LMFDB - Embedded newform 287.3.d.b.286.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(286,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("287.286");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.d (of order $2$, degree $1$, minimal)

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:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	7.7.19468476636329.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 14x^{5} + 56x^{3} - 56x - 15 $ x^7 - 14x^5 + 56x^3 - 56*x - 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			286.2
Root			$-0.957283$ of defining polynomial
Character	$\chi$	$=$	287.286

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.08361 q^{2} +3.35781 q^{3} +5.50864 q^{4} -10.3542 q^{6} +7.00000 q^{7} -4.65206 q^{8} +2.27491 q^{9} +O(q^{10})$	$q-3.08361 q^{2} +3.35781 q^{3} +5.50864 q^{4} -10.3542 q^{6} +7.00000 q^{7} -4.65206 q^{8} +2.27491 q^{9} +18.4970 q^{12} +11.9461 q^{13} -21.5853 q^{14} -7.68944 q^{16} +22.0416 q^{17} -7.01493 q^{18} -0.933175 q^{19} +23.5047 q^{21} -42.2894 q^{23} -15.6207 q^{24} +25.0000 q^{25} -36.8370 q^{26} -22.5816 q^{27} +38.5605 q^{28} +42.3194 q^{32} -67.9677 q^{34} +12.5317 q^{36} +37.3917 q^{37} +2.87755 q^{38} +40.1126 q^{39} -41.0000 q^{41} -72.4793 q^{42} +85.3670 q^{43} +130.404 q^{46} +85.9527 q^{47} -25.8197 q^{48} +49.0000 q^{49} -77.0902 q^{50} +74.0117 q^{51} +65.8065 q^{52} +69.6328 q^{54} -32.5644 q^{56} -3.13343 q^{57} +15.9244 q^{63} -99.7389 q^{64} +121.419 q^{68} -142.000 q^{69} -10.5830 q^{72} -115.301 q^{74} +83.9453 q^{75} -5.14053 q^{76} -123.692 q^{78} -96.2990 q^{81} +126.428 q^{82} +129.479 q^{84} -263.238 q^{86} -108.291 q^{89} +83.6224 q^{91} -232.957 q^{92} -265.044 q^{94} +142.101 q^{96} -143.024 q^{97} -151.097 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 28 q^{4} + 49 q^{7} + 63 q^{9}+O(q^{10}) $ 7 * q + 28 * q^4 + 49 * q^7 + 63 * q^9	$ 7 q + 28 q^{4} + 49 q^{7} + 63 q^{9} - 119 q^{12} + 112 q^{16} + 175 q^{25} + 77 q^{26} + 196 q^{28} + 252 q^{36} - 287 q^{41} - 476 q^{48} + 343 q^{49} + 469 q^{54} + 441 q^{63} + 448 q^{64} - 182 q^{69} - 1001 q^{72} - 973 q^{74} - 917 q^{78} + 567 q^{81} - 833 q^{84} - 721 q^{92} - 1267 q^{94} + 1057 q^{96}+O(q^{100}) $ 7 * q + 28 * q^4 + 49 * q^7 + 63 * q^9 - 119 * q^12 + 112 * q^16 + 175 * q^25 + 77 * q^26 + 196 * q^28 + 252 * q^36 - 287 * q^41 - 476 * q^48 + 343 * q^49 + 469 * q^54 + 441 * q^63 + 448 * q^64 - 182 * q^69 - 1001 * q^72 - 973 * q^74 - 917 * q^78 + 567 * q^81 - 833 * q^84 - 721 * q^92 - 1267 * q^94 + 1057 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.08361	−1.54180	−0.770902	−	0.636954i	$-0.780194\pi$
$2$	−3.08361	−1.54180	−0.770902	+	0.636954i	$0.780194\pi$
$3$	3.35781	1.11927	0.559635	−	0.828739i	$-0.310941\pi$
$3$	3.35781	1.11927	0.559635	+	0.828739i	$0.310941\pi$
$4$	5.50864	1.37716
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	−10.3542	−1.72570
$7$	7.00000	1.00000
$7$	7.00000	1.00000
$8$	−4.65206	−0.581507
$9$	2.27491	0.252768
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	18.4970	1.54142
$13$	11.9461	0.918927	0.459464	−	0.888197i	$-0.348042\pi$
$13$	11.9461	0.918927	0.459464	+	0.888197i	$0.348042\pi$
$14$	−21.5853	−1.54180
$15$	0	0
$16$	−7.68944	−0.480590
$17$	22.0416	1.29657	0.648283	−	0.761399i	$-0.275487\pi$
$17$	22.0416	1.29657	0.648283	+	0.761399i	$0.275487\pi$
$18$	−7.01493	−0.389718
$19$	−0.933175	−0.0491145	−0.0245572	−	0.999698i	$-0.507818\pi$
$19$	−0.933175	−0.0491145	−0.0245572	+	0.999698i	$0.507818\pi$
$20$	0	0
$21$	23.5047	1.11927
$22$	0	0
$23$	−42.2894	−1.83867	−0.919336	−	0.393474i	$-0.871273\pi$
$23$	−42.2894	−1.83867	−0.919336	+	0.393474i	$0.871273\pi$
$24$	−15.6207	−0.650864
$25$	25.0000	1.00000
$26$	−36.8370	−1.41681
$27$	−22.5816	−0.836356
$28$	38.5605	1.37716
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	42.3194	1.32248
$33$	0	0
$34$	−67.9677	−1.99905
$35$	0	0
$36$	12.5317	0.348101
$37$	37.3917	1.01059	0.505293	−	0.862948i	$-0.331384\pi$
$37$	37.3917	1.01059	0.505293	+	0.862948i	$0.331384\pi$
$38$	2.87755	0.0757249
$39$	40.1126	1.02853
$40$	0	0
$41$	−41.0000	−1.00000
$41$	−41.0000	−1.00000
$42$	−72.4793	−1.72570
$43$	85.3670	1.98528	0.992639	−	0.121108i	$-0.0386448\pi$
$43$	85.3670	1.98528	0.992639	+	0.121108i	$0.0386448\pi$
$44$	0	0
$45$	0	0
$46$	130.404	2.83487
$47$	85.9527	1.82878	0.914390	−	0.404834i	$-0.132671\pi$
$47$	85.9527	1.82878	0.914390	+	0.404834i	$0.132671\pi$
$48$	−25.8197	−0.537910
$49$	49.0000	1.00000
$50$	−77.0902	−1.54180
$51$	74.0117	1.45121
$52$	65.8065	1.26551
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	69.6328	1.28950
$55$	0	0
$56$	−32.5644	−0.581507
$57$	−3.13343	−0.0549724
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	15.9244	0.252768
$64$	−99.7389	−1.55842
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	121.419	1.78558
$69$	−142.000	−2.05797
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−10.5830	−0.146986
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−115.301	−1.55813
$75$	83.9453	1.11927
$76$	−5.14053	−0.0676385
$77$	0	0
$78$	−123.692	−1.58579
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	−96.2990	−1.18888
$82$	126.428	1.54180
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	129.479	1.54142
$85$	0	0
$86$	−263.238	−3.06091
$87$	0	0
$88$	0	0
$89$	−108.291	−1.21676	−0.608378	−	0.793647i	$-0.708179\pi$
$89$	−108.291	−1.21676	−0.608378	+	0.793647i	$0.708179\pi$
$90$	0	0
$91$	83.6224	0.918927
$92$	−232.957	−2.53215
$93$	0	0
$94$	−265.044	−2.81962
$95$	0	0
$96$	142.101	1.48022
$97$	−143.024	−1.47447	−0.737236	−	0.675635i	$-0.763870\pi$
$97$	−143.024	−1.47447	−0.737236	+	0.675635i	$0.763870\pi$
$98$	−151.097	−1.54180
$99$	0	0
$100$	137.716	1.37716
$101$	−26.2289	−0.259692	−0.129846	−	0.991534i	$-0.541448\pi$
$101$	−26.2289	−0.259692	−0.129846	+	0.991534i	$0.541448\pi$
$102$	−228.223	−2.23748
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−55.5738	−0.534363
$105$	0	0
$106$	0	0
$107$	−213.884	−1.99892	−0.999458	−	0.0329159i	$-0.989521\pi$
$107$	−213.884	−1.99892	−0.999458	+	0.0329159i	$0.989521\pi$
$108$	−124.394	−1.15180
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	125.554	1.13112
$112$	−53.8261	−0.480590
$113$	191.300	1.69292	0.846462	−	0.532450i	$-0.178728\pi$
$113$	191.300	1.69292	0.846462	+	0.532450i	$0.178728\pi$
$114$	9.66227	0.0847567
$115$	0	0
$116$	0	0
$117$	27.1762	0.232275
$118$	0	0
$119$	154.291	1.29657
$120$	0	0
$121$	121.000	1.00000
$122$	0	0
$123$	−137.670	−1.11927
$124$	0	0
$125$	0	0
$126$	−49.1045	−0.389718
$127$	−230.859	−1.81779	−0.908893	−	0.417029i	$-0.863071\pi$
$127$	−230.859	−1.81779	−0.908893	+	0.417029i	$0.863071\pi$
$128$	138.278	1.08030
$129$	286.646	2.22206
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	−6.53223	−0.0491145
$134$	0	0
$135$	0	0
$136$	−102.539	−0.753963
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	437.873	3.17299
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	288.613	2.04690
$142$	0	0
$143$	0	0
$144$	−17.4928	−0.121478
$145$	0	0
$146$	0	0
$147$	164.533	1.11927
$148$	205.977	1.39174
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	−258.855	−1.72570
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	4.34119	0.0285604
$153$	50.1427	0.327730
$154$	0	0
$155$	0	0
$156$	220.966	1.41645
$157$	−208.285	−1.32666	−0.663328	−	0.748329i	$-0.730857\pi$
$157$	−208.285	−1.32666	−0.663328	+	0.748329i	$0.730857\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−296.026	−1.83867
$162$	296.948	1.83301
$163$	2.09068	0.0128263	0.00641313	−	0.999979i	$-0.497959\pi$
$163$	2.09068	0.0128263	0.00641313	+	0.999979i	$0.497959\pi$
$164$	−225.854	−1.37716
$165$	0	0
$166$	0	0
$167$	−323.159	−1.93508	−0.967542	−	0.252711i	$-0.918678\pi$
$167$	−323.159	−1.93508	−0.967542	+	0.252711i	$0.918678\pi$
$168$	−109.345	−0.650864
$169$	−26.2917	−0.155572
$170$	0	0
$171$	−2.12289	−0.0124146
$172$	470.256	2.73405
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	175.000	1.00000
$176$	0	0
$177$	0	0
$178$	333.928	1.87600
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	287.948	1.59087	0.795437	−	0.606036i	$-0.207241\pi$
$181$	287.948	1.59087	0.795437	+	0.606036i	$0.207241\pi$
$182$	−257.859	−1.41681
$183$	0	0
$184$	196.733	1.06920
$185$	0	0
$186$	0	0
$187$	0	0
$188$	473.482	2.51852
$189$	−158.071	−0.836356
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−334.904	−1.74429
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	441.030	2.27335
$195$	0	0
$196$	269.923	1.37716
$197$	−305.783	−1.55220	−0.776100	−	0.630610i	$-0.782805\pi$
$197$	−305.783	−1.55220	−0.776100	+	0.630610i	$0.782805\pi$
$198$	0	0
$199$	−154.522	−0.776492	−0.388246	−	0.921556i	$-0.626919\pi$
$199$	−154.522	−0.776492	−0.388246	+	0.921556i	$0.626919\pi$
$200$	−116.301	−0.581507
$201$	0	0
$202$	80.8798	0.400395
$203$	0	0
$204$	407.704	1.99855
$205$	0	0
$206$	0	0
$207$	−96.2046	−0.464757
$208$	−91.8585	−0.441627
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	659.535	3.08194
$215$	0	0
$216$	105.051	0.486347
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	263.311	1.19145
$222$	−387.160	−1.74396
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	296.236	1.32248
$225$	56.8727	0.252768
$226$	−589.895	−2.61016
$227$	−202.000	−0.889868	−0.444934	−	0.895563i	$-0.646773\pi$
$227$	−202.000	−0.889868	−0.444934	+	0.895563i	$0.646773\pi$
$228$	−17.2609	−0.0757058
$229$	−332.234	−1.45080	−0.725401	−	0.688327i	$-0.758345\pi$
$229$	−332.234	−1.45080	−0.725401	+	0.688327i	$0.758345\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−83.8007	−0.358123
$235$	0	0
$236$	0	0
$237$	0	0
$238$	−475.774	−1.99905
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	−373.117	−1.54180
$243$	−120.120	−0.494319
$244$	0	0
$245$	0	0
$246$	424.521	1.72570
$247$	−11.1478	−0.0451327
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	87.7216	0.348101
$253$	0	0
$254$	711.878	2.80267
$255$	0	0
$256$	−27.4391	−0.107184
$257$	485.331	1.88845	0.944223	−	0.329306i	$-0.106815\pi$
$257$	485.331	1.88845	0.944223	+	0.329306i	$0.106815\pi$
$258$	−883.905	−3.42599
$259$	261.742	1.01059
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	20.1428	0.0757249
$267$	−363.622	−1.36188
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	−169.488	−0.623117
$273$	280.788	1.02853
$274$	0	0
$275$	0	0
$276$	−782.227	−2.83416
$277$	−553.849	−1.99946	−0.999728	−	0.0233337i	$-0.992572\pi$
$277$	−553.849	−1.99946	−0.999728	+	0.0233337i	$0.992572\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	−889.969	−3.15592
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−287.000	−1.00000
$288$	96.2729	0.334281
$289$	196.833	0.681084
$290$	0	0
$291$	−480.247	−1.65033
$292$	0	0
$293$	422.000	1.44027	0.720137	−	0.693832i	$-0.244079\pi$
$293$	422.000	1.44027	0.720137	+	0.693832i	$0.244079\pi$
$294$	−507.355	−1.72570
$295$	0	0
$296$	−173.948	−0.587663
$297$	0	0
$298$	0	0
$299$	−505.192	−1.68961
$300$	462.425	1.54142
$301$	597.569	1.98528
$302$	0	0
$303$	−88.0719	−0.290666
$304$	7.17559	0.0236039
$305$	0	0
$306$	−154.620	−0.505295
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	482.695	1.55207	0.776037	−	0.630688i	$-0.217227\pi$
$311$	482.695	1.55207	0.776037	+	0.630688i	$0.217227\pi$
$312$	−186.606	−0.598097
$313$	−622.410	−1.98853	−0.994265	−	0.106943i	$-0.965894\pi$
$313$	−622.410	−1.98853	−0.994265	+	0.106943i	$0.965894\pi$
$314$	642.269	2.04544
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−718.183	−2.23733
$322$	912.829	2.83487
$323$	−20.5687	−0.0636802
$324$	−530.476	−1.63727
$325$	298.651	0.918927
$326$	−6.44684	−0.0197756
$327$	0	0
$328$	190.734	0.581507
$329$	601.669	1.82878
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	85.0626	0.255443
$334$	996.496	2.98352
$335$	0	0
$336$	−180.738	−0.537910
$337$	666.653	1.97820	0.989099	−	0.147252i	$-0.0470430\pi$
$337$	666.653	1.97820	0.989099	+	0.147252i	$0.0470430\pi$
$338$	81.0734	0.239862
$339$	642.351	1.89484
$340$	0	0
$341$	0	0
$342$	6.54616	0.0191408
$343$	343.000	1.00000
$344$	−397.132	−1.15445
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−539.631	−1.54180
$351$	−269.761	−0.768550
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	−596.538	−1.67567
$357$	518.082	1.45121
$358$	0	0
$359$	166.950	0.465042	0.232521	−	0.972591i	$-0.425303\pi$
$359$	166.950	0.465042	0.232521	+	0.972591i	$0.425303\pi$
$360$	0	0
$361$	−360.129	−0.997588
$362$	−887.920	−2.45282
$363$	406.295	1.11927
$364$	460.646	1.26551
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	325.182	0.883647
$369$	−93.2712	−0.252768
$370$	0	0
$371$	0	0
$372$	0	0
$373$	568.416	1.52390	0.761952	−	0.647633i	$-0.224241\pi$
$373$	568.416	1.52390	0.761952	+	0.647633i	$0.224241\pi$
$374$	0	0
$375$	0	0
$376$	−399.857	−1.06345
$377$	0	0
$378$	487.430	1.28950
$379$	−715.024	−1.88661	−0.943304	−	0.331931i	$-0.892300\pi$
$379$	−715.024	−1.88661	−0.943304	+	0.331931i	$0.892300\pi$
$380$	0	0
$381$	−775.181	−2.03460
$382$	0	0
$383$	−465.374	−1.21508	−0.607538	−	0.794291i	$-0.707843\pi$
$383$	−465.374	−1.21508	−0.607538	+	0.794291i	$0.707843\pi$
$384$	464.311	1.20914
$385$	0	0
$386$	0	0
$387$	194.202	0.501814
$388$	−787.867	−2.03058
$389$	768.137	1.97464	0.987322	−	0.158729i	$-0.0507396\pi$
$389$	768.137	1.97464	0.987322	+	0.158729i	$0.0507396\pi$
$390$	0	0
$391$	−932.128	−2.38396
$392$	−227.951	−0.581507
$393$	0	0
$394$	942.916	2.39319
$395$	0	0
$396$	0	0
$397$	−682.000	−1.71788	−0.858942	−	0.512073i	$-0.828878\pi$
$397$	−682.000	−1.71788	−0.858942	+	0.512073i	$0.828878\pi$
$398$	476.485	1.19720
$399$	−21.9340	−0.0549724
$400$	−192.236	−0.480590
$401$	−27.2939	−0.0680645	−0.0340323	−	0.999421i	$-0.510835\pi$
$401$	−27.2939	−0.0680645	−0.0340323	+	0.999421i	$0.510835\pi$
$402$	0	0
$403$	0	0
$404$	−144.486	−0.357638
$405$	0	0
$406$	0	0
$407$	0	0
$408$	−344.307	−0.843889
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	296.657	0.716564
$415$	0	0
$416$	505.551	1.21527
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	195.534	0.462256
$424$	0	0
$425$	551.041	1.29657
$426$	0	0
$427$	0	0
$428$	−1178.21	−2.75283
$429$	0	0
$430$	0	0
$431$	−286.000	−0.663573	−0.331787	−	0.943354i	$-0.607651\pi$
$431$	−286.000	−0.663573	−0.331787	+	0.943354i	$0.607651\pi$
$432$	173.640	0.401944
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	39.4635	0.0903054
$438$	0	0
$439$	−851.966	−1.94070	−0.970348	−	0.241710i	$-0.922292\pi$
$439$	−851.966	−1.94070	−0.970348	+	0.241710i	$0.922292\pi$
$440$	0	0
$441$	111.470	0.252768
$442$	−811.947	−1.83698
$443$	814.367	1.83830	0.919151	−	0.393906i	$-0.128877\pi$
$443$	814.367	1.83830	0.919151	+	0.393906i	$0.128877\pi$
$444$	691.633	1.55773
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−698.172	−1.55842
$449$	−106.531	−0.237264	−0.118632	−	0.992938i	$-0.537851\pi$
$449$	−106.531	−0.237264	−0.118632	+	0.992938i	$0.537851\pi$
$450$	−175.373	−0.389718
$451$	0	0
$452$	1053.80	2.33143
$453$	0	0
$454$	622.889	1.37200
$455$	0	0
$456$	14.5769	0.0319669
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	1024.48	2.23685
$459$	−497.735	−1.08439
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	149.704	0.319880
$469$	0	0
$470$	0	0
$471$	−699.382	−1.48489
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−23.3294	−0.0491145
$476$	849.936	1.78558
$477$	0	0
$478$	0	0
$479$	315.983	0.659672	0.329836	−	0.944038i	$-0.393007\pi$
$479$	315.983	0.659672	0.329836	+	0.944038i	$0.393007\pi$
$480$	0	0
$481$	446.683	0.928655
$482$	0	0
$483$	−994.000	−2.05797
$484$	666.546	1.37716
$485$	0	0
$486$	370.402	0.762143
$487$	130.738	0.268456	0.134228	−	0.990950i	$-0.457145\pi$
$487$	130.738	0.268456	0.134228	+	0.990950i	$0.457145\pi$
$488$	0	0
$489$	7.02011	0.0143561
$490$	0	0
$491$	533.512	1.08658	0.543292	−	0.839544i	$-0.317178\pi$
$491$	533.512	1.08658	0.543292	+	0.839544i	$0.317178\pi$
$492$	−758.376	−1.54142
$493$	0	0
$494$	34.3753	0.0695857
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	−1085.11	−2.16588
$502$	0	0
$503$	−1004.97	−1.99795	−0.998974	−	0.0452785i	$-0.985582\pi$
$503$	−1004.97	−1.99795	−0.998974	+	0.0452785i	$0.985582\pi$
$504$	−74.0810	−0.146986
$505$	0	0
$506$	0	0
$507$	−88.2827	−0.174128
$508$	−1271.72	−2.50338
$509$	−1014.83	−1.99376	−0.996881	−	0.0789135i	$-0.974855\pi$
$509$	−1014.83	−1.99376	−0.996881	+	0.0789135i	$0.974855\pi$
$510$	0	0
$511$	0	0
$512$	−468.500	−0.915038
$513$	21.0726	0.0410772
$514$	−1496.57	−2.91161
$515$	0	0
$516$	1579.03	3.06014
$517$	0	0
$518$	−807.109	−1.55813
$519$	0	0
$520$	0	0
$521$	1010.94	1.94039	0.970193	−	0.242332i	$-0.0779123\pi$
$521$	1010.94	1.94039	0.970193	+	0.242332i	$0.0779123\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	587.617	1.11927
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1259.40	2.38071
$530$	0	0
$531$	0	0
$532$	−35.9837	−0.0676385
$533$	−489.788	−0.918927
$534$	1121.27	2.09975
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−1065.69	−1.96985	−0.984924	−	0.172989i	$-0.944657\pi$
$541$	−1065.69	−1.96985	−0.984924	+	0.172989i	$0.944657\pi$
$542$	0	0
$543$	966.877	1.78062
$544$	932.789	1.71469
$545$	0	0
$546$	−865.841	−1.58579
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	660.593	1.19673
$553$	0	0
$554$	1707.85	3.08277
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	1019.80	1.82433
$560$	0	0
$561$	0	0
$562$	0	0
$563$	−219.208	−0.389356	−0.194678	−	0.980867i	$-0.562366\pi$
$563$	−219.208	−0.389356	−0.194678	+	0.980867i	$0.562366\pi$
$564$	1589.87	2.81891
$565$	0	0
$566$	0	0
$567$	−674.093	−1.18888
$568$	0	0
$569$	−305.205	−0.536388	−0.268194	−	0.963365i	$-0.586427\pi$
$569$	−305.205	−0.536388	−0.268194	+	0.963365i	$0.586427\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	884.996	1.54180
$575$	−1057.24	−1.83867
$576$	−226.897	−0.393918
$577$	−279.681	−0.484715	−0.242358	−	0.970187i	$-0.577921\pi$
$577$	−279.681	−0.484715	−0.242358	+	0.970187i	$0.577921\pi$
$578$	−606.957	−1.05010
$579$	0	0
$580$	0	0
$581$	0	0
$582$	1480.89	2.54449
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−1301.28	−2.22062
$587$	1150.12	1.95932	0.979660	−	0.200663i	$-0.0643095\pi$
$587$	1150.12	1.95932	0.979660	+	0.200663i	$0.0643095\pi$
$588$	906.352	1.54142
$589$	0	0
$590$	0	0
$591$	−1026.76	−1.73733
$592$	−287.521	−0.485677
$593$	−367.408	−0.619575	−0.309788	−	0.950806i	$-0.600258\pi$
$593$	−367.408	−0.619575	−0.309788	+	0.950806i	$0.600258\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−518.856	−0.869105
$598$	1557.81	2.60504
$599$	832.822	1.39035	0.695177	−	0.718838i	$-0.255326\pi$
$599$	832.822	1.39035	0.695177	+	0.718838i	$0.255326\pi$
$600$	−390.519	−0.650864
$601$	989.298	1.64609	0.823043	−	0.567979i	$-0.192275\pi$
$601$	989.298	1.64609	0.823043	+	0.567979i	$0.192275\pi$
$602$	−1842.67	−3.06091
$603$	0	0
$604$	0	0
$605$	0	0
$606$	271.579	0.448150
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	−39.4915	−0.0649531
$609$	0	0
$610$	0	0
$611$	1026.80	1.68052
$612$	276.218	0.451337
$613$	1170.04	1.90871	0.954355	−	0.298674i	$-0.0965442\pi$
$613$	1170.04	1.90871	0.954355	+	0.298674i	$0.0965442\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	1167.50	1.89222	0.946108	−	0.323852i	$-0.104978\pi$
$617$	1167.50	1.89222	0.946108	+	0.323852i	$0.104978\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	954.963	1.53778
$622$	−1488.44	−2.39299
$623$	−758.039	−1.21676
$624$	−308.444	−0.494301
$625$	625.000	1.00000
$626$	1919.27	3.06592
$627$	0	0
$628$	−1147.37	−1.82702
$629$	824.173	1.31029
$630$	0	0
$631$	−489.976	−0.776506	−0.388253	−	0.921553i	$-0.626921\pi$
$631$	−489.976	−0.776506	−0.388253	+	0.921553i	$0.626921\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	585.357	0.918927
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	2214.59	3.44952
$643$	−829.902	−1.29067	−0.645336	−	0.763899i	$-0.723283\pi$
$643$	−829.902	−1.29067	−0.645336	+	0.763899i	$0.723283\pi$
$644$	−1630.70	−2.53215
$645$	0	0
$646$	63.4258	0.0981824
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	447.988	0.691340
$649$	0	0
$650$	−920.924	−1.41681
$651$	0	0
$652$	11.5168	0.0176638
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	315.267	0.480590
$657$	0	0
$658$	−1855.31	−2.81962
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	884.147	1.33356
$664$	0	0
$665$	0	0
$666$	−262.300	−0.393844
$667$	0	0
$668$	−1780.17	−2.66492
$669$	0	0
$670$	0	0
$671$	0	0
$672$	994.706	1.48022
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	−2055.70	−3.04999
$675$	−564.540	−0.836356
$676$	−144.832	−0.214248
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	−1980.76	−2.92147
$679$	−1001.17	−1.47447
$680$	0	0
$681$	−678.278	−0.996003
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	−11.6942	−0.0170968
$685$	0	0
$686$	−1057.68	−1.54180
$687$	−1115.58	−1.62384
$688$	−656.424	−0.954105
$689$	0	0
$690$	0	0
$691$	1380.97	1.99852	0.999258	−	0.0385152i	$-0.0122628\pi$
$691$	1380.97	1.99852	0.999258	+	0.0385152i	$0.0122628\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−903.707	−1.29657
$698$	0	0
$699$	0	0
$700$	964.012	1.37716
$701$	805.046	1.14843	0.574213	−	0.818706i	$-0.305308\pi$
$701$	805.046	1.14843	0.574213	+	0.818706i	$0.305308\pi$
$702$	831.838	1.18495
$703$	−34.8930	−0.0496344
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−183.603	−0.259692
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	503.777	0.707552
$713$	0	0
$714$	−1597.56	−2.23748
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−514.809	−0.717004
$719$	−1186.00	−1.64951	−0.824757	−	0.565488i	$-0.808688\pi$
$719$	−1186.00	−1.64951	−0.824757	+	0.565488i	$0.808688\pi$
$720$	0	0
$721$	0	0
$722$	1110.50	1.53809
$723$	0	0
$724$	1586.20	2.19089
$725$	0	0
$726$	−1252.86	−1.72570
$727$	−1244.47	−1.71178	−0.855891	−	0.517156i	$-0.826991\pi$
$727$	−1244.47	−1.71178	−0.855891	+	0.517156i	$0.826991\pi$
$728$	−389.016	−0.534363
$729$	463.352	0.635599
$730$	0	0
$731$	1881.63	2.57405
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	−1789.67	−2.43161
$737$	0	0
$738$	287.612	0.389718
$739$	−1433.42	−1.93967	−0.969837	−	0.243754i	$-0.921621\pi$
$739$	−1433.42	−1.93967	−0.969837	+	0.243754i	$0.921621\pi$
$740$	0	0
$741$	−37.4321	−0.0505157
$742$	0	0
$743$	−1066.27	−1.43508	−0.717541	−	0.696516i	$-0.754732\pi$
$743$	−1066.27	−1.43508	−0.717541	+	0.696516i	$0.754732\pi$
$744$	0	0
$745$	0	0
$746$	−1752.77	−2.34956
$747$	0	0
$748$	0	0
$749$	−1497.19	−1.99892
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−660.928	−0.878893
$753$	0	0
$754$	0	0
$755$	0	0
$756$	−870.758	−1.15180
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	2204.85	2.90878
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	2390.35	3.13695
$763$	0	0
$764$	0	0
$765$	0	0
$766$	1435.03	1.87341
$767$	0	0
$768$	−92.1355	−0.119968
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	1629.65	2.11368
$772$	0	0
$773$	391.374	0.506306	0.253153	−	0.967426i	$-0.418532\pi$
$773$	391.374	0.506306	0.253153	+	0.967426i	$0.418532\pi$
$774$	−598.843	−0.773699
$775$	0	0
$776$	665.355	0.857417
$777$	878.880	1.13112
$778$	−2368.63	−3.04452
$779$	38.2602	0.0491145
$780$	0	0
$781$	0	0
$782$	2874.32	3.67560
$783$	0	0
$784$	−376.782	−0.480590
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−1684.45	−2.13763
$789$	0	0
$790$	0	0
$791$	1339.10	1.69292
$792$	0	0
$793$	0	0
$794$	2103.02	2.64864
$795$	0	0
$796$	−851.206	−1.06935
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	67.6359	0.0847567
$799$	1894.54	2.37113
$800$	1057.99	1.32248
$801$	−246.353	−0.307556
$802$	84.1636	0.104942
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	122.019	0.151013
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	−569.108	−0.697436
$817$	−79.6624	−0.0975060
$818$	0	0
$819$	190.233	0.232275
$820$	0	0
$821$	−1526.34	−1.85912	−0.929562	−	0.368666i	$-0.879815\pi$
$821$	−1526.34	−1.85912	−0.929562	+	0.368666i	$0.879815\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	−529.957	−0.640044
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	−1859.72	−2.23793
$832$	−1191.49	−1.43207
$833$	1080.04	1.29657
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−1302.80	−1.55280	−0.776401	−	0.630240i	$-0.782957\pi$
$839$	−1302.80	−1.55280	−0.776401	+	0.630240i	$0.782957\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	−602.952	−0.712709
$847$	847.000	1.00000
$848$	0	0
$849$	0	0
$850$	−1699.19	−1.99905
$851$	−1581.27	−1.85814
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	995.001	1.16238
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	−963.692	−1.11927
$862$	881.912	1.02310
$863$	578.000	0.669757	0.334878	−	0.942261i	$-0.391305\pi$
$863$	578.000	0.669757	0.334878	+	0.942261i	$0.391305\pi$
$864$	−955.641	−1.10607
$865$	0	0
$866$	0	0
$867$	660.929	0.762318
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−325.366	−0.372699
$874$	−121.690	−0.139233
$875$	0	0
$876$	0	0
$877$	−1126.13	−1.28408	−0.642038	−	0.766673i	$-0.721911\pi$
$877$	−1126.13	−1.28408	−0.642038	+	0.766673i	$0.721911\pi$
$878$	2627.13	2.99217
$879$	1417.00	1.61206
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−343.731	−0.389718
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	1450.48	1.64082
$885$	0	0
$886$	−2511.19	−2.83430
$887$	−1727.12	−1.94714	−0.973571	−	0.228383i	$-0.926656\pi$
$887$	−1727.12	−1.94714	−0.973571	+	0.228383i	$0.926656\pi$
$888$	−584.086	−0.657754
$889$	−1616.01	−1.81779
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−80.2089	−0.0898196
$894$	0	0
$895$	0	0
$896$	967.945	1.08030
$897$	−1696.34	−1.89113
$898$	328.501	0.365814
$899$	0	0
$900$	313.291	0.348101
$901$	0	0
$902$	0	0
$903$	2006.52	2.22206
$904$	−889.940	−0.984447
$905$	0	0
$906$	0	0
$907$	1609.99	1.77507	0.887533	−	0.460744i	$-0.152417\pi$
$907$	1609.99	1.77507	0.887533	+	0.460744i	$0.152417\pi$
$908$	−1112.75	−1.22549
$909$	−59.6684	−0.0656418
$910$	0	0
$911$	1628.15	1.78721	0.893606	−	0.448852i	$-0.148167\pi$
$911$	1628.15	1.78721	0.893606	+	0.448852i	$0.148167\pi$
$912$	24.0943	0.0264192
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−1830.16	−1.99799
$917$	0	0
$918$	1534.82	1.67192
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	934.792	1.01059
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−110.333	−0.118765	−0.0593826	−	0.998235i	$-0.518913\pi$
$929$	−110.333	−0.118765	−0.0593826	+	0.998235i	$0.518913\pi$
$930$	0	0
$931$	−45.7256	−0.0491145
$932$	0	0
$933$	1620.80	1.73719
$934$	0	0
$935$	0	0
$936$	−126.425	−0.135070
$937$	594.865	0.634861	0.317431	−	0.948281i	$-0.397180\pi$
$937$	594.865	0.634861	0.317431	+	0.948281i	$0.397180\pi$
$938$	0	0
$939$	−2089.94	−2.22570
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	2156.62	2.28941
$943$	1733.87	1.83867
$944$	0	0
$945$	0	0
$946$	0	0
$947$	654.964	0.691619	0.345810	−	0.938305i	$-0.387604\pi$
$947$	654.964	0.691619	0.345810	+	0.938305i	$0.387604\pi$
$948$	0	0
$949$	0	0
$950$	71.9387	0.0757249
$951$	0	0
$952$	−717.773	−0.753963
$953$	675.488	0.708802	0.354401	−	0.935094i	$-0.384685\pi$
$953$	675.488	0.708802	0.354401	+	0.935094i	$0.384685\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	−974.368	−1.01709
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	−1377.40	−1.43180
$963$	−486.567	−0.505261
$964$	0	0
$965$	0	0
$966$	3065.11	3.17299
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	−562.899	−0.581507
$969$	−69.0659	−0.0712754
$970$	0	0
$971$	−209.442	−0.215697	−0.107849	−	0.994167i	$-0.534396\pi$
$971$	−209.442	−0.215697	−0.107849	+	0.994167i	$0.534396\pi$
$972$	−661.695	−0.680756
$973$	0	0
$974$	−403.145	−0.413906
$975$	1002.82	1.02853
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	−21.6473	−0.0221342
$979$	0	0
$980$	0	0
$981$	0	0
$982$	−1645.14	−1.67530
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	640.450	0.650864
$985$	0	0
$986$	0	0
$987$	2020.29	2.04690
$988$	−61.4090	−0.0621549
$989$	−3610.12	−3.65028
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	1875.18	1.88082	0.940411	−	0.340039i	$-0.110440\pi$
$997$	1875.18	1.88082	0.940411	+	0.340039i	$0.110440\pi$
$998$	0	0
$999$	−844.364	−0.845209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.b.286.2	yes	7
7.6	odd	2		287.3.d.a.286.2	✓	7
41.40	even	2		287.3.d.a.286.2	✓	7
287.286	odd	2	CM	287.3.d.b.286.2	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.a.286.2	✓	7	7.6	odd	2
287.3.d.a.286.2	✓	7	41.40	even	2
287.3.d.b.286.2	yes	7	1.1	even	1	trivial
287.3.d.b.286.2	yes	7	287.286	odd	2	CM

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.08361 q^{2} +3.35781 q^{3} +5.50864 q^{4} -10.3542 q^{6} +7.00000 q^{7} -4.65206 q^{8} +2.27491 q^{9} +O(q^{10})\)	\(q-3.08361 q^{2} +3.35781 q^{3} +5.50864 q^{4} -10.3542 q^{6} +7.00000 q^{7} -4.65206 q^{8} +2.27491 q^{9} +18.4970 q^{12} +11.9461 q^{13} -21.5853 q^{14} -7.68944 q^{16} +22.0416 q^{17} -7.01493 q^{18} -0.933175 q^{19} +23.5047 q^{21} -42.2894 q^{23} -15.6207 q^{24} +25.0000 q^{25} -36.8370 q^{26} -22.5816 q^{27} +38.5605 q^{28} +42.3194 q^{32} -67.9677 q^{34} +12.5317 q^{36} +37.3917 q^{37} +2.87755 q^{38} +40.1126 q^{39} -41.0000 q^{41} -72.4793 q^{42} +85.3670 q^{43} +130.404 q^{46} +85.9527 q^{47} -25.8197 q^{48} +49.0000 q^{49} -77.0902 q^{50} +74.0117 q^{51} +65.8065 q^{52} +69.6328 q^{54} -32.5644 q^{56} -3.13343 q^{57} +15.9244 q^{63} -99.7389 q^{64} +121.419 q^{68} -142.000 q^{69} -10.5830 q^{72} -115.301 q^{74} +83.9453 q^{75} -5.14053 q^{76} -123.692 q^{78} -96.2990 q^{81} +126.428 q^{82} +129.479 q^{84} -263.238 q^{86} -108.291 q^{89} +83.6224 q^{91} -232.957 q^{92} -265.044 q^{94} +142.101 q^{96} -143.024 q^{97} -151.097 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 28 q^{4} + 49 q^{7} + 63 q^{9}+O(q^{10}) \) 7 * q + 28 * q^4 + 49 * q^7 + 63 * q^9	\( 7 q + 28 q^{4} + 49 q^{7} + 63 q^{9} - 119 q^{12} + 112 q^{16} + 175 q^{25} + 77 q^{26} + 196 q^{28} + 252 q^{36} - 287 q^{41} - 476 q^{48} + 343 q^{49} + 469 q^{54} + 441 q^{63} + 448 q^{64} - 182 q^{69} - 1001 q^{72} - 973 q^{74} - 917 q^{78} + 567 q^{81} - 833 q^{84} - 721 q^{92} - 1267 q^{94} + 1057 q^{96}+O(q^{100}) \) 7 * q + 28 * q^4 + 49 * q^7 + 63 * q^9 - 119 * q^12 + 112 * q^16 + 175 * q^25 + 77 * q^26 + 196 * q^28 + 252 * q^36 - 287 * q^41 - 476 * q^48 + 343 * q^49 + 469 * q^54 + 441 * q^63 + 448 * q^64 - 182 * q^69 - 1001 * q^72 - 973 * q^74 - 917 * q^78 + 567 * q^81 - 833 * q^84 - 721 * q^92 - 1267 * q^94 + 1057 * q^96

Introduction

L-functions

Modular forms

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Database

Properties

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