LMFDB - Embedded newform 5577.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.181057.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 7x^{2} + 2x - 3 $ x^5 - 2x^4 - 4x^3 + 7x^2 + 2x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.44841$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.44841 q^{2} +1.00000 q^{3} +0.0978930 q^{4} -0.404514 q^{5} +1.44841 q^{6} +2.87958 q^{7} -2.75503 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.44841 q^{2} +1.00000 q^{3} +0.0978930 q^{4} -0.404514 q^{5} +1.44841 q^{6} +2.87958 q^{7} -2.75503 q^{8} +1.00000 q^{9} -0.585903 q^{10} -1.00000 q^{11} +0.0978930 q^{12} +4.17082 q^{14} -0.404514 q^{15} -4.18620 q^{16} +1.23539 q^{17} +1.44841 q^{18} +4.83324 q^{19} -0.0395991 q^{20} +2.87958 q^{21} -1.44841 q^{22} +5.99210 q^{23} -2.75503 q^{24} -4.83637 q^{25} +1.00000 q^{27} +0.281891 q^{28} +4.74975 q^{29} -0.585903 q^{30} +6.43354 q^{31} -0.553277 q^{32} -1.00000 q^{33} +1.78934 q^{34} -1.16483 q^{35} +0.0978930 q^{36} -6.09000 q^{37} +7.00052 q^{38} +1.11445 q^{40} -2.29605 q^{41} +4.17082 q^{42} -2.77472 q^{43} -0.0978930 q^{44} -0.404514 q^{45} +8.67903 q^{46} -1.93113 q^{47} -4.18620 q^{48} +1.29199 q^{49} -7.00505 q^{50} +1.23539 q^{51} -4.21042 q^{53} +1.44841 q^{54} +0.404514 q^{55} -7.93334 q^{56} +4.83324 q^{57} +6.87958 q^{58} +7.19647 q^{59} -0.0395991 q^{60} +11.0794 q^{61} +9.31841 q^{62} +2.87958 q^{63} +7.57103 q^{64} -1.44841 q^{66} +15.8396 q^{67} +0.120936 q^{68} +5.99210 q^{69} -1.68715 q^{70} -2.88195 q^{71} -2.75503 q^{72} -6.31312 q^{73} -8.82082 q^{74} -4.83637 q^{75} +0.473141 q^{76} -2.87958 q^{77} -2.73419 q^{79} +1.69338 q^{80} +1.00000 q^{81} -3.32562 q^{82} +3.55488 q^{83} +0.281891 q^{84} -0.499731 q^{85} -4.01893 q^{86} +4.74975 q^{87} +2.75503 q^{88} +5.50461 q^{89} -0.585903 q^{90} +0.586585 q^{92} +6.43354 q^{93} -2.79708 q^{94} -1.95511 q^{95} -0.553277 q^{96} +3.21930 q^{97} +1.87133 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 9 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 9 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 9 q^{7} + 3 q^{8} + 5 q^{9} + 7 q^{10} - 5 q^{11} + 2 q^{12} + 3 q^{14} + 8 q^{15} - 4 q^{16} + 3 q^{17} + 2 q^{18} - 3 q^{19} + 6 q^{20} + 9 q^{21} - 2 q^{22} - q^{23} + 3 q^{24} + 9 q^{25} + 5 q^{27} + 25 q^{28} - 2 q^{29} + 7 q^{30} - 2 q^{31} + 3 q^{32} - 5 q^{33} - 23 q^{34} + 12 q^{35} + 2 q^{36} - q^{37} + 7 q^{38} + 25 q^{40} + 18 q^{41} + 3 q^{42} - 9 q^{43} - 2 q^{44} + 8 q^{45} - 2 q^{46} + 16 q^{47} - 4 q^{48} + 22 q^{49} + 12 q^{50} + 3 q^{51} + 3 q^{53} + 2 q^{54} - 8 q^{55} + 25 q^{56} - 3 q^{57} + 29 q^{58} + 16 q^{59} + 6 q^{60} + 8 q^{61} + 16 q^{62} + 9 q^{63} - q^{64} - 2 q^{66} + 19 q^{67} - 22 q^{68} - q^{69} + 36 q^{70} + 25 q^{71} + 3 q^{72} + 8 q^{73} - 5 q^{74} + 9 q^{75} - 38 q^{76} - 9 q^{77} + 18 q^{79} + 20 q^{80} + 5 q^{81} - 40 q^{82} + 22 q^{83} + 25 q^{84} - 7 q^{85} - 4 q^{86} - 2 q^{87} - 3 q^{88} - 20 q^{89} + 7 q^{90} - 30 q^{92} - 2 q^{93} - 8 q^{94} - 7 q^{95} + 3 q^{96} + 21 q^{97} + 6 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 9 * q^7 + 3 * q^8 + 5 * q^9 + 7 * q^10 - 5 * q^11 + 2 * q^12 + 3 * q^14 + 8 * q^15 - 4 * q^16 + 3 * q^17 + 2 * q^18 - 3 * q^19 + 6 * q^20 + 9 * q^21 - 2 * q^22 - q^23 + 3 * q^24 + 9 * q^25 + 5 * q^27 + 25 * q^28 - 2 * q^29 + 7 * q^30 - 2 * q^31 + 3 * q^32 - 5 * q^33 - 23 * q^34 + 12 * q^35 + 2 * q^36 - q^37 + 7 * q^38 + 25 * q^40 + 18 * q^41 + 3 * q^42 - 9 * q^43 - 2 * q^44 + 8 * q^45 - 2 * q^46 + 16 * q^47 - 4 * q^48 + 22 * q^49 + 12 * q^50 + 3 * q^51 + 3 * q^53 + 2 * q^54 - 8 * q^55 + 25 * q^56 - 3 * q^57 + 29 * q^58 + 16 * q^59 + 6 * q^60 + 8 * q^61 + 16 * q^62 + 9 * q^63 - q^64 - 2 * q^66 + 19 * q^67 - 22 * q^68 - q^69 + 36 * q^70 + 25 * q^71 + 3 * q^72 + 8 * q^73 - 5 * q^74 + 9 * q^75 - 38 * q^76 - 9 * q^77 + 18 * q^79 + 20 * q^80 + 5 * q^81 - 40 * q^82 + 22 * q^83 + 25 * q^84 - 7 * q^85 - 4 * q^86 - 2 * q^87 - 3 * q^88 - 20 * q^89 + 7 * q^90 - 30 * q^92 - 2 * q^93 - 8 * q^94 - 7 * q^95 + 3 * q^96 + 21 * q^97 + 6 * 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 $

$2$	1.44841	1.02418	0.512090	−	0.858932i	$-0.328871\pi$
$2$	1.44841	1.02418	0.512090	+	0.858932i	$0.328871\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0978930	0.0489465
$5$	−0.404514	−0.180904	−0.0904521	−	0.995901i	$-0.528831\pi$
$5$	−0.404514	−0.180904	−0.0904521	+	0.995901i	$0.528831\pi$
$6$	1.44841	0.591311
$7$	2.87958	1.08838	0.544190	−	0.838962i	$-0.316837\pi$
$7$	2.87958	1.08838	0.544190	+	0.838962i	$0.316837\pi$
$8$	−2.75503	−0.974051
$9$	1.00000	0.333333
$10$	−0.585903	−0.185279
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.0978930	0.0282593
$13$	0	0
$13$	0	0
$14$	4.17082	1.11470
$15$	−0.404514	−0.104445
$16$	−4.18620	−1.04655
$17$	1.23539	0.299625	0.149812	−	0.988714i	$-0.452133\pi$
$17$	1.23539	0.299625	0.149812	+	0.988714i	$0.452133\pi$
$18$	1.44841	0.341394
$19$	4.83324	1.10882	0.554411	−	0.832243i	$-0.312944\pi$
$19$	4.83324	1.10882	0.554411	+	0.832243i	$0.312944\pi$
$20$	−0.0395991	−0.00885464
$21$	2.87958	0.628376
$22$	−1.44841	−0.308802
$23$	5.99210	1.24944	0.624720	−	0.780849i	$-0.285213\pi$
$23$	5.99210	1.24944	0.624720	+	0.780849i	$0.285213\pi$
$24$	−2.75503	−0.562368
$25$	−4.83637	−0.967274
$26$	0	0
$27$	1.00000	0.192450
$28$	0.281891	0.0532724
$29$	4.74975	0.882006	0.441003	−	0.897506i	$-0.354623\pi$
$29$	4.74975	0.882006	0.441003	+	0.897506i	$0.354623\pi$
$30$	−0.585903	−0.106971
$31$	6.43354	1.15550	0.577749	−	0.816214i	$-0.303931\pi$
$31$	6.43354	1.15550	0.577749	+	0.816214i	$0.303931\pi$
$32$	−0.553277	−0.0978065
$33$	−1.00000	−0.174078
$34$	1.78934	0.306870
$35$	−1.16483	−0.196893
$36$	0.0978930	0.0163155
$37$	−6.09000	−1.00119	−0.500595	−	0.865682i	$-0.666885\pi$
$37$	−6.09000	−1.00119	−0.500595	+	0.865682i	$0.666885\pi$
$38$	7.00052	1.13563
$39$	0	0
$40$	1.11445	0.176210
$41$	−2.29605	−0.358583	−0.179291	−	0.983796i	$-0.557380\pi$
$41$	−2.29605	−0.358583	−0.179291	+	0.983796i	$0.557380\pi$
$42$	4.17082	0.643571
$43$	−2.77472	−0.423140	−0.211570	−	0.977363i	$-0.567858\pi$
$43$	−2.77472	−0.423140	−0.211570	+	0.977363i	$0.567858\pi$
$44$	−0.0978930	−0.0147579
$45$	−0.404514	−0.0603014
$46$	8.67903	1.27965
$47$	−1.93113	−0.281685	−0.140842	−	0.990032i	$-0.544981\pi$
$47$	−1.93113	−0.281685	−0.140842	+	0.990032i	$0.544981\pi$
$48$	−4.18620	−0.604226
$49$	1.29199	0.184570
$50$	−7.00505	−0.990663
$51$	1.23539	0.172989
$52$	0	0
$53$	−4.21042	−0.578345	−0.289173	−	0.957277i	$-0.593380\pi$
$53$	−4.21042	−0.578345	−0.289173	+	0.957277i	$0.593380\pi$
$54$	1.44841	0.197104
$55$	0.404514	0.0545447
$56$	−7.93334	−1.06014
$57$	4.83324	0.640178
$58$	6.87958	0.903333
$59$	7.19647	0.936900	0.468450	−	0.883490i	$-0.344813\pi$
$59$	7.19647	0.936900	0.468450	+	0.883490i	$0.344813\pi$
$60$	−0.0395991	−0.00511223
$61$	11.0794	1.41858	0.709288	−	0.704919i	$-0.249017\pi$
$61$	11.0794	1.41858	0.709288	+	0.704919i	$0.249017\pi$
$62$	9.31841	1.18344
$63$	2.87958	0.362793
$64$	7.57103	0.946379
$65$	0	0
$66$	−1.44841	−0.178287
$67$	15.8396	1.93511	0.967556	−	0.252656i	$-0.0813040\pi$
$67$	15.8396	1.93511	0.967556	+	0.252656i	$0.0813040\pi$
$68$	0.120936	0.0146656
$69$	5.99210	0.721365
$70$	−1.68715	−0.201654
$71$	−2.88195	−0.342025	−0.171012	−	0.985269i	$-0.554704\pi$
$71$	−2.88195	−0.342025	−0.171012	+	0.985269i	$0.554704\pi$
$72$	−2.75503	−0.324684
$73$	−6.31312	−0.738895	−0.369448	−	0.929252i	$-0.620453\pi$
$73$	−6.31312	−0.738895	−0.369448	+	0.929252i	$0.620453\pi$
$74$	−8.82082	−1.02540
$75$	−4.83637	−0.558456
$76$	0.473141	0.0542730
$77$	−2.87958	−0.328159
$78$	0	0
$79$	−2.73419	−0.307621	−0.153810	−	0.988100i	$-0.549155\pi$
$79$	−2.73419	−0.307621	−0.153810	+	0.988100i	$0.549155\pi$
$80$	1.69338	0.189326
$81$	1.00000	0.111111
$82$	−3.32562	−0.367254
$83$	3.55488	0.390199	0.195099	−	0.980783i	$-0.437497\pi$
$83$	3.55488	0.390199	0.195099	+	0.980783i	$0.437497\pi$
$84$	0.281891	0.0307568
$85$	−0.499731	−0.0542034
$86$	−4.01893	−0.433372
$87$	4.74975	0.509226
$88$	2.75503	0.293687
$89$	5.50461	0.583488	0.291744	−	0.956496i	$-0.405765\pi$
$89$	5.50461	0.583488	0.291744	+	0.956496i	$0.405765\pi$
$90$	−0.585903	−0.0617596
$91$	0	0
$92$	0.586585	0.0611558
$93$	6.43354	0.667127
$94$	−2.79708	−0.288496
$95$	−1.95511	−0.200591
$96$	−0.553277	−0.0564686
$97$	3.21930	0.326870	0.163435	−	0.986554i	$-0.447743\pi$
$97$	3.21930	0.326870	0.163435	+	0.986554i	$0.447743\pi$
$98$	1.87133	0.189033
$99$	−1.00000	−0.100504
$100$	−0.473447	−0.0473447
$101$	14.0055	1.39360	0.696800	−	0.717266i	$-0.254607\pi$
$101$	14.0055	1.39360	0.696800	+	0.717266i	$0.254607\pi$
$102$	1.78934	0.177172
$103$	−13.4197	−1.32228	−0.661140	−	0.750263i	$-0.729927\pi$
$103$	−13.4197	−1.32228	−0.661140	+	0.750263i	$0.729927\pi$
$104$	0	0
$105$	−1.16483	−0.113676
$106$	−6.09841	−0.592330
$107$	−1.75863	−0.170013	−0.0850066	−	0.996380i	$-0.527091\pi$
$107$	−1.75863	−0.170013	−0.0850066	+	0.996380i	$0.527091\pi$
$108$	0.0978930	0.00941976
$109$	9.54438	0.914185	0.457093	−	0.889419i	$-0.348891\pi$
$109$	9.54438	0.914185	0.457093	+	0.889419i	$0.348891\pi$
$110$	0.585903	0.0558636
$111$	−6.09000	−0.578037
$112$	−12.0545	−1.13904
$113$	18.9970	1.78708	0.893542	−	0.448979i	$-0.148212\pi$
$113$	18.9970	1.78708	0.893542	+	0.448979i	$0.148212\pi$
$114$	7.00052	0.655659
$115$	−2.42389	−0.226029
$116$	0.464967	0.0431711
$117$	0	0
$118$	10.4234	0.959556
$119$	3.55739	0.326106
$120$	1.11445	0.101735
$121$	1.00000	0.0909091
$122$	16.0476	1.45288
$123$	−2.29605	−0.207028
$124$	0.629799	0.0565576
$125$	3.97895	0.355888
$126$	4.17082	0.371566
$127$	0.130001	0.0115357	0.00576787	−	0.999983i	$-0.498164\pi$
$127$	0.130001	0.0115357	0.00576787	+	0.999983i	$0.498164\pi$
$128$	12.0725	1.06707
$129$	−2.77472	−0.244300
$130$	0	0
$131$	8.28393	0.723770	0.361885	−	0.932223i	$-0.382133\pi$
$131$	8.28393	0.723770	0.361885	+	0.932223i	$0.382133\pi$
$132$	−0.0978930	−0.00852050
$133$	13.9177	1.20682
$134$	22.9422	1.98191
$135$	−0.404514	−0.0348150
$136$	−3.40353	−0.291850
$137$	20.7228	1.77047	0.885236	−	0.465142i	$-0.153997\pi$
$137$	20.7228	1.77047	0.885236	+	0.465142i	$0.153997\pi$
$138$	8.67903	0.738808
$139$	−6.98036	−0.592067	−0.296033	−	0.955178i	$-0.595664\pi$
$139$	−6.98036	−0.592067	−0.296033	+	0.955178i	$0.595664\pi$
$140$	−0.114029	−0.00963720
$141$	−1.93113	−0.162631
$142$	−4.17425	−0.350295
$143$	0	0
$144$	−4.18620	−0.348850
$145$	−1.92134	−0.159559
$146$	−9.14399	−0.756762
$147$	1.29199	0.106562
$148$	−0.596168	−0.0490047
$149$	19.8557	1.62664	0.813320	−	0.581817i	$-0.197658\pi$
$149$	19.8557	1.62664	0.813320	+	0.581817i	$0.197658\pi$
$150$	−7.00505	−0.571960
$151$	−13.3172	−1.08374	−0.541868	−	0.840463i	$-0.682283\pi$
$151$	−13.3172	−1.08374	−0.541868	+	0.840463i	$0.682283\pi$
$152$	−13.3157	−1.08005
$153$	1.23539	0.0998750
$154$	−4.17082	−0.336094
$155$	−2.60246	−0.209035
$156$	0	0
$157$	21.3752	1.70592	0.852962	−	0.521973i	$-0.174804\pi$
$157$	21.3752	1.70592	0.852962	+	0.521973i	$0.174804\pi$
$158$	−3.96024	−0.315059
$159$	−4.21042	−0.333908
$160$	0.223808	0.0176936
$161$	17.2548	1.35987
$162$	1.44841	0.113798
$163$	−12.1023	−0.947926	−0.473963	−	0.880545i	$-0.657177\pi$
$163$	−12.1023	−0.947926	−0.473963	+	0.880545i	$0.657177\pi$
$164$	−0.224767	−0.0175514
$165$	0.404514	0.0314914
$166$	5.14893	0.399634
$167$	−3.10892	−0.240576	−0.120288	−	0.992739i	$-0.538382\pi$
$167$	−3.10892	−0.240576	−0.120288	+	0.992739i	$0.538382\pi$
$168$	−7.93334	−0.612070
$169$	0	0
$170$	−0.723816	−0.0555141
$171$	4.83324	0.369607
$172$	−0.271625	−0.0207112
$173$	−4.24304	−0.322592	−0.161296	−	0.986906i	$-0.551567\pi$
$173$	−4.24304	−0.322592	−0.161296	+	0.986906i	$0.551567\pi$
$174$	6.87958	0.521540
$175$	−13.9267	−1.05276
$176$	4.18620	0.315547
$177$	7.19647	0.540920
$178$	7.97294	0.597597
$179$	−2.92331	−0.218499	−0.109249	−	0.994014i	$-0.534845\pi$
$179$	−2.92331	−0.218499	−0.109249	+	0.994014i	$0.534845\pi$
$180$	−0.0395991	−0.00295155
$181$	−2.77704	−0.206416	−0.103208	−	0.994660i	$-0.532911\pi$
$181$	−2.77704	−0.206416	−0.103208	+	0.994660i	$0.532911\pi$
$182$	0	0
$183$	11.0794	0.819015
$184$	−16.5084	−1.21702
$185$	2.46349	0.181119
$186$	9.31841	0.683259
$187$	−1.23539	−0.0903403
$188$	−0.189045	−0.0137875
$189$	2.87958	0.209459
$190$	−2.83181	−0.205441
$191$	−22.8688	−1.65473	−0.827363	−	0.561667i	$-0.810160\pi$
$191$	−22.8688	−1.65473	−0.827363	+	0.561667i	$0.810160\pi$
$192$	7.57103	0.546392
$193$	−8.08251	−0.581792	−0.290896	−	0.956755i	$-0.593953\pi$
$193$	−8.08251	−0.581792	−0.290896	+	0.956755i	$0.593953\pi$
$194$	4.66287	0.334774
$195$	0	0
$196$	0.126477	0.00903407
$197$	−22.2566	−1.58571	−0.792857	−	0.609407i	$-0.791407\pi$
$197$	−22.2566	−1.58571	−0.792857	+	0.609407i	$0.791407\pi$
$198$	−1.44841	−0.102934
$199$	−22.5668	−1.59972	−0.799859	−	0.600188i	$-0.795092\pi$
$199$	−22.5668	−1.59972	−0.799859	+	0.600188i	$0.795092\pi$
$200$	13.3243	0.942174
$201$	15.8396	1.11724
$202$	20.2857	1.42730
$203$	13.6773	0.959957
$204$	0.120936	0.00846719
$205$	0.928785	0.0648691
$206$	−19.4372	−1.35425
$207$	5.99210	0.416480
$208$	0	0
$209$	−4.83324	−0.334322
$210$	−1.68715	−0.116425
$211$	−28.5780	−1.96739	−0.983695	−	0.179844i	$-0.942441\pi$
$211$	−28.5780	−1.96739	−0.983695	+	0.179844i	$0.942441\pi$
$212$	−0.412170	−0.0283080
$213$	−2.88195	−0.197468
$214$	−2.54722	−0.174124
$215$	1.12241	0.0765479
$216$	−2.75503	−0.187456
$217$	18.5259	1.25762
$218$	13.8242	0.936291
$219$	−6.31312	−0.426601
$220$	0.0395991	0.00266977
$221$	0	0
$222$	−8.82082	−0.592014
$223$	15.4799	1.03661	0.518306	−	0.855195i	$-0.326563\pi$
$223$	15.4799	1.03661	0.518306	+	0.855195i	$0.326563\pi$
$224$	−1.59321	−0.106451
$225$	−4.83637	−0.322425
$226$	27.5154	1.83030
$227$	13.2754	0.881117	0.440558	−	0.897724i	$-0.354781\pi$
$227$	13.2754	0.881117	0.440558	+	0.897724i	$0.354781\pi$
$228$	0.473141	0.0313345
$229$	27.9909	1.84969	0.924846	−	0.380342i	$-0.124194\pi$
$229$	27.9909	1.84969	0.924846	+	0.380342i	$0.124194\pi$
$230$	−3.51079	−0.231495
$231$	−2.87958	−0.189463
$232$	−13.0857	−0.859118
$233$	−18.2051	−1.19266	−0.596329	−	0.802740i	$-0.703375\pi$
$233$	−18.2051	−1.19266	−0.596329	+	0.802740i	$0.703375\pi$
$234$	0	0
$235$	0.781171	0.0509580
$236$	0.704484	0.0458580
$237$	−2.73419	−0.177605
$238$	5.15257	0.333991
$239$	16.3923	1.06033	0.530166	−	0.847894i	$-0.322130\pi$
$239$	16.3923	1.06033	0.530166	+	0.847894i	$0.322130\pi$
$240$	1.69338	0.109307
$241$	−10.1491	−0.653758	−0.326879	−	0.945066i	$-0.605997\pi$
$241$	−10.1491	−0.653758	−0.326879	+	0.945066i	$0.605997\pi$
$242$	1.44841	0.0931074
$243$	1.00000	0.0641500
$244$	1.08460	0.0694343
$245$	−0.522629	−0.0333895
$246$	−3.32562	−0.212034
$247$	0	0
$248$	−17.7246	−1.12551
$249$	3.55488	0.225281
$250$	5.76315	0.364494
$251$	18.7713	1.18484	0.592418	−	0.805631i	$-0.298173\pi$
$251$	18.7713	1.18484	0.592418	+	0.805631i	$0.298173\pi$
$252$	0.281891	0.0177575
$253$	−5.99210	−0.376720
$254$	0.188295	0.0118147
$255$	−0.499731	−0.0312944
$256$	2.34390	0.146494
$257$	−18.1109	−1.12973	−0.564865	−	0.825183i	$-0.691072\pi$
$257$	−18.1109	−1.12973	−0.564865	+	0.825183i	$0.691072\pi$
$258$	−4.01893	−0.250207
$259$	−17.5366	−1.08967
$260$	0	0
$261$	4.74975	0.294002
$262$	11.9985	0.741272
$263$	25.9168	1.59810	0.799049	−	0.601266i	$-0.205337\pi$
$263$	25.9168	1.59810	0.799049	+	0.601266i	$0.205337\pi$
$264$	2.75503	0.169560
$265$	1.70317	0.104625
$266$	20.1586	1.23600
$267$	5.50461	0.336877
$268$	1.55058	0.0947170
$269$	−21.9328	−1.33727	−0.668634	−	0.743592i	$-0.733121\pi$
$269$	−21.9328	−1.33727	−0.668634	+	0.743592i	$0.733121\pi$
$270$	−0.585903	−0.0356569
$271$	−5.64424	−0.342863	−0.171432	−	0.985196i	$-0.554839\pi$
$271$	−5.64424	−0.342863	−0.171432	+	0.985196i	$0.554839\pi$
$272$	−5.17157	−0.313573
$273$	0	0
$274$	30.0152	1.81328
$275$	4.83637	0.291644
$276$	0.586585	0.0353083
$277$	−5.42988	−0.326250	−0.163125	−	0.986605i	$-0.552157\pi$
$277$	−5.42988	−0.326250	−0.163125	+	0.986605i	$0.552157\pi$
$278$	−10.1104	−0.606383
$279$	6.43354	0.385166
$280$	3.20915	0.191783
$281$	−21.3960	−1.27638	−0.638188	−	0.769881i	$-0.720316\pi$
$281$	−21.3960	−1.27638	−0.638188	+	0.769881i	$0.720316\pi$
$282$	−2.79708	−0.166563
$283$	9.14996	0.543909	0.271954	−	0.962310i	$-0.412330\pi$
$283$	9.14996	0.543909	0.271954	+	0.962310i	$0.412330\pi$
$284$	−0.282123	−0.0167409
$285$	−1.95511	−0.115811
$286$	0	0
$287$	−6.61166	−0.390274
$288$	−0.553277	−0.0326022
$289$	−15.4738	−0.910225
$290$	−2.78289	−0.163417
$291$	3.21930	0.188719
$292$	−0.618011	−0.0361664
$293$	2.37205	0.138577	0.0692884	−	0.997597i	$-0.477927\pi$
$293$	2.37205	0.138577	0.0692884	+	0.997597i	$0.477927\pi$
$294$	1.87133	0.109138
$295$	−2.91107	−0.169489
$296$	16.7781	0.975209
$297$	−1.00000	−0.0580259
$298$	28.7592	1.66597
$299$	0	0
$300$	−0.473447	−0.0273345
$301$	−7.99002	−0.460537
$302$	−19.2887	−1.10994
$303$	14.0055	0.804595
$304$	−20.2329	−1.16044
$305$	−4.48179	−0.256626
$306$	1.78934	0.102290
$307$	11.6946	0.667448	0.333724	−	0.942671i	$-0.391695\pi$
$307$	11.6946	0.667448	0.333724	+	0.942671i	$0.391695\pi$
$308$	−0.281891	−0.0160622
$309$	−13.4197	−0.763419
$310$	−3.76943	−0.214089
$311$	3.94022	0.223429	0.111715	−	0.993740i	$-0.464366\pi$
$311$	3.94022	0.223429	0.111715	+	0.993740i	$0.464366\pi$
$312$	0	0
$313$	−4.96530	−0.280655	−0.140328	−	0.990105i	$-0.544816\pi$
$313$	−4.96530	−0.280655	−0.140328	+	0.990105i	$0.544816\pi$
$314$	30.9600	1.74718
$315$	−1.16483	−0.0656308
$316$	−0.267659	−0.0150570
$317$	2.24582	0.126138	0.0630688	−	0.998009i	$-0.479911\pi$
$317$	2.24582	0.126138	0.0630688	+	0.998009i	$0.479911\pi$
$318$	−6.09841	−0.341982
$319$	−4.74975	−0.265935
$320$	−3.06259	−0.171204
$321$	−1.75863	−0.0981572
$322$	24.9920	1.39275
$323$	5.97091	0.332231
$324$	0.0978930	0.00543850
$325$	0	0
$326$	−17.5291	−0.970847
$327$	9.54438	0.527805
$328$	6.32569	0.349278
$329$	−5.56086	−0.306580
$330$	0.585903	0.0322529
$331$	−4.04258	−0.222200	−0.111100	−	0.993809i	$-0.535437\pi$
$331$	−4.04258	−0.222200	−0.111100	+	0.993809i	$0.535437\pi$
$332$	0.347998	0.0190989
$333$	−6.09000	−0.333730
$334$	−4.50300	−0.246393
$335$	−6.40734	−0.350070
$336$	−12.0545	−0.657628
$337$	−10.1170	−0.551106	−0.275553	−	0.961286i	$-0.588861\pi$
$337$	−10.1170	−0.551106	−0.275553	+	0.961286i	$0.588861\pi$
$338$	0	0
$339$	18.9970	1.03177
$340$	−0.0489202	−0.00265307
$341$	−6.43354	−0.348396
$342$	7.00052	0.378545
$343$	−16.4367	−0.887497
$344$	7.64443	0.412160
$345$	−2.42389	−0.130498
$346$	−6.14567	−0.330393
$347$	−12.2189	−0.655946	−0.327973	−	0.944687i	$-0.606366\pi$
$347$	−12.2189	−0.655946	−0.327973	+	0.944687i	$0.606366\pi$
$348$	0.464967	0.0249249
$349$	1.45900	0.0780984	0.0390492	−	0.999237i	$-0.487567\pi$
$349$	1.45900	0.0780984	0.0390492	+	0.999237i	$0.487567\pi$
$350$	−20.1716	−1.07822
$351$	0	0
$352$	0.553277	0.0294898
$353$	0.732648	0.0389949	0.0194974	−	0.999810i	$-0.493793\pi$
$353$	0.732648	0.0389949	0.0194974	+	0.999810i	$0.493793\pi$
$354$	10.4234	0.554000
$355$	1.16579	0.0618737
$356$	0.538863	0.0285597
$357$	3.55739	0.188277
$358$	−4.23416	−0.223782
$359$	−4.82640	−0.254728	−0.127364	−	0.991856i	$-0.540652\pi$
$359$	−4.82640	−0.254728	−0.127364	+	0.991856i	$0.540652\pi$
$360$	1.11445	0.0587367
$361$	4.36022	0.229485
$362$	−4.02229	−0.211407
$363$	1.00000	0.0524864
$364$	0	0
$365$	2.55375	0.133669
$366$	16.0476	0.838819
$367$	−8.55350	−0.446489	−0.223245	−	0.974762i	$-0.571665\pi$
$367$	−8.55350	−0.446489	−0.223245	+	0.974762i	$0.571665\pi$
$368$	−25.0842	−1.30760
$369$	−2.29605	−0.119528
$370$	3.56815	0.185499
$371$	−12.1242	−0.629459
$372$	0.629799	0.0326536
$373$	−29.3749	−1.52097	−0.760487	−	0.649353i	$-0.775040\pi$
$373$	−29.3749	−1.52097	−0.760487	+	0.649353i	$0.775040\pi$
$374$	−1.78934	−0.0925248
$375$	3.97895	0.205472
$376$	5.32034	0.274375
$377$	0	0
$378$	4.17082	0.214524
$379$	−14.4258	−0.741003	−0.370502	−	0.928832i	$-0.620814\pi$
$379$	−14.4258	−0.741003	−0.370502	+	0.928832i	$0.620814\pi$
$380$	−0.191392	−0.00981821
$381$	0.130001	0.00666016
$382$	−33.1234	−1.69474
$383$	−1.54283	−0.0788347	−0.0394173	−	0.999223i	$-0.512550\pi$
$383$	−1.54283	−0.0788347	−0.0394173	+	0.999223i	$0.512550\pi$
$384$	12.0725	0.616073
$385$	1.16483	0.0593653
$386$	−11.7068	−0.595860
$387$	−2.77472	−0.141047
$388$	0.315147	0.0159992
$389$	−29.5984	−1.50070	−0.750349	−	0.661042i	$-0.770114\pi$
$389$	−29.5984	−1.50070	−0.750349	+	0.661042i	$0.770114\pi$
$390$	0	0
$391$	7.40256	0.374363
$392$	−3.55948	−0.179781
$393$	8.28393	0.417869
$394$	−32.2366	−1.62406
$395$	1.10602	0.0556499
$396$	−0.0978930	−0.00491931
$397$	23.3884	1.17383	0.586916	−	0.809648i	$-0.300342\pi$
$397$	23.3884	1.17383	0.586916	+	0.809648i	$0.300342\pi$
$398$	−32.6860	−1.63840
$399$	13.9177	0.696757
$400$	20.2460	1.01230
$401$	29.5823	1.47727	0.738634	−	0.674106i	$-0.235471\pi$
$401$	29.5823	1.47727	0.738634	+	0.674106i	$0.235471\pi$
$402$	22.9422	1.14425
$403$	0	0
$404$	1.37104	0.0682118
$405$	−0.404514	−0.0201005
$406$	19.8103	0.983170
$407$	6.09000	0.301870
$408$	−3.40353	−0.168500
$409$	20.0551	0.991663	0.495831	−	0.868419i	$-0.334863\pi$
$409$	20.0551	0.991663	0.495831	+	0.868419i	$0.334863\pi$
$410$	1.34526	0.0664377
$411$	20.7228	1.02218
$412$	−1.31369	−0.0647210
$413$	20.7228	1.01970
$414$	8.67903	0.426551
$415$	−1.43800	−0.0705887
$416$	0	0
$417$	−6.98036	−0.341830
$418$	−7.00052	−0.342407
$419$	−2.36336	−0.115458	−0.0577288	−	0.998332i	$-0.518386\pi$
$419$	−2.36336	−0.115458	−0.0577288	+	0.998332i	$0.518386\pi$
$420$	−0.114029	−0.00556404
$421$	−33.6475	−1.63988	−0.819938	−	0.572452i	$-0.805992\pi$
$421$	−33.6475	−1.63988	−0.819938	+	0.572452i	$0.805992\pi$
$422$	−41.3927	−2.01496
$423$	−1.93113	−0.0938950
$424$	11.5998	0.563337
$425$	−5.97478	−0.289819
$426$	−4.17425	−0.202243
$427$	31.9041	1.54395
$428$	−0.172158	−0.00832155
$429$	0	0
$430$	1.62571	0.0783989
$431$	−17.0069	−0.819192	−0.409596	−	0.912267i	$-0.634330\pi$
$431$	−17.0069	−0.819192	−0.409596	+	0.912267i	$0.634330\pi$
$432$	−4.18620	−0.201409
$433$	22.2916	1.07126	0.535632	−	0.844451i	$-0.320073\pi$
$433$	22.2916	1.07126	0.535632	+	0.844451i	$0.320073\pi$
$434$	26.8331	1.28803
$435$	−1.92134	−0.0921212
$436$	0.934328	0.0447462
$437$	28.9613	1.38541
$438$	−9.14399	−0.436917
$439$	−3.72976	−0.178012	−0.0890058	−	0.996031i	$-0.528369\pi$
$439$	−3.72976	−0.178012	−0.0890058	+	0.996031i	$0.528369\pi$
$440$	−1.11445	−0.0531293
$441$	1.29199	0.0615234
$442$	0	0
$443$	17.4170	0.827506	0.413753	−	0.910389i	$-0.364218\pi$
$443$	17.4170	0.827506	0.413753	+	0.910389i	$0.364218\pi$
$444$	−0.596168	−0.0282929
$445$	−2.22669	−0.105555
$446$	22.4213	1.06168
$447$	19.8557	0.939141
$448$	21.8014	1.03002
$449$	12.1693	0.574303	0.287151	−	0.957885i	$-0.407292\pi$
$449$	12.1693	0.574303	0.287151	+	0.957885i	$0.407292\pi$
$450$	−7.00505	−0.330221
$451$	2.29605	0.108117
$452$	1.85967	0.0874716
$453$	−13.3172	−0.625696
$454$	19.2282	0.902423
$455$	0	0
$456$	−13.3157	−0.623566
$457$	9.94645	0.465275	0.232638	−	0.972563i	$-0.425264\pi$
$457$	9.94645	0.465275	0.232638	+	0.972563i	$0.425264\pi$
$458$	40.5423	1.89442
$459$	1.23539	0.0576628
$460$	−0.237282	−0.0110633
$461$	30.9560	1.44177	0.720883	−	0.693057i	$-0.243736\pi$
$461$	30.9560	1.44177	0.720883	+	0.693057i	$0.243736\pi$
$462$	−4.17082	−0.194044
$463$	16.1357	0.749891	0.374945	−	0.927047i	$-0.377661\pi$
$463$	16.1357	0.749891	0.374945	+	0.927047i	$0.377661\pi$
$464$	−19.8834	−0.923064
$465$	−2.60246	−0.120686
$466$	−26.3685	−1.22150
$467$	16.4891	0.763027	0.381513	−	0.924363i	$-0.375403\pi$
$467$	16.4891	0.763027	0.381513	+	0.924363i	$0.375403\pi$
$468$	0	0
$469$	45.6114	2.10614
$470$	1.13146	0.0521902
$471$	21.3752	0.984916
$472$	−19.8265	−0.912589
$473$	2.77472	0.127582
$474$	−3.96024	−0.181900
$475$	−23.3753	−1.07253
$476$	0.348244	0.0159617
$477$	−4.21042	−0.192782
$478$	23.7428	1.08597
$479$	35.1289	1.60508	0.802541	−	0.596597i	$-0.203481\pi$
$479$	35.1289	1.60508	0.802541	+	0.596597i	$0.203481\pi$
$480$	0.223808	0.0102154
$481$	0	0
$482$	−14.7000	−0.669567
$483$	17.2548	0.785119
$484$	0.0978930	0.00444968
$485$	−1.30225	−0.0591323
$486$	1.44841	0.0657012
$487$	−15.9011	−0.720546	−0.360273	−	0.932847i	$-0.617317\pi$
$487$	−15.9011	−0.720546	−0.360273	+	0.932847i	$0.617317\pi$
$488$	−30.5242	−1.38176
$489$	−12.1023	−0.547285
$490$	−0.756981	−0.0341969
$491$	−40.1137	−1.81031	−0.905153	−	0.425086i	$-0.860244\pi$
$491$	−40.1137	−1.81031	−0.905153	+	0.425086i	$0.860244\pi$
$492$	−0.224767	−0.0101333
$493$	5.86777	0.264271
$494$	0	0
$495$	0.404514	0.0181816
$496$	−26.9321	−1.20929
$497$	−8.29882	−0.372253
$498$	5.14893	0.230729
$499$	−7.56383	−0.338604	−0.169302	−	0.985564i	$-0.554151\pi$
$499$	−7.56383	−0.338604	−0.169302	+	0.985564i	$0.554151\pi$
$500$	0.389512	0.0174195
$501$	−3.10892	−0.138896
$502$	27.1886	1.21349
$503$	−16.1326	−0.719318	−0.359659	−	0.933084i	$-0.617107\pi$
$503$	−16.1326	−0.719318	−0.359659	+	0.933084i	$0.617107\pi$
$504$	−7.93334	−0.353379
$505$	−5.66542	−0.252108
$506$	−8.67903	−0.385830
$507$	0	0
$508$	0.0127262	0.000564634 0
$509$	−36.3390	−1.61070	−0.805350	−	0.592800i	$-0.798023\pi$
$509$	−36.3390	−1.61070	−0.805350	+	0.592800i	$0.798023\pi$
$510$	−0.723816	−0.0320511
$511$	−18.1792	−0.804198
$512$	−20.7501	−0.917034
$513$	4.83324	0.213393
$514$	−26.2321	−1.15705
$515$	5.42845	0.239206
$516$	−0.271625	−0.0119576
$517$	1.93113	0.0849312
$518$	−25.4003	−1.11602
$519$	−4.24304	−0.186249
$520$	0	0
$521$	7.15961	0.313668	0.156834	−	0.987625i	$-0.449871\pi$
$521$	7.15961	0.313668	0.156834	+	0.987625i	$0.449871\pi$
$522$	6.87958	0.301111
$523$	−16.7784	−0.733667	−0.366834	−	0.930287i	$-0.619558\pi$
$523$	−16.7784	−0.733667	−0.366834	+	0.930287i	$0.619558\pi$
$524$	0.810939	0.0354260
$525$	−13.9267	−0.607812
$526$	37.5382	1.63674
$527$	7.94790	0.346216
$528$	4.18620	0.182181
$529$	12.9053	0.561101
$530$	2.46689	0.107155
$531$	7.19647	0.312300
$532$	1.36245	0.0590696
$533$	0	0
$534$	7.97294	0.345023
$535$	0.711391	0.0307561
$536$	−43.6385	−1.88490
$537$	−2.92331	−0.126150
$538$	−31.7677	−1.36960
$539$	−1.29199	−0.0556500
$540$	−0.0395991	−0.00170408
$541$	−21.7571	−0.935410	−0.467705	−	0.883885i	$-0.654919\pi$
$541$	−21.7571	−0.935410	−0.467705	+	0.883885i	$0.654919\pi$
$542$	−8.17518	−0.351154
$543$	−2.77704	−0.119174
$544$	−0.683510	−0.0293053
$545$	−3.86084	−0.165380
$546$	0	0
$547$	6.24061	0.266829	0.133415	−	0.991060i	$-0.457406\pi$
$547$	6.24061	0.266829	0.133415	+	0.991060i	$0.457406\pi$
$548$	2.02862	0.0866585
$549$	11.0794	0.472858
$550$	7.00505	0.298696
$551$	22.9567	0.977987
$552$	−16.5084	−0.702646
$553$	−7.87334	−0.334808
$554$	−7.86470	−0.334139
$555$	2.46349	0.104569
$556$	−0.683329	−0.0289796
$557$	−8.00210	−0.339060	−0.169530	−	0.985525i	$-0.554225\pi$
$557$	−8.00210	−0.339060	−0.169530	+	0.985525i	$0.554225\pi$
$558$	9.31841	0.394480
$559$	0	0
$560$	4.87622	0.206058
$561$	−1.23539	−0.0521580
$562$	−30.9901	−1.30724
$563$	−18.9554	−0.798874	−0.399437	−	0.916761i	$-0.630794\pi$
$563$	−18.9554	−0.798874	−0.399437	+	0.916761i	$0.630794\pi$
$564$	−0.189045	−0.00796021
$565$	−7.68454	−0.323291
$566$	13.2529	0.557061
$567$	2.87958	0.120931
$568$	7.93987	0.333150
$569$	44.5230	1.86650	0.933250	−	0.359228i	$-0.116960\pi$
$569$	44.5230	1.86650	0.933250	+	0.359228i	$0.116960\pi$
$570$	−2.83181	−0.118611
$571$	−17.1753	−0.718763	−0.359382	−	0.933191i	$-0.617012\pi$
$571$	−17.1753	−0.718763	−0.359382	+	0.933191i	$0.617012\pi$
$572$	0	0
$573$	−22.8688	−0.955357
$574$	−9.57640	−0.399711
$575$	−28.9800	−1.20855
$576$	7.57103	0.315460
$577$	−5.66586	−0.235873	−0.117936	−	0.993021i	$-0.537628\pi$
$577$	−5.66586	−0.235873	−0.117936	+	0.993021i	$0.537628\pi$
$578$	−22.4124	−0.932235
$579$	−8.08251	−0.335898
$580$	−0.188086	−0.00780984
$581$	10.2366	0.424685
$582$	4.66287	0.193282
$583$	4.21042	0.174378
$584$	17.3929	0.719721
$585$	0	0
$586$	3.43571	0.141928
$587$	−18.0985	−0.747004	−0.373502	−	0.927629i	$-0.621843\pi$
$587$	−18.0985	−0.747004	−0.373502	+	0.927629i	$0.621843\pi$
$588$	0.126477	0.00521582
$589$	31.0949	1.28124
$590$	−4.21643	−0.173588
$591$	−22.2566	−0.915513
$592$	25.4940	1.04780
$593$	23.3821	0.960190	0.480095	−	0.877217i	$-0.340602\pi$
$593$	23.3821	0.960190	0.480095	+	0.877217i	$0.340602\pi$
$594$	−1.44841	−0.0594290
$595$	−1.43902	−0.0589939
$596$	1.94373	0.0796183
$597$	−22.5668	−0.923598
$598$	0	0
$599$	−34.5355	−1.41108	−0.705540	−	0.708670i	$-0.749296\pi$
$599$	−34.5355	−1.41108	−0.705540	+	0.708670i	$0.749296\pi$
$600$	13.3243	0.543964
$601$	−20.8988	−0.852480	−0.426240	−	0.904610i	$-0.640162\pi$
$601$	−20.8988	−0.852480	−0.426240	+	0.904610i	$0.640162\pi$
$602$	−11.5728	−0.471673
$603$	15.8396	0.645037
$604$	−1.30366	−0.0530451
$605$	−0.404514	−0.0164458
$606$	20.2857	0.824051
$607$	−5.15785	−0.209351	−0.104675	−	0.994506i	$-0.533380\pi$
$607$	−5.15785	−0.209351	−0.104675	+	0.994506i	$0.533380\pi$
$608$	−2.67412	−0.108450
$609$	13.6773	0.554231
$610$	−6.49147	−0.262832
$611$	0	0
$612$	0.120936	0.00488853
$613$	5.89337	0.238031	0.119016	−	0.992892i	$-0.462026\pi$
$613$	5.89337	0.238031	0.119016	+	0.992892i	$0.462026\pi$
$614$	16.9386	0.683588
$615$	0.928785	0.0374522
$616$	7.93334	0.319643
$617$	42.2902	1.70254	0.851271	−	0.524727i	$-0.175833\pi$
$617$	42.2902	1.70254	0.851271	+	0.524727i	$0.175833\pi$
$618$	−19.4372	−0.781879
$619$	−25.9026	−1.04111	−0.520556	−	0.853828i	$-0.674275\pi$
$619$	−25.9026	−1.04111	−0.520556	+	0.853828i	$0.674275\pi$
$620$	−0.254763	−0.0102315
$621$	5.99210	0.240455
$622$	5.70706	0.228832
$623$	15.8510	0.635056
$624$	0	0
$625$	22.5723	0.902892
$626$	−7.19179	−0.287442
$627$	−4.83324	−0.193021
$628$	2.09248	0.0834991
$629$	−7.52349	−0.299981
$630$	−1.68715	−0.0672179
$631$	35.5203	1.41404	0.707020	−	0.707193i	$-0.250039\pi$
$631$	35.5203	1.41404	0.707020	+	0.707193i	$0.250039\pi$
$632$	7.53279	0.299638
$633$	−28.5780	−1.13587
$634$	3.25286	0.129188
$635$	−0.0525873	−0.00208687
$636$	−0.412170	−0.0163436
$637$	0	0
$638$	−6.87958	−0.272365
$639$	−2.88195	−0.114008
$640$	−4.88351	−0.193038
$641$	−2.17793	−0.0860231	−0.0430116	−	0.999075i	$-0.513695\pi$
$641$	−2.17793	−0.0860231	−0.0430116	+	0.999075i	$0.513695\pi$
$642$	−2.54722	−0.100531
$643$	37.1835	1.46637	0.733187	−	0.680027i	$-0.238032\pi$
$643$	37.1835	1.46637	0.733187	+	0.680027i	$0.238032\pi$
$644$	1.68912	0.0665607
$645$	1.12241	0.0441949
$646$	8.64834	0.340264
$647$	−46.1767	−1.81539	−0.907696	−	0.419629i	$-0.862160\pi$
$647$	−46.1767	−1.81539	−0.907696	+	0.419629i	$0.862160\pi$
$648$	−2.75503	−0.108228
$649$	−7.19647	−0.282486
$650$	0	0
$651$	18.5259	0.726088
$652$	−1.18473	−0.0463977
$653$	−27.2476	−1.06628	−0.533141	−	0.846027i	$-0.678988\pi$
$653$	−27.2476	−1.06628	−0.533141	+	0.846027i	$0.678988\pi$
$654$	13.8242	0.540568
$655$	−3.35097	−0.130933
$656$	9.61173	0.375275
$657$	−6.31312	−0.246298
$658$	−8.05441	−0.313993
$659$	−0.907115	−0.0353362	−0.0176681	−	0.999844i	$-0.505624\pi$
$659$	−0.907115	−0.0353362	−0.0176681	+	0.999844i	$0.505624\pi$
$660$	0.0395991	0.00154139
$661$	21.6503	0.842097	0.421049	−	0.907038i	$-0.361662\pi$
$661$	21.6503	0.842097	0.421049	+	0.907038i	$0.361662\pi$
$662$	−5.85531	−0.227573
$663$	0	0
$664$	−9.79381	−0.380074
$665$	−5.62991	−0.218319
$666$	−8.82082	−0.341800
$667$	28.4610	1.10201
$668$	−0.304342	−0.0117753
$669$	15.4799	0.598489
$670$	−9.28045	−0.358535
$671$	−11.0794	−0.427716
$672$	−1.59321	−0.0614593
$673$	3.76993	0.145320	0.0726600	−	0.997357i	$-0.476851\pi$
$673$	3.76993	0.145320	0.0726600	+	0.997357i	$0.476851\pi$
$674$	−14.6535	−0.564433
$675$	−4.83637	−0.186152
$676$	0	0
$677$	−32.8356	−1.26197	−0.630986	−	0.775794i	$-0.717350\pi$
$677$	−32.8356	−1.26197	−0.630986	+	0.775794i	$0.717350\pi$
$678$	27.5154	1.05672
$679$	9.27024	0.355759
$680$	1.37677	0.0527969
$681$	13.2754	0.508713
$682$	−9.31841	−0.356820
$683$	22.7722	0.871352	0.435676	−	0.900104i	$-0.356509\pi$
$683$	22.7722	0.871352	0.435676	+	0.900104i	$0.356509\pi$
$684$	0.473141	0.0180910
$685$	−8.38269	−0.320286
$686$	−23.8071	−0.908958
$687$	27.9909	1.06792
$688$	11.6155	0.442838
$689$	0	0
$690$	−3.51079	−0.133653
$691$	−25.6570	−0.976040	−0.488020	−	0.872832i	$-0.662281\pi$
$691$	−25.6570	−0.976040	−0.488020	+	0.872832i	$0.662281\pi$
$692$	−0.415364	−0.0157898
$693$	−2.87958	−0.109386
$694$	−17.6980	−0.671807
$695$	2.82366	0.107107
$696$	−13.0857	−0.496012
$697$	−2.83651	−0.107440
$698$	2.11323	0.0799869
$699$	−18.2051	−0.688581
$700$	−1.36333	−0.0515290
$701$	11.7804	0.444939	0.222469	−	0.974940i	$-0.428588\pi$
$701$	11.7804	0.444939	0.222469	+	0.974940i	$0.428588\pi$
$702$	0	0
$703$	−29.4344	−1.11014
$704$	−7.57103	−0.285344
$705$	0.781171	0.0294206
$706$	1.06117	0.0399378
$707$	40.3300	1.51676
$708$	0.704484	0.0264761
$709$	−11.1214	−0.417674	−0.208837	−	0.977950i	$-0.566968\pi$
$709$	−11.1214	−0.417674	−0.208837	+	0.977950i	$0.566968\pi$
$710$	1.68854	0.0633699
$711$	−2.73419	−0.102540
$712$	−15.1654	−0.568347
$713$	38.5505	1.44373
$714$	5.15257	0.192830
$715$	0	0
$716$	−0.286172	−0.0106947
$717$	16.3923	0.612183
$718$	−6.99061	−0.260887
$719$	14.8744	0.554723	0.277362	−	0.960766i	$-0.410540\pi$
$719$	14.8744	0.554723	0.277362	+	0.960766i	$0.410540\pi$
$720$	1.69338	0.0631085
$721$	−38.6431	−1.43914
$722$	6.31539	0.235034
$723$	−10.1491	−0.377447
$724$	−0.271853	−0.0101033
$725$	−22.9715	−0.853141
$726$	1.44841	0.0537556
$727$	9.26833	0.343743	0.171872	−	0.985119i	$-0.445019\pi$
$727$	9.26833	0.343743	0.171872	+	0.985119i	$0.445019\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.69888	0.136902
$731$	−3.42784	−0.126783
$732$	1.08460	0.0400879
$733$	−21.4862	−0.793611	−0.396805	−	0.917903i	$-0.629881\pi$
$733$	−21.4862	−0.793611	−0.396805	+	0.917903i	$0.629881\pi$
$734$	−12.3890	−0.457286
$735$	−0.522629	−0.0192775
$736$	−3.31529	−0.122203
$737$	−15.8396	−0.583458
$738$	−3.32562	−0.122418
$739$	35.6801	1.31251	0.656256	−	0.754538i	$-0.272139\pi$
$739$	35.6801	1.31251	0.656256	+	0.754538i	$0.272139\pi$
$740$	0.241159	0.00886517
$741$	0	0
$742$	−17.5609	−0.644680
$743$	13.4859	0.494749	0.247374	−	0.968920i	$-0.420432\pi$
$743$	13.4859	0.494749	0.247374	+	0.968920i	$0.420432\pi$
$744$	−17.7246	−0.649816
$745$	−8.03190	−0.294266
$746$	−42.5469	−1.55775
$747$	3.55488	0.130066
$748$	−0.120936	−0.00442184
$749$	−5.06412	−0.185039
$750$	5.76315	0.210441
$751$	−17.9462	−0.654868	−0.327434	−	0.944874i	$-0.606184\pi$
$751$	−17.9462	−0.654868	−0.327434	+	0.944874i	$0.606184\pi$
$752$	8.08412	0.294798
$753$	18.7713	0.684065
$754$	0	0
$755$	5.38699	0.196053
$756$	0.281891	0.0102523
$757$	−38.9014	−1.41390	−0.706948	−	0.707265i	$-0.749929\pi$
$757$	−38.9014	−1.41390	−0.706948	+	0.707265i	$0.749929\pi$
$758$	−20.8945	−0.758921
$759$	−5.99210	−0.217500
$760$	5.38640	0.195385
$761$	−53.8247	−1.95114	−0.975571	−	0.219683i	$-0.929498\pi$
$761$	−53.8247	−1.95114	−0.975571	+	0.219683i	$0.929498\pi$
$762$	0.188295	0.00682121
$763$	27.4838	0.994981
$764$	−2.23869	−0.0809931
$765$	−0.499731	−0.0180678
$766$	−2.23464	−0.0807410
$767$	0	0
$768$	2.34390	0.0845781
$769$	−48.5800	−1.75184	−0.875919	−	0.482457i	$-0.839744\pi$
$769$	−48.5800	−1.75184	−0.875919	+	0.482457i	$0.839744\pi$
$770$	1.68715	0.0608008
$771$	−18.1109	−0.652250
$772$	−0.791221	−0.0284767
$773$	−41.2507	−1.48368	−0.741842	−	0.670575i	$-0.766047\pi$
$773$	−41.2507	−1.48368	−0.741842	+	0.670575i	$0.766047\pi$
$774$	−4.01893	−0.144457
$775$	−31.1150	−1.11768
$776$	−8.86927	−0.318388
$777$	−17.5366	−0.629124
$778$	−42.8706	−1.53699
$779$	−11.0974	−0.397604
$780$	0	0
$781$	2.88195	0.103124
$782$	10.7219	0.383416
$783$	4.74975	0.169742
$784$	−5.40854	−0.193162
$785$	−8.64656	−0.308609
$786$	11.9985	0.427973
$787$	0.562067	0.0200355	0.0100178	−	0.999950i	$-0.496811\pi$
$787$	0.562067	0.0200355	0.0100178	+	0.999950i	$0.496811\pi$
$788$	−2.17876	−0.0776152
$789$	25.9168	0.922662
$790$	1.60197	0.0569956
$791$	54.7033	1.94503
$792$	2.75503	0.0978958
$793$	0	0
$794$	33.8760	1.20222
$795$	1.70317	0.0604053
$796$	−2.20913	−0.0783006
$797$	−11.2823	−0.399639	−0.199820	−	0.979833i	$-0.564036\pi$
$797$	−11.2823	−0.399639	−0.199820	+	0.979833i	$0.564036\pi$
$798$	20.1586	0.713605
$799$	−2.38569	−0.0843998
$800$	2.67585	0.0946056
$801$	5.50461	0.194496
$802$	42.8473	1.51299
$803$	6.31312	0.222785
$804$	1.55058	0.0546849
$805$	−6.97979	−0.246005
$806$	0	0
$807$	−21.9328	−0.772072
$808$	−38.5856	−1.35744
$809$	−20.1030	−0.706783	−0.353392	−	0.935475i	$-0.614972\pi$
$809$	−20.1030	−0.706783	−0.353392	+	0.935475i	$0.614972\pi$
$810$	−0.585903	−0.0205865
$811$	−5.46027	−0.191736	−0.0958681	−	0.995394i	$-0.530563\pi$
$811$	−5.46027	−0.191736	−0.0958681	+	0.995394i	$0.530563\pi$
$812$	1.33891	0.0469866
$813$	−5.64424	−0.197952
$814$	8.82082	0.309169
$815$	4.89555	0.171484
$816$	−5.17157	−0.181041
$817$	−13.4109	−0.469187
$818$	29.0481	1.01564
$819$	0	0
$820$	0.0909216	0.00317512
$821$	16.9701	0.592260	0.296130	−	0.955148i	$-0.404304\pi$
$821$	16.9701	0.592260	0.296130	+	0.955148i	$0.404304\pi$
$822$	30.0152	1.04690
$823$	−45.7397	−1.59439	−0.797194	−	0.603724i	$-0.793683\pi$
$823$	−45.7397	−1.59439	−0.797194	+	0.603724i	$0.793683\pi$
$824$	36.9716	1.28797
$825$	4.83637	0.168381
$826$	30.0152	1.04436
$827$	−25.8174	−0.897760	−0.448880	−	0.893592i	$-0.648177\pi$
$827$	−25.8174	−0.897760	−0.448880	+	0.893592i	$0.648177\pi$
$828$	0.586585	0.0203853
$829$	−4.46809	−0.155183	−0.0775917	−	0.996985i	$-0.524723\pi$
$829$	−4.46809	−0.155183	−0.0775917	+	0.996985i	$0.524723\pi$
$830$	−2.08281	−0.0722956
$831$	−5.42988	−0.188360
$832$	0	0
$833$	1.59611	0.0553018
$834$	−10.1104	−0.350096
$835$	1.25760	0.0435212
$836$	−0.473141	−0.0163639
$837$	6.43354	0.222376
$838$	−3.42311	−0.118249
$839$	−40.6814	−1.40448	−0.702239	−	0.711942i	$-0.747816\pi$
$839$	−40.6814	−1.40448	−0.702239	+	0.711942i	$0.747816\pi$
$840$	3.20915	0.110726
$841$	−6.43991	−0.222066
$842$	−48.7353	−1.67953
$843$	−21.3960	−0.736916
$844$	−2.79759	−0.0962969
$845$	0	0
$846$	−2.79708	−0.0961654
$847$	2.87958	0.0989436
$848$	17.6257	0.605267
$849$	9.14996	0.314026
$850$	−8.65393	−0.296827
$851$	−36.4919	−1.25093
$852$	−0.282123	−0.00966538
$853$	51.5651	1.76556	0.882778	−	0.469790i	$-0.155670\pi$
$853$	51.5651	1.76556	0.882778	+	0.469790i	$0.155670\pi$
$854$	46.2103	1.58128
$855$	−1.95511	−0.0668635
$856$	4.84508	0.165601
$857$	10.5103	0.359024	0.179512	−	0.983756i	$-0.442548\pi$
$857$	10.5103	0.359024	0.179512	+	0.983756i	$0.442548\pi$
$858$	0	0
$859$	−44.7522	−1.52692	−0.763462	−	0.645853i	$-0.776502\pi$
$859$	−44.7522	−1.52692	−0.763462	+	0.645853i	$0.776502\pi$
$860$	0.109876	0.00374675
$861$	−6.61166	−0.225325
$862$	−24.6329	−0.839001
$863$	−8.14973	−0.277420	−0.138710	−	0.990333i	$-0.544296\pi$
$863$	−8.14973	−0.277420	−0.138710	+	0.990333i	$0.544296\pi$
$864$	−0.553277	−0.0188229
$865$	1.71637	0.0583584
$866$	32.2874	1.09717
$867$	−15.4738	−0.525519
$868$	1.81356	0.0615562
$869$	2.73419	0.0927512
$870$	−2.78289	−0.0943488
$871$	0	0
$872$	−26.2951	−0.890463
$873$	3.21930	0.108957
$874$	41.9478	1.41891
$875$	11.4577	0.387341
$876$	−0.618011	−0.0208807
$877$	−53.9568	−1.82199	−0.910996	−	0.412415i	$-0.864685\pi$
$877$	−53.9568	−1.82199	−0.910996	+	0.412415i	$0.864685\pi$
$878$	−5.40222	−0.182316
$879$	2.37205	0.0800074
$880$	−1.69338	−0.0570838
$881$	8.55497	0.288224	0.144112	−	0.989561i	$-0.453967\pi$
$881$	8.55497	0.288224	0.144112	+	0.989561i	$0.453967\pi$
$882$	1.87133	0.0630111
$883$	−18.3554	−0.617709	−0.308855	−	0.951109i	$-0.599946\pi$
$883$	−18.3554	−0.617709	−0.308855	+	0.951109i	$0.599946\pi$
$884$	0	0
$885$	−2.91107	−0.0978547
$886$	25.2269	0.847516
$887$	31.9685	1.07340	0.536699	−	0.843774i	$-0.319671\pi$
$887$	31.9685	1.07340	0.536699	+	0.843774i	$0.319671\pi$
$888$	16.7781	0.563037
$889$	0.374349	0.0125553
$890$	−3.22517	−0.108108
$891$	−1.00000	−0.0335013
$892$	1.51538	0.0507386
$893$	−9.33364	−0.312338
$894$	28.7592	0.961850
$895$	1.18252	0.0395273
$896$	34.7638	1.16138
$897$	0	0
$898$	17.6261	0.588190
$899$	30.5577	1.01916
$900$	−0.473447	−0.0157816
$901$	−5.20149	−0.173287
$902$	3.32562	0.110731
$903$	−7.99002	−0.265891
$904$	−52.3372	−1.74071
$905$	1.12335	0.0373415
$906$	−19.2887	−0.640826
$907$	−53.3962	−1.77299	−0.886496	−	0.462736i	$-0.846868\pi$
$907$	−53.3962	−1.77299	−0.886496	+	0.462736i	$0.846868\pi$
$908$	1.29957	0.0431276
$909$	14.0055	0.464533
$910$	0	0
$911$	−31.2277	−1.03462	−0.517309	−	0.855798i	$-0.673066\pi$
$911$	−31.2277	−1.03462	−0.517309	+	0.855798i	$0.673066\pi$
$912$	−20.2329	−0.669979
$913$	−3.55488	−0.117649
$914$	14.4065	0.476526
$915$	−4.48179	−0.148163
$916$	2.74012	0.0905360
$917$	23.8543	0.787737
$918$	1.78934	0.0590572
$919$	49.9449	1.64753	0.823765	−	0.566932i	$-0.191870\pi$
$919$	49.9449	1.64753	0.823765	+	0.566932i	$0.191870\pi$
$920$	6.67790	0.220164
$921$	11.6946	0.385352
$922$	44.8370	1.47663
$923$	0	0
$924$	−0.281891	−0.00927353
$925$	29.4535	0.968424
$926$	23.3712	0.768024
$927$	−13.4197	−0.440760
$928$	−2.62793	−0.0862659
$929$	37.1748	1.21966	0.609832	−	0.792530i	$-0.291237\pi$
$929$	37.1748	1.21966	0.609832	+	0.792530i	$0.291237\pi$
$930$	−3.76943	−0.123604
$931$	6.24451	0.204655
$932$	−1.78216	−0.0583764
$933$	3.94022	0.128997
$934$	23.8830	0.781477
$935$	0.499731	0.0163429
$936$	0	0
$937$	44.1132	1.44112	0.720558	−	0.693394i	$-0.243886\pi$
$937$	44.1132	1.44112	0.720558	+	0.693394i	$0.243886\pi$
$938$	66.0640	2.15707
$939$	−4.96530	−0.162036
$940$	0.0764712	0.00249422
$941$	−58.9062	−1.92029	−0.960144	−	0.279504i	$-0.909830\pi$
$941$	−58.9062	−1.92029	−0.960144	+	0.279504i	$0.909830\pi$
$942$	30.9600	1.00873
$943$	−13.7582	−0.448028
$944$	−30.1259	−0.980514
$945$	−1.16483	−0.0378920
$946$	4.01893	0.130667
$947$	−11.3616	−0.369202	−0.184601	−	0.982814i	$-0.559099\pi$
$947$	−11.3616	−0.369202	−0.184601	+	0.982814i	$0.559099\pi$
$948$	−0.267659	−0.00869315
$949$	0	0
$950$	−33.8571	−1.09847
$951$	2.24582	0.0728256
$952$	−9.80073	−0.317643
$953$	15.8826	0.514489	0.257245	−	0.966346i	$-0.417185\pi$
$953$	15.8826	0.514489	0.257245	+	0.966346i	$0.417185\pi$
$954$	−6.09841	−0.197443
$955$	9.25074	0.299347
$956$	1.60470	0.0518996
$957$	−4.74975	−0.153537
$958$	50.8811	1.64389
$959$	59.6731	1.92695
$960$	−3.06259	−0.0988447
$961$	10.3905	0.335176
$962$	0	0
$963$	−1.75863	−0.0566711
$964$	−0.993522	−0.0319992
$965$	3.26949	0.105249
$966$	24.9920	0.804103
$967$	−27.1682	−0.873669	−0.436834	−	0.899542i	$-0.643900\pi$
$967$	−27.1682	−0.873669	−0.436834	+	0.899542i	$0.643900\pi$
$968$	−2.75503	−0.0885501
$969$	5.97091	0.191813
$970$	−1.88620	−0.0605621
$971$	−13.0145	−0.417656	−0.208828	−	0.977952i	$-0.566965\pi$
$971$	−13.0145	−0.417656	−0.208828	+	0.977952i	$0.566965\pi$
$972$	0.0978930	0.00313992
$973$	−20.1005	−0.644393
$974$	−23.0313	−0.737970
$975$	0	0
$976$	−46.3807	−1.48461
$977$	−16.4687	−0.526880	−0.263440	−	0.964676i	$-0.584857\pi$
$977$	−16.4687	−0.526880	−0.263440	+	0.964676i	$0.584857\pi$
$978$	−17.5291	−0.560519
$979$	−5.50461	−0.175928
$980$	−0.0511617	−0.00163430
$981$	9.54438	0.304728
$982$	−58.1011	−1.85408
$983$	55.0035	1.75434	0.877169	−	0.480181i	$-0.159429\pi$
$983$	55.0035	1.75434	0.877169	+	0.480181i	$0.159429\pi$
$984$	6.32569	0.201656
$985$	9.00310	0.286863
$986$	8.49893	0.270661
$987$	−5.56086	−0.177004
$988$	0	0
$989$	−16.6264	−0.528688
$990$	0.585903	0.0186212
$991$	23.6827	0.752306	0.376153	−	0.926558i	$-0.377247\pi$
$991$	23.6827	0.752306	0.376153	+	0.926558i	$0.377247\pi$
$992$	−3.55953	−0.113015
$993$	−4.04258	−0.128287
$994$	−12.0201	−0.381254
$995$	9.12859	0.289396
$996$	0.347998	0.0110267
$997$	−40.7188	−1.28958	−0.644789	−	0.764361i	$-0.723055\pi$
$997$	−40.7188	−1.28958	−0.644789	+	0.764361i	$0.723055\pi$
$998$	−10.9555	−0.346791
$999$	−6.09000	−0.192679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.v.1.4		5
13.3	even	3		429.2.i.c.100.2	✓	10
13.9	even	3		429.2.i.c.133.2	yes	10
13.12	even	2		5577.2.a.p.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.c.100.2	✓	10	13.3	even	3
429.2.i.c.133.2	yes	10	13.9	even	3
5577.2.a.p.1.2		5	13.12	even	2
5577.2.a.v.1.4		5	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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+1.44841 q^{2} +1.00000 q^{3} +0.0978930 q^{4} -0.404514 q^{5} +1.44841 q^{6} +2.87958 q^{7} -2.75503 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.44841 q^{2} +1.00000 q^{3} +0.0978930 q^{4} -0.404514 q^{5} +1.44841 q^{6} +2.87958 q^{7} -2.75503 q^{8} +1.00000 q^{9} -0.585903 q^{10} -1.00000 q^{11} +0.0978930 q^{12} +4.17082 q^{14} -0.404514 q^{15} -4.18620 q^{16} +1.23539 q^{17} +1.44841 q^{18} +4.83324 q^{19} -0.0395991 q^{20} +2.87958 q^{21} -1.44841 q^{22} +5.99210 q^{23} -2.75503 q^{24} -4.83637 q^{25} +1.00000 q^{27} +0.281891 q^{28} +4.74975 q^{29} -0.585903 q^{30} +6.43354 q^{31} -0.553277 q^{32} -1.00000 q^{33} +1.78934 q^{34} -1.16483 q^{35} +0.0978930 q^{36} -6.09000 q^{37} +7.00052 q^{38} +1.11445 q^{40} -2.29605 q^{41} +4.17082 q^{42} -2.77472 q^{43} -0.0978930 q^{44} -0.404514 q^{45} +8.67903 q^{46} -1.93113 q^{47} -4.18620 q^{48} +1.29199 q^{49} -7.00505 q^{50} +1.23539 q^{51} -4.21042 q^{53} +1.44841 q^{54} +0.404514 q^{55} -7.93334 q^{56} +4.83324 q^{57} +6.87958 q^{58} +7.19647 q^{59} -0.0395991 q^{60} +11.0794 q^{61} +9.31841 q^{62} +2.87958 q^{63} +7.57103 q^{64} -1.44841 q^{66} +15.8396 q^{67} +0.120936 q^{68} +5.99210 q^{69} -1.68715 q^{70} -2.88195 q^{71} -2.75503 q^{72} -6.31312 q^{73} -8.82082 q^{74} -4.83637 q^{75} +0.473141 q^{76} -2.87958 q^{77} -2.73419 q^{79} +1.69338 q^{80} +1.00000 q^{81} -3.32562 q^{82} +3.55488 q^{83} +0.281891 q^{84} -0.499731 q^{85} -4.01893 q^{86} +4.74975 q^{87} +2.75503 q^{88} +5.50461 q^{89} -0.585903 q^{90} +0.586585 q^{92} +6.43354 q^{93} -2.79708 q^{94} -1.95511 q^{95} -0.553277 q^{96} +3.21930 q^{97} +1.87133 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 9 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 9 * q^7 + 3 * q^8 + 5 * q^9	\( 5 q + 2 q^{2} + 5 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 9 q^{7} + 3 q^{8} + 5 q^{9} + 7 q^{10} - 5 q^{11} + 2 q^{12} + 3 q^{14} + 8 q^{15} - 4 q^{16} + 3 q^{17} + 2 q^{18} - 3 q^{19} + 6 q^{20} + 9 q^{21} - 2 q^{22} - q^{23} + 3 q^{24} + 9 q^{25} + 5 q^{27} + 25 q^{28} - 2 q^{29} + 7 q^{30} - 2 q^{31} + 3 q^{32} - 5 q^{33} - 23 q^{34} + 12 q^{35} + 2 q^{36} - q^{37} + 7 q^{38} + 25 q^{40} + 18 q^{41} + 3 q^{42} - 9 q^{43} - 2 q^{44} + 8 q^{45} - 2 q^{46} + 16 q^{47} - 4 q^{48} + 22 q^{49} + 12 q^{50} + 3 q^{51} + 3 q^{53} + 2 q^{54} - 8 q^{55} + 25 q^{56} - 3 q^{57} + 29 q^{58} + 16 q^{59} + 6 q^{60} + 8 q^{61} + 16 q^{62} + 9 q^{63} - q^{64} - 2 q^{66} + 19 q^{67} - 22 q^{68} - q^{69} + 36 q^{70} + 25 q^{71} + 3 q^{72} + 8 q^{73} - 5 q^{74} + 9 q^{75} - 38 q^{76} - 9 q^{77} + 18 q^{79} + 20 q^{80} + 5 q^{81} - 40 q^{82} + 22 q^{83} + 25 q^{84} - 7 q^{85} - 4 q^{86} - 2 q^{87} - 3 q^{88} - 20 q^{89} + 7 q^{90} - 30 q^{92} - 2 q^{93} - 8 q^{94} - 7 q^{95} + 3 q^{96} + 21 q^{97} + 6 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 5 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 9 * q^7 + 3 * q^8 + 5 * q^9 + 7 * q^10 - 5 * q^11 + 2 * q^12 + 3 * q^14 + 8 * q^15 - 4 * q^16 + 3 * q^17 + 2 * q^18 - 3 * q^19 + 6 * q^20 + 9 * q^21 - 2 * q^22 - q^23 + 3 * q^24 + 9 * q^25 + 5 * q^27 + 25 * q^28 - 2 * q^29 + 7 * q^30 - 2 * q^31 + 3 * q^32 - 5 * q^33 - 23 * q^34 + 12 * q^35 + 2 * q^36 - q^37 + 7 * q^38 + 25 * q^40 + 18 * q^41 + 3 * q^42 - 9 * q^43 - 2 * q^44 + 8 * q^45 - 2 * q^46 + 16 * q^47 - 4 * q^48 + 22 * q^49 + 12 * q^50 + 3 * q^51 + 3 * q^53 + 2 * q^54 - 8 * q^55 + 25 * q^56 - 3 * q^57 + 29 * q^58 + 16 * q^59 + 6 * q^60 + 8 * q^61 + 16 * q^62 + 9 * q^63 - q^64 - 2 * q^66 + 19 * q^67 - 22 * q^68 - q^69 + 36 * q^70 + 25 * q^71 + 3 * q^72 + 8 * q^73 - 5 * q^74 + 9 * q^75 - 38 * q^76 - 9 * q^77 + 18 * q^79 + 20 * q^80 + 5 * q^81 - 40 * q^82 + 22 * q^83 + 25 * q^84 - 7 * q^85 - 4 * q^86 - 2 * q^87 - 3 * q^88 - 20 * q^89 + 7 * q^90 - 30 * q^92 - 2 * q^93 - 8 * q^94 - 7 * q^95 + 3 * q^96 + 21 * q^97 + 6 * q^98 - 5 * q^99

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