525	−1.66180	−0.830900	−	0.556422i	$-0.812174\pi$
$541$	−38.6525	−1.66180	−0.830900	+	0.556422i	$0.812174\pi$
$542$	−12.1591	−0.522276
$543$	7.47214	0.320660
$544$	4.14590	0.177754
$545$	8.74265	0.374494
$546$	0.909830	0.0389371
$547$	7.27051	0.310865	0.155432	−	0.987847i	$-0.450323\pi$
$547$	7.27051	0.310865	0.155432	+	0.987847i	$0.450323\pi$
$548$	−17.0213	−0.727113
$549$	13.7984	0.588900
$550$	−6.45898	−0.275412
$551$	22.4164	0.954971
$552$	−1.47214	−0.0626583
$553$	0.527864	0.0224471
$554$	7.31308	0.310703
$555$	−2.03444	−0.0863572
$556$	30.2705	1.28376
$557$	27.7082	1.17403	0.587017	−	0.809575i	$-0.300302\pi$
$557$	27.7082	1.17403	0.587017	+	0.809575i	$0.300302\pi$
$558$	1.43769	0.0608624
$559$	−19.2705	−0.815056
$560$	−4.34752	−0.183716
$561$	5.47214	0.231034
$562$	−10.5836	−0.446442
$563$	32.7426	1.37994	0.689969	−	0.723839i	$-0.257624\pi$
$563$	32.7426	1.37994	0.689969	+	0.723839i	$0.257624\pi$
$564$	−3.16718	−0.133363
$565$	−8.74265	−0.367806
$566$	10.3475	0.434939
$567$	1.00000	0.0419961
$568$	−5.75580	−0.241508
$569$	−18.8328	−0.789513	−0.394756	−	0.918786i	$-0.629171\pi$
$569$	−18.8328	−0.789513	−0.394756	+	0.918786i	$0.629171\pi$
$570$	−1.58359	−0.0663294
$571$	38.8885	1.62743	0.813717	−	0.581261i	$-0.197440\pi$
$571$	38.8885	1.62743	0.813717	+	0.581261i	$0.197440\pi$
$572$	−24.1672	−1.01048
$573$	6.29180	0.262844
$574$	1.79837	0.0750627
$575$	3.09017	0.128869
$576$	−4.70820	−0.196175
$577$	−16.4721	−0.685744	−0.342872	−	0.939382i	$-0.611400\pi$
$577$	−16.4721	−0.685744	−0.342872	+	0.939382i	$0.611400\pi$
$578$	6.11146	0.254203
$579$	−14.1803	−0.589315
$580$	−19.1459	−0.794990
$581$	−3.00000	−0.124461
$582$	−1.90983	−0.0791650
$583$	18.5066	0.766464
$584$	3.98684	0.164977
$585$	3.29180	0.136099
$586$	−1.30495	−0.0539071
$587$	3.72949	0.153933	0.0769663	−	0.997034i	$-0.475477\pi$
$587$	3.72949	0.153933	0.0769663	+	0.997034i	$0.475477\pi$
$588$	−1.85410	−0.0764619
$589$	11.2918	0.465270
$590$	−3.24420	−0.133562
$591$	−12.8541	−0.528747
$592$	4.63119	0.190341
$593$	19.1246	0.785354	0.392677	−	0.919677i	$-0.371549\pi$
$593$	19.1246	0.785354	0.392677	+	0.919677i	$0.371549\pi$
$594$	2.09017	0.0857607
$595$	1.38197	0.0566551
$596$	30.0000	1.22885
$597$	−18.0344	−0.738101
$598$	−0.909830	−0.0372057
$599$	14.0902	0.575709	0.287854	−	0.957674i	$-0.407058\pi$
$599$	14.0902	0.575709	0.287854	+	0.957674i	$0.407058\pi$
$600$	−4.54915	−0.185718
$601$	−15.6738	−0.639346	−0.319673	−	0.947528i	$-0.603573\pi$
$601$	−15.6738	−0.639346	−0.319673	+	0.947528i	$0.603573\pi$
$602$	−3.09017	−0.125946
$603$	4.14590	0.168834
$604$	−1.41641	−0.0576328
$605$	−26.1803	−1.06438
$606$	0.708204	0.0287688
$607$	20.0902	0.815435	0.407717	−	0.913108i	$-0.366325\pi$
$607$	20.0902	0.815435	0.407717	+	0.913108i	$0.366325\pi$
$608$	12.4377	0.504415
$609$	−7.47214	−0.302786
$610$	7.28367	0.294907
$611$	−4.06888	−0.164609
$612$	1.85410	0.0749476
$613$	−1.65248	−0.0667429	−0.0333714	−	0.999443i	$-0.510624\pi$
$613$	−1.65248	−0.0667429	−0.0333714	+	0.999443i	$0.510624\pi$
$614$	8.67376	0.350045
$615$	6.50658	0.262371
$616$	−8.05573	−0.324575
$617$	−33.3951	−1.34444	−0.672218	−	0.740353i	$-0.734658\pi$
$617$	−33.3951	−1.34444	−0.672218	+	0.740353i	$0.734658\pi$
$618$	1.88854	0.0759684
$619$	43.6180	1.75316	0.876578	−	0.481259i	$-0.159820\pi$
$619$	43.6180	1.75316	0.876578	+	0.481259i	$0.159820\pi$
$620$	−9.64435	−0.387326
$621$	−1.00000	−0.0401286
$622$	−8.21478	−0.329383
$623$	3.14590	0.126038
$624$	−7.49342	−0.299977
$625$	0	0
$626$	0.944272	0.0377407
$627$	16.4164	0.655608
$628$	38.2918	1.52801
$629$	−1.47214	−0.0586979
$630$	0.527864	0.0210306
$631$	−20.7082	−0.824381	−0.412190	−	0.911098i	$-0.635236\pi$
$631$	−20.7082	−0.824381	−0.412190	+	0.911098i	$0.635236\pi$
$632$	0.777088	0.0309109
$633$	26.4164	1.04996
$634$	9.47214	0.376187
$635$	−26.0557	−1.03399
$636$	6.27051	0.248642
$637$	−2.38197	−0.0943769
$638$	−15.6180	−0.618324
$639$	−3.90983	−0.154670
$640$	−13.9443	−0.551196
$641$	27.2148	1.07492	0.537460	−	0.843289i	$-0.319384\pi$
$641$	27.2148	1.07492	0.537460	+	0.843289i	$0.319384\pi$
$642$	−4.50658	−0.177860
$643$	5.14590	0.202934	0.101467	−	0.994839i	$-0.467646\pi$
$643$	5.14590	0.202934	0.101467	+	0.994839i	$0.467646\pi$
$644$	1.85410	0.0730619
$645$	−11.1803	−0.440225
$646$	−1.14590	−0.0450848
$647$	18.3262	0.720479	0.360239	−	0.932860i	$-0.382695\pi$
$647$	18.3262	0.720479	0.360239	+	0.932860i	$0.382695\pi$
$648$	1.47214	0.0578310
$649$	33.6312	1.32014
$650$	−2.81153	−0.110277
$651$	−3.76393	−0.147520
$652$	−5.18847	−0.203196
$653$	−39.5623	−1.54819	−0.774096	−	0.633068i	$-0.781795\pi$
$653$	−39.5623	−1.54819	−0.774096	+	0.633068i	$0.781795\pi$
$654$	2.41641	0.0944890
$655$	24.7984	0.968953
$656$	−14.8115	−0.578293
$657$	2.70820	0.105657
$658$	−0.652476	−0.0254362
$659$	−29.4721	−1.14807	−0.574036	−	0.818830i	$-0.694623\pi$
$659$	−29.4721	−1.14807	−0.574036	+	0.818830i	$0.694623\pi$
$660$	−14.0213	−0.545778
$661$	32.7771	1.27488	0.637440	−	0.770500i	$-0.279993\pi$
$661$	32.7771	1.27488	0.637440	+	0.770500i	$0.279993\pi$
$662$	−7.23607	−0.281238
$663$	2.38197	0.0925079
$664$	−4.41641	−0.171390
$665$	4.14590	0.160771
$666$	−0.562306	−0.0217889
$667$	7.47214	0.289322
$668$	−26.9361	−1.04219
$669$	−20.3262	−0.785858
$670$	2.18847	0.0845480
$671$	−75.5066	−2.91490
$672$	−4.14590	−0.159931
$673$	−32.8885	−1.26776	−0.633880	−	0.773431i	$-0.718539\pi$
$673$	−32.8885	−1.26776	−0.633880	+	0.773431i	$0.718539\pi$
$674$	−4.84095	−0.186466
$675$	−3.09017	−0.118941
$676$	13.5836	0.522446
$677$	−3.61803	−0.139052	−0.0695262	−	0.997580i	$-0.522149\pi$
$677$	−3.61803	−0.139052	−0.0695262	+	0.997580i	$0.522149\pi$
$678$	−2.41641	−0.0928016
$679$	5.00000	0.191882
$680$	2.03444	0.0780173
$681$	−8.79837	−0.337154
$682$	−7.86726	−0.301253
$683$	−34.8885	−1.33497	−0.667487	−	0.744622i	$-0.732630\pi$
$683$	−34.8885	−1.33497	−0.667487	+	0.744622i	$0.732630\pi$
$684$	5.56231	0.212680
$685$	−12.6869	−0.484742
$686$	−0.381966	−0.0145835
$687$	−21.5623	−0.822653
$688$	25.4508	0.970305
$689$	8.05573	0.306899
$690$	−0.527864	−0.0200954
$691$	−1.03444	−0.0393520	−0.0196760	−	0.999806i	$-0.506263\pi$
$691$	−1.03444	−0.0393520	−0.0196760	+	0.999806i	$0.506263\pi$
$692$	17.0213	0.647052
$693$	−5.47214	−0.207869
$694$	2.45085	0.0930330
$695$	22.5623	0.855837
$696$	−11.0000	−0.416954
$697$	4.70820	0.178336
$698$	13.8328	0.523580
$699$	19.2705	0.728878
$700$	5.72949	0.216554
$701$	−20.0344	−0.756690	−0.378345	−	0.925665i	$-0.623507\pi$
$701$	−20.0344	−0.756690	−0.378345	+	0.925665i	$0.623507\pi$
$702$	0.909830	0.0343393
$703$	−4.41641	−0.166568
$704$	25.7639	0.971015
$705$	−2.36068	−0.0889083
$706$	−4.45085	−0.167510
$707$	−1.85410	−0.0697307
$708$	11.3951	0.428255
$709$	30.9230	1.16134	0.580669	−	0.814140i	$-0.302791\pi$
$709$	30.9230	1.16134	0.580669	+	0.814140i	$0.302791\pi$
$710$	−2.06386	−0.0774552
$711$	0.527864	0.0197964
$712$	4.63119	0.173561
$713$	3.76393	0.140960
$714$	0.381966	0.0142947
$715$	−18.0132	−0.673654
$716$	−14.5623	−0.544219
$717$	−17.8541	−0.666774
$718$	6.30495	0.235299
$719$	−28.7082	−1.07064	−0.535318	−	0.844651i	$-0.679808\pi$
$719$	−28.7082	−1.07064	−0.535318	+	0.844651i	$0.679808\pi$
$720$	−4.34752	−0.162023
$721$	−4.94427	−0.184134
$722$	3.81966	0.142153
$723$	−20.4164	−0.759294
$724$	−13.8541	−0.514884
$725$	23.0902	0.857547
$726$	−7.23607	−0.268556
$727$	3.36068	0.124641	0.0623204	−	0.998056i	$-0.480150\pi$
$727$	3.36068	0.124641	0.0623204	+	0.998056i	$0.480150\pi$
$728$	−3.50658	−0.129962
$729$	1.00000	0.0370370
$730$	1.42956	0.0529105
$731$	−8.09017	−0.299226
$732$	−25.5836	−0.945597
$733$	2.18034	0.0805327	0.0402663	−	0.999189i	$-0.487179\pi$
$733$	2.18034	0.0805327	0.0402663	+	0.999189i	$0.487179\pi$
$734$	−9.38197	−0.346295
$735$	−1.38197	−0.0509746
$736$	4.14590	0.152820
$737$	−22.6869	−0.835683
$738$	1.79837	0.0661991
$739$	4.88854	0.179828	0.0899140	−	0.995950i	$-0.471341\pi$
$739$	4.88854	0.179828	0.0899140	+	0.995950i	$0.471341\pi$
$740$	3.77206	0.138664
$741$	7.14590	0.262511
$742$	1.29180	0.0474233
$743$	−22.0344	−0.808365	−0.404183	−	0.914678i	$-0.632444\pi$
$743$	−22.0344	−0.808365	−0.404183	+	0.914678i	$0.632444\pi$
$744$	−5.54102	−0.203144
$745$	22.3607	0.819232
$746$	4.60488	0.168597
$747$	−3.00000	−0.109764
$748$	−10.1459	−0.370971
$749$	11.7984	0.431103
$750$	−4.27051	−0.155937
$751$	−44.3951	−1.62000	−0.810000	−	0.586429i	$-0.800533\pi$
$751$	−44.3951	−1.62000	−0.810000	+	0.586429i	$0.800533\pi$
$752$	5.37384	0.195964
$753$	1.23607	0.0450448
$754$	−6.79837	−0.247582
$755$	−1.05573	−0.0384219
$756$	−1.85410	−0.0674330
$757$	3.11146	0.113088	0.0565439	−	0.998400i	$-0.481992\pi$
$757$	3.11146	0.113088	0.0565439	+	0.998400i	$0.481992\pi$
$758$	−12.3607	−0.448960
$759$	5.47214	0.198626
$760$	6.10333	0.221391
$761$	13.3050	0.482304	0.241152	−	0.970487i	$-0.422475\pi$
$761$	13.3050	0.482304	0.241152	+	0.970487i	$0.422475\pi$
$762$	−7.20163	−0.260887
$763$	−6.32624	−0.229025
$764$	−11.6656	−0.422048
$765$	1.38197	0.0499651
$766$	10.4934	0.379143
$767$	14.6393	0.528595
$768$	5.56231	0.200712
$769$	−17.5967	−0.634555	−0.317277	−	0.948333i	$-0.602769\pi$
$769$	−17.5967	−0.634555	−0.317277	+	0.948333i	$0.602769\pi$
$770$	−2.88854	−0.104096
$771$	−31.5967	−1.13793
$772$	26.2918	0.946262
$773$	−40.0132	−1.43917	−0.719587	−	0.694403i	$-0.755669\pi$
$773$	−40.0132	−1.43917	−0.719587	+	0.694403i	$0.755669\pi$
$774$	−3.09017	−0.111074
$775$	11.6312	0.417805
$776$	7.36068	0.264233
$777$	1.47214	0.0528126
$778$	−3.21478	−0.115256
$779$	14.1246	0.506067
$780$	−6.10333	−0.218534
$781$	21.3951	0.765578
$782$	−0.381966	−0.0136591
$783$	−7.47214	−0.267032
$784$	3.14590	0.112354
$785$	28.5410	1.01867
$786$	6.85410	0.244478
$787$	−30.0344	−1.07061	−0.535306	−	0.844658i	$-0.679804\pi$
$787$	−30.0344	−1.07061	−0.535306	+	0.844658i	$0.679804\pi$
$788$	23.8328	0.849009
$789$	23.6525	0.842050
$790$	0.278640	0.00991358
$791$	6.32624	0.224935
$792$	−8.05573	−0.286248
$793$	−32.8673	−1.16715
$794$	11.3475	0.402709
$795$	4.67376	0.165761
$796$	33.4377	1.18517
$797$	−35.5967	−1.26090	−0.630451	−	0.776229i	$-0.717130\pi$
$797$	−35.5967	−1.26090	−0.630451	+	0.776229i	$0.717130\pi$
$798$	1.14590	0.0405644
$799$	−1.70820	−0.0604319
$800$	12.8115	0.452956
$801$	3.14590	0.111155
$802$	2.13274	0.0753098
$803$	−14.8197	−0.522974
$804$	−7.68692	−0.271097
$805$	1.38197	0.0487079
$806$	−3.42454	−0.120624
$807$	−14.2705	−0.502346
$808$	−2.72949	−0.0960231
$809$	0.965558	0.0339472	0.0169736	−	0.999856i	$-0.494597\pi$
$809$	0.965558	0.0339472	0.0169736	+	0.999856i	$0.494597\pi$
$810$	0.527864	0.0185473
$811$	−10.5279	−0.369683	−0.184842	−	0.982768i	$-0.559177\pi$
$811$	−10.5279	−0.369683	−0.184842	+	0.982768i	$0.559177\pi$
$812$	13.8541	0.486184
$813$	31.8328	1.11643
$814$	3.07701	0.107849
$815$	−3.86726	−0.135464
$816$	−3.14590	−0.110128
$817$	−24.2705	−0.849118
$818$	−8.56231	−0.299374
$819$	−2.38197	−0.0832326
$820$	−12.0639	−0.421288
$821$	20.1803	0.704299	0.352149	−	0.935944i	$-0.385451\pi$
$821$	20.1803	0.704299	0.352149	+	0.935944i	$0.385451\pi$
$822$	−3.50658	−0.122306
$823$	−20.4377	−0.712413	−0.356207	−	0.934407i	$-0.615930\pi$
$823$	−20.4377	−0.712413	−0.356207	+	0.934407i	$0.615930\pi$
$824$	−7.27864	−0.253563
$825$	16.9098	0.588725
$826$	2.34752	0.0816808
$827$	−33.5623	−1.16708	−0.583538	−	0.812086i	$-0.698332\pi$
$827$	−33.5623	−1.16708	−0.583538	+	0.812086i	$0.698332\pi$
$828$	1.85410	0.0644345
$829$	−30.0557	−1.04388	−0.521939	−	0.852983i	$-0.674791\pi$
$829$	−30.0557	−1.04388	−0.521939	+	0.852983i	$0.674791\pi$
$830$	−1.58359	−0.0549673
$831$	−19.1459	−0.664164
$832$	11.2148	0.388803
$833$	−1.00000	−0.0346479
$834$	6.23607	0.215937
$835$	−20.0770	−0.694794
$836$	−30.4377	−1.05271
$837$	−3.76393	−0.130101
$838$	−5.83282	−0.201491
$839$	−15.1459	−0.522894	−0.261447	−	0.965218i	$-0.584200\pi$
$839$	−15.1459	−0.522894	−0.261447	+	0.965218i	$0.584200\pi$
$840$	−2.03444	−0.0701949
$841$	26.8328	0.925270
$842$	5.96556	0.205587
$843$	27.7082	0.954321
$844$	−48.9787	−1.68592
$845$	10.1246	0.348297
$846$	−0.652476	−0.0224326
$847$	18.9443	0.650933
$848$	−10.6393	−0.365356
$849$	−27.0902	−0.929732
$850$	−1.18034	−0.0404853
$851$	−1.47214	−0.0504642
$852$	7.24922	0.248354
$853$	11.3475	0.388532	0.194266	−	0.980949i	$-0.437768\pi$
$853$	11.3475	0.388532	0.194266	+	0.980949i	$0.437768\pi$
$854$	−5.27051	−0.180353
$855$	4.14590	0.141787
$856$	17.3688	0.593654
$857$	27.1246	0.926559	0.463280	−	0.886212i	$-0.346673\pi$
$857$	27.1246	0.926559	0.463280	+	0.886212i	$0.346673\pi$
$858$	−4.97871	−0.169970
$859$	16.8328	0.574328	0.287164	−	0.957881i	$-0.407287\pi$
$859$	16.8328	0.574328	0.287164	+	0.957881i	$0.407287\pi$
$860$	20.7295	0.706870
$861$	−4.70820	−0.160455
$862$	12.2837	0.418383
$863$	14.1803	0.482704	0.241352	−	0.970438i	$-0.422409\pi$
$863$	14.1803	0.482704	0.241352	+	0.970438i	$0.422409\pi$
$864$	−4.14590	−0.141046
$865$	12.6869	0.431368
$866$	5.41641	0.184057
$867$	−16.0000	−0.543388
$868$	6.97871	0.236873
$869$	−2.88854	−0.0979871
$870$	−3.94427	−0.133723
$871$	−9.87539	−0.334615
$872$	−9.31308	−0.315381
$873$	5.00000	0.169224
$874$	−1.14590	−0.0387606
$875$	11.1803	0.377964
$876$	−5.02129	−0.169654
$877$	−15.4164	−0.520575	−0.260288	−	0.965531i	$-0.583817\pi$
$877$	−15.4164	−0.520575	−0.260288	+	0.965531i	$0.583817\pi$
$878$	1.21478	0.0409969
$879$	3.41641	0.115233
$880$	23.7902	0.801969
$881$	−47.4853	−1.59982	−0.799910	−	0.600120i	$-0.795120\pi$
$881$	−47.4853	−1.59982	−0.799910	+	0.600120i	$0.795120\pi$
$882$	−0.381966	−0.0128615
$883$	7.50658	0.252616	0.126308	−	0.991991i	$-0.459687\pi$
$883$	7.50658	0.252616	0.126308	+	0.991991i	$0.459687\pi$
$884$	−4.41641	−0.148540
$885$	8.49342	0.285503
$886$	−1.75078	−0.0588185
$887$	37.1459	1.24724	0.623619	−	0.781729i	$-0.285662\pi$
$887$	37.1459	1.24724	0.623619	+	0.781729i	$0.285662\pi$
$888$	2.16718	0.0727259
$889$	18.8541	0.632346
$890$	1.66061	0.0556637
$891$	−5.47214	−0.183323
$892$	37.6869	1.26185
$893$	−5.12461	−0.171489
$894$	6.18034	0.206701
$895$	−10.8541	−0.362813
$896$	10.0902	0.337089
$897$	2.38197	0.0795315
$898$	−13.9443	−0.465326
$899$	28.1246	0.938008
$900$	5.72949	0.190983
$901$	3.38197	0.112670
$902$	−9.84095	−0.327668
$903$	8.09017	0.269224
$904$	9.31308	0.309749
$905$	−10.3262	−0.343256
$906$	−0.291796	−0.00969428
$907$	23.9656	0.795763	0.397882	−	0.917437i	$-0.369745\pi$
$907$	23.9656	0.795763	0.397882	+	0.917437i	$0.369745\pi$
$908$	16.3131	0.541369
$909$	−1.85410	−0.0614967
$910$	−1.25735	−0.0416809
$911$	−36.1803	−1.19871	−0.599354	−	0.800484i	$-0.704576\pi$
$911$	−36.1803	−1.19871	−0.599354	+	0.800484i	$0.704576\pi$
$912$	−9.43769	−0.312513
$913$	16.4164	0.543304
$914$	−7.22291	−0.238913
$915$	−19.0689	−0.630398
$916$	39.9787	1.32093
$917$	−17.9443	−0.592572
$918$	0.381966	0.0126068
$919$	15.0689	0.497077	0.248538	−	0.968622i	$-0.420050\pi$
$919$	15.0689	0.497077	0.248538	+	0.968622i	$0.420050\pi$
$920$	2.03444	0.0670736
$921$	−22.7082	−0.748261
$922$	−0.236068	−0.00777448
$923$	9.31308	0.306544
$924$	10.1459	0.333776
$925$	−4.54915	−0.149575
$926$	−14.3820	−0.472621
$927$	−4.94427	−0.162391
$928$	30.9787	1.01693
$929$	−54.6180	−1.79196	−0.895980	−	0.444095i	$-0.853525\pi$
$929$	−54.6180	−1.79196	−0.895980	+	0.444095i	$0.853525\pi$
$930$	−1.98684	−0.0651512
$931$	−3.00000	−0.0983210
$932$	−35.7295	−1.17036
$933$	21.5066	0.704094
$934$	−14.8115	−0.484648
$935$	−7.56231	−0.247314
$936$	−3.50658	−0.114616
$937$	44.1246	1.44149	0.720744	−	0.693201i	$-0.243800\pi$
$937$	44.1246	1.44149	0.720744	+	0.693201i	$0.243800\pi$
$938$	−1.58359	−0.0517061
$939$	−2.47214	−0.0806751
$940$	4.37694	0.142760
$941$	26.8328	0.874725	0.437362	−	0.899285i	$-0.355913\pi$
$941$	26.8328	0.874725	0.437362	+	0.899285i	$0.355913\pi$
$942$	7.88854	0.257023
$943$	4.70820	0.153320
$944$	−19.3344	−0.629280
$945$	−1.38197	−0.0449554
$946$	16.9098	0.549786
$947$	−45.4164	−1.47583	−0.737917	−	0.674891i	$-0.764191\pi$
$947$	−45.4164	−1.47583	−0.737917	+	0.674891i	$0.764191\pi$
$948$	−0.978714	−0.0317871
$949$	−6.45085	−0.209403
$950$	−3.54102	−0.114886
$951$	−24.7984	−0.804142
$952$	−1.47214	−0.0477122
$953$	59.6869	1.93345	0.966724	−	0.255820i	$-0.0823454\pi$
$953$	59.6869	1.93345	0.966724	+	0.255820i	$0.0823454\pi$
$954$	1.29180	0.0418234
$955$	−8.69505	−0.281365
$956$	33.1033	1.07064
$957$	40.8885	1.32174
$958$	−6.96556	−0.225047
$959$	9.18034	0.296449
$960$	6.50658	0.209999
$961$	−16.8328	−0.542994
$962$	1.33939	0.0431838
$963$	11.7984	0.380197
$964$	37.8541	1.21920
$965$	19.5967	0.630842
$966$	0.381966	0.0122896
$967$	−21.7771	−0.700304	−0.350152	−	0.936693i	$-0.613870\pi$
$967$	−21.7771	−0.700304	−0.350152	+	0.936693i	$0.613870\pi$
$968$	27.8885	0.896372
$969$	3.00000	0.0963739
$970$	2.63932	0.0847435
$971$	35.9787	1.15461	0.577306	−	0.816528i	$-0.304104\pi$
$971$	35.9787	1.15461	0.577306	+	0.816528i	$0.304104\pi$
$972$	−1.85410	−0.0594703
$973$	−16.3262	−0.523395
$974$	4.85410	0.155535
$975$	7.36068	0.235730
$976$	43.4083	1.38947
$977$	−24.2016	−0.774279	−0.387139	−	0.922021i	$-0.626537\pi$
$977$	−24.2016	−0.774279	−0.387139	+	0.922021i	$0.626537\pi$
$978$	−1.06888	−0.0341791
$979$	−17.2148	−0.550187
$980$	2.56231	0.0818499
$981$	−6.32624	−0.201981
$982$	−6.10333	−0.194765
$983$	−33.3607	−1.06404	−0.532020	−	0.846732i	$-0.678567\pi$
$983$	−33.3607	−1.06404	−0.532020	+	0.846732i	$0.678567\pi$
$984$	−6.93112	−0.220956
$985$	17.7639	0.566006
$986$	−2.85410	−0.0908931
$987$	1.70820	0.0543727
$988$	−13.2492	−0.421514
$989$	−8.09017	−0.257252
$990$	−2.88854	−0.0918039
$991$	14.0902	0.447589	0.223794	−	0.974636i	$-0.428156\pi$
$991$	14.0902	0.447589	0.223794	+	0.974636i	$0.428156\pi$
$992$	15.6049	0.495455
$993$	18.9443	0.601178
$994$	1.49342	0.0473685
$995$	24.9230	0.790112
$996$	5.56231	0.176248
$997$	−40.8885	−1.29495	−0.647477	−	0.762085i	$-0.724176\pi$
$997$	−40.8885	−1.29495	−0.647477	+	0.762085i	$0.724176\pi$
$998$	3.83282	0.121326
$999$	1.47214	0.0465763

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.c.1.2	✓	2
3.2	odd	2		1449.2.a.k.1.1		2
4.3	odd	2		7728.2.a.v.1.2		2
7.6	odd	2		3381.2.a.n.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.c.1.2	✓	2	1.1	even	1	trivial
1449.2.a.k.1.1		2	3.2	odd	2
3381.2.a.n.1.2		2	7.6	odd	2
7728.2.a.v.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)

\(f(q)\)	\(=\)	\(q-0.381966 q^{2} +1.00000 q^{3} -1.85410 q^{4} -1.38197 q^{5} -0.381966 q^{6} +1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.381966 q^{2} +1.00000 q^{3} -1.85410 q^{4} -1.38197 q^{5} -0.381966 q^{6} +1.00000 q^{7} +1.47214 q^{8} +1.00000 q^{9} +0.527864 q^{10} -5.47214 q^{11} -1.85410 q^{12} -2.38197 q^{13} -0.381966 q^{14} -1.38197 q^{15} +3.14590 q^{16} -1.00000 q^{17} -0.381966 q^{18} -3.00000 q^{19} +2.56231 q^{20} +1.00000 q^{21} +2.09017 q^{22} -1.00000 q^{23} +1.47214 q^{24} -3.09017 q^{25} +0.909830 q^{26} +1.00000 q^{27} -1.85410 q^{28} -7.47214 q^{29} +0.527864 q^{30} -3.76393 q^{31} -4.14590 q^{32} -5.47214 q^{33} +0.381966 q^{34} -1.38197 q^{35} -1.85410 q^{36} +1.47214 q^{37} +1.14590 q^{38} -2.38197 q^{39} -2.03444 q^{40} -4.70820 q^{41} -0.381966 q^{42} +8.09017 q^{43} +10.1459 q^{44} -1.38197 q^{45} +0.381966 q^{46} +1.70820 q^{47} +3.14590 q^{48} +1.00000 q^{49} +1.18034 q^{50} -1.00000 q^{51} +4.41641 q^{52} -3.38197 q^{53} -0.381966 q^{54} +7.56231 q^{55} +1.47214 q^{56} -3.00000 q^{57} +2.85410 q^{58} -6.14590 q^{59} +2.56231 q^{60} +13.7984 q^{61} +1.43769 q^{62} +1.00000 q^{63} -4.70820 q^{64} +3.29180 q^{65} +2.09017 q^{66} +4.14590 q^{67} +1.85410 q^{68} -1.00000 q^{69} +0.527864 q^{70} -3.90983 q^{71} +1.47214 q^{72} +2.70820 q^{73} -0.562306 q^{74} -3.09017 q^{75} +5.56231 q^{76} -5.47214 q^{77} +0.909830 q^{78} +0.527864 q^{79} -4.34752 q^{80} +1.00000 q^{81} +1.79837 q^{82} -3.00000 q^{83} -1.85410 q^{84} +1.38197 q^{85} -3.09017 q^{86} -7.47214 q^{87} -8.05573 q^{88} +3.14590 q^{89} +0.527864 q^{90} -2.38197 q^{91} +1.85410 q^{92} -3.76393 q^{93} -0.652476 q^{94} +4.14590 q^{95} -4.14590 q^{96} +5.00000 q^{97} -0.381966 q^{98} -5.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - 3 * q^6 + 2 * q^7 - 6 * q^8 + 2 * q^9	\( 2 q - 3 q^{2} + 2 q^{3} + 3 q^{4} - 5 q^{5} - 3 q^{6} + 2 q^{7} - 6 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} - 7 q^{13} - 3 q^{14} - 5 q^{15} + 13 q^{16} - 2 q^{17} - 3 q^{18} - 6 q^{19} - 15 q^{20} + 2 q^{21} - 7 q^{22} - 2 q^{23} - 6 q^{24} + 5 q^{25} + 13 q^{26} + 2 q^{27} + 3 q^{28} - 6 q^{29} + 10 q^{30} - 12 q^{31} - 15 q^{32} - 2 q^{33} + 3 q^{34} - 5 q^{35} + 3 q^{36} - 6 q^{37} + 9 q^{38} - 7 q^{39} + 25 q^{40} + 4 q^{41} - 3 q^{42} + 5 q^{43} + 27 q^{44} - 5 q^{45} + 3 q^{46} - 10 q^{47} + 13 q^{48} + 2 q^{49} - 20 q^{50} - 2 q^{51} - 18 q^{52} - 9 q^{53} - 3 q^{54} - 5 q^{55} - 6 q^{56} - 6 q^{57} - q^{58} - 19 q^{59} - 15 q^{60} + 3 q^{61} + 23 q^{62} + 2 q^{63} + 4 q^{64} + 20 q^{65} - 7 q^{66} + 15 q^{67} - 3 q^{68} - 2 q^{69} + 10 q^{70} - 19 q^{71} - 6 q^{72} - 8 q^{73} + 19 q^{74} + 5 q^{75} - 9 q^{76} - 2 q^{77} + 13 q^{78} + 10 q^{79} - 40 q^{80} + 2 q^{81} - 21 q^{82} - 6 q^{83} + 3 q^{84} + 5 q^{85} + 5 q^{86} - 6 q^{87} - 34 q^{88} + 13 q^{89} + 10 q^{90} - 7 q^{91} - 3 q^{92} - 12 q^{93} + 30 q^{94} + 15 q^{95} - 15 q^{96} + 10 q^{97} - 3 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 2 * q^3 + 3 * q^4 - 5 * q^5 - 3 * q^6 + 2 * q^7 - 6 * q^8 + 2 * q^9 + 10 * q^10 - 2 * q^11 + 3 * q^12 - 7 * q^13 - 3 * q^14 - 5 * q^15 + 13 * q^16 - 2 * q^17 - 3 * q^18 - 6 * q^19 - 15 * q^20 + 2 * q^21 - 7 * q^22 - 2 * q^23 - 6 * q^24 + 5 * q^25 + 13 * q^26 + 2 * q^27 + 3 * q^28 - 6 * q^29 + 10 * q^30 - 12 * q^31 - 15 * q^32 - 2 * q^33 + 3 * q^34 - 5 * q^35 + 3 * q^36 - 6 * q^37 + 9 * q^38 - 7 * q^39 + 25 * q^40 + 4 * q^41 - 3 * q^42 + 5 * q^43 + 27 * q^44 - 5 * q^45 + 3 * q^46 - 10 * q^47 + 13 * q^48 + 2 * q^49 - 20 * q^50 - 2 * q^51 - 18 * q^52 - 9 * q^53 - 3 * q^54 - 5 * q^55 - 6 * q^56 - 6 * q^57 - q^58 - 19 * q^59 - 15 * q^60 + 3 * q^61 + 23 * q^62 + 2 * q^63 + 4 * q^64 + 20 * q^65 - 7 * q^66 + 15 * q^67 - 3 * q^68 - 2 * q^69 + 10 * q^70 - 19 * q^71 - 6 * q^72 - 8 * q^73 + 19 * q^74 + 5 * q^75 - 9 * q^76 - 2 * q^77 + 13 * q^78 + 10 * q^79 - 40 * q^80 + 2 * q^81 - 21 * q^82 - 6 * q^83 + 3 * q^84 + 5 * q^85 + 5 * q^86 - 6 * q^87 - 34 * q^88 + 13 * q^89 + 10 * q^90 - 7 * q^91 - 3 * q^92 - 12 * q^93 + 30 * q^94 + 15 * q^95 - 15 * q^96 + 10 * q^97 - 3 * q^98 - 2 * q^99

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