LMFDB - Embedded newform 3174.2.a.bd.1.5

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:	$0$
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:	$\Z[a_1, \ldots, a_{5}]$
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			1.5
Root			$-0.830830$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.20362 q^{5} +1.00000 q^{6} -1.51334 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.20362 q^{5} +1.00000 q^{6} -1.51334 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.20362 q^{10} +6.53843 q^{11} +1.00000 q^{12} +2.88612 q^{13} -1.51334 q^{14} +3.20362 q^{15} +1.00000 q^{16} +1.19647 q^{17} +1.00000 q^{18} -0.555554 q^{19} +3.20362 q^{20} -1.51334 q^{21} +6.53843 q^{22} +1.00000 q^{24} +5.26315 q^{25} +2.88612 q^{26} +1.00000 q^{27} -1.51334 q^{28} -8.66918 q^{29} +3.20362 q^{30} -6.73559 q^{31} +1.00000 q^{32} +6.53843 q^{33} +1.19647 q^{34} -4.84815 q^{35} +1.00000 q^{36} +1.45380 q^{37} -0.555554 q^{38} +2.88612 q^{39} +3.20362 q^{40} -1.84796 q^{41} -1.51334 q^{42} -2.17379 q^{43} +6.53843 q^{44} +3.20362 q^{45} -11.4135 q^{47} +1.00000 q^{48} -4.70981 q^{49} +5.26315 q^{50} +1.19647 q^{51} +2.88612 q^{52} -12.0613 q^{53} +1.00000 q^{54} +20.9466 q^{55} -1.51334 q^{56} -0.555554 q^{57} -8.66918 q^{58} +3.96140 q^{59} +3.20362 q^{60} -9.03450 q^{61} -6.73559 q^{62} -1.51334 q^{63} +1.00000 q^{64} +9.24603 q^{65} +6.53843 q^{66} +7.66794 q^{67} +1.19647 q^{68} -4.84815 q^{70} -9.45607 q^{71} +1.00000 q^{72} -0.627598 q^{73} +1.45380 q^{74} +5.26315 q^{75} -0.555554 q^{76} -9.89485 q^{77} +2.88612 q^{78} +13.7721 q^{79} +3.20362 q^{80} +1.00000 q^{81} -1.84796 q^{82} +15.5888 q^{83} -1.51334 q^{84} +3.83304 q^{85} -2.17379 q^{86} -8.66918 q^{87} +6.53843 q^{88} +5.61844 q^{89} +3.20362 q^{90} -4.36768 q^{91} -6.73559 q^{93} -11.4135 q^{94} -1.77978 q^{95} +1.00000 q^{96} +7.24727 q^{97} -4.70981 q^{98} +6.53843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 7 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 7 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 7 q^{7} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 13 q^{11} + 5 q^{12} - 4 q^{13} + 7 q^{14} + 7 q^{15} + 5 q^{16} + 9 q^{17} + 5 q^{18} + 11 q^{19} + 7 q^{20} + 7 q^{21} + 13 q^{22} + 5 q^{24} - 2 q^{25} - 4 q^{26} + 5 q^{27} + 7 q^{28} - 7 q^{29} + 7 q^{30} - 8 q^{31} + 5 q^{32} + 13 q^{33} + 9 q^{34} + q^{35} + 5 q^{36} + 12 q^{37} + 11 q^{38} - 4 q^{39} + 7 q^{40} - 10 q^{41} + 7 q^{42} + 4 q^{43} + 13 q^{44} + 7 q^{45} - 24 q^{47} + 5 q^{48} - 12 q^{49} - 2 q^{50} + 9 q^{51} - 4 q^{52} + 9 q^{53} + 5 q^{54} + 16 q^{55} + 7 q^{56} + 11 q^{57} - 7 q^{58} - 14 q^{59} + 7 q^{60} + 5 q^{61} - 8 q^{62} + 7 q^{63} + 5 q^{64} + 12 q^{65} + 13 q^{66} + 13 q^{67} + 9 q^{68} + q^{70} - 19 q^{71} + 5 q^{72} + 4 q^{73} + 12 q^{74} - 2 q^{75} + 11 q^{76} + 5 q^{77} - 4 q^{78} + 4 q^{79} + 7 q^{80} + 5 q^{81} - 10 q^{82} + 24 q^{83} + 7 q^{84} + 17 q^{85} + 4 q^{86} - 7 q^{87} + 13 q^{88} + 4 q^{89} + 7 q^{90} - 21 q^{91} - 8 q^{93} - 24 q^{94} - 11 q^{95} + 5 q^{96} - 9 q^{97} - 12 q^{98} + 13 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 7 * q^7 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 13 * q^11 + 5 * q^12 - 4 * q^13 + 7 * q^14 + 7 * q^15 + 5 * q^16 + 9 * q^17 + 5 * q^18 + 11 * q^19 + 7 * q^20 + 7 * q^21 + 13 * q^22 + 5 * q^24 - 2 * q^25 - 4 * q^26 + 5 * q^27 + 7 * q^28 - 7 * q^29 + 7 * q^30 - 8 * q^31 + 5 * q^32 + 13 * q^33 + 9 * q^34 + q^35 + 5 * q^36 + 12 * q^37 + 11 * q^38 - 4 * q^39 + 7 * q^40 - 10 * q^41 + 7 * q^42 + 4 * q^43 + 13 * q^44 + 7 * q^45 - 24 * q^47 + 5 * q^48 - 12 * q^49 - 2 * q^50 + 9 * q^51 - 4 * q^52 + 9 * q^53 + 5 * q^54 + 16 * q^55 + 7 * q^56 + 11 * q^57 - 7 * q^58 - 14 * q^59 + 7 * q^60 + 5 * q^61 - 8 * q^62 + 7 * q^63 + 5 * q^64 + 12 * q^65 + 13 * q^66 + 13 * q^67 + 9 * q^68 + q^70 - 19 * q^71 + 5 * q^72 + 4 * q^73 + 12 * q^74 - 2 * q^75 + 11 * q^76 + 5 * q^77 - 4 * q^78 + 4 * q^79 + 7 * q^80 + 5 * q^81 - 10 * q^82 + 24 * q^83 + 7 * q^84 + 17 * q^85 + 4 * q^86 - 7 * q^87 + 13 * q^88 + 4 * q^89 + 7 * q^90 - 21 * q^91 - 8 * q^93 - 24 * q^94 - 11 * q^95 + 5 * q^96 - 9 * q^97 - 12 * q^98 + 13 * 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
$5$	3.20362	1.43270	0.716350	−	0.697741i	$-0.245811\pi$
$5$	3.20362	1.43270	0.716350	+	0.697741i	$0.245811\pi$
$6$	1.00000	0.408248
$7$	−1.51334	−0.571988	−0.285994	−	0.958231i	$-0.592324\pi$
$7$	−1.51334	−0.571988	−0.285994	+	0.958231i	$0.592324\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.20362	1.01307
$11$	6.53843	1.97141	0.985705	−	0.168479i	$-0.0538855\pi$
$11$	6.53843	1.97141	0.985705	+	0.168479i	$0.0538855\pi$
$12$	1.00000	0.288675
$13$	2.88612	0.800466	0.400233	−	0.916413i	$-0.368929\pi$
$13$	2.88612	0.800466	0.400233	+	0.916413i	$0.368929\pi$
$14$	−1.51334	−0.404456
$15$	3.20362	0.827170
$16$	1.00000	0.250000
$17$	1.19647	0.290188	0.145094	−	0.989418i	$-0.453652\pi$
$17$	1.19647	0.290188	0.145094	+	0.989418i	$0.453652\pi$
$18$	1.00000	0.235702
$19$	−0.555554	−0.127453	−0.0637264	−	0.997967i	$-0.520299\pi$
$19$	−0.555554	−0.127453	−0.0637264	+	0.997967i	$0.520299\pi$
$20$	3.20362	0.716350
$21$	−1.51334	−0.330237
$22$	6.53843	1.39400
$23$	0	0
$23$	0	0
$24$	1.00000	0.204124
$25$	5.26315	1.05263
$26$	2.88612	0.566015
$27$	1.00000	0.192450
$28$	−1.51334	−0.285994
$29$	−8.66918	−1.60983	−0.804913	−	0.593393i	$-0.797788\pi$
$29$	−8.66918	−1.60983	−0.804913	+	0.593393i	$0.797788\pi$
$30$	3.20362	0.584898
$31$	−6.73559	−1.20975	−0.604874	−	0.796321i	$-0.706776\pi$
$31$	−6.73559	−1.20975	−0.604874	+	0.796321i	$0.706776\pi$
$32$	1.00000	0.176777
$33$	6.53843	1.13819
$34$	1.19647	0.205194
$35$	−4.84815	−0.819487
$36$	1.00000	0.166667
$37$	1.45380	0.239003	0.119502	−	0.992834i	$-0.461870\pi$
$37$	1.45380	0.239003	0.119502	+	0.992834i	$0.461870\pi$
$38$	−0.555554	−0.0901228
$39$	2.88612	0.462149
$40$	3.20362	0.506536
$41$	−1.84796	−0.288602	−0.144301	−	0.989534i	$-0.546093\pi$
$41$	−1.84796	−0.288602	−0.144301	+	0.989534i	$0.546093\pi$
$42$	−1.51334	−0.233513
$43$	−2.17379	−0.331500	−0.165750	−	0.986168i	$-0.553004\pi$
$43$	−2.17379	−0.331500	−0.165750	+	0.986168i	$0.553004\pi$
$44$	6.53843	0.985705
$45$	3.20362	0.477567
$46$	0	0
$47$	−11.4135	−1.66483	−0.832416	−	0.554152i	$-0.813043\pi$
$47$	−11.4135	−1.66483	−0.832416	+	0.554152i	$0.813043\pi$
$48$	1.00000	0.144338
$49$	−4.70981	−0.672830
$50$	5.26315	0.744322
$51$	1.19647	0.167540
$52$	2.88612	0.400233
$53$	−12.0613	−1.65675	−0.828375	−	0.560175i	$-0.810734\pi$
$53$	−12.0613	−1.65675	−0.828375	+	0.560175i	$0.810734\pi$
$54$	1.00000	0.136083
$55$	20.9466	2.82444
$56$	−1.51334	−0.202228
$57$	−0.555554	−0.0735850
$58$	−8.66918	−1.13832
$59$	3.96140	0.515730	0.257865	−	0.966181i	$-0.416981\pi$
$59$	3.96140	0.515730	0.257865	+	0.966181i	$0.416981\pi$
$60$	3.20362	0.413585
$61$	−9.03450	−1.15675	−0.578375	−	0.815771i	$-0.696313\pi$
$61$	−9.03450	−1.15675	−0.578375	+	0.815771i	$0.696313\pi$
$62$	−6.73559	−0.855420
$63$	−1.51334	−0.190663
$64$	1.00000	0.125000
$65$	9.24603	1.14683
$66$	6.53843	0.804825
$67$	7.66794	0.936788	0.468394	−	0.883520i	$-0.344833\pi$
$67$	7.66794	0.936788	0.468394	+	0.883520i	$0.344833\pi$
$68$	1.19647	0.145094
$69$	0	0
$70$	−4.84815	−0.579465
$71$	−9.45607	−1.12223	−0.561114	−	0.827738i	$-0.689627\pi$
$71$	−9.45607	−1.12223	−0.561114	+	0.827738i	$0.689627\pi$
$72$	1.00000	0.117851
$73$	−0.627598	−0.0734548	−0.0367274	−	0.999325i	$-0.511693\pi$
$73$	−0.627598	−0.0734548	−0.0367274	+	0.999325i	$0.511693\pi$
$74$	1.45380	0.169001
$75$	5.26315	0.607737
$76$	−0.555554	−0.0637264
$77$	−9.89485	−1.12762
$78$	2.88612	0.326789
$79$	13.7721	1.54949	0.774743	−	0.632276i	$-0.217879\pi$
$79$	13.7721	1.54949	0.774743	+	0.632276i	$0.217879\pi$
$80$	3.20362	0.358175
$81$	1.00000	0.111111
$82$	−1.84796	−0.204073
$83$	15.5888	1.71110	0.855549	−	0.517722i	$-0.173220\pi$
$83$	15.5888	1.71110	0.855549	+	0.517722i	$0.173220\pi$
$84$	−1.51334	−0.165119
$85$	3.83304	0.415752
$86$	−2.17379	−0.234406
$87$	−8.66918	−0.929433
$88$	6.53843	0.696999
$89$	5.61844	0.595553	0.297777	−	0.954636i	$-0.403755\pi$
$89$	5.61844	0.595553	0.297777	+	0.954636i	$0.403755\pi$
$90$	3.20362	0.337691
$91$	−4.36768	−0.457857
$92$	0	0
$93$	−6.73559	−0.698448
$94$	−11.4135	−1.17721
$95$	−1.77978	−0.182602
$96$	1.00000	0.102062
$97$	7.24727	0.735848	0.367924	−	0.929856i	$-0.380069\pi$
$97$	7.24727	0.735848	0.367924	+	0.929856i	$0.380069\pi$
$98$	−4.70981	−0.475763
$99$	6.53843	0.657137
$100$	5.26315	0.526315
$101$	−1.02378	−0.101870	−0.0509348	−	0.998702i	$-0.516220\pi$
$101$	−1.02378	−0.101870	−0.0509348	+	0.998702i	$0.516220\pi$
$102$	1.19647	0.118469
$103$	−4.54925	−0.448251	−0.224125	−	0.974560i	$-0.571952\pi$
$103$	−4.54925	−0.448251	−0.224125	+	0.974560i	$0.571952\pi$
$104$	2.88612	0.283008
$105$	−4.84815	−0.473131
$106$	−12.0613	−1.17150
$107$	0.602987	0.0582929	0.0291465	−	0.999575i	$-0.490721\pi$
$107$	0.602987	0.0582929	0.0291465	+	0.999575i	$0.490721\pi$
$108$	1.00000	0.0962250
$109$	5.87577	0.562796	0.281398	−	0.959591i	$-0.409202\pi$
$109$	5.87577	0.562796	0.281398	+	0.959591i	$0.409202\pi$
$110$	20.9466	1.99718
$111$	1.45380	0.137989
$112$	−1.51334	−0.142997
$113$	−12.3076	−1.15781	−0.578903	−	0.815397i	$-0.696519\pi$
$113$	−12.3076	−1.15781	−0.578903	+	0.815397i	$0.696519\pi$
$114$	−0.555554	−0.0520324
$115$	0	0
$116$	−8.66918	−0.804913
$117$	2.88612	0.266822
$118$	3.96140	0.364676
$119$	−1.81067	−0.165984
$120$	3.20362	0.292449
$121$	31.7511	2.88646
$122$	−9.03450	−0.817945
$123$	−1.84796	−0.166625
$124$	−6.73559	−0.604874
$125$	0.843041	0.0754039
$126$	−1.51334	−0.134819
$127$	8.86983	0.787070	0.393535	−	0.919310i	$-0.371252\pi$
$127$	8.86983	0.787070	0.393535	+	0.919310i	$0.371252\pi$
$128$	1.00000	0.0883883
$129$	−2.17379	−0.191391
$130$	9.24603	0.810930
$131$	12.5385	1.09549	0.547745	−	0.836645i	$-0.315486\pi$
$131$	12.5385	1.09549	0.547745	+	0.836645i	$0.315486\pi$
$132$	6.53843	0.569097
$133$	0.840741	0.0729015
$134$	7.66794	0.662409
$135$	3.20362	0.275723
$136$	1.19647	0.102597
$137$	13.6483	1.16606	0.583028	−	0.812452i	$-0.301868\pi$
$137$	13.6483	1.16606	0.583028	+	0.812452i	$0.301868\pi$
$138$	0	0
$139$	−11.6537	−0.988455	−0.494227	−	0.869333i	$-0.664549\pi$
$139$	−11.6537	−0.988455	−0.494227	+	0.869333i	$0.664549\pi$
$140$	−4.84815	−0.409743
$141$	−11.4135	−0.961191
$142$	−9.45607	−0.793536
$143$	18.8707	1.57805
$144$	1.00000	0.0833333
$145$	−27.7727	−2.30640
$146$	−0.627598	−0.0519404
$147$	−4.70981	−0.388459
$148$	1.45380	0.119502
$149$	−17.3034	−1.41755	−0.708776	−	0.705434i	$-0.750752\pi$
$149$	−17.3034	−1.41755	−0.708776	+	0.705434i	$0.750752\pi$
$150$	5.26315	0.429735
$151$	−4.83249	−0.393262	−0.196631	−	0.980478i	$-0.563000\pi$
$151$	−4.83249	−0.393262	−0.196631	+	0.980478i	$0.563000\pi$
$152$	−0.555554	−0.0450614
$153$	1.19647	0.0967292
$154$	−9.89485	−0.797349
$155$	−21.5782	−1.73321
$156$	2.88612	0.231075
$157$	5.05031	0.403059	0.201529	−	0.979482i	$-0.435409\pi$
$157$	5.05031	0.403059	0.201529	+	0.979482i	$0.435409\pi$
$158$	13.7721	1.09565
$159$	−12.0613	−0.956524
$160$	3.20362	0.253268
$161$	0	0
$162$	1.00000	0.0785674
$163$	3.56743	0.279423	0.139711	−	0.990192i	$-0.455383\pi$
$163$	3.56743	0.279423	0.139711	+	0.990192i	$0.455383\pi$
$164$	−1.84796	−0.144301
$165$	20.9466	1.63069
$166$	15.5888	1.20993
$167$	4.56038	0.352893	0.176446	−	0.984310i	$-0.443540\pi$
$167$	4.56038	0.352893	0.176446	+	0.984310i	$0.443540\pi$
$168$	−1.51334	−0.116756
$169$	−4.67030	−0.359254
$170$	3.83304	0.293981
$171$	−0.555554	−0.0424843
$172$	−2.17379	−0.165750
$173$	−15.6132	−1.18705	−0.593525	−	0.804816i	$-0.702264\pi$
$173$	−15.6132	−1.18705	−0.593525	+	0.804816i	$0.702264\pi$
$174$	−8.66918	−0.657209
$175$	−7.96492	−0.602092
$176$	6.53843	0.492853
$177$	3.96140	0.297757
$178$	5.61844	0.421120
$179$	6.40521	0.478748	0.239374	−	0.970927i	$-0.423058\pi$
$179$	6.40521	0.478748	0.239374	+	0.970927i	$0.423058\pi$
$180$	3.20362	0.238783
$181$	22.1363	1.64538	0.822691	−	0.568489i	$-0.192472\pi$
$181$	22.1363	1.64538	0.822691	+	0.568489i	$0.192472\pi$
$182$	−4.36768	−0.323754
$183$	−9.03450	−0.667850
$184$	0	0
$185$	4.65742	0.342420
$186$	−6.73559	−0.493877
$187$	7.82306	0.572079
$188$	−11.4135	−0.832416
$189$	−1.51334	−0.110079
$190$	−1.77978	−0.129119
$191$	2.14915	0.155507	0.0777534	−	0.996973i	$-0.475225\pi$
$191$	2.14915	0.155507	0.0777534	+	0.996973i	$0.475225\pi$
$192$	1.00000	0.0721688
$193$	−11.2460	−0.809506	−0.404753	−	0.914426i	$-0.632643\pi$
$193$	−11.2460	−0.809506	−0.404753	+	0.914426i	$0.632643\pi$
$194$	7.24727	0.520323
$195$	9.24603	0.662122
$196$	−4.70981	−0.336415
$197$	10.4125	0.741860	0.370930	−	0.928661i	$-0.379039\pi$
$197$	10.4125	0.741860	0.370930	+	0.928661i	$0.379039\pi$
$198$	6.53843	0.464666
$199$	−15.0998	−1.07039	−0.535197	−	0.844727i	$-0.679763\pi$
$199$	−15.0998	−1.07039	−0.535197	+	0.844727i	$0.679763\pi$
$200$	5.26315	0.372161
$201$	7.66794	0.540855
$202$	−1.02378	−0.0720327
$203$	13.1194	0.920800
$204$	1.19647	0.0837699
$205$	−5.92014	−0.413480
$206$	−4.54925	−0.316961
$207$	0	0
$208$	2.88612	0.200117
$209$	−3.63245	−0.251262
$210$	−4.84815	−0.334554
$211$	11.4828	0.790512	0.395256	−	0.918571i	$-0.370656\pi$
$211$	11.4828	0.790512	0.395256	+	0.918571i	$0.370656\pi$
$212$	−12.0613	−0.828375
$213$	−9.45607	−0.647919
$214$	0.602987	0.0412193
$215$	−6.96398	−0.474940
$216$	1.00000	0.0680414
$217$	10.1932	0.691961
$218$	5.87577	0.397957
$219$	−0.627598	−0.0424091
$220$	20.9466	1.41222
$221$	3.45317	0.232285
$222$	1.45380	0.0975726
$223$	−15.8063	−1.05847	−0.529235	−	0.848475i	$-0.677521\pi$
$223$	−15.8063	−1.05847	−0.529235	+	0.848475i	$0.677521\pi$
$224$	−1.51334	−0.101114
$225$	5.26315	0.350877
$226$	−12.3076	−0.818692
$227$	2.59469	0.172216	0.0861079	−	0.996286i	$-0.472557\pi$
$227$	2.59469	0.172216	0.0861079	+	0.996286i	$0.472557\pi$
$228$	−0.555554	−0.0367925
$229$	−9.99374	−0.660405	−0.330202	−	0.943910i	$-0.607117\pi$
$229$	−9.99374	−0.660405	−0.330202	+	0.943910i	$0.607117\pi$
$230$	0	0
$231$	−9.89485	−0.651033
$232$	−8.66918	−0.569159
$233$	−27.2948	−1.78814	−0.894070	−	0.447927i	$-0.852162\pi$
$233$	−27.2948	−1.78814	−0.894070	+	0.447927i	$0.852162\pi$
$234$	2.88612	0.188672
$235$	−36.5645	−2.38520
$236$	3.96140	0.257865
$237$	13.7721	0.894597
$238$	−1.81067	−0.117368
$239$	14.3187	0.926198	0.463099	−	0.886306i	$-0.346737\pi$
$239$	14.3187	0.926198	0.463099	+	0.886306i	$0.346737\pi$
$240$	3.20362	0.206792
$241$	−14.1957	−0.914428	−0.457214	−	0.889357i	$-0.651153\pi$
$241$	−14.1957	−0.914428	−0.457214	+	0.889357i	$0.651153\pi$
$242$	31.7511	2.04103
$243$	1.00000	0.0641500
$244$	−9.03450	−0.578375
$245$	−15.0884	−0.963964
$246$	−1.84796	−0.117821
$247$	−1.60340	−0.102022
$248$	−6.73559	−0.427710
$249$	15.5888	0.987903
$250$	0.843041	0.0533186
$251$	−11.9645	−0.755194	−0.377597	−	0.925970i	$-0.623250\pi$
$251$	−11.9645	−0.755194	−0.377597	+	0.925970i	$0.623250\pi$
$252$	−1.51334	−0.0953313
$253$	0	0
$254$	8.86983	0.556543
$255$	3.83304	0.240034
$256$	1.00000	0.0625000
$257$	25.9967	1.62163	0.810815	−	0.585302i	$-0.199024\pi$
$257$	25.9967	1.62163	0.810815	+	0.585302i	$0.199024\pi$
$258$	−2.17379	−0.135334
$259$	−2.20009	−0.136707
$260$	9.24603	0.573414
$261$	−8.66918	−0.536609
$262$	12.5385	0.774629
$263$	−5.74265	−0.354107	−0.177054	−	0.984201i	$-0.556657\pi$
$263$	−5.74265	−0.354107	−0.177054	+	0.984201i	$0.556657\pi$
$264$	6.53843	0.402412
$265$	−38.6398	−2.37363
$266$	0.840741	0.0515491
$267$	5.61844	0.343843
$268$	7.66794	0.468394
$269$	8.17926	0.498699	0.249349	−	0.968414i	$-0.419783\pi$
$269$	8.17926	0.498699	0.249349	+	0.968414i	$0.419783\pi$
$270$	3.20362	0.194966
$271$	−13.5053	−0.820386	−0.410193	−	0.911999i	$-0.634539\pi$
$271$	−13.5053	−0.820386	−0.410193	+	0.911999i	$0.634539\pi$
$272$	1.19647	0.0725469
$273$	−4.36768	−0.264344
$274$	13.6483	0.824526
$275$	34.4128	2.07517
$276$	0	0
$277$	14.9697	0.899440	0.449720	−	0.893169i	$-0.351524\pi$
$277$	14.9697	0.899440	0.449720	+	0.893169i	$0.351524\pi$
$278$	−11.6537	−0.698943
$279$	−6.73559	−0.403249
$280$	−4.84815	−0.289732
$281$	−26.9740	−1.60913	−0.804566	−	0.593863i	$-0.797602\pi$
$281$	−26.9740	−1.60913	−0.804566	+	0.593863i	$0.797602\pi$
$282$	−11.4135	−0.679665
$283$	−13.7193	−0.815528	−0.407764	−	0.913087i	$-0.633691\pi$
$283$	−13.7193	−0.815528	−0.407764	+	0.913087i	$0.633691\pi$
$284$	−9.45607	−0.561114
$285$	−1.77978	−0.105425
$286$	18.8707	1.11585
$287$	2.79658	0.165077
$288$	1.00000	0.0589256
$289$	−15.5685	−0.915791
$290$	−27.7727	−1.63087
$291$	7.24727	0.424842
$292$	−0.627598	−0.0367274
$293$	−9.20499	−0.537761	−0.268881	−	0.963174i	$-0.586654\pi$
$293$	−9.20499	−0.537761	−0.268881	+	0.963174i	$0.586654\pi$
$294$	−4.70981	−0.274682
$295$	12.6908	0.738887
$296$	1.45380	0.0845004
$297$	6.53843	0.379398
$298$	−17.3034	−1.00236
$299$	0	0
$300$	5.26315	0.303868
$301$	3.28968	0.189614
$302$	−4.83249	−0.278078
$303$	−1.02378	−0.0588145
$304$	−0.555554	−0.0318632
$305$	−28.9431	−1.65728
$306$	1.19647	0.0683979
$307$	1.75676	0.100264	0.0501319	−	0.998743i	$-0.484036\pi$
$307$	1.75676	0.100264	0.0501319	+	0.998743i	$0.484036\pi$
$308$	−9.89485	−0.563811
$309$	−4.54925	−0.258798
$310$	−21.5782	−1.22556
$311$	30.3629	1.72172	0.860860	−	0.508841i	$-0.169926\pi$
$311$	30.3629	1.72172	0.860860	+	0.508841i	$0.169926\pi$
$312$	2.88612	0.163395
$313$	−11.0192	−0.622843	−0.311421	−	0.950272i	$-0.600805\pi$
$313$	−11.0192	−0.622843	−0.311421	+	0.950272i	$0.600805\pi$
$314$	5.05031	0.285006
$315$	−4.84815	−0.273162
$316$	13.7721	0.774743
$317$	−10.1471	−0.569920	−0.284960	−	0.958539i	$-0.591980\pi$
$317$	−10.1471	−0.569920	−0.284960	+	0.958539i	$0.591980\pi$
$318$	−12.0613	−0.676365
$319$	−56.6828	−3.17363
$320$	3.20362	0.179088
$321$	0.602987	0.0336554
$322$	0	0
$323$	−0.664706	−0.0369852
$324$	1.00000	0.0555556
$325$	15.1901	0.842595
$326$	3.56743	0.197582
$327$	5.87577	0.324931
$328$	−1.84796	−0.102036
$329$	17.2725	0.952263
$330$	20.9466	1.15307
$331$	29.7790	1.63680	0.818401	−	0.574648i	$-0.194861\pi$
$331$	29.7790	1.63680	0.818401	+	0.574648i	$0.194861\pi$
$332$	15.5888	0.855549
$333$	1.45380	0.0796677
$334$	4.56038	0.249533
$335$	24.5651	1.34214
$336$	−1.51334	−0.0825593
$337$	19.0588	1.03820	0.519100	−	0.854714i	$-0.326267\pi$
$337$	19.0588	1.03820	0.519100	+	0.854714i	$0.326267\pi$
$338$	−4.67030	−0.254031
$339$	−12.3076	−0.668459
$340$	3.83304	0.207876
$341$	−44.0402	−2.38491
$342$	−0.555554	−0.0300409
$343$	17.7209	0.956838
$344$	−2.17379	−0.117203
$345$	0	0
$346$	−15.6132	−0.839371
$347$	−12.1929	−0.654550	−0.327275	−	0.944929i	$-0.606130\pi$
$347$	−12.1929	−0.654550	−0.327275	+	0.944929i	$0.606130\pi$
$348$	−8.66918	−0.464717
$349$	−15.4022	−0.824459	−0.412229	−	0.911080i	$-0.635250\pi$
$349$	−15.4022	−0.824459	−0.412229	+	0.911080i	$0.635250\pi$
$350$	−7.96492	−0.425743
$351$	2.88612	0.154050
$352$	6.53843	0.348499
$353$	18.5308	0.986295	0.493147	−	0.869946i	$-0.335846\pi$
$353$	18.5308	0.986295	0.493147	+	0.869946i	$0.335846\pi$
$354$	3.96140	0.210546
$355$	−30.2936	−1.60782
$356$	5.61844	0.297777
$357$	−1.81067	−0.0958307
$358$	6.40521	0.338526
$359$	11.7601	0.620673	0.310337	−	0.950627i	$-0.399558\pi$
$359$	11.7601	0.620673	0.310337	+	0.950627i	$0.399558\pi$
$360$	3.20362	0.168845
$361$	−18.6914	−0.983756
$362$	22.1363	1.16346
$363$	31.7511	1.66650
$364$	−4.36768	−0.228928
$365$	−2.01058	−0.105239
$366$	−9.03450	−0.472241
$367$	7.81907	0.408152	0.204076	−	0.978955i	$-0.434581\pi$
$367$	7.81907	0.408152	0.204076	+	0.978955i	$0.434581\pi$
$368$	0	0
$369$	−1.84796	−0.0962007
$370$	4.65742	0.242127
$371$	18.2528	0.947640
$372$	−6.73559	−0.349224
$373$	−2.13817	−0.110710	−0.0553550	−	0.998467i	$-0.517629\pi$
$373$	−2.13817	−0.110710	−0.0553550	+	0.998467i	$0.517629\pi$
$374$	7.82306	0.404521
$375$	0.843041	0.0435345
$376$	−11.4135	−0.588607
$377$	−25.0203	−1.28861
$378$	−1.51334	−0.0778377
$379$	21.6725	1.11324	0.556621	−	0.830767i	$-0.312098\pi$
$379$	21.6725	1.11324	0.556621	+	0.830767i	$0.312098\pi$
$380$	−1.77978	−0.0913009
$381$	8.86983	0.454415
$382$	2.14915	0.109960
$383$	−5.00975	−0.255986	−0.127993	−	0.991775i	$-0.540854\pi$
$383$	−5.00975	−0.255986	−0.127993	+	0.991775i	$0.540854\pi$
$384$	1.00000	0.0510310
$385$	−31.6993	−1.61555
$386$	−11.2460	−0.572407
$387$	−2.17379	−0.110500
$388$	7.24727	0.367924
$389$	6.02177	0.305316	0.152658	−	0.988279i	$-0.451217\pi$
$389$	6.02177	0.305316	0.152658	+	0.988279i	$0.451217\pi$
$390$	9.24603	0.468191
$391$	0	0
$392$	−4.70981	−0.237881
$393$	12.5385	0.632482
$394$	10.4125	0.524574
$395$	44.1206	2.21995
$396$	6.53843	0.328568
$397$	24.0018	1.20461	0.602307	−	0.798265i	$-0.294248\pi$
$397$	24.0018	1.20461	0.602307	+	0.798265i	$0.294248\pi$
$398$	−15.0998	−0.756883
$399$	0.840741	0.0420897
$400$	5.26315	0.263158
$401$	14.4766	0.722926	0.361463	−	0.932387i	$-0.382277\pi$
$401$	14.4766	0.722926	0.361463	+	0.932387i	$0.382277\pi$
$402$	7.66794	0.382442
$403$	−19.4397	−0.968362
$404$	−1.02378	−0.0509348
$405$	3.20362	0.159189
$406$	13.1194	0.651104
$407$	9.50557	0.471173
$408$	1.19647	0.0592343
$409$	−32.6435	−1.61412	−0.807059	−	0.590471i	$-0.798942\pi$
$409$	−32.6435	−1.61412	−0.807059	+	0.590471i	$0.798942\pi$
$410$	−5.92014	−0.292375
$411$	13.6483	0.673222
$412$	−4.54925	−0.224125
$413$	−5.99493	−0.294991
$414$	0	0
$415$	49.9407	2.45149
$416$	2.88612	0.141504
$417$	−11.6537	−0.570685
$418$	−3.63245	−0.177669
$419$	36.2427	1.77057	0.885286	−	0.465046i	$-0.153962\pi$
$419$	36.2427	1.77057	0.885286	+	0.465046i	$0.153962\pi$
$420$	−4.84815	−0.236566
$421$	−6.98570	−0.340462	−0.170231	−	0.985404i	$-0.554451\pi$
$421$	−6.98570	−0.340462	−0.170231	+	0.985404i	$0.554451\pi$
$422$	11.4828	0.558976
$423$	−11.4135	−0.554944
$424$	−12.0613	−0.585749
$425$	6.29722	0.305460
$426$	−9.45607	−0.458148
$427$	13.6722	0.661646
$428$	0.602987	0.0291465
$429$	18.8707	0.911086
$430$	−6.96398	−0.335833
$431$	33.3054	1.60426	0.802132	−	0.597146i	$-0.203699\pi$
$431$	33.3054	1.60426	0.802132	+	0.597146i	$0.203699\pi$
$432$	1.00000	0.0481125
$433$	21.5646	1.03633	0.518165	−	0.855281i	$-0.326615\pi$
$433$	21.5646	1.03633	0.518165	+	0.855281i	$0.326615\pi$
$434$	10.1932	0.489290
$435$	−27.7727	−1.33160
$436$	5.87577	0.281398
$437$	0	0
$438$	−0.627598	−0.0299878
$439$	17.2393	0.822785	0.411393	−	0.911458i	$-0.365043\pi$
$439$	17.2393	0.822785	0.411393	+	0.911458i	$0.365043\pi$
$440$	20.9466	0.998591
$441$	−4.70981	−0.224277
$442$	3.45317	0.164251
$443$	18.9166	0.898754	0.449377	−	0.893342i	$-0.351646\pi$
$443$	18.9166	0.898754	0.449377	+	0.893342i	$0.351646\pi$
$444$	1.45380	0.0689943
$445$	17.9993	0.853250
$446$	−15.8063	−0.748452
$447$	−17.3034	−0.818424
$448$	−1.51334	−0.0714985
$449$	23.0511	1.08785	0.543924	−	0.839134i	$-0.316938\pi$
$449$	23.0511	1.08785	0.543924	+	0.839134i	$0.316938\pi$
$450$	5.26315	0.248107
$451$	−12.0827	−0.568953
$452$	−12.3076	−0.578903
$453$	−4.83249	−0.227050
$454$	2.59469	0.121775
$455$	−13.9924	−0.655972
$456$	−0.555554	−0.0260162
$457$	−15.1904	−0.710578	−0.355289	−	0.934757i	$-0.615617\pi$
$457$	−15.1904	−0.710578	−0.355289	+	0.934757i	$0.615617\pi$
$458$	−9.99374	−0.466977
$459$	1.19647	0.0558466
$460$	0	0
$461$	19.2440	0.896281	0.448141	−	0.893963i	$-0.352086\pi$
$461$	19.2440	0.896281	0.448141	+	0.893963i	$0.352086\pi$
$462$	−9.89485	−0.460350
$463$	−3.03240	−0.140927	−0.0704637	−	0.997514i	$-0.522448\pi$
$463$	−3.03240	−0.140927	−0.0704637	+	0.997514i	$0.522448\pi$
$464$	−8.66918	−0.402456
$465$	−21.5782	−1.00067
$466$	−27.2948	−1.26441
$467$	−2.85012	−0.131888	−0.0659439	−	0.997823i	$-0.521006\pi$
$467$	−2.85012	−0.131888	−0.0659439	+	0.997823i	$0.521006\pi$
$468$	2.88612	0.133411
$469$	−11.6042	−0.535831
$470$	−36.5645	−1.68659
$471$	5.05031	0.232706
$472$	3.96140	0.182338
$473$	−14.2132	−0.653522
$474$	13.7721	0.632575
$475$	−2.92397	−0.134161
$476$	−1.81067	−0.0829918
$477$	−12.0613	−0.552250
$478$	14.3187	0.654921
$479$	−37.2607	−1.70249	−0.851243	−	0.524772i	$-0.824151\pi$
$479$	−37.2607	−1.70249	−0.851243	+	0.524772i	$0.824151\pi$
$480$	3.20362	0.146224
$481$	4.19584	0.191314
$482$	−14.1957	−0.646598
$483$	0	0
$484$	31.7511	1.44323
$485$	23.2175	1.05425
$486$	1.00000	0.0453609
$487$	−30.7455	−1.39321	−0.696606	−	0.717454i	$-0.745307\pi$
$487$	−30.7455	−1.39321	−0.696606	+	0.717454i	$0.745307\pi$
$488$	−9.03450	−0.408973
$489$	3.56743	0.161325
$490$	−15.0884	−0.681625
$491$	7.81494	0.352683	0.176342	−	0.984329i	$-0.443574\pi$
$491$	7.81494	0.352683	0.176342	+	0.984329i	$0.443574\pi$
$492$	−1.84796	−0.0833123
$493$	−10.3724	−0.467151
$494$	−1.60340	−0.0721403
$495$	20.9466	0.941480
$496$	−6.73559	−0.302437
$497$	14.3102	0.641901
$498$	15.5888	0.698553
$499$	12.9597	0.580154	0.290077	−	0.957003i	$-0.406319\pi$
$499$	12.9597	0.580154	0.290077	+	0.957003i	$0.406319\pi$
$500$	0.843041	0.0377020
$501$	4.56038	0.203743
$502$	−11.9645	−0.534003
$503$	−19.6304	−0.875276	−0.437638	−	0.899151i	$-0.644185\pi$
$503$	−19.6304	−0.875276	−0.437638	+	0.899151i	$0.644185\pi$
$504$	−1.51334	−0.0674094
$505$	−3.27979	−0.145949
$506$	0	0
$507$	−4.67030	−0.207415
$508$	8.86983	0.393535
$509$	6.25244	0.277134	0.138567	−	0.990353i	$-0.455750\pi$
$509$	6.25244	0.277134	0.138567	+	0.990353i	$0.455750\pi$
$510$	3.83304	0.169730
$511$	0.949767	0.0420152
$512$	1.00000	0.0441942
$513$	−0.555554	−0.0245283
$514$	25.9967	1.14667
$515$	−14.5740	−0.642209
$516$	−2.17379	−0.0956957
$517$	−74.6264	−3.28207
$518$	−2.20009	−0.0966664
$519$	−15.6132	−0.685344
$520$	9.24603	0.405465
$521$	−23.9904	−1.05104	−0.525518	−	0.850782i	$-0.676129\pi$
$521$	−23.9904	−1.05104	−0.525518	+	0.850782i	$0.676129\pi$
$522$	−8.66918	−0.379440
$523$	7.42756	0.324784	0.162392	−	0.986726i	$-0.448079\pi$
$523$	7.42756	0.324784	0.162392	+	0.986726i	$0.448079\pi$
$524$	12.5385	0.547745
$525$	−7.96492	−0.347618
$526$	−5.74265	−0.250392
$527$	−8.05895	−0.351054
$528$	6.53843	0.284549
$529$	0	0
$530$	−38.6398	−1.67841
$531$	3.96140	0.171910
$532$	0.840741	0.0364507
$533$	−5.33343	−0.231016
$534$	5.61844	0.243134
$535$	1.93174	0.0835163
$536$	7.66794	0.331204
$537$	6.40521	0.276405
$538$	8.17926	0.352633
$539$	−30.7948	−1.32642
$540$	3.20362	0.137862
$541$	20.4393	0.878752	0.439376	−	0.898303i	$-0.355200\pi$
$541$	20.4393	0.878752	0.439376	+	0.898303i	$0.355200\pi$
$542$	−13.5053	−0.580101
$543$	22.1363	0.949961
$544$	1.19647	0.0512984
$545$	18.8237	0.806318
$546$	−4.36768	−0.186919
$547$	−9.31027	−0.398078	−0.199039	−	0.979992i	$-0.563782\pi$
$547$	−9.31027	−0.398078	−0.199039	+	0.979992i	$0.563782\pi$
$548$	13.6483	0.583028
$549$	−9.03450	−0.385583
$550$	34.4128	1.46736
$551$	4.81620	0.205177
$552$	0	0
$553$	−20.8419	−0.886287
$554$	14.9697	0.636000
$555$	4.65742	0.197696
$556$	−11.6537	−0.494227
$557$	31.9209	1.35253	0.676265	−	0.736658i	$-0.263597\pi$
$557$	31.9209	1.35253	0.676265	+	0.736658i	$0.263597\pi$
$558$	−6.73559	−0.285140
$559$	−6.27382	−0.265354
$560$	−4.84815	−0.204872
$561$	7.82306	0.330290
$562$	−26.9740	−1.13783
$563$	16.8512	0.710195	0.355097	−	0.934829i	$-0.384448\pi$
$563$	16.8512	0.710195	0.355097	+	0.934829i	$0.384448\pi$
$564$	−11.4135	−0.480595
$565$	−39.4289	−1.65879
$566$	−13.7193	−0.576665
$567$	−1.51334	−0.0635542
$568$	−9.45607	−0.396768
$569$	2.18185	0.0914680	0.0457340	−	0.998954i	$-0.485437\pi$
$569$	2.18185	0.0914680	0.0457340	+	0.998954i	$0.485437\pi$
$570$	−1.77978	−0.0745469
$571$	8.97740	0.375693	0.187846	−	0.982198i	$-0.439849\pi$
$571$	8.97740	0.375693	0.187846	+	0.982198i	$0.439849\pi$
$572$	18.8707	0.789024
$573$	2.14915	0.0897819
$574$	2.79658	0.116727
$575$	0	0
$576$	1.00000	0.0416667
$577$	−41.1842	−1.71452	−0.857261	−	0.514882i	$-0.827836\pi$
$577$	−41.1842	−1.71452	−0.857261	+	0.514882i	$0.827836\pi$
$578$	−15.5685	−0.647562
$579$	−11.2460	−0.467369
$580$	−27.7727	−1.15320
$581$	−23.5912	−0.978727
$582$	7.24727	0.300409
$583$	−78.8620	−3.26613
$584$	−0.627598	−0.0259702
$585$	9.24603	0.382276
$586$	−9.20499	−0.380254
$587$	9.61116	0.396695	0.198348	−	0.980132i	$-0.436443\pi$
$587$	9.61116	0.396695	0.198348	+	0.980132i	$0.436443\pi$
$588$	−4.70981	−0.194229
$589$	3.74198	0.154186
$590$	12.6908	0.522472
$591$	10.4125	0.428313
$592$	1.45380	0.0597508
$593$	−36.4575	−1.49713	−0.748564	−	0.663062i	$-0.769256\pi$
$593$	−36.4575	−1.49713	−0.748564	+	0.663062i	$0.769256\pi$
$594$	6.53843	0.268275
$595$	−5.80068	−0.237805
$596$	−17.3034	−0.708776
$597$	−15.0998	−0.617993
$598$	0	0
$599$	−6.93439	−0.283331	−0.141666	−	0.989915i	$-0.545246\pi$
$599$	−6.93439	−0.283331	−0.141666	+	0.989915i	$0.545246\pi$
$600$	5.26315	0.214867
$601$	16.7707	0.684089	0.342045	−	0.939684i	$-0.388881\pi$
$601$	16.7707	0.684089	0.342045	+	0.939684i	$0.388881\pi$
$602$	3.28968	0.134077
$603$	7.66794	0.312263
$604$	−4.83249	−0.196631
$605$	101.718	4.13543
$606$	−1.02378	−0.0415881
$607$	−10.8715	−0.441259	−0.220629	−	0.975358i	$-0.570811\pi$
$607$	−10.8715	−0.441259	−0.220629	+	0.975358i	$0.570811\pi$
$608$	−0.555554	−0.0225307
$609$	13.1194	0.531624
$610$	−28.9431	−1.17187
$611$	−32.9408	−1.33264
$612$	1.19647	0.0483646
$613$	−20.7458	−0.837914	−0.418957	−	0.908006i	$-0.637604\pi$
$613$	−20.7458	−0.837914	−0.418957	+	0.908006i	$0.637604\pi$
$614$	1.75676	0.0708972
$615$	−5.92014	−0.238723
$616$	−9.89485	−0.398675
$617$	−3.09354	−0.124541	−0.0622706	−	0.998059i	$-0.519834\pi$
$617$	−3.09354	−0.124541	−0.0622706	+	0.998059i	$0.519834\pi$
$618$	−4.54925	−0.182998
$619$	13.0130	0.523038	0.261519	−	0.965198i	$-0.415777\pi$
$619$	13.0130	0.523038	0.261519	+	0.965198i	$0.415777\pi$
$620$	−21.5782	−0.866603
$621$	0	0
$622$	30.3629	1.21744
$623$	−8.50259	−0.340649
$624$	2.88612	0.115537
$625$	−23.6150	−0.944599
$626$	−11.0192	−0.440416
$627$	−3.63245	−0.145066
$628$	5.05031	0.201529
$629$	1.73943	0.0693557
$630$	−4.84815	−0.193155
$631$	−9.82295	−0.391045	−0.195523	−	0.980699i	$-0.562640\pi$
$631$	−9.82295	−0.391045	−0.195523	+	0.980699i	$0.562640\pi$
$632$	13.7721	0.547826
$633$	11.4828	0.456402
$634$	−10.1471	−0.402994
$635$	28.4155	1.12764
$636$	−12.0613	−0.478262
$637$	−13.5931	−0.538578
$638$	−56.6828	−2.24409
$639$	−9.45607	−0.374076
$640$	3.20362	0.126634
$641$	−13.6360	−0.538590	−0.269295	−	0.963058i	$-0.586791\pi$
$641$	−13.6360	−0.538590	−0.269295	+	0.963058i	$0.586791\pi$
$642$	0.602987	0.0237980
$643$	−3.57857	−0.141125	−0.0705626	−	0.997507i	$-0.522479\pi$
$643$	−3.57857	−0.141125	−0.0705626	+	0.997507i	$0.522479\pi$
$644$	0	0
$645$	−6.96398	−0.274207
$646$	−0.664706	−0.0261525
$647$	−26.2492	−1.03196	−0.515982	−	0.856599i	$-0.672573\pi$
$647$	−26.2492	−1.03196	−0.515982	+	0.856599i	$0.672573\pi$
$648$	1.00000	0.0392837
$649$	25.9013	1.01672
$650$	15.1901	0.595805
$651$	10.1932	0.399504
$652$	3.56743	0.139711
$653$	25.7390	1.00725	0.503623	−	0.863923i	$-0.332000\pi$
$653$	25.7390	1.00725	0.503623	+	0.863923i	$0.332000\pi$
$654$	5.87577	0.229761
$655$	40.1684	1.56951
$656$	−1.84796	−0.0721505
$657$	−0.627598	−0.0244849
$658$	17.2725	0.673352
$659$	10.1996	0.397318	0.198659	−	0.980069i	$-0.436341\pi$
$659$	10.1996	0.397318	0.198659	+	0.980069i	$0.436341\pi$
$660$	20.9466	0.815346
$661$	29.9545	1.16509	0.582547	−	0.812797i	$-0.302056\pi$
$661$	29.9545	1.16509	0.582547	+	0.812797i	$0.302056\pi$
$662$	29.7790	1.15739
$663$	3.45317	0.134110
$664$	15.5888	0.604965
$665$	2.69341	0.104446
$666$	1.45380	0.0563336
$667$	0	0
$668$	4.56038	0.176446
$669$	−15.8063	−0.611108
$670$	24.5651	0.949034
$671$	−59.0714	−2.28043
$672$	−1.51334	−0.0583782
$673$	−2.02716	−0.0781413	−0.0390707	−	0.999236i	$-0.512440\pi$
$673$	−2.02716	−0.0781413	−0.0390707	+	0.999236i	$0.512440\pi$
$674$	19.0588	0.734118
$675$	5.26315	0.202579
$676$	−4.67030	−0.179627
$677$	−2.46315	−0.0946664	−0.0473332	−	0.998879i	$-0.515072\pi$
$677$	−2.46315	−0.0946664	−0.0473332	+	0.998879i	$0.515072\pi$
$678$	−12.3076	−0.472672
$679$	−10.9676	−0.420896
$680$	3.83304	0.146990
$681$	2.59469	0.0994288
$682$	−44.0402	−1.68638
$683$	−30.3002	−1.15941	−0.579703	−	0.814828i	$-0.696831\pi$
$683$	−30.3002	−1.15941	−0.579703	+	0.814828i	$0.696831\pi$
$684$	−0.555554	−0.0212421
$685$	43.7240	1.67061
$686$	17.7209	0.676587
$687$	−9.99374	−0.381285
$688$	−2.17379	−0.0828749
$689$	−34.8104	−1.32617
$690$	0	0
$691$	−1.71993	−0.0654294	−0.0327147	−	0.999465i	$-0.510415\pi$
$691$	−1.71993	−0.0654294	−0.0327147	+	0.999465i	$0.510415\pi$
$692$	−15.6132	−0.593525
$693$	−9.89485	−0.375874
$694$	−12.1929	−0.462837
$695$	−37.3340	−1.41616
$696$	−8.66918	−0.328604
$697$	−2.21103	−0.0837487
$698$	−15.4022	−0.582980
$699$	−27.2948	−1.03238
$700$	−7.96492	−0.301046
$701$	0.739062	0.0279140	0.0139570	−	0.999903i	$-0.495557\pi$
$701$	0.739062	0.0279140	0.0139570	+	0.999903i	$0.495557\pi$
$702$	2.88612	0.108930
$703$	−0.807665	−0.0304616
$704$	6.53843	0.246426
$705$	−36.5645	−1.37710
$706$	18.5308	0.697416
$707$	1.54932	0.0582682
$708$	3.96140	0.148878
$709$	−22.5819	−0.848081	−0.424040	−	0.905643i	$-0.639389\pi$
$709$	−22.5819	−0.848081	−0.424040	+	0.905643i	$0.639389\pi$
$710$	−30.2936	−1.13690
$711$	13.7721	0.516496
$712$	5.61844	0.210560
$713$	0	0
$714$	−1.81067	−0.0677626
$715$	60.4545	2.26087
$716$	6.40521	0.239374
$717$	14.3187	0.534741
$718$	11.7601	0.438882
$719$	10.9509	0.408400	0.204200	−	0.978929i	$-0.434541\pi$
$719$	10.9509	0.408400	0.204200	+	0.978929i	$0.434541\pi$
$720$	3.20362	0.119392
$721$	6.88454	0.256394
$722$	−18.6914	−0.695620
$723$	−14.1957	−0.527945
$724$	22.1363	0.822691
$725$	−45.6272	−1.69455
$726$	31.7511	1.17839
$727$	−37.2793	−1.38261	−0.691307	−	0.722562i	$-0.742965\pi$
$727$	−37.2793	−1.38261	−0.691307	+	0.722562i	$0.742965\pi$
$728$	−4.36768	−0.161877
$729$	1.00000	0.0370370
$730$	−2.01058	−0.0744150
$731$	−2.60088	−0.0961971
$732$	−9.03450	−0.333925
$733$	−32.1008	−1.18567	−0.592835	−	0.805324i	$-0.701991\pi$
$733$	−32.1008	−1.18567	−0.592835	+	0.805324i	$0.701991\pi$
$734$	7.81907	0.288607
$735$	−15.0884	−0.556545
$736$	0	0
$737$	50.1363	1.84679
$738$	−1.84796	−0.0680242
$739$	37.5076	1.37974	0.689870	−	0.723934i	$-0.257668\pi$
$739$	37.5076	1.37974	0.689870	+	0.723934i	$0.257668\pi$
$740$	4.65742	0.171210
$741$	−1.60340	−0.0589023
$742$	18.2528	0.670083
$743$	−31.8791	−1.16953	−0.584766	−	0.811202i	$-0.698814\pi$
$743$	−31.8791	−1.16953	−0.584766	+	0.811202i	$0.698814\pi$
$744$	−6.73559	−0.246939
$745$	−55.4335	−2.03093
$746$	−2.13817	−0.0782838
$747$	15.5888	0.570366
$748$	7.82306	0.286039
$749$	−0.912522	−0.0333428
$750$	0.843041	0.0307835
$751$	17.9494	0.654983	0.327491	−	0.944854i	$-0.393797\pi$
$751$	17.9494	0.654983	0.327491	+	0.944854i	$0.393797\pi$
$752$	−11.4135	−0.416208
$753$	−11.9645	−0.436012
$754$	−25.0203	−0.911186
$755$	−15.4814	−0.563427
$756$	−1.51334	−0.0550395
$757$	10.9617	0.398410	0.199205	−	0.979958i	$-0.436164\pi$
$757$	10.9617	0.398410	0.199205	+	0.979958i	$0.436164\pi$
$758$	21.6725	0.787180
$759$	0	0
$760$	−1.77978	−0.0645595
$761$	−0.365855	−0.0132622	−0.00663111	−	0.999978i	$-0.502111\pi$
$761$	−0.365855	−0.0132622	−0.00663111	+	0.999978i	$0.502111\pi$
$762$	8.86983	0.321320
$763$	−8.89201	−0.321912
$764$	2.14915	0.0777534
$765$	3.83304	0.138584
$766$	−5.00975	−0.181010
$767$	11.4331	0.412825
$768$	1.00000	0.0360844
$769$	−0.305975	−0.0110337	−0.00551686	−	0.999985i	$-0.501756\pi$
$769$	−0.305975	−0.0110337	−0.00551686	+	0.999985i	$0.501756\pi$
$770$	−31.6993	−1.14236
$771$	25.9967	0.936249
$772$	−11.2460	−0.404753
$773$	3.53034	0.126977	0.0634887	−	0.997983i	$-0.479777\pi$
$773$	3.53034	0.126977	0.0634887	+	0.997983i	$0.479777\pi$
$774$	−2.17379	−0.0781352
$775$	−35.4504	−1.27342
$776$	7.24727	0.260162
$777$	−2.20009	−0.0789278
$778$	6.02177	0.215891
$779$	1.02664	0.0367832
$780$	9.24603	0.331061
$781$	−61.8278	−2.21237
$782$	0	0
$783$	−8.66918	−0.309811
$784$	−4.70981	−0.168208
$785$	16.1793	0.577462
$786$	12.5385	0.447232
$787$	2.24943	0.0801837	0.0400918	−	0.999196i	$-0.487235\pi$
$787$	2.24943	0.0801837	0.0400918	+	0.999196i	$0.487235\pi$
$788$	10.4125	0.370930
$789$	−5.74265	−0.204444
$790$	44.1206	1.56974
$791$	18.6256	0.662250
$792$	6.53843	0.232333
$793$	−26.0747	−0.925939
$794$	24.0018	0.851790
$795$	−38.6398	−1.37041
$796$	−15.0998	−0.535197
$797$	39.6694	1.40516	0.702581	−	0.711604i	$-0.252031\pi$
$797$	39.6694	1.40516	0.702581	+	0.711604i	$0.252031\pi$
$798$	0.840741	0.0297619
$799$	−13.6560	−0.483113
$800$	5.26315	0.186081
$801$	5.61844	0.198518
$802$	14.4766	0.511186
$803$	−4.10350	−0.144810
$804$	7.66794	0.270427
$805$	0	0
$806$	−19.4397	−0.684735
$807$	8.17926	0.287924
$808$	−1.02378	−0.0360164
$809$	−38.4898	−1.35323	−0.676614	−	0.736338i	$-0.736553\pi$
$809$	−38.4898	−1.35323	−0.676614	+	0.736338i	$0.736553\pi$
$810$	3.20362	0.112564
$811$	−14.4390	−0.507021	−0.253511	−	0.967333i	$-0.581585\pi$
$811$	−14.4390	−0.507021	−0.253511	+	0.967333i	$0.581585\pi$
$812$	13.1194	0.460400
$813$	−13.5053	−0.473650
$814$	9.50557	0.333170
$815$	11.4287	0.400329
$816$	1.19647	0.0418850
$817$	1.20766	0.0422506
$818$	−32.6435	−1.14135
$819$	−4.36768	−0.152619
$820$	−5.92014	−0.206740
$821$	29.2724	1.02161	0.510806	−	0.859696i	$-0.329347\pi$
$821$	29.2724	1.02161	0.510806	+	0.859696i	$0.329347\pi$
$822$	13.6483	0.476040
$823$	−16.6990	−0.582091	−0.291045	−	0.956709i	$-0.594003\pi$
$823$	−16.6990	−0.582091	−0.291045	+	0.956709i	$0.594003\pi$
$824$	−4.54925	−0.158481
$825$	34.4128	1.19810
$826$	−5.99493	−0.208590
$827$	20.3196	0.706582	0.353291	−	0.935514i	$-0.385063\pi$
$827$	20.3196	0.706582	0.353291	+	0.935514i	$0.385063\pi$
$828$	0	0
$829$	0.285271	0.00990788	0.00495394	−	0.999988i	$-0.498423\pi$
$829$	0.285271	0.00990788	0.00495394	+	0.999988i	$0.498423\pi$
$830$	49.9407	1.73347
$831$	14.9697	0.519292
$832$	2.88612	0.100058
$833$	−5.63517	−0.195247
$834$	−11.6537	−0.403535
$835$	14.6097	0.505589
$836$	−3.63245	−0.125631
$837$	−6.73559	−0.232816
$838$	36.2427	1.25198
$839$	24.4524	0.844192	0.422096	−	0.906551i	$-0.361295\pi$
$839$	24.4524	0.844192	0.422096	+	0.906551i	$0.361295\pi$
$840$	−4.84815	−0.167277
$841$	46.1546	1.59154
$842$	−6.98570	−0.240743
$843$	−26.9740	−0.929033
$844$	11.4828	0.395256
$845$	−14.9618	−0.514703
$846$	−11.4135	−0.392405
$847$	−48.0500	−1.65102
$848$	−12.0613	−0.414187
$849$	−13.7193	−0.470845
$850$	6.29722	0.215993
$851$	0	0
$852$	−9.45607	−0.323960
$853$	28.9592	0.991545	0.495773	−	0.868452i	$-0.334885\pi$
$853$	28.9592	0.991545	0.495773	+	0.868452i	$0.334885\pi$
$854$	13.6722	0.467855
$855$	−1.77978	−0.0608673
$856$	0.602987	0.0206097
$857$	−30.4523	−1.04023	−0.520116	−	0.854096i	$-0.674111\pi$
$857$	−30.4523	−1.04023	−0.520116	+	0.854096i	$0.674111\pi$
$858$	18.8707	0.644235
$859$	42.3725	1.44573	0.722866	−	0.690988i	$-0.242824\pi$
$859$	42.3725	1.44573	0.722866	+	0.690988i	$0.242824\pi$
$860$	−6.96398	−0.237470
$861$	2.79658	0.0953072
$862$	33.3054	1.13439
$863$	−49.6854	−1.69131	−0.845655	−	0.533729i	$-0.820790\pi$
$863$	−49.6854	−1.69131	−0.845655	+	0.533729i	$0.820790\pi$
$864$	1.00000	0.0340207
$865$	−50.0187	−1.70069
$866$	21.5646	0.732796
$867$	−15.5685	−0.528732
$868$	10.1932	0.345980
$869$	90.0482	3.05467
$870$	−27.7727	−0.941583
$871$	22.1306	0.749867
$872$	5.87577	0.198979
$873$	7.24727	0.245283
$874$	0	0
$875$	−1.27581	−0.0431301
$876$	−0.627598	−0.0212046
$877$	4.98560	0.168352	0.0841759	−	0.996451i	$-0.473174\pi$
$877$	4.98560	0.168352	0.0841759	+	0.996451i	$0.473174\pi$
$878$	17.2393	0.581797
$879$	−9.20499	−0.310476
$880$	20.9466	0.706110
$881$	−49.2503	−1.65928	−0.829642	−	0.558296i	$-0.811455\pi$
$881$	−49.2503	−1.65928	−0.829642	+	0.558296i	$0.811455\pi$
$882$	−4.70981	−0.158588
$883$	−29.1640	−0.981448	−0.490724	−	0.871315i	$-0.663268\pi$
$883$	−29.1640	−0.981448	−0.490724	+	0.871315i	$0.663268\pi$
$884$	3.45317	0.116143
$885$	12.6908	0.426596
$886$	18.9166	0.635515
$887$	6.09320	0.204590	0.102295	−	0.994754i	$-0.467381\pi$
$887$	6.09320	0.204590	0.102295	+	0.994754i	$0.467381\pi$
$888$	1.45380	0.0487863
$889$	−13.4230	−0.450194
$890$	17.9993	0.603339
$891$	6.53843	0.219046
$892$	−15.8063	−0.529235
$893$	6.34082	0.212188
$894$	−17.3034	−0.578713
$895$	20.5198	0.685903
$896$	−1.51334	−0.0505570
$897$	0	0
$898$	23.0511	0.769225
$899$	58.3920	1.94748
$900$	5.26315	0.175438
$901$	−14.4310	−0.480768
$902$	−12.0827	−0.402311
$903$	3.28968	0.109474
$904$	−12.3076	−0.409346
$905$	70.9163	2.35734
$906$	−4.83249	−0.160549
$907$	2.46052	0.0817004	0.0408502	−	0.999165i	$-0.486993\pi$
$907$	2.46052	0.0817004	0.0408502	+	0.999165i	$0.486993\pi$
$908$	2.59469	0.0861079
$909$	−1.02378	−0.0339565
$910$	−13.9924	−0.463842
$911$	52.4143	1.73656	0.868281	−	0.496073i	$-0.165225\pi$
$911$	52.4143	1.73656	0.868281	+	0.496073i	$0.165225\pi$
$912$	−0.555554	−0.0183962
$913$	101.927	3.37328
$914$	−15.1904	−0.502454
$915$	−28.9431	−0.956828
$916$	−9.99374	−0.330202
$917$	−18.9749	−0.626607
$918$	1.19647	0.0394895
$919$	12.0132	0.396280	0.198140	−	0.980174i	$-0.436510\pi$
$919$	12.0132	0.396280	0.198140	+	0.980174i	$0.436510\pi$
$920$	0	0
$921$	1.75676	0.0578873
$922$	19.2440	0.633767
$923$	−27.2914	−0.898306
$924$	−9.89485	−0.325517
$925$	7.65157	0.251582
$926$	−3.03240	−0.0996507
$927$	−4.54925	−0.149417
$928$	−8.66918	−0.284580
$929$	−17.2437	−0.565747	−0.282874	−	0.959157i	$-0.591288\pi$
$929$	−17.2437	−0.565747	−0.282874	+	0.959157i	$0.591288\pi$
$930$	−21.5782	−0.707578
$931$	2.61656	0.0857541
$932$	−27.2948	−0.894070
$933$	30.3629	0.994036
$934$	−2.85012	−0.0932588
$935$	25.0621	0.819617
$936$	2.88612	0.0943359
$937$	−19.8875	−0.649696	−0.324848	−	0.945766i	$-0.605313\pi$
$937$	−19.8875	−0.649696	−0.324848	+	0.945766i	$0.605313\pi$
$938$	−11.6042	−0.378890
$939$	−11.0192	−0.359598
$940$	−36.5645	−1.19260
$941$	14.7942	0.482278	0.241139	−	0.970491i	$-0.422479\pi$
$941$	14.7942	0.482278	0.241139	+	0.970491i	$0.422479\pi$
$942$	5.05031	0.164548
$943$	0	0
$944$	3.96140	0.128933
$945$	−4.84815	−0.157710
$946$	−14.2132	−0.462110
$947$	−18.1501	−0.589799	−0.294900	−	0.955528i	$-0.595286\pi$
$947$	−18.1501	−0.589799	−0.294900	+	0.955528i	$0.595286\pi$
$948$	13.7721	0.447298
$949$	−1.81132	−0.0587981
$950$	−2.92397	−0.0948660
$951$	−10.1471	−0.329044
$952$	−1.81067	−0.0586841
$953$	26.1661	0.847605	0.423802	−	0.905755i	$-0.360695\pi$
$953$	26.1661	0.847605	0.423802	+	0.905755i	$0.360695\pi$
$954$	−12.0613	−0.390499
$955$	6.88504	0.222795
$956$	14.3187	0.463099
$957$	−56.6828	−1.83229
$958$	−37.2607	−1.20384
$959$	−20.6545	−0.666969
$960$	3.20362	0.103396
$961$	14.3681	0.463488
$962$	4.19584	0.135279
$963$	0.602987	0.0194310
$964$	−14.1957	−0.457214
$965$	−36.0279	−1.15978
$966$	0	0
$967$	−22.8164	−0.733726	−0.366863	−	0.930275i	$-0.619568\pi$
$967$	−22.8164	−0.733726	−0.366863	+	0.930275i	$0.619568\pi$
$968$	31.7511	1.02052
$969$	−0.664706	−0.0213534
$970$	23.2175	0.745468
$971$	2.27238	0.0729240	0.0364620	−	0.999335i	$-0.488391\pi$
$971$	2.27238	0.0729240	0.0364620	+	0.999335i	$0.488391\pi$
$972$	1.00000	0.0320750
$973$	17.6360	0.565384
$974$	−30.7455	−0.985150
$975$	15.1901	0.486473
$976$	−9.03450	−0.289187
$977$	37.7855	1.20887	0.604433	−	0.796656i	$-0.293400\pi$
$977$	37.7855	1.20887	0.604433	+	0.796656i	$0.293400\pi$
$978$	3.56743	0.114074
$979$	36.7358	1.17408
$980$	−15.0884	−0.481982
$981$	5.87577	0.187599
$982$	7.81494	0.249385
$983$	53.3063	1.70021	0.850104	−	0.526615i	$-0.176539\pi$
$983$	53.3063	1.70021	0.850104	+	0.526615i	$0.176539\pi$
$984$	−1.84796	−0.0589107
$985$	33.3577	1.06286
$986$	−10.3724	−0.330326
$987$	17.2725	0.549789
$988$	−1.60340	−0.0510109
$989$	0	0
$990$	20.9466	0.665727
$991$	17.1670	0.545328	0.272664	−	0.962109i	$-0.412095\pi$
$991$	17.1670	0.545328	0.272664	+	0.962109i	$0.412095\pi$
$992$	−6.73559	−0.213855
$993$	29.7790	0.945008
$994$	14.3102	0.453893
$995$	−48.3739	−1.53356
$996$	15.5888	0.493952
$997$	−28.8767	−0.914535	−0.457268	−	0.889329i	$-0.651172\pi$
$997$	−28.8767	−0.914535	−0.457268	+	0.889329i	$0.651172\pi$
$998$	12.9597	0.410231
$999$	1.45380	0.0459962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3174.2.a.bd.1.5		5
3.2	odd	2		9522.2.a.bq.1.1		5
23.15	odd	22		138.2.e.a.133.1	yes	10
23.20	odd	22		138.2.e.a.55.1	✓	10
23.22	odd	2		3174.2.a.bc.1.1		5
69.20	even	22		414.2.i.d.55.1		10
69.38	even	22		414.2.i.d.271.1		10
69.68	even	2		9522.2.a.bt.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.a.55.1	✓	10	23.20	odd	22
138.2.e.a.133.1	yes	10	23.15	odd	22
414.2.i.d.55.1		10	69.20	even	22
414.2.i.d.271.1		10	69.38	even	22
3174.2.a.bc.1.1		5	23.22	odd	2
3174.2.a.bd.1.5		5	1.1	even	1	trivial
9522.2.a.bq.1.1		5	3.2	odd	2
9522.2.a.bt.1.5		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.20362 q^{5} +1.00000 q^{6} -1.51334 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.20362 q^{5} +1.00000 q^{6} -1.51334 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.20362 q^{10} +6.53843 q^{11} +1.00000 q^{12} +2.88612 q^{13} -1.51334 q^{14} +3.20362 q^{15} +1.00000 q^{16} +1.19647 q^{17} +1.00000 q^{18} -0.555554 q^{19} +3.20362 q^{20} -1.51334 q^{21} +6.53843 q^{22} +1.00000 q^{24} +5.26315 q^{25} +2.88612 q^{26} +1.00000 q^{27} -1.51334 q^{28} -8.66918 q^{29} +3.20362 q^{30} -6.73559 q^{31} +1.00000 q^{32} +6.53843 q^{33} +1.19647 q^{34} -4.84815 q^{35} +1.00000 q^{36} +1.45380 q^{37} -0.555554 q^{38} +2.88612 q^{39} +3.20362 q^{40} -1.84796 q^{41} -1.51334 q^{42} -2.17379 q^{43} +6.53843 q^{44} +3.20362 q^{45} -11.4135 q^{47} +1.00000 q^{48} -4.70981 q^{49} +5.26315 q^{50} +1.19647 q^{51} +2.88612 q^{52} -12.0613 q^{53} +1.00000 q^{54} +20.9466 q^{55} -1.51334 q^{56} -0.555554 q^{57} -8.66918 q^{58} +3.96140 q^{59} +3.20362 q^{60} -9.03450 q^{61} -6.73559 q^{62} -1.51334 q^{63} +1.00000 q^{64} +9.24603 q^{65} +6.53843 q^{66} +7.66794 q^{67} +1.19647 q^{68} -4.84815 q^{70} -9.45607 q^{71} +1.00000 q^{72} -0.627598 q^{73} +1.45380 q^{74} +5.26315 q^{75} -0.555554 q^{76} -9.89485 q^{77} +2.88612 q^{78} +13.7721 q^{79} +3.20362 q^{80} +1.00000 q^{81} -1.84796 q^{82} +15.5888 q^{83} -1.51334 q^{84} +3.83304 q^{85} -2.17379 q^{86} -8.66918 q^{87} +6.53843 q^{88} +5.61844 q^{89} +3.20362 q^{90} -4.36768 q^{91} -6.73559 q^{93} -11.4135 q^{94} -1.77978 q^{95} +1.00000 q^{96} +7.24727 q^{97} -4.70981 q^{98} +6.53843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 7 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 7 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} + 5 q^{3} + 5 q^{4} + 7 q^{5} + 5 q^{6} + 7 q^{7} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 13 q^{11} + 5 q^{12} - 4 q^{13} + 7 q^{14} + 7 q^{15} + 5 q^{16} + 9 q^{17} + 5 q^{18} + 11 q^{19} + 7 q^{20} + 7 q^{21} + 13 q^{22} + 5 q^{24} - 2 q^{25} - 4 q^{26} + 5 q^{27} + 7 q^{28} - 7 q^{29} + 7 q^{30} - 8 q^{31} + 5 q^{32} + 13 q^{33} + 9 q^{34} + q^{35} + 5 q^{36} + 12 q^{37} + 11 q^{38} - 4 q^{39} + 7 q^{40} - 10 q^{41} + 7 q^{42} + 4 q^{43} + 13 q^{44} + 7 q^{45} - 24 q^{47} + 5 q^{48} - 12 q^{49} - 2 q^{50} + 9 q^{51} - 4 q^{52} + 9 q^{53} + 5 q^{54} + 16 q^{55} + 7 q^{56} + 11 q^{57} - 7 q^{58} - 14 q^{59} + 7 q^{60} + 5 q^{61} - 8 q^{62} + 7 q^{63} + 5 q^{64} + 12 q^{65} + 13 q^{66} + 13 q^{67} + 9 q^{68} + q^{70} - 19 q^{71} + 5 q^{72} + 4 q^{73} + 12 q^{74} - 2 q^{75} + 11 q^{76} + 5 q^{77} - 4 q^{78} + 4 q^{79} + 7 q^{80} + 5 q^{81} - 10 q^{82} + 24 q^{83} + 7 q^{84} + 17 q^{85} + 4 q^{86} - 7 q^{87} + 13 q^{88} + 4 q^{89} + 7 q^{90} - 21 q^{91} - 8 q^{93} - 24 q^{94} - 11 q^{95} + 5 q^{96} - 9 q^{97} - 12 q^{98} + 13 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 5 * q^3 + 5 * q^4 + 7 * q^5 + 5 * q^6 + 7 * q^7 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 13 * q^11 + 5 * q^12 - 4 * q^13 + 7 * q^14 + 7 * q^15 + 5 * q^16 + 9 * q^17 + 5 * q^18 + 11 * q^19 + 7 * q^20 + 7 * q^21 + 13 * q^22 + 5 * q^24 - 2 * q^25 - 4 * q^26 + 5 * q^27 + 7 * q^28 - 7 * q^29 + 7 * q^30 - 8 * q^31 + 5 * q^32 + 13 * q^33 + 9 * q^34 + q^35 + 5 * q^36 + 12 * q^37 + 11 * q^38 - 4 * q^39 + 7 * q^40 - 10 * q^41 + 7 * q^42 + 4 * q^43 + 13 * q^44 + 7 * q^45 - 24 * q^47 + 5 * q^48 - 12 * q^49 - 2 * q^50 + 9 * q^51 - 4 * q^52 + 9 * q^53 + 5 * q^54 + 16 * q^55 + 7 * q^56 + 11 * q^57 - 7 * q^58 - 14 * q^59 + 7 * q^60 + 5 * q^61 - 8 * q^62 + 7 * q^63 + 5 * q^64 + 12 * q^65 + 13 * q^66 + 13 * q^67 + 9 * q^68 + q^70 - 19 * q^71 + 5 * q^72 + 4 * q^73 + 12 * q^74 - 2 * q^75 + 11 * q^76 + 5 * q^77 - 4 * q^78 + 4 * q^79 + 7 * q^80 + 5 * q^81 - 10 * q^82 + 24 * q^83 + 7 * q^84 + 17 * q^85 + 4 * q^86 - 7 * q^87 + 13 * q^88 + 4 * q^89 + 7 * q^90 - 21 * q^91 - 8 * q^93 - 24 * q^94 - 11 * q^95 + 5 * q^96 - 9 * q^97 - 12 * q^98 + 13 * q^99

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