LMFDB - Embedded newform 3549.2.a.s.1.2

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:	$3$
Coefficient field:	3.3.169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x - 1 $ x^3 - x^2 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.273891$ 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)

$f(q)$	$=$	$q+1.27389 q^{2} -1.00000 q^{3} -0.377203 q^{4} -1.10331 q^{5} -1.27389 q^{6} +1.00000 q^{7} -3.02830 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.27389 q^{2} -1.00000 q^{3} -0.377203 q^{4} -1.10331 q^{5} -1.27389 q^{6} +1.00000 q^{7} -3.02830 q^{8} +1.00000 q^{9} -1.40550 q^{10} +0.348907 q^{11} +0.377203 q^{12} +1.27389 q^{14} +1.10331 q^{15} -3.10331 q^{16} +0.726109 q^{17} +1.27389 q^{18} -2.30219 q^{19} +0.416173 q^{20} -1.00000 q^{21} +0.444469 q^{22} +0.0750160 q^{23} +3.02830 q^{24} -3.78270 q^{25} -1.00000 q^{27} -0.377203 q^{28} +0.480515 q^{29} +1.40550 q^{30} +6.85772 q^{31} +2.10331 q^{32} -0.348907 q^{33} +0.924984 q^{34} -1.10331 q^{35} -0.377203 q^{36} +1.10331 q^{37} -2.93273 q^{38} +3.34116 q^{40} -3.09556 q^{41} -1.27389 q^{42} -4.62280 q^{43} -0.131609 q^{44} -1.10331 q^{45} +0.0955622 q^{46} -4.70769 q^{47} +3.10331 q^{48} +1.00000 q^{49} -4.81875 q^{50} -0.726109 q^{51} +5.54778 q^{53} -1.27389 q^{54} -0.384953 q^{55} -3.02830 q^{56} +2.30219 q^{57} +0.612124 q^{58} +3.92498 q^{59} -0.416173 q^{60} +5.54778 q^{61} +8.73598 q^{62} +1.00000 q^{63} +8.88601 q^{64} -0.444469 q^{66} -8.12386 q^{67} -0.273891 q^{68} -0.0750160 q^{69} -1.40550 q^{70} +9.52936 q^{71} -3.02830 q^{72} +10.4338 q^{73} +1.40550 q^{74} +3.78270 q^{75} +0.868391 q^{76} +0.348907 q^{77} +17.1054 q^{79} +3.42392 q^{80} +1.00000 q^{81} -3.94341 q^{82} +11.9143 q^{83} +0.377203 q^{84} -0.801125 q^{85} -5.88894 q^{86} -0.480515 q^{87} -1.05659 q^{88} +11.9610 q^{89} -1.40550 q^{90} -0.0282963 q^{92} -6.85772 q^{93} -5.99708 q^{94} +2.54003 q^{95} -2.10331 q^{96} -10.1033 q^{97} +1.27389 q^{98} +0.348907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 13 q^{10} + 8 q^{11} - 4 q^{12} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 7 q^{19} + 13 q^{20} - 3 q^{21} + q^{22} + 9 q^{23} - 3 q^{24} + 11 q^{25} - 3 q^{27} + 4 q^{28} - 7 q^{29} - 13 q^{30} + 7 q^{31} + 3 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} - 4 q^{38} + 13 q^{40} - 2 q^{41} - 2 q^{42} - 19 q^{43} + 15 q^{44} - 7 q^{46} + 17 q^{47} + 6 q^{48} + 3 q^{49} + 16 q^{50} - 4 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} - 7 q^{57} - 22 q^{58} + 3 q^{59} - 13 q^{60} + 13 q^{61} - 17 q^{62} + 3 q^{63} + q^{64} - q^{66} - 5 q^{67} + q^{68} - 9 q^{69} + 13 q^{70} - 8 q^{71} + 3 q^{72} + 2 q^{73} - 13 q^{74} - 11 q^{75} + 18 q^{76} + 8 q^{77} - q^{79} + 26 q^{80} + 3 q^{81} - 36 q^{82} - 2 q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} + 7 q^{87} + 21 q^{88} + 19 q^{89} + 13 q^{90} + 12 q^{92} - 7 q^{93} + 7 q^{94} - 3 q^{96} - 27 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 13 * q^10 + 8 * q^11 - 4 * q^12 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 7 * q^19 + 13 * q^20 - 3 * q^21 + q^22 + 9 * q^23 - 3 * q^24 + 11 * q^25 - 3 * q^27 + 4 * q^28 - 7 * q^29 - 13 * q^30 + 7 * q^31 + 3 * q^32 - 8 * q^33 - 6 * q^34 + 4 * q^36 - 4 * q^38 + 13 * q^40 - 2 * q^41 - 2 * q^42 - 19 * q^43 + 15 * q^44 - 7 * q^46 + 17 * q^47 + 6 * q^48 + 3 * q^49 + 16 * q^50 - 4 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 - 7 * q^57 - 22 * q^58 + 3 * q^59 - 13 * q^60 + 13 * q^61 - 17 * q^62 + 3 * q^63 + q^64 - q^66 - 5 * q^67 + q^68 - 9 * q^69 + 13 * q^70 - 8 * q^71 + 3 * q^72 + 2 * q^73 - 13 * q^74 - 11 * q^75 + 18 * q^76 + 8 * q^77 - q^79 + 26 * q^80 + 3 * q^81 - 36 * q^82 - 2 * q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 + 7 * q^87 + 21 * q^88 + 19 * q^89 + 13 * q^90 + 12 * q^92 - 7 * q^93 + 7 * q^94 - 3 * q^96 - 27 * q^97 + 2 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.27389	0.900777	0.450388	−	0.892833i	$-0.351286\pi$
$2$	1.27389	0.900777	0.450388	+	0.892833i	$0.351286\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.377203	−0.188601
$5$	−1.10331	−0.493416	−0.246708	−	0.969090i	$-0.579349\pi$
$5$	−1.10331	−0.493416	−0.246708	+	0.969090i	$0.579349\pi$
$6$	−1.27389	−0.520064
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.02830	−1.07066
$9$	1.00000	0.333333
$10$	−1.40550	−0.444458
$11$	0.348907	0.105199	0.0525996	−	0.998616i	$-0.483249\pi$
$11$	0.348907	0.105199	0.0525996	+	0.998616i	$0.483249\pi$
$12$	0.377203	0.108889
$13$	0	0
$13$	0	0
$14$	1.27389	0.340462
$15$	1.10331	0.284874
$16$	−3.10331	−0.775828
$17$	0.726109	0.176107	0.0880537	−	0.996116i	$-0.471935\pi$
$17$	0.726109	0.176107	0.0880537	+	0.996116i	$0.471935\pi$
$18$	1.27389	0.300259
$19$	−2.30219	−0.528158	−0.264079	−	0.964501i	$-0.585068\pi$
$19$	−2.30219	−0.528158	−0.264079	+	0.964501i	$0.585068\pi$
$20$	0.416173	0.0930590
$21$	−1.00000	−0.218218
$22$	0.444469	0.0947611
$23$	0.0750160	0.0156419	0.00782096	−	0.999969i	$-0.497510\pi$
$23$	0.0750160	0.0156419	0.00782096	+	0.999969i	$0.497510\pi$
$24$	3.02830	0.618148
$25$	−3.78270	−0.756540
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−0.377203	−0.0712846
$29$	0.480515	0.0892294	0.0446147	−	0.999004i	$-0.485794\pi$
$29$	0.480515	0.0892294	0.0446147	+	0.999004i	$0.485794\pi$
$30$	1.40550	0.256608
$31$	6.85772	1.23168	0.615841	−	0.787870i	$-0.288816\pi$
$31$	6.85772	1.23168	0.615841	+	0.787870i	$0.288816\pi$
$32$	2.10331	0.371817
$33$	−0.348907	−0.0607368
$34$	0.924984	0.158633
$35$	−1.10331	−0.186494
$36$	−0.377203	−0.0628671
$37$	1.10331	0.181383	0.0906917	−	0.995879i	$-0.471092\pi$
$37$	1.10331	0.181383	0.0906917	+	0.995879i	$0.471092\pi$
$38$	−2.93273	−0.475752
$39$	0	0
$40$	3.34116	0.528283
$41$	−3.09556	−0.483446	−0.241723	−	0.970345i	$-0.577712\pi$
$41$	−3.09556	−0.483446	−0.241723	+	0.970345i	$0.577712\pi$
$42$	−1.27389	−0.196566
$43$	−4.62280	−0.704970	−0.352485	−	0.935817i	$-0.614663\pi$
$43$	−4.62280	−0.704970	−0.352485	+	0.935817i	$0.614663\pi$
$44$	−0.131609	−0.0198407
$45$	−1.10331	−0.164472
$46$	0.0955622	0.0140899
$47$	−4.70769	−0.686687	−0.343343	−	0.939210i	$-0.611559\pi$
$47$	−4.70769	−0.686687	−0.343343	+	0.939210i	$0.611559\pi$
$48$	3.10331	0.447925
$49$	1.00000	0.142857
$50$	−4.81875	−0.681474
$51$	−0.726109	−0.101676
$52$	0	0
$53$	5.54778	0.762046	0.381023	−	0.924565i	$-0.375572\pi$
$53$	5.54778	0.762046	0.381023	+	0.924565i	$0.375572\pi$
$54$	−1.27389	−0.173355
$55$	−0.384953	−0.0519070
$56$	−3.02830	−0.404673
$57$	2.30219	0.304932
$58$	0.612124	0.0803758
$59$	3.92498	0.510989	0.255495	−	0.966810i	$-0.417762\pi$
$59$	3.92498	0.510989	0.255495	+	0.966810i	$0.417762\pi$
$60$	−0.416173	−0.0537276
$61$	5.54778	0.710321	0.355160	−	0.934805i	$-0.384426\pi$
$61$	5.54778	0.710321	0.355160	+	0.934805i	$0.384426\pi$
$62$	8.73598	1.10947
$63$	1.00000	0.125988
$64$	8.88601	1.11075
$65$	0	0
$66$	−0.444469	−0.0547103
$67$	−8.12386	−0.992487	−0.496244	−	0.868183i	$-0.665288\pi$
$67$	−8.12386	−0.992487	−0.496244	+	0.868183i	$0.665288\pi$
$68$	−0.273891	−0.0332141
$69$	−0.0750160	−0.00903087
$70$	−1.40550	−0.167989
$71$	9.52936	1.13093	0.565463	−	0.824773i	$-0.308697\pi$
$71$	9.52936	1.13093	0.565463	+	0.824773i	$0.308697\pi$
$72$	−3.02830	−0.356888
$73$	10.4338	1.22118	0.610592	−	0.791946i	$-0.290932\pi$
$73$	10.4338	1.22118	0.610592	+	0.791946i	$0.290932\pi$
$74$	1.40550	0.163386
$75$	3.78270	0.436789
$76$	0.868391	0.0996113
$77$	0.348907	0.0397616
$78$	0	0
$79$	17.1054	1.92451	0.962256	−	0.272146i	$-0.0877335\pi$
$79$	17.1054	1.92451	0.962256	+	0.272146i	$0.0877335\pi$
$80$	3.42392	0.382806
$81$	1.00000	0.111111
$82$	−3.94341	−0.435477
$83$	11.9143	1.30777	0.653883	−	0.756596i	$-0.273139\pi$
$83$	11.9143	1.30777	0.653883	+	0.756596i	$0.273139\pi$
$84$	0.377203	0.0411562
$85$	−0.801125	−0.0868943
$86$	−5.88894	−0.635020
$87$	−0.480515	−0.0515166
$88$	−1.05659	−0.112633
$89$	11.9610	1.26787	0.633933	−	0.773388i	$-0.281439\pi$
$89$	11.9610	1.26787	0.633933	+	0.773388i	$0.281439\pi$
$90$	−1.40550	−0.148153
$91$	0	0
$92$	−0.0282963	−0.00295009
$93$	−6.85772	−0.711112
$94$	−5.99708	−0.618551
$95$	2.54003	0.260602
$96$	−2.10331	−0.214668
$97$	−10.1033	−1.02584	−0.512918	−	0.858438i	$-0.671436\pi$
$97$	−10.1033	−1.02584	−0.512918	+	0.858438i	$0.671436\pi$
$98$	1.27389	0.128682
$99$	0.348907	0.0350664
$100$	1.42685	0.142685
$101$	4.07502	0.405479	0.202740	−	0.979233i	$-0.435015\pi$
$101$	4.07502	0.405479	0.202740	+	0.979233i	$0.435015\pi$
$102$	−0.924984	−0.0915871
$103$	−4.11106	−0.405075	−0.202538	−	0.979275i	$-0.564919\pi$
$103$	−4.11106	−0.405075	−0.202538	+	0.979275i	$0.564919\pi$
$104$	0	0
$105$	1.10331	0.107672
$106$	7.06727	0.686434
$107$	−6.17058	−0.596532	−0.298266	−	0.954483i	$-0.596408\pi$
$107$	−6.17058	−0.596532	−0.298266	+	0.954483i	$0.596408\pi$
$108$	0.377203	0.0362964
$109$	8.82167	0.844963	0.422481	−	0.906372i	$-0.361159\pi$
$109$	8.82167	0.844963	0.422481	+	0.906372i	$0.361159\pi$
$110$	−0.490388	−0.0467567
$111$	−1.10331	−0.104722
$112$	−3.10331	−0.293235
$113$	12.0099	1.12979	0.564897	−	0.825161i	$-0.308916\pi$
$113$	12.0099	1.12979	0.564897	+	0.825161i	$0.308916\pi$
$114$	2.93273	0.274676
$115$	−0.0827661	−0.00771798
$116$	−0.181252	−0.0168288
$117$	0	0
$118$	5.00000	0.460287
$119$	0.726109	0.0665623
$120$	−3.34116	−0.305004
$121$	−10.8783	−0.988933
$122$	7.06727	0.639840
$123$	3.09556	0.279117
$124$	−2.58675	−0.232297
$125$	9.69006	0.866706
$126$	1.27389	0.113487
$127$	−5.85772	−0.519788	−0.259894	−	0.965637i	$-0.583688\pi$
$127$	−5.85772	−0.519788	−0.259894	+	0.965637i	$0.583688\pi$
$128$	7.11319	0.628723
$129$	4.62280	0.407015
$130$	0	0
$131$	22.4055	1.95758	0.978789	−	0.204872i	$-0.0656778\pi$
$131$	22.4055	1.95758	0.978789	+	0.204872i	$0.0656778\pi$
$132$	0.131609	0.0114551
$133$	−2.30219	−0.199625
$134$	−10.3489	−0.894009
$135$	1.10331	0.0949580
$136$	−2.19887	−0.188552
$137$	−20.2087	−1.72655	−0.863275	−	0.504734i	$-0.831591\pi$
$137$	−20.2087	−1.72655	−0.863275	+	0.504734i	$0.831591\pi$
$138$	−0.0955622	−0.00813480
$139$	4.27389	0.362507	0.181253	−	0.983436i	$-0.441985\pi$
$139$	4.27389	0.362507	0.181253	+	0.983436i	$0.441985\pi$
$140$	0.416173	0.0351730
$141$	4.70769	0.396459
$142$	12.1394	1.01871
$143$	0	0
$144$	−3.10331	−0.258609
$145$	−0.530158	−0.0440272
$146$	13.2915	1.10001
$147$	−1.00000	−0.0824786
$148$	−0.416173	−0.0342092
$149$	4.89669	0.401152	0.200576	−	0.979678i	$-0.435719\pi$
$149$	4.89669	0.401152	0.200576	+	0.979678i	$0.435719\pi$
$150$	4.81875	0.393449
$151$	8.94553	0.727977	0.363988	−	0.931403i	$-0.381415\pi$
$151$	8.94553	0.727977	0.363988	+	0.931403i	$0.381415\pi$
$152$	6.97170	0.565480
$153$	0.726109	0.0587025
$154$	0.444469	0.0358163
$155$	−7.56620	−0.607732
$156$	0	0
$157$	6.59450	0.526298	0.263149	−	0.964755i	$-0.415239\pi$
$157$	6.59450	0.526298	0.263149	+	0.964755i	$0.415239\pi$
$158$	21.7905	1.73356
$159$	−5.54778	−0.439968
$160$	−2.32061	−0.183460
$161$	0.0750160	0.00591209
$162$	1.27389	0.100086
$163$	9.90444	0.775775	0.387888	−	0.921707i	$-0.373205\pi$
$163$	9.90444	0.775775	0.387888	+	0.921707i	$0.373205\pi$
$164$	1.16765	0.0911785
$165$	0.384953	0.0299685
$166$	15.1775	1.17800
$167$	16.7565	1.29666	0.648330	−	0.761360i	$-0.275468\pi$
$167$	16.7565	1.29666	0.648330	+	0.761360i	$0.275468\pi$
$168$	3.02830	0.233638
$169$	0	0
$170$	−1.02055	−0.0782723
$171$	−2.30219	−0.176053
$172$	1.74373	0.132958
$173$	13.7184	1.04299	0.521494	−	0.853255i	$-0.325375\pi$
$173$	13.7184	1.04299	0.521494	+	0.853255i	$0.325375\pi$
$174$	−0.612124	−0.0464050
$175$	−3.78270	−0.285945
$176$	−1.08277	−0.0816166
$177$	−3.92498	−0.295020
$178$	15.2370	1.14206
$179$	−22.0304	−1.64663	−0.823315	−	0.567584i	$-0.807878\pi$
$179$	−22.0304	−1.64663	−0.823315	+	0.567584i	$0.807878\pi$
$180$	0.416173	0.0310197
$181$	9.43380	0.701208	0.350604	−	0.936524i	$-0.385976\pi$
$181$	9.43380	0.701208	0.350604	+	0.936524i	$0.385976\pi$
$182$	0	0
$183$	−5.54778	−0.410104
$184$	−0.227171	−0.0167473
$185$	−1.21730	−0.0894975
$186$	−8.73598	−0.640553
$187$	0.253344	0.0185264
$188$	1.77575	0.129510
$189$	−1.00000	−0.0727393
$190$	3.23572	0.234744
$191$	−3.37720	−0.244366	−0.122183	−	0.992508i	$-0.538989\pi$
$191$	−3.37720	−0.244366	−0.122183	+	0.992508i	$0.538989\pi$
$192$	−8.88601	−0.641293
$193$	−22.3227	−1.60683	−0.803413	−	0.595423i	$-0.796985\pi$
$193$	−22.3227	−1.60683	−0.803413	+	0.595423i	$0.796985\pi$
$194$	−12.8705	−0.924049
$195$	0	0
$196$	−0.377203	−0.0269431
$197$	25.4514	1.81334	0.906669	−	0.421842i	$-0.138616\pi$
$197$	25.4514	1.81334	0.906669	+	0.421842i	$0.138616\pi$
$198$	0.444469	0.0315870
$199$	−22.3404	−1.58367	−0.791833	−	0.610738i	$-0.790873\pi$
$199$	−22.3404	−1.58367	−0.791833	+	0.610738i	$0.790873\pi$
$200$	11.4551	0.810001
$201$	8.12386	0.573013
$202$	5.19112	0.365246
$203$	0.480515	0.0337256
$204$	0.273891	0.0191762
$205$	3.41537	0.238540
$206$	−5.23704	−0.364882
$207$	0.0750160	0.00521397
$208$	0	0
$209$	−0.803248	−0.0555618
$210$	1.40550	0.0969887
$211$	10.0382	0.691056	0.345528	−	0.938408i	$-0.387700\pi$
$211$	10.0382	0.691056	0.345528	+	0.938408i	$0.387700\pi$
$212$	−2.09264	−0.143723
$213$	−9.52936	−0.652941
$214$	−7.86064	−0.537342
$215$	5.10039	0.347844
$216$	3.02830	0.206049
$217$	6.85772	0.465532
$218$	11.2378	0.761123
$219$	−10.4338	−0.705051
$220$	0.145205	0.00978974
$221$	0	0
$222$	−1.40550	−0.0943309
$223$	5.13453	0.343834	0.171917	−	0.985111i	$-0.445004\pi$
$223$	5.13453	0.343834	0.171917	+	0.985111i	$0.445004\pi$
$224$	2.10331	0.140533
$225$	−3.78270	−0.252180
$226$	15.2993	1.01769
$227$	28.9709	1.92287	0.961433	−	0.275039i	$-0.0886906\pi$
$227$	28.9709	1.92287	0.961433	+	0.275039i	$0.0886906\pi$
$228$	−0.868391	−0.0575106
$229$	−0.679390	−0.0448953	−0.0224477	−	0.999748i	$-0.507146\pi$
$229$	−0.679390	−0.0448953	−0.0224477	+	0.999748i	$0.507146\pi$
$230$	−0.105435	−0.00695218
$231$	−0.348907	−0.0229564
$232$	−1.45514	−0.0955348
$233$	−18.3022	−1.19902	−0.599508	−	0.800369i	$-0.704637\pi$
$233$	−18.3022	−1.19902	−0.599508	+	0.800369i	$0.704637\pi$
$234$	0	0
$235$	5.19405	0.338822
$236$	−1.48052	−0.0963733
$237$	−17.1054	−1.11112
$238$	0.924984	0.0599578
$239$	5.45222	0.352675	0.176337	−	0.984330i	$-0.443575\pi$
$239$	5.45222	0.352675	0.176337	+	0.984330i	$0.443575\pi$
$240$	−3.42392	−0.221013
$241$	15.4621	0.996001	0.498000	−	0.867177i	$-0.334068\pi$
$241$	15.4621	0.996001	0.498000	+	0.867177i	$0.334068\pi$
$242$	−13.8577	−0.890808
$243$	−1.00000	−0.0641500
$244$	−2.09264	−0.133967
$245$	−1.10331	−0.0704880
$246$	3.94341	0.251422
$247$	0	0
$248$	−20.7672	−1.31872
$249$	−11.9143	−0.755039
$250$	12.3441	0.780708
$251$	−8.29444	−0.523540	−0.261770	−	0.965130i	$-0.584306\pi$
$251$	−8.29444	−0.523540	−0.261770	+	0.965130i	$0.584306\pi$
$252$	−0.377203	−0.0237615
$253$	0.0261736	0.00164552
$254$	−7.46209	−0.468213
$255$	0.801125	0.0501684
$256$	−8.71061	−0.544413
$257$	−15.0382	−0.938055	−0.469028	−	0.883184i	$-0.655396\pi$
$257$	−15.0382	−0.938055	−0.469028	+	0.883184i	$0.655396\pi$
$258$	5.88894	0.366629
$259$	1.10331	0.0685565
$260$	0	0
$261$	0.480515	0.0297431
$262$	28.5422	1.76334
$263$	−17.2448	−1.06336	−0.531680	−	0.846945i	$-0.678439\pi$
$263$	−17.2448	−1.06336	−0.531680	+	0.846945i	$0.678439\pi$
$264$	1.05659	0.0650288
$265$	−6.12094	−0.376006
$266$	−2.93273	−0.179817
$267$	−11.9610	−0.732003
$268$	3.06434	0.187185
$269$	−24.2944	−1.48126	−0.740629	−	0.671914i	$-0.765472\pi$
$269$	−24.2944	−1.48126	−0.740629	+	0.671914i	$0.765472\pi$
$270$	1.40550	0.0855360
$271$	−18.3326	−1.11363	−0.556813	−	0.830638i	$-0.687976\pi$
$271$	−18.3326	−1.11363	−0.556813	+	0.830638i	$0.687976\pi$
$272$	−2.25334	−0.136629
$273$	0	0
$274$	−25.7437	−1.55524
$275$	−1.31981	−0.0795875
$276$	0.0282963	0.00170323
$277$	8.45434	0.507972	0.253986	−	0.967208i	$-0.418258\pi$
$277$	8.45434	0.507972	0.253986	+	0.967208i	$0.418258\pi$
$278$	5.44447	0.326538
$279$	6.85772	0.410561
$280$	3.34116	0.199672
$281$	25.0120	1.49209	0.746045	−	0.665895i	$-0.231950\pi$
$281$	25.0120	1.49209	0.746045	+	0.665895i	$0.231950\pi$
$282$	5.99708	0.357121
$283$	27.1415	1.61339	0.806697	−	0.590966i	$-0.201253\pi$
$283$	27.1415	1.61339	0.806697	+	0.590966i	$0.201253\pi$
$284$	−3.59450	−0.213294
$285$	−2.54003	−0.150458
$286$	0	0
$287$	−3.09556	−0.182725
$288$	2.10331	0.123939
$289$	−16.4728	−0.968986
$290$	−0.675364	−0.0396587
$291$	10.1033	0.592267
$292$	−3.93566	−0.230317
$293$	10.5400	0.615755	0.307878	−	0.951426i	$-0.400381\pi$
$293$	10.5400	0.615755	0.307878	+	0.951426i	$0.400381\pi$
$294$	−1.27389	−0.0742948
$295$	−4.33048	−0.252130
$296$	−3.34116	−0.194201
$297$	−0.348907	−0.0202456
$298$	6.23784	0.361349
$299$	0	0
$300$	−1.42685	−0.0823790
$301$	−4.62280	−0.266454
$302$	11.3956	0.655745
$303$	−4.07502	−0.234104
$304$	7.14440	0.409760
$305$	−6.12094	−0.350484
$306$	0.924984	0.0528778
$307$	4.40842	0.251602	0.125801	−	0.992055i	$-0.459850\pi$
$307$	4.40842	0.251602	0.125801	+	0.992055i	$0.459850\pi$
$308$	−0.131609	−0.00749909
$309$	4.11106	0.233870
$310$	−9.63852	−0.547431
$311$	−2.32836	−0.132029	−0.0660146	−	0.997819i	$-0.521028\pi$
$311$	−2.32836	−0.132029	−0.0660146	+	0.997819i	$0.521028\pi$
$312$	0	0
$313$	12.6687	0.716078	0.358039	−	0.933707i	$-0.383445\pi$
$313$	12.6687	0.716078	0.358039	+	0.933707i	$0.383445\pi$
$314$	8.40067	0.474077
$315$	−1.10331	−0.0621646
$316$	−6.45222	−0.362966
$317$	12.2915	0.690360	0.345180	−	0.938536i	$-0.387818\pi$
$317$	12.2915	0.690360	0.345180	+	0.938536i	$0.387818\pi$
$318$	−7.06727	−0.396313
$319$	0.167655	0.00938687
$320$	−9.80405	−0.548063
$321$	6.17058	0.344408
$322$	0.0955622	0.00532547
$323$	−1.67164	−0.0930125
$324$	−0.377203	−0.0209557
$325$	0	0
$326$	12.6172	0.698800
$327$	−8.82167	−0.487840
$328$	9.37428	0.517608
$329$	−4.70769	−0.259543
$330$	0.490388	0.0269950
$331$	−13.2915	−0.730568	−0.365284	−	0.930896i	$-0.619028\pi$
$331$	−13.2915	−0.730568	−0.365284	+	0.930896i	$0.619028\pi$
$332$	−4.49411	−0.246646
$333$	1.10331	0.0604611
$334$	21.3460	1.16800
$335$	8.96315	0.489709
$336$	3.10331	0.169300
$337$	−3.40550	−0.185509	−0.0927547	−	0.995689i	$-0.529567\pi$
$337$	−3.40550	−0.185509	−0.0927547	+	0.995689i	$0.529567\pi$
$338$	0	0
$339$	−12.0099	−0.652287
$340$	0.302187	0.0163884
$341$	2.39270	0.129572
$342$	−2.93273	−0.158584
$343$	1.00000	0.0539949
$344$	13.9992	0.754786
$345$	0.0827661	0.00445598
$346$	17.4757	0.939499
$347$	−33.4981	−1.79827	−0.899137	−	0.437667i	$-0.855805\pi$
$347$	−33.4981	−1.79827	−0.899137	+	0.437667i	$0.855805\pi$
$348$	0.181252	0.00971611
$349$	28.1805	1.50846	0.754232	−	0.656607i	$-0.228009\pi$
$349$	28.1805	1.50846	0.754232	+	0.656607i	$0.228009\pi$
$350$	−4.81875	−0.257573
$351$	0	0
$352$	0.733860	0.0391148
$353$	2.99225	0.159261	0.0796307	−	0.996824i	$-0.474626\pi$
$353$	2.99225	0.159261	0.0796307	+	0.996824i	$0.474626\pi$
$354$	−5.00000	−0.265747
$355$	−10.5139	−0.558018
$356$	−4.51173	−0.239121
$357$	−0.726109	−0.0384298
$358$	−28.0643	−1.48325
$359$	−3.80888	−0.201025	−0.100512	−	0.994936i	$-0.532048\pi$
$359$	−3.80888	−0.201025	−0.100512	+	0.994936i	$0.532048\pi$
$360$	3.34116	0.176094
$361$	−13.6999	−0.721049
$362$	12.0176	0.631632
$363$	10.8783	0.570961
$364$	0	0
$365$	−11.5117	−0.602552
$366$	−7.06727	−0.369412
$367$	−26.4514	−1.38075	−0.690376	−	0.723450i	$-0.742555\pi$
$367$	−26.4514	−1.38075	−0.690376	+	0.723450i	$0.742555\pi$
$368$	−0.232798	−0.0121354
$369$	−3.09556	−0.161149
$370$	−1.55070	−0.0806173
$371$	5.54778	0.288026
$372$	2.58675	0.134117
$373$	2.13161	0.110371	0.0551853	−	0.998476i	$-0.482425\pi$
$373$	2.13161	0.110371	0.0551853	+	0.998476i	$0.482425\pi$
$374$	0.322733	0.0166881
$375$	−9.69006	−0.500393
$376$	14.2563	0.735211
$377$	0	0
$378$	−1.27389	−0.0655219
$379$	13.9434	0.716225	0.358112	−	0.933678i	$-0.383420\pi$
$379$	13.9434	0.716225	0.358112	+	0.933678i	$0.383420\pi$
$380$	−0.958107	−0.0491498
$381$	5.85772	0.300100
$382$	−4.30219	−0.220119
$383$	18.6044	0.950639	0.475320	−	0.879813i	$-0.342332\pi$
$383$	18.6044	0.950639	0.475320	+	0.879813i	$0.342332\pi$
$384$	−7.11319	−0.362993
$385$	−0.384953	−0.0196190
$386$	−28.4367	−1.44739
$387$	−4.62280	−0.234990
$388$	3.81100	0.193474
$389$	−1.23009	−0.0623682	−0.0311841	−	0.999514i	$-0.509928\pi$
$389$	−1.23009	−0.0623682	−0.0311841	+	0.999514i	$0.509928\pi$
$390$	0	0
$391$	0.0544699	0.00275466
$392$	−3.02830	−0.152952
$393$	−22.4055	−1.13021
$394$	32.4223	1.63341
$395$	−18.8726	−0.949585
$396$	−0.131609	−0.00661358
$397$	−29.6142	−1.48630	−0.743148	−	0.669127i	$-0.766668\pi$
$397$	−29.6142	−1.48630	−0.743148	+	0.669127i	$0.766668\pi$
$398$	−28.4592	−1.42653
$399$	2.30219	0.115253
$400$	11.7389	0.586945
$401$	−8.18045	−0.408512	−0.204256	−	0.978917i	$-0.565478\pi$
$401$	−8.18045	−0.408512	−0.204256	+	0.978917i	$0.565478\pi$
$402$	10.3489	0.516157
$403$	0	0
$404$	−1.53711	−0.0764740
$405$	−1.10331	−0.0548240
$406$	0.612124	0.0303792
$407$	0.384953	0.0190814
$408$	2.19887	0.108861
$409$	−10.0673	−0.497794	−0.248897	−	0.968530i	$-0.580068\pi$
$409$	−10.0673	−0.497794	−0.248897	+	0.968530i	$0.580068\pi$
$410$	4.35081	0.214871
$411$	20.2087	0.996824
$412$	1.55070	0.0763977
$413$	3.92498	0.193136
$414$	0.0955622	0.00469663
$415$	−13.1452	−0.645273
$416$	0	0
$417$	−4.27389	−0.209293
$418$	−1.02325	−0.0500488
$419$	9.45997	0.462150	0.231075	−	0.972936i	$-0.425776\pi$
$419$	9.45997	0.462150	0.231075	+	0.972936i	$0.425776\pi$
$420$	−0.416173	−0.0203071
$421$	−31.0643	−1.51398	−0.756992	−	0.653424i	$-0.773332\pi$
$421$	−31.0643	−1.51398	−0.756992	+	0.653424i	$0.773332\pi$
$422$	12.7875	0.622487
$423$	−4.70769	−0.228896
$424$	−16.8003	−0.815896
$425$	−2.74666	−0.133232
$426$	−12.1394	−0.588154
$427$	5.54778	0.268476
$428$	2.32756	0.112507
$429$	0	0
$430$	6.49734	0.313329
$431$	25.2186	1.21474	0.607369	−	0.794420i	$-0.292225\pi$
$431$	25.2186	1.21474	0.607369	+	0.794420i	$0.292225\pi$
$432$	3.10331	0.149308
$433$	3.76991	0.181170	0.0905851	−	0.995889i	$-0.471126\pi$
$433$	3.76991	0.181170	0.0905851	+	0.995889i	$0.471126\pi$
$434$	8.73598	0.419341
$435$	0.530158	0.0254191
$436$	−3.32756	−0.159361
$437$	−0.172701	−0.00826141
$438$	−13.2915	−0.635093
$439$	−22.6348	−1.08030	−0.540150	−	0.841569i	$-0.681632\pi$
$439$	−22.6348	−1.08030	−0.540150	+	0.841569i	$0.681632\pi$
$440$	1.16575	0.0555750
$441$	1.00000	0.0476190
$442$	0	0
$443$	4.64334	0.220612	0.110306	−	0.993898i	$-0.464817\pi$
$443$	4.64334	0.220612	0.110306	+	0.993898i	$0.464817\pi$
$444$	0.416173	0.0197507
$445$	−13.1968	−0.625586
$446$	6.54083	0.309717
$447$	−4.89669	−0.231605
$448$	8.88601	0.419825
$449$	−9.42312	−0.444705	−0.222352	−	0.974966i	$-0.571374\pi$
$449$	−9.42312	−0.444705	−0.222352	+	0.974966i	$0.571374\pi$
$450$	−4.81875	−0.227158
$451$	−1.08006	−0.0508581
$452$	−4.53016	−0.213081
$453$	−8.94553	−0.420298
$454$	36.9058	1.73207
$455$	0	0
$456$	−6.97170	−0.326480
$457$	−12.7162	−0.594840	−0.297420	−	0.954747i	$-0.596126\pi$
$457$	−12.7162	−0.594840	−0.297420	+	0.954747i	$0.596126\pi$
$458$	−0.865468	−0.0404407
$459$	−0.726109	−0.0338919
$460$	0.0312196	0.00145562
$461$	29.7253	1.38445	0.692223	−	0.721684i	$-0.256632\pi$
$461$	29.7253	1.38445	0.692223	+	0.721684i	$0.256632\pi$
$462$	−0.444469	−0.0206786
$463$	15.2838	0.710297	0.355148	−	0.934810i	$-0.384430\pi$
$463$	15.2838	0.710297	0.355148	+	0.934810i	$0.384430\pi$
$464$	−1.49119	−0.0692267
$465$	7.56620	0.350874
$466$	−23.3150	−1.08005
$467$	−26.6503	−1.23323	−0.616614	−	0.787265i	$-0.711496\pi$
$467$	−26.6503	−1.23323	−0.616614	+	0.787265i	$0.711496\pi$
$468$	0	0
$469$	−8.12386	−0.375125
$470$	6.61665	0.305203
$471$	−6.59450	−0.303859
$472$	−11.8860	−0.547098
$473$	−1.61292	−0.0741623
$474$	−21.7905	−1.00087
$475$	8.70849	0.399573
$476$	−0.273891	−0.0125538
$477$	5.54778	0.254015
$478$	6.94553	0.317681
$479$	22.2117	1.01488	0.507439	−	0.861688i	$-0.330592\pi$
$479$	22.2117	1.01488	0.507439	+	0.861688i	$0.330592\pi$
$480$	2.32061	0.105921
$481$	0	0
$482$	19.6970	0.897174
$483$	−0.0750160	−0.00341335
$484$	4.10331	0.186514
$485$	11.1471	0.506164
$486$	−1.27389	−0.0577848
$487$	0.971704	0.0440321	0.0220160	−	0.999758i	$-0.492992\pi$
$487$	0.971704	0.0440321	0.0220160	+	0.999758i	$0.492992\pi$
$488$	−16.8003	−0.760515
$489$	−9.90444	−0.447894
$490$	−1.40550	−0.0634940
$491$	26.9349	1.21555	0.607777	−	0.794108i	$-0.292062\pi$
$491$	26.9349	1.21555	0.607777	+	0.794108i	$0.292062\pi$
$492$	−1.16765	−0.0526419
$493$	0.348907	0.0157140
$494$	0	0
$495$	−0.384953	−0.0173023
$496$	−21.2816	−0.955574
$497$	9.52936	0.427450
$498$	−15.1775	−0.680121
$499$	21.1239	0.945634	0.472817	−	0.881161i	$-0.343237\pi$
$499$	21.1239	0.945634	0.472817	+	0.881161i	$0.343237\pi$
$500$	−3.65512	−0.163462
$501$	−16.7565	−0.748626
$502$	−10.5662	−0.471593
$503$	12.5654	0.560264	0.280132	−	0.959962i	$-0.409622\pi$
$503$	12.5654	0.560264	0.280132	+	0.959962i	$0.409622\pi$
$504$	−3.02830	−0.134891
$505$	−4.49602	−0.200070
$506$	0.0333423	0.00148225
$507$	0	0
$508$	2.20955	0.0980328
$509$	−27.6065	−1.22364	−0.611818	−	0.790998i	$-0.709562\pi$
$509$	−27.6065	−1.22364	−0.611818	+	0.790998i	$0.709562\pi$
$510$	1.02055	0.0451905
$511$	10.4338	0.461564
$512$	−25.3227	−1.11912
$513$	2.30219	0.101644
$514$	−19.1570	−0.844978
$515$	4.53579	0.199871
$516$	−1.74373	−0.0767635
$517$	−1.64254	−0.0722389
$518$	1.40550	0.0617541
$519$	−13.7184	−0.602169
$520$	0	0
$521$	−36.8783	−1.61567	−0.807833	−	0.589411i	$-0.799360\pi$
$521$	−36.8783	−1.61567	−0.807833	+	0.589411i	$0.799360\pi$
$522$	0.612124	0.0267919
$523$	30.8054	1.34702	0.673512	−	0.739176i	$-0.264785\pi$
$523$	30.8054	1.34702	0.673512	+	0.739176i	$0.264785\pi$
$524$	−8.45142	−0.369202
$525$	3.78270	0.165091
$526$	−21.9680	−0.957849
$527$	4.97945	0.216908
$528$	1.08277	0.0471213
$529$	−22.9944	−0.999755
$530$	−7.79740	−0.338697
$531$	3.92498	0.170330
$532$	0.868391	0.0376495
$533$	0	0
$534$	−15.2370	−0.659371
$535$	6.80807	0.294339
$536$	24.6015	1.06262
$537$	22.0304	0.950683
$538$	−30.9485	−1.33428
$539$	0.348907	0.0150285
$540$	−0.416173	−0.0179092
$541$	41.4981	1.78414	0.892072	−	0.451893i	$-0.149251\pi$
$541$	41.4981	1.78414	0.892072	+	0.451893i	$0.149251\pi$
$542$	−23.3537	−1.00313
$543$	−9.43380	−0.404843
$544$	1.52723	0.0654797
$545$	−9.73306	−0.416918
$546$	0	0
$547$	−41.3716	−1.76892	−0.884460	−	0.466615i	$-0.845473\pi$
$547$	−41.3716	−1.76892	−0.884460	+	0.466615i	$0.845473\pi$
$548$	7.62280	0.325630
$549$	5.54778	0.236774
$550$	−1.68129	−0.0716906
$551$	−1.10624	−0.0471272
$552$	0.227171	0.00966903
$553$	17.1054	0.727397
$554$	10.7699	0.457569
$555$	1.21730	0.0516714
$556$	−1.61212	−0.0683693
$557$	−30.0149	−1.27177	−0.635886	−	0.771783i	$-0.719365\pi$
$557$	−30.0149	−1.27177	−0.635886	+	0.771783i	$0.719365\pi$
$558$	8.73598	0.369824
$559$	0	0
$560$	3.42392	0.144687
$561$	−0.253344	−0.0106962
$562$	31.8625	1.34404
$563$	25.9349	1.09302	0.546512	−	0.837451i	$-0.315955\pi$
$563$	25.9349	1.09302	0.546512	+	0.837451i	$0.315955\pi$
$564$	−1.77575	−0.0747727
$565$	−13.2506	−0.557459
$566$	34.5753	1.45331
$567$	1.00000	0.0419961
$568$	−28.8577	−1.21084
$569$	−6.56620	−0.275270	−0.137635	−	0.990483i	$-0.543950\pi$
$569$	−6.56620	−0.275270	−0.137635	+	0.990483i	$0.543950\pi$
$570$	−3.23572	−0.135529
$571$	−30.0539	−1.25772	−0.628858	−	0.777520i	$-0.716477\pi$
$571$	−30.0539	−1.25772	−0.628858	+	0.777520i	$0.716477\pi$
$572$	0	0
$573$	3.37720	0.141085
$574$	−3.94341	−0.164595
$575$	−0.283763	−0.0118337
$576$	8.88601	0.370251
$577$	−21.1706	−0.881343	−0.440671	−	0.897669i	$-0.645260\pi$
$577$	−21.1706	−0.881343	−0.440671	+	0.897669i	$0.645260\pi$
$578$	−20.9845	−0.872840
$579$	22.3227	0.927701
$580$	0.199977	0.00830360
$581$	11.9143	0.494289
$582$	12.8705	0.533500
$583$	1.93566	0.0801667
$584$	−31.5966	−1.30748
$585$	0	0
$586$	13.4268	0.554658
$587$	−0.0312196	−0.00128857	−0.000644286	−	1.00000i	$-0.500205\pi$
$587$	−0.0312196	−0.00128857	−0.000644286		1.00000i	$0.500205\pi$
$588$	0.377203	0.0155556
$589$	−15.7877	−0.650523
$590$	−5.51656	−0.227113
$591$	−25.4514	−1.04693
$592$	−3.42392	−0.140722
$593$	10.3150	0.423586	0.211793	−	0.977315i	$-0.432070\pi$
$593$	10.3150	0.423586	0.211793	+	0.977315i	$0.432070\pi$
$594$	−0.444469	−0.0182368
$595$	−0.801125	−0.0328429
$596$	−1.84704	−0.0756579
$597$	22.3404	0.914330
$598$	0	0
$599$	44.0176	1.79851	0.899256	−	0.437423i	$-0.144109\pi$
$599$	44.0176	1.79851	0.899256	+	0.437423i	$0.144109\pi$
$600$	−11.4551	−0.467654
$601$	5.04672	0.205860	0.102930	−	0.994689i	$-0.467178\pi$
$601$	5.04672	0.205860	0.102930	+	0.994689i	$0.467178\pi$
$602$	−5.88894	−0.240015
$603$	−8.12386	−0.330829
$604$	−3.37428	−0.137297
$605$	12.0021	0.487956
$606$	−5.19112	−0.210875
$607$	16.6482	0.675728	0.337864	−	0.941195i	$-0.390296\pi$
$607$	16.6482	0.675728	0.337864	+	0.941195i	$0.390296\pi$
$608$	−4.84222	−0.196378
$609$	−0.480515	−0.0194715
$610$	−7.79740	−0.315708
$611$	0	0
$612$	−0.273891	−0.0110714
$613$	−38.0120	−1.53529	−0.767645	−	0.640875i	$-0.778572\pi$
$613$	−38.0120	−1.53529	−0.767645	+	0.640875i	$0.778572\pi$
$614$	5.61585	0.226637
$615$	−3.41537	−0.137721
$616$	−1.05659	−0.0425713
$617$	−15.6666	−0.630713	−0.315357	−	0.948973i	$-0.602124\pi$
$617$	−15.6666	−0.630713	−0.315357	+	0.948973i	$0.602124\pi$
$618$	5.23704	0.210665
$619$	−3.26109	−0.131074	−0.0655372	−	0.997850i	$-0.520876\pi$
$619$	−3.26109	−0.131074	−0.0655372	+	0.997850i	$0.520876\pi$
$620$	2.85399	0.114619
$621$	−0.0750160	−0.00301029
$622$	−2.96608	−0.118929
$623$	11.9610	0.479209
$624$	0	0
$625$	8.22234	0.328894
$626$	16.1386	0.645027
$627$	0.803248	0.0320786
$628$	−2.48746	−0.0992606
$629$	0.801125	0.0319430
$630$	−1.40550	−0.0559964
$631$	−1.59955	−0.0636770	−0.0318385	−	0.999493i	$-0.510136\pi$
$631$	−1.59955	−0.0636770	−0.0318385	+	0.999493i	$0.510136\pi$
$632$	−51.8003	−2.06051
$633$	−10.0382	−0.398981
$634$	15.6580	0.621860
$635$	6.46289	0.256472
$636$	2.09264	0.0829785
$637$	0	0
$638$	0.213574	0.00845548
$639$	9.52936	0.376976
$640$	−7.84806	−0.310222
$641$	31.3559	1.23848	0.619241	−	0.785201i	$-0.287440\pi$
$641$	31.3559	1.23848	0.619241	+	0.785201i	$0.287440\pi$
$642$	7.86064	0.310235
$643$	18.6631	0.736000	0.368000	−	0.929826i	$-0.380043\pi$
$643$	18.6631	0.736000	0.368000	+	0.929826i	$0.380043\pi$
$644$	−0.0282963	−0.00111503
$645$	−5.10039	−0.200828
$646$	−2.12949	−0.0837835
$647$	6.53711	0.257000	0.128500	−	0.991709i	$-0.458984\pi$
$647$	6.53711	0.257000	0.128500	+	0.991709i	$0.458984\pi$
$648$	−3.02830	−0.118963
$649$	1.36945	0.0537557
$650$	0	0
$651$	−6.85772	−0.268775
$652$	−3.73598	−0.146312
$653$	15.8521	0.620340	0.310170	−	0.950681i	$-0.399614\pi$
$653$	15.8521	0.620340	0.310170	+	0.950681i	$0.399614\pi$
$654$	−11.2378	−0.439434
$655$	−24.7203	−0.965901
$656$	9.60650	0.375071
$657$	10.4338	0.407061
$658$	−5.99708	−0.233790
$659$	−49.7974	−1.93983	−0.969916	−	0.243441i	$-0.921724\pi$
$659$	−49.7974	−1.93983	−0.969916	+	0.243441i	$0.921724\pi$
$660$	−0.145205	−0.00565211
$661$	−3.57103	−0.138897	−0.0694485	−	0.997586i	$-0.522124\pi$
$661$	−3.57103	−0.138897	−0.0694485	+	0.997586i	$0.522124\pi$
$662$	−16.9319	−0.658078
$663$	0	0
$664$	−36.0801	−1.40018
$665$	2.54003	0.0984982
$666$	1.40550	0.0544620
$667$	0.0360463	0.00139572
$668$	−6.32061	−0.244552
$669$	−5.13453	−0.198512
$670$	11.4181	0.441119
$671$	1.93566	0.0747252
$672$	−2.10331	−0.0811370
$673$	11.7339	0.452307	0.226154	−	0.974092i	$-0.427385\pi$
$673$	11.7339	0.452307	0.226154	+	0.974092i	$0.427385\pi$
$674$	−4.33823	−0.167102
$675$	3.78270	0.145596
$676$	0	0
$677$	17.3326	0.666146	0.333073	−	0.942901i	$-0.391914\pi$
$677$	17.3326	0.666146	0.333073	+	0.942901i	$0.391914\pi$
$678$	−15.2993	−0.587565
$679$	−10.1033	−0.387730
$680$	2.42605	0.0930346
$681$	−28.9709	−1.11017
$682$	3.04804	0.116716
$683$	−16.9640	−0.649108	−0.324554	−	0.945867i	$-0.605214\pi$
$683$	−16.9640	−0.649108	−0.324554	+	0.945867i	$0.605214\pi$
$684$	0.868391	0.0332038
$685$	22.2966	0.851908
$686$	1.27389	0.0486374
$687$	0.679390	0.0259203
$688$	14.3460	0.546935
$689$	0	0
$690$	0.105435	0.00401384
$691$	−36.6425	−1.39395	−0.696974	−	0.717096i	$-0.745471\pi$
$691$	−36.6425	−1.39395	−0.696974	+	0.717096i	$0.745471\pi$
$692$	−5.17460	−0.196709
$693$	0.348907	0.0132539
$694$	−42.6730	−1.61984
$695$	−4.71544	−0.178867
$696$	1.45514	0.0551570
$697$	−2.24772	−0.0851384
$698$	35.8988	1.35879
$699$	18.3022	0.692252
$700$	1.42685	0.0539297
$701$	−14.6092	−0.551782	−0.275891	−	0.961189i	$-0.588973\pi$
$701$	−14.6092	−0.551782	−0.275891	+	0.961189i	$0.588973\pi$
$702$	0	0
$703$	−2.54003	−0.0957991
$704$	3.10039	0.116850
$705$	−5.19405	−0.195619
$706$	3.81180	0.143459
$707$	4.07502	0.153257
$708$	1.48052	0.0556412
$709$	23.5860	0.885789	0.442894	−	0.896574i	$-0.353952\pi$
$709$	23.5860	0.885789	0.442894	+	0.896574i	$0.353952\pi$
$710$	−13.3935	−0.502649
$711$	17.1054	0.641504
$712$	−36.2215	−1.35746
$713$	0.514439	0.0192659
$714$	−0.924984	−0.0346167
$715$	0	0
$716$	8.30994	0.310557
$717$	−5.45222	−0.203617
$718$	−4.85209	−0.181078
$719$	34.1337	1.27297	0.636487	−	0.771288i	$-0.280387\pi$
$719$	34.1337	1.27297	0.636487	+	0.771288i	$0.280387\pi$
$720$	3.42392	0.127602
$721$	−4.11106	−0.153104
$722$	−17.4522	−0.649504
$723$	−15.4621	−0.575041
$724$	−3.55845	−0.132249
$725$	−1.81765	−0.0675057
$726$	13.8577	0.514308
$727$	−15.3481	−0.569230	−0.284615	−	0.958642i	$-0.591866\pi$
$727$	−15.3481	−0.569230	−0.284615	+	0.958642i	$0.591866\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.6647	−0.542765
$731$	−3.35666	−0.124150
$732$	2.09264	0.0773462
$733$	−23.2894	−0.860213	−0.430107	−	0.902778i	$-0.641524\pi$
$733$	−23.2894	−0.860213	−0.430107	+	0.902778i	$0.641524\pi$
$734$	−33.6962	−1.24375
$735$	1.10331	0.0406963
$736$	0.157782	0.00581593
$737$	−2.83447	−0.104409
$738$	−3.94341	−0.145159
$739$	10.2661	0.377646	0.188823	−	0.982011i	$-0.439533\pi$
$739$	10.2661	0.377646	0.188823	+	0.982011i	$0.439533\pi$
$740$	0.459168	0.0168794
$741$	0	0
$742$	7.06727	0.259447
$743$	45.3481	1.66366	0.831830	−	0.555030i	$-0.187293\pi$
$743$	45.3481	1.66366	0.831830	+	0.555030i	$0.187293\pi$
$744$	20.7672	0.761363
$745$	−5.40258	−0.197935
$746$	2.71544	0.0994192
$747$	11.9143	0.435922
$748$	−0.0955622	−0.00349410
$749$	−6.17058	−0.225468
$750$	−12.3441	−0.450742
$751$	−29.6113	−1.08053	−0.540266	−	0.841494i	$-0.681676\pi$
$751$	−29.6113	−1.08053	−0.540266	+	0.841494i	$0.681676\pi$
$752$	14.6094	0.532751
$753$	8.29444	0.302266
$754$	0	0
$755$	−9.86971	−0.359196
$756$	0.377203	0.0137187
$757$	−25.9816	−0.944316	−0.472158	−	0.881514i	$-0.656525\pi$
$757$	−25.9816	−0.944316	−0.472158	+	0.881514i	$0.656525\pi$
$758$	17.7624	0.645159
$759$	−0.0261736	−0.000950041 0
$760$	−7.69197	−0.279017
$761$	54.0665	1.95991	0.979954	−	0.199224i	$-0.0638422\pi$
$761$	54.0665	1.95991	0.979954	+	0.199224i	$0.0638422\pi$
$762$	7.46209	0.270323
$763$	8.82167	0.319366
$764$	1.27389	0.0460877
$765$	−0.801125	−0.0289648
$766$	23.6999	0.856313
$767$	0	0
$768$	8.71061	0.314317
$769$	−25.7934	−0.930133	−0.465066	−	0.885276i	$-0.653970\pi$
$769$	−25.7934	−0.930133	−0.465066	+	0.885276i	$0.653970\pi$
$770$	−0.490388	−0.0176724
$771$	15.0382	0.541586
$772$	8.42020	0.303050
$773$	0.121736	0.00437853	0.00218927	−	0.999998i	$-0.499303\pi$
$773$	0.121736	0.00437853	0.00218927	+	0.999998i	$0.499303\pi$
$774$	−5.88894	−0.211673
$775$	−25.9407	−0.931818
$776$	30.5958	1.09833
$777$	−1.10331	−0.0395811
$778$	−1.56701	−0.0561799
$779$	7.12656	0.255336
$780$	0	0
$781$	3.32486	0.118973
$782$	0.0693886	0.00248133
$783$	−0.480515	−0.0171722
$784$	−3.10331	−0.110833
$785$	−7.27579	−0.259684
$786$	−28.5422	−1.01806
$787$	20.2215	0.720820	0.360410	−	0.932794i	$-0.382637\pi$
$787$	20.2215	0.720820	0.360410	+	0.932794i	$0.382637\pi$
$788$	−9.60035	−0.341998
$789$	17.2448	0.613931
$790$	−24.0417	−0.855364
$791$	12.0099	0.427022
$792$	−1.05659	−0.0375444
$793$	0	0
$794$	−37.7253	−1.33882
$795$	6.12094	0.217087
$796$	8.42685	0.298682
$797$	32.4124	1.14811	0.574054	−	0.818818i	$-0.305370\pi$
$797$	32.4124	1.14811	0.574054	+	0.818818i	$0.305370\pi$
$798$	2.93273	0.103818
$799$	−3.41830	−0.120931
$800$	−7.95620	−0.281294
$801$	11.9610	0.422622
$802$	−10.4210	−0.367978
$803$	3.64042	0.128468
$804$	−3.06434	−0.108071
$805$	−0.0827661	−0.00291712
$806$	0	0
$807$	24.2944	0.855205
$808$	−12.3404	−0.434132
$809$	24.4629	0.860069	0.430035	−	0.902812i	$-0.358501\pi$
$809$	24.4629	0.860069	0.430035	+	0.902812i	$0.358501\pi$
$810$	−1.40550	−0.0493842
$811$	45.2448	1.58876	0.794380	−	0.607421i	$-0.207796\pi$
$811$	45.2448	1.58876	0.794380	+	0.607421i	$0.207796\pi$
$812$	−0.181252	−0.00636069
$813$	18.3326	0.642953
$814$	0.490388	0.0171881
$815$	−10.9277	−0.382780
$816$	2.25334	0.0788828
$817$	10.6425	0.372335
$818$	−12.8246	−0.448401
$819$	0	0
$820$	−1.28829	−0.0449890
$821$	−36.7331	−1.28199	−0.640996	−	0.767544i	$-0.721479\pi$
$821$	−36.7331	−1.28199	−0.640996	+	0.767544i	$0.721479\pi$
$822$	25.7437	0.897916
$823$	42.6476	1.48660	0.743301	−	0.668957i	$-0.233259\pi$
$823$	42.6476	1.48660	0.743301	+	0.668957i	$0.233259\pi$
$824$	12.4495	0.433699
$825$	1.31981	0.0459499
$826$	5.00000	0.173972
$827$	50.0635	1.74088	0.870440	−	0.492275i	$-0.163834\pi$
$827$	50.0635	1.74088	0.870440	+	0.492275i	$0.163834\pi$
$828$	−0.0282963	−0.000983363 0
$829$	25.8911	0.899234	0.449617	−	0.893222i	$-0.351561\pi$
$829$	25.8911	0.899234	0.449617	+	0.893222i	$0.351561\pi$
$830$	−16.7456	−0.581247
$831$	−8.45434	−0.293278
$832$	0	0
$833$	0.726109	0.0251582
$834$	−5.44447	−0.188527
$835$	−18.4877	−0.639793
$836$	0.302987	0.0104790
$837$	−6.85772	−0.237037
$838$	12.0510	0.416294
$839$	28.9349	0.998942	0.499471	−	0.866331i	$-0.333528\pi$
$839$	28.9349	0.998942	0.499471	+	0.866331i	$0.333528\pi$
$840$	−3.34116	−0.115281
$841$	−28.7691	−0.992038
$842$	−39.5726	−1.36376
$843$	−25.0120	−0.861459
$844$	−3.78643	−0.130334
$845$	0	0
$846$	−5.99708	−0.206184
$847$	−10.8783	−0.373782
$848$	−17.2165	−0.591217
$849$	−27.1415	−0.931493
$850$	−3.49894	−0.120013
$851$	0.0827661	0.00283719
$852$	3.59450	0.123146
$853$	−40.3094	−1.38017	−0.690083	−	0.723730i	$-0.742426\pi$
$853$	−40.3094	−1.38017	−0.690083	+	0.723730i	$0.742426\pi$
$854$	7.06727	0.241837
$855$	2.54003	0.0868672
$856$	18.6863	0.638686
$857$	40.0459	1.36794	0.683971	−	0.729509i	$-0.260251\pi$
$857$	40.0459	1.36794	0.683971	+	0.729509i	$0.260251\pi$
$858$	0	0
$859$	6.66659	0.227461	0.113731	−	0.993512i	$-0.463720\pi$
$859$	6.66659	0.227461	0.113731	+	0.993512i	$0.463720\pi$
$860$	−1.92388	−0.0656038
$861$	3.09556	0.105496
$862$	32.1258	1.09421
$863$	5.85289	0.199235	0.0996174	−	0.995026i	$-0.468238\pi$
$863$	5.85289	0.199235	0.0996174	+	0.995026i	$0.468238\pi$
$864$	−2.10331	−0.0715561
$865$	−15.1356	−0.514627
$866$	4.80245	0.163194
$867$	16.4728	0.559444
$868$	−2.58675	−0.0878000
$869$	5.96820	0.202457
$870$	0.675364	0.0228970
$871$	0	0
$872$	−26.7146	−0.904672
$873$	−10.1033	−0.341945
$874$	−0.220002	−0.00744168
$875$	9.69006	0.327584
$876$	3.93566	0.132974
$877$	−4.36733	−0.147474	−0.0737371	−	0.997278i	$-0.523493\pi$
$877$	−4.36733	−0.147474	−0.0737371	+	0.997278i	$0.523493\pi$
$878$	−28.8342	−0.973109
$879$	−10.5400	−0.355506
$880$	1.19463	0.0402709
$881$	3.14733	0.106036	0.0530181	−	0.998594i	$-0.483116\pi$
$881$	3.14733	0.106036	0.0530181	+	0.998594i	$0.483116\pi$
$882$	1.27389	0.0428941
$883$	14.9554	0.503289	0.251645	−	0.967820i	$-0.419029\pi$
$883$	14.9554	0.503289	0.251645	+	0.967820i	$0.419029\pi$
$884$	0	0
$885$	4.33048	0.145568
$886$	5.91511	0.198722
$887$	22.5264	0.756364	0.378182	−	0.925731i	$-0.376549\pi$
$887$	22.5264	0.756364	0.378182	+	0.925731i	$0.376549\pi$
$888$	3.34116	0.112122
$889$	−5.85772	−0.196462
$890$	−16.8112	−0.563513
$891$	0.348907	0.0116888
$892$	−1.93676	−0.0648475
$893$	10.8380	0.362679
$894$	−6.23784	−0.208625
$895$	24.3064	0.812474
$896$	7.11319	0.237635
$897$	0	0
$898$	−12.0040	−0.400580
$899$	3.29524	0.109902
$900$	1.42685	0.0475615
$901$	4.02830	0.134202
$902$	−1.37588	−0.0458118
$903$	4.62280	0.153837
$904$	−36.3695	−1.20963
$905$	−10.4084	−0.345988
$906$	−11.3956	−0.378594
$907$	−18.6532	−0.619370	−0.309685	−	0.950839i	$-0.600224\pi$
$907$	−18.6532	−0.619370	−0.309685	+	0.950839i	$0.600224\pi$
$908$	−10.9279	−0.362655
$909$	4.07502	0.135160
$910$	0	0
$911$	18.3278	0.607226	0.303613	−	0.952795i	$-0.401807\pi$
$911$	18.3278	0.607226	0.303613	+	0.952795i	$0.401807\pi$
$912$	−7.14440	−0.236575
$913$	4.15698	0.137576
$914$	−16.1991	−0.535818
$915$	6.12094	0.202352
$916$	0.256268	0.00846732
$917$	22.4055	0.739895
$918$	−0.924984	−0.0305290
$919$	15.1054	0.498282	0.249141	−	0.968467i	$-0.419852\pi$
$919$	15.1054	0.498282	0.249141	+	0.968467i	$0.419852\pi$
$920$	0.250640	0.00826337
$921$	−4.40842	−0.145262
$922$	37.8668	1.24708
$923$	0	0
$924$	0.131609	0.00432960
$925$	−4.17350	−0.137224
$926$	19.4698	0.639819
$927$	−4.11106	−0.135025
$928$	1.01067	0.0331770
$929$	6.25817	0.205324	0.102662	−	0.994716i	$-0.467264\pi$
$929$	6.25817	0.205324	0.102662	+	0.994716i	$0.467264\pi$
$930$	9.63852	0.316059
$931$	−2.30219	−0.0754511
$932$	6.90364	0.226136
$933$	2.32836	0.0762271
$934$	−33.9496	−1.11086
$935$	−0.279518	−0.00914121
$936$	0	0
$937$	−22.6610	−0.740301	−0.370151	−	0.928972i	$-0.620694\pi$
$937$	−22.6610	−0.740301	−0.370151	+	0.928972i	$0.620694\pi$
$938$	−10.3489	−0.337904
$939$	−12.6687	−0.413428
$940$	−1.95921	−0.0639024
$941$	−17.2944	−0.563783	−0.281891	−	0.959446i	$-0.590962\pi$
$941$	−17.2944	−0.563783	−0.281891	+	0.959446i	$0.590962\pi$
$942$	−8.40067	−0.273709
$943$	−0.232217	−0.00756202
$944$	−12.1805	−0.396440
$945$	1.10331	0.0358908
$946$	−2.05469	−0.0668037
$947$	27.6121	0.897273	0.448637	−	0.893714i	$-0.351910\pi$
$947$	27.6121	0.897273	0.448637	+	0.893714i	$0.351910\pi$
$948$	6.45222	0.209558
$949$	0	0
$950$	11.0937	0.359926
$951$	−12.2915	−0.398580
$952$	−2.19887	−0.0712659
$953$	4.39080	0.142232	0.0711160	−	0.997468i	$-0.477344\pi$
$953$	4.39080	0.142232	0.0711160	+	0.997468i	$0.477344\pi$
$954$	7.06727	0.228811
$955$	3.72611	0.120574
$956$	−2.05659	−0.0665150
$957$	−0.167655	−0.00541951
$958$	28.2952	0.914178
$959$	−20.2087	−0.652574
$960$	9.80405	0.316424
$961$	16.0283	0.517042
$962$	0	0
$963$	−6.17058	−0.198844
$964$	−5.83235	−0.187847
$965$	24.6289	0.792834
$966$	−0.0955622	−0.00307466
$967$	18.4875	0.594517	0.297258	−	0.954797i	$-0.403928\pi$
$967$	18.4875	0.594517	0.297258	+	0.954797i	$0.403928\pi$
$968$	32.9426	1.05882
$969$	1.67164	0.0537008
$970$	14.2002	0.455941
$971$	−52.3374	−1.67959	−0.839794	−	0.542905i	$-0.817324\pi$
$971$	−52.3374	−1.67959	−0.839794	+	0.542905i	$0.817324\pi$
$972$	0.377203	0.0120988
$973$	4.27389	0.137015
$974$	1.23784	0.0396631
$975$	0	0
$976$	−17.2165	−0.551087
$977$	−51.6447	−1.65226	−0.826130	−	0.563480i	$-0.809462\pi$
$977$	−51.6447	−1.65226	−0.826130	+	0.563480i	$0.809462\pi$
$978$	−12.6172	−0.403453
$979$	4.17328	0.133379
$980$	0.416173	0.0132941
$981$	8.82167	0.281654
$982$	34.3121	1.09494
$983$	−37.5419	−1.19740	−0.598701	−	0.800973i	$-0.704316\pi$
$983$	−37.5419	−1.19740	−0.598701	+	0.800973i	$0.704316\pi$
$984$	−9.37428	−0.298841
$985$	−28.0809	−0.894731
$986$	0.444469	0.0141548
$987$	4.70769	0.149847
$988$	0	0
$989$	−0.346784	−0.0110271
$990$	−0.490388	−0.0155856
$991$	−50.5724	−1.60648	−0.803242	−	0.595653i	$-0.796893\pi$
$991$	−50.5724	−1.60648	−0.803242	+	0.595653i	$0.796893\pi$
$992$	14.4239	0.457960
$993$	13.2915	0.421793
$994$	12.1394	0.385037
$995$	24.6484	0.781406
$996$	4.49411	0.142401
$997$	−25.9221	−0.820960	−0.410480	−	0.911870i	$-0.634639\pi$
$997$	−25.9221	−0.820960	−0.410480	+	0.911870i	$0.634639\pi$
$998$	26.9095	0.851805
$999$	−1.10331	−0.0349073

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.s.1.2		3
13.4	even	6		273.2.k.d.211.2	yes	6
13.10	even	6		273.2.k.d.22.2	✓	6
13.12	even	2		3549.2.a.h.1.2		3
39.17	odd	6		819.2.o.d.757.2		6
39.23	odd	6		819.2.o.d.568.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.2	✓	6	13.10	even	6
273.2.k.d.211.2	yes	6	13.4	even	6
819.2.o.d.568.2		6	39.23	odd	6
819.2.o.d.757.2		6	39.17	odd	6
3549.2.a.h.1.2		3	13.12	even	2
3549.2.a.s.1.2		3	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+1.27389 q^{2} -1.00000 q^{3} -0.377203 q^{4} -1.10331 q^{5} -1.27389 q^{6} +1.00000 q^{7} -3.02830 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.27389 q^{2} -1.00000 q^{3} -0.377203 q^{4} -1.10331 q^{5} -1.27389 q^{6} +1.00000 q^{7} -3.02830 q^{8} +1.00000 q^{9} -1.40550 q^{10} +0.348907 q^{11} +0.377203 q^{12} +1.27389 q^{14} +1.10331 q^{15} -3.10331 q^{16} +0.726109 q^{17} +1.27389 q^{18} -2.30219 q^{19} +0.416173 q^{20} -1.00000 q^{21} +0.444469 q^{22} +0.0750160 q^{23} +3.02830 q^{24} -3.78270 q^{25} -1.00000 q^{27} -0.377203 q^{28} +0.480515 q^{29} +1.40550 q^{30} +6.85772 q^{31} +2.10331 q^{32} -0.348907 q^{33} +0.924984 q^{34} -1.10331 q^{35} -0.377203 q^{36} +1.10331 q^{37} -2.93273 q^{38} +3.34116 q^{40} -3.09556 q^{41} -1.27389 q^{42} -4.62280 q^{43} -0.131609 q^{44} -1.10331 q^{45} +0.0955622 q^{46} -4.70769 q^{47} +3.10331 q^{48} +1.00000 q^{49} -4.81875 q^{50} -0.726109 q^{51} +5.54778 q^{53} -1.27389 q^{54} -0.384953 q^{55} -3.02830 q^{56} +2.30219 q^{57} +0.612124 q^{58} +3.92498 q^{59} -0.416173 q^{60} +5.54778 q^{61} +8.73598 q^{62} +1.00000 q^{63} +8.88601 q^{64} -0.444469 q^{66} -8.12386 q^{67} -0.273891 q^{68} -0.0750160 q^{69} -1.40550 q^{70} +9.52936 q^{71} -3.02830 q^{72} +10.4338 q^{73} +1.40550 q^{74} +3.78270 q^{75} +0.868391 q^{76} +0.348907 q^{77} +17.1054 q^{79} +3.42392 q^{80} +1.00000 q^{81} -3.94341 q^{82} +11.9143 q^{83} +0.377203 q^{84} -0.801125 q^{85} -5.88894 q^{86} -0.480515 q^{87} -1.05659 q^{88} +11.9610 q^{89} -1.40550 q^{90} -0.0282963 q^{92} -6.85772 q^{93} -5.99708 q^{94} +2.54003 q^{95} -2.10331 q^{96} -10.1033 q^{97} +1.27389 q^{98} +0.348907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 13 q^{10} + 8 q^{11} - 4 q^{12} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 7 q^{19} + 13 q^{20} - 3 q^{21} + q^{22} + 9 q^{23} - 3 q^{24} + 11 q^{25} - 3 q^{27} + 4 q^{28} - 7 q^{29} - 13 q^{30} + 7 q^{31} + 3 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} - 4 q^{38} + 13 q^{40} - 2 q^{41} - 2 q^{42} - 19 q^{43} + 15 q^{44} - 7 q^{46} + 17 q^{47} + 6 q^{48} + 3 q^{49} + 16 q^{50} - 4 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} - 7 q^{57} - 22 q^{58} + 3 q^{59} - 13 q^{60} + 13 q^{61} - 17 q^{62} + 3 q^{63} + q^{64} - q^{66} - 5 q^{67} + q^{68} - 9 q^{69} + 13 q^{70} - 8 q^{71} + 3 q^{72} + 2 q^{73} - 13 q^{74} - 11 q^{75} + 18 q^{76} + 8 q^{77} - q^{79} + 26 q^{80} + 3 q^{81} - 36 q^{82} - 2 q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} + 7 q^{87} + 21 q^{88} + 19 q^{89} + 13 q^{90} + 12 q^{92} - 7 q^{93} + 7 q^{94} - 3 q^{96} - 27 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 13 * q^10 + 8 * q^11 - 4 * q^12 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 7 * q^19 + 13 * q^20 - 3 * q^21 + q^22 + 9 * q^23 - 3 * q^24 + 11 * q^25 - 3 * q^27 + 4 * q^28 - 7 * q^29 - 13 * q^30 + 7 * q^31 + 3 * q^32 - 8 * q^33 - 6 * q^34 + 4 * q^36 - 4 * q^38 + 13 * q^40 - 2 * q^41 - 2 * q^42 - 19 * q^43 + 15 * q^44 - 7 * q^46 + 17 * q^47 + 6 * q^48 + 3 * q^49 + 16 * q^50 - 4 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 - 7 * q^57 - 22 * q^58 + 3 * q^59 - 13 * q^60 + 13 * q^61 - 17 * q^62 + 3 * q^63 + q^64 - q^66 - 5 * q^67 + q^68 - 9 * q^69 + 13 * q^70 - 8 * q^71 + 3 * q^72 + 2 * q^73 - 13 * q^74 - 11 * q^75 + 18 * q^76 + 8 * q^77 - q^79 + 26 * q^80 + 3 * q^81 - 36 * q^82 - 2 * q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 + 7 * q^87 + 21 * q^88 + 19 * q^89 + 13 * q^90 + 12 * q^92 - 7 * q^93 + 7 * q^94 - 3 * q^96 - 27 * q^97 + 2 * q^98 + 8 * q^99

Introduction

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