LMFDB - Embedded newform 245.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("245.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.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:	$1.95633484952$
Analytic rank:	$0$
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 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} -2.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.58579 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q-0.414214 q^{2} -2.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.58579 q^{8} +2.82843 q^{9} +0.414214 q^{10} +4.82843 q^{11} +4.41421 q^{12} -0.828427 q^{13} +2.41421 q^{15} +3.00000 q^{16} +0.828427 q^{17} -1.17157 q^{18} +2.82843 q^{19} +1.82843 q^{20} -2.00000 q^{22} -2.41421 q^{23} -3.82843 q^{24} +1.00000 q^{25} +0.343146 q^{26} +0.414214 q^{27} -1.00000 q^{29} -1.00000 q^{30} +6.00000 q^{31} -4.41421 q^{32} -11.6569 q^{33} -0.343146 q^{34} -5.17157 q^{36} -1.17157 q^{38} +2.00000 q^{39} -1.58579 q^{40} +2.17157 q^{41} +6.41421 q^{43} -8.82843 q^{44} -2.82843 q^{45} +1.00000 q^{46} -2.00000 q^{47} -7.24264 q^{48} -0.414214 q^{50} -2.00000 q^{51} +1.51472 q^{52} -6.82843 q^{53} -0.171573 q^{54} -4.82843 q^{55} -6.82843 q^{57} +0.414214 q^{58} +12.4853 q^{59} -4.41421 q^{60} +11.4853 q^{61} -2.48528 q^{62} -4.17157 q^{64} +0.828427 q^{65} +4.82843 q^{66} +12.4142 q^{67} -1.51472 q^{68} +5.82843 q^{69} -12.4853 q^{71} +4.48528 q^{72} -4.82843 q^{73} -2.41421 q^{75} -5.17157 q^{76} -0.828427 q^{78} +9.17157 q^{79} -3.00000 q^{80} -9.48528 q^{81} -0.899495 q^{82} +11.7279 q^{83} -0.828427 q^{85} -2.65685 q^{86} +2.41421 q^{87} +7.65685 q^{88} -2.65685 q^{89} +1.17157 q^{90} +4.41421 q^{92} -14.4853 q^{93} +0.828427 q^{94} -2.82843 q^{95} +10.6569 q^{96} -0.343146 q^{97} +13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8}+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 + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8} - 2 q^{10} + 4 q^{11} + 6 q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} - 4 q^{17} - 8 q^{18} - 2 q^{20} - 4 q^{22} - 2 q^{23} - 2 q^{24} + 2 q^{25} + 12 q^{26} - 2 q^{27} - 2 q^{29} - 2 q^{30} + 12 q^{31} - 6 q^{32} - 12 q^{33} - 12 q^{34} - 16 q^{36} - 8 q^{38} + 4 q^{39} - 6 q^{40} + 10 q^{41} + 10 q^{43} - 12 q^{44} + 2 q^{46} - 4 q^{47} - 6 q^{48} + 2 q^{50} - 4 q^{51} + 20 q^{52} - 8 q^{53} - 6 q^{54} - 4 q^{55} - 8 q^{57} - 2 q^{58} + 8 q^{59} - 6 q^{60} + 6 q^{61} + 12 q^{62} - 14 q^{64} - 4 q^{65} + 4 q^{66} + 22 q^{67} - 20 q^{68} + 6 q^{69} - 8 q^{71} - 8 q^{72} - 4 q^{73} - 2 q^{75} - 16 q^{76} + 4 q^{78} + 24 q^{79} - 6 q^{80} - 2 q^{81} + 18 q^{82} - 2 q^{83} + 4 q^{85} + 6 q^{86} + 2 q^{87} + 4 q^{88} + 6 q^{89} + 8 q^{90} + 6 q^{92} - 12 q^{93} - 4 q^{94} + 10 q^{96} - 12 q^{97} + 16 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^10 + 4 * q^11 + 6 * q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 - 4 * q^17 - 8 * q^18 - 2 * q^20 - 4 * q^22 - 2 * q^23 - 2 * q^24 + 2 * q^25 + 12 * q^26 - 2 * q^27 - 2 * q^29 - 2 * q^30 + 12 * q^31 - 6 * q^32 - 12 * q^33 - 12 * q^34 - 16 * q^36 - 8 * q^38 + 4 * q^39 - 6 * q^40 + 10 * q^41 + 10 * q^43 - 12 * q^44 + 2 * q^46 - 4 * q^47 - 6 * q^48 + 2 * q^50 - 4 * q^51 + 20 * q^52 - 8 * q^53 - 6 * q^54 - 4 * q^55 - 8 * q^57 - 2 * q^58 + 8 * q^59 - 6 * q^60 + 6 * q^61 + 12 * q^62 - 14 * q^64 - 4 * q^65 + 4 * q^66 + 22 * q^67 - 20 * q^68 + 6 * q^69 - 8 * q^71 - 8 * q^72 - 4 * q^73 - 2 * q^75 - 16 * q^76 + 4 * q^78 + 24 * q^79 - 6 * q^80 - 2 * q^81 + 18 * q^82 - 2 * q^83 + 4 * q^85 + 6 * q^86 + 2 * q^87 + 4 * q^88 + 6 * q^89 + 8 * q^90 + 6 * q^92 - 12 * q^93 - 4 * q^94 + 10 * q^96 - 12 * q^97 + 16 * 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 $

$2$	−0.414214	−0.292893	−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214	−0.292893	−0.146447	+	0.989219i	$0.546784\pi$
$3$	−2.41421	−1.39385	−0.696923	−	0.717146i	$-0.745448\pi$
$3$	−2.41421	−1.39385	−0.696923	+	0.717146i	$0.745448\pi$
$4$	−1.82843	−0.914214
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.58579	0.560660
$9$	2.82843	0.942809
$10$	0.414214	0.130986
$11$	4.82843	1.45583	0.727913	−	0.685670i	$-0.240491\pi$
$11$	4.82843	1.45583	0.727913	+	0.685670i	$0.240491\pi$
$12$	4.41421	1.27427
$13$	−0.828427	−0.229764	−0.114882	−	0.993379i	$-0.536649\pi$
$13$	−0.828427	−0.229764	−0.114882	+	0.993379i	$0.536649\pi$
$14$	0	0
$15$	2.41421	0.623347
$16$	3.00000	0.750000
$17$	0.828427	0.200923	0.100462	−	0.994941i	$-0.467968\pi$
$17$	0.828427	0.200923	0.100462	+	0.994941i	$0.467968\pi$
$18$	−1.17157	−0.276142
$19$	2.82843	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$19$	2.82843	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$20$	1.82843	0.408849
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−2.41421	−0.503398	−0.251699	−	0.967806i	$-0.580989\pi$
$23$	−2.41421	−0.503398	−0.251699	+	0.967806i	$0.580989\pi$
$24$	−3.82843	−0.781474
$25$	1.00000	0.200000
$26$	0.343146	0.0672964
$27$	0.414214	0.0797154
$28$	0	0
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−1.00000	−0.182574
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	−4.41421	−0.780330
$33$	−11.6569	−2.02920
$34$	−0.343146	−0.0588490
$35$	0	0
$36$	−5.17157	−0.861929
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	−1.17157	−0.190054
$39$	2.00000	0.320256
$40$	−1.58579	−0.250735
$41$	2.17157	0.339143	0.169571	−	0.985518i	$-0.445762\pi$
$41$	2.17157	0.339143	0.169571	+	0.985518i	$0.445762\pi$
$42$	0	0
$43$	6.41421	0.978158	0.489079	−	0.872239i	$-0.337333\pi$
$43$	6.41421	0.978158	0.489079	+	0.872239i	$0.337333\pi$
$44$	−8.82843	−1.33094
$45$	−2.82843	−0.421637
$46$	1.00000	0.147442
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	−7.24264	−1.04539
$49$	0	0
$50$	−0.414214	−0.0585786
$51$	−2.00000	−0.280056
$52$	1.51472	0.210054
$53$	−6.82843	−0.937957	−0.468978	−	0.883210i	$-0.655378\pi$
$53$	−6.82843	−0.937957	−0.468978	+	0.883210i	$0.655378\pi$
$54$	−0.171573	−0.0233481
$55$	−4.82843	−0.651065
$56$	0	0
$57$	−6.82843	−0.904447
$58$	0.414214	0.0543889
$59$	12.4853	1.62545	0.812723	−	0.582651i	$-0.197984\pi$
$59$	12.4853	1.62545	0.812723	+	0.582651i	$0.197984\pi$
$60$	−4.41421	−0.569873
$61$	11.4853	1.47054	0.735270	−	0.677775i	$-0.237055\pi$
$61$	11.4853	1.47054	0.735270	+	0.677775i	$0.237055\pi$
$62$	−2.48528	−0.315631
$63$	0	0
$64$	−4.17157	−0.521447
$65$	0.828427	0.102754
$66$	4.82843	0.594338
$67$	12.4142	1.51664	0.758319	−	0.651884i	$-0.226021\pi$
$67$	12.4142	1.51664	0.758319	+	0.651884i	$0.226021\pi$
$68$	−1.51472	−0.183687
$69$	5.82843	0.701660
$70$	0	0
$71$	−12.4853	−1.48173	−0.740865	−	0.671654i	$-0.765584\pi$
$71$	−12.4853	−1.48173	−0.740865	+	0.671654i	$0.765584\pi$
$72$	4.48528	0.528595
$73$	−4.82843	−0.565125	−0.282562	−	0.959249i	$-0.591184\pi$
$73$	−4.82843	−0.565125	−0.282562	+	0.959249i	$0.591184\pi$
$74$	0	0
$75$	−2.41421	−0.278769
$76$	−5.17157	−0.593220
$77$	0	0
$78$	−0.828427	−0.0938009
$79$	9.17157	1.03188	0.515941	−	0.856624i	$-0.327442\pi$
$79$	9.17157	1.03188	0.515941	+	0.856624i	$0.327442\pi$
$80$	−3.00000	−0.335410
$81$	−9.48528	−1.05392
$82$	−0.899495	−0.0993326
$83$	11.7279	1.28731	0.643653	−	0.765317i	$-0.277418\pi$
$83$	11.7279	1.28731	0.643653	+	0.765317i	$0.277418\pi$
$84$	0	0
$85$	−0.828427	−0.0898555
$86$	−2.65685	−0.286496
$87$	2.41421	0.258831
$88$	7.65685	0.816223
$89$	−2.65685	−0.281626	−0.140813	−	0.990036i	$-0.544972\pi$
$89$	−2.65685	−0.281626	−0.140813	+	0.990036i	$0.544972\pi$
$90$	1.17157	0.123495
$91$	0	0
$92$	4.41421	0.460214
$93$	−14.4853	−1.50205
$94$	0.828427	0.0854457
$95$	−2.82843	−0.290191
$96$	10.6569	1.08766
$97$	−0.343146	−0.0348412	−0.0174206	−	0.999848i	$-0.505545\pi$
$97$	−0.343146	−0.0348412	−0.0174206	+	0.999848i	$0.505545\pi$
$98$	0	0
$99$	13.6569	1.37257
$100$	−1.82843	−0.182843
$101$	−12.3137	−1.22526	−0.612630	−	0.790370i	$-0.709888\pi$
$101$	−12.3137	−1.22526	−0.612630	+	0.790370i	$0.709888\pi$
$102$	0.828427	0.0820265
$103$	−0.414214	−0.0408137	−0.0204068	−	0.999792i	$-0.506496\pi$
$103$	−0.414214	−0.0408137	−0.0204068	+	0.999792i	$0.506496\pi$
$104$	−1.31371	−0.128820
$105$	0	0
$106$	2.82843	0.274721
$107$	2.75736	0.266564	0.133282	−	0.991078i	$-0.457448\pi$
$107$	2.75736	0.266564	0.133282	+	0.991078i	$0.457448\pi$
$108$	−0.757359	−0.0728769
$109$	3.48528	0.333829	0.166915	−	0.985971i	$-0.446620\pi$
$109$	3.48528	0.333829	0.166915	+	0.985971i	$0.446620\pi$
$110$	2.00000	0.190693
$111$	0	0
$112$	0	0
$113$	12.4853	1.17452	0.587258	−	0.809400i	$-0.300207\pi$
$113$	12.4853	1.17452	0.587258	+	0.809400i	$0.300207\pi$
$114$	2.82843	0.264906
$115$	2.41421	0.225127
$116$	1.82843	0.169765
$117$	−2.34315	−0.216624
$118$	−5.17157	−0.476082
$119$	0	0
$120$	3.82843	0.349486
$121$	12.3137	1.11943
$122$	−4.75736	−0.430711
$123$	−5.24264	−0.472713
$124$	−10.9706	−0.985186
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	13.3137	1.18140	0.590700	−	0.806891i	$-0.298852\pi$
$127$	13.3137	1.18140	0.590700	+	0.806891i	$0.298852\pi$
$128$	10.5563	0.933058
$129$	−15.4853	−1.36340
$130$	−0.343146	−0.0300959
$131$	−3.31371	−0.289520	−0.144760	−	0.989467i	$-0.546241\pi$
$131$	−3.31371	−0.289520	−0.144760	+	0.989467i	$0.546241\pi$
$132$	21.3137	1.85512
$133$	0	0
$134$	−5.14214	−0.444213
$135$	−0.414214	−0.0356498
$136$	1.31371	0.112650
$137$	1.65685	0.141555	0.0707773	−	0.997492i	$-0.477452\pi$
$137$	1.65685	0.141555	0.0707773	+	0.997492i	$0.477452\pi$
$138$	−2.41421	−0.205512
$139$	−12.1421	−1.02988	−0.514941	−	0.857225i	$-0.672186\pi$
$139$	−12.1421	−1.02988	−0.514941	+	0.857225i	$0.672186\pi$
$140$	0	0
$141$	4.82843	0.406627
$142$	5.17157	0.433989
$143$	−4.00000	−0.334497
$144$	8.48528	0.707107
$145$	1.00000	0.0830455
$146$	2.00000	0.165521
$147$	0	0
$148$	0	0
$149$	−7.82843	−0.641330	−0.320665	−	0.947193i	$-0.603906\pi$
$149$	−7.82843	−0.641330	−0.320665	+	0.947193i	$0.603906\pi$
$150$	1.00000	0.0816497
$151$	0.343146	0.0279248	0.0139624	−	0.999903i	$-0.495555\pi$
$151$	0.343146	0.0279248	0.0139624	+	0.999903i	$0.495555\pi$
$152$	4.48528	0.363804
$153$	2.34315	0.189432
$154$	0	0
$155$	−6.00000	−0.481932
$156$	−3.65685	−0.292783
$157$	5.31371	0.424080	0.212040	−	0.977261i	$-0.431989\pi$
$157$	5.31371	0.424080	0.212040	+	0.977261i	$0.431989\pi$
$158$	−3.79899	−0.302231
$159$	16.4853	1.30737
$160$	4.41421	0.348974
$161$	0	0
$162$	3.92893	0.308686
$163$	23.6569	1.85295	0.926474	−	0.376359i	$-0.122824\pi$
$163$	23.6569	1.85295	0.926474	+	0.376359i	$0.122824\pi$
$164$	−3.97056	−0.310049
$165$	11.6569	0.907485
$166$	−4.85786	−0.377043
$167$	−19.5858	−1.51559	−0.757797	−	0.652491i	$-0.773724\pi$
$167$	−19.5858	−1.51559	−0.757797	+	0.652491i	$0.773724\pi$
$168$	0	0
$169$	−12.3137	−0.947208
$170$	0.343146	0.0263181
$171$	8.00000	0.611775
$172$	−11.7279	−0.894246
$173$	19.3137	1.46839	0.734197	−	0.678936i	$-0.237559\pi$
$173$	19.3137	1.46839	0.734197	+	0.678936i	$0.237559\pi$
$174$	−1.00000	−0.0758098
$175$	0	0
$176$	14.4853	1.09187
$177$	−30.1421	−2.26562
$178$	1.10051	0.0824863
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	5.17157	0.385466
$181$	8.65685	0.643459	0.321729	−	0.946832i	$-0.395736\pi$
$181$	8.65685	0.643459	0.321729	+	0.946832i	$0.395736\pi$
$182$	0	0
$183$	−27.7279	−2.04971
$184$	−3.82843	−0.282235
$185$	0	0
$186$	6.00000	0.439941
$187$	4.00000	0.292509
$188$	3.65685	0.266704
$189$	0	0
$190$	1.17157	0.0849948
$191$	−7.17157	−0.518917	−0.259458	−	0.965754i	$-0.583544\pi$
$191$	−7.17157	−0.518917	−0.259458	+	0.965754i	$0.583544\pi$
$192$	10.0711	0.726817
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	0.142136	0.0102047
$195$	−2.00000	−0.143223
$196$	0	0
$197$	−23.6569	−1.68548	−0.842741	−	0.538320i	$-0.819059\pi$
$197$	−23.6569	−1.68548	−0.842741	+	0.538320i	$0.819059\pi$
$198$	−5.65685	−0.402015
$199$	−1.65685	−0.117451	−0.0587256	−	0.998274i	$-0.518704\pi$
$199$	−1.65685	−0.117451	−0.0587256	+	0.998274i	$0.518704\pi$
$200$	1.58579	0.112132
$201$	−29.9706	−2.11396
$202$	5.10051	0.358870
$203$	0	0
$204$	3.65685	0.256031
$205$	−2.17157	−0.151669
$206$	0.171573	0.0119540
$207$	−6.82843	−0.474608
$208$	−2.48528	−0.172323
$209$	13.6569	0.944664
$210$	0	0
$211$	3.51472	0.241963	0.120982	−	0.992655i	$-0.461396\pi$
$211$	3.51472	0.241963	0.120982	+	0.992655i	$0.461396\pi$
$212$	12.4853	0.857493
$213$	30.1421	2.06531
$214$	−1.14214	−0.0780748
$215$	−6.41421	−0.437446
$216$	0.656854	0.0446933
$217$	0	0
$218$	−1.44365	−0.0977764
$219$	11.6569	0.787697
$220$	8.82843	0.595212
$221$	−0.686292	−0.0461650
$222$	0	0
$223$	−11.6569	−0.780601	−0.390300	−	0.920688i	$-0.627629\pi$
$223$	−11.6569	−0.780601	−0.390300	+	0.920688i	$0.627629\pi$
$224$	0	0
$225$	2.82843	0.188562
$226$	−5.17157	−0.344008
$227$	−26.9706	−1.79010	−0.895050	−	0.445967i	$-0.852860\pi$
$227$	−26.9706	−1.79010	−0.895050	+	0.445967i	$0.852860\pi$
$228$	12.4853	0.826858
$229$	0.343146	0.0226757	0.0113379	−	0.999936i	$-0.496391\pi$
$229$	0.343146	0.0226757	0.0113379	+	0.999936i	$0.496391\pi$
$230$	−1.00000	−0.0659380
$231$	0	0
$232$	−1.58579	−0.104112
$233$	−11.1716	−0.731874	−0.365937	−	0.930640i	$-0.619251\pi$
$233$	−11.1716	−0.731874	−0.365937	+	0.930640i	$0.619251\pi$
$234$	0.970563	0.0634477
$235$	2.00000	0.130466
$236$	−22.8284	−1.48600
$237$	−22.1421	−1.43829
$238$	0	0
$239$	1.31371	0.0849767	0.0424884	−	0.999097i	$-0.486471\pi$
$239$	1.31371	0.0849767	0.0424884	+	0.999097i	$0.486471\pi$
$240$	7.24264	0.467510
$241$	−16.3431	−1.05275	−0.526377	−	0.850251i	$-0.676450\pi$
$241$	−16.3431	−1.05275	−0.526377	+	0.850251i	$0.676450\pi$
$242$	−5.10051	−0.327873
$243$	21.6569	1.38929
$244$	−21.0000	−1.34439
$245$	0	0
$246$	2.17157	0.138454
$247$	−2.34315	−0.149091
$248$	9.51472	0.604185
$249$	−28.3137	−1.79431
$250$	0.414214	0.0261972
$251$	−13.3137	−0.840354	−0.420177	−	0.907442i	$-0.638032\pi$
$251$	−13.3137	−0.840354	−0.420177	+	0.907442i	$0.638032\pi$
$252$	0	0
$253$	−11.6569	−0.732860
$254$	−5.51472	−0.346024
$255$	2.00000	0.125245
$256$	3.97056	0.248160
$257$	−17.6569	−1.10140	−0.550702	−	0.834702i	$-0.685640\pi$
$257$	−17.6569	−1.10140	−0.550702	+	0.834702i	$0.685640\pi$
$258$	6.41421	0.399331
$259$	0	0
$260$	−1.51472	−0.0939389
$261$	−2.82843	−0.175075
$262$	1.37258	0.0847985
$263$	19.0416	1.17416	0.587079	−	0.809530i	$-0.300278\pi$
$263$	19.0416	1.17416	0.587079	+	0.809530i	$0.300278\pi$
$264$	−18.4853	−1.13769
$265$	6.82843	0.419467
$266$	0	0
$267$	6.41421	0.392543
$268$	−22.6985	−1.38653
$269$	30.4558	1.85693	0.928463	−	0.371425i	$-0.121131\pi$
$269$	30.4558	1.85693	0.928463	+	0.371425i	$0.121131\pi$
$270$	0.171573	0.0104416
$271$	0.485281	0.0294787	0.0147394	−	0.999891i	$-0.495308\pi$
$271$	0.485281	0.0294787	0.0147394	+	0.999891i	$0.495308\pi$
$272$	2.48528	0.150692
$273$	0	0
$274$	−0.686292	−0.0414604
$275$	4.82843	0.291165
$276$	−10.6569	−0.641467
$277$	−12.1421	−0.729550	−0.364775	−	0.931096i	$-0.618854\pi$
$277$	−12.1421	−0.729550	−0.364775	+	0.931096i	$0.618854\pi$
$278$	5.02944	0.301646
$279$	16.9706	1.01600
$280$	0	0
$281$	26.2843	1.56799	0.783994	−	0.620768i	$-0.213179\pi$
$281$	26.2843	1.56799	0.783994	+	0.620768i	$0.213179\pi$
$282$	−2.00000	−0.119098
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	22.8284	1.35462
$285$	6.82843	0.404481
$286$	1.65685	0.0979718
$287$	0	0
$288$	−12.4853	−0.735702
$289$	−16.3137	−0.959630
$290$	−0.414214	−0.0243235
$291$	0.828427	0.0485633
$292$	8.82843	0.516645
$293$	16.0000	0.934730	0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000	0.934730	0.467365	+	0.884064i	$0.345203\pi$
$294$	0	0
$295$	−12.4853	−0.726921
$296$	0	0
$297$	2.00000	0.116052
$298$	3.24264	0.187841
$299$	2.00000	0.115663
$300$	4.41421	0.254855
$301$	0	0
$302$	−0.142136	−0.00817899
$303$	29.7279	1.70782
$304$	8.48528	0.486664
$305$	−11.4853	−0.657645
$306$	−0.970563	−0.0554834
$307$	13.2426	0.755797	0.377899	−	0.925847i	$-0.376647\pi$
$307$	13.2426	0.755797	0.377899	+	0.925847i	$0.376647\pi$
$308$	0	0
$309$	1.00000	0.0568880
$310$	2.48528	0.141154
$311$	18.8284	1.06766	0.533831	−	0.845591i	$-0.320752\pi$
$311$	18.8284	1.06766	0.533831	+	0.845591i	$0.320752\pi$
$312$	3.17157	0.179555
$313$	17.6569	0.998024	0.499012	−	0.866595i	$-0.333696\pi$
$313$	17.6569	0.998024	0.499012	+	0.866595i	$0.333696\pi$
$314$	−2.20101	−0.124210
$315$	0	0
$316$	−16.7696	−0.943361
$317$	25.7990	1.44902	0.724508	−	0.689267i	$-0.242067\pi$
$317$	25.7990	1.44902	0.724508	+	0.689267i	$0.242067\pi$
$318$	−6.82843	−0.382919
$319$	−4.82843	−0.270340
$320$	4.17157	0.233198
$321$	−6.65685	−0.371549
$322$	0	0
$323$	2.34315	0.130376
$324$	17.3431	0.963508
$325$	−0.828427	−0.0459529
$326$	−9.79899	−0.542716
$327$	−8.41421	−0.465307
$328$	3.44365	0.190144
$329$	0	0
$330$	−4.82843	−0.265796
$331$	−10.9706	−0.602997	−0.301498	−	0.953467i	$-0.597487\pi$
$331$	−10.9706	−0.602997	−0.301498	+	0.953467i	$0.597487\pi$
$332$	−21.4437	−1.17687
$333$	0	0
$334$	8.11270	0.443907
$335$	−12.4142	−0.678261
$336$	0	0
$337$	14.8284	0.807756	0.403878	−	0.914813i	$-0.367662\pi$
$337$	14.8284	0.807756	0.403878	+	0.914813i	$0.367662\pi$
$338$	5.10051	0.277431
$339$	−30.1421	−1.63710
$340$	1.51472	0.0821472
$341$	28.9706	1.56884
$342$	−3.31371	−0.179185
$343$	0	0
$344$	10.1716	0.548414
$345$	−5.82843	−0.313792
$346$	−8.00000	−0.430083
$347$	22.0711	1.18484	0.592418	−	0.805630i	$-0.298173\pi$
$347$	22.0711	1.18484	0.592418	+	0.805630i	$0.298173\pi$
$348$	−4.41421	−0.236627
$349$	26.6569	1.42691	0.713454	−	0.700702i	$-0.247130\pi$
$349$	26.6569	1.42691	0.713454	+	0.700702i	$0.247130\pi$
$350$	0	0
$351$	−0.343146	−0.0183158
$352$	−21.3137	−1.13602
$353$	21.1716	1.12685	0.563425	−	0.826168i	$-0.309484\pi$
$353$	21.1716	1.12685	0.563425	+	0.826168i	$0.309484\pi$
$354$	12.4853	0.663585
$355$	12.4853	0.662650
$356$	4.85786	0.257466
$357$	0	0
$358$	4.14214	0.218919
$359$	−10.0000	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	−4.48528	−0.236395
$361$	−11.0000	−0.578947
$362$	−3.58579	−0.188465
$363$	−29.7279	−1.56031
$364$	0	0
$365$	4.82843	0.252731
$366$	11.4853	0.600345
$367$	11.2426	0.586861	0.293431	−	0.955980i	$-0.405203\pi$
$367$	11.2426	0.586861	0.293431	+	0.955980i	$0.405203\pi$
$368$	−7.24264	−0.377549
$369$	6.14214	0.319747
$370$	0	0
$371$	0	0
$372$	26.4853	1.37320
$373$	12.9706	0.671590	0.335795	−	0.941935i	$-0.390995\pi$
$373$	12.9706	0.671590	0.335795	+	0.941935i	$0.390995\pi$
$374$	−1.65685	−0.0856739
$375$	2.41421	0.124669
$376$	−3.17157	−0.163561
$377$	0.828427	0.0426662
$378$	0	0
$379$	21.1716	1.08751	0.543755	−	0.839244i	$-0.317002\pi$
$379$	21.1716	1.08751	0.543755	+	0.839244i	$0.317002\pi$
$380$	5.17157	0.265296
$381$	−32.1421	−1.64669
$382$	2.97056	0.151987
$383$	−16.8995	−0.863524	−0.431762	−	0.901988i	$-0.642108\pi$
$383$	−16.8995	−0.863524	−0.431762	+	0.901988i	$0.642108\pi$
$384$	−25.4853	−1.30054
$385$	0	0
$386$	0.828427	0.0421658
$387$	18.1421	0.922217
$388$	0.627417	0.0318523
$389$	12.3431	0.625822	0.312911	−	0.949782i	$-0.398696\pi$
$389$	12.3431	0.625822	0.312911	+	0.949782i	$0.398696\pi$
$390$	0.828427	0.0419490
$391$	−2.00000	−0.101144
$392$	0	0
$393$	8.00000	0.403547
$394$	9.79899	0.493666
$395$	−9.17157	−0.461472
$396$	−24.9706	−1.25482
$397$	−28.6274	−1.43677	−0.718384	−	0.695646i	$-0.755118\pi$
$397$	−28.6274	−1.43677	−0.718384	+	0.695646i	$0.755118\pi$
$398$	0.686292	0.0344007
$399$	0	0
$400$	3.00000	0.150000
$401$	7.68629	0.383835	0.191918	−	0.981411i	$-0.438529\pi$
$401$	7.68629	0.383835	0.191918	+	0.981411i	$0.438529\pi$
$402$	12.4142	0.619165
$403$	−4.97056	−0.247601
$404$	22.5147	1.12015
$405$	9.48528	0.471327
$406$	0	0
$407$	0	0
$408$	−3.17157	−0.157016
$409$	−24.7990	−1.22623	−0.613116	−	0.789993i	$-0.710084\pi$
$409$	−24.7990	−1.22623	−0.613116	+	0.789993i	$0.710084\pi$
$410$	0.899495	0.0444229
$411$	−4.00000	−0.197305
$412$	0.757359	0.0373124
$413$	0	0
$414$	2.82843	0.139010
$415$	−11.7279	−0.575701
$416$	3.65685	0.179292
$417$	29.3137	1.43550
$418$	−5.65685	−0.276686
$419$	23.3137	1.13895	0.569475	−	0.822009i	$-0.307147\pi$
$419$	23.3137	1.13895	0.569475	+	0.822009i	$0.307147\pi$
$420$	0	0
$421$	−3.48528	−0.169862	−0.0849311	−	0.996387i	$-0.527067\pi$
$421$	−3.48528	−0.169862	−0.0849311	+	0.996387i	$0.527067\pi$
$422$	−1.45584	−0.0708694
$423$	−5.65685	−0.275046
$424$	−10.8284	−0.525875
$425$	0.828427	0.0401846
$426$	−12.4853	−0.604914
$427$	0	0
$428$	−5.04163	−0.243696
$429$	9.65685	0.466237
$430$	2.65685	0.128125
$431$	−21.7990	−1.05002	−0.525010	−	0.851096i	$-0.675938\pi$
$431$	−21.7990	−1.05002	−0.525010	+	0.851096i	$0.675938\pi$
$432$	1.24264	0.0597866
$433$	31.7990	1.52816	0.764081	−	0.645120i	$-0.223193\pi$
$433$	31.7990	1.52816	0.764081	+	0.645120i	$0.223193\pi$
$434$	0	0
$435$	−2.41421	−0.115753
$436$	−6.37258	−0.305191
$437$	−6.82843	−0.326648
$438$	−4.82843	−0.230711
$439$	−33.9411	−1.61992	−0.809961	−	0.586484i	$-0.800512\pi$
$439$	−33.9411	−1.61992	−0.809961	+	0.586484i	$0.800512\pi$
$440$	−7.65685	−0.365026
$441$	0	0
$442$	0.284271	0.0135214
$443$	−12.2132	−0.580267	−0.290133	−	0.956986i	$-0.593700\pi$
$443$	−12.2132	−0.580267	−0.290133	+	0.956986i	$0.593700\pi$
$444$	0	0
$445$	2.65685	0.125947
$446$	4.82843	0.228633
$447$	18.8995	0.893915
$448$	0	0
$449$	−1.82843	−0.0862888	−0.0431444	−	0.999069i	$-0.513738\pi$
$449$	−1.82843	−0.0862888	−0.0431444	+	0.999069i	$0.513738\pi$
$450$	−1.17157	−0.0552285
$451$	10.4853	0.493733
$452$	−22.8284	−1.07376
$453$	−0.828427	−0.0389229
$454$	11.1716	0.524308
$455$	0	0
$456$	−10.8284	−0.507088
$457$	−32.2843	−1.51019	−0.755097	−	0.655613i	$-0.772410\pi$
$457$	−32.2843	−1.51019	−0.755097	+	0.655613i	$0.772410\pi$
$458$	−0.142136	−0.00664156
$459$	0.343146	0.0160167
$460$	−4.41421	−0.205814
$461$	−18.6863	−0.870307	−0.435154	−	0.900356i	$-0.643306\pi$
$461$	−18.6863	−0.870307	−0.435154	+	0.900356i	$0.643306\pi$
$462$	0	0
$463$	11.0416	0.513148	0.256574	−	0.966525i	$-0.417406\pi$
$463$	11.0416	0.513148	0.256574	+	0.966525i	$0.417406\pi$
$464$	−3.00000	−0.139272
$465$	14.4853	0.671739
$466$	4.62742	0.214361
$467$	22.8995	1.05966	0.529831	−	0.848103i	$-0.322255\pi$
$467$	22.8995	1.05966	0.529831	+	0.848103i	$0.322255\pi$
$468$	4.28427	0.198041
$469$	0	0
$470$	−0.828427	−0.0382125
$471$	−12.8284	−0.591103
$472$	19.7990	0.911322
$473$	30.9706	1.42403
$474$	9.17157	0.421264
$475$	2.82843	0.129777
$476$	0	0
$477$	−19.3137	−0.884314
$478$	−0.544156	−0.0248891
$479$	24.3431	1.11227	0.556133	−	0.831093i	$-0.312284\pi$
$479$	24.3431	1.11227	0.556133	+	0.831093i	$0.312284\pi$
$480$	−10.6569	−0.486417
$481$	0	0
$482$	6.76955	0.308345
$483$	0	0
$484$	−22.5147	−1.02340
$485$	0.343146	0.0155814
$486$	−8.97056	−0.406913
$487$	15.6569	0.709480	0.354740	−	0.934965i	$-0.384569\pi$
$487$	15.6569	0.709480	0.354740	+	0.934965i	$0.384569\pi$
$488$	18.2132	0.824473
$489$	−57.1127	−2.58273
$490$	0	0
$491$	−13.3137	−0.600839	−0.300420	−	0.953807i	$-0.597127\pi$
$491$	−13.3137	−0.600839	−0.300420	+	0.953807i	$0.597127\pi$
$492$	9.58579	0.432161
$493$	−0.828427	−0.0373105
$494$	0.970563	0.0436677
$495$	−13.6569	−0.613830
$496$	18.0000	0.808224
$497$	0	0
$498$	11.7279	0.525541
$499$	4.82843	0.216150	0.108075	−	0.994143i	$-0.465531\pi$
$499$	4.82843	0.216150	0.108075	+	0.994143i	$0.465531\pi$
$500$	1.82843	0.0817697
$501$	47.2843	2.11251
$502$	5.51472	0.246134
$503$	−37.8701	−1.68854	−0.844271	−	0.535916i	$-0.819966\pi$
$503$	−37.8701	−1.68854	−0.844271	+	0.535916i	$0.819966\pi$
$504$	0	0
$505$	12.3137	0.547953
$506$	4.82843	0.214650
$507$	29.7279	1.32026
$508$	−24.3431	−1.08005
$509$	−24.6569	−1.09290	−0.546448	−	0.837493i	$-0.684020\pi$
$509$	−24.6569	−1.09290	−0.546448	+	0.837493i	$0.684020\pi$
$510$	−0.828427	−0.0366834
$511$	0	0
$512$	−22.7574	−1.00574
$513$	1.17157	0.0517262
$514$	7.31371	0.322594
$515$	0.414214	0.0182524
$516$	28.3137	1.24644
$517$	−9.65685	−0.424708
$518$	0	0
$519$	−46.6274	−2.04672
$520$	1.31371	0.0576099
$521$	18.9706	0.831115	0.415558	−	0.909567i	$-0.363586\pi$
$521$	18.9706	0.831115	0.415558	+	0.909567i	$0.363586\pi$
$522$	1.17157	0.0512784
$523$	−24.3431	−1.06445	−0.532226	−	0.846602i	$-0.678644\pi$
$523$	−24.3431	−1.06445	−0.532226	+	0.846602i	$0.678644\pi$
$524$	6.05887	0.264683
$525$	0	0
$526$	−7.88730	−0.343903
$527$	4.97056	0.216521
$528$	−34.9706	−1.52190
$529$	−17.1716	−0.746590
$530$	−2.82843	−0.122859
$531$	35.3137	1.53248
$532$	0	0
$533$	−1.79899	−0.0779229
$534$	−2.65685	−0.114973
$535$	−2.75736	−0.119211
$536$	19.6863	0.850318
$537$	24.1421	1.04181
$538$	−12.6152	−0.543881
$539$	0	0
$540$	0.757359	0.0325916
$541$	18.6569	0.802121	0.401060	−	0.916052i	$-0.368642\pi$
$541$	18.6569	0.802121	0.401060	+	0.916052i	$0.368642\pi$
$542$	−0.201010	−0.00863412
$543$	−20.8995	−0.896883
$544$	−3.65685	−0.156786
$545$	−3.48528	−0.149293
$546$	0	0
$547$	5.10051	0.218082	0.109041	−	0.994037i	$-0.465222\pi$
$547$	5.10051	0.218082	0.109041	+	0.994037i	$0.465222\pi$
$548$	−3.02944	−0.129411
$549$	32.4853	1.38644
$550$	−2.00000	−0.0852803
$551$	−2.82843	−0.120495
$552$	9.24264	0.393393
$553$	0	0
$554$	5.02944	0.213680
$555$	0	0
$556$	22.2010	0.941533
$557$	−34.2843	−1.45267	−0.726336	−	0.687340i	$-0.758778\pi$
$557$	−34.2843	−1.45267	−0.726336	+	0.687340i	$0.758778\pi$
$558$	−7.02944	−0.297580
$559$	−5.31371	−0.224746
$560$	0	0
$561$	−9.65685	−0.407713
$562$	−10.8873	−0.459253
$563$	−16.2721	−0.685786	−0.342893	−	0.939374i	$-0.611407\pi$
$563$	−16.2721	−0.685786	−0.342893	+	0.939374i	$0.611407\pi$
$564$	−8.82843	−0.371744
$565$	−12.4853	−0.525260
$566$	5.79899	0.243750
$567$	0	0
$568$	−19.7990	−0.830747
$569$	−3.65685	−0.153303	−0.0766517	−	0.997058i	$-0.524423\pi$
$569$	−3.65685	−0.153303	−0.0766517	+	0.997058i	$0.524423\pi$
$570$	−2.82843	−0.118470
$571$	14.8284	0.620550	0.310275	−	0.950647i	$-0.399579\pi$
$571$	14.8284	0.620550	0.310275	+	0.950647i	$0.399579\pi$
$572$	7.31371	0.305802
$573$	17.3137	0.723291
$574$	0	0
$575$	−2.41421	−0.100680
$576$	−11.7990	−0.491625
$577$	−23.9411	−0.996682	−0.498341	−	0.866981i	$-0.666057\pi$
$577$	−23.9411	−0.996682	−0.498341	+	0.866981i	$0.666057\pi$
$578$	6.75736	0.281069
$579$	4.82843	0.200663
$580$	−1.82843	−0.0759213
$581$	0	0
$582$	−0.343146	−0.0142238
$583$	−32.9706	−1.36550
$584$	−7.65685	−0.316843
$585$	2.34315	0.0968772
$586$	−6.62742	−0.273776
$587$	−22.2843	−0.919770	−0.459885	−	0.887978i	$-0.652109\pi$
$587$	−22.2843	−0.919770	−0.459885	+	0.887978i	$0.652109\pi$
$588$	0	0
$589$	16.9706	0.699260
$590$	5.17157	0.212910
$591$	57.1127	2.34930
$592$	0	0
$593$	−43.7990	−1.79861	−0.899304	−	0.437323i	$-0.855927\pi$
$593$	−43.7990	−1.79861	−0.899304	+	0.437323i	$0.855927\pi$
$594$	−0.828427	−0.0339908
$595$	0	0
$596$	14.3137	0.586312
$597$	4.00000	0.163709
$598$	−0.828427	−0.0338769
$599$	17.6569	0.721440	0.360720	−	0.932674i	$-0.382531\pi$
$599$	17.6569	0.721440	0.360720	+	0.932674i	$0.382531\pi$
$600$	−3.82843	−0.156295
$601$	−8.34315	−0.340324	−0.170162	−	0.985416i	$-0.554429\pi$
$601$	−8.34315	−0.340324	−0.170162	+	0.985416i	$0.554429\pi$
$602$	0	0
$603$	35.1127	1.42990
$604$	−0.627417	−0.0255292
$605$	−12.3137	−0.500623
$606$	−12.3137	−0.500210
$607$	4.21320	0.171009	0.0855043	−	0.996338i	$-0.472750\pi$
$607$	4.21320	0.171009	0.0855043	+	0.996338i	$0.472750\pi$
$608$	−12.4853	−0.506345
$609$	0	0
$610$	4.75736	0.192620
$611$	1.65685	0.0670291
$612$	−4.28427	−0.173181
$613$	−15.4558	−0.624256	−0.312128	−	0.950040i	$-0.601042\pi$
$613$	−15.4558	−0.624256	−0.312128	+	0.950040i	$0.601042\pi$
$614$	−5.48528	−0.221368
$615$	5.24264	0.211404
$616$	0	0
$617$	−11.3137	−0.455473	−0.227736	−	0.973723i	$-0.573132\pi$
$617$	−11.3137	−0.455473	−0.227736	+	0.973723i	$0.573132\pi$
$618$	−0.414214	−0.0166621
$619$	−42.4853	−1.70763	−0.853814	−	0.520578i	$-0.825716\pi$
$619$	−42.4853	−1.70763	−0.853814	+	0.520578i	$0.825716\pi$
$620$	10.9706	0.440588
$621$	−1.00000	−0.0401286
$622$	−7.79899	−0.312711
$623$	0	0
$624$	6.00000	0.240192
$625$	1.00000	0.0400000
$626$	−7.31371	−0.292315
$627$	−32.9706	−1.31672
$628$	−9.71573	−0.387700
$629$	0	0
$630$	0	0
$631$	8.14214	0.324133	0.162067	−	0.986780i	$-0.448184\pi$
$631$	8.14214	0.324133	0.162067	+	0.986780i	$0.448184\pi$
$632$	14.5442	0.578535
$633$	−8.48528	−0.337260
$634$	−10.6863	−0.424407
$635$	−13.3137	−0.528338
$636$	−30.1421	−1.19521
$637$	0	0
$638$	2.00000	0.0791808
$639$	−35.3137	−1.39699
$640$	−10.5563	−0.417276
$641$	14.5147	0.573297	0.286648	−	0.958036i	$-0.407459\pi$
$641$	14.5147	0.573297	0.286648	+	0.958036i	$0.407459\pi$
$642$	2.75736	0.108824
$643$	30.2843	1.19430	0.597148	−	0.802131i	$-0.296301\pi$
$643$	30.2843	1.19430	0.597148	+	0.802131i	$0.296301\pi$
$644$	0	0
$645$	15.4853	0.609732
$646$	−0.970563	−0.0381863
$647$	−17.0416	−0.669976	−0.334988	−	0.942222i	$-0.608732\pi$
$647$	−17.0416	−0.669976	−0.334988	+	0.942222i	$0.608732\pi$
$648$	−15.0416	−0.590891
$649$	60.2843	2.36636
$650$	0.343146	0.0134593
$651$	0	0
$652$	−43.2548	−1.69399
$653$	−24.8284	−0.971611	−0.485806	−	0.874067i	$-0.661474\pi$
$653$	−24.8284	−0.971611	−0.485806	+	0.874067i	$0.661474\pi$
$654$	3.48528	0.136285
$655$	3.31371	0.129477
$656$	6.51472	0.254357
$657$	−13.6569	−0.532805
$658$	0	0
$659$	26.8284	1.04509	0.522544	−	0.852613i	$-0.324983\pi$
$659$	26.8284	1.04509	0.522544	+	0.852613i	$0.324983\pi$
$660$	−21.3137	−0.829635
$661$	−26.1716	−1.01796	−0.508978	−	0.860779i	$-0.669977\pi$
$661$	−26.1716	−1.01796	−0.508978	+	0.860779i	$0.669977\pi$
$662$	4.54416	0.176614
$663$	1.65685	0.0643469
$664$	18.5980	0.721742
$665$	0	0
$666$	0	0
$667$	2.41421	0.0934787
$668$	35.8112	1.38558
$669$	28.1421	1.08804
$670$	5.14214	0.198658
$671$	55.4558	2.14085
$672$	0	0
$673$	18.3431	0.707076	0.353538	−	0.935420i	$-0.384978\pi$
$673$	18.3431	0.707076	0.353538	+	0.935420i	$0.384978\pi$
$674$	−6.14214	−0.236586
$675$	0.414214	0.0159431
$676$	22.5147	0.865951
$677$	−0.142136	−0.00546272	−0.00273136	−	0.999996i	$-0.500869\pi$
$677$	−0.142136	−0.00546272	−0.00273136	+	0.999996i	$0.500869\pi$
$678$	12.4853	0.479494
$679$	0	0
$680$	−1.31371	−0.0503784
$681$	65.1127	2.49512
$682$	−12.0000	−0.459504
$683$	−43.2426	−1.65463	−0.827317	−	0.561736i	$-0.810134\pi$
$683$	−43.2426	−1.65463	−0.827317	+	0.561736i	$0.810134\pi$
$684$	−14.6274	−0.559293
$685$	−1.65685	−0.0633051
$686$	0	0
$687$	−0.828427	−0.0316065
$688$	19.2426	0.733619
$689$	5.65685	0.215509
$690$	2.41421	0.0919075
$691$	4.82843	0.183682	0.0918410	−	0.995774i	$-0.470725\pi$
$691$	4.82843	0.183682	0.0918410	+	0.995774i	$0.470725\pi$
$692$	−35.3137	−1.34243
$693$	0	0
$694$	−9.14214	−0.347031
$695$	12.1421	0.460577
$696$	3.82843	0.145116
$697$	1.79899	0.0681416
$698$	−11.0416	−0.417932
$699$	26.9706	1.02012
$700$	0	0
$701$	−42.7990	−1.61650	−0.808248	−	0.588843i	$-0.799584\pi$
$701$	−42.7990	−1.61650	−0.808248	+	0.588843i	$0.799584\pi$
$702$	0.142136	0.00536456
$703$	0	0
$704$	−20.1421	−0.759135
$705$	−4.82843	−0.181849
$706$	−8.76955	−0.330046
$707$	0	0
$708$	55.1127	2.07126
$709$	38.3137	1.43890	0.719451	−	0.694543i	$-0.244394\pi$
$709$	38.3137	1.43890	0.719451	+	0.694543i	$0.244394\pi$
$710$	−5.17157	−0.194086
$711$	25.9411	0.972868
$712$	−4.21320	−0.157896
$713$	−14.4853	−0.542478
$714$	0	0
$715$	4.00000	0.149592
$716$	18.2843	0.683315
$717$	−3.17157	−0.118445
$718$	4.14214	0.154583
$719$	41.1127	1.53324	0.766622	−	0.642098i	$-0.221936\pi$
$719$	41.1127	1.53324	0.766622	+	0.642098i	$0.221936\pi$
$720$	−8.48528	−0.316228
$721$	0	0
$722$	4.55635	0.169570
$723$	39.4558	1.46738
$724$	−15.8284	−0.588259
$725$	−1.00000	−0.0371391
$726$	12.3137	0.457005
$727$	40.4142	1.49888	0.749440	−	0.662072i	$-0.230323\pi$
$727$	40.4142	1.49888	0.749440	+	0.662072i	$0.230323\pi$
$728$	0	0
$729$	−23.8284	−0.882534
$730$	−2.00000	−0.0740233
$731$	5.31371	0.196535
$732$	50.6985	1.87387
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	−4.65685	−0.171888
$735$	0	0
$736$	10.6569	0.392817
$737$	59.9411	2.20796
$738$	−2.54416	−0.0936517
$739$	41.1127	1.51236	0.756178	−	0.654367i	$-0.227065\pi$
$739$	41.1127	1.51236	0.756178	+	0.654367i	$0.227065\pi$
$740$	0	0
$741$	5.65685	0.207810
$742$	0	0
$743$	−1.92893	−0.0707657	−0.0353828	−	0.999374i	$-0.511265\pi$
$743$	−1.92893	−0.0707657	−0.0353828	+	0.999374i	$0.511265\pi$
$744$	−22.9706	−0.842142
$745$	7.82843	0.286811
$746$	−5.37258	−0.196704
$747$	33.1716	1.21368
$748$	−7.31371	−0.267416
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	−41.6569	−1.52008	−0.760040	−	0.649876i	$-0.774821\pi$
$751$	−41.6569	−1.52008	−0.760040	+	0.649876i	$0.774821\pi$
$752$	−6.00000	−0.218797
$753$	32.1421	1.17132
$754$	−0.343146	−0.0124966
$755$	−0.343146	−0.0124884
$756$	0	0
$757$	19.4558	0.707135	0.353567	−	0.935409i	$-0.384969\pi$
$757$	19.4558	0.707135	0.353567	+	0.935409i	$0.384969\pi$
$758$	−8.76955	−0.318524
$759$	28.1421	1.02149
$760$	−4.48528	−0.162698
$761$	13.3137	0.482622	0.241311	−	0.970448i	$-0.422423\pi$
$761$	13.3137	0.482622	0.241311	+	0.970448i	$0.422423\pi$
$762$	13.3137	0.482305
$763$	0	0
$764$	13.1127	0.474401
$765$	−2.34315	−0.0847166
$766$	7.00000	0.252920
$767$	−10.3431	−0.373469
$768$	−9.58579	−0.345897
$769$	−44.6274	−1.60931	−0.804653	−	0.593745i	$-0.797649\pi$
$769$	−44.6274	−1.60931	−0.804653	+	0.593745i	$0.797649\pi$
$770$	0	0
$771$	42.6274	1.53519
$772$	3.65685	0.131613
$773$	−25.1127	−0.903241	−0.451620	−	0.892210i	$-0.649154\pi$
$773$	−25.1127	−0.903241	−0.451620	+	0.892210i	$0.649154\pi$
$774$	−7.51472	−0.270111
$775$	6.00000	0.215526
$776$	−0.544156	−0.0195341
$777$	0	0
$778$	−5.11270	−0.183299
$779$	6.14214	0.220065
$780$	3.65685	0.130936
$781$	−60.2843	−2.15714
$782$	0.828427	0.0296245
$783$	−0.414214	−0.0148028
$784$	0	0
$785$	−5.31371	−0.189654
$786$	−3.31371	−0.118196
$787$	28.5563	1.01792	0.508962	−	0.860789i	$-0.330029\pi$
$787$	28.5563	1.01792	0.508962	+	0.860789i	$0.330029\pi$
$788$	43.2548	1.54089
$789$	−45.9706	−1.63660
$790$	3.79899	0.135162
$791$	0	0
$792$	21.6569	0.769543
$793$	−9.51472	−0.337878
$794$	11.8579	0.420820
$795$	−16.4853	−0.584673
$796$	3.02944	0.107376
$797$	8.00000	0.283375	0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000	0.283375	0.141687	+	0.989911i	$0.454747\pi$
$798$	0	0
$799$	−1.65685	−0.0586153
$800$	−4.41421	−0.156066
$801$	−7.51472	−0.265520
$802$	−3.18377	−0.112423
$803$	−23.3137	−0.822723
$804$	54.7990	1.93261
$805$	0	0
$806$	2.05887	0.0725208
$807$	−73.5269	−2.58827
$808$	−19.5269	−0.686954
$809$	−9.62742	−0.338482	−0.169241	−	0.985575i	$-0.554132\pi$
$809$	−9.62742	−0.338482	−0.169241	+	0.985575i	$0.554132\pi$
$810$	−3.92893	−0.138049
$811$	−24.6274	−0.864786	−0.432393	−	0.901685i	$-0.642331\pi$
$811$	−24.6274	−0.864786	−0.432393	+	0.901685i	$0.642331\pi$
$812$	0	0
$813$	−1.17157	−0.0410889
$814$	0	0
$815$	−23.6569	−0.828663
$816$	−6.00000	−0.210042
$817$	18.1421	0.634713
$818$	10.2721	0.359155
$819$	0	0
$820$	3.97056	0.138658
$821$	−19.9411	−0.695950	−0.347975	−	0.937504i	$-0.613131\pi$
$821$	−19.9411	−0.695950	−0.347975	+	0.937504i	$0.613131\pi$
$822$	1.65685	0.0577894
$823$	−12.0711	−0.420771	−0.210385	−	0.977619i	$-0.567472\pi$
$823$	−12.0711	−0.420771	−0.210385	+	0.977619i	$0.567472\pi$
$824$	−0.656854	−0.0228826
$825$	−11.6569	−0.405840
$826$	0	0
$827$	16.2132	0.563788	0.281894	−	0.959446i	$-0.409037\pi$
$827$	16.2132	0.563788	0.281894	+	0.959446i	$0.409037\pi$
$828$	12.4853	0.433894
$829$	−6.68629	−0.232225	−0.116112	−	0.993236i	$-0.537043\pi$
$829$	−6.68629	−0.232225	−0.116112	+	0.993236i	$0.537043\pi$
$830$	4.85786	0.168619
$831$	29.3137	1.01688
$832$	3.45584	0.119810
$833$	0	0
$834$	−12.1421	−0.420448
$835$	19.5858	0.677794
$836$	−24.9706	−0.863625
$837$	2.48528	0.0859039
$838$	−9.65685	−0.333590
$839$	−20.8284	−0.719077	−0.359539	−	0.933130i	$-0.617066\pi$
$839$	−20.8284	−0.719077	−0.359539	+	0.933130i	$0.617066\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	1.44365	0.0497515
$843$	−63.4558	−2.18554
$844$	−6.42641	−0.221206
$845$	12.3137	0.423604
$846$	2.34315	0.0805590
$847$	0	0
$848$	−20.4853	−0.703467
$849$	33.7990	1.15998
$850$	−0.343146	−0.0117698
$851$	0	0
$852$	−55.1127	−1.88813
$853$	−53.4558	−1.83029	−0.915147	−	0.403121i	$-0.867925\pi$
$853$	−53.4558	−1.83029	−0.915147	+	0.403121i	$0.867925\pi$
$854$	0	0
$855$	−8.00000	−0.273594
$856$	4.37258	0.149452
$857$	22.2843	0.761216	0.380608	−	0.924736i	$-0.375715\pi$
$857$	22.2843	0.761216	0.380608	+	0.924736i	$0.375715\pi$
$858$	−4.00000	−0.136558
$859$	−46.6274	−1.59091	−0.795453	−	0.606015i	$-0.792767\pi$
$859$	−46.6274	−1.59091	−0.795453	+	0.606015i	$0.792767\pi$
$860$	11.7279	0.399919
$861$	0	0
$862$	9.02944	0.307544
$863$	−16.5563	−0.563585	−0.281792	−	0.959475i	$-0.590929\pi$
$863$	−16.5563	−0.563585	−0.281792	+	0.959475i	$0.590929\pi$
$864$	−1.82843	−0.0622044
$865$	−19.3137	−0.656686
$866$	−13.1716	−0.447588
$867$	39.3848	1.33758
$868$	0	0
$869$	44.2843	1.50224
$870$	1.00000	0.0339032
$871$	−10.2843	−0.348469
$872$	5.52691	0.187165
$873$	−0.970563	−0.0328486
$874$	2.82843	0.0956730
$875$	0	0
$876$	−21.3137	−0.720123
$877$	30.8284	1.04100	0.520501	−	0.853861i	$-0.325745\pi$
$877$	30.8284	1.04100	0.520501	+	0.853861i	$0.325745\pi$
$878$	14.0589	0.474464
$879$	−38.6274	−1.30287
$880$	−14.4853	−0.488299
$881$	3.82843	0.128983	0.0644915	−	0.997918i	$-0.479457\pi$
$881$	3.82843	0.128983	0.0644915	+	0.997918i	$0.479457\pi$
$882$	0	0
$883$	−38.2843	−1.28837	−0.644184	−	0.764870i	$-0.722803\pi$
$883$	−38.2843	−1.28837	−0.644184	+	0.764870i	$0.722803\pi$
$884$	1.25483	0.0422046
$885$	30.1421	1.01322
$886$	5.05887	0.169956
$887$	−44.0711	−1.47976	−0.739881	−	0.672738i	$-0.765118\pi$
$887$	−44.0711	−1.47976	−0.739881	+	0.672738i	$0.765118\pi$
$888$	0	0
$889$	0	0
$890$	−1.10051	−0.0368890
$891$	−45.7990	−1.53432
$892$	21.3137	0.713636
$893$	−5.65685	−0.189299
$894$	−7.82843	−0.261822
$895$	10.0000	0.334263
$896$	0	0
$897$	−4.82843	−0.161216
$898$	0.757359	0.0252734
$899$	−6.00000	−0.200111
$900$	−5.17157	−0.172386
$901$	−5.65685	−0.188457
$902$	−4.34315	−0.144611
$903$	0	0
$904$	19.7990	0.658505
$905$	−8.65685	−0.287764
$906$	0.343146	0.0114003
$907$	28.2132	0.936804	0.468402	−	0.883515i	$-0.344830\pi$
$907$	28.2132	0.936804	0.468402	+	0.883515i	$0.344830\pi$
$908$	49.3137	1.63653
$909$	−34.8284	−1.15519
$910$	0	0
$911$	−49.7990	−1.64991	−0.824957	−	0.565195i	$-0.808801\pi$
$911$	−49.7990	−1.64991	−0.824957	+	0.565195i	$0.808801\pi$
$912$	−20.4853	−0.678335
$913$	56.6274	1.87409
$914$	13.3726	0.442326
$915$	27.7279	0.916657
$916$	−0.627417	−0.0207304
$917$	0	0
$918$	−0.142136	−0.00469117
$919$	19.1127	0.630470	0.315235	−	0.949014i	$-0.397917\pi$
$919$	19.1127	0.630470	0.315235	+	0.949014i	$0.397917\pi$
$920$	3.82843	0.126220
$921$	−31.9706	−1.05347
$922$	7.74012	0.254907
$923$	10.3431	0.340449
$924$	0	0
$925$	0	0
$926$	−4.57359	−0.150298
$927$	−1.17157	−0.0384795
$928$	4.41421	0.144904
$929$	11.4853	0.376820	0.188410	−	0.982090i	$-0.439667\pi$
$929$	11.4853	0.376820	0.188410	+	0.982090i	$0.439667\pi$
$930$	−6.00000	−0.196748
$931$	0	0
$932$	20.4264	0.669089
$933$	−45.4558	−1.48816
$934$	−9.48528	−0.310368
$935$	−4.00000	−0.130814
$936$	−3.71573	−0.121452
$937$	10.6274	0.347183	0.173591	−	0.984818i	$-0.444463\pi$
$937$	10.6274	0.347183	0.173591	+	0.984818i	$0.444463\pi$
$938$	0	0
$939$	−42.6274	−1.39109
$940$	−3.65685	−0.119273
$941$	−10.2843	−0.335258	−0.167629	−	0.985850i	$-0.553611\pi$
$941$	−10.2843	−0.335258	−0.167629	+	0.985850i	$0.553611\pi$
$942$	5.31371	0.173130
$943$	−5.24264	−0.170724
$944$	37.4558	1.21908
$945$	0	0
$946$	−12.8284	−0.417088
$947$	−43.1838	−1.40328	−0.701642	−	0.712530i	$-0.747549\pi$
$947$	−43.1838	−1.40328	−0.701642	+	0.712530i	$0.747549\pi$
$948$	40.4853	1.31490
$949$	4.00000	0.129845
$950$	−1.17157	−0.0380108
$951$	−62.2843	−2.01971
$952$	0	0
$953$	−2.34315	−0.0759019	−0.0379510	−	0.999280i	$-0.512083\pi$
$953$	−2.34315	−0.0759019	−0.0379510	+	0.999280i	$0.512083\pi$
$954$	8.00000	0.259010
$955$	7.17157	0.232067
$956$	−2.40202	−0.0776869
$957$	11.6569	0.376813
$958$	−10.0833	−0.325775
$959$	0	0
$960$	−10.0711	−0.325042
$961$	5.00000	0.161290
$962$	0	0
$963$	7.79899	0.251319
$964$	29.8823	0.962442
$965$	2.00000	0.0643823
$966$	0	0
$967$	−27.5269	−0.885206	−0.442603	−	0.896718i	$-0.645945\pi$
$967$	−27.5269	−0.885206	−0.442603	+	0.896718i	$0.645945\pi$
$968$	19.5269	0.627619
$969$	−5.65685	−0.181724
$970$	−0.142136	−0.00456370
$971$	24.0000	0.770197	0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000	0.770197	0.385098	+	0.922876i	$0.374168\pi$
$972$	−39.5980	−1.27011
$973$	0	0
$974$	−6.48528	−0.207802
$975$	2.00000	0.0640513
$976$	34.4558	1.10290
$977$	21.3137	0.681886	0.340943	−	0.940084i	$-0.389254\pi$
$977$	21.3137	0.681886	0.340943	+	0.940084i	$0.389254\pi$
$978$	23.6569	0.756463
$979$	−12.8284	−0.409998
$980$	0	0
$981$	9.85786	0.314737
$982$	5.51472	0.175982
$983$	14.2132	0.453331	0.226665	−	0.973973i	$-0.427218\pi$
$983$	14.2132	0.453331	0.226665	+	0.973973i	$0.427218\pi$
$984$	−8.31371	−0.265031
$985$	23.6569	0.753770
$986$	0.343146	0.0109280
$987$	0	0
$988$	4.28427	0.136301
$989$	−15.4853	−0.492403
$990$	5.65685	0.179787
$991$	−15.6569	−0.497356	−0.248678	−	0.968586i	$-0.579996\pi$
$991$	−15.6569	−0.497356	−0.248678	+	0.968586i	$0.579996\pi$
$992$	−26.4853	−0.840909
$993$	26.4853	0.840485
$994$	0	0
$995$	1.65685	0.0525258
$996$	51.7696	1.64038
$997$	17.4558	0.552832	0.276416	−	0.961038i	$-0.410853\pi$
$997$	17.4558	0.552832	0.276416	+	0.961038i	$0.410853\pi$
$998$	−2.00000	−0.0633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.a.g.1.1		2
3.2	odd	2		2205.2.a.q.1.2		2
4.3	odd	2		3920.2.a.bv.1.2		2
5.2	odd	4		1225.2.b.h.99.2		4
5.3	odd	4		1225.2.b.h.99.3		4
5.4	even	2		1225.2.a.m.1.2		2
7.2	even	3		245.2.e.e.116.2		4
7.3	odd	6		35.2.e.a.16.2	yes	4
7.4	even	3		245.2.e.e.226.2		4
7.5	odd	6		35.2.e.a.11.2	✓	4
7.6	odd	2		245.2.a.h.1.1		2
21.5	even	6		315.2.j.e.46.1		4
21.17	even	6		315.2.j.e.226.1		4
21.20	even	2		2205.2.a.n.1.2		2
28.3	even	6		560.2.q.k.401.2		4
28.19	even	6		560.2.q.k.81.2		4
28.27	even	2		3920.2.a.bq.1.1		2
35.3	even	12		175.2.k.a.149.2		8
35.12	even	12		175.2.k.a.74.2		8
35.13	even	4		1225.2.b.g.99.3		4
35.17	even	12		175.2.k.a.149.3		8
35.19	odd	6		175.2.e.c.151.1		4
35.24	odd	6		175.2.e.c.51.1		4
35.27	even	4		1225.2.b.g.99.2		4
35.33	even	12		175.2.k.a.74.3		8
35.34	odd	2		1225.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.2	✓	4	7.5	odd	6
35.2.e.a.16.2	yes	4	7.3	odd	6
175.2.e.c.51.1		4	35.24	odd	6
175.2.e.c.151.1		4	35.19	odd	6
175.2.k.a.74.2		8	35.12	even	12
175.2.k.a.74.3		8	35.33	even	12
175.2.k.a.149.2		8	35.3	even	12
175.2.k.a.149.3		8	35.17	even	12
245.2.a.g.1.1		2	1.1	even	1	trivial
245.2.a.h.1.1		2	7.6	odd	2
245.2.e.e.116.2		4	7.2	even	3
245.2.e.e.226.2		4	7.4	even	3
315.2.j.e.46.1		4	21.5	even	6
315.2.j.e.226.1		4	21.17	even	6
560.2.q.k.81.2		4	28.19	even	6
560.2.q.k.401.2		4	28.3	even	6
1225.2.a.k.1.2		2	35.34	odd	2
1225.2.a.m.1.2		2	5.4	even	2
1225.2.b.g.99.2		4	35.27	even	4
1225.2.b.g.99.3		4	35.13	even	4
1225.2.b.h.99.2		4	5.2	odd	4
1225.2.b.h.99.3		4	5.3	odd	4
2205.2.a.n.1.2		2	21.20	even	2
2205.2.a.q.1.2		2	3.2	odd	2
3920.2.a.bq.1.1		2	28.27	even	2
3920.2.a.bv.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} -2.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.58579 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} -2.41421 q^{3} -1.82843 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.58579 q^{8} +2.82843 q^{9} +0.414214 q^{10} +4.82843 q^{11} +4.41421 q^{12} -0.828427 q^{13} +2.41421 q^{15} +3.00000 q^{16} +0.828427 q^{17} -1.17157 q^{18} +2.82843 q^{19} +1.82843 q^{20} -2.00000 q^{22} -2.41421 q^{23} -3.82843 q^{24} +1.00000 q^{25} +0.343146 q^{26} +0.414214 q^{27} -1.00000 q^{29} -1.00000 q^{30} +6.00000 q^{31} -4.41421 q^{32} -11.6569 q^{33} -0.343146 q^{34} -5.17157 q^{36} -1.17157 q^{38} +2.00000 q^{39} -1.58579 q^{40} +2.17157 q^{41} +6.41421 q^{43} -8.82843 q^{44} -2.82843 q^{45} +1.00000 q^{46} -2.00000 q^{47} -7.24264 q^{48} -0.414214 q^{50} -2.00000 q^{51} +1.51472 q^{52} -6.82843 q^{53} -0.171573 q^{54} -4.82843 q^{55} -6.82843 q^{57} +0.414214 q^{58} +12.4853 q^{59} -4.41421 q^{60} +11.4853 q^{61} -2.48528 q^{62} -4.17157 q^{64} +0.828427 q^{65} +4.82843 q^{66} +12.4142 q^{67} -1.51472 q^{68} +5.82843 q^{69} -12.4853 q^{71} +4.48528 q^{72} -4.82843 q^{73} -2.41421 q^{75} -5.17157 q^{76} -0.828427 q^{78} +9.17157 q^{79} -3.00000 q^{80} -9.48528 q^{81} -0.899495 q^{82} +11.7279 q^{83} -0.828427 q^{85} -2.65685 q^{86} +2.41421 q^{87} +7.65685 q^{88} -2.65685 q^{89} +1.17157 q^{90} +4.41421 q^{92} -14.4853 q^{93} +0.828427 q^{94} -2.82843 q^{95} +10.6569 q^{96} -0.343146 q^{97} +13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^8	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 6 q^{8} - 2 q^{10} + 4 q^{11} + 6 q^{12} + 4 q^{13} + 2 q^{15} + 6 q^{16} - 4 q^{17} - 8 q^{18} - 2 q^{20} - 4 q^{22} - 2 q^{23} - 2 q^{24} + 2 q^{25} + 12 q^{26} - 2 q^{27} - 2 q^{29} - 2 q^{30} + 12 q^{31} - 6 q^{32} - 12 q^{33} - 12 q^{34} - 16 q^{36} - 8 q^{38} + 4 q^{39} - 6 q^{40} + 10 q^{41} + 10 q^{43} - 12 q^{44} + 2 q^{46} - 4 q^{47} - 6 q^{48} + 2 q^{50} - 4 q^{51} + 20 q^{52} - 8 q^{53} - 6 q^{54} - 4 q^{55} - 8 q^{57} - 2 q^{58} + 8 q^{59} - 6 q^{60} + 6 q^{61} + 12 q^{62} - 14 q^{64} - 4 q^{65} + 4 q^{66} + 22 q^{67} - 20 q^{68} + 6 q^{69} - 8 q^{71} - 8 q^{72} - 4 q^{73} - 2 q^{75} - 16 q^{76} + 4 q^{78} + 24 q^{79} - 6 q^{80} - 2 q^{81} + 18 q^{82} - 2 q^{83} + 4 q^{85} + 6 q^{86} + 2 q^{87} + 4 q^{88} + 6 q^{89} + 8 q^{90} + 6 q^{92} - 12 q^{93} - 4 q^{94} + 10 q^{96} - 12 q^{97} + 16 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 6 * q^8 - 2 * q^10 + 4 * q^11 + 6 * q^12 + 4 * q^13 + 2 * q^15 + 6 * q^16 - 4 * q^17 - 8 * q^18 - 2 * q^20 - 4 * q^22 - 2 * q^23 - 2 * q^24 + 2 * q^25 + 12 * q^26 - 2 * q^27 - 2 * q^29 - 2 * q^30 + 12 * q^31 - 6 * q^32 - 12 * q^33 - 12 * q^34 - 16 * q^36 - 8 * q^38 + 4 * q^39 - 6 * q^40 + 10 * q^41 + 10 * q^43 - 12 * q^44 + 2 * q^46 - 4 * q^47 - 6 * q^48 + 2 * q^50 - 4 * q^51 + 20 * q^52 - 8 * q^53 - 6 * q^54 - 4 * q^55 - 8 * q^57 - 2 * q^58 + 8 * q^59 - 6 * q^60 + 6 * q^61 + 12 * q^62 - 14 * q^64 - 4 * q^65 + 4 * q^66 + 22 * q^67 - 20 * q^68 + 6 * q^69 - 8 * q^71 - 8 * q^72 - 4 * q^73 - 2 * q^75 - 16 * q^76 + 4 * q^78 + 24 * q^79 - 6 * q^80 - 2 * q^81 + 18 * q^82 - 2 * q^83 + 4 * q^85 + 6 * q^86 + 2 * q^87 + 4 * q^88 + 6 * q^89 + 8 * q^90 + 6 * q^92 - 12 * q^93 - 4 * q^94 + 10 * q^96 - 12 * q^97 + 16 * q^99

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