LMFDB - Embedded newform 6762.2.a.bx.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.56155 q^{10} +3.00000 q^{11} +1.00000 q^{12} -3.12311 q^{13} -2.56155 q^{15} +1.00000 q^{16} -4.68466 q^{17} -1.00000 q^{18} -3.12311 q^{19} -2.56155 q^{20} -3.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} +3.12311 q^{26} +1.00000 q^{27} +0.123106 q^{29} +2.56155 q^{30} -1.68466 q^{31} -1.00000 q^{32} +3.00000 q^{33} +4.68466 q^{34} +1.00000 q^{36} +0.876894 q^{37} +3.12311 q^{38} -3.12311 q^{39} +2.56155 q^{40} -7.12311 q^{41} +12.2462 q^{43} +3.00000 q^{44} -2.56155 q^{45} +1.00000 q^{46} -0.438447 q^{47} +1.00000 q^{48} -1.56155 q^{50} -4.68466 q^{51} -3.12311 q^{52} -0.561553 q^{53} -1.00000 q^{54} -7.68466 q^{55} -3.12311 q^{57} -0.123106 q^{58} +1.43845 q^{59} -2.56155 q^{60} -2.00000 q^{61} +1.68466 q^{62} +1.00000 q^{64} +8.00000 q^{65} -3.00000 q^{66} -2.00000 q^{67} -4.68466 q^{68} -1.00000 q^{69} +0.438447 q^{71} -1.00000 q^{72} +16.9309 q^{73} -0.876894 q^{74} +1.56155 q^{75} -3.12311 q^{76} +3.12311 q^{78} +12.3693 q^{79} -2.56155 q^{80} +1.00000 q^{81} +7.12311 q^{82} -6.56155 q^{83} +12.0000 q^{85} -12.2462 q^{86} +0.123106 q^{87} -3.00000 q^{88} +8.24621 q^{89} +2.56155 q^{90} -1.00000 q^{92} -1.68466 q^{93} +0.438447 q^{94} +8.00000 q^{95} -1.00000 q^{96} +11.6847 q^{97} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 6 q^{11} + 2 q^{12} + 2 q^{13} - q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} - 6 q^{22} - 2 q^{23} - 2 q^{24} - q^{25} - 2 q^{26} + 2 q^{27} - 8 q^{29} + q^{30} + 9 q^{31} - 2 q^{32} + 6 q^{33} - 3 q^{34} + 2 q^{36} + 10 q^{37} - 2 q^{38} + 2 q^{39} + q^{40} - 6 q^{41} + 8 q^{43} + 6 q^{44} - q^{45} + 2 q^{46} - 5 q^{47} + 2 q^{48} + q^{50} + 3 q^{51} + 2 q^{52} + 3 q^{53} - 2 q^{54} - 3 q^{55} + 2 q^{57} + 8 q^{58} + 7 q^{59} - q^{60} - 4 q^{61} - 9 q^{62} + 2 q^{64} + 16 q^{65} - 6 q^{66} - 4 q^{67} + 3 q^{68} - 2 q^{69} + 5 q^{71} - 2 q^{72} + 5 q^{73} - 10 q^{74} - q^{75} + 2 q^{76} - 2 q^{78} - q^{80} + 2 q^{81} + 6 q^{82} - 9 q^{83} + 24 q^{85} - 8 q^{86} - 8 q^{87} - 6 q^{88} + q^{90} - 2 q^{92} + 9 q^{93} + 5 q^{94} + 16 q^{95} - 2 q^{96} + 11 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 6 * q^11 + 2 * q^12 + 2 * q^13 - q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 + 2 * q^19 - q^20 - 6 * q^22 - 2 * q^23 - 2 * q^24 - q^25 - 2 * q^26 + 2 * q^27 - 8 * q^29 + q^30 + 9 * q^31 - 2 * q^32 + 6 * q^33 - 3 * q^34 + 2 * q^36 + 10 * q^37 - 2 * q^38 + 2 * q^39 + q^40 - 6 * q^41 + 8 * q^43 + 6 * q^44 - q^45 + 2 * q^46 - 5 * q^47 + 2 * q^48 + q^50 + 3 * q^51 + 2 * q^52 + 3 * q^53 - 2 * q^54 - 3 * q^55 + 2 * q^57 + 8 * q^58 + 7 * q^59 - q^60 - 4 * q^61 - 9 * q^62 + 2 * q^64 + 16 * q^65 - 6 * q^66 - 4 * q^67 + 3 * q^68 - 2 * q^69 + 5 * q^71 - 2 * q^72 + 5 * q^73 - 10 * q^74 - q^75 + 2 * q^76 - 2 * q^78 - q^80 + 2 * q^81 + 6 * q^82 - 9 * q^83 + 24 * q^85 - 8 * q^86 - 8 * q^87 - 6 * q^88 + q^90 - 2 * q^92 + 9 * q^93 + 5 * q^94 + 16 * q^95 - 2 * q^96 + 11 * q^97 + 6 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.56155	−1.14556	−0.572781	−	0.819709i	$-0.694135\pi$
$5$	−2.56155	−1.14556	−0.572781	+	0.819709i	$0.694135\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.56155	0.810034
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	1.00000	0.288675
$13$	−3.12311	−0.866194	−0.433097	−	0.901347i	$-0.642579\pi$
$13$	−3.12311	−0.866194	−0.433097	+	0.901347i	$0.642579\pi$
$14$	0	0
$15$	−2.56155	−0.661390
$16$	1.00000	0.250000
$17$	−4.68466	−1.13620	−0.568098	−	0.822961i	$-0.692321\pi$
$17$	−4.68466	−1.13620	−0.568098	+	0.822961i	$0.692321\pi$
$18$	−1.00000	−0.235702
$19$	−3.12311	−0.716490	−0.358245	−	0.933628i	$-0.616625\pi$
$19$	−3.12311	−0.716490	−0.358245	+	0.933628i	$0.616625\pi$
$20$	−2.56155	−0.572781
$21$	0	0
$22$	−3.00000	−0.639602
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	1.56155	0.312311
$26$	3.12311	0.612491
$27$	1.00000	0.192450
$28$	0	0
$29$	0.123106	0.0228601	0.0114301	−	0.999935i	$-0.496362\pi$
$29$	0.123106	0.0228601	0.0114301	+	0.999935i	$0.496362\pi$
$30$	2.56155	0.467673
$31$	−1.68466	−0.302574	−0.151287	−	0.988490i	$-0.548342\pi$
$31$	−1.68466	−0.302574	−0.151287	+	0.988490i	$0.548342\pi$
$32$	−1.00000	−0.176777
$33$	3.00000	0.522233
$34$	4.68466	0.803412
$35$	0	0
$36$	1.00000	0.166667
$37$	0.876894	0.144161	0.0720803	−	0.997399i	$-0.477036\pi$
$37$	0.876894	0.144161	0.0720803	+	0.997399i	$0.477036\pi$
$38$	3.12311	0.506635
$39$	−3.12311	−0.500097
$40$	2.56155	0.405017
$41$	−7.12311	−1.11244	−0.556221	−	0.831034i	$-0.687749\pi$
$41$	−7.12311	−1.11244	−0.556221	+	0.831034i	$0.687749\pi$
$42$	0	0
$43$	12.2462	1.86753	0.933765	−	0.357887i	$-0.116503\pi$
$43$	12.2462	1.86753	0.933765	+	0.357887i	$0.116503\pi$
$44$	3.00000	0.452267
$45$	−2.56155	−0.381854
$46$	1.00000	0.147442
$47$	−0.438447	−0.0639541	−0.0319770	−	0.999489i	$-0.510180\pi$
$47$	−0.438447	−0.0639541	−0.0319770	+	0.999489i	$0.510180\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−1.56155	−0.220837
$51$	−4.68466	−0.655983
$52$	−3.12311	−0.433097
$53$	−0.561553	−0.0771352	−0.0385676	−	0.999256i	$-0.512279\pi$
$53$	−0.561553	−0.0771352	−0.0385676	+	0.999256i	$0.512279\pi$
$54$	−1.00000	−0.136083
$55$	−7.68466	−1.03620
$56$	0	0
$57$	−3.12311	−0.413665
$58$	−0.123106	−0.0161646
$59$	1.43845	0.187270	0.0936349	−	0.995607i	$-0.470151\pi$
$59$	1.43845	0.187270	0.0936349	+	0.995607i	$0.470151\pi$
$60$	−2.56155	−0.330695
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	1.68466	0.213952
$63$	0	0
$64$	1.00000	0.125000
$65$	8.00000	0.992278
$66$	−3.00000	−0.369274
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	−4.68466	−0.568098
$69$	−1.00000	−0.120386
$70$	0	0
$71$	0.438447	0.0520341	0.0260171	−	0.999661i	$-0.491718\pi$
$71$	0.438447	0.0520341	0.0260171	+	0.999661i	$0.491718\pi$
$72$	−1.00000	−0.117851
$73$	16.9309	1.98161	0.990804	−	0.135303i	$-0.0432009\pi$
$73$	16.9309	1.98161	0.990804	+	0.135303i	$0.0432009\pi$
$74$	−0.876894	−0.101937
$75$	1.56155	0.180313
$76$	−3.12311	−0.358245
$77$	0	0
$78$	3.12311	0.353622
$79$	12.3693	1.39166	0.695828	−	0.718208i	$-0.255037\pi$
$79$	12.3693	1.39166	0.695828	+	0.718208i	$0.255037\pi$
$80$	−2.56155	−0.286390
$81$	1.00000	0.111111
$82$	7.12311	0.786615
$83$	−6.56155	−0.720224	−0.360112	−	0.932909i	$-0.617262\pi$
$83$	−6.56155	−0.720224	−0.360112	+	0.932909i	$0.617262\pi$
$84$	0	0
$85$	12.0000	1.30158
$86$	−12.2462	−1.32054
$87$	0.123106	0.0131983
$88$	−3.00000	−0.319801
$89$	8.24621	0.874097	0.437048	−	0.899438i	$-0.356024\pi$
$89$	8.24621	0.874097	0.437048	+	0.899438i	$0.356024\pi$
$90$	2.56155	0.270011
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−1.68466	−0.174691
$94$	0.438447	0.0452224
$95$	8.00000	0.820783
$96$	−1.00000	−0.102062
$97$	11.6847	1.18640	0.593199	−	0.805056i	$-0.297865\pi$
$97$	11.6847	1.18640	0.593199	+	0.805056i	$0.297865\pi$
$98$	0	0
$99$	3.00000	0.301511
$100$	1.56155	0.156155
$101$	11.5616	1.15042	0.575209	−	0.818007i	$-0.304921\pi$
$101$	11.5616	1.15042	0.575209	+	0.818007i	$0.304921\pi$
$102$	4.68466	0.463850
$103$	−16.6847	−1.64399	−0.821994	−	0.569496i	$-0.807138\pi$
$103$	−16.6847	−1.64399	−0.821994	+	0.569496i	$0.807138\pi$
$104$	3.12311	0.306246
$105$	0	0
$106$	0.561553	0.0545428
$107$	2.56155	0.247635	0.123817	−	0.992305i	$-0.460486\pi$
$107$	2.56155	0.247635	0.123817	+	0.992305i	$0.460486\pi$
$108$	1.00000	0.0962250
$109$	−12.4384	−1.19139	−0.595694	−	0.803212i	$-0.703123\pi$
$109$	−12.4384	−1.19139	−0.595694	+	0.803212i	$0.703123\pi$
$110$	7.68466	0.732703
$111$	0.876894	0.0832311
$112$	0	0
$113$	−7.12311	−0.670085	−0.335043	−	0.942203i	$-0.608751\pi$
$113$	−7.12311	−0.670085	−0.335043	+	0.942203i	$0.608751\pi$
$114$	3.12311	0.292506
$115$	2.56155	0.238866
$116$	0.123106	0.0114301
$117$	−3.12311	−0.288731
$118$	−1.43845	−0.132420
$119$	0	0
$120$	2.56155	0.233837
$121$	−2.00000	−0.181818
$122$	2.00000	0.181071
$123$	−7.12311	−0.642269
$124$	−1.68466	−0.151287
$125$	8.80776	0.787790
$126$	0	0
$127$	13.6847	1.21432	0.607159	−	0.794581i	$-0.292309\pi$
$127$	13.6847	1.21432	0.607159	+	0.794581i	$0.292309\pi$
$128$	−1.00000	−0.0883883
$129$	12.2462	1.07822
$130$	−8.00000	−0.701646
$131$	−18.5616	−1.62173	−0.810865	−	0.585233i	$-0.801003\pi$
$131$	−18.5616	−1.62173	−0.810865	+	0.585233i	$0.801003\pi$
$132$	3.00000	0.261116
$133$	0	0
$134$	2.00000	0.172774
$135$	−2.56155	−0.220463
$136$	4.68466	0.401706
$137$	20.0540	1.71333	0.856663	−	0.515876i	$-0.172533\pi$
$137$	20.0540	1.71333	0.856663	+	0.515876i	$0.172533\pi$
$138$	1.00000	0.0851257
$139$	18.6847	1.58481	0.792406	−	0.609994i	$-0.208828\pi$
$139$	18.6847	1.58481	0.792406	+	0.609994i	$0.208828\pi$
$140$	0	0
$141$	−0.438447	−0.0369239
$142$	−0.438447	−0.0367937
$143$	−9.36932	−0.783502
$144$	1.00000	0.0833333
$145$	−0.315342	−0.0261877
$146$	−16.9309	−1.40121
$147$	0	0
$148$	0.876894	0.0720803
$149$	−9.12311	−0.747394	−0.373697	−	0.927551i	$-0.621910\pi$
$149$	−9.12311	−0.747394	−0.373697	+	0.927551i	$0.621910\pi$
$150$	−1.56155	−0.127500
$151$	−0.315342	−0.0256621	−0.0128311	−	0.999918i	$-0.504084\pi$
$151$	−0.315342	−0.0256621	−0.0128311	+	0.999918i	$0.504084\pi$
$152$	3.12311	0.253317
$153$	−4.68466	−0.378732
$154$	0	0
$155$	4.31534	0.346617
$156$	−3.12311	−0.250049
$157$	−3.80776	−0.303893	−0.151946	−	0.988389i	$-0.548554\pi$
$157$	−3.80776	−0.303893	−0.151946	+	0.988389i	$0.548554\pi$
$158$	−12.3693	−0.984050
$159$	−0.561553	−0.0445340
$160$	2.56155	0.202509
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	14.0540	1.10079	0.550396	−	0.834904i	$-0.314477\pi$
$163$	14.0540	1.10079	0.550396	+	0.834904i	$0.314477\pi$
$164$	−7.12311	−0.556221
$165$	−7.68466	−0.598250
$166$	6.56155	0.509275
$167$	−13.1231	−1.01550	−0.507748	−	0.861506i	$-0.669522\pi$
$167$	−13.1231	−1.01550	−0.507748	+	0.861506i	$0.669522\pi$
$168$	0	0
$169$	−3.24621	−0.249709
$170$	−12.0000	−0.920358
$171$	−3.12311	−0.238830
$172$	12.2462	0.933765
$173$	−8.43845	−0.641563	−0.320782	−	0.947153i	$-0.603946\pi$
$173$	−8.43845	−0.641563	−0.320782	+	0.947153i	$0.603946\pi$
$174$	−0.123106	−0.00933261
$175$	0	0
$176$	3.00000	0.226134
$177$	1.43845	0.108120
$178$	−8.24621	−0.618080
$179$	−15.1231	−1.13035	−0.565177	−	0.824970i	$-0.691192\pi$
$179$	−15.1231	−1.13035	−0.565177	+	0.824970i	$0.691192\pi$
$180$	−2.56155	−0.190927
$181$	22.9309	1.70444	0.852219	−	0.523185i	$-0.175256\pi$
$181$	22.9309	1.70444	0.852219	+	0.523185i	$0.175256\pi$
$182$	0	0
$183$	−2.00000	−0.147844
$184$	1.00000	0.0737210
$185$	−2.24621	−0.165145
$186$	1.68466	0.123525
$187$	−14.0540	−1.02773
$188$	−0.438447	−0.0319770
$189$	0	0
$190$	−8.00000	−0.580381
$191$	−24.4924	−1.77221	−0.886105	−	0.463485i	$-0.846599\pi$
$191$	−24.4924	−1.77221	−0.886105	+	0.463485i	$0.846599\pi$
$192$	1.00000	0.0721688
$193$	−13.0540	−0.939646	−0.469823	−	0.882761i	$-0.655682\pi$
$193$	−13.0540	−0.939646	−0.469823	+	0.882761i	$0.655682\pi$
$194$	−11.6847	−0.838910
$195$	8.00000	0.572892
$196$	0	0
$197$	0.438447	0.0312381	0.0156190	−	0.999878i	$-0.495028\pi$
$197$	0.438447	0.0312381	0.0156190	+	0.999878i	$0.495028\pi$
$198$	−3.00000	−0.213201
$199$	3.31534	0.235018	0.117509	−	0.993072i	$-0.462509\pi$
$199$	3.31534	0.235018	0.117509	+	0.993072i	$0.462509\pi$
$200$	−1.56155	−0.110418
$201$	−2.00000	−0.141069
$202$	−11.5616	−0.813468
$203$	0	0
$204$	−4.68466	−0.327992
$205$	18.2462	1.27437
$206$	16.6847	1.16248
$207$	−1.00000	−0.0695048
$208$	−3.12311	−0.216548
$209$	−9.36932	−0.648089
$210$	0	0
$211$	13.3153	0.916666	0.458333	−	0.888781i	$-0.348447\pi$
$211$	13.3153	0.916666	0.458333	+	0.888781i	$0.348447\pi$
$212$	−0.561553	−0.0385676
$213$	0.438447	0.0300419
$214$	−2.56155	−0.175104
$215$	−31.3693	−2.13937
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	12.4384	0.842438
$219$	16.9309	1.14408
$220$	−7.68466	−0.518100
$221$	14.6307	0.984166
$222$	−0.876894	−0.0588533
$223$	15.4384	1.03383	0.516917	−	0.856035i	$-0.327079\pi$
$223$	15.4384	1.03383	0.516917	+	0.856035i	$0.327079\pi$
$224$	0	0
$225$	1.56155	0.104104
$226$	7.12311	0.473822
$227$	20.6155	1.36830	0.684150	−	0.729341i	$-0.260173\pi$
$227$	20.6155	1.36830	0.684150	+	0.729341i	$0.260173\pi$
$228$	−3.12311	−0.206833
$229$	−7.31534	−0.483411	−0.241706	−	0.970350i	$-0.577707\pi$
$229$	−7.31534	−0.483411	−0.241706	+	0.970350i	$0.577707\pi$
$230$	−2.56155	−0.168904
$231$	0	0
$232$	−0.123106	−0.00808228
$233$	18.2462	1.19535	0.597675	−	0.801739i	$-0.296092\pi$
$233$	18.2462	1.19535	0.597675	+	0.801739i	$0.296092\pi$
$234$	3.12311	0.204164
$235$	1.12311	0.0732633
$236$	1.43845	0.0936349
$237$	12.3693	0.803473
$238$	0	0
$239$	11.8078	0.763781	0.381890	−	0.924208i	$-0.375273\pi$
$239$	11.8078	0.763781	0.381890	+	0.924208i	$0.375273\pi$
$240$	−2.56155	−0.165348
$241$	10.3153	0.664470	0.332235	−	0.943197i	$-0.392197\pi$
$241$	10.3153	0.664470	0.332235	+	0.943197i	$0.392197\pi$
$242$	2.00000	0.128565
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	7.12311	0.454153
$247$	9.75379	0.620619
$248$	1.68466	0.106976
$249$	−6.56155	−0.415822
$250$	−8.80776	−0.557052
$251$	−8.12311	−0.512726	−0.256363	−	0.966581i	$-0.582524\pi$
$251$	−8.12311	−0.512726	−0.256363	+	0.966581i	$0.582524\pi$
$252$	0	0
$253$	−3.00000	−0.188608
$254$	−13.6847	−0.858652
$255$	12.0000	0.751469
$256$	1.00000	0.0625000
$257$	14.4924	0.904012	0.452006	−	0.892015i	$-0.350708\pi$
$257$	14.4924	0.904012	0.452006	+	0.892015i	$0.350708\pi$
$258$	−12.2462	−0.762416
$259$	0	0
$260$	8.00000	0.496139
$261$	0.123106	0.00762005
$262$	18.5616	1.14674
$263$	−9.12311	−0.562555	−0.281277	−	0.959627i	$-0.590758\pi$
$263$	−9.12311	−0.562555	−0.281277	+	0.959627i	$0.590758\pi$
$264$	−3.00000	−0.184637
$265$	1.43845	0.0883631
$266$	0	0
$267$	8.24621	0.504660
$268$	−2.00000	−0.122169
$269$	8.61553	0.525298	0.262649	−	0.964891i	$-0.415404\pi$
$269$	8.61553	0.525298	0.262649	+	0.964891i	$0.415404\pi$
$270$	2.56155	0.155891
$271$	22.8078	1.38547	0.692736	−	0.721191i	$-0.256405\pi$
$271$	22.8078	1.38547	0.692736	+	0.721191i	$0.256405\pi$
$272$	−4.68466	−0.284049
$273$	0	0
$274$	−20.0540	−1.21150
$275$	4.68466	0.282496
$276$	−1.00000	−0.0601929
$277$	−1.75379	−0.105375	−0.0526875	−	0.998611i	$-0.516779\pi$
$277$	−1.75379	−0.105375	−0.0526875	+	0.998611i	$0.516779\pi$
$278$	−18.6847	−1.12063
$279$	−1.68466	−0.100858
$280$	0	0
$281$	15.1771	0.905389	0.452694	−	0.891666i	$-0.350463\pi$
$281$	15.1771	0.905389	0.452694	+	0.891666i	$0.350463\pi$
$282$	0.438447	0.0261092
$283$	23.3693	1.38916	0.694581	−	0.719415i	$-0.255590\pi$
$283$	23.3693	1.38916	0.694581	+	0.719415i	$0.255590\pi$
$284$	0.438447	0.0260171
$285$	8.00000	0.473879
$286$	9.36932	0.554019
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	4.94602	0.290943
$290$	0.315342	0.0185175
$291$	11.6847	0.684967
$292$	16.9309	0.990804
$293$	−9.43845	−0.551400	−0.275700	−	0.961244i	$-0.588910\pi$
$293$	−9.43845	−0.551400	−0.275700	+	0.961244i	$0.588910\pi$
$294$	0	0
$295$	−3.68466	−0.214529
$296$	−0.876894	−0.0509685
$297$	3.00000	0.174078
$298$	9.12311	0.528487
$299$	3.12311	0.180614
$300$	1.56155	0.0901563
$301$	0	0
$302$	0.315342	0.0181459
$303$	11.5616	0.664194
$304$	−3.12311	−0.179122
$305$	5.12311	0.293348
$306$	4.68466	0.267804
$307$	−4.68466	−0.267368	−0.133684	−	0.991024i	$-0.542681\pi$
$307$	−4.68466	−0.267368	−0.133684	+	0.991024i	$0.542681\pi$
$308$	0	0
$309$	−16.6847	−0.949157
$310$	−4.31534	−0.245095
$311$	4.68466	0.265643	0.132821	−	0.991140i	$-0.457596\pi$
$311$	4.68466	0.265643	0.132821	+	0.991140i	$0.457596\pi$
$312$	3.12311	0.176811
$313$	24.8078	1.40222	0.701109	−	0.713054i	$-0.252689\pi$
$313$	24.8078	1.40222	0.701109	+	0.713054i	$0.252689\pi$
$314$	3.80776	0.214885
$315$	0	0
$316$	12.3693	0.695828
$317$	27.9309	1.56875	0.784377	−	0.620284i	$-0.212983\pi$
$317$	27.9309	1.56875	0.784377	+	0.620284i	$0.212983\pi$
$318$	0.561553	0.0314903
$319$	0.369317	0.0206778
$320$	−2.56155	−0.143195
$321$	2.56155	0.142972
$322$	0	0
$323$	14.6307	0.814073
$324$	1.00000	0.0555556
$325$	−4.87689	−0.270521
$326$	−14.0540	−0.778378
$327$	−12.4384	−0.687848
$328$	7.12311	0.393308
$329$	0	0
$330$	7.68466	0.423027
$331$	−20.4924	−1.12637	−0.563183	−	0.826332i	$-0.690423\pi$
$331$	−20.4924	−1.12637	−0.563183	+	0.826332i	$0.690423\pi$
$332$	−6.56155	−0.360112
$333$	0.876894	0.0480535
$334$	13.1231	0.718064
$335$	5.12311	0.279905
$336$	0	0
$337$	7.43845	0.405198	0.202599	−	0.979262i	$-0.435061\pi$
$337$	7.43845	0.405198	0.202599	+	0.979262i	$0.435061\pi$
$338$	3.24621	0.176571
$339$	−7.12311	−0.386874
$340$	12.0000	0.650791
$341$	−5.05398	−0.273688
$342$	3.12311	0.168878
$343$	0	0
$344$	−12.2462	−0.660271
$345$	2.56155	0.137909
$346$	8.43845	0.453654
$347$	−11.6155	−0.623554	−0.311777	−	0.950155i	$-0.600924\pi$
$347$	−11.6155	−0.623554	−0.311777	+	0.950155i	$0.600924\pi$
$348$	0.123106	0.00659915
$349$	30.0000	1.60586	0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000	1.60586	0.802932	+	0.596071i	$0.203272\pi$
$350$	0	0
$351$	−3.12311	−0.166699
$352$	−3.00000	−0.159901
$353$	−2.63068	−0.140017	−0.0700086	−	0.997546i	$-0.522303\pi$
$353$	−2.63068	−0.140017	−0.0700086	+	0.997546i	$0.522303\pi$
$354$	−1.43845	−0.0764526
$355$	−1.12311	−0.0596083
$356$	8.24621	0.437048
$357$	0	0
$358$	15.1231	0.799281
$359$	−5.12311	−0.270387	−0.135194	−	0.990819i	$-0.543166\pi$
$359$	−5.12311	−0.270387	−0.135194	+	0.990819i	$0.543166\pi$
$360$	2.56155	0.135006
$361$	−9.24621	−0.486643
$362$	−22.9309	−1.20522
$363$	−2.00000	−0.104973
$364$	0	0
$365$	−43.3693	−2.27005
$366$	2.00000	0.104542
$367$	22.5616	1.17770	0.588852	−	0.808241i	$-0.299580\pi$
$367$	22.5616	1.17770	0.588852	+	0.808241i	$0.299580\pi$
$368$	−1.00000	−0.0521286
$369$	−7.12311	−0.370814
$370$	2.24621	0.116775
$371$	0	0
$372$	−1.68466	−0.0873455
$373$	10.4384	0.540482	0.270241	−	0.962793i	$-0.412897\pi$
$373$	10.4384	0.540482	0.270241	+	0.962793i	$0.412897\pi$
$374$	14.0540	0.726714
$375$	8.80776	0.454831
$376$	0.438447	0.0226112
$377$	−0.384472	−0.0198013
$378$	0	0
$379$	12.4924	0.641693	0.320846	−	0.947131i	$-0.396033\pi$
$379$	12.4924	0.641693	0.320846	+	0.947131i	$0.396033\pi$
$380$	8.00000	0.410391
$381$	13.6847	0.701086
$382$	24.4924	1.25314
$383$	−3.75379	−0.191810	−0.0959048	−	0.995391i	$-0.530574\pi$
$383$	−3.75379	−0.191810	−0.0959048	+	0.995391i	$0.530574\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	13.0540	0.664430
$387$	12.2462	0.622510
$388$	11.6847	0.593199
$389$	−25.1231	−1.27379	−0.636896	−	0.770950i	$-0.719782\pi$
$389$	−25.1231	−1.27379	−0.636896	+	0.770950i	$0.719782\pi$
$390$	−8.00000	−0.405096
$391$	4.68466	0.236913
$392$	0	0
$393$	−18.5616	−0.936306
$394$	−0.438447	−0.0220887
$395$	−31.6847	−1.59423
$396$	3.00000	0.150756
$397$	17.3693	0.871741	0.435871	−	0.900009i	$-0.356441\pi$
$397$	17.3693	0.871741	0.435871	+	0.900009i	$0.356441\pi$
$398$	−3.31534	−0.166183
$399$	0	0
$400$	1.56155	0.0780776
$401$	32.3002	1.61299	0.806497	−	0.591238i	$-0.201361\pi$
$401$	32.3002	1.61299	0.806497	+	0.591238i	$0.201361\pi$
$402$	2.00000	0.0997509
$403$	5.26137	0.262087
$404$	11.5616	0.575209
$405$	−2.56155	−0.127285
$406$	0	0
$407$	2.63068	0.130398
$408$	4.68466	0.231925
$409$	−10.3693	−0.512730	−0.256365	−	0.966580i	$-0.582525\pi$
$409$	−10.3693	−0.512730	−0.256365	+	0.966580i	$0.582525\pi$
$410$	−18.2462	−0.901116
$411$	20.0540	0.989190
$412$	−16.6847	−0.821994
$413$	0	0
$414$	1.00000	0.0491473
$415$	16.8078	0.825061
$416$	3.12311	0.153123
$417$	18.6847	0.914992
$418$	9.36932	0.458268
$419$	−16.3002	−0.796316	−0.398158	−	0.917317i	$-0.630350\pi$
$419$	−16.3002	−0.796316	−0.398158	+	0.917317i	$0.630350\pi$
$420$	0	0
$421$	8.93087	0.435264	0.217632	−	0.976031i	$-0.430167\pi$
$421$	8.93087	0.435264	0.217632	+	0.976031i	$0.430167\pi$
$422$	−13.3153	−0.648181
$423$	−0.438447	−0.0213180
$424$	0.561553	0.0272714
$425$	−7.31534	−0.354846
$426$	−0.438447	−0.0212428
$427$	0	0
$428$	2.56155	0.123817
$429$	−9.36932	−0.452355
$430$	31.3693	1.51276
$431$	21.3693	1.02932	0.514662	−	0.857393i	$-0.327917\pi$
$431$	21.3693	1.02932	0.514662	+	0.857393i	$0.327917\pi$
$432$	1.00000	0.0481125
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	0	0
$435$	−0.315342	−0.0151195
$436$	−12.4384	−0.595694
$437$	3.12311	0.149398
$438$	−16.9309	−0.808988
$439$	−26.5616	−1.26771	−0.633857	−	0.773450i	$-0.718529\pi$
$439$	−26.5616	−1.26771	−0.633857	+	0.773450i	$0.718529\pi$
$440$	7.68466	0.366352
$441$	0	0
$442$	−14.6307	−0.695911
$443$	0.946025	0.0449470	0.0224735	−	0.999747i	$-0.492846\pi$
$443$	0.946025	0.0449470	0.0224735	+	0.999747i	$0.492846\pi$
$444$	0.876894	0.0416156
$445$	−21.1231	−1.00133
$446$	−15.4384	−0.731032
$447$	−9.12311	−0.431508
$448$	0	0
$449$	36.4924	1.72218	0.861092	−	0.508449i	$-0.169781\pi$
$449$	36.4924	1.72218	0.861092	+	0.508449i	$0.169781\pi$
$450$	−1.56155	−0.0736123
$451$	−21.3693	−1.00624
$452$	−7.12311	−0.335043
$453$	−0.315342	−0.0148160
$454$	−20.6155	−0.967535
$455$	0	0
$456$	3.12311	0.146253
$457$	38.4233	1.79737	0.898683	−	0.438599i	$-0.144525\pi$
$457$	38.4233	1.79737	0.898683	+	0.438599i	$0.144525\pi$
$458$	7.31534	0.341823
$459$	−4.68466	−0.218661
$460$	2.56155	0.119433
$461$	−8.24621	−0.384064	−0.192032	−	0.981389i	$-0.561508\pi$
$461$	−8.24621	−0.384064	−0.192032	+	0.981389i	$0.561508\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	0.123106	0.00571504
$465$	4.31534	0.200119
$466$	−18.2462	−0.845239
$467$	26.9309	1.24621	0.623106	−	0.782137i	$-0.285871\pi$
$467$	26.9309	1.24621	0.623106	+	0.782137i	$0.285871\pi$
$468$	−3.12311	−0.144366
$469$	0	0
$470$	−1.12311	−0.0518050
$471$	−3.80776	−0.175453
$472$	−1.43845	−0.0662099
$473$	36.7386	1.68924
$474$	−12.3693	−0.568142
$475$	−4.87689	−0.223767
$476$	0	0
$477$	−0.561553	−0.0257117
$478$	−11.8078	−0.540075
$479$	−28.2462	−1.29060	−0.645301	−	0.763928i	$-0.723268\pi$
$479$	−28.2462	−1.29060	−0.645301	+	0.763928i	$0.723268\pi$
$480$	2.56155	0.116918
$481$	−2.73863	−0.124871
$482$	−10.3153	−0.469851
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	−29.9309	−1.35909
$486$	−1.00000	−0.0453609
$487$	17.6847	0.801368	0.400684	−	0.916216i	$-0.368772\pi$
$487$	17.6847	0.801368	0.400684	+	0.916216i	$0.368772\pi$
$488$	2.00000	0.0905357
$489$	14.0540	0.635543
$490$	0	0
$491$	17.9309	0.809209	0.404604	−	0.914492i	$-0.367409\pi$
$491$	17.9309	0.809209	0.404604	+	0.914492i	$0.367409\pi$
$492$	−7.12311	−0.321134
$493$	−0.576708	−0.0259736
$494$	−9.75379	−0.438844
$495$	−7.68466	−0.345400
$496$	−1.68466	−0.0756434
$497$	0	0
$498$	6.56155	0.294030
$499$	−9.80776	−0.439056	−0.219528	−	0.975606i	$-0.570452\pi$
$499$	−9.80776	−0.439056	−0.219528	+	0.975606i	$0.570452\pi$
$500$	8.80776	0.393895
$501$	−13.1231	−0.586297
$502$	8.12311	0.362552
$503$	3.61553	0.161208	0.0806042	−	0.996746i	$-0.474315\pi$
$503$	3.61553	0.161208	0.0806042	+	0.996746i	$0.474315\pi$
$504$	0	0
$505$	−29.6155	−1.31787
$506$	3.00000	0.133366
$507$	−3.24621	−0.144169
$508$	13.6847	0.607159
$509$	1.38447	0.0613656	0.0306828	−	0.999529i	$-0.490232\pi$
$509$	1.38447	0.0613656	0.0306828	+	0.999529i	$0.490232\pi$
$510$	−12.0000	−0.531369
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−3.12311	−0.137888
$514$	−14.4924	−0.639233
$515$	42.7386	1.88329
$516$	12.2462	0.539109
$517$	−1.31534	−0.0578487
$518$	0	0
$519$	−8.43845	−0.370407
$520$	−8.00000	−0.350823
$521$	−8.24621	−0.361273	−0.180637	−	0.983550i	$-0.557816\pi$
$521$	−8.24621	−0.361273	−0.180637	+	0.983550i	$0.557816\pi$
$522$	−0.123106	−0.00538819
$523$	2.63068	0.115032	0.0575159	−	0.998345i	$-0.481682\pi$
$523$	2.63068	0.115032	0.0575159	+	0.998345i	$0.481682\pi$
$524$	−18.5616	−0.810865
$525$	0	0
$526$	9.12311	0.397786
$527$	7.89205	0.343783
$528$	3.00000	0.130558
$529$	1.00000	0.0434783
$530$	−1.43845	−0.0624822
$531$	1.43845	0.0624233
$532$	0	0
$533$	22.2462	0.963590
$534$	−8.24621	−0.356848
$535$	−6.56155	−0.283681
$536$	2.00000	0.0863868
$537$	−15.1231	−0.652610
$538$	−8.61553	−0.371442
$539$	0	0
$540$	−2.56155	−0.110232
$541$	4.63068	0.199089	0.0995443	−	0.995033i	$-0.468261\pi$
$541$	4.63068	0.199089	0.0995443	+	0.995033i	$0.468261\pi$
$542$	−22.8078	−0.979677
$543$	22.9309	0.984058
$544$	4.68466	0.200853
$545$	31.8617	1.36481
$546$	0	0
$547$	−30.0540	−1.28502	−0.642508	−	0.766279i	$-0.722106\pi$
$547$	−30.0540	−1.28502	−0.642508	+	0.766279i	$0.722106\pi$
$548$	20.0540	0.856663
$549$	−2.00000	−0.0853579
$550$	−4.68466	−0.199755
$551$	−0.384472	−0.0163791
$552$	1.00000	0.0425628
$553$	0	0
$554$	1.75379	0.0745113
$555$	−2.24621	−0.0953464
$556$	18.6847	0.792406
$557$	−3.93087	−0.166556	−0.0832781	−	0.996526i	$-0.526539\pi$
$557$	−3.93087	−0.166556	−0.0832781	+	0.996526i	$0.526539\pi$
$558$	1.68466	0.0713173
$559$	−38.2462	−1.61764
$560$	0	0
$561$	−14.0540	−0.593359
$562$	−15.1771	−0.640207
$563$	−24.6155	−1.03742	−0.518710	−	0.854950i	$-0.673588\pi$
$563$	−24.6155	−1.03742	−0.518710	+	0.854950i	$0.673588\pi$
$564$	−0.438447	−0.0184620
$565$	18.2462	0.767624
$566$	−23.3693	−0.982286
$567$	0	0
$568$	−0.438447	−0.0183968
$569$	21.3693	0.895848	0.447924	−	0.894072i	$-0.352163\pi$
$569$	21.3693	0.895848	0.447924	+	0.894072i	$0.352163\pi$
$570$	−8.00000	−0.335083
$571$	−15.3693	−0.643186	−0.321593	−	0.946878i	$-0.604218\pi$
$571$	−15.3693	−0.643186	−0.321593	+	0.946878i	$0.604218\pi$
$572$	−9.36932	−0.391751
$573$	−24.4924	−1.02319
$574$	0	0
$575$	−1.56155	−0.0651213
$576$	1.00000	0.0416667
$577$	27.8769	1.16053	0.580265	−	0.814428i	$-0.302949\pi$
$577$	27.8769	1.16053	0.580265	+	0.814428i	$0.302949\pi$
$578$	−4.94602	−0.205728
$579$	−13.0540	−0.542505
$580$	−0.315342	−0.0130938
$581$	0	0
$582$	−11.6847	−0.484345
$583$	−1.68466	−0.0697714
$584$	−16.9309	−0.700604
$585$	8.00000	0.330759
$586$	9.43845	0.389899
$587$	−44.1771	−1.82338	−0.911692	−	0.410875i	$-0.865223\pi$
$587$	−44.1771	−1.82338	−0.911692	+	0.410875i	$0.865223\pi$
$588$	0	0
$589$	5.26137	0.216791
$590$	3.68466	0.151695
$591$	0.438447	0.0180353
$592$	0.876894	0.0360401
$593$	0.384472	0.0157884	0.00789418	−	0.999969i	$-0.497487\pi$
$593$	0.384472	0.0157884	0.00789418	+	0.999969i	$0.497487\pi$
$594$	−3.00000	−0.123091
$595$	0	0
$596$	−9.12311	−0.373697
$597$	3.31534	0.135688
$598$	−3.12311	−0.127713
$599$	−15.0691	−0.615708	−0.307854	−	0.951434i	$-0.599611\pi$
$599$	−15.0691	−0.615708	−0.307854	+	0.951434i	$0.599611\pi$
$600$	−1.56155	−0.0637501
$601$	−35.9309	−1.46565	−0.732825	−	0.680417i	$-0.761799\pi$
$601$	−35.9309	−1.46565	−0.732825	+	0.680417i	$0.761799\pi$
$602$	0	0
$603$	−2.00000	−0.0814463
$604$	−0.315342	−0.0128311
$605$	5.12311	0.208284
$606$	−11.5616	−0.469656
$607$	−6.31534	−0.256332	−0.128166	−	0.991753i	$-0.540909\pi$
$607$	−6.31534	−0.256332	−0.128166	+	0.991753i	$0.540909\pi$
$608$	3.12311	0.126659
$609$	0	0
$610$	−5.12311	−0.207428
$611$	1.36932	0.0553966
$612$	−4.68466	−0.189366
$613$	10.0540	0.406076	0.203038	−	0.979171i	$-0.434918\pi$
$613$	10.0540	0.406076	0.203038	+	0.979171i	$0.434918\pi$
$614$	4.68466	0.189057
$615$	18.2462	0.735758
$616$	0	0
$617$	−32.0540	−1.29044	−0.645222	−	0.763995i	$-0.723235\pi$
$617$	−32.0540	−1.29044	−0.645222	+	0.763995i	$0.723235\pi$
$618$	16.6847	0.671155
$619$	8.63068	0.346896	0.173448	−	0.984843i	$-0.444509\pi$
$619$	8.63068	0.346896	0.173448	+	0.984843i	$0.444509\pi$
$620$	4.31534	0.173308
$621$	−1.00000	−0.0401286
$622$	−4.68466	−0.187838
$623$	0	0
$624$	−3.12311	−0.125024
$625$	−30.3693	−1.21477
$626$	−24.8078	−0.991518
$627$	−9.36932	−0.374174
$628$	−3.80776	−0.151946
$629$	−4.10795	−0.163795
$630$	0	0
$631$	−34.6155	−1.37802	−0.689011	−	0.724751i	$-0.741955\pi$
$631$	−34.6155	−1.37802	−0.689011	+	0.724751i	$0.741955\pi$
$632$	−12.3693	−0.492025
$633$	13.3153	0.529237
$634$	−27.9309	−1.10928
$635$	−35.0540	−1.39107
$636$	−0.561553	−0.0222670
$637$	0	0
$638$	−0.369317	−0.0146214
$639$	0.438447	0.0173447
$640$	2.56155	0.101254
$641$	40.4384	1.59722	0.798611	−	0.601847i	$-0.205568\pi$
$641$	40.4384	1.59722	0.798611	+	0.601847i	$0.205568\pi$
$642$	−2.56155	−0.101096
$643$	23.8617	0.941015	0.470508	−	0.882396i	$-0.344071\pi$
$643$	23.8617	0.941015	0.470508	+	0.882396i	$0.344071\pi$
$644$	0	0
$645$	−31.3693	−1.23517
$646$	−14.6307	−0.575637
$647$	−29.4233	−1.15675	−0.578374	−	0.815771i	$-0.696313\pi$
$647$	−29.4233	−1.15675	−0.578374	+	0.815771i	$0.696313\pi$
$648$	−1.00000	−0.0392837
$649$	4.31534	0.169392
$650$	4.87689	0.191288
$651$	0	0
$652$	14.0540	0.550396
$653$	9.73863	0.381102	0.190551	−	0.981677i	$-0.438973\pi$
$653$	9.73863	0.381102	0.190551	+	0.981677i	$0.438973\pi$
$654$	12.4384	0.486382
$655$	47.5464	1.85779
$656$	−7.12311	−0.278111
$657$	16.9309	0.660536
$658$	0	0
$659$	45.1771	1.75985	0.879925	−	0.475113i	$-0.157593\pi$
$659$	45.1771	1.75985	0.879925	+	0.475113i	$0.157593\pi$
$660$	−7.68466	−0.299125
$661$	−23.5616	−0.916438	−0.458219	−	0.888839i	$-0.651512\pi$
$661$	−23.5616	−0.916438	−0.458219	+	0.888839i	$0.651512\pi$
$662$	20.4924	0.796461
$663$	14.6307	0.568209
$664$	6.56155	0.254638
$665$	0	0
$666$	−0.876894	−0.0339790
$667$	−0.123106	−0.00476667
$668$	−13.1231	−0.507748
$669$	15.4384	0.596885
$670$	−5.12311	−0.197923
$671$	−6.00000	−0.231627
$672$	0	0
$673$	37.9848	1.46421	0.732104	−	0.681193i	$-0.238538\pi$
$673$	37.9848	1.46421	0.732104	+	0.681193i	$0.238538\pi$
$674$	−7.43845	−0.286518
$675$	1.56155	0.0601042
$676$	−3.24621	−0.124854
$677$	20.5616	0.790245	0.395122	−	0.918629i	$-0.370702\pi$
$677$	20.5616	0.790245	0.395122	+	0.918629i	$0.370702\pi$
$678$	7.12311	0.273561
$679$	0	0
$680$	−12.0000	−0.460179
$681$	20.6155	0.789989
$682$	5.05398	0.193527
$683$	23.0540	0.882136	0.441068	−	0.897474i	$-0.354600\pi$
$683$	23.0540	0.882136	0.441068	+	0.897474i	$0.354600\pi$
$684$	−3.12311	−0.119415
$685$	−51.3693	−1.96272
$686$	0	0
$687$	−7.31534	−0.279098
$688$	12.2462	0.466882
$689$	1.75379	0.0668140
$690$	−2.56155	−0.0975166
$691$	−25.5616	−0.972407	−0.486204	−	0.873846i	$-0.661619\pi$
$691$	−25.5616	−0.972407	−0.486204	+	0.873846i	$0.661619\pi$
$692$	−8.43845	−0.320782
$693$	0	0
$694$	11.6155	0.440919
$695$	−47.8617	−1.81550
$696$	−0.123106	−0.00466631
$697$	33.3693	1.26395
$698$	−30.0000	−1.13552
$699$	18.2462	0.690135
$700$	0	0
$701$	−2.80776	−0.106048	−0.0530239	−	0.998593i	$-0.516886\pi$
$701$	−2.80776	−0.106048	−0.0530239	+	0.998593i	$0.516886\pi$
$702$	3.12311	0.117874
$703$	−2.73863	−0.103290
$704$	3.00000	0.113067
$705$	1.12311	0.0422986
$706$	2.63068	0.0990071
$707$	0	0
$708$	1.43845	0.0540602
$709$	−15.0691	−0.565933	−0.282967	−	0.959130i	$-0.591319\pi$
$709$	−15.0691	−0.565933	−0.282967	+	0.959130i	$0.591319\pi$
$710$	1.12311	0.0421494
$711$	12.3693	0.463886
$712$	−8.24621	−0.309040
$713$	1.68466	0.0630910
$714$	0	0
$715$	24.0000	0.897549
$716$	−15.1231	−0.565177
$717$	11.8078	0.440969
$718$	5.12311	0.191193
$719$	43.8617	1.63577	0.817883	−	0.575384i	$-0.195147\pi$
$719$	43.8617	1.63577	0.817883	+	0.575384i	$0.195147\pi$
$720$	−2.56155	−0.0954634
$721$	0	0
$722$	9.24621	0.344108
$723$	10.3153	0.383632
$724$	22.9309	0.852219
$725$	0.192236	0.00713946
$726$	2.00000	0.0742270
$727$	40.3693	1.49722	0.748608	−	0.663013i	$-0.230723\pi$
$727$	40.3693	1.49722	0.748608	+	0.663013i	$0.230723\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	43.3693	1.60517
$731$	−57.3693	−2.12188
$732$	−2.00000	−0.0739221
$733$	8.93087	0.329869	0.164935	−	0.986305i	$-0.447259\pi$
$733$	8.93087	0.329869	0.164935	+	0.986305i	$0.447259\pi$
$734$	−22.5616	−0.832762
$735$	0	0
$736$	1.00000	0.0368605
$737$	−6.00000	−0.221013
$738$	7.12311	0.262205
$739$	7.94602	0.292299	0.146150	−	0.989262i	$-0.453312\pi$
$739$	7.94602	0.292299	0.146150	+	0.989262i	$0.453312\pi$
$740$	−2.24621	−0.0825724
$741$	9.75379	0.358314
$742$	0	0
$743$	2.87689	0.105543	0.0527715	−	0.998607i	$-0.483195\pi$
$743$	2.87689	0.105543	0.0527715	+	0.998607i	$0.483195\pi$
$744$	1.68466	0.0617626
$745$	23.3693	0.856186
$746$	−10.4384	−0.382179
$747$	−6.56155	−0.240075
$748$	−14.0540	−0.513864
$749$	0	0
$750$	−8.80776	−0.321614
$751$	12.3153	0.449393	0.224697	−	0.974429i	$-0.427861\pi$
$751$	12.3153	0.449393	0.224697	+	0.974429i	$0.427861\pi$
$752$	−0.438447	−0.0159885
$753$	−8.12311	−0.296022
$754$	0.384472	0.0140016
$755$	0.807764	0.0293975
$756$	0	0
$757$	30.4924	1.10827	0.554133	−	0.832428i	$-0.313050\pi$
$757$	30.4924	1.10827	0.554133	+	0.832428i	$0.313050\pi$
$758$	−12.4924	−0.453745
$759$	−3.00000	−0.108893
$760$	−8.00000	−0.290191
$761$	−30.2462	−1.09642	−0.548212	−	0.836339i	$-0.684691\pi$
$761$	−30.2462	−1.09642	−0.548212	+	0.836339i	$0.684691\pi$
$762$	−13.6847	−0.495743
$763$	0	0
$764$	−24.4924	−0.886105
$765$	12.0000	0.433861
$766$	3.75379	0.135630
$767$	−4.49242	−0.162212
$768$	1.00000	0.0360844
$769$	6.94602	0.250480	0.125240	−	0.992126i	$-0.460030\pi$
$769$	6.94602	0.250480	0.125240	+	0.992126i	$0.460030\pi$
$770$	0	0
$771$	14.4924	0.521932
$772$	−13.0540	−0.469823
$773$	−38.8769	−1.39830	−0.699152	−	0.714973i	$-0.746439\pi$
$773$	−38.8769	−1.39830	−0.699152	+	0.714973i	$0.746439\pi$
$774$	−12.2462	−0.440181
$775$	−2.63068	−0.0944969
$776$	−11.6847	−0.419455
$777$	0	0
$778$	25.1231	0.900707
$779$	22.2462	0.797053
$780$	8.00000	0.286446
$781$	1.31534	0.0470666
$782$	−4.68466	−0.167523
$783$	0.123106	0.00439944
$784$	0	0
$785$	9.75379	0.348128
$786$	18.5616	0.662069
$787$	39.8617	1.42092	0.710459	−	0.703739i	$-0.248487\pi$
$787$	39.8617	1.42092	0.710459	+	0.703739i	$0.248487\pi$
$788$	0.438447	0.0156190
$789$	−9.12311	−0.324791
$790$	31.6847	1.12729
$791$	0	0
$792$	−3.00000	−0.106600
$793$	6.24621	0.221809
$794$	−17.3693	−0.616414
$795$	1.43845	0.0510165
$796$	3.31534	0.117509
$797$	45.5464	1.61334	0.806668	−	0.591005i	$-0.201269\pi$
$797$	45.5464	1.61334	0.806668	+	0.591005i	$0.201269\pi$
$798$	0	0
$799$	2.05398	0.0726644
$800$	−1.56155	−0.0552092
$801$	8.24621	0.291366
$802$	−32.3002	−1.14056
$803$	50.7926	1.79243
$804$	−2.00000	−0.0705346
$805$	0	0
$806$	−5.26137	−0.185324
$807$	8.61553	0.303281
$808$	−11.5616	−0.406734
$809$	−7.12311	−0.250435	−0.125218	−	0.992129i	$-0.539963\pi$
$809$	−7.12311	−0.250435	−0.125218	+	0.992129i	$0.539963\pi$
$810$	2.56155	0.0900038
$811$	−14.6847	−0.515648	−0.257824	−	0.966192i	$-0.583005\pi$
$811$	−14.6847	−0.515648	−0.257824	+	0.966192i	$0.583005\pi$
$812$	0	0
$813$	22.8078	0.799903
$814$	−2.63068	−0.0922054
$815$	−36.0000	−1.26102
$816$	−4.68466	−0.163996
$817$	−38.2462	−1.33807
$818$	10.3693	0.362555
$819$	0	0
$820$	18.2462	0.637185
$821$	−15.0000	−0.523504	−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000	−0.523504	−0.261752	+	0.965135i	$0.584300\pi$
$822$	−20.0540	−0.699463
$823$	−50.3542	−1.75524	−0.877618	−	0.479361i	$-0.840869\pi$
$823$	−50.3542	−1.75524	−0.877618	+	0.479361i	$0.840869\pi$
$824$	16.6847	0.581238
$825$	4.68466	0.163099
$826$	0	0
$827$	18.1231	0.630202	0.315101	−	0.949058i	$-0.397962\pi$
$827$	18.1231	0.630202	0.315101	+	0.949058i	$0.397962\pi$
$828$	−1.00000	−0.0347524
$829$	−10.6307	−0.369219	−0.184609	−	0.982812i	$-0.559102\pi$
$829$	−10.6307	−0.369219	−0.184609	+	0.982812i	$0.559102\pi$
$830$	−16.8078	−0.583406
$831$	−1.75379	−0.0608383
$832$	−3.12311	−0.108274
$833$	0	0
$834$	−18.6847	−0.646997
$835$	33.6155	1.16331
$836$	−9.36932	−0.324045
$837$	−1.68466	−0.0582303
$838$	16.3002	0.563081
$839$	15.5076	0.535381	0.267691	−	0.963505i	$-0.413740\pi$
$839$	15.5076	0.535381	0.267691	+	0.963505i	$0.413740\pi$
$840$	0	0
$841$	−28.9848	−0.999477
$842$	−8.93087	−0.307778
$843$	15.1771	0.522726
$844$	13.3153	0.458333
$845$	8.31534	0.286056
$846$	0.438447	0.0150741
$847$	0	0
$848$	−0.561553	−0.0192838
$849$	23.3693	0.802033
$850$	7.31534	0.250914
$851$	−0.876894	−0.0300596
$852$	0.438447	0.0150210
$853$	6.00000	0.205436	0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000	0.205436	0.102718	+	0.994711i	$0.467246\pi$
$854$	0	0
$855$	8.00000	0.273594
$856$	−2.56155	−0.0875521
$857$	−17.5076	−0.598047	−0.299024	−	0.954246i	$-0.596661\pi$
$857$	−17.5076	−0.598047	−0.299024	+	0.954246i	$0.596661\pi$
$858$	9.36932	0.319863
$859$	−31.5616	−1.07687	−0.538433	−	0.842668i	$-0.680984\pi$
$859$	−31.5616	−1.07687	−0.538433	+	0.842668i	$0.680984\pi$
$860$	−31.3693	−1.06968
$861$	0	0
$862$	−21.3693	−0.727842
$863$	47.1771	1.60593	0.802963	−	0.596029i	$-0.203255\pi$
$863$	47.1771	1.60593	0.802963	+	0.596029i	$0.203255\pi$
$864$	−1.00000	−0.0340207
$865$	21.6155	0.734950
$866$	18.0000	0.611665
$867$	4.94602	0.167976
$868$	0	0
$869$	37.1080	1.25880
$870$	0.315342	0.0106911
$871$	6.24621	0.211645
$872$	12.4384	0.421219
$873$	11.6847	0.395466
$874$	−3.12311	−0.105641
$875$	0	0
$876$	16.9309	0.572041
$877$	−20.0000	−0.675352	−0.337676	−	0.941262i	$-0.609641\pi$
$877$	−20.0000	−0.675352	−0.337676	+	0.941262i	$0.609641\pi$
$878$	26.5616	0.896409
$879$	−9.43845	−0.318351
$880$	−7.68466	−0.259050
$881$	15.9460	0.537235	0.268618	−	0.963247i	$-0.413433\pi$
$881$	15.9460	0.537235	0.268618	+	0.963247i	$0.413433\pi$
$882$	0	0
$883$	15.5076	0.521872	0.260936	−	0.965356i	$-0.415969\pi$
$883$	15.5076	0.521872	0.260936	+	0.965356i	$0.415969\pi$
$884$	14.6307	0.492083
$885$	−3.68466	−0.123858
$886$	−0.946025	−0.0317823
$887$	−35.4233	−1.18940	−0.594699	−	0.803949i	$-0.702729\pi$
$887$	−35.4233	−1.18940	−0.594699	+	0.803949i	$0.702729\pi$
$888$	−0.876894	−0.0294266
$889$	0	0
$890$	21.1231	0.708048
$891$	3.00000	0.100504
$892$	15.4384	0.516917
$893$	1.36932	0.0458224
$894$	9.12311	0.305122
$895$	38.7386	1.29489
$896$	0	0
$897$	3.12311	0.104277
$898$	−36.4924	−1.21777
$899$	−0.207391	−0.00691687
$900$	1.56155	0.0520518
$901$	2.63068	0.0876408
$902$	21.3693	0.711520
$903$	0	0
$904$	7.12311	0.236911
$905$	−58.7386	−1.95254
$906$	0.315342	0.0104765
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	20.6155	0.684150
$909$	11.5616	0.383473
$910$	0	0
$911$	10.8769	0.360368	0.180184	−	0.983633i	$-0.442331\pi$
$911$	10.8769	0.360368	0.180184	+	0.983633i	$0.442331\pi$
$912$	−3.12311	−0.103416
$913$	−19.6847	−0.651467
$914$	−38.4233	−1.27093
$915$	5.12311	0.169365
$916$	−7.31534	−0.241706
$917$	0	0
$918$	4.68466	0.154617
$919$	−41.6695	−1.37455	−0.687275	−	0.726397i	$-0.741193\pi$
$919$	−41.6695	−1.37455	−0.687275	+	0.726397i	$0.741193\pi$
$920$	−2.56155	−0.0844519
$921$	−4.68466	−0.154365
$922$	8.24621	0.271575
$923$	−1.36932	−0.0450716
$924$	0	0
$925$	1.36932	0.0450229
$926$	−16.0000	−0.525793
$927$	−16.6847	−0.547996
$928$	−0.123106	−0.00404114
$929$	6.98485	0.229165	0.114583	−	0.993414i	$-0.463447\pi$
$929$	6.98485	0.229165	0.114583	+	0.993414i	$0.463447\pi$
$930$	−4.31534	−0.141506
$931$	0	0
$932$	18.2462	0.597675
$933$	4.68466	0.153369
$934$	−26.9309	−0.881205
$935$	36.0000	1.17733
$936$	3.12311	0.102082
$937$	−36.4233	−1.18990	−0.594949	−	0.803764i	$-0.702828\pi$
$937$	−36.4233	−1.18990	−0.594949	+	0.803764i	$0.702828\pi$
$938$	0	0
$939$	24.8078	0.809571
$940$	1.12311	0.0366317
$941$	17.0540	0.555944	0.277972	−	0.960589i	$-0.410338\pi$
$941$	17.0540	0.555944	0.277972	+	0.960589i	$0.410338\pi$
$942$	3.80776	0.124064
$943$	7.12311	0.231960
$944$	1.43845	0.0468175
$945$	0	0
$946$	−36.7386	−1.19448
$947$	−0.384472	−0.0124937	−0.00624683	−	0.999980i	$-0.501988\pi$
$947$	−0.384472	−0.0124937	−0.00624683	+	0.999980i	$0.501988\pi$
$948$	12.3693	0.401737
$949$	−52.8769	−1.71646
$950$	4.87689	0.158227
$951$	27.9309	0.905721
$952$	0	0
$953$	−11.5616	−0.374515	−0.187258	−	0.982311i	$-0.559960\pi$
$953$	−11.5616	−0.374515	−0.187258	+	0.982311i	$0.559960\pi$
$954$	0.561553	0.0181809
$955$	62.7386	2.03017
$956$	11.8078	0.381890
$957$	0.369317	0.0119383
$958$	28.2462	0.912594
$959$	0	0
$960$	−2.56155	−0.0826738
$961$	−28.1619	−0.908449
$962$	2.73863	0.0882971
$963$	2.56155	0.0825449
$964$	10.3153	0.332235
$965$	33.4384	1.07642
$966$	0	0
$967$	17.0540	0.548419	0.274209	−	0.961670i	$-0.411584\pi$
$967$	17.0540	0.548419	0.274209	+	0.961670i	$0.411584\pi$
$968$	2.00000	0.0642824
$969$	14.6307	0.470005
$970$	29.9309	0.961022
$971$	51.3542	1.64803	0.824017	−	0.566565i	$-0.191728\pi$
$971$	51.3542	1.64803	0.824017	+	0.566565i	$0.191728\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−17.6847	−0.566653
$975$	−4.87689	−0.156186
$976$	−2.00000	−0.0640184
$977$	56.2462	1.79948	0.899738	−	0.436431i	$-0.143758\pi$
$977$	56.2462	1.79948	0.899738	+	0.436431i	$0.143758\pi$
$978$	−14.0540	−0.449397
$979$	24.7386	0.790650
$980$	0	0
$981$	−12.4384	−0.397129
$982$	−17.9309	−0.572197
$983$	−21.8617	−0.697281	−0.348641	−	0.937256i	$-0.613357\pi$
$983$	−21.8617	−0.697281	−0.348641	+	0.937256i	$0.613357\pi$
$984$	7.12311	0.227076
$985$	−1.12311	−0.0357851
$986$	0.576708	0.0183661
$987$	0	0
$988$	9.75379	0.310309
$989$	−12.2462	−0.389407
$990$	7.68466	0.244234
$991$	−39.0540	−1.24059	−0.620295	−	0.784368i	$-0.712987\pi$
$991$	−39.0540	−1.24059	−0.620295	+	0.784368i	$0.712987\pi$
$992$	1.68466	0.0534880
$993$	−20.4924	−0.650307
$994$	0	0
$995$	−8.49242	−0.269228
$996$	−6.56155	−0.207911
$997$	−46.6004	−1.47585	−0.737924	−	0.674883i	$-0.764194\pi$
$997$	−46.6004	−1.47585	−0.737924	+	0.674883i	$0.764194\pi$
$998$	9.80776	0.310459
$999$	0.876894	0.0277437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.bx.1.1		2
7.2	even	3		966.2.i.i.277.2	✓	4
7.4	even	3		966.2.i.i.415.2	yes	4
7.6	odd	2		6762.2.a.br.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.i.277.2	✓	4	7.2	even	3
966.2.i.i.415.2	yes	4	7.4	even	3
6762.2.a.br.1.2		2	7.6	odd	2
6762.2.a.bx.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:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.56155 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.56155 q^{10} +3.00000 q^{11} +1.00000 q^{12} -3.12311 q^{13} -2.56155 q^{15} +1.00000 q^{16} -4.68466 q^{17} -1.00000 q^{18} -3.12311 q^{19} -2.56155 q^{20} -3.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.56155 q^{25} +3.12311 q^{26} +1.00000 q^{27} +0.123106 q^{29} +2.56155 q^{30} -1.68466 q^{31} -1.00000 q^{32} +3.00000 q^{33} +4.68466 q^{34} +1.00000 q^{36} +0.876894 q^{37} +3.12311 q^{38} -3.12311 q^{39} +2.56155 q^{40} -7.12311 q^{41} +12.2462 q^{43} +3.00000 q^{44} -2.56155 q^{45} +1.00000 q^{46} -0.438447 q^{47} +1.00000 q^{48} -1.56155 q^{50} -4.68466 q^{51} -3.12311 q^{52} -0.561553 q^{53} -1.00000 q^{54} -7.68466 q^{55} -3.12311 q^{57} -0.123106 q^{58} +1.43845 q^{59} -2.56155 q^{60} -2.00000 q^{61} +1.68466 q^{62} +1.00000 q^{64} +8.00000 q^{65} -3.00000 q^{66} -2.00000 q^{67} -4.68466 q^{68} -1.00000 q^{69} +0.438447 q^{71} -1.00000 q^{72} +16.9309 q^{73} -0.876894 q^{74} +1.56155 q^{75} -3.12311 q^{76} +3.12311 q^{78} +12.3693 q^{79} -2.56155 q^{80} +1.00000 q^{81} +7.12311 q^{82} -6.56155 q^{83} +12.0000 q^{85} -12.2462 q^{86} +0.123106 q^{87} -3.00000 q^{88} +8.24621 q^{89} +2.56155 q^{90} -1.00000 q^{92} -1.68466 q^{93} +0.438447 q^{94} +8.00000 q^{95} -1.00000 q^{96} +11.6847 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} + 6 q^{11} + 2 q^{12} + 2 q^{13} - q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} - 6 q^{22} - 2 q^{23} - 2 q^{24} - q^{25} - 2 q^{26} + 2 q^{27} - 8 q^{29} + q^{30} + 9 q^{31} - 2 q^{32} + 6 q^{33} - 3 q^{34} + 2 q^{36} + 10 q^{37} - 2 q^{38} + 2 q^{39} + q^{40} - 6 q^{41} + 8 q^{43} + 6 q^{44} - q^{45} + 2 q^{46} - 5 q^{47} + 2 q^{48} + q^{50} + 3 q^{51} + 2 q^{52} + 3 q^{53} - 2 q^{54} - 3 q^{55} + 2 q^{57} + 8 q^{58} + 7 q^{59} - q^{60} - 4 q^{61} - 9 q^{62} + 2 q^{64} + 16 q^{65} - 6 q^{66} - 4 q^{67} + 3 q^{68} - 2 q^{69} + 5 q^{71} - 2 q^{72} + 5 q^{73} - 10 q^{74} - q^{75} + 2 q^{76} - 2 q^{78} - q^{80} + 2 q^{81} + 6 q^{82} - 9 q^{83} + 24 q^{85} - 8 q^{86} - 8 q^{87} - 6 q^{88} + q^{90} - 2 q^{92} + 9 q^{93} + 5 q^{94} + 16 q^{95} - 2 q^{96} + 11 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 + 6 * q^11 + 2 * q^12 + 2 * q^13 - q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 + 2 * q^19 - q^20 - 6 * q^22 - 2 * q^23 - 2 * q^24 - q^25 - 2 * q^26 + 2 * q^27 - 8 * q^29 + q^30 + 9 * q^31 - 2 * q^32 + 6 * q^33 - 3 * q^34 + 2 * q^36 + 10 * q^37 - 2 * q^38 + 2 * q^39 + q^40 - 6 * q^41 + 8 * q^43 + 6 * q^44 - q^45 + 2 * q^46 - 5 * q^47 + 2 * q^48 + q^50 + 3 * q^51 + 2 * q^52 + 3 * q^53 - 2 * q^54 - 3 * q^55 + 2 * q^57 + 8 * q^58 + 7 * q^59 - q^60 - 4 * q^61 - 9 * q^62 + 2 * q^64 + 16 * q^65 - 6 * q^66 - 4 * q^67 + 3 * q^68 - 2 * q^69 + 5 * q^71 - 2 * q^72 + 5 * q^73 - 10 * q^74 - q^75 + 2 * q^76 - 2 * q^78 - q^80 + 2 * q^81 + 6 * q^82 - 9 * q^83 + 24 * q^85 - 8 * q^86 - 8 * q^87 - 6 * q^88 + q^90 - 2 * q^92 + 9 * q^93 + 5 * q^94 + 16 * q^95 - 2 * q^96 + 11 * q^97 + 6 * q^99

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