LMFDB - Embedded newform 287.3.d.b.286.3

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			286.3
Root			$1.48399$ 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)

$f(q)$	$=$	$q-1.79777 q^{2} -0.867827 q^{3} -0.768030 q^{4} +1.56015 q^{6} +7.00000 q^{7} +8.57181 q^{8} -8.24688 q^{9} +O(q^{10})$	$q-1.79777 q^{2} -0.867827 q^{3} -0.768030 q^{4} +1.56015 q^{6} +7.00000 q^{7} +8.57181 q^{8} -8.24688 q^{9} +0.666517 q^{12} -25.1724 q^{13} -12.5844 q^{14} -12.3380 q^{16} -6.49699 q^{17} +14.8260 q^{18} +29.1188 q^{19} -6.07479 q^{21} +45.9547 q^{23} -7.43885 q^{24} +25.0000 q^{25} +45.2541 q^{26} +14.9673 q^{27} -5.37621 q^{28} -12.1064 q^{32} +11.6801 q^{34} +6.33385 q^{36} +53.9367 q^{37} -52.3489 q^{38} +21.8453 q^{39} -41.0000 q^{41} +10.9211 q^{42} +61.3685 q^{43} -82.6159 q^{46} +17.9741 q^{47} +10.7073 q^{48} +49.0000 q^{49} -44.9442 q^{50} +5.63827 q^{51} +19.3331 q^{52} -26.9077 q^{54} +60.0027 q^{56} -25.2701 q^{57} -57.7281 q^{63} +71.1165 q^{64} +4.98989 q^{68} -39.8807 q^{69} -70.6907 q^{72} -96.9656 q^{74} -21.6957 q^{75} -22.3641 q^{76} -39.2727 q^{78} +61.2329 q^{81} +73.7085 q^{82} +4.66562 q^{84} -110.326 q^{86} +161.824 q^{89} -176.207 q^{91} -35.2946 q^{92} -32.3132 q^{94} +10.5062 q^{96} +71.9895 q^{97} -88.0906 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.79777	−0.898884	−0.449442	−	0.893310i	$-0.648377\pi$
$2$	−1.79777	−0.898884	−0.449442	+	0.893310i	$0.648377\pi$
$3$	−0.867827	−0.289276	−0.144638	−	0.989485i	$-0.546202\pi$
$3$	−0.867827	−0.289276	−0.144638	+	0.989485i	$0.546202\pi$
$4$	−0.768030	−0.192007
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	1.56015	0.260025
$7$	7.00000	1.00000
$7$	7.00000	1.00000
$8$	8.57181	1.07148
$9$	−8.24688	−0.916320
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	0.666517	0.0555431
$13$	−25.1724	−1.93634	−0.968168	−	0.250302i	$-0.919470\pi$
$13$	−25.1724	−1.93634	−0.968168	+	0.250302i	$0.919470\pi$
$14$	−12.5844	−0.898884
$15$	0	0
$16$	−12.3380	−0.771126
$17$	−6.49699	−0.382176	−0.191088	−	0.981573i	$-0.561202\pi$
$17$	−6.49699	−0.382176	−0.191088	+	0.981573i	$0.561202\pi$
$18$	14.8260	0.823665
$19$	29.1188	1.53257	0.766285	−	0.642501i	$-0.222103\pi$
$19$	29.1188	1.53257	0.766285	+	0.642501i	$0.222103\pi$
$20$	0	0
$21$	−6.07479	−0.289276
$22$	0	0
$23$	45.9547	1.99803	0.999015	−	0.0443771i	$-0.0141303\pi$
$23$	45.9547	1.99803	0.999015	+	0.0443771i	$0.0141303\pi$
$24$	−7.43885	−0.309952
$25$	25.0000	1.00000
$26$	45.2541	1.74054
$27$	14.9673	0.554345
$28$	−5.37621	−0.192007
$29$	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			$\pi$
$32$	−12.1064	−0.378324
$33$	0	0
$34$	11.6801	0.343532
$35$	0	0
$36$	6.33385	0.175940
$37$	53.9367	1.45775	0.728874	−	0.684648i	$-0.240044\pi$
$37$	53.9367	1.45775	0.728874	+	0.684648i	$0.240044\pi$
$38$	−52.3489	−1.37760
$39$	21.8453	0.560135
$40$	0	0
$41$	−41.0000	−1.00000
$41$	−41.0000	−1.00000
$42$	10.9211	0.260025
$43$	61.3685	1.42717	0.713587	−	0.700567i	$-0.247069\pi$
$43$	61.3685	1.42717	0.713587	+	0.700567i	$0.247069\pi$
$44$	0	0
$45$	0	0
$46$	−82.6159	−1.79600
$47$	17.9741	0.382427	0.191213	−	0.981548i	$-0.438758\pi$
$47$	17.9741	0.382427	0.191213	+	0.981548i	$0.438758\pi$
$48$	10.7073	0.223068
$49$	49.0000	1.00000
$50$	−44.9442	−0.898884
$51$	5.63827	0.110554
$52$	19.3331	0.371791
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	−26.9077	−0.498292
$55$	0	0
$56$	60.0027	1.07148
$57$	−25.2701	−0.443335
$58$	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
$63$	−57.7281	−0.916320
$64$	71.1165	1.11120
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	4.98989	0.0733807
$69$	−39.8807	−0.577981
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−70.6907	−0.981815
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−96.9656	−1.31035
$75$	−21.6957	−0.289276
$76$	−22.3641	−0.294265
$77$	0	0
$78$	−39.2727	−0.503496
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	61.2329	0.755961
$82$	73.7085	0.898884
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	4.66562	0.0555431
$85$	0	0
$86$	−110.326	−1.28286
$87$	0	0
$88$	0	0
$89$	161.824	1.81825	0.909126	−	0.416521i	$-0.136751\pi$
$89$	161.824	1.81825	0.909126	+	0.416521i	$0.136751\pi$
$90$	0	0
$91$	−176.207	−1.93634
$92$	−35.2946	−0.383637
$93$	0	0
$94$	−32.3132	−0.343758
$95$	0	0
$96$	10.5062	0.109440
$97$	71.9895	0.742160	0.371080	−	0.928601i	$-0.378988\pi$
$97$	71.9895	0.742160	0.371080	+	0.928601i	$0.378988\pi$
$98$	−88.0906	−0.898884
$99$	0	0
$100$	−19.2007	−0.192007
$101$	−63.2711	−0.626446	−0.313223	−	0.949680i	$-0.601409\pi$
$101$	−63.2711	−0.626446	−0.313223	+	0.949680i	$0.601409\pi$
$102$	−10.1363	−0.0993755
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−215.773	−2.07474
$105$	0	0
$106$	0	0
$107$	−138.862	−1.29777	−0.648887	−	0.760885i	$-0.724765\pi$
$107$	−138.862	−1.29777	−0.648887	+	0.760885i	$0.724765\pi$
$108$	−11.4953	−0.106438
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	−46.8077	−0.421691
$112$	−86.3661	−0.771126
$113$	−224.566	−1.98731	−0.993657	−	0.112455i	$-0.964129\pi$
$113$	−224.566	−1.98731	−0.993657	+	0.112455i	$0.964129\pi$
$114$	45.4298	0.398507
$115$	0	0
$116$	0	0
$117$	207.593	1.77430
$118$	0	0
$119$	−45.4790	−0.382176
$120$	0	0
$121$	121.000	1.00000
$122$	0	0
$123$	35.5809	0.289276
$124$	0	0
$125$	0	0
$126$	103.782	0.823665
$127$	154.641	1.21764	0.608821	−	0.793308i	$-0.291643\pi$
$127$	154.641	1.21764	0.608821	+	0.793308i	$0.291643\pi$
$128$	−79.4255	−0.620511
$129$	−53.2572	−0.412847
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	203.832	1.53257
$134$	0	0
$135$	0	0
$136$	−55.6910	−0.409493
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	71.6963	0.519538
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	−15.5984	−0.110627
$142$	0	0
$143$	0	0
$144$	101.750	0.706598
$145$	0	0
$146$	0	0
$147$	−42.5235	−0.289276
$148$	−41.4250	−0.279898
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	39.0038	0.260025
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	249.601	1.64211
$153$	53.5799	0.350195
$154$	0	0
$155$	0	0
$156$	−16.7778	−0.107550
$157$	−313.575	−1.99729	−0.998645	−	0.0520353i	$-0.983429\pi$
$157$	−313.575	−1.99729	−0.998645	+	0.0520353i	$0.983429\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	321.683	1.99803
$162$	−110.082	−0.679521
$163$	139.560	0.856194	0.428097	−	0.903733i	$-0.359184\pi$
$163$	139.560	0.856194	0.428097	+	0.903733i	$0.359184\pi$
$164$	31.4892	0.192007
$165$	0	0
$166$	0	0
$167$	−135.496	−0.811351	−0.405675	−	0.914017i	$-0.632964\pi$
$167$	−135.496	−0.811351	−0.405675	+	0.914017i	$0.632964\pi$
$168$	−52.0720	−0.309952
$169$	464.648	2.74940
$170$	0	0
$171$	−240.139	−1.40432
$172$	−47.1328	−0.274028
$173$	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
$178$	−290.923	−1.63440
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	−354.620	−1.95923	−0.979613	−	0.200892i	$-0.935616\pi$
$181$	−354.620	−1.95923	−0.979613	+	0.200892i	$0.935616\pi$
$182$	316.779	1.74054
$183$	0	0
$184$	393.915	2.14084
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−13.8046	−0.0734288
$189$	104.771	0.554345
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−61.7168	−0.321442
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	−129.420	−0.667116
$195$	0	0
$196$	−37.6335	−0.192007
$197$	3.60148	0.0182816	0.00914082	−	0.999958i	$-0.497090\pi$
$197$	3.60148	0.0182816	0.00914082	+	0.999958i	$0.497090\pi$
$198$	0	0
$199$	391.968	1.96969	0.984843	−	0.173447i	$-0.0554904\pi$
$199$	391.968	1.96969	0.984843	+	0.173447i	$0.0554904\pi$
$200$	214.295	1.07148
$201$	0	0
$202$	113.747	0.563103
$203$	0	0
$204$	−4.33036	−0.0212272
$205$	0	0
$206$	0	0
$207$	−378.983	−1.83083
$208$	310.577	1.49316
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	249.641	1.16655
$215$	0	0
$216$	128.297	0.593967
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	163.545	0.740021
$222$	84.1494	0.379051
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	−84.7446	−0.378324
$225$	−206.172	−0.916320
$226$	403.718	1.78636
$227$	−202.000	−0.889868	−0.444934	−	0.895563i	$-0.646773\pi$
$227$	−202.000	−0.889868	−0.444934	+	0.895563i	$0.646773\pi$
$228$	19.4082	0.0851236
$229$	436.116	1.90443	0.952217	−	0.305422i	$-0.0987974\pi$
$229$	436.116	1.90443	0.952217	+	0.305422i	$0.0987974\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−373.205	−1.59489
$235$	0	0
$236$	0	0
$237$	0	0
$238$	81.7606	0.343532
$239$	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			$\pi$
$242$	−217.530	−0.898884
$243$	−187.845	−0.773026
$244$	0	0
$245$	0	0
$246$	−63.9662	−0.260025
$247$	−732.989	−2.96757
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	44.3369	0.175940
$253$	0	0
$254$	−278.008	−1.09452
$255$	0	0
$256$	−141.677	−0.553427
$257$	−510.708	−1.98719	−0.993596	−	0.112989i	$-0.963958\pi$
$257$	−510.708	−1.98719	−0.993596	+	0.112989i	$0.963958\pi$
$258$	95.7441	0.371101
$259$	377.557	1.45775
$260$	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
$266$	−366.442	−1.37760
$267$	−140.436	−0.525976
$268$	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			$\pi$
$272$	80.1600	0.294706
$273$	152.917	0.560135
$274$	0	0
$275$	0	0
$276$	30.6296	0.110977
$277$	493.392	1.78120	0.890599	−	0.454789i	$-0.150285\pi$
$277$	493.392	1.78120	0.890599	+	0.454789i	$0.150285\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	28.0423	0.0994407
$283$	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
$288$	99.8397	0.346666
$289$	−246.789	−0.853941
$290$	0	0
$291$	−62.4744	−0.214689
$292$	0	0
$293$	422.000	1.44027	0.720137	−	0.693832i	$-0.244079\pi$
$293$	422.000	1.44027	0.720137	+	0.693832i	$0.244079\pi$
$294$	76.4474	0.260025
$295$	0	0
$296$	462.335	1.56194
$297$	0	0
$298$	0	0
$299$	−1156.79	−3.86886
$300$	16.6629	0.0555431
$301$	429.579	1.42717
$302$	0	0
$303$	54.9083	0.181216
$304$	−359.268	−1.18180
$305$	0	0
$306$	−96.3242	−0.314785
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	607.658	1.95388	0.976942	−	0.213503i	$-0.0684872\pi$
$311$	607.658	1.95388	0.976942	+	0.213503i	$0.0684872\pi$
$312$	187.253	0.600171
$313$	−335.726	−1.07261	−0.536303	−	0.844025i	$-0.680180\pi$
$313$	−335.726	−1.07261	−0.536303	+	0.844025i	$0.680180\pi$
$314$	563.734	1.79533
$315$	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
$321$	120.508	0.375414
$322$	−578.311	−1.79600
$323$	−189.185	−0.585711
$324$	−47.0287	−0.145150
$325$	−629.309	−1.93634
$326$	−250.896	−0.769619
$327$	0	0
$328$	−351.444	−1.07148
$329$	125.818	0.382427
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	−444.809	−1.33576
$334$	243.590	0.729310
$335$	0	0
$336$	74.9508	0.223068
$337$	−557.571	−1.65451	−0.827257	−	0.561824i	$-0.810100\pi$
$337$	−557.571	−1.65451	−0.827257	+	0.561824i	$0.810100\pi$
$338$	−835.329	−2.47139
$339$	194.885	0.574882
$340$	0	0
$341$	0	0
$342$	431.715	1.26232
$343$	343.000	1.00000
$344$	526.039	1.52918
$345$	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			$\pi$
$350$	−314.609	−0.898884
$351$	−376.762	−1.07340
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	−124.286	−0.349118
$357$	39.4679	0.110554
$358$	0	0
$359$	643.662	1.79293	0.896466	−	0.443113i	$-0.146126\pi$
$359$	643.662	1.79293	0.896466	+	0.443113i	$0.146126\pi$
$360$	0	0
$361$	486.905	1.34877
$362$	637.525	1.76112
$363$	−105.007	−0.289276
$364$	135.332	0.371791
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−566.989	−1.54073
$369$	338.122	0.916320
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−23.3278	−0.0625410	−0.0312705	−	0.999511i	$-0.509955\pi$
$373$	−23.3278	−0.0625410	−0.0312705	+	0.999511i	$0.509955\pi$
$374$	0	0
$375$	0	0
$376$	154.070	0.409762
$377$	0	0
$378$	−188.354	−0.498292
$379$	535.048	1.41174	0.705868	−	0.708344i	$-0.250557\pi$
$379$	535.048	1.41174	0.705868	+	0.708344i	$0.250557\pi$
$380$	0	0
$381$	−134.201	−0.352234
$382$	0	0
$383$	155.301	0.405485	0.202743	−	0.979232i	$-0.435015\pi$
$383$	155.301	0.405485	0.202743	+	0.979232i	$0.435015\pi$
$384$	68.9276	0.179499
$385$	0	0
$386$	0	0
$387$	−506.098	−1.30775
$388$	−55.2901	−0.142500
$389$	−291.322	−0.748898	−0.374449	−	0.927247i	$-0.622168\pi$
$389$	−291.322	−0.748898	−0.374449	+	0.927247i	$0.622168\pi$
$390$	0	0
$391$	−298.567	−0.763599
$392$	420.019	1.07148
$393$	0	0
$394$	−6.47463	−0.0164331
$395$	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	$0.828878\pi$
$398$	−704.667	−1.77052
$399$	−176.891	−0.443335
$400$	−308.450	−0.771126
$401$	787.513	1.96387	0.981936	−	0.189213i	$-0.0605937\pi$
$401$	787.513	1.96387	0.981936	+	0.189213i	$0.0605937\pi$
$402$	0	0
$403$	0	0
$404$	48.5941	0.120282
$405$	0	0
$406$	0	0
$407$	0	0
$408$	48.3302	0.118456
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	681.323	1.64571
$415$	0	0
$416$	304.746	0.732562
$417$	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
$423$	−148.230	−0.350425
$424$	0	0
$425$	−162.425	−0.382176
$426$	0	0
$427$	0	0
$428$	106.650	0.249182
$429$	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	$0.607651\pi$
$432$	−184.667	−0.427469
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1338.15	3.06212
$438$	0	0
$439$	675.515	1.53876	0.769380	−	0.638792i	$-0.220565\pi$
$439$	675.515	1.53876	0.769380	+	0.638792i	$0.220565\pi$
$440$	0	0
$441$	−404.097	−0.916320
$442$	−294.015	−0.665193
$443$	−521.465	−1.17712	−0.588561	−	0.808453i	$-0.700305\pi$
$443$	−521.465	−1.17712	−0.588561	+	0.808453i	$0.700305\pi$
$444$	35.9497	0.0809678
$445$	0	0
$446$	0	0
$447$	0	0
$448$	497.815	1.11120
$449$	482.858	1.07541	0.537703	−	0.843134i	$-0.319292\pi$
$449$	482.858	1.07541	0.537703	+	0.843134i	$0.319292\pi$
$450$	370.649	0.823665
$451$	0	0
$452$	172.474	0.381579
$453$	0	0
$454$	363.149	0.799888
$455$	0	0
$456$	−216.610	−0.475023
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	−784.035	−1.71187
$459$	−97.2425	−0.211857
$460$	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			$\pi$
$468$	−159.438	−0.340679
$469$	0	0
$470$	0	0
$471$	272.129	0.577768
$472$	0	0
$473$	0	0
$474$	0	0
$475$	727.970	1.53257
$476$	34.9292	0.0733807
$477$	0	0
$478$	0	0
$479$	−677.090	−1.41355	−0.706775	−	0.707438i	$-0.749851\pi$
$479$	−677.090	−1.41355	−0.706775	+	0.707438i	$0.749851\pi$
$480$	0	0
$481$	−1357.71	−2.82269
$482$	0	0
$483$	−279.165	−0.577981
$484$	−92.9316	−0.192007
$485$	0	0
$486$	337.702	0.694861
$487$	−673.099	−1.38213	−0.691067	−	0.722791i	$-0.742859\pi$
$487$	−673.099	−1.38213	−0.691067	+	0.722791i	$0.742859\pi$
$488$	0	0
$489$	−121.114	−0.247676
$490$	0	0
$491$	−838.386	−1.70751	−0.853753	−	0.520678i	$-0.825679\pi$
$491$	−838.386	−1.70751	−0.853753	+	0.520678i	$0.825679\pi$
$492$	−27.3272	−0.0555431
$493$	0	0
$494$	1317.74	2.66750
$495$	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
$501$	117.587	0.234704
$502$	0	0
$503$	925.209	1.83938	0.919690	−	0.392644i	$-0.128440\pi$
$503$	925.209	1.83938	0.919690	+	0.392644i	$0.128440\pi$
$504$	−494.835	−0.981815
$505$	0	0
$506$	0	0
$507$	−403.234	−0.795333
$508$	−118.769	−0.233796
$509$	147.500	0.289784	0.144892	−	0.989447i	$-0.453717\pi$
$509$	147.500	0.289784	0.144892	+	0.989447i	$0.453717\pi$
$510$	0	0
$511$	0	0
$512$	572.405	1.11798
$513$	435.830	0.849571
$514$	918.135	1.78626
$515$	0	0
$516$	40.9031	0.0792696
$517$	0	0
$518$	−678.759	−1.31035
$519$	0	0
$520$	0	0
$521$	−471.134	−0.904289	−0.452144	−	0.891945i	$-0.649341\pi$
$521$	−471.134	−0.904289	−0.452144	+	0.891945i	$0.649341\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−151.870	−0.289276
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1582.83	2.99212
$530$	0	0
$531$	0	0
$532$	−156.549	−0.294265
$533$	1032.07	1.93634
$534$	252.471	0.472791
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−810.784	−1.49868	−0.749338	−	0.662187i	$-0.769628\pi$
$541$	−810.784	−1.49868	−0.749338	+	0.662187i	$0.769628\pi$
$542$	0	0
$543$	307.749	0.566757
$544$	78.6550	0.144586
$545$	0	0
$546$	−274.909	−0.503496
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	−341.850	−0.619294
$553$	0	0
$554$	−887.005	−1.60109
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	−1544.79	−2.76349
$560$	0	0
$561$	0	0
$562$	0	0
$563$	1125.54	1.99919	0.999595	−	0.0284664i	$-0.00906235\pi$
$563$	1125.54	1.99919	0.999595	+	0.0284664i	$0.00906235\pi$
$564$	11.9800	0.0212412
$565$	0	0
$566$	0	0
$567$	428.630	0.755961
$568$	0	0
$569$	666.837	1.17195	0.585973	−	0.810331i	$-0.300712\pi$
$569$	666.837	1.17195	0.585973	+	0.810331i	$0.300712\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	515.959	0.898884
$575$	1148.87	1.99803
$576$	−586.489	−1.01821
$577$	737.758	1.27861	0.639305	−	0.768953i	$-0.279222\pi$
$577$	737.758	1.27861	0.639305	+	0.768953i	$0.279222\pi$
$578$	443.670	0.767594
$579$	0	0
$580$	0	0
$581$	0	0
$582$	112.315	0.192980
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−758.658	−1.29464
$587$	901.271	1.53539	0.767693	−	0.640818i	$-0.221405\pi$
$587$	901.271	1.53539	0.767693	+	0.640818i	$0.221405\pi$
$588$	32.6593	0.0555431
$589$	0	0
$590$	0	0
$591$	−3.12546	−0.00528843
$592$	−665.471	−1.12411
$593$	−1017.63	−1.71607	−0.858033	−	0.513595i	$-0.828314\pi$
$593$	−1017.63	−1.71607	−0.858033	+	0.513595i	$0.828314\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−340.160	−0.569782
$598$	2079.64	3.47765
$599$	−1024.90	−1.71101	−0.855507	−	0.517791i	$-0.826754\pi$
$599$	−1024.90	−1.71101	−0.855507	+	0.517791i	$0.826754\pi$
$600$	−185.971	−0.309952
$601$	1150.58	1.91445	0.957223	−	0.289352i	$-0.0934397\pi$
$601$	1150.58	1.91445	0.957223	+	0.289352i	$0.0934397\pi$
$602$	−772.284	−1.28286
$603$	0	0
$604$	0	0
$605$	0	0
$606$	−98.7125	−0.162892
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	−352.523	−0.579808
$609$	0	0
$610$	0	0
$611$	−452.450	−0.740507
$612$	−41.1510	−0.0672402
$613$	−1213.05	−1.97887	−0.989434	−	0.144984i	$-0.953687\pi$
$613$	−1213.05	−1.97887	−0.989434	+	0.144984i	$0.953687\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	1040.37	1.68617	0.843086	−	0.537779i	$-0.180736\pi$
$617$	1040.37	1.68617	0.843086	+	0.537779i	$0.180736\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	687.818	1.10760
$622$	−1092.43	−1.75632
$623$	1132.77	1.81825
$624$	−269.527	−0.431934
$625$	625.000	1.00000
$626$	603.557	0.964149
$627$	0	0
$628$	240.835	0.383495
$629$	−350.426	−0.557116
$630$	0	0
$631$	−1024.81	−1.62411	−0.812053	−	0.583584i	$-0.801650\pi$
$631$	−1024.81	−1.62411	−0.812053	+	0.583584i	$0.801650\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−1233.45	−1.93634
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	−216.645	−0.337454
$643$	−773.073	−1.20229	−0.601145	−	0.799140i	$-0.705289\pi$
$643$	−773.073	−1.20229	−0.601145	+	0.799140i	$0.705289\pi$
$644$	−247.062	−0.383637
$645$	0	0
$646$	340.110	0.526487
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	524.877	0.809995
$649$	0	0
$650$	1131.35	1.74054
$651$	0	0
$652$	−107.186	−0.164396
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	505.858	0.771126
$657$	0	0
$658$	−226.192	−0.343758
$659$	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
$663$	−141.929	−0.214070
$664$	0	0
$665$	0	0
$666$	799.663	1.20070
$667$	0	0
$668$	104.065	0.155785
$669$	0	0
$670$	0	0
$671$	0	0
$672$	73.5436	0.109440
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	1002.38	1.48722
$675$	374.183	0.554345
$676$	−356.864	−0.527905
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	−350.358	−0.516752
$679$	503.926	0.742160
$680$	0	0
$681$	175.301	0.257417
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	184.434	0.269641
$685$	0	0
$686$	−616.634	−0.898884
$687$	−378.473	−0.550907
$688$	−757.165	−1.10053
$689$	0	0
$690$	0	0
$691$	−255.402	−0.369613	−0.184806	−	0.982775i	$-0.559166\pi$
$691$	−255.402	−0.369613	−0.184806	+	0.982775i	$0.559166\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	266.377	0.382176
$698$	0	0
$699$	0	0
$700$	−134.405	−0.192007
$701$	−1298.19	−1.85191	−0.925954	−	0.377637i	$-0.876737\pi$
$701$	−1298.19	−1.85191	−0.925954	+	0.377637i	$0.876737\pi$
$702$	677.332	0.964860
$703$	1570.57	2.23410
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−442.898	−0.626446
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	1387.13	1.94821
$713$	0	0
$714$	−70.9541	−0.0993755
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−1157.16	−1.61164
$719$	−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
$722$	−875.343	−1.21239
$723$	0	0
$724$	272.359	0.376186
$725$	0	0
$726$	188.778	0.260025
$727$	−1363.81	−1.87594	−0.937968	−	0.346721i	$-0.887295\pi$
$727$	−1363.81	−1.87594	−0.937968	+	0.346721i	$0.887295\pi$
$728$	−1510.41	−2.07474
$729$	−388.078	−0.532344
$730$	0	0
$731$	−398.711	−0.545432
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	−556.344	−0.755903
$737$	0	0
$738$	−607.865	−0.823665
$739$	−32.2695	−0.0436665	−0.0218332	−	0.999762i	$-0.506950\pi$
$739$	−32.2695	−0.0436665	−0.0218332	+	0.999762i	$0.506950\pi$
$740$	0	0
$741$	636.108	0.858445
$742$	0	0
$743$	−1474.02	−1.98388	−0.991938	−	0.126726i	$-0.959553\pi$
$743$	−1474.02	−1.98388	−0.991938	+	0.126726i	$0.959553\pi$
$744$	0	0
$745$	0	0
$746$	41.9380	0.0562171
$747$	0	0
$748$	0	0
$749$	−972.032	−1.29777
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−221.764	−0.294899
$753$	0	0
$754$	0	0
$755$	0	0
$756$	−80.4674	−0.106438
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	−961.892	−1.26899
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	241.263	0.316618
$763$	0	0
$764$	0	0
$765$	0	0
$766$	−279.195	−0.364484
$767$	0	0
$768$	122.951	0.160093
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	443.207	0.574846
$772$	0	0
$773$	1413.36	1.82841	0.914203	−	0.405258i	$-0.132818\pi$
$773$	1413.36	1.82841	0.914203	+	0.405258i	$0.132818\pi$
$774$	909.847	1.17551
$775$	0	0
$776$	617.080	0.795207
$777$	−327.654	−0.421691
$778$	523.729	0.673173
$779$	−1193.87	−1.53257
$780$	0	0
$781$	0	0
$782$	536.755	0.686387
$783$	0	0
$784$	−604.562	−0.771126
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−2.76605	−0.00351021
$789$	0	0
$790$	0	0
$791$	−1571.97	−1.98731
$792$	0	0
$793$	0	0
$794$	1226.08	1.54418
$795$	0	0
$796$	−301.043	−0.378195
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	318.008	0.398507
$799$	−116.777	−0.146154
$800$	−302.659	−0.378324
$801$	−1334.55	−1.66610
$802$	−1415.77	−1.76529
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−542.348	−0.671222
$809$	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
$816$	−69.5650	−0.0852512
$817$	1786.98	2.18724
$818$	0	0
$819$	1453.15	1.77430
$820$	0	0
$821$	−1424.94	−1.73561	−0.867807	−	0.496901i	$-0.834471\pi$
$821$	−1424.94	−1.73561	−0.867807	+	0.496901i	$0.834471\pi$
$822$	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			$\pi$
$828$	291.070	0.351534
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	−428.179	−0.515258
$832$	−1790.17	−2.15165
$833$	−318.353	−0.382176
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	1632.63	1.94593	0.972964	−	0.230959i	$-0.0741863\pi$
$839$	1632.63	1.94593	0.972964	+	0.230959i	$0.0741863\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	266.483	0.314992
$847$	847.000	1.00000
$848$	0	0
$849$	0	0
$850$	292.002	0.343532
$851$	2478.64	2.91262
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	−1190.30	−1.39053
$857$	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
$861$	249.066	0.289276
$862$	514.162	0.596475
$863$	578.000	0.669757	0.334878	−	0.942261i	$-0.391305\pi$
$863$	578.000	0.669757	0.334878	+	0.942261i	$0.391305\pi$
$864$	−181.200	−0.209722
$865$	0	0
$866$	0	0
$867$	214.170	0.247024
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−593.688	−0.680056
$874$	−2405.68	−2.75249
$875$	0	0
$876$	0	0
$877$	431.149	0.491619	0.245809	−	0.969318i	$-0.420946\pi$
$877$	431.149	0.491619	0.245809	+	0.969318i	$0.420946\pi$
$878$	−1214.42	−1.38317
$879$	−366.223	−0.416636
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	726.473	0.823665
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	−125.607	−0.142090
$885$	0	0
$886$	937.473	1.05810
$887$	−10.6746	−0.0120345	−0.00601727	−	0.999982i	$-0.501915\pi$
$887$	−10.6746	−0.0120345	−0.00601727	+	0.999982i	$0.501915\pi$
$888$	−401.227	−0.451832
$889$	1082.48	1.21764
$890$	0	0
$891$	0	0
$892$	0	0
$893$	523.384	0.586096
$894$	0	0
$895$	0	0
$896$	−555.978	−0.620511
$897$	1003.89	1.11917
$898$	−868.066	−0.966666
$899$	0	0
$900$	158.346	0.175940
$901$	0	0
$902$	0	0
$903$	−372.800	−0.412847
$904$	−1924.94	−2.12936
$905$	0	0
$906$	0	0
$907$	456.579	0.503395	0.251697	−	0.967806i	$-0.419011\pi$
$907$	456.579	0.503395	0.251697	+	0.967806i	$0.419011\pi$
$908$	155.142	0.170861
$909$	521.789	0.574025
$910$	0	0
$911$	1654.52	1.81616	0.908081	−	0.418795i	$-0.137547\pi$
$911$	1654.52	1.81616	0.908081	+	0.418795i	$0.137547\pi$
$912$	311.783	0.341867
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−334.950	−0.365666
$917$	0	0
$918$	174.819	0.190435
$919$	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
$925$	1348.42	1.45775
$926$	0	0
$927$	0	0
$928$	0	0
$929$	904.140	0.973240	0.486620	−	0.873614i	$-0.338230\pi$
$929$	904.140	0.973240	0.486620	+	0.873614i	$0.338230\pi$
$930$	0	0
$931$	1426.82	1.53257
$932$	0	0
$933$	−527.342	−0.565211
$934$	0	0
$935$	0	0
$936$	1779.45	1.90112
$937$	1600.15	1.70774	0.853871	−	0.520485i	$-0.174249\pi$
$937$	1600.15	1.70774	0.853871	+	0.520485i	$0.174249\pi$
$938$	0	0
$939$	291.352	0.310279
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	−489.224	−0.519346
$943$	−1884.14	−1.99803
$944$	0	0
$945$	0	0
$946$	0	0
$947$	180.974	0.191103	0.0955514	−	0.995424i	$-0.469539\pi$
$947$	180.974	0.191103	0.0955514	+	0.995424i	$0.469539\pi$
$948$	0	0
$949$	0	0
$950$	−1308.72	−1.37760
$951$	0	0
$952$	−389.837	−0.409493
$953$	−1887.91	−1.98102	−0.990510	−	0.137437i	$-0.956113\pi$
$953$	−1887.91	−1.98102	−0.990510	+	0.137437i	$0.956113\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	1217.25	1.27062
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	2440.85	2.53727
$963$	1145.18	1.18918
$964$	0	0
$965$	0	0
$966$	501.874	0.519538
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	1037.19	1.07148
$969$	164.180	0.169432
$970$	0	0
$971$	−1640.05	−1.68903	−0.844514	−	0.535534i	$-0.820110\pi$
$971$	−1640.05	−1.68903	−0.844514	+	0.535534i	$0.820110\pi$
$972$	144.271	0.148427
$973$	0	0
$974$	1210.08	1.24238
$975$	546.131	0.560135
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	217.734	0.222632
$979$	0	0
$980$	0	0
$981$	0	0
$982$	1507.22	1.53485
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	304.993	0.309952
$985$	0	0
$986$	0	0
$987$	−109.189	−0.110627
$988$	562.958	0.569795
$989$	2820.17	2.85153
$990$	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
$997$	−1395.29	−1.39949	−0.699744	−	0.714394i	$-0.746703\pi$
$997$	−1395.29	−1.39949	−0.699744	+	0.714394i	$0.746703\pi$
$998$	0	0
$999$	807.286	0.808094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.b.286.3	yes	7
7.6	odd	2		287.3.d.a.286.3	✓	7
41.40	even	2		287.3.d.a.286.3	✓	7
287.286	odd	2	CM	287.3.d.b.286.3	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.a.286.3	✓	7	7.6	odd	2
287.3.d.a.286.3	✓	7	41.40	even	2
287.3.d.b.286.3	yes	7	1.1	even	1	trivial
287.3.d.b.286.3	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)

\(f(q)\)	\(=\)	\(q-1.79777 q^{2} -0.867827 q^{3} -0.768030 q^{4} +1.56015 q^{6} +7.00000 q^{7} +8.57181 q^{8} -8.24688 q^{9} +O(q^{10})\)	\(q-1.79777 q^{2} -0.867827 q^{3} -0.768030 q^{4} +1.56015 q^{6} +7.00000 q^{7} +8.57181 q^{8} -8.24688 q^{9} +0.666517 q^{12} -25.1724 q^{13} -12.5844 q^{14} -12.3380 q^{16} -6.49699 q^{17} +14.8260 q^{18} +29.1188 q^{19} -6.07479 q^{21} +45.9547 q^{23} -7.43885 q^{24} +25.0000 q^{25} +45.2541 q^{26} +14.9673 q^{27} -5.37621 q^{28} -12.1064 q^{32} +11.6801 q^{34} +6.33385 q^{36} +53.9367 q^{37} -52.3489 q^{38} +21.8453 q^{39} -41.0000 q^{41} +10.9211 q^{42} +61.3685 q^{43} -82.6159 q^{46} +17.9741 q^{47} +10.7073 q^{48} +49.0000 q^{49} -44.9442 q^{50} +5.63827 q^{51} +19.3331 q^{52} -26.9077 q^{54} +60.0027 q^{56} -25.2701 q^{57} -57.7281 q^{63} +71.1165 q^{64} +4.98989 q^{68} -39.8807 q^{69} -70.6907 q^{72} -96.9656 q^{74} -21.6957 q^{75} -22.3641 q^{76} -39.2727 q^{78} +61.2329 q^{81} +73.7085 q^{82} +4.66562 q^{84} -110.326 q^{86} +161.824 q^{89} -176.207 q^{91} -35.2946 q^{92} -32.3132 q^{94} +10.5062 q^{96} +71.9895 q^{97} -88.0906 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 28 q^{4} + 49 q^{7} + 63 q^{9}+O(q^{10}) \) 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

Varieties

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Database

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