LMFDB - Embedded newform 6027.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} +2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} +2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} -2.41421 q^{10} -2.00000 q^{11} -3.82843 q^{12} +1.58579 q^{13} -1.00000 q^{15} +3.00000 q^{16} +6.82843 q^{17} -2.41421 q^{18} -2.82843 q^{19} +3.82843 q^{20} +4.82843 q^{22} +5.24264 q^{23} +4.41421 q^{24} -4.00000 q^{25} -3.82843 q^{26} -1.00000 q^{27} -10.4142 q^{29} +2.41421 q^{30} +3.65685 q^{31} +1.58579 q^{32} +2.00000 q^{33} -16.4853 q^{34} +3.82843 q^{36} -7.82843 q^{37} +6.82843 q^{38} -1.58579 q^{39} -4.41421 q^{40} +1.00000 q^{41} +9.65685 q^{43} -7.65685 q^{44} +1.00000 q^{45} -12.6569 q^{46} -6.65685 q^{47} -3.00000 q^{48} +9.65685 q^{50} -6.82843 q^{51} +6.07107 q^{52} -0.414214 q^{53} +2.41421 q^{54} -2.00000 q^{55} +2.82843 q^{57} +25.1421 q^{58} +10.0000 q^{59} -3.82843 q^{60} -7.31371 q^{61} -8.82843 q^{62} -9.82843 q^{64} +1.58579 q^{65} -4.82843 q^{66} -5.82843 q^{67} +26.1421 q^{68} -5.24264 q^{69} +5.17157 q^{71} -4.41421 q^{72} +3.65685 q^{73} +18.8995 q^{74} +4.00000 q^{75} -10.8284 q^{76} +3.82843 q^{78} -15.4853 q^{79} +3.00000 q^{80} +1.00000 q^{81} -2.41421 q^{82} +3.17157 q^{83} +6.82843 q^{85} -23.3137 q^{86} +10.4142 q^{87} +8.82843 q^{88} -2.82843 q^{89} -2.41421 q^{90} +20.0711 q^{92} -3.65685 q^{93} +16.0711 q^{94} -2.82843 q^{95} -1.58579 q^{96} +2.89949 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{24} - 8 q^{25} - 2 q^{26} - 2 q^{27} - 18 q^{29} + 2 q^{30} - 4 q^{31} + 6 q^{32} + 4 q^{33} - 16 q^{34} + 2 q^{36} - 10 q^{37} + 8 q^{38} - 6 q^{39} - 6 q^{40} + 2 q^{41} + 8 q^{43} - 4 q^{44} + 2 q^{45} - 14 q^{46} - 2 q^{47} - 6 q^{48} + 8 q^{50} - 8 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} - 4 q^{55} + 22 q^{58} + 20 q^{59} - 2 q^{60} + 8 q^{61} - 12 q^{62} - 14 q^{64} + 6 q^{65} - 4 q^{66} - 6 q^{67} + 24 q^{68} - 2 q^{69} + 16 q^{71} - 6 q^{72} - 4 q^{73} + 18 q^{74} + 8 q^{75} - 16 q^{76} + 2 q^{78} - 14 q^{79} + 6 q^{80} + 2 q^{81} - 2 q^{82} + 12 q^{83} + 8 q^{85} - 24 q^{86} + 18 q^{87} + 12 q^{88} - 2 q^{90} + 26 q^{92} + 4 q^{93} + 18 q^{94} - 6 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^24 - 8 * q^25 - 2 * q^26 - 2 * q^27 - 18 * q^29 + 2 * q^30 - 4 * q^31 + 6 * q^32 + 4 * q^33 - 16 * q^34 + 2 * q^36 - 10 * q^37 + 8 * q^38 - 6 * q^39 - 6 * q^40 + 2 * q^41 + 8 * q^43 - 4 * q^44 + 2 * q^45 - 14 * q^46 - 2 * q^47 - 6 * q^48 + 8 * q^50 - 8 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 - 4 * q^55 + 22 * q^58 + 20 * q^59 - 2 * q^60 + 8 * q^61 - 12 * q^62 - 14 * q^64 + 6 * q^65 - 4 * q^66 - 6 * q^67 + 24 * q^68 - 2 * q^69 + 16 * q^71 - 6 * q^72 - 4 * q^73 + 18 * q^74 + 8 * q^75 - 16 * q^76 + 2 * q^78 - 14 * q^79 + 6 * q^80 + 2 * q^81 - 2 * q^82 + 12 * q^83 + 8 * q^85 - 24 * q^86 + 18 * q^87 + 12 * q^88 - 2 * q^90 + 26 * q^92 + 4 * q^93 + 18 * q^94 - 6 * q^96 - 14 * q^97 - 4 * 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 $

$2$	−2.41421	−1.70711	−0.853553	−	0.521005i	$-0.825557\pi$
$2$	−2.41421	−1.70711	−0.853553	+	0.521005i	$0.825557\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.82843	1.91421
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	2.41421	0.985599
$7$	0	0
$7$	0	0
$8$	−4.41421	−1.56066
$9$	1.00000	0.333333
$10$	−2.41421	−0.763441
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−3.82843	−1.10517
$13$	1.58579	0.439818	0.219909	−	0.975520i	$-0.429424\pi$
$13$	1.58579	0.439818	0.219909	+	0.975520i	$0.429424\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	3.00000	0.750000
$17$	6.82843	1.65614	0.828068	−	0.560627i	$-0.189440\pi$
$17$	6.82843	1.65614	0.828068	+	0.560627i	$0.189440\pi$
$18$	−2.41421	−0.569036
$19$	−2.82843	−0.648886	−0.324443	−	0.945905i	$-0.605177\pi$
$19$	−2.82843	−0.648886	−0.324443	+	0.945905i	$0.605177\pi$
$20$	3.82843	0.856062
$21$	0	0
$22$	4.82843	1.02942
$23$	5.24264	1.09317	0.546583	−	0.837405i	$-0.315928\pi$
$23$	5.24264	1.09317	0.546583	+	0.837405i	$0.315928\pi$
$24$	4.41421	0.901048
$25$	−4.00000	−0.800000
$26$	−3.82843	−0.750816
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−10.4142	−1.93387	−0.966935	−	0.255021i	$-0.917918\pi$
$29$	−10.4142	−1.93387	−0.966935	+	0.255021i	$0.917918\pi$
$30$	2.41421	0.440773
$31$	3.65685	0.656790	0.328395	−	0.944540i	$-0.393492\pi$
$31$	3.65685	0.656790	0.328395	+	0.944540i	$0.393492\pi$
$32$	1.58579	0.280330
$33$	2.00000	0.348155
$34$	−16.4853	−2.82720
$35$	0	0
$36$	3.82843	0.638071
$37$	−7.82843	−1.28699	−0.643493	−	0.765452i	$-0.722515\pi$
$37$	−7.82843	−1.28699	−0.643493	+	0.765452i	$0.722515\pi$
$38$	6.82843	1.10772
$39$	−1.58579	−0.253929
$40$	−4.41421	−0.697948
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	9.65685	1.47266	0.736328	−	0.676625i	$-0.236558\pi$
$43$	9.65685	1.47266	0.736328	+	0.676625i	$0.236558\pi$
$44$	−7.65685	−1.15431
$45$	1.00000	0.149071
$46$	−12.6569	−1.86615
$47$	−6.65685	−0.971002	−0.485501	−	0.874236i	$-0.661363\pi$
$47$	−6.65685	−0.971002	−0.485501	+	0.874236i	$0.661363\pi$
$48$	−3.00000	−0.433013
$49$	0	0
$50$	9.65685	1.36569
$51$	−6.82843	−0.956171
$52$	6.07107	0.841906
$53$	−0.414214	−0.0568966	−0.0284483	−	0.999595i	$-0.509057\pi$
$53$	−0.414214	−0.0568966	−0.0284483	+	0.999595i	$0.509057\pi$
$54$	2.41421	0.328533
$55$	−2.00000	−0.269680
$56$	0	0
$57$	2.82843	0.374634
$58$	25.1421	3.30132
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	−3.82843	−0.494248
$61$	−7.31371	−0.936424	−0.468212	−	0.883616i	$-0.655102\pi$
$61$	−7.31371	−0.936424	−0.468212	+	0.883616i	$0.655102\pi$
$62$	−8.82843	−1.12121
$63$	0	0
$64$	−9.82843	−1.22855
$65$	1.58579	0.196693
$66$	−4.82843	−0.594338
$67$	−5.82843	−0.712056	−0.356028	−	0.934475i	$-0.615869\pi$
$67$	−5.82843	−0.712056	−0.356028	+	0.934475i	$0.615869\pi$
$68$	26.1421	3.17020
$69$	−5.24264	−0.631140
$70$	0	0
$71$	5.17157	0.613753	0.306876	−	0.951749i	$-0.400716\pi$
$71$	5.17157	0.613753	0.306876	+	0.951749i	$0.400716\pi$
$72$	−4.41421	−0.520220
$73$	3.65685	0.428002	0.214001	−	0.976833i	$-0.431350\pi$
$73$	3.65685	0.428002	0.214001	+	0.976833i	$0.431350\pi$
$74$	18.8995	2.19702
$75$	4.00000	0.461880
$76$	−10.8284	−1.24211
$77$	0	0
$78$	3.82843	0.433484
$79$	−15.4853	−1.74223	−0.871115	−	0.491079i	$-0.836603\pi$
$79$	−15.4853	−1.74223	−0.871115	+	0.491079i	$0.836603\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	−2.41421	−0.266605
$83$	3.17157	0.348125	0.174063	−	0.984735i	$-0.444310\pi$
$83$	3.17157	0.348125	0.174063	+	0.984735i	$0.444310\pi$
$84$	0	0
$85$	6.82843	0.740647
$86$	−23.3137	−2.51398
$87$	10.4142	1.11652
$88$	8.82843	0.941113
$89$	−2.82843	−0.299813	−0.149906	−	0.988700i	$-0.547897\pi$
$89$	−2.82843	−0.299813	−0.149906	+	0.988700i	$0.547897\pi$
$90$	−2.41421	−0.254480
$91$	0	0
$92$	20.0711	2.09255
$93$	−3.65685	−0.379198
$94$	16.0711	1.65760
$95$	−2.82843	−0.290191
$96$	−1.58579	−0.161849
$97$	2.89949	0.294399	0.147200	−	0.989107i	$-0.452974\pi$
$97$	2.89949	0.294399	0.147200	+	0.989107i	$0.452974\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	−15.3137	−1.53137
$101$	18.9706	1.88764	0.943821	−	0.330458i	$-0.107203\pi$
$101$	18.9706	1.88764	0.943821	+	0.330458i	$0.107203\pi$
$102$	16.4853	1.63229
$103$	−7.58579	−0.747450	−0.373725	−	0.927540i	$-0.621920\pi$
$103$	−7.58579	−0.747450	−0.373725	+	0.927540i	$0.621920\pi$
$104$	−7.00000	−0.686406
$105$	0	0
$106$	1.00000	0.0971286
$107$	−17.7279	−1.71382	−0.856911	−	0.515464i	$-0.827620\pi$
$107$	−17.7279	−1.71382	−0.856911	+	0.515464i	$0.827620\pi$
$108$	−3.82843	−0.368391
$109$	−14.1421	−1.35457	−0.677285	−	0.735720i	$-0.736844\pi$
$109$	−14.1421	−1.35457	−0.677285	+	0.735720i	$0.736844\pi$
$110$	4.82843	0.460372
$111$	7.82843	0.743041
$112$	0	0
$113$	−1.17157	−0.110212	−0.0551062	−	0.998481i	$-0.517550\pi$
$113$	−1.17157	−0.110212	−0.0551062	+	0.998481i	$0.517550\pi$
$114$	−6.82843	−0.639541
$115$	5.24264	0.488879
$116$	−39.8701	−3.70184
$117$	1.58579	0.146606
$118$	−24.1421	−2.22246
$119$	0	0
$120$	4.41421	0.402961
$121$	−7.00000	−0.636364
$122$	17.6569	1.59858
$123$	−1.00000	−0.0901670
$124$	14.0000	1.25724
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−20.9706	−1.86084	−0.930418	−	0.366499i	$-0.880556\pi$
$127$	−20.9706	−1.86084	−0.930418	+	0.366499i	$0.880556\pi$
$128$	20.5563	1.81694
$129$	−9.65685	−0.850239
$130$	−3.82843	−0.335775
$131$	−7.31371	−0.639002	−0.319501	−	0.947586i	$-0.603515\pi$
$131$	−7.31371	−0.639002	−0.319501	+	0.947586i	$0.603515\pi$
$132$	7.65685	0.666444
$133$	0	0
$134$	14.0711	1.21556
$135$	−1.00000	−0.0860663
$136$	−30.1421	−2.58467
$137$	0.899495	0.0768490	0.0384245	−	0.999262i	$-0.487766\pi$
$137$	0.899495	0.0768490	0.0384245	+	0.999262i	$0.487766\pi$
$138$	12.6569	1.07742
$139$	10.5563	0.895378	0.447689	−	0.894189i	$-0.352247\pi$
$139$	10.5563	0.895378	0.447689	+	0.894189i	$0.352247\pi$
$140$	0	0
$141$	6.65685	0.560608
$142$	−12.4853	−1.04774
$143$	−3.17157	−0.265220
$144$	3.00000	0.250000
$145$	−10.4142	−0.864853
$146$	−8.82843	−0.730646
$147$	0	0
$148$	−29.9706	−2.46357
$149$	15.7990	1.29430	0.647152	−	0.762361i	$-0.275960\pi$
$149$	15.7990	1.29430	0.647152	+	0.762361i	$0.275960\pi$
$150$	−9.65685	−0.788479
$151$	5.65685	0.460348	0.230174	−	0.973149i	$-0.426070\pi$
$151$	5.65685	0.460348	0.230174	+	0.973149i	$0.426070\pi$
$152$	12.4853	1.01269
$153$	6.82843	0.552046
$154$	0	0
$155$	3.65685	0.293726
$156$	−6.07107	−0.486074
$157$	−14.8284	−1.18344	−0.591719	−	0.806145i	$-0.701550\pi$
$157$	−14.8284	−1.18344	−0.591719	+	0.806145i	$0.701550\pi$
$158$	37.3848	2.97417
$159$	0.414214	0.0328493
$160$	1.58579	0.125367
$161$	0	0
$162$	−2.41421	−0.189679
$163$	14.4853	1.13457	0.567287	−	0.823520i	$-0.307993\pi$
$163$	14.4853	1.13457	0.567287	+	0.823520i	$0.307993\pi$
$164$	3.82843	0.298950
$165$	2.00000	0.155700
$166$	−7.65685	−0.594287
$167$	−19.1421	−1.48126	−0.740631	−	0.671911i	$-0.765474\pi$
$167$	−19.1421	−1.48126	−0.740631	+	0.671911i	$0.765474\pi$
$168$	0	0
$169$	−10.4853	−0.806560
$170$	−16.4853	−1.26436
$171$	−2.82843	−0.216295
$172$	36.9706	2.81898
$173$	−2.17157	−0.165102	−0.0825508	−	0.996587i	$-0.526307\pi$
$173$	−2.17157	−0.165102	−0.0825508	+	0.996587i	$0.526307\pi$
$174$	−25.1421	−1.90602
$175$	0	0
$176$	−6.00000	−0.452267
$177$	−10.0000	−0.751646
$178$	6.82843	0.511812
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	3.82843	0.285354
$181$	4.48528	0.333388	0.166694	−	0.986009i	$-0.446691\pi$
$181$	4.48528	0.333388	0.166694	+	0.986009i	$0.446691\pi$
$182$	0	0
$183$	7.31371	0.540645
$184$	−23.1421	−1.70606
$185$	−7.82843	−0.575557
$186$	8.82843	0.647332
$187$	−13.6569	−0.998688
$188$	−25.4853	−1.85871
$189$	0	0
$190$	6.82843	0.495386
$191$	6.82843	0.494088	0.247044	−	0.969004i	$-0.420541\pi$
$191$	6.82843	0.494088	0.247044	+	0.969004i	$0.420541\pi$
$192$	9.82843	0.709306
$193$	5.65685	0.407189	0.203595	−	0.979055i	$-0.434738\pi$
$193$	5.65685	0.407189	0.203595	+	0.979055i	$0.434738\pi$
$194$	−7.00000	−0.502571
$195$	−1.58579	−0.113561
$196$	0	0
$197$	−15.1716	−1.08093	−0.540465	−	0.841367i	$-0.681752\pi$
$197$	−15.1716	−1.08093	−0.540465	+	0.841367i	$0.681752\pi$
$198$	4.82843	0.343141
$199$	11.3137	0.802008	0.401004	−	0.916076i	$-0.368661\pi$
$199$	11.3137	0.802008	0.401004	+	0.916076i	$0.368661\pi$
$200$	17.6569	1.24853
$201$	5.82843	0.411106
$202$	−45.7990	−3.22241
$203$	0	0
$204$	−26.1421	−1.83032
$205$	1.00000	0.0698430
$206$	18.3137	1.27598
$207$	5.24264	0.364389
$208$	4.75736	0.329864
$209$	5.65685	0.391293
$210$	0	0
$211$	−0.514719	−0.0354347	−0.0177173	−	0.999843i	$-0.505640\pi$
$211$	−0.514719	−0.0354347	−0.0177173	+	0.999843i	$0.505640\pi$
$212$	−1.58579	−0.108912
$213$	−5.17157	−0.354350
$214$	42.7990	2.92568
$215$	9.65685	0.658592
$216$	4.41421	0.300349
$217$	0	0
$218$	34.1421	2.31240
$219$	−3.65685	−0.247107
$220$	−7.65685	−0.516225
$221$	10.8284	0.728399
$222$	−18.8995	−1.26845
$223$	−20.0711	−1.34406	−0.672029	−	0.740525i	$-0.734577\pi$
$223$	−20.0711	−1.34406	−0.672029	+	0.740525i	$0.734577\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	2.82843	0.188144
$227$	−4.65685	−0.309086	−0.154543	−	0.987986i	$-0.549391\pi$
$227$	−4.65685	−0.309086	−0.154543	+	0.987986i	$0.549391\pi$
$228$	10.8284	0.717130
$229$	−1.24264	−0.0821160	−0.0410580	−	0.999157i	$-0.513073\pi$
$229$	−1.24264	−0.0821160	−0.0410580	+	0.999157i	$0.513073\pi$
$230$	−12.6569	−0.834568
$231$	0	0
$232$	45.9706	3.01812
$233$	0.485281	0.0317918	0.0158959	−	0.999874i	$-0.494940\pi$
$233$	0.485281	0.0317918	0.0158959	+	0.999874i	$0.494940\pi$
$234$	−3.82843	−0.250272
$235$	−6.65685	−0.434245
$236$	38.2843	2.49209
$237$	15.4853	1.00588
$238$	0	0
$239$	18.6274	1.20491	0.602454	−	0.798154i	$-0.294190\pi$
$239$	18.6274	1.20491	0.602454	+	0.798154i	$0.294190\pi$
$240$	−3.00000	−0.193649
$241$	8.14214	0.524481	0.262241	−	0.965003i	$-0.415539\pi$
$241$	8.14214	0.524481	0.262241	+	0.965003i	$0.415539\pi$
$242$	16.8995	1.08634
$243$	−1.00000	−0.0641500
$244$	−28.0000	−1.79252
$245$	0	0
$246$	2.41421	0.153925
$247$	−4.48528	−0.285392
$248$	−16.1421	−1.02503
$249$	−3.17157	−0.200990
$250$	21.7279	1.37419
$251$	22.9706	1.44989	0.724945	−	0.688807i	$-0.241865\pi$
$251$	22.9706	1.44989	0.724945	+	0.688807i	$0.241865\pi$
$252$	0	0
$253$	−10.4853	−0.659204
$254$	50.6274	3.17665
$255$	−6.82843	−0.427613
$256$	−29.9706	−1.87316
$257$	21.4558	1.33838	0.669189	−	0.743092i	$-0.266641\pi$
$257$	21.4558	1.33838	0.669189	+	0.743092i	$0.266641\pi$
$258$	23.3137	1.45145
$259$	0	0
$260$	6.07107	0.376512
$261$	−10.4142	−0.644624
$262$	17.6569	1.09084
$263$	8.82843	0.544384	0.272192	−	0.962243i	$-0.412251\pi$
$263$	8.82843	0.544384	0.272192	+	0.962243i	$0.412251\pi$
$264$	−8.82843	−0.543352
$265$	−0.414214	−0.0254449
$266$	0	0
$267$	2.82843	0.173097
$268$	−22.3137	−1.36303
$269$	−23.1421	−1.41100	−0.705500	−	0.708709i	$-0.749278\pi$
$269$	−23.1421	−1.41100	−0.705500	+	0.708709i	$0.749278\pi$
$270$	2.41421	0.146924
$271$	24.8995	1.51254	0.756268	−	0.654262i	$-0.227020\pi$
$271$	24.8995	1.51254	0.756268	+	0.654262i	$0.227020\pi$
$272$	20.4853	1.24210
$273$	0	0
$274$	−2.17157	−0.131190
$275$	8.00000	0.482418
$276$	−20.0711	−1.20814
$277$	−1.34315	−0.0807018	−0.0403509	−	0.999186i	$-0.512848\pi$
$277$	−1.34315	−0.0807018	−0.0403509	+	0.999186i	$0.512848\pi$
$278$	−25.4853	−1.52851
$279$	3.65685	0.218930
$280$	0	0
$281$	18.8995	1.12745	0.563725	−	0.825963i	$-0.309368\pi$
$281$	18.8995	1.12745	0.563725	+	0.825963i	$0.309368\pi$
$282$	−16.0711	−0.957018
$283$	−5.31371	−0.315867	−0.157934	−	0.987450i	$-0.550483\pi$
$283$	−5.31371	−0.315867	−0.157934	+	0.987450i	$0.550483\pi$
$284$	19.7990	1.17485
$285$	2.82843	0.167542
$286$	7.65685	0.452759
$287$	0	0
$288$	1.58579	0.0934434
$289$	29.6274	1.74279
$290$	25.1421	1.47640
$291$	−2.89949	−0.169971
$292$	14.0000	0.819288
$293$	−4.48528	−0.262033	−0.131016	−	0.991380i	$-0.541824\pi$
$293$	−4.48528	−0.262033	−0.131016	+	0.991380i	$0.541824\pi$
$294$	0	0
$295$	10.0000	0.582223
$296$	34.5563	2.00855
$297$	2.00000	0.116052
$298$	−38.1421	−2.20951
$299$	8.31371	0.480794
$300$	15.3137	0.884137
$301$	0	0
$302$	−13.6569	−0.785864
$303$	−18.9706	−1.08983
$304$	−8.48528	−0.486664
$305$	−7.31371	−0.418782
$306$	−16.4853	−0.942401
$307$	−2.89949	−0.165483	−0.0827415	−	0.996571i	$-0.526368\pi$
$307$	−2.89949	−0.165483	−0.0827415	+	0.996571i	$0.526368\pi$
$308$	0	0
$309$	7.58579	0.431540
$310$	−8.82843	−0.501421
$311$	−11.0000	−0.623753	−0.311876	−	0.950123i	$-0.600957\pi$
$311$	−11.0000	−0.623753	−0.311876	+	0.950123i	$0.600957\pi$
$312$	7.00000	0.396297
$313$	−24.2132	−1.36861	−0.684306	−	0.729195i	$-0.739895\pi$
$313$	−24.2132	−1.36861	−0.684306	+	0.729195i	$0.739895\pi$
$314$	35.7990	2.02025
$315$	0	0
$316$	−59.2843	−3.33500
$317$	11.5858	0.650723	0.325361	−	0.945590i	$-0.394514\pi$
$317$	11.5858	0.650723	0.325361	+	0.945590i	$0.394514\pi$
$318$	−1.00000	−0.0560772
$319$	20.8284	1.16617
$320$	−9.82843	−0.549426
$321$	17.7279	0.989476
$322$	0	0
$323$	−19.3137	−1.07464
$324$	3.82843	0.212690
$325$	−6.34315	−0.351854
$326$	−34.9706	−1.93684
$327$	14.1421	0.782062
$328$	−4.41421	−0.243734
$329$	0	0
$330$	−4.82843	−0.265796
$331$	11.9706	0.657962	0.328981	−	0.944337i	$-0.393295\pi$
$331$	11.9706	0.657962	0.328981	+	0.944337i	$0.393295\pi$
$332$	12.1421	0.666386
$333$	−7.82843	−0.428995
$334$	46.2132	2.52867
$335$	−5.82843	−0.318441
$336$	0	0
$337$	26.1716	1.42566	0.712828	−	0.701339i	$-0.247414\pi$
$337$	26.1716	1.42566	0.712828	+	0.701339i	$0.247414\pi$
$338$	25.3137	1.37688
$339$	1.17157	0.0636311
$340$	26.1421	1.41776
$341$	−7.31371	−0.396060
$342$	6.82843	0.369239
$343$	0	0
$344$	−42.6274	−2.29832
$345$	−5.24264	−0.282254
$346$	5.24264	0.281846
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	39.8701	2.13726
$349$	−7.65685	−0.409862	−0.204931	−	0.978776i	$-0.565697\pi$
$349$	−7.65685	−0.409862	−0.204931	+	0.978776i	$0.565697\pi$
$350$	0	0
$351$	−1.58579	−0.0846430
$352$	−3.17157	−0.169045
$353$	−5.31371	−0.282820	−0.141410	−	0.989951i	$-0.545164\pi$
$353$	−5.31371	−0.282820	−0.141410	+	0.989951i	$0.545164\pi$
$354$	24.1421	1.28314
$355$	5.17157	0.274479
$356$	−10.8284	−0.573905
$357$	0	0
$358$	−28.9706	−1.53114
$359$	−11.9289	−0.629585	−0.314792	−	0.949161i	$-0.601935\pi$
$359$	−11.9289	−0.629585	−0.314792	+	0.949161i	$0.601935\pi$
$360$	−4.41421	−0.232649
$361$	−11.0000	−0.578947
$362$	−10.8284	−0.569129
$363$	7.00000	0.367405
$364$	0	0
$365$	3.65685	0.191408
$366$	−17.6569	−0.922939
$367$	−6.89949	−0.360151	−0.180075	−	0.983653i	$-0.557634\pi$
$367$	−6.89949	−0.360151	−0.180075	+	0.983653i	$0.557634\pi$
$368$	15.7279	0.819875
$369$	1.00000	0.0520579
$370$	18.8995	0.982538
$371$	0	0
$372$	−14.0000	−0.725866
$373$	−35.8284	−1.85513	−0.927563	−	0.373667i	$-0.878100\pi$
$373$	−35.8284	−1.85513	−0.927563	+	0.373667i	$0.878100\pi$
$374$	32.9706	1.70487
$375$	9.00000	0.464758
$376$	29.3848	1.51540
$377$	−16.5147	−0.850551
$378$	0	0
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	−10.8284	−0.555487
$381$	20.9706	1.07435
$382$	−16.4853	−0.843460
$383$	−14.3137	−0.731396	−0.365698	−	0.930734i	$-0.619170\pi$
$383$	−14.3137	−0.731396	−0.365698	+	0.930734i	$0.619170\pi$
$384$	−20.5563	−1.04901
$385$	0	0
$386$	−13.6569	−0.695116
$387$	9.65685	0.490885
$388$	11.1005	0.563543
$389$	−29.4558	−1.49347	−0.746735	−	0.665121i	$-0.768380\pi$
$389$	−29.4558	−1.49347	−0.746735	+	0.665121i	$0.768380\pi$
$390$	3.82843	0.193860
$391$	35.7990	1.81043
$392$	0	0
$393$	7.31371	0.368928
$394$	36.6274	1.84526
$395$	−15.4853	−0.779149
$396$	−7.65685	−0.384771
$397$	−9.17157	−0.460308	−0.230154	−	0.973154i	$-0.573923\pi$
$397$	−9.17157	−0.460308	−0.230154	+	0.973154i	$0.573923\pi$
$398$	−27.3137	−1.36911
$399$	0	0
$400$	−12.0000	−0.600000
$401$	−23.7990	−1.18846	−0.594232	−	0.804293i	$-0.702544\pi$
$401$	−23.7990	−1.18846	−0.594232	+	0.804293i	$0.702544\pi$
$402$	−14.0711	−0.701801
$403$	5.79899	0.288868
$404$	72.6274	3.61335
$405$	1.00000	0.0496904
$406$	0	0
$407$	15.6569	0.776081
$408$	30.1421	1.49226
$409$	15.7990	0.781210	0.390605	−	0.920558i	$-0.372266\pi$
$409$	15.7990	0.781210	0.390605	+	0.920558i	$0.372266\pi$
$410$	−2.41421	−0.119230
$411$	−0.899495	−0.0443688
$412$	−29.0416	−1.43078
$413$	0	0
$414$	−12.6569	−0.622050
$415$	3.17157	0.155686
$416$	2.51472	0.123294
$417$	−10.5563	−0.516947
$418$	−13.6569	−0.667979
$419$	38.8284	1.89689	0.948446	−	0.316938i	$-0.102655\pi$
$419$	38.8284	1.89689	0.948446	+	0.316938i	$0.102655\pi$
$420$	0	0
$421$	0.686292	0.0334478	0.0167239	−	0.999860i	$-0.494676\pi$
$421$	0.686292	0.0334478	0.0167239	+	0.999860i	$0.494676\pi$
$422$	1.24264	0.0604908
$423$	−6.65685	−0.323667
$424$	1.82843	0.0887963
$425$	−27.3137	−1.32491
$426$	12.4853	0.604914
$427$	0	0
$428$	−67.8701	−3.28062
$429$	3.17157	0.153125
$430$	−23.3137	−1.12429
$431$	−17.3137	−0.833972	−0.416986	−	0.908913i	$-0.636914\pi$
$431$	−17.3137	−0.833972	−0.416986	+	0.908913i	$0.636914\pi$
$432$	−3.00000	−0.144338
$433$	−12.1421	−0.583514	−0.291757	−	0.956493i	$-0.594240\pi$
$433$	−12.1421	−0.583514	−0.291757	+	0.956493i	$0.594240\pi$
$434$	0	0
$435$	10.4142	0.499323
$436$	−54.1421	−2.59294
$437$	−14.8284	−0.709340
$438$	8.82843	0.421839
$439$	−14.9706	−0.714506	−0.357253	−	0.934008i	$-0.616287\pi$
$439$	−14.9706	−0.714506	−0.357253	+	0.934008i	$0.616287\pi$
$440$	8.82843	0.420879
$441$	0	0
$442$	−26.1421	−1.24345
$443$	12.6274	0.599947	0.299973	−	0.953948i	$-0.403022\pi$
$443$	12.6274	0.599947	0.299973	+	0.953948i	$0.403022\pi$
$444$	29.9706	1.42234
$445$	−2.82843	−0.134080
$446$	48.4558	2.29445
$447$	−15.7990	−0.747267
$448$	0	0
$449$	17.3137	0.817084	0.408542	−	0.912739i	$-0.366037\pi$
$449$	17.3137	0.817084	0.408542	+	0.912739i	$0.366037\pi$
$450$	9.65685	0.455228
$451$	−2.00000	−0.0941763
$452$	−4.48528	−0.210970
$453$	−5.65685	−0.265782
$454$	11.2426	0.527643
$455$	0	0
$456$	−12.4853	−0.584677
$457$	11.3137	0.529233	0.264616	−	0.964354i	$-0.414755\pi$
$457$	11.3137	0.529233	0.264616	+	0.964354i	$0.414755\pi$
$458$	3.00000	0.140181
$459$	−6.82843	−0.318724
$460$	20.0711	0.935818
$461$	−40.7990	−1.90020	−0.950099	−	0.311948i	$-0.899019\pi$
$461$	−40.7990	−1.90020	−0.950099	+	0.311948i	$0.899019\pi$
$462$	0	0
$463$	−8.17157	−0.379765	−0.189883	−	0.981807i	$-0.560811\pi$
$463$	−8.17157	−0.379765	−0.189883	+	0.981807i	$0.560811\pi$
$464$	−31.2426	−1.45040
$465$	−3.65685	−0.169583
$466$	−1.17157	−0.0542721
$467$	−27.1127	−1.25463	−0.627313	−	0.778767i	$-0.715845\pi$
$467$	−27.1127	−1.25463	−0.627313	+	0.778767i	$0.715845\pi$
$468$	6.07107	0.280635
$469$	0	0
$470$	16.0711	0.741303
$471$	14.8284	0.683258
$472$	−44.1421	−2.03181
$473$	−19.3137	−0.888045
$474$	−37.3848	−1.71714
$475$	11.3137	0.519109
$476$	0	0
$477$	−0.414214	−0.0189655
$478$	−44.9706	−2.05691
$479$	4.97056	0.227111	0.113555	−	0.993532i	$-0.463776\pi$
$479$	4.97056	0.227111	0.113555	+	0.993532i	$0.463776\pi$
$480$	−1.58579	−0.0723809
$481$	−12.4142	−0.566039
$482$	−19.6569	−0.895345
$483$	0	0
$484$	−26.7990	−1.21814
$485$	2.89949	0.131659
$486$	2.41421	0.109511
$487$	16.4853	0.747019	0.373510	−	0.927626i	$-0.378154\pi$
$487$	16.4853	0.747019	0.373510	+	0.927626i	$0.378154\pi$
$488$	32.2843	1.46144
$489$	−14.4853	−0.655047
$490$	0	0
$491$	−19.6569	−0.887101	−0.443551	−	0.896249i	$-0.646281\pi$
$491$	−19.6569	−0.887101	−0.443551	+	0.896249i	$0.646281\pi$
$492$	−3.82843	−0.172599
$493$	−71.1127	−3.20275
$494$	10.8284	0.487194
$495$	−2.00000	−0.0898933
$496$	10.9706	0.492593
$497$	0	0
$498$	7.65685	0.343112
$499$	−10.3431	−0.463023	−0.231511	−	0.972832i	$-0.574367\pi$
$499$	−10.3431	−0.463023	−0.231511	+	0.972832i	$0.574367\pi$
$500$	−34.4558	−1.54091
$501$	19.1421	0.855208
$502$	−55.4558	−2.47512
$503$	25.4853	1.13633	0.568166	−	0.822914i	$-0.307653\pi$
$503$	25.4853	1.13633	0.568166	+	0.822914i	$0.307653\pi$
$504$	0	0
$505$	18.9706	0.844179
$506$	25.3137	1.12533
$507$	10.4853	0.465668
$508$	−80.2843	−3.56204
$509$	−27.6569	−1.22587	−0.612934	−	0.790134i	$-0.710011\pi$
$509$	−27.6569	−1.22587	−0.612934	+	0.790134i	$0.710011\pi$
$510$	16.4853	0.729981
$511$	0	0
$512$	31.2426	1.38074
$513$	2.82843	0.124878
$514$	−51.7990	−2.28476
$515$	−7.58579	−0.334270
$516$	−36.9706	−1.62754
$517$	13.3137	0.585536
$518$	0	0
$519$	2.17157	0.0953215
$520$	−7.00000	−0.306970
$521$	20.8284	0.912510	0.456255	−	0.889849i	$-0.349190\pi$
$521$	20.8284	0.912510	0.456255	+	0.889849i	$0.349190\pi$
$522$	25.1421	1.10044
$523$	9.31371	0.407260	0.203630	−	0.979048i	$-0.434726\pi$
$523$	9.31371	0.407260	0.203630	+	0.979048i	$0.434726\pi$
$524$	−28.0000	−1.22319
$525$	0	0
$526$	−21.3137	−0.929322
$527$	24.9706	1.08773
$528$	6.00000	0.261116
$529$	4.48528	0.195012
$530$	1.00000	0.0434372
$531$	10.0000	0.433963
$532$	0	0
$533$	1.58579	0.0686880
$534$	−6.82843	−0.295495
$535$	−17.7279	−0.766445
$536$	25.7279	1.11128
$537$	−12.0000	−0.517838
$538$	55.8701	2.40873
$539$	0	0
$540$	−3.82843	−0.164749
$541$	−30.7990	−1.32415	−0.662076	−	0.749437i	$-0.730324\pi$
$541$	−30.7990	−1.32415	−0.662076	+	0.749437i	$0.730324\pi$
$542$	−60.1127	−2.58206
$543$	−4.48528	−0.192482
$544$	10.8284	0.464265
$545$	−14.1421	−0.605783
$546$	0	0
$547$	1.34315	0.0574288	0.0287144	−	0.999588i	$-0.490859\pi$
$547$	1.34315	0.0574288	0.0287144	+	0.999588i	$0.490859\pi$
$548$	3.44365	0.147105
$549$	−7.31371	−0.312141
$550$	−19.3137	−0.823539
$551$	29.4558	1.25486
$552$	23.1421	0.984995
$553$	0	0
$554$	3.24264	0.137767
$555$	7.82843	0.332298
$556$	40.4142	1.71394
$557$	−35.7990	−1.51685	−0.758426	−	0.651759i	$-0.774031\pi$
$557$	−35.7990	−1.51685	−0.758426	+	0.651759i	$0.774031\pi$
$558$	−8.82843	−0.373737
$559$	15.3137	0.647701
$560$	0	0
$561$	13.6569	0.576593
$562$	−45.6274	−1.92468
$563$	30.4558	1.28356	0.641780	−	0.766888i	$-0.278196\pi$
$563$	30.4558	1.28356	0.641780	+	0.766888i	$0.278196\pi$
$564$	25.4853	1.07312
$565$	−1.17157	−0.0492884
$566$	12.8284	0.539219
$567$	0	0
$568$	−22.8284	−0.957860
$569$	20.8284	0.873173	0.436587	−	0.899662i	$-0.356187\pi$
$569$	20.8284	0.873173	0.436587	+	0.899662i	$0.356187\pi$
$570$	−6.82843	−0.286011
$571$	−0.686292	−0.0287204	−0.0143602	−	0.999897i	$-0.504571\pi$
$571$	−0.686292	−0.0287204	−0.0143602	+	0.999897i	$0.504571\pi$
$572$	−12.1421	−0.507688
$573$	−6.82843	−0.285262
$574$	0	0
$575$	−20.9706	−0.874533
$576$	−9.82843	−0.409518
$577$	0.485281	0.0202025	0.0101013	−	0.999949i	$-0.496785\pi$
$577$	0.485281	0.0202025	0.0101013	+	0.999949i	$0.496785\pi$
$578$	−71.5269	−2.97513
$579$	−5.65685	−0.235091
$580$	−39.8701	−1.65551
$581$	0	0
$582$	7.00000	0.290159
$583$	0.828427	0.0343099
$584$	−16.1421	−0.667966
$585$	1.58579	0.0655642
$586$	10.8284	0.447318
$587$	−36.9706	−1.52594	−0.762969	−	0.646435i	$-0.776259\pi$
$587$	−36.9706	−1.52594	−0.762969	+	0.646435i	$0.776259\pi$
$588$	0	0
$589$	−10.3431	−0.426182
$590$	−24.1421	−0.993916
$591$	15.1716	0.624075
$592$	−23.4853	−0.965239
$593$	−13.6569	−0.560820	−0.280410	−	0.959880i	$-0.590470\pi$
$593$	−13.6569	−0.560820	−0.280410	+	0.959880i	$0.590470\pi$
$594$	−4.82843	−0.198113
$595$	0	0
$596$	60.4853	2.47757
$597$	−11.3137	−0.463039
$598$	−20.0711	−0.820767
$599$	11.7279	0.479190	0.239595	−	0.970873i	$-0.422985\pi$
$599$	11.7279	0.479190	0.239595	+	0.970873i	$0.422985\pi$
$600$	−17.6569	−0.720838
$601$	−15.5858	−0.635757	−0.317879	−	0.948131i	$-0.602970\pi$
$601$	−15.5858	−0.635757	−0.317879	+	0.948131i	$0.602970\pi$
$602$	0	0
$603$	−5.82843	−0.237352
$604$	21.6569	0.881205
$605$	−7.00000	−0.284590
$606$	45.7990	1.86046
$607$	6.68629	0.271388	0.135694	−	0.990751i	$-0.456674\pi$
$607$	6.68629	0.271388	0.135694	+	0.990751i	$0.456674\pi$
$608$	−4.48528	−0.181902
$609$	0	0
$610$	17.6569	0.714905
$611$	−10.5563	−0.427064
$612$	26.1421	1.05673
$613$	−2.65685	−0.107309	−0.0536547	−	0.998560i	$-0.517087\pi$
$613$	−2.65685	−0.107309	−0.0536547	+	0.998560i	$0.517087\pi$
$614$	7.00000	0.282497
$615$	−1.00000	−0.0403239
$616$	0	0
$617$	−12.0000	−0.483102	−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000	−0.483102	−0.241551	+	0.970388i	$0.577656\pi$
$618$	−18.3137	−0.736685
$619$	−6.89949	−0.277314	−0.138657	−	0.990340i	$-0.544279\pi$
$619$	−6.89949	−0.277314	−0.138657	+	0.990340i	$0.544279\pi$
$620$	14.0000	0.562254
$621$	−5.24264	−0.210380
$622$	26.5563	1.06481
$623$	0	0
$624$	−4.75736	−0.190447
$625$	11.0000	0.440000
$626$	58.4558	2.33637
$627$	−5.65685	−0.225913
$628$	−56.7696	−2.26535
$629$	−53.4558	−2.13142
$630$	0	0
$631$	29.4558	1.17262	0.586309	−	0.810087i	$-0.300580\pi$
$631$	29.4558	1.17262	0.586309	+	0.810087i	$0.300580\pi$
$632$	68.3553	2.71903
$633$	0.514719	0.0204582
$634$	−27.9706	−1.11085
$635$	−20.9706	−0.832191
$636$	1.58579	0.0628805
$637$	0	0
$638$	−50.2843	−1.99077
$639$	5.17157	0.204584
$640$	20.5563	0.812561
$641$	−26.8284	−1.05966	−0.529830	−	0.848104i	$-0.677744\pi$
$641$	−26.8284	−1.05966	−0.529830	+	0.848104i	$0.677744\pi$
$642$	−42.7990	−1.68914
$643$	33.7990	1.33290	0.666451	−	0.745549i	$-0.267813\pi$
$643$	33.7990	1.33290	0.666451	+	0.745549i	$0.267813\pi$
$644$	0	0
$645$	−9.65685	−0.380238
$646$	46.6274	1.83453
$647$	−16.6863	−0.656006	−0.328003	−	0.944677i	$-0.606376\pi$
$647$	−16.6863	−0.656006	−0.328003	+	0.944677i	$0.606376\pi$
$648$	−4.41421	−0.173407
$649$	−20.0000	−0.785069
$650$	15.3137	0.600653
$651$	0	0
$652$	55.4558	2.17182
$653$	6.82843	0.267217	0.133609	−	0.991034i	$-0.457344\pi$
$653$	6.82843	0.267217	0.133609	+	0.991034i	$0.457344\pi$
$654$	−34.1421	−1.33506
$655$	−7.31371	−0.285770
$656$	3.00000	0.117130
$657$	3.65685	0.142667
$658$	0	0
$659$	−24.1421	−0.940444	−0.470222	−	0.882548i	$-0.655826\pi$
$659$	−24.1421	−0.940444	−0.470222	+	0.882548i	$0.655826\pi$
$660$	7.65685	0.298043
$661$	−42.8284	−1.66583	−0.832916	−	0.553399i	$-0.813331\pi$
$661$	−42.8284	−1.66583	−0.832916	+	0.553399i	$0.813331\pi$
$662$	−28.8995	−1.12321
$663$	−10.8284	−0.420541
$664$	−14.0000	−0.543305
$665$	0	0
$666$	18.8995	0.732341
$667$	−54.5980	−2.11404
$668$	−73.2843	−2.83545
$669$	20.0711	0.775992
$670$	14.0711	0.543613
$671$	14.6274	0.564685
$672$	0	0
$673$	−3.02944	−0.116776	−0.0583881	−	0.998294i	$-0.518596\pi$
$673$	−3.02944	−0.116776	−0.0583881	+	0.998294i	$0.518596\pi$
$674$	−63.1838	−2.43375
$675$	4.00000	0.153960
$676$	−40.1421	−1.54393
$677$	37.3137	1.43408	0.717041	−	0.697031i	$-0.245496\pi$
$677$	37.3137	1.43408	0.717041	+	0.697031i	$0.245496\pi$
$678$	−2.82843	−0.108625
$679$	0	0
$680$	−30.1421	−1.15590
$681$	4.65685	0.178451
$682$	17.6569	0.676116
$683$	−23.1127	−0.884383	−0.442191	−	0.896921i	$-0.645799\pi$
$683$	−23.1127	−0.884383	−0.442191	+	0.896921i	$0.645799\pi$
$684$	−10.8284	−0.414035
$685$	0.899495	0.0343679
$686$	0	0
$687$	1.24264	0.0474097
$688$	28.9706	1.10449
$689$	−0.656854	−0.0250242
$690$	12.6569	0.481838
$691$	46.8284	1.78144	0.890719	−	0.454555i	$-0.150202\pi$
$691$	46.8284	1.78144	0.890719	+	0.454555i	$0.150202\pi$
$692$	−8.31371	−0.316040
$693$	0	0
$694$	−28.9706	−1.09971
$695$	10.5563	0.400425
$696$	−45.9706	−1.74251
$697$	6.82843	0.258645
$698$	18.4853	0.699678
$699$	−0.485281	−0.0183550
$700$	0	0
$701$	−42.6274	−1.61002	−0.805008	−	0.593264i	$-0.797839\pi$
$701$	−42.6274	−1.61002	−0.805008	+	0.593264i	$0.797839\pi$
$702$	3.82843	0.144495
$703$	22.1421	0.835106
$704$	19.6569	0.740846
$705$	6.65685	0.250712
$706$	12.8284	0.482804
$707$	0	0
$708$	−38.2843	−1.43881
$709$	14.4853	0.544006	0.272003	−	0.962296i	$-0.412314\pi$
$709$	14.4853	0.544006	0.272003	+	0.962296i	$0.412314\pi$
$710$	−12.4853	−0.468564
$711$	−15.4853	−0.580743
$712$	12.4853	0.467906
$713$	19.1716	0.717981
$714$	0	0
$715$	−3.17157	−0.118610
$716$	45.9411	1.71690
$717$	−18.6274	−0.695654
$718$	28.7990	1.07477
$719$	−35.3137	−1.31698	−0.658490	−	0.752590i	$-0.728804\pi$
$719$	−35.3137	−1.31698	−0.658490	+	0.752590i	$0.728804\pi$
$720$	3.00000	0.111803
$721$	0	0
$722$	26.5563	0.988325
$723$	−8.14214	−0.302809
$724$	17.1716	0.638176
$725$	41.6569	1.54710
$726$	−16.8995	−0.627199
$727$	−47.7990	−1.77277	−0.886383	−	0.462952i	$-0.846790\pi$
$727$	−47.7990	−1.77277	−0.886383	+	0.462952i	$0.846790\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.82843	−0.326755
$731$	65.9411	2.43892
$732$	28.0000	1.03491
$733$	−48.0000	−1.77292	−0.886460	−	0.462805i	$-0.846843\pi$
$733$	−48.0000	−1.77292	−0.886460	+	0.462805i	$0.846843\pi$
$734$	16.6569	0.614816
$735$	0	0
$736$	8.31371	0.306447
$737$	11.6569	0.429386
$738$	−2.41421	−0.0888684
$739$	−28.6863	−1.05524	−0.527621	−	0.849480i	$-0.676916\pi$
$739$	−28.6863	−1.05524	−0.527621	+	0.849480i	$0.676916\pi$
$740$	−29.9706	−1.10174
$741$	4.48528	0.164771
$742$	0	0
$743$	4.62742	0.169763	0.0848817	−	0.996391i	$-0.472949\pi$
$743$	4.62742	0.169763	0.0848817	+	0.996391i	$0.472949\pi$
$744$	16.1421	0.591799
$745$	15.7990	0.578830
$746$	86.4975	3.16690
$747$	3.17157	0.116042
$748$	−52.2843	−1.91170
$749$	0	0
$750$	−21.7279	−0.793392
$751$	22.7990	0.831947	0.415973	−	0.909377i	$-0.363441\pi$
$751$	22.7990	0.831947	0.415973	+	0.909377i	$0.363441\pi$
$752$	−19.9706	−0.728251
$753$	−22.9706	−0.837094
$754$	39.8701	1.45198
$755$	5.65685	0.205874
$756$	0	0
$757$	17.3137	0.629277	0.314639	−	0.949212i	$-0.398117\pi$
$757$	17.3137	0.629277	0.314639	+	0.949212i	$0.398117\pi$
$758$	28.9706	1.05226
$759$	10.4853	0.380592
$760$	12.4853	0.452889
$761$	−37.2843	−1.35155	−0.675777	−	0.737106i	$-0.736192\pi$
$761$	−37.2843	−1.35155	−0.675777	+	0.737106i	$0.736192\pi$
$762$	−50.6274	−1.83404
$763$	0	0
$764$	26.1421	0.945789
$765$	6.82843	0.246882
$766$	34.5563	1.24857
$767$	15.8579	0.572594
$768$	29.9706	1.08147
$769$	−41.4558	−1.49494	−0.747468	−	0.664298i	$-0.768731\pi$
$769$	−41.4558	−1.49494	−0.747468	+	0.664298i	$0.768731\pi$
$770$	0	0
$771$	−21.4558	−0.772713
$772$	21.6569	0.779447
$773$	−14.8284	−0.533341	−0.266671	−	0.963788i	$-0.585924\pi$
$773$	−14.8284	−0.533341	−0.266671	+	0.963788i	$0.585924\pi$
$774$	−23.3137	−0.837994
$775$	−14.6274	−0.525432
$776$	−12.7990	−0.459457
$777$	0	0
$778$	71.1127	2.54951
$779$	−2.82843	−0.101339
$780$	−6.07107	−0.217379
$781$	−10.3431	−0.370107
$782$	−86.4264	−3.09060
$783$	10.4142	0.372174
$784$	0	0
$785$	−14.8284	−0.529249
$786$	−17.6569	−0.629799
$787$	−48.8995	−1.74308	−0.871539	−	0.490326i	$-0.836878\pi$
$787$	−48.8995	−1.74308	−0.871539	+	0.490326i	$0.836878\pi$
$788$	−58.0833	−2.06913
$789$	−8.82843	−0.314300
$790$	37.3848	1.33009
$791$	0	0
$792$	8.82843	0.313704
$793$	−11.5980	−0.411856
$794$	22.1421	0.785795
$795$	0.414214	0.0146906
$796$	43.3137	1.53521
$797$	−5.02944	−0.178152	−0.0890759	−	0.996025i	$-0.528391\pi$
$797$	−5.02944	−0.178152	−0.0890759	+	0.996025i	$0.528391\pi$
$798$	0	0
$799$	−45.4558	−1.60811
$800$	−6.34315	−0.224264
$801$	−2.82843	−0.0999376
$802$	57.4558	2.02884
$803$	−7.31371	−0.258095
$804$	22.3137	0.786944
$805$	0	0
$806$	−14.0000	−0.493129
$807$	23.1421	0.814642
$808$	−83.7401	−2.94597
$809$	−46.3553	−1.62977	−0.814883	−	0.579625i	$-0.803199\pi$
$809$	−46.3553	−1.62977	−0.814883	+	0.579625i	$0.803199\pi$
$810$	−2.41421	−0.0848268
$811$	39.8701	1.40003	0.700014	−	0.714130i	$-0.253177\pi$
$811$	39.8701	1.40003	0.700014	+	0.714130i	$0.253177\pi$
$812$	0	0
$813$	−24.8995	−0.873263
$814$	−37.7990	−1.32485
$815$	14.4853	0.507397
$816$	−20.4853	−0.717128
$817$	−27.3137	−0.955586
$818$	−38.1421	−1.33361
$819$	0	0
$820$	3.82843	0.133694
$821$	−54.4264	−1.89949	−0.949747	−	0.313018i	$-0.898660\pi$
$821$	−54.4264	−1.89949	−0.949747	+	0.313018i	$0.898660\pi$
$822$	2.17157	0.0757423
$823$	5.65685	0.197186	0.0985928	−	0.995128i	$-0.468566\pi$
$823$	5.65685	0.197186	0.0985928	+	0.995128i	$0.468566\pi$
$824$	33.4853	1.16652
$825$	−8.00000	−0.278524
$826$	0	0
$827$	39.5147	1.37406	0.687031	−	0.726628i	$-0.258914\pi$
$827$	39.5147	1.37406	0.687031	+	0.726628i	$0.258914\pi$
$828$	20.0711	0.697518
$829$	−53.1127	−1.84468	−0.922340	−	0.386379i	$-0.873726\pi$
$829$	−53.1127	−1.84468	−0.922340	+	0.386379i	$0.873726\pi$
$830$	−7.65685	−0.265773
$831$	1.34315	0.0465932
$832$	−15.5858	−0.540340
$833$	0	0
$834$	25.4853	0.882483
$835$	−19.1421	−0.662441
$836$	21.6569	0.749018
$837$	−3.65685	−0.126399
$838$	−93.7401	−3.23820
$839$	−51.0833	−1.76359	−0.881795	−	0.471633i	$-0.843665\pi$
$839$	−51.0833	−1.76359	−0.881795	+	0.471633i	$0.843665\pi$
$840$	0	0
$841$	79.4558	2.73986
$842$	−1.65685	−0.0570990
$843$	−18.8995	−0.650933
$844$	−1.97056	−0.0678296
$845$	−10.4853	−0.360705
$846$	16.0711	0.552535
$847$	0	0
$848$	−1.24264	−0.0426725
$849$	5.31371	0.182366
$850$	65.9411	2.26176
$851$	−41.0416	−1.40689
$852$	−19.7990	−0.678302
$853$	−31.1716	−1.06729	−0.533647	−	0.845707i	$-0.679179\pi$
$853$	−31.1716	−1.06729	−0.533647	+	0.845707i	$0.679179\pi$
$854$	0	0
$855$	−2.82843	−0.0967302
$856$	78.2548	2.67470
$857$	55.2843	1.88847	0.944237	−	0.329266i	$-0.106801\pi$
$857$	55.2843	1.88847	0.944237	+	0.329266i	$0.106801\pi$
$858$	−7.65685	−0.261401
$859$	21.7279	0.741347	0.370674	−	0.928763i	$-0.379127\pi$
$859$	21.7279	0.741347	0.370674	+	0.928763i	$0.379127\pi$
$860$	36.9706	1.26069
$861$	0	0
$862$	41.7990	1.42368
$863$	−23.5269	−0.800865	−0.400433	−	0.916326i	$-0.631140\pi$
$863$	−23.5269	−0.800865	−0.400433	+	0.916326i	$0.631140\pi$
$864$	−1.58579	−0.0539496
$865$	−2.17157	−0.0738357
$866$	29.3137	0.996120
$867$	−29.6274	−1.00620
$868$	0	0
$869$	30.9706	1.05060
$870$	−25.1421	−0.852398
$871$	−9.24264	−0.313175
$872$	62.4264	2.11402
$873$	2.89949	0.0981330
$874$	35.7990	1.21092
$875$	0	0
$876$	−14.0000	−0.473016
$877$	−57.5980	−1.94495	−0.972473	−	0.233016i	$-0.925140\pi$
$877$	−57.5980	−1.94495	−0.972473	+	0.233016i	$0.925140\pi$
$878$	36.1421	1.21974
$879$	4.48528	0.151285
$880$	−6.00000	−0.202260
$881$	23.6274	0.796028	0.398014	−	0.917379i	$-0.369700\pi$
$881$	23.6274	0.796028	0.398014	+	0.917379i	$0.369700\pi$
$882$	0	0
$883$	−55.9706	−1.88356	−0.941780	−	0.336231i	$-0.890848\pi$
$883$	−55.9706	−1.88356	−0.941780	+	0.336231i	$0.890848\pi$
$884$	41.4558	1.39431
$885$	−10.0000	−0.336146
$886$	−30.4853	−1.02417
$887$	25.8284	0.867234	0.433617	−	0.901097i	$-0.357237\pi$
$887$	25.8284	0.867234	0.433617	+	0.901097i	$0.357237\pi$
$888$	−34.5563	−1.15964
$889$	0	0
$890$	6.82843	0.228889
$891$	−2.00000	−0.0670025
$892$	−76.8406	−2.57281
$893$	18.8284	0.630069
$894$	38.1421	1.27566
$895$	12.0000	0.401116
$896$	0	0
$897$	−8.31371	−0.277587
$898$	−41.7990	−1.39485
$899$	−38.0833	−1.27015
$900$	−15.3137	−0.510457
$901$	−2.82843	−0.0942286
$902$	4.82843	0.160769
$903$	0	0
$904$	5.17157	0.172004
$905$	4.48528	0.149096
$906$	13.6569	0.453719
$907$	−49.7990	−1.65355	−0.826774	−	0.562534i	$-0.809827\pi$
$907$	−49.7990	−1.65355	−0.826774	+	0.562534i	$0.809827\pi$
$908$	−17.8284	−0.591657
$909$	18.9706	0.629214
$910$	0	0
$911$	2.00000	0.0662630	0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000	0.0662630	0.0331315	+	0.999451i	$0.489452\pi$
$912$	8.48528	0.280976
$913$	−6.34315	−0.209927
$914$	−27.3137	−0.903457
$915$	7.31371	0.241784
$916$	−4.75736	−0.157188
$917$	0	0
$918$	16.4853	0.544095
$919$	33.6274	1.10927	0.554633	−	0.832095i	$-0.312859\pi$
$919$	33.6274	1.10927	0.554633	+	0.832095i	$0.312859\pi$
$920$	−23.1421	−0.762974
$921$	2.89949	0.0955416
$922$	98.4975	3.24384
$923$	8.20101	0.269940
$924$	0	0
$925$	31.3137	1.02959
$926$	19.7279	0.648300
$927$	−7.58579	−0.249150
$928$	−16.5147	−0.542122
$929$	39.9411	1.31043	0.655213	−	0.755444i	$-0.272579\pi$
$929$	39.9411	1.31043	0.655213	+	0.755444i	$0.272579\pi$
$930$	8.82843	0.289496
$931$	0	0
$932$	1.85786	0.0608564
$933$	11.0000	0.360124
$934$	65.4558	2.14178
$935$	−13.6569	−0.446627
$936$	−7.00000	−0.228802
$937$	23.5147	0.768192	0.384096	−	0.923293i	$-0.374513\pi$
$937$	23.5147	0.768192	0.384096	+	0.923293i	$0.374513\pi$
$938$	0	0
$939$	24.2132	0.790168
$940$	−25.4853	−0.831238
$941$	−6.51472	−0.212374	−0.106187	−	0.994346i	$-0.533864\pi$
$941$	−6.51472	−0.212374	−0.106187	+	0.994346i	$0.533864\pi$
$942$	−35.7990	−1.16639
$943$	5.24264	0.170724
$944$	30.0000	0.976417
$945$	0	0
$946$	46.6274	1.51599
$947$	−17.1838	−0.558397	−0.279199	−	0.960233i	$-0.590069\pi$
$947$	−17.1838	−0.558397	−0.279199	+	0.960233i	$0.590069\pi$
$948$	59.2843	1.92546
$949$	5.79899	0.188243
$950$	−27.3137	−0.886174
$951$	−11.5858	−0.375695
$952$	0	0
$953$	−47.1127	−1.52613	−0.763065	−	0.646322i	$-0.776306\pi$
$953$	−47.1127	−1.52613	−0.763065	+	0.646322i	$0.776306\pi$
$954$	1.00000	0.0323762
$955$	6.82843	0.220963
$956$	71.3137	2.30645
$957$	−20.8284	−0.673287
$958$	−12.0000	−0.387702
$959$	0	0
$960$	9.82843	0.317211
$961$	−17.6274	−0.568626
$962$	29.9706	0.966290
$963$	−17.7279	−0.571274
$964$	31.1716	1.00397
$965$	5.65685	0.182101
$966$	0	0
$967$	52.3137	1.68230	0.841148	−	0.540805i	$-0.181880\pi$
$967$	52.3137	1.68230	0.841148	+	0.540805i	$0.181880\pi$
$968$	30.8995	0.993147
$969$	19.3137	0.620446
$970$	−7.00000	−0.224756
$971$	30.3137	0.972813	0.486407	−	0.873733i	$-0.338307\pi$
$971$	30.3137	0.972813	0.486407	+	0.873733i	$0.338307\pi$
$972$	−3.82843	−0.122797
$973$	0	0
$974$	−39.7990	−1.27524
$975$	6.34315	0.203143
$976$	−21.9411	−0.702318
$977$	−54.8284	−1.75412	−0.877058	−	0.480384i	$-0.840497\pi$
$977$	−54.8284	−1.75412	−0.877058	+	0.480384i	$0.840497\pi$
$978$	34.9706	1.11824
$979$	5.65685	0.180794
$980$	0	0
$981$	−14.1421	−0.451524
$982$	47.4558	1.51438
$983$	27.9411	0.891183	0.445592	−	0.895236i	$-0.352993\pi$
$983$	27.9411	0.891183	0.445592	+	0.895236i	$0.352993\pi$
$984$	4.41421	0.140720
$985$	−15.1716	−0.483407
$986$	171.681	5.46744
$987$	0	0
$988$	−17.1716	−0.546301
$989$	50.6274	1.60986
$990$	4.82843	0.153457
$991$	13.9706	0.443790	0.221895	−	0.975071i	$-0.428776\pi$
$991$	13.9706	0.443790	0.221895	+	0.975071i	$0.428776\pi$
$992$	5.79899	0.184118
$993$	−11.9706	−0.379874
$994$	0	0
$995$	11.3137	0.358669
$996$	−12.1421	−0.384738
$997$	−29.1005	−0.921622	−0.460811	−	0.887498i	$-0.652441\pi$
$997$	−29.1005	−0.921622	−0.460811	+	0.887498i	$0.652441\pi$
$998$	24.9706	0.790429
$999$	7.82843	0.247680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.i.1.1		2
7.6	odd	2		861.2.a.e.1.1	✓	2
21.20	even	2		2583.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.a.e.1.1	✓	2	7.6	odd	2
2583.2.a.k.1.2		2	21.20	even	2
6027.2.a.i.1.1		2	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} +2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.41421 q^{2} -1.00000 q^{3} +3.82843 q^{4} +1.00000 q^{5} +2.41421 q^{6} -4.41421 q^{8} +1.00000 q^{9} -2.41421 q^{10} -2.00000 q^{11} -3.82843 q^{12} +1.58579 q^{13} -1.00000 q^{15} +3.00000 q^{16} +6.82843 q^{17} -2.41421 q^{18} -2.82843 q^{19} +3.82843 q^{20} +4.82843 q^{22} +5.24264 q^{23} +4.41421 q^{24} -4.00000 q^{25} -3.82843 q^{26} -1.00000 q^{27} -10.4142 q^{29} +2.41421 q^{30} +3.65685 q^{31} +1.58579 q^{32} +2.00000 q^{33} -16.4853 q^{34} +3.82843 q^{36} -7.82843 q^{37} +6.82843 q^{38} -1.58579 q^{39} -4.41421 q^{40} +1.00000 q^{41} +9.65685 q^{43} -7.65685 q^{44} +1.00000 q^{45} -12.6569 q^{46} -6.65685 q^{47} -3.00000 q^{48} +9.65685 q^{50} -6.82843 q^{51} +6.07107 q^{52} -0.414214 q^{53} +2.41421 q^{54} -2.00000 q^{55} +2.82843 q^{57} +25.1421 q^{58} +10.0000 q^{59} -3.82843 q^{60} -7.31371 q^{61} -8.82843 q^{62} -9.82843 q^{64} +1.58579 q^{65} -4.82843 q^{66} -5.82843 q^{67} +26.1421 q^{68} -5.24264 q^{69} +5.17157 q^{71} -4.41421 q^{72} +3.65685 q^{73} +18.8995 q^{74} +4.00000 q^{75} -10.8284 q^{76} +3.82843 q^{78} -15.4853 q^{79} +3.00000 q^{80} +1.00000 q^{81} -2.41421 q^{82} +3.17157 q^{83} +6.82843 q^{85} -23.3137 q^{86} +10.4142 q^{87} +8.82843 q^{88} -2.82843 q^{89} -2.41421 q^{90} +20.0711 q^{92} -3.65685 q^{93} +16.0711 q^{94} -2.82843 q^{95} -1.58579 q^{96} +2.89949 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} + 6 q^{13} - 2 q^{15} + 6 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{20} + 4 q^{22} + 2 q^{23} + 6 q^{24} - 8 q^{25} - 2 q^{26} - 2 q^{27} - 18 q^{29} + 2 q^{30} - 4 q^{31} + 6 q^{32} + 4 q^{33} - 16 q^{34} + 2 q^{36} - 10 q^{37} + 8 q^{38} - 6 q^{39} - 6 q^{40} + 2 q^{41} + 8 q^{43} - 4 q^{44} + 2 q^{45} - 14 q^{46} - 2 q^{47} - 6 q^{48} + 8 q^{50} - 8 q^{51} - 2 q^{52} + 2 q^{53} + 2 q^{54} - 4 q^{55} + 22 q^{58} + 20 q^{59} - 2 q^{60} + 8 q^{61} - 12 q^{62} - 14 q^{64} + 6 q^{65} - 4 q^{66} - 6 q^{67} + 24 q^{68} - 2 q^{69} + 16 q^{71} - 6 q^{72} - 4 q^{73} + 18 q^{74} + 8 q^{75} - 16 q^{76} + 2 q^{78} - 14 q^{79} + 6 q^{80} + 2 q^{81} - 2 q^{82} + 12 q^{83} + 8 q^{85} - 24 q^{86} + 18 q^{87} + 12 q^{88} - 2 q^{90} + 26 q^{92} + 4 q^{93} + 18 q^{94} - 6 q^{96} - 14 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 6 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 + 6 * q^13 - 2 * q^15 + 6 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^20 + 4 * q^22 + 2 * q^23 + 6 * q^24 - 8 * q^25 - 2 * q^26 - 2 * q^27 - 18 * q^29 + 2 * q^30 - 4 * q^31 + 6 * q^32 + 4 * q^33 - 16 * q^34 + 2 * q^36 - 10 * q^37 + 8 * q^38 - 6 * q^39 - 6 * q^40 + 2 * q^41 + 8 * q^43 - 4 * q^44 + 2 * q^45 - 14 * q^46 - 2 * q^47 - 6 * q^48 + 8 * q^50 - 8 * q^51 - 2 * q^52 + 2 * q^53 + 2 * q^54 - 4 * q^55 + 22 * q^58 + 20 * q^59 - 2 * q^60 + 8 * q^61 - 12 * q^62 - 14 * q^64 + 6 * q^65 - 4 * q^66 - 6 * q^67 + 24 * q^68 - 2 * q^69 + 16 * q^71 - 6 * q^72 - 4 * q^73 + 18 * q^74 + 8 * q^75 - 16 * q^76 + 2 * q^78 - 14 * q^79 + 6 * q^80 + 2 * q^81 - 2 * q^82 + 12 * q^83 + 8 * q^85 - 24 * q^86 + 18 * q^87 + 12 * q^88 - 2 * q^90 + 26 * q^92 + 4 * q^93 + 18 * q^94 - 6 * q^96 - 14 * q^97 - 4 * q^99

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