LMFDB - Embedded newform 549.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [549,2,Mod(1,549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(549, 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("549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 549 = 3^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	549.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:	$4.38378707097$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.91407488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - 2x^{3} + 31x^{2} + 10x - 17 $ x^6 - 11x^4 - 2x^3 + 31x^2 + 10x - 17
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 183)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.27291$ of defining polynomial
Character	$\chi$	$=$	549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27291 q^{2} -0.379697 q^{4} -4.38695 q^{5} -4.03359 q^{7} +3.02914 q^{8} +O(q^{10})$	\(q-1.27291 q^{2} -0.379697 q^{4} -4.38695 q^{5} -4.03359 q^{7} +3.02914 q^{8} +5.58420 q^{10} +0.224693 q^{11} -3.72400 q^{13} +5.13440 q^{14} -3.09644 q^{16} -3.04950 q^{17} +3.50684 q^{19} +1.66571 q^{20} -0.286014 q^{22} +2.98409 q^{23} +14.2453 q^{25} +4.74032 q^{26} +1.53154 q^{28} +5.63910 q^{29} -10.2807 q^{31} -2.11680 q^{32} +3.88174 q^{34} +17.6951 q^{35} +3.79838 q^{37} -4.46390 q^{38} -13.2887 q^{40} +5.34797 q^{41} +1.33704 q^{43} -0.0853150 q^{44} -3.79848 q^{46} -5.56513 q^{47} +9.26982 q^{49} -18.1331 q^{50} +1.41399 q^{52} -11.3740 q^{53} -0.985716 q^{55} -12.2183 q^{56} -7.17807 q^{58} +1.18571 q^{59} -1.00000 q^{61} +13.0865 q^{62} +8.88737 q^{64} +16.3370 q^{65} +10.0018 q^{67} +1.15788 q^{68} -22.5244 q^{70} +9.14594 q^{71} -2.26982 q^{73} -4.83500 q^{74} -1.33153 q^{76} -0.906317 q^{77} +3.86379 q^{79} +13.5839 q^{80} -6.80749 q^{82} -8.57880 q^{83} +13.3780 q^{85} -1.70194 q^{86} +0.680626 q^{88} +1.06401 q^{89} +15.0211 q^{91} -1.13305 q^{92} +7.08391 q^{94} -15.3843 q^{95} +1.57030 q^{97} -11.7997 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 10 q^{4} - 2 q^{5} + 2 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q + 10 * q^4 - 2 * q^5 + 2 * q^7 + 6 * q^8	$ 6 q + 10 q^{4} - 2 q^{5} + 2 q^{7} + 6 q^{8} - 6 q^{10} + 8 q^{11} + 6 q^{13} + 18 q^{14} + 10 q^{16} - 10 q^{17} + 8 q^{19} + 6 q^{20} - 10 q^{22} + 20 q^{25} + 6 q^{26} - 2 q^{28} + 10 q^{29} + 12 q^{32} - 4 q^{34} + 14 q^{35} - 4 q^{37} - 16 q^{38} - 54 q^{40} + 10 q^{41} + 4 q^{43} + 44 q^{44} - 22 q^{46} + 4 q^{47} + 12 q^{49} + 2 q^{50} + 18 q^{52} + 2 q^{53} - 10 q^{55} + 26 q^{56} - 4 q^{58} + 16 q^{59} - 6 q^{61} + 4 q^{62} + 30 q^{64} + 2 q^{65} - 2 q^{67} - 66 q^{68} + 2 q^{70} + 18 q^{71} + 30 q^{73} - 40 q^{74} - 20 q^{76} - 26 q^{77} + 6 q^{79} - 30 q^{80} + 34 q^{82} + 12 q^{83} - 8 q^{85} - 12 q^{86} + 2 q^{88} - 26 q^{89} + 6 q^{91} - 44 q^{92} - 44 q^{94} + 36 q^{95} + 16 q^{97} - 50 q^{98}+O(q^{100}) $ 6 * q + 10 * q^4 - 2 * q^5 + 2 * q^7 + 6 * q^8 - 6 * q^10 + 8 * q^11 + 6 * q^13 + 18 * q^14 + 10 * q^16 - 10 * q^17 + 8 * q^19 + 6 * q^20 - 10 * q^22 + 20 * q^25 + 6 * q^26 - 2 * q^28 + 10 * q^29 + 12 * q^32 - 4 * q^34 + 14 * q^35 - 4 * q^37 - 16 * q^38 - 54 * q^40 + 10 * q^41 + 4 * q^43 + 44 * q^44 - 22 * q^46 + 4 * q^47 + 12 * q^49 + 2 * q^50 + 18 * q^52 + 2 * q^53 - 10 * q^55 + 26 * q^56 - 4 * q^58 + 16 * q^59 - 6 * q^61 + 4 * q^62 + 30 * q^64 + 2 * q^65 - 2 * q^67 - 66 * q^68 + 2 * q^70 + 18 * q^71 + 30 * q^73 - 40 * q^74 - 20 * q^76 - 26 * q^77 + 6 * q^79 - 30 * q^80 + 34 * q^82 + 12 * q^83 - 8 * q^85 - 12 * q^86 + 2 * q^88 - 26 * q^89 + 6 * q^91 - 44 * q^92 - 44 * q^94 + 36 * q^95 + 16 * q^97 - 50 * 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 $

$2$	−1.27291	−0.900084	−0.450042	−	0.893007i	$-0.648591\pi$
$2$	−1.27291	−0.900084	−0.450042	+	0.893007i	$0.648591\pi$
$3$	0	0
$3$	0	0
$4$	−0.379697	−0.189848
$5$	−4.38695	−1.96190	−0.980952	−	0.194249i	$-0.937773\pi$
$5$	−4.38695	−1.96190	−0.980952	+	0.194249i	$0.937773\pi$
$6$	0	0
$7$	−4.03359	−1.52455	−0.762276	−	0.647252i	$-0.775918\pi$
$7$	−4.03359	−1.52455	−0.762276	+	0.647252i	$0.775918\pi$
$8$	3.02914	1.07096
$9$	0	0
$10$	5.58420	1.76588
$11$	0.224693	0.0677474	0.0338737	−	0.999426i	$-0.489216\pi$
$11$	0.224693	0.0677474	0.0338737	+	0.999426i	$0.489216\pi$
$12$	0	0
$13$	−3.72400	−1.03285	−0.516425	−	0.856332i	$-0.672738\pi$
$13$	−3.72400	−1.03285	−0.516425	+	0.856332i	$0.672738\pi$
$14$	5.13440	1.37223
$15$	0	0
$16$	−3.09644	−0.774109
$17$	−3.04950	−0.739613	−0.369806	−	0.929109i	$-0.620576\pi$
$17$	−3.04950	−0.739613	−0.369806	+	0.929109i	$0.620576\pi$
$18$	0	0
$19$	3.50684	0.804524	0.402262	−	0.915525i	$-0.368224\pi$
$19$	3.50684	0.804524	0.402262	+	0.915525i	$0.368224\pi$
$20$	1.66571	0.372464
$21$	0	0
$22$	−0.286014	−0.0609784
$23$	2.98409	0.622225	0.311112	−	0.950373i	$-0.399298\pi$
$23$	2.98409	0.622225	0.311112	+	0.950373i	$0.399298\pi$
$24$	0	0
$25$	14.2453	2.84907
$26$	4.74032	0.929653
$27$	0	0
$28$	1.53154	0.289434
$29$	5.63910	1.04715	0.523577	−	0.851978i	$-0.324597\pi$
$29$	5.63910	1.04715	0.523577	+	0.851978i	$0.324597\pi$
$30$	0	0
$31$	−10.2807	−1.84648	−0.923238	−	0.384229i	$-0.874467\pi$
$31$	−10.2807	−1.84648	−0.923238	+	0.384229i	$0.874467\pi$
$32$	−2.11680	−0.374200
$33$	0	0
$34$	3.88174	0.665714
$35$	17.6951	2.99103
$36$	0	0
$37$	3.79838	0.624449	0.312225	−	0.950008i	$-0.398926\pi$
$37$	3.79838	0.624449	0.312225	+	0.950008i	$0.398926\pi$
$38$	−4.46390	−0.724140
$39$	0	0
$40$	−13.2887	−2.10113
$41$	5.34797	0.835212	0.417606	−	0.908628i	$-0.362869\pi$
$41$	5.34797	0.835212	0.417606	+	0.908628i	$0.362869\pi$
$42$	0	0
$43$	1.33704	0.203897	0.101949	−	0.994790i	$-0.467492\pi$
$43$	1.33704	0.203897	0.101949	+	0.994790i	$0.467492\pi$
$44$	−0.0853150	−0.0128617
$45$	0	0
$46$	−3.79848	−0.560055
$47$	−5.56513	−0.811757	−0.405878	−	0.913927i	$-0.633034\pi$
$47$	−5.56513	−0.811757	−0.405878	+	0.913927i	$0.633034\pi$
$48$	0	0
$49$	9.26982	1.32426
$50$	−18.1331	−2.56440
$51$	0	0
$52$	1.41399	0.196085
$53$	−11.3740	−1.56234	−0.781171	−	0.624317i	$-0.785377\pi$
$53$	−11.3740	−1.56234	−0.781171	+	0.624317i	$0.785377\pi$
$54$	0	0
$55$	−0.985716	−0.132914
$56$	−12.2183	−1.63274
$57$	0	0
$58$	−7.17807	−0.942527
$59$	1.18571	0.154366	0.0771831	−	0.997017i	$-0.475407\pi$
$59$	1.18571	0.154366	0.0771831	+	0.997017i	$0.475407\pi$
$60$	0	0
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	13.0865	1.66198
$63$	0	0
$64$	8.88737	1.11092
$65$	16.3370	2.02635
$66$	0	0
$67$	10.0018	1.22191	0.610955	−	0.791666i	$-0.290786\pi$
$67$	10.0018	1.22191	0.610955	+	0.791666i	$0.290786\pi$
$68$	1.15788	0.140414
$69$	0	0
$70$	−22.5244	−2.69218
$71$	9.14594	1.08542	0.542712	−	0.839919i	$-0.317398\pi$
$71$	9.14594	1.08542	0.542712	+	0.839919i	$0.317398\pi$
$72$	0	0
$73$	−2.26982	−0.265662	−0.132831	−	0.991139i	$-0.542407\pi$
$73$	−2.26982	−0.265662	−0.132831	+	0.991139i	$0.542407\pi$
$74$	−4.83500	−0.562057
$75$	0	0
$76$	−1.33153	−0.152738
$77$	−0.906317	−0.103284
$78$	0	0
$79$	3.86379	0.434710	0.217355	−	0.976093i	$-0.430257\pi$
$79$	3.86379	0.434710	0.217355	+	0.976093i	$0.430257\pi$
$80$	13.5839	1.51873
$81$	0	0
$82$	−6.80749	−0.751762
$83$	−8.57880	−0.941646	−0.470823	−	0.882228i	$-0.656043\pi$
$83$	−8.57880	−0.941646	−0.470823	+	0.882228i	$0.656043\pi$
$84$	0	0
$85$	13.3780	1.45105
$86$	−1.70194	−0.183525
$87$	0	0
$88$	0.680626	0.0725550
$89$	1.06401	0.112785	0.0563925	−	0.998409i	$-0.482040\pi$
$89$	1.06401	0.112785	0.0563925	+	0.998409i	$0.482040\pi$
$90$	0	0
$91$	15.0211	1.57463
$92$	−1.13305	−0.118128
$93$	0	0
$94$	7.08391	0.730650
$95$	−15.3843	−1.57840
$96$	0	0
$97$	1.57030	0.159439	0.0797197	−	0.996817i	$-0.474597\pi$
$97$	1.57030	0.159439	0.0797197	+	0.996817i	$0.474597\pi$
$98$	−11.7997	−1.19195
$99$	0	0
$100$	−5.40891	−0.540891
$101$	−5.10216	−0.507684	−0.253842	−	0.967246i	$-0.581694\pi$
$101$	−5.10216	−0.507684	−0.253842	+	0.967246i	$0.581694\pi$
$102$	0	0
$103$	−2.29154	−0.225792	−0.112896	−	0.993607i	$-0.536013\pi$
$103$	−2.29154	−0.225792	−0.112896	+	0.993607i	$0.536013\pi$
$104$	−11.2805	−1.10615
$105$	0	0
$106$	14.4781	1.40624
$107$	−8.06717	−0.779883	−0.389942	−	0.920840i	$-0.627505\pi$
$107$	−8.06717	−0.779883	−0.389942	+	0.920840i	$0.627505\pi$
$108$	0	0
$109$	−0.471442	−0.0451560	−0.0225780	−	0.999745i	$-0.507187\pi$
$109$	−0.471442	−0.0451560	−0.0225780	+	0.999745i	$0.507187\pi$
$110$	1.25473	0.119634
$111$	0	0
$112$	12.4897	1.18017
$113$	14.4686	1.36109	0.680547	−	0.732704i	$-0.261742\pi$
$113$	14.4686	1.36109	0.680547	+	0.732704i	$0.261742\pi$
$114$	0	0
$115$	−13.0910	−1.22075
$116$	−2.14115	−0.198800
$117$	0	0
$118$	−1.50930	−0.138943
$119$	12.3004	1.12758
$120$	0	0
$121$	−10.9495	−0.995410
$122$	1.27291	0.115244
$123$	0	0
$124$	3.90356	0.350550
$125$	−40.5589	−3.62770
$126$	0	0
$127$	11.5740	1.02703	0.513514	−	0.858081i	$-0.328344\pi$
$127$	11.5740	1.02703	0.513514	+	0.858081i	$0.328344\pi$
$128$	−7.07924	−0.625722
$129$	0	0
$130$	−20.7955	−1.82389
$131$	5.13081	0.448281	0.224141	−	0.974557i	$-0.428043\pi$
$131$	5.13081	0.448281	0.224141	+	0.974557i	$0.428043\pi$
$132$	0	0
$133$	−14.1451	−1.22654
$134$	−12.7314	−1.09982
$135$	0	0
$136$	−9.23737	−0.792098
$137$	−5.86081	−0.500723	−0.250361	−	0.968152i	$-0.580549\pi$
$137$	−5.86081	−0.500723	−0.250361	+	0.968152i	$0.580549\pi$
$138$	0	0
$139$	0.143382	0.0121615	0.00608074	−	0.999982i	$-0.498064\pi$
$139$	0.143382	0.0121615	0.00608074	+	0.999982i	$0.498064\pi$
$140$	−6.71879	−0.567841
$141$	0	0
$142$	−11.6420	−0.976972
$143$	−0.836755	−0.0699729
$144$	0	0
$145$	−24.7385	−2.05442
$146$	2.88928	0.239118
$147$	0	0
$148$	−1.44223	−0.118551
$149$	1.75326	0.143633	0.0718164	−	0.997418i	$-0.477120\pi$
$149$	1.75326	0.143633	0.0718164	+	0.997418i	$0.477120\pi$
$150$	0	0
$151$	−8.48297	−0.690334	−0.345167	−	0.938541i	$-0.612178\pi$
$151$	−8.48297	−0.690334	−0.345167	+	0.938541i	$0.612178\pi$
$152$	10.6227	0.861616
$153$	0	0
$154$	1.15366	0.0929647
$155$	45.1011	3.62261
$156$	0	0
$157$	10.6251	0.847979	0.423989	−	0.905667i	$-0.360629\pi$
$157$	10.6251	0.847979	0.423989	+	0.905667i	$0.360629\pi$
$158$	−4.91826	−0.391276
$159$	0	0
$160$	9.28628	0.734145
$161$	−12.0366	−0.948614
$162$	0	0
$163$	−2.32969	−0.182475	−0.0912377	−	0.995829i	$-0.529082\pi$
$163$	−2.32969	−0.182475	−0.0912377	+	0.995829i	$0.529082\pi$
$164$	−2.03061	−0.158564
$165$	0	0
$166$	10.9201	0.847561
$167$	8.64327	0.668837	0.334418	−	0.942425i	$-0.391460\pi$
$167$	8.64327	0.668837	0.334418	+	0.942425i	$0.391460\pi$
$168$	0	0
$169$	0.868148	0.0667806
$170$	−17.0290	−1.30607
$171$	0	0
$172$	−0.507671	−0.0387096
$173$	21.8579	1.66183	0.830914	−	0.556401i	$-0.187818\pi$
$173$	21.8579	1.66183	0.830914	+	0.556401i	$0.187818\pi$
$174$	0	0
$175$	−57.4598	−4.34356
$176$	−0.695747	−0.0524439
$177$	0	0
$178$	−1.35439	−0.101516
$179$	3.74490	0.279907	0.139954	−	0.990158i	$-0.455305\pi$
$179$	3.74490	0.279907	0.139954	+	0.990158i	$0.455305\pi$
$180$	0	0
$181$	20.1901	1.50072	0.750358	−	0.661032i	$-0.229881\pi$
$181$	20.1901	1.50072	0.750358	+	0.661032i	$0.229881\pi$
$182$	−19.1205	−1.41730
$183$	0	0
$184$	9.03922	0.666380
$185$	−16.6633	−1.22511
$186$	0	0
$187$	−0.685200	−0.0501068
$188$	2.11306	0.154111
$189$	0	0
$190$	19.5829	1.42069
$191$	9.57368	0.692727	0.346364	−	0.938100i	$-0.387416\pi$
$191$	9.57368	0.692727	0.346364	+	0.938100i	$0.387416\pi$
$192$	0	0
$193$	−22.2600	−1.60231	−0.801157	−	0.598455i	$-0.795782\pi$
$193$	−22.2600	−1.60231	−0.801157	+	0.598455i	$0.795782\pi$
$194$	−1.99885	−0.143509
$195$	0	0
$196$	−3.51972	−0.251408
$197$	2.71428	0.193384	0.0966921	−	0.995314i	$-0.469174\pi$
$197$	2.71428	0.193384	0.0966921	+	0.995314i	$0.469174\pi$
$198$	0	0
$199$	5.73717	0.406697	0.203348	−	0.979106i	$-0.434818\pi$
$199$	5.73717	0.406697	0.203348	+	0.979106i	$0.434818\pi$
$200$	43.1512	3.05125
$201$	0	0
$202$	6.49460	0.456959
$203$	−22.7458	−1.59644
$204$	0	0
$205$	−23.4613	−1.63861
$206$	2.91692	0.203232
$207$	0	0
$208$	11.5311	0.799539
$209$	0.787961	0.0545044
$210$	0	0
$211$	6.66296	0.458697	0.229348	−	0.973344i	$-0.426340\pi$
$211$	6.66296	0.458697	0.229348	+	0.973344i	$0.426340\pi$
$212$	4.31868	0.296608
$213$	0	0
$214$	10.2688	0.701960
$215$	−5.86555	−0.400027
$216$	0	0
$217$	41.4683	2.81505
$218$	0.600105	0.0406442
$219$	0	0
$220$	0.374273	0.0252335
$221$	11.3563	0.763909
$222$	0	0
$223$	−14.4281	−0.966176	−0.483088	−	0.875572i	$-0.660485\pi$
$223$	−14.4281	−0.966176	−0.483088	+	0.875572i	$0.660485\pi$
$224$	8.53828	0.570488
$225$	0	0
$226$	−18.4173	−1.22510
$227$	16.4647	1.09280	0.546401	−	0.837524i	$-0.315997\pi$
$227$	16.4647	1.09280	0.546401	+	0.837524i	$0.315997\pi$
$228$	0	0
$229$	4.19646	0.277310	0.138655	−	0.990341i	$-0.455722\pi$
$229$	4.19646	0.277310	0.138655	+	0.990341i	$0.455722\pi$
$230$	16.6637	1.09877
$231$	0	0
$232$	17.0816	1.12146
$233$	−9.04298	−0.592425	−0.296213	−	0.955122i	$-0.595724\pi$
$233$	−9.04298	−0.592425	−0.296213	+	0.955122i	$0.595724\pi$
$234$	0	0
$235$	24.4139	1.59259
$236$	−0.450210	−0.0293062
$237$	0	0
$238$	−15.6574	−1.01492
$239$	18.9364	1.22489	0.612446	−	0.790513i	$-0.290186\pi$
$239$	18.9364	1.22489	0.612446	+	0.790513i	$0.290186\pi$
$240$	0	0
$241$	−24.9704	−1.60848	−0.804241	−	0.594303i	$-0.797428\pi$
$241$	−24.9704	−1.60848	−0.804241	+	0.594303i	$0.797428\pi$
$242$	13.9378	0.895953
$243$	0	0
$244$	0.379697	0.0243076
$245$	−40.6662	−2.59807
$246$	0	0
$247$	−13.0595	−0.830953
$248$	−31.1418	−1.97751
$249$	0	0
$250$	51.6279	3.26523
$251$	7.41779	0.468207	0.234104	−	0.972212i	$-0.424785\pi$
$251$	7.41779	0.468207	0.234104	+	0.972212i	$0.424785\pi$
$252$	0	0
$253$	0.670502	0.0421541
$254$	−14.7327	−0.924411
$255$	0	0
$256$	−8.76349	−0.547718
$257$	−24.7594	−1.54445	−0.772224	−	0.635350i	$-0.780856\pi$
$257$	−24.7594	−1.54445	−0.772224	+	0.635350i	$0.780856\pi$
$258$	0	0
$259$	−15.3211	−0.952006
$260$	−6.20310	−0.384700
$261$	0	0
$262$	−6.53107	−0.403491
$263$	10.2927	0.634674	0.317337	−	0.948313i	$-0.397211\pi$
$263$	10.2927	0.634674	0.317337	+	0.948313i	$0.397211\pi$
$264$	0	0
$265$	49.8973	3.06517
$266$	18.0055	1.10399
$267$	0	0
$268$	−3.79763	−0.231977
$269$	28.8375	1.75825	0.879125	−	0.476591i	$-0.158128\pi$
$269$	28.8375	1.75825	0.879125	+	0.476591i	$0.158128\pi$
$270$	0	0
$271$	23.2356	1.41146	0.705730	−	0.708481i	$-0.250619\pi$
$271$	23.2356	1.41146	0.705730	+	0.708481i	$0.250619\pi$
$272$	9.44259	0.572541
$273$	0	0
$274$	7.46029	0.450693
$275$	3.20083	0.193017
$276$	0	0
$277$	15.0109	0.901916	0.450958	−	0.892545i	$-0.351082\pi$
$277$	15.0109	0.901916	0.450958	+	0.892545i	$0.351082\pi$
$278$	−0.182512	−0.0109464
$279$	0	0
$280$	53.6011	3.20328
$281$	2.79216	0.166566	0.0832830	−	0.996526i	$-0.473459\pi$
$281$	2.79216	0.166566	0.0832830	+	0.996526i	$0.473459\pi$
$282$	0	0
$283$	31.7733	1.88873	0.944364	−	0.328902i	$-0.106679\pi$
$283$	31.7733	1.88873	0.944364	+	0.328902i	$0.106679\pi$
$284$	−3.47268	−0.206066
$285$	0	0
$286$	1.06511	0.0629815
$287$	−21.5715	−1.27332
$288$	0	0
$289$	−7.70055	−0.452973
$290$	31.4899	1.84915
$291$	0	0
$292$	0.861842	0.0504355
$293$	15.5688	0.909541	0.454771	−	0.890609i	$-0.349721\pi$
$293$	15.5688	0.909541	0.454771	+	0.890609i	$0.349721\pi$
$294$	0	0
$295$	−5.20165	−0.302852
$296$	11.5058	0.668763
$297$	0	0
$298$	−2.23175	−0.129282
$299$	−11.1127	−0.642665
$300$	0	0
$301$	−5.39308	−0.310852
$302$	10.7981	0.621359
$303$	0	0
$304$	−10.8587	−0.622790
$305$	4.38695	0.251196
$306$	0	0
$307$	−6.47935	−0.369796	−0.184898	−	0.982758i	$-0.559195\pi$
$307$	−6.47935	−0.369796	−0.184898	+	0.982758i	$0.559195\pi$
$308$	0.344126	0.0196084
$309$	0	0
$310$	−57.4097	−3.26065
$311$	16.5700	0.939601	0.469801	−	0.882773i	$-0.344326\pi$
$311$	16.5700	0.939601	0.469801	+	0.882773i	$0.344326\pi$
$312$	0	0
$313$	24.3360	1.37555	0.687775	−	0.725924i	$-0.258588\pi$
$313$	24.3360	1.37555	0.687775	+	0.725924i	$0.258588\pi$
$314$	−13.5249	−0.763252
$315$	0	0
$316$	−1.46707	−0.0825290
$317$	2.60309	0.146204	0.0731022	−	0.997324i	$-0.476710\pi$
$317$	2.60309	0.146204	0.0731022	+	0.997324i	$0.476710\pi$
$318$	0	0
$319$	1.26706	0.0709420
$320$	−38.9885	−2.17952
$321$	0	0
$322$	15.3215	0.853833
$323$	−10.6941	−0.595036
$324$	0	0
$325$	−53.0496	−2.94266
$326$	2.96549	0.164243
$327$	0	0
$328$	16.1998	0.894482
$329$	22.4474	1.23757
$330$	0	0
$331$	18.0722	0.993337	0.496669	−	0.867940i	$-0.334556\pi$
$331$	18.0722	0.993337	0.496669	+	0.867940i	$0.334556\pi$
$332$	3.25734	0.178770
$333$	0	0
$334$	−11.0021	−0.602009
$335$	−43.8772	−2.39727
$336$	0	0
$337$	2.62041	0.142743	0.0713715	−	0.997450i	$-0.477262\pi$
$337$	2.62041	0.142743	0.0713715	+	0.997450i	$0.477262\pi$
$338$	−1.10507	−0.0601082
$339$	0	0
$340$	−5.07958	−0.275479
$341$	−2.31001	−0.125094
$342$	0	0
$343$	−9.15551	−0.494351
$344$	4.05010	0.218367
$345$	0	0
$346$	−27.8232	−1.49579
$347$	4.08224	0.219146	0.109573	−	0.993979i	$-0.465052\pi$
$347$	4.08224	0.219146	0.109573	+	0.993979i	$0.465052\pi$
$348$	0	0
$349$	−2.83039	−0.151507	−0.0757536	−	0.997127i	$-0.524136\pi$
$349$	−2.83039	−0.151507	−0.0757536	+	0.997127i	$0.524136\pi$
$350$	73.1413	3.90957
$351$	0	0
$352$	−0.475628	−0.0253511
$353$	−16.4482	−0.875447	−0.437724	−	0.899110i	$-0.644215\pi$
$353$	−16.4482	−0.875447	−0.437724	+	0.899110i	$0.644215\pi$
$354$	0	0
$355$	−40.1228	−2.12950
$356$	−0.404001	−0.0214120
$357$	0	0
$358$	−4.76693	−0.251940
$359$	−1.89575	−0.100054	−0.0500269	−	0.998748i	$-0.515931\pi$
$359$	−1.89575	−0.100054	−0.0500269	+	0.998748i	$0.515931\pi$
$360$	0	0
$361$	−6.70208	−0.352741
$362$	−25.7002	−1.35077
$363$	0	0
$364$	−5.70344	−0.298942
$365$	9.95759	0.521204
$366$	0	0
$367$	−10.2685	−0.536010	−0.268005	−	0.963417i	$-0.586364\pi$
$367$	−10.2685	−0.536010	−0.268005	+	0.963417i	$0.586364\pi$
$368$	−9.24003	−0.481670
$369$	0	0
$370$	21.2109	1.10270
$371$	45.8781	2.38187
$372$	0	0
$373$	−16.1905	−0.838310	−0.419155	−	0.907915i	$-0.637674\pi$
$373$	−16.1905	−0.838310	−0.419155	+	0.907915i	$0.637674\pi$
$374$	0.872199	0.0451004
$375$	0	0
$376$	−16.8576	−0.869362
$377$	−21.0000	−1.08155
$378$	0	0
$379$	30.0564	1.54389	0.771946	−	0.635688i	$-0.219283\pi$
$379$	30.0564	1.54389	0.771946	+	0.635688i	$0.219283\pi$
$380$	5.84138	0.299656
$381$	0	0
$382$	−12.1865	−0.623513
$383$	−34.1411	−1.74453	−0.872265	−	0.489034i	$-0.837349\pi$
$383$	−34.1411	−1.74453	−0.872265	+	0.489034i	$0.837349\pi$
$384$	0	0
$385$	3.97597	0.202634
$386$	28.3351	1.44222
$387$	0	0
$388$	−0.596236	−0.0302693
$389$	−5.75261	−0.291669	−0.145834	−	0.989309i	$-0.546587\pi$
$389$	−5.75261	−0.291669	−0.145834	+	0.989309i	$0.546587\pi$
$390$	0	0
$391$	−9.09997	−0.460205
$392$	28.0796	1.41823
$393$	0	0
$394$	−3.45503	−0.174062
$395$	−16.9503	−0.852860
$396$	0	0
$397$	−13.1303	−0.658988	−0.329494	−	0.944158i	$-0.606878\pi$
$397$	−13.1303	−0.658988	−0.329494	+	0.944158i	$0.606878\pi$
$398$	−7.30290	−0.366062
$399$	0	0
$400$	−44.1098	−2.20549
$401$	−21.9000	−1.09363	−0.546816	−	0.837253i	$-0.684160\pi$
$401$	−21.9000	−1.09363	−0.546816	+	0.837253i	$0.684160\pi$
$402$	0	0
$403$	38.2854	1.90713
$404$	1.93727	0.0963830
$405$	0	0
$406$	28.9534	1.43693
$407$	0.853467	0.0423048
$408$	0	0
$409$	35.0840	1.73479	0.867396	−	0.497618i	$-0.165792\pi$
$409$	35.0840	1.73479	0.867396	+	0.497618i	$0.165792\pi$
$410$	29.8641	1.47488
$411$	0	0
$412$	0.870089	0.0428662
$413$	−4.78266	−0.235339
$414$	0	0
$415$	37.6348	1.84742
$416$	7.88294	0.386493
$417$	0	0
$418$	−1.00300	−0.0490586
$419$	23.2529	1.13598	0.567990	−	0.823036i	$-0.307721\pi$
$419$	23.2529	1.13598	0.567990	+	0.823036i	$0.307721\pi$
$420$	0	0
$421$	−9.41978	−0.459092	−0.229546	−	0.973298i	$-0.573724\pi$
$421$	−9.41978	−0.459092	−0.229546	+	0.973298i	$0.573724\pi$
$422$	−8.48135	−0.412866
$423$	0	0
$424$	−34.4535	−1.67321
$425$	−43.4412	−2.10721
$426$	0	0
$427$	4.03359	0.195199
$428$	3.06308	0.148059
$429$	0	0
$430$	7.46632	0.360058
$431$	23.1047	1.11292	0.556458	−	0.830876i	$-0.312160\pi$
$431$	23.1047	1.11292	0.556458	+	0.830876i	$0.312160\pi$
$432$	0	0
$433$	−17.1099	−0.822248	−0.411124	−	0.911579i	$-0.634864\pi$
$433$	−17.1099	−0.822248	−0.411124	+	0.911579i	$0.634864\pi$
$434$	−52.7854	−2.53378
$435$	0	0
$436$	0.179005	0.00857279
$437$	10.4647	0.500595
$438$	0	0
$439$	32.2437	1.53891	0.769455	−	0.638701i	$-0.220528\pi$
$439$	32.2437	1.53891	0.769455	+	0.638701i	$0.220528\pi$
$440$	−2.98587	−0.142346
$441$	0	0
$442$	−14.4556	−0.687583
$443$	30.9460	1.47029	0.735145	−	0.677909i	$-0.237114\pi$
$443$	30.9460	1.47029	0.735145	+	0.677909i	$0.237114\pi$
$444$	0	0
$445$	−4.66777	−0.221273
$446$	18.3657	0.869640
$447$	0	0
$448$	−35.8480	−1.69366
$449$	31.6233	1.49240	0.746199	−	0.665723i	$-0.231877\pi$
$449$	31.6233	1.49240	0.746199	+	0.665723i	$0.231877\pi$
$450$	0	0
$451$	1.20165	0.0565835
$452$	−5.49369	−0.258401
$453$	0	0
$454$	−20.9581	−0.983614
$455$	−65.8967	−3.08928
$456$	0	0
$457$	−31.9247	−1.49338	−0.746688	−	0.665174i	$-0.768357\pi$
$457$	−31.9247	−1.49338	−0.746688	+	0.665174i	$0.768357\pi$
$458$	−5.34172	−0.249602
$459$	0	0
$460$	4.97062	0.231756
$461$	−13.7457	−0.640202	−0.320101	−	0.947383i	$-0.603717\pi$
$461$	−13.7457	−0.640202	−0.320101	+	0.947383i	$0.603717\pi$
$462$	0	0
$463$	6.88887	0.320153	0.160076	−	0.987105i	$-0.448826\pi$
$463$	6.88887	0.320153	0.160076	+	0.987105i	$0.448826\pi$
$464$	−17.4611	−0.810612
$465$	0	0
$466$	11.5109	0.533233
$467$	−20.9191	−0.968018	−0.484009	−	0.875063i	$-0.660820\pi$
$467$	−20.9191	−0.968018	−0.484009	+	0.875063i	$0.660820\pi$
$468$	0	0
$469$	−40.3430	−1.86286
$470$	−31.0768	−1.43346
$471$	0	0
$472$	3.59168	0.165321
$473$	0.300424	0.0138135
$474$	0	0
$475$	49.9561	2.29214
$476$	−4.67043	−0.214069
$477$	0	0
$478$	−24.1043	−1.10251
$479$	−9.35001	−0.427213	−0.213606	−	0.976920i	$-0.568521\pi$
$479$	−9.35001	−0.427213	−0.213606	+	0.976920i	$0.568521\pi$
$480$	0	0
$481$	−14.1451	−0.644963
$482$	31.7851	1.44777
$483$	0	0
$484$	4.15749	0.188977
$485$	−6.88881	−0.312805
$486$	0	0
$487$	−30.1466	−1.36607	−0.683037	−	0.730384i	$-0.739341\pi$
$487$	−30.1466	−1.36607	−0.683037	+	0.730384i	$0.739341\pi$
$488$	−3.02914	−0.137123
$489$	0	0
$490$	51.7645	2.33848
$491$	10.3178	0.465637	0.232819	−	0.972520i	$-0.425205\pi$
$491$	10.3178	0.465637	0.232819	+	0.972520i	$0.425205\pi$
$492$	0	0
$493$	−17.1964	−0.774488
$494$	16.6235	0.747928
$495$	0	0
$496$	31.8337	1.42937
$497$	−36.8909	−1.65478
$498$	0	0
$499$	33.4176	1.49598	0.747988	−	0.663713i	$-0.231020\pi$
$499$	33.4176	1.49598	0.747988	+	0.663713i	$0.231020\pi$
$500$	15.4001	0.688712
$501$	0	0
$502$	−9.44219	−0.421426
$503$	−31.0549	−1.38467	−0.692335	−	0.721577i	$-0.743418\pi$
$503$	−31.0549	−1.38467	−0.692335	+	0.721577i	$0.743418\pi$
$504$	0	0
$505$	22.3829	0.996028
$506$	−0.853490	−0.0379423
$507$	0	0
$508$	−4.39461	−0.194979
$509$	−12.3328	−0.546641	−0.273321	−	0.961923i	$-0.588122\pi$
$509$	−12.3328	−0.546641	−0.273321	+	0.961923i	$0.588122\pi$
$510$	0	0
$511$	9.15551	0.405016
$512$	25.3136	1.11871
$513$	0	0
$514$	31.5165	1.39013
$515$	10.0529	0.442982
$516$	0	0
$517$	−1.25044	−0.0549944
$518$	19.5024	0.856885
$519$	0	0
$520$	49.4871	2.17015
$521$	5.03479	0.220578	0.110289	−	0.993900i	$-0.464822\pi$
$521$	5.03479	0.220578	0.110289	+	0.993900i	$0.464822\pi$
$522$	0	0
$523$	−20.2718	−0.886423	−0.443212	−	0.896417i	$-0.646161\pi$
$523$	−20.2718	−0.886423	−0.443212	+	0.896417i	$0.646161\pi$
$524$	−1.94815	−0.0851054
$525$	0	0
$526$	−13.1017	−0.571260
$527$	31.3511	1.36568
$528$	0	0
$529$	−14.0952	−0.612836
$530$	−63.5148	−2.75891
$531$	0	0
$532$	5.37086	0.232856
$533$	−19.9158	−0.862650
$534$	0	0
$535$	35.3903	1.53006
$536$	30.2968	1.30862
$537$	0	0
$538$	−36.7075	−1.58257
$539$	2.08286	0.0897152
$540$	0	0
$541$	−35.0511	−1.50696	−0.753482	−	0.657469i	$-0.771627\pi$
$541$	−35.0511	−1.50696	−0.753482	+	0.657469i	$0.771627\pi$
$542$	−29.5768	−1.27043
$543$	0	0
$544$	6.45517	0.276763
$545$	2.06820	0.0885918
$546$	0	0
$547$	−16.2324	−0.694048	−0.347024	−	0.937856i	$-0.612808\pi$
$547$	−16.2324	−0.694048	−0.347024	+	0.937856i	$0.612808\pi$
$548$	2.22533	0.0950614
$549$	0	0
$550$	−4.07437	−0.173732
$551$	19.7754	0.842461
$552$	0	0
$553$	−15.5849	−0.662739
$554$	−19.1075	−0.811800
$555$	0	0
$556$	−0.0544415	−0.00230884
$557$	−18.2320	−0.772513	−0.386256	−	0.922391i	$-0.626232\pi$
$557$	−18.2320	−0.772513	−0.386256	+	0.922391i	$0.626232\pi$
$558$	0	0
$559$	−4.97915	−0.210596
$560$	−54.7919	−2.31538
$561$	0	0
$562$	−3.55417	−0.149923
$563$	12.1869	0.513617	0.256809	−	0.966462i	$-0.417329\pi$
$563$	12.1869	0.513617	0.256809	+	0.966462i	$0.417329\pi$
$564$	0	0
$565$	−63.4732	−2.67034
$566$	−40.4446	−1.70001
$567$	0	0
$568$	27.7044	1.16245
$569$	−10.6611	−0.446935	−0.223467	−	0.974711i	$-0.571738\pi$
$569$	−10.6611	−0.446935	−0.223467	+	0.974711i	$0.571738\pi$
$570$	0	0
$571$	7.35619	0.307847	0.153923	−	0.988083i	$-0.450809\pi$
$571$	7.35619	0.307847	0.153923	+	0.988083i	$0.450809\pi$
$572$	0.317713	0.0132842
$573$	0	0
$574$	27.4586	1.14610
$575$	42.5093	1.77276
$576$	0	0
$577$	1.66954	0.0695039	0.0347519	−	0.999396i	$-0.488936\pi$
$577$	1.66954	0.0695039	0.0347519	+	0.999396i	$0.488936\pi$
$578$	9.80211	0.407714
$579$	0	0
$580$	9.39311	0.390027
$581$	34.6033	1.43559
$582$	0	0
$583$	−2.55566	−0.105845
$584$	−6.87561	−0.284515
$585$	0	0
$586$	−19.8178	−0.818664
$587$	15.9947	0.660174	0.330087	−	0.943951i	$-0.392922\pi$
$587$	15.9947	0.660174	0.330087	+	0.943951i	$0.392922\pi$
$588$	0	0
$589$	−36.0529	−1.48553
$590$	6.62124	0.272592
$591$	0	0
$592$	−11.7614	−0.483392
$593$	−11.2366	−0.461432	−0.230716	−	0.973021i	$-0.574107\pi$
$593$	−11.2366	−0.461432	−0.230716	+	0.973021i	$0.574107\pi$
$594$	0	0
$595$	−53.9614	−2.21220
$596$	−0.665707	−0.0272684
$597$	0	0
$598$	14.1455	0.578453
$599$	−24.0333	−0.981974	−0.490987	−	0.871167i	$-0.663364\pi$
$599$	−24.0333	−0.981974	−0.490987	+	0.871167i	$0.663364\pi$
$600$	0	0
$601$	−17.0105	−0.693875	−0.346937	−	0.937888i	$-0.612778\pi$
$601$	−17.0105	−0.693875	−0.346937	+	0.937888i	$0.612778\pi$
$602$	6.86492	0.279793
$603$	0	0
$604$	3.22096	0.131059
$605$	48.0350	1.95290
$606$	0	0
$607$	35.6114	1.44542	0.722710	−	0.691151i	$-0.242896\pi$
$607$	35.6114	1.44542	0.722710	+	0.691151i	$0.242896\pi$
$608$	−7.42326	−0.301053
$609$	0	0
$610$	−5.58420	−0.226098
$611$	20.7245	0.838424
$612$	0	0
$613$	36.5613	1.47670	0.738348	−	0.674420i	$-0.235606\pi$
$613$	36.5613	1.47670	0.738348	+	0.674420i	$0.235606\pi$
$614$	8.24764	0.332848
$615$	0	0
$616$	−2.74536	−0.110614
$617$	−20.1883	−0.812751	−0.406376	−	0.913706i	$-0.633208\pi$
$617$	−20.1883	−0.812751	−0.406376	+	0.913706i	$0.633208\pi$
$618$	0	0
$619$	−26.1304	−1.05027	−0.525135	−	0.851019i	$-0.675985\pi$
$619$	−26.1304	−1.05027	−0.525135	+	0.851019i	$0.675985\pi$
$620$	−17.1247	−0.687746
$621$	0	0
$622$	−21.0922	−0.845720
$623$	−4.29178	−0.171947
$624$	0	0
$625$	106.703	4.26813
$626$	−30.9775	−1.23811
$627$	0	0
$628$	−4.03433	−0.160987
$629$	−11.5832	−0.461850
$630$	0	0
$631$	44.6643	1.77806	0.889029	−	0.457852i	$-0.151381\pi$
$631$	44.6643	1.77806	0.889029	+	0.457852i	$0.151381\pi$
$632$	11.7040	0.465559
$633$	0	0
$634$	−3.31351	−0.131596
$635$	−50.7746	−2.01493
$636$	0	0
$637$	−34.5208	−1.36776
$638$	−1.61286	−0.0638538
$639$	0	0
$640$	31.0563	1.22761
$641$	−42.1165	−1.66350	−0.831752	−	0.555148i	$-0.812662\pi$
$641$	−42.1165	−1.66350	−0.831752	+	0.555148i	$0.812662\pi$
$642$	0	0
$643$	19.6289	0.774089	0.387045	−	0.922061i	$-0.373496\pi$
$643$	19.6289	0.774089	0.387045	+	0.922061i	$0.373496\pi$
$644$	4.57024	0.180093
$645$	0	0
$646$	13.6127	0.535583
$647$	22.5476	0.886439	0.443220	−	0.896413i	$-0.353836\pi$
$647$	22.5476	0.886439	0.443220	+	0.896413i	$0.353836\pi$
$648$	0	0
$649$	0.266420	0.0104579
$650$	67.5275	2.64864
$651$	0	0
$652$	0.884575	0.0346426
$653$	10.8373	0.424096	0.212048	−	0.977259i	$-0.431987\pi$
$653$	10.8373	0.424096	0.212048	+	0.977259i	$0.431987\pi$
$654$	0	0
$655$	−22.5086	−0.879485
$656$	−16.5596	−0.646546
$657$	0	0
$658$	−28.5736	−1.11391
$659$	−38.9487	−1.51723	−0.758614	−	0.651541i	$-0.774123\pi$
$659$	−38.9487	−1.51723	−0.758614	+	0.651541i	$0.774123\pi$
$660$	0	0
$661$	−2.60329	−0.101256	−0.0506282	−	0.998718i	$-0.516122\pi$
$661$	−2.60329	−0.101256	−0.0506282	+	0.998718i	$0.516122\pi$
$662$	−23.0043	−0.894087
$663$	0	0
$664$	−25.9864	−1.00847
$665$	62.0540	2.40635
$666$	0	0
$667$	16.8276	0.651565
$668$	−3.28182	−0.126977
$669$	0	0
$670$	55.8518	2.15774
$671$	−0.224693	−0.00867416
$672$	0	0
$673$	16.8084	0.647918	0.323959	−	0.946071i	$-0.394986\pi$
$673$	16.8084	0.647918	0.323959	+	0.946071i	$0.394986\pi$
$674$	−3.33555	−0.128481
$675$	0	0
$676$	−0.329633	−0.0126782
$677$	12.8509	0.493902	0.246951	−	0.969028i	$-0.420571\pi$
$677$	12.8509	0.493902	0.246951	+	0.969028i	$0.420571\pi$
$678$	0	0
$679$	−6.33392	−0.243074
$680$	40.5239	1.55402
$681$	0	0
$682$	2.94044	0.112595
$683$	−30.9040	−1.18251	−0.591254	−	0.806486i	$-0.701367\pi$
$683$	−30.9040	−1.18251	−0.591254	+	0.806486i	$0.701367\pi$
$684$	0	0
$685$	25.7111	0.982370
$686$	11.6542	0.444958
$687$	0	0
$688$	−4.14007	−0.157839
$689$	42.3568	1.61367
$690$	0	0
$691$	48.3213	1.83823	0.919114	−	0.393991i	$-0.128906\pi$
$691$	48.3213	1.83823	0.919114	+	0.393991i	$0.128906\pi$
$692$	−8.29938	−0.315495
$693$	0	0
$694$	−5.19634	−0.197250
$695$	−0.629009	−0.0238597
$696$	0	0
$697$	−16.3086	−0.617734
$698$	3.60283	0.136369
$699$	0	0
$700$	21.8173	0.824616
$701$	−27.2288	−1.02842	−0.514208	−	0.857665i	$-0.671914\pi$
$701$	−27.2288	−1.02842	−0.514208	+	0.857665i	$0.671914\pi$
$702$	0	0
$703$	13.3203	0.502384
$704$	1.99693	0.0752620
$705$	0	0
$706$	20.9371	0.787976
$707$	20.5800	0.773991
$708$	0	0
$709$	−0.149523	−0.00561544	−0.00280772	−	0.999996i	$-0.500894\pi$
$709$	−0.149523	−0.00561544	−0.00280772	+	0.999996i	$0.500894\pi$
$710$	51.0728	1.91673
$711$	0	0
$712$	3.22304	0.120789
$713$	−30.6786	−1.14892
$714$	0	0
$715$	3.67080	0.137280
$716$	−1.42193	−0.0531399
$717$	0	0
$718$	2.41312	0.0900568
$719$	33.3032	1.24200	0.621000	−	0.783811i	$-0.286727\pi$
$719$	33.3032	1.24200	0.621000	+	0.783811i	$0.286727\pi$
$720$	0	0
$721$	9.24311	0.344232
$722$	8.53115	0.317497
$723$	0	0
$724$	−7.66610	−0.284908
$725$	80.3309	2.98342
$726$	0	0
$727$	−6.63520	−0.246086	−0.123043	−	0.992401i	$-0.539265\pi$
$727$	−6.63520	−0.246086	−0.123043	+	0.992401i	$0.539265\pi$
$728$	45.5009	1.68638
$729$	0	0
$730$	−12.6751	−0.469127
$731$	−4.07732	−0.150805
$732$	0	0
$733$	−29.5213	−1.09039	−0.545197	−	0.838308i	$-0.683545\pi$
$733$	−29.5213	−1.09039	−0.545197	+	0.838308i	$0.683545\pi$
$734$	13.0709	0.482454
$735$	0	0
$736$	−6.31670	−0.232837
$737$	2.24732	0.0827812
$738$	0	0
$739$	−19.1500	−0.704443	−0.352222	−	0.935917i	$-0.614574\pi$
$739$	−19.1500	−0.704443	−0.352222	+	0.935917i	$0.614574\pi$
$740$	6.32700	0.232585
$741$	0	0
$742$	−58.3987	−2.14389
$743$	−48.2813	−1.77127	−0.885635	−	0.464382i	$-0.846276\pi$
$743$	−48.2813	−1.77127	−0.885635	+	0.464382i	$0.846276\pi$
$744$	0	0
$745$	−7.69147	−0.281794
$746$	20.6090	0.754550
$747$	0	0
$748$	0.260168	0.00951269
$749$	32.5396	1.18897
$750$	0	0
$751$	−37.8206	−1.38009	−0.690046	−	0.723765i	$-0.742410\pi$
$751$	−37.8206	−1.38009	−0.690046	+	0.723765i	$0.742410\pi$
$752$	17.2321	0.628389
$753$	0	0
$754$	26.7311	0.973490
$755$	37.2144	1.35437
$756$	0	0
$757$	−9.13474	−0.332008	−0.166004	−	0.986125i	$-0.553086\pi$
$757$	−9.13474	−0.332008	−0.166004	+	0.986125i	$0.553086\pi$
$758$	−38.2591	−1.38963
$759$	0	0
$760$	−46.6014	−1.69041
$761$	5.67109	0.205577	0.102788	−	0.994703i	$-0.467224\pi$
$761$	5.67109	0.205577	0.102788	+	0.994703i	$0.467224\pi$
$762$	0	0
$763$	1.90160	0.0688427
$764$	−3.63509	−0.131513
$765$	0	0
$766$	43.4586	1.57022
$767$	−4.41558	−0.159437
$768$	0	0
$769$	−11.4535	−0.413024	−0.206512	−	0.978444i	$-0.566211\pi$
$769$	−11.4535	−0.413024	−0.206512	+	0.978444i	$0.566211\pi$
$770$	−5.06106	−0.182388
$771$	0	0
$772$	8.45206	0.304196
$773$	−2.80211	−0.100785	−0.0503925	−	0.998729i	$-0.516047\pi$
$773$	−2.80211	−0.100785	−0.0503925	+	0.998729i	$0.516047\pi$
$774$	0	0
$775$	−146.453	−5.26074
$776$	4.75665	0.170754
$777$	0	0
$778$	7.32256	0.262527
$779$	18.7545	0.671948
$780$	0	0
$781$	2.05503	0.0735346
$782$	11.5835	0.414224
$783$	0	0
$784$	−28.7034	−1.02512
$785$	−46.6120	−1.66365
$786$	0	0
$787$	−8.44626	−0.301077	−0.150538	−	0.988604i	$-0.548101\pi$
$787$	−8.44626	−0.301077	−0.150538	+	0.988604i	$0.548101\pi$
$788$	−1.03060	−0.0367137
$789$	0	0
$790$	21.5762	0.767646
$791$	−58.3605	−2.07506
$792$	0	0
$793$	3.72400	0.132243
$794$	16.7136	0.593145
$795$	0	0
$796$	−2.17838	−0.0772107
$797$	18.2987	0.648172	0.324086	−	0.946028i	$-0.394943\pi$
$797$	18.2987	0.648172	0.324086	+	0.946028i	$0.394943\pi$
$798$	0	0
$799$	16.9709	0.600386
$800$	−30.1545	−1.06612
$801$	0	0
$802$	27.8767	0.984361
$803$	−0.510012	−0.0179979
$804$	0	0
$805$	52.8038	1.86109
$806$	−48.7340	−1.71658
$807$	0	0
$808$	−15.4552	−0.543711
$809$	−7.67028	−0.269673	−0.134836	−	0.990868i	$-0.543051\pi$
$809$	−7.67028	−0.269673	−0.134836	+	0.990868i	$0.543051\pi$
$810$	0	0
$811$	2.22925	0.0782795	0.0391397	−	0.999234i	$-0.487538\pi$
$811$	2.22925	0.0782795	0.0391397	+	0.999234i	$0.487538\pi$
$812$	8.63650	0.303082
$813$	0	0
$814$	−1.08639	−0.0380779
$815$	10.2202	0.357999
$816$	0	0
$817$	4.68880	0.164040
$818$	−44.6588	−1.56146
$819$	0	0
$820$	8.90817	0.311087
$821$	0.589300	0.0205667	0.0102834	−	0.999947i	$-0.496727\pi$
$821$	0.589300	0.0205667	0.0102834	+	0.999947i	$0.496727\pi$
$822$	0	0
$823$	−38.3578	−1.33707	−0.668534	−	0.743681i	$-0.733078\pi$
$823$	−38.3578	−1.33707	−0.668534	+	0.743681i	$0.733078\pi$
$824$	−6.94139	−0.241815
$825$	0	0
$826$	6.08790	0.211825
$827$	−12.1313	−0.421846	−0.210923	−	0.977503i	$-0.567647\pi$
$827$	−12.1313	−0.421846	−0.210923	+	0.977503i	$0.567647\pi$
$828$	0	0
$829$	51.3479	1.78339	0.891693	−	0.452641i	$-0.149518\pi$
$829$	51.3479	1.78339	0.891693	+	0.452641i	$0.149518\pi$
$830$	−47.9058	−1.66283
$831$	0	0
$832$	−33.0965	−1.14742
$833$	−28.2683	−0.979439
$834$	0	0
$835$	−37.9176	−1.31219
$836$	−0.299186	−0.0103476
$837$	0	0
$838$	−29.5989	−1.02248
$839$	−29.5044	−1.01860	−0.509302	−	0.860588i	$-0.670096\pi$
$839$	−29.5044	−1.01860	−0.509302	+	0.860588i	$0.670096\pi$
$840$	0	0
$841$	2.79943	0.0965322
$842$	11.9906	0.413222
$843$	0	0
$844$	−2.52990	−0.0870828
$845$	−3.80852	−0.131017
$846$	0	0
$847$	44.1658	1.51756
$848$	35.2189	1.20942
$849$	0	0
$850$	55.2968	1.89666
$851$	11.3347	0.388548
$852$	0	0
$853$	47.5006	1.62639	0.813194	−	0.581993i	$-0.197727\pi$
$853$	47.5006	1.62639	0.813194	+	0.581993i	$0.197727\pi$
$854$	−5.13440	−0.175695
$855$	0	0
$856$	−24.4366	−0.835226
$857$	30.7781	1.05136	0.525680	−	0.850683i	$-0.323811\pi$
$857$	30.7781	1.05136	0.525680	+	0.850683i	$0.323811\pi$
$858$	0	0
$859$	48.9334	1.66958	0.834792	−	0.550565i	$-0.185588\pi$
$859$	48.9334	1.66958	0.834792	+	0.550565i	$0.185588\pi$
$860$	2.22713	0.0759445
$861$	0	0
$862$	−29.4103	−1.00172
$863$	44.1469	1.50278	0.751389	−	0.659860i	$-0.229384\pi$
$863$	44.1469	1.50278	0.751389	+	0.659860i	$0.229384\pi$
$864$	0	0
$865$	−95.8897	−3.26035
$866$	21.7794	0.740093
$867$	0	0
$868$	−15.7454	−0.534432
$869$	0.868166	0.0294505
$870$	0	0
$871$	−37.2465	−1.26205
$872$	−1.42807	−0.0483604
$873$	0	0
$874$	−13.3206	−0.450578
$875$	163.598	5.53061
$876$	0	0
$877$	38.9958	1.31679	0.658397	−	0.752671i	$-0.271235\pi$
$877$	38.9958	1.31679	0.658397	+	0.752671i	$0.271235\pi$
$878$	−41.0434	−1.38515
$879$	0	0
$880$	3.05221	0.102890
$881$	−24.4068	−0.822285	−0.411143	−	0.911571i	$-0.634870\pi$
$881$	−24.4068	−0.822285	−0.411143	+	0.911571i	$0.634870\pi$
$882$	0	0
$883$	6.23399	0.209791	0.104895	−	0.994483i	$-0.466549\pi$
$883$	6.23399	0.209791	0.104895	+	0.994483i	$0.466549\pi$
$884$	−4.31196	−0.145027
$885$	0	0
$886$	−39.3916	−1.32339
$887$	34.9168	1.17239	0.586195	−	0.810170i	$-0.300625\pi$
$887$	34.9168	1.17239	0.586195	+	0.810170i	$0.300625\pi$
$888$	0	0
$889$	−46.6848	−1.56576
$890$	5.94165	0.199165
$891$	0	0
$892$	5.47829	0.183427
$893$	−19.5160	−0.653078
$894$	0	0
$895$	−16.4287	−0.549151
$896$	28.5547	0.953947
$897$	0	0
$898$	−40.2537	−1.34328
$899$	−57.9741	−1.93355
$900$	0	0
$901$	34.6851	1.15553
$902$	−1.52959	−0.0509299
$903$	0	0
$904$	43.8276	1.45768
$905$	−88.5729	−2.94426
$906$	0	0
$907$	29.1767	0.968797	0.484399	−	0.874847i	$-0.339038\pi$
$907$	29.1767	0.968797	0.484399	+	0.874847i	$0.339038\pi$
$908$	−6.25160	−0.207467
$909$	0	0
$910$	83.8806	2.78062
$911$	−40.8114	−1.35214	−0.676071	−	0.736837i	$-0.736319\pi$
$911$	−40.8114	−1.35214	−0.676071	+	0.736837i	$0.736319\pi$
$912$	0	0
$913$	−1.92759	−0.0637941
$914$	40.6374	1.34416
$915$	0	0
$916$	−1.59338	−0.0526468
$917$	−20.6956	−0.683428
$918$	0	0
$919$	−33.1155	−1.09238	−0.546190	−	0.837661i	$-0.683923\pi$
$919$	−33.1155	−1.09238	−0.546190	+	0.837661i	$0.683923\pi$
$920$	−39.6546	−1.30737
$921$	0	0
$922$	17.4971	0.576236
$923$	−34.0594	−1.12108
$924$	0	0
$925$	54.1092	1.77910
$926$	−8.76892	−0.288165
$927$	0	0
$928$	−11.9368	−0.391845
$929$	32.8158	1.07665	0.538325	−	0.842737i	$-0.319057\pi$
$929$	32.8158	1.07665	0.538325	+	0.842737i	$0.319057\pi$
$930$	0	0
$931$	32.5078	1.06540
$932$	3.43359	0.112471
$933$	0	0
$934$	26.6281	0.871298
$935$	3.00594	0.0983048
$936$	0	0
$937$	48.7416	1.59232	0.796160	−	0.605086i	$-0.206861\pi$
$937$	48.7416	1.59232	0.796160	+	0.605086i	$0.206861\pi$
$938$	51.3530	1.67674
$939$	0	0
$940$	−9.26989	−0.302350
$941$	−25.7120	−0.838188	−0.419094	−	0.907943i	$-0.637652\pi$
$941$	−25.7120	−0.838188	−0.419094	+	0.907943i	$0.637652\pi$
$942$	0	0
$943$	15.9588	0.519690
$944$	−3.67147	−0.119496
$945$	0	0
$946$	−0.382413	−0.0124333
$947$	20.9343	0.680274	0.340137	−	0.940376i	$-0.389527\pi$
$947$	20.9343	0.680274	0.340137	+	0.940376i	$0.389527\pi$
$948$	0	0
$949$	8.45280	0.274389
$950$	−63.5897	−2.06312
$951$	0	0
$952$	37.2597	1.20760
$953$	−4.28665	−0.138858	−0.0694291	−	0.997587i	$-0.522118\pi$
$953$	−4.28665	−0.138858	−0.0694291	+	0.997587i	$0.522118\pi$
$954$	0	0
$955$	−41.9993	−1.35907
$956$	−7.19007	−0.232544
$957$	0	0
$958$	11.9017	0.384527
$959$	23.6401	0.763378
$960$	0	0
$961$	74.6937	2.40947
$962$	18.0055	0.580521
$963$	0	0
$964$	9.48116	0.305368
$965$	97.6538	3.14359
$966$	0	0
$967$	60.0910	1.93240	0.966198	−	0.257801i	$-0.0829978\pi$
$967$	60.0910	1.93240	0.966198	+	0.257801i	$0.0829978\pi$
$968$	−33.1676	−1.06605
$969$	0	0
$970$	8.76885	0.281551
$971$	29.4796	0.946046	0.473023	−	0.881050i	$-0.343163\pi$
$971$	29.4796	0.946046	0.473023	+	0.881050i	$0.343163\pi$
$972$	0	0
$973$	−0.578342	−0.0185408
$974$	38.3740	1.22958
$975$	0	0
$976$	3.09644	0.0991145
$977$	58.3853	1.86791	0.933955	−	0.357391i	$-0.116333\pi$
$977$	58.3853	1.86791	0.933955	+	0.357391i	$0.116333\pi$
$978$	0	0
$979$	0.239076	0.00764089
$980$	15.4408	0.493239
$981$	0	0
$982$	−13.1337	−0.419113
$983$	−12.8716	−0.410541	−0.205271	−	0.978705i	$-0.565807\pi$
$983$	−12.8716	−0.410541	−0.205271	+	0.978705i	$0.565807\pi$
$984$	0	0
$985$	−11.9074	−0.379401
$986$	21.8895	0.697105
$987$	0	0
$988$	4.95863	0.157755
$989$	3.98986	0.126870
$990$	0	0
$991$	14.9600	0.475219	0.237609	−	0.971361i	$-0.423636\pi$
$991$	14.9600	0.475219	0.237609	+	0.971361i	$0.423636\pi$
$992$	21.7622	0.690951
$993$	0	0
$994$	46.9589	1.48945
$995$	−25.1687	−0.797901
$996$	0	0
$997$	35.0860	1.11119	0.555593	−	0.831454i	$-0.312491\pi$
$997$	35.0860	1.11119	0.555593	+	0.831454i	$0.312491\pi$
$998$	−42.5376	−1.34650
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	549.2.a.h.1.3		6
3.2	odd	2		183.2.a.c.1.4	✓	6
4.3	odd	2		8784.2.a.ca.1.1		6
12.11	even	2		2928.2.a.bd.1.6		6
15.14	odd	2		4575.2.a.s.1.3		6
21.20	even	2		8967.2.a.y.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.a.c.1.4	✓	6	3.2	odd	2
549.2.a.h.1.3		6	1.1	even	1	trivial
2928.2.a.bd.1.6		6	12.11	even	2
4575.2.a.s.1.3		6	15.14	odd	2
8784.2.a.ca.1.1		6	4.3	odd	2
8967.2.a.y.1.4		6	21.20	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:	\( N \)	\(=\)	\( 549 = 3^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.27291 q^{2} -0.379697 q^{4} -4.38695 q^{5} -4.03359 q^{7} +3.02914 q^{8} +O(q^{10})\)	\(q-1.27291 q^{2} -0.379697 q^{4} -4.38695 q^{5} -4.03359 q^{7} +3.02914 q^{8} +5.58420 q^{10} +0.224693 q^{11} -3.72400 q^{13} +5.13440 q^{14} -3.09644 q^{16} -3.04950 q^{17} +3.50684 q^{19} +1.66571 q^{20} -0.286014 q^{22} +2.98409 q^{23} +14.2453 q^{25} +4.74032 q^{26} +1.53154 q^{28} +5.63910 q^{29} -10.2807 q^{31} -2.11680 q^{32} +3.88174 q^{34} +17.6951 q^{35} +3.79838 q^{37} -4.46390 q^{38} -13.2887 q^{40} +5.34797 q^{41} +1.33704 q^{43} -0.0853150 q^{44} -3.79848 q^{46} -5.56513 q^{47} +9.26982 q^{49} -18.1331 q^{50} +1.41399 q^{52} -11.3740 q^{53} -0.985716 q^{55} -12.2183 q^{56} -7.17807 q^{58} +1.18571 q^{59} -1.00000 q^{61} +13.0865 q^{62} +8.88737 q^{64} +16.3370 q^{65} +10.0018 q^{67} +1.15788 q^{68} -22.5244 q^{70} +9.14594 q^{71} -2.26982 q^{73} -4.83500 q^{74} -1.33153 q^{76} -0.906317 q^{77} +3.86379 q^{79} +13.5839 q^{80} -6.80749 q^{82} -8.57880 q^{83} +13.3780 q^{85} -1.70194 q^{86} +0.680626 q^{88} +1.06401 q^{89} +15.0211 q^{91} -1.13305 q^{92} +7.08391 q^{94} -15.3843 q^{95} +1.57030 q^{97} -11.7997 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 10 q^{4} - 2 q^{5} + 2 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q + 10 * q^4 - 2 * q^5 + 2 * q^7 + 6 * q^8	\( 6 q + 10 q^{4} - 2 q^{5} + 2 q^{7} + 6 q^{8} - 6 q^{10} + 8 q^{11} + 6 q^{13} + 18 q^{14} + 10 q^{16} - 10 q^{17} + 8 q^{19} + 6 q^{20} - 10 q^{22} + 20 q^{25} + 6 q^{26} - 2 q^{28} + 10 q^{29} + 12 q^{32} - 4 q^{34} + 14 q^{35} - 4 q^{37} - 16 q^{38} - 54 q^{40} + 10 q^{41} + 4 q^{43} + 44 q^{44} - 22 q^{46} + 4 q^{47} + 12 q^{49} + 2 q^{50} + 18 q^{52} + 2 q^{53} - 10 q^{55} + 26 q^{56} - 4 q^{58} + 16 q^{59} - 6 q^{61} + 4 q^{62} + 30 q^{64} + 2 q^{65} - 2 q^{67} - 66 q^{68} + 2 q^{70} + 18 q^{71} + 30 q^{73} - 40 q^{74} - 20 q^{76} - 26 q^{77} + 6 q^{79} - 30 q^{80} + 34 q^{82} + 12 q^{83} - 8 q^{85} - 12 q^{86} + 2 q^{88} - 26 q^{89} + 6 q^{91} - 44 q^{92} - 44 q^{94} + 36 q^{95} + 16 q^{97} - 50 q^{98}+O(q^{100}) \) 6 * q + 10 * q^4 - 2 * q^5 + 2 * q^7 + 6 * q^8 - 6 * q^10 + 8 * q^11 + 6 * q^13 + 18 * q^14 + 10 * q^16 - 10 * q^17 + 8 * q^19 + 6 * q^20 - 10 * q^22 + 20 * q^25 + 6 * q^26 - 2 * q^28 + 10 * q^29 + 12 * q^32 - 4 * q^34 + 14 * q^35 - 4 * q^37 - 16 * q^38 - 54 * q^40 + 10 * q^41 + 4 * q^43 + 44 * q^44 - 22 * q^46 + 4 * q^47 + 12 * q^49 + 2 * q^50 + 18 * q^52 + 2 * q^53 - 10 * q^55 + 26 * q^56 - 4 * q^58 + 16 * q^59 - 6 * q^61 + 4 * q^62 + 30 * q^64 + 2 * q^65 - 2 * q^67 - 66 * q^68 + 2 * q^70 + 18 * q^71 + 30 * q^73 - 40 * q^74 - 20 * q^76 - 26 * q^77 + 6 * q^79 - 30 * q^80 + 34 * q^82 + 12 * q^83 - 8 * q^85 - 12 * q^86 + 2 * q^88 - 26 * q^89 + 6 * q^91 - 44 * q^92 - 44 * q^94 + 36 * q^95 + 16 * q^97 - 50 * q^98

Introduction

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