LMFDB - Embedded newform 8006.2.a.c.1.10

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:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.77089 q^{3} +1.00000 q^{4} -0.296987 q^{5} +2.77089 q^{6} +3.25147 q^{7} -1.00000 q^{8} +4.67784 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.77089 q^{3} +1.00000 q^{4} -0.296987 q^{5} +2.77089 q^{6} +3.25147 q^{7} -1.00000 q^{8} +4.67784 q^{9} +0.296987 q^{10} +0.674478 q^{11} -2.77089 q^{12} +5.33914 q^{13} -3.25147 q^{14} +0.822918 q^{15} +1.00000 q^{16} +3.60039 q^{17} -4.67784 q^{18} -7.63503 q^{19} -0.296987 q^{20} -9.00946 q^{21} -0.674478 q^{22} +6.33501 q^{23} +2.77089 q^{24} -4.91180 q^{25} -5.33914 q^{26} -4.64911 q^{27} +3.25147 q^{28} +0.590947 q^{29} -0.822918 q^{30} +5.79006 q^{31} -1.00000 q^{32} -1.86890 q^{33} -3.60039 q^{34} -0.965642 q^{35} +4.67784 q^{36} +1.12363 q^{37} +7.63503 q^{38} -14.7942 q^{39} +0.296987 q^{40} -3.20090 q^{41} +9.00946 q^{42} +10.1621 q^{43} +0.674478 q^{44} -1.38926 q^{45} -6.33501 q^{46} -4.93079 q^{47} -2.77089 q^{48} +3.57204 q^{49} +4.91180 q^{50} -9.97630 q^{51} +5.33914 q^{52} +12.7912 q^{53} +4.64911 q^{54} -0.200311 q^{55} -3.25147 q^{56} +21.1559 q^{57} -0.590947 q^{58} +7.47516 q^{59} +0.822918 q^{60} +12.4722 q^{61} -5.79006 q^{62} +15.2098 q^{63} +1.00000 q^{64} -1.58565 q^{65} +1.86890 q^{66} +9.40104 q^{67} +3.60039 q^{68} -17.5536 q^{69} +0.965642 q^{70} -10.0176 q^{71} -4.67784 q^{72} +5.22712 q^{73} -1.12363 q^{74} +13.6101 q^{75} -7.63503 q^{76} +2.19304 q^{77} +14.7942 q^{78} +12.8617 q^{79} -0.296987 q^{80} -1.15133 q^{81} +3.20090 q^{82} -5.16135 q^{83} -9.00946 q^{84} -1.06927 q^{85} -10.1621 q^{86} -1.63745 q^{87} -0.674478 q^{88} +3.61180 q^{89} +1.38926 q^{90} +17.3601 q^{91} +6.33501 q^{92} -16.0436 q^{93} +4.93079 q^{94} +2.26750 q^{95} +2.77089 q^{96} -1.81646 q^{97} -3.57204 q^{98} +3.15510 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) $ 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * 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
$3$	−2.77089	−1.59978	−0.799888	−	0.600150i	$-0.795108\pi$
$3$	−2.77089	−1.59978	−0.799888	+	0.600150i	$0.795108\pi$
$4$	1.00000	0.500000
$5$	−0.296987	−0.132816	−0.0664082	−	0.997793i	$-0.521154\pi$
$5$	−0.296987	−0.132816	−0.0664082	+	0.997793i	$0.521154\pi$
$6$	2.77089	1.13121
$7$	3.25147	1.22894	0.614470	−	0.788940i	$-0.289370\pi$
$7$	3.25147	1.22894	0.614470	+	0.788940i	$0.289370\pi$
$8$	−1.00000	−0.353553
$9$	4.67784	1.55928
$10$	0.296987	0.0939154
$11$	0.674478	0.203363	0.101681	−	0.994817i	$-0.467578\pi$
$11$	0.674478	0.203363	0.101681	+	0.994817i	$0.467578\pi$
$12$	−2.77089	−0.799888
$13$	5.33914	1.48081	0.740406	−	0.672160i	$-0.234633\pi$
$13$	5.33914	1.48081	0.740406	+	0.672160i	$0.234633\pi$
$14$	−3.25147	−0.868991
$15$	0.822918	0.212476
$16$	1.00000	0.250000
$17$	3.60039	0.873224	0.436612	−	0.899650i	$-0.356178\pi$
$17$	3.60039	0.873224	0.436612	+	0.899650i	$0.356178\pi$
$18$	−4.67784	−1.10258
$19$	−7.63503	−1.75160	−0.875798	−	0.482677i	$-0.839665\pi$
$19$	−7.63503	−1.75160	−0.875798	+	0.482677i	$0.839665\pi$
$20$	−0.296987	−0.0664082
$21$	−9.00946	−1.96603
$22$	−0.674478	−0.143799
$23$	6.33501	1.32094	0.660470	−	0.750852i	$-0.270357\pi$
$23$	6.33501	1.32094	0.660470	+	0.750852i	$0.270357\pi$
$24$	2.77089	0.565606
$25$	−4.91180	−0.982360
$26$	−5.33914	−1.04709
$27$	−4.64911	−0.894723
$28$	3.25147	0.614470
$29$	0.590947	0.109736	0.0548680	−	0.998494i	$-0.482526\pi$
$29$	0.590947	0.109736	0.0548680	+	0.998494i	$0.482526\pi$
$30$	−0.822918	−0.150244
$31$	5.79006	1.03992	0.519962	−	0.854189i	$-0.325946\pi$
$31$	5.79006	1.03992	0.519962	+	0.854189i	$0.325946\pi$
$32$	−1.00000	−0.176777
$33$	−1.86890	−0.325335
$34$	−3.60039	−0.617462
$35$	−0.965642	−0.163223
$36$	4.67784	0.779640
$37$	1.12363	0.184724	0.0923618	−	0.995726i	$-0.470558\pi$
$37$	1.12363	0.184724	0.0923618	+	0.995726i	$0.470558\pi$
$38$	7.63503	1.23857
$39$	−14.7942	−2.36897
$40$	0.296987	0.0469577
$41$	−3.20090	−0.499897	−0.249948	−	0.968259i	$-0.580414\pi$
$41$	−3.20090	−0.499897	−0.249948	+	0.968259i	$0.580414\pi$
$42$	9.00946	1.39019
$43$	10.1621	1.54971	0.774853	−	0.632141i	$-0.217824\pi$
$43$	10.1621	1.54971	0.774853	+	0.632141i	$0.217824\pi$
$44$	0.674478	0.101681
$45$	−1.38926	−0.207098
$46$	−6.33501	−0.934046
$47$	−4.93079	−0.719229	−0.359615	−	0.933101i	$-0.617092\pi$
$47$	−4.93079	−0.719229	−0.359615	+	0.933101i	$0.617092\pi$
$48$	−2.77089	−0.399944
$49$	3.57204	0.510292
$50$	4.91180	0.694633
$51$	−9.97630	−1.39696
$52$	5.33914	0.740406
$53$	12.7912	1.75701	0.878503	−	0.477737i	$-0.158543\pi$
$53$	12.7912	1.75701	0.878503	+	0.477737i	$0.158543\pi$
$54$	4.64911	0.632664
$55$	−0.200311	−0.0270099
$56$	−3.25147	−0.434496
$57$	21.1559	2.80216
$58$	−0.590947	−0.0775951
$59$	7.47516	0.973183	0.486592	−	0.873630i	$-0.338240\pi$
$59$	7.47516	0.973183	0.486592	+	0.873630i	$0.338240\pi$
$60$	0.822918	0.106238
$61$	12.4722	1.59691	0.798454	−	0.602056i	$-0.205652\pi$
$61$	12.4722	1.59691	0.798454	+	0.602056i	$0.205652\pi$
$62$	−5.79006	−0.735338
$63$	15.2098	1.91626
$64$	1.00000	0.125000
$65$	−1.58565	−0.196676
$66$	1.86890	0.230046
$67$	9.40104	1.14852	0.574260	−	0.818673i	$-0.305290\pi$
$67$	9.40104	1.14852	0.574260	+	0.818673i	$0.305290\pi$
$68$	3.60039	0.436612
$69$	−17.5536	−2.11321
$70$	0.965642	0.115416
$71$	−10.0176	−1.18887	−0.594436	−	0.804143i	$-0.702624\pi$
$71$	−10.0176	−1.18887	−0.594436	+	0.804143i	$0.702624\pi$
$72$	−4.67784	−0.551289
$73$	5.22712	0.611788	0.305894	−	0.952066i	$-0.401045\pi$
$73$	5.22712	0.611788	0.305894	+	0.952066i	$0.401045\pi$
$74$	−1.12363	−0.130619
$75$	13.6101	1.57155
$76$	−7.63503	−0.875798
$77$	2.19304	0.249920
$78$	14.7942	1.67511
$79$	12.8617	1.44706	0.723528	−	0.690295i	$-0.242519\pi$
$79$	12.8617	1.44706	0.723528	+	0.690295i	$0.242519\pi$
$80$	−0.296987	−0.0332041
$81$	−1.15133	−0.127925
$82$	3.20090	0.353481
$83$	−5.16135	−0.566532	−0.283266	−	0.959041i	$-0.591418\pi$
$83$	−5.16135	−0.566532	−0.283266	+	0.959041i	$0.591418\pi$
$84$	−9.00946	−0.983013
$85$	−1.06927	−0.115978
$86$	−10.1621	−1.09581
$87$	−1.63745	−0.175553
$88$	−0.674478	−0.0718996
$89$	3.61180	0.382850	0.191425	−	0.981507i	$-0.438689\pi$
$89$	3.61180	0.382850	0.191425	+	0.981507i	$0.438689\pi$
$90$	1.38926	0.146440
$91$	17.3601	1.81983
$92$	6.33501	0.660470
$93$	−16.0436	−1.66365
$94$	4.93079	0.508572
$95$	2.26750	0.232641
$96$	2.77089	0.282803
$97$	−1.81646	−0.184433	−0.0922167	−	0.995739i	$-0.529395\pi$
$97$	−1.81646	−0.184433	−0.0922167	+	0.995739i	$0.529395\pi$
$98$	−3.57204	−0.360831
$99$	3.15510	0.317099
$100$	−4.91180	−0.491180
$101$	−11.9352	−1.18760	−0.593798	−	0.804614i	$-0.702372\pi$
$101$	−11.9352	−1.18760	−0.593798	+	0.804614i	$0.702372\pi$
$102$	9.97630	0.987801
$103$	−0.986194	−0.0971725	−0.0485863	−	0.998819i	$-0.515472\pi$
$103$	−0.986194	−0.0971725	−0.0485863	+	0.998819i	$0.515472\pi$
$104$	−5.33914	−0.523546
$105$	2.67569	0.261121
$106$	−12.7912	−1.24239
$107$	−12.6710	−1.22495	−0.612474	−	0.790491i	$-0.709826\pi$
$107$	−12.6710	−1.22495	−0.612474	+	0.790491i	$0.709826\pi$
$108$	−4.64911	−0.447361
$109$	16.8706	1.61591	0.807957	−	0.589242i	$-0.200573\pi$
$109$	16.8706	1.61591	0.807957	+	0.589242i	$0.200573\pi$
$110$	0.200311	0.0190989
$111$	−3.11346	−0.295516
$112$	3.25147	0.307235
$113$	5.49667	0.517083	0.258542	−	0.966000i	$-0.416758\pi$
$113$	5.49667	0.517083	0.258542	+	0.966000i	$0.416758\pi$
$114$	−21.1559	−1.98143
$115$	−1.88141	−0.175443
$116$	0.590947	0.0548680
$117$	24.9757	2.30900
$118$	−7.47516	−0.688144
$119$	11.7066	1.07314
$120$	−0.822918	−0.0751218
$121$	−10.5451	−0.958644
$122$	−12.4722	−1.12918
$123$	8.86935	0.799723
$124$	5.79006	0.519962
$125$	2.94367	0.263290
$126$	−15.2098	−1.35500
$127$	−5.41414	−0.480427	−0.240214	−	0.970720i	$-0.577217\pi$
$127$	−5.41414	−0.480427	−0.240214	+	0.970720i	$0.577217\pi$
$128$	−1.00000	−0.0883883
$129$	−28.1581	−2.47918
$130$	1.58565	0.139071
$131$	4.11823	0.359812	0.179906	−	0.983684i	$-0.442421\pi$
$131$	4.11823	0.359812	0.179906	+	0.983684i	$0.442421\pi$
$132$	−1.86890	−0.162667
$133$	−24.8251	−2.15261
$134$	−9.40104	−0.812126
$135$	1.38072	0.118834
$136$	−3.60039	−0.308731
$137$	3.15223	0.269313	0.134657	−	0.990892i	$-0.457007\pi$
$137$	3.15223	0.269313	0.134657	+	0.990892i	$0.457007\pi$
$138$	17.5536	1.49426
$139$	−19.4814	−1.65239	−0.826194	−	0.563385i	$-0.809499\pi$
$139$	−19.4814	−1.65239	−0.826194	+	0.563385i	$0.809499\pi$
$140$	−0.965642	−0.0816117
$141$	13.6627	1.15061
$142$	10.0176	0.840659
$143$	3.60113	0.301142
$144$	4.67784	0.389820
$145$	−0.175503	−0.0145747
$146$	−5.22712	−0.432600
$147$	−9.89774	−0.816352
$148$	1.12363	0.0923618
$149$	7.02678	0.575656	0.287828	−	0.957682i	$-0.407067\pi$
$149$	7.02678	0.575656	0.287828	+	0.957682i	$0.407067\pi$
$150$	−13.6101	−1.11126
$151$	−15.5417	−1.26477	−0.632384	−	0.774655i	$-0.717924\pi$
$151$	−15.5417	−1.26477	−0.632384	+	0.774655i	$0.717924\pi$
$152$	7.63503	0.619283
$153$	16.8421	1.36160
$154$	−2.19304	−0.176720
$155$	−1.71957	−0.138119
$156$	−14.7942	−1.18448
$157$	5.35775	0.427595	0.213798	−	0.976878i	$-0.431417\pi$
$157$	5.35775	0.427595	0.213798	+	0.976878i	$0.431417\pi$
$158$	−12.8617	−1.02322
$159$	−35.4430	−2.81081
$160$	0.296987	0.0234789
$161$	20.5981	1.62336
$162$	1.15133	0.0904569
$163$	5.04775	0.395370	0.197685	−	0.980266i	$-0.436658\pi$
$163$	5.04775	0.395370	0.197685	+	0.980266i	$0.436658\pi$
$164$	−3.20090	−0.249948
$165$	0.555040	0.0432098
$166$	5.16135	0.400598
$167$	9.43569	0.730156	0.365078	−	0.930977i	$-0.381042\pi$
$167$	9.43569	0.730156	0.365078	+	0.930977i	$0.381042\pi$
$168$	9.00946	0.695095
$169$	15.5065	1.19280
$170$	1.06927	0.0820092
$171$	−35.7155	−2.73123
$172$	10.1621	0.774853
$173$	0.0136163	0.00103523	0.000517615	−	1.00000i	$-0.499835\pi$
$173$	0.0136163	0.00103523	0.000517615		1.00000i	$0.499835\pi$
$174$	1.63745	0.124135
$175$	−15.9706	−1.20726
$176$	0.674478	0.0508407
$177$	−20.7129	−1.55687
$178$	−3.61180	−0.270716
$179$	−13.6570	−1.02077	−0.510386	−	0.859945i	$-0.670498\pi$
$179$	−13.6570	−1.02077	−0.510386	+	0.859945i	$0.670498\pi$
$180$	−1.38926	−0.103549
$181$	16.7673	1.24630	0.623151	−	0.782101i	$-0.285852\pi$
$181$	16.7673	1.24630	0.623151	+	0.782101i	$0.285852\pi$
$182$	−17.3601	−1.28681
$183$	−34.5592	−2.55469
$184$	−6.33501	−0.467023
$185$	−0.333703	−0.0245343
$186$	16.0436	1.17638
$187$	2.42839	0.177581
$188$	−4.93079	−0.359615
$189$	−15.1164	−1.09956
$190$	−2.26750	−0.164502
$191$	18.8363	1.36295	0.681473	−	0.731843i	$-0.261340\pi$
$191$	18.8363	1.36295	0.681473	+	0.731843i	$0.261340\pi$
$192$	−2.77089	−0.199972
$193$	−3.57532	−0.257357	−0.128679	−	0.991686i	$-0.541074\pi$
$193$	−3.57532	−0.257357	−0.128679	+	0.991686i	$0.541074\pi$
$194$	1.81646	0.130414
$195$	4.39368	0.314638
$196$	3.57204	0.255146
$197$	23.1058	1.64622	0.823109	−	0.567883i	$-0.192237\pi$
$197$	23.1058	1.64622	0.823109	+	0.567883i	$0.192237\pi$
$198$	−3.15510	−0.224223
$199$	−21.9637	−1.55696	−0.778481	−	0.627668i	$-0.784009\pi$
$199$	−21.9637	−1.55696	−0.778481	+	0.627668i	$0.784009\pi$
$200$	4.91180	0.347317
$201$	−26.0493	−1.83737
$202$	11.9352	0.839757
$203$	1.92144	0.134859
$204$	−9.97630	−0.698481
$205$	0.950625	0.0663945
$206$	0.986194	0.0687114
$207$	29.6341	2.05972
$208$	5.33914	0.370203
$209$	−5.14966	−0.356209
$210$	−2.67569	−0.184640
$211$	7.47248	0.514427	0.257213	−	0.966355i	$-0.417196\pi$
$211$	7.47248	0.514427	0.257213	+	0.966355i	$0.417196\pi$
$212$	12.7912	0.878503
$213$	27.7577	1.90193
$214$	12.6710	0.866169
$215$	−3.01801	−0.205827
$216$	4.64911	0.316332
$217$	18.8262	1.27800
$218$	−16.8706	−1.14262
$219$	−14.4838	−0.978724
$220$	−0.200311	−0.0135050
$221$	19.2230	1.29308
$222$	3.11346	0.208962
$223$	−14.2241	−0.952514	−0.476257	−	0.879306i	$-0.658007\pi$
$223$	−14.2241	−0.952514	−0.476257	+	0.879306i	$0.658007\pi$
$224$	−3.25147	−0.217248
$225$	−22.9766	−1.53177
$226$	−5.49667	−0.365633
$227$	−6.85411	−0.454923	−0.227462	−	0.973787i	$-0.573043\pi$
$227$	−6.85411	−0.454923	−0.227462	+	0.973787i	$0.573043\pi$
$228$	21.1559	1.40108
$229$	−14.9392	−0.987208	−0.493604	−	0.869687i	$-0.664321\pi$
$229$	−14.9392	−0.987208	−0.493604	+	0.869687i	$0.664321\pi$
$230$	1.88141	0.124057
$231$	−6.07668	−0.399816
$232$	−0.590947	−0.0387975
$233$	−18.1697	−1.19033	−0.595167	−	0.803602i	$-0.702914\pi$
$233$	−18.1697	−1.19033	−0.595167	+	0.803602i	$0.702914\pi$
$234$	−24.9757	−1.63271
$235$	1.46438	0.0955255
$236$	7.47516	0.486592
$237$	−35.6384	−2.31496
$238$	−11.7066	−0.758824
$239$	−19.1142	−1.23639	−0.618197	−	0.786023i	$-0.712137\pi$
$239$	−19.1142	−1.23639	−0.618197	+	0.786023i	$0.712137\pi$
$240$	0.822918	0.0531191
$241$	−17.3029	−1.11458	−0.557290	−	0.830318i	$-0.688159\pi$
$241$	−17.3029	−1.11458	−0.557290	+	0.830318i	$0.688159\pi$
$242$	10.5451	0.677863
$243$	17.1376	1.09937
$244$	12.4722	0.798454
$245$	−1.06085	−0.0677751
$246$	−8.86935	−0.565489
$247$	−40.7645	−2.59379
$248$	−5.79006	−0.367669
$249$	14.3015	0.906323
$250$	−2.94367	−0.186174
$251$	−12.4657	−0.786831	−0.393415	−	0.919361i	$-0.628707\pi$
$251$	−12.4657	−0.786831	−0.393415	+	0.919361i	$0.628707\pi$
$252$	15.2098	0.958130
$253$	4.27282	0.268630
$254$	5.41414	0.339713
$255$	2.96283	0.185539
$256$	1.00000	0.0625000
$257$	−8.38969	−0.523334	−0.261667	−	0.965158i	$-0.584272\pi$
$257$	−8.38969	−0.523334	−0.261667	+	0.965158i	$0.584272\pi$
$258$	28.1581	1.75305
$259$	3.65345	0.227014
$260$	−1.58565	−0.0983381
$261$	2.76435	0.171109
$262$	−4.11823	−0.254425
$263$	−14.6815	−0.905300	−0.452650	−	0.891688i	$-0.649521\pi$
$263$	−14.6815	−0.905300	−0.452650	+	0.891688i	$0.649521\pi$
$264$	1.86890	0.115023
$265$	−3.79881	−0.233359
$266$	24.8251	1.52212
$267$	−10.0079	−0.612474
$268$	9.40104	0.574260
$269$	2.90076	0.176862	0.0884312	−	0.996082i	$-0.471815\pi$
$269$	2.90076	0.176862	0.0884312	+	0.996082i	$0.471815\pi$
$270$	−1.38072	−0.0840282
$271$	19.8916	1.20833	0.604165	−	0.796860i	$-0.293507\pi$
$271$	19.8916	1.20833	0.604165	+	0.796860i	$0.293507\pi$
$272$	3.60039	0.218306
$273$	−48.1028	−2.91132
$274$	−3.15223	−0.190433
$275$	−3.31290	−0.199775
$276$	−17.5536	−1.05660
$277$	23.2560	1.39732	0.698659	−	0.715455i	$-0.253780\pi$
$277$	23.2560	1.39732	0.698659	+	0.715455i	$0.253780\pi$
$278$	19.4814	1.16842
$279$	27.0850	1.62153
$280$	0.965642	0.0577082
$281$	−8.67427	−0.517464	−0.258732	−	0.965949i	$-0.583305\pi$
$281$	−8.67427	−0.517464	−0.258732	+	0.965949i	$0.583305\pi$
$282$	−13.6627	−0.813601
$283$	18.8124	1.11828	0.559141	−	0.829073i	$-0.311131\pi$
$283$	18.8124	1.11828	0.559141	+	0.829073i	$0.311131\pi$
$284$	−10.0176	−0.594436
$285$	−6.28300	−0.372173
$286$	−3.60113	−0.212940
$287$	−10.4076	−0.614343
$288$	−4.67784	−0.275644
$289$	−4.03717	−0.237481
$290$	0.175503	0.0103059
$291$	5.03321	0.295052
$292$	5.22712	0.305894
$293$	−17.8752	−1.04428	−0.522140	−	0.852860i	$-0.674866\pi$
$293$	−17.8752	−1.04428	−0.522140	+	0.852860i	$0.674866\pi$
$294$	9.89774	0.577248
$295$	−2.22002	−0.129255
$296$	−1.12363	−0.0653097
$297$	−3.13572	−0.181953
$298$	−7.02678	−0.407050
$299$	33.8235	1.95606
$300$	13.6101	0.785777
$301$	33.0418	1.90450
$302$	15.5417	0.894326
$303$	33.0711	1.89989
$304$	−7.63503	−0.437899
$305$	−3.70409	−0.212096
$306$	−16.8421	−0.962797
$307$	−31.6108	−1.80412	−0.902061	−	0.431608i	$-0.857946\pi$
$307$	−31.6108	−1.80412	−0.902061	+	0.431608i	$0.857946\pi$
$308$	2.19304	0.124960
$309$	2.73264	0.155454
$310$	1.71957	0.0976650
$311$	0.134596	0.00763226	0.00381613	−	0.999993i	$-0.498785\pi$
$311$	0.134596	0.00763226	0.00381613	+	0.999993i	$0.498785\pi$
$312$	14.7942	0.837556
$313$	10.9459	0.618701	0.309350	−	0.950948i	$-0.399888\pi$
$313$	10.9459	0.618701	0.309350	+	0.950948i	$0.399888\pi$
$314$	−5.35775	−0.302355
$315$	−4.51712	−0.254511
$316$	12.8617	0.723528
$317$	−16.9101	−0.949768	−0.474884	−	0.880048i	$-0.657510\pi$
$317$	−16.9101	−0.949768	−0.474884	+	0.880048i	$0.657510\pi$
$318$	35.4430	1.98755
$319$	0.398580	0.0223162
$320$	−0.296987	−0.0166021
$321$	35.1099	1.95964
$322$	−20.5981	−1.14789
$323$	−27.4891	−1.52954
$324$	−1.15133	−0.0639627
$325$	−26.2248	−1.45469
$326$	−5.04775	−0.279569
$327$	−46.7467	−2.58510
$328$	3.20090	0.176740
$329$	−16.0323	−0.883889
$330$	−0.555040	−0.0305539
$331$	6.73426	0.370148	0.185074	−	0.982725i	$-0.440747\pi$
$331$	6.73426	0.370148	0.185074	+	0.982725i	$0.440747\pi$
$332$	−5.16135	−0.283266
$333$	5.25616	0.288036
$334$	−9.43569	−0.516298
$335$	−2.79198	−0.152542
$336$	−9.00946	−0.491507
$337$	−2.91281	−0.158671	−0.0793353	−	0.996848i	$-0.525280\pi$
$337$	−2.91281	−0.158671	−0.0793353	+	0.996848i	$0.525280\pi$
$338$	−15.5065	−0.843440
$339$	−15.2307	−0.827217
$340$	−1.06927	−0.0579892
$341$	3.90526	0.211482
$342$	35.7155	1.93127
$343$	−11.1459	−0.601822
$344$	−10.1621	−0.547904
$345$	5.21319	0.280669
$346$	−0.0136163	−0.000732018 0
$347$	−2.89303	−0.155306	−0.0776529	−	0.996980i	$-0.524743\pi$
$347$	−2.89303	−0.155306	−0.0776529	+	0.996980i	$0.524743\pi$
$348$	−1.63745	−0.0877765
$349$	22.0236	1.17890	0.589449	−	0.807806i	$-0.299345\pi$
$349$	22.0236	1.17890	0.589449	+	0.807806i	$0.299345\pi$
$350$	15.9706	0.853662
$351$	−24.8223	−1.32492
$352$	−0.674478	−0.0359498
$353$	−20.7846	−1.10625	−0.553127	−	0.833097i	$-0.686565\pi$
$353$	−20.7846	−1.10625	−0.553127	+	0.833097i	$0.686565\pi$
$354$	20.7129	1.10088
$355$	2.97509	0.157902
$356$	3.61180	0.191425
$357$	−32.4376	−1.71678
$358$	13.6570	0.721795
$359$	8.94474	0.472085	0.236043	−	0.971743i	$-0.424150\pi$
$359$	8.94474	0.472085	0.236043	+	0.971743i	$0.424150\pi$
$360$	1.38926	0.0732202
$361$	39.2937	2.06809
$362$	−16.7673	−0.881269
$363$	29.2193	1.53361
$364$	17.3601	0.909914
$365$	−1.55239	−0.0812555
$366$	34.5592	1.80644
$367$	7.62217	0.397874	0.198937	−	0.980012i	$-0.436251\pi$
$367$	7.62217	0.397874	0.198937	+	0.980012i	$0.436251\pi$
$368$	6.33501	0.330235
$369$	−14.9733	−0.779479
$370$	0.333703	0.0173484
$371$	41.5901	2.15925
$372$	−16.0436	−0.831823
$373$	7.48398	0.387506	0.193753	−	0.981050i	$-0.437934\pi$
$373$	7.48398	0.387506	0.193753	+	0.981050i	$0.437934\pi$
$374$	−2.42839	−0.125569
$375$	−8.15659	−0.421205
$376$	4.93079	0.254286
$377$	3.15515	0.162498
$378$	15.1164	0.777506
$379$	31.8451	1.63577	0.817886	−	0.575380i	$-0.195146\pi$
$379$	31.8451	1.63577	0.817886	+	0.575380i	$0.195146\pi$
$380$	2.26750	0.116320
$381$	15.0020	0.768575
$382$	−18.8363	−0.963748
$383$	12.7476	0.651371	0.325685	−	0.945478i	$-0.394405\pi$
$383$	12.7476	0.651371	0.325685	+	0.945478i	$0.394405\pi$
$384$	2.77089	0.141401
$385$	−0.651304	−0.0331935
$386$	3.57532	0.181979
$387$	47.5367	2.41643
$388$	−1.81646	−0.0922167
$389$	10.5628	0.535556	0.267778	−	0.963481i	$-0.413711\pi$
$389$	10.5628	0.535556	0.267778	+	0.963481i	$0.413711\pi$
$390$	−4.39368	−0.222482
$391$	22.8085	1.15348
$392$	−3.57204	−0.180415
$393$	−11.4112	−0.575617
$394$	−23.1058	−1.16405
$395$	−3.81976	−0.192193
$396$	3.15510	0.158550
$397$	−1.57044	−0.0788181	−0.0394090	−	0.999223i	$-0.512548\pi$
$397$	−1.57044	−0.0788181	−0.0394090	+	0.999223i	$0.512548\pi$
$398$	21.9637	1.10094
$399$	68.7876	3.44369
$400$	−4.91180	−0.245590
$401$	−2.49966	−0.124827	−0.0624136	−	0.998050i	$-0.519880\pi$
$401$	−2.49966	−0.124827	−0.0624136	+	0.998050i	$0.519880\pi$
$402$	26.0493	1.29922
$403$	30.9139	1.53993
$404$	−11.9352	−0.593798
$405$	0.341929	0.0169906
$406$	−1.92144	−0.0953597
$407$	0.757864	0.0375659
$408$	9.97630	0.493900
$409$	35.3447	1.74768	0.873842	−	0.486210i	$-0.161621\pi$
$409$	35.3447	1.74768	0.873842	+	0.486210i	$0.161621\pi$
$410$	−0.950625	−0.0469480
$411$	−8.73449	−0.430841
$412$	−0.986194	−0.0485863
$413$	24.3052	1.19598
$414$	−29.6341	−1.45644
$415$	1.53285	0.0752447
$416$	−5.33914	−0.261773
$417$	53.9808	2.64345
$418$	5.14966	0.251878
$419$	1.27566	0.0623203	0.0311602	−	0.999514i	$-0.490080\pi$
$419$	1.27566	0.0623203	0.0311602	+	0.999514i	$0.490080\pi$
$420$	2.67569	0.130560
$421$	−0.444157	−0.0216469	−0.0108234	−	0.999941i	$-0.503445\pi$
$421$	−0.444157	−0.0216469	−0.0108234	+	0.999941i	$0.503445\pi$
$422$	−7.47248	−0.363755
$423$	−23.0654	−1.12148
$424$	−12.7912	−0.621195
$425$	−17.6844	−0.857820
$426$	−27.7577	−1.34486
$427$	40.5531	1.96250
$428$	−12.6710	−0.612474
$429$	−9.97835	−0.481759
$430$	3.01801	0.145541
$431$	−37.7338	−1.81757	−0.908786	−	0.417263i	$-0.862990\pi$
$431$	−37.7338	−1.81757	−0.908786	+	0.417263i	$0.862990\pi$
$432$	−4.64911	−0.223681
$433$	−6.40596	−0.307851	−0.153925	−	0.988082i	$-0.549192\pi$
$433$	−6.40596	−0.307851	−0.153925	+	0.988082i	$0.549192\pi$
$434$	−18.8262	−0.903686
$435$	0.486300	0.0233163
$436$	16.8706	0.807957
$437$	−48.3680	−2.31375
$438$	14.4838	0.692062
$439$	14.6944	0.701323	0.350662	−	0.936502i	$-0.385957\pi$
$439$	14.6944	0.701323	0.350662	+	0.936502i	$0.385957\pi$
$440$	0.200311	0.00954945
$441$	16.7094	0.795688
$442$	−19.2230	−0.914346
$443$	22.7465	1.08072	0.540359	−	0.841434i	$-0.318288\pi$
$443$	22.7465	1.08072	0.540359	+	0.841434i	$0.318288\pi$
$444$	−3.11346	−0.147758
$445$	−1.07266	−0.0508488
$446$	14.2241	0.673529
$447$	−19.4704	−0.920921
$448$	3.25147	0.153617
$449$	−26.8467	−1.26697	−0.633487	−	0.773754i	$-0.718377\pi$
$449$	−26.8467	−1.26697	−0.633487	+	0.773754i	$0.718377\pi$
$450$	22.9766	1.08313
$451$	−2.15894	−0.101660
$452$	5.49667	0.258542
$453$	43.0645	2.02335
$454$	6.85411	0.321679
$455$	−5.15570	−0.241703
$456$	−21.1559	−0.990714
$457$	2.80748	0.131328	0.0656641	−	0.997842i	$-0.479083\pi$
$457$	2.80748	0.131328	0.0656641	+	0.997842i	$0.479083\pi$
$458$	14.9392	0.698061
$459$	−16.7386	−0.781293
$460$	−1.88141	−0.0877213
$461$	−7.97270	−0.371326	−0.185663	−	0.982614i	$-0.559443\pi$
$461$	−7.97270	−0.371326	−0.185663	+	0.982614i	$0.559443\pi$
$462$	6.07668	0.282713
$463$	−13.1629	−0.611734	−0.305867	−	0.952074i	$-0.598946\pi$
$463$	−13.1629	−0.611734	−0.305867	+	0.952074i	$0.598946\pi$
$464$	0.590947	0.0274340
$465$	4.76474	0.220960
$466$	18.1697	0.841693
$467$	−15.3812	−0.711759	−0.355879	−	0.934532i	$-0.615819\pi$
$467$	−15.3812	−0.711759	−0.355879	+	0.934532i	$0.615819\pi$
$468$	24.9757	1.15450
$469$	30.5672	1.41146
$470$	−1.46438	−0.0675467
$471$	−14.8458	−0.684056
$472$	−7.47516	−0.344072
$473$	6.85412	0.315153
$474$	35.6384	1.63693
$475$	37.5018	1.72070
$476$	11.7066	0.536569
$477$	59.8352	2.73966
$478$	19.1142	0.874263
$479$	11.6366	0.531688	0.265844	−	0.964016i	$-0.414349\pi$
$479$	11.6366	0.531688	0.265844	+	0.964016i	$0.414349\pi$
$480$	−0.822918	−0.0375609
$481$	5.99922	0.273541
$482$	17.3029	0.788127
$483$	−57.0750	−2.59700
$484$	−10.5451	−0.479322
$485$	0.539464	0.0244958
$486$	−17.1376	−0.777375
$487$	2.53502	0.114873	0.0574363	−	0.998349i	$-0.481707\pi$
$487$	2.53502	0.114873	0.0574363	+	0.998349i	$0.481707\pi$
$488$	−12.4722	−0.564592
$489$	−13.9868	−0.632503
$490$	1.06085	0.0479243
$491$	−31.6783	−1.42962	−0.714811	−	0.699318i	$-0.753487\pi$
$491$	−31.6783	−1.42962	−0.714811	+	0.699318i	$0.753487\pi$
$492$	8.86935	0.399861
$493$	2.12764	0.0958241
$494$	40.7645	1.83408
$495$	−0.937022	−0.0421160
$496$	5.79006	0.259981
$497$	−32.5719	−1.46105
$498$	−14.3015	−0.640867
$499$	−26.7437	−1.19721	−0.598606	−	0.801044i	$-0.704278\pi$
$499$	−26.7437	−1.19721	−0.598606	+	0.801044i	$0.704278\pi$
$500$	2.94367	0.131645
$501$	−26.1453	−1.16809
$502$	12.4657	0.556373
$503$	16.1532	0.720235	0.360118	−	0.932907i	$-0.382737\pi$
$503$	16.1532	0.720235	0.360118	+	0.932907i	$0.382737\pi$
$504$	−15.2098	−0.677500
$505$	3.54459	0.157732
$506$	−4.27282	−0.189950
$507$	−42.9667	−1.90822
$508$	−5.41414	−0.240214
$509$	10.9675	0.486126	0.243063	−	0.970010i	$-0.421848\pi$
$509$	10.9675	0.486126	0.243063	+	0.970010i	$0.421848\pi$
$510$	−2.96283	−0.131196
$511$	16.9958	0.751851
$512$	−1.00000	−0.0441942
$513$	35.4961	1.56719
$514$	8.38969	0.370053
$515$	0.292886	0.0129061
$516$	−28.1581	−1.23959
$517$	−3.32571	−0.146264
$518$	−3.65345	−0.160523
$519$	−0.0377294	−0.00165614
$520$	1.58565	0.0695355
$521$	−33.8160	−1.48151	−0.740753	−	0.671778i	$-0.765531\pi$
$521$	−33.8160	−1.48151	−0.740753	+	0.671778i	$0.765531\pi$
$522$	−2.76435	−0.120992
$523$	−32.4017	−1.41683	−0.708413	−	0.705798i	$-0.750588\pi$
$523$	−32.4017	−1.41683	−0.708413	+	0.705798i	$0.750588\pi$
$524$	4.11823	0.179906
$525$	44.2527	1.93135
$526$	14.6815	0.640144
$527$	20.8465	0.908087
$528$	−1.86890	−0.0813336
$529$	17.1323	0.744883
$530$	3.79881	0.165010
$531$	34.9676	1.51747
$532$	−24.8251	−1.07630
$533$	−17.0901	−0.740253
$534$	10.0079	0.433084
$535$	3.76311	0.162693
$536$	−9.40104	−0.406063
$537$	37.8421	1.63301
$538$	−2.90076	−0.125061
$539$	2.40926	0.103774
$540$	1.38072	0.0594169
$541$	19.2561	0.827886	0.413943	−	0.910303i	$-0.364151\pi$
$541$	19.2561	0.827886	0.413943	+	0.910303i	$0.364151\pi$
$542$	−19.8916	−0.854418
$543$	−46.4603	−1.99380
$544$	−3.60039	−0.154366
$545$	−5.01035	−0.214620
$546$	48.1028	2.05861
$547$	−12.3210	−0.526810	−0.263405	−	0.964685i	$-0.584845\pi$
$547$	−12.3210	−0.526810	−0.263405	+	0.964685i	$0.584845\pi$
$548$	3.15223	0.134657
$549$	58.3432	2.49003
$550$	3.31290	0.141262
$551$	−4.51190	−0.192213
$552$	17.5536	0.747131
$553$	41.8195	1.77834
$554$	−23.2560	−0.988053
$555$	0.924655	0.0392494
$556$	−19.4814	−0.826194
$557$	18.2457	0.773095	0.386548	−	0.922269i	$-0.373668\pi$
$557$	18.2457	0.773095	0.386548	+	0.922269i	$0.373668\pi$
$558$	−27.0850	−1.14660
$559$	54.2570	2.29482
$560$	−0.965642	−0.0408058
$561$	−6.72879	−0.284090
$562$	8.67427	0.365902
$563$	27.7892	1.17118	0.585588	−	0.810609i	$-0.300864\pi$
$563$	27.7892	1.17118	0.585588	+	0.810609i	$0.300864\pi$
$564$	13.6627	0.575303
$565$	−1.63244	−0.0686772
$566$	−18.8124	−0.790744
$567$	−3.74351	−0.157213
$568$	10.0176	0.420329
$569$	28.9443	1.21341	0.606705	−	0.794927i	$-0.292491\pi$
$569$	28.9443	1.21341	0.606705	+	0.794927i	$0.292491\pi$
$570$	6.28300	0.263166
$571$	19.9191	0.833587	0.416793	−	0.909001i	$-0.363154\pi$
$571$	19.9191	0.833587	0.416793	+	0.909001i	$0.363154\pi$
$572$	3.60113	0.150571
$573$	−52.1933	−2.18041
$574$	10.4076	0.434406
$575$	−31.1163	−1.29764
$576$	4.67784	0.194910
$577$	26.5869	1.10683	0.553415	−	0.832906i	$-0.313325\pi$
$577$	26.5869	1.10683	0.553415	+	0.832906i	$0.313325\pi$
$578$	4.03717	0.167924
$579$	9.90683	0.411714
$580$	−0.175503	−0.00728737
$581$	−16.7820	−0.696233
$582$	−5.03321	−0.208633
$583$	8.62737	0.357309
$584$	−5.22712	−0.216300
$585$	−7.41744	−0.306673
$586$	17.8752	0.738418
$587$	−27.3915	−1.13057	−0.565283	−	0.824897i	$-0.691233\pi$
$587$	−27.3915	−1.13057	−0.565283	+	0.824897i	$0.691233\pi$
$588$	−9.89774	−0.408176
$589$	−44.2073	−1.82153
$590$	2.22002	0.0913969
$591$	−64.0236	−2.63358
$592$	1.12363	0.0461809
$593$	−23.7239	−0.974224	−0.487112	−	0.873340i	$-0.661950\pi$
$593$	−23.7239	−0.974224	−0.487112	+	0.873340i	$0.661950\pi$
$594$	3.13572	0.128660
$595$	−3.47669	−0.142530
$596$	7.02678	0.287828
$597$	60.8589	2.49079
$598$	−33.8235	−1.38315
$599$	−18.9332	−0.773590	−0.386795	−	0.922166i	$-0.626418\pi$
$599$	−18.9332	−0.773590	−0.386795	+	0.922166i	$0.626418\pi$
$600$	−13.6101	−0.555628
$601$	35.4047	1.44419	0.722094	−	0.691795i	$-0.243180\pi$
$601$	35.4047	1.44419	0.722094	+	0.691795i	$0.243180\pi$
$602$	−33.0418	−1.34668
$603$	43.9766	1.79086
$604$	−15.5417	−0.632384
$605$	3.13175	0.127324
$606$	−33.0711	−1.34342
$607$	−27.7545	−1.12652	−0.563259	−	0.826280i	$-0.690453\pi$
$607$	−27.7545	−1.12652	−0.563259	+	0.826280i	$0.690453\pi$
$608$	7.63503	0.309642
$609$	−5.32411	−0.215744
$610$	3.70409	0.149974
$611$	−26.3262	−1.06504
$612$	16.8421	0.680800
$613$	26.5986	1.07431	0.537154	−	0.843484i	$-0.319500\pi$
$613$	26.5986	1.07431	0.537154	+	0.843484i	$0.319500\pi$
$614$	31.6108	1.27571
$615$	−2.63408	−0.106216
$616$	−2.19304	−0.0883602
$617$	36.6577	1.47578	0.737891	−	0.674920i	$-0.235822\pi$
$617$	36.6577	1.47578	0.737891	+	0.674920i	$0.235822\pi$
$618$	−2.73264	−0.109923
$619$	5.73621	0.230558	0.115279	−	0.993333i	$-0.463224\pi$
$619$	5.73621	0.230558	0.115279	+	0.993333i	$0.463224\pi$
$620$	−1.71957	−0.0690596
$621$	−29.4522	−1.18187
$622$	−0.134596	−0.00539682
$623$	11.7436	0.470499
$624$	−14.7942	−0.592242
$625$	23.6848	0.947391
$626$	−10.9459	−0.437487
$627$	14.2692	0.569855
$628$	5.35775	0.213798
$629$	4.04551	0.161305
$630$	4.51712	0.179966
$631$	−25.9242	−1.03203	−0.516013	−	0.856581i	$-0.672584\pi$
$631$	−25.9242	−1.03203	−0.516013	+	0.856581i	$0.672584\pi$
$632$	−12.8617	−0.511612
$633$	−20.7054	−0.822967
$634$	16.9101	0.671588
$635$	1.60793	0.0638086
$636$	−35.4430	−1.40541
$637$	19.0716	0.755646
$638$	−0.398580	−0.0157799
$639$	−46.8608	−1.85378
$640$	0.296987	0.0117394
$641$	26.2888	1.03834	0.519172	−	0.854670i	$-0.326240\pi$
$641$	26.2888	1.03834	0.519172	+	0.854670i	$0.326240\pi$
$642$	−35.1099	−1.38568
$643$	35.7801	1.41103	0.705514	−	0.708696i	$-0.250716\pi$
$643$	35.7801	1.41103	0.705514	+	0.708696i	$0.250716\pi$
$644$	20.5981	0.811678
$645$	8.36258	0.329276
$646$	27.4891	1.08155
$647$	−10.7741	−0.423574	−0.211787	−	0.977316i	$-0.567928\pi$
$647$	−10.7741	−0.423574	−0.211787	+	0.977316i	$0.567928\pi$
$648$	1.15133	0.0452285
$649$	5.04183	0.197909
$650$	26.2248	1.02862
$651$	−52.1653	−2.04452
$652$	5.04775	0.197685
$653$	0.739825	0.0289516	0.0144758	−	0.999895i	$-0.495392\pi$
$653$	0.739825	0.0289516	0.0144758	+	0.999895i	$0.495392\pi$
$654$	46.7467	1.82794
$655$	−1.22306	−0.0477889
$656$	−3.20090	−0.124974
$657$	24.4516	0.953949
$658$	16.0323	0.625004
$659$	19.5754	0.762549	0.381275	−	0.924462i	$-0.375485\pi$
$659$	19.5754	0.762549	0.381275	+	0.924462i	$0.375485\pi$
$660$	0.555040	0.0216049
$661$	8.85065	0.344250	0.172125	−	0.985075i	$-0.444937\pi$
$661$	8.85065	0.344250	0.172125	+	0.985075i	$0.444937\pi$
$662$	−6.73426	−0.261734
$663$	−53.2649	−2.06864
$664$	5.16135	0.200299
$665$	7.37271	0.285901
$666$	−5.25616	−0.203672
$667$	3.74365	0.144955
$668$	9.43569	0.365078
$669$	39.4134	1.52381
$670$	2.79198	0.107864
$671$	8.41225	0.324751
$672$	9.00946	0.347548
$673$	37.6368	1.45079	0.725395	−	0.688333i	$-0.241657\pi$
$673$	37.6368	1.45079	0.725395	+	0.688333i	$0.241657\pi$
$674$	2.91281	0.112197
$675$	22.8355	0.878939
$676$	15.5065	0.596402
$677$	27.1750	1.04442	0.522210	−	0.852817i	$-0.325108\pi$
$677$	27.1750	1.04442	0.522210	+	0.852817i	$0.325108\pi$
$678$	15.2307	0.584931
$679$	−5.90616	−0.226657
$680$	1.06927	0.0410046
$681$	18.9920	0.727775
$682$	−3.90526	−0.149540
$683$	−11.5995	−0.443843	−0.221921	−	0.975065i	$-0.571233\pi$
$683$	−11.5995	−0.443843	−0.221921	+	0.975065i	$0.571233\pi$
$684$	−35.7155	−1.36562
$685$	−0.936170	−0.0357692
$686$	11.1459	0.425552
$687$	41.3948	1.57931
$688$	10.1621	0.387427
$689$	68.2940	2.60179
$690$	−5.21319	−0.198463
$691$	33.5640	1.27683	0.638417	−	0.769691i	$-0.279590\pi$
$691$	33.5640	1.27683	0.638417	+	0.769691i	$0.279590\pi$
$692$	0.0136163	0.000517615 0
$693$	10.2587	0.389696
$694$	2.89303	0.109818
$695$	5.78571	0.219464
$696$	1.63745	0.0620673
$697$	−11.5245	−0.436522
$698$	−22.0236	−0.833606
$699$	50.3462	1.90427
$700$	−15.9706	−0.603630
$701$	−3.44443	−0.130094	−0.0650471	−	0.997882i	$-0.520720\pi$
$701$	−3.44443	−0.130094	−0.0650471	+	0.997882i	$0.520720\pi$
$702$	24.8223	0.936857
$703$	−8.57896	−0.323561
$704$	0.674478	0.0254203
$705$	−4.05763	−0.152819
$706$	20.7846	0.782239
$707$	−38.8069	−1.45948
$708$	−20.7129	−0.778437
$709$	−21.4704	−0.806337	−0.403168	−	0.915126i	$-0.632091\pi$
$709$	−21.4704	−0.806337	−0.403168	+	0.915126i	$0.632091\pi$
$710$	−2.97509	−0.111653
$711$	60.1651	2.25637
$712$	−3.61180	−0.135358
$713$	36.6800	1.37368
$714$	32.4376	1.21395
$715$	−1.06949	−0.0399966
$716$	−13.6570	−0.510386
$717$	52.9633	1.97795
$718$	−8.94474	−0.333815
$719$	−9.37325	−0.349563	−0.174782	−	0.984607i	$-0.555922\pi$
$719$	−9.37325	−0.349563	−0.174782	+	0.984607i	$0.555922\pi$
$720$	−1.38926	−0.0517745
$721$	−3.20658	−0.119419
$722$	−39.2937	−1.46236
$723$	47.9445	1.78308
$724$	16.7673	0.623151
$725$	−2.90261	−0.107800
$726$	−29.2193	−1.08443
$727$	−7.02365	−0.260493	−0.130246	−	0.991482i	$-0.541577\pi$
$727$	−7.02365	−0.260493	−0.130246	+	0.991482i	$0.541577\pi$
$728$	−17.3601	−0.643406
$729$	−44.0323	−1.63083
$730$	1.55239	0.0574563
$731$	36.5876	1.35324
$732$	−34.5592	−1.27735
$733$	−17.7555	−0.655815	−0.327907	−	0.944710i	$-0.606343\pi$
$733$	−17.7555	−0.655815	−0.327907	+	0.944710i	$0.606343\pi$
$734$	−7.62217	−0.281339
$735$	2.93950	0.108425
$736$	−6.33501	−0.233511
$737$	6.34079	0.233566
$738$	14.9733	0.551175
$739$	2.80219	0.103080	0.0515400	−	0.998671i	$-0.483587\pi$
$739$	2.80219	0.103080	0.0515400	+	0.998671i	$0.483587\pi$
$740$	−0.333703	−0.0122672
$741$	112.954	4.14947
$742$	−41.5901	−1.52682
$743$	−44.0698	−1.61676	−0.808382	−	0.588658i	$-0.799656\pi$
$743$	−44.0698	−1.61676	−0.808382	+	0.588658i	$0.799656\pi$
$744$	16.0436	0.588188
$745$	−2.08686	−0.0764566
$746$	−7.48398	−0.274008
$747$	−24.1440	−0.883382
$748$	2.42839	0.0887906
$749$	−41.1992	−1.50539
$750$	8.15659	0.297837
$751$	6.54192	0.238718	0.119359	−	0.992851i	$-0.461916\pi$
$751$	6.54192	0.238718	0.119359	+	0.992851i	$0.461916\pi$
$752$	−4.93079	−0.179807
$753$	34.5412	1.25875
$754$	−3.15515	−0.114904
$755$	4.61569	0.167982
$756$	−15.1164	−0.549780
$757$	−13.4845	−0.490104	−0.245052	−	0.969510i	$-0.578805\pi$
$757$	−13.4845	−0.490104	−0.245052	+	0.969510i	$0.578805\pi$
$758$	−31.8451	−1.15667
$759$	−11.8395	−0.429747
$760$	−2.26750	−0.0822510
$761$	35.8214	1.29852	0.649262	−	0.760565i	$-0.275078\pi$
$761$	35.8214	1.29852	0.649262	+	0.760565i	$0.275078\pi$
$762$	−15.0020	−0.543465
$763$	54.8543	1.98586
$764$	18.8363	0.681473
$765$	−5.00187	−0.180843
$766$	−12.7476	−0.460589
$767$	39.9110	1.44110
$768$	−2.77089	−0.0999859
$769$	−24.4214	−0.880657	−0.440328	−	0.897837i	$-0.645138\pi$
$769$	−24.4214	−0.880657	−0.440328	+	0.897837i	$0.645138\pi$
$770$	0.651304	0.0234714
$771$	23.2469	0.837217
$772$	−3.57532	−0.128679
$773$	20.4243	0.734611	0.367306	−	0.930100i	$-0.380280\pi$
$773$	20.4243	0.734611	0.367306	+	0.930100i	$0.380280\pi$
$774$	−47.5367	−1.70867
$775$	−28.4396	−1.02158
$776$	1.81646	0.0652071
$777$	−10.1233	−0.363172
$778$	−10.5628	−0.378695
$779$	24.4390	0.875618
$780$	4.39368	0.157319
$781$	−6.75665	−0.241772
$782$	−22.8085	−0.815631
$783$	−2.74738	−0.0981833
$784$	3.57204	0.127573
$785$	−1.59118	−0.0567917
$786$	11.4112	0.407023
$787$	19.7089	0.702546	0.351273	−	0.936273i	$-0.385749\pi$
$787$	19.7089	0.702546	0.351273	+	0.936273i	$0.385749\pi$
$788$	23.1058	0.823109
$789$	40.6808	1.44828
$790$	3.81976	0.135901
$791$	17.8723	0.635464
$792$	−3.15510	−0.112112
$793$	66.5911	2.36472
$794$	1.57044	0.0557328
$795$	10.5261	0.373322
$796$	−21.9637	−0.778481
$797$	−49.4692	−1.75229	−0.876144	−	0.482049i	$-0.839893\pi$
$797$	−49.4692	−1.75229	−0.876144	+	0.482049i	$0.839893\pi$
$798$	−68.7876	−2.43505
$799$	−17.7528	−0.628048
$800$	4.91180	0.173658
$801$	16.8954	0.596970
$802$	2.49966	0.0882662
$803$	3.52558	0.124415
$804$	−26.0493	−0.918687
$805$	−6.11735	−0.215608
$806$	−30.9139	−1.08890
$807$	−8.03769	−0.282940
$808$	11.9352	0.419878
$809$	−2.34250	−0.0823578	−0.0411789	−	0.999152i	$-0.513111\pi$
$809$	−2.34250	−0.0823578	−0.0411789	+	0.999152i	$0.513111\pi$
$810$	−0.341929	−0.0120142
$811$	−12.4923	−0.438664	−0.219332	−	0.975650i	$-0.570388\pi$
$811$	−12.4923	−0.438664	−0.219332	+	0.975650i	$0.570388\pi$
$812$	1.92144	0.0674295
$813$	−55.1175	−1.93305
$814$	−0.757864	−0.0265631
$815$	−1.49911	−0.0525116
$816$	−9.97630	−0.349240
$817$	−77.5880	−2.71446
$818$	−35.3447	−1.23580
$819$	81.2076	2.83762
$820$	0.950625	0.0331973
$821$	−10.4597	−0.365047	−0.182523	−	0.983202i	$-0.558427\pi$
$821$	−10.4597	−0.365047	−0.182523	+	0.983202i	$0.558427\pi$
$822$	8.73449	0.304650
$823$	18.1164	0.631500	0.315750	−	0.948842i	$-0.397744\pi$
$823$	18.1164	0.631500	0.315750	+	0.948842i	$0.397744\pi$
$824$	0.986194	0.0343557
$825$	9.17968	0.319596
$826$	−24.3052	−0.845688
$827$	20.0702	0.697910	0.348955	−	0.937139i	$-0.386537\pi$
$827$	20.0702	0.697910	0.348955	+	0.937139i	$0.386537\pi$
$828$	29.6341	1.02986
$829$	46.2573	1.60658	0.803291	−	0.595587i	$-0.203081\pi$
$829$	46.2573	1.60658	0.803291	+	0.595587i	$0.203081\pi$
$830$	−1.53285	−0.0532061
$831$	−64.4399	−2.23540
$832$	5.33914	0.185102
$833$	12.8608	0.445599
$834$	−53.9808	−1.86920
$835$	−2.80227	−0.0969767
$836$	−5.14966	−0.178105
$837$	−26.9186	−0.930444
$838$	−1.27566	−0.0440671
$839$	30.0539	1.03758	0.518789	−	0.854903i	$-0.326383\pi$
$839$	30.0539	1.03758	0.518789	+	0.854903i	$0.326383\pi$
$840$	−2.67569	−0.0923201
$841$	−28.6508	−0.987958
$842$	0.444157	0.0153067
$843$	24.0355	0.827825
$844$	7.47248	0.257213
$845$	−4.60521	−0.158424
$846$	23.0654	0.793006
$847$	−34.2870	−1.17811
$848$	12.7912	0.439251
$849$	−52.1271	−1.78900
$850$	17.6844	0.606570
$851$	7.11820	0.244009
$852$	27.7577	0.950963
$853$	−22.2093	−0.760431	−0.380215	−	0.924898i	$-0.624150\pi$
$853$	−22.2093	−0.760431	−0.380215	+	0.924898i	$0.624150\pi$
$854$	−40.5531	−1.38770
$855$	10.6070	0.362752
$856$	12.6710	0.433085
$857$	29.0433	0.992102	0.496051	−	0.868293i	$-0.334783\pi$
$857$	29.0433	0.992102	0.496051	+	0.868293i	$0.334783\pi$
$858$	9.97835	0.340655
$859$	47.0264	1.60452	0.802260	−	0.596975i	$-0.203631\pi$
$859$	47.0264	1.60452	0.802260	+	0.596975i	$0.203631\pi$
$860$	−3.01801	−0.102913
$861$	28.8384	0.982811
$862$	37.7338	1.28522
$863$	−29.7243	−1.01183	−0.505914	−	0.862584i	$-0.668845\pi$
$863$	−29.7243	−1.01183	−0.505914	+	0.862584i	$0.668845\pi$
$864$	4.64911	0.158166
$865$	−0.00404387	−0.000137496 0
$866$	6.40596	0.217683
$867$	11.1866	0.379915
$868$	18.8262	0.639002
$869$	8.67494	0.294277
$870$	−0.486300	−0.0164871
$871$	50.1935	1.70074
$872$	−16.8706	−0.571312
$873$	−8.49710	−0.287583
$874$	48.3680	1.63607
$875$	9.57125	0.323567
$876$	−14.4838	−0.489362
$877$	50.3201	1.69919	0.849595	−	0.527436i	$-0.176846\pi$
$877$	50.3201	1.69919	0.849595	+	0.527436i	$0.176846\pi$
$878$	−14.6944	−0.495910
$879$	49.5302	1.67061
$880$	−0.200311	−0.00675248
$881$	28.2691	0.952410	0.476205	−	0.879334i	$-0.342012\pi$
$881$	28.2691	0.952410	0.476205	+	0.879334i	$0.342012\pi$
$882$	−16.7094	−0.562636
$883$	−19.0064	−0.639618	−0.319809	−	0.947482i	$-0.603619\pi$
$883$	−19.0064	−0.639618	−0.319809	+	0.947482i	$0.603619\pi$
$884$	19.2230	0.646540
$885$	6.15144	0.206779
$886$	−22.7465	−0.764184
$887$	−0.680667	−0.0228546	−0.0114273	−	0.999935i	$-0.503637\pi$
$887$	−0.680667	−0.0228546	−0.0114273	+	0.999935i	$0.503637\pi$
$888$	3.11346	0.104481
$889$	−17.6039	−0.590416
$890$	1.07266	0.0359555
$891$	−0.776546	−0.0260153
$892$	−14.2241	−0.476257
$893$	37.6467	1.25980
$894$	19.4704	0.651189
$895$	4.05595	0.135575
$896$	−3.25147	−0.108624
$897$	−93.7213	−3.12926
$898$	26.8467	0.895885
$899$	3.42161	0.114117
$900$	−22.9766	−0.765887
$901$	46.0533	1.53426
$902$	2.15894	0.0718848
$903$	−91.5551	−3.04676
$904$	−5.49667	−0.182817
$905$	−4.97966	−0.165529
$906$	−43.0645	−1.43072
$907$	−42.0355	−1.39577	−0.697883	−	0.716212i	$-0.745874\pi$
$907$	−42.0355	−1.39577	−0.697883	+	0.716212i	$0.745874\pi$
$908$	−6.85411	−0.227462
$909$	−55.8309	−1.85179
$910$	5.15570	0.170910
$911$	19.3085	0.639719	0.319859	−	0.947465i	$-0.396364\pi$
$911$	19.3085	0.639719	0.319859	+	0.947465i	$0.396364\pi$
$912$	21.1559	0.700540
$913$	−3.48122	−0.115211
$914$	−2.80748	−0.0928630
$915$	10.2636	0.339305
$916$	−14.9392	−0.493604
$917$	13.3903	0.442187
$918$	16.7386	0.552457
$919$	−11.9345	−0.393682	−0.196841	−	0.980435i	$-0.563068\pi$
$919$	−11.9345	−0.393682	−0.196841	+	0.980435i	$0.563068\pi$
$920$	1.88141	0.0620283
$921$	87.5901	2.88619
$922$	7.97270	0.262567
$923$	−53.4854	−1.76049
$924$	−6.07668	−0.199908
$925$	−5.51905	−0.181465
$926$	13.1629	0.432561
$927$	−4.61326	−0.151519
$928$	−0.590947	−0.0193988
$929$	43.4879	1.42679	0.713396	−	0.700761i	$-0.247156\pi$
$929$	43.4879	1.42679	0.713396	+	0.700761i	$0.247156\pi$
$930$	−4.76474	−0.156242
$931$	−27.2727	−0.893825
$932$	−18.1697	−0.595167
$933$	−0.372952	−0.0122099
$934$	15.3812	0.503289
$935$	−0.721198	−0.0235857
$936$	−24.9757	−0.816355
$937$	−46.7300	−1.52660	−0.763301	−	0.646042i	$-0.776423\pi$
$937$	−46.7300	−1.52660	−0.763301	+	0.646042i	$0.776423\pi$
$938$	−30.5672	−0.998054
$939$	−30.3300	−0.989782
$940$	1.46438	0.0477627
$941$	−44.2990	−1.44411	−0.722053	−	0.691838i	$-0.756801\pi$
$941$	−44.2990	−1.44411	−0.722053	+	0.691838i	$0.756801\pi$
$942$	14.8458	0.483701
$943$	−20.2777	−0.660334
$944$	7.47516	0.243296
$945$	4.48938	0.146040
$946$	−6.85412	−0.222847
$947$	54.9454	1.78548	0.892742	−	0.450567i	$-0.148778\pi$
$947$	54.9454	1.78548	0.892742	+	0.450567i	$0.148778\pi$
$948$	−35.6384	−1.15748
$949$	27.9084	0.905943
$950$	−37.5018	−1.21672
$951$	46.8562	1.51942
$952$	−11.7066	−0.379412
$953$	−55.1652	−1.78698	−0.893488	−	0.449086i	$-0.851750\pi$
$953$	−55.1652	−1.78698	−0.893488	+	0.449086i	$0.851750\pi$
$954$	−59.8352	−1.93723
$955$	−5.59412	−0.181022
$956$	−19.1142	−0.618197
$957$	−1.10442	−0.0357009
$958$	−11.6366	−0.375960
$959$	10.2494	0.330970
$960$	0.822918	0.0265596
$961$	2.52475	0.0814434
$962$	−5.99922	−0.193423
$963$	−59.2728	−1.91004
$964$	−17.3029	−0.557290
$965$	1.06182	0.0341813
$966$	57.0750	1.83636
$967$	5.56288	0.178890	0.0894451	−	0.995992i	$-0.471491\pi$
$967$	5.56288	0.178890	0.0894451	+	0.995992i	$0.471491\pi$
$968$	10.5451	0.338932
$969$	76.1694	2.44691
$970$	−0.539464	−0.0173211
$971$	−14.2000	−0.455699	−0.227850	−	0.973696i	$-0.573169\pi$
$971$	−14.2000	−0.455699	−0.227850	+	0.973696i	$0.573169\pi$
$972$	17.1376	0.549687
$973$	−63.3431	−2.03069
$974$	−2.53502	−0.0812272
$975$	72.6661	2.32718
$976$	12.4722	0.399227
$977$	−5.20340	−0.166472	−0.0832358	−	0.996530i	$-0.526525\pi$
$977$	−5.20340	−0.166472	−0.0832358	+	0.996530i	$0.526525\pi$
$978$	13.9868	0.447247
$979$	2.43608	0.0778574
$980$	−1.06085	−0.0338876
$981$	78.9181	2.51966
$982$	31.6783	1.01090
$983$	15.0024	0.478501	0.239251	−	0.970958i	$-0.423098\pi$
$983$	15.0024	0.478501	0.239251	+	0.970958i	$0.423098\pi$
$984$	−8.86935	−0.282745
$985$	−6.86211	−0.218645
$986$	−2.12764	−0.0677579
$987$	44.4238	1.41402
$988$	−40.7645	−1.29689
$989$	64.3770	2.04707
$990$	0.937022	0.0297805
$991$	−27.9647	−0.888327	−0.444163	−	0.895946i	$-0.646499\pi$
$991$	−27.9647	−0.888327	−0.444163	+	0.895946i	$0.646499\pi$
$992$	−5.79006	−0.183834
$993$	−18.6599	−0.592154
$994$	32.5719	1.03312
$995$	6.52291	0.206790
$996$	14.3015	0.453162
$997$	−3.48011	−0.110216	−0.0551081	−	0.998480i	$-0.517550\pi$
$997$	−3.48011	−0.110216	−0.0551081	+	0.998480i	$0.517550\pi$
$998$	26.7437	0.846556
$999$	−5.22389	−0.165276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.c.1.10	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.c.1.10	✓	92	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.77089 q^{3} +1.00000 q^{4} -0.296987 q^{5} +2.77089 q^{6} +3.25147 q^{7} -1.00000 q^{8} +4.67784 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.77089 q^{3} +1.00000 q^{4} -0.296987 q^{5} +2.77089 q^{6} +3.25147 q^{7} -1.00000 q^{8} +4.67784 q^{9} +0.296987 q^{10} +0.674478 q^{11} -2.77089 q^{12} +5.33914 q^{13} -3.25147 q^{14} +0.822918 q^{15} +1.00000 q^{16} +3.60039 q^{17} -4.67784 q^{18} -7.63503 q^{19} -0.296987 q^{20} -9.00946 q^{21} -0.674478 q^{22} +6.33501 q^{23} +2.77089 q^{24} -4.91180 q^{25} -5.33914 q^{26} -4.64911 q^{27} +3.25147 q^{28} +0.590947 q^{29} -0.822918 q^{30} +5.79006 q^{31} -1.00000 q^{32} -1.86890 q^{33} -3.60039 q^{34} -0.965642 q^{35} +4.67784 q^{36} +1.12363 q^{37} +7.63503 q^{38} -14.7942 q^{39} +0.296987 q^{40} -3.20090 q^{41} +9.00946 q^{42} +10.1621 q^{43} +0.674478 q^{44} -1.38926 q^{45} -6.33501 q^{46} -4.93079 q^{47} -2.77089 q^{48} +3.57204 q^{49} +4.91180 q^{50} -9.97630 q^{51} +5.33914 q^{52} +12.7912 q^{53} +4.64911 q^{54} -0.200311 q^{55} -3.25147 q^{56} +21.1559 q^{57} -0.590947 q^{58} +7.47516 q^{59} +0.822918 q^{60} +12.4722 q^{61} -5.79006 q^{62} +15.2098 q^{63} +1.00000 q^{64} -1.58565 q^{65} +1.86890 q^{66} +9.40104 q^{67} +3.60039 q^{68} -17.5536 q^{69} +0.965642 q^{70} -10.0176 q^{71} -4.67784 q^{72} +5.22712 q^{73} -1.12363 q^{74} +13.6101 q^{75} -7.63503 q^{76} +2.19304 q^{77} +14.7942 q^{78} +12.8617 q^{79} -0.296987 q^{80} -1.15133 q^{81} +3.20090 q^{82} -5.16135 q^{83} -9.00946 q^{84} -1.06927 q^{85} -10.1621 q^{86} -1.63745 q^{87} -0.674478 q^{88} +3.61180 q^{89} +1.38926 q^{90} +17.3601 q^{91} +6.33501 q^{92} -16.0436 q^{93} +4.93079 q^{94} +2.26750 q^{95} +2.77089 q^{96} -1.81646 q^{97} -3.57204 q^{98} +3.15510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * q^99

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