LMFDB - Embedded newform 8003.2.a.d.1.3

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:	$0$
Dimension:	$179$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
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)

$f(q)$	$=$	$q-2.76009 q^{2} +2.82654 q^{3} +5.61808 q^{4} +3.76331 q^{5} -7.80149 q^{6} -3.62929 q^{7} -9.98623 q^{8} +4.98931 q^{9} +O(q^{10})$	\(q-2.76009 q^{2} +2.82654 q^{3} +5.61808 q^{4} +3.76331 q^{5} -7.80149 q^{6} -3.62929 q^{7} -9.98623 q^{8} +4.98931 q^{9} -10.3871 q^{10} -1.07775 q^{11} +15.8797 q^{12} +5.81881 q^{13} +10.0172 q^{14} +10.6371 q^{15} +16.3267 q^{16} +0.896212 q^{17} -13.7709 q^{18} +8.41489 q^{19} +21.1426 q^{20} -10.2583 q^{21} +2.97469 q^{22} +2.90131 q^{23} -28.2264 q^{24} +9.16251 q^{25} -16.0604 q^{26} +5.62286 q^{27} -20.3896 q^{28} -9.13712 q^{29} -29.3594 q^{30} +6.25916 q^{31} -25.0907 q^{32} -3.04630 q^{33} -2.47362 q^{34} -13.6581 q^{35} +28.0304 q^{36} -3.58525 q^{37} -23.2258 q^{38} +16.4471 q^{39} -37.5813 q^{40} +1.71115 q^{41} +28.3139 q^{42} +10.0771 q^{43} -6.05490 q^{44} +18.7763 q^{45} -8.00787 q^{46} -1.73109 q^{47} +46.1480 q^{48} +6.17173 q^{49} -25.2893 q^{50} +2.53318 q^{51} +32.6906 q^{52} +1.00000 q^{53} -15.5196 q^{54} -4.05591 q^{55} +36.2429 q^{56} +23.7850 q^{57} +25.2193 q^{58} -6.51625 q^{59} +59.7603 q^{60} -4.30525 q^{61} -17.2758 q^{62} -18.1076 q^{63} +36.5990 q^{64} +21.8980 q^{65} +8.40806 q^{66} +3.36514 q^{67} +5.03499 q^{68} +8.20066 q^{69} +37.6977 q^{70} +4.75129 q^{71} -49.8244 q^{72} -12.9804 q^{73} +9.89559 q^{74} +25.8982 q^{75} +47.2756 q^{76} +3.91147 q^{77} -45.3954 q^{78} -1.47616 q^{79} +61.4425 q^{80} +0.925294 q^{81} -4.72291 q^{82} +5.99096 q^{83} -57.6321 q^{84} +3.37272 q^{85} -27.8136 q^{86} -25.8264 q^{87} +10.7627 q^{88} +9.38153 q^{89} -51.8243 q^{90} -21.1181 q^{91} +16.2998 q^{92} +17.6917 q^{93} +4.77796 q^{94} +31.6678 q^{95} -70.9197 q^{96} +3.79417 q^{97} -17.0345 q^{98} -5.37723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) $ 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * 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 $

$2$	−2.76009	−1.95168	−0.975838	−	0.218494i	$-0.929886\pi$
$2$	−2.76009	−1.95168	−0.975838	+	0.218494i	$0.929886\pi$
$3$	2.82654	1.63190	0.815951	−	0.578121i	$-0.196214\pi$
$3$	2.82654	1.63190	0.815951	+	0.578121i	$0.196214\pi$
$4$	5.61808	2.80904
$5$	3.76331	1.68300	0.841502	−	0.540254i	$-0.181672\pi$
$5$	3.76331	1.68300	0.841502	+	0.540254i	$0.181672\pi$
$6$	−7.80149	−3.18494
$7$	−3.62929	−1.37174	−0.685871	−	0.727723i	$-0.740579\pi$
$7$	−3.62929	−1.37174	−0.685871	+	0.727723i	$0.740579\pi$
$8$	−9.98623	−3.53067
$9$	4.98931	1.66310
$10$	−10.3871	−3.28468
$11$	−1.07775	−0.324954	−0.162477	−	0.986712i	$-0.551948\pi$
$11$	−1.07775	−0.324954	−0.162477	+	0.986712i	$0.551948\pi$
$12$	15.8797	4.58408
$13$	5.81881	1.61385	0.806924	−	0.590655i	$-0.201131\pi$
$13$	5.81881	1.61385	0.806924	+	0.590655i	$0.201131\pi$
$14$	10.0172	2.67720
$15$	10.6371	2.74650
$16$	16.3267	4.08168
$17$	0.896212	0.217363	0.108682	−	0.994077i	$-0.465337\pi$
$17$	0.896212	0.217363	0.108682	+	0.994077i	$0.465337\pi$
$18$	−13.7709	−3.24584
$19$	8.41489	1.93051	0.965254	−	0.261313i	$-0.0841555\pi$
$19$	8.41489	1.93051	0.965254	+	0.261313i	$0.0841555\pi$
$20$	21.1426	4.72763
$21$	−10.2583	−2.23855
$22$	2.97469	0.634205
$23$	2.90131	0.604965	0.302483	−	0.953155i	$-0.402185\pi$
$23$	2.90131	0.604965	0.302483	+	0.953155i	$0.402185\pi$
$24$	−28.2264	−5.76170
$25$	9.16251	1.83250
$26$	−16.0604	−3.14971
$27$	5.62286	1.08212
$28$	−20.3896	−3.85328
$29$	−9.13712	−1.69672	−0.848361	−	0.529419i	$-0.822410\pi$
$29$	−9.13712	−1.69672	−0.848361	+	0.529419i	$0.822410\pi$
$30$	−29.3594	−5.36027
$31$	6.25916	1.12418	0.562089	−	0.827077i	$-0.309998\pi$
$31$	6.25916	1.12418	0.562089	+	0.827077i	$0.309998\pi$
$32$	−25.0907	−4.43545
$33$	−3.04630	−0.530293
$34$	−2.47362	−0.424223
$35$	−13.6581	−2.30865
$36$	28.0304	4.67173
$37$	−3.58525	−0.589411	−0.294705	−	0.955588i	$-0.595222\pi$
$37$	−3.58525	−0.589411	−0.294705	+	0.955588i	$0.595222\pi$
$38$	−23.2258	−3.76773
$39$	16.4471	2.63364
$40$	−37.5813	−5.94212
$41$	1.71115	0.267236	0.133618	−	0.991033i	$-0.457340\pi$
$41$	1.71115	0.267236	0.133618	+	0.991033i	$0.457340\pi$
$42$	28.3139	4.36892
$43$	10.0771	1.53674	0.768369	−	0.640007i	$-0.221069\pi$
$43$	10.0771	1.53674	0.768369	+	0.640007i	$0.221069\pi$
$44$	−6.05490	−0.912810
$45$	18.7763	2.79901
$46$	−8.00787	−1.18070
$47$	−1.73109	−0.252506	−0.126253	−	0.991998i	$-0.540295\pi$
$47$	−1.73109	−0.252506	−0.126253	+	0.991998i	$0.540295\pi$
$48$	46.1480	6.66089
$49$	6.17173	0.881676
$50$	−25.2893	−3.57645
$51$	2.53318	0.354715
$52$	32.6906	4.53337
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−15.5196	−2.11195
$55$	−4.05591	−0.546899
$56$	36.2429	4.84316
$57$	23.7850	3.15040
$58$	25.2193	3.31145
$59$	−6.51625	−0.848344	−0.424172	−	0.905582i	$-0.639435\pi$
$59$	−6.51625	−0.848344	−0.424172	+	0.905582i	$0.639435\pi$
$60$	59.7603	7.71503
$61$	−4.30525	−0.551231	−0.275615	−	0.961268i	$-0.588882\pi$
$61$	−4.30525	−0.551231	−0.275615	+	0.961268i	$0.588882\pi$
$62$	−17.2758	−2.19403
$63$	−18.1076	−2.28135
$64$	36.5990	4.57488
$65$	21.8980	2.71611
$66$	8.40806	1.03496
$67$	3.36514	0.411117	0.205559	−	0.978645i	$-0.434099\pi$
$67$	3.36514	0.411117	0.205559	+	0.978645i	$0.434099\pi$
$68$	5.03499	0.610582
$69$	8.20066	0.987244
$70$	37.6977	4.50573
$71$	4.75129	0.563874	0.281937	−	0.959433i	$-0.409023\pi$
$71$	4.75129	0.563874	0.281937	+	0.959433i	$0.409023\pi$
$72$	−49.8244	−5.87186
$73$	−12.9804	−1.51924	−0.759618	−	0.650370i	$-0.774614\pi$
$73$	−12.9804	−1.51924	−0.759618	+	0.650370i	$0.774614\pi$
$74$	9.89559	1.15034
$75$	25.8982	2.99046
$76$	47.2756	5.42288
$77$	3.91147	0.445753
$78$	−45.3954	−5.14002
$79$	−1.47616	−0.166081	−0.0830403	−	0.996546i	$-0.526463\pi$
$79$	−1.47616	−0.166081	−0.0830403	+	0.996546i	$0.526463\pi$
$80$	61.4425	6.86948
$81$	0.925294	0.102810
$82$	−4.72291	−0.521559
$83$	5.99096	0.657594	0.328797	−	0.944401i	$-0.393357\pi$
$83$	5.99096	0.657594	0.328797	+	0.944401i	$0.393357\pi$
$84$	−57.6321	−6.28818
$85$	3.37272	0.365823
$86$	−27.8136	−2.99922
$87$	−25.8264	−2.76888
$88$	10.7627	1.14730
$89$	9.38153	0.994440	0.497220	−	0.867624i	$-0.334354\pi$
$89$	9.38153	0.994440	0.497220	+	0.867624i	$0.334354\pi$
$90$	−51.8243	−5.46276
$91$	−21.1181	−2.21378
$92$	16.2998	1.69937
$93$	17.6917	1.83455
$94$	4.77796	0.492809
$95$	31.6678	3.24905
$96$	−70.9197	−7.23821
$97$	3.79417	0.385239	0.192620	−	0.981273i	$-0.438302\pi$
$97$	3.79417	0.385239	0.192620	+	0.981273i	$0.438302\pi$
$98$	−17.0345	−1.72075
$99$	−5.37723	−0.540432
$100$	51.4757	5.14757
$101$	−15.6041	−1.55267	−0.776334	−	0.630321i	$-0.782923\pi$
$101$	−15.6041	−1.55267	−0.776334	+	0.630321i	$0.782923\pi$
$102$	−6.99179	−0.692290
$103$	1.05160	0.103617	0.0518085	−	0.998657i	$-0.483501\pi$
$103$	1.05160	0.103617	0.0518085	+	0.998657i	$0.483501\pi$
$104$	−58.1080	−5.69796
$105$	−38.6052	−3.76749
$106$	−2.76009	−0.268083
$107$	−16.1287	−1.55922	−0.779609	−	0.626267i	$-0.784582\pi$
$107$	−16.1287	−1.55922	−0.779609	+	0.626267i	$0.784582\pi$
$108$	31.5897	3.03972
$109$	3.34913	0.320788	0.160394	−	0.987053i	$-0.448723\pi$
$109$	3.34913	0.320788	0.160394	+	0.987053i	$0.448723\pi$
$110$	11.1947	1.06737
$111$	−10.1338	−0.961860
$112$	−59.2543	−5.59901
$113$	13.7427	1.29280	0.646401	−	0.762998i	$-0.276273\pi$
$113$	13.7427	1.29280	0.646401	+	0.762998i	$0.276273\pi$
$114$	−65.6487	−6.14856
$115$	10.9185	1.01816
$116$	−51.3331	−4.76616
$117$	29.0319	2.68400
$118$	17.9854	1.65569
$119$	−3.25261	−0.298166
$120$	−106.225	−9.69696
$121$	−9.83845	−0.894405
$122$	11.8829	1.07582
$123$	4.83662	0.436103
$124$	35.1645	3.15786
$125$	15.6648	1.40110
$126$	49.9787	4.45246
$127$	18.1027	1.60636	0.803178	−	0.595739i	$-0.203141\pi$
$127$	18.1027	1.60636	0.803178	+	0.595739i	$0.203141\pi$
$128$	−50.8352	−4.49324
$129$	28.4832	2.50781
$130$	−60.4404	−5.30097
$131$	−18.5012	−1.61646	−0.808229	−	0.588869i	$-0.799573\pi$
$131$	−18.5012	−1.61646	−0.808229	+	0.588869i	$0.799573\pi$
$132$	−17.1144	−1.48962
$133$	−30.5401	−2.64816
$134$	−9.28808	−0.802368
$135$	21.1606	1.82121
$136$	−8.94978	−0.767437
$137$	17.0140	1.45361	0.726804	−	0.686845i	$-0.241005\pi$
$137$	17.0140	1.45361	0.726804	+	0.686845i	$0.241005\pi$
$138$	−22.6345	−1.92678
$139$	−8.21654	−0.696918	−0.348459	−	0.937324i	$-0.613295\pi$
$139$	−8.21654	−0.696918	−0.348459	+	0.937324i	$0.613295\pi$
$140$	−76.7326	−6.48509
$141$	−4.89299	−0.412064
$142$	−13.1140	−1.10050
$143$	−6.27123	−0.524426
$144$	81.4590	6.78825
$145$	−34.3858	−2.85559
$146$	35.8269	2.96506
$147$	17.4446	1.43881
$148$	−20.1422	−1.65568
$149$	7.41925	0.607809	0.303905	−	0.952702i	$-0.401710\pi$
$149$	7.41925	0.607809	0.303905	+	0.952702i	$0.401710\pi$
$150$	−71.4812	−5.83642
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−84.0330	−6.81598
$153$	4.47148	0.361498
$154$	−10.7960	−0.869966
$155$	23.5552	1.89200
$156$	92.4011	7.39801
$157$	4.15950	0.331964	0.165982	−	0.986129i	$-0.446921\pi$
$157$	4.15950	0.331964	0.165982	+	0.986129i	$0.446921\pi$
$158$	4.07432	0.324136
$159$	2.82654	0.224159
$160$	−94.4240	−7.46487
$161$	−10.5297	−0.829856
$162$	−2.55389	−0.200653
$163$	−21.7317	−1.70215	−0.851077	−	0.525040i	$-0.824050\pi$
$163$	−21.7317	−1.70215	−0.851077	+	0.525040i	$0.824050\pi$
$164$	9.61336	0.750677
$165$	−11.4642	−0.892486
$166$	−16.5356	−1.28341
$167$	−7.88218	−0.609942	−0.304971	−	0.952362i	$-0.598647\pi$
$167$	−7.88218	−0.609942	−0.304971	+	0.952362i	$0.598647\pi$
$168$	102.442	7.90356
$169$	20.8586	1.60450
$170$	−9.30901	−0.713969
$171$	41.9845	3.21064
$172$	56.6138	4.31676
$173$	7.35268	0.559014	0.279507	−	0.960144i	$-0.409829\pi$
$173$	7.35268	0.559014	0.279507	+	0.960144i	$0.409829\pi$
$174$	71.2832	5.40396
$175$	−33.2534	−2.51372
$176$	−17.5961	−1.32636
$177$	−18.4184	−1.38441
$178$	−25.8938	−1.94083
$179$	−12.5638	−0.939059	−0.469530	−	0.882917i	$-0.655576\pi$
$179$	−12.5638	−0.939059	−0.469530	+	0.882917i	$0.655576\pi$
$180$	105.487	7.86254
$181$	−0.396151	−0.0294457	−0.0147228	−	0.999892i	$-0.504687\pi$
$181$	−0.396151	−0.0294457	−0.0147228	+	0.999892i	$0.504687\pi$
$182$	58.2879	4.32059
$183$	−12.1689	−0.899555
$184$	−28.9732	−2.13593
$185$	−13.4924	−0.991980
$186$	−48.8308	−3.58045
$187$	−0.965893	−0.0706331
$188$	−9.72541	−0.709299
$189$	−20.4070	−1.48439
$190$	−87.4060	−6.34110
$191$	15.9246	1.15226	0.576132	−	0.817357i	$-0.304561\pi$
$191$	15.9246	1.15226	0.576132	+	0.817357i	$0.304561\pi$
$192$	103.449	7.46576
$193$	22.9823	1.65431	0.827153	−	0.561977i	$-0.189959\pi$
$193$	22.9823	1.65431	0.827153	+	0.561977i	$0.189959\pi$
$194$	−10.4722	−0.751863
$195$	61.8955	4.43243
$196$	34.6733	2.47666
$197$	18.8290	1.34151	0.670756	−	0.741678i	$-0.265970\pi$
$197$	18.8290	1.34151	0.670756	+	0.741678i	$0.265970\pi$
$198$	14.8416	1.05475
$199$	−13.0357	−0.924080	−0.462040	−	0.886859i	$-0.652882\pi$
$199$	−13.0357	−0.924080	−0.462040	+	0.886859i	$0.652882\pi$
$200$	−91.4989	−6.46995
$201$	9.51169	0.670903
$202$	43.0688	3.03031
$203$	33.1613	2.32746
$204$	14.2316	0.996411
$205$	6.43957	0.449759
$206$	−2.90250	−0.202227
$207$	14.4755	1.00612
$208$	95.0020	6.58720
$209$	−9.06916	−0.627327
$210$	106.554	7.35291
$211$	−21.9294	−1.50968	−0.754841	−	0.655908i	$-0.772286\pi$
$211$	−21.9294	−1.50968	−0.754841	+	0.655908i	$0.772286\pi$
$212$	5.61808	0.385852
$213$	13.4297	0.920188
$214$	44.5166	3.04309
$215$	37.9231	2.58634
$216$	−56.1512	−3.82060
$217$	−22.7163	−1.54208
$218$	−9.24389	−0.626075
$219$	−36.6895	−2.47924
$220$	−22.7865	−1.53626
$221$	5.21489	0.350791
$222$	27.9703	1.87724
$223$	−22.8650	−1.53115	−0.765575	−	0.643346i	$-0.777545\pi$
$223$	−22.8650	−1.53115	−0.765575	+	0.643346i	$0.777545\pi$
$224$	91.0613	6.08429
$225$	45.7146	3.04764
$226$	−37.9310	−2.52313
$227$	5.35576	0.355474	0.177737	−	0.984078i	$-0.443122\pi$
$227$	5.35576	0.355474	0.177737	+	0.984078i	$0.443122\pi$
$228$	133.626	8.84961
$229$	22.0979	1.46027	0.730136	−	0.683302i	$-0.239457\pi$
$229$	22.0979	1.46027	0.730136	+	0.683302i	$0.239457\pi$
$230$	−30.1361	−1.98712
$231$	11.0559	0.727425
$232$	91.2454	5.99055
$233$	−14.2648	−0.934518	−0.467259	−	0.884121i	$-0.654758\pi$
$233$	−14.2648	−0.934518	−0.467259	+	0.884121i	$0.654758\pi$
$234$	−80.1305	−5.23829
$235$	−6.51463	−0.424968
$236$	−36.6089	−2.38303
$237$	−4.17241	−0.271027
$238$	8.97749	0.581924
$239$	13.4810	0.872016	0.436008	−	0.899943i	$-0.356392\pi$
$239$	13.4810	0.872016	0.436008	+	0.899943i	$0.356392\pi$
$240$	173.669	11.2103
$241$	−6.90291	−0.444656	−0.222328	−	0.974972i	$-0.571366\pi$
$241$	−6.90291	−0.444656	−0.222328	+	0.974972i	$0.571366\pi$
$242$	27.1550	1.74559
$243$	−14.2532	−0.914344
$244$	−24.1873	−1.54843
$245$	23.2261	1.48386
$246$	−13.3495	−0.851132
$247$	48.9647	3.11555
$248$	−62.5054	−3.96910
$249$	16.9337	1.07313
$250$	−43.2363	−2.73450
$251$	−24.4437	−1.54287	−0.771435	−	0.636308i	$-0.780461\pi$
$251$	−24.4437	−1.54287	−0.771435	+	0.636308i	$0.780461\pi$
$252$	−101.730	−6.40841
$253$	−3.12689	−0.196586
$254$	−49.9651	−3.13509
$255$	9.53313	0.596988
$256$	67.1116	4.19448
$257$	0.545900	0.0340523	0.0170262	−	0.999855i	$-0.494580\pi$
$257$	0.545900	0.0340523	0.0170262	+	0.999855i	$0.494580\pi$
$258$	−78.6161	−4.89443
$259$	13.0119	0.808519
$260$	123.025	7.62967
$261$	−45.5880	−2.82182
$262$	51.0649	3.15480
$263$	−8.29598	−0.511552	−0.255776	−	0.966736i	$-0.582331\pi$
$263$	−8.29598	−0.511552	−0.255776	+	0.966736i	$0.582331\pi$
$264$	30.4211	1.87229
$265$	3.76331	0.231178
$266$	84.2932	5.16835
$267$	26.5172	1.62283
$268$	18.9056	1.15485
$269$	−25.7573	−1.57045	−0.785226	−	0.619210i	$-0.787453\pi$
$269$	−25.7573	−1.57045	−0.785226	+	0.619210i	$0.787453\pi$
$270$	−58.4051	−3.55442
$271$	−1.27460	−0.0774263	−0.0387131	−	0.999250i	$-0.512326\pi$
$271$	−1.27460	−0.0774263	−0.0387131	+	0.999250i	$0.512326\pi$
$272$	14.6322	0.887206
$273$	−59.6912	−3.61268
$274$	−46.9603	−2.83697
$275$	−9.87490	−0.595479
$276$	46.0720	2.77321
$277$	12.0701	0.725220	0.362610	−	0.931941i	$-0.381886\pi$
$277$	12.0701	0.725220	0.362610	+	0.931941i	$0.381886\pi$
$278$	22.6784	1.36016
$279$	31.2289	1.86963
$280$	136.393	8.15106
$281$	−2.40393	−0.143406	−0.0717032	−	0.997426i	$-0.522843\pi$
$281$	−2.40393	−0.143406	−0.0717032	+	0.997426i	$0.522843\pi$
$282$	13.5051	0.804216
$283$	−0.0388912	−0.00231184	−0.00115592	−	0.999999i	$-0.500368\pi$
$283$	−0.0388912	−0.00231184	−0.00115592	+	0.999999i	$0.500368\pi$
$284$	26.6932	1.58395
$285$	89.5103	5.30214
$286$	17.3091	1.02351
$287$	−6.21024	−0.366579
$288$	−125.185	−7.37661
$289$	−16.1968	−0.952753
$290$	94.9079	5.57319
$291$	10.7244	0.628673
$292$	−72.9247	−4.26760
$293$	0.351281	0.0205221	0.0102610	−	0.999947i	$-0.496734\pi$
$293$	0.351281	0.0205221	0.0102610	+	0.999947i	$0.496734\pi$
$294$	−48.1487	−2.80809
$295$	−24.5227	−1.42777
$296$	35.8031	2.08101
$297$	−6.06004	−0.351639
$298$	−20.4778	−1.18625
$299$	16.8822	0.976321
$300$	145.498	8.40034
$301$	−36.5726	−2.10801
$302$	2.76009	0.158825
$303$	−44.1056	−2.53380
$304$	137.387	7.87971
$305$	−16.2020	−0.927723
$306$	−12.3417	−0.705527
$307$	17.9553	1.02476	0.512380	−	0.858759i	$-0.328764\pi$
$307$	17.9553	1.02476	0.512380	+	0.858759i	$0.328764\pi$
$308$	21.9750	1.25214
$309$	2.97238	0.169093
$310$	−65.0143	−3.69257
$311$	8.66264	0.491213	0.245607	−	0.969370i	$-0.421013\pi$
$311$	8.66264	0.491213	0.245607	+	0.969370i	$0.421013\pi$
$312$	−164.244	−9.29851
$313$	25.8381	1.46046	0.730228	−	0.683203i	$-0.239414\pi$
$313$	25.8381	1.46046	0.730228	+	0.683203i	$0.239414\pi$
$314$	−11.4806	−0.647887
$315$	−68.1447	−3.83952
$316$	−8.29317	−0.466527
$317$	−21.5084	−1.20803	−0.604017	−	0.796972i	$-0.706434\pi$
$317$	−21.5084	−1.20803	−0.604017	+	0.796972i	$0.706434\pi$
$318$	−7.80149	−0.437486
$319$	9.84754	0.551357
$320$	137.734	7.69954
$321$	−45.5883	−2.54449
$322$	29.0629	1.61961
$323$	7.54152	0.419622
$324$	5.19838	0.288799
$325$	53.3149	2.95738
$326$	59.9813	3.32206
$327$	9.46644	0.523495
$328$	−17.0879	−0.943521
$329$	6.28263	0.346372
$330$	31.6422	1.74184
$331$	−9.23548	−0.507628	−0.253814	−	0.967253i	$-0.581685\pi$
$331$	−9.23548	−0.507628	−0.253814	+	0.967253i	$0.581685\pi$
$332$	33.6577	1.84721
$333$	−17.8879	−0.980251
$334$	21.7555	1.19041
$335$	12.6641	0.691912
$336$	−167.484	−9.13703
$337$	−29.9472	−1.63133	−0.815665	−	0.578524i	$-0.803629\pi$
$337$	−29.9472	−1.63133	−0.815665	+	0.578524i	$0.803629\pi$
$338$	−57.5715	−3.13147
$339$	38.8442	2.10972
$340$	18.9482	1.02761
$341$	−6.74582	−0.365306
$342$	−115.881	−6.26612
$343$	3.00603	0.162310
$344$	−100.632	−5.42571
$345$	30.8616	1.66153
$346$	−20.2940	−1.09101
$347$	−3.34172	−0.179393	−0.0896964	−	0.995969i	$-0.528590\pi$
$347$	−3.34172	−0.179393	−0.0896964	+	0.995969i	$0.528590\pi$
$348$	−145.095	−7.77791
$349$	−6.98467	−0.373881	−0.186940	−	0.982371i	$-0.559857\pi$
$349$	−6.98467	−0.373881	−0.186940	+	0.982371i	$0.559857\pi$
$350$	91.7823	4.90597
$351$	32.7184	1.74638
$352$	27.0415	1.44132
$353$	2.80226	0.149150	0.0745748	−	0.997215i	$-0.476240\pi$
$353$	2.80226	0.149150	0.0745748	+	0.997215i	$0.476240\pi$
$354$	50.8365	2.70193
$355$	17.8806	0.949003
$356$	52.7062	2.79342
$357$	−9.19362	−0.486578
$358$	34.6771	1.83274
$359$	22.9735	1.21249	0.606247	−	0.795276i	$-0.292674\pi$
$359$	22.9735	1.21249	0.606247	+	0.795276i	$0.292674\pi$
$360$	−187.505	−9.88237
$361$	51.8104	2.72686
$362$	1.09341	0.0574685
$363$	−27.8088	−1.45958
$364$	−118.643	−6.21861
$365$	−48.8491	−2.55688
$366$	33.5874	1.75564
$367$	38.1676	1.99233	0.996167	−	0.0874756i	$-0.0278800\pi$
$367$	38.1676	1.99233	0.996167	+	0.0874756i	$0.0278800\pi$
$368$	47.3688	2.46927
$369$	8.53744	0.444441
$370$	37.2402	1.93603
$371$	−3.62929	−0.188423
$372$	99.3937	5.15332
$373$	2.35527	0.121951	0.0609756	−	0.998139i	$-0.480579\pi$
$373$	2.35527	0.121951	0.0609756	+	0.998139i	$0.480579\pi$
$374$	2.66595	0.137853
$375$	44.2772	2.28646
$376$	17.2871	0.891512
$377$	−53.1672	−2.73825
$378$	56.3251	2.89705
$379$	0.0123932	0.000636595 0	0.000318298	−	1.00000i	$-0.499899\pi$
$379$	0.0123932	0.000636595 0	0.000318298		1.00000i	$0.499899\pi$
$380$	177.913	9.12673
$381$	51.1680	2.62142
$382$	−43.9533	−2.24885
$383$	−10.0787	−0.514998	−0.257499	−	0.966279i	$-0.582898\pi$
$383$	−10.0787	−0.514998	−0.257499	+	0.966279i	$0.582898\pi$
$384$	−143.688	−7.33253
$385$	14.7201	0.750204
$386$	−63.4333	−3.22867
$387$	50.2776	2.55576
$388$	21.3160	1.08215
$389$	8.22458	0.417003	0.208501	−	0.978022i	$-0.433141\pi$
$389$	8.22458	0.417003	0.208501	+	0.978022i	$0.433141\pi$
$390$	−170.837	−8.65067
$391$	2.60019	0.131497
$392$	−61.6323	−3.11290
$393$	−52.2943	−2.63790
$394$	−51.9697	−2.61820
$395$	−5.55524	−0.279514
$396$	−30.2098	−1.51810
$397$	10.5954	0.531769	0.265884	−	0.964005i	$-0.414336\pi$
$397$	10.5954	0.531769	0.265884	+	0.964005i	$0.414336\pi$
$398$	35.9798	1.80351
$399$	−86.3226	−4.32154
$400$	149.594	7.47968
$401$	22.8488	1.14102	0.570508	−	0.821292i	$-0.306746\pi$
$401$	22.8488	1.14102	0.570508	+	0.821292i	$0.306746\pi$
$402$	−26.2531	−1.30939
$403$	36.4209	1.81425
$404$	−87.6653	−4.36151
$405$	3.48217	0.173030
$406$	−91.5280	−4.54246
$407$	3.86400	0.191531
$408$	−25.2969	−1.25238
$409$	−22.9817	−1.13637	−0.568185	−	0.822901i	$-0.692354\pi$
$409$	−22.9817	−1.13637	−0.568185	+	0.822901i	$0.692354\pi$
$410$	−17.7738	−0.877785
$411$	48.0908	2.37215
$412$	5.90796	0.291064
$413$	23.6494	1.16371
$414$	−39.9538	−1.96362
$415$	22.5459	1.10673
$416$	−145.998	−7.15813
$417$	−23.2244	−1.13730
$418$	25.0317	1.22434
$419$	−16.8255	−0.821981	−0.410991	−	0.911640i	$-0.634817\pi$
$419$	−16.8255	−0.821981	−0.410991	+	0.911640i	$0.634817\pi$
$420$	−216.887	−10.5830
$421$	17.7693	0.866020	0.433010	−	0.901389i	$-0.357451\pi$
$421$	17.7693	0.866020	0.433010	+	0.901389i	$0.357451\pi$
$422$	60.5271	2.94641
$423$	−8.63695	−0.419943
$424$	−9.98623	−0.484974
$425$	8.21155	0.398319
$426$	−37.0671	−1.79591
$427$	15.6250	0.756146
$428$	−90.6123	−4.37991
$429$	−17.7259	−0.855813
$430$	−104.671	−5.04769
$431$	8.00947	0.385802	0.192901	−	0.981218i	$-0.438210\pi$
$431$	8.00947	0.385802	0.192901	+	0.981218i	$0.438210\pi$
$432$	91.8028	4.41686
$433$	−0.708775	−0.0340616	−0.0170308	−	0.999855i	$-0.505421\pi$
$433$	−0.708775	−0.0340616	−0.0170308	+	0.999855i	$0.505421\pi$
$434$	62.6990	3.00965
$435$	−97.1928	−4.66004
$436$	18.8157	0.901108
$437$	24.4142	1.16789
$438$	101.266	4.83868
$439$	14.9902	0.715441	0.357720	−	0.933829i	$-0.383554\pi$
$439$	14.9902	0.715441	0.357720	+	0.933829i	$0.383554\pi$
$440$	40.5033	1.93092
$441$	30.7927	1.46632
$442$	−14.3935	−0.684631
$443$	−13.8262	−0.656904	−0.328452	−	0.944521i	$-0.606527\pi$
$443$	−13.8262	−0.656904	−0.328452	+	0.944521i	$0.606527\pi$
$444$	−56.9327	−2.70191
$445$	35.3056	1.67365
$446$	63.1093	2.98831
$447$	20.9708	0.991885
$448$	−132.828	−6.27556
$449$	−20.0797	−0.947621	−0.473810	−	0.880627i	$-0.657122\pi$
$449$	−20.0797	−0.947621	−0.473810	+	0.880627i	$0.657122\pi$
$450$	−126.176	−5.94801
$451$	−1.84419	−0.0868395
$452$	77.2075	3.63153
$453$	−2.82654	−0.132802
$454$	−14.7824	−0.693770
$455$	−79.4741	−3.72580
$456$	−237.522	−11.1230
$457$	28.9334	1.35345	0.676724	−	0.736237i	$-0.263399\pi$
$457$	28.9334	1.35345	0.676724	+	0.736237i	$0.263399\pi$
$458$	−60.9922	−2.84998
$459$	5.03927	0.235213
$460$	61.3412	2.86005
$461$	28.8633	1.34430	0.672148	−	0.740417i	$-0.265372\pi$
$461$	28.8633	1.34430	0.672148	+	0.740417i	$0.265372\pi$
$462$	−30.5153	−1.41970
$463$	−0.248818	−0.0115635	−0.00578177	−	0.999983i	$-0.501840\pi$
$463$	−0.248818	−0.0115635	−0.00578177	+	0.999983i	$0.501840\pi$
$464$	−149.179	−6.92547
$465$	66.5795	3.08755
$466$	39.3721	1.82388
$467$	−30.8222	−1.42628	−0.713140	−	0.701022i	$-0.752728\pi$
$467$	−30.8222	−1.42628	−0.713140	+	0.701022i	$0.752728\pi$
$468$	163.103	7.53946
$469$	−12.2131	−0.563946
$470$	17.9810	0.829400
$471$	11.7570	0.541733
$472$	65.0728	2.99522
$473$	−10.8606	−0.499369
$474$	11.5162	0.528958
$475$	77.1015	3.53766
$476$	−18.2734	−0.837562
$477$	4.98931	0.228445
$478$	−37.2089	−1.70189
$479$	−1.33637	−0.0610602	−0.0305301	−	0.999534i	$-0.509720\pi$
$479$	−1.33637	−0.0610602	−0.0305301	+	0.999534i	$0.509720\pi$
$480$	−266.893	−12.1819
$481$	−20.8619	−0.951219
$482$	19.0526	0.867824
$483$	−29.7626	−1.35424
$484$	−55.2733	−2.51242
$485$	14.2786	0.648359
$486$	39.3401	1.78450
$487$	11.0435	0.500429	0.250215	−	0.968190i	$-0.419499\pi$
$487$	11.0435	0.500429	0.250215	+	0.968190i	$0.419499\pi$
$488$	42.9932	1.94621
$489$	−61.4253	−2.77775
$490$	−64.1062	−2.89602
$491$	−17.9392	−0.809583	−0.404792	−	0.914409i	$-0.632656\pi$
$491$	−17.9392	−0.809583	−0.404792	+	0.914409i	$0.632656\pi$
$492$	27.1725	1.22503
$493$	−8.18880	−0.368805
$494$	−135.147	−6.08054
$495$	−20.2362	−0.909550
$496$	102.191	4.58853
$497$	−17.2438	−0.773490
$498$	−46.7384	−2.09440
$499$	12.1121	0.542211	0.271105	−	0.962550i	$-0.412611\pi$
$499$	12.1121	0.542211	0.271105	+	0.962550i	$0.412611\pi$
$500$	88.0063	3.93576
$501$	−22.2793	−0.995365
$502$	67.4667	3.01119
$503$	12.3358	0.550026	0.275013	−	0.961440i	$-0.411318\pi$
$503$	12.3358	0.550026	0.275013	+	0.961440i	$0.411318\pi$
$504$	180.827	8.05468
$505$	−58.7232	−2.61315
$506$	8.63049	0.383672
$507$	58.9575	2.61839
$508$	101.703	4.51232
$509$	0.399397	0.0177030	0.00885148	−	0.999961i	$-0.497182\pi$
$509$	0.399397	0.0177030	0.00885148	+	0.999961i	$0.497182\pi$
$510$	−26.3123	−1.16513
$511$	47.1095	2.08400
$512$	−83.5635	−3.69302
$513$	47.3158	2.08904
$514$	−1.50673	−0.0664591
$515$	3.95749	0.174388
$516$	160.021	7.04453
$517$	1.86568	0.0820527
$518$	−35.9140	−1.57797
$519$	20.7826	0.912255
$520$	−218.678	−9.58968
$521$	13.9737	0.612201	0.306100	−	0.951999i	$-0.400976\pi$
$521$	13.9737	0.612201	0.306100	+	0.951999i	$0.400976\pi$
$522$	125.827	5.50729
$523$	−33.6176	−1.47000	−0.734998	−	0.678069i	$-0.762817\pi$
$523$	−33.6176	−1.47000	−0.734998	+	0.678069i	$0.762817\pi$
$524$	−103.941	−4.54070
$525$	−93.9919	−4.10214
$526$	22.8976	0.998385
$527$	5.60953	0.244355
$528$	−49.7361	−2.16448
$529$	−14.5824	−0.634017
$530$	−10.3871	−0.451185
$531$	−32.5116	−1.41088
$532$	−171.577	−7.43879
$533$	9.95684	0.431278
$534$	−73.1899	−3.16724
$535$	−60.6972	−2.62417
$536$	−33.6050	−1.45152
$537$	−35.5119	−1.53245
$538$	71.0925	3.06501
$539$	−6.65159	−0.286504
$540$	118.882	5.11586
$541$	−26.8492	−1.15434	−0.577170	−	0.816624i	$-0.695843\pi$
$541$	−26.8492	−1.15434	−0.577170	+	0.816624i	$0.695843\pi$
$542$	3.51800	0.151111
$543$	−1.11974	−0.0480525
$544$	−22.4865	−0.964103
$545$	12.6038	0.539888
$546$	164.753	7.05078
$547$	19.2572	0.823379	0.411689	−	0.911324i	$-0.364939\pi$
$547$	19.2572	0.823379	0.411689	+	0.911324i	$0.364939\pi$
$548$	95.5864	4.08325
$549$	−21.4802	−0.916754
$550$	27.2556	1.16218
$551$	−76.8879	−3.27553
$552$	−81.8937	−3.48563
$553$	5.35740	0.227820
$554$	−33.3144	−1.41540
$555$	−38.1367	−1.61881
$556$	−46.1612	−1.95767
$557$	3.60948	0.152939	0.0764693	−	0.997072i	$-0.475635\pi$
$557$	3.60948	0.152939	0.0764693	+	0.997072i	$0.475635\pi$
$558$	−86.1945	−3.64890
$559$	58.6366	2.48006
$560$	−222.992	−9.42315
$561$	−2.73013	−0.115266
$562$	6.63505	0.279883
$563$	44.2228	1.86377	0.931884	−	0.362756i	$-0.118164\pi$
$563$	44.2228	1.86377	0.931884	+	0.362756i	$0.118164\pi$
$564$	−27.4892	−1.15751
$565$	51.7179	2.17579
$566$	0.107343	0.00451197
$567$	−3.35816	−0.141029
$568$	−47.4475	−1.99085
$569$	12.1116	0.507745	0.253872	−	0.967238i	$-0.418296\pi$
$569$	12.1116	0.507745	0.253872	+	0.967238i	$0.418296\pi$
$570$	−247.056	−10.3481
$571$	−23.7601	−0.994328	−0.497164	−	0.867656i	$-0.665625\pi$
$571$	−23.7601	−0.994328	−0.497164	+	0.867656i	$0.665625\pi$
$572$	−35.2323	−1.47314
$573$	45.0115	1.88038
$574$	17.1408	0.715444
$575$	26.5833	1.10860
$576$	182.604	7.60850
$577$	15.6847	0.652963	0.326482	−	0.945204i	$-0.394137\pi$
$577$	15.6847	0.652963	0.326482	+	0.945204i	$0.394137\pi$
$578$	44.7046	1.85947
$579$	64.9604	2.69966
$580$	−193.183	−8.02147
$581$	−21.7429	−0.902049
$582$	−29.6002	−1.22697
$583$	−1.07775	−0.0446359
$584$	129.625	5.36391
$585$	109.256	4.51718
$586$	−0.969566	−0.0400524
$587$	−12.1521	−0.501572	−0.250786	−	0.968043i	$-0.580689\pi$
$587$	−12.1521	−0.501572	−0.250786	+	0.968043i	$0.580689\pi$
$588$	98.0054	4.04167
$589$	52.6701	2.17024
$590$	67.6848	2.78654
$591$	53.2209	2.18922
$592$	−58.5352	−2.40578
$593$	26.0411	1.06938	0.534689	−	0.845049i	$-0.320429\pi$
$593$	26.0411	1.06938	0.534689	+	0.845049i	$0.320429\pi$
$594$	16.7263	0.686287
$595$	−12.2406	−0.501815
$596$	41.6820	1.70736
$597$	−36.8460	−1.50801
$598$	−46.5963	−1.90546
$599$	−23.8819	−0.975786	−0.487893	−	0.872903i	$-0.662234\pi$
$599$	−23.8819	−0.975786	−0.487893	+	0.872903i	$0.662234\pi$
$600$	−258.625	−10.5583
$601$	−15.3845	−0.627546	−0.313773	−	0.949498i	$-0.601593\pi$
$601$	−15.3845	−0.627546	−0.313773	+	0.949498i	$0.601593\pi$
$602$	100.944	4.11415
$603$	16.7897	0.683730
$604$	−5.61808	−0.228597
$605$	−37.0252	−1.50529
$606$	121.735	4.94517
$607$	15.8619	0.643815	0.321907	−	0.946771i	$-0.395676\pi$
$607$	15.8619	0.643815	0.321907	+	0.946771i	$0.395676\pi$
$608$	−211.135	−8.56266
$609$	93.7315	3.79819
$610$	44.7189	1.81062
$611$	−10.0729	−0.407505
$612$	25.1211	1.01546
$613$	−42.1235	−1.70135	−0.850676	−	0.525690i	$-0.823807\pi$
$613$	−42.1235	−1.70135	−0.850676	+	0.525690i	$0.823807\pi$
$614$	−49.5581	−2.00000
$615$	18.2017	0.733963
$616$	−39.0608	−1.57381
$617$	−28.8842	−1.16283	−0.581416	−	0.813606i	$-0.697501\pi$
$617$	−28.8842	−1.16283	−0.581416	+	0.813606i	$0.697501\pi$
$618$	−8.20402	−0.330014
$619$	20.1239	0.808846	0.404423	−	0.914572i	$-0.367472\pi$
$619$	20.1239	0.808846	0.404423	+	0.914572i	$0.367472\pi$
$620$	132.335	5.31470
$621$	16.3137	0.654645
$622$	−23.9097	−0.958690
$623$	−34.0483	−1.36412
$624$	268.527	10.7497
$625$	13.1390	0.525561
$626$	−71.3155	−2.85034
$627$	−25.6343	−1.02374
$628$	23.3684	0.932502
$629$	−3.21314	−0.128116
$630$	188.085	7.49350
$631$	−7.99029	−0.318088	−0.159044	−	0.987271i	$-0.550841\pi$
$631$	−7.99029	−0.318088	−0.159044	+	0.987271i	$0.550841\pi$
$632$	14.7412	0.586375
$633$	−61.9843	−2.46365
$634$	59.3651	2.35769
$635$	68.1261	2.70350
$636$	15.8797	0.629672
$637$	35.9121	1.42289
$638$	−27.1801	−1.07607
$639$	23.7057	0.937782
$640$	−191.309	−7.56214
$641$	29.5966	1.16900	0.584498	−	0.811395i	$-0.301292\pi$
$641$	29.5966	1.16900	0.584498	+	0.811395i	$0.301292\pi$
$642$	125.828	4.96602
$643$	38.6900	1.52578	0.762892	−	0.646526i	$-0.223779\pi$
$643$	38.6900	1.52578	0.762892	+	0.646526i	$0.223779\pi$
$644$	−59.1567	−2.33110
$645$	107.191	4.22065
$646$	−20.8153	−0.818966
$647$	−42.8369	−1.68409	−0.842047	−	0.539405i	$-0.818649\pi$
$647$	−42.8369	−1.68409	−0.842047	+	0.539405i	$0.818649\pi$
$648$	−9.24019	−0.362989
$649$	7.02290	0.275673
$650$	−147.154	−5.77185
$651$	−64.2084	−2.51653
$652$	−122.090	−4.78143
$653$	37.9529	1.48521	0.742606	−	0.669728i	$-0.233589\pi$
$653$	37.9529	1.48521	0.742606	+	0.669728i	$0.233589\pi$
$654$	−26.1282	−1.02169
$655$	−69.6258	−2.72050
$656$	27.9374	1.09077
$657$	−64.7630	−2.52665
$658$	−17.3406	−0.676007
$659$	13.1906	0.513834	0.256917	−	0.966433i	$-0.417293\pi$
$659$	13.1906	0.513834	0.256917	+	0.966433i	$0.417293\pi$
$660$	−64.4068	−2.50703
$661$	13.2626	0.515856	0.257928	−	0.966164i	$-0.416960\pi$
$661$	13.2626	0.515856	0.257928	+	0.966164i	$0.416960\pi$
$662$	25.4907	0.990726
$663$	14.7401	0.572457
$664$	−59.8271	−2.32174
$665$	−114.932	−4.45686
$666$	49.3722	1.91313
$667$	−26.5096	−1.02646
$668$	−44.2828	−1.71335
$669$	−64.6286	−2.49869
$670$	−34.9539	−1.35039
$671$	4.63999	0.179125
$672$	257.388	9.92896
$673$	−32.4894	−1.25238	−0.626188	−	0.779672i	$-0.715386\pi$
$673$	−32.4894	−1.25238	−0.626188	+	0.779672i	$0.715386\pi$
$674$	82.6570	3.18383
$675$	51.5195	1.98299
$676$	117.185	4.50712
$677$	27.3173	1.04989	0.524945	−	0.851136i	$-0.324086\pi$
$677$	27.3173	1.04989	0.524945	+	0.851136i	$0.324086\pi$
$678$	−107.213	−4.11750
$679$	−13.7701	−0.528449
$680$	−33.6808	−1.29160
$681$	15.1382	0.580099
$682$	18.6190	0.712960
$683$	−2.47015	−0.0945177	−0.0472589	−	0.998883i	$-0.515049\pi$
$683$	−2.47015	−0.0945177	−0.0472589	+	0.998883i	$0.515049\pi$
$684$	235.872	9.01881
$685$	64.0292	2.44643
$686$	−8.29690	−0.316777
$687$	62.4606	2.38302
$688$	164.525	6.27247
$689$	5.81881	0.221679
$690$	−85.1808	−3.24278
$691$	−21.2384	−0.807947	−0.403974	−	0.914771i	$-0.632371\pi$
$691$	−21.2384	−0.807947	−0.403974	+	0.914771i	$0.632371\pi$
$692$	41.3080	1.57029
$693$	19.5155	0.741334
$694$	9.22343	0.350117
$695$	−30.9214	−1.17292
$696$	257.909	9.77600
$697$	1.53355	0.0580873
$698$	19.2783	0.729695
$699$	−40.3200	−1.52504
$700$	−186.820	−7.06114
$701$	5.51018	0.208117	0.104058	−	0.994571i	$-0.466817\pi$
$701$	5.51018	0.208117	0.104058	+	0.994571i	$0.466817\pi$
$702$	−90.3056	−3.40836
$703$	−30.1694	−1.13786
$704$	−39.4447	−1.48663
$705$	−18.4138	−0.693506
$706$	−7.73450	−0.291092
$707$	56.6319	2.12986
$708$	−103.476	−3.88888
$709$	44.3250	1.66466	0.832329	−	0.554281i	$-0.187007\pi$
$709$	44.3250	1.66466	0.832329	+	0.554281i	$0.187007\pi$
$710$	−49.3520	−1.85215
$711$	−7.36501	−0.276209
$712$	−93.6861	−3.51104
$713$	18.1598	0.680089
$714$	25.3752	0.949643
$715$	−23.6006	−0.882612
$716$	−70.5842	−2.63786
$717$	38.1047	1.42304
$718$	−63.4088	−2.36640
$719$	22.6686	0.845397	0.422698	−	0.906270i	$-0.361083\pi$
$719$	22.6686	0.845397	0.422698	+	0.906270i	$0.361083\pi$
$720$	306.556	11.4247
$721$	−3.81655	−0.142136
$722$	−143.001	−5.32195
$723$	−19.5113	−0.725634
$724$	−2.22561	−0.0827142
$725$	−83.7190	−3.10924
$726$	76.7546	2.84863
$727$	17.3058	0.641838	0.320919	−	0.947107i	$-0.396008\pi$
$727$	17.3058	0.641838	0.320919	+	0.947107i	$0.396008\pi$
$728$	210.891	7.81613
$729$	−43.0631	−1.59493
$730$	134.828	4.99020
$731$	9.03118	0.334030
$732$	−68.3662	−2.52689
$733$	−22.2989	−0.823628	−0.411814	−	0.911268i	$-0.635105\pi$
$733$	−22.2989	−0.823628	−0.411814	+	0.911268i	$0.635105\pi$
$734$	−105.346	−3.88839
$735$	65.6496	2.42152
$736$	−72.7958	−2.68329
$737$	−3.62678	−0.133594
$738$	−23.5641	−0.867406
$739$	−23.6322	−0.869325	−0.434662	−	0.900594i	$-0.643132\pi$
$739$	−23.6322	−0.869325	−0.434662	+	0.900594i	$0.643132\pi$
$740$	−75.8014	−2.78651
$741$	138.400	5.08427
$742$	10.0172	0.367741
$743$	−48.6349	−1.78424	−0.892121	−	0.451797i	$-0.850783\pi$
$743$	−48.6349	−1.78424	−0.892121	+	0.451797i	$0.850783\pi$
$744$	−176.674	−6.47718
$745$	27.9210	1.02294
$746$	−6.50075	−0.238009
$747$	29.8908	1.09365
$748$	−5.42647	−0.198411
$749$	58.5356	2.13884
$750$	−122.209	−4.46244
$751$	−18.0417	−0.658352	−0.329176	−	0.944269i	$-0.606771\pi$
$751$	−18.0417	−0.658352	−0.329176	+	0.944269i	$0.606771\pi$
$752$	−28.2630	−1.03065
$753$	−69.0909	−2.51781
$754$	146.746	5.34418
$755$	−3.76331	−0.136961
$756$	−114.648	−4.16971
$757$	−6.10964	−0.222059	−0.111029	−	0.993817i	$-0.535415\pi$
$757$	−6.10964	−0.222059	−0.111029	+	0.993817i	$0.535415\pi$
$758$	−0.0342063	−0.00124243
$759$	−8.83827	−0.320809
$760$	−316.242	−11.4713
$761$	−15.2109	−0.551396	−0.275698	−	0.961244i	$-0.588909\pi$
$761$	−15.2109	−0.551396	−0.275698	+	0.961244i	$0.588909\pi$
$762$	−141.228	−5.11616
$763$	−12.1550	−0.440039
$764$	89.4658	3.23676
$765$	16.8276	0.608402
$766$	27.8181	1.00511
$767$	−37.9168	−1.36910
$768$	189.693	6.84497
$769$	29.6949	1.07082	0.535412	−	0.844591i	$-0.320156\pi$
$769$	29.6949	1.07082	0.535412	+	0.844591i	$0.320156\pi$
$770$	−40.6287	−1.46416
$771$	1.54301	0.0555700
$772$	129.117	4.64701
$773$	19.0366	0.684698	0.342349	−	0.939573i	$-0.388778\pi$
$773$	19.0366	0.684698	0.342349	+	0.939573i	$0.388778\pi$
$774$	−138.771	−4.98801
$775$	57.3496	2.06006
$776$	−37.8894	−1.36015
$777$	36.7786	1.31942
$778$	−22.7006	−0.813854
$779$	14.3991	0.515901
$780$	347.734	12.4509
$781$	−5.12071	−0.183233
$782$	−7.17675	−0.256640
$783$	−51.3768	−1.83606
$784$	100.764	3.59871
$785$	15.6535	0.558697
$786$	144.337	5.14833
$787$	17.6907	0.630604	0.315302	−	0.948991i	$-0.397894\pi$
$787$	17.6907	0.630604	0.315302	+	0.948991i	$0.397894\pi$
$788$	105.783	3.76836
$789$	−23.4489	−0.834803
$790$	15.3329	0.545522
$791$	−49.8761	−1.77339
$792$	53.6983	1.90809
$793$	−25.0514	−0.889603
$794$	−29.2443	−1.03784
$795$	10.6371	0.377260
$796$	−73.2359	−2.59578
$797$	36.0129	1.27564	0.637820	−	0.770185i	$-0.279836\pi$
$797$	36.0129	1.27564	0.637820	+	0.770185i	$0.279836\pi$
$798$	238.258	8.43424
$799$	−1.55142	−0.0548854
$800$	−229.893	−8.12796
$801$	46.8074	1.65386
$802$	−63.0647	−2.22689
$803$	13.9896	0.493682
$804$	53.4375	1.88459
$805$	−39.6265	−1.39665
$806$	−100.525	−3.54083
$807$	−72.8040	−2.56282
$808$	155.826	5.48195
$809$	7.53042	0.264756	0.132378	−	0.991199i	$-0.457739\pi$
$809$	7.53042	0.264756	0.132378	+	0.991199i	$0.457739\pi$
$810$	−9.61109	−0.337699
$811$	38.2139	1.34187	0.670935	−	0.741516i	$-0.265893\pi$
$811$	38.2139	1.34187	0.670935	+	0.741516i	$0.265893\pi$
$812$	186.303	6.53794
$813$	−3.60270	−0.126352
$814$	−10.6650	−0.373807
$815$	−81.7830	−2.86473
$816$	41.3584	1.44783
$817$	84.7974	2.96669
$818$	63.4315	2.21783
$819$	−105.365	−3.68175
$820$	36.1781	1.26339
$821$	−43.8027	−1.52873	−0.764363	−	0.644786i	$-0.776946\pi$
$821$	−43.8027	−1.52873	−0.764363	+	0.644786i	$0.776946\pi$
$822$	−132.735	−4.62966
$823$	−46.5094	−1.62121	−0.810607	−	0.585590i	$-0.800863\pi$
$823$	−46.5094	−1.62121	−0.810607	+	0.585590i	$0.800863\pi$
$824$	−10.5015	−0.365837
$825$	−27.9118	−0.971763
$826$	−65.2743	−2.27118
$827$	−42.5706	−1.48033	−0.740163	−	0.672428i	$-0.765252\pi$
$827$	−42.5706	−1.48033	−0.740163	+	0.672428i	$0.765252\pi$
$828$	81.3248	2.82623
$829$	9.18578	0.319035	0.159518	−	0.987195i	$-0.449006\pi$
$829$	9.18578	0.319035	0.159518	+	0.987195i	$0.449006\pi$
$830$	−62.2285	−2.15998
$831$	34.1165	1.18349
$832$	212.963	7.38316
$833$	5.53118	0.191644
$834$	64.1013	2.21965
$835$	−29.6631	−1.02653
$836$	−50.9513	−1.76219
$837$	35.1944	1.21650
$838$	46.4400	1.60424
$839$	−40.8556	−1.41049	−0.705245	−	0.708963i	$-0.749163\pi$
$839$	−40.8556	−1.41049	−0.705245	+	0.708963i	$0.749163\pi$
$840$	385.521	13.3017
$841$	54.4870	1.87886
$842$	−49.0447	−1.69019
$843$	−6.79479	−0.234025
$844$	−123.201	−4.24076
$845$	78.4973	2.70039
$846$	23.8387	0.819593
$847$	35.7066	1.22689
$848$	16.3267	0.560661
$849$	−0.109928	−0.00377270
$850$	−22.6646	−0.777389
$851$	−10.4019	−0.356573
$852$	75.4492	2.58485
$853$	16.6426	0.569830	0.284915	−	0.958553i	$-0.408035\pi$
$853$	16.6426	0.569830	0.284915	+	0.958553i	$0.408035\pi$
$854$	−43.1263	−1.47575
$855$	158.001	5.40351
$856$	161.065	5.50508
$857$	−0.835667	−0.0285459	−0.0142729	−	0.999898i	$-0.504543\pi$
$857$	−0.835667	−0.0285459	−0.0142729	+	0.999898i	$0.504543\pi$
$858$	48.9249	1.67027
$859$	−47.5044	−1.62083	−0.810415	−	0.585856i	$-0.800758\pi$
$859$	−47.5044	−1.62083	−0.810415	+	0.585856i	$0.800758\pi$
$860$	213.055	7.26513
$861$	−17.5535	−0.598221
$862$	−22.1068	−0.752962
$863$	−32.3639	−1.10168	−0.550840	−	0.834611i	$-0.685692\pi$
$863$	−32.3639	−1.10168	−0.550840	+	0.834611i	$0.685692\pi$
$864$	−141.081	−4.79969
$865$	27.6704	0.940822
$866$	1.95628	0.0664772
$867$	−45.7809	−1.55480
$868$	−127.622	−4.33177
$869$	1.59093	0.0539686
$870$	268.261	9.09489
$871$	19.5811	0.663480
$872$	−33.4452	−1.13260
$873$	18.9303	0.640693
$874$	−67.3854	−2.27934
$875$	−56.8521	−1.92195
$876$	−206.124	−6.96430
$877$	3.66628	0.123801	0.0619007	−	0.998082i	$-0.480284\pi$
$877$	3.66628	0.123801	0.0619007	+	0.998082i	$0.480284\pi$
$878$	−41.3741	−1.39631
$879$	0.992909	0.0334900
$880$	−66.2197	−2.23226
$881$	−18.9671	−0.639019	−0.319510	−	0.947583i	$-0.603518\pi$
$881$	−18.9671	−0.639019	−0.319510	+	0.947583i	$0.603518\pi$
$882$	−84.9905	−2.86178
$883$	30.1430	1.01439	0.507196	−	0.861831i	$-0.330682\pi$
$883$	30.1430	1.01439	0.507196	+	0.861831i	$0.330682\pi$
$884$	29.2977	0.985387
$885$	−69.3143	−2.32997
$886$	38.1616	1.28207
$887$	−16.4007	−0.550682	−0.275341	−	0.961347i	$-0.588791\pi$
$887$	−16.4007	−0.550682	−0.275341	+	0.961347i	$0.588791\pi$
$888$	101.199	3.39601
$889$	−65.7000	−2.20351
$890$	−97.4466	−3.26642
$891$	−0.997236	−0.0334087
$892$	−128.457	−4.30107
$893$	−14.5669	−0.487464
$894$	−57.8812	−1.93584
$895$	−47.2813	−1.58044
$896$	184.496	6.16357
$897$	47.7181	1.59326
$898$	55.4218	1.84945
$899$	−57.1907	−1.90742
$900$	256.829	8.56095
$901$	0.896212	0.0298571
$902$	5.09012	0.169483
$903$	−103.374	−3.44006
$904$	−137.237	−4.56445
$905$	−1.49084	−0.0495572
$906$	7.80149	0.259187
$907$	28.4462	0.944541	0.472271	−	0.881454i	$-0.343435\pi$
$907$	28.4462	0.944541	0.472271	+	0.881454i	$0.343435\pi$
$908$	30.0891	0.998542
$909$	−77.8539	−2.58225
$910$	219.356	7.27157
$911$	−44.4263	−1.47191	−0.735954	−	0.677031i	$-0.763266\pi$
$911$	−44.4263	−1.47191	−0.735954	+	0.677031i	$0.763266\pi$
$912$	388.331	12.8589
$913$	−6.45676	−0.213688
$914$	−79.8588	−2.64149
$915$	−45.7955	−1.51395
$916$	124.148	4.10196
$917$	67.1462	2.21736
$918$	−13.9088	−0.459060
$919$	−14.2993	−0.471690	−0.235845	−	0.971791i	$-0.575786\pi$
$919$	−14.2993	−0.471690	−0.235845	+	0.971791i	$0.575786\pi$
$920$	−109.035	−3.59478
$921$	50.7512	1.67231
$922$	−79.6651	−2.62363
$923$	27.6469	0.910008
$924$	62.1130	2.04337
$925$	−32.8498	−1.08010
$926$	0.686758	0.0225683
$927$	5.24674	0.172326
$928$	229.257	7.52571
$929$	−14.5545	−0.477516	−0.238758	−	0.971079i	$-0.576740\pi$
$929$	−14.5545	−0.477516	−0.238758	+	0.971079i	$0.576740\pi$
$930$	−183.765	−6.02590
$931$	51.9344	1.70208
$932$	−80.1408	−2.62510
$933$	24.4853	0.801612
$934$	85.0719	2.78364
$935$	−3.63495	−0.118876
$936$	−289.919	−9.47629
$937$	46.3421	1.51393	0.756966	−	0.653455i	$-0.226681\pi$
$937$	46.3421	1.51393	0.756966	+	0.653455i	$0.226681\pi$
$938$	33.7091	1.10064
$939$	73.0324	2.38332
$940$	−36.5998	−1.19375
$941$	23.5167	0.766622	0.383311	−	0.923619i	$-0.374784\pi$
$941$	23.5167	0.766622	0.383311	+	0.923619i	$0.374784\pi$
$942$	−32.4503	−1.05729
$943$	4.96457	0.161668
$944$	−106.389	−3.46266
$945$	−76.7978	−2.49823
$946$	29.9761	0.974608
$947$	28.0807	0.912499	0.456250	−	0.889852i	$-0.349192\pi$
$947$	28.0807	0.912499	0.456250	+	0.889852i	$0.349192\pi$
$948$	−23.4410	−0.761327
$949$	−75.5302	−2.45182
$950$	−212.807	−6.90437
$951$	−60.7944	−1.97139
$952$	32.4813	1.05273
$953$	46.4395	1.50432	0.752162	−	0.658978i	$-0.229011\pi$
$953$	46.4395	1.50432	0.752162	+	0.658978i	$0.229011\pi$
$954$	−13.7709	−0.445851
$955$	59.9293	1.93927
$956$	75.7376	2.44953
$957$	27.8344	0.899760
$958$	3.68849	0.119170
$959$	−61.7489	−1.99398
$960$	389.309	12.5649
$961$	8.17708	0.263777
$962$	57.5806	1.85647
$963$	−80.4710	−2.59314
$964$	−38.7811	−1.24906
$965$	86.4897	2.78420
$966$	82.1473	2.64305
$967$	54.4521	1.75106	0.875531	−	0.483161i	$-0.160511\pi$
$967$	54.4521	1.75106	0.875531	+	0.483161i	$0.160511\pi$
$968$	98.2491	3.15784
$969$	21.3164	0.684781
$970$	−39.4103	−1.26539
$971$	36.4022	1.16820	0.584101	−	0.811681i	$-0.301447\pi$
$971$	36.4022	1.16820	0.584101	+	0.811681i	$0.301447\pi$
$972$	−80.0757	−2.56843
$973$	29.8202	0.955992
$974$	−30.4811	−0.976676
$975$	150.697	4.82615
$976$	−70.2905	−2.24995
$977$	−22.9508	−0.734263	−0.367131	−	0.930169i	$-0.619660\pi$
$977$	−22.9508	−0.734263	−0.367131	+	0.930169i	$0.619660\pi$
$978$	169.539	5.42127
$979$	−10.1110	−0.323147
$980$	130.486	4.16824
$981$	16.7098	0.533504
$982$	49.5137	1.58004
$983$	−16.2230	−0.517433	−0.258716	−	0.965953i	$-0.583299\pi$
$983$	−16.2230	−0.517433	−0.258716	+	0.965953i	$0.583299\pi$
$984$	−48.2996	−1.53973
$985$	70.8594	2.25777
$986$	22.6018	0.719788
$987$	17.7581	0.565246
$988$	275.088	8.75170
$989$	29.2367	0.929673
$990$	55.8537	1.77515
$991$	9.93598	0.315627	0.157813	−	0.987469i	$-0.449556\pi$
$991$	9.93598	0.315627	0.157813	+	0.987469i	$0.449556\pi$
$992$	−157.047	−4.98623
$993$	−26.1044	−0.828399
$994$	47.5944	1.50960
$995$	−49.0576	−1.55523
$996$	95.1348	3.01446
$997$	−17.3928	−0.550837	−0.275418	−	0.961324i	$-0.588816\pi$
$997$	−17.3928	−0.550837	−0.275418	+	0.961324i	$0.588816\pi$
$998$	−33.4304	−1.05822
$999$	−20.1593	−0.637813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.d.1.3	✓	179

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.d.1.3	✓	179	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.76009 q^{2} +2.82654 q^{3} +5.61808 q^{4} +3.76331 q^{5} -7.80149 q^{6} -3.62929 q^{7} -9.98623 q^{8} +4.98931 q^{9} +O(q^{10})\)	\(q-2.76009 q^{2} +2.82654 q^{3} +5.61808 q^{4} +3.76331 q^{5} -7.80149 q^{6} -3.62929 q^{7} -9.98623 q^{8} +4.98931 q^{9} -10.3871 q^{10} -1.07775 q^{11} +15.8797 q^{12} +5.81881 q^{13} +10.0172 q^{14} +10.6371 q^{15} +16.3267 q^{16} +0.896212 q^{17} -13.7709 q^{18} +8.41489 q^{19} +21.1426 q^{20} -10.2583 q^{21} +2.97469 q^{22} +2.90131 q^{23} -28.2264 q^{24} +9.16251 q^{25} -16.0604 q^{26} +5.62286 q^{27} -20.3896 q^{28} -9.13712 q^{29} -29.3594 q^{30} +6.25916 q^{31} -25.0907 q^{32} -3.04630 q^{33} -2.47362 q^{34} -13.6581 q^{35} +28.0304 q^{36} -3.58525 q^{37} -23.2258 q^{38} +16.4471 q^{39} -37.5813 q^{40} +1.71115 q^{41} +28.3139 q^{42} +10.0771 q^{43} -6.05490 q^{44} +18.7763 q^{45} -8.00787 q^{46} -1.73109 q^{47} +46.1480 q^{48} +6.17173 q^{49} -25.2893 q^{50} +2.53318 q^{51} +32.6906 q^{52} +1.00000 q^{53} -15.5196 q^{54} -4.05591 q^{55} +36.2429 q^{56} +23.7850 q^{57} +25.2193 q^{58} -6.51625 q^{59} +59.7603 q^{60} -4.30525 q^{61} -17.2758 q^{62} -18.1076 q^{63} +36.5990 q^{64} +21.8980 q^{65} +8.40806 q^{66} +3.36514 q^{67} +5.03499 q^{68} +8.20066 q^{69} +37.6977 q^{70} +4.75129 q^{71} -49.8244 q^{72} -12.9804 q^{73} +9.89559 q^{74} +25.8982 q^{75} +47.2756 q^{76} +3.91147 q^{77} -45.3954 q^{78} -1.47616 q^{79} +61.4425 q^{80} +0.925294 q^{81} -4.72291 q^{82} +5.99096 q^{83} -57.6321 q^{84} +3.37272 q^{85} -27.8136 q^{86} -25.8264 q^{87} +10.7627 q^{88} +9.38153 q^{89} -51.8243 q^{90} -21.1181 q^{91} +16.2998 q^{92} +17.6917 q^{93} +4.77796 q^{94} +31.6678 q^{95} -70.9197 q^{96} +3.79417 q^{97} -17.0345 q^{98} -5.37723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9	\( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 179 * q + 8 * q^2 + 15 * q^3 + 202 * q^4 + 27 * q^5 + 18 * q^6 + 23 * q^7 + 21 * q^8 + 214 * q^9 + 28 * q^10 + 21 * q^11 + 46 * q^12 + 113 * q^13 - 2 * q^14 + 30 * q^15 + 240 * q^16 + 48 * q^17 + 40 * q^18 + 35 * q^19 + 24 * q^20 + 56 * q^21 + 22 * q^22 + 16 * q^23 + 54 * q^24 + 266 * q^25 + 60 * q^27 + 64 * q^28 + 34 * q^29 - 19 * q^30 + 60 * q^31 + 15 * q^32 + 65 * q^33 + 31 * q^34 - 20 * q^35 + 282 * q^36 + 169 * q^37 + 52 * q^38 + 20 * q^39 + 74 * q^40 + 20 * q^41 + 34 * q^42 + 43 * q^43 + 56 * q^44 + 139 * q^45 + 13 * q^46 + 73 * q^47 + 88 * q^48 + 292 * q^49 + 12 * q^50 + 8 * q^51 + 225 * q^52 + 179 * q^53 - 16 * q^54 + 72 * q^55 - 17 * q^56 + 62 * q^57 + 125 * q^58 + 68 * q^59 + 116 * q^60 + 96 * q^61 + 71 * q^62 + 52 * q^63 + 309 * q^64 - 5 * q^65 + 90 * q^67 + 122 * q^68 + 111 * q^69 + 72 * q^70 + 26 * q^71 + 65 * q^72 + 139 * q^73 - 82 * q^74 + 55 * q^75 + 146 * q^76 + 76 * q^77 - 9 * q^78 + 29 * q^79 + 68 * q^80 + 231 * q^81 + 84 * q^82 + 8 * q^83 - 24 * q^84 + 115 * q^85 - 20 * q^86 + 47 * q^87 + 143 * q^88 + 150 * q^89 + 34 * q^90 + 113 * q^91 - 31 * q^92 + 195 * q^93 + 131 * q^94 + 55 * q^95 + 90 * q^96 + 235 * q^97 + 84 * q^98 + 7 * q^99

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