LMFDB - Embedded newform 8011.2.a.b.1.196

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, 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("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.196
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.416963 q^{2} -1.28032 q^{3} -1.82614 q^{4} +0.760612 q^{5} -0.533845 q^{6} +2.95772 q^{7} -1.59536 q^{8} -1.36078 q^{9} +O(q^{10})$	\(q+0.416963 q^{2} -1.28032 q^{3} -1.82614 q^{4} +0.760612 q^{5} -0.533845 q^{6} +2.95772 q^{7} -1.59536 q^{8} -1.36078 q^{9} +0.317147 q^{10} +3.80923 q^{11} +2.33804 q^{12} -6.86702 q^{13} +1.23326 q^{14} -0.973826 q^{15} +2.98708 q^{16} -4.66432 q^{17} -0.567396 q^{18} -3.37601 q^{19} -1.38899 q^{20} -3.78683 q^{21} +1.58831 q^{22} -8.23339 q^{23} +2.04257 q^{24} -4.42147 q^{25} -2.86329 q^{26} +5.58319 q^{27} -5.40122 q^{28} +9.25713 q^{29} -0.406049 q^{30} -4.37865 q^{31} +4.43622 q^{32} -4.87703 q^{33} -1.94485 q^{34} +2.24968 q^{35} +2.48498 q^{36} -1.21419 q^{37} -1.40767 q^{38} +8.79198 q^{39} -1.21345 q^{40} +0.582526 q^{41} -1.57897 q^{42} -7.77152 q^{43} -6.95620 q^{44} -1.03503 q^{45} -3.43302 q^{46} +2.95471 q^{47} -3.82442 q^{48} +1.74812 q^{49} -1.84359 q^{50} +5.97181 q^{51} +12.5402 q^{52} +2.62918 q^{53} +2.32798 q^{54} +2.89735 q^{55} -4.71863 q^{56} +4.32237 q^{57} +3.85988 q^{58} +14.4960 q^{59} +1.77834 q^{60} -11.3958 q^{61} -1.82573 q^{62} -4.02482 q^{63} -4.12442 q^{64} -5.22314 q^{65} -2.03354 q^{66} +13.4845 q^{67} +8.51771 q^{68} +10.5414 q^{69} +0.938032 q^{70} +1.97362 q^{71} +2.17094 q^{72} +15.2228 q^{73} -0.506273 q^{74} +5.66089 q^{75} +6.16508 q^{76} +11.2667 q^{77} +3.66593 q^{78} +8.29785 q^{79} +2.27201 q^{80} -3.06592 q^{81} +0.242891 q^{82} -14.9235 q^{83} +6.91529 q^{84} -3.54773 q^{85} -3.24043 q^{86} -11.8521 q^{87} -6.07709 q^{88} -11.1655 q^{89} -0.431568 q^{90} -20.3107 q^{91} +15.0353 q^{92} +5.60607 q^{93} +1.23201 q^{94} -2.56784 q^{95} -5.67977 q^{96} +16.4114 q^{97} +0.728899 q^{98} -5.18354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	0.416963	0.294837	0.147419	−	0.989074i	$-0.452904\pi$
$2$	0.416963	0.294837	0.147419	+	0.989074i	$0.452904\pi$
$3$	−1.28032	−0.739193	−0.369596	−	0.929192i	$-0.620504\pi$
$3$	−1.28032	−0.739193	−0.369596	+	0.929192i	$0.620504\pi$
$4$	−1.82614	−0.913071
$5$	0.760612	0.340156	0.170078	−	0.985431i	$-0.445598\pi$
$5$	0.760612	0.340156	0.170078	+	0.985431i	$0.445598\pi$
$6$	−0.533845	−0.217941
$7$	2.95772	1.11791	0.558957	−	0.829197i	$-0.311202\pi$
$7$	2.95772	1.11791	0.558957	+	0.829197i	$0.311202\pi$
$8$	−1.59536	−0.564044
$9$	−1.36078	−0.453594
$10$	0.317147	0.100291
$11$	3.80923	1.14853	0.574263	−	0.818671i	$-0.305288\pi$
$11$	3.80923	1.14853	0.574263	+	0.818671i	$0.305288\pi$
$12$	2.33804	0.674935
$13$	−6.86702	−1.90457	−0.952285	−	0.305211i	$-0.901273\pi$
$13$	−6.86702	−1.90457	−0.952285	+	0.305211i	$0.901273\pi$
$14$	1.23326	0.329602
$15$	−0.973826	−0.251441
$16$	2.98708	0.746770
$17$	−4.66432	−1.13126	−0.565632	−	0.824658i	$-0.691368\pi$
$17$	−4.66432	−1.13126	−0.565632	+	0.824658i	$0.691368\pi$
$18$	−0.567396	−0.133736
$19$	−3.37601	−0.774511	−0.387255	−	0.921973i	$-0.626577\pi$
$19$	−3.37601	−0.774511	−0.387255	+	0.921973i	$0.626577\pi$
$20$	−1.38899	−0.310587
$21$	−3.78683	−0.826354
$22$	1.58831	0.338628
$23$	−8.23339	−1.71678	−0.858390	−	0.512997i	$-0.828535\pi$
$23$	−8.23339	−1.71678	−0.858390	+	0.512997i	$0.828535\pi$
$24$	2.04257	0.416937
$25$	−4.42147	−0.884294
$26$	−2.86329	−0.561538
$27$	5.58319	1.07449
$28$	−5.40122	−1.02073
$29$	9.25713	1.71901	0.859503	−	0.511130i	$-0.170773\pi$
$29$	9.25713	1.71901	0.859503	+	0.511130i	$0.170773\pi$
$30$	−0.406049	−0.0741341
$31$	−4.37865	−0.786429	−0.393215	−	0.919447i	$-0.628637\pi$
$31$	−4.37865	−0.786429	−0.393215	+	0.919447i	$0.628637\pi$
$32$	4.43622	0.784220
$33$	−4.87703	−0.848983
$34$	−1.94485	−0.333538
$35$	2.24968	0.380265
$36$	2.48498	0.414164
$37$	−1.21419	−0.199612	−0.0998060	−	0.995007i	$-0.531822\pi$
$37$	−1.21419	−0.199612	−0.0998060	+	0.995007i	$0.531822\pi$
$38$	−1.40767	−0.228354
$39$	8.79198	1.40784
$40$	−1.21345	−0.191863
$41$	0.582526	0.0909752	0.0454876	−	0.998965i	$-0.485516\pi$
$41$	0.582526	0.0909752	0.0454876	+	0.998965i	$0.485516\pi$
$42$	−1.57897	−0.243640
$43$	−7.77152	−1.18514	−0.592572	−	0.805517i	$-0.701888\pi$
$43$	−7.77152	−1.18514	−0.592572	+	0.805517i	$0.701888\pi$
$44$	−6.95620	−1.04869
$45$	−1.03503	−0.154293
$46$	−3.43302	−0.506170
$47$	2.95471	0.430989	0.215495	−	0.976505i	$-0.430864\pi$
$47$	2.95471	0.430989	0.215495	+	0.976505i	$0.430864\pi$
$48$	−3.82442	−0.552007
$49$	1.74812	0.249731
$50$	−1.84359	−0.260723
$51$	5.97181	0.836221
$52$	12.5402	1.73901
$53$	2.62918	0.361145	0.180573	−	0.983562i	$-0.442205\pi$
$53$	2.62918	0.361145	0.180573	+	0.983562i	$0.442205\pi$
$54$	2.32798	0.316798
$55$	2.89735	0.390678
$56$	−4.71863	−0.630553
$57$	4.32237	0.572513
$58$	3.85988	0.506827
$59$	14.4960	1.88722	0.943611	−	0.331057i	$-0.107405\pi$
$59$	14.4960	1.88722	0.943611	+	0.331057i	$0.107405\pi$
$60$	1.77834	0.229583
$61$	−11.3958	−1.45908	−0.729539	−	0.683939i	$-0.760265\pi$
$61$	−11.3958	−1.45908	−0.729539	+	0.683939i	$0.760265\pi$
$62$	−1.82573	−0.231868
$63$	−4.02482	−0.507079
$64$	−4.12442	−0.515553
$65$	−5.22314	−0.647851
$66$	−2.03354	−0.250312
$67$	13.4845	1.64739	0.823697	−	0.567030i	$-0.191908\pi$
$67$	13.4845	1.64739	0.823697	+	0.567030i	$0.191908\pi$
$68$	8.51771	1.03292
$69$	10.5414	1.26903
$70$	0.938032	0.112116
$71$	1.97362	0.234225	0.117113	−	0.993119i	$-0.462636\pi$
$71$	1.97362	0.234225	0.117113	+	0.993119i	$0.462636\pi$
$72$	2.17094	0.255847
$73$	15.2228	1.78169	0.890847	−	0.454304i	$-0.150112\pi$
$73$	15.2228	1.78169	0.890847	+	0.454304i	$0.150112\pi$
$74$	−0.506273	−0.0588530
$75$	5.66089	0.653664
$76$	6.16508	0.707183
$77$	11.2667	1.28395
$78$	3.66593	0.415085
$79$	8.29785	0.933581	0.466791	−	0.884368i	$-0.345410\pi$
$79$	8.29785	0.933581	0.466791	+	0.884368i	$0.345410\pi$
$80$	2.27201	0.254018
$81$	−3.06592	−0.340658
$82$	0.242891	0.0268229
$83$	−14.9235	−1.63807	−0.819035	−	0.573743i	$-0.805491\pi$
$83$	−14.9235	−1.63807	−0.819035	+	0.573743i	$0.805491\pi$
$84$	6.91529	0.754520
$85$	−3.54773	−0.384806
$86$	−3.24043	−0.349425
$87$	−11.8521	−1.27068
$88$	−6.07709	−0.647820
$89$	−11.1655	−1.18354	−0.591769	−	0.806107i	$-0.701570\pi$
$89$	−11.1655	−1.18354	−0.591769	+	0.806107i	$0.701570\pi$
$90$	−0.431568	−0.0454912
$91$	−20.3107	−2.12914
$92$	15.0353	1.56754
$93$	5.60607	0.581323
$94$	1.23201	0.127072
$95$	−2.56784	−0.263454
$96$	−5.67977	−0.579689
$97$	16.4114	1.66633	0.833165	−	0.553024i	$-0.186526\pi$
$97$	16.4114	1.66633	0.833165	+	0.553024i	$0.186526\pi$
$98$	0.728899	0.0736300
$99$	−5.18354	−0.520965
$100$	8.07423	0.807423
$101$	−12.8132	−1.27496	−0.637480	−	0.770467i	$-0.720023\pi$
$101$	−12.8132	−1.27496	−0.637480	+	0.770467i	$0.720023\pi$
$102$	2.49002	0.246549
$103$	8.44565	0.832175	0.416087	−	0.909325i	$-0.363401\pi$
$103$	8.44565	0.832175	0.416087	+	0.909325i	$0.363401\pi$
$104$	10.9554	1.07426
$105$	−2.88031	−0.281089
$106$	1.09627	0.106479
$107$	−17.2144	−1.66418	−0.832088	−	0.554643i	$-0.812855\pi$
$107$	−17.2144	−1.66418	−0.832088	+	0.554643i	$0.812855\pi$
$108$	−10.1957	−0.981082
$109$	−13.0239	−1.24746	−0.623730	−	0.781640i	$-0.714384\pi$
$109$	−13.0239	−1.24746	−0.623730	+	0.781640i	$0.714384\pi$
$110$	1.20809	0.115186
$111$	1.55455	0.147552
$112$	8.83495	0.834824
$113$	−2.57007	−0.241772	−0.120886	−	0.992666i	$-0.538574\pi$
$113$	−2.57007	−0.241772	−0.120886	+	0.992666i	$0.538574\pi$
$114$	1.80227	0.168798
$115$	−6.26241	−0.583973
$116$	−16.9048	−1.56958
$117$	9.34453	0.863902
$118$	6.04430	0.556423
$119$	−13.7958	−1.26465
$120$	1.55360	0.141824
$121$	3.51026	0.319114
$122$	−4.75161	−0.430190
$123$	−0.745819	−0.0672482
$124$	7.99604	0.718066
$125$	−7.16608	−0.640954
$126$	−1.67820	−0.149506
$127$	4.06893	0.361059	0.180530	−	0.983570i	$-0.442219\pi$
$127$	4.06893	0.361059	0.180530	+	0.983570i	$0.442219\pi$
$128$	−10.5922	−0.936224
$129$	9.95002	0.876050
$130$	−2.17785	−0.191010
$131$	22.4197	1.95881	0.979407	−	0.201895i	$-0.0647100\pi$
$131$	22.4197	1.95881	0.979407	+	0.201895i	$0.0647100\pi$
$132$	8.90616	0.775182
$133$	−9.98531	−0.865836
$134$	5.62253	0.485713
$135$	4.24664	0.365493
$136$	7.44126	0.638082
$137$	−18.4285	−1.57445	−0.787225	−	0.616666i	$-0.788483\pi$
$137$	−18.4285	−1.57445	−0.787225	+	0.616666i	$0.788483\pi$
$138$	4.39536	0.374157
$139$	1.82576	0.154859	0.0774294	−	0.996998i	$-0.475329\pi$
$139$	1.82576	0.154859	0.0774294	+	0.996998i	$0.475329\pi$
$140$	−4.10823	−0.347209
$141$	−3.78298	−0.318584
$142$	0.822924	0.0690582
$143$	−26.1581	−2.18745
$144$	−4.06477	−0.338731
$145$	7.04109	0.584730
$146$	6.34734	0.525309
$147$	−2.23815	−0.184599
$148$	2.21729	0.182260
$149$	−5.75033	−0.471085	−0.235543	−	0.971864i	$-0.575687\pi$
$149$	−5.75033	−0.471085	−0.235543	+	0.971864i	$0.575687\pi$
$150$	2.36038	0.192724
$151$	16.2427	1.32181	0.660905	−	0.750469i	$-0.270173\pi$
$151$	16.2427	1.32181	0.660905	+	0.750469i	$0.270173\pi$
$152$	5.38595	0.436858
$153$	6.34712	0.513134
$154$	4.69777	0.378557
$155$	−3.33045	−0.267509
$156$	−16.0554	−1.28546
$157$	19.0025	1.51656	0.758281	−	0.651928i	$-0.226039\pi$
$157$	19.0025	1.51656	0.758281	+	0.651928i	$0.226039\pi$
$158$	3.45989	0.275254
$159$	−3.36618	−0.266956
$160$	3.37424	0.266757
$161$	−24.3521	−1.91921
$162$	−1.27837	−0.100439
$163$	9.20460	0.720960	0.360480	−	0.932767i	$-0.382613\pi$
$163$	9.20460	0.720960	0.360480	+	0.932767i	$0.382613\pi$
$164$	−1.06377	−0.0830668
$165$	−3.70953	−0.288786
$166$	−6.22255	−0.482964
$167$	1.81267	0.140269	0.0701344	−	0.997538i	$-0.477657\pi$
$167$	1.81267	0.140269	0.0701344	+	0.997538i	$0.477657\pi$
$168$	6.04135	0.466100
$169$	34.1560	2.62739
$170$	−1.47927	−0.113455
$171$	4.59402	0.351314
$172$	14.1919	1.08212
$173$	−10.8853	−0.827591	−0.413796	−	0.910370i	$-0.635797\pi$
$173$	−10.8853	−0.827591	−0.413796	+	0.910370i	$0.635797\pi$
$174$	−4.94188	−0.374643
$175$	−13.0775	−0.988564
$176$	11.3785	0.857685
$177$	−18.5595	−1.39502
$178$	−4.65559	−0.348951
$179$	−0.515577	−0.0385361	−0.0192680	−	0.999814i	$-0.506134\pi$
$179$	−0.515577	−0.0385361	−0.0192680	+	0.999814i	$0.506134\pi$
$180$	1.89011	0.140880
$181$	−3.89401	−0.289440	−0.144720	−	0.989473i	$-0.546228\pi$
$181$	−3.89401	−0.289440	−0.144720	+	0.989473i	$0.546228\pi$
$182$	−8.46882	−0.627751
$183$	14.5902	1.07854
$184$	13.1352	0.968340
$185$	−0.923529	−0.0678992
$186$	2.33752	0.171395
$187$	−17.7675	−1.29929
$188$	−5.39573	−0.393524
$189$	16.5135	1.20118
$190$	−1.07069	−0.0776761
$191$	17.7262	1.28262	0.641312	−	0.767281i	$-0.278391\pi$
$191$	17.7262	1.28262	0.641312	+	0.767281i	$0.278391\pi$
$192$	5.28058	0.381093
$193$	−21.0900	−1.51809	−0.759045	−	0.651038i	$-0.774334\pi$
$193$	−21.0900	−1.51809	−0.759045	+	0.651038i	$0.774334\pi$
$194$	6.84296	0.491296
$195$	6.68728	0.478886
$196$	−3.19231	−0.228022
$197$	4.37679	0.311833	0.155917	−	0.987770i	$-0.450167\pi$
$197$	4.37679	0.311833	0.155917	+	0.987770i	$0.450167\pi$
$198$	−2.16134	−0.153600
$199$	7.94392	0.563130	0.281565	−	0.959542i	$-0.409147\pi$
$199$	7.94392	0.563130	0.281565	+	0.959542i	$0.409147\pi$
$200$	7.05383	0.498781
$201$	−17.2645	−1.21774
$202$	−5.34262	−0.375906
$203$	27.3800	1.92170
$204$	−10.9054	−0.763530
$205$	0.443076	0.0309458
$206$	3.52152	0.245356
$207$	11.2039	0.778722
$208$	−20.5123	−1.42228
$209$	−12.8600	−0.889546
$210$	−1.20098	−0.0828755
$211$	8.41497	0.579310	0.289655	−	0.957131i	$-0.406459\pi$
$211$	8.41497	0.579310	0.289655	+	0.957131i	$0.406459\pi$
$212$	−4.80125	−0.329751
$213$	−2.52686	−0.173137
$214$	−7.17775	−0.490661
$215$	−5.91111	−0.403134
$216$	−8.90719	−0.606058
$217$	−12.9508	−0.879160
$218$	−5.43046	−0.367797
$219$	−19.4900	−1.31701
$220$	−5.29097	−0.356717
$221$	32.0300	2.15457
$222$	0.648191	0.0435037
$223$	17.3568	1.16230	0.581150	−	0.813796i	$-0.302603\pi$
$223$	17.3568	1.16230	0.581150	+	0.813796i	$0.302603\pi$
$224$	13.1211	0.876690
$225$	6.01666	0.401111
$226$	−1.07162	−0.0712834
$227$	20.9707	1.39187	0.695936	−	0.718104i	$-0.254990\pi$
$227$	20.9707	1.39187	0.695936	+	0.718104i	$0.254990\pi$
$228$	−7.89327	−0.522745
$229$	−17.1992	−1.13656	−0.568278	−	0.822837i	$-0.692390\pi$
$229$	−17.1992	−1.13656	−0.568278	+	0.822837i	$0.692390\pi$
$230$	−2.61119	−0.172177
$231$	−14.4249	−0.949089
$232$	−14.7684	−0.969596
$233$	−14.7395	−0.965616	−0.482808	−	0.875726i	$-0.660383\pi$
$233$	−14.7395	−0.965616	−0.482808	+	0.875726i	$0.660383\pi$
$234$	3.89632	0.254710
$235$	2.24739	0.146604
$236$	−26.4718	−1.72317
$237$	−10.6239	−0.690096
$238$	−5.75231	−0.372867
$239$	1.21580	0.0786438	0.0393219	−	0.999227i	$-0.487480\pi$
$239$	1.21580	0.0786438	0.0393219	+	0.999227i	$0.487480\pi$
$240$	−2.90890	−0.187768
$241$	−4.09176	−0.263574	−0.131787	−	0.991278i	$-0.542071\pi$
$241$	−4.09176	−0.263574	−0.131787	+	0.991278i	$0.542071\pi$
$242$	1.46365	0.0940867
$243$	−12.8242	−0.822674
$244$	20.8103	1.33224
$245$	1.32964	0.0849475
$246$	−0.310978	−0.0198273
$247$	23.1832	1.47511
$248$	6.98552	0.443581
$249$	19.1069	1.21085
$250$	−2.98799	−0.188977
$251$	−10.4095	−0.657041	−0.328521	−	0.944497i	$-0.606550\pi$
$251$	−10.4095	−0.657041	−0.328521	+	0.944497i	$0.606550\pi$
$252$	7.34989	0.462999
$253$	−31.3629	−1.97177
$254$	1.69659	0.106454
$255$	4.54223	0.284446
$256$	3.83231	0.239519
$257$	14.8592	0.926893	0.463447	−	0.886125i	$-0.346613\pi$
$257$	14.8592	0.926893	0.463447	+	0.886125i	$0.346613\pi$
$258$	4.14879	0.258292
$259$	−3.59124	−0.223149
$260$	9.53819	0.591534
$261$	−12.5969	−0.779732
$262$	9.34816	0.577531
$263$	−0.140178	−0.00864374	−0.00432187	−	0.999991i	$-0.501376\pi$
$263$	−0.140178	−0.00864374	−0.00432187	+	0.999991i	$0.501376\pi$
$264$	7.78062	0.478864
$265$	1.99978	0.122846
$266$	−4.16350	−0.255281
$267$	14.2954	0.874863
$268$	−24.6246	−1.50419
$269$	10.0595	0.613340	0.306670	−	0.951816i	$-0.400785\pi$
$269$	10.0595	0.613340	0.306670	+	0.951816i	$0.400785\pi$
$270$	1.77069	0.107761
$271$	−4.07683	−0.247650	−0.123825	−	0.992304i	$-0.539516\pi$
$271$	−4.07683	−0.247650	−0.123825	+	0.992304i	$0.539516\pi$
$272$	−13.9327	−0.844793
$273$	26.0042	1.57385
$274$	−7.68398	−0.464206
$275$	−16.8424	−1.01564
$276$	−19.2500	−1.15872
$277$	−9.15655	−0.550164	−0.275082	−	0.961421i	$-0.588705\pi$
$277$	−9.15655	−0.550164	−0.275082	+	0.961421i	$0.588705\pi$
$278$	0.761273	0.0456581
$279$	5.95840	0.356720
$280$	−3.58904	−0.214486
$281$	21.3715	1.27492	0.637459	−	0.770484i	$-0.279986\pi$
$281$	21.3715	1.27492	0.637459	+	0.770484i	$0.279986\pi$
$282$	−1.57736	−0.0939304
$283$	11.4211	0.678915	0.339457	−	0.940621i	$-0.389757\pi$
$283$	11.4211	0.678915	0.339457	+	0.940621i	$0.389757\pi$
$284$	−3.60410	−0.213864
$285$	3.28765	0.194744
$286$	−10.9069	−0.644941
$287$	1.72295	0.101702
$288$	−6.03673	−0.355718
$289$	4.75585	0.279756
$290$	2.93587	0.172400
$291$	−21.0119	−1.23174
$292$	−27.7990	−1.62681
$293$	−0.710062	−0.0414822	−0.0207411	−	0.999785i	$-0.506603\pi$
$293$	−0.710062	−0.0414822	−0.0207411	+	0.999785i	$0.506603\pi$
$294$	−0.933224	−0.0544267
$295$	11.0258	0.641950
$296$	1.93707	0.112590
$297$	21.2677	1.23408
$298$	−2.39767	−0.138893
$299$	56.5389	3.26973
$300$	−10.3376	−0.596841
$301$	−22.9860	−1.32489
$302$	6.77259	0.389719
$303$	16.4050	0.942442
$304$	−10.0844	−0.578381
$305$	−8.66775	−0.496314
$306$	2.64651	0.151291
$307$	19.7966	1.12985	0.564926	−	0.825142i	$-0.308905\pi$
$307$	19.7966	1.12985	0.564926	+	0.825142i	$0.308905\pi$
$308$	−20.5745	−1.17234
$309$	−10.8131	−0.615137
$310$	−1.38868	−0.0788714
$311$	28.6806	1.62633	0.813163	−	0.582036i	$-0.197744\pi$
$311$	28.6806	1.62633	0.813163	+	0.582036i	$0.197744\pi$
$312$	−14.0264	−0.794086
$313$	−19.9965	−1.13027	−0.565134	−	0.824999i	$-0.691176\pi$
$313$	−19.9965	−1.13027	−0.565134	+	0.824999i	$0.691176\pi$
$314$	7.92332	0.447139
$315$	−3.06132	−0.172486
$316$	−15.1531	−0.852426
$317$	10.4713	0.588128	0.294064	−	0.955786i	$-0.404992\pi$
$317$	10.4713	0.588128	0.294064	+	0.955786i	$0.404992\pi$
$318$	−1.40357	−0.0787085
$319$	35.2626	1.97433
$320$	−3.13708	−0.175368
$321$	22.0399	1.23015
$322$	−10.1539	−0.565855
$323$	15.7468	0.876175
$324$	5.59881	0.311045
$325$	30.3623	1.68420
$326$	3.83797	0.212566
$327$	16.6747	0.922113
$328$	−0.929337	−0.0513140
$329$	8.73922	0.481809
$330$	−1.54674	−0.0851450
$331$	29.4876	1.62079	0.810394	−	0.585885i	$-0.199253\pi$
$331$	29.4876	1.62079	0.810394	+	0.585885i	$0.199253\pi$
$332$	27.2525	1.49567
$333$	1.65225	0.0905429
$334$	0.755816	0.0413564
$335$	10.2565	0.560371
$336$	−11.3116	−0.617096
$337$	22.1339	1.20571	0.602856	−	0.797850i	$-0.294029\pi$
$337$	22.1339	1.20571	0.602856	+	0.797850i	$0.294029\pi$
$338$	14.2418	0.774651
$339$	3.29051	0.178716
$340$	6.47867	0.351355
$341$	−16.6793	−0.903235
$342$	1.91553	0.103580
$343$	−15.5336	−0.838736
$344$	12.3984	0.668474
$345$	8.01789	0.431669
$346$	−4.53875	−0.244005
$347$	9.19590	0.493662	0.246831	−	0.969059i	$-0.420611\pi$
$347$	9.19590	0.493662	0.246831	+	0.969059i	$0.420611\pi$
$348$	21.6436	1.16022
$349$	−14.0420	−0.751650	−0.375825	−	0.926691i	$-0.622641\pi$
$349$	−14.0420	−0.751650	−0.375825	+	0.926691i	$0.622641\pi$
$350$	−5.45282	−0.291465
$351$	−38.3399	−2.04643
$352$	16.8986	0.900698
$353$	−3.80827	−0.202694	−0.101347	−	0.994851i	$-0.532315\pi$
$353$	−3.80827	−0.202694	−0.101347	+	0.994851i	$0.532315\pi$
$354$	−7.73863	−0.411304
$355$	1.50116	0.0796730
$356$	20.3898	1.08066
$357$	17.6630	0.934823
$358$	−0.214976	−0.0113619
$359$	3.91486	0.206619	0.103309	−	0.994649i	$-0.467057\pi$
$359$	3.91486	0.206619	0.103309	+	0.994649i	$0.467057\pi$
$360$	1.65124	0.0870280
$361$	−7.60253	−0.400133
$362$	−1.62366	−0.0853375
$363$	−4.49425	−0.235887
$364$	37.0903	1.94406
$365$	11.5786	0.606054
$366$	6.08357	0.317993
$367$	−11.2267	−0.586030	−0.293015	−	0.956108i	$-0.594659\pi$
$367$	−11.2267	−0.586030	−0.293015	+	0.956108i	$0.594659\pi$
$368$	−24.5938	−1.28204
$369$	−0.792691	−0.0412658
$370$	−0.385077	−0.0200192
$371$	7.77637	0.403729
$372$	−10.2375	−0.530789
$373$	21.0739	1.09116	0.545582	−	0.838058i	$-0.316309\pi$
$373$	21.0739	1.09116	0.545582	+	0.838058i	$0.316309\pi$
$374$	−7.40837	−0.383078
$375$	9.17487	0.473788
$376$	−4.71383	−0.243097
$377$	−63.5690	−3.27397
$378$	6.88553	0.354153
$379$	17.0993	0.878333	0.439167	−	0.898406i	$-0.355274\pi$
$379$	17.0993	0.878333	0.439167	+	0.898406i	$0.355274\pi$
$380$	4.68923	0.240553
$381$	−5.20953	−0.266892
$382$	7.39116	0.378165
$383$	17.0944	0.873482	0.436741	−	0.899587i	$-0.356133\pi$
$383$	17.0944	0.873482	0.436741	+	0.899587i	$0.356133\pi$
$384$	13.5614	0.692050
$385$	8.56955	0.436745
$386$	−8.79374	−0.447589
$387$	10.5753	0.537575
$388$	−29.9696	−1.52148
$389$	16.4892	0.836036	0.418018	−	0.908439i	$-0.362725\pi$
$389$	16.4892	0.836036	0.418018	+	0.908439i	$0.362725\pi$
$390$	2.78835	0.141193
$391$	38.4031	1.94213
$392$	−2.78887	−0.140859
$393$	−28.7043	−1.44794
$394$	1.82496	0.0919401
$395$	6.31144	0.317563
$396$	9.46588	0.475678
$397$	−16.4577	−0.825990	−0.412995	−	0.910733i	$-0.635517\pi$
$397$	−16.4577	−0.825990	−0.412995	+	0.910733i	$0.635517\pi$
$398$	3.31232	0.166031
$399$	12.7844	0.640020
$400$	−13.2073	−0.660364
$401$	−24.1113	−1.20406	−0.602029	−	0.798474i	$-0.705641\pi$
$401$	−24.1113	−1.20406	−0.602029	+	0.798474i	$0.705641\pi$
$402$	−7.19864	−0.359035
$403$	30.0683	1.49781
$404$	23.3987	1.16413
$405$	−2.33198	−0.115877
$406$	11.4164	0.566589
$407$	−4.62514	−0.229260
$408$	−9.52718	−0.471666
$409$	18.4573	0.912653	0.456327	−	0.889812i	$-0.349165\pi$
$409$	18.4573	0.912653	0.456327	+	0.889812i	$0.349165\pi$
$410$	0.184746	0.00912396
$411$	23.5943	1.16382
$412$	−15.4230	−0.759835
$413$	42.8752	2.10975
$414$	4.67159	0.229596
$415$	−11.3510	−0.557199
$416$	−30.4636	−1.49360
$417$	−2.33755	−0.114471
$418$	−5.36215	−0.262271
$419$	−37.4726	−1.83065	−0.915327	−	0.402711i	$-0.868068\pi$
$419$	−37.4726	−1.83065	−0.915327	+	0.402711i	$0.868068\pi$
$420$	5.25985	0.256654
$421$	19.8504	0.967450	0.483725	−	0.875220i	$-0.339283\pi$
$421$	19.8504	0.967450	0.483725	+	0.875220i	$0.339283\pi$
$422$	3.50873	0.170802
$423$	−4.02072	−0.195494
$424$	−4.19448	−0.203702
$425$	20.6231	1.00037
$426$	−1.05361	−0.0510473
$427$	−33.7055	−1.63112
$428$	31.4359	1.51951
$429$	33.4907	1.61695
$430$	−2.46471	−0.118859
$431$	11.1254	0.535891	0.267946	−	0.963434i	$-0.413655\pi$
$431$	11.1254	0.535891	0.267946	+	0.963434i	$0.413655\pi$
$432$	16.6774	0.802394
$433$	31.2236	1.50051	0.750256	−	0.661148i	$-0.229930\pi$
$433$	31.2236	1.50051	0.750256	+	0.661148i	$0.229930\pi$
$434$	−5.40001	−0.259209
$435$	−9.01484	−0.432228
$436$	23.7834	1.13902
$437$	27.7960	1.32966
$438$	−8.12662	−0.388305
$439$	−0.709051	−0.0338411	−0.0169206	−	0.999857i	$-0.505386\pi$
$439$	−0.709051	−0.0338411	−0.0169206	+	0.999857i	$0.505386\pi$
$440$	−4.62231	−0.220360
$441$	−2.37881	−0.113277
$442$	13.3553	0.635247
$443$	−0.663358	−0.0315171	−0.0157585	−	0.999876i	$-0.505016\pi$
$443$	−0.663358	−0.0315171	−0.0157585	+	0.999876i	$0.505016\pi$
$444$	−2.83884	−0.134725
$445$	−8.49260	−0.402588
$446$	7.23715	0.342689
$447$	7.36226	0.348223
$448$	−12.1989	−0.576344
$449$	−16.1453	−0.761941	−0.380971	−	0.924587i	$-0.624410\pi$
$449$	−16.1453	−0.761941	−0.380971	+	0.924587i	$0.624410\pi$
$450$	2.50872	0.118262
$451$	2.21898	0.104487
$452$	4.69332	0.220755
$453$	−20.7958	−0.977072
$454$	8.74399	0.410376
$455$	−15.4486	−0.724241
$456$	−6.89574	−0.322922
$457$	32.7151	1.53035	0.765173	−	0.643824i	$-0.222653\pi$
$457$	32.7151	1.53035	0.765173	+	0.643824i	$0.222653\pi$
$458$	−7.17143	−0.335099
$459$	−26.0418	−1.21553
$460$	11.4361	0.533209
$461$	32.5814	1.51747	0.758734	−	0.651400i	$-0.225818\pi$
$461$	32.5814	1.51747	0.758734	+	0.651400i	$0.225818\pi$
$462$	−6.01465	−0.279827
$463$	−29.8371	−1.38665	−0.693325	−	0.720625i	$-0.743855\pi$
$463$	−29.8371	−1.38665	−0.693325	+	0.720625i	$0.743855\pi$
$464$	27.6518	1.28370
$465$	4.26405	0.197740
$466$	−6.14581	−0.284699
$467$	−35.6862	−1.65136	−0.825680	−	0.564139i	$-0.809208\pi$
$467$	−35.6862	−1.65136	−0.825680	+	0.564139i	$0.809208\pi$
$468$	−17.0644	−0.788804
$469$	39.8834	1.84164
$470$	0.937078	0.0432242
$471$	−24.3292	−1.12103
$472$	−23.1263	−1.06448
$473$	−29.6035	−1.36117
$474$	−4.42977	−0.203466
$475$	14.9269	0.684895
$476$	25.1930	1.15472
$477$	−3.57774	−0.163813
$478$	0.506945	0.0231871
$479$	1.42951	0.0653161	0.0326581	−	0.999467i	$-0.489603\pi$
$479$	1.42951	0.0653161	0.0326581	+	0.999467i	$0.489603\pi$
$480$	−4.32010	−0.197185
$481$	8.33789	0.380175
$482$	−1.70611	−0.0777113
$483$	31.1784	1.41867
$484$	−6.41023	−0.291374
$485$	12.4827	0.566812
$486$	−5.34722	−0.242555
$487$	11.1440	0.504982	0.252491	−	0.967599i	$-0.418750\pi$
$487$	11.1440	0.504982	0.252491	+	0.967599i	$0.418750\pi$
$488$	18.1803	0.822984
$489$	−11.7848	−0.532928
$490$	0.554410	0.0250457
$491$	−0.982726	−0.0443498	−0.0221749	−	0.999754i	$-0.507059\pi$
$491$	−0.982726	−0.0443498	−0.0221749	+	0.999754i	$0.507059\pi$
$492$	1.36197	0.0614024
$493$	−43.1782	−1.94465
$494$	9.66651	0.434917
$495$	−3.94266	−0.177209
$496$	−13.0794	−0.587282
$497$	5.83741	0.261843
$498$	7.96686	0.357003
$499$	−0.620340	−0.0277702	−0.0138851	−	0.999904i	$-0.504420\pi$
$499$	−0.620340	−0.0277702	−0.0138851	+	0.999904i	$0.504420\pi$
$500$	13.0863	0.585236
$501$	−2.32080	−0.103686
$502$	−4.34037	−0.193720
$503$	−3.22770	−0.143916	−0.0719581	−	0.997408i	$-0.522925\pi$
$503$	−3.22770	−0.143916	−0.0719581	+	0.997408i	$0.522925\pi$
$504$	6.42102	0.286015
$505$	−9.74587	−0.433686
$506$	−13.0772	−0.581350
$507$	−43.7306	−1.94214
$508$	−7.43045	−0.329673
$509$	−0.951735	−0.0421849	−0.0210925	−	0.999778i	$-0.506714\pi$
$509$	−0.951735	−0.0421849	−0.0210925	+	0.999778i	$0.506714\pi$
$510$	1.89394	0.0838651
$511$	45.0248	1.99178
$512$	22.7823	1.00684
$513$	−18.8489	−0.832201
$514$	6.19574	0.273282
$515$	6.42386	0.283069
$516$	−18.1702	−0.799896
$517$	11.2552	0.495003
$518$	−1.49741	−0.0657926
$519$	13.9366	0.611749
$520$	8.33278	0.365416
$521$	8.95807	0.392460	0.196230	−	0.980558i	$-0.437130\pi$
$521$	8.95807	0.392460	0.196230	+	0.980558i	$0.437130\pi$
$522$	−5.25246	−0.229894
$523$	35.3112	1.54405	0.772026	−	0.635591i	$-0.219243\pi$
$523$	35.3112	1.54405	0.772026	+	0.635591i	$0.219243\pi$
$524$	−40.9415	−1.78854
$525$	16.7433	0.730739
$526$	−0.0584490	−0.00254850
$527$	20.4234	0.889658
$528$	−14.5681	−0.633995
$529$	44.7887	1.94733
$530$	0.833834	0.0362194
$531$	−19.7259	−0.856033
$532$	18.2346	0.790570
$533$	−4.00022	−0.173269
$534$	5.96064	0.257942
$535$	−13.0935	−0.566079
$536$	−21.5126	−0.929203
$537$	0.660104	0.0284856
$538$	4.19444	0.180835
$539$	6.65899	0.286823
$540$	−7.75497	−0.333721
$541$	−17.4072	−0.748395	−0.374198	−	0.927349i	$-0.622082\pi$
$541$	−17.4072	−0.748395	−0.374198	+	0.927349i	$0.622082\pi$
$542$	−1.69989	−0.0730164
$543$	4.98558	0.213952
$544$	−20.6919	−0.887159
$545$	−9.90611	−0.424331
$546$	10.8428	0.464029
$547$	−22.1101	−0.945360	−0.472680	−	0.881234i	$-0.656713\pi$
$547$	−22.1101	−0.945360	−0.472680	+	0.881234i	$0.656713\pi$
$548$	33.6530	1.43758
$549$	15.5072	0.661829
$550$	−7.02265	−0.299447
$551$	−31.2522	−1.33139
$552$	−16.8173	−0.715790
$553$	24.5427	1.04366
$554$	−3.81794	−0.162209
$555$	1.18241	0.0501906
$556$	−3.33410	−0.141397
$557$	−30.5805	−1.29574	−0.647868	−	0.761753i	$-0.724339\pi$
$557$	−30.5805	−1.29574	−0.647868	+	0.761753i	$0.724339\pi$
$558$	2.48443	0.105174
$559$	53.3672	2.25719
$560$	6.71997	0.283970
$561$	22.7480	0.960423
$562$	8.91112	0.375893
$563$	8.39301	0.353723	0.176862	−	0.984236i	$-0.443405\pi$
$563$	8.39301	0.353723	0.176862	+	0.984236i	$0.443405\pi$
$564$	6.90825	0.290890
$565$	−1.95483	−0.0822402
$566$	4.76218	0.200169
$567$	−9.06814	−0.380826
$568$	−3.14862	−0.132113
$569$	21.0605	0.882901	0.441451	−	0.897286i	$-0.354464\pi$
$569$	21.0605	0.882901	0.441451	+	0.897286i	$0.354464\pi$
$570$	1.37083	0.0574176
$571$	13.5114	0.565433	0.282717	−	0.959203i	$-0.408764\pi$
$571$	13.5114	0.565433	0.282717	+	0.959203i	$0.408764\pi$
$572$	47.7684	1.99730
$573$	−22.6952	−0.948106
$574$	0.718405	0.0299856
$575$	36.4037	1.51814
$576$	5.61244	0.233852
$577$	−38.9283	−1.62061	−0.810303	−	0.586011i	$-0.800698\pi$
$577$	−38.9283	−1.62061	−0.810303	+	0.586011i	$0.800698\pi$
$578$	1.98301	0.0824825
$579$	27.0019	1.12216
$580$	−12.8580	−0.533900
$581$	−44.1397	−1.83122
$582$	−8.76117	−0.363162
$583$	10.0151	0.414785
$584$	−24.2858	−1.00495
$585$	7.10756	0.293861
$586$	−0.296069	−0.0122305
$587$	−7.18724	−0.296649	−0.148325	−	0.988939i	$-0.547388\pi$
$587$	−7.18724	−0.296649	−0.148325	+	0.988939i	$0.547388\pi$
$588$	4.08718	0.168552
$589$	14.7824	0.609098
$590$	4.59737	0.189271
$591$	−5.60369	−0.230505
$592$	−3.62689	−0.149064
$593$	−4.79467	−0.196894	−0.0984468	−	0.995142i	$-0.531387\pi$
$593$	−4.79467	−0.196894	−0.0984468	+	0.995142i	$0.531387\pi$
$594$	8.86783	0.363851
$595$	−10.4932	−0.430180
$596$	10.5009	0.430134
$597$	−10.1708	−0.416261
$598$	23.5746	0.964037
$599$	29.9630	1.22425	0.612127	−	0.790759i	$-0.290314\pi$
$599$	29.9630	1.22425	0.612127	+	0.790759i	$0.290314\pi$
$600$	−9.03115	−0.368695
$601$	13.5226	0.551598	0.275799	−	0.961215i	$-0.411058\pi$
$601$	13.5226	0.551598	0.275799	+	0.961215i	$0.411058\pi$
$602$	−9.58429	−0.390627
$603$	−18.3495	−0.747249
$604$	−29.6614	−1.20691
$605$	2.66994	0.108549
$606$	6.84026	0.277867
$607$	−25.8020	−1.04727	−0.523636	−	0.851942i	$-0.675425\pi$
$607$	−25.8020	−1.04727	−0.523636	+	0.851942i	$0.675425\pi$
$608$	−14.9767	−0.607386
$609$	−35.0552	−1.42051
$610$	−3.61413	−0.146332
$611$	−20.2901	−0.820849
$612$	−11.5907	−0.468528
$613$	−24.0586	−0.971717	−0.485858	−	0.874038i	$-0.661493\pi$
$613$	−24.0586	−0.971717	−0.485858	+	0.874038i	$0.661493\pi$
$614$	8.25445	0.333122
$615$	−0.567278	−0.0228749
$616$	−17.9743	−0.724207
$617$	3.62248	0.145836	0.0729178	−	0.997338i	$-0.476769\pi$
$617$	3.62248	0.145836	0.0729178	+	0.997338i	$0.476769\pi$
$618$	−4.50867	−0.181365
$619$	−11.0812	−0.445392	−0.222696	−	0.974888i	$-0.571486\pi$
$619$	−11.0812	−0.445392	−0.222696	+	0.974888i	$0.571486\pi$
$620$	6.08188	0.244254
$621$	−45.9686	−1.84466
$622$	11.9587	0.479501
$623$	−33.0244	−1.32309
$624$	26.2624	1.05134
$625$	16.6567	0.666270
$626$	−8.33779	−0.333245
$627$	16.4649	0.657546
$628$	−34.7012	−1.38473
$629$	5.66338	0.225814
$630$	−1.27646	−0.0508553
$631$	−4.51401	−0.179700	−0.0898499	−	0.995955i	$-0.528639\pi$
$631$	−4.51401	−0.179700	−0.0898499	+	0.995955i	$0.528639\pi$
$632$	−13.2380	−0.526581
$633$	−10.7738	−0.428222
$634$	4.36615	0.173402
$635$	3.09488	0.122816
$636$	6.14713	0.243750
$637$	−12.0044	−0.475630
$638$	14.7032	0.582104
$639$	−2.68566	−0.106243
$640$	−8.05652	−0.318462
$641$	27.0620	1.06889	0.534443	−	0.845204i	$-0.320521\pi$
$641$	27.0620	1.06889	0.534443	+	0.845204i	$0.320521\pi$
$642$	9.18981	0.362693
$643$	16.7558	0.660784	0.330392	−	0.943844i	$-0.392819\pi$
$643$	16.7558	0.660784	0.330392	+	0.943844i	$0.392819\pi$
$644$	44.4703	1.75238
$645$	7.56810	0.297994
$646$	6.56583	0.258329
$647$	7.97160	0.313396	0.156698	−	0.987647i	$-0.449915\pi$
$647$	7.97160	0.313396	0.156698	+	0.987647i	$0.449915\pi$
$648$	4.89124	0.192146
$649$	55.2187	2.16752
$650$	12.6600	0.496564
$651$	16.5812	0.649869
$652$	−16.8089	−0.658287
$653$	33.7463	1.32060	0.660298	−	0.751004i	$-0.270430\pi$
$653$	33.7463	1.32060	0.660298	+	0.751004i	$0.270430\pi$
$654$	6.95273	0.271873
$655$	17.0527	0.666302
$656$	1.74005	0.0679375
$657$	−20.7149	−0.808166
$658$	3.64393	0.142055
$659$	27.0917	1.05534	0.527671	−	0.849449i	$-0.323066\pi$
$659$	27.0917	1.05534	0.527671	+	0.849449i	$0.323066\pi$
$660$	6.77413	0.263683
$661$	39.8470	1.54987	0.774934	−	0.632043i	$-0.217783\pi$
$661$	39.8470	1.54987	0.774934	+	0.632043i	$0.217783\pi$
$662$	12.2952	0.477868
$663$	−41.0086	−1.59264
$664$	23.8084	0.923944
$665$	−7.59494	−0.294519
$666$	0.688928	0.0266954
$667$	−76.2176	−2.95116
$668$	−3.31020	−0.128075
$669$	−22.2223	−0.859164
$670$	4.27657	0.165218
$671$	−43.4091	−1.67579
$672$	−16.7992	−0.648043
$673$	−13.8166	−0.532591	−0.266295	−	0.963891i	$-0.585800\pi$
$673$	−13.8166	−0.532591	−0.266295	+	0.963891i	$0.585800\pi$
$674$	9.22902	0.355489
$675$	−24.6859	−0.950162
$676$	−62.3737	−2.39899
$677$	−21.6570	−0.832347	−0.416174	−	0.909285i	$-0.636629\pi$
$677$	−21.6570	−0.832347	−0.416174	+	0.909285i	$0.636629\pi$
$678$	1.37202	0.0526921
$679$	48.5405	1.86281
$680$	5.65991	0.217048
$681$	−26.8492	−1.02886
$682$	−6.95465	−0.266307
$683$	10.9050	0.417267	0.208634	−	0.977994i	$-0.433098\pi$
$683$	10.9050	0.417267	0.208634	+	0.977994i	$0.433098\pi$
$684$	−8.38934	−0.320774
$685$	−14.0169	−0.535558
$686$	−6.47693	−0.247290
$687$	22.0205	0.840134
$688$	−23.2141	−0.885031
$689$	−18.0546	−0.687826
$690$	3.34316	0.127272
$691$	−3.87302	−0.147337	−0.0736684	−	0.997283i	$-0.523471\pi$
$691$	−3.87302	−0.147337	−0.0736684	+	0.997283i	$0.523471\pi$
$692$	19.8780	0.755650
$693$	−15.3315	−0.582394
$694$	3.83435	0.145550
$695$	1.38869	0.0526762
$696$	18.9083	0.716718
$697$	−2.71708	−0.102917
$698$	−5.85498	−0.221614
$699$	18.8712	0.713776
$700$	23.8813	0.902630
$701$	52.6744	1.98948	0.994742	−	0.102413i	$-0.0326563\pi$
$701$	52.6744	1.98948	0.994742	+	0.102413i	$0.0326563\pi$
$702$	−15.9863	−0.603365
$703$	4.09913	0.154602
$704$	−15.7109	−0.592126
$705$	−2.87738	−0.108368
$706$	−1.58791	−0.0597616
$707$	−37.8979	−1.42530
$708$	33.8924	1.27375
$709$	−4.50923	−0.169348	−0.0846739	−	0.996409i	$-0.526985\pi$
$709$	−4.50923	−0.169348	−0.0846739	+	0.996409i	$0.526985\pi$
$710$	0.625926	0.0234906
$711$	−11.2916	−0.423467
$712$	17.8129	0.667568
$713$	36.0512	1.35013
$714$	7.36480	0.275621
$715$	−19.8962	−0.744074
$716$	0.941518	0.0351862
$717$	−1.55662	−0.0581330
$718$	1.63235	0.0609188
$719$	−15.0010	−0.559444	−0.279722	−	0.960081i	$-0.590242\pi$
$719$	−15.0010	−0.559444	−0.279722	+	0.960081i	$0.590242\pi$
$720$	−3.09171	−0.115221
$721$	24.9799	0.930299
$722$	−3.16997	−0.117974
$723$	5.23876	0.194832
$724$	7.11102	0.264279
$725$	−40.9301	−1.52011
$726$	−1.87393	−0.0695482
$727$	−34.0337	−1.26224	−0.631120	−	0.775685i	$-0.717404\pi$
$727$	−34.0337	−1.26224	−0.631120	+	0.775685i	$0.717404\pi$
$728$	32.4029	1.20093
$729$	25.6169	0.948773
$730$	4.82786	0.178687
$731$	36.2488	1.34071
$732$	−26.6438	−0.984783
$733$	51.5518	1.90411	0.952055	−	0.305928i	$-0.0989666\pi$
$733$	51.5518	1.90411	0.952055	+	0.305928i	$0.0989666\pi$
$734$	−4.68112	−0.172783
$735$	−1.70236	−0.0627926
$736$	−36.5251	−1.34633
$737$	51.3656	1.89208
$738$	−0.330522	−0.0121667
$739$	38.4870	1.41577	0.707884	−	0.706329i	$-0.249650\pi$
$739$	38.4870	1.41577	0.707884	+	0.706329i	$0.249650\pi$
$740$	1.68650	0.0619968
$741$	−29.6818	−1.09039
$742$	3.24246	0.119034
$743$	36.1319	1.32555	0.662775	−	0.748819i	$-0.269379\pi$
$743$	36.1319	1.32555	0.662775	+	0.748819i	$0.269379\pi$
$744$	−8.94369	−0.327892
$745$	−4.37377	−0.160242
$746$	8.78701	0.321715
$747$	20.3077	0.743019
$748$	32.4459	1.18634
$749$	−50.9153	−1.86041
$750$	3.82558	0.139690
$751$	27.8911	1.01776	0.508881	−	0.860837i	$-0.330059\pi$
$751$	27.8911	1.01776	0.508881	+	0.860837i	$0.330059\pi$
$752$	8.82597	0.321850
$753$	13.3275	0.485680
$754$	−26.5059	−0.965287
$755$	12.3544	0.449622
$756$	−30.1561	−1.09677
$757$	−14.1409	−0.513960	−0.256980	−	0.966417i	$-0.582727\pi$
$757$	−14.1409	−0.513960	−0.256980	+	0.966417i	$0.582727\pi$
$758$	7.12978	0.258965
$759$	40.1545	1.45752
$760$	4.09662	0.148600
$761$	42.5886	1.54384	0.771918	−	0.635723i	$-0.219298\pi$
$761$	42.5886	1.54384	0.771918	+	0.635723i	$0.219298\pi$
$762$	−2.17218	−0.0786898
$763$	−38.5210	−1.39455
$764$	−32.3706	−1.17113
$765$	4.82770	0.174546
$766$	7.12772	0.257535
$767$	−99.5445	−3.59434
$768$	−4.90658	−0.177051
$769$	−46.3531	−1.67153	−0.835767	−	0.549084i	$-0.814977\pi$
$769$	−46.3531	−1.67153	−0.835767	+	0.549084i	$0.814977\pi$
$770$	3.57318	0.128768
$771$	−19.0246	−0.685153
$772$	38.5133	1.38612
$773$	−6.41242	−0.230639	−0.115319	−	0.993328i	$-0.536789\pi$
$773$	−6.41242	−0.230639	−0.115319	+	0.993328i	$0.536789\pi$
$774$	4.40952	0.158497
$775$	19.3601	0.695435
$776$	−26.1821	−0.939884
$777$	4.59794	0.164950
$778$	6.87538	0.246494
$779$	−1.96661	−0.0704613
$780$	−12.2119	−0.437257
$781$	7.51796	0.269014
$782$	16.0127	0.572612
$783$	51.6844	1.84705
$784$	5.22177	0.186492
$785$	14.4535	0.515868
$786$	−11.9686	−0.426907
$787$	−40.4218	−1.44088	−0.720440	−	0.693517i	$-0.756060\pi$
$787$	−40.4218	−1.44088	−0.720440	+	0.693517i	$0.756060\pi$
$788$	−7.99264	−0.284726
$789$	0.179473	0.00638939
$790$	2.63164	0.0936294
$791$	−7.60156	−0.270280
$792$	8.26960	0.293847
$793$	78.2550	2.77891
$794$	−6.86226	−0.243532
$795$	−2.56036	−0.0908066
$796$	−14.5067	−0.514177
$797$	20.1226	0.712779	0.356389	−	0.934338i	$-0.384008\pi$
$797$	20.1226	0.712779	0.356389	+	0.934338i	$0.384008\pi$
$798$	5.33061	0.188701
$799$	−13.7817	−0.487562
$800$	−19.6146	−0.693481
$801$	15.1938	0.536846
$802$	−10.0535	−0.355001
$803$	57.9872	2.04632
$804$	31.5274	1.11188
$805$	−18.5225	−0.652831
$806$	12.5374	0.441610
$807$	−12.8794	−0.453376
$808$	20.4416	0.719134
$809$	−4.71219	−0.165672	−0.0828359	−	0.996563i	$-0.526398\pi$
$809$	−4.71219	−0.165672	−0.0828359	+	0.996563i	$0.526398\pi$
$810$	−0.972347	−0.0341648
$811$	−34.2920	−1.20416	−0.602078	−	0.798437i	$-0.705660\pi$
$811$	−34.2920	−1.20416	−0.602078	+	0.798437i	$0.705660\pi$
$812$	−49.9998	−1.75465
$813$	5.21965	0.183061
$814$	−1.92851	−0.0675943
$815$	7.00112	0.245239
$816$	17.8383	0.624465
$817$	26.2367	0.917907
$818$	7.69599	0.269084
$819$	27.6385	0.965768
$820$	−0.809119	−0.0282557
$821$	38.8698	1.35657	0.678283	−	0.734801i	$-0.262724\pi$
$821$	38.8698	1.35657	0.678283	+	0.734801i	$0.262724\pi$
$822$	9.83795	0.343138
$823$	−29.9702	−1.04470	−0.522348	−	0.852732i	$-0.674944\pi$
$823$	−29.9702	−1.04470	−0.522348	+	0.852732i	$0.674944\pi$
$824$	−13.4738	−0.469383
$825$	21.5637	0.750750
$826$	17.8774	0.622033
$827$	7.39418	0.257121	0.128560	−	0.991702i	$-0.458964\pi$
$827$	7.39418	0.257121	0.128560	+	0.991702i	$0.458964\pi$
$828$	−20.4598	−0.711028
$829$	13.5829	0.471754	0.235877	−	0.971783i	$-0.424204\pi$
$829$	13.5829	0.471754	0.235877	+	0.971783i	$0.424204\pi$
$830$	−4.73295	−0.164283
$831$	11.7233	0.406677
$832$	28.3225	0.981906
$833$	−8.15377	−0.282511
$834$	−0.974673	−0.0337502
$835$	1.37874	0.0477132
$836$	23.4842	0.812219
$837$	−24.4469	−0.845007
$838$	−15.6247	−0.539745
$839$	22.4028	0.773431	0.386715	−	0.922199i	$-0.373610\pi$
$839$	22.4028	0.773431	0.386715	+	0.922199i	$0.373610\pi$
$840$	4.59512	0.158547
$841$	56.6945	1.95498
$842$	8.27688	0.285240
$843$	−27.3624	−0.942410
$844$	−15.3669	−0.528952
$845$	25.9795	0.893721
$846$	−1.67649	−0.0576390
$847$	10.3824	0.356742
$848$	7.85356	0.269692
$849$	−14.6227	−0.501849
$850$	8.59908	0.294946
$851$	9.99692	0.342690
$852$	4.61440	0.158087
$853$	−38.6772	−1.32428	−0.662142	−	0.749378i	$-0.730352\pi$
$853$	−38.6772	−1.32428	−0.662142	+	0.749378i	$0.730352\pi$
$854$	−14.0539	−0.480915
$855$	3.49427	0.119501
$856$	27.4631	0.938669
$857$	−22.5795	−0.771300	−0.385650	−	0.922645i	$-0.626023\pi$
$857$	−22.5795	−0.771300	−0.385650	+	0.922645i	$0.626023\pi$
$858$	13.9644	0.476736
$859$	0.615306	0.0209940	0.0104970	−	0.999945i	$-0.496659\pi$
$859$	0.615306	0.0209940	0.0104970	+	0.999945i	$0.496659\pi$
$860$	10.7945	0.368090
$861$	−2.20592	−0.0751777
$862$	4.63887	0.158001
$863$	−11.9074	−0.405332	−0.202666	−	0.979248i	$-0.564961\pi$
$863$	−11.9074	−0.405332	−0.202666	+	0.979248i	$0.564961\pi$
$864$	24.7683	0.842633
$865$	−8.27946	−0.281510
$866$	13.0191	0.442406
$867$	−6.08901	−0.206794
$868$	23.6501	0.802736
$869$	31.6084	1.07224
$870$	−3.75885	−0.127437
$871$	−92.5984	−3.13758
$872$	20.7777	0.703623
$873$	−22.3324	−0.755838
$874$	11.5899	0.392034
$875$	−21.1953	−0.716531
$876$	35.5916	1.20253
$877$	−12.2528	−0.413749	−0.206874	−	0.978368i	$-0.566329\pi$
$877$	−12.2528	−0.413749	−0.206874	+	0.978368i	$0.566329\pi$
$878$	−0.295648	−0.00997762
$879$	0.909106	0.0306634
$880$	8.65461	0.291747
$881$	−5.82496	−0.196248	−0.0981240	−	0.995174i	$-0.531284\pi$
$881$	−5.82496	−0.196248	−0.0981240	+	0.995174i	$0.531284\pi$
$882$	−0.991874	−0.0333981
$883$	−19.0075	−0.639654	−0.319827	−	0.947476i	$-0.603625\pi$
$883$	−19.0075	−0.639654	−0.319827	+	0.947476i	$0.603625\pi$
$884$	−58.4913	−1.96727
$885$	−14.1166	−0.474524
$886$	−0.276595	−0.00929240
$887$	8.86588	0.297687	0.148844	−	0.988861i	$-0.452445\pi$
$887$	8.86588	0.297687	0.148844	+	0.988861i	$0.452445\pi$
$888$	−2.48007	−0.0832257
$889$	12.0348	0.403633
$890$	−3.54110	−0.118698
$891$	−11.6788	−0.391255
$892$	−31.6961	−1.06126
$893$	−9.97515	−0.333806
$894$	3.06978	0.102669
$895$	−0.392154	−0.0131083
$896$	−31.3287	−1.04662
$897$	−72.3878	−2.41696
$898$	−6.73197	−0.224649
$899$	−40.5338	−1.35188
$900$	−10.9873	−0.366243
$901$	−12.2633	−0.408550
$902$	0.925230	0.0308068
$903$	29.4294	0.979349
$904$	4.10019	0.136370
$905$	−2.96183	−0.0984546
$906$	−8.67108	−0.288077
$907$	−30.9716	−1.02839	−0.514197	−	0.857672i	$-0.671910\pi$
$907$	−30.9716	−1.02839	−0.514197	+	0.857672i	$0.671910\pi$
$908$	−38.2954	−1.27088
$909$	17.4360	0.578315
$910$	−6.44148	−0.213533
$911$	−32.2059	−1.06703	−0.533514	−	0.845791i	$-0.679129\pi$
$911$	−32.2059	−1.06703	−0.533514	+	0.845791i	$0.679129\pi$
$912$	12.9113	0.427535
$913$	−56.8472	−1.88137
$914$	13.6410	0.451203
$915$	11.0975	0.366872
$916$	31.4082	1.03776
$917$	66.3111	2.18979
$918$	−10.8585	−0.358382
$919$	44.5730	1.47033	0.735164	−	0.677889i	$-0.237105\pi$
$919$	44.5730	1.47033	0.735164	+	0.677889i	$0.237105\pi$
$920$	9.99079	0.329387
$921$	−25.3460	−0.835178
$922$	13.5852	0.447406
$923$	−13.5529	−0.446098
$924$	26.3419	0.866586
$925$	5.36852	0.176516
$926$	−12.4410	−0.408836
$927$	−11.4927	−0.377470
$928$	41.0667	1.34808
$929$	−46.5720	−1.52798	−0.763990	−	0.645229i	$-0.776762\pi$
$929$	−46.5720	−1.52798	−0.763990	+	0.645229i	$0.776762\pi$
$930$	1.77795	0.0583012
$931$	−5.90167	−0.193419
$932$	26.9164	0.881676
$933$	−36.7203	−1.20217
$934$	−14.8798	−0.486882
$935$	−13.5141	−0.441960
$936$	−14.9079	−0.487279
$937$	−23.5077	−0.767964	−0.383982	−	0.923341i	$-0.625447\pi$
$937$	−23.5077	−0.767964	−0.383982	+	0.923341i	$0.625447\pi$
$938$	16.6299	0.542985
$939$	25.6019	0.835486
$940$	−4.10405	−0.133859
$941$	−47.3869	−1.54477	−0.772385	−	0.635155i	$-0.780936\pi$
$941$	−47.3869	−1.54477	−0.772385	+	0.635155i	$0.780936\pi$
$942$	−10.1444	−0.330522
$943$	−4.79616	−0.156184
$944$	43.3008	1.40932
$945$	12.5604	0.408589
$946$	−12.3436	−0.401324
$947$	5.16140	0.167723	0.0838615	−	0.996477i	$-0.473275\pi$
$947$	5.16140	0.167723	0.0838615	+	0.996477i	$0.473275\pi$
$948$	19.4007	0.630107
$949$	−104.535	−3.39336
$950$	6.22398	0.201932
$951$	−13.4066	−0.434740
$952$	22.0092	0.713321
$953$	25.6660	0.831402	0.415701	−	0.909501i	$-0.363536\pi$
$953$	25.6660	0.831402	0.415701	+	0.909501i	$0.363536\pi$
$954$	−1.49178	−0.0482982
$955$	13.4828	0.436292
$956$	−2.22023	−0.0718074
$957$	−45.1474	−1.45941
$958$	0.596053	0.0192576
$959$	−54.5063	−1.76010
$960$	4.01647	0.129631
$961$	−11.8274	−0.381529
$962$	3.47659	0.112090
$963$	23.4250	0.754861
$964$	7.47214	0.240662
$965$	−16.0413	−0.516388
$966$	13.0002	0.418276
$967$	49.1724	1.58128	0.790639	−	0.612283i	$-0.209749\pi$
$967$	49.1724	1.58128	0.790639	+	0.612283i	$0.209749\pi$
$968$	−5.60012	−0.179995
$969$	−20.1609	−0.647662
$970$	5.20484	0.167117
$971$	−54.9914	−1.76476	−0.882380	−	0.470538i	$-0.844060\pi$
$971$	−54.9914	−1.76476	−0.882380	+	0.470538i	$0.844060\pi$
$972$	23.4189	0.751160
$973$	5.40009	0.173119
$974$	4.64662	0.148887
$975$	−38.8735	−1.24495
$976$	−34.0400	−1.08960
$977$	−0.795775	−0.0254591	−0.0127296	−	0.999919i	$-0.504052\pi$
$977$	−0.795775	−0.0254591	−0.0127296	+	0.999919i	$0.504052\pi$
$978$	−4.91383	−0.157127
$979$	−42.5319	−1.35933
$980$	−2.42811	−0.0775631
$981$	17.7227	0.565841
$982$	−0.409760	−0.0130760
$983$	−30.4008	−0.969636	−0.484818	−	0.874615i	$-0.661114\pi$
$983$	−30.4008	−0.969636	−0.484818	+	0.874615i	$0.661114\pi$
$984$	1.18985	0.0379310
$985$	3.32904	0.106072
$986$	−18.0037	−0.573355
$987$	−11.1890	−0.356150
$988$	−42.3358	−1.34688
$989$	63.9859	2.03463
$990$	−1.64394	−0.0522479
$991$	4.49696	0.142851	0.0714254	−	0.997446i	$-0.477245\pi$
$991$	4.49696	0.142851	0.0714254	+	0.997446i	$0.477245\pi$
$992$	−19.4247	−0.616733
$993$	−37.7536	−1.19807
$994$	2.43398	0.0772011
$995$	6.04224	0.191552
$996$	−34.8919	−1.10559
$997$	24.5169	0.776459	0.388230	−	0.921563i	$-0.373087\pi$
$997$	24.5169	0.776459	0.388230	+	0.921563i	$0.373087\pi$
$998$	−0.258659	−0.00818770
$999$	−6.77907	−0.214480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.196	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.196	✓	358	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.416963 q^{2} -1.28032 q^{3} -1.82614 q^{4} +0.760612 q^{5} -0.533845 q^{6} +2.95772 q^{7} -1.59536 q^{8} -1.36078 q^{9} +O(q^{10})\)	\(q+0.416963 q^{2} -1.28032 q^{3} -1.82614 q^{4} +0.760612 q^{5} -0.533845 q^{6} +2.95772 q^{7} -1.59536 q^{8} -1.36078 q^{9} +0.317147 q^{10} +3.80923 q^{11} +2.33804 q^{12} -6.86702 q^{13} +1.23326 q^{14} -0.973826 q^{15} +2.98708 q^{16} -4.66432 q^{17} -0.567396 q^{18} -3.37601 q^{19} -1.38899 q^{20} -3.78683 q^{21} +1.58831 q^{22} -8.23339 q^{23} +2.04257 q^{24} -4.42147 q^{25} -2.86329 q^{26} +5.58319 q^{27} -5.40122 q^{28} +9.25713 q^{29} -0.406049 q^{30} -4.37865 q^{31} +4.43622 q^{32} -4.87703 q^{33} -1.94485 q^{34} +2.24968 q^{35} +2.48498 q^{36} -1.21419 q^{37} -1.40767 q^{38} +8.79198 q^{39} -1.21345 q^{40} +0.582526 q^{41} -1.57897 q^{42} -7.77152 q^{43} -6.95620 q^{44} -1.03503 q^{45} -3.43302 q^{46} +2.95471 q^{47} -3.82442 q^{48} +1.74812 q^{49} -1.84359 q^{50} +5.97181 q^{51} +12.5402 q^{52} +2.62918 q^{53} +2.32798 q^{54} +2.89735 q^{55} -4.71863 q^{56} +4.32237 q^{57} +3.85988 q^{58} +14.4960 q^{59} +1.77834 q^{60} -11.3958 q^{61} -1.82573 q^{62} -4.02482 q^{63} -4.12442 q^{64} -5.22314 q^{65} -2.03354 q^{66} +13.4845 q^{67} +8.51771 q^{68} +10.5414 q^{69} +0.938032 q^{70} +1.97362 q^{71} +2.17094 q^{72} +15.2228 q^{73} -0.506273 q^{74} +5.66089 q^{75} +6.16508 q^{76} +11.2667 q^{77} +3.66593 q^{78} +8.29785 q^{79} +2.27201 q^{80} -3.06592 q^{81} +0.242891 q^{82} -14.9235 q^{83} +6.91529 q^{84} -3.54773 q^{85} -3.24043 q^{86} -11.8521 q^{87} -6.07709 q^{88} -11.1655 q^{89} -0.431568 q^{90} -20.3107 q^{91} +15.0353 q^{92} +5.60607 q^{93} +1.23201 q^{94} -2.56784 q^{95} -5.67977 q^{96} +16.4114 q^{97} +0.728899 q^{98} -5.18354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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