LMFDB - Embedded newform 8006.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.82604 q^{3} +1.00000 q^{4} +3.06326 q^{5} +2.82604 q^{6} +0.692372 q^{7} -1.00000 q^{8} +4.98649 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.82604 q^{3} +1.00000 q^{4} +3.06326 q^{5} +2.82604 q^{6} +0.692372 q^{7} -1.00000 q^{8} +4.98649 q^{9} -3.06326 q^{10} +2.28019 q^{11} -2.82604 q^{12} -1.07870 q^{13} -0.692372 q^{14} -8.65688 q^{15} +1.00000 q^{16} +2.85289 q^{17} -4.98649 q^{18} +0.175144 q^{19} +3.06326 q^{20} -1.95667 q^{21} -2.28019 q^{22} +1.51008 q^{23} +2.82604 q^{24} +4.38355 q^{25} +1.07870 q^{26} -5.61389 q^{27} +0.692372 q^{28} +2.35314 q^{29} +8.65688 q^{30} -6.93214 q^{31} -1.00000 q^{32} -6.44390 q^{33} -2.85289 q^{34} +2.12092 q^{35} +4.98649 q^{36} -4.30129 q^{37} -0.175144 q^{38} +3.04844 q^{39} -3.06326 q^{40} -12.1707 q^{41} +1.95667 q^{42} +12.1281 q^{43} +2.28019 q^{44} +15.2749 q^{45} -1.51008 q^{46} -2.04189 q^{47} -2.82604 q^{48} -6.52062 q^{49} -4.38355 q^{50} -8.06237 q^{51} -1.07870 q^{52} -5.37863 q^{53} +5.61389 q^{54} +6.98481 q^{55} -0.692372 q^{56} -0.494964 q^{57} -2.35314 q^{58} +2.13087 q^{59} -8.65688 q^{60} -4.45670 q^{61} +6.93214 q^{62} +3.45251 q^{63} +1.00000 q^{64} -3.30433 q^{65} +6.44390 q^{66} +0.879153 q^{67} +2.85289 q^{68} -4.26756 q^{69} -2.12092 q^{70} -10.9737 q^{71} -4.98649 q^{72} -11.3514 q^{73} +4.30129 q^{74} -12.3881 q^{75} +0.175144 q^{76} +1.57874 q^{77} -3.04844 q^{78} +12.1508 q^{79} +3.06326 q^{80} +0.905589 q^{81} +12.1707 q^{82} +7.64282 q^{83} -1.95667 q^{84} +8.73913 q^{85} -12.1281 q^{86} -6.65006 q^{87} -2.28019 q^{88} -10.2676 q^{89} -15.2749 q^{90} -0.746859 q^{91} +1.51008 q^{92} +19.5905 q^{93} +2.04189 q^{94} +0.536512 q^{95} +2.82604 q^{96} -12.3896 q^{97} +6.52062 q^{98} +11.3701 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) $ 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.82604	−1.63161	−0.815807	−	0.578325i	$-0.803707\pi$
$3$	−2.82604	−1.63161	−0.815807	+	0.578325i	$0.803707\pi$
$4$	1.00000	0.500000
$5$	3.06326	1.36993	0.684965	−	0.728576i	$-0.259817\pi$
$5$	3.06326	1.36993	0.684965	+	0.728576i	$0.259817\pi$
$6$	2.82604	1.15372
$7$	0.692372	0.261692	0.130846	−	0.991403i	$-0.458231\pi$
$7$	0.692372	0.261692	0.130846	+	0.991403i	$0.458231\pi$
$8$	−1.00000	−0.353553
$9$	4.98649	1.66216
$10$	−3.06326	−0.968687
$11$	2.28019	0.687503	0.343751	−	0.939061i	$-0.388302\pi$
$11$	2.28019	0.687503	0.343751	+	0.939061i	$0.388302\pi$
$12$	−2.82604	−0.815807
$13$	−1.07870	−0.299176	−0.149588	−	0.988748i	$-0.547795\pi$
$13$	−1.07870	−0.299176	−0.149588	+	0.988748i	$0.547795\pi$
$14$	−0.692372	−0.185044
$15$	−8.65688	−2.23520
$16$	1.00000	0.250000
$17$	2.85289	0.691927	0.345963	−	0.938248i	$-0.387552\pi$
$17$	2.85289	0.691927	0.345963	+	0.938248i	$0.387552\pi$
$18$	−4.98649	−1.17533
$19$	0.175144	0.0401809	0.0200904	−	0.999798i	$-0.493605\pi$
$19$	0.175144	0.0401809	0.0200904	+	0.999798i	$0.493605\pi$
$20$	3.06326	0.684965
$21$	−1.95667	−0.426980
$22$	−2.28019	−0.486138
$23$	1.51008	0.314874	0.157437	−	0.987529i	$-0.449677\pi$
$23$	1.51008	0.314874	0.157437	+	0.987529i	$0.449677\pi$
$24$	2.82604	0.576862
$25$	4.38355	0.876711
$26$	1.07870	0.211550
$27$	−5.61389	−1.08039
$28$	0.692372	0.130846
$29$	2.35314	0.436967	0.218484	−	0.975841i	$-0.429889\pi$
$29$	2.35314	0.436967	0.218484	+	0.975841i	$0.429889\pi$
$30$	8.65688	1.58052
$31$	−6.93214	−1.24505	−0.622524	−	0.782601i	$-0.713893\pi$
$31$	−6.93214	−1.24505	−0.622524	+	0.782601i	$0.713893\pi$
$32$	−1.00000	−0.176777
$33$	−6.44390	−1.12174
$34$	−2.85289	−0.489266
$35$	2.12092	0.358500
$36$	4.98649	0.831081
$37$	−4.30129	−0.707127	−0.353564	−	0.935411i	$-0.615030\pi$
$37$	−4.30129	−0.707127	−0.353564	+	0.935411i	$0.615030\pi$
$38$	−0.175144	−0.0284122
$39$	3.04844	0.488140
$40$	−3.06326	−0.484344
$41$	−12.1707	−1.90074	−0.950371	−	0.311118i	$-0.899296\pi$
$41$	−12.1707	−1.90074	−0.950371	+	0.311118i	$0.899296\pi$
$42$	1.95667	0.301921
$43$	12.1281	1.84952	0.924758	−	0.380555i	$-0.124267\pi$
$43$	12.1281	1.84952	0.924758	+	0.380555i	$0.124267\pi$
$44$	2.28019	0.343751
$45$	15.2749	2.27705
$46$	−1.51008	−0.222650
$47$	−2.04189	−0.297841	−0.148920	−	0.988849i	$-0.547580\pi$
$47$	−2.04189	−0.297841	−0.148920	+	0.988849i	$0.547580\pi$
$48$	−2.82604	−0.407903
$49$	−6.52062	−0.931517
$50$	−4.38355	−0.619928
$51$	−8.06237	−1.12896
$52$	−1.07870	−0.149588
$53$	−5.37863	−0.738812	−0.369406	−	0.929268i	$-0.620439\pi$
$53$	−5.37863	−0.738812	−0.369406	+	0.929268i	$0.620439\pi$
$54$	5.61389	0.763953
$55$	6.98481	0.941831
$56$	−0.692372	−0.0925222
$57$	−0.494964	−0.0655596
$58$	−2.35314	−0.308983
$59$	2.13087	0.277415	0.138708	−	0.990333i	$-0.455705\pi$
$59$	2.13087	0.277415	0.138708	+	0.990333i	$0.455705\pi$
$60$	−8.65688	−1.11760
$61$	−4.45670	−0.570622	−0.285311	−	0.958435i	$-0.592097\pi$
$61$	−4.45670	−0.570622	−0.285311	+	0.958435i	$0.592097\pi$
$62$	6.93214	0.880382
$63$	3.45251	0.434975
$64$	1.00000	0.125000
$65$	−3.30433	−0.409851
$66$	6.44390	0.793189
$67$	0.879153	0.107406	0.0537028	−	0.998557i	$-0.482898\pi$
$67$	0.879153	0.107406	0.0537028	+	0.998557i	$0.482898\pi$
$68$	2.85289	0.345963
$69$	−4.26756	−0.513753
$70$	−2.12092	−0.253498
$71$	−10.9737	−1.30233	−0.651167	−	0.758935i	$-0.725720\pi$
$71$	−10.9737	−1.30233	−0.651167	+	0.758935i	$0.725720\pi$
$72$	−4.98649	−0.587663
$73$	−11.3514	−1.32858	−0.664289	−	0.747476i	$-0.731266\pi$
$73$	−11.3514	−1.32858	−0.664289	+	0.747476i	$0.731266\pi$
$74$	4.30129	0.500014
$75$	−12.3881	−1.43045
$76$	0.175144	0.0200904
$77$	1.57874	0.179914
$78$	−3.04844	−0.345167
$79$	12.1508	1.36708	0.683538	−	0.729915i	$-0.260440\pi$
$79$	12.1508	1.36708	0.683538	+	0.729915i	$0.260440\pi$
$80$	3.06326	0.342483
$81$	0.905589	0.100621
$82$	12.1707	1.34403
$83$	7.64282	0.838909	0.419454	−	0.907776i	$-0.362221\pi$
$83$	7.64282	0.838909	0.419454	+	0.907776i	$0.362221\pi$
$84$	−1.95667	−0.213490
$85$	8.73913	0.947892
$86$	−12.1281	−1.30781
$87$	−6.65006	−0.712962
$88$	−2.28019	−0.243069
$89$	−10.2676	−1.08836	−0.544181	−	0.838968i	$-0.683160\pi$
$89$	−10.2676	−1.08836	−0.544181	+	0.838968i	$0.683160\pi$
$90$	−15.2749	−1.61012
$91$	−0.746859	−0.0782921
$92$	1.51008	0.157437
$93$	19.5905	2.03144
$94$	2.04189	0.210605
$95$	0.536512	0.0550450
$96$	2.82604	0.288431
$97$	−12.3896	−1.25797	−0.628986	−	0.777417i	$-0.716530\pi$
$97$	−12.3896	−1.25797	−0.628986	+	0.777417i	$0.716530\pi$
$98$	6.52062	0.658682
$99$	11.3701	1.14274
$100$	4.38355	0.438355
$101$	−5.22039	−0.519449	−0.259724	−	0.965683i	$-0.583632\pi$
$101$	−5.22039	−0.519449	−0.259724	+	0.965683i	$0.583632\pi$
$102$	8.06237	0.798293
$103$	−3.35208	−0.330290	−0.165145	−	0.986269i	$-0.552809\pi$
$103$	−3.35208	−0.330290	−0.165145	+	0.986269i	$0.552809\pi$
$104$	1.07870	0.105775
$105$	−5.99379	−0.584934
$106$	5.37863	0.522419
$107$	−17.2057	−1.66333	−0.831667	−	0.555274i	$-0.812613\pi$
$107$	−17.2057	−1.66333	−0.831667	+	0.555274i	$0.812613\pi$
$108$	−5.61389	−0.540196
$109$	−11.8145	−1.13163	−0.565813	−	0.824534i	$-0.691438\pi$
$109$	−11.8145	−1.13163	−0.565813	+	0.824534i	$0.691438\pi$
$110$	−6.98481	−0.665975
$111$	12.1556	1.15376
$112$	0.692372	0.0654230
$113$	−19.1814	−1.80444	−0.902219	−	0.431279i	$-0.858063\pi$
$113$	−19.1814	−1.80444	−0.902219	+	0.431279i	$0.858063\pi$
$114$	0.494964	0.0463577
$115$	4.62578	0.431356
$116$	2.35314	0.218484
$117$	−5.37890	−0.497280
$118$	−2.13087	−0.196162
$119$	1.97526	0.181072
$120$	8.65688	0.790262
$121$	−5.80074	−0.527340
$122$	4.45670	0.403491
$123$	34.3948	3.10128
$124$	−6.93214	−0.622524
$125$	−1.88833	−0.168898
$126$	−3.45251	−0.307574
$127$	−2.46955	−0.219138	−0.109569	−	0.993979i	$-0.534947\pi$
$127$	−2.46955	−0.219138	−0.109569	+	0.993979i	$0.534947\pi$
$128$	−1.00000	−0.0883883
$129$	−34.2744	−3.01770
$130$	3.30433	0.289809
$131$	−7.50843	−0.656014	−0.328007	−	0.944675i	$-0.606377\pi$
$131$	−7.50843	−0.656014	−0.328007	+	0.944675i	$0.606377\pi$
$132$	−6.44390	−0.560869
$133$	0.121265	0.0105150
$134$	−0.879153	−0.0759473
$135$	−17.1968	−1.48006
$136$	−2.85289	−0.244633
$137$	−7.67740	−0.655925	−0.327962	−	0.944691i	$-0.606362\pi$
$137$	−7.67740	−0.655925	−0.327962	+	0.944691i	$0.606362\pi$
$138$	4.26756	0.363279
$139$	7.67615	0.651083	0.325541	−	0.945528i	$-0.394453\pi$
$139$	7.67615	0.651083	0.325541	+	0.945528i	$0.394453\pi$
$140$	2.12092	0.179250
$141$	5.77047	0.485961
$142$	10.9737	0.920889
$143$	−2.45963	−0.205685
$144$	4.98649	0.415541
$145$	7.20828	0.598615
$146$	11.3514	0.939447
$147$	18.4275	1.51988
$148$	−4.30129	−0.353564
$149$	−7.37986	−0.604582	−0.302291	−	0.953216i	$-0.597751\pi$
$149$	−7.37986	−0.604582	−0.302291	+	0.953216i	$0.597751\pi$
$150$	12.3881	1.01148
$151$	−3.03501	−0.246986	−0.123493	−	0.992345i	$-0.539410\pi$
$151$	−3.03501	−0.246986	−0.123493	+	0.992345i	$0.539410\pi$
$152$	−0.175144	−0.0142061
$153$	14.2259	1.15009
$154$	−1.57874	−0.127218
$155$	−21.2349	−1.70563
$156$	3.04844	0.244070
$157$	12.1397	0.968855	0.484428	−	0.874831i	$-0.339028\pi$
$157$	12.1397	0.968855	0.484428	+	0.874831i	$0.339028\pi$
$158$	−12.1508	−0.966668
$159$	15.2002	1.20546
$160$	−3.06326	−0.242172
$161$	1.04554	0.0824002
$162$	−0.905589	−0.0711498
$163$	2.37411	0.185955	0.0929775	−	0.995668i	$-0.470362\pi$
$163$	2.37411	0.185955	0.0929775	+	0.995668i	$0.470362\pi$
$164$	−12.1707	−0.950371
$165$	−19.7393	−1.53670
$166$	−7.64282	−0.593198
$167$	−3.88661	−0.300755	−0.150377	−	0.988629i	$-0.548049\pi$
$167$	−3.88661	−0.300755	−0.150377	+	0.988629i	$0.548049\pi$
$168$	1.95667	0.150960
$169$	−11.8364	−0.910493
$170$	−8.73913	−0.670261
$171$	0.873355	0.0667871
$172$	12.1281	0.924758
$173$	16.9311	1.28725	0.643623	−	0.765343i	$-0.277430\pi$
$173$	16.9311	1.28725	0.643623	+	0.765343i	$0.277430\pi$
$174$	6.65006	0.504140
$175$	3.03505	0.229428
$176$	2.28019	0.171876
$177$	−6.02191	−0.452634
$178$	10.2676	0.769588
$179$	2.74384	0.205084	0.102542	−	0.994729i	$-0.467302\pi$
$179$	2.74384	0.205084	0.102542	+	0.994729i	$0.467302\pi$
$180$	15.2749	1.13852
$181$	19.9339	1.48168	0.740838	−	0.671684i	$-0.234429\pi$
$181$	19.9339	1.48168	0.740838	+	0.671684i	$0.234429\pi$
$182$	0.746859	0.0553609
$183$	12.5948	0.931034
$184$	−1.51008	−0.111325
$185$	−13.1760	−0.968715
$186$	−19.5905	−1.43644
$187$	6.50512	0.475702
$188$	−2.04189	−0.148920
$189$	−3.88690	−0.282730
$190$	−0.536512	−0.0389227
$191$	3.88094	0.280815	0.140408	−	0.990094i	$-0.455159\pi$
$191$	3.88094	0.280815	0.140408	+	0.990094i	$0.455159\pi$
$192$	−2.82604	−0.203952
$193$	−14.3698	−1.03436	−0.517179	−	0.855877i	$-0.673018\pi$
$193$	−14.3698	−1.03436	−0.517179	+	0.855877i	$0.673018\pi$
$194$	12.3896	0.889520
$195$	9.33815	0.668719
$196$	−6.52062	−0.465759
$197$	−5.03581	−0.358786	−0.179393	−	0.983777i	$-0.557413\pi$
$197$	−5.03581	−0.358786	−0.179393	+	0.983777i	$0.557413\pi$
$198$	−11.3701	−0.808040
$199$	21.6518	1.53486	0.767429	−	0.641134i	$-0.221536\pi$
$199$	21.6518	1.53486	0.767429	+	0.641134i	$0.221536\pi$
$200$	−4.38355	−0.309964
$201$	−2.48452	−0.175245
$202$	5.22039	0.367306
$203$	1.62925	0.114351
$204$	−8.06237	−0.564478
$205$	−37.2820	−2.60389
$206$	3.35208	0.233551
$207$	7.53002	0.523372
$208$	−1.07870	−0.0747941
$209$	0.399362	0.0276245
$210$	5.99379	0.413611
$211$	−18.3389	−1.26250	−0.631251	−	0.775578i	$-0.717458\pi$
$211$	−18.3389	−1.26250	−0.631251	+	0.775578i	$0.717458\pi$
$212$	−5.37863	−0.369406
$213$	31.0120	2.12490
$214$	17.2057	1.17616
$215$	37.1515	2.53371
$216$	5.61389	0.381976
$217$	−4.79962	−0.325819
$218$	11.8145	0.800181
$219$	32.0794	2.16773
$220$	6.98481	0.470916
$221$	−3.07740	−0.207008
$222$	−12.1556	−0.815830
$223$	11.4755	0.768458	0.384229	−	0.923238i	$-0.374467\pi$
$223$	11.4755	0.768458	0.384229	+	0.923238i	$0.374467\pi$
$224$	−0.692372	−0.0462611
$225$	21.8585	1.45724
$226$	19.1814	1.27593
$227$	−6.74186	−0.447473	−0.223736	−	0.974650i	$-0.571825\pi$
$227$	−6.74186	−0.447473	−0.223736	+	0.974650i	$0.571825\pi$
$228$	−0.494964	−0.0327798
$229$	17.7376	1.17213	0.586065	−	0.810264i	$-0.300676\pi$
$229$	17.7376	1.17213	0.586065	+	0.810264i	$0.300676\pi$
$230$	−4.62578	−0.305015
$231$	−4.46158	−0.293550
$232$	−2.35314	−0.154491
$233$	23.5701	1.54413	0.772063	−	0.635546i	$-0.219225\pi$
$233$	23.5701	1.54413	0.772063	+	0.635546i	$0.219225\pi$
$234$	5.37890	0.351630
$235$	−6.25485	−0.408021
$236$	2.13087	0.138708
$237$	−34.3387	−2.23054
$238$	−1.97526	−0.128037
$239$	−8.59370	−0.555880	−0.277940	−	0.960598i	$-0.589652\pi$
$239$	−8.59370	−0.555880	−0.277940	+	0.960598i	$0.589652\pi$
$240$	−8.65688	−0.558799
$241$	14.8029	0.953540	0.476770	−	0.879028i	$-0.341808\pi$
$241$	14.8029	0.953540	0.476770	+	0.879028i	$0.341808\pi$
$242$	5.80074	0.372886
$243$	14.2824	0.916218
$244$	−4.45670	−0.285311
$245$	−19.9743	−1.27611
$246$	−34.3948	−2.19293
$247$	−0.188927	−0.0120212
$248$	6.93214	0.440191
$249$	−21.5989	−1.36877
$250$	1.88833	0.119429
$251$	−9.70408	−0.612516	−0.306258	−	0.951949i	$-0.599077\pi$
$251$	−9.70408	−0.612516	−0.306258	+	0.951949i	$0.599077\pi$
$252$	3.45251	0.217487
$253$	3.44328	0.216477
$254$	2.46955	0.154954
$255$	−24.6971	−1.54659
$256$	1.00000	0.0625000
$257$	4.86077	0.303207	0.151603	−	0.988441i	$-0.451556\pi$
$257$	4.86077	0.303207	0.151603	+	0.988441i	$0.451556\pi$
$258$	34.2744	2.13383
$259$	−2.97809	−0.185050
$260$	−3.30433	−0.204926
$261$	11.7339	0.726311
$262$	7.50843	0.463872
$263$	24.4920	1.51024	0.755119	−	0.655587i	$-0.227579\pi$
$263$	24.4920	1.51024	0.755119	+	0.655587i	$0.227579\pi$
$264$	6.44390	0.396595
$265$	−16.4762	−1.01212
$266$	−0.121265	−0.00743524
$267$	29.0166	1.77579
$268$	0.879153	0.0537028
$269$	−6.53813	−0.398637	−0.199318	−	0.979935i	$-0.563873\pi$
$269$	−6.53813	−0.398637	−0.199318	+	0.979935i	$0.563873\pi$
$270$	17.1968	1.04656
$271$	−21.0283	−1.27738	−0.638688	−	0.769466i	$-0.720523\pi$
$271$	−21.0283	−1.27738	−0.638688	+	0.769466i	$0.720523\pi$
$272$	2.85289	0.172982
$273$	2.11065	0.127743
$274$	7.67740	0.463809
$275$	9.99533	0.602741
$276$	−4.26756	−0.256877
$277$	−2.57394	−0.154653	−0.0773264	−	0.997006i	$-0.524638\pi$
$277$	−2.57394	−0.154653	−0.0773264	+	0.997006i	$0.524638\pi$
$278$	−7.67615	−0.460385
$279$	−34.5670	−2.06947
$280$	−2.12092	−0.126749
$281$	24.1639	1.44150	0.720749	−	0.693196i	$-0.243798\pi$
$281$	24.1639	1.44150	0.720749	+	0.693196i	$0.243798\pi$
$282$	−5.77047	−0.343626
$283$	−18.1926	−1.08144	−0.540719	−	0.841203i	$-0.681848\pi$
$283$	−18.1926	−1.08144	−0.540719	+	0.841203i	$0.681848\pi$
$284$	−10.9737	−0.651167
$285$	−1.51620	−0.0898122
$286$	2.45963	0.145441
$287$	−8.42665	−0.497409
$288$	−4.98649	−0.293832
$289$	−8.86104	−0.521237
$290$	−7.20828	−0.423285
$291$	35.0134	2.05252
$292$	−11.3514	−0.664289
$293$	24.0869	1.40717	0.703586	−	0.710610i	$-0.251581\pi$
$293$	24.0869	1.40717	0.703586	+	0.710610i	$0.251581\pi$
$294$	−18.4275	−1.07471
$295$	6.52740	0.380040
$296$	4.30129	0.250007
$297$	−12.8007	−0.742773
$298$	7.37986	0.427504
$299$	−1.62892	−0.0942030
$300$	−12.3881	−0.715227
$301$	8.39716	0.484004
$302$	3.03501	0.174645
$303$	14.7530	0.847539
$304$	0.175144	0.0100452
$305$	−13.6520	−0.781713
$306$	−14.2259	−0.813240
$307$	4.26161	0.243223	0.121611	−	0.992578i	$-0.461194\pi$
$307$	4.26161	0.243223	0.121611	+	0.992578i	$0.461194\pi$
$308$	1.57874	0.0899570
$309$	9.47311	0.538906
$310$	21.2349	1.20606
$311$	30.9074	1.75260	0.876299	−	0.481767i	$-0.160005\pi$
$311$	30.9074	1.75260	0.876299	+	0.481767i	$0.160005\pi$
$312$	−3.04844	−0.172584
$313$	28.2680	1.59780	0.798901	−	0.601463i	$-0.205415\pi$
$313$	28.2680	1.59780	0.798901	+	0.601463i	$0.205415\pi$
$314$	−12.1397	−0.685084
$315$	10.5759	0.595885
$316$	12.1508	0.683538
$317$	11.8780	0.667133	0.333567	−	0.942727i	$-0.391748\pi$
$317$	11.8780	0.667133	0.333567	+	0.942727i	$0.391748\pi$
$318$	−15.2002	−0.852386
$319$	5.36561	0.300416
$320$	3.06326	0.171241
$321$	48.6239	2.71392
$322$	−1.04554	−0.0582657
$323$	0.499667	0.0278022
$324$	0.905589	0.0503105
$325$	−4.72852	−0.262291
$326$	−2.37411	−0.131490
$327$	33.3883	1.84638
$328$	12.1707	0.672014
$329$	−1.41375	−0.0779426
$330$	19.7393	1.08661
$331$	5.74696	0.315882	0.157941	−	0.987449i	$-0.449514\pi$
$331$	5.74696	0.315882	0.157941	+	0.987449i	$0.449514\pi$
$332$	7.64282	0.419454
$333$	−21.4483	−1.17536
$334$	3.88661	0.212666
$335$	2.69307	0.147138
$336$	−1.95667	−0.106745
$337$	25.2914	1.37771	0.688854	−	0.724900i	$-0.258114\pi$
$337$	25.2914	1.37771	0.688854	+	0.724900i	$0.258114\pi$
$338$	11.8364	0.643816
$339$	54.2074	2.94414
$340$	8.73913	0.473946
$341$	−15.8066	−0.855974
$342$	−0.873355	−0.0472256
$343$	−9.36130	−0.505463
$344$	−12.1281	−0.653903
$345$	−13.0726	−0.703807
$346$	−16.9311	−0.910221
$347$	−0.377875	−0.0202854	−0.0101427	−	0.999949i	$-0.503229\pi$
$347$	−0.377875	−0.0202854	−0.0101427	+	0.999949i	$0.503229\pi$
$348$	−6.65006	−0.356481
$349$	−27.0247	−1.44660	−0.723301	−	0.690533i	$-0.757376\pi$
$349$	−27.0247	−1.44660	−0.723301	+	0.690533i	$0.757376\pi$
$350$	−3.03505	−0.162230
$351$	6.05568	0.323228
$352$	−2.28019	−0.121534
$353$	−2.06081	−0.109686	−0.0548429	−	0.998495i	$-0.517466\pi$
$353$	−2.06081	−0.109686	−0.0548429	+	0.998495i	$0.517466\pi$
$354$	6.02191	0.320061
$355$	−33.6151	−1.78411
$356$	−10.2676	−0.544181
$357$	−5.58216	−0.295439
$358$	−2.74384	−0.145016
$359$	−15.3163	−0.808363	−0.404181	−	0.914679i	$-0.632444\pi$
$359$	−15.3163	−0.808363	−0.404181	+	0.914679i	$0.632444\pi$
$360$	−15.2749	−0.805058
$361$	−18.9693	−0.998385
$362$	−19.9339	−1.04770
$363$	16.3931	0.860415
$364$	−0.746859	−0.0391461
$365$	−34.7722	−1.82006
$366$	−12.5948	−0.658341
$367$	3.85655	0.201310	0.100655	−	0.994921i	$-0.467906\pi$
$367$	3.85655	0.201310	0.100655	+	0.994921i	$0.467906\pi$
$368$	1.51008	0.0787186
$369$	−60.6890	−3.15934
$370$	13.1760	0.684985
$371$	−3.72402	−0.193341
$372$	19.5905	1.01572
$373$	−17.7945	−0.921363	−0.460681	−	0.887566i	$-0.652395\pi$
$373$	−17.7945	−0.921363	−0.460681	+	0.887566i	$0.652395\pi$
$374$	−6.50512	−0.336372
$375$	5.33650	0.275575
$376$	2.04189	0.105303
$377$	−2.53832	−0.130730
$378$	3.88690	0.199921
$379$	−13.0418	−0.669913	−0.334956	−	0.942234i	$-0.608722\pi$
$379$	−13.0418	−0.669913	−0.334956	+	0.942234i	$0.608722\pi$
$380$	0.536512	0.0275225
$381$	6.97905	0.357548
$382$	−3.88094	−0.198566
$383$	13.8945	0.709977	0.354988	−	0.934871i	$-0.384485\pi$
$383$	13.8945	0.709977	0.354988	+	0.934871i	$0.384485\pi$
$384$	2.82604	0.144216
$385$	4.83609	0.246470
$386$	14.3698	0.731401
$387$	60.4766	3.07420
$388$	−12.3896	−0.628986
$389$	13.5860	0.688838	0.344419	−	0.938816i	$-0.388076\pi$
$389$	13.5860	0.688838	0.344419	+	0.938816i	$0.388076\pi$
$390$	−9.33815	−0.472855
$391$	4.30810	0.217870
$392$	6.52062	0.329341
$393$	21.2191	1.07036
$394$	5.03581	0.253700
$395$	37.2211	1.87280
$396$	11.3701	0.571371
$397$	11.8815	0.596316	0.298158	−	0.954517i	$-0.403628\pi$
$397$	11.8815	0.596316	0.298158	+	0.954517i	$0.403628\pi$
$398$	−21.6518	−1.08531
$399$	−0.342700	−0.0171564
$400$	4.38355	0.219178
$401$	−30.0049	−1.49837	−0.749186	−	0.662359i	$-0.769555\pi$
$401$	−30.0049	−1.49837	−0.749186	+	0.662359i	$0.769555\pi$
$402$	2.48452	0.123917
$403$	7.47767	0.372489
$404$	−5.22039	−0.259724
$405$	2.77405	0.137844
$406$	−1.62925	−0.0808583
$407$	−9.80774	−0.486152
$408$	8.06237	0.399147
$409$	−3.71049	−0.183472	−0.0917359	−	0.995783i	$-0.529242\pi$
$409$	−3.71049	−0.183472	−0.0917359	+	0.995783i	$0.529242\pi$
$410$	37.2820	1.84123
$411$	21.6966	1.07022
$412$	−3.35208	−0.165145
$413$	1.47535	0.0725974
$414$	−7.53002	−0.370080
$415$	23.4119	1.14925
$416$	1.07870	0.0528874
$417$	−21.6931	−1.06232
$418$	−0.399362	−0.0195334
$419$	−19.8018	−0.967379	−0.483690	−	0.875240i	$-0.660704\pi$
$419$	−19.8018	−0.967379	−0.483690	+	0.875240i	$0.660704\pi$
$420$	−5.99379	−0.292467
$421$	−26.0484	−1.26952	−0.634761	−	0.772708i	$-0.718902\pi$
$421$	−26.0484	−1.26952	−0.634761	+	0.772708i	$0.718902\pi$
$422$	18.3389	0.892724
$423$	−10.1819	−0.495060
$424$	5.37863	0.261210
$425$	12.5058	0.606620
$426$	−31.0120	−1.50253
$427$	−3.08570	−0.149327
$428$	−17.2057	−0.831667
$429$	6.95101	0.335598
$430$	−37.1515	−1.79160
$431$	−21.3389	−1.02786	−0.513929	−	0.857832i	$-0.671811\pi$
$431$	−21.3389	−1.02786	−0.513929	+	0.857832i	$0.671811\pi$
$432$	−5.61389	−0.270098
$433$	−34.7279	−1.66892	−0.834458	−	0.551072i	$-0.814219\pi$
$433$	−34.7279	−1.66892	−0.834458	+	0.551072i	$0.814219\pi$
$434$	4.79962	0.230389
$435$	−20.3709	−0.976708
$436$	−11.8145	−0.565813
$437$	0.264483	0.0126519
$438$	−32.0794	−1.53281
$439$	35.0226	1.67154	0.835768	−	0.549082i	$-0.185023\pi$
$439$	35.0226	1.67154	0.835768	+	0.549082i	$0.185023\pi$
$440$	−6.98481	−0.332988
$441$	−32.5150	−1.54833
$442$	3.07740	0.146377
$443$	−34.5796	−1.64293	−0.821464	−	0.570261i	$-0.806842\pi$
$443$	−34.5796	−1.64293	−0.821464	+	0.570261i	$0.806842\pi$
$444$	12.1556	0.576879
$445$	−31.4523	−1.49098
$446$	−11.4755	−0.543382
$447$	20.8558	0.986443
$448$	0.692372	0.0327115
$449$	27.6957	1.30704	0.653519	−	0.756910i	$-0.273292\pi$
$449$	27.6957	1.30704	0.653519	+	0.756910i	$0.273292\pi$
$450$	−21.8585	−1.03042
$451$	−27.7515	−1.30677
$452$	−19.1814	−0.902219
$453$	8.57706	0.402985
$454$	6.74186	0.316411
$455$	−2.28782	−0.107255
$456$	0.494964	0.0231788
$457$	5.23659	0.244957	0.122479	−	0.992471i	$-0.460916\pi$
$457$	5.23659	0.244957	0.122479	+	0.992471i	$0.460916\pi$
$458$	−17.7376	−0.828821
$459$	−16.0158	−0.747553
$460$	4.62578	0.215678
$461$	−5.04783	−0.235101	−0.117550	−	0.993067i	$-0.537504\pi$
$461$	−5.04783	−0.235101	−0.117550	+	0.993067i	$0.537504\pi$
$462$	4.46158	0.207571
$463$	−3.00114	−0.139475	−0.0697374	−	0.997565i	$-0.522216\pi$
$463$	−3.00114	−0.139475	−0.0697374	+	0.997565i	$0.522216\pi$
$464$	2.35314	0.109242
$465$	60.0107	2.78293
$466$	−23.5701	−1.09186
$467$	−19.7214	−0.912599	−0.456300	−	0.889826i	$-0.650826\pi$
$467$	−19.7214	−0.912599	−0.456300	+	0.889826i	$0.650826\pi$
$468$	−5.37890	−0.248640
$469$	0.608701	0.0281072
$470$	6.25485	0.288515
$471$	−34.3073	−1.58080
$472$	−2.13087	−0.0980811
$473$	27.6543	1.27155
$474$	34.3387	1.57723
$475$	0.767755	0.0352270
$476$	1.97526	0.0905359
$477$	−26.8205	−1.22803
$478$	8.59370	0.393067
$479$	−17.6085	−0.804554	−0.402277	−	0.915518i	$-0.631781\pi$
$479$	−17.6085	−0.804554	−0.402277	+	0.915518i	$0.631781\pi$
$480$	8.65688	0.395131
$481$	4.63978	0.211556
$482$	−14.8029	−0.674254
$483$	−2.95474	−0.134445
$484$	−5.80074	−0.263670
$485$	−37.9525	−1.72333
$486$	−14.2824	−0.647864
$487$	34.0021	1.54078	0.770390	−	0.637573i	$-0.220062\pi$
$487$	34.0021	1.54078	0.770390	+	0.637573i	$0.220062\pi$
$488$	4.45670	0.201745
$489$	−6.70933	−0.303407
$490$	19.9743	0.902349
$491$	−26.3016	−1.18697	−0.593487	−	0.804844i	$-0.702249\pi$
$491$	−26.3016	−1.18697	−0.593487	+	0.804844i	$0.702249\pi$
$492$	34.3948	1.55064
$493$	6.71325	0.302349
$494$	0.188927	0.00850025
$495$	34.8297	1.56548
$496$	−6.93214	−0.311262
$497$	−7.59786	−0.340810
$498$	21.5989	0.967870
$499$	−32.1334	−1.43849	−0.719244	−	0.694758i	$-0.755511\pi$
$499$	−32.1334	−1.43849	−0.719244	+	0.694758i	$0.755511\pi$
$500$	−1.88833	−0.0844488
$501$	10.9837	0.490716
$502$	9.70408	0.433114
$503$	−14.5127	−0.647089	−0.323544	−	0.946213i	$-0.604874\pi$
$503$	−14.5127	−0.647089	−0.323544	+	0.946213i	$0.604874\pi$
$504$	−3.45251	−0.153787
$505$	−15.9914	−0.711609
$506$	−3.44328	−0.153072
$507$	33.4501	1.48557
$508$	−2.46955	−0.109569
$509$	−12.1659	−0.539245	−0.269623	−	0.962966i	$-0.586899\pi$
$509$	−12.1659	−0.539245	−0.269623	+	0.962966i	$0.586899\pi$
$510$	24.6971	1.09361
$511$	−7.85938	−0.347679
$512$	−1.00000	−0.0441942
$513$	−0.983240	−0.0434111
$514$	−4.86077	−0.214400
$515$	−10.2683	−0.452475
$516$	−34.2744	−1.50885
$517$	−4.65590	−0.204766
$518$	2.97809	0.130850
$519$	−47.8479	−2.10029
$520$	3.30433	0.144904
$521$	5.94487	0.260449	0.130225	−	0.991485i	$-0.458430\pi$
$521$	5.94487	0.260449	0.130225	+	0.991485i	$0.458430\pi$
$522$	−11.7339	−0.513579
$523$	30.0528	1.31412	0.657059	−	0.753839i	$-0.271800\pi$
$523$	30.0528	1.31412	0.657059	+	0.753839i	$0.271800\pi$
$524$	−7.50843	−0.328007
$525$	−8.57717	−0.374338
$526$	−24.4920	−1.06790
$527$	−19.7766	−0.861482
$528$	−6.44390	−0.280435
$529$	−20.7196	−0.900854
$530$	16.4762	0.715678
$531$	10.6255	0.461109
$532$	0.121265	0.00525751
$533$	13.1285	0.568657
$534$	−29.0166	−1.25567
$535$	−52.7054	−2.27865
$536$	−0.879153	−0.0379736
$537$	−7.75419	−0.334618
$538$	6.53813	0.281879
$539$	−14.8682	−0.640421
$540$	−17.1968	−0.740032
$541$	−40.6866	−1.74926	−0.874628	−	0.484795i	$-0.838894\pi$
$541$	−40.6866	−1.74926	−0.874628	+	0.484795i	$0.838894\pi$
$542$	21.0283	0.903242
$543$	−56.3340	−2.41752
$544$	−2.85289	−0.122317
$545$	−36.1909	−1.55025
$546$	−2.11065	−0.0903276
$547$	−13.5945	−0.581260	−0.290630	−	0.956836i	$-0.593865\pi$
$547$	−13.5945	−0.581260	−0.290630	+	0.956836i	$0.593865\pi$
$548$	−7.67740	−0.327962
$549$	−22.2233	−0.948466
$550$	−9.99533	−0.426202
$551$	0.412139	0.0175577
$552$	4.26756	0.181639
$553$	8.41290	0.357753
$554$	2.57394	0.109356
$555$	37.2357	1.58057
$556$	7.67615	0.325541
$557$	26.5051	1.12306	0.561530	−	0.827457i	$-0.310213\pi$
$557$	26.5051	1.12306	0.561530	+	0.827457i	$0.310213\pi$
$558$	34.5670	1.46334
$559$	−13.0825	−0.553332
$560$	2.12092	0.0896251
$561$	−18.3837	−0.776161
$562$	−24.1639	−1.01929
$563$	−30.4753	−1.28438	−0.642190	−	0.766546i	$-0.721974\pi$
$563$	−30.4753	−1.28438	−0.642190	+	0.766546i	$0.721974\pi$
$564$	5.77047	0.242981
$565$	−58.7577	−2.47195
$566$	18.1926	0.764693
$567$	0.627004	0.0263317
$568$	10.9737	0.460444
$569$	−6.29771	−0.264014	−0.132007	−	0.991249i	$-0.542142\pi$
$569$	−6.29771	−0.264014	−0.132007	+	0.991249i	$0.542142\pi$
$570$	1.51620	0.0635068
$571$	−42.2290	−1.76723	−0.883615	−	0.468214i	$-0.844898\pi$
$571$	−42.2290	−1.76723	−0.883615	+	0.468214i	$0.844898\pi$
$572$	−2.45963	−0.102842
$573$	−10.9677	−0.458182
$574$	8.42665	0.351722
$575$	6.61954	0.276054
$576$	4.98649	0.207770
$577$	11.4691	0.477463	0.238732	−	0.971086i	$-0.423268\pi$
$577$	11.4691	0.477463	0.238732	+	0.971086i	$0.423268\pi$
$578$	8.86104	0.368570
$579$	40.6095	1.68767
$580$	7.20828	0.299308
$581$	5.29168	0.219536
$582$	−35.0134	−1.45135
$583$	−12.2643	−0.507936
$584$	11.3514	0.469723
$585$	−16.4770	−0.681239
$586$	−24.0869	−0.995022
$587$	−1.98876	−0.0820847	−0.0410424	−	0.999157i	$-0.513068\pi$
$587$	−1.98876	−0.0820847	−0.0410424	+	0.999157i	$0.513068\pi$
$588$	18.4275	0.759938
$589$	−1.21412	−0.0500271
$590$	−6.52740	−0.268729
$591$	14.2314	0.585401
$592$	−4.30129	−0.176782
$593$	42.5772	1.74844	0.874219	−	0.485532i	$-0.161374\pi$
$593$	42.5772	1.74844	0.874219	+	0.485532i	$0.161374\pi$
$594$	12.8007	0.525220
$595$	6.05073	0.248056
$596$	−7.37986	−0.302291
$597$	−61.1889	−2.50429
$598$	1.62892	0.0666116
$599$	−6.94414	−0.283730	−0.141865	−	0.989886i	$-0.545310\pi$
$599$	−6.94414	−0.283730	−0.141865	+	0.989886i	$0.545310\pi$
$600$	12.3881	0.505742
$601$	43.2980	1.76616	0.883082	−	0.469219i	$-0.155464\pi$
$601$	43.2980	1.76616	0.883082	+	0.469219i	$0.155464\pi$
$602$	−8.39716	−0.342243
$603$	4.38389	0.178526
$604$	−3.03501	−0.123493
$605$	−17.7692	−0.722419
$606$	−14.7530	−0.599301
$607$	4.23105	0.171733	0.0858665	−	0.996307i	$-0.472634\pi$
$607$	4.23105	0.171733	0.0858665	+	0.996307i	$0.472634\pi$
$608$	−0.175144	−0.00710304
$609$	−4.60432	−0.186576
$610$	13.6520	0.552754
$611$	2.20258	0.0891070
$612$	14.2259	0.575047
$613$	−3.81497	−0.154085	−0.0770425	−	0.997028i	$-0.524548\pi$
$613$	−3.81497	−0.154085	−0.0770425	+	0.997028i	$0.524548\pi$
$614$	−4.26161	−0.171985
$615$	105.360	4.24853
$616$	−1.57874	−0.0636092
$617$	7.93363	0.319396	0.159698	−	0.987166i	$-0.448948\pi$
$617$	7.93363	0.319396	0.159698	+	0.987166i	$0.448948\pi$
$618$	−9.47311	−0.381064
$619$	31.4615	1.26454	0.632272	−	0.774747i	$-0.282123\pi$
$619$	31.4615	1.26454	0.632272	+	0.774747i	$0.282123\pi$
$620$	−21.2349	−0.852815
$621$	−8.47744	−0.340188
$622$	−30.9074	−1.23927
$623$	−7.10900	−0.284816
$624$	3.04844	0.122035
$625$	−27.7022	−1.10809
$626$	−28.2680	−1.12982
$627$	−1.12861	−0.0450724
$628$	12.1397	0.484428
$629$	−12.2711	−0.489280
$630$	−10.5759	−0.421355
$631$	12.7590	0.507929	0.253964	−	0.967214i	$-0.418265\pi$
$631$	12.7590	0.507929	0.253964	+	0.967214i	$0.418265\pi$
$632$	−12.1508	−0.483334
$633$	51.8264	2.05992
$634$	−11.8780	−0.471735
$635$	−7.56489	−0.300203
$636$	15.2002	0.602728
$637$	7.03377	0.278688
$638$	−5.36561	−0.212426
$639$	−54.7200	−2.16469
$640$	−3.06326	−0.121086
$641$	22.9302	0.905687	0.452843	−	0.891590i	$-0.350410\pi$
$641$	22.9302	0.905687	0.452843	+	0.891590i	$0.350410\pi$
$642$	−48.6239	−1.91903
$643$	−26.9601	−1.06320	−0.531602	−	0.846994i	$-0.678410\pi$
$643$	−26.9601	−1.06320	−0.531602	+	0.846994i	$0.678410\pi$
$644$	1.04554	0.0412001
$645$	−104.991	−4.13404
$646$	−0.499667	−0.0196591
$647$	33.7313	1.32611	0.663057	−	0.748569i	$-0.269259\pi$
$647$	33.7313	1.32611	0.663057	+	0.748569i	$0.269259\pi$
$648$	−0.905589	−0.0355749
$649$	4.85878	0.190724
$650$	4.72852	0.185468
$651$	13.5639	0.531611
$652$	2.37411	0.0929775
$653$	−30.7541	−1.20350	−0.601750	−	0.798685i	$-0.705530\pi$
$653$	−30.7541	−1.20350	−0.601750	+	0.798685i	$0.705530\pi$
$654$	−33.3883	−1.30559
$655$	−23.0003	−0.898694
$656$	−12.1707	−0.475186
$657$	−56.6035	−2.20831
$658$	1.41375	0.0551137
$659$	36.4077	1.41824	0.709122	−	0.705086i	$-0.249092\pi$
$659$	36.4077	1.41824	0.709122	+	0.705086i	$0.249092\pi$
$660$	−19.7393	−0.768352
$661$	29.6229	1.15220	0.576098	−	0.817380i	$-0.304574\pi$
$661$	29.6229	1.15220	0.576098	+	0.817380i	$0.304574\pi$
$662$	−5.74696	−0.223362
$663$	8.69684	0.337757
$664$	−7.64282	−0.296599
$665$	0.371466	0.0144048
$666$	21.4483	0.831105
$667$	3.55344	0.137590
$668$	−3.88661	−0.150377
$669$	−32.4303	−1.25383
$670$	−2.69307	−0.104043
$671$	−10.1621	−0.392304
$672$	1.95667	0.0754802
$673$	16.4415	0.633772	0.316886	−	0.948464i	$-0.397363\pi$
$673$	16.4415	0.633772	0.316886	+	0.948464i	$0.397363\pi$
$674$	−25.2914	−0.974187
$675$	−24.6088	−0.947192
$676$	−11.8364	−0.455247
$677$	10.0655	0.386850	0.193425	−	0.981115i	$-0.438040\pi$
$677$	10.0655	0.386850	0.193425	+	0.981115i	$0.438040\pi$
$678$	−54.2074	−2.08182
$679$	−8.57821	−0.329201
$680$	−8.73913	−0.335130
$681$	19.0527	0.730103
$682$	15.8066	0.605265
$683$	37.0427	1.41740	0.708701	−	0.705509i	$-0.249282\pi$
$683$	37.0427	1.41740	0.708701	+	0.705509i	$0.249282\pi$
$684$	0.873355	0.0333936
$685$	−23.5179	−0.898571
$686$	9.36130	0.357416
$687$	−50.1270	−1.91246
$688$	12.1281	0.462379
$689$	5.80191	0.221035
$690$	13.0726	0.497666
$691$	−14.3120	−0.544452	−0.272226	−	0.962233i	$-0.587760\pi$
$691$	−14.3120	−0.544452	−0.272226	+	0.962233i	$0.587760\pi$
$692$	16.9311	0.643623
$693$	7.87236	0.299046
$694$	0.377875	0.0143439
$695$	23.5140	0.891939
$696$	6.65006	0.252070
$697$	−34.7216	−1.31517
$698$	27.0247	1.02290
$699$	−66.6099	−2.51942
$700$	3.03505	0.114714
$701$	51.5426	1.94674	0.973368	−	0.229246i	$-0.0736261\pi$
$701$	51.5426	1.94674	0.973368	+	0.229246i	$0.0736261\pi$
$702$	−6.05568	−0.228557
$703$	−0.753346	−0.0284130
$704$	2.28019	0.0859379
$705$	17.6764	0.665733
$706$	2.06081	0.0775596
$707$	−3.61446	−0.135936
$708$	−6.02191	−0.226317
$709$	−33.7053	−1.26583	−0.632915	−	0.774221i	$-0.718142\pi$
$709$	−33.7053	−1.26583	−0.632915	+	0.774221i	$0.718142\pi$
$710$	33.6151	1.26155
$711$	60.5900	2.27230
$712$	10.2676	0.384794
$713$	−10.4681	−0.392034
$714$	5.58216	0.208907
$715$	−7.53449	−0.281774
$716$	2.74384	0.102542
$717$	24.2861	0.906981
$718$	15.3163	0.571599
$719$	7.18676	0.268021	0.134011	−	0.990980i	$-0.457214\pi$
$719$	7.18676	0.268021	0.134011	+	0.990980i	$0.457214\pi$
$720$	15.2749	0.569262
$721$	−2.32089	−0.0864344
$722$	18.9693	0.705965
$723$	−41.8336	−1.55581
$724$	19.9339	0.740838
$725$	10.3151	0.383094
$726$	−16.3931	−0.608405
$727$	17.7029	0.656566	0.328283	−	0.944579i	$-0.393530\pi$
$727$	17.7029	0.656566	0.328283	+	0.944579i	$0.393530\pi$
$728$	0.746859	0.0276805
$729$	−43.0794	−1.59553
$730$	34.7722	1.28698
$731$	34.6001	1.27973
$732$	12.5948	0.465517
$733$	52.4546	1.93746	0.968728	−	0.248127i	$-0.0798149\pi$
$733$	52.4546	1.93746	0.968728	+	0.248127i	$0.0798149\pi$
$734$	−3.85655	−0.142348
$735$	56.4483	2.08213
$736$	−1.51008	−0.0556625
$737$	2.00464	0.0738417
$738$	60.6890	2.23399
$739$	−22.4648	−0.826382	−0.413191	−	0.910644i	$-0.635586\pi$
$739$	−22.4648	−0.826382	−0.413191	+	0.910644i	$0.635586\pi$
$740$	−13.1760	−0.484358
$741$	0.533916	0.0196139
$742$	3.72402	0.136713
$743$	−18.9166	−0.693983	−0.346992	−	0.937868i	$-0.612797\pi$
$743$	−18.9166	−0.693983	−0.346992	+	0.937868i	$0.612797\pi$
$744$	−19.5905	−0.718222
$745$	−22.6064	−0.828235
$746$	17.7945	0.651502
$747$	38.1108	1.39440
$748$	6.50512	0.237851
$749$	−11.9127	−0.435282
$750$	−5.33650	−0.194861
$751$	−35.4191	−1.29246	−0.646230	−	0.763143i	$-0.723655\pi$
$751$	−35.4191	−1.29246	−0.646230	+	0.763143i	$0.723655\pi$
$752$	−2.04189	−0.0744602
$753$	27.4241	0.999389
$754$	2.53832	0.0924403
$755$	−9.29703	−0.338354
$756$	−3.88690	−0.141365
$757$	9.65546	0.350934	0.175467	−	0.984485i	$-0.443857\pi$
$757$	9.65546	0.350934	0.175467	+	0.984485i	$0.443857\pi$
$758$	13.0418	0.473700
$759$	−9.73083	−0.353207
$760$	−0.536512	−0.0194613
$761$	−40.9691	−1.48513	−0.742564	−	0.669775i	$-0.766391\pi$
$761$	−40.9691	−1.48513	−0.742564	+	0.669775i	$0.766391\pi$
$762$	−6.97905	−0.252824
$763$	−8.18005	−0.296138
$764$	3.88094	0.140408
$765$	43.5776	1.57555
$766$	−13.8945	−0.502029
$767$	−2.29856	−0.0829961
$768$	−2.82604	−0.101976
$769$	6.75488	0.243587	0.121794	−	0.992555i	$-0.461135\pi$
$769$	6.75488	0.243587	0.121794	+	0.992555i	$0.461135\pi$
$770$	−4.83609	−0.174281
$771$	−13.7367	−0.494716
$772$	−14.3698	−0.517179
$773$	2.53775	0.0912765	0.0456383	−	0.998958i	$-0.485468\pi$
$773$	2.53775	0.0912765	0.0456383	+	0.998958i	$0.485468\pi$
$774$	−60.4766	−2.17379
$775$	−30.3874	−1.09155
$776$	12.3896	0.444760
$777$	8.41620	0.301929
$778$	−13.5860	−0.487082
$779$	−2.13163	−0.0763735
$780$	9.33815	0.334359
$781$	−25.0220	−0.895358
$782$	−4.30810	−0.154057
$783$	−13.2103	−0.472096
$784$	−6.52062	−0.232879
$785$	37.1871	1.32726
$786$	−21.2191	−0.756860
$787$	−2.30590	−0.0821964	−0.0410982	−	0.999155i	$-0.513086\pi$
$787$	−2.30590	−0.0821964	−0.0410982	+	0.999155i	$0.513086\pi$
$788$	−5.03581	−0.179393
$789$	−69.2152	−2.46413
$790$	−37.2211	−1.32427
$791$	−13.2807	−0.472207
$792$	−11.3701	−0.404020
$793$	4.80742	0.170717
$794$	−11.8815	−0.421659
$795$	46.5622	1.65139
$796$	21.6518	0.767429
$797$	−26.5242	−0.939536	−0.469768	−	0.882790i	$-0.655662\pi$
$797$	−26.5242	−0.939536	−0.469768	+	0.882790i	$0.655662\pi$
$798$	0.342700	0.0121314
$799$	−5.82529	−0.206084
$800$	−4.38355	−0.154982
$801$	−51.1992	−1.80903
$802$	30.0049	1.05951
$803$	−25.8833	−0.913401
$804$	−2.48452	−0.0876223
$805$	3.20276	0.112883
$806$	−7.47767	−0.263390
$807$	18.4770	0.650421
$808$	5.22039	0.183653
$809$	48.5854	1.70817	0.854085	−	0.520133i	$-0.174118\pi$
$809$	48.5854	1.70817	0.854085	+	0.520133i	$0.174118\pi$
$810$	−2.77405	−0.0974703
$811$	6.75928	0.237351	0.118675	−	0.992933i	$-0.462135\pi$
$811$	6.75928	0.237351	0.118675	+	0.992933i	$0.462135\pi$
$812$	1.62925	0.0571755
$813$	59.4267	2.08418
$814$	9.80774	0.343761
$815$	7.27253	0.254745
$816$	−8.06237	−0.282239
$817$	2.12417	0.0743152
$818$	3.71049	0.129734
$819$	−3.72420	−0.130134
$820$	−37.2820	−1.30194
$821$	3.04521	0.106278	0.0531392	−	0.998587i	$-0.483077\pi$
$821$	3.04521	0.106278	0.0531392	+	0.998587i	$0.483077\pi$
$822$	−21.6966	−0.756756
$823$	−9.31957	−0.324860	−0.162430	−	0.986720i	$-0.551933\pi$
$823$	−9.31957	−0.324860	−0.162430	+	0.986720i	$0.551933\pi$
$824$	3.35208	0.116775
$825$	−28.2472	−0.983441
$826$	−1.47535	−0.0513341
$827$	13.7049	0.476567	0.238284	−	0.971196i	$-0.423415\pi$
$827$	13.7049	0.476567	0.238284	+	0.971196i	$0.423415\pi$
$828$	7.53002	0.261686
$829$	−37.5301	−1.30347	−0.651737	−	0.758445i	$-0.725959\pi$
$829$	−37.5301	−1.30347	−0.651737	+	0.758445i	$0.725959\pi$
$830$	−23.4119	−0.812640
$831$	7.27404	0.252334
$832$	−1.07870	−0.0373971
$833$	−18.6026	−0.644542
$834$	21.6931	0.751170
$835$	−11.9057	−0.412014
$836$	0.399362	0.0138122
$837$	38.9162	1.34514
$838$	19.8018	0.684041
$839$	−43.1783	−1.49068	−0.745341	−	0.666684i	$-0.767713\pi$
$839$	−43.1783	−1.49068	−0.745341	+	0.666684i	$0.767713\pi$
$840$	5.99379	0.206805
$841$	−23.4627	−0.809060
$842$	26.0484	0.897688
$843$	−68.2881	−2.35197
$844$	−18.3389	−0.631251
$845$	−36.2580	−1.24731
$846$	10.1819	0.350060
$847$	−4.01627	−0.138001
$848$	−5.37863	−0.184703
$849$	51.4130	1.76449
$850$	−12.5058	−0.428945
$851$	−6.49531	−0.222656
$852$	31.0120	1.06245
$853$	1.79446	0.0614413	0.0307206	−	0.999528i	$-0.490220\pi$
$853$	1.79446	0.0614413	0.0307206	+	0.999528i	$0.490220\pi$
$854$	3.08570	0.105590
$855$	2.67531	0.0914937
$856$	17.2057	0.588078
$857$	51.4351	1.75699	0.878495	−	0.477751i	$-0.158548\pi$
$857$	51.4351	1.75699	0.878495	+	0.477751i	$0.158548\pi$
$858$	−6.95101	−0.237304
$859$	0.953473	0.0325321	0.0162660	−	0.999868i	$-0.494822\pi$
$859$	0.953473	0.0325321	0.0162660	+	0.999868i	$0.494822\pi$
$860$	37.1515	1.26686
$861$	23.8140	0.811580
$862$	21.3389	0.726806
$863$	−51.6708	−1.75889	−0.879447	−	0.475997i	$-0.842087\pi$
$863$	−51.6708	−1.75889	−0.879447	+	0.475997i	$0.842087\pi$
$864$	5.61389	0.190988
$865$	51.8643	1.76344
$866$	34.7279	1.18010
$867$	25.0416	0.850458
$868$	−4.79962	−0.162910
$869$	27.7062	0.939868
$870$	20.3709	0.690637
$871$	−0.948339	−0.0321332
$872$	11.8145	0.400090
$873$	−61.7805	−2.09095
$874$	−0.264483	−0.00894626
$875$	−1.30743	−0.0441992
$876$	32.0794	1.08386
$877$	44.9707	1.51855	0.759277	−	0.650768i	$-0.225553\pi$
$877$	44.9707	1.51855	0.759277	+	0.650768i	$0.225553\pi$
$878$	−35.0226	−1.18196
$879$	−68.0705	−2.29596
$880$	6.98481	0.235458
$881$	31.6458	1.06617	0.533087	−	0.846061i	$-0.321032\pi$
$881$	31.6458	1.06617	0.533087	+	0.846061i	$0.321032\pi$
$882$	32.5150	1.09484
$883$	−26.8434	−0.903353	−0.451676	−	0.892182i	$-0.649174\pi$
$883$	−26.8434	−0.903353	−0.451676	+	0.892182i	$0.649174\pi$
$884$	−3.07740	−0.103504
$885$	−18.4467	−0.620078
$886$	34.5796	1.16172
$887$	32.6200	1.09527	0.547636	−	0.836717i	$-0.315528\pi$
$887$	32.6200	1.09527	0.547636	+	0.836717i	$0.315528\pi$
$888$	−12.1556	−0.407915
$889$	−1.70985	−0.0573466
$890$	31.4523	1.05428
$891$	2.06491	0.0691772
$892$	11.4755	0.384229
$893$	−0.357626	−0.0119675
$894$	−20.8558	−0.697521
$895$	8.40509	0.280951
$896$	−0.692372	−0.0231305
$897$	4.60340	0.153703
$898$	−27.6957	−0.924216
$899$	−16.3123	−0.544045
$900$	21.8585	0.728618
$901$	−15.3446	−0.511204
$902$	27.7515	0.924023
$903$	−23.7307	−0.789707
$904$	19.1814	0.637965
$905$	61.0627	2.02979
$906$	−8.57706	−0.284954
$907$	−18.0937	−0.600792	−0.300396	−	0.953815i	$-0.597119\pi$
$907$	−18.0937	−0.600792	−0.300396	+	0.953815i	$0.597119\pi$
$908$	−6.74186	−0.223736
$909$	−26.0314	−0.863408
$910$	2.28782	0.0758406
$911$	−42.4198	−1.40543	−0.702716	−	0.711470i	$-0.748030\pi$
$911$	−42.4198	−1.40543	−0.702716	+	0.711470i	$0.748030\pi$
$912$	−0.494964	−0.0163899
$913$	17.4271	0.576752
$914$	−5.23659	−0.173211
$915$	38.5811	1.27545
$916$	17.7376	0.586065
$917$	−5.19863	−0.171674
$918$	16.0158	0.528600
$919$	33.8856	1.11778	0.558891	−	0.829241i	$-0.311227\pi$
$919$	33.8856	1.11778	0.558891	+	0.829241i	$0.311227\pi$
$920$	−4.62578	−0.152507
$921$	−12.0435	−0.396846
$922$	5.04783	0.166241
$923$	11.8372	0.389628
$924$	−4.46158	−0.146775
$925$	−18.8549	−0.619946
$926$	3.00114	0.0986236
$927$	−16.7151	−0.548996
$928$	−2.35314	−0.0772456
$929$	−52.3693	−1.71818	−0.859091	−	0.511823i	$-0.828970\pi$
$929$	−52.3693	−1.71818	−0.859091	+	0.511823i	$0.828970\pi$
$930$	−60.0107	−1.96783
$931$	−1.14205	−0.0374292
$932$	23.5701	0.772063
$933$	−87.3455	−2.85956
$934$	19.7214	0.645305
$935$	19.9269	0.651678
$936$	5.37890	0.175815
$937$	−37.9481	−1.23971	−0.619856	−	0.784716i	$-0.712809\pi$
$937$	−37.9481	−1.23971	−0.619856	+	0.784716i	$0.712809\pi$
$938$	−0.608701	−0.0198748
$939$	−79.8864	−2.60699
$940$	−6.25485	−0.204011
$941$	−11.7081	−0.381672	−0.190836	−	0.981622i	$-0.561120\pi$
$941$	−11.7081	−0.381672	−0.190836	+	0.981622i	$0.561120\pi$
$942$	34.3073	1.11779
$943$	−18.3788	−0.598495
$944$	2.13087	0.0693538
$945$	−11.9066	−0.387321
$946$	−27.6543	−0.899120
$947$	16.9802	0.551784	0.275892	−	0.961189i	$-0.411027\pi$
$947$	16.9802	0.551784	0.275892	+	0.961189i	$0.411027\pi$
$948$	−34.3387	−1.11527
$949$	12.2447	0.397479
$950$	−0.767755	−0.0249092
$951$	−33.5676	−1.08850
$952$	−1.97526	−0.0640186
$953$	−12.1950	−0.395034	−0.197517	−	0.980299i	$-0.563288\pi$
$953$	−12.1950	−0.395034	−0.197517	+	0.980299i	$0.563288\pi$
$954$	26.8205	0.868345
$955$	11.8883	0.384697
$956$	−8.59370	−0.277940
$957$	−15.1634	−0.490163
$958$	17.6085	0.568906
$959$	−5.31562	−0.171650
$960$	−8.65688	−0.279400
$961$	17.0545	0.550145
$962$	−4.63978	−0.149593
$963$	−85.7958	−2.76473
$964$	14.8029	0.476770
$965$	−44.0183	−1.41700
$966$	2.95474	0.0950671
$967$	−52.7236	−1.69548	−0.847738	−	0.530415i	$-0.822036\pi$
$967$	−52.7236	−1.69548	−0.847738	+	0.530415i	$0.822036\pi$
$968$	5.80074	0.186443
$969$	−1.41208	−0.0453625
$970$	37.9525	1.21858
$971$	25.3702	0.814169	0.407085	−	0.913390i	$-0.366545\pi$
$971$	25.3702	0.814169	0.407085	+	0.913390i	$0.366545\pi$
$972$	14.2824	0.458109
$973$	5.31476	0.170383
$974$	−34.0021	−1.08950
$975$	13.3630	0.427958
$976$	−4.45670	−0.142655
$977$	−7.93350	−0.253815	−0.126908	−	0.991915i	$-0.540505\pi$
$977$	−7.93350	−0.253815	−0.126908	+	0.991915i	$0.540505\pi$
$978$	6.70933	0.214541
$979$	−23.4120	−0.748252
$980$	−19.9743	−0.638057
$981$	−58.9130	−1.88095
$982$	26.3016	0.839318
$983$	49.3450	1.57386	0.786930	−	0.617042i	$-0.211669\pi$
$983$	49.3450	1.57386	0.786930	+	0.617042i	$0.211669\pi$
$984$	−34.3948	−1.09647
$985$	−15.4260	−0.491513
$986$	−6.71325	−0.213793
$987$	3.99531	0.127172
$988$	−0.188927	−0.00601058
$989$	18.3145	0.582366
$990$	−34.8297	−1.10696
$991$	5.03328	0.159887	0.0799437	−	0.996799i	$-0.474526\pi$
$991$	5.03328	0.159887	0.0799437	+	0.996799i	$0.474526\pi$
$992$	6.93214	0.220096
$993$	−16.2411	−0.515397
$994$	7.59786	0.240989
$995$	66.3251	2.10265
$996$	−21.5989	−0.684387
$997$	23.5351	0.745363	0.372681	−	0.927959i	$-0.378438\pi$
$997$	23.5351	0.745363	0.372681	+	0.927959i	$0.378438\pi$
$998$	32.1334	1.01716
$999$	24.1469	0.763975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.b.1.6	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.b.1.6	✓	75	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.82604 q^{3} +1.00000 q^{4} +3.06326 q^{5} +2.82604 q^{6} +0.692372 q^{7} -1.00000 q^{8} +4.98649 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.82604 q^{3} +1.00000 q^{4} +3.06326 q^{5} +2.82604 q^{6} +0.692372 q^{7} -1.00000 q^{8} +4.98649 q^{9} -3.06326 q^{10} +2.28019 q^{11} -2.82604 q^{12} -1.07870 q^{13} -0.692372 q^{14} -8.65688 q^{15} +1.00000 q^{16} +2.85289 q^{17} -4.98649 q^{18} +0.175144 q^{19} +3.06326 q^{20} -1.95667 q^{21} -2.28019 q^{22} +1.51008 q^{23} +2.82604 q^{24} +4.38355 q^{25} +1.07870 q^{26} -5.61389 q^{27} +0.692372 q^{28} +2.35314 q^{29} +8.65688 q^{30} -6.93214 q^{31} -1.00000 q^{32} -6.44390 q^{33} -2.85289 q^{34} +2.12092 q^{35} +4.98649 q^{36} -4.30129 q^{37} -0.175144 q^{38} +3.04844 q^{39} -3.06326 q^{40} -12.1707 q^{41} +1.95667 q^{42} +12.1281 q^{43} +2.28019 q^{44} +15.2749 q^{45} -1.51008 q^{46} -2.04189 q^{47} -2.82604 q^{48} -6.52062 q^{49} -4.38355 q^{50} -8.06237 q^{51} -1.07870 q^{52} -5.37863 q^{53} +5.61389 q^{54} +6.98481 q^{55} -0.692372 q^{56} -0.494964 q^{57} -2.35314 q^{58} +2.13087 q^{59} -8.65688 q^{60} -4.45670 q^{61} +6.93214 q^{62} +3.45251 q^{63} +1.00000 q^{64} -3.30433 q^{65} +6.44390 q^{66} +0.879153 q^{67} +2.85289 q^{68} -4.26756 q^{69} -2.12092 q^{70} -10.9737 q^{71} -4.98649 q^{72} -11.3514 q^{73} +4.30129 q^{74} -12.3881 q^{75} +0.175144 q^{76} +1.57874 q^{77} -3.04844 q^{78} +12.1508 q^{79} +3.06326 q^{80} +0.905589 q^{81} +12.1707 q^{82} +7.64282 q^{83} -1.95667 q^{84} +8.73913 q^{85} -12.1281 q^{86} -6.65006 q^{87} -2.28019 q^{88} -10.2676 q^{89} -15.2749 q^{90} -0.746859 q^{91} +1.51008 q^{92} +19.5905 q^{93} +2.04189 q^{94} +0.536512 q^{95} +2.82604 q^{96} -12.3896 q^{97} +6.52062 q^{98} +11.3701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9} + 9 q^{10} - 5 q^{11} + q^{12} - 35 q^{13} + 8 q^{14} - 21 q^{15} + 75 q^{16} + 4 q^{17} - 66 q^{18} - 59 q^{19} - 9 q^{20} - 62 q^{21} + 5 q^{22} + 43 q^{23} - q^{24} + 44 q^{25} + 35 q^{26} + 4 q^{27} - 8 q^{28} - 38 q^{29} + 21 q^{30} - 51 q^{31} - 75 q^{32} - 19 q^{33} - 4 q^{34} + 14 q^{35} + 66 q^{36} - 63 q^{37} + 59 q^{38} - 34 q^{39} + 9 q^{40} - 27 q^{41} + 62 q^{42} - 39 q^{43} - 5 q^{44} - 52 q^{45} - 43 q^{46} + 40 q^{47} + q^{48} + 29 q^{49} - 44 q^{50} - 34 q^{51} - 35 q^{52} - 39 q^{53} - 4 q^{54} - 48 q^{55} + 8 q^{56} - 28 q^{57} + 38 q^{58} + 5 q^{59} - 21 q^{60} - 98 q^{61} + 51 q^{62} + 2 q^{63} + 75 q^{64} - q^{65} + 19 q^{66} - 59 q^{67} + 4 q^{68} - 69 q^{69} - 14 q^{70} - 9 q^{71} - 66 q^{72} - 51 q^{73} + 63 q^{74} - q^{75} - 59 q^{76} - 25 q^{77} + 34 q^{78} - 139 q^{79} - 9 q^{80} + 23 q^{81} + 27 q^{82} + 31 q^{83} - 62 q^{84} - 149 q^{85} + 39 q^{86} + q^{87} + 5 q^{88} - 39 q^{89} + 52 q^{90} - 93 q^{91} + 43 q^{92} - 83 q^{93} - 40 q^{94} + 2 q^{95} - q^{96} - 70 q^{97} - 29 q^{98} - 61 q^{99}+O(q^{100}) \) 75 * q - 75 * q^2 + q^3 + 75 * q^4 - 9 * q^5 - q^6 - 8 * q^7 - 75 * q^8 + 66 * q^9 + 9 * q^10 - 5 * q^11 + q^12 - 35 * q^13 + 8 * q^14 - 21 * q^15 + 75 * q^16 + 4 * q^17 - 66 * q^18 - 59 * q^19 - 9 * q^20 - 62 * q^21 + 5 * q^22 + 43 * q^23 - q^24 + 44 * q^25 + 35 * q^26 + 4 * q^27 - 8 * q^28 - 38 * q^29 + 21 * q^30 - 51 * q^31 - 75 * q^32 - 19 * q^33 - 4 * q^34 + 14 * q^35 + 66 * q^36 - 63 * q^37 + 59 * q^38 - 34 * q^39 + 9 * q^40 - 27 * q^41 + 62 * q^42 - 39 * q^43 - 5 * q^44 - 52 * q^45 - 43 * q^46 + 40 * q^47 + q^48 + 29 * q^49 - 44 * q^50 - 34 * q^51 - 35 * q^52 - 39 * q^53 - 4 * q^54 - 48 * q^55 + 8 * q^56 - 28 * q^57 + 38 * q^58 + 5 * q^59 - 21 * q^60 - 98 * q^61 + 51 * q^62 + 2 * q^63 + 75 * q^64 - q^65 + 19 * q^66 - 59 * q^67 + 4 * q^68 - 69 * q^69 - 14 * q^70 - 9 * q^71 - 66 * q^72 - 51 * q^73 + 63 * q^74 - q^75 - 59 * q^76 - 25 * q^77 + 34 * q^78 - 139 * q^79 - 9 * q^80 + 23 * q^81 + 27 * q^82 + 31 * q^83 - 62 * q^84 - 149 * q^85 + 39 * q^86 + q^87 + 5 * q^88 - 39 * q^89 + 52 * q^90 - 93 * q^91 + 43 * q^92 - 83 * q^93 - 40 * q^94 + 2 * q^95 - q^96 - 70 * q^97 - 29 * q^98 - 61 * q^99

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