LMFDB - Embedded newform 7935.2.a.bm.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.0774485$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0774485 q^{2} +1.00000 q^{3} -1.99400 q^{4} +1.00000 q^{5} +0.0774485 q^{6} -3.48186 q^{7} -0.309330 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.0774485 q^{2} +1.00000 q^{3} -1.99400 q^{4} +1.00000 q^{5} +0.0774485 q^{6} -3.48186 q^{7} -0.309330 q^{8} +1.00000 q^{9} +0.0774485 q^{10} -0.122543 q^{11} -1.99400 q^{12} -0.150161 q^{13} -0.269665 q^{14} +1.00000 q^{15} +3.96405 q^{16} -2.68990 q^{17} +0.0774485 q^{18} +3.20531 q^{19} -1.99400 q^{20} -3.48186 q^{21} -0.00949077 q^{22} -0.309330 q^{24} +1.00000 q^{25} -0.0116298 q^{26} +1.00000 q^{27} +6.94284 q^{28} -0.318838 q^{29} +0.0774485 q^{30} +4.15015 q^{31} +0.925669 q^{32} -0.122543 q^{33} -0.208329 q^{34} -3.48186 q^{35} -1.99400 q^{36} +2.32524 q^{37} +0.248246 q^{38} -0.150161 q^{39} -0.309330 q^{40} +0.522379 q^{41} -0.269665 q^{42} -3.64461 q^{43} +0.244351 q^{44} +1.00000 q^{45} +2.89806 q^{47} +3.96405 q^{48} +5.12336 q^{49} +0.0774485 q^{50} -2.68990 q^{51} +0.299422 q^{52} -13.5930 q^{53} +0.0774485 q^{54} -0.122543 q^{55} +1.07704 q^{56} +3.20531 q^{57} -0.0246935 q^{58} -11.7230 q^{59} -1.99400 q^{60} +1.19839 q^{61} +0.321423 q^{62} -3.48186 q^{63} -7.85640 q^{64} -0.150161 q^{65} -0.00949077 q^{66} +14.3576 q^{67} +5.36366 q^{68} -0.269665 q^{70} +10.7769 q^{71} -0.309330 q^{72} +7.64963 q^{73} +0.180086 q^{74} +1.00000 q^{75} -6.39139 q^{76} +0.426677 q^{77} -0.0116298 q^{78} -13.8162 q^{79} +3.96405 q^{80} +1.00000 q^{81} +0.0404575 q^{82} -0.151610 q^{83} +6.94284 q^{84} -2.68990 q^{85} -0.282269 q^{86} -0.318838 q^{87} +0.0379061 q^{88} +3.87082 q^{89} +0.0774485 q^{90} +0.522841 q^{91} +4.15015 q^{93} +0.224451 q^{94} +3.20531 q^{95} +0.925669 q^{96} +15.7821 q^{97} +0.396797 q^{98} -0.122543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 16 q^{14} + 12 q^{15} - 28 q^{17} - 16 q^{19} + 8 q^{20} - 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} - 8 q^{28} - 16 q^{29} + 20 q^{32} - 24 q^{33} - 16 q^{34} - 4 q^{35} + 8 q^{36} - 20 q^{37} - 16 q^{38} - 8 q^{39} - 4 q^{41} - 16 q^{42} + 12 q^{43} - 16 q^{44} + 12 q^{45} + 4 q^{47} + 24 q^{49} - 28 q^{51} - 36 q^{52} - 28 q^{53} - 24 q^{55} - 56 q^{56} - 16 q^{57} + 20 q^{59} + 8 q^{60} - 32 q^{61} + 12 q^{62} - 4 q^{63} - 4 q^{64} - 8 q^{65} + 4 q^{67} - 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} + 36 q^{74} + 12 q^{75} - 8 q^{76} - 28 q^{77} - 36 q^{78} - 40 q^{79} + 12 q^{81} - 28 q^{82} - 100 q^{83} - 8 q^{84} - 28 q^{85} + 20 q^{86} - 16 q^{87} - 80 q^{89} + 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} + 8 q^{97} + 28 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 16 * q^14 + 12 * q^15 - 28 * q^17 - 16 * q^19 + 8 * q^20 - 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 - 8 * q^28 - 16 * q^29 + 20 * q^32 - 24 * q^33 - 16 * q^34 - 4 * q^35 + 8 * q^36 - 20 * q^37 - 16 * q^38 - 8 * q^39 - 4 * q^41 - 16 * q^42 + 12 * q^43 - 16 * q^44 + 12 * q^45 + 4 * q^47 + 24 * q^49 - 28 * q^51 - 36 * q^52 - 28 * q^53 - 24 * q^55 - 56 * q^56 - 16 * q^57 + 20 * q^59 + 8 * q^60 - 32 * q^61 + 12 * q^62 - 4 * q^63 - 4 * q^64 - 8 * q^65 + 4 * q^67 - 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 + 36 * q^74 + 12 * q^75 - 8 * q^76 - 28 * q^77 - 36 * q^78 - 40 * q^79 + 12 * q^81 - 28 * q^82 - 100 * q^83 - 8 * q^84 - 28 * q^85 + 20 * q^86 - 16 * q^87 - 80 * q^89 + 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 + 8 * q^97 + 28 * q^98 - 24 * 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 $

$2$	0.0774485	0.0547644	0.0273822	−	0.999625i	$-0.491283\pi$
$2$	0.0774485	0.0547644	0.0273822	+	0.999625i	$0.491283\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.99400	−0.997001
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0774485	0.0316182
$7$	−3.48186	−1.31602	−0.658010	−	0.753009i	$-0.728602\pi$
$7$	−3.48186	−1.31602	−0.658010	+	0.753009i	$0.728602\pi$
$8$	−0.309330	−0.109365
$9$	1.00000	0.333333
$10$	0.0774485	0.0244914
$11$	−0.122543	−0.0369481	−0.0184740	−	0.999829i	$-0.505881\pi$
$11$	−0.122543	−0.0369481	−0.0184740	+	0.999829i	$0.505881\pi$
$12$	−1.99400	−0.575619
$13$	−0.150161	−0.0416472	−0.0208236	−	0.999783i	$-0.506629\pi$
$13$	−0.150161	−0.0416472	−0.0208236	+	0.999783i	$0.506629\pi$
$14$	−0.269665	−0.0720710
$15$	1.00000	0.258199
$16$	3.96405	0.991012
$17$	−2.68990	−0.652396	−0.326198	−	0.945302i	$-0.605768\pi$
$17$	−2.68990	−0.652396	−0.326198	+	0.945302i	$0.605768\pi$
$18$	0.0774485	0.0182548
$19$	3.20531	0.735348	0.367674	−	0.929955i	$-0.380154\pi$
$19$	3.20531	0.735348	0.367674	+	0.929955i	$0.380154\pi$
$20$	−1.99400	−0.445872
$21$	−3.48186	−0.759804
$22$	−0.00949077	−0.00202344
$23$	0	0
$23$	0	0
$24$	−0.309330	−0.0631416
$25$	1.00000	0.200000
$26$	−0.0116298	−0.00228079
$27$	1.00000	0.192450
$28$	6.94284	1.31207
$29$	−0.318838	−0.0592067	−0.0296033	−	0.999562i	$-0.509424\pi$
$29$	−0.318838	−0.0592067	−0.0296033	+	0.999562i	$0.509424\pi$
$30$	0.0774485	0.0141401
$31$	4.15015	0.745390	0.372695	−	0.927954i	$-0.378434\pi$
$31$	4.15015	0.745390	0.372695	+	0.927954i	$0.378434\pi$
$32$	0.925669	0.163637
$33$	−0.122543	−0.0213320
$34$	−0.208329	−0.0357280
$35$	−3.48186	−0.588542
$36$	−1.99400	−0.332334
$37$	2.32524	0.382266	0.191133	−	0.981564i	$-0.438784\pi$
$37$	2.32524	0.382266	0.191133	+	0.981564i	$0.438784\pi$
$38$	0.248246	0.0402709
$39$	−0.150161	−0.0240450
$40$	−0.309330	−0.0489093
$41$	0.522379	0.0815819	0.0407910	−	0.999168i	$-0.487012\pi$
$41$	0.522379	0.0815819	0.0407910	+	0.999168i	$0.487012\pi$
$42$	−0.269665	−0.0416102
$43$	−3.64461	−0.555797	−0.277899	−	0.960610i	$-0.589638\pi$
$43$	−3.64461	−0.555797	−0.277899	+	0.960610i	$0.589638\pi$
$44$	0.244351	0.0368373
$45$	1.00000	0.149071
$46$	0	0
$47$	2.89806	0.422726	0.211363	−	0.977408i	$-0.432210\pi$
$47$	2.89806	0.422726	0.211363	+	0.977408i	$0.432210\pi$
$48$	3.96405	0.572161
$49$	5.12336	0.731908
$50$	0.0774485	0.0109529
$51$	−2.68990	−0.376661
$52$	0.299422	0.0415223
$53$	−13.5930	−1.86714	−0.933569	−	0.358397i	$-0.883323\pi$
$53$	−13.5930	−1.86714	−0.933569	+	0.358397i	$0.883323\pi$
$54$	0.0774485	0.0105394
$55$	−0.122543	−0.0165237
$56$	1.07704	0.143926
$57$	3.20531	0.424553
$58$	−0.0246935	−0.00324242
$59$	−11.7230	−1.52620	−0.763102	−	0.646278i	$-0.776325\pi$
$59$	−11.7230	−1.52620	−0.763102	+	0.646278i	$0.776325\pi$
$60$	−1.99400	−0.257425
$61$	1.19839	0.153439	0.0767194	−	0.997053i	$-0.475555\pi$
$61$	1.19839	0.153439	0.0767194	+	0.997053i	$0.475555\pi$
$62$	0.321423	0.0408208
$63$	−3.48186	−0.438673
$64$	−7.85640	−0.982050
$65$	−0.150161	−0.0186252
$66$	−0.00949077	−0.00116823
$67$	14.3576	1.75406	0.877028	−	0.480440i	$-0.159523\pi$
$67$	14.3576	1.75406	0.877028	+	0.480440i	$0.159523\pi$
$68$	5.36366	0.650439
$69$	0	0
$70$	−0.269665	−0.0322311
$71$	10.7769	1.27899	0.639494	−	0.768796i	$-0.279144\pi$
$71$	10.7769	1.27899	0.639494	+	0.768796i	$0.279144\pi$
$72$	−0.309330	−0.0364548
$73$	7.64963	0.895321	0.447661	−	0.894204i	$-0.352257\pi$
$73$	7.64963	0.895321	0.447661	+	0.894204i	$0.352257\pi$
$74$	0.180086	0.0209346
$75$	1.00000	0.115470
$76$	−6.39139	−0.733142
$77$	0.426677	0.0486244
$78$	−0.0116298	−0.00131681
$79$	−13.8162	−1.55445	−0.777224	−	0.629224i	$-0.783373\pi$
$79$	−13.8162	−1.55445	−0.777224	+	0.629224i	$0.783373\pi$
$80$	3.96405	0.443194
$81$	1.00000	0.111111
$82$	0.0404575	0.00446779
$83$	−0.151610	−0.0166414	−0.00832070	−	0.999965i	$-0.502649\pi$
$83$	−0.151610	−0.0166414	−0.00832070	+	0.999965i	$0.502649\pi$
$84$	6.94284	0.757526
$85$	−2.68990	−0.291760
$86$	−0.282269	−0.0304379
$87$	−0.318838	−0.0341830
$88$	0.0379061	0.00404081
$89$	3.87082	0.410306	0.205153	−	0.978730i	$-0.434231\pi$
$89$	3.87082	0.410306	0.205153	+	0.978730i	$0.434231\pi$
$90$	0.0774485	0.00816379
$91$	0.522841	0.0548086
$92$	0	0
$93$	4.15015	0.430351
$94$	0.224451	0.0231503
$95$	3.20531	0.328857
$96$	0.925669	0.0944757
$97$	15.7821	1.60242	0.801212	−	0.598380i	$-0.204189\pi$
$97$	15.7821	1.60242	0.801212	+	0.598380i	$0.204189\pi$
$98$	0.396797	0.0400825
$99$	−0.122543	−0.0123160
$100$	−1.99400	−0.199400
$101$	7.08225	0.704711	0.352355	−	0.935866i	$-0.385381\pi$
$101$	7.08225	0.704711	0.352355	+	0.935866i	$0.385381\pi$
$102$	−0.208329	−0.0206276
$103$	−11.7909	−1.16179	−0.580895	−	0.813979i	$-0.697297\pi$
$103$	−11.7909	−1.16179	−0.580895	+	0.813979i	$0.697297\pi$
$104$	0.0464493	0.00455473
$105$	−3.48186	−0.339795
$106$	−1.05276	−0.102253
$107$	11.3579	1.09801	0.549006	−	0.835819i	$-0.315007\pi$
$107$	11.3579	1.09801	0.549006	+	0.835819i	$0.315007\pi$
$108$	−1.99400	−0.191873
$109$	−10.2209	−0.978985	−0.489493	−	0.872007i	$-0.662818\pi$
$109$	−10.2209	−0.978985	−0.489493	+	0.872007i	$0.662818\pi$
$110$	−0.00949077	−0.000904909 0
$111$	2.32524	0.220702
$112$	−13.8023	−1.30419
$113$	−16.0018	−1.50533	−0.752663	−	0.658406i	$-0.771231\pi$
$113$	−16.0018	−1.50533	−0.752663	+	0.658406i	$0.771231\pi$
$114$	0.248246	0.0232504
$115$	0	0
$116$	0.635763	0.0590291
$117$	−0.150161	−0.0138824
$118$	−0.907929	−0.0835817
$119$	9.36584	0.858565
$120$	−0.309330	−0.0282378
$121$	−10.9850	−0.998635
$122$	0.0928139	0.00840298
$123$	0.522379	0.0471014
$124$	−8.27541	−0.743154
$125$	1.00000	0.0894427
$126$	−0.269665	−0.0240237
$127$	−7.35560	−0.652704	−0.326352	−	0.945248i	$-0.605819\pi$
$127$	−7.35560	−0.652704	−0.326352	+	0.945248i	$0.605819\pi$
$128$	−2.45980	−0.217418
$129$	−3.64461	−0.320890
$130$	−0.0116298	−0.00102000
$131$	−20.5745	−1.79760	−0.898799	−	0.438361i	$-0.855559\pi$
$131$	−20.5745	−1.79760	−0.898799	+	0.438361i	$0.855559\pi$
$132$	0.244351	0.0212680
$133$	−11.1604	−0.967732
$134$	1.11197	0.0960598
$135$	1.00000	0.0860663
$136$	0.832064	0.0713489
$137$	0.790270	0.0675173	0.0337587	−	0.999430i	$-0.489252\pi$
$137$	0.790270	0.0675173	0.0337587	+	0.999430i	$0.489252\pi$
$138$	0	0
$139$	−6.81148	−0.577742	−0.288871	−	0.957368i	$-0.593280\pi$
$139$	−6.81148	−0.577742	−0.288871	+	0.957368i	$0.593280\pi$
$140$	6.94284	0.586777
$141$	2.89806	0.244061
$142$	0.834658	0.0700430
$143$	0.0184012	0.00153878
$144$	3.96405	0.330337
$145$	−0.318838	−0.0264780
$146$	0.592452	0.0490317
$147$	5.12336	0.422567
$148$	−4.63652	−0.381120
$149$	−18.0464	−1.47842	−0.739209	−	0.673476i	$-0.764800\pi$
$149$	−18.0464	−1.47842	−0.739209	+	0.673476i	$0.764800\pi$
$150$	0.0774485	0.00632365
$151$	−2.88270	−0.234591	−0.117296	−	0.993097i	$-0.537422\pi$
$151$	−2.88270	−0.234591	−0.117296	+	0.993097i	$0.537422\pi$
$152$	−0.991496	−0.0804210
$153$	−2.68990	−0.217465
$154$	0.0330455	0.00266289
$155$	4.15015	0.333348
$156$	0.299422	0.0239729
$157$	2.58166	0.206039	0.103019	−	0.994679i	$-0.467150\pi$
$157$	2.58166	0.206039	0.103019	+	0.994679i	$0.467150\pi$
$158$	−1.07005	−0.0851284
$159$	−13.5930	−1.07799
$160$	0.925669	0.0731806
$161$	0	0
$162$	0.0774485	0.00608493
$163$	−2.37638	−0.186132	−0.0930662	−	0.995660i	$-0.529667\pi$
$163$	−2.37638	−0.186132	−0.0930662	+	0.995660i	$0.529667\pi$
$164$	−1.04163	−0.0813373
$165$	−0.122543	−0.00953995
$166$	−0.0117420	−0.000911356 0
$167$	11.1767	0.864882	0.432441	−	0.901662i	$-0.357652\pi$
$167$	11.1767	0.864882	0.432441	+	0.901662i	$0.357652\pi$
$168$	1.07704	0.0830957
$169$	−12.9775	−0.998266
$170$	−0.208329	−0.0159781
$171$	3.20531	0.245116
$172$	7.26735	0.554130
$173$	16.4682	1.25206	0.626028	−	0.779800i	$-0.284679\pi$
$173$	16.4682	1.25206	0.626028	+	0.779800i	$0.284679\pi$
$174$	−0.0246935	−0.00187201
$175$	−3.48186	−0.263204
$176$	−0.485766	−0.0366160
$177$	−11.7230	−0.881155
$178$	0.299789	0.0224701
$179$	−6.83739	−0.511051	−0.255525	−	0.966802i	$-0.582248\pi$
$179$	−6.83739	−0.511051	−0.255525	+	0.966802i	$0.582248\pi$
$180$	−1.99400	−0.148624
$181$	−10.3514	−0.769416	−0.384708	−	0.923038i	$-0.625698\pi$
$181$	−10.3514	−0.769416	−0.384708	+	0.923038i	$0.625698\pi$
$182$	0.0404932	0.00300156
$183$	1.19839	0.0885879
$184$	0	0
$185$	2.32524	0.170955
$186$	0.321423	0.0235679
$187$	0.329628	0.0241048
$188$	−5.77874	−0.421458
$189$	−3.48186	−0.253268
$190$	0.248246	0.0180097
$191$	−13.8067	−0.999021	−0.499510	−	0.866308i	$-0.666487\pi$
$191$	−13.8067	−0.999021	−0.499510	+	0.866308i	$0.666487\pi$
$192$	−7.85640	−0.566987
$193$	−15.6957	−1.12980	−0.564900	−	0.825159i	$-0.691085\pi$
$193$	−15.6957	−1.12980	−0.564900	+	0.825159i	$0.691085\pi$
$194$	1.22230	0.0877558
$195$	−0.150161	−0.0107533
$196$	−10.2160	−0.729713
$197$	11.3169	0.806299	0.403149	−	0.915134i	$-0.367916\pi$
$197$	11.3169	0.806299	0.403149	+	0.915134i	$0.367916\pi$
$198$	−0.00949077	−0.000674479 0
$199$	−1.55183	−0.110006	−0.0550032	−	0.998486i	$-0.517517\pi$
$199$	−1.55183	−0.110006	−0.0550032	+	0.998486i	$0.517517\pi$
$200$	−0.309330	−0.0218729
$201$	14.3576	1.01270
$202$	0.548510	0.0385930
$203$	1.11015	0.0779172
$204$	5.36366	0.375531
$205$	0.522379	0.0364846
$206$	−0.913186	−0.0636247
$207$	0	0
$208$	−0.595246	−0.0412729
$209$	−0.392787	−0.0271697
$210$	−0.269665	−0.0186087
$211$	26.1808	1.80236	0.901179	−	0.433447i	$-0.142703\pi$
$211$	26.1808	1.80236	0.901179	+	0.433447i	$0.142703\pi$
$212$	27.1044	1.86154
$213$	10.7769	0.738424
$214$	0.879654	0.0601319
$215$	−3.64461	−0.248560
$216$	−0.309330	−0.0210472
$217$	−14.4503	−0.980948
$218$	−0.791594	−0.0536135
$219$	7.64963	0.516914
$220$	0.244351	0.0164741
$221$	0.403918	0.0271705
$222$	0.180086	0.0120866
$223$	12.0509	0.806987	0.403493	−	0.914983i	$-0.367796\pi$
$223$	12.0509	0.806987	0.403493	+	0.914983i	$0.367796\pi$
$224$	−3.22305	−0.215349
$225$	1.00000	0.0666667
$226$	−1.23932	−0.0824383
$227$	−20.1940	−1.34032	−0.670160	−	0.742216i	$-0.733775\pi$
$227$	−20.1940	−1.34032	−0.670160	+	0.742216i	$0.733775\pi$
$228$	−6.39139	−0.423280
$229$	−18.2714	−1.20741	−0.603705	−	0.797208i	$-0.706310\pi$
$229$	−18.2714	−1.20741	−0.603705	+	0.797208i	$0.706310\pi$
$230$	0	0
$231$	0.426677	0.0280733
$232$	0.0986260	0.00647511
$233$	−7.21642	−0.472763	−0.236382	−	0.971660i	$-0.575962\pi$
$233$	−7.21642	−0.472763	−0.236382	+	0.971660i	$0.575962\pi$
$234$	−0.0116298	−0.000760262 0
$235$	2.89806	0.189049
$236$	23.3757	1.52163
$237$	−13.8162	−0.897461
$238$	0.725371	0.0470188
$239$	−22.2588	−1.43980	−0.719901	−	0.694077i	$-0.755813\pi$
$239$	−22.2588	−1.43980	−0.719901	+	0.694077i	$0.755813\pi$
$240$	3.96405	0.255878
$241$	−17.4490	−1.12399	−0.561995	−	0.827141i	$-0.689966\pi$
$241$	−17.4490	−1.12399	−0.561995	+	0.827141i	$0.689966\pi$
$242$	−0.850771	−0.0546896
$243$	1.00000	0.0641500
$244$	−2.38960	−0.152979
$245$	5.12336	0.327319
$246$	0.0404575	0.00257948
$247$	−0.481313	−0.0306252
$248$	−1.28377	−0.0815192
$249$	−0.151610	−0.00960792
$250$	0.0774485	0.00489828
$251$	−26.1264	−1.64908	−0.824540	−	0.565803i	$-0.808566\pi$
$251$	−26.1264	−1.64908	−0.824540	+	0.565803i	$0.808566\pi$
$252$	6.94284	0.437358
$253$	0	0
$254$	−0.569681	−0.0357449
$255$	−2.68990	−0.168448
$256$	15.5223	0.970143
$257$	23.4736	1.46424	0.732121	−	0.681175i	$-0.238531\pi$
$257$	23.4736	1.46424	0.732121	+	0.681175i	$0.238531\pi$
$258$	−0.282269	−0.0175733
$259$	−8.09615	−0.503070
$260$	0.299422	0.0185693
$261$	−0.318838	−0.0197356
$262$	−1.59346	−0.0984444
$263$	−10.4261	−0.642899	−0.321450	−	0.946927i	$-0.604170\pi$
$263$	−10.4261	−0.642899	−0.321450	+	0.946927i	$0.604170\pi$
$264$	0.0379061	0.00233296
$265$	−13.5930	−0.835010
$266$	−0.864359	−0.0529973
$267$	3.87082	0.236890
$268$	−28.6290	−1.74880
$269$	−2.38704	−0.145541	−0.0727703	−	0.997349i	$-0.523184\pi$
$269$	−2.38704	−0.145541	−0.0727703	+	0.997349i	$0.523184\pi$
$270$	0.0774485	0.00471337
$271$	6.56615	0.398865	0.199433	−	0.979912i	$-0.436090\pi$
$271$	6.56615	0.398865	0.199433	+	0.979912i	$0.436090\pi$
$272$	−10.6629	−0.646532
$273$	0.522841	0.0316438
$274$	0.0612053	0.00369755
$275$	−0.122543	−0.00738961
$276$	0	0
$277$	−12.2650	−0.736932	−0.368466	−	0.929641i	$-0.620117\pi$
$277$	−12.2650	−0.736932	−0.368466	+	0.929641i	$0.620117\pi$
$278$	−0.527539	−0.0316397
$279$	4.15015	0.248463
$280$	1.07704	0.0643656
$281$	−21.8472	−1.30330	−0.651648	−	0.758522i	$-0.725922\pi$
$281$	−21.8472	−1.30330	−0.651648	+	0.758522i	$0.725922\pi$
$282$	0.224451	0.0133658
$283$	4.29021	0.255026	0.127513	−	0.991837i	$-0.459301\pi$
$283$	4.29021	0.255026	0.127513	+	0.991837i	$0.459301\pi$
$284$	−21.4892	−1.27515
$285$	3.20531	0.189866
$286$	0.00142515	8.42706e−5 0
$287$	−1.81885	−0.107363
$288$	0.925669	0.0545456
$289$	−9.76446	−0.574380
$290$	−0.0246935	−0.00145005
$291$	15.7821	0.925160
$292$	−15.2534	−0.892636
$293$	21.3164	1.24532	0.622659	−	0.782493i	$-0.286052\pi$
$293$	21.3164	1.24532	0.622659	+	0.782493i	$0.286052\pi$
$294$	0.396797	0.0231417
$295$	−11.7230	−0.682539
$296$	−0.719264	−0.0418064
$297$	−0.122543	−0.00711066
$298$	−1.39767	−0.0809646
$299$	0	0
$300$	−1.99400	−0.115124
$301$	12.6900	0.731440
$302$	−0.223261	−0.0128472
$303$	7.08225	0.406865
$304$	12.7060	0.728738
$305$	1.19839	0.0686199
$306$	−0.208329	−0.0119093
$307$	−29.2234	−1.66787	−0.833934	−	0.551864i	$-0.813917\pi$
$307$	−29.2234	−1.66787	−0.833934	+	0.551864i	$0.813917\pi$
$308$	−0.850795	−0.0484786
$309$	−11.7909	−0.670760
$310$	0.321423	0.0182556
$311$	18.9974	1.07725	0.538623	−	0.842547i	$-0.318945\pi$
$311$	18.9974	1.07725	0.538623	+	0.842547i	$0.318945\pi$
$312$	0.0464493	0.00262967
$313$	0.839035	0.0474251	0.0237125	−	0.999719i	$-0.492451\pi$
$313$	0.839035	0.0474251	0.0237125	+	0.999719i	$0.492451\pi$
$314$	0.199946	0.0112836
$315$	−3.48186	−0.196181
$316$	27.5496	1.54979
$317$	31.5060	1.76956	0.884778	−	0.466013i	$-0.154310\pi$
$317$	31.5060	1.76956	0.884778	+	0.466013i	$0.154310\pi$
$318$	−1.05276	−0.0590356
$319$	0.0390713	0.00218757
$320$	−7.85640	−0.439186
$321$	11.3579	0.633937
$322$	0	0
$323$	−8.62194	−0.479737
$324$	−1.99400	−0.110778
$325$	−0.150161	−0.00832945
$326$	−0.184047	−0.0101934
$327$	−10.2209	−0.565217
$328$	−0.161587	−0.00892217
$329$	−10.0906	−0.556315
$330$	−0.00949077	−0.000522450 0
$331$	−22.1435	−1.21712	−0.608559	−	0.793509i	$-0.708252\pi$
$331$	−22.1435	−1.21712	−0.608559	+	0.793509i	$0.708252\pi$
$332$	0.302311	0.0165915
$333$	2.32524	0.127422
$334$	0.865622	0.0473647
$335$	14.3576	0.784438
$336$	−13.8023	−0.752975
$337$	−17.0402	−0.928236	−0.464118	−	0.885773i	$-0.653629\pi$
$337$	−17.0402	−0.928236	−0.464118	+	0.885773i	$0.653629\pi$
$338$	−1.00508	−0.0546694
$339$	−16.0018	−0.869100
$340$	5.36366	0.290885
$341$	−0.508572	−0.0275407
$342$	0.248246	0.0134236
$343$	6.53421	0.352814
$344$	1.12738	0.0607845
$345$	0	0
$346$	1.27544	0.0685681
$347$	−27.9081	−1.49818	−0.749092	−	0.662465i	$-0.769510\pi$
$347$	−27.9081	−1.49818	−0.749092	+	0.662465i	$0.769510\pi$
$348$	0.635763	0.0340805
$349$	13.0369	0.697850	0.348925	−	0.937151i	$-0.386547\pi$
$349$	13.0369	0.697850	0.348925	+	0.937151i	$0.386547\pi$
$350$	−0.269665	−0.0144142
$351$	−0.150161	−0.00801501
$352$	−0.113434	−0.00604606
$353$	−12.8361	−0.683197	−0.341598	−	0.939846i	$-0.610968\pi$
$353$	−12.8361	−0.683197	−0.341598	+	0.939846i	$0.610968\pi$
$354$	−0.907929	−0.0482559
$355$	10.7769	0.571981
$356$	−7.71842	−0.409075
$357$	9.36584	0.495693
$358$	−0.529546	−0.0279874
$359$	11.6388	0.614275	0.307137	−	0.951665i	$-0.400629\pi$
$359$	11.6388	0.614275	0.307137	+	0.951665i	$0.400629\pi$
$360$	−0.309330	−0.0163031
$361$	−8.72601	−0.459264
$362$	−0.801704	−0.0421366
$363$	−10.9850	−0.576562
$364$	−1.04255	−0.0546442
$365$	7.64963	0.400400
$366$	0.0928139	0.00485146
$367$	−6.39887	−0.334018	−0.167009	−	0.985955i	$-0.553411\pi$
$367$	−6.39887	−0.334018	−0.167009	+	0.985955i	$0.553411\pi$
$368$	0	0
$369$	0.522379	0.0271940
$370$	0.180086	0.00936223
$371$	47.3288	2.45719
$372$	−8.27541	−0.429060
$373$	11.8683	0.614517	0.307259	−	0.951626i	$-0.400588\pi$
$373$	11.8683	0.614517	0.307259	+	0.951626i	$0.400588\pi$
$374$	0.0255292	0.00132008
$375$	1.00000	0.0516398
$376$	−0.896456	−0.0462312
$377$	0.0478771	0.00246579
$378$	−0.269665	−0.0138701
$379$	−38.4103	−1.97300	−0.986502	−	0.163748i	$-0.947642\pi$
$379$	−38.4103	−1.97300	−0.986502	+	0.163748i	$0.947642\pi$
$380$	−6.39139	−0.327871
$381$	−7.35560	−0.376839
$382$	−1.06931	−0.0547108
$383$	2.27071	0.116028	0.0580140	−	0.998316i	$-0.481523\pi$
$383$	2.27071	0.116028	0.0580140	+	0.998316i	$0.481523\pi$
$384$	−2.45980	−0.125526
$385$	0.426677	0.0217455
$386$	−1.21561	−0.0618728
$387$	−3.64461	−0.185266
$388$	−31.4694	−1.59762
$389$	6.36626	0.322782	0.161391	−	0.986891i	$-0.448402\pi$
$389$	6.36626	0.322782	0.161391	+	0.986891i	$0.448402\pi$
$390$	−0.0116298	−0.000588896 0
$391$	0	0
$392$	−1.58481	−0.0800448
$393$	−20.5745	−1.03784
$394$	0.876481	0.0441565
$395$	−13.8162	−0.695171
$396$	0.244351	0.0122791
$397$	−15.6002	−0.782953	−0.391476	−	0.920188i	$-0.628035\pi$
$397$	−15.6002	−0.782953	−0.391476	+	0.920188i	$0.628035\pi$
$398$	−0.120187	−0.00602444
$399$	−11.1604	−0.558720
$400$	3.96405	0.198202
$401$	−25.1565	−1.25625	−0.628127	−	0.778111i	$-0.716178\pi$
$401$	−25.1565	−1.25625	−0.628127	+	0.778111i	$0.716178\pi$
$402$	1.11197	0.0554602
$403$	−0.623192	−0.0310434
$404$	−14.1220	−0.702597
$405$	1.00000	0.0496904
$406$	0.0859794	0.00426709
$407$	−0.284941	−0.0141240
$408$	0.832064	0.0411933
$409$	23.1444	1.14442	0.572210	−	0.820107i	$-0.306086\pi$
$409$	23.1444	1.14442	0.572210	+	0.820107i	$0.306086\pi$
$410$	0.0404575	0.00199805
$411$	0.790270	0.0389812
$412$	23.5110	1.15831
$413$	40.8179	2.00852
$414$	0	0
$415$	−0.151610	−0.00744226
$416$	−0.139000	−0.00681502
$417$	−6.81148	−0.333560
$418$	−0.0304208	−0.00148793
$419$	−12.6640	−0.618676	−0.309338	−	0.950952i	$-0.600107\pi$
$419$	−12.6640	−0.618676	−0.309338	+	0.950952i	$0.600107\pi$
$420$	6.94284	0.338776
$421$	−2.60380	−0.126901	−0.0634506	−	0.997985i	$-0.520211\pi$
$421$	−2.60380	−0.126901	−0.0634506	+	0.997985i	$0.520211\pi$
$422$	2.02766	0.0987050
$423$	2.89806	0.140909
$424$	4.20471	0.204199
$425$	−2.68990	−0.130479
$426$	0.834658	0.0404393
$427$	−4.17264	−0.201928
$428$	−22.6477	−1.09472
$429$	0.0184012	0.000888418 0
$430$	−0.282269	−0.0136122
$431$	−11.4498	−0.551516	−0.275758	−	0.961227i	$-0.588929\pi$
$431$	−11.4498	−0.551516	−0.275758	+	0.961227i	$0.588929\pi$
$432$	3.96405	0.190720
$433$	0.0910636	0.00437624	0.00218812	−	0.999998i	$-0.499303\pi$
$433$	0.0910636	0.00437624	0.00218812	+	0.999998i	$0.499303\pi$
$434$	−1.11915	−0.0537210
$435$	−0.318838	−0.0152871
$436$	20.3805	0.976049
$437$	0	0
$438$	0.592452	0.0283085
$439$	20.8570	0.995452	0.497726	−	0.867334i	$-0.334169\pi$
$439$	20.8570	0.995452	0.497726	+	0.867334i	$0.334169\pi$
$440$	0.0379061	0.00180710
$441$	5.12336	0.243969
$442$	0.0312829	0.00148797
$443$	−8.82141	−0.419118	−0.209559	−	0.977796i	$-0.567203\pi$
$443$	−8.82141	−0.419118	−0.209559	+	0.977796i	$0.567203\pi$
$444$	−4.63652	−0.220040
$445$	3.87082	0.183494
$446$	0.933324	0.0441942
$447$	−18.0464	−0.853565
$448$	27.3549	1.29240
$449$	4.95512	0.233847	0.116923	−	0.993141i	$-0.462697\pi$
$449$	4.95512	0.233847	0.116923	+	0.993141i	$0.462697\pi$
$450$	0.0774485	0.00365096
$451$	−0.0640139	−0.00301429
$452$	31.9077	1.50081
$453$	−2.88270	−0.135441
$454$	−1.56399	−0.0734019
$455$	0.522841	0.0245111
$456$	−0.991496	−0.0464311
$457$	−29.6720	−1.38800	−0.693998	−	0.719977i	$-0.744152\pi$
$457$	−29.6720	−1.38800	−0.693998	+	0.719977i	$0.744152\pi$
$458$	−1.41510	−0.0661231
$459$	−2.68990	−0.125554
$460$	0	0
$461$	32.4318	1.51050	0.755250	−	0.655437i	$-0.227516\pi$
$461$	32.4318	1.51050	0.755250	+	0.655437i	$0.227516\pi$
$462$	0.0330455	0.00153742
$463$	33.2618	1.54581	0.772903	−	0.634524i	$-0.218804\pi$
$463$	33.2618	1.54581	0.772903	+	0.634524i	$0.218804\pi$
$464$	−1.26389	−0.0586745
$465$	4.15015	0.192459
$466$	−0.558901	−0.0258906
$467$	6.24766	0.289107	0.144554	−	0.989497i	$-0.453825\pi$
$467$	6.24766	0.289107	0.144554	+	0.989497i	$0.453825\pi$
$468$	0.299422	0.0138408
$469$	−49.9911	−2.30837
$470$	0.224451	0.0103531
$471$	2.58166	0.118957
$472$	3.62627	0.166913
$473$	0.446620	0.0205356
$474$	−1.07005	−0.0491489
$475$	3.20531	0.147070
$476$	−18.6755	−0.855991
$477$	−13.5930	−0.622379
$478$	−1.72391	−0.0788499
$479$	−21.6317	−0.988379	−0.494189	−	0.869354i	$-0.664535\pi$
$479$	−21.6317	−0.988379	−0.494189	+	0.869354i	$0.664535\pi$
$480$	0.925669	0.0422508
$481$	−0.349160	−0.0159203
$482$	−1.35140	−0.0615546
$483$	0	0
$484$	21.9041	0.995640
$485$	15.7821	0.716626
$486$	0.0774485	0.00351314
$487$	9.31743	0.422213	0.211107	−	0.977463i	$-0.432293\pi$
$487$	9.31743	0.422213	0.211107	+	0.977463i	$0.432293\pi$
$488$	−0.370699	−0.0167808
$489$	−2.37638	−0.107464
$490$	0.396797	0.0179254
$491$	0.564202	0.0254621	0.0127310	−	0.999919i	$-0.495947\pi$
$491$	0.564202	0.0254621	0.0127310	+	0.999919i	$0.495947\pi$
$492$	−1.04163	−0.0469601
$493$	0.857640	0.0386262
$494$	−0.0372770	−0.00167717
$495$	−0.122543	−0.00550789
$496$	16.4514	0.738690
$497$	−37.5238	−1.68317
$498$	−0.0117420	−0.000526172 0
$499$	32.4148	1.45108	0.725542	−	0.688177i	$-0.241589\pi$
$499$	32.4148	1.45108	0.725542	+	0.688177i	$0.241589\pi$
$500$	−1.99400	−0.0891745
$501$	11.1767	0.499340
$502$	−2.02345	−0.0903109
$503$	−11.8006	−0.526164	−0.263082	−	0.964774i	$-0.584739\pi$
$503$	−11.8006	−0.526164	−0.263082	+	0.964774i	$0.584739\pi$
$504$	1.07704	0.0479753
$505$	7.08225	0.315156
$506$	0	0
$507$	−12.9775	−0.576349
$508$	14.6671	0.650747
$509$	−11.9014	−0.527522	−0.263761	−	0.964588i	$-0.584963\pi$
$509$	−11.9014	−0.527522	−0.263761	+	0.964588i	$0.584963\pi$
$510$	−0.208329	−0.00922494
$511$	−26.6349	−1.17826
$512$	6.12179	0.270547
$513$	3.20531	0.141518
$514$	1.81799	0.0801883
$515$	−11.7909	−0.519568
$516$	7.26735	0.319927
$517$	−0.355137	−0.0156189
$518$	−0.627035	−0.0275503
$519$	16.4682	0.722875
$520$	0.0464493	0.00203694
$521$	−41.5516	−1.82041	−0.910204	−	0.414160i	$-0.864075\pi$
$521$	−41.5516	−1.82041	−0.910204	+	0.414160i	$0.864075\pi$
$522$	−0.0246935	−0.00108081
$523$	−2.18164	−0.0953964	−0.0476982	−	0.998862i	$-0.515189\pi$
$523$	−2.18164	−0.0953964	−0.0476982	+	0.998862i	$0.515189\pi$
$524$	41.0255	1.79221
$525$	−3.48186	−0.151961
$526$	−0.807484	−0.0352080
$527$	−11.1635	−0.486289
$528$	−0.485766	−0.0211402
$529$	0	0
$530$	−1.05276	−0.0457288
$531$	−11.7230	−0.508735
$532$	22.2539	0.964830
$533$	−0.0784411	−0.00339766
$534$	0.299789	0.0129731
$535$	11.3579	0.491046
$536$	−4.44122	−0.191831
$537$	−6.83739	−0.295055
$538$	−0.184873	−0.00797044
$539$	−0.627831	−0.0270426
$540$	−1.99400	−0.0858082
$541$	−19.1708	−0.824218	−0.412109	−	0.911135i	$-0.635208\pi$
$541$	−19.1708	−0.824218	−0.412109	+	0.911135i	$0.635208\pi$
$542$	0.508539	0.0218436
$543$	−10.3514	−0.444223
$544$	−2.48995	−0.106756
$545$	−10.2209	−0.437815
$546$	0.0404932	0.00173295
$547$	0.783501	0.0335001	0.0167500	−	0.999860i	$-0.494668\pi$
$547$	0.783501	0.0335001	0.0167500	+	0.999860i	$0.494668\pi$
$548$	−1.57580	−0.0673149
$549$	1.19839	0.0511462
$550$	−0.00949077	−0.000404688 0
$551$	−1.02197	−0.0435375
$552$	0	0
$553$	48.1062	2.04569
$554$	−0.949906	−0.0403577
$555$	2.32524	0.0987007
$556$	13.5821	0.576009
$557$	32.2113	1.36484	0.682418	−	0.730962i	$-0.260928\pi$
$557$	32.2113	1.36484	0.682418	+	0.730962i	$0.260928\pi$
$558$	0.321423	0.0136069
$559$	0.547278	0.0231474
$560$	−13.8023	−0.583252
$561$	0.329628	0.0139169
$562$	−1.69203	−0.0713742
$563$	3.68471	0.155292	0.0776460	−	0.996981i	$-0.475260\pi$
$563$	3.68471	0.155292	0.0776460	+	0.996981i	$0.475260\pi$
$564$	−5.77874	−0.243329
$565$	−16.0018	−0.673202
$566$	0.332270	0.0139664
$567$	−3.48186	−0.146224
$568$	−3.33363	−0.139876
$569$	−38.3511	−1.60776	−0.803882	−	0.594789i	$-0.797236\pi$
$569$	−38.3511	−1.60776	−0.803882	+	0.594789i	$0.797236\pi$
$570$	0.248246	0.0103979
$571$	−3.30491	−0.138306	−0.0691532	−	0.997606i	$-0.522030\pi$
$571$	−3.30491	−0.138306	−0.0691532	+	0.997606i	$0.522030\pi$
$572$	−0.0366920	−0.00153417
$573$	−13.8067	−0.576785
$574$	−0.140867	−0.00587969
$575$	0	0
$576$	−7.85640	−0.327350
$577$	13.3012	0.553737	0.276869	−	0.960908i	$-0.410703\pi$
$577$	13.3012	0.553737	0.276869	+	0.960908i	$0.410703\pi$
$578$	−0.756243	−0.0314556
$579$	−15.6957	−0.652291
$580$	0.635763	0.0263986
$581$	0.527886	0.0219004
$582$	1.22230	0.0506658
$583$	1.66572	0.0689871
$584$	−2.36626	−0.0979164
$585$	−0.150161	−0.00620840
$586$	1.65093	0.0681991
$587$	31.1044	1.28381	0.641907	−	0.766782i	$-0.278143\pi$
$587$	31.1044	1.28381	0.641907	+	0.766782i	$0.278143\pi$
$588$	−10.2160	−0.421300
$589$	13.3025	0.548120
$590$	−0.907929	−0.0373789
$591$	11.3169	0.465517
$592$	9.21734	0.378830
$593$	−26.6284	−1.09350	−0.546749	−	0.837297i	$-0.684135\pi$
$593$	−26.6284	−1.09350	−0.546749	+	0.837297i	$0.684135\pi$
$594$	−0.00949077	−0.000389411 0
$595$	9.36584	0.383962
$596$	35.9845	1.47398
$597$	−1.55183	−0.0635122
$598$	0	0
$599$	−32.2549	−1.31790	−0.658950	−	0.752187i	$-0.728999\pi$
$599$	−32.2549	−1.31790	−0.658950	+	0.752187i	$0.728999\pi$
$600$	−0.309330	−0.0126283
$601$	16.1792	0.659964	0.329982	−	0.943987i	$-0.392957\pi$
$601$	16.1792	0.659964	0.329982	+	0.943987i	$0.392957\pi$
$602$	0.982823	0.0400569
$603$	14.3576	0.584685
$604$	5.74811	0.233887
$605$	−10.9850	−0.446603
$606$	0.548510	0.0222817
$607$	−22.4212	−0.910050	−0.455025	−	0.890479i	$-0.650370\pi$
$607$	−22.4212	−0.910050	−0.455025	+	0.890479i	$0.650370\pi$
$608$	2.96705	0.120330
$609$	1.11015	0.0449855
$610$	0.0928139	0.00375793
$611$	−0.435176	−0.0176054
$612$	5.36366	0.216813
$613$	−35.2456	−1.42356	−0.711778	−	0.702405i	$-0.752110\pi$
$613$	−35.2456	−1.42356	−0.711778	+	0.702405i	$0.752110\pi$
$614$	−2.26331	−0.0913398
$615$	0.522379	0.0210644
$616$	−0.131984	−0.00531778
$617$	21.7154	0.874229	0.437114	−	0.899406i	$-0.356001\pi$
$617$	21.7154	0.874229	0.437114	+	0.899406i	$0.356001\pi$
$618$	−0.913186	−0.0367337
$619$	21.6812	0.871441	0.435721	−	0.900082i	$-0.356494\pi$
$619$	21.6812	0.871441	0.435721	+	0.900082i	$0.356494\pi$
$620$	−8.27541	−0.332349
$621$	0	0
$622$	1.47132	0.0589947
$623$	−13.4776	−0.539971
$624$	−0.595246	−0.0238289
$625$	1.00000	0.0400000
$626$	0.0649821	0.00259721
$627$	−0.392787	−0.0156864
$628$	−5.14783	−0.205421
$629$	−6.25464	−0.249389
$630$	−0.269665	−0.0107437
$631$	42.4602	1.69031	0.845157	−	0.534519i	$-0.179507\pi$
$631$	42.4602	1.69031	0.845157	+	0.534519i	$0.179507\pi$
$632$	4.27377	0.170002
$633$	26.1808	1.04059
$634$	2.44010	0.0969086
$635$	−7.35560	−0.291898
$636$	27.1044	1.07476
$637$	−0.769330	−0.0304820
$638$	0.00302601	0.000119801 0
$639$	10.7769	0.426329
$640$	−2.45980	−0.0972323
$641$	−2.51082	−0.0991714	−0.0495857	−	0.998770i	$-0.515790\pi$
$641$	−2.51082	−0.0991714	−0.0495857	+	0.998770i	$0.515790\pi$
$642$	0.879654	0.0347172
$643$	47.1823	1.86069	0.930343	−	0.366690i	$-0.119509\pi$
$643$	47.1823	1.86069	0.930343	+	0.366690i	$0.119509\pi$
$644$	0	0
$645$	−3.64461	−0.143506
$646$	−0.667757	−0.0262725
$647$	−12.4526	−0.489561	−0.244780	−	0.969579i	$-0.578716\pi$
$647$	−12.4526	−0.489561	−0.244780	+	0.969579i	$0.578716\pi$
$648$	−0.309330	−0.0121516
$649$	1.43657	0.0563903
$650$	−0.0116298	−0.000456157 0
$651$	−14.4503	−0.566350
$652$	4.73851	0.185574
$653$	−33.7486	−1.32069	−0.660343	−	0.750964i	$-0.729589\pi$
$653$	−33.7486	−1.32069	−0.660343	+	0.750964i	$0.729589\pi$
$654$	−0.791594	−0.0309538
$655$	−20.5745	−0.803910
$656$	2.07074	0.0808486
$657$	7.64963	0.298440
$658$	−0.781506	−0.0304663
$659$	41.2396	1.60646	0.803232	−	0.595666i	$-0.203112\pi$
$659$	41.2396	1.60646	0.803232	+	0.595666i	$0.203112\pi$
$660$	0.244351	0.00951134
$661$	24.1163	0.938015	0.469008	−	0.883194i	$-0.344612\pi$
$661$	24.1163	0.938015	0.469008	+	0.883194i	$0.344612\pi$
$662$	−1.71498	−0.0666547
$663$	0.403918	0.0156869
$664$	0.0468976	0.00181998
$665$	−11.1604	−0.432783
$666$	0.180086	0.00697819
$667$	0	0
$668$	−22.2864	−0.862288
$669$	12.0509	0.465914
$670$	1.11197	0.0429592
$671$	−0.146855	−0.00566926
$672$	−3.22305	−0.124332
$673$	18.6820	0.720140	0.360070	−	0.932925i	$-0.382753\pi$
$673$	18.6820	0.720140	0.360070	+	0.932925i	$0.382753\pi$
$674$	−1.31974	−0.0508343
$675$	1.00000	0.0384900
$676$	25.8771	0.995272
$677$	−3.24032	−0.124535	−0.0622677	−	0.998059i	$-0.519833\pi$
$677$	−3.24032	−0.124535	−0.0622677	+	0.998059i	$0.519833\pi$
$678$	−1.23932	−0.0475958
$679$	−54.9509	−2.10882
$680$	0.832064	0.0319082
$681$	−20.1940	−0.773835
$682$	−0.0393881	−0.00150825
$683$	34.8609	1.33392	0.666958	−	0.745095i	$-0.267596\pi$
$683$	34.8609	1.33392	0.666958	+	0.745095i	$0.267596\pi$
$684$	−6.39139	−0.244381
$685$	0.790270	0.0301947
$686$	0.506065	0.0193216
$687$	−18.2714	−0.697099
$688$	−14.4474	−0.550801
$689$	2.04114	0.0777611
$690$	0	0
$691$	23.0941	0.878542	0.439271	−	0.898355i	$-0.355237\pi$
$691$	23.0941	0.878542	0.439271	+	0.898355i	$0.355237\pi$
$692$	−32.8377	−1.24830
$693$	0.426677	0.0162081
$694$	−2.16144	−0.0820472
$695$	−6.81148	−0.258374
$696$	0.0986260	0.00373841
$697$	−1.40515	−0.0532237
$698$	1.00969	0.0382173
$699$	−7.21642	−0.272950
$700$	6.94284	0.262415
$701$	24.3949	0.921382	0.460691	−	0.887561i	$-0.347602\pi$
$701$	24.3949	0.921382	0.460691	+	0.887561i	$0.347602\pi$
$702$	−0.0116298	−0.000438937 0
$703$	7.45309	0.281099
$704$	0.962746	0.0362849
$705$	2.89806	0.109147
$706$	−0.994137	−0.0374148
$707$	−24.6594	−0.927413
$708$	23.3757	0.878512
$709$	9.01577	0.338594	0.169297	−	0.985565i	$-0.445850\pi$
$709$	9.01577	0.338594	0.169297	+	0.985565i	$0.445850\pi$
$710$	0.834658	0.0313242
$711$	−13.8162	−0.518150
$712$	−1.19736	−0.0448729
$713$	0	0
$714$	0.725371	0.0271463
$715$	0.0184012	0.000688165 0
$716$	13.6338	0.509518
$717$	−22.2588	−0.831270
$718$	0.901412	0.0336404
$719$	27.7308	1.03418	0.517092	−	0.855930i	$-0.327015\pi$
$719$	27.7308	1.03418	0.517092	+	0.855930i	$0.327015\pi$
$720$	3.96405	0.147731
$721$	41.0542	1.52894
$722$	−0.675817	−0.0251513
$723$	−17.4490	−0.648936
$724$	20.6408	0.767109
$725$	−0.318838	−0.0118413
$726$	−0.850771	−0.0315751
$727$	30.1451	1.11802	0.559010	−	0.829161i	$-0.311181\pi$
$727$	30.1451	1.11802	0.559010	+	0.829161i	$0.311181\pi$
$728$	−0.161730	−0.00599412
$729$	1.00000	0.0370370
$730$	0.592452	0.0219277
$731$	9.80361	0.362600
$732$	−2.38960	−0.0883222
$733$	4.16577	0.153866	0.0769332	−	0.997036i	$-0.475487\pi$
$733$	4.16577	0.153866	0.0769332	+	0.997036i	$0.475487\pi$
$734$	−0.495583	−0.0182923
$735$	5.12336	0.188978
$736$	0	0
$737$	−1.75942	−0.0648090
$738$	0.0404575	0.00148926
$739$	15.7522	0.579455	0.289728	−	0.957109i	$-0.406435\pi$
$739$	15.7522	0.579455	0.289728	+	0.957109i	$0.406435\pi$
$740$	−4.63652	−0.170442
$741$	−0.481313	−0.0176815
$742$	3.66555	0.134567
$743$	−50.6258	−1.85728	−0.928640	−	0.370983i	$-0.879021\pi$
$743$	−50.6258	−1.85728	−0.928640	+	0.370983i	$0.879021\pi$
$744$	−1.28377	−0.0470651
$745$	−18.0464	−0.661168
$746$	0.919183	0.0336537
$747$	−0.151610	−0.00554713
$748$	−0.657278	−0.0240325
$749$	−39.5467	−1.44500
$750$	0.0774485	0.00282802
$751$	10.6736	0.389484	0.194742	−	0.980854i	$-0.437613\pi$
$751$	10.6736	0.389484	0.194742	+	0.980854i	$0.437613\pi$
$752$	11.4880	0.418926
$753$	−26.1264	−0.952097
$754$	0.00370801	0.000135038 0
$755$	−2.88270	−0.104912
$756$	6.94284	0.252509
$757$	−11.4031	−0.414452	−0.207226	−	0.978293i	$-0.566444\pi$
$757$	−11.4031	−0.414452	−0.207226	+	0.978293i	$0.566444\pi$
$758$	−2.97482	−0.108050
$759$	0	0
$760$	−0.991496	−0.0359653
$761$	9.39101	0.340424	0.170212	−	0.985407i	$-0.445555\pi$
$761$	9.39101	0.340424	0.170212	+	0.985407i	$0.445555\pi$
$762$	−0.569681	−0.0206374
$763$	35.5878	1.28836
$764$	27.5307	0.996024
$765$	−2.68990	−0.0972534
$766$	0.175863	0.00635420
$767$	1.76034	0.0635622
$768$	15.5223	0.560113
$769$	41.3206	1.49006	0.745029	−	0.667032i	$-0.232436\pi$
$769$	41.3206	1.49006	0.745029	+	0.667032i	$0.232436\pi$
$770$	0.0330455	0.00119088
$771$	23.4736	0.845380
$772$	31.2972	1.12641
$773$	−10.7585	−0.386956	−0.193478	−	0.981105i	$-0.561977\pi$
$773$	−10.7585	−0.386956	−0.193478	+	0.981105i	$0.561977\pi$
$774$	−0.282269	−0.0101460
$775$	4.15015	0.149078
$776$	−4.88186	−0.175248
$777$	−8.09615	−0.290448
$778$	0.493058	0.0176770
$779$	1.67439	0.0599911
$780$	0.299422	0.0107210
$781$	−1.32064	−0.0472561
$782$	0	0
$783$	−0.318838	−0.0113943
$784$	20.3092	0.725330
$785$	2.58166	0.0921434
$786$	−1.59346	−0.0568369
$787$	−32.8202	−1.16991	−0.584957	−	0.811064i	$-0.698889\pi$
$787$	−32.8202	−1.16991	−0.584957	+	0.811064i	$0.698889\pi$
$788$	−22.5660	−0.803881
$789$	−10.4261	−0.371178
$790$	−1.07005	−0.0380706
$791$	55.7162	1.98104
$792$	0.0379061	0.00134694
$793$	−0.179952	−0.00639030
$794$	−1.20821	−0.0428779
$795$	−13.5930	−0.482093
$796$	3.09436	0.109677
$797$	−25.8920	−0.917143	−0.458572	−	0.888657i	$-0.651639\pi$
$797$	−25.8920	−0.917143	−0.458572	+	0.888657i	$0.651639\pi$
$798$	−0.864359	−0.0305980
$799$	−7.79548	−0.275784
$800$	0.925669	0.0327273
$801$	3.87082	0.136769
$802$	−1.94833	−0.0687980
$803$	−0.937407	−0.0330804
$804$	−28.6290	−1.00967
$805$	0	0
$806$	−0.0482653	−0.00170007
$807$	−2.38704	−0.0840278
$808$	−2.19075	−0.0770704
$809$	−46.4747	−1.63396	−0.816982	−	0.576663i	$-0.804355\pi$
$809$	−46.4747	−1.63396	−0.816982	+	0.576663i	$0.804355\pi$
$810$	0.0774485	0.00272126
$811$	−10.4961	−0.368567	−0.184283	−	0.982873i	$-0.558996\pi$
$811$	−10.4961	−0.368567	−0.184283	+	0.982873i	$0.558996\pi$
$812$	−2.21364	−0.0776835
$813$	6.56615	0.230285
$814$	−0.0220683	−0.000773492 0
$815$	−2.37638	−0.0832410
$816$	−10.6629	−0.373275
$817$	−11.6821	−0.408704
$818$	1.79250	0.0626734
$819$	0.522841	0.0182695
$820$	−1.04163	−0.0363751
$821$	−40.0411	−1.39744	−0.698722	−	0.715394i	$-0.746247\pi$
$821$	−40.0411	−1.39744	−0.698722	+	0.715394i	$0.746247\pi$
$822$	0.0612053	0.00213478
$823$	−42.4282	−1.47895	−0.739477	−	0.673182i	$-0.764927\pi$
$823$	−42.4282	−1.47895	−0.739477	+	0.673182i	$0.764927\pi$
$824$	3.64727	0.127059
$825$	−0.122543	−0.00426639
$826$	3.16128	0.109995
$827$	4.03147	0.140188	0.0700940	−	0.997540i	$-0.477670\pi$
$827$	4.03147	0.140188	0.0700940	+	0.997540i	$0.477670\pi$
$828$	0	0
$829$	6.46474	0.224530	0.112265	−	0.993678i	$-0.464189\pi$
$829$	6.46474	0.224530	0.112265	+	0.993678i	$0.464189\pi$
$830$	−0.0117420	−0.000407571 0
$831$	−12.2650	−0.425468
$832$	1.17973	0.0408997
$833$	−13.7813	−0.477494
$834$	−0.527539	−0.0182672
$835$	11.1767	0.386787
$836$	0.783219	0.0270882
$837$	4.15015	0.143450
$838$	−0.980807	−0.0338814
$839$	−36.8309	−1.27154	−0.635772	−	0.771877i	$-0.719318\pi$
$839$	−36.8309	−1.27154	−0.635772	+	0.771877i	$0.719318\pi$
$840$	1.07704	0.0371615
$841$	−28.8983	−0.996495
$842$	−0.201660	−0.00694967
$843$	−21.8472	−0.752458
$844$	−52.2045	−1.79695
$845$	−12.9775	−0.446438
$846$	0.224451	0.00771677
$847$	38.2482	1.31422
$848$	−53.8832	−1.85036
$849$	4.29021	0.147239
$850$	−0.208329	−0.00714561
$851$	0	0
$852$	−21.4892	−0.736209
$853$	−22.4507	−0.768696	−0.384348	−	0.923188i	$-0.625574\pi$
$853$	−22.4507	−0.768696	−0.384348	+	0.923188i	$0.625574\pi$
$854$	−0.323165	−0.0110585
$855$	3.20531	0.109619
$856$	−3.51334	−0.120084
$857$	−55.2589	−1.88761	−0.943804	−	0.330505i	$-0.892781\pi$
$857$	−55.2589	−1.88761	−0.943804	+	0.330505i	$0.892781\pi$
$858$	0.00142515	4.86537e−5 0
$859$	−54.5778	−1.86217	−0.931085	−	0.364802i	$-0.881137\pi$
$859$	−54.5778	−1.86217	−0.931085	+	0.364802i	$0.881137\pi$
$860$	7.26735	0.247815
$861$	−1.81885	−0.0619863
$862$	−0.886769	−0.0302035
$863$	1.15790	0.0394153	0.0197077	−	0.999806i	$-0.493726\pi$
$863$	1.15790	0.0394153	0.0197077	+	0.999806i	$0.493726\pi$
$864$	0.925669	0.0314919
$865$	16.4682	0.559937
$866$	0.00705274	0.000239662 0
$867$	−9.76446	−0.331618
$868$	28.8138	0.978006
$869$	1.69308	0.0574339
$870$	−0.0246935	−0.000837189 0
$871$	−2.15595	−0.0730516
$872$	3.16163	0.107066
$873$	15.7821	0.534142
$874$	0	0
$875$	−3.48186	−0.117708
$876$	−15.2534	−0.515364
$877$	−30.9312	−1.04447	−0.522237	−	0.852801i	$-0.674902\pi$
$877$	−30.9312	−1.04447	−0.522237	+	0.852801i	$0.674902\pi$
$878$	1.61535	0.0545153
$879$	21.3164	0.718985
$880$	−0.485766	−0.0163752
$881$	31.2615	1.05323	0.526613	−	0.850105i	$-0.323462\pi$
$881$	31.2615	1.05323	0.526613	+	0.850105i	$0.323462\pi$
$882$	0.396797	0.0133608
$883$	9.79167	0.329516	0.164758	−	0.986334i	$-0.447316\pi$
$883$	9.79167	0.329516	0.164758	+	0.986334i	$0.447316\pi$
$884$	−0.805413	−0.0270890
$885$	−11.7230	−0.394064
$886$	−0.683206	−0.0229527
$887$	−28.7695	−0.965985	−0.482993	−	0.875624i	$-0.660450\pi$
$887$	−28.7695	−0.965985	−0.482993	+	0.875624i	$0.660450\pi$
$888$	−0.719264	−0.0241369
$889$	25.6112	0.858972
$890$	0.299789	0.0100490
$891$	−0.122543	−0.00410534
$892$	−24.0295	−0.804567
$893$	9.28917	0.310850
$894$	−1.39767	−0.0467450
$895$	−6.83739	−0.228549
$896$	8.56470	0.286126
$897$	0	0
$898$	0.383767	0.0128065
$899$	−1.32323	−0.0441320
$900$	−1.99400	−0.0664667
$901$	36.5637	1.21811
$902$	−0.00495778	−0.000165076 0
$903$	12.6900	0.422297
$904$	4.94984	0.164629
$905$	−10.3514	−0.344094
$906$	−0.223261	−0.00741735
$907$	15.1000	0.501386	0.250693	−	0.968067i	$-0.419342\pi$
$907$	15.1000	0.501386	0.250693	+	0.968067i	$0.419342\pi$
$908$	40.2668	1.33630
$909$	7.08225	0.234904
$910$	0.0404932	0.00134234
$911$	41.7213	1.38229	0.691144	−	0.722717i	$-0.257107\pi$
$911$	41.7213	1.38229	0.691144	+	0.722717i	$0.257107\pi$
$912$	12.7060	0.420737
$913$	0.0185788	0.000614868 0
$914$	−2.29805	−0.0760128
$915$	1.19839	0.0396177
$916$	36.4333	1.20379
$917$	71.6374	2.36568
$918$	−0.208329	−0.00687587
$919$	−30.0337	−0.990721	−0.495361	−	0.868687i	$-0.664964\pi$
$919$	−30.0337	−0.990721	−0.495361	+	0.868687i	$0.664964\pi$
$920$	0	0
$921$	−29.2234	−0.962944
$922$	2.51180	0.0827216
$923$	−1.61828	−0.0532663
$924$	−0.850795	−0.0279891
$925$	2.32524	0.0764533
$926$	2.57608	0.0846551
$927$	−11.7909	−0.387263
$928$	−0.295138	−0.00968839
$929$	27.4627	0.901022	0.450511	−	0.892771i	$-0.351242\pi$
$929$	27.4627	0.901022	0.450511	+	0.892771i	$0.351242\pi$
$930$	0.321423	0.0105399
$931$	16.4219	0.538207
$932$	14.3895	0.471345
$933$	18.9974	0.621948
$934$	0.483872	0.0158328
$935$	0.329628	0.0107800
$936$	0.0464493	0.00151824
$937$	4.29929	0.140452	0.0702258	−	0.997531i	$-0.477628\pi$
$937$	4.29929	0.140452	0.0702258	+	0.997531i	$0.477628\pi$
$938$	−3.87173	−0.126417
$939$	0.839035	0.0273809
$940$	−5.77874	−0.188482
$941$	−47.3293	−1.54289	−0.771445	−	0.636296i	$-0.780466\pi$
$941$	−47.3293	−1.54289	−0.771445	+	0.636296i	$0.780466\pi$
$942$	0.199946	0.00651459
$943$	0	0
$944$	−46.4705	−1.51249
$945$	−3.48186	−0.113265
$946$	0.0345901	0.00112462
$947$	41.2322	1.33987	0.669933	−	0.742422i	$-0.266323\pi$
$947$	41.2322	1.33987	0.669933	+	0.742422i	$0.266323\pi$
$948$	27.5496	0.894770
$949$	−1.14868	−0.0372876
$950$	0.248246	0.00805417
$951$	31.5060	1.02165
$952$	−2.89713	−0.0938966
$953$	0.480977	0.0155804	0.00779019	−	0.999970i	$-0.497520\pi$
$953$	0.480977	0.0155804	0.00779019	+	0.999970i	$0.497520\pi$
$954$	−1.05276	−0.0340842
$955$	−13.8067	−0.446776
$956$	44.3841	1.43548
$957$	0.0390713	0.00126300
$958$	−1.67535	−0.0541280
$959$	−2.75161	−0.0888542
$960$	−7.85640	−0.253564
$961$	−13.7762	−0.444394
$962$	−0.0270420	−0.000871868 0
$963$	11.3579	0.366004
$964$	34.7933	1.12062
$965$	−15.6957	−0.505262
$966$	0	0
$967$	31.7740	1.02178	0.510891	−	0.859645i	$-0.329316\pi$
$967$	31.7740	1.02178	0.510891	+	0.859645i	$0.329316\pi$
$968$	3.39798	0.109215
$969$	−8.62194	−0.276977
$970$	1.22230	0.0392456
$971$	5.61634	0.180237	0.0901185	−	0.995931i	$-0.471275\pi$
$971$	5.61634	0.180237	0.0901185	+	0.995931i	$0.471275\pi$
$972$	−1.99400	−0.0639576
$973$	23.7166	0.760320
$974$	0.721622	0.0231223
$975$	−0.150161	−0.00480901
$976$	4.75049	0.152060
$977$	−45.4913	−1.45540	−0.727698	−	0.685898i	$-0.759410\pi$
$977$	−45.4913	−1.45540	−0.727698	+	0.685898i	$0.759410\pi$
$978$	−0.184047	−0.00588518
$979$	−0.474341	−0.0151600
$980$	−10.2160	−0.326338
$981$	−10.2209	−0.326328
$982$	0.0436966	0.00139442
$983$	54.2736	1.73106	0.865529	−	0.500859i	$-0.166982\pi$
$983$	54.2736	1.73106	0.865529	+	0.500859i	$0.166982\pi$
$984$	−0.161587	−0.00515122
$985$	11.3169	0.360588
$986$	0.0664230	0.00211534
$987$	−10.0906	−0.321189
$988$	0.959738	0.0305333
$989$	0	0
$990$	−0.00949077	−0.000301636 0
$991$	11.0444	0.350837	0.175418	−	0.984494i	$-0.443872\pi$
$991$	11.0444	0.350837	0.175418	+	0.984494i	$0.443872\pi$
$992$	3.84167	0.121973
$993$	−22.1435	−0.702703
$994$	−2.90616	−0.0921779
$995$	−1.55183	−0.0491964
$996$	0.302311	0.00957910
$997$	20.2041	0.639870	0.319935	−	0.947439i	$-0.396339\pi$
$997$	20.2041	0.639870	0.319935	+	0.947439i	$0.396339\pi$
$998$	2.51048	0.0794678
$999$	2.32524	0.0735672

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bm.1.6	yes	12
23.22	odd	2		7935.2.a.bl.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.6	✓	12	23.22	odd	2
7935.2.a.bm.1.6	yes	12	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0774485 q^{2} +1.00000 q^{3} -1.99400 q^{4} +1.00000 q^{5} +0.0774485 q^{6} -3.48186 q^{7} -0.309330 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.0774485 q^{2} +1.00000 q^{3} -1.99400 q^{4} +1.00000 q^{5} +0.0774485 q^{6} -3.48186 q^{7} -0.309330 q^{8} +1.00000 q^{9} +0.0774485 q^{10} -0.122543 q^{11} -1.99400 q^{12} -0.150161 q^{13} -0.269665 q^{14} +1.00000 q^{15} +3.96405 q^{16} -2.68990 q^{17} +0.0774485 q^{18} +3.20531 q^{19} -1.99400 q^{20} -3.48186 q^{21} -0.00949077 q^{22} -0.309330 q^{24} +1.00000 q^{25} -0.0116298 q^{26} +1.00000 q^{27} +6.94284 q^{28} -0.318838 q^{29} +0.0774485 q^{30} +4.15015 q^{31} +0.925669 q^{32} -0.122543 q^{33} -0.208329 q^{34} -3.48186 q^{35} -1.99400 q^{36} +2.32524 q^{37} +0.248246 q^{38} -0.150161 q^{39} -0.309330 q^{40} +0.522379 q^{41} -0.269665 q^{42} -3.64461 q^{43} +0.244351 q^{44} +1.00000 q^{45} +2.89806 q^{47} +3.96405 q^{48} +5.12336 q^{49} +0.0774485 q^{50} -2.68990 q^{51} +0.299422 q^{52} -13.5930 q^{53} +0.0774485 q^{54} -0.122543 q^{55} +1.07704 q^{56} +3.20531 q^{57} -0.0246935 q^{58} -11.7230 q^{59} -1.99400 q^{60} +1.19839 q^{61} +0.321423 q^{62} -3.48186 q^{63} -7.85640 q^{64} -0.150161 q^{65} -0.00949077 q^{66} +14.3576 q^{67} +5.36366 q^{68} -0.269665 q^{70} +10.7769 q^{71} -0.309330 q^{72} +7.64963 q^{73} +0.180086 q^{74} +1.00000 q^{75} -6.39139 q^{76} +0.426677 q^{77} -0.0116298 q^{78} -13.8162 q^{79} +3.96405 q^{80} +1.00000 q^{81} +0.0404575 q^{82} -0.151610 q^{83} +6.94284 q^{84} -2.68990 q^{85} -0.282269 q^{86} -0.318838 q^{87} +0.0379061 q^{88} +3.87082 q^{89} +0.0774485 q^{90} +0.522841 q^{91} +4.15015 q^{93} +0.224451 q^{94} +3.20531 q^{95} +0.925669 q^{96} +15.7821 q^{97} +0.396797 q^{98} -0.122543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 16 q^{14} + 12 q^{15} - 28 q^{17} - 16 q^{19} + 8 q^{20} - 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} - 8 q^{28} - 16 q^{29} + 20 q^{32} - 24 q^{33} - 16 q^{34} - 4 q^{35} + 8 q^{36} - 20 q^{37} - 16 q^{38} - 8 q^{39} - 4 q^{41} - 16 q^{42} + 12 q^{43} - 16 q^{44} + 12 q^{45} + 4 q^{47} + 24 q^{49} - 28 q^{51} - 36 q^{52} - 28 q^{53} - 24 q^{55} - 56 q^{56} - 16 q^{57} + 20 q^{59} + 8 q^{60} - 32 q^{61} + 12 q^{62} - 4 q^{63} - 4 q^{64} - 8 q^{65} + 4 q^{67} - 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} + 36 q^{74} + 12 q^{75} - 8 q^{76} - 28 q^{77} - 36 q^{78} - 40 q^{79} + 12 q^{81} - 28 q^{82} - 100 q^{83} - 8 q^{84} - 28 q^{85} + 20 q^{86} - 16 q^{87} - 80 q^{89} + 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} + 8 q^{97} + 28 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 16 * q^14 + 12 * q^15 - 28 * q^17 - 16 * q^19 + 8 * q^20 - 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 - 8 * q^28 - 16 * q^29 + 20 * q^32 - 24 * q^33 - 16 * q^34 - 4 * q^35 + 8 * q^36 - 20 * q^37 - 16 * q^38 - 8 * q^39 - 4 * q^41 - 16 * q^42 + 12 * q^43 - 16 * q^44 + 12 * q^45 + 4 * q^47 + 24 * q^49 - 28 * q^51 - 36 * q^52 - 28 * q^53 - 24 * q^55 - 56 * q^56 - 16 * q^57 + 20 * q^59 + 8 * q^60 - 32 * q^61 + 12 * q^62 - 4 * q^63 - 4 * q^64 - 8 * q^65 + 4 * q^67 - 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 + 36 * q^74 + 12 * q^75 - 8 * q^76 - 28 * q^77 - 36 * q^78 - 40 * q^79 + 12 * q^81 - 28 * q^82 - 100 * q^83 - 8 * q^84 - 28 * q^85 + 20 * q^86 - 16 * q^87 - 80 * q^89 + 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 + 8 * q^97 + 28 * q^98 - 24 * q^99

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