LMFDB - Embedded newform 4029.2.a.k.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.719826 q^{2} +1.00000 q^{3} -1.48185 q^{4} +1.82945 q^{5} -0.719826 q^{6} +0.414755 q^{7} +2.50633 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.719826 q^{2} +1.00000 q^{3} -1.48185 q^{4} +1.82945 q^{5} -0.719826 q^{6} +0.414755 q^{7} +2.50633 q^{8} +1.00000 q^{9} -1.31688 q^{10} -2.75956 q^{11} -1.48185 q^{12} +0.245564 q^{13} -0.298551 q^{14} +1.82945 q^{15} +1.15958 q^{16} +1.00000 q^{17} -0.719826 q^{18} +0.386626 q^{19} -2.71096 q^{20} +0.414755 q^{21} +1.98641 q^{22} +6.58248 q^{23} +2.50633 q^{24} -1.65313 q^{25} -0.176764 q^{26} +1.00000 q^{27} -0.614604 q^{28} -0.775585 q^{29} -1.31688 q^{30} +2.70422 q^{31} -5.84735 q^{32} -2.75956 q^{33} -0.719826 q^{34} +0.758771 q^{35} -1.48185 q^{36} +7.95789 q^{37} -0.278304 q^{38} +0.245564 q^{39} +4.58519 q^{40} -4.65488 q^{41} -0.298551 q^{42} -1.77108 q^{43} +4.08926 q^{44} +1.82945 q^{45} -4.73824 q^{46} +1.23213 q^{47} +1.15958 q^{48} -6.82798 q^{49} +1.18997 q^{50} +1.00000 q^{51} -0.363890 q^{52} +3.82181 q^{53} -0.719826 q^{54} -5.04847 q^{55} +1.03951 q^{56} +0.386626 q^{57} +0.558286 q^{58} +2.36846 q^{59} -2.71096 q^{60} +5.98058 q^{61} -1.94657 q^{62} +0.414755 q^{63} +1.88991 q^{64} +0.449247 q^{65} +1.98641 q^{66} +9.15259 q^{67} -1.48185 q^{68} +6.58248 q^{69} -0.546183 q^{70} -3.23725 q^{71} +2.50633 q^{72} -3.86850 q^{73} -5.72829 q^{74} -1.65313 q^{75} -0.572922 q^{76} -1.14454 q^{77} -0.176764 q^{78} +1.00000 q^{79} +2.12139 q^{80} +1.00000 q^{81} +3.35070 q^{82} +15.9173 q^{83} -0.614604 q^{84} +1.82945 q^{85} +1.27487 q^{86} -0.775585 q^{87} -6.91637 q^{88} -0.214602 q^{89} -1.31688 q^{90} +0.101849 q^{91} -9.75425 q^{92} +2.70422 q^{93} -0.886922 q^{94} +0.707311 q^{95} -5.84735 q^{96} +18.6375 q^{97} +4.91496 q^{98} -2.75956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	−0.719826	−0.508994	−0.254497	−	0.967074i	$-0.581910\pi$
$2$	−0.719826	−0.508994	−0.254497	+	0.967074i	$0.581910\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.48185	−0.740925
$5$	1.82945	0.818153	0.409076	−	0.912500i	$-0.365851\pi$
$5$	1.82945	0.818153	0.409076	+	0.912500i	$0.365851\pi$
$6$	−0.719826	−0.293868
$7$	0.414755	0.156762	0.0783812	−	0.996923i	$-0.475025\pi$
$7$	0.414755	0.156762	0.0783812	+	0.996923i	$0.475025\pi$
$8$	2.50633	0.886120
$9$	1.00000	0.333333
$10$	−1.31688	−0.416435
$11$	−2.75956	−0.832040	−0.416020	−	0.909356i	$-0.636575\pi$
$11$	−2.75956	−0.832040	−0.416020	+	0.909356i	$0.636575\pi$
$12$	−1.48185	−0.427773
$13$	0.245564	0.0681073	0.0340536	−	0.999420i	$-0.489158\pi$
$13$	0.245564	0.0681073	0.0340536	+	0.999420i	$0.489158\pi$
$14$	−0.298551	−0.0797911
$15$	1.82945	0.472361
$16$	1.15958	0.289895
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.719826	−0.169665
$19$	0.386626	0.0886981	0.0443491	−	0.999016i	$-0.485879\pi$
$19$	0.386626	0.0886981	0.0443491	+	0.999016i	$0.485879\pi$
$20$	−2.71096	−0.606190
$21$	0.414755	0.0905069
$22$	1.98641	0.423503
$23$	6.58248	1.37254	0.686271	−	0.727346i	$-0.259246\pi$
$23$	6.58248	1.37254	0.686271	+	0.727346i	$0.259246\pi$
$24$	2.50633	0.511602
$25$	−1.65313	−0.330626
$26$	−0.176764	−0.0346662
$27$	1.00000	0.192450
$28$	−0.614604	−0.116149
$29$	−0.775585	−0.144022	−0.0720112	−	0.997404i	$-0.522942\pi$
$29$	−0.775585	−0.144022	−0.0720112	+	0.997404i	$0.522942\pi$
$30$	−1.31688	−0.240429
$31$	2.70422	0.485693	0.242846	−	0.970065i	$-0.421919\pi$
$31$	2.70422	0.485693	0.242846	+	0.970065i	$0.421919\pi$
$32$	−5.84735	−1.03368
$33$	−2.75956	−0.480378
$34$	−0.719826	−0.123449
$35$	0.758771	0.128256
$36$	−1.48185	−0.246975
$37$	7.95789	1.30827	0.654134	−	0.756379i	$-0.273033\pi$
$37$	7.95789	1.30827	0.654134	+	0.756379i	$0.273033\pi$
$38$	−0.278304	−0.0451468
$39$	0.245564	0.0393218
$40$	4.58519	0.724982
$41$	−4.65488	−0.726970	−0.363485	−	0.931600i	$-0.618413\pi$
$41$	−4.65488	−0.726970	−0.363485	+	0.931600i	$0.618413\pi$
$42$	−0.298551	−0.0460674
$43$	−1.77108	−0.270088	−0.135044	−	0.990840i	$-0.543118\pi$
$43$	−1.77108	−0.270088	−0.135044	+	0.990840i	$0.543118\pi$
$44$	4.08926	0.616479
$45$	1.82945	0.272718
$46$	−4.73824	−0.698615
$47$	1.23213	0.179725	0.0898626	−	0.995954i	$-0.471357\pi$
$47$	1.23213	0.179725	0.0898626	+	0.995954i	$0.471357\pi$
$48$	1.15958	0.167371
$49$	−6.82798	−0.975426
$50$	1.18997	0.168287
$51$	1.00000	0.140028
$52$	−0.363890	−0.0504624
$53$	3.82181	0.524966	0.262483	−	0.964937i	$-0.415459\pi$
$53$	3.82181	0.524966	0.262483	+	0.964937i	$0.415459\pi$
$54$	−0.719826	−0.0979559
$55$	−5.04847	−0.680736
$56$	1.03951	0.138910
$57$	0.386626	0.0512099
$58$	0.558286	0.0733066
$59$	2.36846	0.308348	0.154174	−	0.988044i	$-0.450728\pi$
$59$	2.36846	0.308348	0.154174	+	0.988044i	$0.450728\pi$
$60$	−2.71096	−0.349984
$61$	5.98058	0.765735	0.382867	−	0.923803i	$-0.374937\pi$
$61$	5.98058	0.765735	0.382867	+	0.923803i	$0.374937\pi$
$62$	−1.94657	−0.247215
$63$	0.414755	0.0522542
$64$	1.88991	0.236239
$65$	0.449247	0.0557222
$66$	1.98641	0.244510
$67$	9.15259	1.11817	0.559083	−	0.829111i	$-0.311153\pi$
$67$	9.15259	1.11817	0.559083	+	0.829111i	$0.311153\pi$
$68$	−1.48185	−0.179701
$69$	6.58248	0.792437
$70$	−0.546183	−0.0652813
$71$	−3.23725	−0.384191	−0.192095	−	0.981376i	$-0.561528\pi$
$71$	−3.23725	−0.384191	−0.192095	+	0.981376i	$0.561528\pi$
$72$	2.50633	0.295373
$73$	−3.86850	−0.452774	−0.226387	−	0.974037i	$-0.572691\pi$
$73$	−3.86850	−0.452774	−0.226387	+	0.974037i	$0.572691\pi$
$74$	−5.72829	−0.665901
$75$	−1.65313	−0.190887
$76$	−0.572922	−0.0657187
$77$	−1.14454	−0.130433
$78$	−0.176764	−0.0200145
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	2.12139	0.237179
$81$	1.00000	0.111111
$82$	3.35070	0.370023
$83$	15.9173	1.74715	0.873574	−	0.486692i	$-0.161796\pi$
$83$	15.9173	1.74715	0.873574	+	0.486692i	$0.161796\pi$
$84$	−0.614604	−0.0670588
$85$	1.82945	0.198431
$86$	1.27487	0.137473
$87$	−0.775585	−0.0831514
$88$	−6.91637	−0.737287
$89$	−0.214602	−0.0227478	−0.0113739	−	0.999935i	$-0.503621\pi$
$89$	−0.214602	−0.0227478	−0.0113739	+	0.999935i	$0.503621\pi$
$90$	−1.31688	−0.138812
$91$	0.101849	0.0106767
$92$	−9.75425	−1.01695
$93$	2.70422	0.280415
$94$	−0.886922	−0.0914790
$95$	0.707311	0.0725686
$96$	−5.84735	−0.596793
$97$	18.6375	1.89235	0.946174	−	0.323660i	$-0.104913\pi$
$97$	18.6375	1.89235	0.946174	+	0.323660i	$0.104913\pi$
$98$	4.91496	0.496486
$99$	−2.75956	−0.277347
$100$	2.44969	0.244969
$101$	4.52955	0.450707	0.225353	−	0.974277i	$-0.427646\pi$
$101$	4.52955	0.450707	0.225353	+	0.974277i	$0.427646\pi$
$102$	−0.719826	−0.0712734
$103$	−4.82523	−0.475444	−0.237722	−	0.971333i	$-0.576401\pi$
$103$	−4.82523	−0.475444	−0.237722	+	0.971333i	$0.576401\pi$
$104$	0.615464	0.0603513
$105$	0.758771	0.0740484
$106$	−2.75104	−0.267204
$107$	−17.0658	−1.64981	−0.824907	−	0.565269i	$-0.808772\pi$
$107$	−17.0658	−1.64981	−0.824907	+	0.565269i	$0.808772\pi$
$108$	−1.48185	−0.142591
$109$	16.0479	1.53711	0.768556	−	0.639782i	$-0.220976\pi$
$109$	16.0479	1.53711	0.768556	+	0.639782i	$0.220976\pi$
$110$	3.63402	0.346490
$111$	7.95789	0.755329
$112$	0.480942	0.0454447
$113$	2.71994	0.255870	0.127935	−	0.991783i	$-0.459165\pi$
$113$	2.71994	0.255870	0.127935	+	0.991783i	$0.459165\pi$
$114$	−0.278304	−0.0260655
$115$	12.0423	1.12295
$116$	1.14930	0.106710
$117$	0.245564	0.0227024
$118$	−1.70488	−0.156947
$119$	0.414755	0.0380205
$120$	4.58519	0.418568
$121$	−3.38481	−0.307710
$122$	−4.30498	−0.389754
$123$	−4.65488	−0.419717
$124$	−4.00725	−0.359862
$125$	−12.1715	−1.08866
$126$	−0.298551	−0.0265970
$127$	9.03607	0.801821	0.400911	−	0.916117i	$-0.368694\pi$
$127$	9.03607	0.801821	0.400911	+	0.916117i	$0.368694\pi$
$128$	10.3343	0.913431
$129$	−1.77108	−0.155935
$130$	−0.323379	−0.0283622
$131$	−10.2707	−0.897360	−0.448680	−	0.893693i	$-0.648106\pi$
$131$	−10.2707	−0.897360	−0.448680	+	0.893693i	$0.648106\pi$
$132$	4.08926	0.355924
$133$	0.160355	0.0139045
$134$	−6.58827	−0.569140
$135$	1.82945	0.157454
$136$	2.50633	0.214916
$137$	4.90565	0.419118	0.209559	−	0.977796i	$-0.432797\pi$
$137$	4.90565	0.419118	0.209559	+	0.977796i	$0.432797\pi$
$138$	−4.73824	−0.403346
$139$	−14.1097	−1.19677	−0.598386	−	0.801208i	$-0.704191\pi$
$139$	−14.1097	−1.19677	−0.598386	+	0.801208i	$0.704191\pi$
$140$	−1.12438	−0.0950279
$141$	1.23213	0.103764
$142$	2.33026	0.195551
$143$	−0.677651	−0.0566680
$144$	1.15958	0.0966318
$145$	−1.41889	−0.117832
$146$	2.78465	0.230459
$147$	−6.82798	−0.563162
$148$	−11.7924	−0.969329
$149$	11.9807	0.981499	0.490750	−	0.871301i	$-0.336723\pi$
$149$	11.9807	0.981499	0.490750	+	0.871301i	$0.336723\pi$
$150$	1.18997	0.0971603
$151$	7.94967	0.646935	0.323467	−	0.946239i	$-0.395151\pi$
$151$	7.94967	0.646935	0.323467	+	0.946239i	$0.395151\pi$
$152$	0.969011	0.0785972
$153$	1.00000	0.0808452
$154$	0.823871	0.0663894
$155$	4.94723	0.397371
$156$	−0.363890	−0.0291345
$157$	−8.53506	−0.681172	−0.340586	−	0.940213i	$-0.610625\pi$
$157$	−8.53506	−0.681172	−0.340586	+	0.940213i	$0.610625\pi$
$158$	−0.719826	−0.0572663
$159$	3.82181	0.303089
$160$	−10.6974	−0.845704
$161$	2.73011	0.215163
$162$	−0.719826	−0.0565549
$163$	8.76964	0.686891	0.343446	−	0.939173i	$-0.388406\pi$
$163$	8.76964	0.686891	0.343446	+	0.939173i	$0.388406\pi$
$164$	6.89784	0.538631
$165$	−5.04847	−0.393023
$166$	−11.4577	−0.889287
$167$	6.48978	0.502194	0.251097	−	0.967962i	$-0.419209\pi$
$167$	6.48978	0.502194	0.251097	+	0.967962i	$0.419209\pi$
$168$	1.03951	0.0802000
$169$	−12.9397	−0.995361
$170$	−1.31688	−0.101000
$171$	0.386626	0.0295660
$172$	2.62448	0.200115
$173$	7.89825	0.600493	0.300246	−	0.953862i	$-0.402931\pi$
$173$	7.89825	0.600493	0.300246	+	0.953862i	$0.402931\pi$
$174$	0.558286	0.0423236
$175$	−0.685643	−0.0518298
$176$	−3.19994	−0.241205
$177$	2.36846	0.178025
$178$	0.154476	0.0115785
$179$	4.81548	0.359926	0.179963	−	0.983673i	$-0.442402\pi$
$179$	4.81548	0.359926	0.179963	+	0.983673i	$0.442402\pi$
$180$	−2.71096	−0.202063
$181$	−13.9833	−1.03937	−0.519686	−	0.854357i	$-0.673951\pi$
$181$	−13.9833	−1.03937	−0.519686	+	0.854357i	$0.673951\pi$
$182$	−0.0733135	−0.00543436
$183$	5.98058	0.442097
$184$	16.4978	1.21624
$185$	14.5585	1.07036
$186$	−1.94657	−0.142729
$187$	−2.75956	−0.201799
$188$	−1.82584	−0.133163
$189$	0.414755	0.0301690
$190$	−0.509141	−0.0369370
$191$	−12.1242	−0.877280	−0.438640	−	0.898663i	$-0.644540\pi$
$191$	−12.1242	−0.877280	−0.438640	+	0.898663i	$0.644540\pi$
$192$	1.88991	0.136393
$193$	−2.70545	−0.194743	−0.0973713	−	0.995248i	$-0.531043\pi$
$193$	−2.70545	−0.194743	−0.0973713	+	0.995248i	$0.531043\pi$
$194$	−13.4157	−0.963193
$195$	0.449247	0.0321712
$196$	10.1180	0.722717
$197$	8.78690	0.626041	0.313020	−	0.949746i	$-0.398659\pi$
$197$	8.78690	0.626041	0.313020	+	0.949746i	$0.398659\pi$
$198$	1.98641	0.141168
$199$	7.23231	0.512685	0.256343	−	0.966586i	$-0.417482\pi$
$199$	7.23231	0.512685	0.256343	+	0.966586i	$0.417482\pi$
$200$	−4.14328	−0.292974
$201$	9.15259	0.645574
$202$	−3.26048	−0.229407
$203$	−0.321677	−0.0225773
$204$	−1.48185	−0.103750
$205$	−8.51585	−0.594773
$206$	3.47332	0.241998
$207$	6.58248	0.457514
$208$	0.284752	0.0197440
$209$	−1.06692	−0.0738004
$210$	−0.546183	−0.0376902
$211$	−25.5292	−1.75750	−0.878750	−	0.477283i	$-0.841622\pi$
$211$	−25.5292	−1.75750	−0.878750	+	0.477283i	$0.841622\pi$
$212$	−5.66335	−0.388961
$213$	−3.23725	−0.221813
$214$	12.2844	0.839745
$215$	−3.24010	−0.220973
$216$	2.50633	0.170534
$217$	1.12159	0.0761384
$218$	−11.5517	−0.782381
$219$	−3.86850	−0.261409
$220$	7.48108	0.504374
$221$	0.245564	0.0165184
$222$	−5.72829	−0.384458
$223$	17.2162	1.15288	0.576441	−	0.817139i	$-0.304441\pi$
$223$	17.2162	1.15288	0.576441	+	0.817139i	$0.304441\pi$
$224$	−2.42522	−0.162041
$225$	−1.65313	−0.110209
$226$	−1.95788	−0.130236
$227$	18.3239	1.21620	0.608099	−	0.793862i	$-0.291933\pi$
$227$	18.3239	1.21620	0.608099	+	0.793862i	$0.291933\pi$
$228$	−0.572922	−0.0379427
$229$	−24.4035	−1.61263	−0.806315	−	0.591486i	$-0.798542\pi$
$229$	−24.4035	−1.61263	−0.806315	+	0.591486i	$0.798542\pi$
$230$	−8.66835	−0.571574
$231$	−1.14454	−0.0753053
$232$	−1.94387	−0.127621
$233$	24.0462	1.57532	0.787659	−	0.616112i	$-0.211293\pi$
$233$	24.0462	1.57532	0.787659	+	0.616112i	$0.211293\pi$
$234$	−0.176764	−0.0115554
$235$	2.25412	0.147043
$236$	−3.50971	−0.228462
$237$	1.00000	0.0649570
$238$	−0.298551	−0.0193522
$239$	22.5991	1.46181	0.730906	−	0.682478i	$-0.239098\pi$
$239$	22.5991	1.46181	0.730906	+	0.682478i	$0.239098\pi$
$240$	2.12139	0.136935
$241$	25.1640	1.62095	0.810477	−	0.585770i	$-0.199208\pi$
$241$	25.1640	1.62095	0.810477	+	0.585770i	$0.199208\pi$
$242$	2.43647	0.156622
$243$	1.00000	0.0641500
$244$	−8.86233	−0.567352
$245$	−12.4914	−0.798047
$246$	3.35070	0.213633
$247$	0.0949416	0.00604099
$248$	6.77767	0.430382
$249$	15.9173	1.00872
$250$	8.76139	0.554119
$251$	−19.9536	−1.25946	−0.629729	−	0.776815i	$-0.716834\pi$
$251$	−19.9536	−1.25946	−0.629729	+	0.776815i	$0.716834\pi$
$252$	−0.614604	−0.0387164
$253$	−18.1648	−1.14201
$254$	−6.50439	−0.408122
$255$	1.82945	0.114564
$256$	−11.2187	−0.701170
$257$	6.37818	0.397860	0.198930	−	0.980014i	$-0.436253\pi$
$257$	6.37818	0.397860	0.198930	+	0.980014i	$0.436253\pi$
$258$	1.27487	0.0793701
$259$	3.30057	0.205087
$260$	−0.665716	−0.0412860
$261$	−0.775585	−0.0480075
$262$	7.39315	0.456751
$263$	28.4679	1.75541	0.877704	−	0.479203i	$-0.159074\pi$
$263$	28.4679	1.75541	0.877704	+	0.479203i	$0.159074\pi$
$264$	−6.91637	−0.425673
$265$	6.99179	0.429502
$266$	−0.115428	−0.00707732
$267$	−0.214602	−0.0131334
$268$	−13.5628	−0.828478
$269$	16.5425	1.00861	0.504307	−	0.863524i	$-0.331748\pi$
$269$	16.5425	1.00861	0.504307	+	0.863524i	$0.331748\pi$
$270$	−1.31688	−0.0801429
$271$	24.4858	1.48741	0.743705	−	0.668508i	$-0.233067\pi$
$271$	24.4858	1.48741	0.743705	+	0.668508i	$0.233067\pi$
$272$	1.15958	0.0703100
$273$	0.101849	0.00616418
$274$	−3.53121	−0.213328
$275$	4.56192	0.275094
$276$	−9.75425	−0.587137
$277$	2.17957	0.130958	0.0654789	−	0.997854i	$-0.479143\pi$
$277$	2.17957	0.130958	0.0654789	+	0.997854i	$0.479143\pi$
$278$	10.1566	0.609149
$279$	2.70422	0.161898
$280$	1.90173	0.113650
$281$	−2.91692	−0.174009	−0.0870043	−	0.996208i	$-0.527729\pi$
$281$	−2.91692	−0.174009	−0.0870043	+	0.996208i	$0.527729\pi$
$282$	−0.886922	−0.0528154
$283$	−9.99042	−0.593869	−0.296934	−	0.954898i	$-0.595964\pi$
$283$	−9.99042	−0.593869	−0.296934	+	0.954898i	$0.595964\pi$
$284$	4.79712	0.284657
$285$	0.707311	0.0418975
$286$	0.487790	0.0288437
$287$	−1.93063	−0.113962
$288$	−5.84735	−0.344558
$289$	1.00000	0.0588235
$290$	1.02135	0.0599760
$291$	18.6375	1.09255
$292$	5.73254	0.335471
$293$	5.35560	0.312877	0.156439	−	0.987688i	$-0.449999\pi$
$293$	5.35560	0.312877	0.156439	+	0.987688i	$0.449999\pi$
$294$	4.91496	0.286646
$295$	4.33297	0.252275
$296$	19.9451	1.15928
$297$	−2.75956	−0.160126
$298$	−8.62404	−0.499577
$299$	1.61642	0.0934801
$300$	2.44969	0.141433
$301$	−0.734565	−0.0423396
$302$	−5.72238	−0.329286
$303$	4.52955	0.260216
$304$	0.448325	0.0257132
$305$	10.9411	0.626488
$306$	−0.719826	−0.0411497
$307$	20.0480	1.14420	0.572099	−	0.820185i	$-0.306129\pi$
$307$	20.0480	1.14420	0.572099	+	0.820185i	$0.306129\pi$
$308$	1.69604	0.0966408
$309$	−4.82523	−0.274498
$310$	−3.56114	−0.202259
$311$	14.8123	0.839931	0.419965	−	0.907540i	$-0.362042\pi$
$311$	14.8123	0.839931	0.419965	+	0.907540i	$0.362042\pi$
$312$	0.615464	0.0348438
$313$	2.76838	0.156478	0.0782390	−	0.996935i	$-0.475070\pi$
$313$	2.76838	0.156478	0.0782390	+	0.996935i	$0.475070\pi$
$314$	6.14376	0.346712
$315$	0.758771	0.0427519
$316$	−1.48185	−0.0833606
$317$	18.8127	1.05662	0.528312	−	0.849050i	$-0.322825\pi$
$317$	18.8127	1.05662	0.528312	+	0.849050i	$0.322825\pi$
$318$	−2.75104	−0.154271
$319$	2.14028	0.119832
$320$	3.45749	0.193280
$321$	−17.0658	−0.952520
$322$	−1.96521	−0.109517
$323$	0.386626	0.0215125
$324$	−1.48185	−0.0823250
$325$	−0.405950	−0.0225180
$326$	−6.31262	−0.349623
$327$	16.0479	0.887452
$328$	−11.6667	−0.644183
$329$	0.511033	0.0281742
$330$	3.63402	0.200046
$331$	−23.3912	−1.28569	−0.642847	−	0.765994i	$-0.722247\pi$
$331$	−23.3912	−1.28569	−0.642847	+	0.765994i	$0.722247\pi$
$332$	−23.5870	−1.29451
$333$	7.95789	0.436089
$334$	−4.67151	−0.255614
$335$	16.7442	0.914831
$336$	0.480942	0.0262375
$337$	−11.9605	−0.651529	−0.325765	−	0.945451i	$-0.605622\pi$
$337$	−11.9605	−0.651529	−0.325765	+	0.945451i	$0.605622\pi$
$338$	9.31433	0.506633
$339$	2.71994	0.147727
$340$	−2.71096	−0.147023
$341$	−7.46248	−0.404116
$342$	−0.278304	−0.0150489
$343$	−5.73522	−0.309673
$344$	−4.43892	−0.239330
$345$	12.0423	0.648335
$346$	−5.68537	−0.305647
$347$	−11.1748	−0.599892	−0.299946	−	0.953956i	$-0.596969\pi$
$347$	−11.1748	−0.599892	−0.299946	+	0.953956i	$0.596969\pi$
$348$	1.14930	0.0616090
$349$	34.0195	1.82102	0.910511	−	0.413485i	$-0.135689\pi$
$349$	34.0195	1.82102	0.910511	+	0.413485i	$0.135689\pi$
$350$	0.493544	0.0263810
$351$	0.245564	0.0131073
$352$	16.1361	0.860059
$353$	−26.9914	−1.43661	−0.718303	−	0.695731i	$-0.755081\pi$
$353$	−26.9914	−1.43661	−0.718303	+	0.695731i	$0.755081\pi$
$354$	−1.70488	−0.0906134
$355$	−5.92237	−0.314327
$356$	0.318009	0.0168544
$357$	0.414755	0.0219511
$358$	−3.46631	−0.183200
$359$	28.5330	1.50591	0.752957	−	0.658069i	$-0.228627\pi$
$359$	28.5330	1.50591	0.752957	+	0.658069i	$0.228627\pi$
$360$	4.58519	0.241661
$361$	−18.8505	−0.992133
$362$	10.0656	0.529034
$363$	−3.38481	−0.177656
$364$	−0.150925	−0.00791061
$365$	−7.07721	−0.370438
$366$	−4.30498	−0.225025
$367$	34.1865	1.78452	0.892261	−	0.451521i	$-0.149118\pi$
$367$	34.1865	1.78452	0.892261	+	0.451521i	$0.149118\pi$
$368$	7.63292	0.397894
$369$	−4.65488	−0.242323
$370$	−10.4796	−0.544808
$371$	1.58511	0.0822950
$372$	−4.00725	−0.207766
$373$	32.4578	1.68060	0.840300	−	0.542121i	$-0.182379\pi$
$373$	32.4578	1.68060	0.840300	+	0.542121i	$0.182379\pi$
$374$	1.98641	0.102715
$375$	−12.1715	−0.628535
$376$	3.08813	0.159258
$377$	−0.190456	−0.00980898
$378$	−0.298551	−0.0153558
$379$	−7.52217	−0.386388	−0.193194	−	0.981161i	$-0.561885\pi$
$379$	−7.52217	−0.386388	−0.193194	+	0.981161i	$0.561885\pi$
$380$	−1.04813	−0.0537679
$381$	9.03607	0.462932
$382$	8.72735	0.446530
$383$	−3.83802	−0.196113	−0.0980567	−	0.995181i	$-0.531263\pi$
$383$	−3.83802	−0.196113	−0.0980567	+	0.995181i	$0.531263\pi$
$384$	10.3343	0.527370
$385$	−2.09388	−0.106714
$386$	1.94745	0.0991228
$387$	−1.77108	−0.0900293
$388$	−27.6179	−1.40209
$389$	4.16830	0.211341	0.105671	−	0.994401i	$-0.466301\pi$
$389$	4.16830	0.211341	0.105671	+	0.994401i	$0.466301\pi$
$390$	−0.323379	−0.0163749
$391$	6.58248	0.332890
$392$	−17.1131	−0.864344
$393$	−10.2707	−0.518091
$394$	−6.32504	−0.318651
$395$	1.82945	0.0920494
$396$	4.08926	0.205493
$397$	−19.5347	−0.980417	−0.490209	−	0.871605i	$-0.663079\pi$
$397$	−19.5347	−0.980417	−0.490209	+	0.871605i	$0.663079\pi$
$398$	−5.20601	−0.260954
$399$	0.160355	0.00802779
$400$	−1.91694	−0.0958470
$401$	−24.1661	−1.20680	−0.603399	−	0.797440i	$-0.706187\pi$
$401$	−24.1661	−1.20680	−0.603399	+	0.797440i	$0.706187\pi$
$402$	−6.58827	−0.328593
$403$	0.664061	0.0330792
$404$	−6.71211	−0.333940
$405$	1.82945	0.0909059
$406$	0.231552	0.0114917
$407$	−21.9603	−1.08853
$408$	2.50633	0.124082
$409$	−20.9646	−1.03663	−0.518316	−	0.855189i	$-0.673441\pi$
$409$	−20.9646	−1.03663	−0.518316	+	0.855189i	$0.673441\pi$
$410$	6.12993	0.302736
$411$	4.90565	0.241978
$412$	7.15026	0.352268
$413$	0.982330	0.0483373
$414$	−4.73824	−0.232872
$415$	29.1198	1.42943
$416$	−1.43590	−0.0704008
$417$	−14.1097	−0.690956
$418$	0.767997	0.0375639
$419$	10.3584	0.506041	0.253021	−	0.967461i	$-0.418576\pi$
$419$	10.3584	0.506041	0.253021	+	0.967461i	$0.418576\pi$
$420$	−1.12438	−0.0548644
$421$	−38.6490	−1.88364	−0.941819	−	0.336121i	$-0.890885\pi$
$421$	−38.6490	−1.88364	−0.941819	+	0.336121i	$0.890885\pi$
$422$	18.3766	0.894557
$423$	1.23213	0.0599084
$424$	9.57870	0.465183
$425$	−1.65313	−0.0801886
$426$	2.33026	0.112901
$427$	2.48047	0.120039
$428$	25.2890	1.22239
$429$	−0.677651	−0.0327173
$430$	2.33231	0.112474
$431$	33.6185	1.61934	0.809672	−	0.586882i	$-0.199645\pi$
$431$	33.6185	1.61934	0.809672	+	0.586882i	$0.199645\pi$
$432$	1.15958	0.0557904
$433$	−3.19007	−0.153305	−0.0766525	−	0.997058i	$-0.524423\pi$
$433$	−3.19007	−0.153305	−0.0766525	+	0.997058i	$0.524423\pi$
$434$	−0.807349	−0.0387540
$435$	−1.41889	−0.0680306
$436$	−23.7806	−1.13889
$437$	2.54496	0.121742
$438$	2.78465	0.133056
$439$	−38.7166	−1.84784	−0.923921	−	0.382582i	$-0.875035\pi$
$439$	−38.7166	−1.84784	−0.923921	+	0.382582i	$0.875035\pi$
$440$	−12.6531	−0.603214
$441$	−6.82798	−0.325142
$442$	−0.176764	−0.00840779
$443$	0.0361883	0.00171936	0.000859680	−	1.00000i	$-0.499726\pi$
$443$	0.0361883	0.00171936	0.000859680		1.00000i	$0.499726\pi$
$444$	−11.7924	−0.559642
$445$	−0.392603	−0.0186112
$446$	−12.3927	−0.586810
$447$	11.9807	0.566669
$448$	0.783849	0.0370334
$449$	3.50805	0.165555	0.0827776	−	0.996568i	$-0.473621\pi$
$449$	3.50805	0.165555	0.0827776	+	0.996568i	$0.473621\pi$
$450$	1.18997	0.0560955
$451$	12.8454	0.604868
$452$	−4.03054	−0.189581
$453$	7.94967	0.373508
$454$	−13.1900	−0.619037
$455$	0.186327	0.00873515
$456$	0.969011	0.0453781
$457$	7.99570	0.374023	0.187011	−	0.982358i	$-0.440120\pi$
$457$	7.99570	0.374023	0.187011	+	0.982358i	$0.440120\pi$
$458$	17.5663	0.820819
$459$	1.00000	0.0466760
$460$	−17.8449	−0.832021
$461$	18.4814	0.860766	0.430383	−	0.902646i	$-0.358378\pi$
$461$	18.4814	0.860766	0.430383	+	0.902646i	$0.358378\pi$
$462$	0.823871	0.0383299
$463$	−26.8168	−1.24628	−0.623142	−	0.782109i	$-0.714144\pi$
$463$	−26.8168	−1.24628	−0.623142	+	0.782109i	$0.714144\pi$
$464$	−0.899354	−0.0417515
$465$	4.94723	0.229422
$466$	−17.3091	−0.801827
$467$	33.0861	1.53104	0.765522	−	0.643410i	$-0.222481\pi$
$467$	33.0861	1.53104	0.765522	+	0.643410i	$0.222481\pi$
$468$	−0.363890	−0.0168208
$469$	3.79608	0.175287
$470$	−1.62258	−0.0748438
$471$	−8.53506	−0.393275
$472$	5.93614	0.273233
$473$	4.88742	0.224724
$474$	−0.719826	−0.0330627
$475$	−0.639143	−0.0293259
$476$	−0.614604	−0.0281703
$477$	3.82181	0.174989
$478$	−16.2674	−0.744053
$479$	13.6621	0.624239	0.312120	−	0.950043i	$-0.398961\pi$
$479$	13.6621	0.624239	0.312120	+	0.950043i	$0.398961\pi$
$480$	−10.6974	−0.488268
$481$	1.95417	0.0891026
$482$	−18.1137	−0.825056
$483$	2.73011	0.124224
$484$	5.01578	0.227990
$485$	34.0962	1.54823
$486$	−0.719826	−0.0326520
$487$	−25.0693	−1.13600	−0.568000	−	0.823029i	$-0.692283\pi$
$487$	−25.0693	−1.13600	−0.568000	+	0.823029i	$0.692283\pi$
$488$	14.9893	0.678533
$489$	8.76964	0.396577
$490$	8.99164	0.406201
$491$	29.1872	1.31720	0.658600	−	0.752493i	$-0.271149\pi$
$491$	29.1872	1.31720	0.658600	+	0.752493i	$0.271149\pi$
$492$	6.89784	0.310979
$493$	−0.775585	−0.0349306
$494$	−0.0683414	−0.00307483
$495$	−5.04847	−0.226912
$496$	3.13577	0.140800
$497$	−1.34266	−0.0602267
$498$	−11.4577	−0.513430
$499$	17.8077	0.797184	0.398592	−	0.917128i	$-0.369499\pi$
$499$	17.8077	0.797184	0.398592	+	0.917128i	$0.369499\pi$
$500$	18.0364	0.806612
$501$	6.48978	0.289942
$502$	14.3631	0.641056
$503$	3.69088	0.164568	0.0822841	−	0.996609i	$-0.473779\pi$
$503$	3.69088	0.164568	0.0822841	+	0.996609i	$0.473779\pi$
$504$	1.03951	0.0463035
$505$	8.28656	0.368747
$506$	13.0755	0.581276
$507$	−12.9397	−0.574672
$508$	−13.3901	−0.594090
$509$	−11.4789	−0.508792	−0.254396	−	0.967100i	$-0.581877\pi$
$509$	−11.4789	−0.508792	−0.254396	+	0.967100i	$0.581877\pi$
$510$	−1.31688	−0.0583125
$511$	−1.60448	−0.0709779
$512$	−12.5931	−0.556540
$513$	0.386626	0.0170700
$514$	−4.59118	−0.202508
$515$	−8.82749	−0.388986
$516$	2.62448	0.115536
$517$	−3.40015	−0.149539
$518$	−2.37584	−0.104388
$519$	7.89825	0.346695
$520$	1.12596	0.0493765
$521$	−25.6691	−1.12458	−0.562291	−	0.826939i	$-0.690080\pi$
$521$	−25.6691	−1.12458	−0.562291	+	0.826939i	$0.690080\pi$
$522$	0.558286	0.0244355
$523$	−40.2412	−1.75962	−0.879812	−	0.475322i	$-0.842332\pi$
$523$	−40.2412	−1.75962	−0.879812	+	0.475322i	$0.842332\pi$
$524$	15.2197	0.664876
$525$	−0.685643	−0.0299239
$526$	−20.4920	−0.893492
$527$	2.70422	0.117798
$528$	−3.19994	−0.139260
$529$	20.3290	0.883871
$530$	−5.03287	−0.218614
$531$	2.36846	0.102783
$532$	−0.237622	−0.0103022
$533$	−1.14307	−0.0495120
$534$	0.154476	0.00668485
$535$	−31.2210	−1.34980
$536$	22.9394	0.990830
$537$	4.81548	0.207803
$538$	−11.9077	−0.513379
$539$	18.8422	0.811593
$540$	−2.71096	−0.116661
$541$	−44.1060	−1.89626	−0.948132	−	0.317876i	$-0.897030\pi$
$541$	−44.1060	−1.89626	−0.948132	+	0.317876i	$0.897030\pi$
$542$	−17.6255	−0.757082
$543$	−13.9833	−0.600082
$544$	−5.84735	−0.250703
$545$	29.3588	1.25759
$546$	−0.0733135	−0.00313753
$547$	−35.4235	−1.51460	−0.757299	−	0.653068i	$-0.773481\pi$
$547$	−35.4235	−1.51460	−0.757299	+	0.653068i	$0.773481\pi$
$548$	−7.26943	−0.310535
$549$	5.98058	0.255245
$550$	−3.28379	−0.140021
$551$	−0.299861	−0.0127745
$552$	16.4978	0.702195
$553$	0.414755	0.0176372
$554$	−1.56891	−0.0666567
$555$	14.5585	0.617975
$556$	20.9085	0.886718
$557$	21.1443	0.895912	0.447956	−	0.894056i	$-0.352152\pi$
$557$	21.1443	0.895912	0.447956	+	0.894056i	$0.352152\pi$
$558$	−1.94657	−0.0824049
$559$	−0.434915	−0.0183950
$560$	0.879857	0.0371807
$561$	−2.75956	−0.116509
$562$	2.09967	0.0885693
$563$	8.02512	0.338218	0.169109	−	0.985597i	$-0.445911\pi$
$563$	8.02512	0.338218	0.169109	+	0.985597i	$0.445911\pi$
$564$	−1.82584	−0.0768817
$565$	4.97598	0.209341
$566$	7.19136	0.302275
$567$	0.414755	0.0174181
$568$	−8.11361	−0.340439
$569$	−36.4770	−1.52919	−0.764597	−	0.644509i	$-0.777062\pi$
$569$	−36.4770	−1.52919	−0.764597	+	0.644509i	$0.777062\pi$
$570$	−0.509141	−0.0213256
$571$	−1.68511	−0.0705195	−0.0352597	−	0.999378i	$-0.511226\pi$
$571$	−1.68511	−0.0705195	−0.0352597	+	0.999378i	$0.511226\pi$
$572$	1.00418	0.0419867
$573$	−12.1242	−0.506498
$574$	1.38972	0.0580058
$575$	−10.8817	−0.453798
$576$	1.88991	0.0787463
$577$	−27.6311	−1.15030	−0.575149	−	0.818048i	$-0.695056\pi$
$577$	−27.6311	−1.15030	−0.575149	+	0.818048i	$0.695056\pi$
$578$	−0.719826	−0.0299408
$579$	−2.70545	−0.112435
$580$	2.10258	0.0873050
$581$	6.60176	0.273887
$582$	−13.4157	−0.556100
$583$	−10.5465	−0.436793
$584$	−9.69572	−0.401212
$585$	0.449247	0.0185741
$586$	−3.85510	−0.159253
$587$	36.6930	1.51448	0.757241	−	0.653136i	$-0.226547\pi$
$587$	36.6930	1.51448	0.757241	+	0.653136i	$0.226547\pi$
$588$	10.1180	0.417261
$589$	1.04552	0.0430800
$590$	−3.11899	−0.128407
$591$	8.78690	0.361445
$592$	9.22782	0.379261
$593$	−28.8174	−1.18339	−0.591695	−	0.806162i	$-0.701541\pi$
$593$	−28.8174	−1.18339	−0.591695	+	0.806162i	$0.701541\pi$
$594$	1.98641	0.0815032
$595$	0.758771	0.0311066
$596$	−17.7536	−0.727217
$597$	7.23231	0.295999
$598$	−1.16354	−0.0475808
$599$	−12.3914	−0.506298	−0.253149	−	0.967427i	$-0.581466\pi$
$599$	−12.3914	−0.506298	−0.253149	+	0.967427i	$0.581466\pi$
$600$	−4.14328	−0.169149
$601$	−16.2368	−0.662313	−0.331157	−	0.943576i	$-0.607439\pi$
$601$	−16.2368	−0.662313	−0.331157	+	0.943576i	$0.607439\pi$
$602$	0.528759	0.0215506
$603$	9.15259	0.372722
$604$	−11.7802	−0.479330
$605$	−6.19232	−0.251754
$606$	−3.26048	−0.132448
$607$	−5.80246	−0.235514	−0.117757	−	0.993042i	$-0.537570\pi$
$607$	−5.80246	−0.235514	−0.117757	+	0.993042i	$0.537570\pi$
$608$	−2.26074	−0.0916851
$609$	−0.321677	−0.0130350
$610$	−7.87572	−0.318879
$611$	0.302568	0.0122406
$612$	−1.48185	−0.0599003
$613$	−23.3330	−0.942411	−0.471205	−	0.882024i	$-0.656181\pi$
$613$	−23.3330	−0.942411	−0.471205	+	0.882024i	$0.656181\pi$
$614$	−14.4310	−0.582390
$615$	−8.51585	−0.343392
$616$	−2.86860	−0.115579
$617$	10.9987	0.442793	0.221396	−	0.975184i	$-0.428939\pi$
$617$	10.9987	0.442793	0.221396	+	0.975184i	$0.428939\pi$
$618$	3.47332	0.139718
$619$	19.2753	0.774739	0.387369	−	0.921925i	$-0.373384\pi$
$619$	19.2753	0.774739	0.387369	+	0.921925i	$0.373384\pi$
$620$	−7.33105	−0.294422
$621$	6.58248	0.264146
$622$	−10.6623	−0.427520
$623$	−0.0890073	−0.00356600
$624$	0.284752	0.0113992
$625$	−14.0015	−0.560060
$626$	−1.99275	−0.0796463
$627$	−1.06692	−0.0426087
$628$	12.6477	0.504698
$629$	7.95789	0.317302
$630$	−0.546183	−0.0217604
$631$	17.4524	0.694768	0.347384	−	0.937723i	$-0.387070\pi$
$631$	17.4524	0.694768	0.347384	+	0.937723i	$0.387070\pi$
$632$	2.50633	0.0996963
$633$	−25.5292	−1.01469
$634$	−13.5418	−0.537815
$635$	16.5310	0.656012
$636$	−5.66335	−0.224566
$637$	−1.67671	−0.0664336
$638$	−1.54063	−0.0609940
$639$	−3.23725	−0.128064
$640$	18.9060	0.747326
$641$	−42.4645	−1.67725	−0.838624	−	0.544711i	$-0.816639\pi$
$641$	−42.4645	−1.67725	−0.838624	+	0.544711i	$0.816639\pi$
$642$	12.2844	0.484827
$643$	10.1855	0.401677	0.200838	−	0.979624i	$-0.435633\pi$
$643$	10.1855	0.401677	0.200838	+	0.979624i	$0.435633\pi$
$644$	−4.04562	−0.159420
$645$	−3.24010	−0.127579
$646$	−0.278304	−0.0109497
$647$	47.0665	1.85037	0.925187	−	0.379511i	$-0.123908\pi$
$647$	47.0665	1.85037	0.925187	+	0.379511i	$0.123908\pi$
$648$	2.50633	0.0984578
$649$	−6.53592	−0.256557
$650$	0.292213	0.0114615
$651$	1.12159	0.0439585
$652$	−12.9953	−0.508935
$653$	−2.16854	−0.0848616	−0.0424308	−	0.999099i	$-0.513510\pi$
$653$	−2.16854	−0.0848616	−0.0424308	+	0.999099i	$0.513510\pi$
$654$	−11.5517	−0.451708
$655$	−18.7898	−0.734177
$656$	−5.39772	−0.210745
$657$	−3.86850	−0.150925
$658$	−0.367855	−0.0143405
$659$	−47.4420	−1.84808	−0.924038	−	0.382300i	$-0.875132\pi$
$659$	−47.4420	−1.84808	−0.924038	+	0.382300i	$0.875132\pi$
$660$	7.48108	0.291201
$661$	−23.1248	−0.899451	−0.449726	−	0.893167i	$-0.648478\pi$
$661$	−23.1248	−0.899451	−0.449726	+	0.893167i	$0.648478\pi$
$662$	16.8376	0.654411
$663$	0.245564	0.00953693
$664$	39.8939	1.54818
$665$	0.293361	0.0113760
$666$	−5.72829	−0.221967
$667$	−5.10527	−0.197677
$668$	−9.61688	−0.372088
$669$	17.2162	0.665617
$670$	−12.0529	−0.465643
$671$	−16.5038	−0.637122
$672$	−2.42522	−0.0935547
$673$	36.0969	1.39143	0.695717	−	0.718316i	$-0.255087\pi$
$673$	36.0969	1.39143	0.695717	+	0.718316i	$0.255087\pi$
$674$	8.60947	0.331624
$675$	−1.65313	−0.0636290
$676$	19.1747	0.737488
$677$	20.6626	0.794130	0.397065	−	0.917791i	$-0.370029\pi$
$677$	20.6626	0.794130	0.397065	+	0.917791i	$0.370029\pi$
$678$	−1.95788	−0.0751920
$679$	7.72997	0.296649
$680$	4.58519	0.175834
$681$	18.3239	0.702172
$682$	5.37169	0.205692
$683$	35.9726	1.37645	0.688227	−	0.725495i	$-0.258389\pi$
$683$	35.9726	1.37645	0.688227	+	0.725495i	$0.258389\pi$
$684$	−0.572922	−0.0219062
$685$	8.97461	0.342902
$686$	4.12836	0.157621
$687$	−24.4035	−0.931053
$688$	−2.05372	−0.0782972
$689$	0.938500	0.0357540
$690$	−8.66835	−0.329998
$691$	−30.6870	−1.16739	−0.583694	−	0.811973i	$-0.698393\pi$
$691$	−30.6870	−1.16739	−0.583694	+	0.811973i	$0.698393\pi$
$692$	−11.7040	−0.444920
$693$	−1.14454	−0.0434775
$694$	8.04388	0.305342
$695$	−25.8130	−0.979142
$696$	−1.94387	−0.0736822
$697$	−4.65488	−0.176316
$698$	−24.4881	−0.926889
$699$	24.0462	0.909510
$700$	1.01602	0.0384020
$701$	−47.7345	−1.80291	−0.901454	−	0.432876i	$-0.857499\pi$
$701$	−47.7345	−1.80291	−0.901454	+	0.432876i	$0.857499\pi$
$702$	−0.176764	−0.00667151
$703$	3.07673	0.116041
$704$	−5.21533	−0.196560
$705$	2.25412	0.0848951
$706$	19.4291	0.731223
$707$	1.87865	0.0706539
$708$	−3.50971	−0.131903
$709$	−0.239120	−0.00898033	−0.00449017	−	0.999990i	$-0.501429\pi$
$709$	−0.239120	−0.00898033	−0.00449017	+	0.999990i	$0.501429\pi$
$710$	4.26308	0.159990
$711$	1.00000	0.0375029
$712$	−0.537864	−0.0201573
$713$	17.8005	0.666634
$714$	−0.298551	−0.0111730
$715$	−1.23972	−0.0463631
$716$	−7.13582	−0.266678
$717$	22.5991	0.843977
$718$	−20.5388	−0.766501
$719$	−30.6832	−1.14429	−0.572145	−	0.820152i	$-0.693889\pi$
$719$	−30.6832	−1.14429	−0.572145	+	0.820152i	$0.693889\pi$
$720$	2.12139	0.0790596
$721$	−2.00128	−0.0745317
$722$	13.5691	0.504989
$723$	25.1640	0.935859
$724$	20.7212	0.770097
$725$	1.28214	0.0476176
$726$	2.43647	0.0904260
$727$	26.1729	0.970701	0.485350	−	0.874320i	$-0.338692\pi$
$727$	26.1729	0.970701	0.485350	+	0.874320i	$0.338692\pi$
$728$	0.255267	0.00946081
$729$	1.00000	0.0370370
$730$	5.09436	0.188551
$731$	−1.77108	−0.0655059
$732$	−8.86233	−0.327561
$733$	7.82983	0.289202	0.144601	−	0.989490i	$-0.453810\pi$
$733$	7.82983	0.289202	0.144601	+	0.989490i	$0.453810\pi$
$734$	−24.6083	−0.908310
$735$	−12.4914	−0.460753
$736$	−38.4901	−1.41876
$737$	−25.2572	−0.930359
$738$	3.35070	0.123341
$739$	31.2670	1.15018	0.575088	−	0.818092i	$-0.304968\pi$
$739$	31.2670	1.15018	0.575088	+	0.818092i	$0.304968\pi$
$740$	−21.5735	−0.793059
$741$	0.0949416	0.00348777
$742$	−1.14101	−0.0418876
$743$	−17.3813	−0.637658	−0.318829	−	0.947812i	$-0.603290\pi$
$743$	−17.3813	−0.637658	−0.318829	+	0.947812i	$0.603290\pi$
$744$	6.77767	0.248481
$745$	21.9181	0.803016
$746$	−23.3640	−0.855415
$747$	15.9173	0.582383
$748$	4.08926	0.149518
$749$	−7.07812	−0.258629
$750$	8.76139	0.319921
$751$	15.6507	0.571103	0.285551	−	0.958363i	$-0.407823\pi$
$751$	15.6507	0.571103	0.285551	+	0.958363i	$0.407823\pi$
$752$	1.42876	0.0521015
$753$	−19.9536	−0.727148
$754$	0.137095	0.00499271
$755$	14.5435	0.529292
$756$	−0.614604	−0.0223529
$757$	45.2503	1.64465	0.822326	−	0.569017i	$-0.192676\pi$
$757$	45.2503	1.64465	0.822326	+	0.569017i	$0.192676\pi$
$758$	5.41466	0.196669
$759$	−18.1648	−0.659339
$760$	1.77275	0.0643045
$761$	33.9249	1.22978	0.614888	−	0.788614i	$-0.289201\pi$
$761$	33.9249	1.22978	0.614888	+	0.788614i	$0.289201\pi$
$762$	−6.50439	−0.235629
$763$	6.65595	0.240962
$764$	17.9663	0.649999
$765$	1.82945	0.0661437
$766$	2.76270	0.0998206
$767$	0.581610	0.0210007
$768$	−11.2187	−0.404821
$769$	−50.3111	−1.81427	−0.907133	−	0.420844i	$-0.861734\pi$
$769$	−50.3111	−1.81427	−0.907133	+	0.420844i	$0.861734\pi$
$770$	1.50723	0.0543167
$771$	6.37818	0.229705
$772$	4.00907	0.144290
$773$	11.3678	0.408871	0.204436	−	0.978880i	$-0.434464\pi$
$773$	11.3678	0.408871	0.204436	+	0.978880i	$0.434464\pi$
$774$	1.27487	0.0458244
$775$	−4.47043	−0.160583
$776$	46.7116	1.67685
$777$	3.30057	0.118407
$778$	−3.00045	−0.107571
$779$	−1.79970	−0.0644809
$780$	−0.665716	−0.0238365
$781$	8.93340	0.319662
$782$	−4.73824	−0.169439
$783$	−0.775585	−0.0277171
$784$	−7.91760	−0.282771
$785$	−15.6144	−0.557303
$786$	7.39315	0.263705
$787$	−18.8362	−0.671436	−0.335718	−	0.941962i	$-0.608979\pi$
$787$	−18.8362	−0.671436	−0.335718	+	0.941962i	$0.608979\pi$
$788$	−13.0209	−0.463850
$789$	28.4679	1.01349
$790$	−1.31688	−0.0468526
$791$	1.12811	0.0401108
$792$	−6.91637	−0.245762
$793$	1.46862	0.0521521
$794$	14.0616	0.499026
$795$	6.99179	0.247973
$796$	−10.7172	−0.379861
$797$	−31.2170	−1.10576	−0.552882	−	0.833259i	$-0.686472\pi$
$797$	−31.2170	−1.10576	−0.552882	+	0.833259i	$0.686472\pi$
$798$	−0.115428	−0.00408610
$799$	1.23213	0.0435898
$800$	9.66643	0.341760
$801$	−0.214602	−0.00758260
$802$	17.3954	0.614252
$803$	10.6754	0.376726
$804$	−13.5628	−0.478322
$805$	4.99459	0.176036
$806$	−0.478008	−0.0168371
$807$	16.5425	0.582324
$808$	11.3525	0.399380
$809$	7.91592	0.278309	0.139154	−	0.990271i	$-0.455562\pi$
$809$	7.91592	0.278309	0.139154	+	0.990271i	$0.455562\pi$
$810$	−1.31688	−0.0462705
$811$	−12.3154	−0.432453	−0.216227	−	0.976343i	$-0.569375\pi$
$811$	−12.3154	−0.432453	−0.216227	+	0.976343i	$0.569375\pi$
$812$	0.476678	0.0167281
$813$	24.4858	0.858756
$814$	15.8076	0.554056
$815$	16.0436	0.561982
$816$	1.15958	0.0405935
$817$	−0.684748	−0.0239563
$818$	15.0909	0.527639
$819$	0.101849	0.00355889
$820$	12.6192	0.440682
$821$	−28.6856	−1.00113	−0.500567	−	0.865698i	$-0.666875\pi$
$821$	−28.6856	−1.00113	−0.500567	+	0.865698i	$0.666875\pi$
$822$	−3.53121	−0.123165
$823$	−10.0482	−0.350259	−0.175130	−	0.984545i	$-0.556034\pi$
$823$	−10.0482	−0.350259	−0.175130	+	0.984545i	$0.556034\pi$
$824$	−12.0936	−0.421300
$825$	4.56192	0.158826
$826$	−0.707107	−0.0246034
$827$	−13.8280	−0.480846	−0.240423	−	0.970668i	$-0.577286\pi$
$827$	−13.8280	−0.480846	−0.240423	+	0.970668i	$0.577286\pi$
$828$	−9.75425	−0.338984
$829$	41.1327	1.42860	0.714300	−	0.699840i	$-0.246745\pi$
$829$	41.1327	1.42860	0.714300	+	0.699840i	$0.246745\pi$
$830$	−20.9612	−0.727573
$831$	2.17957	0.0756085
$832$	0.464095	0.0160896
$833$	−6.82798	−0.236575
$834$	10.1566	0.351693
$835$	11.8727	0.410871
$836$	1.58102	0.0546806
$837$	2.70422	0.0934716
$838$	−7.45625	−0.257572
$839$	−31.3760	−1.08322	−0.541609	−	0.840630i	$-0.682185\pi$
$839$	−31.3760	−1.08322	−0.541609	+	0.840630i	$0.682185\pi$
$840$	1.90173	0.0656158
$841$	−28.3985	−0.979258
$842$	27.8206	0.958760
$843$	−2.91692	−0.100464
$844$	37.8304	1.30218
$845$	−23.6725	−0.814358
$846$	−0.886922	−0.0304930
$847$	−1.40386	−0.0482373
$848$	4.43170	0.152185
$849$	−9.99042	−0.342870
$850$	1.18997	0.0408155
$851$	52.3826	1.79565
$852$	4.79712	0.164347
$853$	−4.24630	−0.145390	−0.0726952	−	0.997354i	$-0.523160\pi$
$853$	−4.24630	−0.145390	−0.0726952	+	0.997354i	$0.523160\pi$
$854$	−1.78551	−0.0610989
$855$	0.707311	0.0241895
$856$	−42.7725	−1.46193
$857$	34.1449	1.16637	0.583184	−	0.812340i	$-0.301807\pi$
$857$	34.1449	1.16637	0.583184	+	0.812340i	$0.301807\pi$
$858$	0.487790	0.0166529
$859$	−22.5724	−0.770160	−0.385080	−	0.922883i	$-0.625826\pi$
$859$	−22.5724	−0.770160	−0.385080	+	0.922883i	$0.625826\pi$
$860$	4.80135	0.163725
$861$	−1.93063	−0.0657958
$862$	−24.1994	−0.824237
$863$	−17.3207	−0.589604	−0.294802	−	0.955558i	$-0.595254\pi$
$863$	−17.3207	−0.589604	−0.294802	+	0.955558i	$0.595254\pi$
$864$	−5.84735	−0.198931
$865$	14.4494	0.491295
$866$	2.29630	0.0780313
$867$	1.00000	0.0339618
$868$	−1.66203	−0.0564129
$869$	−2.75956	−0.0936118
$870$	1.02135	0.0346271
$871$	2.24755	0.0761553
$872$	40.2213	1.36207
$873$	18.6375	0.630782
$874$	−1.83193	−0.0619659
$875$	−5.04820	−0.170660
$876$	5.73254	0.193685
$877$	−53.0590	−1.79167	−0.895837	−	0.444383i	$-0.853423\pi$
$877$	−53.0590	−1.79167	−0.895837	+	0.444383i	$0.853423\pi$
$878$	27.8692	0.940541
$879$	5.35560	0.180640
$880$	−5.85412	−0.197342
$881$	−46.9575	−1.58204	−0.791019	−	0.611791i	$-0.790449\pi$
$881$	−46.9575	−1.58204	−0.791019	+	0.611791i	$0.790449\pi$
$882$	4.91496	0.165495
$883$	27.4476	0.923684	0.461842	−	0.886962i	$-0.347189\pi$
$883$	27.4476	0.923684	0.461842	+	0.886962i	$0.347189\pi$
$884$	−0.363890	−0.0122389
$885$	4.33297	0.145651
$886$	−0.0260493	−0.000875143 0
$887$	38.7268	1.30032	0.650160	−	0.759797i	$-0.274702\pi$
$887$	38.7268	1.30032	0.650160	+	0.759797i	$0.274702\pi$
$888$	19.9451	0.669312
$889$	3.74775	0.125695
$890$	0.282606	0.00947297
$891$	−2.75956	−0.0924489
$892$	−25.5118	−0.854199
$893$	0.476375	0.0159413
$894$	−8.62404	−0.288431
$895$	8.80965	0.294474
$896$	4.28620	0.143192
$897$	1.61642	0.0539708
$898$	−2.52519	−0.0842666
$899$	−2.09735	−0.0699507
$900$	2.44969	0.0816564
$901$	3.82181	0.127323
$902$	−9.24648	−0.307874
$903$	−0.734565	−0.0244448
$904$	6.81705	0.226732
$905$	−25.5817	−0.850365
$906$	−5.72238	−0.190113
$907$	6.62249	0.219896	0.109948	−	0.993937i	$-0.464932\pi$
$907$	6.62249	0.219896	0.109948	+	0.993937i	$0.464932\pi$
$908$	−27.1532	−0.901111
$909$	4.52955	0.150236
$910$	−0.134123	−0.00444614
$911$	36.4150	1.20648	0.603241	−	0.797559i	$-0.293876\pi$
$911$	36.4150	1.20648	0.603241	+	0.797559i	$0.293876\pi$
$912$	0.448325	0.0148455
$913$	−43.9247	−1.45370
$914$	−5.75551	−0.190375
$915$	10.9411	0.361703
$916$	36.1624	1.19484
$917$	−4.25984	−0.140672
$918$	−0.719826	−0.0237578
$919$	−30.1480	−0.994490	−0.497245	−	0.867610i	$-0.665655\pi$
$919$	−30.1480	−0.994490	−0.497245	+	0.867610i	$0.665655\pi$
$920$	30.1819	0.995068
$921$	20.0480	0.660603
$922$	−13.3034	−0.438125
$923$	−0.794953	−0.0261662
$924$	1.69604	0.0557956
$925$	−13.1554	−0.432548
$926$	19.3035	0.634351
$927$	−4.82523	−0.158481
$928$	4.53512	0.148872
$929$	−6.35944	−0.208646	−0.104323	−	0.994543i	$-0.533268\pi$
$929$	−6.35944	−0.208646	−0.104323	+	0.994543i	$0.533268\pi$
$930$	−3.56114	−0.116775
$931$	−2.63988	−0.0865184
$932$	−35.6328	−1.16719
$933$	14.8123	0.484934
$934$	−23.8163	−0.779292
$935$	−5.04847	−0.165103
$936$	0.615464	0.0201171
$937$	−43.7477	−1.42918	−0.714588	−	0.699545i	$-0.753386\pi$
$937$	−43.7477	−1.42918	−0.714588	+	0.699545i	$0.753386\pi$
$938$	−2.73252	−0.0892198
$939$	2.76838	0.0903426
$940$	−3.34027	−0.108948
$941$	−39.9043	−1.30084	−0.650422	−	0.759573i	$-0.725408\pi$
$941$	−39.9043	−1.30084	−0.650422	+	0.759573i	$0.725408\pi$
$942$	6.14376	0.200175
$943$	−30.6407	−0.997797
$944$	2.74643	0.0893886
$945$	0.758771	0.0246828
$946$	−3.51809	−0.114383
$947$	−44.7528	−1.45427	−0.727136	−	0.686494i	$-0.759149\pi$
$947$	−44.7528	−1.45427	−0.727136	+	0.686494i	$0.759149\pi$
$948$	−1.48185	−0.0481283
$949$	−0.949966	−0.0308372
$950$	0.460072	0.0149267
$951$	18.8127	0.610042
$952$	1.03951	0.0336907
$953$	−16.6817	−0.540374	−0.270187	−	0.962808i	$-0.587085\pi$
$953$	−16.6817	−0.540374	−0.270187	+	0.962808i	$0.587085\pi$
$954$	−2.75104	−0.0890681
$955$	−22.1806	−0.717749
$956$	−33.4884	−1.08309
$957$	2.14028	0.0691853
$958$	−9.83436	−0.317734
$959$	2.03464	0.0657019
$960$	3.45749	0.111590
$961$	−23.6872	−0.764102
$962$	−1.40666	−0.0453527
$963$	−17.0658	−0.549938
$964$	−37.2893	−1.20101
$965$	−4.94947	−0.159329
$966$	−1.96521	−0.0632295
$967$	22.2995	0.717102	0.358551	−	0.933510i	$-0.383271\pi$
$967$	22.2995	0.717102	0.358551	+	0.933510i	$0.383271\pi$
$968$	−8.48343	−0.272668
$969$	0.386626	0.0124202
$970$	−24.5433	−0.788039
$971$	−7.79177	−0.250050	−0.125025	−	0.992154i	$-0.539901\pi$
$971$	−7.79177	−0.250050	−0.125025	+	0.992154i	$0.539901\pi$
$972$	−1.48185	−0.0475304
$973$	−5.85207	−0.187609
$974$	18.0455	0.578217
$975$	−0.405950	−0.0130008
$976$	6.93497	0.221983
$977$	13.9986	0.447856	0.223928	−	0.974606i	$-0.428112\pi$
$977$	13.9986	0.447856	0.223928	+	0.974606i	$0.428112\pi$
$978$	−6.31262	−0.201855
$979$	0.592209	0.0189271
$980$	18.5104	0.591293
$981$	16.0479	0.512371
$982$	−21.0097	−0.670447
$983$	−22.6636	−0.722858	−0.361429	−	0.932400i	$-0.617711\pi$
$983$	−22.6636	−0.722858	−0.361429	+	0.932400i	$0.617711\pi$
$984$	−11.6667	−0.371919
$985$	16.0752	0.512197
$986$	0.558286	0.0177795
$987$	0.511033	0.0162664
$988$	−0.140689	−0.00447592
$989$	−11.6581	−0.370707
$990$	3.63402	0.115497
$991$	16.9148	0.537318	0.268659	−	0.963235i	$-0.413420\pi$
$991$	16.9148	0.537318	0.268659	+	0.963235i	$0.413420\pi$
$992$	−15.8125	−0.502049
$993$	−23.3912	−0.742296
$994$	0.966485	0.0306550
$995$	13.2311	0.419455
$996$	−23.5870	−0.747383
$997$	−47.3564	−1.49979	−0.749896	−	0.661555i	$-0.769897\pi$
$997$	−47.3564	−1.49979	−0.749896	+	0.661555i	$0.769897\pi$
$998$	−12.8185	−0.405762
$999$	7.95789	0.251776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.11	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.11	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-0.719826 q^{2} +1.00000 q^{3} -1.48185 q^{4} +1.82945 q^{5} -0.719826 q^{6} +0.414755 q^{7} +2.50633 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.719826 q^{2} +1.00000 q^{3} -1.48185 q^{4} +1.82945 q^{5} -0.719826 q^{6} +0.414755 q^{7} +2.50633 q^{8} +1.00000 q^{9} -1.31688 q^{10} -2.75956 q^{11} -1.48185 q^{12} +0.245564 q^{13} -0.298551 q^{14} +1.82945 q^{15} +1.15958 q^{16} +1.00000 q^{17} -0.719826 q^{18} +0.386626 q^{19} -2.71096 q^{20} +0.414755 q^{21} +1.98641 q^{22} +6.58248 q^{23} +2.50633 q^{24} -1.65313 q^{25} -0.176764 q^{26} +1.00000 q^{27} -0.614604 q^{28} -0.775585 q^{29} -1.31688 q^{30} +2.70422 q^{31} -5.84735 q^{32} -2.75956 q^{33} -0.719826 q^{34} +0.758771 q^{35} -1.48185 q^{36} +7.95789 q^{37} -0.278304 q^{38} +0.245564 q^{39} +4.58519 q^{40} -4.65488 q^{41} -0.298551 q^{42} -1.77108 q^{43} +4.08926 q^{44} +1.82945 q^{45} -4.73824 q^{46} +1.23213 q^{47} +1.15958 q^{48} -6.82798 q^{49} +1.18997 q^{50} +1.00000 q^{51} -0.363890 q^{52} +3.82181 q^{53} -0.719826 q^{54} -5.04847 q^{55} +1.03951 q^{56} +0.386626 q^{57} +0.558286 q^{58} +2.36846 q^{59} -2.71096 q^{60} +5.98058 q^{61} -1.94657 q^{62} +0.414755 q^{63} +1.88991 q^{64} +0.449247 q^{65} +1.98641 q^{66} +9.15259 q^{67} -1.48185 q^{68} +6.58248 q^{69} -0.546183 q^{70} -3.23725 q^{71} +2.50633 q^{72} -3.86850 q^{73} -5.72829 q^{74} -1.65313 q^{75} -0.572922 q^{76} -1.14454 q^{77} -0.176764 q^{78} +1.00000 q^{79} +2.12139 q^{80} +1.00000 q^{81} +3.35070 q^{82} +15.9173 q^{83} -0.614604 q^{84} +1.82945 q^{85} +1.27487 q^{86} -0.775585 q^{87} -6.91637 q^{88} -0.214602 q^{89} -1.31688 q^{90} +0.101849 q^{91} -9.75425 q^{92} +2.70422 q^{93} -0.886922 q^{94} +0.707311 q^{95} -5.84735 q^{96} +18.6375 q^{97} +4.91496 q^{98} -2.75956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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