LMFDB - Embedded newform 8006.2.a.b.1.18

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			1.18
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.74787 q^{3} +1.00000 q^{4} -1.73571 q^{5} +1.74787 q^{6} +2.21934 q^{7} -1.00000 q^{8} +0.0550411 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.74787 q^{3} +1.00000 q^{4} -1.73571 q^{5} +1.74787 q^{6} +2.21934 q^{7} -1.00000 q^{8} +0.0550411 q^{9} +1.73571 q^{10} +2.67308 q^{11} -1.74787 q^{12} -3.26103 q^{13} -2.21934 q^{14} +3.03379 q^{15} +1.00000 q^{16} -1.30973 q^{17} -0.0550411 q^{18} +7.27032 q^{19} -1.73571 q^{20} -3.87911 q^{21} -2.67308 q^{22} +0.554267 q^{23} +1.74787 q^{24} -1.98731 q^{25} +3.26103 q^{26} +5.14740 q^{27} +2.21934 q^{28} +6.55485 q^{29} -3.03379 q^{30} -10.1696 q^{31} -1.00000 q^{32} -4.67220 q^{33} +1.30973 q^{34} -3.85213 q^{35} +0.0550411 q^{36} -3.92760 q^{37} -7.27032 q^{38} +5.69985 q^{39} +1.73571 q^{40} -2.17471 q^{41} +3.87911 q^{42} -3.06341 q^{43} +2.67308 q^{44} -0.0955354 q^{45} -0.554267 q^{46} -9.56855 q^{47} -1.74787 q^{48} -2.07454 q^{49} +1.98731 q^{50} +2.28923 q^{51} -3.26103 q^{52} +9.50333 q^{53} -5.14740 q^{54} -4.63970 q^{55} -2.21934 q^{56} -12.7076 q^{57} -6.55485 q^{58} -2.25435 q^{59} +3.03379 q^{60} +10.9153 q^{61} +10.1696 q^{62} +0.122155 q^{63} +1.00000 q^{64} +5.66021 q^{65} +4.67220 q^{66} +6.83811 q^{67} -1.30973 q^{68} -0.968786 q^{69} +3.85213 q^{70} -4.66048 q^{71} -0.0550411 q^{72} +5.89230 q^{73} +3.92760 q^{74} +3.47355 q^{75} +7.27032 q^{76} +5.93247 q^{77} -5.69985 q^{78} -14.8452 q^{79} -1.73571 q^{80} -9.16209 q^{81} +2.17471 q^{82} +0.906148 q^{83} -3.87911 q^{84} +2.27331 q^{85} +3.06341 q^{86} -11.4570 q^{87} -2.67308 q^{88} +10.9142 q^{89} +0.0955354 q^{90} -7.23733 q^{91} +0.554267 q^{92} +17.7751 q^{93} +9.56855 q^{94} -12.6192 q^{95} +1.74787 q^{96} +6.78254 q^{97} +2.07454 q^{98} +0.147129 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.74787	−1.00913	−0.504566	−	0.863373i	$-0.668347\pi$
$3$	−1.74787	−1.00913	−0.504566	+	0.863373i	$0.668347\pi$
$4$	1.00000	0.500000
$5$	−1.73571	−0.776233	−0.388117	−	0.921610i	$-0.626874\pi$
$5$	−1.73571	−0.776233	−0.388117	+	0.921610i	$0.626874\pi$
$6$	1.74787	0.713564
$7$	2.21934	0.838831	0.419415	−	0.907794i	$-0.362235\pi$
$7$	2.21934	0.838831	0.419415	+	0.907794i	$0.362235\pi$
$8$	−1.00000	−0.353553
$9$	0.0550411	0.0183470
$10$	1.73571	0.548880
$11$	2.67308	0.805965	0.402983	−	0.915208i	$-0.367974\pi$
$11$	2.67308	0.805965	0.402983	+	0.915208i	$0.367974\pi$
$12$	−1.74787	−0.504566
$13$	−3.26103	−0.904448	−0.452224	−	0.891904i	$-0.649369\pi$
$13$	−3.26103	−0.904448	−0.452224	+	0.891904i	$0.649369\pi$
$14$	−2.21934	−0.593143
$15$	3.03379	0.783322
$16$	1.00000	0.250000
$17$	−1.30973	−0.317656	−0.158828	−	0.987306i	$-0.550771\pi$
$17$	−1.30973	−0.317656	−0.158828	+	0.987306i	$0.550771\pi$
$18$	−0.0550411	−0.0129733
$19$	7.27032	1.66793	0.833963	−	0.551820i	$-0.186067\pi$
$19$	7.27032	1.66793	0.833963	+	0.551820i	$0.186067\pi$
$20$	−1.73571	−0.388117
$21$	−3.87911	−0.846491
$22$	−2.67308	−0.569903
$23$	0.554267	0.115573	0.0577864	−	0.998329i	$-0.481596\pi$
$23$	0.554267	0.115573	0.0577864	+	0.998329i	$0.481596\pi$
$24$	1.74787	0.356782
$25$	−1.98731	−0.397462
$26$	3.26103	0.639541
$27$	5.14740	0.990617
$28$	2.21934	0.419415
$29$	6.55485	1.21721	0.608603	−	0.793475i	$-0.291730\pi$
$29$	6.55485	1.21721	0.608603	+	0.793475i	$0.291730\pi$
$30$	−3.03379	−0.553892
$31$	−10.1696	−1.82651	−0.913256	−	0.407386i	$-0.866440\pi$
$31$	−10.1696	−1.82651	−0.913256	+	0.407386i	$0.866440\pi$
$32$	−1.00000	−0.176777
$33$	−4.67220	−0.813325
$34$	1.30973	0.224616
$35$	−3.85213	−0.651128
$36$	0.0550411	0.00917351
$37$	−3.92760	−0.645693	−0.322846	−	0.946451i	$-0.604640\pi$
$37$	−3.92760	−0.645693	−0.322846	+	0.946451i	$0.604640\pi$
$38$	−7.27032	−1.17940
$39$	5.69985	0.912707
$40$	1.73571	0.274440
$41$	−2.17471	−0.339632	−0.169816	−	0.985476i	$-0.554317\pi$
$41$	−2.17471	−0.339632	−0.169816	+	0.985476i	$0.554317\pi$
$42$	3.87911	0.598559
$43$	−3.06341	−0.467166	−0.233583	−	0.972337i	$-0.575045\pi$
$43$	−3.06341	−0.467166	−0.233583	+	0.972337i	$0.575045\pi$
$44$	2.67308	0.402983
$45$	−0.0955354	−0.0142416
$46$	−0.554267	−0.0817223
$47$	−9.56855	−1.39572	−0.697858	−	0.716236i	$-0.745864\pi$
$47$	−9.56855	−1.39572	−0.697858	+	0.716236i	$0.745864\pi$
$48$	−1.74787	−0.252283
$49$	−2.07454	−0.296363
$50$	1.98731	0.281048
$51$	2.28923	0.320556
$52$	−3.26103	−0.452224
$53$	9.50333	1.30538	0.652691	−	0.757624i	$-0.273640\pi$
$53$	9.50333	1.30538	0.652691	+	0.757624i	$0.273640\pi$
$54$	−5.14740	−0.700472
$55$	−4.63970	−0.625617
$56$	−2.21934	−0.296571
$57$	−12.7076	−1.68316
$58$	−6.55485	−0.860695
$59$	−2.25435	−0.293491	−0.146746	−	0.989174i	$-0.546880\pi$
$59$	−2.25435	−0.293491	−0.146746	+	0.989174i	$0.546880\pi$
$60$	3.03379	0.391661
$61$	10.9153	1.39756	0.698780	−	0.715337i	$-0.253727\pi$
$61$	10.9153	1.39756	0.698780	+	0.715337i	$0.253727\pi$
$62$	10.1696	1.29154
$63$	0.122155	0.0153900
$64$	1.00000	0.125000
$65$	5.66021	0.702062
$66$	4.67220	0.575108
$67$	6.83811	0.835409	0.417704	−	0.908583i	$-0.362835\pi$
$67$	6.83811	0.835409	0.417704	+	0.908583i	$0.362835\pi$
$68$	−1.30973	−0.158828
$69$	−0.968786	−0.116628
$70$	3.85213	0.460417
$71$	−4.66048	−0.553097	−0.276549	−	0.961000i	$-0.589191\pi$
$71$	−4.66048	−0.553097	−0.276549	+	0.961000i	$0.589191\pi$
$72$	−0.0550411	−0.00648665
$73$	5.89230	0.689642	0.344821	−	0.938668i	$-0.387940\pi$
$73$	5.89230	0.689642	0.344821	+	0.938668i	$0.387940\pi$
$74$	3.92760	0.456574
$75$	3.47355	0.401091
$76$	7.27032	0.833963
$77$	5.93247	0.676068
$78$	−5.69985	−0.645381
$79$	−14.8452	−1.67022	−0.835108	−	0.550085i	$-0.814595\pi$
$79$	−14.8452	−1.67022	−0.835108	+	0.550085i	$0.814595\pi$
$80$	−1.73571	−0.194058
$81$	−9.16209	−1.01801
$82$	2.17471	0.240156
$83$	0.906148	0.0994627	0.0497313	−	0.998763i	$-0.484163\pi$
$83$	0.906148	0.0994627	0.0497313	+	0.998763i	$0.484163\pi$
$84$	−3.87911	−0.423245
$85$	2.27331	0.246575
$86$	3.06341	0.330336
$87$	−11.4570	−1.22832
$88$	−2.67308	−0.284952
$89$	10.9142	1.15691	0.578454	−	0.815715i	$-0.303656\pi$
$89$	10.9142	1.15691	0.578454	+	0.815715i	$0.303656\pi$
$90$	0.0955354	0.0100703
$91$	−7.23733	−0.758678
$92$	0.554267	0.0577864
$93$	17.7751	1.84319
$94$	9.56855	0.986921
$95$	−12.6192	−1.29470
$96$	1.74787	0.178391
$97$	6.78254	0.688662	0.344331	−	0.938848i	$-0.388106\pi$
$97$	6.78254	0.688662	0.344331	+	0.938848i	$0.388106\pi$
$98$	2.07454	0.209561
$99$	0.147129	0.0147871
$100$	−1.98731	−0.198731
$101$	−5.29099	−0.526474	−0.263237	−	0.964731i	$-0.584790\pi$
$101$	−5.29099	−0.526474	−0.263237	+	0.964731i	$0.584790\pi$
$102$	−2.28923	−0.226668
$103$	10.5560	1.04011	0.520056	−	0.854132i	$-0.325911\pi$
$103$	10.5560	1.04011	0.520056	+	0.854132i	$0.325911\pi$
$104$	3.26103	0.319771
$105$	6.73301	0.657074
$106$	−9.50333	−0.923045
$107$	3.02895	0.292819	0.146410	−	0.989224i	$-0.453228\pi$
$107$	3.02895	0.292819	0.146410	+	0.989224i	$0.453228\pi$
$108$	5.14740	0.495309
$109$	−11.0596	−1.05932	−0.529658	−	0.848212i	$-0.677680\pi$
$109$	−11.0596	−1.05932	−0.529658	+	0.848212i	$0.677680\pi$
$110$	4.63970	0.442378
$111$	6.86492	0.651589
$112$	2.21934	0.209708
$113$	−3.15283	−0.296593	−0.148297	−	0.988943i	$-0.547379\pi$
$113$	−3.15283	−0.296593	−0.148297	+	0.988943i	$0.547379\pi$
$114$	12.7076	1.19017
$115$	−0.962048	−0.0897114
$116$	6.55485	0.608603
$117$	−0.179491	−0.0165939
$118$	2.25435	0.207530
$119$	−2.90673	−0.266459
$120$	−3.03379	−0.276946
$121$	−3.85462	−0.350420
$122$	−10.9153	−0.988223
$123$	3.80110	0.342734
$124$	−10.1696	−0.913256
$125$	12.1279	1.08476
$126$	−0.122155	−0.0108824
$127$	10.2512	0.909645	0.454823	−	0.890582i	$-0.349703\pi$
$127$	10.2512	0.909645	0.454823	+	0.890582i	$0.349703\pi$
$128$	−1.00000	−0.0883883
$129$	5.35444	0.471432
$130$	−5.66021	−0.496433
$131$	3.79715	0.331758	0.165879	−	0.986146i	$-0.446954\pi$
$131$	3.79715	0.331758	0.165879	+	0.986146i	$0.446954\pi$
$132$	−4.67220	−0.406663
$133$	16.1353	1.39911
$134$	−6.83811	−0.590723
$135$	−8.93439	−0.768950
$136$	1.30973	0.112308
$137$	14.7338	1.25879	0.629396	−	0.777085i	$-0.283302\pi$
$137$	14.7338	1.25879	0.629396	+	0.777085i	$0.283302\pi$
$138$	0.968786	0.0824685
$139$	−12.8655	−1.09123	−0.545617	−	0.838035i	$-0.683705\pi$
$139$	−12.8655	−1.09123	−0.545617	+	0.838035i	$0.683705\pi$
$140$	−3.85213	−0.325564
$141$	16.7246	1.40846
$142$	4.66048	0.391099
$143$	−8.71701	−0.728953
$144$	0.0550411	0.00458676
$145$	−11.3773	−0.944836
$146$	−5.89230	−0.487651
$147$	3.62603	0.299070
$148$	−3.92760	−0.322846
$149$	−19.7461	−1.61767	−0.808833	−	0.588038i	$-0.799900\pi$
$149$	−19.7461	−1.61767	−0.808833	+	0.588038i	$0.799900\pi$
$150$	−3.47355	−0.283614
$151$	−2.64835	−0.215520	−0.107760	−	0.994177i	$-0.534368\pi$
$151$	−2.64835	−0.215520	−0.107760	+	0.994177i	$0.534368\pi$
$152$	−7.27032	−0.589701
$153$	−0.0720888	−0.00582803
$154$	−5.93247	−0.478052
$155$	17.6515	1.41780
$156$	5.69985	0.456353
$157$	−1.21317	−0.0968218	−0.0484109	−	0.998828i	$-0.515416\pi$
$157$	−1.21317	−0.0968218	−0.0484109	+	0.998828i	$0.515416\pi$
$158$	14.8452	1.18102
$159$	−16.6106	−1.31730
$160$	1.73571	0.137220
$161$	1.23011	0.0969459
$162$	9.16209	0.719842
$163$	3.51464	0.275288	0.137644	−	0.990482i	$-0.456047\pi$
$163$	3.51464	0.275288	0.137644	+	0.990482i	$0.456047\pi$
$164$	−2.17471	−0.169816
$165$	8.10958	0.631330
$166$	−0.906148	−0.0703307
$167$	18.6662	1.44443	0.722217	−	0.691667i	$-0.243123\pi$
$167$	18.6662	1.44443	0.722217	+	0.691667i	$0.243123\pi$
$168$	3.87911	0.299280
$169$	−2.36567	−0.181974
$170$	−2.27331	−0.174355
$171$	0.400166	0.0306015
$172$	−3.06341	−0.233583
$173$	−10.7300	−0.815786	−0.407893	−	0.913030i	$-0.633736\pi$
$173$	−10.7300	−0.815786	−0.407893	+	0.913030i	$0.633736\pi$
$174$	11.4570	0.868554
$175$	−4.41051	−0.333403
$176$	2.67308	0.201491
$177$	3.94030	0.296171
$178$	−10.9142	−0.818057
$179$	−18.0909	−1.35218	−0.676088	−	0.736821i	$-0.736326\pi$
$179$	−18.0909	−1.35218	−0.676088	+	0.736821i	$0.736326\pi$
$180$	−0.0955354	−0.00712079
$181$	−5.60725	−0.416783	−0.208392	−	0.978045i	$-0.566823\pi$
$181$	−5.60725	−0.416783	−0.208392	+	0.978045i	$0.566823\pi$
$182$	7.23733	0.536467
$183$	−19.0785	−1.41032
$184$	−0.554267	−0.0408611
$185$	6.81717	0.501208
$186$	−17.7751	−1.30333
$187$	−3.50101	−0.256019
$188$	−9.56855	−0.697858
$189$	11.4238	0.830960
$190$	12.6192	0.915491
$191$	−13.6156	−0.985192	−0.492596	−	0.870258i	$-0.663952\pi$
$191$	−13.6156	−0.985192	−0.492596	+	0.870258i	$0.663952\pi$
$192$	−1.74787	−0.126141
$193$	23.1681	1.66767	0.833837	−	0.552010i	$-0.186139\pi$
$193$	23.1681	1.66767	0.833837	+	0.552010i	$0.186139\pi$
$194$	−6.78254	−0.486958
$195$	−9.89330	−0.708474
$196$	−2.07454	−0.148182
$197$	−4.41680	−0.314684	−0.157342	−	0.987544i	$-0.550293\pi$
$197$	−4.41680	−0.314684	−0.157342	+	0.987544i	$0.550293\pi$
$198$	−0.147129	−0.0104560
$199$	−2.00516	−0.142142	−0.0710708	−	0.997471i	$-0.522642\pi$
$199$	−2.00516	−0.142142	−0.0710708	+	0.997471i	$0.522642\pi$
$200$	1.98731	0.140524
$201$	−11.9521	−0.843037
$202$	5.29099	0.372273
$203$	14.5474	1.02103
$204$	2.28923	0.160278
$205$	3.77466	0.263634
$206$	−10.5560	−0.735470
$207$	0.0305075	0.00212042
$208$	−3.26103	−0.226112
$209$	19.4342	1.34429
$210$	−6.73301	−0.464622
$211$	−2.43561	−0.167674	−0.0838371	−	0.996479i	$-0.526718\pi$
$211$	−2.43561	−0.167674	−0.0838371	+	0.996479i	$0.526718\pi$
$212$	9.50333	0.652691
$213$	8.14590	0.558148
$214$	−3.02895	−0.207054
$215$	5.31719	0.362630
$216$	−5.14740	−0.350236
$217$	−22.5697	−1.53213
$218$	11.0596	0.749049
$219$	−10.2990	−0.695940
$220$	−4.63970	−0.312809
$221$	4.27106	0.287303
$222$	−6.86492	−0.460743
$223$	16.0176	1.07262	0.536310	−	0.844021i	$-0.319818\pi$
$223$	16.0176	1.07262	0.536310	+	0.844021i	$0.319818\pi$
$224$	−2.21934	−0.148286
$225$	−0.109384	−0.00729224
$226$	3.15283	0.209723
$227$	−22.1556	−1.47052	−0.735260	−	0.677785i	$-0.762940\pi$
$227$	−22.1556	−1.47052	−0.735260	+	0.677785i	$0.762940\pi$
$228$	−12.7076	−0.841579
$229$	2.05851	0.136030	0.0680151	−	0.997684i	$-0.478333\pi$
$229$	2.05851	0.136030	0.0680151	+	0.997684i	$0.478333\pi$
$230$	0.962048	0.0634355
$231$	−10.3692	−0.682242
$232$	−6.55485	−0.430347
$233$	12.2053	0.799594	0.399797	−	0.916604i	$-0.369081\pi$
$233$	12.2053	0.799594	0.399797	+	0.916604i	$0.369081\pi$
$234$	0.179491	0.0117337
$235$	16.6082	1.08340
$236$	−2.25435	−0.146746
$237$	25.9475	1.68547
$238$	2.90673	0.188415
$239$	8.49060	0.549211	0.274606	−	0.961557i	$-0.411453\pi$
$239$	8.49060	0.549211	0.274606	+	0.961557i	$0.411453\pi$
$240$	3.03379	0.195830
$241$	−7.83678	−0.504811	−0.252406	−	0.967621i	$-0.581222\pi$
$241$	−7.83678	−0.504811	−0.252406	+	0.967621i	$0.581222\pi$
$242$	3.85462	0.247784
$243$	0.571932	0.0366894
$244$	10.9153	0.698780
$245$	3.60081	0.230047
$246$	−3.80110	−0.242349
$247$	−23.7088	−1.50855
$248$	10.1696	0.645769
$249$	−1.58383	−0.100371
$250$	−12.1279	−0.767039
$251$	25.8806	1.63357	0.816785	−	0.576942i	$-0.195754\pi$
$251$	25.8806	1.63357	0.816785	+	0.576942i	$0.195754\pi$
$252$	0.122155	0.00769502
$253$	1.48160	0.0931476
$254$	−10.2512	−0.643216
$255$	−3.97344	−0.248827
$256$	1.00000	0.0625000
$257$	24.6754	1.53921	0.769605	−	0.638520i	$-0.220453\pi$
$257$	24.6754	1.53921	0.769605	+	0.638520i	$0.220453\pi$
$258$	−5.35444	−0.333353
$259$	−8.71666	−0.541627
$260$	5.66021	0.351031
$261$	0.360786	0.0223321
$262$	−3.79715	−0.234588
$263$	7.03600	0.433858	0.216929	−	0.976187i	$-0.430396\pi$
$263$	7.03600	0.433858	0.216929	+	0.976187i	$0.430396\pi$
$264$	4.67220	0.287554
$265$	−16.4950	−1.01328
$266$	−16.1353	−0.989318
$267$	−19.0767	−1.16747
$268$	6.83811	0.417704
$269$	26.0952	1.59105	0.795525	−	0.605921i	$-0.207195\pi$
$269$	26.0952	1.59105	0.795525	+	0.605921i	$0.207195\pi$
$270$	8.93439	0.543730
$271$	−18.5443	−1.12649	−0.563244	−	0.826291i	$-0.690447\pi$
$271$	−18.5443	−1.12649	−0.563244	+	0.826291i	$0.690447\pi$
$272$	−1.30973	−0.0794139
$273$	12.6499	0.765606
$274$	−14.7338	−0.890100
$275$	−5.31224	−0.320340
$276$	−0.968786	−0.0583141
$277$	9.77134	0.587103	0.293551	−	0.955943i	$-0.405163\pi$
$277$	9.77134	0.587103	0.293551	+	0.955943i	$0.405163\pi$
$278$	12.8655	0.771619
$279$	−0.559745	−0.0335111
$280$	3.85213	0.230209
$281$	17.8930	1.06741	0.533703	−	0.845672i	$-0.320800\pi$
$281$	17.8930	1.06741	0.533703	+	0.845672i	$0.320800\pi$
$282$	−16.7246	−0.995933
$283$	24.2772	1.44313	0.721564	−	0.692348i	$-0.243424\pi$
$283$	24.2772	1.44313	0.721564	+	0.692348i	$0.243424\pi$
$284$	−4.66048	−0.276549
$285$	22.0566	1.30652
$286$	8.71701	0.515448
$287$	−4.82641	−0.284894
$288$	−0.0550411	−0.00324333
$289$	−15.2846	−0.899095
$290$	11.3773	0.668100
$291$	−11.8550	−0.694951
$292$	5.89230	0.344821
$293$	1.31178	0.0766352	0.0383176	−	0.999266i	$-0.487800\pi$
$293$	1.31178	0.0766352	0.0383176	+	0.999266i	$0.487800\pi$
$294$	−3.62603	−0.211474
$295$	3.91290	0.227818
$296$	3.92760	0.228287
$297$	13.7594	0.798403
$298$	19.7461	1.14386
$299$	−1.80748	−0.104529
$300$	3.47355	0.200546
$301$	−6.79874	−0.391873
$302$	2.64835	0.152395
$303$	9.24796	0.531281
$304$	7.27032	0.416981
$305$	−18.9458	−1.08483
$306$	0.0720888	0.00412104
$307$	−32.9606	−1.88116	−0.940582	−	0.339568i	$-0.889719\pi$
$307$	−32.9606	−1.88116	−0.940582	+	0.339568i	$0.889719\pi$
$308$	5.93247	0.338034
$309$	−18.4504	−1.04961
$310$	−17.6515	−1.00254
$311$	10.9304	0.619807	0.309903	−	0.950768i	$-0.399703\pi$
$311$	10.9304	0.619807	0.309903	+	0.950768i	$0.399703\pi$
$312$	−5.69985	−0.322691
$313$	18.6025	1.05147	0.525737	−	0.850647i	$-0.323790\pi$
$313$	18.6025	1.05147	0.525737	+	0.850647i	$0.323790\pi$
$314$	1.21317	0.0684633
$315$	−0.212025	−0.0119463
$316$	−14.8452	−0.835108
$317$	22.2111	1.24750	0.623751	−	0.781623i	$-0.285608\pi$
$317$	22.2111	1.24750	0.623751	+	0.781623i	$0.285608\pi$
$318$	16.6106	0.931474
$319$	17.5217	0.981026
$320$	−1.73571	−0.0970292
$321$	−5.29420	−0.295493
$322$	−1.23011	−0.0685511
$323$	−9.52214	−0.529826
$324$	−9.16209	−0.509005
$325$	6.48068	0.359483
$326$	−3.51464	−0.194658
$327$	19.3307	1.06899
$328$	2.17471	0.120078
$329$	−21.2358	−1.17077
$330$	−8.10958	−0.446418
$331$	11.6182	0.638592	0.319296	−	0.947655i	$-0.396554\pi$
$331$	11.6182	0.638592	0.319296	+	0.947655i	$0.396554\pi$
$332$	0.906148	0.0497313
$333$	−0.216179	−0.0118465
$334$	−18.6662	−1.02137
$335$	−11.8690	−0.648472
$336$	−3.87911	−0.211623
$337$	−31.3262	−1.70645	−0.853223	−	0.521546i	$-0.825355\pi$
$337$	−31.3262	−1.70645	−0.853223	+	0.521546i	$0.825355\pi$
$338$	2.36567	0.128675
$339$	5.51073	0.299302
$340$	2.27331	0.123287
$341$	−27.1842	−1.47210
$342$	−0.400166	−0.0216385
$343$	−20.1395	−1.08743
$344$	3.06341	0.165168
$345$	1.68153	0.0905306
$346$	10.7300	0.576848
$347$	20.6101	1.10641	0.553203	−	0.833046i	$-0.313405\pi$
$347$	20.6101	1.10641	0.553203	+	0.833046i	$0.313405\pi$
$348$	−11.4570	−0.614161
$349$	−25.0600	−1.34143	−0.670715	−	0.741715i	$-0.734013\pi$
$349$	−25.0600	−1.34143	−0.670715	+	0.741715i	$0.734013\pi$
$350$	4.41051	0.235752
$351$	−16.7858	−0.895961
$352$	−2.67308	−0.142476
$353$	−7.34342	−0.390851	−0.195425	−	0.980719i	$-0.562609\pi$
$353$	−7.34342	−0.390851	−0.195425	+	0.980719i	$0.562609\pi$
$354$	−3.94030	−0.209425
$355$	8.08924	0.429332
$356$	10.9142	0.578454
$357$	5.08057	0.268892
$358$	18.0909	0.956132
$359$	6.82725	0.360329	0.180164	−	0.983637i	$-0.442337\pi$
$359$	6.82725	0.360329	0.180164	+	0.983637i	$0.442337\pi$
$360$	0.0955354	0.00503516
$361$	33.8576	1.78198
$362$	5.60725	0.294710
$363$	6.73737	0.353620
$364$	−7.23733	−0.379339
$365$	−10.2273	−0.535323
$366$	19.0785	0.997248
$367$	−24.6085	−1.28455	−0.642275	−	0.766474i	$-0.722009\pi$
$367$	−24.6085	−1.28455	−0.642275	+	0.766474i	$0.722009\pi$
$368$	0.554267	0.0288932
$369$	−0.119698	−0.00623124
$370$	−6.81717	−0.354408
$371$	21.0911	1.09499
$372$	17.7751	0.921596
$373$	−37.4692	−1.94008	−0.970041	−	0.242943i	$-0.921887\pi$
$373$	−37.4692	−1.94008	−0.970041	+	0.242943i	$0.921887\pi$
$374$	3.50101	0.181033
$375$	−21.1980	−1.09466
$376$	9.56855	0.493460
$377$	−21.3756	−1.10090
$378$	−11.4238	−0.587577
$379$	−16.1718	−0.830692	−0.415346	−	0.909664i	$-0.636339\pi$
$379$	−16.1718	−0.830692	−0.415346	+	0.909664i	$0.636339\pi$
$380$	−12.6192	−0.647350
$381$	−17.9177	−0.917952
$382$	13.6156	0.696636
$383$	6.08858	0.311112	0.155556	−	0.987827i	$-0.450283\pi$
$383$	6.08858	0.311112	0.155556	+	0.987827i	$0.450283\pi$
$384$	1.74787	0.0891955
$385$	−10.2971	−0.524787
$386$	−23.1681	−1.17922
$387$	−0.168613	−0.00857110
$388$	6.78254	0.344331
$389$	5.94014	0.301177	0.150588	−	0.988597i	$-0.451883\pi$
$389$	5.94014	0.301177	0.150588	+	0.988597i	$0.451883\pi$
$390$	9.89330	0.500966
$391$	−0.725939	−0.0367123
$392$	2.07454	0.104780
$393$	−6.63691	−0.334788
$394$	4.41680	0.222515
$395$	25.7670	1.29648
$396$	0.147129	0.00739353
$397$	−28.9280	−1.45185	−0.725927	−	0.687772i	$-0.758589\pi$
$397$	−28.9280	−1.45185	−0.725927	+	0.687772i	$0.758589\pi$
$398$	2.00516	0.100509
$399$	−28.2024	−1.41188
$400$	−1.98731	−0.0993654
$401$	−33.5317	−1.67449	−0.837247	−	0.546826i	$-0.815836\pi$
$401$	−33.5317	−1.67449	−0.837247	+	0.546826i	$0.815836\pi$
$402$	11.9521	0.596117
$403$	33.1634	1.65198
$404$	−5.29099	−0.263237
$405$	15.9027	0.790214
$406$	−14.5474	−0.721977
$407$	−10.4988	−0.520406
$408$	−2.28923	−0.113334
$409$	−19.6834	−0.973280	−0.486640	−	0.873602i	$-0.661778\pi$
$409$	−19.6834	−0.973280	−0.486640	+	0.873602i	$0.661778\pi$
$410$	−3.77466	−0.186417
$411$	−25.7527	−1.27029
$412$	10.5560	0.520056
$413$	−5.00316	−0.246189
$414$	−0.0305075	−0.00149936
$415$	−1.57281	−0.0772063
$416$	3.26103	0.159885
$417$	22.4871	1.10120
$418$	−19.4342	−0.950557
$419$	−4.35325	−0.212670	−0.106335	−	0.994330i	$-0.533912\pi$
$419$	−4.35325	−0.212670	−0.106335	+	0.994330i	$0.533912\pi$
$420$	6.73301	0.328537
$421$	−16.2820	−0.793535	−0.396768	−	0.917919i	$-0.629868\pi$
$421$	−16.2820	−0.793535	−0.396768	+	0.917919i	$0.629868\pi$
$422$	2.43561	0.118564
$423$	−0.526663	−0.0256072
$424$	−9.50333	−0.461522
$425$	2.60283	0.126256
$426$	−8.14590	−0.394670
$427$	24.2247	1.17232
$428$	3.02895	0.146410
$429$	15.2362	0.735610
$430$	−5.31719	−0.256418
$431$	−33.3637	−1.60707	−0.803537	−	0.595254i	$-0.797051\pi$
$431$	−33.3637	−1.60707	−0.803537	+	0.595254i	$0.797051\pi$
$432$	5.14740	0.247654
$433$	−4.83407	−0.232311	−0.116155	−	0.993231i	$-0.537057\pi$
$433$	−4.83407	−0.232311	−0.116155	+	0.993231i	$0.537057\pi$
$434$	22.5697	1.08338
$435$	19.8861	0.953464
$436$	−11.0596	−0.529658
$437$	4.02970	0.192767
$438$	10.2990	0.492104
$439$	34.5951	1.65114	0.825568	−	0.564303i	$-0.190855\pi$
$439$	34.5951	1.65114	0.825568	+	0.564303i	$0.190855\pi$
$440$	4.63970	0.221189
$441$	−0.114185	−0.00543739
$442$	−4.27106	−0.203154
$443$	13.4493	0.638995	0.319497	−	0.947587i	$-0.396486\pi$
$443$	13.4493	0.638995	0.319497	+	0.947587i	$0.396486\pi$
$444$	6.86492	0.325795
$445$	−18.9440	−0.898030
$446$	−16.0176	−0.758457
$447$	34.5136	1.63244
$448$	2.21934	0.104854
$449$	20.4135	0.963373	0.481686	−	0.876344i	$-0.340024\pi$
$449$	20.4135	0.963373	0.481686	+	0.876344i	$0.340024\pi$
$450$	0.109384	0.00515639
$451$	−5.81317	−0.273732
$452$	−3.15283	−0.148297
$453$	4.62896	0.217488
$454$	22.1556	1.03981
$455$	12.5619	0.588911
$456$	12.7076	0.595086
$457$	0.265371	0.0124136	0.00620678	−	0.999981i	$-0.498024\pi$
$457$	0.265371	0.0124136	0.00620678	+	0.999981i	$0.498024\pi$
$458$	−2.05851	−0.0961878
$459$	−6.74169	−0.314675
$460$	−0.962048	−0.0448557
$461$	12.2186	0.569078	0.284539	−	0.958664i	$-0.408159\pi$
$461$	12.2186	0.569078	0.284539	+	0.958664i	$0.408159\pi$
$462$	10.3692	0.482418
$463$	−33.7450	−1.56826	−0.784131	−	0.620595i	$-0.786891\pi$
$463$	−33.7450	−1.56826	−0.784131	+	0.620595i	$0.786891\pi$
$464$	6.55485	0.304301
$465$	−30.8524	−1.43075
$466$	−12.2053	−0.565398
$467$	−13.5665	−0.627781	−0.313890	−	0.949459i	$-0.601632\pi$
$467$	−13.5665	−0.627781	−0.313890	+	0.949459i	$0.601632\pi$
$468$	−0.179491	−0.00829696
$469$	15.1761	0.700766
$470$	−16.6082	−0.766081
$471$	2.12047	0.0977060
$472$	2.25435	0.103765
$473$	−8.18875	−0.376519
$474$	−25.9475	−1.19181
$475$	−14.4484	−0.662937
$476$	−2.90673	−0.133230
$477$	0.523073	0.0239499
$478$	−8.49060	−0.388351
$479$	−39.6038	−1.80954	−0.904772	−	0.425897i	$-0.859959\pi$
$479$	−39.6038	−1.80954	−0.904772	+	0.425897i	$0.859959\pi$
$480$	−3.03379	−0.138473
$481$	12.8080	0.583995
$482$	7.83678	0.356956
$483$	−2.15006	−0.0978312
$484$	−3.85462	−0.175210
$485$	−11.7725	−0.534563
$486$	−0.571932	−0.0259434
$487$	−4.52853	−0.205207	−0.102604	−	0.994722i	$-0.532717\pi$
$487$	−4.52853	−0.205207	−0.102604	+	0.994722i	$0.532717\pi$
$488$	−10.9153	−0.494112
$489$	−6.14313	−0.277802
$490$	−3.60081	−0.162668
$491$	2.14133	0.0966367	0.0483183	−	0.998832i	$-0.484614\pi$
$491$	2.14133	0.0966367	0.0483183	+	0.998832i	$0.484614\pi$
$492$	3.80110	0.171367
$493$	−8.58507	−0.386652
$494$	23.7088	1.06671
$495$	−0.255374	−0.0114782
$496$	−10.1696	−0.456628
$497$	−10.3432	−0.463955
$498$	1.58383	0.0709730
$499$	−24.5841	−1.10054	−0.550268	−	0.834988i	$-0.685475\pi$
$499$	−24.5841	−1.10054	−0.550268	+	0.834988i	$0.685475\pi$
$500$	12.1279	0.542378
$501$	−32.6260	−1.45762
$502$	−25.8806	−1.15511
$503$	−0.417848	−0.0186309	−0.00931546	−	0.999957i	$-0.502965\pi$
$503$	−0.417848	−0.0186309	−0.00931546	+	0.999957i	$0.502965\pi$
$504$	−0.122155	−0.00544120
$505$	9.18364	0.408666
$506$	−1.48160	−0.0658653
$507$	4.13487	0.183636
$508$	10.2512	0.454823
$509$	−16.8625	−0.747416	−0.373708	−	0.927546i	$-0.621914\pi$
$509$	−16.8625	−0.747416	−0.373708	+	0.927546i	$0.621914\pi$
$510$	3.97344	0.175947
$511$	13.0770	0.578493
$512$	−1.00000	−0.0441942
$513$	37.4232	1.65228
$514$	−24.6754	−1.08839
$515$	−18.3221	−0.807369
$516$	5.35444	0.235716
$517$	−25.5775	−1.12490
$518$	8.71666	0.382988
$519$	18.7546	0.823235
$520$	−5.66021	−0.248217
$521$	−35.0758	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$521$	−35.0758	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$522$	−0.360786	−0.0157912
$523$	−35.6722	−1.55984	−0.779918	−	0.625881i	$-0.784739\pi$
$523$	−35.6722	−1.55984	−0.779918	+	0.625881i	$0.784739\pi$
$524$	3.79715	0.165879
$525$	7.70898	0.336448
$526$	−7.03600	−0.306784
$527$	13.3194	0.580202
$528$	−4.67220	−0.203331
$529$	−22.6928	−0.986643
$530$	16.4950	0.716498
$531$	−0.124082	−0.00538469
$532$	16.1353	0.699554
$533$	7.09179	0.307179
$534$	19.0767	0.825528
$535$	−5.25737	−0.227296
$536$	−6.83811	−0.295362
$537$	31.6205	1.36452
$538$	−26.0952	−1.12504
$539$	−5.54543	−0.238859
$540$	−8.93439	−0.384475
$541$	−6.00659	−0.258243	−0.129122	−	0.991629i	$-0.541216\pi$
$541$	−6.00659	−0.258243	−0.129122	+	0.991629i	$0.541216\pi$
$542$	18.5443	0.796547
$543$	9.80072	0.420589
$544$	1.30973	0.0561541
$545$	19.1962	0.822276
$546$	−12.6499	−0.541366
$547$	−42.0128	−1.79634	−0.898169	−	0.439650i	$-0.855103\pi$
$547$	−42.0128	−1.79634	−0.898169	+	0.439650i	$0.855103\pi$
$548$	14.7338	0.629396
$549$	0.600789	0.0256410
$550$	5.31224	0.226515
$551$	47.6559	2.03021
$552$	0.968786	0.0412343
$553$	−32.9465	−1.40103
$554$	−9.77134	−0.415144
$555$	−11.9155	−0.505785
$556$	−12.8655	−0.545617
$557$	−28.4804	−1.20675	−0.603377	−	0.797456i	$-0.706178\pi$
$557$	−28.4804	−1.20675	−0.603377	+	0.797456i	$0.706178\pi$
$558$	0.559745	0.0236959
$559$	9.98988	0.422527
$560$	−3.85213	−0.162782
$561$	6.11931	0.258357
$562$	−17.8930	−0.754770
$563$	8.28017	0.348967	0.174484	−	0.984660i	$-0.444174\pi$
$563$	8.28017	0.348967	0.174484	+	0.984660i	$0.444174\pi$
$564$	16.7246	0.704231
$565$	5.47240	0.230226
$566$	−24.2772	−1.02045
$567$	−20.3338	−0.853938
$568$	4.66048	0.195549
$569$	−5.04542	−0.211515	−0.105757	−	0.994392i	$-0.533727\pi$
$569$	−5.04542	−0.211515	−0.105757	+	0.994392i	$0.533727\pi$
$570$	−22.0566	−0.923851
$571$	15.9127	0.665926	0.332963	−	0.942940i	$-0.391952\pi$
$571$	15.9127	0.665926	0.332963	+	0.942940i	$0.391952\pi$
$572$	−8.71701	−0.364477
$573$	23.7983	0.994189
$574$	4.82641	0.201450
$575$	−1.10150	−0.0459357
$576$	0.0550411	0.00229338
$577$	−41.9905	−1.74809	−0.874045	−	0.485845i	$-0.838512\pi$
$577$	−41.9905	−1.74809	−0.874045	+	0.485845i	$0.838512\pi$
$578$	15.2846	0.635756
$579$	−40.4947	−1.68290
$580$	−11.3773	−0.472418
$581$	2.01105	0.0834323
$582$	11.8550	0.491404
$583$	25.4032	1.05209
$584$	−5.89230	−0.243825
$585$	0.311544	0.0128808
$586$	−1.31178	−0.0541893
$587$	−35.0248	−1.44563	−0.722813	−	0.691044i	$-0.757151\pi$
$587$	−35.0248	−1.44563	−0.722813	+	0.691044i	$0.757151\pi$
$588$	3.62603	0.149535
$589$	−73.9362	−3.04649
$590$	−3.91290	−0.161091
$591$	7.71999	0.317558
$592$	−3.92760	−0.161423
$593$	4.40724	0.180984	0.0904919	−	0.995897i	$-0.471156\pi$
$593$	4.40724	0.180984	0.0904919	+	0.995897i	$0.471156\pi$
$594$	−13.7594	−0.564556
$595$	5.04524	0.206835
$596$	−19.7461	−0.808833
$597$	3.50475	0.143440
$598$	1.80748	0.0739135
$599$	−29.0796	−1.18816	−0.594080	−	0.804406i	$-0.702484\pi$
$599$	−29.0796	−1.18816	−0.594080	+	0.804406i	$0.702484\pi$
$600$	−3.47355	−0.141807
$601$	0.264684	0.0107967	0.00539835	−	0.999985i	$-0.498282\pi$
$601$	0.264684	0.0107967	0.00539835	+	0.999985i	$0.498282\pi$
$602$	6.79874	0.277096
$603$	0.376377	0.0153273
$604$	−2.64835	−0.107760
$605$	6.69051	0.272008
$606$	−9.24796	−0.375673
$607$	−31.4882	−1.27807	−0.639034	−	0.769179i	$-0.720666\pi$
$607$	−31.4882	−1.27807	−0.639034	+	0.769179i	$0.720666\pi$
$608$	−7.27032	−0.294850
$609$	−25.4270	−1.03035
$610$	18.9458	0.767092
$611$	31.2034	1.26235
$612$	−0.0720888	−0.00291402
$613$	14.4271	0.582704	0.291352	−	0.956616i	$-0.405895\pi$
$613$	14.4271	0.582704	0.291352	+	0.956616i	$0.405895\pi$
$614$	32.9606	1.33018
$615$	−6.59761	−0.266041
$616$	−5.93247	−0.239026
$617$	−18.1341	−0.730053	−0.365026	−	0.930997i	$-0.618940\pi$
$617$	−18.1341	−0.730053	−0.365026	+	0.930997i	$0.618940\pi$
$618$	18.4504	0.742186
$619$	16.2149	0.651730	0.325865	−	0.945416i	$-0.394344\pi$
$619$	16.2149	0.651730	0.325865	+	0.945416i	$0.394344\pi$
$620$	17.6515	0.708900
$621$	2.85303	0.114488
$622$	−10.9304	−0.438270
$623$	24.2224	0.970449
$624$	5.69985	0.228177
$625$	−11.1141	−0.444562
$626$	−18.6025	−0.743505
$627$	−33.9684	−1.35657
$628$	−1.21317	−0.0484109
$629$	5.14408	0.205108
$630$	0.212025	0.00844728
$631$	−0.454143	−0.0180791	−0.00903957	−	0.999959i	$-0.502877\pi$
$631$	−0.454143	−0.0180791	−0.00903957	+	0.999959i	$0.502877\pi$
$632$	14.8452	0.590511
$633$	4.25712	0.169205
$634$	−22.2111	−0.882117
$635$	−17.7931	−0.706097
$636$	−16.6106	−0.658651
$637$	6.76515	0.268045
$638$	−17.5217	−0.693690
$639$	−0.256518	−0.0101477
$640$	1.73571	0.0686100
$641$	−7.46583	−0.294883	−0.147441	−	0.989071i	$-0.547104\pi$
$641$	−7.46583	−0.294883	−0.147441	+	0.989071i	$0.547104\pi$
$642$	5.29420	0.208945
$643$	30.4528	1.20094	0.600470	−	0.799647i	$-0.294980\pi$
$643$	30.4528	1.20094	0.600470	+	0.799647i	$0.294980\pi$
$644$	1.23011	0.0484730
$645$	−9.29375	−0.365941
$646$	9.52214	0.374644
$647$	20.6375	0.811343	0.405672	−	0.914019i	$-0.367038\pi$
$647$	20.6375	0.811343	0.405672	+	0.914019i	$0.367038\pi$
$648$	9.16209	0.359921
$649$	−6.02606	−0.236544
$650$	−6.48068	−0.254193
$651$	39.4489	1.54613
$652$	3.51464	0.137644
$653$	−34.9386	−1.36725	−0.683626	−	0.729832i	$-0.739598\pi$
$653$	−34.9386	−1.36725	−0.683626	+	0.729832i	$0.739598\pi$
$654$	−19.3307	−0.755889
$655$	−6.59075	−0.257522
$656$	−2.17471	−0.0849080
$657$	0.324319	0.0126529
$658$	21.2358	0.827859
$659$	−23.7853	−0.926544	−0.463272	−	0.886216i	$-0.653325\pi$
$659$	−23.7853	−0.926544	−0.463272	+	0.886216i	$0.653325\pi$
$660$	8.10958	0.315665
$661$	−1.13289	−0.0440644	−0.0220322	−	0.999757i	$-0.507014\pi$
$661$	−1.13289	−0.0440644	−0.0220322	+	0.999757i	$0.507014\pi$
$662$	−11.6182	−0.451553
$663$	−7.46525	−0.289926
$664$	−0.906148	−0.0351654
$665$	−28.0062	−1.08603
$666$	0.216179	0.00837677
$667$	3.63314	0.140676
$668$	18.6662	0.722217
$669$	−27.9967	−1.08242
$670$	11.8690	0.458539
$671$	29.1775	1.12638
$672$	3.87911	0.149640
$673$	−10.5614	−0.407113	−0.203557	−	0.979063i	$-0.565250\pi$
$673$	−10.5614	−0.407113	−0.203557	+	0.979063i	$0.565250\pi$
$674$	31.3262	1.20664
$675$	−10.2295	−0.393732
$676$	−2.36567	−0.0909872
$677$	47.9082	1.84126	0.920631	−	0.390434i	$-0.127675\pi$
$677$	47.9082	1.84126	0.920631	+	0.390434i	$0.127675\pi$
$678$	−5.51073	−0.211638
$679$	15.0527	0.577671
$680$	−2.27331	−0.0871774
$681$	38.7251	1.48395
$682$	27.1842	1.04094
$683$	−25.6191	−0.980288	−0.490144	−	0.871641i	$-0.663056\pi$
$683$	−25.6191	−0.980288	−0.490144	+	0.871641i	$0.663056\pi$
$684$	0.400166	0.0153007
$685$	−25.5736	−0.977116
$686$	20.1395	0.768929
$687$	−3.59800	−0.137272
$688$	−3.06341	−0.116791
$689$	−30.9907	−1.18065
$690$	−1.68153	−0.0640148
$691$	2.78768	0.106048	0.0530242	−	0.998593i	$-0.483114\pi$
$691$	2.78768	0.106048	0.0530242	+	0.998593i	$0.483114\pi$
$692$	−10.7300	−0.407893
$693$	0.326530	0.0124038
$694$	−20.6101	−0.782348
$695$	22.3307	0.847052
$696$	11.4570	0.434277
$697$	2.84827	0.107886
$698$	25.0600	0.948535
$699$	−21.3332	−0.806896
$700$	−4.41051	−0.166702
$701$	28.4684	1.07524	0.537618	−	0.843189i	$-0.319324\pi$
$701$	28.4684	1.07524	0.537618	+	0.843189i	$0.319324\pi$
$702$	16.7858	0.633540
$703$	−28.5549	−1.07697
$704$	2.67308	0.100746
$705$	−29.0290	−1.09330
$706$	7.34342	0.276373
$707$	−11.7425	−0.441622
$708$	3.94030	0.148086
$709$	−27.7267	−1.04130	−0.520649	−	0.853771i	$-0.674310\pi$
$709$	−27.7267	−1.04130	−0.520649	+	0.853771i	$0.674310\pi$
$710$	−8.08924	−0.303584
$711$	−0.817096	−0.0306435
$712$	−10.9142	−0.409029
$713$	−5.63667	−0.211095
$714$	−5.08057	−0.190136
$715$	15.1302	0.565838
$716$	−18.0909	−0.676088
$717$	−14.8404	−0.554227
$718$	−6.82725	−0.254791
$719$	−6.99370	−0.260821	−0.130411	−	0.991460i	$-0.541630\pi$
$719$	−6.99370	−0.260821	−0.130411	+	0.991460i	$0.541630\pi$
$720$	−0.0955354	−0.00356039
$721$	23.4273	0.872477
$722$	−33.8576	−1.26005
$723$	13.6977	0.509421
$724$	−5.60725	−0.208392
$725$	−13.0265	−0.483793
$726$	−6.73737	−0.250047
$727$	29.7784	1.10442	0.552210	−	0.833705i	$-0.313785\pi$
$727$	29.7784	1.10442	0.552210	+	0.833705i	$0.313785\pi$
$728$	7.23733	0.268233
$729$	26.4866	0.980986
$730$	10.2273	0.378531
$731$	4.01223	0.148398
$732$	−19.0785	−0.705161
$733$	−27.9727	−1.03319	−0.516597	−	0.856228i	$-0.672802\pi$
$733$	−27.9727	−1.03319	−0.516597	+	0.856228i	$0.672802\pi$
$734$	24.6085	0.908315
$735$	−6.29373	−0.232148
$736$	−0.554267	−0.0204306
$737$	18.2789	0.673310
$738$	0.119698	0.00440615
$739$	42.9463	1.57980	0.789902	−	0.613233i	$-0.210131\pi$
$739$	42.9463	1.57980	0.789902	+	0.613233i	$0.210131\pi$
$740$	6.81717	0.250604
$741$	41.4398	1.52233
$742$	−21.0911	−0.774278
$743$	38.1538	1.39973	0.699864	−	0.714276i	$-0.253244\pi$
$743$	38.1538	1.39973	0.699864	+	0.714276i	$0.253244\pi$
$744$	−17.7751	−0.651666
$745$	34.2736	1.25569
$746$	37.4692	1.37184
$747$	0.0498754	0.00182484
$748$	−3.50101	−0.128010
$749$	6.72225	0.245626
$750$	21.1980	0.774043
$751$	19.6603	0.717416	0.358708	−	0.933450i	$-0.383217\pi$
$751$	19.6603	0.717416	0.358708	+	0.933450i	$0.383217\pi$
$752$	−9.56855	−0.348929
$753$	−45.2359	−1.64849
$754$	21.3756	0.778453
$755$	4.59677	0.167293
$756$	11.4238	0.415480
$757$	−30.1867	−1.09715	−0.548577	−	0.836100i	$-0.684830\pi$
$757$	−30.1867	−1.09715	−0.548577	+	0.836100i	$0.684830\pi$
$758$	16.1718	0.587388
$759$	−2.58965	−0.0939982
$760$	12.6192	0.457745
$761$	16.6604	0.603940	0.301970	−	0.953317i	$-0.402356\pi$
$761$	16.6604	0.603940	0.301970	+	0.953317i	$0.402356\pi$
$762$	17.9177	0.649090
$763$	−24.5449	−0.888586
$764$	−13.6156	−0.492596
$765$	0.125125	0.00452391
$766$	−6.08858	−0.219989
$767$	7.35150	0.265447
$768$	−1.74787	−0.0630707
$769$	16.2160	0.584764	0.292382	−	0.956302i	$-0.405552\pi$
$769$	16.2160	0.584764	0.292382	+	0.956302i	$0.405552\pi$
$770$	10.2971	0.371080
$771$	−43.1294	−1.55327
$772$	23.1681	0.833837
$773$	−23.5150	−0.845777	−0.422889	−	0.906182i	$-0.638984\pi$
$773$	−23.5150	−0.845777	−0.422889	+	0.906182i	$0.638984\pi$
$774$	0.168613	0.00606068
$775$	20.2101	0.725969
$776$	−6.78254	−0.243479
$777$	15.2356	0.546573
$778$	−5.94014	−0.212964
$779$	−15.8108	−0.566481
$780$	−9.89330	−0.354237
$781$	−12.4579	−0.445777
$782$	0.725939	0.0259595
$783$	33.7404	1.20579
$784$	−2.07454	−0.0740908
$785$	2.10572	0.0751563
$786$	6.63691	0.236731
$787$	49.6419	1.76954	0.884771	−	0.466026i	$-0.154315\pi$
$787$	49.6419	1.76954	0.884771	+	0.466026i	$0.154315\pi$
$788$	−4.41680	−0.157342
$789$	−12.2980	−0.437820
$790$	−25.7670	−0.916748
$791$	−6.99719	−0.248791
$792$	−0.147129	−0.00522802
$793$	−35.5951	−1.26402
$794$	28.9280	1.02662
$795$	28.8311	1.02253
$796$	−2.00516	−0.0710708
$797$	−33.2443	−1.17757	−0.588787	−	0.808288i	$-0.700394\pi$
$797$	−33.2443	−1.17757	−0.588787	+	0.808288i	$0.700394\pi$
$798$	28.2024	0.998352
$799$	12.5322	0.443357
$800$	1.98731	0.0702620
$801$	0.600732	0.0212258
$802$	33.5317	1.18405
$803$	15.7506	0.555827
$804$	−11.9521	−0.421519
$805$	−2.13511	−0.0752527
$806$	−33.1634	−1.16813
$807$	−45.6109	−1.60558
$808$	5.29099	0.186137
$809$	18.6203	0.654656	0.327328	−	0.944911i	$-0.393852\pi$
$809$	18.6203	0.654656	0.327328	+	0.944911i	$0.393852\pi$
$810$	−15.9027	−0.558765
$811$	−43.1977	−1.51688	−0.758438	−	0.651745i	$-0.774037\pi$
$811$	−43.1977	−1.51688	−0.758438	+	0.651745i	$0.774037\pi$
$812$	14.5474	0.510515
$813$	32.4130	1.13677
$814$	10.4988	0.367983
$815$	−6.10041	−0.213688
$816$	2.28923	0.0801391
$817$	−22.2720	−0.779198
$818$	19.6834	0.688213
$819$	−0.398350	−0.0139195
$820$	3.77466	0.131817
$821$	4.27152	0.149077	0.0745385	−	0.997218i	$-0.476252\pi$
$821$	4.27152	0.149077	0.0745385	+	0.997218i	$0.476252\pi$
$822$	25.7527	0.898229
$823$	−38.9406	−1.35738	−0.678692	−	0.734423i	$-0.737453\pi$
$823$	−38.9406	−1.35738	−0.678692	+	0.734423i	$0.737453\pi$
$824$	−10.5560	−0.367735
$825$	9.28510	0.323266
$826$	5.00316	0.174082
$827$	−3.56698	−0.124036	−0.0620181	−	0.998075i	$-0.519754\pi$
$827$	−3.56698	−0.124036	−0.0620181	+	0.998075i	$0.519754\pi$
$828$	0.0305075	0.00106021
$829$	−35.0920	−1.21879	−0.609397	−	0.792865i	$-0.708588\pi$
$829$	−35.0920	−1.21879	−0.609397	+	0.792865i	$0.708588\pi$
$830$	1.57281	0.0545931
$831$	−17.0790	−0.592464
$832$	−3.26103	−0.113056
$833$	2.71709	0.0941415
$834$	−22.4871	−0.778665
$835$	−32.3991	−1.12122
$836$	19.4342	0.672145
$837$	−52.3469	−1.80937
$838$	4.35325	0.150380
$839$	2.99989	0.103568	0.0517839	−	0.998658i	$-0.483509\pi$
$839$	2.99989	0.103568	0.0517839	+	0.998658i	$0.483509\pi$
$840$	−6.73301	−0.232311
$841$	13.9661	0.481590
$842$	16.2820	0.561114
$843$	−31.2746	−1.07715
$844$	−2.43561	−0.0838371
$845$	4.10611	0.141255
$846$	0.526663	0.0181071
$847$	−8.55470	−0.293943
$848$	9.50333	0.326346
$849$	−42.4333	−1.45631
$850$	−2.60283	−0.0892764
$851$	−2.17694	−0.0746245
$852$	8.14590	0.279074
$853$	−34.9791	−1.19766	−0.598831	−	0.800876i	$-0.704368\pi$
$853$	−34.9791	−1.19766	−0.598831	+	0.800876i	$0.704368\pi$
$854$	−24.2247	−0.828952
$855$	−0.694573	−0.0237539
$856$	−3.02895	−0.103527
$857$	34.7639	1.18751	0.593756	−	0.804645i	$-0.297645\pi$
$857$	34.7639	1.18751	0.593756	+	0.804645i	$0.297645\pi$
$858$	−15.2362	−0.520155
$859$	10.4521	0.356622	0.178311	−	0.983974i	$-0.442937\pi$
$859$	10.4521	0.356622	0.178311	+	0.983974i	$0.442937\pi$
$860$	5.31719	0.181315
$861$	8.43592	0.287495
$862$	33.3637	1.13637
$863$	−7.21203	−0.245500	−0.122750	−	0.992438i	$-0.539171\pi$
$863$	−7.21203	−0.245500	−0.122750	+	0.992438i	$0.539171\pi$
$864$	−5.14740	−0.175118
$865$	18.6242	0.633240
$866$	4.83407	0.164269
$867$	26.7155	0.907305
$868$	−22.5697	−0.766067
$869$	−39.6825	−1.34614
$870$	−19.8861	−0.674201
$871$	−22.2993	−0.755583
$872$	11.0596	0.374524
$873$	0.373318	0.0126349
$874$	−4.02970	−0.136307
$875$	26.9160	0.909927
$876$	−10.2990	−0.347970
$877$	−24.7388	−0.835369	−0.417685	−	0.908592i	$-0.637158\pi$
$877$	−24.7388	−0.835369	−0.417685	+	0.908592i	$0.637158\pi$
$878$	−34.5951	−1.16753
$879$	−2.29282	−0.0773350
$880$	−4.63970	−0.156404
$881$	−33.4510	−1.12699	−0.563497	−	0.826118i	$-0.690544\pi$
$881$	−33.4510	−1.12699	−0.563497	+	0.826118i	$0.690544\pi$
$882$	0.114185	0.00384481
$883$	36.9016	1.24184	0.620919	−	0.783875i	$-0.286760\pi$
$883$	36.9016	1.24184	0.620919	+	0.783875i	$0.286760\pi$
$884$	4.27106	0.143651
$885$	−6.83923	−0.229898
$886$	−13.4493	−0.451837
$887$	1.33734	0.0449036	0.0224518	−	0.999748i	$-0.492853\pi$
$887$	1.33734	0.0449036	0.0224518	+	0.999748i	$0.492853\pi$
$888$	−6.86492	−0.230372
$889$	22.7508	0.763038
$890$	18.9440	0.635003
$891$	−24.4910	−0.820481
$892$	16.0176	0.536310
$893$	−69.5665	−2.32795
$894$	−34.5136	−1.15431
$895$	31.4005	1.04960
$896$	−2.21934	−0.0741428
$897$	3.15924	0.105484
$898$	−20.4135	−0.681207
$899$	−66.6602	−2.22324
$900$	−0.109384	−0.00364612
$901$	−12.4468	−0.414662
$902$	5.81317	0.193558
$903$	11.8833	0.395451
$904$	3.15283	0.104862
$905$	9.73256	0.323521
$906$	−4.62896	−0.153787
$907$	−26.6012	−0.883279	−0.441639	−	0.897193i	$-0.645603\pi$
$907$	−26.6012	−0.883279	−0.441639	+	0.897193i	$0.645603\pi$
$908$	−22.1556	−0.735260
$909$	−0.291222	−0.00965922
$910$	−12.5619	−0.416423
$911$	−17.2266	−0.570741	−0.285371	−	0.958417i	$-0.592117\pi$
$911$	−17.2266	−0.570741	−0.285371	+	0.958417i	$0.592117\pi$
$912$	−12.7076	−0.420789
$913$	2.42221	0.0801635
$914$	−0.265371	−0.00877771
$915$	33.1147	1.09474
$916$	2.05851	0.0680151
$917$	8.42714	0.278289
$918$	6.74169	0.222509
$919$	−42.5073	−1.40219	−0.701093	−	0.713070i	$-0.747304\pi$
$919$	−42.5073	−1.40219	−0.701093	+	0.713070i	$0.747304\pi$
$920$	0.962048	0.0317178
$921$	57.6108	1.89834
$922$	−12.2186	−0.402399
$923$	15.1980	0.500247
$924$	−10.3692	−0.341121
$925$	7.80534	0.256638
$926$	33.7450	1.10893
$927$	0.581012	0.0190829
$928$	−6.55485	−0.215174
$929$	−8.38068	−0.274961	−0.137481	−	0.990504i	$-0.543900\pi$
$929$	−8.38068	−0.274961	−0.137481	+	0.990504i	$0.543900\pi$
$930$	30.8524	1.01169
$931$	−15.0826	−0.494312
$932$	12.2053	0.399797
$933$	−19.1049	−0.625467
$934$	13.5665	0.443908
$935$	6.07674	0.198731
$936$	0.179491	0.00586684
$937$	50.1068	1.63692	0.818460	−	0.574564i	$-0.194828\pi$
$937$	50.1068	1.63692	0.818460	+	0.574564i	$0.194828\pi$
$938$	−15.1761	−0.495517
$939$	−32.5147	−1.06108
$940$	16.6082	0.541701
$941$	−14.5266	−0.473553	−0.236777	−	0.971564i	$-0.576091\pi$
$941$	−14.5266	−0.473553	−0.236777	+	0.971564i	$0.576091\pi$
$942$	−2.12047	−0.0690885
$943$	−1.20537	−0.0392522
$944$	−2.25435	−0.0733728
$945$	−19.8284	−0.645019
$946$	8.18875	0.266239
$947$	30.0670	0.977047	0.488523	−	0.872551i	$-0.337536\pi$
$947$	30.0670	0.977047	0.488523	+	0.872551i	$0.337536\pi$
$948$	25.9475	0.842735
$949$	−19.2150	−0.623745
$950$	14.4484	0.468767
$951$	−38.8221	−1.25889
$952$	2.90673	0.0942076
$953$	−6.01559	−0.194864	−0.0974320	−	0.995242i	$-0.531063\pi$
$953$	−6.01559	−0.194864	−0.0974320	+	0.995242i	$0.531063\pi$
$954$	−0.523073	−0.0169351
$955$	23.6328	0.764739
$956$	8.49060	0.274606
$957$	−30.6256	−0.989984
$958$	39.6038	1.27954
$959$	32.6992	1.05591
$960$	3.03379	0.0979152
$961$	72.4205	2.33615
$962$	−12.8080	−0.412947
$963$	0.166716	0.00537236
$964$	−7.83678	−0.252406
$965$	−40.2131	−1.29450
$966$	2.15006	0.0691771
$967$	5.04306	0.162174	0.0810870	−	0.996707i	$-0.474161\pi$
$967$	5.04306	0.162174	0.0810870	+	0.996707i	$0.474161\pi$
$968$	3.85462	0.123892
$969$	16.6434	0.534664
$970$	11.7725	0.377993
$971$	33.6161	1.07879	0.539396	−	0.842052i	$-0.318653\pi$
$971$	33.6161	1.07879	0.539396	+	0.842052i	$0.318653\pi$
$972$	0.571932	0.0183447
$973$	−28.5528	−0.915361
$974$	4.52853	0.145103
$975$	−11.3274	−0.362766
$976$	10.9153	0.349390
$977$	−29.7031	−0.950288	−0.475144	−	0.879908i	$-0.657604\pi$
$977$	−29.7031	−0.950288	−0.475144	+	0.879908i	$0.657604\pi$
$978$	6.14313	0.196436
$979$	29.1747	0.932427
$980$	3.60081	0.115024
$981$	−0.608731	−0.0194353
$982$	−2.14133	−0.0683325
$983$	25.7669	0.821835	0.410918	−	0.911672i	$-0.365208\pi$
$983$	25.7669	0.821835	0.410918	+	0.911672i	$0.365208\pi$
$984$	−3.80110	−0.121175
$985$	7.66629	0.244268
$986$	8.58507	0.273404
$987$	37.1174	1.18146
$988$	−23.7088	−0.754276
$989$	−1.69795	−0.0539916
$990$	0.255374	0.00811632
$991$	−34.1366	−1.08439	−0.542193	−	0.840254i	$-0.682406\pi$
$991$	−34.1366	−1.08439	−0.542193	+	0.840254i	$0.682406\pi$
$992$	10.1696	0.322885
$993$	−20.3070	−0.644424
$994$	10.3432	0.328066
$995$	3.48037	0.110335
$996$	−1.58383	−0.0501855
$997$	−6.74715	−0.213684	−0.106842	−	0.994276i	$-0.534074\pi$
$997$	−6.74715	−0.213684	−0.106842	+	0.994276i	$0.534074\pi$
$998$	24.5841	0.778197
$999$	−20.2169	−0.639634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.b.1.18	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.b.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.74787 q^{3} +1.00000 q^{4} -1.73571 q^{5} +1.74787 q^{6} +2.21934 q^{7} -1.00000 q^{8} +0.0550411 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.74787 q^{3} +1.00000 q^{4} -1.73571 q^{5} +1.74787 q^{6} +2.21934 q^{7} -1.00000 q^{8} +0.0550411 q^{9} +1.73571 q^{10} +2.67308 q^{11} -1.74787 q^{12} -3.26103 q^{13} -2.21934 q^{14} +3.03379 q^{15} +1.00000 q^{16} -1.30973 q^{17} -0.0550411 q^{18} +7.27032 q^{19} -1.73571 q^{20} -3.87911 q^{21} -2.67308 q^{22} +0.554267 q^{23} +1.74787 q^{24} -1.98731 q^{25} +3.26103 q^{26} +5.14740 q^{27} +2.21934 q^{28} +6.55485 q^{29} -3.03379 q^{30} -10.1696 q^{31} -1.00000 q^{32} -4.67220 q^{33} +1.30973 q^{34} -3.85213 q^{35} +0.0550411 q^{36} -3.92760 q^{37} -7.27032 q^{38} +5.69985 q^{39} +1.73571 q^{40} -2.17471 q^{41} +3.87911 q^{42} -3.06341 q^{43} +2.67308 q^{44} -0.0955354 q^{45} -0.554267 q^{46} -9.56855 q^{47} -1.74787 q^{48} -2.07454 q^{49} +1.98731 q^{50} +2.28923 q^{51} -3.26103 q^{52} +9.50333 q^{53} -5.14740 q^{54} -4.63970 q^{55} -2.21934 q^{56} -12.7076 q^{57} -6.55485 q^{58} -2.25435 q^{59} +3.03379 q^{60} +10.9153 q^{61} +10.1696 q^{62} +0.122155 q^{63} +1.00000 q^{64} +5.66021 q^{65} +4.67220 q^{66} +6.83811 q^{67} -1.30973 q^{68} -0.968786 q^{69} +3.85213 q^{70} -4.66048 q^{71} -0.0550411 q^{72} +5.89230 q^{73} +3.92760 q^{74} +3.47355 q^{75} +7.27032 q^{76} +5.93247 q^{77} -5.69985 q^{78} -14.8452 q^{79} -1.73571 q^{80} -9.16209 q^{81} +2.17471 q^{82} +0.906148 q^{83} -3.87911 q^{84} +2.27331 q^{85} +3.06341 q^{86} -11.4570 q^{87} -2.67308 q^{88} +10.9142 q^{89} +0.0955354 q^{90} -7.23733 q^{91} +0.554267 q^{92} +17.7751 q^{93} +9.56855 q^{94} -12.6192 q^{95} +1.74787 q^{96} +6.78254 q^{97} +2.07454 q^{98} +0.147129 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 75 q^{2} + q^{3} + 75 q^{4} - 9 q^{5} - q^{6} - 8 q^{7} - 75 q^{8} + 66 q^{9}+O(q^{10}) \) 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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