LMFDB - Embedded newform 8003.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9042767376$
Analytic rank:	$1$
Dimension:	$147$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28070 q^{2} -3.18519 q^{3} +3.20158 q^{4} -4.19393 q^{5} +7.26446 q^{6} -3.02488 q^{7} -2.74045 q^{8} +7.14546 q^{9} +O(q^{10})$	\(q-2.28070 q^{2} -3.18519 q^{3} +3.20158 q^{4} -4.19393 q^{5} +7.26446 q^{6} -3.02488 q^{7} -2.74045 q^{8} +7.14546 q^{9} +9.56509 q^{10} -0.923883 q^{11} -10.1977 q^{12} -4.47580 q^{13} +6.89885 q^{14} +13.3585 q^{15} -0.153032 q^{16} +1.29874 q^{17} -16.2966 q^{18} -0.764782 q^{19} -13.4272 q^{20} +9.63484 q^{21} +2.10710 q^{22} -3.12718 q^{23} +8.72886 q^{24} +12.5890 q^{25} +10.2080 q^{26} -13.2041 q^{27} -9.68442 q^{28} -6.50995 q^{29} -30.4666 q^{30} +0.995985 q^{31} +5.82992 q^{32} +2.94275 q^{33} -2.96204 q^{34} +12.6861 q^{35} +22.8768 q^{36} -9.58649 q^{37} +1.74424 q^{38} +14.2563 q^{39} +11.4932 q^{40} -4.26086 q^{41} -21.9742 q^{42} -9.20390 q^{43} -2.95789 q^{44} -29.9675 q^{45} +7.13216 q^{46} +1.20998 q^{47} +0.487438 q^{48} +2.14992 q^{49} -28.7118 q^{50} -4.13675 q^{51} -14.3297 q^{52} +1.00000 q^{53} +30.1145 q^{54} +3.87470 q^{55} +8.28954 q^{56} +2.43598 q^{57} +14.8472 q^{58} -13.7028 q^{59} +42.7683 q^{60} +13.6487 q^{61} -2.27154 q^{62} -21.6142 q^{63} -12.9902 q^{64} +18.7712 q^{65} -6.71151 q^{66} -15.6287 q^{67} +4.15804 q^{68} +9.96068 q^{69} -28.9333 q^{70} +12.0718 q^{71} -19.5818 q^{72} -11.6532 q^{73} +21.8639 q^{74} -40.0985 q^{75} -2.44851 q^{76} +2.79464 q^{77} -32.5143 q^{78} +7.23914 q^{79} +0.641807 q^{80} +20.6212 q^{81} +9.71773 q^{82} -3.14316 q^{83} +30.8467 q^{84} -5.44684 q^{85} +20.9913 q^{86} +20.7355 q^{87} +2.53185 q^{88} -13.6179 q^{89} +68.3469 q^{90} +13.5388 q^{91} -10.0119 q^{92} -3.17241 q^{93} -2.75959 q^{94} +3.20744 q^{95} -18.5694 q^{96} -14.3531 q^{97} -4.90333 q^{98} -6.60157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) $ 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.28070	−1.61270	−0.806348	−	0.591441i	$-0.798559\pi$
$2$	−2.28070	−1.61270	−0.806348	+	0.591441i	$0.798559\pi$
$3$	−3.18519	−1.83897	−0.919486	−	0.393122i	$-0.871395\pi$
$3$	−3.18519	−1.83897	−0.919486	+	0.393122i	$0.871395\pi$
$4$	3.20158	1.60079
$5$	−4.19393	−1.87558	−0.937791	−	0.347200i	$-0.887132\pi$
$5$	−4.19393	−1.87558	−0.937791	+	0.347200i	$0.887132\pi$
$6$	7.26446	2.96571
$7$	−3.02488	−1.14330	−0.571649	−	0.820498i	$-0.693696\pi$
$7$	−3.02488	−1.14330	−0.571649	+	0.820498i	$0.693696\pi$
$8$	−2.74045	−0.968895
$9$	7.14546	2.38182
$10$	9.56509	3.02475
$11$	−0.923883	−0.278561	−0.139281	−	0.990253i	$-0.544479\pi$
$11$	−0.923883	−0.278561	−0.139281	+	0.990253i	$0.544479\pi$
$12$	−10.1977	−2.94381
$13$	−4.47580	−1.24136	−0.620682	−	0.784062i	$-0.713144\pi$
$13$	−4.47580	−1.24136	−0.620682	+	0.784062i	$0.713144\pi$
$14$	6.89885	1.84379
$15$	13.3585	3.44914
$16$	−0.153032	−0.0382581
$17$	1.29874	0.314992	0.157496	−	0.987520i	$-0.449658\pi$
$17$	1.29874	0.314992	0.157496	+	0.987520i	$0.449658\pi$
$18$	−16.2966	−3.84115
$19$	−0.764782	−0.175453	−0.0877265	−	0.996145i	$-0.527960\pi$
$19$	−0.764782	−0.175453	−0.0877265	+	0.996145i	$0.527960\pi$
$20$	−13.4272	−3.00242
$21$	9.63484	2.10249
$22$	2.10710	0.449235
$23$	−3.12718	−0.652063	−0.326031	−	0.945359i	$-0.605712\pi$
$23$	−3.12718	−0.652063	−0.326031	+	0.945359i	$0.605712\pi$
$24$	8.72886	1.78177
$25$	12.5890	2.51781
$26$	10.2080	2.00195
$27$	−13.2041	−2.54113
$28$	−9.68442	−1.83018
$29$	−6.50995	−1.20887	−0.604434	−	0.796655i	$-0.706601\pi$
$29$	−6.50995	−1.20887	−0.604434	+	0.796655i	$0.706601\pi$
$30$	−30.4666	−5.56242
$31$	0.995985	0.178884	0.0894421	−	0.995992i	$-0.471492\pi$
$31$	0.995985	0.178884	0.0894421	+	0.995992i	$0.471492\pi$
$32$	5.82992	1.03059
$33$	2.94275	0.512266
$34$	−2.96204	−0.507986
$35$	12.6861	2.14435
$36$	22.8768	3.81280
$37$	−9.58649	−1.57601	−0.788005	−	0.615669i	$-0.788886\pi$
$37$	−9.58649	−1.57601	−0.788005	+	0.615669i	$0.788886\pi$
$38$	1.74424	0.282953
$39$	14.2563	2.28284
$40$	11.4932	1.81724
$41$	−4.26086	−0.665434	−0.332717	−	0.943027i	$-0.607965\pi$
$41$	−4.26086	−0.665434	−0.332717	+	0.943027i	$0.607965\pi$
$42$	−21.9742	−3.39069
$43$	−9.20390	−1.40358	−0.701791	−	0.712383i	$-0.747616\pi$
$43$	−9.20390	−1.40358	−0.701791	+	0.712383i	$0.747616\pi$
$44$	−2.95789	−0.445918
$45$	−29.9675	−4.46730
$46$	7.13216	1.05158
$47$	1.20998	0.176493	0.0882466	−	0.996099i	$-0.471874\pi$
$47$	1.20998	0.176493	0.0882466	+	0.996099i	$0.471874\pi$
$48$	0.487438	0.0703556
$49$	2.14992	0.307132
$50$	−28.7118	−4.06046
$51$	−4.13675	−0.579261
$52$	−14.3297	−1.98717
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	30.1145	4.09807
$55$	3.87470	0.522464
$56$	8.28954	1.10774
$57$	2.43598	0.322653
$58$	14.8472	1.94954
$59$	−13.7028	−1.78396	−0.891978	−	0.452079i	$-0.850682\pi$
$59$	−13.7028	−1.78396	−0.891978	+	0.452079i	$0.850682\pi$
$60$	42.7683	5.52136
$61$	13.6487	1.74754	0.873769	−	0.486340i	$-0.161668\pi$
$61$	13.6487	1.74754	0.873769	+	0.486340i	$0.161668\pi$
$62$	−2.27154	−0.288486
$63$	−21.6142	−2.72313
$64$	−12.9902	−1.62378
$65$	18.7712	2.32828
$66$	−6.71151	−0.826130
$67$	−15.6287	−1.90935	−0.954675	−	0.297651i	$-0.903797\pi$
$67$	−15.6287	−1.90935	−0.954675	+	0.297651i	$0.903797\pi$
$68$	4.15804	0.504236
$69$	9.96068	1.19913
$70$	−28.9333	−3.45819
$71$	12.0718	1.43266	0.716329	−	0.697762i	$-0.245821\pi$
$71$	12.0718	1.43266	0.716329	+	0.697762i	$0.245821\pi$
$72$	−19.5818	−2.30773
$73$	−11.6532	−1.36391	−0.681954	−	0.731395i	$-0.738870\pi$
$73$	−11.6532	−1.36391	−0.681954	+	0.731395i	$0.738870\pi$
$74$	21.8639	2.54163
$75$	−40.0985	−4.63018
$76$	−2.44851	−0.280864
$77$	2.79464	0.318479
$78$	−32.5143	−3.68152
$79$	7.23914	0.814466	0.407233	−	0.913324i	$-0.366494\pi$
$79$	7.23914	0.814466	0.407233	+	0.913324i	$0.366494\pi$
$80$	0.641807	0.0717563
$81$	20.6212	2.29124
$82$	9.71773	1.07314
$83$	−3.14316	−0.345007	−0.172503	−	0.985009i	$-0.555186\pi$
$83$	−3.14316	−0.345007	−0.172503	+	0.985009i	$0.555186\pi$
$84$	30.8467	3.36566
$85$	−5.44684	−0.590793
$86$	20.9913	2.26355
$87$	20.7355	2.22307
$88$	2.53185	0.269896
$89$	−13.6179	−1.44349	−0.721747	−	0.692157i	$-0.756661\pi$
$89$	−13.6179	−1.44349	−0.721747	+	0.692157i	$0.756661\pi$
$90$	68.3469	7.20440
$91$	13.5388	1.41925
$92$	−10.0119	−1.04382
$93$	−3.17241	−0.328963
$94$	−2.75959	−0.284630
$95$	3.20744	0.329077
$96$	−18.5694	−1.89523
$97$	−14.3531	−1.45733	−0.728667	−	0.684868i	$-0.759860\pi$
$97$	−14.3531	−1.45733	−0.728667	+	0.684868i	$0.759860\pi$
$98$	−4.90333	−0.495311
$99$	−6.60157	−0.663482
$100$	40.3049	4.03049
$101$	4.23134	0.421034	0.210517	−	0.977590i	$-0.432485\pi$
$101$	4.23134	0.421034	0.210517	+	0.977590i	$0.432485\pi$
$102$	9.43468	0.934172
$103$	−13.0633	−1.28717	−0.643583	−	0.765376i	$-0.722553\pi$
$103$	−13.0633	−1.28717	−0.643583	+	0.765376i	$0.722553\pi$
$104$	12.2657	1.20275
$105$	−40.4078	−3.94340
$106$	−2.28070	−0.221521
$107$	11.1038	1.07345	0.536723	−	0.843758i	$-0.319662\pi$
$107$	11.1038	1.07345	0.536723	+	0.843758i	$0.319662\pi$
$108$	−42.2740	−4.06781
$109$	−15.6377	−1.49782	−0.748910	−	0.662672i	$-0.769422\pi$
$109$	−15.6377	−1.49782	−0.748910	+	0.662672i	$0.769422\pi$
$110$	−8.83702	−0.842577
$111$	30.5348	2.89824
$112$	0.462906	0.0437405
$113$	11.3901	1.07149	0.535747	−	0.844379i	$-0.320030\pi$
$113$	11.3901	1.07149	0.535747	+	0.844379i	$0.320030\pi$
$114$	−5.55573	−0.520342
$115$	13.1152	1.22300
$116$	−20.8421	−1.93514
$117$	−31.9817	−2.95671
$118$	31.2520	2.87698
$119$	−3.92855	−0.360130
$120$	−36.6082	−3.34186
$121$	−10.1464	−0.922404
$122$	−31.1286	−2.81825
$123$	13.5717	1.22371
$124$	3.18873	0.286356
$125$	−31.8279	−2.84677
$126$	49.2954	4.39158
$127$	19.3416	1.71629	0.858147	−	0.513405i	$-0.171616\pi$
$127$	19.3416	1.71629	0.858147	+	0.513405i	$0.171616\pi$
$128$	17.9669	1.58807
$129$	29.3162	2.58115
$130$	−42.8115	−3.75481
$131$	12.9748	1.13362	0.566808	−	0.823850i	$-0.308178\pi$
$131$	12.9748	1.13362	0.566808	+	0.823850i	$0.308178\pi$
$132$	9.42145	0.820032
$133$	2.31338	0.200595
$134$	35.6443	3.07920
$135$	55.3770	4.76609
$136$	−3.55914	−0.305194
$137$	7.75851	0.662854	0.331427	−	0.943481i	$-0.392470\pi$
$137$	7.75851	0.662854	0.331427	+	0.943481i	$0.392470\pi$
$138$	−22.7173	−1.93383
$139$	1.64505	0.139532	0.0697658	−	0.997563i	$-0.477775\pi$
$139$	1.64505	0.139532	0.0697658	+	0.997563i	$0.477775\pi$
$140$	40.6158	3.43266
$141$	−3.85401	−0.324566
$142$	−27.5321	−2.31044
$143$	4.13512	0.345796
$144$	−1.09349	−0.0911239
$145$	27.3023	2.26733
$146$	26.5775	2.19957
$147$	−6.84792	−0.564807
$148$	−30.6919	−2.52286
$149$	−13.9331	−1.14145	−0.570724	−	0.821142i	$-0.693337\pi$
$149$	−13.9331	−1.14145	−0.570724	+	0.821142i	$0.693337\pi$
$150$	91.4526	7.46708
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	2.09585	0.169996
$153$	9.28012	0.750253
$154$	−6.37373	−0.513610
$155$	−4.17709	−0.335512
$156$	45.6427	3.65434
$157$	−3.85333	−0.307529	−0.153765	−	0.988108i	$-0.549140\pi$
$157$	−3.85333	−0.307529	−0.153765	+	0.988108i	$0.549140\pi$
$158$	−16.5103	−1.31349
$159$	−3.18519	−0.252602
$160$	−24.4503	−1.93296
$161$	9.45937	0.745503
$162$	−47.0307	−3.69508
$163$	6.24854	0.489423	0.244712	−	0.969596i	$-0.421307\pi$
$163$	6.24854	0.489423	0.244712	+	0.969596i	$0.421307\pi$
$164$	−13.6415	−1.06522
$165$	−12.3417	−0.960798
$166$	7.16860	0.556392
$167$	−16.3905	−1.26833	−0.634166	−	0.773197i	$-0.718657\pi$
$167$	−16.3905	−1.26833	−0.634166	+	0.773197i	$0.718657\pi$
$168$	−26.4038	−2.03710
$169$	7.03283	0.540987
$170$	12.4226	0.952770
$171$	−5.46472	−0.417897
$172$	−29.4671	−2.24684
$173$	−3.16731	−0.240806	−0.120403	−	0.992725i	$-0.538419\pi$
$173$	−3.16731	−0.240806	−0.120403	+	0.992725i	$0.538419\pi$
$174$	−47.2913	−3.58514
$175$	−38.0804	−2.87861
$176$	0.141384	0.0106572
$177$	43.6461	3.28064
$178$	31.0583	2.32792
$179$	17.6026	1.31568	0.657839	−	0.753158i	$-0.271471\pi$
$179$	17.6026	1.31568	0.657839	+	0.753158i	$0.271471\pi$
$180$	−95.9436	−7.15121
$181$	0.345417	0.0256746	0.0128373	−	0.999918i	$-0.495914\pi$
$181$	0.345417	0.0256746	0.0128373	+	0.999918i	$0.495914\pi$
$182$	−30.8779	−2.28882
$183$	−43.4738	−3.21368
$184$	8.56988	0.631780
$185$	40.2051	2.95594
$186$	7.23530	0.530518
$187$	−1.19989	−0.0877444
$188$	3.87384	0.282529
$189$	39.9408	2.90527
$190$	−7.31521	−0.530701
$191$	14.2267	1.02941	0.514705	−	0.857367i	$-0.327901\pi$
$191$	14.2267	1.02941	0.514705	+	0.857367i	$0.327901\pi$
$192$	41.3763	2.98608
$193$	1.13422	0.0816428	0.0408214	−	0.999166i	$-0.487003\pi$
$193$	1.13422	0.0816428	0.0408214	+	0.999166i	$0.487003\pi$
$194$	32.7350	2.35024
$195$	−59.7899	−4.28165
$196$	6.88316	0.491654
$197$	17.0245	1.21295	0.606473	−	0.795104i	$-0.292584\pi$
$197$	17.0245	1.21295	0.606473	+	0.795104i	$0.292584\pi$
$198$	15.0562	1.07000
$199$	15.0261	1.06517	0.532586	−	0.846376i	$-0.321220\pi$
$199$	15.0261	1.06517	0.532586	+	0.846376i	$0.321220\pi$
$200$	−34.4996	−2.43949
$201$	49.7804	3.51124
$202$	−9.65040	−0.679000
$203$	19.6918	1.38210
$204$	−13.2441	−0.927276
$205$	17.8697	1.24808
$206$	29.7935	2.07581
$207$	−22.3452	−1.55310
$208$	0.684944	0.0474923
$209$	0.706569	0.0488744
$210$	92.1581	6.35951
$211$	−20.4091	−1.40502	−0.702510	−	0.711674i	$-0.747937\pi$
$211$	−20.4091	−1.40502	−0.702510	+	0.711674i	$0.747937\pi$
$212$	3.20158	0.219886
$213$	−38.4510	−2.63462
$214$	−25.3245	−1.73114
$215$	38.6005	2.63253
$216$	36.1851	2.46208
$217$	−3.01274	−0.204518
$218$	35.6649	2.41553
$219$	37.1178	2.50819
$220$	12.4052	0.836357
$221$	−5.81292	−0.391020
$222$	−69.6407	−4.67398
$223$	4.60387	0.308298	0.154149	−	0.988048i	$-0.450736\pi$
$223$	4.60387	0.308298	0.154149	+	0.988048i	$0.450736\pi$
$224$	−17.6348	−1.17828
$225$	89.9545	5.99696
$226$	−25.9775	−1.72799
$227$	20.3445	1.35031	0.675155	−	0.737676i	$-0.264077\pi$
$227$	20.3445	1.35031	0.675155	+	0.737676i	$0.264077\pi$
$228$	7.79899	0.516501
$229$	4.62827	0.305845	0.152922	−	0.988238i	$-0.451132\pi$
$229$	4.62827	0.305845	0.152922	+	0.988238i	$0.451132\pi$
$230$	−29.9118	−1.97232
$231$	−8.90147	−0.585673
$232$	17.8402	1.17127
$233$	28.5949	1.87331	0.936656	−	0.350251i	$-0.113904\pi$
$233$	28.5949	1.87331	0.936656	+	0.350251i	$0.113904\pi$
$234$	72.9405	4.76827
$235$	−5.07456	−0.331028
$236$	−43.8707	−2.85574
$237$	−23.0580	−1.49778
$238$	8.95983	0.580780
$239$	−2.34518	−0.151697	−0.0758487	−	0.997119i	$-0.524167\pi$
$239$	−2.34518	−0.151697	−0.0758487	+	0.997119i	$0.524167\pi$
$240$	−2.04428	−0.131958
$241$	23.0746	1.48637	0.743184	−	0.669087i	$-0.233315\pi$
$241$	23.0746	1.48637	0.743184	+	0.669087i	$0.233315\pi$
$242$	23.1410	1.48756
$243$	−26.0702	−1.67241
$244$	43.6975	2.79745
$245$	−9.01663	−0.576051
$246$	−30.9528	−1.97348
$247$	3.42302	0.217801
$248$	−2.72945	−0.173320
$249$	10.0116	0.634458
$250$	72.5898	4.59098
$251$	2.61443	0.165022	0.0825108	−	0.996590i	$-0.473706\pi$
$251$	2.61443	0.165022	0.0825108	+	0.996590i	$0.473706\pi$
$252$	−69.1996	−4.35916
$253$	2.88915	0.181639
$254$	−44.1124	−2.76786
$255$	17.3492	1.08645
$256$	−14.9967	−0.937293
$257$	8.69076	0.542115	0.271057	−	0.962563i	$-0.412627\pi$
$257$	8.69076	0.542115	0.271057	+	0.962563i	$0.412627\pi$
$258$	−66.8614	−4.16261
$259$	28.9980	1.80185
$260$	60.0976	3.72709
$261$	−46.5166	−2.87930
$262$	−29.5917	−1.82818
$263$	−22.4252	−1.38280	−0.691398	−	0.722474i	$-0.743005\pi$
$263$	−22.4252	−1.38280	−0.691398	+	0.722474i	$0.743005\pi$
$264$	−8.06444	−0.496332
$265$	−4.19393	−0.257631
$266$	−5.27612	−0.323499
$267$	43.3756	2.65455
$268$	−50.0366	−3.05647
$269$	−17.6447	−1.07582	−0.537909	−	0.843003i	$-0.680785\pi$
$269$	−17.6447	−1.07582	−0.537909	+	0.843003i	$0.680785\pi$
$270$	−126.298	−7.68626
$271$	−10.5130	−0.638618	−0.319309	−	0.947651i	$-0.603451\pi$
$271$	−10.5130	−0.638618	−0.319309	+	0.947651i	$0.603451\pi$
$272$	−0.198750	−0.0120510
$273$	−43.1237	−2.60996
$274$	−17.6948	−1.06898
$275$	−11.6308	−0.701364
$276$	31.8900	1.91955
$277$	−13.5494	−0.814104	−0.407052	−	0.913405i	$-0.633443\pi$
$277$	−13.5494	−0.814104	−0.407052	+	0.913405i	$0.633443\pi$
$278$	−3.75187	−0.225022
$279$	7.11677	0.426070
$280$	−34.7657	−2.07765
$281$	10.8621	0.647976	0.323988	−	0.946061i	$-0.394976\pi$
$281$	10.8621	0.647976	0.323988	+	0.946061i	$0.394976\pi$
$282$	8.78983	0.523427
$283$	26.7150	1.58804	0.794020	−	0.607892i	$-0.207985\pi$
$283$	26.7150	1.58804	0.794020	+	0.607892i	$0.207985\pi$
$284$	38.6489	2.29339
$285$	−10.2163	−0.605163
$286$	−9.43096	−0.557664
$287$	12.8886	0.760790
$288$	41.6574	2.45469
$289$	−15.3133	−0.900780
$290$	−62.2682	−3.65652
$291$	45.7173	2.68000
$292$	−37.3088	−2.18333
$293$	−8.55087	−0.499547	−0.249774	−	0.968304i	$-0.580356\pi$
$293$	−8.55087	−0.499547	−0.249774	+	0.968304i	$0.580356\pi$
$294$	15.6180	0.910863
$295$	57.4687	3.34595
$296$	26.2713	1.52699
$297$	12.1990	0.707859
$298$	31.7773	1.84081
$299$	13.9967	0.809448
$300$	−128.379	−7.41195
$301$	27.8407	1.60471
$302$	−2.28070	−0.131239
$303$	−13.4776	−0.774269
$304$	0.117037	0.00671251
$305$	−57.2417	−3.27765
$306$	−21.1651	−1.20993
$307$	−14.4888	−0.826920	−0.413460	−	0.910522i	$-0.635680\pi$
$307$	−14.4888	−0.826920	−0.413460	+	0.910522i	$0.635680\pi$
$308$	8.94727	0.509818
$309$	41.6092	2.36706
$310$	9.52668	0.541079
$311$	−13.5809	−0.770100	−0.385050	−	0.922896i	$-0.625816\pi$
$311$	−13.5809	−0.770100	−0.385050	+	0.922896i	$0.625816\pi$
$312$	−39.0687	−2.21183
$313$	9.01267	0.509426	0.254713	−	0.967017i	$-0.418019\pi$
$313$	9.01267	0.509426	0.254713	+	0.967017i	$0.418019\pi$
$314$	8.78828	0.495951
$315$	90.6483	5.10746
$316$	23.1767	1.30379
$317$	13.4044	0.752866	0.376433	−	0.926444i	$-0.377151\pi$
$317$	13.4044	0.752866	0.376433	+	0.926444i	$0.377151\pi$
$318$	7.26446	0.407371
$319$	6.01443	0.336744
$320$	54.4800	3.04553
$321$	−35.3678	−1.97404
$322$	−21.5740	−1.20227
$323$	−0.993256	−0.0552663
$324$	66.0204	3.66780
$325$	−56.3461	−3.12552
$326$	−14.2510	−0.789291
$327$	49.8091	2.75445
$328$	11.6767	0.644736
$329$	−3.66004	−0.201785
$330$	28.1476	1.54948
$331$	13.3603	0.734349	0.367175	−	0.930152i	$-0.380325\pi$
$331$	13.3603	0.734349	0.367175	+	0.930152i	$0.380325\pi$
$332$	−10.0631	−0.552284
$333$	−68.4999	−3.75377
$334$	37.3817	2.04544
$335$	65.5457	3.58114
$336$	−1.47444	−0.0804375
$337$	−1.62078	−0.0882896	−0.0441448	−	0.999025i	$-0.514056\pi$
$337$	−1.62078	−0.0882896	−0.0441448	+	0.999025i	$0.514056\pi$
$338$	−16.0398	−0.872447
$339$	−36.2798	−1.97045
$340$	−17.4385	−0.945736
$341$	−0.920174	−0.0498302
$342$	12.4634	0.673942
$343$	14.6709	0.792155
$344$	25.2228	1.35992
$345$	−41.7744	−2.24906
$346$	7.22369	0.388348
$347$	−5.10977	−0.274307	−0.137154	−	0.990550i	$-0.543795\pi$
$347$	−5.10977	−0.274307	−0.137154	+	0.990550i	$0.543795\pi$
$348$	66.3863	3.55868
$349$	3.34659	0.179139	0.0895693	−	0.995981i	$-0.471451\pi$
$349$	3.34659	0.179139	0.0895693	+	0.995981i	$0.471451\pi$
$350$	86.8499	4.64232
$351$	59.0989	3.15447
$352$	−5.38616	−0.287083
$353$	−0.355246	−0.0189078	−0.00945392	−	0.999955i	$-0.503009\pi$
$353$	−0.355246	−0.0189078	−0.00945392	+	0.999955i	$0.503009\pi$
$354$	−99.5437	−5.29069
$355$	−50.6283	−2.68707
$356$	−43.5988	−2.31073
$357$	12.5132	0.662268
$358$	−40.1462	−2.12179
$359$	−21.0679	−1.11192	−0.555960	−	0.831209i	$-0.687649\pi$
$359$	−21.0679	−1.11192	−0.555960	+	0.831209i	$0.687649\pi$
$360$	82.1245	4.32834
$361$	−18.4151	−0.969216
$362$	−0.787791	−0.0414054
$363$	32.3184	1.69627
$364$	43.3456	2.27192
$365$	48.8729	2.55812
$366$	99.1506	5.18268
$367$	32.1036	1.67579	0.837897	−	0.545829i	$-0.183785\pi$
$367$	32.1036	1.67579	0.837897	+	0.545829i	$0.183785\pi$
$368$	0.478561	0.0249467
$369$	−30.4458	−1.58494
$370$	−91.6956	−4.76703
$371$	−3.02488	−0.157044
$372$	−10.1567	−0.526601
$373$	−15.8397	−0.820148	−0.410074	−	0.912052i	$-0.634497\pi$
$373$	−15.8397	−0.820148	−0.410074	+	0.912052i	$0.634497\pi$
$374$	2.73658	0.141505
$375$	101.378	5.23514
$376$	−3.31588	−0.171003
$377$	29.1373	1.50065
$378$	−91.0930	−4.68532
$379$	−2.42234	−0.124427	−0.0622136	−	0.998063i	$-0.519816\pi$
$379$	−2.42234	−0.124427	−0.0622136	+	0.998063i	$0.519816\pi$
$380$	10.2689	0.526783
$381$	−61.6069	−3.15622
$382$	−32.4469	−1.66013
$383$	−0.331527	−0.0169402	−0.00847011	−	0.999964i	$-0.502696\pi$
$383$	−0.331527	−0.0169402	−0.00847011	+	0.999964i	$0.502696\pi$
$384$	−57.2281	−2.92041
$385$	−11.7205	−0.597333
$386$	−2.58681	−0.131665
$387$	−65.7661	−3.34308
$388$	−45.9526	−2.33289
$389$	24.9615	1.26560	0.632800	−	0.774315i	$-0.281906\pi$
$389$	24.9615	1.26560	0.632800	+	0.774315i	$0.281906\pi$
$390$	136.363	6.90500
$391$	−4.06141	−0.205394
$392$	−5.89175	−0.297578
$393$	−41.3274	−2.08469
$394$	−38.8277	−1.95611
$395$	−30.3604	−1.52760
$396$	−21.1355	−1.06210
$397$	35.1544	1.76435	0.882175	−	0.470922i	$-0.156079\pi$
$397$	35.1544	1.76435	0.882175	+	0.470922i	$0.156079\pi$
$398$	−34.2700	−1.71780
$399$	−7.36856	−0.368889
$400$	−1.92653	−0.0963266
$401$	21.2163	1.05949	0.529747	−	0.848156i	$-0.322287\pi$
$401$	21.2163	1.05949	0.529747	+	0.848156i	$0.322287\pi$
$402$	−113.534	−5.66257
$403$	−4.45784	−0.222061
$404$	13.5470	0.673987
$405$	−86.4838	−4.29741
$406$	−44.9111	−2.22890
$407$	8.85680	0.439015
$408$	11.3365	0.561243
$409$	−7.83486	−0.387409	−0.193705	−	0.981060i	$-0.562050\pi$
$409$	−7.83486	−0.387409	−0.193705	+	0.981060i	$0.562050\pi$
$410$	−40.7555	−2.01277
$411$	−24.7124	−1.21897
$412$	−41.8233	−2.06049
$413$	41.4494	2.03959
$414$	50.9625	2.50467
$415$	13.1822	0.647089
$416$	−26.0936	−1.27934
$417$	−5.23981	−0.256595
$418$	−1.61147	−0.0788196
$419$	−1.13472	−0.0554347	−0.0277174	−	0.999616i	$-0.508824\pi$
$419$	−1.13472	−0.0554347	−0.0277174	+	0.999616i	$0.508824\pi$
$420$	−129.369	−6.31256
$421$	−29.0068	−1.41371	−0.706853	−	0.707361i	$-0.749886\pi$
$421$	−29.0068	−1.41371	−0.706853	+	0.707361i	$0.749886\pi$
$422$	46.5470	2.26587
$423$	8.64584	0.420375
$424$	−2.74045	−0.133088
$425$	16.3499	0.793089
$426$	87.6951	4.24884
$427$	−41.2858	−1.99796
$428$	35.5498	1.71836
$429$	−13.1712	−0.635909
$430$	−88.0361	−4.24548
$431$	14.8490	0.715249	0.357625	−	0.933865i	$-0.383587\pi$
$431$	14.8490	0.715249	0.357625	+	0.933865i	$0.383587\pi$
$432$	2.02065	0.0972188
$433$	16.7672	0.805778	0.402889	−	0.915249i	$-0.368006\pi$
$433$	16.7672	0.805778	0.402889	+	0.915249i	$0.368006\pi$
$434$	6.87115	0.329826
$435$	−86.9630	−4.16956
$436$	−50.0654	−2.39770
$437$	2.39161	0.114406
$438$	−84.6545	−4.04495
$439$	−5.23419	−0.249814	−0.124907	−	0.992168i	$-0.539863\pi$
$439$	−5.23419	−0.249814	−0.124907	+	0.992168i	$0.539863\pi$
$440$	−10.6184	−0.506213
$441$	15.3622	0.731533
$442$	13.2575	0.630596
$443$	30.7971	1.46321	0.731606	−	0.681728i	$-0.238771\pi$
$443$	30.7971	1.46321	0.731606	+	0.681728i	$0.238771\pi$
$444$	97.7598	4.63947
$445$	57.1125	2.70739
$446$	−10.5000	−0.497191
$447$	44.3798	2.09909
$448$	39.2939	1.85646
$449$	3.55970	0.167992	0.0839962	−	0.996466i	$-0.473232\pi$
$449$	3.55970	0.167992	0.0839962	+	0.996466i	$0.473232\pi$
$450$	−205.159	−9.67129
$451$	3.93653	0.185364
$452$	36.4665	1.71524
$453$	−3.18519	−0.149653
$454$	−46.3996	−2.17764
$455$	−56.7807	−2.66192
$456$	−6.67567	−0.312617
$457$	−2.28399	−0.106841	−0.0534204	−	0.998572i	$-0.517012\pi$
$457$	−2.28399	−0.106841	−0.0534204	+	0.998572i	$0.517012\pi$
$458$	−10.5557	−0.493235
$459$	−17.1487	−0.800434
$460$	41.9894	1.95776
$461$	−2.89345	−0.134761	−0.0673807	−	0.997727i	$-0.521464\pi$
$461$	−2.89345	−0.134761	−0.0673807	+	0.997727i	$0.521464\pi$
$462$	20.3016	0.944514
$463$	37.2766	1.73239	0.866194	−	0.499707i	$-0.166559\pi$
$463$	37.2766	1.73239	0.866194	+	0.499707i	$0.166559\pi$
$464$	0.996234	0.0462490
$465$	13.3048	0.616997
$466$	−65.2162	−3.02108
$467$	−24.0339	−1.11216	−0.556079	−	0.831130i	$-0.687695\pi$
$467$	−24.0339	−1.11216	−0.556079	+	0.831130i	$0.687695\pi$
$468$	−102.392	−4.73307
$469$	47.2750	2.18296
$470$	11.5735	0.533847
$471$	12.2736	0.565537
$472$	37.5519	1.72846
$473$	8.50333	0.390983
$474$	52.5884	2.41547
$475$	−9.62788	−0.441757
$476$	−12.5776	−0.576492
$477$	7.14546	0.327168
$478$	5.34866	0.244642
$479$	3.13467	0.143227	0.0716134	−	0.997432i	$-0.477185\pi$
$479$	3.13467	0.143227	0.0716134	+	0.997432i	$0.477185\pi$
$480$	77.8788	3.55466
$481$	42.9073	1.95640
$482$	−52.6263	−2.39706
$483$	−30.1299	−1.37096
$484$	−32.4847	−1.47658
$485$	60.1958	2.73335
$486$	59.4583	2.69708
$487$	−16.8106	−0.761759	−0.380879	−	0.924625i	$-0.624379\pi$
$487$	−16.8106	−0.761759	−0.380879	+	0.924625i	$0.624379\pi$
$488$	−37.4036	−1.69318
$489$	−19.9028	−0.900036
$490$	20.5642	0.928996
$491$	37.6338	1.69839	0.849195	−	0.528080i	$-0.177088\pi$
$491$	37.6338	1.69839	0.849195	+	0.528080i	$0.177088\pi$
$492$	43.4508	1.95891
$493$	−8.45476	−0.380783
$494$	−7.80686	−0.351247
$495$	27.6865	1.24442
$496$	−0.152418	−0.00684377
$497$	−36.5158	−1.63796
$498$	−22.8334	−1.02319
$499$	35.0687	1.56989	0.784946	−	0.619564i	$-0.212690\pi$
$499$	35.0687	1.56989	0.784946	+	0.619564i	$0.212690\pi$
$500$	−101.900	−4.55709
$501$	52.2068	2.33243
$502$	−5.96273	−0.266130
$503$	−26.5937	−1.18575	−0.592877	−	0.805293i	$-0.702008\pi$
$503$	−26.5937	−1.18575	−0.592877	+	0.805293i	$0.702008\pi$
$504$	59.2325	2.63843
$505$	−17.7459	−0.789683
$506$	−6.58928	−0.292929
$507$	−22.4009	−0.994859
$508$	61.9239	2.74743
$509$	−2.80087	−0.124147	−0.0620733	−	0.998072i	$-0.519771\pi$
$509$	−2.80087	−0.124147	−0.0620733	+	0.998072i	$0.519771\pi$
$510$	−39.5684	−1.75212
$511$	35.2497	1.55935
$512$	−1.73092	−0.0764967
$513$	10.0982	0.445849
$514$	−19.8210	−0.874267
$515$	54.7866	2.41419
$516$	93.8583	4.13188
$517$	−1.11788	−0.0491642
$518$	−66.1357	−2.90584
$519$	10.0885	0.442836
$520$	−51.4415	−2.25586
$521$	−11.6091	−0.508606	−0.254303	−	0.967125i	$-0.581846\pi$
$521$	−11.6091	−0.508606	−0.254303	+	0.967125i	$0.581846\pi$
$522$	106.090	4.64344
$523$	−24.2243	−1.05925	−0.529627	−	0.848231i	$-0.677668\pi$
$523$	−24.2243	−1.05925	−0.529627	+	0.848231i	$0.677668\pi$
$524$	41.5400	1.81468
$525$	121.293	5.29368
$526$	51.1451	2.23003
$527$	1.29353	0.0563470
$528$	−0.450336	−0.0195983
$529$	−13.2207	−0.574814
$530$	9.56509	0.415481
$531$	−97.9129	−4.24906
$532$	7.40647	0.321111
$533$	19.0708	0.826046
$534$	−98.9267	−4.28098
$535$	−46.5686	−2.01334
$536$	42.8296	1.84996
$537$	−56.0676	−2.41950
$538$	40.2423	1.73497
$539$	−1.98628	−0.0855550
$540$	177.294	7.62952
$541$	9.19952	0.395518	0.197759	−	0.980251i	$-0.436634\pi$
$541$	9.19952	0.395518	0.197759	+	0.980251i	$0.436634\pi$
$542$	23.9769	1.02990
$543$	−1.10022	−0.0472149
$544$	7.57157	0.324628
$545$	65.5834	2.80928
$546$	98.3521	4.20908
$547$	−15.9436	−0.681699	−0.340849	−	0.940118i	$-0.610715\pi$
$547$	−15.9436	−0.681699	−0.340849	+	0.940118i	$0.610715\pi$
$548$	24.8395	1.06109
$549$	97.5263	4.16232
$550$	26.5263	1.13109
$551$	4.97869	0.212100
$552$	−27.2967	−1.16183
$553$	−21.8975	−0.931178
$554$	30.9021	1.31290
$555$	−128.061	−5.43588
$556$	5.26677	0.223361
$557$	−31.9348	−1.35312	−0.676560	−	0.736387i	$-0.736530\pi$
$557$	−31.9348	−1.35312	−0.676560	+	0.736387i	$0.736530\pi$
$558$	−16.2312	−0.687122
$559$	41.1949	1.74236
$560$	−1.94139	−0.0820388
$561$	3.82187	0.161360
$562$	−24.7731	−1.04499
$563$	15.0485	0.634218	0.317109	−	0.948389i	$-0.397288\pi$
$563$	15.0485	0.634218	0.317109	+	0.948389i	$0.397288\pi$
$564$	−12.3389	−0.519563
$565$	−47.7694	−2.00967
$566$	−60.9287	−2.56103
$567$	−62.3767	−2.61958
$568$	−33.0821	−1.38810
$569$	10.6755	0.447542	0.223771	−	0.974642i	$-0.428163\pi$
$569$	10.6755	0.447542	0.223771	+	0.974642i	$0.428163\pi$
$570$	23.3004	0.975944
$571$	42.1317	1.76315	0.881577	−	0.472039i	$-0.156482\pi$
$571$	42.1317	1.76315	0.881577	+	0.472039i	$0.156482\pi$
$572$	13.2389	0.553547
$573$	−45.3149	−1.89306
$574$	−29.3950	−1.22692
$575$	−39.3682	−1.64177
$576$	−92.8210	−3.86754
$577$	−23.0688	−0.960368	−0.480184	−	0.877168i	$-0.659430\pi$
$577$	−23.0688	−0.960368	−0.480184	+	0.877168i	$0.659430\pi$
$578$	34.9249	1.45269
$579$	−3.61270	−0.150139
$580$	87.4105	3.62952
$581$	9.50770	0.394446
$582$	−104.267	−4.32202
$583$	−0.923883	−0.0382633
$584$	31.9351	1.32148
$585$	134.129	5.54555
$586$	19.5020	0.805618
$587$	13.3305	0.550208	0.275104	−	0.961414i	$-0.411288\pi$
$587$	13.3305	0.550208	0.275104	+	0.961414i	$0.411288\pi$
$588$	−21.9242	−0.904139
$589$	−0.761712	−0.0313858
$590$	−131.069	−5.39601
$591$	−54.2263	−2.23057
$592$	1.46704	0.0602952
$593$	−7.22150	−0.296551	−0.148276	−	0.988946i	$-0.547372\pi$
$593$	−7.22150	−0.296551	−0.148276	+	0.988946i	$0.547372\pi$
$594$	−27.8223	−1.14156
$595$	16.4761	0.675453
$596$	−44.6081	−1.82722
$597$	−47.8610	−1.95882
$598$	−31.9222	−1.30539
$599$	−35.4745	−1.44945	−0.724725	−	0.689038i	$-0.758033\pi$
$599$	−35.4745	−1.44945	−0.724725	+	0.689038i	$0.758033\pi$
$600$	109.888	4.48616
$601$	−41.0514	−1.67452	−0.837261	−	0.546804i	$-0.815844\pi$
$601$	−41.0514	−1.67452	−0.837261	+	0.546804i	$0.815844\pi$
$602$	−63.4963	−2.58792
$603$	−111.674	−4.54773
$604$	3.20158	0.130271
$605$	42.5535	1.73004
$606$	30.7384	1.24866
$607$	−40.0247	−1.62455	−0.812276	−	0.583273i	$-0.801772\pi$
$607$	−40.0247	−1.62455	−0.812276	+	0.583273i	$0.801772\pi$
$608$	−4.45862	−0.180821
$609$	−62.7223	−2.54164
$610$	130.551	5.28586
$611$	−5.41562	−0.219093
$612$	29.7111	1.20100
$613$	−31.6985	−1.28029	−0.640145	−	0.768254i	$-0.721126\pi$
$613$	−31.6985	−1.28029	−0.640145	+	0.768254i	$0.721126\pi$
$614$	33.0446	1.33357
$615$	−56.9186	−2.29518
$616$	−7.65856	−0.308572
$617$	16.9635	0.682927	0.341463	−	0.939895i	$-0.389078\pi$
$617$	16.9635	0.682927	0.341463	+	0.939895i	$0.389078\pi$
$618$	−94.8980	−3.81736
$619$	−4.74653	−0.190779	−0.0953896	−	0.995440i	$-0.530410\pi$
$619$	−4.74653	−0.190779	−0.0953896	+	0.995440i	$0.530410\pi$
$620$	−13.3733	−0.537085
$621$	41.2916	1.65697
$622$	30.9738	1.24194
$623$	41.1926	1.65034
$624$	−2.18168	−0.0873370
$625$	70.5388	2.82155
$626$	−20.5552	−0.821550
$627$	−2.25056	−0.0898787
$628$	−12.3367	−0.492290
$629$	−12.4504	−0.496430
$630$	−206.741	−8.23678
$631$	−15.1281	−0.602239	−0.301120	−	0.953586i	$-0.597360\pi$
$631$	−15.1281	−0.602239	−0.301120	+	0.953586i	$0.597360\pi$
$632$	−19.8385	−0.789132
$633$	65.0069	2.58379
$634$	−30.5714	−1.21414
$635$	−81.1175	−3.21905
$636$	−10.1977	−0.404364
$637$	−9.62264	−0.381263
$638$	−13.7171	−0.543065
$639$	86.2585	3.41233
$640$	−75.3520	−2.97855
$641$	47.1250	1.86132	0.930662	−	0.365879i	$-0.119232\pi$
$641$	47.1250	1.86132	0.930662	+	0.365879i	$0.119232\pi$
$642$	80.6633	3.18353
$643$	27.6183	1.08916	0.544580	−	0.838709i	$-0.316689\pi$
$643$	27.6183	1.08916	0.544580	+	0.838709i	$0.316689\pi$
$644$	30.2849	1.19339
$645$	−122.950	−4.84115
$646$	2.26532	0.0891277
$647$	−37.4574	−1.47260	−0.736301	−	0.676654i	$-0.763429\pi$
$647$	−37.4574	−1.47260	−0.736301	+	0.676654i	$0.763429\pi$
$648$	−56.5113	−2.21997
$649$	12.6598	0.496941
$650$	128.508	5.04051
$651$	9.59616	0.376103
$652$	20.0052	0.783464
$653$	40.7652	1.59527	0.797633	−	0.603143i	$-0.206085\pi$
$653$	40.7652	1.59527	0.797633	+	0.603143i	$0.206085\pi$
$654$	−113.599	−4.44209
$655$	−54.4155	−2.12619
$656$	0.652050	0.0254583
$657$	−83.2677	−3.24858
$658$	8.34745	0.325417
$659$	30.5964	1.19187	0.595933	−	0.803034i	$-0.296782\pi$
$659$	30.5964	1.19187	0.595933	+	0.803034i	$0.296782\pi$
$660$	−39.5129	−1.53804
$661$	2.45174	0.0953616	0.0476808	−	0.998863i	$-0.484817\pi$
$661$	2.45174	0.0953616	0.0476808	+	0.998863i	$0.484817\pi$
$662$	−30.4708	−1.18428
$663$	18.5153	0.719074
$664$	8.61367	0.334275
$665$	−9.70214	−0.376233
$666$	156.228	6.05369
$667$	20.3578	0.788257
$668$	−52.4755	−2.03034
$669$	−14.6642	−0.566951
$670$	−149.490	−5.77530
$671$	−12.6098	−0.486797
$672$	56.1703	2.16682
$673$	−17.9842	−0.693241	−0.346621	−	0.938005i	$-0.612671\pi$
$673$	−17.9842	−0.693241	−0.346621	+	0.938005i	$0.612671\pi$
$674$	3.69651	0.142384
$675$	−166.227	−6.39807
$676$	22.5162	0.866007
$677$	−14.4968	−0.557157	−0.278578	−	0.960413i	$-0.589863\pi$
$677$	−14.4968	−0.557157	−0.278578	+	0.960413i	$0.589863\pi$
$678$	82.7432	3.17773
$679$	43.4164	1.66617
$680$	14.9268	0.572416
$681$	−64.8011	−2.48318
$682$	2.09864	0.0803610
$683$	−4.47242	−0.171132	−0.0855661	−	0.996332i	$-0.527270\pi$
$683$	−4.47242	−0.171132	−0.0855661	+	0.996332i	$0.527270\pi$
$684$	−17.4958	−0.668967
$685$	−32.5386	−1.24324
$686$	−33.4599	−1.27751
$687$	−14.7419	−0.562440
$688$	1.40850	0.0536984
$689$	−4.47580	−0.170515
$690$	95.2748	3.62705
$691$	−15.1844	−0.577641	−0.288820	−	0.957383i	$-0.593263\pi$
$691$	−15.1844	−0.577641	−0.288820	+	0.957383i	$0.593263\pi$
$692$	−10.1404	−0.385481
$693$	19.9690	0.758559
$694$	11.6539	0.442374
$695$	−6.89924	−0.261703
$696$	−56.8244	−2.15392
$697$	−5.53376	−0.209606
$698$	−7.63255	−0.288896
$699$	−91.0802	−3.44497
$700$	−121.918	−4.60805
$701$	−7.19552	−0.271771	−0.135886	−	0.990725i	$-0.543388\pi$
$701$	−7.19552	−0.271771	−0.135886	+	0.990725i	$0.543388\pi$
$702$	−134.787	−5.08720
$703$	7.33158	0.276516
$704$	12.0014	0.452321
$705$	16.1634	0.608751
$706$	0.810209	0.0304926
$707$	−12.7993	−0.481367
$708$	139.737	5.25163
$709$	26.0825	0.979549	0.489775	−	0.871849i	$-0.337079\pi$
$709$	26.0825	0.979549	0.489775	+	0.871849i	$0.337079\pi$
$710$	115.468	4.33343
$711$	51.7269	1.93991
$712$	37.3191	1.39859
$713$	−3.11463	−0.116644
$714$	−28.5388	−1.06804
$715$	−17.3424	−0.648569
$716$	56.3561	2.10613
$717$	7.46987	0.278967
$718$	48.0495	1.79319
$719$	−15.2180	−0.567536	−0.283768	−	0.958893i	$-0.591585\pi$
$719$	−15.2180	−0.567536	−0.283768	+	0.958893i	$0.591585\pi$
$720$	4.58601	0.170910
$721$	39.5150	1.47162
$722$	41.9993	1.56305
$723$	−73.4972	−2.73339
$724$	1.10588	0.0410997
$725$	−81.9540	−3.04370
$726$	−73.7085	−2.73558
$727$	−20.3329	−0.754107	−0.377054	−	0.926191i	$-0.623063\pi$
$727$	−20.3329	−0.754107	−0.377054	+	0.926191i	$0.623063\pi$
$728$	−37.1023	−1.37510
$729$	21.1751	0.784265
$730$	−111.464	−4.12548
$731$	−11.9535	−0.442117
$732$	−139.185	−5.14442
$733$	−20.5153	−0.757749	−0.378874	−	0.925448i	$-0.623689\pi$
$733$	−20.5153	−0.757749	−0.378874	+	0.925448i	$0.623689\pi$
$734$	−73.2186	−2.70255
$735$	28.7197	1.05934
$736$	−18.2312	−0.672012
$737$	14.4391	0.531871
$738$	69.4376	2.55603
$739$	23.2022	0.853508	0.426754	−	0.904368i	$-0.359657\pi$
$739$	23.2022	0.853508	0.426754	+	0.904368i	$0.359657\pi$
$740$	128.720	4.73184
$741$	−10.9030	−0.400531
$742$	6.89885	0.253265
$743$	13.3108	0.488325	0.244162	−	0.969734i	$-0.421487\pi$
$743$	13.3108	0.488325	0.244162	+	0.969734i	$0.421487\pi$
$744$	8.69381	0.318731
$745$	58.4346	2.14088
$746$	36.1256	1.32265
$747$	−22.4593	−0.821744
$748$	−3.84154	−0.140461
$749$	−33.5878	−1.22727
$750$	−231.213	−8.44269
$751$	−15.1166	−0.551611	−0.275806	−	0.961213i	$-0.588945\pi$
$751$	−15.1166	−0.551611	−0.275806	+	0.961213i	$0.588945\pi$
$752$	−0.185166	−0.00675230
$753$	−8.32748	−0.303470
$754$	−66.4533	−2.42009
$755$	−4.19393	−0.152633
$756$	127.874	4.65073
$757$	17.0184	0.618544	0.309272	−	0.950974i	$-0.399915\pi$
$757$	17.0184	0.618544	0.309272	+	0.950974i	$0.399915\pi$
$758$	5.52462	0.200663
$759$	−9.20251	−0.334030
$760$	−8.78983	−0.318841
$761$	10.2783	0.372586	0.186293	−	0.982494i	$-0.440353\pi$
$761$	10.2783	0.372586	0.186293	+	0.982494i	$0.440353\pi$
$762$	140.507	5.09002
$763$	47.3022	1.71246
$764$	45.5481	1.64787
$765$	−38.9202	−1.40716
$766$	0.756113	0.0273195
$767$	61.3312	2.21454
$768$	47.7674	1.72366
$769$	13.8801	0.500530	0.250265	−	0.968177i	$-0.419482\pi$
$769$	13.8801	0.500530	0.250265	+	0.968177i	$0.419482\pi$
$770$	26.7310	0.963317
$771$	−27.6817	−0.996934
$772$	3.63129	0.130693
$773$	−25.4302	−0.914662	−0.457331	−	0.889297i	$-0.651195\pi$
$773$	−25.4302	−0.914662	−0.457331	+	0.889297i	$0.651195\pi$
$774$	149.993	5.39137
$775$	12.5385	0.450396
$776$	39.3338	1.41200
$777$	−92.3643	−3.31355
$778$	−56.9297	−2.04103
$779$	3.25863	0.116752
$780$	−191.422	−6.85402
$781$	−11.1529	−0.399083
$782$	9.26285	0.331239
$783$	85.9579	3.07189
$784$	−0.329008	−0.0117503
$785$	16.1606	0.576796
$786$	94.2552	3.36197
$787$	−36.1771	−1.28958	−0.644788	−	0.764362i	$-0.723054\pi$
$787$	−36.1771	−1.28958	−0.644788	+	0.764362i	$0.723054\pi$
$788$	54.5053	1.94167
$789$	71.4286	2.54292
$790$	69.2430	2.46355
$791$	−34.4538	−1.22504
$792$	18.0912	0.642844
$793$	−61.0890	−2.16933
$794$	−80.1766	−2.84536
$795$	13.3585	0.473776
$796$	48.1073	1.70512
$797$	25.1496	0.890845	0.445422	−	0.895321i	$-0.353054\pi$
$797$	25.1496	0.890845	0.445422	+	0.895321i	$0.353054\pi$
$798$	16.8054	0.594906
$799$	1.57145	0.0555939
$800$	73.3931	2.59484
$801$	−97.3061	−3.43814
$802$	−48.3881	−1.70864
$803$	10.7662	0.379932
$804$	159.376	5.62077
$805$	−39.6719	−1.39825
$806$	10.1670	0.358116
$807$	56.2018	1.97840
$808$	−11.5958	−0.407937
$809$	−0.967526	−0.0340164	−0.0170082	−	0.999855i	$-0.505414\pi$
$809$	−0.967526	−0.0340164	−0.0170082	+	0.999855i	$0.505414\pi$
$810$	197.243	6.93043
$811$	27.3523	0.960469	0.480235	−	0.877140i	$-0.340551\pi$
$811$	27.3523	0.960469	0.480235	+	0.877140i	$0.340551\pi$
$812$	63.0451	2.21245
$813$	33.4859	1.17440
$814$	−20.1997	−0.707998
$815$	−26.2059	−0.917953
$816$	0.633057	0.0221614
$817$	7.03898	0.246263
$818$	17.8690	0.624773
$819$	96.7408	3.38040
$820$	57.2114	1.99791
$821$	5.04773	0.176167	0.0880835	−	0.996113i	$-0.471926\pi$
$821$	5.04773	0.176167	0.0880835	+	0.996113i	$0.471926\pi$
$822$	56.3614	1.96583
$823$	30.3368	1.05747	0.528737	−	0.848786i	$-0.322666\pi$
$823$	30.3368	1.05747	0.528737	+	0.848786i	$0.322666\pi$
$824$	35.7993	1.24713
$825$	37.0464	1.28979
$826$	−94.5337	−3.28925
$827$	15.9798	0.555673	0.277836	−	0.960628i	$-0.410383\pi$
$827$	15.9798	0.555673	0.277836	+	0.960628i	$0.410383\pi$
$828$	−71.5399	−2.48618
$829$	−30.7643	−1.06849	−0.534244	−	0.845330i	$-0.679404\pi$
$829$	−30.7643	−1.06849	−0.534244	+	0.845330i	$0.679404\pi$
$830$	−30.0646	−1.04356
$831$	43.1575	1.49712
$832$	58.1417	2.01570
$833$	2.79220	0.0967440
$834$	11.9504	0.413810
$835$	68.7405	2.37886
$836$	2.26214	0.0782378
$837$	−13.1511	−0.454568
$838$	2.58795	0.0893994
$839$	3.02422	0.104408	0.0522038	−	0.998636i	$-0.483375\pi$
$839$	3.02422	0.104408	0.0522038	+	0.998636i	$0.483375\pi$
$840$	110.736	3.82074
$841$	13.3795	0.461360
$842$	66.1558	2.27988
$843$	−34.5977	−1.19161
$844$	−65.3414	−2.24914
$845$	−29.4952	−1.01466
$846$	−19.7185	−0.677938
$847$	30.6918	1.05458
$848$	−0.153032	−0.00525516
$849$	−85.0923	−2.92036
$850$	−37.2893	−1.27901
$851$	29.9787	1.02766
$852$	−123.104	−4.21748
$853$	35.2885	1.20826	0.604128	−	0.796888i	$-0.293522\pi$
$853$	35.2885	1.20826	0.604128	+	0.796888i	$0.293522\pi$
$854$	94.1604	3.22210
$855$	22.9186	0.783801
$856$	−30.4294	−1.04006
$857$	−12.9007	−0.440678	−0.220339	−	0.975423i	$-0.570716\pi$
$857$	−12.9007	−0.440678	−0.220339	+	0.975423i	$0.570716\pi$
$858$	30.0394	1.02553
$859$	6.85720	0.233965	0.116982	−	0.993134i	$-0.462678\pi$
$859$	6.85720	0.233965	0.116982	+	0.993134i	$0.462678\pi$
$860$	123.583	4.21414
$861$	−41.0527	−1.39907
$862$	−33.8660	−1.15348
$863$	16.7398	0.569828	0.284914	−	0.958553i	$-0.408035\pi$
$863$	16.7398	0.569828	0.284914	+	0.958553i	$0.408035\pi$
$864$	−76.9787	−2.61887
$865$	13.2835	0.451652
$866$	−38.2408	−1.29948
$867$	48.7757	1.65651
$868$	−9.64554	−0.327391
$869$	−6.68811	−0.226879
$870$	198.336	6.72423
$871$	69.9510	2.37020
$872$	42.8543	1.45123
$873$	−102.559	−3.47111
$874$	−5.45455	−0.184503
$875$	96.2757	3.25471
$876$	118.836	4.01509
$877$	25.3400	0.855670	0.427835	−	0.903857i	$-0.359276\pi$
$877$	25.3400	0.855670	0.427835	+	0.903857i	$0.359276\pi$
$878$	11.9376	0.402875
$879$	27.2362	0.918653
$880$	−0.592955	−0.0199885
$881$	−36.0743	−1.21538	−0.607688	−	0.794176i	$-0.707903\pi$
$881$	−36.0743	−1.21538	−0.607688	+	0.794176i	$0.707903\pi$
$882$	−35.0365	−1.17974
$883$	21.4519	0.721915	0.360958	−	0.932582i	$-0.382450\pi$
$883$	21.4519	0.721915	0.360958	+	0.932582i	$0.382450\pi$
$884$	−18.6106	−0.625941
$885$	−183.049	−6.15312
$886$	−70.2388	−2.35972
$887$	−32.9499	−1.10635	−0.553174	−	0.833066i	$-0.686584\pi$
$887$	−32.9499	−1.10635	−0.553174	+	0.833066i	$0.686584\pi$
$888$	−83.6791	−2.80809
$889$	−58.5062	−1.96224
$890$	−130.256	−4.36620
$891$	−19.0516	−0.638251
$892$	14.7397	0.493521
$893$	−0.925369	−0.0309663
$894$	−101.217	−3.38520
$895$	−73.8240	−2.46766
$896$	−54.3478	−1.81563
$897$	−44.5821	−1.48855
$898$	−8.11859	−0.270921
$899$	−6.48381	−0.216247
$900$	287.997	9.59989
$901$	1.29874	0.0432674
$902$	−8.97804	−0.298936
$903$	−88.6781	−2.95102
$904$	−31.2141	−1.03816
$905$	−1.44865	−0.0481548
$906$	7.26446	0.241346
$907$	−35.4305	−1.17645	−0.588224	−	0.808698i	$-0.700173\pi$
$907$	−35.4305	−1.17645	−0.588224	+	0.808698i	$0.700173\pi$
$908$	65.1345	2.16157
$909$	30.2348	1.00283
$910$	129.500	4.29287
$911$	34.2354	1.13427	0.567135	−	0.823625i	$-0.308052\pi$
$911$	34.2354	1.13427	0.567135	+	0.823625i	$0.308052\pi$
$912$	−0.372784	−0.0123441
$913$	2.90391	0.0961055
$914$	5.20910	0.172302
$915$	182.326	6.02751
$916$	14.8178	0.489594
$917$	−39.2474	−1.29606
$918$	39.1111	1.29086
$919$	−23.0102	−0.759036	−0.379518	−	0.925184i	$-0.623910\pi$
$919$	−23.0102	−0.759036	−0.379518	+	0.925184i	$0.623910\pi$
$920$	−35.9415	−1.18496
$921$	46.1497	1.52068
$922$	6.59908	0.217329
$923$	−54.0310	−1.77845
$924$	−28.4988	−0.937541
$925$	−120.685	−3.96809
$926$	−85.0166	−2.79382
$927$	−93.3434	−3.06580
$928$	−37.9525	−1.24585
$929$	4.14539	0.136006	0.0680030	−	0.997685i	$-0.478337\pi$
$929$	4.14539	0.136006	0.0680030	+	0.997685i	$0.478337\pi$
$930$	−30.3443	−0.995030
$931$	−1.64422	−0.0538872
$932$	91.5488	2.99878
$933$	43.2577	1.41619
$934$	54.8141	1.79357
$935$	5.03224	0.164572
$936$	87.6441	2.86474
$937$	26.0812	0.852035	0.426018	−	0.904715i	$-0.359916\pi$
$937$	26.0812	0.852035	0.426018	+	0.904715i	$0.359916\pi$
$938$	−107.820	−3.52045
$939$	−28.7071	−0.936821
$940$	−16.2466	−0.529906
$941$	7.99742	0.260708	0.130354	−	0.991467i	$-0.458389\pi$
$941$	7.99742	0.260708	0.130354	+	0.991467i	$0.458389\pi$
$942$	−27.9924	−0.912040
$943$	13.3245	0.433905
$944$	2.09698	0.0682508
$945$	−167.509	−5.44907
$946$	−19.3935	−0.630538
$947$	34.9839	1.13682	0.568412	−	0.822744i	$-0.307558\pi$
$947$	34.9839	1.13682	0.568412	+	0.822744i	$0.307558\pi$
$948$	−73.8223	−2.39764
$949$	52.1576	1.69311
$950$	21.9583	0.712421
$951$	−42.6956	−1.38450
$952$	10.7660	0.348928
$953$	−12.6709	−0.410450	−0.205225	−	0.978715i	$-0.565793\pi$
$953$	−12.6709	−0.410450	−0.205225	+	0.978715i	$0.565793\pi$
$954$	−16.2966	−0.527623
$955$	−59.6659	−1.93074
$956$	−7.50830	−0.242836
$957$	−19.1571	−0.619262
$958$	−7.14923	−0.230981
$959$	−23.4686	−0.757840
$960$	−173.529	−5.60064
$961$	−30.0080	−0.968000
$962$	−97.8585	−3.15508
$963$	79.3419	2.55676
$964$	73.8754	2.37937
$965$	−4.75683	−0.153128
$966$	68.7172	2.21094
$967$	−46.5301	−1.49631	−0.748154	−	0.663526i	$-0.769059\pi$
$967$	−46.5301	−1.49631	−0.748154	+	0.663526i	$0.769059\pi$
$968$	27.8058	0.893712
$969$	3.16371	0.101633
$970$	−137.288	−4.40806
$971$	49.9686	1.60357	0.801784	−	0.597614i	$-0.203885\pi$
$971$	49.9686	1.60357	0.801784	+	0.597614i	$0.203885\pi$
$972$	−83.4660	−2.67717
$973$	−4.97610	−0.159526
$974$	38.3398	1.22849
$975$	179.473	5.74774
$976$	−2.08870	−0.0668576
$977$	−16.7965	−0.537368	−0.268684	−	0.963228i	$-0.586589\pi$
$977$	−16.7965	−0.537368	−0.268684	+	0.963228i	$0.586589\pi$
$978$	45.3923	1.45148
$979$	12.5813	0.402101
$980$	−28.8675	−0.922138
$981$	−111.739	−3.56754
$982$	−85.8313	−2.73899
$983$	4.26172	0.135928	0.0679639	−	0.997688i	$-0.478350\pi$
$983$	4.26172	0.135928	0.0679639	+	0.997688i	$0.478350\pi$
$984$	−37.1924	−1.18565
$985$	−71.3995	−2.27498
$986$	19.2827	0.614088
$987$	11.6579	0.371076
$988$	10.9591	0.348654
$989$	28.7823	0.915223
$990$	−63.1445	−2.00687
$991$	−11.3886	−0.361771	−0.180886	−	0.983504i	$-0.557896\pi$
$991$	−11.3886	−0.361771	−0.180886	+	0.983504i	$0.557896\pi$
$992$	5.80651	0.184357
$993$	−42.5552	−1.35045
$994$	83.2815	2.64153
$995$	−63.0184	−1.99782
$996$	32.0529	1.01564
$997$	−5.46600	−0.173110	−0.0865550	−	0.996247i	$-0.527586\pi$
$997$	−5.46600	−0.173110	−0.0865550	+	0.996247i	$0.527586\pi$
$998$	−79.9812	−2.53176
$999$	126.581	4.00484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.a.1.19	✓	147

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.19	✓	147	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.28070 q^{2} -3.18519 q^{3} +3.20158 q^{4} -4.19393 q^{5} +7.26446 q^{6} -3.02488 q^{7} -2.74045 q^{8} +7.14546 q^{9} +O(q^{10})\)	\(q-2.28070 q^{2} -3.18519 q^{3} +3.20158 q^{4} -4.19393 q^{5} +7.26446 q^{6} -3.02488 q^{7} -2.74045 q^{8} +7.14546 q^{9} +9.56509 q^{10} -0.923883 q^{11} -10.1977 q^{12} -4.47580 q^{13} +6.89885 q^{14} +13.3585 q^{15} -0.153032 q^{16} +1.29874 q^{17} -16.2966 q^{18} -0.764782 q^{19} -13.4272 q^{20} +9.63484 q^{21} +2.10710 q^{22} -3.12718 q^{23} +8.72886 q^{24} +12.5890 q^{25} +10.2080 q^{26} -13.2041 q^{27} -9.68442 q^{28} -6.50995 q^{29} -30.4666 q^{30} +0.995985 q^{31} +5.82992 q^{32} +2.94275 q^{33} -2.96204 q^{34} +12.6861 q^{35} +22.8768 q^{36} -9.58649 q^{37} +1.74424 q^{38} +14.2563 q^{39} +11.4932 q^{40} -4.26086 q^{41} -21.9742 q^{42} -9.20390 q^{43} -2.95789 q^{44} -29.9675 q^{45} +7.13216 q^{46} +1.20998 q^{47} +0.487438 q^{48} +2.14992 q^{49} -28.7118 q^{50} -4.13675 q^{51} -14.3297 q^{52} +1.00000 q^{53} +30.1145 q^{54} +3.87470 q^{55} +8.28954 q^{56} +2.43598 q^{57} +14.8472 q^{58} -13.7028 q^{59} +42.7683 q^{60} +13.6487 q^{61} -2.27154 q^{62} -21.6142 q^{63} -12.9902 q^{64} +18.7712 q^{65} -6.71151 q^{66} -15.6287 q^{67} +4.15804 q^{68} +9.96068 q^{69} -28.9333 q^{70} +12.0718 q^{71} -19.5818 q^{72} -11.6532 q^{73} +21.8639 q^{74} -40.0985 q^{75} -2.44851 q^{76} +2.79464 q^{77} -32.5143 q^{78} +7.23914 q^{79} +0.641807 q^{80} +20.6212 q^{81} +9.71773 q^{82} -3.14316 q^{83} +30.8467 q^{84} -5.44684 q^{85} +20.9913 q^{86} +20.7355 q^{87} +2.53185 q^{88} -13.6179 q^{89} +68.3469 q^{90} +13.5388 q^{91} -10.0119 q^{92} -3.17241 q^{93} -2.75959 q^{94} +3.20744 q^{95} -18.5694 q^{96} -14.3531 q^{97} -4.90333 q^{98} -6.60157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

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