LMFDB - Embedded newform 4882.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4882,2,Mod(1,4882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4882, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4882.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4882 = 2 \cdot 2441 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4882.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:	$38.9829662668$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	4882.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} +3.00000 q^{5} -3.23607 q^{6} -4.23607 q^{7} -1.00000 q^{8} +7.47214 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} +3.00000 q^{5} -3.23607 q^{6} -4.23607 q^{7} -1.00000 q^{8} +7.47214 q^{9} -3.00000 q^{10} -2.23607 q^{11} +3.23607 q^{12} -4.38197 q^{13} +4.23607 q^{14} +9.70820 q^{15} +1.00000 q^{16} -7.47214 q^{17} -7.47214 q^{18} -7.23607 q^{19} +3.00000 q^{20} -13.7082 q^{21} +2.23607 q^{22} -1.00000 q^{23} -3.23607 q^{24} +4.00000 q^{25} +4.38197 q^{26} +14.4721 q^{27} -4.23607 q^{28} +8.61803 q^{29} -9.70820 q^{30} -7.00000 q^{31} -1.00000 q^{32} -7.23607 q^{33} +7.47214 q^{34} -12.7082 q^{35} +7.47214 q^{36} -8.94427 q^{37} +7.23607 q^{38} -14.1803 q^{39} -3.00000 q^{40} +5.38197 q^{41} +13.7082 q^{42} -7.23607 q^{43} -2.23607 q^{44} +22.4164 q^{45} +1.00000 q^{46} +7.00000 q^{47} +3.23607 q^{48} +10.9443 q^{49} -4.00000 q^{50} -24.1803 q^{51} -4.38197 q^{52} +2.70820 q^{53} -14.4721 q^{54} -6.70820 q^{55} +4.23607 q^{56} -23.4164 q^{57} -8.61803 q^{58} -9.32624 q^{59} +9.70820 q^{60} +5.09017 q^{61} +7.00000 q^{62} -31.6525 q^{63} +1.00000 q^{64} -13.1459 q^{65} +7.23607 q^{66} -5.38197 q^{67} -7.47214 q^{68} -3.23607 q^{69} +12.7082 q^{70} +7.85410 q^{71} -7.47214 q^{72} +14.7984 q^{73} +8.94427 q^{74} +12.9443 q^{75} -7.23607 q^{76} +9.47214 q^{77} +14.1803 q^{78} -15.0902 q^{79} +3.00000 q^{80} +24.4164 q^{81} -5.38197 q^{82} -3.14590 q^{83} -13.7082 q^{84} -22.4164 q^{85} +7.23607 q^{86} +27.8885 q^{87} +2.23607 q^{88} +1.61803 q^{89} -22.4164 q^{90} +18.5623 q^{91} -1.00000 q^{92} -22.6525 q^{93} -7.00000 q^{94} -21.7082 q^{95} -3.23607 q^{96} +6.09017 q^{97} -10.9443 q^{98} -16.7082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{12} - 11 q^{13} + 4 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{17} - 6 q^{18} - 10 q^{19} + 6 q^{20} - 14 q^{21} - 2 q^{23} - 2 q^{24} + 8 q^{25} + 11 q^{26} + 20 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 14 q^{31} - 2 q^{32} - 10 q^{33} + 6 q^{34} - 12 q^{35} + 6 q^{36} + 10 q^{38} - 6 q^{39} - 6 q^{40} + 13 q^{41} + 14 q^{42} - 10 q^{43} + 18 q^{45} + 2 q^{46} + 14 q^{47} + 2 q^{48} + 4 q^{49} - 8 q^{50} - 26 q^{51} - 11 q^{52} - 8 q^{53} - 20 q^{54} + 4 q^{56} - 20 q^{57} - 15 q^{58} - 3 q^{59} + 6 q^{60} - q^{61} + 14 q^{62} - 32 q^{63} + 2 q^{64} - 33 q^{65} + 10 q^{66} - 13 q^{67} - 6 q^{68} - 2 q^{69} + 12 q^{70} + 9 q^{71} - 6 q^{72} + 5 q^{73} + 8 q^{75} - 10 q^{76} + 10 q^{77} + 6 q^{78} - 19 q^{79} + 6 q^{80} + 22 q^{81} - 13 q^{82} - 13 q^{83} - 14 q^{84} - 18 q^{85} + 10 q^{86} + 20 q^{87} + q^{89} - 18 q^{90} + 17 q^{91} - 2 q^{92} - 14 q^{93} - 14 q^{94} - 30 q^{95} - 2 q^{96} + q^{97} - 4 q^{98} - 20 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9 - 6 * q^10 + 2 * q^12 - 11 * q^13 + 4 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^17 - 6 * q^18 - 10 * q^19 + 6 * q^20 - 14 * q^21 - 2 * q^23 - 2 * q^24 + 8 * q^25 + 11 * q^26 + 20 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 14 * q^31 - 2 * q^32 - 10 * q^33 + 6 * q^34 - 12 * q^35 + 6 * q^36 + 10 * q^38 - 6 * q^39 - 6 * q^40 + 13 * q^41 + 14 * q^42 - 10 * q^43 + 18 * q^45 + 2 * q^46 + 14 * q^47 + 2 * q^48 + 4 * q^49 - 8 * q^50 - 26 * q^51 - 11 * q^52 - 8 * q^53 - 20 * q^54 + 4 * q^56 - 20 * q^57 - 15 * q^58 - 3 * q^59 + 6 * q^60 - q^61 + 14 * q^62 - 32 * q^63 + 2 * q^64 - 33 * q^65 + 10 * q^66 - 13 * q^67 - 6 * q^68 - 2 * q^69 + 12 * q^70 + 9 * q^71 - 6 * q^72 + 5 * q^73 + 8 * q^75 - 10 * q^76 + 10 * q^77 + 6 * q^78 - 19 * q^79 + 6 * q^80 + 22 * q^81 - 13 * q^82 - 13 * q^83 - 14 * q^84 - 18 * q^85 + 10 * q^86 + 20 * q^87 + q^89 - 18 * q^90 + 17 * q^91 - 2 * q^92 - 14 * q^93 - 14 * q^94 - 30 * q^95 - 2 * q^96 + q^97 - 4 * q^98 - 20 * 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
$3$	3.23607	1.86834	0.934172	−	0.356822i	$-0.116140\pi$
$3$	3.23607	1.86834	0.934172	+	0.356822i	$0.116140\pi$
$4$	1.00000	0.500000
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	−3.23607	−1.32112
$7$	−4.23607	−1.60108	−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−4.23607	−1.60108	−0.800542	+	0.599277i	$0.795455\pi$
$8$	−1.00000	−0.353553
$9$	7.47214	2.49071
$10$	−3.00000	−0.948683
$11$	−2.23607	−0.674200	−0.337100	−	0.941469i	$-0.609446\pi$
$11$	−2.23607	−0.674200	−0.337100	+	0.941469i	$0.609446\pi$
$12$	3.23607	0.934172
$13$	−4.38197	−1.21534	−0.607669	−	0.794190i	$-0.707895\pi$
$13$	−4.38197	−1.21534	−0.607669	+	0.794190i	$0.707895\pi$
$14$	4.23607	1.13214
$15$	9.70820	2.50665
$16$	1.00000	0.250000
$17$	−7.47214	−1.81226	−0.906130	−	0.423000i	$-0.860977\pi$
$17$	−7.47214	−1.81226	−0.906130	+	0.423000i	$0.860977\pi$
$18$	−7.47214	−1.76120
$19$	−7.23607	−1.66007	−0.830034	−	0.557713i	$-0.811679\pi$
$19$	−7.23607	−1.66007	−0.830034	+	0.557713i	$0.811679\pi$
$20$	3.00000	0.670820
$21$	−13.7082	−2.99138
$22$	2.23607	0.476731
$23$	−1.00000	−0.208514	−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000	−0.208514	−0.104257	+	0.994550i	$0.533247\pi$
$24$	−3.23607	−0.660560
$25$	4.00000	0.800000
$26$	4.38197	0.859374
$27$	14.4721	2.78516
$28$	−4.23607	−0.800542
$29$	8.61803	1.60033	0.800164	−	0.599781i	$-0.204746\pi$
$29$	8.61803	1.60033	0.800164	+	0.599781i	$0.204746\pi$
$30$	−9.70820	−1.77247
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−1.00000	−0.176777
$33$	−7.23607	−1.25964
$34$	7.47214	1.28146
$35$	−12.7082	−2.14808
$36$	7.47214	1.24536
$37$	−8.94427	−1.47043	−0.735215	−	0.677834i	$-0.762919\pi$
$37$	−8.94427	−1.47043	−0.735215	+	0.677834i	$0.762919\pi$
$38$	7.23607	1.17385
$39$	−14.1803	−2.27067
$40$	−3.00000	−0.474342
$41$	5.38197	0.840522	0.420261	−	0.907403i	$-0.361939\pi$
$41$	5.38197	0.840522	0.420261	+	0.907403i	$0.361939\pi$
$42$	13.7082	2.11522
$43$	−7.23607	−1.10349	−0.551745	−	0.834013i	$-0.686038\pi$
$43$	−7.23607	−1.10349	−0.551745	+	0.834013i	$0.686038\pi$
$44$	−2.23607	−0.337100
$45$	22.4164	3.34164
$46$	1.00000	0.147442
$47$	7.00000	1.02105	0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000	1.02105	0.510527	+	0.859861i	$0.329450\pi$
$48$	3.23607	0.467086
$49$	10.9443	1.56347
$50$	−4.00000	−0.565685
$51$	−24.1803	−3.38592
$52$	−4.38197	−0.607669
$53$	2.70820	0.372000	0.186000	−	0.982550i	$-0.440447\pi$
$53$	2.70820	0.372000	0.186000	+	0.982550i	$0.440447\pi$
$54$	−14.4721	−1.96941
$55$	−6.70820	−0.904534
$56$	4.23607	0.566068
$57$	−23.4164	−3.10158
$58$	−8.61803	−1.13160
$59$	−9.32624	−1.21417	−0.607086	−	0.794636i	$-0.707662\pi$
$59$	−9.32624	−1.21417	−0.607086	+	0.794636i	$0.707662\pi$
$60$	9.70820	1.25332
$61$	5.09017	0.651729	0.325865	−	0.945416i	$-0.394345\pi$
$61$	5.09017	0.651729	0.325865	+	0.945416i	$0.394345\pi$
$62$	7.00000	0.889001
$63$	−31.6525	−3.98784
$64$	1.00000	0.125000
$65$	−13.1459	−1.63055
$66$	7.23607	0.890698
$67$	−5.38197	−0.657512	−0.328756	−	0.944415i	$-0.606629\pi$
$67$	−5.38197	−0.657512	−0.328756	+	0.944415i	$0.606629\pi$
$68$	−7.47214	−0.906130
$69$	−3.23607	−0.389577
$70$	12.7082	1.51892
$71$	7.85410	0.932110	0.466055	−	0.884756i	$-0.345675\pi$
$71$	7.85410	0.932110	0.466055	+	0.884756i	$0.345675\pi$
$72$	−7.47214	−0.880600
$73$	14.7984	1.73202	0.866009	−	0.500028i	$-0.166677\pi$
$73$	14.7984	1.73202	0.866009	+	0.500028i	$0.166677\pi$
$74$	8.94427	1.03975
$75$	12.9443	1.49468
$76$	−7.23607	−0.830034
$77$	9.47214	1.07945
$78$	14.1803	1.60561
$79$	−15.0902	−1.69778	−0.848888	−	0.528572i	$-0.822728\pi$
$79$	−15.0902	−1.69778	−0.848888	+	0.528572i	$0.822728\pi$
$80$	3.00000	0.335410
$81$	24.4164	2.71293
$82$	−5.38197	−0.594339
$83$	−3.14590	−0.345307	−0.172654	−	0.984983i	$-0.555234\pi$
$83$	−3.14590	−0.345307	−0.172654	+	0.984983i	$0.555234\pi$
$84$	−13.7082	−1.49569
$85$	−22.4164	−2.43140
$86$	7.23607	0.780285
$87$	27.8885	2.98997
$88$	2.23607	0.238366
$89$	1.61803	0.171511	0.0857556	−	0.996316i	$-0.472670\pi$
$89$	1.61803	0.171511	0.0857556	+	0.996316i	$0.472670\pi$
$90$	−22.4164	−2.36290
$91$	18.5623	1.94586
$92$	−1.00000	−0.104257
$93$	−22.6525	−2.34895
$94$	−7.00000	−0.721995
$95$	−21.7082	−2.22721
$96$	−3.23607	−0.330280
$97$	6.09017	0.618363	0.309182	−	0.951003i	$-0.399945\pi$
$97$	6.09017	0.618363	0.309182	+	0.951003i	$0.399945\pi$
$98$	−10.9443	−1.10554
$99$	−16.7082	−1.67924
$100$	4.00000	0.400000
$101$	−3.94427	−0.392470	−0.196235	−	0.980557i	$-0.562871\pi$
$101$	−3.94427	−0.392470	−0.196235	+	0.980557i	$0.562871\pi$
$102$	24.1803	2.39421
$103$	−12.7082	−1.25218	−0.626088	−	0.779752i	$-0.715345\pi$
$103$	−12.7082	−1.25218	−0.626088	+	0.779752i	$0.715345\pi$
$104$	4.38197	0.429687
$105$	−41.1246	−4.01335
$106$	−2.70820	−0.263044
$107$	13.4721	1.30240	0.651200	−	0.758906i	$-0.274266\pi$
$107$	13.4721	1.30240	0.651200	+	0.758906i	$0.274266\pi$
$108$	14.4721	1.39258
$109$	4.09017	0.391767	0.195884	−	0.980627i	$-0.437243\pi$
$109$	4.09017	0.391767	0.195884	+	0.980627i	$0.437243\pi$
$110$	6.70820	0.639602
$111$	−28.9443	−2.74727
$112$	−4.23607	−0.400271
$113$	−9.85410	−0.926996	−0.463498	−	0.886098i	$-0.653406\pi$
$113$	−9.85410	−0.926996	−0.463498	+	0.886098i	$0.653406\pi$
$114$	23.4164	2.19315
$115$	−3.00000	−0.279751
$116$	8.61803	0.800164
$117$	−32.7426	−3.02706
$118$	9.32624	0.858550
$119$	31.6525	2.90158
$120$	−9.70820	−0.886234
$121$	−6.00000	−0.545455
$122$	−5.09017	−0.460842
$123$	17.4164	1.57038
$124$	−7.00000	−0.628619
$125$	−3.00000	−0.268328
$126$	31.6525	2.81983
$127$	−11.0902	−0.984093	−0.492047	−	0.870569i	$-0.663751\pi$
$127$	−11.0902	−0.984093	−0.492047	+	0.870569i	$0.663751\pi$
$128$	−1.00000	−0.0883883
$129$	−23.4164	−2.06170
$130$	13.1459	1.15297
$131$	12.0344	1.05145	0.525727	−	0.850653i	$-0.323793\pi$
$131$	12.0344	1.05145	0.525727	+	0.850653i	$0.323793\pi$
$132$	−7.23607	−0.629819
$133$	30.6525	2.65791
$134$	5.38197	0.464931
$135$	43.4164	3.73669
$136$	7.47214	0.640730
$137$	8.14590	0.695951	0.347976	−	0.937504i	$-0.386869\pi$
$137$	8.14590	0.695951	0.347976	+	0.937504i	$0.386869\pi$
$138$	3.23607	0.275472
$139$	−0.527864	−0.0447728	−0.0223864	−	0.999749i	$-0.507126\pi$
$139$	−0.527864	−0.0447728	−0.0223864	+	0.999749i	$0.507126\pi$
$140$	−12.7082	−1.07404
$141$	22.6525	1.90768
$142$	−7.85410	−0.659102
$143$	9.79837	0.819381
$144$	7.47214	0.622678
$145$	25.8541	2.14707
$146$	−14.7984	−1.22472
$147$	35.4164	2.92110
$148$	−8.94427	−0.735215
$149$	−0.618034	−0.0506313	−0.0253157	−	0.999680i	$-0.508059\pi$
$149$	−0.618034	−0.0506313	−0.0253157	+	0.999680i	$0.508059\pi$
$150$	−12.9443	−1.05690
$151$	10.3262	0.840337	0.420169	−	0.907446i	$-0.361971\pi$
$151$	10.3262	0.840337	0.420169	+	0.907446i	$0.361971\pi$
$152$	7.23607	0.586923
$153$	−55.8328	−4.51382
$154$	−9.47214	−0.763286
$155$	−21.0000	−1.68676
$156$	−14.1803	−1.13534
$157$	−5.38197	−0.429528	−0.214764	−	0.976666i	$-0.568898\pi$
$157$	−5.38197	−0.429528	−0.214764	+	0.976666i	$0.568898\pi$
$158$	15.0902	1.20051
$159$	8.76393	0.695025
$160$	−3.00000	−0.237171
$161$	4.23607	0.333849
$162$	−24.4164	−1.91833
$163$	−25.4721	−1.99513	−0.997566	−	0.0697310i	$-0.977786\pi$
$163$	−25.4721	−1.99513	−0.997566	+	0.0697310i	$0.977786\pi$
$164$	5.38197	0.420261
$165$	−21.7082	−1.68998
$166$	3.14590	0.244169
$167$	21.8885	1.69379	0.846893	−	0.531763i	$-0.178470\pi$
$167$	21.8885	1.69379	0.846893	+	0.531763i	$0.178470\pi$
$168$	13.7082	1.05761
$169$	6.20163	0.477048
$170$	22.4164	1.71926
$171$	−54.0689	−4.13475
$172$	−7.23607	−0.551745
$173$	−7.94427	−0.603992	−0.301996	−	0.953309i	$-0.597653\pi$
$173$	−7.94427	−0.603992	−0.301996	+	0.953309i	$0.597653\pi$
$174$	−27.8885	−2.11423
$175$	−16.9443	−1.28087
$176$	−2.23607	−0.168550
$177$	−30.1803	−2.26849
$178$	−1.61803	−0.121277
$179$	2.61803	0.195681	0.0978405	−	0.995202i	$-0.468806\pi$
$179$	2.61803	0.195681	0.0978405	+	0.995202i	$0.468806\pi$
$180$	22.4164	1.67082
$181$	−2.76393	−0.205441	−0.102721	−	0.994710i	$-0.532755\pi$
$181$	−2.76393	−0.205441	−0.102721	+	0.994710i	$0.532755\pi$
$182$	−18.5623	−1.37593
$183$	16.4721	1.21766
$184$	1.00000	0.0737210
$185$	−26.8328	−1.97279
$186$	22.6525	1.66096
$187$	16.7082	1.22182
$188$	7.00000	0.510527
$189$	−61.3050	−4.45928
$190$	21.7082	1.57488
$191$	11.5279	0.834127	0.417063	−	0.908877i	$-0.363059\pi$
$191$	11.5279	0.834127	0.417063	+	0.908877i	$0.363059\pi$
$192$	3.23607	0.233543
$193$	−3.29180	−0.236949	−0.118474	−	0.992957i	$-0.537800\pi$
$193$	−3.29180	−0.236949	−0.118474	+	0.992957i	$0.537800\pi$
$194$	−6.09017	−0.437249
$195$	−42.5410	−3.04643
$196$	10.9443	0.781734
$197$	−22.4164	−1.59710	−0.798551	−	0.601927i	$-0.794400\pi$
$197$	−22.4164	−1.59710	−0.798551	+	0.601927i	$0.794400\pi$
$198$	16.7082	1.18740
$199$	−9.14590	−0.648336	−0.324168	−	0.946000i	$-0.605084\pi$
$199$	−9.14590	−0.648336	−0.324168	+	0.946000i	$0.605084\pi$
$200$	−4.00000	−0.282843
$201$	−17.4164	−1.22846
$202$	3.94427	0.277518
$203$	−36.5066	−2.56226
$204$	−24.1803	−1.69296
$205$	16.1459	1.12768
$206$	12.7082	0.885423
$207$	−7.47214	−0.519349
$208$	−4.38197	−0.303835
$209$	16.1803	1.11922
$210$	41.1246	2.83787
$211$	−20.3262	−1.39932	−0.699658	−	0.714478i	$-0.746664\pi$
$211$	−20.3262	−1.39932	−0.699658	+	0.714478i	$0.746664\pi$
$212$	2.70820	0.186000
$213$	25.4164	1.74150
$214$	−13.4721	−0.920936
$215$	−21.7082	−1.48049
$216$	−14.4721	−0.984704
$217$	29.6525	2.01294
$218$	−4.09017	−0.277021
$219$	47.8885	3.23601
$220$	−6.70820	−0.452267
$221$	32.7426	2.20251
$222$	28.9443	1.94261
$223$	−13.2361	−0.886353	−0.443176	−	0.896434i	$-0.646148\pi$
$223$	−13.2361	−0.886353	−0.443176	+	0.896434i	$0.646148\pi$
$224$	4.23607	0.283034
$225$	29.8885	1.99257
$226$	9.85410	0.655485
$227$	5.76393	0.382566	0.191283	−	0.981535i	$-0.438735\pi$
$227$	5.76393	0.382566	0.191283	+	0.981535i	$0.438735\pi$
$228$	−23.4164	−1.55079
$229$	−27.3607	−1.80804	−0.904022	−	0.427485i	$-0.859400\pi$
$229$	−27.3607	−1.80804	−0.904022	+	0.427485i	$0.859400\pi$
$230$	3.00000	0.197814
$231$	30.6525	2.01678
$232$	−8.61803	−0.565802
$233$	14.7426	0.965823	0.482911	−	0.875669i	$-0.339579\pi$
$233$	14.7426	0.965823	0.482911	+	0.875669i	$0.339579\pi$
$234$	32.7426	2.14045
$235$	21.0000	1.36989
$236$	−9.32624	−0.607086
$237$	−48.8328	−3.17203
$238$	−31.6525	−2.05173
$239$	−14.1459	−0.915022	−0.457511	−	0.889204i	$-0.651259\pi$
$239$	−14.1459	−0.915022	−0.457511	+	0.889204i	$0.651259\pi$
$240$	9.70820	0.626662
$241$	−12.1246	−0.781015	−0.390507	−	0.920600i	$-0.627700\pi$
$241$	−12.1246	−0.781015	−0.390507	+	0.920600i	$0.627700\pi$
$242$	6.00000	0.385695
$243$	35.5967	2.28353
$244$	5.09017	0.325865
$245$	32.8328	2.09761
$246$	−17.4164	−1.11043
$247$	31.7082	2.01754
$248$	7.00000	0.444500
$249$	−10.1803	−0.645153
$250$	3.00000	0.189737
$251$	21.0344	1.32768	0.663841	−	0.747874i	$-0.268925\pi$
$251$	21.0344	1.32768	0.663841	+	0.747874i	$0.268925\pi$
$252$	−31.6525	−1.99392
$253$	2.23607	0.140580
$254$	11.0902	0.695859
$255$	−72.5410	−4.54269
$256$	1.00000	0.0625000
$257$	14.0902	0.878921	0.439460	−	0.898262i	$-0.355170\pi$
$257$	14.0902	0.878921	0.439460	+	0.898262i	$0.355170\pi$
$258$	23.4164	1.45784
$259$	37.8885	2.35428
$260$	−13.1459	−0.815274
$261$	64.3951	3.98596
$262$	−12.0344	−0.743490
$263$	0.472136	0.0291132	0.0145566	−	0.999894i	$-0.495366\pi$
$263$	0.472136	0.0291132	0.0145566	+	0.999894i	$0.495366\pi$
$264$	7.23607	0.445349
$265$	8.12461	0.499091
$266$	−30.6525	−1.87942
$267$	5.23607	0.320442
$268$	−5.38197	−0.328756
$269$	9.09017	0.554237	0.277119	−	0.960836i	$-0.410620\pi$
$269$	9.09017	0.554237	0.277119	+	0.960836i	$0.410620\pi$
$270$	−43.4164	−2.64224
$271$	−11.9443	−0.725563	−0.362781	−	0.931874i	$-0.618173\pi$
$271$	−11.9443	−0.725563	−0.362781	+	0.931874i	$0.618173\pi$
$272$	−7.47214	−0.453065
$273$	60.0689	3.63553
$274$	−8.14590	−0.492112
$275$	−8.94427	−0.539360
$276$	−3.23607	−0.194788
$277$	6.32624	0.380107	0.190053	−	0.981774i	$-0.439134\pi$
$277$	6.32624	0.380107	0.190053	+	0.981774i	$0.439134\pi$
$278$	0.527864	0.0316592
$279$	−52.3050	−3.13142
$280$	12.7082	0.759460
$281$	8.90983	0.531516	0.265758	−	0.964040i	$-0.414378\pi$
$281$	8.90983	0.531516	0.265758	+	0.964040i	$0.414378\pi$
$282$	−22.6525	−1.34894
$283$	21.9787	1.30650	0.653249	−	0.757143i	$-0.273405\pi$
$283$	21.9787	1.30650	0.653249	+	0.757143i	$0.273405\pi$
$284$	7.85410	0.466055
$285$	−70.2492	−4.16120
$286$	−9.79837	−0.579390
$287$	−22.7984	−1.34575
$288$	−7.47214	−0.440300
$289$	38.8328	2.28428
$290$	−25.8541	−1.51821
$291$	19.7082	1.15532
$292$	14.7984	0.866009
$293$	13.7639	0.804097	0.402049	−	0.915618i	$-0.368298\pi$
$293$	13.7639	0.804097	0.402049	+	0.915618i	$0.368298\pi$
$294$	−35.4164	−2.06553
$295$	−27.9787	−1.62898
$296$	8.94427	0.519875
$297$	−32.3607	−1.87776
$298$	0.618034	0.0358017
$299$	4.38197	0.253416
$300$	12.9443	0.747338
$301$	30.6525	1.76678
$302$	−10.3262	−0.594208
$303$	−12.7639	−0.733269
$304$	−7.23607	−0.415017
$305$	15.2705	0.874387
$306$	55.8328	3.19175
$307$	−11.8541	−0.676549	−0.338275	−	0.941047i	$-0.609843\pi$
$307$	−11.8541	−0.676549	−0.338275	+	0.941047i	$0.609843\pi$
$308$	9.47214	0.539725
$309$	−41.1246	−2.33950
$310$	21.0000	1.19272
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	14.1803	0.802804
$313$	4.52786	0.255930	0.127965	−	0.991779i	$-0.459155\pi$
$313$	4.52786	0.255930	0.127965	+	0.991779i	$0.459155\pi$
$314$	5.38197	0.303722
$315$	−94.9574	−5.35024
$316$	−15.0902	−0.848888
$317$	−2.81966	−0.158368	−0.0791839	−	0.996860i	$-0.525231\pi$
$317$	−2.81966	−0.158368	−0.0791839	+	0.996860i	$0.525231\pi$
$318$	−8.76393	−0.491457
$319$	−19.2705	−1.07894
$320$	3.00000	0.167705
$321$	43.5967	2.43333
$322$	−4.23607	−0.236067
$323$	54.0689	3.00847
$324$	24.4164	1.35647
$325$	−17.5279	−0.972271
$326$	25.4721	1.41077
$327$	13.2361	0.731956
$328$	−5.38197	−0.297169
$329$	−29.6525	−1.63479
$330$	21.7082	1.19500
$331$	23.9443	1.31610	0.658048	−	0.752976i	$-0.271382\pi$
$331$	23.9443	1.31610	0.658048	+	0.752976i	$0.271382\pi$
$332$	−3.14590	−0.172654
$333$	−66.8328	−3.66242
$334$	−21.8885	−1.19769
$335$	−16.1459	−0.882145
$336$	−13.7082	−0.747844
$337$	−7.09017	−0.386226	−0.193113	−	0.981177i	$-0.561858\pi$
$337$	−7.09017	−0.386226	−0.193113	+	0.981177i	$0.561858\pi$
$338$	−6.20163	−0.337324
$339$	−31.8885	−1.73195
$340$	−22.4164	−1.21570
$341$	15.6525	0.847629
$342$	54.0689	2.92371
$343$	−16.7082	−0.902158
$344$	7.23607	0.390143
$345$	−9.70820	−0.522672
$346$	7.94427	0.427087
$347$	−1.90983	−0.102525	−0.0512625	−	0.998685i	$-0.516325\pi$
$347$	−1.90983	−0.102525	−0.0512625	+	0.998685i	$0.516325\pi$
$348$	27.8885	1.49498
$349$	33.4164	1.78874	0.894370	−	0.447329i	$-0.147625\pi$
$349$	33.4164	1.78874	0.894370	+	0.447329i	$0.147625\pi$
$350$	16.9443	0.905709
$351$	−63.4164	−3.38492
$352$	2.23607	0.119183
$353$	5.00000	0.266123	0.133062	−	0.991108i	$-0.457519\pi$
$353$	5.00000	0.266123	0.133062	+	0.991108i	$0.457519\pi$
$354$	30.1803	1.60407
$355$	23.5623	1.25056
$356$	1.61803	0.0857556
$357$	102.430	5.42115
$358$	−2.61803	−0.138367
$359$	−13.3262	−0.703332	−0.351666	−	0.936126i	$-0.614385\pi$
$359$	−13.3262	−0.703332	−0.351666	+	0.936126i	$0.614385\pi$
$360$	−22.4164	−1.18145
$361$	33.3607	1.75583
$362$	2.76393	0.145269
$363$	−19.4164	−1.01910
$364$	18.5623	0.972929
$365$	44.3951	2.32375
$366$	−16.4721	−0.861012
$367$	15.3607	0.801821	0.400910	−	0.916117i	$-0.368694\pi$
$367$	15.3607	0.801821	0.400910	+	0.916117i	$0.368694\pi$
$368$	−1.00000	−0.0521286
$369$	40.2148	2.09350
$370$	26.8328	1.39497
$371$	−11.4721	−0.595604
$372$	−22.6525	−1.17448
$373$	33.2148	1.71980	0.859898	−	0.510466i	$-0.170527\pi$
$373$	33.2148	1.71980	0.859898	+	0.510466i	$0.170527\pi$
$374$	−16.7082	−0.863961
$375$	−9.70820	−0.501329
$376$	−7.00000	−0.360997
$377$	−37.7639	−1.94494
$378$	61.3050	3.15319
$379$	11.4721	0.589284	0.294642	−	0.955608i	$-0.404800\pi$
$379$	11.4721	0.589284	0.294642	+	0.955608i	$0.404800\pi$
$380$	−21.7082	−1.11361
$381$	−35.8885	−1.83863
$382$	−11.5279	−0.589817
$383$	−24.4164	−1.24762	−0.623810	−	0.781576i	$-0.714416\pi$
$383$	−24.4164	−1.24762	−0.623810	+	0.781576i	$0.714416\pi$
$384$	−3.23607	−0.165140
$385$	28.4164	1.44823
$386$	3.29180	0.167548
$387$	−54.0689	−2.74848
$388$	6.09017	0.309182
$389$	−18.2361	−0.924605	−0.462303	−	0.886722i	$-0.652977\pi$
$389$	−18.2361	−0.924605	−0.462303	+	0.886722i	$0.652977\pi$
$390$	42.5410	2.15415
$391$	7.47214	0.377882
$392$	−10.9443	−0.552769
$393$	38.9443	1.96448
$394$	22.4164	1.12932
$395$	−45.2705	−2.27781
$396$	−16.7082	−0.839619
$397$	−14.7082	−0.738184	−0.369092	−	0.929393i	$-0.620331\pi$
$397$	−14.7082	−0.738184	−0.369092	+	0.929393i	$0.620331\pi$
$398$	9.14590	0.458442
$399$	99.1935	4.96589
$400$	4.00000	0.200000
$401$	34.4508	1.72039	0.860197	−	0.509962i	$-0.170341\pi$
$401$	34.4508	1.72039	0.860197	+	0.509962i	$0.170341\pi$
$402$	17.4164	0.868651
$403$	30.6738	1.52797
$404$	−3.94427	−0.196235
$405$	73.2492	3.63978
$406$	36.5066	1.81179
$407$	20.0000	0.991363
$408$	24.1803	1.19711
$409$	−19.7426	−0.976211	−0.488106	−	0.872785i	$-0.662312\pi$
$409$	−19.7426	−0.976211	−0.488106	+	0.872785i	$0.662312\pi$
$410$	−16.1459	−0.797389
$411$	26.3607	1.30028
$412$	−12.7082	−0.626088
$413$	39.5066	1.94399
$414$	7.47214	0.367235
$415$	−9.43769	−0.463278
$416$	4.38197	0.214844
$417$	−1.70820	−0.0836511
$418$	−16.1803	−0.791406
$419$	21.1803	1.03473	0.517364	−	0.855766i	$-0.326913\pi$
$419$	21.1803	1.03473	0.517364	+	0.855766i	$0.326913\pi$
$420$	−41.1246	−2.00668
$421$	27.1459	1.32301	0.661505	−	0.749941i	$-0.269918\pi$
$421$	27.1459	1.32301	0.661505	+	0.749941i	$0.269918\pi$
$422$	20.3262	0.989466
$423$	52.3050	2.54315
$424$	−2.70820	−0.131522
$425$	−29.8885	−1.44981
$426$	−25.4164	−1.23143
$427$	−21.5623	−1.04347
$428$	13.4721	0.651200
$429$	31.7082	1.53089
$430$	21.7082	1.04686
$431$	20.1246	0.969368	0.484684	−	0.874689i	$-0.338935\pi$
$431$	20.1246	0.969368	0.484684	+	0.874689i	$0.338935\pi$
$432$	14.4721	0.696291
$433$	−17.5066	−0.841312	−0.420656	−	0.907220i	$-0.638200\pi$
$433$	−17.5066	−0.841312	−0.420656	+	0.907220i	$0.638200\pi$
$434$	−29.6525	−1.42336
$435$	83.6656	4.01146
$436$	4.09017	0.195884
$437$	7.23607	0.346148
$438$	−47.8885	−2.28820
$439$	−19.7639	−0.943281	−0.471641	−	0.881791i	$-0.656338\pi$
$439$	−19.7639	−0.943281	−0.471641	+	0.881791i	$0.656338\pi$
$440$	6.70820	0.319801
$441$	81.7771	3.89415
$442$	−32.7426	−1.55741
$443$	14.7984	0.703092	0.351546	−	0.936171i	$-0.385656\pi$
$443$	14.7984	0.703092	0.351546	+	0.936171i	$0.385656\pi$
$444$	−28.9443	−1.37363
$445$	4.85410	0.230107
$446$	13.2361	0.626746
$447$	−2.00000	−0.0945968
$448$	−4.23607	−0.200135
$449$	−22.6525	−1.06904	−0.534518	−	0.845157i	$-0.679507\pi$
$449$	−22.6525	−1.06904	−0.534518	+	0.845157i	$0.679507\pi$
$450$	−29.8885	−1.40896
$451$	−12.0344	−0.566680
$452$	−9.85410	−0.463498
$453$	33.4164	1.57004
$454$	−5.76393	−0.270515
$455$	55.6869	2.61064
$456$	23.4164	1.09657
$457$	−4.20163	−0.196544	−0.0982719	−	0.995160i	$-0.531331\pi$
$457$	−4.20163	−0.196544	−0.0982719	+	0.995160i	$0.531331\pi$
$458$	27.3607	1.27848
$459$	−108.138	−5.04744
$460$	−3.00000	−0.139876
$461$	−18.5279	−0.862929	−0.431464	−	0.902130i	$-0.642003\pi$
$461$	−18.5279	−0.862929	−0.431464	+	0.902130i	$0.642003\pi$
$462$	−30.6525	−1.42608
$463$	−13.6180	−0.632884	−0.316442	−	0.948612i	$-0.602488\pi$
$463$	−13.6180	−0.632884	−0.316442	+	0.948612i	$0.602488\pi$
$464$	8.61803	0.400082
$465$	−67.9574	−3.15145
$466$	−14.7426	−0.682940
$467$	−3.41641	−0.158093	−0.0790463	−	0.996871i	$-0.525187\pi$
$467$	−3.41641	−0.158093	−0.0790463	+	0.996871i	$0.525187\pi$
$468$	−32.7426	−1.51353
$469$	22.7984	1.05273
$470$	−21.0000	−0.968658
$471$	−17.4164	−0.802506
$472$	9.32624	0.429275
$473$	16.1803	0.743973
$474$	48.8328	2.24297
$475$	−28.9443	−1.32805
$476$	31.6525	1.45079
$477$	20.2361	0.926546
$478$	14.1459	0.647018
$479$	−34.7082	−1.58586	−0.792929	−	0.609314i	$-0.791445\pi$
$479$	−34.7082	−1.58586	−0.792929	+	0.609314i	$0.791445\pi$
$480$	−9.70820	−0.443117
$481$	39.1935	1.78707
$482$	12.1246	0.552261
$483$	13.7082	0.623745
$484$	−6.00000	−0.272727
$485$	18.2705	0.829621
$486$	−35.5967	−1.61470
$487$	−9.00000	−0.407829	−0.203914	−	0.978989i	$-0.565366\pi$
$487$	−9.00000	−0.407829	−0.203914	+	0.978989i	$0.565366\pi$
$488$	−5.09017	−0.230421
$489$	−82.4296	−3.72759
$490$	−32.8328	−1.48324
$491$	6.52786	0.294598	0.147299	−	0.989092i	$-0.452942\pi$
$491$	6.52786	0.294598	0.147299	+	0.989092i	$0.452942\pi$
$492$	17.4164	0.785192
$493$	−64.3951	−2.90021
$494$	−31.7082	−1.42662
$495$	−50.1246	−2.25293
$496$	−7.00000	−0.314309
$497$	−33.2705	−1.49239
$498$	10.1803	0.456192
$499$	7.94427	0.355634	0.177817	−	0.984064i	$-0.443096\pi$
$499$	7.94427	0.355634	0.177817	+	0.984064i	$0.443096\pi$
$500$	−3.00000	−0.134164
$501$	70.8328	3.16458
$502$	−21.0344	−0.938813
$503$	−21.2361	−0.946869	−0.473435	−	0.880829i	$-0.656986\pi$
$503$	−21.2361	−0.946869	−0.473435	+	0.880829i	$0.656986\pi$
$504$	31.6525	1.40991
$505$	−11.8328	−0.526553
$506$	−2.23607	−0.0994053
$507$	20.0689	0.891290
$508$	−11.0902	−0.492047
$509$	−35.8328	−1.58826	−0.794131	−	0.607747i	$-0.792074\pi$
$509$	−35.8328	−1.58826	−0.794131	+	0.607747i	$0.792074\pi$
$510$	72.5410	3.21217
$511$	−62.6869	−2.77311
$512$	−1.00000	−0.0441942
$513$	−104.721	−4.62356
$514$	−14.0902	−0.621491
$515$	−38.1246	−1.67997
$516$	−23.4164	−1.03085
$517$	−15.6525	−0.688395
$518$	−37.8885	−1.66473
$519$	−25.7082	−1.12846
$520$	13.1459	0.576486
$521$	12.8541	0.563148	0.281574	−	0.959539i	$-0.409143\pi$
$521$	12.8541	0.563148	0.281574	+	0.959539i	$0.409143\pi$
$522$	−64.3951	−2.81850
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	12.0344	0.525727
$525$	−54.8328	−2.39310
$526$	−0.472136	−0.0205861
$527$	52.3050	2.27844
$528$	−7.23607	−0.314909
$529$	−22.0000	−0.956522
$530$	−8.12461	−0.352911
$531$	−69.6869	−3.02415
$532$	30.6525	1.32895
$533$	−23.5836	−1.02152
$534$	−5.23607	−0.226587
$535$	40.4164	1.74735
$536$	5.38197	0.232466
$537$	8.47214	0.365600
$538$	−9.09017	−0.391905
$539$	−24.4721	−1.05409
$540$	43.4164	1.86834
$541$	32.5967	1.40144	0.700722	−	0.713435i	$-0.252861\pi$
$541$	32.5967	1.40144	0.700722	+	0.713435i	$0.252861\pi$
$542$	11.9443	0.513050
$543$	−8.94427	−0.383835
$544$	7.47214	0.320365
$545$	12.2705	0.525611
$546$	−60.0689	−2.57071
$547$	−29.6525	−1.26785	−0.633924	−	0.773395i	$-0.718557\pi$
$547$	−29.6525	−1.26785	−0.633924	+	0.773395i	$0.718557\pi$
$548$	8.14590	0.347976
$549$	38.0344	1.62327
$550$	8.94427	0.381385
$551$	−62.3607	−2.65665
$552$	3.23607	0.137736
$553$	63.9230	2.71828
$554$	−6.32624	−0.268776
$555$	−86.8328	−3.68585
$556$	−0.527864	−0.0223864
$557$	−19.7639	−0.837425	−0.418712	−	0.908119i	$-0.637518\pi$
$557$	−19.7639	−0.837425	−0.418712	+	0.908119i	$0.637518\pi$
$558$	52.3050	2.21425
$559$	31.7082	1.34111
$560$	−12.7082	−0.537020
$561$	54.0689	2.28279
$562$	−8.90983	−0.375838
$563$	24.0689	1.01438	0.507191	−	0.861834i	$-0.330684\pi$
$563$	24.0689	1.01438	0.507191	+	0.861834i	$0.330684\pi$
$564$	22.6525	0.953841
$565$	−29.5623	−1.24370
$566$	−21.9787	−0.923834
$567$	−103.430	−4.34363
$568$	−7.85410	−0.329551
$569$	22.7639	0.954314	0.477157	−	0.878818i	$-0.341667\pi$
$569$	22.7639	0.954314	0.477157	+	0.878818i	$0.341667\pi$
$570$	70.2492	2.94242
$571$	37.1803	1.55595	0.777974	−	0.628296i	$-0.216247\pi$
$571$	37.1803	1.55595	0.777974	+	0.628296i	$0.216247\pi$
$572$	9.79837	0.409691
$573$	37.3050	1.55844
$574$	22.7984	0.951586
$575$	−4.00000	−0.166812
$576$	7.47214	0.311339
$577$	−28.7984	−1.19889	−0.599446	−	0.800415i	$-0.704612\pi$
$577$	−28.7984	−1.19889	−0.599446	+	0.800415i	$0.704612\pi$
$578$	−38.8328	−1.61523
$579$	−10.6525	−0.442702
$580$	25.8541	1.07353
$581$	13.3262	0.552866
$582$	−19.7082	−0.816931
$583$	−6.05573	−0.250803
$584$	−14.7984	−0.612361
$585$	−98.2279	−4.06123
$586$	−13.7639	−0.568583
$587$	−29.2361	−1.20670	−0.603351	−	0.797476i	$-0.706168\pi$
$587$	−29.2361	−1.20670	−0.603351	+	0.797476i	$0.706168\pi$
$588$	35.4164	1.46055
$589$	50.6525	2.08710
$590$	27.9787	1.15187
$591$	−72.5410	−2.98394
$592$	−8.94427	−0.367607
$593$	0.909830	0.0373622	0.0186811	−	0.999825i	$-0.494053\pi$
$593$	0.909830	0.0373622	0.0186811	+	0.999825i	$0.494053\pi$
$594$	32.3607	1.32777
$595$	94.9574	3.89287
$596$	−0.618034	−0.0253157
$597$	−29.5967	−1.21131
$598$	−4.38197	−0.179192
$599$	−20.2918	−0.829100	−0.414550	−	0.910026i	$-0.636061\pi$
$599$	−20.2918	−0.829100	−0.414550	+	0.910026i	$0.636061\pi$
$600$	−12.9443	−0.528448
$601$	4.58359	0.186969	0.0934843	−	0.995621i	$-0.470200\pi$
$601$	4.58359	0.186969	0.0934843	+	0.995621i	$0.470200\pi$
$602$	−30.6525	−1.24930
$603$	−40.2148	−1.63767
$604$	10.3262	0.420169
$605$	−18.0000	−0.731804
$606$	12.7639	0.518499
$607$	−29.8541	−1.21174	−0.605870	−	0.795563i	$-0.707175\pi$
$607$	−29.8541	−1.21174	−0.605870	+	0.795563i	$0.707175\pi$
$608$	7.23607	0.293461
$609$	−118.138	−4.78718
$610$	−15.2705	−0.618285
$611$	−30.6738	−1.24093
$612$	−55.8328	−2.25691
$613$	−42.0689	−1.69915	−0.849573	−	0.527471i	$-0.823140\pi$
$613$	−42.0689	−1.69915	−0.849573	+	0.527471i	$0.823140\pi$
$614$	11.8541	0.478393
$615$	52.2492	2.10689
$616$	−9.47214	−0.381643
$617$	−42.1591	−1.69726	−0.848630	−	0.528987i	$-0.822572\pi$
$617$	−42.1591	−1.69726	−0.848630	+	0.528987i	$0.822572\pi$
$618$	41.1246	1.65427
$619$	19.7639	0.794379	0.397190	−	0.917737i	$-0.369985\pi$
$619$	19.7639	0.794379	0.397190	+	0.917737i	$0.369985\pi$
$620$	−21.0000	−0.843380
$621$	−14.4721	−0.580747
$622$	−16.0000	−0.641542
$623$	−6.85410	−0.274604
$624$	−14.1803	−0.567668
$625$	−29.0000	−1.16000
$626$	−4.52786	−0.180970
$627$	52.3607	2.09108
$628$	−5.38197	−0.214764
$629$	66.8328	2.66480
$630$	94.9574	3.78319
$631$	14.3050	0.569471	0.284736	−	0.958606i	$-0.408094\pi$
$631$	14.3050	0.569471	0.284736	+	0.958606i	$0.408094\pi$
$632$	15.0902	0.600255
$633$	−65.7771	−2.61440
$634$	2.81966	0.111983
$635$	−33.2705	−1.32030
$636$	8.76393	0.347513
$637$	−47.9574	−1.90014
$638$	19.2705	0.762927
$639$	58.6869	2.32162
$640$	−3.00000	−0.118585
$641$	−30.1803	−1.19205	−0.596026	−	0.802965i	$-0.703254\pi$
$641$	−30.1803	−1.19205	−0.596026	+	0.802965i	$0.703254\pi$
$642$	−43.5967	−1.72063
$643$	−3.11146	−0.122704	−0.0613519	−	0.998116i	$-0.519541\pi$
$643$	−3.11146	−0.122704	−0.0613519	+	0.998116i	$0.519541\pi$
$644$	4.23607	0.166924
$645$	−70.2492	−2.76606
$646$	−54.0689	−2.12731
$647$	40.7639	1.60260	0.801298	−	0.598266i	$-0.204143\pi$
$647$	40.7639	1.60260	0.801298	+	0.598266i	$0.204143\pi$
$648$	−24.4164	−0.959167
$649$	20.8541	0.818595
$650$	17.5279	0.687499
$651$	95.9574	3.76087
$652$	−25.4721	−0.997566
$653$	−19.1803	−0.750585	−0.375292	−	0.926906i	$-0.622458\pi$
$653$	−19.1803	−0.750585	−0.375292	+	0.926906i	$0.622458\pi$
$654$	−13.2361	−0.517571
$655$	36.1033	1.41067
$656$	5.38197	0.210130
$657$	110.575	4.31396
$658$	29.6525	1.15597
$659$	4.85410	0.189089	0.0945445	−	0.995521i	$-0.469861\pi$
$659$	4.85410	0.189089	0.0945445	+	0.995521i	$0.469861\pi$
$660$	−21.7082	−0.844991
$661$	−39.0344	−1.51826	−0.759132	−	0.650937i	$-0.774376\pi$
$661$	−39.0344	−1.51826	−0.759132	+	0.650937i	$0.774376\pi$
$662$	−23.9443	−0.930621
$663$	105.957	4.11505
$664$	3.14590	0.122085
$665$	91.9574	3.56596
$666$	66.8328	2.58972
$667$	−8.61803	−0.333692
$668$	21.8885	0.846893
$669$	−42.8328	−1.65601
$670$	16.1459	0.623770
$671$	−11.3820	−0.439396
$672$	13.7082	0.528805
$673$	−27.8885	−1.07502	−0.537512	−	0.843256i	$-0.680636\pi$
$673$	−27.8885	−1.07502	−0.537512	+	0.843256i	$0.680636\pi$
$674$	7.09017	0.273103
$675$	57.8885	2.22813
$676$	6.20163	0.238524
$677$	43.9443	1.68892	0.844458	−	0.535622i	$-0.179923\pi$
$677$	43.9443	1.68892	0.844458	+	0.535622i	$0.179923\pi$
$678$	31.8885	1.22467
$679$	−25.7984	−0.990051
$680$	22.4164	0.859630
$681$	18.6525	0.714764
$682$	−15.6525	−0.599364
$683$	−21.7082	−0.830641	−0.415321	−	0.909675i	$-0.636331\pi$
$683$	−21.7082	−0.830641	−0.415321	+	0.909675i	$0.636331\pi$
$684$	−54.0689	−2.06738
$685$	24.4377	0.933716
$686$	16.7082	0.637922
$687$	−88.5410	−3.37805
$688$	−7.23607	−0.275873
$689$	−11.8673	−0.452107
$690$	9.70820	0.369585
$691$	8.79837	0.334706	0.167353	−	0.985897i	$-0.446478\pi$
$691$	8.79837	0.334706	0.167353	+	0.985897i	$0.446478\pi$
$692$	−7.94427	−0.301996
$693$	70.7771	2.68860
$694$	1.90983	0.0724962
$695$	−1.58359	−0.0600691
$696$	−27.8885	−1.05711
$697$	−40.2148	−1.52324
$698$	−33.4164	−1.26483
$699$	47.7082	1.80449
$700$	−16.9443	−0.640433
$701$	36.2705	1.36992	0.684959	−	0.728581i	$-0.259820\pi$
$701$	36.2705	1.36992	0.684959	+	0.728581i	$0.259820\pi$
$702$	63.4164	2.39350
$703$	64.7214	2.44101
$704$	−2.23607	−0.0842750
$705$	67.9574	2.55942
$706$	−5.00000	−0.188177
$707$	16.7082	0.628377
$708$	−30.1803	−1.13425
$709$	−5.12461	−0.192459	−0.0962294	−	0.995359i	$-0.530678\pi$
$709$	−5.12461	−0.192459	−0.0962294	+	0.995359i	$0.530678\pi$
$710$	−23.5623	−0.884278
$711$	−112.756	−4.22867
$712$	−1.61803	−0.0606384
$713$	7.00000	0.262152
$714$	−102.430	−3.83333
$715$	29.3951	1.09932
$716$	2.61803	0.0978405
$717$	−45.7771	−1.70958
$718$	13.3262	0.497331
$719$	2.76393	0.103077	0.0515386	−	0.998671i	$-0.483587\pi$
$719$	2.76393	0.103077	0.0515386	+	0.998671i	$0.483587\pi$
$720$	22.4164	0.835410
$721$	53.8328	2.00484
$722$	−33.3607	−1.24156
$723$	−39.2361	−1.45921
$724$	−2.76393	−0.102721
$725$	34.4721	1.28026
$726$	19.4164	0.720610
$727$	−20.2148	−0.749725	−0.374862	−	0.927080i	$-0.622310\pi$
$727$	−20.2148	−0.749725	−0.374862	+	0.927080i	$0.622310\pi$
$728$	−18.5623	−0.687965
$729$	41.9443	1.55349
$730$	−44.3951	−1.64314
$731$	54.0689	1.99981
$732$	16.4721	0.608828
$733$	−27.1459	−1.00266	−0.501328	−	0.865257i	$-0.667155\pi$
$733$	−27.1459	−1.00266	−0.501328	+	0.865257i	$0.667155\pi$
$734$	−15.3607	−0.566973
$735$	106.249	3.91906
$736$	1.00000	0.0368605
$737$	12.0344	0.443294
$738$	−40.2148	−1.48033
$739$	−5.74265	−0.211247	−0.105623	−	0.994406i	$-0.533684\pi$
$739$	−5.74265	−0.211247	−0.105623	+	0.994406i	$0.533684\pi$
$740$	−26.8328	−0.986394
$741$	102.610	3.76947
$742$	11.4721	0.421155
$743$	−50.9574	−1.86945	−0.934723	−	0.355376i	$-0.884353\pi$
$743$	−50.9574	−1.86945	−0.934723	+	0.355376i	$0.884353\pi$
$744$	22.6525	0.830480
$745$	−1.85410	−0.0679290
$746$	−33.2148	−1.21608
$747$	−23.5066	−0.860061
$748$	16.7082	0.610912
$749$	−57.0689	−2.08525
$750$	9.70820	0.354493
$751$	−22.5066	−0.821277	−0.410638	−	0.911798i	$-0.634694\pi$
$751$	−22.5066	−0.821277	−0.410638	+	0.911798i	$0.634694\pi$
$752$	7.00000	0.255264
$753$	68.0689	2.48057
$754$	37.7639	1.37528
$755$	30.9787	1.12743
$756$	−61.3050	−2.22964
$757$	−17.7082	−0.643616	−0.321808	−	0.946805i	$-0.604290\pi$
$757$	−17.7082	−0.643616	−0.321808	+	0.946805i	$0.604290\pi$
$758$	−11.4721	−0.416687
$759$	7.23607	0.262653
$760$	21.7082	0.787439
$761$	−6.47214	−0.234615	−0.117307	−	0.993096i	$-0.537426\pi$
$761$	−6.47214	−0.234615	−0.117307	+	0.993096i	$0.537426\pi$
$762$	35.8885	1.30010
$763$	−17.3262	−0.627252
$764$	11.5279	0.417063
$765$	−167.498	−6.05592
$766$	24.4164	0.882201
$767$	40.8673	1.47563
$768$	3.23607	0.116772
$769$	5.43769	0.196088	0.0980441	−	0.995182i	$-0.468741\pi$
$769$	5.43769	0.196088	0.0980441	+	0.995182i	$0.468741\pi$
$770$	−28.4164	−1.02406
$771$	45.5967	1.64213
$772$	−3.29180	−0.118474
$773$	−31.0689	−1.11747	−0.558735	−	0.829346i	$-0.688713\pi$
$773$	−31.0689	−1.11747	−0.558735	+	0.829346i	$0.688713\pi$
$774$	54.0689	1.94347
$775$	−28.0000	−1.00579
$776$	−6.09017	−0.218624
$777$	122.610	4.39861
$778$	18.2361	0.653795
$779$	−38.9443	−1.39532
$780$	−42.5410	−1.52321
$781$	−17.5623	−0.628429
$782$	−7.47214	−0.267203
$783$	124.721	4.45718
$784$	10.9443	0.390867
$785$	−16.1459	−0.576272
$786$	−38.9443	−1.38910
$787$	33.5410	1.19561	0.597804	−	0.801642i	$-0.296040\pi$
$787$	33.5410	1.19561	0.597804	+	0.801642i	$0.296040\pi$
$788$	−22.4164	−0.798551
$789$	1.52786	0.0543934
$790$	45.2705	1.61065
$791$	41.7426	1.48420
$792$	16.7082	0.593700
$793$	−22.3050	−0.792072
$794$	14.7082	0.521975
$795$	26.2918	0.932474
$796$	−9.14590	−0.324168
$797$	11.2016	0.396782	0.198391	−	0.980123i	$-0.436428\pi$
$797$	11.2016	0.396782	0.198391	+	0.980123i	$0.436428\pi$
$798$	−99.1935	−3.51141
$799$	−52.3050	−1.85042
$800$	−4.00000	−0.141421
$801$	12.0902	0.427185
$802$	−34.4508	−1.21650
$803$	−33.0902	−1.16773
$804$	−17.4164	−0.614229
$805$	12.7082	0.447905
$806$	−30.6738	−1.08044
$807$	29.4164	1.03551
$808$	3.94427	0.138759
$809$	14.1246	0.496595	0.248297	−	0.968684i	$-0.420129\pi$
$809$	14.1246	0.496595	0.248297	+	0.968684i	$0.420129\pi$
$810$	−73.2492	−2.57372
$811$	−15.9230	−0.559132	−0.279566	−	0.960127i	$-0.590191\pi$
$811$	−15.9230	−0.559132	−0.279566	+	0.960127i	$0.590191\pi$
$812$	−36.5066	−1.28113
$813$	−38.6525	−1.35560
$814$	−20.0000	−0.701000
$815$	−76.4164	−2.67675
$816$	−24.1803	−0.846481
$817$	52.3607	1.83187
$818$	19.7426	0.690285
$819$	138.700	4.84657
$820$	16.1459	0.563839
$821$	−20.6180	−0.719574	−0.359787	−	0.933034i	$-0.617151\pi$
$821$	−20.6180	−0.719574	−0.359787	+	0.933034i	$0.617151\pi$
$822$	−26.3607	−0.919434
$823$	−15.8885	−0.553840	−0.276920	−	0.960893i	$-0.589314\pi$
$823$	−15.8885	−0.553840	−0.276920	+	0.960893i	$0.589314\pi$
$824$	12.7082	0.442711
$825$	−28.9443	−1.00771
$826$	−39.5066	−1.37461
$827$	−23.5623	−0.819342	−0.409671	−	0.912233i	$-0.634356\pi$
$827$	−23.5623	−0.819342	−0.409671	+	0.912233i	$0.634356\pi$
$828$	−7.47214	−0.259675
$829$	25.3820	0.881552	0.440776	−	0.897617i	$-0.354703\pi$
$829$	25.3820	0.881552	0.440776	+	0.897617i	$0.354703\pi$
$830$	9.43769	0.327587
$831$	20.4721	0.710171
$832$	−4.38197	−0.151917
$833$	−81.7771	−2.83341
$834$	1.70820	0.0591503
$835$	65.6656	2.27245
$836$	16.1803	0.559609
$837$	−101.305	−3.50161
$838$	−21.1803	−0.731663
$839$	−9.67376	−0.333975	−0.166988	−	0.985959i	$-0.553404\pi$
$839$	−9.67376	−0.333975	−0.166988	+	0.985959i	$0.553404\pi$
$840$	41.1246	1.41893
$841$	45.2705	1.56105
$842$	−27.1459	−0.935509
$843$	28.8328	0.993055
$844$	−20.3262	−0.699658
$845$	18.6049	0.640027
$846$	−52.3050	−1.79828
$847$	25.4164	0.873318
$848$	2.70820	0.0930001
$849$	71.1246	2.44099
$850$	29.8885	1.02517
$851$	8.94427	0.306606
$852$	25.4164	0.870752
$853$	−26.9787	−0.923734	−0.461867	−	0.886949i	$-0.652820\pi$
$853$	−26.9787	−0.923734	−0.461867	+	0.886949i	$0.652820\pi$
$854$	21.5623	0.737847
$855$	−162.207	−5.54735
$856$	−13.4721	−0.460468
$857$	−31.9443	−1.09120	−0.545598	−	0.838047i	$-0.683697\pi$
$857$	−31.9443	−1.09120	−0.545598	+	0.838047i	$0.683697\pi$
$858$	−31.7082	−1.08250
$859$	19.5410	0.666731	0.333365	−	0.942798i	$-0.391816\pi$
$859$	19.5410	0.666731	0.333365	+	0.942798i	$0.391816\pi$
$860$	−21.7082	−0.740244
$861$	−73.7771	−2.51432
$862$	−20.1246	−0.685447
$863$	3.67376	0.125056	0.0625282	−	0.998043i	$-0.480084\pi$
$863$	3.67376	0.125056	0.0625282	+	0.998043i	$0.480084\pi$
$864$	−14.4721	−0.492352
$865$	−23.8328	−0.810340
$866$	17.5066	0.594898
$867$	125.666	4.26783
$868$	29.6525	1.00647
$869$	33.7426	1.14464
$870$	−83.6656	−2.83653
$871$	23.5836	0.799100
$872$	−4.09017	−0.138511
$873$	45.5066	1.54016
$874$	−7.23607	−0.244764
$875$	12.7082	0.429616
$876$	47.8885	1.61800
$877$	28.0689	0.947819	0.473909	−	0.880574i	$-0.342842\pi$
$877$	28.0689	0.947819	0.473909	+	0.880574i	$0.342842\pi$
$878$	19.7639	0.667000
$879$	44.5410	1.50233
$880$	−6.70820	−0.226134
$881$	−4.61803	−0.155586	−0.0777928	−	0.996970i	$-0.524787\pi$
$881$	−4.61803	−0.155586	−0.0777928	+	0.996970i	$0.524787\pi$
$882$	−81.7771	−2.75358
$883$	26.5623	0.893893	0.446946	−	0.894561i	$-0.352511\pi$
$883$	26.5623	0.893893	0.446946	+	0.894561i	$0.352511\pi$
$884$	32.7426	1.10125
$885$	−90.5410	−3.04350
$886$	−14.7984	−0.497161
$887$	21.0344	0.706267	0.353134	−	0.935573i	$-0.385116\pi$
$887$	21.0344	0.706267	0.353134	+	0.935573i	$0.385116\pi$
$888$	28.9443	0.971306
$889$	46.9787	1.57562
$890$	−4.85410	−0.162710
$891$	−54.5967	−1.82906
$892$	−13.2361	−0.443176
$893$	−50.6525	−1.69502
$894$	2.00000	0.0668900
$895$	7.85410	0.262534
$896$	4.23607	0.141517
$897$	14.1803	0.473468
$898$	22.6525	0.755923
$899$	−60.3262	−2.01199
$900$	29.8885	0.996285
$901$	−20.2361	−0.674161
$902$	12.0344	0.400703
$903$	99.1935	3.30095
$904$	9.85410	0.327743
$905$	−8.29180	−0.275629
$906$	−33.4164	−1.11019
$907$	45.3262	1.50503	0.752517	−	0.658573i	$-0.228840\pi$
$907$	45.3262	1.50503	0.752517	+	0.658573i	$0.228840\pi$
$908$	5.76393	0.191283
$909$	−29.4721	−0.977529
$910$	−55.6869	−1.84600
$911$	−5.61803	−0.186134	−0.0930669	−	0.995660i	$-0.529667\pi$
$911$	−5.61803	−0.186134	−0.0930669	+	0.995660i	$0.529667\pi$
$912$	−23.4164	−0.775395
$913$	7.03444	0.232806
$914$	4.20163	0.138977
$915$	49.4164	1.63366
$916$	−27.3607	−0.904022
$917$	−50.9787	−1.68347
$918$	108.138	3.56908
$919$	−18.6869	−0.616425	−0.308212	−	0.951318i	$-0.599731\pi$
$919$	−18.6869	−0.616425	−0.308212	+	0.951318i	$0.599731\pi$
$920$	3.00000	0.0989071
$921$	−38.3607	−1.26403
$922$	18.5279	0.610183
$923$	−34.4164	−1.13283
$924$	30.6525	1.00839
$925$	−35.7771	−1.17634
$926$	13.6180	0.447516
$927$	−94.9574	−3.11881
$928$	−8.61803	−0.282901
$929$	36.9098	1.21097	0.605486	−	0.795856i	$-0.292979\pi$
$929$	36.9098	1.21097	0.605486	+	0.795856i	$0.292979\pi$
$930$	67.9574	2.22841
$931$	−79.1935	−2.59546
$932$	14.7426	0.482911
$933$	51.7771	1.69511
$934$	3.41641	0.111788
$935$	50.1246	1.63925
$936$	32.7426	1.07023
$937$	−2.14590	−0.0701034	−0.0350517	−	0.999385i	$-0.511160\pi$
$937$	−2.14590	−0.0701034	−0.0350517	+	0.999385i	$0.511160\pi$
$938$	−22.7984	−0.744393
$939$	14.6525	0.478165
$940$	21.0000	0.684944
$941$	50.3262	1.64059	0.820294	−	0.571942i	$-0.193810\pi$
$941$	50.3262	1.64059	0.820294	+	0.571942i	$0.193810\pi$
$942$	17.4164	0.567457
$943$	−5.38197	−0.175261
$944$	−9.32624	−0.303543
$945$	−183.915	−5.98275
$946$	−16.1803	−0.526068
$947$	−13.8754	−0.450890	−0.225445	−	0.974256i	$-0.572384\pi$
$947$	−13.8754	−0.450890	−0.225445	+	0.974256i	$0.572384\pi$
$948$	−48.8328	−1.58602
$949$	−64.8460	−2.10499
$950$	28.9443	0.939076
$951$	−9.12461	−0.295886
$952$	−31.6525	−1.02586
$953$	−41.0000	−1.32812	−0.664060	−	0.747679i	$-0.731168\pi$
$953$	−41.0000	−1.32812	−0.664060	+	0.747679i	$0.731168\pi$
$954$	−20.2361	−0.655167
$955$	34.5836	1.11910
$956$	−14.1459	−0.457511
$957$	−62.3607	−2.01583
$958$	34.7082	1.12137
$959$	−34.5066	−1.11428
$960$	9.70820	0.313331
$961$	18.0000	0.580645
$962$	−39.1935	−1.26365
$963$	100.666	3.24390
$964$	−12.1246	−0.390507
$965$	−9.87539	−0.317900
$966$	−13.7082	−0.441054
$967$	20.7082	0.665931	0.332965	−	0.942939i	$-0.391951\pi$
$967$	20.7082	0.665931	0.332965	+	0.942939i	$0.391951\pi$
$968$	6.00000	0.192847
$969$	174.971	5.62086
$970$	−18.2705	−0.586631
$971$	58.1803	1.86710	0.933548	−	0.358452i	$-0.116695\pi$
$971$	58.1803	1.86710	0.933548	+	0.358452i	$0.116695\pi$
$972$	35.5967	1.14177
$973$	2.23607	0.0716850
$974$	9.00000	0.288379
$975$	−56.7214	−1.81654
$976$	5.09017	0.162932
$977$	28.4508	0.910223	0.455112	−	0.890434i	$-0.349599\pi$
$977$	28.4508	0.910223	0.455112	+	0.890434i	$0.349599\pi$
$978$	82.4296	2.63581
$979$	−3.61803	−0.115633
$980$	32.8328	1.04881
$981$	30.5623	0.975779
$982$	−6.52786	−0.208313
$983$	16.2016	0.516752	0.258376	−	0.966044i	$-0.416813\pi$
$983$	16.2016	0.516752	0.258376	+	0.966044i	$0.416813\pi$
$984$	−17.4164	−0.555215
$985$	−67.2492	−2.14274
$986$	64.3951	2.05076
$987$	−95.9574	−3.05436
$988$	31.7082	1.00877
$989$	7.23607	0.230094
$990$	50.1246	1.59306
$991$	28.1246	0.893408	0.446704	−	0.894682i	$-0.352598\pi$
$991$	28.1246	0.893408	0.446704	+	0.894682i	$0.352598\pi$
$992$	7.00000	0.222250
$993$	77.4853	2.45892
$994$	33.2705	1.05528
$995$	−27.4377	−0.869833
$996$	−10.1803	−0.322576
$997$	−27.3607	−0.866521	−0.433261	−	0.901269i	$-0.642637\pi$
$997$	−27.3607	−0.866521	−0.433261	+	0.901269i	$0.642637\pi$
$998$	−7.94427	−0.251472
$999$	−129.443	−4.09539

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4882.2.a.c.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4882.2.a.c.1.2	✓	2	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:	\( N \)	\(=\)	\( 4882 = 2 \cdot 2441 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4882.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} +3.00000 q^{5} -3.23607 q^{6} -4.23607 q^{7} -1.00000 q^{8} +7.47214 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +3.23607 q^{3} +1.00000 q^{4} +3.00000 q^{5} -3.23607 q^{6} -4.23607 q^{7} -1.00000 q^{8} +7.47214 q^{9} -3.00000 q^{10} -2.23607 q^{11} +3.23607 q^{12} -4.38197 q^{13} +4.23607 q^{14} +9.70820 q^{15} +1.00000 q^{16} -7.47214 q^{17} -7.47214 q^{18} -7.23607 q^{19} +3.00000 q^{20} -13.7082 q^{21} +2.23607 q^{22} -1.00000 q^{23} -3.23607 q^{24} +4.00000 q^{25} +4.38197 q^{26} +14.4721 q^{27} -4.23607 q^{28} +8.61803 q^{29} -9.70820 q^{30} -7.00000 q^{31} -1.00000 q^{32} -7.23607 q^{33} +7.47214 q^{34} -12.7082 q^{35} +7.47214 q^{36} -8.94427 q^{37} +7.23607 q^{38} -14.1803 q^{39} -3.00000 q^{40} +5.38197 q^{41} +13.7082 q^{42} -7.23607 q^{43} -2.23607 q^{44} +22.4164 q^{45} +1.00000 q^{46} +7.00000 q^{47} +3.23607 q^{48} +10.9443 q^{49} -4.00000 q^{50} -24.1803 q^{51} -4.38197 q^{52} +2.70820 q^{53} -14.4721 q^{54} -6.70820 q^{55} +4.23607 q^{56} -23.4164 q^{57} -8.61803 q^{58} -9.32624 q^{59} +9.70820 q^{60} +5.09017 q^{61} +7.00000 q^{62} -31.6525 q^{63} +1.00000 q^{64} -13.1459 q^{65} +7.23607 q^{66} -5.38197 q^{67} -7.47214 q^{68} -3.23607 q^{69} +12.7082 q^{70} +7.85410 q^{71} -7.47214 q^{72} +14.7984 q^{73} +8.94427 q^{74} +12.9443 q^{75} -7.23607 q^{76} +9.47214 q^{77} +14.1803 q^{78} -15.0902 q^{79} +3.00000 q^{80} +24.4164 q^{81} -5.38197 q^{82} -3.14590 q^{83} -13.7082 q^{84} -22.4164 q^{85} +7.23607 q^{86} +27.8885 q^{87} +2.23607 q^{88} +1.61803 q^{89} -22.4164 q^{90} +18.5623 q^{91} -1.00000 q^{92} -22.6525 q^{93} -7.00000 q^{94} -21.7082 q^{95} -3.23607 q^{96} +6.09017 q^{97} -10.9443 q^{98} -16.7082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 6 q^{5} - 2 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9} - 6 q^{10} + 2 q^{12} - 11 q^{13} + 4 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{17} - 6 q^{18} - 10 q^{19} + 6 q^{20} - 14 q^{21} - 2 q^{23} - 2 q^{24} + 8 q^{25} + 11 q^{26} + 20 q^{27} - 4 q^{28} + 15 q^{29} - 6 q^{30} - 14 q^{31} - 2 q^{32} - 10 q^{33} + 6 q^{34} - 12 q^{35} + 6 q^{36} + 10 q^{38} - 6 q^{39} - 6 q^{40} + 13 q^{41} + 14 q^{42} - 10 q^{43} + 18 q^{45} + 2 q^{46} + 14 q^{47} + 2 q^{48} + 4 q^{49} - 8 q^{50} - 26 q^{51} - 11 q^{52} - 8 q^{53} - 20 q^{54} + 4 q^{56} - 20 q^{57} - 15 q^{58} - 3 q^{59} + 6 q^{60} - q^{61} + 14 q^{62} - 32 q^{63} + 2 q^{64} - 33 q^{65} + 10 q^{66} - 13 q^{67} - 6 q^{68} - 2 q^{69} + 12 q^{70} + 9 q^{71} - 6 q^{72} + 5 q^{73} + 8 q^{75} - 10 q^{76} + 10 q^{77} + 6 q^{78} - 19 q^{79} + 6 q^{80} + 22 q^{81} - 13 q^{82} - 13 q^{83} - 14 q^{84} - 18 q^{85} + 10 q^{86} + 20 q^{87} + q^{89} - 18 q^{90} + 17 q^{91} - 2 q^{92} - 14 q^{93} - 14 q^{94} - 30 q^{95} - 2 q^{96} + q^{97} - 4 q^{98} - 20 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + 6 * q^5 - 2 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9 - 6 * q^10 + 2 * q^12 - 11 * q^13 + 4 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^17 - 6 * q^18 - 10 * q^19 + 6 * q^20 - 14 * q^21 - 2 * q^23 - 2 * q^24 + 8 * q^25 + 11 * q^26 + 20 * q^27 - 4 * q^28 + 15 * q^29 - 6 * q^30 - 14 * q^31 - 2 * q^32 - 10 * q^33 + 6 * q^34 - 12 * q^35 + 6 * q^36 + 10 * q^38 - 6 * q^39 - 6 * q^40 + 13 * q^41 + 14 * q^42 - 10 * q^43 + 18 * q^45 + 2 * q^46 + 14 * q^47 + 2 * q^48 + 4 * q^49 - 8 * q^50 - 26 * q^51 - 11 * q^52 - 8 * q^53 - 20 * q^54 + 4 * q^56 - 20 * q^57 - 15 * q^58 - 3 * q^59 + 6 * q^60 - q^61 + 14 * q^62 - 32 * q^63 + 2 * q^64 - 33 * q^65 + 10 * q^66 - 13 * q^67 - 6 * q^68 - 2 * q^69 + 12 * q^70 + 9 * q^71 - 6 * q^72 + 5 * q^73 + 8 * q^75 - 10 * q^76 + 10 * q^77 + 6 * q^78 - 19 * q^79 + 6 * q^80 + 22 * q^81 - 13 * q^82 - 13 * q^83 - 14 * q^84 - 18 * q^85 + 10 * q^86 + 20 * q^87 + q^89 - 18 * q^90 + 17 * q^91 - 2 * q^92 - 14 * q^93 - 14 * q^94 - 30 * q^95 - 2 * q^96 + q^97 - 4 * q^98 - 20 * q^99

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