LMFDB - Embedded newform 4003.2.a.c.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.39320 q^{2} +3.24043 q^{3} +3.72738 q^{4} +2.56572 q^{5} -7.75497 q^{6} -2.79627 q^{7} -4.13396 q^{8} +7.50035 q^{9} +O(q^{10})$	\(q-2.39320 q^{2} +3.24043 q^{3} +3.72738 q^{4} +2.56572 q^{5} -7.75497 q^{6} -2.79627 q^{7} -4.13396 q^{8} +7.50035 q^{9} -6.14026 q^{10} +3.51490 q^{11} +12.0783 q^{12} +1.02927 q^{13} +6.69203 q^{14} +8.31401 q^{15} +2.43862 q^{16} -3.64469 q^{17} -17.9498 q^{18} +2.31545 q^{19} +9.56340 q^{20} -9.06112 q^{21} -8.41183 q^{22} +2.99496 q^{23} -13.3958 q^{24} +1.58289 q^{25} -2.46325 q^{26} +14.5831 q^{27} -10.4228 q^{28} -4.24330 q^{29} -19.8970 q^{30} +3.21604 q^{31} +2.43184 q^{32} +11.3898 q^{33} +8.72245 q^{34} -7.17444 q^{35} +27.9567 q^{36} +3.62174 q^{37} -5.54132 q^{38} +3.33529 q^{39} -10.6066 q^{40} -5.65051 q^{41} +21.6850 q^{42} +8.47151 q^{43} +13.1014 q^{44} +19.2438 q^{45} -7.16753 q^{46} +10.2753 q^{47} +7.90215 q^{48} +0.819148 q^{49} -3.78818 q^{50} -11.8103 q^{51} +3.83650 q^{52} -5.05786 q^{53} -34.9001 q^{54} +9.01822 q^{55} +11.5597 q^{56} +7.50304 q^{57} +10.1550 q^{58} -0.487214 q^{59} +30.9895 q^{60} +3.39301 q^{61} -7.69660 q^{62} -20.9730 q^{63} -10.6971 q^{64} +2.64082 q^{65} -27.2579 q^{66} +0.382019 q^{67} -13.5852 q^{68} +9.70495 q^{69} +17.1698 q^{70} -5.02956 q^{71} -31.0062 q^{72} -9.64474 q^{73} -8.66754 q^{74} +5.12925 q^{75} +8.63057 q^{76} -9.82861 q^{77} -7.98199 q^{78} +9.13895 q^{79} +6.25679 q^{80} +24.7543 q^{81} +13.5228 q^{82} -7.62765 q^{83} -33.7742 q^{84} -9.35124 q^{85} -20.2740 q^{86} -13.7501 q^{87} -14.5305 q^{88} +8.23006 q^{89} -46.0541 q^{90} -2.87813 q^{91} +11.1634 q^{92} +10.4213 q^{93} -24.5909 q^{94} +5.94079 q^{95} +7.88021 q^{96} +5.19890 q^{97} -1.96038 q^{98} +26.3630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.39320	−1.69224	−0.846122	−	0.532989i	$-0.821069\pi$
$2$	−2.39320	−1.69224	−0.846122	+	0.532989i	$0.821069\pi$
$3$	3.24043	1.87086	0.935430	−	0.353512i	$-0.115013\pi$
$3$	3.24043	1.87086	0.935430	+	0.353512i	$0.115013\pi$
$4$	3.72738	1.86369
$5$	2.56572	1.14742	0.573711	−	0.819058i	$-0.305503\pi$
$5$	2.56572	1.14742	0.573711	+	0.819058i	$0.305503\pi$
$6$	−7.75497	−3.16595
$7$	−2.79627	−1.05689	−0.528446	−	0.848967i	$-0.677225\pi$
$7$	−2.79627	−1.05689	−0.528446	+	0.848967i	$0.677225\pi$
$8$	−4.13396	−1.46158
$9$	7.50035	2.50012
$10$	−6.14026	−1.94172
$11$	3.51490	1.05978	0.529891	−	0.848066i	$-0.322233\pi$
$11$	3.51490	1.05978	0.529891	+	0.848066i	$0.322233\pi$
$12$	12.0783	3.48671
$13$	1.02927	0.285469	0.142735	−	0.989761i	$-0.454410\pi$
$13$	1.02927	0.285469	0.142735	+	0.989761i	$0.454410\pi$
$14$	6.69203	1.78852
$15$	8.31401	2.14667
$16$	2.43862	0.609654
$17$	−3.64469	−0.883967	−0.441984	−	0.897023i	$-0.645725\pi$
$17$	−3.64469	−0.883967	−0.441984	+	0.897023i	$0.645725\pi$
$18$	−17.9498	−4.23081
$19$	2.31545	0.531201	0.265600	−	0.964083i	$-0.414430\pi$
$19$	2.31545	0.531201	0.265600	+	0.964083i	$0.414430\pi$
$20$	9.56340	2.13844
$21$	−9.06112	−1.97730
$22$	−8.41183	−1.79341
$23$	2.99496	0.624493	0.312246	−	0.950001i	$-0.398919\pi$
$23$	2.99496	0.624493	0.312246	+	0.950001i	$0.398919\pi$
$24$	−13.3958	−2.73441
$25$	1.58289	0.316579
$26$	−2.46325	−0.483084
$27$	14.5831	2.80651
$28$	−10.4228	−1.96972
$29$	−4.24330	−0.787961	−0.393980	−	0.919119i	$-0.628902\pi$
$29$	−4.24330	−0.787961	−0.393980	+	0.919119i	$0.628902\pi$
$30$	−19.8970	−3.63269
$31$	3.21604	0.577617	0.288809	−	0.957387i	$-0.406741\pi$
$31$	3.21604	0.577617	0.288809	+	0.957387i	$0.406741\pi$
$32$	2.43184	0.429893
$33$	11.3898	1.98270
$34$	8.72245	1.49589
$35$	−7.17444	−1.21270
$36$	27.9567	4.65945
$37$	3.62174	0.595411	0.297705	−	0.954658i	$-0.403779\pi$
$37$	3.62174	0.595411	0.297705	+	0.954658i	$0.403779\pi$
$38$	−5.54132	−0.898922
$39$	3.33529	0.534073
$40$	−10.6066	−1.67705
$41$	−5.65051	−0.882462	−0.441231	−	0.897394i	$-0.645458\pi$
$41$	−5.65051	−0.882462	−0.441231	+	0.897394i	$0.645458\pi$
$42$	21.6850	3.34607
$43$	8.47151	1.29189	0.645946	−	0.763383i	$-0.276463\pi$
$43$	8.47151	1.29189	0.645946	+	0.763383i	$0.276463\pi$
$44$	13.1014	1.97511
$45$	19.2438	2.86869
$46$	−7.16753	−1.05679
$47$	10.2753	1.49881	0.749407	−	0.662110i	$-0.230339\pi$
$47$	10.2753	1.49881	0.749407	+	0.662110i	$0.230339\pi$
$48$	7.90215	1.14058
$49$	0.819148	0.117021
$50$	−3.78818	−0.535729
$51$	−11.8103	−1.65378
$52$	3.83650	0.532027
$53$	−5.05786	−0.694751	−0.347375	−	0.937726i	$-0.612927\pi$
$53$	−5.05786	−0.694751	−0.347375	+	0.937726i	$0.612927\pi$
$54$	−34.9001	−4.74930
$55$	9.01822	1.21602
$56$	11.5597	1.54473
$57$	7.50304	0.993802
$58$	10.1550	1.33342
$59$	−0.487214	−0.0634299	−0.0317150	−	0.999497i	$-0.510097\pi$
$59$	−0.487214	−0.0634299	−0.0317150	+	0.999497i	$0.510097\pi$
$60$	30.9895	4.00073
$61$	3.39301	0.434430	0.217215	−	0.976124i	$-0.430303\pi$
$61$	3.39301	0.434430	0.217215	+	0.976124i	$0.430303\pi$
$62$	−7.69660	−0.977470
$63$	−20.9730	−2.64236
$64$	−10.6971	−1.33714
$65$	2.64082	0.327554
$66$	−27.2579	−3.35522
$67$	0.382019	0.0466710	0.0233355	−	0.999728i	$-0.492571\pi$
$67$	0.382019	0.0466710	0.0233355	+	0.999728i	$0.492571\pi$
$68$	−13.5852	−1.64744
$69$	9.70495	1.16834
$70$	17.1698	2.05219
$71$	−5.02956	−0.596899	−0.298450	−	0.954425i	$-0.596469\pi$
$71$	−5.02956	−0.596899	−0.298450	+	0.954425i	$0.596469\pi$
$72$	−31.0062	−3.65411
$73$	−9.64474	−1.12883	−0.564416	−	0.825491i	$-0.690899\pi$
$73$	−9.64474	−1.12883	−0.564416	+	0.825491i	$0.690899\pi$
$74$	−8.66754	−1.00758
$75$	5.12925	0.592275
$76$	8.63057	0.989994
$77$	−9.82861	−1.12007
$78$	−7.98199	−0.903783
$79$	9.13895	1.02821	0.514106	−	0.857727i	$-0.328124\pi$
$79$	9.13895	1.02821	0.514106	+	0.857727i	$0.328124\pi$
$80$	6.25679	0.699531
$81$	24.7543	2.75047
$82$	13.5228	1.49334
$83$	−7.62765	−0.837243	−0.418622	−	0.908161i	$-0.637487\pi$
$83$	−7.62765	−0.837243	−0.418622	+	0.908161i	$0.637487\pi$
$84$	−33.7742	−3.68507
$85$	−9.35124	−1.01428
$86$	−20.2740	−2.18620
$87$	−13.7501	−1.47416
$88$	−14.5305	−1.54895
$89$	8.23006	0.872385	0.436192	−	0.899853i	$-0.356327\pi$
$89$	8.23006	0.872385	0.436192	+	0.899853i	$0.356327\pi$
$90$	−46.0541	−4.85453
$91$	−2.87813	−0.301710
$92$	11.1634	1.16386
$93$	10.4213	1.08064
$94$	−24.5909	−2.53636
$95$	5.94079	0.609512
$96$	7.88021	0.804270
$97$	5.19890	0.527868	0.263934	−	0.964541i	$-0.414980\pi$
$97$	5.19890	0.527868	0.263934	+	0.964541i	$0.414980\pi$
$98$	−1.96038	−0.198028
$99$	26.3630	2.64958
$100$	5.90005	0.590005
$101$	0.980373	0.0975508	0.0487754	−	0.998810i	$-0.484468\pi$
$101$	0.980373	0.0975508	0.0487754	+	0.998810i	$0.484468\pi$
$102$	28.2645	2.79860
$103$	9.87016	0.972536	0.486268	−	0.873810i	$-0.338358\pi$
$103$	9.87016	0.972536	0.486268	+	0.873810i	$0.338358\pi$
$104$	−4.25498	−0.417235
$105$	−23.2482	−2.26880
$106$	12.1045	1.17569
$107$	−0.364181	−0.0352067	−0.0176033	−	0.999845i	$-0.505604\pi$
$107$	−0.364181	−0.0352067	−0.0176033	+	0.999845i	$0.505604\pi$
$108$	54.3566	5.23047
$109$	−4.06581	−0.389434	−0.194717	−	0.980859i	$-0.562379\pi$
$109$	−4.06581	−0.389434	−0.194717	+	0.980859i	$0.562379\pi$
$110$	−21.5824	−2.05780
$111$	11.7360	1.11393
$112$	−6.81904	−0.644339
$113$	−8.80074	−0.827904	−0.413952	−	0.910299i	$-0.635852\pi$
$113$	−8.80074	−0.827904	−0.413952	+	0.910299i	$0.635852\pi$
$114$	−17.9562	−1.68176
$115$	7.68422	0.716557
$116$	−15.8164	−1.46852
$117$	7.71992	0.713707
$118$	1.16600	0.107339
$119$	10.1916	0.934258
$120$	−34.3698	−3.13752
$121$	1.35450	0.123136
$122$	−8.12013	−0.735162
$123$	−18.3101	−1.65096
$124$	11.9874	1.07650
$125$	−8.76732	−0.784173
$126$	50.1926	4.47151
$127$	1.96533	0.174395	0.0871975	−	0.996191i	$-0.472209\pi$
$127$	1.96533	0.174395	0.0871975	+	0.996191i	$0.472209\pi$
$128$	20.7366	1.83287
$129$	27.4513	2.41695
$130$	−6.32001	−0.554301
$131$	16.1691	1.41270	0.706351	−	0.707861i	$-0.250340\pi$
$131$	16.1691	1.41270	0.706351	+	0.707861i	$0.250340\pi$
$132$	42.4540	3.69515
$133$	−6.47463	−0.561422
$134$	−0.914245	−0.0789788
$135$	37.4160	3.22025
$136$	15.0670	1.29199
$137$	7.28342	0.622265	0.311132	−	0.950367i	$-0.399292\pi$
$137$	7.28342	0.622265	0.311132	+	0.950367i	$0.399292\pi$
$138$	−23.2258	−1.97711
$139$	−1.44687	−0.122722	−0.0613611	−	0.998116i	$-0.519544\pi$
$139$	−1.44687	−0.122722	−0.0613611	+	0.998116i	$0.519544\pi$
$140$	−26.7419	−2.26010
$141$	33.2965	2.80407
$142$	12.0367	1.01010
$143$	3.61779	0.302535
$144$	18.2905	1.52421
$145$	−10.8871	−0.904124
$146$	23.0817	1.91026
$147$	2.65439	0.218930
$148$	13.4996	1.10966
$149$	2.08460	0.170777	0.0853886	−	0.996348i	$-0.472787\pi$
$149$	2.08460	0.170777	0.0853886	+	0.996348i	$0.472787\pi$
$150$	−12.2753	−1.00227
$151$	−10.8854	−0.885841	−0.442921	−	0.896561i	$-0.646058\pi$
$151$	−10.8854	−0.885841	−0.442921	+	0.896561i	$0.646058\pi$
$152$	−9.57199	−0.776391
$153$	−27.3365	−2.21002
$154$	23.5218	1.89544
$155$	8.25144	0.662771
$156$	12.4319	0.995348
$157$	6.84560	0.546338	0.273169	−	0.961966i	$-0.411928\pi$
$157$	6.84560	0.546338	0.273169	+	0.961966i	$0.411928\pi$
$158$	−21.8713	−1.73999
$159$	−16.3896	−1.29978
$160$	6.23942	0.493269
$161$	−8.37474	−0.660022
$162$	−59.2418	−4.65447
$163$	5.76269	0.451369	0.225685	−	0.974200i	$-0.427538\pi$
$163$	5.76269	0.451369	0.225685	+	0.974200i	$0.427538\pi$
$164$	−21.0616	−1.64464
$165$	29.2229	2.27500
$166$	18.2545	1.41682
$167$	8.27564	0.640388	0.320194	−	0.947352i	$-0.396252\pi$
$167$	8.27564	0.640388	0.320194	+	0.947352i	$0.396252\pi$
$168$	37.4583	2.88997
$169$	−11.9406	−0.918507
$170$	22.3793	1.71642
$171$	17.3667	1.32806
$172$	31.5765	2.40769
$173$	20.1595	1.53270	0.766349	−	0.642424i	$-0.222071\pi$
$173$	20.1595	1.53270	0.766349	+	0.642424i	$0.222071\pi$
$174$	32.9067	2.49465
$175$	−4.42621	−0.334590
$176$	8.57148	0.646100
$177$	−1.57878	−0.118668
$178$	−19.6961	−1.47629
$179$	19.4815	1.45611	0.728057	−	0.685517i	$-0.240424\pi$
$179$	19.4815	1.45611	0.728057	+	0.685517i	$0.240424\pi$
$180$	71.7289	5.34636
$181$	−11.8313	−0.879416	−0.439708	−	0.898141i	$-0.644918\pi$
$181$	−11.8313	−0.879416	−0.439708	+	0.898141i	$0.644918\pi$
$182$	6.88793	0.510568
$183$	10.9948	0.812758
$184$	−12.3811	−0.912744
$185$	9.29236	0.683188
$186$	−24.9403	−1.82871
$187$	−12.8107	−0.936812
$188$	38.3002	2.79333
$189$	−40.7782	−2.96618
$190$	−14.2175	−1.03144
$191$	18.8169	1.36154	0.680772	−	0.732496i	$-0.261645\pi$
$191$	18.8169	1.36154	0.680772	+	0.732496i	$0.261645\pi$
$192$	−34.6632	−2.50160
$193$	−23.4427	−1.68744	−0.843720	−	0.536784i	$-0.819639\pi$
$193$	−23.4427	−1.68744	−0.843720	+	0.536784i	$0.819639\pi$
$194$	−12.4420	−0.893282
$195$	8.55740	0.612808
$196$	3.05328	0.218091
$197$	26.0328	1.85476	0.927379	−	0.374124i	$-0.122057\pi$
$197$	26.0328	1.85476	0.927379	+	0.374124i	$0.122057\pi$
$198$	−63.0917	−4.48373
$199$	−27.0208	−1.91546	−0.957728	−	0.287677i	$-0.907117\pi$
$199$	−27.0208	−1.91546	−0.957728	+	0.287677i	$0.907117\pi$
$200$	−6.54363	−0.462704
$201$	1.23790	0.0873149
$202$	−2.34622	−0.165080
$203$	11.8654	0.832790
$204$	−44.0217	−3.08213
$205$	−14.4976	−1.01256
$206$	−23.6212	−1.64577
$207$	22.4633	1.56131
$208$	2.51000	0.174038
$209$	8.13857	0.562957
$210$	55.6376	3.83936
$211$	−16.7660	−1.15422	−0.577109	−	0.816667i	$-0.695819\pi$
$211$	−16.7660	−1.15422	−0.577109	+	0.816667i	$0.695819\pi$
$212$	−18.8526	−1.29480
$213$	−16.2979	−1.11671
$214$	0.871555	0.0595783
$215$	21.7355	1.48235
$216$	−60.2858	−4.10193
$217$	−8.99292	−0.610479
$218$	9.73027	0.659017
$219$	−31.2531	−2.11189
$220$	33.6144	2.26628
$221$	−3.75139	−0.252346
$222$	−28.0865	−1.88504
$223$	16.6625	1.11581	0.557903	−	0.829906i	$-0.311606\pi$
$223$	16.6625	1.11581	0.557903	+	0.829906i	$0.311606\pi$
$224$	−6.80010	−0.454351
$225$	11.8723	0.791485
$226$	21.0619	1.40102
$227$	−17.2095	−1.14223	−0.571116	−	0.820870i	$-0.693489\pi$
$227$	−17.2095	−1.14223	−0.571116	+	0.820870i	$0.693489\pi$
$228$	27.9667	1.85214
$229$	−23.7039	−1.56640	−0.783199	−	0.621771i	$-0.786413\pi$
$229$	−23.7039	−1.56640	−0.783199	+	0.621771i	$0.786413\pi$
$230$	−18.3898	−1.21259
$231$	−31.8489	−2.09550
$232$	17.5416	1.15167
$233$	−5.94633	−0.389557	−0.194779	−	0.980847i	$-0.562399\pi$
$233$	−5.94633	−0.389557	−0.194779	+	0.980847i	$0.562399\pi$
$234$	−18.4753	−1.20777
$235$	26.3636	1.71977
$236$	−1.81603	−0.118214
$237$	29.6141	1.92364
$238$	−24.3904	−1.58099
$239$	−7.67611	−0.496526	−0.248263	−	0.968693i	$-0.579860\pi$
$239$	−7.67611	−0.496526	−0.248263	+	0.968693i	$0.579860\pi$
$240$	20.2747	1.30872
$241$	−13.2541	−0.853770	−0.426885	−	0.904306i	$-0.640389\pi$
$241$	−13.2541	−0.853770	−0.426885	+	0.904306i	$0.640389\pi$
$242$	−3.24158	−0.208377
$243$	36.4651	2.33924
$244$	12.6470	0.809643
$245$	2.10170	0.134273
$246$	43.8196	2.79383
$247$	2.38323	0.151642
$248$	−13.2950	−0.844232
$249$	−24.7168	−1.56637
$250$	20.9819	1.32701
$251$	−12.1700	−0.768161	−0.384081	−	0.923300i	$-0.625482\pi$
$251$	−12.1700	−0.768161	−0.384081	+	0.923300i	$0.625482\pi$
$252$	−78.1746	−4.92453
$253$	10.5270	0.661826
$254$	−4.70342	−0.295119
$255$	−30.3020	−1.89758
$256$	−28.2325	−1.76453
$257$	16.8474	1.05091	0.525457	−	0.850820i	$-0.323894\pi$
$257$	16.8474	1.05091	0.525457	+	0.850820i	$0.323894\pi$
$258$	−65.6963	−4.09007
$259$	−10.1274	−0.629285
$260$	9.84336	0.610460
$261$	−31.8262	−1.97000
$262$	−38.6959	−2.39064
$263$	−10.6177	−0.654718	−0.327359	−	0.944900i	$-0.606159\pi$
$263$	−10.6177	−0.654718	−0.327359	+	0.944900i	$0.606159\pi$
$264$	−47.0848	−2.89787
$265$	−12.9770	−0.797173
$266$	15.4951	0.950063
$267$	26.6689	1.63211
$268$	1.42393	0.0869804
$269$	−18.0469	−1.10034	−0.550170	−	0.835053i	$-0.685437\pi$
$269$	−18.0469	−1.10034	−0.550170	+	0.835053i	$0.685437\pi$
$270$	−89.5437	−5.44946
$271$	−23.0879	−1.40249	−0.701244	−	0.712921i	$-0.747372\pi$
$271$	−23.0879	−1.40249	−0.701244	+	0.712921i	$0.747372\pi$
$272$	−8.88800	−0.538914
$273$	−9.32637	−0.564458
$274$	−17.4307	−1.05302
$275$	5.56371	0.335504
$276$	36.1741	2.17742
$277$	19.4987	1.17156	0.585782	−	0.810469i	$-0.300788\pi$
$277$	19.4987	1.17156	0.585782	+	0.810469i	$0.300788\pi$
$278$	3.46265	0.207676
$279$	24.1214	1.44411
$280$	29.6589	1.77246
$281$	0.311221	0.0185659	0.00928294	−	0.999957i	$-0.497045\pi$
$281$	0.311221	0.0185659	0.00928294	+	0.999957i	$0.497045\pi$
$282$	−79.6850	−4.74517
$283$	−7.03041	−0.417915	−0.208957	−	0.977925i	$-0.567007\pi$
$283$	−7.03041	−0.417915	−0.208957	+	0.977925i	$0.567007\pi$
$284$	−18.7471	−1.11244
$285$	19.2507	1.14031
$286$	−8.65808	−0.511963
$287$	15.8004	0.932667
$288$	18.2397	1.07478
$289$	−3.71624	−0.218602
$290$	26.0549	1.53000
$291$	16.8466	0.987568
$292$	−35.9496	−2.10379
$293$	3.91062	0.228461	0.114230	−	0.993454i	$-0.463560\pi$
$293$	3.91062	0.228461	0.114230	+	0.993454i	$0.463560\pi$
$294$	−6.35247	−0.370484
$295$	−1.25005	−0.0727809
$296$	−14.9721	−0.870238
$297$	51.2580	2.97429
$298$	−4.98886	−0.288997
$299$	3.08264	0.178274
$300$	19.1187	1.10382
$301$	−23.6887	−1.36539
$302$	26.0509	1.49906
$303$	3.17683	0.182504
$304$	5.64649	0.323849
$305$	8.70549	0.498475
$306$	65.4215	3.73990
$307$	25.2624	1.44180	0.720902	−	0.693037i	$-0.243728\pi$
$307$	25.2624	1.44180	0.720902	+	0.693037i	$0.243728\pi$
$308$	−36.6350	−2.08747
$309$	31.9835	1.81948
$310$	−19.7473	−1.12157
$311$	21.0704	1.19479	0.597395	−	0.801947i	$-0.296202\pi$
$311$	21.0704	1.19479	0.597395	+	0.801947i	$0.296202\pi$
$312$	−13.7880	−0.780589
$313$	−8.77657	−0.496081	−0.248041	−	0.968750i	$-0.579787\pi$
$313$	−8.77657	−0.496081	−0.248041	+	0.968750i	$0.579787\pi$
$314$	−16.3829	−0.924538
$315$	−53.8109	−3.03190
$316$	34.0644	1.91627
$317$	−31.9380	−1.79382	−0.896908	−	0.442216i	$-0.854192\pi$
$317$	−31.9380	−1.79382	−0.896908	+	0.442216i	$0.854192\pi$
$318$	39.2236	2.19955
$319$	−14.9148	−0.835066
$320$	−27.4457	−1.53426
$321$	−1.18010	−0.0658668
$322$	20.0424	1.11692
$323$	−8.43910	−0.469564
$324$	92.2686	5.12603
$325$	1.62923	0.0903736
$326$	−13.7913	−0.763827
$327$	−13.1749	−0.728576
$328$	23.3590	1.28979
$329$	−28.7327	−1.58408
$330$	−69.9360	−3.84985
$331$	−8.71438	−0.478986	−0.239493	−	0.970898i	$-0.576981\pi$
$331$	−8.71438	−0.478986	−0.239493	+	0.970898i	$0.576981\pi$
$332$	−28.4312	−1.56036
$333$	27.1643	1.48860
$334$	−19.8052	−1.08369
$335$	0.980151	0.0535514
$336$	−22.0966	−1.20547
$337$	25.4145	1.38442	0.692208	−	0.721698i	$-0.256638\pi$
$337$	25.4145	1.38442	0.692208	+	0.721698i	$0.256638\pi$
$338$	28.5762	1.55434
$339$	−28.5181	−1.54889
$340$	−34.8556	−1.89031
$341$	11.3040	0.612148
$342$	−41.5619	−2.24741
$343$	17.2834	0.933213
$344$	−35.0209	−1.88820
$345$	24.9001	1.34058
$346$	−48.2456	−2.59370
$347$	−5.40936	−0.290390	−0.145195	−	0.989403i	$-0.546381\pi$
$347$	−5.40936	−0.290390	−0.145195	+	0.989403i	$0.546381\pi$
$348$	−51.2519	−2.74739
$349$	4.76821	0.255237	0.127618	−	0.991823i	$-0.459267\pi$
$349$	4.76821	0.255237	0.127618	+	0.991823i	$0.459267\pi$
$350$	10.5928	0.566208
$351$	15.0100	0.801173
$352$	8.54768	0.455593
$353$	−24.2744	−1.29199	−0.645997	−	0.763340i	$-0.723558\pi$
$353$	−24.2744	−1.29199	−0.645997	+	0.763340i	$0.723558\pi$
$354$	3.77833	0.200816
$355$	−12.9044	−0.684896
$356$	30.6766	1.62586
$357$	33.0250	1.74787
$358$	−46.6230	−2.46410
$359$	15.2658	0.805699	0.402849	−	0.915266i	$-0.368020\pi$
$359$	15.2658	0.805699	0.402849	+	0.915266i	$0.368020\pi$
$360$	−79.5531	−4.19281
$361$	−13.6387	−0.717826
$362$	28.3147	1.48819
$363$	4.38915	0.230371
$364$	−10.7279	−0.562295
$365$	−24.7457	−1.29525
$366$	−26.3127	−1.37538
$367$	0.287626	0.0150140	0.00750698	−	0.999972i	$-0.497610\pi$
$367$	0.287626	0.0150140	0.00750698	+	0.999972i	$0.497610\pi$
$368$	7.30356	0.380725
$369$	−42.3809	−2.20626
$370$	−22.2384	−1.15612
$371$	14.1432	0.734277
$372$	38.8443	2.01398
$373$	−1.93480	−0.100180	−0.0500902	−	0.998745i	$-0.515951\pi$
$373$	−1.93480	−0.100180	−0.0500902	+	0.998745i	$0.515951\pi$
$374$	30.6585	1.58531
$375$	−28.4098	−1.46708
$376$	−42.4779	−2.19063
$377$	−4.36752	−0.224939
$378$	97.5903	5.01950
$379$	−19.8120	−1.01767	−0.508836	−	0.860863i	$-0.669924\pi$
$379$	−19.8120	−1.01767	−0.508836	+	0.860863i	$0.669924\pi$
$380$	22.1436	1.13594
$381$	6.36851	0.326269
$382$	−45.0325	−2.30406
$383$	−36.9164	−1.88634	−0.943171	−	0.332308i	$-0.892173\pi$
$383$	−36.9164	−1.88634	−0.943171	+	0.332308i	$0.892173\pi$
$384$	67.1953	3.42905
$385$	−25.2174	−1.28520
$386$	56.1029	2.85556
$387$	63.5393	3.22988
$388$	19.3783	0.983784
$389$	10.2935	0.521899	0.260950	−	0.965352i	$-0.415964\pi$
$389$	10.2935	0.521899	0.260950	+	0.965352i	$0.415964\pi$
$390$	−20.4795	−1.03702
$391$	−10.9157	−0.552031
$392$	−3.38633	−0.171035
$393$	52.3948	2.64297
$394$	−62.3015	−3.13870
$395$	23.4479	1.17979
$396$	98.2649	4.93800
$397$	23.3327	1.17103	0.585517	−	0.810660i	$-0.300892\pi$
$397$	23.3327	1.17103	0.585517	+	0.810660i	$0.300892\pi$
$398$	64.6661	3.24142
$399$	−20.9806	−1.05034
$400$	3.86007	0.193004
$401$	19.8949	0.993504	0.496752	−	0.867893i	$-0.334526\pi$
$401$	19.8949	0.993504	0.496752	+	0.867893i	$0.334526\pi$
$402$	−2.96254	−0.147758
$403$	3.31018	0.164892
$404$	3.65423	0.181805
$405$	63.5124	3.15595
$406$	−28.3963	−1.40928
$407$	12.7300	0.631005
$408$	48.8235	2.41713
$409$	−1.15423	−0.0570729	−0.0285365	−	0.999593i	$-0.509085\pi$
$409$	−1.15423	−0.0570729	−0.0285365	+	0.999593i	$0.509085\pi$
$410$	34.6956	1.71349
$411$	23.6014	1.16417
$412$	36.7899	1.81251
$413$	1.36238	0.0670386
$414$	−53.7590	−2.64211
$415$	−19.5704	−0.960672
$416$	2.50303	0.122721
$417$	−4.68849	−0.229596
$418$	−19.4772	−0.952660
$419$	3.46098	0.169080	0.0845399	−	0.996420i	$-0.473058\pi$
$419$	3.46098	0.169080	0.0845399	+	0.996420i	$0.473058\pi$
$420$	−86.6551	−4.22834
$421$	23.6303	1.15167	0.575834	−	0.817566i	$-0.304677\pi$
$421$	23.6303	1.15167	0.575834	+	0.817566i	$0.304677\pi$
$422$	40.1243	1.95322
$423$	77.0688	3.74721
$424$	20.9090	1.01543
$425$	−5.76916	−0.279845
$426$	39.0041	1.88975
$427$	−9.48778	−0.459146
$428$	−1.35744	−0.0656144
$429$	11.7232	0.566001
$430$	−52.0172	−2.50849
$431$	−29.3418	−1.41334	−0.706671	−	0.707542i	$-0.749804\pi$
$431$	−29.3418	−1.41334	−0.706671	+	0.707542i	$0.749804\pi$
$432$	35.5625	1.71100
$433$	−17.4920	−0.840610	−0.420305	−	0.907383i	$-0.638077\pi$
$433$	−17.4920	−0.840610	−0.420305	+	0.907383i	$0.638077\pi$
$434$	21.5218	1.03308
$435$	−35.2788	−1.69149
$436$	−15.1548	−0.725784
$437$	6.93469	0.331731
$438$	74.7947	3.57383
$439$	26.6785	1.27329	0.636647	−	0.771155i	$-0.280321\pi$
$439$	26.6785	1.27329	0.636647	+	0.771155i	$0.280321\pi$
$440$	−37.2810	−1.77730
$441$	6.14390	0.292567
$442$	8.97780	0.427030
$443$	−17.4828	−0.830631	−0.415316	−	0.909677i	$-0.636329\pi$
$443$	−17.4828	−0.830631	−0.415316	+	0.909677i	$0.636329\pi$
$444$	43.7445	2.07602
$445$	21.1160	1.00099
$446$	−39.8767	−1.88822
$447$	6.75500	0.319500
$448$	29.9120	1.41321
$449$	−32.5296	−1.53517	−0.767584	−	0.640949i	$-0.778541\pi$
$449$	−32.5296	−1.53517	−0.767584	+	0.640949i	$0.778541\pi$
$450$	−28.4127	−1.33939
$451$	−19.8610	−0.935217
$452$	−32.8037	−1.54296
$453$	−35.2733	−1.65728
$454$	41.1856	1.93294
$455$	−7.38447	−0.346189
$456$	−31.0173	−1.45252
$457$	20.3357	0.951263	0.475632	−	0.879645i	$-0.342220\pi$
$457$	20.3357	0.951263	0.475632	+	0.879645i	$0.342220\pi$
$458$	56.7281	2.65073
$459$	−53.1507	−2.48086
$460$	28.6420	1.33544
$461$	36.5773	1.70358	0.851788	−	0.523887i	$-0.175519\pi$
$461$	36.5773	1.70358	0.851788	+	0.523887i	$0.175519\pi$
$462$	76.2206	3.54610
$463$	−11.8926	−0.552697	−0.276349	−	0.961057i	$-0.589124\pi$
$463$	−11.8926	−0.552697	−0.276349	+	0.961057i	$0.589124\pi$
$464$	−10.3478	−0.480383
$465$	26.7382	1.23995
$466$	14.2307	0.659226
$467$	19.7127	0.912195	0.456097	−	0.889930i	$-0.349247\pi$
$467$	19.7127	0.912195	0.456097	+	0.889930i	$0.349247\pi$
$468$	28.7751	1.33013
$469$	−1.06823	−0.0493262
$470$	−63.0933	−2.91028
$471$	22.1827	1.02212
$472$	2.01413	0.0927077
$473$	29.7765	1.36912
$474$	−70.8723	−3.25527
$475$	3.66511	0.168167
$476$	37.9878	1.74117
$477$	−37.9358	−1.73696
$478$	18.3704	0.840244
$479$	−31.6469	−1.44598	−0.722992	−	0.690857i	$-0.757234\pi$
$479$	−31.6469	−1.44598	−0.722992	+	0.690857i	$0.757234\pi$
$480$	20.2184	0.922838
$481$	3.72777	0.169972
$482$	31.7196	1.44479
$483$	−27.1377	−1.23481
$484$	5.04874	0.229488
$485$	13.3389	0.605688
$486$	−87.2681	−3.95856
$487$	−14.4351	−0.654118	−0.327059	−	0.945004i	$-0.606058\pi$
$487$	−14.4351	−0.654118	−0.327059	+	0.945004i	$0.606058\pi$
$488$	−14.0266	−0.634953
$489$	18.6736	0.844448
$490$	−5.02978	−0.227222
$491$	−25.8128	−1.16492	−0.582459	−	0.812860i	$-0.697909\pi$
$491$	−25.8128	−1.16492	−0.582459	+	0.812860i	$0.697909\pi$
$492$	−68.2486	−3.07689
$493$	15.4655	0.696532
$494$	−5.70354	−0.256615
$495$	67.6399	3.04019
$496$	7.84268	0.352147
$497$	14.0640	0.630858
$498$	59.1522	2.65067
$499$	−14.8504	−0.664793	−0.332397	−	0.943140i	$-0.607857\pi$
$499$	−14.8504	−0.664793	−0.332397	+	0.943140i	$0.607857\pi$
$500$	−32.6792	−1.46146
$501$	26.8166	1.19808
$502$	29.1251	1.29992
$503$	18.5348	0.826426	0.413213	−	0.910634i	$-0.364407\pi$
$503$	18.5348	0.826426	0.413213	+	0.910634i	$0.364407\pi$
$504$	86.7018	3.86201
$505$	2.51536	0.111932
$506$	−25.1931	−1.11997
$507$	−38.6926	−1.71840
$508$	7.32555	0.325019
$509$	1.60638	0.0712015	0.0356008	−	0.999366i	$-0.488666\pi$
$509$	1.60638	0.0712015	0.0356008	+	0.999366i	$0.488666\pi$
$510$	72.5185	3.21118
$511$	26.9693	1.19305
$512$	26.0926	1.15314
$513$	33.7664	1.49082
$514$	−40.3192	−1.77840
$515$	25.3240	1.11591
$516$	102.321	4.50445
$517$	36.1168	1.58841
$518$	24.2368	1.06490
$519$	65.3254	2.86746
$520$	−10.9171	−0.478745
$521$	26.0587	1.14165	0.570826	−	0.821071i	$-0.306623\pi$
$521$	26.0587	1.14165	0.570826	+	0.821071i	$0.306623\pi$
$522$	76.1664	3.33371
$523$	−6.65022	−0.290794	−0.145397	−	0.989373i	$-0.546446\pi$
$523$	−6.65022	−0.290794	−0.145397	+	0.989373i	$0.546446\pi$
$524$	60.2685	2.63284
$525$	−14.3428	−0.625971
$526$	25.4103	1.10794
$527$	−11.7215	−0.510595
$528$	27.7752	1.20876
$529$	−14.0302	−0.610009
$530$	31.0566	1.34901
$531$	−3.65428	−0.158582
$532$	−24.1334	−1.04632
$533$	−5.81593	−0.251916
$534$	−63.8239	−2.76193
$535$	−0.934384	−0.0403969
$536$	−1.57925	−0.0682133
$537$	63.1282	2.72418
$538$	43.1898	1.86204
$539$	2.87922	0.124017
$540$	139.464	6.00156
$541$	−5.19518	−0.223358	−0.111679	−	0.993744i	$-0.535623\pi$
$541$	−5.19518	−0.223358	−0.111679	+	0.993744i	$0.535623\pi$
$542$	55.2538	2.37335
$543$	−38.3385	−1.64526
$544$	−8.86332	−0.380012
$545$	−10.4317	−0.446845
$546$	22.3198	0.955201
$547$	−6.07215	−0.259626	−0.129813	−	0.991538i	$-0.541438\pi$
$547$	−6.07215	−0.259626	−0.129813	+	0.991538i	$0.541438\pi$
$548$	27.1481	1.15971
$549$	25.4488	1.08613
$550$	−13.3150	−0.567755
$551$	−9.82515	−0.418565
$552$	−40.1199	−1.70762
$553$	−25.5550	−1.08671
$554$	−46.6642	−1.98257
$555$	30.1112	1.27815
$556$	−5.39305	−0.228716
$557$	−0.316767	−0.0134218	−0.00671092	−	0.999977i	$-0.502136\pi$
$557$	−0.316767	−0.0134218	−0.00671092	+	0.999977i	$0.502136\pi$
$558$	−57.7273	−2.44379
$559$	8.71951	0.368796
$560$	−17.4957	−0.739329
$561$	−41.5121	−1.75264
$562$	−0.744813	−0.0314180
$563$	30.7402	1.29554	0.647772	−	0.761834i	$-0.275701\pi$
$563$	30.7402	1.29554	0.647772	+	0.761834i	$0.275701\pi$
$564$	124.109	5.22592
$565$	−22.5802	−0.949956
$566$	16.8252	0.707214
$567$	−69.2197	−2.90695
$568$	20.7920	0.872414
$569$	22.2385	0.932287	0.466143	−	0.884709i	$-0.345643\pi$
$569$	22.2385	0.932287	0.466143	+	0.884709i	$0.345643\pi$
$570$	−46.0706	−1.92969
$571$	−24.6105	−1.02992	−0.514958	−	0.857215i	$-0.672193\pi$
$571$	−24.6105	−1.02992	−0.514958	+	0.857215i	$0.672193\pi$
$572$	13.4849	0.563832
$573$	60.9748	2.54726
$574$	−37.8134	−1.57830
$575$	4.74071	0.197701
$576$	−80.2321	−3.34300
$577$	−18.3153	−0.762474	−0.381237	−	0.924477i	$-0.624502\pi$
$577$	−18.3153	−0.762474	−0.381237	+	0.924477i	$0.624502\pi$
$578$	8.89368	0.369928
$579$	−75.9642	−3.15696
$580$	−40.5804	−1.68501
$581$	21.3290	0.884876
$582$	−40.3173	−1.67121
$583$	−17.7779	−0.736284
$584$	39.8710	1.64987
$585$	19.8071	0.818924
$586$	−9.35886	−0.386611
$587$	−30.9110	−1.27583	−0.637917	−	0.770105i	$-0.720204\pi$
$587$	−30.9110	−1.27583	−0.637917	+	0.770105i	$0.720204\pi$
$588$	9.89392	0.408019
$589$	7.44657	0.306831
$590$	2.99162	0.123163
$591$	84.3572	3.46999
$592$	8.83204	0.362995
$593$	36.4996	1.49886	0.749429	−	0.662084i	$-0.230328\pi$
$593$	36.4996	1.49886	0.749429	+	0.662084i	$0.230328\pi$
$594$	−122.670	−5.03322
$595$	26.1486	1.07199
$596$	7.77011	0.318276
$597$	−87.5589	−3.58355
$598$	−7.37735	−0.301682
$599$	−28.0381	−1.14561	−0.572804	−	0.819692i	$-0.694144\pi$
$599$	−28.0381	−1.14561	−0.572804	+	0.819692i	$0.694144\pi$
$600$	−21.2041	−0.865655
$601$	47.5005	1.93759	0.968794	−	0.247868i	$-0.0797300\pi$
$601$	47.5005	1.93759	0.968794	+	0.247868i	$0.0797300\pi$
$602$	56.6916	2.31058
$603$	2.86528	0.116683
$604$	−40.5740	−1.65093
$605$	3.47526	0.141289
$606$	−7.60277	−0.308841
$607$	−7.03650	−0.285603	−0.142801	−	0.989751i	$-0.545611\pi$
$607$	−7.03650	−0.285603	−0.142801	+	0.989751i	$0.545611\pi$
$608$	5.63081	0.228360
$609$	38.4490	1.55803
$610$	−20.8339	−0.843541
$611$	10.5762	0.427865
$612$	−101.893	−4.11880
$613$	19.1407	0.773087	0.386544	−	0.922271i	$-0.373669\pi$
$613$	19.1407	0.773087	0.386544	+	0.922271i	$0.373669\pi$
$614$	−60.4580	−2.43989
$615$	−46.9784	−1.89435
$616$	40.6311	1.63708
$617$	4.21003	0.169489	0.0847447	−	0.996403i	$-0.472993\pi$
$617$	4.21003	0.169489	0.0847447	+	0.996403i	$0.472993\pi$
$618$	−76.5428	−3.07900
$619$	−16.9723	−0.682176	−0.341088	−	0.940031i	$-0.610795\pi$
$619$	−16.9723	−0.682176	−0.341088	+	0.940031i	$0.610795\pi$
$620$	30.7563	1.23520
$621$	43.6757	1.75265
$622$	−50.4255	−2.02188
$623$	−23.0135	−0.922017
$624$	8.13348	0.325600
$625$	−30.4089	−1.21636
$626$	21.0040	0.839491
$627$	26.3724	1.05321
$628$	25.5162	1.01821
$629$	−13.2001	−0.526324
$630$	128.780	5.13071
$631$	−36.1788	−1.44026	−0.720128	−	0.693841i	$-0.755917\pi$
$631$	−36.1788	−1.44026	−0.720128	+	0.693841i	$0.755917\pi$
$632$	−37.7801	−1.50281
$633$	−54.3289	−2.15938
$634$	76.4339	3.03558
$635$	5.04248	0.200105
$636$	−61.0904	−2.42239
$637$	0.843128	0.0334060
$638$	35.6939	1.41314
$639$	−37.7235	−1.49232
$640$	53.2042	2.10308
$641$	−21.9630	−0.867485	−0.433743	−	0.901037i	$-0.642807\pi$
$641$	−21.9630	−0.867485	−0.433743	+	0.901037i	$0.642807\pi$
$642$	2.82421	0.111463
$643$	−18.7695	−0.740196	−0.370098	−	0.928993i	$-0.620676\pi$
$643$	−18.7695	−0.740196	−0.370098	+	0.928993i	$0.620676\pi$
$644$	−31.2158	−1.23008
$645$	70.4322	2.77326
$646$	20.1964	0.794617
$647$	−29.1688	−1.14674	−0.573372	−	0.819295i	$-0.694365\pi$
$647$	−29.1688	−1.14674	−0.573372	+	0.819295i	$0.694365\pi$
$648$	−102.333	−4.02003
$649$	−1.71251	−0.0672218
$650$	−3.89907	−0.152934
$651$	−29.1409	−1.14212
$652$	21.4798	0.841213
$653$	42.2753	1.65436	0.827179	−	0.561938i	$-0.189944\pi$
$653$	42.2753	1.65436	0.827179	+	0.561938i	$0.189944\pi$
$654$	31.5302	1.23293
$655$	41.4854	1.62097
$656$	−13.7794	−0.537997
$657$	−72.3390	−2.82221
$658$	68.7629	2.68066
$659$	0.760019	0.0296061	0.0148031	−	0.999890i	$-0.495288\pi$
$659$	0.760019	0.0296061	0.0148031	+	0.999890i	$0.495288\pi$
$660$	108.925	4.23989
$661$	10.2330	0.398019	0.199010	−	0.979998i	$-0.436228\pi$
$661$	10.2330	0.398019	0.199010	+	0.979998i	$0.436228\pi$
$662$	20.8552	0.810561
$663$	−12.1561	−0.472103
$664$	31.5324	1.22370
$665$	−16.6121	−0.644188
$666$	−65.0096	−2.51907
$667$	−12.7085	−0.492076
$668$	30.8465	1.19349
$669$	53.9937	2.08752
$670$	−2.34569	−0.0906220
$671$	11.9261	0.460401
$672$	−22.0352	−0.850027
$673$	−19.4212	−0.748631	−0.374316	−	0.927301i	$-0.622122\pi$
$673$	−19.4212	−0.748631	−0.374316	+	0.927301i	$0.622122\pi$
$674$	−60.8219	−2.34277
$675$	23.0834	0.888482
$676$	−44.5072	−1.71181
$677$	−7.74032	−0.297485	−0.148742	−	0.988876i	$-0.547522\pi$
$677$	−7.74032	−0.297485	−0.148742	+	0.988876i	$0.547522\pi$
$678$	68.2495	2.62111
$679$	−14.5375	−0.557900
$680$	38.6577	1.48245
$681$	−55.7659	−2.13696
$682$	−27.0528	−1.03590
$683$	−21.0024	−0.803633	−0.401817	−	0.915720i	$-0.631621\pi$
$683$	−21.0024	−0.803633	−0.401817	+	0.915720i	$0.631621\pi$
$684$	64.7323	2.47510
$685$	18.6872	0.714001
$686$	−41.3624	−1.57923
$687$	−76.8107	−2.93051
$688$	20.6588	0.787608
$689$	−5.20593	−0.198330
$690$	−59.5909	−2.26859
$691$	−3.77905	−0.143762	−0.0718810	−	0.997413i	$-0.522900\pi$
$691$	−3.77905	−0.143762	−0.0718810	+	0.997413i	$0.522900\pi$
$692$	75.1422	2.85648
$693$	−73.7181	−2.80032
$694$	12.9457	0.491411
$695$	−3.71227	−0.140814
$696$	56.8424	2.15460
$697$	20.5944	0.780068
$698$	−11.4113	−0.431923
$699$	−19.2686	−0.728807
$700$	−16.4982	−0.623572
$701$	32.7511	1.23699	0.618496	−	0.785788i	$-0.287742\pi$
$701$	32.7511	1.23699	0.618496	+	0.785788i	$0.287742\pi$
$702$	−35.9218	−1.35578
$703$	8.38596	0.316283
$704$	−37.5992	−1.41707
$705$	85.4293	3.21745
$706$	58.0933	2.18637
$707$	−2.74139	−0.103101
$708$	−5.88472	−0.221161
$709$	−8.26321	−0.310331	−0.155166	−	0.987888i	$-0.549591\pi$
$709$	−8.26321	−0.310331	−0.155166	+	0.987888i	$0.549591\pi$
$710$	30.8828	1.15901
$711$	68.5454	2.57065
$712$	−34.0228	−1.27506
$713$	9.63191	0.360718
$714$	−79.0352	−2.95782
$715$	9.28223	0.347136
$716$	72.6149	2.71375
$717$	−24.8739	−0.928931
$718$	−36.5341	−1.36344
$719$	42.8474	1.59794	0.798969	−	0.601372i	$-0.205379\pi$
$719$	42.8474	1.59794	0.798969	+	0.601372i	$0.205379\pi$
$720$	46.9282	1.74891
$721$	−27.5997	−1.02787
$722$	32.6400	1.21474
$723$	−42.9488	−1.59728
$724$	−44.0999	−1.63896
$725$	−6.71669	−0.249452
$726$	−10.5041	−0.389844
$727$	−43.6731	−1.61975	−0.809874	−	0.586604i	$-0.800464\pi$
$727$	−43.6731	−1.61975	−0.809874	+	0.586604i	$0.800464\pi$
$728$	11.8981	0.440973
$729$	43.8997	1.62592
$730$	59.2212	2.19187
$731$	−30.8760	−1.14199
$732$	40.9818	1.51473
$733$	−48.5002	−1.79140	−0.895699	−	0.444662i	$-0.853324\pi$
$733$	−48.5002	−1.79140	−0.895699	+	0.444662i	$0.853324\pi$
$734$	−0.688345	−0.0254073
$735$	6.81041	0.251206
$736$	7.28328	0.268465
$737$	1.34276	0.0494611
$738$	101.426	3.73353
$739$	41.5990	1.53024	0.765122	−	0.643886i	$-0.222679\pi$
$739$	41.5990	1.53024	0.765122	+	0.643886i	$0.222679\pi$
$740$	34.6362	1.27325
$741$	7.72269	0.283700
$742$	−33.8474	−1.24258
$743$	−10.9455	−0.401552	−0.200776	−	0.979637i	$-0.564346\pi$
$743$	−10.9455	−0.401552	−0.200776	+	0.979637i	$0.564346\pi$
$744$	−43.0814	−1.57944
$745$	5.34849	0.195954
$746$	4.63036	0.169530
$747$	−57.2101	−2.09321
$748$	−47.7504	−1.74593
$749$	1.01835	0.0372097
$750$	67.9903	2.48265
$751$	−5.11517	−0.186655	−0.0933276	−	0.995635i	$-0.529750\pi$
$751$	−5.11517	−0.186655	−0.0933276	+	0.995635i	$0.529750\pi$
$752$	25.0576	0.913758
$753$	−39.4359	−1.43712
$754$	10.4523	0.380651
$755$	−27.9288	−1.01643
$756$	−151.996	−5.52804
$757$	−37.9332	−1.37871	−0.689353	−	0.724425i	$-0.742105\pi$
$757$	−37.9332	−1.37871	−0.689353	+	0.724425i	$0.742105\pi$
$758$	47.4139	1.72215
$759$	34.1119	1.23818
$760$	−24.5590	−0.890848
$761$	28.7658	1.04276	0.521379	−	0.853325i	$-0.325418\pi$
$761$	28.7658	1.04276	0.521379	+	0.853325i	$0.325418\pi$
$762$	−15.2411	−0.552127
$763$	11.3691	0.411590
$764$	70.1378	2.53750
$765$	−70.1376	−2.53583
$766$	88.3482	3.19215
$767$	−0.501477	−0.0181073
$768$	−91.4852	−3.30119
$769$	−12.0086	−0.433043	−0.216521	−	0.976278i	$-0.569471\pi$
$769$	−12.0086	−0.433043	−0.216521	+	0.976278i	$0.569471\pi$
$770$	60.3502	2.17487
$771$	54.5928	1.96611
$772$	−87.3798	−3.14487
$773$	52.3196	1.88180	0.940902	−	0.338678i	$-0.109980\pi$
$773$	52.3196	1.88180	0.940902	+	0.338678i	$0.109980\pi$
$774$	−152.062	−5.46575
$775$	5.09065	0.182861
$776$	−21.4921	−0.771520
$777$	−32.8170	−1.17730
$778$	−24.6343	−0.883181
$779$	−13.0835	−0.468765
$780$	31.8967	1.14208
$781$	−17.6784	−0.632583
$782$	26.1234	0.934172
$783$	−61.8803	−2.21142
$784$	1.99759	0.0713424
$785$	17.5639	0.626881
$786$	−125.391	−4.47255
$787$	25.7897	0.919302	0.459651	−	0.888100i	$-0.347974\pi$
$787$	25.7897	0.919302	0.459651	+	0.888100i	$0.347974\pi$
$788$	97.0341	3.45670
$789$	−34.4060	−1.22489
$790$	−56.1155	−1.99650
$791$	24.6093	0.875005
$792$	−108.984	−3.87256
$793$	3.49233	0.124016
$794$	−55.8397	−1.98168
$795$	−42.0511	−1.49140
$796$	−100.717	−3.56982
$797$	45.2666	1.60342	0.801712	−	0.597710i	$-0.203923\pi$
$797$	45.2666	1.60342	0.801712	+	0.597710i	$0.203923\pi$
$798$	50.2106	1.77744
$799$	−37.4505	−1.32490
$800$	3.84935	0.136095
$801$	61.7284	2.18107
$802$	−47.6124	−1.68125
$803$	−33.9003	−1.19631
$804$	4.61414	0.162728
$805$	−21.4872	−0.757324
$806$	−7.92192	−0.279038
$807$	−58.4796	−2.05858
$808$	−4.05283	−0.142578
$809$	−16.1748	−0.568677	−0.284338	−	0.958724i	$-0.591774\pi$
$809$	−16.1748	−0.568677	−0.284338	+	0.958724i	$0.591774\pi$
$810$	−151.997	−5.34065
$811$	−19.5970	−0.688142	−0.344071	−	0.938944i	$-0.611806\pi$
$811$	−19.5970	−0.688142	−0.344071	+	0.938944i	$0.611806\pi$
$812$	44.2270	1.55206
$813$	−74.8145	−2.62386
$814$	−30.4655	−1.06781
$815$	14.7854	0.517911
$816$	−28.8009	−1.00823
$817$	19.6154	0.686254
$818$	2.76229	0.0965813
$819$	−21.5870	−0.754311
$820$	−54.0381	−1.88709
$821$	−10.2871	−0.359021	−0.179511	−	0.983756i	$-0.557451\pi$
$821$	−10.2871	−0.359021	−0.179511	+	0.983756i	$0.557451\pi$
$822$	−56.4827	−1.97006
$823$	51.2301	1.78577	0.892884	−	0.450286i	$-0.148678\pi$
$823$	51.2301	1.78577	0.892884	+	0.450286i	$0.148678\pi$
$824$	−40.8029	−1.42144
$825$	18.0288	0.627682
$826$	−3.26045	−0.113446
$827$	−50.6261	−1.76044	−0.880221	−	0.474564i	$-0.842606\pi$
$827$	−50.6261	−1.76044	−0.880221	+	0.474564i	$0.842606\pi$
$828$	83.7292	2.90979
$829$	53.2843	1.85064	0.925320	−	0.379186i	$-0.123796\pi$
$829$	53.2843	1.85064	0.925320	+	0.379186i	$0.123796\pi$
$830$	46.8357	1.62569
$831$	63.1841	2.19183
$832$	−11.0103	−0.381712
$833$	−2.98554	−0.103443
$834$	11.2205	0.388533
$835$	21.2329	0.734796
$836$	30.3356	1.04918
$837$	46.8997	1.62109
$838$	−8.28279	−0.286124
$839$	25.0546	0.864980	0.432490	−	0.901639i	$-0.357635\pi$
$839$	25.0546	0.864980	0.432490	+	0.901639i	$0.357635\pi$
$840$	96.1074	3.31602
$841$	−10.9944	−0.379118
$842$	−56.5518	−1.94891
$843$	1.00849	0.0347342
$844$	−62.4933	−2.15111
$845$	−30.6362	−1.05392
$846$	−184.441	−6.34120
$847$	−3.78755	−0.130142
$848$	−12.3342	−0.423558
$849$	−22.7815	−0.781860
$850$	13.8067	0.473567
$851$	10.8470	0.371830
$852$	−60.7486	−2.08121
$853$	33.6958	1.15372	0.576861	−	0.816842i	$-0.304277\pi$
$853$	33.6958	1.15372	0.576861	+	0.816842i	$0.304277\pi$
$854$	22.7061	0.776987
$855$	44.5580	1.52385
$856$	1.50551	0.0514573
$857$	−5.19775	−0.177552	−0.0887758	−	0.996052i	$-0.528295\pi$
$857$	−5.19775	−0.177552	−0.0887758	+	0.996052i	$0.528295\pi$
$858$	−28.0559	−0.957812
$859$	46.5223	1.58732	0.793660	−	0.608362i	$-0.208173\pi$
$859$	46.5223	1.58732	0.793660	+	0.608362i	$0.208173\pi$
$860$	81.0164	2.76264
$861$	51.2000	1.74489
$862$	70.2205	2.39172
$863$	26.9573	0.917637	0.458818	−	0.888530i	$-0.348273\pi$
$863$	26.9573	0.917637	0.458818	+	0.888530i	$0.348273\pi$
$864$	35.4637	1.20650
$865$	51.7235	1.75865
$866$	41.8617	1.42252
$867$	−12.0422	−0.408974
$868$	−33.5201	−1.13774
$869$	32.1225	1.08968
$870$	84.4291	2.86241
$871$	0.393202	0.0133231
$872$	16.8079	0.569187
$873$	38.9936	1.31973
$874$	−16.5961	−0.561370
$875$	24.5158	0.828786
$876$	−116.492	−3.93590
$877$	−42.2271	−1.42591	−0.712953	−	0.701212i	$-0.752643\pi$
$877$	−42.2271	−1.42591	−0.712953	+	0.701212i	$0.752643\pi$
$878$	−63.8468	−2.15473
$879$	12.6721	0.427418
$880$	21.9920	0.741350
$881$	40.1694	1.35334	0.676671	−	0.736286i	$-0.263422\pi$
$881$	40.1694	1.35334	0.676671	+	0.736286i	$0.263422\pi$
$882$	−14.7036	−0.495095
$883$	20.2122	0.680194	0.340097	−	0.940390i	$-0.389540\pi$
$883$	20.2122	0.680194	0.340097	+	0.940390i	$0.389540\pi$
$884$	−13.9829	−0.470294
$885$	−4.05070	−0.136163
$886$	41.8397	1.40563
$887$	31.7475	1.06598	0.532989	−	0.846122i	$-0.321069\pi$
$887$	31.7475	1.06598	0.532989	+	0.846122i	$0.321069\pi$
$888$	−48.5161	−1.62809
$889$	−5.49561	−0.184317
$890$	−50.5347	−1.69393
$891$	87.0086	2.91490
$892$	62.1076	2.07952
$893$	23.7921	0.796171
$894$	−16.1660	−0.540673
$895$	49.9839	1.67078
$896$	−57.9852	−1.93715
$897$	9.98906	0.333525
$898$	77.8497	2.59788
$899$	−13.6466	−0.455140
$900$	44.2525	1.47508
$901$	18.4343	0.614137
$902$	47.5312	1.58262
$903$	−76.7613	−2.55446
$904$	36.3819	1.21005
$905$	−30.3558	−1.00906
$906$	84.4159	2.80453
$907$	40.6477	1.34968	0.674842	−	0.737963i	$-0.264212\pi$
$907$	40.6477	1.34968	0.674842	+	0.737963i	$0.264212\pi$
$908$	−64.1462	−2.12877
$909$	7.35315	0.243889
$910$	17.6725	0.585837
$911$	17.7696	0.588734	0.294367	−	0.955692i	$-0.404891\pi$
$911$	17.7696	0.588734	0.294367	+	0.955692i	$0.404891\pi$
$912$	18.2970	0.605876
$913$	−26.8104	−0.887295
$914$	−48.6673	−1.60977
$915$	28.2095	0.932577
$916$	−88.3535	−2.91928
$917$	−45.2133	−1.49307
$918$	127.200	4.19823
$919$	−39.6066	−1.30650	−0.653251	−	0.757142i	$-0.726595\pi$
$919$	−39.6066	−1.30650	−0.653251	+	0.757142i	$0.726595\pi$
$920$	−31.7663	−1.04730
$921$	81.8611	2.69741
$922$	−87.5366	−2.88287
$923$	−5.17680	−0.170396
$924$	−118.713	−3.90537
$925$	5.73284	0.188494
$926$	28.4614	0.935299
$927$	74.0297	2.43145
$928$	−10.3190	−0.338739
$929$	−42.8988	−1.40746	−0.703732	−	0.710466i	$-0.748484\pi$
$929$	−42.8988	−1.40746	−0.703732	+	0.710466i	$0.748484\pi$
$930$	−63.9896	−2.09830
$931$	1.89670	0.0621617
$932$	−22.1643	−0.726015
$933$	68.2769	2.23529
$934$	−47.1763	−1.54366
$935$	−32.8686	−1.07492
$936$	−31.9139	−1.04314
$937$	−5.07215	−0.165700	−0.0828500	−	0.996562i	$-0.526402\pi$
$937$	−5.07215	−0.165700	−0.0828500	+	0.996562i	$0.526402\pi$
$938$	2.55648	0.0834720
$939$	−28.4398	−0.928099
$940$	98.2673	3.20513
$941$	−43.7577	−1.42646	−0.713231	−	0.700929i	$-0.752769\pi$
$941$	−43.7577	−1.42646	−0.713231	+	0.700929i	$0.752769\pi$
$942$	−53.0874	−1.72968
$943$	−16.9231	−0.551091
$944$	−1.18813	−0.0386703
$945$	−104.625	−3.40346
$946$	−71.2609	−2.31689
$947$	49.6028	1.61187	0.805936	−	0.592002i	$-0.201662\pi$
$947$	49.6028	1.61187	0.805936	+	0.592002i	$0.201662\pi$
$948$	110.383	3.58507
$949$	−9.92708	−0.322247
$950$	−8.77133	−0.284580
$951$	−103.493	−3.35598
$952$	−42.1315	−1.36549
$953$	−1.93027	−0.0625275	−0.0312637	−	0.999511i	$-0.509953\pi$
$953$	−1.93027	−0.0625275	−0.0312637	+	0.999511i	$0.509953\pi$
$954$	90.7877	2.93936
$955$	48.2788	1.56227
$956$	−28.6118	−0.925372
$957$	−48.3302	−1.56229
$958$	75.7372	2.44696
$959$	−20.3664	−0.657667
$960$	−88.9358	−2.87039
$961$	−20.6571	−0.666358
$962$	−8.92127	−0.287633
$963$	−2.73148	−0.0880209
$964$	−49.4030	−1.59116
$965$	−60.1472	−1.93621
$966$	64.9458	2.08960
$967$	12.8335	0.412697	0.206349	−	0.978479i	$-0.433842\pi$
$967$	12.8335	0.412697	0.206349	+	0.978479i	$0.433842\pi$
$968$	−5.59945	−0.179973
$969$	−27.3463	−0.878489
$970$	−31.9226	−1.02497
$971$	−9.00915	−0.289117	−0.144559	−	0.989496i	$-0.546176\pi$
$971$	−9.00915	−0.289117	−0.144559	+	0.989496i	$0.546176\pi$
$972$	135.919	4.35962
$973$	4.04586	0.129704
$974$	34.5461	1.10693
$975$	5.27941	0.169076
$976$	8.27424	0.264852
$977$	−2.46127	−0.0787430	−0.0393715	−	0.999225i	$-0.512536\pi$
$977$	−2.46127	−0.0787430	−0.0393715	+	0.999225i	$0.512536\pi$
$978$	−44.6895	−1.42901
$979$	28.9278	0.924537
$980$	7.83385	0.250243
$981$	−30.4950	−0.973631
$982$	61.7752	1.97132
$983$	−40.2839	−1.28486	−0.642428	−	0.766346i	$-0.722073\pi$
$983$	−40.2839	−1.28486	−0.642428	+	0.766346i	$0.722073\pi$
$984$	75.6932	2.41301
$985$	66.7927	2.12819
$986$	−37.0120	−1.17870
$987$	−93.1061	−2.96360
$988$	8.88322	0.282613
$989$	25.3718	0.806778
$990$	−161.875	−5.14474
$991$	9.57445	0.304142	0.152071	−	0.988370i	$-0.451406\pi$
$991$	9.57445	0.304142	0.152071	+	0.988370i	$0.451406\pi$
$992$	7.82090	0.248314
$993$	−28.2383	−0.896115
$994$	−33.6580	−1.06757
$995$	−69.3277	−2.19784
$996$	−92.1291	−2.91922
$997$	9.22173	0.292055	0.146028	−	0.989281i	$-0.453351\pi$
$997$	9.22173	0.292055	0.146028	+	0.989281i	$0.453351\pi$
$998$	35.5398	1.12499
$999$	52.8161	1.67103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.c.1.15	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.c.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.39320 q^{2} +3.24043 q^{3} +3.72738 q^{4} +2.56572 q^{5} -7.75497 q^{6} -2.79627 q^{7} -4.13396 q^{8} +7.50035 q^{9} +O(q^{10})\)	\(q-2.39320 q^{2} +3.24043 q^{3} +3.72738 q^{4} +2.56572 q^{5} -7.75497 q^{6} -2.79627 q^{7} -4.13396 q^{8} +7.50035 q^{9} -6.14026 q^{10} +3.51490 q^{11} +12.0783 q^{12} +1.02927 q^{13} +6.69203 q^{14} +8.31401 q^{15} +2.43862 q^{16} -3.64469 q^{17} -17.9498 q^{18} +2.31545 q^{19} +9.56340 q^{20} -9.06112 q^{21} -8.41183 q^{22} +2.99496 q^{23} -13.3958 q^{24} +1.58289 q^{25} -2.46325 q^{26} +14.5831 q^{27} -10.4228 q^{28} -4.24330 q^{29} -19.8970 q^{30} +3.21604 q^{31} +2.43184 q^{32} +11.3898 q^{33} +8.72245 q^{34} -7.17444 q^{35} +27.9567 q^{36} +3.62174 q^{37} -5.54132 q^{38} +3.33529 q^{39} -10.6066 q^{40} -5.65051 q^{41} +21.6850 q^{42} +8.47151 q^{43} +13.1014 q^{44} +19.2438 q^{45} -7.16753 q^{46} +10.2753 q^{47} +7.90215 q^{48} +0.819148 q^{49} -3.78818 q^{50} -11.8103 q^{51} +3.83650 q^{52} -5.05786 q^{53} -34.9001 q^{54} +9.01822 q^{55} +11.5597 q^{56} +7.50304 q^{57} +10.1550 q^{58} -0.487214 q^{59} +30.9895 q^{60} +3.39301 q^{61} -7.69660 q^{62} -20.9730 q^{63} -10.6971 q^{64} +2.64082 q^{65} -27.2579 q^{66} +0.382019 q^{67} -13.5852 q^{68} +9.70495 q^{69} +17.1698 q^{70} -5.02956 q^{71} -31.0062 q^{72} -9.64474 q^{73} -8.66754 q^{74} +5.12925 q^{75} +8.63057 q^{76} -9.82861 q^{77} -7.98199 q^{78} +9.13895 q^{79} +6.25679 q^{80} +24.7543 q^{81} +13.5228 q^{82} -7.62765 q^{83} -33.7742 q^{84} -9.35124 q^{85} -20.2740 q^{86} -13.7501 q^{87} -14.5305 q^{88} +8.23006 q^{89} -46.0541 q^{90} -2.87813 q^{91} +11.1634 q^{92} +10.4213 q^{93} -24.5909 q^{94} +5.94079 q^{95} +7.88021 q^{96} +5.19890 q^{97} -1.96038 q^{98} +26.3630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 22 q^{2} + 16 q^{3} + 196 q^{4} + 61 q^{5} + 7 q^{6} + 21 q^{7} + 60 q^{8} + 221 q^{9}+O(q^{10}) \) 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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