LMFDB - Embedded newform 4598.2.a.bb.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			$-0.618034$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -2.00000 q^{6} +1.85410 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -2.00000 q^{6} +1.85410 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.618034 q^{10} -2.00000 q^{12} -6.47214 q^{13} +1.85410 q^{14} +1.23607 q^{15} +1.00000 q^{16} +5.61803 q^{17} +1.00000 q^{18} +1.00000 q^{19} -0.618034 q^{20} -3.70820 q^{21} -1.14590 q^{23} -2.00000 q^{24} -4.61803 q^{25} -6.47214 q^{26} +4.00000 q^{27} +1.85410 q^{28} +1.52786 q^{29} +1.23607 q^{30} +2.00000 q^{31} +1.00000 q^{32} +5.61803 q^{34} -1.14590 q^{35} +1.00000 q^{36} +4.00000 q^{37} +1.00000 q^{38} +12.9443 q^{39} -0.618034 q^{40} -9.23607 q^{41} -3.70820 q^{42} +2.09017 q^{43} -0.618034 q^{45} -1.14590 q^{46} +3.61803 q^{47} -2.00000 q^{48} -3.56231 q^{49} -4.61803 q^{50} -11.2361 q^{51} -6.47214 q^{52} -9.23607 q^{53} +4.00000 q^{54} +1.85410 q^{56} -2.00000 q^{57} +1.52786 q^{58} -12.4721 q^{59} +1.23607 q^{60} +10.5623 q^{61} +2.00000 q^{62} +1.85410 q^{63} +1.00000 q^{64} +4.00000 q^{65} +7.23607 q^{67} +5.61803 q^{68} +2.29180 q^{69} -1.14590 q^{70} -12.9443 q^{71} +1.00000 q^{72} -14.0000 q^{73} +4.00000 q^{74} +9.23607 q^{75} +1.00000 q^{76} +12.9443 q^{78} -9.70820 q^{79} -0.618034 q^{80} -11.0000 q^{81} -9.23607 q^{82} +10.7984 q^{83} -3.70820 q^{84} -3.47214 q^{85} +2.09017 q^{86} -3.05573 q^{87} +6.76393 q^{89} -0.618034 q^{90} -12.0000 q^{91} -1.14590 q^{92} -4.00000 q^{93} +3.61803 q^{94} -0.618034 q^{95} -2.00000 q^{96} -4.76393 q^{97} -3.56231 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9} + q^{10} - 4 q^{12} - 4 q^{13} - 3 q^{14} - 2 q^{15} + 2 q^{16} + 9 q^{17} + 2 q^{18} + 2 q^{19} + q^{20} + 6 q^{21} - 9 q^{23} - 4 q^{24} - 7 q^{25} - 4 q^{26} + 8 q^{27} - 3 q^{28} + 12 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 9 q^{34} - 9 q^{35} + 2 q^{36} + 8 q^{37} + 2 q^{38} + 8 q^{39} + q^{40} - 14 q^{41} + 6 q^{42} - 7 q^{43} + q^{45} - 9 q^{46} + 5 q^{47} - 4 q^{48} + 13 q^{49} - 7 q^{50} - 18 q^{51} - 4 q^{52} - 14 q^{53} + 8 q^{54} - 3 q^{56} - 4 q^{57} + 12 q^{58} - 16 q^{59} - 2 q^{60} + q^{61} + 4 q^{62} - 3 q^{63} + 2 q^{64} + 8 q^{65} + 10 q^{67} + 9 q^{68} + 18 q^{69} - 9 q^{70} - 8 q^{71} + 2 q^{72} - 28 q^{73} + 8 q^{74} + 14 q^{75} + 2 q^{76} + 8 q^{78} - 6 q^{79} + q^{80} - 22 q^{81} - 14 q^{82} - 3 q^{83} + 6 q^{84} + 2 q^{85} - 7 q^{86} - 24 q^{87} + 18 q^{89} + q^{90} - 24 q^{91} - 9 q^{92} - 8 q^{93} + 5 q^{94} + q^{95} - 4 q^{96} - 14 q^{97} + 13 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9 + q^10 - 4 * q^12 - 4 * q^13 - 3 * q^14 - 2 * q^15 + 2 * q^16 + 9 * q^17 + 2 * q^18 + 2 * q^19 + q^20 + 6 * q^21 - 9 * q^23 - 4 * q^24 - 7 * q^25 - 4 * q^26 + 8 * q^27 - 3 * q^28 + 12 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 9 * q^34 - 9 * q^35 + 2 * q^36 + 8 * q^37 + 2 * q^38 + 8 * q^39 + q^40 - 14 * q^41 + 6 * q^42 - 7 * q^43 + q^45 - 9 * q^46 + 5 * q^47 - 4 * q^48 + 13 * q^49 - 7 * q^50 - 18 * q^51 - 4 * q^52 - 14 * q^53 + 8 * q^54 - 3 * q^56 - 4 * q^57 + 12 * q^58 - 16 * q^59 - 2 * q^60 + q^61 + 4 * q^62 - 3 * q^63 + 2 * q^64 + 8 * q^65 + 10 * q^67 + 9 * q^68 + 18 * q^69 - 9 * q^70 - 8 * q^71 + 2 * q^72 - 28 * q^73 + 8 * q^74 + 14 * q^75 + 2 * q^76 + 8 * q^78 - 6 * q^79 + q^80 - 22 * q^81 - 14 * q^82 - 3 * q^83 + 6 * q^84 + 2 * q^85 - 7 * q^86 - 24 * q^87 + 18 * q^89 + q^90 - 24 * q^91 - 9 * q^92 - 8 * q^93 + 5 * q^94 + q^95 - 4 * q^96 - 14 * q^97 + 13 * 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
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	1.00000	0.500000
$5$	−0.618034	−0.276393	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034	−0.276393	−0.138197	+	0.990405i	$0.544131\pi$
$6$	−2.00000	−0.816497
$7$	1.85410	0.700785	0.350392	−	0.936603i	$-0.386048\pi$
$7$	1.85410	0.700785	0.350392	+	0.936603i	$0.386048\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.618034	−0.195440
$11$	0	0
$11$	0	0
$12$	−2.00000	−0.577350
$13$	−6.47214	−1.79505	−0.897524	−	0.440966i	$-0.854636\pi$
$13$	−6.47214	−1.79505	−0.897524	+	0.440966i	$0.854636\pi$
$14$	1.85410	0.495530
$15$	1.23607	0.319151
$16$	1.00000	0.250000
$17$	5.61803	1.36257	0.681287	−	0.732017i	$-0.261421\pi$
$17$	5.61803	1.36257	0.681287	+	0.732017i	$0.261421\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.618034	−0.138197
$21$	−3.70820	−0.809196
$22$	0	0
$23$	−1.14590	−0.238936	−0.119468	−	0.992838i	$-0.538119\pi$
$23$	−1.14590	−0.238936	−0.119468	+	0.992838i	$0.538119\pi$
$24$	−2.00000	−0.408248
$25$	−4.61803	−0.923607
$26$	−6.47214	−1.26929
$27$	4.00000	0.769800
$28$	1.85410	0.350392
$29$	1.52786	0.283717	0.141859	−	0.989887i	$-0.454692\pi$
$29$	1.52786	0.283717	0.141859	+	0.989887i	$0.454692\pi$
$30$	1.23607	0.225674
$31$	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
$34$	5.61803	0.963485
$35$	−1.14590	−0.193692
$36$	1.00000	0.166667
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	1.00000	0.162221
$39$	12.9443	2.07274
$40$	−0.618034	−0.0977198
$41$	−9.23607	−1.44243	−0.721216	−	0.692711i	$-0.756416\pi$
$41$	−9.23607	−1.44243	−0.721216	+	0.692711i	$0.756416\pi$
$42$	−3.70820	−0.572188
$43$	2.09017	0.318748	0.159374	−	0.987218i	$-0.449052\pi$
$43$	2.09017	0.318748	0.159374	+	0.987218i	$0.449052\pi$
$44$	0	0
$45$	−0.618034	−0.0921311
$46$	−1.14590	−0.168953
$47$	3.61803	0.527744	0.263872	−	0.964558i	$-0.415000\pi$
$47$	3.61803	0.527744	0.263872	+	0.964558i	$0.415000\pi$
$48$	−2.00000	−0.288675
$49$	−3.56231	−0.508901
$50$	−4.61803	−0.653089
$51$	−11.2361	−1.57336
$52$	−6.47214	−0.897524
$53$	−9.23607	−1.26867	−0.634336	−	0.773058i	$-0.718726\pi$
$53$	−9.23607	−1.26867	−0.634336	+	0.773058i	$0.718726\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	1.85410	0.247765
$57$	−2.00000	−0.264906
$58$	1.52786	0.200618
$59$	−12.4721	−1.62373	−0.811867	−	0.583843i	$-0.801549\pi$
$59$	−12.4721	−1.62373	−0.811867	+	0.583843i	$0.801549\pi$
$60$	1.23607	0.159576
$61$	10.5623	1.35236	0.676182	−	0.736734i	$-0.263633\pi$
$61$	10.5623	1.35236	0.676182	+	0.736734i	$0.263633\pi$
$62$	2.00000	0.254000
$63$	1.85410	0.233595
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	7.23607	0.884026	0.442013	−	0.897009i	$-0.354264\pi$
$67$	7.23607	0.884026	0.442013	+	0.897009i	$0.354264\pi$
$68$	5.61803	0.681287
$69$	2.29180	0.275900
$70$	−1.14590	−0.136961
$71$	−12.9443	−1.53620	−0.768101	−	0.640328i	$-0.778798\pi$
$71$	−12.9443	−1.53620	−0.768101	+	0.640328i	$0.778798\pi$
$72$	1.00000	0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	4.00000	0.464991
$75$	9.23607	1.06649
$76$	1.00000	0.114708
$77$	0	0
$78$	12.9443	1.46565
$79$	−9.70820	−1.09226	−0.546129	−	0.837701i	$-0.683899\pi$
$79$	−9.70820	−1.09226	−0.546129	+	0.837701i	$0.683899\pi$
$80$	−0.618034	−0.0690983
$81$	−11.0000	−1.22222
$82$	−9.23607	−1.01995
$83$	10.7984	1.18528	0.592638	−	0.805469i	$-0.298087\pi$
$83$	10.7984	1.18528	0.592638	+	0.805469i	$0.298087\pi$
$84$	−3.70820	−0.404598
$85$	−3.47214	−0.376606
$86$	2.09017	0.225389
$87$	−3.05573	−0.327608
$88$	0	0
$89$	6.76393	0.716975	0.358488	−	0.933534i	$-0.383293\pi$
$89$	6.76393	0.716975	0.358488	+	0.933534i	$0.383293\pi$
$90$	−0.618034	−0.0651465
$91$	−12.0000	−1.25794
$92$	−1.14590	−0.119468
$93$	−4.00000	−0.414781
$94$	3.61803	0.373172
$95$	−0.618034	−0.0634089
$96$	−2.00000	−0.204124
$97$	−4.76393	−0.483704	−0.241852	−	0.970313i	$-0.577755\pi$
$97$	−4.76393	−0.483704	−0.241852	+	0.970313i	$0.577755\pi$
$98$	−3.56231	−0.359847
$99$	0	0
$100$	−4.61803	−0.461803
$101$	5.56231	0.553470	0.276735	−	0.960946i	$-0.410748\pi$
$101$	5.56231	0.553470	0.276735	+	0.960946i	$0.410748\pi$
$102$	−11.2361	−1.11254
$103$	−9.23607	−0.910057	−0.455028	−	0.890477i	$-0.650371\pi$
$103$	−9.23607	−0.910057	−0.455028	+	0.890477i	$0.650371\pi$
$104$	−6.47214	−0.634645
$105$	2.29180	0.223656
$106$	−9.23607	−0.897086
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	4.00000	0.384900
$109$	−1.23607	−0.118394	−0.0591969	−	0.998246i	$-0.518854\pi$
$109$	−1.23607	−0.118394	−0.0591969	+	0.998246i	$0.518854\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	1.85410	0.175196
$113$	14.4721	1.36142	0.680712	−	0.732551i	$-0.261671\pi$
$113$	14.4721	1.36142	0.680712	+	0.732551i	$0.261671\pi$
$114$	−2.00000	−0.187317
$115$	0.708204	0.0660404
$116$	1.52786	0.141859
$117$	−6.47214	−0.598349
$118$	−12.4721	−1.14815
$119$	10.4164	0.954871
$120$	1.23607	0.112837
$121$	0	0
$122$	10.5623	0.956266
$123$	18.4721	1.66558
$124$	2.00000	0.179605
$125$	5.94427	0.531672
$126$	1.85410	0.165177
$127$	7.41641	0.658100	0.329050	−	0.944313i	$-0.393272\pi$
$127$	7.41641	0.658100	0.329050	+	0.944313i	$0.393272\pi$
$128$	1.00000	0.0883883
$129$	−4.18034	−0.368058
$130$	4.00000	0.350823
$131$	−0.909830	−0.0794922	−0.0397461	−	0.999210i	$-0.512655\pi$
$131$	−0.909830	−0.0794922	−0.0397461	+	0.999210i	$0.512655\pi$
$132$	0	0
$133$	1.85410	0.160771
$134$	7.23607	0.625101
$135$	−2.47214	−0.212768
$136$	5.61803	0.481742
$137$	−15.0902	−1.28924	−0.644620	−	0.764503i	$-0.722984\pi$
$137$	−15.0902	−1.28924	−0.644620	+	0.764503i	$0.722984\pi$
$138$	2.29180	0.195091
$139$	5.32624	0.451766	0.225883	−	0.974154i	$-0.427473\pi$
$139$	5.32624	0.451766	0.225883	+	0.974154i	$0.427473\pi$
$140$	−1.14590	−0.0968461
$141$	−7.23607	−0.609387
$142$	−12.9443	−1.08626
$143$	0	0
$144$	1.00000	0.0833333
$145$	−0.944272	−0.0784175
$146$	−14.0000	−1.15865
$147$	7.12461	0.587628
$148$	4.00000	0.328798
$149$	−20.4721	−1.67714	−0.838571	−	0.544792i	$-0.816609\pi$
$149$	−20.4721	−1.67714	−0.838571	+	0.544792i	$0.816609\pi$
$150$	9.23607	0.754122
$151$	−0.291796	−0.0237460	−0.0118730	−	0.999930i	$-0.503779\pi$
$151$	−0.291796	−0.0237460	−0.0118730	+	0.999930i	$0.503779\pi$
$152$	1.00000	0.0811107
$153$	5.61803	0.454191
$154$	0	0
$155$	−1.23607	−0.0992834
$156$	12.9443	1.03637
$157$	7.67376	0.612433	0.306216	−	0.951962i	$-0.400937\pi$
$157$	7.67376	0.612433	0.306216	+	0.951962i	$0.400937\pi$
$158$	−9.70820	−0.772343
$159$	18.4721	1.46494
$160$	−0.618034	−0.0488599
$161$	−2.12461	−0.167443
$162$	−11.0000	−0.864242
$163$	−16.3262	−1.27877	−0.639385	−	0.768887i	$-0.720811\pi$
$163$	−16.3262	−1.27877	−0.639385	+	0.768887i	$0.720811\pi$
$164$	−9.23607	−0.721216
$165$	0	0
$166$	10.7984	0.838116
$167$	−25.4164	−1.96678	−0.983390	−	0.181503i	$-0.941904\pi$
$167$	−25.4164	−1.96678	−0.983390	+	0.181503i	$0.941904\pi$
$168$	−3.70820	−0.286094
$169$	28.8885	2.22220
$170$	−3.47214	−0.266301
$171$	1.00000	0.0764719
$172$	2.09017	0.159374
$173$	−3.05573	−0.232323	−0.116161	−	0.993230i	$-0.537059\pi$
$173$	−3.05573	−0.232323	−0.116161	+	0.993230i	$0.537059\pi$
$174$	−3.05573	−0.231654
$175$	−8.56231	−0.647249
$176$	0	0
$177$	24.9443	1.87493
$178$	6.76393	0.506978
$179$	−20.1803	−1.50835	−0.754175	−	0.656674i	$-0.771963\pi$
$179$	−20.1803	−1.50835	−0.754175	+	0.656674i	$0.771963\pi$
$180$	−0.618034	−0.0460655
$181$	−13.7082	−1.01892	−0.509461	−	0.860494i	$-0.670155\pi$
$181$	−13.7082	−1.01892	−0.509461	+	0.860494i	$0.670155\pi$
$182$	−12.0000	−0.889499
$183$	−21.1246	−1.56158
$184$	−1.14590	−0.0844767
$185$	−2.47214	−0.181755
$186$	−4.00000	−0.293294
$187$	0	0
$188$	3.61803	0.263872
$189$	7.41641	0.539464
$190$	−0.618034	−0.0448369
$191$	−24.0344	−1.73907	−0.869536	−	0.493870i	$-0.835582\pi$
$191$	−24.0344	−1.73907	−0.869536	+	0.493870i	$0.835582\pi$
$192$	−2.00000	−0.144338
$193$	−21.1246	−1.52058	−0.760291	−	0.649582i	$-0.774944\pi$
$193$	−21.1246	−1.52058	−0.760291	+	0.649582i	$0.774944\pi$
$194$	−4.76393	−0.342030
$195$	−8.00000	−0.572892
$196$	−3.56231	−0.254450
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	−5.56231	−0.394301	−0.197151	−	0.980373i	$-0.563169\pi$
$199$	−5.56231	−0.394301	−0.197151	+	0.980373i	$0.563169\pi$
$200$	−4.61803	−0.326544
$201$	−14.4721	−1.02079
$202$	5.56231	0.391362
$203$	2.83282	0.198825
$204$	−11.2361	−0.786682
$205$	5.70820	0.398678
$206$	−9.23607	−0.643507
$207$	−1.14590	−0.0796454
$208$	−6.47214	−0.448762
$209$	0	0
$210$	2.29180	0.158149
$211$	−11.4164	−0.785938	−0.392969	−	0.919552i	$-0.628552\pi$
$211$	−11.4164	−0.785938	−0.392969	+	0.919552i	$0.628552\pi$
$212$	−9.23607	−0.634336
$213$	25.8885	1.77385
$214$	6.00000	0.410152
$215$	−1.29180	−0.0880998
$216$	4.00000	0.272166
$217$	3.70820	0.251729
$218$	−1.23607	−0.0837171
$219$	28.0000	1.89206
$220$	0	0
$221$	−36.3607	−2.44588
$222$	−8.00000	−0.536925
$223$	3.70820	0.248320	0.124160	−	0.992262i	$-0.460376\pi$
$223$	3.70820	0.248320	0.124160	+	0.992262i	$0.460376\pi$
$224$	1.85410	0.123882
$225$	−4.61803	−0.307869
$226$	14.4721	0.962672
$227$	0	0		−	1.00000i	$-0.5\pi$
$227$	0	0			1.00000i	$0.5\pi$
$228$	−2.00000	−0.132453
$229$	24.2705	1.60384	0.801920	−	0.597431i	$-0.203812\pi$
$229$	24.2705	1.60384	0.801920	+	0.597431i	$0.203812\pi$
$230$	0.708204	0.0466976
$231$	0	0
$232$	1.52786	0.100309
$233$	−18.7984	−1.23152	−0.615761	−	0.787933i	$-0.711151\pi$
$233$	−18.7984	−1.23152	−0.615761	+	0.787933i	$0.711151\pi$
$234$	−6.47214	−0.423097
$235$	−2.23607	−0.145865
$236$	−12.4721	−0.811867
$237$	19.4164	1.26123
$238$	10.4164	0.675195
$239$	2.67376	0.172951	0.0864756	−	0.996254i	$-0.472440\pi$
$239$	2.67376	0.172951	0.0864756	+	0.996254i	$0.472440\pi$
$240$	1.23607	0.0797878
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	0	0
$243$	10.0000	0.641500
$244$	10.5623	0.676182
$245$	2.20163	0.140657
$246$	18.4721	1.17774
$247$	−6.47214	−0.411812
$248$	2.00000	0.127000
$249$	−21.5967	−1.36864
$250$	5.94427	0.375949
$251$	10.8541	0.685105	0.342552	−	0.939499i	$-0.388709\pi$
$251$	10.8541	0.685105	0.342552	+	0.939499i	$0.388709\pi$
$252$	1.85410	0.116797
$253$	0	0
$254$	7.41641	0.465347
$255$	6.94427	0.434867
$256$	1.00000	0.0625000
$257$	−10.9443	−0.682685	−0.341342	−	0.939939i	$-0.610882\pi$
$257$	−10.9443	−0.682685	−0.341342	+	0.939939i	$0.610882\pi$
$258$	−4.18034	−0.260257
$259$	7.41641	0.460833
$260$	4.00000	0.248069
$261$	1.52786	0.0945724
$262$	−0.909830	−0.0562095
$263$	6.47214	0.399089	0.199544	−	0.979889i	$-0.436054\pi$
$263$	6.47214	0.399089	0.199544	+	0.979889i	$0.436054\pi$
$264$	0	0
$265$	5.70820	0.350652
$266$	1.85410	0.113682
$267$	−13.5279	−0.827892
$268$	7.23607	0.442013
$269$	18.6525	1.13726	0.568631	−	0.822593i	$-0.307473\pi$
$269$	18.6525	1.13726	0.568631	+	0.822593i	$0.307473\pi$
$270$	−2.47214	−0.150449
$271$	−31.2148	−1.89616	−0.948081	−	0.318028i	$-0.896980\pi$
$271$	−31.2148	−1.89616	−0.948081	+	0.318028i	$0.896980\pi$
$272$	5.61803	0.340643
$273$	24.0000	1.45255
$274$	−15.0902	−0.911631
$275$	0	0
$276$	2.29180	0.137950
$277$	−3.52786	−0.211969	−0.105984	−	0.994368i	$-0.533799\pi$
$277$	−3.52786	−0.211969	−0.105984	+	0.994368i	$0.533799\pi$
$278$	5.32624	0.319447
$279$	2.00000	0.119737
$280$	−1.14590	−0.0684805
$281$	4.65248	0.277543	0.138772	−	0.990324i	$-0.455685\pi$
$281$	4.65248	0.277543	0.138772	+	0.990324i	$0.455685\pi$
$282$	−7.23607	−0.430902
$283$	−9.56231	−0.568420	−0.284210	−	0.958762i	$-0.591731\pi$
$283$	−9.56231	−0.568420	−0.284210	+	0.958762i	$0.591731\pi$
$284$	−12.9443	−0.768101
$285$	1.23607	0.0732183
$286$	0	0
$287$	−17.1246	−1.01083
$288$	1.00000	0.0589256
$289$	14.5623	0.856606
$290$	−0.944272	−0.0554496
$291$	9.52786	0.558533
$292$	−14.0000	−0.819288
$293$	0.652476	0.0381180	0.0190590	−	0.999818i	$-0.493933\pi$
$293$	0.652476	0.0381180	0.0190590	+	0.999818i	$0.493933\pi$
$294$	7.12461	0.415516
$295$	7.70820	0.448789
$296$	4.00000	0.232495
$297$	0	0
$298$	−20.4721	−1.18592
$299$	7.41641	0.428902
$300$	9.23607	0.533245
$301$	3.87539	0.223374
$302$	−0.291796	−0.0167910
$303$	−11.1246	−0.639092
$304$	1.00000	0.0573539
$305$	−6.52786	−0.373784
$306$	5.61803	0.321162
$307$	−27.4164	−1.56474	−0.782369	−	0.622816i	$-0.785989\pi$
$307$	−27.4164	−1.56474	−0.782369	+	0.622816i	$0.785989\pi$
$308$	0	0
$309$	18.4721	1.05084
$310$	−1.23607	−0.0702039
$311$	−4.20163	−0.238252	−0.119126	−	0.992879i	$-0.538009\pi$
$311$	−4.20163	−0.238252	−0.119126	+	0.992879i	$0.538009\pi$
$312$	12.9443	0.732825
$313$	−0.0901699	−0.00509671	−0.00254835	−	0.999997i	$-0.500811\pi$
$313$	−0.0901699	−0.00509671	−0.00254835	+	0.999997i	$0.500811\pi$
$314$	7.67376	0.433055
$315$	−1.14590	−0.0645640
$316$	−9.70820	−0.546129
$317$	2.18034	0.122460	0.0612300	−	0.998124i	$-0.480498\pi$
$317$	2.18034	0.122460	0.0612300	+	0.998124i	$0.480498\pi$
$318$	18.4721	1.03587
$319$	0	0
$320$	−0.618034	−0.0345492
$321$	−12.0000	−0.669775
$322$	−2.12461	−0.118400
$323$	5.61803	0.312596
$324$	−11.0000	−0.611111
$325$	29.8885	1.65792
$326$	−16.3262	−0.904227
$327$	2.47214	0.136709
$328$	−9.23607	−0.509977
$329$	6.70820	0.369835
$330$	0	0
$331$	−9.70820	−0.533611	−0.266806	−	0.963750i	$-0.585968\pi$
$331$	−9.70820	−0.533611	−0.266806	+	0.963750i	$0.585968\pi$
$332$	10.7984	0.592638
$333$	4.00000	0.219199
$334$	−25.4164	−1.39072
$335$	−4.47214	−0.244339
$336$	−3.70820	−0.202299
$337$	−17.0557	−0.929085	−0.464542	−	0.885551i	$-0.653781\pi$
$337$	−17.0557	−0.929085	−0.464542	+	0.885551i	$0.653781\pi$
$338$	28.8885	1.57133
$339$	−28.9443	−1.57204
$340$	−3.47214	−0.188303
$341$	0	0
$342$	1.00000	0.0540738
$343$	−19.5836	−1.05741
$344$	2.09017	0.112694
$345$	−1.41641	−0.0762568
$346$	−3.05573	−0.164277
$347$	8.56231	0.459649	0.229824	−	0.973232i	$-0.426185\pi$
$347$	8.56231	0.459649	0.229824	+	0.973232i	$0.426185\pi$
$348$	−3.05573	−0.163804
$349$	20.9787	1.12296	0.561482	−	0.827489i	$-0.310231\pi$
$349$	20.9787	1.12296	0.561482	+	0.827489i	$0.310231\pi$
$350$	−8.56231	−0.457675
$351$	−25.8885	−1.38183
$352$	0	0
$353$	15.3820	0.818699	0.409350	−	0.912378i	$-0.365756\pi$
$353$	15.3820	0.818699	0.409350	+	0.912378i	$0.365756\pi$
$354$	24.9443	1.32577
$355$	8.00000	0.424596
$356$	6.76393	0.358488
$357$	−20.8328	−1.10259
$358$	−20.1803	−1.06656
$359$	−6.09017	−0.321427	−0.160713	−	0.987001i	$-0.551379\pi$
$359$	−6.09017	−0.321427	−0.160713	+	0.987001i	$0.551379\pi$
$360$	−0.618034	−0.0325733
$361$	1.00000	0.0526316
$362$	−13.7082	−0.720487
$363$	0	0
$364$	−12.0000	−0.628971
$365$	8.65248	0.452891
$366$	−21.1246	−1.10420
$367$	−21.5623	−1.12554	−0.562772	−	0.826612i	$-0.690265\pi$
$367$	−21.5623	−1.12554	−0.562772	+	0.826612i	$0.690265\pi$
$368$	−1.14590	−0.0597341
$369$	−9.23607	−0.480810
$370$	−2.47214	−0.128520
$371$	−17.1246	−0.889066
$372$	−4.00000	−0.207390
$373$	−30.3607	−1.57202	−0.786008	−	0.618216i	$-0.787856\pi$
$373$	−30.3607	−1.57202	−0.786008	+	0.618216i	$0.787856\pi$
$374$	0	0
$375$	−11.8885	−0.613922
$376$	3.61803	0.186586
$377$	−9.88854	−0.509286
$378$	7.41641	0.381459
$379$	1.23607	0.0634925	0.0317463	−	0.999496i	$-0.489893\pi$
$379$	1.23607	0.0634925	0.0317463	+	0.999496i	$0.489893\pi$
$380$	−0.618034	−0.0317045
$381$	−14.8328	−0.759908
$382$	−24.0344	−1.22971
$383$	14.9443	0.763617	0.381808	−	0.924242i	$-0.375301\pi$
$383$	14.9443	0.763617	0.381808	+	0.924242i	$0.375301\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	−21.1246	−1.07521
$387$	2.09017	0.106249
$388$	−4.76393	−0.241852
$389$	13.0344	0.660872	0.330436	−	0.943828i	$-0.392804\pi$
$389$	13.0344	0.660872	0.330436	+	0.943828i	$0.392804\pi$
$390$	−8.00000	−0.405096
$391$	−6.43769	−0.325568
$392$	−3.56231	−0.179924
$393$	1.81966	0.0917897
$394$	−18.0000	−0.906827
$395$	6.00000	0.301893
$396$	0	0
$397$	20.8541	1.04664	0.523319	−	0.852137i	$-0.324694\pi$
$397$	20.8541	1.04664	0.523319	+	0.852137i	$0.324694\pi$
$398$	−5.56231	−0.278813
$399$	−3.70820	−0.185642
$400$	−4.61803	−0.230902
$401$	12.4721	0.622829	0.311414	−	0.950274i	$-0.399197\pi$
$401$	12.4721	0.622829	0.311414	+	0.950274i	$0.399197\pi$
$402$	−14.4721	−0.721805
$403$	−12.9443	−0.644800
$404$	5.56231	0.276735
$405$	6.79837	0.337814
$406$	2.83282	0.140590
$407$	0	0
$408$	−11.2361	−0.556268
$409$	−22.9443	−1.13452	−0.567261	−	0.823538i	$-0.691997\pi$
$409$	−22.9443	−1.13452	−0.567261	+	0.823538i	$0.691997\pi$
$410$	5.70820	0.281908
$411$	30.1803	1.48869
$412$	−9.23607	−0.455028
$413$	−23.1246	−1.13789
$414$	−1.14590	−0.0563178
$415$	−6.67376	−0.327602
$416$	−6.47214	−0.317323
$417$	−10.6525	−0.521654
$418$	0	0
$419$	9.32624	0.455617	0.227808	−	0.973706i	$-0.426844\pi$
$419$	9.32624	0.455617	0.227808	+	0.973706i	$0.426844\pi$
$420$	2.29180	0.111828
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	−11.4164	−0.555742
$423$	3.61803	0.175915
$424$	−9.23607	−0.448543
$425$	−25.9443	−1.25848
$426$	25.8885	1.25430
$427$	19.5836	0.947716
$428$	6.00000	0.290021
$429$	0	0
$430$	−1.29180	−0.0622959
$431$	35.8885	1.72869	0.864345	−	0.502899i	$-0.167733\pi$
$431$	35.8885	1.72869	0.864345	+	0.502899i	$0.167733\pi$
$432$	4.00000	0.192450
$433$	5.52786	0.265652	0.132826	−	0.991139i	$-0.457595\pi$
$433$	5.52786	0.265652	0.132826	+	0.991139i	$0.457595\pi$
$434$	3.70820	0.177999
$435$	1.88854	0.0905487
$436$	−1.23607	−0.0591969
$437$	−1.14590	−0.0548157
$438$	28.0000	1.33789
$439$	23.1246	1.10368	0.551839	−	0.833951i	$-0.313926\pi$
$439$	23.1246	1.10368	0.551839	+	0.833951i	$0.313926\pi$
$440$	0	0
$441$	−3.56231	−0.169634
$442$	−36.3607	−1.72950
$443$	14.2148	0.675365	0.337682	−	0.941260i	$-0.390357\pi$
$443$	14.2148	0.675365	0.337682	+	0.941260i	$0.390357\pi$
$444$	−8.00000	−0.379663
$445$	−4.18034	−0.198167
$446$	3.70820	0.175589
$447$	40.9443	1.93660
$448$	1.85410	0.0875981
$449$	−8.18034	−0.386054	−0.193027	−	0.981193i	$-0.561831\pi$
$449$	−8.18034	−0.386054	−0.193027	+	0.981193i	$0.561831\pi$
$450$	−4.61803	−0.217696
$451$	0	0
$452$	14.4721	0.680712
$453$	0.583592	0.0274196
$454$	0	0
$455$	7.41641	0.347687
$456$	−2.00000	−0.0936586
$457$	−23.3820	−1.09376	−0.546881	−	0.837210i	$-0.684185\pi$
$457$	−23.3820	−1.09376	−0.546881	+	0.837210i	$0.684185\pi$
$458$	24.2705	1.13409
$459$	22.4721	1.04891
$460$	0.708204	0.0330202
$461$	5.20163	0.242264	0.121132	−	0.992636i	$-0.461348\pi$
$461$	5.20163	0.242264	0.121132	+	0.992636i	$0.461348\pi$
$462$	0	0
$463$	2.79837	0.130051	0.0650257	−	0.997884i	$-0.479287\pi$
$463$	2.79837	0.130051	0.0650257	+	0.997884i	$0.479287\pi$
$464$	1.52786	0.0709293
$465$	2.47214	0.114643
$466$	−18.7984	−0.870818
$467$	31.0902	1.43868	0.719341	−	0.694657i	$-0.244444\pi$
$467$	31.0902	1.43868	0.719341	+	0.694657i	$0.244444\pi$
$468$	−6.47214	−0.299175
$469$	13.4164	0.619512
$470$	−2.23607	−0.103142
$471$	−15.3475	−0.707177
$472$	−12.4721	−0.574077
$473$	0	0
$474$	19.4164	0.891825
$475$	−4.61803	−0.211890
$476$	10.4164	0.477435
$477$	−9.23607	−0.422891
$478$	2.67376	0.122295
$479$	−10.0902	−0.461032	−0.230516	−	0.973069i	$-0.574041\pi$
$479$	−10.0902	−0.461032	−0.230516	+	0.973069i	$0.574041\pi$
$480$	1.23607	0.0564185
$481$	−25.8885	−1.18042
$482$	10.0000	0.455488
$483$	4.24922	0.193346
$484$	0	0
$485$	2.94427	0.133693
$486$	10.0000	0.453609
$487$	10.0000	0.453143	0.226572	−	0.973995i	$-0.427248\pi$
$487$	10.0000	0.453143	0.226572	+	0.973995i	$0.427248\pi$
$488$	10.5623	0.478133
$489$	32.6525	1.47660
$490$	2.20163	0.0994593
$491$	−10.1459	−0.457878	−0.228939	−	0.973441i	$-0.573526\pi$
$491$	−10.1459	−0.457878	−0.228939	+	0.973441i	$0.573526\pi$
$492$	18.4721	0.832788
$493$	8.58359	0.386586
$494$	−6.47214	−0.291195
$495$	0	0
$496$	2.00000	0.0898027
$497$	−24.0000	−1.07655
$498$	−21.5967	−0.967773
$499$	17.5623	0.786197	0.393098	−	0.919496i	$-0.371403\pi$
$499$	17.5623	0.786197	0.393098	+	0.919496i	$0.371403\pi$
$500$	5.94427	0.265836
$501$	50.8328	2.27104
$502$	10.8541	0.484442
$503$	−29.3050	−1.30664	−0.653322	−	0.757080i	$-0.726625\pi$
$503$	−29.3050	−1.30664	−0.653322	+	0.757080i	$0.726625\pi$
$504$	1.85410	0.0825883
$505$	−3.43769	−0.152975
$506$	0	0
$507$	−57.7771	−2.56597
$508$	7.41641	0.329050
$509$	20.2918	0.899418	0.449709	−	0.893175i	$-0.351528\pi$
$509$	20.2918	0.899418	0.449709	+	0.893175i	$0.351528\pi$
$510$	6.94427	0.307498
$511$	−25.9574	−1.14829
$512$	1.00000	0.0441942
$513$	4.00000	0.176604
$514$	−10.9443	−0.482731
$515$	5.70820	0.251534
$516$	−4.18034	−0.184029
$517$	0	0
$518$	7.41641	0.325858
$519$	6.11146	0.268263
$520$	4.00000	0.175412
$521$	2.18034	0.0955224	0.0477612	−	0.998859i	$-0.484791\pi$
$521$	2.18034	0.0955224	0.0477612	+	0.998859i	$0.484791\pi$
$522$	1.52786	0.0668728
$523$	−29.1246	−1.27353	−0.636765	−	0.771058i	$-0.719728\pi$
$523$	−29.1246	−1.27353	−0.636765	+	0.771058i	$0.719728\pi$
$524$	−0.909830	−0.0397461
$525$	17.1246	0.747379
$526$	6.47214	0.282199
$527$	11.2361	0.489451
$528$	0	0
$529$	−21.6869	−0.942909
$530$	5.70820	0.247949
$531$	−12.4721	−0.541245
$532$	1.85410	0.0803855
$533$	59.7771	2.58923
$534$	−13.5279	−0.585408
$535$	−3.70820	−0.160320
$536$	7.23607	0.312551
$537$	40.3607	1.74169
$538$	18.6525	0.804165
$539$	0	0
$540$	−2.47214	−0.106384
$541$	27.1459	1.16709	0.583547	−	0.812080i	$-0.301665\pi$
$541$	27.1459	1.16709	0.583547	+	0.812080i	$0.301665\pi$
$542$	−31.2148	−1.34079
$543$	27.4164	1.17655
$544$	5.61803	0.240871
$545$	0.763932	0.0327233
$546$	24.0000	1.02711
$547$	6.29180	0.269018	0.134509	−	0.990912i	$-0.457054\pi$
$547$	6.29180	0.269018	0.134509	+	0.990912i	$0.457054\pi$
$548$	−15.0902	−0.644620
$549$	10.5623	0.450788
$550$	0	0
$551$	1.52786	0.0650892
$552$	2.29180	0.0975453
$553$	−18.0000	−0.765438
$554$	−3.52786	−0.149885
$555$	4.94427	0.209873
$556$	5.32624	0.225883
$557$	35.4508	1.50210	0.751050	−	0.660245i	$-0.229548\pi$
$557$	35.4508	1.50210	0.751050	+	0.660245i	$0.229548\pi$
$558$	2.00000	0.0846668
$559$	−13.5279	−0.572168
$560$	−1.14590	−0.0484230
$561$	0	0
$562$	4.65248	0.196253
$563$	−9.70820	−0.409152	−0.204576	−	0.978851i	$-0.565582\pi$
$563$	−9.70820	−0.409152	−0.204576	+	0.978851i	$0.565582\pi$
$564$	−7.23607	−0.304693
$565$	−8.94427	−0.376288
$566$	−9.56231	−0.401934
$567$	−20.3951	−0.856515
$568$	−12.9443	−0.543130
$569$	−16.6525	−0.698108	−0.349054	−	0.937103i	$-0.613497\pi$
$569$	−16.6525	−0.698108	−0.349054	+	0.937103i	$0.613497\pi$
$570$	1.23607	0.0517732
$571$	6.14590	0.257198	0.128599	−	0.991697i	$-0.458952\pi$
$571$	6.14590	0.257198	0.128599	+	0.991697i	$0.458952\pi$
$572$	0	0
$573$	48.0689	2.00811
$574$	−17.1246	−0.714767
$575$	5.29180	0.220683
$576$	1.00000	0.0416667
$577$	12.4721	0.519222	0.259611	−	0.965713i	$-0.416406\pi$
$577$	12.4721	0.519222	0.259611	+	0.965713i	$0.416406\pi$
$578$	14.5623	0.605712
$579$	42.2492	1.75582
$580$	−0.944272	−0.0392088
$581$	20.0213	0.830623
$582$	9.52786	0.394943
$583$	0	0
$584$	−14.0000	−0.579324
$585$	4.00000	0.165380
$586$	0.652476	0.0269535
$587$	28.9443	1.19466	0.597329	−	0.801996i	$-0.296229\pi$
$587$	28.9443	1.19466	0.597329	+	0.801996i	$0.296229\pi$
$588$	7.12461	0.293814
$589$	2.00000	0.0824086
$590$	7.70820	0.317342
$591$	36.0000	1.48084
$592$	4.00000	0.164399
$593$	−44.4508	−1.82538	−0.912689	−	0.408655i	$-0.865998\pi$
$593$	−44.4508	−1.82538	−0.912689	+	0.408655i	$0.865998\pi$
$594$	0	0
$595$	−6.43769	−0.263920
$596$	−20.4721	−0.838571
$597$	11.1246	0.455300
$598$	7.41641	0.303279
$599$	15.5967	0.637266	0.318633	−	0.947878i	$-0.396776\pi$
$599$	15.5967	0.637266	0.318633	+	0.947878i	$0.396776\pi$
$600$	9.23607	0.377061
$601$	31.7082	1.29340	0.646702	−	0.762743i	$-0.276148\pi$
$601$	31.7082	1.29340	0.646702	+	0.762743i	$0.276148\pi$
$602$	3.87539	0.157949
$603$	7.23607	0.294675
$604$	−0.291796	−0.0118730
$605$	0	0
$606$	−11.1246	−0.451906
$607$	24.9443	1.01246	0.506228	−	0.862399i	$-0.331039\pi$
$607$	24.9443	1.01246	0.506228	+	0.862399i	$0.331039\pi$
$608$	1.00000	0.0405554
$609$	−5.66563	−0.229583
$610$	−6.52786	−0.264305
$611$	−23.4164	−0.947326
$612$	5.61803	0.227096
$613$	−7.72949	−0.312191	−0.156096	−	0.987742i	$-0.549891\pi$
$613$	−7.72949	−0.312191	−0.156096	+	0.987742i	$0.549891\pi$
$614$	−27.4164	−1.10644
$615$	−11.4164	−0.460354
$616$	0	0
$617$	42.7214	1.71990	0.859949	−	0.510381i	$-0.170495\pi$
$617$	42.7214	1.71990	0.859949	+	0.510381i	$0.170495\pi$
$618$	18.4721	0.743058
$619$	12.5623	0.504922	0.252461	−	0.967607i	$-0.418760\pi$
$619$	12.5623	0.504922	0.252461	+	0.967607i	$0.418760\pi$
$620$	−1.23607	−0.0496417
$621$	−4.58359	−0.183933
$622$	−4.20163	−0.168470
$623$	12.5410	0.502445
$624$	12.9443	0.518186
$625$	19.4164	0.776656
$626$	−0.0901699	−0.00360392
$627$	0	0
$628$	7.67376	0.306216
$629$	22.4721	0.896023
$630$	−1.14590	−0.0456537
$631$	−24.3607	−0.969783	−0.484892	−	0.874574i	$-0.661141\pi$
$631$	−24.3607	−0.969783	−0.484892	+	0.874574i	$0.661141\pi$
$632$	−9.70820	−0.386172
$633$	22.8328	0.907523
$634$	2.18034	0.0865924
$635$	−4.58359	−0.181894
$636$	18.4721	0.732468
$637$	23.0557	0.913501
$638$	0	0
$639$	−12.9443	−0.512067
$640$	−0.618034	−0.0244299
$641$	21.3050	0.841495	0.420747	−	0.907178i	$-0.361768\pi$
$641$	21.3050	0.841495	0.420747	+	0.907178i	$0.361768\pi$
$642$	−12.0000	−0.473602
$643$	20.9230	0.825122	0.412561	−	0.910930i	$-0.364634\pi$
$643$	20.9230	0.825122	0.412561	+	0.910930i	$0.364634\pi$
$644$	−2.12461	−0.0837214
$645$	2.58359	0.101729
$646$	5.61803	0.221039
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	−11.0000	−0.432121
$649$	0	0
$650$	29.8885	1.17233
$651$	−7.41641	−0.290672
$652$	−16.3262	−0.639385
$653$	−1.61803	−0.0633186	−0.0316593	−	0.999499i	$-0.510079\pi$
$653$	−1.61803	−0.0633186	−0.0316593	+	0.999499i	$0.510079\pi$
$654$	2.47214	0.0966682
$655$	0.562306	0.0219711
$656$	−9.23607	−0.360608
$657$	−14.0000	−0.546192
$658$	6.70820	0.261513
$659$	20.2918	0.790456	0.395228	−	0.918583i	$-0.370666\pi$
$659$	20.2918	0.790456	0.395228	+	0.918583i	$0.370666\pi$
$660$	0	0
$661$	19.5967	0.762225	0.381113	−	0.924529i	$-0.375541\pi$
$661$	19.5967	0.762225	0.381113	+	0.924529i	$0.375541\pi$
$662$	−9.70820	−0.377320
$663$	72.7214	2.82426
$664$	10.7984	0.419058
$665$	−1.14590	−0.0444360
$666$	4.00000	0.154997
$667$	−1.75078	−0.0677903
$668$	−25.4164	−0.983390
$669$	−7.41641	−0.286735
$670$	−4.47214	−0.172774
$671$	0	0
$672$	−3.70820	−0.143047
$673$	−45.0132	−1.73513	−0.867565	−	0.497324i	$-0.834316\pi$
$673$	−45.0132	−1.73513	−0.867565	+	0.497324i	$0.834316\pi$
$674$	−17.0557	−0.656962
$675$	−18.4721	−0.710993
$676$	28.8885	1.11110
$677$	33.7082	1.29551	0.647756	−	0.761848i	$-0.275708\pi$
$677$	33.7082	1.29551	0.647756	+	0.761848i	$0.275708\pi$
$678$	−28.9443	−1.11160
$679$	−8.83282	−0.338972
$680$	−3.47214	−0.133150
$681$	0	0
$682$	0	0
$683$	−20.0689	−0.767914	−0.383957	−	0.923351i	$-0.625439\pi$
$683$	−20.0689	−0.767914	−0.383957	+	0.923351i	$0.625439\pi$
$684$	1.00000	0.0382360
$685$	9.32624	0.356337
$686$	−19.5836	−0.747705
$687$	−48.5410	−1.85196
$688$	2.09017	0.0796870
$689$	59.7771	2.27733
$690$	−1.41641	−0.0539217
$691$	−20.3262	−0.773247	−0.386623	−	0.922238i	$-0.626359\pi$
$691$	−20.3262	−0.773247	−0.386623	+	0.922238i	$0.626359\pi$
$692$	−3.05573	−0.116161
$693$	0	0
$694$	8.56231	0.325021
$695$	−3.29180	−0.124865
$696$	−3.05573	−0.115827
$697$	−51.8885	−1.96542
$698$	20.9787	0.794056
$699$	37.5967	1.42204
$700$	−8.56231	−0.323625
$701$	14.7426	0.556822	0.278411	−	0.960462i	$-0.410192\pi$
$701$	14.7426	0.556822	0.278411	+	0.960462i	$0.410192\pi$
$702$	−25.8885	−0.977100
$703$	4.00000	0.150863
$704$	0	0
$705$	4.47214	0.168430
$706$	15.3820	0.578908
$707$	10.3131	0.387863
$708$	24.9443	0.937463
$709$	5.20163	0.195351	0.0976756	−	0.995218i	$-0.468859\pi$
$709$	5.20163	0.195351	0.0976756	+	0.995218i	$0.468859\pi$
$710$	8.00000	0.300235
$711$	−9.70820	−0.364086
$712$	6.76393	0.253489
$713$	−2.29180	−0.0858284
$714$	−20.8328	−0.779649
$715$	0	0
$716$	−20.1803	−0.754175
$717$	−5.34752	−0.199707
$718$	−6.09017	−0.227283
$719$	−20.3262	−0.758041	−0.379020	−	0.925388i	$-0.623739\pi$
$719$	−20.3262	−0.758041	−0.379020	+	0.925388i	$0.623739\pi$
$720$	−0.618034	−0.0230328
$721$	−17.1246	−0.637754
$722$	1.00000	0.0372161
$723$	−20.0000	−0.743808
$724$	−13.7082	−0.509461
$725$	−7.05573	−0.262043
$726$	0	0
$727$	18.8541	0.699260	0.349630	−	0.936888i	$-0.386307\pi$
$727$	18.8541	0.699260	0.349630	+	0.936888i	$0.386307\pi$
$728$	−12.0000	−0.444750
$729$	13.0000	0.481481
$730$	8.65248	0.320242
$731$	11.7426	0.434317
$732$	−21.1246	−0.780788
$733$	44.3262	1.63723	0.818613	−	0.574345i	$-0.194743\pi$
$733$	44.3262	1.63723	0.818613	+	0.574345i	$0.194743\pi$
$734$	−21.5623	−0.795879
$735$	−4.40325	−0.162416
$736$	−1.14590	−0.0422384
$737$	0	0
$738$	−9.23607	−0.339984
$739$	−43.4508	−1.59837	−0.799183	−	0.601088i	$-0.794734\pi$
$739$	−43.4508	−1.59837	−0.799183	+	0.601088i	$0.794734\pi$
$740$	−2.47214	−0.0908775
$741$	12.9443	0.475520
$742$	−17.1246	−0.628664
$743$	28.6525	1.05116	0.525579	−	0.850745i	$-0.323849\pi$
$743$	28.6525	1.05116	0.525579	+	0.850745i	$0.323849\pi$
$744$	−4.00000	−0.146647
$745$	12.6525	0.463551
$746$	−30.3607	−1.11158
$747$	10.7984	0.395092
$748$	0	0
$749$	11.1246	0.406484
$750$	−11.8885	−0.434108
$751$	−37.4164	−1.36534	−0.682672	−	0.730725i	$-0.739182\pi$
$751$	−37.4164	−1.36534	−0.682672	+	0.730725i	$0.739182\pi$
$752$	3.61803	0.131936
$753$	−21.7082	−0.791091
$754$	−9.88854	−0.360120
$755$	0.180340	0.00656324
$756$	7.41641	0.269732
$757$	1.41641	0.0514802	0.0257401	−	0.999669i	$-0.491806\pi$
$757$	1.41641	0.0514802	0.0257401	+	0.999669i	$0.491806\pi$
$758$	1.23607	0.0448960
$759$	0	0
$760$	−0.618034	−0.0224184
$761$	51.3050	1.85980	0.929902	−	0.367809i	$-0.119892\pi$
$761$	51.3050	1.85980	0.929902	+	0.367809i	$0.119892\pi$
$762$	−14.8328	−0.537336
$763$	−2.29180	−0.0829686
$764$	−24.0344	−0.869536
$765$	−3.47214	−0.125535
$766$	14.9443	0.539958
$767$	80.7214	2.91468
$768$	−2.00000	−0.0721688
$769$	34.5066	1.24434	0.622170	−	0.782883i	$-0.286251\pi$
$769$	34.5066	1.24434	0.622170	+	0.782883i	$0.286251\pi$
$770$	0	0
$771$	21.8885	0.788297
$772$	−21.1246	−0.760291
$773$	−33.5967	−1.20839	−0.604196	−	0.796836i	$-0.706505\pi$
$773$	−33.5967	−1.20839	−0.604196	+	0.796836i	$0.706505\pi$
$774$	2.09017	0.0751296
$775$	−9.23607	−0.331769
$776$	−4.76393	−0.171015
$777$	−14.8328	−0.532124
$778$	13.0344	0.467307
$779$	−9.23607	−0.330916
$780$	−8.00000	−0.286446
$781$	0	0
$782$	−6.43769	−0.230211
$783$	6.11146	0.218406
$784$	−3.56231	−0.127225
$785$	−4.74265	−0.169272
$786$	1.81966	0.0649051
$787$	−42.9443	−1.53080	−0.765399	−	0.643556i	$-0.777458\pi$
$787$	−42.9443	−1.53080	−0.765399	+	0.643556i	$0.777458\pi$
$788$	−18.0000	−0.641223
$789$	−12.9443	−0.460828
$790$	6.00000	0.213470
$791$	26.8328	0.954065
$792$	0	0
$793$	−68.3607	−2.42756
$794$	20.8541	0.740084
$795$	−11.4164	−0.404898
$796$	−5.56231	−0.197151
$797$	−53.7771	−1.90488	−0.952441	−	0.304723i	$-0.901436\pi$
$797$	−53.7771	−1.90488	−0.952441	+	0.304723i	$0.901436\pi$
$798$	−3.70820	−0.131269
$799$	20.3262	0.719091
$800$	−4.61803	−0.163272
$801$	6.76393	0.238992
$802$	12.4721	0.440406
$803$	0	0
$804$	−14.4721	−0.510393
$805$	1.31308	0.0462801
$806$	−12.9443	−0.455943
$807$	−37.3050	−1.31320
$808$	5.56231	0.195681
$809$	5.56231	0.195560	0.0977801	−	0.995208i	$-0.468826\pi$
$809$	5.56231	0.195560	0.0977801	+	0.995208i	$0.468826\pi$
$810$	6.79837	0.238871
$811$	−40.2492	−1.41334	−0.706671	−	0.707543i	$-0.749804\pi$
$811$	−40.2492	−1.41334	−0.706671	+	0.707543i	$0.749804\pi$
$812$	2.83282	0.0994123
$813$	62.4296	2.18950
$814$	0	0
$815$	10.0902	0.353443
$816$	−11.2361	−0.393341
$817$	2.09017	0.0731258
$818$	−22.9443	−0.802228
$819$	−12.0000	−0.419314
$820$	5.70820	0.199339
$821$	3.90983	0.136454	0.0682270	−	0.997670i	$-0.478266\pi$
$821$	3.90983	0.136454	0.0682270	+	0.997670i	$0.478266\pi$
$822$	30.1803	1.05266
$823$	13.8541	0.482924	0.241462	−	0.970410i	$-0.422373\pi$
$823$	13.8541	0.482924	0.241462	+	0.970410i	$0.422373\pi$
$824$	−9.23607	−0.321754
$825$	0	0
$826$	−23.1246	−0.804608
$827$	28.2492	0.982322	0.491161	−	0.871069i	$-0.336573\pi$
$827$	28.2492	0.982322	0.491161	+	0.871069i	$0.336573\pi$
$828$	−1.14590	−0.0398227
$829$	−18.8328	−0.654091	−0.327045	−	0.945009i	$-0.606053\pi$
$829$	−18.8328	−0.654091	−0.327045	+	0.945009i	$0.606053\pi$
$830$	−6.67376	−0.231650
$831$	7.05573	0.244760
$832$	−6.47214	−0.224381
$833$	−20.0132	−0.693415
$834$	−10.6525	−0.368865
$835$	15.7082	0.543605
$836$	0	0
$837$	8.00000	0.276520
$838$	9.32624	0.322170
$839$	−24.1803	−0.834798	−0.417399	−	0.908723i	$-0.637058\pi$
$839$	−24.1803	−0.834798	−0.417399	+	0.908723i	$0.637058\pi$
$840$	2.29180	0.0790745
$841$	−26.6656	−0.919505
$842$	28.0000	0.964944
$843$	−9.30495	−0.320480
$844$	−11.4164	−0.392969
$845$	−17.8541	−0.614200
$846$	3.61803	0.124391
$847$	0	0
$848$	−9.23607	−0.317168
$849$	19.1246	0.656355
$850$	−25.9443	−0.889881
$851$	−4.58359	−0.157124
$852$	25.8885	0.886927
$853$	−4.27051	−0.146219	−0.0731097	−	0.997324i	$-0.523292\pi$
$853$	−4.27051	−0.146219	−0.0731097	+	0.997324i	$0.523292\pi$
$854$	19.5836	0.670137
$855$	−0.618034	−0.0211363
$856$	6.00000	0.205076
$857$	−19.0132	−0.649477	−0.324739	−	0.945804i	$-0.605276\pi$
$857$	−19.0132	−0.649477	−0.324739	+	0.945804i	$0.605276\pi$
$858$	0	0
$859$	33.6869	1.14938	0.574691	−	0.818370i	$-0.305122\pi$
$859$	33.6869	1.14938	0.574691	+	0.818370i	$0.305122\pi$
$860$	−1.29180	−0.0440499
$861$	34.2492	1.16721
$862$	35.8885	1.22237
$863$	48.1803	1.64008	0.820039	−	0.572308i	$-0.193952\pi$
$863$	48.1803	1.64008	0.820039	+	0.572308i	$0.193952\pi$
$864$	4.00000	0.136083
$865$	1.88854	0.0642124
$866$	5.52786	0.187844
$867$	−29.1246	−0.989124
$868$	3.70820	0.125865
$869$	0	0
$870$	1.88854	0.0640276
$871$	−46.8328	−1.58687
$872$	−1.23607	−0.0418585
$873$	−4.76393	−0.161235
$874$	−1.14590	−0.0387606
$875$	11.0213	0.372587
$876$	28.0000	0.946032
$877$	−14.5836	−0.492453	−0.246226	−	0.969212i	$-0.579191\pi$
$877$	−14.5836	−0.492453	−0.246226	+	0.969212i	$0.579191\pi$
$878$	23.1246	0.780418
$879$	−1.30495	−0.0440149
$880$	0	0
$881$	25.4164	0.856301	0.428150	−	0.903708i	$-0.359165\pi$
$881$	25.4164	0.856301	0.428150	+	0.903708i	$0.359165\pi$
$882$	−3.56231	−0.119949
$883$	−24.3951	−0.820961	−0.410481	−	0.911869i	$-0.634639\pi$
$883$	−24.3951	−0.820961	−0.410481	+	0.911869i	$0.634639\pi$
$884$	−36.3607	−1.22294
$885$	−15.4164	−0.518217
$886$	14.2148	0.477555
$887$	12.1115	0.406663	0.203331	−	0.979110i	$-0.434823\pi$
$887$	12.1115	0.406663	0.203331	+	0.979110i	$0.434823\pi$
$888$	−8.00000	−0.268462
$889$	13.7508	0.461186
$890$	−4.18034	−0.140125
$891$	0	0
$892$	3.70820	0.124160
$893$	3.61803	0.121073
$894$	40.9443	1.36938
$895$	12.4721	0.416898
$896$	1.85410	0.0619412
$897$	−14.8328	−0.495253
$898$	−8.18034	−0.272981
$899$	3.05573	0.101914
$900$	−4.61803	−0.153934
$901$	−51.8885	−1.72866
$902$	0	0
$903$	−7.75078	−0.257930
$904$	14.4721	0.481336
$905$	8.47214	0.281623
$906$	0.583592	0.0193886
$907$	−30.8328	−1.02379	−0.511893	−	0.859049i	$-0.671056\pi$
$907$	−30.8328	−1.02379	−0.511893	+	0.859049i	$0.671056\pi$
$908$	0	0
$909$	5.56231	0.184490
$910$	7.41641	0.245852
$911$	13.4164	0.444505	0.222253	−	0.974989i	$-0.428659\pi$
$911$	13.4164	0.444505	0.222253	+	0.974989i	$0.428659\pi$
$912$	−2.00000	−0.0662266
$913$	0	0
$914$	−23.3820	−0.773407
$915$	13.0557	0.431609
$916$	24.2705	0.801920
$917$	−1.68692	−0.0557069
$918$	22.4721	0.741691
$919$	−28.6869	−0.946294	−0.473147	−	0.880983i	$-0.656882\pi$
$919$	−28.6869	−0.946294	−0.473147	+	0.880983i	$0.656882\pi$
$920$	0.708204	0.0233488
$921$	54.8328	1.80680
$922$	5.20163	0.171306
$923$	83.7771	2.75756
$924$	0	0
$925$	−18.4721	−0.607360
$926$	2.79837	0.0919603
$927$	−9.23607	−0.303352
$928$	1.52786	0.0501546
$929$	48.2705	1.58370	0.791852	−	0.610713i	$-0.209117\pi$
$929$	48.2705	1.58370	0.791852	+	0.610713i	$0.209117\pi$
$930$	2.47214	0.0810645
$931$	−3.56231	−0.116750
$932$	−18.7984	−0.615761
$933$	8.40325	0.275110
$934$	31.0902	1.01730
$935$	0	0
$936$	−6.47214	−0.211548
$937$	56.8115	1.85595	0.927976	−	0.372640i	$-0.121547\pi$
$937$	56.8115	1.85595	0.927976	+	0.372640i	$0.121547\pi$
$938$	13.4164	0.438061
$939$	0.180340	0.00588517
$940$	−2.23607	−0.0729325
$941$	8.94427	0.291575	0.145787	−	0.989316i	$-0.453428\pi$
$941$	8.94427	0.291575	0.145787	+	0.989316i	$0.453428\pi$
$942$	−15.3475	−0.500049
$943$	10.5836	0.344649
$944$	−12.4721	−0.405933
$945$	−4.58359	−0.149104
$946$	0	0
$947$	−37.9230	−1.23233	−0.616166	−	0.787617i	$-0.711315\pi$
$947$	−37.9230	−1.23233	−0.616166	+	0.787617i	$0.711315\pi$
$948$	19.4164	0.630616
$949$	90.6099	2.94132
$950$	−4.61803	−0.149829
$951$	−4.36068	−0.141405
$952$	10.4164	0.337598
$953$	49.7771	1.61244	0.806219	−	0.591617i	$-0.201510\pi$
$953$	49.7771	1.61244	0.806219	+	0.591617i	$0.201510\pi$
$954$	−9.23607	−0.299029
$955$	14.8541	0.480667
$956$	2.67376	0.0864756
$957$	0	0
$958$	−10.0902	−0.325999
$959$	−27.9787	−0.903480
$960$	1.23607	0.0398939
$961$	−27.0000	−0.870968
$962$	−25.8885	−0.834680
$963$	6.00000	0.193347
$964$	10.0000	0.322078
$965$	13.0557	0.420279
$966$	4.24922	0.136717
$967$	−58.2705	−1.87385	−0.936927	−	0.349526i	$-0.886343\pi$
$967$	−58.2705	−1.87385	−0.936927	+	0.349526i	$0.886343\pi$
$968$	0	0
$969$	−11.2361	−0.360955
$970$	2.94427	0.0945349
$971$	−34.3607	−1.10269	−0.551343	−	0.834278i	$-0.685885\pi$
$971$	−34.3607	−1.10269	−0.551343	+	0.834278i	$0.685885\pi$
$972$	10.0000	0.320750
$973$	9.87539	0.316590
$974$	10.0000	0.320421
$975$	−59.7771	−1.91440
$976$	10.5623	0.338091
$977$	8.83282	0.282587	0.141293	−	0.989968i	$-0.454874\pi$
$977$	8.83282	0.282587	0.141293	+	0.989968i	$0.454874\pi$
$978$	32.6525	1.04411
$979$	0	0
$980$	2.20163	0.0703284
$981$	−1.23607	−0.0394646
$982$	−10.1459	−0.323769
$983$	−58.1378	−1.85431	−0.927153	−	0.374682i	$-0.877752\pi$
$983$	−58.1378	−1.85431	−0.927153	+	0.374682i	$0.877752\pi$
$984$	18.4721	0.588870
$985$	11.1246	0.354460
$986$	8.58359	0.273357
$987$	−13.4164	−0.427049
$988$	−6.47214	−0.205906
$989$	−2.39512	−0.0761604
$990$	0	0
$991$	−26.3607	−0.837375	−0.418687	−	0.908130i	$-0.637510\pi$
$991$	−26.3607	−0.837375	−0.418687	+	0.908130i	$0.637510\pi$
$992$	2.00000	0.0635001
$993$	19.4164	0.616161
$994$	−24.0000	−0.761234
$995$	3.43769	0.108982
$996$	−21.5967	−0.684319
$997$	−21.2705	−0.673644	−0.336822	−	0.941568i	$-0.609352\pi$
$997$	−21.2705	−0.673644	−0.336822	+	0.941568i	$0.609352\pi$
$998$	17.5623	0.555925
$999$	16.0000	0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bb.1.1		2
11.5	even	5		418.2.f.d.267.1	yes	4
11.9	even	5		418.2.f.d.191.1	✓	4
11.10	odd	2		4598.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.d.191.1	✓	4	11.9	even	5
418.2.f.d.267.1	yes	4	11.5	even	5
4598.2.a.t.1.1		2	11.10	odd	2
4598.2.a.bb.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -2.00000 q^{6} +1.85410 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.00000 q^{3} +1.00000 q^{4} -0.618034 q^{5} -2.00000 q^{6} +1.85410 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.618034 q^{10} -2.00000 q^{12} -6.47214 q^{13} +1.85410 q^{14} +1.23607 q^{15} +1.00000 q^{16} +5.61803 q^{17} +1.00000 q^{18} +1.00000 q^{19} -0.618034 q^{20} -3.70820 q^{21} -1.14590 q^{23} -2.00000 q^{24} -4.61803 q^{25} -6.47214 q^{26} +4.00000 q^{27} +1.85410 q^{28} +1.52786 q^{29} +1.23607 q^{30} +2.00000 q^{31} +1.00000 q^{32} +5.61803 q^{34} -1.14590 q^{35} +1.00000 q^{36} +4.00000 q^{37} +1.00000 q^{38} +12.9443 q^{39} -0.618034 q^{40} -9.23607 q^{41} -3.70820 q^{42} +2.09017 q^{43} -0.618034 q^{45} -1.14590 q^{46} +3.61803 q^{47} -2.00000 q^{48} -3.56231 q^{49} -4.61803 q^{50} -11.2361 q^{51} -6.47214 q^{52} -9.23607 q^{53} +4.00000 q^{54} +1.85410 q^{56} -2.00000 q^{57} +1.52786 q^{58} -12.4721 q^{59} +1.23607 q^{60} +10.5623 q^{61} +2.00000 q^{62} +1.85410 q^{63} +1.00000 q^{64} +4.00000 q^{65} +7.23607 q^{67} +5.61803 q^{68} +2.29180 q^{69} -1.14590 q^{70} -12.9443 q^{71} +1.00000 q^{72} -14.0000 q^{73} +4.00000 q^{74} +9.23607 q^{75} +1.00000 q^{76} +12.9443 q^{78} -9.70820 q^{79} -0.618034 q^{80} -11.0000 q^{81} -9.23607 q^{82} +10.7984 q^{83} -3.70820 q^{84} -3.47214 q^{85} +2.09017 q^{86} -3.05573 q^{87} +6.76393 q^{89} -0.618034 q^{90} -12.0000 q^{91} -1.14590 q^{92} -4.00000 q^{93} +3.61803 q^{94} -0.618034 q^{95} -2.00000 q^{96} -4.76393 q^{97} -3.56231 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 4 q^{3} + 2 q^{4} + q^{5} - 4 q^{6} - 3 q^{7} + 2 q^{8} + 2 q^{9} + q^{10} - 4 q^{12} - 4 q^{13} - 3 q^{14} - 2 q^{15} + 2 q^{16} + 9 q^{17} + 2 q^{18} + 2 q^{19} + q^{20} + 6 q^{21} - 9 q^{23} - 4 q^{24} - 7 q^{25} - 4 q^{26} + 8 q^{27} - 3 q^{28} + 12 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 9 q^{34} - 9 q^{35} + 2 q^{36} + 8 q^{37} + 2 q^{38} + 8 q^{39} + q^{40} - 14 q^{41} + 6 q^{42} - 7 q^{43} + q^{45} - 9 q^{46} + 5 q^{47} - 4 q^{48} + 13 q^{49} - 7 q^{50} - 18 q^{51} - 4 q^{52} - 14 q^{53} + 8 q^{54} - 3 q^{56} - 4 q^{57} + 12 q^{58} - 16 q^{59} - 2 q^{60} + q^{61} + 4 q^{62} - 3 q^{63} + 2 q^{64} + 8 q^{65} + 10 q^{67} + 9 q^{68} + 18 q^{69} - 9 q^{70} - 8 q^{71} + 2 q^{72} - 28 q^{73} + 8 q^{74} + 14 q^{75} + 2 q^{76} + 8 q^{78} - 6 q^{79} + q^{80} - 22 q^{81} - 14 q^{82} - 3 q^{83} + 6 q^{84} + 2 q^{85} - 7 q^{86} - 24 q^{87} + 18 q^{89} + q^{90} - 24 q^{91} - 9 q^{92} - 8 q^{93} + 5 q^{94} + q^{95} - 4 q^{96} - 14 q^{97} + 13 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 4 * q^3 + 2 * q^4 + q^5 - 4 * q^6 - 3 * q^7 + 2 * q^8 + 2 * q^9 + q^10 - 4 * q^12 - 4 * q^13 - 3 * q^14 - 2 * q^15 + 2 * q^16 + 9 * q^17 + 2 * q^18 + 2 * q^19 + q^20 + 6 * q^21 - 9 * q^23 - 4 * q^24 - 7 * q^25 - 4 * q^26 + 8 * q^27 - 3 * q^28 + 12 * q^29 - 2 * q^30 + 4 * q^31 + 2 * q^32 + 9 * q^34 - 9 * q^35 + 2 * q^36 + 8 * q^37 + 2 * q^38 + 8 * q^39 + q^40 - 14 * q^41 + 6 * q^42 - 7 * q^43 + q^45 - 9 * q^46 + 5 * q^47 - 4 * q^48 + 13 * q^49 - 7 * q^50 - 18 * q^51 - 4 * q^52 - 14 * q^53 + 8 * q^54 - 3 * q^56 - 4 * q^57 + 12 * q^58 - 16 * q^59 - 2 * q^60 + q^61 + 4 * q^62 - 3 * q^63 + 2 * q^64 + 8 * q^65 + 10 * q^67 + 9 * q^68 + 18 * q^69 - 9 * q^70 - 8 * q^71 + 2 * q^72 - 28 * q^73 + 8 * q^74 + 14 * q^75 + 2 * q^76 + 8 * q^78 - 6 * q^79 + q^80 - 22 * q^81 - 14 * q^82 - 3 * q^83 + 6 * q^84 + 2 * q^85 - 7 * q^86 - 24 * q^87 + 18 * q^89 + q^90 - 24 * q^91 - 9 * q^92 - 8 * q^93 + 5 * q^94 + q^95 - 4 * q^96 - 14 * q^97 + 13 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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