LMFDB - Embedded newform 5290.2.a.u.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{24})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 4x^{2} + 1 $ x^4 - 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.517638$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} +5.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} +5.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +1.00000 q^{10} -5.27792 q^{11} +2.41421 q^{12} -5.86370 q^{13} -5.18154 q^{14} -2.41421 q^{15} +1.00000 q^{16} -4.21441 q^{17} -2.82843 q^{18} -1.98174 q^{19} -1.00000 q^{20} +12.5093 q^{21} +5.27792 q^{22} -2.41421 q^{24} +1.00000 q^{25} +5.86370 q^{26} -0.414214 q^{27} +5.18154 q^{28} -0.889012 q^{29} +2.41421 q^{30} +6.68216 q^{31} -1.00000 q^{32} -12.7420 q^{33} +4.21441 q^{34} -5.18154 q^{35} +2.82843 q^{36} -4.82843 q^{37} +1.98174 q^{38} -14.1562 q^{39} +1.00000 q^{40} -3.39355 q^{41} -12.5093 q^{42} +3.19980 q^{43} -5.27792 q^{44} -2.82843 q^{45} +1.11099 q^{47} +2.41421 q^{48} +19.8484 q^{49} -1.00000 q^{50} -10.1745 q^{51} -5.86370 q^{52} -3.24728 q^{53} +0.414214 q^{54} +5.27792 q^{55} -5.18154 q^{56} -4.78434 q^{57} +0.889012 q^{58} +3.00000 q^{59} -2.41421 q^{60} +4.09978 q^{61} -6.68216 q^{62} +14.6556 q^{63} +1.00000 q^{64} +5.86370 q^{65} +12.7420 q^{66} -10.6705 q^{67} -4.21441 q^{68} +5.18154 q^{70} -6.90895 q^{71} -2.82843 q^{72} +4.44485 q^{73} +4.82843 q^{74} +2.41421 q^{75} -1.98174 q^{76} -27.3477 q^{77} +14.1562 q^{78} -17.4375 q^{79} -1.00000 q^{80} -9.48528 q^{81} +3.39355 q^{82} +3.74907 q^{83} +12.5093 q^{84} +4.21441 q^{85} -3.19980 q^{86} -2.14626 q^{87} +5.27792 q^{88} -10.7785 q^{89} +2.82843 q^{90} -30.3830 q^{91} +16.1322 q^{93} -1.11099 q^{94} +1.98174 q^{95} -2.41421 q^{96} +1.11439 q^{97} -19.8484 q^{98} -14.9282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{12} - 8 q^{13} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} + 4 q^{28} - 12 q^{29} + 4 q^{30} + 28 q^{31} - 4 q^{32} - 16 q^{33} + 12 q^{34} - 4 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} + 4 q^{40} - 8 q^{41} - 4 q^{42} + 12 q^{43} - 4 q^{47} + 4 q^{48} + 12 q^{49} - 4 q^{50} - 16 q^{51} - 8 q^{52} - 20 q^{53} - 4 q^{54} - 4 q^{56} + 12 q^{57} + 12 q^{58} + 12 q^{59} - 4 q^{60} - 28 q^{62} + 4 q^{64} + 8 q^{65} + 16 q^{66} - 12 q^{67} - 12 q^{68} + 4 q^{70} + 20 q^{71} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 8 q^{76} - 24 q^{77} + 16 q^{78} + 4 q^{79} - 4 q^{80} - 4 q^{81} + 8 q^{82} - 12 q^{83} + 4 q^{84} + 12 q^{85} - 12 q^{86} + 4 q^{87} - 40 q^{89} - 32 q^{91} + 36 q^{93} + 4 q^{94} - 8 q^{95} - 4 q^{96} - 16 q^{97} - 12 q^{98} - 32 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 + 4 * q^12 - 8 * q^13 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 12 * q^17 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 + 4 * q^28 - 12 * q^29 + 4 * q^30 + 28 * q^31 - 4 * q^32 - 16 * q^33 + 12 * q^34 - 4 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 + 4 * q^40 - 8 * q^41 - 4 * q^42 + 12 * q^43 - 4 * q^47 + 4 * q^48 + 12 * q^49 - 4 * q^50 - 16 * q^51 - 8 * q^52 - 20 * q^53 - 4 * q^54 - 4 * q^56 + 12 * q^57 + 12 * q^58 + 12 * q^59 - 4 * q^60 - 28 * q^62 + 4 * q^64 + 8 * q^65 + 16 * q^66 - 12 * q^67 - 12 * q^68 + 4 * q^70 + 20 * q^71 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 8 * q^76 - 24 * q^77 + 16 * q^78 + 4 * q^79 - 4 * q^80 - 4 * q^81 + 8 * q^82 - 12 * q^83 + 4 * q^84 + 12 * q^85 - 12 * q^86 + 4 * q^87 - 40 * q^89 - 32 * q^91 + 36 * q^93 + 4 * q^94 - 8 * q^95 - 4 * q^96 - 16 * q^97 - 12 * q^98 - 32 * 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	$-0.254552\pi$
$3$	2.41421	1.39385	0.696923	+	0.717146i	$0.254552\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.41421	−0.985599
$7$	5.18154	1.95844	0.979219	−	0.202805i	$-0.0650058\pi$
$7$	5.18154	1.95844	0.979219	+	0.202805i	$0.0650058\pi$
$8$	−1.00000	−0.353553
$9$	2.82843	0.942809
$10$	1.00000	0.316228
$11$	−5.27792	−1.59135	−0.795676	−	0.605723i	$-0.792884\pi$
$11$	−5.27792	−1.59135	−0.795676	+	0.605723i	$0.792884\pi$
$12$	2.41421	0.696923
$13$	−5.86370	−1.62630	−0.813149	−	0.582055i	$-0.802249\pi$
$13$	−5.86370	−1.62630	−0.813149	+	0.582055i	$0.802249\pi$
$14$	−5.18154	−1.38482
$15$	−2.41421	−0.623347
$16$	1.00000	0.250000
$17$	−4.21441	−1.02215	−0.511073	−	0.859538i	$-0.670752\pi$
$17$	−4.21441	−1.02215	−0.511073	+	0.859538i	$0.670752\pi$
$18$	−2.82843	−0.666667
$19$	−1.98174	−0.454642	−0.227321	−	0.973820i	$-0.572997\pi$
$19$	−1.98174	−0.454642	−0.227321	+	0.973820i	$0.572997\pi$
$20$	−1.00000	−0.223607
$21$	12.5093	2.72976
$22$	5.27792	1.12526
$23$	0	0
$23$	0	0
$24$	−2.41421	−0.492799
$25$	1.00000	0.200000
$26$	5.86370	1.14997
$27$	−0.414214	−0.0797154
$28$	5.18154	0.979219
$29$	−0.889012	−0.165085	−0.0825427	−	0.996588i	$-0.526304\pi$
$29$	−0.889012	−0.165085	−0.0825427	+	0.996588i	$0.526304\pi$
$30$	2.41421	0.440773
$31$	6.68216	1.20015	0.600076	−	0.799943i	$-0.295137\pi$
$31$	6.68216	1.20015	0.600076	+	0.799943i	$0.295137\pi$
$32$	−1.00000	−0.176777
$33$	−12.7420	−2.21810
$34$	4.21441	0.722766
$35$	−5.18154	−0.875840
$36$	2.82843	0.471405
$37$	−4.82843	−0.793789	−0.396894	−	0.917864i	$-0.629912\pi$
$37$	−4.82843	−0.793789	−0.396894	+	0.917864i	$0.629912\pi$
$38$	1.98174	0.321481
$39$	−14.1562	−2.26681
$40$	1.00000	0.158114
$41$	−3.39355	−0.529983	−0.264992	−	0.964251i	$-0.585369\pi$
$41$	−3.39355	−0.529983	−0.264992	+	0.964251i	$0.585369\pi$
$42$	−12.5093	−1.93023
$43$	3.19980	0.487965	0.243983	−	0.969780i	$-0.421546\pi$
$43$	3.19980	0.487965	0.243983	+	0.969780i	$0.421546\pi$
$44$	−5.27792	−0.795676
$45$	−2.82843	−0.421637
$46$	0	0
$47$	1.11099	0.162054	0.0810271	−	0.996712i	$-0.474180\pi$
$47$	1.11099	0.162054	0.0810271	+	0.996712i	$0.474180\pi$
$48$	2.41421	0.348462
$49$	19.8484	2.83548
$50$	−1.00000	−0.141421
$51$	−10.1745	−1.42471
$52$	−5.86370	−0.813149
$53$	−3.24728	−0.446049	−0.223024	−	0.974813i	$-0.571593\pi$
$53$	−3.24728	−0.446049	−0.223024	+	0.974813i	$0.571593\pi$
$54$	0.414214	0.0563673
$55$	5.27792	0.711674
$56$	−5.18154	−0.692412
$57$	−4.78434	−0.633702
$58$	0.889012	0.116733
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	−2.41421	−0.311674
$61$	4.09978	0.524923	0.262461	−	0.964943i	$-0.415466\pi$
$61$	4.09978	0.524923	0.262461	+	0.964943i	$0.415466\pi$
$62$	−6.68216	−0.848636
$63$	14.6556	1.84643
$64$	1.00000	0.125000
$65$	5.86370	0.727303
$66$	12.7420	1.56843
$67$	−10.6705	−1.30361	−0.651803	−	0.758389i	$-0.725987\pi$
$67$	−10.6705	−1.30361	−0.651803	+	0.758389i	$0.725987\pi$
$68$	−4.21441	−0.511073
$69$	0	0
$70$	5.18154	0.619313
$71$	−6.90895	−0.819941	−0.409971	−	0.912099i	$-0.634461\pi$
$71$	−6.90895	−0.819941	−0.409971	+	0.912099i	$0.634461\pi$
$72$	−2.82843	−0.333333
$73$	4.44485	0.520230	0.260115	−	0.965578i	$-0.416240\pi$
$73$	4.44485	0.520230	0.260115	+	0.965578i	$0.416240\pi$
$74$	4.82843	0.561293
$75$	2.41421	0.278769
$76$	−1.98174	−0.227321
$77$	−27.3477	−3.11656
$78$	14.1562	1.60288
$79$	−17.4375	−1.96188	−0.980939	−	0.194317i	$-0.937751\pi$
$79$	−17.4375	−1.96188	−0.980939	+	0.194317i	$0.937751\pi$
$80$	−1.00000	−0.111803
$81$	−9.48528	−1.05392
$82$	3.39355	0.374755
$83$	3.74907	0.411514	0.205757	−	0.978603i	$-0.434034\pi$
$83$	3.74907	0.411514	0.205757	+	0.978603i	$0.434034\pi$
$84$	12.5093	1.36488
$85$	4.21441	0.457117
$86$	−3.19980	−0.345043
$87$	−2.14626	−0.230104
$88$	5.27792	0.562628
$89$	−10.7785	−1.14252	−0.571261	−	0.820768i	$-0.693546\pi$
$89$	−10.7785	−1.14252	−0.571261	+	0.820768i	$0.693546\pi$
$90$	2.82843	0.298142
$91$	−30.3830	−3.18501
$92$	0	0
$93$	16.1322	1.67283
$94$	−1.11099	−0.114590
$95$	1.98174	0.203322
$96$	−2.41421	−0.246400
$97$	1.11439	0.113149	0.0565745	−	0.998398i	$-0.481982\pi$
$97$	1.11439	0.113149	0.0565745	+	0.998398i	$0.481982\pi$
$98$	−19.8484	−2.00499
$99$	−14.9282	−1.50034
$100$	1.00000	0.100000
$101$	−16.2925	−1.62117	−0.810584	−	0.585623i	$-0.800850\pi$
$101$	−16.2925	−1.62117	−0.810584	+	0.585623i	$0.800850\pi$
$102$	10.1745	1.00742
$103$	9.36913	0.923168	0.461584	−	0.887096i	$-0.347281\pi$
$103$	9.36913	0.923168	0.461584	+	0.887096i	$0.347281\pi$
$104$	5.86370	0.574983
$105$	−12.5093	−1.22079
$106$	3.24728	0.315404
$107$	5.07107	0.490239	0.245119	−	0.969493i	$-0.421173\pi$
$107$	5.07107	0.490239	0.245119	+	0.969493i	$0.421173\pi$
$108$	−0.414214	−0.0398577
$109$	−15.2521	−1.46089	−0.730443	−	0.682974i	$-0.760686\pi$
$109$	−15.2521	−1.46089	−0.730443	+	0.682974i	$0.760686\pi$
$110$	−5.27792	−0.503230
$111$	−11.6569	−1.10642
$112$	5.18154	0.489610
$113$	−5.40665	−0.508615	−0.254307	−	0.967123i	$-0.581848\pi$
$113$	−5.40665	−0.508615	−0.254307	+	0.967123i	$0.581848\pi$
$114$	4.78434	0.448095
$115$	0	0
$116$	−0.889012	−0.0825427
$117$	−16.5851	−1.53329
$118$	−3.00000	−0.276172
$119$	−21.8372	−2.00181
$120$	2.41421	0.220387
$121$	16.8564	1.53240
$122$	−4.09978	−0.371176
$123$	−8.19275	−0.738716
$124$	6.68216	0.600076
$125$	−1.00000	−0.0894427
$126$	−14.6556	−1.30563
$127$	−5.04524	−0.447693	−0.223846	−	0.974624i	$-0.571861\pi$
$127$	−5.04524	−0.447693	−0.223846	+	0.974624i	$0.571861\pi$
$128$	−1.00000	−0.0883883
$129$	7.72500	0.680149
$130$	−5.86370	−0.514281
$131$	2.90702	0.253988	0.126994	−	0.991903i	$-0.459467\pi$
$131$	2.90702	0.253988	0.126994	+	0.991903i	$0.459467\pi$
$132$	−12.7420	−1.10905
$133$	−10.2685	−0.890389
$134$	10.6705	0.921788
$135$	0.414214	0.0356498
$136$	4.21441	0.361383
$137$	−17.6420	−1.50726	−0.753629	−	0.657300i	$-0.771698\pi$
$137$	−17.6420	−1.50726	−0.753629	+	0.657300i	$0.771698\pi$
$138$	0	0
$139$	−9.09049	−0.771045	−0.385523	−	0.922698i	$-0.625979\pi$
$139$	−9.09049	−0.771045	−0.385523	+	0.922698i	$0.625979\pi$
$140$	−5.18154	−0.437920
$141$	2.68216	0.225879
$142$	6.90895	0.579786
$143$	30.9481	2.58801
$144$	2.82843	0.235702
$145$	0.889012	0.0738284
$146$	−4.44485	−0.367858
$147$	47.9182	3.95223
$148$	−4.82843	−0.396894
$149$	−11.3743	−0.931818	−0.465909	−	0.884833i	$-0.654273\pi$
$149$	−11.3743	−0.931818	−0.465909	+	0.884833i	$0.654273\pi$
$150$	−2.41421	−0.197120
$151$	12.2633	0.997974	0.498987	−	0.866610i	$-0.333706\pi$
$151$	12.2633	0.997974	0.498987	+	0.866610i	$0.333706\pi$
$152$	1.98174	0.160740
$153$	−11.9202	−0.963688
$154$	27.3477	2.20374
$155$	−6.68216	−0.536724
$156$	−14.1562	−1.13341
$157$	−12.4994	−0.997559	−0.498779	−	0.866729i	$-0.666218\pi$
$157$	−12.4994	−0.997559	−0.498779	+	0.866729i	$0.666218\pi$
$158$	17.4375	1.38726
$159$	−7.83964	−0.621724
$160$	1.00000	0.0790569
$161$	0	0
$162$	9.48528	0.745234
$163$	−11.0504	−0.865534	−0.432767	−	0.901506i	$-0.642463\pi$
$163$	−11.0504	−0.865534	−0.432767	+	0.901506i	$0.642463\pi$
$164$	−3.39355	−0.264992
$165$	12.7420	0.991965
$166$	−3.74907	−0.290984
$167$	10.6973	0.827781	0.413891	−	0.910327i	$-0.364170\pi$
$167$	10.6973	0.827781	0.413891	+	0.910327i	$0.364170\pi$
$168$	−12.5093	−0.965117
$169$	21.3830	1.64485
$170$	−4.21441	−0.323231
$171$	−5.60521	−0.428641
$172$	3.19980	0.243983
$173$	−6.80917	−0.517692	−0.258846	−	0.965919i	$-0.583342\pi$
$173$	−6.80917	−0.517692	−0.258846	+	0.965919i	$0.583342\pi$
$174$	2.14626	0.162708
$175$	5.18154	0.391688
$176$	−5.27792	−0.397838
$177$	7.24264	0.544390
$178$	10.7785	0.807886
$179$	18.6086	1.39087	0.695436	−	0.718588i	$-0.255211\pi$
$179$	18.6086	1.39087	0.695436	+	0.718588i	$0.255211\pi$
$180$	−2.82843	−0.210819
$181$	−18.4994	−1.37505	−0.687524	−	0.726162i	$-0.741302\pi$
$181$	−18.4994	−1.37505	−0.687524	+	0.726162i	$0.741302\pi$
$182$	30.3830	2.25214
$183$	9.89774	0.731662
$184$	0	0
$185$	4.82843	0.354993
$186$	−16.1322	−1.18287
$187$	22.2433	1.62659
$188$	1.11099	0.0810271
$189$	−2.14626	−0.156118
$190$	−1.98174	−0.143771
$191$	−13.5690	−0.981821	−0.490911	−	0.871210i	$-0.663336\pi$
$191$	−13.5690	−0.981821	−0.490911	+	0.871210i	$0.663336\pi$
$192$	2.41421	0.174231
$193$	2.99927	0.215892	0.107946	−	0.994157i	$-0.465573\pi$
$193$	2.99927	0.215892	0.107946	+	0.994157i	$0.465573\pi$
$194$	−1.11439	−0.0800084
$195$	14.1562	1.01375
$196$	19.8484	1.41774
$197$	27.7108	1.97431	0.987157	−	0.159752i	$-0.0510695\pi$
$197$	27.7108	1.97431	0.987157	+	0.159752i	$0.0510695\pi$
$198$	14.9282	1.06090
$199$	3.99587	0.283260	0.141630	−	0.989920i	$-0.454766\pi$
$199$	3.99587	0.283260	0.141630	+	0.989920i	$0.454766\pi$
$200$	−1.00000	−0.0707107
$201$	−25.7608	−1.81703
$202$	16.2925	1.14634
$203$	−4.60645	−0.323309
$204$	−10.1745	−0.712357
$205$	3.39355	0.237016
$206$	−9.36913	−0.652778
$207$	0	0
$208$	−5.86370	−0.406575
$209$	10.4595	0.723496
$210$	12.5093	0.863227
$211$	20.9683	1.44352	0.721758	−	0.692145i	$-0.243334\pi$
$211$	20.9683	1.44352	0.721758	+	0.692145i	$0.243334\pi$
$212$	−3.24728	−0.223024
$213$	−16.6797	−1.14287
$214$	−5.07107	−0.346651
$215$	−3.19980	−0.218225
$216$	0.414214	0.0281837
$217$	34.6239	2.35042
$218$	15.2521	1.03300
$219$	10.7308	0.725121
$220$	5.27792	0.355837
$221$	24.7121	1.66231
$222$	11.6569	0.782357
$223$	−9.39355	−0.629039	−0.314519	−	0.949251i	$-0.601843\pi$
$223$	−9.39355	−0.629039	−0.314519	+	0.949251i	$0.601843\pi$
$224$	−5.18154	−0.346206
$225$	2.82843	0.188562
$226$	5.40665	0.359645
$227$	21.4052	1.42071	0.710356	−	0.703842i	$-0.248534\pi$
$227$	21.4052	1.42071	0.710356	+	0.703842i	$0.248534\pi$
$228$	−4.78434	−0.316851
$229$	5.71744	0.377819	0.188909	−	0.981995i	$-0.439505\pi$
$229$	5.71744	0.377819	0.188909	+	0.981995i	$0.439505\pi$
$230$	0	0
$231$	−66.0233	−4.34401
$232$	0.889012	0.0583665
$233$	5.49525	0.360006	0.180003	−	0.983666i	$-0.442389\pi$
$233$	5.49525	0.360006	0.180003	+	0.983666i	$0.442389\pi$
$234$	16.5851	1.08420
$235$	−1.11099	−0.0724729
$236$	3.00000	0.195283
$237$	−42.0980	−2.73456
$238$	21.8372	1.41549
$239$	2.30463	0.149074	0.0745372	−	0.997218i	$-0.476252\pi$
$239$	2.30463	0.149074	0.0745372	+	0.997218i	$0.476252\pi$
$240$	−2.41421	−0.155837
$241$	17.1392	1.10403	0.552017	−	0.833833i	$-0.313858\pi$
$241$	17.1392	1.10403	0.552017	+	0.833833i	$0.313858\pi$
$242$	−16.8564	−1.08357
$243$	−21.6569	−1.38929
$244$	4.09978	0.262461
$245$	−19.8484	−1.26807
$246$	8.19275	0.522351
$247$	11.6203	0.739384
$248$	−6.68216	−0.424318
$249$	9.05105	0.573587
$250$	1.00000	0.0632456
$251$	−14.9172	−0.941568	−0.470784	−	0.882249i	$-0.656029\pi$
$251$	−14.9172	−0.941568	−0.470784	+	0.882249i	$0.656029\pi$
$252$	14.6556	0.923217
$253$	0	0
$254$	5.04524	0.316567
$255$	10.1745	0.637151
$256$	1.00000	0.0625000
$257$	−0.443437	−0.0276609	−0.0138304	−	0.999904i	$-0.504403\pi$
$257$	−0.443437	−0.0276609	−0.0138304	+	0.999904i	$0.504403\pi$
$258$	−7.72500	−0.480938
$259$	−25.0187	−1.55459
$260$	5.86370	0.363651
$261$	−2.51451	−0.155644
$262$	−2.90702	−0.179597
$263$	−16.2147	−0.999840	−0.499920	−	0.866072i	$-0.666637\pi$
$263$	−16.2147	−0.999840	−0.499920	+	0.866072i	$0.666637\pi$
$264$	12.7420	0.784217
$265$	3.24728	0.199479
$266$	10.2685	0.629600
$267$	−26.0217	−1.59250
$268$	−10.6705	−0.651803
$269$	−12.5334	−0.764175	−0.382088	−	0.924126i	$-0.624795\pi$
$269$	−12.5334	−0.764175	−0.382088	+	0.924126i	$0.624795\pi$
$270$	−0.414214	−0.0252082
$271$	−0.914107	−0.0555280	−0.0277640	−	0.999615i	$-0.508839\pi$
$271$	−0.914107	−0.0555280	−0.0277640	+	0.999615i	$0.508839\pi$
$272$	−4.21441	−0.255536
$273$	−73.3511	−4.43941
$274$	17.6420	1.06579
$275$	−5.27792	−0.318270
$276$	0	0
$277$	7.84644	0.471447	0.235723	−	0.971820i	$-0.424254\pi$
$277$	7.84644	0.471447	0.235723	+	0.971820i	$0.424254\pi$
$278$	9.09049	0.545211
$279$	18.9000	1.13151
$280$	5.18154	0.309656
$281$	13.0029	0.775689	0.387845	−	0.921725i	$-0.373220\pi$
$281$	13.0029	0.775689	0.387845	+	0.921725i	$0.373220\pi$
$282$	−2.68216	−0.159720
$283$	−9.44725	−0.561581	−0.280790	−	0.959769i	$-0.590597\pi$
$283$	−9.44725	−0.561581	−0.280790	+	0.959769i	$0.590597\pi$
$284$	−6.90895	−0.409971
$285$	4.78434	0.283400
$286$	−30.9481	−1.83000
$287$	−17.5838	−1.03794
$288$	−2.82843	−0.166667
$289$	0.761275	0.0447809
$290$	−0.889012	−0.0522046
$291$	2.69037	0.157712
$292$	4.44485	0.260115
$293$	−11.8365	−0.691494	−0.345747	−	0.938328i	$-0.612374\pi$
$293$	−11.8365	−0.691494	−0.345747	+	0.938328i	$0.612374\pi$
$294$	−47.9182	−2.79465
$295$	−3.00000	−0.174667
$296$	4.82843	0.280647
$297$	2.18618	0.126855
$298$	11.3743	0.658895
$299$	0	0
$300$	2.41421	0.139385
$301$	16.5799	0.955649
$302$	−12.2633	−0.705674
$303$	−39.3336	−2.25966
$304$	−1.98174	−0.113661
$305$	−4.09978	−0.234752
$306$	11.9202	0.681430
$307$	−3.09122	−0.176425	−0.0882125	−	0.996102i	$-0.528115\pi$
$307$	−3.09122	−0.176425	−0.0882125	+	0.996102i	$0.528115\pi$
$308$	−27.3477	−1.55828
$309$	22.6191	1.28676
$310$	6.68216	0.379521
$311$	−3.45214	−0.195753	−0.0978765	−	0.995199i	$-0.531205\pi$
$311$	−3.45214	−0.195753	−0.0978765	+	0.995199i	$0.531205\pi$
$312$	14.1562	0.801439
$313$	−3.47647	−0.196502	−0.0982509	−	0.995162i	$-0.531325\pi$
$313$	−3.47647	−0.196502	−0.0982509	+	0.995162i	$0.531325\pi$
$314$	12.4994	0.705381
$315$	−14.6556	−0.825750
$316$	−17.4375	−0.980939
$317$	2.80917	0.157779	0.0788894	−	0.996883i	$-0.474863\pi$
$317$	2.80917	0.157779	0.0788894	+	0.996883i	$0.474863\pi$
$318$	7.83964	0.439625
$319$	4.69213	0.262709
$320$	−1.00000	−0.0559017
$321$	12.2426	0.683318
$322$	0	0
$323$	8.35187	0.464710
$324$	−9.48528	−0.526960
$325$	−5.86370	−0.325260
$326$	11.0504	0.612025
$327$	−36.8218	−2.03625
$328$	3.39355	0.187377
$329$	5.75663	0.317373
$330$	−12.7420	−0.701425
$331$	11.5334	0.633934	0.316967	−	0.948437i	$-0.397336\pi$
$331$	11.5334	0.633934	0.316967	+	0.948437i	$0.397336\pi$
$332$	3.74907	0.205757
$333$	−13.6569	−0.748391
$334$	−10.6973	−0.585330
$335$	10.6705	0.582990
$336$	12.5093	0.682441
$337$	−26.6773	−1.45320	−0.726602	−	0.687059i	$-0.758901\pi$
$337$	−26.6773	−1.45320	−0.726602	+	0.687059i	$0.758901\pi$
$338$	−21.3830	−1.16308
$339$	−13.0528	−0.708931
$340$	4.21441	0.228559
$341$	−35.2679	−1.90986
$342$	5.60521	0.303095
$343$	66.5743	3.59467
$344$	−3.19980	−0.172522
$345$	0	0
$346$	6.80917	0.366063
$347$	24.6148	1.32139	0.660696	−	0.750654i	$-0.270261\pi$
$347$	24.6148	1.32139	0.660696	+	0.750654i	$0.270261\pi$
$348$	−2.14626	−0.115052
$349$	−27.9469	−1.49596	−0.747981	−	0.663720i	$-0.768977\pi$
$349$	−27.9469	−1.49596	−0.747981	+	0.663720i	$0.768977\pi$
$350$	−5.18154	−0.276965
$351$	2.42883	0.129641
$352$	5.27792	0.281314
$353$	−34.3319	−1.82730	−0.913651	−	0.406500i	$-0.866749\pi$
$353$	−34.3319	−1.82730	−0.913651	+	0.406500i	$0.866749\pi$
$354$	−7.24264	−0.384942
$355$	6.90895	0.366689
$356$	−10.7785	−0.571261
$357$	−52.7195	−2.79021
$358$	−18.6086	−0.983495
$359$	6.57028	0.346766	0.173383	−	0.984854i	$-0.444530\pi$
$359$	6.57028	0.346766	0.173383	+	0.984854i	$0.444530\pi$
$360$	2.82843	0.149071
$361$	−15.0727	−0.793300
$362$	18.4994	0.972306
$363$	40.6950	2.13593
$364$	−30.3830	−1.59250
$365$	−4.44485	−0.232654
$366$	−9.89774	−0.517363
$367$	30.3741	1.58551	0.792757	−	0.609538i	$-0.208645\pi$
$367$	30.3741	1.58551	0.792757	+	0.609538i	$0.208645\pi$
$368$	0	0
$369$	−9.59841	−0.499673
$370$	−4.82843	−0.251018
$371$	−16.8259	−0.873559
$372$	16.1322	0.836414
$373$	16.6822	0.863770	0.431885	−	0.901929i	$-0.357849\pi$
$373$	16.6822	0.863770	0.431885	+	0.901929i	$0.357849\pi$
$374$	−22.2433	−1.15017
$375$	−2.41421	−0.124669
$376$	−1.11099	−0.0572948
$377$	5.21290	0.268478
$378$	2.14626	0.110392
$379$	11.1798	0.574269	0.287134	−	0.957890i	$-0.407297\pi$
$379$	11.1798	0.574269	0.287134	+	0.957890i	$0.407297\pi$
$380$	1.98174	0.101661
$381$	−12.1803	−0.624015
$382$	13.5690	0.694252
$383$	5.17260	0.264308	0.132154	−	0.991229i	$-0.457811\pi$
$383$	5.17260	0.264308	0.132154	+	0.991229i	$0.457811\pi$
$384$	−2.41421	−0.123200
$385$	27.3477	1.39377
$386$	−2.99927	−0.152659
$387$	9.05040	0.460058
$388$	1.11439	0.0565745
$389$	0.00480803	0.000243777 0	0.000121888	−	1.00000i	$-0.499961\pi$
$389$	0.00480803	0.000243777 0	0.000121888		1.00000i	$0.499961\pi$
$390$	−14.1562	−0.716829
$391$	0	0
$392$	−19.8484	−1.00249
$393$	7.01818	0.354020
$394$	−27.7108	−1.39605
$395$	17.4375	0.877378
$396$	−14.9282	−0.750170
$397$	−2.22892	−0.111866	−0.0559332	−	0.998435i	$-0.517813\pi$
$397$	−2.22892	−0.111866	−0.0559332	+	0.998435i	$0.517813\pi$
$398$	−3.99587	−0.200295
$399$	−24.7903	−1.24107
$400$	1.00000	0.0500000
$401$	16.8818	0.843034	0.421517	−	0.906820i	$-0.361498\pi$
$401$	16.8818	0.843034	0.421517	+	0.906820i	$0.361498\pi$
$402$	25.7608	1.28483
$403$	−39.1822	−1.95181
$404$	−16.2925	−0.810584
$405$	9.48528	0.471327
$406$	4.60645	0.228614
$407$	25.4840	1.26320
$408$	10.1745	0.503712
$409$	−11.5909	−0.573135	−0.286568	−	0.958060i	$-0.592514\pi$
$409$	−11.5909	−0.573135	−0.286568	+	0.958060i	$0.592514\pi$
$410$	−3.39355	−0.167595
$411$	−42.5915	−2.10089
$412$	9.36913	0.461584
$413$	15.5446	0.764901
$414$	0	0
$415$	−3.74907	−0.184034
$416$	5.86370	0.287492
$417$	−21.9464	−1.07472
$418$	−10.4595	−0.511589
$419$	26.8180	1.31014	0.655072	−	0.755566i	$-0.272638\pi$
$419$	26.8180	1.31014	0.655072	+	0.755566i	$0.272638\pi$
$420$	−12.5093	−0.610394
$421$	35.2486	1.71791	0.858957	−	0.512048i	$-0.171113\pi$
$421$	35.2486	1.71791	0.858957	+	0.512048i	$0.171113\pi$
$422$	−20.9683	−1.02072
$423$	3.14235	0.152786
$424$	3.24728	0.157702
$425$	−4.21441	−0.204429
$426$	16.6797	0.808133
$427$	21.2432	1.02803
$428$	5.07107	0.245119
$429$	74.7154	3.60729
$430$	3.19980	0.154308
$431$	32.2843	1.55508	0.777539	−	0.628834i	$-0.216468\pi$
$431$	32.2843	1.55508	0.777539	+	0.628834i	$0.216468\pi$
$432$	−0.414214	−0.0199289
$433$	−10.7926	−0.518661	−0.259330	−	0.965789i	$-0.583502\pi$
$433$	−10.7926	−0.518661	−0.259330	+	0.965789i	$0.583502\pi$
$434$	−34.6239	−1.66200
$435$	2.14626	0.102906
$436$	−15.2521	−0.730443
$437$	0	0
$438$	−10.7308	−0.512738
$439$	31.1226	1.48540	0.742700	−	0.669624i	$-0.233545\pi$
$439$	31.1226	1.48540	0.742700	+	0.669624i	$0.233545\pi$
$440$	−5.27792	−0.251615
$441$	56.1396	2.67332
$442$	−24.7121	−1.17543
$443$	3.21342	0.152674	0.0763370	−	0.997082i	$-0.475678\pi$
$443$	3.21342	0.152674	0.0763370	+	0.997082i	$0.475678\pi$
$444$	−11.6569	−0.553210
$445$	10.7785	0.510952
$446$	9.39355	0.444797
$447$	−27.4600	−1.29881
$448$	5.18154	0.244805
$449$	−29.7812	−1.40546	−0.702731	−	0.711456i	$-0.748036\pi$
$449$	−29.7812	−1.40546	−0.702731	+	0.711456i	$0.748036\pi$
$450$	−2.82843	−0.133333
$451$	17.9109	0.843390
$452$	−5.40665	−0.254307
$453$	29.6062	1.39102
$454$	−21.4052	−1.00460
$455$	30.3830	1.42438
$456$	4.78434	0.224047
$457$	12.8763	0.602329	0.301165	−	0.953572i	$-0.402625\pi$
$457$	12.8763	0.602329	0.301165	+	0.953572i	$0.402625\pi$
$458$	−5.71744	−0.267158
$459$	1.74567	0.0814808
$460$	0	0
$461$	5.28345	0.246075	0.123037	−	0.992402i	$-0.460736\pi$
$461$	5.28345	0.246075	0.123037	+	0.992402i	$0.460736\pi$
$462$	66.0233	3.07168
$463$	13.0139	0.604806	0.302403	−	0.953180i	$-0.402211\pi$
$463$	13.0139	0.604806	0.302403	+	0.953180i	$0.402211\pi$
$464$	−0.889012	−0.0412713
$465$	−16.1322	−0.748111
$466$	−5.49525	−0.254562
$467$	−19.6166	−0.907747	−0.453874	−	0.891066i	$-0.649958\pi$
$467$	−19.6166	−0.907747	−0.453874	+	0.891066i	$0.649958\pi$
$468$	−16.5851	−0.766645
$469$	−55.2895	−2.55303
$470$	1.11099	0.0512461
$471$	−30.1762	−1.39044
$472$	−3.00000	−0.138086
$473$	−16.8883	−0.776524
$474$	42.0980	1.93362
$475$	−1.98174	−0.0909285
$476$	−21.8372	−1.00090
$477$	−9.18471	−0.420539
$478$	−2.30463	−0.105411
$479$	14.6364	0.668752	0.334376	−	0.942440i	$-0.391474\pi$
$479$	14.6364	0.668752	0.334376	+	0.942440i	$0.391474\pi$
$480$	2.41421	0.110193
$481$	28.3125	1.29094
$482$	−17.1392	−0.780670
$483$	0	0
$484$	16.8564	0.766200
$485$	−1.11439	−0.0506018
$486$	21.6569	0.982375
$487$	11.4445	0.518600	0.259300	−	0.965797i	$-0.416508\pi$
$487$	11.4445	0.518600	0.259300	+	0.965797i	$0.416508\pi$
$488$	−4.09978	−0.185588
$489$	−26.6780	−1.20642
$490$	19.8484	0.896658
$491$	23.9294	1.07992	0.539960	−	0.841690i	$-0.318439\pi$
$491$	23.9294	1.07992	0.539960	+	0.841690i	$0.318439\pi$
$492$	−8.19275	−0.369358
$493$	3.74666	0.168741
$494$	−11.6203	−0.522824
$495$	14.9282	0.670973
$496$	6.68216	0.300038
$497$	−35.7990	−1.60580
$498$	−9.05105	−0.405587
$499$	36.5779	1.63745	0.818726	−	0.574184i	$-0.194681\pi$
$499$	36.5779	1.63745	0.818726	+	0.574184i	$0.194681\pi$
$500$	−1.00000	−0.0447214
$501$	25.8255	1.15380
$502$	14.9172	0.665789
$503$	23.9741	1.06895	0.534477	−	0.845183i	$-0.320509\pi$
$503$	23.9741	1.06895	0.534477	+	0.845183i	$0.320509\pi$
$504$	−14.6556	−0.652813
$505$	16.2925	0.725008
$506$	0	0
$507$	51.6232	2.29267
$508$	−5.04524	−0.223846
$509$	−20.1783	−0.894388	−0.447194	−	0.894437i	$-0.647577\pi$
$509$	−20.1783	−0.894388	−0.447194	+	0.894437i	$0.647577\pi$
$510$	−10.1745	−0.450534
$511$	23.0311	1.01884
$512$	−1.00000	−0.0441942
$513$	0.820863	0.0362420
$514$	0.443437	0.0195592
$515$	−9.36913	−0.412853
$516$	7.72500	0.340074
$517$	−5.86370	−0.257885
$518$	25.0187	1.09926
$519$	−16.4388	−0.721583
$520$	−5.86370	−0.257140
$521$	−10.5031	−0.460150	−0.230075	−	0.973173i	$-0.573897\pi$
$521$	−10.5031	−0.460150	−0.230075	+	0.973173i	$0.573897\pi$
$522$	2.51451	0.110057
$523$	−41.2321	−1.80295	−0.901477	−	0.432827i	$-0.857516\pi$
$523$	−41.2321	−1.80295	−0.901477	+	0.432827i	$0.857516\pi$
$524$	2.90702	0.126994
$525$	12.5093	0.545953
$526$	16.2147	0.706994
$527$	−28.1614	−1.22673
$528$	−12.7420	−0.554525
$529$	0	0
$530$	−3.24728	−0.141053
$531$	8.48528	0.368230
$532$	−10.2685	−0.445194
$533$	19.8988	0.861911
$534$	26.0217	1.12607
$535$	−5.07107	−0.219241
$536$	10.6705	0.460894
$537$	44.9251	1.93866
$538$	12.5334	0.540354
$539$	−104.758	−4.51225
$540$	0.414214	0.0178249
$541$	−20.4635	−0.879796	−0.439898	−	0.898048i	$-0.644985\pi$
$541$	−20.4635	−0.879796	−0.439898	+	0.898048i	$0.644985\pi$
$542$	0.914107	0.0392642
$543$	−44.6614	−1.91661
$544$	4.21441	0.180691
$545$	15.2521	0.653328
$546$	73.3511	3.13914
$547$	19.1127	0.817200	0.408600	−	0.912714i	$-0.366017\pi$
$547$	19.1127	0.817200	0.408600	+	0.912714i	$0.366017\pi$
$548$	−17.6420	−0.753629
$549$	11.5959	0.494902
$550$	5.27792	0.225051
$551$	1.76179	0.0750548
$552$	0	0
$553$	−90.3534	−3.84222
$554$	−7.84644	−0.333363
$555$	11.6569	0.494806
$556$	−9.09049	−0.385523
$557$	23.7019	1.00428	0.502141	−	0.864786i	$-0.332546\pi$
$557$	23.7019	1.00428	0.502141	+	0.864786i	$0.332546\pi$
$558$	−18.9000	−0.800101
$559$	−18.7627	−0.793577
$560$	−5.18154	−0.218960
$561$	53.7001	2.26722
$562$	−13.0029	−0.548495
$563$	36.7595	1.54923	0.774614	−	0.632434i	$-0.217944\pi$
$563$	36.7595	1.54923	0.774614	+	0.632434i	$0.217944\pi$
$564$	2.68216	0.112939
$565$	5.40665	0.227459
$566$	9.44725	0.397098
$567$	−49.1484	−2.06404
$568$	6.90895	0.289893
$569$	5.63276	0.236137	0.118069	−	0.993005i	$-0.462330\pi$
$569$	5.63276	0.236137	0.118069	+	0.993005i	$0.462330\pi$
$570$	−4.78434	−0.200394
$571$	23.8578	0.998417	0.499209	−	0.866482i	$-0.333624\pi$
$571$	23.8578	0.998417	0.499209	+	0.866482i	$0.333624\pi$
$572$	30.9481	1.29401
$573$	−32.7586	−1.36851
$574$	17.5838	0.733934
$575$	0	0
$576$	2.82843	0.117851
$577$	−0.355389	−0.0147950	−0.00739751	−	0.999973i	$-0.502355\pi$
$577$	−0.355389	−0.0147950	−0.00739751	+	0.999973i	$0.502355\pi$
$578$	−0.761275	−0.0316648
$579$	7.24088	0.300921
$580$	0.889012	0.0369142
$581$	19.4259	0.805924
$582$	−2.69037	−0.111519
$583$	17.1389	0.709821
$584$	−4.44485	−0.183929
$585$	16.5851	0.685708
$586$	11.8365	0.488960
$587$	−6.02481	−0.248671	−0.124335	−	0.992240i	$-0.539680\pi$
$587$	−6.02481	−0.248671	−0.124335	+	0.992240i	$0.539680\pi$
$588$	47.9182	1.97611
$589$	−13.2423	−0.545640
$590$	3.00000	0.123508
$591$	66.8998	2.75189
$592$	−4.82843	−0.198447
$593$	−31.1404	−1.27878	−0.639391	−	0.768882i	$-0.720813\pi$
$593$	−31.1404	−1.27878	−0.639391	+	0.768882i	$0.720813\pi$
$594$	−2.18618	−0.0897002
$595$	21.8372	0.895236
$596$	−11.3743	−0.465909
$597$	9.64689	0.394821
$598$	0	0
$599$	−27.0379	−1.10474	−0.552370	−	0.833599i	$-0.686277\pi$
$599$	−27.0379	−1.10474	−0.552370	+	0.833599i	$0.686277\pi$
$600$	−2.41421	−0.0985599
$601$	32.1076	1.30970	0.654848	−	0.755760i	$-0.272733\pi$
$601$	32.1076	1.30970	0.654848	+	0.755760i	$0.272733\pi$
$602$	−16.5799	−0.675746
$603$	−30.1806	−1.22905
$604$	12.2633	0.498987
$605$	−16.8564	−0.685310
$606$	39.3336	1.59782
$607$	9.71064	0.394143	0.197071	−	0.980389i	$-0.436857\pi$
$607$	9.71064	0.394143	0.197071	+	0.980389i	$0.436857\pi$
$608$	1.98174	0.0803702
$609$	−11.1210	−0.450644
$610$	4.09978	0.165995
$611$	−6.51451	−0.263549
$612$	−11.9202	−0.481844
$613$	−26.6704	−1.07721	−0.538603	−	0.842559i	$-0.681048\pi$
$613$	−26.6704	−1.07721	−0.538603	+	0.842559i	$0.681048\pi$
$614$	3.09122	0.124751
$615$	8.19275	0.330364
$616$	27.3477	1.10187
$617$	−25.2187	−1.01527	−0.507633	−	0.861573i	$-0.669480\pi$
$617$	−25.2187	−1.01527	−0.507633	+	0.861573i	$0.669480\pi$
$618$	−22.6191	−0.909873
$619$	−20.5984	−0.827921	−0.413960	−	0.910295i	$-0.635855\pi$
$619$	−20.5984	−0.827921	−0.413960	+	0.910295i	$0.635855\pi$
$620$	−6.68216	−0.268362
$621$	0	0
$622$	3.45214	0.138418
$623$	−55.8494	−2.23756
$624$	−14.1562	−0.566703
$625$	1.00000	0.0400000
$626$	3.47647	0.138948
$627$	25.2514	1.00844
$628$	−12.4994	−0.498779
$629$	20.3490	0.811367
$630$	14.6556	0.583893
$631$	43.6747	1.73866	0.869330	−	0.494232i	$-0.164551\pi$
$631$	43.6747	1.73866	0.869330	+	0.494232i	$0.164551\pi$
$632$	17.4375	0.693628
$633$	50.6219	2.01204
$634$	−2.80917	−0.111566
$635$	5.04524	0.200214
$636$	−7.83964	−0.310862
$637$	−116.385	−4.61134
$638$	−4.69213	−0.185763
$639$	−19.5415	−0.773048
$640$	1.00000	0.0395285
$641$	−34.5169	−1.36334	−0.681668	−	0.731662i	$-0.738745\pi$
$641$	−34.5169	−1.36334	−0.681668	+	0.731662i	$0.738745\pi$
$642$	−12.2426	−0.483178
$643$	−14.9620	−0.590044	−0.295022	−	0.955490i	$-0.595327\pi$
$643$	−14.9620	−0.590044	−0.295022	+	0.955490i	$0.595327\pi$
$644$	0	0
$645$	−7.72500	−0.304172
$646$	−8.35187	−0.328600
$647$	−30.7657	−1.20952	−0.604762	−	0.796406i	$-0.706732\pi$
$647$	−30.7657	−1.20952	−0.604762	+	0.796406i	$0.706732\pi$
$648$	9.48528	0.372617
$649$	−15.8338	−0.621529
$650$	5.86370	0.229993
$651$	83.5895	3.27613
$652$	−11.0504	−0.432767
$653$	−18.1415	−0.709930	−0.354965	−	0.934880i	$-0.615507\pi$
$653$	−18.1415	−0.709930	−0.354965	+	0.934880i	$0.615507\pi$
$654$	36.8218	1.43985
$655$	−2.90702	−0.113587
$656$	−3.39355	−0.132496
$657$	12.5719	0.490477
$658$	−5.75663	−0.224417
$659$	−39.6933	−1.54623	−0.773116	−	0.634265i	$-0.781303\pi$
$659$	−39.6933	−1.54623	−0.773116	+	0.634265i	$0.781303\pi$
$660$	12.7420	0.495982
$661$	−11.9122	−0.463330	−0.231665	−	0.972796i	$-0.574417\pi$
$661$	−11.9122	−0.463330	−0.231665	+	0.972796i	$0.574417\pi$
$662$	−11.5334	−0.448259
$663$	59.6602	2.31701
$664$	−3.74907	−0.145492
$665$	10.2685	0.398194
$666$	13.6569	0.529192
$667$	0	0
$668$	10.6973	0.413891
$669$	−22.6780	−0.876783
$670$	−10.6705	−0.412236
$671$	−21.6383	−0.835336
$672$	−12.5093	−0.482558
$673$	−22.3626	−0.862014	−0.431007	−	0.902349i	$-0.641841\pi$
$673$	−22.3626	−0.862014	−0.431007	+	0.902349i	$0.641841\pi$
$674$	26.6773	1.02757
$675$	−0.414214	−0.0159431
$676$	21.3830	0.822424
$677$	−7.92051	−0.304410	−0.152205	−	0.988349i	$-0.548637\pi$
$677$	−7.92051	−0.304410	−0.152205	+	0.988349i	$0.548637\pi$
$678$	13.0528	0.501290
$679$	5.77425	0.221595
$680$	−4.21441	−0.161615
$681$	51.6767	1.98026
$682$	35.2679	1.35048
$683$	21.3214	0.815841	0.407920	−	0.913018i	$-0.366254\pi$
$683$	21.3214	0.815841	0.407920	+	0.913018i	$0.366254\pi$
$684$	−5.60521	−0.214320
$685$	17.6420	0.674066
$686$	−66.5743	−2.54182
$687$	13.8031	0.526622
$688$	3.19980	0.121991
$689$	19.0411	0.725409
$690$	0	0
$691$	7.72061	0.293706	0.146853	−	0.989158i	$-0.453086\pi$
$691$	7.72061	0.293706	0.146853	+	0.989158i	$0.453086\pi$
$692$	−6.80917	−0.258846
$693$	−77.3511	−2.93832
$694$	−24.6148	−0.934365
$695$	9.09049	0.344822
$696$	2.14626	0.0813539
$697$	14.3018	0.541720
$698$	27.9469	1.05781
$699$	13.2667	0.501793
$700$	5.18154	0.195844
$701$	−11.9739	−0.452250	−0.226125	−	0.974098i	$-0.572606\pi$
$701$	−11.9739	−0.452250	−0.226125	+	0.974098i	$0.572606\pi$
$702$	−2.42883	−0.0916701
$703$	9.56869	0.360890
$704$	−5.27792	−0.198919
$705$	−2.68216	−0.101016
$706$	34.3319	1.29210
$707$	−84.4204	−3.17496
$708$	7.24264	0.272195
$709$	31.1894	1.17134	0.585671	−	0.810549i	$-0.300831\pi$
$709$	31.1894	1.17134	0.585671	+	0.810549i	$0.300831\pi$
$710$	−6.90895	−0.259288
$711$	−49.3208	−1.84968
$712$	10.7785	0.403943
$713$	0	0
$714$	52.7195	1.97298
$715$	−30.9481	−1.15739
$716$	18.6086	0.695436
$717$	5.56388	0.207787
$718$	−6.57028	−0.245201
$719$	46.1685	1.72180	0.860898	−	0.508778i	$-0.169903\pi$
$719$	46.1685	1.72180	0.860898	+	0.508778i	$0.169903\pi$
$720$	−2.82843	−0.105409
$721$	48.5465	1.80797
$722$	15.0727	0.560948
$723$	41.3777	1.53885
$724$	−18.4994	−0.687524
$725$	−0.889012	−0.0330171
$726$	−40.6950	−1.51033
$727$	−1.95618	−0.0725508	−0.0362754	−	0.999342i	$-0.511549\pi$
$727$	−1.95618	−0.0725508	−0.0362754	+	0.999342i	$0.511549\pi$
$728$	30.3830	1.12607
$729$	−23.8284	−0.882534
$730$	4.44485	0.164511
$731$	−13.4853	−0.498771
$732$	9.89774	0.365831
$733$	−10.0100	−0.369727	−0.184863	−	0.982764i	$-0.559184\pi$
$733$	−10.0100	−0.369727	−0.184863	+	0.982764i	$0.559184\pi$
$734$	−30.3741	−1.12113
$735$	−47.9182	−1.76749
$736$	0	0
$737$	56.3179	2.07449
$738$	9.59841	0.353322
$739$	−11.2913	−0.415357	−0.207678	−	0.978197i	$-0.566591\pi$
$739$	−11.2913	−0.415357	−0.207678	+	0.978197i	$0.566591\pi$
$740$	4.82843	0.177497
$741$	28.0540	1.03059
$742$	16.8259	0.617700
$743$	33.3889	1.22492	0.612460	−	0.790501i	$-0.290180\pi$
$743$	33.3889	1.22492	0.612460	+	0.790501i	$0.290180\pi$
$744$	−16.1322	−0.591434
$745$	11.3743	0.416722
$746$	−16.6822	−0.610777
$747$	10.6040	0.387979
$748$	22.2433	0.813296
$749$	26.2759	0.960102
$750$	2.41421	0.0881546
$751$	−6.98569	−0.254911	−0.127456	−	0.991844i	$-0.540681\pi$
$751$	−6.98569	−0.254911	−0.127456	+	0.991844i	$0.540681\pi$
$752$	1.11099	0.0405136
$753$	−36.0134	−1.31240
$754$	−5.21290	−0.189843
$755$	−12.2633	−0.446307
$756$	−2.14626	−0.0780589
$757$	−1.94045	−0.0705267	−0.0352634	−	0.999378i	$-0.511227\pi$
$757$	−1.94045	−0.0705267	−0.0352634	+	0.999378i	$0.511227\pi$
$758$	−11.1798	−0.406069
$759$	0	0
$760$	−1.98174	−0.0718853
$761$	−12.1457	−0.440283	−0.220142	−	0.975468i	$-0.570652\pi$
$761$	−12.1457	−0.440283	−0.220142	+	0.975468i	$0.570652\pi$
$762$	12.1803	0.441246
$763$	−79.0293	−2.86105
$764$	−13.5690	−0.490911
$765$	11.9202	0.430974
$766$	−5.17260	−0.186894
$767$	−17.5911	−0.635178
$768$	2.41421	0.0871154
$769$	−21.7199	−0.783239	−0.391619	−	0.920127i	$-0.628085\pi$
$769$	−21.7199	−0.783239	−0.391619	+	0.920127i	$0.628085\pi$
$770$	−27.3477	−0.985544
$771$	−1.07055	−0.0385550
$772$	2.99927	0.107946
$773$	2.75891	0.0992309	0.0496155	−	0.998768i	$-0.484200\pi$
$773$	2.75891	0.0992309	0.0496155	+	0.998768i	$0.484200\pi$
$774$	−9.05040	−0.325310
$775$	6.68216	0.240030
$776$	−1.11439	−0.0400042
$777$	−60.4005	−2.16685
$778$	−0.00480803	−0.000172376 0
$779$	6.72513	0.240953
$780$	14.1562	0.506874
$781$	36.4648	1.30481
$782$	0	0
$783$	0.368241	0.0131599
$784$	19.8484	0.708870
$785$	12.4994	0.446122
$786$	−7.01818	−0.250330
$787$	20.6715	0.736859	0.368430	−	0.929656i	$-0.379896\pi$
$787$	20.6715	0.736859	0.368430	+	0.929656i	$0.379896\pi$
$788$	27.7108	0.987157
$789$	−39.1457	−1.39362
$790$	−17.4375	−0.620400
$791$	−28.0148	−0.996091
$792$	14.9282	0.530451
$793$	−24.0399	−0.853681
$794$	2.22892	0.0791015
$795$	7.83964	0.278043
$796$	3.99587	0.141630
$797$	−10.2223	−0.362093	−0.181047	−	0.983474i	$-0.557949\pi$
$797$	−10.2223	−0.362093	−0.181047	+	0.983474i	$0.557949\pi$
$798$	24.7903	0.877566
$799$	−4.68216	−0.165643
$800$	−1.00000	−0.0353553
$801$	−30.4863	−1.07718
$802$	−16.8818	−0.596115
$803$	−23.4595	−0.827869
$804$	−25.7608	−0.908513
$805$	0	0
$806$	39.1822	1.38013
$807$	−30.2583	−1.06514
$808$	16.2925	0.573169
$809$	13.0871	0.460118	0.230059	−	0.973177i	$-0.426108\pi$
$809$	13.0871	0.460118	0.230059	+	0.973177i	$0.426108\pi$
$810$	−9.48528	−0.333279
$811$	−48.6529	−1.70843	−0.854217	−	0.519916i	$-0.825963\pi$
$811$	−48.6529	−1.70843	−0.854217	+	0.519916i	$0.825963\pi$
$812$	−4.60645	−0.161655
$813$	−2.20685	−0.0773976
$814$	−25.4840	−0.893215
$815$	11.0504	0.387079
$816$	−10.1745	−0.356178
$817$	−6.34117	−0.221850
$818$	11.5909	0.405268
$819$	−85.9361	−3.00285
$820$	3.39355	0.118508
$821$	−25.0119	−0.872921	−0.436461	−	0.899723i	$-0.643768\pi$
$821$	−25.0119	−0.872921	−0.436461	+	0.899723i	$0.643768\pi$
$822$	42.5915	1.48555
$823$	−51.8740	−1.80821	−0.904107	−	0.427306i	$-0.859463\pi$
$823$	−51.8740	−1.80821	−0.904107	+	0.427306i	$0.859463\pi$
$824$	−9.36913	−0.326389
$825$	−12.7420	−0.443620
$826$	−15.5446	−0.540867
$827$	−30.9960	−1.07784	−0.538918	−	0.842358i	$-0.681167\pi$
$827$	−30.9960	−1.07784	−0.538918	+	0.842358i	$0.681167\pi$
$828$	0	0
$829$	13.8345	0.480491	0.240246	−	0.970712i	$-0.422772\pi$
$829$	13.8345	0.480491	0.240246	+	0.970712i	$0.422772\pi$
$830$	3.74907	0.130132
$831$	18.9430	0.657125
$832$	−5.86370	−0.203287
$833$	−83.6492	−2.89827
$834$	21.9464	0.759941
$835$	−10.6973	−0.370195
$836$	10.4595	0.361748
$837$	−2.76784	−0.0956706
$838$	−26.8180	−0.926412
$839$	21.2275	0.732856	0.366428	−	0.930446i	$-0.380581\pi$
$839$	21.2275	0.732856	0.366428	+	0.930446i	$0.380581\pi$
$840$	12.5093	0.431613
$841$	−28.2097	−0.972747
$842$	−35.2486	−1.21475
$843$	31.3918	1.08119
$844$	20.9683	0.721758
$845$	−21.3830	−0.735598
$846$	−3.14235	−0.108036
$847$	87.3422	3.00111
$848$	−3.24728	−0.111512
$849$	−22.8077	−0.782757
$850$	4.21441	0.144553
$851$	0	0
$852$	−16.6797	−0.571436
$853$	−48.4901	−1.66027	−0.830135	−	0.557563i	$-0.811736\pi$
$853$	−48.4901	−1.66027	−0.830135	+	0.557563i	$0.811736\pi$
$854$	−21.2432	−0.726926
$855$	5.60521	0.191694
$856$	−5.07107	−0.173326
$857$	28.0408	0.957854	0.478927	−	0.877855i	$-0.341026\pi$
$857$	28.0408	0.957854	0.478927	+	0.877855i	$0.341026\pi$
$858$	−74.7154	−2.55074
$859$	11.5724	0.394844	0.197422	−	0.980319i	$-0.436743\pi$
$859$	11.5724	0.394844	0.197422	+	0.980319i	$0.436743\pi$
$860$	−3.19980	−0.109112
$861$	−42.4511	−1.44673
$862$	−32.2843	−1.09961
$863$	53.8138	1.83184	0.915921	−	0.401359i	$-0.131462\pi$
$863$	53.8138	1.83184	0.915921	+	0.401359i	$0.131462\pi$
$864$	0.414214	0.0140918
$865$	6.80917	0.231519
$866$	10.7926	0.366749
$867$	1.83788	0.0624177
$868$	34.6239	1.17521
$869$	92.0339	3.12204
$870$	−2.14626	−0.0727652
$871$	62.5685	2.12005
$872$	15.2521	0.516501
$873$	3.15197	0.106678
$874$	0	0
$875$	−5.18154	−0.175168
$876$	10.7308	0.362560
$877$	−41.1389	−1.38916	−0.694581	−	0.719415i	$-0.744410\pi$
$877$	−41.1389	−1.38916	−0.694581	+	0.719415i	$0.744410\pi$
$878$	−31.1226	−1.05034
$879$	−28.5758	−0.963837
$880$	5.27792	0.177919
$881$	30.4226	1.02496	0.512481	−	0.858698i	$-0.328726\pi$
$881$	30.4226	1.02496	0.512481	+	0.858698i	$0.328726\pi$
$882$	−56.1396	−1.89032
$883$	−25.6071	−0.861749	−0.430874	−	0.902412i	$-0.641795\pi$
$883$	−25.6071	−0.861749	−0.430874	+	0.902412i	$0.641795\pi$
$884$	24.7121	0.831157
$885$	−7.24264	−0.243459
$886$	−3.21342	−0.107957
$887$	25.6099	0.859895	0.429948	−	0.902854i	$-0.358532\pi$
$887$	25.6099	0.859895	0.429948	+	0.902854i	$0.358532\pi$
$888$	11.6569	0.391178
$889$	−26.1421	−0.876779
$890$	−10.7785	−0.361297
$891$	50.0625	1.67716
$892$	−9.39355	−0.314519
$893$	−2.20169	−0.0736767
$894$	27.4600	0.918399
$895$	−18.6086	−0.622017
$896$	−5.18154	−0.173103
$897$	0	0
$898$	29.7812	0.993812
$899$	−5.94052	−0.198127
$900$	2.82843	0.0942809
$901$	13.6854	0.455927
$902$	−17.9109	−0.596367
$903$	40.0274	1.33203
$904$	5.40665	0.179823
$905$	18.4994	0.614940
$906$	−29.6062	−0.983601
$907$	11.5928	0.384934	0.192467	−	0.981303i	$-0.438351\pi$
$907$	11.5928	0.384934	0.192467	+	0.981303i	$0.438351\pi$
$908$	21.4052	0.710356
$909$	−46.0822	−1.52845
$910$	−30.3830	−1.00719
$911$	−34.7647	−1.15181	−0.575903	−	0.817518i	$-0.695349\pi$
$911$	−34.7647	−1.15181	−0.575903	+	0.817518i	$0.695349\pi$
$912$	−4.78434	−0.158425
$913$	−19.7873	−0.654863
$914$	−12.8763	−0.425911
$915$	−9.89774	−0.327209
$916$	5.71744	0.188909
$917$	15.0629	0.497419
$918$	−1.74567	−0.0576156
$919$	7.08657	0.233764	0.116882	−	0.993146i	$-0.462710\pi$
$919$	7.08657	0.233764	0.116882	+	0.993146i	$0.462710\pi$
$920$	0	0
$921$	−7.46286	−0.245910
$922$	−5.28345	−0.174001
$923$	40.5120	1.33347
$924$	−66.0233	−2.17201
$925$	−4.82843	−0.158758
$926$	−13.0139	−0.427663
$927$	26.4999	0.870371
$928$	0.889012	0.0291832
$929$	−20.1225	−0.660199	−0.330099	−	0.943946i	$-0.607082\pi$
$929$	−20.1225	−0.660199	−0.330099	+	0.943946i	$0.607082\pi$
$930$	16.1322	0.528995
$931$	−39.3343	−1.28913
$932$	5.49525	0.180003
$933$	−8.33421	−0.272850
$934$	19.6166	0.641874
$935$	−22.2433	−0.727434
$936$	16.5851	0.542100
$937$	33.1079	1.08159	0.540793	−	0.841156i	$-0.318124\pi$
$937$	33.1079	1.08159	0.540793	+	0.841156i	$0.318124\pi$
$938$	55.2895	1.80527
$939$	−8.39295	−0.273894
$940$	−1.11099	−0.0362364
$941$	57.3787	1.87049	0.935246	−	0.353999i	$-0.115179\pi$
$941$	57.3787	1.87049	0.935246	+	0.353999i	$0.115179\pi$
$942$	30.1762	0.983193
$943$	0	0
$944$	3.00000	0.0976417
$945$	2.14626	0.0698180
$946$	16.8883	0.549085
$947$	−35.2177	−1.14442	−0.572211	−	0.820106i	$-0.693914\pi$
$947$	−35.2177	−1.14442	−0.572211	+	0.820106i	$0.693914\pi$
$948$	−42.0980	−1.36728
$949$	−26.0633	−0.846049
$950$	1.98174	0.0642961
$951$	6.78194	0.219919
$952$	21.8372	0.707746
$953$	24.2421	0.785280	0.392640	−	0.919692i	$-0.371562\pi$
$953$	24.2421	0.785280	0.392640	+	0.919692i	$0.371562\pi$
$954$	9.18471	0.297366
$955$	13.5690	0.439084
$956$	2.30463	0.0745372
$957$	11.3278	0.366176
$958$	−14.6364	−0.472879
$959$	−91.4127	−2.95187
$960$	−2.41421	−0.0779184
$961$	13.6513	0.440364
$962$	−28.3125	−0.912830
$963$	14.3431	0.462201
$964$	17.1392	0.552017
$965$	−2.99927	−0.0965500
$966$	0	0
$967$	59.1442	1.90195	0.950975	−	0.309267i	$-0.100084\pi$
$967$	59.1442	1.90195	0.950975	+	0.309267i	$0.100084\pi$
$968$	−16.8564	−0.541785
$969$	20.1632	0.647735
$970$	1.11439	0.0357808
$971$	55.3713	1.77695	0.888475	−	0.458924i	$-0.151765\pi$
$971$	55.3713	1.77695	0.888475	+	0.458924i	$0.151765\pi$
$972$	−21.6569	−0.694644
$973$	−47.1027	−1.51004
$974$	−11.4445	−0.366705
$975$	−14.1562	−0.453362
$976$	4.09978	0.131231
$977$	34.3493	1.09893	0.549466	−	0.835516i	$-0.314831\pi$
$977$	34.3493	1.09893	0.549466	+	0.835516i	$0.314831\pi$
$978$	26.6780	0.853069
$979$	56.8882	1.81816
$980$	−19.8484	−0.634033
$981$	−43.1394	−1.37734
$982$	−23.9294	−0.763619
$983$	23.1331	0.737830	0.368915	−	0.929463i	$-0.379729\pi$
$983$	23.1331	0.737830	0.368915	+	0.929463i	$0.379729\pi$
$984$	8.19275	0.261175
$985$	−27.7108	−0.882940
$986$	−3.74666	−0.119318
$987$	13.8977	0.442370
$988$	11.6203	0.369692
$989$	0	0
$990$	−14.9282	−0.474449
$991$	39.6120	1.25832	0.629158	−	0.777277i	$-0.283400\pi$
$991$	39.6120	1.25832	0.629158	+	0.777277i	$0.283400\pi$
$992$	−6.68216	−0.212159
$993$	27.8441	0.883606
$994$	35.7990	1.13548
$995$	−3.99587	−0.126678
$996$	9.05105	0.286793
$997$	0.566153	0.0179302	0.00896512	−	0.999960i	$-0.497146\pi$
$997$	0.566153	0.0179302	0.00896512	+	0.999960i	$0.497146\pi$
$998$	−36.5779	−1.15785
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.u.1.4	✓	4
23.22	odd	2		5290.2.a.v.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.u.1.4	✓	4	1.1	even	1	trivial
5290.2.a.v.1.3	yes	4	23.22	odd	2

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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} +5.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.41421 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.41421 q^{6} +5.18154 q^{7} -1.00000 q^{8} +2.82843 q^{9} +1.00000 q^{10} -5.27792 q^{11} +2.41421 q^{12} -5.86370 q^{13} -5.18154 q^{14} -2.41421 q^{15} +1.00000 q^{16} -4.21441 q^{17} -2.82843 q^{18} -1.98174 q^{19} -1.00000 q^{20} +12.5093 q^{21} +5.27792 q^{22} -2.41421 q^{24} +1.00000 q^{25} +5.86370 q^{26} -0.414214 q^{27} +5.18154 q^{28} -0.889012 q^{29} +2.41421 q^{30} +6.68216 q^{31} -1.00000 q^{32} -12.7420 q^{33} +4.21441 q^{34} -5.18154 q^{35} +2.82843 q^{36} -4.82843 q^{37} +1.98174 q^{38} -14.1562 q^{39} +1.00000 q^{40} -3.39355 q^{41} -12.5093 q^{42} +3.19980 q^{43} -5.27792 q^{44} -2.82843 q^{45} +1.11099 q^{47} +2.41421 q^{48} +19.8484 q^{49} -1.00000 q^{50} -10.1745 q^{51} -5.86370 q^{52} -3.24728 q^{53} +0.414214 q^{54} +5.27792 q^{55} -5.18154 q^{56} -4.78434 q^{57} +0.889012 q^{58} +3.00000 q^{59} -2.41421 q^{60} +4.09978 q^{61} -6.68216 q^{62} +14.6556 q^{63} +1.00000 q^{64} +5.86370 q^{65} +12.7420 q^{66} -10.6705 q^{67} -4.21441 q^{68} +5.18154 q^{70} -6.90895 q^{71} -2.82843 q^{72} +4.44485 q^{73} +4.82843 q^{74} +2.41421 q^{75} -1.98174 q^{76} -27.3477 q^{77} +14.1562 q^{78} -17.4375 q^{79} -1.00000 q^{80} -9.48528 q^{81} +3.39355 q^{82} +3.74907 q^{83} +12.5093 q^{84} +4.21441 q^{85} -3.19980 q^{86} -2.14626 q^{87} +5.27792 q^{88} -10.7785 q^{89} +2.82843 q^{90} -30.3830 q^{91} +16.1322 q^{93} -1.11099 q^{94} +1.98174 q^{95} -2.41421 q^{96} +1.11439 q^{97} -19.8484 q^{98} -14.9282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{10} + 4 q^{12} - 8 q^{13} - 4 q^{14} - 4 q^{15} + 4 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 4 q^{25} + 8 q^{26} + 4 q^{27} + 4 q^{28} - 12 q^{29} + 4 q^{30} + 28 q^{31} - 4 q^{32} - 16 q^{33} + 12 q^{34} - 4 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} + 4 q^{40} - 8 q^{41} - 4 q^{42} + 12 q^{43} - 4 q^{47} + 4 q^{48} + 12 q^{49} - 4 q^{50} - 16 q^{51} - 8 q^{52} - 20 q^{53} - 4 q^{54} - 4 q^{56} + 12 q^{57} + 12 q^{58} + 12 q^{59} - 4 q^{60} - 28 q^{62} + 4 q^{64} + 8 q^{65} + 16 q^{66} - 12 q^{67} - 12 q^{68} + 4 q^{70} + 20 q^{71} - 16 q^{73} + 8 q^{74} + 4 q^{75} + 8 q^{76} - 24 q^{77} + 16 q^{78} + 4 q^{79} - 4 q^{80} - 4 q^{81} + 8 q^{82} - 12 q^{83} + 4 q^{84} + 12 q^{85} - 12 q^{86} + 4 q^{87} - 40 q^{89} - 32 q^{91} + 36 q^{93} + 4 q^{94} - 8 q^{95} - 4 q^{96} - 16 q^{97} - 12 q^{98} - 32 q^{99}+O(q^{100}) \) 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 + 4 * q^12 - 8 * q^13 - 4 * q^14 - 4 * q^15 + 4 * q^16 - 12 * q^17 + 8 * q^19 - 4 * q^20 + 4 * q^21 - 4 * q^24 + 4 * q^25 + 8 * q^26 + 4 * q^27 + 4 * q^28 - 12 * q^29 + 4 * q^30 + 28 * q^31 - 4 * q^32 - 16 * q^33 + 12 * q^34 - 4 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 + 4 * q^40 - 8 * q^41 - 4 * q^42 + 12 * q^43 - 4 * q^47 + 4 * q^48 + 12 * q^49 - 4 * q^50 - 16 * q^51 - 8 * q^52 - 20 * q^53 - 4 * q^54 - 4 * q^56 + 12 * q^57 + 12 * q^58 + 12 * q^59 - 4 * q^60 - 28 * q^62 + 4 * q^64 + 8 * q^65 + 16 * q^66 - 12 * q^67 - 12 * q^68 + 4 * q^70 + 20 * q^71 - 16 * q^73 + 8 * q^74 + 4 * q^75 + 8 * q^76 - 24 * q^77 + 16 * q^78 + 4 * q^79 - 4 * q^80 - 4 * q^81 + 8 * q^82 - 12 * q^83 + 4 * q^84 + 12 * q^85 - 12 * q^86 + 4 * q^87 - 40 * q^89 - 32 * q^91 + 36 * q^93 + 4 * q^94 - 8 * q^95 - 4 * q^96 - 16 * q^97 - 12 * q^98 - 32 * q^99

Introduction

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