LMFDB - Embedded newform 5070.2.a.ca.1.1

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			1.1
Root			$-3.64466$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.66808 q^{11} +1.00000 q^{12} -3.64466 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} -6.31274 q^{19} -1.00000 q^{20} -3.64466 q^{21} +1.66808 q^{22} +1.24453 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} -3.64466 q^{28} +10.0448 q^{29} -1.00000 q^{30} +4.21957 q^{31} +1.00000 q^{32} +1.66808 q^{33} +4.00000 q^{34} +3.64466 q^{35} +1.00000 q^{36} -9.86423 q^{37} -6.31274 q^{38} -1.00000 q^{40} +9.28932 q^{41} -3.64466 q^{42} -7.57286 q^{43} +1.66808 q^{44} -1.00000 q^{45} +1.24453 q^{46} +6.82522 q^{47} +1.00000 q^{48} +6.28354 q^{49} +1.00000 q^{50} +4.00000 q^{51} -0.848634 q^{53} +1.00000 q^{54} -1.66808 q^{55} -3.64466 q^{56} -6.31274 q^{57} +10.0448 q^{58} +6.10876 q^{59} -1.00000 q^{60} +7.46410 q^{61} +4.21957 q^{62} -3.64466 q^{63} +1.00000 q^{64} +1.66808 q^{66} +14.7534 q^{67} +4.00000 q^{68} +1.24453 q^{69} +3.64466 q^{70} +3.51093 q^{71} +1.00000 q^{72} -12.2175 q^{73} -9.86423 q^{74} +1.00000 q^{75} -6.31274 q^{76} -6.07957 q^{77} +9.93398 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.28932 q^{82} +7.95317 q^{83} -3.64466 q^{84} -4.00000 q^{85} -7.57286 q^{86} +10.0448 q^{87} +1.66808 q^{88} -5.95162 q^{89} -1.00000 q^{90} +1.24453 q^{92} +4.21957 q^{93} +6.82522 q^{94} +6.31274 q^{95} +1.00000 q^{96} +2.75342 q^{97} +6.28354 q^{98} +1.66808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−3.64466	−1.37755	−0.688776	−	0.724974i	$-0.741852\pi$
$7$	−3.64466	−1.37755	−0.688776	+	0.724974i	$0.741852\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	1.66808	0.502944	0.251472	−	0.967865i	$-0.419085\pi$
$11$	1.66808	0.502944	0.251472	+	0.967865i	$0.419085\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−3.64466	−0.974076
$15$	−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
$19$	−6.31274	−1.44824	−0.724120	−	0.689674i	$-0.757754\pi$
$19$	−6.31274	−1.44824	−0.724120	+	0.689674i	$0.757754\pi$
$20$	−1.00000	−0.223607
$21$	−3.64466	−0.795330
$22$	1.66808	0.355635
$23$	1.24453	0.259503	0.129752	−	0.991547i	$-0.458582\pi$
$23$	1.24453	0.259503	0.129752	+	0.991547i	$0.458582\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	−3.64466	−0.688776
$29$	10.0448	1.86527	0.932635	−	0.360821i	$-0.117504\pi$
$29$	10.0448	1.86527	0.932635	+	0.360821i	$0.117504\pi$
$30$	−1.00000	−0.182574
$31$	4.21957	0.757857	0.378928	−	0.925426i	$-0.376293\pi$
$31$	4.21957	0.757857	0.378928	+	0.925426i	$0.376293\pi$
$32$	1.00000	0.176777
$33$	1.66808	0.290375
$34$	4.00000	0.685994
$35$	3.64466	0.616060
$36$	1.00000	0.166667
$37$	−9.86423	−1.62167	−0.810835	−	0.585275i	$-0.800986\pi$
$37$	−9.86423	−1.62167	−0.810835	+	0.585275i	$0.800986\pi$
$38$	−6.31274	−1.02406
$39$	0	0
$40$	−1.00000	−0.158114
$41$	9.28932	1.45075	0.725374	−	0.688355i	$-0.241667\pi$
$41$	9.28932	1.45075	0.725374	+	0.688355i	$0.241667\pi$
$42$	−3.64466	−0.562383
$43$	−7.57286	−1.15485	−0.577425	−	0.816443i	$-0.695943\pi$
$43$	−7.57286	−1.15485	−0.577425	+	0.816443i	$0.695943\pi$
$44$	1.66808	0.251472
$45$	−1.00000	−0.149071
$46$	1.24453	0.183496
$47$	6.82522	0.995560	0.497780	−	0.867303i	$-0.334149\pi$
$47$	6.82522	0.995560	0.497780	+	0.867303i	$0.334149\pi$
$48$	1.00000	0.144338
$49$	6.28354	0.897649
$50$	1.00000	0.141421
$51$	4.00000	0.560112
$52$	0	0
$53$	−0.848634	−0.116569	−0.0582844	−	0.998300i	$-0.518563\pi$
$53$	−0.848634	−0.116569	−0.0582844	+	0.998300i	$0.518563\pi$
$54$	1.00000	0.136083
$55$	−1.66808	−0.224923
$56$	−3.64466	−0.487038
$57$	−6.31274	−0.836142
$58$	10.0448	1.31895
$59$	6.10876	0.795293	0.397646	−	0.917539i	$-0.369827\pi$
$59$	6.10876	0.795293	0.397646	+	0.917539i	$0.369827\pi$
$60$	−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	$0.341420\pi$
$62$	4.21957	0.535886
$63$	−3.64466	−0.459184
$64$	1.00000	0.125000
$65$	0	0
$66$	1.66808	0.205326
$67$	14.7534	1.80242	0.901209	−	0.433386i	$-0.142681\pi$
$67$	14.7534	1.80242	0.901209	+	0.433386i	$0.142681\pi$
$68$	4.00000	0.485071
$69$	1.24453	0.149824
$70$	3.64466	0.435620
$71$	3.51093	0.416671	0.208336	−	0.978057i	$-0.433195\pi$
$71$	3.51093	0.416671	0.208336	+	0.978057i	$0.433195\pi$
$72$	1.00000	0.117851
$73$	−12.2175	−1.42995	−0.714976	−	0.699149i	$-0.753563\pi$
$73$	−12.2175	−1.42995	−0.714976	+	0.699149i	$0.753563\pi$
$74$	−9.86423	−1.14669
$75$	1.00000	0.115470
$76$	−6.31274	−0.724120
$77$	−6.07957	−0.692831
$78$	0	0
$79$	9.93398	1.11766	0.558830	−	0.829282i	$-0.311250\pi$
$79$	9.93398	1.11766	0.558830	+	0.829282i	$0.311250\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	9.28932	1.02583
$83$	7.95317	0.872974	0.436487	−	0.899711i	$-0.356223\pi$
$83$	7.95317	0.872974	0.436487	+	0.899711i	$0.356223\pi$
$84$	−3.64466	−0.397665
$85$	−4.00000	−0.433861
$86$	−7.57286	−0.816603
$87$	10.0448	1.07691
$88$	1.66808	0.177817
$89$	−5.95162	−0.630870	−0.315435	−	0.948947i	$-0.602150\pi$
$89$	−5.95162	−0.630870	−0.315435	+	0.948947i	$0.602150\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	1.24453	0.129752
$93$	4.21957	0.437549
$94$	6.82522	0.703967
$95$	6.31274	0.647673
$96$	1.00000	0.102062
$97$	2.75342	0.279568	0.139784	−	0.990182i	$-0.455359\pi$
$97$	2.75342	0.279568	0.139784	+	0.990182i	$0.455359\pi$
$98$	6.28354	0.634734
$99$	1.66808	0.167648
$100$	1.00000	0.100000
$101$	5.33615	0.530967	0.265483	−	0.964115i	$-0.414468\pi$
$101$	5.33615	0.530967	0.265483	+	0.964115i	$0.414468\pi$
$102$	4.00000	0.396059
$103$	7.51248	0.740227	0.370113	−	0.928987i	$-0.379319\pi$
$103$	7.51248	0.740227	0.370113	+	0.928987i	$0.379319\pi$
$104$	0	0
$105$	3.64466	0.355682
$106$	−0.848634	−0.0824266
$107$	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
$109$	0.663848	0.0635851	0.0317926	−	0.999494i	$-0.489878\pi$
$109$	0.663848	0.0635851	0.0317926	+	0.999494i	$0.489878\pi$
$110$	−1.66808	−0.159045
$111$	−9.86423	−0.936271
$112$	−3.64466	−0.344388
$113$	−17.8700	−1.68107	−0.840534	−	0.541758i	$-0.817759\pi$
$113$	−17.8700	−1.68107	−0.840534	+	0.541758i	$0.817759\pi$
$114$	−6.31274	−0.591242
$115$	−1.24453	−0.116053
$116$	10.0448	0.932635
$117$	0	0
$118$	6.10876	0.562357
$119$	−14.5786	−1.33642
$120$	−1.00000	−0.0912871
$121$	−8.21752	−0.747047
$122$	7.46410	0.675768
$123$	9.28932	0.837590
$124$	4.21957	0.378928
$125$	−1.00000	−0.0894427
$126$	−3.64466	−0.324692
$127$	14.4407	1.28140	0.640702	−	0.767790i	$-0.278643\pi$
$127$	14.4407	1.28140	0.640702	+	0.767790i	$0.278643\pi$
$128$	1.00000	0.0883883
$129$	−7.57286	−0.666753
$130$	0	0
$131$	−10.8892	−0.951393	−0.475697	−	0.879609i	$-0.657804\pi$
$131$	−10.8892	−0.951393	−0.475697	+	0.879609i	$0.657804\pi$
$132$	1.66808	0.145187
$133$	23.0078	1.99503
$134$	14.7534	1.27450
$135$	−1.00000	−0.0860663
$136$	4.00000	0.342997
$137$	7.03696	0.601208	0.300604	−	0.953749i	$-0.402812\pi$
$137$	7.03696	0.601208	0.300604	+	0.953749i	$0.402812\pi$
$138$	1.24453	0.105942
$139$	11.6447	0.987687	0.493844	−	0.869551i	$-0.335592\pi$
$139$	11.6447	0.987687	0.493844	+	0.869551i	$0.335592\pi$
$140$	3.64466	0.308030
$141$	6.82522	0.574787
$142$	3.51093	0.294631
$143$	0	0
$144$	1.00000	0.0833333
$145$	−10.0448	−0.834174
$146$	−12.2175	−1.01113
$147$	6.28354	0.518258
$148$	−9.86423	−0.810835
$149$	0.772609	0.0632946	0.0316473	−	0.999499i	$-0.489925\pi$
$149$	0.772609	0.0632946	0.0316473	+	0.999499i	$0.489925\pi$
$150$	1.00000	0.0816497
$151$	9.77838	0.795754	0.397877	−	0.917439i	$-0.369747\pi$
$151$	9.77838	0.795754	0.397877	+	0.917439i	$0.369747\pi$
$152$	−6.31274	−0.512030
$153$	4.00000	0.323381
$154$	−6.07957	−0.489906
$155$	−4.21957	−0.338924
$156$	0	0
$157$	−12.0135	−0.958786	−0.479393	−	0.877600i	$-0.659143\pi$
$157$	−12.0135	−0.958786	−0.479393	+	0.877600i	$0.659143\pi$
$158$	9.93398	0.790305
$159$	−0.848634	−0.0673011
$160$	−1.00000	−0.0790569
$161$	−4.53590	−0.357479
$162$	1.00000	0.0785674
$163$	−10.0916	−0.790437	−0.395218	−	0.918587i	$-0.629331\pi$
$163$	−10.0916	−0.790437	−0.395218	+	0.918587i	$0.629331\pi$
$164$	9.28932	0.725374
$165$	−1.66808	−0.129860
$166$	7.95317	0.617285
$167$	7.89701	0.611089	0.305545	−	0.952178i	$-0.401161\pi$
$167$	7.89701	0.611089	0.305545	+	0.952178i	$0.401161\pi$
$168$	−3.64466	−0.281192
$169$	0	0
$170$	−4.00000	−0.306786
$171$	−6.31274	−0.482747
$172$	−7.57286	−0.577425
$173$	−0.440685	−0.0335047	−0.0167523	−	0.999860i	$-0.505333\pi$
$173$	−0.440685	−0.0335047	−0.0167523	+	0.999860i	$0.505333\pi$
$174$	10.0448	0.761493
$175$	−3.64466	−0.275510
$176$	1.66808	0.125736
$177$	6.10876	0.459163
$178$	−5.95162	−0.446093
$179$	−19.6368	−1.46773	−0.733863	−	0.679297i	$-0.762285\pi$
$179$	−19.6368	−1.46773	−0.733863	+	0.679297i	$0.762285\pi$
$180$	−1.00000	−0.0745356
$181$	−6.21752	−0.462145	−0.231072	−	0.972937i	$-0.574223\pi$
$181$	−6.21752	−0.462145	−0.231072	+	0.972937i	$0.574223\pi$
$182$	0	0
$183$	7.46410	0.551762
$184$	1.24453	0.0917482
$185$	9.86423	0.725232
$186$	4.21957	0.309394
$187$	6.67230	0.487927
$188$	6.82522	0.497780
$189$	−3.64466	−0.265110
$190$	6.31274	0.457974
$191$	15.6816	1.13468	0.567341	−	0.823483i	$-0.307972\pi$
$191$	15.6816	1.13468	0.567341	+	0.823483i	$0.307972\pi$
$192$	1.00000	0.0721688
$193$	−8.12795	−0.585063	−0.292531	−	0.956256i	$-0.594498\pi$
$193$	−8.12795	−0.585063	−0.292531	+	0.956256i	$0.594498\pi$
$194$	2.75342	0.197684
$195$	0	0
$196$	6.28354	0.448825
$197$	0.891239	0.0634981	0.0317491	−	0.999496i	$-0.489892\pi$
$197$	0.891239	0.0634981	0.0317491	+	0.999496i	$0.489892\pi$
$198$	1.66808	0.118545
$199$	0.361116	0.0255988	0.0127994	−	0.999918i	$-0.495926\pi$
$199$	0.361116	0.0255988	0.0127994	+	0.999918i	$0.495926\pi$
$200$	1.00000	0.0707107
$201$	14.7534	1.04063
$202$	5.33615	0.375450
$203$	−36.6098	−2.56951
$204$	4.00000	0.280056
$205$	−9.28932	−0.648794
$206$	7.51248	0.523419
$207$	1.24453	0.0865010
$208$	0	0
$209$	−10.5301	−0.728384
$210$	3.64466	0.251505
$211$	2.22739	0.153340	0.0766700	−	0.997057i	$-0.475571\pi$
$211$	2.22739	0.153340	0.0766700	+	0.997057i	$0.475571\pi$
$212$	−0.848634	−0.0582844
$213$	3.51093	0.240565
$214$	16.9282	1.15719
$215$	7.57286	0.516465
$216$	1.00000	0.0680414
$217$	−15.3789	−1.04399
$218$	0.663848	0.0449615
$219$	−12.2175	−0.825584
$220$	−1.66808	−0.112462
$221$	0	0
$222$	−9.86423	−0.662044
$223$	6.08380	0.407401	0.203701	−	0.979033i	$-0.434703\pi$
$223$	6.08380	0.407401	0.203701	+	0.979033i	$0.434703\pi$
$224$	−3.64466	−0.243519
$225$	1.00000	0.0666667
$226$	−17.8700	−1.18869
$227$	15.3205	1.01686	0.508429	−	0.861104i	$-0.330226\pi$
$227$	15.3205	1.01686	0.508429	+	0.861104i	$0.330226\pi$
$228$	−6.31274	−0.418071
$229$	22.2644	1.47127	0.735635	−	0.677378i	$-0.236884\pi$
$229$	22.2644	1.47127	0.735635	+	0.677378i	$0.236884\pi$
$230$	−1.24453	−0.0820621
$231$	−6.07957	−0.400006
$232$	10.0448	0.659473
$233$	−10.8366	−0.709928	−0.354964	−	0.934880i	$-0.615507\pi$
$233$	−10.8366	−0.709928	−0.354964	+	0.934880i	$0.615507\pi$
$234$	0	0
$235$	−6.82522	−0.445228
$236$	6.10876	0.397646
$237$	9.93398	0.645281
$238$	−14.5786	−0.944993
$239$	16.4975	1.06714	0.533568	−	0.845757i	$-0.320851\pi$
$239$	16.4975	1.06714	0.533568	+	0.845757i	$0.320851\pi$
$240$	−1.00000	−0.0645497
$241$	4.40435	0.283709	0.141855	−	0.989887i	$-0.454693\pi$
$241$	4.40435	0.283709	0.141855	+	0.989887i	$0.454693\pi$
$242$	−8.21752	−0.528242
$243$	1.00000	0.0641500
$244$	7.46410	0.477840
$245$	−6.28354	−0.401441
$246$	9.28932	0.592265
$247$	0	0
$248$	4.21957	0.267943
$249$	7.95317	0.504011
$250$	−1.00000	−0.0632456
$251$	11.9453	0.753984	0.376992	−	0.926217i	$-0.376959\pi$
$251$	11.9453	0.753984	0.376992	+	0.926217i	$0.376959\pi$
$252$	−3.64466	−0.229592
$253$	2.07598	0.130515
$254$	14.4407	0.906089
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	19.4621	1.21401	0.607005	−	0.794698i	$-0.292371\pi$
$257$	19.4621	1.21401	0.607005	+	0.794698i	$0.292371\pi$
$258$	−7.57286	−0.471466
$259$	35.9518	2.23393
$260$	0	0
$261$	10.0448	0.621757
$262$	−10.8892	−0.672737
$263$	2.03478	0.125470	0.0627350	−	0.998030i	$-0.480018\pi$
$263$	2.03478	0.125470	0.0627350	+	0.998030i	$0.480018\pi$
$264$	1.66808	0.102663
$265$	0.848634	0.0521312
$266$	23.0078	1.41070
$267$	−5.95162	−0.364233
$268$	14.7534	0.901209
$269$	20.5287	1.25166	0.625829	−	0.779960i	$-0.284761\pi$
$269$	20.5287	1.25166	0.625829	+	0.779960i	$0.284761\pi$
$270$	−1.00000	−0.0608581
$271$	−25.5401	−1.55145	−0.775725	−	0.631072i	$-0.782615\pi$
$271$	−25.5401	−1.55145	−0.775725	+	0.631072i	$0.782615\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	7.03696	0.425119
$275$	1.66808	0.100589
$276$	1.24453	0.0749121
$277$	18.0604	1.08514	0.542572	−	0.840010i	$-0.317451\pi$
$277$	18.0604	1.08514	0.542572	+	0.840010i	$0.317451\pi$
$278$	11.6447	0.698400
$279$	4.21957	0.252619
$280$	3.64466	0.217810
$281$	−20.2175	−1.20608	−0.603038	−	0.797712i	$-0.706043\pi$
$281$	−20.2175	−1.20608	−0.603038	+	0.797712i	$0.706043\pi$
$282$	6.82522	0.406436
$283$	8.69149	0.516656	0.258328	−	0.966057i	$-0.416829\pi$
$283$	8.69149	0.516656	0.258328	+	0.966057i	$0.416829\pi$
$284$	3.51093	0.208336
$285$	6.31274	0.373934
$286$	0	0
$287$	−33.8564	−1.99848
$288$	1.00000	0.0589256
$289$	−1.00000	−0.0588235
$290$	−10.0448	−0.589850
$291$	2.75342	0.161408
$292$	−12.2175	−0.714976
$293$	7.54790	0.440953	0.220476	−	0.975392i	$-0.429239\pi$
$293$	7.54790	0.440953	0.220476	+	0.975392i	$0.429239\pi$
$294$	6.28354	0.366464
$295$	−6.10876	−0.355666
$296$	−9.86423	−0.573347
$297$	1.66808	0.0967916
$298$	0.772609	0.0447560
$299$	0	0
$300$	1.00000	0.0577350
$301$	27.6005	1.59087
$302$	9.77838	0.562683
$303$	5.33615	0.306554
$304$	−6.31274	−0.362060
$305$	−7.46410	−0.427393
$306$	4.00000	0.228665
$307$	−26.0427	−1.48634	−0.743169	−	0.669104i	$-0.766678\pi$
$307$	−26.0427	−1.48634	−0.743169	+	0.669104i	$0.766678\pi$
$308$	−6.07957	−0.346416
$309$	7.51248	0.427370
$310$	−4.21957	−0.239655
$311$	−25.3789	−1.43910	−0.719552	−	0.694438i	$-0.755653\pi$
$311$	−25.3789	−1.43910	−0.719552	+	0.694438i	$0.755653\pi$
$312$	0	0
$313$	−31.4600	−1.77822	−0.889112	−	0.457689i	$-0.848677\pi$
$313$	−31.4600	−1.77822	−0.889112	+	0.457689i	$0.848677\pi$
$314$	−12.0135	−0.677964
$315$	3.64466	0.205353
$316$	9.93398	0.558830
$317$	−24.7093	−1.38781	−0.693905	−	0.720066i	$-0.744111\pi$
$317$	−24.7093	−1.38781	−0.693905	+	0.720066i	$0.744111\pi$
$318$	−0.848634	−0.0475890
$319$	16.7555	0.938126
$320$	−1.00000	−0.0559017
$321$	16.9282	0.944840
$322$	−4.53590	−0.252776
$323$	−25.2509	−1.40500
$324$	1.00000	0.0555556
$325$	0	0
$326$	−10.0916	−0.558923
$327$	0.663848	0.0367109
$328$	9.28932	0.512917
$329$	−24.8756	−1.37144
$330$	−1.66808	−0.0918246
$331$	5.60360	0.308002	0.154001	−	0.988071i	$-0.450784\pi$
$331$	5.60360	0.308002	0.154001	+	0.988071i	$0.450784\pi$
$332$	7.95317	0.436487
$333$	−9.86423	−0.540556
$334$	7.89701	0.432105
$335$	−14.7534	−0.806065
$336$	−3.64466	−0.198832
$337$	−21.7868	−1.18680	−0.593402	−	0.804906i	$-0.702216\pi$
$337$	−21.7868	−1.18680	−0.593402	+	0.804906i	$0.702216\pi$
$338$	0	0
$339$	−17.8700	−0.970565
$340$	−4.00000	−0.216930
$341$	7.03856	0.381159
$342$	−6.31274	−0.341354
$343$	2.61124	0.140994
$344$	−7.57286	−0.408301
$345$	−1.24453	−0.0670034
$346$	−0.440685	−0.0236914
$347$	9.68162	0.519737	0.259868	−	0.965644i	$-0.416321\pi$
$347$	9.68162	0.519737	0.259868	+	0.965644i	$0.416321\pi$
$348$	10.0448	0.538457
$349$	−19.3205	−1.03420	−0.517102	−	0.855924i	$-0.672989\pi$
$349$	−19.3205	−1.03420	−0.517102	+	0.855924i	$0.672989\pi$
$350$	−3.64466	−0.194815
$351$	0	0
$352$	1.66808	0.0889087
$353$	−22.9750	−1.22284	−0.611419	−	0.791307i	$-0.709401\pi$
$353$	−22.9750	−1.22284	−0.611419	+	0.791307i	$0.709401\pi$
$354$	6.10876	0.324677
$355$	−3.51093	−0.186341
$356$	−5.95162	−0.315435
$357$	−14.5786	−0.771583
$358$	−19.6368	−1.03784
$359$	2.21752	0.117036	0.0585182	−	0.998286i	$-0.481362\pi$
$359$	2.21752	0.117036	0.0585182	+	0.998286i	$0.481362\pi$
$360$	−1.00000	−0.0527046
$361$	20.8506	1.09740
$362$	−6.21752	−0.326786
$363$	−8.21752	−0.431308
$364$	0	0
$365$	12.2175	0.639494
$366$	7.46410	0.390155
$367$	−6.08112	−0.317432	−0.158716	−	0.987324i	$-0.550735\pi$
$367$	−6.08112	−0.317432	−0.158716	+	0.987324i	$0.550735\pi$
$368$	1.24453	0.0648758
$369$	9.28932	0.483583
$370$	9.86423	0.512817
$371$	3.09298	0.160580
$372$	4.21957	0.218774
$373$	15.6781	0.811780	0.405890	−	0.913922i	$-0.366962\pi$
$373$	15.6781	0.811780	0.405890	+	0.913922i	$0.366962\pi$
$374$	6.67230	0.345017
$375$	−1.00000	−0.0516398
$376$	6.82522	0.351984
$377$	0	0
$378$	−3.64466	−0.187461
$379$	30.7166	1.57781	0.788903	−	0.614518i	$-0.210650\pi$
$379$	30.7166	1.57781	0.788903	+	0.614518i	$0.210650\pi$
$380$	6.31274	0.323837
$381$	14.4407	0.739819
$382$	15.6816	0.802342
$383$	−20.0619	−1.02512	−0.512558	−	0.858652i	$-0.671302\pi$
$383$	−20.0619	−1.02512	−0.512558	+	0.858652i	$0.671302\pi$
$384$	1.00000	0.0510310
$385$	6.07957	0.309844
$386$	−8.12795	−0.413702
$387$	−7.57286	−0.384950
$388$	2.75342	0.139784
$389$	−27.0314	−1.37055	−0.685273	−	0.728287i	$-0.740317\pi$
$389$	−27.0314	−1.37055	−0.685273	+	0.728287i	$0.740317\pi$
$390$	0	0
$391$	4.97813	0.251755
$392$	6.28354	0.317367
$393$	−10.8892	−0.549287
$394$	0.891239	0.0449000
$395$	−9.93398	−0.499833
$396$	1.66808	0.0838240
$397$	−3.73628	−0.187518	−0.0937592	−	0.995595i	$-0.529888\pi$
$397$	−3.73628	−0.187518	−0.0937592	+	0.995595i	$0.529888\pi$
$398$	0.361116	0.0181011
$399$	23.0078	1.15183
$400$	1.00000	0.0500000
$401$	−28.0911	−1.40280	−0.701402	−	0.712766i	$-0.747442\pi$
$401$	−28.0911	−1.40280	−0.701402	+	0.712766i	$0.747442\pi$
$402$	14.7534	0.735834
$403$	0	0
$404$	5.33615	0.265483
$405$	−1.00000	−0.0496904
$406$	−36.6098	−1.81692
$407$	−16.4543	−0.815609
$408$	4.00000	0.198030
$409$	−27.3804	−1.35388	−0.676938	−	0.736040i	$-0.736693\pi$
$409$	−27.3804	−1.35388	−0.676938	+	0.736040i	$0.736693\pi$
$410$	−9.28932	−0.458767
$411$	7.03696	0.347108
$412$	7.51248	0.370113
$413$	−22.2644	−1.09556
$414$	1.24453	0.0611654
$415$	−7.95317	−0.390406
$416$	0	0
$417$	11.6447	0.570241
$418$	−10.5301	−0.515045
$419$	−13.1614	−0.642975	−0.321487	−	0.946914i	$-0.604183\pi$
$419$	−13.1614	−0.642975	−0.321487	+	0.946914i	$0.604183\pi$
$420$	3.64466	0.177841
$421$	−1.29341	−0.0630370	−0.0315185	−	0.999503i	$-0.510034\pi$
$421$	−1.29341	−0.0630370	−0.0315185	+	0.999503i	$0.510034\pi$
$422$	2.22739	0.108428
$423$	6.82522	0.331853
$424$	−0.848634	−0.0412133
$425$	4.00000	0.194029
$426$	3.51093	0.170105
$427$	−27.2041	−1.31650
$428$	16.9282	0.818256
$429$	0	0
$430$	7.57286	0.365196
$431$	12.1279	0.584183	0.292091	−	0.956390i	$-0.405649\pi$
$431$	12.1279	0.584183	0.292091	+	0.956390i	$0.405649\pi$
$432$	1.00000	0.0481125
$433$	−2.07802	−0.0998633	−0.0499317	−	0.998753i	$-0.515900\pi$
$433$	−2.07802	−0.0998633	−0.0499317	+	0.998753i	$0.515900\pi$
$434$	−15.3789	−0.738210
$435$	−10.0448	−0.481611
$436$	0.663848	0.0317926
$437$	−7.85641	−0.375823
$438$	−12.2175	−0.583776
$439$	−2.39640	−0.114374	−0.0571869	−	0.998363i	$-0.518213\pi$
$439$	−2.39640	−0.114374	−0.0571869	+	0.998363i	$0.518213\pi$
$440$	−1.66808	−0.0795224
$441$	6.28354	0.299216
$442$	0	0
$443$	21.9959	1.04506	0.522529	−	0.852622i	$-0.324989\pi$
$443$	21.9959	1.04506	0.522529	+	0.852622i	$0.324989\pi$
$444$	−9.86423	−0.468136
$445$	5.95162	0.282134
$446$	6.08380	0.288076
$447$	0.772609	0.0365432
$448$	−3.64466	−0.172194
$449$	29.2253	1.37923	0.689613	−	0.724178i	$-0.257780\pi$
$449$	29.2253	1.37923	0.689613	+	0.724178i	$0.257780\pi$
$450$	1.00000	0.0471405
$451$	15.4953	0.729645
$452$	−17.8700	−0.840534
$453$	9.77838	0.459429
$454$	15.3205	0.719027
$455$	0	0
$456$	−6.31274	−0.295621
$457$	−39.6432	−1.85443	−0.927216	−	0.374526i	$-0.877805\pi$
$457$	−39.6432	−1.85443	−0.927216	+	0.374526i	$0.877805\pi$
$458$	22.2644	1.04034
$459$	4.00000	0.186704
$460$	−1.24453	−0.0580266
$461$	−16.6758	−0.776672	−0.388336	−	0.921518i	$-0.626950\pi$
$461$	−16.6758	−0.776672	−0.388336	+	0.921518i	$0.626950\pi$
$462$	−6.07957	−0.282847
$463$	−32.2175	−1.49728	−0.748638	−	0.662979i	$-0.769292\pi$
$463$	−32.2175	−1.49728	−0.748638	+	0.662979i	$0.769292\pi$
$464$	10.0448	0.466318
$465$	−4.21957	−0.195678
$466$	−10.8366	−0.501995
$467$	6.88137	0.318432	0.159216	−	0.987244i	$-0.449103\pi$
$467$	6.88137	0.318432	0.159216	+	0.987244i	$0.449103\pi$
$468$	0	0
$469$	−53.7712	−2.48292
$470$	−6.82522	−0.314824
$471$	−12.0135	−0.553555
$472$	6.10876	0.281179
$473$	−12.6321	−0.580825
$474$	9.93398	0.456283
$475$	−6.31274	−0.289648
$476$	−14.5786	−0.668211
$477$	−0.848634	−0.0388563
$478$	16.4975	0.754579
$479$	18.9709	0.866805	0.433402	−	0.901201i	$-0.357313\pi$
$479$	18.9709	0.866805	0.433402	+	0.901201i	$0.357313\pi$
$480$	−1.00000	−0.0456435
$481$	0	0
$482$	4.40435	0.200613
$483$	−4.53590	−0.206391
$484$	−8.21752	−0.373524
$485$	−2.75342	−0.125026
$486$	1.00000	0.0453609
$487$	−1.91620	−0.0868314	−0.0434157	−	0.999057i	$-0.513824\pi$
$487$	−1.91620	−0.0868314	−0.0434157	+	0.999057i	$0.513824\pi$
$488$	7.46410	0.337884
$489$	−10.0916	−0.456359
$490$	−6.28354	−0.283862
$491$	−33.6375	−1.51804	−0.759019	−	0.651069i	$-0.774321\pi$
$491$	−33.6375	−1.51804	−0.759019	+	0.651069i	$0.774321\pi$
$492$	9.28932	0.418795
$493$	40.1791	1.80958
$494$	0	0
$495$	−1.66808	−0.0749744
$496$	4.21957	0.189464
$497$	−12.7962	−0.573986
$498$	7.95317	0.356390
$499$	−1.82522	−0.0817080	−0.0408540	−	0.999165i	$-0.513008\pi$
$499$	−1.82522	−0.0817080	−0.0408540	+	0.999165i	$0.513008\pi$
$500$	−1.00000	−0.0447214
$501$	7.89701	0.352813
$502$	11.9453	0.533147
$503$	−19.9985	−0.891687	−0.445843	−	0.895111i	$-0.647096\pi$
$503$	−19.9985	−0.891687	−0.445843	+	0.895111i	$0.647096\pi$
$504$	−3.64466	−0.162346
$505$	−5.33615	−0.237456
$506$	2.07598	0.0922884
$507$	0	0
$508$	14.4407	0.640702
$509$	5.89124	0.261125	0.130562	−	0.991440i	$-0.458322\pi$
$509$	5.89124	0.261125	0.130562	+	0.991440i	$0.458322\pi$
$510$	−4.00000	−0.177123
$511$	44.5287	1.96983
$512$	1.00000	0.0441942
$513$	−6.31274	−0.278714
$514$	19.4621	0.858434
$515$	−7.51248	−0.331040
$516$	−7.57286	−0.333377
$517$	11.3850	0.500711
$518$	35.9518	1.57963
$519$	−0.440685	−0.0193439
$520$	0	0
$521$	32.0370	1.40356	0.701782	−	0.712391i	$-0.252388\pi$
$521$	32.0370	1.40356	0.701782	+	0.712391i	$0.252388\pi$
$522$	10.0448	0.439648
$523$	38.7186	1.69305	0.846523	−	0.532352i	$-0.178692\pi$
$523$	38.7186	1.69305	0.846523	+	0.532352i	$0.178692\pi$
$524$	−10.8892	−0.475697
$525$	−3.64466	−0.159066
$526$	2.03478	0.0887207
$527$	16.8783	0.735229
$528$	1.66808	0.0725937
$529$	−21.4511	−0.932658
$530$	0.848634	0.0368623
$531$	6.10876	0.265098
$532$	23.0078	0.997513
$533$	0	0
$534$	−5.95162	−0.257552
$535$	−16.9282	−0.731870
$536$	14.7534	0.637251
$537$	−19.6368	−0.847392
$538$	20.5287	0.885056
$539$	10.4814	0.451467
$540$	−1.00000	−0.0430331
$541$	25.9616	1.11618	0.558089	−	0.829781i	$-0.311535\pi$
$541$	25.9616	1.11618	0.558089	+	0.829781i	$0.311535\pi$
$542$	−25.5401	−1.09704
$543$	−6.21752	−0.266819
$544$	4.00000	0.171499
$545$	−0.663848	−0.0284361
$546$	0	0
$547$	−17.7596	−0.759348	−0.379674	−	0.925120i	$-0.623964\pi$
$547$	−17.7596	−0.759348	−0.379674	+	0.925120i	$0.623964\pi$
$548$	7.03696	0.300604
$549$	7.46410	0.318560
$550$	1.66808	0.0711270
$551$	−63.4101	−2.70136
$552$	1.24453	0.0529708
$553$	−36.2060	−1.53963
$554$	18.0604	0.767312
$555$	9.86423	0.418713
$556$	11.6447	0.493844
$557$	26.2202	1.11099	0.555493	−	0.831521i	$-0.312530\pi$
$557$	26.2202	1.11099	0.555493	+	0.831521i	$0.312530\pi$
$558$	4.21957	0.178629
$559$	0	0
$560$	3.64466	0.154015
$561$	6.67230	0.281705
$562$	−20.2175	−0.852825
$563$	−25.9928	−1.09547	−0.547733	−	0.836653i	$-0.684509\pi$
$563$	−25.9928	−1.09547	−0.547733	+	0.836653i	$0.684509\pi$
$564$	6.82522	0.287394
$565$	17.8700	0.751797
$566$	8.69149	0.365331
$567$	−3.64466	−0.153061
$568$	3.51093	0.147316
$569$	−25.4699	−1.06775	−0.533876	−	0.845563i	$-0.679265\pi$
$569$	−25.4699	−1.06775	−0.533876	+	0.845563i	$0.679265\pi$
$570$	6.31274	0.264411
$571$	8.44491	0.353409	0.176704	−	0.984264i	$-0.443456\pi$
$571$	8.44491	0.353409	0.176704	+	0.984264i	$0.443456\pi$
$572$	0	0
$573$	15.6816	0.655109
$574$	−33.8564	−1.41314
$575$	1.24453	0.0519006
$576$	1.00000	0.0416667
$577$	35.4216	1.47462	0.737311	−	0.675554i	$-0.236095\pi$
$577$	35.4216	1.47462	0.737311	+	0.675554i	$0.236095\pi$
$578$	−1.00000	−0.0415945
$579$	−8.12795	−0.337786
$580$	−10.0448	−0.417087
$581$	−28.9866	−1.20257
$582$	2.75342	0.114133
$583$	−1.41559	−0.0586276
$584$	−12.2175	−0.505565
$585$	0	0
$586$	7.54790	0.311801
$587$	27.3789	1.13005	0.565024	−	0.825075i	$-0.308867\pi$
$587$	27.3789	1.13005	0.565024	+	0.825075i	$0.308867\pi$
$588$	6.28354	0.259129
$589$	−26.6370	−1.09756
$590$	−6.10876	−0.251494
$591$	0.891239	0.0366607
$592$	−9.86423	−0.405417
$593$	12.0619	0.495324	0.247662	−	0.968846i	$-0.420338\pi$
$593$	12.0619	0.495324	0.247662	+	0.968846i	$0.420338\pi$
$594$	1.66808	0.0684420
$595$	14.5786	0.597666
$596$	0.772609	0.0316473
$597$	0.361116	0.0147795
$598$	0	0
$599$	−28.6129	−1.16909	−0.584546	−	0.811360i	$-0.698727\pi$
$599$	−28.6129	−1.16909	−0.584546	+	0.811360i	$0.698727\pi$
$600$	1.00000	0.0408248
$601$	−19.1676	−0.781862	−0.390931	−	0.920420i	$-0.627847\pi$
$601$	−19.1676	−0.781862	−0.390931	+	0.920420i	$0.627847\pi$
$602$	27.6005	1.12491
$603$	14.7534	0.600806
$604$	9.77838	0.397877
$605$	8.21752	0.334090
$606$	5.33615	0.216766
$607$	18.9382	0.768678	0.384339	−	0.923192i	$-0.374429\pi$
$607$	18.9382	0.768678	0.384339	+	0.923192i	$0.374429\pi$
$608$	−6.31274	−0.256015
$609$	−36.6098	−1.48351
$610$	−7.46410	−0.302213
$611$	0	0
$612$	4.00000	0.161690
$613$	−17.9694	−0.725779	−0.362890	−	0.931832i	$-0.618210\pi$
$613$	−17.9694	−0.725779	−0.362890	+	0.931832i	$0.618210\pi$
$614$	−26.0427	−1.05100
$615$	−9.28932	−0.374582
$616$	−6.07957	−0.244953
$617$	18.0151	0.725260	0.362630	−	0.931933i	$-0.381879\pi$
$617$	18.0151	0.725260	0.362630	+	0.931933i	$0.381879\pi$
$618$	7.51248	0.302196
$619$	25.0505	1.00687	0.503433	−	0.864035i	$-0.332070\pi$
$619$	25.0505	1.00687	0.503433	+	0.864035i	$0.332070\pi$
$620$	−4.21957	−0.169462
$621$	1.24453	0.0499414
$622$	−25.3789	−1.01760
$623$	21.6916	0.869057
$624$	0	0
$625$	1.00000	0.0400000
$626$	−31.4600	−1.25739
$627$	−10.5301	−0.420533
$628$	−12.0135	−0.479393
$629$	−39.4569	−1.57325
$630$	3.64466	0.145207
$631$	−1.41727	−0.0564206	−0.0282103	−	0.999602i	$-0.508981\pi$
$631$	−1.41727	−0.0564206	−0.0282103	+	0.999602i	$0.508981\pi$
$632$	9.93398	0.395152
$633$	2.22739	0.0885308
$634$	−24.7093	−0.981330
$635$	−14.4407	−0.573061
$636$	−0.848634	−0.0336505
$637$	0	0
$638$	16.7555	0.663355
$639$	3.51093	0.138890
$640$	−1.00000	−0.0395285
$641$	4.61970	0.182467	0.0912335	−	0.995830i	$-0.470919\pi$
$641$	4.61970	0.182467	0.0912335	+	0.995830i	$0.470919\pi$
$642$	16.9282	0.668103
$643$	−48.0896	−1.89647	−0.948234	−	0.317573i	$-0.897132\pi$
$643$	−48.0896	−1.89647	−0.948234	+	0.317573i	$0.897132\pi$
$644$	−4.53590	−0.178739
$645$	7.57286	0.298181
$646$	−25.2509	−0.993485
$647$	3.74565	0.147257	0.0736283	−	0.997286i	$-0.476542\pi$
$647$	3.74565	0.147257	0.0736283	+	0.997286i	$0.476542\pi$
$648$	1.00000	0.0392837
$649$	10.1899	0.399988
$650$	0	0
$651$	−15.3789	−0.602746
$652$	−10.0916	−0.395218
$653$	42.2899	1.65493	0.827466	−	0.561516i	$-0.189782\pi$
$653$	42.2899	1.65493	0.827466	+	0.561516i	$0.189782\pi$
$654$	0.663848	0.0259585
$655$	10.8892	0.425476
$656$	9.28932	0.362687
$657$	−12.2175	−0.476651
$658$	−24.8756	−0.969752
$659$	−29.1750	−1.13650	−0.568248	−	0.822858i	$-0.692378\pi$
$659$	−29.1750	−1.13650	−0.568248	+	0.822858i	$0.692378\pi$
$660$	−1.66808	−0.0649298
$661$	44.4662	1.72954	0.864768	−	0.502172i	$-0.167465\pi$
$661$	44.4662	1.72954	0.864768	+	0.502172i	$0.167465\pi$
$662$	5.60360	0.217790
$663$	0	0
$664$	7.95317	0.308643
$665$	−23.0078	−0.892203
$666$	−9.86423	−0.382231
$667$	12.5011	0.484043
$668$	7.89701	0.305545
$669$	6.08380	0.235213
$670$	−14.7534	−0.569974
$671$	12.4507	0.480654
$672$	−3.64466	−0.140596
$673$	7.90633	0.304767	0.152383	−	0.988321i	$-0.451305\pi$
$673$	7.90633	0.304767	0.152383	+	0.988321i	$0.451305\pi$
$674$	−21.7868	−0.839198
$675$	1.00000	0.0384900
$676$	0	0
$677$	−7.05615	−0.271190	−0.135595	−	0.990764i	$-0.543295\pi$
$677$	−7.05615	−0.271190	−0.135595	+	0.990764i	$0.543295\pi$
$678$	−17.8700	−0.686293
$679$	−10.0353	−0.385119
$680$	−4.00000	−0.153393
$681$	15.3205	0.587083
$682$	7.03856	0.269520
$683$	−5.95317	−0.227792	−0.113896	−	0.993493i	$-0.536333\pi$
$683$	−5.95317	−0.227792	−0.113896	+	0.993493i	$0.536333\pi$
$684$	−6.31274	−0.241373
$685$	−7.03696	−0.268869
$686$	2.61124	0.0996976
$687$	22.2644	0.849438
$688$	−7.57286	−0.288713
$689$	0	0
$690$	−1.24453	−0.0473786
$691$	18.7591	0.713628	0.356814	−	0.934175i	$-0.383863\pi$
$691$	18.7591	0.713628	0.356814	+	0.934175i	$0.383863\pi$
$692$	−0.440685	−0.0167523
$693$	−6.07957	−0.230944
$694$	9.68162	0.367509
$695$	−11.6447	−0.441707
$696$	10.0448	0.380747
$697$	37.1573	1.40743
$698$	−19.3205	−0.731292
$699$	−10.8366	−0.409877
$700$	−3.64466	−0.137755
$701$	28.5298	1.07755	0.538777	−	0.842448i	$-0.318887\pi$
$701$	28.5298	1.07755	0.538777	+	0.842448i	$0.318887\pi$
$702$	0	0
$703$	62.2703	2.34857
$704$	1.66808	0.0628680
$705$	−6.82522	−0.257053
$706$	−22.9750	−0.864677
$707$	−19.4485	−0.731435
$708$	6.10876	0.229581
$709$	−23.1926	−0.871015	−0.435507	−	0.900185i	$-0.643431\pi$
$709$	−23.1926	−0.871015	−0.435507	+	0.900185i	$0.643431\pi$
$710$	−3.51093	−0.131763
$711$	9.93398	0.372553
$712$	−5.95162	−0.223046
$713$	5.25139	0.196666
$714$	−14.5786	−0.545592
$715$	0	0
$716$	−19.6368	−0.733863
$717$	16.4975	0.616111
$718$	2.21752	0.0827572
$719$	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
$721$	−27.3804	−1.01970
$722$	20.8506	0.775980
$723$	4.40435	0.163800
$724$	−6.21752	−0.231072
$725$	10.0448	0.373054
$726$	−8.21752	−0.304981
$727$	−3.82677	−0.141927	−0.0709634	−	0.997479i	$-0.522607\pi$
$727$	−3.82677	−0.141927	−0.0709634	+	0.997479i	$0.522607\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.2175	0.452191
$731$	−30.2915	−1.12037
$732$	7.46410	0.275881
$733$	−12.9340	−0.477727	−0.238864	−	0.971053i	$-0.576775\pi$
$733$	−12.9340	−0.477727	−0.238864	+	0.971053i	$0.576775\pi$
$734$	−6.08112	−0.224458
$735$	−6.28354	−0.231772
$736$	1.24453	0.0458741
$737$	24.6098	0.906515
$738$	9.28932	0.341945
$739$	35.3462	1.30023	0.650115	−	0.759836i	$-0.274721\pi$
$739$	35.3462	1.30023	0.650115	+	0.759836i	$0.274721\pi$
$740$	9.86423	0.362616
$741$	0	0
$742$	3.09298	0.113547
$743$	−37.0953	−1.36090	−0.680448	−	0.732796i	$-0.738215\pi$
$743$	−37.0953	−1.36090	−0.680448	+	0.732796i	$0.738215\pi$
$744$	4.21957	0.154697
$745$	−0.772609	−0.0283062
$746$	15.6781	0.574015
$747$	7.95317	0.290991
$748$	6.67230	0.243964
$749$	−61.6975	−2.25438
$750$	−1.00000	−0.0365148
$751$	−9.65807	−0.352428	−0.176214	−	0.984352i	$-0.556385\pi$
$751$	−9.65807	−0.352428	−0.176214	+	0.984352i	$0.556385\pi$
$752$	6.82522	0.248890
$753$	11.9453	0.435313
$754$	0	0
$755$	−9.77838	−0.355872
$756$	−3.64466	−0.132555
$757$	−43.6885	−1.58789	−0.793943	−	0.607992i	$-0.791975\pi$
$757$	−43.6885	−1.58789	−0.793943	+	0.607992i	$0.791975\pi$
$758$	30.7166	1.11568
$759$	2.07598	0.0753531
$760$	6.31274	0.228987
$761$	39.9007	1.44640	0.723200	−	0.690639i	$-0.242671\pi$
$761$	39.9007	1.44640	0.723200	+	0.690639i	$0.242671\pi$
$762$	14.4407	0.523131
$763$	−2.41950	−0.0875918
$764$	15.6816	0.567341
$765$	−4.00000	−0.144620
$766$	−20.0619	−0.724867
$767$	0	0
$768$	1.00000	0.0360844
$769$	−17.5588	−0.633187	−0.316594	−	0.948561i	$-0.602539\pi$
$769$	−17.5588	−0.633187	−0.316594	+	0.948561i	$0.602539\pi$
$770$	6.07957	0.219092
$771$	19.4621	0.700909
$772$	−8.12795	−0.292531
$773$	−12.8372	−0.461723	−0.230861	−	0.972987i	$-0.574154\pi$
$773$	−12.8372	−0.461723	−0.230861	+	0.972987i	$0.574154\pi$
$774$	−7.57286	−0.272201
$775$	4.21957	0.151571
$776$	2.75342	0.0988420
$777$	35.9518	1.28976
$778$	−27.0314	−0.969122
$779$	−58.6410	−2.10103
$780$	0	0
$781$	5.85651	0.209562
$782$	4.97813	0.178018
$783$	10.0448	0.358971
$784$	6.28354	0.224412
$785$	12.0135	0.428782
$786$	−10.8892	−0.388405
$787$	−6.95735	−0.248003	−0.124001	−	0.992282i	$-0.539573\pi$
$787$	−6.95735	−0.248003	−0.124001	+	0.992282i	$0.539573\pi$
$788$	0.891239	0.0317491
$789$	2.03478	0.0724402
$790$	−9.93398	−0.353435
$791$	65.1301	2.31576
$792$	1.66808	0.0592725
$793$	0	0
$794$	−3.73628	−0.132596
$795$	0.848634	0.0300979
$796$	0.361116	0.0127994
$797$	34.1354	1.20914	0.604569	−	0.796553i	$-0.293345\pi$
$797$	34.1354	1.20914	0.604569	+	0.796553i	$0.293345\pi$
$798$	23.0078	0.814466
$799$	27.3009	0.965835
$800$	1.00000	0.0353553
$801$	−5.95162	−0.210290
$802$	−28.0911	−0.991932
$803$	−20.3798	−0.719186
$804$	14.7534	0.520313
$805$	4.53590	0.159869
$806$	0	0
$807$	20.5287	0.722645
$808$	5.33615	0.187725
$809$	−3.32770	−0.116996	−0.0584978	−	0.998288i	$-0.518631\pi$
$809$	−3.32770	−0.116996	−0.0584978	+	0.998288i	$0.518631\pi$
$810$	−1.00000	−0.0351364
$811$	20.6083	0.723655	0.361827	−	0.932245i	$-0.382153\pi$
$811$	20.6083	0.723655	0.361827	+	0.932245i	$0.382153\pi$
$812$	−36.6098	−1.28475
$813$	−25.5401	−0.895730
$814$	−16.4543	−0.576722
$815$	10.0916	0.353494
$816$	4.00000	0.140028
$817$	47.8055	1.67250
$818$	−27.3804	−0.957335
$819$	0	0
$820$	−9.28932	−0.324397
$821$	1.58005	0.0551442	0.0275721	−	0.999620i	$-0.491222\pi$
$821$	1.58005	0.0551442	0.0275721	+	0.999620i	$0.491222\pi$
$822$	7.03696	0.245442
$823$	37.5168	1.30776	0.653878	−	0.756600i	$-0.273141\pi$
$823$	37.5168	1.30776	0.653878	+	0.756600i	$0.273141\pi$
$824$	7.51248	0.261710
$825$	1.66808	0.0580750
$826$	−22.2644	−0.774676
$827$	−49.4912	−1.72098	−0.860489	−	0.509469i	$-0.829842\pi$
$827$	−49.4912	−1.72098	−0.860489	+	0.509469i	$0.829842\pi$
$828$	1.24453	0.0432505
$829$	49.1385	1.70665	0.853326	−	0.521378i	$-0.174582\pi$
$829$	49.1385	1.70665	0.853326	+	0.521378i	$0.174582\pi$
$830$	−7.95317	−0.276058
$831$	18.0604	0.626508
$832$	0	0
$833$	25.1342	0.870848
$834$	11.6447	0.403222
$835$	−7.89701	−0.273287
$836$	−10.5301	−0.364192
$837$	4.21957	0.145850
$838$	−13.1614	−0.454652
$839$	−21.5421	−0.743717	−0.371858	−	0.928289i	$-0.621279\pi$
$839$	−21.5421	−0.743717	−0.371858	+	0.928289i	$0.621279\pi$
$840$	3.64466	0.125753
$841$	71.8977	2.47923
$842$	−1.29341	−0.0445739
$843$	−20.2175	−0.696328
$844$	2.22739	0.0766700
$845$	0	0
$846$	6.82522	0.234656
$847$	29.9501	1.02910
$848$	−0.848634	−0.0291422
$849$	8.69149	0.298291
$850$	4.00000	0.137199
$851$	−12.2764	−0.420828
$852$	3.51093	0.120283
$853$	2.79821	0.0958088	0.0479044	−	0.998852i	$-0.484746\pi$
$853$	2.79821	0.0958088	0.0479044	+	0.998852i	$0.484746\pi$
$854$	−27.2041	−0.930905
$855$	6.31274	0.215891
$856$	16.9282	0.578594
$857$	48.9658	1.67264	0.836320	−	0.548242i	$-0.184703\pi$
$857$	48.9658	1.67264	0.836320	+	0.548242i	$0.184703\pi$
$858$	0	0
$859$	4.22739	0.144237	0.0721184	−	0.997396i	$-0.477024\pi$
$859$	4.22739	0.144237	0.0721184	+	0.997396i	$0.477024\pi$
$860$	7.57286	0.258232
$861$	−33.8564	−1.15382
$862$	12.1279	0.413080
$863$	19.0285	0.647738	0.323869	−	0.946102i	$-0.395016\pi$
$863$	19.0285	0.647738	0.323869	+	0.946102i	$0.395016\pi$
$864$	1.00000	0.0340207
$865$	0.440685	0.0149837
$866$	−2.07802	−0.0706141
$867$	−1.00000	−0.0339618
$868$	−15.3789	−0.521994
$869$	16.5706	0.562120
$870$	−10.0448	−0.340550
$871$	0	0
$872$	0.663848	0.0224807
$873$	2.75342	0.0931892
$874$	−7.85641	−0.265747
$875$	3.64466	0.123212
$876$	−12.2175	−0.412792
$877$	−13.5473	−0.457459	−0.228729	−	0.973490i	$-0.573457\pi$
$877$	−13.5473	−0.457459	−0.228729	+	0.973490i	$0.573457\pi$
$878$	−2.39640	−0.0808745
$879$	7.54790	0.254584
$880$	−1.66808	−0.0562308
$881$	4.98081	0.167808	0.0839039	−	0.996474i	$-0.473261\pi$
$881$	4.98081	0.167808	0.0839039	+	0.996474i	$0.473261\pi$
$882$	6.28354	0.211578
$883$	−30.9829	−1.04266	−0.521330	−	0.853355i	$-0.674564\pi$
$883$	−30.9829	−1.04266	−0.521330	+	0.853355i	$0.674564\pi$
$884$	0	0
$885$	−6.10876	−0.205344
$886$	21.9959	0.738967
$887$	17.1765	0.576731	0.288365	−	0.957520i	$-0.406888\pi$
$887$	17.1765	0.576731	0.288365	+	0.957520i	$0.406888\pi$
$888$	−9.86423	−0.331022
$889$	−52.6314	−1.76520
$890$	5.95162	0.199499
$891$	1.66808	0.0558826
$892$	6.08380	0.203701
$893$	−43.0858	−1.44181
$894$	0.772609	0.0258399
$895$	19.6368	0.656387
$896$	−3.64466	−0.121760
$897$	0	0
$898$	29.2253	0.975261
$899$	42.3847	1.41361
$900$	1.00000	0.0333333
$901$	−3.39454	−0.113088
$902$	15.4953	0.515937
$903$	27.6005	0.918487
$904$	−17.8700	−0.594347
$905$	6.21752	0.206677
$906$	9.77838	0.324865
$907$	−25.0797	−0.832758	−0.416379	−	0.909191i	$-0.636701\pi$
$907$	−25.0797	−0.832758	−0.416379	+	0.909191i	$0.636701\pi$
$908$	15.3205	0.508429
$909$	5.33615	0.176989
$910$	0	0
$911$	18.2332	0.604092	0.302046	−	0.953293i	$-0.402330\pi$
$911$	18.2332	0.604092	0.302046	+	0.953293i	$0.402330\pi$
$912$	−6.31274	−0.209036
$913$	13.2665	0.439057
$914$	−39.6432	−1.31128
$915$	−7.46410	−0.246756
$916$	22.2644	0.735635
$917$	39.6874	1.31059
$918$	4.00000	0.132020
$919$	−34.3882	−1.13436	−0.567181	−	0.823593i	$-0.691966\pi$
$919$	−34.3882	−1.13436	−0.567181	+	0.823593i	$0.691966\pi$
$920$	−1.24453	−0.0410310
$921$	−26.0427	−0.858137
$922$	−16.6758	−0.549190
$923$	0	0
$924$	−6.07957	−0.200003
$925$	−9.86423	−0.324334
$926$	−32.2175	−1.05873
$927$	7.51248	0.246742
$928$	10.0448	0.329736
$929$	−31.0904	−1.02004	−0.510022	−	0.860161i	$-0.670363\pi$
$929$	−31.0904	−1.02004	−0.510022	+	0.860161i	$0.670363\pi$
$930$	−4.21957	−0.138365
$931$	−39.6663	−1.30001
$932$	−10.8366	−0.354964
$933$	−25.3789	−0.830868
$934$	6.88137	0.225165
$935$	−6.67230	−0.218208
$936$	0	0
$937$	−18.8783	−0.616726	−0.308363	−	0.951269i	$-0.599781\pi$
$937$	−18.8783	−0.616726	−0.308363	+	0.951269i	$0.599781\pi$
$938$	−53.7712	−1.75569
$939$	−31.4600	−1.02666
$940$	−6.82522	−0.222614
$941$	28.9398	0.943409	0.471705	−	0.881757i	$-0.343639\pi$
$941$	28.9398	0.943409	0.471705	+	0.881757i	$0.343639\pi$
$942$	−12.0135	−0.391423
$943$	11.5609	0.376473
$944$	6.10876	0.198823
$945$	3.64466	0.118561
$946$	−12.6321	−0.410705
$947$	−7.86896	−0.255707	−0.127853	−	0.991793i	$-0.540809\pi$
$947$	−7.86896	−0.255707	−0.127853	+	0.991793i	$0.540809\pi$
$948$	9.93398	0.322641
$949$	0	0
$950$	−6.31274	−0.204812
$951$	−24.7093	−0.801253
$952$	−14.5786	−0.472496
$953$	−55.0968	−1.78476	−0.892381	−	0.451283i	$-0.850967\pi$
$953$	−55.0968	−1.78476	−0.892381	+	0.451283i	$0.850967\pi$
$954$	−0.848634	−0.0274755
$955$	−15.6816	−0.507445
$956$	16.4975	0.533568
$957$	16.7555	0.541627
$958$	18.9709	0.612923
$959$	−25.6473	−0.828196
$960$	−1.00000	−0.0322749
$961$	−13.1952	−0.425653
$962$	0	0
$963$	16.9282	0.545504
$964$	4.40435	0.141855
$965$	8.12795	0.261648
$966$	−4.53590	−0.145940
$967$	−31.5523	−1.01465	−0.507326	−	0.861754i	$-0.669366\pi$
$967$	−31.5523	−1.01465	−0.507326	+	0.861754i	$0.669366\pi$
$968$	−8.21752	−0.264121
$969$	−25.2509	−0.811177
$970$	−2.75342	−0.0884070
$971$	3.67585	0.117964	0.0589818	−	0.998259i	$-0.481215\pi$
$971$	3.67585	0.117964	0.0589818	+	0.998259i	$0.481215\pi$
$972$	1.00000	0.0320750
$973$	−42.4408	−1.36059
$974$	−1.91620	−0.0613991
$975$	0	0
$976$	7.46410	0.238920
$977$	42.0205	1.34435	0.672177	−	0.740391i	$-0.265359\pi$
$977$	42.0205	1.34435	0.672177	+	0.740391i	$0.265359\pi$
$978$	−10.0916	−0.322694
$979$	−9.92775	−0.317292
$980$	−6.28354	−0.200720
$981$	0.663848	0.0211950
$982$	−33.6375	−1.07341
$983$	−13.4307	−0.428372	−0.214186	−	0.976793i	$-0.568710\pi$
$983$	−13.4307	−0.428372	−0.214186	+	0.976793i	$0.568710\pi$
$984$	9.28932	0.296133
$985$	−0.891239	−0.0283972
$986$	40.1791	1.27956
$987$	−24.8756	−0.791799
$988$	0	0
$989$	−9.42468	−0.299687
$990$	−1.66808	−0.0530149
$991$	43.7988	1.39132	0.695658	−	0.718373i	$-0.255113\pi$
$991$	43.7988	1.39132	0.695658	+	0.718373i	$0.255113\pi$
$992$	4.21957	0.133971
$993$	5.60360	0.177825
$994$	−12.7962	−0.405870
$995$	−0.361116	−0.0114481
$996$	7.95317	0.252006
$997$	−23.5125	−0.744648	−0.372324	−	0.928103i	$-0.621439\pi$
$997$	−23.5125	−0.744648	−0.372324	+	0.928103i	$0.621439\pi$
$998$	−1.82522	−0.0577763
$999$	−9.86423	−0.312090

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5070.2.a.ca.1.1		4
13.2	odd	12		390.2.bb.c.121.3	✓	8
13.5	odd	4		5070.2.b.ba.1351.1		8
13.7	odd	12		390.2.bb.c.361.3	yes	8
13.8	odd	4		5070.2.b.ba.1351.8		8
13.12	even	2		5070.2.a.bz.1.4		4
39.2	even	12		1170.2.bs.f.901.1		8
39.20	even	12		1170.2.bs.f.361.1		8
65.2	even	12		1950.2.y.j.199.3		8
65.7	even	12		1950.2.y.k.49.2		8
65.28	even	12		1950.2.y.k.199.2		8
65.33	even	12		1950.2.y.j.49.3		8
65.54	odd	12		1950.2.bc.g.901.2		8
65.59	odd	12		1950.2.bc.g.751.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bb.c.121.3	✓	8	13.2	odd	12
390.2.bb.c.361.3	yes	8	13.7	odd	12
1170.2.bs.f.361.1		8	39.20	even	12
1170.2.bs.f.901.1		8	39.2	even	12
1950.2.y.j.49.3		8	65.33	even	12
1950.2.y.j.199.3		8	65.2	even	12
1950.2.y.k.49.2		8	65.7	even	12
1950.2.y.k.199.2		8	65.28	even	12
1950.2.bc.g.751.2		8	65.59	odd	12
1950.2.bc.g.901.2		8	65.54	odd	12
5070.2.a.bz.1.4		4	13.12	even	2
5070.2.a.ca.1.1		4	1.1	even	1	trivial
5070.2.b.ba.1351.1		8	13.5	odd	4
5070.2.b.ba.1351.8		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.64466 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.66808 q^{11} +1.00000 q^{12} -3.64466 q^{14} -1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{18} -6.31274 q^{19} -1.00000 q^{20} -3.64466 q^{21} +1.66808 q^{22} +1.24453 q^{23} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} -3.64466 q^{28} +10.0448 q^{29} -1.00000 q^{30} +4.21957 q^{31} +1.00000 q^{32} +1.66808 q^{33} +4.00000 q^{34} +3.64466 q^{35} +1.00000 q^{36} -9.86423 q^{37} -6.31274 q^{38} -1.00000 q^{40} +9.28932 q^{41} -3.64466 q^{42} -7.57286 q^{43} +1.66808 q^{44} -1.00000 q^{45} +1.24453 q^{46} +6.82522 q^{47} +1.00000 q^{48} +6.28354 q^{49} +1.00000 q^{50} +4.00000 q^{51} -0.848634 q^{53} +1.00000 q^{54} -1.66808 q^{55} -3.64466 q^{56} -6.31274 q^{57} +10.0448 q^{58} +6.10876 q^{59} -1.00000 q^{60} +7.46410 q^{61} +4.21957 q^{62} -3.64466 q^{63} +1.00000 q^{64} +1.66808 q^{66} +14.7534 q^{67} +4.00000 q^{68} +1.24453 q^{69} +3.64466 q^{70} +3.51093 q^{71} +1.00000 q^{72} -12.2175 q^{73} -9.86423 q^{74} +1.00000 q^{75} -6.31274 q^{76} -6.07957 q^{77} +9.93398 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.28932 q^{82} +7.95317 q^{83} -3.64466 q^{84} -4.00000 q^{85} -7.57286 q^{86} +10.0448 q^{87} +1.66808 q^{88} -5.95162 q^{89} -1.00000 q^{90} +1.24453 q^{92} +4.21957 q^{93} +6.82522 q^{94} +6.31274 q^{95} +1.00000 q^{96} +2.75342 q^{97} +6.28354 q^{98} +1.66808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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