LMFDB - Embedded newform 4655.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4655,2,Mod(1,4655)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4655, 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("4655.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4655 = 5 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4655.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:	$37.1703621409$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.11344.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 4x + 3 $ x^4 - 2x^3 - 4x^2 + 4*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.552409$ of defining polynomial
Character	$\chi$	$=$	4655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14243 q^{2} +2.87834 q^{3} +2.59002 q^{4} +1.00000 q^{5} -6.16666 q^{6} -1.26409 q^{8} +5.28487 q^{9} +O(q^{10})$	\(q-2.14243 q^{2} +2.87834 q^{3} +2.59002 q^{4} +1.00000 q^{5} -6.16666 q^{6} -1.26409 q^{8} +5.28487 q^{9} -2.14243 q^{10} -1.10482 q^{11} +7.45498 q^{12} -1.77353 q^{13} +2.87834 q^{15} -2.47182 q^{16} -7.75669 q^{17} -11.3225 q^{18} -1.00000 q^{19} +2.59002 q^{20} +2.36700 q^{22} -6.65187 q^{23} -3.63849 q^{24} +1.00000 q^{25} +3.79966 q^{26} +6.57664 q^{27} +7.75669 q^{29} -6.16666 q^{30} -6.57664 q^{31} +7.82389 q^{32} -3.18005 q^{33} +16.6182 q^{34} +13.6879 q^{36} -1.40652 q^{37} +2.14243 q^{38} -5.10482 q^{39} -1.26409 q^{40} -2.81995 q^{41} +3.10482 q^{43} -2.86151 q^{44} +5.28487 q^{45} +14.2512 q^{46} -1.46492 q^{47} -7.11475 q^{48} -2.14243 q^{50} -22.3264 q^{51} -4.59348 q^{52} -2.59348 q^{53} -14.0900 q^{54} -1.10482 q^{55} -2.87834 q^{57} -16.6182 q^{58} +5.38969 q^{59} +7.45498 q^{60} -4.07523 q^{61} +14.0900 q^{62} -11.8185 q^{64} -1.77353 q^{65} +6.81305 q^{66} -15.8151 q^{67} -20.0900 q^{68} -19.1464 q^{69} +7.14638 q^{71} -6.68055 q^{72} -0.243310 q^{73} +3.01339 q^{74} +2.87834 q^{75} -2.59002 q^{76} +10.9367 q^{78} -9.38969 q^{79} -2.47182 q^{80} +3.07523 q^{81} +6.04156 q^{82} -8.86151 q^{83} -7.75669 q^{85} -6.65187 q^{86} +22.3264 q^{87} +1.39659 q^{88} -0.813048 q^{89} -11.3225 q^{90} -17.2285 q^{92} -18.9298 q^{93} +3.13849 q^{94} -1.00000 q^{95} +22.5199 q^{96} -3.19689 q^{97} -5.83882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{5} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^5 - 12 * q^8 + 8 * q^9	$ 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{5} - 12 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 6 q^{12} - 2 q^{13} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 34 q^{18} - 4 q^{19} + 8 q^{20} + 4 q^{22} - 8 q^{23} + 24 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 4 q^{29} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 4 q^{34} + 40 q^{36} - 6 q^{37} + 2 q^{38} - 12 q^{39} - 12 q^{40} - 16 q^{41} + 4 q^{43} + 24 q^{44} + 8 q^{45} + 12 q^{47} - 38 q^{48} - 2 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} + 20 q^{54} + 4 q^{55} + 2 q^{57} - 4 q^{58} - 6 q^{60} - 20 q^{61} - 20 q^{62} - 4 q^{64} - 2 q^{65} + 28 q^{66} - 18 q^{67} - 4 q^{68} - 28 q^{69} - 20 q^{71} - 52 q^{72} - 28 q^{73} + 32 q^{74} - 2 q^{75} - 8 q^{76} + 12 q^{78} - 16 q^{79} + 4 q^{80} + 16 q^{81} - 16 q^{82} - 4 q^{85} - 8 q^{86} + 36 q^{87} - 12 q^{88} - 4 q^{89} - 34 q^{90} - 28 q^{92} - 40 q^{93} + 48 q^{94} - 4 q^{95} + 52 q^{96} - 30 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^5 - 12 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 6 * q^12 - 2 * q^13 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 34 * q^18 - 4 * q^19 + 8 * q^20 + 4 * q^22 - 8 * q^23 + 24 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 4 * q^29 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 4 * q^34 + 40 * q^36 - 6 * q^37 + 2 * q^38 - 12 * q^39 - 12 * q^40 - 16 * q^41 + 4 * q^43 + 24 * q^44 + 8 * q^45 + 12 * q^47 - 38 * q^48 - 2 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 + 20 * q^54 + 4 * q^55 + 2 * q^57 - 4 * q^58 - 6 * q^60 - 20 * q^61 - 20 * q^62 - 4 * q^64 - 2 * q^65 + 28 * q^66 - 18 * q^67 - 4 * q^68 - 28 * q^69 - 20 * q^71 - 52 * q^72 - 28 * q^73 + 32 * q^74 - 2 * q^75 - 8 * q^76 + 12 * q^78 - 16 * q^79 + 4 * q^80 + 16 * q^81 - 16 * q^82 - 4 * q^85 - 8 * q^86 + 36 * q^87 - 12 * q^88 - 4 * q^89 - 34 * q^90 - 28 * q^92 - 40 * q^93 + 48 * q^94 - 4 * q^95 + 52 * q^96 - 30 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.14243	−1.51493	−0.757465	−	0.652876i	$-0.773562\pi$
$2$	−2.14243	−1.51493	−0.757465	+	0.652876i	$0.773562\pi$
$3$	2.87834	1.66181	0.830907	−	0.556412i	$-0.187822\pi$
$3$	2.87834	1.66181	0.830907	+	0.556412i	$0.187822\pi$
$4$	2.59002	1.29501
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.16666	−2.51753
$7$	0	0
$7$	0	0
$8$	−1.26409	−0.446923
$9$	5.28487	1.76162
$10$	−2.14243	−0.677497
$11$	−1.10482	−0.333115	−0.166558	−	0.986032i	$-0.553265\pi$
$11$	−1.10482	−0.333115	−0.166558	+	0.986032i	$0.553265\pi$
$12$	7.45498	2.15207
$13$	−1.77353	−0.491888	−0.245944	−	0.969284i	$-0.579098\pi$
$13$	−1.77353	−0.491888	−0.245944	+	0.969284i	$0.579098\pi$
$14$	0	0
$15$	2.87834	0.743185
$16$	−2.47182	−0.617955
$17$	−7.75669	−1.88127	−0.940637	−	0.339415i	$-0.889771\pi$
$17$	−7.75669	−1.88127	−0.940637	+	0.339415i	$0.889771\pi$
$18$	−11.3225	−2.66874
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.59002	0.579147
$21$	0	0
$22$	2.36700	0.504647
$23$	−6.65187	−1.38701	−0.693505	−	0.720451i	$-0.743935\pi$
$23$	−6.65187	−1.38701	−0.693505	+	0.720451i	$0.743935\pi$
$24$	−3.63849	−0.742703
$25$	1.00000	0.200000
$26$	3.79966	0.745175
$27$	6.57664	1.26567
$28$	0	0
$29$	7.75669	1.44038	0.720191	−	0.693776i	$-0.244054\pi$
$29$	7.75669	1.44038	0.720191	+	0.693776i	$0.244054\pi$
$30$	−6.16666	−1.12587
$31$	−6.57664	−1.18120	−0.590600	−	0.806965i	$-0.701109\pi$
$31$	−6.57664	−1.18120	−0.590600	+	0.806965i	$0.701109\pi$
$32$	7.82389	1.38308
$33$	−3.18005	−0.553576
$34$	16.6182	2.85000
$35$	0	0
$36$	13.6879	2.28132
$37$	−1.40652	−0.231231	−0.115616	−	0.993294i	$-0.536884\pi$
$37$	−1.40652	−0.231231	−0.115616	+	0.993294i	$0.536884\pi$
$38$	2.14243	0.347549
$39$	−5.10482	−0.817425
$40$	−1.26409	−0.199870
$41$	−2.81995	−0.440402	−0.220201	−	0.975454i	$-0.570671\pi$
$41$	−2.81995	−0.440402	−0.220201	+	0.975454i	$0.570671\pi$
$42$	0	0
$43$	3.10482	0.473480	0.236740	−	0.971573i	$-0.423921\pi$
$43$	3.10482	0.473480	0.236740	+	0.971573i	$0.423921\pi$
$44$	−2.86151	−0.431389
$45$	5.28487	0.787822
$46$	14.2512	2.10122
$47$	−1.46492	−0.213680	−0.106840	−	0.994276i	$-0.534073\pi$
$47$	−1.46492	−0.213680	−0.106840	+	0.994276i	$0.534073\pi$
$48$	−7.11475	−1.02693
$49$	0	0
$50$	−2.14243	−0.302986
$51$	−22.3264	−3.12633
$52$	−4.59348	−0.637001
$53$	−2.59348	−0.356241	−0.178121	−	0.984009i	$-0.557002\pi$
$53$	−2.59348	−0.356241	−0.178121	+	0.984009i	$0.557002\pi$
$54$	−14.0900	−1.91741
$55$	−1.10482	−0.148974
$56$	0	0
$57$	−2.87834	−0.381246
$58$	−16.6182	−2.18208
$59$	5.38969	0.701678	0.350839	−	0.936436i	$-0.385897\pi$
$59$	5.38969	0.701678	0.350839	+	0.936436i	$0.385897\pi$
$60$	7.45498	0.962434
$61$	−4.07523	−0.521780	−0.260890	−	0.965369i	$-0.584016\pi$
$61$	−4.07523	−0.521780	−0.260890	+	0.965369i	$0.584016\pi$
$62$	14.0900	1.78943
$63$	0	0
$64$	−11.8185	−1.47732
$65$	−1.77353	−0.219979
$66$	6.81305	0.838628
$67$	−15.8151	−1.93212	−0.966060	−	0.258318i	$-0.916832\pi$
$67$	−15.8151	−1.93212	−0.966060	+	0.258318i	$0.916832\pi$
$68$	−20.0900	−2.43627
$69$	−19.1464	−2.30495
$70$	0	0
$71$	7.14638	0.848119	0.424059	−	0.905634i	$-0.360605\pi$
$71$	7.14638	0.848119	0.424059	+	0.905634i	$0.360605\pi$
$72$	−6.68055	−0.787310
$73$	−0.243310	−0.0284773	−0.0142387	−	0.999899i	$-0.504532\pi$
$73$	−0.243310	−0.0284773	−0.0142387	+	0.999899i	$0.504532\pi$
$74$	3.01339	0.350299
$75$	2.87834	0.332363
$76$	−2.59002	−0.297096
$77$	0	0
$78$	10.9367	1.23834
$79$	−9.38969	−1.05642	−0.528211	−	0.849113i	$-0.677137\pi$
$79$	−9.38969	−1.05642	−0.528211	+	0.849113i	$0.677137\pi$
$80$	−2.47182	−0.276358
$81$	3.07523	0.341692
$82$	6.04156	0.667178
$83$	−8.86151	−0.972677	−0.486338	−	0.873771i	$-0.661668\pi$
$83$	−8.86151	−0.972677	−0.486338	+	0.873771i	$0.661668\pi$
$84$	0	0
$85$	−7.75669	−0.841331
$86$	−6.65187	−0.717290
$87$	22.3264	2.39364
$88$	1.39659	0.148877
$89$	−0.813048	−0.0861829	−0.0430914	−	0.999071i	$-0.513721\pi$
$89$	−0.813048	−0.0861829	−0.0430914	+	0.999071i	$0.513721\pi$
$90$	−11.3225	−1.19349
$91$	0	0
$92$	−17.2285	−1.79620
$93$	−18.9298	−1.96293
$94$	3.13849	0.323711
$95$	−1.00000	−0.102598
$96$	22.5199	2.29842
$97$	−3.19689	−0.324595	−0.162297	−	0.986742i	$-0.551890\pi$
$97$	−3.19689	−0.324595	−0.162297	+	0.986742i	$0.551890\pi$
$98$	0	0
$99$	−5.83882	−0.586824
$100$	2.59002	0.259002
$101$	3.01887	0.300389	0.150195	−	0.988656i	$-0.452010\pi$
$101$	3.01887	0.300389	0.150195	+	0.988656i	$0.452010\pi$
$102$	47.8329	4.73616
$103$	−6.05839	−0.596951	−0.298476	−	0.954417i	$-0.596478\pi$
$103$	−6.05839	−0.596951	−0.298476	+	0.954417i	$0.596478\pi$
$104$	2.24190	0.219836
$105$	0	0
$106$	5.55635	0.539681
$107$	20.3848	1.97068	0.985338	−	0.170616i	$-0.0545759\pi$
$107$	20.3848	1.97068	0.985338	+	0.170616i	$0.0545759\pi$
$108$	17.0337	1.63906
$109$	4.72710	0.452774	0.226387	−	0.974037i	$-0.427309\pi$
$109$	4.72710	0.452774	0.226387	+	0.974037i	$0.427309\pi$
$110$	2.36700	0.225685
$111$	−4.04846	−0.384263
$112$	0	0
$113$	−7.98316	−0.750993	−0.375496	−	0.926824i	$-0.622528\pi$
$113$	−7.98316	−0.750993	−0.375496	+	0.926824i	$0.622528\pi$
$114$	6.16666	0.577561
$115$	−6.65187	−0.620290
$116$	20.0900	1.86531
$117$	−9.37285	−0.866520
$118$	−11.5471	−1.06299
$119$	0	0
$120$	−3.63849	−0.332147
$121$	−9.77938	−0.889034
$122$	8.73091	0.790460
$123$	−8.11679	−0.731866
$124$	−17.0337	−1.52967
$125$	1.00000	0.0894427
$126$	0	0
$127$	4.63503	0.411293	0.205646	−	0.978626i	$-0.434070\pi$
$127$	4.63503	0.411293	0.205646	+	0.978626i	$0.434070\pi$
$128$	9.67265	0.854950
$129$	8.93674	0.786836
$130$	3.79966	0.333252
$131$	−15.5134	−1.35541	−0.677705	−	0.735334i	$-0.737025\pi$
$131$	−15.5134	−1.35541	−0.677705	+	0.735334i	$0.737025\pi$
$132$	−8.23641	−0.716887
$133$	0	0
$134$	33.8828	2.92703
$135$	6.57664	0.566027
$136$	9.80515	0.840785
$137$	−0.813048	−0.0694634	−0.0347317	−	0.999397i	$-0.511058\pi$
$137$	−0.813048	−0.0694634	−0.0347317	+	0.999397i	$0.511058\pi$
$138$	41.0199	3.49184
$139$	12.7687	1.08302	0.541512	−	0.840693i	$-0.317852\pi$
$139$	12.7687	1.08302	0.541512	+	0.840693i	$0.317852\pi$
$140$	0	0
$141$	−4.21654	−0.355097
$142$	−15.3106	−1.28484
$143$	1.95942	0.163855
$144$	−13.0632	−1.08860
$145$	7.75669	0.644158
$146$	0.521277	0.0431412
$147$	0	0
$148$	−3.64293	−0.299447
$149$	−13.7982	−1.13040	−0.565198	−	0.824955i	$-0.691200\pi$
$149$	−13.7982	−1.13040	−0.565198	+	0.824955i	$0.691200\pi$
$150$	−6.16666	−0.503506
$151$	5.02269	0.408740	0.204370	−	0.978894i	$-0.434485\pi$
$151$	5.02269	0.408740	0.204370	+	0.978894i	$0.434485\pi$
$152$	1.26409	0.102531
$153$	−40.9931	−3.31409
$154$	0	0
$155$	−6.57664	−0.528248
$156$	−13.2216	−1.05858
$157$	−7.18695	−0.573581	−0.286791	−	0.957993i	$-0.592588\pi$
$157$	−7.18695	−0.573581	−0.286791	+	0.957993i	$0.592588\pi$
$158$	20.1168	1.60041
$159$	−7.46492	−0.592007
$160$	7.82389	0.618533
$161$	0	0
$162$	−6.58848	−0.517640
$163$	7.25528	0.568277	0.284139	−	0.958783i	$-0.408292\pi$
$163$	7.25528	0.568277	0.284139	+	0.958783i	$0.408292\pi$
$164$	−7.30374	−0.570326
$165$	−3.18005	−0.247567
$166$	18.9852	1.47354
$167$	7.33129	0.567312	0.283656	−	0.958926i	$-0.408453\pi$
$167$	7.33129	0.567312	0.283656	+	0.958926i	$0.408453\pi$
$168$	0	0
$169$	−9.85461	−0.758047
$170$	16.6182	1.27456
$171$	−5.28487	−0.404144
$172$	8.04156	0.613163
$173$	5.77353	0.438953	0.219477	−	0.975618i	$-0.429565\pi$
$173$	5.77353	0.438953	0.219477	+	0.975618i	$0.429565\pi$
$174$	−47.8329	−3.62620
$175$	0	0
$176$	2.73091	0.205850
$177$	15.5134	1.16606
$178$	1.74190	0.130561
$179$	−4.48379	−0.335134	−0.167567	−	0.985861i	$-0.553591\pi$
$179$	−4.48379	−0.335134	−0.167567	+	0.985861i	$0.553591\pi$
$180$	13.6879	1.02024
$181$	2.73400	0.203217	0.101608	−	0.994824i	$-0.467601\pi$
$181$	2.73400	0.203217	0.101608	+	0.994824i	$0.467601\pi$
$182$	0	0
$183$	−11.7299	−0.867101
$184$	8.40856	0.619887
$185$	−1.40652	−0.103410
$186$	40.5559	2.97371
$187$	8.56974	0.626681
$188$	−3.79418	−0.276719
$189$	0	0
$190$	2.14243	0.155429
$191$	−17.7230	−1.28239	−0.641196	−	0.767377i	$-0.721562\pi$
$191$	−17.7230	−1.28239	−0.641196	+	0.767377i	$0.721562\pi$
$192$	−34.0178	−2.45502
$193$	−13.5371	−0.974423	−0.487212	−	0.873284i	$-0.661986\pi$
$193$	−13.5371	−0.974423	−0.487212	+	0.873284i	$0.661986\pi$
$194$	6.84912	0.491738
$195$	−5.10482	−0.365564
$196$	0	0
$197$	−21.5134	−1.53276	−0.766382	−	0.642385i	$-0.777945\pi$
$197$	−21.5134	−1.53276	−0.766382	+	0.642385i	$0.777945\pi$
$198$	12.5093	0.888997
$199$	−7.09410	−0.502888	−0.251444	−	0.967872i	$-0.580905\pi$
$199$	−7.09410	−0.502888	−0.251444	+	0.967872i	$0.580905\pi$
$200$	−1.26409	−0.0893846
$201$	−45.5213	−3.21082
$202$	−6.46774	−0.455068
$203$	0	0
$204$	−57.8260	−4.04863
$205$	−2.81995	−0.196954
$206$	12.9797	0.904339
$207$	−35.1543	−2.44339
$208$	4.38384	0.303964
$209$	1.10482	0.0764219
$210$	0	0
$211$	11.0604	0.761431	0.380716	−	0.924692i	$-0.375678\pi$
$211$	11.0604	0.761431	0.380716	+	0.924692i	$0.375678\pi$
$212$	−6.71717	−0.461337
$213$	20.5697	1.40942
$214$	−43.6731	−2.98543
$215$	3.10482	0.211747
$216$	−8.31346	−0.565659
$217$	0	0
$218$	−10.1275	−0.685921
$219$	−0.700331	−0.0473240
$220$	−2.86151	−0.192923
$221$	13.7567	0.925375
$222$	8.67356	0.582131
$223$	12.6350	0.846104	0.423052	−	0.906105i	$-0.360959\pi$
$223$	12.6350	0.846104	0.423052	+	0.906105i	$0.360959\pi$
$224$	0	0
$225$	5.28487	0.352325
$226$	17.1034	1.13770
$227$	6.62813	0.439925	0.219962	−	0.975508i	$-0.429407\pi$
$227$	6.62813	0.439925	0.219962	+	0.975508i	$0.429407\pi$
$228$	−7.45498	−0.493718
$229$	0.0752308	0.00497139	0.00248570	−	0.999997i	$-0.499209\pi$
$229$	0.0752308	0.00497139	0.00248570	+	0.999997i	$0.499209\pi$
$230$	14.2512	0.939696
$231$	0	0
$232$	−9.80515	−0.643740
$233$	9.51338	0.623242	0.311621	−	0.950206i	$-0.399128\pi$
$233$	9.51338	0.623242	0.311621	+	0.950206i	$0.399128\pi$
$234$	20.0807	1.31272
$235$	−1.46492	−0.0955607
$236$	13.9594	0.908681
$237$	−27.0268	−1.75558
$238$	0	0
$239$	−2.92984	−0.189515	−0.0947577	−	0.995500i	$-0.530208\pi$
$239$	−2.92984	−0.189515	−0.0947577	+	0.995500i	$0.530208\pi$
$240$	−7.11475	−0.459255
$241$	9.42743	0.607274	0.303637	−	0.952788i	$-0.401799\pi$
$241$	9.42743	0.607274	0.303637	+	0.952788i	$0.401799\pi$
$242$	20.9517	1.34682
$243$	−10.8783	−0.697846
$244$	−10.5549	−0.675711
$245$	0	0
$246$	17.3897	1.10873
$247$	1.77353	0.112847
$248$	8.31346	0.527905
$249$	−25.5065	−1.61641
$250$	−2.14243	−0.135499
$251$	14.9298	0.942363	0.471181	−	0.882036i	$-0.343828\pi$
$251$	14.9298	0.942363	0.471181	+	0.882036i	$0.343828\pi$
$252$	0	0
$253$	7.34911	0.462035
$254$	−9.93026	−0.623080
$255$	−22.3264	−1.39814
$256$	2.91405	0.182128
$257$	15.1295	0.943755	0.471877	−	0.881664i	$-0.343576\pi$
$257$	15.1295	0.943755	0.471877	+	0.881664i	$0.343576\pi$
$258$	−19.1464	−1.19200
$259$	0	0
$260$	−4.59348	−0.284875
$261$	40.9931	2.53741
$262$	33.2364	2.05335
$263$	−15.2216	−0.938605	−0.469302	−	0.883038i	$-0.655495\pi$
$263$	−15.2216	−0.938605	−0.469302	+	0.883038i	$0.655495\pi$
$264$	4.01987	0.247406
$265$	−2.59348	−0.159316
$266$	0	0
$267$	−2.34023	−0.143220
$268$	−40.9615	−2.50212
$269$	−11.5203	−0.702404	−0.351202	−	0.936300i	$-0.614227\pi$
$269$	−11.5203	−0.702404	−0.351202	+	0.936300i	$0.614227\pi$
$270$	−14.0900	−0.857491
$271$	−2.16118	−0.131282	−0.0656411	−	0.997843i	$-0.520909\pi$
$271$	−2.16118	−0.131282	−0.0656411	+	0.997843i	$0.520909\pi$
$272$	19.1731	1.16254
$273$	0	0
$274$	1.74190	0.105232
$275$	−1.10482	−0.0666231
$276$	−49.5896	−2.98494
$277$	23.4205	1.40720	0.703602	−	0.710595i	$-0.251574\pi$
$277$	23.4205	1.40720	0.703602	+	0.710595i	$0.251574\pi$
$278$	−27.3560	−1.64070
$279$	−34.7567	−2.08083
$280$	0	0
$281$	25.6824	1.53209	0.766043	−	0.642789i	$-0.222223\pi$
$281$	25.6824	1.53209	0.766043	+	0.642789i	$0.222223\pi$
$282$	9.03366	0.537947
$283$	−7.38587	−0.439045	−0.219522	−	0.975607i	$-0.570450\pi$
$283$	−7.38587	−0.439045	−0.219522	+	0.975607i	$0.570450\pi$
$284$	18.5093	1.09832
$285$	−2.87834	−0.170498
$286$	−4.19794	−0.248229
$287$	0	0
$288$	41.3482	2.43647
$289$	43.1662	2.53919
$290$	−16.6182	−0.975854
$291$	−9.20174	−0.539416
$292$	−0.630180	−0.0368785
$293$	24.1522	1.41099	0.705494	−	0.708716i	$-0.250725\pi$
$293$	24.1522	1.41099	0.705494	+	0.708716i	$0.250725\pi$
$294$	0	0
$295$	5.38969	0.313800
$296$	1.77797	0.103343
$297$	−7.26600	−0.421616
$298$	29.5618	1.71247
$299$	11.7973	0.682253
$300$	7.45498	0.430414
$301$	0	0
$302$	−10.7608	−0.619213
$303$	8.68936	0.499190
$304$	2.47182	0.141769
$305$	−4.07523	−0.233347
$306$	87.8250	5.02062
$307$	−4.38482	−0.250255	−0.125127	−	0.992141i	$-0.539934\pi$
$307$	−4.38482	−0.250255	−0.125127	+	0.992141i	$0.539934\pi$
$308$	0	0
$309$	−17.4381	−0.992022
$310$	14.0900	0.800259
$311$	15.7123	0.890963	0.445481	−	0.895291i	$-0.353033\pi$
$311$	15.7123	0.890963	0.445481	+	0.895291i	$0.353033\pi$
$312$	6.45295	0.365326
$313$	−24.7794	−1.40061	−0.700307	−	0.713842i	$-0.746953\pi$
$313$	−24.7794	−1.40061	−0.700307	+	0.713842i	$0.746953\pi$
$314$	15.3976	0.868935
$315$	0	0
$316$	−24.3195	−1.36808
$317$	−27.3798	−1.53780	−0.768900	−	0.639369i	$-0.779196\pi$
$317$	−27.3798	−1.53780	−0.768900	+	0.639369i	$0.779196\pi$
$318$	15.9931	0.896848
$319$	−8.56974	−0.479813
$320$	−11.8185	−0.660676
$321$	58.6745	3.27489
$322$	0	0
$323$	7.75669	0.431594
$324$	7.96492	0.442496
$325$	−1.77353	−0.0983775
$326$	−15.5440	−0.860900
$327$	13.6062	0.752426
$328$	3.56467	0.196826
$329$	0	0
$330$	6.81305	0.375046
$331$	4.70033	0.258354	0.129177	−	0.991622i	$-0.458767\pi$
$331$	4.70033	0.258354	0.129177	+	0.991622i	$0.458767\pi$
$332$	−22.9515	−1.25963
$333$	−7.43329	−0.407342
$334$	−15.7068	−0.859439
$335$	−15.8151	−0.864070
$336$	0	0
$337$	−20.6360	−1.12412	−0.562058	−	0.827098i	$-0.689990\pi$
$337$	−20.6360	−1.12412	−0.562058	+	0.827098i	$0.689990\pi$
$338$	21.1128	1.14839
$339$	−22.9783	−1.24801
$340$	−20.0900	−1.08953
$341$	7.26600	0.393476
$342$	11.3225	0.612250
$343$	0	0
$344$	−3.92477	−0.211609
$345$	−19.1464	−1.03081
$346$	−12.3694	−0.664983
$347$	30.0148	1.61128	0.805639	−	0.592407i	$-0.201822\pi$
$347$	30.0148	1.61128	0.805639	+	0.592407i	$0.201822\pi$
$348$	57.8260	3.09980
$349$	14.7340	0.788693	0.394347	−	0.918962i	$-0.370971\pi$
$349$	14.7340	0.788693	0.394347	+	0.918962i	$0.370971\pi$
$350$	0	0
$351$	−11.6638	−0.622570
$352$	−8.64399	−0.460726
$353$	29.6302	1.57705	0.788527	−	0.615000i	$-0.210844\pi$
$353$	29.6302	1.57705	0.788527	+	0.615000i	$0.210844\pi$
$354$	−33.2364	−1.76649
$355$	7.14638	0.379290
$356$	−2.10581	−0.111608
$357$	0	0
$358$	9.60623	0.507705
$359$	21.7577	1.14833	0.574163	−	0.818741i	$-0.305328\pi$
$359$	21.7577	1.14833	0.574163	+	0.818741i	$0.305328\pi$
$360$	−6.68055	−0.352096
$361$	1.00000	0.0526316
$362$	−5.85742	−0.307859
$363$	−28.1484	−1.47741
$364$	0	0
$365$	−0.243310	−0.0127355
$366$	25.1306	1.31360
$367$	−30.0347	−1.56780	−0.783898	−	0.620889i	$-0.786772\pi$
$367$	−30.0347	−1.56780	−0.783898	+	0.620889i	$0.786772\pi$
$368$	16.4422	0.857111
$369$	−14.9031	−0.775823
$370$	3.01339	0.156658
$371$	0	0
$372$	−49.0287	−2.54202
$373$	−37.3055	−1.93161	−0.965803	−	0.259277i	$-0.916516\pi$
$373$	−37.3055	−1.93161	−0.965803	+	0.259277i	$0.916516\pi$
$374$	−18.3601	−0.949378
$375$	2.87834	0.148637
$376$	1.85179	0.0954987
$377$	−13.7567	−0.708506
$378$	0	0
$379$	−14.7794	−0.759166	−0.379583	−	0.925158i	$-0.623932\pi$
$379$	−14.7794	−0.759166	−0.379583	+	0.925158i	$0.623932\pi$
$380$	−2.59002	−0.132865
$381$	13.3412	0.683492
$382$	37.9704	1.94273
$383$	29.0020	1.48193	0.740967	−	0.671541i	$-0.234367\pi$
$383$	29.0020	1.48193	0.740967	+	0.671541i	$0.234367\pi$
$384$	27.8412	1.42077
$385$	0	0
$386$	29.0024	1.47618
$387$	16.4086	0.834094
$388$	−8.28001	−0.420354
$389$	21.1987	1.07481	0.537407	−	0.843323i	$-0.319404\pi$
$389$	21.1987	1.07481	0.537407	+	0.843323i	$0.319404\pi$
$390$	10.9367	0.553803
$391$	51.5965	2.60935
$392$	0	0
$393$	−44.6529	−2.25244
$394$	46.0910	2.32203
$395$	−9.38969	−0.472446
$396$	−15.1227	−0.759944
$397$	−10.3856	−0.521238	−0.260619	−	0.965442i	$-0.583927\pi$
$397$	−10.3856	−0.521238	−0.260619	+	0.965442i	$0.583927\pi$
$398$	15.1987	0.761840
$399$	0	0
$400$	−2.47182	−0.123591
$401$	25.6638	1.28159	0.640796	−	0.767712i	$-0.278605\pi$
$401$	25.6638	1.28159	0.640796	+	0.767712i	$0.278605\pi$
$402$	97.5263	4.86417
$403$	11.6638	0.581017
$404$	7.81896	0.389008
$405$	3.07523	0.152809
$406$	0	0
$407$	1.55395	0.0770266
$408$	28.2226	1.39723
$409$	−5.71611	−0.282644	−0.141322	−	0.989964i	$-0.545135\pi$
$409$	−5.71611	−0.282644	−0.141322	+	0.989964i	$0.545135\pi$
$410$	6.04156	0.298371
$411$	−2.34023	−0.115435
$412$	−15.6914	−0.773059
$413$	0	0
$414$	75.3157	3.70156
$415$	−8.86151	−0.434994
$416$	−13.8759	−0.680321
$417$	36.7526	1.79978
$418$	−2.36700	−0.115774
$419$	−15.4303	−0.753818	−0.376909	−	0.926250i	$-0.623013\pi$
$419$	−15.4303	−0.753818	−0.376909	+	0.926250i	$0.623013\pi$
$420$	0	0
$421$	−1.18005	−0.0575121	−0.0287561	−	0.999586i	$-0.509155\pi$
$421$	−1.18005	−0.0575121	−0.0287561	+	0.999586i	$0.509155\pi$
$422$	−23.6962	−1.15352
$423$	−7.74190	−0.376424
$424$	3.27839	0.159213
$425$	−7.75669	−0.376255
$426$	−44.0693	−2.13517
$427$	0	0
$428$	52.7972	2.55205
$429$	5.63990	0.272297
$430$	−6.65187	−0.320782
$431$	−14.0255	−0.675585	−0.337792	−	0.941221i	$-0.609680\pi$
$431$	−14.0255	−0.675585	−0.337792	+	0.941221i	$0.609680\pi$
$432$	−16.2563	−0.782130
$433$	−25.5894	−1.22975	−0.614874	−	0.788625i	$-0.710793\pi$
$433$	−25.5894	−1.22975	−0.614874	+	0.788625i	$0.710793\pi$
$434$	0	0
$435$	22.3264	1.07047
$436$	12.2433	0.586348
$437$	6.65187	0.318202
$438$	1.50041	0.0716925
$439$	21.9732	1.04873	0.524363	−	0.851495i	$-0.324304\pi$
$439$	21.9732	1.04873	0.524363	+	0.851495i	$0.324304\pi$
$440$	1.39659	0.0665798
$441$	0	0
$442$	−29.4728	−1.40188
$443$	−19.3721	−0.920395	−0.460197	−	0.887817i	$-0.652221\pi$
$443$	−19.3721	−0.920395	−0.460197	+	0.887817i	$0.652221\pi$
$444$	−10.4856	−0.497625
$445$	−0.813048	−0.0385422
$446$	−27.0697	−1.28179
$447$	−39.7161	−1.87851
$448$	0	0
$449$	−19.1841	−0.905355	−0.452677	−	0.891674i	$-0.649531\pi$
$449$	−19.1841	−0.905355	−0.452677	+	0.891674i	$0.649531\pi$
$450$	−11.3225	−0.533747
$451$	3.11553	0.146705
$452$	−20.6766	−0.972545
$453$	14.4570	0.679250
$454$	−14.2003	−0.666455
$455$	0	0
$456$	3.63849	0.170388
$457$	8.36010	0.391069	0.195534	−	0.980697i	$-0.437356\pi$
$457$	8.36010	0.391069	0.195534	+	0.980697i	$0.437356\pi$
$458$	−0.161177	−0.00753131
$459$	−51.0130	−2.38108
$460$	−17.2285	−0.803283
$461$	25.0268	1.16561	0.582806	−	0.812611i	$-0.301955\pi$
$461$	25.0268	1.16561	0.582806	+	0.812611i	$0.301955\pi$
$462$	0	0
$463$	32.3749	1.50459	0.752294	−	0.658827i	$-0.228947\pi$
$463$	32.3749	1.50459	0.752294	+	0.658827i	$0.228947\pi$
$464$	−19.1731	−0.890091
$465$	−18.9298	−0.877850
$466$	−20.3818	−0.944168
$467$	−15.2216	−0.704372	−0.352186	−	0.935930i	$-0.614562\pi$
$467$	−15.2216	−0.704372	−0.352186	+	0.935930i	$0.614562\pi$
$468$	−24.2759	−1.12215
$469$	0	0
$470$	3.13849	0.144768
$471$	−20.6865	−0.953185
$472$	−6.81305	−0.313596
$473$	−3.43026	−0.157724
$474$	57.9031	2.65958
$475$	−1.00000	−0.0458831
$476$	0	0
$477$	−13.7062	−0.627563
$478$	6.27698	0.287103
$479$	20.0485	0.916038	0.458019	−	0.888943i	$-0.348559\pi$
$479$	20.0485	0.916038	0.458019	+	0.888943i	$0.348559\pi$
$480$	22.5199	1.02789
$481$	2.49451	0.113740
$482$	−20.1977	−0.919978
$483$	0	0
$484$	−25.3288	−1.15131
$485$	−3.19689	−0.145163
$486$	23.3061	1.05719
$487$	−31.6508	−1.43424	−0.717118	−	0.696952i	$-0.754539\pi$
$487$	−31.6508	−1.43424	−0.717118	+	0.696952i	$0.754539\pi$
$488$	5.15146	0.233195
$489$	20.8832	0.944371
$490$	0	0
$491$	24.8033	1.11936	0.559679	−	0.828710i	$-0.310924\pi$
$491$	24.8033	1.11936	0.559679	+	0.828710i	$0.310924\pi$
$492$	−21.0227	−0.947776
$493$	−60.1662	−2.70975
$494$	−3.79966	−0.170955
$495$	−5.83882	−0.262436
$496$	16.2563	0.729928
$497$	0	0
$498$	54.6460	2.44874
$499$	−33.0237	−1.47834	−0.739171	−	0.673518i	$-0.764783\pi$
$499$	−33.0237	−1.47834	−0.739171	+	0.673518i	$0.764783\pi$
$500$	2.59002	0.115829
$501$	21.1020	0.942767
$502$	−31.9862	−1.42761
$503$	3.54396	0.158017	0.0790087	−	0.996874i	$-0.474825\pi$
$503$	3.54396	0.158017	0.0790087	+	0.996874i	$0.474825\pi$
$504$	0	0
$505$	3.01887	0.134338
$506$	−15.7450	−0.699950
$507$	−28.3650	−1.25973
$508$	12.0049	0.532629
$509$	2.11679	0.0938250	0.0469125	−	0.998899i	$-0.485062\pi$
$509$	2.11679	0.0938250	0.0469125	+	0.998899i	$0.485062\pi$
$510$	47.8329	2.11808
$511$	0	0
$512$	−25.5885	−1.13086
$513$	−6.57664	−0.290366
$514$	−32.4140	−1.42972
$515$	−6.05839	−0.266965
$516$	23.1464	1.01896
$517$	1.61847	0.0711802
$518$	0	0
$519$	16.6182	0.729458
$520$	2.24190	0.0983136
$521$	8.60748	0.377101	0.188550	−	0.982064i	$-0.439621\pi$
$521$	8.60748	0.377101	0.188550	+	0.982064i	$0.439621\pi$
$522$	−87.8250	−3.84400
$523$	−36.8349	−1.61068	−0.805340	−	0.592814i	$-0.798017\pi$
$523$	−36.8349	−1.61068	−0.805340	+	0.592814i	$0.798017\pi$
$524$	−40.1800	−1.75527
$525$	0	0
$526$	32.6113	1.42192
$527$	51.0130	2.22216
$528$	7.86051	0.342085
$529$	21.2474	0.923799
$530$	5.55635	0.241353
$531$	28.4838	1.23609
$532$	0	0
$533$	5.00125	0.216628
$534$	5.01379	0.216968
$535$	20.3848	0.881313
$536$	19.9917	0.863509
$537$	−12.9059	−0.556931
$538$	24.6814	1.06409
$539$	0	0
$540$	17.0337	0.733012
$541$	−32.0079	−1.37613	−0.688063	−	0.725651i	$-0.741539\pi$
$541$	−32.0079	−1.37613	−0.688063	+	0.725651i	$0.741539\pi$
$542$	4.63018	0.198883
$543$	7.86941	0.337709
$544$	−60.6875	−2.60196
$545$	4.72710	0.202487
$546$	0	0
$547$	17.6240	0.753550	0.376775	−	0.926305i	$-0.377033\pi$
$547$	17.6240	0.753550	0.376775	+	0.926305i	$0.377033\pi$
$548$	−2.10581	−0.0899559
$549$	−21.5371	−0.919179
$550$	2.36700	0.100929
$551$	−7.75669	−0.330446
$552$	24.2027	1.03014
$553$	0	0
$554$	−50.1769	−2.13181
$555$	−4.04846	−0.171848
$556$	33.0711	1.40253
$557$	−34.6865	−1.46972	−0.734858	−	0.678221i	$-0.762751\pi$
$557$	−34.6865	−1.46972	−0.734858	+	0.678221i	$0.762751\pi$
$558$	74.4639	3.15231
$559$	−5.50648	−0.232899
$560$	0	0
$561$	24.6667	1.04143
$562$	−55.0229	−2.32100
$563$	−13.5073	−0.569263	−0.284632	−	0.958637i	$-0.591871\pi$
$563$	−13.5073	−0.569263	−0.284632	+	0.958637i	$0.591871\pi$
$564$	−10.9209	−0.459855
$565$	−7.98316	−0.335854
$566$	15.8238	0.665122
$567$	0	0
$568$	−9.03366	−0.379044
$569$	32.3588	1.35655	0.678276	−	0.734807i	$-0.262727\pi$
$569$	32.3588	1.35655	0.678276	+	0.734807i	$0.262727\pi$
$570$	6.16666	0.258293
$571$	−8.93293	−0.373831	−0.186916	−	0.982376i	$-0.559849\pi$
$571$	−8.93293	−0.373831	−0.186916	+	0.982376i	$0.559849\pi$
$572$	5.07496	0.212195
$573$	−51.0130	−2.13110
$574$	0	0
$575$	−6.65187	−0.277402
$576$	−62.4594	−2.60248
$577$	−14.9059	−0.620541	−0.310270	−	0.950648i	$-0.600420\pi$
$577$	−14.9059	−0.620541	−0.310270	+	0.950648i	$0.600420\pi$
$578$	−92.4808	−3.84669
$579$	−38.9645	−1.61931
$580$	20.0900	0.834193
$581$	0	0
$582$	19.7141	0.817177
$583$	2.86532	0.118669
$584$	0.307566	0.0127272
$585$	−9.37285	−0.387520
$586$	−51.7446	−2.13755
$587$	−7.37207	−0.304278	−0.152139	−	0.988359i	$-0.548616\pi$
$587$	−7.37207	−0.304278	−0.152139	+	0.988359i	$0.548616\pi$
$588$	0	0
$589$	6.57664	0.270986
$590$	−11.5471	−0.475385
$591$	−61.9229	−2.54717
$592$	3.47668	0.142890
$593$	17.6853	0.726247	0.363124	−	0.931741i	$-0.381710\pi$
$593$	17.6853	0.726247	0.363124	+	0.931741i	$0.381710\pi$
$594$	15.5669	0.638718
$595$	0	0
$596$	−35.7378	−1.46388
$597$	−20.4193	−0.835705
$598$	−25.2749	−1.03357
$599$	5.30657	0.216821	0.108410	−	0.994106i	$-0.465424\pi$
$599$	5.30657	0.216821	0.108410	+	0.994106i	$0.465424\pi$
$600$	−3.63849	−0.148541
$601$	−43.7875	−1.78613	−0.893065	−	0.449927i	$-0.851450\pi$
$601$	−43.7875	−1.78613	−0.893065	+	0.449927i	$0.851450\pi$
$602$	0	0
$603$	−83.5806	−3.40367
$604$	13.0089	0.529324
$605$	−9.77938	−0.397588
$606$	−18.6164	−0.756239
$607$	7.24535	0.294080	0.147040	−	0.989131i	$-0.453025\pi$
$607$	7.24535	0.294080	0.147040	+	0.989131i	$0.453025\pi$
$608$	−7.82389	−0.317301
$609$	0	0
$610$	8.73091	0.353504
$611$	2.59807	0.105107
$612$	−106.173	−4.29179
$613$	20.8962	0.843988	0.421994	−	0.906599i	$-0.361330\pi$
$613$	20.8962	0.843988	0.421994	+	0.906599i	$0.361330\pi$
$614$	9.39419	0.379119
$615$	−8.11679	−0.327301
$616$	0	0
$617$	−22.0494	−0.887677	−0.443839	−	0.896107i	$-0.646384\pi$
$617$	−22.0494	−0.887677	−0.443839	+	0.896107i	$0.646384\pi$
$618$	37.3601	1.50284
$619$	0.0484607	0.00194780	0.000973900	−	1.00000i	$-0.499690\pi$
$619$	0.0484607	0.00194780	0.000973900		1.00000i	$0.499690\pi$
$620$	−17.0337	−0.684088
$621$	−43.7470	−1.75550
$622$	−33.6626	−1.34975
$623$	0	0
$624$	12.6182	0.505132
$625$	1.00000	0.0400000
$626$	53.0882	2.12183
$627$	3.18005	0.126999
$628$	−18.6144	−0.742795
$629$	10.9100	0.435009
$630$	0	0
$631$	−32.6182	−1.29851	−0.649255	−	0.760571i	$-0.724919\pi$
$631$	−32.6182	−1.29851	−0.649255	+	0.760571i	$0.724919\pi$
$632$	11.8694	0.472140
$633$	31.8357	1.26536
$634$	58.6593	2.32966
$635$	4.63503	0.183936
$636$	−19.3343	−0.766656
$637$	0	0
$638$	18.3601	0.726883
$639$	37.7677	1.49407
$640$	9.67265	0.382345
$641$	−13.4136	−0.529806	−0.264903	−	0.964275i	$-0.585340\pi$
$641$	−13.4136	−0.529806	−0.264903	+	0.964275i	$0.585340\pi$
$642$	−125.706	−4.96123
$643$	−23.8052	−0.938783	−0.469392	−	0.882990i	$-0.655527\pi$
$643$	−23.8052	−0.938783	−0.469392	+	0.882990i	$0.655527\pi$
$644$	0	0
$645$	8.93674	0.351884
$646$	−16.6182	−0.653834
$647$	48.4580	1.90508	0.952540	−	0.304412i	$-0.0984601\pi$
$647$	48.4580	1.90508	0.952540	+	0.304412i	$0.0984601\pi$
$648$	−3.88737	−0.152710
$649$	−5.95463	−0.233740
$650$	3.79966	0.149035
$651$	0	0
$652$	18.7914	0.735926
$653$	22.2351	0.870128	0.435064	−	0.900399i	$-0.356726\pi$
$653$	22.2351	0.870128	0.435064	+	0.900399i	$0.356726\pi$
$654$	−29.1504	−1.13987
$655$	−15.5134	−0.606158
$656$	6.97041	0.272149
$657$	−1.28586	−0.0501663
$658$	0	0
$659$	−10.7072	−0.417095	−0.208547	−	0.978012i	$-0.566874\pi$
$659$	−10.7072	−0.417095	−0.208547	+	0.978012i	$0.566874\pi$
$660$	−8.23641	−0.320602
$661$	44.7980	1.74244	0.871220	−	0.490893i	$-0.163330\pi$
$661$	44.7980	1.74244	0.871220	+	0.490893i	$0.163330\pi$
$662$	−10.0702	−0.391388
$663$	39.5965	1.53780
$664$	11.2017	0.434712
$665$	0	0
$666$	15.9253	0.617095
$667$	−51.5965	−1.99782
$668$	18.9882	0.734677
$669$	36.3680	1.40607
$670$	33.8828	1.30901
$671$	4.50239	0.173813
$672$	0	0
$673$	−43.2772	−1.66821	−0.834106	−	0.551604i	$-0.814016\pi$
$673$	−43.2772	−1.66821	−0.834106	+	0.551604i	$0.814016\pi$
$674$	44.2113	1.70296
$675$	6.57664	0.253135
$676$	−25.5237	−0.981680
$677$	−11.5330	−0.443251	−0.221625	−	0.975132i	$-0.571136\pi$
$677$	−11.5330	−0.443251	−0.221625	+	0.975132i	$0.571136\pi$
$678$	49.2295	1.89065
$679$	0	0
$680$	9.80515	0.376010
$681$	19.0780	0.731072
$682$	−15.5669	−0.596088
$683$	0.916090	0.0350532	0.0175266	−	0.999846i	$-0.494421\pi$
$683$	0.916090	0.0350532	0.0175266	+	0.999846i	$0.494421\pi$
$684$	−13.6879	−0.523372
$685$	−0.813048	−0.0310650
$686$	0	0
$687$	0.216540	0.00826153
$688$	−7.67456	−0.292590
$689$	4.59960	0.175231
$690$	41.0199	1.56160
$691$	−14.8278	−0.564077	−0.282039	−	0.959403i	$-0.591011\pi$
$691$	−14.8278	−0.564077	−0.282039	+	0.959403i	$0.591011\pi$
$692$	14.9536	0.568450
$693$	0	0
$694$	−64.3047	−2.44097
$695$	12.7687	0.484343
$696$	−28.2226	−1.06978
$697$	21.8735	0.828517
$698$	−31.5666	−1.19481
$699$	27.3828	1.03571
$700$	0	0
$701$	36.1722	1.36620	0.683102	−	0.730323i	$-0.260631\pi$
$701$	36.1722	1.36620	0.683102	+	0.730323i	$0.260631\pi$
$702$	24.9890	0.943150
$703$	1.40652	0.0530481
$704$	13.0573	0.492117
$705$	−4.21654	−0.158804
$706$	−63.4807	−2.38913
$707$	0	0
$708$	40.1800	1.51006
$709$	10.4331	0.391823	0.195911	−	0.980622i	$-0.437234\pi$
$709$	10.4331	0.391823	0.195911	+	0.980622i	$0.437234\pi$
$710$	−15.3106	−0.574598
$711$	−49.6233	−1.86102
$712$	1.02777	0.0385171
$713$	43.7470	1.63834
$714$	0	0
$715$	1.95942	0.0732783
$716$	−11.6131	−0.434003
$717$	−8.43308	−0.314939
$718$	−46.6144	−1.73963
$719$	−7.73373	−0.288420	−0.144210	−	0.989547i	$-0.546064\pi$
$719$	−7.73373	−0.288420	−0.144210	+	0.989547i	$0.546064\pi$
$720$	−13.0632	−0.486839
$721$	0	0
$722$	−2.14243	−0.0797331
$723$	27.1354	1.00918
$724$	7.08114	0.263168
$725$	7.75669	0.288076
$726$	60.3061	2.23817
$727$	39.5241	1.46587	0.732934	−	0.680300i	$-0.238151\pi$
$727$	39.5241	1.46587	0.732934	+	0.680300i	$0.238151\pi$
$728$	0	0
$729$	−40.5373	−1.50138
$730$	0.521277	0.0192933
$731$	−24.0831	−0.890746
$732$	−30.3808	−1.12291
$733$	−50.7498	−1.87449	−0.937243	−	0.348677i	$-0.886631\pi$
$733$	−50.7498	−1.87449	−0.937243	+	0.348677i	$0.886631\pi$
$734$	64.3473	2.37510
$735$	0	0
$736$	−52.0435	−1.91835
$737$	17.4728	0.643619
$738$	31.9288	1.17532
$739$	0.419276	0.0154233	0.00771165	−	0.999970i	$-0.497545\pi$
$739$	0.419276	0.0154233	0.00771165	+	0.999970i	$0.497545\pi$
$740$	−3.64293	−0.133917
$741$	5.10482	0.187530
$742$	0	0
$743$	19.5511	0.717259	0.358630	−	0.933480i	$-0.383244\pi$
$743$	19.5511	0.717259	0.358630	+	0.933480i	$0.383244\pi$
$744$	23.9290	0.877280
$745$	−13.7982	−0.505529
$746$	79.9246	2.92625
$747$	−46.8319	−1.71349
$748$	22.1958	0.811560
$749$	0	0
$750$	−6.16666	−0.225175
$751$	8.76768	0.319937	0.159969	−	0.987122i	$-0.448861\pi$
$751$	8.76768	0.319937	0.159969	+	0.987122i	$0.448861\pi$
$752$	3.62102	0.132045
$753$	42.9732	1.56603
$754$	29.4728	1.07334
$755$	5.02269	0.182794
$756$	0	0
$757$	−48.0535	−1.74653	−0.873267	−	0.487241i	$-0.838003\pi$
$757$	−48.0535	−1.74653	−0.873267	+	0.487241i	$0.838003\pi$
$758$	31.6638	1.15008
$759$	21.1533	0.767815
$760$	1.26409	0.0458533
$761$	−29.3947	−1.06556	−0.532779	−	0.846254i	$-0.678852\pi$
$761$	−29.3947	−1.06556	−0.532779	+	0.846254i	$0.678852\pi$
$762$	−28.5827	−1.03544
$763$	0	0
$764$	−45.9031	−1.66071
$765$	−40.9931	−1.48211
$766$	−62.1350	−2.24503
$767$	−9.55875	−0.345146
$768$	8.38765	0.302663
$769$	13.3790	0.482458	0.241229	−	0.970468i	$-0.422449\pi$
$769$	13.3790	0.482458	0.241229	+	0.970468i	$0.422449\pi$
$770$	0	0
$771$	43.5480	1.56834
$772$	−35.0615	−1.26189
$773$	−0.133625	−0.00480617	−0.00240309	−	0.999997i	$-0.500765\pi$
$773$	−0.133625	−0.00480617	−0.00240309	+	0.999997i	$0.500765\pi$
$774$	−35.1543	−1.26359
$775$	−6.57664	−0.236240
$776$	4.04115	0.145069
$777$	0	0
$778$	−45.4167	−1.62827
$779$	2.81995	0.101035
$780$	−13.2216	−0.473410
$781$	−7.89545	−0.282522
$782$	−110.542	−3.95298
$783$	51.0130	1.82305
$784$	0	0
$785$	−7.18695	−0.256513
$786$	95.6658	3.41229
$787$	4.84060	0.172549	0.0862744	−	0.996271i	$-0.472504\pi$
$787$	4.84060	0.172549	0.0862744	+	0.996271i	$0.472504\pi$
$788$	−55.7202	−1.98495
$789$	−43.8130	−1.55979
$790$	20.1168	0.715723
$791$	0	0
$792$	7.38079	0.262265
$793$	7.22753	0.256657
$794$	22.2505	0.789640
$795$	−7.46492	−0.264753
$796$	−18.3739	−0.651246
$797$	−11.6993	−0.414410	−0.207205	−	0.978298i	$-0.566437\pi$
$797$	−11.6993	−0.414410	−0.207205	+	0.978298i	$0.566437\pi$
$798$	0	0
$799$	11.3629	0.401991
$800$	7.82389	0.276616
$801$	−4.29685	−0.151822
$802$	−54.9831	−1.94152
$803$	0.268814	0.00948624
$804$	−117.901	−4.15806
$805$	0	0
$806$	−24.9890	−0.880200
$807$	−33.1593	−1.16726
$808$	−3.81613	−0.134251
$809$	−33.1987	−1.16720	−0.583601	−	0.812040i	$-0.698357\pi$
$809$	−33.1987	−1.16720	−0.583601	+	0.812040i	$0.698357\pi$
$810$	−6.58848	−0.231496
$811$	26.5766	0.933232	0.466616	−	0.884460i	$-0.345473\pi$
$811$	26.5766	0.933232	0.466616	+	0.884460i	$0.345473\pi$
$812$	0	0
$813$	−6.22061	−0.218166
$814$	−3.32924	−0.116690
$815$	7.25528	0.254141
$816$	55.1869	1.93193
$817$	−3.10482	−0.108624
$818$	12.2464	0.428185
$819$	0	0
$820$	−7.30374	−0.255058
$821$	25.5807	0.892773	0.446387	−	0.894840i	$-0.352711\pi$
$821$	25.5807	0.892773	0.446387	+	0.894840i	$0.352711\pi$
$822$	5.01379	0.174876
$823$	12.9783	0.452395	0.226198	−	0.974081i	$-0.427371\pi$
$823$	12.9783	0.452395	0.226198	+	0.974081i	$0.427371\pi$
$824$	7.65835	0.266791
$825$	−3.18005	−0.110715
$826$	0	0
$827$	−12.5167	−0.435248	−0.217624	−	0.976033i	$-0.569831\pi$
$827$	−12.5167	−0.435248	−0.217624	+	0.976033i	$0.569831\pi$
$828$	−91.0504	−3.16422
$829$	19.4391	0.675149	0.337574	−	0.941299i	$-0.390394\pi$
$829$	19.4391	0.675149	0.337574	+	0.941299i	$0.390394\pi$
$830$	18.9852	0.658986
$831$	67.4124	2.33851
$832$	20.9605	0.726674
$833$	0	0
$834$	−78.7400	−2.72654
$835$	7.33129	0.253710
$836$	2.86151	0.0989673
$837$	−43.2522	−1.49501
$838$	33.0583	1.14198
$839$	43.9972	1.51895	0.759475	−	0.650536i	$-0.225456\pi$
$839$	43.9972	1.51895	0.759475	+	0.650536i	$0.225456\pi$
$840$	0	0
$841$	31.1662	1.07470
$842$	2.52818	0.0871268
$843$	73.9229	2.54604
$844$	28.6468	0.986063
$845$	−9.85461	−0.339009
$846$	16.5865	0.570256
$847$	0	0
$848$	6.41061	0.220141
$849$	−21.2591	−0.729610
$850$	16.6182	0.569999
$851$	9.35601	0.320720
$852$	53.2761	1.82521
$853$	−3.30374	−0.113118	−0.0565590	−	0.998399i	$-0.518013\pi$
$853$	−3.30374	−0.113118	−0.0565590	+	0.998399i	$0.518013\pi$
$854$	0	0
$855$	−5.28487	−0.180739
$856$	−25.7682	−0.880740
$857$	−6.02374	−0.205767	−0.102883	−	0.994693i	$-0.532807\pi$
$857$	−6.02374	−0.205767	−0.102883	+	0.994693i	$0.532807\pi$
$858$	−12.0831	−0.412511
$859$	36.0158	1.22884	0.614421	−	0.788978i	$-0.289390\pi$
$859$	36.0158	1.22884	0.614421	+	0.788978i	$0.289390\pi$
$860$	8.04156	0.274215
$861$	0	0
$862$	30.0487	1.02346
$863$	29.9250	1.01866	0.509329	−	0.860572i	$-0.329894\pi$
$863$	29.9250	1.01866	0.509329	+	0.860572i	$0.329894\pi$
$864$	51.4549	1.75053
$865$	5.77353	0.196306
$866$	54.8236	1.86298
$867$	124.247	4.21966
$868$	0	0
$869$	10.3739	0.351911
$870$	−47.8329	−1.62169
$871$	28.0485	0.950386
$872$	−5.97548	−0.202355
$873$	−16.8951	−0.571813
$874$	−14.2512	−0.482054
$875$	0	0
$876$	−1.81388	−0.0612852
$877$	0.618980	0.0209015	0.0104507	−	0.999945i	$-0.496673\pi$
$877$	0.618980	0.0209015	0.0104507	+	0.999945i	$0.496673\pi$
$878$	−47.0762	−1.58874
$879$	69.5184	2.34480
$880$	2.73091	0.0920591
$881$	21.2423	0.715672	0.357836	−	0.933784i	$-0.383515\pi$
$881$	21.2423	0.715672	0.357836	+	0.933784i	$0.383515\pi$
$882$	0	0
$883$	−48.8971	−1.64552	−0.822760	−	0.568389i	$-0.807567\pi$
$883$	−48.8971	−1.64552	−0.822760	+	0.568389i	$0.807567\pi$
$884$	35.6302	1.19837
$885$	15.5134	0.521477
$886$	41.5034	1.39433
$887$	−58.2797	−1.95684	−0.978421	−	0.206622i	$-0.933753\pi$
$887$	−58.2797	−1.95684	−0.978421	+	0.206622i	$0.933753\pi$
$888$	5.11762	0.171736
$889$	0	0
$890$	1.74190	0.0583887
$891$	−3.39757	−0.113823
$892$	32.7251	1.09572
$893$	1.46492	0.0490216
$894$	85.0892	2.84581
$895$	−4.48379	−0.149877
$896$	0	0
$897$	33.9566	1.13378
$898$	41.1007	1.37155
$899$	−51.0130	−1.70138
$900$	13.6879	0.456265
$901$	20.1168	0.670187
$902$	−6.67483	−0.222247
$903$	0	0
$904$	10.0914	0.335636
$905$	2.73400	0.0908814
$906$	−30.9732	−1.02902
$907$	−36.5154	−1.21247	−0.606237	−	0.795284i	$-0.707322\pi$
$907$	−36.5154	−1.21247	−0.606237	+	0.795284i	$0.707322\pi$
$908$	17.1670	0.569708
$909$	15.9543	0.529172
$910$	0	0
$911$	6.62735	0.219574	0.109787	−	0.993955i	$-0.464983\pi$
$911$	6.62735	0.219574	0.109787	+	0.993955i	$0.464983\pi$
$912$	7.11475	0.235593
$913$	9.79036	0.324014
$914$	−17.9110	−0.592442
$915$	−11.7299	−0.387779
$916$	0.194850	0.00643802
$917$	0	0
$918$	109.292	3.60717
$919$	7.91688	0.261154	0.130577	−	0.991438i	$-0.458317\pi$
$919$	7.91688	0.261154	0.130577	+	0.991438i	$0.458317\pi$
$920$	8.40856	0.277222
$921$	−12.6210	−0.415877
$922$	−53.6182	−1.76582
$923$	−12.6743	−0.417179
$924$	0	0
$925$	−1.40652	−0.0462462
$926$	−69.3611	−2.27935
$927$	−32.0178	−1.05160
$928$	60.6875	1.99217
$929$	−35.8597	−1.17652	−0.588259	−	0.808673i	$-0.700186\pi$
$929$	−35.8597	−1.17652	−0.588259	+	0.808673i	$0.700186\pi$
$930$	40.5559	1.32988
$931$	0	0
$932$	24.6399	0.807106
$933$	45.2254	1.48061
$934$	32.6113	1.06707
$935$	8.56974	0.280260
$936$	11.8481	0.387268
$937$	11.4420	0.373793	0.186896	−	0.982380i	$-0.440157\pi$
$937$	11.4420	0.373793	0.186896	+	0.982380i	$0.440157\pi$
$938$	0	0
$939$	−71.3236	−2.32756
$940$	−3.79418	−0.123752
$941$	0.360100	0.0117389	0.00586945	−	0.999983i	$-0.498132\pi$
$941$	0.360100	0.0117389	0.00586945	+	0.999983i	$0.498132\pi$
$942$	44.3195	1.44401
$943$	18.7579	0.610843
$944$	−13.3223	−0.433605
$945$	0	0
$946$	7.34911	0.238940
$947$	2.63807	0.0857256	0.0428628	−	0.999081i	$-0.486352\pi$
$947$	2.63807	0.0857256	0.0428628	+	0.999081i	$0.486352\pi$
$948$	−70.0000	−2.27349
$949$	0.431517	0.0140076
$950$	2.14243	0.0695097
$951$	−78.8084	−2.55554
$952$	0	0
$953$	10.4430	0.338282	0.169141	−	0.985592i	$-0.445901\pi$
$953$	10.4430	0.338282	0.169141	+	0.985592i	$0.445901\pi$
$954$	29.3646	0.950714
$955$	−17.7230	−0.573503
$956$	−7.58835	−0.245425
$957$	−24.6667	−0.797360
$958$	−42.9525	−1.38773
$959$	0	0
$960$	−34.0178	−1.09792
$961$	12.2522	0.395232
$962$	−5.34432	−0.172308
$963$	107.731	3.47159
$964$	24.4173	0.786428
$965$	−13.5371	−0.435775
$966$	0	0
$967$	33.2732	1.06999	0.534996	−	0.844854i	$-0.320313\pi$
$967$	33.2732	1.06999	0.534996	+	0.844854i	$0.320313\pi$
$968$	12.3620	0.397330
$969$	22.3264	0.717228
$970$	6.84912	0.219912
$971$	−23.5657	−0.756258	−0.378129	−	0.925753i	$-0.623432\pi$
$971$	−23.5657	−0.756258	−0.378129	+	0.925753i	$0.623432\pi$
$972$	−28.1752	−0.903719
$973$	0	0
$974$	67.8098	2.17277
$975$	−5.10482	−0.163485
$976$	10.0732	0.322437
$977$	0.402439	0.0128752	0.00643759	−	0.999979i	$-0.497951\pi$
$977$	0.402439	0.0128752	0.00643759	+	0.999979i	$0.497951\pi$
$978$	−44.7409	−1.43066
$979$	0.898271	0.0287089
$980$	0	0
$981$	24.9821	0.797617
$982$	−53.1395	−1.69575
$983$	−11.4927	−0.366561	−0.183281	−	0.983061i	$-0.558672\pi$
$983$	−11.4927	−0.366561	−0.183281	+	0.983061i	$0.558672\pi$
$984$	10.2603	0.327088
$985$	−21.5134	−0.685473
$986$	128.902	4.10508
$987$	0	0
$988$	4.59348	0.146138
$989$	−20.6529	−0.656723
$990$	12.5093	0.397571
$991$	6.05761	0.192426	0.0962132	−	0.995361i	$-0.469327\pi$
$991$	6.05761	0.192426	0.0962132	+	0.995361i	$0.469327\pi$
$992$	−51.4549	−1.63370
$993$	13.5292	0.429335
$994$	0	0
$995$	−7.09410	−0.224898
$996$	−66.0624	−2.09327
$997$	48.1086	1.52362	0.761808	−	0.647803i	$-0.224312\pi$
$997$	48.1086	1.52362	0.761808	+	0.647803i	$0.224312\pi$
$998$	70.7510	2.23959
$999$	−9.25020	−0.292663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4655.2.a.y.1.2		4
7.6	odd	2		95.2.a.b.1.2	✓	4
21.20	even	2		855.2.a.m.1.3		4
28.27	even	2		1520.2.a.t.1.4		4
35.13	even	4		475.2.b.e.324.7		8
35.27	even	4		475.2.b.e.324.2		8
35.34	odd	2		475.2.a.i.1.3		4
56.13	odd	2		6080.2.a.cc.1.4		4
56.27	even	2		6080.2.a.ch.1.1		4
105.104	even	2		4275.2.a.bo.1.2		4
133.132	even	2		1805.2.a.p.1.3		4
140.139	even	2		7600.2.a.cf.1.1		4
665.664	even	2		9025.2.a.bf.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.a.b.1.2	✓	4	7.6	odd	2
475.2.a.i.1.3		4	35.34	odd	2
475.2.b.e.324.2		8	35.27	even	4
475.2.b.e.324.7		8	35.13	even	4
855.2.a.m.1.3		4	21.20	even	2
1520.2.a.t.1.4		4	28.27	even	2
1805.2.a.p.1.3		4	133.132	even	2
4275.2.a.bo.1.2		4	105.104	even	2
4655.2.a.y.1.2		4	1.1	even	1	trivial
6080.2.a.cc.1.4		4	56.13	odd	2
6080.2.a.ch.1.1		4	56.27	even	2
7600.2.a.cf.1.1		4	140.139	even	2
9025.2.a.bf.1.2		4	665.664	even	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:	\( N \)	\(=\)	\( 4655 = 5 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4655.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14243 q^{2} +2.87834 q^{3} +2.59002 q^{4} +1.00000 q^{5} -6.16666 q^{6} -1.26409 q^{8} +5.28487 q^{9} +O(q^{10})\)	\(q-2.14243 q^{2} +2.87834 q^{3} +2.59002 q^{4} +1.00000 q^{5} -6.16666 q^{6} -1.26409 q^{8} +5.28487 q^{9} -2.14243 q^{10} -1.10482 q^{11} +7.45498 q^{12} -1.77353 q^{13} +2.87834 q^{15} -2.47182 q^{16} -7.75669 q^{17} -11.3225 q^{18} -1.00000 q^{19} +2.59002 q^{20} +2.36700 q^{22} -6.65187 q^{23} -3.63849 q^{24} +1.00000 q^{25} +3.79966 q^{26} +6.57664 q^{27} +7.75669 q^{29} -6.16666 q^{30} -6.57664 q^{31} +7.82389 q^{32} -3.18005 q^{33} +16.6182 q^{34} +13.6879 q^{36} -1.40652 q^{37} +2.14243 q^{38} -5.10482 q^{39} -1.26409 q^{40} -2.81995 q^{41} +3.10482 q^{43} -2.86151 q^{44} +5.28487 q^{45} +14.2512 q^{46} -1.46492 q^{47} -7.11475 q^{48} -2.14243 q^{50} -22.3264 q^{51} -4.59348 q^{52} -2.59348 q^{53} -14.0900 q^{54} -1.10482 q^{55} -2.87834 q^{57} -16.6182 q^{58} +5.38969 q^{59} +7.45498 q^{60} -4.07523 q^{61} +14.0900 q^{62} -11.8185 q^{64} -1.77353 q^{65} +6.81305 q^{66} -15.8151 q^{67} -20.0900 q^{68} -19.1464 q^{69} +7.14638 q^{71} -6.68055 q^{72} -0.243310 q^{73} +3.01339 q^{74} +2.87834 q^{75} -2.59002 q^{76} +10.9367 q^{78} -9.38969 q^{79} -2.47182 q^{80} +3.07523 q^{81} +6.04156 q^{82} -8.86151 q^{83} -7.75669 q^{85} -6.65187 q^{86} +22.3264 q^{87} +1.39659 q^{88} -0.813048 q^{89} -11.3225 q^{90} -17.2285 q^{92} -18.9298 q^{93} +3.13849 q^{94} -1.00000 q^{95} +22.5199 q^{96} -3.19689 q^{97} -5.83882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{5} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^5 - 12 * q^8 + 8 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} + 8 q^{4} + 4 q^{5} - 12 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 6 q^{12} - 2 q^{13} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 34 q^{18} - 4 q^{19} + 8 q^{20} + 4 q^{22} - 8 q^{23} + 24 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{27} + 4 q^{29} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 4 q^{34} + 40 q^{36} - 6 q^{37} + 2 q^{38} - 12 q^{39} - 12 q^{40} - 16 q^{41} + 4 q^{43} + 24 q^{44} + 8 q^{45} + 12 q^{47} - 38 q^{48} - 2 q^{50} - 36 q^{51} - 18 q^{52} - 10 q^{53} + 20 q^{54} + 4 q^{55} + 2 q^{57} - 4 q^{58} - 6 q^{60} - 20 q^{61} - 20 q^{62} - 4 q^{64} - 2 q^{65} + 28 q^{66} - 18 q^{67} - 4 q^{68} - 28 q^{69} - 20 q^{71} - 52 q^{72} - 28 q^{73} + 32 q^{74} - 2 q^{75} - 8 q^{76} + 12 q^{78} - 16 q^{79} + 4 q^{80} + 16 q^{81} - 16 q^{82} - 4 q^{85} - 8 q^{86} + 36 q^{87} - 12 q^{88} - 4 q^{89} - 34 q^{90} - 28 q^{92} - 40 q^{93} + 48 q^{94} - 4 q^{95} + 52 q^{96} - 30 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 + 8 * q^4 + 4 * q^5 - 12 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 6 * q^12 - 2 * q^13 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 34 * q^18 - 4 * q^19 + 8 * q^20 + 4 * q^22 - 8 * q^23 + 24 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^27 + 4 * q^29 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 4 * q^34 + 40 * q^36 - 6 * q^37 + 2 * q^38 - 12 * q^39 - 12 * q^40 - 16 * q^41 + 4 * q^43 + 24 * q^44 + 8 * q^45 + 12 * q^47 - 38 * q^48 - 2 * q^50 - 36 * q^51 - 18 * q^52 - 10 * q^53 + 20 * q^54 + 4 * q^55 + 2 * q^57 - 4 * q^58 - 6 * q^60 - 20 * q^61 - 20 * q^62 - 4 * q^64 - 2 * q^65 + 28 * q^66 - 18 * q^67 - 4 * q^68 - 28 * q^69 - 20 * q^71 - 52 * q^72 - 28 * q^73 + 32 * q^74 - 2 * q^75 - 8 * q^76 + 12 * q^78 - 16 * q^79 + 4 * q^80 + 16 * q^81 - 16 * q^82 - 4 * q^85 - 8 * q^86 + 36 * q^87 - 12 * q^88 - 4 * q^89 - 34 * q^90 - 28 * q^92 - 40 * q^93 + 48 * q^94 - 4 * q^95 + 52 * q^96 - 30 * q^97 - 4 * q^99

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