LMFDB - Embedded newform 1334.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, 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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 16x^{7} + 44x^{6} + 87x^{5} - 209x^{4} - 160x^{3} + 348x^{2} + 12x - 100 $ x^9 - 3x^8 - 16x^7 + 44x^6 + 87x^5 - 209x^4 - 160x^3 + 348x^2 + 12x - 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.783963$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.783963 q^{3} +1.00000 q^{4} -1.63370 q^{5} +0.783963 q^{6} -4.03607 q^{7} -1.00000 q^{8} -2.38540 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.783963 q^{3} +1.00000 q^{4} -1.63370 q^{5} +0.783963 q^{6} -4.03607 q^{7} -1.00000 q^{8} -2.38540 q^{9} +1.63370 q^{10} +0.505327 q^{11} -0.783963 q^{12} -4.58492 q^{13} +4.03607 q^{14} +1.28076 q^{15} +1.00000 q^{16} -1.56693 q^{17} +2.38540 q^{18} -0.836555 q^{19} -1.63370 q^{20} +3.16413 q^{21} -0.505327 q^{22} -1.00000 q^{23} +0.783963 q^{24} -2.33101 q^{25} +4.58492 q^{26} +4.22196 q^{27} -4.03607 q^{28} +1.00000 q^{29} -1.28076 q^{30} +2.50533 q^{31} -1.00000 q^{32} -0.396158 q^{33} +1.56693 q^{34} +6.59374 q^{35} -2.38540 q^{36} +3.34753 q^{37} +0.836555 q^{38} +3.59441 q^{39} +1.63370 q^{40} +1.34753 q^{41} -3.16413 q^{42} -2.07325 q^{43} +0.505327 q^{44} +3.89704 q^{45} +1.00000 q^{46} +4.89334 q^{47} -0.783963 q^{48} +9.28986 q^{49} +2.33101 q^{50} +1.22842 q^{51} -4.58492 q^{52} -5.13710 q^{53} -4.22196 q^{54} -0.825554 q^{55} +4.03607 q^{56} +0.655828 q^{57} -1.00000 q^{58} -5.55849 q^{59} +1.28076 q^{60} +10.6036 q^{61} -2.50533 q^{62} +9.62765 q^{63} +1.00000 q^{64} +7.49040 q^{65} +0.396158 q^{66} -2.29208 q^{67} -1.56693 q^{68} +0.783963 q^{69} -6.59374 q^{70} -9.76324 q^{71} +2.38540 q^{72} +0.224247 q^{73} -3.34753 q^{74} +1.82743 q^{75} -0.836555 q^{76} -2.03953 q^{77} -3.59441 q^{78} +10.4269 q^{79} -1.63370 q^{80} +3.84635 q^{81} -1.34753 q^{82} -14.3979 q^{83} +3.16413 q^{84} +2.55990 q^{85} +2.07325 q^{86} -0.783963 q^{87} -0.505327 q^{88} -2.55096 q^{89} -3.89704 q^{90} +18.5050 q^{91} -1.00000 q^{92} -1.96408 q^{93} -4.89334 q^{94} +1.36668 q^{95} +0.783963 q^{96} +10.6144 q^{97} -9.28986 q^{98} -1.20541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * 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
$3$	−0.783963	−0.452621	−0.226311	−	0.974055i	$-0.572666\pi$
$3$	−0.783963	−0.452621	−0.226311	+	0.974055i	$0.572666\pi$
$4$	1.00000	0.500000
$5$	−1.63370	−0.730614	−0.365307	−	0.930887i	$-0.619036\pi$
$5$	−1.63370	−0.730614	−0.365307	+	0.930887i	$0.619036\pi$
$6$	0.783963	0.320052
$7$	−4.03607	−1.52549	−0.762746	−	0.646699i	$-0.776149\pi$
$7$	−4.03607	−1.52549	−0.762746	+	0.646699i	$0.776149\pi$
$8$	−1.00000	−0.353553
$9$	−2.38540	−0.795134
$10$	1.63370	0.516622
$11$	0.505327	0.152362	0.0761809	−	0.997094i	$-0.475727\pi$
$11$	0.505327	0.152362	0.0761809	+	0.997094i	$0.475727\pi$
$12$	−0.783963	−0.226311
$13$	−4.58492	−1.27163	−0.635814	−	0.771843i	$-0.719335\pi$
$13$	−4.58492	−1.27163	−0.635814	+	0.771843i	$0.719335\pi$
$14$	4.03607	1.07869
$15$	1.28076	0.330692
$16$	1.00000	0.250000
$17$	−1.56693	−0.380037	−0.190019	−	0.981780i	$-0.560855\pi$
$17$	−1.56693	−0.380037	−0.190019	+	0.981780i	$0.560855\pi$
$18$	2.38540	0.562245
$19$	−0.836555	−0.191919	−0.0959594	−	0.995385i	$-0.530592\pi$
$19$	−0.836555	−0.191919	−0.0959594	+	0.995385i	$0.530592\pi$
$20$	−1.63370	−0.365307
$21$	3.16413	0.690470
$22$	−0.505327	−0.107736
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.783963	0.160026
$25$	−2.33101	−0.466202
$26$	4.58492	0.899176
$27$	4.22196	0.812516
$28$	−4.03607	−0.762746
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.28076	−0.233834
$31$	2.50533	0.449970	0.224985	−	0.974362i	$-0.427767\pi$
$31$	2.50533	0.449970	0.224985	+	0.974362i	$0.427767\pi$
$32$	−1.00000	−0.176777
$33$	−0.396158	−0.0689622
$34$	1.56693	0.268727
$35$	6.59374	1.11455
$36$	−2.38540	−0.397567
$37$	3.34753	0.550331	0.275166	−	0.961397i	$-0.411267\pi$
$37$	3.34753	0.550331	0.275166	+	0.961397i	$0.411267\pi$
$38$	0.836555	0.135707
$39$	3.59441	0.575566
$40$	1.63370	0.258311
$41$	1.34753	0.210449	0.105225	−	0.994448i	$-0.466444\pi$
$41$	1.34753	0.210449	0.105225	+	0.994448i	$0.466444\pi$
$42$	−3.16413	−0.488236
$43$	−2.07325	−0.316168	−0.158084	−	0.987426i	$-0.550532\pi$
$43$	−2.07325	−0.316168	−0.158084	+	0.987426i	$0.550532\pi$
$44$	0.505327	0.0761809
$45$	3.89704	0.580936
$46$	1.00000	0.147442
$47$	4.89334	0.713768	0.356884	−	0.934149i	$-0.383839\pi$
$47$	4.89334	0.713768	0.356884	+	0.934149i	$0.383839\pi$
$48$	−0.783963	−0.113155
$49$	9.28986	1.32712
$50$	2.33101	0.329655
$51$	1.22842	0.172013
$52$	−4.58492	−0.635814
$53$	−5.13710	−0.705635	−0.352817	−	0.935692i	$-0.614776\pi$
$53$	−5.13710	−0.705635	−0.352817	+	0.935692i	$0.614776\pi$
$54$	−4.22196	−0.574536
$55$	−0.825554	−0.111318
$56$	4.03607	0.539343
$57$	0.655828	0.0868665
$58$	−1.00000	−0.131306
$59$	−5.55849	−0.723654	−0.361827	−	0.932245i	$-0.617847\pi$
$59$	−5.55849	−0.723654	−0.361827	+	0.932245i	$0.617847\pi$
$60$	1.28076	0.165346
$61$	10.6036	1.35766	0.678828	−	0.734297i	$-0.262488\pi$
$61$	10.6036	1.35766	0.678828	+	0.734297i	$0.262488\pi$
$62$	−2.50533	−0.318177
$63$	9.62765	1.21297
$64$	1.00000	0.125000
$65$	7.49040	0.929069
$66$	0.396158	0.0487636
$67$	−2.29208	−0.280022	−0.140011	−	0.990150i	$-0.544714\pi$
$67$	−2.29208	−0.280022	−0.140011	+	0.990150i	$0.544714\pi$
$68$	−1.56693	−0.190019
$69$	0.783963	0.0943781
$70$	−6.59374	−0.788103
$71$	−9.76324	−1.15868	−0.579342	−	0.815085i	$-0.696690\pi$
$71$	−9.76324	−1.15868	−0.579342	+	0.815085i	$0.696690\pi$
$72$	2.38540	0.281122
$73$	0.224247	0.0262461	0.0131231	−	0.999914i	$-0.495823\pi$
$73$	0.224247	0.0262461	0.0131231	+	0.999914i	$0.495823\pi$
$74$	−3.34753	−0.389143
$75$	1.82743	0.211013
$76$	−0.836555	−0.0959594
$77$	−2.03953	−0.232426
$78$	−3.59441	−0.406986
$79$	10.4269	1.17312	0.586558	−	0.809907i	$-0.300483\pi$
$79$	10.4269	1.17312	0.586558	+	0.809907i	$0.300483\pi$
$80$	−1.63370	−0.182654
$81$	3.84635	0.427372
$82$	−1.34753	−0.148810
$83$	−14.3979	−1.58037	−0.790187	−	0.612866i	$-0.790016\pi$
$83$	−14.3979	−1.58037	−0.790187	+	0.612866i	$0.790016\pi$
$84$	3.16413	0.345235
$85$	2.55990	0.277661
$86$	2.07325	0.223565
$87$	−0.783963	−0.0840497
$88$	−0.505327	−0.0538680
$89$	−2.55096	−0.270401	−0.135201	−	0.990818i	$-0.543168\pi$
$89$	−2.55096	−0.270401	−0.135201	+	0.990818i	$0.543168\pi$
$90$	−3.89704	−0.410784
$91$	18.5050	1.93986
$92$	−1.00000	−0.104257
$93$	−1.96408	−0.203666
$94$	−4.89334	−0.504710
$95$	1.36668	0.140219
$96$	0.783963	0.0800129
$97$	10.6144	1.07773	0.538867	−	0.842391i	$-0.318853\pi$
$97$	10.6144	1.07773	0.538867	+	0.842391i	$0.318853\pi$
$98$	−9.28986	−0.938418
$99$	−1.20541	−0.121148
$100$	−2.33101	−0.233101
$101$	3.50228	0.348490	0.174245	−	0.984702i	$-0.444252\pi$
$101$	3.50228	0.348490	0.174245	+	0.984702i	$0.444252\pi$
$102$	−1.22842	−0.121631
$103$	−3.62302	−0.356987	−0.178493	−	0.983941i	$-0.557122\pi$
$103$	−3.62302	−0.356987	−0.178493	+	0.983941i	$0.557122\pi$
$104$	4.58492	0.449588
$105$	−5.16925	−0.504467
$106$	5.13710	0.498959
$107$	−10.0055	−0.967268	−0.483634	−	0.875270i	$-0.660683\pi$
$107$	−10.0055	−0.967268	−0.483634	+	0.875270i	$0.660683\pi$
$108$	4.22196	0.406258
$109$	10.3064	0.987173	0.493586	−	0.869697i	$-0.335686\pi$
$109$	10.3064	0.987173	0.493586	+	0.869697i	$0.335686\pi$
$110$	0.825554	0.0787135
$111$	−2.62434	−0.249092
$112$	−4.03607	−0.381373
$113$	11.7530	1.10563	0.552813	−	0.833305i	$-0.313554\pi$
$113$	11.7530	1.10563	0.552813	+	0.833305i	$0.313554\pi$
$114$	−0.655828	−0.0614239
$115$	1.63370	0.152344
$116$	1.00000	0.0928477
$117$	10.9369	1.01111
$118$	5.55849	0.511700
$119$	6.32425	0.579743
$120$	−1.28076	−0.116917
$121$	−10.7446	−0.976786
$122$	−10.6036	−0.960008
$123$	−1.05642	−0.0952539
$124$	2.50533	0.224985
$125$	11.9767	1.07123
$126$	−9.62765	−0.857699
$127$	2.76856	0.245670	0.122835	−	0.992427i	$-0.460801\pi$
$127$	2.76856	0.245670	0.122835	+	0.992427i	$0.460801\pi$
$128$	−1.00000	−0.0883883
$129$	1.62535	0.143104
$130$	−7.49040	−0.656951
$131$	−8.85548	−0.773707	−0.386853	−	0.922141i	$-0.626438\pi$
$131$	−8.85548	−0.773707	−0.386853	+	0.922141i	$0.626438\pi$
$132$	−0.396158	−0.0344811
$133$	3.37639	0.292770
$134$	2.29208	0.198005
$135$	−6.89743	−0.593636
$136$	1.56693	0.134363
$137$	5.04370	0.430913	0.215456	−	0.976513i	$-0.430876\pi$
$137$	5.04370	0.430913	0.215456	+	0.976513i	$0.430876\pi$
$138$	−0.783963	−0.0667354
$139$	16.8620	1.43021	0.715107	−	0.699015i	$-0.246378\pi$
$139$	16.8620	1.43021	0.715107	+	0.699015i	$0.246378\pi$
$140$	6.59374	0.557273
$141$	−3.83620	−0.323066
$142$	9.76324	0.819313
$143$	−2.31688	−0.193747
$144$	−2.38540	−0.198783
$145$	−1.63370	−0.135672
$146$	−0.224247	−0.0185588
$147$	−7.28291	−0.600684
$148$	3.34753	0.275166
$149$	16.7450	1.37180	0.685901	−	0.727695i	$-0.259409\pi$
$149$	16.7450	1.37180	0.685901	+	0.727695i	$0.259409\pi$
$150$	−1.82743	−0.149209
$151$	3.47099	0.282465	0.141233	−	0.989976i	$-0.454893\pi$
$151$	3.47099	0.282465	0.141233	+	0.989976i	$0.454893\pi$
$152$	0.836555	0.0678535
$153$	3.73777	0.302180
$154$	2.03953	0.164350
$155$	−4.09296	−0.328755
$156$	3.59441	0.287783
$157$	−9.65046	−0.770191	−0.385095	−	0.922877i	$-0.625831\pi$
$157$	−9.65046	−0.770191	−0.385095	+	0.922877i	$0.625831\pi$
$158$	−10.4269	−0.829518
$159$	4.02730	0.319385
$160$	1.63370	0.129156
$161$	4.03607	0.318087
$162$	−3.84635	−0.302198
$163$	−4.67830	−0.366433	−0.183216	−	0.983073i	$-0.558651\pi$
$163$	−4.67830	−0.366433	−0.183216	+	0.983073i	$0.558651\pi$
$164$	1.34753	0.105225
$165$	0.647204	0.0503848
$166$	14.3979	1.11749
$167$	23.5742	1.82422	0.912111	−	0.409942i	$-0.134451\pi$
$167$	23.5742	1.82422	0.912111	+	0.409942i	$0.134451\pi$
$168$	−3.16413	−0.244118
$169$	8.02146	0.617036
$170$	−2.55990	−0.196336
$171$	1.99552	0.152601
$172$	−2.07325	−0.158084
$173$	−12.4214	−0.944382	−0.472191	−	0.881496i	$-0.656537\pi$
$173$	−12.4214	−0.944382	−0.472191	+	0.881496i	$0.656537\pi$
$174$	0.783963	0.0594321
$175$	9.40813	0.711188
$176$	0.505327	0.0380904
$177$	4.35765	0.327541
$178$	2.55096	0.191203
$179$	−16.3067	−1.21882	−0.609409	−	0.792856i	$-0.708593\pi$
$179$	−16.3067	−1.21882	−0.609409	+	0.792856i	$0.708593\pi$
$180$	3.89704	0.290468
$181$	4.45042	0.330797	0.165398	−	0.986227i	$-0.447109\pi$
$181$	4.45042	0.330797	0.165398	+	0.986227i	$0.447109\pi$
$182$	−18.5050	−1.37169
$183$	−8.31286	−0.614504
$184$	1.00000	0.0737210
$185$	−5.46888	−0.402080
$186$	1.96408	0.144014
$187$	−0.791813	−0.0579031
$188$	4.89334	0.356884
$189$	−17.0401	−1.23949
$190$	−1.36668	−0.0991496
$191$	−15.7486	−1.13953	−0.569764	−	0.821808i	$-0.692966\pi$
$191$	−15.7486	−1.13953	−0.569764	+	0.821808i	$0.692966\pi$
$192$	−0.783963	−0.0565777
$193$	8.36682	0.602257	0.301128	−	0.953584i	$-0.402637\pi$
$193$	8.36682	0.602257	0.301128	+	0.953584i	$0.402637\pi$
$194$	−10.6144	−0.762073
$195$	−5.87219	−0.420517
$196$	9.28986	0.663562
$197$	7.49551	0.534033	0.267017	−	0.963692i	$-0.413962\pi$
$197$	7.49551	0.534033	0.267017	+	0.963692i	$0.413962\pi$
$198$	1.20541	0.0856646
$199$	3.38562	0.240000	0.120000	−	0.992774i	$-0.461711\pi$
$199$	3.38562	0.240000	0.120000	+	0.992774i	$0.461711\pi$
$200$	2.33101	0.164827
$201$	1.79690	0.126744
$202$	−3.50228	−0.246419
$203$	−4.03607	−0.283277
$204$	1.22842	0.0860065
$205$	−2.20147	−0.153757
$206$	3.62302	0.252428
$207$	2.38540	0.165797
$208$	−4.58492	−0.317907
$209$	−0.422733	−0.0292411
$210$	5.16925	0.356712
$211$	28.7269	1.97764	0.988821	−	0.149104i	$-0.0476390\pi$
$211$	28.7269	1.97764	0.988821	+	0.149104i	$0.0476390\pi$
$212$	−5.13710	−0.352817
$213$	7.65402	0.524445
$214$	10.0055	0.683962
$215$	3.38708	0.230997
$216$	−4.22196	−0.287268
$217$	−10.1117	−0.686425
$218$	−10.3064	−0.698037
$219$	−0.175801	−0.0118796
$220$	−0.825554	−0.0556589
$221$	7.18426	0.483266
$222$	2.62434	0.176134
$223$	−20.8672	−1.39737	−0.698685	−	0.715430i	$-0.746231\pi$
$223$	−20.8672	−1.39737	−0.698685	+	0.715430i	$0.746231\pi$
$224$	4.03607	0.269671
$225$	5.56040	0.370693
$226$	−11.7530	−0.781796
$227$	−19.4820	−1.29307	−0.646534	−	0.762885i	$-0.723782\pi$
$227$	−19.4820	−1.29307	−0.646534	+	0.762885i	$0.723782\pi$
$228$	0.655828	0.0434333
$229$	21.9333	1.44939	0.724697	−	0.689067i	$-0.241980\pi$
$229$	21.9333	1.44939	0.724697	+	0.689067i	$0.241980\pi$
$230$	−1.63370	−0.107723
$231$	1.59892	0.105201
$232$	−1.00000	−0.0656532
$233$	−15.8904	−1.04101	−0.520507	−	0.853857i	$-0.674257\pi$
$233$	−15.8904	−1.04101	−0.520507	+	0.853857i	$0.674257\pi$
$234$	−10.9369	−0.714966
$235$	−7.99427	−0.521489
$236$	−5.55849	−0.361827
$237$	−8.17429	−0.530977
$238$	−6.32425	−0.409940
$239$	−0.364083	−0.0235506	−0.0117753	−	0.999931i	$-0.503748\pi$
$239$	−0.364083	−0.0235506	−0.0117753	+	0.999931i	$0.503748\pi$
$240$	1.28076	0.0826729
$241$	−8.31634	−0.535703	−0.267851	−	0.963460i	$-0.586314\pi$
$241$	−8.31634	−0.535703	−0.267851	+	0.963460i	$0.586314\pi$
$242$	10.7446	0.690692
$243$	−15.6813	−1.00595
$244$	10.6036	0.678828
$245$	−15.1769	−0.969615
$246$	1.05642	0.0673547
$247$	3.83553	0.244049
$248$	−2.50533	−0.159088
$249$	11.2874	0.715311
$250$	−11.9767	−0.757473
$251$	−16.4590	−1.03888	−0.519441	−	0.854506i	$-0.673860\pi$
$251$	−16.4590	−1.03888	−0.519441	+	0.854506i	$0.673860\pi$
$252$	9.62765	0.606485
$253$	−0.505327	−0.0317696
$254$	−2.76856	−0.173715
$255$	−2.00687	−0.125675
$256$	1.00000	0.0625000
$257$	−0.197300	−0.0123072	−0.00615360	−	0.999981i	$-0.501959\pi$
$257$	−0.197300	−0.0123072	−0.00615360	+	0.999981i	$0.501959\pi$
$258$	−1.62535	−0.101190
$259$	−13.5109	−0.839525
$260$	7.49040	0.464535
$261$	−2.38540	−0.147653
$262$	8.85548	0.547093
$263$	−21.6188	−1.33307	−0.666535	−	0.745473i	$-0.732223\pi$
$263$	−21.6188	−1.33307	−0.666535	+	0.745473i	$0.732223\pi$
$264$	0.396158	0.0243818
$265$	8.39250	0.515547
$266$	−3.37639	−0.207020
$267$	1.99986	0.122389
$268$	−2.29208	−0.140011
$269$	10.8505	0.661568	0.330784	−	0.943707i	$-0.392687\pi$
$269$	10.8505	0.661568	0.330784	+	0.943707i	$0.392687\pi$
$270$	6.89743	0.419764
$271$	−6.39473	−0.388452	−0.194226	−	0.980957i	$-0.562220\pi$
$271$	−6.39473	−0.388452	−0.194226	+	0.980957i	$0.562220\pi$
$272$	−1.56693	−0.0950093
$273$	−14.5073	−0.878020
$274$	−5.04370	−0.304701
$275$	−1.17792	−0.0710314
$276$	0.783963	0.0471890
$277$	1.71168	0.102845	0.0514225	−	0.998677i	$-0.483624\pi$
$277$	1.71168	0.102845	0.0514225	+	0.998677i	$0.483624\pi$
$278$	−16.8620	−1.01131
$279$	−5.97621	−0.357786
$280$	−6.59374	−0.394051
$281$	−4.59608	−0.274179	−0.137090	−	0.990559i	$-0.543775\pi$
$281$	−4.59608	−0.274179	−0.137090	+	0.990559i	$0.543775\pi$
$282$	3.83620	0.228442
$283$	−6.61166	−0.393023	−0.196511	−	0.980502i	$-0.562961\pi$
$283$	−6.61166	−0.393023	−0.196511	+	0.980502i	$0.562961\pi$
$284$	−9.76324	−0.579342
$285$	−1.07143	−0.0634660
$286$	2.31688	0.137000
$287$	−5.43874	−0.321039
$288$	2.38540	0.140561
$289$	−14.5447	−0.855572
$290$	1.63370	0.0959344
$291$	−8.32133	−0.487805
$292$	0.224247	0.0131231
$293$	28.4775	1.66367	0.831837	−	0.555020i	$-0.187289\pi$
$293$	28.4775	1.66367	0.831837	+	0.555020i	$0.187289\pi$
$294$	7.28291	0.424748
$295$	9.08093	0.528712
$296$	−3.34753	−0.194571
$297$	2.13347	0.123796
$298$	−16.7450	−0.970010
$299$	4.58492	0.265153
$300$	1.82743	0.105507
$301$	8.36779	0.482312
$302$	−3.47099	−0.199733
$303$	−2.74566	−0.157734
$304$	−0.836555	−0.0479797
$305$	−17.3232	−0.991924
$306$	−3.73777	−0.213674
$307$	15.4720	0.883035	0.441517	−	0.897253i	$-0.354440\pi$
$307$	15.4720	0.883035	0.441517	+	0.897253i	$0.354440\pi$
$308$	−2.03953	−0.116213
$309$	2.84031	0.161580
$310$	4.09296	0.232465
$311$	−22.2372	−1.26096	−0.630478	−	0.776207i	$-0.717141\pi$
$311$	−22.2372	−1.26096	−0.630478	+	0.776207i	$0.717141\pi$
$312$	−3.59441	−0.203493
$313$	−6.91882	−0.391075	−0.195537	−	0.980696i	$-0.562645\pi$
$313$	−6.91882	−0.391075	−0.195537	+	0.980696i	$0.562645\pi$
$314$	9.65046	0.544607
$315$	−15.7287	−0.886213
$316$	10.4269	0.586558
$317$	−25.9005	−1.45472	−0.727360	−	0.686257i	$-0.759253\pi$
$317$	−25.9005	−1.45472	−0.727360	+	0.686257i	$0.759253\pi$
$318$	−4.02730	−0.225840
$319$	0.505327	0.0282929
$320$	−1.63370	−0.0913268
$321$	7.84394	0.437806
$322$	−4.03607	−0.224921
$323$	1.31083	0.0729363
$324$	3.84635	0.213686
$325$	10.6875	0.592836
$326$	4.67830	0.259107
$327$	−8.07983	−0.446815
$328$	−1.34753	−0.0744051
$329$	−19.7499	−1.08885
$330$	−0.647204	−0.0356274
$331$	−25.2543	−1.38810	−0.694050	−	0.719927i	$-0.744175\pi$
$331$	−25.2543	−1.38810	−0.694050	+	0.719927i	$0.744175\pi$
$332$	−14.3979	−0.790187
$333$	−7.98521	−0.437587
$334$	−23.5742	−1.28992
$335$	3.74457	0.204588
$336$	3.16413	0.172617
$337$	−21.4218	−1.16692	−0.583459	−	0.812143i	$-0.698301\pi$
$337$	−21.4218	−1.16692	−0.583459	+	0.812143i	$0.698301\pi$
$338$	−8.02146	−0.436310
$339$	−9.21390	−0.500430
$340$	2.55990	0.138830
$341$	1.26601	0.0685582
$342$	−1.99552	−0.107905
$343$	−9.24204	−0.499023
$344$	2.07325	0.111782
$345$	−1.28076	−0.0689540
$346$	12.4214	0.667779
$347$	7.14148	0.383375	0.191687	−	0.981456i	$-0.438604\pi$
$347$	7.14148	0.383375	0.191687	+	0.981456i	$0.438604\pi$
$348$	−0.783963	−0.0420248
$349$	19.0626	1.02040	0.510200	−	0.860056i	$-0.329571\pi$
$349$	19.0626	1.02040	0.510200	+	0.860056i	$0.329571\pi$
$350$	−9.40813	−0.502886
$351$	−19.3573	−1.03322
$352$	−0.505327	−0.0269340
$353$	0.544274	0.0289688	0.0144844	−	0.999895i	$-0.495389\pi$
$353$	0.544274	0.0289688	0.0144844	+	0.999895i	$0.495389\pi$
$354$	−4.35765	−0.231607
$355$	15.9502	0.846551
$356$	−2.55096	−0.135201
$357$	−4.95798	−0.262404
$358$	16.3067	0.861835
$359$	−3.74446	−0.197625	−0.0988124	−	0.995106i	$-0.531504\pi$
$359$	−3.74446	−0.197625	−0.0988124	+	0.995106i	$0.531504\pi$
$360$	−3.89704	−0.205392
$361$	−18.3002	−0.963167
$362$	−4.45042	−0.233909
$363$	8.42341	0.442114
$364$	18.5050	0.969928
$365$	−0.366353	−0.0191758
$366$	8.31286	0.434520
$367$	7.97213	0.416142	0.208071	−	0.978114i	$-0.433282\pi$
$367$	7.97213	0.416142	0.208071	+	0.978114i	$0.433282\pi$
$368$	−1.00000	−0.0521286
$369$	−3.21441	−0.167335
$370$	5.46888	0.284313
$371$	20.7337	1.07644
$372$	−1.96408	−0.101833
$373$	0.495427	0.0256523	0.0128261	−	0.999918i	$-0.495917\pi$
$373$	0.495427	0.0256523	0.0128261	+	0.999918i	$0.495917\pi$
$374$	0.791813	0.0409437
$375$	−9.38929	−0.484861
$376$	−4.89334	−0.252355
$377$	−4.58492	−0.236135
$378$	17.0401	0.876449
$379$	23.7275	1.21880	0.609401	−	0.792862i	$-0.291410\pi$
$379$	23.7275	1.21880	0.609401	+	0.792862i	$0.291410\pi$
$380$	1.36668	0.0701093
$381$	−2.17045	−0.111195
$382$	15.7486	0.805768
$383$	22.5487	1.15218	0.576092	−	0.817385i	$-0.304577\pi$
$383$	22.5487	1.15218	0.576092	+	0.817385i	$0.304577\pi$
$384$	0.783963	0.0400065
$385$	3.33199	0.169814
$386$	−8.36682	−0.425860
$387$	4.94554	0.251396
$388$	10.6144	0.538867
$389$	15.8992	0.806123	0.403062	−	0.915173i	$-0.367946\pi$
$389$	15.8992	0.806123	0.403062	+	0.915173i	$0.367946\pi$
$390$	5.87219	0.297350
$391$	1.56693	0.0792432
$392$	−9.28986	−0.469209
$393$	6.94237	0.350196
$394$	−7.49551	−0.377618
$395$	−17.0344	−0.857095
$396$	−1.20541	−0.0605740
$397$	28.6392	1.43736	0.718681	−	0.695340i	$-0.244746\pi$
$397$	28.6392	1.43736	0.718681	+	0.695340i	$0.244746\pi$
$398$	−3.38562	−0.169706
$399$	−2.64697	−0.132514
$400$	−2.33101	−0.116551
$401$	5.84046	0.291659	0.145829	−	0.989310i	$-0.453415\pi$
$401$	5.84046	0.291659	0.145829	+	0.989310i	$0.453415\pi$
$402$	−1.79690	−0.0896214
$403$	−11.4867	−0.572194
$404$	3.50228	0.174245
$405$	−6.28379	−0.312244
$406$	4.03607	0.200307
$407$	1.69160	0.0838494
$408$	−1.22842	−0.0608157
$409$	−11.1117	−0.549438	−0.274719	−	0.961524i	$-0.588585\pi$
$409$	−11.1117	−0.549438	−0.274719	+	0.961524i	$0.588585\pi$
$410$	2.20147	0.108723
$411$	−3.95408	−0.195040
$412$	−3.62302	−0.178493
$413$	22.4345	1.10393
$414$	−2.38540	−0.117236
$415$	23.5219	1.15464
$416$	4.58492	0.224794
$417$	−13.2192	−0.647345
$418$	0.422733	0.0206766
$419$	27.4336	1.34022	0.670110	−	0.742262i	$-0.266247\pi$
$419$	27.4336	1.34022	0.670110	+	0.742262i	$0.266247\pi$
$420$	−5.16925	−0.252234
$421$	−22.3496	−1.08925	−0.544625	−	0.838679i	$-0.683328\pi$
$421$	−22.3496	−1.08925	−0.544625	+	0.838679i	$0.683328\pi$
$422$	−28.7269	−1.39840
$423$	−11.6726	−0.567541
$424$	5.13710	0.249480
$425$	3.65254	0.177174
$426$	−7.65402	−0.370838
$427$	−42.7970	−2.07109
$428$	−10.0055	−0.483634
$429$	1.81635	0.0876942
$430$	−3.38708	−0.163340
$431$	−3.77275	−0.181727	−0.0908634	−	0.995863i	$-0.528963\pi$
$431$	−3.77275	−0.181727	−0.0908634	+	0.995863i	$0.528963\pi$
$432$	4.22196	0.203129
$433$	16.8614	0.810305	0.405153	−	0.914249i	$-0.367218\pi$
$433$	16.8614	0.810305	0.405153	+	0.914249i	$0.367218\pi$
$434$	10.1117	0.485376
$435$	1.28076	0.0614079
$436$	10.3064	0.493586
$437$	0.836555	0.0400178
$438$	0.175801	0.00840011
$439$	33.4870	1.59825	0.799124	−	0.601167i	$-0.205297\pi$
$439$	33.4870	1.59825	0.799124	+	0.601167i	$0.205297\pi$
$440$	0.825554	0.0393568
$441$	−22.1601	−1.05524
$442$	−7.18426	−0.341720
$443$	−4.35102	−0.206723	−0.103362	−	0.994644i	$-0.532960\pi$
$443$	−4.35102	−0.206723	−0.103362	+	0.994644i	$0.532960\pi$
$444$	−2.62434	−0.124546
$445$	4.16752	0.197559
$446$	20.8672	0.988089
$447$	−13.1274	−0.620906
$448$	−4.03607	−0.190686
$449$	−39.3943	−1.85913	−0.929566	−	0.368656i	$-0.879818\pi$
$449$	−39.3943	−1.85913	−0.929566	+	0.368656i	$0.879818\pi$
$450$	−5.56040	−0.262120
$451$	0.680945	0.0320644
$452$	11.7530	0.552813
$453$	−2.72113	−0.127850
$454$	19.4820	0.914338
$455$	−30.2318	−1.41729
$456$	−0.655828	−0.0307120
$457$	26.1035	1.22107	0.610535	−	0.791989i	$-0.290954\pi$
$457$	26.1035	1.22107	0.610535	+	0.791989i	$0.290954\pi$
$458$	−21.9333	−1.02488
$459$	−6.61552	−0.308786
$460$	1.63370	0.0761718
$461$	6.18681	0.288149	0.144074	−	0.989567i	$-0.453980\pi$
$461$	6.18681	0.288149	0.144074	+	0.989567i	$0.453980\pi$
$462$	−1.59892	−0.0743885
$463$	−4.31269	−0.200428	−0.100214	−	0.994966i	$-0.531953\pi$
$463$	−4.31269	−0.200428	−0.100214	+	0.994966i	$0.531953\pi$
$464$	1.00000	0.0464238
$465$	3.20873	0.148801
$466$	15.8904	0.736109
$467$	31.2058	1.44403	0.722016	−	0.691876i	$-0.243216\pi$
$467$	31.2058	1.44403	0.722016	+	0.691876i	$0.243216\pi$
$468$	10.9369	0.505557
$469$	9.25098	0.427170
$470$	7.99427	0.368748
$471$	7.56561	0.348605
$472$	5.55849	0.255850
$473$	−1.04767	−0.0481719
$474$	8.17429	0.375457
$475$	1.95002	0.0894730
$476$	6.32425	0.289872
$477$	12.2540	0.561074
$478$	0.364083	0.0166528
$479$	11.0450	0.504659	0.252329	−	0.967641i	$-0.418803\pi$
$479$	11.0450	0.504659	0.252329	+	0.967641i	$0.418803\pi$
$480$	−1.28076	−0.0584586
$481$	−15.3482	−0.699816
$482$	8.31634	0.378799
$483$	−3.16413	−0.143973
$484$	−10.7446	−0.488393
$485$	−17.3409	−0.787408
$486$	15.6813	0.711317
$487$	−22.3697	−1.01367	−0.506833	−	0.862044i	$-0.669184\pi$
$487$	−22.3697	−1.01367	−0.506833	+	0.862044i	$0.669184\pi$
$488$	−10.6036	−0.480004
$489$	3.66761	0.165855
$490$	15.1769	0.685622
$491$	25.2411	1.13911	0.569557	−	0.821952i	$-0.307115\pi$
$491$	25.2411	1.13911	0.569557	+	0.821952i	$0.307115\pi$
$492$	−1.05642	−0.0476270
$493$	−1.56693	−0.0705711
$494$	−3.83553	−0.172569
$495$	1.96928	0.0885125
$496$	2.50533	0.112492
$497$	39.4051	1.76756
$498$	−11.2874	−0.505801
$499$	−17.4741	−0.782249	−0.391124	−	0.920338i	$-0.627914\pi$
$499$	−17.4741	−0.782249	−0.391124	+	0.920338i	$0.627914\pi$
$500$	11.9767	0.535614
$501$	−18.4813	−0.825682
$502$	16.4590	0.734601
$503$	−27.2195	−1.21366	−0.606829	−	0.794833i	$-0.707559\pi$
$503$	−27.2195	−1.21366	−0.606829	+	0.794833i	$0.707559\pi$
$504$	−9.62765	−0.428850
$505$	−5.72168	−0.254612
$506$	0.505327	0.0224645
$507$	−6.28853	−0.279284
$508$	2.76856	0.122835
$509$	−6.61058	−0.293009	−0.146504	−	0.989210i	$-0.546802\pi$
$509$	−6.61058	−0.293009	−0.146504	+	0.989210i	$0.546802\pi$
$510$	2.00687	0.0888657
$511$	−0.905076	−0.0400382
$512$	−1.00000	−0.0441942
$513$	−3.53190	−0.155937
$514$	0.197300	0.00870251
$515$	5.91894	0.260820
$516$	1.62535	0.0715522
$517$	2.47274	0.108751
$518$	13.5109	0.593634
$519$	9.73792	0.427447
$520$	−7.49040	−0.328476
$521$	3.41145	0.149458	0.0747292	−	0.997204i	$-0.476191\pi$
$521$	3.41145	0.149458	0.0747292	+	0.997204i	$0.476191\pi$
$522$	2.38540	0.104406
$523$	−16.7231	−0.731250	−0.365625	−	0.930762i	$-0.619145\pi$
$523$	−16.7231	−0.731250	−0.365625	+	0.930762i	$0.619145\pi$
$524$	−8.85548	−0.386853
$525$	−7.37563	−0.321899
$526$	21.6188	0.942623
$527$	−3.92568	−0.171005
$528$	−0.396158	−0.0172405
$529$	1.00000	0.0434783
$530$	−8.39250	−0.364547
$531$	13.2592	0.575402
$532$	3.37639	0.146385
$533$	−6.17833	−0.267613
$534$	−1.99986	−0.0865424
$535$	16.3460	0.706700
$536$	2.29208	0.0990026
$537$	12.7838	0.551663
$538$	−10.8505	−0.467799
$539$	4.69442	0.202203
$540$	−6.89743	−0.296818
$541$	4.96991	0.213673	0.106837	−	0.994277i	$-0.465928\pi$
$541$	4.96991	0.213673	0.106837	+	0.994277i	$0.465928\pi$
$542$	6.39473	0.274677
$543$	−3.48896	−0.149726
$544$	1.56693	0.0671817
$545$	−16.8376	−0.721243
$546$	14.5073	0.620854
$547$	−28.6621	−1.22550	−0.612750	−	0.790276i	$-0.709937\pi$
$547$	−28.6621	−1.22550	−0.612750	+	0.790276i	$0.709937\pi$
$548$	5.04370	0.215456
$549$	−25.2939	−1.07952
$550$	1.17792	0.0502268
$551$	−0.836555	−0.0356384
$552$	−0.783963	−0.0333677
$553$	−42.0836	−1.78958
$554$	−1.71168	−0.0727224
$555$	4.28740	0.181990
$556$	16.8620	0.715107
$557$	−4.17698	−0.176984	−0.0884922	−	0.996077i	$-0.528205\pi$
$557$	−4.17698	−0.176984	−0.0884922	+	0.996077i	$0.528205\pi$
$558$	5.97621	0.252993
$559$	9.50569	0.402048
$560$	6.59374	0.278636
$561$	0.620752	0.0262082
$562$	4.59608	0.193874
$563$	13.6531	0.575411	0.287705	−	0.957719i	$-0.407108\pi$
$563$	13.6531	0.575411	0.287705	+	0.957719i	$0.407108\pi$
$564$	−3.83620	−0.161533
$565$	−19.2009	−0.807787
$566$	6.61166	0.277909
$567$	−15.5241	−0.651952
$568$	9.76324	0.409656
$569$	28.3799	1.18975	0.594873	−	0.803820i	$-0.297202\pi$
$569$	28.3799	1.18975	0.594873	+	0.803820i	$0.297202\pi$
$570$	1.07143	0.0448772
$571$	13.7068	0.573613	0.286806	−	0.957989i	$-0.407406\pi$
$571$	13.7068	0.573613	0.286806	+	0.957989i	$0.407406\pi$
$572$	−2.31688	−0.0968737
$573$	12.3463	0.515775
$574$	5.43874	0.227009
$575$	2.33101	0.0972099
$576$	−2.38540	−0.0993917
$577$	23.6988	0.986595	0.493298	−	0.869861i	$-0.335791\pi$
$577$	23.6988	0.986595	0.493298	+	0.869861i	$0.335791\pi$
$578$	14.5447	0.604981
$579$	−6.55928	−0.272594
$580$	−1.63370	−0.0678359
$581$	58.1109	2.41085
$582$	8.32133	0.344930
$583$	−2.59591	−0.107512
$584$	−0.224247	−0.00927940
$585$	−17.8676	−0.738734
$586$	−28.4775	−1.17639
$587$	−22.3986	−0.924487	−0.462244	−	0.886753i	$-0.652955\pi$
$587$	−22.3986	−0.924487	−0.462244	+	0.886753i	$0.652955\pi$
$588$	−7.28291	−0.300342
$589$	−2.09584	−0.0863577
$590$	−9.08093	−0.373856
$591$	−5.87621	−0.241715
$592$	3.34753	0.137583
$593$	7.52660	0.309081	0.154540	−	0.987986i	$-0.450610\pi$
$593$	7.52660	0.309081	0.154540	+	0.987986i	$0.450610\pi$
$594$	−2.13347	−0.0875372
$595$	−10.3320	−0.423569
$596$	16.7450	0.685901
$597$	−2.65420	−0.108629
$598$	−4.58492	−0.187491
$599$	2.36529	0.0966433	0.0483216	−	0.998832i	$-0.484613\pi$
$599$	2.36529	0.0966433	0.0483216	+	0.998832i	$0.484613\pi$
$600$	−1.82743	−0.0746044
$601$	9.65543	0.393853	0.196927	−	0.980418i	$-0.436904\pi$
$601$	9.65543	0.393853	0.196927	+	0.980418i	$0.436904\pi$
$602$	−8.36779	−0.341046
$603$	5.46752	0.222655
$604$	3.47099	0.141233
$605$	17.5536	0.713654
$606$	2.74566	0.111535
$607$	31.4747	1.27752	0.638759	−	0.769407i	$-0.279448\pi$
$607$	31.4747	1.27752	0.638759	+	0.769407i	$0.279448\pi$
$608$	0.836555	0.0339268
$609$	3.16413	0.128217
$610$	17.3232	0.701396
$611$	−22.4356	−0.907646
$612$	3.73777	0.151090
$613$	41.3895	1.67171	0.835853	−	0.548953i	$-0.184973\pi$
$613$	41.3895	1.67171	0.835853	+	0.548953i	$0.184973\pi$
$614$	−15.4720	−0.624400
$615$	1.72587	0.0695939
$616$	2.03953	0.0821752
$617$	33.3394	1.34219	0.671096	−	0.741370i	$-0.265824\pi$
$617$	33.3394	1.34219	0.671096	+	0.741370i	$0.265824\pi$
$618$	−2.84031	−0.114254
$619$	−6.43997	−0.258844	−0.129422	−	0.991590i	$-0.541312\pi$
$619$	−6.43997	−0.258844	−0.129422	+	0.991590i	$0.541312\pi$
$620$	−4.09296	−0.164377
$621$	−4.22196	−0.169421
$622$	22.2372	0.891631
$623$	10.2959	0.412495
$624$	3.59441	0.143891
$625$	−7.91132	−0.316453
$626$	6.91882	0.276532
$627$	0.331407	0.0132351
$628$	−9.65046	−0.385095
$629$	−5.24536	−0.209146
$630$	15.7287	0.626647
$631$	27.1150	1.07943	0.539715	−	0.841848i	$-0.318532\pi$
$631$	27.1150	1.07943	0.539715	+	0.841848i	$0.318532\pi$
$632$	−10.4269	−0.414759
$633$	−22.5208	−0.895123
$634$	25.9005	1.02864
$635$	−4.52301	−0.179490
$636$	4.02730	0.159693
$637$	−42.5932	−1.68761
$638$	−0.505327	−0.0200061
$639$	23.2893	0.921308
$640$	1.63370	0.0645778
$641$	−16.4041	−0.647923	−0.323962	−	0.946070i	$-0.605015\pi$
$641$	−16.4041	−0.647923	−0.323962	+	0.946070i	$0.605015\pi$
$642$	−7.84394	−0.309576
$643$	−2.89696	−0.114245	−0.0571225	−	0.998367i	$-0.518193\pi$
$643$	−2.89696	−0.114245	−0.0571225	+	0.998367i	$0.518193\pi$
$644$	4.03607	0.159043
$645$	−2.65535	−0.104554
$646$	−1.31083	−0.0515737
$647$	44.5357	1.75088	0.875440	−	0.483326i	$-0.160572\pi$
$647$	44.5357	1.75088	0.875440	+	0.483326i	$0.160572\pi$
$648$	−3.84635	−0.151099
$649$	−2.80885	−0.110257
$650$	−10.6875	−0.419198
$651$	7.92718	0.310691
$652$	−4.67830	−0.183216
$653$	12.7216	0.497833	0.248916	−	0.968525i	$-0.419926\pi$
$653$	12.7216	0.497833	0.248916	+	0.968525i	$0.419926\pi$
$654$	8.07983	0.315946
$655$	14.4672	0.565281
$656$	1.34753	0.0526124
$657$	−0.534919	−0.0208692
$658$	19.7499	0.769930
$659$	−14.6022	−0.568822	−0.284411	−	0.958702i	$-0.591798\pi$
$659$	−14.6022	−0.568822	−0.284411	+	0.958702i	$0.591798\pi$
$660$	0.647204	0.0251924
$661$	31.0482	1.20763	0.603817	−	0.797123i	$-0.293646\pi$
$661$	31.0482	1.20763	0.603817	+	0.797123i	$0.293646\pi$
$662$	25.2543	0.981535
$663$	−5.63219	−0.218736
$664$	14.3979	0.558746
$665$	−5.51603	−0.213902
$666$	7.98521	0.309421
$667$	−1.00000	−0.0387202
$668$	23.5742	0.912111
$669$	16.3591	0.632479
$670$	−3.74457	−0.144665
$671$	5.35830	0.206855
$672$	−3.16413	−0.122059
$673$	31.3004	1.20654	0.603271	−	0.797536i	$-0.293864\pi$
$673$	31.3004	1.20654	0.603271	+	0.797536i	$0.293864\pi$
$674$	21.4218	0.825136
$675$	−9.84143	−0.378797
$676$	8.02146	0.308518
$677$	0.152100	0.00584569	0.00292285	−	0.999996i	$-0.499070\pi$
$677$	0.152100	0.00584569	0.00292285	+	0.999996i	$0.499070\pi$
$678$	9.21390	0.353858
$679$	−42.8406	−1.64407
$680$	−2.55990	−0.0981679
$681$	15.2732	0.585270
$682$	−1.26601	−0.0484780
$683$	−13.3579	−0.511127	−0.255564	−	0.966792i	$-0.582261\pi$
$683$	−13.3579	−0.511127	−0.255564	+	0.966792i	$0.582261\pi$
$684$	1.99552	0.0763006
$685$	−8.23992	−0.314831
$686$	9.24204	0.352863
$687$	−17.1949	−0.656027
$688$	−2.07325	−0.0790420
$689$	23.5532	0.897305
$690$	1.28076	0.0487578
$691$	19.1829	0.729752	0.364876	−	0.931056i	$-0.381111\pi$
$691$	19.1829	0.729752	0.364876	+	0.931056i	$0.381111\pi$
$692$	−12.4214	−0.472191
$693$	4.86511	0.184810
$694$	−7.14148	−0.271087
$695$	−27.5475	−1.04493
$696$	0.783963	0.0297160
$697$	−2.11150	−0.0799786
$698$	−19.0626	−0.721531
$699$	12.4575	0.471186
$700$	9.40813	0.355594
$701$	43.0156	1.62468	0.812339	−	0.583185i	$-0.198194\pi$
$701$	43.0156	1.62468	0.812339	+	0.583185i	$0.198194\pi$
$702$	19.3573	0.730595
$703$	−2.80040	−0.105619
$704$	0.505327	0.0190452
$705$	6.26722	0.236037
$706$	−0.544274	−0.0204840
$707$	−14.1354	−0.531618
$708$	4.35765	0.163771
$709$	12.0147	0.451223	0.225611	−	0.974217i	$-0.427562\pi$
$709$	12.0147	0.451223	0.225611	+	0.974217i	$0.427562\pi$
$710$	−15.9502	−0.598602
$711$	−24.8723	−0.932784
$712$	2.55096	0.0956013
$713$	−2.50533	−0.0938252
$714$	4.95798	0.185548
$715$	3.78510	0.141555
$716$	−16.3067	−0.609409
$717$	0.285428	0.0106595
$718$	3.74446	0.139742
$719$	−41.4448	−1.54563	−0.772815	−	0.634632i	$-0.781152\pi$
$719$	−41.4448	−1.54563	−0.772815	+	0.634632i	$0.781152\pi$
$720$	3.89704	0.145234
$721$	14.6228	0.544580
$722$	18.3002	0.681062
$723$	6.51970	0.242470
$724$	4.45042	0.165398
$725$	−2.33101	−0.0865716
$726$	−8.42341	−0.312622
$727$	−22.1712	−0.822283	−0.411141	−	0.911572i	$-0.634870\pi$
$727$	−22.1712	−0.822283	−0.411141	+	0.911572i	$0.634870\pi$
$728$	−18.5050	−0.685843
$729$	0.754492	0.0279441
$730$	0.366353	0.0135593
$731$	3.24865	0.120156
$732$	−8.31286	−0.307252
$733$	22.0966	0.816155	0.408078	−	0.912947i	$-0.366199\pi$
$733$	22.0966	0.816155	0.408078	+	0.912947i	$0.366199\pi$
$734$	−7.97213	−0.294257
$735$	11.8981	0.438869
$736$	1.00000	0.0368605
$737$	−1.15825	−0.0426646
$738$	3.21441	0.118324
$739$	36.9867	1.36058	0.680289	−	0.732944i	$-0.261854\pi$
$739$	36.9867	1.36058	0.680289	+	0.732944i	$0.261854\pi$
$740$	−5.46888	−0.201040
$741$	−3.00692	−0.110462
$742$	−20.7337	−0.761158
$743$	16.9485	0.621779	0.310890	−	0.950446i	$-0.399373\pi$
$743$	16.9485	0.621779	0.310890	+	0.950446i	$0.399373\pi$
$744$	1.96408	0.0720068
$745$	−27.3563	−1.00226
$746$	−0.495427	−0.0181389
$747$	34.3447	1.25661
$748$	−0.791813	−0.0289516
$749$	40.3829	1.47556
$750$	9.38929	0.342848
$751$	−30.3287	−1.10671	−0.553355	−	0.832946i	$-0.686653\pi$
$751$	−30.3287	−1.10671	−0.553355	+	0.832946i	$0.686653\pi$
$752$	4.89334	0.178442
$753$	12.9032	0.470220
$754$	4.58492	0.166973
$755$	−5.67057	−0.206373
$756$	−17.0401	−0.619743
$757$	−18.0737	−0.656900	−0.328450	−	0.944521i	$-0.606526\pi$
$757$	−18.0737	−0.656900	−0.328450	+	0.944521i	$0.606526\pi$
$758$	−23.7275	−0.861823
$759$	0.396158	0.0143796
$760$	−1.36668	−0.0495748
$761$	−3.53795	−0.128251	−0.0641253	−	0.997942i	$-0.520426\pi$
$761$	−3.53795	−0.128251	−0.0641253	+	0.997942i	$0.520426\pi$
$762$	2.17045	0.0786271
$763$	−41.5973	−1.50592
$764$	−15.7486	−0.569764
$765$	−6.10640	−0.220777
$766$	−22.5487	−0.814717
$767$	25.4852	0.920218
$768$	−0.783963	−0.0282888
$769$	17.8120	0.642317	0.321158	−	0.947025i	$-0.395928\pi$
$769$	17.8120	0.642317	0.321158	+	0.947025i	$0.395928\pi$
$770$	−3.33199	−0.120077
$771$	0.154676	0.00557050
$772$	8.36682	0.301128
$773$	33.7239	1.21296	0.606482	−	0.795097i	$-0.292580\pi$
$773$	33.7239	1.21296	0.606482	+	0.795097i	$0.292580\pi$
$774$	−4.94554	−0.177764
$775$	−5.83995	−0.209777
$776$	−10.6144	−0.381036
$777$	10.5920	0.379987
$778$	−15.8992	−0.570015
$779$	−1.12729	−0.0403892
$780$	−5.87219	−0.210258
$781$	−4.93363	−0.176539
$782$	−1.56693	−0.0560334
$783$	4.22196	0.150880
$784$	9.28986	0.331781
$785$	15.7660	0.562713
$786$	−6.94237	−0.247626
$787$	5.25900	0.187463	0.0937315	−	0.995598i	$-0.470120\pi$
$787$	5.25900	0.187463	0.0937315	+	0.995598i	$0.470120\pi$
$788$	7.49551	0.267017
$789$	16.9483	0.603376
$790$	17.0344	0.606058
$791$	−47.4358	−1.68662
$792$	1.20541	0.0428323
$793$	−48.6168	−1.72643
$794$	−28.6392	−1.01637
$795$	−6.57941	−0.233348
$796$	3.38562	0.120000
$797$	27.2907	0.966685	0.483342	−	0.875431i	$-0.339423\pi$
$797$	27.2907	0.966685	0.483342	+	0.875431i	$0.339423\pi$
$798$	2.64697	0.0937017
$799$	−7.66754	−0.271258
$800$	2.33101	0.0824137
$801$	6.08507	0.215005
$802$	−5.84046	−0.206234
$803$	0.113318	0.00399890
$804$	1.79690	0.0633719
$805$	−6.59374	−0.232399
$806$	11.4867	0.404602
$807$	−8.50641	−0.299440
$808$	−3.50228	−0.123210
$809$	20.0952	0.706511	0.353255	−	0.935527i	$-0.385075\pi$
$809$	20.0952	0.706511	0.353255	+	0.935527i	$0.385075\pi$
$810$	6.28379	0.220790
$811$	−3.43666	−0.120677	−0.0603387	−	0.998178i	$-0.519218\pi$
$811$	−3.43666	−0.120677	−0.0603387	+	0.998178i	$0.519218\pi$
$812$	−4.03607	−0.141638
$813$	5.01323	0.175822
$814$	−1.69160	−0.0592905
$815$	7.64296	0.267721
$816$	1.22842	0.0430032
$817$	1.73439	0.0606786
$818$	11.1117	0.388512
$819$	−44.1420	−1.54245
$820$	−2.20147	−0.0768787
$821$	−30.7940	−1.07472	−0.537359	−	0.843354i	$-0.680578\pi$
$821$	−30.7940	−1.07472	−0.537359	+	0.843354i	$0.680578\pi$
$822$	3.95408	0.137914
$823$	−8.37938	−0.292087	−0.146043	−	0.989278i	$-0.546654\pi$
$823$	−8.37938	−0.292087	−0.146043	+	0.989278i	$0.546654\pi$
$824$	3.62302	0.126214
$825$	0.923448	0.0321503
$826$	−22.4345	−0.780595
$827$	−10.5498	−0.366851	−0.183426	−	0.983034i	$-0.558719\pi$
$827$	−10.5498	−0.366851	−0.183426	+	0.983034i	$0.558719\pi$
$828$	2.38540	0.0828984
$829$	−24.1926	−0.840245	−0.420123	−	0.907467i	$-0.638013\pi$
$829$	−24.1926	−0.840245	−0.420123	+	0.907467i	$0.638013\pi$
$830$	−23.5219	−0.816456
$831$	−1.34189	−0.0465498
$832$	−4.58492	−0.158953
$833$	−14.5566	−0.504356
$834$	13.2192	0.457742
$835$	−38.5132	−1.33280
$836$	−0.422733	−0.0146205
$837$	10.5774	0.365608
$838$	−27.4336	−0.947678
$839$	2.57558	0.0889188	0.0444594	−	0.999011i	$-0.485843\pi$
$839$	2.57558	0.0889188	0.0444594	+	0.999011i	$0.485843\pi$
$840$	5.16925	0.178356
$841$	1.00000	0.0344828
$842$	22.3496	0.770217
$843$	3.60316	0.124099
$844$	28.7269	0.988821
$845$	−13.1047	−0.450815
$846$	11.6726	0.401312
$847$	43.3661	1.49008
$848$	−5.13710	−0.176409
$849$	5.18330	0.177890
$850$	−3.65254	−0.125281
$851$	−3.34753	−0.114752
$852$	7.65402	0.262222
$853$	−6.19770	−0.212205	−0.106103	−	0.994355i	$-0.533837\pi$
$853$	−6.19770	−0.212205	−0.106103	+	0.994355i	$0.533837\pi$
$854$	42.7970	1.46448
$855$	−3.26009	−0.111493
$856$	10.0055	0.341981
$857$	−50.8471	−1.73690	−0.868451	−	0.495774i	$-0.834884\pi$
$857$	−50.8471	−1.73690	−0.868451	+	0.495774i	$0.834884\pi$
$858$	−1.81635	−0.0620092
$859$	12.0213	0.410160	0.205080	−	0.978745i	$-0.434255\pi$
$859$	12.0213	0.410160	0.205080	+	0.978745i	$0.434255\pi$
$860$	3.38708	0.115499
$861$	4.26377	0.145309
$862$	3.77275	0.128500
$863$	−56.0102	−1.90661	−0.953305	−	0.302008i	$-0.902343\pi$
$863$	−56.0102	−1.90661	−0.953305	+	0.302008i	$0.902343\pi$
$864$	−4.22196	−0.143634
$865$	20.2929	0.689979
$866$	−16.8614	−0.572972
$867$	11.4025	0.387250
$868$	−10.1117	−0.343213
$869$	5.26898	0.178738
$870$	−1.28076	−0.0434219
$871$	10.5090	0.356083
$872$	−10.3064	−0.349018
$873$	−25.3197	−0.856942
$874$	−0.836555	−0.0282969
$875$	−48.3388	−1.63415
$876$	−0.175801	−0.00593978
$877$	10.8354	0.365886	0.182943	−	0.983124i	$-0.441438\pi$
$877$	10.8354	0.365886	0.182943	+	0.983124i	$0.441438\pi$
$878$	−33.4870	−1.13013
$879$	−22.3253	−0.753014
$880$	−0.825554	−0.0278294
$881$	25.8698	0.871575	0.435788	−	0.900050i	$-0.356470\pi$
$881$	25.8698	0.871575	0.435788	+	0.900050i	$0.356470\pi$
$882$	22.1601	0.746168
$883$	48.7143	1.63937	0.819683	−	0.572818i	$-0.194150\pi$
$883$	48.7143	1.63937	0.819683	+	0.572818i	$0.194150\pi$
$884$	7.18426	0.241633
$885$	−7.11911	−0.239306
$886$	4.35102	0.146175
$887$	43.1636	1.44929	0.724646	−	0.689121i	$-0.242003\pi$
$887$	43.1636	1.44929	0.724646	+	0.689121i	$0.242003\pi$
$888$	2.62434	0.0880672
$889$	−11.1741	−0.374767
$890$	−4.16752	−0.139695
$891$	1.94366	0.0651151
$892$	−20.8672	−0.698685
$893$	−4.09355	−0.136985
$894$	13.1274	0.439047
$895$	26.6403	0.890486
$896$	4.03607	0.134836
$897$	−3.59441	−0.120014
$898$	39.3943	1.31460
$899$	2.50533	0.0835573
$900$	5.56040	0.185347
$901$	8.04949	0.268167
$902$	−0.680945	−0.0226730
$903$	−6.56004	−0.218305
$904$	−11.7530	−0.390898
$905$	−7.27066	−0.241685
$906$	2.72113	0.0904035
$907$	39.9621	1.32692	0.663460	−	0.748212i	$-0.269087\pi$
$907$	39.9621	1.32692	0.663460	+	0.748212i	$0.269087\pi$
$908$	−19.4820	−0.646534
$909$	−8.35434	−0.277096
$910$	30.2318	1.00217
$911$	14.3672	0.476006	0.238003	−	0.971264i	$-0.423507\pi$
$911$	14.3672	0.476006	0.238003	+	0.971264i	$0.423507\pi$
$912$	0.655828	0.0217166
$913$	−7.27564	−0.240788
$914$	−26.1035	−0.863427
$915$	13.5807	0.448966
$916$	21.9333	0.724697
$917$	35.7413	1.18028
$918$	6.61552	0.218345
$919$	−39.3329	−1.29747	−0.648736	−	0.761014i	$-0.724702\pi$
$919$	−39.3329	−1.29747	−0.648736	+	0.761014i	$0.724702\pi$
$920$	−1.63370	−0.0538616
$921$	−12.1295	−0.399680
$922$	−6.18681	−0.203752
$923$	44.7636	1.47341
$924$	1.59892	0.0526006
$925$	−7.80314	−0.256566
$926$	4.31269	0.141724
$927$	8.64236	0.283852
$928$	−1.00000	−0.0328266
$929$	17.6399	0.578747	0.289373	−	0.957216i	$-0.406553\pi$
$929$	17.6399	0.578747	0.289373	+	0.957216i	$0.406553\pi$
$930$	−3.20873	−0.105218
$931$	−7.77148	−0.254700
$932$	−15.8904	−0.520507
$933$	17.4332	0.570736
$934$	−31.2058	−1.02108
$935$	1.29359	0.0423049
$936$	−10.9369	−0.357483
$937$	23.7371	0.775456	0.387728	−	0.921774i	$-0.373260\pi$
$937$	23.7371	0.775456	0.387728	+	0.921774i	$0.373260\pi$
$938$	−9.25098	−0.302055
$939$	5.42410	0.177009
$940$	−7.99427	−0.260744
$941$	31.3024	1.02043	0.510215	−	0.860047i	$-0.329566\pi$
$941$	31.3024	1.02043	0.510215	+	0.860047i	$0.329566\pi$
$942$	−7.56561	−0.246501
$943$	−1.34753	−0.0438817
$944$	−5.55849	−0.180913
$945$	27.8385	0.905586
$946$	1.04767	0.0340627
$947$	−9.97246	−0.324061	−0.162031	−	0.986786i	$-0.551804\pi$
$947$	−9.97246	−0.324061	−0.162031	+	0.986786i	$0.551804\pi$
$948$	−8.17429	−0.265489
$949$	−1.02815	−0.0333753
$950$	−1.95002	−0.0632670
$951$	20.3051	0.658437
$952$	−6.32425	−0.204970
$953$	39.8218	1.28996	0.644978	−	0.764201i	$-0.276867\pi$
$953$	39.8218	1.28996	0.644978	+	0.764201i	$0.276867\pi$
$954$	−12.2540	−0.396739
$955$	25.7285	0.832556
$956$	−0.364083	−0.0117753
$957$	−0.396158	−0.0128060
$958$	−11.0450	−0.356847
$959$	−20.3567	−0.657354
$960$	1.28076	0.0413365
$961$	−24.7233	−0.797527
$962$	15.3482	0.494845
$963$	23.8671	0.769108
$964$	−8.31634	−0.267851
$965$	−13.6689	−0.440018
$966$	3.16413	0.101804
$967$	9.44290	0.303663	0.151832	−	0.988406i	$-0.451483\pi$
$967$	9.44290	0.303663	0.151832	+	0.988406i	$0.451483\pi$
$968$	10.7446	0.345346
$969$	−1.02764	−0.0330125
$970$	17.3409	0.556781
$971$	−25.0586	−0.804169	−0.402084	−	0.915603i	$-0.631714\pi$
$971$	−25.0586	−0.804169	−0.402084	+	0.915603i	$0.631714\pi$
$972$	−15.6813	−0.502977
$973$	−68.0561	−2.18178
$974$	22.3697	0.716771
$975$	−8.37860	−0.268330
$976$	10.6036	0.339414
$977$	−21.8931	−0.700421	−0.350210	−	0.936671i	$-0.613890\pi$
$977$	−21.8931	−0.700421	−0.350210	+	0.936671i	$0.613890\pi$
$978$	−3.66761	−0.117277
$979$	−1.28907	−0.0411988
$980$	−15.1769	−0.484808
$981$	−24.5849	−0.784935
$982$	−25.2411	−0.805475
$983$	−45.0201	−1.43592	−0.717959	−	0.696085i	$-0.754924\pi$
$983$	−45.0201	−1.43592	−0.717959	+	0.696085i	$0.754924\pi$
$984$	1.05642	0.0336773
$985$	−12.2454	−0.390172
$986$	1.56693	0.0499013
$987$	15.4832	0.492835
$988$	3.83553	0.122025
$989$	2.07325	0.0659256
$990$	−1.96928	−0.0625878
$991$	29.8226	0.947345	0.473672	−	0.880701i	$-0.342928\pi$
$991$	29.8226	0.947345	0.473672	+	0.880701i	$0.342928\pi$
$992$	−2.50533	−0.0795442
$993$	19.7984	0.628284
$994$	−39.4051	−1.24985
$995$	−5.53110	−0.175348
$996$	11.2874	0.357655
$997$	−6.32951	−0.200458	−0.100229	−	0.994964i	$-0.531957\pi$
$997$	−6.32951	−0.200458	−0.100229	+	0.994964i	$0.531957\pi$
$998$	17.4741	0.553133
$999$	14.1331	0.447153

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.j.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.j.1.5	✓	9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.783963 q^{3} +1.00000 q^{4} -1.63370 q^{5} +0.783963 q^{6} -4.03607 q^{7} -1.00000 q^{8} -2.38540 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.783963 q^{3} +1.00000 q^{4} -1.63370 q^{5} +0.783963 q^{6} -4.03607 q^{7} -1.00000 q^{8} -2.38540 q^{9} +1.63370 q^{10} +0.505327 q^{11} -0.783963 q^{12} -4.58492 q^{13} +4.03607 q^{14} +1.28076 q^{15} +1.00000 q^{16} -1.56693 q^{17} +2.38540 q^{18} -0.836555 q^{19} -1.63370 q^{20} +3.16413 q^{21} -0.505327 q^{22} -1.00000 q^{23} +0.783963 q^{24} -2.33101 q^{25} +4.58492 q^{26} +4.22196 q^{27} -4.03607 q^{28} +1.00000 q^{29} -1.28076 q^{30} +2.50533 q^{31} -1.00000 q^{32} -0.396158 q^{33} +1.56693 q^{34} +6.59374 q^{35} -2.38540 q^{36} +3.34753 q^{37} +0.836555 q^{38} +3.59441 q^{39} +1.63370 q^{40} +1.34753 q^{41} -3.16413 q^{42} -2.07325 q^{43} +0.505327 q^{44} +3.89704 q^{45} +1.00000 q^{46} +4.89334 q^{47} -0.783963 q^{48} +9.28986 q^{49} +2.33101 q^{50} +1.22842 q^{51} -4.58492 q^{52} -5.13710 q^{53} -4.22196 q^{54} -0.825554 q^{55} +4.03607 q^{56} +0.655828 q^{57} -1.00000 q^{58} -5.55849 q^{59} +1.28076 q^{60} +10.6036 q^{61} -2.50533 q^{62} +9.62765 q^{63} +1.00000 q^{64} +7.49040 q^{65} +0.396158 q^{66} -2.29208 q^{67} -1.56693 q^{68} +0.783963 q^{69} -6.59374 q^{70} -9.76324 q^{71} +2.38540 q^{72} +0.224247 q^{73} -3.34753 q^{74} +1.82743 q^{75} -0.836555 q^{76} -2.03953 q^{77} -3.59441 q^{78} +10.4269 q^{79} -1.63370 q^{80} +3.84635 q^{81} -1.34753 q^{82} -14.3979 q^{83} +3.16413 q^{84} +2.55990 q^{85} +2.07325 q^{86} -0.783963 q^{87} -0.505327 q^{88} -2.55096 q^{89} -3.89704 q^{90} +18.5050 q^{91} -1.00000 q^{92} -1.96408 q^{93} -4.89334 q^{94} +1.36668 q^{95} +0.783963 q^{96} +10.6144 q^{97} -9.28986 q^{98} -1.20541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 5 q^{5} + 3 q^{6} + 6 q^{7} - 9 q^{8} + 14 q^{9} - 5 q^{10} - 3 q^{11} - 3 q^{12} + 13 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 2 q^{17} - 14 q^{18} + 16 q^{19} + 5 q^{20} + 8 q^{21} + 3 q^{22} - 9 q^{23} + 3 q^{24} + 20 q^{25} - 13 q^{26} - 21 q^{27} + 6 q^{28} + 9 q^{29} + 3 q^{30} + 15 q^{31} - 9 q^{32} + 13 q^{33} - 2 q^{34} + 14 q^{36} + 12 q^{37} - 16 q^{38} - 5 q^{39} - 5 q^{40} - 6 q^{41} - 8 q^{42} - 3 q^{43} - 3 q^{44} + 20 q^{45} + 9 q^{46} - 19 q^{47} - 3 q^{48} + 37 q^{49} - 20 q^{50} + 6 q^{51} + 13 q^{52} + 5 q^{53} + 21 q^{54} + q^{55} - 6 q^{56} - 20 q^{57} - 9 q^{58} + 12 q^{59} - 3 q^{60} + 12 q^{61} - 15 q^{62} + 6 q^{63} + 9 q^{64} + 19 q^{65} - 13 q^{66} - 6 q^{67} + 2 q^{68} + 3 q^{69} + 12 q^{71} - 14 q^{72} - 12 q^{74} + 16 q^{75} + 16 q^{76} + 34 q^{77} + 5 q^{78} + 29 q^{79} + 5 q^{80} + 5 q^{81} + 6 q^{82} + 24 q^{83} + 8 q^{84} + 12 q^{85} + 3 q^{86} - 3 q^{87} + 3 q^{88} - 2 q^{89} - 20 q^{90} + 58 q^{91} - 9 q^{92} + 7 q^{93} + 19 q^{94} + 6 q^{95} + 3 q^{96} + 12 q^{97} - 37 q^{98} - 20 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 5 * q^5 + 3 * q^6 + 6 * q^7 - 9 * q^8 + 14 * q^9 - 5 * q^10 - 3 * q^11 - 3 * q^12 + 13 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 2 * q^17 - 14 * q^18 + 16 * q^19 + 5 * q^20 + 8 * q^21 + 3 * q^22 - 9 * q^23 + 3 * q^24 + 20 * q^25 - 13 * q^26 - 21 * q^27 + 6 * q^28 + 9 * q^29 + 3 * q^30 + 15 * q^31 - 9 * q^32 + 13 * q^33 - 2 * q^34 + 14 * q^36 + 12 * q^37 - 16 * q^38 - 5 * q^39 - 5 * q^40 - 6 * q^41 - 8 * q^42 - 3 * q^43 - 3 * q^44 + 20 * q^45 + 9 * q^46 - 19 * q^47 - 3 * q^48 + 37 * q^49 - 20 * q^50 + 6 * q^51 + 13 * q^52 + 5 * q^53 + 21 * q^54 + q^55 - 6 * q^56 - 20 * q^57 - 9 * q^58 + 12 * q^59 - 3 * q^60 + 12 * q^61 - 15 * q^62 + 6 * q^63 + 9 * q^64 + 19 * q^65 - 13 * q^66 - 6 * q^67 + 2 * q^68 + 3 * q^69 + 12 * q^71 - 14 * q^72 - 12 * q^74 + 16 * q^75 + 16 * q^76 + 34 * q^77 + 5 * q^78 + 29 * q^79 + 5 * q^80 + 5 * q^81 + 6 * q^82 + 24 * q^83 + 8 * q^84 + 12 * q^85 + 3 * q^86 - 3 * q^87 + 3 * q^88 - 2 * q^89 - 20 * q^90 + 58 * q^91 - 9 * q^92 + 7 * q^93 + 19 * q^94 + 6 * q^95 + 3 * q^96 + 12 * q^97 - 37 * q^98 - 20 * q^99

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