LMFDB - Embedded newform 3549.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.24698$ 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)

$f(q)$	$=$	$q-1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -1.00000 q^{5} -1.24698 q^{6} +1.00000 q^{7} +3.04892 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -1.00000 q^{5} -1.24698 q^{6} +1.00000 q^{7} +3.04892 q^{8} +1.00000 q^{9} +1.24698 q^{10} +1.24698 q^{11} -0.445042 q^{12} -1.24698 q^{14} -1.00000 q^{15} -2.91185 q^{16} -3.80194 q^{17} -1.24698 q^{18} -0.664874 q^{19} +0.445042 q^{20} +1.00000 q^{21} -1.55496 q^{22} -2.30798 q^{23} +3.04892 q^{24} -4.00000 q^{25} +1.00000 q^{27} -0.445042 q^{28} +4.29590 q^{29} +1.24698 q^{30} +1.80194 q^{31} -2.46681 q^{32} +1.24698 q^{33} +4.74094 q^{34} -1.00000 q^{35} -0.445042 q^{36} -2.78017 q^{37} +0.829085 q^{38} -3.04892 q^{40} -0.829085 q^{41} -1.24698 q^{42} -8.00000 q^{43} -0.554958 q^{44} -1.00000 q^{45} +2.87800 q^{46} +9.07606 q^{47} -2.91185 q^{48} +1.00000 q^{49} +4.98792 q^{50} -3.80194 q^{51} -12.0858 q^{53} -1.24698 q^{54} -1.24698 q^{55} +3.04892 q^{56} -0.664874 q^{57} -5.35690 q^{58} +0.902165 q^{59} +0.445042 q^{60} -7.91185 q^{61} -2.24698 q^{62} +1.00000 q^{63} +8.89977 q^{64} -1.55496 q^{66} +8.40581 q^{67} +1.69202 q^{68} -2.30798 q^{69} +1.24698 q^{70} -6.74094 q^{71} +3.04892 q^{72} +3.40581 q^{73} +3.46681 q^{74} -4.00000 q^{75} +0.295897 q^{76} +1.24698 q^{77} -13.8388 q^{79} +2.91185 q^{80} +1.00000 q^{81} +1.03385 q^{82} +8.92692 q^{83} -0.445042 q^{84} +3.80194 q^{85} +9.97584 q^{86} +4.29590 q^{87} +3.80194 q^{88} -0.682333 q^{89} +1.24698 q^{90} +1.02715 q^{92} +1.80194 q^{93} -11.3177 q^{94} +0.664874 q^{95} -2.46681 q^{96} -10.5211 q^{97} -1.24698 q^{98} +1.24698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{9} - q^{10} - q^{11} - q^{12} + q^{14} - 3 q^{15} - 5 q^{16} - 7 q^{17} + q^{18} - 3 q^{19} + q^{20} + 3 q^{21} - 5 q^{22} - 12 q^{23} - 12 q^{25} + 3 q^{27} - q^{28} - q^{29} - q^{30} + q^{31} - 4 q^{32} - q^{33} - 3 q^{35} - q^{36} - 7 q^{37} - 8 q^{38} + 8 q^{41} + q^{42} - 24 q^{43} - 2 q^{44} - 3 q^{45} - 11 q^{46} + 12 q^{47} - 5 q^{48} + 3 q^{49} - 4 q^{50} - 7 q^{51} + q^{53} + q^{54} + q^{55} - 3 q^{57} - 12 q^{58} + 21 q^{59} + q^{60} - 20 q^{61} - 2 q^{62} + 3 q^{63} + 4 q^{64} - 5 q^{66} + 12 q^{67} - 12 q^{69} - q^{70} - 6 q^{71} - 3 q^{73} + 7 q^{74} - 12 q^{75} - 13 q^{76} - q^{77} - 9 q^{79} + 5 q^{80} + 3 q^{81} + 19 q^{82} - 2 q^{83} - q^{84} + 7 q^{85} - 8 q^{86} - q^{87} + 7 q^{88} - 19 q^{89} - q^{90} - 3 q^{92} + q^{93} - 17 q^{94} + 3 q^{95} - 4 q^{96} - 16 q^{97} + q^{98} - q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^9 - q^10 - q^11 - q^12 + q^14 - 3 * q^15 - 5 * q^16 - 7 * q^17 + q^18 - 3 * q^19 + q^20 + 3 * q^21 - 5 * q^22 - 12 * q^23 - 12 * q^25 + 3 * q^27 - q^28 - q^29 - q^30 + q^31 - 4 * q^32 - q^33 - 3 * q^35 - q^36 - 7 * q^37 - 8 * q^38 + 8 * q^41 + q^42 - 24 * q^43 - 2 * q^44 - 3 * q^45 - 11 * q^46 + 12 * q^47 - 5 * q^48 + 3 * q^49 - 4 * q^50 - 7 * q^51 + q^53 + q^54 + q^55 - 3 * q^57 - 12 * q^58 + 21 * q^59 + q^60 - 20 * q^61 - 2 * q^62 + 3 * q^63 + 4 * q^64 - 5 * q^66 + 12 * q^67 - 12 * q^69 - q^70 - 6 * q^71 - 3 * q^73 + 7 * q^74 - 12 * q^75 - 13 * q^76 - q^77 - 9 * q^79 + 5 * q^80 + 3 * q^81 + 19 * q^82 - 2 * q^83 - q^84 + 7 * q^85 - 8 * q^86 - q^87 + 7 * q^88 - 19 * q^89 - q^90 - 3 * q^92 + q^93 - 17 * q^94 + 3 * q^95 - 4 * q^96 - 16 * q^97 + q^98 - 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 $

$2$	−1.24698	−0.881748	−0.440874	−	0.897569i	$-0.645331\pi$
$2$	−1.24698	−0.881748	−0.440874	+	0.897569i	$0.645331\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.445042	−0.222521
$5$	−1.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−1.24698	−0.509077
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.04892	1.07796
$9$	1.00000	0.333333
$10$	1.24698	0.394330
$11$	1.24698	0.375978	0.187989	−	0.982171i	$-0.439803\pi$
$11$	1.24698	0.375978	0.187989	+	0.982171i	$0.439803\pi$
$12$	−0.445042	−0.128473
$13$	0	0
$13$	0	0
$14$	−1.24698	−0.333269
$15$	−1.00000	−0.258199
$16$	−2.91185	−0.727963
$17$	−3.80194	−0.922105	−0.461053	−	0.887373i	$-0.652528\pi$
$17$	−3.80194	−0.922105	−0.461053	+	0.887373i	$0.652528\pi$
$18$	−1.24698	−0.293916
$19$	−0.664874	−0.152533	−0.0762663	−	0.997087i	$-0.524300\pi$
$19$	−0.664874	−0.152533	−0.0762663	+	0.997087i	$0.524300\pi$
$20$	0.445042	0.0995144
$21$	1.00000	0.218218
$22$	−1.55496	−0.331518
$23$	−2.30798	−0.481247	−0.240623	−	0.970619i	$-0.577352\pi$
$23$	−2.30798	−0.481247	−0.240623	+	0.970619i	$0.577352\pi$
$24$	3.04892	0.622358
$25$	−4.00000	−0.800000
$26$	0	0
$27$	1.00000	0.192450
$28$	−0.445042	−0.0841050
$29$	4.29590	0.797728	0.398864	−	0.917010i	$-0.369405\pi$
$29$	4.29590	0.797728	0.398864	+	0.917010i	$0.369405\pi$
$30$	1.24698	0.227666
$31$	1.80194	0.323638	0.161819	−	0.986820i	$-0.448264\pi$
$31$	1.80194	0.323638	0.161819	+	0.986820i	$0.448264\pi$
$32$	−2.46681	−0.436075
$33$	1.24698	0.217071
$34$	4.74094	0.813064
$35$	−1.00000	−0.169031
$36$	−0.445042	−0.0741736
$37$	−2.78017	−0.457057	−0.228528	−	0.973537i	$-0.573391\pi$
$37$	−2.78017	−0.457057	−0.228528	+	0.973537i	$0.573391\pi$
$38$	0.829085	0.134495
$39$	0	0
$40$	−3.04892	−0.482076
$41$	−0.829085	−0.129481	−0.0647406	−	0.997902i	$-0.520622\pi$
$41$	−0.829085	−0.129481	−0.0647406	+	0.997902i	$0.520622\pi$
$42$	−1.24698	−0.192413
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−0.554958	−0.0836631
$45$	−1.00000	−0.149071
$46$	2.87800	0.424338
$47$	9.07606	1.32388	0.661940	−	0.749557i	$-0.269733\pi$
$47$	9.07606	1.32388	0.661940	+	0.749557i	$0.269733\pi$
$48$	−2.91185	−0.420290
$49$	1.00000	0.142857
$50$	4.98792	0.705398
$51$	−3.80194	−0.532378
$52$	0	0
$53$	−12.0858	−1.66011	−0.830053	−	0.557685i	$-0.811690\pi$
$53$	−12.0858	−1.66011	−0.830053	+	0.557685i	$0.811690\pi$
$54$	−1.24698	−0.169692
$55$	−1.24698	−0.168143
$56$	3.04892	0.407429
$57$	−0.664874	−0.0880648
$58$	−5.35690	−0.703395
$59$	0.902165	0.117452	0.0587260	−	0.998274i	$-0.481296\pi$
$59$	0.902165	0.117452	0.0587260	+	0.998274i	$0.481296\pi$
$60$	0.445042	0.0574547
$61$	−7.91185	−1.01301	−0.506505	−	0.862237i	$-0.669063\pi$
$61$	−7.91185	−1.01301	−0.506505	+	0.862237i	$0.669063\pi$
$62$	−2.24698	−0.285367
$63$	1.00000	0.125988
$64$	8.89977	1.11247
$65$	0	0
$66$	−1.55496	−0.191402
$67$	8.40581	1.02693	0.513467	−	0.858109i	$-0.328361\pi$
$67$	8.40581	1.02693	0.513467	+	0.858109i	$0.328361\pi$
$68$	1.69202	0.205188
$69$	−2.30798	−0.277848
$70$	1.24698	0.149043
$71$	−6.74094	−0.800002	−0.400001	−	0.916515i	$-0.630990\pi$
$71$	−6.74094	−0.800002	−0.400001	+	0.916515i	$0.630990\pi$
$72$	3.04892	0.359318
$73$	3.40581	0.398620	0.199310	−	0.979936i	$-0.436130\pi$
$73$	3.40581	0.398620	0.199310	+	0.979936i	$0.436130\pi$
$74$	3.46681	0.403009
$75$	−4.00000	−0.461880
$76$	0.295897	0.0339417
$77$	1.24698	0.142107
$78$	0	0
$79$	−13.8388	−1.55698	−0.778492	−	0.627655i	$-0.784015\pi$
$79$	−13.8388	−1.55698	−0.778492	+	0.627655i	$0.784015\pi$
$80$	2.91185	0.325555
$81$	1.00000	0.111111
$82$	1.03385	0.114170
$83$	8.92692	0.979857	0.489928	−	0.871763i	$-0.337023\pi$
$83$	8.92692	0.979857	0.489928	+	0.871763i	$0.337023\pi$
$84$	−0.445042	−0.0485580
$85$	3.80194	0.412378
$86$	9.97584	1.07572
$87$	4.29590	0.460568
$88$	3.80194	0.405288
$89$	−0.682333	−0.0723271	−0.0361636	−	0.999346i	$-0.511514\pi$
$89$	−0.682333	−0.0723271	−0.0361636	+	0.999346i	$0.511514\pi$
$90$	1.24698	0.131443
$91$	0	0
$92$	1.02715	0.107087
$93$	1.80194	0.186852
$94$	−11.3177	−1.16733
$95$	0.664874	0.0682147
$96$	−2.46681	−0.251768
$97$	−10.5211	−1.06826	−0.534128	−	0.845403i	$-0.679360\pi$
$97$	−10.5211	−1.06826	−0.534128	+	0.845403i	$0.679360\pi$
$98$	−1.24698	−0.125964
$99$	1.24698	0.125326
$100$	1.78017	0.178017
$101$	3.92154	0.390208	0.195104	−	0.980783i	$-0.437496\pi$
$101$	3.92154	0.390208	0.195104	+	0.980783i	$0.437496\pi$
$102$	4.74094	0.469423
$103$	4.72886	0.465948	0.232974	−	0.972483i	$-0.425154\pi$
$103$	4.72886	0.465948	0.232974	+	0.972483i	$0.425154\pi$
$104$	0	0
$105$	−1.00000	−0.0975900
$106$	15.0707	1.46379
$107$	5.29052	0.511454	0.255727	−	0.966749i	$-0.417685\pi$
$107$	5.29052	0.511454	0.255727	+	0.966749i	$0.417685\pi$
$108$	−0.445042	−0.0428242
$109$	−3.85086	−0.368845	−0.184423	−	0.982847i	$-0.559041\pi$
$109$	−3.85086	−0.368845	−0.184423	+	0.982847i	$0.559041\pi$
$110$	1.55496	0.148259
$111$	−2.78017	−0.263882
$112$	−2.91185	−0.275144
$113$	14.5254	1.36644	0.683218	−	0.730214i	$-0.260580\pi$
$113$	14.5254	1.36644	0.683218	+	0.730214i	$0.260580\pi$
$114$	0.829085	0.0776509
$115$	2.30798	0.215220
$116$	−1.91185	−0.177511
$117$	0	0
$118$	−1.12498	−0.103563
$119$	−3.80194	−0.348523
$120$	−3.04892	−0.278327
$121$	−9.44504	−0.858640
$122$	9.86592	0.893218
$123$	−0.829085	−0.0747561
$124$	−0.801938	−0.0720161
$125$	9.00000	0.804984
$126$	−1.24698	−0.111090
$127$	20.0954	1.78318	0.891591	−	0.452841i	$-0.149590\pi$
$127$	20.0954	1.78318	0.891591	+	0.452841i	$0.149590\pi$
$128$	−6.16421	−0.544844
$129$	−8.00000	−0.704361
$130$	0	0
$131$	−4.46681	−0.390267	−0.195134	−	0.980777i	$-0.562514\pi$
$131$	−4.46681	−0.390267	−0.195134	+	0.980777i	$0.562514\pi$
$132$	−0.554958	−0.0483029
$133$	−0.664874	−0.0576519
$134$	−10.4819	−0.905496
$135$	−1.00000	−0.0860663
$136$	−11.5918	−0.993988
$137$	−11.1903	−0.956051	−0.478026	−	0.878346i	$-0.658647\pi$
$137$	−11.1903	−0.956051	−0.478026	+	0.878346i	$0.658647\pi$
$138$	2.87800	0.244992
$139$	−14.0218	−1.18931	−0.594656	−	0.803981i	$-0.702712\pi$
$139$	−14.0218	−1.18931	−0.594656	+	0.803981i	$0.702712\pi$
$140$	0.445042	0.0376129
$141$	9.07606	0.764343
$142$	8.40581	0.705400
$143$	0	0
$144$	−2.91185	−0.242654
$145$	−4.29590	−0.356755
$146$	−4.24698	−0.351483
$147$	1.00000	0.0824786
$148$	1.23729	0.101705
$149$	4.09246	0.335267	0.167634	−	0.985849i	$-0.446387\pi$
$149$	4.09246	0.335267	0.167634	+	0.985849i	$0.446387\pi$
$150$	4.98792	0.407262
$151$	−7.43967	−0.605431	−0.302716	−	0.953081i	$-0.597893\pi$
$151$	−7.43967	−0.605431	−0.302716	+	0.953081i	$0.597893\pi$
$152$	−2.02715	−0.164423
$153$	−3.80194	−0.307368
$154$	−1.55496	−0.125302
$155$	−1.80194	−0.144735
$156$	0	0
$157$	−13.7192	−1.09491	−0.547454	−	0.836835i	$-0.684403\pi$
$157$	−13.7192	−1.09491	−0.547454	+	0.836835i	$0.684403\pi$
$158$	17.2567	1.37287
$159$	−12.0858	−0.958463
$160$	2.46681	0.195019
$161$	−2.30798	−0.181894
$162$	−1.24698	−0.0979720
$163$	−7.66487	−0.600359	−0.300180	−	0.953883i	$-0.597047\pi$
$163$	−7.66487	−0.600359	−0.300180	+	0.953883i	$0.597047\pi$
$164$	0.368977	0.0288123
$165$	−1.24698	−0.0970772
$166$	−11.1317	−0.863986
$167$	3.03684	0.234997	0.117499	−	0.993073i	$-0.462512\pi$
$167$	3.03684	0.234997	0.117499	+	0.993073i	$0.462512\pi$
$168$	3.04892	0.235229
$169$	0	0
$170$	−4.74094	−0.363613
$171$	−0.664874	−0.0508442
$172$	3.56033	0.271473
$173$	−18.0073	−1.36907	−0.684535	−	0.728980i	$-0.739995\pi$
$173$	−18.0073	−1.36907	−0.684535	+	0.728980i	$0.739995\pi$
$174$	−5.35690	−0.406105
$175$	−4.00000	−0.302372
$176$	−3.63102	−0.273699
$177$	0.902165	0.0678109
$178$	0.850855	0.0637743
$179$	−20.5308	−1.53454	−0.767272	−	0.641322i	$-0.778386\pi$
$179$	−20.5308	−1.53454	−0.767272	+	0.641322i	$0.778386\pi$
$180$	0.445042	0.0331715
$181$	2.56465	0.190629	0.0953143	−	0.995447i	$-0.469614\pi$
$181$	2.56465	0.190629	0.0953143	+	0.995447i	$0.469614\pi$
$182$	0	0
$183$	−7.91185	−0.584861
$184$	−7.03684	−0.518762
$185$	2.78017	0.204402
$186$	−2.24698	−0.164757
$187$	−4.74094	−0.346692
$188$	−4.03923	−0.294591
$189$	1.00000	0.0727393
$190$	−0.829085	−0.0601481
$191$	−1.78554	−0.129197	−0.0645987	−	0.997911i	$-0.520577\pi$
$191$	−1.78554	−0.129197	−0.0645987	+	0.997911i	$0.520577\pi$
$192$	8.89977	0.642286
$193$	−8.84415	−0.636616	−0.318308	−	0.947987i	$-0.603115\pi$
$193$	−8.84415	−0.636616	−0.318308	+	0.947987i	$0.603115\pi$
$194$	13.1196	0.941933
$195$	0	0
$196$	−0.445042	−0.0317887
$197$	3.73125	0.265841	0.132920	−	0.991127i	$-0.457565\pi$
$197$	3.73125	0.265841	0.132920	+	0.991127i	$0.457565\pi$
$198$	−1.55496	−0.110506
$199$	−22.9976	−1.63026	−0.815129	−	0.579280i	$-0.803334\pi$
$199$	−22.9976	−1.63026	−0.815129	+	0.579280i	$0.803334\pi$
$200$	−12.1957	−0.862364
$201$	8.40581	0.592900
$202$	−4.89008	−0.344065
$203$	4.29590	0.301513
$204$	1.69202	0.118465
$205$	0.829085	0.0579058
$206$	−5.89679	−0.410849
$207$	−2.30798	−0.160416
$208$	0	0
$209$	−0.829085	−0.0573490
$210$	1.24698	0.0860498
$211$	8.20105	0.564583	0.282292	−	0.959329i	$-0.408905\pi$
$211$	8.20105	0.564583	0.282292	+	0.959329i	$0.408905\pi$
$212$	5.37867	0.369408
$213$	−6.74094	−0.461882
$214$	−6.59717	−0.450973
$215$	8.00000	0.545595
$216$	3.04892	0.207453
$217$	1.80194	0.122324
$218$	4.80194	0.325228
$219$	3.40581	0.230144
$220$	0.554958	0.0374153
$221$	0	0
$222$	3.46681	0.232677
$223$	−27.1933	−1.82100	−0.910498	−	0.413513i	$-0.864302\pi$
$223$	−27.1933	−1.82100	−0.910498	+	0.413513i	$0.864302\pi$
$224$	−2.46681	−0.164821
$225$	−4.00000	−0.266667
$226$	−18.1129	−1.20485
$227$	−9.40581	−0.624286	−0.312143	−	0.950035i	$-0.601047\pi$
$227$	−9.40581	−0.624286	−0.312143	+	0.950035i	$0.601047\pi$
$228$	0.295897	0.0195963
$229$	−15.5961	−1.03062	−0.515310	−	0.857004i	$-0.672323\pi$
$229$	−15.5961	−1.03062	−0.515310	+	0.857004i	$0.672323\pi$
$230$	−2.87800	−0.189770
$231$	1.24698	0.0820452
$232$	13.0978	0.859915
$233$	7.13036	0.467125	0.233563	−	0.972342i	$-0.424962\pi$
$233$	7.13036	0.467125	0.233563	+	0.972342i	$0.424962\pi$
$234$	0	0
$235$	−9.07606	−0.592057
$236$	−0.401501	−0.0261355
$237$	−13.8388	−0.898925
$238$	4.74094	0.307309
$239$	−3.05861	−0.197845	−0.0989224	−	0.995095i	$-0.531540\pi$
$239$	−3.05861	−0.197845	−0.0989224	+	0.995095i	$0.531540\pi$
$240$	2.91185	0.187959
$241$	−24.2664	−1.56313	−0.781567	−	0.623822i	$-0.785579\pi$
$241$	−24.2664	−1.56313	−0.781567	+	0.623822i	$0.785579\pi$
$242$	11.7778	0.757104
$243$	1.00000	0.0641500
$244$	3.52111	0.225416
$245$	−1.00000	−0.0638877
$246$	1.03385	0.0659160
$247$	0	0
$248$	5.49396	0.348867
$249$	8.92692	0.565721
$250$	−11.2228	−0.709793
$251$	15.4601	0.975833	0.487917	−	0.872890i	$-0.337757\pi$
$251$	15.4601	0.975833	0.487917	+	0.872890i	$0.337757\pi$
$252$	−0.445042	−0.0280350
$253$	−2.87800	−0.180938
$254$	−25.0586	−1.57232
$255$	3.80194	0.238087
$256$	−10.1129	−0.632056
$257$	−27.1987	−1.69661	−0.848303	−	0.529512i	$-0.822375\pi$
$257$	−27.1987	−1.69661	−0.848303	+	0.529512i	$0.822375\pi$
$258$	9.97584	0.621068
$259$	−2.78017	−0.172751
$260$	0	0
$261$	4.29590	0.265909
$262$	5.57002	0.344117
$263$	9.70410	0.598381	0.299190	−	0.954193i	$-0.403283\pi$
$263$	9.70410	0.598381	0.299190	+	0.954193i	$0.403283\pi$
$264$	3.80194	0.233993
$265$	12.0858	0.742422
$266$	0.829085	0.0508345
$267$	−0.682333	−0.0417581
$268$	−3.74094	−0.228514
$269$	26.8189	1.63518	0.817589	−	0.575802i	$-0.195310\pi$
$269$	26.8189	1.63518	0.817589	+	0.575802i	$0.195310\pi$
$270$	1.24698	0.0758888
$271$	28.6353	1.73947	0.869736	−	0.493517i	$-0.164289\pi$
$271$	28.6353	1.73947	0.869736	+	0.493517i	$0.164289\pi$
$272$	11.0707	0.671259
$273$	0	0
$274$	13.9541	0.842996
$275$	−4.98792	−0.300783
$276$	1.02715	0.0618270
$277$	−27.1943	−1.63395	−0.816975	−	0.576673i	$-0.804351\pi$
$277$	−27.1943	−1.63395	−0.816975	+	0.576673i	$0.804351\pi$
$278$	17.4849	1.04867
$279$	1.80194	0.107879
$280$	−3.04892	−0.182208
$281$	29.0629	1.73375	0.866874	−	0.498527i	$-0.166126\pi$
$281$	29.0629	1.73375	0.866874	+	0.498527i	$0.166126\pi$
$282$	−11.3177	−0.673957
$283$	15.1927	0.903111	0.451556	−	0.892243i	$-0.350869\pi$
$283$	15.1927	0.903111	0.451556	+	0.892243i	$0.350869\pi$
$284$	3.00000	0.178017
$285$	0.664874	0.0393838
$286$	0	0
$287$	−0.829085	−0.0489393
$288$	−2.46681	−0.145358
$289$	−2.54527	−0.149722
$290$	5.35690	0.314568
$291$	−10.5211	−0.616758
$292$	−1.51573	−0.0887014
$293$	−29.4959	−1.72317	−0.861584	−	0.507615i	$-0.830527\pi$
$293$	−29.4959	−1.72317	−0.861584	+	0.507615i	$0.830527\pi$
$294$	−1.24698	−0.0727253
$295$	−0.902165	−0.0525261
$296$	−8.47650	−0.492687
$297$	1.24698	0.0723571
$298$	−5.10321	−0.295621
$299$	0	0
$300$	1.78017	0.102778
$301$	−8.00000	−0.461112
$302$	9.27711	0.533838
$303$	3.92154	0.225287
$304$	1.93602	0.111038
$305$	7.91185	0.453031
$306$	4.74094	0.271021
$307$	−32.7415	−1.86866	−0.934329	−	0.356412i	$-0.884000\pi$
$307$	−32.7415	−1.86866	−0.934329	+	0.356412i	$0.884000\pi$
$308$	−0.554958	−0.0316217
$309$	4.72886	0.269015
$310$	2.24698	0.127620
$311$	2.59956	0.147408	0.0737039	−	0.997280i	$-0.476518\pi$
$311$	2.59956	0.147408	0.0737039	+	0.997280i	$0.476518\pi$
$312$	0	0
$313$	−11.9511	−0.675515	−0.337758	−	0.941233i	$-0.609668\pi$
$313$	−11.9511	−0.675515	−0.337758	+	0.941233i	$0.609668\pi$
$314$	17.1075	0.965433
$315$	−1.00000	−0.0563436
$316$	6.15883	0.346461
$317$	−1.93602	−0.108738	−0.0543688	−	0.998521i	$-0.517315\pi$
$317$	−1.93602	−0.108738	−0.0543688	+	0.998521i	$0.517315\pi$
$318$	15.0707	0.845122
$319$	5.35690	0.299929
$320$	−8.89977	−0.497512
$321$	5.29052	0.295288
$322$	2.87800	0.160385
$323$	2.52781	0.140651
$324$	−0.445042	−0.0247245
$325$	0	0
$326$	9.55794	0.529365
$327$	−3.85086	−0.212953
$328$	−2.52781	−0.139575
$329$	9.07606	0.500380
$330$	1.55496	0.0855976
$331$	22.9312	1.26041	0.630207	−	0.776427i	$-0.282970\pi$
$331$	22.9312	1.26041	0.630207	+	0.776427i	$0.282970\pi$
$332$	−3.97285	−0.218039
$333$	−2.78017	−0.152352
$334$	−3.78687	−0.207208
$335$	−8.40581	−0.459259
$336$	−2.91185	−0.158855
$337$	−2.25129	−0.122636	−0.0613178	−	0.998118i	$-0.519530\pi$
$337$	−2.25129	−0.122636	−0.0613178	+	0.998118i	$0.519530\pi$
$338$	0	0
$339$	14.5254	0.788912
$340$	−1.69202	−0.0917627
$341$	2.24698	0.121681
$342$	0.829085	0.0448318
$343$	1.00000	0.0539949
$344$	−24.3913	−1.31509
$345$	2.30798	0.124257
$346$	22.4547	1.20717
$347$	7.34721	0.394419	0.197209	−	0.980361i	$-0.436812\pi$
$347$	7.34721	0.394419	0.197209	+	0.980361i	$0.436812\pi$
$348$	−1.91185	−0.102486
$349$	2.51035	0.134376	0.0671880	−	0.997740i	$-0.478597\pi$
$349$	2.51035	0.134376	0.0671880	+	0.997740i	$0.478597\pi$
$350$	4.98792	0.266615
$351$	0	0
$352$	−3.07606	−0.163955
$353$	−17.9825	−0.957114	−0.478557	−	0.878056i	$-0.658840\pi$
$353$	−17.9825	−0.957114	−0.478557	+	0.878056i	$0.658840\pi$
$354$	−1.12498	−0.0597921
$355$	6.74094	0.357772
$356$	0.303667	0.0160943
$357$	−3.80194	−0.201220
$358$	25.6015	1.35308
$359$	−16.8442	−0.889000	−0.444500	−	0.895779i	$-0.646619\pi$
$359$	−16.8442	−0.889000	−0.444500	+	0.895779i	$0.646619\pi$
$360$	−3.04892	−0.160692
$361$	−18.5579	−0.976734
$362$	−3.19806	−0.168086
$363$	−9.44504	−0.495736
$364$	0	0
$365$	−3.40581	−0.178268
$366$	9.86592	0.515700
$367$	−22.2416	−1.16100	−0.580501	−	0.814259i	$-0.697143\pi$
$367$	−22.2416	−1.16100	−0.580501	+	0.814259i	$0.697143\pi$
$368$	6.72050	0.350330
$369$	−0.829085	−0.0431604
$370$	−3.46681	−0.180231
$371$	−12.0858	−0.627461
$372$	−0.801938	−0.0415785
$373$	6.74871	0.349435	0.174717	−	0.984619i	$-0.444099\pi$
$373$	6.74871	0.349435	0.174717	+	0.984619i	$0.444099\pi$
$374$	5.91185	0.305695
$375$	9.00000	0.464758
$376$	27.6722	1.42708
$377$	0	0
$378$	−1.24698	−0.0641377
$379$	−12.8498	−0.660049	−0.330025	−	0.943972i	$-0.607057\pi$
$379$	−12.8498	−0.660049	−0.330025	+	0.943972i	$0.607057\pi$
$380$	−0.295897	−0.0151792
$381$	20.0954	1.02952
$382$	2.22654	0.113920
$383$	33.0315	1.68783	0.843914	−	0.536478i	$-0.180246\pi$
$383$	33.0315	1.68783	0.843914	+	0.536478i	$0.180246\pi$
$384$	−6.16421	−0.314566
$385$	−1.24698	−0.0635520
$386$	11.0285	0.561335
$387$	−8.00000	−0.406663
$388$	4.68233	0.237709
$389$	17.5047	0.887524	0.443762	−	0.896145i	$-0.353644\pi$
$389$	17.5047	0.887524	0.443762	+	0.896145i	$0.353644\pi$
$390$	0	0
$391$	8.77479	0.443760
$392$	3.04892	0.153994
$393$	−4.46681	−0.225321
$394$	−4.65279	−0.234404
$395$	13.8388	0.696304
$396$	−0.554958	−0.0278877
$397$	−20.9487	−1.05138	−0.525692	−	0.850675i	$-0.676194\pi$
$397$	−20.9487	−1.05138	−0.525692	+	0.850675i	$0.676194\pi$
$398$	28.6775	1.43748
$399$	−0.664874	−0.0332854
$400$	11.6474	0.582371
$401$	−17.8224	−0.890007	−0.445004	−	0.895529i	$-0.646798\pi$
$401$	−17.8224	−0.890007	−0.445004	+	0.895529i	$0.646798\pi$
$402$	−10.4819	−0.522789
$403$	0	0
$404$	−1.74525	−0.0868295
$405$	−1.00000	−0.0496904
$406$	−5.35690	−0.265858
$407$	−3.46681	−0.171843
$408$	−11.5918	−0.573879
$409$	−7.54719	−0.373184	−0.186592	−	0.982437i	$-0.559744\pi$
$409$	−7.54719	−0.373184	−0.186592	+	0.982437i	$0.559744\pi$
$410$	−1.03385	−0.0510583
$411$	−11.1903	−0.551976
$412$	−2.10454	−0.103683
$413$	0.902165	0.0443927
$414$	2.87800	0.141446
$415$	−8.92692	−0.438205
$416$	0	0
$417$	−14.0218	−0.686649
$418$	1.03385	0.0505673
$419$	−12.6823	−0.619573	−0.309786	−	0.950806i	$-0.600257\pi$
$419$	−12.6823	−0.619573	−0.309786	+	0.950806i	$0.600257\pi$
$420$	0.445042	0.0217158
$421$	15.9661	0.778142	0.389071	−	0.921208i	$-0.372796\pi$
$421$	15.9661	0.778142	0.389071	+	0.921208i	$0.372796\pi$
$422$	−10.2265	−0.497820
$423$	9.07606	0.441293
$424$	−36.8485	−1.78952
$425$	15.2078	0.737684
$426$	8.40581	0.407263
$427$	−7.91185	−0.382881
$428$	−2.35450	−0.113809
$429$	0	0
$430$	−9.97584	−0.481078
$431$	22.5405	1.08574	0.542868	−	0.839818i	$-0.317338\pi$
$431$	22.5405	1.08574	0.542868	+	0.839818i	$0.317338\pi$
$432$	−2.91185	−0.140097
$433$	26.7982	1.28784	0.643920	−	0.765093i	$-0.277307\pi$
$433$	26.7982	1.28784	0.643920	+	0.765093i	$0.277307\pi$
$434$	−2.24698	−0.107858
$435$	−4.29590	−0.205972
$436$	1.71379	0.0820757
$437$	1.53452	0.0734058
$438$	−4.24698	−0.202929
$439$	−26.8049	−1.27933	−0.639665	−	0.768654i	$-0.720927\pi$
$439$	−26.8049	−1.27933	−0.639665	+	0.768654i	$0.720927\pi$
$440$	−3.80194	−0.181250
$441$	1.00000	0.0476190
$442$	0	0
$443$	5.23059	0.248513	0.124256	−	0.992250i	$-0.460345\pi$
$443$	5.23059	0.248513	0.124256	+	0.992250i	$0.460345\pi$
$444$	1.23729	0.0587192
$445$	0.682333	0.0323457
$446$	33.9095	1.60566
$447$	4.09246	0.193567
$448$	8.89977	0.420475
$449$	37.1903	1.75512	0.877559	−	0.479468i	$-0.159170\pi$
$449$	37.1903	1.75512	0.877559	+	0.479468i	$0.159170\pi$
$450$	4.98792	0.235133
$451$	−1.03385	−0.0486822
$452$	−6.46442	−0.304061
$453$	−7.43967	−0.349546
$454$	11.7289	0.550463
$455$	0	0
$456$	−2.02715	−0.0949299
$457$	−8.91484	−0.417019	−0.208509	−	0.978020i	$-0.566861\pi$
$457$	−8.91484	−0.417019	−0.208509	+	0.978020i	$0.566861\pi$
$458$	19.4480	0.908747
$459$	−3.80194	−0.177459
$460$	−1.02715	−0.0478910
$461$	5.40880	0.251913	0.125956	−	0.992036i	$-0.459800\pi$
$461$	5.40880	0.251913	0.125956	+	0.992036i	$0.459800\pi$
$462$	−1.55496	−0.0723432
$463$	−5.50902	−0.256026	−0.128013	−	0.991772i	$-0.540860\pi$
$463$	−5.50902	−0.256026	−0.128013	+	0.991772i	$0.540860\pi$
$464$	−12.5090	−0.580717
$465$	−1.80194	−0.0835629
$466$	−8.89141	−0.411887
$467$	3.10752	0.143799	0.0718995	−	0.997412i	$-0.477094\pi$
$467$	3.10752	0.143799	0.0718995	+	0.997412i	$0.477094\pi$
$468$	0	0
$469$	8.40581	0.388144
$470$	11.3177	0.522045
$471$	−13.7192	−0.632146
$472$	2.75063	0.126608
$473$	−9.97584	−0.458689
$474$	17.2567	0.792625
$475$	2.65950	0.122026
$476$	1.69202	0.0775537
$477$	−12.0858	−0.553369
$478$	3.81402	0.174449
$479$	−29.8528	−1.36401	−0.682004	−	0.731348i	$-0.738891\pi$
$479$	−29.8528	−1.36401	−0.682004	+	0.731348i	$0.738891\pi$
$480$	2.46681	0.112594
$481$	0	0
$482$	30.2597	1.37829
$483$	−2.30798	−0.105017
$484$	4.20344	0.191065
$485$	10.5211	0.477739
$486$	−1.24698	−0.0565641
$487$	34.9269	1.58269	0.791345	−	0.611370i	$-0.209381\pi$
$487$	34.9269	1.58269	0.791345	+	0.611370i	$0.209381\pi$
$488$	−24.1226	−1.09198
$489$	−7.66487	−0.346618
$490$	1.24698	0.0563328
$491$	−10.1226	−0.456826	−0.228413	−	0.973564i	$-0.573354\pi$
$491$	−10.1226	−0.456826	−0.228413	+	0.973564i	$0.573354\pi$
$492$	0.368977	0.0166348
$493$	−16.3327	−0.735589
$494$	0	0
$495$	−1.24698	−0.0560476
$496$	−5.24698	−0.235596
$497$	−6.74094	−0.302372
$498$	−11.1317	−0.498823
$499$	−8.19136	−0.366696	−0.183348	−	0.983048i	$-0.558693\pi$
$499$	−8.19136	−0.366696	−0.183348	+	0.983048i	$0.558693\pi$
$500$	−4.00538	−0.179126
$501$	3.03684	0.135676
$502$	−19.2784	−0.860439
$503$	27.0137	1.20448	0.602242	−	0.798314i	$-0.294274\pi$
$503$	27.0137	1.20448	0.602242	+	0.798314i	$0.294274\pi$
$504$	3.04892	0.135810
$505$	−3.92154	−0.174506
$506$	3.58881	0.159542
$507$	0	0
$508$	−8.94331	−0.396795
$509$	−22.8170	−1.01135	−0.505673	−	0.862725i	$-0.668756\pi$
$509$	−22.8170	−1.01135	−0.505673	+	0.862725i	$0.668756\pi$
$510$	−4.74094	−0.209932
$511$	3.40581	0.150664
$512$	24.9390	1.10216
$513$	−0.664874	−0.0293549
$514$	33.9162	1.49598
$515$	−4.72886	−0.208378
$516$	3.56033	0.156735
$517$	11.3177	0.497750
$518$	3.46681	0.152323
$519$	−18.0073	−0.790433
$520$	0	0
$521$	−0.967476	−0.0423859	−0.0211929	−	0.999775i	$-0.506746\pi$
$521$	−0.967476	−0.0423859	−0.0211929	+	0.999775i	$0.506746\pi$
$522$	−5.35690	−0.234465
$523$	9.93256	0.434320	0.217160	−	0.976136i	$-0.430321\pi$
$523$	9.93256	0.434320	0.217160	+	0.976136i	$0.430321\pi$
$524$	1.98792	0.0868426
$525$	−4.00000	−0.174574
$526$	−12.1008	−0.527621
$527$	−6.85086	−0.298428
$528$	−3.63102	−0.158020
$529$	−17.6732	−0.768402
$530$	−15.0707	−0.654629
$531$	0.902165	0.0391506
$532$	0.295897	0.0128288
$533$	0	0
$534$	0.850855	0.0368201
$535$	−5.29052	−0.228729
$536$	25.6286	1.10699
$537$	−20.5308	−0.885969
$538$	−33.4426	−1.44181
$539$	1.24698	0.0537112
$540$	0.445042	0.0191516
$541$	−1.08516	−0.0466548	−0.0233274	−	0.999728i	$-0.507426\pi$
$541$	−1.08516	−0.0466548	−0.0233274	+	0.999728i	$0.507426\pi$
$542$	−35.7077	−1.53378
$543$	2.56465	0.110060
$544$	9.37867	0.402107
$545$	3.85086	0.164953
$546$	0	0
$547$	10.3400	0.442108	0.221054	−	0.975262i	$-0.429050\pi$
$547$	10.3400	0.442108	0.221054	+	0.975262i	$0.429050\pi$
$548$	4.98015	0.212741
$549$	−7.91185	−0.337670
$550$	6.21983	0.265215
$551$	−2.85623	−0.121680
$552$	−7.03684	−0.299508
$553$	−13.8388	−0.588485
$554$	33.9108	1.44073
$555$	2.78017	0.118012
$556$	6.24027	0.264647
$557$	−36.6805	−1.55420	−0.777102	−	0.629375i	$-0.783311\pi$
$557$	−36.6805	−1.55420	−0.777102	+	0.629375i	$0.783311\pi$
$558$	−2.24698	−0.0951222
$559$	0	0
$560$	2.91185	0.123048
$561$	−4.74094	−0.200163
$562$	−36.2409	−1.52873
$563$	6.46548	0.272488	0.136244	−	0.990675i	$-0.456497\pi$
$563$	6.46548	0.272488	0.136244	+	0.990675i	$0.456497\pi$
$564$	−4.03923	−0.170082
$565$	−14.5254	−0.611089
$566$	−18.9450	−0.796316
$567$	1.00000	0.0419961
$568$	−20.5526	−0.862366
$569$	−2.57002	−0.107741	−0.0538705	−	0.998548i	$-0.517156\pi$
$569$	−2.57002	−0.107741	−0.0538705	+	0.998548i	$0.517156\pi$
$570$	−0.829085	−0.0347265
$571$	−27.5260	−1.15193	−0.575964	−	0.817475i	$-0.695373\pi$
$571$	−27.5260	−1.15193	−0.575964	+	0.817475i	$0.695373\pi$
$572$	0	0
$573$	−1.78554	−0.0745922
$574$	1.03385	0.0431521
$575$	9.23191	0.384997
$576$	8.89977	0.370824
$577$	31.2422	1.30063	0.650315	−	0.759665i	$-0.274637\pi$
$577$	31.2422	1.30063	0.650315	+	0.759665i	$0.274637\pi$
$578$	3.17390	0.132017
$579$	−8.84415	−0.367550
$580$	1.91185	0.0793854
$581$	8.92692	0.370351
$582$	13.1196	0.543825
$583$	−15.0707	−0.624164
$584$	10.3840	0.429695
$585$	0	0
$586$	36.7808	1.51940
$587$	−47.4456	−1.95829	−0.979145	−	0.203161i	$-0.934879\pi$
$587$	−47.4456	−1.95829	−0.979145	+	0.203161i	$0.934879\pi$
$588$	−0.445042	−0.0183532
$589$	−1.19806	−0.0493653
$590$	1.12498	0.0463148
$591$	3.73125	0.153483
$592$	8.09544	0.332721
$593$	−18.8968	−0.775998	−0.387999	−	0.921660i	$-0.626834\pi$
$593$	−18.8968	−0.775998	−0.387999	+	0.921660i	$0.626834\pi$
$594$	−1.55496	−0.0638007
$595$	3.80194	0.155864
$596$	−1.82132	−0.0746040
$597$	−22.9976	−0.941229
$598$	0	0
$599$	−17.9825	−0.734747	−0.367373	−	0.930074i	$-0.619743\pi$
$599$	−17.9825	−0.734747	−0.367373	+	0.930074i	$0.619743\pi$
$600$	−12.1957	−0.497886
$601$	−21.4819	−0.876264	−0.438132	−	0.898911i	$-0.644360\pi$
$601$	−21.4819	−0.876264	−0.438132	+	0.898911i	$0.644360\pi$
$602$	9.97584	0.406585
$603$	8.40581	0.342311
$604$	3.31096	0.134721
$605$	9.44504	0.383996
$606$	−4.89008	−0.198646
$607$	−21.4537	−0.870777	−0.435389	−	0.900243i	$-0.643389\pi$
$607$	−21.4537	−0.870777	−0.435389	+	0.900243i	$0.643389\pi$
$608$	1.64012	0.0665157
$609$	4.29590	0.174079
$610$	−9.86592	−0.399459
$611$	0	0
$612$	1.69202	0.0683959
$613$	15.5405	0.627674	0.313837	−	0.949477i	$-0.398385\pi$
$613$	15.5405	0.627674	0.313837	+	0.949477i	$0.398385\pi$
$614$	40.8280	1.64768
$615$	0.829085	0.0334319
$616$	3.80194	0.153184
$617$	2.42566	0.0976536	0.0488268	−	0.998807i	$-0.484452\pi$
$617$	2.42566	0.0976536	0.0488268	+	0.998807i	$0.484452\pi$
$618$	−5.89679	−0.237204
$619$	33.4892	1.34604	0.673022	−	0.739623i	$-0.264996\pi$
$619$	33.4892	1.34604	0.673022	+	0.739623i	$0.264996\pi$
$620$	0.801938	0.0322066
$621$	−2.30798	−0.0926160
$622$	−3.24160	−0.129976
$623$	−0.682333	−0.0273371
$624$	0	0
$625$	11.0000	0.440000
$626$	14.9028	0.595634
$627$	−0.829085	−0.0331105
$628$	6.10560	0.243640
$629$	10.5700	0.421454
$630$	1.24698	0.0496809
$631$	39.0907	1.55617	0.778087	−	0.628156i	$-0.216190\pi$
$631$	39.0907	1.55617	0.778087	+	0.628156i	$0.216190\pi$
$632$	−42.1933	−1.67836
$633$	8.20105	0.325962
$634$	2.41417	0.0958791
$635$	−20.0954	−0.797463
$636$	5.37867	0.213278
$637$	0	0
$638$	−6.67994	−0.264461
$639$	−6.74094	−0.266667
$640$	6.16421	0.243662
$641$	−10.7047	−0.422810	−0.211405	−	0.977399i	$-0.567804\pi$
$641$	−10.7047	−0.422810	−0.211405	+	0.977399i	$0.567804\pi$
$642$	−6.59717	−0.260370
$643$	32.6679	1.28829	0.644147	−	0.764901i	$-0.277212\pi$
$643$	32.6679	1.28829	0.644147	+	0.764901i	$0.277212\pi$
$644$	1.02715	0.0404753
$645$	8.00000	0.315000
$646$	−3.15213	−0.124019
$647$	48.0267	1.88812	0.944062	−	0.329769i	$-0.106971\pi$
$647$	48.0267	1.88812	0.944062	+	0.329769i	$0.106971\pi$
$648$	3.04892	0.119773
$649$	1.12498	0.0441594
$650$	0	0
$651$	1.80194	0.0706235
$652$	3.41119	0.133593
$653$	31.3207	1.22567	0.612836	−	0.790210i	$-0.290029\pi$
$653$	31.3207	1.22567	0.612836	+	0.790210i	$0.290029\pi$
$654$	4.80194	0.187771
$655$	4.46681	0.174533
$656$	2.41417	0.0942577
$657$	3.40581	0.132873
$658$	−11.3177	−0.441209
$659$	12.6383	0.492319	0.246159	−	0.969229i	$-0.420831\pi$
$659$	12.6383	0.492319	0.246159	+	0.969229i	$0.420831\pi$
$660$	0.554958	0.0216017
$661$	21.5483	0.838130	0.419065	−	0.907956i	$-0.362358\pi$
$661$	21.5483	0.838130	0.419065	+	0.907956i	$0.362358\pi$
$662$	−28.5948	−1.11137
$663$	0	0
$664$	27.2174	1.05624
$665$	0.664874	0.0257827
$666$	3.46681	0.134336
$667$	−9.91484	−0.383904
$668$	−1.35152	−0.0522918
$669$	−27.1933	−1.05135
$670$	10.4819	0.404950
$671$	−9.86592	−0.380870
$672$	−2.46681	−0.0951593
$673$	26.5176	1.02218	0.511090	−	0.859527i	$-0.329242\pi$
$673$	26.5176	1.02218	0.511090	+	0.859527i	$0.329242\pi$
$674$	2.80731	0.108134
$675$	−4.00000	−0.153960
$676$	0	0
$677$	14.5670	0.559857	0.279928	−	0.960021i	$-0.409689\pi$
$677$	14.5670	0.559857	0.279928	+	0.960021i	$0.409689\pi$
$678$	−18.1129	−0.695622
$679$	−10.5211	−0.403763
$680$	11.5918	0.444525
$681$	−9.40581	−0.360432
$682$	−2.80194	−0.107292
$683$	40.9503	1.56692	0.783461	−	0.621441i	$-0.213453\pi$
$683$	40.9503	1.56692	0.783461	+	0.621441i	$0.213453\pi$
$684$	0.295897	0.0113139
$685$	11.1903	0.427559
$686$	−1.24698	−0.0476099
$687$	−15.5961	−0.595029
$688$	23.2948	0.888107
$689$	0	0
$690$	−2.87800	−0.109564
$691$	28.4650	1.08286	0.541430	−	0.840746i	$-0.317883\pi$
$691$	28.4650	1.08286	0.541430	+	0.840746i	$0.317883\pi$
$692$	8.01400	0.304647
$693$	1.24698	0.0473688
$694$	−9.16182	−0.347778
$695$	14.0218	0.531876
$696$	13.0978	0.496472
$697$	3.15213	0.119395
$698$	−3.13036	−0.118486
$699$	7.13036	0.269695
$700$	1.78017	0.0672840
$701$	−32.9506	−1.24453	−0.622264	−	0.782808i	$-0.713787\pi$
$701$	−32.9506	−1.24453	−0.622264	+	0.782808i	$0.713787\pi$
$702$	0	0
$703$	1.84846	0.0697161
$704$	11.0978	0.418265
$705$	−9.07606	−0.341824
$706$	22.4239	0.843933
$707$	3.92154	0.147485
$708$	−0.401501	−0.0150893
$709$	−18.9869	−0.713066	−0.356533	−	0.934283i	$-0.616041\pi$
$709$	−18.9869	−0.713066	−0.356533	+	0.934283i	$0.616041\pi$
$710$	−8.40581	−0.315465
$711$	−13.8388	−0.518995
$712$	−2.08038	−0.0779654
$713$	−4.15883	−0.155750
$714$	4.74094	0.177425
$715$	0	0
$716$	9.13706	0.341468
$717$	−3.05861	−0.114226
$718$	21.0043	0.783874
$719$	−27.9017	−1.04056	−0.520279	−	0.853996i	$-0.674172\pi$
$719$	−27.9017	−1.04056	−0.520279	+	0.853996i	$0.674172\pi$
$720$	2.91185	0.108518
$721$	4.72886	0.176112
$722$	23.1414	0.861233
$723$	−24.2664	−0.902476
$724$	−1.14138	−0.0424189
$725$	−17.1836	−0.638182
$726$	11.7778	0.437114
$727$	6.13898	0.227682	0.113841	−	0.993499i	$-0.463685\pi$
$727$	6.13898	0.227682	0.113841	+	0.993499i	$0.463685\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.24698	0.157188
$731$	30.4155	1.12496
$732$	3.52111	0.130144
$733$	−32.9511	−1.21708	−0.608538	−	0.793525i	$-0.708244\pi$
$733$	−32.9511	−1.21708	−0.608538	+	0.793525i	$0.708244\pi$
$734$	27.7348	1.02371
$735$	−1.00000	−0.0368856
$736$	5.69335	0.209860
$737$	10.4819	0.386105
$738$	1.03385	0.0380566
$739$	−40.4868	−1.48933	−0.744665	−	0.667438i	$-0.767391\pi$
$739$	−40.4868	−1.48933	−0.744665	+	0.667438i	$0.767391\pi$
$740$	−1.23729	−0.0454837
$741$	0	0
$742$	15.0707	0.553262
$743$	−31.6862	−1.16245	−0.581226	−	0.813742i	$-0.697427\pi$
$743$	−31.6862	−1.16245	−0.581226	+	0.813742i	$0.697427\pi$
$744$	5.49396	0.201418
$745$	−4.09246	−0.149936
$746$	−8.41550	−0.308113
$747$	8.92692	0.326619
$748$	2.10992	0.0771462
$749$	5.29052	0.193311
$750$	−11.2228	−0.409799
$751$	2.69202	0.0982333	0.0491166	−	0.998793i	$-0.484359\pi$
$751$	2.69202	0.0982333	0.0491166	+	0.998793i	$0.484359\pi$
$752$	−26.4282	−0.963736
$753$	15.4601	0.563398
$754$	0	0
$755$	7.43967	0.270757
$756$	−0.445042	−0.0161860
$757$	49.4379	1.79685	0.898425	−	0.439127i	$-0.144712\pi$
$757$	49.4379	1.79685	0.898425	+	0.439127i	$0.144712\pi$
$758$	16.0234	0.581997
$759$	−2.87800	−0.104465
$760$	2.02715	0.0735324
$761$	−38.3545	−1.39035	−0.695175	−	0.718841i	$-0.744673\pi$
$761$	−38.3545	−1.39035	−0.695175	+	0.718841i	$0.744673\pi$
$762$	−25.0586	−0.907778
$763$	−3.85086	−0.139410
$764$	0.794642	0.0287491
$765$	3.80194	0.137459
$766$	−41.1896	−1.48824
$767$	0	0
$768$	−10.1129	−0.364918
$769$	−9.24267	−0.333299	−0.166650	−	0.986016i	$-0.553295\pi$
$769$	−9.24267	−0.333299	−0.166650	+	0.986016i	$0.553295\pi$
$770$	1.55496	0.0560368
$771$	−27.1987	−0.979536
$772$	3.93602	0.141660
$773$	−41.6431	−1.49780	−0.748899	−	0.662684i	$-0.769417\pi$
$773$	−41.6431	−1.49780	−0.748899	+	0.662684i	$0.769417\pi$
$774$	9.97584	0.358574
$775$	−7.20775	−0.258910
$776$	−32.0780	−1.15153
$777$	−2.78017	−0.0997380
$778$	−21.8280	−0.782572
$779$	0.551237	0.0197501
$780$	0	0
$781$	−8.40581	−0.300784
$782$	−10.9420	−0.391285
$783$	4.29590	0.153523
$784$	−2.91185	−0.103995
$785$	13.7192	0.489658
$786$	5.57002	0.198676
$787$	23.3263	0.831492	0.415746	−	0.909481i	$-0.363520\pi$
$787$	23.3263	0.831492	0.415746	+	0.909481i	$0.363520\pi$
$788$	−1.66056	−0.0591551
$789$	9.70410	0.345475
$790$	−17.2567	−0.613965
$791$	14.5254	0.516464
$792$	3.80194	0.135096
$793$	0	0
$794$	26.1226	0.927056
$795$	12.0858	0.428637
$796$	10.2349	0.362766
$797$	15.8696	0.562132	0.281066	−	0.959689i	$-0.409312\pi$
$797$	15.8696	0.562132	0.281066	+	0.959689i	$0.409312\pi$
$798$	0.829085	0.0293493
$799$	−34.5066	−1.22076
$800$	9.86725	0.348860
$801$	−0.682333	−0.0241090
$802$	22.2241	0.784762
$803$	4.24698	0.149873
$804$	−3.74094	−0.131933
$805$	2.30798	0.0813456
$806$	0	0
$807$	26.8189	0.944071
$808$	11.9565	0.420627
$809$	30.9912	1.08959	0.544796	−	0.838569i	$-0.316607\pi$
$809$	30.9912	1.08959	0.544796	+	0.838569i	$0.316607\pi$
$810$	1.24698	0.0438144
$811$	22.1517	0.777850	0.388925	−	0.921269i	$-0.372847\pi$
$811$	22.1517	0.777850	0.388925	+	0.921269i	$0.372847\pi$
$812$	−1.91185	−0.0670929
$813$	28.6353	1.00429
$814$	4.32304	0.151523
$815$	7.66487	0.268489
$816$	11.0707	0.387552
$817$	5.31900	0.186088
$818$	9.41119	0.329055
$819$	0	0
$820$	−0.368977	−0.0128853
$821$	32.2097	1.12413	0.562063	−	0.827095i	$-0.310008\pi$
$821$	32.2097	1.12413	0.562063	+	0.827095i	$0.310008\pi$
$822$	13.9541	0.486704
$823$	−23.2948	−0.812007	−0.406003	−	0.913872i	$-0.633078\pi$
$823$	−23.2948	−0.812007	−0.406003	+	0.913872i	$0.633078\pi$
$824$	14.4179	0.502271
$825$	−4.98792	−0.173657
$826$	−1.12498	−0.0391431
$827$	31.3889	1.09150	0.545750	−	0.837948i	$-0.316245\pi$
$827$	31.3889	1.09150	0.545750	+	0.837948i	$0.316245\pi$
$828$	1.02715	0.0356958
$829$	−16.1065	−0.559400	−0.279700	−	0.960087i	$-0.590235\pi$
$829$	−16.1065	−0.559400	−0.279700	+	0.960087i	$0.590235\pi$
$830$	11.1317	0.386386
$831$	−27.1943	−0.943361
$832$	0	0
$833$	−3.80194	−0.131729
$834$	17.4849	0.605451
$835$	−3.03684	−0.105094
$836$	0.368977	0.0127614
$837$	1.80194	0.0622841
$838$	15.8146	0.546307
$839$	14.1817	0.489606	0.244803	−	0.969573i	$-0.421277\pi$
$839$	14.1817	0.489606	0.244803	+	0.969573i	$0.421277\pi$
$840$	−3.04892	−0.105198
$841$	−10.5453	−0.363630
$842$	−19.9095	−0.686125
$843$	29.0629	1.00098
$844$	−3.64981	−0.125632
$845$	0	0
$846$	−11.3177	−0.389109
$847$	−9.44504	−0.324535
$848$	35.1919	1.20850
$849$	15.1927	0.521412
$850$	−18.9638	−0.650451
$851$	6.41657	0.219957
$852$	3.00000	0.102778
$853$	9.48486	0.324755	0.162378	−	0.986729i	$-0.448084\pi$
$853$	9.48486	0.324755	0.162378	+	0.986729i	$0.448084\pi$
$854$	9.86592	0.337605
$855$	0.664874	0.0227382
$856$	16.1304	0.551324
$857$	31.6853	1.08235	0.541175	−	0.840910i	$-0.317980\pi$
$857$	31.6853	1.08235	0.541175	+	0.840910i	$0.317980\pi$
$858$	0	0
$859$	36.0103	1.22865	0.614327	−	0.789051i	$-0.289427\pi$
$859$	36.0103	1.22865	0.614327	+	0.789051i	$0.289427\pi$
$860$	−3.56033	−0.121406
$861$	−0.829085	−0.0282551
$862$	−28.1075	−0.957346
$863$	31.0213	1.05598	0.527989	−	0.849251i	$-0.322946\pi$
$863$	31.0213	1.05598	0.527989	+	0.849251i	$0.322946\pi$
$864$	−2.46681	−0.0839227
$865$	18.0073	0.612266
$866$	−33.4168	−1.13555
$867$	−2.54527	−0.0864419
$868$	−0.801938	−0.0272195
$869$	−17.2567	−0.585392
$870$	5.35690	0.181616
$871$	0	0
$872$	−11.7409	−0.397598
$873$	−10.5211	−0.356085
$874$	−1.91351	−0.0647254
$875$	9.00000	0.304256
$876$	−1.51573	−0.0512118
$877$	50.8273	1.71632	0.858158	−	0.513386i	$-0.171609\pi$
$877$	50.8273	1.71632	0.858158	+	0.513386i	$0.171609\pi$
$878$	33.4252	1.12805
$879$	−29.4959	−0.994871
$880$	3.63102	0.122402
$881$	16.2999	0.549159	0.274580	−	0.961564i	$-0.411461\pi$
$881$	16.2999	0.549159	0.274580	+	0.961564i	$0.411461\pi$
$882$	−1.24698	−0.0419880
$883$	−56.4669	−1.90026	−0.950132	−	0.311849i	$-0.899052\pi$
$883$	−56.4669	−1.90026	−0.950132	+	0.311849i	$0.899052\pi$
$884$	0	0
$885$	−0.902165	−0.0303260
$886$	−6.52243	−0.219125
$887$	−50.7717	−1.70475	−0.852373	−	0.522935i	$-0.824837\pi$
$887$	−50.7717	−1.70475	−0.852373	+	0.522935i	$0.824837\pi$
$888$	−8.47650	−0.284453
$889$	20.0954	0.673979
$890$	−0.850855	−0.0285207
$891$	1.24698	0.0417754
$892$	12.1021	0.405210
$893$	−6.03444	−0.201935
$894$	−5.10321	−0.170677
$895$	20.5308	0.686269
$896$	−6.16421	−0.205932
$897$	0	0
$898$	−46.3755	−1.54757
$899$	7.74094	0.258175
$900$	1.78017	0.0593389
$901$	45.9493	1.53079
$902$	1.28919	0.0429254
$903$	−8.00000	−0.266223
$904$	44.2868	1.47296
$905$	−2.56465	−0.0852517
$906$	9.27711	0.308211
$907$	2.24698	0.0746097	0.0373049	−	0.999304i	$-0.488123\pi$
$907$	2.24698	0.0746097	0.0373049	+	0.999304i	$0.488123\pi$
$908$	4.18598	0.138917
$909$	3.92154	0.130069
$910$	0	0
$911$	11.2295	0.372051	0.186025	−	0.982545i	$-0.440439\pi$
$911$	11.2295	0.372051	0.186025	+	0.982545i	$0.440439\pi$
$912$	1.93602	0.0641079
$913$	11.1317	0.368405
$914$	11.1166	0.367705
$915$	7.91185	0.261558
$916$	6.94092	0.229334
$917$	−4.46681	−0.147507
$918$	4.74094	0.156474
$919$	12.6364	0.416836	0.208418	−	0.978040i	$-0.433169\pi$
$919$	12.6364	0.416836	0.208418	+	0.978040i	$0.433169\pi$
$920$	7.03684	0.231998
$921$	−32.7415	−1.07887
$922$	−6.74466	−0.222124
$923$	0	0
$924$	−0.554958	−0.0182568
$925$	11.1207	0.365645
$926$	6.86964	0.225750
$927$	4.72886	0.155316
$928$	−10.5972	−0.347869
$929$	8.00730	0.262711	0.131355	−	0.991335i	$-0.458067\pi$
$929$	8.00730	0.262711	0.131355	+	0.991335i	$0.458067\pi$
$930$	2.24698	0.0736814
$931$	−0.664874	−0.0217904
$932$	−3.17331	−0.103945
$933$	2.59956	0.0851059
$934$	−3.87502	−0.126794
$935$	4.74094	0.155045
$936$	0	0
$937$	6.48486	0.211851	0.105926	−	0.994374i	$-0.466219\pi$
$937$	6.48486	0.211851	0.105926	+	0.994374i	$0.466219\pi$
$938$	−10.4819	−0.342245
$939$	−11.9511	−0.390009
$940$	4.03923	0.131745
$941$	37.6896	1.22865	0.614323	−	0.789054i	$-0.289429\pi$
$941$	37.6896	1.22865	0.614323	+	0.789054i	$0.289429\pi$
$942$	17.1075	0.557393
$943$	1.91351	0.0623125
$944$	−2.62697	−0.0855007
$945$	−1.00000	−0.0325300
$946$	12.4397	0.404448
$947$	−11.2174	−0.364518	−0.182259	−	0.983251i	$-0.558341\pi$
$947$	−11.2174	−0.364518	−0.182259	+	0.983251i	$0.558341\pi$
$948$	6.15883	0.200030
$949$	0	0
$950$	−3.31634	−0.107596
$951$	−1.93602	−0.0627797
$952$	−11.5918	−0.375692
$953$	−38.7415	−1.25496	−0.627481	−	0.778632i	$-0.715914\pi$
$953$	−38.7415	−1.25496	−0.627481	+	0.778632i	$0.715914\pi$
$954$	15.0707	0.487932
$955$	1.78554	0.0577789
$956$	1.36121	0.0440246
$957$	5.35690	0.173164
$958$	37.2258	1.20271
$959$	−11.1903	−0.361353
$960$	−8.89977	−0.287239
$961$	−27.7530	−0.895259
$962$	0	0
$963$	5.29052	0.170485
$964$	10.7995	0.347830
$965$	8.84415	0.284703
$966$	2.87800	0.0925982
$967$	11.2258	0.360997	0.180499	−	0.983575i	$-0.442229\pi$
$967$	11.2258	0.360997	0.180499	+	0.983575i	$0.442229\pi$
$968$	−28.7972	−0.925576
$969$	2.52781	0.0812050
$970$	−13.1196	−0.421245
$971$	−2.34913	−0.0753870	−0.0376935	−	0.999289i	$-0.512001\pi$
$971$	−2.34913	−0.0753870	−0.0376935	+	0.999289i	$0.512001\pi$
$972$	−0.445042	−0.0142747
$973$	−14.0218	−0.449517
$974$	−43.5532	−1.39553
$975$	0	0
$976$	23.0382	0.737434
$977$	29.4873	0.943381	0.471690	−	0.881764i	$-0.343644\pi$
$977$	29.4873	0.943381	0.471690	+	0.881764i	$0.343644\pi$
$978$	9.55794	0.305629
$979$	−0.850855	−0.0271934
$980$	0.445042	0.0142163
$981$	−3.85086	−0.122948
$982$	12.6227	0.402805
$983$	−8.99867	−0.287013	−0.143507	−	0.989649i	$-0.545838\pi$
$983$	−8.99867	−0.287013	−0.143507	+	0.989649i	$0.545838\pi$
$984$	−2.52781	−0.0805837
$985$	−3.73125	−0.118888
$986$	20.3666	0.648604
$987$	9.07606	0.288894
$988$	0	0
$989$	18.4638	0.587116
$990$	1.55496	0.0494198
$991$	−23.5338	−0.747575	−0.373788	−	0.927514i	$-0.621941\pi$
$991$	−23.5338	−0.747575	−0.373788	+	0.927514i	$0.621941\pi$
$992$	−4.44504	−0.141130
$993$	22.9312	0.727701
$994$	8.40581	0.266616
$995$	22.9976	0.729073
$996$	−3.97285	−0.125885
$997$	37.8812	1.19971	0.599856	−	0.800108i	$-0.295225\pi$
$997$	37.8812	1.19971	0.599856	+	0.800108i	$0.295225\pi$
$998$	10.2145	0.323333
$999$	−2.78017	−0.0879606

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.p.1.1	yes	3
13.12	even	2		3549.2.a.j.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.j.1.3	✓	3	13.12	even	2
3549.2.a.p.1.1	yes	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)

\(f(q)\)	\(=\)	\(q-1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -1.00000 q^{5} -1.24698 q^{6} +1.00000 q^{7} +3.04892 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.24698 q^{2} +1.00000 q^{3} -0.445042 q^{4} -1.00000 q^{5} -1.24698 q^{6} +1.00000 q^{7} +3.04892 q^{8} +1.00000 q^{9} +1.24698 q^{10} +1.24698 q^{11} -0.445042 q^{12} -1.24698 q^{14} -1.00000 q^{15} -2.91185 q^{16} -3.80194 q^{17} -1.24698 q^{18} -0.664874 q^{19} +0.445042 q^{20} +1.00000 q^{21} -1.55496 q^{22} -2.30798 q^{23} +3.04892 q^{24} -4.00000 q^{25} +1.00000 q^{27} -0.445042 q^{28} +4.29590 q^{29} +1.24698 q^{30} +1.80194 q^{31} -2.46681 q^{32} +1.24698 q^{33} +4.74094 q^{34} -1.00000 q^{35} -0.445042 q^{36} -2.78017 q^{37} +0.829085 q^{38} -3.04892 q^{40} -0.829085 q^{41} -1.24698 q^{42} -8.00000 q^{43} -0.554958 q^{44} -1.00000 q^{45} +2.87800 q^{46} +9.07606 q^{47} -2.91185 q^{48} +1.00000 q^{49} +4.98792 q^{50} -3.80194 q^{51} -12.0858 q^{53} -1.24698 q^{54} -1.24698 q^{55} +3.04892 q^{56} -0.664874 q^{57} -5.35690 q^{58} +0.902165 q^{59} +0.445042 q^{60} -7.91185 q^{61} -2.24698 q^{62} +1.00000 q^{63} +8.89977 q^{64} -1.55496 q^{66} +8.40581 q^{67} +1.69202 q^{68} -2.30798 q^{69} +1.24698 q^{70} -6.74094 q^{71} +3.04892 q^{72} +3.40581 q^{73} +3.46681 q^{74} -4.00000 q^{75} +0.295897 q^{76} +1.24698 q^{77} -13.8388 q^{79} +2.91185 q^{80} +1.00000 q^{81} +1.03385 q^{82} +8.92692 q^{83} -0.445042 q^{84} +3.80194 q^{85} +9.97584 q^{86} +4.29590 q^{87} +3.80194 q^{88} -0.682333 q^{89} +1.24698 q^{90} +1.02715 q^{92} +1.80194 q^{93} -11.3177 q^{94} +0.664874 q^{95} -2.46681 q^{96} -10.5211 q^{97} -1.24698 q^{98} +1.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} - q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{9} - q^{10} - q^{11} - q^{12} + q^{14} - 3 q^{15} - 5 q^{16} - 7 q^{17} + q^{18} - 3 q^{19} + q^{20} + 3 q^{21} - 5 q^{22} - 12 q^{23} - 12 q^{25} + 3 q^{27} - q^{28} - q^{29} - q^{30} + q^{31} - 4 q^{32} - q^{33} - 3 q^{35} - q^{36} - 7 q^{37} - 8 q^{38} + 8 q^{41} + q^{42} - 24 q^{43} - 2 q^{44} - 3 q^{45} - 11 q^{46} + 12 q^{47} - 5 q^{48} + 3 q^{49} - 4 q^{50} - 7 q^{51} + q^{53} + q^{54} + q^{55} - 3 q^{57} - 12 q^{58} + 21 q^{59} + q^{60} - 20 q^{61} - 2 q^{62} + 3 q^{63} + 4 q^{64} - 5 q^{66} + 12 q^{67} - 12 q^{69} - q^{70} - 6 q^{71} - 3 q^{73} + 7 q^{74} - 12 q^{75} - 13 q^{76} - q^{77} - 9 q^{79} + 5 q^{80} + 3 q^{81} + 19 q^{82} - 2 q^{83} - q^{84} + 7 q^{85} - 8 q^{86} - q^{87} + 7 q^{88} - 19 q^{89} - q^{90} - 3 q^{92} + q^{93} - 17 q^{94} + 3 q^{95} - 4 q^{96} - 16 q^{97} + q^{98} - q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 - q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^9 - q^10 - q^11 - q^12 + q^14 - 3 * q^15 - 5 * q^16 - 7 * q^17 + q^18 - 3 * q^19 + q^20 + 3 * q^21 - 5 * q^22 - 12 * q^23 - 12 * q^25 + 3 * q^27 - q^28 - q^29 - q^30 + q^31 - 4 * q^32 - q^33 - 3 * q^35 - q^36 - 7 * q^37 - 8 * q^38 + 8 * q^41 + q^42 - 24 * q^43 - 2 * q^44 - 3 * q^45 - 11 * q^46 + 12 * q^47 - 5 * q^48 + 3 * q^49 - 4 * q^50 - 7 * q^51 + q^53 + q^54 + q^55 - 3 * q^57 - 12 * q^58 + 21 * q^59 + q^60 - 20 * q^61 - 2 * q^62 + 3 * q^63 + 4 * q^64 - 5 * q^66 + 12 * q^67 - 12 * q^69 - q^70 - 6 * q^71 - 3 * q^73 + 7 * q^74 - 12 * q^75 - 13 * q^76 - q^77 - 9 * q^79 + 5 * q^80 + 3 * q^81 + 19 * q^82 - 2 * q^83 - q^84 + 7 * q^85 - 8 * q^86 - q^87 + 7 * q^88 - 19 * q^89 - q^90 - 3 * q^92 + q^93 - 17 * q^94 + 3 * q^95 - 4 * q^96 - 16 * q^97 + q^98 - q^99

Introduction

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