LMFDB - Embedded newform 1449.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1449,4,Mod(1,1449)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1449, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1449.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1449 = 3^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1449.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$85.4937675983$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} +7.00000 q^{7} +21.0000 q^{8} +O(q^{10})$

\(q-3.00000 q^{2} +1.00000 q^{4} -3.00000 q^{5} +7.00000 q^{7} +21.0000 q^{8} +9.00000 q^{10} +30.0000 q^{11} +11.0000 q^{13} -21.0000 q^{14} -71.0000 q^{16} -78.0000 q^{17} +74.0000 q^{19} -3.00000 q^{20} -90.0000 q^{22} -23.0000 q^{23} -116.000 q^{25} -33.0000 q^{26} +7.00000 q^{28} -9.00000 q^{29} +56.0000 q^{31} +45.0000 q^{32} +234.000 q^{34} -21.0000 q^{35} -169.000 q^{37} -222.000 q^{38} -63.0000 q^{40} -225.000 q^{41} +47.0000 q^{43} +30.0000 q^{44} +69.0000 q^{46} -255.000 q^{47} +49.0000 q^{49} +348.000 q^{50} +11.0000 q^{52} +102.000 q^{53} -90.0000 q^{55} +147.000 q^{56} +27.0000 q^{58} -24.0000 q^{59} +722.000 q^{61} -168.000 q^{62} +433.000 q^{64} -33.0000 q^{65} +884.000 q^{67} -78.0000 q^{68} +63.0000 q^{70} -90.0000 q^{71} +578.000 q^{73} +507.000 q^{74} +74.0000 q^{76} +210.000 q^{77} -484.000 q^{79} +213.000 q^{80} +675.000 q^{82} -756.000 q^{83} +234.000 q^{85} -141.000 q^{86} +630.000 q^{88} -1416.00 q^{89} +77.0000 q^{91} -23.0000 q^{92} +765.000 q^{94} -222.000 q^{95} +1019.00 q^{97} -147.000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	0	0
$3$	0	0
$4$	1.00000	0.125000
$5$	−3.00000	−0.268328	−0.134164	−	0.990959i	$-0.542835\pi$
$5$	−3.00000	−0.268328	−0.134164	+	0.990959i	$0.542835\pi$
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	21.0000	0.928078
$9$	0	0
$10$	9.00000	0.284605
$11$	30.0000	0.822304	0.411152	−	0.911567i	$-0.365127\pi$
$11$	30.0000	0.822304	0.411152	+	0.911567i	$0.365127\pi$
$12$	0	0
$13$	11.0000	0.234681	0.117340	−	0.993092i	$-0.462563\pi$
$13$	11.0000	0.234681	0.117340	+	0.993092i	$0.462563\pi$
$14$	−21.0000	−0.400892
$15$	0	0
$16$	−71.0000	−1.10938
$17$	−78.0000	−1.11281	−0.556405	−	0.830911i	$-0.687820\pi$
$17$	−78.0000	−1.11281	−0.556405	+	0.830911i	$0.687820\pi$
$18$	0	0
$19$	74.0000	0.893514	0.446757	−	0.894655i	$-0.352579\pi$
$19$	74.0000	0.893514	0.446757	+	0.894655i	$0.352579\pi$
$20$	−3.00000	−0.0335410
$21$	0	0
$22$	−90.0000	−0.872185
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	0	0
$25$	−116.000	−0.928000
$26$	−33.0000	−0.248917
$27$	0	0
$28$	7.00000	0.0472456
$29$	−9.00000	−0.0576296	−0.0288148	−	0.999585i	$-0.509173\pi$
$29$	−9.00000	−0.0576296	−0.0288148	+	0.999585i	$0.509173\pi$
$30$	0	0
$31$	56.0000	0.324448	0.162224	−	0.986754i	$-0.448133\pi$
$31$	56.0000	0.324448	0.162224	+	0.986754i	$0.448133\pi$
$32$	45.0000	0.248592
$33$	0	0
$34$	234.000	1.18031
$35$	−21.0000	−0.101419
$36$	0	0
$37$	−169.000	−0.750903	−0.375452	−	0.926842i	$-0.622512\pi$
$37$	−169.000	−0.750903	−0.375452	+	0.926842i	$0.622512\pi$
$38$	−222.000	−0.947715
$39$	0	0
$40$	−63.0000	−0.249029
$41$	−225.000	−0.857051	−0.428526	−	0.903530i	$-0.640967\pi$
$41$	−225.000	−0.857051	−0.428526	+	0.903530i	$0.640967\pi$
$42$	0	0
$43$	47.0000	0.166684	0.0833422	−	0.996521i	$-0.473441\pi$
$43$	47.0000	0.166684	0.0833422	+	0.996521i	$0.473441\pi$
$44$	30.0000	0.102788
$45$	0	0
$46$	69.0000	0.221163
$47$	−255.000	−0.791395	−0.395698	−	0.918381i	$-0.629497\pi$
$47$	−255.000	−0.791395	−0.395698	+	0.918381i	$0.629497\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	348.000	0.984293
$51$	0	0
$52$	11.0000	0.0293351
$53$	102.000	0.264354	0.132177	−	0.991226i	$-0.457803\pi$
$53$	102.000	0.264354	0.132177	+	0.991226i	$0.457803\pi$
$54$	0	0
$55$	−90.0000	−0.220647
$56$	147.000	0.350780
$57$	0	0
$58$	27.0000	0.0611254
$59$	−24.0000	−0.0529582	−0.0264791	−	0.999649i	$-0.508430\pi$
$59$	−24.0000	−0.0529582	−0.0264791	+	0.999649i	$0.508430\pi$
$60$	0	0
$61$	722.000	1.51545	0.757726	−	0.652572i	$-0.226310\pi$
$61$	722.000	1.51545	0.757726	+	0.652572i	$0.226310\pi$
$62$	−168.000	−0.344129
$63$	0	0
$64$	433.000	0.845703
$65$	−33.0000	−0.0629715
$66$	0	0
$67$	884.000	1.61191	0.805954	−	0.591979i	$-0.201653\pi$
$67$	884.000	1.61191	0.805954	+	0.591979i	$0.201653\pi$
$68$	−78.0000	−0.139101
$69$	0	0
$70$	63.0000	0.107571
$71$	−90.0000	−0.150437	−0.0752186	−	0.997167i	$-0.523965\pi$
$71$	−90.0000	−0.150437	−0.0752186	+	0.997167i	$0.523965\pi$
$72$	0	0
$73$	578.000	0.926709	0.463355	−	0.886173i	$-0.346646\pi$
$73$	578.000	0.926709	0.463355	+	0.886173i	$0.346646\pi$
$74$	507.000	0.796453
$75$	0	0
$76$	74.0000	0.111689
$77$	210.000	0.310802
$78$	0	0
$79$	−484.000	−0.689294	−0.344647	−	0.938732i	$-0.612001\pi$
$79$	−484.000	−0.689294	−0.344647	+	0.938732i	$0.612001\pi$
$80$	213.000	0.297677
$81$	0	0
$82$	675.000	0.909040
$83$	−756.000	−0.999780	−0.499890	−	0.866089i	$-0.666626\pi$
$83$	−756.000	−0.999780	−0.499890	+	0.866089i	$0.666626\pi$
$84$	0	0
$85$	234.000	0.298598
$86$	−141.000	−0.176796
$87$	0	0
$88$	630.000	0.763162
$89$	−1416.00	−1.68647	−0.843234	−	0.537546i	$-0.819351\pi$
$89$	−1416.00	−1.68647	−0.843234	+	0.537546i	$0.819351\pi$
$90$	0	0
$91$	77.0000	0.0887010
$92$	−23.0000	−0.0260643
$93$	0	0
$94$	765.000	0.839401
$95$	−222.000	−0.239755
$96$	0	0
$97$	1019.00	1.06664	0.533318	−	0.845915i	$-0.320945\pi$
$97$	1019.00	1.06664	0.533318	+	0.845915i	$0.320945\pi$
$98$	−147.000	−0.151523
$99$	0	0
$100$	−116.000	−0.116000
$101$	−1518.00	−1.49551	−0.747756	−	0.663974i	$-0.768869\pi$
$101$	−1518.00	−1.49551	−0.747756	+	0.663974i	$0.768869\pi$
$102$	0	0
$103$	−367.000	−0.351083	−0.175542	−	0.984472i	$-0.556168\pi$
$103$	−367.000	−0.351083	−0.175542	+	0.984472i	$0.556168\pi$
$104$	231.000	0.217802
$105$	0	0
$106$	−306.000	−0.280390
$107$	1626.00	1.46908	0.734539	−	0.678566i	$-0.237398\pi$
$107$	1626.00	1.46908	0.734539	+	0.678566i	$0.237398\pi$
$108$	0	0
$109$	−2005.00	−1.76187	−0.880937	−	0.473234i	$-0.843086\pi$
$109$	−2005.00	−1.76187	−0.880937	+	0.473234i	$0.843086\pi$
$110$	270.000	0.234032
$111$	0	0
$112$	−497.000	−0.419304
$113$	1017.00	0.846649	0.423324	−	0.905978i	$-0.360863\pi$
$113$	1017.00	0.846649	0.423324	+	0.905978i	$0.360863\pi$
$114$	0	0
$115$	69.0000	0.0559503
$116$	−9.00000	−0.00720370
$117$	0	0
$118$	72.0000	0.0561707
$119$	−546.000	−0.420603
$120$	0	0
$121$	−431.000	−0.323817
$122$	−2166.00	−1.60738
$123$	0	0
$124$	56.0000	0.0405560
$125$	723.000	0.517337
$126$	0	0
$127$	1721.00	1.20247	0.601236	−	0.799071i	$-0.294675\pi$
$127$	1721.00	1.20247	0.601236	+	0.799071i	$0.294675\pi$
$128$	−1659.00	−1.14560
$129$	0	0
$130$	99.0000	0.0667913
$131$	2562.00	1.70873	0.854363	−	0.519677i	$-0.173948\pi$
$131$	2562.00	1.70873	0.854363	+	0.519677i	$0.173948\pi$
$132$	0	0
$133$	518.000	0.337717
$134$	−2652.00	−1.70969
$135$	0	0
$136$	−1638.00	−1.03277
$137$	−951.000	−0.593061	−0.296531	−	0.955023i	$-0.595830\pi$
$137$	−951.000	−0.593061	−0.296531	+	0.955023i	$0.595830\pi$
$138$	0	0
$139$	1937.00	1.18197	0.590986	−	0.806682i	$-0.298739\pi$
$139$	1937.00	1.18197	0.590986	+	0.806682i	$0.298739\pi$
$140$	−21.0000	−0.0126773
$141$	0	0
$142$	270.000	0.159563
$143$	330.000	0.192979
$144$	0	0
$145$	27.0000	0.0154636
$146$	−1734.00	−0.982924
$147$	0	0
$148$	−169.000	−0.0938629
$149$	−3036.00	−1.66925	−0.834627	−	0.550816i	$-0.814317\pi$
$149$	−3036.00	−1.66925	−0.834627	+	0.550816i	$0.814317\pi$
$150$	0	0
$151$	2873.00	1.54835	0.774177	−	0.632969i	$-0.218164\pi$
$151$	2873.00	1.54835	0.774177	+	0.632969i	$0.218164\pi$
$152$	1554.00	0.829250
$153$	0	0
$154$	−630.000	−0.329655
$155$	−168.000	−0.0870586
$156$	0	0
$157$	−3274.00	−1.66429	−0.832145	−	0.554558i	$-0.812888\pi$
$157$	−3274.00	−1.66429	−0.832145	+	0.554558i	$0.812888\pi$
$158$	1452.00	0.731107
$159$	0	0
$160$	−135.000	−0.0667043
$161$	−161.000	−0.0788110
$162$	0	0
$163$	−2554.00	−1.22727	−0.613634	−	0.789591i	$-0.710293\pi$
$163$	−2554.00	−1.22727	−0.613634	+	0.789591i	$0.710293\pi$
$164$	−225.000	−0.107131
$165$	0	0
$166$	2268.00	1.06043
$167$	1800.00	0.834061	0.417030	−	0.908892i	$-0.363071\pi$
$167$	1800.00	0.834061	0.417030	+	0.908892i	$0.363071\pi$
$168$	0	0
$169$	−2076.00	−0.944925
$170$	−702.000	−0.316711
$171$	0	0
$172$	47.0000	0.0208356
$173$	−4278.00	−1.88006	−0.940030	−	0.341092i	$-0.889203\pi$
$173$	−4278.00	−1.88006	−0.940030	+	0.341092i	$0.889203\pi$
$174$	0	0
$175$	−812.000	−0.350751
$176$	−2130.00	−0.912243
$177$	0	0
$178$	4248.00	1.78877
$179$	−2895.00	−1.20884	−0.604420	−	0.796666i	$-0.706595\pi$
$179$	−2895.00	−1.20884	−0.604420	+	0.796666i	$0.706595\pi$
$180$	0	0
$181$	182.000	0.0747401	0.0373700	−	0.999301i	$-0.488102\pi$
$181$	182.000	0.0747401	0.0373700	+	0.999301i	$0.488102\pi$
$182$	−231.000	−0.0940816
$183$	0	0
$184$	−483.000	−0.193518
$185$	507.000	0.201489
$186$	0	0
$187$	−2340.00	−0.915068
$188$	−255.000	−0.0989244
$189$	0	0
$190$	666.000	0.254299
$191$	1032.00	0.390958	0.195479	−	0.980708i	$-0.437374\pi$
$191$	1032.00	0.390958	0.195479	+	0.980708i	$0.437374\pi$
$192$	0	0
$193$	1523.00	0.568020	0.284010	−	0.958821i	$-0.408335\pi$
$193$	1523.00	0.568020	0.284010	+	0.958821i	$0.408335\pi$
$194$	−3057.00	−1.13134
$195$	0	0
$196$	49.0000	0.0178571
$197$	−891.000	−0.322239	−0.161120	−	0.986935i	$-0.551510\pi$
$197$	−891.000	−0.322239	−0.161120	+	0.986935i	$0.551510\pi$
$198$	0	0
$199$	3755.00	1.33761	0.668806	−	0.743437i	$-0.266806\pi$
$199$	3755.00	1.33761	0.668806	+	0.743437i	$0.266806\pi$
$200$	−2436.00	−0.861256
$201$	0	0
$202$	4554.00	1.58623
$203$	−63.0000	−0.0217819
$204$	0	0
$205$	675.000	0.229971
$206$	1101.00	0.372380
$207$	0	0
$208$	−781.000	−0.260349
$209$	2220.00	0.734740
$210$	0	0
$211$	20.0000	0.00652539	0.00326269	−	0.999995i	$-0.498961\pi$
$211$	20.0000	0.00652539	0.00326269	+	0.999995i	$0.498961\pi$
$212$	102.000	0.0330443
$213$	0	0
$214$	−4878.00	−1.55819
$215$	−141.000	−0.0447261
$216$	0	0
$217$	392.000	0.122630
$218$	6015.00	1.86875
$219$	0	0
$220$	−90.0000	−0.0275809
$221$	−858.000	−0.261155
$222$	0	0
$223$	2792.00	0.838413	0.419207	−	0.907891i	$-0.362308\pi$
$223$	2792.00	0.838413	0.419207	+	0.907891i	$0.362308\pi$
$224$	315.000	0.0939590
$225$	0	0
$226$	−3051.00	−0.898007
$227$	−105.000	−0.0307009	−0.0153504	−	0.999882i	$-0.504886\pi$
$227$	−105.000	−0.0307009	−0.0153504	+	0.999882i	$0.504886\pi$
$228$	0	0
$229$	74.0000	0.0213540	0.0106770	−	0.999943i	$-0.496601\pi$
$229$	74.0000	0.0213540	0.0106770	+	0.999943i	$0.496601\pi$
$230$	−207.000	−0.0593442
$231$	0	0
$232$	−189.000	−0.0534847
$233$	−570.000	−0.160266	−0.0801329	−	0.996784i	$-0.525534\pi$
$233$	−570.000	−0.160266	−0.0801329	+	0.996784i	$0.525534\pi$
$234$	0	0
$235$	765.000	0.212354
$236$	−24.0000	−0.00661978
$237$	0	0
$238$	1638.00	0.446117
$239$	−4482.00	−1.21304	−0.606520	−	0.795068i	$-0.707435\pi$
$239$	−4482.00	−1.21304	−0.606520	+	0.795068i	$0.707435\pi$
$240$	0	0
$241$	−2995.00	−0.800518	−0.400259	−	0.916402i	$-0.631080\pi$
$241$	−2995.00	−0.800518	−0.400259	+	0.916402i	$0.631080\pi$
$242$	1293.00	0.343459
$243$	0	0
$244$	722.000	0.189432
$245$	−147.000	−0.0383326
$246$	0	0
$247$	814.000	0.209691
$248$	1176.00	0.301113
$249$	0	0
$250$	−2169.00	−0.548718
$251$	−3537.00	−0.889456	−0.444728	−	0.895666i	$-0.646700\pi$
$251$	−3537.00	−0.889456	−0.444728	+	0.895666i	$0.646700\pi$
$252$	0	0
$253$	−690.000	−0.171462
$254$	−5163.00	−1.27542
$255$	0	0
$256$	1513.00	0.369385
$257$	1194.00	0.289804	0.144902	−	0.989446i	$-0.453713\pi$
$257$	1194.00	0.289804	0.144902	+	0.989446i	$0.453713\pi$
$258$	0	0
$259$	−1183.00	−0.283815
$260$	−33.0000	−0.00787144
$261$	0	0
$262$	−7686.00	−1.81238
$263$	−7161.00	−1.67896	−0.839479	−	0.543391i	$-0.817140\pi$
$263$	−7161.00	−1.67896	−0.839479	+	0.543391i	$0.817140\pi$
$264$	0	0
$265$	−306.000	−0.0709337
$266$	−1554.00	−0.358202
$267$	0	0
$268$	884.000	0.201488
$269$	−3966.00	−0.898927	−0.449463	−	0.893299i	$-0.648385\pi$
$269$	−3966.00	−0.898927	−0.449463	+	0.893299i	$0.648385\pi$
$270$	0	0
$271$	542.000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	542.000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	5538.00	1.23452
$273$	0	0
$274$	2853.00	0.629037
$275$	−3480.00	−0.763098
$276$	0	0
$277$	−7504.00	−1.62770	−0.813848	−	0.581078i	$-0.802631\pi$
$277$	−7504.00	−1.62770	−0.813848	+	0.581078i	$0.802631\pi$
$278$	−5811.00	−1.25367
$279$	0	0
$280$	−441.000	−0.0941243
$281$	5211.00	1.10627	0.553136	−	0.833091i	$-0.313431\pi$
$281$	5211.00	1.10627	0.553136	+	0.833091i	$0.313431\pi$
$282$	0	0
$283$	−3976.00	−0.835154	−0.417577	−	0.908641i	$-0.637121\pi$
$283$	−3976.00	−0.835154	−0.417577	+	0.908641i	$0.637121\pi$
$284$	−90.0000	−0.0188046
$285$	0	0
$286$	−990.000	−0.204685
$287$	−1575.00	−0.323935
$288$	0	0
$289$	1171.00	0.238347
$290$	−81.0000	−0.0164017
$291$	0	0
$292$	578.000	0.115839
$293$	−9234.00	−1.84115	−0.920573	−	0.390569i	$-0.872278\pi$
$293$	−9234.00	−1.84115	−0.920573	+	0.390569i	$0.872278\pi$
$294$	0	0
$295$	72.0000	0.0142102
$296$	−3549.00	−0.696897
$297$	0	0
$298$	9108.00	1.77051
$299$	−253.000	−0.0489343
$300$	0	0
$301$	329.000	0.0630008
$302$	−8619.00	−1.64228
$303$	0	0
$304$	−5254.00	−0.991242
$305$	−2166.00	−0.406639
$306$	0	0
$307$	227.000	0.0422006	0.0211003	−	0.999777i	$-0.493283\pi$
$307$	227.000	0.0422006	0.0211003	+	0.999777i	$0.493283\pi$
$308$	210.000	0.0388502
$309$	0	0
$310$	504.000	0.0923396
$311$	8760.00	1.59722	0.798608	−	0.601852i	$-0.205570\pi$
$311$	8760.00	1.59722	0.798608	+	0.601852i	$0.205570\pi$
$312$	0	0
$313$	−7558.00	−1.36487	−0.682434	−	0.730948i	$-0.739078\pi$
$313$	−7558.00	−1.36487	−0.682434	+	0.730948i	$0.739078\pi$
$314$	9822.00	1.76525
$315$	0	0
$316$	−484.000	−0.0861618
$317$	7125.00	1.26240	0.631199	−	0.775621i	$-0.282563\pi$
$317$	7125.00	1.26240	0.631199	+	0.775621i	$0.282563\pi$
$318$	0	0
$319$	−270.000	−0.0473890
$320$	−1299.00	−0.226926
$321$	0	0
$322$	483.000	0.0835917
$323$	−5772.00	−0.994312
$324$	0	0
$325$	−1276.00	−0.217784
$326$	7662.00	1.30171
$327$	0	0
$328$	−4725.00	−0.795410
$329$	−1785.00	−0.299119
$330$	0	0
$331$	−3382.00	−0.561606	−0.280803	−	0.959765i	$-0.590601\pi$
$331$	−3382.00	−0.561606	−0.280803	+	0.959765i	$0.590601\pi$
$332$	−756.000	−0.124973
$333$	0	0
$334$	−5400.00	−0.884655
$335$	−2652.00	−0.432520
$336$	0	0
$337$	398.000	0.0643337	0.0321668	−	0.999483i	$-0.489759\pi$
$337$	398.000	0.0643337	0.0321668	+	0.999483i	$0.489759\pi$
$338$	6228.00	1.00224
$339$	0	0
$340$	234.000	0.0373248
$341$	1680.00	0.266795
$342$	0	0
$343$	343.000	0.0539949
$344$	987.000	0.154696
$345$	0	0
$346$	12834.0	1.99410
$347$	−4047.00	−0.626093	−0.313047	−	0.949738i	$-0.601350\pi$
$347$	−4047.00	−0.626093	−0.313047	+	0.949738i	$0.601350\pi$
$348$	0	0
$349$	2018.00	0.309516	0.154758	−	0.987952i	$-0.450540\pi$
$349$	2018.00	0.309516	0.154758	+	0.987952i	$0.450540\pi$
$350$	2436.00	0.372028
$351$	0	0
$352$	1350.00	0.204418
$353$	−7467.00	−1.12586	−0.562930	−	0.826505i	$-0.690326\pi$
$353$	−7467.00	−1.12586	−0.562930	+	0.826505i	$0.690326\pi$
$354$	0	0
$355$	270.000	0.0403665
$356$	−1416.00	−0.210809
$357$	0	0
$358$	8685.00	1.28217
$359$	1689.00	0.248306	0.124153	−	0.992263i	$-0.460379\pi$
$359$	1689.00	0.248306	0.124153	+	0.992263i	$0.460379\pi$
$360$	0	0
$361$	−1383.00	−0.201633
$362$	−546.000	−0.0792738
$363$	0	0
$364$	77.0000	0.0110876
$365$	−1734.00	−0.248662
$366$	0	0
$367$	−11365.0	−1.61648	−0.808240	−	0.588853i	$-0.799580\pi$
$367$	−11365.0	−1.61648	−0.808240	+	0.588853i	$0.799580\pi$
$368$	1633.00	0.231321
$369$	0	0
$370$	−1521.00	−0.213711
$371$	714.000	0.0999165
$372$	0	0
$373$	−9538.00	−1.32402	−0.662009	−	0.749496i	$-0.730296\pi$
$373$	−9538.00	−1.32402	−0.662009	+	0.749496i	$0.730296\pi$
$374$	7020.00	0.970576
$375$	0	0
$376$	−5355.00	−0.734476
$377$	−99.0000	−0.0135246
$378$	0	0
$379$	−10735.0	−1.45493	−0.727467	−	0.686143i	$-0.759303\pi$
$379$	−10735.0	−1.45493	−0.727467	+	0.686143i	$0.759303\pi$
$380$	−222.000	−0.0299694
$381$	0	0
$382$	−3096.00	−0.414673
$383$	7926.00	1.05744	0.528720	−	0.848796i	$-0.322672\pi$
$383$	7926.00	1.05744	0.528720	+	0.848796i	$0.322672\pi$
$384$	0	0
$385$	−630.000	−0.0833968
$386$	−4569.00	−0.602477
$387$	0	0
$388$	1019.00	0.133330
$389$	5016.00	0.653782	0.326891	−	0.945062i	$-0.393999\pi$
$389$	5016.00	0.653782	0.326891	+	0.945062i	$0.393999\pi$
$390$	0	0
$391$	1794.00	0.232037
$392$	1029.00	0.132583
$393$	0	0
$394$	2673.00	0.341786
$395$	1452.00	0.184957
$396$	0	0
$397$	−3346.00	−0.423000	−0.211500	−	0.977378i	$-0.567835\pi$
$397$	−3346.00	−0.423000	−0.211500	+	0.977378i	$0.567835\pi$
$398$	−11265.0	−1.41875
$399$	0	0
$400$	8236.00	1.02950
$401$	−2946.00	−0.366873	−0.183437	−	0.983032i	$-0.558722\pi$
$401$	−2946.00	−0.366873	−0.183437	+	0.983032i	$0.558722\pi$
$402$	0	0
$403$	616.000	0.0761418
$404$	−1518.00	−0.186939
$405$	0	0
$406$	189.000	0.0231032
$407$	−5070.00	−0.617471
$408$	0	0
$409$	−10942.0	−1.32285	−0.661427	−	0.750010i	$-0.730049\pi$
$409$	−10942.0	−1.32285	−0.661427	+	0.750010i	$0.730049\pi$
$410$	−2025.00	−0.243921
$411$	0	0
$412$	−367.000	−0.0438854
$413$	−168.000	−0.0200163
$414$	0	0
$415$	2268.00	0.268269
$416$	495.000	0.0583398
$417$	0	0
$418$	−6660.00	−0.779309
$419$	1872.00	0.218265	0.109133	−	0.994027i	$-0.465193\pi$
$419$	1872.00	0.218265	0.109133	+	0.994027i	$0.465193\pi$
$420$	0	0
$421$	−5965.00	−0.690538	−0.345269	−	0.938504i	$-0.612212\pi$
$421$	−5965.00	−0.690538	−0.345269	+	0.938504i	$0.612212\pi$
$422$	−60.0000	−0.00692122
$423$	0	0
$424$	2142.00	0.245341
$425$	9048.00	1.03269
$426$	0	0
$427$	5054.00	0.572787
$428$	1626.00	0.183635
$429$	0	0
$430$	423.000	0.0474392
$431$	3099.00	0.346342	0.173171	−	0.984892i	$-0.444599\pi$
$431$	3099.00	0.346342	0.173171	+	0.984892i	$0.444599\pi$
$432$	0	0
$433$	8237.00	0.914192	0.457096	−	0.889417i	$-0.348890\pi$
$433$	8237.00	0.914192	0.457096	+	0.889417i	$0.348890\pi$
$434$	−1176.00	−0.130069
$435$	0	0
$436$	−2005.00	−0.220234
$437$	−1702.00	−0.186311
$438$	0	0
$439$	−6802.00	−0.739503	−0.369751	−	0.929131i	$-0.620557\pi$
$439$	−6802.00	−0.739503	−0.369751	+	0.929131i	$0.620557\pi$
$440$	−1890.00	−0.204778
$441$	0	0
$442$	2574.00	0.276997
$443$	−7293.00	−0.782169	−0.391085	−	0.920355i	$-0.627900\pi$
$443$	−7293.00	−0.782169	−0.391085	+	0.920355i	$0.627900\pi$
$444$	0	0
$445$	4248.00	0.452527
$446$	−8376.00	−0.889272
$447$	0	0
$448$	3031.00	0.319646
$449$	324.000	0.0340546	0.0170273	−	0.999855i	$-0.494580\pi$
$449$	324.000	0.0340546	0.0170273	+	0.999855i	$0.494580\pi$
$450$	0	0
$451$	−6750.00	−0.704756
$452$	1017.00	0.105831
$453$	0	0
$454$	315.000	0.0325632
$455$	−231.000	−0.0238010
$456$	0	0
$457$	−15334.0	−1.56957	−0.784786	−	0.619767i	$-0.787227\pi$
$457$	−15334.0	−1.56957	−0.784786	+	0.619767i	$0.787227\pi$
$458$	−222.000	−0.0226493
$459$	0	0
$460$	69.0000	0.00699379
$461$	9648.00	0.974734	0.487367	−	0.873197i	$-0.337957\pi$
$461$	9648.00	0.974734	0.487367	+	0.873197i	$0.337957\pi$
$462$	0	0
$463$	4331.00	0.434727	0.217364	−	0.976091i	$-0.430254\pi$
$463$	4331.00	0.434727	0.217364	+	0.976091i	$0.430254\pi$
$464$	639.000	0.0639328
$465$	0	0
$466$	1710.00	0.169988
$467$	−8535.00	−0.845723	−0.422862	−	0.906194i	$-0.638974\pi$
$467$	−8535.00	−0.845723	−0.422862	+	0.906194i	$0.638974\pi$
$468$	0	0
$469$	6188.00	0.609244
$470$	−2295.00	−0.225235
$471$	0	0
$472$	−504.000	−0.0491493
$473$	1410.00	0.137065
$474$	0	0
$475$	−8584.00	−0.829181
$476$	−546.000	−0.0525754
$477$	0	0
$478$	13446.0	1.28662
$479$	−4920.00	−0.469312	−0.234656	−	0.972078i	$-0.575396\pi$
$479$	−4920.00	−0.469312	−0.234656	+	0.972078i	$0.575396\pi$
$480$	0	0
$481$	−1859.00	−0.176223
$482$	8985.00	0.849078
$483$	0	0
$484$	−431.000	−0.0404771
$485$	−3057.00	−0.286209
$486$	0	0
$487$	1379.00	0.128313	0.0641565	−	0.997940i	$-0.479564\pi$
$487$	1379.00	0.128313	0.0641565	+	0.997940i	$0.479564\pi$
$488$	15162.0	1.40646
$489$	0	0
$490$	441.000	0.0406579
$491$	−1836.00	−0.168753	−0.0843763	−	0.996434i	$-0.526890\pi$
$491$	−1836.00	−0.168753	−0.0843763	+	0.996434i	$0.526890\pi$
$492$	0	0
$493$	702.000	0.0641308
$494$	−2442.00	−0.222410
$495$	0	0
$496$	−3976.00	−0.359935
$497$	−630.000	−0.0568599
$498$	0	0
$499$	6392.00	0.573437	0.286719	−	0.958015i	$-0.407436\pi$
$499$	6392.00	0.573437	0.286719	+	0.958015i	$0.407436\pi$
$500$	723.000	0.0646671
$501$	0	0
$502$	10611.0	0.943411
$503$	8874.00	0.786624	0.393312	−	0.919405i	$-0.371329\pi$
$503$	8874.00	0.786624	0.393312	+	0.919405i	$0.371329\pi$
$504$	0	0
$505$	4554.00	0.401288
$506$	2070.00	0.181863
$507$	0	0
$508$	1721.00	0.150309
$509$	5892.00	0.513081	0.256541	−	0.966533i	$-0.417417\pi$
$509$	5892.00	0.513081	0.256541	+	0.966533i	$0.417417\pi$
$510$	0	0
$511$	4046.00	0.350263
$512$	8733.00	0.753804
$513$	0	0
$514$	−3582.00	−0.307384
$515$	1101.00	0.0942055
$516$	0	0
$517$	−7650.00	−0.650767
$518$	3549.00	0.301031
$519$	0	0
$520$	−693.000	−0.0584424
$521$	−14118.0	−1.18718	−0.593590	−	0.804768i	$-0.702290\pi$
$521$	−14118.0	−1.18718	−0.593590	+	0.804768i	$0.702290\pi$
$522$	0	0
$523$	17030.0	1.42384	0.711922	−	0.702259i	$-0.247825\pi$
$523$	17030.0	1.42384	0.711922	+	0.702259i	$0.247825\pi$
$524$	2562.00	0.213591
$525$	0	0
$526$	21483.0	1.78080
$527$	−4368.00	−0.361049
$528$	0	0
$529$	529.000	0.0434783
$530$	918.000	0.0752366
$531$	0	0
$532$	518.000	0.0422146
$533$	−2475.00	−0.201133
$534$	0	0
$535$	−4878.00	−0.394195
$536$	18564.0	1.49598
$537$	0	0
$538$	11898.0	0.953456
$539$	1470.00	0.117472
$540$	0	0
$541$	−12850.0	−1.02119	−0.510596	−	0.859821i	$-0.670575\pi$
$541$	−12850.0	−1.02119	−0.510596	+	0.859821i	$0.670575\pi$
$542$	−1626.00	−0.128861
$543$	0	0
$544$	−3510.00	−0.276636
$545$	6015.00	0.472760
$546$	0	0
$547$	−10942.0	−0.855295	−0.427647	−	0.903946i	$-0.640657\pi$
$547$	−10942.0	−0.855295	−0.427647	+	0.903946i	$0.640657\pi$
$548$	−951.000	−0.0741327
$549$	0	0
$550$	10440.0	0.809387
$551$	−666.000	−0.0514928
$552$	0	0
$553$	−3388.00	−0.260529
$554$	22512.0	1.72643
$555$	0	0
$556$	1937.00	0.147747
$557$	24150.0	1.83711	0.918553	−	0.395297i	$-0.129358\pi$
$557$	24150.0	1.83711	0.918553	+	0.395297i	$0.129358\pi$
$558$	0	0
$559$	517.000	0.0391177
$560$	1491.00	0.112511
$561$	0	0
$562$	−15633.0	−1.17338
$563$	5943.00	0.444880	0.222440	−	0.974946i	$-0.428598\pi$
$563$	5943.00	0.444880	0.222440	+	0.974946i	$0.428598\pi$
$564$	0	0
$565$	−3051.00	−0.227180
$566$	11928.0	0.885815
$567$	0	0
$568$	−1890.00	−0.139617
$569$	−7689.00	−0.566502	−0.283251	−	0.959046i	$-0.591413\pi$
$569$	−7689.00	−0.566502	−0.283251	+	0.959046i	$0.591413\pi$
$570$	0	0
$571$	10172.0	0.745508	0.372754	−	0.927930i	$-0.378414\pi$
$571$	10172.0	0.745508	0.372754	+	0.927930i	$0.378414\pi$
$572$	330.000	0.0241224
$573$	0	0
$574$	4725.00	0.343585
$575$	2668.00	0.193501
$576$	0	0
$577$	14924.0	1.07677	0.538383	−	0.842700i	$-0.319035\pi$
$577$	14924.0	1.07677	0.538383	+	0.842700i	$0.319035\pi$
$578$	−3513.00	−0.252805
$579$	0	0
$580$	27.0000	0.00193296
$581$	−5292.00	−0.377882
$582$	0	0
$583$	3060.00	0.217380
$584$	12138.0	0.860058
$585$	0	0
$586$	27702.0	1.95283
$587$	8244.00	0.579670	0.289835	−	0.957077i	$-0.406400\pi$
$587$	8244.00	0.579670	0.289835	+	0.957077i	$0.406400\pi$
$588$	0	0
$589$	4144.00	0.289899
$590$	−216.000	−0.0150722
$591$	0	0
$592$	11999.0	0.833034
$593$	843.000	0.0583775	0.0291888	−	0.999574i	$-0.490708\pi$
$593$	843.000	0.0583775	0.0291888	+	0.999574i	$0.490708\pi$
$594$	0	0
$595$	1638.00	0.112860
$596$	−3036.00	−0.208657
$597$	0	0
$598$	759.000	0.0519027
$599$	11136.0	0.759607	0.379804	−	0.925067i	$-0.375992\pi$
$599$	11136.0	0.759607	0.379804	+	0.925067i	$0.375992\pi$
$600$	0	0
$601$	−178.000	−0.0120812	−0.00604058	−	0.999982i	$-0.501923\pi$
$601$	−178.000	−0.0120812	−0.00604058	+	0.999982i	$0.501923\pi$
$602$	−987.000	−0.0668225
$603$	0	0
$604$	2873.00	0.193544
$605$	1293.00	0.0868891
$606$	0	0
$607$	1406.00	0.0940161	0.0470081	−	0.998895i	$-0.485031\pi$
$607$	1406.00	0.0940161	0.0470081	+	0.998895i	$0.485031\pi$
$608$	3330.00	0.222121
$609$	0	0
$610$	6498.00	0.431305
$611$	−2805.00	−0.185725
$612$	0	0
$613$	27029.0	1.78090	0.890449	−	0.455082i	$-0.150390\pi$
$613$	27029.0	1.78090	0.890449	+	0.455082i	$0.150390\pi$
$614$	−681.000	−0.0447605
$615$	0	0
$616$	4410.00	0.288448
$617$	15822.0	1.03237	0.516183	−	0.856478i	$-0.327352\pi$
$617$	15822.0	1.03237	0.516183	+	0.856478i	$0.327352\pi$
$618$	0	0
$619$	−27646.0	−1.79513	−0.897566	−	0.440880i	$-0.854666\pi$
$619$	−27646.0	−1.79513	−0.897566	+	0.440880i	$0.854666\pi$
$620$	−168.000	−0.0108823
$621$	0	0
$622$	−26280.0	−1.69410
$623$	−9912.00	−0.637425
$624$	0	0
$625$	12331.0	0.789184
$626$	22674.0	1.44766
$627$	0	0
$628$	−3274.00	−0.208036
$629$	13182.0	0.835613
$630$	0	0
$631$	22682.0	1.43099	0.715496	−	0.698617i	$-0.246201\pi$
$631$	22682.0	1.43099	0.715496	+	0.698617i	$0.246201\pi$
$632$	−10164.0	−0.639719
$633$	0	0
$634$	−21375.0	−1.33897
$635$	−5163.00	−0.322657
$636$	0	0
$637$	539.000	0.0335258
$638$	810.000	0.0502636
$639$	0	0
$640$	4977.00	0.307396
$641$	−25557.0	−1.57479	−0.787395	−	0.616448i	$-0.788571\pi$
$641$	−25557.0	−1.57479	−0.787395	+	0.616448i	$0.788571\pi$
$642$	0	0
$643$	10406.0	0.638216	0.319108	−	0.947718i	$-0.396617\pi$
$643$	10406.0	0.638216	0.319108	+	0.947718i	$0.396617\pi$
$644$	−161.000	−0.00985138
$645$	0	0
$646$	17316.0	1.05463
$647$	−15252.0	−0.926767	−0.463383	−	0.886158i	$-0.653365\pi$
$647$	−15252.0	−0.926767	−0.463383	+	0.886158i	$0.653365\pi$
$648$	0	0
$649$	−720.000	−0.0435477
$650$	3828.00	0.230995
$651$	0	0
$652$	−2554.00	−0.153409
$653$	−15573.0	−0.933260	−0.466630	−	0.884453i	$-0.654532\pi$
$653$	−15573.0	−0.933260	−0.466630	+	0.884453i	$0.654532\pi$
$654$	0	0
$655$	−7686.00	−0.458499
$656$	15975.0	0.950791
$657$	0	0
$658$	5355.00	0.317264
$659$	8424.00	0.497955	0.248978	−	0.968509i	$-0.419905\pi$
$659$	8424.00	0.497955	0.248978	+	0.968509i	$0.419905\pi$
$660$	0	0
$661$	−24496.0	−1.44143	−0.720714	−	0.693232i	$-0.756186\pi$
$661$	−24496.0	−1.44143	−0.720714	+	0.693232i	$0.756186\pi$
$662$	10146.0	0.595673
$663$	0	0
$664$	−15876.0	−0.927874
$665$	−1554.00	−0.0906189
$666$	0	0
$667$	207.000	0.0120166
$668$	1800.00	0.104258
$669$	0	0
$670$	7956.00	0.458757
$671$	21660.0	1.24616
$672$	0	0
$673$	24131.0	1.38214	0.691071	−	0.722787i	$-0.257139\pi$
$673$	24131.0	1.38214	0.691071	+	0.722787i	$0.257139\pi$
$674$	−1194.00	−0.0682361
$675$	0	0
$676$	−2076.00	−0.118116
$677$	−21414.0	−1.21567	−0.607834	−	0.794064i	$-0.707961\pi$
$677$	−21414.0	−1.21567	−0.607834	+	0.794064i	$0.707961\pi$
$678$	0	0
$679$	7133.00	0.403151
$680$	4914.00	0.277122
$681$	0	0
$682$	−5040.00	−0.282979
$683$	15780.0	0.884048	0.442024	−	0.897003i	$-0.354261\pi$
$683$	15780.0	0.884048	0.442024	+	0.897003i	$0.354261\pi$
$684$	0	0
$685$	2853.00	0.159135
$686$	−1029.00	−0.0572703
$687$	0	0
$688$	−3337.00	−0.184916
$689$	1122.00	0.0620389
$690$	0	0
$691$	5699.00	0.313748	0.156874	−	0.987619i	$-0.449858\pi$
$691$	5699.00	0.313748	0.156874	+	0.987619i	$0.449858\pi$
$692$	−4278.00	−0.235007
$693$	0	0
$694$	12141.0	0.664072
$695$	−5811.00	−0.317157
$696$	0	0
$697$	17550.0	0.953736
$698$	−6054.00	−0.328291
$699$	0	0
$700$	−812.000	−0.0438439
$701$	−29970.0	−1.61477	−0.807383	−	0.590027i	$-0.799117\pi$
$701$	−29970.0	−1.61477	−0.807383	+	0.590027i	$0.799117\pi$
$702$	0	0
$703$	−12506.0	−0.670943
$704$	12990.0	0.695425
$705$	0	0
$706$	22401.0	1.19415
$707$	−10626.0	−0.565250
$708$	0	0
$709$	−24874.0	−1.31758	−0.658789	−	0.752328i	$-0.728931\pi$
$709$	−24874.0	−1.31758	−0.658789	+	0.752328i	$0.728931\pi$
$710$	−810.000	−0.0428152
$711$	0	0
$712$	−29736.0	−1.56517
$713$	−1288.00	−0.0676521
$714$	0	0
$715$	−990.000	−0.0517817
$716$	−2895.00	−0.151105
$717$	0	0
$718$	−5067.00	−0.263369
$719$	−2343.00	−0.121529	−0.0607644	−	0.998152i	$-0.519354\pi$
$719$	−2343.00	−0.121529	−0.0607644	+	0.998152i	$0.519354\pi$
$720$	0	0
$721$	−2569.00	−0.132697
$722$	4149.00	0.213864
$723$	0	0
$724$	182.000	0.00934251
$725$	1044.00	0.0534803
$726$	0	0
$727$	19424.0	0.990916	0.495458	−	0.868632i	$-0.335000\pi$
$727$	19424.0	0.990916	0.495458	+	0.868632i	$0.335000\pi$
$728$	1617.00	0.0823214
$729$	0	0
$730$	5202.00	0.263746
$731$	−3666.00	−0.185488
$732$	0	0
$733$	5816.00	0.293068	0.146534	−	0.989206i	$-0.453188\pi$
$733$	5816.00	0.293068	0.146534	+	0.989206i	$0.453188\pi$
$734$	34095.0	1.71454
$735$	0	0
$736$	−1035.00	−0.0518351
$737$	26520.0	1.32548
$738$	0	0
$739$	11450.0	0.569953	0.284976	−	0.958535i	$-0.408014\pi$
$739$	11450.0	0.569953	0.284976	+	0.958535i	$0.408014\pi$
$740$	507.000	0.0251861
$741$	0	0
$742$	−2142.00	−0.105977
$743$	−25632.0	−1.26561	−0.632804	−	0.774312i	$-0.718096\pi$
$743$	−25632.0	−1.26561	−0.632804	+	0.774312i	$0.718096\pi$
$744$	0	0
$745$	9108.00	0.447908
$746$	28614.0	1.40433
$747$	0	0
$748$	−2340.00	−0.114384
$749$	11382.0	0.555259
$750$	0	0
$751$	−24640.0	−1.19724	−0.598619	−	0.801034i	$-0.704284\pi$
$751$	−24640.0	−1.19724	−0.598619	+	0.801034i	$0.704284\pi$
$752$	18105.0	0.877954
$753$	0	0
$754$	297.000	0.0143450
$755$	−8619.00	−0.415467
$756$	0	0
$757$	38126.0	1.83053	0.915266	−	0.402850i	$-0.131980\pi$
$757$	38126.0	1.83053	0.915266	+	0.402850i	$0.131980\pi$
$758$	32205.0	1.54319
$759$	0	0
$760$	−4662.00	−0.222511
$761$	−10758.0	−0.512454	−0.256227	−	0.966617i	$-0.582479\pi$
$761$	−10758.0	−0.512454	−0.256227	+	0.966617i	$0.582479\pi$
$762$	0	0
$763$	−14035.0	−0.665925
$764$	1032.00	0.0488697
$765$	0	0
$766$	−23778.0	−1.12158
$767$	−264.000	−0.0124283
$768$	0	0
$769$	33779.0	1.58401	0.792004	−	0.610516i	$-0.209038\pi$
$769$	33779.0	1.58401	0.792004	+	0.610516i	$0.209038\pi$
$770$	1890.00	0.0884557
$771$	0	0
$772$	1523.00	0.0710026
$773$	33285.0	1.54874	0.774371	−	0.632731i	$-0.218066\pi$
$773$	33285.0	1.54874	0.774371	+	0.632731i	$0.218066\pi$
$774$	0	0
$775$	−6496.00	−0.301088
$776$	21399.0	0.989922
$777$	0	0
$778$	−15048.0	−0.693441
$779$	−16650.0	−0.765787
$780$	0	0
$781$	−2700.00	−0.123705
$782$	−5382.00	−0.246112
$783$	0	0
$784$	−3479.00	−0.158482
$785$	9822.00	0.446576
$786$	0	0
$787$	−12724.0	−0.576317	−0.288159	−	0.957583i	$-0.593043\pi$
$787$	−12724.0	−0.576317	−0.288159	+	0.957583i	$0.593043\pi$
$788$	−891.000	−0.0402799
$789$	0	0
$790$	−4356.00	−0.196177
$791$	7119.00	0.320003
$792$	0	0
$793$	7942.00	0.355648
$794$	10038.0	0.448659
$795$	0	0
$796$	3755.00	0.167202
$797$	−5463.00	−0.242797	−0.121399	−	0.992604i	$-0.538738\pi$
$797$	−5463.00	−0.242797	−0.121399	+	0.992604i	$0.538738\pi$
$798$	0	0
$799$	19890.0	0.880673
$800$	−5220.00	−0.230694
$801$	0	0
$802$	8838.00	0.389128
$803$	17340.0	0.762037
$804$	0	0
$805$	483.000	0.0211472
$806$	−1848.00	−0.0807606
$807$	0	0
$808$	−31878.0	−1.38795
$809$	−32298.0	−1.40363	−0.701815	−	0.712359i	$-0.747627\pi$
$809$	−32298.0	−1.40363	−0.701815	+	0.712359i	$0.747627\pi$
$810$	0	0
$811$	14321.0	0.620072	0.310036	−	0.950725i	$-0.399659\pi$
$811$	14321.0	0.620072	0.310036	+	0.950725i	$0.399659\pi$
$812$	−63.0000	−0.00272274
$813$	0	0
$814$	15210.0	0.654927
$815$	7662.00	0.329311
$816$	0	0
$817$	3478.00	0.148935
$818$	32826.0	1.40310
$819$	0	0
$820$	675.000	0.0287464
$821$	−24222.0	−1.02966	−0.514832	−	0.857291i	$-0.672146\pi$
$821$	−24222.0	−1.02966	−0.514832	+	0.857291i	$0.672146\pi$
$822$	0	0
$823$	−35215.0	−1.49152	−0.745758	−	0.666217i	$-0.767913\pi$
$823$	−35215.0	−1.49152	−0.745758	+	0.666217i	$0.767913\pi$
$824$	−7707.00	−0.325833
$825$	0	0
$826$	504.000	0.0212305
$827$	−8694.00	−0.365562	−0.182781	−	0.983154i	$-0.558510\pi$
$827$	−8694.00	−0.365562	−0.182781	+	0.983154i	$0.558510\pi$
$828$	0	0
$829$	−16558.0	−0.693707	−0.346854	−	0.937919i	$-0.612750\pi$
$829$	−16558.0	−0.693707	−0.346854	+	0.937919i	$0.612750\pi$
$830$	−6804.00	−0.284543
$831$	0	0
$832$	4763.00	0.198470
$833$	−3822.00	−0.158973
$834$	0	0
$835$	−5400.00	−0.223802
$836$	2220.00	0.0918425
$837$	0	0
$838$	−5616.00	−0.231505
$839$	−11376.0	−0.468109	−0.234054	−	0.972224i	$-0.575199\pi$
$839$	−11376.0	−0.468109	−0.234054	+	0.972224i	$0.575199\pi$
$840$	0	0
$841$	−24308.0	−0.996679
$842$	17895.0	0.732426
$843$	0	0
$844$	20.0000	0.000815673 0
$845$	6228.00	0.253550
$846$	0	0
$847$	−3017.00	−0.122391
$848$	−7242.00	−0.293268
$849$	0	0
$850$	−27144.0	−1.09533
$851$	3887.00	0.156574
$852$	0	0
$853$	−18043.0	−0.724244	−0.362122	−	0.932131i	$-0.617948\pi$
$853$	−18043.0	−0.724244	−0.362122	+	0.932131i	$0.617948\pi$
$854$	−15162.0	−0.607533
$855$	0	0
$856$	34146.0	1.36342
$857$	6087.00	0.242623	0.121312	−	0.992614i	$-0.461290\pi$
$857$	6087.00	0.242623	0.121312	+	0.992614i	$0.461290\pi$
$858$	0	0
$859$	2045.00	0.0812276	0.0406138	−	0.999175i	$-0.487069\pi$
$859$	2045.00	0.0812276	0.0406138	+	0.999175i	$0.487069\pi$
$860$	−141.000	−0.00559077
$861$	0	0
$862$	−9297.00	−0.367352
$863$	29112.0	1.14830	0.574151	−	0.818750i	$-0.305332\pi$
$863$	29112.0	1.14830	0.574151	+	0.818750i	$0.305332\pi$
$864$	0	0
$865$	12834.0	0.504473
$866$	−24711.0	−0.969647
$867$	0	0
$868$	392.000	0.0153287
$869$	−14520.0	−0.566809
$870$	0	0
$871$	9724.00	0.378284
$872$	−42105.0	−1.63516
$873$	0	0
$874$	5106.00	0.197612
$875$	5061.00	0.195535
$876$	0	0
$877$	−40588.0	−1.56278	−0.781391	−	0.624042i	$-0.785489\pi$
$877$	−40588.0	−1.56278	−0.781391	+	0.624042i	$0.785489\pi$
$878$	20406.0	0.784361
$879$	0	0
$880$	6390.00	0.244781
$881$	16362.0	0.625709	0.312855	−	0.949801i	$-0.398715\pi$
$881$	16362.0	0.625709	0.312855	+	0.949801i	$0.398715\pi$
$882$	0	0
$883$	524.000	0.0199706	0.00998528	−	0.999950i	$-0.496822\pi$
$883$	524.000	0.0199706	0.00998528	+	0.999950i	$0.496822\pi$
$884$	−858.000	−0.0326444
$885$	0	0
$886$	21879.0	0.829616
$887$	−36480.0	−1.38092	−0.690461	−	0.723369i	$-0.742592\pi$
$887$	−36480.0	−1.38092	−0.690461	+	0.723369i	$0.742592\pi$
$888$	0	0
$889$	12047.0	0.454492
$890$	−12744.0	−0.479977
$891$	0	0
$892$	2792.00	0.104802
$893$	−18870.0	−0.707123
$894$	0	0
$895$	8685.00	0.324366
$896$	−11613.0	−0.432995
$897$	0	0
$898$	−972.000	−0.0361203
$899$	−504.000	−0.0186978
$900$	0	0
$901$	−7956.00	−0.294176
$902$	20250.0	0.747507
$903$	0	0
$904$	21357.0	0.785756
$905$	−546.000	−0.0200549
$906$	0	0
$907$	−9259.00	−0.338964	−0.169482	−	0.985533i	$-0.554209\pi$
$907$	−9259.00	−0.338964	−0.169482	+	0.985533i	$0.554209\pi$
$908$	−105.000	−0.00383761
$909$	0	0
$910$	693.000	0.0252448
$911$	−7839.00	−0.285091	−0.142545	−	0.989788i	$-0.545529\pi$
$911$	−7839.00	−0.285091	−0.142545	+	0.989788i	$0.545529\pi$
$912$	0	0
$913$	−22680.0	−0.822123
$914$	46002.0	1.66478
$915$	0	0
$916$	74.0000	0.00266925
$917$	17934.0	0.645837
$918$	0	0
$919$	−11374.0	−0.408263	−0.204131	−	0.978943i	$-0.565437\pi$
$919$	−11374.0	−0.408263	−0.204131	+	0.978943i	$0.565437\pi$
$920$	1449.00	0.0519262
$921$	0	0
$922$	−28944.0	−1.03386
$923$	−990.000	−0.0353047
$924$	0	0
$925$	19604.0	0.696838
$926$	−12993.0	−0.461098
$927$	0	0
$928$	−405.000	−0.0143263
$929$	−8121.00	−0.286804	−0.143402	−	0.989664i	$-0.545804\pi$
$929$	−8121.00	−0.286804	−0.143402	+	0.989664i	$0.545804\pi$
$930$	0	0
$931$	3626.00	0.127645
$932$	−570.000	−0.0200332
$933$	0	0
$934$	25605.0	0.897025
$935$	7020.00	0.245539
$936$	0	0
$937$	1739.00	0.0606304	0.0303152	−	0.999540i	$-0.490349\pi$
$937$	1739.00	0.0606304	0.0303152	+	0.999540i	$0.490349\pi$
$938$	−18564.0	−0.646201
$939$	0	0
$940$	765.000	0.0265442
$941$	−21327.0	−0.738831	−0.369416	−	0.929264i	$-0.620442\pi$
$941$	−21327.0	−0.738831	−0.369416	+	0.929264i	$0.620442\pi$
$942$	0	0
$943$	5175.00	0.178708
$944$	1704.00	0.0587505
$945$	0	0
$946$	−4230.00	−0.145380
$947$	−24249.0	−0.832087	−0.416044	−	0.909345i	$-0.636584\pi$
$947$	−24249.0	−0.832087	−0.416044	+	0.909345i	$0.636584\pi$
$948$	0	0
$949$	6358.00	0.217481
$950$	25752.0	0.879479
$951$	0	0
$952$	−11466.0	−0.390352
$953$	−35118.0	−1.19369	−0.596843	−	0.802358i	$-0.703579\pi$
$953$	−35118.0	−1.19369	−0.596843	+	0.802358i	$0.703579\pi$
$954$	0	0
$955$	−3096.00	−0.104905
$956$	−4482.00	−0.151630
$957$	0	0
$958$	14760.0	0.497781
$959$	−6657.00	−0.224156
$960$	0	0
$961$	−26655.0	−0.894733
$962$	5577.00	0.186912
$963$	0	0
$964$	−2995.00	−0.100065
$965$	−4569.00	−0.152416
$966$	0	0
$967$	32672.0	1.08652	0.543258	−	0.839566i	$-0.317191\pi$
$967$	32672.0	1.08652	0.543258	+	0.839566i	$0.317191\pi$
$968$	−9051.00	−0.300527
$969$	0	0
$970$	9171.00	0.303570
$971$	2796.00	0.0924077	0.0462039	−	0.998932i	$-0.485288\pi$
$971$	2796.00	0.0924077	0.0462039	+	0.998932i	$0.485288\pi$
$972$	0	0
$973$	13559.0	0.446744
$974$	−4137.00	−0.136097
$975$	0	0
$976$	−51262.0	−1.68121
$977$	44265.0	1.44950	0.724751	−	0.689011i	$-0.241955\pi$
$977$	44265.0	1.44950	0.724751	+	0.689011i	$0.241955\pi$
$978$	0	0
$979$	−42480.0	−1.38679
$980$	−147.000	−0.00479157
$981$	0	0
$982$	5508.00	0.178989
$983$	1416.00	0.0459444	0.0229722	−	0.999736i	$-0.492687\pi$
$983$	1416.00	0.0459444	0.0229722	+	0.999736i	$0.492687\pi$
$984$	0	0
$985$	2673.00	0.0864658
$986$	−2106.00	−0.0680210
$987$	0	0
$988$	814.000	0.0262113
$989$	−1081.00	−0.0347561
$990$	0	0
$991$	60068.0	1.92545	0.962726	−	0.270479i	$-0.0871819\pi$
$991$	60068.0	1.92545	0.962726	+	0.270479i	$0.0871819\pi$
$992$	2520.00	0.0806553
$993$	0	0
$994$	1890.00	0.0603090
$995$	−11265.0	−0.358919
$996$	0	0
$997$	−4426.00	−0.140595	−0.0702973	−	0.997526i	$-0.522395\pi$
$997$	−4426.00	−0.140595	−0.0702973	+	0.997526i	$0.522395\pi$
$998$	−19176.0	−0.608222
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1449.4.a.a.1.1	✓	1
3.2	odd	2		1449.4.a.b.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1449.4.a.a.1.1	✓	1	1.1	even	1	trivial
1449.4.a.b.1.1	yes	1	3.2	odd	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:	\( N \)	\(=\)	\( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1449.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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