LMFDB - Embedded newform 4334.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.352502 q^{3} +1.00000 q^{4} -2.30147 q^{5} -0.352502 q^{6} +2.78311 q^{7} +1.00000 q^{8} -2.87574 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.352502 q^{3} +1.00000 q^{4} -2.30147 q^{5} -0.352502 q^{6} +2.78311 q^{7} +1.00000 q^{8} -2.87574 q^{9} -2.30147 q^{10} -1.00000 q^{11} -0.352502 q^{12} +2.55119 q^{13} +2.78311 q^{14} +0.811273 q^{15} +1.00000 q^{16} -2.24672 q^{17} -2.87574 q^{18} +1.37057 q^{19} -2.30147 q^{20} -0.981053 q^{21} -1.00000 q^{22} +4.45181 q^{23} -0.352502 q^{24} +0.296751 q^{25} +2.55119 q^{26} +2.07121 q^{27} +2.78311 q^{28} +1.67278 q^{29} +0.811273 q^{30} +4.85127 q^{31} +1.00000 q^{32} +0.352502 q^{33} -2.24672 q^{34} -6.40524 q^{35} -2.87574 q^{36} +0.216166 q^{37} +1.37057 q^{38} -0.899299 q^{39} -2.30147 q^{40} +5.79023 q^{41} -0.981053 q^{42} -6.26065 q^{43} -1.00000 q^{44} +6.61843 q^{45} +4.45181 q^{46} -11.3421 q^{47} -0.352502 q^{48} +0.745706 q^{49} +0.296751 q^{50} +0.791975 q^{51} +2.55119 q^{52} -4.29578 q^{53} +2.07121 q^{54} +2.30147 q^{55} +2.78311 q^{56} -0.483130 q^{57} +1.67278 q^{58} -2.83155 q^{59} +0.811273 q^{60} +11.9152 q^{61} +4.85127 q^{62} -8.00351 q^{63} +1.00000 q^{64} -5.87147 q^{65} +0.352502 q^{66} +11.4814 q^{67} -2.24672 q^{68} -1.56927 q^{69} -6.40524 q^{70} +7.34829 q^{71} -2.87574 q^{72} +9.18695 q^{73} +0.216166 q^{74} -0.104605 q^{75} +1.37057 q^{76} -2.78311 q^{77} -0.899299 q^{78} +7.70621 q^{79} -2.30147 q^{80} +7.89712 q^{81} +5.79023 q^{82} +8.24125 q^{83} -0.981053 q^{84} +5.17076 q^{85} -6.26065 q^{86} -0.589660 q^{87} -1.00000 q^{88} +4.26928 q^{89} +6.61843 q^{90} +7.10023 q^{91} +4.45181 q^{92} -1.71008 q^{93} -11.3421 q^{94} -3.15433 q^{95} -0.352502 q^{96} +9.36625 q^{97} +0.745706 q^{98} +2.87574 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * 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
$3$	−0.352502	−0.203517	−0.101759	−	0.994809i	$-0.532447\pi$
$3$	−0.352502	−0.203517	−0.101759	+	0.994809i	$0.532447\pi$
$4$	1.00000	0.500000
$5$	−2.30147	−1.02925	−0.514624	−	0.857416i	$-0.672068\pi$
$5$	−2.30147	−1.02925	−0.514624	+	0.857416i	$0.672068\pi$
$6$	−0.352502	−0.143908
$7$	2.78311	1.05192	0.525959	−	0.850510i	$-0.323707\pi$
$7$	2.78311	1.05192	0.525959	+	0.850510i	$0.323707\pi$
$8$	1.00000	0.353553
$9$	−2.87574	−0.958581
$10$	−2.30147	−0.727788
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.352502	−0.101759
$13$	2.55119	0.707572	0.353786	−	0.935326i	$-0.384894\pi$
$13$	2.55119	0.707572	0.353786	+	0.935326i	$0.384894\pi$
$14$	2.78311	0.743818
$15$	0.811273	0.209470
$16$	1.00000	0.250000
$17$	−2.24672	−0.544910	−0.272455	−	0.962168i	$-0.587836\pi$
$17$	−2.24672	−0.544910	−0.272455	+	0.962168i	$0.587836\pi$
$18$	−2.87574	−0.677819
$19$	1.37057	0.314431	0.157215	−	0.987564i	$-0.449748\pi$
$19$	1.37057	0.314431	0.157215	+	0.987564i	$0.449748\pi$
$20$	−2.30147	−0.514624
$21$	−0.981053	−0.214083
$22$	−1.00000	−0.213201
$23$	4.45181	0.928266	0.464133	−	0.885766i	$-0.346366\pi$
$23$	4.45181	0.928266	0.464133	+	0.885766i	$0.346366\pi$
$24$	−0.352502	−0.0719542
$25$	0.296751	0.0593501
$26$	2.55119	0.500329
$27$	2.07121	0.398605
$28$	2.78311	0.525959
$29$	1.67278	0.310628	0.155314	−	0.987865i	$-0.450361\pi$
$29$	1.67278	0.310628	0.155314	+	0.987865i	$0.450361\pi$
$30$	0.811273	0.148117
$31$	4.85127	0.871313	0.435657	−	0.900113i	$-0.356516\pi$
$31$	4.85127	0.871313	0.435657	+	0.900113i	$0.356516\pi$
$32$	1.00000	0.176777
$33$	0.352502	0.0613628
$34$	−2.24672	−0.385310
$35$	−6.40524	−1.08268
$36$	−2.87574	−0.479290
$37$	0.216166	0.0355375	0.0177687	−	0.999842i	$-0.494344\pi$
$37$	0.216166	0.0355375	0.0177687	+	0.999842i	$0.494344\pi$
$38$	1.37057	0.222336
$39$	−0.899299	−0.144003
$40$	−2.30147	−0.363894
$41$	5.79023	0.904282	0.452141	−	0.891946i	$-0.350660\pi$
$41$	5.79023	0.904282	0.452141	+	0.891946i	$0.350660\pi$
$42$	−0.981053	−0.151380
$43$	−6.26065	−0.954740	−0.477370	−	0.878703i	$-0.658410\pi$
$43$	−6.26065	−0.954740	−0.477370	+	0.878703i	$0.658410\pi$
$44$	−1.00000	−0.150756
$45$	6.61843	0.986617
$46$	4.45181	0.656383
$47$	−11.3421	−1.65442	−0.827209	−	0.561894i	$-0.810073\pi$
$47$	−11.3421	−1.65442	−0.827209	+	0.561894i	$0.810073\pi$
$48$	−0.352502	−0.0508793
$49$	0.745706	0.106529
$50$	0.296751	0.0419669
$51$	0.791975	0.110899
$52$	2.55119	0.353786
$53$	−4.29578	−0.590070	−0.295035	−	0.955486i	$-0.595331\pi$
$53$	−4.29578	−0.590070	−0.295035	+	0.955486i	$0.595331\pi$
$54$	2.07121	0.281856
$55$	2.30147	0.310330
$56$	2.78311	0.371909
$57$	−0.483130	−0.0639921
$58$	1.67278	0.219647
$59$	−2.83155	−0.368637	−0.184318	−	0.982867i	$-0.559008\pi$
$59$	−2.83155	−0.368637	−0.184318	+	0.982867i	$0.559008\pi$
$60$	0.811273	0.104735
$61$	11.9152	1.52558	0.762792	−	0.646644i	$-0.223828\pi$
$61$	11.9152	1.52558	0.762792	+	0.646644i	$0.223828\pi$
$62$	4.85127	0.616111
$63$	−8.00351	−1.00835
$64$	1.00000	0.125000
$65$	−5.87147	−0.728266
$66$	0.352502	0.0433900
$67$	11.4814	1.40268	0.701340	−	0.712827i	$-0.252586\pi$
$67$	11.4814	1.40268	0.701340	+	0.712827i	$0.252586\pi$
$68$	−2.24672	−0.272455
$69$	−1.56927	−0.188918
$70$	−6.40524	−0.765572
$71$	7.34829	0.872081	0.436041	−	0.899927i	$-0.356380\pi$
$71$	7.34829	0.872081	0.436041	+	0.899927i	$0.356380\pi$
$72$	−2.87574	−0.338909
$73$	9.18695	1.07525	0.537626	−	0.843184i	$-0.319321\pi$
$73$	9.18695	1.07525	0.537626	+	0.843184i	$0.319321\pi$
$74$	0.216166	0.0251288
$75$	−0.104605	−0.0120788
$76$	1.37057	0.157215
$77$	−2.78311	−0.317165
$78$	−0.899299	−0.101826
$79$	7.70621	0.867016	0.433508	−	0.901150i	$-0.357276\pi$
$79$	7.70621	0.867016	0.433508	+	0.901150i	$0.357276\pi$
$80$	−2.30147	−0.257312
$81$	7.89712	0.877458
$82$	5.79023	0.639424
$83$	8.24125	0.904595	0.452297	−	0.891867i	$-0.350605\pi$
$83$	8.24125	0.904595	0.452297	+	0.891867i	$0.350605\pi$
$84$	−0.981053	−0.107042
$85$	5.17076	0.560847
$86$	−6.26065	−0.675103
$87$	−0.589660	−0.0632182
$88$	−1.00000	−0.106600
$89$	4.26928	0.452543	0.226271	−	0.974064i	$-0.427346\pi$
$89$	4.26928	0.452543	0.226271	+	0.974064i	$0.427346\pi$
$90$	6.61843	0.697643
$91$	7.10023	0.744307
$92$	4.45181	0.464133
$93$	−1.71008	−0.177327
$94$	−11.3421	−1.16985
$95$	−3.15433	−0.323627
$96$	−0.352502	−0.0359771
$97$	9.36625	0.950999	0.475499	−	0.879716i	$-0.342267\pi$
$97$	9.36625	0.950999	0.475499	+	0.879716i	$0.342267\pi$
$98$	0.745706	0.0753277
$99$	2.87574	0.289023
$100$	0.296751	0.0296751
$101$	−1.76551	−0.175674	−0.0878372	−	0.996135i	$-0.527996\pi$
$101$	−1.76551	−0.175674	−0.0878372	+	0.996135i	$0.527996\pi$
$102$	0.791975	0.0784172
$103$	−5.46062	−0.538051	−0.269026	−	0.963133i	$-0.586702\pi$
$103$	−5.46062	−0.538051	−0.269026	+	0.963133i	$0.586702\pi$
$104$	2.55119	0.250164
$105$	2.25786	0.220345
$106$	−4.29578	−0.417243
$107$	17.0234	1.64571	0.822857	−	0.568249i	$-0.192379\pi$
$107$	17.0234	1.64571	0.822857	+	0.568249i	$0.192379\pi$
$108$	2.07121	0.199303
$109$	7.94526	0.761018	0.380509	−	0.924777i	$-0.375749\pi$
$109$	7.94526	0.761018	0.380509	+	0.924777i	$0.375749\pi$
$110$	2.30147	0.219436
$111$	−0.0761990	−0.00723249
$112$	2.78311	0.262979
$113$	−1.53679	−0.144569	−0.0722845	−	0.997384i	$-0.523029\pi$
$113$	−1.53679	−0.144569	−0.0722845	+	0.997384i	$0.523029\pi$
$114$	−0.483130	−0.0452493
$115$	−10.2457	−0.955415
$116$	1.67278	0.155314
$117$	−7.33655	−0.678265
$118$	−2.83155	−0.260665
$119$	−6.25288	−0.573200
$120$	0.811273	0.0740587
$121$	1.00000	0.0909091
$122$	11.9152	1.07875
$123$	−2.04107	−0.184037
$124$	4.85127	0.435657
$125$	10.8244	0.968161
$126$	−8.00351	−0.713009
$127$	8.25381	0.732407	0.366204	−	0.930535i	$-0.380657\pi$
$127$	8.25381	0.732407	0.366204	+	0.930535i	$0.380657\pi$
$128$	1.00000	0.0883883
$129$	2.20689	0.194306
$130$	−5.87147	−0.514962
$131$	−0.923986	−0.0807290	−0.0403645	−	0.999185i	$-0.512852\pi$
$131$	−0.923986	−0.0807290	−0.0403645	+	0.999185i	$0.512852\pi$
$132$	0.352502	0.0306814
$133$	3.81445	0.330755
$134$	11.4814	0.991844
$135$	−4.76683	−0.410263
$136$	−2.24672	−0.192655
$137$	0.567311	0.0484687	0.0242343	−	0.999706i	$-0.492285\pi$
$137$	0.567311	0.0484687	0.0242343	+	0.999706i	$0.492285\pi$
$138$	−1.56927	−0.133585
$139$	−11.9964	−1.01752	−0.508762	−	0.860907i	$-0.669897\pi$
$139$	−11.9964	−1.01752	−0.508762	+	0.860907i	$0.669897\pi$
$140$	−6.40524	−0.541341
$141$	3.99812	0.336703
$142$	7.34829	0.616655
$143$	−2.55119	−0.213341
$144$	−2.87574	−0.239645
$145$	−3.84985	−0.319713
$146$	9.18695	0.760318
$147$	−0.262863	−0.0216806
$148$	0.216166	0.0177687
$149$	16.0511	1.31496	0.657479	−	0.753473i	$-0.271623\pi$
$149$	16.0511	1.31496	0.657479	+	0.753473i	$0.271623\pi$
$150$	−0.104605	−0.00854099
$151$	−21.1791	−1.72353	−0.861765	−	0.507307i	$-0.830641\pi$
$151$	−21.1791	−1.72353	−0.861765	+	0.507307i	$0.830641\pi$
$152$	1.37057	0.111168
$153$	6.46099	0.522340
$154$	−2.78311	−0.224269
$155$	−11.1650	−0.896797
$156$	−0.899299	−0.0720015
$157$	−6.85909	−0.547415	−0.273708	−	0.961813i	$-0.588250\pi$
$157$	−6.85909	−0.547415	−0.273708	+	0.961813i	$0.588250\pi$
$158$	7.70621	0.613073
$159$	1.51427	0.120090
$160$	−2.30147	−0.181947
$161$	12.3899	0.976458
$162$	7.89712	0.620456
$163$	13.4130	1.05059	0.525293	−	0.850922i	$-0.323956\pi$
$163$	13.4130	1.05059	0.525293	+	0.850922i	$0.323956\pi$
$164$	5.79023	0.452141
$165$	−0.811273	−0.0631575
$166$	8.24125	0.639645
$167$	−4.69870	−0.363597	−0.181798	−	0.983336i	$-0.558192\pi$
$167$	−4.69870	−0.363597	−0.181798	+	0.983336i	$0.558192\pi$
$168$	−0.981053	−0.0756899
$169$	−6.49145	−0.499342
$170$	5.17076	0.396579
$171$	−3.94141	−0.301407
$172$	−6.26065	−0.477370
$173$	−20.9777	−1.59491	−0.797454	−	0.603380i	$-0.793820\pi$
$173$	−20.9777	−1.59491	−0.797454	+	0.603380i	$0.793820\pi$
$174$	−0.589660	−0.0447020
$175$	0.825890	0.0624314
$176$	−1.00000	−0.0753778
$177$	0.998129	0.0750239
$178$	4.26928	0.319996
$179$	−10.7189	−0.801168	−0.400584	−	0.916260i	$-0.631193\pi$
$179$	−10.7189	−0.801168	−0.400584	+	0.916260i	$0.631193\pi$
$180$	6.61843	0.493308
$181$	17.5060	1.30121	0.650606	−	0.759415i	$-0.274515\pi$
$181$	17.5060	1.30121	0.650606	+	0.759415i	$0.274515\pi$
$182$	7.10023	0.526304
$183$	−4.20013	−0.310483
$184$	4.45181	0.328191
$185$	−0.497499	−0.0365768
$186$	−1.71008	−0.125389
$187$	2.24672	0.164297
$188$	−11.3421	−0.827209
$189$	5.76442	0.419300
$190$	−3.15433	−0.228839
$191$	11.9060	0.861491	0.430746	−	0.902473i	$-0.358251\pi$
$191$	11.9060	0.861491	0.430746	+	0.902473i	$0.358251\pi$
$192$	−0.352502	−0.0254397
$193$	10.1689	0.731972	0.365986	−	0.930620i	$-0.380732\pi$
$193$	10.1689	0.731972	0.365986	+	0.930620i	$0.380732\pi$
$194$	9.36625	0.672457
$195$	2.06971	0.148215
$196$	0.745706	0.0532647
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	2.87574	0.204370
$199$	5.74366	0.407157	0.203579	−	0.979059i	$-0.434743\pi$
$199$	5.74366	0.407157	0.203579	+	0.979059i	$0.434743\pi$
$200$	0.296751	0.0209834
$201$	−4.04723	−0.285470
$202$	−1.76551	−0.124221
$203$	4.65554	0.326755
$204$	0.791975	0.0554493
$205$	−13.3260	−0.930730
$206$	−5.46062	−0.380460
$207$	−12.8022	−0.889817
$208$	2.55119	0.176893
$209$	−1.37057	−0.0948044
$210$	2.25786	0.155807
$211$	5.04209	0.347112	0.173556	−	0.984824i	$-0.444474\pi$
$211$	5.04209	0.347112	0.173556	+	0.984824i	$0.444474\pi$
$212$	−4.29578	−0.295035
$213$	−2.59029	−0.177484
$214$	17.0234	1.16370
$215$	14.4087	0.982663
$216$	2.07121	0.140928
$217$	13.5016	0.916549
$218$	7.94526	0.538121
$219$	−3.23842	−0.218832
$220$	2.30147	0.155165
$221$	−5.73181	−0.385563
$222$	−0.0761990	−0.00511414
$223$	−6.07573	−0.406861	−0.203431	−	0.979089i	$-0.565209\pi$
$223$	−6.07573	−0.406861	−0.203431	+	0.979089i	$0.565209\pi$
$224$	2.78311	0.185954
$225$	−0.853378	−0.0568919
$226$	−1.53679	−0.102226
$227$	−19.2536	−1.27791	−0.638954	−	0.769245i	$-0.720632\pi$
$227$	−19.2536	−1.27791	−0.638954	+	0.769245i	$0.720632\pi$
$228$	−0.483130	−0.0319961
$229$	25.7224	1.69978	0.849891	−	0.526959i	$-0.176668\pi$
$229$	25.7224	1.69978	0.849891	+	0.526959i	$0.176668\pi$
$230$	−10.2457	−0.675580
$231$	0.981053	0.0645486
$232$	1.67278	0.109824
$233$	14.5122	0.950725	0.475362	−	0.879790i	$-0.342317\pi$
$233$	14.5122	0.950725	0.475362	+	0.879790i	$0.342317\pi$
$234$	−7.33655	−0.479605
$235$	26.1035	1.70281
$236$	−2.83155	−0.184318
$237$	−2.71646	−0.176453
$238$	−6.25288	−0.405314
$239$	−7.54852	−0.488273	−0.244137	−	0.969741i	$-0.578505\pi$
$239$	−7.54852	−0.488273	−0.244137	+	0.969741i	$0.578505\pi$
$240$	0.811273	0.0523674
$241$	14.0384	0.904291	0.452145	−	0.891944i	$-0.350659\pi$
$241$	14.0384	0.904291	0.452145	+	0.891944i	$0.350659\pi$
$242$	1.00000	0.0642824
$243$	−8.99739	−0.577183
$244$	11.9152	0.762792
$245$	−1.71622	−0.109645
$246$	−2.04107	−0.130134
$247$	3.49658	0.222482
$248$	4.85127	0.308056
$249$	−2.90506	−0.184101
$250$	10.8244	0.684593
$251$	−2.14826	−0.135597	−0.0677984	−	0.997699i	$-0.521597\pi$
$251$	−2.14826	−0.135597	−0.0677984	+	0.997699i	$0.521597\pi$
$252$	−8.00351	−0.504174
$253$	−4.45181	−0.279883
$254$	8.25381	0.517890
$255$	−1.82270	−0.114142
$256$	1.00000	0.0625000
$257$	16.9321	1.05619	0.528097	−	0.849184i	$-0.322906\pi$
$257$	16.9321	1.05619	0.528097	+	0.849184i	$0.322906\pi$
$258$	2.20689	0.137395
$259$	0.601614	0.0373825
$260$	−5.87147	−0.364133
$261$	−4.81049	−0.297762
$262$	−0.923986	−0.0570840
$263$	−13.6803	−0.843562	−0.421781	−	0.906698i	$-0.638595\pi$
$263$	−13.6803	−0.843562	−0.421781	+	0.906698i	$0.638595\pi$
$264$	0.352502	0.0216950
$265$	9.88659	0.607328
$266$	3.81445	0.233879
$267$	−1.50493	−0.0921002
$268$	11.4814	0.701340
$269$	16.9118	1.03113	0.515565	−	0.856851i	$-0.327582\pi$
$269$	16.9118	1.03113	0.515565	+	0.856851i	$0.327582\pi$
$270$	−4.76683	−0.290100
$271$	−16.3170	−0.991190	−0.495595	−	0.868554i	$-0.665050\pi$
$271$	−16.3170	−0.991190	−0.495595	+	0.868554i	$0.665050\pi$
$272$	−2.24672	−0.136228
$273$	−2.50285	−0.151479
$274$	0.567311	0.0342725
$275$	−0.296751	−0.0178947
$276$	−1.56927	−0.0944591
$277$	0.324701	0.0195094	0.00975470	−	0.999952i	$-0.496895\pi$
$277$	0.324701	0.0195094	0.00975470	+	0.999952i	$0.496895\pi$
$278$	−11.9964	−0.719498
$279$	−13.9510	−0.835224
$280$	−6.40524	−0.382786
$281$	3.10530	0.185247	0.0926234	−	0.995701i	$-0.470475\pi$
$281$	3.10530	0.185247	0.0926234	+	0.995701i	$0.470475\pi$
$282$	3.99812	0.238085
$283$	12.3332	0.733133	0.366567	−	0.930392i	$-0.380533\pi$
$283$	12.3332	0.733133	0.366567	+	0.930392i	$0.380533\pi$
$284$	7.34829	0.436041
$285$	1.11191	0.0658637
$286$	−2.55119	−0.150855
$287$	16.1149	0.951230
$288$	−2.87574	−0.169455
$289$	−11.9522	−0.703073
$290$	−3.84985	−0.226071
$291$	−3.30162	−0.193545
$292$	9.18695	0.537626
$293$	−18.2534	−1.06637	−0.533187	−	0.845997i	$-0.679006\pi$
$293$	−18.2534	−1.06637	−0.533187	+	0.845997i	$0.679006\pi$
$294$	−0.262863	−0.0153305
$295$	6.51672	0.379418
$296$	0.216166	0.0125644
$297$	−2.07121	−0.120184
$298$	16.0511	0.929815
$299$	11.3574	0.656814
$300$	−0.104605	−0.00603939
$301$	−17.4241	−1.00431
$302$	−21.1791	−1.21872
$303$	0.622345	0.0357528
$304$	1.37057	0.0786077
$305$	−27.4224	−1.57020
$306$	6.46099	0.369350
$307$	2.22490	0.126982	0.0634908	−	0.997982i	$-0.479777\pi$
$307$	2.22490	0.126982	0.0634908	+	0.997982i	$0.479777\pi$
$308$	−2.78311	−0.158582
$309$	1.92488	0.109503
$310$	−11.1650	−0.634131
$311$	−12.2891	−0.696853	−0.348426	−	0.937336i	$-0.613284\pi$
$311$	−12.2891	−0.696853	−0.348426	+	0.937336i	$0.613284\pi$
$312$	−0.899299	−0.0509128
$313$	5.02275	0.283902	0.141951	−	0.989874i	$-0.454662\pi$
$313$	5.02275	0.283902	0.141951	+	0.989874i	$0.454662\pi$
$314$	−6.85909	−0.387081
$315$	18.4198	1.03784
$316$	7.70621	0.433508
$317$	−20.4888	−1.15077	−0.575383	−	0.817884i	$-0.695147\pi$
$317$	−20.4888	−1.15077	−0.575383	+	0.817884i	$0.695147\pi$
$318$	1.51427	0.0849161
$319$	−1.67278	−0.0936578
$320$	−2.30147	−0.128656
$321$	−6.00079	−0.334931
$322$	12.3899	0.690460
$323$	−3.07929	−0.171337
$324$	7.89712	0.438729
$325$	0.757066	0.0419945
$326$	13.4130	0.742876
$327$	−2.80072	−0.154880
$328$	5.79023	0.319712
$329$	−31.5664	−1.74031
$330$	−0.811273	−0.0446591
$331$	30.5438	1.67884	0.839420	−	0.543483i	$-0.182895\pi$
$331$	30.5438	1.67884	0.839420	+	0.543483i	$0.182895\pi$
$332$	8.24125	0.452297
$333$	−0.621638	−0.0340655
$334$	−4.69870	−0.257102
$335$	−26.4241	−1.44370
$336$	−0.981053	−0.0535208
$337$	−5.35277	−0.291584	−0.145792	−	0.989315i	$-0.546573\pi$
$337$	−5.35277	−0.291584	−0.145792	+	0.989315i	$0.546573\pi$
$338$	−6.49145	−0.353088
$339$	0.541722	0.0294223
$340$	5.17076	0.280424
$341$	−4.85127	−0.262711
$342$	−3.94141	−0.213127
$343$	−17.4064	−0.939857
$344$	−6.26065	−0.337551
$345$	3.61163	0.194443
$346$	−20.9777	−1.12777
$347$	10.1087	0.542662	0.271331	−	0.962486i	$-0.412536\pi$
$347$	10.1087	0.542662	0.271331	+	0.962486i	$0.412536\pi$
$348$	−0.589660	−0.0316091
$349$	31.3957	1.68058	0.840288	−	0.542141i	$-0.182386\pi$
$349$	31.3957	1.68058	0.840288	+	0.542141i	$0.182386\pi$
$350$	0.825890	0.0441457
$351$	5.28405	0.282042
$352$	−1.00000	−0.0533002
$353$	−3.30536	−0.175927	−0.0879634	−	0.996124i	$-0.528036\pi$
$353$	−3.30536	−0.175927	−0.0879634	+	0.996124i	$0.528036\pi$
$354$	0.998129	0.0530499
$355$	−16.9118	−0.897587
$356$	4.26928	0.226271
$357$	2.20415	0.116656
$358$	−10.7189	−0.566511
$359$	−24.9360	−1.31607	−0.658036	−	0.752987i	$-0.728612\pi$
$359$	−24.9360	−1.31607	−0.658036	+	0.752987i	$0.728612\pi$
$360$	6.61843	0.348822
$361$	−17.1215	−0.901133
$362$	17.5060	0.920096
$363$	−0.352502	−0.0185016
$364$	7.10023	0.372153
$365$	−21.1435	−1.10670
$366$	−4.20013	−0.219544
$367$	17.0827	0.891709	0.445855	−	0.895105i	$-0.352900\pi$
$367$	17.0827	0.891709	0.445855	+	0.895105i	$0.352900\pi$
$368$	4.45181	0.232066
$369$	−16.6512	−0.866828
$370$	−0.497499	−0.0258637
$371$	−11.9556	−0.620705
$372$	−1.71008	−0.0886637
$373$	19.0044	0.984012	0.492006	−	0.870592i	$-0.336264\pi$
$373$	19.0044	0.984012	0.492006	+	0.870592i	$0.336264\pi$
$374$	2.24672	0.116175
$375$	−3.81562	−0.197038
$376$	−11.3421	−0.584925
$377$	4.26758	0.219792
$378$	5.76442	0.296490
$379$	22.8225	1.17232	0.586158	−	0.810197i	$-0.300640\pi$
$379$	22.8225	1.17232	0.586158	+	0.810197i	$0.300640\pi$
$380$	−3.15433	−0.161814
$381$	−2.90949	−0.149058
$382$	11.9060	0.609166
$383$	33.7892	1.72655	0.863273	−	0.504738i	$-0.168411\pi$
$383$	33.7892	1.72655	0.863273	+	0.504738i	$0.168411\pi$
$384$	−0.352502	−0.0179886
$385$	6.40524	0.326441
$386$	10.1689	0.517582
$387$	18.0040	0.915195
$388$	9.36625	0.475499
$389$	20.5486	1.04186	0.520928	−	0.853601i	$-0.325586\pi$
$389$	20.5486	1.04186	0.520928	+	0.853601i	$0.325586\pi$
$390$	2.06971	0.104804
$391$	−10.0020	−0.505821
$392$	0.745706	0.0376638
$393$	0.325707	0.0164298
$394$	−1.00000	−0.0503793
$395$	−17.7356	−0.892374
$396$	2.87574	0.144511
$397$	−29.3159	−1.47132	−0.735662	−	0.677349i	$-0.763129\pi$
$397$	−29.3159	−1.47132	−0.735662	+	0.677349i	$0.763129\pi$
$398$	5.74366	0.287904
$399$	−1.34460	−0.0673144
$400$	0.296751	0.0148375
$401$	−6.54009	−0.326596	−0.163298	−	0.986577i	$-0.552213\pi$
$401$	−6.54009	−0.326596	−0.163298	+	0.986577i	$0.552213\pi$
$402$	−4.04723	−0.201858
$403$	12.3765	0.616516
$404$	−1.76551	−0.0878372
$405$	−18.1750	−0.903121
$406$	4.65554	0.231051
$407$	−0.216166	−0.0107149
$408$	0.791975	0.0392086
$409$	−28.6504	−1.41667	−0.708336	−	0.705876i	$-0.750554\pi$
$409$	−28.6504	−1.41667	−0.708336	+	0.705876i	$0.750554\pi$
$410$	−13.3260	−0.658126
$411$	−0.199978	−0.00986421
$412$	−5.46062	−0.269026
$413$	−7.88052	−0.387775
$414$	−12.8022	−0.629196
$415$	−18.9670	−0.931052
$416$	2.55119	0.125082
$417$	4.22877	0.207084
$418$	−1.37057	−0.0670369
$419$	35.3294	1.72596	0.862978	−	0.505242i	$-0.168597\pi$
$419$	35.3294	1.72596	0.862978	+	0.505242i	$0.168597\pi$
$420$	2.25786	0.110172
$421$	−27.1150	−1.32150	−0.660751	−	0.750605i	$-0.729762\pi$
$421$	−27.1150	−1.32150	−0.660751	+	0.750605i	$0.729762\pi$
$422$	5.04209	0.245445
$423$	32.6170	1.58589
$424$	−4.29578	−0.208621
$425$	−0.666716	−0.0323405
$426$	−2.59029	−0.125500
$427$	33.1613	1.60479
$428$	17.0234	0.822857
$429$	0.899299	0.0434186
$430$	14.4087	0.694848
$431$	−1.49198	−0.0718663	−0.0359331	−	0.999354i	$-0.511440\pi$
$431$	−1.49198	−0.0718663	−0.0359331	+	0.999354i	$0.511440\pi$
$432$	2.07121	0.0996513
$433$	30.2113	1.45186	0.725932	−	0.687767i	$-0.241409\pi$
$433$	30.2113	1.45186	0.725932	+	0.687767i	$0.241409\pi$
$434$	13.5016	0.648098
$435$	1.35708	0.0650671
$436$	7.94526	0.380509
$437$	6.10152	0.291875
$438$	−3.23842	−0.154738
$439$	−11.3055	−0.539583	−0.269791	−	0.962919i	$-0.586955\pi$
$439$	−11.3055	−0.539583	−0.269791	+	0.962919i	$0.586955\pi$
$440$	2.30147	0.109718
$441$	−2.14446	−0.102117
$442$	−5.73181	−0.272634
$443$	21.9930	1.04492	0.522459	−	0.852664i	$-0.325015\pi$
$443$	21.9930	1.04492	0.522459	+	0.852664i	$0.325015\pi$
$444$	−0.0761990	−0.00361625
$445$	−9.82560	−0.465778
$446$	−6.07573	−0.287694
$447$	−5.65805	−0.267617
$448$	2.78311	0.131490
$449$	−18.0675	−0.852657	−0.426329	−	0.904568i	$-0.640193\pi$
$449$	−18.0675	−0.852657	−0.426329	+	0.904568i	$0.640193\pi$
$450$	−0.853378	−0.0402286
$451$	−5.79023	−0.272651
$452$	−1.53679	−0.0722845
$453$	7.46568	0.350768
$454$	−19.2536	−0.903617
$455$	−16.3410	−0.766076
$456$	−0.483130	−0.0226246
$457$	−39.4476	−1.84528	−0.922641	−	0.385660i	$-0.873974\pi$
$457$	−39.4476	−1.84528	−0.922641	+	0.385660i	$0.873974\pi$
$458$	25.7224	1.20193
$459$	−4.65344	−0.217204
$460$	−10.2457	−0.477707
$461$	−20.9277	−0.974700	−0.487350	−	0.873207i	$-0.662036\pi$
$461$	−20.9277	−0.974700	−0.487350	+	0.873207i	$0.662036\pi$
$462$	0.981053	0.0456427
$463$	29.6302	1.37703	0.688516	−	0.725221i	$-0.258262\pi$
$463$	29.6302	1.37703	0.688516	+	0.725221i	$0.258262\pi$
$464$	1.67278	0.0776570
$465$	3.93570	0.182514
$466$	14.5122	0.672264
$467$	−11.2148	−0.518960	−0.259480	−	0.965748i	$-0.583551\pi$
$467$	−11.2148	−0.518960	−0.259480	+	0.965748i	$0.583551\pi$
$468$	−7.33655	−0.339132
$469$	31.9541	1.47550
$470$	26.1035	1.20407
$471$	2.41785	0.111408
$472$	−2.83155	−0.130333
$473$	6.26065	0.287865
$474$	−2.71646	−0.124771
$475$	0.406718	0.0186615
$476$	−6.25288	−0.286600
$477$	12.3535	0.565630
$478$	−7.54852	−0.345261
$479$	−10.6588	−0.487014	−0.243507	−	0.969899i	$-0.578298\pi$
$479$	−10.6588	−0.487014	−0.243507	+	0.969899i	$0.578298\pi$
$480$	0.811273	0.0370294
$481$	0.551480	0.0251453
$482$	14.0384	0.639430
$483$	−4.36746	−0.198726
$484$	1.00000	0.0454545
$485$	−21.5561	−0.978813
$486$	−8.99739	−0.408130
$487$	−0.382018	−0.0173109	−0.00865544	−	0.999963i	$-0.502755\pi$
$487$	−0.382018	−0.0173109	−0.00865544	+	0.999963i	$0.502755\pi$
$488$	11.9152	0.539375
$489$	−4.72811	−0.213812
$490$	−1.71622	−0.0775308
$491$	10.3902	0.468905	0.234453	−	0.972128i	$-0.424670\pi$
$491$	10.3902	0.468905	0.234453	+	0.972128i	$0.424670\pi$
$492$	−2.04107	−0.0920186
$493$	−3.75828	−0.169264
$494$	3.49658	0.157319
$495$	−6.61843	−0.297476
$496$	4.85127	0.217828
$497$	20.4511	0.917357
$498$	−2.90506	−0.130179
$499$	−30.0476	−1.34512	−0.672558	−	0.740044i	$-0.734804\pi$
$499$	−30.0476	−1.34512	−0.672558	+	0.740044i	$0.734804\pi$
$500$	10.8244	0.484081
$501$	1.65630	0.0739982
$502$	−2.14826	−0.0958814
$503$	−18.3852	−0.819755	−0.409878	−	0.912141i	$-0.634429\pi$
$503$	−18.3852	−0.819755	−0.409878	+	0.912141i	$0.634429\pi$
$504$	−8.00351	−0.356505
$505$	4.06325	0.180812
$506$	−4.45181	−0.197907
$507$	2.28825	0.101625
$508$	8.25381	0.366204
$509$	−37.4041	−1.65791	−0.828955	−	0.559316i	$-0.811064\pi$
$509$	−37.4041	−1.65791	−0.828955	+	0.559316i	$0.811064\pi$
$510$	−1.82270	−0.0807107
$511$	25.5683	1.13108
$512$	1.00000	0.0441942
$513$	2.83875	0.125334
$514$	16.9321	0.746842
$515$	12.5674	0.553788
$516$	2.20689	0.0971530
$517$	11.3421	0.498826
$518$	0.601614	0.0264334
$519$	7.39470	0.324591
$520$	−5.87147	−0.257481
$521$	28.4682	1.24721	0.623607	−	0.781738i	$-0.285667\pi$
$521$	28.4682	1.24721	0.623607	+	0.781738i	$0.285667\pi$
$522$	−4.81049	−0.210549
$523$	−4.19648	−0.183499	−0.0917496	−	0.995782i	$-0.529246\pi$
$523$	−4.19648	−0.183499	−0.0917496	+	0.995782i	$0.529246\pi$
$524$	−0.923986	−0.0403645
$525$	−0.291128	−0.0127059
$526$	−13.6803	−0.596488
$527$	−10.8994	−0.474787
$528$	0.352502	0.0153407
$529$	−3.18143	−0.138323
$530$	9.88659	0.429446
$531$	8.14281	0.353368
$532$	3.81445	0.165378
$533$	14.7720	0.639845
$534$	−1.50493	−0.0651247
$535$	−39.1788	−1.69385
$536$	11.4814	0.495922
$537$	3.77843	0.163051
$538$	16.9118	0.729119
$539$	−0.745706	−0.0321198
$540$	−4.76683	−0.205132
$541$	8.92079	0.383535	0.191767	−	0.981440i	$-0.438578\pi$
$541$	8.92079	0.383535	0.191767	+	0.981440i	$0.438578\pi$
$542$	−16.3170	−0.700877
$543$	−6.17091	−0.264819
$544$	−2.24672	−0.0963274
$545$	−18.2858	−0.783276
$546$	−2.50285	−0.107112
$547$	−20.7775	−0.888382	−0.444191	−	0.895932i	$-0.646509\pi$
$547$	−20.7775	−0.888382	−0.444191	+	0.895932i	$0.646509\pi$
$548$	0.567311	0.0242343
$549$	−34.2650	−1.46239
$550$	−0.296751	−0.0126535
$551$	2.29267	0.0976710
$552$	−1.56927	−0.0667926
$553$	21.4472	0.912029
$554$	0.324701	0.0137952
$555$	0.175370	0.00744402
$556$	−11.9964	−0.508762
$557$	−35.1793	−1.49060	−0.745298	−	0.666732i	$-0.767693\pi$
$557$	−35.1793	−1.49060	−0.745298	+	0.666732i	$0.767693\pi$
$558$	−13.9510	−0.590592
$559$	−15.9721	−0.675547
$560$	−6.40524	−0.270671
$561$	−0.791975	−0.0334372
$562$	3.10530	0.130989
$563$	−27.9331	−1.17724	−0.588620	−	0.808410i	$-0.700329\pi$
$563$	−27.9331	−1.17724	−0.588620	+	0.808410i	$0.700329\pi$
$564$	3.99812	0.168351
$565$	3.53687	0.148797
$566$	12.3332	0.518403
$567$	21.9786	0.923013
$568$	7.34829	0.308327
$569$	−34.2222	−1.43467	−0.717334	−	0.696730i	$-0.754638\pi$
$569$	−34.2222	−1.43467	−0.717334	+	0.696730i	$0.754638\pi$
$570$	1.11191	0.0465727
$571$	−10.0028	−0.418605	−0.209302	−	0.977851i	$-0.567119\pi$
$571$	−10.0028	−0.418605	−0.209302	+	0.977851i	$0.567119\pi$
$572$	−2.55119	−0.106670
$573$	−4.19691	−0.175328
$574$	16.1149	0.672621
$575$	1.32108	0.0550927
$576$	−2.87574	−0.119823
$577$	−8.10186	−0.337285	−0.168642	−	0.985677i	$-0.553938\pi$
$577$	−8.10186	−0.337285	−0.168642	+	0.985677i	$0.553938\pi$
$578$	−11.9522	−0.497148
$579$	−3.58455	−0.148969
$580$	−3.84985	−0.159856
$581$	22.9363	0.951559
$582$	−3.30162	−0.136857
$583$	4.29578	0.177913
$584$	9.18695	0.380159
$585$	16.8848	0.698102
$586$	−18.2534	−0.754041
$587$	−5.50988	−0.227417	−0.113709	−	0.993514i	$-0.536273\pi$
$587$	−5.50988	−0.227417	−0.113709	+	0.993514i	$0.536273\pi$
$588$	−0.262863	−0.0108403
$589$	6.64901	0.273968
$590$	6.51672	0.268289
$591$	0.352502	0.0145000
$592$	0.216166	0.00888437
$593$	2.86114	0.117493	0.0587464	−	0.998273i	$-0.481290\pi$
$593$	2.86114	0.117493	0.0587464	+	0.998273i	$0.481290\pi$
$594$	−2.07121	−0.0849829
$595$	14.3908	0.589965
$596$	16.0511	0.657479
$597$	−2.02465	−0.0828635
$598$	11.3574	0.464438
$599$	−38.4703	−1.57185	−0.785927	−	0.618319i	$-0.787814\pi$
$599$	−38.4703	−1.57185	−0.785927	+	0.618319i	$0.787814\pi$
$600$	−0.104605	−0.00427049
$601$	34.7471	1.41736	0.708681	−	0.705529i	$-0.249291\pi$
$601$	34.7471	1.41736	0.708681	+	0.705529i	$0.249291\pi$
$602$	−17.4241	−0.710152
$603$	−33.0176	−1.34458
$604$	−21.1791	−0.861765
$605$	−2.30147	−0.0935679
$606$	0.622345	0.0252810
$607$	11.6993	0.474858	0.237429	−	0.971405i	$-0.423695\pi$
$607$	11.6993	0.474858	0.237429	+	0.971405i	$0.423695\pi$
$608$	1.37057	0.0555840
$609$	−1.64109	−0.0665003
$610$	−27.4224	−1.11030
$611$	−28.9359	−1.17062
$612$	6.46099	0.261170
$613$	−39.0524	−1.57731	−0.788655	−	0.614836i	$-0.789222\pi$
$613$	−39.0524	−1.57731	−0.788655	+	0.614836i	$0.789222\pi$
$614$	2.22490	0.0897896
$615$	4.69746	0.189420
$616$	−2.78311	−0.112135
$617$	−7.12867	−0.286989	−0.143495	−	0.989651i	$-0.545834\pi$
$617$	−7.12867	−0.286989	−0.143495	+	0.989651i	$0.545834\pi$
$618$	1.92488	0.0774301
$619$	11.4553	0.460426	0.230213	−	0.973140i	$-0.426058\pi$
$619$	11.4553	0.460426	0.230213	+	0.973140i	$0.426058\pi$
$620$	−11.1650	−0.448398
$621$	9.22064	0.370011
$622$	−12.2891	−0.492749
$623$	11.8819	0.476037
$624$	−0.899299	−0.0360008
$625$	−26.3957	−1.05583
$626$	5.02275	0.200749
$627$	0.483130	0.0192943
$628$	−6.85909	−0.273708
$629$	−0.485665	−0.0193647
$630$	18.4198	0.733863
$631$	−20.3957	−0.811941	−0.405971	−	0.913886i	$-0.633067\pi$
$631$	−20.3957	−0.811941	−0.405971	+	0.913886i	$0.633067\pi$
$632$	7.70621	0.306536
$633$	−1.77735	−0.0706433
$634$	−20.4888	−0.813715
$635$	−18.9959	−0.753828
$636$	1.51427	0.0600448
$637$	1.90243	0.0753772
$638$	−1.67278	−0.0662261
$639$	−21.1318	−0.835960
$640$	−2.30147	−0.0909735
$641$	−16.1416	−0.637553	−0.318777	−	0.947830i	$-0.603272\pi$
$641$	−16.1416	−0.637553	−0.318777	+	0.947830i	$0.603272\pi$
$642$	−6.00079	−0.236832
$643$	14.1603	0.558428	0.279214	−	0.960229i	$-0.409926\pi$
$643$	14.1603	0.558428	0.279214	+	0.960229i	$0.409926\pi$
$644$	12.3899	0.488229
$645$	−5.07909	−0.199989
$646$	−3.07929	−0.121153
$647$	−39.5895	−1.55642	−0.778211	−	0.628003i	$-0.783873\pi$
$647$	−39.5895	−1.55642	−0.778211	+	0.628003i	$0.783873\pi$
$648$	7.89712	0.310228
$649$	2.83155	0.111148
$650$	0.757066	0.0296946
$651$	−4.75935	−0.186534
$652$	13.4130	0.525293
$653$	−39.8831	−1.56075	−0.780374	−	0.625313i	$-0.784971\pi$
$653$	−39.8831	−1.56075	−0.780374	+	0.625313i	$0.784971\pi$
$654$	−2.80072	−0.109517
$655$	2.12652	0.0830901
$656$	5.79023	0.226071
$657$	−26.4193	−1.03072
$658$	−31.5664	−1.23059
$659$	−50.9518	−1.98480	−0.992400	−	0.123056i	$-0.960730\pi$
$659$	−50.9518	−1.98480	−0.992400	+	0.123056i	$0.960730\pi$
$660$	−0.811273	−0.0315787
$661$	−46.1247	−1.79404	−0.897022	−	0.441986i	$-0.854274\pi$
$661$	−46.1247	−1.79404	−0.897022	+	0.441986i	$0.854274\pi$
$662$	30.5438	1.18712
$663$	2.02048	0.0784688
$664$	8.24125	0.319823
$665$	−8.77884	−0.340429
$666$	−0.621638	−0.0240880
$667$	7.44690	0.288345
$668$	−4.69870	−0.181798
$669$	2.14171	0.0828033
$670$	−26.4241	−1.02085
$671$	−11.9152	−0.459981
$672$	−0.981053	−0.0378449
$673$	−1.24637	−0.0480441	−0.0240220	−	0.999711i	$-0.507647\pi$
$673$	−1.24637	−0.0480441	−0.0240220	+	0.999711i	$0.507647\pi$
$674$	−5.35277	−0.206181
$675$	0.614634	0.0236573
$676$	−6.49145	−0.249671
$677$	42.7342	1.64241	0.821204	−	0.570635i	$-0.193303\pi$
$677$	42.7342	1.64241	0.821204	+	0.570635i	$0.193303\pi$
$678$	0.541722	0.0208047
$679$	26.0673	1.00037
$680$	5.17076	0.198290
$681$	6.78695	0.260076
$682$	−4.85127	−0.185765
$683$	25.4363	0.973293	0.486646	−	0.873599i	$-0.338220\pi$
$683$	25.4363	0.973293	0.486646	+	0.873599i	$0.338220\pi$
$684$	−3.94141	−0.150704
$685$	−1.30565	−0.0498862
$686$	−17.4064	−0.664579
$687$	−9.06720	−0.345935
$688$	−6.26065	−0.238685
$689$	−10.9593	−0.417517
$690$	3.61163	0.137492
$691$	10.3495	0.393714	0.196857	−	0.980432i	$-0.436927\pi$
$691$	10.3495	0.393714	0.196857	+	0.980432i	$0.436927\pi$
$692$	−20.9777	−0.797454
$693$	8.00351	0.304028
$694$	10.1087	0.383720
$695$	27.6094	1.04728
$696$	−0.589660	−0.0223510
$697$	−13.0090	−0.492753
$698$	31.3957	1.18835
$699$	−5.11558	−0.193489
$700$	0.825890	0.0312157
$701$	−20.0349	−0.756707	−0.378353	−	0.925661i	$-0.623510\pi$
$701$	−20.0349	−0.756707	−0.378353	+	0.925661i	$0.623510\pi$
$702$	5.28405	0.199434
$703$	0.296271	0.0111741
$704$	−1.00000	−0.0376889
$705$	−9.20155	−0.346550
$706$	−3.30536	−0.124399
$707$	−4.91360	−0.184795
$708$	0.998129	0.0375120
$709$	−5.35837	−0.201238	−0.100619	−	0.994925i	$-0.532082\pi$
$709$	−5.35837	−0.201238	−0.100619	+	0.994925i	$0.532082\pi$
$710$	−16.9118	−0.634690
$711$	−22.1611	−0.831105
$712$	4.26928	0.159998
$713$	21.5969	0.808810
$714$	2.20415	0.0824884
$715$	5.87147	0.219581
$716$	−10.7189	−0.400584
$717$	2.66087	0.0993721
$718$	−24.9360	−0.930603
$719$	16.9361	0.631611	0.315805	−	0.948824i	$-0.397725\pi$
$719$	16.9361	0.631611	0.315805	+	0.948824i	$0.397725\pi$
$720$	6.61843	0.246654
$721$	−15.1975	−0.565985
$722$	−17.1215	−0.637197
$723$	−4.94856	−0.184039
$724$	17.5060	0.650606
$725$	0.496399	0.0184358
$726$	−0.352502	−0.0130826
$727$	47.2091	1.75089	0.875444	−	0.483319i	$-0.160569\pi$
$727$	47.2091	1.75089	0.875444	+	0.483319i	$0.160569\pi$
$728$	7.10023	0.263152
$729$	−20.5198	−0.759991
$730$	−21.1435	−0.782555
$731$	14.0659	0.520247
$732$	−4.20013	−0.155241
$733$	8.34078	0.308074	0.154037	−	0.988065i	$-0.450773\pi$
$733$	8.34078	0.308074	0.154037	+	0.988065i	$0.450773\pi$
$734$	17.0827	0.630534
$735$	0.604971	0.0223147
$736$	4.45181	0.164096
$737$	−11.4814	−0.422924
$738$	−16.6512	−0.612940
$739$	−15.6395	−0.575307	−0.287653	−	0.957735i	$-0.592875\pi$
$739$	−15.6395	−0.575307	−0.287653	+	0.957735i	$0.592875\pi$
$740$	−0.497499	−0.0182884
$741$	−1.23255	−0.0452790
$742$	−11.9556	−0.438905
$743$	−10.8094	−0.396559	−0.198279	−	0.980146i	$-0.563535\pi$
$743$	−10.8094	−0.396559	−0.198279	+	0.980146i	$0.563535\pi$
$744$	−1.71008	−0.0626947
$745$	−36.9411	−1.35342
$746$	19.0044	0.695802
$747$	−23.6997	−0.867127
$748$	2.24672	0.0821483
$749$	47.3780	1.73115
$750$	−3.81562	−0.139327
$751$	41.5146	1.51489	0.757444	−	0.652900i	$-0.226448\pi$
$751$	41.5146	1.51489	0.757444	+	0.652900i	$0.226448\pi$
$752$	−11.3421	−0.413605
$753$	0.757266	0.0275963
$754$	4.26758	0.155416
$755$	48.7430	1.77394
$756$	5.76442	0.209650
$757$	28.0434	1.01925	0.509627	−	0.860395i	$-0.329783\pi$
$757$	28.0434	1.01925	0.509627	+	0.860395i	$0.329783\pi$
$758$	22.8225	0.828952
$759$	1.56927	0.0569610
$760$	−3.15433	−0.114419
$761$	−7.36743	−0.267069	−0.133535	−	0.991044i	$-0.542633\pi$
$761$	−7.36743	−0.267069	−0.133535	+	0.991044i	$0.542633\pi$
$762$	−2.90949	−0.105400
$763$	22.1125	0.800528
$764$	11.9060	0.430746
$765$	−14.8698	−0.537617
$766$	33.7892	1.22085
$767$	−7.22381	−0.260837
$768$	−0.352502	−0.0127198
$769$	−3.42391	−0.123469	−0.0617347	−	0.998093i	$-0.519663\pi$
$769$	−3.42391	−0.123469	−0.0617347	+	0.998093i	$0.519663\pi$
$770$	6.40524	0.230829
$771$	−5.96860	−0.214954
$772$	10.1689	0.365986
$773$	4.97524	0.178947	0.0894734	−	0.995989i	$-0.471482\pi$
$773$	4.97524	0.178947	0.0894734	+	0.995989i	$0.471482\pi$
$774$	18.0040	0.647140
$775$	1.43962	0.0517125
$776$	9.36625	0.336229
$777$	−0.212070	−0.00760798
$778$	20.5486	0.736703
$779$	7.93593	0.284334
$780$	2.06971	0.0741074
$781$	−7.34829	−0.262942
$782$	−10.0020	−0.357670
$783$	3.46469	0.123818
$784$	0.745706	0.0266324
$785$	15.7860	0.563426
$786$	0.325707	0.0116176
$787$	−10.7499	−0.383194	−0.191597	−	0.981474i	$-0.561367\pi$
$787$	−10.7499	−0.383194	−0.191597	+	0.981474i	$0.561367\pi$
$788$	−1.00000	−0.0356235
$789$	4.82233	0.171679
$790$	−17.7356	−0.631004
$791$	−4.27706	−0.152075
$792$	2.87574	0.102185
$793$	30.3979	1.07946
$794$	−29.3159	−1.04038
$795$	−3.48505	−0.123602
$796$	5.74366	0.203579
$797$	31.7247	1.12375	0.561873	−	0.827224i	$-0.310081\pi$
$797$	31.7247	1.12375	0.561873	+	0.827224i	$0.310081\pi$
$798$	−1.34460	−0.0475985
$799$	25.4826	0.901509
$800$	0.296751	0.0104917
$801$	−12.2773	−0.433799
$802$	−6.54009	−0.230939
$803$	−9.18695	−0.324201
$804$	−4.04723	−0.142735
$805$	−28.5149	−1.00502
$806$	12.3765	0.435943
$807$	−5.96144	−0.209853
$808$	−1.76551	−0.0621103
$809$	−8.28001	−0.291110	−0.145555	−	0.989350i	$-0.546497\pi$
$809$	−8.28001	−0.291110	−0.145555	+	0.989350i	$0.546497\pi$
$810$	−18.1750	−0.638603
$811$	2.71509	0.0953396	0.0476698	−	0.998863i	$-0.484820\pi$
$811$	2.71509	0.0953396	0.0476698	+	0.998863i	$0.484820\pi$
$812$	4.65554	0.163377
$813$	5.75180	0.201724
$814$	−0.216166	−0.00757661
$815$	−30.8695	−1.08131
$816$	0.791975	0.0277247
$817$	−8.58067	−0.300199
$818$	−28.6504	−1.00174
$819$	−20.4184	−0.713478
$820$	−13.3260	−0.465365
$821$	−5.50775	−0.192222	−0.0961109	−	0.995371i	$-0.530640\pi$
$821$	−5.50775	−0.192222	−0.0961109	+	0.995371i	$0.530640\pi$
$822$	−0.199978	−0.00697505
$823$	−50.1813	−1.74921	−0.874606	−	0.484835i	$-0.838880\pi$
$823$	−50.1813	−1.74921	−0.874606	+	0.484835i	$0.838880\pi$
$824$	−5.46062	−0.190230
$825$	0.104605	0.00364189
$826$	−7.88052	−0.274198
$827$	3.89525	0.135451	0.0677255	−	0.997704i	$-0.478426\pi$
$827$	3.89525	0.135451	0.0677255	+	0.997704i	$0.478426\pi$
$828$	−12.8022	−0.444909
$829$	37.0095	1.28539	0.642696	−	0.766121i	$-0.277816\pi$
$829$	37.0095	1.28539	0.642696	+	0.766121i	$0.277816\pi$
$830$	−18.9670	−0.658353
$831$	−0.114458	−0.00397050
$832$	2.55119	0.0884465
$833$	−1.67539	−0.0580490
$834$	4.22877	0.146430
$835$	10.8139	0.374231
$836$	−1.37057	−0.0474022
$837$	10.0480	0.347310
$838$	35.3294	1.22044
$839$	−46.2042	−1.59515	−0.797573	−	0.603222i	$-0.793883\pi$
$839$	−46.2042	−1.59515	−0.797573	+	0.603222i	$0.793883\pi$
$840$	2.25786	0.0779036
$841$	−26.2018	−0.903510
$842$	−27.1150	−0.934444
$843$	−1.09463	−0.0377009
$844$	5.04209	0.173556
$845$	14.9399	0.513947
$846$	32.6170	1.12140
$847$	2.78311	0.0956288
$848$	−4.29578	−0.147518
$849$	−4.34748	−0.149205
$850$	−0.666716	−0.0228682
$851$	0.962329	0.0329882
$852$	−2.59029	−0.0887418
$853$	56.5807	1.93728	0.968642	−	0.248459i	$-0.0799242\pi$
$853$	56.5807	1.93728	0.968642	+	0.248459i	$0.0799242\pi$
$854$	33.1613	1.13476
$855$	9.07103	0.310223
$856$	17.0234	0.581848
$857$	46.7522	1.59703	0.798513	−	0.601978i	$-0.205620\pi$
$857$	46.7522	1.59703	0.798513	+	0.601978i	$0.205620\pi$
$858$	0.899299	0.0307016
$859$	−32.2235	−1.09945	−0.549726	−	0.835345i	$-0.685268\pi$
$859$	−32.2235	−1.09945	−0.549726	+	0.835345i	$0.685268\pi$
$860$	14.4087	0.491332
$861$	−5.68053	−0.193592
$862$	−1.49198	−0.0508171
$863$	−36.5941	−1.24568	−0.622839	−	0.782350i	$-0.714021\pi$
$863$	−36.5941	−1.24568	−0.622839	+	0.782350i	$0.714021\pi$
$864$	2.07121	0.0704641
$865$	48.2796	1.64155
$866$	30.2113	1.02662
$867$	4.21319	0.143088
$868$	13.5016	0.458275
$869$	−7.70621	−0.261415
$870$	1.35708	0.0460094
$871$	29.2913	0.992497
$872$	7.94526	0.269060
$873$	−26.9349	−0.911609
$874$	6.10152	0.206387
$875$	30.1254	1.01843
$876$	−3.23842	−0.109416
$877$	−10.1194	−0.341706	−0.170853	−	0.985297i	$-0.554652\pi$
$877$	−10.1194	−0.341706	−0.170853	+	0.985297i	$0.554652\pi$
$878$	−11.3055	−0.381543
$879$	6.43436	0.217026
$880$	2.30147	0.0775824
$881$	−7.25997	−0.244595	−0.122297	−	0.992494i	$-0.539026\pi$
$881$	−7.25997	−0.244595	−0.122297	+	0.992494i	$0.539026\pi$
$882$	−2.14446	−0.0722076
$883$	−0.612783	−0.0206218	−0.0103109	−	0.999947i	$-0.503282\pi$
$883$	−0.612783	−0.0206218	−0.0103109	+	0.999947i	$0.503282\pi$
$884$	−5.73181	−0.192782
$885$	−2.29716	−0.0772182
$886$	21.9930	0.738869
$887$	43.7842	1.47013	0.735065	−	0.677997i	$-0.237152\pi$
$887$	43.7842	1.47013	0.735065	+	0.677997i	$0.237152\pi$
$888$	−0.0761990	−0.00255707
$889$	22.9713	0.770432
$890$	−9.82560	−0.329355
$891$	−7.89712	−0.264563
$892$	−6.07573	−0.203431
$893$	−15.5452	−0.520200
$894$	−5.65805	−0.189234
$895$	24.6692	0.824600
$896$	2.78311	0.0929772
$897$	−4.00350	−0.133673
$898$	−18.0675	−0.602920
$899$	8.11511	0.270654
$900$	−0.853378	−0.0284459
$901$	9.65142	0.321535
$902$	−5.79023	−0.192794
$903$	6.14203	0.204394
$904$	−1.53679	−0.0511129
$905$	−40.2895	−1.33927
$906$	7.46568	0.248031
$907$	−21.8451	−0.725356	−0.362678	−	0.931915i	$-0.618137\pi$
$907$	−21.8451	−0.725356	−0.362678	+	0.931915i	$0.618137\pi$
$908$	−19.2536	−0.638954
$909$	5.07714	0.168398
$910$	−16.3410	−0.541697
$911$	34.0831	1.12922	0.564611	−	0.825357i	$-0.309026\pi$
$911$	34.0831	1.12922	0.564611	+	0.825357i	$0.309026\pi$
$912$	−0.483130	−0.0159980
$913$	−8.24125	−0.272746
$914$	−39.4476	−1.30481
$915$	9.66646	0.319563
$916$	25.7224	0.849891
$917$	−2.57156	−0.0849202
$918$	−4.65344	−0.153586
$919$	−37.2944	−1.23023	−0.615114	−	0.788438i	$-0.710890\pi$
$919$	−37.2944	−1.23023	−0.615114	+	0.788438i	$0.710890\pi$
$920$	−10.2457	−0.337790
$921$	−0.784282	−0.0258430
$922$	−20.9277	−0.689217
$923$	18.7468	0.617060
$924$	0.981053	0.0322743
$925$	0.0641474	0.00210915
$926$	29.6302	0.973709
$927$	15.7033	0.515766
$928$	1.67278	0.0549118
$929$	−34.8481	−1.14333	−0.571664	−	0.820488i	$-0.693702\pi$
$929$	−34.8481	−1.14333	−0.571664	+	0.820488i	$0.693702\pi$
$930$	3.93570	0.129057
$931$	1.02204	0.0334961
$932$	14.5122	0.475362
$933$	4.33195	0.141822
$934$	−11.2148	−0.366960
$935$	−5.17076	−0.169102
$936$	−7.33655	−0.239803
$937$	60.5606	1.97843	0.989214	−	0.146474i	$-0.0467926\pi$
$937$	60.5606	1.97843	0.989214	+	0.146474i	$0.0467926\pi$
$938$	31.9541	1.04334
$939$	−1.77053	−0.0577791
$940$	26.1035	0.851403
$941$	45.4680	1.48222	0.741108	−	0.671386i	$-0.234301\pi$
$941$	45.4680	1.48222	0.741108	+	0.671386i	$0.234301\pi$
$942$	2.41785	0.0787777
$943$	25.7770	0.839414
$944$	−2.83155	−0.0921592
$945$	−13.2666	−0.431563
$946$	6.26065	0.203551
$947$	34.0813	1.10749	0.553747	−	0.832685i	$-0.313197\pi$
$947$	34.0813	1.10749	0.553747	+	0.832685i	$0.313197\pi$
$948$	−2.71646	−0.0882264
$949$	23.4376	0.760818
$950$	0.406718	0.0131957
$951$	7.22236	0.234201
$952$	−6.25288	−0.202657
$953$	−8.06685	−0.261311	−0.130655	−	0.991428i	$-0.541708\pi$
$953$	−8.06685	−0.261311	−0.130655	+	0.991428i	$0.541708\pi$
$954$	12.3535	0.399961
$955$	−27.4014	−0.886687
$956$	−7.54852	−0.244137
$957$	0.589660	0.0190610
$958$	−10.6588	−0.344371
$959$	1.57889	0.0509850
$960$	0.811273	0.0261837
$961$	−7.46522	−0.240813
$962$	0.551480	0.0177804
$963$	−48.9549	−1.57755
$964$	14.0384	0.452145
$965$	−23.4033	−0.753380
$966$	−4.36746	−0.140521
$967$	23.2739	0.748437	0.374218	−	0.927341i	$-0.377911\pi$
$967$	23.2739	0.748437	0.374218	+	0.927341i	$0.377911\pi$
$968$	1.00000	0.0321412
$969$	1.08546	0.0348700
$970$	−21.5561	−0.692125
$971$	45.7461	1.46806	0.734031	−	0.679116i	$-0.237637\pi$
$971$	45.7461	1.46806	0.734031	+	0.679116i	$0.237637\pi$
$972$	−8.99739	−0.288591
$973$	−33.3874	−1.07035
$974$	−0.382018	−0.0122406
$975$	−0.266868	−0.00854660
$976$	11.9152	0.381396
$977$	−39.3189	−1.25792	−0.628962	−	0.777436i	$-0.716520\pi$
$977$	−39.3189	−1.25792	−0.628962	+	0.777436i	$0.716520\pi$
$978$	−4.72811	−0.151188
$979$	−4.26928	−0.136447
$980$	−1.71622	−0.0548226
$981$	−22.8485	−0.729497
$982$	10.3902	0.331566
$983$	35.4181	1.12966	0.564831	−	0.825207i	$-0.308942\pi$
$983$	35.4181	1.12966	0.564831	+	0.825207i	$0.308942\pi$
$984$	−2.04107	−0.0650669
$985$	2.30147	0.0733308
$986$	−3.75828	−0.119688
$987$	11.1272	0.354183
$988$	3.49658	0.111241
$989$	−27.8712	−0.886252
$990$	−6.61843	−0.210347
$991$	21.6368	0.687315	0.343657	−	0.939095i	$-0.388334\pi$
$991$	21.6368	0.687315	0.343657	+	0.939095i	$0.388334\pi$
$992$	4.85127	0.154028
$993$	−10.7668	−0.341673
$994$	20.4511	0.648669
$995$	−13.2188	−0.419065
$996$	−2.90506	−0.0920504
$997$	−26.0434	−0.824804	−0.412402	−	0.911002i	$-0.635310\pi$
$997$	−26.0434	−0.824804	−0.412402	+	0.911002i	$0.635310\pi$
$998$	−30.0476	−0.951141
$999$	0.447726	0.0141654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.f.1.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.f.1.10	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.352502 q^{3} +1.00000 q^{4} -2.30147 q^{5} -0.352502 q^{6} +2.78311 q^{7} +1.00000 q^{8} -2.87574 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.352502 q^{3} +1.00000 q^{4} -2.30147 q^{5} -0.352502 q^{6} +2.78311 q^{7} +1.00000 q^{8} -2.87574 q^{9} -2.30147 q^{10} -1.00000 q^{11} -0.352502 q^{12} +2.55119 q^{13} +2.78311 q^{14} +0.811273 q^{15} +1.00000 q^{16} -2.24672 q^{17} -2.87574 q^{18} +1.37057 q^{19} -2.30147 q^{20} -0.981053 q^{21} -1.00000 q^{22} +4.45181 q^{23} -0.352502 q^{24} +0.296751 q^{25} +2.55119 q^{26} +2.07121 q^{27} +2.78311 q^{28} +1.67278 q^{29} +0.811273 q^{30} +4.85127 q^{31} +1.00000 q^{32} +0.352502 q^{33} -2.24672 q^{34} -6.40524 q^{35} -2.87574 q^{36} +0.216166 q^{37} +1.37057 q^{38} -0.899299 q^{39} -2.30147 q^{40} +5.79023 q^{41} -0.981053 q^{42} -6.26065 q^{43} -1.00000 q^{44} +6.61843 q^{45} +4.45181 q^{46} -11.3421 q^{47} -0.352502 q^{48} +0.745706 q^{49} +0.296751 q^{50} +0.791975 q^{51} +2.55119 q^{52} -4.29578 q^{53} +2.07121 q^{54} +2.30147 q^{55} +2.78311 q^{56} -0.483130 q^{57} +1.67278 q^{58} -2.83155 q^{59} +0.811273 q^{60} +11.9152 q^{61} +4.85127 q^{62} -8.00351 q^{63} +1.00000 q^{64} -5.87147 q^{65} +0.352502 q^{66} +11.4814 q^{67} -2.24672 q^{68} -1.56927 q^{69} -6.40524 q^{70} +7.34829 q^{71} -2.87574 q^{72} +9.18695 q^{73} +0.216166 q^{74} -0.104605 q^{75} +1.37057 q^{76} -2.78311 q^{77} -0.899299 q^{78} +7.70621 q^{79} -2.30147 q^{80} +7.89712 q^{81} +5.79023 q^{82} +8.24125 q^{83} -0.981053 q^{84} +5.17076 q^{85} -6.26065 q^{86} -0.589660 q^{87} -1.00000 q^{88} +4.26928 q^{89} +6.61843 q^{90} +7.10023 q^{91} +4.45181 q^{92} -1.71008 q^{93} -11.3421 q^{94} -3.15433 q^{95} -0.352502 q^{96} +9.36625 q^{97} +0.745706 q^{98} +2.87574 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9	\( 24 q + 24 q^{2} + 8 q^{3} + 24 q^{4} + 8 q^{6} + 11 q^{7} + 24 q^{8} + 28 q^{9} - 24 q^{11} + 8 q^{12} + 9 q^{13} + 11 q^{14} + 6 q^{15} + 24 q^{16} - q^{17} + 28 q^{18} + 35 q^{19} + 21 q^{21} - 24 q^{22} + 13 q^{23} + 8 q^{24} + 38 q^{25} + 9 q^{26} + 23 q^{27} + 11 q^{28} + 15 q^{29} + 6 q^{30} + 31 q^{31} + 24 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 28 q^{36} + 13 q^{37} + 35 q^{38} + 31 q^{39} + 16 q^{41} + 21 q^{42} + 35 q^{43} - 24 q^{44} + 13 q^{45} + 13 q^{46} + 46 q^{47} + 8 q^{48} + 55 q^{49} + 38 q^{50} + 18 q^{51} + 9 q^{52} + 6 q^{53} + 23 q^{54} + 11 q^{56} + 18 q^{57} + 15 q^{58} + 13 q^{59} + 6 q^{60} + 60 q^{61} + 31 q^{62} + 52 q^{63} + 24 q^{64} - 9 q^{65} - 8 q^{66} + 28 q^{67} - q^{68} + 21 q^{69} + 28 q^{70} + 10 q^{71} + 28 q^{72} + 3 q^{73} + 13 q^{74} + 48 q^{75} + 35 q^{76} - 11 q^{77} + 31 q^{78} + 47 q^{79} + 16 q^{81} + 16 q^{82} + 66 q^{83} + 21 q^{84} + 37 q^{85} + 35 q^{86} + 34 q^{87} - 24 q^{88} - 5 q^{89} + 13 q^{90} + q^{91} + 13 q^{92} - 16 q^{93} + 46 q^{94} + 9 q^{95} + 8 q^{96} + 24 q^{97} + 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q + 24 * q^2 + 8 * q^3 + 24 * q^4 + 8 * q^6 + 11 * q^7 + 24 * q^8 + 28 * q^9 - 24 * q^11 + 8 * q^12 + 9 * q^13 + 11 * q^14 + 6 * q^15 + 24 * q^16 - q^17 + 28 * q^18 + 35 * q^19 + 21 * q^21 - 24 * q^22 + 13 * q^23 + 8 * q^24 + 38 * q^25 + 9 * q^26 + 23 * q^27 + 11 * q^28 + 15 * q^29 + 6 * q^30 + 31 * q^31 + 24 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 28 * q^36 + 13 * q^37 + 35 * q^38 + 31 * q^39 + 16 * q^41 + 21 * q^42 + 35 * q^43 - 24 * q^44 + 13 * q^45 + 13 * q^46 + 46 * q^47 + 8 * q^48 + 55 * q^49 + 38 * q^50 + 18 * q^51 + 9 * q^52 + 6 * q^53 + 23 * q^54 + 11 * q^56 + 18 * q^57 + 15 * q^58 + 13 * q^59 + 6 * q^60 + 60 * q^61 + 31 * q^62 + 52 * q^63 + 24 * q^64 - 9 * q^65 - 8 * q^66 + 28 * q^67 - q^68 + 21 * q^69 + 28 * q^70 + 10 * q^71 + 28 * q^72 + 3 * q^73 + 13 * q^74 + 48 * q^75 + 35 * q^76 - 11 * q^77 + 31 * q^78 + 47 * q^79 + 16 * q^81 + 16 * q^82 + 66 * q^83 + 21 * q^84 + 37 * q^85 + 35 * q^86 + 34 * q^87 - 24 * q^88 - 5 * q^89 + 13 * q^90 + q^91 + 13 * q^92 - 16 * q^93 + 46 * q^94 + 9 * q^95 + 8 * q^96 + 24 * q^97 + 55 * q^98 - 28 * q^99

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