LMFDB - Embedded newform 4598.2.a.bn.1.3

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:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.12489$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -3.12489 q^{5} +2.12489 q^{6} -0.515138 q^{7} +1.00000 q^{8} +1.51514 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -3.12489 q^{5} +2.12489 q^{6} -0.515138 q^{7} +1.00000 q^{8} +1.51514 q^{9} -3.12489 q^{10} +2.12489 q^{12} -0.484862 q^{13} -0.515138 q^{14} -6.64002 q^{15} +1.00000 q^{16} -1.51514 q^{17} +1.51514 q^{18} -1.00000 q^{19} -3.12489 q^{20} -1.09461 q^{21} +0.515138 q^{23} +2.12489 q^{24} +4.76491 q^{25} -0.484862 q^{26} -3.15516 q^{27} -0.515138 q^{28} -2.60975 q^{29} -6.64002 q^{30} -5.28005 q^{31} +1.00000 q^{32} -1.51514 q^{34} +1.60975 q^{35} +1.51514 q^{36} -10.6097 q^{37} -1.00000 q^{38} -1.03028 q^{39} -3.12489 q^{40} -6.09461 q^{41} -1.09461 q^{42} +1.03028 q^{43} -4.73463 q^{45} +0.515138 q^{46} +9.01468 q^{47} +2.12489 q^{48} -6.73463 q^{49} +4.76491 q^{50} -3.21949 q^{51} -0.484862 q^{52} -0.670300 q^{53} -3.15516 q^{54} -0.515138 q^{56} -2.12489 q^{57} -2.60975 q^{58} -2.90539 q^{59} -6.64002 q^{60} +9.92007 q^{61} -5.28005 q^{62} -0.780505 q^{63} +1.00000 q^{64} +1.51514 q^{65} -2.06055 q^{67} -1.51514 q^{68} +1.09461 q^{69} +1.60975 q^{70} -2.64002 q^{71} +1.51514 q^{72} -7.52982 q^{73} -10.6097 q^{74} +10.1249 q^{75} -1.00000 q^{76} -1.03028 q^{78} +1.60975 q^{79} -3.12489 q^{80} -11.2498 q^{81} -6.09461 q^{82} -1.60975 q^{83} -1.09461 q^{84} +4.73463 q^{85} +1.03028 q^{86} -5.54541 q^{87} -1.06433 q^{89} -4.73463 q^{90} +0.249771 q^{91} +0.515138 q^{92} -11.2195 q^{93} +9.01468 q^{94} +3.12489 q^{95} +2.12489 q^{96} +7.76491 q^{97} -6.73463 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 - 2 * q^6 - 2 * q^7 + 3 * q^8 + 5 * q^9	$ 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} - 2 q^{12} - q^{13} - 2 q^{14} - 12 q^{15} + 3 q^{16} - 5 q^{17} + 5 q^{18} - 3 q^{19} - q^{20} + 6 q^{21} + 2 q^{23} - 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + q^{29} - 12 q^{30} + 3 q^{32} - 5 q^{34} - 4 q^{35} + 5 q^{36} - 23 q^{37} - 3 q^{38} - 4 q^{39} - q^{40} - 9 q^{41} + 6 q^{42} + 4 q^{43} + 3 q^{45} + 2 q^{46} - 6 q^{47} - 2 q^{48} - 3 q^{49} - 2 q^{50} + 8 q^{51} - q^{52} + 5 q^{53} - 2 q^{54} - 2 q^{56} + 2 q^{57} + q^{58} - 18 q^{59} - 12 q^{60} + 6 q^{61} - 20 q^{63} + 3 q^{64} + 5 q^{65} - 8 q^{67} - 5 q^{68} - 6 q^{69} - 4 q^{70} + 5 q^{72} + 10 q^{73} - 23 q^{74} + 22 q^{75} - 3 q^{76} - 4 q^{78} - 4 q^{79} - q^{80} - 17 q^{81} - 9 q^{82} + 4 q^{83} + 6 q^{84} - 3 q^{85} + 4 q^{86} - 18 q^{87} + 7 q^{89} + 3 q^{90} - 16 q^{91} + 2 q^{92} - 16 q^{93} - 6 q^{94} + q^{95} - 2 q^{96} + 7 q^{97} - 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 - 2 * q^6 - 2 * q^7 + 3 * q^8 + 5 * q^9 - q^10 - 2 * q^12 - q^13 - 2 * q^14 - 12 * q^15 + 3 * q^16 - 5 * q^17 + 5 * q^18 - 3 * q^19 - q^20 + 6 * q^21 + 2 * q^23 - 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + q^29 - 12 * q^30 + 3 * q^32 - 5 * q^34 - 4 * q^35 + 5 * q^36 - 23 * q^37 - 3 * q^38 - 4 * q^39 - q^40 - 9 * q^41 + 6 * q^42 + 4 * q^43 + 3 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 3 * q^49 - 2 * q^50 + 8 * q^51 - q^52 + 5 * q^53 - 2 * q^54 - 2 * q^56 + 2 * q^57 + q^58 - 18 * q^59 - 12 * q^60 + 6 * q^61 - 20 * q^63 + 3 * q^64 + 5 * q^65 - 8 * q^67 - 5 * q^68 - 6 * q^69 - 4 * q^70 + 5 * q^72 + 10 * q^73 - 23 * q^74 + 22 * q^75 - 3 * q^76 - 4 * q^78 - 4 * q^79 - q^80 - 17 * q^81 - 9 * q^82 + 4 * q^83 + 6 * q^84 - 3 * q^85 + 4 * q^86 - 18 * q^87 + 7 * q^89 + 3 * q^90 - 16 * q^91 + 2 * q^92 - 16 * q^93 - 6 * q^94 + q^95 - 2 * q^96 + 7 * q^97 - 3 * 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
$3$	2.12489	1.22680	0.613402	−	0.789771i	$-0.289801\pi$
$3$	2.12489	1.22680	0.613402	+	0.789771i	$0.289801\pi$
$4$	1.00000	0.500000
$5$	−3.12489	−1.39749	−0.698746	−	0.715370i	$-0.746258\pi$
$5$	−3.12489	−1.39749	−0.698746	+	0.715370i	$0.746258\pi$
$6$	2.12489	0.867481
$7$	−0.515138	−0.194704	−0.0973519	−	0.995250i	$-0.531037\pi$
$7$	−0.515138	−0.194704	−0.0973519	+	0.995250i	$0.531037\pi$
$8$	1.00000	0.353553
$9$	1.51514	0.505046
$10$	−3.12489	−0.988176
$11$	0	0
$11$	0	0
$12$	2.12489	0.613402
$13$	−0.484862	−0.134477	−0.0672383	−	0.997737i	$-0.521419\pi$
$13$	−0.484862	−0.134477	−0.0672383	+	0.997737i	$0.521419\pi$
$14$	−0.515138	−0.137676
$15$	−6.64002	−1.71445
$16$	1.00000	0.250000
$17$	−1.51514	−0.367475	−0.183737	−	0.982975i	$-0.558820\pi$
$17$	−1.51514	−0.367475	−0.183737	+	0.982975i	$0.558820\pi$
$18$	1.51514	0.357121
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.12489	−0.698746
$21$	−1.09461	−0.238863
$22$	0	0
$23$	0.515138	0.107414	0.0537069	−	0.998557i	$-0.482896\pi$
$23$	0.515138	0.107414	0.0537069	+	0.998557i	$0.482896\pi$
$24$	2.12489	0.433740
$25$	4.76491	0.952982
$26$	−0.484862	−0.0950893
$27$	−3.15516	−0.607211
$28$	−0.515138	−0.0973519
$29$	−2.60975	−0.484618	−0.242309	−	0.970199i	$-0.577905\pi$
$29$	−2.60975	−0.484618	−0.242309	+	0.970199i	$0.577905\pi$
$30$	−6.64002	−1.21230
$31$	−5.28005	−0.948324	−0.474162	−	0.880438i	$-0.657249\pi$
$31$	−5.28005	−0.948324	−0.474162	+	0.880438i	$0.657249\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−1.51514	−0.259844
$35$	1.60975	0.272097
$36$	1.51514	0.252523
$37$	−10.6097	−1.74423	−0.872116	−	0.489299i	$-0.837253\pi$
$37$	−10.6097	−1.74423	−0.872116	+	0.489299i	$0.837253\pi$
$38$	−1.00000	−0.162221
$39$	−1.03028	−0.164976
$40$	−3.12489	−0.494088
$41$	−6.09461	−0.951818	−0.475909	−	0.879495i	$-0.657881\pi$
$41$	−6.09461	−0.951818	−0.475909	+	0.879495i	$0.657881\pi$
$42$	−1.09461	−0.168902
$43$	1.03028	0.157116	0.0785578	−	0.996910i	$-0.474968\pi$
$43$	1.03028	0.157116	0.0785578	+	0.996910i	$0.474968\pi$
$44$	0	0
$45$	−4.73463	−0.705797
$46$	0.515138	0.0759530
$47$	9.01468	1.31493	0.657463	−	0.753487i	$-0.271630\pi$
$47$	9.01468	1.31493	0.657463	+	0.753487i	$0.271630\pi$
$48$	2.12489	0.306701
$49$	−6.73463	−0.962090
$50$	4.76491	0.673860
$51$	−3.21949	−0.450819
$52$	−0.484862	−0.0672383
$53$	−0.670300	−0.0920727	−0.0460364	−	0.998940i	$-0.514659\pi$
$53$	−0.670300	−0.0920727	−0.0460364	+	0.998940i	$0.514659\pi$
$54$	−3.15516	−0.429363
$55$	0	0
$56$	−0.515138	−0.0688382
$57$	−2.12489	−0.281448
$58$	−2.60975	−0.342677
$59$	−2.90539	−0.378250	−0.189125	−	0.981953i	$-0.560565\pi$
$59$	−2.90539	−0.378250	−0.189125	+	0.981953i	$0.560565\pi$
$60$	−6.64002	−0.857223
$61$	9.92007	1.27013	0.635067	−	0.772457i	$-0.280972\pi$
$61$	9.92007	1.27013	0.635067	+	0.772457i	$0.280972\pi$
$62$	−5.28005	−0.670567
$63$	−0.780505	−0.0983344
$64$	1.00000	0.125000
$65$	1.51514	0.187930
$66$	0	0
$67$	−2.06055	−0.251737	−0.125868	−	0.992047i	$-0.540172\pi$
$67$	−2.06055	−0.251737	−0.125868	+	0.992047i	$0.540172\pi$
$68$	−1.51514	−0.183737
$69$	1.09461	0.131775
$70$	1.60975	0.192402
$71$	−2.64002	−0.313313	−0.156657	−	0.987653i	$-0.550072\pi$
$71$	−2.64002	−0.313313	−0.156657	+	0.987653i	$0.550072\pi$
$72$	1.51514	0.178561
$73$	−7.52982	−0.881299	−0.440649	−	0.897679i	$-0.645252\pi$
$73$	−7.52982	−0.881299	−0.440649	+	0.897679i	$0.645252\pi$
$74$	−10.6097	−1.23336
$75$	10.1249	1.16912
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−1.03028	−0.116656
$79$	1.60975	0.181111	0.0905554	−	0.995891i	$-0.471136\pi$
$79$	1.60975	0.181111	0.0905554	+	0.995891i	$0.471136\pi$
$80$	−3.12489	−0.349373
$81$	−11.2498	−1.24997
$82$	−6.09461	−0.673037
$83$	−1.60975	−0.176693	−0.0883464	−	0.996090i	$-0.528158\pi$
$83$	−1.60975	−0.176693	−0.0883464	+	0.996090i	$0.528158\pi$
$84$	−1.09461	−0.119432
$85$	4.73463	0.513543
$86$	1.03028	0.111098
$87$	−5.54541	−0.594531
$88$	0	0
$89$	−1.06433	−0.112819	−0.0564095	−	0.998408i	$-0.517965\pi$
$89$	−1.06433	−0.112819	−0.0564095	+	0.998408i	$0.517965\pi$
$90$	−4.73463	−0.499074
$91$	0.249771	0.0261831
$92$	0.515138	0.0537069
$93$	−11.2195	−1.16341
$94$	9.01468	0.929793
$95$	3.12489	0.320606
$96$	2.12489	0.216870
$97$	7.76491	0.788407	0.394204	−	0.919023i	$-0.371021\pi$
$97$	7.76491	0.788407	0.394204	+	0.919023i	$0.371021\pi$
$98$	−6.73463	−0.680301
$99$	0	0
$100$	4.76491	0.476491
$101$	6.70058	0.666732	0.333366	−	0.942797i	$-0.391815\pi$
$101$	6.70058	0.666732	0.333366	+	0.942797i	$0.391815\pi$
$102$	−3.21949	−0.318777
$103$	−7.54920	−0.743844	−0.371922	−	0.928264i	$-0.621301\pi$
$103$	−7.54920	−0.743844	−0.371922	+	0.928264i	$0.621301\pi$
$104$	−0.484862	−0.0475446
$105$	3.42053	0.333809
$106$	−0.670300	−0.0651052
$107$	−4.84484	−0.468368	−0.234184	−	0.972192i	$-0.575242\pi$
$107$	−4.84484	−0.468368	−0.234184	+	0.972192i	$0.575242\pi$
$108$	−3.15516	−0.303606
$109$	7.82924	0.749905	0.374953	−	0.927044i	$-0.377659\pi$
$109$	7.82924	0.749905	0.374953	+	0.927044i	$0.377659\pi$
$110$	0	0
$111$	−22.5445	−2.13983
$112$	−0.515138	−0.0486760
$113$	−10.8751	−1.02304	−0.511522	−	0.859270i	$-0.670918\pi$
$113$	−10.8751	−1.02304	−0.511522	+	0.859270i	$0.670918\pi$
$114$	−2.12489	−0.199014
$115$	−1.60975	−0.150110
$116$	−2.60975	−0.242309
$117$	−0.734633	−0.0679168
$118$	−2.90539	−0.267463
$119$	0.780505	0.0715488
$120$	−6.64002	−0.606148
$121$	0	0
$122$	9.92007	0.898121
$123$	−12.9503	−1.16769
$124$	−5.28005	−0.474162
$125$	0.734633	0.0657076
$126$	−0.780505	−0.0695329
$127$	−0.780505	−0.0692586	−0.0346293	−	0.999400i	$-0.511025\pi$
$127$	−0.780505	−0.0692586	−0.0346293	+	0.999400i	$0.511025\pi$
$128$	1.00000	0.0883883
$129$	2.18922	0.192750
$130$	1.51514	0.132886
$131$	−18.3103	−1.59978	−0.799890	−	0.600146i	$-0.795109\pi$
$131$	−18.3103	−1.59978	−0.799890	+	0.600146i	$0.795109\pi$
$132$	0	0
$133$	0.515138	0.0446681
$134$	−2.06055	−0.178005
$135$	9.85952	0.848572
$136$	−1.51514	−0.129922
$137$	0.969724	0.0828491	0.0414246	−	0.999142i	$-0.486810\pi$
$137$	0.969724	0.0828491	0.0414246	+	0.999142i	$0.486810\pi$
$138$	1.09461	0.0931793
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	1.60975	0.136048
$141$	19.1552	1.61316
$142$	−2.64002	−0.221546
$143$	0	0
$144$	1.51514	0.126262
$145$	8.15516	0.677249
$146$	−7.52982	−0.623172
$147$	−14.3103	−1.18030
$148$	−10.6097	−0.872116
$149$	−16.0752	−1.31693	−0.658467	−	0.752609i	$-0.728795\pi$
$149$	−16.0752	−1.31693	−0.658467	+	0.752609i	$0.728795\pi$
$150$	10.1249	0.826693
$151$	22.2304	1.80908	0.904542	−	0.426385i	$-0.140213\pi$
$151$	22.2304	1.80908	0.904542	+	0.426385i	$0.140213\pi$
$152$	−1.00000	−0.0811107
$153$	−2.29564	−0.185592
$154$	0	0
$155$	16.4995	1.32528
$156$	−1.03028	−0.0824881
$157$	−20.2304	−1.61456	−0.807281	−	0.590168i	$-0.799062\pi$
$157$	−20.2304	−1.61456	−0.807281	+	0.590168i	$0.799062\pi$
$158$	1.60975	0.128065
$159$	−1.42431	−0.112955
$160$	−3.12489	−0.247044
$161$	−0.265367	−0.0209139
$162$	−11.2498	−0.883865
$163$	−9.03028	−0.707306	−0.353653	−	0.935377i	$-0.615061\pi$
$163$	−9.03028	−0.707306	−0.353653	+	0.935377i	$0.615061\pi$
$164$	−6.09461	−0.475909
$165$	0	0
$166$	−1.60975	−0.124941
$167$	12.2498	0.947916	0.473958	−	0.880548i	$-0.342825\pi$
$167$	12.2498	0.947916	0.473958	+	0.880548i	$0.342825\pi$
$168$	−1.09461	−0.0844509
$169$	−12.7649	−0.981916
$170$	4.73463	0.363130
$171$	−1.51514	−0.115866
$172$	1.03028	0.0785578
$173$	23.5942	1.79383	0.896915	−	0.442203i	$-0.145803\pi$
$173$	23.5942	1.79383	0.896915	+	0.442203i	$0.145803\pi$
$174$	−5.54541	−0.420397
$175$	−2.45459	−0.185549
$176$	0	0
$177$	−6.17362	−0.464038
$178$	−1.06433	−0.0797751
$179$	−23.6547	−1.76804	−0.884018	−	0.467453i	$-0.845172\pi$
$179$	−23.6547	−1.76804	−0.884018	+	0.467453i	$0.845172\pi$
$180$	−4.73463	−0.352899
$181$	−15.7044	−1.16730	−0.583648	−	0.812007i	$-0.698375\pi$
$181$	−15.7044	−1.16730	−0.583648	+	0.812007i	$0.698375\pi$
$182$	0.249771	0.0185142
$183$	21.0790	1.55821
$184$	0.515138	0.0379765
$185$	33.1542	2.43755
$186$	−11.2195	−0.822653
$187$	0	0
$188$	9.01468	0.657463
$189$	1.62534	0.118226
$190$	3.12489	0.226703
$191$	18.0450	1.30569	0.652844	−	0.757493i	$-0.273576\pi$
$191$	18.0450	1.30569	0.652844	+	0.757493i	$0.273576\pi$
$192$	2.12489	0.153350
$193$	−18.2645	−1.31470	−0.657352	−	0.753584i	$-0.728323\pi$
$193$	−18.2645	−1.31470	−0.657352	+	0.753584i	$0.728323\pi$
$194$	7.76491	0.557488
$195$	3.21949	0.230553
$196$	−6.73463	−0.481045
$197$	21.5445	1.53498	0.767491	−	0.641060i	$-0.221505\pi$
$197$	21.5445	1.53498	0.767491	+	0.641060i	$0.221505\pi$
$198$	0	0
$199$	2.18922	0.155190	0.0775948	−	0.996985i	$-0.475276\pi$
$199$	2.18922	0.155190	0.0775948	+	0.996985i	$0.475276\pi$
$200$	4.76491	0.336930
$201$	−4.37844	−0.308831
$202$	6.70058	0.471451
$203$	1.34438	0.0943570
$204$	−3.21949	−0.225410
$205$	19.0450	1.33016
$206$	−7.54920	−0.525977
$207$	0.780505	0.0542489
$208$	−0.484862	−0.0336191
$209$	0	0
$210$	3.42053	0.236039
$211$	16.5639	1.14030	0.570152	−	0.821539i	$-0.306884\pi$
$211$	16.5639	1.14030	0.570152	+	0.821539i	$0.306884\pi$
$212$	−0.670300	−0.0460364
$213$	−5.60975	−0.384374
$214$	−4.84484	−0.331186
$215$	−3.21949	−0.219568
$216$	−3.15516	−0.214682
$217$	2.71995	0.184642
$218$	7.82924	0.530263
$219$	−16.0000	−1.08118
$220$	0	0
$221$	0.734633	0.0494167
$222$	−22.5445	−1.51309
$223$	−15.7990	−1.05798	−0.528989	−	0.848629i	$-0.677429\pi$
$223$	−15.7990	−1.05798	−0.528989	+	0.848629i	$0.677429\pi$
$224$	−0.515138	−0.0344191
$225$	7.21949	0.481300
$226$	−10.8751	−0.723402
$227$	22.2791	1.47872	0.739359	−	0.673312i	$-0.235129\pi$
$227$	22.2791	1.47872	0.739359	+	0.673312i	$0.235129\pi$
$228$	−2.12489	−0.140724
$229$	2.98440	0.197215	0.0986075	−	0.995126i	$-0.468561\pi$
$229$	2.98440	0.197215	0.0986075	+	0.995126i	$0.468561\pi$
$230$	−1.60975	−0.106144
$231$	0	0
$232$	−2.60975	−0.171338
$233$	1.96972	0.129041	0.0645205	−	0.997916i	$-0.479448\pi$
$233$	1.96972	0.129041	0.0645205	+	0.997916i	$0.479448\pi$
$234$	−0.734633	−0.0480244
$235$	−28.1698	−1.83760
$236$	−2.90539	−0.189125
$237$	3.42053	0.222187
$238$	0.780505	0.0505926
$239$	−28.3553	−1.83415	−0.917075	−	0.398714i	$-0.869457\pi$
$239$	−28.3553	−1.83415	−0.917075	+	0.398714i	$0.869457\pi$
$240$	−6.64002	−0.428612
$241$	−3.07901	−0.198337	−0.0991683	−	0.995071i	$-0.531618\pi$
$241$	−3.07901	−0.198337	−0.0991683	+	0.995071i	$0.531618\pi$
$242$	0	0
$243$	−14.4390	−0.926262
$244$	9.92007	0.635067
$245$	21.0450	1.34451
$246$	−12.9503	−0.825684
$247$	0.484862	0.0308510
$248$	−5.28005	−0.335283
$249$	−3.42053	−0.216767
$250$	0.734633	0.0464623
$251$	−12.7493	−0.804729	−0.402365	−	0.915479i	$-0.631812\pi$
$251$	−12.7493	−0.804729	−0.402365	+	0.915479i	$0.631812\pi$
$252$	−0.780505	−0.0491672
$253$	0	0
$254$	−0.780505	−0.0489733
$255$	10.0606	0.630016
$256$	1.00000	0.0625000
$257$	−6.95504	−0.433844	−0.216922	−	0.976189i	$-0.569602\pi$
$257$	−6.95504	−0.433844	−0.216922	+	0.976189i	$0.569602\pi$
$258$	2.18922	0.136295
$259$	5.46548	0.339609
$260$	1.51514	0.0939649
$261$	−3.95413	−0.244754
$262$	−18.3103	−1.13122
$263$	10.6888	0.659097	0.329549	−	0.944139i	$-0.393103\pi$
$263$	10.6888	0.659097	0.329549	+	0.944139i	$0.393103\pi$
$264$	0	0
$265$	2.09461	0.128671
$266$	0.515138	0.0315851
$267$	−2.26159	−0.138407
$268$	−2.06055	−0.125868
$269$	−4.92007	−0.299982	−0.149991	−	0.988687i	$-0.547924\pi$
$269$	−4.92007	−0.299982	−0.149991	+	0.988687i	$0.547924\pi$
$270$	9.85952	0.600031
$271$	9.52982	0.578895	0.289448	−	0.957194i	$-0.406528\pi$
$271$	9.52982	0.578895	0.289448	+	0.957194i	$0.406528\pi$
$272$	−1.51514	−0.0918687
$273$	0.530734	0.0321215
$274$	0.969724	0.0585832
$275$	0	0
$276$	1.09461	0.0658877
$277$	−13.5639	−0.814974	−0.407487	−	0.913211i	$-0.633595\pi$
$277$	−13.5639	−0.814974	−0.407487	+	0.913211i	$0.633595\pi$
$278$	4.00000	0.239904
$279$	−8.00000	−0.478947
$280$	1.60975	0.0962008
$281$	−2.57947	−0.153878	−0.0769392	−	0.997036i	$-0.524515\pi$
$281$	−2.57947	−0.153878	−0.0769392	+	0.997036i	$0.524515\pi$
$282$	19.1552	1.14067
$283$	17.7796	1.05689	0.528443	−	0.848969i	$-0.322776\pi$
$283$	17.7796	1.05689	0.528443	+	0.848969i	$0.322776\pi$
$284$	−2.64002	−0.156657
$285$	6.64002	0.393321
$286$	0	0
$287$	3.13957	0.185323
$288$	1.51514	0.0892804
$289$	−14.7044	−0.864962
$290$	8.15516	0.478888
$291$	16.4995	0.967220
$292$	−7.52982	−0.440649
$293$	−1.95035	−0.113940	−0.0569702	−	0.998376i	$-0.518144\pi$
$293$	−1.95035	−0.113940	−0.0569702	+	0.998376i	$0.518144\pi$
$294$	−14.3103	−0.834595
$295$	9.07901	0.528601
$296$	−10.6097	−0.616679
$297$	0	0
$298$	−16.0752	−0.931213
$299$	−0.249771	−0.0144446
$300$	10.1249	0.584561
$301$	−0.530734	−0.0305910
$302$	22.2304	1.27922
$303$	14.2380	0.817949
$304$	−1.00000	−0.0573539
$305$	−30.9991	−1.77500
$306$	−2.29564	−0.131233
$307$	20.1542	1.15026	0.575132	−	0.818061i	$-0.304951\pi$
$307$	20.1542	1.15026	0.575132	+	0.818061i	$0.304951\pi$
$308$	0	0
$309$	−16.0412	−0.912551
$310$	16.4995	0.937111
$311$	−4.90917	−0.278374	−0.139187	−	0.990266i	$-0.544449\pi$
$311$	−4.90917	−0.278374	−0.139187	+	0.990266i	$0.544449\pi$
$312$	−1.03028	−0.0583279
$313$	−27.5601	−1.55779	−0.778894	−	0.627155i	$-0.784219\pi$
$313$	−27.5601	−1.55779	−0.778894	+	0.627155i	$0.784219\pi$
$314$	−20.2304	−1.14167
$315$	2.43899	0.137421
$316$	1.60975	0.0905554
$317$	28.2791	1.58831	0.794157	−	0.607713i	$-0.207913\pi$
$317$	28.2791	1.58831	0.794157	+	0.607713i	$0.207913\pi$
$318$	−1.42431	−0.0798713
$319$	0	0
$320$	−3.12489	−0.174686
$321$	−10.2947	−0.574596
$322$	−0.265367	−0.0147883
$323$	1.51514	0.0843045
$324$	−11.2498	−0.624987
$325$	−2.31032	−0.128154
$326$	−9.03028	−0.500141
$327$	16.6362	0.919986
$328$	−6.09461	−0.336519
$329$	−4.64380	−0.256021
$330$	0	0
$331$	26.0937	1.43424	0.717120	−	0.696950i	$-0.245460\pi$
$331$	26.0937	1.43424	0.717120	+	0.696950i	$0.245460\pi$
$332$	−1.60975	−0.0883464
$333$	−16.0752	−0.880917
$334$	12.2498	0.670278
$335$	6.43899	0.351800
$336$	−1.09461	−0.0597158
$337$	−19.2148	−1.04670	−0.523348	−	0.852119i	$-0.675317\pi$
$337$	−19.2148	−1.04670	−0.523348	+	0.852119i	$0.675317\pi$
$338$	−12.7649	−0.694320
$339$	−23.1084	−1.25507
$340$	4.73463	0.256772
$341$	0	0
$342$	−1.51514	−0.0819293
$343$	7.07523	0.382027
$344$	1.03028	0.0555488
$345$	−3.42053	−0.184155
$346$	23.5942	1.26843
$347$	3.17076	0.170215	0.0851076	−	0.996372i	$-0.472877\pi$
$347$	3.17076	0.170215	0.0851076	+	0.996372i	$0.472877\pi$
$348$	−5.54541	−0.297265
$349$	−11.5445	−0.617963	−0.308981	−	0.951068i	$-0.599988\pi$
$349$	−11.5445	−0.617963	−0.308981	+	0.951068i	$0.599988\pi$
$350$	−2.45459	−0.131203
$351$	1.52982	0.0816556
$352$	0	0
$353$	5.43899	0.289488	0.144744	−	0.989469i	$-0.453764\pi$
$353$	5.43899	0.289488	0.144744	+	0.989469i	$0.453764\pi$
$354$	−6.17362	−0.328124
$355$	8.24977	0.437852
$356$	−1.06433	−0.0564095
$357$	1.65848	0.0877763
$358$	−23.6547	−1.25019
$359$	37.0890	1.95748	0.978741	−	0.205099i	$-0.0657518\pi$
$359$	37.0890	1.95748	0.978741	+	0.205099i	$0.0657518\pi$
$360$	−4.73463	−0.249537
$361$	1.00000	0.0526316
$362$	−15.7044	−0.825403
$363$	0	0
$364$	0.249771	0.0130915
$365$	23.5298	1.23161
$366$	21.0790	1.10182
$367$	11.8245	0.617236	0.308618	−	0.951186i	$-0.400133\pi$
$367$	11.8245	0.617236	0.308618	+	0.951186i	$0.400133\pi$
$368$	0.515138	0.0268534
$369$	−9.23417	−0.480712
$370$	33.1542	1.72361
$371$	0.345297	0.0179269
$372$	−11.2195	−0.581704
$373$	−29.4948	−1.52719	−0.763593	−	0.645698i	$-0.776566\pi$
$373$	−29.4948	−1.52719	−0.763593	+	0.645698i	$0.776566\pi$
$374$	0	0
$375$	1.56101	0.0806102
$376$	9.01468	0.464897
$377$	1.26537	0.0651697
$378$	1.62534	0.0835987
$379$	29.4655	1.51354	0.756770	−	0.653681i	$-0.226776\pi$
$379$	29.4655	1.51354	0.756770	+	0.653681i	$0.226776\pi$
$380$	3.12489	0.160303
$381$	−1.65848	−0.0849667
$382$	18.0450	0.923260
$383$	11.8789	0.606983	0.303492	−	0.952834i	$-0.401848\pi$
$383$	11.8789	0.606983	0.303492	+	0.952834i	$0.401848\pi$
$384$	2.12489	0.108435
$385$	0	0
$386$	−18.2645	−0.929636
$387$	1.56101	0.0793506
$388$	7.76491	0.394204
$389$	13.6244	0.690786	0.345393	−	0.938458i	$-0.387746\pi$
$389$	13.6244	0.690786	0.345393	+	0.938458i	$0.387746\pi$
$390$	3.21949	0.163025
$391$	−0.780505	−0.0394718
$392$	−6.73463	−0.340150
$393$	−38.9073	−1.96262
$394$	21.5445	1.08540
$395$	−5.03028	−0.253101
$396$	0	0
$397$	17.7943	0.893069	0.446534	−	0.894766i	$-0.352658\pi$
$397$	17.7943	0.893069	0.446534	+	0.894766i	$0.352658\pi$
$398$	2.18922	0.109736
$399$	1.09461	0.0547990
$400$	4.76491	0.238245
$401$	19.0256	0.950092	0.475046	−	0.879961i	$-0.342431\pi$
$401$	19.0256	0.950092	0.475046	+	0.879961i	$0.342431\pi$
$402$	−4.37844	−0.218377
$403$	2.56009	0.127527
$404$	6.70058	0.333366
$405$	35.1542	1.74683
$406$	1.34438	0.0667205
$407$	0	0
$408$	−3.21949	−0.159389
$409$	5.58325	0.276074	0.138037	−	0.990427i	$-0.455921\pi$
$409$	5.58325	0.276074	0.138037	+	0.990427i	$0.455921\pi$
$410$	19.0450	0.940563
$411$	2.06055	0.101640
$412$	−7.54920	−0.371922
$413$	1.49668	0.0736467
$414$	0.780505	0.0383597
$415$	5.03028	0.246927
$416$	−0.484862	−0.0237723
$417$	8.49954	0.416224
$418$	0	0
$419$	20.1698	0.985361	0.492681	−	0.870210i	$-0.336017\pi$
$419$	20.1698	0.985361	0.492681	+	0.870210i	$0.336017\pi$
$420$	3.42053	0.166905
$421$	−17.8292	−0.868944	−0.434472	−	0.900685i	$-0.643065\pi$
$421$	−17.8292	−0.868944	−0.434472	+	0.900685i	$0.643065\pi$
$422$	16.5639	0.806317
$423$	13.6585	0.664098
$424$	−0.670300	−0.0325526
$425$	−7.21949	−0.350197
$426$	−5.60975	−0.271793
$427$	−5.11021	−0.247300
$428$	−4.84484	−0.234184
$429$	0	0
$430$	−3.21949	−0.155258
$431$	10.7687	0.518710	0.259355	−	0.965782i	$-0.416490\pi$
$431$	10.7687	0.518710	0.259355	+	0.965782i	$0.416490\pi$
$432$	−3.15516	−0.151803
$433$	40.6353	1.95281	0.976405	−	0.215949i	$-0.0692846\pi$
$433$	40.6353	1.95281	0.976405	+	0.215949i	$0.0692846\pi$
$434$	2.71995	0.130562
$435$	17.3288	0.830852
$436$	7.82924	0.374953
$437$	−0.515138	−0.0246424
$438$	−16.0000	−0.764510
$439$	−15.0596	−0.718757	−0.359379	−	0.933192i	$-0.617011\pi$
$439$	−15.0596	−0.718757	−0.359379	+	0.933192i	$0.617011\pi$
$440$	0	0
$441$	−10.2039	−0.485900
$442$	0.734633	0.0349429
$443$	−26.1892	−1.24429	−0.622144	−	0.782903i	$-0.713738\pi$
$443$	−26.1892	−1.24429	−0.622144	+	0.782903i	$0.713738\pi$
$444$	−22.5445	−1.06991
$445$	3.32592	0.157664
$446$	−15.7990	−0.748103
$447$	−34.1580	−1.61562
$448$	−0.515138	−0.0243380
$449$	30.5748	1.44291	0.721456	−	0.692460i	$-0.243473\pi$
$449$	30.5748	1.44291	0.721456	+	0.692460i	$0.243473\pi$
$450$	7.21949	0.340330
$451$	0	0
$452$	−10.8751	−0.511522
$453$	47.2370	2.21939
$454$	22.2791	1.04561
$455$	−0.780505	−0.0365907
$456$	−2.12489	−0.0995069
$457$	−16.4693	−0.770400	−0.385200	−	0.922833i	$-0.625867\pi$
$457$	−16.4693	−0.770400	−0.385200	+	0.922833i	$0.625867\pi$
$458$	2.98440	0.139452
$459$	4.78051	0.223135
$460$	−1.60975	−0.0750549
$461$	21.8742	1.01878	0.509391	−	0.860535i	$-0.329871\pi$
$461$	21.8742	1.01878	0.509391	+	0.860535i	$0.329871\pi$
$462$	0	0
$463$	27.8089	1.29239	0.646196	−	0.763172i	$-0.276359\pi$
$463$	27.8089	1.29239	0.646196	+	0.763172i	$0.276359\pi$
$464$	−2.60975	−0.121154
$465$	35.0596	1.62585
$466$	1.96972	0.0912457
$467$	20.3709	0.942652	0.471326	−	0.881959i	$-0.343776\pi$
$467$	20.3709	0.942652	0.471326	+	0.881959i	$0.343776\pi$
$468$	−0.734633	−0.0339584
$469$	1.06147	0.0490141
$470$	−28.1698	−1.29938
$471$	−42.9873	−1.98075
$472$	−2.90539	−0.133731
$473$	0	0
$474$	3.42053	0.157110
$475$	−4.76491	−0.218629
$476$	0.780505	0.0357744
$477$	−1.01560	−0.0465010
$478$	−28.3553	−1.29694
$479$	32.2342	1.47282	0.736409	−	0.676537i	$-0.236520\pi$
$479$	32.2342	1.47282	0.736409	+	0.676537i	$0.236520\pi$
$480$	−6.64002	−0.303074
$481$	5.14426	0.234558
$482$	−3.07901	−0.140245
$483$	−0.563875	−0.0256572
$484$	0	0
$485$	−24.2645	−1.10179
$486$	−14.4390	−0.654966
$487$	−1.81078	−0.0820543	−0.0410272	−	0.999158i	$-0.513063\pi$
$487$	−1.81078	−0.0820543	−0.0410272	+	0.999158i	$0.513063\pi$
$488$	9.92007	0.449060
$489$	−19.1883	−0.867725
$490$	21.0450	0.950714
$491$	4.65940	0.210276	0.105138	−	0.994458i	$-0.466472\pi$
$491$	4.65940	0.210276	0.105138	+	0.994458i	$0.466472\pi$
$492$	−12.9503	−0.583847
$493$	3.95413	0.178085
$494$	0.484862	0.0218150
$495$	0	0
$496$	−5.28005	−0.237081
$497$	1.35998	0.0610033
$498$	−3.42053	−0.153278
$499$	−7.63911	−0.341973	−0.170987	−	0.985273i	$-0.554696\pi$
$499$	−7.63911	−0.341973	−0.170987	+	0.985273i	$0.554696\pi$
$500$	0.734633	0.0328538
$501$	26.0294	1.16291
$502$	−12.7493	−0.569030
$503$	8.26537	0.368535	0.184267	−	0.982876i	$-0.441009\pi$
$503$	8.26537	0.368535	0.184267	+	0.982876i	$0.441009\pi$
$504$	−0.780505	−0.0347665
$505$	−20.9385	−0.931752
$506$	0	0
$507$	−27.1240	−1.20462
$508$	−0.780505	−0.0346293
$509$	11.3756	0.504213	0.252107	−	0.967699i	$-0.418877\pi$
$509$	11.3756	0.504213	0.252107	+	0.967699i	$0.418877\pi$
$510$	10.0606	0.445489
$511$	3.87890	0.171592
$512$	1.00000	0.0441942
$513$	3.15516	0.139304
$514$	−6.95504	−0.306774
$515$	23.5904	1.03952
$516$	2.18922	0.0963750
$517$	0	0
$518$	5.46548	0.240140
$519$	50.1349	2.20068
$520$	1.51514	0.0664432
$521$	−2.62065	−0.114813	−0.0574063	−	0.998351i	$-0.518283\pi$
$521$	−2.62065	−0.114813	−0.0574063	+	0.998351i	$0.518283\pi$
$522$	−3.95413	−0.173067
$523$	15.3150	0.669679	0.334840	−	0.942275i	$-0.391318\pi$
$523$	15.3150	0.669679	0.334840	+	0.942275i	$0.391318\pi$
$524$	−18.3103	−0.799890
$525$	−5.21571	−0.227632
$526$	10.6888	0.466052
$527$	8.00000	0.348485
$528$	0	0
$529$	−22.7346	−0.988462
$530$	2.09461	0.0909840
$531$	−4.40207	−0.191033
$532$	0.515138	0.0223341
$533$	2.95504	0.127997
$534$	−2.26159	−0.0978684
$535$	15.1396	0.654540
$536$	−2.06055	−0.0890023
$537$	−50.2635	−2.16903
$538$	−4.92007	−0.212119
$539$	0	0
$540$	9.85952	0.424286
$541$	−9.09839	−0.391170	−0.195585	−	0.980687i	$-0.562661\pi$
$541$	−9.09839	−0.391170	−0.195585	+	0.980687i	$0.562661\pi$
$542$	9.52982	0.409341
$543$	−33.3700	−1.43204
$544$	−1.51514	−0.0649610
$545$	−24.4655	−1.04799
$546$	0.530734	0.0227133
$547$	19.6547	0.840374	0.420187	−	0.907437i	$-0.361964\pi$
$547$	19.6547	0.840374	0.420187	+	0.907437i	$0.361964\pi$
$548$	0.969724	0.0414246
$549$	15.0303	0.641477
$550$	0	0
$551$	2.60975	0.111179
$552$	1.09461	0.0465897
$553$	−0.829242	−0.0352630
$554$	−13.5639	−0.576274
$555$	70.4490	2.99039
$556$	4.00000	0.169638
$557$	−16.2791	−0.689769	−0.344884	−	0.938645i	$-0.612082\pi$
$557$	−16.2791	−0.689769	−0.344884	+	0.938645i	$0.612082\pi$
$558$	−8.00000	−0.338667
$559$	−0.499542	−0.0211284
$560$	1.60975	0.0680242
$561$	0	0
$562$	−2.57947	−0.108808
$563$	18.0038	0.758769	0.379384	−	0.925239i	$-0.376136\pi$
$563$	18.0038	0.758769	0.379384	+	0.925239i	$0.376136\pi$
$564$	19.1552	0.806578
$565$	33.9835	1.42970
$566$	17.7796	0.747332
$567$	5.79518	0.243375
$568$	−2.64002	−0.110773
$569$	−15.0303	−0.630102	−0.315051	−	0.949075i	$-0.602022\pi$
$569$	−15.0303	−0.630102	−0.315051	+	0.949075i	$0.602022\pi$
$570$	6.64002	0.278120
$571$	−22.5189	−0.942387	−0.471194	−	0.882030i	$-0.656177\pi$
$571$	−22.5189	−0.942387	−0.471194	+	0.882030i	$0.656177\pi$
$572$	0	0
$573$	38.3435	1.60182
$574$	3.13957	0.131043
$575$	2.45459	0.102363
$576$	1.51514	0.0631308
$577$	−19.2947	−0.803250	−0.401625	−	0.915804i	$-0.631554\pi$
$577$	−19.2947	−0.803250	−0.401625	+	0.915804i	$0.631554\pi$
$578$	−14.7044	−0.611621
$579$	−38.8099	−1.61288
$580$	8.15516	0.338625
$581$	0.829242	0.0344028
$582$	16.4995	0.683928
$583$	0	0
$584$	−7.52982	−0.311586
$585$	2.29564	0.0949132
$586$	−1.95035	−0.0805681
$587$	−7.51044	−0.309989	−0.154995	−	0.987915i	$-0.549536\pi$
$587$	−7.51044	−0.309989	−0.154995	+	0.987915i	$0.549536\pi$
$588$	−14.3103	−0.590148
$589$	5.28005	0.217561
$590$	9.07901	0.373777
$591$	45.7796	1.88312
$592$	−10.6097	−0.436058
$593$	−17.2110	−0.706772	−0.353386	−	0.935478i	$-0.614970\pi$
$593$	−17.2110	−0.706772	−0.353386	+	0.935478i	$0.614970\pi$
$594$	0	0
$595$	−2.43899	−0.0999888
$596$	−16.0752	−0.658467
$597$	4.65184	0.190387
$598$	−0.249771	−0.0102139
$599$	−27.5592	−1.12604	−0.563019	−	0.826444i	$-0.690360\pi$
$599$	−27.5592	−1.12604	−0.563019	+	0.826444i	$0.690360\pi$
$600$	10.1249	0.413347
$601$	21.5757	0.880091	0.440045	−	0.897976i	$-0.354962\pi$
$601$	21.5757	0.880091	0.440045	+	0.897976i	$0.354962\pi$
$602$	−0.530734	−0.0216311
$603$	−3.12202	−0.127139
$604$	22.2304	0.904542
$605$	0	0
$606$	14.2380	0.578377
$607$	−35.8889	−1.45668	−0.728342	−	0.685213i	$-0.759709\pi$
$607$	−35.8889	−1.45668	−0.728342	+	0.685213i	$0.759709\pi$
$608$	−1.00000	−0.0405554
$609$	2.85665	0.115757
$610$	−30.9991	−1.25512
$611$	−4.37088	−0.176827
$612$	−2.29564	−0.0927959
$613$	5.12489	0.206992	0.103496	−	0.994630i	$-0.466997\pi$
$613$	5.12489	0.206992	0.103496	+	0.994630i	$0.466997\pi$
$614$	20.1542	0.813359
$615$	40.4683	1.63184
$616$	0	0
$617$	−1.28096	−0.0515697	−0.0257848	−	0.999668i	$-0.508208\pi$
$617$	−1.28096	−0.0515697	−0.0257848	+	0.999668i	$0.508208\pi$
$618$	−16.0412	−0.645271
$619$	−12.9092	−0.518863	−0.259432	−	0.965761i	$-0.583535\pi$
$619$	−12.9092	−0.518863	−0.259432	+	0.965761i	$0.583535\pi$
$620$	16.4995	0.662638
$621$	−1.62534	−0.0652228
$622$	−4.90917	−0.196840
$623$	0.548279	0.0219663
$624$	−1.03028	−0.0412441
$625$	−26.1202	−1.04481
$626$	−27.5601	−1.10152
$627$	0	0
$628$	−20.2304	−0.807281
$629$	16.0752	0.640961
$630$	2.43899	0.0971717
$631$	−15.2039	−0.605258	−0.302629	−	0.953108i	$-0.597864\pi$
$631$	−15.2039	−0.605258	−0.302629	+	0.953108i	$0.597864\pi$
$632$	1.60975	0.0640323
$633$	35.1963	1.39893
$634$	28.2791	1.12311
$635$	2.43899	0.0967883
$636$	−1.42431	−0.0564776
$637$	3.26537	0.129379
$638$	0	0
$639$	−4.00000	−0.158238
$640$	−3.12489	−0.123522
$641$	−0.775808	−0.0306426	−0.0153213	−	0.999883i	$-0.504877\pi$
$641$	−0.775808	−0.0306426	−0.0153213	+	0.999883i	$0.504877\pi$
$642$	−10.2947	−0.406300
$643$	39.5904	1.56129	0.780646	−	0.624974i	$-0.214890\pi$
$643$	39.5904	1.56129	0.780646	+	0.624974i	$0.214890\pi$
$644$	−0.265367	−0.0104569
$645$	−6.84106	−0.269366
$646$	1.51514	0.0596123
$647$	−13.0147	−0.511660	−0.255830	−	0.966722i	$-0.582349\pi$
$647$	−13.0147	−0.511660	−0.255830	+	0.966722i	$0.582349\pi$
$648$	−11.2498	−0.441933
$649$	0	0
$650$	−2.31032	−0.0906183
$651$	5.77959	0.226520
$652$	−9.03028	−0.353653
$653$	−49.2782	−1.92841	−0.964203	−	0.265166i	$-0.914573\pi$
$653$	−49.2782	−1.92841	−0.964203	+	0.265166i	$0.914573\pi$
$654$	16.6362	0.650529
$655$	57.2177	2.23568
$656$	−6.09461	−0.237955
$657$	−11.4087	−0.445096
$658$	−4.64380	−0.181034
$659$	−25.0890	−0.977328	−0.488664	−	0.872472i	$-0.662516\pi$
$659$	−25.0890	−0.977328	−0.488664	+	0.872472i	$0.662516\pi$
$660$	0	0
$661$	−18.9882	−0.738555	−0.369277	−	0.929319i	$-0.620395\pi$
$661$	−18.9882	−0.738555	−0.369277	+	0.929319i	$0.620395\pi$
$662$	26.0937	1.01416
$663$	1.56101	0.0606246
$664$	−1.60975	−0.0624703
$665$	−1.60975	−0.0624233
$666$	−16.0752	−0.622903
$667$	−1.34438	−0.0520546
$668$	12.2498	0.473958
$669$	−33.5710	−1.29793
$670$	6.43899	0.248760
$671$	0	0
$672$	−1.09461	−0.0422255
$673$	−34.4196	−1.32678	−0.663389	−	0.748274i	$-0.730883\pi$
$673$	−34.4196	−1.32678	−0.663389	+	0.748274i	$0.730883\pi$
$674$	−19.2148	−0.740126
$675$	−15.0341	−0.578661
$676$	−12.7649	−0.490958
$677$	14.0185	0.538773	0.269387	−	0.963032i	$-0.413179\pi$
$677$	14.0185	0.538773	0.269387	+	0.963032i	$0.413179\pi$
$678$	−23.1084	−0.887472
$679$	−4.00000	−0.153506
$680$	4.73463	0.181565
$681$	47.3406	1.81410
$682$	0	0
$683$	20.8780	0.798874	0.399437	−	0.916761i	$-0.369206\pi$
$683$	20.8780	0.798874	0.399437	+	0.916761i	$0.369206\pi$
$684$	−1.51514	−0.0579328
$685$	−3.03028	−0.115781
$686$	7.07523	0.270134
$687$	6.34152	0.241944
$688$	1.03028	0.0392789
$689$	0.325003	0.0123816
$690$	−3.42053	−0.130217
$691$	−27.8889	−1.06094	−0.530471	−	0.847703i	$-0.677985\pi$
$691$	−27.8889	−1.06094	−0.530471	+	0.847703i	$0.677985\pi$
$692$	23.5942	0.896915
$693$	0	0
$694$	3.17076	0.120360
$695$	−12.4995	−0.474135
$696$	−5.54541	−0.210198
$697$	9.23417	0.349769
$698$	−11.5445	−0.436966
$699$	4.18544	0.158308
$700$	−2.45459	−0.0927746
$701$	38.5436	1.45577	0.727885	−	0.685699i	$-0.240503\pi$
$701$	38.5436	1.45577	0.727885	+	0.685699i	$0.240503\pi$
$702$	1.52982	0.0577393
$703$	10.6097	0.400154
$704$	0	0
$705$	−59.8577	−2.25437
$706$	5.43899	0.204699
$707$	−3.45172	−0.129815
$708$	−6.17362	−0.232019
$709$	45.9688	1.72639	0.863197	−	0.504867i	$-0.168458\pi$
$709$	45.9688	1.72639	0.863197	+	0.504867i	$0.168458\pi$
$710$	8.24977	0.309608
$711$	2.43899	0.0914693
$712$	−1.06433	−0.0398876
$713$	−2.71995	−0.101863
$714$	1.65848	0.0620672
$715$	0	0
$716$	−23.6547	−0.884018
$717$	−60.2517	−2.25014
$718$	37.0890	1.38415
$719$	24.3784	0.909162	0.454581	−	0.890705i	$-0.349789\pi$
$719$	24.3784	0.909162	0.454581	+	0.890705i	$0.349789\pi$
$720$	−4.73463	−0.176449
$721$	3.88888	0.144829
$722$	1.00000	0.0372161
$723$	−6.54255	−0.243320
$724$	−15.7044	−0.583648
$725$	−12.4352	−0.461832
$726$	0	0
$727$	32.5739	1.20810	0.604049	−	0.796947i	$-0.293553\pi$
$727$	32.5739	1.20810	0.604049	+	0.796947i	$0.293553\pi$
$728$	0.249771	0.00925712
$729$	3.06811	0.113634
$730$	23.5298	0.870878
$731$	−1.56101	−0.0577361
$732$	21.0790	0.779103
$733$	−27.9154	−1.03108	−0.515539	−	0.856866i	$-0.672408\pi$
$733$	−27.9154	−1.03108	−0.515539	+	0.856866i	$0.672408\pi$
$734$	11.8245	0.436452
$735$	44.7181	1.64945
$736$	0.515138	0.0189882
$737$	0	0
$738$	−9.23417	−0.339915
$739$	−50.8586	−1.87086	−0.935432	−	0.353507i	$-0.884989\pi$
$739$	−50.8586	−1.87086	−0.935432	+	0.353507i	$0.884989\pi$
$740$	33.1542	1.21877
$741$	1.03028	0.0378481
$742$	0.345297	0.0126762
$743$	24.3709	0.894081	0.447040	−	0.894514i	$-0.352478\pi$
$743$	24.3709	0.894081	0.447040	+	0.894514i	$0.352478\pi$
$744$	−11.2195	−0.411327
$745$	50.2333	1.84040
$746$	−29.4948	−1.07988
$747$	−2.43899	−0.0892380
$748$	0	0
$749$	2.49576	0.0911931
$750$	1.56101	0.0570000
$751$	−48.8392	−1.78217	−0.891084	−	0.453838i	$-0.850055\pi$
$751$	−48.8392	−1.78217	−0.891084	+	0.453838i	$0.850055\pi$
$752$	9.01468	0.328732
$753$	−27.0908	−0.987245
$754$	1.26537	0.0460820
$755$	−69.4674	−2.52818
$756$	1.62534	0.0591132
$757$	−4.27627	−0.155424	−0.0777118	−	0.996976i	$-0.524761\pi$
$757$	−4.27627	−0.155424	−0.0777118	+	0.996976i	$0.524761\pi$
$758$	29.4655	1.07023
$759$	0	0
$760$	3.12489	0.113352
$761$	−1.65940	−0.0601532	−0.0300766	−	0.999548i	$-0.509575\pi$
$761$	−1.65940	−0.0601532	−0.0300766	+	0.999548i	$0.509575\pi$
$762$	−1.65848	−0.0600805
$763$	−4.03314	−0.146009
$764$	18.0450	0.652844
$765$	7.17362	0.259363
$766$	11.8789	0.429202
$767$	1.40871	0.0508657
$768$	2.12489	0.0766752
$769$	−3.15046	−0.113609	−0.0568043	−	0.998385i	$-0.518091\pi$
$769$	−3.15046	−0.113609	−0.0568043	+	0.998385i	$0.518091\pi$
$770$	0	0
$771$	−14.7787	−0.532241
$772$	−18.2645	−0.657352
$773$	−35.9338	−1.29245	−0.646225	−	0.763147i	$-0.723653\pi$
$773$	−35.9338	−1.29245	−0.646225	+	0.763147i	$0.723653\pi$
$774$	1.56101	0.0561094
$775$	−25.1589	−0.903736
$776$	7.76491	0.278744
$777$	11.6135	0.416633
$778$	13.6244	0.488459
$779$	6.09461	0.218362
$780$	3.21949	0.115276
$781$	0	0
$782$	−0.780505	−0.0279108
$783$	8.23417	0.294265
$784$	−6.73463	−0.240523
$785$	63.2177	2.25634
$786$	−38.9073	−1.38778
$787$	−8.44277	−0.300952	−0.150476	−	0.988614i	$-0.548081\pi$
$787$	−8.44277	−0.300952	−0.150476	+	0.988614i	$0.548081\pi$
$788$	21.5445	0.767491
$789$	22.7124	0.808583
$790$	−5.03028	−0.178969
$791$	5.60219	0.199191
$792$	0	0
$793$	−4.80986	−0.170803
$794$	17.7943	0.631495
$795$	4.45080	0.157854
$796$	2.18922	0.0775948
$797$	34.3784	1.21775	0.608873	−	0.793267i	$-0.291622\pi$
$797$	34.3784	1.21775	0.608873	+	0.793267i	$0.291622\pi$
$798$	1.09461	0.0387488
$799$	−13.6585	−0.483202
$800$	4.76491	0.168465
$801$	−1.61261	−0.0569788
$802$	19.0256	0.671817
$803$	0	0
$804$	−4.37844	−0.154416
$805$	0.829242	0.0292269
$806$	2.56009	0.0901755
$807$	−10.4546	−0.368019
$808$	6.70058	0.235725
$809$	−20.4158	−0.717782	−0.358891	−	0.933379i	$-0.616845\pi$
$809$	−20.4158	−0.717782	−0.358891	+	0.933379i	$0.616845\pi$
$810$	35.1542	1.23519
$811$	8.84484	0.310584	0.155292	−	0.987869i	$-0.450368\pi$
$811$	8.84484	0.310584	0.155292	+	0.987869i	$0.450368\pi$
$812$	1.34438	0.0471785
$813$	20.2498	0.710190
$814$	0	0
$815$	28.2186	0.988454
$816$	−3.21949	−0.112705
$817$	−1.03028	−0.0360448
$818$	5.58325	0.195214
$819$	0.378437	0.0132237
$820$	19.0450	0.665079
$821$	7.69966	0.268720	0.134360	−	0.990933i	$-0.457102\pi$
$821$	7.69966	0.268720	0.134360	+	0.990933i	$0.457102\pi$
$822$	2.06055	0.0718700
$823$	−41.1433	−1.43417	−0.717083	−	0.696987i	$-0.754523\pi$
$823$	−41.1433	−1.43417	−0.717083	+	0.696987i	$0.754523\pi$
$824$	−7.54920	−0.262989
$825$	0	0
$826$	1.49668	0.0520761
$827$	−44.3472	−1.54210	−0.771052	−	0.636772i	$-0.780269\pi$
$827$	−44.3472	−1.54210	−0.771052	+	0.636772i	$0.780269\pi$
$828$	0.780505	0.0271244
$829$	−50.7252	−1.76176	−0.880880	−	0.473339i	$-0.843048\pi$
$829$	−50.7252	−1.76176	−0.880880	+	0.473339i	$0.843048\pi$
$830$	5.03028	0.174603
$831$	−28.8217	−0.999813
$832$	−0.484862	−0.0168096
$833$	10.2039	0.353544
$834$	8.49954	0.294315
$835$	−38.2791	−1.32470
$836$	0	0
$837$	16.6594	0.575833
$838$	20.1698	0.696756
$839$	−7.92007	−0.273431	−0.136716	−	0.990610i	$-0.543655\pi$
$839$	−7.92007	−0.273431	−0.136716	+	0.990610i	$0.543655\pi$
$840$	3.42053	0.118019
$841$	−22.1892	−0.765145
$842$	−17.8292	−0.614436
$843$	−5.48108	−0.188778
$844$	16.5639	0.570152
$845$	39.8889	1.37222
$846$	13.6585	0.469588
$847$	0	0
$848$	−0.670300	−0.0230182
$849$	37.7796	1.29659
$850$	−7.21949	−0.247627
$851$	−5.46548	−0.187354
$852$	−5.60975	−0.192187
$853$	−41.1055	−1.40743	−0.703713	−	0.710484i	$-0.748476\pi$
$853$	−41.1055	−1.40743	−0.703713	+	0.710484i	$0.748476\pi$
$854$	−5.11021	−0.174868
$855$	4.73463	0.161921
$856$	−4.84484	−0.165593
$857$	21.2195	0.724844	0.362422	−	0.932014i	$-0.381950\pi$
$857$	21.2195	0.724844	0.362422	+	0.932014i	$0.381950\pi$
$858$	0	0
$859$	20.3297	0.693640	0.346820	−	0.937932i	$-0.387261\pi$
$859$	20.3297	0.693640	0.346820	+	0.937932i	$0.387261\pi$
$860$	−3.21949	−0.109784
$861$	6.67122	0.227354
$862$	10.7687	0.366783
$863$	−39.2782	−1.33705	−0.668523	−	0.743691i	$-0.733073\pi$
$863$	−39.2782	−1.33705	−0.668523	+	0.743691i	$0.733073\pi$
$864$	−3.15516	−0.107341
$865$	−73.7290	−2.50686
$866$	40.6353	1.38084
$867$	−31.2451	−1.06114
$868$	2.71995	0.0923212
$869$	0	0
$870$	17.3288	0.587501
$871$	0.999083	0.0338526
$872$	7.82924	0.265132
$873$	11.7649	0.398182
$874$	−0.515138	−0.0174248
$875$	−0.378437	−0.0127935
$876$	−16.0000	−0.540590
$877$	45.6656	1.54202	0.771009	−	0.636824i	$-0.219752\pi$
$877$	45.6656	1.54202	0.771009	+	0.636824i	$0.219752\pi$
$878$	−15.0596	−0.508238
$879$	−4.14426	−0.139783
$880$	0	0
$881$	34.9301	1.17682	0.588412	−	0.808561i	$-0.299753\pi$
$881$	34.9301	1.17682	0.588412	+	0.808561i	$0.299753\pi$
$882$	−10.2039	−0.343583
$883$	−7.58039	−0.255100	−0.127550	−	0.991832i	$-0.540711\pi$
$883$	−7.58039	−0.255100	−0.127550	+	0.991832i	$0.540711\pi$
$884$	0.734633	0.0247084
$885$	19.2919	0.648489
$886$	−26.1892	−0.879844
$887$	−34.6987	−1.16507	−0.582535	−	0.812806i	$-0.697939\pi$
$887$	−34.6987	−1.16507	−0.582535	+	0.812806i	$0.697939\pi$
$888$	−22.5445	−0.756544
$889$	0.402068	0.0134849
$890$	3.32592	0.111485
$891$	0	0
$892$	−15.7990	−0.528989
$893$	−9.01468	−0.301665
$894$	−34.1580	−1.14242
$895$	73.9182	2.47081
$896$	−0.515138	−0.0172096
$897$	−0.530734	−0.0177207
$898$	30.5748	1.02029
$899$	13.7796	0.459575
$900$	7.21949	0.240650
$901$	1.01560	0.0338344
$902$	0	0
$903$	−1.12775	−0.0375292
$904$	−10.8751	−0.361701
$905$	49.0743	1.63129
$906$	47.2370	1.56935
$907$	−38.2148	−1.26890	−0.634451	−	0.772963i	$-0.718774\pi$
$907$	−38.2148	−1.26890	−0.634451	+	0.772963i	$0.718774\pi$
$908$	22.2791	0.739359
$909$	10.1523	0.336730
$910$	−0.780505	−0.0258735
$911$	6.51136	0.215731	0.107865	−	0.994166i	$-0.465598\pi$
$911$	6.51136	0.215731	0.107865	+	0.994166i	$0.465598\pi$
$912$	−2.12489	−0.0703620
$913$	0	0
$914$	−16.4693	−0.544755
$915$	−65.8695	−2.17758
$916$	2.98440	0.0986075
$917$	9.43234	0.311483
$918$	4.78051	0.157780
$919$	−38.4390	−1.26799	−0.633993	−	0.773339i	$-0.718585\pi$
$919$	−38.4390	−1.26799	−0.633993	+	0.773339i	$0.718585\pi$
$920$	−1.60975	−0.0530718
$921$	42.8255	1.41115
$922$	21.8742	0.720388
$923$	1.28005	0.0421333
$924$	0	0
$925$	−50.5545	−1.66222
$926$	27.8089	0.913859
$927$	−11.4381	−0.375676
$928$	−2.60975	−0.0856692
$929$	−40.6878	−1.33492	−0.667462	−	0.744643i	$-0.732620\pi$
$929$	−40.6878	−1.33492	−0.667462	+	0.744643i	$0.732620\pi$
$930$	35.0596	1.14965
$931$	6.73463	0.220719
$932$	1.96972	0.0645205
$933$	−10.4314	−0.341510
$934$	20.3709	0.666555
$935$	0	0
$936$	−0.734633	−0.0240122
$937$	−41.6206	−1.35969	−0.679844	−	0.733357i	$-0.737952\pi$
$937$	−41.6206	−1.35969	−0.679844	+	0.733357i	$0.737952\pi$
$938$	1.06147	0.0346582
$939$	−58.5620	−1.91110
$940$	−28.1698	−0.918799
$941$	−44.5436	−1.45208	−0.726040	−	0.687653i	$-0.758641\pi$
$941$	−44.5436	−1.45208	−0.726040	+	0.687653i	$0.758641\pi$
$942$	−42.9873	−1.40060
$943$	−3.13957	−0.102238
$944$	−2.90539	−0.0945624
$945$	−5.07901	−0.165220
$946$	0	0
$947$	3.75779	0.122112	0.0610559	−	0.998134i	$-0.480553\pi$
$947$	3.75779	0.122112	0.0610559	+	0.998134i	$0.480553\pi$
$948$	3.42053	0.111094
$949$	3.65092	0.118514
$950$	−4.76491	−0.154594
$951$	60.0899	1.94855
$952$	0.780505	0.0252963
$953$	−18.1022	−0.586387	−0.293193	−	0.956053i	$-0.594718\pi$
$953$	−18.1022	−0.586387	−0.293193	+	0.956053i	$0.594718\pi$
$954$	−1.01560	−0.0328811
$955$	−56.3884	−1.82469
$956$	−28.3553	−0.917075
$957$	0	0
$958$	32.2342	1.04144
$959$	−0.499542	−0.0161310
$960$	−6.64002	−0.214306
$961$	−3.12110	−0.100681
$962$	5.14426	0.165858
$963$	−7.34060	−0.236548
$964$	−3.07901	−0.0991683
$965$	57.0743	1.83729
$966$	−0.563875	−0.0181424
$967$	−6.45459	−0.207565	−0.103783	−	0.994600i	$-0.533095\pi$
$967$	−6.45459	−0.207565	−0.103783	+	0.994600i	$0.533095\pi$
$968$	0	0
$969$	3.21949	0.103425
$970$	−24.2645	−0.779085
$971$	42.5033	1.36400	0.681998	−	0.731354i	$-0.261111\pi$
$971$	42.5033	1.36400	0.681998	+	0.731354i	$0.261111\pi$
$972$	−14.4390	−0.463131
$973$	−2.06055	−0.0660583
$974$	−1.81078	−0.0580212
$975$	−4.90917	−0.157219
$976$	9.92007	0.317534
$977$	38.2351	1.22325	0.611624	−	0.791148i	$-0.290516\pi$
$977$	38.2351	1.22325	0.611624	+	0.791148i	$0.290516\pi$
$978$	−19.1883	−0.613574
$979$	0	0
$980$	21.0450	0.672256
$981$	11.8624	0.378737
$982$	4.65940	0.148687
$983$	51.7602	1.65089	0.825447	−	0.564479i	$-0.190923\pi$
$983$	51.7602	1.65089	0.825447	+	0.564479i	$0.190923\pi$
$984$	−12.9503	−0.412842
$985$	−67.3241	−2.14512
$986$	3.95413	0.125925
$987$	−9.86755	−0.314088
$988$	0.484862	0.0154255
$989$	0.530734	0.0168764
$990$	0	0
$991$	23.6391	0.750921	0.375460	−	0.926838i	$-0.377485\pi$
$991$	23.6391	0.750921	0.375460	+	0.926838i	$0.377485\pi$
$992$	−5.28005	−0.167642
$993$	55.4461	1.75953
$994$	1.35998	0.0431358
$995$	−6.84106	−0.216876
$996$	−3.42053	−0.108384
$997$	−27.6244	−0.874874	−0.437437	−	0.899249i	$-0.644114\pi$
$997$	−27.6244	−0.874874	−0.437437	+	0.899249i	$0.644114\pi$
$998$	−7.63911	−0.241812
$999$	33.4755	1.05912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bn.1.3	yes	3
11.10	odd	2		4598.2.a.bk.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.bk.1.3	✓	3	11.10	odd	2
4598.2.a.bn.1.3	yes	3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -3.12489 q^{5} +2.12489 q^{6} -0.515138 q^{7} +1.00000 q^{8} +1.51514 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.12489 q^{3} +1.00000 q^{4} -3.12489 q^{5} +2.12489 q^{6} -0.515138 q^{7} +1.00000 q^{8} +1.51514 q^{9} -3.12489 q^{10} +2.12489 q^{12} -0.484862 q^{13} -0.515138 q^{14} -6.64002 q^{15} +1.00000 q^{16} -1.51514 q^{17} +1.51514 q^{18} -1.00000 q^{19} -3.12489 q^{20} -1.09461 q^{21} +0.515138 q^{23} +2.12489 q^{24} +4.76491 q^{25} -0.484862 q^{26} -3.15516 q^{27} -0.515138 q^{28} -2.60975 q^{29} -6.64002 q^{30} -5.28005 q^{31} +1.00000 q^{32} -1.51514 q^{34} +1.60975 q^{35} +1.51514 q^{36} -10.6097 q^{37} -1.00000 q^{38} -1.03028 q^{39} -3.12489 q^{40} -6.09461 q^{41} -1.09461 q^{42} +1.03028 q^{43} -4.73463 q^{45} +0.515138 q^{46} +9.01468 q^{47} +2.12489 q^{48} -6.73463 q^{49} +4.76491 q^{50} -3.21949 q^{51} -0.484862 q^{52} -0.670300 q^{53} -3.15516 q^{54} -0.515138 q^{56} -2.12489 q^{57} -2.60975 q^{58} -2.90539 q^{59} -6.64002 q^{60} +9.92007 q^{61} -5.28005 q^{62} -0.780505 q^{63} +1.00000 q^{64} +1.51514 q^{65} -2.06055 q^{67} -1.51514 q^{68} +1.09461 q^{69} +1.60975 q^{70} -2.64002 q^{71} +1.51514 q^{72} -7.52982 q^{73} -10.6097 q^{74} +10.1249 q^{75} -1.00000 q^{76} -1.03028 q^{78} +1.60975 q^{79} -3.12489 q^{80} -11.2498 q^{81} -6.09461 q^{82} -1.60975 q^{83} -1.09461 q^{84} +4.73463 q^{85} +1.03028 q^{86} -5.54541 q^{87} -1.06433 q^{89} -4.73463 q^{90} +0.249771 q^{91} +0.515138 q^{92} -11.2195 q^{93} +9.01468 q^{94} +3.12489 q^{95} +2.12489 q^{96} +7.76491 q^{97} -6.73463 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 - 2 * q^6 - 2 * q^7 + 3 * q^8 + 5 * q^9	\( 3 q + 3 q^{2} - 2 q^{3} + 3 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} + 3 q^{8} + 5 q^{9} - q^{10} - 2 q^{12} - q^{13} - 2 q^{14} - 12 q^{15} + 3 q^{16} - 5 q^{17} + 5 q^{18} - 3 q^{19} - q^{20} + 6 q^{21} + 2 q^{23} - 2 q^{24} - 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + q^{29} - 12 q^{30} + 3 q^{32} - 5 q^{34} - 4 q^{35} + 5 q^{36} - 23 q^{37} - 3 q^{38} - 4 q^{39} - q^{40} - 9 q^{41} + 6 q^{42} + 4 q^{43} + 3 q^{45} + 2 q^{46} - 6 q^{47} - 2 q^{48} - 3 q^{49} - 2 q^{50} + 8 q^{51} - q^{52} + 5 q^{53} - 2 q^{54} - 2 q^{56} + 2 q^{57} + q^{58} - 18 q^{59} - 12 q^{60} + 6 q^{61} - 20 q^{63} + 3 q^{64} + 5 q^{65} - 8 q^{67} - 5 q^{68} - 6 q^{69} - 4 q^{70} + 5 q^{72} + 10 q^{73} - 23 q^{74} + 22 q^{75} - 3 q^{76} - 4 q^{78} - 4 q^{79} - q^{80} - 17 q^{81} - 9 q^{82} + 4 q^{83} + 6 q^{84} - 3 q^{85} + 4 q^{86} - 18 q^{87} + 7 q^{89} + 3 q^{90} - 16 q^{91} + 2 q^{92} - 16 q^{93} - 6 q^{94} + q^{95} - 2 q^{96} + 7 q^{97} - 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 - 2 * q^3 + 3 * q^4 - q^5 - 2 * q^6 - 2 * q^7 + 3 * q^8 + 5 * q^9 - q^10 - 2 * q^12 - q^13 - 2 * q^14 - 12 * q^15 + 3 * q^16 - 5 * q^17 + 5 * q^18 - 3 * q^19 - q^20 + 6 * q^21 + 2 * q^23 - 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + q^29 - 12 * q^30 + 3 * q^32 - 5 * q^34 - 4 * q^35 + 5 * q^36 - 23 * q^37 - 3 * q^38 - 4 * q^39 - q^40 - 9 * q^41 + 6 * q^42 + 4 * q^43 + 3 * q^45 + 2 * q^46 - 6 * q^47 - 2 * q^48 - 3 * q^49 - 2 * q^50 + 8 * q^51 - q^52 + 5 * q^53 - 2 * q^54 - 2 * q^56 + 2 * q^57 + q^58 - 18 * q^59 - 12 * q^60 + 6 * q^61 - 20 * q^63 + 3 * q^64 + 5 * q^65 - 8 * q^67 - 5 * q^68 - 6 * q^69 - 4 * q^70 + 5 * q^72 + 10 * q^73 - 23 * q^74 + 22 * q^75 - 3 * q^76 - 4 * q^78 - 4 * q^79 - q^80 - 17 * q^81 - 9 * q^82 + 4 * q^83 + 6 * q^84 - 3 * q^85 + 4 * q^86 - 18 * q^87 + 7 * q^89 + 3 * q^90 - 16 * q^91 + 2 * q^92 - 16 * q^93 - 6 * q^94 + q^95 - 2 * q^96 + 7 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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