LMFDB - Embedded newform 8011.2.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.79741 q^{2} +3.22245 q^{3} +5.82553 q^{4} -0.295886 q^{5} -9.01452 q^{6} +1.71950 q^{7} -10.7016 q^{8} +7.38416 q^{9} +O(q^{10})$	\(q-2.79741 q^{2} +3.22245 q^{3} +5.82553 q^{4} -0.295886 q^{5} -9.01452 q^{6} +1.71950 q^{7} -10.7016 q^{8} +7.38416 q^{9} +0.827715 q^{10} +4.76010 q^{11} +18.7725 q^{12} -0.569413 q^{13} -4.81015 q^{14} -0.953476 q^{15} +18.2857 q^{16} +2.37635 q^{17} -20.6566 q^{18} +4.95583 q^{19} -1.72369 q^{20} +5.54099 q^{21} -13.3160 q^{22} +6.53282 q^{23} -34.4853 q^{24} -4.91245 q^{25} +1.59289 q^{26} +14.1277 q^{27} +10.0170 q^{28} +9.48955 q^{29} +2.66727 q^{30} -5.25196 q^{31} -29.7496 q^{32} +15.3392 q^{33} -6.64765 q^{34} -0.508775 q^{35} +43.0167 q^{36} +2.25957 q^{37} -13.8635 q^{38} -1.83490 q^{39} +3.16645 q^{40} -2.41689 q^{41} -15.5005 q^{42} -6.28325 q^{43} +27.7301 q^{44} -2.18487 q^{45} -18.2750 q^{46} +3.48677 q^{47} +58.9248 q^{48} -4.04333 q^{49} +13.7422 q^{50} +7.65768 q^{51} -3.31713 q^{52} -12.6934 q^{53} -39.5211 q^{54} -1.40845 q^{55} -18.4014 q^{56} +15.9699 q^{57} -26.5462 q^{58} +13.6200 q^{59} -5.55450 q^{60} +6.78837 q^{61} +14.6919 q^{62} +12.6971 q^{63} +46.6505 q^{64} +0.168481 q^{65} -42.9100 q^{66} -12.4057 q^{67} +13.8435 q^{68} +21.0517 q^{69} +1.42325 q^{70} -6.95038 q^{71} -79.0223 q^{72} +9.90863 q^{73} -6.32097 q^{74} -15.8301 q^{75} +28.8704 q^{76} +8.18499 q^{77} +5.13299 q^{78} -1.84979 q^{79} -5.41049 q^{80} +23.3734 q^{81} +6.76103 q^{82} +8.47139 q^{83} +32.2792 q^{84} -0.703129 q^{85} +17.5769 q^{86} +30.5796 q^{87} -50.9407 q^{88} +2.21152 q^{89} +6.11198 q^{90} -0.979105 q^{91} +38.0572 q^{92} -16.9242 q^{93} -9.75396 q^{94} -1.46636 q^{95} -95.8665 q^{96} -4.85889 q^{97} +11.3109 q^{98} +35.1494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.79741	−1.97807	−0.989036	−	0.147678i	$-0.952820\pi$
$2$	−2.79741	−1.97807	−0.989036	+	0.147678i	$0.952820\pi$
$3$	3.22245	1.86048	0.930240	−	0.366951i	$-0.119598\pi$
$3$	3.22245	1.86048	0.930240	+	0.366951i	$0.119598\pi$
$4$	5.82553	2.91276
$5$	−0.295886	−0.132324	−0.0661620	−	0.997809i	$-0.521075\pi$
$5$	−0.295886	−0.132324	−0.0661620	+	0.997809i	$0.521075\pi$
$6$	−9.01452	−3.68016
$7$	1.71950	0.649909	0.324955	−	0.945730i	$-0.394651\pi$
$7$	1.71950	0.649909	0.324955	+	0.945730i	$0.394651\pi$
$8$	−10.7016	−3.78358
$9$	7.38416	2.46139
$10$	0.827715	0.261746
$11$	4.76010	1.43522	0.717612	−	0.696443i	$-0.245235\pi$
$11$	4.76010	1.43522	0.717612	+	0.696443i	$0.245235\pi$
$12$	18.7725	5.41914
$13$	−0.569413	−0.157927	−0.0789634	−	0.996878i	$-0.525161\pi$
$13$	−0.569413	−0.157927	−0.0789634	+	0.996878i	$0.525161\pi$
$14$	−4.81015	−1.28557
$15$	−0.953476	−0.246186
$16$	18.2857	4.57143
$17$	2.37635	0.576351	0.288175	−	0.957578i	$-0.406951\pi$
$17$	2.37635	0.576351	0.288175	+	0.957578i	$0.406951\pi$
$18$	−20.6566	−4.86880
$19$	4.95583	1.13695	0.568473	−	0.822702i	$-0.307534\pi$
$19$	4.95583	1.13695	0.568473	+	0.822702i	$0.307534\pi$
$20$	−1.72369	−0.385429
$21$	5.54099	1.20914
$22$	−13.3160	−2.83898
$23$	6.53282	1.36219	0.681094	−	0.732196i	$-0.261505\pi$
$23$	6.53282	1.36219	0.681094	+	0.732196i	$0.261505\pi$
$24$	−34.4853	−7.03929
$25$	−4.91245	−0.982490
$26$	1.59289	0.312391
$27$	14.1277	2.71888
$28$	10.0170	1.89303
$29$	9.48955	1.76217	0.881083	−	0.472962i	$-0.156815\pi$
$29$	9.48955	1.76217	0.881083	+	0.472962i	$0.156815\pi$
$30$	2.66727	0.486974
$31$	−5.25196	−0.943280	−0.471640	−	0.881791i	$-0.656338\pi$
$31$	−5.25196	−0.943280	−0.471640	+	0.881791i	$0.656338\pi$
$32$	−29.7496	−5.25904
$33$	15.3392	2.67021
$34$	−6.64765	−1.14006
$35$	−0.508775	−0.0859986
$36$	43.0167	7.16944
$37$	2.25957	0.371472	0.185736	−	0.982600i	$-0.440533\pi$
$37$	2.25957	0.371472	0.185736	+	0.982600i	$0.440533\pi$
$38$	−13.8635	−2.24896
$39$	−1.83490	−0.293820
$40$	3.16645	0.500659
$41$	−2.41689	−0.377454	−0.188727	−	0.982030i	$-0.560436\pi$
$41$	−2.41689	−0.377454	−0.188727	+	0.982030i	$0.560436\pi$
$42$	−15.5005	−2.39177
$43$	−6.28325	−0.958187	−0.479094	−	0.877764i	$-0.659035\pi$
$43$	−6.28325	−0.958187	−0.479094	+	0.877764i	$0.659035\pi$
$44$	27.7301	4.18047
$45$	−2.18487	−0.325701
$46$	−18.2750	−2.69450
$47$	3.48677	0.508598	0.254299	−	0.967126i	$-0.418155\pi$
$47$	3.48677	0.508598	0.254299	+	0.967126i	$0.418155\pi$
$48$	58.9248	8.50506
$49$	−4.04333	−0.577618
$50$	13.7422	1.94344
$51$	7.65768	1.07229
$52$	−3.31713	−0.460004
$53$	−12.6934	−1.74357	−0.871787	−	0.489884i	$-0.837039\pi$
$53$	−12.6934	−1.74357	−0.871787	+	0.489884i	$0.837039\pi$
$54$	−39.5211	−5.37814
$55$	−1.40845	−0.189915
$56$	−18.4014	−2.45899
$57$	15.9699	2.11527
$58$	−26.5462	−3.48569
$59$	13.6200	1.77317	0.886584	−	0.462567i	$-0.153072\pi$
$59$	13.6200	1.77317	0.886584	+	0.462567i	$0.153072\pi$
$60$	−5.55450	−0.717083
$61$	6.78837	0.869162	0.434581	−	0.900633i	$-0.356896\pi$
$61$	6.78837	0.869162	0.434581	+	0.900633i	$0.356896\pi$
$62$	14.6919	1.86588
$63$	12.6971	1.59968
$64$	46.6505	5.83131
$65$	0.168481	0.0208975
$66$	−42.9100	−5.28186
$67$	−12.4057	−1.51560	−0.757799	−	0.652488i	$-0.773725\pi$
$67$	−12.4057	−1.51560	−0.757799	+	0.652488i	$0.773725\pi$
$68$	13.8435	1.67877
$69$	21.0517	2.53432
$70$	1.42325	0.170111
$71$	−6.95038	−0.824858	−0.412429	−	0.910990i	$-0.635320\pi$
$71$	−6.95038	−0.824858	−0.412429	+	0.910990i	$0.635320\pi$
$72$	−79.0223	−9.31287
$73$	9.90863	1.15972	0.579859	−	0.814717i	$-0.303108\pi$
$73$	9.90863	1.15972	0.579859	+	0.814717i	$0.303108\pi$
$74$	−6.32097	−0.734798
$75$	−15.8301	−1.82790
$76$	28.8704	3.31166
$77$	8.18499	0.932766
$78$	5.13299	0.581197
$79$	−1.84979	−0.208118	−0.104059	−	0.994571i	$-0.533183\pi$
$79$	−1.84979	−0.208118	−0.104059	+	0.994571i	$0.533183\pi$
$80$	−5.41049	−0.604911
$81$	23.3734	2.59704
$82$	6.76103	0.746631
$83$	8.47139	0.929856	0.464928	−	0.885349i	$-0.346080\pi$
$83$	8.47139	0.929856	0.464928	+	0.885349i	$0.346080\pi$
$84$	32.2792	3.52195
$85$	−0.703129	−0.0762651
$86$	17.5769	1.89536
$87$	30.5796	3.27847
$88$	−50.9407	−5.43029
$89$	2.21152	0.234421	0.117210	−	0.993107i	$-0.462605\pi$
$89$	2.21152	0.234421	0.117210	+	0.993107i	$0.462605\pi$
$90$	6.11198	0.644259
$91$	−0.979105	−0.102638
$92$	38.0572	3.96773
$93$	−16.9242	−1.75495
$94$	−9.75396	−1.00604
$95$	−1.46636	−0.150445
$96$	−95.8665	−9.78434
$97$	−4.85889	−0.493346	−0.246673	−	0.969099i	$-0.579337\pi$
$97$	−4.85889	−0.493346	−0.246673	+	0.969099i	$0.579337\pi$
$98$	11.3109	1.14257
$99$	35.1494	3.53264
$100$	−28.6176	−2.86176
$101$	7.18760	0.715193	0.357597	−	0.933876i	$-0.383596\pi$
$101$	7.18760	0.715193	0.357597	+	0.933876i	$0.383596\pi$
$102$	−21.4217	−2.12106
$103$	9.39259	0.925480	0.462740	−	0.886494i	$-0.346866\pi$
$103$	9.39259	0.925480	0.462740	+	0.886494i	$0.346866\pi$
$104$	6.09363	0.597530
$105$	−1.63950	−0.159999
$106$	35.5087	3.44891
$107$	−15.3956	−1.48834	−0.744172	−	0.667988i	$-0.767156\pi$
$107$	−15.3956	−1.48834	−0.744172	+	0.667988i	$0.767156\pi$
$108$	82.3015	7.91946
$109$	−8.19652	−0.785084	−0.392542	−	0.919734i	$-0.628404\pi$
$109$	−8.19652	−0.785084	−0.392542	+	0.919734i	$0.628404\pi$
$110$	3.94001	0.375665
$111$	7.28136	0.691116
$112$	31.4423	2.97102
$113$	−8.19462	−0.770885	−0.385443	−	0.922732i	$-0.625951\pi$
$113$	−8.19462	−0.770885	−0.385443	+	0.922732i	$0.625951\pi$
$114$	−44.6745	−4.18415
$115$	−1.93297	−0.180250
$116$	55.2817	5.13277
$117$	−4.20464	−0.388719
$118$	−38.1007	−3.50745
$119$	4.08614	0.374576
$120$	10.2037	0.931467
$121$	11.6586	1.05987
$122$	−18.9899	−1.71926
$123$	−7.78828	−0.702246
$124$	−30.5955	−2.74755
$125$	2.93295	0.262331
$126$	−35.5189	−3.16428
$127$	9.45115	0.838654	0.419327	−	0.907835i	$-0.362266\pi$
$127$	9.45115	0.838654	0.419327	+	0.907835i	$0.362266\pi$
$128$	−71.0016	−6.27572
$129$	−20.2475	−1.78269
$130$	−0.471312	−0.0413368
$131$	1.36787	0.119512	0.0597558	−	0.998213i	$-0.480968\pi$
$131$	1.36787	0.119512	0.0597558	+	0.998213i	$0.480968\pi$
$132$	89.3588	7.77769
$133$	8.52155	0.738912
$134$	34.7039	2.99796
$135$	−4.18019	−0.359774
$136$	−25.4308	−2.18067
$137$	−20.0197	−1.71040	−0.855199	−	0.518300i	$-0.826565\pi$
$137$	−20.0197	−1.71040	−0.855199	+	0.518300i	$0.826565\pi$
$138$	−58.8903	−5.01307
$139$	−0.356925	−0.0302740	−0.0151370	−	0.999885i	$-0.504818\pi$
$139$	−0.356925	−0.0302740	−0.0151370	+	0.999885i	$0.504818\pi$
$140$	−2.96388	−0.250494
$141$	11.2359	0.946237
$142$	19.4431	1.63163
$143$	−2.71047	−0.226661
$144$	135.025	11.2521
$145$	−2.80782	−0.233177
$146$	−27.7186	−2.29400
$147$	−13.0294	−1.07465
$148$	13.1632	1.08201
$149$	0.411045	0.0336741	0.0168370	−	0.999858i	$-0.494640\pi$
$149$	0.411045	0.0336741	0.0168370	+	0.999858i	$0.494640\pi$
$150$	44.2834	3.61572
$151$	−13.2413	−1.07756	−0.538780	−	0.842447i	$-0.681115\pi$
$151$	−13.2413	−1.07756	−0.538780	+	0.842447i	$0.681115\pi$
$152$	−53.0353	−4.30173
$153$	17.5474	1.41862
$154$	−22.8968	−1.84508
$155$	1.55398	0.124819
$156$	−10.6893	−0.855828
$157$	−13.2152	−1.05469	−0.527345	−	0.849651i	$-0.676812\pi$
$157$	−13.2152	−1.05469	−0.527345	+	0.849651i	$0.676812\pi$
$158$	5.17464	0.411672
$159$	−40.9039	−3.24389
$160$	8.80248	0.695897
$161$	11.2332	0.885299
$162$	−65.3850	−5.13713
$163$	−24.1635	−1.89263	−0.946317	−	0.323241i	$-0.895228\pi$
$163$	−24.1635	−1.89263	−0.946317	+	0.323241i	$0.895228\pi$
$164$	−14.0796	−1.09943
$165$	−4.53864	−0.353333
$166$	−23.6980	−1.83932
$167$	−18.9667	−1.46768	−0.733842	−	0.679320i	$-0.762275\pi$
$167$	−18.9667	−1.46768	−0.733842	+	0.679320i	$0.762275\pi$
$168$	−59.2974	−4.57490
$169$	−12.6758	−0.975059
$170$	1.96694	0.150858
$171$	36.5947	2.79847
$172$	−36.6033	−2.79097
$173$	23.9198	1.81859	0.909293	−	0.416156i	$-0.136623\pi$
$173$	23.9198	1.81859	0.909293	+	0.416156i	$0.136623\pi$
$174$	−85.5437	−6.48505
$175$	−8.44695	−0.638530
$176$	87.0420	6.56104
$177$	43.8896	3.29895
$178$	−6.18654	−0.463701
$179$	0.794507	0.0593843	0.0296921	−	0.999559i	$-0.490547\pi$
$179$	0.794507	0.0593843	0.0296921	+	0.999559i	$0.490547\pi$
$180$	−12.7280	−0.948690
$181$	−11.9035	−0.884781	−0.442390	−	0.896823i	$-0.645869\pi$
$181$	−11.9035	−0.884781	−0.442390	+	0.896823i	$0.645869\pi$
$182$	2.73896	0.203026
$183$	21.8752	1.61706
$184$	−69.9116	−5.15395
$185$	−0.668576	−0.0491547
$186$	47.3439	3.47142
$187$	11.3117	0.827193
$188$	20.3123	1.48143
$189$	24.2926	1.76703
$190$	4.10202	0.297592
$191$	10.0934	0.730333	0.365166	−	0.930942i	$-0.381012\pi$
$191$	10.0934	0.730333	0.365166	+	0.930942i	$0.381012\pi$
$192$	150.329	10.8490
$193$	−1.57834	−0.113612	−0.0568058	−	0.998385i	$-0.518092\pi$
$193$	−1.57834	−0.113612	−0.0568058	+	0.998385i	$0.518092\pi$
$194$	13.5923	0.975873
$195$	0.542922	0.0388794
$196$	−23.5545	−1.68247
$197$	−5.31119	−0.378407	−0.189203	−	0.981938i	$-0.560591\pi$
$197$	−5.31119	−0.378407	−0.189203	+	0.981938i	$0.560591\pi$
$198$	−98.3273	−6.98782
$199$	−15.9935	−1.13375	−0.566875	−	0.823804i	$-0.691848\pi$
$199$	−15.9935	−1.13375	−0.566875	+	0.823804i	$0.691848\pi$
$200$	52.5711	3.71734
$201$	−39.9767	−2.81974
$202$	−20.1067	−1.41470
$203$	16.3173	1.14525
$204$	44.6100	3.12333
$205$	0.715122	0.0499463
$206$	−26.2750	−1.83066
$207$	48.2394	3.35287
$208$	−10.4121	−0.721952
$209$	23.5903	1.63177
$210$	4.58636	0.316489
$211$	−10.6108	−0.730477	−0.365239	−	0.930914i	$-0.619013\pi$
$211$	−10.6108	−0.730477	−0.365239	+	0.930914i	$0.619013\pi$
$212$	−73.9459	−5.07862
$213$	−22.3972	−1.53463
$214$	43.0678	2.94405
$215$	1.85912	0.126791
$216$	−151.189	−10.2871
$217$	−9.03074	−0.613047
$218$	22.9291	1.55295
$219$	31.9300	2.15763
$220$	−8.20494	−0.553177
$221$	−1.35313	−0.0910213
$222$	−20.3690	−1.36708
$223$	9.82366	0.657841	0.328921	−	0.944358i	$-0.393315\pi$
$223$	9.82366	0.657841	0.328921	+	0.944358i	$0.393315\pi$
$224$	−51.1544	−3.41790
$225$	−36.2743	−2.41829
$226$	22.9238	1.52487
$227$	−17.8725	−1.18624	−0.593118	−	0.805115i	$-0.702103\pi$
$227$	−17.8725	−1.18624	−0.593118	+	0.805115i	$0.702103\pi$
$228$	93.0332	6.16127
$229$	−26.3659	−1.74231	−0.871153	−	0.491012i	$-0.836627\pi$
$229$	−26.3659	−1.74231	−0.871153	+	0.491012i	$0.836627\pi$
$230$	5.40731	0.356548
$231$	26.3757	1.73539
$232$	−101.553	−6.66730
$233$	16.6028	1.08768	0.543842	−	0.839187i	$-0.316969\pi$
$233$	16.6028	1.08768	0.543842	+	0.839187i	$0.316969\pi$
$234$	11.7621	0.768914
$235$	−1.03169	−0.0672998
$236$	79.3435	5.16482
$237$	−5.96086	−0.387199
$238$	−11.4306	−0.740937
$239$	−8.62053	−0.557616	−0.278808	−	0.960347i	$-0.589939\pi$
$239$	−8.62053	−0.557616	−0.278808	+	0.960347i	$0.589939\pi$
$240$	−17.4350	−1.12542
$241$	8.51174	0.548289	0.274145	−	0.961688i	$-0.411605\pi$
$241$	8.51174	0.548289	0.274145	+	0.961688i	$0.411605\pi$
$242$	−32.6139	−2.09650
$243$	32.9362	2.11286
$244$	39.5459	2.53166
$245$	1.19636	0.0764328
$246$	21.7871	1.38909
$247$	−2.82192	−0.179554
$248$	56.2044	3.56898
$249$	27.2986	1.72998
$250$	−8.20468	−0.518910
$251$	−11.7387	−0.740938	−0.370469	−	0.928845i	$-0.620803\pi$
$251$	−11.7387	−0.740938	−0.370469	+	0.928845i	$0.620803\pi$
$252$	73.9671	4.65949
$253$	31.0969	1.95505
$254$	−26.4388	−1.65892
$255$	−2.26580	−0.141890
$256$	105.320	6.58250
$257$	−9.19620	−0.573643	−0.286822	−	0.957984i	$-0.592599\pi$
$257$	−9.19620	−0.573643	−0.286822	+	0.957984i	$0.592599\pi$
$258$	56.6405	3.52628
$259$	3.88534	0.241423
$260$	0.981492	0.0608696
$261$	70.0724	4.33737
$262$	−3.82650	−0.236402
$263$	21.2195	1.30845	0.654225	−	0.756300i	$-0.272995\pi$
$263$	21.2195	1.30845	0.654225	+	0.756300i	$0.272995\pi$
$264$	−164.154	−10.1030
$265$	3.75580	0.230717
$266$	−23.8383	−1.46162
$267$	7.12651	0.436135
$268$	−72.2698	−4.41458
$269$	21.2646	1.29652	0.648261	−	0.761418i	$-0.275496\pi$
$269$	21.2646	1.29652	0.648261	+	0.761418i	$0.275496\pi$
$270$	11.6937	0.711658
$271$	13.0106	0.790336	0.395168	−	0.918609i	$-0.370686\pi$
$271$	13.0106	0.790336	0.395168	+	0.918609i	$0.370686\pi$
$272$	43.4534	2.63475
$273$	−3.15511	−0.190956
$274$	56.0034	3.38329
$275$	−23.3838	−1.41009
$276$	122.637	7.38189
$277$	16.6991	1.00335	0.501677	−	0.865055i	$-0.332717\pi$
$277$	16.6991	1.00335	0.501677	+	0.865055i	$0.332717\pi$
$278$	0.998468	0.0598841
$279$	−38.7813	−2.32178
$280$	5.44470	0.325383
$281$	−9.93377	−0.592599	−0.296299	−	0.955095i	$-0.595753\pi$
$281$	−9.93377	−0.592599	−0.296299	+	0.955095i	$0.595753\pi$
$282$	−31.4316	−1.87172
$283$	0.728183	0.0432860	0.0216430	−	0.999766i	$-0.493110\pi$
$283$	0.728183	0.0432860	0.0216430	+	0.999766i	$0.493110\pi$
$284$	−40.4896	−2.40262
$285$	−4.72527	−0.279901
$286$	7.58230	0.448351
$287$	−4.15583	−0.245311
$288$	−219.676	−12.9445
$289$	−11.3529	−0.667820
$290$	7.85464	0.461240
$291$	−15.6575	−0.917861
$292$	57.7230	3.37799
$293$	16.7529	0.978715	0.489358	−	0.872083i	$-0.337231\pi$
$293$	16.7529	0.978715	0.489358	+	0.872083i	$0.337231\pi$
$294$	36.4486	2.12573
$295$	−4.02995	−0.234633
$296$	−24.1811	−1.40550
$297$	67.2494	3.90221
$298$	−1.14986	−0.0666097
$299$	−3.71988	−0.215126
$300$	−92.2188	−5.32425
$301$	−10.8040	−0.622735
$302$	37.0413	2.13149
$303$	23.1617	1.33060
$304$	90.6211	5.19748
$305$	−2.00858	−0.115011
$306$	−49.0873	−2.80614
$307$	7.32258	0.417922	0.208961	−	0.977924i	$-0.432992\pi$
$307$	7.32258	0.417922	0.208961	+	0.977924i	$0.432992\pi$
$308$	47.6819	2.71693
$309$	30.2671	1.72184
$310$	−4.34713	−0.246900
$311$	19.9093	1.12895	0.564475	−	0.825450i	$-0.309079\pi$
$311$	19.9093	1.12895	0.564475	+	0.825450i	$0.309079\pi$
$312$	19.6364	1.11169
$313$	−0.567200	−0.0320600	−0.0160300	−	0.999872i	$-0.505103\pi$
$313$	−0.567200	−0.0320600	−0.0160300	+	0.999872i	$0.505103\pi$
$314$	36.9684	2.08625
$315$	−3.75688	−0.211676
$316$	−10.7760	−0.606199
$317$	−0.427611	−0.0240170	−0.0120085	−	0.999928i	$-0.503823\pi$
$317$	−0.427611	−0.0240170	−0.0120085	+	0.999928i	$0.503823\pi$
$318$	114.425	6.41664
$319$	45.1712	2.52910
$320$	−13.8032	−0.771623
$321$	−49.6114	−2.76904
$322$	−31.4239	−1.75118
$323$	11.7768	0.655280
$324$	136.162	7.56456
$325$	2.79722	0.155162
$326$	67.5954	3.74376
$327$	−26.4129	−1.46063
$328$	25.8645	1.42813
$329$	5.99550	0.330543
$330$	12.6965	0.698917
$331$	−9.46313	−0.520141	−0.260070	−	0.965590i	$-0.583746\pi$
$331$	−9.46313	−0.520141	−0.260070	+	0.965590i	$0.583746\pi$
$332$	49.3503	2.70845
$333$	16.6851	0.914336
$334$	53.0576	2.90318
$335$	3.67067	0.200550
$336$	101.321	5.52752
$337$	−10.2290	−0.557209	−0.278604	−	0.960406i	$-0.589872\pi$
$337$	−10.2290	−0.557209	−0.278604	+	0.960406i	$0.589872\pi$
$338$	35.4594	1.92874
$339$	−26.4067	−1.43422
$340$	−4.09610	−0.222142
$341$	−24.9999	−1.35382
$342$	−102.371	−5.53556
$343$	−18.9890	−1.02531
$344$	67.2408	3.62538
$345$	−6.22889	−0.335352
$346$	−66.9135	−3.59729
$347$	−12.8192	−0.688169	−0.344084	−	0.938939i	$-0.611811\pi$
$347$	−12.8192	−0.688169	−0.344084	+	0.938939i	$0.611811\pi$
$348$	178.142	9.54942
$349$	−26.4986	−1.41844	−0.709218	−	0.704989i	$-0.750952\pi$
$349$	−26.4986	−1.41844	−0.709218	+	0.704989i	$0.750952\pi$
$350$	23.6296	1.26306
$351$	−8.04452	−0.429385
$352$	−141.611	−7.54790
$353$	−24.2714	−1.29184	−0.645919	−	0.763406i	$-0.723526\pi$
$353$	−24.2714	−1.29184	−0.645919	+	0.763406i	$0.723526\pi$
$354$	−122.777	−6.52555
$355$	2.05652	0.109149
$356$	12.8833	0.682812
$357$	13.1674	0.696891
$358$	−2.22257	−0.117466
$359$	18.8896	0.996954	0.498477	−	0.866903i	$-0.333893\pi$
$359$	18.8896	0.996954	0.498477	+	0.866903i	$0.333893\pi$
$360$	23.3816	1.23232
$361$	5.56030	0.292647
$362$	33.2990	1.75016
$363$	37.5691	1.97187
$364$	−5.70381	−0.298961
$365$	−2.93182	−0.153459
$366$	−61.1939	−3.19866
$367$	−4.58029	−0.239089	−0.119545	−	0.992829i	$-0.538143\pi$
$367$	−4.58029	−0.239089	−0.119545	+	0.992829i	$0.538143\pi$
$368$	119.457	6.22715
$369$	−17.8467	−0.929060
$370$	1.87028	0.0972314
$371$	−21.8263	−1.13317
$372$	−98.5922	−5.11177
$373$	−22.7896	−1.18000	−0.590002	−	0.807402i	$-0.700873\pi$
$373$	−22.7896	−1.18000	−0.590002	+	0.807402i	$0.700873\pi$
$374$	−31.6435	−1.63625
$375$	9.45128	0.488062
$376$	−37.3140	−1.92433
$377$	−5.40348	−0.278293
$378$	−67.9565	−3.49530
$379$	5.56494	0.285852	0.142926	−	0.989733i	$-0.454349\pi$
$379$	5.56494	0.285852	0.142926	+	0.989733i	$0.454349\pi$
$380$	−8.54232	−0.438212
$381$	30.4558	1.56030
$382$	−28.2354	−1.44465
$383$	2.56511	0.131071	0.0655355	−	0.997850i	$-0.479124\pi$
$383$	2.56511	0.131071	0.0655355	+	0.997850i	$0.479124\pi$
$384$	−228.799	−11.6758
$385$	−2.42182	−0.123427
$386$	4.41528	0.224732
$387$	−46.3966	−2.35847
$388$	−28.3056	−1.43700
$389$	25.0265	1.26889	0.634447	−	0.772966i	$-0.281228\pi$
$389$	25.0265	1.26889	0.634447	+	0.772966i	$0.281228\pi$
$390$	−1.51878	−0.0769063
$391$	15.5243	0.785098
$392$	43.2700	2.18547
$393$	4.40789	0.222349
$394$	14.8576	0.748515
$395$	0.547327	0.0275390
$396$	204.764	10.2898
$397$	−32.4397	−1.62810	−0.814050	−	0.580795i	$-0.802742\pi$
$397$	−32.4397	−1.62810	−0.814050	+	0.580795i	$0.802742\pi$
$398$	44.7405	2.24264
$399$	27.4602	1.37473
$400$	−89.8278	−4.49139
$401$	−35.4524	−1.77041	−0.885204	−	0.465202i	$-0.845982\pi$
$401$	−35.4524	−1.77041	−0.885204	+	0.465202i	$0.845982\pi$
$402$	111.831	5.57764
$403$	2.99054	0.148969
$404$	41.8716	2.08319
$405$	−6.91584	−0.343651
$406$	−45.6462	−2.26538
$407$	10.7558	0.533146
$408$	−81.9493	−4.05710
$409$	25.4003	1.25596	0.627982	−	0.778228i	$-0.283881\pi$
$409$	25.4003	1.25596	0.627982	+	0.778228i	$0.283881\pi$
$410$	−2.00049	−0.0987972
$411$	−64.5124	−3.18216
$412$	54.7168	2.69571
$413$	23.4195	1.15240
$414$	−134.946	−6.63222
$415$	−2.50656	−0.123042
$416$	16.9398	0.830543
$417$	−1.15017	−0.0563242
$418$	−65.9918	−3.22776
$419$	26.0223	1.27127	0.635637	−	0.771988i	$-0.280737\pi$
$419$	26.0223	1.27127	0.635637	+	0.771988i	$0.280737\pi$
$420$	−9.55095	−0.466039
$421$	32.0370	1.56139	0.780694	−	0.624913i	$-0.214866\pi$
$421$	32.0370	1.56139	0.780694	+	0.624913i	$0.214866\pi$
$422$	29.6828	1.44494
$423$	25.7469	1.25186
$424$	135.840	6.59696
$425$	−11.6737	−0.566259
$426$	62.6543	3.03561
$427$	11.6726	0.564876
$428$	−89.6873	−4.33520
$429$	−8.73433	−0.421698
$430$	−5.20074	−0.250802
$431$	5.74291	0.276626	0.138313	−	0.990389i	$-0.455832\pi$
$431$	5.74291	0.276626	0.138313	+	0.990389i	$0.455832\pi$
$432$	258.336	12.4292
$433$	0.125801	0.00604559	0.00302280	−	0.999995i	$-0.499038\pi$
$433$	0.125801	0.00604559	0.00302280	+	0.999995i	$0.499038\pi$
$434$	25.2627	1.21265
$435$	−9.04805	−0.433821
$436$	−47.7491	−2.28677
$437$	32.3756	1.54873
$438$	−89.3216	−4.26795
$439$	26.4347	1.26166	0.630829	−	0.775922i	$-0.282715\pi$
$439$	26.4347	1.26166	0.630829	+	0.775922i	$0.282715\pi$
$440$	15.0726	0.718559
$441$	−29.8566	−1.42174
$442$	3.78526	0.180047
$443$	12.5625	0.596864	0.298432	−	0.954431i	$-0.403536\pi$
$443$	12.5625	0.596864	0.298432	+	0.954431i	$0.403536\pi$
$444$	42.4178	2.01306
$445$	−0.654357	−0.0310195
$446$	−27.4809	−1.30126
$447$	1.32457	0.0626500
$448$	80.2155	3.78983
$449$	−30.2232	−1.42632	−0.713161	−	0.701000i	$-0.752737\pi$
$449$	−30.2232	−1.42632	−0.713161	+	0.701000i	$0.752737\pi$
$450$	101.474	4.78355
$451$	−11.5046	−0.541731
$452$	−47.7380	−2.24541
$453$	−42.6693	−2.00478
$454$	49.9967	2.34646
$455$	0.289703	0.0135815
$456$	−170.904	−8.00329
$457$	−33.5684	−1.57026	−0.785131	−	0.619330i	$-0.787404\pi$
$457$	−33.5684	−1.57026	−0.785131	+	0.619330i	$0.787404\pi$
$458$	73.7563	3.44640
$459$	33.5725	1.56703
$460$	−11.2606	−0.525027
$461$	37.7660	1.75894	0.879469	−	0.475955i	$-0.157898\pi$
$461$	37.7660	1.75894	0.879469	+	0.475955i	$0.157898\pi$
$462$	−73.7837	−3.43273
$463$	−22.4431	−1.04302	−0.521510	−	0.853245i	$-0.674631\pi$
$463$	−22.4431	−1.04302	−0.521510	+	0.853245i	$0.674631\pi$
$464$	173.523	8.05562
$465$	5.00762	0.232223
$466$	−46.4449	−2.15152
$467$	18.9509	0.876945	0.438473	−	0.898745i	$-0.355520\pi$
$467$	18.9509	0.876945	0.438473	+	0.898745i	$0.355520\pi$
$468$	−24.4943	−1.13225
$469$	−21.3316	−0.985001
$470$	2.88605	0.133124
$471$	−42.5853	−1.96223
$472$	−145.755	−6.70893
$473$	−29.9089	−1.37521
$474$	16.6750	0.765908
$475$	−24.3453	−1.11704
$476$	23.8039	1.09105
$477$	−93.7302	−4.29161
$478$	24.1152	1.10300
$479$	7.22302	0.330028	0.165014	−	0.986291i	$-0.447233\pi$
$479$	7.22302	0.330028	0.165014	+	0.986291i	$0.447233\pi$
$480$	28.3655	1.29470
$481$	−1.28663	−0.0586654
$482$	−23.8109	−1.08456
$483$	36.1983	1.64708
$484$	67.9174	3.08715
$485$	1.43768	0.0652815
$486$	−92.1362	−4.17938
$487$	17.4232	0.789519	0.394760	−	0.918784i	$-0.370828\pi$
$487$	17.4232	0.789519	0.394760	+	0.918784i	$0.370828\pi$
$488$	−72.6464	−3.28855
$489$	−77.8657	−3.52121
$490$	−3.34672	−0.151189
$491$	−12.8614	−0.580425	−0.290213	−	0.956962i	$-0.593726\pi$
$491$	−12.8614	−0.580425	−0.290213	+	0.956962i	$0.593726\pi$
$492$	−45.3709	−2.04548
$493$	22.5505	1.01563
$494$	7.89408	0.355171
$495$	−10.4002	−0.467454
$496$	−96.0360	−4.31214
$497$	−11.9512	−0.536083
$498$	−76.3655	−3.42202
$499$	7.21194	0.322851	0.161425	−	0.986885i	$-0.448391\pi$
$499$	7.21194	0.322851	0.161425	+	0.986885i	$0.448391\pi$
$500$	17.0860	0.764109
$501$	−61.1190	−2.73060
$502$	32.8379	1.46563
$503$	−11.0130	−0.491046	−0.245523	−	0.969391i	$-0.578960\pi$
$503$	−11.0130	−0.491046	−0.245523	+	0.969391i	$0.578960\pi$
$504$	−135.879	−6.05252
$505$	−2.12671	−0.0946373
$506$	−86.9909	−3.86722
$507$	−40.8470	−1.81408
$508$	55.0579	2.44280
$509$	26.1184	1.15768	0.578839	−	0.815442i	$-0.303506\pi$
$509$	26.1184	1.15768	0.578839	+	0.815442i	$0.303506\pi$
$510$	6.33837	0.280668
$511$	17.0379	0.753711
$512$	−152.620	−6.74493
$513$	70.0147	3.09122
$514$	25.7256	1.13471
$515$	−2.77913	−0.122463
$516$	−117.952	−5.19255
$517$	16.5974	0.729953
$518$	−10.8689	−0.477552
$519$	77.0802	3.38345
$520$	−1.80302	−0.0790676
$521$	−39.7475	−1.74137	−0.870684	−	0.491842i	$-0.836324\pi$
$521$	−39.7475	−1.74137	−0.870684	+	0.491842i	$0.836324\pi$
$522$	−196.021	−8.57963
$523$	−13.0059	−0.568707	−0.284353	−	0.958720i	$-0.591779\pi$
$523$	−13.0059	−0.568707	−0.284353	+	0.958720i	$0.591779\pi$
$524$	7.96858	0.348109
$525$	−27.2199	−1.18797
$526$	−59.3597	−2.58821
$527$	−12.4805	−0.543660
$528$	280.488	12.2067
$529$	19.6778	0.855556
$530$	−10.5065	−0.456374
$531$	100.572	4.36445
$532$	49.6425	2.15228
$533$	1.37621	0.0596101
$534$	−19.9358	−0.862706
$535$	4.55532	0.196944
$536$	132.761	5.73439
$537$	2.56026	0.110483
$538$	−59.4858	−2.56461
$539$	−19.2466	−0.829012
$540$	−24.3518	−1.04794
$541$	15.1102	0.649640	0.324820	−	0.945776i	$-0.394696\pi$
$541$	15.1102	0.649640	0.324820	+	0.945776i	$0.394696\pi$
$542$	−36.3960	−1.56334
$543$	−38.3584	−1.64612
$544$	−70.6956	−3.03105
$545$	2.42523	0.103886
$546$	8.82617	0.377725
$547$	29.5247	1.26238	0.631192	−	0.775626i	$-0.282566\pi$
$547$	29.5247	1.26238	0.631192	+	0.775626i	$0.282566\pi$
$548$	−116.625	−4.98199
$549$	50.1264	2.13934
$550$	65.4141	2.78927
$551$	47.0286	2.00349
$552$	−225.286	−9.58883
$553$	−3.18072	−0.135258
$554$	−46.7144	−1.98471
$555$	−2.15445	−0.0914513
$556$	−2.07928	−0.0881811
$557$	−38.6394	−1.63720	−0.818602	−	0.574361i	$-0.805251\pi$
$557$	−38.6394	−1.63720	−0.818602	+	0.574361i	$0.805251\pi$
$558$	108.487	4.59264
$559$	3.57777	0.151324
$560$	−9.30332	−0.393137
$561$	36.4513	1.53898
$562$	27.7889	1.17220
$563$	−6.83895	−0.288227	−0.144114	−	0.989561i	$-0.546033\pi$
$563$	−6.83895	−0.288227	−0.144114	+	0.989561i	$0.546033\pi$
$564$	65.4553	2.75617
$565$	2.42467	0.102007
$566$	−2.03703	−0.0856227
$567$	40.1904	1.68784
$568$	74.3801	3.12092
$569$	37.6671	1.57909	0.789543	−	0.613696i	$-0.210318\pi$
$569$	37.6671	1.57909	0.789543	+	0.613696i	$0.210318\pi$
$570$	13.2185	0.553663
$571$	−39.8856	−1.66916	−0.834581	−	0.550885i	$-0.814290\pi$
$571$	−39.8856	−1.66916	−0.834581	+	0.550885i	$0.814290\pi$
$572$	−15.7899	−0.660209
$573$	32.5254	1.35877
$574$	11.6256	0.485242
$575$	−32.0922	−1.33834
$576$	344.475	14.3531
$577$	36.2466	1.50896	0.754482	−	0.656320i	$-0.227888\pi$
$577$	36.2466	1.50896	0.754482	+	0.656320i	$0.227888\pi$
$578$	31.7589	1.32100
$579$	−5.08613	−0.211372
$580$	−16.3570	−0.679189
$581$	14.5665	0.604322
$582$	43.8006	1.81559
$583$	−60.4220	−2.50242
$584$	−106.038	−4.38789
$585$	1.24409	0.0514369
$586$	−46.8648	−1.93597
$587$	6.83881	0.282268	0.141134	−	0.989991i	$-0.454925\pi$
$587$	6.83881	0.282268	0.141134	+	0.989991i	$0.454925\pi$
$588$	−75.9032	−3.13019
$589$	−26.0279	−1.07246
$590$	11.2734	0.464120
$591$	−17.1150	−0.704018
$592$	41.3180	1.69816
$593$	−28.5848	−1.17384	−0.586919	−	0.809646i	$-0.699659\pi$
$593$	−28.5848	−1.17384	−0.586919	+	0.809646i	$0.699659\pi$
$594$	−188.125	−7.71884
$595$	−1.20903	−0.0495654
$596$	2.39455	0.0980847
$597$	−51.5382	−2.10932
$598$	10.4060	0.425535
$599$	−34.1841	−1.39673	−0.698363	−	0.715744i	$-0.746088\pi$
$599$	−34.1841	−1.39673	−0.698363	+	0.715744i	$0.746088\pi$
$600$	169.407	6.91603
$601$	19.6808	0.802798	0.401399	−	0.915903i	$-0.368524\pi$
$601$	19.6808	0.802798	0.401399	+	0.915903i	$0.368524\pi$
$602$	30.2234	1.23181
$603$	−91.6057	−3.73047
$604$	−77.1374	−3.13868
$605$	−3.44960	−0.140246
$606$	−64.7928	−2.63203
$607$	−15.8421	−0.643010	−0.321505	−	0.946908i	$-0.604189\pi$
$607$	−15.8421	−0.643010	−0.321505	+	0.946908i	$0.604189\pi$
$608$	−147.434	−5.97924
$609$	52.5815	2.13071
$610$	5.61884	0.227500
$611$	−1.98542	−0.0803213
$612$	102.223	4.13211
$613$	−16.4098	−0.662785	−0.331393	−	0.943493i	$-0.607519\pi$
$613$	−16.4098	−0.662785	−0.331393	+	0.943493i	$0.607519\pi$
$614$	−20.4843	−0.826679
$615$	2.30444	0.0929240
$616$	−87.5924	−3.52920
$617$	7.90787	0.318359	0.159179	−	0.987250i	$-0.449115\pi$
$617$	7.90787	0.318359	0.159179	+	0.987250i	$0.449115\pi$
$618$	−84.6697	−3.40592
$619$	−8.42971	−0.338819	−0.169409	−	0.985546i	$-0.554186\pi$
$619$	−8.42971	−0.338819	−0.169409	+	0.985546i	$0.554186\pi$
$620$	9.05276	0.363567
$621$	92.2939	3.70363
$622$	−55.6944	−2.23314
$623$	3.80271	0.152352
$624$	−33.5526	−1.34318
$625$	23.6944	0.947778
$626$	1.58669	0.0634170
$627$	76.0184	3.03588
$628$	−76.9856	−3.07206
$629$	5.36955	0.214098
$630$	10.5095	0.418710
$631$	11.2052	0.446070	0.223035	−	0.974810i	$-0.428404\pi$
$631$	11.2052	0.446070	0.223035	+	0.974810i	$0.428404\pi$
$632$	19.7957	0.787432
$633$	−34.1927	−1.35904
$634$	1.19621	0.0475074
$635$	−2.79646	−0.110974
$636$	−238.287	−9.44868
$637$	2.30232	0.0912214
$638$	−126.363	−5.00275
$639$	−51.3227	−2.03029
$640$	21.0084	0.830428
$641$	−15.1899	−0.599965	−0.299982	−	0.953945i	$-0.596981\pi$
$641$	−15.1899	−0.599965	−0.299982	+	0.953945i	$0.596981\pi$
$642$	138.784	5.47735
$643$	29.7505	1.17325	0.586623	−	0.809860i	$-0.300457\pi$
$643$	29.7505	1.17325	0.586623	+	0.809860i	$0.300457\pi$
$644$	65.4392	2.57867
$645$	5.99093	0.235893
$646$	−32.9447	−1.29619
$647$	−1.57306	−0.0618435	−0.0309218	−	0.999522i	$-0.509844\pi$
$647$	−1.57306	−0.0618435	−0.0309218	+	0.999522i	$0.509844\pi$
$648$	−250.132	−9.82612
$649$	64.8324	2.54490
$650$	−7.82497	−0.306921
$651$	−29.1011	−1.14056
$652$	−140.765	−5.51280
$653$	17.8432	0.698259	0.349130	−	0.937074i	$-0.386477\pi$
$653$	17.8432	0.698259	0.349130	+	0.937074i	$0.386477\pi$
$654$	73.8877	2.88924
$655$	−0.404734	−0.0158142
$656$	−44.1945	−1.72551
$657$	73.1669	2.85451
$658$	−16.7719	−0.653837
$659$	−18.3868	−0.716250	−0.358125	−	0.933674i	$-0.616584\pi$
$659$	−18.3868	−0.716250	−0.358125	+	0.933674i	$0.616584\pi$
$660$	−26.4400	−1.02918
$661$	−42.3139	−1.64582	−0.822909	−	0.568173i	$-0.807651\pi$
$661$	−42.3139	−1.64582	−0.822909	+	0.568173i	$0.807651\pi$
$662$	26.4723	1.02888
$663$	−4.36038	−0.169343
$664$	−90.6573	−3.51819
$665$	−2.52140	−0.0977758
$666$	−46.6750	−1.80862
$667$	61.9936	2.40040
$668$	−110.491	−4.27502
$669$	31.6562	1.22390
$670$	−10.2684	−0.396702
$671$	32.3133	1.24744
$672$	−164.842	−6.35893
$673$	−0.406318	−0.0156624	−0.00783120	−	0.999969i	$-0.502493\pi$
$673$	−0.406318	−0.0156624	−0.00783120	+	0.999969i	$0.502493\pi$
$674$	28.6147	1.10220
$675$	−69.4018	−2.67128
$676$	−73.8431	−2.84012
$677$	1.18167	0.0454151	0.0227076	−	0.999742i	$-0.492771\pi$
$677$	1.18167	0.0454151	0.0227076	+	0.999742i	$0.492771\pi$
$678$	73.8706	2.83698
$679$	−8.35486	−0.320630
$680$	7.52460	0.288555
$681$	−57.5930	−2.20697
$682$	69.9350	2.67795
$683$	−24.5351	−0.938808	−0.469404	−	0.882983i	$-0.655531\pi$
$683$	−24.5351	−0.938808	−0.469404	+	0.882983i	$0.655531\pi$
$684$	213.183	8.15127
$685$	5.92354	0.226327
$686$	53.1201	2.02813
$687$	−84.9626	−3.24152
$688$	−114.894	−4.38029
$689$	7.22780	0.275357
$690$	17.4248	0.663350
$691$	29.6416	1.12762	0.563809	−	0.825905i	$-0.309335\pi$
$691$	29.6416	1.12762	0.563809	+	0.825905i	$0.309335\pi$
$692$	139.345	5.29712
$693$	60.4393	2.29590
$694$	35.8605	1.36125
$695$	0.105609	0.00400598
$696$	−327.250	−12.4044
$697$	−5.74338	−0.217546
$698$	74.1275	2.80577
$699$	53.5016	2.02362
$700$	−49.2080	−1.85989
$701$	25.1416	0.949586	0.474793	−	0.880098i	$-0.342523\pi$
$701$	25.1416	0.949586	0.474793	+	0.880098i	$0.342523\pi$
$702$	22.5038	0.849353
$703$	11.1981	0.422344
$704$	222.061	8.36925
$705$	−3.32455	−0.125210
$706$	67.8973	2.55535
$707$	12.3591	0.464811
$708$	255.680	9.60905
$709$	18.8533	0.708052	0.354026	−	0.935236i	$-0.384812\pi$
$709$	18.8533	0.708052	0.354026	+	0.935236i	$0.384812\pi$
$710$	−5.75293	−0.215904
$711$	−13.6592	−0.512259
$712$	−23.6668	−0.886951
$713$	−34.3101	−1.28492
$714$	−36.8346	−1.37850
$715$	0.801988	0.0299926
$716$	4.62843	0.172972
$717$	−27.7792	−1.03743
$718$	−52.8420	−1.97205
$719$	−10.5637	−0.393961	−0.196981	−	0.980407i	$-0.563114\pi$
$719$	−10.5637	−0.393961	−0.196981	+	0.980407i	$0.563114\pi$
$720$	−39.9519	−1.48892
$721$	16.1506	0.601478
$722$	−15.5545	−0.578877
$723$	27.4286	1.02008
$724$	−69.3442	−2.57716
$725$	−46.6170	−1.73131
$726$	−105.096	−3.90049
$727$	37.2633	1.38202	0.691009	−	0.722846i	$-0.257166\pi$
$727$	37.2633	1.38202	0.691009	+	0.722846i	$0.257166\pi$
$728$	10.4780	0.388340
$729$	36.0151	1.33389
$730$	8.20152	0.303552
$731$	−14.9312	−0.552252
$732$	127.434	4.71011
$733$	−46.5415	−1.71905	−0.859525	−	0.511094i	$-0.829240\pi$
$733$	−46.5415	−1.71905	−0.859525	+	0.511094i	$0.829240\pi$
$734$	12.8130	0.472936
$735$	3.85521	0.142202
$736$	−194.349	−7.16380
$737$	−59.0524	−2.17522
$738$	49.9245	1.83775
$739$	28.3079	1.04132	0.520661	−	0.853763i	$-0.325685\pi$
$739$	28.3079	1.04132	0.520661	+	0.853763i	$0.325685\pi$
$740$	−3.89481	−0.143176
$741$	−9.09348	−0.334057
$742$	61.0572	2.24148
$743$	12.2210	0.448346	0.224173	−	0.974549i	$-0.428032\pi$
$743$	12.2210	0.448346	0.224173	+	0.974549i	$0.428032\pi$
$744$	181.116	6.64002
$745$	−0.121622	−0.00445589
$746$	63.7521	2.33413
$747$	62.5541	2.28873
$748$	65.8966	2.40942
$749$	−26.4726	−0.967289
$750$	−26.4392	−0.965421
$751$	24.7590	0.903470	0.451735	−	0.892152i	$-0.350805\pi$
$751$	24.7590	0.903470	0.451735	+	0.892152i	$0.350805\pi$
$752$	63.7582	2.32502
$753$	−37.8272	−1.37850
$754$	15.1158	0.550484
$755$	3.91790	0.142587
$756$	141.517	5.14693
$757$	−11.2940	−0.410487	−0.205243	−	0.978711i	$-0.565799\pi$
$757$	−11.2940	−0.410487	−0.205243	+	0.978711i	$0.565799\pi$
$758$	−15.5674	−0.565435
$759$	100.208	3.63732
$760$	15.6924	0.569223
$761$	−29.7177	−1.07726	−0.538632	−	0.842541i	$-0.681059\pi$
$761$	−29.7177	−1.07726	−0.538632	+	0.842541i	$0.681059\pi$
$762$	−85.1975	−3.08638
$763$	−14.0939	−0.510234
$764$	58.7994	2.12729
$765$	−5.19202	−0.187718
$766$	−7.17568	−0.259268
$767$	−7.75539	−0.280031
$768$	339.388	12.2466
$769$	16.8909	0.609102	0.304551	−	0.952496i	$-0.401494\pi$
$769$	16.8909	0.609102	0.304551	+	0.952496i	$0.401494\pi$
$770$	6.77484	0.244148
$771$	−29.6343	−1.06725
$772$	−9.19469	−0.330924
$773$	1.52842	0.0549733	0.0274866	−	0.999622i	$-0.491250\pi$
$773$	1.52842	0.0549733	0.0274866	+	0.999622i	$0.491250\pi$
$774$	129.790	4.66522
$775$	25.8000	0.926764
$776$	51.9979	1.86662
$777$	12.5203	0.449163
$778$	−70.0095	−2.50996
$779$	−11.9777	−0.429145
$780$	3.16281	0.113247
$781$	−33.0845	−1.18386
$782$	−43.4279	−1.55298
$783$	134.066	4.79112
$784$	−73.9352	−2.64054
$785$	3.91019	0.139561
$786$	−12.3307	−0.439822
$787$	15.9095	0.567113	0.283556	−	0.958956i	$-0.408486\pi$
$787$	15.9095	0.567113	0.283556	+	0.958956i	$0.408486\pi$
$788$	−30.9405	−1.10221
$789$	68.3787	2.43434
$790$	−1.53110	−0.0544741
$791$	−14.0906	−0.501006
$792$	−376.154	−13.3661
$793$	−3.86539	−0.137264
$794$	90.7472	3.22050
$795$	12.1029	0.429244
$796$	−93.1706	−3.30235
$797$	−10.8307	−0.383644	−0.191822	−	0.981430i	$-0.561440\pi$
$797$	−10.8307	−0.383644	−0.191822	+	0.981430i	$0.561440\pi$
$798$	−76.8177	−2.71932
$799$	8.28581	0.293131
$800$	146.144	5.16695
$801$	16.3302	0.577000
$802$	99.1751	3.50199
$803$	47.1661	1.66446
$804$	−232.885	−8.21324
$805$	−3.32374	−0.117146
$806$	−8.36577	−0.294672
$807$	68.5239	2.41216
$808$	−76.9188	−2.70599
$809$	36.6948	1.29012	0.645059	−	0.764132i	$-0.276833\pi$
$809$	36.6948	1.29012	0.645059	+	0.764132i	$0.276833\pi$
$810$	19.3465	0.679766
$811$	−6.32762	−0.222193	−0.111096	−	0.993810i	$-0.535436\pi$
$811$	−6.32762	−0.222193	−0.111096	+	0.993810i	$0.535436\pi$
$812$	95.0567	3.33584
$813$	41.9259	1.47041
$814$	−30.0885	−1.05460
$815$	7.14964	0.250441
$816$	140.026	4.90190
$817$	−31.1388	−1.08941
$818$	−71.0552	−2.48439
$819$	−7.22987	−0.252632
$820$	4.16596	0.145482
$821$	22.1814	0.774135	0.387068	−	0.922051i	$-0.373488\pi$
$821$	22.1814	0.774135	0.387068	+	0.922051i	$0.373488\pi$
$822$	180.468	6.29454
$823$	6.55122	0.228361	0.114181	−	0.993460i	$-0.463576\pi$
$823$	6.55122	0.228361	0.114181	+	0.993460i	$0.463576\pi$
$824$	−100.516	−3.50163
$825$	−75.3530	−2.62345
$826$	−65.5141	−2.27953
$827$	26.9579	0.937419	0.468710	−	0.883352i	$-0.344719\pi$
$827$	26.9579	0.937419	0.468710	+	0.883352i	$0.344719\pi$
$828$	281.020	9.76613
$829$	18.4142	0.639550	0.319775	−	0.947493i	$-0.396393\pi$
$829$	18.4142	0.639550	0.319775	+	0.947493i	$0.396393\pi$
$830$	7.01189	0.243386
$831$	53.8121	1.86672
$832$	−26.5634	−0.920921
$833$	−9.60837	−0.332910
$834$	3.21751	0.111413
$835$	5.61196	0.194210
$836$	137.426	4.75297
$837$	−74.1983	−2.56467
$838$	−72.7953	−2.51467
$839$	−20.9821	−0.724382	−0.362191	−	0.932104i	$-0.617971\pi$
$839$	−20.9821	−0.724382	−0.362191	+	0.932104i	$0.617971\pi$
$840$	17.5453	0.605369
$841$	61.0516	2.10523
$842$	−89.6208	−3.08854
$843$	−32.0110	−1.10252
$844$	−61.8135	−2.12771
$845$	3.75058	0.129024
$846$	−72.0248	−2.47626
$847$	20.0469	0.688820
$848$	−232.108	−7.97064
$849$	2.34653	0.0805327
$850$	32.6563	1.12010
$851$	14.7614	0.506014
$852$	−130.476	−4.47002
$853$	25.7414	0.881368	0.440684	−	0.897662i	$-0.354736\pi$
$853$	25.7414	0.881368	0.440684	+	0.897662i	$0.354736\pi$
$854$	−32.6531	−1.11737
$855$	−10.8278	−0.370304
$856$	164.757	5.63128
$857$	40.3727	1.37911	0.689553	−	0.724236i	$-0.257807\pi$
$857$	40.3727	1.37911	0.689553	+	0.724236i	$0.257807\pi$
$858$	24.4336	0.834148
$859$	40.0981	1.36813	0.684065	−	0.729421i	$-0.260210\pi$
$859$	40.0981	1.36813	0.684065	+	0.729421i	$0.260210\pi$
$860$	10.8304	0.369313
$861$	−13.3919	−0.456396
$862$	−16.0653	−0.547186
$863$	40.7029	1.38554	0.692771	−	0.721157i	$-0.256390\pi$
$863$	40.7029	1.38554	0.692771	+	0.721157i	$0.256390\pi$
$864$	−420.294	−14.2987
$865$	−7.07752	−0.240643
$866$	−0.351916	−0.0119586
$867$	−36.5842	−1.24247
$868$	−52.6088	−1.78566
$869$	−8.80520	−0.298696
$870$	25.3112	0.858129
$871$	7.06397	0.239354
$872$	87.7159	2.97043
$873$	−35.8789	−1.21432
$874$	−90.5680	−3.06351
$875$	5.04321	0.170491
$876$	186.009	6.28467
$877$	−24.9584	−0.842787	−0.421393	−	0.906878i	$-0.638459\pi$
$877$	−24.9584	−0.842787	−0.421393	+	0.906878i	$0.638459\pi$
$878$	−73.9488	−2.49565
$879$	53.9853	1.82088
$880$	−25.7545	−0.868183
$881$	38.0745	1.28276	0.641382	−	0.767222i	$-0.278362\pi$
$881$	38.0745	1.28276	0.641382	+	0.767222i	$0.278362\pi$
$882$	83.5212	2.81231
$883$	58.9922	1.98525	0.992623	−	0.121242i	$-0.0386877\pi$
$883$	58.9922	1.98525	0.992623	+	0.121242i	$0.0386877\pi$
$884$	−7.88269	−0.265124
$885$	−12.9863	−0.436530
$886$	−35.1426	−1.18064
$887$	−1.20170	−0.0403492	−0.0201746	−	0.999796i	$-0.506422\pi$
$887$	−1.20170	−0.0403492	−0.0201746	+	0.999796i	$0.506422\pi$
$888$	−77.9221	−2.61490
$889$	16.2512	0.545049
$890$	1.83051	0.0613588
$891$	111.260	3.72734
$892$	57.2280	1.91614
$893$	17.2799	0.578249
$894$	−3.70537	−0.123926
$895$	−0.235083	−0.00785797
$896$	−122.087	−4.07865
$897$	−11.9871	−0.400238
$898$	84.5469	2.82137
$899$	−49.8388	−1.66222
$900$	−211.317	−7.04391
$901$	−30.1641	−1.00491
$902$	32.1832	1.07158
$903$	−34.8155	−1.15859
$904$	87.6955	2.91671
$905$	3.52208	0.117078
$906$	119.364	3.96559
$907$	9.69436	0.321896	0.160948	−	0.986963i	$-0.448545\pi$
$907$	9.69436	0.321896	0.160948	+	0.986963i	$0.448545\pi$
$908$	−104.117	−3.45523
$909$	53.0744	1.76037
$910$	−0.810420	−0.0268652
$911$	−17.4515	−0.578194	−0.289097	−	0.957300i	$-0.593355\pi$
$911$	−17.4515	−0.578194	−0.289097	+	0.957300i	$0.593355\pi$
$912$	292.022	9.66980
$913$	40.3247	1.33455
$914$	93.9046	3.10609
$915$	−6.47255	−0.213976
$916$	−153.595	−5.07493
$917$	2.35205	0.0776716
$918$	−93.9162	−3.09970
$919$	17.5880	0.580174	0.290087	−	0.957000i	$-0.406316\pi$
$919$	17.5880	0.580174	0.290087	+	0.957000i	$0.406316\pi$
$920$	20.6858	0.681992
$921$	23.5966	0.777535
$922$	−105.647	−3.47931
$923$	3.95764	0.130267
$924$	153.652	5.05479
$925$	−11.1001	−0.364967
$926$	62.7827	2.06317
$927$	69.3564	2.27796
$928$	−282.310	−9.26729
$929$	27.6489	0.907129	0.453565	−	0.891223i	$-0.350152\pi$
$929$	27.6489	0.907129	0.453565	+	0.891223i	$0.350152\pi$
$930$	−14.0084	−0.459353
$931$	−20.0381	−0.656721
$932$	96.7200	3.16817
$933$	64.1565	2.10039
$934$	−53.0137	−1.73466
$935$	−3.34697	−0.109458
$936$	44.9964	1.47075
$937$	−19.5903	−0.639988	−0.319994	−	0.947420i	$-0.603681\pi$
$937$	−19.5903	−0.639988	−0.319994	+	0.947420i	$0.603681\pi$
$938$	59.6733	1.94840
$939$	−1.82777	−0.0596471
$940$	−6.01012	−0.196029
$941$	−27.4102	−0.893547	−0.446773	−	0.894647i	$-0.647427\pi$
$941$	−27.4102	−0.893547	−0.446773	+	0.894647i	$0.647427\pi$
$942$	119.129	3.88143
$943$	−15.7891	−0.514163
$944$	249.051	8.10592
$945$	−7.18783	−0.233820
$946$	83.6677	2.72027
$947$	−25.5165	−0.829173	−0.414587	−	0.910010i	$-0.636074\pi$
$947$	−25.5165	−0.829173	−0.414587	+	0.910010i	$0.636074\pi$
$948$	−34.7252	−1.12782
$949$	−5.64211	−0.183151
$950$	68.1039	2.20958
$951$	−1.37795	−0.0446832
$952$	−43.7282	−1.41724
$953$	27.3734	0.886710	0.443355	−	0.896346i	$-0.353788\pi$
$953$	27.3734	0.886710	0.443355	+	0.896346i	$0.353788\pi$
$954$	262.202	8.48911
$955$	−2.98649	−0.0966406
$956$	−50.2192	−1.62420
$957$	145.562	4.70535
$958$	−20.2058	−0.652820
$959$	−34.4238	−1.11160
$960$	−44.4801	−1.43559
$961$	−3.41689	−0.110222
$962$	3.59924	0.116044
$963$	−113.683	−3.66339
$964$	49.5854	1.59704
$965$	0.467009	0.0150336
$966$	−101.262	−3.25804
$967$	−52.5651	−1.69038	−0.845189	−	0.534467i	$-0.820512\pi$
$967$	−52.5651	−1.69038	−0.845189	+	0.534467i	$0.820512\pi$
$968$	−124.765	−4.01011
$969$	37.9502	1.21914
$970$	−4.02178	−0.129132
$971$	1.44469	0.0463622	0.0231811	−	0.999731i	$-0.492621\pi$
$971$	1.44469	0.0463622	0.0231811	+	0.999731i	$0.492621\pi$
$972$	191.871	6.15426
$973$	−0.613733	−0.0196754
$974$	−48.7399	−1.56173
$975$	9.01388	0.288675
$976$	124.130	3.97332
$977$	−10.9340	−0.349810	−0.174905	−	0.984585i	$-0.555962\pi$
$977$	−10.9340	−0.349810	−0.174905	+	0.984585i	$0.555962\pi$
$978$	217.823	6.96520
$979$	10.5271	0.336446
$980$	6.96944	0.222631
$981$	−60.5244	−1.93240
$982$	35.9786	1.14812
$983$	−11.1197	−0.354663	−0.177331	−	0.984151i	$-0.556746\pi$
$983$	−11.1197	−0.354663	−0.177331	+	0.984151i	$0.556746\pi$
$984$	83.3470	2.65701
$985$	1.57150	0.0500723
$986$	−63.0832	−2.00898
$987$	19.3202	0.614968
$988$	−16.4392	−0.523000
$989$	−41.0474	−1.30523
$990$	29.0936	0.924657
$991$	27.7737	0.882261	0.441131	−	0.897443i	$-0.354578\pi$
$991$	27.7737	0.882261	0.441131	+	0.897443i	$0.354578\pi$
$992$	156.244	4.96075
$993$	−30.4944	−0.967712
$994$	33.4324	1.06041
$995$	4.73225	0.150022
$996$	159.029	5.03902
$997$	34.8657	1.10421	0.552104	−	0.833775i	$-0.313825\pi$
$997$	34.8657	1.10421	0.552104	+	0.833775i	$0.313825\pi$
$998$	−20.1748	−0.638622
$999$	31.9227	1.00999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.2	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.79741 q^{2} +3.22245 q^{3} +5.82553 q^{4} -0.295886 q^{5} -9.01452 q^{6} +1.71950 q^{7} -10.7016 q^{8} +7.38416 q^{9} +O(q^{10})\)	\(q-2.79741 q^{2} +3.22245 q^{3} +5.82553 q^{4} -0.295886 q^{5} -9.01452 q^{6} +1.71950 q^{7} -10.7016 q^{8} +7.38416 q^{9} +0.827715 q^{10} +4.76010 q^{11} +18.7725 q^{12} -0.569413 q^{13} -4.81015 q^{14} -0.953476 q^{15} +18.2857 q^{16} +2.37635 q^{17} -20.6566 q^{18} +4.95583 q^{19} -1.72369 q^{20} +5.54099 q^{21} -13.3160 q^{22} +6.53282 q^{23} -34.4853 q^{24} -4.91245 q^{25} +1.59289 q^{26} +14.1277 q^{27} +10.0170 q^{28} +9.48955 q^{29} +2.66727 q^{30} -5.25196 q^{31} -29.7496 q^{32} +15.3392 q^{33} -6.64765 q^{34} -0.508775 q^{35} +43.0167 q^{36} +2.25957 q^{37} -13.8635 q^{38} -1.83490 q^{39} +3.16645 q^{40} -2.41689 q^{41} -15.5005 q^{42} -6.28325 q^{43} +27.7301 q^{44} -2.18487 q^{45} -18.2750 q^{46} +3.48677 q^{47} +58.9248 q^{48} -4.04333 q^{49} +13.7422 q^{50} +7.65768 q^{51} -3.31713 q^{52} -12.6934 q^{53} -39.5211 q^{54} -1.40845 q^{55} -18.4014 q^{56} +15.9699 q^{57} -26.5462 q^{58} +13.6200 q^{59} -5.55450 q^{60} +6.78837 q^{61} +14.6919 q^{62} +12.6971 q^{63} +46.6505 q^{64} +0.168481 q^{65} -42.9100 q^{66} -12.4057 q^{67} +13.8435 q^{68} +21.0517 q^{69} +1.42325 q^{70} -6.95038 q^{71} -79.0223 q^{72} +9.90863 q^{73} -6.32097 q^{74} -15.8301 q^{75} +28.8704 q^{76} +8.18499 q^{77} +5.13299 q^{78} -1.84979 q^{79} -5.41049 q^{80} +23.3734 q^{81} +6.76103 q^{82} +8.47139 q^{83} +32.2792 q^{84} -0.703129 q^{85} +17.5769 q^{86} +30.5796 q^{87} -50.9407 q^{88} +2.21152 q^{89} +6.11198 q^{90} -0.979105 q^{91} +38.0572 q^{92} -16.9242 q^{93} -9.75396 q^{94} -1.46636 q^{95} -95.8665 q^{96} -4.85889 q^{97} +11.3109 q^{98} +35.1494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 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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