LMFDB - Embedded newform 4003.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34196 q^{2} -1.89472 q^{3} +3.48479 q^{4} -4.06412 q^{5} +4.43736 q^{6} +3.16270 q^{7} -3.47733 q^{8} +0.589962 q^{9} +O(q^{10})$	\(q-2.34196 q^{2} -1.89472 q^{3} +3.48479 q^{4} -4.06412 q^{5} +4.43736 q^{6} +3.16270 q^{7} -3.47733 q^{8} +0.589962 q^{9} +9.51803 q^{10} +5.59916 q^{11} -6.60270 q^{12} -4.59164 q^{13} -7.40692 q^{14} +7.70037 q^{15} +1.17419 q^{16} +4.80028 q^{17} -1.38167 q^{18} -5.33357 q^{19} -14.1626 q^{20} -5.99242 q^{21} -13.1130 q^{22} -4.15524 q^{23} +6.58856 q^{24} +11.5171 q^{25} +10.7535 q^{26} +4.56635 q^{27} +11.0213 q^{28} +9.77771 q^{29} -18.0340 q^{30} -0.132664 q^{31} +4.20474 q^{32} -10.6088 q^{33} -11.2421 q^{34} -12.8536 q^{35} +2.05589 q^{36} +1.55645 q^{37} +12.4910 q^{38} +8.69987 q^{39} +14.1323 q^{40} -3.68566 q^{41} +14.0340 q^{42} +9.30922 q^{43} +19.5119 q^{44} -2.39768 q^{45} +9.73143 q^{46} +7.95349 q^{47} -2.22477 q^{48} +3.00264 q^{49} -26.9726 q^{50} -9.09519 q^{51} -16.0009 q^{52} +10.7581 q^{53} -10.6942 q^{54} -22.7557 q^{55} -10.9977 q^{56} +10.1056 q^{57} -22.8990 q^{58} +12.0183 q^{59} +26.8342 q^{60} +2.39663 q^{61} +0.310695 q^{62} +1.86587 q^{63} -12.1957 q^{64} +18.6610 q^{65} +24.8455 q^{66} -2.16009 q^{67} +16.7280 q^{68} +7.87302 q^{69} +30.1026 q^{70} -2.27280 q^{71} -2.05149 q^{72} -13.9412 q^{73} -3.64515 q^{74} -21.8217 q^{75} -18.5864 q^{76} +17.7084 q^{77} -20.3748 q^{78} -17.2667 q^{79} -4.77207 q^{80} -10.4218 q^{81} +8.63168 q^{82} +7.58184 q^{83} -20.8823 q^{84} -19.5089 q^{85} -21.8019 q^{86} -18.5260 q^{87} -19.4701 q^{88} -6.84345 q^{89} +5.61527 q^{90} -14.5220 q^{91} -14.4802 q^{92} +0.251362 q^{93} -18.6268 q^{94} +21.6763 q^{95} -7.96680 q^{96} -15.7665 q^{97} -7.03208 q^{98} +3.30329 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) $ 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * 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 $

$2$	−2.34196	−1.65602	−0.828009	−	0.560715i	$-0.810526\pi$
$2$	−2.34196	−1.65602	−0.828009	+	0.560715i	$0.810526\pi$
$3$	−1.89472	−1.09392	−0.546958	−	0.837160i	$-0.684214\pi$
$3$	−1.89472	−1.09392	−0.546958	+	0.837160i	$0.684214\pi$
$4$	3.48479	1.74240
$5$	−4.06412	−1.81753	−0.908765	−	0.417307i	$-0.862974\pi$
$5$	−4.06412	−1.81753	−0.908765	+	0.417307i	$0.862974\pi$
$6$	4.43736	1.81155
$7$	3.16270	1.19539	0.597693	−	0.801725i	$-0.296084\pi$
$7$	3.16270	1.19539	0.597693	+	0.801725i	$0.296084\pi$
$8$	−3.47733	−1.22942
$9$	0.589962	0.196654
$10$	9.51803	3.00986
$11$	5.59916	1.68821	0.844105	−	0.536178i	$-0.180132\pi$
$11$	5.59916	1.68821	0.844105	+	0.536178i	$0.180132\pi$
$12$	−6.60270	−1.90604
$13$	−4.59164	−1.27349	−0.636746	−	0.771074i	$-0.719720\pi$
$13$	−4.59164	−1.27349	−0.636746	+	0.771074i	$0.719720\pi$
$14$	−7.40692	−1.97958
$15$	7.70037	1.98823
$16$	1.17419	0.293548
$17$	4.80028	1.16424	0.582120	−	0.813103i	$-0.302224\pi$
$17$	4.80028	1.16424	0.582120	+	0.813103i	$0.302224\pi$
$18$	−1.38167	−0.325662
$19$	−5.33357	−1.22361	−0.611803	−	0.791010i	$-0.709555\pi$
$19$	−5.33357	−1.22361	−0.611803	+	0.791010i	$0.709555\pi$
$20$	−14.1626	−3.16686
$21$	−5.99242	−1.30765
$22$	−13.1130	−2.79571
$23$	−4.15524	−0.866428	−0.433214	−	0.901291i	$-0.642621\pi$
$23$	−4.15524	−0.866428	−0.433214	+	0.901291i	$0.642621\pi$
$24$	6.58856	1.34488
$25$	11.5171	2.30342
$26$	10.7535	2.10893
$27$	4.56635	0.878794
$28$	11.0213	2.08284
$29$	9.77771	1.81567	0.907837	−	0.419323i	$-0.137732\pi$
$29$	9.77771	1.81567	0.907837	+	0.419323i	$0.137732\pi$
$30$	−18.0340	−3.29254
$31$	−0.132664	−0.0238272	−0.0119136	−	0.999929i	$-0.503792\pi$
$31$	−0.132664	−0.0238272	−0.0119136	+	0.999929i	$0.503792\pi$
$32$	4.20474	0.743300
$33$	−10.6088	−1.84676
$34$	−11.2421	−1.92800
$35$	−12.8536	−2.17265
$36$	2.05589	0.342649
$37$	1.55645	0.255879	0.127939	−	0.991782i	$-0.459164\pi$
$37$	1.55645	0.255879	0.127939	+	0.991782i	$0.459164\pi$
$38$	12.4910	2.02631
$39$	8.69987	1.39309
$40$	14.1323	2.23451
$41$	−3.68566	−0.575603	−0.287802	−	0.957690i	$-0.592924\pi$
$41$	−3.68566	−0.575603	−0.287802	+	0.957690i	$0.592924\pi$
$42$	14.0340	2.16550
$43$	9.30922	1.41964	0.709821	−	0.704382i	$-0.248776\pi$
$43$	9.30922	1.41964	0.709821	+	0.704382i	$0.248776\pi$
$44$	19.5119	2.94153
$45$	−2.39768	−0.357425
$46$	9.73143	1.43482
$47$	7.95349	1.16014	0.580068	−	0.814568i	$-0.303026\pi$
$47$	7.95349	1.16014	0.580068	+	0.814568i	$0.303026\pi$
$48$	−2.22477	−0.321117
$49$	3.00264	0.428949
$50$	−26.9726	−3.81450
$51$	−9.09519	−1.27358
$52$	−16.0009	−2.21893
$53$	10.7581	1.47774	0.738868	−	0.673850i	$-0.235360\pi$
$53$	10.7581	1.47774	0.738868	+	0.673850i	$0.235360\pi$
$54$	−10.6942	−1.45530
$55$	−22.7557	−3.06837
$56$	−10.9977	−1.46963
$57$	10.1056	1.33852
$58$	−22.8990	−3.00679
$59$	12.0183	1.56464	0.782322	−	0.622874i	$-0.214035\pi$
$59$	12.0183	1.56464	0.782322	+	0.622874i	$0.214035\pi$
$60$	26.8342	3.46428
$61$	2.39663	0.306857	0.153428	−	0.988160i	$-0.450969\pi$
$61$	2.39663	0.306857	0.153428	+	0.988160i	$0.450969\pi$
$62$	0.310695	0.0394583
$63$	1.86587	0.235077
$64$	−12.1957	−1.52447
$65$	18.6610	2.31461
$66$	24.8455	3.05827
$67$	−2.16009	−0.263897	−0.131948	−	0.991257i	$-0.542123\pi$
$67$	−2.16009	−0.263897	−0.131948	+	0.991257i	$0.542123\pi$
$68$	16.7280	2.02857
$69$	7.87302	0.947800
$70$	30.1026	3.59795
$71$	−2.27280	−0.269732	−0.134866	−	0.990864i	$-0.543060\pi$
$71$	−2.27280	−0.269732	−0.134866	+	0.990864i	$0.543060\pi$
$72$	−2.05149	−0.241771
$73$	−13.9412	−1.63169	−0.815847	−	0.578267i	$-0.803729\pi$
$73$	−13.9412	−1.63169	−0.815847	+	0.578267i	$0.803729\pi$
$74$	−3.64515	−0.423740
$75$	−21.8217	−2.51975
$76$	−18.5864	−2.13201
$77$	17.7084	2.01806
$78$	−20.3748	−2.30699
$79$	−17.2667	−1.94266	−0.971328	−	0.237744i	$-0.923592\pi$
$79$	−17.2667	−1.94266	−0.971328	+	0.237744i	$0.923592\pi$
$80$	−4.77207	−0.533533
$81$	−10.4218	−1.15798
$82$	8.63168	0.953209
$83$	7.58184	0.832215	0.416107	−	0.909316i	$-0.363394\pi$
$83$	7.58184	0.832215	0.416107	+	0.909316i	$0.363394\pi$
$84$	−20.8823	−2.27845
$85$	−19.5089	−2.11604
$86$	−21.8019	−2.35095
$87$	−18.5260	−1.98620
$88$	−19.4701	−2.07552
$89$	−6.84345	−0.725404	−0.362702	−	0.931905i	$-0.618146\pi$
$89$	−6.84345	−0.725404	−0.362702	+	0.931905i	$0.618146\pi$
$90$	5.61527	0.591901
$91$	−14.5220	−1.52232
$92$	−14.4802	−1.50966
$93$	0.251362	0.0260650
$94$	−18.6268	−1.92120
$95$	21.6763	2.22394
$96$	−7.96680	−0.813109
$97$	−15.7665	−1.60084	−0.800420	−	0.599439i	$-0.795390\pi$
$97$	−15.7665	−1.60084	−0.800420	+	0.599439i	$0.795390\pi$
$98$	−7.03208	−0.710348
$99$	3.30329	0.331993
$100$	40.1347	4.01347
$101$	−15.8106	−1.57321	−0.786605	−	0.617457i	$-0.788163\pi$
$101$	−15.8106	−1.57321	−0.786605	+	0.617457i	$0.788163\pi$
$102$	21.3006	2.10907
$103$	14.1609	1.39532	0.697659	−	0.716430i	$-0.254225\pi$
$103$	14.1609	1.39532	0.697659	+	0.716430i	$0.254225\pi$
$104$	15.9666	1.56566
$105$	24.3539	2.37670
$106$	−25.1950	−2.44716
$107$	−2.67185	−0.258297	−0.129149	−	0.991625i	$-0.541224\pi$
$107$	−2.67185	−0.258297	−0.129149	+	0.991625i	$0.541224\pi$
$108$	15.9128	1.53121
$109$	−4.31831	−0.413619	−0.206809	−	0.978381i	$-0.566308\pi$
$109$	−4.31831	−0.413619	−0.206809	+	0.978381i	$0.566308\pi$
$110$	53.2930	5.08128
$111$	−2.94903	−0.279910
$112$	3.71362	0.350904
$113$	−4.99336	−0.469736	−0.234868	−	0.972027i	$-0.575466\pi$
$113$	−4.99336	−0.469736	−0.234868	+	0.972027i	$0.575466\pi$
$114$	−23.6670	−2.21662
$115$	16.8874	1.57476
$116$	34.0733	3.16362
$117$	−2.70889	−0.250437
$118$	−28.1463	−2.59108
$119$	15.1818	1.39172
$120$	−26.7767	−2.44437
$121$	20.3506	1.85005
$122$	−5.61281	−0.508160
$123$	6.98329	0.629662
$124$	−0.462308	−0.0415165
$125$	−26.4863	−2.36900
$126$	−4.36980	−0.389292
$127$	12.0313	1.06760	0.533801	−	0.845610i	$-0.320763\pi$
$127$	12.0313	1.06760	0.533801	+	0.845610i	$0.320763\pi$
$128$	20.1525	1.78124
$129$	−17.6384	−1.55297
$130$	−43.7034	−3.83304
$131$	−8.20236	−0.716643	−0.358322	−	0.933598i	$-0.616651\pi$
$131$	−8.20236	−0.716643	−0.358322	+	0.933598i	$0.616651\pi$
$132$	−36.9696	−3.21779
$133$	−16.8685	−1.46268
$134$	5.05885	0.437018
$135$	−18.5582	−1.59723
$136$	−16.6922	−1.43134
$137$	−5.94864	−0.508226	−0.254113	−	0.967174i	$-0.581784\pi$
$137$	−5.94864	−0.508226	−0.254113	+	0.967174i	$0.581784\pi$
$138$	−18.4383	−1.56957
$139$	−2.87726	−0.244046	−0.122023	−	0.992527i	$-0.538938\pi$
$139$	−2.87726	−0.244046	−0.122023	+	0.992527i	$0.538938\pi$
$140$	−44.7921	−3.78562
$141$	−15.0696	−1.26909
$142$	5.32281	0.446680
$143$	−25.7093	−2.14992
$144$	0.692729	0.0577274
$145$	−39.7378	−3.30004
$146$	32.6498	2.70212
$147$	−5.68917	−0.469235
$148$	5.42390	0.445842
$149$	1.16436	0.0953878	0.0476939	−	0.998862i	$-0.484813\pi$
$149$	1.16436	0.0953878	0.0476939	+	0.998862i	$0.484813\pi$
$150$	51.1055	4.17275
$151$	7.96515	0.648194	0.324097	−	0.946024i	$-0.394940\pi$
$151$	7.96515	0.648194	0.324097	+	0.946024i	$0.394940\pi$
$152$	18.5466	1.50433
$153$	2.83198	0.228952
$154$	−41.4725	−3.34195
$155$	0.539165	0.0433067
$156$	30.3172	2.42732
$157$	15.0675	1.20251	0.601257	−	0.799056i	$-0.294667\pi$
$157$	15.0675	1.20251	0.601257	+	0.799056i	$0.294667\pi$
$158$	40.4380	3.21707
$159$	−20.3836	−1.61652
$160$	−17.0886	−1.35097
$161$	−13.1418	−1.03572
$162$	24.4075	1.91764
$163$	12.5273	0.981214	0.490607	−	0.871381i	$-0.336775\pi$
$163$	12.5273	0.981214	0.490607	+	0.871381i	$0.336775\pi$
$164$	−12.8438	−1.00293
$165$	43.1156	3.35655
$166$	−17.7564	−1.37816
$167$	−16.0652	−1.24316	−0.621580	−	0.783350i	$-0.713509\pi$
$167$	−16.0652	−1.24316	−0.621580	+	0.783350i	$0.713509\pi$
$168$	20.8376	1.60766
$169$	8.08317	0.621782
$170$	45.6892	3.50420
$171$	−3.14660	−0.240627
$172$	32.4407	2.47358
$173$	1.17632	0.0894338	0.0447169	−	0.999000i	$-0.485761\pi$
$173$	1.17632	0.0894338	0.0447169	+	0.999000i	$0.485761\pi$
$174$	43.3872	3.28918
$175$	36.4251	2.75348
$176$	6.57450	0.495571
$177$	−22.7712	−1.71159
$178$	16.0271	1.20128
$179$	16.1286	1.20551	0.602753	−	0.797928i	$-0.294071\pi$
$179$	16.1286	1.20551	0.602753	+	0.797928i	$0.294071\pi$
$180$	−8.35540	−0.622775
$181$	−9.88410	−0.734680	−0.367340	−	0.930087i	$-0.619731\pi$
$181$	−9.88410	−0.734680	−0.367340	+	0.930087i	$0.619731\pi$
$182$	34.0099	2.52098
$183$	−4.54094	−0.335676
$184$	14.4491	1.06521
$185$	−6.32560	−0.465067
$186$	−0.588680	−0.0431641
$187$	26.8775	1.96548
$188$	27.7162	2.02142
$189$	14.4420	1.05050
$190$	−50.7651	−3.68289
$191$	8.08293	0.584860	0.292430	−	0.956287i	$-0.405536\pi$
$191$	8.08293	0.584860	0.292430	+	0.956287i	$0.405536\pi$
$192$	23.1075	1.66764
$193$	13.1816	0.948836	0.474418	−	0.880300i	$-0.342659\pi$
$193$	13.1816	0.948836	0.474418	+	0.880300i	$0.342659\pi$
$194$	36.9245	2.65102
$195$	−35.3573	−2.53199
$196$	10.4636	0.747399
$197$	7.21903	0.514334	0.257167	−	0.966367i	$-0.417211\pi$
$197$	7.21903	0.514334	0.257167	+	0.966367i	$0.417211\pi$
$198$	−7.73618	−0.549787
$199$	3.24740	0.230202	0.115101	−	0.993354i	$-0.463281\pi$
$199$	3.24740	0.230202	0.115101	+	0.993354i	$0.463281\pi$
$200$	−40.0487	−2.83187
$201$	4.09276	0.288681
$202$	37.0277	2.60526
$203$	30.9239	2.17043
$204$	−31.6948	−2.21908
$205$	14.9790	1.04618
$206$	−33.1644	−2.31067
$207$	−2.45143	−0.170386
$208$	−5.39147	−0.373832
$209$	−29.8635	−2.06570
$210$	−57.0360	−3.93586
$211$	−5.03731	−0.346783	−0.173391	−	0.984853i	$-0.555473\pi$
$211$	−5.03731	−0.346783	−0.173391	+	0.984853i	$0.555473\pi$
$212$	37.4897	2.57480
$213$	4.30632	0.295064
$214$	6.25737	0.427745
$215$	−37.8338	−2.58024
$216$	−15.8787	−1.08041
$217$	−0.419577	−0.0284828
$218$	10.1133	0.684960
$219$	26.4147	1.78494
$220$	−79.2988	−5.34632
$221$	−22.0412	−1.48265
$222$	6.90653	0.463536
$223$	15.0556	1.00819	0.504097	−	0.863647i	$-0.331825\pi$
$223$	15.0556	1.00819	0.504097	+	0.863647i	$0.331825\pi$
$224$	13.2983	0.888531
$225$	6.79464	0.452976
$226$	11.6943	0.777892
$227$	−2.00794	−0.133272	−0.0666359	−	0.997777i	$-0.521227\pi$
$227$	−2.00794	−0.133272	−0.0666359	+	0.997777i	$0.521227\pi$
$228$	35.2160	2.33224
$229$	−7.06117	−0.466615	−0.233308	−	0.972403i	$-0.574955\pi$
$229$	−7.06117	−0.466615	−0.233308	+	0.972403i	$0.574955\pi$
$230$	−39.5497	−2.60783
$231$	−33.5525	−2.20759
$232$	−34.0003	−2.23223
$233$	−21.3694	−1.39995	−0.699977	−	0.714165i	$-0.746806\pi$
$233$	−21.3694	−1.39995	−0.699977	+	0.714165i	$0.746806\pi$
$234$	6.34413	0.414729
$235$	−32.3239	−2.10858
$236$	41.8812	2.72623
$237$	32.7156	2.12510
$238$	−35.5553	−2.30471
$239$	5.28312	0.341737	0.170868	−	0.985294i	$-0.445343\pi$
$239$	5.28312	0.341737	0.170868	+	0.985294i	$0.445343\pi$
$240$	9.04173	0.583641
$241$	−18.2101	−1.17302	−0.586509	−	0.809943i	$-0.699498\pi$
$241$	−18.2101	−1.17302	−0.586509	+	0.809943i	$0.699498\pi$
$242$	−47.6603	−3.06372
$243$	6.04740	0.387941
$244$	8.35175	0.534666
$245$	−12.2031	−0.779628
$246$	−16.3546	−1.04273
$247$	24.4899	1.55825
$248$	0.461318	0.0292937
$249$	−14.3655	−0.910374
$250$	62.0299	3.92311
$251$	19.9923	1.26190	0.630951	−	0.775823i	$-0.282665\pi$
$251$	19.9923	1.26190	0.630951	+	0.775823i	$0.282665\pi$
$252$	6.50217	0.409598
$253$	−23.2659	−1.46271
$254$	−28.1768	−1.76797
$255$	36.9640	2.31477
$256$	−22.8049	−1.42531
$257$	9.53494	0.594773	0.297387	−	0.954757i	$-0.403885\pi$
$257$	9.53494	0.594773	0.297387	+	0.954757i	$0.403885\pi$
$258$	41.3084	2.57175
$259$	4.92257	0.305874
$260$	65.0297	4.03297
$261$	5.76847	0.357059
$262$	19.2096	1.18677
$263$	17.8563	1.10107	0.550535	−	0.834812i	$-0.314424\pi$
$263$	17.8563	1.10107	0.550535	+	0.834812i	$0.314424\pi$
$264$	36.8904	2.27045
$265$	−43.7222	−2.68583
$266$	39.5053	2.42223
$267$	12.9664	0.793532
$268$	−7.52746	−0.459813
$269$	14.9685	0.912648	0.456324	−	0.889814i	$-0.349166\pi$
$269$	14.9685	0.912648	0.456324	+	0.889814i	$0.349166\pi$
$270$	43.4626	2.64505
$271$	0.641322	0.0389575	0.0194788	−	0.999810i	$-0.493799\pi$
$271$	0.641322	0.0389575	0.0194788	+	0.999810i	$0.493799\pi$
$272$	5.63646	0.341761
$273$	27.5150	1.66529
$274$	13.9315	0.841632
$275$	64.4861	3.88866
$276$	27.4358	1.65144
$277$	−16.7074	−1.00385	−0.501926	−	0.864911i	$-0.667375\pi$
$277$	−16.7074	−1.00385	−0.501926	+	0.864911i	$0.667375\pi$
$278$	6.73843	0.404144
$279$	−0.0782669	−0.00468572
$280$	44.6961	2.67111
$281$	−29.8919	−1.78320	−0.891601	−	0.452822i	$-0.850417\pi$
$281$	−29.8919	−1.78320	−0.891601	+	0.452822i	$0.850417\pi$
$282$	35.2925	2.10164
$283$	−24.4290	−1.45215	−0.726076	−	0.687614i	$-0.758658\pi$
$283$	−24.4290	−1.45215	−0.726076	+	0.687614i	$0.758658\pi$
$284$	−7.92023	−0.469979
$285$	−41.0705	−2.43281
$286$	60.2103	3.56031
$287$	−11.6566	−0.688068
$288$	2.48064	0.146173
$289$	6.04271	0.355453
$290$	93.0645	5.46493
$291$	29.8730	1.75119
$292$	−48.5822	−2.84306
$293$	−19.5340	−1.14119	−0.570593	−	0.821233i	$-0.693287\pi$
$293$	−19.5340	−1.14119	−0.570593	+	0.821233i	$0.693287\pi$
$294$	13.3238	0.777061
$295$	−48.8437	−2.84379
$296$	−5.41228	−0.314583
$297$	25.5677	1.48359
$298$	−2.72688	−0.157964
$299$	19.0794	1.10339
$300$	−76.0440	−4.39040
$301$	29.4422	1.69702
$302$	−18.6541	−1.07342
$303$	29.9566	1.72096
$304$	−6.26265	−0.359187
$305$	−9.74019	−0.557721
$306$	−6.63240	−0.379149
$307$	0.261102	0.0149019	0.00745093	−	0.999972i	$-0.497628\pi$
$307$	0.261102	0.0149019	0.00745093	+	0.999972i	$0.497628\pi$
$308$	61.7102	3.51627
$309$	−26.8310	−1.52636
$310$	−1.26270	−0.0717168
$311$	2.78486	0.157915	0.0789576	−	0.996878i	$-0.474841\pi$
$311$	2.78486	0.157915	0.0789576	+	0.996878i	$0.474841\pi$
$312$	−30.2523	−1.71270
$313$	4.24954	0.240198	0.120099	−	0.992762i	$-0.461679\pi$
$313$	4.24954	0.240198	0.120099	+	0.992762i	$0.461679\pi$
$314$	−35.2874	−1.99138
$315$	−7.58312	−0.427260
$316$	−60.1709	−3.38488
$317$	−7.24390	−0.406858	−0.203429	−	0.979090i	$-0.565209\pi$
$317$	−7.24390	−0.406858	−0.203429	+	0.979090i	$0.565209\pi$
$318$	47.7375	2.67699
$319$	54.7469	3.06524
$320$	49.5650	2.77077
$321$	5.06240	0.282556
$322$	30.7775	1.71517
$323$	−25.6027	−1.42457
$324$	−36.3179	−2.01766
$325$	−52.8824	−2.93339
$326$	−29.3385	−1.62491
$327$	8.18198	0.452464
$328$	12.8162	0.707659
$329$	25.1545	1.38681
$330$	−100.975	−5.55850
$331$	−21.3414	−1.17303	−0.586516	−	0.809938i	$-0.699501\pi$
$331$	−21.3414	−1.17303	−0.586516	+	0.809938i	$0.699501\pi$
$332$	26.4211	1.45005
$333$	0.918245	0.0503195
$334$	37.6241	2.05870
$335$	8.77887	0.479641
$336$	−7.03626	−0.383859
$337$	35.2178	1.91844	0.959218	−	0.282667i	$-0.0912190\pi$
$337$	35.2178	1.91844	0.959218	+	0.282667i	$0.0912190\pi$
$338$	−18.9305	−1.02968
$339$	9.46103	0.513852
$340$	−67.9846	−3.68698
$341$	−0.742810	−0.0402254
$342$	7.36923	0.398482
$343$	−12.6424	−0.682626
$344$	−32.3712	−1.74534
$345$	−31.9969	−1.72266
$346$	−2.75489	−0.148104
$347$	−8.85399	−0.475307	−0.237653	−	0.971350i	$-0.576378\pi$
$347$	−8.85399	−0.475307	−0.237653	+	0.971350i	$0.576378\pi$
$348$	−64.5593	−3.46074
$349$	28.1363	1.50610	0.753050	−	0.657964i	$-0.228582\pi$
$349$	28.1363	1.50610	0.753050	+	0.657964i	$0.228582\pi$
$350$	−85.3062	−4.55981
$351$	−20.9670	−1.11914
$352$	23.5430	1.25485
$353$	−6.28531	−0.334533	−0.167267	−	0.985912i	$-0.553494\pi$
$353$	−6.28531	−0.334533	−0.167267	+	0.985912i	$0.553494\pi$
$354$	53.3294	2.83443
$355$	9.23693	0.490246
$356$	−23.8480	−1.26394
$357$	−28.7653	−1.52242
$358$	−37.7725	−1.99634
$359$	−30.4246	−1.60575	−0.802876	−	0.596147i	$-0.796698\pi$
$359$	−30.4246	−1.60575	−0.802876	+	0.596147i	$0.796698\pi$
$360$	8.33751	0.439425
$361$	9.44702	0.497211
$362$	23.1482	1.21664
$363$	−38.5587	−2.02380
$364$	−50.6060	−2.65248
$365$	56.6588	2.96566
$366$	10.6347	0.555885
$367$	20.0395	1.04605	0.523026	−	0.852317i	$-0.324803\pi$
$367$	20.0395	1.04605	0.523026	+	0.852317i	$0.324803\pi$
$368$	−4.87906	−0.254338
$369$	−2.17440	−0.113195
$370$	14.8143	0.770160
$371$	34.0246	1.76647
$372$	0.875944	0.0454156
$373$	18.7242	0.969502	0.484751	−	0.874652i	$-0.338910\pi$
$373$	18.7242	0.969502	0.484751	+	0.874652i	$0.338910\pi$
$374$	−62.9462	−3.25487
$375$	50.1841	2.59149
$376$	−27.6569	−1.42630
$377$	−44.8957	−2.31225
$378$	−33.8226	−1.73964
$379$	13.8010	0.708909	0.354454	−	0.935073i	$-0.384667\pi$
$379$	13.8010	0.708909	0.354454	+	0.935073i	$0.384667\pi$
$380$	75.5374	3.87499
$381$	−22.7959	−1.16787
$382$	−18.9299	−0.968539
$383$	−0.632437	−0.0323160	−0.0161580	−	0.999869i	$-0.505143\pi$
$383$	−0.632437	−0.0323160	−0.0161580	+	0.999869i	$0.505143\pi$
$384$	−38.1833	−1.94853
$385$	−71.9693	−3.66789
$386$	−30.8709	−1.57129
$387$	5.49208	0.279178
$388$	−54.9428	−2.78930
$389$	32.6105	1.65342	0.826710	−	0.562629i	$-0.190210\pi$
$389$	32.6105	1.65342	0.826710	+	0.562629i	$0.190210\pi$
$390$	82.8056	4.19303
$391$	−19.9463	−1.00873
$392$	−10.4412	−0.527359
$393$	15.5412	0.783948
$394$	−16.9067	−0.851747
$395$	70.1740	3.53084
$396$	11.5113	0.578463
$397$	9.52323	0.477957	0.238979	−	0.971025i	$-0.423187\pi$
$397$	9.52323	0.477957	0.238979	+	0.971025i	$0.423187\pi$
$398$	−7.60530	−0.381219
$399$	31.9610	1.60005
$400$	13.5233	0.676165
$401$	−1.93808	−0.0967832	−0.0483916	−	0.998828i	$-0.515410\pi$
$401$	−1.93808	−0.0967832	−0.0483916	+	0.998828i	$0.515410\pi$
$402$	−9.58510	−0.478061
$403$	0.609148	0.0303438
$404$	−55.0965	−2.74115
$405$	42.3556	2.10467
$406$	−72.4227	−3.59428
$407$	8.71480	0.431977
$408$	31.6270	1.56577
$409$	33.4374	1.65337	0.826687	−	0.562663i	$-0.190223\pi$
$409$	33.4374	1.65337	0.826687	+	0.562663i	$0.190223\pi$
$410$	−35.0802	−1.73249
$411$	11.2710	0.555957
$412$	49.3479	2.43120
$413$	38.0101	1.87036
$414$	5.74117	0.282163
$415$	−30.8135	−1.51258
$416$	−19.3067	−0.946587
$417$	5.45159	0.266966
$418$	69.9393	3.42084
$419$	20.3242	0.992902	0.496451	−	0.868065i	$-0.334636\pi$
$419$	20.3242	0.992902	0.496451	+	0.868065i	$0.334636\pi$
$420$	84.8684	4.14115
$421$	−9.61186	−0.468454	−0.234227	−	0.972182i	$-0.575256\pi$
$421$	−9.61186	−0.468454	−0.234227	+	0.972182i	$0.575256\pi$
$422$	11.7972	0.574279
$423$	4.69225	0.228145
$424$	−37.4094	−1.81676
$425$	55.2853	2.68173
$426$	−10.0852	−0.488631
$427$	7.57980	0.366812
$428$	−9.31084	−0.450056
$429$	48.7120	2.35184
$430$	88.6054	4.27293
$431$	−22.6012	−1.08866	−0.544331	−	0.838870i	$-0.683216\pi$
$431$	−22.6012	−1.08866	−0.544331	+	0.838870i	$0.683216\pi$
$432$	5.36177	0.257968
$433$	−17.4977	−0.840884	−0.420442	−	0.907319i	$-0.638125\pi$
$433$	−17.4977	−0.840884	−0.420442	+	0.907319i	$0.638125\pi$
$434$	0.982635	0.0471680
$435$	75.2920	3.60997
$436$	−15.0484	−0.720688
$437$	22.1623	1.06017
$438$	−61.8622	−2.95589
$439$	−19.5837	−0.934681	−0.467340	−	0.884078i	$-0.654788\pi$
$439$	−19.5837	−0.934681	−0.467340	+	0.884078i	$0.654788\pi$
$440$	79.1290	3.77233
$441$	1.77144	0.0843545
$442$	51.6196	2.45529
$443$	27.5231	1.30766	0.653831	−	0.756640i	$-0.273161\pi$
$443$	27.5231	1.30766	0.653831	+	0.756640i	$0.273161\pi$
$444$	−10.2768	−0.487714
$445$	27.8126	1.31844
$446$	−35.2596	−1.66959
$447$	−2.20613	−0.104346
$448$	−38.5714	−1.82233
$449$	6.87377	0.324393	0.162197	−	0.986758i	$-0.448142\pi$
$449$	6.87377	0.324393	0.162197	+	0.986758i	$0.448142\pi$
$450$	−15.9128	−0.750137
$451$	−20.6366	−0.971739
$452$	−17.4008	−0.818467
$453$	−15.0917	−0.709071
$454$	4.70253	0.220701
$455$	59.0190	2.76686
$456$	−35.1406	−1.64561
$457$	11.2935	0.528285	0.264143	−	0.964484i	$-0.414911\pi$
$457$	11.2935	0.528285	0.264143	+	0.964484i	$0.414911\pi$
$458$	16.5370	0.772723
$459$	21.9198	1.02313
$460$	58.8491	2.74386
$461$	−9.70031	−0.451788	−0.225894	−	0.974152i	$-0.572530\pi$
$461$	−9.70031	−0.451788	−0.225894	+	0.974152i	$0.572530\pi$
$462$	78.5788	3.65582
$463$	31.9880	1.48661	0.743305	−	0.668953i	$-0.233257\pi$
$463$	31.9880	1.48661	0.743305	+	0.668953i	$0.233257\pi$
$464$	11.4809	0.532988
$465$	−1.02157	−0.0473740
$466$	50.0463	2.31835
$467$	7.00803	0.324293	0.162147	−	0.986767i	$-0.448158\pi$
$467$	7.00803	0.324293	0.162147	+	0.986767i	$0.448158\pi$
$468$	−9.43993	−0.436361
$469$	−6.83170	−0.315459
$470$	75.7015	3.49185
$471$	−28.5486	−1.31545
$472$	−41.7915	−1.92361
$473$	52.1238	2.39666
$474$	−76.6186	−3.51921
$475$	−61.4273	−2.81848
$476$	52.9055	2.42492
$477$	6.34686	0.290603
$478$	−12.3729	−0.565922
$479$	24.1558	1.10371	0.551854	−	0.833941i	$-0.313921\pi$
$479$	24.1558	1.10371	0.551854	+	0.833941i	$0.313921\pi$
$480$	32.3781	1.47785
$481$	−7.14665	−0.325859
$482$	42.6474	1.94254
$483$	24.9000	1.13299
$484$	70.9176	3.22353
$485$	64.0768	2.90958
$486$	−14.1628	−0.642438
$487$	10.1678	0.460748	0.230374	−	0.973102i	$-0.426005\pi$
$487$	10.1678	0.460748	0.230374	+	0.973102i	$0.426005\pi$
$488$	−8.33386	−0.377256
$489$	−23.7357	−1.07337
$490$	28.5792	1.29108
$491$	17.8240	0.804386	0.402193	−	0.915555i	$-0.368248\pi$
$491$	17.8240	0.804386	0.402193	+	0.915555i	$0.368248\pi$
$492$	24.3353	1.09712
$493$	46.9357	2.11388
$494$	−57.3544	−2.58049
$495$	−13.4250	−0.603408
$496$	−0.155774	−0.00699445
$497$	−7.18817	−0.322434
$498$	33.6434	1.50760
$499$	−26.9964	−1.20852	−0.604262	−	0.796786i	$-0.706532\pi$
$499$	−26.9964	−1.20852	−0.604262	+	0.796786i	$0.706532\pi$
$500$	−92.2992	−4.12774
$501$	30.4390	1.35991
$502$	−46.8212	−2.08973
$503$	12.3233	0.549467	0.274734	−	0.961520i	$-0.411410\pi$
$503$	12.3233	0.549467	0.274734	+	0.961520i	$0.411410\pi$
$504$	−6.48824	−0.289009
$505$	64.2560	2.85936
$506$	54.4878	2.42228
$507$	−15.3153	−0.680178
$508$	41.9265	1.86019
$509$	−0.613117	−0.0271759	−0.0135880	−	0.999908i	$-0.504325\pi$
$509$	−0.613117	−0.0271759	−0.0135880	+	0.999908i	$0.504325\pi$
$510$	−86.5682	−3.83331
$511$	−44.0918	−1.95051
$512$	13.1033	0.579089
$513$	−24.3549	−1.07530
$514$	−22.3305	−0.984955
$515$	−57.5518	−2.53604
$516$	−61.4660	−2.70589
$517$	44.5328	1.95855
$518$	−11.5285	−0.506533
$519$	−2.22879	−0.0978332
$520$	−64.8904	−2.84563
$521$	−13.3204	−0.583578	−0.291789	−	0.956483i	$-0.594250\pi$
$521$	−13.3204	−0.583578	−0.291789	+	0.956483i	$0.594250\pi$
$522$	−13.5095	−0.591297
$523$	7.12252	0.311446	0.155723	−	0.987801i	$-0.450229\pi$
$523$	7.12252	0.311446	0.155723	+	0.987801i	$0.450229\pi$
$524$	−28.5835	−1.24868
$525$	−69.0153	−3.01207
$526$	−41.8189	−1.82339
$527$	−0.636827	−0.0277406
$528$	−12.4568	−0.542114
$529$	−5.73396	−0.249303
$530$	102.396	4.44779
$531$	7.09031	0.307693
$532$	−58.7831	−2.54857
$533$	16.9232	0.733026
$534$	−30.3669	−1.31410
$535$	10.8587	0.469463
$536$	7.51134	0.324441
$537$	−30.5591	−1.31872
$538$	−35.0558	−1.51136
$539$	16.8123	0.724156
$540$	−64.6714	−2.78302
$541$	8.77727	0.377364	0.188682	−	0.982038i	$-0.439578\pi$
$541$	8.77727	0.377364	0.188682	+	0.982038i	$0.439578\pi$
$542$	−1.50195	−0.0645144
$543$	18.7276	0.803678
$544$	20.1839	0.865379
$545$	17.5501	0.751765
$546$	−64.4392	−2.75774
$547$	−26.3213	−1.12542	−0.562709	−	0.826655i	$-0.690241\pi$
$547$	−26.3213	−1.12542	−0.562709	+	0.826655i	$0.690241\pi$
$548$	−20.7298	−0.885532
$549$	1.41392	0.0603446
$550$	−151.024	−6.43968
$551$	−52.1501	−2.22167
$552$	−27.3771	−1.16525
$553$	−54.6093	−2.32222
$554$	39.1282	1.66240
$555$	11.9852	0.508745
$556$	−10.0266	−0.425224
$557$	38.4138	1.62765	0.813823	−	0.581113i	$-0.197382\pi$
$557$	38.4138	1.62765	0.813823	+	0.581113i	$0.197382\pi$
$558$	0.183298	0.00775964
$559$	−42.7446	−1.80790
$560$	−15.0926	−0.637778
$561$	−50.9254	−2.15007
$562$	70.0058	2.95301
$563$	−16.0296	−0.675569	−0.337784	−	0.941223i	$-0.609677\pi$
$563$	−16.0296	−0.675569	−0.337784	+	0.941223i	$0.609677\pi$
$564$	−52.5145	−2.21126
$565$	20.2936	0.853760
$566$	57.2118	2.40479
$567$	−32.9611	−1.38424
$568$	7.90327	0.331614
$569$	34.9494	1.46516	0.732578	−	0.680683i	$-0.238317\pi$
$569$	34.9494	1.46516	0.732578	+	0.680683i	$0.238317\pi$
$570$	96.1856	4.02877
$571$	−7.88836	−0.330118	−0.165059	−	0.986284i	$-0.552781\pi$
$571$	−7.88836	−0.330118	−0.165059	+	0.986284i	$0.552781\pi$
$572$	−89.5917	−3.74602
$573$	−15.3149	−0.639788
$574$	27.2994	1.13945
$575$	−47.8563	−1.99575
$576$	−7.19502	−0.299792
$577$	20.7664	0.864515	0.432258	−	0.901750i	$-0.357717\pi$
$577$	20.7664	0.864515	0.432258	+	0.901750i	$0.357717\pi$
$578$	−14.1518	−0.588637
$579$	−24.9755	−1.03795
$580$	−138.478	−5.74999
$581$	23.9790	0.994818
$582$	−69.9615	−2.90000
$583$	60.2363	2.49473
$584$	48.4782	2.00604
$585$	11.0093	0.455177
$586$	45.7478	1.88982
$587$	39.7603	1.64108	0.820542	−	0.571586i	$-0.193672\pi$
$587$	39.7603	1.64108	0.820542	+	0.571586i	$0.193672\pi$
$588$	−19.8256	−0.817593
$589$	0.707576	0.0291552
$590$	114.390	4.70937
$591$	−13.6780	−0.562639
$592$	1.82757	0.0751127
$593$	−15.3053	−0.628513	−0.314257	−	0.949338i	$-0.601755\pi$
$593$	−15.3053	−0.628513	−0.314257	+	0.949338i	$0.601755\pi$
$594$	−59.8786	−2.45685
$595$	−61.7008	−2.52949
$596$	4.05754	0.166203
$597$	−6.15292	−0.251822
$598$	−44.6832	−1.82723
$599$	23.0462	0.941644	0.470822	−	0.882228i	$-0.343957\pi$
$599$	23.0462	0.941644	0.470822	+	0.882228i	$0.343957\pi$
$600$	75.8811	3.09783
$601$	−12.6853	−0.517445	−0.258723	−	0.965952i	$-0.583302\pi$
$601$	−12.6853	−0.517445	−0.258723	+	0.965952i	$0.583302\pi$
$602$	−68.9526	−2.81030
$603$	−1.27437	−0.0518963
$604$	27.7569	1.12941
$605$	−82.7073	−3.36253
$606$	−70.1572	−2.84994
$607$	12.2482	0.497138	0.248569	−	0.968614i	$-0.420040\pi$
$607$	12.2482	0.497138	0.248569	+	0.968614i	$0.420040\pi$
$608$	−22.4263	−0.909507
$609$	−58.5921	−2.37427
$610$	22.8112	0.923597
$611$	−36.5196	−1.47742
$612$	9.86887	0.398925
$613$	−46.5406	−1.87976	−0.939878	−	0.341510i	$-0.889062\pi$
$613$	−46.5406	−1.87976	−0.939878	+	0.341510i	$0.889062\pi$
$614$	−0.611490	−0.0246777
$615$	−28.3809	−1.14443
$616$	−61.5781	−2.48105
$617$	26.5930	1.07059	0.535296	−	0.844664i	$-0.320200\pi$
$617$	26.5930	1.07059	0.535296	+	0.844664i	$0.320200\pi$
$618$	62.8372	2.52768
$619$	34.4712	1.38552	0.692758	−	0.721170i	$-0.256396\pi$
$619$	34.4712	1.38552	0.692758	+	0.721170i	$0.256396\pi$
$620$	1.87888	0.0754575
$621$	−18.9743	−0.761411
$622$	−6.52205	−0.261510
$623$	−21.6438	−0.867139
$624$	10.2153	0.408941
$625$	50.0580	2.00232
$626$	−9.95228	−0.397773
$627$	56.5830	2.25971
$628$	52.5069	2.09526
$629$	7.47139	0.297904
$630$	17.7594	0.707551
$631$	23.1379	0.921106	0.460553	−	0.887632i	$-0.347651\pi$
$631$	23.1379	0.921106	0.460553	+	0.887632i	$0.347651\pi$
$632$	60.0420	2.38834
$633$	9.54430	0.379352
$634$	16.9650	0.673764
$635$	−48.8966	−1.94040
$636$	−71.0325	−2.81662
$637$	−13.7871	−0.546263
$638$	−128.215	−5.07609
$639$	−1.34086	−0.0530438
$640$	−81.9022	−3.23747
$641$	−28.5719	−1.12852	−0.564262	−	0.825596i	$-0.690839\pi$
$641$	−28.5719	−1.12852	−0.564262	+	0.825596i	$0.690839\pi$
$642$	−11.8560	−0.467918
$643$	28.5210	1.12476	0.562379	−	0.826880i	$-0.309886\pi$
$643$	28.5210	1.12476	0.562379	+	0.826880i	$0.309886\pi$
$644$	−45.7963	−1.80463
$645$	71.6845	2.82257
$646$	59.9605	2.35911
$647$	4.25473	0.167271	0.0836354	−	0.996496i	$-0.473347\pi$
$647$	4.25473	0.167271	0.0836354	+	0.996496i	$0.473347\pi$
$648$	36.2401	1.42365
$649$	67.2922	2.64145
$650$	123.849	4.85774
$651$	0.794981	0.0311578
$652$	43.6550	1.70966
$653$	−9.52702	−0.372821	−0.186411	−	0.982472i	$-0.559685\pi$
$653$	−9.52702	−0.372821	−0.186411	+	0.982472i	$0.559685\pi$
$654$	−19.1619	−0.749289
$655$	33.3354	1.30252
$656$	−4.32768	−0.168967
$657$	−8.22478	−0.320879
$658$	−58.9108	−2.29658
$659$	19.6043	0.763675	0.381837	−	0.924229i	$-0.375291\pi$
$659$	19.6043	0.763675	0.381837	+	0.924229i	$0.375291\pi$
$660$	150.249	5.84843
$661$	−30.2185	−1.17536	−0.587681	−	0.809092i	$-0.699959\pi$
$661$	−30.2185	−1.17536	−0.587681	+	0.809092i	$0.699959\pi$
$662$	49.9809	1.94256
$663$	41.7618	1.62190
$664$	−26.3645	−1.02314
$665$	68.5555	2.65847
$666$	−2.15050	−0.0833300
$667$	−40.6287	−1.57315
$668$	−55.9838	−2.16608
$669$	−28.5260	−1.10288
$670$	−20.5598	−0.794294
$671$	13.4191	0.518039
$672$	−25.1966	−0.971979
$673$	9.13421	0.352098	0.176049	−	0.984381i	$-0.443668\pi$
$673$	9.13421	0.352098	0.176049	+	0.984381i	$0.443668\pi$
$674$	−82.4788	−3.17697
$675$	52.5910	2.02423
$676$	28.1682	1.08339
$677$	3.48343	0.133879	0.0669395	−	0.997757i	$-0.478677\pi$
$677$	3.48343	0.133879	0.0669395	+	0.997757i	$0.478677\pi$
$678$	−22.1574	−0.850949
$679$	−49.8645	−1.91362
$680$	67.8390	2.60151
$681$	3.80449	0.145788
$682$	1.73963	0.0666140
$683$	−25.8033	−0.987335	−0.493668	−	0.869651i	$-0.664344\pi$
$683$	−25.8033	−0.987335	−0.493668	+	0.869651i	$0.664344\pi$
$684$	−10.9653	−0.419267
$685$	24.1760	0.923717
$686$	29.6081	1.13044
$687$	13.3789	0.510438
$688$	10.9308	0.416734
$689$	−49.3973	−1.88189
$690$	74.9356	2.85275
$691$	11.4009	0.433711	0.216856	−	0.976204i	$-0.430420\pi$
$691$	11.4009	0.433711	0.216856	+	0.976204i	$0.430420\pi$
$692$	4.09923	0.155829
$693$	10.4473	0.396860
$694$	20.7357	0.787117
$695$	11.6935	0.443560
$696$	64.4210	2.44187
$697$	−17.6922	−0.670140
$698$	−65.8941	−2.49413
$699$	40.4890	1.53143
$700$	126.934	4.79765
$701$	37.9243	1.43238	0.716190	−	0.697905i	$-0.245884\pi$
$701$	37.9243	1.43238	0.716190	+	0.697905i	$0.245884\pi$
$702$	49.1040	1.85331
$703$	−8.30143	−0.313094
$704$	−68.2859	−2.57362
$705$	61.2448	2.30661
$706$	14.7200	0.553993
$707$	−50.0040	−1.88059
$708$	−79.3530	−2.98227
$709$	−33.3004	−1.25062	−0.625312	−	0.780375i	$-0.715028\pi$
$709$	−33.3004	−1.25062	−0.625312	+	0.780375i	$0.715028\pi$
$710$	−21.6326	−0.811856
$711$	−10.1867	−0.382031
$712$	23.7969	0.891828
$713$	0.551253	0.0206446
$714$	67.3673	2.52116
$715$	104.486	3.90755
$716$	56.2047	2.10047
$717$	−10.0100	−0.373831
$718$	71.2534	2.65915
$719$	4.61966	0.172284	0.0861421	−	0.996283i	$-0.472546\pi$
$719$	4.61966	0.172284	0.0861421	+	0.996283i	$0.472546\pi$
$720$	−2.81534	−0.104921
$721$	44.7867	1.66795
$722$	−22.1246	−0.823391
$723$	34.5031	1.28318
$724$	−34.4440	−1.28010
$725$	112.611	4.18226
$726$	90.3030	3.35146
$727$	21.4774	0.796553	0.398276	−	0.917265i	$-0.369608\pi$
$727$	21.4774	0.796553	0.398276	+	0.917265i	$0.369608\pi$
$728$	50.4977	1.87157
$729$	19.8074	0.733606
$730$	−132.693	−4.91118
$731$	44.6869	1.65280
$732$	−15.8242	−0.584880
$733$	19.3447	0.714514	0.357257	−	0.934006i	$-0.383712\pi$
$733$	19.3447	0.714514	0.357257	+	0.934006i	$0.383712\pi$
$734$	−46.9317	−1.73228
$735$	23.1215	0.852849
$736$	−17.4717	−0.644016
$737$	−12.0947	−0.445513
$738$	5.09236	0.187452
$739$	−5.60363	−0.206133	−0.103067	−	0.994674i	$-0.532865\pi$
$739$	−5.60363	−0.206133	−0.103067	+	0.994674i	$0.532865\pi$
$740$	−22.0434	−0.810331
$741$	−46.4014	−1.70460
$742$	−79.6843	−2.92530
$743$	19.7233	0.723578	0.361789	−	0.932260i	$-0.382166\pi$
$743$	19.7233	0.723578	0.361789	+	0.932260i	$0.382166\pi$
$744$	−0.874068	−0.0320449
$745$	−4.73209	−0.173370
$746$	−43.8514	−1.60551
$747$	4.47299	0.163658
$748$	93.6627	3.42465
$749$	−8.45024	−0.308765
$750$	−117.529	−4.29156
$751$	−32.3025	−1.17874	−0.589368	−	0.807865i	$-0.700623\pi$
$751$	−32.3025	−1.17874	−0.589368	+	0.807865i	$0.700623\pi$
$752$	9.33893	0.340556
$753$	−37.8798	−1.38042
$754$	105.144	3.82912
$755$	−32.3713	−1.17811
$756$	50.3272	1.83038
$757$	−30.9493	−1.12487	−0.562436	−	0.826841i	$-0.690136\pi$
$757$	−30.9493	−1.12487	−0.562436	+	0.826841i	$0.690136\pi$
$758$	−32.3214	−1.17397
$759$	44.0823	1.60009
$760$	−75.3756	−2.73416
$761$	−17.3883	−0.630325	−0.315163	−	0.949038i	$-0.602059\pi$
$761$	−17.3883	−0.630325	−0.315163	+	0.949038i	$0.602059\pi$
$762$	53.3871	1.93401
$763$	−13.6575	−0.494434
$764$	28.1673	1.01906
$765$	−11.5095	−0.416128
$766$	1.48114	0.0535159
$767$	−55.1836	−1.99256
$768$	43.2089	1.55917
$769$	−44.5928	−1.60806	−0.804028	−	0.594591i	$-0.797314\pi$
$769$	−44.5928	−1.60806	−0.804028	+	0.594591i	$0.797314\pi$
$770$	168.549	6.07410
$771$	−18.0660	−0.650632
$772$	45.9353	1.65325
$773$	43.2678	1.55623	0.778117	−	0.628120i	$-0.216175\pi$
$773$	43.2678	1.55623	0.778117	+	0.628120i	$0.216175\pi$
$774$	−12.8623	−0.462324
$775$	−1.52791	−0.0548841
$776$	54.8252	1.96811
$777$	−9.32689	−0.334600
$778$	−76.3726	−2.73809
$779$	19.6577	0.704311
$780$	−123.213	−4.41173
$781$	−12.7258	−0.455364
$782$	46.7136	1.67047
$783$	44.6484	1.59560
$784$	3.52569	0.125917
$785$	−61.2360	−2.18561
$786$	−36.3968	−1.29823
$787$	−17.9471	−0.639747	−0.319873	−	0.947460i	$-0.603640\pi$
$787$	−17.9471	−0.639747	−0.319873	+	0.947460i	$0.603640\pi$
$788$	25.1568	0.896174
$789$	−33.8328	−1.20448
$790$	−164.345	−5.84713
$791$	−15.7925	−0.561516
$792$	−11.4866	−0.408159
$793$	−11.0045	−0.390780
$794$	−22.3031	−0.791506
$795$	82.8413	2.93808
$796$	11.3165	0.401104
$797$	−6.99950	−0.247935	−0.123967	−	0.992286i	$-0.539562\pi$
$797$	−6.99950	−0.247935	−0.123967	+	0.992286i	$0.539562\pi$
$798$	−74.8515	−2.64972
$799$	38.1790	1.35067
$800$	48.4264	1.71213
$801$	−4.03737	−0.142654
$802$	4.53892	0.160275
$803$	−78.0590	−2.75464
$804$	14.2624	0.502997
$805$	53.4098	1.88245
$806$	−1.42660	−0.0502499
$807$	−28.3612	−0.998361
$808$	54.9785	1.93414
$809$	−30.3896	−1.06844	−0.534221	−	0.845345i	$-0.679395\pi$
$809$	−30.3896	−1.06844	−0.534221	+	0.845345i	$0.679395\pi$
$810$	−99.1953	−3.48537
$811$	33.8095	1.18721	0.593606	−	0.804756i	$-0.297704\pi$
$811$	33.8095	1.18721	0.593606	+	0.804756i	$0.297704\pi$
$812$	107.763	3.78175
$813$	−1.21512	−0.0426163
$814$	−20.4098	−0.715361
$815$	−50.9125	−1.78339
$816$	−10.6795	−0.373858
$817$	−49.6514	−1.73708
$818$	−78.3092	−2.73802
$819$	−8.56740	−0.299369
$820$	52.1986	1.82285
$821$	34.2786	1.19633	0.598165	−	0.801373i	$-0.295897\pi$
$821$	34.2786	1.19633	0.598165	+	0.801373i	$0.295897\pi$
$822$	−26.3963	−0.920676
$823$	−3.37653	−0.117699	−0.0588493	−	0.998267i	$-0.518743\pi$
$823$	−3.37653	−0.117699	−0.0588493	+	0.998267i	$0.518743\pi$
$824$	−49.2423	−1.71544
$825$	−122.183	−4.25387
$826$	−89.0183	−3.09734
$827$	11.3084	0.393232	0.196616	−	0.980481i	$-0.437005\pi$
$827$	11.3084	0.393232	0.196616	+	0.980481i	$0.437005\pi$
$828$	−8.54274	−0.296881
$829$	−30.7774	−1.06894	−0.534472	−	0.845186i	$-0.679489\pi$
$829$	−30.7774	−1.06894	−0.534472	+	0.845186i	$0.679489\pi$
$830$	72.1641	2.50485
$831$	31.6559	1.09813
$832$	55.9984	1.94140
$833$	14.4135	0.499400
$834$	−12.7674	−0.442100
$835$	65.2909	2.25948
$836$	−104.068	−3.59927
$837$	−0.605792	−0.0209392
$838$	−47.5985	−1.64426
$839$	19.1455	0.660977	0.330489	−	0.943810i	$-0.392786\pi$
$839$	19.1455	0.660977	0.330489	+	0.943810i	$0.392786\pi$
$840$	−84.6867	−2.92197
$841$	66.6036	2.29667
$842$	22.5106	0.775768
$843$	56.6368	1.95067
$844$	−17.5540	−0.604233
$845$	−32.8510	−1.13011
$846$	−10.9891	−0.377812
$847$	64.3627	2.21153
$848$	12.6321	0.433787
$849$	46.2861	1.58853
$850$	−129.476	−4.44100
$851$	−6.46742	−0.221700
$852$	15.0066	0.514118
$853$	43.5067	1.48964	0.744820	−	0.667265i	$-0.232535\pi$
$853$	43.5067	1.48964	0.744820	+	0.667265i	$0.232535\pi$
$854$	−17.7516	−0.607448
$855$	12.7882	0.437347
$856$	9.29090	0.317556
$857$	10.4837	0.358117	0.179059	−	0.983838i	$-0.442695\pi$
$857$	10.4837	0.358117	0.179059	+	0.983838i	$0.442695\pi$
$858$	−114.082	−3.89468
$859$	48.1138	1.64162	0.820810	−	0.571201i	$-0.193522\pi$
$859$	48.1138	1.64162	0.820810	+	0.571201i	$0.193522\pi$
$860$	−131.843	−4.49581
$861$	22.0860	0.752689
$862$	52.9312	1.80284
$863$	−13.8070	−0.469996	−0.234998	−	0.971996i	$-0.575508\pi$
$863$	−13.8070	−0.469996	−0.234998	+	0.971996i	$0.575508\pi$
$864$	19.2003	0.653208
$865$	−4.78070	−0.162549
$866$	40.9789	1.39252
$867$	−11.4492	−0.388836
$868$	−1.46214	−0.0496283
$869$	−96.6790	−3.27961
$870$	−176.331	−5.97818
$871$	9.91835	0.336071
$872$	15.0162	0.508512
$873$	−9.30160	−0.314812
$874$	−51.9033	−1.75565
$875$	−83.7680	−2.83188
$876$	92.0496	3.11007
$877$	28.5026	0.962464	0.481232	−	0.876593i	$-0.340189\pi$
$877$	28.5026	0.962464	0.481232	+	0.876593i	$0.340189\pi$
$878$	45.8644	1.54785
$879$	37.0114	1.24836
$880$	−26.7196	−0.900716
$881$	−23.4700	−0.790724	−0.395362	−	0.918525i	$-0.629381\pi$
$881$	−23.4700	−0.790724	−0.395362	+	0.918525i	$0.629381\pi$
$882$	−4.14866	−0.139693
$883$	−6.64052	−0.223471	−0.111736	−	0.993738i	$-0.535641\pi$
$883$	−6.64052	−0.223471	−0.111736	+	0.993738i	$0.535641\pi$
$884$	−76.8089	−2.58336
$885$	92.5451	3.11087
$886$	−64.4581	−2.16551
$887$	−26.8120	−0.900259	−0.450130	−	0.892963i	$-0.648622\pi$
$887$	−26.8120	−0.900259	−0.450130	+	0.892963i	$0.648622\pi$
$888$	10.2548	0.344127
$889$	38.0512	1.27620
$890$	−65.1361	−2.18337
$891$	−58.3535	−1.95492
$892$	52.4655	1.75667
$893$	−42.4205	−1.41955
$894$	5.16667	0.172799
$895$	−65.5484	−2.19104
$896$	63.7362	2.12928
$897$	−36.1501	−1.20702
$898$	−16.0981	−0.537201
$899$	−1.29715	−0.0432625
$900$	23.6779	0.789264
$901$	51.6419	1.72044
$902$	48.3301	1.60922
$903$	−55.7848	−1.85640
$904$	17.3636	0.577504
$905$	40.1702	1.33530
$906$	35.3442	1.17423
$907$	−13.7447	−0.456385	−0.228192	−	0.973616i	$-0.573281\pi$
$907$	−13.7447	−0.456385	−0.228192	+	0.973616i	$0.573281\pi$
$908$	−6.99726	−0.232212
$909$	−9.32762	−0.309378
$910$	−138.220	−4.58196
$911$	−8.26440	−0.273812	−0.136906	−	0.990584i	$-0.543716\pi$
$911$	−8.26440	−0.273812	−0.136906	+	0.990584i	$0.543716\pi$
$912$	11.8660	0.392921
$913$	42.4519	1.40495
$914$	−26.4488	−0.874850
$915$	18.4549	0.610101
$916$	−24.6067	−0.813029
$917$	−25.9416	−0.856666
$918$	−51.3353	−1.69432
$919$	−7.54936	−0.249030	−0.124515	−	0.992218i	$-0.539738\pi$
$919$	−7.54936	−0.249030	−0.124515	+	0.992218i	$0.539738\pi$
$920$	−58.7231	−1.93604
$921$	−0.494714	−0.0163014
$922$	22.7178	0.748170
$923$	10.4359	0.343501
$924$	−116.924	−3.84650
$925$	17.9258	0.589395
$926$	−74.9148	−2.46185
$927$	8.35441	0.274395
$928$	41.1127	1.34959
$929$	35.4602	1.16341	0.581706	−	0.813399i	$-0.302385\pi$
$929$	35.4602	1.16341	0.581706	+	0.813399i	$0.302385\pi$
$930$	2.39247	0.0784522
$931$	−16.0148	−0.524865
$932$	−74.4678	−2.43927
$933$	−5.27654	−0.172746
$934$	−16.4126	−0.537035
$935$	−109.234	−3.57232
$936$	9.41971	0.307893
$937$	−3.99175	−0.130405	−0.0652024	−	0.997872i	$-0.520769\pi$
$937$	−3.99175	−0.130405	−0.0652024	+	0.997872i	$0.520769\pi$
$938$	15.9996	0.522406
$939$	−8.05169	−0.262757
$940$	−112.642	−3.67398
$941$	25.7831	0.840504	0.420252	−	0.907408i	$-0.361942\pi$
$941$	25.7831	0.840504	0.420252	+	0.907408i	$0.361942\pi$
$942$	66.8598	2.17841
$943$	15.3148	0.498719
$944$	14.1118	0.459299
$945$	−58.6939	−1.90931
$946$	−122.072	−3.96891
$947$	−41.7089	−1.35536	−0.677678	−	0.735359i	$-0.737014\pi$
$947$	−41.7089	−1.35536	−0.677678	+	0.735359i	$0.737014\pi$
$948$	114.007	3.70277
$949$	64.0130	2.07795
$950$	143.860	4.66745
$951$	13.7252	0.445069
$952$	−52.7922	−1.71101
$953$	35.4747	1.14914	0.574569	−	0.818456i	$-0.305170\pi$
$953$	35.4747	1.14914	0.574569	+	0.818456i	$0.305170\pi$
$954$	−14.8641	−0.481243
$955$	−32.8500	−1.06300
$956$	18.4106	0.595441
$957$	−103.730	−3.35312
$958$	−56.5720	−1.82776
$959$	−18.8137	−0.607527
$960$	−93.9117	−3.03099
$961$	−30.9824	−0.999432
$962$	16.7372	0.539629
$963$	−1.57629	−0.0507952
$964$	−63.4585	−2.04386
$965$	−53.5718	−1.72454
$966$	−58.3148	−1.87625
$967$	17.0130	0.547100	0.273550	−	0.961858i	$-0.411802\pi$
$967$	17.0130	0.547100	0.273550	+	0.961858i	$0.411802\pi$
$968$	−70.7657	−2.27450
$969$	48.5099	1.55836
$970$	−150.066	−4.81831
$971$	−10.2644	−0.329400	−0.164700	−	0.986344i	$-0.552666\pi$
$971$	−10.2644	−0.329400	−0.164700	+	0.986344i	$0.552666\pi$
$972$	21.0739	0.675947
$973$	−9.09988	−0.291729
$974$	−23.8127	−0.763008
$975$	100.197	3.20888
$976$	2.81410	0.0900773
$977$	45.5027	1.45576	0.727881	−	0.685704i	$-0.240505\pi$
$977$	45.5027	1.45576	0.727881	+	0.685704i	$0.240505\pi$
$978$	55.5882	1.77751
$979$	−38.3176	−1.22463
$980$	−42.5253	−1.35842
$981$	−2.54763	−0.0813397
$982$	−41.7432	−1.33208
$983$	23.0587	0.735459	0.367730	−	0.929933i	$-0.380135\pi$
$983$	23.0587	0.735459	0.367730	+	0.929933i	$0.380135\pi$
$984$	−24.2832	−0.774120
$985$	−29.3390	−0.934819
$986$	−109.922	−3.50062
$987$	−47.6606	−1.51705
$988$	85.3421	2.71509
$989$	−38.6821	−1.23002
$990$	31.4408	0.999254
$991$	23.6496	0.751256	0.375628	−	0.926771i	$-0.377427\pi$
$991$	23.6496	0.751256	0.375628	+	0.926771i	$0.377427\pi$
$992$	−0.557820	−0.0177108
$993$	40.4360	1.28320
$994$	16.8344	0.533956
$995$	−13.1978	−0.418400
$996$	−50.0606	−1.58623
$997$	35.6067	1.12768	0.563838	−	0.825886i	$-0.309324\pi$
$997$	35.6067	1.12768	0.563838	+	0.825886i	$0.309324\pi$
$998$	63.2246	2.00134
$999$	7.10728	0.224864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.18	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.18	✓	179	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34196 q^{2} -1.89472 q^{3} +3.48479 q^{4} -4.06412 q^{5} +4.43736 q^{6} +3.16270 q^{7} -3.47733 q^{8} +0.589962 q^{9} +O(q^{10})\)	\(q-2.34196 q^{2} -1.89472 q^{3} +3.48479 q^{4} -4.06412 q^{5} +4.43736 q^{6} +3.16270 q^{7} -3.47733 q^{8} +0.589962 q^{9} +9.51803 q^{10} +5.59916 q^{11} -6.60270 q^{12} -4.59164 q^{13} -7.40692 q^{14} +7.70037 q^{15} +1.17419 q^{16} +4.80028 q^{17} -1.38167 q^{18} -5.33357 q^{19} -14.1626 q^{20} -5.99242 q^{21} -13.1130 q^{22} -4.15524 q^{23} +6.58856 q^{24} +11.5171 q^{25} +10.7535 q^{26} +4.56635 q^{27} +11.0213 q^{28} +9.77771 q^{29} -18.0340 q^{30} -0.132664 q^{31} +4.20474 q^{32} -10.6088 q^{33} -11.2421 q^{34} -12.8536 q^{35} +2.05589 q^{36} +1.55645 q^{37} +12.4910 q^{38} +8.69987 q^{39} +14.1323 q^{40} -3.68566 q^{41} +14.0340 q^{42} +9.30922 q^{43} +19.5119 q^{44} -2.39768 q^{45} +9.73143 q^{46} +7.95349 q^{47} -2.22477 q^{48} +3.00264 q^{49} -26.9726 q^{50} -9.09519 q^{51} -16.0009 q^{52} +10.7581 q^{53} -10.6942 q^{54} -22.7557 q^{55} -10.9977 q^{56} +10.1056 q^{57} -22.8990 q^{58} +12.0183 q^{59} +26.8342 q^{60} +2.39663 q^{61} +0.310695 q^{62} +1.86587 q^{63} -12.1957 q^{64} +18.6610 q^{65} +24.8455 q^{66} -2.16009 q^{67} +16.7280 q^{68} +7.87302 q^{69} +30.1026 q^{70} -2.27280 q^{71} -2.05149 q^{72} -13.9412 q^{73} -3.64515 q^{74} -21.8217 q^{75} -18.5864 q^{76} +17.7084 q^{77} -20.3748 q^{78} -17.2667 q^{79} -4.77207 q^{80} -10.4218 q^{81} +8.63168 q^{82} +7.58184 q^{83} -20.8823 q^{84} -19.5089 q^{85} -21.8019 q^{86} -18.5260 q^{87} -19.4701 q^{88} -6.84345 q^{89} +5.61527 q^{90} -14.5220 q^{91} -14.4802 q^{92} +0.251362 q^{93} -18.6268 q^{94} +21.6763 q^{95} -7.96680 q^{96} -15.7665 q^{97} -7.03208 q^{98} +3.30329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9} + 9 q^{10} + 46 q^{11} + 33 q^{12} + 47 q^{13} + 22 q^{14} + 36 q^{15} + 222 q^{16} + 103 q^{17} + 43 q^{18} + 12 q^{19} + 102 q^{20} + 50 q^{21} + 39 q^{22} + 121 q^{23} - 3 q^{24} + 246 q^{25} + 52 q^{26} + 49 q^{27} + 41 q^{28} + 138 q^{29} + 28 q^{30} + 5 q^{31} + 137 q^{32} + 63 q^{33} + 2 q^{34} + 72 q^{35} + 279 q^{36} + 118 q^{37} + 123 q^{38} + q^{39} + 9 q^{40} + 50 q^{41} + 48 q^{42} + 48 q^{43} + 108 q^{44} + 158 q^{45} + 13 q^{46} + 85 q^{47} + 50 q^{48} + 230 q^{49} + 78 q^{50} + 15 q^{51} + 41 q^{52} + 399 q^{53} - 5 q^{54} + 24 q^{55} + 53 q^{56} + 45 q^{57} + 27 q^{58} + 48 q^{59} + 66 q^{60} + 46 q^{61} + 81 q^{62} + 78 q^{63} + 252 q^{64} + 153 q^{65} + 6 q^{66} + 70 q^{67} + 240 q^{68} + 120 q^{69} - 31 q^{70} + 86 q^{71} + 89 q^{72} + 45 q^{73} + 68 q^{74} + 17 q^{75} - 13 q^{76} + 362 q^{77} + 69 q^{78} + 31 q^{79} + 169 q^{80} + 303 q^{81} + 25 q^{82} + 106 q^{83} + 13 q^{84} + 115 q^{85} + 95 q^{86} + 32 q^{87} + 83 q^{88} + 105 q^{89} - 38 q^{90} + 3 q^{91} + 310 q^{92} + 298 q^{93} - 17 q^{94} + 102 q^{95} - 82 q^{96} + 34 q^{97} + 81 q^{98} + 58 q^{99}+O(q^{100}) \) 179 * q + 22 * q^2 + 16 * q^3 + 196 * q^4 + 61 * q^5 + 7 * q^6 + 21 * q^7 + 60 * q^8 + 221 * q^9 + 9 * q^10 + 46 * q^11 + 33 * q^12 + 47 * q^13 + 22 * q^14 + 36 * q^15 + 222 * q^16 + 103 * q^17 + 43 * q^18 + 12 * q^19 + 102 * q^20 + 50 * q^21 + 39 * q^22 + 121 * q^23 - 3 * q^24 + 246 * q^25 + 52 * q^26 + 49 * q^27 + 41 * q^28 + 138 * q^29 + 28 * q^30 + 5 * q^31 + 137 * q^32 + 63 * q^33 + 2 * q^34 + 72 * q^35 + 279 * q^36 + 118 * q^37 + 123 * q^38 + q^39 + 9 * q^40 + 50 * q^41 + 48 * q^42 + 48 * q^43 + 108 * q^44 + 158 * q^45 + 13 * q^46 + 85 * q^47 + 50 * q^48 + 230 * q^49 + 78 * q^50 + 15 * q^51 + 41 * q^52 + 399 * q^53 - 5 * q^54 + 24 * q^55 + 53 * q^56 + 45 * q^57 + 27 * q^58 + 48 * q^59 + 66 * q^60 + 46 * q^61 + 81 * q^62 + 78 * q^63 + 252 * q^64 + 153 * q^65 + 6 * q^66 + 70 * q^67 + 240 * q^68 + 120 * q^69 - 31 * q^70 + 86 * q^71 + 89 * q^72 + 45 * q^73 + 68 * q^74 + 17 * q^75 - 13 * q^76 + 362 * q^77 + 69 * q^78 + 31 * q^79 + 169 * q^80 + 303 * q^81 + 25 * q^82 + 106 * q^83 + 13 * q^84 + 115 * q^85 + 95 * q^86 + 32 * q^87 + 83 * q^88 + 105 * q^89 - 38 * q^90 + 3 * q^91 + 310 * q^92 + 298 * q^93 - 17 * q^94 + 102 * q^95 - 82 * q^96 + 34 * q^97 + 81 * q^98 + 58 * q^99

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