LMFDB - Embedded newform 8003.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$1$
Dimension:	$147$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46705 q^{2} +3.03255 q^{3} +4.08634 q^{4} -1.27620 q^{5} -7.48147 q^{6} +0.505683 q^{7} -5.14712 q^{8} +6.19639 q^{9} +O(q^{10})$	\(q-2.46705 q^{2} +3.03255 q^{3} +4.08634 q^{4} -1.27620 q^{5} -7.48147 q^{6} +0.505683 q^{7} -5.14712 q^{8} +6.19639 q^{9} +3.14846 q^{10} +3.60482 q^{11} +12.3921 q^{12} -4.00989 q^{13} -1.24755 q^{14} -3.87016 q^{15} +4.52551 q^{16} -0.211286 q^{17} -15.2868 q^{18} +8.35902 q^{19} -5.21500 q^{20} +1.53351 q^{21} -8.89327 q^{22} -5.98834 q^{23} -15.6089 q^{24} -3.37131 q^{25} +9.89261 q^{26} +9.69322 q^{27} +2.06640 q^{28} -4.12124 q^{29} +9.54787 q^{30} -2.75210 q^{31} -0.870443 q^{32} +10.9318 q^{33} +0.521254 q^{34} -0.645355 q^{35} +25.3206 q^{36} -10.0449 q^{37} -20.6221 q^{38} -12.1602 q^{39} +6.56876 q^{40} -5.67790 q^{41} -3.78325 q^{42} -3.32994 q^{43} +14.7305 q^{44} -7.90785 q^{45} +14.7735 q^{46} -1.62890 q^{47} +13.7239 q^{48} -6.74428 q^{49} +8.31719 q^{50} -0.640737 q^{51} -16.3858 q^{52} +1.00000 q^{53} -23.9137 q^{54} -4.60048 q^{55} -2.60281 q^{56} +25.3492 q^{57} +10.1673 q^{58} +13.9626 q^{59} -15.8148 q^{60} -6.70397 q^{61} +6.78956 q^{62} +3.13341 q^{63} -6.90360 q^{64} +5.11744 q^{65} -26.9693 q^{66} -3.66555 q^{67} -0.863387 q^{68} -18.1600 q^{69} +1.59212 q^{70} +0.532971 q^{71} -31.8935 q^{72} -14.0603 q^{73} +24.7812 q^{74} -10.2237 q^{75} +34.1578 q^{76} +1.82290 q^{77} +29.9999 q^{78} -12.1696 q^{79} -5.77547 q^{80} +10.8061 q^{81} +14.0077 q^{82} -12.5846 q^{83} +6.26646 q^{84} +0.269644 q^{85} +8.21513 q^{86} -12.4979 q^{87} -18.5544 q^{88} -13.2819 q^{89} +19.5091 q^{90} -2.02774 q^{91} -24.4704 q^{92} -8.34588 q^{93} +4.01859 q^{94} -10.6678 q^{95} -2.63967 q^{96} +6.76479 q^{97} +16.6385 q^{98} +22.3368 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) $ 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46705	−1.74447	−0.872234	−	0.489088i	$-0.837330\pi$
$2$	−2.46705	−1.74447	−0.872234	+	0.489088i	$0.837330\pi$
$3$	3.03255	1.75085	0.875423	−	0.483357i	$-0.160583\pi$
$3$	3.03255	1.75085	0.875423	+	0.483357i	$0.160583\pi$
$4$	4.08634	2.04317
$5$	−1.27620	−0.570735	−0.285368	−	0.958418i	$-0.592116\pi$
$5$	−1.27620	−0.570735	−0.285368	+	0.958418i	$0.592116\pi$
$6$	−7.48147	−3.05430
$7$	0.505683	0.191130	0.0955652	−	0.995423i	$-0.469534\pi$
$7$	0.505683	0.191130	0.0955652	+	0.995423i	$0.469534\pi$
$8$	−5.14712	−1.81978
$9$	6.19639	2.06546
$10$	3.14846	0.995630
$11$	3.60482	1.08689	0.543447	−	0.839444i	$-0.317119\pi$
$11$	3.60482	1.08689	0.543447	+	0.839444i	$0.317119\pi$
$12$	12.3921	3.57728
$13$	−4.00989	−1.11214	−0.556072	−	0.831134i	$-0.687692\pi$
$13$	−4.00989	−1.11214	−0.556072	+	0.831134i	$0.687692\pi$
$14$	−1.24755	−0.333421
$15$	−3.87016	−0.999270
$16$	4.52551	1.13138
$17$	−0.211286	−0.0512444	−0.0256222	−	0.999672i	$-0.508157\pi$
$17$	−0.211286	−0.0512444	−0.0256222	+	0.999672i	$0.508157\pi$
$18$	−15.2868	−3.60314
$19$	8.35902	1.91769	0.958846	−	0.283927i	$-0.0916375\pi$
$19$	8.35902	1.91769	0.958846	+	0.283927i	$0.0916375\pi$
$20$	−5.21500	−1.16611
$21$	1.53351	0.334640
$22$	−8.89327	−1.89605
$23$	−5.98834	−1.24866	−0.624328	−	0.781163i	$-0.714627\pi$
$23$	−5.98834	−1.24866	−0.624328	+	0.781163i	$0.714627\pi$
$24$	−15.6089	−3.18616
$25$	−3.37131	−0.674261
$26$	9.89261	1.94010
$27$	9.69322	1.86546
$28$	2.06640	0.390512
$29$	−4.12124	−0.765294	−0.382647	−	0.923895i	$-0.624988\pi$
$29$	−4.12124	−0.765294	−0.382647	+	0.923895i	$0.624988\pi$
$30$	9.54787	1.74320
$31$	−2.75210	−0.494291	−0.247145	−	0.968978i	$-0.579493\pi$
$31$	−2.75210	−0.494291	−0.247145	+	0.968978i	$0.579493\pi$
$32$	−0.870443	−0.153874
$33$	10.9318	1.90298
$34$	0.521254	0.0893943
$35$	−0.645355	−0.109085
$36$	25.3206	4.22009
$37$	−10.0449	−1.65137	−0.825683	−	0.564134i	$-0.809210\pi$
$37$	−10.0449	−1.65137	−0.825683	+	0.564134i	$0.809210\pi$
$38$	−20.6221	−3.34535
$39$	−12.1602	−1.94719
$40$	6.56876	1.03861
$41$	−5.67790	−0.886739	−0.443370	−	0.896339i	$-0.646217\pi$
$41$	−5.67790	−0.886739	−0.443370	+	0.896339i	$0.646217\pi$
$42$	−3.78325	−0.583769
$43$	−3.32994	−0.507811	−0.253905	−	0.967229i	$-0.581715\pi$
$43$	−3.32994	−0.507811	−0.253905	+	0.967229i	$0.581715\pi$
$44$	14.7305	2.22071
$45$	−7.90785	−1.17883
$46$	14.7735	2.17824
$47$	−1.62890	−0.237600	−0.118800	−	0.992918i	$-0.537905\pi$
$47$	−1.62890	−0.237600	−0.118800	+	0.992918i	$0.537905\pi$
$48$	13.7239	1.98087
$49$	−6.74428	−0.963469
$50$	8.31719	1.17623
$51$	−0.640737	−0.0897211
$52$	−16.3858	−2.27230
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−23.9137	−3.25424
$55$	−4.60048	−0.620328
$56$	−2.60281	−0.347815
$57$	25.3492	3.35758
$58$	10.1673	1.33503
$59$	13.9626	1.81777	0.908885	−	0.417047i	$-0.136935\pi$
$59$	13.9626	1.81777	0.908885	+	0.417047i	$0.136935\pi$
$60$	−15.8148	−2.04168
$61$	−6.70397	−0.858355	−0.429178	−	0.903220i	$-0.641197\pi$
$61$	−6.70397	−0.858355	−0.429178	+	0.903220i	$0.641197\pi$
$62$	6.78956	0.862275
$63$	3.13341	0.394773
$64$	−6.90360	−0.862950
$65$	5.11744	0.634740
$66$	−26.9693	−3.31969
$67$	−3.66555	−0.447818	−0.223909	−	0.974610i	$-0.571882\pi$
$67$	−3.66555	−0.447818	−0.223909	+	0.974610i	$0.571882\pi$
$68$	−0.863387	−0.104701
$69$	−18.1600	−2.18620
$70$	1.59212	0.190295
$71$	0.532971	0.0632520	0.0316260	−	0.999500i	$-0.489931\pi$
$71$	0.532971	0.0632520	0.0316260	+	0.999500i	$0.489931\pi$
$72$	−31.8935	−3.75869
$73$	−14.0603	−1.64563	−0.822817	−	0.568307i	$-0.807599\pi$
$73$	−14.0603	−1.64563	−0.822817	+	0.568307i	$0.807599\pi$
$74$	24.7812	2.88076
$75$	−10.2237	−1.18053
$76$	34.1578	3.91817
$77$	1.82290	0.207738
$78$	29.9999	3.39682
$79$	−12.1696	−1.36919	−0.684595	−	0.728923i	$-0.740021\pi$
$79$	−12.1696	−1.36919	−0.684595	+	0.728923i	$0.740021\pi$
$80$	−5.77547	−0.645718
$81$	10.8061	1.20067
$82$	14.0077	1.54689
$83$	−12.5846	−1.38134	−0.690670	−	0.723170i	$-0.742684\pi$
$83$	−12.5846	−1.38134	−0.690670	+	0.723170i	$0.742684\pi$
$84$	6.26646	0.683727
$85$	0.269644	0.0292470
$86$	8.21513	0.885860
$87$	−12.4979	−1.33991
$88$	−18.5544	−1.97791
$89$	−13.2819	−1.40788	−0.703941	−	0.710258i	$-0.748578\pi$
$89$	−13.2819	−1.40788	−0.703941	+	0.710258i	$0.748578\pi$
$90$	19.5091	2.05644
$91$	−2.02774	−0.212564
$92$	−24.4704	−2.55122
$93$	−8.34588	−0.865427
$94$	4.01859	0.414486
$95$	−10.6678	−1.09449
$96$	−2.63967	−0.269410
$97$	6.76479	0.686860	0.343430	−	0.939178i	$-0.388411\pi$
$97$	6.76479	0.686860	0.343430	+	0.939178i	$0.388411\pi$
$98$	16.6385	1.68074
$99$	22.3368	2.24494
$100$	−13.7763	−1.37763
$101$	−2.26858	−0.225732	−0.112866	−	0.993610i	$-0.536003\pi$
$101$	−2.26858	−0.225732	−0.112866	+	0.993610i	$0.536003\pi$
$102$	1.58073	0.156516
$103$	8.91277	0.878202	0.439101	−	0.898438i	$-0.355297\pi$
$103$	8.91277	0.878202	0.439101	+	0.898438i	$0.355297\pi$
$104$	20.6394	2.02386
$105$	−1.95707	−0.190991
$106$	−2.46705	−0.239621
$107$	−7.00485	−0.677184	−0.338592	−	0.940933i	$-0.609951\pi$
$107$	−7.00485	−0.677184	−0.338592	+	0.940933i	$0.609951\pi$
$108$	39.6098	3.81146
$109$	−11.3176	−1.08403	−0.542017	−	0.840368i	$-0.682339\pi$
$109$	−11.3176	−1.08403	−0.542017	+	0.840368i	$0.682339\pi$
$110$	11.3496	1.08214
$111$	−30.4616	−2.89129
$112$	2.28848	0.216241
$113$	5.19702	0.488895	0.244447	−	0.969663i	$-0.421393\pi$
$113$	5.19702	0.488895	0.244447	+	0.969663i	$0.421393\pi$
$114$	−62.5378	−5.85720
$115$	7.64234	0.712652
$116$	−16.8408	−1.56363
$117$	−24.8468	−2.29709
$118$	−34.4463	−3.17104
$119$	−0.106844	−0.00979436
$120$	19.9201	1.81845
$121$	1.99471	0.181337
$122$	16.5390	1.49737
$123$	−17.2185	−1.55254
$124$	−11.2460	−1.00992
$125$	10.6835	0.955560
$126$	−7.73029	−0.688669
$127$	9.47482	0.840754	0.420377	−	0.907349i	$-0.361898\pi$
$127$	9.47482	0.840754	0.420377	+	0.907349i	$0.361898\pi$
$128$	18.7724	1.65926
$129$	−10.0982	−0.889099
$130$	−12.6250	−1.10728
$131$	7.60547	0.664493	0.332246	−	0.943193i	$-0.392193\pi$
$131$	7.60547	0.664493	0.332246	+	0.943193i	$0.392193\pi$
$132$	44.6711	3.88812
$133$	4.22702	0.366529
$134$	9.04310	0.781205
$135$	−12.3705	−1.06468
$136$	1.08751	0.0932536
$137$	0.541000	0.0462207	0.0231104	−	0.999733i	$-0.492643\pi$
$137$	0.541000	0.0462207	0.0231104	+	0.999733i	$0.492643\pi$
$138$	44.8016	3.81376
$139$	1.32998	0.112807	0.0564037	−	0.998408i	$-0.482037\pi$
$139$	1.32998	0.112807	0.0564037	+	0.998408i	$0.482037\pi$
$140$	−2.63714	−0.222879
$141$	−4.93974	−0.416001
$142$	−1.31487	−0.110341
$143$	−14.4549	−1.20878
$144$	28.0418	2.33682
$145$	5.25953	0.436781
$146$	34.6875	2.87076
$147$	−20.4524	−1.68689
$148$	−41.0468	−3.37402
$149$	6.67058	0.546475	0.273238	−	0.961947i	$-0.411905\pi$
$149$	6.67058	0.546475	0.273238	+	0.961947i	$0.411905\pi$
$150$	25.2223	2.05939
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−43.0249	−3.48978
$153$	−1.30921	−0.105843
$154$	−4.49718	−0.362393
$155$	3.51223	0.282109
$156$	−49.6908	−3.97845
$157$	0.927070	0.0739883	0.0369941	−	0.999315i	$-0.488222\pi$
$157$	0.927070	0.0739883	0.0369941	+	0.999315i	$0.488222\pi$
$158$	30.0231	2.38851
$159$	3.03255	0.240497
$160$	1.11086	0.0878214
$161$	−3.02820	−0.238656
$162$	−26.6591	−2.09454
$163$	−15.8171	−1.23889	−0.619447	−	0.785039i	$-0.712643\pi$
$163$	−15.8171	−1.23889	−0.619447	+	0.785039i	$0.712643\pi$
$164$	−23.2019	−1.81176
$165$	−13.9512	−1.08610
$166$	31.0469	2.40971
$167$	−3.35919	−0.259942	−0.129971	−	0.991518i	$-0.541488\pi$
$167$	−3.35919	−0.259942	−0.129971	+	0.991518i	$0.541488\pi$
$168$	−7.89317	−0.608971
$169$	3.07923	0.236864
$170$	−0.665226	−0.0510205
$171$	51.7958	3.96092
$172$	−13.6073	−1.03754
$173$	12.6191	0.959409	0.479704	−	0.877430i	$-0.340744\pi$
$173$	12.6191	0.959409	0.479704	+	0.877430i	$0.340744\pi$
$174$	30.8329	2.33744
$175$	−1.70481	−0.128872
$176$	16.3137	1.22969
$177$	42.3422	3.18264
$178$	32.7672	2.45601
$179$	0.476539	0.0356182	0.0178091	−	0.999841i	$-0.494331\pi$
$179$	0.476539	0.0356182	0.0178091	+	0.999841i	$0.494331\pi$
$180$	−32.3142	−2.40856
$181$	4.01548	0.298468	0.149234	−	0.988802i	$-0.452319\pi$
$181$	4.01548	0.298468	0.149234	+	0.988802i	$0.452319\pi$
$182$	5.00253	0.370812
$183$	−20.3302	−1.50285
$184$	30.8227	2.27228
$185$	12.8193	0.942493
$186$	20.5897	1.50971
$187$	−0.761648	−0.0556972
$188$	−6.65626	−0.485458
$189$	4.90170	0.356546
$190$	26.3180	1.90931
$191$	10.9222	0.790299	0.395150	−	0.918617i	$-0.370693\pi$
$191$	10.9222	0.790299	0.395150	+	0.918617i	$0.370693\pi$
$192$	−20.9355	−1.51089
$193$	−9.46895	−0.681590	−0.340795	−	0.940138i	$-0.610696\pi$
$193$	−9.46895	−0.681590	−0.340795	+	0.940138i	$0.610696\pi$
$194$	−16.6891	−1.19821
$195$	15.5189	1.11133
$196$	−27.5595	−1.96853
$197$	8.69704	0.619639	0.309819	−	0.950795i	$-0.399731\pi$
$197$	8.69704	0.619639	0.309819	+	0.950795i	$0.399731\pi$
$198$	−55.1062	−3.91622
$199$	9.05125	0.641626	0.320813	−	0.947143i	$-0.396044\pi$
$199$	9.05125	0.641626	0.320813	+	0.947143i	$0.396044\pi$
$200$	17.3525	1.22701
$201$	−11.1160	−0.784061
$202$	5.59670	0.393782
$203$	−2.08404	−0.146271
$204$	−2.61827	−0.183316
$205$	7.24615	0.506093
$206$	−21.9883	−1.53200
$207$	−37.1061	−2.57905
$208$	−18.1468	−1.25826
$209$	30.1328	2.08433
$210$	4.82820	0.333178
$211$	20.4671	1.40901	0.704506	−	0.709698i	$-0.251169\pi$
$211$	20.4671	1.40901	0.704506	+	0.709698i	$0.251169\pi$
$212$	4.08634	0.280651
$213$	1.61626	0.110744
$214$	17.2813	1.18133
$215$	4.24968	0.289826
$216$	−49.8921	−3.39473
$217$	−1.39169	−0.0944740
$218$	27.9212	1.89106
$219$	−42.6386	−2.88125
$220$	−18.7991	−1.26744
$221$	0.847234	0.0569912
$222$	75.1504	5.04376
$223$	−7.36186	−0.492987	−0.246493	−	0.969144i	$-0.579278\pi$
$223$	−7.36186	−0.492987	−0.246493	+	0.969144i	$0.579278\pi$
$224$	−0.440169	−0.0294100
$225$	−20.8899	−1.39266
$226$	−12.8213	−0.852861
$227$	18.8909	1.25383	0.626916	−	0.779087i	$-0.284317\pi$
$227$	18.8909	1.25383	0.626916	+	0.779087i	$0.284317\pi$
$228$	103.586	6.86012
$229$	−3.71537	−0.245519	−0.122759	−	0.992436i	$-0.539174\pi$
$229$	−3.71537	−0.245519	−0.122759	+	0.992436i	$0.539174\pi$
$230$	−18.8540	−1.24320
$231$	5.52803	0.363718
$232$	21.2125	1.39267
$233$	8.70658	0.570387	0.285194	−	0.958470i	$-0.407942\pi$
$233$	8.70658	0.570387	0.285194	+	0.958470i	$0.407942\pi$
$234$	61.2985	4.00721
$235$	2.07881	0.135607
$236$	57.0558	3.71402
$237$	−36.9051	−2.39724
$238$	0.263589	0.0170860
$239$	10.9659	0.709324	0.354662	−	0.934995i	$-0.384596\pi$
$239$	10.9659	0.709324	0.354662	+	0.934995i	$0.384596\pi$
$240$	−17.5144	−1.13055
$241$	24.3045	1.56559	0.782795	−	0.622280i	$-0.213794\pi$
$241$	24.3045	1.56559	0.782795	+	0.622280i	$0.213794\pi$
$242$	−4.92105	−0.316337
$243$	3.69030	0.236733
$244$	−27.3947	−1.75377
$245$	8.60708	0.549886
$246$	42.4790	2.70836
$247$	−33.5188	−2.13275
$248$	14.1654	0.899501
$249$	−38.1635	−2.41851
$250$	−26.3567	−1.66694
$251$	20.3108	1.28201	0.641005	−	0.767537i	$-0.278518\pi$
$251$	20.3108	1.28201	0.641005	+	0.767537i	$0.278518\pi$
$252$	12.8042	0.806588
$253$	−21.5869	−1.35716
$254$	−23.3749	−1.46667
$255$	0.817710	0.0512070
$256$	−32.5053	−2.03158
$257$	−29.3366	−1.82996	−0.914982	−	0.403494i	$-0.867796\pi$
$257$	−29.3366	−1.82996	−0.914982	+	0.403494i	$0.867796\pi$
$258$	24.9128	1.55101
$259$	−5.07952	−0.315626
$260$	20.9116	1.29688
$261$	−25.5368	−1.58069
$262$	−18.7631	−1.15919
$263$	−23.7291	−1.46320	−0.731598	−	0.681736i	$-0.761225\pi$
$263$	−23.7291	−1.46320	−0.731598	+	0.681736i	$0.761225\pi$
$264$	−56.2673	−3.46301
$265$	−1.27620	−0.0783965
$266$	−10.4283	−0.639399
$267$	−40.2782	−2.46499
$268$	−14.9787	−0.914969
$269$	−20.1885	−1.23091	−0.615456	−	0.788171i	$-0.711028\pi$
$269$	−20.1885	−1.23091	−0.615456	+	0.788171i	$0.711028\pi$
$270$	30.5187	1.85731
$271$	−18.1001	−1.09950	−0.549751	−	0.835328i	$-0.685277\pi$
$271$	−18.1001	−1.09950	−0.549751	+	0.835328i	$0.685277\pi$
$272$	−0.956178	−0.0579768
$273$	−6.14922	−0.372168
$274$	−1.33467	−0.0806307
$275$	−12.1529	−0.732850
$276$	−74.2079	−4.46679
$277$	−5.52362	−0.331882	−0.165941	−	0.986136i	$-0.553066\pi$
$277$	−5.52362	−0.331882	−0.165941	+	0.986136i	$0.553066\pi$
$278$	−3.28113	−0.196789
$279$	−17.0530	−1.02094
$280$	3.32172	0.198510
$281$	14.5629	0.868748	0.434374	−	0.900733i	$-0.356970\pi$
$281$	14.5629	0.868748	0.434374	+	0.900733i	$0.356970\pi$
$282$	12.1866	0.725701
$283$	21.5393	1.28038	0.640189	−	0.768218i	$-0.278856\pi$
$283$	21.5393	1.28038	0.640189	+	0.768218i	$0.278856\pi$
$284$	2.17790	0.129235
$285$	−32.3507	−1.91629
$286$	35.6611	2.10868
$287$	−2.87122	−0.169483
$288$	−5.39360	−0.317821
$289$	−16.9554	−0.997374
$290$	−12.9755	−0.761950
$291$	20.5146	1.20259
$292$	−57.4552	−3.36231
$293$	20.7483	1.21213	0.606064	−	0.795416i	$-0.292747\pi$
$293$	20.7483	1.21213	0.606064	+	0.795416i	$0.292747\pi$
$294$	50.4572	2.94272
$295$	−17.8191	−1.03747
$296$	51.7021	3.00512
$297$	34.9423	2.02756
$298$	−16.4567	−0.953309
$299$	24.0126	1.38868
$300$	−41.7774	−2.41202
$301$	−1.68390	−0.0970581
$302$	−2.46705	−0.141963
$303$	−6.87959	−0.395222
$304$	37.8289	2.16963
$305$	8.55563	0.489894
$306$	3.22989	0.184641
$307$	−33.9786	−1.93926	−0.969631	−	0.244571i	$-0.921353\pi$
$307$	−33.9786	−1.93926	−0.969631	+	0.244571i	$0.921353\pi$
$308$	7.44898	0.424445
$309$	27.0285	1.53760
$310$	−8.66486	−0.492131
$311$	16.8098	0.953195	0.476597	−	0.879122i	$-0.341870\pi$
$311$	16.8098	0.953195	0.476597	+	0.879122i	$0.341870\pi$
$312$	62.5900	3.54346
$313$	14.1293	0.798637	0.399318	−	0.916812i	$-0.369247\pi$
$313$	14.1293	0.798637	0.399318	+	0.916812i	$0.369247\pi$
$314$	−2.28713	−0.129070
$315$	−3.99887	−0.225311
$316$	−49.7293	−2.79749
$317$	−28.3807	−1.59402	−0.797008	−	0.603968i	$-0.793585\pi$
$317$	−28.3807	−1.59402	−0.797008	+	0.603968i	$0.793585\pi$
$318$	−7.48147	−0.419540
$319$	−14.8563	−0.831793
$320$	8.81039	0.492516
$321$	−21.2426	−1.18565
$322$	7.47074	0.416328
$323$	−1.76615	−0.0982710
$324$	44.1573	2.45318
$325$	13.5186	0.749875
$326$	39.0217	2.16121
$327$	−34.3214	−1.89798
$328$	29.2248	1.61367
$329$	−0.823710	−0.0454126
$330$	34.4183	1.89467
$331$	−17.2988	−0.950829	−0.475414	−	0.879762i	$-0.657702\pi$
$331$	−17.2988	−0.950829	−0.475414	+	0.879762i	$0.657702\pi$
$332$	−51.4250	−2.82232
$333$	−62.2419	−3.41083
$334$	8.28728	0.453460
$335$	4.67798	0.255586
$336$	6.93993	0.378604
$337$	3.86708	0.210653	0.105327	−	0.994438i	$-0.466411\pi$
$337$	3.86708	0.210653	0.105327	+	0.994438i	$0.466411\pi$
$338$	−7.59663	−0.413202
$339$	15.7602	0.855979
$340$	1.10186	0.0597566
$341$	−9.92080	−0.537241
$342$	−127.783	−6.90970
$343$	−6.95026	−0.375279
$344$	17.1396	0.924104
$345$	23.1758	1.24774
$346$	−31.1318	−1.67366
$347$	3.69657	0.198442	0.0992211	−	0.995065i	$-0.468365\pi$
$347$	3.69657	0.198442	0.0992211	+	0.995065i	$0.468365\pi$
$348$	−51.0706	−2.73767
$349$	20.0654	1.07408	0.537038	−	0.843558i	$-0.319543\pi$
$349$	20.0654	1.07408	0.537038	+	0.843558i	$0.319543\pi$
$350$	4.20586	0.224813
$351$	−38.8688	−2.07466
$352$	−3.13779	−0.167245
$353$	2.79936	0.148995	0.0744974	−	0.997221i	$-0.476265\pi$
$353$	2.79936	0.148995	0.0744974	+	0.997221i	$0.476265\pi$
$354$	−104.460	−5.55201
$355$	−0.680179	−0.0361001
$356$	−54.2746	−2.87655
$357$	−0.324010	−0.0171484
$358$	−1.17565	−0.0621349
$359$	−3.22430	−0.170172	−0.0850859	−	0.996374i	$-0.527116\pi$
$359$	−3.22430	−0.170172	−0.0850859	+	0.996374i	$0.527116\pi$
$360$	40.7026	2.14522
$361$	50.8733	2.67754
$362$	−9.90640	−0.520669
$363$	6.04907	0.317494
$364$	−8.28603	−0.434306
$365$	17.9438	0.939221
$366$	50.1555	2.62167
$367$	−5.81148	−0.303357	−0.151678	−	0.988430i	$-0.548468\pi$
$367$	−5.81148	−0.303357	−0.151678	+	0.988430i	$0.548468\pi$
$368$	−27.1003	−1.41270
$369$	−35.1825	−1.83153
$370$	−31.6258	−1.64415
$371$	0.505683	0.0262538
$372$	−34.1041	−1.76822
$373$	−24.7943	−1.28380	−0.641900	−	0.766789i	$-0.721853\pi$
$373$	−24.7943	−1.28380	−0.641900	+	0.766789i	$0.721853\pi$
$374$	1.87902	0.0971620
$375$	32.3983	1.67304
$376$	8.38416	0.432380
$377$	16.5257	0.851117
$378$	−12.0928	−0.621984
$379$	0.991750	0.0509428	0.0254714	−	0.999676i	$-0.491891\pi$
$379$	0.991750	0.0509428	0.0254714	+	0.999676i	$0.491891\pi$
$380$	−43.5923	−2.23624
$381$	28.7329	1.47203
$382$	−26.9455	−1.37865
$383$	−26.9312	−1.37612	−0.688061	−	0.725653i	$-0.741538\pi$
$383$	−26.9312	−1.37612	−0.688061	+	0.725653i	$0.741538\pi$
$384$	56.9284	2.90511
$385$	−2.32639	−0.118564
$386$	23.3604	1.18901
$387$	−20.6336	−1.04886
$388$	27.6432	1.40337
$389$	10.5700	0.535920	0.267960	−	0.963430i	$-0.413650\pi$
$389$	10.5700	0.535920	0.267960	+	0.963430i	$0.413650\pi$
$390$	−38.2859	−1.93868
$391$	1.26525	0.0639866
$392$	34.7136	1.75330
$393$	23.0640	1.16342
$394$	−21.4561	−1.08094
$395$	15.5309	0.781446
$396$	91.2760	4.58679
$397$	9.46384	0.474976	0.237488	−	0.971390i	$-0.423676\pi$
$397$	9.46384	0.474976	0.237488	+	0.971390i	$0.423676\pi$
$398$	−22.3299	−1.11930
$399$	12.8187	0.641736
$400$	−15.2569	−0.762844
$401$	−37.4186	−1.86860	−0.934299	−	0.356490i	$-0.883973\pi$
$401$	−37.4186	−1.86860	−0.934299	+	0.356490i	$0.883973\pi$
$402$	27.4237	1.36777
$403$	11.0356	0.549723
$404$	−9.27019	−0.461209
$405$	−13.7907	−0.685267
$406$	5.14144	0.255165
$407$	−36.2099	−1.79486
$408$	3.29795	0.163273
$409$	32.5846	1.61120	0.805601	−	0.592458i	$-0.201842\pi$
$409$	32.5846	1.61120	0.805601	+	0.592458i	$0.201842\pi$
$410$	−17.8766	−0.882864
$411$	1.64061	0.0809254
$412$	36.4207	1.79432
$413$	7.06063	0.347431
$414$	91.5426	4.49907
$415$	16.0605	0.788380
$416$	3.49038	0.171130
$417$	4.03324	0.197509
$418$	−74.3391	−3.63604
$419$	−7.23713	−0.353557	−0.176779	−	0.984251i	$-0.556568\pi$
$419$	−7.23713	−0.353557	−0.176779	+	0.984251i	$0.556568\pi$
$420$	−7.99727	−0.390227
$421$	5.73681	0.279595	0.139798	−	0.990180i	$-0.455355\pi$
$421$	5.73681	0.279595	0.139798	+	0.990180i	$0.455355\pi$
$422$	−50.4933	−2.45798
$423$	−10.0933	−0.490754
$424$	−5.14712	−0.249966
$425$	0.712310	0.0345521
$426$	−3.98740	−0.193190
$427$	−3.39009	−0.164058
$428$	−28.6242	−1.38360
$429$	−43.8354	−2.11639
$430$	−10.4842	−0.505592
$431$	−2.71739	−0.130892	−0.0654460	−	0.997856i	$-0.520847\pi$
$431$	−2.71739	−0.130892	−0.0654460	+	0.997856i	$0.520847\pi$
$432$	43.8668	2.11054
$433$	−12.9222	−0.621002	−0.310501	−	0.950573i	$-0.600497\pi$
$433$	−12.9222	−0.621002	−0.310501	+	0.950573i	$0.600497\pi$
$434$	3.43337	0.164807
$435$	15.9498	0.764736
$436$	−46.2478	−2.21487
$437$	−50.0567	−2.39454
$438$	105.192	5.02625
$439$	−16.4584	−0.785517	−0.392758	−	0.919642i	$-0.628479\pi$
$439$	−16.4584	−0.785517	−0.392758	+	0.919642i	$0.628479\pi$
$440$	23.6792	1.12886
$441$	−41.7902	−1.99001
$442$	−2.09017	−0.0994193
$443$	9.02804	0.428935	0.214468	−	0.976731i	$-0.431198\pi$
$443$	9.02804	0.428935	0.214468	+	0.976731i	$0.431198\pi$
$444$	−124.477	−5.90740
$445$	16.9505	0.803528
$446$	18.1621	0.860000
$447$	20.2289	0.956794
$448$	−3.49104	−0.164936
$449$	25.6714	1.21151	0.605753	−	0.795653i	$-0.292872\pi$
$449$	25.6714	1.21151	0.605753	+	0.795653i	$0.292872\pi$
$450$	51.5365	2.42945
$451$	−20.4678	−0.963791
$452$	21.2368	0.998895
$453$	3.03255	0.142482
$454$	−46.6048	−2.18727
$455$	2.58780	0.121318
$456$	−130.475	−6.11006
$457$	−10.9152	−0.510592	−0.255296	−	0.966863i	$-0.582173\pi$
$457$	−10.9152	−0.510592	−0.255296	+	0.966863i	$0.582173\pi$
$458$	9.16601	0.428300
$459$	−2.04804	−0.0955945
$460$	31.2292	1.45607
$461$	14.7791	0.688331	0.344165	−	0.938909i	$-0.388162\pi$
$461$	14.7791	0.688331	0.344165	+	0.938909i	$0.388162\pi$
$462$	−13.6379	−0.634495
$463$	3.09037	0.143622	0.0718108	−	0.997418i	$-0.477122\pi$
$463$	3.09037	0.143622	0.0718108	+	0.997418i	$0.477122\pi$
$464$	−18.6507	−0.865837
$465$	10.6510	0.493930
$466$	−21.4796	−0.995023
$467$	1.91433	0.0885849	0.0442924	−	0.999019i	$-0.485897\pi$
$467$	1.91433	0.0885849	0.0442924	+	0.999019i	$0.485897\pi$
$468$	−101.533	−4.69335
$469$	−1.85361	−0.0855916
$470$	−5.12854	−0.236562
$471$	2.81139	0.129542
$472$	−71.8669	−3.30794
$473$	−12.0038	−0.551936
$474$	91.0467	4.18192
$475$	−28.1808	−1.29302
$476$	−0.436601	−0.0200116
$477$	6.19639	0.283713
$478$	−27.0534	−1.23739
$479$	31.3564	1.43271	0.716356	−	0.697735i	$-0.245809\pi$
$479$	31.3564	1.43271	0.716356	+	0.697735i	$0.245809\pi$
$480$	3.36875	0.153762
$481$	40.2788	1.83656
$482$	−59.9604	−2.73112
$483$	−9.18320	−0.417850
$484$	8.15107	0.370503
$485$	−8.63324	−0.392015
$486$	−9.10417	−0.412974
$487$	7.02256	0.318223	0.159111	−	0.987261i	$-0.449137\pi$
$487$	7.02256	0.318223	0.159111	+	0.987261i	$0.449137\pi$
$488$	34.5061	1.56202
$489$	−47.9663	−2.16911
$490$	−21.2341	−0.959259
$491$	13.3963	0.604566	0.302283	−	0.953218i	$-0.402251\pi$
$491$	13.3963	0.604566	0.302283	+	0.953218i	$0.402251\pi$
$492$	−70.3609	−3.17211
$493$	0.870760	0.0392171
$494$	82.6926	3.72051
$495$	−28.5064	−1.28127
$496$	−12.4546	−0.559230
$497$	0.269514	0.0120894
$498$	94.1514	4.21902
$499$	−23.9793	−1.07346	−0.536730	−	0.843754i	$-0.680341\pi$
$499$	−23.9793	−1.07346	−0.536730	+	0.843754i	$0.680341\pi$
$500$	43.6564	1.95237
$501$	−10.1869	−0.455118
$502$	−50.1079	−2.23643
$503$	23.8166	1.06193	0.530965	−	0.847394i	$-0.321830\pi$
$503$	23.8166	1.06193	0.530965	+	0.847394i	$0.321830\pi$
$504$	−16.1280	−0.718399
$505$	2.89517	0.128833
$506$	53.2559	2.36751
$507$	9.33795	0.414713
$508$	38.7174	1.71781
$509$	−4.80173	−0.212833	−0.106416	−	0.994322i	$-0.533938\pi$
$509$	−4.80173	−0.212833	−0.106416	+	0.994322i	$0.533938\pi$
$510$	−2.01733	−0.0893290
$511$	−7.11006	−0.314531
$512$	42.6475	1.88477
$513$	81.0259	3.57738
$514$	72.3748	3.19232
$515$	−11.3745	−0.501221
$516$	−41.2648	−1.81658
$517$	−5.87190	−0.258246
$518$	12.5314	0.550600
$519$	38.2680	1.67978
$520$	−26.3400	−1.15509
$521$	−35.3692	−1.54955	−0.774775	−	0.632237i	$-0.782137\pi$
$521$	−35.3692	−1.54955	−0.774775	+	0.632237i	$0.782137\pi$
$522$	63.0005	2.75746
$523$	14.2094	0.621333	0.310667	−	0.950519i	$-0.399448\pi$
$523$	14.2094	0.621333	0.310667	+	0.950519i	$0.399448\pi$
$524$	31.0785	1.35767
$525$	−5.16994	−0.225635
$526$	58.5408	2.55250
$527$	0.581479	0.0253296
$528$	49.4720	2.15299
$529$	12.8602	0.559140
$530$	3.14846	0.136760
$531$	86.5174	3.75454
$532$	17.2731	0.748882
$533$	22.7678	0.986182
$534$	99.3684	4.30009
$535$	8.93961	0.386493
$536$	18.8670	0.814931
$537$	1.44513	0.0623620
$538$	49.8060	2.14729
$539$	−24.3119	−1.04719
$540$	−50.5502	−2.17533
$541$	20.6875	0.889425	0.444712	−	0.895673i	$-0.353306\pi$
$541$	20.6875	0.889425	0.444712	+	0.895673i	$0.353306\pi$
$542$	44.6539	1.91805
$543$	12.1772	0.522572
$544$	0.183913	0.00788518
$545$	14.4436	0.618696
$546$	15.1704	0.649235
$547$	34.2593	1.46482	0.732412	−	0.680862i	$-0.238395\pi$
$547$	34.2593	1.46482	0.732412	+	0.680862i	$0.238395\pi$
$548$	2.21071	0.0944369
$549$	−41.5404	−1.77290
$550$	29.9819	1.27843
$551$	−34.4495	−1.46760
$552$	93.4715	3.97841
$553$	−6.15398	−0.261694
$554$	13.6270	0.578958
$555$	38.8752	1.65016
$556$	5.43476	0.230485
$557$	6.35009	0.269062	0.134531	−	0.990909i	$-0.457047\pi$
$557$	6.35009	0.269062	0.134531	+	0.990909i	$0.457047\pi$
$558$	42.0708	1.78100
$559$	13.3527	0.564759
$560$	−2.92056	−0.123416
$561$	−2.30974	−0.0975172
$562$	−35.9274	−1.51550
$563$	20.2401	0.853020	0.426510	−	0.904483i	$-0.359743\pi$
$563$	20.2401	0.853020	0.426510	+	0.904483i	$0.359743\pi$
$564$	−20.1855	−0.849962
$565$	−6.63245	−0.279029
$566$	−53.1385	−2.23358
$567$	5.46445	0.229485
$568$	−2.74326	−0.115105
$569$	22.8052	0.956045	0.478022	−	0.878348i	$-0.341354\pi$
$569$	22.8052	0.956045	0.478022	+	0.878348i	$0.341354\pi$
$570$	79.8109	3.34291
$571$	−33.6677	−1.40895	−0.704475	−	0.709728i	$-0.748818\pi$
$571$	−33.6677	−1.40895	−0.704475	+	0.709728i	$0.748818\pi$
$572$	−59.0678	−2.46975
$573$	33.1220	1.38369
$574$	7.08345	0.295657
$575$	20.1885	0.841920
$576$	−42.7774	−1.78239
$577$	6.39105	0.266063	0.133031	−	0.991112i	$-0.457529\pi$
$577$	6.39105	0.266063	0.133031	+	0.991112i	$0.457529\pi$
$578$	41.8297	1.73989
$579$	−28.7151	−1.19336
$580$	21.4923	0.892418
$581$	−6.36383	−0.264016
$582$	−50.6106	−2.09788
$583$	3.60482	0.149296
$584$	72.3700	2.99469
$585$	31.7096	1.31103
$586$	−51.1871	−2.11452
$587$	−15.0260	−0.620191	−0.310095	−	0.950705i	$-0.600361\pi$
$587$	−15.0260	−0.620191	−0.310095	+	0.950705i	$0.600361\pi$
$588$	−83.5756	−3.44660
$589$	−23.0048	−0.947897
$590$	43.9605	1.80983
$591$	26.3743	1.08489
$592$	−45.4582	−1.86832
$593$	−35.2076	−1.44580	−0.722902	−	0.690950i	$-0.757192\pi$
$593$	−35.2076	−1.44580	−0.722902	+	0.690950i	$0.757192\pi$
$594$	−86.2044	−3.53701
$595$	0.136354	0.00558999
$596$	27.2583	1.11654
$597$	27.4484	1.12339
$598$	−59.2403	−2.42252
$599$	−6.03354	−0.246524	−0.123262	−	0.992374i	$-0.539335\pi$
$599$	−6.03354	−0.246524	−0.123262	+	0.992374i	$0.539335\pi$
$600$	52.6224	2.14830
$601$	29.8430	1.21732	0.608661	−	0.793430i	$-0.291707\pi$
$601$	29.8430	1.21732	0.608661	+	0.793430i	$0.291707\pi$
$602$	4.15426	0.169315
$603$	−22.7132	−0.924952
$604$	4.08634	0.166271
$605$	−2.54565	−0.103496
$606$	16.9723	0.689453
$607$	−2.22671	−0.0903794	−0.0451897	−	0.998978i	$-0.514389\pi$
$607$	−2.22671	−0.0903794	−0.0451897	+	0.998978i	$0.514389\pi$
$608$	−7.27605	−0.295083
$609$	−6.31997	−0.256098
$610$	−21.1072	−0.854604
$611$	6.53173	0.264245
$612$	−5.34988	−0.216256
$613$	26.0278	1.05125	0.525627	−	0.850715i	$-0.323831\pi$
$613$	26.0278	1.05125	0.525627	+	0.850715i	$0.323831\pi$
$614$	83.8270	3.38298
$615$	21.9744	0.886092
$616$	−9.38266	−0.378038
$617$	9.44303	0.380162	0.190081	−	0.981768i	$-0.439125\pi$
$617$	9.44303	0.380162	0.190081	+	0.981768i	$0.439125\pi$
$618$	−66.6806	−2.68229
$619$	16.0005	0.643113	0.321556	−	0.946890i	$-0.395794\pi$
$619$	16.0005	0.643113	0.321556	+	0.946890i	$0.395794\pi$
$620$	14.3522	0.576398
$621$	−58.0463	−2.32932
$622$	−41.4706	−1.66282
$623$	−6.71646	−0.269089
$624$	−55.0312	−2.20301
$625$	3.22223	0.128889
$626$	−34.8578	−1.39320
$627$	91.3792	3.64933
$628$	3.78833	0.151171
$629$	2.12234	0.0846233
$630$	9.86541	0.393048
$631$	−49.0602	−1.95305	−0.976527	−	0.215394i	$-0.930896\pi$
$631$	−49.0602	−1.95305	−0.976527	+	0.215394i	$0.930896\pi$
$632$	62.6385	2.49163
$633$	62.0675	2.46696
$634$	70.0165	2.78071
$635$	−12.0918	−0.479848
$636$	12.3921	0.491377
$637$	27.0439	1.07152
$638$	36.6513	1.45104
$639$	3.30249	0.130645
$640$	−23.9574	−0.947000
$641$	2.65253	0.104769	0.0523844	−	0.998627i	$-0.483318\pi$
$641$	2.65253	0.104769	0.0523844	+	0.998627i	$0.483318\pi$
$642$	52.4066	2.06832
$643$	−47.0497	−1.85546	−0.927729	−	0.373254i	$-0.878242\pi$
$643$	−47.0497	−1.85546	−0.927729	+	0.373254i	$0.878242\pi$
$644$	−12.3743	−0.487615
$645$	12.8874	0.507440
$646$	4.35717	0.171431
$647$	34.7567	1.36643	0.683214	−	0.730218i	$-0.260582\pi$
$647$	34.7567	1.36643	0.683214	+	0.730218i	$0.260582\pi$
$648$	−55.6200	−2.18496
$649$	50.3325	1.97572
$650$	−33.3510	−1.30813
$651$	−4.22037	−0.165409
$652$	−64.6342	−2.53127
$653$	21.7673	0.851822	0.425911	−	0.904765i	$-0.359954\pi$
$653$	21.7673	0.851822	0.425911	+	0.904765i	$0.359954\pi$
$654$	84.6726	3.31096
$655$	−9.70612	−0.379250
$656$	−25.6954	−1.00324
$657$	−87.1231	−3.39899
$658$	2.03213	0.0792208
$659$	38.8066	1.51169	0.755845	−	0.654751i	$-0.227226\pi$
$659$	38.8066	1.51169	0.755845	+	0.654751i	$0.227226\pi$
$660$	−57.0094	−2.21909
$661$	−0.607797	−0.0236406	−0.0118203	−	0.999930i	$-0.503763\pi$
$661$	−0.607797	−0.0236406	−0.0118203	+	0.999930i	$0.503763\pi$
$662$	42.6771	1.65869
$663$	2.56928	0.0997827
$664$	64.7744	2.51374
$665$	−5.39454	−0.209191
$666$	153.554	5.95010
$667$	24.6794	0.955589
$668$	−13.7268	−0.531105
$669$	−22.3252	−0.863144
$670$	−11.5408	−0.445861
$671$	−24.1666	−0.932941
$672$	−1.33484	−0.0514924
$673$	34.5206	1.33067	0.665336	−	0.746544i	$-0.268288\pi$
$673$	34.5206	1.33067	0.665336	+	0.746544i	$0.268288\pi$
$674$	−9.54028	−0.367478
$675$	−32.6788	−1.25781
$676$	12.5828	0.483954
$677$	−11.1077	−0.426905	−0.213452	−	0.976953i	$-0.568471\pi$
$677$	−11.1077	−0.426905	−0.213452	+	0.976953i	$0.568471\pi$
$678$	−38.8813	−1.49323
$679$	3.42084	0.131280
$680$	−1.38789	−0.0532231
$681$	57.2876	2.19527
$682$	24.4751	0.937201
$683$	26.0260	0.995858	0.497929	−	0.867218i	$-0.334094\pi$
$683$	26.0260	0.995858	0.497929	+	0.867218i	$0.334094\pi$
$684$	211.655	8.09284
$685$	−0.690426	−0.0263798
$686$	17.1466	0.654662
$687$	−11.2671	−0.429866
$688$	−15.0697	−0.574526
$689$	−4.00989	−0.152765
$690$	−57.1759	−2.17665
$691$	6.12721	0.233090	0.116545	−	0.993185i	$-0.462818\pi$
$691$	6.12721	0.233090	0.116545	+	0.993185i	$0.462818\pi$
$692$	51.5658	1.96024
$693$	11.2954	0.429076
$694$	−9.11962	−0.346176
$695$	−1.69733	−0.0643832
$696$	64.3280	2.43835
$697$	1.19966	0.0454404
$698$	−49.5024	−1.87369
$699$	26.4032	0.998660
$700$	−6.96645	−0.263307
$701$	−9.56244	−0.361168	−0.180584	−	0.983560i	$-0.557799\pi$
$701$	−9.56244	−0.361168	−0.180584	+	0.983560i	$0.557799\pi$
$702$	95.8913	3.61918
$703$	−83.9653	−3.16681
$704$	−24.8862	−0.937934
$705$	6.30411	0.237427
$706$	−6.90616	−0.259917
$707$	−1.14718	−0.0431442
$708$	173.025	6.50267
$709$	−46.9459	−1.76309	−0.881544	−	0.472101i	$-0.843496\pi$
$709$	−46.9459	−1.76309	−0.881544	+	0.472101i	$0.843496\pi$
$710$	1.67804	0.0629756
$711$	−75.4078	−2.82801
$712$	68.3637	2.56204
$713$	16.4805	0.617199
$714$	0.799349	0.0299149
$715$	18.4474	0.689895
$716$	1.94730	0.0727742
$717$	33.2547	1.24192
$718$	7.95451	0.296860
$719$	37.6905	1.40562	0.702810	−	0.711378i	$-0.251928\pi$
$719$	37.6905	1.40562	0.702810	+	0.711378i	$0.251928\pi$
$720$	−35.7871	−1.33371
$721$	4.50704	0.167851
$722$	−125.507	−4.67089
$723$	73.7047	2.74111
$724$	16.4086	0.609822
$725$	13.8939	0.516008
$726$	−14.9234	−0.553858
$727$	−21.0718	−0.781508	−0.390754	−	0.920495i	$-0.627786\pi$
$727$	−21.0718	−0.781508	−0.390754	+	0.920495i	$0.627786\pi$
$728$	10.4370	0.386821
$729$	−21.2271	−0.786190
$730$	−44.2683	−1.63844
$731$	0.703570	0.0260225
$732$	−83.0760	−3.07058
$733$	28.6528	1.05832	0.529158	−	0.848523i	$-0.322508\pi$
$733$	28.6528	1.05832	0.529158	+	0.848523i	$0.322508\pi$
$734$	14.3372	0.529196
$735$	26.1014	0.962766
$736$	5.21251	0.192136
$737$	−13.2136	−0.486731
$738$	86.7970	3.19504
$739$	13.9635	0.513655	0.256827	−	0.966457i	$-0.417323\pi$
$739$	13.9635	0.513655	0.256827	+	0.966457i	$0.417323\pi$
$740$	52.3840	1.92567
$741$	−101.648	−3.73412
$742$	−1.24755	−0.0457989
$743$	−47.3542	−1.73726	−0.868628	−	0.495465i	$-0.834998\pi$
$743$	−47.3542	−1.73726	−0.868628	+	0.495465i	$0.834998\pi$
$744$	42.9572	1.57489
$745$	−8.51302	−0.311893
$746$	61.1688	2.23955
$747$	−77.9791	−2.85311
$748$	−3.11235	−0.113799
$749$	−3.54224	−0.129430
$750$	−79.9282	−2.91856
$751$	5.14620	0.187788	0.0938938	−	0.995582i	$-0.470069\pi$
$751$	5.14620	0.187788	0.0938938	+	0.995582i	$0.470069\pi$
$752$	−7.37163	−0.268816
$753$	61.5938	2.24460
$754$	−40.7698	−1.48475
$755$	−1.27620	−0.0464458
$756$	20.0300	0.728485
$757$	21.3165	0.774762	0.387381	−	0.921920i	$-0.373380\pi$
$757$	21.3165	0.774762	0.387381	+	0.921920i	$0.373380\pi$
$758$	−2.44670	−0.0888681
$759$	−65.4634	−2.37617
$760$	54.9085	1.99174
$761$	−25.7997	−0.935240	−0.467620	−	0.883930i	$-0.654888\pi$
$761$	−25.7997	−0.935240	−0.467620	+	0.883930i	$0.654888\pi$
$762$	−70.8856	−2.56791
$763$	−5.72314	−0.207192
$764$	44.6317	1.61472
$765$	1.67082	0.0604086
$766$	66.4408	2.40060
$767$	−55.9883	−2.02162
$768$	−98.5742	−3.55699
$769$	−51.7391	−1.86576	−0.932879	−	0.360189i	$-0.882712\pi$
$769$	−51.7391	−1.86576	−0.932879	+	0.360189i	$0.882712\pi$
$770$	5.73931	0.206831
$771$	−88.9647	−3.20399
$772$	−38.6934	−1.39261
$773$	−7.00500	−0.251952	−0.125976	−	0.992033i	$-0.540206\pi$
$773$	−7.00500	−0.251952	−0.125976	+	0.992033i	$0.540206\pi$
$774$	50.9041	1.82971
$775$	9.27815	0.333281
$776$	−34.8192	−1.24993
$777$	−15.4039	−0.552613
$778$	−26.0767	−0.934896
$779$	−47.4617	−1.70049
$780$	63.4156	2.27064
$781$	1.92126	0.0687481
$782$	−3.12144	−0.111623
$783$	−39.9481	−1.42763
$784$	−30.5213	−1.09005
$785$	−1.18313	−0.0422277
$786$	−56.9001	−2.02956
$787$	−24.9058	−0.887795	−0.443898	−	0.896078i	$-0.646405\pi$
$787$	−24.9058	−0.887795	−0.443898	+	0.896078i	$0.646405\pi$
$788$	35.5391	1.26603
$789$	−71.9597	−2.56183
$790$	−38.3156	−1.36321
$791$	2.62805	0.0934426
$792$	−114.970	−4.08529
$793$	26.8822	0.954615
$794$	−23.3478	−0.828582
$795$	−3.87016	−0.137260
$796$	36.9865	1.31095
$797$	−6.36490	−0.225456	−0.112728	−	0.993626i	$-0.535959\pi$
$797$	−6.36490	−0.225456	−0.112728	+	0.993626i	$0.535959\pi$
$798$	−31.6243	−1.11949
$799$	0.344165	0.0121757
$800$	2.93453	0.103751
$801$	−82.3001	−2.90793
$802$	92.3137	3.25971
$803$	−50.6848	−1.78863
$804$	−45.4237	−1.60197
$805$	3.86460	0.136209
$806$	−27.2254	−0.958974
$807$	−61.2226	−2.15514
$808$	11.6766	0.410783
$809$	7.26443	0.255404	0.127702	−	0.991813i	$-0.459240\pi$
$809$	7.26443	0.255404	0.127702	+	0.991813i	$0.459240\pi$
$810$	34.0224	1.19543
$811$	35.6721	1.25262	0.626309	−	0.779575i	$-0.284565\pi$
$811$	35.6721	1.25262	0.626309	+	0.779575i	$0.284565\pi$
$812$	−8.51611	−0.298857
$813$	−54.8895	−1.92506
$814$	89.3317	3.13108
$815$	20.1859	0.707080
$816$	−2.89966	−0.101508
$817$	−27.8350	−0.973825
$818$	−80.3878	−2.81069
$819$	−12.5646	−0.439044
$820$	29.6103	1.03404
$821$	11.5991	0.404810	0.202405	−	0.979302i	$-0.435124\pi$
$821$	11.5991	0.404810	0.202405	+	0.979302i	$0.435124\pi$
$822$	−4.04747	−0.141172
$823$	−29.1712	−1.01684	−0.508421	−	0.861108i	$-0.669771\pi$
$823$	−29.1712	−1.01684	−0.508421	+	0.861108i	$0.669771\pi$
$824$	−45.8751	−1.59813
$825$	−36.8545	−1.28311
$826$	−17.4189	−0.606083
$827$	−21.9220	−0.762303	−0.381152	−	0.924513i	$-0.624472\pi$
$827$	−21.9220	−0.762303	−0.381152	+	0.924513i	$0.624472\pi$
$828$	−151.628	−5.26944
$829$	19.4836	0.676693	0.338347	−	0.941022i	$-0.390132\pi$
$829$	19.4836	0.676693	0.338347	+	0.941022i	$0.390132\pi$
$830$	−39.6221	−1.37530
$831$	−16.7507	−0.581074
$832$	27.6827	0.959724
$833$	1.42497	0.0493724
$834$	−9.95021	−0.344548
$835$	4.28700	0.148358
$836$	123.133	4.25864
$837$	−26.6767	−0.922081
$838$	17.8544	0.616769
$839$	−12.2233	−0.421996	−0.210998	−	0.977487i	$-0.567671\pi$
$839$	−12.2233	−0.421996	−0.210998	+	0.977487i	$0.567671\pi$
$840$	10.0733	0.347561
$841$	−12.0154	−0.414325
$842$	−14.1530	−0.487745
$843$	44.1627	1.52104
$844$	83.6355	2.87885
$845$	−3.92973	−0.135187
$846$	24.9007	0.856105
$847$	1.00869	0.0346591
$848$	4.52551	0.155407
$849$	65.3191	2.24174
$850$	−1.75731	−0.0602751
$851$	60.1521	2.06199
$852$	6.60460	0.226270
$853$	−34.6379	−1.18598	−0.592990	−	0.805210i	$-0.702053\pi$
$853$	−34.6379	−1.18598	−0.592990	+	0.805210i	$0.702053\pi$
$854$	8.36352	0.286194
$855$	−66.1019	−2.26064
$856$	36.0548	1.23233
$857$	−29.0317	−0.991703	−0.495852	−	0.868407i	$-0.665144\pi$
$857$	−29.0317	−0.991703	−0.495852	+	0.868407i	$0.665144\pi$
$858$	108.144	3.69198
$859$	−47.1596	−1.60906	−0.804532	−	0.593909i	$-0.797584\pi$
$859$	−47.1596	−1.60906	−0.804532	+	0.593909i	$0.797584\pi$
$860$	17.3656	0.592164
$861$	−8.70713	−0.296738
$862$	6.70394	0.228337
$863$	−37.8998	−1.29012	−0.645061	−	0.764131i	$-0.723168\pi$
$863$	−37.8998	−1.29012	−0.645061	+	0.764131i	$0.723168\pi$
$864$	−8.43740	−0.287046
$865$	−16.1045	−0.547568
$866$	31.8798	1.08332
$867$	−51.4181	−1.74625
$868$	−5.68692	−0.193027
$869$	−43.8693	−1.48816
$870$	−39.3490	−1.33406
$871$	14.6985	0.498038
$872$	58.2532	1.97270
$873$	41.9173	1.41868
$874$	123.492	4.17719
$875$	5.40246	0.182637
$876$	−174.236	−5.88689
$877$	−49.3538	−1.66656	−0.833279	−	0.552853i	$-0.813539\pi$
$877$	−49.3538	−1.66656	−0.833279	+	0.552853i	$0.813539\pi$
$878$	40.6037	1.37031
$879$	62.9203	2.12225
$880$	−20.8195	−0.701826
$881$	12.0768	0.406879	0.203439	−	0.979088i	$-0.434788\pi$
$881$	12.0768	0.406879	0.203439	+	0.979088i	$0.434788\pi$
$882$	103.099	3.47151
$883$	−38.6385	−1.30029	−0.650144	−	0.759811i	$-0.725291\pi$
$883$	−38.6385	−1.30029	−0.650144	+	0.759811i	$0.725291\pi$
$884$	3.46209	0.116443
$885$	−54.0373	−1.81644
$886$	−22.2726	−0.748264
$887$	2.20974	0.0741958	0.0370979	−	0.999312i	$-0.488189\pi$
$887$	2.20974	0.0741958	0.0370979	+	0.999312i	$0.488189\pi$
$888$	156.789	5.26151
$889$	4.79126	0.160694
$890$	−41.8176	−1.40173
$891$	38.9539	1.30500
$892$	−30.0831	−1.00726
$893$	−13.6160	−0.455644
$894$	−49.9057	−1.66910
$895$	−0.608161	−0.0203286
$896$	9.49290	0.317136
$897$	72.8195	2.43137
$898$	−63.3326	−2.11343
$899$	11.3420	0.378278
$900$	−85.3634	−2.84545
$901$	−0.211286	−0.00703896
$902$	50.4951	1.68130
$903$	−5.10650	−0.169934
$904$	−26.7497	−0.889681
$905$	−5.12457	−0.170346
$906$	−7.48147	−0.248555
$907$	41.6964	1.38451	0.692254	−	0.721654i	$-0.256618\pi$
$907$	41.6964	1.38451	0.692254	+	0.721654i	$0.256618\pi$
$908$	77.1946	2.56179
$909$	−14.0570	−0.466241
$910$	−6.38424	−0.211636
$911$	−0.891986	−0.0295528	−0.0147764	−	0.999891i	$-0.504704\pi$
$911$	−0.891986	−0.0295528	−0.0147764	+	0.999891i	$0.504704\pi$
$912$	114.718	3.79870
$913$	−45.3652	−1.50137
$914$	26.9284	0.890711
$915$	25.9454	0.857729
$916$	−15.1823	−0.501637
$917$	3.84596	0.127005
$918$	5.05263	0.166762
$919$	−32.7862	−1.08152	−0.540759	−	0.841178i	$-0.681863\pi$
$919$	−32.7862	−1.08152	−0.540759	+	0.841178i	$0.681863\pi$
$920$	−39.3360	−1.29687
$921$	−103.042	−3.39535
$922$	−36.4608	−1.20077
$923$	−2.13715	−0.0703453
$924$	22.5894	0.743138
$925$	33.8643	1.11345
$926$	−7.62410	−0.250544
$927$	55.2270	1.81389
$928$	3.58730	0.117759
$929$	16.6133	0.545064	0.272532	−	0.962147i	$-0.412139\pi$
$929$	16.6133	0.545064	0.272532	+	0.962147i	$0.412139\pi$
$930$	−26.2767	−0.861645
$931$	−56.3756	−1.84764
$932$	35.5781	1.16540
$933$	50.9765	1.66890
$934$	−4.72276	−0.154534
$935$	0.972017	0.0317884
$936$	127.890	4.18020
$937$	16.6824	0.544992	0.272496	−	0.962157i	$-0.412151\pi$
$937$	16.6824	0.544992	0.272496	+	0.962157i	$0.412151\pi$
$938$	4.57295	0.149312
$939$	42.8479	1.39829
$940$	8.49474	0.277068
$941$	−39.1944	−1.27770	−0.638850	−	0.769331i	$-0.720590\pi$
$941$	−39.1944	−1.27770	−0.638850	+	0.769331i	$0.720590\pi$
$942$	−6.93585	−0.225982
$943$	34.0012	1.10723
$944$	63.1877	2.05659
$945$	−6.25557	−0.203494
$946$	29.6141	0.962836
$947$	44.8834	1.45852	0.729258	−	0.684239i	$-0.239866\pi$
$947$	44.8834	1.45852	0.729258	+	0.684239i	$0.239866\pi$
$948$	−150.807	−4.89798
$949$	56.3803	1.83018
$950$	69.5235	2.25564
$951$	−86.0659	−2.79088
$952$	0.549938	0.0178236
$953$	15.9911	0.518004	0.259002	−	0.965877i	$-0.416606\pi$
$953$	15.9911	0.518004	0.259002	+	0.965877i	$0.416606\pi$
$954$	−15.2868	−0.494929
$955$	−13.9389	−0.451052
$956$	44.8104	1.44927
$957$	−45.0526	−1.45634
$958$	−77.3579	−2.49932
$959$	0.273575	0.00883419
$960$	26.7180	0.862320
$961$	−23.4260	−0.755677
$962$	−99.3700	−3.20382
$963$	−43.4048	−1.39870
$964$	99.3164	3.19877
$965$	12.0843	0.389008
$966$	22.6554	0.728926
$967$	−54.6858	−1.75858	−0.879288	−	0.476290i	$-0.841981\pi$
$967$	−54.6858	−1.75858	−0.879288	+	0.476290i	$0.841981\pi$
$968$	−10.2670	−0.329994
$969$	−5.35593	−0.172057
$970$	21.2987	0.683859
$971$	−9.30124	−0.298491	−0.149245	−	0.988800i	$-0.547684\pi$
$971$	−9.30124	−0.298491	−0.149245	+	0.988800i	$0.547684\pi$
$972$	15.0798	0.483686
$973$	0.672549	0.0215609
$974$	−17.3250	−0.555129
$975$	40.9958	1.31292
$976$	−30.3389	−0.971125
$977$	−18.1886	−0.581905	−0.290953	−	0.956737i	$-0.593972\pi$
$977$	−18.1886	−0.581905	−0.290953	+	0.956737i	$0.593972\pi$
$978$	118.335	3.78395
$979$	−47.8790	−1.53022
$980$	35.1715	1.12351
$981$	−70.1285	−2.23903
$982$	−33.0493	−1.05465
$983$	−27.9579	−0.891720	−0.445860	−	0.895103i	$-0.647102\pi$
$983$	−27.9579	−0.891720	−0.445860	+	0.895103i	$0.647102\pi$
$984$	88.6258	2.82529
$985$	−11.0992	−0.353650
$986$	−2.14821	−0.0684129
$987$	−2.49794	−0.0795105
$988$	−136.969	−4.35757
$989$	19.9408	0.634081
$990$	70.3266	2.23513
$991$	−44.6402	−1.41804	−0.709022	−	0.705187i	$-0.750863\pi$
$991$	−44.6402	−1.41804	−0.709022	+	0.705187i	$0.750863\pi$
$992$	2.39554	0.0760585
$993$	−52.4596	−1.66476
$994$	−0.664906	−0.0210895
$995$	−11.5512	−0.366199
$996$	−155.949	−4.94144
$997$	1.90100	0.0602053	0.0301027	−	0.999547i	$-0.490417\pi$
$997$	1.90100	0.0602053	0.0301027	+	0.999547i	$0.490417\pi$
$998$	59.1581	1.87262
$999$	−97.3671	−3.08056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.a.1.9	✓	147

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.9	✓	147	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46705 q^{2} +3.03255 q^{3} +4.08634 q^{4} -1.27620 q^{5} -7.48147 q^{6} +0.505683 q^{7} -5.14712 q^{8} +6.19639 q^{9} +O(q^{10})\)	\(q-2.46705 q^{2} +3.03255 q^{3} +4.08634 q^{4} -1.27620 q^{5} -7.48147 q^{6} +0.505683 q^{7} -5.14712 q^{8} +6.19639 q^{9} +3.14846 q^{10} +3.60482 q^{11} +12.3921 q^{12} -4.00989 q^{13} -1.24755 q^{14} -3.87016 q^{15} +4.52551 q^{16} -0.211286 q^{17} -15.2868 q^{18} +8.35902 q^{19} -5.21500 q^{20} +1.53351 q^{21} -8.89327 q^{22} -5.98834 q^{23} -15.6089 q^{24} -3.37131 q^{25} +9.89261 q^{26} +9.69322 q^{27} +2.06640 q^{28} -4.12124 q^{29} +9.54787 q^{30} -2.75210 q^{31} -0.870443 q^{32} +10.9318 q^{33} +0.521254 q^{34} -0.645355 q^{35} +25.3206 q^{36} -10.0449 q^{37} -20.6221 q^{38} -12.1602 q^{39} +6.56876 q^{40} -5.67790 q^{41} -3.78325 q^{42} -3.32994 q^{43} +14.7305 q^{44} -7.90785 q^{45} +14.7735 q^{46} -1.62890 q^{47} +13.7239 q^{48} -6.74428 q^{49} +8.31719 q^{50} -0.640737 q^{51} -16.3858 q^{52} +1.00000 q^{53} -23.9137 q^{54} -4.60048 q^{55} -2.60281 q^{56} +25.3492 q^{57} +10.1673 q^{58} +13.9626 q^{59} -15.8148 q^{60} -6.70397 q^{61} +6.78956 q^{62} +3.13341 q^{63} -6.90360 q^{64} +5.11744 q^{65} -26.9693 q^{66} -3.66555 q^{67} -0.863387 q^{68} -18.1600 q^{69} +1.59212 q^{70} +0.532971 q^{71} -31.8935 q^{72} -14.0603 q^{73} +24.7812 q^{74} -10.2237 q^{75} +34.1578 q^{76} +1.82290 q^{77} +29.9999 q^{78} -12.1696 q^{79} -5.77547 q^{80} +10.8061 q^{81} +14.0077 q^{82} -12.5846 q^{83} +6.26646 q^{84} +0.269644 q^{85} +8.21513 q^{86} -12.4979 q^{87} -18.5544 q^{88} -13.2819 q^{89} +19.5091 q^{90} -2.02774 q^{91} -24.4704 q^{92} -8.34588 q^{93} +4.01859 q^{94} -10.6678 q^{95} -2.63967 q^{96} +6.76479 q^{97} +16.6385 q^{98} +22.3368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

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