LMFDB - Embedded newform 5070.2.a.bz.1.3

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			1.3
Root			$-1.32258$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.32258 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.32258 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.61335 q^{11} +1.00000 q^{12} -1.32258 q^{14} +1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -2.29078 q^{19} +1.00000 q^{20} +1.32258 q^{21} -4.61335 q^{22} +8.66799 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +1.32258 q^{28} -2.02283 q^{29} -1.00000 q^{30} +10.1321 q^{31} -1.00000 q^{32} +4.61335 q^{33} -4.00000 q^{34} +1.32258 q^{35} +1.00000 q^{36} -6.80951 q^{37} +2.29078 q^{38} -1.00000 q^{40} -4.64516 q^{41} -1.32258 q^{42} +8.60562 q^{43} +4.61335 q^{44} +1.00000 q^{45} -8.66799 q^{46} -9.10926 q^{47} +1.00000 q^{48} -5.25078 q^{49} -1.00000 q^{50} +4.00000 q^{51} +0.826674 q^{53} -1.00000 q^{54} +4.61335 q^{55} -1.32258 q^{56} -2.29078 q^{57} +2.02283 q^{58} +3.14152 q^{59} +1.00000 q^{60} +0.535898 q^{61} -10.1321 q^{62} +1.32258 q^{63} +1.00000 q^{64} -4.61335 q^{66} -3.18106 q^{67} +4.00000 q^{68} +8.66799 q^{69} -1.32258 q^{70} +11.3360 q^{71} -1.00000 q^{72} -6.28304 q^{73} +6.80951 q^{74} +1.00000 q^{75} -2.29078 q^{76} +6.10153 q^{77} +2.96774 q^{79} +1.00000 q^{80} +1.00000 q^{81} +4.64516 q^{82} -15.8719 q^{83} +1.32258 q^{84} +4.00000 q^{85} -8.60562 q^{86} -2.02283 q^{87} -4.61335 q^{88} -11.8641 q^{89} -1.00000 q^{90} +8.66799 q^{92} +10.1321 q^{93} +9.10926 q^{94} -2.29078 q^{95} -1.00000 q^{96} +8.81894 q^{97} +5.25078 q^{98} +4.61335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1.32258	0.499888	0.249944	−	0.968260i	$-0.419588\pi$
$7$	1.32258	0.499888	0.249944	+	0.968260i	$0.419588\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	4.61335	1.39098	0.695489	−	0.718536i	$-0.255188\pi$
$11$	4.61335	1.39098	0.695489	+	0.718536i	$0.255188\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.32258	−0.353474
$15$	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
$19$	−2.29078	−0.525540	−0.262770	−	0.964859i	$-0.584636\pi$
$19$	−2.29078	−0.525540	−0.262770	+	0.964859i	$0.584636\pi$
$20$	1.00000	0.223607
$21$	1.32258	0.288611
$22$	−4.61335	−0.983571
$23$	8.66799	1.80740	0.903700	−	0.428166i	$-0.140840\pi$
$23$	8.66799	1.80740	0.903700	+	0.428166i	$0.140840\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	1.32258	0.249944
$29$	−2.02283	−0.375629	−0.187815	−	0.982204i	$-0.560140\pi$
$29$	−2.02283	−0.375629	−0.187815	+	0.982204i	$0.560140\pi$
$30$	−1.00000	−0.182574
$31$	10.1321	1.81978	0.909888	−	0.414853i	$-0.136167\pi$
$31$	10.1321	1.81978	0.909888	+	0.414853i	$0.136167\pi$
$32$	−1.00000	−0.176777
$33$	4.61335	0.803082
$34$	−4.00000	−0.685994
$35$	1.32258	0.223557
$36$	1.00000	0.166667
$37$	−6.80951	−1.11948	−0.559738	−	0.828670i	$-0.689098\pi$
$37$	−6.80951	−1.11948	−0.559738	+	0.828670i	$0.689098\pi$
$38$	2.29078	0.371613
$39$	0	0
$40$	−1.00000	−0.158114
$41$	−4.64516	−0.725452	−0.362726	−	0.931896i	$-0.618154\pi$
$41$	−4.64516	−0.725452	−0.362726	+	0.931896i	$0.618154\pi$
$42$	−1.32258	−0.204078
$43$	8.60562	1.31235	0.656173	−	0.754611i	$-0.272174\pi$
$43$	8.60562	1.31235	0.656173	+	0.754611i	$0.272174\pi$
$44$	4.61335	0.695489
$45$	1.00000	0.149071
$46$	−8.66799	−1.27802
$47$	−9.10926	−1.32872	−0.664361	−	0.747412i	$-0.731296\pi$
$47$	−9.10926	−1.32872	−0.664361	+	0.747412i	$0.731296\pi$
$48$	1.00000	0.144338
$49$	−5.25078	−0.750112
$50$	−1.00000	−0.141421
$51$	4.00000	0.560112
$52$	0	0
$53$	0.826674	0.113552	0.0567762	−	0.998387i	$-0.481918\pi$
$53$	0.826674	0.113552	0.0567762	+	0.998387i	$0.481918\pi$
$54$	−1.00000	−0.136083
$55$	4.61335	0.622065
$56$	−1.32258	−0.176737
$57$	−2.29078	−0.303421
$58$	2.02283	0.265610
$59$	3.14152	0.408991	0.204496	−	0.978867i	$-0.434445\pi$
$59$	3.14152	0.408991	0.204496	+	0.978867i	$0.434445\pi$
$60$	1.00000	0.129099
$61$	0.535898	0.0686148	0.0343074	−	0.999411i	$-0.489077\pi$
$61$	0.535898	0.0686148	0.0343074	+	0.999411i	$0.489077\pi$
$62$	−10.1321	−1.28678
$63$	1.32258	0.166629
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.61335	−0.567865
$67$	−3.18106	−0.388628	−0.194314	−	0.980939i	$-0.562248\pi$
$67$	−3.18106	−0.388628	−0.194314	+	0.980939i	$0.562248\pi$
$68$	4.00000	0.485071
$69$	8.66799	1.04350
$70$	−1.32258	−0.158079
$71$	11.3360	1.34533	0.672666	−	0.739946i	$-0.265149\pi$
$71$	11.3360	1.34533	0.672666	+	0.739946i	$0.265149\pi$
$72$	−1.00000	−0.117851
$73$	−6.28304	−0.735375	−0.367687	−	0.929949i	$-0.619850\pi$
$73$	−6.28304	−0.735375	−0.367687	+	0.929949i	$0.619850\pi$
$74$	6.80951	0.791589
$75$	1.00000	0.115470
$76$	−2.29078	−0.262770
$77$	6.10153	0.695334
$78$	0	0
$79$	2.96774	0.333897	0.166948	−	0.985966i	$-0.446609\pi$
$79$	2.96774	0.333897	0.166948	+	0.985966i	$0.446609\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	4.64516	0.512972
$83$	−15.8719	−1.74216	−0.871082	−	0.491138i	$-0.836581\pi$
$83$	−15.8719	−1.74216	−0.871082	+	0.491138i	$0.836581\pi$
$84$	1.32258	0.144305
$85$	4.00000	0.433861
$86$	−8.60562	−0.927968
$87$	−2.02283	−0.216870
$88$	−4.61335	−0.491785
$89$	−11.8641	−1.25760	−0.628798	−	0.777569i	$-0.716453\pi$
$89$	−11.8641	−1.25760	−0.628798	+	0.777569i	$0.716453\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	8.66799	0.903700
$93$	10.1321	1.05065
$94$	9.10926	0.939549
$95$	−2.29078	−0.235029
$96$	−1.00000	−0.102062
$97$	8.81894	0.895428	0.447714	−	0.894177i	$-0.352238\pi$
$97$	8.81894	0.895428	0.447714	+	0.894177i	$0.352238\pi$
$98$	5.25078	0.530409
$99$	4.61335	0.463660
$100$	1.00000	0.100000
$101$	−7.22671	−0.719085	−0.359542	−	0.933129i	$-0.617067\pi$
$101$	−7.22671	−0.719085	−0.359542	+	0.933129i	$0.617067\pi$
$102$	−4.00000	−0.396059
$103$	18.4000	1.81301	0.906505	−	0.422196i	$-0.138740\pi$
$103$	18.4000	1.81301	0.906505	+	0.422196i	$0.138740\pi$
$104$	0	0
$105$	1.32258	0.129071
$106$	−0.826674	−0.0802936
$107$	3.07180	0.296962	0.148481	−	0.988915i	$-0.452562\pi$
$107$	3.07180	0.296962	0.148481	+	0.988915i	$0.452562\pi$
$108$	1.00000	0.0962250
$109$	−13.2267	−1.26689	−0.633445	−	0.773788i	$-0.718360\pi$
$109$	−13.2267	−1.26689	−0.633445	+	0.773788i	$0.718360\pi$
$110$	−4.61335	−0.439866
$111$	−6.80951	−0.646330
$112$	1.32258	0.124972
$113$	−8.08643	−0.760708	−0.380354	−	0.924841i	$-0.624198\pi$
$113$	−8.08643	−0.760708	−0.380354	+	0.924841i	$0.624198\pi$
$114$	2.29078	0.214551
$115$	8.66799	0.808294
$116$	−2.02283	−0.187815
$117$	0	0
$118$	−3.14152	−0.289201
$119$	5.29032	0.484963
$120$	−1.00000	−0.0912871
$121$	10.2830	0.934822
$122$	−0.535898	−0.0485180
$123$	−4.64516	−0.418840
$124$	10.1321	0.909888
$125$	1.00000	0.0894427
$126$	−1.32258	−0.117825
$127$	11.4718	1.01796	0.508980	−	0.860778i	$-0.330023\pi$
$127$	11.4718	1.01796	0.508980	+	0.860778i	$0.330023\pi$
$128$	−1.00000	−0.0883883
$129$	8.60562	0.757683
$130$	0	0
$131$	−15.9906	−1.39710	−0.698551	−	0.715560i	$-0.746172\pi$
$131$	−15.9906	−1.39710	−0.698551	+	0.715560i	$0.746172\pi$
$132$	4.61335	0.401541
$133$	−3.02973	−0.262711
$134$	3.18106	0.274802
$135$	1.00000	0.0860663
$136$	−4.00000	−0.342997
$137$	16.0697	1.37293	0.686465	−	0.727163i	$-0.259162\pi$
$137$	16.0697	1.37293	0.686465	+	0.727163i	$0.259162\pi$
$138$	−8.66799	−0.737868
$139$	9.32258	0.790731	0.395365	−	0.918524i	$-0.370618\pi$
$139$	9.32258	0.790731	0.395365	+	0.918524i	$0.370618\pi$
$140$	1.32258	0.111778
$141$	−9.10926	−0.767138
$142$	−11.3360	−0.951294
$143$	0	0
$144$	1.00000	0.0833333
$145$	−2.02283	−0.167987
$146$	6.28304	0.519988
$147$	−5.25078	−0.433077
$148$	−6.80951	−0.559738
$149$	−4.08519	−0.334672	−0.167336	−	0.985900i	$-0.553516\pi$
$149$	−4.08519	−0.334672	−0.167336	+	0.985900i	$0.553516\pi$
$150$	−1.00000	−0.0816497
$151$	−19.9811	−1.62604	−0.813021	−	0.582235i	$-0.802178\pi$
$151$	−19.9811	−1.62604	−0.813021	+	0.582235i	$0.802178\pi$
$152$	2.29078	0.185806
$153$	4.00000	0.323381
$154$	−6.10153	−0.491675
$155$	10.1321	0.813829
$156$	0	0
$157$	7.13379	0.569338	0.284669	−	0.958626i	$-0.408116\pi$
$157$	7.13379	0.569338	0.284669	+	0.958626i	$0.408116\pi$
$158$	−2.96774	−0.236101
$159$	0.826674	0.0655595
$160$	−1.00000	−0.0790569
$161$	11.4641	0.903498
$162$	−1.00000	−0.0785674
$163$	−9.89470	−0.775012	−0.387506	−	0.921867i	$-0.626663\pi$
$163$	−9.89470	−0.775012	−0.387506	+	0.921867i	$0.626663\pi$
$164$	−4.64516	−0.362726
$165$	4.61335	0.359149
$166$	15.8719	1.23190
$167$	−24.0375	−1.86007	−0.930037	−	0.367465i	$-0.880226\pi$
$167$	−24.0375	−1.86007	−0.930037	+	0.367465i	$0.880226\pi$
$168$	−1.32258	−0.102039
$169$	0	0
$170$	−4.00000	−0.306786
$171$	−2.29078	−0.175180
$172$	8.60562	0.656173
$173$	2.52817	0.192213	0.0961065	−	0.995371i	$-0.469361\pi$
$173$	2.52817	0.192213	0.0961065	+	0.995371i	$0.469361\pi$
$174$	2.02283	0.153350
$175$	1.32258	0.0999776
$176$	4.61335	0.347745
$177$	3.14152	0.236131
$178$	11.8641	0.889255
$179$	−6.27568	−0.469066	−0.234533	−	0.972108i	$-0.575356\pi$
$179$	−6.27568	−0.469066	−0.234533	+	0.972108i	$0.575356\pi$
$180$	1.00000	0.0745356
$181$	12.2830	0.912991	0.456496	−	0.889726i	$-0.349104\pi$
$181$	12.2830	0.912991	0.456496	+	0.889726i	$0.349104\pi$
$182$	0	0
$183$	0.535898	0.0396147
$184$	−8.66799	−0.639012
$185$	−6.80951	−0.500645
$186$	−10.1321	−0.742921
$187$	18.4534	1.34945
$188$	−9.10926	−0.664361
$189$	1.32258	0.0962035
$190$	2.29078	0.166190
$191$	−9.74715	−0.705279	−0.352639	−	0.935759i	$-0.614716\pi$
$191$	−9.74715	−0.705279	−0.352639	+	0.935759i	$0.614716\pi$
$192$	1.00000	0.0721688
$193$	13.7626	0.990654	0.495327	−	0.868707i	$-0.335048\pi$
$193$	13.7626	0.990654	0.495327	+	0.868707i	$0.335048\pi$
$194$	−8.81894	−0.633163
$195$	0	0
$196$	−5.25078	−0.375056
$197$	−10.1415	−0.722554	−0.361277	−	0.932459i	$-0.617659\pi$
$197$	−10.1415	−0.722554	−0.361277	+	0.932459i	$0.617659\pi$
$198$	−4.61335	−0.327857
$199$	9.57336	0.678638	0.339319	−	0.940671i	$-0.389803\pi$
$199$	9.57336	0.678638	0.339319	+	0.940671i	$0.389803\pi$
$200$	−1.00000	−0.0707107
$201$	−3.18106	−0.224375
$202$	7.22671	0.508470
$203$	−2.67535	−0.187773
$204$	4.00000	0.280056
$205$	−4.64516	−0.324432
$206$	−18.4000	−1.28199
$207$	8.66799	0.602467
$208$	0	0
$209$	−10.5682	−0.731015
$210$	−1.32258	−0.0912667
$211$	−1.08519	−0.0747074	−0.0373537	−	0.999302i	$-0.511893\pi$
$211$	−1.08519	−0.0747074	−0.0373537	+	0.999302i	$0.511893\pi$
$212$	0.826674	0.0567762
$213$	11.3360	0.776728
$214$	−3.07180	−0.209984
$215$	8.60562	0.586899
$216$	−1.00000	−0.0680414
$217$	13.4005	0.909685
$218$	13.2267	0.895826
$219$	−6.28304	−0.424569
$220$	4.61335	0.311032
$221$	0	0
$222$	6.80951	0.457024
$223$	24.9416	1.67021	0.835106	−	0.550089i	$-0.185406\pi$
$223$	24.9416	1.67021	0.835106	+	0.550089i	$0.185406\pi$
$224$	−1.32258	−0.0883686
$225$	1.00000	0.0666667
$226$	8.08643	0.537902
$227$	19.3205	1.28235	0.641174	−	0.767396i	$-0.278448\pi$
$227$	19.3205	1.28235	0.641174	+	0.767396i	$0.278448\pi$
$228$	−2.29078	−0.151710
$229$	4.15491	0.274564	0.137282	−	0.990532i	$-0.456163\pi$
$229$	4.15491	0.274564	0.137282	+	0.990532i	$0.456163\pi$
$230$	−8.66799	−0.571550
$231$	6.10153	0.401451
$232$	2.02283	0.132805
$233$	−16.9665	−1.11151	−0.555756	−	0.831346i	$-0.687571\pi$
$233$	−16.9665	−1.11151	−0.555756	+	0.831346i	$0.687571\pi$
$234$	0	0
$235$	−9.10926	−0.594223
$236$	3.14152	0.204496
$237$	2.96774	0.192775
$238$	−5.29032	−0.342920
$239$	6.34416	0.410370	0.205185	−	0.978723i	$-0.434220\pi$
$239$	6.34416	0.410370	0.205185	+	0.978723i	$0.434220\pi$
$240$	1.00000	0.0645497
$241$	24.1855	1.55792	0.778962	−	0.627072i	$-0.215747\pi$
$241$	24.1855	1.55792	0.778962	+	0.627072i	$0.215747\pi$
$242$	−10.2830	−0.661019
$243$	1.00000	0.0641500
$244$	0.535898	0.0343074
$245$	−5.25078	−0.335460
$246$	4.64516	0.296165
$247$	0	0
$248$	−10.1321	−0.643388
$249$	−15.8719	−1.00584
$250$	−1.00000	−0.0632456
$251$	8.82497	0.557027	0.278514	−	0.960432i	$-0.410158\pi$
$251$	8.82497	0.557027	0.278514	+	0.960432i	$0.410158\pi$
$252$	1.32258	0.0833147
$253$	39.9885	2.51406
$254$	−11.4718	−0.719807
$255$	4.00000	0.250490
$256$	1.00000	0.0625000
$257$	8.38494	0.523038	0.261519	−	0.965198i	$-0.415777\pi$
$257$	8.38494	0.523038	0.261519	+	0.965198i	$0.415777\pi$
$258$	−8.60562	−0.535763
$259$	−9.00612	−0.559613
$260$	0	0
$261$	−2.02283	−0.125210
$262$	15.9906	0.987900
$263$	1.92130	0.118472	0.0592361	−	0.998244i	$-0.481134\pi$
$263$	1.92130	0.118472	0.0592361	+	0.998244i	$0.481134\pi$
$264$	−4.61335	−0.283932
$265$	0.826674	0.0507822
$266$	3.02973	0.185765
$267$	−11.8641	−0.726073
$268$	−3.18106	−0.194314
$269$	−32.3098	−1.96996	−0.984982	−	0.172655i	$-0.944766\pi$
$269$	−32.3098	−1.96996	−0.984982	+	0.172655i	$0.944766\pi$
$270$	−1.00000	−0.0608581
$271$	−23.4526	−1.42464	−0.712322	−	0.701853i	$-0.752356\pi$
$271$	−23.4526	−1.42464	−0.712322	+	0.701853i	$0.752356\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−16.0697	−0.970808
$275$	4.61335	0.278196
$276$	8.66799	0.521751
$277$	−9.00566	−0.541098	−0.270549	−	0.962706i	$-0.587205\pi$
$277$	−9.00566	−0.541098	−0.270549	+	0.962706i	$0.587205\pi$
$278$	−9.32258	−0.559131
$279$	10.1321	0.606592
$280$	−1.32258	−0.0790393
$281$	1.71696	0.102425	0.0512125	−	0.998688i	$-0.483691\pi$
$281$	1.71696	0.102425	0.0512125	+	0.998688i	$0.483691\pi$
$282$	9.10926	0.542449
$283$	−1.54929	−0.0920957	−0.0460479	−	0.998939i	$-0.514663\pi$
$283$	−1.54929	−0.0920957	−0.0460479	+	0.998939i	$0.514663\pi$
$284$	11.3360	0.672666
$285$	−2.29078	−0.135694
$286$	0	0
$287$	−6.14359	−0.362645
$288$	−1.00000	−0.0589256
$289$	−1.00000	−0.0588235
$290$	2.02283	0.118784
$291$	8.81894	0.516976
$292$	−6.28304	−0.367687
$293$	30.4057	1.77632	0.888160	−	0.459535i	$-0.151984\pi$
$293$	30.4057	1.77632	0.888160	+	0.459535i	$0.151984\pi$
$294$	5.25078	0.306232
$295$	3.14152	0.182906
$296$	6.80951	0.395795
$297$	4.61335	0.267694
$298$	4.08519	0.236649
$299$	0	0
$300$	1.00000	0.0577350
$301$	11.3816	0.656026
$302$	19.9811	1.14978
$303$	−7.22671	−0.415164
$304$	−2.29078	−0.131385
$305$	0.535898	0.0306855
$306$	−4.00000	−0.228665
$307$	9.82622	0.560812	0.280406	−	0.959882i	$-0.409531\pi$
$307$	9.82622	0.560812	0.280406	+	0.959882i	$0.409531\pi$
$308$	6.10153	0.347667
$309$	18.4000	1.04674
$310$	−10.1321	−0.575464
$311$	3.40049	0.192824	0.0964121	−	0.995342i	$-0.469263\pi$
$311$	3.40049	0.192824	0.0964121	+	0.995342i	$0.469263\pi$
$312$	0	0
$313$	−16.2340	−0.917599	−0.458800	−	0.888540i	$-0.651720\pi$
$313$	−16.2340	−0.917599	−0.458800	+	0.888540i	$0.651720\pi$
$314$	−7.13379	−0.402583
$315$	1.32258	0.0745189
$316$	2.96774	0.166948
$317$	−23.5231	−1.32119	−0.660596	−	0.750742i	$-0.729696\pi$
$317$	−23.5231	−1.32119	−0.660596	+	0.750742i	$0.729696\pi$
$318$	−0.826674	−0.0463576
$319$	−9.33201	−0.522493
$320$	1.00000	0.0559017
$321$	3.07180	0.171451
$322$	−11.4641	−0.638869
$323$	−9.16310	−0.509849
$324$	1.00000	0.0555556
$325$	0	0
$326$	9.89470	0.548016
$327$	−13.2267	−0.731439
$328$	4.64516	0.256486
$329$	−12.0477	−0.664213
$330$	−4.61335	−0.253957
$331$	−18.0904	−0.994338	−0.497169	−	0.867654i	$-0.665627\pi$
$331$	−18.0904	−0.994338	−0.497169	+	0.867654i	$0.665627\pi$
$332$	−15.8719	−0.871082
$333$	−6.80951	−0.373159
$334$	24.0375	1.31527
$335$	−3.18106	−0.173800
$336$	1.32258	0.0721526
$337$	5.69900	0.310444	0.155222	−	0.987880i	$-0.450391\pi$
$337$	5.69900	0.310444	0.155222	+	0.987880i	$0.450391\pi$
$338$	0	0
$339$	−8.08643	−0.439195
$340$	4.00000	0.216930
$341$	46.7429	2.53127
$342$	2.29078	0.123871
$343$	−16.2026	−0.874860
$344$	−8.60562	−0.463984
$345$	8.66799	0.466669
$346$	−2.52817	−0.135915
$347$	−15.7471	−0.845351	−0.422676	−	0.906281i	$-0.638909\pi$
$347$	−15.7471	−0.845351	−0.422676	+	0.906281i	$0.638909\pi$
$348$	−2.02283	−0.108435
$349$	−15.3205	−0.820088	−0.410044	−	0.912066i	$-0.634487\pi$
$349$	−15.3205	−0.820088	−0.410044	+	0.912066i	$0.634487\pi$
$350$	−1.32258	−0.0706949
$351$	0	0
$352$	−4.61335	−0.245893
$353$	1.19993	0.0638657	0.0319328	−	0.999490i	$-0.489834\pi$
$353$	1.19993	0.0638657	0.0319328	+	0.999490i	$0.489834\pi$
$354$	−3.14152	−0.166970
$355$	11.3360	0.601651
$356$	−11.8641	−0.628798
$357$	5.29032	0.279993
$358$	6.27568	0.331680
$359$	16.2830	0.859386	0.429693	−	0.902975i	$-0.358622\pi$
$359$	16.2830	0.859386	0.429693	+	0.902975i	$0.358622\pi$
$360$	−1.00000	−0.0527046
$361$	−13.7523	−0.723808
$362$	−12.2830	−0.645582
$363$	10.2830	0.539720
$364$	0	0
$365$	−6.28304	−0.328870
$366$	−0.535898	−0.0280119
$367$	−19.6345	−1.02491	−0.512456	−	0.858714i	$-0.671264\pi$
$367$	−19.6345	−1.02491	−0.512456	+	0.858714i	$0.671264\pi$
$368$	8.66799	0.451850
$369$	−4.64516	−0.241817
$370$	6.80951	0.354009
$371$	1.09334	0.0567635
$372$	10.1321	0.525324
$373$	−2.55748	−0.132421	−0.0662106	−	0.997806i	$-0.521091\pi$
$373$	−2.55748	−0.132421	−0.0662106	+	0.997806i	$0.521091\pi$
$374$	−18.4534	−0.954204
$375$	1.00000	0.0516398
$376$	9.10926	0.469774
$377$	0	0
$378$	−1.32258	−0.0680262
$379$	−15.1088	−0.776087	−0.388044	−	0.921641i	$-0.626849\pi$
$379$	−15.1088	−0.776087	−0.388044	+	0.921641i	$0.626849\pi$
$380$	−2.29078	−0.117514
$381$	11.4718	0.587720
$382$	9.74715	0.498707
$383$	18.7303	0.957076	0.478538	−	0.878067i	$-0.341167\pi$
$383$	18.7303	0.957076	0.478538	+	0.878067i	$0.341167\pi$
$384$	−1.00000	−0.0510310
$385$	6.10153	0.310963
$386$	−13.7626	−0.700498
$387$	8.60562	0.437448
$388$	8.81894	0.447714
$389$	−6.96899	−0.353342	−0.176671	−	0.984270i	$-0.556533\pi$
$389$	−6.96899	−0.353342	−0.176671	+	0.984270i	$0.556533\pi$
$390$	0	0
$391$	34.6719	1.75344
$392$	5.25078	0.265205
$393$	−15.9906	−0.806617
$394$	10.1415	0.510922
$395$	2.96774	0.149323
$396$	4.61335	0.231830
$397$	−18.5721	−0.932108	−0.466054	−	0.884756i	$-0.654325\pi$
$397$	−18.5721	−0.932108	−0.466054	+	0.884756i	$0.654325\pi$
$398$	−9.57336	−0.479869
$399$	−3.02973	−0.151676
$400$	1.00000	0.0500000
$401$	29.6904	1.48267	0.741333	−	0.671138i	$-0.234194\pi$
$401$	29.6904	1.48267	0.741333	+	0.671138i	$0.234194\pi$
$402$	3.18106	0.158657
$403$	0	0
$404$	−7.22671	−0.359542
$405$	1.00000	0.0496904
$406$	2.67535	0.132775
$407$	−31.4147	−1.55717
$408$	−4.00000	−0.198030
$409$	24.3355	1.20331	0.601657	−	0.798755i	$-0.294507\pi$
$409$	24.3355	1.20331	0.601657	+	0.798755i	$0.294507\pi$
$410$	4.64516	0.229408
$411$	16.0697	0.792661
$412$	18.4000	0.906505
$413$	4.15491	0.204450
$414$	−8.66799	−0.426008
$415$	−15.8719	−0.779119
$416$	0	0
$417$	9.32258	0.456529
$418$	10.5682	0.516906
$419$	−2.88255	−0.140822	−0.0704109	−	0.997518i	$-0.522431\pi$
$419$	−2.88255	−0.140822	−0.0704109	+	0.997518i	$0.522431\pi$
$420$	1.32258	0.0645353
$421$	4.94707	0.241106	0.120553	−	0.992707i	$-0.461533\pi$
$421$	4.94707	0.241106	0.120553	+	0.992707i	$0.461533\pi$
$422$	1.08519	0.0528261
$423$	−9.10926	−0.442907
$424$	−0.826674	−0.0401468
$425$	4.00000	0.194029
$426$	−11.3360	−0.549230
$427$	0.708768	0.0342997
$428$	3.07180	0.148481
$429$	0	0
$430$	−8.60562	−0.415000
$431$	−17.7626	−0.855595	−0.427797	−	0.903875i	$-0.640710\pi$
$431$	−17.7626	−0.855595	−0.427797	+	0.903875i	$0.640710\pi$
$432$	1.00000	0.0481125
$433$	35.8375	1.72224	0.861121	−	0.508400i	$-0.169763\pi$
$433$	35.8375	1.72224	0.861121	+	0.508400i	$0.169763\pi$
$434$	−13.4005	−0.643244
$435$	−2.02283	−0.0969871
$436$	−13.2267	−0.633445
$437$	−19.8564	−0.949861
$438$	6.28304	0.300215
$439$	10.0904	0.481588	0.240794	−	0.970576i	$-0.422592\pi$
$439$	10.0904	0.481588	0.240794	+	0.970576i	$0.422592\pi$
$440$	−4.61335	−0.219933
$441$	−5.25078	−0.250037
$442$	0	0
$443$	13.6981	0.650816	0.325408	−	0.945574i	$-0.394498\pi$
$443$	13.6981	0.650816	0.325408	+	0.945574i	$0.394498\pi$
$444$	−6.80951	−0.323165
$445$	−11.8641	−0.562414
$446$	−24.9416	−1.18102
$447$	−4.08519	−0.193223
$448$	1.32258	0.0624860
$449$	15.3128	0.722655	0.361327	−	0.932439i	$-0.382324\pi$
$449$	15.3128	0.722655	0.361327	+	0.932439i	$0.382324\pi$
$450$	−1.00000	−0.0471405
$451$	−21.4298	−1.00909
$452$	−8.08643	−0.380354
$453$	−19.9811	−0.938795
$454$	−19.3205	−0.906756
$455$	0	0
$456$	2.29078	0.107275
$457$	−15.5554	−0.727651	−0.363826	−	0.931467i	$-0.618530\pi$
$457$	−15.5554	−0.727651	−0.363826	+	0.931467i	$0.618530\pi$
$458$	−4.15491	−0.194146
$459$	4.00000	0.186704
$460$	8.66799	0.404147
$461$	−15.6431	−0.728571	−0.364286	−	0.931287i	$-0.618687\pi$
$461$	−15.6431	−0.728571	−0.364286	+	0.931287i	$0.618687\pi$
$462$	−6.10153	−0.283869
$463$	13.7170	0.637481	0.318741	−	0.947842i	$-0.396740\pi$
$463$	13.7170	0.637481	0.318741	+	0.947842i	$0.396740\pi$
$464$	−2.02283	−0.0939073
$465$	10.1321	0.469864
$466$	16.9665	0.785958
$467$	0.943666	0.0436677	0.0218338	−	0.999762i	$-0.493050\pi$
$467$	0.943666	0.0436677	0.0218338	+	0.999762i	$0.493050\pi$
$468$	0	0
$469$	−4.20720	−0.194271
$470$	9.10926	0.420179
$471$	7.13379	0.328708
$472$	−3.14152	−0.144600
$473$	39.7008	1.82544
$474$	−2.96774	−0.136313
$475$	−2.29078	−0.105108
$476$	5.29032	0.242481
$477$	0.826674	0.0378508
$478$	−6.34416	−0.290175
$479$	11.1020	0.507263	0.253631	−	0.967301i	$-0.418375\pi$
$479$	11.1020	0.507263	0.253631	+	0.967301i	$0.418375\pi$
$480$	−1.00000	−0.0456435
$481$	0	0
$482$	−24.1855	−1.10162
$483$	11.4641	0.521635
$484$	10.2830	0.467411
$485$	8.81894	0.400448
$486$	−1.00000	−0.0453609
$487$	32.9416	1.49273	0.746363	−	0.665539i	$-0.231798\pi$
$487$	32.9416	1.49273	0.746363	+	0.665539i	$0.231798\pi$
$488$	−0.535898	−0.0242590
$489$	−9.89470	−0.447454
$490$	5.25078	0.237206
$491$	28.4513	1.28399	0.641996	−	0.766708i	$-0.278107\pi$
$491$	28.4513	1.28399	0.641996	+	0.766708i	$0.278107\pi$
$492$	−4.64516	−0.209420
$493$	−8.09130	−0.364414
$494$	0	0
$495$	4.61335	0.207355
$496$	10.1321	0.454944
$497$	14.9927	0.672516
$498$	15.8719	0.711235
$499$	4.10926	0.183956	0.0919779	−	0.995761i	$-0.470681\pi$
$499$	4.10926	0.183956	0.0919779	+	0.995761i	$0.470681\pi$
$500$	1.00000	0.0447214
$501$	−24.0375	−1.07391
$502$	−8.82497	−0.393878
$503$	5.73601	0.255756	0.127878	−	0.991790i	$-0.459183\pi$
$503$	5.73601	0.255756	0.127878	+	0.991790i	$0.459183\pi$
$504$	−1.32258	−0.0589124
$505$	−7.22671	−0.321584
$506$	−39.9885	−1.77771
$507$	0	0
$508$	11.4718	0.508980
$509$	−15.1415	−0.671136	−0.335568	−	0.942016i	$-0.608928\pi$
$509$	−15.1415	−0.671136	−0.335568	+	0.942016i	$0.608928\pi$
$510$	−4.00000	−0.177123
$511$	−8.30983	−0.367605
$512$	−1.00000	−0.0441942
$513$	−2.29078	−0.101140
$514$	−8.38494	−0.369844
$515$	18.4000	0.810802
$516$	8.60562	0.378841
$517$	−42.0243	−1.84822
$518$	9.00612	0.395706
$519$	2.52817	0.110974
$520$	0	0
$521$	8.93027	0.391242	0.195621	−	0.980680i	$-0.437328\pi$
$521$	8.93027	0.391242	0.195621	+	0.980680i	$0.437328\pi$
$522$	2.02283	0.0885367
$523$	−9.81687	−0.429262	−0.214631	−	0.976695i	$-0.568855\pi$
$523$	−9.81687	−0.429262	−0.214631	+	0.976695i	$0.568855\pi$
$524$	−15.9906	−0.698551
$525$	1.32258	0.0577221
$526$	−1.92130	−0.0837725
$527$	40.5283	1.76544
$528$	4.61335	0.200771
$529$	52.1340	2.26669
$530$	−0.826674	−0.0359084
$531$	3.14152	0.136330
$532$	−3.02973	−0.131356
$533$	0	0
$534$	11.8641	0.513411
$535$	3.07180	0.132805
$536$	3.18106	0.137401
$537$	−6.27568	−0.270816
$538$	32.3098	1.39298
$539$	−24.2237	−1.04339
$540$	1.00000	0.0430331
$541$	3.80826	0.163730	0.0818650	−	0.996643i	$-0.473912\pi$
$541$	3.80826	0.163730	0.0818650	+	0.996643i	$0.473912\pi$
$542$	23.4526	1.00738
$543$	12.2830	0.527116
$544$	−4.00000	−0.171499
$545$	−13.2267	−0.566570
$546$	0	0
$547$	45.5847	1.94906	0.974530	−	0.224257i	$-0.0719954\pi$
$547$	45.5847	1.94906	0.974530	+	0.224257i	$0.0719954\pi$
$548$	16.0697	0.686465
$549$	0.535898	0.0228716
$550$	−4.61335	−0.196714
$551$	4.63384	0.197408
$552$	−8.66799	−0.368934
$553$	3.92507	0.166911
$554$	9.00566	0.382614
$555$	−6.80951	−0.289047
$556$	9.32258	0.395365
$557$	36.8591	1.56177	0.780885	−	0.624674i	$-0.214768\pi$
$557$	36.8591	1.56177	0.780885	+	0.624674i	$0.214768\pi$
$558$	−10.1321	−0.428925
$559$	0	0
$560$	1.32258	0.0558892
$561$	18.4534	0.779104
$562$	−1.71696	−0.0724254
$563$	33.7739	1.42340	0.711701	−	0.702483i	$-0.247925\pi$
$563$	33.7739	1.42340	0.711701	+	0.702483i	$0.247925\pi$
$564$	−9.10926	−0.383569
$565$	−8.08643	−0.340199
$566$	1.54929	0.0651215
$567$	1.32258	0.0555431
$568$	−11.3360	−0.475647
$569$	−25.4318	−1.06616	−0.533079	−	0.846065i	$-0.678965\pi$
$569$	−25.4318	−1.06616	−0.533079	+	0.846065i	$0.678965\pi$
$570$	2.29078	0.0959500
$571$	−13.3682	−0.559443	−0.279722	−	0.960081i	$-0.590242\pi$
$571$	−13.3682	−0.559443	−0.279722	+	0.960081i	$0.590242\pi$
$572$	0	0
$573$	−9.74715	−0.407193
$574$	6.14359	0.256429
$575$	8.66799	0.361480
$576$	1.00000	0.0416667
$577$	9.57428	0.398582	0.199291	−	0.979940i	$-0.436136\pi$
$577$	9.57428	0.398582	0.199291	+	0.979940i	$0.436136\pi$
$578$	1.00000	0.0415945
$579$	13.7626	0.571954
$580$	−2.02283	−0.0839933
$581$	−20.9918	−0.870887
$582$	−8.81894	−0.365557
$583$	3.81374	0.157949
$584$	6.28304	0.259994
$585$	0	0
$586$	−30.4057	−1.25605
$587$	1.40049	0.0578045	0.0289023	−	0.999582i	$-0.490799\pi$
$587$	1.40049	0.0578045	0.0289023	+	0.999582i	$0.490799\pi$
$588$	−5.25078	−0.216539
$589$	−23.2103	−0.956365
$590$	−3.14152	−0.129334
$591$	−10.1415	−0.417166
$592$	−6.80951	−0.279869
$593$	−10.7303	−0.440643	−0.220321	−	0.975427i	$-0.570711\pi$
$593$	−10.7303	−0.440643	−0.220321	+	0.975427i	$0.570711\pi$
$594$	−4.61335	−0.189288
$595$	5.29032	0.216882
$596$	−4.08519	−0.167336
$597$	9.57336	0.391812
$598$	0	0
$599$	−40.7967	−1.66691	−0.833453	−	0.552590i	$-0.813640\pi$
$599$	−40.7967	−1.66691	−0.833453	+	0.552590i	$0.813640\pi$
$600$	−1.00000	−0.0408248
$601$	42.8832	1.74924	0.874621	−	0.484808i	$-0.161110\pi$
$601$	42.8832	1.74924	0.874621	+	0.484808i	$0.161110\pi$
$602$	−11.3816	−0.463880
$603$	−3.18106	−0.129543
$604$	−19.9811	−0.813021
$605$	10.2830	0.418065
$606$	7.22671	0.293565
$607$	−6.87233	−0.278939	−0.139470	−	0.990226i	$-0.544540\pi$
$607$	−6.87233	−0.278939	−0.139470	+	0.990226i	$0.544540\pi$
$608$	2.29078	0.0929032
$609$	−2.67535	−0.108411
$610$	−0.535898	−0.0216979
$611$	0	0
$612$	4.00000	0.161690
$613$	−0.761361	−0.0307511	−0.0153755	−	0.999882i	$-0.504894\pi$
$613$	−0.761361	−0.0307511	−0.0153755	+	0.999882i	$0.504894\pi$
$614$	−9.82622	−0.396554
$615$	−4.64516	−0.187311
$616$	−6.10153	−0.245838
$617$	−24.6022	−0.990448	−0.495224	−	0.868765i	$-0.664914\pi$
$617$	−24.6022	−0.990448	−0.495224	+	0.868765i	$0.664914\pi$
$618$	−18.4000	−0.740158
$619$	17.2035	0.691468	0.345734	−	0.938333i	$-0.387630\pi$
$619$	17.2035	0.691468	0.345734	+	0.938333i	$0.387630\pi$
$620$	10.1321	0.406914
$621$	8.66799	0.347834
$622$	−3.40049	−0.136347
$623$	−15.6913	−0.628657
$624$	0	0
$625$	1.00000	0.0400000
$626$	16.2340	0.648841
$627$	−10.5682	−0.422052
$628$	7.13379	0.284669
$629$	−27.2380	−1.08605
$630$	−1.32258	−0.0526928
$631$	2.40777	0.0958517	0.0479259	−	0.998851i	$-0.484739\pi$
$631$	2.40777	0.0958517	0.0479259	+	0.998851i	$0.484739\pi$
$632$	−2.96774	−0.118050
$633$	−1.08519	−0.0431323
$634$	23.5231	0.934223
$635$	11.4718	0.455246
$636$	0.826674	0.0327797
$637$	0	0
$638$	9.33201	0.369458
$639$	11.3360	0.448444
$640$	−1.00000	−0.0395285
$641$	−19.4775	−0.769315	−0.384657	−	0.923059i	$-0.625680\pi$
$641$	−19.4775	−0.769315	−0.384657	+	0.923059i	$0.625680\pi$
$642$	−3.07180	−0.121234
$643$	23.9543	0.944667	0.472334	−	0.881420i	$-0.343412\pi$
$643$	23.9543	0.944667	0.472334	+	0.881420i	$0.343412\pi$
$644$	11.4641	0.451749
$645$	8.60562	0.338846
$646$	9.16310	0.360517
$647$	18.2108	0.715940	0.357970	−	0.933733i	$-0.383469\pi$
$647$	18.2108	0.715940	0.357970	+	0.933733i	$0.383469\pi$
$648$	−1.00000	−0.0392837
$649$	14.4930	0.568898
$650$	0	0
$651$	13.4005	0.525207
$652$	−9.89470	−0.387506
$653$	−48.1585	−1.88459	−0.942294	−	0.334787i	$-0.891336\pi$
$653$	−48.1585	−1.88459	−0.942294	+	0.334787i	$0.891336\pi$
$654$	13.2267	0.517205
$655$	−15.9906	−0.624803
$656$	−4.64516	−0.181363
$657$	−6.28304	−0.245125
$658$	12.0477	0.469669
$659$	−36.8254	−1.43451	−0.717257	−	0.696809i	$-0.754603\pi$
$659$	−36.8254	−1.43451	−0.717257	+	0.696809i	$0.754603\pi$
$660$	4.61335	0.179575
$661$	22.5318	0.876384	0.438192	−	0.898881i	$-0.355619\pi$
$661$	22.5318	0.876384	0.438192	+	0.898881i	$0.355619\pi$
$662$	18.0904	0.703103
$663$	0	0
$664$	15.8719	0.615948
$665$	−3.02973	−0.117488
$666$	6.80951	0.263863
$667$	−17.5338	−0.678912
$668$	−24.0375	−0.930037
$669$	24.9416	0.964298
$670$	3.18106	0.122895
$671$	2.47229	0.0954417
$672$	−1.32258	−0.0510196
$673$	23.7437	0.915254	0.457627	−	0.889144i	$-0.348700\pi$
$673$	23.7437	0.915254	0.457627	+	0.889144i	$0.348700\pi$
$674$	−5.69900	−0.219517
$675$	1.00000	0.0384900
$676$	0	0
$677$	1.16559	0.0447975	0.0223987	−	0.999749i	$-0.492870\pi$
$677$	1.16559	0.0447975	0.0223987	+	0.999749i	$0.492870\pi$
$678$	8.08643	0.310558
$679$	11.6638	0.447614
$680$	−4.00000	−0.153393
$681$	19.3205	0.740363
$682$	−46.7429	−1.78988
$683$	13.8719	0.530792	0.265396	−	0.964139i	$-0.414497\pi$
$683$	13.8719	0.530792	0.265396	+	0.964139i	$0.414497\pi$
$684$	−2.29078	−0.0875900
$685$	16.0697	0.613993
$686$	16.2026	0.618620
$687$	4.15491	0.158520
$688$	8.60562	0.328086
$689$	0	0
$690$	−8.66799	−0.329985
$691$	−41.2190	−1.56804	−0.784022	−	0.620733i	$-0.786835\pi$
$691$	−41.2190	−1.56804	−0.784022	+	0.620733i	$0.786835\pi$
$692$	2.52817	0.0961065
$693$	6.10153	0.231778
$694$	15.7471	0.597753
$695$	9.32258	0.353626
$696$	2.02283	0.0766750
$697$	−18.5806	−0.703792
$698$	15.3205	0.579890
$699$	−16.9665	−0.641732
$700$	1.32258	0.0499888
$701$	23.0112	0.869122	0.434561	−	0.900642i	$-0.356904\pi$
$701$	23.0112	0.869122	0.434561	+	0.900642i	$0.356904\pi$
$702$	0	0
$703$	15.5991	0.588329
$704$	4.61335	0.173872
$705$	−9.10926	−0.343075
$706$	−1.19993	−0.0451599
$707$	−9.55790	−0.359462
$708$	3.14152	0.118066
$709$	−17.0831	−0.641570	−0.320785	−	0.947152i	$-0.603947\pi$
$709$	−17.0831	−0.641570	−0.320785	+	0.947152i	$0.603947\pi$
$710$	−11.3360	−0.425431
$711$	2.96774	0.111299
$712$	11.8641	0.444627
$713$	87.8248	3.28906
$714$	−5.29032	−0.197985
$715$	0	0
$716$	−6.27568	−0.234533
$717$	6.34416	0.236927
$718$	−16.2830	−0.607678
$719$	−43.7128	−1.63021	−0.815106	−	0.579311i	$-0.803322\pi$
$719$	−43.7128	−1.63021	−0.815106	+	0.579311i	$0.803322\pi$
$720$	1.00000	0.0372678
$721$	24.3355	0.906302
$722$	13.7523	0.511809
$723$	24.1855	0.899467
$724$	12.2830	0.456496
$725$	−2.02283	−0.0751259
$726$	−10.2830	−0.381640
$727$	−31.8453	−1.18108	−0.590538	−	0.807010i	$-0.701084\pi$
$727$	−31.8453	−1.18108	−0.590538	+	0.807010i	$0.701084\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.28304	0.232546
$731$	34.4225	1.27316
$732$	0.535898	0.0198074
$733$	5.96774	0.220423	0.110212	−	0.993908i	$-0.464847\pi$
$733$	5.96774	0.220423	0.110212	+	0.993908i	$0.464847\pi$
$734$	19.6345	0.724722
$735$	−5.25078	−0.193678
$736$	−8.66799	−0.319506
$737$	−14.6753	−0.540573
$738$	4.64516	0.170991
$739$	−10.8292	−0.398357	−0.199179	−	0.979963i	$-0.563827\pi$
$739$	−10.8292	−0.398357	−0.199179	+	0.979963i	$0.563827\pi$
$740$	−6.80951	−0.250322
$741$	0	0
$742$	−1.09334	−0.0401378
$743$	19.8503	0.728237	0.364118	−	0.931353i	$-0.381370\pi$
$743$	19.8503	0.728237	0.364118	+	0.931353i	$0.381370\pi$
$744$	−10.1321	−0.371460
$745$	−4.08519	−0.149670
$746$	2.55748	0.0936359
$747$	−15.8719	−0.580721
$748$	18.4534	0.674724
$749$	4.06270	0.148448
$750$	−1.00000	−0.0365148
$751$	−15.3308	−0.559428	−0.279714	−	0.960083i	$-0.590240\pi$
$751$	−15.3308	−0.559428	−0.279714	+	0.960083i	$0.590240\pi$
$752$	−9.10926	−0.332181
$753$	8.82497	0.321600
$754$	0	0
$755$	−19.9811	−0.727188
$756$	1.32258	0.0481018
$757$	45.1633	1.64149	0.820744	−	0.571297i	$-0.193559\pi$
$757$	45.1633	1.64149	0.820744	+	0.571297i	$0.193559\pi$
$758$	15.1088	0.548776
$759$	39.9885	1.45149
$760$	2.29078	0.0830952
$761$	−21.7058	−0.786835	−0.393418	−	0.919360i	$-0.628707\pi$
$761$	−21.7058	−0.786835	−0.393418	+	0.919360i	$0.628707\pi$
$762$	−11.4718	−0.415581
$763$	−17.4934	−0.633303
$764$	−9.74715	−0.352639
$765$	4.00000	0.144620
$766$	−18.7303	−0.676755
$767$	0	0
$768$	1.00000	0.0360844
$769$	42.1132	1.51864	0.759321	−	0.650717i	$-0.225531\pi$
$769$	42.1132	1.51864	0.759321	+	0.650717i	$0.225531\pi$
$770$	−6.10153	−0.219884
$771$	8.38494	0.301976
$772$	13.7626	0.495327
$773$	−29.7605	−1.07041	−0.535206	−	0.844722i	$-0.679766\pi$
$773$	−29.7605	−1.07041	−0.535206	+	0.844722i	$0.679766\pi$
$774$	−8.60562	−0.309323
$775$	10.1321	0.363955
$776$	−8.81894	−0.316582
$777$	−9.00612	−0.323093
$778$	6.96899	0.249850
$779$	10.6410	0.381254
$780$	0	0
$781$	52.2969	1.87133
$782$	−34.6719	−1.23987
$783$	−2.02283	−0.0722899
$784$	−5.25078	−0.187528
$785$	7.13379	0.254616
$786$	15.9906	0.570365
$787$	−41.0448	−1.46309	−0.731545	−	0.681793i	$-0.761200\pi$
$787$	−41.0448	−1.46309	−0.731545	+	0.681793i	$0.761200\pi$
$788$	−10.1415	−0.361277
$789$	1.92130	0.0684000
$790$	−2.96774	−0.105587
$791$	−10.6950	−0.380269
$792$	−4.61335	−0.163928
$793$	0	0
$794$	18.5721	0.659100
$795$	0.826674	0.0293191
$796$	9.57336	0.339319
$797$	45.2526	1.60293	0.801464	−	0.598043i	$-0.204055\pi$
$797$	45.2526	1.60293	0.801464	+	0.598043i	$0.204055\pi$
$798$	3.02973	0.107251
$799$	−36.4370	−1.28905
$800$	−1.00000	−0.0353553
$801$	−11.8641	−0.419199
$802$	−29.6904	−1.04840
$803$	−28.9859	−1.02289
$804$	−3.18106	−0.112187
$805$	11.4641	0.404056
$806$	0	0
$807$	−32.3098	−1.13736
$808$	7.22671	0.254235
$809$	−28.4534	−1.00037	−0.500184	−	0.865919i	$-0.666734\pi$
$809$	−28.4534	−1.00037	−0.500184	+	0.865919i	$0.666734\pi$
$810$	−1.00000	−0.0351364
$811$	44.4114	1.55949	0.779747	−	0.626095i	$-0.215348\pi$
$811$	44.4114	1.55949	0.779747	+	0.626095i	$0.215348\pi$
$812$	−2.67535	−0.0938863
$813$	−23.4526	−0.822518
$814$	31.4147	1.10108
$815$	−9.89470	−0.346596
$816$	4.00000	0.140028
$817$	−19.7135	−0.689690
$818$	−24.3355	−0.850871
$819$	0	0
$820$	−4.64516	−0.162216
$821$	−45.1683	−1.57638	−0.788192	−	0.615429i	$-0.788983\pi$
$821$	−45.1683	−1.57638	−0.788192	+	0.615429i	$0.788983\pi$
$822$	−16.0697	−0.560496
$823$	2.41799	0.0842859	0.0421430	−	0.999112i	$-0.486582\pi$
$823$	2.41799	0.0842859	0.0421430	+	0.999112i	$0.486582\pi$
$824$	−18.4000	−0.640996
$825$	4.61335	0.160616
$826$	−4.15491	−0.144568
$827$	4.26832	0.148424	0.0742120	−	0.997242i	$-0.476356\pi$
$827$	4.26832	0.148424	0.0742120	+	0.997242i	$0.476356\pi$
$828$	8.66799	0.301233
$829$	−42.9852	−1.49294	−0.746468	−	0.665421i	$-0.768252\pi$
$829$	−42.9852	−1.49294	−0.746468	+	0.665421i	$0.768252\pi$
$830$	15.8719	0.550921
$831$	−9.00566	−0.312403
$832$	0	0
$833$	−21.0031	−0.727715
$834$	−9.32258	−0.322815
$835$	−24.0375	−0.831851
$836$	−10.5682	−0.365507
$837$	10.1321	0.350216
$838$	2.88255	0.0995761
$839$	−23.3016	−0.804462	−0.402231	−	0.915538i	$-0.631765\pi$
$839$	−23.3016	−0.804462	−0.402231	+	0.915538i	$0.631765\pi$
$840$	−1.32258	−0.0456333
$841$	−24.9082	−0.858903
$842$	−4.94707	−0.170487
$843$	1.71696	0.0591351
$844$	−1.08519	−0.0373537
$845$	0	0
$846$	9.10926	0.313183
$847$	13.6001	0.467307
$848$	0.826674	0.0283881
$849$	−1.54929	−0.0531715
$850$	−4.00000	−0.137199
$851$	−59.0247	−2.02334
$852$	11.3360	0.388364
$853$	20.8418	0.713609	0.356804	−	0.934179i	$-0.383866\pi$
$853$	20.8418	0.713609	0.356804	+	0.934179i	$0.383866\pi$
$854$	−0.708768	−0.0242536
$855$	−2.29078	−0.0783429
$856$	−3.07180	−0.104992
$857$	−36.7250	−1.25450	−0.627250	−	0.778818i	$-0.715820\pi$
$857$	−36.7250	−1.25450	−0.627250	+	0.778818i	$0.715820\pi$
$858$	0	0
$859$	0.914812	0.0312130	0.0156065	−	0.999878i	$-0.495032\pi$
$859$	0.914812	0.0312130	0.0156065	+	0.999878i	$0.495032\pi$
$860$	8.60562	0.293449
$861$	−6.14359	−0.209373
$862$	17.7626	0.604997
$863$	−33.6104	−1.14411	−0.572056	−	0.820215i	$-0.693854\pi$
$863$	−33.6104	−1.14411	−0.572056	+	0.820215i	$0.693854\pi$
$864$	−1.00000	−0.0340207
$865$	2.52817	0.0859603
$866$	−35.8375	−1.21781
$867$	−1.00000	−0.0339618
$868$	13.4005	0.454842
$869$	13.6912	0.464443
$870$	2.02283	0.0685802
$871$	0	0
$872$	13.2267	0.447913
$873$	8.81894	0.298476
$874$	19.8564	0.671653
$875$	1.32258	0.0447114
$876$	−6.28304	−0.212284
$877$	24.3213	0.821273	0.410637	−	0.911799i	$-0.365307\pi$
$877$	24.3213	0.821273	0.410637	+	0.911799i	$0.365307\pi$
$878$	−10.0904	−0.340534
$879$	30.4057	1.02556
$880$	4.61335	0.155516
$881$	−9.90413	−0.333679	−0.166839	−	0.985984i	$-0.553356\pi$
$881$	−9.90413	−0.333679	−0.166839	+	0.985984i	$0.553356\pi$
$882$	5.25078	0.176803
$883$	43.9718	1.47977	0.739884	−	0.672734i	$-0.234880\pi$
$883$	43.9718	1.47977	0.739884	+	0.672734i	$0.234880\pi$
$884$	0	0
$885$	3.14152	0.105601
$886$	−13.6981	−0.460196
$887$	50.5614	1.69769	0.848843	−	0.528645i	$-0.177300\pi$
$887$	50.5614	1.69769	0.848843	+	0.528645i	$0.177300\pi$
$888$	6.80951	0.228512
$889$	15.1724	0.508866
$890$	11.8641	0.397687
$891$	4.61335	0.154553
$892$	24.9416	0.835106
$893$	20.8673	0.698297
$894$	4.08519	0.136629
$895$	−6.27568	−0.209773
$896$	−1.32258	−0.0441843
$897$	0	0
$898$	−15.3128	−0.510994
$899$	−20.4954	−0.683562
$900$	1.00000	0.0333333
$901$	3.30669	0.110162
$902$	21.4298	0.713533
$903$	11.3816	0.378757
$904$	8.08643	0.268951
$905$	12.2830	0.408302
$906$	19.9811	0.663829
$907$	14.2435	0.472948	0.236474	−	0.971638i	$-0.424008\pi$
$907$	14.2435	0.472948	0.236474	+	0.971638i	$0.424008\pi$
$908$	19.3205	0.641174
$909$	−7.22671	−0.239695
$910$	0	0
$911$	21.8108	0.722623	0.361311	−	0.932445i	$-0.382329\pi$
$911$	21.8108	0.722623	0.361311	+	0.932445i	$0.382329\pi$
$912$	−2.29078	−0.0758551
$913$	−73.2226	−2.42331
$914$	15.5554	0.514527
$915$	0.535898	0.0177163
$916$	4.15491	0.137282
$917$	−21.1488	−0.698395
$918$	−4.00000	−0.132020
$919$	−5.30578	−0.175022	−0.0875108	−	0.996164i	$-0.527891\pi$
$919$	−5.30578	−0.175022	−0.0875108	+	0.996164i	$0.527891\pi$
$920$	−8.66799	−0.285775
$921$	9.82622	0.323785
$922$	15.6431	0.515178
$923$	0	0
$924$	6.10153	0.200726
$925$	−6.80951	−0.223895
$926$	−13.7170	−0.450767
$927$	18.4000	0.604336
$928$	2.02283	0.0664025
$929$	44.3408	1.45477	0.727386	−	0.686228i	$-0.240735\pi$
$929$	44.3408	1.45477	0.727386	+	0.686228i	$0.240735\pi$
$930$	−10.1321	−0.332244
$931$	12.0284	0.394214
$932$	−16.9665	−0.555756
$933$	3.40049	0.111327
$934$	−0.943666	−0.0308777
$935$	18.4534	0.603491
$936$	0	0
$937$	38.5283	1.25867	0.629333	−	0.777136i	$-0.283328\pi$
$937$	38.5283	1.25867	0.629333	+	0.777136i	$0.283328\pi$
$938$	4.20720	0.137370
$939$	−16.2340	−0.529776
$940$	−9.10926	−0.297111
$941$	−28.8637	−0.940929	−0.470465	−	0.882419i	$-0.655914\pi$
$941$	−28.8637	−0.940929	−0.470465	+	0.882419i	$0.655914\pi$
$942$	−7.13379	−0.232431
$943$	−40.2642	−1.31118
$944$	3.14152	0.102248
$945$	1.32258	0.0430235
$946$	−39.7008	−1.29078
$947$	−49.2346	−1.59991	−0.799955	−	0.600060i	$-0.795143\pi$
$947$	−49.2346	−1.59991	−0.799955	+	0.600060i	$0.795143\pi$
$948$	2.96774	0.0963877
$949$	0	0
$950$	2.29078	0.0743226
$951$	−23.5231	−0.762790
$952$	−5.29032	−0.171460
$953$	−26.5097	−0.858732	−0.429366	−	0.903131i	$-0.641263\pi$
$953$	−26.5097	−0.858732	−0.429366	+	0.903131i	$0.641263\pi$
$954$	−0.826674	−0.0267645
$955$	−9.74715	−0.315410
$956$	6.34416	0.205185
$957$	−9.33201	−0.301661
$958$	−11.1020	−0.358689
$959$	21.2535	0.686311
$960$	1.00000	0.0322749
$961$	71.6592	2.31159
$962$	0	0
$963$	3.07180	0.0989873
$964$	24.1855	0.778962
$965$	13.7626	0.443034
$966$	−11.4641	−0.368851
$967$	−52.3877	−1.68468	−0.842338	−	0.538950i	$-0.818821\pi$
$967$	−52.3877	−1.68468	−0.842338	+	0.538950i	$0.818821\pi$
$968$	−10.2830	−0.330510
$969$	−9.16310	−0.294361
$970$	−8.81894	−0.283159
$971$	−28.6431	−0.919200	−0.459600	−	0.888126i	$-0.652007\pi$
$971$	−28.6431	−0.919200	−0.459600	+	0.888126i	$0.652007\pi$
$972$	1.00000	0.0320750
$973$	12.3299	0.395277
$974$	−32.9416	−1.05552
$975$	0	0
$976$	0.535898	0.0171537
$977$	40.5499	1.29731	0.648654	−	0.761084i	$-0.275332\pi$
$977$	40.5499	1.29731	0.648654	+	0.761084i	$0.275332\pi$
$978$	9.89470	0.316397
$979$	−54.7335	−1.74929
$980$	−5.25078	−0.167730
$981$	−13.2267	−0.422296
$982$	−28.4513	−0.907919
$983$	22.4160	0.714958	0.357479	−	0.933921i	$-0.383636\pi$
$983$	22.4160	0.714958	0.357479	+	0.933921i	$0.383636\pi$
$984$	4.64516	0.148082
$985$	−10.1415	−0.323136
$986$	8.09130	0.257680
$987$	−12.0477	−0.383483
$988$	0	0
$989$	74.5934	2.37193
$990$	−4.61335	−0.146622
$991$	−28.5688	−0.907518	−0.453759	−	0.891125i	$-0.649917\pi$
$991$	−28.5688	−0.907518	−0.453759	+	0.891125i	$0.649917\pi$
$992$	−10.1321	−0.321694
$993$	−18.0904	−0.574081
$994$	−14.9927	−0.475540
$995$	9.57336	0.303496
$996$	−15.8719	−0.502919
$997$	−34.4000	−1.08946	−0.544730	−	0.838611i	$-0.683368\pi$
$997$	−34.4000	−1.08946	−0.544730	+	0.838611i	$0.683368\pi$
$998$	−4.10926	−0.130076
$999$	−6.80951	−0.215443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.bz.1.3		4
13.2	odd	12		390.2.bb.c.121.2	✓	8
13.5	odd	4		5070.2.b.ba.1351.7		8
13.7	odd	12		390.2.bb.c.361.2	yes	8
13.8	odd	4		5070.2.b.ba.1351.2		8
13.12	even	2		5070.2.a.ca.1.2		4
39.2	even	12		1170.2.bs.f.901.4		8
39.20	even	12		1170.2.bs.f.361.4		8
65.2	even	12		1950.2.y.k.199.4		8
65.7	even	12		1950.2.y.j.49.1		8
65.28	even	12		1950.2.y.j.199.1		8
65.33	even	12		1950.2.y.k.49.4		8
65.54	odd	12		1950.2.bc.g.901.3		8
65.59	odd	12		1950.2.bc.g.751.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.2	✓	8	13.2	odd	12
390.2.bb.c.361.2	yes	8	13.7	odd	12
1170.2.bs.f.361.4		8	39.20	even	12
1170.2.bs.f.901.4		8	39.2	even	12
1950.2.y.j.49.1		8	65.7	even	12
1950.2.y.j.199.1		8	65.28	even	12
1950.2.y.k.49.4		8	65.33	even	12
1950.2.y.k.199.4		8	65.2	even	12
1950.2.bc.g.751.3		8	65.59	odd	12
1950.2.bc.g.901.3		8	65.54	odd	12
5070.2.a.bz.1.3		4	1.1	even	1	trivial
5070.2.a.ca.1.2		4	13.12	even	2
5070.2.b.ba.1351.2		8	13.8	odd	4
5070.2.b.ba.1351.7		8	13.5	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.32258 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.32258 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +4.61335 q^{11} +1.00000 q^{12} -1.32258 q^{14} +1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} -2.29078 q^{19} +1.00000 q^{20} +1.32258 q^{21} -4.61335 q^{22} +8.66799 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +1.32258 q^{28} -2.02283 q^{29} -1.00000 q^{30} +10.1321 q^{31} -1.00000 q^{32} +4.61335 q^{33} -4.00000 q^{34} +1.32258 q^{35} +1.00000 q^{36} -6.80951 q^{37} +2.29078 q^{38} -1.00000 q^{40} -4.64516 q^{41} -1.32258 q^{42} +8.60562 q^{43} +4.61335 q^{44} +1.00000 q^{45} -8.66799 q^{46} -9.10926 q^{47} +1.00000 q^{48} -5.25078 q^{49} -1.00000 q^{50} +4.00000 q^{51} +0.826674 q^{53} -1.00000 q^{54} +4.61335 q^{55} -1.32258 q^{56} -2.29078 q^{57} +2.02283 q^{58} +3.14152 q^{59} +1.00000 q^{60} +0.535898 q^{61} -10.1321 q^{62} +1.32258 q^{63} +1.00000 q^{64} -4.61335 q^{66} -3.18106 q^{67} +4.00000 q^{68} +8.66799 q^{69} -1.32258 q^{70} +11.3360 q^{71} -1.00000 q^{72} -6.28304 q^{73} +6.80951 q^{74} +1.00000 q^{75} -2.29078 q^{76} +6.10153 q^{77} +2.96774 q^{79} +1.00000 q^{80} +1.00000 q^{81} +4.64516 q^{82} -15.8719 q^{83} +1.32258 q^{84} +4.00000 q^{85} -8.60562 q^{86} -2.02283 q^{87} -4.61335 q^{88} -11.8641 q^{89} -1.00000 q^{90} +8.66799 q^{92} +10.1321 q^{93} +9.10926 q^{94} -2.29078 q^{95} -1.00000 q^{96} +8.81894 q^{97} +5.25078 q^{98} +4.61335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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