LMFDB - Embedded newform 483.2.a.i.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:	$0$
Dimension:	$4$
Coefficient field:	4.4.24197.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - x + 2 $ x^4 - 6*x^2 - x + 2
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			$0.509552$ 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)

$f(q)$	$=$	$q-0.509552 q^{2} -1.00000 q^{3} -1.74036 q^{4} +4.41546 q^{5} +0.509552 q^{6} +1.00000 q^{7} +1.90591 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.509552 q^{2} -1.00000 q^{3} -1.74036 q^{4} +4.41546 q^{5} +0.509552 q^{6} +1.00000 q^{7} +1.90591 q^{8} +1.00000 q^{9} -2.24991 q^{10} -1.67510 q^{11} +1.74036 q^{12} -4.66537 q^{13} -0.509552 q^{14} -4.41546 q^{15} +2.50955 q^{16} +6.24991 q^{17} -0.509552 q^{18} -0.694209 q^{19} -7.68447 q^{20} -1.00000 q^{21} +0.853553 q^{22} -1.00000 q^{23} -1.90591 q^{24} +14.4963 q^{25} +2.37725 q^{26} -1.00000 q^{27} -1.74036 q^{28} +5.60012 q^{29} +2.24991 q^{30} +4.24991 q^{31} -5.09056 q^{32} +1.67510 q^{33} -3.18466 q^{34} +4.41546 q^{35} -1.74036 q^{36} +9.26901 q^{37} +0.353736 q^{38} +4.66537 q^{39} +8.41546 q^{40} -5.15582 q^{41} +0.509552 q^{42} +4.20376 q^{43} +2.91528 q^{44} +4.41546 q^{45} +0.509552 q^{46} -1.92501 q^{47} -2.50955 q^{48} +1.00000 q^{49} -7.38662 q^{50} -6.24991 q^{51} +8.11940 q^{52} -1.84066 q^{53} +0.509552 q^{54} -7.39636 q^{55} +1.90591 q^{56} +0.694209 q^{57} -2.85355 q^{58} +9.39779 q^{59} +7.68447 q^{60} +7.72125 q^{61} -2.16555 q^{62} +1.00000 q^{63} -2.42520 q^{64} -20.5998 q^{65} -0.853553 q^{66} -8.22728 q^{67} -10.8771 q^{68} +1.00000 q^{69} -2.24991 q^{70} -10.6654 q^{71} +1.90591 q^{72} -11.9117 q^{73} -4.72305 q^{74} -14.4963 q^{75} +1.20817 q^{76} -1.67510 q^{77} -2.37725 q^{78} +0.581012 q^{79} +11.0808 q^{80} +1.00000 q^{81} +2.62716 q^{82} +6.95032 q^{83} +1.74036 q^{84} +27.5962 q^{85} -2.14204 q^{86} -5.60012 q^{87} -3.19259 q^{88} -13.4963 q^{89} -2.24991 q^{90} -4.66537 q^{91} +1.74036 q^{92} -4.24991 q^{93} +0.980895 q^{94} -3.06525 q^{95} +5.09056 q^{96} +10.0999 q^{97} -0.509552 q^{98} -1.67510 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{4} + 5 q^{5} + 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 4 * q^4 + 5 * q^5 + 4 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q - 4 q^{3} + 4 q^{4} + 5 q^{5} + 4 q^{7} - 3 q^{8} + 4 q^{9} + 4 q^{10} - 5 q^{11} - 4 q^{12} + 7 q^{13} - 5 q^{15} + 8 q^{16} + 12 q^{17} + 3 q^{19} - q^{20} - 4 q^{21} - q^{22} - 4 q^{23} + 3 q^{24} + 7 q^{25} + 5 q^{26} - 4 q^{27} + 4 q^{28} + 6 q^{29} - 4 q^{30} + 4 q^{31} - 6 q^{32} + 5 q^{33} - 9 q^{34} + 5 q^{35} + 4 q^{36} + 20 q^{37} + 23 q^{38} - 7 q^{39} + 21 q^{40} + 3 q^{41} + 9 q^{43} - 27 q^{44} + 5 q^{45} + 7 q^{47} - 8 q^{48} + 4 q^{49} + 3 q^{50} - 12 q^{51} + 38 q^{52} - 6 q^{53} - 21 q^{55} - 3 q^{56} - 3 q^{57} - 7 q^{58} - 2 q^{59} + q^{60} + 24 q^{61} - 9 q^{62} + 4 q^{63} - 21 q^{64} - 14 q^{65} + q^{66} + q^{67} - 13 q^{68} + 4 q^{69} + 4 q^{70} - 17 q^{71} - 3 q^{72} + 16 q^{73} - 33 q^{74} - 7 q^{75} - 25 q^{76} - 5 q^{77} - 5 q^{78} - 10 q^{79} + 6 q^{80} + 4 q^{81} - 7 q^{82} + 8 q^{83} - 4 q^{84} + 17 q^{85} - 35 q^{86} - 6 q^{87} - 12 q^{88} - 3 q^{89} + 4 q^{90} + 7 q^{91} - 4 q^{92} - 4 q^{93} + 8 q^{94} - 3 q^{95} + 6 q^{96} - 2 q^{97} - 5 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^4 + 5 * q^5 + 4 * q^7 - 3 * q^8 + 4 * q^9 + 4 * q^10 - 5 * q^11 - 4 * q^12 + 7 * q^13 - 5 * q^15 + 8 * q^16 + 12 * q^17 + 3 * q^19 - q^20 - 4 * q^21 - q^22 - 4 * q^23 + 3 * q^24 + 7 * q^25 + 5 * q^26 - 4 * q^27 + 4 * q^28 + 6 * q^29 - 4 * q^30 + 4 * q^31 - 6 * q^32 + 5 * q^33 - 9 * q^34 + 5 * q^35 + 4 * q^36 + 20 * q^37 + 23 * q^38 - 7 * q^39 + 21 * q^40 + 3 * q^41 + 9 * q^43 - 27 * q^44 + 5 * q^45 + 7 * q^47 - 8 * q^48 + 4 * q^49 + 3 * q^50 - 12 * q^51 + 38 * q^52 - 6 * q^53 - 21 * q^55 - 3 * q^56 - 3 * q^57 - 7 * q^58 - 2 * q^59 + q^60 + 24 * q^61 - 9 * q^62 + 4 * q^63 - 21 * q^64 - 14 * q^65 + q^66 + q^67 - 13 * q^68 + 4 * q^69 + 4 * q^70 - 17 * q^71 - 3 * q^72 + 16 * q^73 - 33 * q^74 - 7 * q^75 - 25 * q^76 - 5 * q^77 - 5 * q^78 - 10 * q^79 + 6 * q^80 + 4 * q^81 - 7 * q^82 + 8 * q^83 - 4 * q^84 + 17 * q^85 - 35 * q^86 - 6 * q^87 - 12 * q^88 - 3 * q^89 + 4 * q^90 + 7 * q^91 - 4 * q^92 - 4 * q^93 + 8 * q^94 - 3 * q^95 + 6 * q^96 - 2 * q^97 - 5 * 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 $

$2$	−0.509552	−0.360308	−0.180154	−	0.983638i	$-0.557660\pi$
$2$	−0.509552	−0.360308	−0.180154	+	0.983638i	$0.557660\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.74036	−0.870178
$5$	4.41546	1.97465	0.987327	−	0.158699i	$-0.0507301\pi$
$5$	4.41546	1.97465	0.987327	+	0.158699i	$0.0507301\pi$
$6$	0.509552	0.208024
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.90591	0.673840
$9$	1.00000	0.333333
$10$	−2.24991	−0.711484
$11$	−1.67510	−0.505063	−0.252531	−	0.967589i	$-0.581263\pi$
$11$	−1.67510	−0.505063	−0.252531	+	0.967589i	$0.581263\pi$
$12$	1.74036	0.502398
$13$	−4.66537	−1.29394	−0.646970	−	0.762515i	$-0.723964\pi$
$13$	−4.66537	−1.29394	−0.646970	+	0.762515i	$0.723964\pi$
$14$	−0.509552	−0.136184
$15$	−4.41546	−1.14007
$16$	2.50955	0.627388
$17$	6.24991	1.51583	0.757913	−	0.652356i	$-0.226219\pi$
$17$	6.24991	1.51583	0.757913	+	0.652356i	$0.226219\pi$
$18$	−0.509552	−0.120103
$19$	−0.694209	−0.159262	−0.0796312	−	0.996824i	$-0.525374\pi$
$19$	−0.694209	−0.159262	−0.0796312	+	0.996824i	$0.525374\pi$
$20$	−7.68447	−1.71830
$21$	−1.00000	−0.218218
$22$	0.853553	0.181978
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.90591	−0.389042
$25$	14.4963	2.89926
$26$	2.37725	0.466217
$27$	−1.00000	−0.192450
$28$	−1.74036	−0.328896
$29$	5.60012	1.03992	0.519958	−	0.854192i	$-0.325948\pi$
$29$	5.60012	1.03992	0.519958	+	0.854192i	$0.325948\pi$
$30$	2.24991	0.410775
$31$	4.24991	0.763306	0.381653	−	0.924306i	$-0.375355\pi$
$31$	4.24991	0.763306	0.381653	+	0.924306i	$0.375355\pi$
$32$	−5.09056	−0.899893
$33$	1.67510	0.291598
$34$	−3.18466	−0.546164
$35$	4.41546	0.746349
$36$	−1.74036	−0.290059
$37$	9.26901	1.52382	0.761908	−	0.647685i	$-0.224263\pi$
$37$	9.26901	1.52382	0.761908	+	0.647685i	$0.224263\pi$
$38$	0.353736	0.0573835
$39$	4.66537	0.747057
$40$	8.41546	1.33060
$41$	−5.15582	−0.805203	−0.402602	−	0.915375i	$-0.631894\pi$
$41$	−5.15582	−0.805203	−0.402602	+	0.915375i	$0.631894\pi$
$42$	0.509552	0.0786257
$43$	4.20376	0.641068	0.320534	−	0.947237i	$-0.396138\pi$
$43$	4.20376	0.641068	0.320534	+	0.947237i	$0.396138\pi$
$44$	2.91528	0.439495
$45$	4.41546	0.658218
$46$	0.509552	0.0751294
$47$	−1.92501	−0.280792	−0.140396	−	0.990095i	$-0.544838\pi$
$47$	−1.92501	−0.280792	−0.140396	+	0.990095i	$0.544838\pi$
$48$	−2.50955	−0.362223
$49$	1.00000	0.142857
$50$	−7.38662	−1.04463
$51$	−6.24991	−0.875162
$52$	8.11940	1.12596
$53$	−1.84066	−0.252833	−0.126417	−	0.991977i	$-0.540348\pi$
$53$	−1.84066	−0.252833	−0.126417	+	0.991977i	$0.540348\pi$
$54$	0.509552	0.0693413
$55$	−7.39636	−0.997324
$56$	1.90591	0.254688
$57$	0.694209	0.0919502
$58$	−2.85355	−0.374690
$59$	9.39779	1.22349	0.611744	−	0.791056i	$-0.290468\pi$
$59$	9.39779	1.22349	0.611744	+	0.791056i	$0.290468\pi$
$60$	7.68447	0.992061
$61$	7.72125	0.988605	0.494302	−	0.869290i	$-0.335424\pi$
$61$	7.72125	0.988605	0.494302	+	0.869290i	$0.335424\pi$
$62$	−2.16555	−0.275025
$63$	1.00000	0.125988
$64$	−2.42520	−0.303149
$65$	−20.5998	−2.55508
$66$	−0.853553	−0.105065
$67$	−8.22728	−1.00512	−0.502561	−	0.864542i	$-0.667609\pi$
$67$	−8.22728	−1.00512	−0.502561	+	0.864542i	$0.667609\pi$
$68$	−10.8771	−1.31904
$69$	1.00000	0.120386
$70$	−2.24991	−0.268916
$71$	−10.6654	−1.26575	−0.632873	−	0.774255i	$-0.718125\pi$
$71$	−10.6654	−1.26575	−0.632873	+	0.774255i	$0.718125\pi$
$72$	1.90591	0.224613
$73$	−11.9117	−1.39416	−0.697082	−	0.716991i	$-0.745519\pi$
$73$	−11.9117	−1.39416	−0.697082	+	0.716991i	$0.745519\pi$
$74$	−4.72305	−0.549043
$75$	−14.4963	−1.67389
$76$	1.20817	0.138587
$77$	−1.67510	−0.190896
$78$	−2.37725	−0.269171
$79$	0.581012	0.0653689	0.0326845	−	0.999466i	$-0.489594\pi$
$79$	0.581012	0.0653689	0.0326845	+	0.999466i	$0.489594\pi$
$80$	11.0808	1.23887
$81$	1.00000	0.111111
$82$	2.62716	0.290121
$83$	6.95032	0.762897	0.381449	−	0.924390i	$-0.375425\pi$
$83$	6.95032	0.762897	0.381449	+	0.924390i	$0.375425\pi$
$84$	1.74036	0.189888
$85$	27.5962	2.99323
$86$	−2.14204	−0.230982
$87$	−5.60012	−0.600396
$88$	−3.19259	−0.340332
$89$	−13.4963	−1.43060	−0.715302	−	0.698816i	$-0.753711\pi$
$89$	−13.4963	−1.43060	−0.715302	+	0.698816i	$0.753711\pi$
$90$	−2.24991	−0.237161
$91$	−4.66537	−0.489064
$92$	1.74036	0.181445
$93$	−4.24991	−0.440695
$94$	0.980895	0.101172
$95$	−3.06525	−0.314488
$96$	5.09056	0.519554
$97$	10.0999	1.02549	0.512746	−	0.858540i	$-0.328628\pi$
$97$	10.0999	1.02549	0.512746	+	0.858540i	$0.328628\pi$
$98$	−0.509552	−0.0514726
$99$	−1.67510	−0.168354
$100$	−25.2287	−2.52287
$101$	−13.7830	−1.37146	−0.685729	−	0.727857i	$-0.740516\pi$
$101$	−13.7830	−1.37146	−0.685729	+	0.727857i	$0.740516\pi$
$102$	3.18466	0.315328
$103$	16.5553	1.63125	0.815623	−	0.578584i	$-0.196395\pi$
$103$	16.5553	1.63125	0.815623	+	0.578584i	$0.196395\pi$
$104$	−8.89176	−0.871909
$105$	−4.41546	−0.430905
$106$	0.937911	0.0910979
$107$	−1.33463	−0.129024	−0.0645118	−	0.997917i	$-0.520549\pi$
$107$	−1.33463	−0.129024	−0.0645118	+	0.997917i	$0.520549\pi$
$108$	1.74036	0.167466
$109$	4.00794	0.383891	0.191945	−	0.981406i	$-0.438520\pi$
$109$	4.00794	0.383891	0.191945	+	0.981406i	$0.438520\pi$
$110$	3.76883	0.359344
$111$	−9.26901	−0.879776
$112$	2.50955	0.237130
$113$	−9.06525	−0.852787	−0.426394	−	0.904538i	$-0.640216\pi$
$113$	−9.06525	−0.852787	−0.426394	+	0.904538i	$0.640216\pi$
$114$	−0.353736	−0.0331304
$115$	−4.41546	−0.411744
$116$	−9.74620	−0.904912
$117$	−4.66537	−0.431314
$118$	−4.78867	−0.440832
$119$	6.24991	0.572928
$120$	−8.41546	−0.768223
$121$	−8.19403	−0.744911
$122$	−3.93438	−0.356202
$123$	5.15582	0.464884
$124$	−7.39636	−0.664212
$125$	41.9305	3.75038
$126$	−0.509552	−0.0453945
$127$	−21.4977	−1.90761	−0.953807	−	0.300419i	$-0.902873\pi$
$127$	−21.4977	−1.90761	−0.953807	+	0.300419i	$0.902873\pi$
$128$	11.4169	1.00912
$129$	−4.20376	−0.370121
$130$	10.4967	0.920618
$131$	1.17529	0.102685	0.0513426	−	0.998681i	$-0.483650\pi$
$131$	1.17529	0.102685	0.0513426	+	0.998681i	$0.483650\pi$
$132$	−2.91528	−0.253742
$133$	−0.694209	−0.0601956
$134$	4.19223	0.362153
$135$	−4.41546	−0.380022
$136$	11.9117	1.02142
$137$	15.8562	1.35469	0.677345	−	0.735666i	$-0.263131\pi$
$137$	15.8562	1.35469	0.677345	+	0.735666i	$0.263131\pi$
$138$	−0.509552	−0.0433760
$139$	−1.93438	−0.164072	−0.0820361	−	0.996629i	$-0.526142\pi$
$139$	−1.93438	−0.164072	−0.0820361	+	0.996629i	$0.526142\pi$
$140$	−7.68447	−0.649457
$141$	1.92501	0.162115
$142$	5.43457	0.456059
$143$	7.81498	0.653521
$144$	2.50955	0.209129
$145$	24.7271	2.05347
$146$	6.06966	0.502329
$147$	−1.00000	−0.0824786
$148$	−16.1314	−1.32599
$149$	2.61301	0.214067	0.107033	−	0.994255i	$-0.465865\pi$
$149$	2.61301	0.214067	0.107033	+	0.994255i	$0.465865\pi$
$150$	7.38662	0.603115
$151$	−9.26281	−0.753797	−0.376898	−	0.926255i	$-0.623009\pi$
$151$	−9.26281	−0.753797	−0.376898	+	0.926255i	$0.623009\pi$
$152$	−1.32310	−0.107317
$153$	6.24991	0.505275
$154$	0.853553	0.0687813
$155$	18.7653	1.50727
$156$	−8.11940	−0.650073
$157$	−7.77504	−0.620516	−0.310258	−	0.950652i	$-0.600415\pi$
$157$	−7.77504	−0.620516	−0.310258	+	0.950652i	$0.600415\pi$
$158$	−0.296056	−0.0235530
$159$	1.84066	0.145973
$160$	−22.4772	−1.77698
$161$	−1.00000	−0.0788110
$162$	−0.509552	−0.0400342
$163$	−7.12077	−0.557742	−0.278871	−	0.960329i	$-0.589960\pi$
$163$	−7.12077	−0.557742	−0.278871	+	0.960329i	$0.589960\pi$
$164$	8.97296	0.700670
$165$	7.39636	0.575805
$166$	−3.54156	−0.274878
$167$	−11.9867	−0.927562	−0.463781	−	0.885950i	$-0.653507\pi$
$167$	−11.9867	−0.927562	−0.463781	+	0.885950i	$0.653507\pi$
$168$	−1.90591	−0.147044
$169$	8.76567	0.674282
$170$	−14.0617	−1.07849
$171$	−0.694209	−0.0530875
$172$	−7.31604	−0.557843
$173$	−2.09993	−0.159655	−0.0798275	−	0.996809i	$-0.525437\pi$
$173$	−2.09993	−0.159655	−0.0798275	+	0.996809i	$0.525437\pi$
$174$	2.85355	0.216327
$175$	14.4963	1.09582
$176$	−4.20376	−0.316870
$177$	−9.39779	−0.706381
$178$	6.87707	0.515458
$179$	−15.9726	−1.19385	−0.596924	−	0.802298i	$-0.703611\pi$
$179$	−15.9726	−1.19385	−0.596924	+	0.802298i	$0.703611\pi$
$180$	−7.68447	−0.572767
$181$	−2.89970	−0.215533	−0.107767	−	0.994176i	$-0.534370\pi$
$181$	−2.89970	−0.215533	−0.107767	+	0.994176i	$0.534370\pi$
$182$	2.37725	0.176214
$183$	−7.72125	−0.570771
$184$	−1.90591	−0.140505
$185$	40.9270	3.00901
$186$	2.16555	0.158786
$187$	−10.4692	−0.765587
$188$	3.35021	0.244339
$189$	−1.00000	−0.0727393
$190$	1.56191	0.113313
$191$	−21.5486	−1.55921	−0.779603	−	0.626275i	$-0.784579\pi$
$191$	−21.5486	−1.55921	−0.779603	+	0.626275i	$0.784579\pi$
$192$	2.42520	0.175023
$193$	4.58722	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$193$	4.58722	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$194$	−5.14645	−0.369493
$195$	20.5998	1.47518
$196$	−1.74036	−0.124311
$197$	−11.8656	−0.845389	−0.422695	−	0.906272i	$-0.638916\pi$
$197$	−11.8656	−0.845389	−0.422695	+	0.906272i	$0.638916\pi$
$198$	0.853553	0.0606594
$199$	−2.52866	−0.179252	−0.0896259	−	0.995976i	$-0.528567\pi$
$199$	−2.52866	−0.179252	−0.0896259	+	0.995976i	$0.528567\pi$
$200$	27.6286	1.95364
$201$	8.22728	0.580307
$202$	7.02315	0.494147
$203$	5.60012	0.393051
$204$	10.8771	0.761547
$205$	−22.7653	−1.59000
$206$	−8.43581	−0.587751
$207$	−1.00000	−0.0695048
$208$	−11.7080	−0.811803
$209$	1.16287	0.0804376
$210$	2.24991	0.155258
$211$	−21.9797	−1.51314	−0.756572	−	0.653911i	$-0.773127\pi$
$211$	−21.9797	−1.51314	−0.756572	+	0.653911i	$0.773127\pi$
$212$	3.20340	0.220010
$213$	10.6654	0.730779
$214$	0.680065	0.0464883
$215$	18.5615	1.26589
$216$	−1.90591	−0.129681
$217$	4.24991	0.288503
$218$	−2.04225	−0.138319
$219$	11.9117	0.804921
$220$	12.8723	0.867850
$221$	−29.1581	−1.96139
$222$	4.72305	0.316990
$223$	0.0302726	0.00202720	0.00101360	−	0.999999i	$-0.499677\pi$
$223$	0.0302726	0.00202720	0.00101360	+	0.999999i	$0.499677\pi$
$224$	−5.09056	−0.340128
$225$	14.4963	0.966419
$226$	4.61922	0.307266
$227$	21.2393	1.40970	0.704852	−	0.709355i	$-0.251014\pi$
$227$	21.2393	1.40970	0.704852	+	0.709355i	$0.251014\pi$
$228$	−1.20817	−0.0800131
$229$	17.4360	1.15220	0.576102	−	0.817378i	$-0.304573\pi$
$229$	17.4360	1.15220	0.576102	+	0.817378i	$0.304573\pi$
$230$	2.24991	0.148355
$231$	1.67510	0.110214
$232$	10.6733	0.700737
$233$	−11.2082	−0.734272	−0.367136	−	0.930167i	$-0.619662\pi$
$233$	−11.2082	−0.734272	−0.367136	+	0.930167i	$0.619662\pi$
$234$	2.37725	0.155406
$235$	−8.49982	−0.554467
$236$	−16.3555	−1.06465
$237$	−0.581012	−0.0377408
$238$	−3.18466	−0.206431
$239$	−18.5654	−1.20090	−0.600449	−	0.799663i	$-0.705011\pi$
$239$	−18.5654	−1.20090	−0.600449	+	0.799663i	$0.705011\pi$
$240$	−11.0808	−0.715264
$241$	−13.6556	−0.879637	−0.439818	−	0.898087i	$-0.644957\pi$
$241$	−13.6556	−0.879637	−0.439818	+	0.898087i	$0.644957\pi$
$242$	4.17529	0.268398
$243$	−1.00000	−0.0641500
$244$	−13.4377	−0.860262
$245$	4.41546	0.282093
$246$	−2.62716	−0.167502
$247$	3.23874	0.206076
$248$	8.09993	0.514346
$249$	−6.95032	−0.440459
$250$	−21.3658	−1.35129
$251$	0.604526	0.0381574	0.0190787	−	0.999818i	$-0.493927\pi$
$251$	0.604526	0.0381574	0.0190787	+	0.999818i	$0.493927\pi$
$252$	−1.74036	−0.109632
$253$	1.67510	0.105313
$254$	10.9542	0.687329
$255$	−27.5962	−1.72814
$256$	−0.967116	−0.0604447
$257$	14.1602	0.883291	0.441645	−	0.897190i	$-0.354395\pi$
$257$	14.1602	0.883291	0.441645	+	0.897190i	$0.354395\pi$
$258$	2.14204	0.133357
$259$	9.26901	0.575948
$260$	35.8509	2.22338
$261$	5.60012	0.346639
$262$	−0.598870	−0.0369983
$263$	20.5788	1.26895	0.634473	−	0.772945i	$-0.281217\pi$
$263$	20.5788	1.26895	0.634473	+	0.772945i	$0.281217\pi$
$264$	3.19259	0.196491
$265$	−8.12734	−0.499259
$266$	0.353736	0.0216889
$267$	13.4963	0.825960
$268$	14.3184	0.874635
$269$	−0.496655	−0.0302816	−0.0151408	−	0.999885i	$-0.504820\pi$
$269$	−0.496655	−0.0302816	−0.0151408	+	0.999885i	$0.504820\pi$
$270$	2.24991	0.136925
$271$	24.0547	1.46122	0.730609	−	0.682797i	$-0.239236\pi$
$271$	24.0547	1.46122	0.730609	+	0.682797i	$0.239236\pi$
$272$	15.6845	0.951011
$273$	4.66537	0.282361
$274$	−8.07958	−0.488105
$275$	−24.2828	−1.46431
$276$	−1.74036	−0.104757
$277$	23.2402	1.39637	0.698183	−	0.715919i	$-0.253992\pi$
$277$	23.2402	1.39637	0.698183	+	0.715919i	$0.253992\pi$
$278$	0.985670	0.0591165
$279$	4.24991	0.254435
$280$	8.41546	0.502920
$281$	−15.0697	−0.898985	−0.449492	−	0.893284i	$-0.648395\pi$
$281$	−15.0697	−0.898985	−0.449492	+	0.893284i	$0.648395\pi$
$282$	−0.980895	−0.0584114
$283$	9.22691	0.548483	0.274241	−	0.961661i	$-0.411573\pi$
$283$	9.22691	0.548483	0.274241	+	0.961661i	$0.411573\pi$
$284$	18.5615	1.10142
$285$	3.06525	0.181570
$286$	−3.98214	−0.235469
$287$	−5.15582	−0.304338
$288$	−5.09056	−0.299964
$289$	22.0614	1.29773
$290$	−12.5998	−0.739883
$291$	−10.0999	−0.592069
$292$	20.7307	1.21317
$293$	−12.3881	−0.723718	−0.361859	−	0.932233i	$-0.617858\pi$
$293$	−12.3881	−0.723718	−0.361859	+	0.932233i	$0.617858\pi$
$294$	0.509552	0.0297177
$295$	41.4956	2.41596
$296$	17.6659	1.02681
$297$	1.67510	0.0971994
$298$	−1.33147	−0.0771299
$299$	4.66537	0.269805
$300$	25.2287	1.45658
$301$	4.20376	0.242301
$302$	4.71989	0.271599
$303$	13.7830	0.791811
$304$	−1.74215	−0.0999194
$305$	34.0929	1.95215
$306$	−3.18466	−0.182055
$307$	0.823281	0.0469871	0.0234936	−	0.999724i	$-0.492521\pi$
$307$	0.823281	0.0469871	0.0234936	+	0.999724i	$0.492521\pi$
$308$	2.91528	0.166113
$309$	−16.5553	−0.941800
$310$	−9.56191	−0.543080
$311$	−30.6632	−1.73875	−0.869375	−	0.494152i	$-0.835479\pi$
$311$	−30.6632	−1.73875	−0.869375	+	0.494152i	$0.835479\pi$
$312$	8.89176	0.503397
$313$	13.1323	0.742282	0.371141	−	0.928577i	$-0.378967\pi$
$313$	13.1323	0.742282	0.371141	+	0.928577i	$0.378967\pi$
$314$	3.96179	0.223577
$315$	4.41546	0.248783
$316$	−1.01117	−0.0568826
$317$	−15.2269	−0.855229	−0.427614	−	0.903961i	$-0.640646\pi$
$317$	−15.2269	−0.855229	−0.427614	+	0.903961i	$0.640646\pi$
$318$	−0.937911	−0.0525954
$319$	−9.38078	−0.525223
$320$	−10.7084	−0.598615
$321$	1.33463	0.0744918
$322$	0.509552	0.0283962
$323$	−4.33874	−0.241414
$324$	−1.74036	−0.0966865
$325$	−67.6305	−3.75147
$326$	3.62841	0.200959
$327$	−4.00794	−0.221639
$328$	−9.82651	−0.542578
$329$	−1.92501	−0.106129
$330$	−3.76883	−0.207467
$331$	25.5674	1.40531	0.702655	−	0.711530i	$-0.251998\pi$
$331$	25.5674	1.40531	0.702655	+	0.711530i	$0.251998\pi$
$332$	−12.0960	−0.663857
$333$	9.26901	0.507939
$334$	6.10787	0.334208
$335$	−36.3272	−1.98477
$336$	−2.50955	−0.136907
$337$	16.2890	0.887318	0.443659	−	0.896196i	$-0.353680\pi$
$337$	16.2890	0.887318	0.443659	+	0.896196i	$0.353680\pi$
$338$	−4.46657	−0.242949
$339$	9.06525	0.492357
$340$	−48.0273	−2.60464
$341$	−7.11904	−0.385518
$342$	0.353736	0.0191278
$343$	1.00000	0.0539949
$344$	8.01198	0.431977
$345$	4.41546	0.237720
$346$	1.07003	0.0575250
$347$	21.6729	1.16346	0.581732	−	0.813380i	$-0.302375\pi$
$347$	21.6729	1.16346	0.581732	+	0.813380i	$0.302375\pi$
$348$	9.74620	0.522451
$349$	−21.5198	−1.15193	−0.575964	−	0.817475i	$-0.695373\pi$
$349$	−21.5198	−1.15193	−0.575964	+	0.817475i	$0.695373\pi$
$350$	−7.38662	−0.394831
$351$	4.66537	0.249019
$352$	8.52722	0.454503
$353$	−20.1852	−1.07435	−0.537174	−	0.843471i	$-0.680508\pi$
$353$	−20.1852	−1.07435	−0.537174	+	0.843471i	$0.680508\pi$
$354$	4.78867	0.254515
$355$	−47.0925	−2.49941
$356$	23.4884	1.24488
$357$	−6.24991	−0.330780
$358$	8.13887	0.430153
$359$	23.2492	1.22705	0.613524	−	0.789676i	$-0.289751\pi$
$359$	23.2492	1.22705	0.613524	+	0.789676i	$0.289751\pi$
$360$	8.41546	0.443534
$361$	−18.5181	−0.974635
$362$	1.47755	0.0776583
$363$	8.19403	0.430075
$364$	8.11940	0.425572
$365$	−52.5959	−2.75299
$366$	3.93438	0.205653
$367$	27.7171	1.44682	0.723409	−	0.690419i	$-0.242574\pi$
$367$	27.7171	1.44682	0.723409	+	0.690419i	$0.242574\pi$
$368$	−2.50955	−0.130819
$369$	−5.15582	−0.268401
$370$	−20.8544	−1.08417
$371$	−1.84066	−0.0955621
$372$	7.39636	0.383483
$373$	−24.7303	−1.28048	−0.640242	−	0.768173i	$-0.721166\pi$
$373$	−24.7303	−1.28048	−0.640242	+	0.768173i	$0.721166\pi$
$374$	5.33463	0.275847
$375$	−41.9305	−2.16528
$376$	−3.66890	−0.189209
$377$	−26.1266	−1.34559
$378$	0.509552	0.0262086
$379$	−3.11140	−0.159822	−0.0799109	−	0.996802i	$-0.525464\pi$
$379$	−3.11140	−0.159822	−0.0799109	+	0.996802i	$0.525464\pi$
$380$	5.33463	0.273661
$381$	21.4977	1.10136
$382$	10.9802	0.561794
$383$	−18.9503	−0.968316	−0.484158	−	0.874980i	$-0.660874\pi$
$383$	−18.9503	−0.968316	−0.484158	+	0.874980i	$0.660874\pi$
$384$	−11.4169	−0.582616
$385$	−7.39636	−0.376953
$386$	−2.33743	−0.118972
$387$	4.20376	0.213689
$388$	−17.5775	−0.892362
$389$	−20.1693	−1.02262	−0.511312	−	0.859395i	$-0.670840\pi$
$389$	−20.1693	−1.02262	−0.511312	+	0.859395i	$0.670840\pi$
$390$	−10.4967	−0.531519
$391$	−6.24991	−0.316071
$392$	1.90591	0.0962629
$393$	−1.17529	−0.0592854
$394$	6.04615	0.304600
$395$	2.56543	0.129081
$396$	2.91528	0.146498
$397$	8.41634	0.422404	0.211202	−	0.977442i	$-0.432262\pi$
$397$	8.41634	0.422404	0.211202	+	0.977442i	$0.432262\pi$
$398$	1.28848	0.0645859
$399$	0.694209	0.0347539
$400$	36.3792	1.81896
$401$	−5.86329	−0.292799	−0.146399	−	0.989226i	$-0.546768\pi$
$401$	−5.86329	−0.292799	−0.146399	+	0.989226i	$0.546768\pi$
$402$	−4.19223	−0.209089
$403$	−19.8274	−0.987673
$404$	23.9873	1.19341
$405$	4.41546	0.219406
$406$	−2.85355	−0.141619
$407$	−15.5266	−0.769623
$408$	−11.9117	−0.589719
$409$	−26.2686	−1.29890	−0.649451	−	0.760404i	$-0.725001\pi$
$409$	−26.2686	−1.29890	−0.649451	+	0.760404i	$0.725001\pi$
$410$	11.6001	0.572889
$411$	−15.8562	−0.782130
$412$	−28.8122	−1.41947
$413$	9.39779	0.462435
$414$	0.509552	0.0250431
$415$	30.6889	1.50646
$416$	23.7494	1.16441
$417$	1.93438	0.0947271
$418$	−0.592544	−0.0289823
$419$	−0.800648	−0.0391142	−0.0195571	−	0.999809i	$-0.506226\pi$
$419$	−0.800648	−0.0391142	−0.0195571	+	0.999809i	$0.506226\pi$
$420$	7.68447	0.374964
$421$	23.3845	1.13969	0.569846	−	0.821751i	$-0.307003\pi$
$421$	23.3845	1.13969	0.569846	+	0.821751i	$0.307003\pi$
$422$	11.1998	0.545198
$423$	−1.92501	−0.0935973
$424$	−3.50812	−0.170369
$425$	90.6005	4.39477
$426$	−5.43457	−0.263306
$427$	7.72125	0.373658
$428$	2.32273	0.112274
$429$	−7.81498	−0.377311
$430$	−9.45808	−0.456109
$431$	−33.4853	−1.61293	−0.806465	−	0.591281i	$-0.798622\pi$
$431$	−33.4853	−1.61293	−0.806465	+	0.591281i	$0.798622\pi$
$432$	−2.50955	−0.120741
$433$	24.1373	1.15996	0.579982	−	0.814629i	$-0.303059\pi$
$433$	24.1373	1.15996	0.579982	+	0.814629i	$0.303059\pi$
$434$	−2.16555	−0.103950
$435$	−24.7271	−1.18557
$436$	−6.97524	−0.334053
$437$	0.694209	0.0332085
$438$	−6.06966	−0.290020
$439$	−16.4469	−0.784968	−0.392484	−	0.919759i	$-0.628384\pi$
$439$	−16.4469	−0.784968	−0.392484	+	0.919759i	$0.628384\pi$
$440$	−14.0968	−0.672037
$441$	1.00000	0.0476190
$442$	14.8576	0.706704
$443$	9.58542	0.455417	0.227709	−	0.973729i	$-0.426877\pi$
$443$	9.58542	0.455417	0.227709	+	0.973729i	$0.426877\pi$
$444$	16.1314	0.765562
$445$	−59.5923	−2.82495
$446$	−0.0154255	−0.000730417 0
$447$	−2.61301	−0.123591
$448$	−2.42520	−0.114580
$449$	4.17319	0.196945	0.0984725	−	0.995140i	$-0.468604\pi$
$449$	4.17319	0.196945	0.0984725	+	0.995140i	$0.468604\pi$
$450$	−7.38662	−0.348209
$451$	8.63653	0.406678
$452$	15.7768	0.742077
$453$	9.26281	0.435205
$454$	−10.8226	−0.507927
$455$	−20.5998	−0.965731
$456$	1.32310	0.0619598
$457$	8.02668	0.375472	0.187736	−	0.982220i	$-0.439885\pi$
$457$	8.02668	0.375472	0.187736	+	0.982220i	$0.439885\pi$
$458$	−8.88456	−0.415148
$459$	−6.24991	−0.291721
$460$	7.68447	0.358290
$461$	11.6192	0.541158	0.270579	−	0.962698i	$-0.412785\pi$
$461$	11.6192	0.541158	0.270579	+	0.962698i	$0.412785\pi$
$462$	−0.853553	−0.0397109
$463$	−35.8714	−1.66708	−0.833542	−	0.552456i	$-0.813691\pi$
$463$	−35.8714	−1.66708	−0.833542	+	0.552456i	$0.813691\pi$
$464$	14.0538	0.652431
$465$	−18.7653	−0.870220
$466$	5.71115	0.264564
$467$	−13.1731	−0.609579	−0.304790	−	0.952420i	$-0.598586\pi$
$467$	−13.1731	−0.609579	−0.304790	+	0.952420i	$0.598586\pi$
$468$	8.11940	0.375320
$469$	−8.22728	−0.379900
$470$	4.33110	0.199779
$471$	7.77504	0.358255
$472$	17.9113	0.824435
$473$	−7.04174	−0.323779
$474$	0.296056	0.0135983
$475$	−10.0635	−0.461743
$476$	−10.8771	−0.498550
$477$	−1.84066	−0.0842778
$478$	9.46006	0.432693
$479$	5.23080	0.239002	0.119501	−	0.992834i	$-0.461871\pi$
$479$	5.23080	0.239002	0.119501	+	0.992834i	$0.461871\pi$
$480$	22.4772	1.02594
$481$	−43.2434	−1.97173
$482$	6.95826	0.316940
$483$	1.00000	0.0455016
$484$	14.2605	0.648206
$485$	44.5959	2.02499
$486$	0.509552	0.0231138
$487$	28.9779	1.31311	0.656557	−	0.754277i	$-0.272012\pi$
$487$	28.9779	1.31311	0.656557	+	0.754277i	$0.272012\pi$
$488$	14.7160	0.666162
$489$	7.12077	0.322012
$490$	−2.24991	−0.101641
$491$	−16.6912	−0.753262	−0.376631	−	0.926363i	$-0.622917\pi$
$491$	−16.6912	−0.753262	−0.376631	+	0.926363i	$0.622917\pi$
$492$	−8.97296	−0.404532
$493$	35.0002	1.57633
$494$	−1.65031	−0.0742509
$495$	−7.39636	−0.332441
$496$	10.6654	0.478889
$497$	−10.6654	−0.478407
$498$	3.54156	0.158701
$499$	9.57213	0.428507	0.214254	−	0.976778i	$-0.431268\pi$
$499$	9.57213	0.428507	0.214254	+	0.976778i	$0.431268\pi$
$500$	−72.9740	−3.26350
$501$	11.9867	0.535528
$502$	−0.308038	−0.0137484
$503$	−20.6348	−0.920060	−0.460030	−	0.887903i	$-0.652161\pi$
$503$	−20.6348	−0.920060	−0.460030	+	0.887903i	$0.652161\pi$
$504$	1.90591	0.0848959
$505$	−60.8582	−2.70815
$506$	−0.853553	−0.0379451
$507$	−8.76567	−0.389297
$508$	37.4137	1.65996
$509$	6.23665	0.276434	0.138217	−	0.990402i	$-0.455863\pi$
$509$	6.23665	0.276434	0.138217	+	0.990402i	$0.455863\pi$
$510$	14.0617	0.622664
$511$	−11.9117	−0.526945
$512$	−22.3410	−0.987342
$513$	0.694209	0.0306501
$514$	−7.21538	−0.318257
$515$	73.0994	3.22115
$516$	7.31604	0.322071
$517$	3.22460	0.141818
$518$	−4.72305	−0.207519
$519$	2.09993	0.0921769
$520$	−39.2612	−1.72172
$521$	12.6615	0.554709	0.277355	−	0.960768i	$-0.410542\pi$
$521$	12.6615	0.554709	0.277355	+	0.960768i	$0.410542\pi$
$522$	−2.85355	−0.124897
$523$	43.3446	1.89533	0.947663	−	0.319272i	$-0.103438\pi$
$523$	43.3446	1.89533	0.947663	+	0.319272i	$0.103438\pi$
$524$	−2.04542	−0.0893545
$525$	−14.4963	−0.632670
$526$	−10.4860	−0.457211
$527$	26.5615	1.15704
$528$	4.20376	0.182945
$529$	1.00000	0.0434783
$530$	4.14131	0.179887
$531$	9.39779	0.407829
$532$	1.20817	0.0523809
$533$	24.0538	1.04189
$534$	−6.87707	−0.297600
$535$	−5.89301	−0.254777
$536$	−15.6804	−0.677291
$537$	15.9726	0.689268
$538$	0.253072	0.0109107
$539$	−1.67510	−0.0721518
$540$	7.68447	0.330687
$541$	5.87439	0.252560	0.126280	−	0.991995i	$-0.459696\pi$
$541$	5.87439	0.252560	0.126280	+	0.991995i	$0.459696\pi$
$542$	−12.2571	−0.526488
$543$	2.89970	0.124438
$544$	−31.8156	−1.36408
$545$	17.6969	0.758051
$546$	−2.37725	−0.101737
$547$	13.8580	0.592524	0.296262	−	0.955107i	$-0.404260\pi$
$547$	13.8580	0.592524	0.296262	+	0.955107i	$0.404260\pi$
$548$	−27.5955	−1.17882
$549$	7.72125	0.329535
$550$	12.3734	0.527602
$551$	−3.88765	−0.165620
$552$	1.90591	0.0811208
$553$	0.581012	0.0247071
$554$	−11.8421	−0.503122
$555$	−40.9270	−1.73725
$556$	3.36652	0.142772
$557$	−18.5921	−0.787773	−0.393887	−	0.919159i	$-0.628870\pi$
$557$	−18.5921	−0.787773	−0.393887	+	0.919159i	$0.628870\pi$
$558$	−2.16555	−0.0916751
$559$	−19.6121	−0.829503
$560$	11.0808	0.468251
$561$	10.4692	0.442012
$562$	7.67882	0.323911
$563$	5.09582	0.214763	0.107382	−	0.994218i	$-0.465753\pi$
$563$	5.09582	0.214763	0.107382	+	0.994218i	$0.465753\pi$
$564$	−3.35021	−0.141069
$565$	−40.0273	−1.68396
$566$	−4.70160	−0.197623
$567$	1.00000	0.0419961
$568$	−20.3272	−0.852911
$569$	−29.3028	−1.22844	−0.614218	−	0.789136i	$-0.710529\pi$
$569$	−29.3028	−1.22844	−0.614218	+	0.789136i	$0.710529\pi$
$570$	−1.56191	−0.0654211
$571$	−5.10736	−0.213736	−0.106868	−	0.994273i	$-0.534082\pi$
$571$	−5.10736	−0.213736	−0.106868	+	0.994273i	$0.534082\pi$
$572$	−13.6008	−0.568680
$573$	21.5486	0.900208
$574$	2.62716	0.109656
$575$	−14.4963	−0.604537
$576$	−2.42520	−0.101050
$577$	24.7379	1.02985	0.514926	−	0.857235i	$-0.327819\pi$
$577$	24.7379	1.02985	0.514926	+	0.857235i	$0.327819\pi$
$578$	−11.2414	−0.467581
$579$	−4.58722	−0.190638
$580$	−43.0340	−1.78689
$581$	6.95032	0.288348
$582$	5.14645	0.213327
$583$	3.08329	0.127697
$584$	−22.7027	−0.939444
$585$	−20.5998	−0.851695
$586$	6.31236	0.260761
$587$	38.8319	1.60276	0.801382	−	0.598152i	$-0.204098\pi$
$587$	38.8319	1.60276	0.801382	+	0.598152i	$0.204098\pi$
$588$	1.74036	0.0717711
$589$	−2.95032	−0.121566
$590$	−21.1442	−0.870492
$591$	11.8656	0.488086
$592$	23.2611	0.956024
$593$	36.9162	1.51596	0.757982	−	0.652275i	$-0.226185\pi$
$593$	36.9162	1.51596	0.757982	+	0.652275i	$0.226185\pi$
$594$	−0.853553	−0.0350217
$595$	27.5962	1.13133
$596$	−4.54758	−0.186276
$597$	2.52866	0.103491
$598$	−2.37725	−0.0972130
$599$	40.4224	1.65161	0.825807	−	0.563953i	$-0.190720\pi$
$599$	40.4224	1.65161	0.825807	+	0.563953i	$0.190720\pi$
$600$	−27.6286	−1.12793
$601$	2.98464	0.121746	0.0608730	−	0.998146i	$-0.480612\pi$
$601$	2.98464	0.121746	0.0608730	+	0.998146i	$0.480612\pi$
$602$	−2.14204	−0.0873029
$603$	−8.22728	−0.335041
$604$	16.1206	0.655937
$605$	−36.1804	−1.47094
$606$	−7.02315	−0.285296
$607$	−29.1893	−1.18476	−0.592378	−	0.805660i	$-0.701811\pi$
$607$	−29.1893	−1.18476	−0.592378	+	0.805660i	$0.701811\pi$
$608$	3.53392	0.143319
$609$	−5.60012	−0.226928
$610$	−17.3721	−0.703376
$611$	8.98090	0.363328
$612$	−10.8771	−0.439679
$613$	−5.88595	−0.237731	−0.118866	−	0.992910i	$-0.537926\pi$
$613$	−5.88595	−0.237731	−0.118866	+	0.992910i	$0.537926\pi$
$614$	−0.419505	−0.0169298
$615$	22.7653	0.917986
$616$	−3.19259	−0.128633
$617$	−8.07326	−0.325017	−0.162509	−	0.986707i	$-0.551959\pi$
$617$	−8.07326	−0.325017	−0.162509	+	0.986707i	$0.551959\pi$
$618$	8.43581	0.339338
$619$	10.8589	0.436457	0.218228	−	0.975898i	$-0.429972\pi$
$619$	10.8589	0.436457	0.218228	+	0.975898i	$0.429972\pi$
$620$	−32.6583	−1.31159
$621$	1.00000	0.0401286
$622$	15.6245	0.626486
$623$	−13.4963	−0.540717
$624$	11.7080	0.468695
$625$	112.661	4.50644
$626$	−6.69160	−0.267450
$627$	−1.16287	−0.0464406
$628$	13.5313	0.539959
$629$	57.9305	2.30984
$630$	−2.24991	−0.0896385
$631$	23.1891	0.923145	0.461572	−	0.887103i	$-0.347285\pi$
$631$	23.1891	0.923145	0.461572	+	0.887103i	$0.347285\pi$
$632$	1.10736	0.0440482
$633$	21.9797	0.873614
$634$	7.75891	0.308146
$635$	−94.9223	−3.76688
$636$	−3.20340	−0.127023
$637$	−4.66537	−0.184849
$638$	4.78000	0.189242
$639$	−10.6654	−0.421915
$640$	50.4108	1.99266
$641$	−46.7138	−1.84509	−0.922543	−	0.385895i	$-0.873893\pi$
$641$	−46.7138	−1.84509	−0.922543	+	0.385895i	$0.873893\pi$
$642$	−0.680065	−0.0268400
$643$	33.7524	1.33106	0.665532	−	0.746369i	$-0.268205\pi$
$643$	33.7524	1.33106	0.665532	+	0.746369i	$0.268205\pi$
$644$	1.74036	0.0685796
$645$	−18.5615	−0.730860
$646$	2.21082	0.0869834
$647$	18.9277	0.744124	0.372062	−	0.928208i	$-0.378651\pi$
$647$	18.9277	0.744124	0.372062	+	0.928208i	$0.378651\pi$
$648$	1.90591	0.0748711
$649$	−15.7423	−0.617938
$650$	34.4613	1.35168
$651$	−4.24991	−0.166567
$652$	12.3927	0.485335
$653$	−10.1696	−0.397967	−0.198984	−	0.980003i	$-0.563764\pi$
$653$	−10.1696	−0.397967	−0.198984	+	0.980003i	$0.563764\pi$
$654$	2.04225	0.0798585
$655$	5.18943	0.202768
$656$	−12.9388	−0.505175
$657$	−11.9117	−0.464722
$658$	0.980895	0.0382393
$659$	−4.60754	−0.179484	−0.0897421	−	0.995965i	$-0.528604\pi$
$659$	−4.60754	−0.179484	−0.0897421	+	0.995965i	$0.528604\pi$
$660$	−12.8723	−0.501053
$661$	−31.1205	−1.21045	−0.605223	−	0.796056i	$-0.706916\pi$
$661$	−31.1205	−1.21045	−0.605223	+	0.796056i	$0.706916\pi$
$662$	−13.0279	−0.506345
$663$	29.1581	1.13241
$664$	13.2467	0.514071
$665$	−3.06525	−0.118865
$666$	−4.72305	−0.183014
$667$	−5.60012	−0.216837
$668$	20.8612	0.807144
$669$	−0.0302726	−0.00117041
$670$	18.5106	0.715128
$671$	−12.9339	−0.499308
$672$	5.09056	0.196373
$673$	−36.9447	−1.42411	−0.712057	−	0.702122i	$-0.752236\pi$
$673$	−36.9447	−1.42411	−0.712057	+	0.702122i	$0.752236\pi$
$674$	−8.30010	−0.319708
$675$	−14.4963	−0.557962
$676$	−15.2554	−0.586746
$677$	0.331401	0.0127368	0.00636838	−	0.999980i	$-0.497973\pi$
$677$	0.331401	0.0127368	0.00636838	+	0.999980i	$0.497973\pi$
$678$	−4.61922	−0.177400
$679$	10.0999	0.387600
$680$	52.5959	2.01696
$681$	−21.2393	−0.813893
$682$	3.62752	0.138905
$683$	−16.8856	−0.646109	−0.323055	−	0.946380i	$-0.604710\pi$
$683$	−16.8856	−0.646109	−0.323055	+	0.946380i	$0.604710\pi$
$684$	1.20817	0.0461956
$685$	70.0126	2.67504
$686$	−0.509552	−0.0194548
$687$	−17.4360	−0.665225
$688$	10.5496	0.402198
$689$	8.58734	0.327152
$690$	−2.24991	−0.0856526
$691$	−11.1963	−0.425929	−0.212964	−	0.977060i	$-0.568312\pi$
$691$	−11.1963	−0.425929	−0.212964	+	0.977060i	$0.568312\pi$
$692$	3.65463	0.138928
$693$	−1.67510	−0.0636319
$694$	−11.0435	−0.419206
$695$	−8.54119	−0.323986
$696$	−10.6733	−0.404571
$697$	−32.2234	−1.22055
$698$	10.9655	0.415049
$699$	11.2082	0.423932
$700$	−25.2287	−0.953556
$701$	9.50609	0.359040	0.179520	−	0.983754i	$-0.442546\pi$
$701$	9.50609	0.359040	0.179520	+	0.983754i	$0.442546\pi$
$702$	−2.37725	−0.0897235
$703$	−6.43463	−0.242687
$704$	4.06245	0.153110
$705$	8.49982	0.320122
$706$	10.2854	0.387096
$707$	−13.7830	−0.518362
$708$	16.3555	0.614677
$709$	36.2890	1.36286	0.681431	−	0.731882i	$-0.261358\pi$
$709$	36.2890	1.36286	0.681431	+	0.731882i	$0.261358\pi$
$710$	23.9961	0.900558
$711$	0.581012	0.0217896
$712$	−25.7227	−0.963998
$713$	−4.24991	−0.159160
$714$	3.18466	0.119183
$715$	34.5067	1.29048
$716$	27.7980	1.03886
$717$	18.5654	0.693339
$718$	−11.8467	−0.442115
$719$	−33.5772	−1.25222	−0.626109	−	0.779736i	$-0.715353\pi$
$719$	−33.5772	−1.25222	−0.626109	+	0.779736i	$0.715353\pi$
$720$	11.0808	0.412958
$721$	16.5553	0.616553
$722$	9.43593	0.351169
$723$	13.6556	0.507858
$724$	5.04651	0.187552
$725$	81.1809	3.01498
$726$	−4.17529	−0.154959
$727$	37.5410	1.39232	0.696159	−	0.717887i	$-0.254891\pi$
$727$	37.5410	1.39232	0.696159	+	0.717887i	$0.254891\pi$
$728$	−8.89176	−0.329551
$729$	1.00000	0.0370370
$730$	26.8004	0.991925
$731$	26.2731	0.971747
$732$	13.4377	0.496673
$733$	24.2222	0.894668	0.447334	−	0.894367i	$-0.352374\pi$
$733$	24.2222	0.894668	0.447334	+	0.894367i	$0.352374\pi$
$734$	−14.1233	−0.521300
$735$	−4.41546	−0.162867
$736$	5.09056	0.187641
$737$	13.7815	0.507650
$738$	2.62716	0.0967071
$739$	−19.4377	−0.715028	−0.357514	−	0.933908i	$-0.616376\pi$
$739$	−19.4377	−0.715028	−0.357514	+	0.933908i	$0.616376\pi$
$740$	−71.2275	−2.61837
$741$	−3.23874	−0.118978
$742$	0.937911	0.0344318
$743$	35.7282	1.31074	0.655370	−	0.755308i	$-0.272513\pi$
$743$	35.7282	1.31074	0.655370	+	0.755308i	$0.272513\pi$
$744$	−8.09993	−0.296958
$745$	11.5377	0.422707
$746$	12.6014	0.461369
$747$	6.95032	0.254299
$748$	18.2202	0.666197
$749$	−1.33463	−0.0487664
$750$	21.3658	0.780168
$751$	14.4795	0.528363	0.264182	−	0.964473i	$-0.414898\pi$
$751$	14.4795	0.528363	0.264182	+	0.964473i	$0.414898\pi$
$752$	−4.83092	−0.176166
$753$	−0.604526	−0.0220302
$754$	13.3129	0.484826
$755$	−40.8996	−1.48849
$756$	1.74036	0.0632961
$757$	21.8034	0.792460	0.396230	−	0.918151i	$-0.370318\pi$
$757$	21.8034	0.792460	0.396230	+	0.918151i	$0.370318\pi$
$758$	1.58542	0.0575851
$759$	−1.67510	−0.0608024
$760$	−5.84209	−0.211915
$761$	−5.98196	−0.216846	−0.108423	−	0.994105i	$-0.534580\pi$
$761$	−5.98196	−0.216846	−0.108423	+	0.994105i	$0.534580\pi$
$762$	−10.9542	−0.396829
$763$	4.00794	0.145097
$764$	37.5023	1.35679
$765$	27.5962	0.997744
$766$	9.65619	0.348892
$767$	−43.8441	−1.58312
$768$	0.967116	0.0348978
$769$	−16.0694	−0.579476	−0.289738	−	0.957106i	$-0.593568\pi$
$769$	−16.0694	−0.579476	−0.289738	+	0.957106i	$0.593568\pi$
$770$	3.76883	0.135819
$771$	−14.1602	−0.509968
$772$	−7.98340	−0.287329
$773$	36.5039	1.31295	0.656476	−	0.754347i	$-0.272046\pi$
$773$	36.5039	1.31295	0.656476	+	0.754347i	$0.272046\pi$
$774$	−2.14204	−0.0769939
$775$	61.6079	2.21302
$776$	19.2495	0.691018
$777$	−9.26901	−0.332524
$778$	10.2773	0.368460
$779$	3.57921	0.128239
$780$	−35.8509	−1.28367
$781$	17.8656	0.639282
$782$	3.18466	0.113883
$783$	−5.60012	−0.200132
$784$	2.50955	0.0896269
$785$	−34.3304	−1.22530
$786$	0.598870	0.0213610
$787$	−44.7402	−1.59482	−0.797408	−	0.603440i	$-0.793796\pi$
$787$	−44.7402	−1.59482	−0.797408	+	0.603440i	$0.793796\pi$
$788$	20.6504	0.735639
$789$	−20.5788	−0.732626
$790$	−1.30722	−0.0465089
$791$	−9.06525	−0.322323
$792$	−3.19259	−0.113444
$793$	−36.0225	−1.27920
$794$	−4.28857	−0.152196
$795$	8.12734	0.288247
$796$	4.40076	0.155981
$797$	−11.3919	−0.403521	−0.201761	−	0.979435i	$-0.564666\pi$
$797$	−11.3919	−0.403521	−0.201761	+	0.979435i	$0.564666\pi$
$798$	−0.353736	−0.0125221
$799$	−12.0312	−0.425632
$800$	−73.7943	−2.60902
$801$	−13.4963	−0.476868
$802$	2.98765	0.105498
$803$	19.9534	0.704141
$804$	−14.3184	−0.504971
$805$	−4.41546	−0.155625
$806$	10.1031	0.355866
$807$	0.496655	0.0174831
$808$	−26.2691	−0.924143
$809$	−23.4803	−0.825523	−0.412761	−	0.910839i	$-0.635436\pi$
$809$	−23.4803	−0.825523	−0.412761	+	0.910839i	$0.635436\pi$
$810$	−2.24991	−0.0790537
$811$	−0.320003	−0.0112368	−0.00561841	−	0.999984i	$-0.501788\pi$
$811$	−0.320003	−0.0112368	−0.00561841	+	0.999984i	$0.501788\pi$
$812$	−9.74620	−0.342025
$813$	−24.0547	−0.843634
$814$	7.91160	0.277301
$815$	−31.4415	−1.10135
$816$	−15.6845	−0.549066
$817$	−2.91829	−0.102098
$818$	13.3853	0.468004
$819$	−4.66537	−0.163021
$820$	39.6197	1.38358
$821$	50.4892	1.76208	0.881042	−	0.473038i	$-0.156843\pi$
$821$	50.4892	1.76208	0.881042	+	0.473038i	$0.156843\pi$
$822$	8.07958	0.281808
$823$	−29.6259	−1.03270	−0.516348	−	0.856379i	$-0.672709\pi$
$823$	−29.6259	−1.03270	−0.516348	+	0.856379i	$0.672709\pi$
$824$	31.5529	1.09920
$825$	24.2828	0.845418
$826$	−4.78867	−0.166619
$827$	−3.13318	−0.108951	−0.0544757	−	0.998515i	$-0.517349\pi$
$827$	−3.13318	−0.108951	−0.0544757	+	0.998515i	$0.517349\pi$
$828$	1.74036	0.0604816
$829$	−20.1070	−0.698345	−0.349172	−	0.937059i	$-0.613537\pi$
$829$	−20.1070	−0.698345	−0.349172	+	0.937059i	$0.613537\pi$
$830$	−15.6376	−0.542789
$831$	−23.2402	−0.806193
$832$	11.3144	0.392257
$833$	6.24991	0.216547
$834$	−0.985670	−0.0341309
$835$	−52.9270	−1.83161
$836$	−2.02381	−0.0699950
$837$	−4.24991	−0.146898
$838$	0.407972	0.0140932
$839$	−6.63075	−0.228919	−0.114460	−	0.993428i	$-0.536514\pi$
$839$	−6.63075	−0.228919	−0.114460	+	0.993428i	$0.536514\pi$
$840$	−8.41546	−0.290361
$841$	2.36131	0.0814244
$842$	−11.9156	−0.410640
$843$	15.0697	0.519029
$844$	38.2525	1.31670
$845$	38.7045	1.33147
$846$	0.980895	0.0337239
$847$	−8.19403	−0.281550
$848$	−4.61922	−0.158625
$849$	−9.22691	−0.316667
$850$	−46.1657	−1.58347
$851$	−9.26901	−0.317738
$852$	−18.5615	−0.635908
$853$	−36.1804	−1.23879	−0.619397	−	0.785078i	$-0.712623\pi$
$853$	−36.1804	−1.23879	−0.619397	+	0.785078i	$0.712623\pi$
$854$	−3.93438	−0.134632
$855$	−3.06525	−0.104829
$856$	−2.54368	−0.0869413
$857$	12.6983	0.433764	0.216882	−	0.976198i	$-0.430411\pi$
$857$	12.6983	0.433764	0.216882	+	0.976198i	$0.430411\pi$
$858$	3.98214	0.135948
$859$	49.2759	1.68127	0.840636	−	0.541600i	$-0.182181\pi$
$859$	49.2759	1.68127	0.840636	+	0.541600i	$0.182181\pi$
$860$	−32.3037	−1.10155
$861$	5.15582	0.175710
$862$	17.0625	0.581152
$863$	−3.28011	−0.111656	−0.0558282	−	0.998440i	$-0.517780\pi$
$863$	−3.28011	−0.111656	−0.0558282	+	0.998440i	$0.517780\pi$
$864$	5.09056	0.173185
$865$	−9.27218	−0.315263
$866$	−12.2992	−0.417944
$867$	−22.0614	−0.749243
$868$	−7.39636	−0.251049
$869$	−0.973255	−0.0330154
$870$	12.5998	0.427172
$871$	38.3833	1.30057
$872$	7.63876	0.258681
$873$	10.0999	0.341831
$874$	−0.353736	−0.0119653
$875$	41.9305	1.41751
$876$	−20.7307	−0.700425
$877$	7.64380	0.258113	0.129056	−	0.991637i	$-0.458805\pi$
$877$	7.64380	0.258113	0.129056	+	0.991637i	$0.458805\pi$
$878$	8.38056	0.282830
$879$	12.3881	0.417839
$880$	−18.5615	−0.625709
$881$	5.21611	0.175735	0.0878676	−	0.996132i	$-0.471995\pi$
$881$	5.21611	0.175735	0.0878676	+	0.996132i	$0.471995\pi$
$882$	−0.509552	−0.0171575
$883$	−45.2052	−1.52127	−0.760637	−	0.649177i	$-0.775113\pi$
$883$	−45.2052	−1.52127	−0.760637	+	0.649177i	$0.775113\pi$
$884$	50.7455	1.70676
$885$	−41.4956	−1.39486
$886$	−4.88428	−0.164090
$887$	−8.59600	−0.288626	−0.144313	−	0.989532i	$-0.546097\pi$
$887$	−8.59600	−0.288626	−0.144313	+	0.989532i	$0.546097\pi$
$888$	−17.6659	−0.592828
$889$	−21.4977	−0.721010
$890$	30.3654	1.01785
$891$	−1.67510	−0.0561181
$892$	−0.0526851	−0.00176403
$893$	1.33636	0.0447196
$894$	1.33147	0.0445310
$895$	−70.5263	−2.35744
$896$	11.4169	0.381412
$897$	−4.66537	−0.155772
$898$	−2.12646	−0.0709609
$899$	23.8000	0.793774
$900$	−25.2287	−0.840957
$901$	−11.5039	−0.383251
$902$	−4.40076	−0.146529
$903$	−4.20376	−0.139892
$904$	−17.2775	−0.574642
$905$	−12.8035	−0.425603
$906$	−4.71989	−0.156808
$907$	2.50429	0.0831537	0.0415769	−	0.999135i	$-0.486762\pi$
$907$	2.50429	0.0831537	0.0415769	+	0.999135i	$0.486762\pi$
$908$	−36.9640	−1.22669
$909$	−13.7830	−0.457152
$910$	10.4967	0.347961
$911$	29.5776	0.979951	0.489975	−	0.871736i	$-0.337006\pi$
$911$	29.5776	0.979951	0.489975	+	0.871736i	$0.337006\pi$
$912$	1.74215	0.0576885
$913$	−11.6425	−0.385311
$914$	−4.09001	−0.135286
$915$	−34.0929	−1.12708
$916$	−30.3448	−1.00262
$917$	1.17529	0.0388114
$918$	3.18466	0.105109
$919$	23.5583	0.777117	0.388558	−	0.921424i	$-0.372973\pi$
$919$	23.5583	0.777117	0.388558	+	0.921424i	$0.372973\pi$
$920$	−8.41546	−0.277450
$921$	−0.823281	−0.0271280
$922$	−5.92057	−0.194984
$923$	49.7579	1.63780
$924$	−2.91528	−0.0959056
$925$	134.366	4.41794
$926$	18.2783	0.600664
$927$	16.5553	0.543749
$928$	−28.5078	−0.935813
$929$	−37.9337	−1.24456	−0.622281	−	0.782794i	$-0.713794\pi$
$929$	−37.9337	−1.24456	−0.622281	+	0.782794i	$0.713794\pi$
$930$	9.56191	0.313547
$931$	−0.694209	−0.0227518
$932$	19.5062	0.638947
$933$	30.6632	1.00387
$934$	6.71240	0.219636
$935$	−46.2265	−1.51177
$936$	−8.89176	−0.290636
$937$	−42.3490	−1.38348	−0.691741	−	0.722146i	$-0.743156\pi$
$937$	−42.3490	−1.38348	−0.691741	+	0.722146i	$0.743156\pi$
$938$	4.19223	0.136881
$939$	−13.1323	−0.428556
$940$	14.7927	0.482485
$941$	−33.9735	−1.10750	−0.553752	−	0.832682i	$-0.686804\pi$
$941$	−33.9735	−1.10750	−0.553752	+	0.832682i	$0.686804\pi$
$942$	−3.96179	−0.129082
$943$	5.15582	0.167896
$944$	23.5842	0.767602
$945$	−4.41546	−0.143635
$946$	3.58813	0.116660
$947$	−27.7471	−0.901659	−0.450829	−	0.892610i	$-0.648872\pi$
$947$	−27.7471	−0.901659	−0.450829	+	0.892610i	$0.648872\pi$
$948$	1.01117	0.0328412
$949$	55.5727	1.80397
$950$	5.12786	0.166370
$951$	15.2269	0.493766
$952$	11.9117	0.386062
$953$	−6.25582	−0.202646	−0.101323	−	0.994854i	$-0.532308\pi$
$953$	−6.25582	−0.202646	−0.101323	+	0.994854i	$0.532308\pi$
$954$	0.937911	0.0303660
$955$	−95.1472	−3.07889
$956$	32.3105	1.04500
$957$	9.38078	0.303237
$958$	−2.66537	−0.0861142
$959$	15.8562	0.512024
$960$	10.7084	0.345611
$961$	−12.9383	−0.417364
$962$	22.0348	0.710429
$963$	−1.33463	−0.0430079
$964$	23.7657	0.765441
$965$	20.2547	0.652021
$966$	−0.509552	−0.0163946
$967$	43.1613	1.38797	0.693987	−	0.719988i	$-0.255853\pi$
$967$	43.1613	1.38797	0.693987	+	0.719988i	$0.255853\pi$
$968$	−15.6171	−0.501951
$969$	4.33874	0.139381
$970$	−22.7239	−0.729621
$971$	6.69189	0.214753	0.107377	−	0.994218i	$-0.465755\pi$
$971$	6.69189	0.214753	0.107377	+	0.994218i	$0.465755\pi$
$972$	1.74036	0.0558220
$973$	−1.93438	−0.0620135
$974$	−14.7658	−0.473125
$975$	67.6305	2.16591
$976$	19.3769	0.620239
$977$	−47.1871	−1.50965	−0.754825	−	0.655926i	$-0.772278\pi$
$977$	−47.1871	−1.50965	−0.754825	+	0.655926i	$0.772278\pi$
$978$	−3.62841	−0.116024
$979$	22.6077	0.722545
$980$	−7.68447	−0.245472
$981$	4.00794	0.127964
$982$	8.50502	0.271406
$983$	18.4505	0.588480	0.294240	−	0.955732i	$-0.404934\pi$
$983$	18.4505	0.588480	0.294240	+	0.955732i	$0.404934\pi$
$984$	9.82651	0.313258
$985$	−52.3921	−1.66935
$986$	−17.8344	−0.567965
$987$	1.92501	0.0612738
$988$	−5.63656	−0.179323
$989$	−4.20376	−0.133672
$990$	3.76883	0.119781
$991$	−24.3764	−0.774342	−0.387171	−	0.922008i	$-0.626548\pi$
$991$	−24.3764	−0.774342	−0.387171	+	0.922008i	$0.626548\pi$
$992$	−21.6344	−0.686894
$993$	−25.5674	−0.811356
$994$	5.43457	0.172374
$995$	−11.1652	−0.353960
$996$	12.0960	0.383278
$997$	59.5570	1.88619	0.943094	−	0.332525i	$-0.107901\pi$
$997$	59.5570	1.88619	0.943094	+	0.332525i	$0.107901\pi$
$998$	−4.87750	−0.154395
$999$	−9.26901	−0.293259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.a.i.1.2	✓	4
3.2	odd	2		1449.2.a.p.1.3		4
4.3	odd	2		7728.2.a.cd.1.4		4
7.6	odd	2		3381.2.a.w.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.i.1.2	✓	4	1.1	even	1	trivial
1449.2.a.p.1.3		4	3.2	odd	2
3381.2.a.w.1.2		4	7.6	odd	2
7728.2.a.cd.1.4		4	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)

\(f(q)\)	\(=\)	\(q-0.509552 q^{2} -1.00000 q^{3} -1.74036 q^{4} +4.41546 q^{5} +0.509552 q^{6} +1.00000 q^{7} +1.90591 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.509552 q^{2} -1.00000 q^{3} -1.74036 q^{4} +4.41546 q^{5} +0.509552 q^{6} +1.00000 q^{7} +1.90591 q^{8} +1.00000 q^{9} -2.24991 q^{10} -1.67510 q^{11} +1.74036 q^{12} -4.66537 q^{13} -0.509552 q^{14} -4.41546 q^{15} +2.50955 q^{16} +6.24991 q^{17} -0.509552 q^{18} -0.694209 q^{19} -7.68447 q^{20} -1.00000 q^{21} +0.853553 q^{22} -1.00000 q^{23} -1.90591 q^{24} +14.4963 q^{25} +2.37725 q^{26} -1.00000 q^{27} -1.74036 q^{28} +5.60012 q^{29} +2.24991 q^{30} +4.24991 q^{31} -5.09056 q^{32} +1.67510 q^{33} -3.18466 q^{34} +4.41546 q^{35} -1.74036 q^{36} +9.26901 q^{37} +0.353736 q^{38} +4.66537 q^{39} +8.41546 q^{40} -5.15582 q^{41} +0.509552 q^{42} +4.20376 q^{43} +2.91528 q^{44} +4.41546 q^{45} +0.509552 q^{46} -1.92501 q^{47} -2.50955 q^{48} +1.00000 q^{49} -7.38662 q^{50} -6.24991 q^{51} +8.11940 q^{52} -1.84066 q^{53} +0.509552 q^{54} -7.39636 q^{55} +1.90591 q^{56} +0.694209 q^{57} -2.85355 q^{58} +9.39779 q^{59} +7.68447 q^{60} +7.72125 q^{61} -2.16555 q^{62} +1.00000 q^{63} -2.42520 q^{64} -20.5998 q^{65} -0.853553 q^{66} -8.22728 q^{67} -10.8771 q^{68} +1.00000 q^{69} -2.24991 q^{70} -10.6654 q^{71} +1.90591 q^{72} -11.9117 q^{73} -4.72305 q^{74} -14.4963 q^{75} +1.20817 q^{76} -1.67510 q^{77} -2.37725 q^{78} +0.581012 q^{79} +11.0808 q^{80} +1.00000 q^{81} +2.62716 q^{82} +6.95032 q^{83} +1.74036 q^{84} +27.5962 q^{85} -2.14204 q^{86} -5.60012 q^{87} -3.19259 q^{88} -13.4963 q^{89} -2.24991 q^{90} -4.66537 q^{91} +1.74036 q^{92} -4.24991 q^{93} +0.980895 q^{94} -3.06525 q^{95} +5.09056 q^{96} +10.0999 q^{97} -0.509552 q^{98} -1.67510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{4} + 5 q^{5} + 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 4 * q^4 + 5 * q^5 + 4 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q - 4 q^{3} + 4 q^{4} + 5 q^{5} + 4 q^{7} - 3 q^{8} + 4 q^{9} + 4 q^{10} - 5 q^{11} - 4 q^{12} + 7 q^{13} - 5 q^{15} + 8 q^{16} + 12 q^{17} + 3 q^{19} - q^{20} - 4 q^{21} - q^{22} - 4 q^{23} + 3 q^{24} + 7 q^{25} + 5 q^{26} - 4 q^{27} + 4 q^{28} + 6 q^{29} - 4 q^{30} + 4 q^{31} - 6 q^{32} + 5 q^{33} - 9 q^{34} + 5 q^{35} + 4 q^{36} + 20 q^{37} + 23 q^{38} - 7 q^{39} + 21 q^{40} + 3 q^{41} + 9 q^{43} - 27 q^{44} + 5 q^{45} + 7 q^{47} - 8 q^{48} + 4 q^{49} + 3 q^{50} - 12 q^{51} + 38 q^{52} - 6 q^{53} - 21 q^{55} - 3 q^{56} - 3 q^{57} - 7 q^{58} - 2 q^{59} + q^{60} + 24 q^{61} - 9 q^{62} + 4 q^{63} - 21 q^{64} - 14 q^{65} + q^{66} + q^{67} - 13 q^{68} + 4 q^{69} + 4 q^{70} - 17 q^{71} - 3 q^{72} + 16 q^{73} - 33 q^{74} - 7 q^{75} - 25 q^{76} - 5 q^{77} - 5 q^{78} - 10 q^{79} + 6 q^{80} + 4 q^{81} - 7 q^{82} + 8 q^{83} - 4 q^{84} + 17 q^{85} - 35 q^{86} - 6 q^{87} - 12 q^{88} - 3 q^{89} + 4 q^{90} + 7 q^{91} - 4 q^{92} - 4 q^{93} + 8 q^{94} - 3 q^{95} + 6 q^{96} - 2 q^{97} - 5 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^4 + 5 * q^5 + 4 * q^7 - 3 * q^8 + 4 * q^9 + 4 * q^10 - 5 * q^11 - 4 * q^12 + 7 * q^13 - 5 * q^15 + 8 * q^16 + 12 * q^17 + 3 * q^19 - q^20 - 4 * q^21 - q^22 - 4 * q^23 + 3 * q^24 + 7 * q^25 + 5 * q^26 - 4 * q^27 + 4 * q^28 + 6 * q^29 - 4 * q^30 + 4 * q^31 - 6 * q^32 + 5 * q^33 - 9 * q^34 + 5 * q^35 + 4 * q^36 + 20 * q^37 + 23 * q^38 - 7 * q^39 + 21 * q^40 + 3 * q^41 + 9 * q^43 - 27 * q^44 + 5 * q^45 + 7 * q^47 - 8 * q^48 + 4 * q^49 + 3 * q^50 - 12 * q^51 + 38 * q^52 - 6 * q^53 - 21 * q^55 - 3 * q^56 - 3 * q^57 - 7 * q^58 - 2 * q^59 + q^60 + 24 * q^61 - 9 * q^62 + 4 * q^63 - 21 * q^64 - 14 * q^65 + q^66 + q^67 - 13 * q^68 + 4 * q^69 + 4 * q^70 - 17 * q^71 - 3 * q^72 + 16 * q^73 - 33 * q^74 - 7 * q^75 - 25 * q^76 - 5 * q^77 - 5 * q^78 - 10 * q^79 + 6 * q^80 + 4 * q^81 - 7 * q^82 + 8 * q^83 - 4 * q^84 + 17 * q^85 - 35 * q^86 - 6 * q^87 - 12 * q^88 - 3 * q^89 + 4 * q^90 + 7 * q^91 - 4 * q^92 - 4 * q^93 + 8 * q^94 - 3 * q^95 + 6 * q^96 - 2 * q^97 - 5 * q^99

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