LMFDB - Embedded newform 3549.2.a.bb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 $ x^8 - 2x^7 - 9x^6 + 14x^5 + 25x^4 - 24x^3 - 16x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.775848$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.775848 q^{2} +1.00000 q^{3} -1.39806 q^{4} +3.03444 q^{5} +0.775848 q^{6} -1.00000 q^{7} -2.63638 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.775848 q^{2} +1.00000 q^{3} -1.39806 q^{4} +3.03444 q^{5} +0.775848 q^{6} -1.00000 q^{7} -2.63638 q^{8} +1.00000 q^{9} +2.35426 q^{10} -6.14359 q^{11} -1.39806 q^{12} -0.775848 q^{14} +3.03444 q^{15} +0.750691 q^{16} +6.44544 q^{17} +0.775848 q^{18} -4.32282 q^{19} -4.24233 q^{20} -1.00000 q^{21} -4.76649 q^{22} -8.92243 q^{23} -2.63638 q^{24} +4.20781 q^{25} +1.00000 q^{27} +1.39806 q^{28} -2.44946 q^{29} +2.35426 q^{30} -3.00419 q^{31} +5.85518 q^{32} -6.14359 q^{33} +5.00068 q^{34} -3.03444 q^{35} -1.39806 q^{36} -2.38830 q^{37} -3.35385 q^{38} -7.99993 q^{40} +0.945057 q^{41} -0.775848 q^{42} -5.28909 q^{43} +8.58910 q^{44} +3.03444 q^{45} -6.92245 q^{46} +0.212978 q^{47} +0.750691 q^{48} +1.00000 q^{49} +3.26462 q^{50} +6.44544 q^{51} +4.03626 q^{53} +0.775848 q^{54} -18.6423 q^{55} +2.63638 q^{56} -4.32282 q^{57} -1.90041 q^{58} -1.72328 q^{59} -4.24233 q^{60} -13.5329 q^{61} -2.33080 q^{62} -1.00000 q^{63} +3.04135 q^{64} -4.76649 q^{66} -6.35099 q^{67} -9.01111 q^{68} -8.92243 q^{69} -2.35426 q^{70} -7.06708 q^{71} -2.63638 q^{72} +1.75626 q^{73} -1.85296 q^{74} +4.20781 q^{75} +6.04356 q^{76} +6.14359 q^{77} +17.3116 q^{79} +2.27793 q^{80} +1.00000 q^{81} +0.733221 q^{82} -4.99898 q^{83} +1.39806 q^{84} +19.5583 q^{85} -4.10353 q^{86} -2.44946 q^{87} +16.1968 q^{88} -3.56786 q^{89} +2.35426 q^{90} +12.4741 q^{92} -3.00419 q^{93} +0.165239 q^{94} -13.1173 q^{95} +5.85518 q^{96} -1.57496 q^{97} +0.775848 q^{98} -6.14359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * 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 $

$2$	0.775848	0.548607	0.274304	−	0.961643i	$-0.411553\pi$
$2$	0.775848	0.548607	0.274304	+	0.961643i	$0.411553\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.39806	−0.699030
$5$	3.03444	1.35704	0.678521	−	0.734581i	$-0.262621\pi$
$5$	3.03444	1.35704	0.678521	+	0.734581i	$0.262621\pi$
$6$	0.775848	0.316739
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.63638	−0.932100
$9$	1.00000	0.333333
$10$	2.35426	0.744483
$11$	−6.14359	−1.85236	−0.926180	−	0.377081i	$-0.876928\pi$
$11$	−6.14359	−1.85236	−0.926180	+	0.377081i	$0.876928\pi$
$12$	−1.39806	−0.403585
$13$	0	0
$13$	0	0
$14$	−0.775848	−0.207354
$15$	3.03444	0.783488
$16$	0.750691	0.187673
$17$	6.44544	1.56325	0.781624	−	0.623749i	$-0.214391\pi$
$17$	6.44544	1.56325	0.781624	+	0.623749i	$0.214391\pi$
$18$	0.775848	0.182869
$19$	−4.32282	−0.991722	−0.495861	−	0.868402i	$-0.665148\pi$
$19$	−4.32282	−0.991722	−0.495861	+	0.868402i	$0.665148\pi$
$20$	−4.24233	−0.948613
$21$	−1.00000	−0.218218
$22$	−4.76649	−1.01622
$23$	−8.92243	−1.86045	−0.930227	−	0.366984i	$-0.880390\pi$
$23$	−8.92243	−1.86045	−0.930227	+	0.366984i	$0.880390\pi$
$24$	−2.63638	−0.538148
$25$	4.20781	0.841563
$26$	0	0
$27$	1.00000	0.192450
$28$	1.39806	0.264208
$29$	−2.44946	−0.454853	−0.227426	−	0.973795i	$-0.573031\pi$
$29$	−2.44946	−0.454853	−0.227426	+	0.973795i	$0.573031\pi$
$30$	2.35426	0.429828
$31$	−3.00419	−0.539568	−0.269784	−	0.962921i	$-0.586952\pi$
$31$	−3.00419	−0.539568	−0.269784	+	0.962921i	$0.586952\pi$
$32$	5.85518	1.03506
$33$	−6.14359	−1.06946
$34$	5.00068	0.857610
$35$	−3.03444	−0.512914
$36$	−1.39806	−0.233010
$37$	−2.38830	−0.392634	−0.196317	−	0.980541i	$-0.562898\pi$
$37$	−2.38830	−0.392634	−0.196317	+	0.980541i	$0.562898\pi$
$38$	−3.35385	−0.544066
$39$	0	0
$40$	−7.99993	−1.26490
$41$	0.945057	0.147593	0.0737966	−	0.997273i	$-0.476488\pi$
$41$	0.945057	0.147593	0.0737966	+	0.997273i	$0.476488\pi$
$42$	−0.775848	−0.119716
$43$	−5.28909	−0.806579	−0.403289	−	0.915073i	$-0.632133\pi$
$43$	−5.28909	−0.806579	−0.403289	+	0.915073i	$0.632133\pi$
$44$	8.58910	1.29486
$45$	3.03444	0.452347
$46$	−6.92245	−1.02066
$47$	0.212978	0.0310661	0.0155331	−	0.999879i	$-0.495055\pi$
$47$	0.212978	0.0310661	0.0155331	+	0.999879i	$0.495055\pi$
$48$	0.750691	0.108353
$49$	1.00000	0.142857
$50$	3.26462	0.461687
$51$	6.44544	0.902542
$52$	0	0
$53$	4.03626	0.554422	0.277211	−	0.960809i	$-0.410590\pi$
$53$	4.03626	0.554422	0.277211	+	0.960809i	$0.410590\pi$
$54$	0.775848	0.105580
$55$	−18.6423	−2.51373
$56$	2.63638	0.352301
$57$	−4.32282	−0.572571
$58$	−1.90041	−0.249536
$59$	−1.72328	−0.224352	−0.112176	−	0.993688i	$-0.535782\pi$
$59$	−1.72328	−0.224352	−0.112176	+	0.993688i	$0.535782\pi$
$60$	−4.24233	−0.547682
$61$	−13.5329	−1.73271	−0.866355	−	0.499428i	$-0.833543\pi$
$61$	−13.5329	−1.73271	−0.866355	+	0.499428i	$0.833543\pi$
$62$	−2.33080	−0.296011
$63$	−1.00000	−0.125988
$64$	3.04135	0.380168
$65$	0	0
$66$	−4.76649	−0.586714
$67$	−6.35099	−0.775898	−0.387949	−	0.921681i	$-0.626816\pi$
$67$	−6.35099	−0.775898	−0.387949	+	0.921681i	$0.626816\pi$
$68$	−9.01111	−1.09276
$69$	−8.92243	−1.07413
$70$	−2.35426	−0.281388
$71$	−7.06708	−0.838708	−0.419354	−	0.907823i	$-0.637743\pi$
$71$	−7.06708	−0.838708	−0.419354	+	0.907823i	$0.637743\pi$
$72$	−2.63638	−0.310700
$73$	1.75626	0.205554	0.102777	−	0.994704i	$-0.467227\pi$
$73$	1.75626	0.205554	0.102777	+	0.994704i	$0.467227\pi$
$74$	−1.85296	−0.215402
$75$	4.20781	0.485876
$76$	6.04356	0.693244
$77$	6.14359	0.700127
$78$	0	0
$79$	17.3116	1.94771	0.973856	−	0.227168i	$-0.0729467\pi$
$79$	17.3116	1.94771	0.973856	+	0.227168i	$0.0729467\pi$
$80$	2.27793	0.254680
$81$	1.00000	0.111111
$82$	0.733221	0.0809707
$83$	−4.99898	−0.548709	−0.274355	−	0.961629i	$-0.588464\pi$
$83$	−4.99898	−0.548709	−0.274355	+	0.961629i	$0.588464\pi$
$84$	1.39806	0.152541
$85$	19.5583	2.12139
$86$	−4.10353	−0.442495
$87$	−2.44946	−0.262609
$88$	16.1968	1.72659
$89$	−3.56786	−0.378192	−0.189096	−	0.981959i	$-0.560556\pi$
$89$	−3.56786	−0.378192	−0.189096	+	0.981959i	$0.560556\pi$
$90$	2.35426	0.248161
$91$	0	0
$92$	12.4741	1.30051
$93$	−3.00419	−0.311520
$94$	0.165239	0.0170431
$95$	−13.1173	−1.34581
$96$	5.85518	0.597592
$97$	−1.57496	−0.159913	−0.0799567	−	0.996798i	$-0.525478\pi$
$97$	−1.57496	−0.159913	−0.0799567	+	0.996798i	$0.525478\pi$
$98$	0.775848	0.0783725
$99$	−6.14359	−0.617454
$100$	−5.88277	−0.588277
$101$	−8.54623	−0.850381	−0.425191	−	0.905104i	$-0.639793\pi$
$101$	−8.54623	−0.850381	−0.425191	+	0.905104i	$0.639793\pi$
$102$	5.00068	0.495141
$103$	−1.58051	−0.155733	−0.0778663	−	0.996964i	$-0.524811\pi$
$103$	−1.58051	−0.155733	−0.0778663	+	0.996964i	$0.524811\pi$
$104$	0	0
$105$	−3.03444	−0.296131
$106$	3.13152	0.304160
$107$	−3.66169	−0.353989	−0.176994	−	0.984212i	$-0.556637\pi$
$107$	−3.66169	−0.353989	−0.176994	+	0.984212i	$0.556637\pi$
$108$	−1.39806	−0.134528
$109$	−3.05967	−0.293063	−0.146532	−	0.989206i	$-0.546811\pi$
$109$	−3.05967	−0.293063	−0.146532	+	0.989206i	$0.546811\pi$
$110$	−14.4636	−1.37905
$111$	−2.38830	−0.226687
$112$	−0.750691	−0.0709336
$113$	−11.7783	−1.10801	−0.554007	−	0.832512i	$-0.686902\pi$
$113$	−11.7783	−1.10801	−0.554007	+	0.832512i	$0.686902\pi$
$114$	−3.35385	−0.314117
$115$	−27.0745	−2.52471
$116$	3.42449	0.317956
$117$	0	0
$118$	−1.33700	−0.123081
$119$	−6.44544	−0.590853
$120$	−7.99993	−0.730290
$121$	26.7436	2.43124
$122$	−10.4995	−0.950578
$123$	0.945057	0.0852129
$124$	4.20004	0.377175
$125$	−2.40384	−0.215006
$126$	−0.775848	−0.0691180
$127$	0.679874	0.0603290	0.0301645	−	0.999545i	$-0.490397\pi$
$127$	0.679874	0.0603290	0.0301645	+	0.999545i	$0.490397\pi$
$128$	−9.35073	−0.826496
$129$	−5.28909	−0.465678
$130$	0	0
$131$	−14.3741	−1.25587	−0.627936	−	0.778265i	$-0.716100\pi$
$131$	−14.3741	−1.25587	−0.627936	+	0.778265i	$0.716100\pi$
$132$	8.58910	0.747585
$133$	4.32282	0.374836
$134$	−4.92741	−0.425663
$135$	3.03444	0.261163
$136$	−16.9926	−1.45710
$137$	10.1813	0.869844	0.434922	−	0.900468i	$-0.356776\pi$
$137$	10.1813	0.869844	0.434922	+	0.900468i	$0.356776\pi$
$138$	−6.92245	−0.589278
$139$	12.3525	1.04773	0.523863	−	0.851802i	$-0.324490\pi$
$139$	12.3525	1.04773	0.523863	+	0.851802i	$0.324490\pi$
$140$	4.24233	0.358542
$141$	0.212978	0.0179360
$142$	−5.48298	−0.460122
$143$	0	0
$144$	0.750691	0.0625576
$145$	−7.43273	−0.617254
$146$	1.36259	0.112769
$147$	1.00000	0.0824786
$148$	3.33898	0.274463
$149$	−11.9803	−0.981462	−0.490731	−	0.871311i	$-0.663270\pi$
$149$	−11.9803	−0.981462	−0.490731	+	0.871311i	$0.663270\pi$
$150$	3.26462	0.266555
$151$	−16.0560	−1.30662	−0.653309	−	0.757092i	$-0.726620\pi$
$151$	−16.0560	−1.30662	−0.653309	+	0.757092i	$0.726620\pi$
$152$	11.3966	0.924385
$153$	6.44544	0.521083
$154$	4.76649	0.384095
$155$	−9.11603	−0.732217
$156$	0	0
$157$	18.9571	1.51294	0.756470	−	0.654028i	$-0.226922\pi$
$157$	18.9571	1.51294	0.756470	+	0.654028i	$0.226922\pi$
$158$	13.4312	1.06853
$159$	4.03626	0.320096
$160$	17.7672	1.40462
$161$	8.92243	0.703186
$162$	0.775848	0.0609564
$163$	7.24567	0.567524	0.283762	−	0.958895i	$-0.408417\pi$
$163$	7.24567	0.567524	0.283762	+	0.958895i	$0.408417\pi$
$164$	−1.32125	−0.103172
$165$	−18.6423	−1.45130
$166$	−3.87845	−0.301026
$167$	11.0746	0.856975	0.428487	−	0.903548i	$-0.359047\pi$
$167$	11.0746	0.856975	0.428487	+	0.903548i	$0.359047\pi$
$168$	2.63638	0.203401
$169$	0	0
$170$	15.1743	1.16381
$171$	−4.32282	−0.330574
$172$	7.39446	0.563823
$173$	4.57650	0.347945	0.173972	−	0.984751i	$-0.444340\pi$
$173$	4.57650	0.347945	0.173972	+	0.984751i	$0.444340\pi$
$174$	−1.90041	−0.144069
$175$	−4.20781	−0.318081
$176$	−4.61193	−0.347638
$177$	−1.72328	−0.129530
$178$	−2.76811	−0.207479
$179$	3.25636	0.243392	0.121696	−	0.992567i	$-0.461167\pi$
$179$	3.25636	0.243392	0.121696	+	0.992567i	$0.461167\pi$
$180$	−4.24233	−0.316204
$181$	20.2771	1.50718	0.753591	−	0.657343i	$-0.228320\pi$
$181$	20.2771	1.50718	0.753591	+	0.657343i	$0.228320\pi$
$182$	0	0
$183$	−13.5329	−1.00038
$184$	23.5229	1.73413
$185$	−7.24714	−0.532820
$186$	−2.33080	−0.170902
$187$	−39.5981	−2.89570
$188$	−0.297757	−0.0217161
$189$	−1.00000	−0.0727393
$190$	−10.1770	−0.738321
$191$	23.9229	1.73100	0.865499	−	0.500910i	$-0.167001\pi$
$191$	23.9229	1.73100	0.865499	+	0.500910i	$0.167001\pi$
$192$	3.04135	0.219490
$193$	−8.43437	−0.607119	−0.303559	−	0.952812i	$-0.598175\pi$
$193$	−8.43437	−0.607119	−0.303559	+	0.952812i	$0.598175\pi$
$194$	−1.22193	−0.0877297
$195$	0	0
$196$	−1.39806	−0.0998614
$197$	23.9756	1.70819	0.854096	−	0.520116i	$-0.174111\pi$
$197$	23.9756	1.70819	0.854096	+	0.520116i	$0.174111\pi$
$198$	−4.76649	−0.338740
$199$	−10.4194	−0.738612	−0.369306	−	0.929308i	$-0.620405\pi$
$199$	−10.4194	−0.738612	−0.369306	+	0.929308i	$0.620405\pi$
$200$	−11.0934	−0.784421
$201$	−6.35099	−0.447965
$202$	−6.63057	−0.466525
$203$	2.44946	0.171918
$204$	−9.01111	−0.630904
$205$	2.86772	0.200290
$206$	−1.22624	−0.0854360
$207$	−8.92243	−0.620151
$208$	0	0
$209$	26.5576	1.83703
$210$	−2.35426	−0.162460
$211$	8.18369	0.563389	0.281694	−	0.959504i	$-0.409104\pi$
$211$	8.18369	0.563389	0.281694	+	0.959504i	$0.409104\pi$
$212$	−5.64293	−0.387558
$213$	−7.06708	−0.484228
$214$	−2.84091	−0.194201
$215$	−16.0494	−1.09456
$216$	−2.63638	−0.179383
$217$	3.00419	0.203938
$218$	−2.37384	−0.160777
$219$	1.75626	0.118677
$220$	26.0631	1.75717
$221$	0	0
$222$	−1.85296	−0.124362
$223$	−7.63142	−0.511038	−0.255519	−	0.966804i	$-0.582246\pi$
$223$	−7.63142	−0.511038	−0.255519	+	0.966804i	$0.582246\pi$
$224$	−5.85518	−0.391216
$225$	4.20781	0.280521
$226$	−9.13820	−0.607864
$227$	−8.44391	−0.560442	−0.280221	−	0.959936i	$-0.590408\pi$
$227$	−8.44391	−0.560442	−0.280221	+	0.959936i	$0.590408\pi$
$228$	6.04356	0.400244
$229$	−19.3696	−1.27998	−0.639991	−	0.768382i	$-0.721062\pi$
$229$	−19.3696	−1.27998	−0.639991	+	0.768382i	$0.721062\pi$
$230$	−21.0057	−1.38508
$231$	6.14359	0.404218
$232$	6.45769	0.423968
$233$	3.12399	0.204660	0.102330	−	0.994751i	$-0.467370\pi$
$233$	3.12399	0.204660	0.102330	+	0.994751i	$0.467370\pi$
$234$	0	0
$235$	0.646270	0.0421580
$236$	2.40925	0.156829
$237$	17.3116	1.12451
$238$	−5.00068	−0.324146
$239$	22.3164	1.44353	0.721765	−	0.692138i	$-0.243331\pi$
$239$	22.3164	1.44353	0.721765	+	0.692138i	$0.243331\pi$
$240$	2.27793	0.147039
$241$	−21.9939	−1.41675	−0.708376	−	0.705835i	$-0.750572\pi$
$241$	−21.9939	−1.41675	−0.708376	+	0.705835i	$0.750572\pi$
$242$	20.7490	1.33380
$243$	1.00000	0.0641500
$244$	18.9198	1.21122
$245$	3.03444	0.193863
$246$	0.733221	0.0467484
$247$	0	0
$248$	7.92018	0.502932
$249$	−4.99898	−0.316797
$250$	−1.86502	−0.117954
$251$	1.49983	0.0946687	0.0473344	−	0.998879i	$-0.484927\pi$
$251$	1.49983	0.0946687	0.0473344	+	0.998879i	$0.484927\pi$
$252$	1.39806	0.0880695
$253$	54.8157	3.44623
$254$	0.527479	0.0330970
$255$	19.5583	1.22479
$256$	−13.3374	−0.833590
$257$	−8.93391	−0.557282	−0.278641	−	0.960395i	$-0.589884\pi$
$257$	−8.93391	−0.557282	−0.278641	+	0.960395i	$0.589884\pi$
$258$	−4.10353	−0.255475
$259$	2.38830	0.148402
$260$	0	0
$261$	−2.44946	−0.151618
$262$	−11.1521	−0.688981
$263$	−10.4624	−0.645137	−0.322568	−	0.946546i	$-0.604546\pi$
$263$	−10.4624	−0.645137	−0.322568	+	0.946546i	$0.604546\pi$
$264$	16.1968	0.996845
$265$	12.2478	0.752374
$266$	3.35385	0.205638
$267$	−3.56786	−0.218349
$268$	8.87907	0.542376
$269$	2.91690	0.177846	0.0889232	−	0.996038i	$-0.471657\pi$
$269$	2.91690	0.177846	0.0889232	+	0.996038i	$0.471657\pi$
$270$	2.35426	0.143276
$271$	22.6664	1.37689	0.688444	−	0.725289i	$-0.258294\pi$
$271$	22.6664	1.37689	0.688444	+	0.725289i	$0.258294\pi$
$272$	4.83853	0.293379
$273$	0	0
$274$	7.89912	0.477203
$275$	−25.8511	−1.55888
$276$	12.4741	0.750852
$277$	0.227605	0.0136755	0.00683773	−	0.999977i	$-0.497823\pi$
$277$	0.227605	0.0136755	0.00683773	+	0.999977i	$0.497823\pi$
$278$	9.58367	0.574790
$279$	−3.00419	−0.179856
$280$	7.99993	0.478087
$281$	−11.1627	−0.665908	−0.332954	−	0.942943i	$-0.608045\pi$
$281$	−11.1627	−0.665908	−0.332954	+	0.942943i	$0.608045\pi$
$282$	0.165239	0.00983984
$283$	−20.0679	−1.19291	−0.596456	−	0.802646i	$-0.703425\pi$
$283$	−20.0679	−1.19291	−0.596456	+	0.802646i	$0.703425\pi$
$284$	9.88020	0.586282
$285$	−13.1173	−0.777003
$286$	0	0
$287$	−0.945057	−0.0557850
$288$	5.85518	0.345020
$289$	24.5437	1.44375
$290$	−5.76667	−0.338630
$291$	−1.57496	−0.0923260
$292$	−2.45535	−0.143689
$293$	3.68811	0.215461	0.107731	−	0.994180i	$-0.465642\pi$
$293$	3.68811	0.215461	0.107731	+	0.994180i	$0.465642\pi$
$294$	0.775848	0.0452484
$295$	−5.22919	−0.304455
$296$	6.29645	0.365974
$297$	−6.14359	−0.356487
$298$	−9.29487	−0.538438
$299$	0	0
$300$	−5.88277	−0.339642
$301$	5.28909	0.304858
$302$	−12.4570	−0.716820
$303$	−8.54623	−0.490968
$304$	−3.24510	−0.186119
$305$	−41.0648	−2.35136
$306$	5.00068	0.285870
$307$	−25.5280	−1.45696	−0.728479	−	0.685068i	$-0.759772\pi$
$307$	−25.5280	−1.45696	−0.728479	+	0.685068i	$0.759772\pi$
$308$	−8.58910	−0.489409
$309$	−1.58051	−0.0899122
$310$	−7.07265	−0.401700
$311$	−15.7918	−0.895469	−0.447734	−	0.894167i	$-0.647769\pi$
$311$	−15.7918	−0.895469	−0.447734	+	0.894167i	$0.647769\pi$
$312$	0	0
$313$	4.21208	0.238081	0.119041	−	0.992889i	$-0.462018\pi$
$313$	4.21208	0.238081	0.119041	+	0.992889i	$0.462018\pi$
$314$	14.7078	0.830010
$315$	−3.03444	−0.170971
$316$	−24.2027	−1.36151
$317$	−23.6448	−1.32802	−0.664011	−	0.747723i	$-0.731147\pi$
$317$	−23.6448	−1.32802	−0.664011	+	0.747723i	$0.731147\pi$
$318$	3.13152	0.175607
$319$	15.0484	0.842551
$320$	9.22878	0.515904
$321$	−3.66169	−0.204376
$322$	6.92245	0.385773
$323$	−27.8625	−1.55031
$324$	−1.39806	−0.0776700
$325$	0	0
$326$	5.62154	0.311348
$327$	−3.05967	−0.169200
$328$	−2.49153	−0.137572
$329$	−0.212978	−0.0117419
$330$	−14.4636	−0.796196
$331$	3.54791	0.195011	0.0975055	−	0.995235i	$-0.468914\pi$
$331$	3.54791	0.195011	0.0975055	+	0.995235i	$0.468914\pi$
$332$	6.98887	0.383564
$333$	−2.38830	−0.130878
$334$	8.59217	0.470143
$335$	−19.2717	−1.05293
$336$	−0.750691	−0.0409536
$337$	18.4037	1.00251	0.501256	−	0.865299i	$-0.332871\pi$
$337$	18.4037	1.00251	0.501256	+	0.865299i	$0.332871\pi$
$338$	0	0
$339$	−11.7783	−0.639712
$340$	−27.3437	−1.48292
$341$	18.4565	0.999475
$342$	−3.35385	−0.181355
$343$	−1.00000	−0.0539949
$344$	13.9440	0.751812
$345$	−27.0745	−1.45764
$346$	3.55067	0.190885
$347$	−20.9993	−1.12730	−0.563651	−	0.826013i	$-0.690604\pi$
$347$	−20.9993	−1.12730	−0.563651	+	0.826013i	$0.690604\pi$
$348$	3.42449	0.183572
$349$	−2.26426	−0.121203	−0.0606016	−	0.998162i	$-0.519302\pi$
$349$	−2.26426	−0.121203	−0.0606016	+	0.998162i	$0.519302\pi$
$350$	−3.26462	−0.174501
$351$	0	0
$352$	−35.9718	−1.91730
$353$	1.84815	0.0983670	0.0491835	−	0.998790i	$-0.484338\pi$
$353$	1.84815	0.0983670	0.0491835	+	0.998790i	$0.484338\pi$
$354$	−1.33700	−0.0710610
$355$	−21.4446	−1.13816
$356$	4.98808	0.264367
$357$	−6.44544	−0.341129
$358$	2.52644	0.133527
$359$	10.1169	0.533949	0.266974	−	0.963704i	$-0.413976\pi$
$359$	10.1169	0.533949	0.266974	+	0.963704i	$0.413976\pi$
$360$	−7.99993	−0.421633
$361$	−0.313249	−0.0164868
$362$	15.7319	0.826851
$363$	26.7436	1.40368
$364$	0	0
$365$	5.32926	0.278946
$366$	−10.4995	−0.548816
$367$	−15.8078	−0.825160	−0.412580	−	0.910921i	$-0.635372\pi$
$367$	−15.8078	−0.825160	−0.412580	+	0.910921i	$0.635372\pi$
$368$	−6.69799	−0.349157
$369$	0.945057	0.0491977
$370$	−5.62268	−0.292309
$371$	−4.03626	−0.209552
$372$	4.20004	0.217762
$373$	−11.1828	−0.579025	−0.289512	−	0.957174i	$-0.593493\pi$
$373$	−11.1828	−0.579025	−0.289512	+	0.957174i	$0.593493\pi$
$374$	−30.7221	−1.58860
$375$	−2.40384	−0.124134
$376$	−0.561492	−0.0289567
$377$	0	0
$378$	−0.775848	−0.0399053
$379$	27.4187	1.40841	0.704203	−	0.709999i	$-0.251305\pi$
$379$	27.4187	1.40841	0.704203	+	0.709999i	$0.251305\pi$
$380$	18.3388	0.940761
$381$	0.679874	0.0348310
$382$	18.5605	0.949639
$383$	3.90039	0.199301	0.0996503	−	0.995023i	$-0.468228\pi$
$383$	3.90039	0.199301	0.0996503	+	0.995023i	$0.468228\pi$
$384$	−9.35073	−0.477178
$385$	18.6423	0.950101
$386$	−6.54379	−0.333070
$387$	−5.28909	−0.268860
$388$	2.20189	0.111784
$389$	−20.5060	−1.03970	−0.519848	−	0.854259i	$-0.674012\pi$
$389$	−20.5060	−1.03970	−0.519848	+	0.854259i	$0.674012\pi$
$390$	0	0
$391$	−57.5090	−2.90835
$392$	−2.63638	−0.133157
$393$	−14.3741	−0.725078
$394$	18.6014	0.937126
$395$	52.5311	2.64313
$396$	8.58910	0.431619
$397$	−30.9953	−1.55561	−0.777804	−	0.628506i	$-0.783667\pi$
$397$	−30.9953	−1.55561	−0.777804	+	0.628506i	$0.783667\pi$
$398$	−8.08388	−0.405208
$399$	4.32282	0.216412
$400$	3.15877	0.157938
$401$	15.5871	0.778384	0.389192	−	0.921157i	$-0.372754\pi$
$401$	15.5871	0.778384	0.389192	+	0.921157i	$0.372754\pi$
$402$	−4.92741	−0.245757
$403$	0	0
$404$	11.9481	0.594442
$405$	3.03444	0.150782
$406$	1.90041	0.0943156
$407$	14.6727	0.727299
$408$	−16.9926	−0.841260
$409$	−19.2111	−0.949925	−0.474963	−	0.880006i	$-0.657538\pi$
$409$	−19.2111	−0.949925	−0.474963	+	0.880006i	$0.657538\pi$
$410$	2.22491	0.109881
$411$	10.1813	0.502205
$412$	2.20965	0.108862
$413$	1.72328	0.0847971
$414$	−6.92245	−0.340220
$415$	−15.1691	−0.744621
$416$	0	0
$417$	12.3525	0.604905
$418$	20.6047	1.00781
$419$	20.8500	1.01859	0.509294	−	0.860593i	$-0.329907\pi$
$419$	20.8500	1.01859	0.509294	+	0.860593i	$0.329907\pi$
$420$	4.24233	0.207004
$421$	3.31213	0.161423	0.0807116	−	0.996737i	$-0.474281\pi$
$421$	3.31213	0.161423	0.0807116	+	0.996737i	$0.474281\pi$
$422$	6.34930	0.309079
$423$	0.212978	0.0103554
$424$	−10.6411	−0.516777
$425$	27.1212	1.31557
$426$	−5.48298	−0.265651
$427$	13.5329	0.654903
$428$	5.11926	0.247449
$429$	0	0
$430$	−12.4519	−0.600484
$431$	28.3773	1.36689	0.683443	−	0.730004i	$-0.260482\pi$
$431$	28.3773	1.36689	0.683443	+	0.730004i	$0.260482\pi$
$432$	0.750691	0.0361176
$433$	21.1954	1.01859	0.509293	−	0.860593i	$-0.329907\pi$
$433$	21.1954	1.01859	0.509293	+	0.860593i	$0.329907\pi$
$434$	2.33080	0.111882
$435$	−7.43273	−0.356372
$436$	4.27760	0.204860
$437$	38.5700	1.84505
$438$	1.36259	0.0651070
$439$	12.5732	0.600084	0.300042	−	0.953926i	$-0.402999\pi$
$439$	12.5732	0.600084	0.300042	+	0.953926i	$0.402999\pi$
$440$	49.1482	2.34305
$441$	1.00000	0.0476190
$442$	0	0
$443$	10.7230	0.509465	0.254732	−	0.967012i	$-0.418013\pi$
$443$	10.7230	0.509465	0.254732	+	0.967012i	$0.418013\pi$
$444$	3.33898	0.158461
$445$	−10.8264	−0.513222
$446$	−5.92082	−0.280359
$447$	−11.9803	−0.566648
$448$	−3.04135	−0.143690
$449$	−11.1853	−0.527868	−0.263934	−	0.964541i	$-0.585020\pi$
$449$	−11.1853	−0.527868	−0.263934	+	0.964541i	$0.585020\pi$
$450$	3.26462	0.153896
$451$	−5.80604	−0.273396
$452$	16.4668	0.774535
$453$	−16.0560	−0.754376
$454$	−6.55119	−0.307463
$455$	0	0
$456$	11.3966	0.533694
$457$	−2.50156	−0.117018	−0.0585090	−	0.998287i	$-0.518635\pi$
$457$	−2.50156	−0.117018	−0.0585090	+	0.998287i	$0.518635\pi$
$458$	−15.0279	−0.702208
$459$	6.44544	0.300847
$460$	37.8518	1.76485
$461$	−8.73331	−0.406751	−0.203375	−	0.979101i	$-0.565191\pi$
$461$	−8.73331	−0.406751	−0.203375	+	0.979101i	$0.565191\pi$
$462$	4.76649	0.221757
$463$	12.0840	0.561591	0.280795	−	0.959768i	$-0.409402\pi$
$463$	12.0840	0.561591	0.280795	+	0.959768i	$0.409402\pi$
$464$	−1.83879	−0.0853635
$465$	−9.11603	−0.422746
$466$	2.42375	0.112278
$467$	3.44741	0.159527	0.0797635	−	0.996814i	$-0.474583\pi$
$467$	3.44741	0.159527	0.0797635	+	0.996814i	$0.474583\pi$
$468$	0	0
$469$	6.35099	0.293262
$470$	0.501407	0.0231282
$471$	18.9571	0.873496
$472$	4.54322	0.209119
$473$	32.4940	1.49407
$474$	13.4312	0.616915
$475$	−18.1896	−0.834596
$476$	9.01111	0.413024
$477$	4.03626	0.184807
$478$	17.3142	0.791931
$479$	12.6504	0.578012	0.289006	−	0.957327i	$-0.406675\pi$
$479$	12.6504	0.578012	0.289006	+	0.957327i	$0.406675\pi$
$480$	17.7672	0.810957
$481$	0	0
$482$	−17.0639	−0.777241
$483$	8.92243	0.405984
$484$	−37.3892	−1.69951
$485$	−4.77913	−0.217009
$486$	0.775848	0.0351932
$487$	−7.71599	−0.349645	−0.174822	−	0.984600i	$-0.555935\pi$
$487$	−7.71599	−0.349645	−0.174822	+	0.984600i	$0.555935\pi$
$488$	35.6778	1.61506
$489$	7.24567	0.327660
$490$	2.35426	0.106355
$491$	4.65613	0.210128	0.105064	−	0.994465i	$-0.466495\pi$
$491$	4.65613	0.210128	0.105064	+	0.994465i	$0.466495\pi$
$492$	−1.32125	−0.0595664
$493$	−15.7878	−0.711048
$494$	0	0
$495$	−18.6423	−0.837910
$496$	−2.25522	−0.101262
$497$	7.06708	0.317002
$498$	−3.87845	−0.173797
$499$	−32.4249	−1.45154	−0.725769	−	0.687938i	$-0.758516\pi$
$499$	−32.4249	−1.45154	−0.725769	+	0.687938i	$0.758516\pi$
$500$	3.36071	0.150296
$501$	11.0746	0.494775
$502$	1.16364	0.0519359
$503$	−0.292607	−0.0130467	−0.00652335	−	0.999979i	$-0.502076\pi$
$503$	−0.292607	−0.0130467	−0.00652335	+	0.999979i	$0.502076\pi$
$504$	2.63638	0.117434
$505$	−25.9330	−1.15400
$506$	42.5286	1.89063
$507$	0	0
$508$	−0.950504	−0.0421718
$509$	−4.83466	−0.214293	−0.107146	−	0.994243i	$-0.534171\pi$
$509$	−4.83466	−0.214293	−0.107146	+	0.994243i	$0.534171\pi$
$510$	15.1743	0.671927
$511$	−1.75626	−0.0776923
$512$	8.35364	0.369182
$513$	−4.32282	−0.190857
$514$	−6.93135	−0.305729
$515$	−4.79597	−0.211336
$516$	7.39446	0.325523
$517$	−1.30845	−0.0575456
$518$	1.85296	0.0814142
$519$	4.57650	0.200886
$520$	0	0
$521$	35.8024	1.56853	0.784265	−	0.620425i	$-0.213040\pi$
$521$	35.8024	1.56853	0.784265	+	0.620425i	$0.213040\pi$
$522$	−1.90041	−0.0831785
$523$	40.0519	1.75135	0.875673	−	0.482904i	$-0.160418\pi$
$523$	40.0519	1.75135	0.875673	+	0.482904i	$0.160418\pi$
$524$	20.0959	0.877892
$525$	−4.20781	−0.183644
$526$	−8.11720	−0.353927
$527$	−19.3633	−0.843480
$528$	−4.61193	−0.200709
$529$	56.6097	2.46129
$530$	9.50241	0.412758
$531$	−1.72328	−0.0747840
$532$	−6.04356	−0.262021
$533$	0	0
$534$	−2.76811	−0.119788
$535$	−11.1112	−0.480378
$536$	16.7436	0.723214
$537$	3.25636	0.140522
$538$	2.26307	0.0975679
$539$	−6.14359	−0.264623
$540$	−4.24233	−0.182561
$541$	24.0781	1.03520	0.517599	−	0.855623i	$-0.326826\pi$
$541$	24.0781	1.03520	0.517599	+	0.855623i	$0.326826\pi$
$542$	17.5857	0.755371
$543$	20.2771	0.870172
$544$	37.7392	1.61805
$545$	−9.28438	−0.397699
$546$	0	0
$547$	−30.4282	−1.30102	−0.650508	−	0.759500i	$-0.725444\pi$
$547$	−30.4282	−1.30102	−0.650508	+	0.759500i	$0.725444\pi$
$548$	−14.2340	−0.608047
$549$	−13.5329	−0.577570
$550$	−20.0565	−0.855212
$551$	10.5886	0.451088
$552$	23.5229	1.00120
$553$	−17.3116	−0.736166
$554$	0.176587	0.00750246
$555$	−7.24714	−0.307624
$556$	−17.2695	−0.732392
$557$	−27.7922	−1.17759	−0.588797	−	0.808281i	$-0.700398\pi$
$557$	−27.7922	−1.17759	−0.588797	+	0.808281i	$0.700398\pi$
$558$	−2.33080	−0.0986704
$559$	0	0
$560$	−2.27793	−0.0962599
$561$	−39.5981	−1.67183
$562$	−8.66053	−0.365322
$563$	46.4805	1.95892	0.979461	−	0.201636i	$-0.0646257\pi$
$563$	46.4805	1.95892	0.979461	+	0.201636i	$0.0646257\pi$
$564$	−0.297757	−0.0125378
$565$	−35.7407	−1.50362
$566$	−15.5696	−0.654441
$567$	−1.00000	−0.0419961
$568$	18.6315	0.781760
$569$	12.4367	0.521373	0.260686	−	0.965424i	$-0.416051\pi$
$569$	12.4367	0.521373	0.260686	+	0.965424i	$0.416051\pi$
$570$	−10.1770	−0.426270
$571$	−11.1120	−0.465022	−0.232511	−	0.972594i	$-0.574694\pi$
$571$	−11.1120	−0.465022	−0.232511	+	0.972594i	$0.574694\pi$
$572$	0	0
$573$	23.9229	0.999392
$574$	−0.733221	−0.0306040
$575$	−37.5439	−1.56569
$576$	3.04135	0.126723
$577$	−19.5793	−0.815097	−0.407549	−	0.913183i	$-0.633616\pi$
$577$	−19.5793	−0.815097	−0.407549	+	0.913183i	$0.633616\pi$
$578$	19.0422	0.792050
$579$	−8.43437	−0.350520
$580$	10.3914	0.431479
$581$	4.99898	0.207393
$582$	−1.22193	−0.0506507
$583$	−24.7971	−1.02699
$584$	−4.63016	−0.191597
$585$	0	0
$586$	2.86141	0.118204
$587$	−8.31074	−0.343021	−0.171511	−	0.985182i	$-0.554865\pi$
$587$	−8.31074	−0.343021	−0.171511	+	0.985182i	$0.554865\pi$
$588$	−1.39806	−0.0576550
$589$	12.9866	0.535102
$590$	−4.05706	−0.167026
$591$	23.9756	0.986225
$592$	−1.79287	−0.0736866
$593$	0.319656	0.0131267	0.00656336	−	0.999978i	$-0.497911\pi$
$593$	0.319656	0.0131267	0.00656336	+	0.999978i	$0.497911\pi$
$594$	−4.76649	−0.195571
$595$	−19.5583	−0.801812
$596$	16.7491	0.686072
$597$	−10.4194	−0.426438
$598$	0	0
$599$	9.32910	0.381177	0.190588	−	0.981670i	$-0.438960\pi$
$599$	9.32910	0.381177	0.190588	+	0.981670i	$0.438960\pi$
$600$	−11.0934	−0.452886
$601$	33.0347	1.34751	0.673757	−	0.738953i	$-0.264679\pi$
$601$	33.0347	1.34751	0.673757	+	0.738953i	$0.264679\pi$
$602$	4.10353	0.167247
$603$	−6.35099	−0.258633
$604$	22.4472	0.913365
$605$	81.1519	3.29929
$606$	−6.63057	−0.269349
$607$	22.2603	0.903518	0.451759	−	0.892140i	$-0.350797\pi$
$607$	22.2603	0.903518	0.451759	+	0.892140i	$0.350797\pi$
$608$	−25.3109	−1.02649
$609$	2.44946	0.0992570
$610$	−31.8600	−1.28997
$611$	0	0
$612$	−9.01111	−0.364253
$613$	−42.8352	−1.73010	−0.865048	−	0.501689i	$-0.832712\pi$
$613$	−42.8352	−1.73010	−0.865048	+	0.501689i	$0.832712\pi$
$614$	−19.8058	−0.799298
$615$	2.86772	0.115637
$616$	−16.1968	−0.652588
$617$	25.7494	1.03663	0.518316	−	0.855189i	$-0.326559\pi$
$617$	25.7494	1.03663	0.518316	+	0.855189i	$0.326559\pi$
$618$	−1.22624	−0.0493265
$619$	−28.8141	−1.15814	−0.579068	−	0.815279i	$-0.696583\pi$
$619$	−28.8141	−1.15814	−0.579068	+	0.815279i	$0.696583\pi$
$620$	12.7448	0.511842
$621$	−8.92243	−0.358045
$622$	−12.2520	−0.491261
$623$	3.56786	0.142943
$624$	0	0
$625$	−28.3334	−1.13333
$626$	3.26794	0.130613
$627$	26.5576	1.06061
$628$	−26.5031	−1.05759
$629$	−15.3936	−0.613784
$630$	−2.35426	−0.0937961
$631$	15.7317	0.626270	0.313135	−	0.949709i	$-0.398621\pi$
$631$	15.7317	0.626270	0.313135	+	0.949709i	$0.398621\pi$
$632$	−45.6400	−1.81546
$633$	8.18369	0.325273
$634$	−18.3447	−0.728563
$635$	2.06303	0.0818690
$636$	−5.64293	−0.223757
$637$	0	0
$638$	11.6753	0.462230
$639$	−7.06708	−0.279569
$640$	−28.3742	−1.12159
$641$	−6.35719	−0.251094	−0.125547	−	0.992088i	$-0.540069\pi$
$641$	−6.35719	−0.251094	−0.125547	+	0.992088i	$0.540069\pi$
$642$	−2.84091	−0.112122
$643$	25.5573	1.00788	0.503940	−	0.863739i	$-0.331883\pi$
$643$	25.5573	1.00788	0.503940	+	0.863739i	$0.331883\pi$
$644$	−12.4741	−0.491548
$645$	−16.0494	−0.631945
$646$	−21.6170	−0.850511
$647$	45.4611	1.78726	0.893630	−	0.448804i	$-0.148150\pi$
$647$	45.4611	1.78726	0.893630	+	0.448804i	$0.148150\pi$
$648$	−2.63638	−0.103567
$649$	10.5871	0.415581
$650$	0	0
$651$	3.00419	0.117743
$652$	−10.1299	−0.396717
$653$	−4.54208	−0.177745	−0.0888727	−	0.996043i	$-0.528326\pi$
$653$	−4.54208	−0.177745	−0.0888727	+	0.996043i	$0.528326\pi$
$654$	−2.37384	−0.0928244
$655$	−43.6174	−1.70427
$656$	0.709446	0.0276992
$657$	1.75626	0.0685182
$658$	−0.165239	−0.00644168
$659$	33.1528	1.29145	0.645724	−	0.763571i	$-0.276556\pi$
$659$	33.1528	1.29145	0.645724	+	0.763571i	$0.276556\pi$
$660$	26.0631	1.01450
$661$	−0.979180	−0.0380857	−0.0190428	−	0.999819i	$-0.506062\pi$
$661$	−0.979180	−0.0380857	−0.0190428	+	0.999819i	$0.506062\pi$
$662$	2.75264	0.106984
$663$	0	0
$664$	13.1792	0.511452
$665$	13.1173	0.508668
$666$	−1.85296	−0.0718006
$667$	21.8551	0.846233
$668$	−15.4829	−0.599051
$669$	−7.63142	−0.295048
$670$	−14.9519	−0.577643
$671$	83.1405	3.20961
$672$	−5.85518	−0.225868
$673$	−23.7677	−0.916176	−0.458088	−	0.888907i	$-0.651466\pi$
$673$	−23.7677	−0.916176	−0.458088	+	0.888907i	$0.651466\pi$
$674$	14.2785	0.549986
$675$	4.20781	0.161959
$676$	0	0
$677$	7.86778	0.302383	0.151192	−	0.988504i	$-0.451689\pi$
$677$	7.86778	0.302383	0.151192	+	0.988504i	$0.451689\pi$
$678$	−9.13820	−0.350951
$679$	1.57496	0.0604416
$680$	−51.5630	−1.97735
$681$	−8.44391	−0.323571
$682$	14.3194	0.548320
$683$	32.5934	1.24715	0.623576	−	0.781763i	$-0.285679\pi$
$683$	32.5934	1.24715	0.623576	+	0.781763i	$0.285679\pi$
$684$	6.04356	0.231081
$685$	30.8944	1.18042
$686$	−0.775848	−0.0296220
$687$	−19.3696	−0.738998
$688$	−3.97047	−0.151373
$689$	0	0
$690$	−21.0057	−0.799675
$691$	−4.05922	−0.154420	−0.0772100	−	0.997015i	$-0.524601\pi$
$691$	−4.05922	−0.154420	−0.0772100	+	0.997015i	$0.524601\pi$
$692$	−6.39822	−0.243224
$693$	6.14359	0.233376
$694$	−16.2923	−0.618446
$695$	37.4829	1.42181
$696$	6.45769	0.244778
$697$	6.09131	0.230725
$698$	−1.75672	−0.0664930
$699$	3.12399	0.118160
$700$	5.88277	0.222348
$701$	−16.8527	−0.636518	−0.318259	−	0.948004i	$-0.603098\pi$
$701$	−16.8527	−0.636518	−0.318259	+	0.948004i	$0.603098\pi$
$702$	0	0
$703$	10.3242	0.389383
$704$	−18.6848	−0.704209
$705$	0.646270	0.0243399
$706$	1.43388	0.0539649
$707$	8.54623	0.321414
$708$	2.40925	0.0905452
$709$	26.0407	0.977980	0.488990	−	0.872289i	$-0.337365\pi$
$709$	26.0407	0.977980	0.488990	+	0.872289i	$0.337365\pi$
$710$	−16.6378	−0.624404
$711$	17.3116	0.649237
$712$	9.40622	0.352513
$713$	26.8047	1.00384
$714$	−5.00068	−0.187146
$715$	0	0
$716$	−4.55259	−0.170138
$717$	22.3164	0.833422
$718$	7.84916	0.292928
$719$	−6.45677	−0.240797	−0.120399	−	0.992726i	$-0.538417\pi$
$719$	−6.45677	−0.240797	−0.120399	+	0.992726i	$0.538417\pi$
$720$	2.27793	0.0848933
$721$	1.58051	0.0588614
$722$	−0.243034	−0.00904478
$723$	−21.9939	−0.817963
$724$	−28.3485	−1.05357
$725$	−10.3069	−0.382787
$726$	20.7490	0.770068
$727$	6.77208	0.251162	0.125581	−	0.992083i	$-0.459920\pi$
$727$	6.77208	0.251162	0.125581	+	0.992083i	$0.459920\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.13469	0.153032
$731$	−34.0905	−1.26088
$732$	18.9198	0.699296
$733$	14.1788	0.523708	0.261854	−	0.965108i	$-0.415666\pi$
$733$	14.1788	0.523708	0.261854	+	0.965108i	$0.415666\pi$
$734$	−12.2644	−0.452689
$735$	3.03444	0.111927
$736$	−52.2424	−1.92568
$737$	39.0179	1.43724
$738$	0.733221	0.0269902
$739$	19.3647	0.712343	0.356172	−	0.934421i	$-0.384082\pi$
$739$	19.3647	0.712343	0.356172	+	0.934421i	$0.384082\pi$
$740$	10.1319	0.372457
$741$	0	0
$742$	−3.13152	−0.114962
$743$	−25.7462	−0.944536	−0.472268	−	0.881455i	$-0.656565\pi$
$743$	−25.7462	−0.944536	−0.472268	+	0.881455i	$0.656565\pi$
$744$	7.92018	0.290368
$745$	−36.3534	−1.33189
$746$	−8.67617	−0.317657
$747$	−4.99898	−0.182903
$748$	55.3605	2.02418
$749$	3.66169	0.133795
$750$	−1.86502	−0.0681008
$751$	−19.8564	−0.724570	−0.362285	−	0.932067i	$-0.618003\pi$
$751$	−19.8564	−0.724570	−0.362285	+	0.932067i	$0.618003\pi$
$752$	0.159881	0.00583026
$753$	1.49983	0.0546570
$754$	0	0
$755$	−48.7209	−1.77313
$756$	1.39806	0.0508469
$757$	−29.8079	−1.08339	−0.541694	−	0.840576i	$-0.682217\pi$
$757$	−29.8079	−1.08339	−0.541694	+	0.840576i	$0.682217\pi$
$758$	21.2728	0.772662
$759$	54.8157	1.98968
$760$	34.5822	1.25443
$761$	10.9585	0.397244	0.198622	−	0.980076i	$-0.436353\pi$
$761$	10.9585	0.397244	0.198622	+	0.980076i	$0.436353\pi$
$762$	0.527479	0.0191085
$763$	3.05967	0.110767
$764$	−33.4456	−1.21002
$765$	19.5583	0.707131
$766$	3.02611	0.109338
$767$	0	0
$768$	−13.3374	−0.481273
$769$	−8.10274	−0.292192	−0.146096	−	0.989270i	$-0.546671\pi$
$769$	−8.10274	−0.292192	−0.146096	+	0.989270i	$0.546671\pi$
$770$	14.4636	0.521232
$771$	−8.93391	−0.321747
$772$	11.7917	0.424394
$773$	20.5433	0.738890	0.369445	−	0.929253i	$-0.379548\pi$
$773$	20.5433	0.738890	0.369445	+	0.929253i	$0.379548\pi$
$774$	−4.10353	−0.147498
$775$	−12.6411	−0.454081
$776$	4.15220	0.149055
$777$	2.38830	0.0856797
$778$	−15.9096	−0.570385
$779$	−4.08531	−0.146371
$780$	0	0
$781$	43.4172	1.55359
$782$	−44.6182	−1.59554
$783$	−2.44946	−0.0875365
$784$	0.750691	0.0268104
$785$	57.5241	2.05312
$786$	−11.1521	−0.397783
$787$	−34.6346	−1.23459	−0.617295	−	0.786732i	$-0.711771\pi$
$787$	−34.6346	−1.23459	−0.617295	+	0.786732i	$0.711771\pi$
$788$	−33.5193	−1.19408
$789$	−10.4624	−0.372470
$790$	40.7561	1.45004
$791$	11.7783	0.418790
$792$	16.1968	0.575529
$793$	0	0
$794$	−24.0476	−0.853419
$795$	12.2478	0.434384
$796$	14.5670	0.516312
$797$	−39.0702	−1.38394	−0.691969	−	0.721927i	$-0.743257\pi$
$797$	−39.0702	−1.38394	−0.691969	+	0.721927i	$0.743257\pi$
$798$	3.35385	0.118725
$799$	1.37274	0.0485641
$800$	24.6375	0.871067
$801$	−3.56786	−0.126064
$802$	12.0932	0.427027
$803$	−10.7897	−0.380761
$804$	8.87907	0.313141
$805$	27.0745	0.954252
$806$	0	0
$807$	2.91690	0.102680
$808$	22.5311	0.792641
$809$	−35.6907	−1.25482	−0.627410	−	0.778689i	$-0.715885\pi$
$809$	−35.6907	−1.25482	−0.627410	+	0.778689i	$0.715885\pi$
$810$	2.35426	0.0827204
$811$	34.8691	1.22442	0.612209	−	0.790696i	$-0.290281\pi$
$811$	34.8691	1.22442	0.612209	+	0.790696i	$0.290281\pi$
$812$	−3.42449	−0.120176
$813$	22.6664	0.794947
$814$	11.3838	0.399002
$815$	21.9865	0.770154
$816$	4.83853	0.169383
$817$	22.8638	0.799902
$818$	−14.9049	−0.521136
$819$	0	0
$820$	−4.00924	−0.140009
$821$	41.6711	1.45433	0.727166	−	0.686461i	$-0.240837\pi$
$821$	41.6711	1.45433	0.727166	+	0.686461i	$0.240837\pi$
$822$	7.89912	0.275513
$823$	15.2353	0.531070	0.265535	−	0.964101i	$-0.414451\pi$
$823$	15.2353	0.531070	0.265535	+	0.964101i	$0.414451\pi$
$824$	4.16683	0.145158
$825$	−25.8511	−0.900018
$826$	1.33700	0.0465203
$827$	−31.0121	−1.07839	−0.539197	−	0.842179i	$-0.681272\pi$
$827$	−31.0121	−1.07839	−0.539197	+	0.842179i	$0.681272\pi$
$828$	12.4741	0.433504
$829$	−14.2252	−0.494063	−0.247031	−	0.969007i	$-0.579455\pi$
$829$	−14.2252	−0.494063	−0.247031	+	0.969007i	$0.579455\pi$
$830$	−11.7689	−0.408505
$831$	0.227605	0.00789553
$832$	0	0
$833$	6.44544	0.223321
$834$	9.58367	0.331855
$835$	33.6050	1.16295
$836$	−37.1291	−1.28414
$837$	−3.00419	−0.103840
$838$	16.1764	0.558805
$839$	−13.5745	−0.468643	−0.234321	−	0.972159i	$-0.575287\pi$
$839$	−13.5745	−0.468643	−0.234321	+	0.972159i	$0.575287\pi$
$840$	7.99993	0.276024
$841$	−23.0002	−0.793109
$842$	2.56971	0.0885579
$843$	−11.1627	−0.384462
$844$	−11.4413	−0.393825
$845$	0	0
$846$	0.165239	0.00568103
$847$	−26.7436	−0.918922
$848$	3.02998	0.104050
$849$	−20.0679	−0.688728
$850$	21.0419	0.721732
$851$	21.3094	0.730477
$852$	9.88020	0.338490
$853$	33.8621	1.15942	0.579708	−	0.814824i	$-0.303167\pi$
$853$	33.8621	1.15942	0.579708	+	0.814824i	$0.303167\pi$
$854$	10.4995	0.359285
$855$	−13.1173	−0.448603
$856$	9.65360	0.329953
$857$	37.5517	1.28274	0.641370	−	0.767232i	$-0.278366\pi$
$857$	37.5517	1.28274	0.641370	+	0.767232i	$0.278366\pi$
$858$	0	0
$859$	−23.9785	−0.818134	−0.409067	−	0.912504i	$-0.634146\pi$
$859$	−23.9785	−0.818134	−0.409067	+	0.912504i	$0.634146\pi$
$860$	22.4380	0.765131
$861$	−0.945057	−0.0322075
$862$	22.0165	0.749884
$863$	45.2748	1.54117	0.770585	−	0.637337i	$-0.219964\pi$
$863$	45.2748	1.54117	0.770585	+	0.637337i	$0.219964\pi$
$864$	5.85518	0.199197
$865$	13.8871	0.472176
$866$	16.4444	0.558804
$867$	24.5437	0.833548
$868$	−4.20004	−0.142559
$869$	−106.356	−3.60786
$870$	−5.76667	−0.195508
$871$	0	0
$872$	8.06645	0.273164
$873$	−1.57496	−0.0533045
$874$	29.9245	1.01221
$875$	2.40384	0.0812647
$876$	−2.45535	−0.0829587
$877$	−16.5695	−0.559512	−0.279756	−	0.960071i	$-0.590253\pi$
$877$	−16.5695	−0.559512	−0.279756	+	0.960071i	$0.590253\pi$
$878$	9.75486	0.329211
$879$	3.68811	0.124397
$880$	−13.9946	−0.471759
$881$	4.11912	0.138777	0.0693883	−	0.997590i	$-0.477895\pi$
$881$	4.11912	0.138777	0.0693883	+	0.997590i	$0.477895\pi$
$882$	0.775848	0.0261242
$883$	−57.7416	−1.94316	−0.971580	−	0.236710i	$-0.923931\pi$
$883$	−57.7416	−1.94316	−0.971580	+	0.236710i	$0.923931\pi$
$884$	0	0
$885$	−5.22919	−0.175777
$886$	8.31941	0.279496
$887$	50.8905	1.70874	0.854368	−	0.519669i	$-0.173945\pi$
$887$	50.8905	1.70874	0.854368	+	0.519669i	$0.173945\pi$
$888$	6.29645	0.211295
$889$	−0.679874	−0.0228022
$890$	−8.39967	−0.281558
$891$	−6.14359	−0.205818
$892$	10.6692	0.357231
$893$	−0.920667	−0.0308090
$894$	−9.29487	−0.310867
$895$	9.88122	0.330293
$896$	9.35073	0.312386
$897$	0	0
$898$	−8.67811	−0.289592
$899$	7.35863	0.245424
$900$	−5.88277	−0.196092
$901$	26.0154	0.866700
$902$	−4.50460	−0.149987
$903$	5.28909	0.176010
$904$	31.0522	1.03278
$905$	61.5295	2.04531
$906$	−12.4570	−0.413856
$907$	−57.3525	−1.90436	−0.952179	−	0.305539i	$-0.901163\pi$
$907$	−57.3525	−1.90436	−0.952179	+	0.305539i	$0.901163\pi$
$908$	11.8051	0.391766
$909$	−8.54623	−0.283460
$910$	0	0
$911$	35.1349	1.16407	0.582036	−	0.813163i	$-0.302256\pi$
$911$	35.1349	1.16407	0.582036	+	0.813163i	$0.302256\pi$
$912$	−3.24510	−0.107456
$913$	30.7117	1.01641
$914$	−1.94083	−0.0641970
$915$	−41.0648	−1.35756
$916$	27.0799	0.894746
$917$	14.3741	0.474675
$918$	5.00068	0.165047
$919$	17.0967	0.563968	0.281984	−	0.959419i	$-0.409007\pi$
$919$	17.0967	0.563968	0.281984	+	0.959419i	$0.409007\pi$
$920$	71.3787	2.35329
$921$	−25.5280	−0.841175
$922$	−6.77572	−0.223147
$923$	0	0
$924$	−8.58910	−0.282561
$925$	−10.0495	−0.330426
$926$	9.37534	0.308093
$927$	−1.58051	−0.0519108
$928$	−14.3420	−0.470799
$929$	−29.6472	−0.972692	−0.486346	−	0.873766i	$-0.661670\pi$
$929$	−29.6472	−0.972692	−0.486346	+	0.873766i	$0.661670\pi$
$930$	−7.07265	−0.231921
$931$	−4.32282	−0.141675
$932$	−4.36753	−0.143063
$933$	−15.7918	−0.516999
$934$	2.67466	0.0875177
$935$	−120.158	−3.92959
$936$	0	0
$937$	−6.82549	−0.222979	−0.111489	−	0.993766i	$-0.535562\pi$
$937$	−6.82549	−0.222979	−0.111489	+	0.993766i	$0.535562\pi$
$938$	4.92741	0.160886
$939$	4.21208	0.137456
$940$	−0.903524	−0.0294697
$941$	−44.6666	−1.45609	−0.728045	−	0.685529i	$-0.759571\pi$
$941$	−44.6666	−1.45609	−0.728045	+	0.685529i	$0.759571\pi$
$942$	14.7078	0.479207
$943$	−8.43220	−0.274590
$944$	−1.29365	−0.0421048
$945$	−3.03444	−0.0987103
$946$	25.2104	0.819660
$947$	55.1630	1.79256	0.896278	−	0.443493i	$-0.146261\pi$
$947$	55.1630	1.79256	0.896278	+	0.443493i	$0.146261\pi$
$948$	−24.2027	−0.786067
$949$	0	0
$950$	−14.1124	−0.457866
$951$	−23.6448	−0.766734
$952$	16.9926	0.550734
$953$	−29.3026	−0.949204	−0.474602	−	0.880201i	$-0.657408\pi$
$953$	−29.3026	−0.949204	−0.474602	+	0.880201i	$0.657408\pi$
$954$	3.13152	0.101387
$955$	72.5925	2.34904
$956$	−31.1997	−1.00907
$957$	15.0484	0.486447
$958$	9.81479	0.317101
$959$	−10.1813	−0.328770
$960$	9.22878	0.297857
$961$	−21.9748	−0.708866
$962$	0	0
$963$	−3.66169	−0.117996
$964$	30.7488	0.990353
$965$	−25.5936	−0.823886
$966$	6.92245	0.222726
$967$	−7.07095	−0.227387	−0.113693	−	0.993516i	$-0.536268\pi$
$967$	−7.07095	−0.227387	−0.113693	+	0.993516i	$0.536268\pi$
$968$	−70.5064	−2.26616
$969$	−27.8625	−0.895071
$970$	−3.70788	−0.119053
$971$	7.29702	0.234172	0.117086	−	0.993122i	$-0.462645\pi$
$971$	7.29702	0.234172	0.117086	+	0.993122i	$0.462645\pi$
$972$	−1.39806	−0.0448428
$973$	−12.3525	−0.396003
$974$	−5.98644	−0.191818
$975$	0	0
$976$	−10.1590	−0.325183
$977$	−17.6491	−0.564646	−0.282323	−	0.959319i	$-0.591105\pi$
$977$	−17.6491	−0.564646	−0.282323	+	0.959319i	$0.591105\pi$
$978$	5.62154	0.179757
$979$	21.9194	0.700548
$980$	−4.24233	−0.135516
$981$	−3.05967	−0.0976877
$982$	3.61245	0.115278
$983$	−36.1510	−1.15304	−0.576520	−	0.817083i	$-0.695590\pi$
$983$	−36.1510	−1.15304	−0.576520	+	0.817083i	$0.695590\pi$
$984$	−2.49153	−0.0794270
$985$	72.7525	2.31809
$986$	−12.2490	−0.390086
$987$	−0.212978	−0.00677918
$988$	0	0
$989$	47.1915	1.50060
$990$	−14.4636	−0.459684
$991$	−2.19876	−0.0698459	−0.0349230	−	0.999390i	$-0.511119\pi$
$991$	−2.19876	−0.0698459	−0.0349230	+	0.999390i	$0.511119\pi$
$992$	−17.5901	−0.558485
$993$	3.54791	0.112590
$994$	5.48298	0.173910
$995$	−31.6170	−1.00233
$996$	6.98887	0.221451
$997$	−36.4487	−1.15434	−0.577171	−	0.816623i	$-0.695843\pi$
$997$	−36.4487	−1.15434	−0.577171	+	0.816623i	$0.695843\pi$
$998$	−25.1568	−0.796325
$999$	−2.38830	−0.0755624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bb.1.6		8
13.6	odd	12		273.2.bd.a.127.3	yes	16
13.11	odd	12		273.2.bd.a.43.3	✓	16
13.12	even	2		3549.2.a.bd.1.3		8
39.11	even	12		819.2.ct.b.316.6		16
39.32	even	12		819.2.ct.b.127.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.3	✓	16	13.11	odd	12
273.2.bd.a.127.3	yes	16	13.6	odd	12
819.2.ct.b.127.6		16	39.32	even	12
819.2.ct.b.316.6		16	39.11	even	12
3549.2.a.bb.1.6		8	1.1	even	1	trivial
3549.2.a.bd.1.3		8	13.12	even	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+0.775848 q^{2} +1.00000 q^{3} -1.39806 q^{4} +3.03444 q^{5} +0.775848 q^{6} -1.00000 q^{7} -2.63638 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.775848 q^{2} +1.00000 q^{3} -1.39806 q^{4} +3.03444 q^{5} +0.775848 q^{6} -1.00000 q^{7} -2.63638 q^{8} +1.00000 q^{9} +2.35426 q^{10} -6.14359 q^{11} -1.39806 q^{12} -0.775848 q^{14} +3.03444 q^{15} +0.750691 q^{16} +6.44544 q^{17} +0.775848 q^{18} -4.32282 q^{19} -4.24233 q^{20} -1.00000 q^{21} -4.76649 q^{22} -8.92243 q^{23} -2.63638 q^{24} +4.20781 q^{25} +1.00000 q^{27} +1.39806 q^{28} -2.44946 q^{29} +2.35426 q^{30} -3.00419 q^{31} +5.85518 q^{32} -6.14359 q^{33} +5.00068 q^{34} -3.03444 q^{35} -1.39806 q^{36} -2.38830 q^{37} -3.35385 q^{38} -7.99993 q^{40} +0.945057 q^{41} -0.775848 q^{42} -5.28909 q^{43} +8.58910 q^{44} +3.03444 q^{45} -6.92245 q^{46} +0.212978 q^{47} +0.750691 q^{48} +1.00000 q^{49} +3.26462 q^{50} +6.44544 q^{51} +4.03626 q^{53} +0.775848 q^{54} -18.6423 q^{55} +2.63638 q^{56} -4.32282 q^{57} -1.90041 q^{58} -1.72328 q^{59} -4.24233 q^{60} -13.5329 q^{61} -2.33080 q^{62} -1.00000 q^{63} +3.04135 q^{64} -4.76649 q^{66} -6.35099 q^{67} -9.01111 q^{68} -8.92243 q^{69} -2.35426 q^{70} -7.06708 q^{71} -2.63638 q^{72} +1.75626 q^{73} -1.85296 q^{74} +4.20781 q^{75} +6.04356 q^{76} +6.14359 q^{77} +17.3116 q^{79} +2.27793 q^{80} +1.00000 q^{81} +0.733221 q^{82} -4.99898 q^{83} +1.39806 q^{84} +19.5583 q^{85} -4.10353 q^{86} -2.44946 q^{87} +16.1968 q^{88} -3.56786 q^{89} +2.35426 q^{90} +12.4741 q^{92} -3.00419 q^{93} +0.165239 q^{94} -13.1173 q^{95} +5.85518 q^{96} -1.57496 q^{97} +0.775848 q^{98} -6.14359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * q^99

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