LMFDB - Embedded newform 230.2.a.a.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(1,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
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			1.2
Root			$-1.79129$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.79129 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.79129 q^{6} +2.79129 q^{7} -1.00000 q^{8} +0.208712 q^{9} +1.00000 q^{10} +3.79129 q^{11} +1.79129 q^{12} +1.20871 q^{13} -2.79129 q^{14} -1.79129 q^{15} +1.00000 q^{16} -3.79129 q^{17} -0.208712 q^{18} +1.20871 q^{19} -1.00000 q^{20} +5.00000 q^{21} -3.79129 q^{22} +1.00000 q^{23} -1.79129 q^{24} +1.00000 q^{25} -1.20871 q^{26} -5.00000 q^{27} +2.79129 q^{28} -1.58258 q^{29} +1.79129 q^{30} +10.3739 q^{31} -1.00000 q^{32} +6.79129 q^{33} +3.79129 q^{34} -2.79129 q^{35} +0.208712 q^{36} -4.00000 q^{37} -1.20871 q^{38} +2.16515 q^{39} +1.00000 q^{40} -2.20871 q^{41} -5.00000 q^{42} -7.16515 q^{43} +3.79129 q^{44} -0.208712 q^{45} -1.00000 q^{46} -13.5826 q^{47} +1.79129 q^{48} +0.791288 q^{49} -1.00000 q^{50} -6.79129 q^{51} +1.20871 q^{52} +6.00000 q^{53} +5.00000 q^{54} -3.79129 q^{55} -2.79129 q^{56} +2.16515 q^{57} +1.58258 q^{58} -4.41742 q^{59} -1.79129 q^{60} -3.37386 q^{61} -10.3739 q^{62} +0.582576 q^{63} +1.00000 q^{64} -1.20871 q^{65} -6.79129 q^{66} -7.16515 q^{67} -3.79129 q^{68} +1.79129 q^{69} +2.79129 q^{70} -5.37386 q^{71} -0.208712 q^{72} -14.7477 q^{73} +4.00000 q^{74} +1.79129 q^{75} +1.20871 q^{76} +10.5826 q^{77} -2.16515 q^{78} +8.00000 q^{79} -1.00000 q^{80} -9.58258 q^{81} +2.20871 q^{82} -6.00000 q^{83} +5.00000 q^{84} +3.79129 q^{85} +7.16515 q^{86} -2.83485 q^{87} -3.79129 q^{88} -3.16515 q^{89} +0.208712 q^{90} +3.37386 q^{91} +1.00000 q^{92} +18.5826 q^{93} +13.5826 q^{94} -1.20871 q^{95} -1.79129 q^{96} +14.9564 q^{97} -0.791288 q^{98} +0.791288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 5 q^{9} + 2 q^{10} + 3 q^{11} - q^{12} + 7 q^{13} - q^{14} + q^{15} + 2 q^{16} - 3 q^{17} - 5 q^{18} + 7 q^{19} - 2 q^{20} + 10 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 + q^6 + q^7 - 2 * q^8 + 5 * q^9 + 2 * q^10 + 3 * q^11 - q^12 + 7 * q^13 - q^14 + q^15 + 2 * q^16 - 3 * q^17 - 5 * q^18 + 7 * q^19 - 2 * q^20 + 10 * q^21 - 3 * q^22 + 2 * q^23 + q^24 + 2 * q^25 - 7 * q^26 - 10 * q^27 + q^28 + 6 * q^29 - q^30 + 7 * q^31 - 2 * q^32 + 9 * q^33 + 3 * q^34 - q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 14 * q^39 + 2 * q^40 - 9 * q^41 - 10 * q^42 + 4 * q^43 + 3 * q^44 - 5 * q^45 - 2 * q^46 - 18 * q^47 - q^48 - 3 * q^49 - 2 * q^50 - 9 * q^51 + 7 * q^52 + 12 * q^53 + 10 * q^54 - 3 * q^55 - q^56 - 14 * q^57 - 6 * q^58 - 18 * q^59 + q^60 + 7 * q^61 - 7 * q^62 - 8 * q^63 + 2 * q^64 - 7 * q^65 - 9 * q^66 + 4 * q^67 - 3 * q^68 - q^69 + q^70 + 3 * q^71 - 5 * q^72 - 2 * q^73 + 8 * q^74 - q^75 + 7 * q^76 + 12 * q^77 + 14 * q^78 + 16 * q^79 - 2 * q^80 - 10 * q^81 + 9 * q^82 - 12 * q^83 + 10 * q^84 + 3 * q^85 - 4 * q^86 - 24 * q^87 - 3 * q^88 + 12 * q^89 + 5 * q^90 - 7 * q^91 + 2 * q^92 + 28 * q^93 + 18 * q^94 - 7 * q^95 + q^96 + 7 * q^97 + 3 * q^98 - 3 * q^99

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.79129	1.03420	0.517100	−	0.855925i	$-0.327011\pi$
$3$	1.79129	1.03420	0.517100	+	0.855925i	$0.327011\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.79129	−0.731290
$7$	2.79129	1.05501	0.527504	−	0.849553i	$-0.323128\pi$
$7$	2.79129	1.05501	0.527504	+	0.849553i	$0.323128\pi$
$8$	−1.00000	−0.353553
$9$	0.208712	0.0695707
$10$	1.00000	0.316228
$11$	3.79129	1.14312	0.571558	−	0.820562i	$-0.306339\pi$
$11$	3.79129	1.14312	0.571558	+	0.820562i	$0.306339\pi$
$12$	1.79129	0.517100
$13$	1.20871	0.335236	0.167618	−	0.985852i	$-0.446392\pi$
$13$	1.20871	0.335236	0.167618	+	0.985852i	$0.446392\pi$
$14$	−2.79129	−0.746003
$15$	−1.79129	−0.462509
$16$	1.00000	0.250000
$17$	−3.79129	−0.919522	−0.459761	−	0.888043i	$-0.652065\pi$
$17$	−3.79129	−0.919522	−0.459761	+	0.888043i	$0.652065\pi$
$18$	−0.208712	−0.0491939
$19$	1.20871	0.277298	0.138649	−	0.990342i	$-0.455724\pi$
$19$	1.20871	0.277298	0.138649	+	0.990342i	$0.455724\pi$
$20$	−1.00000	−0.223607
$21$	5.00000	1.09109
$22$	−3.79129	−0.808305
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.79129	−0.365645
$25$	1.00000	0.200000
$26$	−1.20871	−0.237048
$27$	−5.00000	−0.962250
$28$	2.79129	0.527504
$29$	−1.58258	−0.293877	−0.146938	−	0.989146i	$-0.546942\pi$
$29$	−1.58258	−0.293877	−0.146938	+	0.989146i	$0.546942\pi$
$30$	1.79129	0.327043
$31$	10.3739	1.86320	0.931600	−	0.363484i	$-0.118413\pi$
$31$	10.3739	1.86320	0.931600	+	0.363484i	$0.118413\pi$
$32$	−1.00000	−0.176777
$33$	6.79129	1.18221
$34$	3.79129	0.650201
$35$	−2.79129	−0.471814
$36$	0.208712	0.0347854
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−1.20871	−0.196079
$39$	2.16515	0.346702
$40$	1.00000	0.158114
$41$	−2.20871	−0.344943	−0.172471	−	0.985015i	$-0.555175\pi$
$41$	−2.20871	−0.344943	−0.172471	+	0.985015i	$0.555175\pi$
$42$	−5.00000	−0.771517
$43$	−7.16515	−1.09268	−0.546338	−	0.837565i	$-0.683978\pi$
$43$	−7.16515	−1.09268	−0.546338	+	0.837565i	$0.683978\pi$
$44$	3.79129	0.571558
$45$	−0.208712	−0.0311130
$46$	−1.00000	−0.147442
$47$	−13.5826	−1.98122	−0.990611	−	0.136710i	$-0.956347\pi$
$47$	−13.5826	−1.98122	−0.990611	+	0.136710i	$0.956347\pi$
$48$	1.79129	0.258550
$49$	0.791288	0.113041
$50$	−1.00000	−0.141421
$51$	−6.79129	−0.950971
$52$	1.20871	0.167618
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	5.00000	0.680414
$55$	−3.79129	−0.511217
$56$	−2.79129	−0.373002
$57$	2.16515	0.286781
$58$	1.58258	0.207802
$59$	−4.41742	−0.575100	−0.287550	−	0.957766i	$-0.592841\pi$
$59$	−4.41742	−0.575100	−0.287550	+	0.957766i	$0.592841\pi$
$60$	−1.79129	−0.231254
$61$	−3.37386	−0.431979	−0.215989	−	0.976396i	$-0.569298\pi$
$61$	−3.37386	−0.431979	−0.215989	+	0.976396i	$0.569298\pi$
$62$	−10.3739	−1.31748
$63$	0.582576	0.0733976
$64$	1.00000	0.125000
$65$	−1.20871	−0.149922
$66$	−6.79129	−0.835950
$67$	−7.16515	−0.875363	−0.437681	−	0.899130i	$-0.644200\pi$
$67$	−7.16515	−0.875363	−0.437681	+	0.899130i	$0.644200\pi$
$68$	−3.79129	−0.459761
$69$	1.79129	0.215646
$70$	2.79129	0.333623
$71$	−5.37386	−0.637760	−0.318880	−	0.947795i	$-0.603307\pi$
$71$	−5.37386	−0.637760	−0.318880	+	0.947795i	$0.603307\pi$
$72$	−0.208712	−0.0245970
$73$	−14.7477	−1.72609	−0.863045	−	0.505126i	$-0.831446\pi$
$73$	−14.7477	−1.72609	−0.863045	+	0.505126i	$0.831446\pi$
$74$	4.00000	0.464991
$75$	1.79129	0.206840
$76$	1.20871	0.138649
$77$	10.5826	1.20600
$78$	−2.16515	−0.245155
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	−9.58258	−1.06473
$82$	2.20871	0.243911
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	5.00000	0.545545
$85$	3.79129	0.411223
$86$	7.16515	0.772638
$87$	−2.83485	−0.303928
$88$	−3.79129	−0.404153
$89$	−3.16515	−0.335505	−0.167753	−	0.985829i	$-0.553651\pi$
$89$	−3.16515	−0.335505	−0.167753	+	0.985829i	$0.553651\pi$
$90$	0.208712	0.0220002
$91$	3.37386	0.353677
$92$	1.00000	0.104257
$93$	18.5826	1.92692
$94$	13.5826	1.40094
$95$	−1.20871	−0.124011
$96$	−1.79129	−0.182823
$97$	14.9564	1.51860	0.759298	−	0.650743i	$-0.225542\pi$
$97$	14.9564	1.51860	0.759298	+	0.650743i	$0.225542\pi$
$98$	−0.791288	−0.0799321
$99$	0.791288	0.0795274
$100$	1.00000	0.100000
$101$	13.5826	1.35152	0.675758	−	0.737123i	$-0.263816\pi$
$101$	13.5826	1.35152	0.675758	+	0.737123i	$0.263816\pi$
$102$	6.79129	0.672438
$103$	7.37386	0.726568	0.363284	−	0.931678i	$-0.381655\pi$
$103$	7.37386	0.726568	0.363284	+	0.931678i	$0.381655\pi$
$104$	−1.20871	−0.118524
$105$	−5.00000	−0.487950
$106$	−6.00000	−0.582772
$107$	13.5826	1.31308	0.656539	−	0.754292i	$-0.272020\pi$
$107$	13.5826	1.31308	0.656539	+	0.754292i	$0.272020\pi$
$108$	−5.00000	−0.481125
$109$	10.3739	0.993636	0.496818	−	0.867855i	$-0.334502\pi$
$109$	10.3739	0.993636	0.496818	+	0.867855i	$0.334502\pi$
$110$	3.79129	0.361485
$111$	−7.16515	−0.680086
$112$	2.79129	0.263752
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−2.16515	−0.202785
$115$	−1.00000	−0.0932505
$116$	−1.58258	−0.146938
$117$	0.252273	0.0233226
$118$	4.41742	0.406657
$119$	−10.5826	−0.970103
$120$	1.79129	0.163521
$121$	3.37386	0.306715
$122$	3.37386	0.305455
$123$	−3.95644	−0.356740
$124$	10.3739	0.931600
$125$	−1.00000	−0.0894427
$126$	−0.582576	−0.0519000
$127$	−14.7477	−1.30865	−0.654325	−	0.756214i	$-0.727047\pi$
$127$	−14.7477	−1.30865	−0.654325	+	0.756214i	$0.727047\pi$
$128$	−1.00000	−0.0883883
$129$	−12.8348	−1.13005
$130$	1.20871	0.106011
$131$	9.16515	0.800763	0.400381	−	0.916349i	$-0.368878\pi$
$131$	9.16515	0.800763	0.400381	+	0.916349i	$0.368878\pi$
$132$	6.79129	0.591106
$133$	3.37386	0.292551
$134$	7.16515	0.618975
$135$	5.00000	0.430331
$136$	3.79129	0.325100
$137$	−0.791288	−0.0676043	−0.0338021	−	0.999429i	$-0.510762\pi$
$137$	−0.791288	−0.0676043	−0.0338021	+	0.999429i	$0.510762\pi$
$138$	−1.79129	−0.152485
$139$	−14.7477	−1.25089	−0.625443	−	0.780270i	$-0.715082\pi$
$139$	−14.7477	−1.25089	−0.625443	+	0.780270i	$0.715082\pi$
$140$	−2.79129	−0.235907
$141$	−24.3303	−2.04898
$142$	5.37386	0.450965
$143$	4.58258	0.383214
$144$	0.208712	0.0173927
$145$	1.58258	0.131426
$146$	14.7477	1.22053
$147$	1.41742	0.116907
$148$	−4.00000	−0.328798
$149$	12.7913	1.04790	0.523952	−	0.851748i	$-0.324457\pi$
$149$	12.7913	1.04790	0.523952	+	0.851748i	$0.324457\pi$
$150$	−1.79129	−0.146258
$151$	−6.20871	−0.505258	−0.252629	−	0.967563i	$-0.581295\pi$
$151$	−6.20871	−0.505258	−0.252629	+	0.967563i	$0.581295\pi$
$152$	−1.20871	−0.0980395
$153$	−0.791288	−0.0639718
$154$	−10.5826	−0.852768
$155$	−10.3739	−0.833249
$156$	2.16515	0.173351
$157$	12.7477	1.01738	0.508690	−	0.860950i	$-0.330130\pi$
$157$	12.7477	1.01738	0.508690	+	0.860950i	$0.330130\pi$
$158$	−8.00000	−0.636446
$159$	10.7477	0.852350
$160$	1.00000	0.0790569
$161$	2.79129	0.219984
$162$	9.58258	0.752878
$163$	22.3739	1.75246	0.876228	−	0.481897i	$-0.160052\pi$
$163$	22.3739	1.75246	0.876228	+	0.481897i	$0.160052\pi$
$164$	−2.20871	−0.172471
$165$	−6.79129	−0.528701
$166$	6.00000	0.465690
$167$	−18.3303	−1.41844	−0.709221	−	0.704987i	$-0.750953\pi$
$167$	−18.3303	−1.41844	−0.709221	+	0.704987i	$0.750953\pi$
$168$	−5.00000	−0.385758
$169$	−11.5390	−0.887617
$170$	−3.79129	−0.290779
$171$	0.252273	0.0192918
$172$	−7.16515	−0.546338
$173$	−14.2087	−1.08027	−0.540134	−	0.841579i	$-0.681627\pi$
$173$	−14.2087	−1.08027	−0.540134	+	0.841579i	$0.681627\pi$
$174$	2.83485	0.214909
$175$	2.79129	0.211002
$176$	3.79129	0.285779
$177$	−7.91288	−0.594768
$178$	3.16515	0.237238
$179$	−16.7477	−1.25178	−0.625892	−	0.779910i	$-0.715265\pi$
$179$	−16.7477	−1.25178	−0.625892	+	0.779910i	$0.715265\pi$
$180$	−0.208712	−0.0155565
$181$	13.5390	1.00635	0.503174	−	0.864185i	$-0.332166\pi$
$181$	13.5390	1.00635	0.503174	+	0.864185i	$0.332166\pi$
$182$	−3.37386	−0.250087
$183$	−6.04356	−0.446753
$184$	−1.00000	−0.0737210
$185$	4.00000	0.294086
$186$	−18.5826	−1.36254
$187$	−14.3739	−1.05112
$188$	−13.5826	−0.990611
$189$	−13.9564	−1.01518
$190$	1.20871	0.0876892
$191$	16.4174	1.18792	0.593962	−	0.804493i	$-0.297563\pi$
$191$	16.4174	1.18792	0.593962	+	0.804493i	$0.297563\pi$
$192$	1.79129	0.129275
$193$	6.74773	0.485712	0.242856	−	0.970062i	$-0.421916\pi$
$193$	6.74773	0.485712	0.242856	+	0.970062i	$0.421916\pi$
$194$	−14.9564	−1.07381
$195$	−2.16515	−0.155050
$196$	0.791288	0.0565206
$197$	20.5390	1.46334	0.731672	−	0.681657i	$-0.238740\pi$
$197$	20.5390	1.46334	0.731672	+	0.681657i	$0.238740\pi$
$198$	−0.791288	−0.0562344
$199$	20.3303	1.44118	0.720588	−	0.693363i	$-0.243872\pi$
$199$	20.3303	1.44118	0.720588	+	0.693363i	$0.243872\pi$
$200$	−1.00000	−0.0707107
$201$	−12.8348	−0.905300
$202$	−13.5826	−0.955667
$203$	−4.41742	−0.310042
$204$	−6.79129	−0.475485
$205$	2.20871	0.154263
$206$	−7.37386	−0.513761
$207$	0.208712	0.0145065
$208$	1.20871	0.0838091
$209$	4.58258	0.316983
$210$	5.00000	0.345033
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	6.00000	0.412082
$213$	−9.62614	−0.659572
$214$	−13.5826	−0.928486
$215$	7.16515	0.488659
$216$	5.00000	0.340207
$217$	28.9564	1.96569
$218$	−10.3739	−0.702607
$219$	−26.4174	−1.78512
$220$	−3.79129	−0.255609
$221$	−4.58258	−0.308257
$222$	7.16515	0.480893
$223$	11.1652	0.747674	0.373837	−	0.927494i	$-0.378042\pi$
$223$	11.1652	0.747674	0.373837	+	0.927494i	$0.378042\pi$
$224$	−2.79129	−0.186501
$225$	0.208712	0.0139141
$226$	−6.00000	−0.399114
$227$	4.74773	0.315118	0.157559	−	0.987510i	$-0.449638\pi$
$227$	4.74773	0.315118	0.157559	+	0.987510i	$0.449638\pi$
$228$	2.16515	0.143391
$229$	−16.3303	−1.07914	−0.539568	−	0.841942i	$-0.681413\pi$
$229$	−16.3303	−1.07914	−0.539568	+	0.841942i	$0.681413\pi$
$230$	1.00000	0.0659380
$231$	18.9564	1.24724
$232$	1.58258	0.103901
$233$	7.58258	0.496751	0.248376	−	0.968664i	$-0.420103\pi$
$233$	7.58258	0.496751	0.248376	+	0.968664i	$0.420103\pi$
$234$	−0.252273	−0.0164916
$235$	13.5826	0.886030
$236$	−4.41742	−0.287550
$237$	14.3303	0.930853
$238$	10.5826	0.685966
$239$	3.16515	0.204737	0.102368	−	0.994747i	$-0.467358\pi$
$239$	3.16515	0.204737	0.102368	+	0.994747i	$0.467358\pi$
$240$	−1.79129	−0.115627
$241$	−28.0000	−1.80364	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−28.0000	−1.80364	−0.901819	+	0.432113i	$0.857768\pi$
$242$	−3.37386	−0.216880
$243$	−2.16515	−0.138895
$244$	−3.37386	−0.215989
$245$	−0.791288	−0.0505535
$246$	3.95644	0.252253
$247$	1.46099	0.0929603
$248$	−10.3739	−0.658741
$249$	−10.7477	−0.681110
$250$	1.00000	0.0632456
$251$	30.7913	1.94353	0.971764	−	0.235953i	$-0.0758212\pi$
$251$	30.7913	1.94353	0.971764	+	0.235953i	$0.0758212\pi$
$252$	0.582576	0.0366988
$253$	3.79129	0.238356
$254$	14.7477	0.925355
$255$	6.79129	0.425287
$256$	1.00000	0.0625000
$257$	22.7477	1.41896	0.709482	−	0.704723i	$-0.248929\pi$
$257$	22.7477	1.41896	0.709482	+	0.704723i	$0.248929\pi$
$258$	12.8348	0.799063
$259$	−11.1652	−0.693769
$260$	−1.20871	−0.0749611
$261$	−0.330303	−0.0204452
$262$	−9.16515	−0.566225
$263$	15.7913	0.973733	0.486866	−	0.873477i	$-0.338140\pi$
$263$	15.7913	0.973733	0.486866	+	0.873477i	$0.338140\pi$
$264$	−6.79129	−0.417975
$265$	−6.00000	−0.368577
$266$	−3.37386	−0.206865
$267$	−5.66970	−0.346980
$268$	−7.16515	−0.437681
$269$	16.7477	1.02113	0.510563	−	0.859840i	$-0.329437\pi$
$269$	16.7477	1.02113	0.510563	+	0.859840i	$0.329437\pi$
$270$	−5.00000	−0.304290
$271$	−23.1216	−1.40454	−0.702268	−	0.711912i	$-0.747829\pi$
$271$	−23.1216	−1.40454	−0.702268	+	0.711912i	$0.747829\pi$
$272$	−3.79129	−0.229881
$273$	6.04356	0.365773
$274$	0.791288	0.0478034
$275$	3.79129	0.228623
$276$	1.79129	0.107823
$277$	−1.16515	−0.0700072	−0.0350036	−	0.999387i	$-0.511144\pi$
$277$	−1.16515	−0.0700072	−0.0350036	+	0.999387i	$0.511144\pi$
$278$	14.7477	0.884510
$279$	2.16515	0.129624
$280$	2.79129	0.166811
$281$	−16.7477	−0.999086	−0.499543	−	0.866289i	$-0.666499\pi$
$281$	−16.7477	−0.999086	−0.499543	+	0.866289i	$0.666499\pi$
$282$	24.3303	1.44885
$283$	−28.3303	−1.68406	−0.842031	−	0.539429i	$-0.818640\pi$
$283$	−28.3303	−1.68406	−0.842031	+	0.539429i	$0.818640\pi$
$284$	−5.37386	−0.318880
$285$	−2.16515	−0.128252
$286$	−4.58258	−0.270973
$287$	−6.16515	−0.363917
$288$	−0.208712	−0.0122985
$289$	−2.62614	−0.154479
$290$	−1.58258	−0.0929320
$291$	26.7913	1.57053
$292$	−14.7477	−0.863045
$293$	−27.4955	−1.60630	−0.803151	−	0.595776i	$-0.796845\pi$
$293$	−27.4955	−1.60630	−0.803151	+	0.595776i	$0.796845\pi$
$294$	−1.41742	−0.0826659
$295$	4.41742	0.257192
$296$	4.00000	0.232495
$297$	−18.9564	−1.09996
$298$	−12.7913	−0.740979
$299$	1.20871	0.0699016
$300$	1.79129	0.103420
$301$	−20.0000	−1.15278
$302$	6.20871	0.357271
$303$	24.3303	1.39774
$304$	1.20871	0.0693244
$305$	3.37386	0.193187
$306$	0.791288	0.0452349
$307$	16.5390	0.943931	0.471966	−	0.881617i	$-0.343545\pi$
$307$	16.5390	0.943931	0.471966	+	0.881617i	$0.343545\pi$
$308$	10.5826	0.602998
$309$	13.2087	0.751417
$310$	10.3739	0.589196
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−2.16515	−0.122578
$313$	−18.3739	−1.03855	−0.519276	−	0.854607i	$-0.673798\pi$
$313$	−18.3739	−1.03855	−0.519276	+	0.854607i	$0.673798\pi$
$314$	−12.7477	−0.719396
$315$	−0.582576	−0.0328244
$316$	8.00000	0.450035
$317$	5.20871	0.292550	0.146275	−	0.989244i	$-0.453271\pi$
$317$	5.20871	0.292550	0.146275	+	0.989244i	$0.453271\pi$
$318$	−10.7477	−0.602703
$319$	−6.00000	−0.335936
$320$	−1.00000	−0.0559017
$321$	24.3303	1.35799
$322$	−2.79129	−0.155552
$323$	−4.58258	−0.254981
$324$	−9.58258	−0.532365
$325$	1.20871	0.0670473
$326$	−22.3739	−1.23917
$327$	18.5826	1.02762
$328$	2.20871	0.121956
$329$	−37.9129	−2.09020
$330$	6.79129	0.373848
$331$	6.74773	0.370889	0.185444	−	0.982655i	$-0.440628\pi$
$331$	6.74773	0.370889	0.185444	+	0.982655i	$0.440628\pi$
$332$	−6.00000	−0.329293
$333$	−0.834849	−0.0457494
$334$	18.3303	1.00299
$335$	7.16515	0.391474
$336$	5.00000	0.272772
$337$	−16.7913	−0.914680	−0.457340	−	0.889292i	$-0.651198\pi$
$337$	−16.7913	−0.914680	−0.457340	+	0.889292i	$0.651198\pi$
$338$	11.5390	0.627640
$339$	10.7477	0.583736
$340$	3.79129	0.205611
$341$	39.3303	2.12986
$342$	−0.252273	−0.0136414
$343$	−17.3303	−0.935748
$344$	7.16515	0.386319
$345$	−1.79129	−0.0964397
$346$	14.2087	0.763865
$347$	9.79129	0.525624	0.262812	−	0.964847i	$-0.415350\pi$
$347$	9.79129	0.525624	0.262812	+	0.964847i	$0.415350\pi$
$348$	−2.83485	−0.151964
$349$	26.0000	1.39175	0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000	1.39175	0.695874	+	0.718164i	$0.255017\pi$
$350$	−2.79129	−0.149201
$351$	−6.04356	−0.322581
$352$	−3.79129	−0.202076
$353$	−15.1652	−0.807160	−0.403580	−	0.914944i	$-0.632234\pi$
$353$	−15.1652	−0.807160	−0.403580	+	0.914944i	$0.632234\pi$
$354$	7.91288	0.420565
$355$	5.37386	0.285215
$356$	−3.16515	−0.167753
$357$	−18.9564	−1.00328
$358$	16.7477	0.885145
$359$	−9.16515	−0.483718	−0.241859	−	0.970311i	$-0.577757\pi$
$359$	−9.16515	−0.483718	−0.241859	+	0.970311i	$0.577757\pi$
$360$	0.208712	0.0110001
$361$	−17.5390	−0.923106
$362$	−13.5390	−0.711595
$363$	6.04356	0.317205
$364$	3.37386	0.176838
$365$	14.7477	0.771931
$366$	6.04356	0.315902
$367$	−0.834849	−0.0435787	−0.0217894	−	0.999763i	$-0.506936\pi$
$367$	−0.834849	−0.0435787	−0.0217894	+	0.999763i	$0.506936\pi$
$368$	1.00000	0.0521286
$369$	−0.460985	−0.0239979
$370$	−4.00000	−0.207950
$371$	16.7477	0.869499
$372$	18.5826	0.963462
$373$	−14.7477	−0.763608	−0.381804	−	0.924243i	$-0.624697\pi$
$373$	−14.7477	−0.763608	−0.381804	+	0.924243i	$0.624697\pi$
$374$	14.3739	0.743255
$375$	−1.79129	−0.0925017
$376$	13.5826	0.700468
$377$	−1.91288	−0.0985183
$378$	13.9564	0.717842
$379$	7.37386	0.378770	0.189385	−	0.981903i	$-0.439351\pi$
$379$	7.37386	0.378770	0.189385	+	0.981903i	$0.439351\pi$
$380$	−1.20871	−0.0620056
$381$	−26.4174	−1.35341
$382$	−16.4174	−0.839989
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	−1.79129	−0.0914113
$385$	−10.5826	−0.539338
$386$	−6.74773	−0.343450
$387$	−1.49545	−0.0760182
$388$	14.9564	0.759298
$389$	29.7042	1.50606	0.753031	−	0.657986i	$-0.228591\pi$
$389$	29.7042	1.50606	0.753031	+	0.657986i	$0.228591\pi$
$390$	2.16515	0.109637
$391$	−3.79129	−0.191734
$392$	−0.791288	−0.0399661
$393$	16.4174	0.828150
$394$	−20.5390	−1.03474
$395$	−8.00000	−0.402524
$396$	0.791288	0.0397637
$397$	16.5390	0.830069	0.415035	−	0.909806i	$-0.363769\pi$
$397$	16.5390	0.830069	0.415035	+	0.909806i	$0.363769\pi$
$398$	−20.3303	−1.01907
$399$	6.04356	0.302556
$400$	1.00000	0.0500000
$401$	22.7477	1.13597	0.567984	−	0.823040i	$-0.307724\pi$
$401$	22.7477	1.13597	0.567984	+	0.823040i	$0.307724\pi$
$402$	12.8348	0.640144
$403$	12.5390	0.624613
$404$	13.5826	0.675758
$405$	9.58258	0.476162
$406$	4.41742	0.219233
$407$	−15.1652	−0.751709
$408$	6.79129	0.336219
$409$	−22.7913	−1.12696	−0.563478	−	0.826131i	$-0.690537\pi$
$409$	−22.7913	−1.12696	−0.563478	+	0.826131i	$0.690537\pi$
$410$	−2.20871	−0.109081
$411$	−1.41742	−0.0699164
$412$	7.37386	0.363284
$413$	−12.3303	−0.606735
$414$	−0.208712	−0.0102576
$415$	6.00000	0.294528
$416$	−1.20871	−0.0592620
$417$	−26.4174	−1.29367
$418$	−4.58258	−0.224141
$419$	39.1652	1.91334	0.956671	−	0.291170i	$-0.0940444\pi$
$419$	39.1652	1.91334	0.956671	+	0.291170i	$0.0940444\pi$
$420$	−5.00000	−0.243975
$421$	−23.1216	−1.12688	−0.563439	−	0.826158i	$-0.690522\pi$
$421$	−23.1216	−1.12688	−0.563439	+	0.826158i	$0.690522\pi$
$422$	10.0000	0.486792
$423$	−2.83485	−0.137835
$424$	−6.00000	−0.291386
$425$	−3.79129	−0.183904
$426$	9.62614	0.466388
$427$	−9.41742	−0.455741
$428$	13.5826	0.656539
$429$	8.20871	0.396320
$430$	−7.16515	−0.345534
$431$	−19.9129	−0.959170	−0.479585	−	0.877496i	$-0.659213\pi$
$431$	−19.9129	−0.959170	−0.479585	+	0.877496i	$0.659213\pi$
$432$	−5.00000	−0.240563
$433$	1.53901	0.0739603	0.0369802	−	0.999316i	$-0.488226\pi$
$433$	1.53901	0.0739603	0.0369802	+	0.999316i	$0.488226\pi$
$434$	−28.9564	−1.38995
$435$	2.83485	0.135921
$436$	10.3739	0.496818
$437$	1.20871	0.0578205
$438$	26.4174	1.26227
$439$	25.5390	1.21891	0.609455	−	0.792820i	$-0.291388\pi$
$439$	25.5390	1.21891	0.609455	+	0.792820i	$0.291388\pi$
$440$	3.79129	0.180743
$441$	0.165151	0.00786435
$442$	4.58258	0.217971
$443$	−35.2087	−1.67282	−0.836408	−	0.548107i	$-0.815349\pi$
$443$	−35.2087	−1.67282	−0.836408	+	0.548107i	$0.815349\pi$
$444$	−7.16515	−0.340043
$445$	3.16515	0.150043
$446$	−11.1652	−0.528685
$447$	22.9129	1.08374
$448$	2.79129	0.131876
$449$	25.1216	1.18556	0.592781	−	0.805364i	$-0.298030\pi$
$449$	25.1216	1.18556	0.592781	+	0.805364i	$0.298030\pi$
$450$	−0.208712	−0.00983879
$451$	−8.37386	−0.394310
$452$	6.00000	0.282216
$453$	−11.1216	−0.522538
$454$	−4.74773	−0.222822
$455$	−3.37386	−0.158169
$456$	−2.16515	−0.101393
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	16.3303	0.763065
$459$	18.9564	0.884811
$460$	−1.00000	−0.0466252
$461$	−1.25227	−0.0583242	−0.0291621	−	0.999575i	$-0.509284\pi$
$461$	−1.25227	−0.0583242	−0.0291621	+	0.999575i	$0.509284\pi$
$462$	−18.9564	−0.881933
$463$	−10.0000	−0.464739	−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000	−0.464739	−0.232370	+	0.972628i	$0.574648\pi$
$464$	−1.58258	−0.0734692
$465$	−18.5826	−0.861746
$466$	−7.58258	−0.351256
$467$	25.9129	1.19911	0.599553	−	0.800335i	$-0.295345\pi$
$467$	25.9129	1.19911	0.599553	+	0.800335i	$0.295345\pi$
$468$	0.252273	0.0116613
$469$	−20.0000	−0.923514
$470$	−13.5826	−0.626517
$471$	22.8348	1.05217
$472$	4.41742	0.203328
$473$	−27.1652	−1.24905
$474$	−14.3303	−0.658213
$475$	1.20871	0.0554595
$476$	−10.5826	−0.485052
$477$	1.25227	0.0573376
$478$	−3.16515	−0.144771
$479$	−39.4955	−1.80459	−0.902297	−	0.431116i	$-0.858120\pi$
$479$	−39.4955	−1.80459	−0.902297	+	0.431116i	$0.858120\pi$
$480$	1.79129	0.0817607
$481$	−4.83485	−0.220450
$482$	28.0000	1.27537
$483$	5.00000	0.227508
$484$	3.37386	0.153357
$485$	−14.9564	−0.679137
$486$	2.16515	0.0982133
$487$	15.5826	0.706114	0.353057	−	0.935602i	$-0.385142\pi$
$487$	15.5826	0.706114	0.353057	+	0.935602i	$0.385142\pi$
$488$	3.37386	0.152728
$489$	40.0780	1.81239
$490$	0.791288	0.0357467
$491$	−16.7477	−0.755814	−0.377907	−	0.925843i	$-0.623356\pi$
$491$	−16.7477	−0.755814	−0.377907	+	0.925843i	$0.623356\pi$
$492$	−3.95644	−0.178370
$493$	6.00000	0.270226
$494$	−1.46099	−0.0657328
$495$	−0.791288	−0.0355657
$496$	10.3739	0.465800
$497$	−15.0000	−0.672842
$498$	10.7477	0.481617
$499$	23.1652	1.03701	0.518507	−	0.855073i	$-0.326488\pi$
$499$	23.1652	1.03701	0.518507	+	0.855073i	$0.326488\pi$
$500$	−1.00000	−0.0447214
$501$	−32.8348	−1.46695
$502$	−30.7913	−1.37428
$503$	18.7913	0.837862	0.418931	−	0.908018i	$-0.362405\pi$
$503$	18.7913	0.837862	0.418931	+	0.908018i	$0.362405\pi$
$504$	−0.582576	−0.0259500
$505$	−13.5826	−0.604417
$506$	−3.79129	−0.168543
$507$	−20.6697	−0.917973
$508$	−14.7477	−0.654325
$509$	7.25227	0.321451	0.160726	−	0.986999i	$-0.448617\pi$
$509$	7.25227	0.321451	0.160726	+	0.986999i	$0.448617\pi$
$510$	−6.79129	−0.300723
$511$	−41.1652	−1.82104
$512$	−1.00000	−0.0441942
$513$	−6.04356	−0.266830
$514$	−22.7477	−1.00336
$515$	−7.37386	−0.324931
$516$	−12.8348	−0.565023
$517$	−51.4955	−2.26477
$518$	11.1652	0.490569
$519$	−25.4519	−1.11721
$520$	1.20871	0.0530055
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	0.330303	0.0144570
$523$	−1.16515	−0.0509485	−0.0254743	−	0.999675i	$-0.508110\pi$
$523$	−1.16515	−0.0509485	−0.0254743	+	0.999675i	$0.508110\pi$
$524$	9.16515	0.400381
$525$	5.00000	0.218218
$526$	−15.7913	−0.688533
$527$	−39.3303	−1.71325
$528$	6.79129	0.295553
$529$	1.00000	0.0434783
$530$	6.00000	0.260623
$531$	−0.921970	−0.0400101
$532$	3.37386	0.146276
$533$	−2.66970	−0.115637
$534$	5.66970	0.245352
$535$	−13.5826	−0.587226
$536$	7.16515	0.309487
$537$	−30.0000	−1.29460
$538$	−16.7477	−0.722046
$539$	3.00000	0.129219
$540$	5.00000	0.215166
$541$	38.3303	1.64795	0.823974	−	0.566627i	$-0.191752\pi$
$541$	38.3303	1.64795	0.823974	+	0.566627i	$0.191752\pi$
$542$	23.1216	0.993157
$543$	24.2523	1.04076
$544$	3.79129	0.162550
$545$	−10.3739	−0.444367
$546$	−6.04356	−0.258641
$547$	15.1216	0.646553	0.323276	−	0.946305i	$-0.395216\pi$
$547$	15.1216	0.646553	0.323276	+	0.946305i	$0.395216\pi$
$548$	−0.791288	−0.0338021
$549$	−0.704166	−0.0300531
$550$	−3.79129	−0.161661
$551$	−1.91288	−0.0814914
$552$	−1.79129	−0.0762423
$553$	22.3303	0.949581
$554$	1.16515	0.0495025
$555$	7.16515	0.304144
$556$	−14.7477	−0.625443
$557$	30.3303	1.28514	0.642568	−	0.766229i	$-0.277869\pi$
$557$	30.3303	1.28514	0.642568	+	0.766229i	$0.277869\pi$
$558$	−2.16515	−0.0916582
$559$	−8.66061	−0.366305
$560$	−2.79129	−0.117953
$561$	−25.7477	−1.08707
$562$	16.7477	0.706460
$563$	3.16515	0.133395	0.0666976	−	0.997773i	$-0.478754\pi$
$563$	3.16515	0.133395	0.0666976	+	0.997773i	$0.478754\pi$
$564$	−24.3303	−1.02449
$565$	−6.00000	−0.252422
$566$	28.3303	1.19081
$567$	−26.7477	−1.12330
$568$	5.37386	0.225482
$569$	15.4955	0.649603	0.324802	−	0.945782i	$-0.394702\pi$
$569$	15.4955	0.649603	0.324802	+	0.945782i	$0.394702\pi$
$570$	2.16515	0.0906882
$571$	30.1216	1.26055	0.630275	−	0.776372i	$-0.282942\pi$
$571$	30.1216	1.26055	0.630275	+	0.776372i	$0.282942\pi$
$572$	4.58258	0.191607
$573$	29.4083	1.22855
$574$	6.16515	0.257328
$575$	1.00000	0.0417029
$576$	0.208712	0.00869634
$577$	22.8348	0.950627	0.475314	−	0.879816i	$-0.342335\pi$
$577$	22.8348	0.950627	0.475314	+	0.879816i	$0.342335\pi$
$578$	2.62614	0.109233
$579$	12.0871	0.502324
$580$	1.58258	0.0657129
$581$	−16.7477	−0.694813
$582$	−26.7913	−1.11053
$583$	22.7477	0.942115
$584$	14.7477	0.610265
$585$	−0.252273	−0.0104302
$586$	27.4955	1.13583
$587$	−26.2087	−1.08175	−0.540875	−	0.841103i	$-0.681907\pi$
$587$	−26.2087	−1.08175	−0.540875	+	0.841103i	$0.681907\pi$
$588$	1.41742	0.0584536
$589$	12.5390	0.516661
$590$	−4.41742	−0.181862
$591$	36.7913	1.51339
$592$	−4.00000	−0.164399
$593$	13.9129	0.571333	0.285667	−	0.958329i	$-0.407785\pi$
$593$	13.9129	0.571333	0.285667	+	0.958329i	$0.407785\pi$
$594$	18.9564	0.777792
$595$	10.5826	0.433843
$596$	12.7913	0.523952
$597$	36.4174	1.49047
$598$	−1.20871	−0.0494279
$599$	−40.1216	−1.63932	−0.819662	−	0.572848i	$-0.805839\pi$
$599$	−40.1216	−1.63932	−0.819662	+	0.572848i	$0.805839\pi$
$600$	−1.79129	−0.0731290
$601$	−22.7913	−0.929676	−0.464838	−	0.885396i	$-0.653887\pi$
$601$	−22.7913	−0.929676	−0.464838	+	0.885396i	$0.653887\pi$
$602$	20.0000	0.815139
$603$	−1.49545	−0.0608996
$604$	−6.20871	−0.252629
$605$	−3.37386	−0.137167
$606$	−24.3303	−0.988351
$607$	−28.0000	−1.13648	−0.568242	−	0.822861i	$-0.692376\pi$
$607$	−28.0000	−1.13648	−0.568242	+	0.822861i	$0.692376\pi$
$608$	−1.20871	−0.0490198
$609$	−7.91288	−0.320646
$610$	−3.37386	−0.136604
$611$	−16.4174	−0.664178
$612$	−0.791288	−0.0319859
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	−16.5390	−0.667460
$615$	3.95644	0.159539
$616$	−10.5826	−0.426384
$617$	44.8693	1.80637	0.903185	−	0.429251i	$-0.141222\pi$
$617$	44.8693	1.80637	0.903185	+	0.429251i	$0.141222\pi$
$618$	−13.2087	−0.531332
$619$	2.79129	0.112191	0.0560957	−	0.998425i	$-0.482135\pi$
$619$	2.79129	0.112191	0.0560957	+	0.998425i	$0.482135\pi$
$620$	−10.3739	−0.416624
$621$	−5.00000	−0.200643
$622$	−12.0000	−0.481156
$623$	−8.83485	−0.353961
$624$	2.16515	0.0866754
$625$	1.00000	0.0400000
$626$	18.3739	0.734367
$627$	8.20871	0.327824
$628$	12.7477	0.508690
$629$	15.1652	0.604674
$630$	0.582576	0.0232104
$631$	−17.9129	−0.713100	−0.356550	−	0.934276i	$-0.616047\pi$
$631$	−17.9129	−0.713100	−0.356550	+	0.934276i	$0.616047\pi$
$632$	−8.00000	−0.318223
$633$	−17.9129	−0.711973
$634$	−5.20871	−0.206864
$635$	14.7477	0.585246
$636$	10.7477	0.426175
$637$	0.956439	0.0378955
$638$	6.00000	0.237542
$639$	−1.12159	−0.0443694
$640$	1.00000	0.0395285
$641$	−3.16515	−0.125016	−0.0625080	−	0.998044i	$-0.519910\pi$
$641$	−3.16515	−0.125016	−0.0625080	+	0.998044i	$0.519910\pi$
$642$	−24.3303	−0.960240
$643$	−20.7477	−0.818210	−0.409105	−	0.912487i	$-0.634159\pi$
$643$	−20.7477	−0.818210	−0.409105	+	0.912487i	$0.634159\pi$
$644$	2.79129	0.109992
$645$	12.8348	0.505372
$646$	4.58258	0.180299
$647$	2.83485	0.111449	0.0557247	−	0.998446i	$-0.482253\pi$
$647$	2.83485	0.111449	0.0557247	+	0.998446i	$0.482253\pi$
$648$	9.58258	0.376439
$649$	−16.7477	−0.657406
$650$	−1.20871	−0.0474096
$651$	51.8693	2.03292
$652$	22.3739	0.876228
$653$	35.5390	1.39075	0.695375	−	0.718647i	$-0.255238\pi$
$653$	35.5390	1.39075	0.695375	+	0.718647i	$0.255238\pi$
$654$	−18.5826	−0.726636
$655$	−9.16515	−0.358112
$656$	−2.20871	−0.0862357
$657$	−3.07803	−0.120085
$658$	37.9129	1.47800
$659$	−27.1652	−1.05820	−0.529102	−	0.848558i	$-0.677471\pi$
$659$	−27.1652	−1.05820	−0.529102	+	0.848558i	$0.677471\pi$
$660$	−6.79129	−0.264351
$661$	−39.3739	−1.53147	−0.765733	−	0.643159i	$-0.777624\pi$
$661$	−39.3739	−1.53147	−0.765733	+	0.643159i	$0.777624\pi$
$662$	−6.74773	−0.262258
$663$	−8.20871	−0.318800
$664$	6.00000	0.232845
$665$	−3.37386	−0.130833
$666$	0.834849	0.0323497
$667$	−1.58258	−0.0612776
$668$	−18.3303	−0.709221
$669$	20.0000	0.773245
$670$	−7.16515	−0.276814
$671$	−12.7913	−0.493802
$672$	−5.00000	−0.192879
$673$	38.0000	1.46479	0.732396	−	0.680879i	$-0.238402\pi$
$673$	38.0000	1.46479	0.732396	+	0.680879i	$0.238402\pi$
$674$	16.7913	0.646776
$675$	−5.00000	−0.192450
$676$	−11.5390	−0.443808
$677$	−30.6606	−1.17838	−0.589191	−	0.807993i	$-0.700554\pi$
$677$	−30.6606	−1.17838	−0.589191	+	0.807993i	$0.700554\pi$
$678$	−10.7477	−0.412764
$679$	41.7477	1.60213
$680$	−3.79129	−0.145389
$681$	8.50455	0.325895
$682$	−39.3303	−1.50604
$683$	2.37386	0.0908334	0.0454167	−	0.998968i	$-0.485538\pi$
$683$	2.37386	0.0908334	0.0454167	+	0.998968i	$0.485538\pi$
$684$	0.252273	0.00964590
$685$	0.791288	0.0302336
$686$	17.3303	0.661674
$687$	−29.2523	−1.11604
$688$	−7.16515	−0.273169
$689$	7.25227	0.276290
$690$	1.79129	0.0681932
$691$	15.2523	0.580224	0.290112	−	0.956993i	$-0.406307\pi$
$691$	15.2523	0.580224	0.290112	+	0.956993i	$0.406307\pi$
$692$	−14.2087	−0.540134
$693$	2.20871	0.0839020
$694$	−9.79129	−0.371672
$695$	14.7477	0.559413
$696$	2.83485	0.107455
$697$	8.37386	0.317183
$698$	−26.0000	−0.984115
$699$	13.5826	0.513740
$700$	2.79129	0.105501
$701$	9.62614	0.363574	0.181787	−	0.983338i	$-0.441812\pi$
$701$	9.62614	0.363574	0.181787	+	0.983338i	$0.441812\pi$
$702$	6.04356	0.228100
$703$	−4.83485	−0.182350
$704$	3.79129	0.142890
$705$	24.3303	0.916332
$706$	15.1652	0.570748
$707$	37.9129	1.42586
$708$	−7.91288	−0.297384
$709$	34.5390	1.29714	0.648570	−	0.761155i	$-0.275367\pi$
$709$	34.5390	1.29714	0.648570	+	0.761155i	$0.275367\pi$
$710$	−5.37386	−0.201678
$711$	1.66970	0.0626185
$712$	3.16515	0.118619
$713$	10.3739	0.388504
$714$	18.9564	0.709427
$715$	−4.58258	−0.171379
$716$	−16.7477	−0.625892
$717$	5.66970	0.211739
$718$	9.16515	0.342040
$719$	−29.5390	−1.10162	−0.550810	−	0.834631i	$-0.685681\pi$
$719$	−29.5390	−1.10162	−0.550810	+	0.834631i	$0.685681\pi$
$720$	−0.208712	−0.00777824
$721$	20.5826	0.766535
$722$	17.5390	0.652735
$723$	−50.1561	−1.86532
$724$	13.5390	0.503174
$725$	−1.58258	−0.0587754
$726$	−6.04356	−0.224298
$727$	−2.12159	−0.0786854	−0.0393427	−	0.999226i	$-0.512526\pi$
$727$	−2.12159	−0.0786854	−0.0393427	+	0.999226i	$0.512526\pi$
$728$	−3.37386	−0.125044
$729$	24.8693	0.921086
$730$	−14.7477	−0.545838
$731$	27.1652	1.00474
$732$	−6.04356	−0.223376
$733$	26.0000	0.960332	0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000	0.960332	0.480166	+	0.877178i	$0.340576\pi$
$734$	0.834849	0.0308148
$735$	−1.41742	−0.0522825
$736$	−1.00000	−0.0368605
$737$	−27.1652	−1.00064
$738$	0.460985	0.0169691
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	4.00000	0.147043
$741$	2.61704	0.0961395
$742$	−16.7477	−0.614828
$743$	9.95644	0.365266	0.182633	−	0.983181i	$-0.441538\pi$
$743$	9.95644	0.365266	0.182633	+	0.983181i	$0.441538\pi$
$744$	−18.5826	−0.681270
$745$	−12.7913	−0.468637
$746$	14.7477	0.539953
$747$	−1.25227	−0.0458183
$748$	−14.3739	−0.525561
$749$	37.9129	1.38531
$750$	1.79129	0.0654086
$751$	18.7477	0.684114	0.342057	−	0.939679i	$-0.388876\pi$
$751$	18.7477	0.684114	0.342057	+	0.939679i	$0.388876\pi$
$752$	−13.5826	−0.495306
$753$	55.1561	2.01000
$754$	1.91288	0.0696629
$755$	6.20871	0.225958
$756$	−13.9564	−0.507591
$757$	26.3303	0.956991	0.478496	−	0.878090i	$-0.341182\pi$
$757$	26.3303	0.956991	0.478496	+	0.878090i	$0.341182\pi$
$758$	−7.37386	−0.267831
$759$	6.79129	0.246508
$760$	1.20871	0.0438446
$761$	−33.9564	−1.23092	−0.615460	−	0.788168i	$-0.711030\pi$
$761$	−33.9564	−1.23092	−0.615460	+	0.788168i	$0.711030\pi$
$762$	26.4174	0.957002
$763$	28.9564	1.04829
$764$	16.4174	0.593962
$765$	0.791288	0.0286091
$766$	24.0000	0.867155
$767$	−5.33939	−0.192794
$768$	1.79129	0.0646375
$769$	−3.66970	−0.132333	−0.0661663	−	0.997809i	$-0.521077\pi$
$769$	−3.66970	−0.132333	−0.0661663	+	0.997809i	$0.521077\pi$
$770$	10.5826	0.381370
$771$	40.7477	1.46749
$772$	6.74773	0.242856
$773$	−21.4955	−0.773138	−0.386569	−	0.922261i	$-0.626340\pi$
$773$	−21.4955	−0.773138	−0.386569	+	0.922261i	$0.626340\pi$
$774$	1.49545	0.0537530
$775$	10.3739	0.372640
$776$	−14.9564	−0.536905
$777$	−20.0000	−0.717496
$778$	−29.7042	−1.06495
$779$	−2.66970	−0.0956518
$780$	−2.16515	−0.0775249
$781$	−20.3739	−0.729034
$782$	3.79129	0.135576
$783$	7.91288	0.282783
$784$	0.791288	0.0282603
$785$	−12.7477	−0.454986
$786$	−16.4174	−0.585590
$787$	−8.41742	−0.300049	−0.150024	−	0.988682i	$-0.547935\pi$
$787$	−8.41742	−0.300049	−0.150024	+	0.988682i	$0.547935\pi$
$788$	20.5390	0.731672
$789$	28.2867	1.00703
$790$	8.00000	0.284627
$791$	16.7477	0.595481
$792$	−0.791288	−0.0281172
$793$	−4.07803	−0.144815
$794$	−16.5390	−0.586948
$795$	−10.7477	−0.381183
$796$	20.3303	0.720588
$797$	−49.9129	−1.76800	−0.884002	−	0.467482i	$-0.845161\pi$
$797$	−49.9129	−1.76800	−0.884002	+	0.467482i	$0.845161\pi$
$798$	−6.04356	−0.213940
$799$	51.4955	1.82178
$800$	−1.00000	−0.0353553
$801$	−0.660606	−0.0233413
$802$	−22.7477	−0.803250
$803$	−55.9129	−1.97312
$804$	−12.8348	−0.452650
$805$	−2.79129	−0.0983800
$806$	−12.5390	−0.441668
$807$	30.0000	1.05605
$808$	−13.5826	−0.477833
$809$	11.0436	0.388271	0.194135	−	0.980975i	$-0.437810\pi$
$809$	11.0436	0.388271	0.194135	+	0.980975i	$0.437810\pi$
$810$	−9.58258	−0.336697
$811$	−47.9129	−1.68245	−0.841224	−	0.540686i	$-0.818165\pi$
$811$	−47.9129	−1.68245	−0.841224	+	0.540686i	$0.818165\pi$
$812$	−4.41742	−0.155021
$813$	−41.4174	−1.45257
$814$	15.1652	0.531538
$815$	−22.3739	−0.783722
$816$	−6.79129	−0.237743
$817$	−8.66061	−0.302996
$818$	22.7913	0.796879
$819$	0.704166	0.0246056
$820$	2.20871	0.0771316
$821$	2.83485	0.0989369	0.0494684	−	0.998776i	$-0.484247\pi$
$821$	2.83485	0.0989369	0.0494684	+	0.998776i	$0.484247\pi$
$822$	1.41742	0.0494383
$823$	41.1652	1.43493	0.717463	−	0.696596i	$-0.245303\pi$
$823$	41.1652	1.43493	0.717463	+	0.696596i	$0.245303\pi$
$824$	−7.37386	−0.256881
$825$	6.79129	0.236442
$826$	12.3303	0.429026
$827$	41.0780	1.42842	0.714212	−	0.699930i	$-0.246785\pi$
$827$	41.0780	1.42842	0.714212	+	0.699930i	$0.246785\pi$
$828$	0.208712	0.00725325
$829$	−31.4955	−1.09388	−0.546941	−	0.837171i	$-0.684208\pi$
$829$	−31.4955	−1.09388	−0.546941	+	0.837171i	$0.684208\pi$
$830$	−6.00000	−0.208263
$831$	−2.08712	−0.0724014
$832$	1.20871	0.0419046
$833$	−3.00000	−0.103944
$834$	26.4174	0.914761
$835$	18.3303	0.634346
$836$	4.58258	0.158492
$837$	−51.8693	−1.79287
$838$	−39.1652	−1.35294
$839$	−22.4174	−0.773935	−0.386968	−	0.922093i	$-0.626478\pi$
$839$	−22.4174	−0.773935	−0.386968	+	0.922093i	$0.626478\pi$
$840$	5.00000	0.172516
$841$	−26.4955	−0.913636
$842$	23.1216	0.796823
$843$	−30.0000	−1.03325
$844$	−10.0000	−0.344214
$845$	11.5390	0.396954
$846$	2.83485	0.0974641
$847$	9.41742	0.323587
$848$	6.00000	0.206041
$849$	−50.7477	−1.74166
$850$	3.79129	0.130040
$851$	−4.00000	−0.137118
$852$	−9.62614	−0.329786
$853$	8.46099	0.289699	0.144849	−	0.989454i	$-0.453730\pi$
$853$	8.46099	0.289699	0.144849	+	0.989454i	$0.453730\pi$
$854$	9.41742	0.322258
$855$	−0.252273	−0.00862755
$856$	−13.5826	−0.464243
$857$	9.16515	0.313076	0.156538	−	0.987672i	$-0.449967\pi$
$857$	9.16515	0.313076	0.156538	+	0.987672i	$0.449967\pi$
$858$	−8.20871	−0.280241
$859$	0.747727	0.0255121	0.0127561	−	0.999919i	$-0.495940\pi$
$859$	0.747727	0.0255121	0.0127561	+	0.999919i	$0.495940\pi$
$860$	7.16515	0.244330
$861$	−11.0436	−0.376364
$862$	19.9129	0.678235
$863$	−31.5826	−1.07508	−0.537542	−	0.843237i	$-0.680647\pi$
$863$	−31.5826	−1.07508	−0.537542	+	0.843237i	$0.680647\pi$
$864$	5.00000	0.170103
$865$	14.2087	0.483111
$866$	−1.53901	−0.0522979
$867$	−4.70417	−0.159762
$868$	28.9564	0.982846
$869$	30.3303	1.02889
$870$	−2.83485	−0.0961104
$871$	−8.66061	−0.293453
$872$	−10.3739	−0.351303
$873$	3.12159	0.105650
$874$	−1.20871	−0.0408853
$875$	−2.79129	−0.0943628
$876$	−26.4174	−0.892562
$877$	7.70417	0.260151	0.130076	−	0.991504i	$-0.458478\pi$
$877$	7.70417	0.260151	0.130076	+	0.991504i	$0.458478\pi$
$878$	−25.5390	−0.861900
$879$	−49.2523	−1.66124
$880$	−3.79129	−0.127804
$881$	−6.33030	−0.213273	−0.106637	−	0.994298i	$-0.534008\pi$
$881$	−6.33030	−0.213273	−0.106637	+	0.994298i	$0.534008\pi$
$882$	−0.165151	−0.00556094
$883$	−12.0436	−0.405298	−0.202649	−	0.979251i	$-0.564955\pi$
$883$	−12.0436	−0.405298	−0.202649	+	0.979251i	$0.564955\pi$
$884$	−4.58258	−0.154129
$885$	7.91288	0.265989
$886$	35.2087	1.18286
$887$	−3.16515	−0.106275	−0.0531377	−	0.998587i	$-0.516922\pi$
$887$	−3.16515	−0.106275	−0.0531377	+	0.998587i	$0.516922\pi$
$888$	7.16515	0.240447
$889$	−41.1652	−1.38063
$890$	−3.16515	−0.106096
$891$	−36.3303	−1.21711
$892$	11.1652	0.373837
$893$	−16.4174	−0.549388
$894$	−22.9129	−0.766321
$895$	16.7477	0.559815
$896$	−2.79129	−0.0932504
$897$	2.16515	0.0722923
$898$	−25.1216	−0.838318
$899$	−16.4174	−0.547552
$900$	0.208712	0.00695707
$901$	−22.7477	−0.757837
$902$	8.37386	0.278819
$903$	−35.8258	−1.19221
$904$	−6.00000	−0.199557
$905$	−13.5390	−0.450052
$906$	11.1216	0.369490
$907$	−20.7477	−0.688917	−0.344458	−	0.938802i	$-0.611937\pi$
$907$	−20.7477	−0.688917	−0.344458	+	0.938802i	$0.611937\pi$
$908$	4.74773	0.157559
$909$	2.83485	0.0940260
$910$	3.37386	0.111842
$911$	13.5826	0.450011	0.225005	−	0.974358i	$-0.427760\pi$
$911$	13.5826	0.450011	0.225005	+	0.974358i	$0.427760\pi$
$912$	2.16515	0.0716953
$913$	−22.7477	−0.752840
$914$	10.0000	0.330771
$915$	6.04356	0.199794
$916$	−16.3303	−0.539568
$917$	25.5826	0.844811
$918$	−18.9564	−0.625656
$919$	−36.8348	−1.21507	−0.607535	−	0.794293i	$-0.707841\pi$
$919$	−36.8348	−1.21507	−0.607535	+	0.794293i	$0.707841\pi$
$920$	1.00000	0.0329690
$921$	29.6261	0.976214
$922$	1.25227	0.0412414
$923$	−6.49545	−0.213800
$924$	18.9564	0.623621
$925$	−4.00000	−0.131519
$926$	10.0000	0.328620
$927$	1.53901	0.0505479
$928$	1.58258	0.0519506
$929$	−39.4955	−1.29580	−0.647902	−	0.761724i	$-0.724353\pi$
$929$	−39.4955	−1.29580	−0.647902	+	0.761724i	$0.724353\pi$
$930$	18.5826	0.609347
$931$	0.956439	0.0313460
$932$	7.58258	0.248376
$933$	21.4955	0.703730
$934$	−25.9129	−0.847895
$935$	14.3739	0.470076
$936$	−0.252273	−0.00824580
$937$	58.3739	1.90699	0.953495	−	0.301407i	$-0.0974564\pi$
$937$	58.3739	1.90699	0.953495	+	0.301407i	$0.0974564\pi$
$938$	20.0000	0.653023
$939$	−32.9129	−1.07407
$940$	13.5826	0.443015
$941$	54.9564	1.79153	0.895764	−	0.444529i	$-0.146629\pi$
$941$	54.9564	1.79153	0.895764	+	0.444529i	$0.146629\pi$
$942$	−22.8348	−0.744000
$943$	−2.20871	−0.0719256
$944$	−4.41742	−0.143775
$945$	13.9564	0.454003
$946$	27.1652	0.883215
$947$	−29.5390	−0.959889	−0.479945	−	0.877299i	$-0.659343\pi$
$947$	−29.5390	−0.959889	−0.479945	+	0.877299i	$0.659343\pi$
$948$	14.3303	0.465427
$949$	−17.8258	−0.578649
$950$	−1.20871	−0.0392158
$951$	9.33030	0.302556
$952$	10.5826	0.342983
$953$	−26.5390	−0.859683	−0.429842	−	0.902904i	$-0.641431\pi$
$953$	−26.5390	−0.859683	−0.429842	+	0.902904i	$0.641431\pi$
$954$	−1.25227	−0.0405438
$955$	−16.4174	−0.531255
$956$	3.16515	0.102368
$957$	−10.7477	−0.347425
$958$	39.4955	1.27604
$959$	−2.20871	−0.0713230
$960$	−1.79129	−0.0578136
$961$	76.6170	2.47152
$962$	4.83485	0.155882
$963$	2.83485	0.0913517
$964$	−28.0000	−0.901819
$965$	−6.74773	−0.217217
$966$	−5.00000	−0.160872
$967$	−5.25227	−0.168902	−0.0844509	−	0.996428i	$-0.526914\pi$
$967$	−5.25227	−0.168902	−0.0844509	+	0.996428i	$0.526914\pi$
$968$	−3.37386	−0.108440
$969$	−8.20871	−0.263702
$970$	14.9564	0.480222
$971$	−6.95644	−0.223243	−0.111621	−	0.993751i	$-0.535604\pi$
$971$	−6.95644	−0.223243	−0.111621	+	0.993751i	$0.535604\pi$
$972$	−2.16515	−0.0694473
$973$	−41.1652	−1.31969
$974$	−15.5826	−0.499298
$975$	2.16515	0.0693403
$976$	−3.37386	−0.107995
$977$	7.12159	0.227840	0.113920	−	0.993490i	$-0.463659\pi$
$977$	7.12159	0.227840	0.113920	+	0.993490i	$0.463659\pi$
$978$	−40.0780	−1.28155
$979$	−12.0000	−0.383522
$980$	−0.791288	−0.0252768
$981$	2.16515	0.0691280
$982$	16.7477	0.534441
$983$	−0.626136	−0.0199707	−0.00998533	−	0.999950i	$-0.503178\pi$
$983$	−0.626136	−0.0199707	−0.00998533	+	0.999950i	$0.503178\pi$
$984$	3.95644	0.126127
$985$	−20.5390	−0.654427
$986$	−6.00000	−0.191079
$987$	−67.9129	−2.16169
$988$	1.46099	0.0464801
$989$	−7.16515	−0.227839
$990$	0.791288	0.0251488
$991$	−37.7913	−1.20048	−0.600240	−	0.799820i	$-0.704928\pi$
$991$	−37.7913	−1.20048	−0.600240	+	0.799820i	$0.704928\pi$
$992$	−10.3739	−0.329370
$993$	12.0871	0.383573
$994$	15.0000	0.475771
$995$	−20.3303	−0.644514
$996$	−10.7477	−0.340555
$997$	11.4955	0.364065	0.182032	−	0.983293i	$-0.441732\pi$
$997$	11.4955	0.364065	0.182032	+	0.983293i	$0.441732\pi$
$998$	−23.1652	−0.733280
$999$	20.0000	0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.a.a.1.2	✓	2
3.2	odd	2		2070.2.a.x.1.2		2
4.3	odd	2		1840.2.a.n.1.1		2
5.2	odd	4		1150.2.b.g.599.1		4
5.3	odd	4		1150.2.b.g.599.4		4
5.4	even	2		1150.2.a.o.1.1		2
8.3	odd	2		7360.2.a.bk.1.2		2
8.5	even	2		7360.2.a.bq.1.1		2
20.19	odd	2		9200.2.a.bs.1.2		2
23.22	odd	2		5290.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.a.1.2	✓	2	1.1	even	1	trivial
1150.2.a.o.1.1		2	5.4	even	2
1150.2.b.g.599.1		4	5.2	odd	4
1150.2.b.g.599.4		4	5.3	odd	4
1840.2.a.n.1.1		2	4.3	odd	2
2070.2.a.x.1.2		2	3.2	odd	2
5290.2.a.e.1.2		2	23.22	odd	2
7360.2.a.bk.1.2		2	8.3	odd	2
7360.2.a.bq.1.1		2	8.5	even	2
9200.2.a.bs.1.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.79129 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.79129 q^{6} +2.79129 q^{7} -1.00000 q^{8} +0.208712 q^{9} +1.00000 q^{10} +3.79129 q^{11} +1.79129 q^{12} +1.20871 q^{13} -2.79129 q^{14} -1.79129 q^{15} +1.00000 q^{16} -3.79129 q^{17} -0.208712 q^{18} +1.20871 q^{19} -1.00000 q^{20} +5.00000 q^{21} -3.79129 q^{22} +1.00000 q^{23} -1.79129 q^{24} +1.00000 q^{25} -1.20871 q^{26} -5.00000 q^{27} +2.79129 q^{28} -1.58258 q^{29} +1.79129 q^{30} +10.3739 q^{31} -1.00000 q^{32} +6.79129 q^{33} +3.79129 q^{34} -2.79129 q^{35} +0.208712 q^{36} -4.00000 q^{37} -1.20871 q^{38} +2.16515 q^{39} +1.00000 q^{40} -2.20871 q^{41} -5.00000 q^{42} -7.16515 q^{43} +3.79129 q^{44} -0.208712 q^{45} -1.00000 q^{46} -13.5826 q^{47} +1.79129 q^{48} +0.791288 q^{49} -1.00000 q^{50} -6.79129 q^{51} +1.20871 q^{52} +6.00000 q^{53} +5.00000 q^{54} -3.79129 q^{55} -2.79129 q^{56} +2.16515 q^{57} +1.58258 q^{58} -4.41742 q^{59} -1.79129 q^{60} -3.37386 q^{61} -10.3739 q^{62} +0.582576 q^{63} +1.00000 q^{64} -1.20871 q^{65} -6.79129 q^{66} -7.16515 q^{67} -3.79129 q^{68} +1.79129 q^{69} +2.79129 q^{70} -5.37386 q^{71} -0.208712 q^{72} -14.7477 q^{73} +4.00000 q^{74} +1.79129 q^{75} +1.20871 q^{76} +10.5826 q^{77} -2.16515 q^{78} +8.00000 q^{79} -1.00000 q^{80} -9.58258 q^{81} +2.20871 q^{82} -6.00000 q^{83} +5.00000 q^{84} +3.79129 q^{85} +7.16515 q^{86} -2.83485 q^{87} -3.79129 q^{88} -3.16515 q^{89} +0.208712 q^{90} +3.37386 q^{91} +1.00000 q^{92} +18.5826 q^{93} +13.5826 q^{94} -1.20871 q^{95} -1.79129 q^{96} +14.9564 q^{97} -0.791288 q^{98} +0.791288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} - 2 q^{5} + q^{6} + q^{7} - 2 q^{8} + 5 q^{9} + 2 q^{10} + 3 q^{11} - q^{12} + 7 q^{13} - q^{14} + q^{15} + 2 q^{16} - 3 q^{17} - 5 q^{18} + 7 q^{19} - 2 q^{20} + 10 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 - 2 * q^5 + q^6 + q^7 - 2 * q^8 + 5 * q^9 + 2 * q^10 + 3 * q^11 - q^12 + 7 * q^13 - q^14 + q^15 + 2 * q^16 - 3 * q^17 - 5 * q^18 + 7 * q^19 - 2 * q^20 + 10 * q^21 - 3 * q^22 + 2 * q^23 + q^24 + 2 * q^25 - 7 * q^26 - 10 * q^27 + q^28 + 6 * q^29 - q^30 + 7 * q^31 - 2 * q^32 + 9 * q^33 + 3 * q^34 - q^35 + 5 * q^36 - 8 * q^37 - 7 * q^38 - 14 * q^39 + 2 * q^40 - 9 * q^41 - 10 * q^42 + 4 * q^43 + 3 * q^44 - 5 * q^45 - 2 * q^46 - 18 * q^47 - q^48 - 3 * q^49 - 2 * q^50 - 9 * q^51 + 7 * q^52 + 12 * q^53 + 10 * q^54 - 3 * q^55 - q^56 - 14 * q^57 - 6 * q^58 - 18 * q^59 + q^60 + 7 * q^61 - 7 * q^62 - 8 * q^63 + 2 * q^64 - 7 * q^65 - 9 * q^66 + 4 * q^67 - 3 * q^68 - q^69 + q^70 + 3 * q^71 - 5 * q^72 - 2 * q^73 + 8 * q^74 - q^75 + 7 * q^76 + 12 * q^77 + 14 * q^78 + 16 * q^79 - 2 * q^80 - 10 * q^81 + 9 * q^82 - 12 * q^83 + 10 * q^84 + 3 * q^85 - 4 * q^86 - 24 * q^87 - 3 * q^88 + 12 * q^89 + 5 * q^90 - 7 * q^91 + 2 * q^92 + 28 * q^93 + 18 * q^94 - 7 * q^95 + q^96 + 7 * q^97 + 3 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more