LMFDB - Embedded newform 4598.2.a.bj.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.56155 q^{6} -3.56155 q^{7} +1.00000 q^{8} -0.561553 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.56155 q^{6} -3.56155 q^{7} +1.00000 q^{8} -0.561553 q^{9} +2.00000 q^{10} -1.56155 q^{12} +3.56155 q^{13} -3.56155 q^{14} -3.12311 q^{15} +1.00000 q^{16} -3.56155 q^{17} -0.561553 q^{18} +1.00000 q^{19} +2.00000 q^{20} +5.56155 q^{21} +5.56155 q^{23} -1.56155 q^{24} -1.00000 q^{25} +3.56155 q^{26} +5.56155 q^{27} -3.56155 q^{28} -6.68466 q^{29} -3.12311 q^{30} +2.00000 q^{31} +1.00000 q^{32} -3.56155 q^{34} -7.12311 q^{35} -0.561553 q^{36} +3.12311 q^{37} +1.00000 q^{38} -5.56155 q^{39} +2.00000 q^{40} -2.00000 q^{41} +5.56155 q^{42} -1.12311 q^{45} +5.56155 q^{46} +8.00000 q^{47} -1.56155 q^{48} +5.68466 q^{49} -1.00000 q^{50} +5.56155 q^{51} +3.56155 q^{52} -7.80776 q^{53} +5.56155 q^{54} -3.56155 q^{56} -1.56155 q^{57} -6.68466 q^{58} +4.68466 q^{59} -3.12311 q^{60} +10.2462 q^{61} +2.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +7.12311 q^{65} +4.68466 q^{67} -3.56155 q^{68} -8.68466 q^{69} -7.12311 q^{70} +6.00000 q^{71} -0.561553 q^{72} -2.68466 q^{73} +3.12311 q^{74} +1.56155 q^{75} +1.00000 q^{76} -5.56155 q^{78} +4.00000 q^{79} +2.00000 q^{80} -7.00000 q^{81} -2.00000 q^{82} +2.24621 q^{83} +5.56155 q^{84} -7.12311 q^{85} +10.4384 q^{87} -9.12311 q^{89} -1.12311 q^{90} -12.6847 q^{91} +5.56155 q^{92} -3.12311 q^{93} +8.00000 q^{94} +2.00000 q^{95} -1.56155 q^{96} +1.12311 q^{97} +5.68466 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 2 q^{8} + 3 q^{9} + 4 q^{10} + q^{12} + 3 q^{13} - 3 q^{14} + 2 q^{15} + 2 q^{16} - 3 q^{17} + 3 q^{18} + 2 q^{19} + 4 q^{20} + 7 q^{21} + 7 q^{23} + q^{24} - 2 q^{25} + 3 q^{26} + 7 q^{27} - 3 q^{28} - q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} - 3 q^{34} - 6 q^{35} + 3 q^{36} - 2 q^{37} + 2 q^{38} - 7 q^{39} + 4 q^{40} - 4 q^{41} + 7 q^{42} + 6 q^{45} + 7 q^{46} + 16 q^{47} + q^{48} - q^{49} - 2 q^{50} + 7 q^{51} + 3 q^{52} + 5 q^{53} + 7 q^{54} - 3 q^{56} + q^{57} - q^{58} - 3 q^{59} + 2 q^{60} + 4 q^{61} + 4 q^{62} + 4 q^{63} + 2 q^{64} + 6 q^{65} - 3 q^{67} - 3 q^{68} - 5 q^{69} - 6 q^{70} + 12 q^{71} + 3 q^{72} + 7 q^{73} - 2 q^{74} - q^{75} + 2 q^{76} - 7 q^{78} + 8 q^{79} + 4 q^{80} - 14 q^{81} - 4 q^{82} - 12 q^{83} + 7 q^{84} - 6 q^{85} + 25 q^{87} - 10 q^{89} + 6 q^{90} - 13 q^{91} + 7 q^{92} + 2 q^{93} + 16 q^{94} + 4 q^{95} + q^{96} - 6 q^{97} - q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 2 * q^8 + 3 * q^9 + 4 * q^10 + q^12 + 3 * q^13 - 3 * q^14 + 2 * q^15 + 2 * q^16 - 3 * q^17 + 3 * q^18 + 2 * q^19 + 4 * q^20 + 7 * q^21 + 7 * q^23 + q^24 - 2 * q^25 + 3 * q^26 + 7 * q^27 - 3 * q^28 - q^29 + 2 * q^30 + 4 * q^31 + 2 * q^32 - 3 * q^34 - 6 * q^35 + 3 * q^36 - 2 * q^37 + 2 * q^38 - 7 * q^39 + 4 * q^40 - 4 * q^41 + 7 * q^42 + 6 * q^45 + 7 * q^46 + 16 * q^47 + q^48 - q^49 - 2 * q^50 + 7 * q^51 + 3 * q^52 + 5 * q^53 + 7 * q^54 - 3 * q^56 + q^57 - q^58 - 3 * q^59 + 2 * q^60 + 4 * q^61 + 4 * q^62 + 4 * q^63 + 2 * q^64 + 6 * q^65 - 3 * q^67 - 3 * q^68 - 5 * q^69 - 6 * q^70 + 12 * q^71 + 3 * q^72 + 7 * q^73 - 2 * q^74 - q^75 + 2 * q^76 - 7 * q^78 + 8 * q^79 + 4 * q^80 - 14 * q^81 - 4 * q^82 - 12 * q^83 + 7 * q^84 - 6 * q^85 + 25 * q^87 - 10 * q^89 + 6 * q^90 - 13 * q^91 + 7 * q^92 + 2 * q^93 + 16 * q^94 + 4 * q^95 + q^96 - 6 * q^97 - q^98

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
$3$	−1.56155	−0.901563	−0.450781	−	0.892634i	$-0.648855\pi$
$3$	−1.56155	−0.901563	−0.450781	+	0.892634i	$0.648855\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	−1.56155	−0.637501
$7$	−3.56155	−1.34614	−0.673070	−	0.739579i	$-0.735025\pi$
$7$	−3.56155	−1.34614	−0.673070	+	0.739579i	$0.735025\pi$
$8$	1.00000	0.353553
$9$	−0.561553	−0.187184
$10$	2.00000	0.632456
$11$	0	0
$11$	0	0
$12$	−1.56155	−0.450781
$13$	3.56155	0.987797	0.493899	−	0.869520i	$-0.335571\pi$
$13$	3.56155	0.987797	0.493899	+	0.869520i	$0.335571\pi$
$14$	−3.56155	−0.951865
$15$	−3.12311	−0.806382
$16$	1.00000	0.250000
$17$	−3.56155	−0.863803	−0.431902	−	0.901921i	$-0.642157\pi$
$17$	−3.56155	−0.863803	−0.431902	+	0.901921i	$0.642157\pi$
$18$	−0.561553	−0.132359
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.00000	0.447214
$21$	5.56155	1.21363
$22$	0	0
$23$	5.56155	1.15966	0.579832	−	0.814736i	$-0.303118\pi$
$23$	5.56155	1.15966	0.579832	+	0.814736i	$0.303118\pi$
$24$	−1.56155	−0.318751
$25$	−1.00000	−0.200000
$26$	3.56155	0.698478
$27$	5.56155	1.07032
$28$	−3.56155	−0.673070
$29$	−6.68466	−1.24131	−0.620655	−	0.784084i	$-0.713133\pi$
$29$	−6.68466	−1.24131	−0.620655	+	0.784084i	$0.713133\pi$
$30$	−3.12311	−0.570198
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.56155	−0.610801
$35$	−7.12311	−1.20402
$36$	−0.561553	−0.0935921
$37$	3.12311	0.513435	0.256718	−	0.966486i	$-0.417359\pi$
$37$	3.12311	0.513435	0.256718	+	0.966486i	$0.417359\pi$
$38$	1.00000	0.162221
$39$	−5.56155	−0.890561
$40$	2.00000	0.316228
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	5.56155	0.858166
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	−1.12311	−0.167423
$46$	5.56155	0.820006
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.56155	−0.225391
$49$	5.68466	0.812094
$50$	−1.00000	−0.141421
$51$	5.56155	0.778773
$52$	3.56155	0.493899
$53$	−7.80776	−1.07248	−0.536239	−	0.844066i	$-0.680156\pi$
$53$	−7.80776	−1.07248	−0.536239	+	0.844066i	$0.680156\pi$
$54$	5.56155	0.756831
$55$	0	0
$56$	−3.56155	−0.475933
$57$	−1.56155	−0.206833
$58$	−6.68466	−0.877739
$59$	4.68466	0.609891	0.304945	−	0.952370i	$-0.401362\pi$
$59$	4.68466	0.609891	0.304945	+	0.952370i	$0.401362\pi$
$60$	−3.12311	−0.403191
$61$	10.2462	1.31189	0.655946	−	0.754807i	$-0.272270\pi$
$61$	10.2462	1.31189	0.655946	+	0.754807i	$0.272270\pi$
$62$	2.00000	0.254000
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	7.12311	0.883513
$66$	0	0
$67$	4.68466	0.572322	0.286161	−	0.958182i	$-0.407621\pi$
$67$	4.68466	0.572322	0.286161	+	0.958182i	$0.407621\pi$
$68$	−3.56155	−0.431902
$69$	−8.68466	−1.04551
$70$	−7.12311	−0.851374
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−0.561553	−0.0661796
$73$	−2.68466	−0.314216	−0.157108	−	0.987581i	$-0.550217\pi$
$73$	−2.68466	−0.314216	−0.157108	+	0.987581i	$0.550217\pi$
$74$	3.12311	0.363054
$75$	1.56155	0.180313
$76$	1.00000	0.114708
$77$	0	0
$78$	−5.56155	−0.629722
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	2.00000	0.223607
$81$	−7.00000	−0.777778
$82$	−2.00000	−0.220863
$83$	2.24621	0.246554	0.123277	−	0.992372i	$-0.460660\pi$
$83$	2.24621	0.246554	0.123277	+	0.992372i	$0.460660\pi$
$84$	5.56155	0.606815
$85$	−7.12311	−0.772609
$86$	0	0
$87$	10.4384	1.11912
$88$	0	0
$89$	−9.12311	−0.967047	−0.483524	−	0.875331i	$-0.660643\pi$
$89$	−9.12311	−0.967047	−0.483524	+	0.875331i	$0.660643\pi$
$90$	−1.12311	−0.118386
$91$	−12.6847	−1.32971
$92$	5.56155	0.579832
$93$	−3.12311	−0.323851
$94$	8.00000	0.825137
$95$	2.00000	0.205196
$96$	−1.56155	−0.159375
$97$	1.12311	0.114034	0.0570170	−	0.998373i	$-0.481841\pi$
$97$	1.12311	0.114034	0.0570170	+	0.998373i	$0.481841\pi$
$98$	5.68466	0.574237
$99$	0	0
$100$	−1.00000	−0.100000
$101$	15.1231	1.50481	0.752403	−	0.658703i	$-0.228895\pi$
$101$	15.1231	1.50481	0.752403	+	0.658703i	$0.228895\pi$
$102$	5.56155	0.550676
$103$	11.3693	1.12025	0.560126	−	0.828407i	$-0.310753\pi$
$103$	11.3693	1.12025	0.560126	+	0.828407i	$0.310753\pi$
$104$	3.56155	0.349239
$105$	11.1231	1.08550
$106$	−7.80776	−0.758357
$107$	−18.9309	−1.83012	−0.915058	−	0.403322i	$-0.867855\pi$
$107$	−18.9309	−1.83012	−0.915058	+	0.403322i	$0.867855\pi$
$108$	5.56155	0.535161
$109$	18.6847	1.78967	0.894833	−	0.446401i	$-0.147295\pi$
$109$	18.6847	1.78967	0.894833	+	0.446401i	$0.147295\pi$
$110$	0	0
$111$	−4.87689	−0.462894
$112$	−3.56155	−0.336535
$113$	5.12311	0.481941	0.240971	−	0.970532i	$-0.422534\pi$
$113$	5.12311	0.481941	0.240971	+	0.970532i	$0.422534\pi$
$114$	−1.56155	−0.146253
$115$	11.1231	1.03723
$116$	−6.68466	−0.620655
$117$	−2.00000	−0.184900
$118$	4.68466	0.431258
$119$	12.6847	1.16280
$120$	−3.12311	−0.285099
$121$	0	0
$122$	10.2462	0.927648
$123$	3.12311	0.281601
$124$	2.00000	0.179605
$125$	−12.0000	−1.07331
$126$	2.00000	0.178174
$127$	14.2462	1.26415	0.632073	−	0.774909i	$-0.282204\pi$
$127$	14.2462	1.26415	0.632073	+	0.774909i	$0.282204\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	7.12311	0.624738
$131$	7.12311	0.622349	0.311174	−	0.950353i	$-0.399278\pi$
$131$	7.12311	0.622349	0.311174	+	0.950353i	$0.399278\pi$
$132$	0	0
$133$	−3.56155	−0.308826
$134$	4.68466	0.404693
$135$	11.1231	0.957325
$136$	−3.56155	−0.305401
$137$	8.43845	0.720945	0.360473	−	0.932770i	$-0.382615\pi$
$137$	8.43845	0.720945	0.360473	+	0.932770i	$0.382615\pi$
$138$	−8.68466	−0.739287
$139$	17.3693	1.47325	0.736623	−	0.676303i	$-0.236419\pi$
$139$	17.3693	1.47325	0.736623	+	0.676303i	$0.236419\pi$
$140$	−7.12311	−0.602012
$141$	−12.4924	−1.05205
$142$	6.00000	0.503509
$143$	0	0
$144$	−0.561553	−0.0467961
$145$	−13.3693	−1.11026
$146$	−2.68466	−0.222184
$147$	−8.87689	−0.732154
$148$	3.12311	0.256718
$149$	15.1231	1.23893	0.619467	−	0.785023i	$-0.287349\pi$
$149$	15.1231	1.23893	0.619467	+	0.785023i	$0.287349\pi$
$150$	1.56155	0.127500
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	1.00000	0.0811107
$153$	2.00000	0.161690
$154$	0	0
$155$	4.00000	0.321288
$156$	−5.56155	−0.445281
$157$	18.4924	1.47586	0.737928	−	0.674879i	$-0.235804\pi$
$157$	18.4924	1.47586	0.737928	+	0.674879i	$0.235804\pi$
$158$	4.00000	0.318223
$159$	12.1922	0.966907
$160$	2.00000	0.158114
$161$	−19.8078	−1.56107
$162$	−7.00000	−0.549972
$163$	−13.3693	−1.04717	−0.523583	−	0.851975i	$-0.675405\pi$
$163$	−13.3693	−1.04717	−0.523583	+	0.851975i	$0.675405\pi$
$164$	−2.00000	−0.156174
$165$	0	0
$166$	2.24621	0.174340
$167$	25.3693	1.96314	0.981568	−	0.191111i	$-0.0612092\pi$
$167$	25.3693	1.96314	0.981568	+	0.191111i	$0.0612092\pi$
$168$	5.56155	0.429083
$169$	−0.315342	−0.0242570
$170$	−7.12311	−0.546317
$171$	−0.561553	−0.0429430
$172$	0	0
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	10.4384	0.791337
$175$	3.56155	0.269228
$176$	0	0
$177$	−7.31534	−0.549855
$178$	−9.12311	−0.683806
$179$	22.2462	1.66276	0.831380	−	0.555704i	$-0.187551\pi$
$179$	22.2462	1.66276	0.831380	+	0.555704i	$0.187551\pi$
$180$	−1.12311	−0.0837114
$181$	−19.1231	−1.42141	−0.710705	−	0.703491i	$-0.751624\pi$
$181$	−19.1231	−1.42141	−0.710705	+	0.703491i	$0.751624\pi$
$182$	−12.6847	−0.940249
$183$	−16.0000	−1.18275
$184$	5.56155	0.410003
$185$	6.24621	0.459231
$186$	−3.12311	−0.228997
$187$	0	0
$188$	8.00000	0.583460
$189$	−19.8078	−1.44080
$190$	2.00000	0.145095
$191$	−20.6847	−1.49669	−0.748345	−	0.663310i	$-0.769151\pi$
$191$	−20.6847	−1.49669	−0.748345	+	0.663310i	$0.769151\pi$
$192$	−1.56155	−0.112695
$193$	1.12311	0.0808429	0.0404215	−	0.999183i	$-0.487130\pi$
$193$	1.12311	0.0808429	0.0404215	+	0.999183i	$0.487130\pi$
$194$	1.12311	0.0806343
$195$	−11.1231	−0.796542
$196$	5.68466	0.406047
$197$	−1.75379	−0.124952	−0.0624761	−	0.998046i	$-0.519900\pi$
$197$	−1.75379	−0.124952	−0.0624761	+	0.998046i	$0.519900\pi$
$198$	0	0
$199$	−0.684658	−0.0485341	−0.0242671	−	0.999706i	$-0.507725\pi$
$199$	−0.684658	−0.0485341	−0.0242671	+	0.999706i	$0.507725\pi$
$200$	−1.00000	−0.0707107
$201$	−7.31534	−0.515984
$202$	15.1231	1.06406
$203$	23.8078	1.67098
$204$	5.56155	0.389387
$205$	−4.00000	−0.279372
$206$	11.3693	0.792138
$207$	−3.12311	−0.217071
$208$	3.56155	0.246949
$209$	0	0
$210$	11.1231	0.767567
$211$	12.6847	0.873248	0.436624	−	0.899644i	$-0.356174\pi$
$211$	12.6847	0.873248	0.436624	+	0.899644i	$0.356174\pi$
$212$	−7.80776	−0.536239
$213$	−9.36932	−0.641975
$214$	−18.9309	−1.29409
$215$	0	0
$216$	5.56155	0.378416
$217$	−7.12311	−0.483548
$218$	18.6847	1.26548
$219$	4.19224	0.283285
$220$	0	0
$221$	−12.6847	−0.853262
$222$	−4.87689	−0.327316
$223$	−24.7386	−1.65662	−0.828311	−	0.560269i	$-0.810698\pi$
$223$	−24.7386	−1.65662	−0.828311	+	0.560269i	$0.810698\pi$
$224$	−3.56155	−0.237966
$225$	0.561553	0.0374369
$226$	5.12311	0.340784
$227$	17.1771	1.14008	0.570041	−	0.821616i	$-0.306927\pi$
$227$	17.1771	1.14008	0.570041	+	0.821616i	$0.306927\pi$
$228$	−1.56155	−0.103416
$229$	21.1231	1.39585	0.697927	−	0.716169i	$-0.254106\pi$
$229$	21.1231	1.39585	0.697927	+	0.716169i	$0.254106\pi$
$230$	11.1231	0.733436
$231$	0	0
$232$	−6.68466	−0.438869
$233$	−20.7386	−1.35863	−0.679317	−	0.733845i	$-0.737724\pi$
$233$	−20.7386	−1.35863	−0.679317	+	0.733845i	$0.737724\pi$
$234$	−2.00000	−0.130744
$235$	16.0000	1.04372
$236$	4.68466	0.304945
$237$	−6.24621	−0.405735
$238$	12.6847	0.822224
$239$	4.93087	0.318951	0.159476	−	0.987202i	$-0.449020\pi$
$239$	4.93087	0.318951	0.159476	+	0.987202i	$0.449020\pi$
$240$	−3.12311	−0.201596
$241$	−21.6155	−1.39238	−0.696189	−	0.717858i	$-0.745123\pi$
$241$	−21.6155	−1.39238	−0.696189	+	0.717858i	$0.745123\pi$
$242$	0	0
$243$	−5.75379	−0.369106
$244$	10.2462	0.655946
$245$	11.3693	0.726359
$246$	3.12311	0.199122
$247$	3.56155	0.226616
$248$	2.00000	0.127000
$249$	−3.50758	−0.222284
$250$	−12.0000	−0.758947
$251$	8.87689	0.560305	0.280152	−	0.959956i	$-0.409615\pi$
$251$	8.87689	0.560305	0.280152	+	0.959956i	$0.409615\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	14.2462	0.893887
$255$	11.1231	0.696556
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	0	0
$259$	−11.1231	−0.691156
$260$	7.12311	0.441756
$261$	3.75379	0.232354
$262$	7.12311	0.440067
$263$	−17.1231	−1.05586	−0.527928	−	0.849289i	$-0.677031\pi$
$263$	−17.1231	−1.05586	−0.527928	+	0.849289i	$0.677031\pi$
$264$	0	0
$265$	−15.6155	−0.959254
$266$	−3.56155	−0.218373
$267$	14.2462	0.871854
$268$	4.68466	0.286161
$269$	11.1231	0.678188	0.339094	−	0.940753i	$-0.389880\pi$
$269$	11.1231	0.678188	0.339094	+	0.940753i	$0.389880\pi$
$270$	11.1231	0.676931
$271$	−13.3153	−0.808849	−0.404425	−	0.914571i	$-0.632528\pi$
$271$	−13.3153	−0.808849	−0.404425	+	0.914571i	$0.632528\pi$
$272$	−3.56155	−0.215951
$273$	19.8078	1.19882
$274$	8.43845	0.509785
$275$	0	0
$276$	−8.68466	−0.522755
$277$	24.4924	1.47161	0.735804	−	0.677195i	$-0.236805\pi$
$277$	24.4924	1.47161	0.735804	+	0.677195i	$0.236805\pi$
$278$	17.3693	1.04174
$279$	−1.12311	−0.0672386
$280$	−7.12311	−0.425687
$281$	0.630683	0.0376234	0.0188117	−	0.999823i	$-0.494012\pi$
$281$	0.630683	0.0376234	0.0188117	+	0.999823i	$0.494012\pi$
$282$	−12.4924	−0.743913
$283$	13.3693	0.794723	0.397362	−	0.917662i	$-0.369926\pi$
$283$	13.3693	0.794723	0.397362	+	0.917662i	$0.369926\pi$
$284$	6.00000	0.356034
$285$	−3.12311	−0.184997
$286$	0	0
$287$	7.12311	0.420464
$288$	−0.561553	−0.0330898
$289$	−4.31534	−0.253844
$290$	−13.3693	−0.785073
$291$	−1.75379	−0.102809
$292$	−2.68466	−0.157108
$293$	24.9309	1.45648	0.728238	−	0.685324i	$-0.240339\pi$
$293$	24.9309	1.45648	0.728238	+	0.685324i	$0.240339\pi$
$294$	−8.87689	−0.517711
$295$	9.36932	0.545503
$296$	3.12311	0.181527
$297$	0	0
$298$	15.1231	0.876058
$299$	19.8078	1.14551
$300$	1.56155	0.0901563
$301$	0	0
$302$	−4.00000	−0.230174
$303$	−23.6155	−1.35668
$304$	1.00000	0.0573539
$305$	20.4924	1.17339
$306$	2.00000	0.114332
$307$	5.75379	0.328386	0.164193	−	0.986428i	$-0.447498\pi$
$307$	5.75379	0.328386	0.164193	+	0.986428i	$0.447498\pi$
$308$	0	0
$309$	−17.7538	−1.00998
$310$	4.00000	0.227185
$311$	15.8078	0.896376	0.448188	−	0.893939i	$-0.352070\pi$
$311$	15.8078	0.896376	0.448188	+	0.893939i	$0.352070\pi$
$312$	−5.56155	−0.314861
$313$	3.56155	0.201311	0.100655	−	0.994921i	$-0.467906\pi$
$313$	3.56155	0.201311	0.100655	+	0.994921i	$0.467906\pi$
$314$	18.4924	1.04359
$315$	4.00000	0.225374
$316$	4.00000	0.225018
$317$	30.0540	1.68800	0.844000	−	0.536344i	$-0.180195\pi$
$317$	30.0540	1.68800	0.844000	+	0.536344i	$0.180195\pi$
$318$	12.1922	0.683707
$319$	0	0
$320$	2.00000	0.111803
$321$	29.5616	1.64996
$322$	−19.8078	−1.10384
$323$	−3.56155	−0.198170
$324$	−7.00000	−0.388889
$325$	−3.56155	−0.197559
$326$	−13.3693	−0.740458
$327$	−29.1771	−1.61350
$328$	−2.00000	−0.110432
$329$	−28.4924	−1.57084
$330$	0	0
$331$	−10.4384	−0.573749	−0.286874	−	0.957968i	$-0.592616\pi$
$331$	−10.4384	−0.573749	−0.286874	+	0.957968i	$0.592616\pi$
$332$	2.24621	0.123277
$333$	−1.75379	−0.0961070
$334$	25.3693	1.38815
$335$	9.36932	0.511900
$336$	5.56155	0.303408
$337$	−2.87689	−0.156714	−0.0783572	−	0.996925i	$-0.524967\pi$
$337$	−2.87689	−0.156714	−0.0783572	+	0.996925i	$0.524967\pi$
$338$	−0.315342	−0.0171523
$339$	−8.00000	−0.434500
$340$	−7.12311	−0.386305
$341$	0	0
$342$	−0.561553	−0.0303653
$343$	4.68466	0.252948
$344$	0	0
$345$	−17.3693	−0.935133
$346$	−18.0000	−0.967686
$347$	31.6155	1.69721	0.848605	−	0.529027i	$-0.177443\pi$
$347$	31.6155	1.69721	0.848605	+	0.529027i	$0.177443\pi$
$348$	10.4384	0.559560
$349$	19.6155	1.05000	0.524998	−	0.851104i	$-0.324066\pi$
$349$	19.6155	1.05000	0.524998	+	0.851104i	$0.324066\pi$
$350$	3.56155	0.190373
$351$	19.8078	1.05726
$352$	0	0
$353$	−23.1771	−1.23359	−0.616796	−	0.787123i	$-0.711570\pi$
$353$	−23.1771	−1.23359	−0.616796	+	0.787123i	$0.711570\pi$
$354$	−7.31534	−0.388806
$355$	12.0000	0.636894
$356$	−9.12311	−0.483524
$357$	−19.8078	−1.04834
$358$	22.2462	1.17575
$359$	−12.9309	−0.682465	−0.341233	−	0.939979i	$-0.610844\pi$
$359$	−12.9309	−0.682465	−0.341233	+	0.939979i	$0.610844\pi$
$360$	−1.12311	−0.0591929
$361$	1.00000	0.0526316
$362$	−19.1231	−1.00509
$363$	0	0
$364$	−12.6847	−0.664857
$365$	−5.36932	−0.281043
$366$	−16.0000	−0.836333
$367$	13.7538	0.717942	0.358971	−	0.933349i	$-0.383128\pi$
$367$	13.7538	0.717942	0.358971	+	0.933349i	$0.383128\pi$
$368$	5.56155	0.289916
$369$	1.12311	0.0584665
$370$	6.24621	0.324725
$371$	27.8078	1.44371
$372$	−3.12311	−0.161925
$373$	−7.56155	−0.391522	−0.195761	−	0.980652i	$-0.562718\pi$
$373$	−7.56155	−0.391522	−0.195761	+	0.980652i	$0.562718\pi$
$374$	0	0
$375$	18.7386	0.967659
$376$	8.00000	0.412568
$377$	−23.8078	−1.22616
$378$	−19.8078	−1.01880
$379$	2.43845	0.125255	0.0626273	−	0.998037i	$-0.480052\pi$
$379$	2.43845	0.125255	0.0626273	+	0.998037i	$0.480052\pi$
$380$	2.00000	0.102598
$381$	−22.2462	−1.13971
$382$	−20.6847	−1.05832
$383$	−2.00000	−0.102195	−0.0510976	−	0.998694i	$-0.516272\pi$
$383$	−2.00000	−0.102195	−0.0510976	+	0.998694i	$0.516272\pi$
$384$	−1.56155	−0.0796877
$385$	0	0
$386$	1.12311	0.0571646
$387$	0	0
$388$	1.12311	0.0570170
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	−11.1231	−0.563240
$391$	−19.8078	−1.00172
$392$	5.68466	0.287119
$393$	−11.1231	−0.561086
$394$	−1.75379	−0.0883546
$395$	8.00000	0.402524
$396$	0	0
$397$	−26.9848	−1.35433	−0.677165	−	0.735831i	$-0.736792\pi$
$397$	−26.9848	−1.35433	−0.677165	+	0.735831i	$0.736792\pi$
$398$	−0.684658	−0.0343188
$399$	5.56155	0.278426
$400$	−1.00000	−0.0500000
$401$	−24.2462	−1.21080	−0.605399	−	0.795922i	$-0.706986\pi$
$401$	−24.2462	−1.21080	−0.605399	+	0.795922i	$0.706986\pi$
$402$	−7.31534	−0.364856
$403$	7.12311	0.354827
$404$	15.1231	0.752403
$405$	−14.0000	−0.695666
$406$	23.8078	1.18156
$407$	0	0
$408$	5.56155	0.275338
$409$	0.246211	0.0121744	0.00608718	−	0.999981i	$-0.498062\pi$
$409$	0.246211	0.0121744	0.00608718	+	0.999981i	$0.498062\pi$
$410$	−4.00000	−0.197546
$411$	−13.1771	−0.649977
$412$	11.3693	0.560126
$413$	−16.6847	−0.820998
$414$	−3.12311	−0.153492
$415$	4.49242	0.220524
$416$	3.56155	0.174619
$417$	−27.1231	−1.32822
$418$	0	0
$419$	−23.1231	−1.12964	−0.564819	−	0.825215i	$-0.691054\pi$
$419$	−23.1231	−1.12964	−0.564819	+	0.825215i	$0.691054\pi$
$420$	11.1231	0.542752
$421$	−1.06913	−0.0521062	−0.0260531	−	0.999661i	$-0.508294\pi$
$421$	−1.06913	−0.0521062	−0.0260531	+	0.999661i	$0.508294\pi$
$422$	12.6847	0.617480
$423$	−4.49242	−0.218429
$424$	−7.80776	−0.379179
$425$	3.56155	0.172761
$426$	−9.36932	−0.453945
$427$	−36.4924	−1.76599
$428$	−18.9309	−0.915058
$429$	0	0
$430$	0	0
$431$	25.8617	1.24572	0.622858	−	0.782335i	$-0.285971\pi$
$431$	25.8617	1.24572	0.622858	+	0.782335i	$0.285971\pi$
$432$	5.56155	0.267580
$433$	31.3693	1.50751	0.753757	−	0.657154i	$-0.228240\pi$
$433$	31.3693	1.50751	0.753757	+	0.657154i	$0.228240\pi$
$434$	−7.12311	−0.341920
$435$	20.8769	1.00097
$436$	18.6847	0.894833
$437$	5.56155	0.266045
$438$	4.19224	0.200313
$439$	−31.6155	−1.50893	−0.754463	−	0.656342i	$-0.772103\pi$
$439$	−31.6155	−1.50893	−0.754463	+	0.656342i	$0.772103\pi$
$440$	0	0
$441$	−3.19224	−0.152011
$442$	−12.6847	−0.603348
$443$	−17.8617	−0.848637	−0.424318	−	0.905513i	$-0.639486\pi$
$443$	−17.8617	−0.848637	−0.424318	+	0.905513i	$0.639486\pi$
$444$	−4.87689	−0.231447
$445$	−18.2462	−0.864953
$446$	−24.7386	−1.17141
$447$	−23.6155	−1.11698
$448$	−3.56155	−0.168268
$449$	−17.6155	−0.831328	−0.415664	−	0.909518i	$-0.636451\pi$
$449$	−17.6155	−0.831328	−0.415664	+	0.909518i	$0.636451\pi$
$450$	0.561553	0.0264719
$451$	0	0
$452$	5.12311	0.240971
$453$	6.24621	0.293473
$454$	17.1771	0.806160
$455$	−25.3693	−1.18933
$456$	−1.56155	−0.0731264
$457$	−32.4384	−1.51741	−0.758703	−	0.651436i	$-0.774167\pi$
$457$	−32.4384	−1.51741	−0.758703	+	0.651436i	$0.774167\pi$
$458$	21.1231	0.987018
$459$	−19.8078	−0.924547
$460$	11.1231	0.518617
$461$	22.7386	1.05904	0.529522	−	0.848296i	$-0.322371\pi$
$461$	22.7386	1.05904	0.529522	+	0.848296i	$0.322371\pi$
$462$	0	0
$463$	36.4924	1.69595	0.847973	−	0.530039i	$-0.177823\pi$
$463$	36.4924	1.69595	0.847973	+	0.530039i	$0.177823\pi$
$464$	−6.68466	−0.310327
$465$	−6.24621	−0.289661
$466$	−20.7386	−0.960699
$467$	26.2462	1.21453	0.607265	−	0.794499i	$-0.292267\pi$
$467$	26.2462	1.21453	0.607265	+	0.794499i	$0.292267\pi$
$468$	−2.00000	−0.0924500
$469$	−16.6847	−0.770426
$470$	16.0000	0.738025
$471$	−28.8769	−1.33058
$472$	4.68466	0.215629
$473$	0	0
$474$	−6.24621	−0.286898
$475$	−1.00000	−0.0458831
$476$	12.6847	0.581400
$477$	4.38447	0.200751
$478$	4.93087	0.225533
$479$	−11.3693	−0.519477	−0.259739	−	0.965679i	$-0.583636\pi$
$479$	−11.3693	−0.519477	−0.259739	+	0.965679i	$0.583636\pi$
$480$	−3.12311	−0.142550
$481$	11.1231	0.507170
$482$	−21.6155	−0.984560
$483$	30.9309	1.40740
$484$	0	0
$485$	2.24621	0.101995
$486$	−5.75379	−0.260997
$487$	22.8769	1.03665	0.518326	−	0.855183i	$-0.326556\pi$
$487$	22.8769	1.03665	0.518326	+	0.855183i	$0.326556\pi$
$488$	10.2462	0.463824
$489$	20.8769	0.944086
$490$	11.3693	0.513613
$491$	14.6307	0.660273	0.330137	−	0.943933i	$-0.392905\pi$
$491$	14.6307	0.660273	0.330137	+	0.943933i	$0.392905\pi$
$492$	3.12311	0.140800
$493$	23.8078	1.07225
$494$	3.56155	0.160242
$495$	0	0
$496$	2.00000	0.0898027
$497$	−21.3693	−0.958545
$498$	−3.50758	−0.157178
$499$	26.2462	1.17494	0.587471	−	0.809245i	$-0.300124\pi$
$499$	26.2462	1.17494	0.587471	+	0.809245i	$0.300124\pi$
$500$	−12.0000	−0.536656
$501$	−39.6155	−1.76989
$502$	8.87689	0.396195
$503$	−9.31534	−0.415351	−0.207675	−	0.978198i	$-0.566590\pi$
$503$	−9.31534	−0.415351	−0.207675	+	0.978198i	$0.566590\pi$
$504$	2.00000	0.0890871
$505$	30.2462	1.34594
$506$	0	0
$507$	0.492423	0.0218693
$508$	14.2462	0.632073
$509$	−6.63068	−0.293900	−0.146950	−	0.989144i	$-0.546946\pi$
$509$	−6.63068	−0.293900	−0.146950	+	0.989144i	$0.546946\pi$
$510$	11.1231	0.492539
$511$	9.56155	0.422978
$512$	1.00000	0.0441942
$513$	5.56155	0.245549
$514$	−22.0000	−0.970378
$515$	22.7386	1.00198
$516$	0	0
$517$	0	0
$518$	−11.1231	−0.488721
$519$	28.1080	1.23380
$520$	7.12311	0.312369
$521$	1.12311	0.0492042	0.0246021	−	0.999697i	$-0.492168\pi$
$521$	1.12311	0.0492042	0.0246021	+	0.999697i	$0.492168\pi$
$522$	3.75379	0.164299
$523$	6.05398	0.264722	0.132361	−	0.991202i	$-0.457744\pi$
$523$	6.05398	0.264722	0.132361	+	0.991202i	$0.457744\pi$
$524$	7.12311	0.311174
$525$	−5.56155	−0.242726
$526$	−17.1231	−0.746603
$527$	−7.12311	−0.310287
$528$	0	0
$529$	7.93087	0.344820
$530$	−15.6155	−0.678295
$531$	−2.63068	−0.114162
$532$	−3.56155	−0.154413
$533$	−7.12311	−0.308536
$534$	14.2462	0.616494
$535$	−37.8617	−1.63691
$536$	4.68466	0.202346
$537$	−34.7386	−1.49908
$538$	11.1231	0.479551
$539$	0	0
$540$	11.1231	0.478662
$541$	−43.2311	−1.85865	−0.929324	−	0.369265i	$-0.879609\pi$
$541$	−43.2311	−1.85865	−0.929324	+	0.369265i	$0.879609\pi$
$542$	−13.3153	−0.571943
$543$	29.8617	1.28149
$544$	−3.56155	−0.152700
$545$	37.3693	1.60073
$546$	19.8078	0.847694
$547$	−6.73863	−0.288123	−0.144062	−	0.989569i	$-0.546016\pi$
$547$	−6.73863	−0.288123	−0.144062	+	0.989569i	$0.546016\pi$
$548$	8.43845	0.360473
$549$	−5.75379	−0.245566
$550$	0	0
$551$	−6.68466	−0.284776
$552$	−8.68466	−0.369644
$553$	−14.2462	−0.605811
$554$	24.4924	1.04058
$555$	−9.75379	−0.414025
$556$	17.3693	0.736623
$557$	−8.87689	−0.376126	−0.188063	−	0.982157i	$-0.560221\pi$
$557$	−8.87689	−0.376126	−0.188063	+	0.982157i	$0.560221\pi$
$558$	−1.12311	−0.0475449
$559$	0	0
$560$	−7.12311	−0.301006
$561$	0	0
$562$	0.630683	0.0266038
$563$	−6.73863	−0.284000	−0.142000	−	0.989867i	$-0.545353\pi$
$563$	−6.73863	−0.284000	−0.142000	+	0.989867i	$0.545353\pi$
$564$	−12.4924	−0.526026
$565$	10.2462	0.431061
$566$	13.3693	0.561954
$567$	24.9309	1.04700
$568$	6.00000	0.251754
$569$	−3.36932	−0.141249	−0.0706246	−	0.997503i	$-0.522499\pi$
$569$	−3.36932	−0.141249	−0.0706246	+	0.997503i	$0.522499\pi$
$570$	−3.12311	−0.130812
$571$	−35.6155	−1.49046	−0.745232	−	0.666806i	$-0.767661\pi$
$571$	−35.6155	−1.49046	−0.745232	+	0.666806i	$0.767661\pi$
$572$	0	0
$573$	32.3002	1.34936
$574$	7.12311	0.297313
$575$	−5.56155	−0.231933
$576$	−0.561553	−0.0233980
$577$	3.94602	0.164275	0.0821376	−	0.996621i	$-0.473825\pi$
$577$	3.94602	0.164275	0.0821376	+	0.996621i	$0.473825\pi$
$578$	−4.31534	−0.179495
$579$	−1.75379	−0.0728850
$580$	−13.3693	−0.555131
$581$	−8.00000	−0.331896
$582$	−1.75379	−0.0726969
$583$	0	0
$584$	−2.68466	−0.111092
$585$	−4.00000	−0.165380
$586$	24.9309	1.02988
$587$	−7.50758	−0.309871	−0.154935	−	0.987925i	$-0.549517\pi$
$587$	−7.50758	−0.309871	−0.154935	+	0.987925i	$0.549517\pi$
$588$	−8.87689	−0.366077
$589$	2.00000	0.0824086
$590$	9.36932	0.385729
$591$	2.73863	0.112652
$592$	3.12311	0.128359
$593$	−34.0000	−1.39621	−0.698106	−	0.715994i	$-0.745974\pi$
$593$	−34.0000	−1.39621	−0.698106	+	0.715994i	$0.745974\pi$
$594$	0	0
$595$	25.3693	1.04004
$596$	15.1231	0.619467
$597$	1.06913	0.0437566
$598$	19.8078	0.810000
$599$	39.8617	1.62871	0.814353	−	0.580370i	$-0.197092\pi$
$599$	39.8617	1.62871	0.814353	+	0.580370i	$0.197092\pi$
$600$	1.56155	0.0637501
$601$	3.36932	0.137437	0.0687187	−	0.997636i	$-0.478109\pi$
$601$	3.36932	0.137437	0.0687187	+	0.997636i	$0.478109\pi$
$602$	0	0
$603$	−2.63068	−0.107130
$604$	−4.00000	−0.162758
$605$	0	0
$606$	−23.6155	−0.959315
$607$	−27.6155	−1.12088	−0.560440	−	0.828195i	$-0.689368\pi$
$607$	−27.6155	−1.12088	−0.560440	+	0.828195i	$0.689368\pi$
$608$	1.00000	0.0405554
$609$	−37.1771	−1.50649
$610$	20.4924	0.829714
$611$	28.4924	1.15268
$612$	2.00000	0.0808452
$613$	−1.75379	−0.0708349	−0.0354174	−	0.999373i	$-0.511276\pi$
$613$	−1.75379	−0.0708349	−0.0354174	+	0.999373i	$0.511276\pi$
$614$	5.75379	0.232204
$615$	6.24621	0.251872
$616$	0	0
$617$	−4.73863	−0.190770	−0.0953851	−	0.995440i	$-0.530408\pi$
$617$	−4.73863	−0.190770	−0.0953851	+	0.995440i	$0.530408\pi$
$618$	−17.7538	−0.714162
$619$	−26.2462	−1.05492	−0.527462	−	0.849579i	$-0.676856\pi$
$619$	−26.2462	−1.05492	−0.527462	+	0.849579i	$0.676856\pi$
$620$	4.00000	0.160644
$621$	30.9309	1.24121
$622$	15.8078	0.633834
$623$	32.4924	1.30178
$624$	−5.56155	−0.222640
$625$	−19.0000	−0.760000
$626$	3.56155	0.142348
$627$	0	0
$628$	18.4924	0.737928
$629$	−11.1231	−0.443507
$630$	4.00000	0.159364
$631$	36.4924	1.45274	0.726370	−	0.687304i	$-0.241206\pi$
$631$	36.4924	1.45274	0.726370	+	0.687304i	$0.241206\pi$
$632$	4.00000	0.159111
$633$	−19.8078	−0.787288
$634$	30.0540	1.19360
$635$	28.4924	1.13069
$636$	12.1922	0.483454
$637$	20.2462	0.802184
$638$	0	0
$639$	−3.36932	−0.133288
$640$	2.00000	0.0790569
$641$	−9.61553	−0.379791	−0.189895	−	0.981804i	$-0.560815\pi$
$641$	−9.61553	−0.379791	−0.189895	+	0.981804i	$0.560815\pi$
$642$	29.5616	1.16670
$643$	−37.3693	−1.47370	−0.736851	−	0.676055i	$-0.763688\pi$
$643$	−37.3693	−1.47370	−0.736851	+	0.676055i	$0.763688\pi$
$644$	−19.8078	−0.780535
$645$	0	0
$646$	−3.56155	−0.140127
$647$	22.5464	0.886390	0.443195	−	0.896425i	$-0.353845\pi$
$647$	22.5464	0.886390	0.443195	+	0.896425i	$0.353845\pi$
$648$	−7.00000	−0.274986
$649$	0	0
$650$	−3.56155	−0.139696
$651$	11.1231	0.435949
$652$	−13.3693	−0.523583
$653$	25.6155	1.00241	0.501207	−	0.865328i	$-0.332890\pi$
$653$	25.6155	1.00241	0.501207	+	0.865328i	$0.332890\pi$
$654$	−29.1771	−1.14091
$655$	14.2462	0.556646
$656$	−2.00000	−0.0780869
$657$	1.50758	0.0588162
$658$	−28.4924	−1.11075
$659$	−47.4233	−1.84735	−0.923675	−	0.383178i	$-0.874830\pi$
$659$	−47.4233	−1.84735	−0.923675	+	0.383178i	$0.874830\pi$
$660$	0	0
$661$	−22.4384	−0.872754	−0.436377	−	0.899764i	$-0.643739\pi$
$661$	−22.4384	−0.872754	−0.436377	+	0.899764i	$0.643739\pi$
$662$	−10.4384	−0.405702
$663$	19.8078	0.769270
$664$	2.24621	0.0871699
$665$	−7.12311	−0.276222
$666$	−1.75379	−0.0679579
$667$	−37.1771	−1.43950
$668$	25.3693	0.981568
$669$	38.6307	1.49355
$670$	9.36932	0.361968
$671$	0	0
$672$	5.56155	0.214542
$673$	18.8769	0.727651	0.363825	−	0.931467i	$-0.381470\pi$
$673$	18.8769	0.727651	0.363825	+	0.931467i	$0.381470\pi$
$674$	−2.87689	−0.110814
$675$	−5.56155	−0.214064
$676$	−0.315342	−0.0121285
$677$	39.1771	1.50570	0.752849	−	0.658194i	$-0.228679\pi$
$677$	39.1771	1.50570	0.752849	+	0.658194i	$0.228679\pi$
$678$	−8.00000	−0.307238
$679$	−4.00000	−0.153506
$680$	−7.12311	−0.273159
$681$	−26.8229	−1.02786
$682$	0	0
$683$	−4.49242	−0.171898	−0.0859489	−	0.996300i	$-0.527392\pi$
$683$	−4.49242	−0.171898	−0.0859489	+	0.996300i	$0.527392\pi$
$684$	−0.561553	−0.0214715
$685$	16.8769	0.644833
$686$	4.68466	0.178861
$687$	−32.9848	−1.25845
$688$	0	0
$689$	−27.8078	−1.05939
$690$	−17.3693	−0.661239
$691$	−43.6155	−1.65921	−0.829606	−	0.558349i	$-0.811435\pi$
$691$	−43.6155	−1.65921	−0.829606	+	0.558349i	$0.811435\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	31.6155	1.20011
$695$	34.7386	1.31771
$696$	10.4384	0.395668
$697$	7.12311	0.269807
$698$	19.6155	0.742459
$699$	32.3845	1.22489
$700$	3.56155	0.134614
$701$	−24.9848	−0.943665	−0.471832	−	0.881688i	$-0.656407\pi$
$701$	−24.9848	−0.943665	−0.471832	+	0.881688i	$0.656407\pi$
$702$	19.8078	0.747596
$703$	3.12311	0.117790
$704$	0	0
$705$	−24.9848	−0.940984
$706$	−23.1771	−0.872281
$707$	−53.8617	−2.02568
$708$	−7.31534	−0.274927
$709$	−9.50758	−0.357065	−0.178532	−	0.983934i	$-0.557135\pi$
$709$	−9.50758	−0.357065	−0.178532	+	0.983934i	$0.557135\pi$
$710$	12.0000	0.450352
$711$	−2.24621	−0.0842395
$712$	−9.12311	−0.341903
$713$	11.1231	0.416564
$714$	−19.8078	−0.741287
$715$	0	0
$716$	22.2462	0.831380
$717$	−7.69981	−0.287555
$718$	−12.9309	−0.482576
$719$	−6.43845	−0.240114	−0.120057	−	0.992767i	$-0.538308\pi$
$719$	−6.43845	−0.240114	−0.120057	+	0.992767i	$0.538308\pi$
$720$	−1.12311	−0.0418557
$721$	−40.4924	−1.50802
$722$	1.00000	0.0372161
$723$	33.7538	1.25532
$724$	−19.1231	−0.710705
$725$	6.68466	0.248262
$726$	0	0
$727$	−39.4233	−1.46213	−0.731064	−	0.682308i	$-0.760976\pi$
$727$	−39.4233	−1.46213	−0.731064	+	0.682308i	$0.760976\pi$
$728$	−12.6847	−0.470125
$729$	29.9848	1.11055
$730$	−5.36932	−0.198727
$731$	0	0
$732$	−16.0000	−0.591377
$733$	48.1080	1.77691	0.888454	−	0.458966i	$-0.151780\pi$
$733$	48.1080	1.77691	0.888454	+	0.458966i	$0.151780\pi$
$734$	13.7538	0.507662
$735$	−17.7538	−0.654858
$736$	5.56155	0.205002
$737$	0	0
$738$	1.12311	0.0413421
$739$	−20.9848	−0.771940	−0.385970	−	0.922511i	$-0.626133\pi$
$739$	−20.9848	−0.771940	−0.385970	+	0.922511i	$0.626133\pi$
$740$	6.24621	0.229615
$741$	−5.56155	−0.204309
$742$	27.8078	1.02086
$743$	25.7538	0.944815	0.472407	−	0.881380i	$-0.343385\pi$
$743$	25.7538	0.944815	0.472407	+	0.881380i	$0.343385\pi$
$744$	−3.12311	−0.114499
$745$	30.2462	1.10814
$746$	−7.56155	−0.276848
$747$	−1.26137	−0.0461510
$748$	0	0
$749$	67.4233	2.46359
$750$	18.7386	0.684238
$751$	−41.2311	−1.50454	−0.752271	−	0.658853i	$-0.771042\pi$
$751$	−41.2311	−1.50454	−0.752271	+	0.658853i	$0.771042\pi$
$752$	8.00000	0.291730
$753$	−13.8617	−0.505150
$754$	−23.8078	−0.867028
$755$	−8.00000	−0.291150
$756$	−19.8078	−0.720401
$757$	−9.50758	−0.345559	−0.172779	−	0.984961i	$-0.555275\pi$
$757$	−9.50758	−0.345559	−0.172779	+	0.984961i	$0.555275\pi$
$758$	2.43845	0.0885684
$759$	0	0
$760$	2.00000	0.0725476
$761$	22.1922	0.804468	0.402234	−	0.915537i	$-0.368234\pi$
$761$	22.1922	0.804468	0.402234	+	0.915537i	$0.368234\pi$
$762$	−22.2462	−0.805895
$763$	−66.5464	−2.40914
$764$	−20.6847	−0.748345
$765$	4.00000	0.144620
$766$	−2.00000	−0.0722629
$767$	16.6847	0.602448
$768$	−1.56155	−0.0563477
$769$	1.31534	0.0474324	0.0237162	−	0.999719i	$-0.492450\pi$
$769$	1.31534	0.0474324	0.0237162	+	0.999719i	$0.492450\pi$
$770$	0	0
$771$	34.3542	1.23723
$772$	1.12311	0.0404215
$773$	9.06913	0.326194	0.163097	−	0.986610i	$-0.447852\pi$
$773$	9.06913	0.326194	0.163097	+	0.986610i	$0.447852\pi$
$774$	0	0
$775$	−2.00000	−0.0718421
$776$	1.12311	0.0403171
$777$	17.3693	0.623121
$778$	18.0000	0.645331
$779$	−2.00000	−0.0716574
$780$	−11.1231	−0.398271
$781$	0	0
$782$	−19.8078	−0.708324
$783$	−37.1771	−1.32860
$784$	5.68466	0.203024
$785$	36.9848	1.32005
$786$	−11.1231	−0.396748
$787$	−3.31534	−0.118179	−0.0590896	−	0.998253i	$-0.518820\pi$
$787$	−3.31534	−0.118179	−0.0590896	+	0.998253i	$0.518820\pi$
$788$	−1.75379	−0.0624761
$789$	26.7386	0.951921
$790$	8.00000	0.284627
$791$	−18.2462	−0.648761
$792$	0	0
$793$	36.4924	1.29588
$794$	−26.9848	−0.957656
$795$	24.3845	0.864828
$796$	−0.684658	−0.0242671
$797$	−35.8078	−1.26838	−0.634188	−	0.773179i	$-0.718665\pi$
$797$	−35.8078	−1.26838	−0.634188	+	0.773179i	$0.718665\pi$
$798$	5.56155	0.196877
$799$	−28.4924	−1.00799
$800$	−1.00000	−0.0353553
$801$	5.12311	0.181016
$802$	−24.2462	−0.856163
$803$	0	0
$804$	−7.31534	−0.257992
$805$	−39.6155	−1.39626
$806$	7.12311	0.250901
$807$	−17.3693	−0.611429
$808$	15.1231	0.532029
$809$	−36.9309	−1.29842	−0.649210	−	0.760609i	$-0.724900\pi$
$809$	−36.9309	−1.29842	−0.649210	+	0.760609i	$0.724900\pi$
$810$	−14.0000	−0.491910
$811$	−20.6847	−0.726337	−0.363168	−	0.931724i	$-0.618305\pi$
$811$	−20.6847	−0.726337	−0.363168	+	0.931724i	$0.618305\pi$
$812$	23.8078	0.835489
$813$	20.7926	0.729229
$814$	0	0
$815$	−26.7386	−0.936613
$816$	5.56155	0.194693
$817$	0	0
$818$	0.246211	0.00860857
$819$	7.12311	0.248901
$820$	−4.00000	−0.139686
$821$	−44.9848	−1.56998	−0.784991	−	0.619507i	$-0.787332\pi$
$821$	−44.9848	−1.56998	−0.784991	+	0.619507i	$0.787332\pi$
$822$	−13.1771	−0.459603
$823$	14.9309	0.520457	0.260229	−	0.965547i	$-0.416202\pi$
$823$	14.9309	0.520457	0.260229	+	0.965547i	$0.416202\pi$
$824$	11.3693	0.396069
$825$	0	0
$826$	−16.6847	−0.580534
$827$	−21.0691	−0.732645	−0.366323	−	0.930488i	$-0.619383\pi$
$827$	−21.0691	−0.732645	−0.366323	+	0.930488i	$0.619383\pi$
$828$	−3.12311	−0.108535
$829$	−33.1771	−1.15229	−0.576144	−	0.817348i	$-0.695443\pi$
$829$	−33.1771	−1.15229	−0.576144	+	0.817348i	$0.695443\pi$
$830$	4.49242	0.155934
$831$	−38.2462	−1.32675
$832$	3.56155	0.123475
$833$	−20.2462	−0.701490
$834$	−27.1231	−0.939196
$835$	50.7386	1.75588
$836$	0	0
$837$	11.1231	0.384471
$838$	−23.1231	−0.798774
$839$	1.12311	0.0387739	0.0193870	−	0.999812i	$-0.493829\pi$
$839$	1.12311	0.0387739	0.0193870	+	0.999812i	$0.493829\pi$
$840$	11.1231	0.383784
$841$	15.6847	0.540850
$842$	−1.06913	−0.0368447
$843$	−0.984845	−0.0339199
$844$	12.6847	0.436624
$845$	−0.630683	−0.0216962
$846$	−4.49242	−0.154453
$847$	0	0
$848$	−7.80776	−0.268120
$849$	−20.8769	−0.716493
$850$	3.56155	0.122160
$851$	17.3693	0.595413
$852$	−9.36932	−0.320988
$853$	−38.3542	−1.31322	−0.656611	−	0.754230i	$-0.728011\pi$
$853$	−38.3542	−1.31322	−0.656611	+	0.754230i	$0.728011\pi$
$854$	−36.4924	−1.24874
$855$	−1.12311	−0.0384094
$856$	−18.9309	−0.647044
$857$	10.0000	0.341593	0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000	0.341593	0.170797	+	0.985306i	$0.445366\pi$
$858$	0	0
$859$	−41.8617	−1.42830	−0.714152	−	0.699991i	$-0.753188\pi$
$859$	−41.8617	−1.42830	−0.714152	+	0.699991i	$0.753188\pi$
$860$	0	0
$861$	−11.1231	−0.379074
$862$	25.8617	0.880854
$863$	−16.2462	−0.553027	−0.276514	−	0.961010i	$-0.589179\pi$
$863$	−16.2462	−0.553027	−0.276514	+	0.961010i	$0.589179\pi$
$864$	5.56155	0.189208
$865$	−36.0000	−1.22404
$866$	31.3693	1.06597
$867$	6.73863	0.228856
$868$	−7.12311	−0.241774
$869$	0	0
$870$	20.8769	0.707793
$871$	16.6847	0.565338
$872$	18.6847	0.632742
$873$	−0.630683	−0.0213454
$874$	5.56155	0.188122
$875$	42.7386	1.44483
$876$	4.19224	0.141643
$877$	40.4384	1.36551	0.682755	−	0.730648i	$-0.260782\pi$
$877$	40.4384	1.36551	0.682755	+	0.730648i	$0.260782\pi$
$878$	−31.6155	−1.06697
$879$	−38.9309	−1.31311
$880$	0	0
$881$	−28.7386	−0.968229	−0.484115	−	0.875005i	$-0.660858\pi$
$881$	−28.7386	−0.968229	−0.484115	+	0.875005i	$0.660858\pi$
$882$	−3.19224	−0.107488
$883$	−54.7386	−1.84210	−0.921051	−	0.389442i	$-0.872668\pi$
$883$	−54.7386	−1.84210	−0.921051	+	0.389442i	$0.872668\pi$
$884$	−12.6847	−0.426631
$885$	−14.6307	−0.491805
$886$	−17.8617	−0.600077
$887$	32.0000	1.07445	0.537227	−	0.843437i	$-0.319472\pi$
$887$	32.0000	1.07445	0.537227	+	0.843437i	$0.319472\pi$
$888$	−4.87689	−0.163658
$889$	−50.7386	−1.70172
$890$	−18.2462	−0.611614
$891$	0	0
$892$	−24.7386	−0.828311
$893$	8.00000	0.267710
$894$	−23.6155	−0.789821
$895$	44.4924	1.48722
$896$	−3.56155	−0.118983
$897$	−30.9309	−1.03275
$898$	−17.6155	−0.587838
$899$	−13.3693	−0.445892
$900$	0.561553	0.0187184
$901$	27.8078	0.926411
$902$	0	0
$903$	0	0
$904$	5.12311	0.170392
$905$	−38.2462	−1.27135
$906$	6.24621	0.207516
$907$	56.7926	1.88577	0.942884	−	0.333122i	$-0.108102\pi$
$907$	56.7926	1.88577	0.942884	+	0.333122i	$0.108102\pi$
$908$	17.1771	0.570041
$909$	−8.49242	−0.281676
$910$	−25.3693	−0.840985
$911$	−46.9848	−1.55668	−0.778339	−	0.627845i	$-0.783937\pi$
$911$	−46.9848	−1.55668	−0.778339	+	0.627845i	$0.783937\pi$
$912$	−1.56155	−0.0517082
$913$	0	0
$914$	−32.4384	−1.07297
$915$	−32.0000	−1.05789
$916$	21.1231	0.697927
$917$	−25.3693	−0.837769
$918$	−19.8078	−0.653754
$919$	−28.4384	−0.938098	−0.469049	−	0.883172i	$-0.655403\pi$
$919$	−28.4384	−0.938098	−0.469049	+	0.883172i	$0.655403\pi$
$920$	11.1231	0.366718
$921$	−8.98485	−0.296061
$922$	22.7386	0.748857
$923$	21.3693	0.703380
$924$	0	0
$925$	−3.12311	−0.102687
$926$	36.4924	1.19922
$927$	−6.38447	−0.209694
$928$	−6.68466	−0.219435
$929$	−16.9309	−0.555484	−0.277742	−	0.960656i	$-0.589586\pi$
$929$	−16.9309	−0.555484	−0.277742	+	0.960656i	$0.589586\pi$
$930$	−6.24621	−0.204821
$931$	5.68466	0.186307
$932$	−20.7386	−0.679317
$933$	−24.6847	−0.808139
$934$	26.2462	0.858802
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	54.3002	1.77391	0.886955	−	0.461856i	$-0.152816\pi$
$937$	54.3002	1.77391	0.886955	+	0.461856i	$0.152816\pi$
$938$	−16.6847	−0.544773
$939$	−5.56155	−0.181494
$940$	16.0000	0.521862
$941$	−20.4384	−0.666274	−0.333137	−	0.942878i	$-0.608107\pi$
$941$	−20.4384	−0.666274	−0.333137	+	0.942878i	$0.608107\pi$
$942$	−28.8769	−0.940860
$943$	−11.1231	−0.362218
$944$	4.68466	0.152473
$945$	−39.6155	−1.28869
$946$	0	0
$947$	28.9848	0.941881	0.470940	−	0.882165i	$-0.343915\pi$
$947$	28.9848	0.941881	0.470940	+	0.882165i	$0.343915\pi$
$948$	−6.24621	−0.202868
$949$	−9.56155	−0.310381
$950$	−1.00000	−0.0324443
$951$	−46.9309	−1.52184
$952$	12.6847	0.411112
$953$	9.12311	0.295526	0.147763	−	0.989023i	$-0.452793\pi$
$953$	9.12311	0.295526	0.147763	+	0.989023i	$0.452793\pi$
$954$	4.38447	0.141953
$955$	−41.3693	−1.33868
$956$	4.93087	0.159476
$957$	0	0
$958$	−11.3693	−0.367326
$959$	−30.0540	−0.970493
$960$	−3.12311	−0.100798
$961$	−27.0000	−0.870968
$962$	11.1231	0.358623
$963$	10.6307	0.342569
$964$	−21.6155	−0.696189
$965$	2.24621	0.0723081
$966$	30.9309	0.995184
$967$	3.86174	0.124185	0.0620926	−	0.998070i	$-0.480223\pi$
$967$	3.86174	0.124185	0.0620926	+	0.998070i	$0.480223\pi$
$968$	0	0
$969$	5.56155	0.178663
$970$	2.24621	0.0721215
$971$	−14.2462	−0.457183	−0.228591	−	0.973522i	$-0.573412\pi$
$971$	−14.2462	−0.457183	−0.228591	+	0.973522i	$0.573412\pi$
$972$	−5.75379	−0.184553
$973$	−61.8617	−1.98320
$974$	22.8769	0.733023
$975$	5.56155	0.178112
$976$	10.2462	0.327973
$977$	55.3693	1.77142	0.885711	−	0.464238i	$-0.153672\pi$
$977$	55.3693	1.77142	0.885711	+	0.464238i	$0.153672\pi$
$978$	20.8769	0.667569
$979$	0	0
$980$	11.3693	0.363180
$981$	−10.4924	−0.334997
$982$	14.6307	0.466884
$983$	−48.2462	−1.53882	−0.769408	−	0.638758i	$-0.779448\pi$
$983$	−48.2462	−1.53882	−0.769408	+	0.638758i	$0.779448\pi$
$984$	3.12311	0.0995610
$985$	−3.50758	−0.111761
$986$	23.8078	0.758194
$987$	44.4924	1.41621
$988$	3.56155	0.113308
$989$	0	0
$990$	0	0
$991$	21.1231	0.670998	0.335499	−	0.942041i	$-0.391095\pi$
$991$	21.1231	0.670998	0.335499	+	0.942041i	$0.391095\pi$
$992$	2.00000	0.0635001
$993$	16.3002	0.517271
$994$	−21.3693	−0.677794
$995$	−1.36932	−0.0434103
$996$	−3.50758	−0.111142
$997$	53.3693	1.69022	0.845112	−	0.534590i	$-0.179534\pi$
$997$	53.3693	1.69022	0.845112	+	0.534590i	$0.179534\pi$
$998$	26.2462	0.830809
$999$	17.3693	0.549541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bj.1.1		2
11.10	odd	2		418.2.a.e.1.1	✓	2
33.32	even	2		3762.2.a.y.1.2		2
44.43	even	2		3344.2.a.k.1.2		2
209.208	even	2		7942.2.a.x.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.e.1.1	✓	2	11.10	odd	2
3344.2.a.k.1.2		2	44.43	even	2
3762.2.a.y.1.2		2	33.32	even	2
4598.2.a.bj.1.1		2	1.1	even	1	trivial
7942.2.a.x.1.2		2	209.208	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.56155 q^{6} -3.56155 q^{7} +1.00000 q^{8} -0.561553 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.56155 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.56155 q^{6} -3.56155 q^{7} +1.00000 q^{8} -0.561553 q^{9} +2.00000 q^{10} -1.56155 q^{12} +3.56155 q^{13} -3.56155 q^{14} -3.12311 q^{15} +1.00000 q^{16} -3.56155 q^{17} -0.561553 q^{18} +1.00000 q^{19} +2.00000 q^{20} +5.56155 q^{21} +5.56155 q^{23} -1.56155 q^{24} -1.00000 q^{25} +3.56155 q^{26} +5.56155 q^{27} -3.56155 q^{28} -6.68466 q^{29} -3.12311 q^{30} +2.00000 q^{31} +1.00000 q^{32} -3.56155 q^{34} -7.12311 q^{35} -0.561553 q^{36} +3.12311 q^{37} +1.00000 q^{38} -5.56155 q^{39} +2.00000 q^{40} -2.00000 q^{41} +5.56155 q^{42} -1.12311 q^{45} +5.56155 q^{46} +8.00000 q^{47} -1.56155 q^{48} +5.68466 q^{49} -1.00000 q^{50} +5.56155 q^{51} +3.56155 q^{52} -7.80776 q^{53} +5.56155 q^{54} -3.56155 q^{56} -1.56155 q^{57} -6.68466 q^{58} +4.68466 q^{59} -3.12311 q^{60} +10.2462 q^{61} +2.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +7.12311 q^{65} +4.68466 q^{67} -3.56155 q^{68} -8.68466 q^{69} -7.12311 q^{70} +6.00000 q^{71} -0.561553 q^{72} -2.68466 q^{73} +3.12311 q^{74} +1.56155 q^{75} +1.00000 q^{76} -5.56155 q^{78} +4.00000 q^{79} +2.00000 q^{80} -7.00000 q^{81} -2.00000 q^{82} +2.24621 q^{83} +5.56155 q^{84} -7.12311 q^{85} +10.4384 q^{87} -9.12311 q^{89} -1.12311 q^{90} -12.6847 q^{91} +5.56155 q^{92} -3.12311 q^{93} +8.00000 q^{94} +2.00000 q^{95} -1.56155 q^{96} +1.12311 q^{97} +5.68466 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 4 q^{5} + q^{6} - 3 q^{7} + 2 q^{8} + 3 q^{9} + 4 q^{10} + q^{12} + 3 q^{13} - 3 q^{14} + 2 q^{15} + 2 q^{16} - 3 q^{17} + 3 q^{18} + 2 q^{19} + 4 q^{20} + 7 q^{21} + 7 q^{23} + q^{24} - 2 q^{25} + 3 q^{26} + 7 q^{27} - 3 q^{28} - q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} - 3 q^{34} - 6 q^{35} + 3 q^{36} - 2 q^{37} + 2 q^{38} - 7 q^{39} + 4 q^{40} - 4 q^{41} + 7 q^{42} + 6 q^{45} + 7 q^{46} + 16 q^{47} + q^{48} - q^{49} - 2 q^{50} + 7 q^{51} + 3 q^{52} + 5 q^{53} + 7 q^{54} - 3 q^{56} + q^{57} - q^{58} - 3 q^{59} + 2 q^{60} + 4 q^{61} + 4 q^{62} + 4 q^{63} + 2 q^{64} + 6 q^{65} - 3 q^{67} - 3 q^{68} - 5 q^{69} - 6 q^{70} + 12 q^{71} + 3 q^{72} + 7 q^{73} - 2 q^{74} - q^{75} + 2 q^{76} - 7 q^{78} + 8 q^{79} + 4 q^{80} - 14 q^{81} - 4 q^{82} - 12 q^{83} + 7 q^{84} - 6 q^{85} + 25 q^{87} - 10 q^{89} + 6 q^{90} - 13 q^{91} + 7 q^{92} + 2 q^{93} + 16 q^{94} + 4 q^{95} + q^{96} - 6 q^{97} - q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 4 * q^5 + q^6 - 3 * q^7 + 2 * q^8 + 3 * q^9 + 4 * q^10 + q^12 + 3 * q^13 - 3 * q^14 + 2 * q^15 + 2 * q^16 - 3 * q^17 + 3 * q^18 + 2 * q^19 + 4 * q^20 + 7 * q^21 + 7 * q^23 + q^24 - 2 * q^25 + 3 * q^26 + 7 * q^27 - 3 * q^28 - q^29 + 2 * q^30 + 4 * q^31 + 2 * q^32 - 3 * q^34 - 6 * q^35 + 3 * q^36 - 2 * q^37 + 2 * q^38 - 7 * q^39 + 4 * q^40 - 4 * q^41 + 7 * q^42 + 6 * q^45 + 7 * q^46 + 16 * q^47 + q^48 - q^49 - 2 * q^50 + 7 * q^51 + 3 * q^52 + 5 * q^53 + 7 * q^54 - 3 * q^56 + q^57 - q^58 - 3 * q^59 + 2 * q^60 + 4 * q^61 + 4 * q^62 + 4 * q^63 + 2 * q^64 + 6 * q^65 - 3 * q^67 - 3 * q^68 - 5 * q^69 - 6 * q^70 + 12 * q^71 + 3 * q^72 + 7 * q^73 - 2 * q^74 - q^75 + 2 * q^76 - 7 * q^78 + 8 * q^79 + 4 * q^80 - 14 * q^81 - 4 * q^82 - 12 * q^83 + 7 * q^84 - 6 * q^85 + 25 * q^87 - 10 * q^89 + 6 * q^90 - 13 * q^91 + 7 * q^92 + 2 * q^93 + 16 * q^94 + 4 * q^95 + q^96 - 6 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more