LMFDB - Embedded newform 1155.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.352076.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 3x^{2} + 8x - 4 $ x^5 - x^4 - 8x^3 + 3x^2 + 8*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.06028$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.346466 q^{2} +1.00000 q^{3} -1.87996 q^{4} -1.00000 q^{5} +0.346466 q^{6} +1.00000 q^{7} -1.34427 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.346466 q^{2} +1.00000 q^{3} -1.87996 q^{4} -1.00000 q^{5} +0.346466 q^{6} +1.00000 q^{7} -1.34427 q^{8} +1.00000 q^{9} -0.346466 q^{10} +1.00000 q^{11} -1.87996 q^{12} +3.69074 q^{13} +0.346466 q^{14} -1.00000 q^{15} +3.29418 q^{16} -8.05410 q^{17} +0.346466 q^{18} +4.87996 q^{19} +1.87996 q^{20} +1.00000 q^{21} +0.346466 q^{22} +3.57289 q^{23} -1.34427 q^{24} +1.00000 q^{25} +1.27871 q^{26} +1.00000 q^{27} -1.87996 q^{28} +3.98492 q^{29} -0.346466 q^{30} -0.383670 q^{31} +3.82987 q^{32} +1.00000 q^{33} -2.79047 q^{34} -1.00000 q^{35} -1.87996 q^{36} -1.48340 q^{37} +1.69074 q^{38} +3.69074 q^{39} +1.34427 q^{40} +6.17195 q^{41} +0.346466 q^{42} +8.94915 q^{43} -1.87996 q^{44} -1.00000 q^{45} +1.23788 q^{46} +9.24332 q^{47} +3.29418 q^{48} +1.00000 q^{49} +0.346466 q^{50} -8.05410 q^{51} -6.93845 q^{52} -2.29418 q^{53} +0.346466 q^{54} -1.00000 q^{55} -1.34427 q^{56} +4.87996 q^{57} +1.38064 q^{58} +9.05191 q^{59} +1.87996 q^{60} -4.95437 q^{61} -0.132929 q^{62} +1.00000 q^{63} -5.26144 q^{64} -3.69074 q^{65} +0.346466 q^{66} +7.86707 q^{67} +15.1414 q^{68} +3.57289 q^{69} -0.346466 q^{70} -8.25074 q^{71} -1.34427 q^{72} +11.5482 q^{73} -0.513947 q^{74} +1.00000 q^{75} -9.17414 q^{76} +1.00000 q^{77} +1.27871 q^{78} +6.30926 q^{79} -3.29418 q^{80} +1.00000 q^{81} +2.13837 q^{82} -12.2614 q^{83} -1.87996 q^{84} +8.05410 q^{85} +3.10057 q^{86} +3.98492 q^{87} -1.34427 q^{88} +11.7165 q^{89} -0.346466 q^{90} +3.69074 q^{91} -6.71690 q^{92} -0.383670 q^{93} +3.20249 q^{94} -4.87996 q^{95} +3.82987 q^{96} -16.7091 q^{97} +0.346466 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + q^98 + 5 * 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 $

$2$	0.346466	0.244988	0.122494	−	0.992469i	$-0.460911\pi$
$2$	0.346466	0.244988	0.122494	+	0.992469i	$0.460911\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.87996	−0.939981
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.346466	0.141444
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.34427	−0.475272
$9$	1.00000	0.333333
$10$	−0.346466	−0.109562
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.87996	−0.542698
$13$	3.69074	1.02363	0.511813	−	0.859097i	$-0.328974\pi$
$13$	3.69074	1.02363	0.511813	+	0.859097i	$0.328974\pi$
$14$	0.346466	0.0925968
$15$	−1.00000	−0.258199
$16$	3.29418	0.823545
$17$	−8.05410	−1.95341	−0.976703	−	0.214594i	$-0.931157\pi$
$17$	−8.05410	−1.95341	−0.976703	+	0.214594i	$0.931157\pi$
$18$	0.346466	0.0816627
$19$	4.87996	1.11954	0.559770	−	0.828648i	$-0.310889\pi$
$19$	4.87996	1.11954	0.559770	+	0.828648i	$0.310889\pi$
$20$	1.87996	0.420372
$21$	1.00000	0.218218
$22$	0.346466	0.0738667
$23$	3.57289	0.745000	0.372500	−	0.928032i	$-0.378501\pi$
$23$	3.57289	0.745000	0.372500	+	0.928032i	$0.378501\pi$
$24$	−1.34427	−0.274399
$25$	1.00000	0.200000
$26$	1.27871	0.250777
$27$	1.00000	0.192450
$28$	−1.87996	−0.355279
$29$	3.98492	0.739981	0.369990	−	0.929036i	$-0.379361\pi$
$29$	3.98492	0.739981	0.369990	+	0.929036i	$0.379361\pi$
$30$	−0.346466	−0.0632557
$31$	−0.383670	−0.0689092	−0.0344546	−	0.999406i	$-0.510969\pi$
$31$	−0.383670	−0.0689092	−0.0344546	+	0.999406i	$0.510969\pi$
$32$	3.82987	0.677031
$33$	1.00000	0.174078
$34$	−2.79047	−0.478562
$35$	−1.00000	−0.169031
$36$	−1.87996	−0.313327
$37$	−1.48340	−0.243870	−0.121935	−	0.992538i	$-0.538910\pi$
$37$	−1.48340	−0.243870	−0.121935	+	0.992538i	$0.538910\pi$
$38$	1.69074	0.274274
$39$	3.69074	0.590991
$40$	1.34427	0.212548
$41$	6.17195	0.963896	0.481948	−	0.876200i	$-0.339929\pi$
$41$	6.17195	0.963896	0.481948	+	0.876200i	$0.339929\pi$
$42$	0.346466	0.0534608
$43$	8.94915	1.36473	0.682366	−	0.731011i	$-0.260951\pi$
$43$	8.94915	1.36473	0.682366	+	0.731011i	$0.260951\pi$
$44$	−1.87996	−0.283415
$45$	−1.00000	−0.149071
$46$	1.23788	0.182516
$47$	9.24332	1.34828	0.674139	−	0.738605i	$-0.264515\pi$
$47$	9.24332	1.34828	0.674139	+	0.738605i	$0.264515\pi$
$48$	3.29418	0.475474
$49$	1.00000	0.142857
$50$	0.346466	0.0489976
$51$	−8.05410	−1.12780
$52$	−6.93845	−0.962190
$53$	−2.29418	−0.315130	−0.157565	−	0.987509i	$-0.550364\pi$
$53$	−2.29418	−0.315130	−0.157565	+	0.987509i	$0.550364\pi$
$54$	0.346466	0.0471480
$55$	−1.00000	−0.134840
$56$	−1.34427	−0.179636
$57$	4.87996	0.646367
$58$	1.38064	0.181287
$59$	9.05191	1.17846	0.589229	−	0.807966i	$-0.299432\pi$
$59$	9.05191	1.17846	0.589229	+	0.807966i	$0.299432\pi$
$60$	1.87996	0.242702
$61$	−4.95437	−0.634342	−0.317171	−	0.948368i	$-0.602733\pi$
$61$	−4.95437	−0.634342	−0.317171	+	0.948368i	$0.602733\pi$
$62$	−0.132929	−0.0168820
$63$	1.00000	0.125988
$64$	−5.26144	−0.657680
$65$	−3.69074	−0.457780
$66$	0.346466	0.0426470
$67$	7.86707	0.961116	0.480558	−	0.876963i	$-0.340434\pi$
$67$	7.86707	0.961116	0.480558	+	0.876963i	$0.340434\pi$
$68$	15.1414	1.83616
$69$	3.57289	0.430126
$70$	−0.346466	−0.0414106
$71$	−8.25074	−0.979183	−0.489591	−	0.871952i	$-0.662854\pi$
$71$	−8.25074	−0.979183	−0.489591	+	0.871952i	$0.662854\pi$
$72$	−1.34427	−0.158424
$73$	11.5482	1.35161	0.675807	−	0.737078i	$-0.263795\pi$
$73$	11.5482	1.35161	0.675807	+	0.737078i	$0.263795\pi$
$74$	−0.513947	−0.0597452
$75$	1.00000	0.115470
$76$	−9.17414	−1.05235
$77$	1.00000	0.113961
$78$	1.27871	0.144786
$79$	6.30926	0.709847	0.354924	−	0.934895i	$-0.384507\pi$
$79$	6.30926	0.709847	0.354924	+	0.934895i	$0.384507\pi$
$80$	−3.29418	−0.368300
$81$	1.00000	0.111111
$82$	2.13837	0.236143
$83$	−12.2614	−1.34587	−0.672934	−	0.739703i	$-0.734966\pi$
$83$	−12.2614	−1.34587	−0.672934	+	0.739703i	$0.734966\pi$
$84$	−1.87996	−0.205121
$85$	8.05410	0.873590
$86$	3.10057	0.334343
$87$	3.98492	0.427228
$88$	−1.34427	−0.143300
$89$	11.7165	1.24195	0.620973	−	0.783832i	$-0.286738\pi$
$89$	11.7165	1.24195	0.620973	+	0.783832i	$0.286738\pi$
$90$	−0.346466	−0.0365207
$91$	3.69074	0.386895
$92$	−6.71690	−0.700285
$93$	−0.383670	−0.0397848
$94$	3.20249	0.330312
$95$	−4.87996	−0.500673
$96$	3.82987	0.390884
$97$	−16.7091	−1.69655	−0.848274	−	0.529557i	$-0.822358\pi$
$97$	−16.7091	−1.69655	−0.848274	+	0.529557i	$0.822358\pi$
$98$	0.346466	0.0349983
$99$	1.00000	0.100504
$100$	−1.87996	−0.187996
$101$	−11.2202	−1.11645	−0.558226	−	0.829689i	$-0.688518\pi$
$101$	−11.2202	−1.11645	−0.558226	+	0.829689i	$0.688518\pi$
$102$	−2.79047	−0.276298
$103$	6.57070	0.647430	0.323715	−	0.946155i	$-0.395068\pi$
$103$	6.57070	0.647430	0.323715	+	0.946155i	$0.395068\pi$
$104$	−4.96136	−0.486502
$105$	−1.00000	−0.0975900
$106$	−0.794854	−0.0772031
$107$	−8.83652	−0.854259	−0.427130	−	0.904190i	$-0.640475\pi$
$107$	−8.83652	−0.854259	−0.427130	+	0.904190i	$0.640475\pi$
$108$	−1.87996	−0.180899
$109$	−8.24636	−0.789858	−0.394929	−	0.918712i	$-0.629231\pi$
$109$	−8.24636	−0.789858	−0.394929	+	0.918712i	$0.629231\pi$
$110$	−0.346466	−0.0330342
$111$	−1.48340	−0.140798
$112$	3.29418	0.311271
$113$	−4.67262	−0.439563	−0.219782	−	0.975549i	$-0.570535\pi$
$113$	−4.67262	−0.439563	−0.219782	+	0.975549i	$0.570535\pi$
$114$	1.69074	0.158352
$115$	−3.57289	−0.333174
$116$	−7.49149	−0.695568
$117$	3.69074	0.341209
$118$	3.13618	0.288708
$119$	−8.05410	−0.738318
$120$	1.34427	0.122715
$121$	1.00000	0.0909091
$122$	−1.71652	−0.155406
$123$	6.17195	0.556506
$124$	0.721286	0.0647734
$125$	−1.00000	−0.0894427
$126$	0.346466	0.0308656
$127$	20.3005	1.80137	0.900687	−	0.434468i	$-0.143064\pi$
$127$	20.3005	1.80137	0.900687	+	0.434468i	$0.143064\pi$
$128$	−9.48264	−0.838155
$129$	8.94915	0.787928
$130$	−1.27871	−0.112151
$131$	−14.0107	−1.22412	−0.612059	−	0.790812i	$-0.709658\pi$
$131$	−14.0107	−1.22412	−0.612059	+	0.790812i	$0.709658\pi$
$132$	−1.87996	−0.163630
$133$	4.87996	0.423146
$134$	2.72567	0.235462
$135$	−1.00000	−0.0860663
$136$	10.8269	0.928400
$137$	−8.37844	−0.715819	−0.357909	−	0.933756i	$-0.616510\pi$
$137$	−8.37844	−0.715819	−0.357909	+	0.933756i	$0.616510\pi$
$138$	1.23788	0.105376
$139$	−13.5482	−1.14914	−0.574572	−	0.818454i	$-0.694831\pi$
$139$	−13.5482	−1.14914	−0.574572	+	0.818454i	$0.694831\pi$
$140$	1.87996	0.158886
$141$	9.24332	0.778428
$142$	−2.85860	−0.239888
$143$	3.69074	0.308635
$144$	3.29418	0.274515
$145$	−3.98492	−0.330929
$146$	4.00105	0.331130
$147$	1.00000	0.0824786
$148$	2.78874	0.229233
$149$	−0.560003	−0.0458772	−0.0229386	−	0.999737i	$-0.507302\pi$
$149$	−0.560003	−0.0458772	−0.0229386	+	0.999737i	$0.507302\pi$
$150$	0.346466	0.0282888
$151$	5.20430	0.423520	0.211760	−	0.977322i	$-0.432080\pi$
$151$	5.20430	0.423520	0.211760	+	0.977322i	$0.432080\pi$
$152$	−6.56000	−0.532086
$153$	−8.05410	−0.651136
$154$	0.346466	0.0279190
$155$	0.383670	0.0308171
$156$	−6.93845	−0.555520
$157$	−16.5405	−1.32008	−0.660039	−	0.751231i	$-0.729460\pi$
$157$	−16.5405	−1.32008	−0.660039	+	0.751231i	$0.729460\pi$
$158$	2.18594	0.173904
$159$	−2.29418	−0.181940
$160$	−3.82987	−0.302778
$161$	3.57289	0.281583
$162$	0.346466	0.0272209
$163$	−11.9035	−0.932355	−0.466178	−	0.884691i	$-0.654369\pi$
$163$	−11.9035	−0.932355	−0.466178	+	0.884691i	$0.654369\pi$
$164$	−11.6030	−0.906044
$165$	−1.00000	−0.0778499
$166$	−4.24817	−0.329722
$167$	−21.2823	−1.64688	−0.823439	−	0.567405i	$-0.807947\pi$
$167$	−21.2823	−1.64688	−0.823439	+	0.567405i	$0.807947\pi$
$168$	−1.34427	−0.103713
$169$	0.621555	0.0478119
$170$	2.79047	0.214019
$171$	4.87996	0.373180
$172$	−16.8240	−1.28282
$173$	25.4897	1.93794	0.968972	−	0.247169i	$-0.0795004\pi$
$173$	25.4897	1.93794	0.968972	+	0.247169i	$0.0795004\pi$
$174$	1.38064	0.104666
$175$	1.00000	0.0755929
$176$	3.29418	0.248308
$177$	9.05191	0.680383
$178$	4.05936	0.304262
$179$	13.8317	1.03383	0.516914	−	0.856037i	$-0.327081\pi$
$179$	13.8317	1.03383	0.516914	+	0.856037i	$0.327081\pi$
$180$	1.87996	0.140124
$181$	22.4823	1.67109	0.835547	−	0.549419i	$-0.185151\pi$
$181$	22.4823	1.67109	0.835547	+	0.549419i	$0.185151\pi$
$182$	1.27871	0.0947846
$183$	−4.95437	−0.366238
$184$	−4.80294	−0.354078
$185$	1.48340	0.109062
$186$	−0.132929	−0.00974680
$187$	−8.05410	−0.588974
$188$	−17.3771	−1.26735
$189$	1.00000	0.0727393
$190$	−1.69074	−0.122659
$191$	7.57655	0.548220	0.274110	−	0.961698i	$-0.411617\pi$
$191$	7.57655	0.548220	0.274110	+	0.961698i	$0.411617\pi$
$192$	−5.26144	−0.379712
$193$	−10.4529	−0.752413	−0.376206	−	0.926536i	$-0.622772\pi$
$193$	−10.4529	−0.752413	−0.376206	+	0.926536i	$0.622772\pi$
$194$	−5.78912	−0.415634
$195$	−3.69074	−0.264299
$196$	−1.87996	−0.134283
$197$	−19.3825	−1.38095	−0.690474	−	0.723357i	$-0.742598\pi$
$197$	−19.3825	−1.38095	−0.690474	+	0.723357i	$0.742598\pi$
$198$	0.346466	0.0246222
$199$	−9.62699	−0.682440	−0.341220	−	0.939984i	$-0.610840\pi$
$199$	−9.62699	−0.682440	−0.341220	+	0.939984i	$0.610840\pi$
$200$	−1.34427	−0.0950545
$201$	7.86707	0.554900
$202$	−3.88741	−0.273517
$203$	3.98492	0.279686
$204$	15.1414	1.06011
$205$	−6.17195	−0.431068
$206$	2.27652	0.158613
$207$	3.57289	0.248333
$208$	12.1580	0.843002
$209$	4.87996	0.337554
$210$	−0.346466	−0.0239084
$211$	21.4915	1.47954	0.739768	−	0.672862i	$-0.234935\pi$
$211$	21.4915	1.47954	0.739768	+	0.672862i	$0.234935\pi$
$212$	4.31297	0.296216
$213$	−8.25074	−0.565332
$214$	−3.06155	−0.209283
$215$	−8.94915	−0.610327
$216$	−1.34427	−0.0914662
$217$	−0.383670	−0.0260452
$218$	−2.85708	−0.193506
$219$	11.5482	0.780355
$220$	1.87996	0.126747
$221$	−29.7256	−1.99956
$222$	−0.513947	−0.0344939
$223$	12.5449	0.840070	0.420035	−	0.907508i	$-0.362018\pi$
$223$	12.5449	0.840070	0.420035	+	0.907508i	$0.362018\pi$
$224$	3.82987	0.255894
$225$	1.00000	0.0666667
$226$	−1.61890	−0.107688
$227$	−20.2208	−1.34210	−0.671052	−	0.741411i	$-0.734157\pi$
$227$	−20.2208	−1.34210	−0.671052	+	0.741411i	$0.734157\pi$
$228$	−9.17414	−0.607572
$229$	−10.2315	−0.676118	−0.338059	−	0.941125i	$-0.609770\pi$
$229$	−10.2315	−0.676118	−0.338059	+	0.941125i	$0.609770\pi$
$230$	−1.23788	−0.0816237
$231$	1.00000	0.0657952
$232$	−5.35682	−0.351692
$233$	20.8703	1.36726	0.683630	−	0.729829i	$-0.260400\pi$
$233$	20.8703	1.36726	0.683630	+	0.729829i	$0.260400\pi$
$234$	1.27871	0.0835922
$235$	−9.24332	−0.602968
$236$	−17.0172	−1.10773
$237$	6.30926	0.409831
$238$	−2.79047	−0.180879
$239$	0.436717	0.0282489	0.0141244	−	0.999900i	$-0.495504\pi$
$239$	0.436717	0.0282489	0.0141244	+	0.999900i	$0.495504\pi$
$240$	−3.29418	−0.212638
$241$	7.24417	0.466638	0.233319	−	0.972400i	$-0.425041\pi$
$241$	7.24417	0.466638	0.233319	+	0.972400i	$0.425041\pi$
$242$	0.346466	0.0222717
$243$	1.00000	0.0641500
$244$	9.31403	0.596269
$245$	−1.00000	−0.0638877
$246$	2.13837	0.136337
$247$	18.0107	1.14599
$248$	0.515758	0.0327507
$249$	−12.2614	−0.777037
$250$	−0.346466	−0.0219124
$251$	−6.37301	−0.402261	−0.201130	−	0.979565i	$-0.564461\pi$
$251$	−6.37301	−0.402261	−0.201130	+	0.979565i	$0.564461\pi$
$252$	−1.87996	−0.118426
$253$	3.57289	0.224626
$254$	7.03341	0.441316
$255$	8.05410	0.504367
$256$	7.23747	0.452342
$257$	18.3589	1.14520	0.572600	−	0.819835i	$-0.305935\pi$
$257$	18.3589	1.14520	0.572600	+	0.819835i	$0.305935\pi$
$258$	3.10057	0.193033
$259$	−1.48340	−0.0921741
$260$	6.93845	0.430304
$261$	3.98492	0.246660
$262$	−4.85421	−0.299894
$263$	−5.17414	−0.319051	−0.159526	−	0.987194i	$-0.550996\pi$
$263$	−5.17414	−0.319051	−0.159526	+	0.987194i	$0.550996\pi$
$264$	−1.34427	−0.0827343
$265$	2.29418	0.140930
$266$	1.69074	0.103666
$267$	11.7165	0.717037
$268$	−14.7898	−0.903430
$269$	−25.7121	−1.56769	−0.783847	−	0.620954i	$-0.786745\pi$
$269$	−25.7121	−1.56769	−0.783847	+	0.620954i	$0.786745\pi$
$270$	−0.346466	−0.0210852
$271$	24.7525	1.50361	0.751803	−	0.659388i	$-0.229185\pi$
$271$	24.7525	1.50361	0.751803	+	0.659388i	$0.229185\pi$
$272$	−26.5316	−1.60872
$273$	3.69074	0.223374
$274$	−2.90284	−0.175367
$275$	1.00000	0.0603023
$276$	−6.71690	−0.404310
$277$	11.8086	0.709507	0.354754	−	0.934960i	$-0.384565\pi$
$277$	11.8086	0.709507	0.354754	+	0.934960i	$0.384565\pi$
$278$	−4.69399	−0.281527
$279$	−0.383670	−0.0229697
$280$	1.34427	0.0803357
$281$	18.9297	1.12925	0.564625	−	0.825348i	$-0.309021\pi$
$281$	18.9297	1.12925	0.564625	+	0.825348i	$0.309021\pi$
$282$	3.20249	0.190706
$283$	17.0290	1.01227	0.506135	−	0.862454i	$-0.331074\pi$
$283$	17.0290	1.01227	0.506135	+	0.862454i	$0.331074\pi$
$284$	15.5111	0.920413
$285$	−4.87996	−0.289064
$286$	1.27871	0.0756120
$287$	6.17195	0.364319
$288$	3.82987	0.225677
$289$	47.8686	2.81580
$290$	−1.38064	−0.0810738
$291$	−16.7091	−0.979503
$292$	−21.7102	−1.27049
$293$	−7.66082	−0.447550	−0.223775	−	0.974641i	$-0.571838\pi$
$293$	−7.66082	−0.447550	−0.223775	+	0.974641i	$0.571838\pi$
$294$	0.346466	0.0202063
$295$	−9.05191	−0.527023
$296$	1.99410	0.115905
$297$	1.00000	0.0580259
$298$	−0.194022	−0.0112394
$299$	13.1866	0.762602
$300$	−1.87996	−0.108540
$301$	8.94915	0.515820
$302$	1.80311	0.103757
$303$	−11.2202	−0.644583
$304$	16.0755	0.921991
$305$	4.95437	0.283686
$306$	−2.79047	−0.159521
$307$	−6.16415	−0.351807	−0.175903	−	0.984407i	$-0.556285\pi$
$307$	−6.16415	−0.351807	−0.175903	+	0.984407i	$0.556285\pi$
$308$	−1.87996	−0.107121
$309$	6.57070	0.373794
$310$	0.132929	0.00754984
$311$	−33.0085	−1.87174	−0.935869	−	0.352347i	$-0.885384\pi$
$311$	−33.0085	−1.87174	−0.935869	+	0.352347i	$0.885384\pi$
$312$	−4.96136	−0.280882
$313$	−22.3005	−1.26050	−0.630248	−	0.776394i	$-0.717047\pi$
$313$	−22.3005	−1.26050	−0.630248	+	0.776394i	$0.717047\pi$
$314$	−5.73073	−0.323404
$315$	−1.00000	−0.0563436
$316$	−11.8612	−0.667243
$317$	−15.9175	−0.894016	−0.447008	−	0.894530i	$-0.647511\pi$
$317$	−15.9175	−0.894016	−0.447008	+	0.894530i	$0.647511\pi$
$318$	−0.794854	−0.0445732
$319$	3.98492	0.223113
$320$	5.26144	0.294123
$321$	−8.83652	−0.493207
$322$	1.23788	0.0689846
$323$	−39.3037	−2.18692
$324$	−1.87996	−0.104442
$325$	3.69074	0.204725
$326$	−4.12416	−0.228416
$327$	−8.24636	−0.456025
$328$	−8.29679	−0.458113
$329$	9.24332	0.509601
$330$	−0.346466	−0.0190723
$331$	−12.8066	−0.703915	−0.351957	−	0.936016i	$-0.614484\pi$
$331$	−12.8066	−0.703915	−0.351957	+	0.936016i	$0.614484\pi$
$332$	23.0510	1.26509
$333$	−1.48340	−0.0812899
$334$	−7.37360	−0.403466
$335$	−7.86707	−0.429824
$336$	3.29418	0.179712
$337$	−2.14363	−0.116771	−0.0583854	−	0.998294i	$-0.518595\pi$
$337$	−2.14363	−0.116771	−0.0583854	+	0.998294i	$0.518595\pi$
$338$	0.215348	0.0117134
$339$	−4.67262	−0.253782
$340$	−15.1414	−0.821158
$341$	−0.383670	−0.0207769
$342$	1.69074	0.0914247
$343$	1.00000	0.0539949
$344$	−12.0301	−0.648619
$345$	−3.57289	−0.192358
$346$	8.83130	0.474774
$347$	20.0650	1.07715	0.538573	−	0.842579i	$-0.318964\pi$
$347$	20.0650	1.07715	0.538573	+	0.842579i	$0.318964\pi$
$348$	−7.49149	−0.401586
$349$	18.9588	1.01484	0.507419	−	0.861699i	$-0.330599\pi$
$349$	18.9588	1.01484	0.507419	+	0.861699i	$0.330599\pi$
$350$	0.346466	0.0185194
$351$	3.69074	0.196997
$352$	3.82987	0.204133
$353$	−22.5530	−1.20038	−0.600189	−	0.799858i	$-0.704908\pi$
$353$	−22.5530	−1.20038	−0.600189	+	0.799858i	$0.704908\pi$
$354$	3.13618	0.166686
$355$	8.25074	0.437904
$356$	−22.0265	−1.16740
$357$	−8.05410	−0.426268
$358$	4.79220	0.253276
$359$	8.75407	0.462022	0.231011	−	0.972951i	$-0.425797\pi$
$359$	8.75407	0.462022	0.231011	+	0.972951i	$0.425797\pi$
$360$	1.34427	0.0708494
$361$	4.81402	0.253370
$362$	7.78933	0.409398
$363$	1.00000	0.0524864
$364$	−6.93845	−0.363673
$365$	−11.5482	−0.604460
$366$	−1.71652	−0.0897239
$367$	−32.2438	−1.68311	−0.841555	−	0.540171i	$-0.818359\pi$
$367$	−32.2438	−1.68311	−0.841555	+	0.540171i	$0.818359\pi$
$368$	11.7697	0.613540
$369$	6.17195	0.321299
$370$	0.513947	0.0267189
$371$	−2.29418	−0.119108
$372$	0.721286	0.0373969
$373$	0.0309728	0.00160371	0.000801856	−	1.00000i	$-0.499745\pi$
$373$	0.0309728	0.00160371	0.000801856		1.00000i	$0.499745\pi$
$374$	−2.79047	−0.144292
$375$	−1.00000	−0.0516398
$376$	−12.4256	−0.640799
$377$	14.7073	0.757464
$378$	0.346466	0.0178203
$379$	−0.294179	−0.0151109	−0.00755547	−	0.999971i	$-0.502405\pi$
$379$	−0.294179	−0.0151109	−0.00755547	+	0.999971i	$0.502405\pi$
$380$	9.17414	0.470623
$381$	20.3005	1.04002
$382$	2.62502	0.134308
$383$	−6.85443	−0.350245	−0.175122	−	0.984547i	$-0.556032\pi$
$383$	−6.85443	−0.350245	−0.175122	+	0.984547i	$0.556032\pi$
$384$	−9.48264	−0.483909
$385$	−1.00000	−0.0509647
$386$	−3.62156	−0.184332
$387$	8.94915	0.454911
$388$	31.4124	1.59472
$389$	5.88763	0.298514	0.149257	−	0.988798i	$-0.452312\pi$
$389$	5.88763	0.298514	0.149257	+	0.988798i	$0.452312\pi$
$390$	−1.27871	−0.0647502
$391$	−28.7764	−1.45529
$392$	−1.34427	−0.0678961
$393$	−14.0107	−0.706745
$394$	−6.71538	−0.338316
$395$	−6.30926	−0.317453
$396$	−1.87996	−0.0944716
$397$	−29.8336	−1.49730	−0.748652	−	0.662963i	$-0.769299\pi$
$397$	−29.8336	−1.49730	−0.748652	+	0.662963i	$0.769299\pi$
$398$	−3.33542	−0.167190
$399$	4.87996	0.244304
$400$	3.29418	0.164709
$401$	−8.01066	−0.400034	−0.200017	−	0.979792i	$-0.564100\pi$
$401$	−8.01066	−0.400034	−0.200017	+	0.979792i	$0.564100\pi$
$402$	2.72567	0.135944
$403$	−1.41603	−0.0705374
$404$	21.0935	1.04944
$405$	−1.00000	−0.0496904
$406$	1.38064	0.0685199
$407$	−1.48340	−0.0735295
$408$	10.8269	0.536012
$409$	−28.1499	−1.39192	−0.695961	−	0.718080i	$-0.745021\pi$
$409$	−28.1499	−1.39192	−0.695961	+	0.718080i	$0.745021\pi$
$410$	−2.13837	−0.105606
$411$	−8.37844	−0.413278
$412$	−12.3527	−0.608572
$413$	9.05191	0.445415
$414$	1.23788	0.0608387
$415$	12.2614	0.601890
$416$	14.1350	0.693027
$417$	−13.5482	−0.663458
$418$	1.69074	0.0826968
$419$	−2.73379	−0.133555	−0.0667773	−	0.997768i	$-0.521272\pi$
$419$	−2.73379	−0.133555	−0.0667773	+	0.997768i	$0.521272\pi$
$420$	1.87996	0.0917327
$421$	31.9974	1.55946	0.779729	−	0.626117i	$-0.215357\pi$
$421$	31.9974	1.55946	0.779729	+	0.626117i	$0.215357\pi$
$422$	7.44606	0.362469
$423$	9.24332	0.449426
$424$	3.08400	0.149772
$425$	−8.05410	−0.390681
$426$	−2.85860	−0.138500
$427$	−4.95437	−0.239759
$428$	16.6123	0.802987
$429$	3.69074	0.178191
$430$	−3.10057	−0.149523
$431$	24.3439	1.17260	0.586302	−	0.810092i	$-0.300583\pi$
$431$	24.3439	1.17260	0.586302	+	0.810092i	$0.300583\pi$
$432$	3.29418	0.158491
$433$	−32.2120	−1.54801	−0.774005	−	0.633179i	$-0.781750\pi$
$433$	−32.2120	−1.54801	−0.774005	+	0.633179i	$0.781750\pi$
$434$	−0.132929	−0.00638078
$435$	−3.98492	−0.191062
$436$	15.5028	0.742451
$437$	17.4356	0.834057
$438$	4.00105	0.191178
$439$	18.8240	0.898421	0.449211	−	0.893426i	$-0.351705\pi$
$439$	18.8240	0.898421	0.449211	+	0.893426i	$0.351705\pi$
$440$	1.34427	0.0640857
$441$	1.00000	0.0476190
$442$	−10.2989	−0.489868
$443$	−15.2485	−0.724480	−0.362240	−	0.932085i	$-0.617988\pi$
$443$	−15.2485	−0.724480	−0.362240	+	0.932085i	$0.617988\pi$
$444$	2.78874	0.132348
$445$	−11.7165	−0.555415
$446$	4.34638	0.205807
$447$	−0.560003	−0.0264872
$448$	−5.26144	−0.248580
$449$	14.4193	0.680488	0.340244	−	0.940337i	$-0.389490\pi$
$449$	14.4193	0.680488	0.340244	+	0.940337i	$0.389490\pi$
$450$	0.346466	0.0163325
$451$	6.17195	0.290626
$452$	8.78435	0.413181
$453$	5.20430	0.244520
$454$	−7.00582	−0.328799
$455$	−3.69074	−0.173025
$456$	−6.56000	−0.307200
$457$	−22.0266	−1.03036	−0.515180	−	0.857082i	$-0.672275\pi$
$457$	−22.0266	−1.03036	−0.515180	+	0.857082i	$0.672275\pi$
$458$	−3.54487	−0.165641
$459$	−8.05410	−0.375933
$460$	6.71690	0.313177
$461$	6.36074	0.296249	0.148125	−	0.988969i	$-0.452676\pi$
$461$	6.36074	0.296249	0.148125	+	0.988969i	$0.452676\pi$
$462$	0.346466	0.0161190
$463$	−0.751450	−0.0349229	−0.0174614	−	0.999848i	$-0.505558\pi$
$463$	−0.751450	−0.0349229	−0.0174614	+	0.999848i	$0.505558\pi$
$464$	13.1270	0.609407
$465$	0.383670	0.0177923
$466$	7.23085	0.334963
$467$	−4.76734	−0.220606	−0.110303	−	0.993898i	$-0.535182\pi$
$467$	−4.76734	−0.220606	−0.110303	+	0.993898i	$0.535182\pi$
$468$	−6.93845	−0.320730
$469$	7.86707	0.363268
$470$	−3.20249	−0.147720
$471$	−16.5405	−0.762148
$472$	−12.1682	−0.560089
$473$	8.94915	0.411482
$474$	2.18594	0.100404
$475$	4.87996	0.223908
$476$	15.1414	0.694005
$477$	−2.29418	−0.105043
$478$	0.151307	0.00692064
$479$	−4.14254	−0.189277	−0.0946387	−	0.995512i	$-0.530170\pi$
$479$	−4.14254	−0.189277	−0.0946387	+	0.995512i	$0.530170\pi$
$480$	−3.82987	−0.174809
$481$	−5.47485	−0.249631
$482$	2.50985	0.114321
$483$	3.57289	0.162572
$484$	−1.87996	−0.0854528
$485$	16.7091	0.758720
$486$	0.346466	0.0157160
$487$	3.45770	0.156683	0.0783416	−	0.996927i	$-0.475038\pi$
$487$	3.45770	0.156683	0.0783416	+	0.996927i	$0.475038\pi$
$488$	6.66003	0.301485
$489$	−11.9035	−0.538296
$490$	−0.346466	−0.0156517
$491$	5.93078	0.267652	0.133826	−	0.991005i	$-0.457274\pi$
$491$	5.93078	0.267652	0.133826	+	0.991005i	$0.457274\pi$
$492$	−11.6030	−0.523105
$493$	−32.0949	−1.44548
$494$	6.24008	0.280754
$495$	−1.00000	−0.0449467
$496$	−1.26388	−0.0567498
$497$	−8.25074	−0.370096
$498$	−4.24817	−0.190365
$499$	42.7153	1.91220	0.956101	−	0.293038i	$-0.0946662\pi$
$499$	42.7153	1.91220	0.956101	+	0.293038i	$0.0946662\pi$
$500$	1.87996	0.0840744
$501$	−21.2823	−0.950825
$502$	−2.20803	−0.0985491
$503$	−16.1231	−0.718892	−0.359446	−	0.933166i	$-0.617034\pi$
$503$	−16.1231	−0.718892	−0.359446	+	0.933166i	$0.617034\pi$
$504$	−1.34427	−0.0598787
$505$	11.2202	0.499292
$506$	1.23788	0.0550307
$507$	0.621555	0.0276042
$508$	−38.1641	−1.69326
$509$	7.82258	0.346730	0.173365	−	0.984858i	$-0.444536\pi$
$509$	7.82258	0.346730	0.173365	+	0.984858i	$0.444536\pi$
$510$	2.79047	0.123564
$511$	11.5482	0.510862
$512$	21.4728	0.948973
$513$	4.87996	0.215456
$514$	6.36074	0.280560
$515$	−6.57070	−0.289540
$516$	−16.8240	−0.740637
$517$	9.24332	0.406521
$518$	−0.513947	−0.0225816
$519$	25.4897	1.11887
$520$	4.96136	0.217570
$521$	−1.66938	−0.0731367	−0.0365684	−	0.999331i	$-0.511643\pi$
$521$	−1.66938	−0.0731367	−0.0365684	+	0.999331i	$0.511643\pi$
$522$	1.38064	0.0604288
$523$	−9.24749	−0.404365	−0.202182	−	0.979348i	$-0.564803\pi$
$523$	−9.24749	−0.404365	−0.202182	+	0.979348i	$0.564803\pi$
$524$	26.3395	1.15065
$525$	1.00000	0.0436436
$526$	−1.79266	−0.0781638
$527$	3.09012	0.134608
$528$	3.29418	0.143361
$529$	−10.2344	−0.444976
$530$	0.794854	0.0345263
$531$	9.05191	0.392819
$532$	−9.17414	−0.397749
$533$	22.7790	0.986670
$534$	4.05936	0.175666
$535$	8.83652	0.382036
$536$	−10.5755	−0.456792
$537$	13.8317	0.596881
$538$	−8.90836	−0.384067
$539$	1.00000	0.0430730
$540$	1.87996	0.0809007
$541$	29.0137	1.24740	0.623698	−	0.781665i	$-0.285629\pi$
$541$	29.0137	1.24740	0.623698	+	0.781665i	$0.285629\pi$
$542$	8.57588	0.368366
$543$	22.4823	0.964806
$544$	−30.8461	−1.32252
$545$	8.24636	0.353235
$546$	1.27871	0.0547239
$547$	−35.6928	−1.52611	−0.763057	−	0.646331i	$-0.776303\pi$
$547$	−35.6928	−1.52611	−0.763057	+	0.646331i	$0.776303\pi$
$548$	15.7512	0.672856
$549$	−4.95437	−0.211447
$550$	0.346466	0.0147733
$551$	19.4462	0.828438
$552$	−4.80294	−0.204427
$553$	6.30926	0.268297
$554$	4.09126	0.173821
$555$	1.48340	0.0629669
$556$	25.4701	1.08017
$557$	16.6602	0.705915	0.352958	−	0.935639i	$-0.385176\pi$
$557$	16.6602	0.705915	0.352958	+	0.935639i	$0.385176\pi$
$558$	−0.132929	−0.00562732
$559$	33.0290	1.39698
$560$	−3.29418	−0.139204
$561$	−8.05410	−0.340044
$562$	6.55848	0.276653
$563$	26.4077	1.11295	0.556475	−	0.830864i	$-0.312154\pi$
$563$	26.4077	1.11295	0.556475	+	0.830864i	$0.312154\pi$
$564$	−17.3771	−0.731708
$565$	4.67262	0.196579
$566$	5.89997	0.247994
$567$	1.00000	0.0419961
$568$	11.0913	0.465379
$569$	−7.71029	−0.323232	−0.161616	−	0.986854i	$-0.551671\pi$
$569$	−7.71029	−0.323232	−0.161616	+	0.986854i	$0.551671\pi$
$570$	−1.69074	−0.0708173
$571$	−0.443244	−0.0185492	−0.00927460	−	0.999957i	$-0.502952\pi$
$571$	−0.443244	−0.0185492	−0.00927460	+	0.999957i	$0.502952\pi$
$572$	−6.93845	−0.290111
$573$	7.57655	0.316515
$574$	2.13837	0.0892538
$575$	3.57289	0.149000
$576$	−5.26144	−0.219227
$577$	43.5368	1.81246	0.906230	−	0.422785i	$-0.138947\pi$
$577$	43.5368	1.81246	0.906230	+	0.422785i	$0.138947\pi$
$578$	16.5848	0.689837
$579$	−10.4529	−0.434406
$580$	7.49149	0.311067
$581$	−12.2614	−0.508690
$582$	−5.78912	−0.239967
$583$	−2.29418	−0.0950152
$584$	−15.5239	−0.642385
$585$	−3.69074	−0.152593
$586$	−2.65421	−0.109644
$587$	−4.04521	−0.166964	−0.0834819	−	0.996509i	$-0.526604\pi$
$587$	−4.04521	−0.166964	−0.0834819	+	0.996509i	$0.526604\pi$
$588$	−1.87996	−0.0775283
$589$	−1.87230	−0.0771466
$590$	−3.13618	−0.129114
$591$	−19.3825	−0.797291
$592$	−4.88659	−0.200838
$593$	−10.3225	−0.423894	−0.211947	−	0.977281i	$-0.567980\pi$
$593$	−10.3225	−0.423894	−0.211947	+	0.977281i	$0.567980\pi$
$594$	0.346466	0.0142157
$595$	8.05410	0.330186
$596$	1.05278	0.0431237
$597$	−9.62699	−0.394007
$598$	4.56871	0.186828
$599$	6.67608	0.272777	0.136389	−	0.990655i	$-0.456450\pi$
$599$	6.67608	0.272777	0.136389	+	0.990655i	$0.456450\pi$
$600$	−1.34427	−0.0548797
$601$	14.8933	0.607509	0.303755	−	0.952750i	$-0.401760\pi$
$601$	14.8933	0.607509	0.303755	+	0.952750i	$0.401760\pi$
$602$	3.10057	0.126370
$603$	7.86707	0.320372
$604$	−9.78389	−0.398101
$605$	−1.00000	−0.0406558
$606$	−3.88741	−0.157915
$607$	27.7040	1.12447	0.562235	−	0.826978i	$-0.309942\pi$
$607$	27.7040	1.12447	0.562235	+	0.826978i	$0.309942\pi$
$608$	18.6896	0.757963
$609$	3.98492	0.161477
$610$	1.71652	0.0694998
$611$	34.1147	1.38013
$612$	15.1414	0.612055
$613$	34.3733	1.38832	0.694162	−	0.719818i	$-0.255775\pi$
$613$	34.3733	1.38832	0.694162	+	0.719818i	$0.255775\pi$
$614$	−2.13567	−0.0861885
$615$	−6.17195	−0.248877
$616$	−1.34427	−0.0541623
$617$	−22.1082	−0.890043	−0.445021	−	0.895520i	$-0.646804\pi$
$617$	−22.1082	−0.890043	−0.445021	+	0.895520i	$0.646804\pi$
$618$	2.27652	0.0915752
$619$	−44.9783	−1.80783	−0.903915	−	0.427711i	$-0.859320\pi$
$619$	−44.9783	−1.80783	−0.903915	+	0.427711i	$0.859320\pi$
$620$	−0.721286	−0.0289675
$621$	3.57289	0.143375
$622$	−11.4363	−0.458554
$623$	11.7165	0.469411
$624$	12.1580	0.486708
$625$	1.00000	0.0400000
$626$	−7.72634	−0.308807
$627$	4.87996	0.194887
$628$	31.0956	1.24085
$629$	11.9475	0.476377
$630$	−0.346466	−0.0138035
$631$	33.2160	1.32231	0.661154	−	0.750251i	$-0.270067\pi$
$631$	33.2160	1.32231	0.661154	+	0.750251i	$0.270067\pi$
$632$	−8.48137	−0.337371
$633$	21.4915	0.854210
$634$	−5.51487	−0.219024
$635$	−20.3005	−0.805599
$636$	4.31297	0.171020
$637$	3.69074	0.146232
$638$	1.38064	0.0546599
$639$	−8.25074	−0.326394
$640$	9.48264	0.374834
$641$	−2.69656	−0.106508	−0.0532539	−	0.998581i	$-0.516959\pi$
$641$	−2.69656	−0.106508	−0.0532539	+	0.998581i	$0.516959\pi$
$642$	−3.06155	−0.120830
$643$	−17.8226	−0.702854	−0.351427	−	0.936215i	$-0.614303\pi$
$643$	−17.8226	−0.702854	−0.351427	+	0.936215i	$0.614303\pi$
$644$	−6.71690	−0.264683
$645$	−8.94915	−0.352372
$646$	−13.6174	−0.535769
$647$	7.87251	0.309500	0.154750	−	0.987954i	$-0.450543\pi$
$647$	7.87251	0.309500	0.154750	+	0.987954i	$0.450543\pi$
$648$	−1.34427	−0.0528080
$649$	9.05191	0.355319
$650$	1.27871	0.0501553
$651$	−0.383670	−0.0150372
$652$	22.3782	0.876396
$653$	44.0968	1.72564	0.862821	−	0.505509i	$-0.168695\pi$
$653$	44.0968	1.72564	0.862821	+	0.505509i	$0.168695\pi$
$654$	−2.85708	−0.111721
$655$	14.0107	0.547442
$656$	20.3315	0.793812
$657$	11.5482	0.450538
$658$	3.20249	0.124846
$659$	27.8400	1.08449	0.542247	−	0.840219i	$-0.317574\pi$
$659$	27.8400	1.08449	0.542247	+	0.840219i	$0.317574\pi$
$660$	1.87996	0.0731774
$661$	−8.51221	−0.331087	−0.165543	−	0.986203i	$-0.552938\pi$
$661$	−8.51221	−0.331087	−0.165543	+	0.986203i	$0.552938\pi$
$662$	−4.43705	−0.172451
$663$	−29.7256	−1.15445
$664$	16.4827	0.639654
$665$	−4.87996	−0.189237
$666$	−0.513947	−0.0199151
$667$	14.2377	0.551285
$668$	40.0100	1.54803
$669$	12.5449	0.485015
$670$	−2.72567	−0.105302
$671$	−4.95437	−0.191261
$672$	3.82987	0.147740
$673$	−3.74379	−0.144312	−0.0721562	−	0.997393i	$-0.522988\pi$
$673$	−3.74379	−0.144312	−0.0721562	+	0.997393i	$0.522988\pi$
$674$	−0.742693	−0.0286075
$675$	1.00000	0.0384900
$676$	−1.16850	−0.0449423
$677$	37.5997	1.44507	0.722537	−	0.691332i	$-0.242976\pi$
$677$	37.5997	1.44507	0.722537	+	0.691332i	$0.242976\pi$
$678$	−1.61890	−0.0621736
$679$	−16.7091	−0.641235
$680$	−10.8269	−0.415193
$681$	−20.2208	−0.774864
$682$	−0.132929	−0.00509010
$683$	−15.4275	−0.590318	−0.295159	−	0.955448i	$-0.595373\pi$
$683$	−15.4275	−0.590318	−0.295159	+	0.955448i	$0.595373\pi$
$684$	−9.17414	−0.350782
$685$	8.37844	0.320124
$686$	0.346466	0.0132281
$687$	−10.2315	−0.390357
$688$	29.4801	1.12392
$689$	−8.46721	−0.322575
$690$	−1.23788	−0.0471255
$691$	−38.3345	−1.45831	−0.729157	−	0.684347i	$-0.760087\pi$
$691$	−38.3345	−1.45831	−0.729157	+	0.684347i	$0.760087\pi$
$692$	−47.9196	−1.82163
$693$	1.00000	0.0379869
$694$	6.95184	0.263888
$695$	13.5482	0.513913
$696$	−5.35682	−0.203050
$697$	−49.7095	−1.88288
$698$	6.56856	0.248624
$699$	20.8703	0.789388
$700$	−1.87996	−0.0710559
$701$	13.5585	0.512099	0.256049	−	0.966664i	$-0.417579\pi$
$701$	13.5585	0.512099	0.256049	+	0.966664i	$0.417579\pi$
$702$	1.27871	0.0482620
$703$	−7.23894	−0.273022
$704$	−5.26144	−0.198298
$705$	−9.24332	−0.348124
$706$	−7.81386	−0.294078
$707$	−11.2202	−0.421979
$708$	−17.0172	−0.639547
$709$	6.09910	0.229057	0.114528	−	0.993420i	$-0.463464\pi$
$709$	6.09910	0.229057	0.114528	+	0.993420i	$0.463464\pi$
$710$	2.85860	0.107281
$711$	6.30926	0.236616
$712$	−15.7502	−0.590262
$713$	−1.37081	−0.0513374
$714$	−2.79047	−0.104431
$715$	−3.69074	−0.138026
$716$	−26.0030	−0.971779
$717$	0.436717	0.0163095
$718$	3.03298	0.113190
$719$	−22.8581	−0.852463	−0.426231	−	0.904614i	$-0.640159\pi$
$719$	−22.8581	−0.852463	−0.426231	+	0.904614i	$0.640159\pi$
$720$	−3.29418	−0.122767
$721$	6.57070	0.244706
$722$	1.66789	0.0620726
$723$	7.24417	0.269413
$724$	−42.2658	−1.57080
$725$	3.98492	0.147996
$726$	0.346466	0.0128585
$727$	−35.7901	−1.32738	−0.663691	−	0.748006i	$-0.731011\pi$
$727$	−35.7901	−1.32738	−0.663691	+	0.748006i	$0.731011\pi$
$728$	−4.96136	−0.183880
$729$	1.00000	0.0370370
$730$	−4.00105	−0.148086
$731$	−72.0773	−2.66588
$732$	9.31403	0.344256
$733$	3.01655	0.111419	0.0557094	−	0.998447i	$-0.482258\pi$
$733$	3.01655	0.111419	0.0557094	+	0.998447i	$0.482258\pi$
$734$	−11.1714	−0.412342
$735$	−1.00000	−0.0368856
$736$	13.6837	0.504388
$737$	7.86707	0.289787
$738$	2.13837	0.0787144
$739$	−20.2596	−0.745261	−0.372631	−	0.927980i	$-0.621544\pi$
$739$	−20.2596	−0.745261	−0.372631	+	0.927980i	$0.621544\pi$
$740$	−2.78874	−0.102516
$741$	18.0107	0.661638
$742$	−0.794854	−0.0291800
$743$	−20.9489	−0.768541	−0.384270	−	0.923221i	$-0.625547\pi$
$743$	−20.9489	−0.768541	−0.384270	+	0.923221i	$0.625547\pi$
$744$	0.515758	0.0189086
$745$	0.560003	0.0205169
$746$	0.0107310	0.000392890 0
$747$	−12.2614	−0.448623
$748$	15.1414	0.553624
$749$	−8.83652	−0.322880
$750$	−0.346466	−0.0126511
$751$	−10.5150	−0.383699	−0.191850	−	0.981424i	$-0.561449\pi$
$751$	−10.5150	−0.383699	−0.191850	+	0.981424i	$0.561449\pi$
$752$	30.4492	1.11037
$753$	−6.37301	−0.232245
$754$	5.09557	0.185570
$755$	−5.20430	−0.189404
$756$	−1.87996	−0.0683735
$757$	26.9162	0.978284	0.489142	−	0.872204i	$-0.337310\pi$
$757$	26.9162	0.978284	0.489142	+	0.872204i	$0.337310\pi$
$758$	−0.101923	−0.00370200
$759$	3.57289	0.129688
$760$	6.56000	0.237956
$761$	36.1259	1.30956	0.654781	−	0.755818i	$-0.272761\pi$
$761$	36.1259	1.30956	0.654781	+	0.755818i	$0.272761\pi$
$762$	7.03341	0.254794
$763$	−8.24636	−0.298538
$764$	−14.2436	−0.515317
$765$	8.05410	0.291197
$766$	−2.37482	−0.0858059
$767$	33.4082	1.20630
$768$	7.23747	0.261160
$769$	−7.11490	−0.256570	−0.128285	−	0.991737i	$-0.540947\pi$
$769$	−7.11490	−0.256570	−0.128285	+	0.991737i	$0.540947\pi$
$770$	−0.346466	−0.0124858
$771$	18.3589	0.661181
$772$	19.6510	0.707254
$773$	−10.5530	−0.379567	−0.189783	−	0.981826i	$-0.560779\pi$
$773$	−10.5530	−0.379567	−0.189783	+	0.981826i	$0.560779\pi$
$774$	3.10057	0.111448
$775$	−0.383670	−0.0137818
$776$	22.4616	0.806323
$777$	−1.48340	−0.0532167
$778$	2.03986	0.0731325
$779$	30.1189	1.07912
$780$	6.93845	0.248436
$781$	−8.25074	−0.295235
$782$	−9.97005	−0.356528
$783$	3.98492	0.142409
$784$	3.29418	0.117649
$785$	16.5405	0.590357
$786$	−4.85421	−0.173144
$787$	−30.6250	−1.09166	−0.545832	−	0.837895i	$-0.683786\pi$
$787$	−30.6250	−1.09166	−0.545832	+	0.837895i	$0.683786\pi$
$788$	36.4384	1.29806
$789$	−5.17414	−0.184204
$790$	−2.18594	−0.0777723
$791$	−4.67262	−0.166139
$792$	−1.34427	−0.0477667
$793$	−18.2853	−0.649330
$794$	−10.3363	−0.366822
$795$	2.29418	0.0813661
$796$	18.0984	0.641480
$797$	36.4866	1.29242	0.646212	−	0.763158i	$-0.276352\pi$
$797$	36.4866	1.29242	0.646212	+	0.763158i	$0.276352\pi$
$798$	1.69074	0.0598515
$799$	−74.4467	−2.63373
$800$	3.82987	0.135406
$801$	11.7165	0.413982
$802$	−2.77542	−0.0980035
$803$	11.5482	0.407527
$804$	−14.7898	−0.521596
$805$	−3.57289	−0.125928
$806$	−0.490605	−0.0172808
$807$	−25.7121	−0.905109
$808$	15.0830	0.530618
$809$	−12.6521	−0.444825	−0.222412	−	0.974953i	$-0.571393\pi$
$809$	−12.6521	−0.444825	−0.222412	+	0.974953i	$0.571393\pi$
$810$	−0.346466	−0.0121736
$811$	4.82148	0.169305	0.0846525	−	0.996411i	$-0.473022\pi$
$811$	4.82148	0.169305	0.0846525	+	0.996411i	$0.473022\pi$
$812$	−7.49149	−0.262900
$813$	24.7525	0.868107
$814$	−0.513947	−0.0180139
$815$	11.9035	0.416962
$816$	−26.5316	−0.928793
$817$	43.6715	1.52787
$818$	−9.75296	−0.341004
$819$	3.69074	0.128965
$820$	11.6030	0.405195
$821$	−9.25424	−0.322975	−0.161488	−	0.986875i	$-0.551629\pi$
$821$	−9.25424	−0.322975	−0.161488	+	0.986875i	$0.551629\pi$
$822$	−2.90284	−0.101248
$823$	−54.6966	−1.90660	−0.953301	−	0.302021i	$-0.902339\pi$
$823$	−54.6966	−1.90660	−0.953301	+	0.302021i	$0.902339\pi$
$824$	−8.83282	−0.307706
$825$	1.00000	0.0348155
$826$	3.13618	0.109122
$827$	22.4997	0.782390	0.391195	−	0.920308i	$-0.372062\pi$
$827$	22.4997	0.782390	0.391195	+	0.920308i	$0.372062\pi$
$828$	−6.71690	−0.233428
$829$	47.9977	1.66703	0.833515	−	0.552497i	$-0.186325\pi$
$829$	47.9977	1.66703	0.833515	+	0.552497i	$0.186325\pi$
$830$	4.24817	0.147456
$831$	11.8086	0.409634
$832$	−19.4186	−0.673219
$833$	−8.05410	−0.279058
$834$	−4.69399	−0.162539
$835$	21.2823	0.736506
$836$	−9.17414	−0.317294
$837$	−0.383670	−0.0132616
$838$	−0.947166	−0.0327193
$839$	−56.0400	−1.93472	−0.967359	−	0.253412i	$-0.918447\pi$
$839$	−56.0400	−1.93472	−0.967359	+	0.253412i	$0.918447\pi$
$840$	1.34427	0.0463818
$841$	−13.1204	−0.452429
$842$	11.0860	0.382049
$843$	18.9297	0.651973
$844$	−40.4032	−1.39073
$845$	−0.621555	−0.0213821
$846$	3.20249	0.110104
$847$	1.00000	0.0343604
$848$	−7.55743	−0.259523
$849$	17.0290	0.584435
$850$	−2.79047	−0.0957123
$851$	−5.30003	−0.181683
$852$	15.5111	0.531401
$853$	−2.66849	−0.0913672	−0.0456836	−	0.998956i	$-0.514547\pi$
$853$	−2.66849	−0.0913672	−0.0456836	+	0.998956i	$0.514547\pi$
$854$	−1.71652	−0.0587381
$855$	−4.87996	−0.166891
$856$	11.8787	0.406006
$857$	−51.2959	−1.75223	−0.876117	−	0.482099i	$-0.839874\pi$
$857$	−51.2959	−1.75223	−0.876117	+	0.482099i	$0.839874\pi$
$858$	1.27871	0.0436546
$859$	−39.0707	−1.33308	−0.666538	−	0.745471i	$-0.732224\pi$
$859$	−39.0707	−1.33308	−0.666538	+	0.745471i	$0.732224\pi$
$860$	16.8240	0.573695
$861$	6.17195	0.210339
$862$	8.43432	0.287274
$863$	−44.3974	−1.51130	−0.755652	−	0.654973i	$-0.772680\pi$
$863$	−44.3974	−1.51130	−0.755652	+	0.654973i	$0.772680\pi$
$864$	3.82987	0.130295
$865$	−25.4897	−0.866675
$866$	−11.1604	−0.379244
$867$	47.8686	1.62570
$868$	0.721286	0.0244820
$869$	6.30926	0.214027
$870$	−1.38064	−0.0468080
$871$	29.0353	0.983824
$872$	11.0854	0.375398
$873$	−16.7091	−0.565516
$874$	6.04083	0.204334
$875$	−1.00000	−0.0338062
$876$	−21.7102	−0.733519
$877$	−0.264983	−0.00894784	−0.00447392	−	0.999990i	$-0.501424\pi$
$877$	−0.264983	−0.00894784	−0.00447392	+	0.999990i	$0.501424\pi$
$878$	6.52188	0.220103
$879$	−7.66082	−0.258393
$880$	−3.29418	−0.111047
$881$	−19.1957	−0.646720	−0.323360	−	0.946276i	$-0.604812\pi$
$881$	−19.1957	−0.646720	−0.323360	+	0.946276i	$0.604812\pi$
$882$	0.346466	0.0116661
$883$	−16.5938	−0.558426	−0.279213	−	0.960229i	$-0.590074\pi$
$883$	−16.5938	−0.558426	−0.279213	+	0.960229i	$0.590074\pi$
$884$	55.8830	1.87955
$885$	−9.05191	−0.304277
$886$	−5.28310	−0.177489
$887$	27.1523	0.911685	0.455843	−	0.890060i	$-0.349338\pi$
$887$	27.1523	0.911685	0.455843	+	0.890060i	$0.349338\pi$
$888$	1.99410	0.0669175
$889$	20.3005	0.680856
$890$	−4.05936	−0.136070
$891$	1.00000	0.0335013
$892$	−23.5840	−0.789650
$893$	45.1071	1.50945
$894$	−0.194022	−0.00648906
$895$	−13.8317	−0.462342
$896$	−9.48264	−0.316793
$897$	13.1866	0.440288
$898$	4.99578	0.166711
$899$	−1.52890	−0.0509915
$900$	−1.87996	−0.0626654
$901$	18.4775	0.615576
$902$	2.13837	0.0711999
$903$	8.94915	0.297809
$904$	6.28128	0.208912
$905$	−22.4823	−0.747336
$906$	1.80311	0.0599044
$907$	5.56569	0.184806	0.0924028	−	0.995722i	$-0.470545\pi$
$907$	5.56569	0.184806	0.0924028	+	0.995722i	$0.470545\pi$
$908$	38.0144	1.26155
$909$	−11.2202	−0.372150
$910$	−1.27871	−0.0423890
$911$	−36.6294	−1.21359	−0.606793	−	0.794860i	$-0.707544\pi$
$911$	−36.6294	−1.21359	−0.606793	+	0.794860i	$0.707544\pi$
$912$	16.0755	0.532312
$913$	−12.2614	−0.405794
$914$	−7.63146	−0.252426
$915$	4.95437	0.163786
$916$	19.2349	0.635538
$917$	−14.0107	−0.462673
$918$	−2.79047	−0.0920992
$919$	−44.8730	−1.48022	−0.740111	−	0.672484i	$-0.765227\pi$
$919$	−44.8730	−1.48022	−0.740111	+	0.672484i	$0.765227\pi$
$920$	4.80294	0.158348
$921$	−6.16415	−0.203116
$922$	2.20378	0.0725776
$923$	−30.4513	−1.00232
$924$	−1.87996	−0.0618462
$925$	−1.48340	−0.0487739
$926$	−0.260352	−0.00855569
$927$	6.57070	0.215810
$928$	15.2617	0.500990
$929$	1.09423	0.0359004	0.0179502	−	0.999839i	$-0.494286\pi$
$929$	1.09423	0.0359004	0.0179502	+	0.999839i	$0.494286\pi$
$930$	0.132929	0.00435890
$931$	4.87996	0.159934
$932$	−39.2354	−1.28520
$933$	−33.0085	−1.08065
$934$	−1.65172	−0.0540459
$935$	8.05410	0.263397
$936$	−4.96136	−0.162167
$937$	−35.1612	−1.14867	−0.574333	−	0.818622i	$-0.694739\pi$
$937$	−35.1612	−1.14867	−0.574333	+	0.818622i	$0.694739\pi$
$938$	2.72567	0.0889963
$939$	−22.3005	−0.727748
$940$	17.3771	0.566778
$941$	11.3841	0.371112	0.185556	−	0.982634i	$-0.440591\pi$
$941$	11.3841	0.371112	0.185556	+	0.982634i	$0.440591\pi$
$942$	−5.73073	−0.186717
$943$	22.0517	0.718102
$944$	29.8186	0.970513
$945$	−1.00000	−0.0325300
$946$	3.10057	0.100808
$947$	−14.3145	−0.465157	−0.232579	−	0.972578i	$-0.574716\pi$
$947$	−14.3145	−0.465157	−0.232579	+	0.972578i	$0.574716\pi$
$948$	−11.8612	−0.385233
$949$	42.6214	1.38355
$950$	1.69074	0.0548548
$951$	−15.9175	−0.516161
$952$	10.8269	0.350902
$953$	−41.8177	−1.35461	−0.677304	−	0.735703i	$-0.736852\pi$
$953$	−41.8177	−1.35461	−0.677304	+	0.735703i	$0.736852\pi$
$954$	−0.794854	−0.0257344
$955$	−7.57655	−0.245172
$956$	−0.821011	−0.0265534
$957$	3.98492	0.128814
$958$	−1.43525	−0.0463707
$959$	−8.37844	−0.270554
$960$	5.26144	0.169812
$961$	−30.8528	−0.995252
$962$	−1.89685	−0.0611568
$963$	−8.83652	−0.284753
$964$	−13.6188	−0.438630
$965$	10.4529	0.336489
$966$	1.23788	0.0398283
$967$	11.5066	0.370026	0.185013	−	0.982736i	$-0.440767\pi$
$967$	11.5066	0.370026	0.185013	+	0.982736i	$0.440767\pi$
$968$	−1.34427	−0.0432066
$969$	−39.3037	−1.26262
$970$	5.78912	0.185877
$971$	25.5857	0.821083	0.410542	−	0.911842i	$-0.365340\pi$
$971$	25.5857	0.821083	0.410542	+	0.911842i	$0.365340\pi$
$972$	−1.87996	−0.0602998
$973$	−13.5482	−0.434335
$974$	1.19797	0.0383856
$975$	3.69074	0.118198
$976$	−16.3206	−0.522409
$977$	25.9826	0.831256	0.415628	−	0.909535i	$-0.363562\pi$
$977$	25.9826	0.831256	0.415628	+	0.909535i	$0.363562\pi$
$978$	−4.12416	−0.131876
$979$	11.7165	0.374461
$980$	1.87996	0.0600532
$981$	−8.24636	−0.263286
$982$	2.05481	0.0655717
$983$	0.992582	0.0316585	0.0158292	−	0.999875i	$-0.494961\pi$
$983$	0.992582	0.0316585	0.0158292	+	0.999875i	$0.494961\pi$
$984$	−8.29679	−0.264492
$985$	19.3825	0.617579
$986$	−11.1198	−0.354126
$987$	9.24332	0.294218
$988$	−33.8594	−1.07721
$989$	31.9743	1.01672
$990$	−0.346466	−0.0110114
$991$	−0.600585	−0.0190782	−0.00953911	−	0.999955i	$-0.503036\pi$
$991$	−0.600585	−0.0190782	−0.00953911	+	0.999955i	$0.503036\pi$
$992$	−1.46941	−0.0466537
$993$	−12.8066	−0.406405
$994$	−2.85860	−0.0906692
$995$	9.62699	0.305196
$996$	23.0510	0.730400
$997$	−12.1506	−0.384814	−0.192407	−	0.981315i	$-0.561629\pi$
$997$	−12.1506	−0.384814	−0.192407	+	0.981315i	$0.561629\pi$
$998$	14.7994	0.468467
$999$	−1.48340	−0.0469327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.w.1.3	✓	5
3.2	odd	2		3465.2.a.bm.1.3		5
5.4	even	2		5775.2.a.cg.1.3		5
7.6	odd	2		8085.2.a.bv.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.w.1.3	✓	5	1.1	even	1	trivial
3465.2.a.bm.1.3		5	3.2	odd	2
5775.2.a.cg.1.3		5	5.4	even	2
8085.2.a.bv.1.3		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q+0.346466 q^{2} +1.00000 q^{3} -1.87996 q^{4} -1.00000 q^{5} +0.346466 q^{6} +1.00000 q^{7} -1.34427 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.346466 q^{2} +1.00000 q^{3} -1.87996 q^{4} -1.00000 q^{5} +0.346466 q^{6} +1.00000 q^{7} -1.34427 q^{8} +1.00000 q^{9} -0.346466 q^{10} +1.00000 q^{11} -1.87996 q^{12} +3.69074 q^{13} +0.346466 q^{14} -1.00000 q^{15} +3.29418 q^{16} -8.05410 q^{17} +0.346466 q^{18} +4.87996 q^{19} +1.87996 q^{20} +1.00000 q^{21} +0.346466 q^{22} +3.57289 q^{23} -1.34427 q^{24} +1.00000 q^{25} +1.27871 q^{26} +1.00000 q^{27} -1.87996 q^{28} +3.98492 q^{29} -0.346466 q^{30} -0.383670 q^{31} +3.82987 q^{32} +1.00000 q^{33} -2.79047 q^{34} -1.00000 q^{35} -1.87996 q^{36} -1.48340 q^{37} +1.69074 q^{38} +3.69074 q^{39} +1.34427 q^{40} +6.17195 q^{41} +0.346466 q^{42} +8.94915 q^{43} -1.87996 q^{44} -1.00000 q^{45} +1.23788 q^{46} +9.24332 q^{47} +3.29418 q^{48} +1.00000 q^{49} +0.346466 q^{50} -8.05410 q^{51} -6.93845 q^{52} -2.29418 q^{53} +0.346466 q^{54} -1.00000 q^{55} -1.34427 q^{56} +4.87996 q^{57} +1.38064 q^{58} +9.05191 q^{59} +1.87996 q^{60} -4.95437 q^{61} -0.132929 q^{62} +1.00000 q^{63} -5.26144 q^{64} -3.69074 q^{65} +0.346466 q^{66} +7.86707 q^{67} +15.1414 q^{68} +3.57289 q^{69} -0.346466 q^{70} -8.25074 q^{71} -1.34427 q^{72} +11.5482 q^{73} -0.513947 q^{74} +1.00000 q^{75} -9.17414 q^{76} +1.00000 q^{77} +1.27871 q^{78} +6.30926 q^{79} -3.29418 q^{80} +1.00000 q^{81} +2.13837 q^{82} -12.2614 q^{83} -1.87996 q^{84} +8.05410 q^{85} +3.10057 q^{86} +3.98492 q^{87} -1.34427 q^{88} +11.7165 q^{89} -0.346466 q^{90} +3.69074 q^{91} -6.71690 q^{92} -0.383670 q^{93} +3.20249 q^{94} -4.87996 q^{95} +3.82987 q^{96} -16.7091 q^{97} +0.346466 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} + 5 q^{3} + 9 q^{4} - 5 q^{5} + q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} + 5 q^{11} + 9 q^{12} + 8 q^{13} + q^{14} - 5 q^{15} + 13 q^{16} + q^{18} + 6 q^{19} - 9 q^{20} + 5 q^{21} + q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} - 10 q^{26} + 5 q^{27} + 9 q^{28} + 6 q^{29} - q^{30} + 10 q^{31} + 7 q^{32} + 5 q^{33} - 4 q^{34} - 5 q^{35} + 9 q^{36} + 4 q^{37} - 2 q^{38} + 8 q^{39} - 3 q^{40} + q^{42} + 9 q^{44} - 5 q^{45} + 34 q^{46} - 2 q^{47} + 13 q^{48} + 5 q^{49} + q^{50} + 6 q^{52} - 8 q^{53} + q^{54} - 5 q^{55} + 3 q^{56} + 6 q^{57} - 4 q^{59} - 9 q^{60} + 16 q^{61} - 24 q^{62} + 5 q^{63} + 13 q^{64} - 8 q^{65} + q^{66} + 16 q^{67} + 18 q^{68} - 2 q^{69} - q^{70} - 6 q^{71} + 3 q^{72} + 2 q^{73} - 18 q^{74} + 5 q^{75} - 24 q^{76} + 5 q^{77} - 10 q^{78} + 42 q^{79} - 13 q^{80} + 5 q^{81} - 42 q^{82} - 22 q^{83} + 9 q^{84} + 2 q^{86} + 6 q^{87} + 3 q^{88} - 10 q^{89} - q^{90} + 8 q^{91} - 32 q^{92} + 10 q^{93} + 12 q^{94} - 6 q^{95} + 7 q^{96} - 2 q^{97} + q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 9 * q^4 - 5 * q^5 + q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - q^10 + 5 * q^11 + 9 * q^12 + 8 * q^13 + q^14 - 5 * q^15 + 13 * q^16 + q^18 + 6 * q^19 - 9 * q^20 + 5 * q^21 + q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 - 10 * q^26 + 5 * q^27 + 9 * q^28 + 6 * q^29 - q^30 + 10 * q^31 + 7 * q^32 + 5 * q^33 - 4 * q^34 - 5 * q^35 + 9 * q^36 + 4 * q^37 - 2 * q^38 + 8 * q^39 - 3 * q^40 + q^42 + 9 * q^44 - 5 * q^45 + 34 * q^46 - 2 * q^47 + 13 * q^48 + 5 * q^49 + q^50 + 6 * q^52 - 8 * q^53 + q^54 - 5 * q^55 + 3 * q^56 + 6 * q^57 - 4 * q^59 - 9 * q^60 + 16 * q^61 - 24 * q^62 + 5 * q^63 + 13 * q^64 - 8 * q^65 + q^66 + 16 * q^67 + 18 * q^68 - 2 * q^69 - q^70 - 6 * q^71 + 3 * q^72 + 2 * q^73 - 18 * q^74 + 5 * q^75 - 24 * q^76 + 5 * q^77 - 10 * q^78 + 42 * q^79 - 13 * q^80 + 5 * q^81 - 42 * q^82 - 22 * q^83 + 9 * q^84 + 2 * q^86 + 6 * q^87 + 3 * q^88 - 10 * q^89 - q^90 + 8 * q^91 - 32 * q^92 + 10 * q^93 + 12 * q^94 - 6 * q^95 + 7 * q^96 - 2 * q^97 + q^98 + 5 * q^99

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