LMFDB - Embedded newform 5070.2.a.ca.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5070,2,Mod(1,5070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5070, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5070.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5070.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:	$40.4841538248$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.131472.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 19x^{2} + 20x + 52 $ x^4 - 2x^3 - 19x^2 + 20*x + 52
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$4.64466$ of defining polynomial
Character	$\chi$	$=$	5070.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.40013 q^{11} +1.00000 q^{12} +4.64466 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +8.04479 q^{19} -1.00000 q^{20} +4.64466 q^{21} -4.40013 q^{22} -0.976584 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +4.64466 q^{28} -4.31274 q^{29} -1.00000 q^{30} +6.44069 q^{31} +1.00000 q^{32} -4.40013 q^{33} +4.00000 q^{34} -4.64466 q^{35} +1.00000 q^{36} -3.79603 q^{37} +8.04479 q^{38} -1.00000 q^{40} -7.28932 q^{41} +4.64466 q^{42} +0.716456 q^{43} -4.40013 q^{44} -1.00000 q^{45} -0.976584 q^{46} -9.75342 q^{47} +1.00000 q^{48} +14.5729 q^{49} +1.00000 q^{50} +4.00000 q^{51} +13.5089 q^{53} +1.00000 q^{54} +4.40013 q^{55} +4.64466 q^{56} +8.04479 q^{57} -4.31274 q^{58} -2.18056 q^{59} -1.00000 q^{60} +7.46410 q^{61} +6.44069 q^{62} +4.64466 q^{63} +1.00000 q^{64} -4.40013 q^{66} -1.82522 q^{67} +4.00000 q^{68} -0.976584 q^{69} -4.64466 q^{70} +7.95317 q^{71} +1.00000 q^{72} +4.36112 q^{73} -3.79603 q^{74} +1.00000 q^{75} +8.04479 q^{76} -20.4371 q^{77} -14.9340 q^{79} -1.00000 q^{80} +1.00000 q^{81} -7.28932 q^{82} +3.51093 q^{83} +4.64466 q^{84} -4.00000 q^{85} +0.716456 q^{86} -4.31274 q^{87} -4.40013 q^{88} -8.17274 q^{89} -1.00000 q^{90} -0.976584 q^{92} +6.44069 q^{93} -9.75342 q^{94} -8.04479 q^{95} +1.00000 q^{96} -13.8252 q^{97} +14.5729 q^{98} -4.40013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 2 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 4 q^{16} + 16 q^{17} + 4 q^{18} - 4 q^{20} + 2 q^{21} - 2 q^{22} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{27} + 2 q^{28} + 8 q^{29} - 4 q^{30} + 4 q^{31} + 4 q^{32} - 2 q^{33} + 16 q^{34} - 2 q^{35} + 4 q^{36} - 10 q^{37} - 4 q^{40} + 4 q^{41} + 2 q^{42} + 14 q^{43} - 2 q^{44} - 4 q^{45} + 4 q^{46} + 8 q^{47} + 4 q^{48} + 14 q^{49} + 4 q^{50} + 16 q^{51} + 8 q^{53} + 4 q^{54} + 2 q^{55} + 2 q^{56} + 8 q^{58} - 6 q^{59} - 4 q^{60} + 16 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{66} + 12 q^{67} + 16 q^{68} + 4 q^{69} - 2 q^{70} + 16 q^{71} + 4 q^{72} + 12 q^{73} - 10 q^{74} + 4 q^{75} - 8 q^{77} - 10 q^{79} - 4 q^{80} + 4 q^{81} + 4 q^{82} + 16 q^{83} + 2 q^{84} - 16 q^{85} + 14 q^{86} + 8 q^{87} - 2 q^{88} - 4 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} + 8 q^{94} + 4 q^{96} - 36 q^{97} + 14 q^{98} - 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 2 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 4 * q^16 + 16 * q^17 + 4 * q^18 - 4 * q^20 + 2 * q^21 - 2 * q^22 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^27 + 2 * q^28 + 8 * q^29 - 4 * q^30 + 4 * q^31 + 4 * q^32 - 2 * q^33 + 16 * q^34 - 2 * q^35 + 4 * q^36 - 10 * q^37 - 4 * q^40 + 4 * q^41 + 2 * q^42 + 14 * q^43 - 2 * q^44 - 4 * q^45 + 4 * q^46 + 8 * q^47 + 4 * q^48 + 14 * q^49 + 4 * q^50 + 16 * q^51 + 8 * q^53 + 4 * q^54 + 2 * q^55 + 2 * q^56 + 8 * q^58 - 6 * q^59 - 4 * q^60 + 16 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 - 2 * q^66 + 12 * q^67 + 16 * q^68 + 4 * q^69 - 2 * q^70 + 16 * q^71 + 4 * q^72 + 12 * q^73 - 10 * q^74 + 4 * q^75 - 8 * q^77 - 10 * q^79 - 4 * q^80 + 4 * q^81 + 4 * q^82 + 16 * q^83 + 2 * q^84 - 16 * q^85 + 14 * q^86 + 8 * q^87 - 2 * q^88 - 4 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 + 8 * q^94 + 4 * q^96 - 36 * q^97 + 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	4.64466	1.75552	0.877758	−	0.479104i	$-0.159038\pi$
$7$	4.64466	1.75552	0.877758	+	0.479104i	$0.159038\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−4.40013	−1.32669	−0.663344	−	0.748315i	$-0.730863\pi$
$11$	−4.40013	−1.32669	−0.663344	+	0.748315i	$0.730863\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	4.64466	1.24134
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	1.00000	0.235702
$19$	8.04479	1.84560	0.922800	−	0.385279i	$-0.125895\pi$
$19$	8.04479	1.84560	0.922800	+	0.385279i	$0.125895\pi$
$20$	−1.00000	−0.223607
$21$	4.64466	1.01355
$22$	−4.40013	−0.938110
$23$	−0.976584	−0.203632	−0.101816	−	0.994803i	$-0.532465\pi$
$23$	−0.976584	−0.203632	−0.101816	+	0.994803i	$0.532465\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	4.64466	0.877758
$29$	−4.31274	−0.800855	−0.400427	−	0.916328i	$-0.631138\pi$
$29$	−4.31274	−0.800855	−0.400427	+	0.916328i	$0.631138\pi$
$30$	−1.00000	−0.182574
$31$	6.44069	1.15678	0.578391	−	0.815760i	$-0.303681\pi$
$31$	6.44069	1.15678	0.578391	+	0.815760i	$0.303681\pi$
$32$	1.00000	0.176777
$33$	−4.40013	−0.765964
$34$	4.00000	0.685994
$35$	−4.64466	−0.785091
$36$	1.00000	0.166667
$37$	−3.79603	−0.624063	−0.312031	−	0.950072i	$-0.601009\pi$
$37$	−3.79603	−0.624063	−0.312031	+	0.950072i	$0.601009\pi$
$38$	8.04479	1.30504
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−7.28932	−1.13840	−0.569200	−	0.822199i	$-0.692747\pi$
$41$	−7.28932	−1.13840	−0.569200	+	0.822199i	$0.692747\pi$
$42$	4.64466	0.716687
$43$	0.716456	0.109259	0.0546293	−	0.998507i	$-0.482602\pi$
$43$	0.716456	0.109259	0.0546293	+	0.998507i	$0.482602\pi$
$44$	−4.40013	−0.663344
$45$	−1.00000	−0.149071
$46$	−0.976584	−0.143989
$47$	−9.75342	−1.42268	−0.711341	−	0.702847i	$-0.751912\pi$
$47$	−9.75342	−1.42268	−0.711341	+	0.702847i	$0.751912\pi$
$48$	1.00000	0.144338
$49$	14.5729	2.08184
$50$	1.00000	0.141421
$51$	4.00000	0.560112
$52$	0	0
$53$	13.5089	1.85559	0.927794	−	0.373092i	$-0.121703\pi$
$53$	13.5089	1.85559	0.927794	+	0.373092i	$0.121703\pi$
$54$	1.00000	0.136083
$55$	4.40013	0.593313
$56$	4.64466	0.620669
$57$	8.04479	1.06556
$58$	−4.31274	−0.566290
$59$	−2.18056	−0.283884	−0.141942	−	0.989875i	$-0.545335\pi$
$59$	−2.18056	−0.283884	−0.141942	+	0.989875i	$0.545335\pi$
$60$	−1.00000	−0.129099
$61$	7.46410	0.955680	0.477840	−	0.878447i	$-0.341420\pi$
$61$	7.46410	0.955680	0.477840	+	0.878447i	$0.341420\pi$
$62$	6.44069	0.817968
$63$	4.64466	0.585172
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.40013	−0.541618
$67$	−1.82522	−0.222986	−0.111493	−	0.993765i	$-0.535563\pi$
$67$	−1.82522	−0.222986	−0.111493	+	0.993765i	$0.535563\pi$
$68$	4.00000	0.485071
$69$	−0.976584	−0.117567
$70$	−4.64466	−0.555143
$71$	7.95317	0.943867	0.471934	−	0.881634i	$-0.343556\pi$
$71$	7.95317	0.943867	0.471934	+	0.881634i	$0.343556\pi$
$72$	1.00000	0.117851
$73$	4.36112	0.510430	0.255215	−	0.966884i	$-0.417854\pi$
$73$	4.36112	0.510430	0.255215	+	0.966884i	$0.417854\pi$
$74$	−3.79603	−0.441279
$75$	1.00000	0.115470
$76$	8.04479	0.922800
$77$	−20.4371	−2.32902
$78$	0	0
$79$	−14.9340	−1.68020	−0.840102	−	0.542429i	$-0.817505\pi$
$79$	−14.9340	−1.68020	−0.840102	+	0.542429i	$0.817505\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−7.28932	−0.804971
$83$	3.51093	0.385375	0.192688	−	0.981260i	$-0.438280\pi$
$83$	3.51093	0.385375	0.192688	+	0.981260i	$0.438280\pi$
$84$	4.64466	0.506774
$85$	−4.00000	−0.433861
$86$	0.716456	0.0772575
$87$	−4.31274	−0.462374
$88$	−4.40013	−0.469055
$89$	−8.17274	−0.866308	−0.433154	−	0.901320i	$-0.642599\pi$
$89$	−8.17274	−0.866308	−0.433154	+	0.901320i	$0.642599\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−0.976584	−0.101816
$93$	6.44069	0.667868
$94$	−9.75342	−1.00599
$95$	−8.04479	−0.825378
$96$	1.00000	0.102062
$97$	−13.8252	−1.40374	−0.701869	−	0.712306i	$-0.747651\pi$
$97$	−13.8252	−1.40374	−0.701869	+	0.712306i	$0.747651\pi$
$98$	14.5729	1.47208
$99$	−4.40013	−0.442229
$100$	1.00000	0.100000
$101$	−6.80025	−0.676651	−0.338325	−	0.941029i	$-0.609860\pi$
$101$	−6.80025	−0.676651	−0.338325	+	0.941029i	$0.609860\pi$
$102$	4.00000	0.396059
$103$	5.29137	0.521374	0.260687	−	0.965423i	$-0.416051\pi$
$103$	5.29137	0.521374	0.260687	+	0.965423i	$0.416051\pi$
$104$	0	0
$105$	−4.64466	−0.453272
$106$	13.5089	1.31210
$107$	16.9282	1.63651	0.818256	−	0.574855i	$-0.194941\pi$
$107$	16.9282	1.63651	0.818256	+	0.574855i	$0.194941\pi$
$108$	1.00000	0.0962250
$109$	12.8003	1.22604	0.613021	−	0.790067i	$-0.289954\pi$
$109$	12.8003	1.22604	0.613021	+	0.790067i	$0.289954\pi$
$110$	4.40013	0.419536
$111$	−3.79603	−0.360303
$112$	4.64466	0.438879
$113$	13.0662	1.22916	0.614580	−	0.788854i	$-0.289325\pi$
$113$	13.0662	1.22916	0.614580	+	0.788854i	$0.289325\pi$
$114$	8.04479	0.753463
$115$	0.976584	0.0910669
$116$	−4.31274	−0.400427
$117$	0	0
$118$	−2.18056	−0.200737
$119$	18.5786	1.70310
$120$	−1.00000	−0.0912871
$121$	8.36112	0.760101
$122$	7.46410	0.675768
$123$	−7.28932	−0.657256
$124$	6.44069	0.578391
$125$	−1.00000	−0.0894427
$126$	4.64466	0.413779
$127$	12.2196	1.08431	0.542156	−	0.840278i	$-0.317608\pi$
$127$	12.2196	1.08431	0.542156	+	0.840278i	$0.317608\pi$
$128$	1.00000	0.0883883
$129$	0.716456	0.0630805
$130$	0	0
$131$	−0.378757	−0.0330921	−0.0165461	−	0.999863i	$-0.505267\pi$
$131$	−0.378757	−0.0330921	−0.0165461	+	0.999863i	$0.505267\pi$
$132$	−4.40013	−0.382982
$133$	37.3653	3.23998
$134$	−1.82522	−0.157675
$135$	−1.00000	−0.0860663
$136$	4.00000	0.342997
$137$	−1.25235	−0.106996	−0.0534979	−	0.998568i	$-0.517037\pi$
$137$	−1.25235	−0.106996	−0.0534979	+	0.998568i	$0.517037\pi$
$138$	−0.976584	−0.0831323
$139$	3.35534	0.284596	0.142298	−	0.989824i	$-0.454551\pi$
$139$	3.35534	0.284596	0.142298	+	0.989824i	$0.454551\pi$
$140$	−4.64466	−0.392545
$141$	−9.75342	−0.821386
$142$	7.95317	0.667415
$143$	0	0
$144$	1.00000	0.0833333
$145$	4.31274	0.358153
$146$	4.36112	0.360929
$147$	14.5729	1.20195
$148$	−3.79603	−0.312031
$149$	4.61970	0.378460	0.189230	−	0.981933i	$-0.439401\pi$
$149$	4.61970	0.378460	0.189230	+	0.981933i	$0.439401\pi$
$150$	1.00000	0.0816497
$151$	−11.2425	−0.914901	−0.457450	−	0.889235i	$-0.651237\pi$
$151$	−11.2425	−0.914901	−0.457450	+	0.889235i	$0.651237\pi$
$152$	8.04479	0.652518
$153$	4.00000	0.323381
$154$	−20.4371	−1.64687
$155$	−6.44069	−0.517328
$156$	0	0
$157$	−1.50311	−0.119961	−0.0599807	−	0.998200i	$-0.519104\pi$
$157$	−1.50311	−0.119961	−0.0599807	+	0.998200i	$0.519104\pi$
$158$	−14.9340	−1.18808
$159$	13.5089	1.07132
$160$	−1.00000	−0.0790569
$161$	−4.53590	−0.357479
$162$	1.00000	0.0785674
$163$	−0.176330	−0.0138112	−0.00690561	−	0.999976i	$-0.502198\pi$
$163$	−0.176330	−0.0138112	−0.00690561	+	0.999976i	$0.502198\pi$
$164$	−7.28932	−0.569200
$165$	4.40013	0.342549
$166$	3.51093	0.272501
$167$	−8.68162	−0.671804	−0.335902	−	0.941897i	$-0.609041\pi$
$167$	−8.68162	−0.671804	−0.335902	+	0.941897i	$0.609041\pi$
$168$	4.64466	0.358343
$169$	0	0
$170$	−4.00000	−0.306786
$171$	8.04479	0.615200
$172$	0.716456	0.0546293
$173$	1.78043	0.135364	0.0676818	−	0.997707i	$-0.478440\pi$
$173$	1.78043	0.135364	0.0676818	+	0.997707i	$0.478440\pi$
$174$	−4.31274	−0.326948
$175$	4.64466	0.351103
$176$	−4.40013	−0.331672
$177$	−2.18056	−0.163901
$178$	−8.17274	−0.612572
$179$	−17.4157	−1.30171	−0.650856	−	0.759201i	$-0.725590\pi$
$179$	−17.4157	−1.30171	−0.650856	+	0.759201i	$0.725590\pi$
$180$	−1.00000	−0.0745356
$181$	10.3611	0.770136	0.385068	−	0.922888i	$-0.374178\pi$
$181$	10.3611	0.770136	0.385068	+	0.922888i	$0.374178\pi$
$182$	0	0
$183$	7.46410	0.551762
$184$	−0.976584	−0.0719947
$185$	3.79603	0.279089
$186$	6.44069	0.472254
$187$	−17.6005	−1.28708
$188$	−9.75342	−0.711341
$189$	4.64466	0.337849
$190$	−8.04479	−0.583630
$191$	−0.897014	−0.0649057	−0.0324528	−	0.999473i	$-0.510332\pi$
$191$	−0.897014	−0.0649057	−0.0324528	+	0.999473i	$0.510332\pi$
$192$	1.00000	0.0721688
$193$	−20.2644	−1.45866	−0.729330	−	0.684162i	$-0.760168\pi$
$193$	−20.2644	−1.45866	−0.729330	+	0.684162i	$0.760168\pi$
$194$	−13.8252	−0.992593
$195$	0	0
$196$	14.5729	1.04092
$197$	9.18056	0.654088	0.327044	−	0.945009i	$-0.393948\pi$
$197$	9.18056	0.654088	0.327044	+	0.945009i	$0.393948\pi$
$198$	−4.40013	−0.312703
$199$	−16.2175	−1.14963	−0.574815	−	0.818284i	$-0.694926\pi$
$199$	−16.2175	−1.14963	−0.574815	+	0.818284i	$0.694926\pi$
$200$	1.00000	0.0707107
$201$	−1.82522	−0.128741
$202$	−6.80025	−0.478464
$203$	−20.0312	−1.40591
$204$	4.00000	0.280056
$205$	7.28932	0.509108
$206$	5.29137	0.368667
$207$	−0.976584	−0.0678773
$208$	0	0
$209$	−35.3981	−2.44854
$210$	−4.64466	−0.320512
$211$	−1.61970	−0.111504	−0.0557522	−	0.998445i	$-0.517756\pi$
$211$	−1.61970	−0.111504	−0.0557522	+	0.998445i	$0.517756\pi$
$212$	13.5089	0.927794
$213$	7.95317	0.544942
$214$	16.9282	1.15719
$215$	−0.716456	−0.0488619
$216$	1.00000	0.0680414
$217$	29.9148	2.03075
$218$	12.8003	0.866943
$219$	4.36112	0.294697
$220$	4.40013	0.296656
$221$	0	0
$222$	−3.79603	−0.254773
$223$	2.23671	0.149781	0.0748906	−	0.997192i	$-0.476139\pi$
$223$	2.23671	0.149781	0.0748906	+	0.997192i	$0.476139\pi$
$224$	4.64466	0.310334
$225$	1.00000	0.0666667
$226$	13.0662	0.869148
$227$	15.3205	1.01686	0.508429	−	0.861104i	$-0.330226\pi$
$227$	15.3205	1.01686	0.508429	+	0.861104i	$0.330226\pi$
$228$	8.04479	0.532779
$229$	10.1279	0.669274	0.334637	−	0.942347i	$-0.391386\pi$
$229$	10.1279	0.669274	0.334637	+	0.942347i	$0.391386\pi$
$230$	0.976584	0.0643940
$231$	−20.4371	−1.34466
$232$	−4.31274	−0.283145
$233$	−20.7519	−1.35950	−0.679750	−	0.733444i	$-0.737912\pi$
$233$	−20.7519	−1.35950	−0.679750	+	0.733444i	$0.737912\pi$
$234$	0	0
$235$	9.75342	0.636243
$236$	−2.18056	−0.141942
$237$	−14.9340	−0.970066
$238$	18.5786	1.20427
$239$	−24.3539	−1.57532	−0.787662	−	0.616107i	$-0.788709\pi$
$239$	−24.3539	−1.57532	−0.787662	+	0.616107i	$0.788709\pi$
$240$	−1.00000	−0.0645497
$241$	−19.8685	−1.27984	−0.639920	−	0.768442i	$-0.721032\pi$
$241$	−19.8685	−1.27984	−0.639920	+	0.768442i	$0.721032\pi$
$242$	8.36112	0.537473
$243$	1.00000	0.0641500
$244$	7.46410	0.477840
$245$	−14.5729	−0.931026
$246$	−7.28932	−0.464750
$247$	0	0
$248$	6.44069	0.408984
$249$	3.51093	0.222496
$250$	−1.00000	−0.0632456
$251$	13.5713	0.856614	0.428307	−	0.903633i	$-0.359110\pi$
$251$	13.5713	0.856614	0.428307	+	0.903633i	$0.359110\pi$
$252$	4.64466	0.292586
$253$	4.29709	0.270156
$254$	12.2196	0.766724
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	0.662300	0.0413132	0.0206566	−	0.999787i	$-0.493424\pi$
$257$	0.662300	0.0413132	0.0206566	+	0.999787i	$0.493424\pi$
$258$	0.716456	0.0446046
$259$	−17.6312	−1.09555
$260$	0	0
$261$	−4.31274	−0.266952
$262$	−0.378757	−0.0233997
$263$	30.7498	1.89612	0.948058	−	0.318098i	$-0.103044\pi$
$263$	30.7498	1.89612	0.948058	+	0.318098i	$0.103044\pi$
$264$	−4.40013	−0.270809
$265$	−13.5089	−0.829844
$266$	37.3653	2.29101
$267$	−8.17274	−0.500163
$268$	−1.82522	−0.111493
$269$	−3.74410	−0.228282	−0.114141	−	0.993465i	$-0.536412\pi$
$269$	−3.74410	−0.228282	−0.114141	+	0.993465i	$0.536412\pi$
$270$	−1.00000	−0.0608581
$271$	−27.7612	−1.68637	−0.843186	−	0.537622i	$-0.819323\pi$
$271$	−27.7612	−1.68637	−0.843186	+	0.537622i	$0.819323\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−1.25235	−0.0756575
$275$	−4.40013	−0.265338
$276$	−0.976584	−0.0587834
$277$	11.9922	0.720540	0.360270	−	0.932848i	$-0.382685\pi$
$277$	11.9922	0.720540	0.360270	+	0.932848i	$0.382685\pi$
$278$	3.35534	0.201240
$279$	6.44069	0.385594
$280$	−4.64466	−0.277572
$281$	−3.63888	−0.217078	−0.108539	−	0.994092i	$-0.534617\pi$
$281$	−3.63888	−0.217078	−0.108539	+	0.994092i	$0.534617\pi$
$282$	−9.75342	−0.580808
$283$	4.84441	0.287970	0.143985	−	0.989580i	$-0.454008\pi$
$283$	4.84441	0.287970	0.143985	+	0.989580i	$0.454008\pi$
$284$	7.95317	0.471934
$285$	−8.04479	−0.476532
$286$	0	0
$287$	−33.8564	−1.99848
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	4.31274	0.253253
$291$	−13.8252	−0.810449
$292$	4.36112	0.255215
$293$	3.70081	0.216204	0.108102	−	0.994140i	$-0.465523\pi$
$293$	3.70081	0.216204	0.108102	+	0.994140i	$0.465523\pi$
$294$	14.5729	0.849907
$295$	2.18056	0.126957
$296$	−3.79603	−0.220640
$297$	−4.40013	−0.255321
$298$	4.61970	0.267612
$299$	0	0
$300$	1.00000	0.0577350
$301$	3.32770	0.191805
$302$	−11.2425	−0.646932
$303$	−6.80025	−0.390664
$304$	8.04479	0.461400
$305$	−7.46410	−0.427393
$306$	4.00000	0.228665
$307$	7.11454	0.406048	0.203024	−	0.979174i	$-0.434923\pi$
$307$	7.11454	0.406048	0.203024	+	0.979174i	$0.434923\pi$
$308$	−20.4371	−1.16451
$309$	5.29137	0.301015
$310$	−6.44069	−0.365806
$311$	19.9148	1.12926	0.564632	−	0.825343i	$-0.309018\pi$
$311$	19.9148	1.12926	0.564632	+	0.825343i	$0.309018\pi$
$312$	0	0
$313$	6.13950	0.347025	0.173513	−	0.984832i	$-0.444488\pi$
$313$	6.13950	0.347025	0.173513	+	0.984832i	$0.444488\pi$
$314$	−1.50311	−0.0848255
$315$	−4.64466	−0.261697
$316$	−14.9340	−0.840102
$317$	7.85286	0.441061	0.220530	−	0.975380i	$-0.429221\pi$
$317$	7.85286	0.441061	0.220530	+	0.975380i	$0.429221\pi$
$318$	13.5089	0.757541
$319$	18.9766	1.06248
$320$	−1.00000	−0.0559017
$321$	16.9282	0.944840
$322$	−4.53590	−0.252776
$323$	32.1791	1.79050
$324$	1.00000	0.0555556
$325$	0	0
$326$	−0.176330	−0.00976601
$327$	12.8003	0.707856
$328$	−7.28932	−0.402485
$329$	−45.3013	−2.49754
$330$	4.40013	0.242219
$331$	−31.9959	−1.75865	−0.879327	−	0.476218i	$-0.842007\pi$
$331$	−31.9959	−1.75865	−0.879327	+	0.476218i	$0.842007\pi$
$332$	3.51093	0.192688
$333$	−3.79603	−0.208021
$334$	−8.68162	−0.475037
$335$	1.82522	0.0997223
$336$	4.64466	0.253387
$337$	35.6432	1.94161	0.970806	−	0.239867i	$-0.0771039\pi$
$337$	35.6432	1.94161	0.970806	+	0.239867i	$0.0771039\pi$
$338$	0	0
$339$	13.0662	0.709656
$340$	−4.00000	−0.216930
$341$	−28.3398	−1.53469
$342$	8.04479	0.435012
$343$	35.1734	1.89918
$344$	0.716456	0.0386287
$345$	0.976584	0.0525775
$346$	1.78043	0.0957166
$347$	−6.89701	−0.370251	−0.185126	−	0.982715i	$-0.559269\pi$
$347$	−6.89701	−0.370251	−0.185126	+	0.982715i	$0.559269\pi$
$348$	−4.31274	−0.231187
$349$	−19.3205	−1.03420	−0.517102	−	0.855924i	$-0.672989\pi$
$349$	−19.3205	−1.03420	−0.517102	+	0.855924i	$0.672989\pi$
$350$	4.64466	0.248267
$351$	0	0
$352$	−4.40013	−0.234528
$353$	−27.4173	−1.45927	−0.729637	−	0.683835i	$-0.760311\pi$
$353$	−27.4173	−1.45927	−0.729637	+	0.683835i	$0.760311\pi$
$354$	−2.18056	−0.115895
$355$	−7.95317	−0.422110
$356$	−8.17274	−0.433154
$357$	18.5786	0.983286
$358$	−17.4157	−0.920449
$359$	−14.3611	−0.757951	−0.378975	−	0.925407i	$-0.623723\pi$
$359$	−14.3611	−0.757951	−0.378975	+	0.925407i	$0.623723\pi$
$360$	−1.00000	−0.0527046
$361$	45.7186	2.40624
$362$	10.3611	0.544568
$363$	8.36112	0.438845
$364$	0	0
$365$	−4.36112	−0.228271
$366$	7.46410	0.390155
$367$	−13.7753	−0.719064	−0.359532	−	0.933133i	$-0.617064\pi$
$367$	−13.7753	−0.719064	−0.359532	+	0.933133i	$0.617064\pi$
$368$	−0.976584	−0.0509079
$369$	−7.28932	−0.379467
$370$	3.79603	0.197346
$371$	62.7442	3.25752
$372$	6.44069	0.333934
$373$	−33.4627	−1.73263	−0.866316	−	0.499496i	$-0.833519\pi$
$373$	−33.4627	−1.73263	−0.866316	+	0.499496i	$0.833519\pi$
$374$	−17.6005	−0.910101
$375$	−1.00000	−0.0516398
$376$	−9.75342	−0.502994
$377$	0	0
$378$	4.64466	0.238896
$379$	−33.3768	−1.71445	−0.857227	−	0.514939i	$-0.827814\pi$
$379$	−33.3768	−1.71445	−0.857227	+	0.514939i	$0.827814\pi$
$380$	−8.04479	−0.412689
$381$	12.2196	0.626027
$382$	−0.897014	−0.0458952
$383$	−7.33038	−0.374565	−0.187282	−	0.982306i	$-0.559968\pi$
$383$	−7.33038	−0.374565	−0.187282	+	0.982306i	$0.559968\pi$
$384$	1.00000	0.0510310
$385$	20.4371	1.04157
$386$	−20.2644	−1.03143
$387$	0.716456	0.0364195
$388$	−13.8252	−0.701869
$389$	32.6198	1.65389	0.826946	−	0.562282i	$-0.190076\pi$
$389$	32.6198	1.65389	0.826946	+	0.562282i	$0.190076\pi$
$390$	0	0
$391$	−3.90633	−0.197552
$392$	14.5729	0.736041
$393$	−0.378757	−0.0191058
$394$	9.18056	0.462510
$395$	14.9340	0.751410
$396$	−4.40013	−0.221115
$397$	14.4683	0.726145	0.363072	−	0.931761i	$-0.381728\pi$
$397$	14.4683	0.726145	0.363072	+	0.931761i	$0.381728\pi$
$398$	−16.2175	−0.812911
$399$	37.3653	1.87060
$400$	1.00000	0.0500000
$401$	7.28727	0.363909	0.181955	−	0.983307i	$-0.441758\pi$
$401$	7.28727	0.363909	0.181955	+	0.983307i	$0.441758\pi$
$402$	−1.82522	−0.0910336
$403$	0	0
$404$	−6.80025	−0.338325
$405$	−1.00000	−0.0496904
$406$	−20.0312	−0.994131
$407$	16.7030	0.827937
$408$	4.00000	0.198030
$409$	24.5766	1.21523	0.607617	−	0.794230i	$-0.292126\pi$
$409$	24.5766	1.21523	0.607617	+	0.794230i	$0.292126\pi$
$410$	7.28932	0.359994
$411$	−1.25235	−0.0617741
$412$	5.29137	0.260687
$413$	−10.1279	−0.498364
$414$	−0.976584	−0.0479965
$415$	−3.51093	−0.172345
$416$	0	0
$417$	3.35534	0.164312
$418$	−35.3981	−1.73138
$419$	15.5537	0.759847	0.379923	−	0.925018i	$-0.375950\pi$
$419$	15.5537	0.759847	0.379923	+	0.925018i	$0.375950\pi$
$420$	−4.64466	−0.226636
$421$	−22.3143	−1.08753	−0.543766	−	0.839237i	$-0.683002\pi$
$421$	−22.3143	−1.08753	−0.543766	+	0.839237i	$0.683002\pi$
$422$	−1.61970	−0.0788456
$423$	−9.75342	−0.474228
$424$	13.5089	0.656050
$425$	4.00000	0.194029
$426$	7.95317	0.385332
$427$	34.6682	1.67771
$428$	16.9282	0.818256
$429$	0	0
$430$	−0.716456	−0.0345506
$431$	24.2644	1.16877	0.584386	−	0.811476i	$-0.301335\pi$
$431$	24.2644	1.16877	0.584386	+	0.811476i	$0.301335\pi$
$432$	1.00000	0.0481125
$433$	−23.0989	−1.11006	−0.555031	−	0.831830i	$-0.687294\pi$
$433$	−23.0989	−1.11006	−0.555031	+	0.831830i	$0.687294\pi$
$434$	29.9148	1.43596
$435$	4.31274	0.206780
$436$	12.8003	0.613021
$437$	−7.85641	−0.375823
$438$	4.36112	0.208382
$439$	−39.9959	−1.90890	−0.954450	−	0.298370i	$-0.903557\pi$
$439$	−39.9959	−1.90890	−0.954450	+	0.298370i	$0.903557\pi$
$440$	4.40013	0.209768
$441$	14.5729	0.693946
$442$	0	0
$443$	−15.6036	−0.741350	−0.370675	−	0.928763i	$-0.620874\pi$
$443$	−15.6036	−0.741350	−0.370675	+	0.928763i	$0.620874\pi$
$444$	−3.79603	−0.180151
$445$	8.17274	0.387425
$446$	2.23671	0.105911
$447$	4.61970	0.218504
$448$	4.64466	0.219440
$449$	27.0042	1.27441	0.637203	−	0.770696i	$-0.280091\pi$
$449$	27.0042	1.27441	0.637203	+	0.770696i	$0.280091\pi$
$450$	1.00000	0.0471405
$451$	32.0739	1.51030
$452$	13.0662	0.614580
$453$	−11.2425	−0.528218
$454$	15.3205	0.719027
$455$	0	0
$456$	8.04479	0.376732
$457$	17.7868	0.832033	0.416017	−	0.909357i	$-0.363426\pi$
$457$	17.7868	0.832033	0.416017	+	0.909357i	$0.363426\pi$
$458$	10.1279	0.473248
$459$	4.00000	0.186704
$460$	0.976584	0.0455334
$461$	−24.9652	−1.16274	−0.581372	−	0.813638i	$-0.697484\pi$
$461$	−24.9652	−1.16274	−0.581372	+	0.813638i	$0.697484\pi$
$462$	−20.4371	−0.950820
$463$	−15.6389	−0.726801	−0.363400	−	0.931633i	$-0.618384\pi$
$463$	−15.6389	−0.726801	−0.363400	+	0.931633i	$0.618384\pi$
$464$	−4.31274	−0.200214
$465$	−6.44069	−0.298680
$466$	−20.7519	−0.961312
$467$	2.43914	0.112870	0.0564349	−	0.998406i	$-0.482027\pi$
$467$	2.43914	0.112870	0.0564349	+	0.998406i	$0.482027\pi$
$468$	0	0
$469$	−8.47751	−0.391455
$470$	9.75342	0.449892
$471$	−1.50311	−0.0692598
$472$	−2.18056	−0.100368
$473$	−3.15250	−0.144952
$474$	−14.9340	−0.685940
$475$	8.04479	0.369120
$476$	18.5786	0.851550
$477$	13.5089	0.618529
$478$	−24.3539	−1.11392
$479$	−14.1863	−0.648190	−0.324095	−	0.946025i	$-0.605060\pi$
$479$	−14.1863	−0.648190	−0.324095	+	0.946025i	$0.605060\pi$
$480$	−1.00000	−0.0456435
$481$	0	0
$482$	−19.8685	−0.904983
$483$	−4.53590	−0.206391
$484$	8.36112	0.380051
$485$	13.8252	0.627771
$486$	1.00000	0.0453609
$487$	−5.76329	−0.261160	−0.130580	−	0.991438i	$-0.541684\pi$
$487$	−5.76329	−0.261160	−0.130580	+	0.991438i	$0.541684\pi$
$488$	7.46410	0.337884
$489$	−0.176330	−0.00797392
$490$	−14.5729	−0.658335
$491$	−1.07534	−0.0485295	−0.0242647	−	0.999706i	$-0.507724\pi$
$491$	−1.07534	−0.0485295	−0.0242647	+	0.999706i	$0.507724\pi$
$492$	−7.28932	−0.328628
$493$	−17.2509	−0.776943
$494$	0	0
$495$	4.40013	0.197771
$496$	6.44069	0.289195
$497$	36.9398	1.65697
$498$	3.51093	0.157329
$499$	14.7534	0.660454	0.330227	−	0.943902i	$-0.392875\pi$
$499$	14.7534	0.660454	0.330227	+	0.943902i	$0.392875\pi$
$500$	−1.00000	−0.0447214
$501$	−8.68162	−0.387866
$502$	13.5713	0.605717
$503$	−26.6618	−1.18879	−0.594395	−	0.804173i	$-0.702609\pi$
$503$	−26.6618	−1.18879	−0.594395	+	0.804173i	$0.702609\pi$
$504$	4.64466	0.206890
$505$	6.80025	0.302607
$506$	4.29709	0.191029
$507$	0	0
$508$	12.2196	0.542156
$509$	14.1806	0.628542	0.314271	−	0.949333i	$-0.398240\pi$
$509$	14.1806	0.628542	0.314271	+	0.949333i	$0.398240\pi$
$510$	−4.00000	−0.177123
$511$	20.2559	0.896068
$512$	1.00000	0.0441942
$513$	8.04479	0.355186
$514$	0.662300	0.0292128
$515$	−5.29137	−0.233165
$516$	0.716456	0.0315402
$517$	42.9163	1.88746
$518$	−17.6312	−0.774673
$519$	1.78043	0.0781523
$520$	0	0
$521$	23.7476	1.04040	0.520202	−	0.854043i	$-0.325857\pi$
$521$	23.7476	1.04040	0.520202	+	0.854043i	$0.325857\pi$
$522$	−4.31274	−0.188763
$523$	13.8506	0.605646	0.302823	−	0.953047i	$-0.402071\pi$
$523$	13.8506	0.605646	0.302823	+	0.953047i	$0.402071\pi$
$524$	−0.378757	−0.0165461
$525$	4.64466	0.202710
$526$	30.7498	1.34076
$527$	25.7627	1.12224
$528$	−4.40013	−0.191491
$529$	−22.0463	−0.958534
$530$	−13.5089	−0.586789
$531$	−2.18056	−0.0946282
$532$	37.3653	1.61999
$533$	0	0
$534$	−8.17274	−0.353669
$535$	−16.9282	−0.731870
$536$	−1.82522	−0.0788374
$537$	−17.4157	−0.751544
$538$	−3.74410	−0.161420
$539$	−64.1224	−2.76195
$540$	−1.00000	−0.0430331
$541$	−14.8898	−0.640164	−0.320082	−	0.947390i	$-0.603710\pi$
$541$	−14.8898	−0.640164	−0.320082	+	0.947390i	$0.603710\pi$
$542$	−27.7612	−1.19245
$543$	10.3611	0.444638
$544$	4.00000	0.171499
$545$	−12.8003	−0.548303
$546$	0	0
$547$	−22.2019	−0.949284	−0.474642	−	0.880179i	$-0.657422\pi$
$547$	−22.2019	−0.949284	−0.474642	+	0.880179i	$0.657422\pi$
$548$	−1.25235	−0.0534979
$549$	7.46410	0.318560
$550$	−4.40013	−0.187622
$551$	−34.6950	−1.47806
$552$	−0.976584	−0.0415662
$553$	−69.3632	−2.94963
$554$	11.9922	0.509499
$555$	3.79603	0.161132
$556$	3.35534	0.142298
$557$	−1.89969	−0.0804927	−0.0402463	−	0.999190i	$-0.512814\pi$
$557$	−1.89969	−0.0804927	−0.0402463	+	0.999190i	$0.512814\pi$
$558$	6.44069	0.272656
$559$	0	0
$560$	−4.64466	−0.196273
$561$	−17.6005	−0.743094
$562$	−3.63888	−0.153497
$563$	−1.72000	−0.0724894	−0.0362447	−	0.999343i	$-0.511540\pi$
$563$	−1.72000	−0.0724894	−0.0362447	+	0.999343i	$0.511540\pi$
$564$	−9.75342	−0.410693
$565$	−13.0662	−0.549697
$566$	4.84441	0.203626
$567$	4.64466	0.195057
$568$	7.95317	0.333707
$569$	−0.601920	−0.0252338	−0.0126169	−	0.999920i	$-0.504016\pi$
$569$	−0.601920	−0.0252338	−0.0126169	+	0.999920i	$0.504016\pi$
$570$	−8.04479	−0.336959
$571$	−11.9808	−0.501381	−0.250691	−	0.968067i	$-0.580658\pi$
$571$	−11.9808	−0.501381	−0.250691	+	0.968067i	$0.580658\pi$
$572$	0	0
$573$	−0.897014	−0.0374733
$574$	−33.8564	−1.41314
$575$	−0.976584	−0.0407264
$576$	1.00000	0.0416667
$577$	−43.0293	−1.79133	−0.895667	−	0.444725i	$-0.853301\pi$
$577$	−43.0293	−1.79133	−0.895667	+	0.444725i	$0.853301\pi$
$578$	−1.00000	−0.0415945
$579$	−20.2644	−0.842158
$580$	4.31274	0.179077
$581$	16.3071	0.676532
$582$	−13.8252	−0.573074
$583$	−59.4408	−2.46179
$584$	4.36112	0.180464
$585$	0	0
$586$	3.70081	0.152879
$587$	−17.9148	−0.739423	−0.369711	−	0.929147i	$-0.620543\pi$
$587$	−17.9148	−0.739423	−0.369711	+	0.929147i	$0.620543\pi$
$588$	14.5729	0.600975
$589$	51.8139	2.13496
$590$	2.18056	0.0897722
$591$	9.18056	0.377638
$592$	−3.79603	−0.156016
$593$	−0.669624	−0.0274981	−0.0137491	−	0.999905i	$-0.504377\pi$
$593$	−0.669624	−0.0274981	−0.0137491	+	0.999905i	$0.504377\pi$
$594$	−4.40013	−0.180539
$595$	−18.5786	−0.761650
$596$	4.61970	0.189230
$597$	−16.2175	−0.663739
$598$	0	0
$599$	1.29241	0.0528066	0.0264033	−	0.999651i	$-0.491595\pi$
$599$	1.29241	0.0528066	0.0264033	+	0.999651i	$0.491595\pi$
$600$	1.00000	0.0408248
$601$	−11.4734	−0.468011	−0.234005	−	0.972235i	$-0.575183\pi$
$601$	−11.4734	−0.468011	−0.234005	+	0.972235i	$0.575183\pi$
$602$	3.32770	0.135627
$603$	−1.82522	−0.0743286
$604$	−11.2425	−0.457450
$605$	−8.36112	−0.339928
$606$	−6.80025	−0.276241
$607$	−24.1344	−0.979583	−0.489792	−	0.871839i	$-0.662927\pi$
$607$	−24.1344	−0.979583	−0.489792	+	0.871839i	$0.662927\pi$
$608$	8.04479	0.326259
$609$	−20.0312	−0.811705
$610$	−7.46410	−0.302213
$611$	0	0
$612$	4.00000	0.161690
$613$	28.9502	1.16929	0.584644	−	0.811290i	$-0.301234\pi$
$613$	28.9502	1.16929	0.584644	+	0.811290i	$0.301234\pi$
$614$	7.11454	0.287119
$615$	7.28932	0.293934
$616$	−20.4371	−0.823434
$617$	0.841311	0.0338699	0.0169349	−	0.999857i	$-0.494609\pi$
$617$	0.841311	0.0338699	0.0169349	+	0.999857i	$0.494609\pi$
$618$	5.29137	0.212850
$619$	6.25076	0.251239	0.125620	−	0.992078i	$-0.459908\pi$
$619$	6.25076	0.251239	0.125620	+	0.992078i	$0.459908\pi$
$620$	−6.44069	−0.258664
$621$	−0.976584	−0.0391889
$622$	19.9148	0.798510
$623$	−37.9596	−1.52082
$624$	0	0
$625$	1.00000	0.0400000
$626$	6.13950	0.245384
$627$	−35.3981	−1.41366
$628$	−1.50311	−0.0599807
$629$	−15.1841	−0.605430
$630$	−4.64466	−0.185048
$631$	3.02496	0.120422	0.0602110	−	0.998186i	$-0.480823\pi$
$631$	3.02496	0.120422	0.0602110	+	0.998186i	$0.480823\pi$
$632$	−14.9340	−0.594042
$633$	−1.61970	−0.0643771
$634$	7.85286	0.311877
$635$	−12.2196	−0.484919
$636$	13.5089	0.535662
$637$	0	0
$638$	18.9766	0.751290
$639$	7.95317	0.314622
$640$	−1.00000	−0.0395285
$641$	0.772609	0.0305162	0.0152581	−	0.999884i	$-0.495143\pi$
$641$	0.772609	0.0305162	0.0152581	+	0.999884i	$0.495143\pi$
$642$	16.9282	0.668103
$643$	−19.3745	−0.764057	−0.382028	−	0.924151i	$-0.624774\pi$
$643$	−19.3745	−0.764057	−0.382028	+	0.924151i	$0.624774\pi$
$644$	−4.53590	−0.178739
$645$	−0.716456	−0.0282104
$646$	32.1791	1.26607
$647$	−27.1905	−1.06897	−0.534485	−	0.845178i	$-0.679494\pi$
$647$	−27.1905	−1.06897	−0.534485	+	0.845178i	$0.679494\pi$
$648$	1.00000	0.0392837
$649$	9.59473	0.376626
$650$	0	0
$651$	29.9148	1.17245
$652$	−0.176330	−0.00690561
$653$	15.7960	0.618144	0.309072	−	0.951039i	$-0.399982\pi$
$653$	15.7960	0.618144	0.309072	+	0.951039i	$0.399982\pi$
$654$	12.8003	0.500530
$655$	0.378757	0.0147993
$656$	−7.28932	−0.284600
$657$	4.36112	0.170143
$658$	−45.3013	−1.76603
$659$	30.4762	1.18719	0.593593	−	0.804766i	$-0.297709\pi$
$659$	30.4762	1.18719	0.593593	+	0.804766i	$0.297709\pi$
$660$	4.40013	0.171275
$661$	27.8876	1.08470	0.542351	−	0.840152i	$-0.317534\pi$
$661$	27.8876	1.08470	0.542351	+	0.840152i	$0.317534\pi$
$662$	−31.9959	−1.24356
$663$	0	0
$664$	3.51093	0.136251
$665$	−37.3653	−1.44896
$666$	−3.79603	−0.147093
$667$	4.21175	0.163079
$668$	−8.68162	−0.335902
$669$	2.23671	0.0864762
$670$	1.82522	0.0705143
$671$	−32.8430	−1.26789
$672$	4.64466	0.179172
$673$	−0.978131	−0.0377042	−0.0188521	−	0.999822i	$-0.506001\pi$
$673$	−0.978131	−0.0377042	−0.0188521	+	0.999822i	$0.506001\pi$
$674$	35.6432	1.37293
$675$	1.00000	0.0384900
$676$	0	0
$677$	−19.1926	−0.737630	−0.368815	−	0.929503i	$-0.620236\pi$
$677$	−19.1926	−0.737630	−0.368815	+	0.929503i	$0.620236\pi$
$678$	13.0662	0.501803
$679$	−64.2134	−2.46429
$680$	−4.00000	−0.153393
$681$	15.3205	0.587083
$682$	−28.3398	−1.08519
$683$	−1.51093	−0.0578143	−0.0289071	−	0.999582i	$-0.509203\pi$
$683$	−1.51093	−0.0578143	−0.0289071	+	0.999582i	$0.509203\pi$
$684$	8.04479	0.307600
$685$	1.25235	0.0478500
$686$	35.1734	1.34293
$687$	10.1279	0.386405
$688$	0.716456	0.0273146
$689$	0	0
$690$	0.976584	0.0371779
$691$	33.1166	1.25981	0.629907	−	0.776670i	$-0.283093\pi$
$691$	33.1166	1.25981	0.629907	+	0.776670i	$0.283093\pi$
$692$	1.78043	0.0676818
$693$	−20.4371	−0.776341
$694$	−6.89701	−0.261807
$695$	−3.35534	−0.127275
$696$	−4.31274	−0.163474
$697$	−29.1573	−1.10441
$698$	−19.3205	−0.731292
$699$	−20.7519	−0.784908
$700$	4.64466	0.175552
$701$	−27.8695	−1.05262	−0.526308	−	0.850294i	$-0.676424\pi$
$701$	−27.8695	−1.05262	−0.526308	+	0.850294i	$0.676424\pi$
$702$	0	0
$703$	−30.5382	−1.15177
$704$	−4.40013	−0.165836
$705$	9.75342	0.367335
$706$	−27.4173	−1.03186
$707$	−31.5849	−1.18787
$708$	−2.18056	−0.0819504
$709$	−11.0562	−0.415223	−0.207611	−	0.978211i	$-0.566569\pi$
$709$	−11.0562	−0.415223	−0.207611	+	0.978211i	$0.566569\pi$
$710$	−7.95317	−0.298477
$711$	−14.9340	−0.560068
$712$	−8.17274	−0.306286
$713$	−6.28987	−0.235557
$714$	18.5786	0.695288
$715$	0	0
$716$	−17.4157	−0.650856
$717$	−24.3539	−0.909514
$718$	−14.3611	−0.535952
$719$	11.7128	0.436814	0.218407	−	0.975858i	$-0.429914\pi$
$719$	11.7128	0.436814	0.218407	+	0.975858i	$0.429914\pi$
$720$	−1.00000	−0.0372678
$721$	24.5766	0.915280
$722$	45.7186	1.70147
$723$	−19.8685	−0.738916
$724$	10.3611	0.385068
$725$	−4.31274	−0.160171
$726$	8.36112	0.310310
$727$	19.4152	0.720071	0.360035	−	0.932939i	$-0.382765\pi$
$727$	19.4152	0.720071	0.360035	+	0.932939i	$0.382765\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.36112	−0.161412
$731$	2.86583	0.105996
$732$	7.46410	0.275881
$733$	11.9340	0.440792	0.220396	−	0.975411i	$-0.429265\pi$
$733$	11.9340	0.440792	0.220396	+	0.975411i	$0.429265\pi$
$734$	−13.7753	−0.508455
$735$	−14.5729	−0.537528
$736$	−0.976584	−0.0359973
$737$	8.03119	0.295833
$738$	−7.28932	−0.268324
$739$	−19.8628	−0.730666	−0.365333	−	0.930877i	$-0.619045\pi$
$739$	−19.8628	−0.730666	−0.365333	+	0.930877i	$0.619045\pi$
$740$	3.79603	0.139545
$741$	0	0
$742$	62.7442	2.30341
$743$	16.4877	0.604873	0.302437	−	0.953169i	$-0.402200\pi$
$743$	16.4877	0.604873	0.302437	+	0.953169i	$0.402200\pi$
$744$	6.44069	0.236127
$745$	−4.61970	−0.169253
$746$	−33.4627	−1.22516
$747$	3.51093	0.128458
$748$	−17.6005	−0.643538
$749$	78.6257	2.87292
$750$	−1.00000	−0.0365148
$751$	−46.6624	−1.70274	−0.851368	−	0.524569i	$-0.824227\pi$
$751$	−46.6624	−1.70274	−0.851368	+	0.524569i	$0.824227\pi$
$752$	−9.75342	−0.355671
$753$	13.5713	0.494566
$754$	0	0
$755$	11.2425	0.409156
$756$	4.64466	0.168925
$757$	2.63597	0.0958061	0.0479030	−	0.998852i	$-0.484746\pi$
$757$	2.63597	0.0958061	0.0479030	+	0.998852i	$0.484746\pi$
$758$	−33.3768	−1.21230
$759$	4.29709	0.155975
$760$	−8.04479	−0.291815
$761$	0.0800681	0.00290246	0.00145123	−	0.999999i	$-0.499538\pi$
$761$	0.0800681	0.00290246	0.00145123	+	0.999999i	$0.499538\pi$
$762$	12.2196	0.442668
$763$	59.4528	2.15234
$764$	−0.897014	−0.0324528
$765$	−4.00000	−0.144620
$766$	−7.33038	−0.264857
$767$	0	0
$768$	1.00000	0.0360844
$769$	5.68317	0.204940	0.102470	−	0.994736i	$-0.467325\pi$
$769$	5.68317	0.204940	0.102470	+	0.994736i	$0.467325\pi$
$770$	20.4371	0.736502
$771$	0.662300	0.0238522
$772$	−20.2644	−0.729330
$773$	7.58851	0.272940	0.136470	−	0.990644i	$-0.456424\pi$
$773$	7.58851	0.272940	0.136470	+	0.990644i	$0.456424\pi$
$774$	0.716456	0.0257525
$775$	6.44069	0.231356
$776$	−13.8252	−0.496296
$777$	−17.6312	−0.632517
$778$	32.6198	1.16948
$779$	−58.6410	−2.10103
$780$	0	0
$781$	−34.9949	−1.25222
$782$	−3.90633	−0.139690
$783$	−4.31274	−0.154125
$784$	14.5729	0.520459
$785$	1.50311	0.0536484
$786$	−0.378757	−0.0135098
$787$	−4.73623	−0.168828	−0.0844142	−	0.996431i	$-0.526902\pi$
$787$	−4.73623	−0.168828	−0.0844142	+	0.996431i	$0.526902\pi$
$788$	9.18056	0.327044
$789$	30.7498	1.09472
$790$	14.9340	0.531327
$791$	60.6878	2.15781
$792$	−4.40013	−0.156352
$793$	0	0
$794$	14.4683	0.513462
$795$	−13.5089	−0.479111
$796$	−16.2175	−0.574815
$797$	−41.0636	−1.45455	−0.727274	−	0.686347i	$-0.759213\pi$
$797$	−41.0636	−1.45455	−0.727274	+	0.686347i	$0.759213\pi$
$798$	37.3653	1.32272
$799$	−39.0137	−1.38020
$800$	1.00000	0.0353553
$801$	−8.17274	−0.288769
$802$	7.28727	0.257323
$803$	−19.1895	−0.677181
$804$	−1.82522	−0.0643705
$805$	4.53590	0.159869
$806$	0	0
$807$	−3.74410	−0.131799
$808$	−6.80025	−0.239232
$809$	−27.6005	−0.970382	−0.485191	−	0.874408i	$-0.661250\pi$
$809$	−27.6005	−0.970382	−0.485191	+	0.874408i	$0.661250\pi$
$810$	−1.00000	−0.0351364
$811$	10.6930	0.375482	0.187741	−	0.982219i	$-0.439883\pi$
$811$	10.6930	0.375482	0.187741	+	0.982219i	$0.439883\pi$
$812$	−20.0312	−0.702957
$813$	−27.7612	−0.973628
$814$	16.7030	0.585440
$815$	0.176330	0.00617657
$816$	4.00000	0.140028
$817$	5.76374	0.201648
$818$	24.5766	0.859300
$819$	0	0
$820$	7.28932	0.254554
$821$	17.5635	0.612972	0.306486	−	0.951875i	$-0.400847\pi$
$821$	17.5635	0.612972	0.306486	+	0.951875i	$0.400847\pi$
$822$	−1.25235	−0.0436809
$823$	−38.7130	−1.34945	−0.674725	−	0.738069i	$-0.735738\pi$
$823$	−38.7130	−1.34945	−0.674725	+	0.738069i	$0.735738\pi$
$824$	5.29137	0.184333
$825$	−4.40013	−0.153193
$826$	−10.1279	−0.352396
$827$	−28.4703	−0.990010	−0.495005	−	0.868890i	$-0.664834\pi$
$827$	−28.4703	−0.990010	−0.495005	+	0.868890i	$0.664834\pi$
$828$	−0.976584	−0.0339386
$829$	8.28709	0.287822	0.143911	−	0.989591i	$-0.454032\pi$
$829$	8.28709	0.287822	0.143911	+	0.989591i	$0.454032\pi$
$830$	−3.51093	−0.121866
$831$	11.9922	0.416004
$832$	0	0
$833$	58.2915	2.01968
$834$	3.35534	0.116186
$835$	8.68162	0.300440
$836$	−35.3981	−1.22427
$837$	6.44069	0.222623
$838$	15.5537	0.537293
$839$	−42.5630	−1.46944	−0.734719	−	0.678372i	$-0.762686\pi$
$839$	−42.5630	−1.46944	−0.734719	+	0.678372i	$0.762686\pi$
$840$	−4.64466	−0.160256
$841$	−10.4003	−0.358631
$842$	−22.3143	−0.769001
$843$	−3.63888	−0.125330
$844$	−1.61970	−0.0557522
$845$	0	0
$846$	−9.75342	−0.335330
$847$	38.8345	1.33437
$848$	13.5089	0.463897
$849$	4.84441	0.166260
$850$	4.00000	0.137199
$851$	3.70714	0.127079
$852$	7.95317	0.272471
$853$	−28.1380	−0.963425	−0.481713	−	0.876329i	$-0.659985\pi$
$853$	−28.1380	−0.963425	−0.481713	+	0.876329i	$0.659985\pi$
$854$	34.6682	1.18632
$855$	−8.04479	−0.275126
$856$	16.9282	0.578594
$857$	10.3355	0.353053	0.176526	−	0.984296i	$-0.443514\pi$
$857$	10.3355	0.353053	0.176526	+	0.984296i	$0.443514\pi$
$858$	0	0
$859$	0.380304	0.0129758	0.00648791	−	0.999979i	$-0.497935\pi$
$859$	0.380304	0.0129758	0.00648791	+	0.999979i	$0.497935\pi$
$860$	−0.716456	−0.0244310
$861$	−33.8564	−1.15382
$862$	24.2644	0.826447
$863$	47.1484	1.60495	0.802475	−	0.596685i	$-0.203516\pi$
$863$	47.1484	1.60495	0.802475	+	0.596685i	$0.203516\pi$
$864$	1.00000	0.0340207
$865$	−1.78043	−0.0605365
$866$	−23.0989	−0.784932
$867$	−1.00000	−0.0339618
$868$	29.9148	1.01537
$869$	65.7114	2.22911
$870$	4.31274	0.146215
$871$	0	0
$872$	12.8003	0.433471
$873$	−13.8252	−0.467913
$874$	−7.85641	−0.265747
$875$	−4.64466	−0.157018
$876$	4.36112	0.147348
$877$	−40.0412	−1.35209	−0.676047	−	0.736858i	$-0.736309\pi$
$877$	−40.0412	−1.35209	−0.676047	+	0.736858i	$0.736309\pi$
$878$	−39.9959	−1.34980
$879$	3.70081	0.124825
$880$	4.40013	0.148328
$881$	−15.4449	−0.520352	−0.260176	−	0.965561i	$-0.583781\pi$
$881$	−15.4449	−0.520352	−0.260176	+	0.965561i	$0.583781\pi$
$882$	14.5729	0.490694
$883$	6.02142	0.202637	0.101318	−	0.994854i	$-0.467694\pi$
$883$	6.02142	0.202637	0.101318	+	0.994854i	$0.467694\pi$
$884$	0	0
$885$	2.18056	0.0732987
$886$	−15.6036	−0.524213
$887$	−49.1380	−1.64989	−0.824947	−	0.565210i	$-0.808795\pi$
$887$	−49.1380	−1.64989	−0.824947	+	0.565210i	$0.808795\pi$
$888$	−3.79603	−0.127386
$889$	56.7557	1.90353
$890$	8.17274	0.273951
$891$	−4.40013	−0.147410
$892$	2.23671	0.0748906
$893$	−78.4642	−2.62570
$894$	4.61970	0.154506
$895$	17.4157	0.582143
$896$	4.64466	0.155167
$897$	0	0
$898$	27.0042	0.901141
$899$	−27.7770	−0.926414
$900$	1.00000	0.0333333
$901$	54.0356	1.80019
$902$	32.0739	1.06795
$903$	3.32770	0.110739
$904$	13.0662	0.434574
$905$	−10.3611	−0.344415
$906$	−11.2425	−0.373507
$907$	16.3669	0.543454	0.271727	−	0.962374i	$-0.412405\pi$
$907$	16.3669	0.543454	0.271727	+	0.962374i	$0.412405\pi$
$908$	15.3205	0.508429
$909$	−6.80025	−0.225550
$910$	0	0
$911$	−10.4819	−0.347280	−0.173640	−	0.984809i	$-0.555553\pi$
$911$	−10.4819	−0.347280	−0.173640	+	0.984809i	$0.555553\pi$
$912$	8.04479	0.266389
$913$	−15.4486	−0.511273
$914$	17.7868	0.588336
$915$	−7.46410	−0.246756
$916$	10.1279	0.334637
$917$	−1.75920	−0.0580938
$918$	4.00000	0.132020
$919$	3.21130	0.105931	0.0529655	−	0.998596i	$-0.483133\pi$
$919$	3.21130	0.105931	0.0529655	+	0.998596i	$0.483133\pi$
$920$	0.976584	0.0321970
$921$	7.11454	0.234432
$922$	−24.9652	−0.822184
$923$	0	0
$924$	−20.4371	−0.672331
$925$	−3.79603	−0.124813
$926$	−15.6389	−0.513926
$927$	5.29137	0.173791
$928$	−4.31274	−0.141572
$929$	−46.4788	−1.52492	−0.762460	−	0.647036i	$-0.776008\pi$
$929$	−46.4788	−1.52492	−0.762460	+	0.647036i	$0.776008\pi$
$930$	−6.44069	−0.211198
$931$	117.236	3.84224
$932$	−20.7519	−0.679750
$933$	19.9148	0.651981
$934$	2.43914	0.0798110
$935$	17.6005	0.575598
$936$	0	0
$937$	−27.7627	−0.906969	−0.453485	−	0.891264i	$-0.649819\pi$
$937$	−27.7627	−0.906969	−0.453485	+	0.891264i	$0.649819\pi$
$938$	−8.47751	−0.276801
$939$	6.13950	0.200355
$940$	9.75342	0.318122
$941$	−20.7962	−0.677935	−0.338968	−	0.940798i	$-0.610078\pi$
$941$	−20.7962	−0.677935	−0.338968	+	0.940798i	$0.610078\pi$
$942$	−1.50311	−0.0489741
$943$	7.11863	0.231814
$944$	−2.18056	−0.0709711
$945$	−4.64466	−0.151091
$946$	−3.15250	−0.102497
$947$	−9.05925	−0.294386	−0.147193	−	0.989108i	$-0.547024\pi$
$947$	−9.05925	−0.294386	−0.147193	+	0.989108i	$0.547024\pi$
$948$	−14.9340	−0.485033
$949$	0	0
$950$	8.04479	0.261007
$951$	7.85286	0.254646
$952$	18.5786	0.602137
$953$	−15.2762	−0.494845	−0.247423	−	0.968908i	$-0.579584\pi$
$953$	−15.2762	−0.494845	−0.247423	+	0.968908i	$0.579584\pi$
$954$	13.5089	0.437366
$955$	0.897014	0.0290267
$956$	−24.3539	−0.787662
$957$	18.9766	0.613426
$958$	−14.1863	−0.458340
$959$	−5.81676	−0.187833
$960$	−1.00000	−0.0322749
$961$	10.4824	0.338143
$962$	0	0
$963$	16.9282	0.545504
$964$	−19.8685	−0.639920
$965$	20.2644	0.652333
$966$	−4.53590	−0.145940
$967$	46.3036	1.48902	0.744511	−	0.667610i	$-0.232683\pi$
$967$	46.3036	1.48902	0.744511	+	0.667610i	$0.232683\pi$
$968$	8.36112	0.268736
$969$	32.1791	1.03374
$970$	13.8252	0.443901
$971$	11.9652	0.383981	0.191990	−	0.981397i	$-0.438506\pi$
$971$	11.9652	0.383981	0.191990	+	0.981397i	$0.438506\pi$
$972$	1.00000	0.0320750
$973$	15.5844	0.499613
$974$	−5.76329	−0.184668
$975$	0	0
$976$	7.46410	0.238920
$977$	1.76415	0.0564403	0.0282201	−	0.999602i	$-0.491016\pi$
$977$	1.76415	0.0564403	0.0282201	+	0.999602i	$0.491016\pi$
$978$	−0.176330	−0.00563841
$979$	35.9611	1.14932
$980$	−14.5729	−0.465513
$981$	12.8003	0.408681
$982$	−1.07534	−0.0343155
$983$	−54.2821	−1.73133	−0.865666	−	0.500623i	$-0.833104\pi$
$983$	−54.2821	−1.73133	−0.865666	+	0.500623i	$0.833104\pi$
$984$	−7.28932	−0.232375
$985$	−9.18056	−0.292517
$986$	−17.2509	−0.549382
$987$	−45.3013	−1.44196
$988$	0	0
$989$	−0.699680	−0.0222485
$990$	4.40013	0.139845
$991$	−17.4783	−0.555218	−0.277609	−	0.960694i	$-0.589542\pi$
$991$	−17.4783	−0.555218	−0.277609	+	0.960694i	$0.589542\pi$
$992$	6.44069	0.204492
$993$	−31.9959	−1.01536
$994$	36.9398	1.17166
$995$	16.2175	0.514130
$996$	3.51093	0.111248
$997$	−21.2914	−0.674304	−0.337152	−	0.941450i	$-0.609464\pi$
$997$	−21.2914	−0.674304	−0.337152	+	0.941450i	$0.609464\pi$
$998$	14.7534	0.467011
$999$	−3.79603	−0.120101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.ca.1.4		4
13.2	odd	12		390.2.bb.c.121.4	✓	8
13.5	odd	4		5070.2.b.ba.1351.4		8
13.7	odd	12		390.2.bb.c.361.4	yes	8
13.8	odd	4		5070.2.b.ba.1351.5		8
13.12	even	2		5070.2.a.bz.1.1		4
39.2	even	12		1170.2.bs.f.901.2		8
39.20	even	12		1170.2.bs.f.361.2		8
65.2	even	12		1950.2.y.j.199.4		8
65.7	even	12		1950.2.y.k.49.1		8
65.28	even	12		1950.2.y.k.199.1		8
65.33	even	12		1950.2.y.j.49.4		8
65.54	odd	12		1950.2.bc.g.901.1		8
65.59	odd	12		1950.2.bc.g.751.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.4	✓	8	13.2	odd	12
390.2.bb.c.361.4	yes	8	13.7	odd	12
1170.2.bs.f.361.2		8	39.20	even	12
1170.2.bs.f.901.2		8	39.2	even	12
1950.2.y.j.49.4		8	65.33	even	12
1950.2.y.j.199.4		8	65.2	even	12
1950.2.y.k.49.1		8	65.7	even	12
1950.2.y.k.199.1		8	65.28	even	12
1950.2.bc.g.751.1		8	65.59	odd	12
1950.2.bc.g.901.1		8	65.54	odd	12
5070.2.a.bz.1.1		4	13.12	even	2
5070.2.a.ca.1.4		4	1.1	even	1	trivial
5070.2.b.ba.1351.4		8	13.5	odd	4
5070.2.b.ba.1351.5		8	13.8	odd	4

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:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.40013 q^{11} +1.00000 q^{12} +4.64466 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} +8.04479 q^{19} -1.00000 q^{20} +4.64466 q^{21} -4.40013 q^{22} -0.976584 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +4.64466 q^{28} -4.31274 q^{29} -1.00000 q^{30} +6.44069 q^{31} +1.00000 q^{32} -4.40013 q^{33} +4.00000 q^{34} -4.64466 q^{35} +1.00000 q^{36} -3.79603 q^{37} +8.04479 q^{38} -1.00000 q^{40} -7.28932 q^{41} +4.64466 q^{42} +0.716456 q^{43} -4.40013 q^{44} -1.00000 q^{45} -0.976584 q^{46} -9.75342 q^{47} +1.00000 q^{48} +14.5729 q^{49} +1.00000 q^{50} +4.00000 q^{51} +13.5089 q^{53} +1.00000 q^{54} +4.40013 q^{55} +4.64466 q^{56} +8.04479 q^{57} -4.31274 q^{58} -2.18056 q^{59} -1.00000 q^{60} +7.46410 q^{61} +6.44069 q^{62} +4.64466 q^{63} +1.00000 q^{64} -4.40013 q^{66} -1.82522 q^{67} +4.00000 q^{68} -0.976584 q^{69} -4.64466 q^{70} +7.95317 q^{71} +1.00000 q^{72} +4.36112 q^{73} -3.79603 q^{74} +1.00000 q^{75} +8.04479 q^{76} -20.4371 q^{77} -14.9340 q^{79} -1.00000 q^{80} +1.00000 q^{81} -7.28932 q^{82} +3.51093 q^{83} +4.64466 q^{84} -4.00000 q^{85} +0.716456 q^{86} -4.31274 q^{87} -4.40013 q^{88} -8.17274 q^{89} -1.00000 q^{90} -0.976584 q^{92} +6.44069 q^{93} -9.75342 q^{94} -8.04479 q^{95} +1.00000 q^{96} -13.8252 q^{97} +14.5729 q^{98} -4.40013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} - 2 q^{11} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 4 q^{16} + 16 q^{17} + 4 q^{18} - 4 q^{20} + 2 q^{21} - 2 q^{22} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 4 q^{27} + 2 q^{28} + 8 q^{29} - 4 q^{30} + 4 q^{31} + 4 q^{32} - 2 q^{33} + 16 q^{34} - 2 q^{35} + 4 q^{36} - 10 q^{37} - 4 q^{40} + 4 q^{41} + 2 q^{42} + 14 q^{43} - 2 q^{44} - 4 q^{45} + 4 q^{46} + 8 q^{47} + 4 q^{48} + 14 q^{49} + 4 q^{50} + 16 q^{51} + 8 q^{53} + 4 q^{54} + 2 q^{55} + 2 q^{56} + 8 q^{58} - 6 q^{59} - 4 q^{60} + 16 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} - 2 q^{66} + 12 q^{67} + 16 q^{68} + 4 q^{69} - 2 q^{70} + 16 q^{71} + 4 q^{72} + 12 q^{73} - 10 q^{74} + 4 q^{75} - 8 q^{77} - 10 q^{79} - 4 q^{80} + 4 q^{81} + 4 q^{82} + 16 q^{83} + 2 q^{84} - 16 q^{85} + 14 q^{86} + 8 q^{87} - 2 q^{88} - 4 q^{89} - 4 q^{90} + 4 q^{92} + 4 q^{93} + 8 q^{94} + 4 q^{96} - 36 q^{97} + 14 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 - 2 * q^11 + 4 * q^12 + 2 * q^14 - 4 * q^15 + 4 * q^16 + 16 * q^17 + 4 * q^18 - 4 * q^20 + 2 * q^21 - 2 * q^22 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 4 * q^27 + 2 * q^28 + 8 * q^29 - 4 * q^30 + 4 * q^31 + 4 * q^32 - 2 * q^33 + 16 * q^34 - 2 * q^35 + 4 * q^36 - 10 * q^37 - 4 * q^40 + 4 * q^41 + 2 * q^42 + 14 * q^43 - 2 * q^44 - 4 * q^45 + 4 * q^46 + 8 * q^47 + 4 * q^48 + 14 * q^49 + 4 * q^50 + 16 * q^51 + 8 * q^53 + 4 * q^54 + 2 * q^55 + 2 * q^56 + 8 * q^58 - 6 * q^59 - 4 * q^60 + 16 * q^61 + 4 * q^62 + 2 * q^63 + 4 * q^64 - 2 * q^66 + 12 * q^67 + 16 * q^68 + 4 * q^69 - 2 * q^70 + 16 * q^71 + 4 * q^72 + 12 * q^73 - 10 * q^74 + 4 * q^75 - 8 * q^77 - 10 * q^79 - 4 * q^80 + 4 * q^81 + 4 * q^82 + 16 * q^83 + 2 * q^84 - 16 * q^85 + 14 * q^86 + 8 * q^87 - 2 * q^88 - 4 * q^89 - 4 * q^90 + 4 * q^92 + 4 * q^93 + 8 * q^94 + 4 * q^96 - 36 * q^97 + 14 * q^98 - 2 * q^99

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