LMFDB - Embedded newform 3549.2.a.bg.1.11

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:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.29981$ 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)

$f(q)$	$=$	$q+1.29981 q^{2} +1.00000 q^{3} -0.310501 q^{4} -1.99349 q^{5} +1.29981 q^{6} +1.00000 q^{7} -3.00321 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.29981 q^{2} +1.00000 q^{3} -0.310501 q^{4} -1.99349 q^{5} +1.29981 q^{6} +1.00000 q^{7} -3.00321 q^{8} +1.00000 q^{9} -2.59115 q^{10} -2.23452 q^{11} -0.310501 q^{12} +1.29981 q^{14} -1.99349 q^{15} -3.28259 q^{16} -0.168513 q^{17} +1.29981 q^{18} +6.89127 q^{19} +0.618982 q^{20} +1.00000 q^{21} -2.90445 q^{22} +1.53967 q^{23} -3.00321 q^{24} -1.02599 q^{25} +1.00000 q^{27} -0.310501 q^{28} +8.81373 q^{29} -2.59115 q^{30} +0.0996388 q^{31} +1.73968 q^{32} -2.23452 q^{33} -0.219034 q^{34} -1.99349 q^{35} -0.310501 q^{36} -4.91920 q^{37} +8.95732 q^{38} +5.98686 q^{40} -0.944193 q^{41} +1.29981 q^{42} +7.75243 q^{43} +0.693822 q^{44} -1.99349 q^{45} +2.00128 q^{46} +1.08393 q^{47} -3.28259 q^{48} +1.00000 q^{49} -1.33359 q^{50} -0.168513 q^{51} +12.0106 q^{53} +1.29981 q^{54} +4.45450 q^{55} -3.00321 q^{56} +6.89127 q^{57} +11.4562 q^{58} -9.17434 q^{59} +0.618982 q^{60} -3.27054 q^{61} +0.129511 q^{62} +1.00000 q^{63} +8.82643 q^{64} -2.90445 q^{66} +8.51847 q^{67} +0.0523235 q^{68} +1.53967 q^{69} -2.59115 q^{70} -6.19104 q^{71} -3.00321 q^{72} +13.2207 q^{73} -6.39401 q^{74} -1.02599 q^{75} -2.13975 q^{76} -2.23452 q^{77} +10.1866 q^{79} +6.54381 q^{80} +1.00000 q^{81} -1.22727 q^{82} +0.338076 q^{83} -0.310501 q^{84} +0.335929 q^{85} +10.0767 q^{86} +8.81373 q^{87} +6.71073 q^{88} +7.96124 q^{89} -2.59115 q^{90} -0.478070 q^{92} +0.0996388 q^{93} +1.40890 q^{94} -13.7377 q^{95} +1.73968 q^{96} +14.8575 q^{97} +1.29981 q^{98} -2.23452 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.29981	0.919102	0.459551	−	0.888151i	$-0.348010\pi$
$2$	1.29981	0.919102	0.459551	+	0.888151i	$0.348010\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.310501	−0.155251
$5$	−1.99349	−0.891516	−0.445758	−	0.895153i	$-0.647066\pi$
$5$	−1.99349	−0.891516	−0.445758	+	0.895153i	$0.647066\pi$
$6$	1.29981	0.530644
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.00321	−1.06179
$9$	1.00000	0.333333
$10$	−2.59115	−0.819395
$11$	−2.23452	−0.673734	−0.336867	−	0.941552i	$-0.609367\pi$
$11$	−2.23452	−0.673734	−0.336867	+	0.941552i	$0.609367\pi$
$12$	−0.310501	−0.0896340
$13$	0	0
$13$	0	0
$14$	1.29981	0.347388
$15$	−1.99349	−0.514717
$16$	−3.28259	−0.820647
$17$	−0.168513	−0.0408704	−0.0204352	−	0.999791i	$-0.506505\pi$
$17$	−0.168513	−0.0408704	−0.0204352	+	0.999791i	$0.506505\pi$
$18$	1.29981	0.306367
$19$	6.89127	1.58097	0.790483	−	0.612484i	$-0.209830\pi$
$19$	6.89127	1.58097	0.790483	+	0.612484i	$0.209830\pi$
$20$	0.618982	0.138408
$21$	1.00000	0.218218
$22$	−2.90445	−0.619230
$23$	1.53967	0.321044	0.160522	−	0.987032i	$-0.448682\pi$
$23$	1.53967	0.321044	0.160522	+	0.987032i	$0.448682\pi$
$24$	−3.00321	−0.613027
$25$	−1.02599	−0.205199
$26$	0	0
$27$	1.00000	0.192450
$28$	−0.310501	−0.0586792
$29$	8.81373	1.63667	0.818335	−	0.574742i	$-0.194898\pi$
$29$	8.81373	1.63667	0.818335	+	0.574742i	$0.194898\pi$
$30$	−2.59115	−0.473078
$31$	0.0996388	0.0178956	0.00894782	−	0.999960i	$-0.497152\pi$
$31$	0.0996388	0.0178956	0.00894782	+	0.999960i	$0.497152\pi$
$32$	1.73968	0.307535
$33$	−2.23452	−0.388980
$34$	−0.219034	−0.0375641
$35$	−1.99349	−0.336961
$36$	−0.310501	−0.0517502
$37$	−4.91920	−0.808712	−0.404356	−	0.914602i	$-0.632504\pi$
$37$	−4.91920	−0.808712	−0.404356	+	0.914602i	$0.632504\pi$
$38$	8.95732	1.45307
$39$	0	0
$40$	5.98686	0.946606
$41$	−0.944193	−0.147458	−0.0737291	−	0.997278i	$-0.523490\pi$
$41$	−0.944193	−0.147458	−0.0737291	+	0.997278i	$0.523490\pi$
$42$	1.29981	0.200565
$43$	7.75243	1.18223	0.591117	−	0.806586i	$-0.298687\pi$
$43$	7.75243	1.18223	0.591117	+	0.806586i	$0.298687\pi$
$44$	0.693822	0.104598
$45$	−1.99349	−0.297172
$46$	2.00128	0.295072
$47$	1.08393	0.158107	0.0790536	−	0.996870i	$-0.474810\pi$
$47$	1.08393	0.158107	0.0790536	+	0.996870i	$0.474810\pi$
$48$	−3.28259	−0.473801
$49$	1.00000	0.142857
$50$	−1.33359	−0.188599
$51$	−0.168513	−0.0235965
$52$	0	0
$53$	12.0106	1.64978	0.824890	−	0.565294i	$-0.191237\pi$
$53$	12.0106	1.64978	0.824890	+	0.565294i	$0.191237\pi$
$54$	1.29981	0.176881
$55$	4.45450	0.600645
$56$	−3.00321	−0.401320
$57$	6.89127	0.912771
$58$	11.4562	1.50427
$59$	−9.17434	−1.19440	−0.597199	−	0.802093i	$-0.703720\pi$
$59$	−9.17434	−1.19440	−0.597199	+	0.802093i	$0.703720\pi$
$60$	0.618982	0.0799102
$61$	−3.27054	−0.418750	−0.209375	−	0.977835i	$-0.567143\pi$
$61$	−3.27054	−0.418750	−0.209375	+	0.977835i	$0.567143\pi$
$62$	0.129511	0.0164479
$63$	1.00000	0.125988
$64$	8.82643	1.10330
$65$	0	0
$66$	−2.90445	−0.357513
$67$	8.51847	1.04070	0.520348	−	0.853954i	$-0.325802\pi$
$67$	8.51847	1.04070	0.520348	+	0.853954i	$0.325802\pi$
$68$	0.0523235	0.00634515
$69$	1.53967	0.185355
$70$	−2.59115	−0.309702
$71$	−6.19104	−0.734741	−0.367371	−	0.930075i	$-0.619742\pi$
$71$	−6.19104	−0.734741	−0.367371	+	0.930075i	$0.619742\pi$
$72$	−3.00321	−0.353931
$73$	13.2207	1.54736	0.773682	−	0.633574i	$-0.218413\pi$
$73$	13.2207	1.54736	0.773682	+	0.633574i	$0.218413\pi$
$74$	−6.39401	−0.743289
$75$	−1.02599	−0.118472
$76$	−2.13975	−0.245446
$77$	−2.23452	−0.254647
$78$	0	0
$79$	10.1866	1.14608	0.573039	−	0.819528i	$-0.305764\pi$
$79$	10.1866	1.14608	0.573039	+	0.819528i	$0.305764\pi$
$80$	6.54381	0.731620
$81$	1.00000	0.111111
$82$	−1.22727	−0.135529
$83$	0.338076	0.0371087	0.0185543	−	0.999828i	$-0.494094\pi$
$83$	0.338076	0.0371087	0.0185543	+	0.999828i	$0.494094\pi$
$84$	−0.310501	−0.0338785
$85$	0.335929	0.0364366
$86$	10.0767	1.08659
$87$	8.81373	0.944931
$88$	6.71073	0.715366
$89$	7.96124	0.843890	0.421945	−	0.906621i	$-0.361348\pi$
$89$	7.96124	0.843890	0.421945	+	0.906621i	$0.361348\pi$
$90$	−2.59115	−0.273132
$91$	0	0
$92$	−0.478070	−0.0498423
$93$	0.0996388	0.0103321
$94$	1.40890	0.145317
$95$	−13.7377	−1.40946
$96$	1.73968	0.177556
$97$	14.8575	1.50855	0.754274	−	0.656560i	$-0.227989\pi$
$97$	14.8575	1.50855	0.754274	+	0.656560i	$0.227989\pi$
$98$	1.29981	0.131300
$99$	−2.23452	−0.224578
$100$	0.318572	0.0318572
$101$	−6.98055	−0.694590	−0.347295	−	0.937756i	$-0.612900\pi$
$101$	−6.98055	−0.694590	−0.347295	+	0.937756i	$0.612900\pi$
$102$	−0.219034	−0.0216876
$103$	8.36180	0.823913	0.411956	−	0.911204i	$-0.364846\pi$
$103$	8.36180	0.823913	0.411956	+	0.911204i	$0.364846\pi$
$104$	0	0
$105$	−1.99349	−0.194545
$106$	15.6114	1.51632
$107$	16.7289	1.61725	0.808624	−	0.588326i	$-0.200213\pi$
$107$	16.7289	1.61725	0.808624	+	0.588326i	$0.200213\pi$
$108$	−0.310501	−0.0298780
$109$	−8.00198	−0.766451	−0.383226	−	0.923655i	$-0.625187\pi$
$109$	−8.00198	−0.766451	−0.383226	+	0.923655i	$0.625187\pi$
$110$	5.78999	0.552054
$111$	−4.91920	−0.466910
$112$	−3.28259	−0.310175
$113$	1.04525	0.0983287	0.0491643	−	0.998791i	$-0.484344\pi$
$113$	1.04525	0.0983287	0.0491643	+	0.998791i	$0.484344\pi$
$114$	8.95732	0.838930
$115$	−3.06932	−0.286216
$116$	−2.73668	−0.254094
$117$	0	0
$118$	−11.9249	−1.09777
$119$	−0.168513	−0.0154475
$120$	5.98686	0.546523
$121$	−6.00691	−0.546083
$122$	−4.25107	−0.384874
$123$	−0.944193	−0.0851350
$124$	−0.0309380	−0.00277831
$125$	12.0128	1.07445
$126$	1.29981	0.115796
$127$	14.7776	1.31130	0.655650	−	0.755065i	$-0.272395\pi$
$127$	14.7776	1.31130	0.655650	+	0.755065i	$0.272395\pi$
$128$	7.99328	0.706513
$129$	7.75243	0.682563
$130$	0	0
$131$	−13.6465	−1.19230	−0.596151	−	0.802872i	$-0.703304\pi$
$131$	−13.6465	−1.19230	−0.596151	+	0.802872i	$0.703304\pi$
$132$	0.693822	0.0603895
$133$	6.89127	0.597549
$134$	11.0724	0.956507
$135$	−1.99349	−0.171572
$136$	0.506079	0.0433959
$137$	−8.57759	−0.732833	−0.366417	−	0.930451i	$-0.619415\pi$
$137$	−8.57759	−0.732833	−0.366417	+	0.930451i	$0.619415\pi$
$138$	2.00128	0.170360
$139$	2.79628	0.237177	0.118589	−	0.992943i	$-0.462163\pi$
$139$	2.79628	0.237177	0.118589	+	0.992943i	$0.462163\pi$
$140$	0.618982	0.0523135
$141$	1.08393	0.0912832
$142$	−8.04716	−0.675302
$143$	0	0
$144$	−3.28259	−0.273549
$145$	−17.5701	−1.45912
$146$	17.1843	1.42219
$147$	1.00000	0.0824786
$148$	1.52742	0.125553
$149$	−0.948225	−0.0776816	−0.0388408	−	0.999245i	$-0.512367\pi$
$149$	−0.948225	−0.0776816	−0.0388408	+	0.999245i	$0.512367\pi$
$150$	−1.33359	−0.108887
$151$	−16.9937	−1.38293	−0.691463	−	0.722412i	$-0.743033\pi$
$151$	−16.9937	−1.38293	−0.691463	+	0.722412i	$0.743033\pi$
$152$	−20.6959	−1.67866
$153$	−0.168513	−0.0136235
$154$	−2.90445	−0.234047
$155$	−0.198629	−0.0159543
$156$	0	0
$157$	16.5425	1.32023	0.660117	−	0.751163i	$-0.270507\pi$
$157$	16.5425	1.32023	0.660117	+	0.751163i	$0.270507\pi$
$158$	13.2406	1.05336
$159$	12.0106	0.952500
$160$	−3.46804	−0.274173
$161$	1.53967	0.121343
$162$	1.29981	0.102122
$163$	−13.0285	−1.02047	−0.510234	−	0.860036i	$-0.670441\pi$
$163$	−13.0285	−1.02047	−0.510234	+	0.860036i	$0.670441\pi$
$164$	0.293173	0.0228930
$165$	4.45450	0.346782
$166$	0.439434	0.0341067
$167$	−9.63809	−0.745818	−0.372909	−	0.927868i	$-0.621640\pi$
$167$	−9.63809	−0.745818	−0.372909	+	0.927868i	$0.621640\pi$
$168$	−3.00321	−0.231702
$169$	0	0
$170$	0.436643	0.0334890
$171$	6.89127	0.526988
$172$	−2.40714	−0.183543
$173$	−21.7199	−1.65133	−0.825667	−	0.564158i	$-0.809201\pi$
$173$	−21.7199	−1.65133	−0.825667	+	0.564158i	$0.809201\pi$
$174$	11.4562	0.868489
$175$	−1.02599	−0.0775578
$176$	7.33501	0.552897
$177$	−9.17434	−0.689586
$178$	10.3481	0.775622
$179$	−14.4043	−1.07663	−0.538315	−	0.842743i	$-0.680939\pi$
$179$	−14.4043	−1.07663	−0.538315	+	0.842743i	$0.680939\pi$
$180$	0.618982	0.0461362
$181$	0.246871	0.0183498	0.00917488	−	0.999958i	$-0.497080\pi$
$181$	0.246871	0.0183498	0.00917488	+	0.999958i	$0.497080\pi$
$182$	0	0
$183$	−3.27054	−0.241765
$184$	−4.62395	−0.340882
$185$	9.80638	0.720980
$186$	0.129511	0.00949622
$187$	0.376546	0.0275357
$188$	−0.336561	−0.0245462
$189$	1.00000	0.0727393
$190$	−17.8563	−1.29543
$191$	8.32325	0.602249	0.301124	−	0.953585i	$-0.402638\pi$
$191$	8.32325	0.602249	0.301124	+	0.953585i	$0.402638\pi$
$192$	8.82643	0.636992
$193$	−17.2173	−1.23933	−0.619664	−	0.784868i	$-0.712731\pi$
$193$	−17.2173	−1.23933	−0.619664	+	0.784868i	$0.712731\pi$
$194$	19.3118	1.38651
$195$	0	0
$196$	−0.310501	−0.0221787
$197$	13.8565	0.987231	0.493616	−	0.869680i	$-0.335675\pi$
$197$	13.8565	0.987231	0.493616	+	0.869680i	$0.335675\pi$
$198$	−2.90445	−0.206410
$199$	13.0628	0.925995	0.462997	−	0.886360i	$-0.346774\pi$
$199$	13.0628	0.925995	0.462997	+	0.886360i	$0.346774\pi$
$200$	3.08127	0.217879
$201$	8.51847	0.600846
$202$	−9.07337	−0.638400
$203$	8.81373	0.618603
$204$	0.0523235	0.00366337
$205$	1.88224	0.131461
$206$	10.8687	0.757260
$207$	1.53967	0.107015
$208$	0	0
$209$	−15.3987	−1.06515
$210$	−2.59115	−0.178807
$211$	1.40177	0.0965017	0.0482508	−	0.998835i	$-0.484635\pi$
$211$	1.40177	0.0965017	0.0482508	+	0.998835i	$0.484635\pi$
$212$	−3.72930	−0.256129
$213$	−6.19104	−0.424203
$214$	21.7444	1.48642
$215$	−15.4544	−1.05398
$216$	−3.00321	−0.204342
$217$	0.0996388	0.00676392
$218$	−10.4010	−0.704447
$219$	13.2207	0.893371
$220$	−1.38313	−0.0932505
$221$	0	0
$222$	−6.39401	−0.429138
$223$	−7.12243	−0.476953	−0.238476	−	0.971148i	$-0.576648\pi$
$223$	−7.12243	−0.476953	−0.238476	+	0.971148i	$0.576648\pi$
$224$	1.73968	0.116237
$225$	−1.02599	−0.0683996
$226$	1.35862	0.0903741
$227$	−13.5583	−0.899896	−0.449948	−	0.893055i	$-0.648557\pi$
$227$	−13.5583	−0.899896	−0.449948	+	0.893055i	$0.648557\pi$
$228$	−2.13975	−0.141708
$229$	12.6022	0.832776	0.416388	−	0.909187i	$-0.363296\pi$
$229$	12.6022	0.832776	0.416388	+	0.909187i	$0.363296\pi$
$230$	−3.98953	−0.263062
$231$	−2.23452	−0.147021
$232$	−26.4695	−1.73781
$233$	14.9463	0.979167	0.489584	−	0.871956i	$-0.337149\pi$
$233$	14.9463	0.979167	0.489584	+	0.871956i	$0.337149\pi$
$234$	0	0
$235$	−2.16080	−0.140955
$236$	2.84865	0.185431
$237$	10.1866	0.661688
$238$	−0.219034	−0.0141979
$239$	−28.5654	−1.84774	−0.923870	−	0.382707i	$-0.874992\pi$
$239$	−28.5654	−1.84774	−0.923870	+	0.382707i	$0.874992\pi$
$240$	6.54381	0.422401
$241$	24.4026	1.57191	0.785954	−	0.618285i	$-0.212172\pi$
$241$	24.4026	1.57191	0.785954	+	0.618285i	$0.212172\pi$
$242$	−7.80783	−0.501906
$243$	1.00000	0.0641500
$244$	1.01551	0.0650111
$245$	−1.99349	−0.127359
$246$	−1.22727	−0.0782478
$247$	0	0
$248$	−0.299236	−0.0190015
$249$	0.338076	0.0214247
$250$	15.6143	0.987534
$251$	2.73250	0.172474	0.0862370	−	0.996275i	$-0.472516\pi$
$251$	2.73250	0.172474	0.0862370	+	0.996275i	$0.472516\pi$
$252$	−0.310501	−0.0195597
$253$	−3.44043	−0.216298
$254$	19.2080	1.20522
$255$	0.335929	0.0210367
$256$	−7.26312	−0.453945
$257$	4.38194	0.273338	0.136669	−	0.990617i	$-0.456360\pi$
$257$	4.38194	0.273338	0.136669	+	0.990617i	$0.456360\pi$
$258$	10.0767	0.627345
$259$	−4.91920	−0.305664
$260$	0	0
$261$	8.81373	0.545556
$262$	−17.7378	−1.09585
$263$	−20.7701	−1.28074	−0.640369	−	0.768067i	$-0.721219\pi$
$263$	−20.7701	−1.28074	−0.640369	+	0.768067i	$0.721219\pi$
$264$	6.71073	0.413017
$265$	−23.9430	−1.47080
$266$	8.95732	0.549209
$267$	7.96124	0.487220
$268$	−2.64500	−0.161569
$269$	20.1473	1.22840	0.614201	−	0.789150i	$-0.289478\pi$
$269$	20.1473	1.22840	0.614201	+	0.789150i	$0.289478\pi$
$270$	−2.59115	−0.157693
$271$	16.1869	0.983284	0.491642	−	0.870797i	$-0.336397\pi$
$271$	16.1869	0.983284	0.491642	+	0.870797i	$0.336397\pi$
$272$	0.553158	0.0335401
$273$	0	0
$274$	−11.1492	−0.673549
$275$	2.29261	0.138249
$276$	−0.478070	−0.0287764
$277$	−21.9043	−1.31610	−0.658052	−	0.752972i	$-0.728619\pi$
$277$	−21.9043	−1.31610	−0.658052	+	0.752972i	$0.728619\pi$
$278$	3.63463	0.217990
$279$	0.0996388	0.00596522
$280$	5.98686	0.357784
$281$	−19.5379	−1.16553	−0.582765	−	0.812640i	$-0.698029\pi$
$281$	−19.5379	−1.16553	−0.582765	+	0.812640i	$0.698029\pi$
$282$	1.40890	0.0838987
$283$	23.9022	1.42084	0.710418	−	0.703780i	$-0.248506\pi$
$283$	23.9022	1.42084	0.710418	+	0.703780i	$0.248506\pi$
$284$	1.92233	0.114069
$285$	−13.7377	−0.813750
$286$	0	0
$287$	−0.944193	−0.0557339
$288$	1.73968	0.102512
$289$	−16.9716	−0.998330
$290$	−22.8377	−1.34108
$291$	14.8575	0.870960
$292$	−4.10504	−0.240229
$293$	17.9823	1.05054	0.525268	−	0.850937i	$-0.323965\pi$
$293$	17.9823	1.05054	0.525268	+	0.850937i	$0.323965\pi$
$294$	1.29981	0.0758063
$295$	18.2890	1.06483
$296$	14.7734	0.858685
$297$	−2.23452	−0.129660
$298$	−1.23251	−0.0713974
$299$	0	0
$300$	0.318572	0.0183928
$301$	7.75243	0.446842
$302$	−22.0885	−1.27105
$303$	−6.98055	−0.401022
$304$	−22.6212	−1.29741
$305$	6.51979	0.373322
$306$	−0.219034	−0.0125214
$307$	28.7026	1.63814	0.819071	−	0.573692i	$-0.194489\pi$
$307$	28.7026	1.63814	0.819071	+	0.573692i	$0.194489\pi$
$308$	0.693822	0.0395342
$309$	8.36180	0.475686
$310$	−0.258179	−0.0146636
$311$	22.0690	1.25142	0.625710	−	0.780056i	$-0.284809\pi$
$311$	22.0690	1.25142	0.625710	+	0.780056i	$0.284809\pi$
$312$	0	0
$313$	20.6739	1.16856	0.584280	−	0.811552i	$-0.301377\pi$
$313$	20.6739	1.16856	0.584280	+	0.811552i	$0.301377\pi$
$314$	21.5020	1.21343
$315$	−1.99349	−0.112320
$316$	−3.16294	−0.177929
$317$	−22.1697	−1.24518	−0.622588	−	0.782550i	$-0.713919\pi$
$317$	−22.1697	−1.24518	−0.622588	+	0.782550i	$0.713919\pi$
$318$	15.6114	0.875445
$319$	−19.6945	−1.10268
$320$	−17.5954	−0.983613
$321$	16.7289	0.933718
$322$	2.00128	0.111527
$323$	−1.16127	−0.0646146
$324$	−0.310501	−0.0172501
$325$	0	0
$326$	−16.9345	−0.937914
$327$	−8.00198	−0.442511
$328$	2.83561	0.156570
$329$	1.08393	0.0597589
$330$	5.78999	0.318728
$331$	−1.69293	−0.0930516	−0.0465258	−	0.998917i	$-0.514815\pi$
$331$	−1.69293	−0.0930516	−0.0465258	+	0.998917i	$0.514815\pi$
$332$	−0.104973	−0.00576115
$333$	−4.91920	−0.269571
$334$	−12.5277	−0.685483
$335$	−16.9815	−0.927798
$336$	−3.28259	−0.179080
$337$	21.8236	1.18881	0.594404	−	0.804167i	$-0.297388\pi$
$337$	21.8236	1.18881	0.594404	+	0.804167i	$0.297388\pi$
$338$	0	0
$339$	1.04525	0.0567701
$340$	−0.104306	−0.00565681
$341$	−0.222645	−0.0120569
$342$	8.95732	0.484356
$343$	1.00000	0.0539949
$344$	−23.2821	−1.25529
$345$	−3.06932	−0.165247
$346$	−28.2317	−1.51774
$347$	−15.6894	−0.842251	−0.421125	−	0.907002i	$-0.638365\pi$
$347$	−15.6894	−0.842251	−0.421125	+	0.907002i	$0.638365\pi$
$348$	−2.73668	−0.146701
$349$	−26.8967	−1.43975	−0.719873	−	0.694106i	$-0.755800\pi$
$349$	−26.8967	−1.43975	−0.719873	+	0.694106i	$0.755800\pi$
$350$	−1.33359	−0.0712836
$351$	0	0
$352$	−3.88736	−0.207197
$353$	19.0891	1.01601	0.508005	−	0.861354i	$-0.330383\pi$
$353$	19.0891	1.01601	0.508005	+	0.861354i	$0.330383\pi$
$354$	−11.9249	−0.633800
$355$	12.3418	0.655034
$356$	−2.47198	−0.131014
$357$	−0.168513	−0.00891864
$358$	−18.7229	−0.989534
$359$	24.0829	1.27105	0.635523	−	0.772082i	$-0.280784\pi$
$359$	24.0829	1.27105	0.635523	+	0.772082i	$0.280784\pi$
$360$	5.98686	0.315535
$361$	28.4896	1.49945
$362$	0.320884	0.0168653
$363$	−6.00691	−0.315281
$364$	0	0
$365$	−26.3553	−1.37950
$366$	−4.25107	−0.222207
$367$	−33.8964	−1.76938	−0.884688	−	0.466184i	$-0.845628\pi$
$367$	−33.8964	−1.76938	−0.884688	+	0.466184i	$0.845628\pi$
$368$	−5.05411	−0.263463
$369$	−0.944193	−0.0491527
$370$	12.7464	0.662654
$371$	12.0106	0.623558
$372$	−0.0309380	−0.00160406
$373$	−5.12346	−0.265283	−0.132641	−	0.991164i	$-0.542346\pi$
$373$	−5.12346	−0.265283	−0.132641	+	0.991164i	$0.542346\pi$
$374$	0.489437	0.0253082
$375$	12.0128	0.620336
$376$	−3.25526	−0.167877
$377$	0	0
$378$	1.29981	0.0668549
$379$	−13.3411	−0.685285	−0.342643	−	0.939466i	$-0.611322\pi$
$379$	−13.3411	−0.685285	−0.342643	+	0.939466i	$0.611322\pi$
$380$	4.26557	0.218819
$381$	14.7776	0.757079
$382$	10.8186	0.553528
$383$	−18.3151	−0.935856	−0.467928	−	0.883767i	$-0.654999\pi$
$383$	−18.3151	−0.935856	−0.467928	+	0.883767i	$0.654999\pi$
$384$	7.99328	0.407906
$385$	4.45450	0.227022
$386$	−22.3791	−1.13907
$387$	7.75243	0.394078
$388$	−4.61326	−0.234203
$389$	7.76659	0.393782	0.196891	−	0.980425i	$-0.436915\pi$
$389$	7.76659	0.393782	0.196891	+	0.980425i	$0.436915\pi$
$390$	0	0
$391$	−0.259454	−0.0131212
$392$	−3.00321	−0.151685
$393$	−13.6465	−0.688376
$394$	18.0107	0.907367
$395$	−20.3068	−1.02175
$396$	0.693822	0.0348659
$397$	−34.9079	−1.75198	−0.875989	−	0.482332i	$-0.839790\pi$
$397$	−34.9079	−1.75198	−0.875989	+	0.482332i	$0.839790\pi$
$398$	16.9791	0.851084
$399$	6.89127	0.344995
$400$	3.36791	0.168396
$401$	13.5850	0.678403	0.339201	−	0.940714i	$-0.389843\pi$
$401$	13.5850	0.678403	0.339201	+	0.940714i	$0.389843\pi$
$402$	11.0724	0.552239
$403$	0	0
$404$	2.16747	0.107836
$405$	−1.99349	−0.0990574
$406$	11.4562	0.568559
$407$	10.9921	0.544856
$408$	0.506079	0.0250546
$409$	−32.2850	−1.59639	−0.798195	−	0.602400i	$-0.794211\pi$
$409$	−32.2850	−1.59639	−0.798195	+	0.602400i	$0.794211\pi$
$410$	2.44655	0.120826
$411$	−8.57759	−0.423101
$412$	−2.59635	−0.127913
$413$	−9.17434	−0.451440
$414$	2.00128	0.0983574
$415$	−0.673952	−0.0330830
$416$	0	0
$417$	2.79628	0.136934
$418$	−20.0153	−0.978982
$419$	−7.57878	−0.370247	−0.185124	−	0.982715i	$-0.559269\pi$
$419$	−7.57878	−0.370247	−0.185124	+	0.982715i	$0.559269\pi$
$420$	0.618982	0.0302032
$421$	−8.75402	−0.426645	−0.213322	−	0.976982i	$-0.568429\pi$
$421$	−8.75402	−0.426645	−0.213322	+	0.976982i	$0.568429\pi$
$422$	1.82203	0.0886949
$423$	1.08393	0.0527024
$424$	−36.0702	−1.75173
$425$	0.172893	0.00838655
$426$	−8.04716	−0.389886
$427$	−3.27054	−0.158272
$428$	−5.19436	−0.251079
$429$	0	0
$430$	−20.0877	−0.968716
$431$	6.43018	0.309731	0.154866	−	0.987936i	$-0.450506\pi$
$431$	6.43018	0.309731	0.154866	+	0.987936i	$0.450506\pi$
$432$	−3.28259	−0.157934
$433$	14.6413	0.703615	0.351808	−	0.936072i	$-0.385567\pi$
$433$	14.6413	0.703615	0.351808	+	0.936072i	$0.385567\pi$
$434$	0.129511	0.00621674
$435$	−17.5701	−0.842422
$436$	2.48463	0.118992
$437$	10.6103	0.507559
$438$	17.1843	0.821099
$439$	27.4546	1.31034	0.655168	−	0.755484i	$-0.272598\pi$
$439$	27.4546	1.31034	0.655168	+	0.755484i	$0.272598\pi$
$440$	−13.3778	−0.637761
$441$	1.00000	0.0476190
$442$	0	0
$443$	25.4047	1.20701	0.603506	−	0.797358i	$-0.293770\pi$
$443$	25.4047	1.20701	0.603506	+	0.797358i	$0.293770\pi$
$444$	1.52742	0.0724881
$445$	−15.8707	−0.752342
$446$	−9.25778	−0.438369
$447$	−0.948225	−0.0448495
$448$	8.82643	0.417009
$449$	−8.66570	−0.408960	−0.204480	−	0.978871i	$-0.565550\pi$
$449$	−8.66570	−0.408960	−0.204480	+	0.978871i	$0.565550\pi$
$450$	−1.33359	−0.0628662
$451$	2.10982	0.0993475
$452$	−0.324551	−0.0152656
$453$	−16.9937	−0.798433
$454$	−17.6232	−0.827096
$455$	0	0
$456$	−20.6959	−0.969174
$457$	31.5437	1.47555	0.737775	−	0.675047i	$-0.235876\pi$
$457$	31.5437	1.47555	0.737775	+	0.675047i	$0.235876\pi$
$458$	16.3804	0.765406
$459$	−0.168513	−0.00786550
$460$	0.953028	0.0444352
$461$	−18.5257	−0.862829	−0.431415	−	0.902154i	$-0.641985\pi$
$461$	−18.5257	−0.862829	−0.431415	+	0.902154i	$0.641985\pi$
$462$	−2.90445	−0.135127
$463$	3.91466	0.181930	0.0909649	−	0.995854i	$-0.471005\pi$
$463$	3.91466	0.181930	0.0909649	+	0.995854i	$0.471005\pi$
$464$	−28.9318	−1.34313
$465$	−0.198629	−0.00921120
$466$	19.4274	0.899955
$467$	−22.9029	−1.05982	−0.529909	−	0.848055i	$-0.677774\pi$
$467$	−22.9029	−1.05982	−0.529909	+	0.848055i	$0.677774\pi$
$468$	0	0
$469$	8.51847	0.393346
$470$	−2.80863	−0.129552
$471$	16.5425	0.762237
$472$	27.5524	1.26820
$473$	−17.3230	−0.796511
$474$	13.2406	0.608159
$475$	−7.07040	−0.324412
$476$	0.0523235	0.00239824
$477$	12.0106	0.549926
$478$	−37.1295	−1.69826
$479$	10.5619	0.482588	0.241294	−	0.970452i	$-0.422428\pi$
$479$	10.5619	0.482588	0.241294	+	0.970452i	$0.422428\pi$
$480$	−3.46804	−0.158294
$481$	0	0
$482$	31.7186	1.44474
$483$	1.53967	0.0700575
$484$	1.86515	0.0847797
$485$	−29.6182	−1.34489
$486$	1.29981	0.0589605
$487$	−10.8592	−0.492076	−0.246038	−	0.969260i	$-0.579129\pi$
$487$	−10.8592	−0.492076	−0.246038	+	0.969260i	$0.579129\pi$
$488$	9.82210	0.444626
$489$	−13.0285	−0.589167
$490$	−2.59115	−0.117056
$491$	19.6903	0.888613	0.444306	−	0.895875i	$-0.353450\pi$
$491$	19.6903	0.888613	0.444306	+	0.895875i	$0.353450\pi$
$492$	0.293173	0.0132173
$493$	−1.48523	−0.0668913
$494$	0	0
$495$	4.45450	0.200215
$496$	−0.327073	−0.0146860
$497$	−6.19104	−0.277706
$498$	0.439434	0.0196915
$499$	23.1892	1.03809	0.519045	−	0.854747i	$-0.326288\pi$
$499$	23.1892	1.03809	0.519045	+	0.854747i	$0.326288\pi$
$500$	−3.72998	−0.166810
$501$	−9.63809	−0.430598
$502$	3.55172	0.158521
$503$	−17.2440	−0.768871	−0.384435	−	0.923152i	$-0.625604\pi$
$503$	−17.2440	−0.768871	−0.384435	+	0.923152i	$0.625604\pi$
$504$	−3.00321	−0.133773
$505$	13.9157	0.619239
$506$	−4.47190	−0.198800
$507$	0	0
$508$	−4.58846	−0.203580
$509$	8.87248	0.393266	0.196633	−	0.980477i	$-0.436999\pi$
$509$	8.87248	0.393266	0.196633	+	0.980477i	$0.436999\pi$
$510$	0.436643	0.0193349
$511$	13.2207	0.584849
$512$	−25.4272	−1.12374
$513$	6.89127	0.304257
$514$	5.69568	0.251226
$515$	−16.6692	−0.734531
$516$	−2.40714	−0.105968
$517$	−2.42206	−0.106522
$518$	−6.39401	−0.280937
$519$	−21.7199	−0.953398
$520$	0	0
$521$	−16.5018	−0.722956	−0.361478	−	0.932381i	$-0.617728\pi$
$521$	−16.5018	−0.722956	−0.361478	+	0.932381i	$0.617728\pi$
$522$	11.4562	0.501422
$523$	−26.6069	−1.16344	−0.581720	−	0.813389i	$-0.697620\pi$
$523$	−26.6069	−1.16344	−0.581720	+	0.813389i	$0.697620\pi$
$524$	4.23726	0.185106
$525$	−1.02599	−0.0447780
$526$	−26.9971	−1.17713
$527$	−0.0167904	−0.000731402 0
$528$	7.33501	0.319215
$529$	−20.6294	−0.896931
$530$	−31.1212	−1.35182
$531$	−9.17434	−0.398133
$532$	−2.13975	−0.0927698
$533$	0	0
$534$	10.3481	0.447805
$535$	−33.3490	−1.44180
$536$	−25.5827	−1.10500
$537$	−14.4043	−0.621593
$538$	26.1876	1.12903
$539$	−2.23452	−0.0962477
$540$	0.618982	0.0266367
$541$	8.60187	0.369823	0.184912	−	0.982755i	$-0.440800\pi$
$541$	8.60187	0.369823	0.184912	+	0.982755i	$0.440800\pi$
$542$	21.0398	0.903739
$543$	0.246871	0.0105942
$544$	−0.293159	−0.0125691
$545$	15.9519	0.683304
$546$	0	0
$547$	−35.2695	−1.50801	−0.754007	−	0.656867i	$-0.771881\pi$
$547$	−35.2695	−1.50801	−0.754007	+	0.656867i	$0.771881\pi$
$548$	2.66335	0.113773
$549$	−3.27054	−0.139583
$550$	2.97994	0.127065
$551$	60.7378	2.58752
$552$	−4.62395	−0.196808
$553$	10.1866	0.433177
$554$	−28.4714	−1.20963
$555$	9.80638	0.416258
$556$	−0.868249	−0.0368219
$557$	29.0820	1.23225	0.616123	−	0.787650i	$-0.288703\pi$
$557$	29.0820	1.23225	0.616123	+	0.787650i	$0.288703\pi$
$558$	0.129511	0.00548265
$559$	0	0
$560$	6.54381	0.276526
$561$	0.376546	0.0158978
$562$	−25.3954	−1.07124
$563$	21.7125	0.915074	0.457537	−	0.889191i	$-0.348732\pi$
$563$	21.7125	0.915074	0.457537	+	0.889191i	$0.348732\pi$
$564$	−0.336561	−0.0141718
$565$	−2.08369	−0.0876616
$566$	31.0682	1.30589
$567$	1.00000	0.0419961
$568$	18.5930	0.780144
$569$	−42.5801	−1.78505	−0.892525	−	0.450998i	$-0.851068\pi$
$569$	−42.5801	−1.78505	−0.892525	+	0.450998i	$0.851068\pi$
$570$	−17.8563	−0.747920
$571$	−14.4690	−0.605509	−0.302754	−	0.953069i	$-0.597906\pi$
$571$	−14.4690	−0.605509	−0.302754	+	0.953069i	$0.597906\pi$
$572$	0	0
$573$	8.32325	0.347709
$574$	−1.22727	−0.0512252
$575$	−1.57969	−0.0658778
$576$	8.82643	0.367768
$577$	12.3774	0.515277	0.257639	−	0.966241i	$-0.417056\pi$
$577$	12.3774	0.515277	0.257639	+	0.966241i	$0.417056\pi$
$578$	−22.0598	−0.917567
$579$	−17.2173	−0.715526
$580$	5.45554	0.226529
$581$	0.338076	0.0140258
$582$	19.3118	0.800502
$583$	−26.8379	−1.11151
$584$	−39.7044	−1.64298
$585$	0	0
$586$	23.3735	0.965550
$587$	−46.2313	−1.90817	−0.954086	−	0.299534i	$-0.903169\pi$
$587$	−46.2313	−1.90817	−0.954086	+	0.299534i	$0.903169\pi$
$588$	−0.310501	−0.0128049
$589$	0.686637	0.0282924
$590$	23.7721	0.978683
$591$	13.8565	0.569978
$592$	16.1477	0.663666
$593$	45.4459	1.86624	0.933120	−	0.359565i	$-0.117075\pi$
$593$	45.4459	1.86624	0.933120	+	0.359565i	$0.117075\pi$
$594$	−2.90445	−0.119171
$595$	0.335929	0.0137717
$596$	0.294425	0.0120601
$597$	13.0628	0.534623
$598$	0	0
$599$	27.7068	1.13207	0.566035	−	0.824381i	$-0.308477\pi$
$599$	27.7068	1.13207	0.566035	+	0.824381i	$0.308477\pi$
$600$	3.08127	0.125792
$601$	34.5036	1.40743	0.703716	−	0.710481i	$-0.251523\pi$
$601$	34.5036	1.40743	0.703716	+	0.710481i	$0.251523\pi$
$602$	10.0767	0.410694
$603$	8.51847	0.346899
$604$	5.27656	0.214700
$605$	11.9747	0.486842
$606$	−9.07337	−0.368580
$607$	22.1561	0.899290	0.449645	−	0.893207i	$-0.351551\pi$
$607$	22.1561	0.899290	0.449645	+	0.893207i	$0.351551\pi$
$608$	11.9886	0.486203
$609$	8.81373	0.357150
$610$	8.47447	0.343121
$611$	0	0
$612$	0.0523235	0.00211505
$613$	8.13812	0.328696	0.164348	−	0.986402i	$-0.447448\pi$
$613$	8.13812	0.328696	0.164348	+	0.986402i	$0.447448\pi$
$614$	37.3078	1.50562
$615$	1.88224	0.0758992
$616$	6.71073	0.270383
$617$	−34.3640	−1.38344	−0.691722	−	0.722164i	$-0.743148\pi$
$617$	−34.3640	−1.38344	−0.691722	+	0.722164i	$0.743148\pi$
$618$	10.8687	0.437204
$619$	−22.8723	−0.919317	−0.459658	−	0.888096i	$-0.652028\pi$
$619$	−22.8723	−0.919317	−0.459658	+	0.888096i	$0.652028\pi$
$620$	0.0616746	0.00247691
$621$	1.53967	0.0617849
$622$	28.6855	1.15018
$623$	7.96124	0.318960
$624$	0	0
$625$	−18.8174	−0.752695
$626$	26.8721	1.07403
$627$	−15.3987	−0.614964
$628$	−5.13646	−0.204967
$629$	0.828948	0.0330523
$630$	−2.59115	−0.103234
$631$	16.5005	0.656874	0.328437	−	0.944526i	$-0.393478\pi$
$631$	16.5005	0.656874	0.328437	+	0.944526i	$0.393478\pi$
$632$	−30.5923	−1.21690
$633$	1.40177	0.0557153
$634$	−28.8164	−1.14444
$635$	−29.4590	−1.16904
$636$	−3.72930	−0.147876
$637$	0	0
$638$	−25.5990	−1.01348
$639$	−6.19104	−0.244914
$640$	−15.9345	−0.629868
$641$	−35.2485	−1.39223	−0.696115	−	0.717930i	$-0.745090\pi$
$641$	−35.2485	−1.39223	−0.696115	+	0.717930i	$0.745090\pi$
$642$	21.7444	0.858183
$643$	4.35068	0.171574	0.0857871	−	0.996313i	$-0.472660\pi$
$643$	4.35068	0.171574	0.0857871	+	0.996313i	$0.472660\pi$
$644$	−0.478070	−0.0188386
$645$	−15.4544	−0.608516
$646$	−1.50942	−0.0593875
$647$	−36.0405	−1.41690	−0.708450	−	0.705761i	$-0.750605\pi$
$647$	−36.0405	−1.41690	−0.708450	+	0.705761i	$0.750605\pi$
$648$	−3.00321	−0.117977
$649$	20.5003	0.804706
$650$	0	0
$651$	0.0996388	0.00390515
$652$	4.04535	0.158428
$653$	−19.4384	−0.760683	−0.380342	−	0.924846i	$-0.624194\pi$
$653$	−19.4384	−0.760683	−0.380342	+	0.924846i	$0.624194\pi$
$654$	−10.4010	−0.406713
$655$	27.2042	1.06296
$656$	3.09939	0.121011
$657$	13.2207	0.515788
$658$	1.40890	0.0549246
$659$	19.6182	0.764217	0.382109	−	0.924117i	$-0.375198\pi$
$659$	19.6182	0.764217	0.382109	+	0.924117i	$0.375198\pi$
$660$	−1.38313	−0.0538382
$661$	6.96154	0.270773	0.135386	−	0.990793i	$-0.456772\pi$
$661$	6.96154	0.270773	0.135386	+	0.990793i	$0.456772\pi$
$662$	−2.20048	−0.0855240
$663$	0	0
$664$	−1.01531	−0.0394018
$665$	−13.7377	−0.532724
$666$	−6.39401	−0.247763
$667$	13.5703	0.525442
$668$	2.99264	0.115789
$669$	−7.12243	−0.275369
$670$	−22.0727	−0.852741
$671$	7.30809	0.282126
$672$	1.73968	0.0671097
$673$	23.6004	0.909728	0.454864	−	0.890561i	$-0.349688\pi$
$673$	23.6004	0.909728	0.454864	+	0.890561i	$0.349688\pi$
$674$	28.3665	1.09264
$675$	−1.02599	−0.0394905
$676$	0	0
$677$	19.0748	0.733105	0.366552	−	0.930397i	$-0.380538\pi$
$677$	19.0748	0.733105	0.366552	+	0.930397i	$0.380538\pi$
$678$	1.35862	0.0521775
$679$	14.8575	0.570177
$680$	−1.00886	−0.0386881
$681$	−13.5583	−0.519555
$682$	−0.289396	−0.0110815
$683$	−17.7879	−0.680633	−0.340317	−	0.940311i	$-0.610534\pi$
$683$	−17.7879	−0.680633	−0.340317	+	0.940311i	$0.610534\pi$
$684$	−2.13975	−0.0818153
$685$	17.0994	0.653333
$686$	1.29981	0.0496269
$687$	12.6022	0.480803
$688$	−25.4480	−0.970196
$689$	0	0
$690$	−3.98953	−0.151879
$691$	−22.9906	−0.874603	−0.437302	−	0.899315i	$-0.644066\pi$
$691$	−22.9906	−0.874603	−0.437302	+	0.899315i	$0.644066\pi$
$692$	6.74406	0.256371
$693$	−2.23452	−0.0848825
$694$	−20.3932	−0.774115
$695$	−5.57436	−0.211448
$696$	−26.4695	−1.00332
$697$	0.159109	0.00602667
$698$	−34.9605	−1.32327
$699$	14.9463	0.565322
$700$	0.318572	0.0120409
$701$	6.30757	0.238234	0.119117	−	0.992880i	$-0.461994\pi$
$701$	6.30757	0.238234	0.119117	+	0.992880i	$0.461994\pi$
$702$	0	0
$703$	−33.8995	−1.27855
$704$	−19.7228	−0.743333
$705$	−2.16080	−0.0813805
$706$	24.8121	0.933817
$707$	−6.98055	−0.262531
$708$	2.84865	0.107059
$709$	−10.9014	−0.409412	−0.204706	−	0.978823i	$-0.565624\pi$
$709$	−10.9014	−0.409412	−0.204706	+	0.978823i	$0.565624\pi$
$710$	16.0419	0.602043
$711$	10.1866	0.382026
$712$	−23.9093	−0.896037
$713$	0.153411	0.00574529
$714$	−0.219034	−0.00819715
$715$	0	0
$716$	4.47257	0.167148
$717$	−28.5654	−1.06679
$718$	31.3031	1.16822
$719$	5.44927	0.203223	0.101612	−	0.994824i	$-0.467600\pi$
$719$	5.44927	0.203223	0.101612	+	0.994824i	$0.467600\pi$
$720$	6.54381	0.243873
$721$	8.36180	0.311410
$722$	37.0310	1.37815
$723$	24.4026	0.907541
$724$	−0.0766537	−0.00284881
$725$	−9.04283	−0.335842
$726$	−7.80783	−0.289776
$727$	33.5071	1.24271	0.621355	−	0.783529i	$-0.286582\pi$
$727$	33.5071	1.24271	0.621355	+	0.783529i	$0.286582\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−34.2568	−1.26790
$731$	−1.30638	−0.0483183
$732$	1.01551	0.0375342
$733$	48.1935	1.78007	0.890033	−	0.455895i	$-0.150681\pi$
$733$	48.1935	1.78007	0.890033	+	0.455895i	$0.150681\pi$
$734$	−44.0587	−1.62624
$735$	−1.99349	−0.0735310
$736$	2.67854	0.0987323
$737$	−19.0347	−0.701152
$738$	−1.22727	−0.0451764
$739$	42.2008	1.55238	0.776190	−	0.630499i	$-0.217150\pi$
$739$	42.2008	1.55238	0.776190	+	0.630499i	$0.217150\pi$
$740$	−3.04489	−0.111933
$741$	0	0
$742$	15.6114	0.573114
$743$	−17.3622	−0.636956	−0.318478	−	0.947930i	$-0.603172\pi$
$743$	−17.3622	−0.636956	−0.318478	+	0.947930i	$0.603172\pi$
$744$	−0.299236	−0.0109705
$745$	1.89028	0.0692544
$746$	−6.65951	−0.243822
$747$	0.338076	0.0123696
$748$	−0.116918	−0.00427494
$749$	16.7289	0.611262
$750$	15.6143	0.570153
$751$	−17.2502	−0.629470	−0.314735	−	0.949180i	$-0.601916\pi$
$751$	−17.2502	−0.629470	−0.314735	+	0.949180i	$0.601916\pi$
$752$	−3.55809	−0.129750
$753$	2.73250	0.0995779
$754$	0	0
$755$	33.8767	1.23290
$756$	−0.310501	−0.0112928
$757$	−27.7065	−1.00701	−0.503506	−	0.863992i	$-0.667957\pi$
$757$	−27.7065	−1.00701	−0.503506	+	0.863992i	$0.667957\pi$
$758$	−17.3408	−0.629847
$759$	−3.44043	−0.124880
$760$	41.2571	1.49655
$761$	6.49989	0.235621	0.117810	−	0.993036i	$-0.462412\pi$
$761$	6.49989	0.235621	0.117810	+	0.993036i	$0.462412\pi$
$762$	19.2080	0.695833
$763$	−8.00198	−0.289691
$764$	−2.58438	−0.0934995
$765$	0.335929	0.0121455
$766$	−23.8061	−0.860148
$767$	0	0
$768$	−7.26312	−0.262085
$769$	−16.2258	−0.585117	−0.292559	−	0.956248i	$-0.594507\pi$
$769$	−16.2258	−0.585117	−0.292559	+	0.956248i	$0.594507\pi$
$770$	5.78999	0.208657
$771$	4.38194	0.157812
$772$	5.34599	0.192406
$773$	−15.1651	−0.545451	−0.272725	−	0.962092i	$-0.587925\pi$
$773$	−15.1651	−0.545451	−0.272725	+	0.962092i	$0.587925\pi$
$774$	10.0767	0.362198
$775$	−0.102229	−0.00367216
$776$	−44.6200	−1.60177
$777$	−4.91920	−0.176475
$778$	10.0951	0.361926
$779$	−6.50668	−0.233126
$780$	0	0
$781$	13.8340	0.495020
$782$	−0.337241	−0.0120597
$783$	8.81373	0.314977
$784$	−3.28259	−0.117235
$785$	−32.9773	−1.17701
$786$	−17.7378	−0.632688
$787$	35.6231	1.26983	0.634913	−	0.772584i	$-0.281036\pi$
$787$	35.6231	1.26983	0.634913	+	0.772584i	$0.281036\pi$
$788$	−4.30245	−0.153268
$789$	−20.7701	−0.739435
$790$	−26.3949	−0.939090
$791$	1.04525	0.0371647
$792$	6.71073	0.238455
$793$	0	0
$794$	−45.3735	−1.61025
$795$	−23.9430	−0.849170
$796$	−4.05600	−0.143761
$797$	27.7190	0.981856	0.490928	−	0.871200i	$-0.336658\pi$
$797$	27.7190	0.981856	0.490928	+	0.871200i	$0.336658\pi$
$798$	8.95732	0.317086
$799$	−0.182656	−0.00646190
$800$	−1.78490	−0.0631059
$801$	7.96124	0.281297
$802$	17.6579	0.623522
$803$	−29.5419	−1.04251
$804$	−2.64500	−0.0932818
$805$	−3.06932	−0.108179
$806$	0	0
$807$	20.1473	0.709218
$808$	20.9640	0.737512
$809$	−53.4008	−1.87747	−0.938735	−	0.344639i	$-0.888001\pi$
$809$	−53.4008	−1.87747	−0.938735	+	0.344639i	$0.888001\pi$
$810$	−2.59115	−0.0910439
$811$	36.7023	1.28879	0.644397	−	0.764691i	$-0.277109\pi$
$811$	36.7023	1.28879	0.644397	+	0.764691i	$0.277109\pi$
$812$	−2.73668	−0.0960385
$813$	16.1869	0.567699
$814$	14.2876	0.500779
$815$	25.9721	0.909763
$816$	0.553158	0.0193644
$817$	53.4241	1.86907
$818$	−41.9642	−1.46725
$819$	0	0
$820$	−0.584438	−0.0204095
$821$	42.0190	1.46647	0.733236	−	0.679974i	$-0.238009\pi$
$821$	42.0190	1.46647	0.733236	+	0.679974i	$0.238009\pi$
$822$	−11.1492	−0.388874
$823$	−51.9482	−1.81080	−0.905400	−	0.424559i	$-0.860429\pi$
$823$	−51.9482	−1.81080	−0.905400	+	0.424559i	$0.860429\pi$
$824$	−25.1122	−0.874825
$825$	2.29261	0.0798183
$826$	−11.9249	−0.414920
$827$	13.0284	0.453042	0.226521	−	0.974006i	$-0.427265\pi$
$827$	13.0284	0.453042	0.226521	+	0.974006i	$0.427265\pi$
$828$	−0.478070	−0.0166141
$829$	−8.22530	−0.285677	−0.142838	−	0.989746i	$-0.545623\pi$
$829$	−8.22530	−0.285677	−0.142838	+	0.989746i	$0.545623\pi$
$830$	−0.876008	−0.0304067
$831$	−21.9043	−0.759853
$832$	0	0
$833$	−0.168513	−0.00583862
$834$	3.63463	0.125857
$835$	19.2134	0.664909
$836$	4.78131	0.165365
$837$	0.0996388	0.00344402
$838$	−9.85095	−0.340295
$839$	−39.8317	−1.37514	−0.687572	−	0.726116i	$-0.741324\pi$
$839$	−39.8317	−1.37514	−0.687572	+	0.726116i	$0.741324\pi$
$840$	5.98686	0.206566
$841$	48.6819	1.67869
$842$	−11.3785	−0.392130
$843$	−19.5379	−0.672920
$844$	−0.435251	−0.0149819
$845$	0	0
$846$	1.40890	0.0484389
$847$	−6.00691	−0.206400
$848$	−39.4257	−1.35389
$849$	23.9022	0.820320
$850$	0.224728	0.00770809
$851$	−7.57395	−0.259632
$852$	1.92233	0.0658578
$853$	31.4971	1.07844	0.539220	−	0.842165i	$-0.318719\pi$
$853$	31.4971	1.07844	0.539220	+	0.842165i	$0.318719\pi$
$854$	−4.25107	−0.145469
$855$	−13.7377	−0.469819
$856$	−50.2405	−1.71718
$857$	24.9026	0.850658	0.425329	−	0.905039i	$-0.360158\pi$
$857$	24.9026	0.850658	0.425329	+	0.905039i	$0.360158\pi$
$858$	0	0
$859$	57.6219	1.96603	0.983016	−	0.183519i	$-0.0587490\pi$
$859$	57.6219	1.96603	0.983016	+	0.183519i	$0.0587490\pi$
$860$	4.79861	0.163631
$861$	−0.944193	−0.0321780
$862$	8.35800	0.284675
$863$	42.6303	1.45115	0.725576	−	0.688142i	$-0.241573\pi$
$863$	42.6303	1.45115	0.725576	+	0.688142i	$0.241573\pi$
$864$	1.73968	0.0591852
$865$	43.2984	1.47219
$866$	19.0309	0.646695
$867$	−16.9716	−0.576386
$868$	−0.0309380	−0.00105010
$869$	−22.7621	−0.772151
$870$	−22.8377	−0.774272
$871$	0	0
$872$	24.0316	0.813813
$873$	14.8575	0.502849
$874$	13.7913	0.466499
$875$	12.0128	0.406106
$876$	−4.10504	−0.138696
$877$	44.6625	1.50814	0.754072	−	0.656792i	$-0.228087\pi$
$877$	44.6625	1.50814	0.754072	+	0.656792i	$0.228087\pi$
$878$	35.6856	1.20433
$879$	17.9823	0.606527
$880$	−14.6223	−0.492917
$881$	−9.04872	−0.304859	−0.152430	−	0.988314i	$-0.548710\pi$
$881$	−9.04872	−0.304859	−0.152430	+	0.988314i	$0.548710\pi$
$882$	1.29981	0.0437668
$883$	0.876086	0.0294826	0.0147413	−	0.999891i	$-0.495308\pi$
$883$	0.876086	0.0294826	0.0147413	+	0.999891i	$0.495308\pi$
$884$	0	0
$885$	18.2890	0.614777
$886$	33.0212	1.10937
$887$	−14.8426	−0.498366	−0.249183	−	0.968456i	$-0.580162\pi$
$887$	−14.8426	−0.498366	−0.249183	+	0.968456i	$0.580162\pi$
$888$	14.7734	0.495762
$889$	14.7776	0.495625
$890$	−20.6288	−0.691479
$891$	−2.23452	−0.0748593
$892$	2.21152	0.0740473
$893$	7.46964	0.249962
$894$	−1.23251	−0.0412213
$895$	28.7149	0.959834
$896$	7.99328	0.267037
$897$	0	0
$898$	−11.2637	−0.375876
$899$	0.878189	0.0292893
$900$	0.318572	0.0106191
$901$	−2.02394	−0.0674271
$902$	2.74236	0.0913105
$903$	7.75243	0.257985
$904$	−3.13910	−0.104405
$905$	−0.492135	−0.0163591
$906$	−22.0885	−0.733841
$907$	30.2415	1.00415	0.502076	−	0.864824i	$-0.332570\pi$
$907$	30.2415	1.00415	0.502076	+	0.864824i	$0.332570\pi$
$908$	4.20987	0.139709
$909$	−6.98055	−0.231530
$910$	0	0
$911$	1.72413	0.0571229	0.0285614	−	0.999592i	$-0.490907\pi$
$911$	1.72413	0.0571229	0.0285614	+	0.999592i	$0.490907\pi$
$912$	−22.6212	−0.749062
$913$	−0.755439	−0.0250014
$914$	41.0007	1.35618
$915$	6.51979	0.215538
$916$	−3.91299	−0.129289
$917$	−13.6465	−0.450648
$918$	−0.219034	−0.00722920
$919$	−14.1914	−0.468131	−0.234066	−	0.972221i	$-0.575203\pi$
$919$	−14.1914	−0.468131	−0.234066	+	0.972221i	$0.575203\pi$
$920$	9.21781	0.303902
$921$	28.7026	0.945782
$922$	−24.0799	−0.793029
$923$	0	0
$924$	0.693822	0.0228251
$925$	5.04707	0.165947
$926$	5.08831	0.167212
$927$	8.36180	0.274638
$928$	15.3331	0.503334
$929$	46.0189	1.50983	0.754916	−	0.655821i	$-0.227678\pi$
$929$	46.0189	1.50983	0.754916	+	0.655821i	$0.227678\pi$
$930$	−0.258179	−0.00846603
$931$	6.89127	0.225852
$932$	−4.64086	−0.152016
$933$	22.0690	0.722507
$934$	−29.7693	−0.974081
$935$	−0.750640	−0.0245486
$936$	0	0
$937$	45.9281	1.50041	0.750203	−	0.661208i	$-0.229956\pi$
$937$	45.9281	1.50041	0.750203	+	0.661208i	$0.229956\pi$
$938$	11.0724	0.361525
$939$	20.6739	0.674668
$940$	0.670932	0.0218834
$941$	−10.3266	−0.336638	−0.168319	−	0.985733i	$-0.553834\pi$
$941$	−10.3266	−0.336638	−0.168319	+	0.985733i	$0.553834\pi$
$942$	21.5020	0.700574
$943$	−1.45375	−0.0473405
$944$	30.1156	0.980179
$945$	−1.99349	−0.0648483
$946$	−22.5165	−0.732075
$947$	38.6597	1.25627	0.628135	−	0.778104i	$-0.283818\pi$
$947$	38.6597	1.25627	0.628135	+	0.778104i	$0.283818\pi$
$948$	−3.16294	−0.102728
$949$	0	0
$950$	−9.19015	−0.298168
$951$	−22.1697	−0.718903
$952$	0.506079	0.0164021
$953$	3.49088	0.113081	0.0565404	−	0.998400i	$-0.481993\pi$
$953$	3.49088	0.113081	0.0565404	+	0.998400i	$0.481993\pi$
$954$	15.6114	0.505439
$955$	−16.5923	−0.536915
$956$	8.86958	0.286863
$957$	−19.6945	−0.636632
$958$	13.7285	0.443548
$959$	−8.57759	−0.276985
$960$	−17.5954	−0.567889
$961$	−30.9901	−0.999680
$962$	0	0
$963$	16.7289	0.539082
$964$	−7.57703	−0.244040
$965$	34.3225	1.10488
$966$	2.00128	0.0643900
$967$	−27.3810	−0.880513	−0.440257	−	0.897872i	$-0.645113\pi$
$967$	−27.3810	−0.880513	−0.440257	+	0.897872i	$0.645113\pi$
$968$	18.0400	0.579827
$969$	−1.16127	−0.0373053
$970$	−38.4980	−1.23610
$971$	−35.1329	−1.12747	−0.563735	−	0.825956i	$-0.690636\pi$
$971$	−35.1329	−1.12747	−0.563735	+	0.825956i	$0.690636\pi$
$972$	−0.310501	−0.00995933
$973$	2.79628	0.0896446
$974$	−14.1148	−0.452268
$975$	0	0
$976$	10.7358	0.343645
$977$	−16.4403	−0.525973	−0.262987	−	0.964799i	$-0.584707\pi$
$977$	−16.4403	−0.525973	−0.262987	+	0.964799i	$0.584707\pi$
$978$	−16.9345	−0.541505
$979$	−17.7896	−0.568557
$980$	0.618982	0.0197726
$981$	−8.00198	−0.255484
$982$	25.5936	0.816726
$983$	−15.8250	−0.504739	−0.252370	−	0.967631i	$-0.581210\pi$
$983$	−15.8250	−0.504739	−0.252370	+	0.967631i	$0.581210\pi$
$984$	2.83561	0.0903958
$985$	−27.6227	−0.880133
$986$	−1.93051	−0.0614799
$987$	1.08393	0.0345018
$988$	0	0
$989$	11.9362	0.379549
$990$	5.78999	0.184018
$991$	−27.8250	−0.883890	−0.441945	−	0.897042i	$-0.645711\pi$
$991$	−27.8250	−0.883890	−0.441945	+	0.897042i	$0.645711\pi$
$992$	0.173340	0.00550355
$993$	−1.69293	−0.0537234
$994$	−8.04716	−0.255240
$995$	−26.0405	−0.825539
$996$	−0.104973	−0.00332620
$997$	−36.7129	−1.16271	−0.581355	−	0.813650i	$-0.697477\pi$
$997$	−36.7129	−1.16271	−0.581355	+	0.813650i	$0.697477\pi$
$998$	30.1414	0.954110
$999$	−4.91920	−0.155637

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bg.1.11	✓	15
13.12	even	2		3549.2.a.bh.1.5	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.11	✓	15	1.1	even	1	trivial
3549.2.a.bh.1.5	yes	15	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)

\(f(q)\)	\(=\)	\(q+1.29981 q^{2} +1.00000 q^{3} -0.310501 q^{4} -1.99349 q^{5} +1.29981 q^{6} +1.00000 q^{7} -3.00321 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.29981 q^{2} +1.00000 q^{3} -0.310501 q^{4} -1.99349 q^{5} +1.29981 q^{6} +1.00000 q^{7} -3.00321 q^{8} +1.00000 q^{9} -2.59115 q^{10} -2.23452 q^{11} -0.310501 q^{12} +1.29981 q^{14} -1.99349 q^{15} -3.28259 q^{16} -0.168513 q^{17} +1.29981 q^{18} +6.89127 q^{19} +0.618982 q^{20} +1.00000 q^{21} -2.90445 q^{22} +1.53967 q^{23} -3.00321 q^{24} -1.02599 q^{25} +1.00000 q^{27} -0.310501 q^{28} +8.81373 q^{29} -2.59115 q^{30} +0.0996388 q^{31} +1.73968 q^{32} -2.23452 q^{33} -0.219034 q^{34} -1.99349 q^{35} -0.310501 q^{36} -4.91920 q^{37} +8.95732 q^{38} +5.98686 q^{40} -0.944193 q^{41} +1.29981 q^{42} +7.75243 q^{43} +0.693822 q^{44} -1.99349 q^{45} +2.00128 q^{46} +1.08393 q^{47} -3.28259 q^{48} +1.00000 q^{49} -1.33359 q^{50} -0.168513 q^{51} +12.0106 q^{53} +1.29981 q^{54} +4.45450 q^{55} -3.00321 q^{56} +6.89127 q^{57} +11.4562 q^{58} -9.17434 q^{59} +0.618982 q^{60} -3.27054 q^{61} +0.129511 q^{62} +1.00000 q^{63} +8.82643 q^{64} -2.90445 q^{66} +8.51847 q^{67} +0.0523235 q^{68} +1.53967 q^{69} -2.59115 q^{70} -6.19104 q^{71} -3.00321 q^{72} +13.2207 q^{73} -6.39401 q^{74} -1.02599 q^{75} -2.13975 q^{76} -2.23452 q^{77} +10.1866 q^{79} +6.54381 q^{80} +1.00000 q^{81} -1.22727 q^{82} +0.338076 q^{83} -0.310501 q^{84} +0.335929 q^{85} +10.0767 q^{86} +8.81373 q^{87} +6.71073 q^{88} +7.96124 q^{89} -2.59115 q^{90} -0.478070 q^{92} +0.0996388 q^{93} +1.40890 q^{94} -13.7377 q^{95} +1.73968 q^{96} +14.8575 q^{97} +1.29981 q^{98} -2.23452 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

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