LMFDB - Embedded newform 2006.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, 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("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} + 4 $ x^4 - 6*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.28825$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} -1.28825 q^{5} -2.41421 q^{6} +2.70246 q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} -1.28825 q^{5} -2.41421 q^{6} +2.70246 q^{7} +1.00000 q^{8} +2.82843 q^{9} -1.28825 q^{10} +0.288246 q^{11} -2.41421 q^{12} -6.11010 q^{13} +2.70246 q^{14} +3.11010 q^{15} +1.00000 q^{16} -1.00000 q^{17} +2.82843 q^{18} +3.39835 q^{19} -1.28825 q^{20} -6.52431 q^{21} +0.288246 q^{22} -1.12597 q^{23} -2.41421 q^{24} -3.34042 q^{25} -6.11010 q^{26} +0.414214 q^{27} +2.70246 q^{28} +9.24839 q^{29} +3.11010 q^{30} -7.34617 q^{31} +1.00000 q^{32} -0.695886 q^{33} -1.00000 q^{34} -3.48143 q^{35} +2.82843 q^{36} +3.39835 q^{38} +14.7511 q^{39} -1.28825 q^{40} -10.0486 q^{41} -6.52431 q^{42} +7.45052 q^{43} +0.288246 q^{44} -3.64371 q^{45} -1.12597 q^{46} -4.90222 q^{47} -2.41421 q^{48} +0.303286 q^{49} -3.34042 q^{50} +2.41421 q^{51} -6.11010 q^{52} +1.18389 q^{53} +0.414214 q^{54} -0.371331 q^{55} +2.70246 q^{56} -8.20433 q^{57} +9.24839 q^{58} +1.00000 q^{59} +3.11010 q^{60} -6.58224 q^{61} -7.34617 q^{62} +7.64371 q^{63} +1.00000 q^{64} +7.87131 q^{65} -0.695886 q^{66} -9.22103 q^{67} -1.00000 q^{68} +2.71833 q^{69} -3.48143 q^{70} -9.08849 q^{71} +2.82843 q^{72} +0.591531 q^{73} +8.06450 q^{75} +3.39835 q^{76} +0.778972 q^{77} +14.7511 q^{78} -7.88718 q^{79} -1.28825 q^{80} -9.48528 q^{81} -10.0486 q^{82} -15.3369 q^{83} -6.52431 q^{84} +1.28825 q^{85} +7.45052 q^{86} -22.3276 q^{87} +0.288246 q^{88} -12.1383 q^{89} -3.64371 q^{90} -16.5123 q^{91} -1.12597 q^{92} +17.7352 q^{93} -4.90222 q^{94} -4.37790 q^{95} -2.41421 q^{96} +12.6584 q^{97} +0.303286 q^{98} +0.815282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} + 4 q^{10} - 8 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 4 q^{16} - 4 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} - 8 q^{22} - 8 q^{23} - 4 q^{24} - 4 q^{25} - 12 q^{26} - 4 q^{27} - 4 q^{28} + 8 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{33} - 4 q^{34} - 20 q^{35} - 8 q^{38} + 8 q^{39} + 4 q^{40} - 4 q^{41} - 8 q^{42} + 8 q^{43} - 8 q^{44} - 8 q^{45} - 8 q^{46} - 12 q^{47} - 4 q^{48} + 4 q^{49} - 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 4 q^{54} - 20 q^{55} - 4 q^{56} + 8 q^{57} + 8 q^{58} + 4 q^{59} + 4 q^{61} - 8 q^{62} + 24 q^{63} + 4 q^{64} - 4 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 12 q^{69} - 20 q^{70} - 20 q^{71} - 4 q^{73} + 12 q^{75} - 8 q^{76} + 24 q^{77} + 8 q^{78} - 12 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 16 q^{83} - 8 q^{84} - 4 q^{85} + 8 q^{86} - 20 q^{87} - 8 q^{88} - 32 q^{89} - 8 q^{90} + 8 q^{91} - 8 q^{92} + 4 q^{93} - 12 q^{94} - 28 q^{95} - 4 q^{96} + 24 q^{97} + 4 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 + 4 * q^10 - 8 * q^11 - 4 * q^12 - 12 * q^13 - 4 * q^14 + 4 * q^16 - 4 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 - 8 * q^22 - 8 * q^23 - 4 * q^24 - 4 * q^25 - 12 * q^26 - 4 * q^27 - 4 * q^28 + 8 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^33 - 4 * q^34 - 20 * q^35 - 8 * q^38 + 8 * q^39 + 4 * q^40 - 4 * q^41 - 8 * q^42 + 8 * q^43 - 8 * q^44 - 8 * q^45 - 8 * q^46 - 12 * q^47 - 4 * q^48 + 4 * q^49 - 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 4 * q^54 - 20 * q^55 - 4 * q^56 + 8 * q^57 + 8 * q^58 + 4 * q^59 + 4 * q^61 - 8 * q^62 + 24 * q^63 + 4 * q^64 - 4 * q^65 + 4 * q^66 - 16 * q^67 - 4 * q^68 + 12 * q^69 - 20 * q^70 - 20 * q^71 - 4 * q^73 + 12 * q^75 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 12 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 16 * q^83 - 8 * q^84 - 4 * q^85 + 8 * q^86 - 20 * q^87 - 8 * q^88 - 32 * q^89 - 8 * q^90 + 8 * q^91 - 8 * q^92 + 4 * q^93 - 12 * q^94 - 28 * q^95 - 4 * q^96 + 24 * q^97 + 4 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.41421	−1.39385	−0.696923	−	0.717146i	$-0.745448\pi$
$3$	−2.41421	−1.39385	−0.696923	+	0.717146i	$0.745448\pi$
$4$	1.00000	0.500000
$5$	−1.28825	−0.576121	−0.288060	−	0.957612i	$-0.593010\pi$
$5$	−1.28825	−0.576121	−0.288060	+	0.957612i	$0.593010\pi$
$6$	−2.41421	−0.985599
$7$	2.70246	1.02143	0.510717	−	0.859749i	$-0.329380\pi$
$7$	2.70246	1.02143	0.510717	+	0.859749i	$0.329380\pi$
$8$	1.00000	0.353553
$9$	2.82843	0.942809
$10$	−1.28825	−0.407379
$11$	0.288246	0.0869093	0.0434547	−	0.999055i	$-0.486164\pi$
$11$	0.288246	0.0869093	0.0434547	+	0.999055i	$0.486164\pi$
$12$	−2.41421	−0.696923
$13$	−6.11010	−1.69464	−0.847318	−	0.531085i	$-0.821784\pi$
$13$	−6.11010	−1.69464	−0.847318	+	0.531085i	$0.821784\pi$
$14$	2.70246	0.722263
$15$	3.11010	0.803024
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.82843	0.666667
$19$	3.39835	0.779634	0.389817	−	0.920892i	$-0.372538\pi$
$19$	3.39835	0.779634	0.389817	+	0.920892i	$0.372538\pi$
$20$	−1.28825	−0.288060
$21$	−6.52431	−1.42372
$22$	0.288246	0.0614542
$23$	−1.12597	−0.234781	−0.117390	−	0.993086i	$-0.537453\pi$
$23$	−1.12597	−0.234781	−0.117390	+	0.993086i	$0.537453\pi$
$24$	−2.41421	−0.492799
$25$	−3.34042	−0.668085
$26$	−6.11010	−1.19829
$27$	0.414214	0.0797154
$28$	2.70246	0.510717
$29$	9.24839	1.71738	0.858691	−	0.512494i	$-0.171278\pi$
$29$	9.24839	1.71738	0.858691	+	0.512494i	$0.171278\pi$
$30$	3.11010	0.567824
$31$	−7.34617	−1.31941	−0.659705	−	0.751524i	$-0.729319\pi$
$31$	−7.34617	−1.31941	−0.659705	+	0.751524i	$0.729319\pi$
$32$	1.00000	0.176777
$33$	−0.695886	−0.121138
$34$	−1.00000	−0.171499
$35$	−3.48143	−0.588469
$36$	2.82843	0.471405
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	3.39835	0.551284
$39$	14.7511	2.36206
$40$	−1.28825	−0.203690
$41$	−10.0486	−1.56933	−0.784666	−	0.619919i	$-0.787166\pi$
$41$	−10.0486	−1.56933	−0.784666	+	0.619919i	$0.787166\pi$
$42$	−6.52431	−1.00672
$43$	7.45052	1.13619	0.568097	−	0.822962i	$-0.307680\pi$
$43$	7.45052	1.13619	0.568097	+	0.822962i	$0.307680\pi$
$44$	0.288246	0.0434547
$45$	−3.64371	−0.543172
$46$	−1.12597	−0.166015
$47$	−4.90222	−0.715062	−0.357531	−	0.933901i	$-0.616381\pi$
$47$	−4.90222	−0.715062	−0.357531	+	0.933901i	$0.616381\pi$
$48$	−2.41421	−0.348462
$49$	0.303286	0.0433265
$50$	−3.34042	−0.472407
$51$	2.41421	0.338058
$52$	−6.11010	−0.847318
$53$	1.18389	0.162620	0.0813099	−	0.996689i	$-0.474090\pi$
$53$	1.18389	0.162620	0.0813099	+	0.996689i	$0.474090\pi$
$54$	0.414214	0.0563673
$55$	−0.371331	−0.0500703
$56$	2.70246	0.361131
$57$	−8.20433	−1.08669
$58$	9.24839	1.21437
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	3.11010	0.401512
$61$	−6.58224	−0.842769	−0.421384	−	0.906882i	$-0.638456\pi$
$61$	−6.58224	−0.842769	−0.421384	+	0.906882i	$0.638456\pi$
$62$	−7.34617	−0.932964
$63$	7.64371	0.963017
$64$	1.00000	0.125000
$65$	7.87131	0.976316
$66$	−0.695886	−0.0856577
$67$	−9.22103	−1.12653	−0.563264	−	0.826277i	$-0.690455\pi$
$67$	−9.22103	−1.12653	−0.563264	+	0.826277i	$0.690455\pi$
$68$	−1.00000	−0.121268
$69$	2.71833	0.327248
$70$	−3.48143	−0.416111
$71$	−9.08849	−1.07861	−0.539303	−	0.842112i	$-0.681312\pi$
$71$	−9.08849	−1.07861	−0.539303	+	0.842112i	$0.681312\pi$
$72$	2.82843	0.333333
$73$	0.591531	0.0692335	0.0346167	−	0.999401i	$-0.488979\pi$
$73$	0.591531	0.0692335	0.0346167	+	0.999401i	$0.488979\pi$
$74$	0	0
$75$	8.06450	0.931208
$76$	3.39835	0.389817
$77$	0.778972	0.0887721
$78$	14.7511	1.67023
$79$	−7.88718	−0.887377	−0.443688	−	0.896181i	$-0.646330\pi$
$79$	−7.88718	−0.887377	−0.443688	+	0.896181i	$0.646330\pi$
$80$	−1.28825	−0.144030
$81$	−9.48528	−1.05392
$82$	−10.0486	−1.10969
$83$	−15.3369	−1.68344	−0.841720	−	0.539914i	$-0.818457\pi$
$83$	−15.3369	−1.68344	−0.841720	+	0.539914i	$0.818457\pi$
$84$	−6.52431	−0.711861
$85$	1.28825	0.139730
$86$	7.45052	0.803411
$87$	−22.3276	−2.39377
$88$	0.288246	0.0307271
$89$	−12.1383	−1.28666	−0.643328	−	0.765591i	$-0.722447\pi$
$89$	−12.1383	−1.28666	−0.643328	+	0.765591i	$0.722447\pi$
$90$	−3.64371	−0.384081
$91$	−16.5123	−1.73096
$92$	−1.12597	−0.117390
$93$	17.7352	1.83906
$94$	−4.90222	−0.505625
$95$	−4.37790	−0.449163
$96$	−2.41421	−0.246400
$97$	12.6584	1.28527	0.642633	−	0.766174i	$-0.277842\pi$
$97$	12.6584	1.28527	0.642633	+	0.766174i	$0.277842\pi$
$98$	0.303286	0.0306365
$99$	0.815282	0.0819389
$100$	−3.34042	−0.334042
$101$	−10.9211	−1.08669	−0.543345	−	0.839509i	$-0.682843\pi$
$101$	−10.9211	−1.08669	−0.543345	+	0.839509i	$0.682843\pi$
$102$	2.41421	0.239043
$103$	−0.593911	−0.0585198	−0.0292599	−	0.999572i	$-0.509315\pi$
$103$	−0.593911	−0.0585198	−0.0292599	+	0.999572i	$0.509315\pi$
$104$	−6.11010	−0.599145
$105$	8.40492	0.820236
$106$	1.18389	0.114990
$107$	5.54593	0.536145	0.268072	−	0.963399i	$-0.413613\pi$
$107$	5.54593	0.536145	0.268072	+	0.963399i	$0.413613\pi$
$108$	0.414214	0.0398577
$109$	2.17240	0.208078	0.104039	−	0.994573i	$-0.466823\pi$
$109$	2.17240	0.208078	0.104039	+	0.994573i	$0.466823\pi$
$110$	−0.371331	−0.0354050
$111$	0	0
$112$	2.70246	0.255358
$113$	19.6476	1.84829	0.924143	−	0.382046i	$-0.124780\pi$
$113$	19.6476	1.84829	0.924143	+	0.382046i	$0.124780\pi$
$114$	−8.20433	−0.768406
$115$	1.45052	0.135262
$116$	9.24839	0.858691
$117$	−17.2820	−1.59772
$118$	1.00000	0.0920575
$119$	−2.70246	−0.247734
$120$	3.11010	0.283912
$121$	−10.9169	−0.992447
$122$	−6.58224	−0.595928
$123$	24.2595	2.18741
$124$	−7.34617	−0.659705
$125$	10.7445	0.961019
$126$	7.64371	0.680956
$127$	−11.9949	−1.06438	−0.532188	−	0.846626i	$-0.678630\pi$
$127$	−11.9949	−1.06438	−0.532188	+	0.846626i	$0.678630\pi$
$128$	1.00000	0.0883883
$129$	−17.9872	−1.58368
$130$	7.87131	0.690360
$131$	−0.755808	−0.0660352	−0.0330176	−	0.999455i	$-0.510512\pi$
$131$	−0.755808	−0.0660352	−0.0330176	+	0.999455i	$0.510512\pi$
$132$	−0.695886	−0.0605691
$133$	9.18389	0.796344
$134$	−9.22103	−0.796575
$135$	−0.533609	−0.0459257
$136$	−1.00000	−0.0857493
$137$	−12.9551	−1.10683	−0.553415	−	0.832905i	$-0.686676\pi$
$137$	−12.9551	−1.10683	−0.553415	+	0.832905i	$0.686676\pi$
$138$	2.71833	0.231399
$139$	−17.8044	−1.51015	−0.755076	−	0.655637i	$-0.772400\pi$
$139$	−17.8044	−1.51015	−0.755076	+	0.655637i	$0.772400\pi$
$140$	−3.48143	−0.294235
$141$	11.8350	0.996687
$142$	−9.08849	−0.762689
$143$	−1.76121	−0.147280
$144$	2.82843	0.235702
$145$	−11.9142	−0.989420
$146$	0.591531	0.0489555
$147$	−0.732196	−0.0603905
$148$	0	0
$149$	−21.7121	−1.77872	−0.889360	−	0.457207i	$-0.848850\pi$
$149$	−21.7121	−1.77872	−0.889360	+	0.457207i	$0.848850\pi$
$150$	8.06450	0.658463
$151$	−8.50032	−0.691746	−0.345873	−	0.938281i	$-0.612417\pi$
$151$	−8.50032	−0.691746	−0.345873	+	0.938281i	$0.612417\pi$
$152$	3.39835	0.275642
$153$	−2.82843	−0.228665
$154$	0.778972	0.0627714
$155$	9.46367	0.760140
$156$	14.7511	1.18103
$157$	20.1030	1.60439	0.802197	−	0.597059i	$-0.203664\pi$
$157$	20.1030	1.60439	0.802197	+	0.597059i	$0.203664\pi$
$158$	−7.88718	−0.627470
$159$	−2.85816	−0.226667
$160$	−1.28825	−0.101845
$161$	−3.04288	−0.239813
$162$	−9.48528	−0.745234
$163$	−16.9737	−1.32948	−0.664740	−	0.747075i	$-0.731458\pi$
$163$	−16.9737	−1.32948	−0.664740	+	0.747075i	$0.731458\pi$
$164$	−10.0486	−0.784666
$165$	0.896473	0.0697903
$166$	−15.3369	−1.19037
$167$	14.7352	1.14025	0.570123	−	0.821560i	$-0.306896\pi$
$167$	14.7352	1.14025	0.570123	+	0.821560i	$0.306896\pi$
$168$	−6.52431	−0.503362
$169$	24.3333	1.87179
$170$	1.28825	0.0988039
$171$	9.61197	0.735046
$172$	7.45052	0.568097
$173$	−6.74149	−0.512546	−0.256273	−	0.966604i	$-0.582495\pi$
$173$	−6.74149	−0.512546	−0.256273	+	0.966604i	$0.582495\pi$
$174$	−22.3276	−1.69265
$175$	−9.02736	−0.682404
$176$	0.288246	0.0217273
$177$	−2.41421	−0.181463
$178$	−12.1383	−0.909803
$179$	4.56262	0.341026	0.170513	−	0.985355i	$-0.445457\pi$
$179$	4.56262	0.341026	0.170513	+	0.985355i	$0.445457\pi$
$180$	−3.64371	−0.271586
$181$	6.78939	0.504652	0.252326	−	0.967642i	$-0.418805\pi$
$181$	6.78939	0.504652	0.252326	+	0.967642i	$0.418805\pi$
$182$	−16.5123	−1.22397
$183$	15.8909	1.17469
$184$	−1.12597	−0.0830075
$185$	0	0
$186$	17.7352	1.30041
$187$	−0.288246	−0.0210786
$188$	−4.90222	−0.357531
$189$	1.11940	0.0814240
$190$	−4.37790	−0.317607
$191$	7.43548	0.538013	0.269006	−	0.963138i	$-0.413305\pi$
$191$	7.43548	0.538013	0.269006	+	0.963138i	$0.413305\pi$
$192$	−2.41421	−0.174231
$193$	−24.8700	−1.79018	−0.895089	−	0.445887i	$-0.852888\pi$
$193$	−24.8700	−1.79018	−0.895089	+	0.445887i	$0.852888\pi$
$194$	12.6584	0.908821
$195$	−19.0030	−1.36083
$196$	0.303286	0.0216633
$197$	14.5120	1.03394	0.516968	−	0.856004i	$-0.327060\pi$
$197$	14.5120	1.03394	0.516968	+	0.856004i	$0.327060\pi$
$198$	0.815282	0.0579395
$199$	−12.7619	−0.904669	−0.452335	−	0.891848i	$-0.649409\pi$
$199$	−12.7619	−0.904669	−0.452335	+	0.891848i	$0.649409\pi$
$200$	−3.34042	−0.236204
$201$	22.2615	1.57021
$202$	−10.9211	−0.768406
$203$	24.9934	1.75419
$204$	2.41421	0.169029
$205$	12.9451	0.904125
$206$	−0.593911	−0.0413797
$207$	−3.18472	−0.221353
$208$	−6.11010	−0.423659
$209$	0.979558	0.0677575
$210$	8.40492	0.579994
$211$	−1.20550	−0.0829903	−0.0414951	−	0.999139i	$-0.513212\pi$
$211$	−1.20550	−0.0829903	−0.0414951	+	0.999139i	$0.513212\pi$
$212$	1.18389	0.0813099
$213$	21.9415	1.50341
$214$	5.54593	0.379112
$215$	−9.59810	−0.654585
$216$	0.414214	0.0281837
$217$	−19.8527	−1.34769
$218$	2.17240	0.147134
$219$	−1.42808	−0.0965009
$220$	−0.371331	−0.0250351
$221$	6.11010	0.411010
$222$	0	0
$223$	6.06450	0.406109	0.203054	−	0.979167i	$-0.434913\pi$
$223$	6.06450	0.406109	0.203054	+	0.979167i	$0.434913\pi$
$224$	2.70246	0.180566
$225$	−9.44814	−0.629876
$226$	19.6476	1.30694
$227$	23.5091	1.56035	0.780176	−	0.625559i	$-0.215129\pi$
$227$	23.5091	1.56035	0.780176	+	0.625559i	$0.215129\pi$
$228$	−8.20433	−0.543345
$229$	6.55790	0.433358	0.216679	−	0.976243i	$-0.430477\pi$
$229$	6.55790	0.433358	0.216679	+	0.976243i	$0.430477\pi$
$230$	1.45052	0.0956447
$231$	−1.88060	−0.123735
$232$	9.24839	0.607186
$233$	13.6101	0.891626	0.445813	−	0.895126i	$-0.352915\pi$
$233$	13.6101	0.891626	0.445813	+	0.895126i	$0.352915\pi$
$234$	−17.2820	−1.12976
$235$	6.31526	0.411962
$236$	1.00000	0.0650945
$237$	19.0413	1.23687
$238$	−2.70246	−0.175174
$239$	21.2124	1.37211	0.686057	−	0.727548i	$-0.259340\pi$
$239$	21.2124	1.37211	0.686057	+	0.727548i	$0.259340\pi$
$240$	3.11010	0.200756
$241$	30.1060	1.93930	0.969650	−	0.244499i	$-0.0786233\pi$
$241$	30.1060	1.93930	0.969650	+	0.244499i	$0.0786233\pi$
$242$	−10.9169	−0.701766
$243$	21.6569	1.38929
$244$	−6.58224	−0.421384
$245$	−0.390706	−0.0249613
$246$	24.2595	1.54673
$247$	−20.7642	−1.32120
$248$	−7.34617	−0.466482
$249$	37.0265	2.34646
$250$	10.7445	0.679543
$251$	−24.3240	−1.53532	−0.767659	−	0.640858i	$-0.778579\pi$
$251$	−24.3240	−1.53532	−0.767659	+	0.640858i	$0.778579\pi$
$252$	7.64371	0.481508
$253$	−0.324555	−0.0204046
$254$	−11.9949	−0.752627
$255$	−3.11010	−0.194762
$256$	1.00000	0.0625000
$257$	−8.34544	−0.520575	−0.260287	−	0.965531i	$-0.583817\pi$
$257$	−8.34544	−0.520575	−0.260287	+	0.965531i	$0.583817\pi$
$258$	−17.9872	−1.11983
$259$	0	0
$260$	7.87131	0.488158
$261$	26.1584	1.61916
$262$	−0.755808	−0.0466940
$263$	−7.09695	−0.437617	−0.218808	−	0.975768i	$-0.570217\pi$
$263$	−7.09695	−0.437617	−0.218808	+	0.975768i	$0.570217\pi$
$264$	−0.695886	−0.0428289
$265$	−1.52514	−0.0936887
$266$	9.18389	0.563100
$267$	29.3044	1.79340
$268$	−9.22103	−0.563264
$269$	27.9946	1.70686	0.853429	−	0.521209i	$-0.174519\pi$
$269$	27.9946	1.70686	0.853429	+	0.521209i	$0.174519\pi$
$270$	−0.533609	−0.0324744
$271$	−9.52752	−0.578756	−0.289378	−	0.957215i	$-0.593448\pi$
$271$	−9.52752	−0.578756	−0.289378	+	0.957215i	$0.593448\pi$
$272$	−1.00000	−0.0606339
$273$	39.8642	2.41269
$274$	−12.9551	−0.782647
$275$	−0.962862	−0.0580628
$276$	2.71833	0.163624
$277$	10.5510	0.633950	0.316975	−	0.948434i	$-0.397333\pi$
$277$	10.5510	0.633950	0.316975	+	0.948434i	$0.397333\pi$
$278$	−17.8044	−1.06784
$279$	−20.7781	−1.24395
$280$	−3.48143	−0.208055
$281$	7.52012	0.448613	0.224306	−	0.974519i	$-0.427988\pi$
$281$	7.52012	0.448613	0.224306	+	0.974519i	$0.427988\pi$
$282$	11.8350	0.704764
$283$	0.267461	0.0158989	0.00794945	−	0.999968i	$-0.497470\pi$
$283$	0.267461	0.0158989	0.00794945	+	0.999968i	$0.497470\pi$
$284$	−9.08849	−0.539303
$285$	10.5692	0.626065
$286$	−1.76121	−0.104143
$287$	−27.1560	−1.60297
$288$	2.82843	0.166667
$289$	1.00000	0.0588235
$290$	−11.9142	−0.699625
$291$	−30.5601	−1.79146
$292$	0.591531	0.0346167
$293$	19.8113	1.15739	0.578694	−	0.815544i	$-0.303562\pi$
$293$	19.8113	1.15739	0.578694	+	0.815544i	$0.303562\pi$
$294$	−0.732196	−0.0427025
$295$	−1.28825	−0.0750046
$296$	0	0
$297$	0.119395	0.00692801
$298$	−21.7121	−1.25775
$299$	6.87978	0.397868
$300$	8.06450	0.465604
$301$	20.1347	1.16055
$302$	−8.50032	−0.489139
$303$	26.3659	1.51468
$304$	3.39835	0.194908
$305$	8.47954	0.485537
$306$	−2.82843	−0.161690
$307$	−2.38792	−0.136286	−0.0681430	−	0.997676i	$-0.521707\pi$
$307$	−2.38792	−0.136286	−0.0681430	+	0.997676i	$0.521707\pi$
$308$	0.778972	0.0443860
$309$	1.43383	0.0815676
$310$	9.46367	0.537500
$311$	22.9308	1.30029	0.650143	−	0.759812i	$-0.274709\pi$
$311$	22.9308	1.30029	0.650143	+	0.759812i	$0.274709\pi$
$312$	14.7511	0.835116
$313$	5.12095	0.289453	0.144727	−	0.989472i	$-0.453770\pi$
$313$	5.12095	0.289453	0.144727	+	0.989472i	$0.453770\pi$
$314$	20.1030	1.13448
$315$	−9.84697	−0.554814
$316$	−7.88718	−0.443688
$317$	29.8349	1.67569	0.837846	−	0.545906i	$-0.183815\pi$
$317$	29.8349	1.67569	0.837846	+	0.545906i	$0.183815\pi$
$318$	−2.85816	−0.160278
$319$	2.66581	0.149257
$320$	−1.28825	−0.0720151
$321$	−13.3891	−0.747304
$322$	−3.04288	−0.169573
$323$	−3.39835	−0.189089
$324$	−9.48528	−0.526960
$325$	20.4103	1.13216
$326$	−16.9737	−0.940084
$327$	−5.24464	−0.290029
$328$	−10.0486	−0.554843
$329$	−13.2480	−0.730388
$330$	0.896473	0.0493492
$331$	−20.4037	−1.12149	−0.560746	−	0.827988i	$-0.689485\pi$
$331$	−20.4037	−1.12149	−0.560746	+	0.827988i	$0.689485\pi$
$332$	−15.3369	−0.841720
$333$	0	0
$334$	14.7352	0.806275
$335$	11.8789	0.649016
$336$	−6.52431	−0.355930
$337$	−16.4068	−0.893734	−0.446867	−	0.894600i	$-0.647460\pi$
$337$	−16.4068	−0.893734	−0.446867	+	0.894600i	$0.647460\pi$
$338$	24.3333	1.32356
$339$	−47.4334	−2.57623
$340$	1.28825	0.0698649
$341$	−2.11750	−0.114669
$342$	9.61197	0.519756
$343$	−18.0976	−0.977178
$344$	7.45052	0.401705
$345$	−3.50187	−0.188535
$346$	−6.74149	−0.362425
$347$	27.8484	1.49498	0.747491	−	0.664271i	$-0.231258\pi$
$347$	27.8484	1.49498	0.747491	+	0.664271i	$0.231258\pi$
$348$	−22.3276	−1.19688
$349$	−24.4273	−1.30756	−0.653780	−	0.756684i	$-0.726818\pi$
$349$	−24.4273	−1.30756	−0.653780	+	0.756684i	$0.726818\pi$
$350$	−9.02736	−0.482533
$351$	−2.53089	−0.135089
$352$	0.288246	0.0153635
$353$	−4.44040	−0.236339	−0.118169	−	0.992993i	$-0.537703\pi$
$353$	−4.44040	−0.236339	−0.118169	+	0.992993i	$0.537703\pi$
$354$	−2.41421	−0.128314
$355$	11.7082	0.621407
$356$	−12.1383	−0.643328
$357$	6.52431	0.345303
$358$	4.56262	0.241142
$359$	5.75819	0.303906	0.151953	−	0.988388i	$-0.451444\pi$
$359$	5.75819	0.303906	0.151953	+	0.988388i	$0.451444\pi$
$360$	−3.64371	−0.192040
$361$	−7.45125	−0.392171
$362$	6.78939	0.356843
$363$	26.3558	1.38332
$364$	−16.5123	−0.865479
$365$	−0.762037	−0.0398869
$366$	15.8909	0.830632
$367$	−13.6982	−0.715039	−0.357520	−	0.933906i	$-0.616378\pi$
$367$	−13.6982	−0.715039	−0.357520	+	0.933906i	$0.616378\pi$
$368$	−1.12597	−0.0586951
$369$	−28.4218	−1.47958
$370$	0	0
$371$	3.19942	0.166105
$372$	17.7352	0.919528
$373$	−5.44312	−0.281834	−0.140917	−	0.990021i	$-0.545005\pi$
$373$	−5.44312	−0.281834	−0.140917	+	0.990021i	$0.545005\pi$
$374$	−0.288246	−0.0149048
$375$	−25.9396	−1.33951
$376$	−4.90222	−0.252813
$377$	−56.5086	−2.91034
$378$	1.11940	0.0575755
$379$	−36.1977	−1.85935	−0.929676	−	0.368379i	$-0.879913\pi$
$379$	−36.1977	−1.85935	−0.929676	+	0.368379i	$0.879913\pi$
$380$	−4.37790	−0.224582
$381$	28.9582	1.48358
$382$	7.43548	0.380432
$383$	−9.06679	−0.463292	−0.231646	−	0.972800i	$-0.574411\pi$
$383$	−9.06679	−0.463292	−0.231646	+	0.972800i	$0.574411\pi$
$384$	−2.41421	−0.123200
$385$	−1.00351	−0.0511435
$386$	−24.8700	−1.26585
$387$	21.0733	1.07121
$388$	12.6584	0.642633
$389$	16.8048	0.852038	0.426019	−	0.904714i	$-0.359916\pi$
$389$	16.8048	0.852038	0.426019	+	0.904714i	$0.359916\pi$
$390$	−19.0030	−0.962255
$391$	1.12597	0.0569426
$392$	0.303286	0.0153182
$393$	1.82468	0.0920430
$394$	14.5120	0.731104
$395$	10.1606	0.511236
$396$	0.815282	0.0409694
$397$	−13.4733	−0.676204	−0.338102	−	0.941110i	$-0.609785\pi$
$397$	−13.4733	−0.676204	−0.338102	+	0.941110i	$0.609785\pi$
$398$	−12.7619	−0.639698
$399$	−22.1719	−1.10998
$400$	−3.34042	−0.167021
$401$	18.6668	0.932175	0.466088	−	0.884739i	$-0.345663\pi$
$401$	18.6668	0.932175	0.466088	+	0.884739i	$0.345663\pi$
$402$	22.2615	1.11030
$403$	44.8858	2.23592
$404$	−10.9211	−0.543345
$405$	12.2194	0.607185
$406$	24.9934	1.24040
$407$	0	0
$408$	2.41421	0.119521
$409$	12.4382	0.615030	0.307515	−	0.951543i	$-0.400503\pi$
$409$	12.4382	0.615030	0.307515	+	0.951543i	$0.400503\pi$
$410$	12.9451	0.639313
$411$	31.2764	1.54275
$412$	−0.593911	−0.0292599
$413$	2.70246	0.132979
$414$	−3.18472	−0.156520
$415$	19.7577	0.969865
$416$	−6.11010	−0.299572
$417$	42.9837	2.10492
$418$	0.979558	0.0479118
$419$	−18.2673	−0.892415	−0.446207	−	0.894930i	$-0.647226\pi$
$419$	−18.2673	−0.892415	−0.446207	+	0.894930i	$0.647226\pi$
$420$	8.40492	0.410118
$421$	6.22137	0.303211	0.151606	−	0.988441i	$-0.451556\pi$
$421$	6.22137	0.303211	0.151606	+	0.988441i	$0.451556\pi$
$422$	−1.20550	−0.0586830
$423$	−13.8656	−0.674167
$424$	1.18389	0.0574948
$425$	3.34042	0.162034
$426$	21.9415	1.06307
$427$	−17.7882	−0.860832
$428$	5.54593	0.268072
$429$	4.25194	0.205285
$430$	−9.59810	−0.462862
$431$	−14.0096	−0.674818	−0.337409	−	0.941358i	$-0.609551\pi$
$431$	−14.0096	−0.674818	−0.337409	+	0.941358i	$0.609551\pi$
$432$	0.414214	0.0199289
$433$	−22.7622	−1.09388	−0.546942	−	0.837171i	$-0.684208\pi$
$433$	−22.7622	−1.09388	−0.546942	+	0.837171i	$0.684208\pi$
$434$	−19.8527	−0.952961
$435$	28.7634	1.37910
$436$	2.17240	0.104039
$437$	−3.82643	−0.183043
$438$	−1.42808	−0.0682364
$439$	3.08373	0.147178	0.0735892	−	0.997289i	$-0.476555\pi$
$439$	3.08373	0.147178	0.0735892	+	0.997289i	$0.476555\pi$
$440$	−0.371331	−0.0177025
$441$	0.857821	0.0408486
$442$	6.11010	0.290628
$443$	−5.83542	−0.277249	−0.138625	−	0.990345i	$-0.544268\pi$
$443$	−5.83542	−0.277249	−0.138625	+	0.990345i	$0.544268\pi$
$444$	0	0
$445$	15.6371	0.741269
$446$	6.06450	0.287162
$447$	52.4175	2.47926
$448$	2.70246	0.127679
$449$	−10.7028	−0.505094	−0.252547	−	0.967585i	$-0.581268\pi$
$449$	−10.7028	−0.505094	−0.252547	+	0.967585i	$0.581268\pi$
$450$	−9.44814	−0.445390
$451$	−2.89647	−0.136390
$452$	19.6476	0.924143
$453$	20.5216	0.964188
$454$	23.5091	1.10334
$455$	21.2719	0.997242
$456$	−8.20433	−0.384203
$457$	−29.2423	−1.36790	−0.683948	−	0.729530i	$-0.739739\pi$
$457$	−29.2423	−1.36790	−0.683948	+	0.729530i	$0.739739\pi$
$458$	6.55790	0.306431
$459$	−0.414214	−0.0193338
$460$	1.45052	0.0676310
$461$	30.3738	1.41465	0.707325	−	0.706888i	$-0.249902\pi$
$461$	30.3738	1.41465	0.707325	+	0.706888i	$0.249902\pi$
$462$	−1.88060	−0.0874937
$463$	28.0834	1.30515	0.652573	−	0.757726i	$-0.273690\pi$
$463$	28.0834	1.30515	0.652573	+	0.757726i	$0.273690\pi$
$464$	9.24839	0.429346
$465$	−22.8473	−1.05952
$466$	13.6101	0.630475
$467$	14.4243	0.667479	0.333739	−	0.942665i	$-0.391689\pi$
$467$	14.4243	0.667479	0.333739	+	0.942665i	$0.391689\pi$
$468$	−17.2820	−0.798859
$469$	−24.9195	−1.15067
$470$	6.31526	0.291301
$471$	−48.5329	−2.23628
$472$	1.00000	0.0460287
$473$	2.14758	0.0987459
$474$	19.0413	0.874597
$475$	−11.3519	−0.520861
$476$	−2.70246	−0.123867
$477$	3.34855	0.153319
$478$	21.2124	0.970231
$479$	−6.86829	−0.313820	−0.156910	−	0.987613i	$-0.550153\pi$
$479$	−6.86829	−0.313820	−0.156910	+	0.987613i	$0.550153\pi$
$480$	3.11010	0.141956
$481$	0	0
$482$	30.1060	1.37129
$483$	7.34617	0.334262
$484$	−10.9169	−0.496223
$485$	−16.3071	−0.740469
$486$	21.6569	0.982375
$487$	−23.3812	−1.05950	−0.529752	−	0.848152i	$-0.677715\pi$
$487$	−23.3812	−1.05950	−0.529752	+	0.848152i	$0.677715\pi$
$488$	−6.58224	−0.297964
$489$	40.9781	1.85309
$490$	−0.390706	−0.0176503
$491$	12.3875	0.559040	0.279520	−	0.960140i	$-0.409825\pi$
$491$	12.3875	0.559040	0.279520	+	0.960140i	$0.409825\pi$
$492$	24.2595	1.09370
$493$	−9.24839	−0.416526
$494$	−20.7642	−0.934227
$495$	−1.05028	−0.0472067
$496$	−7.34617	−0.329853
$497$	−24.5613	−1.10172
$498$	37.0265	1.65920
$499$	29.5868	1.32449	0.662244	−	0.749288i	$-0.269604\pi$
$499$	29.5868	1.32449	0.662244	+	0.749288i	$0.269604\pi$
$500$	10.7445	0.480509
$501$	−35.5740	−1.58933
$502$	−24.3240	−1.08563
$503$	−11.3863	−0.507691	−0.253846	−	0.967245i	$-0.581696\pi$
$503$	−11.3863	−0.507691	−0.253846	+	0.967245i	$0.581696\pi$
$504$	7.64371	0.340478
$505$	14.0691	0.626065
$506$	−0.324555	−0.0144282
$507$	−58.7458	−2.60899
$508$	−11.9949	−0.532188
$509$	−11.2877	−0.500319	−0.250160	−	0.968205i	$-0.580483\pi$
$509$	−11.2877	−0.500319	−0.250160	+	0.968205i	$0.580483\pi$
$510$	−3.11010	−0.137718
$511$	1.59859	0.0707174
$512$	1.00000	0.0441942
$513$	1.40764	0.0621489
$514$	−8.34544	−0.368102
$515$	0.765103	0.0337145
$516$	−17.9872	−0.791840
$517$	−1.41304	−0.0621455
$518$	0	0
$519$	16.2754	0.714411
$520$	7.87131	0.345180
$521$	−0.147581	−0.00646562	−0.00323281	−	0.999995i	$-0.501029\pi$
$521$	−0.147581	−0.00646562	−0.00323281	+	0.999995i	$0.501029\pi$
$522$	26.1584	1.14492
$523$	23.8600	1.04333	0.521663	−	0.853152i	$-0.325312\pi$
$523$	23.8600	1.04333	0.521663	+	0.853152i	$0.325312\pi$
$524$	−0.755808	−0.0330176
$525$	21.7940	0.951167
$526$	−7.09695	−0.309442
$527$	7.34617	0.320004
$528$	−0.695886	−0.0302846
$529$	−21.7322	−0.944878
$530$	−1.52514	−0.0662479
$531$	2.82843	0.122743
$532$	9.18389	0.398172
$533$	61.3981	2.65945
$534$	29.3044	1.26813
$535$	−7.14452	−0.308884
$536$	−9.22103	−0.398288
$537$	−11.0151	−0.475339
$538$	27.9946	1.20693
$539$	0.0874207	0.00376548
$540$	−0.533609	−0.0229629
$541$	−12.5343	−0.538890	−0.269445	−	0.963016i	$-0.586840\pi$
$541$	−12.5343	−0.538890	−0.269445	+	0.963016i	$0.586840\pi$
$542$	−9.52752	−0.409242
$543$	−16.3910	−0.703407
$544$	−1.00000	−0.0428746
$545$	−2.79859	−0.119878
$546$	39.8642	1.70603
$547$	5.34647	0.228598	0.114299	−	0.993446i	$-0.463538\pi$
$547$	5.34647	0.228598	0.114299	+	0.993446i	$0.463538\pi$
$548$	−12.9551	−0.553415
$549$	−18.6174	−0.794570
$550$	−0.962862	−0.0410566
$551$	31.4292	1.33893
$552$	2.71833	0.115700
$553$	−21.3148	−0.906396
$554$	10.5510	0.448270
$555$	0	0
$556$	−17.8044	−0.755076
$557$	30.5783	1.29565	0.647823	−	0.761791i	$-0.275680\pi$
$557$	30.5783	1.29565	0.647823	+	0.761791i	$0.275680\pi$
$558$	−20.7781	−0.879607
$559$	−45.5234	−1.92544
$560$	−3.48143	−0.147117
$561$	0.695886	0.0293803
$562$	7.52012	0.317217
$563$	−45.2200	−1.90579	−0.952897	−	0.303293i	$-0.901914\pi$
$563$	−45.2200	−1.90579	−0.952897	+	0.303293i	$0.901914\pi$
$564$	11.8350	0.498343
$565$	−25.3109	−1.06484
$566$	0.267461	0.0112422
$567$	−25.6336	−1.07651
$568$	−9.08849	−0.381344
$569$	−25.3137	−1.06121	−0.530603	−	0.847621i	$-0.678034\pi$
$569$	−25.3137	−1.06121	−0.530603	+	0.847621i	$0.678034\pi$
$570$	10.5692	0.442695
$571$	−3.33921	−0.139742	−0.0698709	−	0.997556i	$-0.522259\pi$
$571$	−3.33921	−0.139742	−0.0698709	+	0.997556i	$0.522259\pi$
$572$	−1.76121	−0.0736399
$573$	−17.9508	−0.749907
$574$	−27.1560	−1.13347
$575$	3.76121	0.156853
$576$	2.82843	0.117851
$577$	33.9186	1.41205	0.706024	−	0.708187i	$-0.250487\pi$
$577$	33.9186	1.41205	0.706024	+	0.708187i	$0.250487\pi$
$578$	1.00000	0.0415945
$579$	60.0414	2.49523
$580$	−11.9142	−0.494710
$581$	−41.4473	−1.71952
$582$	−30.5601	−1.26676
$583$	0.341251	0.0141332
$584$	0.591531	0.0244777
$585$	22.2634	0.920479
$586$	19.8113	0.818398
$587$	25.1420	1.03772	0.518861	−	0.854858i	$-0.326356\pi$
$587$	25.1420	1.03772	0.518861	+	0.854858i	$0.326356\pi$
$588$	−0.732196	−0.0301953
$589$	−24.9648	−1.02866
$590$	−1.28825	−0.0530362
$591$	−35.0351	−1.44115
$592$	0	0
$593$	3.84659	0.157961	0.0789803	−	0.996876i	$-0.474834\pi$
$593$	3.84659	0.157961	0.0789803	+	0.996876i	$0.474834\pi$
$594$	0.119395	0.00489885
$595$	3.48143	0.142725
$596$	−21.7121	−0.889360
$597$	30.8100	1.26097
$598$	6.87978	0.281335
$599$	−8.75044	−0.357533	−0.178767	−	0.983891i	$-0.557211\pi$
$599$	−8.75044	−0.357533	−0.178767	+	0.983891i	$0.557211\pi$
$600$	8.06450	0.329232
$601$	20.5231	0.837153	0.418577	−	0.908182i	$-0.362529\pi$
$601$	20.5231	0.837153	0.418577	+	0.908182i	$0.362529\pi$
$602$	20.1347	0.820631
$603$	−26.0810	−1.06210
$604$	−8.50032	−0.345873
$605$	14.0637	0.571769
$606$	26.3659	1.07104
$607$	−47.3580	−1.92220	−0.961102	−	0.276195i	$-0.910927\pi$
$607$	−47.3580	−1.92220	−0.961102	+	0.276195i	$0.910927\pi$
$608$	3.39835	0.137821
$609$	−60.3394	−2.44507
$610$	8.47954	0.343326
$611$	29.9530	1.21177
$612$	−2.82843	−0.114332
$613$	−41.0174	−1.65668	−0.828338	−	0.560228i	$-0.810713\pi$
$613$	−41.0174	−1.65668	−0.828338	+	0.560228i	$0.810713\pi$
$614$	−2.38792	−0.0963687
$615$	−31.2522	−1.26021
$616$	0.778972	0.0313857
$617$	39.3776	1.58528	0.792640	−	0.609689i	$-0.208706\pi$
$617$	39.3776	1.58528	0.792640	+	0.609689i	$0.208706\pi$
$618$	1.43383	0.0576770
$619$	17.7093	0.711798	0.355899	−	0.934524i	$-0.384175\pi$
$619$	17.7093	0.711798	0.355899	+	0.934524i	$0.384175\pi$
$620$	9.46367	0.380070
$621$	−0.466391	−0.0187156
$622$	22.9308	0.919441
$623$	−32.8032	−1.31423
$624$	14.7511	0.590516
$625$	2.86054	0.114422
$626$	5.12095	0.204674
$627$	−2.36486	−0.0944435
$628$	20.1030	0.802197
$629$	0	0
$630$	−9.84697	−0.392313
$631$	28.5377	1.13607	0.568033	−	0.823006i	$-0.307705\pi$
$631$	28.5377	1.13607	0.568033	+	0.823006i	$0.307705\pi$
$632$	−7.88718	−0.313735
$633$	2.91034	0.115676
$634$	29.8349	1.18489
$635$	15.4524	0.613209
$636$	−2.85816	−0.113334
$637$	−1.85311	−0.0734227
$638$	2.66581	0.105540
$639$	−25.7061	−1.01692
$640$	−1.28825	−0.0509224
$641$	−33.5738	−1.32608	−0.663042	−	0.748582i	$-0.730735\pi$
$641$	−33.5738	−1.32608	−0.663042	+	0.748582i	$0.730735\pi$
$642$	−13.3891	−0.528424
$643$	18.8890	0.744911	0.372455	−	0.928050i	$-0.378516\pi$
$643$	18.8890	0.744911	0.372455	+	0.928050i	$0.378516\pi$
$644$	−3.04288	−0.119906
$645$	23.1719	0.912392
$646$	−3.39835	−0.133706
$647$	−8.48226	−0.333472	−0.166736	−	0.986002i	$-0.553323\pi$
$647$	−8.48226	−0.333472	−0.166736	+	0.986002i	$0.553323\pi$
$648$	−9.48528	−0.372617
$649$	0.288246	0.0113146
$650$	20.4103	0.800559
$651$	47.9287	1.87847
$652$	−16.9737	−0.664740
$653$	30.1680	1.18057	0.590283	−	0.807196i	$-0.299016\pi$
$653$	30.1680	1.18057	0.590283	+	0.807196i	$0.299016\pi$
$654$	−5.24464	−0.205082
$655$	0.973666	0.0380443
$656$	−10.0486	−0.392333
$657$	1.67310	0.0652740
$658$	−13.2480	−0.516462
$659$	23.6815	0.922500	0.461250	−	0.887270i	$-0.347401\pi$
$659$	23.6815	0.922500	0.461250	+	0.887270i	$0.347401\pi$
$660$	0.896473	0.0348952
$661$	−13.6445	−0.530711	−0.265355	−	0.964151i	$-0.585489\pi$
$661$	−13.6445	−0.530711	−0.265355	+	0.964151i	$0.585489\pi$
$662$	−20.4037	−0.793014
$663$	−14.7511	−0.572885
$664$	−15.3369	−0.595186
$665$	−11.8311	−0.458791
$666$	0	0
$667$	−10.4134	−0.403208
$668$	14.7352	0.570123
$669$	−14.6410	−0.566053
$670$	11.8789	0.458924
$671$	−1.89730	−0.0732445
$672$	−6.52431	−0.251681
$673$	12.6236	0.486603	0.243301	−	0.969951i	$-0.421770\pi$
$673$	12.6236	0.486603	0.243301	+	0.969951i	$0.421770\pi$
$674$	−16.4068	−0.631965
$675$	−1.38365	−0.0532567
$676$	24.3333	0.935897
$677$	−11.5950	−0.445634	−0.222817	−	0.974860i	$-0.571525\pi$
$677$	−11.5950	−0.445634	−0.222817	+	0.974860i	$0.571525\pi$
$678$	−47.4334	−1.82167
$679$	34.2088	1.31281
$680$	1.28825	0.0494020
$681$	−56.7560	−2.17489
$682$	−2.11750	−0.0810833
$683$	−27.8494	−1.06563	−0.532813	−	0.846233i	$-0.678865\pi$
$683$	−27.8494	−1.06563	−0.532813	+	0.846233i	$0.678865\pi$
$684$	9.61197	0.367523
$685$	16.6894	0.637668
$686$	−18.0976	−0.690969
$687$	−15.8322	−0.604035
$688$	7.45052	0.284049
$689$	−7.23369	−0.275582
$690$	−3.50187	−0.133314
$691$	−30.7325	−1.16912	−0.584560	−	0.811351i	$-0.698733\pi$
$691$	−30.7325	−1.16912	−0.584560	+	0.811351i	$0.698733\pi$
$692$	−6.74149	−0.256273
$693$	2.20327	0.0836951
$694$	27.8484	1.05711
$695$	22.9365	0.870030
$696$	−22.3276	−0.846325
$697$	10.0486	0.380619
$698$	−24.4273	−0.924585
$699$	−32.8576	−1.24279
$700$	−9.02736	−0.341202
$701$	−3.59016	−0.135599	−0.0677993	−	0.997699i	$-0.521598\pi$
$701$	−3.59016	−0.135599	−0.0677993	+	0.997699i	$0.521598\pi$
$702$	−2.53089	−0.0955221
$703$	0	0
$704$	0.288246	0.0108637
$705$	−15.2464	−0.574212
$706$	−4.44040	−0.167117
$707$	−29.5138	−1.10998
$708$	−2.41421	−0.0907317
$709$	7.22141	0.271206	0.135603	−	0.990763i	$-0.456703\pi$
$709$	7.22141	0.271206	0.135603	+	0.990763i	$0.456703\pi$
$710$	11.7082	0.439401
$711$	−22.3083	−0.836627
$712$	−12.1383	−0.454901
$713$	8.27155	0.309772
$714$	6.52431	0.244166
$715$	2.26887	0.0848509
$716$	4.56262	0.170513
$717$	−51.2112	−1.91252
$718$	5.75819	0.214894
$719$	−49.1662	−1.83359	−0.916796	−	0.399356i	$-0.869234\pi$
$719$	−49.1662	−1.83359	−0.916796	+	0.399356i	$0.869234\pi$
$720$	−3.64371	−0.135793
$721$	−1.60502	−0.0597741
$722$	−7.45125	−0.277307
$723$	−72.6824	−2.70309
$724$	6.78939	0.252326
$725$	−30.8935	−1.14736
$726$	26.3558	0.978154
$727$	−1.12835	−0.0418481	−0.0209240	−	0.999781i	$-0.506661\pi$
$727$	−1.12835	−0.0418481	−0.0209240	+	0.999781i	$0.506661\pi$
$728$	−16.5123	−0.611986
$729$	−23.8284	−0.882534
$730$	−0.762037	−0.0282043
$731$	−7.45052	−0.275568
$732$	15.8909	0.587345
$733$	48.9912	1.80953	0.904766	−	0.425910i	$-0.140046\pi$
$733$	48.9912	1.80953	0.904766	+	0.425910i	$0.140046\pi$
$734$	−13.6982	−0.505609
$735$	0.943249	0.0347922
$736$	−1.12597	−0.0415037
$737$	−2.65792	−0.0979058
$738$	−28.4218	−1.04622
$739$	45.9765	1.69127	0.845637	−	0.533759i	$-0.179221\pi$
$739$	45.9765	1.69127	0.845637	+	0.533759i	$0.179221\pi$
$740$	0	0
$741$	50.1293	1.84155
$742$	3.19942	0.117454
$743$	27.3388	1.00296	0.501481	−	0.865169i	$-0.332789\pi$
$743$	27.3388	1.00296	0.501481	+	0.865169i	$0.332789\pi$
$744$	17.7352	0.650205
$745$	27.9705	1.02476
$746$	−5.44312	−0.199287
$747$	−43.3792	−1.58716
$748$	−0.288246	−0.0105393
$749$	14.9876	0.547636
$750$	−25.9396	−0.947178
$751$	−37.7804	−1.37863	−0.689313	−	0.724463i	$-0.742088\pi$
$751$	−37.7804	−1.37863	−0.689313	+	0.724463i	$0.742088\pi$
$752$	−4.90222	−0.178765
$753$	58.7234	2.14000
$754$	−56.5086	−2.05792
$755$	10.9505	0.398530
$756$	1.11940	0.0407120
$757$	−40.5763	−1.47477	−0.737385	−	0.675473i	$-0.763939\pi$
$757$	−40.5763	−1.47477	−0.737385	+	0.675473i	$0.763939\pi$
$758$	−36.1977	−1.31476
$759$	0.783546	0.0284409
$760$	−4.37790	−0.158803
$761$	−1.16575	−0.0422583	−0.0211292	−	0.999777i	$-0.506726\pi$
$761$	−1.16575	−0.0422583	−0.0211292	+	0.999777i	$0.506726\pi$
$762$	28.9582	1.04905
$763$	5.87082	0.212538
$764$	7.43548	0.269006
$765$	3.64371	0.131739
$766$	−9.06679	−0.327597
$767$	−6.11010	−0.220623
$768$	−2.41421	−0.0871154
$769$	15.5230	0.559772	0.279886	−	0.960033i	$-0.409703\pi$
$769$	15.5230	0.559772	0.279886	+	0.960033i	$0.409703\pi$
$770$	−1.00351	−0.0361639
$771$	20.1477	0.725601
$772$	−24.8700	−0.895089
$773$	1.06869	0.0384380	0.0192190	−	0.999815i	$-0.493882\pi$
$773$	1.06869	0.0384380	0.0192190	+	0.999815i	$0.493882\pi$
$774$	21.0733	0.757463
$775$	24.5393	0.881478
$776$	12.6584	0.454410
$777$	0	0
$778$	16.8048	0.602482
$779$	−34.1487	−1.22350
$780$	−19.0030	−0.680417
$781$	−2.61972	−0.0937408
$782$	1.12597	0.0402645
$783$	3.83081	0.136902
$784$	0.303286	0.0108316
$785$	−25.8976	−0.924325
$786$	1.82468	0.0650842
$787$	21.4565	0.764843	0.382421	−	0.923988i	$-0.375090\pi$
$787$	21.4565	0.764843	0.382421	+	0.923988i	$0.375090\pi$
$788$	14.5120	0.516968
$789$	17.1336	0.609971
$790$	10.1606	0.361499
$791$	53.0967	1.88790
$792$	0.815282	0.0289698
$793$	40.2181	1.42819
$794$	−13.4733	−0.478148
$795$	3.68202	0.130588
$796$	−12.7619	−0.452335
$797$	−18.6479	−0.660544	−0.330272	−	0.943886i	$-0.607140\pi$
$797$	−18.6479	−0.660544	−0.330272	+	0.943886i	$0.607140\pi$
$798$	−22.1719	−0.784876
$799$	4.90222	0.173428
$800$	−3.34042	−0.118102
$801$	−34.3323	−1.21307
$802$	18.6668	0.659147
$803$	0.170506	0.00601704
$804$	22.2615	0.785104
$805$	3.91998	0.138161
$806$	44.8858	1.58104
$807$	−67.5848	−2.37910
$808$	−10.9211	−0.384203
$809$	−7.49068	−0.263358	−0.131679	−	0.991292i	$-0.542037\pi$
$809$	−7.49068	−0.263358	−0.131679	+	0.991292i	$0.542037\pi$
$810$	12.2194	0.429345
$811$	−38.7604	−1.36106	−0.680531	−	0.732720i	$-0.738251\pi$
$811$	−38.7604	−1.36106	−0.680531	+	0.732720i	$0.738251\pi$
$812$	24.9934	0.877096
$813$	23.0015	0.806697
$814$	0	0
$815$	21.8663	0.765941
$816$	2.41421	0.0845144
$817$	25.3195	0.885816
$818$	12.4382	0.434892
$819$	−46.7038	−1.63196
$820$	12.9451	0.452062
$821$	34.6391	1.20891	0.604456	−	0.796638i	$-0.293390\pi$
$821$	34.6391	1.20891	0.604456	+	0.796638i	$0.293390\pi$
$822$	31.2764	1.09089
$823$	26.4572	0.922240	0.461120	−	0.887338i	$-0.347448\pi$
$823$	26.4572	0.922240	0.461120	+	0.887338i	$0.347448\pi$
$824$	−0.593911	−0.0206899
$825$	2.32456	0.0809306
$826$	2.70246	0.0940306
$827$	−48.3015	−1.67961	−0.839805	−	0.542889i	$-0.817331\pi$
$827$	−48.3015	−1.67961	−0.839805	+	0.542889i	$0.817331\pi$
$828$	−3.18472	−0.110677
$829$	−26.8422	−0.932268	−0.466134	−	0.884714i	$-0.654354\pi$
$829$	−26.8422	−0.932268	−0.466134	+	0.884714i	$0.654354\pi$
$830$	19.7577	0.685798
$831$	−25.4724	−0.883629
$832$	−6.11010	−0.211830
$833$	−0.303286	−0.0105082
$834$	42.9837	1.48840
$835$	−18.9826	−0.656919
$836$	0.979558	0.0338787
$837$	−3.04288	−0.105177
$838$	−18.2673	−0.631033
$839$	−35.0390	−1.20968	−0.604841	−	0.796346i	$-0.706763\pi$
$839$	−35.0390	−1.20968	−0.604841	+	0.796346i	$0.706763\pi$
$840$	8.40492	0.289997
$841$	56.5326	1.94940
$842$	6.22137	0.214403
$843$	−18.1552	−0.625298
$844$	−1.20550	−0.0414951
$845$	−31.3473	−1.07838
$846$	−13.8656	−0.476708
$847$	−29.5025	−1.01372
$848$	1.18389	0.0406550
$849$	−0.645708	−0.0221606
$850$	3.34042	0.114576
$851$	0	0
$852$	21.9415	0.751705
$853$	49.6898	1.70135	0.850673	−	0.525695i	$-0.176195\pi$
$853$	49.6898	1.70135	0.850673	+	0.525695i	$0.176195\pi$
$854$	−17.7882	−0.608700
$855$	−12.3826	−0.423475
$856$	5.54593	0.189556
$857$	−26.9260	−0.919774	−0.459887	−	0.887977i	$-0.652110\pi$
$857$	−26.9260	−0.919774	−0.459887	+	0.887977i	$0.652110\pi$
$858$	4.25194	0.145159
$859$	−7.17085	−0.244666	−0.122333	−	0.992489i	$-0.539038\pi$
$859$	−7.17085	−0.244666	−0.122333	+	0.992489i	$0.539038\pi$
$860$	−9.59810	−0.327293
$861$	65.5604	2.23429
$862$	−14.0096	−0.477169
$863$	14.1211	0.480686	0.240343	−	0.970688i	$-0.422740\pi$
$863$	14.1211	0.480686	0.240343	+	0.970688i	$0.422740\pi$
$864$	0.414214	0.0140918
$865$	8.68470	0.295289
$866$	−22.7622	−0.773492
$867$	−2.41421	−0.0819910
$868$	−19.8527	−0.673845
$869$	−2.27344	−0.0771213
$870$	28.7634	0.975171
$871$	56.3414	1.90906
$872$	2.17240	0.0735668
$873$	35.8034	1.21176
$874$	−3.82643	−0.129431
$875$	29.0366	0.981617
$876$	−1.42808	−0.0482504
$877$	8.94276	0.301975	0.150988	−	0.988536i	$-0.451755\pi$
$877$	8.94276	0.301975	0.150988	+	0.988536i	$0.451755\pi$
$878$	3.08373	0.104071
$879$	−47.8287	−1.61322
$880$	−0.371331	−0.0125176
$881$	35.8573	1.20806	0.604031	−	0.796961i	$-0.293560\pi$
$881$	35.8573	1.20806	0.604031	+	0.796961i	$0.293560\pi$
$882$	0.857821	0.0288843
$883$	25.5689	0.860460	0.430230	−	0.902719i	$-0.358432\pi$
$883$	25.5689	0.860460	0.430230	+	0.902719i	$0.358432\pi$
$884$	6.11010	0.205505
$885$	3.11010	0.104545
$886$	−5.83542	−0.196045
$887$	−44.5341	−1.49531	−0.747654	−	0.664088i	$-0.768820\pi$
$887$	−44.5341	−1.49531	−0.747654	+	0.664088i	$0.768820\pi$
$888$	0	0
$889$	−32.4157	−1.08719
$890$	15.6371	0.524157
$891$	−2.73409	−0.0915955
$892$	6.06450	0.203054
$893$	−16.6594	−0.557487
$894$	52.4175	1.75310
$895$	−5.87778	−0.196472
$896$	2.70246	0.0902828
$897$	−16.6093	−0.554567
$898$	−10.7028	−0.357156
$899$	−67.9402	−2.26593
$900$	−9.44814	−0.314938
$901$	−1.18389	−0.0394411
$902$	−2.89647	−0.0964420
$903$	−48.6096	−1.61762
$904$	19.6476	0.653468
$905$	−8.74641	−0.290740
$906$	20.5216	0.681784
$907$	22.9420	0.761778	0.380889	−	0.924621i	$-0.375618\pi$
$907$	22.9420	0.761778	0.380889	+	0.924621i	$0.375618\pi$
$908$	23.5091	0.780176
$909$	−30.8896	−1.02454
$910$	21.2719	0.705156
$911$	38.9392	1.29011	0.645056	−	0.764135i	$-0.276834\pi$
$911$	38.9392	1.29011	0.645056	+	0.764135i	$0.276834\pi$
$912$	−8.20433	−0.271673
$913$	−4.42079	−0.146307
$914$	−29.2423	−0.967249
$915$	−20.4714	−0.676764
$916$	6.55790	0.216679
$917$	−2.04254	−0.0674506
$918$	−0.414214	−0.0136711
$919$	33.5975	1.10828	0.554140	−	0.832423i	$-0.313047\pi$
$919$	33.5975	1.10828	0.554140	+	0.832423i	$0.313047\pi$
$920$	1.45052	0.0478223
$921$	5.76496	0.189962
$922$	30.3738	1.00031
$923$	55.5316	1.82784
$924$	−1.88060	−0.0618674
$925$	0	0
$926$	28.0834	0.922877
$927$	−1.67983	−0.0551730
$928$	9.24839	0.303593
$929$	−9.49968	−0.311674	−0.155837	−	0.987783i	$-0.549808\pi$
$929$	−9.49968	−0.311674	−0.155837	+	0.987783i	$0.549808\pi$
$930$	−22.8473	−0.749193
$931$	1.03067	0.0337788
$932$	13.6101	0.445813
$933$	−55.3598	−1.81240
$934$	14.4243	0.471979
$935$	0.371331	0.0121438
$936$	−17.2820	−0.564879
$937$	31.6126	1.03274	0.516369	−	0.856366i	$-0.327283\pi$
$937$	31.6126	1.03274	0.516369	+	0.856366i	$0.327283\pi$
$938$	−24.9195	−0.813649
$939$	−12.3631	−0.403453
$940$	6.31526	0.205981
$941$	−6.50270	−0.211982	−0.105991	−	0.994367i	$-0.533801\pi$
$941$	−6.50270	−0.211982	−0.105991	+	0.994367i	$0.533801\pi$
$942$	−48.5329	−1.58129
$943$	11.3144	0.368449
$944$	1.00000	0.0325472
$945$	−1.44206	−0.0469101
$946$	2.14758	0.0698239
$947$	40.0940	1.30288	0.651441	−	0.758700i	$-0.274165\pi$
$947$	40.0940	1.30288	0.651441	+	0.758700i	$0.274165\pi$
$948$	19.0413	0.618434
$949$	−3.61431	−0.117326
$950$	−11.3519	−0.368305
$951$	−72.0277	−2.33566
$952$	−2.70246	−0.0875872
$953$	−59.9727	−1.94270	−0.971352	−	0.237644i	$-0.923625\pi$
$953$	−59.9727	−1.94270	−0.971352	+	0.237644i	$0.923625\pi$
$954$	3.34855	0.108413
$955$	−9.57873	−0.309960
$956$	21.2124	0.686057
$957$	−6.43583	−0.208041
$958$	−6.86829	−0.221904
$959$	−35.0107	−1.13055
$960$	3.11010	0.100378
$961$	22.9662	0.740845
$962$	0	0
$963$	15.6862	0.505482
$964$	30.1060	0.969650
$965$	32.0386	1.03136
$966$	7.34617	0.236359
$967$	−22.5995	−0.726750	−0.363375	−	0.931643i	$-0.618376\pi$
$967$	−22.5995	−0.726750	−0.363375	+	0.931643i	$0.618376\pi$
$968$	−10.9169	−0.350883
$969$	8.20433	0.263561
$970$	−16.3071	−0.523591
$971$	23.6286	0.758277	0.379139	−	0.925340i	$-0.376220\pi$
$971$	23.6286	0.758277	0.379139	+	0.925340i	$0.376220\pi$
$972$	21.6569	0.694644
$973$	−48.1158	−1.54252
$974$	−23.3812	−0.749183
$975$	−49.2749	−1.57806
$976$	−6.58224	−0.210692
$977$	−6.50607	−0.208147	−0.104074	−	0.994570i	$-0.533188\pi$
$977$	−6.50607	−0.208147	−0.104074	+	0.994570i	$0.533188\pi$
$978$	40.9781	1.31033
$979$	−3.49881	−0.111822
$980$	−0.390706	−0.0124807
$981$	6.14448	0.196178
$982$	12.3875	0.395301
$983$	37.9672	1.21097	0.605483	−	0.795858i	$-0.292980\pi$
$983$	37.9672	1.21097	0.605483	+	0.795858i	$0.292980\pi$
$984$	24.2595	0.773366
$985$	−18.6950	−0.595673
$986$	−9.24839	−0.294529
$987$	31.9836	1.01805
$988$	−20.7642	−0.660598
$989$	−8.38905	−0.266756
$990$	−1.05028	−0.0333802
$991$	9.97855	0.316979	0.158489	−	0.987361i	$-0.449338\pi$
$991$	9.97855	0.316979	0.158489	+	0.987361i	$0.449338\pi$
$992$	−7.34617	−0.233241
$993$	49.2590	1.56319
$994$	−24.5613	−0.779036
$995$	16.4405	0.521199
$996$	37.0265	1.17323
$997$	−47.2108	−1.49518	−0.747590	−	0.664160i	$-0.768789\pi$
$997$	−47.2108	−1.49518	−0.747590	+	0.664160i	$0.768789\pi$
$998$	29.5868	0.936554
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.r.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.r.1.1	✓	4	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} -1.28825 q^{5} -2.41421 q^{6} +2.70246 q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} -1.28825 q^{5} -2.41421 q^{6} +2.70246 q^{7} +1.00000 q^{8} +2.82843 q^{9} -1.28825 q^{10} +0.288246 q^{11} -2.41421 q^{12} -6.11010 q^{13} +2.70246 q^{14} +3.11010 q^{15} +1.00000 q^{16} -1.00000 q^{17} +2.82843 q^{18} +3.39835 q^{19} -1.28825 q^{20} -6.52431 q^{21} +0.288246 q^{22} -1.12597 q^{23} -2.41421 q^{24} -3.34042 q^{25} -6.11010 q^{26} +0.414214 q^{27} +2.70246 q^{28} +9.24839 q^{29} +3.11010 q^{30} -7.34617 q^{31} +1.00000 q^{32} -0.695886 q^{33} -1.00000 q^{34} -3.48143 q^{35} +2.82843 q^{36} +3.39835 q^{38} +14.7511 q^{39} -1.28825 q^{40} -10.0486 q^{41} -6.52431 q^{42} +7.45052 q^{43} +0.288246 q^{44} -3.64371 q^{45} -1.12597 q^{46} -4.90222 q^{47} -2.41421 q^{48} +0.303286 q^{49} -3.34042 q^{50} +2.41421 q^{51} -6.11010 q^{52} +1.18389 q^{53} +0.414214 q^{54} -0.371331 q^{55} +2.70246 q^{56} -8.20433 q^{57} +9.24839 q^{58} +1.00000 q^{59} +3.11010 q^{60} -6.58224 q^{61} -7.34617 q^{62} +7.64371 q^{63} +1.00000 q^{64} +7.87131 q^{65} -0.695886 q^{66} -9.22103 q^{67} -1.00000 q^{68} +2.71833 q^{69} -3.48143 q^{70} -9.08849 q^{71} +2.82843 q^{72} +0.591531 q^{73} +8.06450 q^{75} +3.39835 q^{76} +0.778972 q^{77} +14.7511 q^{78} -7.88718 q^{79} -1.28825 q^{80} -9.48528 q^{81} -10.0486 q^{82} -15.3369 q^{83} -6.52431 q^{84} +1.28825 q^{85} +7.45052 q^{86} -22.3276 q^{87} +0.288246 q^{88} -12.1383 q^{89} -3.64371 q^{90} -16.5123 q^{91} -1.12597 q^{92} +17.7352 q^{93} -4.90222 q^{94} -4.37790 q^{95} -2.41421 q^{96} +12.6584 q^{97} +0.303286 q^{98} +0.815282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} + 4 q^{10} - 8 q^{11} - 4 q^{12} - 12 q^{13} - 4 q^{14} + 4 q^{16} - 4 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} - 8 q^{22} - 8 q^{23} - 4 q^{24} - 4 q^{25} - 12 q^{26} - 4 q^{27} - 4 q^{28} + 8 q^{29} - 8 q^{31} + 4 q^{32} + 4 q^{33} - 4 q^{34} - 20 q^{35} - 8 q^{38} + 8 q^{39} + 4 q^{40} - 4 q^{41} - 8 q^{42} + 8 q^{43} - 8 q^{44} - 8 q^{45} - 8 q^{46} - 12 q^{47} - 4 q^{48} + 4 q^{49} - 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 4 q^{54} - 20 q^{55} - 4 q^{56} + 8 q^{57} + 8 q^{58} + 4 q^{59} + 4 q^{61} - 8 q^{62} + 24 q^{63} + 4 q^{64} - 4 q^{65} + 4 q^{66} - 16 q^{67} - 4 q^{68} + 12 q^{69} - 20 q^{70} - 20 q^{71} - 4 q^{73} + 12 q^{75} - 8 q^{76} + 24 q^{77} + 8 q^{78} - 12 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 16 q^{83} - 8 q^{84} - 4 q^{85} + 8 q^{86} - 20 q^{87} - 8 q^{88} - 32 q^{89} - 8 q^{90} + 8 q^{91} - 8 q^{92} + 4 q^{93} - 12 q^{94} - 28 q^{95} - 4 q^{96} + 24 q^{97} + 4 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 + 4 * q^10 - 8 * q^11 - 4 * q^12 - 12 * q^13 - 4 * q^14 + 4 * q^16 - 4 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 - 8 * q^22 - 8 * q^23 - 4 * q^24 - 4 * q^25 - 12 * q^26 - 4 * q^27 - 4 * q^28 + 8 * q^29 - 8 * q^31 + 4 * q^32 + 4 * q^33 - 4 * q^34 - 20 * q^35 - 8 * q^38 + 8 * q^39 + 4 * q^40 - 4 * q^41 - 8 * q^42 + 8 * q^43 - 8 * q^44 - 8 * q^45 - 8 * q^46 - 12 * q^47 - 4 * q^48 + 4 * q^49 - 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 4 * q^54 - 20 * q^55 - 4 * q^56 + 8 * q^57 + 8 * q^58 + 4 * q^59 + 4 * q^61 - 8 * q^62 + 24 * q^63 + 4 * q^64 - 4 * q^65 + 4 * q^66 - 16 * q^67 - 4 * q^68 + 12 * q^69 - 20 * q^70 - 20 * q^71 - 4 * q^73 + 12 * q^75 - 8 * q^76 + 24 * q^77 + 8 * q^78 - 12 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 16 * q^83 - 8 * q^84 - 4 * q^85 + 8 * q^86 - 20 * q^87 - 8 * q^88 - 32 * q^89 - 8 * q^90 + 8 * q^91 - 8 * q^92 + 4 * q^93 - 12 * q^94 - 28 * q^95 - 4 * q^96 + 24 * q^97 + 4 * q^98 + 8 * q^99

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