LMFDB - Embedded newform 4923.2.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4923,2,Mod(1,4923)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4923, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4923.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4923 = 3^{2} \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4923.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$39.3103529151$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 $ x^18 - 4x^17 - 18x^16 + 84x^15 + 116x^14 - 708x^13 - 282x^12 + 3104x^11 - 137x^10 - 7703x^9 + 2068x^8 + 11068x^7 - 4274x^6 - 9021x^5 + 4048x^4 + 3834x^3 - 1851x^2 - 654*x + 328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 547)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.52216$ of defining polynomial
Character	$\chi$	$=$	4923.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52216 q^{2} +0.316965 q^{4} -1.24712 q^{5} -0.899316 q^{7} +2.56184 q^{8} +O(q^{10})$	\(q-1.52216 q^{2} +0.316965 q^{4} -1.24712 q^{5} -0.899316 q^{7} +2.56184 q^{8} +1.89831 q^{10} -3.77827 q^{11} -4.29029 q^{13} +1.36890 q^{14} -4.53346 q^{16} +7.86362 q^{17} -6.61960 q^{19} -0.395293 q^{20} +5.75113 q^{22} -3.37854 q^{23} -3.44470 q^{25} +6.53050 q^{26} -0.285052 q^{28} +2.81309 q^{29} -1.72157 q^{31} +1.77696 q^{32} -11.9697 q^{34} +1.12155 q^{35} -4.86769 q^{37} +10.0761 q^{38} -3.19492 q^{40} -5.86463 q^{41} +7.30517 q^{43} -1.19758 q^{44} +5.14268 q^{46} -2.08319 q^{47} -6.19123 q^{49} +5.24338 q^{50} -1.35987 q^{52} -3.26386 q^{53} +4.71195 q^{55} -2.30391 q^{56} -4.28196 q^{58} +6.21926 q^{59} +12.5220 q^{61} +2.62050 q^{62} +6.36212 q^{64} +5.35050 q^{65} -10.3052 q^{67} +2.49250 q^{68} -1.70718 q^{70} -16.3692 q^{71} -15.5143 q^{73} +7.40939 q^{74} -2.09818 q^{76} +3.39786 q^{77} +5.15466 q^{79} +5.65376 q^{80} +8.92689 q^{82} -6.55843 q^{83} -9.80686 q^{85} -11.1196 q^{86} -9.67935 q^{88} +4.60031 q^{89} +3.85833 q^{91} -1.07088 q^{92} +3.17095 q^{94} +8.25541 q^{95} +9.16155 q^{97} +9.42403 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} + 16 q^{4} + 27 q^{5} - 11 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^2 + 16 * q^4 + 27 * q^5 - 11 * q^7 + 12 * q^8	$ 18 q + 4 q^{2} + 16 q^{4} + 27 q^{5} - 11 q^{7} + 12 q^{8} - 5 q^{10} - 2 q^{11} - 25 q^{13} + 7 q^{14} + 8 q^{16} + 30 q^{17} + 4 q^{19} + 41 q^{20} - 24 q^{22} + 26 q^{23} + 31 q^{25} + 18 q^{26} - 16 q^{28} + 18 q^{29} - 5 q^{31} + 28 q^{32} + 5 q^{34} + 9 q^{35} - 18 q^{37} + 45 q^{38} + 7 q^{40} + 17 q^{41} + 8 q^{43} - 12 q^{44} + 30 q^{46} + 52 q^{47} + 29 q^{49} - 13 q^{50} - 14 q^{52} + 60 q^{53} + 11 q^{55} - 7 q^{56} + 14 q^{58} + 8 q^{59} - 26 q^{61} - 4 q^{62} + 44 q^{64} + 6 q^{65} + 12 q^{67} + 61 q^{68} + 35 q^{70} + q^{71} - 2 q^{73} - 16 q^{74} + 66 q^{76} + 73 q^{77} + 18 q^{79} + 32 q^{80} + 44 q^{82} + 43 q^{83} + 51 q^{85} - 4 q^{86} - 17 q^{88} + 28 q^{89} - q^{91} + 68 q^{92} + 78 q^{94} + 18 q^{95} - 34 q^{97} - 34 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 + 16 * q^4 + 27 * q^5 - 11 * q^7 + 12 * q^8 - 5 * q^10 - 2 * q^11 - 25 * q^13 + 7 * q^14 + 8 * q^16 + 30 * q^17 + 4 * q^19 + 41 * q^20 - 24 * q^22 + 26 * q^23 + 31 * q^25 + 18 * q^26 - 16 * q^28 + 18 * q^29 - 5 * q^31 + 28 * q^32 + 5 * q^34 + 9 * q^35 - 18 * q^37 + 45 * q^38 + 7 * q^40 + 17 * q^41 + 8 * q^43 - 12 * q^44 + 30 * q^46 + 52 * q^47 + 29 * q^49 - 13 * q^50 - 14 * q^52 + 60 * q^53 + 11 * q^55 - 7 * q^56 + 14 * q^58 + 8 * q^59 - 26 * q^61 - 4 * q^62 + 44 * q^64 + 6 * q^65 + 12 * q^67 + 61 * q^68 + 35 * q^70 + q^71 - 2 * q^73 - 16 * q^74 + 66 * q^76 + 73 * q^77 + 18 * q^79 + 32 * q^80 + 44 * q^82 + 43 * q^83 + 51 * q^85 - 4 * q^86 - 17 * q^88 + 28 * q^89 - q^91 + 68 * q^92 + 78 * q^94 + 18 * q^95 - 34 * q^97 - 34 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.52216	−1.07633	−0.538164	−	0.842840i	$-0.680882\pi$
$2$	−1.52216	−1.07633	−0.538164	+	0.842840i	$0.680882\pi$
$3$	0	0
$3$	0	0
$4$	0.316965	0.158483
$5$	−1.24712	−0.557728	−0.278864	−	0.960331i	$-0.589958\pi$
$5$	−1.24712	−0.557728	−0.278864	+	0.960331i	$0.589958\pi$
$6$	0	0
$7$	−0.899316	−0.339909	−0.169955	−	0.985452i	$-0.554362\pi$
$7$	−0.899316	−0.339909	−0.169955	+	0.985452i	$0.554362\pi$
$8$	2.56184	0.905749
$9$	0	0
$10$	1.89831	0.600298
$11$	−3.77827	−1.13919	−0.569596	−	0.821925i	$-0.692900\pi$
$11$	−3.77827	−1.13919	−0.569596	+	0.821925i	$0.692900\pi$
$12$	0	0
$13$	−4.29029	−1.18991	−0.594957	−	0.803758i	$-0.702831\pi$
$13$	−4.29029	−1.18991	−0.594957	+	0.803758i	$0.702831\pi$
$14$	1.36890	0.365854
$15$	0	0
$16$	−4.53346	−1.13337
$17$	7.86362	1.90721	0.953604	−	0.301063i	$-0.0973415\pi$
$17$	7.86362	1.90721	0.953604	+	0.301063i	$0.0973415\pi$
$18$	0	0
$19$	−6.61960	−1.51864	−0.759320	−	0.650718i	$-0.774468\pi$
$19$	−6.61960	−1.51864	−0.759320	+	0.650718i	$0.774468\pi$
$20$	−0.395293	−0.0883902
$21$	0	0
$22$	5.75113	1.22614
$23$	−3.37854	−0.704475	−0.352238	−	0.935911i	$-0.614579\pi$
$23$	−3.37854	−0.704475	−0.352238	+	0.935911i	$0.614579\pi$
$24$	0	0
$25$	−3.44470	−0.688940
$26$	6.53050	1.28074
$27$	0	0
$28$	−0.285052	−0.0538697
$29$	2.81309	0.522377	0.261189	−	0.965288i	$-0.415886\pi$
$29$	2.81309	0.522377	0.261189	+	0.965288i	$0.415886\pi$
$30$	0	0
$31$	−1.72157	−0.309202	−0.154601	−	0.987977i	$-0.549409\pi$
$31$	−1.72157	−0.309202	−0.154601	+	0.987977i	$0.549409\pi$
$32$	1.77696	0.314125
$33$	0	0
$34$	−11.9697	−2.05278
$35$	1.12155	0.189577
$36$	0	0
$37$	−4.86769	−0.800243	−0.400122	−	0.916462i	$-0.631032\pi$
$37$	−4.86769	−0.800243	−0.400122	+	0.916462i	$0.631032\pi$
$38$	10.0761	1.63456
$39$	0	0
$40$	−3.19492	−0.505161
$41$	−5.86463	−0.915901	−0.457951	−	0.888978i	$-0.651416\pi$
$41$	−5.86463	−0.915901	−0.457951	+	0.888978i	$0.651416\pi$
$42$	0	0
$43$	7.30517	1.11403	0.557014	−	0.830503i	$-0.311947\pi$
$43$	7.30517	1.11403	0.557014	+	0.830503i	$0.311947\pi$
$44$	−1.19758	−0.180542
$45$	0	0
$46$	5.14268	0.758247
$47$	−2.08319	−0.303865	−0.151932	−	0.988391i	$-0.548550\pi$
$47$	−2.08319	−0.303865	−0.151932	+	0.988391i	$0.548550\pi$
$48$	0	0
$49$	−6.19123	−0.884462
$50$	5.24338	0.741525
$51$	0	0
$52$	−1.35987	−0.188581
$53$	−3.26386	−0.448325	−0.224163	−	0.974552i	$-0.571965\pi$
$53$	−3.26386	−0.448325	−0.224163	+	0.974552i	$0.571965\pi$
$54$	0	0
$55$	4.71195	0.635359
$56$	−2.30391	−0.307873
$57$	0	0
$58$	−4.28196	−0.562250
$59$	6.21926	0.809679	0.404840	−	0.914388i	$-0.367327\pi$
$59$	6.21926	0.809679	0.404840	+	0.914388i	$0.367327\pi$
$60$	0	0
$61$	12.5220	1.60327	0.801636	−	0.597812i	$-0.203963\pi$
$61$	12.5220	1.60327	0.801636	+	0.597812i	$0.203963\pi$
$62$	2.62050	0.332803
$63$	0	0
$64$	6.36212	0.795264
$65$	5.35050	0.663648
$66$	0	0
$67$	−10.3052	−1.25898	−0.629491	−	0.777008i	$-0.716737\pi$
$67$	−10.3052	−1.25898	−0.629491	+	0.777008i	$0.716737\pi$
$68$	2.49250	0.302259
$69$	0	0
$70$	−1.70718	−0.204047
$71$	−16.3692	−1.94267	−0.971334	−	0.237718i	$-0.923601\pi$
$71$	−16.3692	−1.94267	−0.971334	+	0.237718i	$0.923601\pi$
$72$	0	0
$73$	−15.5143	−1.81581	−0.907907	−	0.419172i	$-0.862320\pi$
$73$	−15.5143	−1.81581	−0.907907	+	0.419172i	$0.862320\pi$
$74$	7.40939	0.861324
$75$	0	0
$76$	−2.09818	−0.240678
$77$	3.39786	0.387222
$78$	0	0
$79$	5.15466	0.579945	0.289973	−	0.957035i	$-0.406354\pi$
$79$	5.15466	0.579945	0.289973	+	0.957035i	$0.406354\pi$
$80$	5.65376	0.632109
$81$	0	0
$82$	8.92689	0.985811
$83$	−6.55843	−0.719881	−0.359941	−	0.932975i	$-0.617203\pi$
$83$	−6.55843	−0.719881	−0.359941	+	0.932975i	$0.617203\pi$
$84$	0	0
$85$	−9.80686	−1.06370
$86$	−11.1196	−1.19906
$87$	0	0
$88$	−9.67935	−1.03182
$89$	4.60031	0.487632	0.243816	−	0.969822i	$-0.421601\pi$
$89$	4.60031	0.487632	0.243816	+	0.969822i	$0.421601\pi$
$90$	0	0
$91$	3.85833	0.404463
$92$	−1.07088	−0.111647
$93$	0	0
$94$	3.17095	0.327058
$95$	8.25541	0.846987
$96$	0	0
$97$	9.16155	0.930215	0.465107	−	0.885254i	$-0.346016\pi$
$97$	9.16155	0.930215	0.465107	+	0.885254i	$0.346016\pi$
$98$	9.42403	0.951971
$99$	0	0
$100$	−1.09185	−0.109185
$101$	11.0854	1.10304	0.551521	−	0.834161i	$-0.314048\pi$
$101$	11.0854	1.10304	0.551521	+	0.834161i	$0.314048\pi$
$102$	0	0
$103$	−4.38943	−0.432503	−0.216252	−	0.976338i	$-0.569383\pi$
$103$	−4.38943	−0.432503	−0.216252	+	0.976338i	$0.569383\pi$
$104$	−10.9911	−1.07776
$105$	0	0
$106$	4.96811	0.482545
$107$	19.0618	1.84277	0.921385	−	0.388650i	$-0.127059\pi$
$107$	19.0618	1.84277	0.921385	+	0.388650i	$0.127059\pi$
$108$	0	0
$109$	4.54306	0.435147	0.217573	−	0.976044i	$-0.430186\pi$
$109$	4.54306	0.435147	0.217573	+	0.976044i	$0.430186\pi$
$110$	−7.17233	−0.683855
$111$	0	0
$112$	4.07701	0.385242
$113$	−11.6865	−1.09937	−0.549685	−	0.835372i	$-0.685252\pi$
$113$	−11.6865	−1.09937	−0.549685	+	0.835372i	$0.685252\pi$
$114$	0	0
$115$	4.21344	0.392905
$116$	0.891651	0.0827877
$117$	0	0
$118$	−9.46670	−0.871481
$119$	−7.07188	−0.648278
$120$	0	0
$121$	3.27535	0.297759
$122$	−19.0604	−1.72565
$123$	0	0
$124$	−0.545677	−0.0490032
$125$	10.5315	0.941968
$126$	0	0
$127$	−13.7079	−1.21638	−0.608189	−	0.793792i	$-0.708104\pi$
$127$	−13.7079	−1.21638	−0.608189	+	0.793792i	$0.708104\pi$
$128$	−13.2381	−1.17009
$129$	0	0
$130$	−8.14430	−0.714303
$131$	−15.4415	−1.34913	−0.674563	−	0.738217i	$-0.735668\pi$
$131$	−15.4415	−1.34913	−0.674563	+	0.738217i	$0.735668\pi$
$132$	0	0
$133$	5.95311	0.516200
$134$	15.6862	1.35508
$135$	0	0
$136$	20.1454	1.72745
$137$	−0.634397	−0.0542002	−0.0271001	−	0.999633i	$-0.508627\pi$
$137$	−0.634397	−0.0542002	−0.0271001	+	0.999633i	$0.508627\pi$
$138$	0	0
$139$	8.90062	0.754941	0.377470	−	0.926022i	$-0.376794\pi$
$139$	8.90062	0.754941	0.377470	+	0.926022i	$0.376794\pi$
$140$	0.355493	0.0300446
$141$	0	0
$142$	24.9165	2.09095
$143$	16.2099	1.35554
$144$	0	0
$145$	−3.50825	−0.291344
$146$	23.6152	1.95441
$147$	0	0
$148$	−1.54289	−0.126825
$149$	−0.864000	−0.0707816	−0.0353908	−	0.999374i	$-0.511268\pi$
$149$	−0.864000	−0.0707816	−0.0353908	+	0.999374i	$0.511268\pi$
$150$	0	0
$151$	9.82722	0.799728	0.399864	−	0.916575i	$-0.369057\pi$
$151$	9.82722	0.799728	0.399864	+	0.916575i	$0.369057\pi$
$152$	−16.9584	−1.37551
$153$	0	0
$154$	−5.17208	−0.416778
$155$	2.14699	0.172451
$156$	0	0
$157$	−11.4355	−0.912656	−0.456328	−	0.889812i	$-0.650836\pi$
$157$	−11.4355	−0.912656	−0.456328	+	0.889812i	$0.650836\pi$
$158$	−7.84621	−0.624211
$159$	0	0
$160$	−2.21608	−0.175196
$161$	3.03838	0.239458
$162$	0	0
$163$	−19.1215	−1.49771	−0.748854	−	0.662735i	$-0.769396\pi$
$163$	−19.1215	−1.49771	−0.748854	+	0.662735i	$0.769396\pi$
$164$	−1.85888	−0.145154
$165$	0	0
$166$	9.98297	0.774828
$167$	−13.2573	−1.02588	−0.512942	−	0.858423i	$-0.671444\pi$
$167$	−13.2573	−1.02588	−0.512942	+	0.858423i	$0.671444\pi$
$168$	0	0
$169$	5.40662	0.415893
$170$	14.9276	1.14489
$171$	0	0
$172$	2.31549	0.176554
$173$	1.24666	0.0947815	0.0473907	−	0.998876i	$-0.484909\pi$
$173$	1.24666	0.0947815	0.0473907	+	0.998876i	$0.484909\pi$
$174$	0	0
$175$	3.09787	0.234177
$176$	17.1287	1.29112
$177$	0	0
$178$	−7.00240	−0.524852
$179$	−0.595954	−0.0445437	−0.0222718	−	0.999752i	$-0.507090\pi$
$179$	−0.595954	−0.0445437	−0.0222718	+	0.999752i	$0.507090\pi$
$180$	0	0
$181$	−9.48635	−0.705115	−0.352557	−	0.935790i	$-0.614688\pi$
$181$	−9.48635	−0.705115	−0.352557	+	0.935790i	$0.614688\pi$
$182$	−5.87298	−0.435335
$183$	0	0
$184$	−8.65531	−0.638078
$185$	6.07058	0.446318
$186$	0	0
$187$	−29.7109	−2.17268
$188$	−0.660299	−0.0481573
$189$	0	0
$190$	−12.5660	−0.911637
$191$	−7.23592	−0.523573	−0.261786	−	0.965126i	$-0.584312\pi$
$191$	−7.23592	−0.523573	−0.261786	+	0.965126i	$0.584312\pi$
$192$	0	0
$193$	4.36945	0.314520	0.157260	−	0.987557i	$-0.449734\pi$
$193$	4.36945	0.314520	0.157260	+	0.987557i	$0.449734\pi$
$194$	−13.9453	−1.00122
$195$	0	0
$196$	−1.96241	−0.140172
$197$	19.5262	1.39118	0.695592	−	0.718437i	$-0.255142\pi$
$197$	19.5262	1.39118	0.695592	+	0.718437i	$0.255142\pi$
$198$	0	0
$199$	0.0647319	0.00458872	0.00229436	−	0.999997i	$-0.499270\pi$
$199$	0.0647319	0.00458872	0.00229436	+	0.999997i	$0.499270\pi$
$200$	−8.82479	−0.624007
$201$	0	0
$202$	−16.8738	−1.18723
$203$	−2.52985	−0.177561
$204$	0	0
$205$	7.31388	0.510824
$206$	6.68141	0.465516
$207$	0	0
$208$	19.4499	1.34861
$209$	25.0106	1.73002
$210$	0	0
$211$	9.65449	0.664642	0.332321	−	0.943166i	$-0.392168\pi$
$211$	9.65449	0.664642	0.332321	+	0.943166i	$0.392168\pi$
$212$	−1.03453	−0.0710518
$213$	0	0
$214$	−29.0150	−1.98343
$215$	−9.11040	−0.621324
$216$	0	0
$217$	1.54823	0.105101
$218$	−6.91526	−0.468361
$219$	0	0
$220$	1.49352	0.100693
$221$	−33.7372	−2.26941
$222$	0	0
$223$	12.7892	0.856429	0.428215	−	0.903677i	$-0.359143\pi$
$223$	12.7892	0.856429	0.428215	+	0.903677i	$0.359143\pi$
$224$	−1.59805	−0.106774
$225$	0	0
$226$	17.7887	1.18328
$227$	−4.94823	−0.328426	−0.164213	−	0.986425i	$-0.552508\pi$
$227$	−4.94823	−0.328426	−0.164213	+	0.986425i	$0.552508\pi$
$228$	0	0
$229$	−26.7697	−1.76899	−0.884496	−	0.466548i	$-0.845497\pi$
$229$	−26.7697	−1.76899	−0.884496	+	0.466548i	$0.845497\pi$
$230$	−6.41352	−0.422895
$231$	0	0
$232$	7.20670	0.473143
$233$	22.2664	1.45872	0.729361	−	0.684129i	$-0.239818\pi$
$233$	22.2664	1.45872	0.729361	+	0.684129i	$0.239818\pi$
$234$	0	0
$235$	2.59798	0.169474
$236$	1.97129	0.128320
$237$	0	0
$238$	10.7645	0.697760
$239$	18.3982	1.19008	0.595041	−	0.803695i	$-0.297136\pi$
$239$	18.3982	1.19008	0.595041	+	0.803695i	$0.297136\pi$
$240$	0	0
$241$	21.7977	1.40411	0.702056	−	0.712122i	$-0.252266\pi$
$241$	21.7977	1.40411	0.702056	+	0.712122i	$0.252266\pi$
$242$	−4.98560	−0.320486
$243$	0	0
$244$	3.96903	0.254091
$245$	7.72119	0.493289
$246$	0	0
$247$	28.4000	1.80705
$248$	−4.41038	−0.280060
$249$	0	0
$250$	−16.0307	−1.01387
$251$	22.0114	1.38935	0.694674	−	0.719325i	$-0.255549\pi$
$251$	22.0114	1.38935	0.694674	+	0.719325i	$0.255549\pi$
$252$	0	0
$253$	12.7651	0.802533
$254$	20.8656	1.30922
$255$	0	0
$256$	7.42619	0.464137
$257$	−9.18964	−0.573234	−0.286617	−	0.958045i	$-0.592531\pi$
$257$	−9.18964	−0.573234	−0.286617	+	0.958045i	$0.592531\pi$
$258$	0	0
$259$	4.37759	0.272010
$260$	1.69592	0.105177
$261$	0	0
$262$	23.5043	1.45210
$263$	15.6117	0.962656	0.481328	−	0.876540i	$-0.340155\pi$
$263$	15.6117	0.962656	0.481328	+	0.876540i	$0.340155\pi$
$264$	0	0
$265$	4.07041	0.250043
$266$	−9.06157	−0.555600
$267$	0	0
$268$	−3.26639	−0.199527
$269$	17.8631	1.08913	0.544566	−	0.838718i	$-0.316694\pi$
$269$	17.8631	1.08913	0.544566	+	0.838718i	$0.316694\pi$
$270$	0	0
$271$	−16.5337	−1.00435	−0.502174	−	0.864767i	$-0.667466\pi$
$271$	−16.5337	−1.00435	−0.502174	+	0.864767i	$0.667466\pi$
$272$	−35.6494	−2.16156
$273$	0	0
$274$	0.965653	0.0583372
$275$	13.0150	0.784835
$276$	0	0
$277$	28.3672	1.70442	0.852210	−	0.523199i	$-0.175262\pi$
$277$	28.3672	1.70442	0.852210	+	0.523199i	$0.175262\pi$
$278$	−13.5482	−0.812564
$279$	0	0
$280$	2.87324	0.171709
$281$	−1.04933	−0.0625977	−0.0312988	−	0.999510i	$-0.509964\pi$
$281$	−1.04933	−0.0625977	−0.0312988	+	0.999510i	$0.509964\pi$
$282$	0	0
$283$	−13.8367	−0.822505	−0.411253	−	0.911521i	$-0.634909\pi$
$283$	−13.8367	−0.822505	−0.411253	+	0.911521i	$0.634909\pi$
$284$	−5.18847	−0.307879
$285$	0	0
$286$	−24.6740	−1.45901
$287$	5.27415	0.311323
$288$	0	0
$289$	44.8365	2.63744
$290$	5.34011	0.313582
$291$	0	0
$292$	−4.91750	−0.287775
$293$	−8.25156	−0.482061	−0.241031	−	0.970517i	$-0.577485\pi$
$293$	−8.25156	−0.482061	−0.241031	+	0.970517i	$0.577485\pi$
$294$	0	0
$295$	−7.75615	−0.451581
$296$	−12.4703	−0.724819
$297$	0	0
$298$	1.31514	0.0761842
$299$	14.4949	0.838264
$300$	0	0
$301$	−6.56965	−0.378669
$302$	−14.9586	−0.860770
$303$	0	0
$304$	30.0097	1.72117
$305$	−15.6163	−0.894189
$306$	0	0
$307$	−5.46378	−0.311835	−0.155917	−	0.987770i	$-0.549833\pi$
$307$	−5.46378	−0.311835	−0.155917	+	0.987770i	$0.549833\pi$
$308$	1.07700	0.0613680
$309$	0	0
$310$	−3.26806	−0.185614
$311$	18.4424	1.04577	0.522887	−	0.852402i	$-0.324855\pi$
$311$	18.4424	1.04577	0.522887	+	0.852402i	$0.324855\pi$
$312$	0	0
$313$	−21.9260	−1.23933	−0.619664	−	0.784867i	$-0.712731\pi$
$313$	−21.9260	−1.23933	−0.619664	+	0.784867i	$0.712731\pi$
$314$	17.4067	0.982317
$315$	0	0
$316$	1.63385	0.0919112
$317$	7.73837	0.434630	0.217315	−	0.976102i	$-0.430270\pi$
$317$	7.73837	0.434630	0.217315	+	0.976102i	$0.430270\pi$
$318$	0	0
$319$	−10.6286	−0.595088
$320$	−7.93430	−0.443541
$321$	0	0
$322$	−4.62489	−0.257735
$323$	−52.0540	−2.89636
$324$	0	0
$325$	14.7788	0.819779
$326$	29.1059	1.61203
$327$	0	0
$328$	−15.0243	−0.829577
$329$	1.87345	0.103286
$330$	0	0
$331$	−21.2914	−1.17028	−0.585140	−	0.810932i	$-0.698960\pi$
$331$	−21.2914	−1.17028	−0.585140	+	0.810932i	$0.698960\pi$
$332$	−2.07879	−0.114089
$333$	0	0
$334$	20.1798	1.10419
$335$	12.8518	0.702169
$336$	0	0
$337$	21.3815	1.16472	0.582362	−	0.812930i	$-0.302129\pi$
$337$	21.3815	1.16472	0.582362	+	0.812930i	$0.302129\pi$
$338$	−8.22972	−0.447638
$339$	0	0
$340$	−3.10843	−0.168578
$341$	6.50455	0.352241
$342$	0	0
$343$	11.8631	0.640546
$344$	18.7147	1.00903
$345$	0	0
$346$	−1.89761	−0.102016
$347$	7.25286	0.389354	0.194677	−	0.980867i	$-0.437634\pi$
$347$	7.25286	0.389354	0.194677	+	0.980867i	$0.437634\pi$
$348$	0	0
$349$	24.7806	1.32647	0.663236	−	0.748410i	$-0.269182\pi$
$349$	24.7806	1.32647	0.663236	+	0.748410i	$0.269182\pi$
$350$	−4.71545	−0.252051
$351$	0	0
$352$	−6.71384	−0.357849
$353$	24.3581	1.29645	0.648227	−	0.761447i	$-0.275511\pi$
$353$	24.3581	1.29645	0.648227	+	0.761447i	$0.275511\pi$
$354$	0	0
$355$	20.4143	1.08348
$356$	1.45814	0.0772811
$357$	0	0
$358$	0.907136	0.0479436
$359$	−24.9267	−1.31558	−0.657790	−	0.753201i	$-0.728509\pi$
$359$	−24.9267	−1.31558	−0.657790	+	0.753201i	$0.728509\pi$
$360$	0	0
$361$	24.8191	1.30627
$362$	14.4397	0.758935
$363$	0	0
$364$	1.22296	0.0641003
$365$	19.3482	1.01273
$366$	0	0
$367$	−2.52376	−0.131739	−0.0658695	−	0.997828i	$-0.520982\pi$
$367$	−2.52376	−0.131739	−0.0658695	+	0.997828i	$0.520982\pi$
$368$	15.3165	0.798428
$369$	0	0
$370$	−9.24038	−0.480384
$371$	2.93524	0.152390
$372$	0	0
$373$	27.2959	1.41333	0.706664	−	0.707549i	$-0.250199\pi$
$373$	27.2959	1.41333	0.706664	+	0.707549i	$0.250199\pi$
$374$	45.2247	2.33851
$375$	0	0
$376$	−5.33681	−0.275225
$377$	−12.0690	−0.621584
$378$	0	0
$379$	−8.84527	−0.454351	−0.227175	−	0.973854i	$-0.572949\pi$
$379$	−8.84527	−0.454351	−0.227175	+	0.973854i	$0.572949\pi$
$380$	2.61668	0.134233
$381$	0	0
$382$	11.0142	0.563536
$383$	9.56433	0.488715	0.244357	−	0.969685i	$-0.421423\pi$
$383$	9.56433	0.488715	0.244357	+	0.969685i	$0.421423\pi$
$384$	0	0
$385$	−4.23753	−0.215964
$386$	−6.65099	−0.338527
$387$	0	0
$388$	2.90389	0.147423
$389$	0.0942924	0.00478081	0.00239041	−	0.999997i	$-0.499239\pi$
$389$	0.0942924	0.00478081	0.00239041	+	0.999997i	$0.499239\pi$
$390$	0	0
$391$	−26.5676	−1.34358
$392$	−15.8610	−0.801100
$393$	0	0
$394$	−29.7220	−1.49737
$395$	−6.42847	−0.323451
$396$	0	0
$397$	−29.4428	−1.47769	−0.738847	−	0.673873i	$-0.764629\pi$
$397$	−29.4428	−1.47769	−0.738847	+	0.673873i	$0.764629\pi$
$398$	−0.0985322	−0.00493897
$399$	0	0
$400$	15.6164	0.780821
$401$	28.1453	1.40551	0.702756	−	0.711431i	$-0.251953\pi$
$401$	28.1453	1.40551	0.702756	+	0.711431i	$0.251953\pi$
$402$	0	0
$403$	7.38602	0.367924
$404$	3.51370	0.174813
$405$	0	0
$406$	3.85084	0.191114
$407$	18.3915	0.911631
$408$	0	0
$409$	10.4165	0.515062	0.257531	−	0.966270i	$-0.417091\pi$
$409$	10.4165	0.515062	0.257531	+	0.966270i	$0.417091\pi$
$410$	−11.1329	−0.549814
$411$	0	0
$412$	−1.39130	−0.0685443
$413$	−5.59308	−0.275218
$414$	0	0
$415$	8.17913	0.401498
$416$	−7.62367	−0.373781
$417$	0	0
$418$	−38.0702	−1.86207
$419$	10.1329	0.495026	0.247513	−	0.968885i	$-0.420387\pi$
$419$	10.1329	0.495026	0.247513	+	0.968885i	$0.420387\pi$
$420$	0	0
$421$	−34.9879	−1.70521	−0.852603	−	0.522559i	$-0.824977\pi$
$421$	−34.9879	−1.70521	−0.852603	+	0.522559i	$0.824977\pi$
$422$	−14.6957	−0.715373
$423$	0	0
$424$	−8.36150	−0.406070
$425$	−27.0878	−1.31395
$426$	0	0
$427$	−11.2612	−0.544967
$428$	6.04192	0.292047
$429$	0	0
$430$	13.8675	0.668749
$431$	−5.20902	−0.250910	−0.125455	−	0.992099i	$-0.540039\pi$
$431$	−5.20902	−0.250910	−0.125455	+	0.992099i	$0.540039\pi$
$432$	0	0
$433$	15.2360	0.732196	0.366098	−	0.930576i	$-0.380693\pi$
$433$	15.2360	0.732196	0.366098	+	0.930576i	$0.380693\pi$
$434$	−2.35665	−0.113123
$435$	0	0
$436$	1.43999	0.0689632
$437$	22.3646	1.06984
$438$	0	0
$439$	1.92960	0.0920947	0.0460473	−	0.998939i	$-0.485337\pi$
$439$	1.92960	0.0920947	0.0460473	+	0.998939i	$0.485337\pi$
$440$	12.0713	0.575476
$441$	0	0
$442$	51.3534	2.44263
$443$	−12.2961	−0.584204	−0.292102	−	0.956387i	$-0.594355\pi$
$443$	−12.2961	−0.584204	−0.292102	+	0.956387i	$0.594355\pi$
$444$	0	0
$445$	−5.73712	−0.271966
$446$	−19.4672	−0.921799
$447$	0	0
$448$	−5.72155	−0.270318
$449$	−26.8719	−1.26816	−0.634082	−	0.773266i	$-0.718622\pi$
$449$	−26.8719	−1.26816	−0.634082	+	0.773266i	$0.718622\pi$
$450$	0	0
$451$	22.1582	1.04339
$452$	−3.70421	−0.174231
$453$	0	0
$454$	7.53199	0.353494
$455$	−4.81179	−0.225580
$456$	0	0
$457$	−0.906919	−0.0424239	−0.0212119	−	0.999775i	$-0.506752\pi$
$457$	−0.906919	−0.0424239	−0.0212119	+	0.999775i	$0.506752\pi$
$458$	40.7477	1.90402
$459$	0	0
$460$	1.33551	0.0622687
$461$	−4.46280	−0.207853	−0.103927	−	0.994585i	$-0.533141\pi$
$461$	−4.46280	−0.207853	−0.103927	+	0.994585i	$0.533141\pi$
$462$	0	0
$463$	23.4974	1.09202	0.546009	−	0.837779i	$-0.316146\pi$
$463$	23.4974	1.09202	0.546009	+	0.837779i	$0.316146\pi$
$464$	−12.7530	−0.592045
$465$	0	0
$466$	−33.8930	−1.57006
$467$	−8.31369	−0.384712	−0.192356	−	0.981325i	$-0.561613\pi$
$467$	−8.31369	−0.384712	−0.192356	+	0.981325i	$0.561613\pi$
$468$	0	0
$469$	9.26764	0.427940
$470$	−3.95454	−0.182409
$471$	0	0
$472$	15.9328	0.733366
$473$	−27.6009	−1.26909
$474$	0	0
$475$	22.8025	1.04625
$476$	−2.24154	−0.102741
$477$	0	0
$478$	−28.0050	−1.28092
$479$	−21.3313	−0.974651	−0.487325	−	0.873220i	$-0.662027\pi$
$479$	−21.3313	−0.974651	−0.487325	+	0.873220i	$0.662027\pi$
$480$	0	0
$481$	20.8838	0.952220
$482$	−33.1795	−1.51129
$483$	0	0
$484$	1.03817	0.0471896
$485$	−11.4255	−0.518806
$486$	0	0
$487$	15.0513	0.682038	0.341019	−	0.940056i	$-0.389228\pi$
$487$	15.0513	0.682038	0.341019	+	0.940056i	$0.389228\pi$
$488$	32.0793	1.45216
$489$	0	0
$490$	−11.7529	−0.530941
$491$	43.1675	1.94812	0.974060	−	0.226289i	$-0.0726595\pi$
$491$	43.1675	1.94812	0.974060	+	0.226289i	$0.0726595\pi$
$492$	0	0
$493$	22.1211	0.996282
$494$	−43.2293	−1.94498
$495$	0	0
$496$	7.80465	0.350439
$497$	14.7211	0.660331
$498$	0	0
$499$	16.8824	0.755759	0.377880	−	0.925855i	$-0.376653\pi$
$499$	16.8824	0.755759	0.377880	+	0.925855i	$0.376653\pi$
$500$	3.33813	0.149286
$501$	0	0
$502$	−33.5048	−1.49539
$503$	13.4026	0.597592	0.298796	−	0.954317i	$-0.403415\pi$
$503$	13.4026	0.597592	0.298796	+	0.954317i	$0.403415\pi$
$504$	0	0
$505$	−13.8248	−0.615197
$506$	−19.4304	−0.863789
$507$	0	0
$508$	−4.34492	−0.192775
$509$	17.5986	0.780045	0.390022	−	0.920805i	$-0.372467\pi$
$509$	17.5986	0.780045	0.390022	+	0.920805i	$0.372467\pi$
$510$	0	0
$511$	13.9523	0.617212
$512$	15.1723	0.670527
$513$	0	0
$514$	13.9881	0.616988
$515$	5.47413	0.241219
$516$	0	0
$517$	7.87086	0.346160
$518$	−6.66338	−0.292772
$519$	0	0
$520$	13.7071	0.601098
$521$	9.08215	0.397896	0.198948	−	0.980010i	$-0.436247\pi$
$521$	9.08215	0.397896	0.198948	+	0.980010i	$0.436247\pi$
$522$	0	0
$523$	12.7052	0.555561	0.277780	−	0.960645i	$-0.410401\pi$
$523$	12.7052	0.555561	0.277780	+	0.960645i	$0.410401\pi$
$524$	−4.89440	−0.213813
$525$	0	0
$526$	−23.7634	−1.03613
$527$	−13.5377	−0.589713
$528$	0	0
$529$	−11.5854	−0.503715
$530$	−6.19581	−0.269129
$531$	0	0
$532$	1.88693	0.0818087
$533$	25.1610	1.08984
$534$	0	0
$535$	−23.7723	−1.02776
$536$	−26.4004	−1.14032
$537$	0	0
$538$	−27.1905	−1.17226
$539$	23.3922	1.00757
$540$	0	0
$541$	37.0432	1.59261	0.796306	−	0.604894i	$-0.206785\pi$
$541$	37.0432	1.59261	0.796306	+	0.604894i	$0.206785\pi$
$542$	25.1668	1.08101
$543$	0	0
$544$	13.9733	0.599102
$545$	−5.66573	−0.242693
$546$	0	0
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−0.201082	−0.00858980
$549$	0	0
$550$	−19.8109	−0.844740
$551$	−18.6215	−0.793303
$552$	0	0
$553$	−4.63567	−0.197129
$554$	−43.1794	−1.83452
$555$	0	0
$556$	2.82119	0.119645
$557$	46.3948	1.96581	0.982905	−	0.184111i	$-0.0589406\pi$
$557$	46.3948	1.96581	0.982905	+	0.184111i	$0.0589406\pi$
$558$	0	0
$559$	−31.3413	−1.32560
$560$	−5.08451	−0.214860
$561$	0	0
$562$	1.59724	0.0673757
$563$	25.5383	1.07631	0.538155	−	0.842846i	$-0.319122\pi$
$563$	25.5383	1.07631	0.538155	+	0.842846i	$0.319122\pi$
$564$	0	0
$565$	14.5744	0.613149
$566$	21.0616	0.885286
$567$	0	0
$568$	−41.9354	−1.75957
$569$	−34.7766	−1.45791	−0.728956	−	0.684560i	$-0.759994\pi$
$569$	−34.7766	−1.45791	−0.728956	+	0.684560i	$0.759994\pi$
$570$	0	0
$571$	−18.0804	−0.756643	−0.378322	−	0.925674i	$-0.623499\pi$
$571$	−18.0804	−0.756643	−0.378322	+	0.925674i	$0.623499\pi$
$572$	5.13798	0.214830
$573$	0	0
$574$	−8.02809	−0.335086
$575$	11.6381	0.485341
$576$	0	0
$577$	17.7760	0.740025	0.370012	−	0.929027i	$-0.379353\pi$
$577$	17.7760	0.740025	0.370012	+	0.929027i	$0.379353\pi$
$578$	−68.2483	−2.83876
$579$	0	0
$580$	−1.11199	−0.0461730
$581$	5.89810	0.244694
$582$	0	0
$583$	12.3317	0.510729
$584$	−39.7453	−1.64467
$585$	0	0
$586$	12.5602	0.518856
$587$	12.4600	0.514279	0.257139	−	0.966374i	$-0.417220\pi$
$587$	12.4600	0.514279	0.257139	+	0.966374i	$0.417220\pi$
$588$	0	0
$589$	11.3961	0.469567
$590$	11.8061	0.486049
$591$	0	0
$592$	22.0675	0.906968
$593$	5.62287	0.230904	0.115452	−	0.993313i	$-0.463168\pi$
$593$	5.62287	0.230904	0.115452	+	0.993313i	$0.463168\pi$
$594$	0	0
$595$	8.81946	0.361563
$596$	−0.273858	−0.0112177
$597$	0	0
$598$	−22.0636	−0.902248
$599$	−19.3513	−0.790673	−0.395337	−	0.918536i	$-0.629372\pi$
$599$	−19.3513	−0.790673	−0.395337	+	0.918536i	$0.629372\pi$
$600$	0	0
$601$	−25.3645	−1.03464	−0.517321	−	0.855792i	$-0.673071\pi$
$601$	−25.3645	−1.03464	−0.517321	+	0.855792i	$0.673071\pi$
$602$	10.0001	0.407572
$603$	0	0
$604$	3.11489	0.126743
$605$	−4.08474	−0.166068
$606$	0	0
$607$	13.9505	0.566235	0.283117	−	0.959085i	$-0.408631\pi$
$607$	13.9505	0.566235	0.283117	+	0.959085i	$0.408631\pi$
$608$	−11.7628	−0.477043
$609$	0	0
$610$	23.7705	0.962441
$611$	8.93750	0.361573
$612$	0	0
$613$	25.5058	1.03017	0.515084	−	0.857139i	$-0.327761\pi$
$613$	25.5058	1.03017	0.515084	+	0.857139i	$0.327761\pi$
$614$	8.31674	0.335636
$615$	0	0
$616$	8.70479	0.350726
$617$	−7.43879	−0.299474	−0.149737	−	0.988726i	$-0.547843\pi$
$617$	−7.43879	−0.299474	−0.149737	+	0.988726i	$0.547843\pi$
$618$	0	0
$619$	10.5397	0.423626	0.211813	−	0.977310i	$-0.432063\pi$
$619$	10.5397	0.423626	0.211813	+	0.977310i	$0.432063\pi$
$620$	0.680522	0.0273304
$621$	0	0
$622$	−28.0723	−1.12560
$623$	−4.13713	−0.165751
$624$	0	0
$625$	4.08945	0.163578
$626$	33.3748	1.33392
$627$	0	0
$628$	−3.62467	−0.144640
$629$	−38.2777	−1.52623
$630$	0	0
$631$	23.4904	0.935139	0.467570	−	0.883956i	$-0.345130\pi$
$631$	23.4904	0.935139	0.467570	+	0.883956i	$0.345130\pi$
$632$	13.2055	0.525285
$633$	0	0
$634$	−11.7790	−0.467805
$635$	17.0953	0.678408
$636$	0	0
$637$	26.5622	1.05243
$638$	16.1784	0.640510
$639$	0	0
$640$	16.5094	0.652592
$641$	12.1894	0.481454	0.240727	−	0.970593i	$-0.422614\pi$
$641$	12.1894	0.481454	0.240727	+	0.970593i	$0.422614\pi$
$642$	0	0
$643$	−45.5594	−1.79669	−0.898343	−	0.439295i	$-0.855228\pi$
$643$	−45.5594	−1.79669	−0.898343	+	0.439295i	$0.855228\pi$
$644$	0.963060	0.0379499
$645$	0	0
$646$	79.2344	3.11744
$647$	13.8400	0.544107	0.272054	−	0.962282i	$-0.412297\pi$
$647$	13.8400	0.544107	0.272054	+	0.962282i	$0.412297\pi$
$648$	0	0
$649$	−23.4981	−0.922380
$650$	−22.4956	−0.882351
$651$	0	0
$652$	−6.06084	−0.237361
$653$	37.0134	1.44845	0.724224	−	0.689565i	$-0.242198\pi$
$653$	37.0134	1.44845	0.724224	+	0.689565i	$0.242198\pi$
$654$	0	0
$655$	19.2573	0.752445
$656$	26.5871	1.03805
$657$	0	0
$658$	−2.85168	−0.111170
$659$	−4.58672	−0.178673	−0.0893366	−	0.996001i	$-0.528475\pi$
$659$	−4.58672	−0.178673	−0.0893366	+	0.996001i	$0.528475\pi$
$660$	0	0
$661$	33.9504	1.32052	0.660259	−	0.751038i	$-0.270446\pi$
$661$	33.9504	1.32052	0.660259	+	0.751038i	$0.270446\pi$
$662$	32.4088	1.25961
$663$	0	0
$664$	−16.8017	−0.652032
$665$	−7.42422	−0.287899
$666$	0	0
$667$	−9.50414	−0.368002
$668$	−4.20212	−0.162585
$669$	0	0
$670$	−19.5625	−0.755764
$671$	−47.3114	−1.82644
$672$	0	0
$673$	−19.4772	−0.750792	−0.375396	−	0.926865i	$-0.622493\pi$
$673$	−19.4772	−0.750792	−0.375396	+	0.926865i	$0.622493\pi$
$674$	−32.5460	−1.25363
$675$	0	0
$676$	1.71371	0.0659119
$677$	−4.07259	−0.156523	−0.0782613	−	0.996933i	$-0.524937\pi$
$677$	−4.07259	−0.156523	−0.0782613	+	0.996933i	$0.524937\pi$
$678$	0	0
$679$	−8.23913	−0.316189
$680$	−25.1236	−0.963448
$681$	0	0
$682$	−9.90095	−0.379127
$683$	0.965668	0.0369503	0.0184751	−	0.999829i	$-0.494119\pi$
$683$	0.965668	0.0369503	0.0184751	+	0.999829i	$0.494119\pi$
$684$	0	0
$685$	0.791168	0.0302290
$686$	−18.0575	−0.689438
$687$	0	0
$688$	−33.1177	−1.26260
$689$	14.0029	0.533468
$690$	0	0
$691$	−9.03055	−0.343538	−0.171769	−	0.985137i	$-0.554948\pi$
$691$	−9.03055	−0.343538	−0.171769	+	0.985137i	$0.554948\pi$
$692$	0.395147	0.0150212
$693$	0	0
$694$	−11.0400	−0.419073
$695$	−11.1001	−0.421051
$696$	0	0
$697$	−46.1172	−1.74681
$698$	−37.7199	−1.42772
$699$	0	0
$700$	0.981918	0.0371130
$701$	−9.28360	−0.350637	−0.175318	−	0.984512i	$-0.556095\pi$
$701$	−9.28360	−0.350637	−0.175318	+	0.984512i	$0.556095\pi$
$702$	0	0
$703$	32.2221	1.21528
$704$	−24.0378	−0.905959
$705$	0	0
$706$	−37.0770	−1.39541
$707$	−9.96930	−0.374934
$708$	0	0
$709$	−42.7085	−1.60395	−0.801976	−	0.597357i	$-0.796218\pi$
$709$	−42.7085	−1.60395	−0.801976	+	0.597357i	$0.796218\pi$
$710$	−31.0738	−1.16618
$711$	0	0
$712$	11.7853	0.441672
$713$	5.81639	0.217825
$714$	0	0
$715$	−20.2156	−0.756022
$716$	−0.188897	−0.00705940
$717$	0	0
$718$	37.9424	1.41600
$719$	−3.48301	−0.129895	−0.0649473	−	0.997889i	$-0.520688\pi$
$719$	−3.48301	−0.129895	−0.0649473	+	0.997889i	$0.520688\pi$
$720$	0	0
$721$	3.94748	0.147012
$722$	−37.7786	−1.40597
$723$	0	0
$724$	−3.00684	−0.111748
$725$	−9.69024	−0.359887
$726$	0	0
$727$	−43.5536	−1.61531	−0.807657	−	0.589652i	$-0.799265\pi$
$727$	−43.5536	−1.61531	−0.807657	+	0.589652i	$0.799265\pi$
$728$	9.88444	0.366342
$729$	0	0
$730$	−29.4510	−1.09003
$731$	57.4451	2.12468
$732$	0	0
$733$	35.9769	1.32884	0.664418	−	0.747361i	$-0.268679\pi$
$733$	35.9769	1.32884	0.664418	+	0.747361i	$0.268679\pi$
$734$	3.84155	0.141794
$735$	0	0
$736$	−6.00353	−0.221293
$737$	38.9359	1.43422
$738$	0	0
$739$	−9.01253	−0.331531	−0.165766	−	0.986165i	$-0.553010\pi$
$739$	−9.01253	−0.331531	−0.165766	+	0.986165i	$0.553010\pi$
$740$	1.92416	0.0707336
$741$	0	0
$742$	−4.46790	−0.164022
$743$	27.7846	1.01932	0.509658	−	0.860377i	$-0.329772\pi$
$743$	27.7846	1.01932	0.509658	+	0.860377i	$0.329772\pi$
$744$	0	0
$745$	1.07751	0.0394769
$746$	−41.5487	−1.52120
$747$	0	0
$748$	−9.41733	−0.344332
$749$	−17.1425	−0.626375
$750$	0	0
$751$	−35.3238	−1.28898	−0.644492	−	0.764611i	$-0.722931\pi$
$751$	−35.3238	−1.28898	−0.644492	+	0.764611i	$0.722931\pi$
$752$	9.44407	0.344390
$753$	0	0
$754$	18.3709	0.669028
$755$	−12.2557	−0.446030
$756$	0	0
$757$	−7.21058	−0.262073	−0.131036	−	0.991378i	$-0.541830\pi$
$757$	−7.21058	−0.262073	−0.131036	+	0.991378i	$0.541830\pi$
$758$	13.4639	0.489031
$759$	0	0
$760$	21.1491	0.767158
$761$	−15.5783	−0.564712	−0.282356	−	0.959310i	$-0.591116\pi$
$761$	−15.5783	−0.564712	−0.282356	+	0.959310i	$0.591116\pi$
$762$	0	0
$763$	−4.08565	−0.147910
$764$	−2.29353	−0.0829772
$765$	0	0
$766$	−14.5584	−0.526017
$767$	−26.6825	−0.963448
$768$	0	0
$769$	24.1433	0.870629	0.435314	−	0.900279i	$-0.356637\pi$
$769$	24.1433	0.870629	0.435314	+	0.900279i	$0.356637\pi$
$770$	6.45019	0.232449
$771$	0	0
$772$	1.38496	0.0498460
$773$	23.9888	0.862818	0.431409	−	0.902156i	$-0.358017\pi$
$773$	23.9888	0.862818	0.431409	+	0.902156i	$0.358017\pi$
$774$	0	0
$775$	5.93028	0.213022
$776$	23.4705	0.842541
$777$	0	0
$778$	−0.143528	−0.00514572
$779$	38.8215	1.39092
$780$	0	0
$781$	61.8474	2.21307
$782$	40.4401	1.44613
$783$	0	0
$784$	28.0677	1.00242
$785$	14.2615	0.509013
$786$	0	0
$787$	−5.35961	−0.191050	−0.0955248	−	0.995427i	$-0.530453\pi$
$787$	−5.35961	−0.191050	−0.0955248	+	0.995427i	$0.530453\pi$
$788$	6.18913	0.220479
$789$	0	0
$790$	9.78515	0.348140
$791$	10.5098	0.373686
$792$	0	0
$793$	−53.7229	−1.90776
$794$	44.8167	1.59048
$795$	0	0
$796$	0.0205178	0.000727233 0
$797$	19.3882	0.686766	0.343383	−	0.939195i	$-0.388427\pi$
$797$	19.3882	0.686766	0.343383	+	0.939195i	$0.388427\pi$
$798$	0	0
$799$	−16.3814	−0.579533
$800$	−6.12109	−0.216413
$801$	0	0
$802$	−42.8417	−1.51279
$803$	58.6173	2.06856
$804$	0	0
$805$	−3.78921	−0.133552
$806$	−11.2427	−0.396007
$807$	0	0
$808$	28.3992	0.999079
$809$	35.6076	1.25190	0.625948	−	0.779865i	$-0.284712\pi$
$809$	35.6076	1.25190	0.625948	+	0.779865i	$0.284712\pi$
$810$	0	0
$811$	7.02922	0.246829	0.123415	−	0.992355i	$-0.460615\pi$
$811$	7.02922	0.246829	0.123415	+	0.992355i	$0.460615\pi$
$812$	−0.801876	−0.0281403
$813$	0	0
$814$	−27.9947	−0.981214
$815$	23.8467	0.835314
$816$	0	0
$817$	−48.3573	−1.69181
$818$	−15.8555	−0.554376
$819$	0	0
$820$	2.31825	0.0809567
$821$	11.9108	0.415691	0.207845	−	0.978162i	$-0.433355\pi$
$821$	11.9108	0.415691	0.207845	+	0.978162i	$0.433355\pi$
$822$	0	0
$823$	38.1506	1.32985	0.664924	−	0.746911i	$-0.268464\pi$
$823$	38.1506	1.32985	0.664924	+	0.746911i	$0.268464\pi$
$824$	−11.2450	−0.391740
$825$	0	0
$826$	8.51355	0.296224
$827$	−22.1837	−0.771404	−0.385702	−	0.922623i	$-0.626041\pi$
$827$	−22.1837	−0.771404	−0.385702	+	0.922623i	$0.626041\pi$
$828$	0	0
$829$	−26.7091	−0.927646	−0.463823	−	0.885928i	$-0.653523\pi$
$829$	−26.7091	−0.927646	−0.463823	+	0.885928i	$0.653523\pi$
$830$	−12.4499	−0.432143
$831$	0	0
$832$	−27.2953	−0.946296
$833$	−48.6855	−1.68685
$834$	0	0
$835$	16.5335	0.572164
$836$	7.92751	0.274179
$837$	0	0
$838$	−15.4239	−0.532810
$839$	24.3713	0.841392	0.420696	−	0.907202i	$-0.361786\pi$
$839$	24.3713	0.841392	0.420696	+	0.907202i	$0.361786\pi$
$840$	0	0
$841$	−21.0865	−0.727122
$842$	53.2571	1.83536
$843$	0	0
$844$	3.06014	0.105334
$845$	−6.74268	−0.231955
$846$	0	0
$847$	−2.94557	−0.101211
$848$	14.7966	0.508117
$849$	0	0
$850$	41.2319	1.41424
$851$	16.4457	0.563751
$852$	0	0
$853$	−21.5357	−0.737369	−0.368685	−	0.929555i	$-0.620192\pi$
$853$	−21.5357	−0.737369	−0.368685	+	0.929555i	$0.620192\pi$
$854$	17.1413	0.586564
$855$	0	0
$856$	48.8333	1.66909
$857$	−10.1092	−0.345325	−0.172663	−	0.984981i	$-0.555237\pi$
$857$	−10.1092	−0.345325	−0.172663	+	0.984981i	$0.555237\pi$
$858$	0	0
$859$	29.3539	1.00154	0.500771	−	0.865580i	$-0.333050\pi$
$859$	29.3539	1.00154	0.500771	+	0.865580i	$0.333050\pi$
$860$	−2.88768	−0.0984691
$861$	0	0
$862$	7.92895	0.270061
$863$	−9.84744	−0.335211	−0.167605	−	0.985854i	$-0.553603\pi$
$863$	−9.84744	−0.335211	−0.167605	+	0.985854i	$0.553603\pi$
$864$	0	0
$865$	−1.55473	−0.0528622
$866$	−23.1916	−0.788083
$867$	0	0
$868$	0.490735	0.0166566
$869$	−19.4757	−0.660669
$870$	0	0
$871$	44.2124	1.49808
$872$	11.6386	0.394134
$873$	0	0
$874$	−34.0425	−1.15150
$875$	−9.47117	−0.320184
$876$	0	0
$877$	−32.9822	−1.11373	−0.556864	−	0.830603i	$-0.687996\pi$
$877$	−32.9822	−1.11373	−0.556864	+	0.830603i	$0.687996\pi$
$878$	−2.93715	−0.0991241
$879$	0	0
$880$	−21.3614	−0.720094
$881$	−34.3375	−1.15686	−0.578429	−	0.815733i	$-0.696334\pi$
$881$	−34.3375	−1.15686	−0.578429	+	0.815733i	$0.696334\pi$
$882$	0	0
$883$	12.5688	0.422974	0.211487	−	0.977381i	$-0.432169\pi$
$883$	12.5688	0.422974	0.211487	+	0.977381i	$0.432169\pi$
$884$	−10.6935	−0.359662
$885$	0	0
$886$	18.7166	0.628795
$887$	−34.7329	−1.16622	−0.583109	−	0.812394i	$-0.698164\pi$
$887$	−34.7329	−1.16622	−0.583109	+	0.812394i	$0.698164\pi$
$888$	0	0
$889$	12.3277	0.413458
$890$	8.73281	0.292724
$891$	0	0
$892$	4.05374	0.135729
$893$	13.7899	0.461461
$894$	0	0
$895$	0.743224	0.0248432
$896$	11.9052	0.397725
$897$	0	0
$898$	40.9033	1.36496
$899$	−4.84292	−0.161520
$900$	0	0
$901$	−25.6657	−0.855050
$902$	−33.7282	−1.12303
$903$	0	0
$904$	−29.9389	−0.995754
$905$	11.8306	0.393262
$906$	0	0
$907$	18.5744	0.616753	0.308376	−	0.951264i	$-0.400214\pi$
$907$	18.5744	0.616753	0.308376	+	0.951264i	$0.400214\pi$
$908$	−1.56842	−0.0520498
$909$	0	0
$910$	7.32430	0.242798
$911$	4.83712	0.160261	0.0801304	−	0.996784i	$-0.474466\pi$
$911$	4.83712	0.160261	0.0801304	+	0.996784i	$0.474466\pi$
$912$	0	0
$913$	24.7795	0.820083
$914$	1.38047	0.0456620
$915$	0	0
$916$	−8.48506	−0.280354
$917$	13.8867	0.458580
$918$	0	0
$919$	57.3488	1.89176	0.945881	−	0.324513i	$-0.105200\pi$
$919$	57.3488	1.89176	0.945881	+	0.324513i	$0.105200\pi$
$920$	10.7942	0.355874
$921$	0	0
$922$	6.79309	0.223718
$923$	70.2287	2.31161
$924$	0	0
$925$	16.7677	0.551319
$926$	−35.7668	−1.17537
$927$	0	0
$928$	4.99874	0.164092
$929$	−46.6546	−1.53069	−0.765344	−	0.643622i	$-0.777431\pi$
$929$	−46.6546	−1.53069	−0.765344	+	0.643622i	$0.777431\pi$
$930$	0	0
$931$	40.9835	1.34318
$932$	7.05768	0.231182
$933$	0	0
$934$	12.6547	0.414076
$935$	37.0530	1.21176
$936$	0	0
$937$	20.5835	0.672433	0.336217	−	0.941785i	$-0.390853\pi$
$937$	20.5835	0.672433	0.336217	+	0.941785i	$0.390853\pi$
$938$	−14.1068	−0.460604
$939$	0	0
$940$	0.823470	0.0268586
$941$	−26.4195	−0.861251	−0.430625	−	0.902531i	$-0.641707\pi$
$941$	−26.4195	−0.861251	−0.430625	+	0.902531i	$0.641707\pi$
$942$	0	0
$943$	19.8139	0.645230
$944$	−28.1948	−0.917663
$945$	0	0
$946$	42.0130	1.36596
$947$	−30.9279	−1.00502	−0.502510	−	0.864571i	$-0.667590\pi$
$947$	−30.9279	−1.00502	−0.502510	+	0.864571i	$0.667590\pi$
$948$	0	0
$949$	66.5610	2.16066
$950$	−34.7090	−1.12611
$951$	0	0
$952$	−18.1171	−0.587177
$953$	−31.9144	−1.03381	−0.516905	−	0.856043i	$-0.672916\pi$
$953$	−31.9144	−1.03381	−0.516905	+	0.856043i	$0.672916\pi$
$954$	0	0
$955$	9.02404	0.292011
$956$	5.83160	0.188607
$957$	0	0
$958$	32.4696	1.04904
$959$	0.570523	0.0184232
$960$	0	0
$961$	−28.0362	−0.904394
$962$	−31.7885	−1.02490
$963$	0	0
$964$	6.90911	0.222527
$965$	−5.44922	−0.175416
$966$	0	0
$967$	25.3550	0.815363	0.407682	−	0.913124i	$-0.366337\pi$
$967$	25.3550	0.815363	0.407682	+	0.913124i	$0.366337\pi$
$968$	8.39094	0.269695
$969$	0	0
$970$	17.3915	0.558406
$971$	−4.38779	−0.140811	−0.0704054	−	0.997518i	$-0.522429\pi$
$971$	−4.38779	−0.140811	−0.0704054	+	0.997518i	$0.522429\pi$
$972$	0	0
$973$	−8.00447	−0.256611
$974$	−22.9104	−0.734097
$975$	0	0
$976$	−56.7678	−1.81709
$977$	−3.45588	−0.110563	−0.0552817	−	0.998471i	$-0.517606\pi$
$977$	−3.45588	−0.110563	−0.0552817	+	0.998471i	$0.517606\pi$
$978$	0	0
$979$	−17.3812	−0.555506
$980$	2.44735	0.0781777
$981$	0	0
$982$	−65.7077	−2.09682
$983$	−56.4424	−1.80023	−0.900117	−	0.435648i	$-0.856519\pi$
$983$	−56.4424	−1.80023	−0.900117	+	0.435648i	$0.856519\pi$
$984$	0	0
$985$	−24.3515	−0.775902
$986$	−33.6717	−1.07233
$987$	0	0
$988$	9.00182	0.286386
$989$	−24.6808	−0.784805
$990$	0	0
$991$	−55.5706	−1.76526	−0.882629	−	0.470069i	$-0.844229\pi$
$991$	−55.5706	−1.76526	−0.882629	+	0.470069i	$0.844229\pi$
$992$	−3.05915	−0.0971281
$993$	0	0
$994$	−22.4078	−0.710733
$995$	−0.0807282	−0.00255926
$996$	0	0
$997$	−20.1408	−0.637866	−0.318933	−	0.947777i	$-0.603324\pi$
$997$	−20.1408	−0.637866	−0.318933	+	0.947777i	$0.603324\pi$
$998$	−25.6977	−0.813445
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4923.2.a.l.1.4		18
3.2	odd	2		547.2.a.b.1.15	✓	18
12.11	even	2		8752.2.a.s.1.14		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.a.b.1.15	✓	18	3.2	odd	2
4923.2.a.l.1.4		18	1.1	even	1	trivial
8752.2.a.s.1.14		18	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4923 = 3^{2} \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4923.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52216 q^{2} +0.316965 q^{4} -1.24712 q^{5} -0.899316 q^{7} +2.56184 q^{8} +O(q^{10})\)	\(q-1.52216 q^{2} +0.316965 q^{4} -1.24712 q^{5} -0.899316 q^{7} +2.56184 q^{8} +1.89831 q^{10} -3.77827 q^{11} -4.29029 q^{13} +1.36890 q^{14} -4.53346 q^{16} +7.86362 q^{17} -6.61960 q^{19} -0.395293 q^{20} +5.75113 q^{22} -3.37854 q^{23} -3.44470 q^{25} +6.53050 q^{26} -0.285052 q^{28} +2.81309 q^{29} -1.72157 q^{31} +1.77696 q^{32} -11.9697 q^{34} +1.12155 q^{35} -4.86769 q^{37} +10.0761 q^{38} -3.19492 q^{40} -5.86463 q^{41} +7.30517 q^{43} -1.19758 q^{44} +5.14268 q^{46} -2.08319 q^{47} -6.19123 q^{49} +5.24338 q^{50} -1.35987 q^{52} -3.26386 q^{53} +4.71195 q^{55} -2.30391 q^{56} -4.28196 q^{58} +6.21926 q^{59} +12.5220 q^{61} +2.62050 q^{62} +6.36212 q^{64} +5.35050 q^{65} -10.3052 q^{67} +2.49250 q^{68} -1.70718 q^{70} -16.3692 q^{71} -15.5143 q^{73} +7.40939 q^{74} -2.09818 q^{76} +3.39786 q^{77} +5.15466 q^{79} +5.65376 q^{80} +8.92689 q^{82} -6.55843 q^{83} -9.80686 q^{85} -11.1196 q^{86} -9.67935 q^{88} +4.60031 q^{89} +3.85833 q^{91} -1.07088 q^{92} +3.17095 q^{94} +8.25541 q^{95} +9.16155 q^{97} +9.42403 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} + 16 q^{4} + 27 q^{5} - 11 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^2 + 16 * q^4 + 27 * q^5 - 11 * q^7 + 12 * q^8	\( 18 q + 4 q^{2} + 16 q^{4} + 27 q^{5} - 11 q^{7} + 12 q^{8} - 5 q^{10} - 2 q^{11} - 25 q^{13} + 7 q^{14} + 8 q^{16} + 30 q^{17} + 4 q^{19} + 41 q^{20} - 24 q^{22} + 26 q^{23} + 31 q^{25} + 18 q^{26} - 16 q^{28} + 18 q^{29} - 5 q^{31} + 28 q^{32} + 5 q^{34} + 9 q^{35} - 18 q^{37} + 45 q^{38} + 7 q^{40} + 17 q^{41} + 8 q^{43} - 12 q^{44} + 30 q^{46} + 52 q^{47} + 29 q^{49} - 13 q^{50} - 14 q^{52} + 60 q^{53} + 11 q^{55} - 7 q^{56} + 14 q^{58} + 8 q^{59} - 26 q^{61} - 4 q^{62} + 44 q^{64} + 6 q^{65} + 12 q^{67} + 61 q^{68} + 35 q^{70} + q^{71} - 2 q^{73} - 16 q^{74} + 66 q^{76} + 73 q^{77} + 18 q^{79} + 32 q^{80} + 44 q^{82} + 43 q^{83} + 51 q^{85} - 4 q^{86} - 17 q^{88} + 28 q^{89} - q^{91} + 68 q^{92} + 78 q^{94} + 18 q^{95} - 34 q^{97} - 34 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 + 16 * q^4 + 27 * q^5 - 11 * q^7 + 12 * q^8 - 5 * q^10 - 2 * q^11 - 25 * q^13 + 7 * q^14 + 8 * q^16 + 30 * q^17 + 4 * q^19 + 41 * q^20 - 24 * q^22 + 26 * q^23 + 31 * q^25 + 18 * q^26 - 16 * q^28 + 18 * q^29 - 5 * q^31 + 28 * q^32 + 5 * q^34 + 9 * q^35 - 18 * q^37 + 45 * q^38 + 7 * q^40 + 17 * q^41 + 8 * q^43 - 12 * q^44 + 30 * q^46 + 52 * q^47 + 29 * q^49 - 13 * q^50 - 14 * q^52 + 60 * q^53 + 11 * q^55 - 7 * q^56 + 14 * q^58 + 8 * q^59 - 26 * q^61 - 4 * q^62 + 44 * q^64 + 6 * q^65 + 12 * q^67 + 61 * q^68 + 35 * q^70 + q^71 - 2 * q^73 - 16 * q^74 + 66 * q^76 + 73 * q^77 + 18 * q^79 + 32 * q^80 + 44 * q^82 + 43 * q^83 + 51 * q^85 - 4 * q^86 - 17 * q^88 + 28 * q^89 - q^91 + 68 * q^92 + 78 * q^94 + 18 * q^95 - 34 * q^97 - 34 * q^98

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