LMFDB - Embedded newform 8003.2.a.a.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.68460 q^{2} -1.10941 q^{3} +5.20709 q^{4} +3.69885 q^{5} +2.97832 q^{6} +2.40865 q^{7} -8.60976 q^{8} -1.76921 q^{9} +O(q^{10})$	\(q-2.68460 q^{2} -1.10941 q^{3} +5.20709 q^{4} +3.69885 q^{5} +2.97832 q^{6} +2.40865 q^{7} -8.60976 q^{8} -1.76921 q^{9} -9.92993 q^{10} +0.422417 q^{11} -5.77679 q^{12} +0.251181 q^{13} -6.46626 q^{14} -4.10353 q^{15} +12.6996 q^{16} +6.41367 q^{17} +4.74963 q^{18} -6.84321 q^{19} +19.2602 q^{20} -2.67217 q^{21} -1.13402 q^{22} -5.31209 q^{23} +9.55174 q^{24} +8.68147 q^{25} -0.674321 q^{26} +5.29101 q^{27} +12.5420 q^{28} -10.4444 q^{29} +11.0164 q^{30} -4.08973 q^{31} -16.8738 q^{32} -0.468633 q^{33} -17.2181 q^{34} +8.90922 q^{35} -9.21244 q^{36} -11.8129 q^{37} +18.3713 q^{38} -0.278662 q^{39} -31.8462 q^{40} +4.62078 q^{41} +7.17372 q^{42} +7.18487 q^{43} +2.19956 q^{44} -6.54405 q^{45} +14.2609 q^{46} -0.848440 q^{47} -14.0890 q^{48} -1.19842 q^{49} -23.3063 q^{50} -7.11538 q^{51} +1.30792 q^{52} +1.00000 q^{53} -14.2042 q^{54} +1.56246 q^{55} -20.7379 q^{56} +7.59191 q^{57} +28.0391 q^{58} -4.14649 q^{59} -21.3675 q^{60} +6.42455 q^{61} +10.9793 q^{62} -4.26141 q^{63} +19.9004 q^{64} +0.929080 q^{65} +1.25809 q^{66} +6.65552 q^{67} +33.3965 q^{68} +5.89328 q^{69} -23.9177 q^{70} +9.53426 q^{71} +15.2325 q^{72} -6.09687 q^{73} +31.7129 q^{74} -9.63130 q^{75} -35.6332 q^{76} +1.01745 q^{77} +0.748098 q^{78} +9.59628 q^{79} +46.9739 q^{80} -0.562253 q^{81} -12.4049 q^{82} -11.5895 q^{83} -13.9142 q^{84} +23.7232 q^{85} -19.2885 q^{86} +11.5871 q^{87} -3.63691 q^{88} +4.12878 q^{89} +17.5682 q^{90} +0.605006 q^{91} -27.6605 q^{92} +4.53719 q^{93} +2.27772 q^{94} -25.3120 q^{95} +18.7200 q^{96} +6.55809 q^{97} +3.21729 q^{98} -0.747345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.68460	−1.89830	−0.949150	−	0.314824i	$-0.898055\pi$
$2$	−2.68460	−1.89830	−0.949150	+	0.314824i	$0.898055\pi$
$3$	−1.10941	−0.640518	−0.320259	−	0.947330i	$-0.603770\pi$
$3$	−1.10941	−0.640518	−0.320259	+	0.947330i	$0.603770\pi$
$4$	5.20709	2.60354
$5$	3.69885	1.65417	0.827087	−	0.562073i	$-0.189996\pi$
$5$	3.69885	1.65417	0.827087	+	0.562073i	$0.189996\pi$
$6$	2.97832	1.21589
$7$	2.40865	0.910383	0.455191	−	0.890394i	$-0.349571\pi$
$7$	2.40865	0.910383	0.455191	+	0.890394i	$0.349571\pi$
$8$	−8.60976	−3.04401
$9$	−1.76921	−0.589737
$10$	−9.92993	−3.14012
$11$	0.422417	0.127363	0.0636817	−	0.997970i	$-0.479716\pi$
$11$	0.422417	0.127363	0.0636817	+	0.997970i	$0.479716\pi$
$12$	−5.77679	−1.66762
$13$	0.251181	0.0696651	0.0348325	−	0.999393i	$-0.488910\pi$
$13$	0.251181	0.0696651	0.0348325	+	0.999393i	$0.488910\pi$
$14$	−6.46626	−1.72818
$15$	−4.10353	−1.05953
$16$	12.6996	3.17490
$17$	6.41367	1.55554	0.777771	−	0.628547i	$-0.216350\pi$
$17$	6.41367	1.55554	0.777771	+	0.628547i	$0.216350\pi$
$18$	4.74963	1.11950
$19$	−6.84321	−1.56994	−0.784970	−	0.619534i	$-0.787322\pi$
$19$	−6.84321	−1.56994	−0.784970	+	0.619534i	$0.787322\pi$
$20$	19.2602	4.30672
$21$	−2.67217	−0.583116
$22$	−1.13402	−0.241774
$23$	−5.31209	−1.10765	−0.553824	−	0.832634i	$-0.686832\pi$
$23$	−5.31209	−1.10765	−0.553824	+	0.832634i	$0.686832\pi$
$24$	9.55174	1.94974
$25$	8.68147	1.73629
$26$	−0.674321	−0.132245
$27$	5.29101	1.01825
$28$	12.5420	2.37022
$29$	−10.4444	−1.93948	−0.969741	−	0.244138i	$-0.921495\pi$
$29$	−10.4444	−1.93948	−0.969741	+	0.244138i	$0.921495\pi$
$30$	11.0164	2.01130
$31$	−4.08973	−0.734538	−0.367269	−	0.930115i	$-0.619707\pi$
$31$	−4.08973	−0.734538	−0.367269	+	0.930115i	$0.619707\pi$
$32$	−16.8738	−2.98290
$33$	−0.468633	−0.0815786
$34$	−17.2181	−2.95289
$35$	8.90922	1.50593
$36$	−9.21244	−1.53541
$37$	−11.8129	−1.94203	−0.971014	−	0.239021i	$-0.923174\pi$
$37$	−11.8129	−1.94203	−0.971014	+	0.239021i	$0.923174\pi$
$38$	18.3713	2.98022
$39$	−0.278662	−0.0446217
$40$	−31.8462	−5.03532
$41$	4.62078	0.721644	0.360822	−	0.932635i	$-0.382496\pi$
$41$	4.62078	0.721644	0.360822	+	0.932635i	$0.382496\pi$
$42$	7.17372	1.10693
$43$	7.18487	1.09568	0.547842	−	0.836582i	$-0.315450\pi$
$43$	7.18487	1.09568	0.547842	+	0.836582i	$0.315450\pi$
$44$	2.19956	0.331596
$45$	−6.54405	−0.975529
$46$	14.2609	2.10265
$47$	−0.848440	−0.123758	−0.0618789	−	0.998084i	$-0.519709\pi$
$47$	−0.848440	−0.123758	−0.0618789	+	0.998084i	$0.519709\pi$
$48$	−14.0890	−2.03358
$49$	−1.19842	−0.171203
$50$	−23.3063	−3.29601
$51$	−7.11538	−0.996352
$52$	1.30792	0.181376
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−14.2042	−1.93295
$55$	1.56246	0.210682
$56$	−20.7379	−2.77121
$57$	7.59191	1.00557
$58$	28.0391	3.68172
$59$	−4.14649	−0.539827	−0.269913	−	0.962885i	$-0.586995\pi$
$59$	−4.14649	−0.539827	−0.269913	+	0.962885i	$0.586995\pi$
$60$	−21.3675	−2.75853
$61$	6.42455	0.822579	0.411290	−	0.911505i	$-0.365078\pi$
$61$	6.42455	0.822579	0.411290	+	0.911505i	$0.365078\pi$
$62$	10.9793	1.39437
$63$	−4.26141	−0.536887
$64$	19.9004	2.48755
$65$	0.929080	0.115238
$66$	1.25809	0.154861
$67$	6.65552	0.813102	0.406551	−	0.913628i	$-0.366731\pi$
$67$	6.65552	0.813102	0.406551	+	0.913628i	$0.366731\pi$
$68$	33.3965	4.04992
$69$	5.89328	0.709468
$70$	−23.9177	−2.85871
$71$	9.53426	1.13151	0.565754	−	0.824574i	$-0.308585\pi$
$71$	9.53426	1.13151	0.565754	+	0.824574i	$0.308585\pi$
$72$	15.2325	1.79517
$73$	−6.09687	−0.713585	−0.356793	−	0.934184i	$-0.616130\pi$
$73$	−6.09687	−0.713585	−0.356793	+	0.934184i	$0.616130\pi$
$74$	31.7129	3.68655
$75$	−9.63130	−1.11213
$76$	−35.6332	−4.08741
$77$	1.01745	0.115950
$78$	0.748098	0.0847054
$79$	9.59628	1.07967	0.539833	−	0.841772i	$-0.318487\pi$
$79$	9.59628	1.07967	0.539833	+	0.841772i	$0.318487\pi$
$80$	46.9739	5.25184
$81$	−0.562253	−0.0624726
$82$	−12.4049	−1.36990
$83$	−11.5895	−1.27211	−0.636056	−	0.771643i	$-0.719435\pi$
$83$	−11.5895	−1.27211	−0.636056	+	0.771643i	$0.719435\pi$
$84$	−13.9142	−1.51817
$85$	23.7232	2.57314
$86$	−19.2885	−2.07994
$87$	11.5871	1.24227
$88$	−3.63691	−0.387696
$89$	4.12878	0.437650	0.218825	−	0.975764i	$-0.429778\pi$
$89$	4.12878	0.437650	0.218825	+	0.975764i	$0.429778\pi$
$90$	17.5682	1.85185
$91$	0.605006	0.0634219
$92$	−27.6605	−2.88381
$93$	4.53719	0.470484
$94$	2.27772	0.234929
$95$	−25.3120	−2.59695
$96$	18.7200	1.91060
$97$	6.55809	0.665873	0.332936	−	0.942949i	$-0.391961\pi$
$97$	6.55809	0.665873	0.332936	+	0.942949i	$0.391961\pi$
$98$	3.21729	0.324996
$99$	−0.747345	−0.0751110
$100$	45.2052	4.52052
$101$	3.12152	0.310603	0.155302	−	0.987867i	$-0.450365\pi$
$101$	3.12152	0.310603	0.155302	+	0.987867i	$0.450365\pi$
$102$	19.1020	1.89138
$103$	7.14889	0.704401	0.352200	−	0.935925i	$-0.385434\pi$
$103$	7.14889	0.704401	0.352200	+	0.935925i	$0.385434\pi$
$104$	−2.16261	−0.212061
$105$	−9.88396	−0.964576
$106$	−2.68460	−0.260752
$107$	−12.4007	−1.19882	−0.599409	−	0.800443i	$-0.704598\pi$
$107$	−12.4007	−1.19882	−0.599409	+	0.800443i	$0.704598\pi$
$108$	27.5507	2.65107
$109$	−6.94264	−0.664985	−0.332492	−	0.943106i	$-0.607890\pi$
$109$	−6.94264	−0.664985	−0.332492	+	0.943106i	$0.607890\pi$
$110$	−4.19457	−0.399937
$111$	13.1053	1.24390
$112$	30.5888	2.89037
$113$	−13.1266	−1.23485	−0.617424	−	0.786630i	$-0.711824\pi$
$113$	−13.1266	−1.23485	−0.617424	+	0.786630i	$0.711824\pi$
$114$	−20.3813	−1.90888
$115$	−19.6486	−1.83224
$116$	−54.3850	−5.04952
$117$	−0.444392	−0.0410841
$118$	11.1317	1.02475
$119$	15.4483	1.41614
$120$	35.3304	3.22521
$121$	−10.8216	−0.983779
$122$	−17.2474	−1.56150
$123$	−5.12633	−0.462226
$124$	−21.2956	−1.91240
$125$	13.6172	1.21796
$126$	11.4402	1.01917
$127$	−5.66593	−0.502770	−0.251385	−	0.967887i	$-0.580886\pi$
$127$	−5.66593	−0.502770	−0.251385	+	0.967887i	$0.580886\pi$
$128$	−19.6769	−1.73921
$129$	−7.97096	−0.701804
$130$	−2.49421	−0.218757
$131$	5.70822	0.498730	0.249365	−	0.968410i	$-0.419778\pi$
$131$	5.70822	0.498730	0.249365	+	0.968410i	$0.419778\pi$
$132$	−2.44021	−0.212393
$133$	−16.4829	−1.42925
$134$	−17.8674	−1.54351
$135$	19.5706	1.68437
$136$	−55.2201	−4.73508
$137$	7.00384	0.598378	0.299189	−	0.954194i	$-0.403284\pi$
$137$	7.00384	0.598378	0.299189	+	0.954194i	$0.403284\pi$
$138$	−15.8211	−1.34678
$139$	3.39123	0.287640	0.143820	−	0.989604i	$-0.454061\pi$
$139$	3.39123	0.287640	0.143820	+	0.989604i	$0.454061\pi$
$140$	46.3911	3.92076
$141$	0.941267	0.0792690
$142$	−25.5957	−2.14794
$143$	0.106103	0.00887279
$144$	−22.4683	−1.87236
$145$	−38.6323	−3.20824
$146$	16.3677	1.35460
$147$	1.32954	0.109659
$148$	−61.5108	−5.05616
$149$	−11.7924	−0.966067	−0.483034	−	0.875602i	$-0.660465\pi$
$149$	−11.7924	−0.966067	−0.483034	+	0.875602i	$0.660465\pi$
$150$	25.8562	2.11115
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	58.9183	4.77891
$153$	−11.3471	−0.917361
$154$	−2.73146	−0.220107
$155$	−15.1273	−1.21505
$156$	−1.45102	−0.116175
$157$	−18.3779	−1.46672	−0.733359	−	0.679842i	$-0.762048\pi$
$157$	−18.3779	−1.46672	−0.733359	+	0.679842i	$0.762048\pi$
$158$	−25.7622	−2.04953
$159$	−1.10941	−0.0879818
$160$	−62.4138	−4.93424
$161$	−12.7949	−1.00838
$162$	1.50943	0.118592
$163$	6.11633	0.479068	0.239534	−	0.970888i	$-0.423005\pi$
$163$	6.11633	0.479068	0.239534	+	0.970888i	$0.423005\pi$
$164$	24.0608	1.87883
$165$	−1.73340	−0.134945
$166$	31.1132	2.41485
$167$	5.31882	0.411583	0.205791	−	0.978596i	$-0.434023\pi$
$167$	5.31882	0.411583	0.205791	+	0.978596i	$0.434023\pi$
$168$	23.0068	1.77501
$169$	−12.9369	−0.995147
$170$	−63.6873	−4.88459
$171$	12.1071	0.925852
$172$	37.4123	2.85266
$173$	−17.9677	−1.36606	−0.683029	−	0.730391i	$-0.739338\pi$
$173$	−17.9677	−1.36606	−0.683029	+	0.730391i	$0.739338\pi$
$174$	−31.1069	−2.35820
$175$	20.9106	1.58069
$176$	5.36452	0.404366
$177$	4.60015	0.345768
$178$	−11.0841	−0.830791
$179$	20.2771	1.51558	0.757790	−	0.652499i	$-0.226279\pi$
$179$	20.2771	1.51558	0.757790	+	0.652499i	$0.226279\pi$
$180$	−34.0754	−2.53983
$181$	−10.9578	−0.814486	−0.407243	−	0.913320i	$-0.633510\pi$
$181$	−10.9578	−0.814486	−0.407243	+	0.913320i	$0.633510\pi$
$182$	−1.62420	−0.120394
$183$	−7.12745	−0.526877
$184$	45.7358	3.37169
$185$	−43.6941	−3.21246
$186$	−12.1805	−0.893120
$187$	2.70924	0.198119
$188$	−4.41790	−0.322209
$189$	12.7442	0.927001
$190$	67.9526	4.92980
$191$	22.6780	1.64092	0.820462	−	0.571701i	$-0.193716\pi$
$191$	22.6780	1.64092	0.820462	+	0.571701i	$0.193716\pi$
$192$	−22.0776	−1.59332
$193$	−23.7891	−1.71237	−0.856187	−	0.516666i	$-0.827173\pi$
$193$	−23.7891	−1.71237	−0.856187	+	0.516666i	$0.827173\pi$
$194$	−17.6059	−1.26403
$195$	−1.03073	−0.0738121
$196$	−6.24030	−0.445736
$197$	0.358983	0.0255765	0.0127882	−	0.999918i	$-0.495929\pi$
$197$	0.358983	0.0255765	0.0127882	+	0.999918i	$0.495929\pi$
$198$	2.00632	0.142583
$199$	−26.3548	−1.86824	−0.934122	−	0.356954i	$-0.883815\pi$
$199$	−26.3548	−1.86824	−0.934122	+	0.356954i	$0.883815\pi$
$200$	−74.7454	−5.28530
$201$	−7.38370	−0.520806
$202$	−8.38005	−0.589618
$203$	−25.1569	−1.76567
$204$	−37.0504	−2.59405
$205$	17.0916	1.19373
$206$	−19.1919	−1.33716
$207$	9.39822	0.653221
$208$	3.18990	0.221179
$209$	−2.89069	−0.199953
$210$	26.5345	1.83105
$211$	−7.84408	−0.540009	−0.270004	−	0.962859i	$-0.587025\pi$
$211$	−7.84408	−0.540009	−0.270004	+	0.962859i	$0.587025\pi$
$212$	5.20709	0.357624
$213$	−10.5774	−0.724751
$214$	33.2908	2.27572
$215$	26.5758	1.81245
$216$	−45.5543	−3.09958
$217$	−9.85072	−0.668710
$218$	18.6382	1.26234
$219$	6.76393	0.457064
$220$	8.13585	0.548519
$221$	1.61099	0.108367
$222$	−35.1826	−2.36130
$223$	−19.6293	−1.31448	−0.657238	−	0.753683i	$-0.728275\pi$
$223$	−19.6293	−1.31448	−0.657238	+	0.753683i	$0.728275\pi$
$224$	−40.6431	−2.71558
$225$	−15.3594	−1.02396
$226$	35.2398	2.34411
$227$	4.38074	0.290760	0.145380	−	0.989376i	$-0.453560\pi$
$227$	4.38074	0.290760	0.145380	+	0.989376i	$0.453560\pi$
$228$	39.5318	2.61806
$229$	−27.5553	−1.82091	−0.910453	−	0.413613i	$-0.864267\pi$
$229$	−27.5553	−1.82091	−0.910453	+	0.413613i	$0.864267\pi$
$230$	52.7487	3.47815
$231$	−1.12877	−0.0742677
$232$	89.9240	5.90380
$233$	27.8461	1.82426	0.912128	−	0.409906i	$-0.134438\pi$
$233$	27.8461	1.82426	0.912128	+	0.409906i	$0.134438\pi$
$234$	1.19302	0.0779899
$235$	−3.13825	−0.204717
$236$	−21.5911	−1.40546
$237$	−10.6462	−0.691545
$238$	−41.4724	−2.68826
$239$	−24.0133	−1.55329	−0.776647	−	0.629936i	$-0.783081\pi$
$239$	−24.0133	−1.55329	−0.776647	+	0.629936i	$0.783081\pi$
$240$	−52.1132	−3.36389
$241$	−19.3224	−1.24467	−0.622334	−	0.782752i	$-0.713815\pi$
$241$	−19.3224	−1.24467	−0.622334	+	0.782752i	$0.713815\pi$
$242$	29.0516	1.86751
$243$	−15.2492	−0.978240
$244$	33.4532	2.14162
$245$	−4.43279	−0.283200
$246$	13.7622	0.877443
$247$	−1.71888	−0.109370
$248$	35.2116	2.23594
$249$	12.8575	0.814810
$250$	−36.5568	−2.31205
$251$	15.6179	0.985790	0.492895	−	0.870089i	$-0.335939\pi$
$251$	15.6179	0.985790	0.492895	+	0.870089i	$0.335939\pi$
$252$	−22.1895	−1.39781
$253$	−2.24392	−0.141074
$254$	15.2108	0.954408
$255$	−26.3187	−1.64814
$256$	13.0238	0.813991
$257$	15.5362	0.969119	0.484559	−	0.874758i	$-0.338980\pi$
$257$	15.5362	0.969119	0.484559	+	0.874758i	$0.338980\pi$
$258$	21.3989	1.33224
$259$	−28.4531	−1.76799
$260$	4.83780	0.300028
$261$	18.4784	1.14378
$262$	−15.3243	−0.946739
$263$	13.8165	0.851960	0.425980	−	0.904733i	$-0.359929\pi$
$263$	13.8165	0.851960	0.425980	+	0.904733i	$0.359929\pi$
$264$	4.03482	0.248326
$265$	3.69885	0.227218
$266$	44.2499	2.71314
$267$	−4.58050	−0.280322
$268$	34.6559	2.11695
$269$	−15.2943	−0.932511	−0.466255	−	0.884650i	$-0.654397\pi$
$269$	−15.2943	−0.932511	−0.466255	+	0.884650i	$0.654397\pi$
$270$	−52.5393	−3.19744
$271$	24.7216	1.50173	0.750867	−	0.660454i	$-0.229636\pi$
$271$	24.7216	1.50173	0.750867	+	0.660454i	$0.229636\pi$
$272$	81.4509	4.93869
$273$	−0.671199	−0.0406228
$274$	−18.8025	−1.13590
$275$	3.66720	0.221141
$276$	30.6868	1.84713
$277$	−0.841344	−0.0505515	−0.0252757	−	0.999681i	$-0.508046\pi$
$277$	−0.841344	−0.0505515	−0.0252757	+	0.999681i	$0.508046\pi$
$278$	−9.10411	−0.546028
$279$	7.23560	0.433184
$280$	−76.7062	−4.58407
$281$	−10.0173	−0.597584	−0.298792	−	0.954318i	$-0.596584\pi$
$281$	−10.0173	−0.597584	−0.298792	+	0.954318i	$0.596584\pi$
$282$	−2.52693	−0.150476
$283$	−5.83736	−0.346995	−0.173497	−	0.984834i	$-0.555507\pi$
$283$	−5.83736	−0.346995	−0.173497	+	0.984834i	$0.555507\pi$
$284$	49.6457	2.94593
$285$	28.0813	1.66339
$286$	−0.284845	−0.0168432
$287$	11.1298	0.656972
$288$	29.8534	1.75913
$289$	24.1351	1.41971
$290$	103.712	6.09021
$291$	−7.27560	−0.426503
$292$	−31.7470	−1.85785
$293$	−30.8236	−1.80073	−0.900367	−	0.435132i	$-0.856702\pi$
$293$	−30.8236	−1.80073	−0.900367	+	0.435132i	$0.856702\pi$
$294$	−3.56929	−0.208165
$295$	−15.3372	−0.892968
$296$	101.706	5.91155
$297$	2.23501	0.129688
$298$	31.6578	1.83389
$299$	−1.33430	−0.0771643
$300$	−50.1511	−2.89547
$301$	17.3058	0.997491
$302$	−2.68460	−0.154481
$303$	−3.46305	−0.198947
$304$	−86.9059	−4.98440
$305$	23.7634	1.36069
$306$	30.4625	1.74143
$307$	−11.9556	−0.682345	−0.341172	−	0.940001i	$-0.610824\pi$
$307$	−11.9556	−0.682345	−0.341172	+	0.940001i	$0.610824\pi$
$308$	5.29797	0.301880
$309$	−7.93104	−0.451181
$310$	40.6108	2.30654
$311$	22.2850	1.26367	0.631833	−	0.775105i	$-0.282303\pi$
$311$	22.2850	1.26367	0.631833	+	0.775105i	$0.282303\pi$
$312$	2.39922	0.135829
$313$	4.71618	0.266574	0.133287	−	0.991077i	$-0.457447\pi$
$313$	4.71618	0.266574	0.133287	+	0.991077i	$0.457447\pi$
$314$	49.3374	2.78427
$315$	−15.7623	−0.888104
$316$	49.9687	2.81096
$317$	10.3423	0.580880	0.290440	−	0.956893i	$-0.406198\pi$
$317$	10.3423	0.580880	0.290440	+	0.956893i	$0.406198\pi$
$318$	2.97832	0.167016
$319$	−4.41190	−0.247019
$320$	73.6084	4.11484
$321$	13.7574	0.767864
$322$	34.3493	1.91421
$323$	−43.8900	−2.44211
$324$	−2.92770	−0.162650
$325$	2.18062	0.120959
$326$	−16.4199	−0.909415
$327$	7.70223	0.425934
$328$	−39.7838	−2.19669
$329$	−2.04359	−0.112667
$330$	4.65350	0.256167
$331$	−13.0154	−0.715390	−0.357695	−	0.933838i	$-0.616437\pi$
$331$	−13.0154	−0.715390	−0.357695	+	0.933838i	$0.616437\pi$
$332$	−60.3475	−3.31200
$333$	20.8995	1.14529
$334$	−14.2789	−0.781307
$335$	24.6178	1.34501
$336$	−33.9355	−1.85133
$337$	−26.4531	−1.44099	−0.720497	−	0.693458i	$-0.756086\pi$
$337$	−26.4531	−1.44099	−0.720497	+	0.693458i	$0.756086\pi$
$338$	34.7305	1.88909
$339$	14.5628	0.790942
$340$	123.529	6.69928
$341$	−1.72757	−0.0935533
$342$	−32.5027	−1.75754
$343$	−19.7471	−1.06624
$344$	−61.8600	−3.33527
$345$	21.7983	1.17358
$346$	48.2361	2.59319
$347$	−33.8934	−1.81949	−0.909745	−	0.415167i	$-0.863723\pi$
$347$	−33.8934	−1.81949	−0.909745	+	0.415167i	$0.863723\pi$
$348$	60.3353	3.23431
$349$	−21.1298	−1.13105	−0.565526	−	0.824730i	$-0.691327\pi$
$349$	−21.1298	−1.13105	−0.565526	+	0.824730i	$0.691327\pi$
$350$	−56.1366	−3.00063
$351$	1.32900	0.0709368
$352$	−7.12780	−0.379913
$353$	24.4569	1.30171	0.650856	−	0.759201i	$-0.274410\pi$
$353$	24.4569	1.30171	0.650856	+	0.759201i	$0.274410\pi$
$354$	−12.3496	−0.656372
$355$	35.2658	1.87171
$356$	21.4989	1.13944
$357$	−17.1384	−0.907062
$358$	−54.4359	−2.87703
$359$	12.8541	0.678414	0.339207	−	0.940712i	$-0.389841\pi$
$359$	12.8541	0.678414	0.339207	+	0.940712i	$0.389841\pi$
$360$	56.3426	2.96952
$361$	27.8295	1.46471
$362$	29.4173	1.54614
$363$	12.0055	0.630127
$364$	3.15032	0.165122
$365$	−22.5514	−1.18039
$366$	19.1344	1.00017
$367$	−3.53727	−0.184644	−0.0923219	−	0.995729i	$-0.529429\pi$
$367$	−3.53727	−0.184644	−0.0923219	+	0.995729i	$0.529429\pi$
$368$	−67.4614	−3.51667
$369$	−8.17513	−0.425580
$370$	117.301	6.09821
$371$	2.40865	0.125051
$372$	23.6255	1.22493
$373$	25.6743	1.32936	0.664682	−	0.747126i	$-0.268567\pi$
$373$	25.6743	1.32936	0.664682	+	0.747126i	$0.268567\pi$
$374$	−7.27323	−0.376090
$375$	−15.1071	−0.780125
$376$	7.30486	0.376720
$377$	−2.62344	−0.135114
$378$	−34.2130	−1.75973
$379$	17.1002	0.878378	0.439189	−	0.898395i	$-0.355266\pi$
$379$	17.1002	0.878378	0.439189	+	0.898395i	$0.355266\pi$
$380$	−131.802	−6.76129
$381$	6.28583	0.322033
$382$	−60.8814	−3.11497
$383$	−37.2884	−1.90535	−0.952675	−	0.303992i	$-0.901680\pi$
$383$	−37.2884	−1.90535	−0.952675	+	0.303992i	$0.901680\pi$
$384$	21.8297	1.11399
$385$	3.76340	0.191801
$386$	63.8642	3.25060
$387$	−12.7116	−0.646165
$388$	34.1485	1.73363
$389$	−20.1803	−1.02318	−0.511590	−	0.859230i	$-0.670943\pi$
$389$	−20.1803	−1.02318	−0.511590	+	0.859230i	$0.670943\pi$
$390$	2.76710	0.140118
$391$	−34.0700	−1.72299
$392$	10.3181	0.521145
$393$	−6.33275	−0.319445
$394$	−0.963726	−0.0485518
$395$	35.4952	1.78596
$396$	−3.89149	−0.195555
$397$	−2.69672	−0.135345	−0.0676723	−	0.997708i	$-0.521557\pi$
$397$	−2.69672	−0.135345	−0.0676723	+	0.997708i	$0.521557\pi$
$398$	70.7522	3.54649
$399$	18.2862	0.915457
$400$	110.251	5.51256
$401$	11.7273	0.585635	0.292817	−	0.956168i	$-0.405407\pi$
$401$	11.7273	0.585635	0.292817	+	0.956168i	$0.405407\pi$
$402$	19.8223	0.988646
$403$	−1.02726	−0.0511716
$404$	16.2540	0.808669
$405$	−2.07969	−0.103341
$406$	67.5363	3.35177
$407$	−4.98997	−0.247344
$408$	61.2617	3.03290
$409$	28.0470	1.38684	0.693418	−	0.720536i	$-0.256104\pi$
$409$	28.0470	1.38684	0.693418	+	0.720536i	$0.256104\pi$
$410$	−45.8840	−2.26605
$411$	−7.77012	−0.383272
$412$	37.2249	1.83394
$413$	−9.98742	−0.491449
$414$	−25.2305	−1.24001
$415$	−42.8677	−2.10430
$416$	−4.23839	−0.207804
$417$	−3.76226	−0.184239
$418$	7.76034	0.379571
$419$	27.9249	1.36422	0.682111	−	0.731248i	$-0.261062\pi$
$419$	27.9249	1.36422	0.682111	+	0.731248i	$0.261062\pi$
$420$	−51.4667	−2.51132
$421$	−16.2871	−0.793787	−0.396894	−	0.917865i	$-0.629912\pi$
$421$	−16.2871	−0.793787	−0.396894	+	0.917865i	$0.629912\pi$
$422$	21.0582	1.02510
$423$	1.50107	0.0729845
$424$	−8.60976	−0.418127
$425$	55.6801	2.70088
$426$	28.3961	1.37579
$427$	15.4745	0.748862
$428$	−64.5714	−3.12117
$429$	−0.117712	−0.00568318
$430$	−71.3453	−3.44058
$431$	5.37506	0.258908	0.129454	−	0.991585i	$-0.458678\pi$
$431$	5.37506	0.258908	0.129454	+	0.991585i	$0.458678\pi$
$432$	67.1936	3.23285
$433$	14.6297	0.703057	0.351528	−	0.936177i	$-0.385662\pi$
$433$	14.6297	0.703057	0.351528	+	0.936177i	$0.385662\pi$
$434$	26.4453	1.26941
$435$	42.8591	2.05493
$436$	−36.1510	−1.73132
$437$	36.3517	1.73894
$438$	−18.1585	−0.867644
$439$	25.7466	1.22882	0.614409	−	0.788987i	$-0.289394\pi$
$439$	25.7466	1.22882	0.614409	+	0.788987i	$0.289394\pi$
$440$	−13.4524	−0.641316
$441$	2.12027	0.100965
$442$	−4.32487	−0.205713
$443$	13.8857	0.659728	0.329864	−	0.944028i	$-0.392997\pi$
$443$	13.8857	0.659728	0.329864	+	0.944028i	$0.392997\pi$
$444$	68.2406	3.23856
$445$	15.2717	0.723949
$446$	52.6969	2.49527
$447$	13.0825	0.618783
$448$	47.9329	2.26462
$449$	−31.0109	−1.46349	−0.731747	−	0.681577i	$-0.761295\pi$
$449$	−31.0109	−1.46349	−0.731747	+	0.681577i	$0.761295\pi$
$450$	41.2338	1.94378
$451$	1.95189	0.0919111
$452$	−68.3515	−3.21498
$453$	−1.10941	−0.0521246
$454$	−11.7606	−0.551950
$455$	2.23783	0.104911
$456$	−65.3645	−3.06097
$457$	13.1507	0.615165	0.307582	−	0.951521i	$-0.400480\pi$
$457$	13.1507	0.615165	0.307582	+	0.951521i	$0.400480\pi$
$458$	73.9750	3.45663
$459$	33.9347	1.58394
$460$	−102.312	−4.77033
$461$	34.5660	1.60990	0.804950	−	0.593342i	$-0.202192\pi$
$461$	34.5660	1.60990	0.804950	+	0.593342i	$0.202192\pi$
$462$	3.03030	0.140982
$463$	−30.1337	−1.40043	−0.700216	−	0.713931i	$-0.746913\pi$
$463$	−30.1337	−1.40043	−0.700216	+	0.713931i	$0.746913\pi$
$464$	−132.640	−6.15766
$465$	16.7824	0.778263
$466$	−74.7556	−3.46298
$467$	−25.8263	−1.19510	−0.597549	−	0.801832i	$-0.703859\pi$
$467$	−25.8263	−1.19510	−0.597549	+	0.801832i	$0.703859\pi$
$468$	−2.31399	−0.106964
$469$	16.0308	0.740234
$470$	8.42496	0.388614
$471$	20.3886	0.939458
$472$	35.7002	1.64324
$473$	3.03501	0.139550
$474$	28.5808	1.31276
$475$	−59.4091	−2.72588
$476$	80.4404	3.68698
$477$	−1.76921	−0.0810067
$478$	64.4663	2.94862
$479$	−3.93260	−0.179685	−0.0898425	−	0.995956i	$-0.528636\pi$
$479$	−3.93260	−0.179685	−0.0898425	+	0.995956i	$0.528636\pi$
$480$	69.2424	3.16047
$481$	−2.96718	−0.135292
$482$	51.8731	2.36275
$483$	14.1948	0.645887
$484$	−56.3488	−2.56131
$485$	24.2574	1.10147
$486$	40.9382	1.85699
$487$	−26.8192	−1.21529	−0.607647	−	0.794208i	$-0.707886\pi$
$487$	−26.8192	−1.21529	−0.607647	+	0.794208i	$0.707886\pi$
$488$	−55.3138	−2.50394
$489$	−6.78551	−0.306851
$490$	11.9003	0.537599
$491$	31.0623	1.40182	0.700910	−	0.713249i	$-0.252777\pi$
$491$	31.0623	1.40182	0.700910	+	0.713249i	$0.252777\pi$
$492$	−26.6933	−1.20343
$493$	−66.9871	−3.01695
$494$	4.61452	0.207617
$495$	−2.76432	−0.124247
$496$	−51.9379	−2.33208
$497$	22.9647	1.03011
$498$	−34.5172	−1.54675
$499$	−21.6511	−0.969238	−0.484619	−	0.874725i	$-0.661042\pi$
$499$	−21.6511	−0.969238	−0.484619	+	0.874725i	$0.661042\pi$
$500$	70.9060	3.17101
$501$	−5.90074	−0.263626
$502$	−41.9277	−1.87133
$503$	−9.85667	−0.439487	−0.219744	−	0.975558i	$-0.570522\pi$
$503$	−9.85667	−0.439487	−0.219744	+	0.975558i	$0.570522\pi$
$504$	36.6897	1.63429
$505$	11.5460	0.513792
$506$	6.02403	0.267801
$507$	14.3523	0.637409
$508$	−29.5030	−1.30898
$509$	26.5234	1.17563	0.587815	−	0.808996i	$-0.299988\pi$
$509$	26.5234	1.17563	0.587815	+	0.808996i	$0.299988\pi$
$510$	70.6552	3.12867
$511$	−14.6852	−0.649636
$512$	4.38989	0.194008
$513$	−36.2075	−1.59860
$514$	−41.7084	−1.83968
$515$	26.4426	1.16520
$516$	−41.5055	−1.82718
$517$	−0.358396	−0.0157622
$518$	76.3852	3.35617
$519$	19.9335	0.874984
$520$	−7.99915	−0.350786
$521$	−20.5967	−0.902360	−0.451180	−	0.892433i	$-0.648997\pi$
$521$	−20.5967	−0.902360	−0.451180	+	0.892433i	$0.648997\pi$
$522$	−49.6072	−2.17125
$523$	−21.2519	−0.929282	−0.464641	−	0.885499i	$-0.653817\pi$
$523$	−21.2519	−0.929282	−0.464641	+	0.885499i	$0.653817\pi$
$524$	29.7232	1.29846
$525$	−23.1984	−1.01246
$526$	−37.0917	−1.61728
$527$	−26.2302	−1.14260
$528$	−5.95145	−0.259004
$529$	5.21831	0.226883
$530$	−9.92993	−0.431329
$531$	7.33601	0.318356
$532$	−85.8277	−3.72110
$533$	1.16065	0.0502734
$534$	12.2968	0.532136
$535$	−45.8682	−1.98305
$536$	−57.3024	−2.47509
$537$	−22.4956	−0.970755
$538$	41.0592	1.77019
$539$	−0.506235	−0.0218051
$540$	101.906	4.38533
$541$	−13.6041	−0.584884	−0.292442	−	0.956283i	$-0.594468\pi$
$541$	−13.6041	−0.584884	−0.292442	+	0.956283i	$0.594468\pi$
$542$	−66.3678	−2.85074
$543$	12.1567	0.521693
$544$	−108.223	−4.64003
$545$	−25.6798	−1.10000
$546$	1.80190	0.0771143
$547$	9.48556	0.405573	0.202787	−	0.979223i	$-0.435000\pi$
$547$	9.48556	0.405573	0.202787	+	0.979223i	$0.435000\pi$
$548$	36.4696	1.55790
$549$	−11.3664	−0.485106
$550$	−9.84498	−0.419791
$551$	71.4734	3.04487
$552$	−50.7397	−2.15963
$553$	23.1140	0.982909
$554$	2.25867	0.0959619
$555$	48.4746	2.05763
$556$	17.6584	0.748885
$557$	−17.1216	−0.725467	−0.362733	−	0.931893i	$-0.618156\pi$
$557$	−17.1216	−0.725467	−0.362733	+	0.931893i	$0.618156\pi$
$558$	−19.4247	−0.822314
$559$	1.80470	0.0763308
$560$	113.143	4.78118
$561$	−3.00566	−0.126899
$562$	26.8925	1.13439
$563$	36.1538	1.52370	0.761851	−	0.647752i	$-0.224291\pi$
$563$	36.1538	1.52370	0.761851	+	0.647752i	$0.224291\pi$
$564$	4.90126	0.206380
$565$	−48.5534	−2.04266
$566$	15.6710	0.658700
$567$	−1.35427	−0.0568739
$568$	−82.0876	−3.44432
$569$	3.07615	0.128959	0.0644794	−	0.997919i	$-0.479461\pi$
$569$	3.07615	0.128959	0.0644794	+	0.997919i	$0.479461\pi$
$570$	−75.3872	−3.15762
$571$	9.79045	0.409718	0.204859	−	0.978792i	$-0.434326\pi$
$571$	9.79045	0.409718	0.204859	+	0.978792i	$0.434326\pi$
$572$	0.552488	0.0231007
$573$	−25.1592	−1.05104
$574$	−29.8791	−1.24713
$575$	−46.1168	−1.92320
$576$	−35.2080	−1.46700
$577$	29.6088	1.23263	0.616316	−	0.787499i	$-0.288624\pi$
$577$	29.6088	1.23263	0.616316	+	0.787499i	$0.288624\pi$
$578$	−64.7932	−2.69504
$579$	26.3918	1.09681
$580$	−201.162	−8.35280
$581$	−27.9150	−1.15811
$582$	19.5321	0.809631
$583$	0.422417	0.0174947
$584$	52.4926	2.17216
$585$	−1.64374	−0.0679603
$586$	82.7491	3.41833
$587$	−19.3155	−0.797237	−0.398619	−	0.917117i	$-0.630510\pi$
$587$	−19.3155	−0.797237	−0.398619	+	0.917117i	$0.630510\pi$
$588$	6.92304	0.285502
$589$	27.9869	1.15318
$590$	41.1743	1.69512
$591$	−0.398259	−0.0163822
$592$	−150.019	−6.16574
$593$	−18.5814	−0.763046	−0.381523	−	0.924359i	$-0.624600\pi$
$593$	−18.5814	−0.763046	−0.381523	+	0.924359i	$0.624600\pi$
$594$	−6.00011	−0.246188
$595$	57.1407	2.34254
$596$	−61.4038	−2.51520
$597$	29.2383	1.19664
$598$	3.58205	0.146481
$599$	−33.9653	−1.38778	−0.693892	−	0.720079i	$-0.744106\pi$
$599$	−33.9653	−1.38778	−0.693892	+	0.720079i	$0.744106\pi$
$600$	82.9232	3.38532
$601$	−14.7053	−0.599842	−0.299921	−	0.953964i	$-0.596960\pi$
$601$	−14.7053	−0.599842	−0.299921	+	0.953964i	$0.596960\pi$
$602$	−46.4592	−1.89354
$603$	−11.7750	−0.479516
$604$	5.20709	0.211873
$605$	−40.0273	−1.62734
$606$	9.29690	0.377661
$607$	33.5391	1.36131	0.680654	−	0.732605i	$-0.261696\pi$
$607$	33.5391	1.36131	0.680654	+	0.732605i	$0.261696\pi$
$608$	115.471	4.68298
$609$	27.9093	1.13094
$610$	−63.7954	−2.58300
$611$	−0.213112	−0.00862159
$612$	−59.0855	−2.38839
$613$	−36.5461	−1.47608	−0.738041	−	0.674756i	$-0.764249\pi$
$613$	−36.5461	−1.47608	−0.738041	+	0.674756i	$0.764249\pi$
$614$	32.0962	1.29530
$615$	−18.9615	−0.764602
$616$	−8.76002	−0.352951
$617$	0.902052	0.0363153	0.0181576	−	0.999835i	$-0.494220\pi$
$617$	0.902052	0.0363153	0.0181576	+	0.999835i	$0.494220\pi$
$618$	21.2917	0.856477
$619$	−5.49963	−0.221049	−0.110524	−	0.993873i	$-0.535253\pi$
$619$	−5.49963	−0.221049	−0.110524	+	0.993873i	$0.535253\pi$
$620$	−78.7692	−3.16345
$621$	−28.1063	−1.12787
$622$	−59.8263	−2.39882
$623$	9.94477	0.398429
$624$	−3.53890	−0.141669
$625$	6.96062	0.278425
$626$	−12.6611	−0.506038
$627$	3.20695	0.128073
$628$	−95.6954	−3.81866
$629$	−75.7640	−3.02091
$630$	42.3155	1.68589
$631$	6.63965	0.264320	0.132160	−	0.991228i	$-0.457809\pi$
$631$	6.63965	0.264320	0.132160	+	0.991228i	$0.457809\pi$
$632$	−82.6216	−3.28651
$633$	8.70229	0.345885
$634$	−27.7649	−1.10268
$635$	−20.9574	−0.831669
$636$	−5.77679	−0.229065
$637$	−0.301021	−0.0119269
$638$	11.8442	0.468916
$639$	−16.8681	−0.667293
$640$	−72.7818	−2.87695
$641$	−27.4083	−1.08256	−0.541282	−	0.840841i	$-0.682061\pi$
$641$	−27.4083	−1.08256	−0.541282	+	0.840841i	$0.682061\pi$
$642$	−36.9332	−1.45764
$643$	−32.1767	−1.26893	−0.634463	−	0.772954i	$-0.718779\pi$
$643$	−32.1767	−1.26893	−0.634463	+	0.772954i	$0.718779\pi$
$644$	−66.6244	−2.62537
$645$	−29.4834	−1.16091
$646$	117.827	4.63585
$647$	−22.2502	−0.874745	−0.437373	−	0.899280i	$-0.644091\pi$
$647$	−22.2502	−0.874745	−0.437373	+	0.899280i	$0.644091\pi$
$648$	4.84086	0.190167
$649$	−1.75155	−0.0687542
$650$	−5.85410	−0.229617
$651$	10.9285	0.428321
$652$	31.8483	1.24727
$653$	1.49422	0.0584733	0.0292366	−	0.999573i	$-0.490692\pi$
$653$	1.49422	0.0584733	0.0292366	+	0.999573i	$0.490692\pi$
$654$	−20.6774	−0.808551
$655$	21.1138	0.824986
$656$	58.6820	2.29115
$657$	10.7867	0.420828
$658$	5.48623	0.213876
$659$	18.1372	0.706525	0.353263	−	0.935524i	$-0.385072\pi$
$659$	18.1372	0.706525	0.353263	+	0.935524i	$0.385072\pi$
$660$	−9.02598	−0.351336
$661$	−1.77087	−0.0688788	−0.0344394	−	0.999407i	$-0.510965\pi$
$661$	−1.77087	−0.0688788	−0.0344394	+	0.999407i	$0.510965\pi$
$662$	34.9411	1.35803
$663$	−1.78725	−0.0694109
$664$	99.7827	3.87232
$665$	−60.9676	−2.36422
$666$	−56.1069	−2.17410
$667$	55.4817	2.14826
$668$	27.6956	1.07157
$669$	21.7769	0.841945
$670$	−66.0889	−2.55324
$671$	2.71384	0.104767
$672$	45.0898	1.73938
$673$	25.8793	0.997572	0.498786	−	0.866725i	$-0.333779\pi$
$673$	25.8793	0.997572	0.498786	+	0.866725i	$0.333779\pi$
$674$	71.0161	2.73544
$675$	45.9337	1.76799
$676$	−67.3636	−2.59091
$677$	−19.4343	−0.746919	−0.373459	−	0.927646i	$-0.621829\pi$
$677$	−19.4343	−0.746919	−0.373459	+	0.927646i	$0.621829\pi$
$678$	−39.0953	−1.50145
$679$	15.7961	0.606199
$680$	−204.251	−7.83266
$681$	−4.86003	−0.186237
$682$	4.63784	0.177592
$683$	23.9516	0.916484	0.458242	−	0.888827i	$-0.348479\pi$
$683$	23.9516	0.916484	0.458242	+	0.888827i	$0.348479\pi$
$684$	63.0427	2.41050
$685$	25.9061	0.989822
$686$	53.0131	2.02405
$687$	30.5701	1.16632
$688$	91.2450	3.47868
$689$	0.251181	0.00956923
$690$	−58.5199	−2.22781
$691$	−1.07671	−0.0409598	−0.0204799	−	0.999790i	$-0.506519\pi$
$691$	−1.07671	−0.0409598	−0.0204799	+	0.999790i	$0.506519\pi$
$692$	−93.5594	−3.55659
$693$	−1.80009	−0.0683798
$694$	90.9902	3.45394
$695$	12.5436	0.475808
$696$	−99.7624	−3.78149
$697$	29.6361	1.12255
$698$	56.7251	2.14708
$699$	−30.8927	−1.16847
$700$	108.883	4.11540
$701$	22.2917	0.841946	0.420973	−	0.907073i	$-0.361689\pi$
$701$	22.2917	0.841946	0.420973	+	0.907073i	$0.361689\pi$
$702$	−3.56784	−0.134659
$703$	80.8381	3.04887
$704$	8.40625	0.316822
$705$	3.48160	0.131125
$706$	−65.6572	−2.47104
$707$	7.51865	0.282768
$708$	23.9534	0.900223
$709$	−37.2903	−1.40047	−0.700233	−	0.713915i	$-0.746920\pi$
$709$	−37.2903	−1.40047	−0.700233	+	0.713915i	$0.746920\pi$
$710$	−94.6746	−3.55307
$711$	−16.9778	−0.636719
$712$	−35.5478	−1.33221
$713$	21.7250	0.813609
$714$	46.0099	1.72188
$715$	0.392459	0.0146771
$716$	105.585	3.94588
$717$	26.6406	0.994912
$718$	−34.5082	−1.28783
$719$	9.92089	0.369987	0.184993	−	0.982740i	$-0.440774\pi$
$719$	9.92089	0.369987	0.184993	+	0.982740i	$0.440774\pi$
$720$	−83.1067	−3.09720
$721$	17.2191	0.641274
$722$	−74.7111	−2.78046
$723$	21.4365	0.797232
$724$	−57.0582	−2.12055
$725$	−90.6730	−3.36751
$726$	−32.2301	−1.19617
$727$	−23.0345	−0.854303	−0.427152	−	0.904180i	$-0.640483\pi$
$727$	−23.0345	−0.854303	−0.427152	+	0.904180i	$0.640483\pi$
$728$	−5.20895	−0.193057
$729$	18.6044	0.689052
$730$	60.5416	2.24074
$731$	46.0814	1.70438
$732$	−37.1133	−1.37175
$733$	19.9804	0.737992	0.368996	−	0.929431i	$-0.379702\pi$
$733$	19.9804	0.737992	0.368996	+	0.929431i	$0.379702\pi$
$734$	9.49616	0.350509
$735$	4.91777	0.181395
$736$	89.6354	3.30400
$737$	2.81141	0.103559
$738$	21.9470	0.807880
$739$	−31.9500	−1.17530	−0.587651	−	0.809115i	$-0.699947\pi$
$739$	−31.9500	−1.17530	−0.587651	+	0.809115i	$0.699947\pi$
$740$	−227.519	−8.36377
$741$	1.90694	0.0700534
$742$	−6.46626	−0.237384
$743$	25.3216	0.928958	0.464479	−	0.885584i	$-0.346242\pi$
$743$	25.3216	0.928958	0.464479	+	0.885584i	$0.346242\pi$
$744$	−39.0641	−1.43216
$745$	−43.6181	−1.59804
$746$	−68.9252	−2.52353
$747$	20.5043	0.750212
$748$	14.1073	0.515812
$749$	−29.8688	−1.09138
$750$	40.5564	1.48091
$751$	26.9408	0.983084	0.491542	−	0.870854i	$-0.336433\pi$
$751$	26.9408	0.983084	0.491542	+	0.870854i	$0.336433\pi$
$752$	−10.7748	−0.392918
$753$	−17.3266	−0.631416
$754$	7.04290	0.256487
$755$	3.69885	0.134615
$756$	66.3600	2.41349
$757$	−3.13857	−0.114073	−0.0570367	−	0.998372i	$-0.518165\pi$
$757$	−3.13857	−0.114073	−0.0570367	+	0.998372i	$0.518165\pi$
$758$	−45.9072	−1.66743
$759$	2.48942	0.0903603
$760$	217.930	7.90515
$761$	28.3473	1.02759	0.513794	−	0.857914i	$-0.328240\pi$
$761$	28.3473	1.02759	0.513794	+	0.857914i	$0.328240\pi$
$762$	−16.8750	−0.611315
$763$	−16.7224	−0.605390
$764$	118.086	4.27222
$765$	−41.9713	−1.51748
$766$	100.105	3.61693
$767$	−1.04152	−0.0376071
$768$	−14.4488	−0.521375
$769$	14.2229	0.512891	0.256445	−	0.966559i	$-0.417449\pi$
$769$	14.2229	0.512891	0.256445	+	0.966559i	$0.417449\pi$
$770$	−10.1032	−0.364096
$771$	−17.2359	−0.620737
$772$	−123.872	−4.45824
$773$	−6.18281	−0.222380	−0.111190	−	0.993799i	$-0.535466\pi$
$773$	−6.18281	−0.222380	−0.111190	+	0.993799i	$0.535466\pi$
$774$	34.1255	1.22662
$775$	−35.5049	−1.27537
$776$	−56.4635	−2.02692
$777$	31.5661	1.13243
$778$	54.1760	1.94230
$779$	−31.6209	−1.13294
$780$	−5.36710	−0.192173
$781$	4.02743	0.144113
$782$	91.4643	3.27076
$783$	−55.2615	−1.97489
$784$	−15.2195	−0.543553
$785$	−67.9771	−2.42621
$786$	17.0009	0.606403
$787$	−18.3835	−0.655301	−0.327650	−	0.944799i	$-0.606257\pi$
$787$	−18.3835	−0.655301	−0.327650	+	0.944799i	$0.606257\pi$
$788$	1.86925	0.0665894
$789$	−15.3281	−0.545695
$790$	−95.2904	−3.39028
$791$	−31.6174	−1.12419
$792$	6.43446	0.228639
$793$	1.61372	0.0573051
$794$	7.23962	0.256925
$795$	−4.10353	−0.145537
$796$	−137.232	−4.86406
$797$	−17.2566	−0.611261	−0.305630	−	0.952150i	$-0.598867\pi$
$797$	−17.2566	−0.611261	−0.305630	+	0.952150i	$0.598867\pi$
$798$	−49.0913	−1.73781
$799$	−5.44161	−0.192510
$800$	−146.490	−5.17920
$801$	−7.30469	−0.258098
$802$	−31.4832	−1.11171
$803$	−2.57542	−0.0908847
$804$	−38.4476	−1.35594
$805$	−47.3266	−1.66804
$806$	2.75779	0.0971391
$807$	16.9676	0.597290
$808$	−26.8756	−0.945479
$809$	37.0853	1.30385	0.651926	−	0.758283i	$-0.273961\pi$
$809$	37.0853	1.30385	0.651926	+	0.758283i	$0.273961\pi$
$810$	5.58314	0.196171
$811$	53.0584	1.86313	0.931566	−	0.363573i	$-0.118443\pi$
$811$	53.0584	1.86313	0.931566	+	0.363573i	$0.118443\pi$
$812$	−130.994	−4.59700
$813$	−27.4264	−0.961886
$814$	13.3961	0.469532
$815$	22.6234	0.792462
$816$	−90.3624	−3.16332
$817$	−49.1676	−1.72016
$818$	−75.2950	−2.63263
$819$	−1.07038	−0.0374022
$820$	88.9972	3.10792
$821$	11.2244	0.391733	0.195866	−	0.980631i	$-0.437248\pi$
$821$	11.2244	0.391733	0.195866	+	0.980631i	$0.437248\pi$
$822$	20.8597	0.727565
$823$	−2.79535	−0.0974398	−0.0487199	−	0.998812i	$-0.515514\pi$
$823$	−2.79535	−0.0974398	−0.0487199	+	0.998812i	$0.515514\pi$
$824$	−61.5502	−2.14420
$825$	−4.06843	−0.141644
$826$	26.8122	0.932917
$827$	−34.8103	−1.21047	−0.605236	−	0.796046i	$-0.706921\pi$
$827$	−34.8103	−1.21047	−0.605236	+	0.796046i	$0.706921\pi$
$828$	48.9373	1.70069
$829$	6.00671	0.208622	0.104311	−	0.994545i	$-0.466736\pi$
$829$	6.00671	0.208622	0.104311	+	0.994545i	$0.466736\pi$
$830$	115.083	3.99458
$831$	0.933395	0.0323791
$832$	4.99859	0.173295
$833$	−7.68629	−0.266314
$834$	10.1002	0.349740
$835$	19.6735	0.680830
$836$	−15.0521	−0.520586
$837$	−21.6388	−0.747946
$838$	−74.9674	−2.58970
$839$	36.5665	1.26242	0.631208	−	0.775613i	$-0.282559\pi$
$839$	36.5665	1.26242	0.631208	+	0.775613i	$0.282559\pi$
$840$	85.0985	2.93618
$841$	80.0860	2.76159
$842$	43.7245	1.50685
$843$	11.1133	0.382763
$844$	−40.8448	−1.40594
$845$	−47.8517	−1.64615
$846$	−4.02978	−0.138547
$847$	−26.0653	−0.895615
$848$	12.6996	0.436106
$849$	6.47602	0.222256
$850$	−149.479	−5.12708
$851$	62.7512	2.15108
$852$	−55.0774	−1.88692
$853$	−44.1275	−1.51090	−0.755449	−	0.655208i	$-0.772581\pi$
$853$	−44.1275	−1.51090	−0.755449	+	0.655208i	$0.772581\pi$
$854$	−41.5428	−1.42157
$855$	44.7823	1.53152
$856$	106.767	3.64921
$857$	−0.861790	−0.0294382	−0.0147191	−	0.999892i	$-0.504685\pi$
$857$	−0.861790	−0.0294382	−0.0147191	+	0.999892i	$0.504685\pi$
$858$	0.316009	0.0107884
$859$	13.7160	0.467985	0.233992	−	0.972238i	$-0.424821\pi$
$859$	13.7160	0.467985	0.233992	+	0.972238i	$0.424821\pi$
$860$	138.382	4.71880
$861$	−12.3475	−0.420802
$862$	−14.4299	−0.491484
$863$	3.71153	0.126342	0.0631709	−	0.998003i	$-0.479879\pi$
$863$	3.71153	0.126342	0.0631709	+	0.998003i	$0.479879\pi$
$864$	−89.2796	−3.03735
$865$	−66.4598	−2.25970
$866$	−39.2748	−1.33461
$867$	−26.7757	−0.909351
$868$	−51.2936	−1.74102
$869$	4.05363	0.137510
$870$	−115.060	−3.90088
$871$	1.67174	0.0566448
$872$	59.7745	2.02422
$873$	−11.6026	−0.392690
$874$	−97.5900	−3.30103
$875$	32.7990	1.10881
$876$	35.2204	1.18999
$877$	−38.3063	−1.29351	−0.646756	−	0.762697i	$-0.723875\pi$
$877$	−38.3063	−1.29351	−0.646756	+	0.762697i	$0.723875\pi$
$878$	−69.1194	−2.33267
$879$	34.1960	1.15340
$880$	19.8426	0.668892
$881$	41.6891	1.40454	0.702270	−	0.711911i	$-0.252170\pi$
$881$	41.6891	1.40454	0.702270	+	0.711911i	$0.252170\pi$
$882$	−5.69207	−0.191662
$883$	−33.5716	−1.12977	−0.564887	−	0.825168i	$-0.691080\pi$
$883$	−33.5716	−1.12977	−0.564887	+	0.825168i	$0.691080\pi$
$884$	8.38857	0.282138
$885$	17.0153	0.571961
$886$	−37.2775	−1.25236
$887$	−42.9135	−1.44089	−0.720447	−	0.693510i	$-0.756064\pi$
$887$	−42.9135	−1.44089	−0.720447	+	0.693510i	$0.756064\pi$
$888$	−112.834	−3.78645
$889$	−13.6472	−0.457713
$890$	−40.9985	−1.37427
$891$	−0.237505	−0.00795672
$892$	−102.212	−3.42230
$893$	5.80605	0.194292
$894$	−35.1214	−1.17464
$895$	75.0018	2.50703
$896$	−47.3946	−1.58334
$897$	1.48028	0.0494251
$898$	83.2519	2.77815
$899$	42.7149	1.42462
$900$	−79.9776	−2.66592
$901$	6.41367	0.213670
$902$	−5.24006	−0.174475
$903$	−19.1992	−0.638910
$904$	113.017	3.75889
$905$	−40.5312	−1.34730
$906$	2.97832	0.0989481
$907$	−11.5853	−0.384684	−0.192342	−	0.981328i	$-0.561608\pi$
$907$	−11.5853	−0.384684	−0.192342	+	0.981328i	$0.561608\pi$
$908$	22.8109	0.757007
$909$	−5.52264	−0.183174
$910$	−6.00767	−0.199152
$911$	4.69718	0.155624	0.0778122	−	0.996968i	$-0.475207\pi$
$911$	4.69718	0.155624	0.0778122	+	0.996968i	$0.475207\pi$
$912$	96.4142	3.19259
$913$	−4.89560	−0.162021
$914$	−35.3045	−1.16777
$915$	−26.3634	−0.871546
$916$	−143.483	−4.74081
$917$	13.7491	0.454035
$918$	−91.1013	−3.00679
$919$	57.8288	1.90760	0.953799	−	0.300446i	$-0.0971356\pi$
$919$	57.8288	1.90760	0.953799	+	0.300446i	$0.0971356\pi$
$920$	169.170	5.57736
$921$	13.2637	0.437054
$922$	−92.7960	−3.05607
$923$	2.39482	0.0788266
$924$	−5.87761	−0.193359
$925$	−102.553	−3.37193
$926$	80.8971	2.65844
$927$	−12.6479	−0.415411
$928$	176.238	5.78528
$929$	−5.52424	−0.181245	−0.0906223	−	0.995885i	$-0.528886\pi$
$929$	−5.52424	−0.181245	−0.0906223	+	0.995885i	$0.528886\pi$
$930$	−45.0540	−1.47738
$931$	8.20106	0.268779
$932$	144.997	4.74953
$933$	−24.7232	−0.809400
$934$	69.3333	2.26865
$935$	10.0211	0.327724
$936$	3.82611	0.125060
$937$	19.5058	0.637225	0.318613	−	0.947885i	$-0.396783\pi$
$937$	19.5058	0.637225	0.318613	+	0.947885i	$0.396783\pi$
$938$	−43.0363	−1.40519
$939$	−5.23218	−0.170746
$940$	−16.3412	−0.532990
$941$	15.5876	0.508140	0.254070	−	0.967186i	$-0.418231\pi$
$941$	15.5876	0.508140	0.254070	+	0.967186i	$0.418231\pi$
$942$	−54.7353	−1.78337
$943$	−24.5460	−0.799327
$944$	−52.6587	−1.71389
$945$	47.1387	1.53342
$946$	−8.14780	−0.264908
$947$	−21.8073	−0.708643	−0.354322	−	0.935124i	$-0.615288\pi$
$947$	−21.8073	−0.708643	−0.354322	+	0.935124i	$0.615288\pi$
$948$	−55.4357	−1.80047
$949$	−1.53142	−0.0497120
$950$	159.490	5.17453
$951$	−11.4738	−0.372064
$952$	−133.006	−4.31074
$953$	−44.8271	−1.45209	−0.726046	−	0.687646i	$-0.758644\pi$
$953$	−44.8271	−1.45209	−0.726046	+	0.687646i	$0.758644\pi$
$954$	4.74963	0.153775
$955$	83.8825	2.71437
$956$	−125.040	−4.04407
$957$	4.89460	0.158220
$958$	10.5575	0.341096
$959$	16.8698	0.544753
$960$	−81.6618	−2.63562
$961$	−14.2741	−0.460454
$962$	7.96569	0.256824
$963$	21.9394	0.706987
$964$	−100.614	−3.24055
$965$	−87.9921	−2.83257
$966$	−38.1075	−1.22609
$967$	−25.9922	−0.835852	−0.417926	−	0.908481i	$-0.637243\pi$
$967$	−25.9922	−0.835852	−0.417926	+	0.908481i	$0.637243\pi$
$968$	93.1710	2.99463
$969$	48.6920	1.56421
$970$	−65.1214	−2.09092
$971$	31.9426	1.02509	0.512544	−	0.858661i	$-0.328703\pi$
$971$	31.9426	1.02509	0.512544	+	0.858661i	$0.328703\pi$
$972$	−79.4042	−2.54689
$973$	8.16828	0.261863
$974$	71.9988	2.30699
$975$	−2.41920	−0.0774764
$976$	81.5892	2.61161
$977$	17.1781	0.549576	0.274788	−	0.961505i	$-0.411392\pi$
$977$	17.1781	0.549576	0.274788	+	0.961505i	$0.411392\pi$
$978$	18.2164	0.582496
$979$	1.74407	0.0557406
$980$	−23.0819	−0.737325
$981$	12.2830	0.392166
$982$	−83.3899	−2.66108
$983$	−19.8613	−0.633476	−0.316738	−	0.948513i	$-0.602588\pi$
$983$	−19.8613	−0.633476	−0.316738	+	0.948513i	$0.602588\pi$
$984$	44.1365	1.40702
$985$	1.32782	0.0423079
$986$	179.834	5.72707
$987$	2.26718	0.0721651
$988$	−8.95038	−0.284749
$989$	−38.1667	−1.21363
$990$	7.42109	0.235858
$991$	−43.4147	−1.37911	−0.689556	−	0.724232i	$-0.742194\pi$
$991$	−43.4147	−1.37911	−0.689556	+	0.724232i	$0.742194\pi$
$992$	69.0095	2.19105
$993$	14.4394	0.458220
$994$	−61.6510	−1.95545
$995$	−97.4825	−3.09040
$996$	66.9500	2.12139
$997$	−8.01943	−0.253978	−0.126989	−	0.991904i	$-0.540531\pi$
$997$	−8.01943	−0.253978	−0.126989	+	0.991904i	$0.540531\pi$
$998$	58.1247	1.83991
$999$	−62.5021	−1.97748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.a.1.6	✓	147

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.68460 q^{2} -1.10941 q^{3} +5.20709 q^{4} +3.69885 q^{5} +2.97832 q^{6} +2.40865 q^{7} -8.60976 q^{8} -1.76921 q^{9} +O(q^{10})\)	\(q-2.68460 q^{2} -1.10941 q^{3} +5.20709 q^{4} +3.69885 q^{5} +2.97832 q^{6} +2.40865 q^{7} -8.60976 q^{8} -1.76921 q^{9} -9.92993 q^{10} +0.422417 q^{11} -5.77679 q^{12} +0.251181 q^{13} -6.46626 q^{14} -4.10353 q^{15} +12.6996 q^{16} +6.41367 q^{17} +4.74963 q^{18} -6.84321 q^{19} +19.2602 q^{20} -2.67217 q^{21} -1.13402 q^{22} -5.31209 q^{23} +9.55174 q^{24} +8.68147 q^{25} -0.674321 q^{26} +5.29101 q^{27} +12.5420 q^{28} -10.4444 q^{29} +11.0164 q^{30} -4.08973 q^{31} -16.8738 q^{32} -0.468633 q^{33} -17.2181 q^{34} +8.90922 q^{35} -9.21244 q^{36} -11.8129 q^{37} +18.3713 q^{38} -0.278662 q^{39} -31.8462 q^{40} +4.62078 q^{41} +7.17372 q^{42} +7.18487 q^{43} +2.19956 q^{44} -6.54405 q^{45} +14.2609 q^{46} -0.848440 q^{47} -14.0890 q^{48} -1.19842 q^{49} -23.3063 q^{50} -7.11538 q^{51} +1.30792 q^{52} +1.00000 q^{53} -14.2042 q^{54} +1.56246 q^{55} -20.7379 q^{56} +7.59191 q^{57} +28.0391 q^{58} -4.14649 q^{59} -21.3675 q^{60} +6.42455 q^{61} +10.9793 q^{62} -4.26141 q^{63} +19.9004 q^{64} +0.929080 q^{65} +1.25809 q^{66} +6.65552 q^{67} +33.3965 q^{68} +5.89328 q^{69} -23.9177 q^{70} +9.53426 q^{71} +15.2325 q^{72} -6.09687 q^{73} +31.7129 q^{74} -9.63130 q^{75} -35.6332 q^{76} +1.01745 q^{77} +0.748098 q^{78} +9.59628 q^{79} +46.9739 q^{80} -0.562253 q^{81} -12.4049 q^{82} -11.5895 q^{83} -13.9142 q^{84} +23.7232 q^{85} -19.2885 q^{86} +11.5871 q^{87} -3.63691 q^{88} +4.12878 q^{89} +17.5682 q^{90} +0.605006 q^{91} -27.6605 q^{92} +4.53719 q^{93} +2.27772 q^{94} -25.3120 q^{95} +18.7200 q^{96} +6.55809 q^{97} +3.21729 q^{98} -0.747345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 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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