LMFDB - Embedded newform 4010.2.a.o.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.34023 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.34023 q^{6} +0.629438 q^{7} +1.00000 q^{8} -1.20379 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.34023 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.34023 q^{6} +0.629438 q^{7} +1.00000 q^{8} -1.20379 q^{9} -1.00000 q^{10} +5.31691 q^{11} -1.34023 q^{12} -2.28111 q^{13} +0.629438 q^{14} +1.34023 q^{15} +1.00000 q^{16} -5.32344 q^{17} -1.20379 q^{18} +3.82801 q^{19} -1.00000 q^{20} -0.843589 q^{21} +5.31691 q^{22} +2.83265 q^{23} -1.34023 q^{24} +1.00000 q^{25} -2.28111 q^{26} +5.63403 q^{27} +0.629438 q^{28} +6.56764 q^{29} +1.34023 q^{30} -9.22718 q^{31} +1.00000 q^{32} -7.12586 q^{33} -5.32344 q^{34} -0.629438 q^{35} -1.20379 q^{36} -1.66635 q^{37} +3.82801 q^{38} +3.05720 q^{39} -1.00000 q^{40} -11.4383 q^{41} -0.843589 q^{42} +7.74664 q^{43} +5.31691 q^{44} +1.20379 q^{45} +2.83265 q^{46} +6.08505 q^{47} -1.34023 q^{48} -6.60381 q^{49} +1.00000 q^{50} +7.13462 q^{51} -2.28111 q^{52} +11.4820 q^{53} +5.63403 q^{54} -5.31691 q^{55} +0.629438 q^{56} -5.13040 q^{57} +6.56764 q^{58} +2.23753 q^{59} +1.34023 q^{60} -1.18470 q^{61} -9.22718 q^{62} -0.757714 q^{63} +1.00000 q^{64} +2.28111 q^{65} -7.12586 q^{66} +13.2856 q^{67} -5.32344 q^{68} -3.79639 q^{69} -0.629438 q^{70} +4.77151 q^{71} -1.20379 q^{72} -7.38932 q^{73} -1.66635 q^{74} -1.34023 q^{75} +3.82801 q^{76} +3.34667 q^{77} +3.05720 q^{78} -8.69240 q^{79} -1.00000 q^{80} -3.93950 q^{81} -11.4383 q^{82} +8.56961 q^{83} -0.843589 q^{84} +5.32344 q^{85} +7.74664 q^{86} -8.80212 q^{87} +5.31691 q^{88} +3.05594 q^{89} +1.20379 q^{90} -1.43582 q^{91} +2.83265 q^{92} +12.3665 q^{93} +6.08505 q^{94} -3.82801 q^{95} -1.34023 q^{96} -4.45503 q^{97} -6.60381 q^{98} -6.40047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.34023	−0.773780	−0.386890	−	0.922126i	$-0.626451\pi$
$3$	−1.34023	−0.773780	−0.386890	+	0.922126i	$0.626451\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.34023	−0.547145
$7$	0.629438	0.237905	0.118953	−	0.992900i	$-0.462046\pi$
$7$	0.629438	0.237905	0.118953	+	0.992900i	$0.462046\pi$
$8$	1.00000	0.353553
$9$	−1.20379	−0.401265
$10$	−1.00000	−0.316228
$11$	5.31691	1.60311	0.801555	−	0.597922i	$-0.204007\pi$
$11$	5.31691	1.60311	0.801555	+	0.597922i	$0.204007\pi$
$12$	−1.34023	−0.386890
$13$	−2.28111	−0.632665	−0.316333	−	0.948648i	$-0.602452\pi$
$13$	−2.28111	−0.632665	−0.316333	+	0.948648i	$0.602452\pi$
$14$	0.629438	0.168224
$15$	1.34023	0.346045
$16$	1.00000	0.250000
$17$	−5.32344	−1.29112	−0.645562	−	0.763708i	$-0.723377\pi$
$17$	−5.32344	−1.29112	−0.645562	+	0.763708i	$0.723377\pi$
$18$	−1.20379	−0.283737
$19$	3.82801	0.878207	0.439103	−	0.898437i	$-0.355296\pi$
$19$	3.82801	0.878207	0.439103	+	0.898437i	$0.355296\pi$
$20$	−1.00000	−0.223607
$21$	−0.843589	−0.184086
$22$	5.31691	1.13357
$23$	2.83265	0.590648	0.295324	−	0.955397i	$-0.404572\pi$
$23$	2.83265	0.590648	0.295324	+	0.955397i	$0.404572\pi$
$24$	−1.34023	−0.273572
$25$	1.00000	0.200000
$26$	−2.28111	−0.447362
$27$	5.63403	1.08427
$28$	0.629438	0.118953
$29$	6.56764	1.21958	0.609790	−	0.792563i	$-0.291254\pi$
$29$	6.56764	1.21958	0.609790	+	0.792563i	$0.291254\pi$
$30$	1.34023	0.244691
$31$	−9.22718	−1.65725	−0.828625	−	0.559804i	$-0.810876\pi$
$31$	−9.22718	−1.65725	−0.828625	+	0.559804i	$0.810876\pi$
$32$	1.00000	0.176777
$33$	−7.12586	−1.24045
$34$	−5.32344	−0.912963
$35$	−0.629438	−0.106394
$36$	−1.20379	−0.200632
$37$	−1.66635	−0.273947	−0.136973	−	0.990575i	$-0.543738\pi$
$37$	−1.66635	−0.273947	−0.136973	+	0.990575i	$0.543738\pi$
$38$	3.82801	0.620986
$39$	3.05720	0.489544
$40$	−1.00000	−0.158114
$41$	−11.4383	−1.78636	−0.893178	−	0.449704i	$-0.851529\pi$
$41$	−11.4383	−1.78636	−0.893178	+	0.449704i	$0.851529\pi$
$42$	−0.843589	−0.130169
$43$	7.74664	1.18135	0.590676	−	0.806909i	$-0.298861\pi$
$43$	7.74664	1.18135	0.590676	+	0.806909i	$0.298861\pi$
$44$	5.31691	0.801555
$45$	1.20379	0.179451
$46$	2.83265	0.417651
$47$	6.08505	0.887596	0.443798	−	0.896127i	$-0.353631\pi$
$47$	6.08505	0.887596	0.443798	+	0.896127i	$0.353631\pi$
$48$	−1.34023	−0.193445
$49$	−6.60381	−0.943401
$50$	1.00000	0.141421
$51$	7.13462	0.999046
$52$	−2.28111	−0.316333
$53$	11.4820	1.57717	0.788586	−	0.614925i	$-0.210814\pi$
$53$	11.4820	1.57717	0.788586	+	0.614925i	$0.210814\pi$
$54$	5.63403	0.766695
$55$	−5.31691	−0.716932
$56$	0.629438	0.0841122
$57$	−5.13040	−0.679539
$58$	6.56764	0.862373
$59$	2.23753	0.291302	0.145651	−	0.989336i	$-0.453472\pi$
$59$	2.23753	0.291302	0.145651	+	0.989336i	$0.453472\pi$
$60$	1.34023	0.173022
$61$	−1.18470	−0.151685	−0.0758427	−	0.997120i	$-0.524165\pi$
$61$	−1.18470	−0.151685	−0.0758427	+	0.997120i	$0.524165\pi$
$62$	−9.22718	−1.17185
$63$	−0.757714	−0.0954630
$64$	1.00000	0.125000
$65$	2.28111	0.282936
$66$	−7.12586	−0.877133
$67$	13.2856	1.62309	0.811545	−	0.584290i	$-0.198627\pi$
$67$	13.2856	1.62309	0.811545	+	0.584290i	$0.198627\pi$
$68$	−5.32344	−0.645562
$69$	−3.79639	−0.457031
$70$	−0.629438	−0.0752323
$71$	4.77151	0.566273	0.283137	−	0.959080i	$-0.408625\pi$
$71$	4.77151	0.566273	0.283137	+	0.959080i	$0.408625\pi$
$72$	−1.20379	−0.141869
$73$	−7.38932	−0.864855	−0.432427	−	0.901669i	$-0.642343\pi$
$73$	−7.38932	−0.864855	−0.432427	+	0.901669i	$0.642343\pi$
$74$	−1.66635	−0.193710
$75$	−1.34023	−0.154756
$76$	3.82801	0.439103
$77$	3.34667	0.381388
$78$	3.05720	0.346160
$79$	−8.69240	−0.977971	−0.488986	−	0.872292i	$-0.662633\pi$
$79$	−8.69240	−0.977971	−0.488986	+	0.872292i	$0.662633\pi$
$80$	−1.00000	−0.111803
$81$	−3.93950	−0.437722
$82$	−11.4383	−1.26314
$83$	8.56961	0.940636	0.470318	−	0.882497i	$-0.344139\pi$
$83$	8.56961	0.940636	0.470318	+	0.882497i	$0.344139\pi$
$84$	−0.843589	−0.0920432
$85$	5.32344	0.577408
$86$	7.74664	0.835341
$87$	−8.80212	−0.943687
$88$	5.31691	0.566785
$89$	3.05594	0.323929	0.161965	−	0.986797i	$-0.448217\pi$
$89$	3.05594	0.323929	0.161965	+	0.986797i	$0.448217\pi$
$90$	1.20379	0.126891
$91$	−1.43582	−0.150514
$92$	2.83265	0.295324
$93$	12.3665	1.28235
$94$	6.08505	0.627625
$95$	−3.82801	−0.392746
$96$	−1.34023	−0.136786
$97$	−4.45503	−0.452339	−0.226170	−	0.974088i	$-0.572620\pi$
$97$	−4.45503	−0.452339	−0.226170	+	0.974088i	$0.572620\pi$
$98$	−6.60381	−0.667085
$99$	−6.40047	−0.643271
$100$	1.00000	0.100000
$101$	9.42901	0.938222	0.469111	−	0.883139i	$-0.344574\pi$
$101$	9.42901	0.938222	0.469111	+	0.883139i	$0.344574\pi$
$102$	7.13462	0.706432
$103$	18.9131	1.86356	0.931781	−	0.363022i	$-0.118255\pi$
$103$	18.9131	1.86356	0.931781	+	0.363022i	$0.118255\pi$
$104$	−2.28111	−0.223681
$105$	0.843589	0.0823259
$106$	11.4820	1.11523
$107$	10.4972	1.01480	0.507401	−	0.861710i	$-0.330606\pi$
$107$	10.4972	1.01480	0.507401	+	0.861710i	$0.330606\pi$
$108$	5.63403	0.542135
$109$	−2.07688	−0.198929	−0.0994647	−	0.995041i	$-0.531713\pi$
$109$	−2.07688	−0.198929	−0.0994647	+	0.995041i	$0.531713\pi$
$110$	−5.31691	−0.506948
$111$	2.23329	0.211975
$112$	0.629438	0.0594763
$113$	2.25851	0.212463	0.106232	−	0.994341i	$-0.466122\pi$
$113$	2.25851	0.212463	0.106232	+	0.994341i	$0.466122\pi$
$114$	−5.13040	−0.480506
$115$	−2.83265	−0.264146
$116$	6.56764	0.609790
$117$	2.74598	0.253866
$118$	2.23753	0.205981
$119$	−3.35078	−0.307165
$120$	1.34023	0.122345
$121$	17.2695	1.56996
$122$	−1.18470	−0.107258
$123$	15.3298	1.38225
$124$	−9.22718	−0.828625
$125$	−1.00000	−0.0894427
$126$	−0.757714	−0.0675026
$127$	20.6592	1.83320	0.916602	−	0.399801i	$-0.130921\pi$
$127$	20.6592	1.83320	0.916602	+	0.399801i	$0.130921\pi$
$128$	1.00000	0.0883883
$129$	−10.3822	−0.914106
$130$	2.28111	0.200066
$131$	−10.6019	−0.926289	−0.463145	−	0.886283i	$-0.653279\pi$
$131$	−10.6019	−0.926289	−0.463145	+	0.886283i	$0.653279\pi$
$132$	−7.12586	−0.620227
$133$	2.40950	0.208930
$134$	13.2856	1.14770
$135$	−5.63403	−0.484900
$136$	−5.32344	−0.456481
$137$	7.13318	0.609429	0.304715	−	0.952444i	$-0.401439\pi$
$137$	7.13318	0.609429	0.304715	+	0.952444i	$0.401439\pi$
$138$	−3.79639	−0.323170
$139$	18.0646	1.53222	0.766109	−	0.642711i	$-0.222190\pi$
$139$	18.0646	1.53222	0.766109	+	0.642711i	$0.222190\pi$
$140$	−0.629438	−0.0531972
$141$	−8.15535	−0.686804
$142$	4.77151	0.400416
$143$	−12.1284	−1.01423
$144$	−1.20379	−0.100316
$145$	−6.56764	−0.545413
$146$	−7.38932	−0.611545
$147$	8.85059	0.729985
$148$	−1.66635	−0.136973
$149$	−17.1741	−1.40696	−0.703478	−	0.710717i	$-0.748370\pi$
$149$	−17.1741	−1.40696	−0.703478	+	0.710717i	$0.748370\pi$
$150$	−1.34023	−0.109429
$151$	−8.13794	−0.662256	−0.331128	−	0.943586i	$-0.607429\pi$
$151$	−8.13794	−0.662256	−0.331128	+	0.943586i	$0.607429\pi$
$152$	3.82801	0.310493
$153$	6.40833	0.518083
$154$	3.34667	0.269682
$155$	9.22718	0.741145
$156$	3.05720	0.244772
$157$	−5.43917	−0.434093	−0.217047	−	0.976161i	$-0.569642\pi$
$157$	−5.43917	−0.434093	−0.217047	+	0.976161i	$0.569642\pi$
$158$	−8.69240	−0.691530
$159$	−15.3885	−1.22038
$160$	−1.00000	−0.0790569
$161$	1.78298	0.140518
$162$	−3.93950	−0.309516
$163$	21.9943	1.72273	0.861364	−	0.507989i	$-0.169611\pi$
$163$	21.9943	1.72273	0.861364	+	0.507989i	$0.169611\pi$
$164$	−11.4383	−0.893178
$165$	7.12586	0.554748
$166$	8.56961	0.665130
$167$	−7.59260	−0.587533	−0.293766	−	0.955877i	$-0.594909\pi$
$167$	−7.59260	−0.587533	−0.293766	+	0.955877i	$0.594909\pi$
$168$	−0.843589	−0.0650843
$169$	−7.79655	−0.599735
$170$	5.32344	0.408289
$171$	−4.60814	−0.352393
$172$	7.74664	0.590676
$173$	−6.17284	−0.469313	−0.234656	−	0.972078i	$-0.575396\pi$
$173$	−6.17284	−0.469313	−0.234656	+	0.972078i	$0.575396\pi$
$174$	−8.80212	−0.667287
$175$	0.629438	0.0475811
$176$	5.31691	0.400777
$177$	−2.99880	−0.225403
$178$	3.05594	0.229053
$179$	15.4641	1.15584	0.577920	−	0.816093i	$-0.303864\pi$
$179$	15.4641	1.15584	0.577920	+	0.816093i	$0.303864\pi$
$180$	1.20379	0.0897255
$181$	19.2301	1.42936	0.714681	−	0.699451i	$-0.246572\pi$
$181$	19.2301	1.42936	0.714681	+	0.699451i	$0.246572\pi$
$182$	−1.43582	−0.106430
$183$	1.58777	0.117371
$184$	2.83265	0.208826
$185$	1.66635	0.122513
$186$	12.3665	0.906756
$187$	−28.3043	−2.06981
$188$	6.08505	0.443798
$189$	3.54628	0.257954
$190$	−3.82801	−0.277713
$191$	−6.42413	−0.464834	−0.232417	−	0.972616i	$-0.574663\pi$
$191$	−6.42413	−0.464834	−0.232417	+	0.972616i	$0.574663\pi$
$192$	−1.34023	−0.0967225
$193$	14.6142	1.05195	0.525975	−	0.850500i	$-0.323700\pi$
$193$	14.6142	1.05195	0.525975	+	0.850500i	$0.323700\pi$
$194$	−4.45503	−0.319852
$195$	−3.05720	−0.218931
$196$	−6.60381	−0.471701
$197$	−0.508433	−0.0362243	−0.0181122	−	0.999836i	$-0.505766\pi$
$197$	−0.508433	−0.0362243	−0.0181122	+	0.999836i	$0.505766\pi$
$198$	−6.40047	−0.454861
$199$	−3.23551	−0.229359	−0.114680	−	0.993403i	$-0.536584\pi$
$199$	−3.23551	−0.229359	−0.114680	+	0.993403i	$0.536584\pi$
$200$	1.00000	0.0707107
$201$	−17.8057	−1.25591
$202$	9.42901	0.663423
$203$	4.13392	0.290145
$204$	7.13462	0.499523
$205$	11.4383	0.798882
$206$	18.9131	1.31774
$207$	−3.40993	−0.237006
$208$	−2.28111	−0.158166
$209$	20.3532	1.40786
$210$	0.843589	0.0582132
$211$	−27.7651	−1.91143	−0.955715	−	0.294293i	$-0.904916\pi$
$211$	−27.7651	−1.91143	−0.955715	+	0.294293i	$0.904916\pi$
$212$	11.4820	0.788586
$213$	−6.39489	−0.438171
$214$	10.4972	0.717574
$215$	−7.74664	−0.528316
$216$	5.63403	0.383347
$217$	−5.80794	−0.394269
$218$	−2.07688	−0.140664
$219$	9.90336	0.669207
$220$	−5.31691	−0.358466
$221$	12.1433	0.816849
$222$	2.23329	0.149889
$223$	15.9113	1.06550	0.532751	−	0.846272i	$-0.321158\pi$
$223$	15.9113	1.06550	0.532751	+	0.846272i	$0.321158\pi$
$224$	0.629438	0.0420561
$225$	−1.20379	−0.0802530
$226$	2.25851	0.150234
$227$	−2.09312	−0.138925	−0.0694627	−	0.997585i	$-0.522128\pi$
$227$	−2.09312	−0.138925	−0.0694627	+	0.997585i	$0.522128\pi$
$228$	−5.13040	−0.339769
$229$	26.4539	1.74812	0.874062	−	0.485813i	$-0.161477\pi$
$229$	26.4539	1.74812	0.874062	+	0.485813i	$0.161477\pi$
$230$	−2.83265	−0.186779
$231$	−4.48529	−0.295110
$232$	6.56764	0.431187
$233$	2.96586	0.194300	0.0971499	−	0.995270i	$-0.469027\pi$
$233$	2.96586	0.194300	0.0971499	+	0.995270i	$0.469027\pi$
$234$	2.74598	0.179511
$235$	−6.08505	−0.396945
$236$	2.23753	0.145651
$237$	11.6498	0.756734
$238$	−3.35078	−0.217199
$239$	24.3398	1.57441	0.787205	−	0.616691i	$-0.211527\pi$
$239$	24.3398	1.57441	0.787205	+	0.616691i	$0.211527\pi$
$240$	1.34023	0.0865112
$241$	24.9195	1.60521	0.802605	−	0.596511i	$-0.203447\pi$
$241$	24.9195	1.60521	0.802605	+	0.596511i	$0.203447\pi$
$242$	17.2695	1.11013
$243$	−11.6223	−0.745570
$244$	−1.18470	−0.0758427
$245$	6.60381	0.421902
$246$	15.3298	0.977395
$247$	−8.73211	−0.555611
$248$	−9.22718	−0.585926
$249$	−11.4852	−0.727845
$250$	−1.00000	−0.0632456
$251$	20.4819	1.29281	0.646403	−	0.762996i	$-0.276273\pi$
$251$	20.4819	1.29281	0.646403	+	0.762996i	$0.276273\pi$
$252$	−0.757714	−0.0477315
$253$	15.0609	0.946873
$254$	20.6592	1.29627
$255$	−7.13462	−0.446787
$256$	1.00000	0.0625000
$257$	−3.01936	−0.188342	−0.0941712	−	0.995556i	$-0.530020\pi$
$257$	−3.01936	−0.188342	−0.0941712	+	0.995556i	$0.530020\pi$
$258$	−10.3822	−0.646370
$259$	−1.04887	−0.0651734
$260$	2.28111	0.141468
$261$	−7.90609	−0.489375
$262$	−10.6019	−0.654986
$263$	18.6660	1.15099	0.575496	−	0.817804i	$-0.304809\pi$
$263$	18.6660	1.15099	0.575496	+	0.817804i	$0.304809\pi$
$264$	−7.12586	−0.438567
$265$	−11.4820	−0.705333
$266$	2.40950	0.147736
$267$	−4.09565	−0.250650
$268$	13.2856	0.811545
$269$	−16.2551	−0.991090	−0.495545	−	0.868582i	$-0.665032\pi$
$269$	−16.2551	−0.991090	−0.495545	+	0.868582i	$0.665032\pi$
$270$	−5.63403	−0.342876
$271$	−18.7394	−1.13834	−0.569168	−	0.822222i	$-0.692734\pi$
$271$	−18.7394	−1.13834	−0.569168	+	0.822222i	$0.692734\pi$
$272$	−5.32344	−0.322781
$273$	1.92432	0.116465
$274$	7.13318	0.430931
$275$	5.31691	0.320622
$276$	−3.79639	−0.228516
$277$	−3.07414	−0.184707	−0.0923536	−	0.995726i	$-0.529439\pi$
$277$	−3.07414	−0.184707	−0.0923536	+	0.995726i	$0.529439\pi$
$278$	18.0646	1.08344
$279$	11.1076	0.664996
$280$	−0.629438	−0.0376161
$281$	−27.4092	−1.63510	−0.817549	−	0.575859i	$-0.804668\pi$
$281$	−27.4092	−1.63510	−0.817549	+	0.575859i	$0.804668\pi$
$282$	−8.15535	−0.485644
$283$	29.3144	1.74256	0.871280	−	0.490786i	$-0.163290\pi$
$283$	29.3144	1.74256	0.871280	+	0.490786i	$0.163290\pi$
$284$	4.77151	0.283137
$285$	5.13040	0.303899
$286$	−12.1284	−0.717170
$287$	−7.19968	−0.424983
$288$	−1.20379	−0.0709343
$289$	11.3390	0.667003
$290$	−6.56764	−0.385665
$291$	5.97074	0.350011
$292$	−7.38932	−0.432427
$293$	5.55713	0.324651	0.162326	−	0.986737i	$-0.448101\pi$
$293$	5.55713	0.324651	0.162326	+	0.986737i	$0.448101\pi$
$294$	8.85059	0.516177
$295$	−2.23753	−0.130274
$296$	−1.66635	−0.0968549
$297$	29.9557	1.73820
$298$	−17.1741	−0.994868
$299$	−6.46157	−0.373682
$300$	−1.34023	−0.0773780
$301$	4.87603	0.281050
$302$	−8.13794	−0.468286
$303$	−12.6370	−0.725977
$304$	3.82801	0.219552
$305$	1.18470	0.0678358
$306$	6.40833	0.366340
$307$	−21.0370	−1.20065	−0.600324	−	0.799757i	$-0.704962\pi$
$307$	−21.0370	−1.20065	−0.600324	+	0.799757i	$0.704962\pi$
$308$	3.34667	0.190694
$309$	−25.3478	−1.44199
$310$	9.22718	0.524069
$311$	6.17151	0.349954	0.174977	−	0.984572i	$-0.444015\pi$
$311$	6.17151	0.349954	0.174977	+	0.984572i	$0.444015\pi$
$312$	3.05720	0.173080
$313$	−5.22818	−0.295514	−0.147757	−	0.989024i	$-0.547205\pi$
$313$	−5.22818	−0.295514	−0.147757	+	0.989024i	$0.547205\pi$
$314$	−5.43917	−0.306950
$315$	0.757714	0.0426924
$316$	−8.69240	−0.488986
$317$	−6.30363	−0.354047	−0.177024	−	0.984207i	$-0.556647\pi$
$317$	−6.30363	−0.354047	−0.177024	+	0.984207i	$0.556647\pi$
$318$	−15.3885	−0.862942
$319$	34.9196	1.95512
$320$	−1.00000	−0.0559017
$321$	−14.0686	−0.785234
$322$	1.78298	0.0993614
$323$	−20.3782	−1.13387
$324$	−3.93950	−0.218861
$325$	−2.28111	−0.126533
$326$	21.9943	1.21815
$327$	2.78349	0.153928
$328$	−11.4383	−0.631572
$329$	3.83017	0.211164
$330$	7.12586	0.392266
$331$	27.9884	1.53838	0.769192	−	0.639018i	$-0.220659\pi$
$331$	27.9884	1.53838	0.769192	+	0.639018i	$0.220659\pi$
$332$	8.56961	0.470318
$333$	2.00595	0.109925
$334$	−7.59260	−0.415448
$335$	−13.2856	−0.725868
$336$	−0.843589	−0.0460216
$337$	−25.8306	−1.40708	−0.703541	−	0.710655i	$-0.748399\pi$
$337$	−25.8306	−1.40708	−0.703541	+	0.710655i	$0.748399\pi$
$338$	−7.79655	−0.424077
$339$	−3.02692	−0.164400
$340$	5.32344	0.288704
$341$	−49.0601	−2.65675
$342$	−4.60814	−0.249180
$343$	−8.56276	−0.462345
$344$	7.74664	0.417671
$345$	3.79639	0.204391
$346$	−6.17284	−0.331854
$347$	−22.5211	−1.20900	−0.604498	−	0.796607i	$-0.706626\pi$
$347$	−22.5211	−1.20900	−0.604498	+	0.796607i	$0.706626\pi$
$348$	−8.80212	−0.471843
$349$	2.99048	0.160077	0.0800384	−	0.996792i	$-0.474496\pi$
$349$	2.99048	0.160077	0.0800384	+	0.996792i	$0.474496\pi$
$350$	0.629438	0.0336449
$351$	−12.8518	−0.685980
$352$	5.31691	0.283392
$353$	4.08481	0.217413	0.108706	−	0.994074i	$-0.465329\pi$
$353$	4.08481	0.217413	0.108706	+	0.994074i	$0.465329\pi$
$354$	−2.99880	−0.159384
$355$	−4.77151	−0.253245
$356$	3.05594	0.161965
$357$	4.49080	0.237678
$358$	15.4641	0.817303
$359$	−13.7648	−0.726477	−0.363238	−	0.931696i	$-0.618329\pi$
$359$	−13.7648	−0.726477	−0.363238	+	0.931696i	$0.618329\pi$
$360$	1.20379	0.0634455
$361$	−4.34631	−0.228753
$362$	19.2301	1.01071
$363$	−23.1451	−1.21480
$364$	−1.43582	−0.0752572
$365$	7.38932	0.386775
$366$	1.58777	0.0829939
$367$	−6.22540	−0.324963	−0.162482	−	0.986712i	$-0.551950\pi$
$367$	−6.22540	−0.324963	−0.162482	+	0.986712i	$0.551950\pi$
$368$	2.83265	0.147662
$369$	13.7693	0.716802
$370$	1.66635	0.0866296
$371$	7.22720	0.375218
$372$	12.3665	0.641173
$373$	5.47137	0.283297	0.141648	−	0.989917i	$-0.454760\pi$
$373$	5.47137	0.283297	0.141648	+	0.989917i	$0.454760\pi$
$374$	−28.3043	−1.46358
$375$	1.34023	0.0692090
$376$	6.08505	0.313813
$377$	−14.9815	−0.771586
$378$	3.54628	0.182401
$379$	−19.6499	−1.00935	−0.504674	−	0.863310i	$-0.668387\pi$
$379$	−19.6499	−1.00935	−0.504674	+	0.863310i	$0.668387\pi$
$380$	−3.82801	−0.196373
$381$	−27.6879	−1.41850
$382$	−6.42413	−0.328687
$383$	12.8627	0.657251	0.328626	−	0.944460i	$-0.393415\pi$
$383$	12.8627	0.657251	0.328626	+	0.944460i	$0.393415\pi$
$384$	−1.34023	−0.0683931
$385$	−3.34667	−0.170562
$386$	14.6142	0.743841
$387$	−9.32536	−0.474035
$388$	−4.45503	−0.226170
$389$	29.5389	1.49768	0.748841	−	0.662750i	$-0.230611\pi$
$389$	29.5389	1.49768	0.748841	+	0.662750i	$0.230611\pi$
$390$	−3.05720	−0.154807
$391$	−15.0794	−0.762600
$392$	−6.60381	−0.333543
$393$	14.2089	0.716744
$394$	−0.508433	−0.0256145
$395$	8.69240	0.437362
$396$	−6.40047	−0.321636
$397$	−24.9989	−1.25466	−0.627329	−	0.778755i	$-0.715852\pi$
$397$	−24.9989	−1.25466	−0.627329	+	0.778755i	$0.715852\pi$
$398$	−3.23551	−0.162182
$399$	−3.22927	−0.161666
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−17.8057	−0.888065
$403$	21.0482	1.04848
$404$	9.42901	0.469111
$405$	3.93950	0.195755
$406$	4.13392	0.205163
$407$	−8.85986	−0.439167
$408$	7.13462	0.353216
$409$	26.7097	1.32071	0.660355	−	0.750954i	$-0.270406\pi$
$409$	26.7097	1.32071	0.660355	+	0.750954i	$0.270406\pi$
$410$	11.4383	0.564895
$411$	−9.56008	−0.471564
$412$	18.9131	0.931781
$413$	1.40839	0.0693022
$414$	−3.40993	−0.167589
$415$	−8.56961	−0.420665
$416$	−2.28111	−0.111840
$417$	−24.2106	−1.18560
$418$	20.3532	0.995508
$419$	6.67207	0.325952	0.162976	−	0.986630i	$-0.447891\pi$
$419$	6.67207	0.325952	0.162976	+	0.986630i	$0.447891\pi$
$420$	0.843589	0.0411630
$421$	5.32703	0.259624	0.129812	−	0.991539i	$-0.458563\pi$
$421$	5.32703	0.259624	0.129812	+	0.991539i	$0.458563\pi$
$422$	−27.7651	−1.35159
$423$	−7.32515	−0.356161
$424$	11.4820	0.557614
$425$	−5.32344	−0.258225
$426$	−6.39489	−0.309834
$427$	−0.745696	−0.0360868
$428$	10.4972	0.507401
$429$	16.2549	0.784792
$430$	−7.74664	−0.373576
$431$	−33.4408	−1.61079	−0.805393	−	0.592741i	$-0.798046\pi$
$431$	−33.4408	−1.61079	−0.805393	+	0.592741i	$0.798046\pi$
$432$	5.63403	0.271068
$433$	−1.71070	−0.0822109	−0.0411054	−	0.999155i	$-0.513088\pi$
$433$	−1.71070	−0.0822109	−0.0411054	+	0.999155i	$0.513088\pi$
$434$	−5.80794	−0.278790
$435$	8.80212	0.422029
$436$	−2.07688	−0.0994647
$437$	10.8434	0.518711
$438$	9.90336	0.473201
$439$	17.6151	0.840721	0.420360	−	0.907357i	$-0.361904\pi$
$439$	17.6151	0.840721	0.420360	+	0.907357i	$0.361904\pi$
$440$	−5.31691	−0.253474
$441$	7.94963	0.378554
$442$	12.1433	0.577600
$443$	−28.8753	−1.37191	−0.685955	−	0.727644i	$-0.740615\pi$
$443$	−28.8753	−1.37191	−0.685955	+	0.727644i	$0.740615\pi$
$444$	2.23329	0.105987
$445$	−3.05594	−0.144866
$446$	15.9113	0.753424
$447$	23.0171	1.08867
$448$	0.629438	0.0297382
$449$	23.8510	1.12560	0.562799	−	0.826593i	$-0.309724\pi$
$449$	23.8510	1.12560	0.562799	+	0.826593i	$0.309724\pi$
$450$	−1.20379	−0.0567474
$451$	−60.8162	−2.86372
$452$	2.25851	0.106232
$453$	10.9067	0.512440
$454$	−2.09312	−0.0982350
$455$	1.43582	0.0673121
$456$	−5.13040	−0.240253
$457$	−17.9314	−0.838797	−0.419399	−	0.907802i	$-0.637759\pi$
$457$	−17.9314	−0.838797	−0.419399	+	0.907802i	$0.637759\pi$
$458$	26.4539	1.23611
$459$	−29.9925	−1.39993
$460$	−2.83265	−0.132073
$461$	23.5048	1.09473	0.547363	−	0.836895i	$-0.315632\pi$
$461$	23.5048	1.09473	0.547363	+	0.836895i	$0.315632\pi$
$462$	−4.48529	−0.208675
$463$	26.4428	1.22890	0.614452	−	0.788955i	$-0.289377\pi$
$463$	26.4428	1.22890	0.614452	+	0.788955i	$0.289377\pi$
$464$	6.56764	0.304895
$465$	−12.3665	−0.573483
$466$	2.96586	0.137391
$467$	−28.7680	−1.33122	−0.665612	−	0.746298i	$-0.731830\pi$
$467$	−28.7680	−1.33122	−0.665612	+	0.746298i	$0.731830\pi$
$468$	2.74598	0.126933
$469$	8.36244	0.386142
$470$	−6.08505	−0.280683
$471$	7.28972	0.335893
$472$	2.23753	0.102991
$473$	41.1882	1.89383
$474$	11.6498	0.535092
$475$	3.82801	0.175641
$476$	−3.35078	−0.153583
$477$	−13.8219	−0.632864
$478$	24.3398	1.11328
$479$	−18.1118	−0.827548	−0.413774	−	0.910380i	$-0.635790\pi$
$479$	−18.1118	−0.827548	−0.413774	+	0.910380i	$0.635790\pi$
$480$	1.34023	0.0611727
$481$	3.80113	0.173317
$482$	24.9195	1.13505
$483$	−2.38959	−0.108730
$484$	17.2695	0.784979
$485$	4.45503	0.202292
$486$	−11.6223	−0.527198
$487$	−28.4853	−1.29079	−0.645396	−	0.763849i	$-0.723307\pi$
$487$	−28.4853	−1.29079	−0.645396	+	0.763849i	$0.723307\pi$
$488$	−1.18470	−0.0536289
$489$	−29.4773	−1.33301
$490$	6.60381	0.298330
$491$	−35.4381	−1.59930	−0.799649	−	0.600467i	$-0.794981\pi$
$491$	−35.4381	−1.59930	−0.799649	+	0.600467i	$0.794981\pi$
$492$	15.3298	0.691123
$493$	−34.9625	−1.57463
$494$	−8.73211	−0.392876
$495$	6.40047	0.287680
$496$	−9.22718	−0.414313
$497$	3.00337	0.134719
$498$	−11.4852	−0.514664
$499$	−31.8386	−1.42529	−0.712647	−	0.701523i	$-0.752504\pi$
$499$	−31.8386	−1.42529	−0.712647	+	0.701523i	$0.752504\pi$
$500$	−1.00000	−0.0447214
$501$	10.1758	0.454621
$502$	20.4819	0.914152
$503$	−35.4420	−1.58028	−0.790141	−	0.612925i	$-0.789993\pi$
$503$	−35.4420	−1.58028	−0.790141	+	0.612925i	$0.789993\pi$
$504$	−0.757714	−0.0337513
$505$	−9.42901	−0.419585
$506$	15.0609	0.669540
$507$	10.4491	0.464063
$508$	20.6592	0.916602
$509$	28.4404	1.26060	0.630299	−	0.776352i	$-0.282932\pi$
$509$	28.4404	1.26060	0.630299	+	0.776352i	$0.282932\pi$
$510$	−7.13462	−0.315926
$511$	−4.65112	−0.205754
$512$	1.00000	0.0441942
$513$	21.5672	0.952214
$514$	−3.01936	−0.133178
$515$	−18.9131	−0.833410
$516$	−10.3822	−0.457053
$517$	32.3537	1.42291
$518$	−1.04887	−0.0460846
$519$	8.27301	0.363145
$520$	2.28111	0.100033
$521$	35.6515	1.56192	0.780960	−	0.624581i	$-0.214730\pi$
$521$	35.6515	1.56192	0.780960	+	0.624581i	$0.214730\pi$
$522$	−7.90609	−0.346040
$523$	−14.4347	−0.631183	−0.315592	−	0.948895i	$-0.602203\pi$
$523$	−14.4347	−0.631183	−0.315592	+	0.948895i	$0.602203\pi$
$524$	−10.6019	−0.463145
$525$	−0.843589	−0.0368173
$526$	18.6660	0.813875
$527$	49.1204	2.13972
$528$	−7.12586	−0.310113
$529$	−14.9761	−0.651135
$530$	−11.4820	−0.498745
$531$	−2.69353	−0.116889
$532$	2.40950	0.104465
$533$	26.0919	1.13016
$534$	−4.09565	−0.177236
$535$	−10.4972	−0.453834
$536$	13.2856	0.573849
$537$	−20.7254	−0.894366
$538$	−16.2551	−0.700807
$539$	−35.1119	−1.51237
$540$	−5.63403	−0.242450
$541$	−8.30805	−0.357191	−0.178595	−	0.983923i	$-0.557155\pi$
$541$	−8.30805	−0.357191	−0.178595	+	0.983923i	$0.557155\pi$
$542$	−18.7394	−0.804924
$543$	−25.7727	−1.10601
$544$	−5.32344	−0.228241
$545$	2.07688	0.0889640
$546$	1.92432	0.0823532
$547$	13.0099	0.556263	0.278132	−	0.960543i	$-0.410285\pi$
$547$	13.0099	0.556263	0.278132	+	0.960543i	$0.410285\pi$
$548$	7.13318	0.304715
$549$	1.42614	0.0608660
$550$	5.31691	0.226714
$551$	25.1410	1.07104
$552$	−3.79639	−0.161585
$553$	−5.47133	−0.232665
$554$	−3.07414	−0.130608
$555$	−2.23329	−0.0947979
$556$	18.0646	0.766109
$557$	−18.1936	−0.770886	−0.385443	−	0.922732i	$-0.625951\pi$
$557$	−18.1936	−0.770886	−0.385443	+	0.922732i	$0.625951\pi$
$558$	11.1076	0.470223
$559$	−17.6709	−0.747400
$560$	−0.629438	−0.0265986
$561$	37.9341	1.60158
$562$	−27.4092	−1.15619
$563$	−39.7579	−1.67559	−0.837797	−	0.545982i	$-0.816157\pi$
$563$	−39.7579	−1.67559	−0.837797	+	0.545982i	$0.816157\pi$
$564$	−8.15535	−0.343402
$565$	−2.25851	−0.0950164
$566$	29.3144	1.23218
$567$	−2.47967	−0.104136
$568$	4.77151	0.200208
$569$	−39.9296	−1.67393	−0.836967	−	0.547253i	$-0.815674\pi$
$569$	−39.9296	−1.67393	−0.836967	+	0.547253i	$0.815674\pi$
$570$	5.13040	0.214889
$571$	−9.49782	−0.397471	−0.198736	−	0.980053i	$-0.563684\pi$
$571$	−9.49782	−0.397471	−0.198736	+	0.980053i	$0.563684\pi$
$572$	−12.1284	−0.507116
$573$	8.60978	0.359679
$574$	−7.19968	−0.300509
$575$	2.83265	0.118130
$576$	−1.20379	−0.0501581
$577$	15.2081	0.633120	0.316560	−	0.948572i	$-0.397472\pi$
$577$	15.2081	0.633120	0.316560	+	0.948572i	$0.397472\pi$
$578$	11.3390	0.471642
$579$	−19.5863	−0.813978
$580$	−6.56764	−0.272706
$581$	5.39404	0.223782
$582$	5.97074	0.247495
$583$	61.0487	2.52838
$584$	−7.38932	−0.305772
$585$	−2.74598	−0.113532
$586$	5.55713	0.229563
$587$	17.6775	0.729628	0.364814	−	0.931080i	$-0.381133\pi$
$587$	17.6775	0.729628	0.364814	+	0.931080i	$0.381133\pi$
$588$	8.85059	0.364992
$589$	−35.3218	−1.45541
$590$	−2.23753	−0.0921177
$591$	0.681414	0.0280296
$592$	−1.66635	−0.0684867
$593$	−20.7323	−0.851375	−0.425688	−	0.904870i	$-0.639968\pi$
$593$	−20.7323	−0.851375	−0.425688	+	0.904870i	$0.639968\pi$
$594$	29.9557	1.22910
$595$	3.35078	0.137369
$596$	−17.1741	−0.703478
$597$	4.33632	0.177474
$598$	−6.46157	−0.264233
$599$	−31.0075	−1.26693	−0.633467	−	0.773770i	$-0.718369\pi$
$599$	−31.0075	−1.26693	−0.633467	+	0.773770i	$0.718369\pi$
$600$	−1.34023	−0.0547145
$601$	−13.6646	−0.557391	−0.278695	−	0.960380i	$-0.589902\pi$
$601$	−13.6646	−0.557391	−0.278695	+	0.960380i	$0.589902\pi$
$602$	4.87603	0.198732
$603$	−15.9931	−0.651289
$604$	−8.13794	−0.331128
$605$	−17.2695	−0.702107
$606$	−12.6370	−0.513343
$607$	20.6053	0.836343	0.418172	−	0.908368i	$-0.362671\pi$
$607$	20.6053	0.836343	0.418172	+	0.908368i	$0.362671\pi$
$608$	3.82801	0.155246
$609$	−5.54039	−0.224508
$610$	1.18470	0.0479672
$611$	−13.8807	−0.561551
$612$	6.40833	0.259041
$613$	−16.8456	−0.680387	−0.340194	−	0.940355i	$-0.610493\pi$
$613$	−16.8456	−0.680387	−0.340194	+	0.940355i	$0.610493\pi$
$614$	−21.0370	−0.848986
$615$	−15.3298	−0.618159
$616$	3.34667	0.134841
$617$	15.9981	0.644058	0.322029	−	0.946730i	$-0.395635\pi$
$617$	15.9981	0.644058	0.322029	+	0.946730i	$0.395635\pi$
$618$	−25.3478	−1.01964
$619$	−6.03036	−0.242381	−0.121190	−	0.992629i	$-0.538671\pi$
$619$	−6.03036	−0.242381	−0.121190	+	0.992629i	$0.538671\pi$
$620$	9.22718	0.370572
$621$	15.9592	0.640422
$622$	6.17151	0.247455
$623$	1.92353	0.0770645
$624$	3.05720	0.122386
$625$	1.00000	0.0400000
$626$	−5.22818	−0.208960
$627$	−27.2779	−1.08937
$628$	−5.43917	−0.217047
$629$	8.87074	0.353700
$630$	0.757714	0.0301881
$631$	8.58121	0.341612	0.170806	−	0.985305i	$-0.445363\pi$
$631$	8.58121	0.341612	0.170806	+	0.985305i	$0.445363\pi$
$632$	−8.69240	−0.345765
$633$	37.2116	1.47903
$634$	−6.30363	−0.250349
$635$	−20.6592	−0.819834
$636$	−15.3885	−0.610192
$637$	15.0640	0.596857
$638$	34.9196	1.38248
$639$	−5.74391	−0.227226
$640$	−1.00000	−0.0395285
$641$	18.5696	0.733454	0.366727	−	0.930329i	$-0.380478\pi$
$641$	18.5696	0.733454	0.366727	+	0.930329i	$0.380478\pi$
$642$	−14.0686	−0.555244
$643$	10.1652	0.400875	0.200438	−	0.979706i	$-0.435764\pi$
$643$	10.1652	0.400875	0.200438	+	0.979706i	$0.435764\pi$
$644$	1.78298	0.0702591
$645$	10.3822	0.408800
$646$	−20.3782	−0.801770
$647$	−30.5276	−1.20016	−0.600081	−	0.799939i	$-0.704865\pi$
$647$	−30.5276	−1.20016	−0.600081	+	0.799939i	$0.704865\pi$
$648$	−3.93950	−0.154758
$649$	11.8968	0.466988
$650$	−2.28111	−0.0894724
$651$	7.78395	0.305077
$652$	21.9943	0.861364
$653$	50.0685	1.95933	0.979666	−	0.200636i	$-0.0643009\pi$
$653$	50.0685	1.95933	0.979666	+	0.200636i	$0.0643009\pi$
$654$	2.78349	0.108843
$655$	10.6019	0.414249
$656$	−11.4383	−0.446589
$657$	8.89523	0.347036
$658$	3.83017	0.149315
$659$	−30.9445	−1.20543	−0.602713	−	0.797958i	$-0.705914\pi$
$659$	−30.9445	−1.20543	−0.602713	+	0.797958i	$0.705914\pi$
$660$	7.12586	0.277374
$661$	−36.4966	−1.41955	−0.709777	−	0.704426i	$-0.751204\pi$
$661$	−36.4966	−1.41955	−0.709777	+	0.704426i	$0.751204\pi$
$662$	27.9884	1.08780
$663$	−16.2748	−0.632062
$664$	8.56961	0.332565
$665$	−2.40950	−0.0934363
$666$	2.00595	0.0777289
$667$	18.6038	0.720343
$668$	−7.59260	−0.293766
$669$	−21.3248	−0.824465
$670$	−13.2856	−0.513266
$671$	−6.29895	−0.243168
$672$	−0.843589	−0.0325422
$673$	−2.44617	−0.0942931	−0.0471465	−	0.998888i	$-0.515013\pi$
$673$	−2.44617	−0.0942931	−0.0471465	+	0.998888i	$0.515013\pi$
$674$	−25.8306	−0.994957
$675$	5.63403	0.216854
$676$	−7.79655	−0.299867
$677$	24.4195	0.938516	0.469258	−	0.883061i	$-0.344521\pi$
$677$	24.4195	0.938516	0.469258	+	0.883061i	$0.344521\pi$
$678$	−3.02692	−0.116248
$679$	−2.80416	−0.107614
$680$	5.32344	0.204145
$681$	2.80526	0.107498
$682$	−49.0601	−1.87861
$683$	13.1769	0.504200	0.252100	−	0.967701i	$-0.418879\pi$
$683$	13.1769	0.504200	0.252100	+	0.967701i	$0.418879\pi$
$684$	−4.60814	−0.176197
$685$	−7.13318	−0.272545
$686$	−8.56276	−0.326928
$687$	−35.4542	−1.35266
$688$	7.74664	0.295338
$689$	−26.1916	−0.997822
$690$	3.79639	0.144526
$691$	28.6386	1.08947	0.544733	−	0.838610i	$-0.316631\pi$
$691$	28.6386	1.08947	0.544733	+	0.838610i	$0.316631\pi$
$692$	−6.17284	−0.234656
$693$	−4.02870	−0.153038
$694$	−22.5211	−0.854889
$695$	−18.0646	−0.685229
$696$	−8.80212	−0.333644
$697$	60.8909	2.30641
$698$	2.99048	0.113191
$699$	−3.97492	−0.150345
$700$	0.629438	0.0237905
$701$	−30.4278	−1.14924	−0.574621	−	0.818420i	$-0.694850\pi$
$701$	−30.4278	−1.14924	−0.574621	+	0.818420i	$0.694850\pi$
$702$	−12.8518	−0.485061
$703$	−6.37883	−0.240582
$704$	5.31691	0.200389
$705$	8.15535	0.307148
$706$	4.08481	0.153734
$707$	5.93498	0.223208
$708$	−2.99880	−0.112702
$709$	−6.64889	−0.249704	−0.124852	−	0.992175i	$-0.539846\pi$
$709$	−6.64889	−0.249704	−0.124852	+	0.992175i	$0.539846\pi$
$710$	−4.77151	−0.179071
$711$	10.4639	0.392425
$712$	3.05594	0.114526
$713$	−26.1374	−0.978852
$714$	4.49080	0.168064
$715$	12.1284	0.453578
$716$	15.4641	0.577920
$717$	−32.6208	−1.21825
$718$	−13.7648	−0.513697
$719$	35.1901	1.31237	0.656184	−	0.754601i	$-0.272169\pi$
$719$	35.1901	1.31237	0.656184	+	0.754601i	$0.272169\pi$
$720$	1.20379	0.0448628
$721$	11.9046	0.443351
$722$	−4.34631	−0.161753
$723$	−33.3978	−1.24208
$724$	19.2301	0.714681
$725$	6.56764	0.243916
$726$	−23.1451	−0.858995
$727$	12.0548	0.447086	0.223543	−	0.974694i	$-0.428238\pi$
$727$	12.0548	0.447086	0.223543	+	0.974694i	$0.428238\pi$
$728$	−1.43582	−0.0532149
$729$	27.3950	1.01463
$730$	7.38932	0.273491
$731$	−41.2388	−1.52527
$732$	1.58777	0.0586856
$733$	15.6326	0.577402	0.288701	−	0.957419i	$-0.406777\pi$
$733$	15.6326	0.577402	0.288701	+	0.957419i	$0.406777\pi$
$734$	−6.22540	−0.229784
$735$	−8.85059	−0.326459
$736$	2.83265	0.104413
$737$	70.6381	2.60199
$738$	13.7693	0.506855
$739$	38.3245	1.40979	0.704895	−	0.709311i	$-0.250994\pi$
$739$	38.3245	1.40979	0.704895	+	0.709311i	$0.250994\pi$
$740$	1.66635	0.0612564
$741$	11.7030	0.429920
$742$	7.22720	0.265319
$743$	32.8123	1.20377	0.601883	−	0.798585i	$-0.294418\pi$
$743$	32.8123	1.20377	0.601883	+	0.798585i	$0.294418\pi$
$744$	12.3665	0.453378
$745$	17.1741	0.629210
$746$	5.47137	0.200321
$747$	−10.3160	−0.377444
$748$	−28.3043	−1.03491
$749$	6.60734	0.241427
$750$	1.34023	0.0489381
$751$	−16.5408	−0.603583	−0.301791	−	0.953374i	$-0.597585\pi$
$751$	−16.5408	−0.603583	−0.301791	+	0.953374i	$0.597585\pi$
$752$	6.08505	0.221899
$753$	−27.4504	−1.00035
$754$	−14.9815	−0.545594
$755$	8.13794	0.296170
$756$	3.54628	0.128977
$757$	−39.8431	−1.44812	−0.724061	−	0.689736i	$-0.757727\pi$
$757$	−39.8431	−1.44812	−0.724061	+	0.689736i	$0.757727\pi$
$758$	−19.6499	−0.713717
$759$	−20.1851	−0.732671
$760$	−3.82801	−0.138857
$761$	−17.8598	−0.647416	−0.323708	−	0.946157i	$-0.604929\pi$
$761$	−17.8598	−0.647416	−0.323708	+	0.946157i	$0.604929\pi$
$762$	−27.6879	−1.00303
$763$	−1.30727	−0.0473264
$764$	−6.42413	−0.232417
$765$	−6.40833	−0.231694
$766$	12.8627	0.464747
$767$	−5.10405	−0.184296
$768$	−1.34023	−0.0483612
$769$	12.9146	0.465714	0.232857	−	0.972511i	$-0.425193\pi$
$769$	12.9146	0.465714	0.232857	+	0.972511i	$0.425193\pi$
$770$	−3.34667	−0.120606
$771$	4.04662	0.145736
$772$	14.6142	0.525975
$773$	−22.1021	−0.794958	−0.397479	−	0.917611i	$-0.630115\pi$
$773$	−22.1021	−0.794958	−0.397479	+	0.917611i	$0.630115\pi$
$774$	−9.32536	−0.335193
$775$	−9.22718	−0.331450
$776$	−4.45503	−0.159926
$777$	1.40572	0.0504299
$778$	29.5389	1.05902
$779$	−43.7858	−1.56879
$780$	−3.05720	−0.109465
$781$	25.3697	0.907798
$782$	−15.0794	−0.539240
$783$	37.0023	1.32235
$784$	−6.60381	−0.235850
$785$	5.43917	0.194132
$786$	14.2089	0.506815
$787$	−39.8347	−1.41995	−0.709976	−	0.704225i	$-0.751294\pi$
$787$	−39.8347	−1.41995	−0.709976	+	0.704225i	$0.751294\pi$
$788$	−0.508433	−0.0181122
$789$	−25.0166	−0.890615
$790$	8.69240	0.309262
$791$	1.42160	0.0505461
$792$	−6.40047	−0.227431
$793$	2.70243	0.0959661
$794$	−24.9989	−0.887177
$795$	15.3885	0.545772
$796$	−3.23551	−0.114680
$797$	21.6879	0.768223	0.384112	−	0.923287i	$-0.374508\pi$
$797$	21.6879	0.768223	0.384112	+	0.923287i	$0.374508\pi$
$798$	−3.22927	−0.114315
$799$	−32.3934	−1.14600
$800$	1.00000	0.0353553
$801$	−3.67873	−0.129981
$802$	−1.00000	−0.0353112
$803$	−39.2884	−1.38646
$804$	−17.8057	−0.627957
$805$	−1.78298	−0.0628417
$806$	21.0482	0.741391
$807$	21.7855	0.766886
$808$	9.42901	0.331711
$809$	−41.1605	−1.44713	−0.723563	−	0.690258i	$-0.757497\pi$
$809$	−41.1605	−1.44713	−0.723563	+	0.690258i	$0.757497\pi$
$810$	3.93950	0.138420
$811$	39.5183	1.38767	0.693837	−	0.720132i	$-0.255919\pi$
$811$	39.5183	1.38767	0.693837	+	0.720132i	$0.255919\pi$
$812$	4.13392	0.145072
$813$	25.1150	0.880821
$814$	−8.85986	−0.310538
$815$	−21.9943	−0.770427
$816$	7.13462	0.249762
$817$	29.6542	1.03747
$818$	26.7097	0.933883
$819$	1.72843	0.0603961
$820$	11.4383	0.399441
$821$	−30.3012	−1.05752	−0.528760	−	0.848772i	$-0.677343\pi$
$821$	−30.3012	−1.05752	−0.528760	+	0.848772i	$0.677343\pi$
$822$	−9.56008	−0.333446
$823$	5.46676	0.190559	0.0952796	−	0.995451i	$-0.469625\pi$
$823$	5.46676	0.190559	0.0952796	+	0.995451i	$0.469625\pi$
$824$	18.9131	0.658868
$825$	−7.12586	−0.248091
$826$	1.40839	0.0490041
$827$	−11.1014	−0.386035	−0.193018	−	0.981195i	$-0.561827\pi$
$827$	−11.1014	−0.386035	−0.193018	+	0.981195i	$0.561827\pi$
$828$	−3.40993	−0.118503
$829$	−2.71132	−0.0941679	−0.0470840	−	0.998891i	$-0.514993\pi$
$829$	−2.71132	−0.0941679	−0.0470840	+	0.998891i	$0.514993\pi$
$830$	−8.56961	−0.297455
$831$	4.12004	0.142923
$832$	−2.28111	−0.0790831
$833$	35.1550	1.21805
$834$	−24.2106	−0.838345
$835$	7.59260	0.262753
$836$	20.3532	0.703931
$837$	−51.9862	−1.79691
$838$	6.67207	0.230483
$839$	−15.7230	−0.542817	−0.271409	−	0.962464i	$-0.587489\pi$
$839$	−15.7230	−0.542817	−0.271409	+	0.962464i	$0.587489\pi$
$840$	0.843589	0.0291066
$841$	14.1339	0.487376
$842$	5.32703	0.183582
$843$	36.7346	1.26521
$844$	−27.7651	−0.955715
$845$	7.79655	0.268210
$846$	−7.32515	−0.251844
$847$	10.8701	0.373502
$848$	11.4820	0.394293
$849$	−39.2879	−1.34836
$850$	−5.32344	−0.182593
$851$	−4.72019	−0.161806
$852$	−6.39489	−0.219085
$853$	37.3631	1.27929	0.639644	−	0.768672i	$-0.279082\pi$
$853$	37.3631	1.27929	0.639644	+	0.768672i	$0.279082\pi$
$854$	−0.745696	−0.0255172
$855$	4.60814	0.157595
$856$	10.4972	0.358787
$857$	−23.4620	−0.801447	−0.400724	−	0.916199i	$-0.631241\pi$
$857$	−23.4620	−0.801447	−0.400724	+	0.916199i	$0.631241\pi$
$858$	16.2549	0.554932
$859$	54.0259	1.84334	0.921671	−	0.387973i	$-0.126825\pi$
$859$	54.0259	1.84334	0.921671	+	0.387973i	$0.126825\pi$
$860$	−7.74664	−0.264158
$861$	9.64919	0.328844
$862$	−33.4408	−1.13900
$863$	−6.10933	−0.207964	−0.103982	−	0.994579i	$-0.533158\pi$
$863$	−6.10933	−0.207964	−0.103982	+	0.994579i	$0.533158\pi$
$864$	5.63403	0.191674
$865$	6.17284	0.209883
$866$	−1.71070	−0.0581319
$867$	−15.1969	−0.516113
$868$	−5.80794	−0.197134
$869$	−46.2167	−1.56779
$870$	8.80212	0.298420
$871$	−30.3058	−1.02687
$872$	−2.07688	−0.0703322
$873$	5.36293	0.181508
$874$	10.8434	0.366784
$875$	−0.629438	−0.0212789
$876$	9.90336	0.334604
$877$	20.9116	0.706134	0.353067	−	0.935598i	$-0.385139\pi$
$877$	20.9116	0.706134	0.353067	+	0.935598i	$0.385139\pi$
$878$	17.6151	0.594479
$879$	−7.44781	−0.251209
$880$	−5.31691	−0.179233
$881$	−3.90738	−0.131643	−0.0658215	−	0.997831i	$-0.520967\pi$
$881$	−3.90738	−0.131643	−0.0658215	+	0.997831i	$0.520967\pi$
$882$	7.94963	0.267678
$883$	−18.3091	−0.616149	−0.308075	−	0.951362i	$-0.599685\pi$
$883$	−18.3091	−0.616149	−0.308075	+	0.951362i	$0.599685\pi$
$884$	12.1433	0.408425
$885$	2.99880	0.100803
$886$	−28.8753	−0.970086
$887$	−18.1268	−0.608639	−0.304320	−	0.952570i	$-0.598429\pi$
$887$	−18.1268	−0.608639	−0.304320	+	0.952570i	$0.598429\pi$
$888$	2.23329	0.0749443
$889$	13.0037	0.436129
$890$	−3.05594	−0.102435
$891$	−20.9459	−0.701716
$892$	15.9113	0.532751
$893$	23.2937	0.779493
$894$	23.0171	0.769808
$895$	−15.4641	−0.516908
$896$	0.629438	0.0210281
$897$	8.65997	0.289148
$898$	23.8510	0.795919
$899$	−60.6008	−2.02115
$900$	−1.20379	−0.0401265
$901$	−61.1237	−2.03633
$902$	−60.8162	−2.02496
$903$	−6.53498	−0.217471
$904$	2.25851	0.0751171
$905$	−19.2301	−0.639230
$906$	10.9067	0.362350
$907$	24.7582	0.822083	0.411042	−	0.911617i	$-0.365165\pi$
$907$	24.7582	0.822083	0.411042	+	0.911617i	$0.365165\pi$
$908$	−2.09312	−0.0694627
$909$	−11.3506	−0.376475
$910$	1.43582	0.0475968
$911$	−22.3430	−0.740256	−0.370128	−	0.928981i	$-0.620686\pi$
$911$	−22.3430	−0.740256	−0.370128	+	0.928981i	$0.620686\pi$
$912$	−5.13040	−0.169885
$913$	45.5638	1.50794
$914$	−17.9314	−0.593119
$915$	−1.58777	−0.0524900
$916$	26.4539	0.874062
$917$	−6.67322	−0.220369
$918$	−29.9925	−0.989899
$919$	5.75870	0.189962	0.0949809	−	0.995479i	$-0.469721\pi$
$919$	5.75870	0.189962	0.0949809	+	0.995479i	$0.469721\pi$
$920$	−2.83265	−0.0933896
$921$	28.1944	0.929037
$922$	23.5048	0.774088
$923$	−10.8843	−0.358261
$924$	−4.48529	−0.147555
$925$	−1.66635	−0.0547894
$926$	26.4428	0.868966
$927$	−22.7675	−0.747782
$928$	6.56764	0.215593
$929$	−54.0304	−1.77268	−0.886340	−	0.463034i	$-0.846761\pi$
$929$	−54.0304	−1.77268	−0.886340	+	0.463034i	$0.846761\pi$
$930$	−12.3665	−0.405514
$931$	−25.2795	−0.828501
$932$	2.96586	0.0971499
$933$	−8.27122	−0.270788
$934$	−28.7680	−0.941318
$935$	28.3043	0.925649
$936$	2.74598	0.0897553
$937$	−50.3099	−1.64355	−0.821777	−	0.569809i	$-0.807017\pi$
$937$	−50.3099	−1.64355	−0.821777	+	0.569809i	$0.807017\pi$
$938$	8.36244	0.273043
$939$	7.00694	0.228663
$940$	−6.08505	−0.198473
$941$	15.5962	0.508423	0.254212	−	0.967149i	$-0.418184\pi$
$941$	15.5962	0.508423	0.254212	+	0.967149i	$0.418184\pi$
$942$	7.28972	0.237512
$943$	−32.4006	−1.05511
$944$	2.23753	0.0728254
$945$	−3.54628	−0.115360
$946$	41.1882	1.33914
$947$	17.7022	0.575244	0.287622	−	0.957744i	$-0.407135\pi$
$947$	17.7022	0.575244	0.287622	+	0.957744i	$0.407135\pi$
$948$	11.6498	0.378367
$949$	16.8558	0.547163
$950$	3.82801	0.124197
$951$	8.44829	0.273954
$952$	−3.35078	−0.108599
$953$	−4.08470	−0.132316	−0.0661581	−	0.997809i	$-0.521074\pi$
$953$	−4.08470	−0.132316	−0.0661581	+	0.997809i	$0.521074\pi$
$954$	−13.8219	−0.447502
$955$	6.42413	0.207880
$956$	24.3398	0.787205
$957$	−46.8001	−1.51283
$958$	−18.1118	−0.585165
$959$	4.48990	0.144986
$960$	1.34023	0.0432556
$961$	54.1408	1.74648
$962$	3.80113	0.122553
$963$	−12.6365	−0.407205
$964$	24.9195	0.802605
$965$	−14.6142	−0.470446
$966$	−2.38959	−0.0768839
$967$	7.95894	0.255942	0.127971	−	0.991778i	$-0.459154\pi$
$967$	7.95894	0.255942	0.127971	+	0.991778i	$0.459154\pi$
$968$	17.2695	0.555064
$969$	27.3114	0.877369
$970$	4.45503	0.143042
$971$	23.4050	0.751101	0.375551	−	0.926802i	$-0.377454\pi$
$971$	23.4050	0.751101	0.375551	+	0.926802i	$0.377454\pi$
$972$	−11.6223	−0.372785
$973$	11.3705	0.364523
$974$	−28.4853	−0.912727
$975$	3.05720	0.0979087
$976$	−1.18470	−0.0379214
$977$	−16.2942	−0.521297	−0.260649	−	0.965434i	$-0.583936\pi$
$977$	−16.2942	−0.521297	−0.260649	+	0.965434i	$0.583936\pi$
$978$	−29.4773	−0.942582
$979$	16.2482	0.519294
$980$	6.60381	0.210951
$981$	2.50014	0.0798234
$982$	−35.4381	−1.13088
$983$	9.48816	0.302625	0.151313	−	0.988486i	$-0.451650\pi$
$983$	9.48816	0.302625	0.151313	+	0.988486i	$0.451650\pi$
$984$	15.3298	0.488698
$985$	0.508433	0.0162000
$986$	−34.9625	−1.11343
$987$	−5.13329	−0.163394
$988$	−8.73211	−0.277805
$989$	21.9435	0.697763
$990$	6.40047	0.203420
$991$	0.420600	0.0133608	0.00668039	−	0.999978i	$-0.497874\pi$
$991$	0.420600	0.0133608	0.00668039	+	0.999978i	$0.497874\pi$
$992$	−9.22718	−0.292963
$993$	−37.5108	−1.19037
$994$	3.00337	0.0952610
$995$	3.23551	0.102573
$996$	−11.4852	−0.363923
$997$	59.9534	1.89874	0.949371	−	0.314156i	$-0.101722\pi$
$997$	59.9534	1.89874	0.949371	+	0.314156i	$0.101722\pi$
$998$	−31.8386	−1.00783
$999$	−9.38830	−0.297033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.o.1.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.o.1.7	✓	22	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.34023 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.34023 q^{6} +0.629438 q^{7} +1.00000 q^{8} -1.20379 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.34023 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.34023 q^{6} +0.629438 q^{7} +1.00000 q^{8} -1.20379 q^{9} -1.00000 q^{10} +5.31691 q^{11} -1.34023 q^{12} -2.28111 q^{13} +0.629438 q^{14} +1.34023 q^{15} +1.00000 q^{16} -5.32344 q^{17} -1.20379 q^{18} +3.82801 q^{19} -1.00000 q^{20} -0.843589 q^{21} +5.31691 q^{22} +2.83265 q^{23} -1.34023 q^{24} +1.00000 q^{25} -2.28111 q^{26} +5.63403 q^{27} +0.629438 q^{28} +6.56764 q^{29} +1.34023 q^{30} -9.22718 q^{31} +1.00000 q^{32} -7.12586 q^{33} -5.32344 q^{34} -0.629438 q^{35} -1.20379 q^{36} -1.66635 q^{37} +3.82801 q^{38} +3.05720 q^{39} -1.00000 q^{40} -11.4383 q^{41} -0.843589 q^{42} +7.74664 q^{43} +5.31691 q^{44} +1.20379 q^{45} +2.83265 q^{46} +6.08505 q^{47} -1.34023 q^{48} -6.60381 q^{49} +1.00000 q^{50} +7.13462 q^{51} -2.28111 q^{52} +11.4820 q^{53} +5.63403 q^{54} -5.31691 q^{55} +0.629438 q^{56} -5.13040 q^{57} +6.56764 q^{58} +2.23753 q^{59} +1.34023 q^{60} -1.18470 q^{61} -9.22718 q^{62} -0.757714 q^{63} +1.00000 q^{64} +2.28111 q^{65} -7.12586 q^{66} +13.2856 q^{67} -5.32344 q^{68} -3.79639 q^{69} -0.629438 q^{70} +4.77151 q^{71} -1.20379 q^{72} -7.38932 q^{73} -1.66635 q^{74} -1.34023 q^{75} +3.82801 q^{76} +3.34667 q^{77} +3.05720 q^{78} -8.69240 q^{79} -1.00000 q^{80} -3.93950 q^{81} -11.4383 q^{82} +8.56961 q^{83} -0.843589 q^{84} +5.32344 q^{85} +7.74664 q^{86} -8.80212 q^{87} +5.31691 q^{88} +3.05594 q^{89} +1.20379 q^{90} -1.43582 q^{91} +2.83265 q^{92} +12.3665 q^{93} +6.08505 q^{94} -3.82801 q^{95} -1.34023 q^{96} -4.45503 q^{97} -6.60381 q^{98} -6.40047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9	\( 22 q + 22 q^{2} + 2 q^{3} + 22 q^{4} - 22 q^{5} + 2 q^{6} + 13 q^{7} + 22 q^{8} + 32 q^{9} - 22 q^{10} - 3 q^{11} + 2 q^{12} + 6 q^{13} + 13 q^{14} - 2 q^{15} + 22 q^{16} + 17 q^{17} + 32 q^{18} + 13 q^{19} - 22 q^{20} + 16 q^{21} - 3 q^{22} + 19 q^{23} + 2 q^{24} + 22 q^{25} + 6 q^{26} + 14 q^{27} + 13 q^{28} + 14 q^{29} - 2 q^{30} + 13 q^{31} + 22 q^{32} + 12 q^{33} + 17 q^{34} - 13 q^{35} + 32 q^{36} + 35 q^{37} + 13 q^{38} + 30 q^{39} - 22 q^{40} - 5 q^{41} + 16 q^{42} + 19 q^{43} - 3 q^{44} - 32 q^{45} + 19 q^{46} + 29 q^{47} + 2 q^{48} + 61 q^{49} + 22 q^{50} + q^{51} + 6 q^{52} + 29 q^{53} + 14 q^{54} + 3 q^{55} + 13 q^{56} + 33 q^{57} + 14 q^{58} - 4 q^{59} - 2 q^{60} + 20 q^{61} + 13 q^{62} + 50 q^{63} + 22 q^{64} - 6 q^{65} + 12 q^{66} + 48 q^{67} + 17 q^{68} + 19 q^{69} - 13 q^{70} + 2 q^{71} + 32 q^{72} + 16 q^{73} + 35 q^{74} + 2 q^{75} + 13 q^{76} + 53 q^{77} + 30 q^{78} + 29 q^{79} - 22 q^{80} + 54 q^{81} - 5 q^{82} + 13 q^{83} + 16 q^{84} - 17 q^{85} + 19 q^{86} + 56 q^{87} - 3 q^{88} + 20 q^{89} - 32 q^{90} + 42 q^{91} + 19 q^{92} + 50 q^{93} + 29 q^{94} - 13 q^{95} + 2 q^{96} + 36 q^{97} + 61 q^{98} - q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 + 2 * q^3 + 22 * q^4 - 22 * q^5 + 2 * q^6 + 13 * q^7 + 22 * q^8 + 32 * q^9 - 22 * q^10 - 3 * q^11 + 2 * q^12 + 6 * q^13 + 13 * q^14 - 2 * q^15 + 22 * q^16 + 17 * q^17 + 32 * q^18 + 13 * q^19 - 22 * q^20 + 16 * q^21 - 3 * q^22 + 19 * q^23 + 2 * q^24 + 22 * q^25 + 6 * q^26 + 14 * q^27 + 13 * q^28 + 14 * q^29 - 2 * q^30 + 13 * q^31 + 22 * q^32 + 12 * q^33 + 17 * q^34 - 13 * q^35 + 32 * q^36 + 35 * q^37 + 13 * q^38 + 30 * q^39 - 22 * q^40 - 5 * q^41 + 16 * q^42 + 19 * q^43 - 3 * q^44 - 32 * q^45 + 19 * q^46 + 29 * q^47 + 2 * q^48 + 61 * q^49 + 22 * q^50 + q^51 + 6 * q^52 + 29 * q^53 + 14 * q^54 + 3 * q^55 + 13 * q^56 + 33 * q^57 + 14 * q^58 - 4 * q^59 - 2 * q^60 + 20 * q^61 + 13 * q^62 + 50 * q^63 + 22 * q^64 - 6 * q^65 + 12 * q^66 + 48 * q^67 + 17 * q^68 + 19 * q^69 - 13 * q^70 + 2 * q^71 + 32 * q^72 + 16 * q^73 + 35 * q^74 + 2 * q^75 + 13 * q^76 + 53 * q^77 + 30 * q^78 + 29 * q^79 - 22 * q^80 + 54 * q^81 - 5 * q^82 + 13 * q^83 + 16 * q^84 - 17 * q^85 + 19 * q^86 + 56 * q^87 - 3 * q^88 + 20 * q^89 - 32 * q^90 + 42 * q^91 + 19 * q^92 + 50 * q^93 + 29 * q^94 - 13 * q^95 + 2 * q^96 + 36 * q^97 + 61 * q^98 - q^99

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