LMFDB - Embedded newform 5819.2.a.u.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.29534 q^{2} -3.02840 q^{3} +3.26860 q^{4} +1.86081 q^{5} +6.95122 q^{6} -4.83491 q^{7} -2.91187 q^{8} +6.17120 q^{9} -4.27120 q^{10} +1.00000 q^{11} -9.89863 q^{12} -0.671797 q^{13} +11.0978 q^{14} -5.63528 q^{15} +0.146550 q^{16} -0.875601 q^{17} -14.1650 q^{18} -7.70453 q^{19} +6.08225 q^{20} +14.6420 q^{21} -2.29534 q^{22} +8.81832 q^{24} -1.53738 q^{25} +1.54201 q^{26} -9.60366 q^{27} -15.8034 q^{28} -1.40702 q^{29} +12.9349 q^{30} -3.64474 q^{31} +5.48737 q^{32} -3.02840 q^{33} +2.00980 q^{34} -8.99686 q^{35} +20.1712 q^{36} -4.24239 q^{37} +17.6845 q^{38} +2.03447 q^{39} -5.41845 q^{40} -3.16461 q^{41} -33.6085 q^{42} -10.8915 q^{43} +3.26860 q^{44} +11.4834 q^{45} -6.28698 q^{47} -0.443811 q^{48} +16.3764 q^{49} +3.52882 q^{50} +2.65167 q^{51} -2.19584 q^{52} -2.70334 q^{53} +22.0437 q^{54} +1.86081 q^{55} +14.0787 q^{56} +23.3324 q^{57} +3.22960 q^{58} +9.21157 q^{59} -18.4195 q^{60} -6.49923 q^{61} +8.36593 q^{62} -29.8372 q^{63} -12.8885 q^{64} -1.25009 q^{65} +6.95122 q^{66} -7.53522 q^{67} -2.86199 q^{68} +20.6509 q^{70} +8.65293 q^{71} -17.9698 q^{72} -5.71063 q^{73} +9.73775 q^{74} +4.65581 q^{75} -25.1830 q^{76} -4.83491 q^{77} -4.66981 q^{78} -1.14344 q^{79} +0.272701 q^{80} +10.5701 q^{81} +7.26386 q^{82} +4.29543 q^{83} +47.8590 q^{84} -1.62933 q^{85} +24.9997 q^{86} +4.26102 q^{87} -2.91187 q^{88} -4.97553 q^{89} -26.3584 q^{90} +3.24808 q^{91} +11.0377 q^{93} +14.4308 q^{94} -14.3367 q^{95} -16.6179 q^{96} -0.0547066 q^{97} -37.5894 q^{98} +6.17120 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * 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 $

$2$	−2.29534	−1.62305	−0.811526	−	0.584316i	$-0.801363\pi$
$2$	−2.29534	−1.62305	−0.811526	+	0.584316i	$0.801363\pi$
$3$	−3.02840	−1.74845	−0.874224	−	0.485524i	$-0.838629\pi$
$3$	−3.02840	−1.74845	−0.874224	+	0.485524i	$0.838629\pi$
$4$	3.26860	1.63430
$5$	1.86081	0.832180	0.416090	−	0.909323i	$-0.363400\pi$
$5$	1.86081	0.832180	0.416090	+	0.909323i	$0.363400\pi$
$6$	6.95122	2.83782
$7$	−4.83491	−1.82742	−0.913712	−	0.406361i	$-0.866797\pi$
$7$	−4.83491	−1.82742	−0.913712	+	0.406361i	$0.866797\pi$
$8$	−2.91187	−1.02950
$9$	6.17120	2.05707
$10$	−4.27120	−1.35067
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−9.89863	−2.85749
$13$	−0.671797	−0.186323	−0.0931616	−	0.995651i	$-0.529697\pi$
$13$	−0.671797	−0.186323	−0.0931616	+	0.995651i	$0.529697\pi$
$14$	11.0978	2.96601
$15$	−5.63528	−1.45502
$16$	0.146550	0.0366374
$17$	−0.875601	−0.212364	−0.106182	−	0.994347i	$-0.533863\pi$
$17$	−0.875601	−0.212364	−0.106182	+	0.994347i	$0.533863\pi$
$18$	−14.1650	−3.33873
$19$	−7.70453	−1.76754	−0.883770	−	0.467921i	$-0.845003\pi$
$19$	−7.70453	−1.76754	−0.883770	+	0.467921i	$0.845003\pi$
$20$	6.08225	1.36003
$21$	14.6420	3.19516
$22$	−2.29534	−0.489369
$23$	0	0
$23$	0	0
$24$	8.81832	1.80003
$25$	−1.53738	−0.307477
$26$	1.54201	0.302412
$27$	−9.60366	−1.84823
$28$	−15.8034	−2.98656
$29$	−1.40702	−0.261277	−0.130639	−	0.991430i	$-0.541703\pi$
$29$	−1.40702	−0.261277	−0.130639	+	0.991430i	$0.541703\pi$
$30$	12.9349	2.36158
$31$	−3.64474	−0.654614	−0.327307	−	0.944918i	$-0.606141\pi$
$31$	−3.64474	−0.654614	−0.327307	+	0.944918i	$0.606141\pi$
$32$	5.48737	0.970039
$33$	−3.02840	−0.527177
$34$	2.00980	0.344679
$35$	−8.99686	−1.52075
$36$	20.1712	3.36187
$37$	−4.24239	−0.697445	−0.348723	−	0.937226i	$-0.613384\pi$
$37$	−4.24239	−0.697445	−0.348723	+	0.937226i	$0.613384\pi$
$38$	17.6845	2.86881
$39$	2.03447	0.325776
$40$	−5.41845	−0.856732
$41$	−3.16461	−0.494229	−0.247114	−	0.968986i	$-0.579482\pi$
$41$	−3.16461	−0.494229	−0.247114	+	0.968986i	$0.579482\pi$
$42$	−33.6085	−5.18591
$43$	−10.8915	−1.66093	−0.830467	−	0.557067i	$-0.811927\pi$
$43$	−10.8915	−1.66093	−0.830467	+	0.557067i	$0.811927\pi$
$44$	3.26860	0.492760
$45$	11.4834	1.71185
$46$	0	0
$47$	−6.28698	−0.917051	−0.458525	−	0.888681i	$-0.651622\pi$
$47$	−6.28698	−0.917051	−0.458525	+	0.888681i	$0.651622\pi$
$48$	−0.443811	−0.0640586
$49$	16.3764	2.33948
$50$	3.52882	0.499051
$51$	2.65167	0.371308
$52$	−2.19584	−0.304508
$53$	−2.70334	−0.371332	−0.185666	−	0.982613i	$-0.559444\pi$
$53$	−2.70334	−0.371332	−0.185666	+	0.982613i	$0.559444\pi$
$54$	22.0437	2.99977
$55$	1.86081	0.250912
$56$	14.0787	1.88134
$57$	23.3324	3.09045
$58$	3.22960	0.424067
$59$	9.21157	1.19924	0.599622	−	0.800283i	$-0.295318\pi$
$59$	9.21157	1.19924	0.599622	+	0.800283i	$0.295318\pi$
$60$	−18.4195	−2.37794
$61$	−6.49923	−0.832141	−0.416070	−	0.909332i	$-0.636593\pi$
$61$	−6.49923	−0.832141	−0.416070	+	0.909332i	$0.636593\pi$
$62$	8.36593	1.06247
$63$	−29.8372	−3.75914
$64$	−12.8885	−1.61106
$65$	−1.25009	−0.155054
$66$	6.95122	0.855635
$67$	−7.53522	−0.920574	−0.460287	−	0.887770i	$-0.652253\pi$
$67$	−7.53522	−0.920574	−0.460287	+	0.887770i	$0.652253\pi$
$68$	−2.86199	−0.347067
$69$	0	0
$70$	20.6509	2.46825
$71$	8.65293	1.02691	0.513457	−	0.858115i	$-0.328365\pi$
$71$	8.65293	1.02691	0.513457	+	0.858115i	$0.328365\pi$
$72$	−17.9698	−2.11776
$73$	−5.71063	−0.668379	−0.334189	−	0.942506i	$-0.608463\pi$
$73$	−5.71063	−0.668379	−0.334189	+	0.942506i	$0.608463\pi$
$74$	9.73775	1.13199
$75$	4.65581	0.537607
$76$	−25.1830	−2.88869
$77$	−4.83491	−0.550989
$78$	−4.66981	−0.528752
$79$	−1.14344	−0.128647	−0.0643236	−	0.997929i	$-0.520489\pi$
$79$	−1.14344	−0.128647	−0.0643236	+	0.997929i	$0.520489\pi$
$80$	0.272701	0.0304889
$81$	10.5701	1.17446
$82$	7.26386	0.802159
$83$	4.29543	0.471485	0.235742	−	0.971816i	$-0.424248\pi$
$83$	4.29543	0.471485	0.235742	+	0.971816i	$0.424248\pi$
$84$	47.8590	5.22184
$85$	−1.62933	−0.176725
$86$	24.9997	2.69578
$87$	4.26102	0.456829
$88$	−2.91187	−0.310407
$89$	−4.97553	−0.527405	−0.263702	−	0.964604i	$-0.584944\pi$
$89$	−4.97553	−0.527405	−0.263702	+	0.964604i	$0.584944\pi$
$90$	−26.3584	−2.77842
$91$	3.24808	0.340491
$92$	0	0
$93$	11.0377	1.14456
$94$	14.4308	1.48842
$95$	−14.3367	−1.47091
$96$	−16.6179	−1.69606
$97$	−0.0547066	−0.00555462	−0.00277731	−	0.999996i	$-0.500884\pi$
$97$	−0.0547066	−0.00555462	−0.00277731	+	0.999996i	$0.500884\pi$
$98$	−37.5894	−3.79710
$99$	6.17120	0.620229
$100$	−5.02509	−0.502509
$101$	10.1948	1.01442	0.507211	−	0.861822i	$-0.330676\pi$
$101$	10.1948	1.01442	0.507211	+	0.861822i	$0.330676\pi$
$102$	−6.08649	−0.602652
$103$	−17.3880	−1.71329	−0.856644	−	0.515908i	$-0.827455\pi$
$103$	−17.3880	−1.71329	−0.856644	+	0.515908i	$0.827455\pi$
$104$	1.95619	0.191820
$105$	27.2461	2.65894
$106$	6.20509	0.602692
$107$	−3.71713	−0.359349	−0.179674	−	0.983726i	$-0.557504\pi$
$107$	−3.71713	−0.359349	−0.179674	+	0.983726i	$0.557504\pi$
$108$	−31.3905	−3.02056
$109$	−8.17987	−0.783490	−0.391745	−	0.920074i	$-0.628128\pi$
$109$	−8.17987	−0.783490	−0.391745	+	0.920074i	$0.628128\pi$
$110$	−4.27120	−0.407243
$111$	12.8477	1.21945
$112$	−0.708555	−0.0669522
$113$	6.43887	0.605718	0.302859	−	0.953035i	$-0.402059\pi$
$113$	6.43887	0.605718	0.302859	+	0.953035i	$0.402059\pi$
$114$	−53.5558	−5.01596
$115$	0	0
$116$	−4.59899	−0.427005
$117$	−4.14580	−0.383279
$118$	−21.1437	−1.94644
$119$	4.23345	0.388080
$120$	16.4092	1.49795
$121$	1.00000	0.0909091
$122$	14.9180	1.35061
$123$	9.58369	0.864132
$124$	−11.9132	−1.06984
$125$	−12.1648	−1.08806
$126$	68.4866	6.10128
$127$	−15.4542	−1.37134	−0.685669	−	0.727914i	$-0.740490\pi$
$127$	−15.4542	−1.37134	−0.685669	+	0.727914i	$0.740490\pi$
$128$	18.6088	1.64480
$129$	32.9837	2.90406
$130$	2.86938	0.251661
$131$	17.5047	1.52940	0.764698	−	0.644389i	$-0.222888\pi$
$131$	17.5047	1.52940	0.764698	+	0.644389i	$0.222888\pi$
$132$	−9.89863	−0.861565
$133$	37.2507	3.23005
$134$	17.2959	1.49414
$135$	−17.8706	−1.53806
$136$	2.54964	0.218630
$137$	3.32728	0.284269	0.142135	−	0.989847i	$-0.454603\pi$
$137$	3.32728	0.284269	0.142135	+	0.989847i	$0.454603\pi$
$138$	0	0
$139$	−4.20453	−0.356624	−0.178312	−	0.983974i	$-0.557064\pi$
$139$	−4.20453	−0.356624	−0.178312	+	0.983974i	$0.557064\pi$
$140$	−29.4071	−2.48536
$141$	19.0395	1.60341
$142$	−19.8614	−1.66674
$143$	−0.671797	−0.0561785
$144$	0.904388	0.0753657
$145$	−2.61820	−0.217430
$146$	13.1079	1.08481
$147$	−49.5942	−4.09046
$148$	−13.8667	−1.13984
$149$	4.39091	0.359718	0.179859	−	0.983692i	$-0.442436\pi$
$149$	4.39091	0.359718	0.179859	+	0.983692i	$0.442436\pi$
$150$	−10.6867	−0.872564
$151$	0.473668	0.0385465	0.0192733	−	0.999814i	$-0.493865\pi$
$151$	0.473668	0.0385465	0.0192733	+	0.999814i	$0.493865\pi$
$152$	22.4346	1.81969
$153$	−5.40351	−0.436848
$154$	11.0978	0.894285
$155$	−6.78217	−0.544757
$156$	6.64987	0.532416
$157$	19.1308	1.52681	0.763403	−	0.645923i	$-0.223527\pi$
$157$	19.1308	1.52681	0.763403	+	0.645923i	$0.223527\pi$
$158$	2.62459	0.208801
$159$	8.18679	0.649255
$160$	10.2110	0.807247
$161$	0	0
$162$	−24.2621	−1.90621
$163$	−1.24590	−0.0975864	−0.0487932	−	0.998809i	$-0.515538\pi$
$163$	−1.24590	−0.0975864	−0.0487932	+	0.998809i	$0.515538\pi$
$164$	−10.3438	−0.807718
$165$	−5.63528	−0.438706
$166$	−9.85949	−0.765245
$167$	−4.94076	−0.382327	−0.191164	−	0.981558i	$-0.561226\pi$
$167$	−4.94076	−0.382327	−0.191164	+	0.981558i	$0.561226\pi$
$168$	−42.6358	−3.28942
$169$	−12.5487	−0.965284
$170$	3.73987	0.286835
$171$	−47.5462	−3.63595
$172$	−35.5999	−2.71447
$173$	−18.9345	−1.43956	−0.719780	−	0.694202i	$-0.755757\pi$
$173$	−18.9345	−1.43956	−0.719780	+	0.694202i	$0.755757\pi$
$174$	−9.78050	−0.741458
$175$	7.43311	0.561890
$176$	0.146550	0.0110466
$177$	−27.8963	−2.09682
$178$	11.4205	0.856006
$179$	−11.8023	−0.882145	−0.441072	−	0.897472i	$-0.645402\pi$
$179$	−11.8023	−0.882145	−0.441072	+	0.897472i	$0.645402\pi$
$180$	37.5348	2.79768
$181$	−5.50887	−0.409471	−0.204736	−	0.978817i	$-0.565633\pi$
$181$	−5.50887	−0.409471	−0.204736	+	0.978817i	$0.565633\pi$
$182$	−7.45546	−0.552636
$183$	19.6823	1.45495
$184$	0	0
$185$	−7.89429	−0.580400
$186$	−25.3354	−1.85768
$187$	−0.875601	−0.0640303
$188$	−20.5496	−1.49874
$189$	46.4329	3.37749
$190$	32.9076	2.38737
$191$	−7.93312	−0.574020	−0.287010	−	0.957928i	$-0.592661\pi$
$191$	−7.93312	−0.574020	−0.287010	+	0.957928i	$0.592661\pi$
$192$	39.0315	2.81686
$193$	4.98694	0.358968	0.179484	−	0.983761i	$-0.442557\pi$
$193$	4.98694	0.358968	0.179484	+	0.983761i	$0.442557\pi$
$194$	0.125570	0.00901543
$195$	3.78577	0.271104
$196$	53.5278	3.82342
$197$	−22.8065	−1.62490	−0.812448	−	0.583034i	$-0.801865\pi$
$197$	−22.8065	−1.62490	−0.812448	+	0.583034i	$0.801865\pi$
$198$	−14.1650	−1.00666
$199$	−0.478830	−0.0339434	−0.0169717	−	0.999856i	$-0.505403\pi$
$199$	−0.478830	−0.0339434	−0.0169717	+	0.999856i	$0.505403\pi$
$200$	4.47667	0.316548
$201$	22.8197	1.60957
$202$	−23.4006	−1.64646
$203$	6.80282	0.477464
$204$	8.66725	0.606829
$205$	−5.88873	−0.411287
$206$	39.9114	2.78076
$207$	0	0
$208$	−0.0984518	−0.00682640
$209$	−7.70453	−0.532933
$210$	−62.5391	−4.31561
$211$	−10.8655	−0.748013	−0.374006	−	0.927426i	$-0.622016\pi$
$211$	−10.8655	−0.748013	−0.374006	+	0.927426i	$0.622016\pi$
$212$	−8.83614	−0.606868
$213$	−26.2045	−1.79550
$214$	8.53209	0.583242
$215$	−20.2670	−1.38220
$216$	27.9647	1.90275
$217$	17.6220	1.19626
$218$	18.7756	1.27164
$219$	17.2941	1.16862
$220$	6.08225	0.410065
$221$	0.588227	0.0395684
$222$	−29.4898	−1.97923
$223$	−6.16572	−0.412887	−0.206443	−	0.978459i	$-0.566189\pi$
$223$	−6.16572	−0.412887	−0.206443	+	0.978459i	$0.566189\pi$
$224$	−26.5309	−1.77267
$225$	−9.48750	−0.632500
$226$	−14.7794	−0.983112
$227$	−17.0330	−1.13052	−0.565259	−	0.824914i	$-0.691224\pi$
$227$	−17.0330	−1.13052	−0.565259	+	0.824914i	$0.691224\pi$
$228$	76.2643	5.05072
$229$	−6.20190	−0.409833	−0.204917	−	0.978779i	$-0.565692\pi$
$229$	−6.20190	−0.409833	−0.204917	+	0.978779i	$0.565692\pi$
$230$	0	0
$231$	14.6420	0.963376
$232$	4.09707	0.268986
$233$	−17.1995	−1.12678	−0.563388	−	0.826193i	$-0.690502\pi$
$233$	−17.1995	−1.12678	−0.563388	+	0.826193i	$0.690502\pi$
$234$	9.51603	0.622082
$235$	−11.6989	−0.763151
$236$	30.1089	1.95993
$237$	3.46279	0.224933
$238$	−9.71723	−0.629874
$239$	−10.5745	−0.684007	−0.342004	−	0.939699i	$-0.611106\pi$
$239$	−10.5745	−0.684007	−0.342004	+	0.939699i	$0.611106\pi$
$240$	−0.825849	−0.0533083
$241$	−19.5194	−1.25736	−0.628678	−	0.777666i	$-0.716403\pi$
$241$	−19.5194	−1.25736	−0.628678	+	0.777666i	$0.716403\pi$
$242$	−2.29534	−0.147550
$243$	−3.19955	−0.205251
$244$	−21.2434	−1.35997
$245$	30.4733	1.94687
$246$	−21.9979	−1.40253
$247$	5.17588	0.329334
$248$	10.6130	0.673928
$249$	−13.0083	−0.824366
$250$	27.9225	1.76597
$251$	−27.4068	−1.72990	−0.864950	−	0.501858i	$-0.832650\pi$
$251$	−27.4068	−1.72990	−0.864950	+	0.501858i	$0.832650\pi$
$252$	−97.5259	−6.14356
$253$	0	0
$254$	35.4727	2.22575
$255$	4.93426	0.308995
$256$	−16.9365	−1.05853
$257$	−0.455059	−0.0283858	−0.0141929	−	0.999899i	$-0.504518\pi$
$257$	−0.455059	−0.0283858	−0.0141929	+	0.999899i	$0.504518\pi$
$258$	−75.7090	−4.71344
$259$	20.5116	1.27453
$260$	−4.08604	−0.253405
$261$	−8.68301	−0.537465
$262$	−40.1794	−2.48229
$263$	−6.12697	−0.377805	−0.188902	−	0.981996i	$-0.560493\pi$
$263$	−6.12697	−0.377805	−0.188902	+	0.981996i	$0.560493\pi$
$264$	8.81832	0.542730
$265$	−5.03040	−0.309015
$266$	−85.5032	−5.24254
$267$	15.0679	0.922139
$268$	−24.6296	−1.50449
$269$	26.1172	1.59239	0.796195	−	0.605039i	$-0.206843\pi$
$269$	26.1172	1.59239	0.796195	+	0.605039i	$0.206843\pi$
$270$	41.0192	2.49635
$271$	−27.6809	−1.68150	−0.840748	−	0.541426i	$-0.817885\pi$
$271$	−27.6809	−1.68150	−0.840748	+	0.541426i	$0.817885\pi$
$272$	−0.128319	−0.00778049
$273$	−9.83649	−0.595331
$274$	−7.63726	−0.461384
$275$	−1.53738	−0.0927077
$276$	0	0
$277$	−23.3693	−1.40412	−0.702062	−	0.712116i	$-0.747737\pi$
$277$	−23.3693	−1.40412	−0.702062	+	0.712116i	$0.747737\pi$
$278$	9.65085	0.578819
$279$	−22.4924	−1.34659
$280$	26.1977	1.56561
$281$	−16.0124	−0.955221	−0.477611	−	0.878572i	$-0.658497\pi$
$281$	−16.0124	−0.955221	−0.477611	+	0.878572i	$0.658497\pi$
$282$	−43.7022	−2.60243
$283$	−25.7375	−1.52993	−0.764967	−	0.644069i	$-0.777245\pi$
$283$	−25.7375	−1.52993	−0.764967	+	0.644069i	$0.777245\pi$
$284$	28.2830	1.67829
$285$	43.4172	2.57181
$286$	1.54201	0.0911807
$287$	15.3006	0.903166
$288$	33.8636	1.99543
$289$	−16.2333	−0.954901
$290$	6.00967	0.352900
$291$	0.165673	0.00971195
$292$	−18.6658	−1.09233
$293$	15.6646	0.915137	0.457569	−	0.889174i	$-0.348720\pi$
$293$	15.6646	0.915137	0.457569	+	0.889174i	$0.348720\pi$
$294$	113.836	6.63903
$295$	17.1410	0.997987
$296$	12.3533	0.718022
$297$	−9.60366	−0.557261
$298$	−10.0787	−0.583841
$299$	0	0
$300$	15.2180	0.878611
$301$	52.6593	3.03523
$302$	−1.08723	−0.0625630
$303$	−30.8740	−1.77366
$304$	−1.12910	−0.0647582
$305$	−12.0938	−0.692491
$306$	12.4029	0.709027
$307$	24.9438	1.42362	0.711810	−	0.702372i	$-0.247876\pi$
$307$	24.9438	1.42362	0.711810	+	0.702372i	$0.247876\pi$
$308$	−15.8034	−0.900482
$309$	52.6577	2.99559
$310$	15.5674	0.884169
$311$	1.60505	0.0910143	0.0455072	−	0.998964i	$-0.485510\pi$
$311$	1.60505	0.0910143	0.0455072	+	0.998964i	$0.485510\pi$
$312$	−5.92412	−0.335387
$313$	13.4008	0.757455	0.378728	−	0.925508i	$-0.376362\pi$
$313$	13.4008	0.757455	0.378728	+	0.925508i	$0.376362\pi$
$314$	−43.9118	−2.47809
$315$	−55.5214	−3.12828
$316$	−3.73745	−0.210248
$317$	32.2996	1.81413	0.907064	−	0.420992i	$-0.138318\pi$
$317$	32.2996	1.81413	0.907064	+	0.420992i	$0.138318\pi$
$318$	−18.7915	−1.05377
$319$	−1.40702	−0.0787780
$320$	−23.9830	−1.34069
$321$	11.2570	0.628302
$322$	0	0
$323$	6.74609	0.375363
$324$	34.5495	1.91942
$325$	1.03281	0.0572900
$326$	2.85977	0.158388
$327$	24.7719	1.36989
$328$	9.21494	0.508810
$329$	30.3970	1.67584
$330$	12.9349	0.712043
$331$	1.07418	0.0590422	0.0295211	−	0.999564i	$-0.490602\pi$
$331$	1.07418	0.0590422	0.0295211	+	0.999564i	$0.490602\pi$
$332$	14.0401	0.770548
$333$	−26.1807	−1.43469
$334$	11.3407	0.620537
$335$	−14.0216	−0.766083
$336$	2.14579	0.117062
$337$	−2.35061	−0.128046	−0.0640229	−	0.997948i	$-0.520393\pi$
$337$	−2.35061	−0.128046	−0.0640229	+	0.997948i	$0.520393\pi$
$338$	28.8035	1.56671
$339$	−19.4995	−1.05907
$340$	−5.32562	−0.288822
$341$	−3.64474	−0.197374
$342$	109.135	5.90134
$343$	−45.3339	−2.44780
$344$	31.7146	1.70994
$345$	0	0
$346$	43.4611	2.33648
$347$	−19.0048	−1.02023	−0.510115	−	0.860106i	$-0.670397\pi$
$347$	−19.0048	−1.02023	−0.510115	+	0.860106i	$0.670397\pi$
$348$	13.9276	0.746596
$349$	13.7070	0.733717	0.366859	−	0.930277i	$-0.380433\pi$
$349$	13.7070	0.733717	0.366859	+	0.930277i	$0.380433\pi$
$350$	−17.0615	−0.911978
$351$	6.45172	0.344367
$352$	5.48737	0.292478
$353$	−16.9871	−0.904134	−0.452067	−	0.891984i	$-0.649313\pi$
$353$	−16.9871	−0.904134	−0.452067	+	0.891984i	$0.649313\pi$
$354$	64.0316	3.40324
$355$	16.1015	0.854577
$356$	−16.2630	−0.861938
$357$	−12.8206	−0.678537
$358$	27.0903	1.43177
$359$	21.4127	1.13012	0.565059	−	0.825051i	$-0.308853\pi$
$359$	21.4127	1.13012	0.565059	+	0.825051i	$0.308853\pi$
$360$	−33.4383	−1.76235
$361$	40.3598	2.12420
$362$	12.6447	0.664593
$363$	−3.02840	−0.158950
$364$	10.6167	0.556465
$365$	−10.6264	−0.556211
$366$	−45.1775	−2.36147
$367$	6.38742	0.333421	0.166710	−	0.986006i	$-0.446686\pi$
$367$	6.38742	0.333421	0.166710	+	0.986006i	$0.446686\pi$
$368$	0	0
$369$	−19.5294	−1.01666
$370$	18.1201	0.942020
$371$	13.0704	0.678582
$372$	36.0779	1.87055
$373$	23.9688	1.24106	0.620529	−	0.784184i	$-0.286918\pi$
$373$	23.9688	1.24106	0.620529	+	0.784184i	$0.286918\pi$
$374$	2.00980	0.103925
$375$	36.8400	1.90241
$376$	18.3069	0.944107
$377$	0.945233	0.0486820
$378$	−106.579	−5.48185
$379$	−3.87842	−0.199221	−0.0996105	−	0.995027i	$-0.531760\pi$
$379$	−3.87842	−0.199221	−0.0996105	+	0.995027i	$0.531760\pi$
$380$	−46.8609	−2.40391
$381$	46.8014	2.39771
$382$	18.2092	0.931665
$383$	20.8605	1.06592	0.532962	−	0.846139i	$-0.321079\pi$
$383$	20.8605	1.06592	0.532962	+	0.846139i	$0.321079\pi$
$384$	−56.3548	−2.87584
$385$	−8.99686	−0.458522
$386$	−11.4467	−0.582624
$387$	−67.2135	−3.41665
$388$	−0.178814	−0.00907791
$389$	−19.5845	−0.992974	−0.496487	−	0.868044i	$-0.665377\pi$
$389$	−19.5845	−0.992974	−0.496487	+	0.868044i	$0.665377\pi$
$390$	−8.68963	−0.440017
$391$	0	0
$392$	−47.6859	−2.40850
$393$	−53.0113	−2.67407
$394$	52.3487	2.63729
$395$	−2.12773	−0.107058
$396$	20.1712	1.01364
$397$	17.7687	0.891786	0.445893	−	0.895086i	$-0.352886\pi$
$397$	17.7687	0.891786	0.445893	+	0.895086i	$0.352886\pi$
$398$	1.09908	0.0550919
$399$	−112.810	−5.64757
$400$	−0.225303	−0.0112652
$401$	−6.40641	−0.319921	−0.159960	−	0.987123i	$-0.551137\pi$
$401$	−6.40641	−0.319921	−0.159960	+	0.987123i	$0.551137\pi$
$402$	−52.3790	−2.61242
$403$	2.44853	0.121970
$404$	33.3228	1.65787
$405$	19.6690	0.977360
$406$	−15.6148	−0.774950
$407$	−4.24239	−0.210288
$408$	−7.72133	−0.382263
$409$	17.6565	0.873056	0.436528	−	0.899691i	$-0.356208\pi$
$409$	17.6565	0.873056	0.436528	+	0.899691i	$0.356208\pi$
$410$	13.5167	0.667541
$411$	−10.0763	−0.497029
$412$	−56.8343	−2.80003
$413$	−44.5371	−2.19153
$414$	0	0
$415$	7.99299	0.392360
$416$	−3.68640	−0.180741
$417$	12.7330	0.623538
$418$	17.6845	0.864979
$419$	15.5272	0.758551	0.379276	−	0.925284i	$-0.376173\pi$
$419$	15.5272	0.758551	0.379276	+	0.925284i	$0.376173\pi$
$420$	89.0565	4.34551
$421$	−22.0707	−1.07566	−0.537830	−	0.843053i	$-0.680756\pi$
$421$	−22.0707	−1.07566	−0.537830	+	0.843053i	$0.680756\pi$
$422$	24.9401	1.21406
$423$	−38.7982	−1.88643
$424$	7.87178	0.382288
$425$	1.34613	0.0652971
$426$	60.1484	2.91420
$427$	31.4232	1.52067
$428$	−12.1498	−0.587284
$429$	2.03447	0.0982252
$430$	46.5197	2.24338
$431$	−22.0505	−1.06213	−0.531067	−	0.847330i	$-0.678209\pi$
$431$	−22.0505	−1.06213	−0.531067	+	0.847330i	$0.678209\pi$
$432$	−1.40741	−0.0677143
$433$	−11.6288	−0.558842	−0.279421	−	0.960169i	$-0.590143\pi$
$433$	−11.6288	−0.558842	−0.279421	+	0.960169i	$0.590143\pi$
$434$	−40.4485	−1.94159
$435$	7.92895	0.380164
$436$	−26.7367	−1.28046
$437$	0	0
$438$	−39.6958	−1.89674
$439$	6.18385	0.295139	0.147570	−	0.989052i	$-0.452855\pi$
$439$	6.18385	0.295139	0.147570	+	0.989052i	$0.452855\pi$
$440$	−5.41845	−0.258314
$441$	101.062	4.81247
$442$	−1.35018	−0.0642216
$443$	5.59713	0.265928	0.132964	−	0.991121i	$-0.457551\pi$
$443$	5.59713	0.265928	0.132964	+	0.991121i	$0.457551\pi$
$444$	41.9939	1.99294
$445$	−9.25852	−0.438896
$446$	14.1524	0.670137
$447$	−13.2974	−0.628947
$448$	62.3147	2.94409
$449$	4.14649	0.195685	0.0978426	−	0.995202i	$-0.468806\pi$
$449$	4.14649	0.195685	0.0978426	+	0.995202i	$0.468806\pi$
$450$	21.7771	1.02658
$451$	−3.16461	−0.149016
$452$	21.0461	0.989925
$453$	−1.43445	−0.0673965
$454$	39.0965	1.83489
$455$	6.04407	0.283350
$456$	−67.9410	−3.18163
$457$	30.2338	1.41428	0.707140	−	0.707074i	$-0.249985\pi$
$457$	30.2338	1.41428	0.707140	+	0.707074i	$0.249985\pi$
$458$	14.2355	0.665181
$459$	8.40898	0.392497
$460$	0	0
$461$	−23.3135	−1.08582	−0.542910	−	0.839791i	$-0.682677\pi$
$461$	−23.3135	−1.08582	−0.542910	+	0.839791i	$0.682677\pi$
$462$	−33.6085	−1.56361
$463$	8.81820	0.409817	0.204908	−	0.978781i	$-0.434310\pi$
$463$	8.81820	0.409817	0.204908	+	0.978781i	$0.434310\pi$
$464$	−0.206199	−0.00957253
$465$	20.5391	0.952479
$466$	39.4787	1.82882
$467$	25.1224	1.16253	0.581264	−	0.813715i	$-0.302559\pi$
$467$	25.1224	1.16253	0.581264	+	0.813715i	$0.302559\pi$
$468$	−13.5510	−0.626393
$469$	36.4321	1.68228
$470$	26.8530	1.23863
$471$	−57.9357	−2.66954
$472$	−26.8229	−1.23463
$473$	−10.8915	−0.500791
$474$	−7.94830	−0.365078
$475$	11.8448	0.543477
$476$	13.8375	0.634239
$477$	−16.6828	−0.763855
$478$	24.2721	1.11018
$479$	−12.4863	−0.570514	−0.285257	−	0.958451i	$-0.592079\pi$
$479$	−12.4863	−0.570514	−0.285257	+	0.958451i	$0.592079\pi$
$480$	−30.9228	−1.41143
$481$	2.85003	0.129950
$482$	44.8037	2.04075
$483$	0	0
$484$	3.26860	0.148573
$485$	−0.101799	−0.00462244
$486$	7.34407	0.333134
$487$	17.4876	0.792437	0.396218	−	0.918156i	$-0.370322\pi$
$487$	17.4876	0.792437	0.396218	+	0.918156i	$0.370322\pi$
$488$	18.9249	0.856691
$489$	3.77308	0.170625
$490$	−69.9468	−3.15987
$491$	−12.4301	−0.560963	−0.280482	−	0.959859i	$-0.590494\pi$
$491$	−12.4301	−0.560963	−0.280482	+	0.959859i	$0.590494\pi$
$492$	31.3253	1.41225
$493$	1.23199	0.0554860
$494$	−11.8804	−0.534526
$495$	11.4834	0.516142
$496$	−0.534136	−0.0239834
$497$	−41.8361	−1.87661
$498$	29.8585	1.33799
$499$	−41.0461	−1.83747	−0.918737	−	0.394869i	$-0.870790\pi$
$499$	−41.0461	−1.83747	−0.918737	+	0.394869i	$0.870790\pi$
$500$	−39.7620	−1.77821
$501$	14.9626	0.668479
$502$	62.9079	2.80772
$503$	25.1877	1.12306	0.561531	−	0.827456i	$-0.310213\pi$
$503$	25.1877	1.12306	0.561531	+	0.827456i	$0.310213\pi$
$504$	86.8822	3.87004
$505$	18.9706	0.844182
$506$	0	0
$507$	38.0024	1.68775
$508$	−50.5136	−2.24118
$509$	17.2888	0.766314	0.383157	−	0.923683i	$-0.374837\pi$
$509$	17.2888	0.766314	0.383157	+	0.923683i	$0.374837\pi$
$510$	−11.3258	−0.501515
$511$	27.6104	1.22141
$512$	1.65764	0.0732581
$513$	73.9917	3.26681
$514$	1.04452	0.0460716
$515$	−32.3557	−1.42576
$516$	107.811	4.74610
$517$	−6.28698	−0.276501
$518$	−47.0812	−2.06863
$519$	57.3411	2.51700
$520$	3.64010	0.159629
$521$	−7.83905	−0.343435	−0.171718	−	0.985146i	$-0.554932\pi$
$521$	−7.83905	−0.343435	−0.171718	+	0.985146i	$0.554932\pi$
$522$	19.9305	0.872334
$523$	−16.4195	−0.717976	−0.358988	−	0.933342i	$-0.616878\pi$
$523$	−16.4195	−0.717976	−0.358988	+	0.933342i	$0.616878\pi$
$524$	57.2160	2.49949
$525$	−22.5104	−0.982436
$526$	14.0635	0.613197
$527$	3.19134	0.139017
$528$	−0.443811	−0.0193144
$529$	0	0
$530$	11.5465	0.501548
$531$	56.8464	2.46693
$532$	121.758	5.27887
$533$	2.12597	0.0920862
$534$	−34.5860	−1.49668
$535$	−6.91688	−0.299043
$536$	21.9416	0.947734
$537$	35.7421	1.54238
$538$	−59.9478	−2.58453
$539$	16.3764	0.705380
$540$	−58.4119	−2.51365
$541$	20.2280	0.869671	0.434835	−	0.900510i	$-0.356807\pi$
$541$	20.2280	0.869671	0.434835	+	0.900510i	$0.356807\pi$
$542$	63.5372	2.72916
$543$	16.6831	0.715938
$544$	−4.80474	−0.206002
$545$	−15.2212	−0.652004
$546$	22.5781	0.966254
$547$	−23.7276	−1.01452	−0.507259	−	0.861793i	$-0.669341\pi$
$547$	−23.7276	−1.01452	−0.507259	+	0.861793i	$0.669341\pi$
$548$	10.8756	0.464581
$549$	−40.1080	−1.71177
$550$	3.52882	0.150469
$551$	10.8404	0.461818
$552$	0	0
$553$	5.52843	0.235093
$554$	53.6405	2.27897
$555$	23.9071	1.01480
$556$	−13.7429	−0.582830
$557$	−11.3993	−0.483005	−0.241503	−	0.970400i	$-0.577640\pi$
$557$	−11.3993	−0.483005	−0.241503	+	0.970400i	$0.577640\pi$
$558$	51.6278	2.18558
$559$	7.31687	0.309470
$560$	−1.31849	−0.0557163
$561$	2.65167	0.111954
$562$	36.7540	1.55037
$563$	22.3009	0.939870	0.469935	−	0.882701i	$-0.344277\pi$
$563$	22.3009	0.939870	0.469935	+	0.882701i	$0.344277\pi$
$564$	62.2325	2.62046
$565$	11.9815	0.504066
$566$	59.0763	2.48316
$567$	−51.1056	−2.14623
$568$	−25.1962	−1.05721
$569$	9.08903	0.381032	0.190516	−	0.981684i	$-0.438984\pi$
$569$	9.08903	0.381032	0.190516	+	0.981684i	$0.438984\pi$
$570$	−99.6573	−4.17418
$571$	32.2137	1.34810	0.674050	−	0.738686i	$-0.264553\pi$
$571$	32.2137	1.34810	0.674050	+	0.738686i	$0.264553\pi$
$572$	−2.19584	−0.0918126
$573$	24.0246	1.00364
$574$	−35.1201	−1.46589
$575$	0	0
$576$	−79.5375	−3.31406
$577$	−19.1592	−0.797610	−0.398805	−	0.917036i	$-0.630575\pi$
$577$	−19.1592	−0.797610	−0.398805	+	0.917036i	$0.630575\pi$
$578$	37.2610	1.54986
$579$	−15.1024	−0.627636
$580$	−8.55785	−0.355345
$581$	−20.7680	−0.861603
$582$	−0.380277	−0.0157630
$583$	−2.70334	−0.111961
$584$	16.6286	0.688098
$585$	−7.71454	−0.318957
$586$	−35.9557	−1.48532
$587$	−42.7664	−1.76516	−0.882580	−	0.470162i	$-0.844195\pi$
$587$	−42.7664	−1.76516	−0.882580	+	0.470162i	$0.844195\pi$
$588$	−162.104	−6.68504
$589$	28.0810	1.15706
$590$	−39.3445	−1.61979
$591$	69.0672	2.84104
$592$	−0.621722	−0.0255526
$593$	7.28055	0.298976	0.149488	−	0.988764i	$-0.452237\pi$
$593$	7.28055	0.298976	0.149488	+	0.988764i	$0.452237\pi$
$594$	22.0437	0.904464
$595$	7.87766	0.322952
$596$	14.3521	0.587887
$597$	1.45009	0.0593482
$598$	0	0
$599$	7.67861	0.313740	0.156870	−	0.987619i	$-0.449860\pi$
$599$	7.67861	0.313740	0.156870	+	0.987619i	$0.449860\pi$
$600$	−13.5571	−0.553468
$601$	0.795081	0.0324320	0.0162160	−	0.999869i	$-0.494838\pi$
$601$	0.795081	0.0324320	0.0162160	+	0.999869i	$0.494838\pi$
$602$	−120.871	−4.92634
$603$	−46.5014	−1.89368
$604$	1.54823	0.0629966
$605$	1.86081	0.0756527
$606$	70.8664	2.87875
$607$	26.1590	1.06176	0.530881	−	0.847447i	$-0.321861\pi$
$607$	26.1590	1.06176	0.530881	+	0.847447i	$0.321861\pi$
$608$	−42.2776	−1.71458
$609$	−20.6017	−0.834821
$610$	27.7595	1.12395
$611$	4.22358	0.170868
$612$	−17.6619	−0.713941
$613$	−1.74845	−0.0706194	−0.0353097	−	0.999376i	$-0.511242\pi$
$613$	−1.74845	−0.0706194	−0.0353097	+	0.999376i	$0.511242\pi$
$614$	−57.2546	−2.31061
$615$	17.8334	0.719114
$616$	14.0787	0.567245
$617$	−21.0955	−0.849271	−0.424636	−	0.905364i	$-0.639598\pi$
$617$	−21.0955	−0.849271	−0.424636	+	0.905364i	$0.639598\pi$
$618$	−120.868	−4.86201
$619$	36.9587	1.48550	0.742748	−	0.669571i	$-0.233522\pi$
$619$	36.9587	1.48550	0.742748	+	0.669571i	$0.233522\pi$
$620$	−22.1682	−0.890297
$621$	0	0
$622$	−3.68415	−0.147721
$623$	24.0562	0.963793
$624$	0.298151	0.0119356
$625$	−14.9495	−0.597982
$626$	−30.7593	−1.22939
$627$	23.3324	0.931806
$628$	62.5310	2.49526
$629$	3.71464	0.148113
$630$	127.441	5.07736
$631$	22.8809	0.910875	0.455437	−	0.890268i	$-0.349483\pi$
$631$	22.8809	0.910875	0.455437	+	0.890268i	$0.349483\pi$
$632$	3.32956	0.132443
$633$	32.9051	1.30786
$634$	−74.1388	−2.94443
$635$	−28.7573	−1.14120
$636$	26.7593	1.06108
$637$	−11.0016	−0.435900
$638$	3.22960	0.127861
$639$	53.3990	2.11243
$640$	34.6274	1.36877
$641$	14.6863	0.580075	0.290037	−	0.957015i	$-0.406332\pi$
$641$	14.6863	0.580075	0.290037	+	0.957015i	$0.406332\pi$
$642$	−25.8386	−1.01977
$643$	−25.5413	−1.00725	−0.503624	−	0.863923i	$-0.668000\pi$
$643$	−25.5413	−1.00725	−0.503624	+	0.863923i	$0.668000\pi$
$644$	0	0
$645$	61.3765	2.41670
$646$	−15.4846	−0.609233
$647$	12.8250	0.504203	0.252102	−	0.967701i	$-0.418878\pi$
$647$	12.8250	0.504203	0.252102	+	0.967701i	$0.418878\pi$
$648$	−30.7789	−1.20911
$649$	9.21157	0.361586
$650$	−2.37065	−0.0929847
$651$	−53.3664	−2.09159
$652$	−4.07235	−0.159486
$653$	2.52854	0.0989494	0.0494747	−	0.998775i	$-0.484245\pi$
$653$	2.52854	0.0989494	0.0494747	+	0.998775i	$0.484245\pi$
$654$	−56.8600	−2.22340
$655$	32.5730	1.27273
$656$	−0.463772	−0.0181073
$657$	−35.2414	−1.37490
$658$	−69.7716	−2.71998
$659$	18.9446	0.737975	0.368988	−	0.929434i	$-0.379704\pi$
$659$	18.9446	0.737975	0.368988	+	0.929434i	$0.379704\pi$
$660$	−18.4195	−0.716977
$661$	16.8011	0.653487	0.326744	−	0.945113i	$-0.394049\pi$
$661$	16.8011	0.653487	0.326744	+	0.945113i	$0.394049\pi$
$662$	−2.46561	−0.0958285
$663$	−1.78138	−0.0691833
$664$	−12.5078	−0.485395
$665$	69.3165	2.68798
$666$	60.0936	2.32858
$667$	0	0
$668$	−16.1494	−0.624838
$669$	18.6723	0.721911
$670$	32.1844	1.24339
$671$	−6.49923	−0.250900
$672$	80.3463	3.09942
$673$	10.4735	0.403725	0.201863	−	0.979414i	$-0.435301\pi$
$673$	10.4735	0.403725	0.201863	+	0.979414i	$0.435301\pi$
$674$	5.39545	0.207825
$675$	14.7645	0.568286
$676$	−41.0167	−1.57756
$677$	−2.61344	−0.100443	−0.0502213	−	0.998738i	$-0.515993\pi$
$677$	−2.61344	−0.100443	−0.0502213	+	0.998738i	$0.515993\pi$
$678$	44.7580	1.71892
$679$	0.264502	0.0101506
$680$	4.74440	0.181939
$681$	51.5826	1.97665
$682$	8.36593	0.320348
$683$	25.1735	0.963236	0.481618	−	0.876381i	$-0.340049\pi$
$683$	25.1735	0.963236	0.481618	+	0.876381i	$0.340049\pi$
$684$	−155.410	−5.94223
$685$	6.19145	0.236563
$686$	104.057	3.97291
$687$	18.7818	0.716572
$688$	−1.59614	−0.0608524
$689$	1.81610	0.0691878
$690$	0	0
$691$	−25.6904	−0.977309	−0.488654	−	0.872477i	$-0.662512\pi$
$691$	−25.6904	−0.977309	−0.488654	+	0.872477i	$0.662512\pi$
$692$	−61.8892	−2.35267
$693$	−29.8372	−1.13342
$694$	43.6225	1.65589
$695$	−7.82384	−0.296775
$696$	−12.4076	−0.470307
$697$	2.77093	0.104957
$698$	−31.4622	−1.19086
$699$	52.0869	1.97011
$700$	24.2959	0.918298
$701$	−35.8879	−1.35547	−0.677734	−	0.735307i	$-0.737038\pi$
$701$	−35.8879	−1.35547	−0.677734	+	0.735307i	$0.737038\pi$
$702$	−14.8089	−0.558926
$703$	32.6857	1.23276
$704$	−12.8885	−0.485753
$705$	35.4289	1.33433
$706$	38.9913	1.46746
$707$	−49.2911	−1.85378
$708$	−91.1819	−3.42683
$709$	−33.5227	−1.25897	−0.629486	−	0.777012i	$-0.716734\pi$
$709$	−33.5227	−1.25897	−0.629486	+	0.777012i	$0.716734\pi$
$710$	−36.9584	−1.38702
$711$	−7.05640	−0.264636
$712$	14.4881	0.542965
$713$	0	0
$714$	29.4276	1.10130
$715$	−1.25009	−0.0467506
$716$	−38.5770	−1.44169
$717$	32.0238	1.19595
$718$	−49.1494	−1.83424
$719$	45.7326	1.70554	0.852770	−	0.522287i	$-0.174921\pi$
$719$	45.7326	1.70554	0.852770	+	0.522287i	$0.174921\pi$
$720$	1.68290	0.0627178
$721$	84.0693	3.13090
$722$	−92.6395	−3.44769
$723$	59.1125	2.19842
$724$	−18.0063	−0.669199
$725$	2.16313	0.0803366
$726$	6.95122	0.257984
$727$	−24.4311	−0.906101	−0.453051	−	0.891485i	$-0.649664\pi$
$727$	−24.4311	−0.906101	−0.453051	+	0.891485i	$0.649664\pi$
$728$	−9.45801	−0.350537
$729$	−22.0208	−0.815587
$730$	24.3912	0.902760
$731$	9.53659	0.352723
$732$	64.3334	2.37783
$733$	9.69778	0.358196	0.179098	−	0.983831i	$-0.442682\pi$
$733$	9.69778	0.358196	0.179098	+	0.983831i	$0.442682\pi$
$734$	−14.6613	−0.541160
$735$	−92.2854	−3.40400
$736$	0	0
$737$	−7.53522	−0.277563
$738$	44.8267	1.65009
$739$	32.3210	1.18895	0.594474	−	0.804115i	$-0.297360\pi$
$739$	32.3210	1.18895	0.594474	+	0.804115i	$0.297360\pi$
$740$	−25.8033	−0.948548
$741$	−15.6746	−0.575822
$742$	−30.0011	−1.10137
$743$	12.8639	0.471930	0.235965	−	0.971762i	$-0.424175\pi$
$743$	12.8639	0.471930	0.235965	+	0.971762i	$0.424175\pi$
$744$	−32.1405	−1.17833
$745$	8.17066	0.299350
$746$	−55.0166	−2.01430
$747$	26.5080	0.969876
$748$	−2.86199	−0.104645
$749$	17.9720	0.656683
$750$	−84.5604	−3.08771
$751$	−22.4842	−0.820461	−0.410230	−	0.911982i	$-0.634552\pi$
$751$	−22.4842	−0.820461	−0.410230	+	0.911982i	$0.634552\pi$
$752$	−0.921356	−0.0335984
$753$	82.9986	3.02464
$754$	−2.16963	−0.0790134
$755$	0.881406	0.0320776
$756$	151.770	5.51984
$757$	−16.2586	−0.590930	−0.295465	−	0.955354i	$-0.595475\pi$
$757$	−16.2586	−0.590930	−0.295465	+	0.955354i	$0.595475\pi$
$758$	8.90230	0.323346
$759$	0	0
$760$	41.7466	1.51431
$761$	−24.5165	−0.888722	−0.444361	−	0.895848i	$-0.646569\pi$
$761$	−24.5165	−0.888722	−0.444361	+	0.895848i	$0.646569\pi$
$762$	−107.425	−3.89161
$763$	39.5490	1.43177
$764$	−25.9302	−0.938121
$765$	−10.0549	−0.363536
$766$	−47.8821	−1.73005
$767$	−6.18831	−0.223447
$768$	51.2906	1.85079
$769$	32.8639	1.18510	0.592552	−	0.805532i	$-0.298121\pi$
$769$	32.8639	1.18510	0.592552	+	0.805532i	$0.298121\pi$
$770$	20.6509	0.744206
$771$	1.37810	0.0496311
$772$	16.3003	0.586661
$773$	−38.9309	−1.40025	−0.700123	−	0.714022i	$-0.746872\pi$
$773$	−38.9309	−1.40025	−0.700123	+	0.714022i	$0.746872\pi$
$774$	154.278	5.54541
$775$	5.60336	0.201279
$776$	0.159299	0.00571849
$777$	−62.1173	−2.22845
$778$	44.9532	1.61165
$779$	24.3818	0.873569
$780$	12.3742	0.443066
$781$	8.65293	0.309626
$782$	0	0
$783$	13.5126	0.482899
$784$	2.39995	0.0857126
$785$	35.5988	1.27058
$786$	121.679	4.34015
$787$	14.1003	0.502622	0.251311	−	0.967906i	$-0.419138\pi$
$787$	14.1003	0.502622	0.251311	+	0.967906i	$0.419138\pi$
$788$	−74.5453	−2.65557
$789$	18.5549	0.660572
$790$	4.88386	0.173760
$791$	−31.1314	−1.10690
$792$	−17.9698	−0.638528
$793$	4.36616	0.155047
$794$	−40.7853	−1.44742
$795$	15.2341	0.540297
$796$	−1.56510	−0.0554737
$797$	11.8651	0.420283	0.210141	−	0.977671i	$-0.432608\pi$
$797$	11.8651	0.420283	0.210141	+	0.977671i	$0.432608\pi$
$798$	258.938	9.16630
$799$	5.50489	0.194749
$800$	−8.43618	−0.298264
$801$	−30.7050	−1.08491
$802$	14.7049	0.519249
$803$	−5.71063	−0.201524
$804$	74.5884	2.63053
$805$	0	0
$806$	−5.62021	−0.197963
$807$	−79.0932	−2.78421
$808$	−29.6860	−1.04435
$809$	20.8928	0.734553	0.367276	−	0.930112i	$-0.380290\pi$
$809$	20.8928	0.734553	0.367276	+	0.930112i	$0.380290\pi$
$810$	−45.1471	−1.58631
$811$	−2.34337	−0.0822869	−0.0411434	−	0.999153i	$-0.513100\pi$
$811$	−2.34337	−0.0822869	−0.0411434	+	0.999153i	$0.513100\pi$
$812$	22.2357	0.780320
$813$	83.8289	2.94001
$814$	9.73775	0.341308
$815$	−2.31838	−0.0812095
$816$	0.388602	0.0136038
$817$	83.9137	2.93577
$818$	−40.5276	−1.41702
$819$	20.0446	0.700414
$820$	−19.2479	−0.672167
$821$	−9.00362	−0.314229	−0.157114	−	0.987580i	$-0.550219\pi$
$821$	−9.00362	−0.314229	−0.157114	+	0.987580i	$0.550219\pi$
$822$	23.1287	0.806705
$823$	22.2583	0.775874	0.387937	−	0.921686i	$-0.373188\pi$
$823$	22.2583	0.775874	0.387937	+	0.921686i	$0.373188\pi$
$824$	50.6316	1.76383
$825$	4.65581	0.162094
$826$	102.228	3.55697
$827$	11.9922	0.417010	0.208505	−	0.978021i	$-0.433140\pi$
$827$	11.9922	0.417010	0.208505	+	0.978021i	$0.433140\pi$
$828$	0	0
$829$	−38.5858	−1.34014	−0.670069	−	0.742299i	$-0.733736\pi$
$829$	−38.5858	−1.34014	−0.670069	+	0.742299i	$0.733736\pi$
$830$	−18.3466	−0.636822
$831$	70.7715	2.45504
$832$	8.65846	0.300178
$833$	−14.3392	−0.496823
$834$	−29.2266	−1.01203
$835$	−9.19381	−0.318165
$836$	−25.1830	−0.870973
$837$	35.0028	1.20988
$838$	−35.6402	−1.23117
$839$	15.6697	0.540979	0.270489	−	0.962723i	$-0.412814\pi$
$839$	15.6697	0.540979	0.270489	+	0.962723i	$0.412814\pi$
$840$	−79.3371	−2.73739
$841$	−27.0203	−0.931734
$842$	50.6598	1.74585
$843$	48.4920	1.67015
$844$	−35.5150	−1.22248
$845$	−23.3507	−0.803290
$846$	89.0553	3.06178
$847$	−4.83491	−0.166130
$848$	−0.396174	−0.0136047
$849$	77.9434	2.67501
$850$	−3.08984	−0.105981
$851$	0	0
$852$	−85.6521	−2.93439
$853$	14.6906	0.502995	0.251497	−	0.967858i	$-0.419077\pi$
$853$	14.6906	0.502995	0.251497	+	0.967858i	$0.419077\pi$
$854$	−72.1270	−2.46814
$855$	−88.4745	−3.02576
$856$	10.8238	0.369951
$857$	45.0625	1.53931	0.769653	−	0.638462i	$-0.220429\pi$
$857$	45.0625	1.53931	0.769653	+	0.638462i	$0.220429\pi$
$858$	−4.66981	−0.159425
$859$	53.4365	1.82323	0.911615	−	0.411044i	$-0.134836\pi$
$859$	53.4365	1.82323	0.911615	+	0.411044i	$0.134836\pi$
$860$	−66.2447	−2.25892
$861$	−46.3363	−1.57914
$862$	50.6135	1.72390
$863$	−48.7362	−1.65900	−0.829500	−	0.558506i	$-0.811375\pi$
$863$	−48.7362	−1.65900	−0.829500	+	0.558506i	$0.811375\pi$
$864$	−52.6988	−1.79285
$865$	−35.2335	−1.19797
$866$	26.6920	0.907031
$867$	49.1610	1.66959
$868$	57.5993	1.95505
$869$	−1.14344	−0.0387886
$870$	−18.1997	−0.617027
$871$	5.06214	0.171524
$872$	23.8188	0.806605
$873$	−0.337606	−0.0114262
$874$	0	0
$875$	58.8159	1.98834
$876$	56.5274	1.90988
$877$	−27.8376	−0.940011	−0.470005	−	0.882664i	$-0.655748\pi$
$877$	−27.8376	−0.940011	−0.470005	+	0.882664i	$0.655748\pi$
$878$	−14.1941	−0.479026
$879$	−47.4387	−1.60007
$880$	0.272701	0.00919276
$881$	−11.0905	−0.373649	−0.186825	−	0.982393i	$-0.559820\pi$
$881$	−11.0905	−0.373649	−0.186825	+	0.982393i	$0.559820\pi$
$882$	−231.972	−7.81089
$883$	−26.0935	−0.878118	−0.439059	−	0.898458i	$-0.644688\pi$
$883$	−26.0935	−0.878118	−0.439059	+	0.898458i	$0.644688\pi$
$884$	1.92268	0.0646667
$885$	−51.9098	−1.74493
$886$	−12.8473	−0.431615
$887$	7.90798	0.265524	0.132762	−	0.991148i	$-0.457615\pi$
$887$	7.90798	0.265524	0.132762	+	0.991148i	$0.457615\pi$
$888$	−37.4108	−1.25542
$889$	74.7196	2.50602
$890$	21.2515	0.712351
$891$	10.5701	0.354112
$892$	−20.1533	−0.674781
$893$	48.4382	1.62092
$894$	30.5222	1.02081
$895$	−21.9618	−0.734103
$896$	−89.9718	−3.00575
$897$	0	0
$898$	−9.51763	−0.317607
$899$	5.12822	0.171036
$900$	−31.0108	−1.03369
$901$	2.36705	0.0788578
$902$	7.26386	0.241860
$903$	−159.473	−5.30694
$904$	−18.7492	−0.623588
$905$	−10.2510	−0.340754
$906$	3.29257	0.109388
$907$	−19.1968	−0.637420	−0.318710	−	0.947852i	$-0.603250\pi$
$907$	−19.1968	−0.637420	−0.318710	+	0.947852i	$0.603250\pi$
$908$	−55.6740	−1.84761
$909$	62.9143	2.08674
$910$	−13.8732	−0.459892
$911$	12.9473	0.428963	0.214482	−	0.976728i	$-0.431194\pi$
$911$	12.9473	0.428963	0.214482	+	0.976728i	$0.431194\pi$
$912$	3.41936	0.113226
$913$	4.29543	0.142158
$914$	−69.3971	−2.29545
$915$	36.6249	1.21078
$916$	−20.2715	−0.669791
$917$	−84.6338	−2.79486
$918$	−19.3015	−0.637044
$919$	−12.3388	−0.407019	−0.203509	−	0.979073i	$-0.565235\pi$
$919$	−12.3388	−0.407019	−0.203509	+	0.979073i	$0.565235\pi$
$920$	0	0
$921$	−75.5399	−2.48912
$922$	53.5126	1.76234
$923$	−5.81302	−0.191338
$924$	47.8590	1.57445
$925$	6.52218	0.214448
$926$	−20.2408	−0.665154
$927$	−107.305	−3.52435
$928$	−7.72084	−0.253449
$929$	42.4304	1.39210	0.696048	−	0.717995i	$-0.254940\pi$
$929$	42.4304	1.39210	0.696048	+	0.717995i	$0.254940\pi$
$930$	−47.1443	−1.54592
$931$	−126.172	−4.13513
$932$	−56.2182	−1.84149
$933$	−4.86075	−0.159134
$934$	−57.6646	−1.88684
$935$	−1.62933	−0.0532847
$936$	12.0720	0.394587
$937$	−8.80913	−0.287782	−0.143891	−	0.989594i	$-0.545961\pi$
$937$	−8.80913	−0.287782	−0.143891	+	0.989594i	$0.545961\pi$
$938$	−83.6243	−2.73043
$939$	−40.5828	−1.32437
$940$	−38.2390	−1.24722
$941$	−52.6368	−1.71591	−0.857956	−	0.513723i	$-0.828266\pi$
$941$	−52.6368	−1.71591	−0.857956	+	0.513723i	$0.828266\pi$
$942$	132.982	4.33280
$943$	0	0
$944$	1.34995	0.0439372
$945$	86.4028	2.81068
$946$	24.9997	0.812810
$947$	−4.96505	−0.161342	−0.0806712	−	0.996741i	$-0.525706\pi$
$947$	−4.96505	−0.161342	−0.0806712	+	0.996741i	$0.525706\pi$
$948$	11.3185	0.367608
$949$	3.83639	0.124534
$950$	−27.1879	−0.882092
$951$	−97.8162	−3.17191
$952$	−12.3273	−0.399530
$953$	−28.7734	−0.932062	−0.466031	−	0.884768i	$-0.654316\pi$
$953$	−28.7734	−0.932062	−0.466031	+	0.884768i	$0.654316\pi$
$954$	38.2929	1.23978
$955$	−14.7620	−0.477688
$956$	−34.5638	−1.11787
$957$	4.26102	0.137739
$958$	28.6603	0.925974
$959$	−16.0871	−0.519480
$960$	72.6302	2.34413
$961$	−17.7159	−0.571480
$962$	−6.54180	−0.210916
$963$	−22.9392	−0.739204
$964$	−63.8011	−2.05490
$965$	9.27975	0.298726
$966$	0	0
$967$	−17.9251	−0.576432	−0.288216	−	0.957565i	$-0.593062\pi$
$967$	−17.9251	−0.576432	−0.288216	+	0.957565i	$0.593062\pi$
$968$	−2.91187	−0.0935912
$969$	−20.4299	−0.656302
$970$	0.233663	0.00750246
$971$	58.9528	1.89188	0.945942	−	0.324335i	$-0.105140\pi$
$971$	58.9528	1.89188	0.945942	+	0.324335i	$0.105140\pi$
$972$	−10.4581	−0.335442
$973$	20.3285	0.651703
$974$	−40.1399	−1.28617
$975$	−3.12776	−0.100169
$976$	−0.952460	−0.0304875
$977$	15.0718	0.482190	0.241095	−	0.970501i	$-0.422493\pi$
$977$	15.0718	0.482190	0.241095	+	0.970501i	$0.422493\pi$
$978$	−8.66052	−0.276933
$979$	−4.97553	−0.159019
$980$	99.6052	3.18177
$981$	−50.4796	−1.61169
$982$	28.5314	0.910473
$983$	3.17567	0.101288	0.0506440	−	0.998717i	$-0.483873\pi$
$983$	3.17567	0.101288	0.0506440	+	0.998717i	$0.483873\pi$
$984$	−27.9065	−0.889627
$985$	−42.4386	−1.35221
$986$	−2.82784	−0.0900567
$987$	−92.0543	−2.93012
$988$	16.9179	0.538230
$989$	0	0
$990$	−26.3584	−0.837726
$991$	−3.26920	−0.103850	−0.0519248	−	0.998651i	$-0.516536\pi$
$991$	−3.26920	−0.103850	−0.0519248	+	0.998651i	$0.516536\pi$
$992$	−20.0000	−0.635001
$993$	−3.25304	−0.103232
$994$	96.0283	3.04583
$995$	−0.891012	−0.0282470
$996$	−42.5189	−1.34726
$997$	10.3816	0.328788	0.164394	−	0.986395i	$-0.447433\pi$
$997$	10.3816	0.328788	0.164394	+	0.986395i	$0.447433\pi$
$998$	94.2148	2.98232
$999$	40.7425	1.28904

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.7		60
23.4	even	11		253.2.i.b.177.11	✓	120
23.6	even	11		253.2.i.b.243.11	yes	120
23.22	odd	2		5819.2.a.t.1.7		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.177.11	✓	120	23.4	even	11
253.2.i.b.243.11	yes	120	23.6	even	11
5819.2.a.t.1.7		60	23.22	odd	2
5819.2.a.u.1.7		60	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29534 q^{2} -3.02840 q^{3} +3.26860 q^{4} +1.86081 q^{5} +6.95122 q^{6} -4.83491 q^{7} -2.91187 q^{8} +6.17120 q^{9} -4.27120 q^{10} +1.00000 q^{11} -9.89863 q^{12} -0.671797 q^{13} +11.0978 q^{14} -5.63528 q^{15} +0.146550 q^{16} -0.875601 q^{17} -14.1650 q^{18} -7.70453 q^{19} +6.08225 q^{20} +14.6420 q^{21} -2.29534 q^{22} +8.81832 q^{24} -1.53738 q^{25} +1.54201 q^{26} -9.60366 q^{27} -15.8034 q^{28} -1.40702 q^{29} +12.9349 q^{30} -3.64474 q^{31} +5.48737 q^{32} -3.02840 q^{33} +2.00980 q^{34} -8.99686 q^{35} +20.1712 q^{36} -4.24239 q^{37} +17.6845 q^{38} +2.03447 q^{39} -5.41845 q^{40} -3.16461 q^{41} -33.6085 q^{42} -10.8915 q^{43} +3.26860 q^{44} +11.4834 q^{45} -6.28698 q^{47} -0.443811 q^{48} +16.3764 q^{49} +3.52882 q^{50} +2.65167 q^{51} -2.19584 q^{52} -2.70334 q^{53} +22.0437 q^{54} +1.86081 q^{55} +14.0787 q^{56} +23.3324 q^{57} +3.22960 q^{58} +9.21157 q^{59} -18.4195 q^{60} -6.49923 q^{61} +8.36593 q^{62} -29.8372 q^{63} -12.8885 q^{64} -1.25009 q^{65} +6.95122 q^{66} -7.53522 q^{67} -2.86199 q^{68} +20.6509 q^{70} +8.65293 q^{71} -17.9698 q^{72} -5.71063 q^{73} +9.73775 q^{74} +4.65581 q^{75} -25.1830 q^{76} -4.83491 q^{77} -4.66981 q^{78} -1.14344 q^{79} +0.272701 q^{80} +10.5701 q^{81} +7.26386 q^{82} +4.29543 q^{83} +47.8590 q^{84} -1.62933 q^{85} +24.9997 q^{86} +4.26102 q^{87} -2.91187 q^{88} -4.97553 q^{89} -26.3584 q^{90} +3.24808 q^{91} +11.0377 q^{93} +14.4308 q^{94} -14.3367 q^{95} -16.6179 q^{96} -0.0547066 q^{97} -37.5894 q^{98} +6.17120 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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