LMFDB - Embedded newform 4998.2.a.bv.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4998,2,Mod(1,4998)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4998, 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("4998.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4998.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:	$39.9092309302$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 714)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	4998.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41421 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41421 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.41421 q^{10} +4.82843 q^{11} +1.00000 q^{12} +5.65685 q^{13} -2.41421 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.00000 q^{19} -2.41421 q^{20} -4.82843 q^{22} +1.58579 q^{23} -1.00000 q^{24} +0.828427 q^{25} -5.65685 q^{26} +1.00000 q^{27} -1.17157 q^{29} +2.41421 q^{30} +6.00000 q^{31} -1.00000 q^{32} +4.82843 q^{33} +1.00000 q^{34} +1.00000 q^{36} -4.41421 q^{37} -3.00000 q^{38} +5.65685 q^{39} +2.41421 q^{40} -9.65685 q^{41} +4.17157 q^{43} +4.82843 q^{44} -2.41421 q^{45} -1.58579 q^{46} +10.0000 q^{47} +1.00000 q^{48} -0.828427 q^{50} -1.00000 q^{51} +5.65685 q^{52} -8.82843 q^{53} -1.00000 q^{54} -11.6569 q^{55} +3.00000 q^{57} +1.17157 q^{58} +10.6569 q^{59} -2.41421 q^{60} +12.4853 q^{61} -6.00000 q^{62} +1.00000 q^{64} -13.6569 q^{65} -4.82843 q^{66} -6.65685 q^{67} -1.00000 q^{68} +1.58579 q^{69} -0.414214 q^{71} -1.00000 q^{72} +5.17157 q^{73} +4.41421 q^{74} +0.828427 q^{75} +3.00000 q^{76} -5.65685 q^{78} +0.343146 q^{79} -2.41421 q^{80} +1.00000 q^{81} +9.65685 q^{82} +9.65685 q^{83} +2.41421 q^{85} -4.17157 q^{86} -1.17157 q^{87} -4.82843 q^{88} -16.3137 q^{89} +2.41421 q^{90} +1.58579 q^{92} +6.00000 q^{93} -10.0000 q^{94} -7.24264 q^{95} -1.00000 q^{96} +1.65685 q^{97} +4.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{12} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 6 q^{19} - 2 q^{20} - 4 q^{22} + 6 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{27} - 8 q^{29} + 2 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 2 q^{34} + 2 q^{36} - 6 q^{37} - 6 q^{38} + 2 q^{40} - 8 q^{41} + 14 q^{43} + 4 q^{44} - 2 q^{45} - 6 q^{46} + 20 q^{47} + 2 q^{48} + 4 q^{50} - 2 q^{51} - 12 q^{53} - 2 q^{54} - 12 q^{55} + 6 q^{57} + 8 q^{58} + 10 q^{59} - 2 q^{60} + 8 q^{61} - 12 q^{62} + 2 q^{64} - 16 q^{65} - 4 q^{66} - 2 q^{67} - 2 q^{68} + 6 q^{69} + 2 q^{71} - 2 q^{72} + 16 q^{73} + 6 q^{74} - 4 q^{75} + 6 q^{76} + 12 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 8 q^{83} + 2 q^{85} - 14 q^{86} - 8 q^{87} - 4 q^{88} - 10 q^{89} + 2 q^{90} + 6 q^{92} + 12 q^{93} - 20 q^{94} - 6 q^{95} - 2 q^{96} - 8 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^12 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 + 6 * q^19 - 2 * q^20 - 4 * q^22 + 6 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^27 - 8 * q^29 + 2 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 2 * q^34 + 2 * q^36 - 6 * q^37 - 6 * q^38 + 2 * q^40 - 8 * q^41 + 14 * q^43 + 4 * q^44 - 2 * q^45 - 6 * q^46 + 20 * q^47 + 2 * q^48 + 4 * q^50 - 2 * q^51 - 12 * q^53 - 2 * q^54 - 12 * q^55 + 6 * q^57 + 8 * q^58 + 10 * q^59 - 2 * q^60 + 8 * q^61 - 12 * q^62 + 2 * q^64 - 16 * q^65 - 4 * q^66 - 2 * q^67 - 2 * q^68 + 6 * q^69 + 2 * q^71 - 2 * q^72 + 16 * q^73 + 6 * q^74 - 4 * q^75 + 6 * q^76 + 12 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 8 * q^83 + 2 * q^85 - 14 * q^86 - 8 * q^87 - 4 * q^88 - 10 * q^89 + 2 * q^90 + 6 * q^92 + 12 * q^93 - 20 * q^94 - 6 * q^95 - 2 * q^96 - 8 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.41421	−1.07967	−0.539835	−	0.841771i	$-0.681513\pi$
$5$	−2.41421	−1.07967	−0.539835	+	0.841771i	$0.681513\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.41421	0.763441
$11$	4.82843	1.45583	0.727913	−	0.685670i	$-0.240491\pi$
$11$	4.82843	1.45583	0.727913	+	0.685670i	$0.240491\pi$
$12$	1.00000	0.288675
$13$	5.65685	1.56893	0.784465	−	0.620174i	$-0.212938\pi$
$13$	5.65685	1.56893	0.784465	+	0.620174i	$0.212938\pi$
$14$	0	0
$15$	−2.41421	−0.623347
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	−2.41421	−0.539835
$21$	0	0
$22$	−4.82843	−1.02942
$23$	1.58579	0.330659	0.165330	−	0.986238i	$-0.447131\pi$
$23$	1.58579	0.330659	0.165330	+	0.986238i	$0.447131\pi$
$24$	−1.00000	−0.204124
$25$	0.828427	0.165685
$26$	−5.65685	−1.10940
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.17157	−0.217556	−0.108778	−	0.994066i	$-0.534694\pi$
$29$	−1.17157	−0.217556	−0.108778	+	0.994066i	$0.534694\pi$
$30$	2.41421	0.440773
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	−1.00000	−0.176777
$33$	4.82843	0.840521
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.41421	−0.725692	−0.362846	−	0.931849i	$-0.618195\pi$
$37$	−4.41421	−0.725692	−0.362846	+	0.931849i	$0.618195\pi$
$38$	−3.00000	−0.486664
$39$	5.65685	0.905822
$40$	2.41421	0.381721
$41$	−9.65685	−1.50815	−0.754074	−	0.656790i	$-0.771914\pi$
$41$	−9.65685	−1.50815	−0.754074	+	0.656790i	$0.771914\pi$
$42$	0	0
$43$	4.17157	0.636159	0.318079	−	0.948064i	$-0.396962\pi$
$43$	4.17157	0.636159	0.318079	+	0.948064i	$0.396962\pi$
$44$	4.82843	0.727913
$45$	−2.41421	−0.359890
$46$	−1.58579	−0.233811
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−0.828427	−0.117157
$51$	−1.00000	−0.140028
$52$	5.65685	0.784465
$53$	−8.82843	−1.21268	−0.606339	−	0.795206i	$-0.707362\pi$
$53$	−8.82843	−1.21268	−0.606339	+	0.795206i	$0.707362\pi$
$54$	−1.00000	−0.136083
$55$	−11.6569	−1.57181
$56$	0	0
$57$	3.00000	0.397360
$58$	1.17157	0.153835
$59$	10.6569	1.38740	0.693702	−	0.720262i	$-0.255978\pi$
$59$	10.6569	1.38740	0.693702	+	0.720262i	$0.255978\pi$
$60$	−2.41421	−0.311674
$61$	12.4853	1.59858	0.799288	−	0.600948i	$-0.205210\pi$
$61$	12.4853	1.59858	0.799288	+	0.600948i	$0.205210\pi$
$62$	−6.00000	−0.762001
$63$	0	0
$64$	1.00000	0.125000
$65$	−13.6569	−1.69392
$66$	−4.82843	−0.594338
$67$	−6.65685	−0.813264	−0.406632	−	0.913592i	$-0.633297\pi$
$67$	−6.65685	−0.813264	−0.406632	+	0.913592i	$0.633297\pi$
$68$	−1.00000	−0.121268
$69$	1.58579	0.190906
$70$	0	0
$71$	−0.414214	−0.0491581	−0.0245791	−	0.999698i	$-0.507825\pi$
$71$	−0.414214	−0.0491581	−0.0245791	+	0.999698i	$0.507825\pi$
$72$	−1.00000	−0.117851
$73$	5.17157	0.605287	0.302643	−	0.953104i	$-0.402131\pi$
$73$	5.17157	0.605287	0.302643	+	0.953104i	$0.402131\pi$
$74$	4.41421	0.513142
$75$	0.828427	0.0956585
$76$	3.00000	0.344124
$77$	0	0
$78$	−5.65685	−0.640513
$79$	0.343146	0.0386069	0.0193035	−	0.999814i	$-0.493855\pi$
$79$	0.343146	0.0386069	0.0193035	+	0.999814i	$0.493855\pi$
$80$	−2.41421	−0.269917
$81$	1.00000	0.111111
$82$	9.65685	1.06642
$83$	9.65685	1.05998	0.529989	−	0.848005i	$-0.322196\pi$
$83$	9.65685	1.05998	0.529989	+	0.848005i	$0.322196\pi$
$84$	0	0
$85$	2.41421	0.261858
$86$	−4.17157	−0.449832
$87$	−1.17157	−0.125606
$88$	−4.82843	−0.514712
$89$	−16.3137	−1.72925	−0.864625	−	0.502418i	$-0.832444\pi$
$89$	−16.3137	−1.72925	−0.864625	+	0.502418i	$0.832444\pi$
$90$	2.41421	0.254480
$91$	0	0
$92$	1.58579	0.165330
$93$	6.00000	0.622171
$94$	−10.0000	−1.03142
$95$	−7.24264	−0.743079
$96$	−1.00000	−0.102062
$97$	1.65685	0.168228	0.0841140	−	0.996456i	$-0.473194\pi$
$97$	1.65685	0.168228	0.0841140	+	0.996456i	$0.473194\pi$
$98$	0	0
$99$	4.82843	0.485275
$100$	0.828427	0.0828427
$101$	−11.3137	−1.12576	−0.562878	−	0.826540i	$-0.690306\pi$
$101$	−11.3137	−1.12576	−0.562878	+	0.826540i	$0.690306\pi$
$102$	1.00000	0.0990148
$103$	−3.65685	−0.360321	−0.180160	−	0.983637i	$-0.557662\pi$
$103$	−3.65685	−0.360321	−0.180160	+	0.983637i	$0.557662\pi$
$104$	−5.65685	−0.554700
$105$	0	0
$106$	8.82843	0.857493
$107$	−10.1421	−0.980477	−0.490239	−	0.871588i	$-0.663090\pi$
$107$	−10.1421	−0.980477	−0.490239	+	0.871588i	$0.663090\pi$
$108$	1.00000	0.0962250
$109$	−14.5563	−1.39425	−0.697123	−	0.716952i	$-0.745537\pi$
$109$	−14.5563	−1.39425	−0.697123	+	0.716952i	$0.745537\pi$
$110$	11.6569	1.11144
$111$	−4.41421	−0.418979
$112$	0	0
$113$	6.48528	0.610084	0.305042	−	0.952339i	$-0.401330\pi$
$113$	6.48528	0.610084	0.305042	+	0.952339i	$0.401330\pi$
$114$	−3.00000	−0.280976
$115$	−3.82843	−0.357003
$116$	−1.17157	−0.108778
$117$	5.65685	0.522976
$118$	−10.6569	−0.981043
$119$	0	0
$120$	2.41421	0.220387
$121$	12.3137	1.11943
$122$	−12.4853	−1.13036
$123$	−9.65685	−0.870729
$124$	6.00000	0.538816
$125$	10.0711	0.900784
$126$	0	0
$127$	13.1716	1.16879	0.584394	−	0.811470i	$-0.301332\pi$
$127$	13.1716	1.16879	0.584394	+	0.811470i	$0.301332\pi$
$128$	−1.00000	−0.0883883
$129$	4.17157	0.367287
$130$	13.6569	1.19779
$131$	−3.65685	−0.319501	−0.159750	−	0.987157i	$-0.551069\pi$
$131$	−3.65685	−0.319501	−0.159750	+	0.987157i	$0.551069\pi$
$132$	4.82843	0.420261
$133$	0	0
$134$	6.65685	0.575065
$135$	−2.41421	−0.207782
$136$	1.00000	0.0857493
$137$	−10.1716	−0.869016	−0.434508	−	0.900668i	$-0.643078\pi$
$137$	−10.1716	−0.869016	−0.434508	+	0.900668i	$0.643078\pi$
$138$	−1.58579	−0.134991
$139$	−14.1421	−1.19952	−0.599760	−	0.800180i	$-0.704737\pi$
$139$	−14.1421	−1.19952	−0.599760	+	0.800180i	$0.704737\pi$
$140$	0	0
$141$	10.0000	0.842152
$142$	0.414214	0.0347600
$143$	27.3137	2.28409
$144$	1.00000	0.0833333
$145$	2.82843	0.234888
$146$	−5.17157	−0.428002
$147$	0	0
$148$	−4.41421	−0.362846
$149$	−20.8284	−1.70633	−0.853166	−	0.521640i	$-0.825320\pi$
$149$	−20.8284	−1.70633	−0.853166	+	0.521640i	$0.825320\pi$
$150$	−0.828427	−0.0676408
$151$	−2.82843	−0.230174	−0.115087	−	0.993355i	$-0.536715\pi$
$151$	−2.82843	−0.230174	−0.115087	+	0.993355i	$0.536715\pi$
$152$	−3.00000	−0.243332
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−14.4853	−1.16349
$156$	5.65685	0.452911
$157$	−10.9706	−0.875546	−0.437773	−	0.899085i	$-0.644233\pi$
$157$	−10.9706	−0.875546	−0.437773	+	0.899085i	$0.644233\pi$
$158$	−0.343146	−0.0272992
$159$	−8.82843	−0.700140
$160$	2.41421	0.190860
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	16.4853	1.29123	0.645613	−	0.763664i	$-0.276602\pi$
$163$	16.4853	1.29123	0.645613	+	0.763664i	$0.276602\pi$
$164$	−9.65685	−0.754074
$165$	−11.6569	−0.907485
$166$	−9.65685	−0.749517
$167$	8.89949	0.688664	0.344332	−	0.938848i	$-0.388105\pi$
$167$	8.89949	0.688664	0.344332	+	0.938848i	$0.388105\pi$
$168$	0	0
$169$	19.0000	1.46154
$170$	−2.41421	−0.185162
$171$	3.00000	0.229416
$172$	4.17157	0.318079
$173$	21.2426	1.61505	0.807524	−	0.589835i	$-0.200807\pi$
$173$	21.2426	1.61505	0.807524	+	0.589835i	$0.200807\pi$
$174$	1.17157	0.0888167
$175$	0	0
$176$	4.82843	0.363956
$177$	10.6569	0.801018
$178$	16.3137	1.22276
$179$	7.48528	0.559476	0.279738	−	0.960076i	$-0.409752\pi$
$179$	7.48528	0.559476	0.279738	+	0.960076i	$0.409752\pi$
$180$	−2.41421	−0.179945
$181$	18.5563	1.37928	0.689641	−	0.724151i	$-0.257768\pi$
$181$	18.5563	1.37928	0.689641	+	0.724151i	$0.257768\pi$
$182$	0	0
$183$	12.4853	0.922939
$184$	−1.58579	−0.116906
$185$	10.6569	0.783508
$186$	−6.00000	−0.439941
$187$	−4.82843	−0.353090
$188$	10.0000	0.729325
$189$	0	0
$190$	7.24264	0.525436
$191$	20.9706	1.51738	0.758688	−	0.651454i	$-0.225841\pi$
$191$	20.9706	1.51738	0.758688	+	0.651454i	$0.225841\pi$
$192$	1.00000	0.0721688
$193$	2.48528	0.178894	0.0894472	−	0.995992i	$-0.471490\pi$
$193$	2.48528	0.178894	0.0894472	+	0.995992i	$0.471490\pi$
$194$	−1.65685	−0.118955
$195$	−13.6569	−0.977988
$196$	0	0
$197$	4.75736	0.338948	0.169474	−	0.985535i	$-0.445793\pi$
$197$	4.75736	0.338948	0.169474	+	0.985535i	$0.445793\pi$
$198$	−4.82843	−0.343141
$199$	24.5563	1.74075	0.870377	−	0.492386i	$-0.163875\pi$
$199$	24.5563	1.74075	0.870377	+	0.492386i	$0.163875\pi$
$200$	−0.828427	−0.0585786
$201$	−6.65685	−0.469538
$202$	11.3137	0.796030
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	23.3137	1.62830
$206$	3.65685	0.254785
$207$	1.58579	0.110220
$208$	5.65685	0.392232
$209$	14.4853	1.00197
$210$	0	0
$211$	19.6569	1.35323	0.676617	−	0.736335i	$-0.263445\pi$
$211$	19.6569	1.35323	0.676617	+	0.736335i	$0.263445\pi$
$212$	−8.82843	−0.606339
$213$	−0.414214	−0.0283814
$214$	10.1421	0.693302
$215$	−10.0711	−0.686841
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	14.5563	0.985880
$219$	5.17157	0.349463
$220$	−11.6569	−0.785905
$221$	−5.65685	−0.380521
$222$	4.41421	0.296263
$223$	−18.1421	−1.21489	−0.607444	−	0.794363i	$-0.707805\pi$
$223$	−18.1421	−1.21489	−0.607444	+	0.794363i	$0.707805\pi$
$224$	0	0
$225$	0.828427	0.0552285
$226$	−6.48528	−0.431394
$227$	3.65685	0.242714	0.121357	−	0.992609i	$-0.461275\pi$
$227$	3.65685	0.242714	0.121357	+	0.992609i	$0.461275\pi$
$228$	3.00000	0.198680
$229$	3.51472	0.232259	0.116130	−	0.993234i	$-0.462951\pi$
$229$	3.51472	0.232259	0.116130	+	0.993234i	$0.462951\pi$
$230$	3.82843	0.252439
$231$	0	0
$232$	1.17157	0.0769175
$233$	−0.828427	−0.0542721	−0.0271360	−	0.999632i	$-0.508639\pi$
$233$	−0.828427	−0.0542721	−0.0271360	+	0.999632i	$0.508639\pi$
$234$	−5.65685	−0.369800
$235$	−24.1421	−1.57486
$236$	10.6569	0.693702
$237$	0.343146	0.0222897
$238$	0	0
$239$	−3.51472	−0.227348	−0.113674	−	0.993518i	$-0.536262\pi$
$239$	−3.51472	−0.227348	−0.113674	+	0.993518i	$0.536262\pi$
$240$	−2.41421	−0.155837
$241$	5.65685	0.364390	0.182195	−	0.983262i	$-0.441680\pi$
$241$	5.65685	0.364390	0.182195	+	0.983262i	$0.441680\pi$
$242$	−12.3137	−0.791555
$243$	1.00000	0.0641500
$244$	12.4853	0.799288
$245$	0	0
$246$	9.65685	0.615699
$247$	16.9706	1.07981
$248$	−6.00000	−0.381000
$249$	9.65685	0.611978
$250$	−10.0711	−0.636950
$251$	−31.3137	−1.97650	−0.988252	−	0.152834i	$-0.951160\pi$
$251$	−31.3137	−1.97650	−0.988252	+	0.152834i	$0.951160\pi$
$252$	0	0
$253$	7.65685	0.481382
$254$	−13.1716	−0.826458
$255$	2.41421	0.151184
$256$	1.00000	0.0625000
$257$	17.1421	1.06930	0.534649	−	0.845075i	$-0.320444\pi$
$257$	17.1421	1.06930	0.534649	+	0.845075i	$0.320444\pi$
$258$	−4.17157	−0.259711
$259$	0	0
$260$	−13.6569	−0.846962
$261$	−1.17157	−0.0725185
$262$	3.65685	0.225921
$263$	31.4558	1.93965	0.969825	−	0.243801i	$-0.0783945\pi$
$263$	31.4558	1.93965	0.969825	+	0.243801i	$0.0783945\pi$
$264$	−4.82843	−0.297169
$265$	21.3137	1.30929
$266$	0	0
$267$	−16.3137	−0.998383
$268$	−6.65685	−0.406632
$269$	−7.72792	−0.471180	−0.235590	−	0.971853i	$-0.575702\pi$
$269$	−7.72792	−0.471180	−0.235590	+	0.971853i	$0.575702\pi$
$270$	2.41421	0.146924
$271$	32.6274	1.98197	0.990987	−	0.133956i	$-0.0427682\pi$
$271$	32.6274	1.98197	0.990987	+	0.133956i	$0.0427682\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	10.1716	0.614487
$275$	4.00000	0.241209
$276$	1.58579	0.0954531
$277$	26.1421	1.57073	0.785364	−	0.619034i	$-0.212476\pi$
$277$	26.1421	1.57073	0.785364	+	0.619034i	$0.212476\pi$
$278$	14.1421	0.848189
$279$	6.00000	0.359211
$280$	0	0
$281$	1.34315	0.0801254	0.0400627	−	0.999197i	$-0.487244\pi$
$281$	1.34315	0.0801254	0.0400627	+	0.999197i	$0.487244\pi$
$282$	−10.0000	−0.595491
$283$	16.4853	0.979948	0.489974	−	0.871737i	$-0.337006\pi$
$283$	16.4853	0.979948	0.489974	+	0.871737i	$0.337006\pi$
$284$	−0.414214	−0.0245791
$285$	−7.24264	−0.429017
$286$	−27.3137	−1.61509
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−2.82843	−0.166091
$291$	1.65685	0.0971265
$292$	5.17157	0.302643
$293$	11.5147	0.672697	0.336349	−	0.941738i	$-0.390808\pi$
$293$	11.5147	0.672697	0.336349	+	0.941738i	$0.390808\pi$
$294$	0	0
$295$	−25.7279	−1.49794
$296$	4.41421	0.256571
$297$	4.82843	0.280174
$298$	20.8284	1.20656
$299$	8.97056	0.518781
$300$	0.828427	0.0478293
$301$	0	0
$302$	2.82843	0.162758
$303$	−11.3137	−0.649956
$304$	3.00000	0.172062
$305$	−30.1421	−1.72593
$306$	1.00000	0.0571662
$307$	10.5147	0.600107	0.300053	−	0.953922i	$-0.402996\pi$
$307$	10.5147	0.600107	0.300053	+	0.953922i	$0.402996\pi$
$308$	0	0
$309$	−3.65685	−0.208031
$310$	14.4853	0.822709
$311$	−12.7574	−0.723403	−0.361702	−	0.932294i	$-0.617804\pi$
$311$	−12.7574	−0.723403	−0.361702	+	0.932294i	$0.617804\pi$
$312$	−5.65685	−0.320256
$313$	−9.79899	−0.553872	−0.276936	−	0.960888i	$-0.589319\pi$
$313$	−9.79899	−0.553872	−0.276936	+	0.960888i	$0.589319\pi$
$314$	10.9706	0.619105
$315$	0	0
$316$	0.343146	0.0193035
$317$	−18.8995	−1.06150	−0.530751	−	0.847528i	$-0.678090\pi$
$317$	−18.8995	−1.06150	−0.530751	+	0.847528i	$0.678090\pi$
$318$	8.82843	0.495074
$319$	−5.65685	−0.316723
$320$	−2.41421	−0.134959
$321$	−10.1421	−0.566079
$322$	0	0
$323$	−3.00000	−0.166924
$324$	1.00000	0.0555556
$325$	4.68629	0.259949
$326$	−16.4853	−0.913035
$327$	−14.5563	−0.804968
$328$	9.65685	0.533211
$329$	0	0
$330$	11.6569	0.641689
$331$	11.8284	0.650149	0.325075	−	0.945688i	$-0.394611\pi$
$331$	11.8284	0.650149	0.325075	+	0.945688i	$0.394611\pi$
$332$	9.65685	0.529989
$333$	−4.41421	−0.241897
$334$	−8.89949	−0.486959
$335$	16.0711	0.878056
$336$	0	0
$337$	−10.1421	−0.552477	−0.276239	−	0.961089i	$-0.589088\pi$
$337$	−10.1421	−0.552477	−0.276239	+	0.961089i	$0.589088\pi$
$338$	−19.0000	−1.03346
$339$	6.48528	0.352232
$340$	2.41421	0.130929
$341$	28.9706	1.56884
$342$	−3.00000	−0.162221
$343$	0	0
$344$	−4.17157	−0.224916
$345$	−3.82843	−0.206116
$346$	−21.2426	−1.14201
$347$	−16.0000	−0.858925	−0.429463	−	0.903085i	$-0.641297\pi$
$347$	−16.0000	−0.858925	−0.429463	+	0.903085i	$0.641297\pi$
$348$	−1.17157	−0.0628029
$349$	−27.7990	−1.48805	−0.744023	−	0.668154i	$-0.767085\pi$
$349$	−27.7990	−1.48805	−0.744023	+	0.668154i	$0.767085\pi$
$350$	0	0
$351$	5.65685	0.301941
$352$	−4.82843	−0.257356
$353$	4.31371	0.229596	0.114798	−	0.993389i	$-0.463378\pi$
$353$	4.31371	0.229596	0.114798	+	0.993389i	$0.463378\pi$
$354$	−10.6569	−0.566405
$355$	1.00000	0.0530745
$356$	−16.3137	−0.864625
$357$	0	0
$358$	−7.48528	−0.395609
$359$	−20.6274	−1.08867	−0.544337	−	0.838867i	$-0.683219\pi$
$359$	−20.6274	−1.08867	−0.544337	+	0.838867i	$0.683219\pi$
$360$	2.41421	0.127240
$361$	−10.0000	−0.526316
$362$	−18.5563	−0.975300
$363$	12.3137	0.646302
$364$	0	0
$365$	−12.4853	−0.653509
$366$	−12.4853	−0.652616
$367$	9.58579	0.500374	0.250187	−	0.968198i	$-0.419508\pi$
$367$	9.58579	0.500374	0.250187	+	0.968198i	$0.419508\pi$
$368$	1.58579	0.0826648
$369$	−9.65685	−0.502716
$370$	−10.6569	−0.554023
$371$	0	0
$372$	6.00000	0.311086
$373$	−20.1421	−1.04292	−0.521460	−	0.853276i	$-0.674612\pi$
$373$	−20.1421	−1.04292	−0.521460	+	0.853276i	$0.674612\pi$
$374$	4.82843	0.249672
$375$	10.0711	0.520068
$376$	−10.0000	−0.515711
$377$	−6.62742	−0.341329
$378$	0	0
$379$	10.6274	0.545894	0.272947	−	0.962029i	$-0.412002\pi$
$379$	10.6274	0.545894	0.272947	+	0.962029i	$0.412002\pi$
$380$	−7.24264	−0.371540
$381$	13.1716	0.674800
$382$	−20.9706	−1.07295
$383$	20.3431	1.03949	0.519743	−	0.854323i	$-0.326028\pi$
$383$	20.3431	1.03949	0.519743	+	0.854323i	$0.326028\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−2.48528	−0.126497
$387$	4.17157	0.212053
$388$	1.65685	0.0841140
$389$	−9.17157	−0.465017	−0.232509	−	0.972594i	$-0.574693\pi$
$389$	−9.17157	−0.465017	−0.232509	+	0.972594i	$0.574693\pi$
$390$	13.6569	0.691542
$391$	−1.58579	−0.0801967
$392$	0	0
$393$	−3.65685	−0.184464
$394$	−4.75736	−0.239672
$395$	−0.828427	−0.0416827
$396$	4.82843	0.242638
$397$	29.8701	1.49914	0.749568	−	0.661928i	$-0.230261\pi$
$397$	29.8701	1.49914	0.749568	+	0.661928i	$0.230261\pi$
$398$	−24.5563	−1.23090
$399$	0	0
$400$	0.828427	0.0414214
$401$	11.4558	0.572078	0.286039	−	0.958218i	$-0.407661\pi$
$401$	11.4558	0.572078	0.286039	+	0.958218i	$0.407661\pi$
$402$	6.65685	0.332014
$403$	33.9411	1.69073
$404$	−11.3137	−0.562878
$405$	−2.41421	−0.119963
$406$	0	0
$407$	−21.3137	−1.05648
$408$	1.00000	0.0495074
$409$	17.3137	0.856108	0.428054	−	0.903753i	$-0.359199\pi$
$409$	17.3137	0.856108	0.428054	+	0.903753i	$0.359199\pi$
$410$	−23.3137	−1.15138
$411$	−10.1716	−0.501727
$412$	−3.65685	−0.180160
$413$	0	0
$414$	−1.58579	−0.0779372
$415$	−23.3137	−1.14442
$416$	−5.65685	−0.277350
$417$	−14.1421	−0.692543
$418$	−14.4853	−0.708498
$419$	24.4853	1.19618	0.598092	−	0.801427i	$-0.295926\pi$
$419$	24.4853	1.19618	0.598092	+	0.801427i	$0.295926\pi$
$420$	0	0
$421$	−16.0000	−0.779792	−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000	−0.779792	−0.389896	+	0.920859i	$0.627489\pi$
$422$	−19.6569	−0.956881
$423$	10.0000	0.486217
$424$	8.82843	0.428746
$425$	−0.828427	−0.0401846
$426$	0.414214	0.0200687
$427$	0	0
$428$	−10.1421	−0.490239
$429$	27.3137	1.31872
$430$	10.0711	0.485670
$431$	7.24264	0.348866	0.174433	−	0.984669i	$-0.444191\pi$
$431$	7.24264	0.348866	0.174433	+	0.984669i	$0.444191\pi$
$432$	1.00000	0.0481125
$433$	−12.5147	−0.601419	−0.300709	−	0.953716i	$-0.597223\pi$
$433$	−12.5147	−0.601419	−0.300709	+	0.953716i	$0.597223\pi$
$434$	0	0
$435$	2.82843	0.135613
$436$	−14.5563	−0.697123
$437$	4.75736	0.227575
$438$	−5.17157	−0.247107
$439$	−0.899495	−0.0429306	−0.0214653	−	0.999770i	$-0.506833\pi$
$439$	−0.899495	−0.0429306	−0.0214653	+	0.999770i	$0.506833\pi$
$440$	11.6569	0.555719
$441$	0	0
$442$	5.65685	0.269069
$443$	11.1421	0.529379	0.264689	−	0.964334i	$-0.414731\pi$
$443$	11.1421	0.529379	0.264689	+	0.964334i	$0.414731\pi$
$444$	−4.41421	−0.209489
$445$	39.3848	1.86702
$446$	18.1421	0.859055
$447$	−20.8284	−0.985151
$448$	0	0
$449$	−13.8579	−0.653993	−0.326997	−	0.945026i	$-0.606037\pi$
$449$	−13.8579	−0.653993	−0.326997	+	0.945026i	$0.606037\pi$
$450$	−0.828427	−0.0390524
$451$	−46.6274	−2.19560
$452$	6.48528	0.305042
$453$	−2.82843	−0.132891
$454$	−3.65685	−0.171625
$455$	0	0
$456$	−3.00000	−0.140488
$457$	−38.4558	−1.79889	−0.899444	−	0.437036i	$-0.856028\pi$
$457$	−38.4558	−1.79889	−0.899444	+	0.437036i	$0.856028\pi$
$458$	−3.51472	−0.164232
$459$	−1.00000	−0.0466760
$460$	−3.82843	−0.178501
$461$	−4.62742	−0.215520	−0.107760	−	0.994177i	$-0.534368\pi$
$461$	−4.62742	−0.215520	−0.107760	+	0.994177i	$0.534368\pi$
$462$	0	0
$463$	19.3137	0.897584	0.448792	−	0.893636i	$-0.351854\pi$
$463$	19.3137	0.897584	0.448792	+	0.893636i	$0.351854\pi$
$464$	−1.17157	−0.0543889
$465$	−14.4853	−0.671739
$466$	0.828427	0.0383761
$467$	−3.48528	−0.161280	−0.0806398	−	0.996743i	$-0.525696\pi$
$467$	−3.48528	−0.161280	−0.0806398	+	0.996743i	$0.525696\pi$
$468$	5.65685	0.261488
$469$	0	0
$470$	24.1421	1.11359
$471$	−10.9706	−0.505497
$472$	−10.6569	−0.490521
$473$	20.1421	0.926136
$474$	−0.343146	−0.0157612
$475$	2.48528	0.114033
$476$	0	0
$477$	−8.82843	−0.404226
$478$	3.51472	0.160759
$479$	14.2132	0.649418	0.324709	−	0.945814i	$-0.394734\pi$
$479$	14.2132	0.649418	0.324709	+	0.945814i	$0.394734\pi$
$480$	2.41421	0.110193
$481$	−24.9706	−1.13856
$482$	−5.65685	−0.257663
$483$	0	0
$484$	12.3137	0.559714
$485$	−4.00000	−0.181631
$486$	−1.00000	−0.0453609
$487$	2.27208	0.102958	0.0514788	−	0.998674i	$-0.483607\pi$
$487$	2.27208	0.102958	0.0514788	+	0.998674i	$0.483607\pi$
$488$	−12.4853	−0.565182
$489$	16.4853	0.745490
$490$	0	0
$491$	−0.798990	−0.0360579	−0.0180290	−	0.999837i	$-0.505739\pi$
$491$	−0.798990	−0.0360579	−0.0180290	+	0.999837i	$0.505739\pi$
$492$	−9.65685	−0.435365
$493$	1.17157	0.0527650
$494$	−16.9706	−0.763542
$495$	−11.6569	−0.523937
$496$	6.00000	0.269408
$497$	0	0
$498$	−9.65685	−0.432734
$499$	34.6274	1.55014	0.775068	−	0.631878i	$-0.217716\pi$
$499$	34.6274	1.55014	0.775068	+	0.631878i	$0.217716\pi$
$500$	10.0711	0.450392
$501$	8.89949	0.397600
$502$	31.3137	1.39760
$503$	15.2426	0.679636	0.339818	−	0.940491i	$-0.389635\pi$
$503$	15.2426	0.679636	0.339818	+	0.940491i	$0.389635\pi$
$504$	0	0
$505$	27.3137	1.21544
$506$	−7.65685	−0.340389
$507$	19.0000	0.843820
$508$	13.1716	0.584394
$509$	34.2843	1.51962	0.759812	−	0.650143i	$-0.225291\pi$
$509$	34.2843	1.51962	0.759812	+	0.650143i	$0.225291\pi$
$510$	−2.41421	−0.106903
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	3.00000	0.132453
$514$	−17.1421	−0.756107
$515$	8.82843	0.389027
$516$	4.17157	0.183643
$517$	48.2843	2.12354
$518$	0	0
$519$	21.2426	0.932448
$520$	13.6569	0.598893
$521$	−23.7990	−1.04265	−0.521326	−	0.853357i	$-0.674563\pi$
$521$	−23.7990	−1.04265	−0.521326	+	0.853357i	$0.674563\pi$
$522$	1.17157	0.0512784
$523$	−6.62742	−0.289797	−0.144898	−	0.989447i	$-0.546286\pi$
$523$	−6.62742	−0.289797	−0.144898	+	0.989447i	$0.546286\pi$
$524$	−3.65685	−0.159750
$525$	0	0
$526$	−31.4558	−1.37154
$527$	−6.00000	−0.261364
$528$	4.82843	0.210130
$529$	−20.4853	−0.890664
$530$	−21.3137	−0.925808
$531$	10.6569	0.462468
$532$	0	0
$533$	−54.6274	−2.36618
$534$	16.3137	0.705963
$535$	24.4853	1.05859
$536$	6.65685	0.287532
$537$	7.48528	0.323014
$538$	7.72792	0.333174
$539$	0	0
$540$	−2.41421	−0.103891
$541$	−39.7990	−1.71109	−0.855546	−	0.517727i	$-0.826778\pi$
$541$	−39.7990	−1.71109	−0.855546	+	0.517727i	$0.826778\pi$
$542$	−32.6274	−1.40147
$543$	18.5563	0.796329
$544$	1.00000	0.0428746
$545$	35.1421	1.50532
$546$	0	0
$547$	−33.3137	−1.42439	−0.712196	−	0.701981i	$-0.752299\pi$
$547$	−33.3137	−1.42439	−0.712196	+	0.701981i	$0.752299\pi$
$548$	−10.1716	−0.434508
$549$	12.4853	0.532859
$550$	−4.00000	−0.170561
$551$	−3.51472	−0.149732
$552$	−1.58579	−0.0674956
$553$	0	0
$554$	−26.1421	−1.11067
$555$	10.6569	0.452358
$556$	−14.1421	−0.599760
$557$	−16.0000	−0.677942	−0.338971	−	0.940797i	$-0.610079\pi$
$557$	−16.0000	−0.677942	−0.338971	+	0.940797i	$0.610079\pi$
$558$	−6.00000	−0.254000
$559$	23.5980	0.998088
$560$	0	0
$561$	−4.82843	−0.203856
$562$	−1.34315	−0.0566572
$563$	−17.9706	−0.757369	−0.378684	−	0.925526i	$-0.623623\pi$
$563$	−17.9706	−0.757369	−0.378684	+	0.925526i	$0.623623\pi$
$564$	10.0000	0.421076
$565$	−15.6569	−0.658689
$566$	−16.4853	−0.692928
$567$	0	0
$568$	0.414214	0.0173800
$569$	37.1421	1.55708	0.778540	−	0.627595i	$-0.215961\pi$
$569$	37.1421	1.55708	0.778540	+	0.627595i	$0.215961\pi$
$570$	7.24264	0.303361
$571$	−9.31371	−0.389767	−0.194883	−	0.980826i	$-0.562433\pi$
$571$	−9.31371	−0.389767	−0.194883	+	0.980826i	$0.562433\pi$
$572$	27.3137	1.14204
$573$	20.9706	0.876058
$574$	0	0
$575$	1.31371	0.0547854
$576$	1.00000	0.0416667
$577$	21.3137	0.887301	0.443651	−	0.896200i	$-0.353683\pi$
$577$	21.3137	0.887301	0.443651	+	0.896200i	$0.353683\pi$
$578$	−1.00000	−0.0415945
$579$	2.48528	0.103285
$580$	2.82843	0.117444
$581$	0	0
$582$	−1.65685	−0.0686788
$583$	−42.6274	−1.76545
$584$	−5.17157	−0.214001
$585$	−13.6569	−0.564641
$586$	−11.5147	−0.475669
$587$	8.17157	0.337277	0.168638	−	0.985678i	$-0.446063\pi$
$587$	8.17157	0.337277	0.168638	+	0.985678i	$0.446063\pi$
$588$	0	0
$589$	18.0000	0.741677
$590$	25.7279	1.05920
$591$	4.75736	0.195692
$592$	−4.41421	−0.181423
$593$	18.6863	0.767354	0.383677	−	0.923467i	$-0.374658\pi$
$593$	18.6863	0.767354	0.383677	+	0.923467i	$0.374658\pi$
$594$	−4.82843	−0.198113
$595$	0	0
$596$	−20.8284	−0.853166
$597$	24.5563	1.00502
$598$	−8.97056	−0.366834
$599$	−10.9706	−0.448245	−0.224123	−	0.974561i	$-0.571952\pi$
$599$	−10.9706	−0.448245	−0.224123	+	0.974561i	$0.571952\pi$
$600$	−0.828427	−0.0338204
$601$	−24.1421	−0.984778	−0.492389	−	0.870375i	$-0.663876\pi$
$601$	−24.1421	−0.984778	−0.492389	+	0.870375i	$0.663876\pi$
$602$	0	0
$603$	−6.65685	−0.271088
$604$	−2.82843	−0.115087
$605$	−29.7279	−1.20861
$606$	11.3137	0.459588
$607$	36.2132	1.46985	0.734924	−	0.678149i	$-0.237218\pi$
$607$	36.2132	1.46985	0.734924	+	0.678149i	$0.237218\pi$
$608$	−3.00000	−0.121666
$609$	0	0
$610$	30.1421	1.22042
$611$	56.5685	2.28852
$612$	−1.00000	−0.0404226
$613$	−36.6274	−1.47937	−0.739684	−	0.672955i	$-0.765025\pi$
$613$	−36.6274	−1.47937	−0.739684	+	0.672955i	$0.765025\pi$
$614$	−10.5147	−0.424340
$615$	23.3137	0.940099
$616$	0	0
$617$	−32.3431	−1.30209	−0.651043	−	0.759041i	$-0.725668\pi$
$617$	−32.3431	−1.30209	−0.651043	+	0.759041i	$0.725668\pi$
$618$	3.65685	0.147100
$619$	−9.31371	−0.374350	−0.187175	−	0.982327i	$-0.559933\pi$
$619$	−9.31371	−0.374350	−0.187175	+	0.982327i	$0.559933\pi$
$620$	−14.4853	−0.581743
$621$	1.58579	0.0636354
$622$	12.7574	0.511524
$623$	0	0
$624$	5.65685	0.226455
$625$	−28.4558	−1.13823
$626$	9.79899	0.391646
$627$	14.4853	0.578486
$628$	−10.9706	−0.437773
$629$	4.41421	0.176006
$630$	0	0
$631$	46.2843	1.84255	0.921274	−	0.388914i	$-0.127150\pi$
$631$	46.2843	1.84255	0.921274	+	0.388914i	$0.127150\pi$
$632$	−0.343146	−0.0136496
$633$	19.6569	0.781290
$634$	18.8995	0.750595
$635$	−31.7990	−1.26190
$636$	−8.82843	−0.350070
$637$	0	0
$638$	5.65685	0.223957
$639$	−0.414214	−0.0163860
$640$	2.41421	0.0954302
$641$	−32.6274	−1.28871	−0.644353	−	0.764728i	$-0.722873\pi$
$641$	−32.6274	−1.28871	−0.644353	+	0.764728i	$0.722873\pi$
$642$	10.1421	0.400278
$643$	1.37258	0.0541294	0.0270647	−	0.999634i	$-0.491384\pi$
$643$	1.37258	0.0541294	0.0270647	+	0.999634i	$0.491384\pi$
$644$	0	0
$645$	−10.0711	−0.396548
$646$	3.00000	0.118033
$647$	−21.3137	−0.837928	−0.418964	−	0.908003i	$-0.637607\pi$
$647$	−21.3137	−0.837928	−0.418964	+	0.908003i	$0.637607\pi$
$648$	−1.00000	−0.0392837
$649$	51.4558	2.01982
$650$	−4.68629	−0.183811
$651$	0	0
$652$	16.4853	0.645613
$653$	25.2426	0.987821	0.493910	−	0.869513i	$-0.335567\pi$
$653$	25.2426	0.987821	0.493910	+	0.869513i	$0.335567\pi$
$654$	14.5563	0.569198
$655$	8.82843	0.344955
$656$	−9.65685	−0.377037
$657$	5.17157	0.201762
$658$	0	0
$659$	−2.37258	−0.0924227	−0.0462114	−	0.998932i	$-0.514715\pi$
$659$	−2.37258	−0.0924227	−0.0462114	+	0.998932i	$0.514715\pi$
$660$	−11.6569	−0.453742
$661$	39.1716	1.52360	0.761799	−	0.647814i	$-0.224316\pi$
$661$	39.1716	1.52360	0.761799	+	0.647814i	$0.224316\pi$
$662$	−11.8284	−0.459725
$663$	−5.65685	−0.219694
$664$	−9.65685	−0.374759
$665$	0	0
$666$	4.41421	0.171047
$667$	−1.85786	−0.0719368
$668$	8.89949	0.344332
$669$	−18.1421	−0.701415
$670$	−16.0711	−0.620880
$671$	60.2843	2.32725
$672$	0	0
$673$	16.0000	0.616755	0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000	0.616755	0.308377	+	0.951264i	$0.400214\pi$
$674$	10.1421	0.390660
$675$	0.828427	0.0318862
$676$	19.0000	0.730769
$677$	40.4853	1.55598	0.777988	−	0.628279i	$-0.216240\pi$
$677$	40.4853	1.55598	0.777988	+	0.628279i	$0.216240\pi$
$678$	−6.48528	−0.249066
$679$	0	0
$680$	−2.41421	−0.0925809
$681$	3.65685	0.140131
$682$	−28.9706	−1.10934
$683$	4.20101	0.160747	0.0803736	−	0.996765i	$-0.474389\pi$
$683$	4.20101	0.160747	0.0803736	+	0.996765i	$0.474389\pi$
$684$	3.00000	0.114708
$685$	24.5563	0.938250
$686$	0	0
$687$	3.51472	0.134095
$688$	4.17157	0.159040
$689$	−49.9411	−1.90261
$690$	3.82843	0.145746
$691$	−23.3137	−0.886895	−0.443448	−	0.896300i	$-0.646245\pi$
$691$	−23.3137	−0.886895	−0.443448	+	0.896300i	$0.646245\pi$
$692$	21.2426	0.807524
$693$	0	0
$694$	16.0000	0.607352
$695$	34.1421	1.29509
$696$	1.17157	0.0444084
$697$	9.65685	0.365779
$698$	27.7990	1.05221
$699$	−0.828427	−0.0313340
$700$	0	0
$701$	−20.2843	−0.766126	−0.383063	−	0.923722i	$-0.625131\pi$
$701$	−20.2843	−0.766126	−0.383063	+	0.923722i	$0.625131\pi$
$702$	−5.65685	−0.213504
$703$	−13.2426	−0.499456
$704$	4.82843	0.181978
$705$	−24.1421	−0.909245
$706$	−4.31371	−0.162349
$707$	0	0
$708$	10.6569	0.400509
$709$	−29.8701	−1.12179	−0.560897	−	0.827886i	$-0.689544\pi$
$709$	−29.8701	−1.12179	−0.560897	+	0.827886i	$0.689544\pi$
$710$	−1.00000	−0.0375293
$711$	0.343146	0.0128690
$712$	16.3137	0.611382
$713$	9.51472	0.356329
$714$	0	0
$715$	−65.9411	−2.46606
$716$	7.48528	0.279738
$717$	−3.51472	−0.131260
$718$	20.6274	0.769808
$719$	−46.9706	−1.75171	−0.875853	−	0.482578i	$-0.839701\pi$
$719$	−46.9706	−1.75171	−0.875853	+	0.482578i	$0.839701\pi$
$720$	−2.41421	−0.0899724
$721$	0	0
$722$	10.0000	0.372161
$723$	5.65685	0.210381
$724$	18.5563	0.689641
$725$	−0.970563	−0.0360458
$726$	−12.3137	−0.457005
$727$	−46.1421	−1.71132	−0.855659	−	0.517541i	$-0.826848\pi$
$727$	−46.1421	−1.71132	−0.855659	+	0.517541i	$0.826848\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.4853	0.462101
$731$	−4.17157	−0.154291
$732$	12.4853	0.461469
$733$	−50.1421	−1.85204	−0.926021	−	0.377472i	$-0.876793\pi$
$733$	−50.1421	−1.85204	−0.926021	+	0.377472i	$0.876793\pi$
$734$	−9.58579	−0.353818
$735$	0	0
$736$	−1.58579	−0.0584529
$737$	−32.1421	−1.18397
$738$	9.65685	0.355474
$739$	21.3431	0.785120	0.392560	−	0.919726i	$-0.371589\pi$
$739$	21.3431	0.785120	0.392560	+	0.919726i	$0.371589\pi$
$740$	10.6569	0.391754
$741$	16.9706	0.623429
$742$	0	0
$743$	−9.02944	−0.331258	−0.165629	−	0.986188i	$-0.552965\pi$
$743$	−9.02944	−0.331258	−0.165629	+	0.986188i	$0.552965\pi$
$744$	−6.00000	−0.219971
$745$	50.2843	1.84227
$746$	20.1421	0.737456
$747$	9.65685	0.353326
$748$	−4.82843	−0.176545
$749$	0	0
$750$	−10.0711	−0.367743
$751$	42.8995	1.56542	0.782712	−	0.622384i	$-0.213836\pi$
$751$	42.8995	1.56542	0.782712	+	0.622384i	$0.213836\pi$
$752$	10.0000	0.364662
$753$	−31.3137	−1.14113
$754$	6.62742	0.241356
$755$	6.82843	0.248512
$756$	0	0
$757$	37.4558	1.36136	0.680678	−	0.732583i	$-0.261685\pi$
$757$	37.4558	1.36136	0.680678	+	0.732583i	$0.261685\pi$
$758$	−10.6274	−0.386005
$759$	7.65685	0.277926
$760$	7.24264	0.262718
$761$	−24.5147	−0.888658	−0.444329	−	0.895864i	$-0.646558\pi$
$761$	−24.5147	−0.888658	−0.444329	+	0.895864i	$0.646558\pi$
$762$	−13.1716	−0.477156
$763$	0	0
$764$	20.9706	0.758688
$765$	2.41421	0.0872861
$766$	−20.3431	−0.735028
$767$	60.2843	2.17674
$768$	1.00000	0.0360844
$769$	−24.3137	−0.876775	−0.438387	−	0.898786i	$-0.644450\pi$
$769$	−24.3137	−0.876775	−0.438387	+	0.898786i	$0.644450\pi$
$770$	0	0
$771$	17.1421	0.617359
$772$	2.48528	0.0894472
$773$	42.9706	1.54554	0.772772	−	0.634684i	$-0.218870\pi$
$773$	42.9706	1.54554	0.772772	+	0.634684i	$0.218870\pi$
$774$	−4.17157	−0.149944
$775$	4.97056	0.178548
$776$	−1.65685	−0.0594776
$777$	0	0
$778$	9.17157	0.328817
$779$	−28.9706	−1.03798
$780$	−13.6569	−0.488994
$781$	−2.00000	−0.0715656
$782$	1.58579	0.0567076
$783$	−1.17157	−0.0418686
$784$	0	0
$785$	26.4853	0.945300
$786$	3.65685	0.130436
$787$	−37.1127	−1.32292	−0.661462	−	0.749978i	$-0.730064\pi$
$787$	−37.1127	−1.32292	−0.661462	+	0.749978i	$0.730064\pi$
$788$	4.75736	0.169474
$789$	31.4558	1.11986
$790$	0.828427	0.0294741
$791$	0	0
$792$	−4.82843	−0.171571
$793$	70.6274	2.50805
$794$	−29.8701	−1.06005
$795$	21.3137	0.755919
$796$	24.5563	0.870377
$797$	−44.7696	−1.58582	−0.792909	−	0.609339i	$-0.791435\pi$
$797$	−44.7696	−1.58582	−0.792909	+	0.609339i	$0.791435\pi$
$798$	0	0
$799$	−10.0000	−0.353775
$800$	−0.828427	−0.0292893
$801$	−16.3137	−0.576417
$802$	−11.4558	−0.404520
$803$	24.9706	0.881192
$804$	−6.65685	−0.234769
$805$	0	0
$806$	−33.9411	−1.19553
$807$	−7.72792	−0.272036
$808$	11.3137	0.398015
$809$	−21.7990	−0.766412	−0.383206	−	0.923663i	$-0.625180\pi$
$809$	−21.7990	−0.766412	−0.383206	+	0.923663i	$0.625180\pi$
$810$	2.41421	0.0848268
$811$	−39.9411	−1.40252	−0.701261	−	0.712904i	$-0.747379\pi$
$811$	−39.9411	−1.40252	−0.701261	+	0.712904i	$0.747379\pi$
$812$	0	0
$813$	32.6274	1.14429
$814$	21.3137	0.747045
$815$	−39.7990	−1.39410
$816$	−1.00000	−0.0350070
$817$	12.5147	0.437835
$818$	−17.3137	−0.605360
$819$	0	0
$820$	23.3137	0.814150
$821$	10.4142	0.363459	0.181729	−	0.983349i	$-0.441831\pi$
$821$	10.4142	0.363459	0.181729	+	0.983349i	$0.441831\pi$
$822$	10.1716	0.354774
$823$	−12.6274	−0.440164	−0.220082	−	0.975481i	$-0.570633\pi$
$823$	−12.6274	−0.440164	−0.220082	+	0.975481i	$0.570633\pi$
$824$	3.65685	0.127393
$825$	4.00000	0.139262
$826$	0	0
$827$	24.1421	0.839504	0.419752	−	0.907639i	$-0.362117\pi$
$827$	24.1421	0.839504	0.419752	+	0.907639i	$0.362117\pi$
$828$	1.58579	0.0551099
$829$	8.62742	0.299643	0.149821	−	0.988713i	$-0.452130\pi$
$829$	8.62742	0.299643	0.149821	+	0.988713i	$0.452130\pi$
$830$	23.3137	0.809231
$831$	26.1421	0.906861
$832$	5.65685	0.196116
$833$	0	0
$834$	14.1421	0.489702
$835$	−21.4853	−0.743529
$836$	14.4853	0.500984
$837$	6.00000	0.207390
$838$	−24.4853	−0.845830
$839$	32.7574	1.13091	0.565455	−	0.824779i	$-0.308701\pi$
$839$	32.7574	1.13091	0.565455	+	0.824779i	$0.308701\pi$
$840$	0	0
$841$	−27.6274	−0.952670
$842$	16.0000	0.551396
$843$	1.34315	0.0462604
$844$	19.6569	0.676617
$845$	−45.8701	−1.57798
$846$	−10.0000	−0.343807
$847$	0	0
$848$	−8.82843	−0.303169
$849$	16.4853	0.565773
$850$	0.828427	0.0284148
$851$	−7.00000	−0.239957
$852$	−0.414214	−0.0141907
$853$	7.79899	0.267032	0.133516	−	0.991047i	$-0.457373\pi$
$853$	7.79899	0.267032	0.133516	+	0.991047i	$0.457373\pi$
$854$	0	0
$855$	−7.24264	−0.247693
$856$	10.1421	0.346651
$857$	26.7696	0.914430	0.457215	−	0.889356i	$-0.348847\pi$
$857$	26.7696	0.914430	0.457215	+	0.889356i	$0.348847\pi$
$858$	−27.3137	−0.932475
$859$	−6.51472	−0.222279	−0.111140	−	0.993805i	$-0.535450\pi$
$859$	−6.51472	−0.222279	−0.111140	+	0.993805i	$0.535450\pi$
$860$	−10.0711	−0.343421
$861$	0	0
$862$	−7.24264	−0.246685
$863$	−19.1127	−0.650604	−0.325302	−	0.945610i	$-0.605466\pi$
$863$	−19.1127	−0.650604	−0.325302	+	0.945610i	$0.605466\pi$
$864$	−1.00000	−0.0340207
$865$	−51.2843	−1.74372
$866$	12.5147	0.425267
$867$	1.00000	0.0339618
$868$	0	0
$869$	1.65685	0.0562049
$870$	−2.82843	−0.0958927
$871$	−37.6569	−1.27595
$872$	14.5563	0.492940
$873$	1.65685	0.0560760
$874$	−4.75736	−0.160920
$875$	0	0
$876$	5.17157	0.174731
$877$	18.1421	0.612616	0.306308	−	0.951932i	$-0.400906\pi$
$877$	18.1421	0.612616	0.306308	+	0.951932i	$0.400906\pi$
$878$	0.899495	0.0303565
$879$	11.5147	0.388382
$880$	−11.6569	−0.392952
$881$	20.2843	0.683394	0.341697	−	0.939810i	$-0.388998\pi$
$881$	20.2843	0.683394	0.341697	+	0.939810i	$0.388998\pi$
$882$	0	0
$883$	11.3137	0.380737	0.190368	−	0.981713i	$-0.439032\pi$
$883$	11.3137	0.380737	0.190368	+	0.981713i	$0.439032\pi$
$884$	−5.65685	−0.190261
$885$	−25.7279	−0.864835
$886$	−11.1421	−0.374327
$887$	6.68629	0.224504	0.112252	−	0.993680i	$-0.464194\pi$
$887$	6.68629	0.224504	0.112252	+	0.993680i	$0.464194\pi$
$888$	4.41421	0.148131
$889$	0	0
$890$	−39.3848	−1.32018
$891$	4.82843	0.161758
$892$	−18.1421	−0.607444
$893$	30.0000	1.00391
$894$	20.8284	0.696607
$895$	−18.0711	−0.604049
$896$	0	0
$897$	8.97056	0.299518
$898$	13.8579	0.462443
$899$	−7.02944	−0.234445
$900$	0.828427	0.0276142
$901$	8.82843	0.294118
$902$	46.6274	1.55252
$903$	0	0
$904$	−6.48528	−0.215697
$905$	−44.7990	−1.48917
$906$	2.82843	0.0939682
$907$	−50.4853	−1.67634	−0.838168	−	0.545412i	$-0.816373\pi$
$907$	−50.4853	−1.67634	−0.838168	+	0.545412i	$0.816373\pi$
$908$	3.65685	0.121357
$909$	−11.3137	−0.375252
$910$	0	0
$911$	2.21320	0.0733267	0.0366634	−	0.999328i	$-0.488327\pi$
$911$	2.21320	0.0733267	0.0366634	+	0.999328i	$0.488327\pi$
$912$	3.00000	0.0993399
$913$	46.6274	1.54314
$914$	38.4558	1.27201
$915$	−30.1421	−0.996468
$916$	3.51472	0.116130
$917$	0	0
$918$	1.00000	0.0330049
$919$	−14.8284	−0.489145	−0.244572	−	0.969631i	$-0.578648\pi$
$919$	−14.8284	−0.489145	−0.244572	+	0.969631i	$0.578648\pi$
$920$	3.82843	0.126220
$921$	10.5147	0.346472
$922$	4.62742	0.152396
$923$	−2.34315	−0.0771256
$924$	0	0
$925$	−3.65685	−0.120237
$926$	−19.3137	−0.634688
$927$	−3.65685	−0.120107
$928$	1.17157	0.0384588
$929$	−24.8284	−0.814594	−0.407297	−	0.913296i	$-0.633529\pi$
$929$	−24.8284	−0.814594	−0.407297	+	0.913296i	$0.633529\pi$
$930$	14.4853	0.474991
$931$	0	0
$932$	−0.828427	−0.0271360
$933$	−12.7574	−0.417657
$934$	3.48528	0.114042
$935$	11.6569	0.381220
$936$	−5.65685	−0.184900
$937$	−35.8284	−1.17046	−0.585232	−	0.810866i	$-0.698997\pi$
$937$	−35.8284	−1.17046	−0.585232	+	0.810866i	$0.698997\pi$
$938$	0	0
$939$	−9.79899	−0.319778
$940$	−24.1421	−0.787430
$941$	−24.2721	−0.791247	−0.395624	−	0.918413i	$-0.629471\pi$
$941$	−24.2721	−0.791247	−0.395624	+	0.918413i	$0.629471\pi$
$942$	10.9706	0.357440
$943$	−15.3137	−0.498683
$944$	10.6569	0.346851
$945$	0	0
$946$	−20.1421	−0.654877
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0.343146	0.0111449
$949$	29.2548	0.949652
$950$	−2.48528	−0.0806332
$951$	−18.8995	−0.612858
$952$	0	0
$953$	−0.372583	−0.0120691	−0.00603457	−	0.999982i	$-0.501921\pi$
$953$	−0.372583	−0.0120691	−0.00603457	+	0.999982i	$0.501921\pi$
$954$	8.82843	0.285831
$955$	−50.6274	−1.63826
$956$	−3.51472	−0.113674
$957$	−5.65685	−0.182860
$958$	−14.2132	−0.459208
$959$	0	0
$960$	−2.41421	−0.0779184
$961$	5.00000	0.161290
$962$	24.9706	0.805083
$963$	−10.1421	−0.326826
$964$	5.65685	0.182195
$965$	−6.00000	−0.193147
$966$	0	0
$967$	−23.5147	−0.756182	−0.378091	−	0.925768i	$-0.623419\pi$
$967$	−23.5147	−0.756182	−0.378091	+	0.925768i	$0.623419\pi$
$968$	−12.3137	−0.395778
$969$	−3.00000	−0.0963739
$970$	4.00000	0.128432
$971$	−11.3431	−0.364019	−0.182009	−	0.983297i	$-0.558260\pi$
$971$	−11.3431	−0.364019	−0.182009	+	0.983297i	$0.558260\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−2.27208	−0.0728021
$975$	4.68629	0.150081
$976$	12.4853	0.399644
$977$	50.1127	1.60325	0.801624	−	0.597829i	$-0.203970\pi$
$977$	50.1127	1.60325	0.801624	+	0.597829i	$0.203970\pi$
$978$	−16.4853	−0.527141
$979$	−78.7696	−2.51749
$980$	0	0
$981$	−14.5563	−0.464748
$982$	0.798990	0.0254968
$983$	−27.7279	−0.884383	−0.442192	−	0.896921i	$-0.645799\pi$
$983$	−27.7279	−0.884383	−0.442192	+	0.896921i	$0.645799\pi$
$984$	9.65685	0.307849
$985$	−11.4853	−0.365951
$986$	−1.17157	−0.0373105
$987$	0	0
$988$	16.9706	0.539906
$989$	6.61522	0.210352
$990$	11.6569	0.370479
$991$	1.92893	0.0612746	0.0306373	−	0.999531i	$-0.490246\pi$
$991$	1.92893	0.0612746	0.0306373	+	0.999531i	$0.490246\pi$
$992$	−6.00000	−0.190500
$993$	11.8284	0.375364
$994$	0	0
$995$	−59.2843	−1.87944
$996$	9.65685	0.305989
$997$	23.7990	0.753722	0.376861	−	0.926270i	$-0.377004\pi$
$997$	23.7990	0.753722	0.376861	+	0.926270i	$0.377004\pi$
$998$	−34.6274	−1.09611
$999$	−4.41421	−0.139660

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.bv.1.1		2
7.2	even	3		714.2.i.n.613.2	yes	4
7.4	even	3		714.2.i.n.205.2	✓	4
7.6	odd	2		4998.2.a.bt.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.i.n.205.2	✓	4	7.4	even	3
714.2.i.n.613.2	yes	4	7.2	even	3
4998.2.a.bt.1.2		2	7.6	odd	2
4998.2.a.bv.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:	\( N \)	\(=\)	\( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4998.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41421 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.41421 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.41421 q^{10} +4.82843 q^{11} +1.00000 q^{12} +5.65685 q^{13} -2.41421 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +3.00000 q^{19} -2.41421 q^{20} -4.82843 q^{22} +1.58579 q^{23} -1.00000 q^{24} +0.828427 q^{25} -5.65685 q^{26} +1.00000 q^{27} -1.17157 q^{29} +2.41421 q^{30} +6.00000 q^{31} -1.00000 q^{32} +4.82843 q^{33} +1.00000 q^{34} +1.00000 q^{36} -4.41421 q^{37} -3.00000 q^{38} +5.65685 q^{39} +2.41421 q^{40} -9.65685 q^{41} +4.17157 q^{43} +4.82843 q^{44} -2.41421 q^{45} -1.58579 q^{46} +10.0000 q^{47} +1.00000 q^{48} -0.828427 q^{50} -1.00000 q^{51} +5.65685 q^{52} -8.82843 q^{53} -1.00000 q^{54} -11.6569 q^{55} +3.00000 q^{57} +1.17157 q^{58} +10.6569 q^{59} -2.41421 q^{60} +12.4853 q^{61} -6.00000 q^{62} +1.00000 q^{64} -13.6569 q^{65} -4.82843 q^{66} -6.65685 q^{67} -1.00000 q^{68} +1.58579 q^{69} -0.414214 q^{71} -1.00000 q^{72} +5.17157 q^{73} +4.41421 q^{74} +0.828427 q^{75} +3.00000 q^{76} -5.65685 q^{78} +0.343146 q^{79} -2.41421 q^{80} +1.00000 q^{81} +9.65685 q^{82} +9.65685 q^{83} +2.41421 q^{85} -4.17157 q^{86} -1.17157 q^{87} -4.82843 q^{88} -16.3137 q^{89} +2.41421 q^{90} +1.58579 q^{92} +6.00000 q^{93} -10.0000 q^{94} -7.24264 q^{95} -1.00000 q^{96} +1.65685 q^{97} +4.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 2 q^{12} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 6 q^{19} - 2 q^{20} - 4 q^{22} + 6 q^{23} - 2 q^{24} - 4 q^{25} + 2 q^{27} - 8 q^{29} + 2 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 2 q^{34} + 2 q^{36} - 6 q^{37} - 6 q^{38} + 2 q^{40} - 8 q^{41} + 14 q^{43} + 4 q^{44} - 2 q^{45} - 6 q^{46} + 20 q^{47} + 2 q^{48} + 4 q^{50} - 2 q^{51} - 12 q^{53} - 2 q^{54} - 12 q^{55} + 6 q^{57} + 8 q^{58} + 10 q^{59} - 2 q^{60} + 8 q^{61} - 12 q^{62} + 2 q^{64} - 16 q^{65} - 4 q^{66} - 2 q^{67} - 2 q^{68} + 6 q^{69} + 2 q^{71} - 2 q^{72} + 16 q^{73} + 6 q^{74} - 4 q^{75} + 6 q^{76} + 12 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 8 q^{83} + 2 q^{85} - 14 q^{86} - 8 q^{87} - 4 q^{88} - 10 q^{89} + 2 q^{90} + 6 q^{92} + 12 q^{93} - 20 q^{94} - 6 q^{95} - 2 q^{96} - 8 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 2 * q^12 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 + 6 * q^19 - 2 * q^20 - 4 * q^22 + 6 * q^23 - 2 * q^24 - 4 * q^25 + 2 * q^27 - 8 * q^29 + 2 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 2 * q^34 + 2 * q^36 - 6 * q^37 - 6 * q^38 + 2 * q^40 - 8 * q^41 + 14 * q^43 + 4 * q^44 - 2 * q^45 - 6 * q^46 + 20 * q^47 + 2 * q^48 + 4 * q^50 - 2 * q^51 - 12 * q^53 - 2 * q^54 - 12 * q^55 + 6 * q^57 + 8 * q^58 + 10 * q^59 - 2 * q^60 + 8 * q^61 - 12 * q^62 + 2 * q^64 - 16 * q^65 - 4 * q^66 - 2 * q^67 - 2 * q^68 + 6 * q^69 + 2 * q^71 - 2 * q^72 + 16 * q^73 + 6 * q^74 - 4 * q^75 + 6 * q^76 + 12 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 8 * q^83 + 2 * q^85 - 14 * q^86 - 8 * q^87 - 4 * q^88 - 10 * q^89 + 2 * q^90 + 6 * q^92 + 12 * q^93 - 20 * q^94 - 6 * q^95 - 2 * q^96 - 8 * q^97 + 4 * q^99

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