LMFDB - Embedded newform 3174.2.a.bb.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3174,2,Mod(1,3174)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3174, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3174.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3174 = 2 \cdot 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3174.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:	$25.3445176016$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.91899$ of defining polynomial
Character	$\chi$	$=$	3174.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.324635 q^{5} -1.00000 q^{6} +2.43232 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.324635 q^{5} -1.00000 q^{6} +2.43232 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.324635 q^{10} -3.40009 q^{11} -1.00000 q^{12} +0.269342 q^{13} +2.43232 q^{14} +0.324635 q^{15} +1.00000 q^{16} -4.84815 q^{17} +1.00000 q^{18} -4.02509 q^{19} -0.324635 q^{20} -2.43232 q^{21} -3.40009 q^{22} -1.00000 q^{24} -4.89461 q^{25} +0.269342 q^{26} -1.00000 q^{27} +2.43232 q^{28} +2.00935 q^{29} +0.324635 q^{30} -9.50557 q^{31} +1.00000 q^{32} +3.40009 q^{33} -4.84815 q^{34} -0.789617 q^{35} +1.00000 q^{36} +2.01732 q^{37} -4.02509 q^{38} -0.269342 q^{39} -0.324635 q^{40} -2.60502 q^{41} -2.43232 q^{42} -3.93559 q^{43} -3.40009 q^{44} -0.324635 q^{45} +5.19874 q^{47} -1.00000 q^{48} -1.08380 q^{49} -4.89461 q^{50} +4.84815 q^{51} +0.269342 q^{52} +1.08001 q^{53} -1.00000 q^{54} +1.10379 q^{55} +2.43232 q^{56} +4.02509 q^{57} +2.00935 q^{58} +9.90548 q^{59} +0.324635 q^{60} -4.35062 q^{61} -9.50557 q^{62} +2.43232 q^{63} +1.00000 q^{64} -0.0874378 q^{65} +3.40009 q^{66} -10.2730 q^{67} -4.84815 q^{68} -0.789617 q^{70} +11.4304 q^{71} +1.00000 q^{72} -1.13935 q^{73} +2.01732 q^{74} +4.89461 q^{75} -4.02509 q^{76} -8.27012 q^{77} -0.269342 q^{78} -16.0547 q^{79} -0.324635 q^{80} +1.00000 q^{81} -2.60502 q^{82} +1.05529 q^{83} -2.43232 q^{84} +1.57388 q^{85} -3.93559 q^{86} -2.00935 q^{87} -3.40009 q^{88} +2.74085 q^{89} -0.324635 q^{90} +0.655127 q^{91} +9.50557 q^{93} +5.19874 q^{94} +1.30668 q^{95} -1.00000 q^{96} +13.6079 q^{97} -1.08380 q^{98} -3.40009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9} + q^{10} - 11 q^{11} - 5 q^{12} + 12 q^{13} - 11 q^{14} - q^{15} + 5 q^{16} + q^{17} + 5 q^{18} - 15 q^{19} + q^{20} + 11 q^{21} - 11 q^{22} - 5 q^{24} + 6 q^{25} + 12 q^{26} - 5 q^{27} - 11 q^{28} + q^{29} - q^{30} - 18 q^{31} + 5 q^{32} + 11 q^{33} + q^{34} - 11 q^{35} + 5 q^{36} - 10 q^{37} - 15 q^{38} - 12 q^{39} + q^{40} - 16 q^{41} + 11 q^{42} - 18 q^{43} - 11 q^{44} + q^{45} - 4 q^{47} - 5 q^{48} + 20 q^{49} + 6 q^{50} - q^{51} + 12 q^{52} + q^{53} - 5 q^{54} - 22 q^{55} - 11 q^{56} + 15 q^{57} + q^{58} + 2 q^{59} - q^{60} + q^{61} - 18 q^{62} - 11 q^{63} + 5 q^{64} - 24 q^{65} + 11 q^{66} - 29 q^{67} + q^{68} - 11 q^{70} - 11 q^{71} + 5 q^{72} - 8 q^{73} - 10 q^{74} - 6 q^{75} - 15 q^{76} + 11 q^{77} - 12 q^{78} - 40 q^{79} + q^{80} + 5 q^{81} - 16 q^{82} - 8 q^{83} + 11 q^{84} - 13 q^{85} - 18 q^{86} - q^{87} - 11 q^{88} - 2 q^{89} + q^{90} - 33 q^{91} + 18 q^{93} - 4 q^{94} - 3 q^{95} - 5 q^{96} - 17 q^{97} + 20 q^{98} - 11 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9 + q^10 - 11 * q^11 - 5 * q^12 + 12 * q^13 - 11 * q^14 - q^15 + 5 * q^16 + q^17 + 5 * q^18 - 15 * q^19 + q^20 + 11 * q^21 - 11 * q^22 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 5 * q^27 - 11 * q^28 + q^29 - q^30 - 18 * q^31 + 5 * q^32 + 11 * q^33 + q^34 - 11 * q^35 + 5 * q^36 - 10 * q^37 - 15 * q^38 - 12 * q^39 + q^40 - 16 * q^41 + 11 * q^42 - 18 * q^43 - 11 * q^44 + q^45 - 4 * q^47 - 5 * q^48 + 20 * q^49 + 6 * q^50 - q^51 + 12 * q^52 + q^53 - 5 * q^54 - 22 * q^55 - 11 * q^56 + 15 * q^57 + q^58 + 2 * q^59 - q^60 + q^61 - 18 * q^62 - 11 * q^63 + 5 * q^64 - 24 * q^65 + 11 * q^66 - 29 * q^67 + q^68 - 11 * q^70 - 11 * q^71 + 5 * q^72 - 8 * q^73 - 10 * q^74 - 6 * q^75 - 15 * q^76 + 11 * q^77 - 12 * q^78 - 40 * q^79 + q^80 + 5 * q^81 - 16 * q^82 - 8 * q^83 + 11 * q^84 - 13 * q^85 - 18 * q^86 - q^87 - 11 * q^88 - 2 * q^89 + q^90 - 33 * q^91 + 18 * q^93 - 4 * q^94 - 3 * q^95 - 5 * q^96 - 17 * q^97 + 20 * q^98 - 11 * 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
$5$	−0.324635	−0.145181	−0.0725905	−	0.997362i	$-0.523127\pi$
$5$	−0.324635	−0.145181	−0.0725905	+	0.997362i	$0.523127\pi$
$6$	−1.00000	−0.408248
$7$	2.43232	0.919332	0.459666	−	0.888092i	$-0.347969\pi$
$7$	2.43232	0.919332	0.459666	+	0.888092i	$0.347969\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.324635	−0.102659
$11$	−3.40009	−1.02517	−0.512583	−	0.858638i	$-0.671311\pi$
$11$	−3.40009	−1.02517	−0.512583	+	0.858638i	$0.671311\pi$
$12$	−1.00000	−0.288675
$13$	0.269342	0.0747021	0.0373510	−	0.999302i	$-0.488108\pi$
$13$	0.269342	0.0747021	0.0373510	+	0.999302i	$0.488108\pi$
$14$	2.43232	0.650066
$15$	0.324635	0.0838203
$16$	1.00000	0.250000
$17$	−4.84815	−1.17585	−0.587925	−	0.808916i	$-0.700055\pi$
$17$	−4.84815	−1.17585	−0.587925	+	0.808916i	$0.700055\pi$
$18$	1.00000	0.235702
$19$	−4.02509	−0.923419	−0.461710	−	0.887031i	$-0.652764\pi$
$19$	−4.02509	−0.923419	−0.461710	+	0.887031i	$0.652764\pi$
$20$	−0.324635	−0.0725905
$21$	−2.43232	−0.530776
$22$	−3.40009	−0.724901
$23$	0	0
$23$	0	0
$24$	−1.00000	−0.204124
$25$	−4.89461	−0.978922
$26$	0.269342	0.0528223
$27$	−1.00000	−0.192450
$28$	2.43232	0.459666
$29$	2.00935	0.373128	0.186564	−	0.982443i	$-0.440265\pi$
$29$	2.00935	0.373128	0.186564	+	0.982443i	$0.440265\pi$
$30$	0.324635	0.0592699
$31$	−9.50557	−1.70725	−0.853625	−	0.520888i	$-0.825601\pi$
$31$	−9.50557	−1.70725	−0.853625	+	0.520888i	$0.825601\pi$
$32$	1.00000	0.176777
$33$	3.40009	0.591880
$34$	−4.84815	−0.831451
$35$	−0.789617	−0.133470
$36$	1.00000	0.166667
$37$	2.01732	0.331645	0.165823	−	0.986156i	$-0.446972\pi$
$37$	2.01732	0.331645	0.165823	+	0.986156i	$0.446972\pi$
$38$	−4.02509	−0.652956
$39$	−0.269342	−0.0431293
$40$	−0.324635	−0.0513293
$41$	−2.60502	−0.406836	−0.203418	−	0.979092i	$-0.565205\pi$
$41$	−2.60502	−0.406836	−0.203418	+	0.979092i	$0.565205\pi$
$42$	−2.43232	−0.375316
$43$	−3.93559	−0.600172	−0.300086	−	0.953912i	$-0.597015\pi$
$43$	−3.93559	−0.600172	−0.300086	+	0.953912i	$0.597015\pi$
$44$	−3.40009	−0.512583
$45$	−0.324635	−0.0483937
$46$	0	0
$47$	5.19874	0.758314	0.379157	−	0.925332i	$-0.376214\pi$
$47$	5.19874	0.758314	0.379157	+	0.925332i	$0.376214\pi$
$48$	−1.00000	−0.144338
$49$	−1.08380	−0.154829
$50$	−4.89461	−0.692203
$51$	4.84815	0.678877
$52$	0.269342	0.0373510
$53$	1.08001	0.148351	0.0741754	−	0.997245i	$-0.476368\pi$
$53$	1.08001	0.148351	0.0741754	+	0.997245i	$0.476368\pi$
$54$	−1.00000	−0.136083
$55$	1.10379	0.148835
$56$	2.43232	0.325033
$57$	4.02509	0.533136
$58$	2.00935	0.263841
$59$	9.90548	1.28958	0.644792	−	0.764358i	$-0.276944\pi$
$59$	9.90548	1.28958	0.644792	+	0.764358i	$0.276944\pi$
$60$	0.324635	0.0419102
$61$	−4.35062	−0.557040	−0.278520	−	0.960430i	$-0.589844\pi$
$61$	−4.35062	−0.557040	−0.278520	+	0.960430i	$0.589844\pi$
$62$	−9.50557	−1.20721
$63$	2.43232	0.306444
$64$	1.00000	0.125000
$65$	−0.0874378	−0.0108453
$66$	3.40009	0.418522
$67$	−10.2730	−1.25504	−0.627521	−	0.778600i	$-0.715930\pi$
$67$	−10.2730	−1.25504	−0.627521	+	0.778600i	$0.715930\pi$
$68$	−4.84815	−0.587925
$69$	0	0
$70$	−0.789617	−0.0943772
$71$	11.4304	1.35654	0.678268	−	0.734814i	$-0.262731\pi$
$71$	11.4304	1.35654	0.678268	+	0.734814i	$0.262731\pi$
$72$	1.00000	0.117851
$73$	−1.13935	−0.133351	−0.0666756	−	0.997775i	$-0.521239\pi$
$73$	−1.13935	−0.133351	−0.0666756	+	0.997775i	$0.521239\pi$
$74$	2.01732	0.234509
$75$	4.89461	0.565181
$76$	−4.02509	−0.461710
$77$	−8.27012	−0.942467
$78$	−0.269342	−0.0304970
$79$	−16.0547	−1.80629	−0.903145	−	0.429335i	$-0.858748\pi$
$79$	−16.0547	−1.80629	−0.903145	+	0.429335i	$0.858748\pi$
$80$	−0.324635	−0.0362953
$81$	1.00000	0.111111
$82$	−2.60502	−0.287676
$83$	1.05529	0.115833	0.0579167	−	0.998321i	$-0.481554\pi$
$83$	1.05529	0.115833	0.0579167	+	0.998321i	$0.481554\pi$
$84$	−2.43232	−0.265388
$85$	1.57388	0.170711
$86$	−3.93559	−0.424385
$87$	−2.00935	−0.215425
$88$	−3.40009	−0.362451
$89$	2.74085	0.290529	0.145265	−	0.989393i	$-0.453597\pi$
$89$	2.74085	0.290529	0.145265	+	0.989393i	$0.453597\pi$
$90$	−0.324635	−0.0342195
$91$	0.655127	0.0686760
$92$	0	0
$93$	9.50557	0.985681
$94$	5.19874	0.536209
$95$	1.30668	0.134063
$96$	−1.00000	−0.102062
$97$	13.6079	1.38167	0.690836	−	0.723011i	$-0.257242\pi$
$97$	13.6079	1.38167	0.690836	+	0.723011i	$0.257242\pi$
$98$	−1.08380	−0.109481
$99$	−3.40009	−0.341722
$100$	−4.89461	−0.489461
$101$	15.9029	1.58240	0.791198	−	0.611560i	$-0.209458\pi$
$101$	15.9029	1.58240	0.791198	+	0.611560i	$0.209458\pi$
$102$	4.84815	0.480038
$103$	−13.9721	−1.37672	−0.688358	−	0.725371i	$-0.741668\pi$
$103$	−13.9721	−1.37672	−0.688358	+	0.725371i	$0.741668\pi$
$104$	0.269342	0.0264112
$105$	0.789617	0.0770587
$106$	1.08001	0.104900
$107$	−10.7919	−1.04329	−0.521644	−	0.853163i	$-0.674681\pi$
$107$	−10.7919	−1.04329	−0.521644	+	0.853163i	$0.674681\pi$
$108$	−1.00000	−0.0962250
$109$	−16.3580	−1.56681	−0.783404	−	0.621513i	$-0.786518\pi$
$109$	−16.3580	−1.56681	−0.783404	+	0.621513i	$0.786518\pi$
$110$	1.10379	0.105242
$111$	−2.01732	−0.191476
$112$	2.43232	0.229833
$113$	−19.9598	−1.87766	−0.938830	−	0.344382i	$-0.888089\pi$
$113$	−19.9598	−1.87766	−0.938830	+	0.344382i	$0.888089\pi$
$114$	4.02509	0.376984
$115$	0	0
$116$	2.00935	0.186564
$117$	0.269342	0.0249007
$118$	9.90548	0.911873
$119$	−11.7923	−1.08100
$120$	0.324635	0.0296350
$121$	0.560608	0.0509643
$122$	−4.35062	−0.393887
$123$	2.60502	0.234887
$124$	−9.50557	−0.853625
$125$	3.21214	0.287302
$126$	2.43232	0.216689
$127$	−5.44618	−0.483270	−0.241635	−	0.970367i	$-0.577684\pi$
$127$	−5.44618	−0.483270	−0.241635	+	0.970367i	$0.577684\pi$
$128$	1.00000	0.0883883
$129$	3.93559	0.346509
$130$	−0.0874378	−0.00766881
$131$	15.3071	1.33739	0.668694	−	0.743537i	$-0.266853\pi$
$131$	15.3071	1.33739	0.668694	+	0.743537i	$0.266853\pi$
$132$	3.40009	0.295940
$133$	−9.79032	−0.848929
$134$	−10.2730	−0.887448
$135$	0.324635	0.0279401
$136$	−4.84815	−0.415725
$137$	17.0753	1.45884	0.729419	−	0.684067i	$-0.239791\pi$
$137$	17.0753	1.45884	0.729419	+	0.684067i	$0.239791\pi$
$138$	0	0
$139$	16.2779	1.38067	0.690337	−	0.723488i	$-0.257462\pi$
$139$	16.2779	1.38067	0.690337	+	0.723488i	$0.257462\pi$
$140$	−0.789617	−0.0667348
$141$	−5.19874	−0.437813
$142$	11.4304	0.959216
$143$	−0.915787	−0.0765820
$144$	1.00000	0.0833333
$145$	−0.652306	−0.0541711
$146$	−1.13935	−0.0942935
$147$	1.08380	0.0893907
$148$	2.01732	0.165823
$149$	1.63045	0.133571	0.0667857	−	0.997767i	$-0.478726\pi$
$149$	1.63045	0.133571	0.0667857	+	0.997767i	$0.478726\pi$
$150$	4.89461	0.399643
$151$	−11.7663	−0.957530	−0.478765	−	0.877943i	$-0.658915\pi$
$151$	−11.7663	−0.957530	−0.478765	+	0.877943i	$0.658915\pi$
$152$	−4.02509	−0.326478
$153$	−4.84815	−0.391950
$154$	−8.27012	−0.666425
$155$	3.08584	0.247860
$156$	−0.269342	−0.0215646
$157$	−10.0065	−0.798607	−0.399303	−	0.916819i	$-0.630748\pi$
$157$	−10.0065	−0.798607	−0.399303	+	0.916819i	$0.630748\pi$
$158$	−16.0547	−1.27724
$159$	−1.08001	−0.0856504
$160$	−0.324635	−0.0256646
$161$	0	0
$162$	1.00000	0.0785674
$163$	−15.9393	−1.24846	−0.624230	−	0.781241i	$-0.714587\pi$
$163$	−15.9393	−1.24846	−0.624230	+	0.781241i	$0.714587\pi$
$164$	−2.60502	−0.203418
$165$	−1.10379	−0.0859297
$166$	1.05529	0.0819066
$167$	−9.53697	−0.737993	−0.368997	−	0.929431i	$-0.620299\pi$
$167$	−9.53697	−0.737993	−0.368997	+	0.929431i	$0.620299\pi$
$168$	−2.43232	−0.187658
$169$	−12.9275	−0.994420
$170$	1.57388	0.120711
$171$	−4.02509	−0.307806
$172$	−3.93559	−0.300086
$173$	−24.7305	−1.88022	−0.940112	−	0.340865i	$-0.889280\pi$
$173$	−24.7305	−1.88022	−0.940112	+	0.340865i	$0.889280\pi$
$174$	−2.00935	−0.152329
$175$	−11.9053	−0.899954
$176$	−3.40009	−0.256291
$177$	−9.90548	−0.744541
$178$	2.74085	0.205435
$179$	−26.3484	−1.96937	−0.984684	−	0.174348i	$-0.944218\pi$
$179$	−26.3484	−1.96937	−0.984684	+	0.174348i	$0.944218\pi$
$180$	−0.324635	−0.0241968
$181$	18.1768	1.35107	0.675535	−	0.737328i	$-0.263913\pi$
$181$	18.1768	1.35107	0.675535	+	0.737328i	$0.263913\pi$
$182$	0.655127	0.0485613
$183$	4.35062	0.321607
$184$	0	0
$185$	−0.654892	−0.0481486
$186$	9.50557	0.696982
$187$	16.4841	1.20544
$188$	5.19874	0.379157
$189$	−2.43232	−0.176925
$190$	1.30668	0.0947969
$191$	−7.85270	−0.568201	−0.284101	−	0.958794i	$-0.591695\pi$
$191$	−7.85270	−0.568201	−0.284101	+	0.958794i	$0.591695\pi$
$192$	−1.00000	−0.0721688
$193$	23.5784	1.69721	0.848604	−	0.529028i	$-0.177443\pi$
$193$	23.5784	1.69721	0.848604	+	0.529028i	$0.177443\pi$
$194$	13.6079	0.976990
$195$	0.0874378	0.00626155
$196$	−1.08380	−0.0774146
$197$	9.26049	0.659783	0.329891	−	0.944019i	$-0.392988\pi$
$197$	9.26049	0.659783	0.329891	+	0.944019i	$0.392988\pi$
$198$	−3.40009	−0.241634
$199$	25.7180	1.82310	0.911552	−	0.411185i	$-0.134885\pi$
$199$	25.7180	1.82310	0.911552	+	0.411185i	$0.134885\pi$
$200$	−4.89461	−0.346101
$201$	10.2730	0.724599
$202$	15.9029	1.11892
$203$	4.88740	0.343028
$204$	4.84815	0.339438
$205$	0.845680	0.0590649
$206$	−13.9721	−0.973485
$207$	0	0
$208$	0.269342	0.0186755
$209$	13.6857	0.946658
$210$	0.789617	0.0544887
$211$	19.6782	1.35470	0.677350	−	0.735660i	$-0.263128\pi$
$211$	19.6782	1.35470	0.677350	+	0.735660i	$0.263128\pi$
$212$	1.08001	0.0741754
$213$	−11.4304	−0.783197
$214$	−10.7919	−0.737716
$215$	1.27763	0.0871336
$216$	−1.00000	−0.0680414
$217$	−23.1206	−1.56953
$218$	−16.3580	−1.10790
$219$	1.13935	0.0769903
$220$	1.10379	0.0744173
$221$	−1.30581	−0.0878384
$222$	−2.01732	−0.135394
$223$	−4.79039	−0.320788	−0.160394	−	0.987053i	$-0.551277\pi$
$223$	−4.79039	−0.320788	−0.160394	+	0.987053i	$0.551277\pi$
$224$	2.43232	0.162516
$225$	−4.89461	−0.326307
$226$	−19.9598	−1.32771
$227$	−6.03416	−0.400501	−0.200251	−	0.979745i	$-0.564176\pi$
$227$	−6.03416	−0.400501	−0.200251	+	0.979745i	$0.564176\pi$
$228$	4.02509	0.266568
$229$	−7.27420	−0.480692	−0.240346	−	0.970687i	$-0.577261\pi$
$229$	−7.27420	−0.480692	−0.240346	+	0.970687i	$0.577261\pi$
$230$	0	0
$231$	8.27012	0.544134
$232$	2.00935	0.131921
$233$	8.41855	0.551517	0.275759	−	0.961227i	$-0.411071\pi$
$233$	8.41855	0.551517	0.275759	+	0.961227i	$0.411071\pi$
$234$	0.269342	0.0176074
$235$	−1.68769	−0.110093
$236$	9.90548	0.644792
$237$	16.0547	1.04286
$238$	−11.7923	−0.764379
$239$	−5.16012	−0.333781	−0.166890	−	0.985975i	$-0.553373\pi$
$239$	−5.16012	−0.333781	−0.166890	+	0.985975i	$0.553373\pi$
$240$	0.324635	0.0209551
$241$	−15.6301	−1.00682	−0.503411	−	0.864047i	$-0.667922\pi$
$241$	−15.6301	−1.00682	−0.503411	+	0.864047i	$0.667922\pi$
$242$	0.560608	0.0360372
$243$	−1.00000	−0.0641500
$244$	−4.35062	−0.278520
$245$	0.351841	0.0224783
$246$	2.60502	0.166090
$247$	−1.08413	−0.0689813
$248$	−9.50557	−0.603604
$249$	−1.05529	−0.0668765
$250$	3.21214	0.203153
$251$	13.8839	0.876345	0.438172	−	0.898891i	$-0.355626\pi$
$251$	13.8839	0.876345	0.438172	+	0.898891i	$0.355626\pi$
$252$	2.43232	0.153222
$253$	0	0
$254$	−5.44618	−0.341724
$255$	−1.57388	−0.0985601
$256$	1.00000	0.0625000
$257$	−9.84808	−0.614307	−0.307153	−	0.951660i	$-0.599376\pi$
$257$	−9.84808	−0.614307	−0.307153	+	0.951660i	$0.599376\pi$
$258$	3.93559	0.245019
$259$	4.90677	0.304892
$260$	−0.0874378	−0.00542266
$261$	2.00935	0.124376
$262$	15.3071	0.945677
$263$	−0.229051	−0.0141239	−0.00706195	−	0.999975i	$-0.502248\pi$
$263$	−0.229051	−0.0141239	−0.00706195	+	0.999975i	$0.502248\pi$
$264$	3.40009	0.209261
$265$	−0.350609	−0.0215377
$266$	−9.79032	−0.600283
$267$	−2.74085	−0.167737
$268$	−10.2730	−0.627521
$269$	−0.432758	−0.0263857	−0.0131928	−	0.999913i	$-0.504200\pi$
$269$	−0.432758	−0.0263857	−0.0131928	+	0.999913i	$0.504200\pi$
$270$	0.324635	0.0197566
$271$	−7.28255	−0.442383	−0.221192	−	0.975230i	$-0.570995\pi$
$271$	−7.28255	−0.442383	−0.221192	+	0.975230i	$0.570995\pi$
$272$	−4.84815	−0.293962
$273$	−0.655127	−0.0396501
$274$	17.0753	1.03155
$275$	16.6421	1.00356
$276$	0	0
$277$	−24.9693	−1.50026	−0.750130	−	0.661291i	$-0.770009\pi$
$277$	−24.9693	−1.50026	−0.750130	+	0.661291i	$0.770009\pi$
$278$	16.2779	0.976285
$279$	−9.50557	−0.569083
$280$	−0.789617	−0.0471886
$281$	7.32093	0.436730	0.218365	−	0.975867i	$-0.429928\pi$
$281$	7.32093	0.436730	0.218365	+	0.975867i	$0.429928\pi$
$282$	−5.19874	−0.309581
$283$	−10.4946	−0.623837	−0.311918	−	0.950109i	$-0.600972\pi$
$283$	−10.4946	−0.623837	−0.311918	+	0.950109i	$0.600972\pi$
$284$	11.4304	0.678268
$285$	−1.30668	−0.0774013
$286$	−0.915787	−0.0541516
$287$	−6.33625	−0.374017
$288$	1.00000	0.0589256
$289$	6.50456	0.382621
$290$	−0.652306	−0.0383047
$291$	−13.6079	−0.797709
$292$	−1.13935	−0.0666756
$293$	16.1874	0.945677	0.472839	−	0.881149i	$-0.343229\pi$
$293$	16.1874	0.945677	0.472839	+	0.881149i	$0.343229\pi$
$294$	1.08380	0.0632088
$295$	−3.21566	−0.187223
$296$	2.01732	0.117254
$297$	3.40009	0.197293
$298$	1.63045	0.0944492
$299$	0	0
$300$	4.89461	0.282591
$301$	−9.57262	−0.551757
$302$	−11.7663	−0.677076
$303$	−15.9029	−0.913597
$304$	−4.02509	−0.230855
$305$	1.41236	0.0808717
$306$	−4.84815	−0.277150
$307$	17.8501	1.01876	0.509380	−	0.860541i	$-0.329875\pi$
$307$	17.8501	1.01876	0.509380	+	0.860541i	$0.329875\pi$
$308$	−8.27012	−0.471234
$309$	13.9721	0.794847
$310$	3.08584	0.175264
$311$	−14.7357	−0.835586	−0.417793	−	0.908542i	$-0.637196\pi$
$311$	−14.7357	−0.835586	−0.417793	+	0.908542i	$0.637196\pi$
$312$	−0.269342	−0.0152485
$313$	5.71682	0.323134	0.161567	−	0.986862i	$-0.448345\pi$
$313$	5.71682	0.323134	0.161567	+	0.986862i	$0.448345\pi$
$314$	−10.0065	−0.564700
$315$	−0.789617	−0.0444899
$316$	−16.0547	−0.903145
$317$	−7.00248	−0.393298	−0.196649	−	0.980474i	$-0.563006\pi$
$317$	−7.00248	−0.393298	−0.196649	+	0.980474i	$0.563006\pi$
$318$	−1.08001	−0.0605640
$319$	−6.83198	−0.382518
$320$	−0.324635	−0.0181476
$321$	10.7919	0.602343
$322$	0	0
$323$	19.5143	1.08580
$324$	1.00000	0.0555556
$325$	−1.31833	−0.0731275
$326$	−15.9393	−0.882794
$327$	16.3580	0.904597
$328$	−2.60502	−0.143838
$329$	12.6450	0.697142
$330$	−1.10379	−0.0607615
$331$	19.5035	1.07201	0.536004	−	0.844215i	$-0.319933\pi$
$331$	19.5035	1.07201	0.536004	+	0.844215i	$0.319933\pi$
$332$	1.05529	0.0579167
$333$	2.01732	0.110548
$334$	−9.53697	−0.521840
$335$	3.33496	0.182208
$336$	−2.43232	−0.132694
$337$	20.3735	1.10981	0.554906	−	0.831913i	$-0.312754\pi$
$337$	20.3735	1.10981	0.554906	+	0.831913i	$0.312754\pi$
$338$	−12.9275	−0.703161
$339$	19.9598	1.08407
$340$	1.57388	0.0853555
$341$	32.3198	1.75021
$342$	−4.02509	−0.217652
$343$	−19.6624	−1.06167
$344$	−3.93559	−0.212193
$345$	0	0
$346$	−24.7305	−1.32952
$347$	−1.87358	−0.100579	−0.0502896	−	0.998735i	$-0.516014\pi$
$347$	−1.87358	−0.100579	−0.0502896	+	0.998735i	$0.516014\pi$
$348$	−2.00935	−0.107713
$349$	16.4616	0.881172	0.440586	−	0.897710i	$-0.354771\pi$
$349$	16.4616	0.881172	0.440586	+	0.897710i	$0.354771\pi$
$350$	−11.9053	−0.636364
$351$	−0.269342	−0.0143764
$352$	−3.40009	−0.181225
$353$	−8.08237	−0.430181	−0.215090	−	0.976594i	$-0.569005\pi$
$353$	−8.08237	−0.430181	−0.215090	+	0.976594i	$0.569005\pi$
$354$	−9.90548	−0.526470
$355$	−3.71070	−0.196943
$356$	2.74085	0.145265
$357$	11.7923	0.624113
$358$	−26.3484	−1.39255
$359$	−17.8120	−0.940083	−0.470042	−	0.882644i	$-0.655761\pi$
$359$	−17.8120	−0.940083	−0.470042	+	0.882644i	$0.655761\pi$
$360$	−0.324635	−0.0171098
$361$	−2.79864	−0.147297
$362$	18.1768	0.955350
$363$	−0.560608	−0.0294243
$364$	0.655127	0.0343380
$365$	0.369874	0.0193601
$366$	4.35062	0.227411
$367$	4.22445	0.220515	0.110257	−	0.993903i	$-0.464833\pi$
$367$	4.22445	0.220515	0.110257	+	0.993903i	$0.464833\pi$
$368$	0	0
$369$	−2.60502	−0.135612
$370$	−0.654892	−0.0340462
$371$	2.62693	0.136384
$372$	9.50557	0.492841
$373$	6.77016	0.350545	0.175273	−	0.984520i	$-0.443919\pi$
$373$	6.77016	0.350545	0.175273	+	0.984520i	$0.443919\pi$
$374$	16.4841	0.852375
$375$	−3.21214	−0.165874
$376$	5.19874	0.268105
$377$	0.541204	0.0278734
$378$	−2.43232	−0.125105
$379$	−8.78615	−0.451314	−0.225657	−	0.974207i	$-0.572453\pi$
$379$	−8.78615	−0.451314	−0.225657	+	0.974207i	$0.572453\pi$
$380$	1.30668	0.0670315
$381$	5.44618	0.279016
$382$	−7.85270	−0.401779
$383$	23.0045	1.17547	0.587737	−	0.809052i	$-0.300019\pi$
$383$	23.0045	1.17547	0.587737	+	0.809052i	$0.300019\pi$
$384$	−1.00000	−0.0510310
$385$	2.68477	0.136828
$386$	23.5784	1.20011
$387$	−3.93559	−0.200057
$388$	13.6079	0.690836
$389$	6.52670	0.330917	0.165458	−	0.986217i	$-0.447090\pi$
$389$	6.52670	0.330917	0.165458	+	0.986217i	$0.447090\pi$
$390$	0.0874378	0.00442759
$391$	0	0
$392$	−1.08380	−0.0547404
$393$	−15.3071	−0.772142
$394$	9.26049	0.466537
$395$	5.21190	0.262239
$396$	−3.40009	−0.170861
$397$	34.7651	1.74481	0.872404	−	0.488785i	$-0.162560\pi$
$397$	34.7651	1.74481	0.872404	+	0.488785i	$0.162560\pi$
$398$	25.7180	1.28913
$399$	9.79032	0.490129
$400$	−4.89461	−0.244731
$401$	4.23343	0.211408	0.105704	−	0.994398i	$-0.466290\pi$
$401$	4.23343	0.211408	0.105704	+	0.994398i	$0.466290\pi$
$402$	10.2730	0.512369
$403$	−2.56025	−0.127535
$404$	15.9029	0.791198
$405$	−0.324635	−0.0161312
$406$	4.88740	0.242557
$407$	−6.85907	−0.339991
$408$	4.84815	0.240019
$409$	23.7882	1.17625	0.588126	−	0.808769i	$-0.299866\pi$
$409$	23.7882	1.17625	0.588126	+	0.808769i	$0.299866\pi$
$410$	0.845680	0.0417652
$411$	−17.0753	−0.842260
$412$	−13.9721	−0.688358
$413$	24.0933	1.18555
$414$	0	0
$415$	−0.342585	−0.0168168
$416$	0.269342	0.0132056
$417$	−16.2779	−0.797133
$418$	13.6857	0.669388
$419$	−22.3001	−1.08943	−0.544717	−	0.838620i	$-0.683363\pi$
$419$	−22.3001	−1.08943	−0.544717	+	0.838620i	$0.683363\pi$
$420$	0.789617	0.0385294
$421$	23.9034	1.16498	0.582491	−	0.812837i	$-0.302078\pi$
$421$	23.9034	1.16498	0.582491	+	0.812837i	$0.302078\pi$
$422$	19.6782	0.957918
$423$	5.19874	0.252771
$424$	1.08001	0.0524499
$425$	23.7298	1.15107
$426$	−11.4304	−0.553804
$427$	−10.5821	−0.512105
$428$	−10.7919	−0.521644
$429$	0.915787	0.0442146
$430$	1.27763	0.0616127
$431$	−10.0745	−0.485269	−0.242635	−	0.970118i	$-0.578012\pi$
$431$	−10.0745	−0.485269	−0.242635	+	0.970118i	$0.578012\pi$
$432$	−1.00000	−0.0481125
$433$	32.9245	1.58225	0.791125	−	0.611655i	$-0.209496\pi$
$433$	32.9245	1.58225	0.791125	+	0.611655i	$0.209496\pi$
$434$	−23.1206	−1.10982
$435$	0.652306	0.0312757
$436$	−16.3580	−0.783404
$437$	0	0
$438$	1.13935	0.0544404
$439$	−17.6807	−0.843852	−0.421926	−	0.906630i	$-0.638646\pi$
$439$	−17.6807	−0.843852	−0.421926	+	0.906630i	$0.638646\pi$
$440$	1.10379	0.0526210
$441$	−1.08380	−0.0516097
$442$	−1.30581	−0.0621111
$443$	−32.6096	−1.54933	−0.774665	−	0.632371i	$-0.782082\pi$
$443$	−32.6096	−1.54933	−0.774665	+	0.632371i	$0.782082\pi$
$444$	−2.01732	−0.0957378
$445$	−0.889774	−0.0421793
$446$	−4.79039	−0.226832
$447$	−1.63045	−0.0771174
$448$	2.43232	0.114916
$449$	35.3685	1.66914	0.834572	−	0.550898i	$-0.185715\pi$
$449$	35.3685	1.66914	0.834572	+	0.550898i	$0.185715\pi$
$450$	−4.89461	−0.230734
$451$	8.85730	0.417074
$452$	−19.9598	−0.938830
$453$	11.7663	0.552830
$454$	−6.03416	−0.283197
$455$	−0.212677	−0.00997045
$456$	4.02509	0.188492
$457$	8.77948	0.410687	0.205343	−	0.978690i	$-0.434169\pi$
$457$	8.77948	0.410687	0.205343	+	0.978690i	$0.434169\pi$
$458$	−7.27420	−0.339901
$459$	4.84815	0.226292
$460$	0	0
$461$	12.7701	0.594765	0.297382	−	0.954758i	$-0.403886\pi$
$461$	12.7701	0.594765	0.297382	+	0.954758i	$0.403886\pi$
$462$	8.27012	0.384761
$463$	15.8063	0.734579	0.367290	−	0.930107i	$-0.380286\pi$
$463$	15.8063	0.734579	0.367290	+	0.930107i	$0.380286\pi$
$464$	2.00935	0.0932819
$465$	−3.08584	−0.143102
$466$	8.41855	0.389982
$467$	−3.47362	−0.160740	−0.0803700	−	0.996765i	$-0.525610\pi$
$467$	−3.47362	−0.160740	−0.0803700	+	0.996765i	$0.525610\pi$
$468$	0.269342	0.0124503
$469$	−24.9872	−1.15380
$470$	−1.68769	−0.0778474
$471$	10.0065	0.461076
$472$	9.90548	0.455936
$473$	13.3814	0.615275
$474$	16.0547	0.737415
$475$	19.7013	0.903956
$476$	−11.7923	−0.540498
$477$	1.08001	0.0494503
$478$	−5.16012	−0.236019
$479$	−0.885748	−0.0404709	−0.0202354	−	0.999795i	$-0.506442\pi$
$479$	−0.885748	−0.0404709	−0.0202354	+	0.999795i	$0.506442\pi$
$480$	0.324635	0.0148175
$481$	0.543349	0.0247746
$482$	−15.6301	−0.711931
$483$	0	0
$484$	0.560608	0.0254822
$485$	−4.41760	−0.200593
$486$	−1.00000	−0.0453609
$487$	−3.28852	−0.149017	−0.0745085	−	0.997220i	$-0.523739\pi$
$487$	−3.28852	−0.149017	−0.0745085	+	0.997220i	$0.523739\pi$
$488$	−4.35062	−0.196943
$489$	15.9393	0.720798
$490$	0.351841	0.0158945
$491$	24.1044	1.08781	0.543907	−	0.839145i	$-0.316944\pi$
$491$	24.1044	1.08781	0.543907	+	0.839145i	$0.316944\pi$
$492$	2.60502	0.117443
$493$	−9.74165	−0.438742
$494$	−1.08413	−0.0487772
$495$	1.10379	0.0496116
$496$	−9.50557	−0.426812
$497$	27.8024	1.24711
$498$	−1.05529	−0.0472888
$499$	13.5901	0.608375	0.304187	−	0.952612i	$-0.401615\pi$
$499$	13.5901	0.608375	0.304187	+	0.952612i	$0.401615\pi$
$500$	3.21214	0.143651
$501$	9.53697	0.426081
$502$	13.8839	0.619669
$503$	16.4428	0.733149	0.366575	−	0.930389i	$-0.380530\pi$
$503$	16.4428	0.733149	0.366575	+	0.930389i	$0.380530\pi$
$504$	2.43232	0.108344
$505$	−5.16263	−0.229734
$506$	0	0
$507$	12.9275	0.574128
$508$	−5.44618	−0.241635
$509$	−25.3556	−1.12387	−0.561934	−	0.827182i	$-0.689943\pi$
$509$	−25.3556	−1.12387	−0.561934	+	0.827182i	$0.689943\pi$
$510$	−1.57388	−0.0696925
$511$	−2.77127	−0.122594
$512$	1.00000	0.0441942
$513$	4.02509	0.177712
$514$	−9.84808	−0.434380
$515$	4.53584	0.199873
$516$	3.93559	0.173255
$517$	−17.6762	−0.777398
$518$	4.90677	0.215591
$519$	24.7305	1.08555
$520$	−0.0874378	−0.00383440
$521$	−33.3911	−1.46289	−0.731445	−	0.681900i	$-0.761154\pi$
$521$	−33.3911	−1.46289	−0.731445	+	0.681900i	$0.761154\pi$
$522$	2.00935	0.0879470
$523$	−8.13303	−0.355633	−0.177816	−	0.984064i	$-0.556903\pi$
$523$	−8.13303	−0.355633	−0.177816	+	0.984064i	$0.556903\pi$
$524$	15.3071	0.668694
$525$	11.9053	0.519589
$526$	−0.229051	−0.00998711
$527$	46.0844	2.00747
$528$	3.40009	0.147970
$529$	0	0
$530$	−0.350609	−0.0152295
$531$	9.90548	0.429861
$532$	−9.79032	−0.424464
$533$	−0.701642	−0.0303915
$534$	−2.74085	−0.118608
$535$	3.50341	0.151466
$536$	−10.2730	−0.443724
$537$	26.3484	1.13702
$538$	−0.432758	−0.0186575
$539$	3.68503	0.158726
$540$	0.324635	0.0139701
$541$	8.92929	0.383900	0.191950	−	0.981405i	$-0.438519\pi$
$541$	8.92929	0.383900	0.191950	+	0.981405i	$0.438519\pi$
$542$	−7.28255	−0.312812
$543$	−18.1768	−0.780040
$544$	−4.84815	−0.207863
$545$	5.31036	0.227471
$546$	−0.655127	−0.0280369
$547$	18.3908	0.786335	0.393168	−	0.919467i	$-0.371379\pi$
$547$	18.3908	0.786335	0.393168	+	0.919467i	$0.371379\pi$
$548$	17.0753	0.729419
$549$	−4.35062	−0.185680
$550$	16.6421	0.709622
$551$	−8.08783	−0.344553
$552$	0	0
$553$	−39.0501	−1.66058
$554$	−24.9693	−1.06084
$555$	0.654892	0.0277986
$556$	16.2779	0.690337
$557$	15.0330	0.636968	0.318484	−	0.947928i	$-0.396826\pi$
$557$	15.0330	0.636968	0.318484	+	0.947928i	$0.396826\pi$
$558$	−9.50557	−0.402403
$559$	−1.06002	−0.0448341
$560$	−0.789617	−0.0333674
$561$	−16.4841	−0.695961
$562$	7.32093	0.308815
$563$	45.8315	1.93157	0.965785	−	0.259346i	$-0.0835068\pi$
$563$	45.8315	1.93157	0.965785	+	0.259346i	$0.0835068\pi$
$564$	−5.19874	−0.218906
$565$	6.47964	0.272601
$566$	−10.4946	−0.441119
$567$	2.43232	0.102148
$568$	11.4304	0.479608
$569$	−35.3665	−1.48264	−0.741321	−	0.671150i	$-0.765801\pi$
$569$	−35.3665	−1.48264	−0.741321	+	0.671150i	$0.765801\pi$
$570$	−1.30668	−0.0547310
$571$	−21.0408	−0.880528	−0.440264	−	0.897868i	$-0.645115\pi$
$571$	−21.0408	−0.880528	−0.440264	+	0.897868i	$0.645115\pi$
$572$	−0.915787	−0.0382910
$573$	7.85270	0.328051
$574$	−6.33625	−0.264470
$575$	0	0
$576$	1.00000	0.0416667
$577$	−17.0656	−0.710452	−0.355226	−	0.934780i	$-0.615596\pi$
$577$	−17.0656	−0.710452	−0.355226	+	0.934780i	$0.615596\pi$
$578$	6.50456	0.270554
$579$	−23.5784	−0.979884
$580$	−0.652306	−0.0270855
$581$	2.56681	0.106489
$582$	−13.6079	−0.564066
$583$	−3.67213	−0.152084
$584$	−1.13935	−0.0471467
$585$	−0.0874378	−0.00361511
$586$	16.1874	0.668695
$587$	−3.20673	−0.132356	−0.0661780	−	0.997808i	$-0.521081\pi$
$587$	−3.20673	−0.132356	−0.0661780	+	0.997808i	$0.521081\pi$
$588$	1.08380	0.0446953
$589$	38.2608	1.57651
$590$	−3.21566	−0.132387
$591$	−9.26049	−0.380926
$592$	2.01732	0.0829114
$593$	−8.15422	−0.334854	−0.167427	−	0.985884i	$-0.553546\pi$
$593$	−8.15422	−0.334854	−0.167427	+	0.985884i	$0.553546\pi$
$594$	3.40009	0.139507
$595$	3.82818	0.156940
$596$	1.63045	0.0667857
$597$	−25.7180	−1.05257
$598$	0	0
$599$	−44.6481	−1.82427	−0.912136	−	0.409888i	$-0.865568\pi$
$599$	−44.6481	−1.82427	−0.912136	+	0.409888i	$0.865568\pi$
$600$	4.89461	0.199822
$601$	−27.7579	−1.13227	−0.566135	−	0.824312i	$-0.691562\pi$
$601$	−27.7579	−1.13227	−0.566135	+	0.824312i	$0.691562\pi$
$602$	−9.57262	−0.390151
$603$	−10.2730	−0.418347
$604$	−11.7663	−0.478765
$605$	−0.181993	−0.00739906
$606$	−15.9029	−0.646011
$607$	−23.5817	−0.957153	−0.478577	−	0.878046i	$-0.658847\pi$
$607$	−23.5817	−0.957153	−0.478577	+	0.878046i	$0.658847\pi$
$608$	−4.02509	−0.163239
$609$	−4.88740	−0.198047
$610$	1.41236	0.0571849
$611$	1.40024	0.0566477
$612$	−4.84815	−0.195975
$613$	32.8468	1.32667	0.663336	−	0.748322i	$-0.269140\pi$
$613$	32.8468	1.32667	0.663336	+	0.748322i	$0.269140\pi$
$614$	17.8501	0.720373
$615$	−0.845680	−0.0341011
$616$	−8.27012	−0.333212
$617$	23.3881	0.941571	0.470786	−	0.882248i	$-0.343971\pi$
$617$	23.3881	0.941571	0.470786	+	0.882248i	$0.343971\pi$
$618$	13.9721	0.562042
$619$	12.4486	0.500350	0.250175	−	0.968201i	$-0.419512\pi$
$619$	12.4486	0.500350	0.250175	+	0.968201i	$0.419512\pi$
$620$	3.08584	0.123930
$621$	0	0
$622$	−14.7357	−0.590848
$623$	6.66662	0.267093
$624$	−0.269342	−0.0107823
$625$	23.4303	0.937212
$626$	5.71682	0.228490
$627$	−13.6857	−0.546553
$628$	−10.0065	−0.399303
$629$	−9.78027	−0.389965
$630$	−0.789617	−0.0314591
$631$	−32.4757	−1.29284	−0.646419	−	0.762982i	$-0.723734\pi$
$631$	−32.4757	−1.29284	−0.646419	+	0.762982i	$0.723734\pi$
$632$	−16.0547	−0.638620
$633$	−19.6782	−0.782137
$634$	−7.00248	−0.278104
$635$	1.76802	0.0701617
$636$	−1.08001	−0.0428252
$637$	−0.291914	−0.0115661
$638$	−6.83198	−0.270481
$639$	11.4304	0.452179
$640$	−0.324635	−0.0128323
$641$	−3.78968	−0.149683	−0.0748416	−	0.997195i	$-0.523845\pi$
$641$	−3.78968	−0.149683	−0.0748416	+	0.997195i	$0.523845\pi$
$642$	10.7919	0.425920
$643$	−16.4223	−0.647634	−0.323817	−	0.946120i	$-0.604966\pi$
$643$	−16.4223	−0.647634	−0.323817	+	0.946120i	$0.604966\pi$
$644$	0	0
$645$	−1.27763	−0.0503066
$646$	19.5143	0.767778
$647$	−5.18571	−0.203871	−0.101936	−	0.994791i	$-0.532504\pi$
$647$	−5.18571	−0.203871	−0.101936	+	0.994791i	$0.532504\pi$
$648$	1.00000	0.0392837
$649$	−33.6795	−1.32204
$650$	−1.31833	−0.0517090
$651$	23.1206	0.906168
$652$	−15.9393	−0.624230
$653$	−25.7770	−1.00873	−0.504366	−	0.863490i	$-0.668274\pi$
$653$	−25.7770	−1.00873	−0.504366	+	0.863490i	$0.668274\pi$
$654$	16.3580	0.639647
$655$	−4.96922	−0.194164
$656$	−2.60502	−0.101709
$657$	−1.13935	−0.0444504
$658$	12.6450	0.492954
$659$	43.8640	1.70870	0.854349	−	0.519700i	$-0.173956\pi$
$659$	43.8640	1.70870	0.854349	+	0.519700i	$0.173956\pi$
$660$	−1.10379	−0.0429649
$661$	−9.43101	−0.366824	−0.183412	−	0.983036i	$-0.558714\pi$
$661$	−9.43101	−0.366824	−0.183412	+	0.983036i	$0.558714\pi$
$662$	19.5035	0.758024
$663$	1.30581	0.0507135
$664$	1.05529	0.0409533
$665$	3.17828	0.123248
$666$	2.01732	0.0781696
$667$	0	0
$668$	−9.53697	−0.368997
$669$	4.79039	0.185207
$670$	3.33496	0.128841
$671$	14.7925	0.571059
$672$	−2.43232	−0.0938289
$673$	−8.94031	−0.344624	−0.172312	−	0.985042i	$-0.555124\pi$
$673$	−8.94031	−0.344624	−0.172312	+	0.985042i	$0.555124\pi$
$674$	20.3735	0.784756
$675$	4.89461	0.188394
$676$	−12.9275	−0.497210
$677$	35.3761	1.35961	0.679807	−	0.733391i	$-0.262063\pi$
$677$	35.3761	1.35961	0.679807	+	0.733391i	$0.262063\pi$
$678$	19.9598	0.766551
$679$	33.0988	1.27022
$680$	1.57388	0.0603555
$681$	6.03416	0.231229
$682$	32.3198	1.23759
$683$	29.2895	1.12073	0.560366	−	0.828245i	$-0.310661\pi$
$683$	29.2895	1.12073	0.560366	+	0.828245i	$0.310661\pi$
$684$	−4.02509	−0.153903
$685$	−5.54322	−0.211796
$686$	−19.6624	−0.750715
$687$	7.27420	0.277528
$688$	−3.93559	−0.150043
$689$	0.290892	0.0110821
$690$	0	0
$691$	−20.9634	−0.797487	−0.398744	−	0.917062i	$-0.630554\pi$
$691$	−20.9634	−0.797487	−0.398744	+	0.917062i	$0.630554\pi$
$692$	−24.7305	−0.940112
$693$	−8.27012	−0.314156
$694$	−1.87358	−0.0711203
$695$	−5.28438	−0.200448
$696$	−2.00935	−0.0761644
$697$	12.6295	0.478377
$698$	16.4616	0.623083
$699$	−8.41855	−0.318419
$700$	−11.9053	−0.449977
$701$	32.1001	1.21240	0.606202	−	0.795311i	$-0.292692\pi$
$701$	32.1001	1.21240	0.606202	+	0.795311i	$0.292692\pi$
$702$	−0.269342	−0.0101657
$703$	−8.11990	−0.306248
$704$	−3.40009	−0.128146
$705$	1.68769	0.0635622
$706$	−8.08237	−0.304184
$707$	38.6810	1.45475
$708$	−9.90548	−0.372271
$709$	33.7537	1.26765	0.633824	−	0.773477i	$-0.281484\pi$
$709$	33.7537	1.26765	0.633824	+	0.773477i	$0.281484\pi$
$710$	−3.71070	−0.139260
$711$	−16.0547	−0.602097
$712$	2.74085	0.102718
$713$	0	0
$714$	11.7923	0.441315
$715$	0.297296	0.0111183
$716$	−26.3484	−0.984684
$717$	5.16012	0.192708
$718$	−17.8120	−0.664739
$719$	−46.9884	−1.75237	−0.876185	−	0.481974i	$-0.839920\pi$
$719$	−46.9884	−1.75237	−0.876185	+	0.481974i	$0.839920\pi$
$720$	−0.324635	−0.0120984
$721$	−33.9848	−1.26566
$722$	−2.79864	−0.104154
$723$	15.6301	0.581289
$724$	18.1768	0.675535
$725$	−9.83501	−0.365263
$726$	−0.560608	−0.0208061
$727$	−16.8502	−0.624939	−0.312470	−	0.949928i	$-0.601156\pi$
$727$	−16.8502	−0.624939	−0.312470	+	0.949928i	$0.601156\pi$
$728$	0.655127	0.0242806
$729$	1.00000	0.0370370
$730$	0.369874	0.0136896
$731$	19.0803	0.705711
$732$	4.35062	0.160804
$733$	−10.6895	−0.394825	−0.197413	−	0.980321i	$-0.563254\pi$
$733$	−10.6895	−0.394825	−0.197413	+	0.980321i	$0.563254\pi$
$734$	4.22445	0.155927
$735$	−0.351841	−0.0129778
$736$	0	0
$737$	34.9290	1.28663
$738$	−2.60502	−0.0958921
$739$	24.8920	0.915668	0.457834	−	0.889038i	$-0.348625\pi$
$739$	24.8920	0.915668	0.457834	+	0.889038i	$0.348625\pi$
$740$	−0.654892	−0.0240743
$741$	1.08413	0.0398264
$742$	2.62693	0.0964378
$743$	−38.1691	−1.40029	−0.700145	−	0.714001i	$-0.746881\pi$
$743$	−38.1691	−1.40029	−0.700145	+	0.714001i	$0.746881\pi$
$744$	9.50557	0.348491
$745$	−0.529300	−0.0193920
$746$	6.77016	0.247873
$747$	1.05529	0.0386111
$748$	16.4841	0.602720
$749$	−26.2493	−0.959128
$750$	−3.21214	−0.117291
$751$	−44.2589	−1.61503	−0.807514	−	0.589848i	$-0.799188\pi$
$751$	−44.2589	−1.61503	−0.807514	+	0.589848i	$0.799188\pi$
$752$	5.19874	0.189579
$753$	−13.8839	−0.505958
$754$	0.541204	0.0197095
$755$	3.81976	0.139015
$756$	−2.43232	−0.0884627
$757$	9.78484	0.355636	0.177818	−	0.984063i	$-0.443096\pi$
$757$	9.78484	0.355636	0.177818	+	0.984063i	$0.443096\pi$
$758$	−8.78615	−0.319128
$759$	0	0
$760$	1.30668	0.0473984
$761$	23.9490	0.868150	0.434075	−	0.900877i	$-0.357075\pi$
$761$	23.9490	0.868150	0.434075	+	0.900877i	$0.357075\pi$
$762$	5.44618	0.197294
$763$	−39.7878	−1.44042
$764$	−7.85270	−0.284101
$765$	1.57388	0.0569037
$766$	23.0045	0.831186
$767$	2.66796	0.0963345
$768$	−1.00000	−0.0360844
$769$	27.6827	0.998265	0.499132	−	0.866526i	$-0.333652\pi$
$769$	27.6827	0.998265	0.499132	+	0.866526i	$0.333652\pi$
$770$	2.68477	0.0967523
$771$	9.84808	0.354670
$772$	23.5784	0.848604
$773$	33.8343	1.21693	0.608467	−	0.793579i	$-0.291785\pi$
$773$	33.8343	1.21693	0.608467	+	0.793579i	$0.291785\pi$
$774$	−3.93559	−0.141462
$775$	46.5261	1.67127
$776$	13.6079	0.488495
$777$	−4.90677	−0.176030
$778$	6.52670	0.233993
$779$	10.4854	0.375680
$780$	0.0874378	0.00313078
$781$	−38.8643	−1.39067
$782$	0	0
$783$	−2.00935	−0.0718084
$784$	−1.08380	−0.0387073
$785$	3.24846	0.115943
$786$	−15.3071	−0.545987
$787$	−24.4836	−0.872745	−0.436372	−	0.899766i	$-0.643737\pi$
$787$	−24.4836	−0.872745	−0.436372	+	0.899766i	$0.643737\pi$
$788$	9.26049	0.329891
$789$	0.229051	0.00815444
$790$	5.21190	0.185431
$791$	−48.5487	−1.72619
$792$	−3.40009	−0.120817
$793$	−1.17181	−0.0416121
$794$	34.7651	1.23377
$795$	0.350609	0.0124348
$796$	25.7180	0.911552
$797$	8.69614	0.308033	0.154017	−	0.988068i	$-0.450779\pi$
$797$	8.69614	0.308033	0.154017	+	0.988068i	$0.450779\pi$
$798$	9.79032	0.346574
$799$	−25.2043	−0.891663
$800$	−4.89461	−0.173051
$801$	2.74085	0.0968430
$802$	4.23343	0.149488
$803$	3.87390	0.136707
$804$	10.2730	0.362299
$805$	0	0
$806$	−2.56025	−0.0901809
$807$	0.432758	0.0152338
$808$	15.9029	0.559462
$809$	18.5536	0.652308	0.326154	−	0.945317i	$-0.394247\pi$
$809$	18.5536	0.652308	0.326154	+	0.945317i	$0.394247\pi$
$810$	−0.324635	−0.0114065
$811$	−21.5690	−0.757390	−0.378695	−	0.925521i	$-0.623627\pi$
$811$	−21.5690	−0.757390	−0.378695	+	0.925521i	$0.623627\pi$
$812$	4.88740	0.171514
$813$	7.28255	0.255410
$814$	−6.85907	−0.240410
$815$	5.17444	0.181253
$816$	4.84815	0.169719
$817$	15.8411	0.554210
$818$	23.7882	0.831736
$819$	0.655127	0.0228920
$820$	0.845680	0.0295324
$821$	6.92328	0.241624	0.120812	−	0.992675i	$-0.461450\pi$
$821$	6.92328	0.241624	0.120812	+	0.992675i	$0.461450\pi$
$822$	−17.0753	−0.595568
$823$	−31.3176	−1.09166	−0.545831	−	0.837895i	$-0.683786\pi$
$823$	−31.3176	−1.09166	−0.545831	+	0.837895i	$0.683786\pi$
$824$	−13.9721	−0.486743
$825$	−16.6421	−0.579404
$826$	24.0933	0.838314
$827$	4.77095	0.165902	0.0829511	−	0.996554i	$-0.473565\pi$
$827$	4.77095	0.165902	0.0829511	+	0.996554i	$0.473565\pi$
$828$	0	0
$829$	−1.94168	−0.0674372	−0.0337186	−	0.999431i	$-0.510735\pi$
$829$	−1.94168	−0.0674372	−0.0337186	+	0.999431i	$0.510735\pi$
$830$	−0.342585	−0.0118913
$831$	24.9693	0.866175
$832$	0.269342	0.00933776
$833$	5.25445	0.182056
$834$	−16.2779	−0.563658
$835$	3.09603	0.107143
$836$	13.6857	0.473329
$837$	9.50557	0.328560
$838$	−22.3001	−0.770346
$839$	45.8225	1.58197	0.790985	−	0.611836i	$-0.209569\pi$
$839$	45.8225	1.58197	0.790985	+	0.611836i	$0.209569\pi$
$840$	0.789617	0.0272444
$841$	−24.9625	−0.860776
$842$	23.9034	0.823766
$843$	−7.32093	−0.252146
$844$	19.6782	0.677350
$845$	4.19670	0.144371
$846$	5.19874	0.178736
$847$	1.36358	0.0468531
$848$	1.08001	0.0370877
$849$	10.4946	0.360172
$850$	23.7298	0.813926
$851$	0	0
$852$	−11.4304	−0.391598
$853$	−19.1208	−0.654685	−0.327342	−	0.944906i	$-0.606153\pi$
$853$	−19.1208	−0.654685	−0.327342	+	0.944906i	$0.606153\pi$
$854$	−10.5821	−0.362113
$855$	1.30668	0.0446877
$856$	−10.7919	−0.368858
$857$	9.48763	0.324091	0.162046	−	0.986783i	$-0.448191\pi$
$857$	9.48763	0.324091	0.162046	+	0.986783i	$0.448191\pi$
$858$	0.915787	0.0312645
$859$	39.2043	1.33763	0.668817	−	0.743427i	$-0.266801\pi$
$859$	39.2043	1.33763	0.668817	+	0.743427i	$0.266801\pi$
$860$	1.27763	0.0435668
$861$	6.33625	0.215939
$862$	−10.0745	−0.343137
$863$	12.9692	0.441477	0.220739	−	0.975333i	$-0.429153\pi$
$863$	12.9692	0.441477	0.220739	+	0.975333i	$0.429153\pi$
$864$	−1.00000	−0.0340207
$865$	8.02838	0.272973
$866$	32.9245	1.11882
$867$	−6.50456	−0.220907
$868$	−23.1206	−0.784765
$869$	54.5873	1.85175
$870$	0.652306	0.0221153
$871$	−2.76694	−0.0937542
$872$	−16.3580	−0.553950
$873$	13.6079	0.460558
$874$	0	0
$875$	7.81295	0.264126
$876$	1.13935	0.0384952
$877$	28.5809	0.965108	0.482554	−	0.875866i	$-0.339709\pi$
$877$	28.5809	0.965108	0.482554	+	0.875866i	$0.339709\pi$
$878$	−17.6807	−0.596694
$879$	−16.1874	−0.545987
$880$	1.10379	0.0372087
$881$	−33.5556	−1.13052	−0.565259	−	0.824913i	$-0.691224\pi$
$881$	−33.5556	−1.13052	−0.565259	+	0.824913i	$0.691224\pi$
$882$	−1.08380	−0.0364936
$883$	21.6186	0.727524	0.363762	−	0.931492i	$-0.381492\pi$
$883$	21.6186	0.727524	0.363762	+	0.931492i	$0.381492\pi$
$884$	−1.30581	−0.0439192
$885$	3.21566	0.108093
$886$	−32.6096	−1.09554
$887$	−39.1158	−1.31338	−0.656690	−	0.754161i	$-0.728044\pi$
$887$	−39.1158	−1.31338	−0.656690	+	0.754161i	$0.728044\pi$
$888$	−2.01732	−0.0676968
$889$	−13.2469	−0.444285
$890$	−0.889774	−0.0298253
$891$	−3.40009	−0.113907
$892$	−4.79039	−0.160394
$893$	−20.9254	−0.700242
$894$	−1.63045	−0.0545303
$895$	8.55359	0.285915
$896$	2.43232	0.0812582
$897$	0	0
$898$	35.3685	1.18026
$899$	−19.1000	−0.637022
$900$	−4.89461	−0.163154
$901$	−5.23605	−0.174438
$902$	8.85730	0.294916
$903$	9.57262	0.318557
$904$	−19.9598	−0.663853
$905$	−5.90081	−0.196150
$906$	11.7663	0.390910
$907$	18.6215	0.618317	0.309158	−	0.951011i	$-0.399953\pi$
$907$	18.6215	0.618317	0.309158	+	0.951011i	$0.399953\pi$
$908$	−6.03416	−0.200251
$909$	15.9029	0.527465
$910$	−0.212677	−0.00705018
$911$	−16.2164	−0.537273	−0.268637	−	0.963242i	$-0.586573\pi$
$911$	−16.2164	−0.537273	−0.268637	+	0.963242i	$0.586573\pi$
$912$	4.02509	0.133284
$913$	−3.58809	−0.118748
$914$	8.77948	0.290400
$915$	−1.41236	−0.0466913
$916$	−7.27420	−0.240346
$917$	37.2318	1.22950
$918$	4.84815	0.160013
$919$	−7.51602	−0.247930	−0.123965	−	0.992287i	$-0.539561\pi$
$919$	−7.51602	−0.247930	−0.123965	+	0.992287i	$0.539561\pi$
$920$	0	0
$921$	−17.8501	−0.588182
$922$	12.7701	0.420562
$923$	3.07868	0.101336
$924$	8.27012	0.272067
$925$	−9.87400	−0.324655
$926$	15.8063	0.519426
$927$	−13.9721	−0.458905
$928$	2.00935	0.0659603
$929$	16.8540	0.552962	0.276481	−	0.961019i	$-0.410832\pi$
$929$	16.8540	0.552962	0.276481	+	0.961019i	$0.410832\pi$
$930$	−3.08584	−0.101189
$931$	4.36241	0.142972
$932$	8.41855	0.275759
$933$	14.7357	0.482426
$934$	−3.47362	−0.113660
$935$	−5.35133	−0.175007
$936$	0.269342	0.00880372
$937$	0.877608	0.0286702	0.0143351	−	0.999897i	$-0.495437\pi$
$937$	0.877608	0.0286702	0.0143351	+	0.999897i	$0.495437\pi$
$938$	−24.9872	−0.815859
$939$	−5.71682	−0.186561
$940$	−1.68769	−0.0550465
$941$	−13.9836	−0.455851	−0.227926	−	0.973679i	$-0.573194\pi$
$941$	−13.9836	−0.455851	−0.227926	+	0.973679i	$0.573194\pi$
$942$	10.0065	0.326030
$943$	0	0
$944$	9.90548	0.322396
$945$	0.789617	0.0256862
$946$	13.3814	0.435065
$947$	−24.6457	−0.800876	−0.400438	−	0.916324i	$-0.631142\pi$
$947$	−24.6457	−0.800876	−0.400438	+	0.916324i	$0.631142\pi$
$948$	16.0547	0.521431
$949$	−0.306876	−0.00996161
$950$	19.7013	0.639193
$951$	7.00248	0.227071
$952$	−11.7923	−0.382190
$953$	−56.1029	−1.81735	−0.908675	−	0.417504i	$-0.862905\pi$
$953$	−56.1029	−1.81735	−0.908675	+	0.417504i	$0.862905\pi$
$954$	1.08001	0.0349666
$955$	2.54926	0.0824921
$956$	−5.16012	−0.166890
$957$	6.83198	0.220847
$958$	−0.885748	−0.0286172
$959$	41.5325	1.34116
$960$	0.324635	0.0104775
$961$	59.3558	1.91470
$962$	0.543349	0.0175183
$963$	−10.7919	−0.347763
$964$	−15.6301	−0.503411
$965$	−7.65436	−0.246403
$966$	0	0
$967$	−38.0371	−1.22319	−0.611596	−	0.791170i	$-0.709472\pi$
$967$	−38.0371	−1.22319	−0.611596	+	0.791170i	$0.709472\pi$
$968$	0.560608	0.0180186
$969$	−19.5143	−0.626888
$970$	−4.41760	−0.141841
$971$	−46.8643	−1.50395	−0.751974	−	0.659193i	$-0.770898\pi$
$971$	−46.8643	−1.50395	−0.751974	+	0.659193i	$0.770898\pi$
$972$	−1.00000	−0.0320750
$973$	39.5932	1.26930
$974$	−3.28852	−0.105371
$975$	1.31833	0.0422202
$976$	−4.35062	−0.139260
$977$	6.32527	0.202363	0.101182	−	0.994868i	$-0.467738\pi$
$977$	6.32527	0.202363	0.101182	+	0.994868i	$0.467738\pi$
$978$	15.9393	0.509681
$979$	−9.31912	−0.297840
$980$	0.351841	0.0112391
$981$	−16.3580	−0.522269
$982$	24.1044	0.769201
$983$	29.8592	0.952361	0.476181	−	0.879348i	$-0.342021\pi$
$983$	29.8592	0.952361	0.476181	+	0.879348i	$0.342021\pi$
$984$	2.60502	0.0830450
$985$	−3.00628	−0.0957880
$986$	−9.74165	−0.310237
$987$	−12.6450	−0.402495
$988$	−1.08413	−0.0344907
$989$	0	0
$990$	1.10379	0.0350807
$991$	8.95060	0.284325	0.142163	−	0.989843i	$-0.454594\pi$
$991$	8.95060	0.284325	0.142163	+	0.989843i	$0.454594\pi$
$992$	−9.50557	−0.301802
$993$	−19.5035	−0.618924
$994$	27.8024	0.881838
$995$	−8.34897	−0.264680
$996$	−1.05529	−0.0334382
$997$	16.7521	0.530545	0.265272	−	0.964174i	$-0.414538\pi$
$997$	16.7521	0.530545	0.265272	+	0.964174i	$0.414538\pi$
$998$	13.5901	0.430186
$999$	−2.01732	−0.0638252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3174.2.a.bb.1.2		5
3.2	odd	2		9522.2.a.br.1.4		5
23.11	odd	22		138.2.e.b.121.1	yes	10
23.21	odd	22		138.2.e.b.73.1	✓	10
23.22	odd	2		3174.2.a.ba.1.4		5
69.11	even	22		414.2.i.e.397.1		10
69.44	even	22		414.2.i.e.73.1		10
69.68	even	2		9522.2.a.bs.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.73.1	✓	10	23.21	odd	22
138.2.e.b.121.1	yes	10	23.11	odd	22
414.2.i.e.73.1		10	69.44	even	22
414.2.i.e.397.1		10	69.11	even	22
3174.2.a.ba.1.4		5	23.22	odd	2
3174.2.a.bb.1.2		5	1.1	even	1	trivial
9522.2.a.br.1.4		5	3.2	odd	2
9522.2.a.bs.1.2		5	69.68	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3174 = 2 \cdot 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3174.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.324635 q^{5} -1.00000 q^{6} +2.43232 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.324635 q^{5} -1.00000 q^{6} +2.43232 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.324635 q^{10} -3.40009 q^{11} -1.00000 q^{12} +0.269342 q^{13} +2.43232 q^{14} +0.324635 q^{15} +1.00000 q^{16} -4.84815 q^{17} +1.00000 q^{18} -4.02509 q^{19} -0.324635 q^{20} -2.43232 q^{21} -3.40009 q^{22} -1.00000 q^{24} -4.89461 q^{25} +0.269342 q^{26} -1.00000 q^{27} +2.43232 q^{28} +2.00935 q^{29} +0.324635 q^{30} -9.50557 q^{31} +1.00000 q^{32} +3.40009 q^{33} -4.84815 q^{34} -0.789617 q^{35} +1.00000 q^{36} +2.01732 q^{37} -4.02509 q^{38} -0.269342 q^{39} -0.324635 q^{40} -2.60502 q^{41} -2.43232 q^{42} -3.93559 q^{43} -3.40009 q^{44} -0.324635 q^{45} +5.19874 q^{47} -1.00000 q^{48} -1.08380 q^{49} -4.89461 q^{50} +4.84815 q^{51} +0.269342 q^{52} +1.08001 q^{53} -1.00000 q^{54} +1.10379 q^{55} +2.43232 q^{56} +4.02509 q^{57} +2.00935 q^{58} +9.90548 q^{59} +0.324635 q^{60} -4.35062 q^{61} -9.50557 q^{62} +2.43232 q^{63} +1.00000 q^{64} -0.0874378 q^{65} +3.40009 q^{66} -10.2730 q^{67} -4.84815 q^{68} -0.789617 q^{70} +11.4304 q^{71} +1.00000 q^{72} -1.13935 q^{73} +2.01732 q^{74} +4.89461 q^{75} -4.02509 q^{76} -8.27012 q^{77} -0.269342 q^{78} -16.0547 q^{79} -0.324635 q^{80} +1.00000 q^{81} -2.60502 q^{82} +1.05529 q^{83} -2.43232 q^{84} +1.57388 q^{85} -3.93559 q^{86} -2.00935 q^{87} -3.40009 q^{88} +2.74085 q^{89} -0.324635 q^{90} +0.655127 q^{91} +9.50557 q^{93} +5.19874 q^{94} +1.30668 q^{95} -1.00000 q^{96} +13.6079 q^{97} -1.08380 q^{98} -3.40009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9} + q^{10} - 11 q^{11} - 5 q^{12} + 12 q^{13} - 11 q^{14} - q^{15} + 5 q^{16} + q^{17} + 5 q^{18} - 15 q^{19} + q^{20} + 11 q^{21} - 11 q^{22} - 5 q^{24} + 6 q^{25} + 12 q^{26} - 5 q^{27} - 11 q^{28} + q^{29} - q^{30} - 18 q^{31} + 5 q^{32} + 11 q^{33} + q^{34} - 11 q^{35} + 5 q^{36} - 10 q^{37} - 15 q^{38} - 12 q^{39} + q^{40} - 16 q^{41} + 11 q^{42} - 18 q^{43} - 11 q^{44} + q^{45} - 4 q^{47} - 5 q^{48} + 20 q^{49} + 6 q^{50} - q^{51} + 12 q^{52} + q^{53} - 5 q^{54} - 22 q^{55} - 11 q^{56} + 15 q^{57} + q^{58} + 2 q^{59} - q^{60} + q^{61} - 18 q^{62} - 11 q^{63} + 5 q^{64} - 24 q^{65} + 11 q^{66} - 29 q^{67} + q^{68} - 11 q^{70} - 11 q^{71} + 5 q^{72} - 8 q^{73} - 10 q^{74} - 6 q^{75} - 15 q^{76} + 11 q^{77} - 12 q^{78} - 40 q^{79} + q^{80} + 5 q^{81} - 16 q^{82} - 8 q^{83} + 11 q^{84} - 13 q^{85} - 18 q^{86} - q^{87} - 11 q^{88} - 2 q^{89} + q^{90} - 33 q^{91} + 18 q^{93} - 4 q^{94} - 3 q^{95} - 5 q^{96} - 17 q^{97} + 20 q^{98} - 11 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9 + q^10 - 11 * q^11 - 5 * q^12 + 12 * q^13 - 11 * q^14 - q^15 + 5 * q^16 + q^17 + 5 * q^18 - 15 * q^19 + q^20 + 11 * q^21 - 11 * q^22 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 5 * q^27 - 11 * q^28 + q^29 - q^30 - 18 * q^31 + 5 * q^32 + 11 * q^33 + q^34 - 11 * q^35 + 5 * q^36 - 10 * q^37 - 15 * q^38 - 12 * q^39 + q^40 - 16 * q^41 + 11 * q^42 - 18 * q^43 - 11 * q^44 + q^45 - 4 * q^47 - 5 * q^48 + 20 * q^49 + 6 * q^50 - q^51 + 12 * q^52 + q^53 - 5 * q^54 - 22 * q^55 - 11 * q^56 + 15 * q^57 + q^58 + 2 * q^59 - q^60 + q^61 - 18 * q^62 - 11 * q^63 + 5 * q^64 - 24 * q^65 + 11 * q^66 - 29 * q^67 + q^68 - 11 * q^70 - 11 * q^71 + 5 * q^72 - 8 * q^73 - 10 * q^74 - 6 * q^75 - 15 * q^76 + 11 * q^77 - 12 * q^78 - 40 * q^79 + q^80 + 5 * q^81 - 16 * q^82 - 8 * q^83 + 11 * q^84 - 13 * q^85 - 18 * q^86 - q^87 - 11 * q^88 - 2 * q^89 + q^90 - 33 * q^91 + 18 * q^93 - 4 * q^94 - 3 * q^95 - 5 * q^96 - 17 * q^97 + 20 * q^98 - 11 * q^99

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