LMFDB - Embedded newform 287.3.d.a.286.7

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			286.7
Root			$2.80779$ 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)

$f(q)$	$=$	$q+3.88369 q^{2} +1.79404 q^{3} +11.0831 q^{4} +6.96751 q^{6} -7.00000 q^{7} +27.5084 q^{8} -5.78141 q^{9} +O(q^{10})$	$q+3.88369 q^{2} +1.79404 q^{3} +11.0831 q^{4} +6.96751 q^{6} -7.00000 q^{7} +27.5084 q^{8} -5.78141 q^{9} +19.8835 q^{12} +0.743300 q^{13} -27.1858 q^{14} +62.5018 q^{16} +30.1432 q^{17} -22.4532 q^{18} -37.2437 q^{19} -12.5583 q^{21} -40.5180 q^{23} +49.3512 q^{24} +25.0000 q^{25} +2.88675 q^{26} -26.5185 q^{27} -77.5814 q^{28} +132.704 q^{32} +117.067 q^{34} -64.0757 q^{36} -61.3957 q^{37} -144.643 q^{38} +1.33351 q^{39} +41.0000 q^{41} -48.7725 q^{42} -8.84177 q^{43} -157.359 q^{46} +93.9519 q^{47} +112.131 q^{48} +49.0000 q^{49} +97.0923 q^{50} +54.0783 q^{51} +8.23804 q^{52} -102.990 q^{54} -192.559 q^{56} -66.8169 q^{57} +40.4699 q^{63} +265.375 q^{64} +334.079 q^{68} -72.6911 q^{69} -159.037 q^{72} -238.442 q^{74} +44.8511 q^{75} -412.774 q^{76} +5.17895 q^{78} +4.45741 q^{81} +159.231 q^{82} -139.184 q^{84} -34.3387 q^{86} -36.2726 q^{89} -5.20310 q^{91} -449.063 q^{92} +364.880 q^{94} +238.077 q^{96} -13.3032 q^{97} +190.301 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.88369	1.94185	0.970923	−	0.239394i	$-0.0769486\pi$
$2$	3.88369	1.94185	0.970923	+	0.239394i	$0.0769486\pi$
$3$	1.79404	0.598014	0.299007	−	0.954251i	$-0.403345\pi$
$3$	1.79404	0.598014	0.299007	+	0.954251i	$0.403345\pi$
$4$	11.0831	2.77076
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	6.96751	1.16125
$7$	−7.00000	−1.00000
$7$	−7.00000	−1.00000
$8$	27.5084	3.43855
$9$	−5.78141	−0.642379
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	19.8835	1.65696
$13$	0.743300	0.0571769	0.0285885	−	0.999591i	$-0.490899\pi$
$13$	0.743300	0.0571769	0.0285885	+	0.999591i	$0.490899\pi$
$14$	−27.1858	−1.94185
$15$	0	0
$16$	62.5018	3.90636
$17$	30.1432	1.77313	0.886566	−	0.462602i	$-0.153084\pi$
$17$	30.1432	1.77313	0.886566	+	0.462602i	$0.153084\pi$
$18$	−22.4532	−1.24740
$19$	−37.2437	−1.96020	−0.980098	−	0.198512i	$-0.936389\pi$
$19$	−37.2437	−1.96020	−0.980098	+	0.198512i	$0.936389\pi$
$20$	0	0
$21$	−12.5583	−0.598014
$22$	0	0
$23$	−40.5180	−1.76165	−0.880827	−	0.473439i	$-0.843013\pi$
$23$	−40.5180	−1.76165	−0.880827	+	0.473439i	$0.843013\pi$
$24$	49.3512	2.05630
$25$	25.0000	1.00000
$26$	2.88675	0.111029
$27$	−26.5185	−0.982166
$28$	−77.5814	−2.77076
$29$	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			$\pi$
$32$	132.704	4.14701
$33$	0	0
$34$	117.067	3.44315
$35$	0	0
$36$	−64.0757	−1.77988
$37$	−61.3957	−1.65934	−0.829672	−	0.558251i	$-0.811473\pi$
$37$	−61.3957	−1.65934	−0.829672	+	0.558251i	$0.811473\pi$
$38$	−144.643	−3.80640
$39$	1.33351	0.0341926
$40$	0	0
$41$	41.0000	1.00000
$41$	41.0000	1.00000
$42$	−48.7725	−1.16125
$43$	−8.84177	−0.205622	−0.102811	−	0.994701i	$-0.532784\pi$
$43$	−8.84177	−0.205622	−0.102811	+	0.994701i	$0.532784\pi$
$44$	0	0
$45$	0	0
$46$	−157.359	−3.42086
$47$	93.9519	1.99898	0.999488	−	0.0319957i	$-0.0101863\pi$
$47$	93.9519	1.99898	0.999488	+	0.0319957i	$0.0101863\pi$
$48$	112.131	2.33606
$49$	49.0000	1.00000
$50$	97.0923	1.94185
$51$	54.0783	1.06036
$52$	8.23804	0.158424
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	−102.990	−1.90721
$55$	0	0
$56$	−192.559	−3.43855
$57$	−66.8169	−1.17223
$58$	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
$63$	40.4699	0.642379
$64$	265.375	4.14648
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	334.079	4.91293
$69$	−72.6911	−1.05349
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	−159.037	−2.20885
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−238.442	−3.22219
$75$	44.8511	0.598014
$76$	−412.774	−5.43124
$77$	0	0
$78$	5.17895	0.0663968
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	4.45741	0.0550298
$82$	159.231	1.94185
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	−139.184	−1.65696
$85$	0	0
$86$	−34.3387	−0.399287
$87$	0	0
$88$	0	0
$89$	−36.2726	−0.407558	−0.203779	−	0.979017i	$-0.565322\pi$
$89$	−36.2726	−0.407558	−0.203779	+	0.979017i	$0.565322\pi$
$90$	0	0
$91$	−5.20310	−0.0571769
$92$	−449.063	−4.88112
$93$	0	0
$94$	364.880	3.88170
$95$	0	0
$96$	238.077	2.47997
$97$	−13.3032	−0.137147	−0.0685734	−	0.997646i	$-0.521845\pi$
$97$	−13.3032	−0.137147	−0.0685734	+	0.997646i	$0.521845\pi$
$98$	190.301	1.94185
$99$	0	0
$100$	277.076	2.77076
$101$	−140.239	−1.38851	−0.694255	−	0.719729i	$-0.744266\pi$
$101$	−140.239	−1.38851	−0.694255	+	0.719729i	$0.744266\pi$
$102$	210.023	2.05905
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	20.4470	0.196606
$105$	0	0
$106$	0	0
$107$	40.7263	0.380619	0.190310	−	0.981724i	$-0.439051\pi$
$107$	40.7263	0.380619	0.190310	+	0.981724i	$0.439051\pi$
$108$	−293.906	−2.72135
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	−110.147	−0.992312
$112$	−437.513	−3.90636
$113$	213.354	1.88809	0.944046	−	0.329814i	$-0.106986\pi$
$113$	213.354	1.88809	0.944046	+	0.329814i	$0.106986\pi$
$114$	−259.496	−2.27628
$115$	0	0
$116$	0	0
$117$	−4.29732	−0.0367293
$118$	0	0
$119$	−211.003	−1.77313
$120$	0	0
$121$	121.000	1.00000
$122$	0	0
$123$	73.5557	0.598014
$124$	0	0
$125$	0	0
$126$	157.172	1.24740
$127$	162.037	1.27588	0.637942	−	0.770084i	$-0.279786\pi$
$127$	162.037	1.27588	0.637942	+	0.770084i	$0.279786\pi$
$128$	499.817	3.90482
$129$	−15.8625	−0.122965
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	260.706	1.96020
$134$	0	0
$135$	0	0
$136$	829.192	6.09700
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	−282.310	−2.04572
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	168.554	1.19542
$142$	0	0
$143$	0	0
$144$	−361.349	−2.50937
$145$	0	0
$146$	0	0
$147$	87.9081	0.598014
$148$	−680.452	−4.59765
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	174.188	1.16125
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	−1024.52	−6.74023
$153$	−174.270	−1.13902
$154$	0	0
$155$	0	0
$156$	14.7794	0.0947397
$157$	182.736	1.16392	0.581962	−	0.813216i	$-0.302285\pi$
$157$	182.736	1.16392	0.581962	+	0.813216i	$0.302285\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	283.626	1.76165
$162$	17.3112	0.106859
$163$	−253.568	−1.55563	−0.777817	−	0.628491i	$-0.783673\pi$
$163$	−253.568	−1.55563	−0.777817	+	0.628491i	$0.783673\pi$
$164$	454.405	2.77076
$165$	0	0
$166$	0	0
$167$	−154.199	−0.923346	−0.461673	−	0.887050i	$-0.652751\pi$
$167$	−154.199	−0.923346	−0.461673	+	0.887050i	$0.652751\pi$
$168$	−345.458	−2.05630
$169$	−168.448	−0.996731
$170$	0	0
$171$	215.321	1.25919
$172$	−97.9937	−0.569731
$173$	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
$178$	−140.872	−0.791414
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	−351.055	−1.93953	−0.969765	−	0.244041i	$-0.921527\pi$
$181$	−351.055	−1.93953	−0.969765	+	0.244041i	$0.921527\pi$
$182$	−20.2072	−0.111029
$183$	0	0
$184$	−1114.59	−6.05753
$185$	0	0
$186$	0	0
$187$	0	0
$188$	1041.27	5.53869
$189$	185.629	0.982166
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	476.094	2.47966
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	−51.6657	−0.266318
$195$	0	0
$196$	543.070	2.77076
$197$	310.274	1.57500	0.787498	−	0.616317i	$-0.211376\pi$
$197$	310.274	1.57500	0.787498	+	0.616317i	$0.211376\pi$
$198$	0	0
$199$	19.9200	0.100101	0.0500503	−	0.998747i	$-0.484062\pi$
$199$	19.9200	0.100101	0.0500503	+	0.998747i	$0.484062\pi$
$200$	687.710	3.43855
$201$	0	0
$202$	−544.647	−2.69627
$203$	0	0
$204$	599.352	2.93800
$205$	0	0
$206$	0	0
$207$	234.251	1.13165
$208$	46.4576	0.223354
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	158.168	0.739104
$215$	0	0
$216$	−729.481	−3.37722
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	22.4055	0.101382
$222$	−427.775	−1.92692
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	−928.930	−4.14701
$225$	−144.535	−0.642379
$226$	828.603	3.66638
$227$	202.000	0.889868	0.444934	−	0.895563i	$-0.353227\pi$
$227$	202.000	0.889868	0.444934	+	0.895563i	$0.353227\pi$
$228$	−740.535	−3.24796
$229$	453.619	1.98087	0.990436	−	0.137976i	$-0.0440598\pi$
$229$	453.619	1.98087	0.990436	+	0.137976i	$0.0440598\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−16.6895	−0.0713225
$235$	0	0
$236$	0	0
$237$	0	0
$238$	−819.469	−3.44315
$239$	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			$\pi$
$242$	469.927	1.94185
$243$	246.663	1.01507
$244$	0	0
$245$	0	0
$246$	285.668	1.16125
$247$	−27.6833	−0.112078
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	448.530	1.77988
$253$	0	0
$254$	629.303	2.47757
$255$	0	0
$256$	879.635	3.43607
$257$	−434.934	−1.69235	−0.846175	−	0.532905i	$-0.821100\pi$
$257$	−434.934	−1.69235	−0.846175	+	0.532905i	$0.821100\pi$
$258$	−61.6051	−0.238779
$259$	429.770	1.65934
$260$	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
$266$	1012.50	3.80640
$267$	−65.0746	−0.243725
$268$	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			$\pi$
$272$	1884.01	6.92650
$273$	−9.33459	−0.0341926
$274$	0	0
$275$	0	0
$276$	−805.639	−2.91898
$277$	−335.213	−1.21015	−0.605077	−	0.796167i	$-0.706858\pi$
$277$	−335.213	−1.21015	−0.605077	+	0.796167i	$0.706858\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	654.610	2.32131
$283$	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
$288$	−767.218	−2.66395
$289$	619.615	2.14400
$290$	0	0
$291$	−23.8666	−0.0820158
$292$	0	0
$293$	−422.000	−1.44027	−0.720137	−	0.693832i	$-0.755921\pi$
$293$	−422.000	−1.44027	−0.720137	+	0.693832i	$0.755921\pi$
$294$	341.408	1.16125
$295$	0	0
$296$	−1688.90	−5.70574
$297$	0	0
$298$	0	0
$299$	−30.1171	−0.100726
$300$	497.087	1.65696
$301$	61.8924	0.205622
$302$	0	0
$303$	−251.596	−0.830349
$304$	−2327.80	−7.65724
$305$	0	0
$306$	−676.813	−2.21181
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−275.043	−0.884381	−0.442191	−	0.896921i	$-0.645799\pi$
$311$	−275.043	−0.884381	−0.442191	+	0.896921i	$0.645799\pi$
$312$	36.6828	0.117573
$313$	−203.767	−0.651012	−0.325506	−	0.945540i	$-0.605535\pi$
$313$	−203.767	−0.651012	−0.325506	+	0.945540i	$0.605535\pi$
$314$	709.691	2.26016
$315$	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
$321$	73.0647	0.227616
$322$	1101.52	3.42086
$323$	−1122.65	−3.47569
$324$	49.4017	0.152474
$325$	18.5825	0.0571769
$326$	−984.781	−3.02080
$327$	0	0
$328$	1127.84	3.43855
$329$	−657.663	−1.99898
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	354.954	1.06593
$334$	−598.860	−1.79299
$335$	0	0
$336$	−784.917	−2.33606
$337$	338.056	1.00313	0.501566	−	0.865119i	$-0.332757\pi$
$337$	338.056	1.00313	0.501566	+	0.865119i	$0.332757\pi$
$338$	−654.198	−1.93550
$339$	382.767	1.12911
$340$	0	0
$341$	0	0
$342$	836.242	2.44515
$343$	−343.000	−1.00000
$344$	−243.223	−0.707043
$345$	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			$\pi$
$350$	−679.646	−1.94185
$351$	−19.7112	−0.0561572
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	−402.011	−1.12925
$357$	−378.548	−1.06036
$358$	0	0
$359$	−453.407	−1.26297	−0.631486	−	0.775387i	$-0.717555\pi$
$359$	−453.407	−1.26297	−0.631486	+	0.775387i	$0.717555\pi$
$360$	0	0
$361$	1026.10	2.84237
$362$	−1363.39	−3.76627
$363$	217.079	0.598014
$364$	−57.6662	−0.158424
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−2532.45	−6.88166
$369$	−237.038	−0.642379
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−597.506	−1.60189	−0.800946	−	0.598737i	$-0.795670\pi$
$373$	−597.506	−1.60189	−0.800946	+	0.598737i	$0.795670\pi$
$374$	0	0
$375$	0	0
$376$	2584.46	6.87357
$377$	0	0
$378$	720.927	1.90721
$379$	−249.099	−0.657252	−0.328626	−	0.944460i	$-0.606586\pi$
$379$	−249.099	−0.657252	−0.328626	+	0.944460i	$0.606586\pi$
$380$	0	0
$381$	290.702	0.762997
$382$	0	0
$383$	−185.531	−0.484416	−0.242208	−	0.970224i	$-0.577872\pi$
$383$	−185.531	−0.484416	−0.242208	+	0.970224i	$0.577872\pi$
$384$	896.693	2.33514
$385$	0	0
$386$	0	0
$387$	51.1179	0.132088
$388$	−147.441	−0.380002
$389$	−638.486	−1.64135	−0.820677	−	0.571393i	$-0.806403\pi$
$389$	−638.486	−1.64135	−0.820677	+	0.571393i	$0.806403\pi$
$390$	0	0
$391$	−1221.34	−3.12364
$392$	1347.91	3.43855
$393$	0	0
$394$	1205.01	3.05840
$395$	0	0
$396$	0	0
$397$	682.000	1.71788	0.858942	−	0.512073i	$-0.171122\pi$
$397$	682.000	1.71788	0.858942	+	0.512073i	$0.171122\pi$
$398$	77.3632	0.194380
$399$	467.718	1.17223
$400$	1562.55	3.90636
$401$	−323.182	−0.805941	−0.402970	−	0.915213i	$-0.632022\pi$
$401$	−323.182	−0.805941	−0.402970	+	0.915213i	$0.632022\pi$
$402$	0	0
$403$	0	0
$404$	−1554.28	−3.84723
$405$	0	0
$406$	0	0
$407$	0	0
$408$	1487.61	3.64609
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	909.760	2.19749
$415$	0	0
$416$	98.6391	0.237113
$417$	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
$423$	−543.174	−1.28410
$424$	0	0
$425$	753.581	1.77313
$426$	0	0
$427$	0	0
$428$	451.372	1.05461
$429$	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	$0.607651\pi$
$432$	−1657.45	−3.83670
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1509.04	3.45319
$438$	0	0
$439$	365.271	0.832051	0.416026	−	0.909353i	$-0.363423\pi$
$439$	365.271	0.832051	0.416026	+	0.909353i	$0.363423\pi$
$440$	0	0
$441$	−283.289	−0.642379
$442$	87.0160	0.196869
$443$	−582.294	−1.31443	−0.657216	−	0.753702i	$-0.728266\pi$
$443$	−582.294	−1.31443	−0.657216	+	0.753702i	$0.728266\pi$
$444$	−1220.76	−2.74946
$445$	0	0
$446$	0	0
$447$	0	0
$448$	−1857.62	−4.14648
$449$	−763.548	−1.70055	−0.850276	−	0.526337i	$-0.823565\pi$
$449$	−763.548	−1.70055	−0.850276	+	0.526337i	$0.823565\pi$
$450$	−561.330	−1.24740
$451$	0	0
$452$	2364.62	5.23146
$453$	0	0
$454$	784.505	1.72799
$455$	0	0
$456$	−1838.02	−4.03075
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	1761.72	3.84655
$459$	−799.353	−1.74151
$460$	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			$\pi$
$468$	−47.6275	−0.101768
$469$	0	0
$470$	0	0
$471$	327.836	0.696043
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−931.093	−1.96020
$476$	−2338.55	−4.91293
$477$	0	0
$478$	0	0
$479$	−904.092	−1.88746	−0.943728	−	0.330722i	$-0.892708\pi$
$479$	−904.092	−1.88746	−0.943728	+	0.330722i	$0.892708\pi$
$480$	0	0
$481$	−45.6355	−0.0948762
$482$	0	0
$483$	508.838	1.05349
$484$	1341.05	2.77076
$485$	0	0
$486$	957.963	1.97112
$487$	−970.078	−1.99195	−0.995974	−	0.0896447i	$-0.971427\pi$
$487$	−970.078	−1.99195	−0.995974	+	0.0896447i	$0.971427\pi$
$488$	0	0
$489$	−454.912	−0.930291
$490$	0	0
$491$	977.207	1.99024	0.995119	−	0.0986847i	$-0.0314635\pi$
$491$	977.207	1.99024	0.995119	+	0.0986847i	$0.0314635\pi$
$492$	815.222	1.65696
$493$	0	0
$494$	−107.513	−0.217638
$495$	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
$501$	−276.639	−0.552174
$502$	0	0
$503$	662.200	1.31650	0.658251	−	0.752799i	$-0.271297\pi$
$503$	662.200	1.31650	0.658251	+	0.752799i	$0.271297\pi$
$504$	1113.26	2.20885
$505$	0	0
$506$	0	0
$507$	−302.202	−0.596059
$508$	1795.87	3.53517
$509$	−949.182	−1.86480	−0.932398	−	0.361432i	$-0.882288\pi$
$509$	−949.182	−1.86480	−0.932398	+	0.361432i	$0.882288\pi$
$510$	0	0
$511$	0	0
$512$	1416.96	2.76750
$513$	987.647	1.92524
$514$	−1689.15	−3.28628
$515$	0	0
$516$	−175.805	−0.340707
$517$	0	0
$518$	1669.09	3.22219
$519$	0	0
$520$	0	0
$521$	801.267	1.53794	0.768970	−	0.639285i	$-0.220769\pi$
$521$	801.267	1.53794	0.768970	+	0.639285i	$0.220769\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−313.957	−0.598014
$526$	0	0
$527$	0	0
$528$	0	0
$529$	1112.71	2.10342
$530$	0	0
$531$	0	0
$532$	2889.42	5.43124
$533$	30.4753	0.0571769
$534$	−252.730	−0.473277
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	54.6565	0.101029	0.0505143	−	0.998723i	$-0.483914\pi$
$541$	54.6565	0.101029	0.0505143	+	0.998723i	$0.483914\pi$
$542$	0	0
$543$	−629.807	−1.15987
$544$	4000.14	7.35319
$545$	0	0
$546$	−36.2526	−0.0663968
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	−1999.61	−3.62249
$553$	0	0
$554$	−1301.86	−2.34993
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	−6.57209	−0.0117569
$560$	0	0
$561$	0	0
$562$	0	0
$563$	281.707	0.500367	0.250183	−	0.968198i	$-0.419509\pi$
$563$	281.707	0.500367	0.250183	+	0.968198i	$0.419509\pi$
$564$	1868.09	3.31221
$565$	0	0
$566$	0	0
$567$	−31.2019	−0.0550298
$568$	0	0
$569$	1136.74	1.99778	0.998890	−	0.0471008i	$-0.0149982\pi$
$569$	1136.74	1.99778	0.998890	+	0.0471008i	$0.0149982\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	−1114.62	−1.94185
$575$	−1012.95	−1.76165
$576$	−1534.24	−2.66361
$577$	1049.71	1.81926	0.909630	−	0.415419i	$-0.136365\pi$
$577$	1049.71	1.81926	0.909630	+	0.415419i	$0.136365\pi$
$578$	2406.39	4.16331
$579$	0	0
$580$	0	0
$581$	0	0
$582$	−92.6905	−0.159262
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−1638.92	−2.79679
$587$	26.2545	0.0447265	0.0223633	−	0.999750i	$-0.492881\pi$
$587$	26.2545	0.0447265	0.0223633	+	0.999750i	$0.492881\pi$
$588$	974.290	1.65696
$589$	0	0
$590$	0	0
$591$	556.645	0.941870
$592$	−3837.35	−6.48200
$593$	−820.295	−1.38330	−0.691648	−	0.722235i	$-0.743115\pi$
$593$	−820.295	−1.38330	−0.691648	+	0.722235i	$0.743115\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	35.7374	0.0598616
$598$	−116.965	−0.195594
$599$	−376.700	−0.628881	−0.314441	−	0.949277i	$-0.601817\pi$
$599$	−376.700	−0.628881	−0.314441	+	0.949277i	$0.601817\pi$
$600$	1233.78	2.05630
$601$	−445.454	−0.741189	−0.370594	−	0.928795i	$-0.620846\pi$
$601$	−445.454	−0.741189	−0.370594	+	0.928795i	$0.620846\pi$
$602$	240.371	0.399287
$603$	0	0
$604$	0	0
$605$	0	0
$606$	−977.119	−1.61241
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	−4942.40	−8.12895
$609$	0	0
$610$	0	0
$611$	69.8344	0.114295
$612$	−1931.45	−3.15596
$613$	1015.79	1.65709	0.828543	−	0.559925i	$-0.189170\pi$
$613$	1015.79	1.65709	0.828543	+	0.559925i	$0.189170\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	129.821	0.210407	0.105203	−	0.994451i	$-0.466451\pi$
$617$	129.821	0.210407	0.105203	+	0.994451i	$0.466451\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	1074.48	1.73024
$622$	−1068.18	−1.71733
$623$	253.908	0.407558
$624$	83.3470	0.133569
$625$	625.000	1.00000
$626$	−791.367	−1.26416
$627$	0	0
$628$	2025.27	3.22496
$629$	−1850.67	−2.94224
$630$	0	0
$631$	946.059	1.49930	0.749651	−	0.661834i	$-0.230221\pi$
$631$	946.059	1.49930	0.749651	+	0.661834i	$0.230221\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	36.4217	0.0571769
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	283.761	0.441995
$643$	−1173.95	−1.82574	−0.912871	−	0.408248i	$-0.866140\pi$
$643$	−1173.95	−1.82574	−0.912871	+	0.408248i	$0.866140\pi$
$644$	3143.44	4.88112
$645$	0	0
$646$	−4360.01	−6.74925
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	122.616	0.189222
$649$	0	0
$650$	72.1687	0.111029
$651$	0	0
$652$	−2810.31	−4.31029
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	2562.58	3.90636
$657$	0	0
$658$	−2554.16	−3.88170
$659$	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
$663$	40.1964	0.0606280
$664$	0	0
$665$	0	0
$666$	1378.53	2.06987
$667$	0	0
$668$	−1708.99	−2.55837
$669$	0	0
$670$	0	0
$671$	0	0
$672$	−1666.54	−2.47997
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	1312.90	1.94793
$675$	−662.962	−0.982166
$676$	−1866.91	−2.76170
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	1486.55	2.19255
$679$	93.1227	0.137147
$680$	0	0
$681$	362.397	0.532154
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	2386.42	3.48891
$685$	0	0
$686$	−1332.11	−1.94185
$687$	813.813	1.18459
$688$	−552.627	−0.803236
$689$	0	0
$690$	0	0
$691$	1267.31	1.83402	0.917011	−	0.398861i	$-0.130594\pi$
$691$	1267.31	1.83402	0.917011	+	0.398861i	$0.130594\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	1235.87	1.77313
$698$	0	0
$699$	0	0
$700$	−1939.53	−2.77076
$701$	−227.299	−0.324249	−0.162125	−	0.986770i	$-0.551835\pi$
$701$	−227.299	−0.324249	−0.162125	+	0.986770i	$0.551835\pi$
$702$	−76.5522	−0.109049
$703$	2286.61	3.25264
$704$	0	0
$705$	0	0
$706$	0	0
$707$	981.676	1.38851
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	−997.801	−1.40141
$713$	0	0
$714$	−1470.16	−2.05905
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−1760.89	−2.45250
$719$	1186.00	1.64951	0.824757	−	0.565488i	$-0.191312\pi$
$719$	1186.00	1.64951	0.824757	+	0.565488i	$0.191312\pi$
$720$	0	0
$721$	0	0
$722$	3985.04	5.51945
$723$	0	0
$724$	−3890.76	−5.37398
$725$	0	0
$726$	843.068	1.16125
$727$	456.173	0.627473	0.313736	−	0.949510i	$-0.398419\pi$
$727$	456.173	0.627473	0.313736	+	0.949510i	$0.398419\pi$
$728$	−143.129	−0.196606
$729$	402.407	0.551999
$730$	0	0
$731$	−266.520	−0.364596
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	−5376.92	−7.30559
$737$	0	0
$738$	−920.582	−1.24740
$739$	1447.78	1.95911	0.979554	−	0.201182i	$-0.0644783\pi$
$739$	1447.78	1.95911	0.979554	+	0.201182i	$0.0644783\pi$
$740$	0	0
$741$	−49.6650	−0.0670243
$742$	0	0
$743$	−771.806	−1.03877	−0.519385	−	0.854540i	$-0.673839\pi$
$743$	−771.806	−1.03877	−0.519385	+	0.854540i	$0.673839\pi$
$744$	0	0
$745$	0	0
$746$	−2320.53	−3.11063
$747$	0	0
$748$	0	0
$749$	−285.084	−0.380619
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	5872.16	7.80873
$753$	0	0
$754$	0	0
$755$	0	0
$756$	2057.34	2.72135
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	−967.422	−1.27628
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	1129.00	1.48162
$763$	0	0
$764$	0	0
$765$	0	0
$766$	−720.546	−0.940661
$767$	0	0
$768$	1578.10	2.05482
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	−780.290	−1.01205
$772$	0	0
$773$	−1371.05	−1.77368	−0.886839	−	0.462078i	$-0.847104\pi$
$773$	−1371.05	−1.77368	−0.886839	+	0.462078i	$0.847104\pi$
$774$	198.526	0.256494
$775$	0	0
$776$	−365.951	−0.471586
$777$	771.026	0.992312
$778$	−2479.68	−3.18725
$779$	−1526.99	−1.96020
$780$	0	0
$781$	0	0
$782$	−4743.33	−6.06563
$783$	0	0
$784$	3062.59	3.90636
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	3438.79	4.36394
$789$	0	0
$790$	0	0
$791$	−1493.48	−1.88809
$792$	0	0
$793$	0	0
$794$	2648.68	3.33587
$795$	0	0
$796$	220.775	0.277355
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	1816.47	2.27628
$799$	2832.01	3.54445
$800$	3317.61	4.14701
$801$	209.707	0.261806
$802$	−1255.14	−1.56501
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−3857.76	−4.77446
$809$	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
$816$	3379.99	4.14215
$817$	329.300	0.403060
$818$	0	0
$819$	30.0813	0.0367293
$820$	0	0
$821$	−250.529	−0.305151	−0.152576	−	0.988292i	$-0.548757\pi$
$821$	−250.529	−0.305151	−0.152576	+	0.988292i	$0.548757\pi$
$822$	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			$\pi$
$828$	2596.22	3.13553
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	−601.386	−0.723689
$832$	197.253	0.237083
$833$	1477.02	1.77313
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	1639.10	1.95364	0.976819	−	0.214066i	$-0.0686709\pi$
$839$	1639.10	1.95364	0.976819	+	0.214066i	$0.0686709\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	−2109.52	−2.49352
$847$	−847.000	−1.00000
$848$	0	0
$849$	0	0
$850$	2926.68	3.44315
$851$	2487.63	2.92319
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	1120.31	1.30878
$857$	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
$861$	−514.890	−0.598014
$862$	−1110.74	−1.28856
$863$	578.000	0.669757	0.334878	−	0.942261i	$-0.391305\pi$
$863$	578.000	0.669757	0.334878	+	0.942261i	$0.391305\pi$
$864$	−3519.12	−4.07305
$865$	0	0
$866$	0	0
$867$	1111.62	1.28214
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	76.9115	0.0881003
$874$	5860.66	6.70556
$875$	0	0
$876$	0	0
$877$	349.230	0.398210	0.199105	−	0.979978i	$-0.436197\pi$
$877$	349.230	0.398210	0.199105	+	0.979978i	$0.436197\pi$
$878$	1418.60	1.61572
$879$	−757.086	−0.861304
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	−1100.21	−1.24740
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	248.321	0.280906
$885$	0	0
$886$	−2261.45	−2.55243
$887$	−1731.87	−1.95250	−0.976249	−	0.216651i	$-0.930487\pi$
$887$	−1731.87	−1.95250	−0.976249	+	0.216651i	$0.930487\pi$
$888$	−3029.95	−3.41211
$889$	−1134.26	−1.27588
$890$	0	0
$891$	0	0
$892$	0	0
$893$	−3499.12	−3.91839
$894$	0	0
$895$	0	0
$896$	−3498.72	−3.90482
$897$	−54.0313	−0.0602356
$898$	−2965.38	−3.30221
$899$	0	0
$900$	−1601.89	−1.77988
$901$	0	0
$902$	0	0
$903$	111.038	0.122965
$904$	5869.03	6.49230
$905$	0	0
$906$	0	0
$907$	−1813.18	−1.99910	−0.999549	−	0.0300296i	$-0.990440\pi$
$907$	−1813.18	−1.99910	−0.999549	+	0.0300296i	$0.990440\pi$
$908$	2238.78	2.46561
$909$	810.782	0.891949
$910$	0	0
$911$	435.007	0.477505	0.238752	−	0.971080i	$-0.423262\pi$
$911$	435.007	0.477505	0.238752	+	0.971080i	$0.423262\pi$
$912$	−4176.18	−4.57914
$913$	0	0
$914$	0	0
$915$	0	0
$916$	5027.49	5.48852
$917$	0	0
$918$	−3104.44	−3.38174
$919$	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
$925$	−1534.89	−1.65934
$926$	0	0
$927$	0	0
$928$	0	0
$929$	1518.87	1.63495	0.817476	−	0.575962i	$-0.195373\pi$
$929$	1518.87	1.63495	0.817476	+	0.575962i	$0.195373\pi$
$930$	0	0
$931$	−1824.94	−1.96020
$932$	0	0
$933$	−493.438	−0.528873
$934$	0	0
$935$	0	0
$936$	−118.212	−0.126295
$937$	1307.00	1.39488	0.697439	−	0.716644i	$-0.254323\pi$
$937$	1307.00	1.39488	0.697439	+	0.716644i	$0.254323\pi$
$938$	0	0
$939$	−365.566	−0.389315
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	1273.22	1.35161
$943$	−1661.24	−1.76165
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−981.068	−1.03597	−0.517987	−	0.855388i	$-0.673319\pi$
$947$	−981.068	−1.03597	−0.517987	+	0.855388i	$0.673319\pi$
$948$	0	0
$949$	0	0
$950$	−3616.08	−3.80640
$951$	0	0
$952$	−5804.34	−6.09700
$953$	164.712	0.172836	0.0864178	−	0.996259i	$-0.472458\pi$
$953$	164.712	0.172836	0.0864178	+	0.996259i	$0.472458\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	−3511.21	−3.66515
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	−177.234	−0.184235
$963$	−235.455	−0.244502
$964$	0	0
$965$	0	0
$966$	1976.17	2.04572
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	3328.51	3.43855
$969$	−2014.08	−2.07851
$970$	0	0
$971$	1835.66	1.89049	0.945243	−	0.326368i	$-0.105825\pi$
$971$	1835.66	1.89049	0.945243	+	0.326368i	$0.105825\pi$
$972$	2733.78	2.81253
$973$	0	0
$974$	−3767.48	−3.86805
$975$	33.3378	0.0341926
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	−1766.74	−1.80648
$979$	0	0
$980$	0	0
$981$	0	0
$982$	3795.17	3.86473
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	2023.40	2.05630
$985$	0	0
$986$	0	0
$987$	−1179.88	−1.19542
$988$	−306.815	−0.310542
$989$	358.251	0.362236
$990$	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
$997$	−639.045	−0.640968	−0.320484	−	0.947254i	$-0.603846\pi$
$997$	−639.045	−0.640968	−0.320484	+	0.947254i	$0.603846\pi$
$998$	0	0
$999$	1628.12	1.62975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.a.286.7	✓	7
7.6	odd	2		287.3.d.b.286.7	yes	7
41.40	even	2		287.3.d.b.286.7	yes	7
287.286	odd	2	CM	287.3.d.a.286.7	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.a.286.7	✓	7	1.1	even	1	trivial
287.3.d.a.286.7	✓	7	287.286	odd	2	CM
287.3.d.b.286.7	yes	7	7.6	odd	2
287.3.d.b.286.7	yes	7	41.40	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.88369 q^{2} +1.79404 q^{3} +11.0831 q^{4} +6.96751 q^{6} -7.00000 q^{7} +27.5084 q^{8} -5.78141 q^{9} +O(q^{10})\)	\(q+3.88369 q^{2} +1.79404 q^{3} +11.0831 q^{4} +6.96751 q^{6} -7.00000 q^{7} +27.5084 q^{8} -5.78141 q^{9} +19.8835 q^{12} +0.743300 q^{13} -27.1858 q^{14} +62.5018 q^{16} +30.1432 q^{17} -22.4532 q^{18} -37.2437 q^{19} -12.5583 q^{21} -40.5180 q^{23} +49.3512 q^{24} +25.0000 q^{25} +2.88675 q^{26} -26.5185 q^{27} -77.5814 q^{28} +132.704 q^{32} +117.067 q^{34} -64.0757 q^{36} -61.3957 q^{37} -144.643 q^{38} +1.33351 q^{39} +41.0000 q^{41} -48.7725 q^{42} -8.84177 q^{43} -157.359 q^{46} +93.9519 q^{47} +112.131 q^{48} +49.0000 q^{49} +97.0923 q^{50} +54.0783 q^{51} +8.23804 q^{52} -102.990 q^{54} -192.559 q^{56} -66.8169 q^{57} +40.4699 q^{63} +265.375 q^{64} +334.079 q^{68} -72.6911 q^{69} -159.037 q^{72} -238.442 q^{74} +44.8511 q^{75} -412.774 q^{76} +5.17895 q^{78} +4.45741 q^{81} +159.231 q^{82} -139.184 q^{84} -34.3387 q^{86} -36.2726 q^{89} -5.20310 q^{91} -449.063 q^{92} +364.880 q^{94} +238.077 q^{96} -13.3032 q^{97} +190.301 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 28 q^{4} - 49 q^{7} + 63 q^{9}+O(q^{10}) \) 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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Representations

Groups

Database

Properties

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