LMFDB - Embedded newform 1050.4.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,4,Mod(1,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, 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("1050.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1050.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:	$61.9520055060$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1050.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -12.0000 q^{12} -26.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -18.0000 q^{17} +18.0000 q^{18} +92.0000 q^{19} +21.0000 q^{21} -24.0000 q^{24} -52.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} -6.00000 q^{29} -4.00000 q^{31} +32.0000 q^{32} -36.0000 q^{34} +36.0000 q^{36} -410.000 q^{37} +184.000 q^{38} +78.0000 q^{39} +174.000 q^{41} +42.0000 q^{42} -248.000 q^{43} -420.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} +54.0000 q^{51} -104.000 q^{52} -102.000 q^{53} -54.0000 q^{54} -56.0000 q^{56} -276.000 q^{57} -12.0000 q^{58} -588.000 q^{59} +650.000 q^{61} -8.00000 q^{62} -63.0000 q^{63} +64.0000 q^{64} -152.000 q^{67} -72.0000 q^{68} -168.000 q^{71} +72.0000 q^{72} +610.000 q^{73} -820.000 q^{74} +368.000 q^{76} +156.000 q^{78} -1048.00 q^{79} +81.0000 q^{81} +348.000 q^{82} +684.000 q^{83} +84.0000 q^{84} -496.000 q^{86} +18.0000 q^{87} -834.000 q^{89} +182.000 q^{91} +12.0000 q^{93} -840.000 q^{94} -96.0000 q^{96} -110.000 q^{97} +98.0000 q^{98} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−12.0000	−0.288675
$13$	−26.0000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−26.0000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−18.0000	−0.256802	−0.128401	−	0.991722i	$-0.540985\pi$
$17$	−18.0000	−0.256802	−0.128401	+	0.991722i	$0.540985\pi$
$18$	18.0000	0.235702
$19$	92.0000	1.11086	0.555428	−	0.831565i	$-0.312555\pi$
$19$	92.0000	1.11086	0.555428	+	0.831565i	$0.312555\pi$
$20$	0	0
$21$	21.0000	0.218218
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	−52.0000	−0.392232
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−6.00000	−0.0384197	−0.0192099	−	0.999815i	$-0.506115\pi$
$29$	−6.00000	−0.0384197	−0.0192099	+	0.999815i	$0.506115\pi$
$30$	0	0
$31$	−4.00000	−0.0231749	−0.0115874	−	0.999933i	$-0.503688\pi$
$31$	−4.00000	−0.0231749	−0.0115874	+	0.999933i	$0.503688\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−36.0000	−0.181587
$35$	0	0
$36$	36.0000	0.166667
$37$	−410.000	−1.82172	−0.910859	−	0.412717i	$-0.864580\pi$
$37$	−410.000	−1.82172	−0.910859	+	0.412717i	$0.864580\pi$
$38$	184.000	0.785493
$39$	78.0000	0.320256
$40$	0	0
$41$	174.000	0.662786	0.331393	−	0.943493i	$-0.392481\pi$
$41$	174.000	0.662786	0.331393	+	0.943493i	$0.392481\pi$
$42$	42.0000	0.154303
$43$	−248.000	−0.879527	−0.439763	−	0.898114i	$-0.644938\pi$
$43$	−248.000	−0.879527	−0.439763	+	0.898114i	$0.644938\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−420.000	−1.30347	−0.651737	−	0.758445i	$-0.725959\pi$
$47$	−420.000	−1.30347	−0.651737	+	0.758445i	$0.725959\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	0	0
$51$	54.0000	0.148265
$52$	−104.000	−0.277350
$53$	−102.000	−0.264354	−0.132177	−	0.991226i	$-0.542197\pi$
$53$	−102.000	−0.264354	−0.132177	+	0.991226i	$0.542197\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	−56.0000	−0.133631
$57$	−276.000	−0.641353
$58$	−12.0000	−0.0271668
$59$	−588.000	−1.29748	−0.648738	−	0.761012i	$-0.724703\pi$
$59$	−588.000	−1.29748	−0.648738	+	0.761012i	$0.724703\pi$
$60$	0	0
$61$	650.000	1.36433	0.682164	−	0.731199i	$-0.261039\pi$
$61$	650.000	1.36433	0.682164	+	0.731199i	$0.261039\pi$
$62$	−8.00000	−0.0163871
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	0	0
$66$	0	0
$67$	−152.000	−0.277161	−0.138580	−	0.990351i	$-0.544254\pi$
$67$	−152.000	−0.277161	−0.138580	+	0.990351i	$0.544254\pi$
$68$	−72.0000	−0.128401
$69$	0	0
$70$	0	0
$71$	−168.000	−0.280816	−0.140408	−	0.990094i	$-0.544841\pi$
$71$	−168.000	−0.280816	−0.140408	+	0.990094i	$0.544841\pi$
$72$	72.0000	0.117851
$73$	610.000	0.978015	0.489008	−	0.872280i	$-0.337359\pi$
$73$	610.000	0.978015	0.489008	+	0.872280i	$0.337359\pi$
$74$	−820.000	−1.28815
$75$	0	0
$76$	368.000	0.555428
$77$	0	0
$78$	156.000	0.226455
$79$	−1048.00	−1.49252	−0.746261	−	0.665654i	$-0.768153\pi$
$79$	−1048.00	−1.49252	−0.746261	+	0.665654i	$0.768153\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	348.000	0.468661
$83$	684.000	0.904563	0.452282	−	0.891875i	$-0.350610\pi$
$83$	684.000	0.904563	0.452282	+	0.891875i	$0.350610\pi$
$84$	84.0000	0.109109
$85$	0	0
$86$	−496.000	−0.621919
$87$	18.0000	0.0221816
$88$	0	0
$89$	−834.000	−0.993301	−0.496651	−	0.867951i	$-0.665437\pi$
$89$	−834.000	−0.993301	−0.496651	+	0.867951i	$0.665437\pi$
$90$	0	0
$91$	182.000	0.209657
$92$	0	0
$93$	12.0000	0.0133800
$94$	−840.000	−0.921696
$95$	0	0
$96$	−96.0000	−0.102062
$97$	−110.000	−0.115142	−0.0575712	−	0.998341i	$-0.518336\pi$
$97$	−110.000	−0.115142	−0.0575712	+	0.998341i	$0.518336\pi$
$98$	98.0000	0.101015
$99$	0	0
$100$	0	0
$101$	−1374.00	−1.35364	−0.676822	−	0.736146i	$-0.736643\pi$
$101$	−1374.00	−1.35364	−0.676822	+	0.736146i	$0.736643\pi$
$102$	108.000	0.104839
$103$	−1184.00	−1.13265	−0.566325	−	0.824182i	$-0.691635\pi$
$103$	−1184.00	−1.13265	−0.566325	+	0.824182i	$0.691635\pi$
$104$	−208.000	−0.196116
$105$	0	0
$106$	−204.000	−0.186927
$107$	276.000	0.249364	0.124682	−	0.992197i	$-0.460209\pi$
$107$	276.000	0.249364	0.124682	+	0.992197i	$0.460209\pi$
$108$	−108.000	−0.0962250
$109$	−1594.00	−1.40071	−0.700356	−	0.713794i	$-0.746975\pi$
$109$	−1594.00	−1.40071	−0.700356	+	0.713794i	$0.746975\pi$
$110$	0	0
$111$	1230.00	1.05177
$112$	−112.000	−0.0944911
$113$	−738.000	−0.614382	−0.307191	−	0.951648i	$-0.599389\pi$
$113$	−738.000	−0.614382	−0.307191	+	0.951648i	$0.599389\pi$
$114$	−552.000	−0.453505
$115$	0	0
$116$	−24.0000	−0.0192099
$117$	−234.000	−0.184900
$118$	−1176.00	−0.917454
$119$	126.000	0.0970622
$120$	0	0
$121$	−1331.00	−1.00000
$122$	1300.00	0.964725
$123$	−522.000	−0.382660
$124$	−16.0000	−0.0115874
$125$	0	0
$126$	−126.000	−0.0890871
$127$	−776.000	−0.542196	−0.271098	−	0.962552i	$-0.587387\pi$
$127$	−776.000	−0.542196	−0.271098	+	0.962552i	$0.587387\pi$
$128$	128.000	0.0883883
$129$	744.000	0.507795
$130$	0	0
$131$	588.000	0.392166	0.196083	−	0.980587i	$-0.437178\pi$
$131$	588.000	0.392166	0.196083	+	0.980587i	$0.437178\pi$
$132$	0	0
$133$	−644.000	−0.419864
$134$	−304.000	−0.195982
$135$	0	0
$136$	−144.000	−0.0907934
$137$	−1242.00	−0.774534	−0.387267	−	0.921968i	$-0.626581\pi$
$137$	−1242.00	−0.774534	−0.387267	+	0.921968i	$0.626581\pi$
$138$	0	0
$139$	−724.000	−0.441790	−0.220895	−	0.975298i	$-0.570898\pi$
$139$	−724.000	−0.441790	−0.220895	+	0.975298i	$0.570898\pi$
$140$	0	0
$141$	1260.00	0.752561
$142$	−336.000	−0.198567
$143$	0	0
$144$	144.000	0.0833333
$145$	0	0
$146$	1220.00	0.691561
$147$	−147.000	−0.0824786
$148$	−1640.00	−0.910859
$149$	−1566.00	−0.861018	−0.430509	−	0.902586i	$-0.641666\pi$
$149$	−1566.00	−0.861018	−0.430509	+	0.902586i	$0.641666\pi$
$150$	0	0
$151$	1208.00	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	1208.00	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	736.000	0.392747
$153$	−162.000	−0.0856008
$154$	0	0
$155$	0	0
$156$	312.000	0.160128
$157$	2374.00	1.20679	0.603394	−	0.797443i	$-0.293815\pi$
$157$	2374.00	1.20679	0.603394	+	0.797443i	$0.293815\pi$
$158$	−2096.00	−1.05537
$159$	306.000	0.152625
$160$	0	0
$161$	0	0
$162$	162.000	0.0785674
$163$	400.000	0.192211	0.0961056	−	0.995371i	$-0.469361\pi$
$163$	400.000	0.192211	0.0961056	+	0.995371i	$0.469361\pi$
$164$	696.000	0.331393
$165$	0	0
$166$	1368.00	0.639623
$167$	−1260.00	−0.583843	−0.291921	−	0.956442i	$-0.594295\pi$
$167$	−1260.00	−0.583843	−0.291921	+	0.956442i	$0.594295\pi$
$168$	168.000	0.0771517
$169$	−1521.00	−0.692308
$170$	0	0
$171$	828.000	0.370285
$172$	−992.000	−0.439763
$173$	−258.000	−0.113384	−0.0566918	−	0.998392i	$-0.518055\pi$
$173$	−258.000	−0.113384	−0.0566918	+	0.998392i	$0.518055\pi$
$174$	36.0000	0.0156848
$175$	0	0
$176$	0	0
$177$	1764.00	0.749098
$178$	−1668.00	−0.702370
$179$	2784.00	1.16249	0.581246	−	0.813728i	$-0.302566\pi$
$179$	2784.00	1.16249	0.581246	+	0.813728i	$0.302566\pi$
$180$	0	0
$181$	−70.0000	−0.0287462	−0.0143731	−	0.999897i	$-0.504575\pi$
$181$	−70.0000	−0.0287462	−0.0143731	+	0.999897i	$0.504575\pi$
$182$	364.000	0.148250
$183$	−1950.00	−0.787695
$184$	0	0
$185$	0	0
$186$	24.0000	0.00946110
$187$	0	0
$188$	−1680.00	−0.651737
$189$	189.000	0.0727393
$190$	0	0
$191$	792.000	0.300037	0.150019	−	0.988683i	$-0.452067\pi$
$191$	792.000	0.300037	0.150019	+	0.988683i	$0.452067\pi$
$192$	−192.000	−0.0721688
$193$	214.000	0.0798138	0.0399069	−	0.999203i	$-0.487294\pi$
$193$	214.000	0.0798138	0.0399069	+	0.999203i	$0.487294\pi$
$194$	−220.000	−0.0814179
$195$	0	0
$196$	196.000	0.0714286
$197$	−2766.00	−1.00035	−0.500176	−	0.865924i	$-0.666731\pi$
$197$	−2766.00	−1.00035	−0.500176	+	0.865924i	$0.666731\pi$
$198$	0	0
$199$	−2020.00	−0.719568	−0.359784	−	0.933036i	$-0.617150\pi$
$199$	−2020.00	−0.719568	−0.359784	+	0.933036i	$0.617150\pi$
$200$	0	0
$201$	456.000	0.160019
$202$	−2748.00	−0.957171
$203$	42.0000	0.0145213
$204$	216.000	0.0741325
$205$	0	0
$206$	−2368.00	−0.800905
$207$	0	0
$208$	−416.000	−0.138675
$209$	0	0
$210$	0	0
$211$	356.000	0.116152	0.0580759	−	0.998312i	$-0.481503\pi$
$211$	356.000	0.116152	0.0580759	+	0.998312i	$0.481503\pi$
$212$	−408.000	−0.132177
$213$	504.000	0.162129
$214$	552.000	0.176327
$215$	0	0
$216$	−216.000	−0.0680414
$217$	28.0000	0.00875928
$218$	−3188.00	−0.990452
$219$	−1830.00	−0.564657
$220$	0	0
$221$	468.000	0.142448
$222$	2460.00	0.743713
$223$	2176.00	0.653434	0.326717	−	0.945122i	$-0.394058\pi$
$223$	2176.00	0.653434	0.326717	+	0.945122i	$0.394058\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	−1476.00	−0.434434
$227$	1716.00	0.501740	0.250870	−	0.968021i	$-0.419283\pi$
$227$	1716.00	0.501740	0.250870	+	0.968021i	$0.419283\pi$
$228$	−1104.00	−0.320676
$229$	−5734.00	−1.65464	−0.827322	−	0.561728i	$-0.810137\pi$
$229$	−5734.00	−1.65464	−0.827322	+	0.561728i	$0.810137\pi$
$230$	0	0
$231$	0	0
$232$	−48.0000	−0.0135834
$233$	−1770.00	−0.497668	−0.248834	−	0.968546i	$-0.580047\pi$
$233$	−1770.00	−0.497668	−0.248834	+	0.968546i	$0.580047\pi$
$234$	−468.000	−0.130744
$235$	0	0
$236$	−2352.00	−0.648738
$237$	3144.00	0.861708
$238$	252.000	0.0686333
$239$	6072.00	1.64337	0.821684	−	0.569943i	$-0.193035\pi$
$239$	6072.00	1.64337	0.821684	+	0.569943i	$0.193035\pi$
$240$	0	0
$241$	−4054.00	−1.08357	−0.541787	−	0.840516i	$-0.682252\pi$
$241$	−4054.00	−1.08357	−0.541787	+	0.840516i	$0.682252\pi$
$242$	−2662.00	−0.707107
$243$	−243.000	−0.0641500
$244$	2600.00	0.682164
$245$	0	0
$246$	−1044.00	−0.270581
$247$	−2392.00	−0.616192
$248$	−32.0000	−0.00819356
$249$	−2052.00	−0.522250
$250$	0	0
$251$	1788.00	0.449632	0.224816	−	0.974401i	$-0.427822\pi$
$251$	1788.00	0.449632	0.224816	+	0.974401i	$0.427822\pi$
$252$	−252.000	−0.0629941
$253$	0	0
$254$	−1552.00	−0.383390
$255$	0	0
$256$	256.000	0.0625000
$257$	5550.00	1.34708	0.673540	−	0.739151i	$-0.264773\pi$
$257$	5550.00	1.34708	0.673540	+	0.739151i	$0.264773\pi$
$258$	1488.00	0.359065
$259$	2870.00	0.688545
$260$	0	0
$261$	−54.0000	−0.0128066
$262$	1176.00	0.277304
$263$	−4368.00	−1.02412	−0.512058	−	0.858951i	$-0.671117\pi$
$263$	−4368.00	−1.02412	−0.512058	+	0.858951i	$0.671117\pi$
$264$	0	0
$265$	0	0
$266$	−1288.00	−0.296889
$267$	2502.00	0.573483
$268$	−608.000	−0.138580
$269$	−102.000	−0.0231191	−0.0115596	−	0.999933i	$-0.503680\pi$
$269$	−102.000	−0.0231191	−0.0115596	+	0.999933i	$0.503680\pi$
$270$	0	0
$271$	8180.00	1.83358	0.916789	−	0.399372i	$-0.130772\pi$
$271$	8180.00	1.83358	0.916789	+	0.399372i	$0.130772\pi$
$272$	−288.000	−0.0642006
$273$	−546.000	−0.121046
$274$	−2484.00	−0.547679
$275$	0	0
$276$	0	0
$277$	−3410.00	−0.739664	−0.369832	−	0.929099i	$-0.620585\pi$
$277$	−3410.00	−0.739664	−0.369832	+	0.929099i	$0.620585\pi$
$278$	−1448.00	−0.312393
$279$	−36.0000	−0.00772496
$280$	0	0
$281$	5058.00	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	5058.00	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	2520.00	0.532141
$283$	5572.00	1.17039	0.585196	−	0.810892i	$-0.301018\pi$
$283$	5572.00	1.17039	0.585196	+	0.810892i	$0.301018\pi$
$284$	−672.000	−0.140408
$285$	0	0
$286$	0	0
$287$	−1218.00	−0.250510
$288$	288.000	0.0589256
$289$	−4589.00	−0.934053
$290$	0	0
$291$	330.000	0.0664775
$292$	2440.00	0.489008
$293$	5790.00	1.15446	0.577228	−	0.816583i	$-0.304135\pi$
$293$	5790.00	1.15446	0.577228	+	0.816583i	$0.304135\pi$
$294$	−294.000	−0.0583212
$295$	0	0
$296$	−3280.00	−0.644075
$297$	0	0
$298$	−3132.00	−0.608832
$299$	0	0
$300$	0	0
$301$	1736.00	0.332430
$302$	2416.00	0.460348
$303$	4122.00	0.781527
$304$	1472.00	0.277714
$305$	0	0
$306$	−324.000	−0.0605289
$307$	−3452.00	−0.641746	−0.320873	−	0.947122i	$-0.603976\pi$
$307$	−3452.00	−0.641746	−0.320873	+	0.947122i	$0.603976\pi$
$308$	0	0
$309$	3552.00	0.653936
$310$	0	0
$311$	−3696.00	−0.673894	−0.336947	−	0.941524i	$-0.609394\pi$
$311$	−3696.00	−0.673894	−0.336947	+	0.941524i	$0.609394\pi$
$312$	624.000	0.113228
$313$	7018.00	1.26735	0.633675	−	0.773599i	$-0.281545\pi$
$313$	7018.00	1.26735	0.633675	+	0.773599i	$0.281545\pi$
$314$	4748.00	0.853328
$315$	0	0
$316$	−4192.00	−0.746261
$317$	−9486.00	−1.68072	−0.840358	−	0.542032i	$-0.817655\pi$
$317$	−9486.00	−1.68072	−0.840358	+	0.542032i	$0.817655\pi$
$318$	612.000	0.107922
$319$	0	0
$320$	0	0
$321$	−828.000	−0.143970
$322$	0	0
$323$	−1656.00	−0.285270
$324$	324.000	0.0555556
$325$	0	0
$326$	800.000	0.135914
$327$	4782.00	0.808701
$328$	1392.00	0.234330
$329$	2940.00	0.492667
$330$	0	0
$331$	5852.00	0.971767	0.485884	−	0.874023i	$-0.338498\pi$
$331$	5852.00	0.971767	0.485884	+	0.874023i	$0.338498\pi$
$332$	2736.00	0.452282
$333$	−3690.00	−0.607240
$334$	−2520.00	−0.412839
$335$	0	0
$336$	336.000	0.0545545
$337$	5686.00	0.919098	0.459549	−	0.888152i	$-0.348011\pi$
$337$	5686.00	0.919098	0.459549	+	0.888152i	$0.348011\pi$
$338$	−3042.00	−0.489535
$339$	2214.00	0.354714
$340$	0	0
$341$	0	0
$342$	1656.00	0.261831
$343$	−343.000	−0.0539949
$344$	−1984.00	−0.310960
$345$	0	0
$346$	−516.000	−0.0801744
$347$	7764.00	1.20113	0.600567	−	0.799575i	$-0.294942\pi$
$347$	7764.00	1.20113	0.600567	+	0.799575i	$0.294942\pi$
$348$	72.0000	0.0110908
$349$	−3070.00	−0.470869	−0.235435	−	0.971890i	$-0.575651\pi$
$349$	−3070.00	−0.470869	−0.235435	+	0.971890i	$0.575651\pi$
$350$	0	0
$351$	702.000	0.106752
$352$	0	0
$353$	4518.00	0.681215	0.340607	−	0.940206i	$-0.389367\pi$
$353$	4518.00	0.681215	0.340607	+	0.940206i	$0.389367\pi$
$354$	3528.00	0.529692
$355$	0	0
$356$	−3336.00	−0.496651
$357$	−378.000	−0.0560389
$358$	5568.00	0.822005
$359$	12552.0	1.84532	0.922659	−	0.385617i	$-0.126011\pi$
$359$	12552.0	1.84532	0.922659	+	0.385617i	$0.126011\pi$
$360$	0	0
$361$	1605.00	0.233999
$362$	−140.000	−0.0203266
$363$	3993.00	0.577350
$364$	728.000	0.104828
$365$	0	0
$366$	−3900.00	−0.556984
$367$	−5096.00	−0.724820	−0.362410	−	0.932019i	$-0.618046\pi$
$367$	−5096.00	−0.724820	−0.362410	+	0.932019i	$0.618046\pi$
$368$	0	0
$369$	1566.00	0.220929
$370$	0	0
$371$	714.000	0.0999165
$372$	48.0000	0.00669001
$373$	8782.00	1.21907	0.609537	−	0.792757i	$-0.291355\pi$
$373$	8782.00	1.21907	0.609537	+	0.792757i	$0.291355\pi$
$374$	0	0
$375$	0	0
$376$	−3360.00	−0.460848
$377$	156.000	0.0213114
$378$	378.000	0.0514344
$379$	−3196.00	−0.433160	−0.216580	−	0.976265i	$-0.569490\pi$
$379$	−3196.00	−0.433160	−0.216580	+	0.976265i	$0.569490\pi$
$380$	0	0
$381$	2328.00	0.313037
$382$	1584.00	0.212158
$383$	8148.00	1.08706	0.543529	−	0.839390i	$-0.317088\pi$
$383$	8148.00	1.08706	0.543529	+	0.839390i	$0.317088\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	428.000	0.0564369
$387$	−2232.00	−0.293176
$388$	−440.000	−0.0575712
$389$	354.000	0.0461401	0.0230701	−	0.999734i	$-0.492656\pi$
$389$	354.000	0.0461401	0.0230701	+	0.999734i	$0.492656\pi$
$390$	0	0
$391$	0	0
$392$	392.000	0.0505076
$393$	−1764.00	−0.226417
$394$	−5532.00	−0.707356
$395$	0	0
$396$	0	0
$397$	−9914.00	−1.25332	−0.626662	−	0.779291i	$-0.715579\pi$
$397$	−9914.00	−1.25332	−0.626662	+	0.779291i	$0.715579\pi$
$398$	−4040.00	−0.508811
$399$	1932.00	0.242408
$400$	0	0
$401$	5490.00	0.683685	0.341842	−	0.939757i	$-0.388949\pi$
$401$	5490.00	0.683685	0.341842	+	0.939757i	$0.388949\pi$
$402$	912.000	0.113150
$403$	104.000	0.0128551
$404$	−5496.00	−0.676822
$405$	0	0
$406$	84.0000	0.0102681
$407$	0	0
$408$	432.000	0.0524196
$409$	−6166.00	−0.745450	−0.372725	−	0.927942i	$-0.621577\pi$
$409$	−6166.00	−0.745450	−0.372725	+	0.927942i	$0.621577\pi$
$410$	0	0
$411$	3726.00	0.447178
$412$	−4736.00	−0.566325
$413$	4116.00	0.490400
$414$	0	0
$415$	0	0
$416$	−832.000	−0.0980581
$417$	2172.00	0.255068
$418$	0	0
$419$	6132.00	0.714959	0.357479	−	0.933921i	$-0.383636\pi$
$419$	6132.00	0.714959	0.357479	+	0.933921i	$0.383636\pi$
$420$	0	0
$421$	−3202.00	−0.370679	−0.185340	−	0.982675i	$-0.559339\pi$
$421$	−3202.00	−0.370679	−0.185340	+	0.982675i	$0.559339\pi$
$422$	712.000	0.0821318
$423$	−3780.00	−0.434491
$424$	−816.000	−0.0934634
$425$	0	0
$426$	1008.00	0.114643
$427$	−4550.00	−0.515667
$428$	1104.00	0.124682
$429$	0	0
$430$	0	0
$431$	−5712.00	−0.638370	−0.319185	−	0.947692i	$-0.603409\pi$
$431$	−5712.00	−0.638370	−0.319185	+	0.947692i	$0.603409\pi$
$432$	−432.000	−0.0481125
$433$	9490.00	1.05326	0.526629	−	0.850096i	$-0.323456\pi$
$433$	9490.00	1.05326	0.526629	+	0.850096i	$0.323456\pi$
$434$	56.0000	0.00619375
$435$	0	0
$436$	−6376.00	−0.700356
$437$	0	0
$438$	−3660.00	−0.399273
$439$	11828.0	1.28592	0.642961	−	0.765899i	$-0.277706\pi$
$439$	11828.0	1.28592	0.642961	+	0.765899i	$0.277706\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	936.000	0.100726
$443$	−7164.00	−0.768334	−0.384167	−	0.923264i	$-0.625511\pi$
$443$	−7164.00	−0.768334	−0.384167	+	0.923264i	$0.625511\pi$
$444$	4920.00	0.525885
$445$	0	0
$446$	4352.00	0.462047
$447$	4698.00	0.497109
$448$	−448.000	−0.0472456
$449$	7722.00	0.811634	0.405817	−	0.913954i	$-0.366987\pi$
$449$	7722.00	0.811634	0.405817	+	0.913954i	$0.366987\pi$
$450$	0	0
$451$	0	0
$452$	−2952.00	−0.307191
$453$	−3624.00	−0.375873
$454$	3432.00	0.354784
$455$	0	0
$456$	−2208.00	−0.226752
$457$	−13394.0	−1.37100	−0.685498	−	0.728075i	$-0.740415\pi$
$457$	−13394.0	−1.37100	−0.685498	+	0.728075i	$0.740415\pi$
$458$	−11468.0	−1.17001
$459$	486.000	0.0494217
$460$	0	0
$461$	8682.00	0.877139	0.438569	−	0.898697i	$-0.355485\pi$
$461$	8682.00	0.877139	0.438569	+	0.898697i	$0.355485\pi$
$462$	0	0
$463$	6640.00	0.666495	0.333247	−	0.942839i	$-0.391856\pi$
$463$	6640.00	0.666495	0.333247	+	0.942839i	$0.391856\pi$
$464$	−96.0000	−0.00960493
$465$	0	0
$466$	−3540.00	−0.351904
$467$	3372.00	0.334128	0.167064	−	0.985946i	$-0.446571\pi$
$467$	3372.00	0.334128	0.167064	+	0.985946i	$0.446571\pi$
$468$	−936.000	−0.0924500
$469$	1064.00	0.104757
$470$	0	0
$471$	−7122.00	−0.696740
$472$	−4704.00	−0.458727
$473$	0	0
$474$	6288.00	0.609319
$475$	0	0
$476$	504.000	0.0485311
$477$	−918.000	−0.0881181
$478$	12144.0	1.16204
$479$	14040.0	1.33926	0.669628	−	0.742696i	$-0.266453\pi$
$479$	14040.0	1.33926	0.669628	+	0.742696i	$0.266453\pi$
$480$	0	0
$481$	10660.0	1.01051
$482$	−8108.00	−0.766202
$483$	0	0
$484$	−5324.00	−0.500000
$485$	0	0
$486$	−486.000	−0.0453609
$487$	−18704.0	−1.74037	−0.870184	−	0.492727i	$-0.836000\pi$
$487$	−18704.0	−1.74037	−0.870184	+	0.492727i	$0.836000\pi$
$488$	5200.00	0.482363
$489$	−1200.00	−0.110973
$490$	0	0
$491$	−16440.0	−1.51105	−0.755526	−	0.655118i	$-0.772619\pi$
$491$	−16440.0	−1.51105	−0.755526	+	0.655118i	$0.772619\pi$
$492$	−2088.00	−0.191330
$493$	108.000	0.00986628
$494$	−4784.00	−0.435713
$495$	0	0
$496$	−64.0000	−0.00579372
$497$	1176.00	0.106138
$498$	−4104.00	−0.369286
$499$	−5860.00	−0.525711	−0.262855	−	0.964835i	$-0.584664\pi$
$499$	−5860.00	−0.525711	−0.262855	+	0.964835i	$0.584664\pi$
$500$	0	0
$501$	3780.00	0.337082
$502$	3576.00	0.317938
$503$	13380.0	1.18605	0.593027	−	0.805183i	$-0.297933\pi$
$503$	13380.0	1.18605	0.593027	+	0.805183i	$0.297933\pi$
$504$	−504.000	−0.0445435
$505$	0	0
$506$	0	0
$507$	4563.00	0.399704
$508$	−3104.00	−0.271098
$509$	−7590.00	−0.660945	−0.330472	−	0.943816i	$-0.607208\pi$
$509$	−7590.00	−0.660945	−0.330472	+	0.943816i	$0.607208\pi$
$510$	0	0
$511$	−4270.00	−0.369655
$512$	512.000	0.0441942
$513$	−2484.00	−0.213784
$514$	11100.0	0.952529
$515$	0	0
$516$	2976.00	0.253897
$517$	0	0
$518$	5740.00	0.486875
$519$	774.000	0.0654621
$520$	0	0
$521$	−22626.0	−1.90262	−0.951308	−	0.308242i	$-0.900259\pi$
$521$	−22626.0	−1.90262	−0.951308	+	0.308242i	$0.900259\pi$
$522$	−108.000	−0.00905562
$523$	−12476.0	−1.04309	−0.521546	−	0.853223i	$-0.674645\pi$
$523$	−12476.0	−1.04309	−0.521546	+	0.853223i	$0.674645\pi$
$524$	2352.00	0.196083
$525$	0	0
$526$	−8736.00	−0.724159
$527$	72.0000	0.00595136
$528$	0	0
$529$	−12167.0	−1.00000
$530$	0	0
$531$	−5292.00	−0.432492
$532$	−2576.00	−0.209932
$533$	−4524.00	−0.367648
$534$	5004.00	0.405514
$535$	0	0
$536$	−1216.00	−0.0979910
$537$	−8352.00	−0.671165
$538$	−204.000	−0.0163477
$539$	0	0
$540$	0	0
$541$	10046.0	0.798357	0.399179	−	0.916873i	$-0.369295\pi$
$541$	10046.0	0.798357	0.399179	+	0.916873i	$0.369295\pi$
$542$	16360.0	1.29654
$543$	210.000	0.0165966
$544$	−576.000	−0.0453967
$545$	0	0
$546$	−1092.00	−0.0855921
$547$	14392.0	1.12497	0.562484	−	0.826808i	$-0.309846\pi$
$547$	14392.0	1.12497	0.562484	+	0.826808i	$0.309846\pi$
$548$	−4968.00	−0.387267
$549$	5850.00	0.454776
$550$	0	0
$551$	−552.000	−0.0426787
$552$	0	0
$553$	7336.00	0.564120
$554$	−6820.00	−0.523022
$555$	0	0
$556$	−2896.00	−0.220895
$557$	21474.0	1.63354	0.816771	−	0.576962i	$-0.195762\pi$
$557$	21474.0	1.63354	0.816771	+	0.576962i	$0.195762\pi$
$558$	−72.0000	−0.00546237
$559$	6448.00	0.487874
$560$	0	0
$561$	0	0
$562$	10116.0	0.759284
$563$	16332.0	1.22258	0.611289	−	0.791407i	$-0.290651\pi$
$563$	16332.0	1.22258	0.611289	+	0.791407i	$0.290651\pi$
$564$	5040.00	0.376281
$565$	0	0
$566$	11144.0	0.827592
$567$	−567.000	−0.0419961
$568$	−1344.00	−0.0992834
$569$	19146.0	1.41062	0.705309	−	0.708900i	$-0.250808\pi$
$569$	19146.0	1.41062	0.705309	+	0.708900i	$0.250808\pi$
$570$	0	0
$571$	−18484.0	−1.35470	−0.677348	−	0.735663i	$-0.736871\pi$
$571$	−18484.0	−1.35470	−0.677348	+	0.735663i	$0.736871\pi$
$572$	0	0
$573$	−2376.00	−0.173227
$574$	−2436.00	−0.177137
$575$	0	0
$576$	576.000	0.0416667
$577$	−24590.0	−1.77417	−0.887084	−	0.461608i	$-0.847273\pi$
$577$	−24590.0	−1.77417	−0.887084	+	0.461608i	$0.847273\pi$
$578$	−9178.00	−0.660475
$579$	−642.000	−0.0460805
$580$	0	0
$581$	−4788.00	−0.341893
$582$	660.000	0.0470067
$583$	0	0
$584$	4880.00	0.345781
$585$	0	0
$586$	11580.0	0.816323
$587$	19476.0	1.36944	0.684719	−	0.728807i	$-0.259925\pi$
$587$	19476.0	1.36944	0.684719	+	0.728807i	$0.259925\pi$
$588$	−588.000	−0.0412393
$589$	−368.000	−0.0257439
$590$	0	0
$591$	8298.00	0.577553
$592$	−6560.00	−0.455430
$593$	19758.0	1.36824	0.684118	−	0.729371i	$-0.260187\pi$
$593$	19758.0	1.36824	0.684118	+	0.729371i	$0.260187\pi$
$594$	0	0
$595$	0	0
$596$	−6264.00	−0.430509
$597$	6060.00	0.415443
$598$	0	0
$599$	−26976.0	−1.84008	−0.920041	−	0.391821i	$-0.871845\pi$
$599$	−26976.0	−1.84008	−0.920041	+	0.391821i	$0.871845\pi$
$600$	0	0
$601$	−22798.0	−1.54734	−0.773669	−	0.633590i	$-0.781581\pi$
$601$	−22798.0	−1.54734	−0.773669	+	0.633590i	$0.781581\pi$
$602$	3472.00	0.235063
$603$	−1368.00	−0.0923868
$604$	4832.00	0.325515
$605$	0	0
$606$	8244.00	0.552623
$607$	−11936.0	−0.798134	−0.399067	−	0.916922i	$-0.630666\pi$
$607$	−11936.0	−0.798134	−0.399067	+	0.916922i	$0.630666\pi$
$608$	2944.00	0.196373
$609$	−126.000	−0.00838387
$610$	0	0
$611$	10920.0	0.723038
$612$	−648.000	−0.0428004
$613$	−19034.0	−1.25412	−0.627060	−	0.778971i	$-0.715742\pi$
$613$	−19034.0	−1.25412	−0.627060	+	0.778971i	$0.715742\pi$
$614$	−6904.00	−0.453783
$615$	0	0
$616$	0	0
$617$	−954.000	−0.0622473	−0.0311237	−	0.999516i	$-0.509909\pi$
$617$	−954.000	−0.0622473	−0.0311237	+	0.999516i	$0.509909\pi$
$618$	7104.00	0.462403
$619$	11108.0	0.721273	0.360637	−	0.932706i	$-0.382559\pi$
$619$	11108.0	0.721273	0.360637	+	0.932706i	$0.382559\pi$
$620$	0	0
$621$	0	0
$622$	−7392.00	−0.476515
$623$	5838.00	0.375433
$624$	1248.00	0.0800641
$625$	0	0
$626$	14036.0	0.896152
$627$	0	0
$628$	9496.00	0.603394
$629$	7380.00	0.467822
$630$	0	0
$631$	−8536.00	−0.538531	−0.269265	−	0.963066i	$-0.586781\pi$
$631$	−8536.00	−0.538531	−0.269265	+	0.963066i	$0.586781\pi$
$632$	−8384.00	−0.527686
$633$	−1068.00	−0.0670603
$634$	−18972.0	−1.18845
$635$	0	0
$636$	1224.00	0.0763125
$637$	−1274.00	−0.0792429
$638$	0	0
$639$	−1512.00	−0.0936053
$640$	0	0
$641$	−10158.0	−0.625923	−0.312962	−	0.949766i	$-0.601321\pi$
$641$	−10158.0	−0.625923	−0.312962	+	0.949766i	$0.601321\pi$
$642$	−1656.00	−0.101802
$643$	22732.0	1.39419	0.697094	−	0.716980i	$-0.254476\pi$
$643$	22732.0	1.39419	0.697094	+	0.716980i	$0.254476\pi$
$644$	0	0
$645$	0	0
$646$	−3312.00	−0.201717
$647$	19500.0	1.18489	0.592445	−	0.805611i	$-0.298163\pi$
$647$	19500.0	1.18489	0.592445	+	0.805611i	$0.298163\pi$
$648$	648.000	0.0392837
$649$	0	0
$650$	0	0
$651$	−84.0000	−0.00505717
$652$	1600.00	0.0961056
$653$	16218.0	0.971913	0.485957	−	0.873983i	$-0.338471\pi$
$653$	16218.0	0.971913	0.485957	+	0.873983i	$0.338471\pi$
$654$	9564.00	0.571838
$655$	0	0
$656$	2784.00	0.165697
$657$	5490.00	0.326005
$658$	5880.00	0.348368
$659$	−1968.00	−0.116331	−0.0581657	−	0.998307i	$-0.518525\pi$
$659$	−1968.00	−0.116331	−0.0581657	+	0.998307i	$0.518525\pi$
$660$	0	0
$661$	−15694.0	−0.923488	−0.461744	−	0.887013i	$-0.652776\pi$
$661$	−15694.0	−0.923488	−0.461744	+	0.887013i	$0.652776\pi$
$662$	11704.0	0.687143
$663$	−1404.00	−0.0822426
$664$	5472.00	0.319811
$665$	0	0
$666$	−7380.00	−0.429383
$667$	0	0
$668$	−5040.00	−0.291921
$669$	−6528.00	−0.377260
$670$	0	0
$671$	0	0
$672$	672.000	0.0385758
$673$	−20018.0	−1.14656	−0.573282	−	0.819358i	$-0.694330\pi$
$673$	−20018.0	−1.14656	−0.573282	+	0.819358i	$0.694330\pi$
$674$	11372.0	0.649901
$675$	0	0
$676$	−6084.00	−0.346154
$677$	−3834.00	−0.217655	−0.108828	−	0.994061i	$-0.534710\pi$
$677$	−3834.00	−0.217655	−0.108828	+	0.994061i	$0.534710\pi$
$678$	4428.00	0.250821
$679$	770.000	0.0435197
$680$	0	0
$681$	−5148.00	−0.289680
$682$	0	0
$683$	26172.0	1.46624	0.733121	−	0.680098i	$-0.238063\pi$
$683$	26172.0	1.46624	0.733121	+	0.680098i	$0.238063\pi$
$684$	3312.00	0.185143
$685$	0	0
$686$	−686.000	−0.0381802
$687$	17202.0	0.955309
$688$	−3968.00	−0.219882
$689$	2652.00	0.146637
$690$	0	0
$691$	10244.0	0.563965	0.281983	−	0.959419i	$-0.409008\pi$
$691$	10244.0	0.563965	0.281983	+	0.959419i	$0.409008\pi$
$692$	−1032.00	−0.0566918
$693$	0	0
$694$	15528.0	0.849330
$695$	0	0
$696$	144.000	0.00784239
$697$	−3132.00	−0.170205
$698$	−6140.00	−0.332955
$699$	5310.00	0.287329
$700$	0	0
$701$	7386.00	0.397953	0.198977	−	0.980004i	$-0.436238\pi$
$701$	7386.00	0.397953	0.198977	+	0.980004i	$0.436238\pi$
$702$	1404.00	0.0754851
$703$	−37720.0	−2.02367
$704$	0	0
$705$	0	0
$706$	9036.00	0.481692
$707$	9618.00	0.511630
$708$	7056.00	0.374549
$709$	−28330.0	−1.50064	−0.750321	−	0.661073i	$-0.770101\pi$
$709$	−28330.0	−1.50064	−0.750321	+	0.661073i	$0.770101\pi$
$710$	0	0
$711$	−9432.00	−0.497507
$712$	−6672.00	−0.351185
$713$	0	0
$714$	−756.000	−0.0396255
$715$	0	0
$716$	11136.0	0.581246
$717$	−18216.0	−0.948799
$718$	25104.0	1.30484
$719$	3024.00	0.156851	0.0784257	−	0.996920i	$-0.475011\pi$
$719$	3024.00	0.156851	0.0784257	+	0.996920i	$0.475011\pi$
$720$	0	0
$721$	8288.00	0.428102
$722$	3210.00	0.165462
$723$	12162.0	0.625601
$724$	−280.000	−0.0143731
$725$	0	0
$726$	7986.00	0.408248
$727$	12376.0	0.631362	0.315681	−	0.948865i	$-0.397767\pi$
$727$	12376.0	0.631362	0.315681	+	0.948865i	$0.397767\pi$
$728$	1456.00	0.0741249
$729$	729.000	0.0370370
$730$	0	0
$731$	4464.00	0.225865
$732$	−7800.00	−0.393847
$733$	−506.000	−0.0254973	−0.0127487	−	0.999919i	$-0.504058\pi$
$733$	−506.000	−0.0254973	−0.0127487	+	0.999919i	$0.504058\pi$
$734$	−10192.0	−0.512525
$735$	0	0
$736$	0	0
$737$	0	0
$738$	3132.00	0.156220
$739$	6428.00	0.319970	0.159985	−	0.987119i	$-0.448855\pi$
$739$	6428.00	0.319970	0.159985	+	0.987119i	$0.448855\pi$
$740$	0	0
$741$	7176.00	0.355758
$742$	1428.00	0.0706517
$743$	−32568.0	−1.60808	−0.804040	−	0.594575i	$-0.797320\pi$
$743$	−32568.0	−1.60808	−0.804040	+	0.594575i	$0.797320\pi$
$744$	96.0000	0.00473055
$745$	0	0
$746$	17564.0	0.862016
$747$	6156.00	0.301521
$748$	0	0
$749$	−1932.00	−0.0942507
$750$	0	0
$751$	28928.0	1.40559	0.702795	−	0.711393i	$-0.251935\pi$
$751$	28928.0	1.40559	0.702795	+	0.711393i	$0.251935\pi$
$752$	−6720.00	−0.325869
$753$	−5364.00	−0.259595
$754$	312.000	0.0150695
$755$	0	0
$756$	756.000	0.0363696
$757$	−5042.00	−0.242080	−0.121040	−	0.992648i	$-0.538623\pi$
$757$	−5042.00	−0.242080	−0.121040	+	0.992648i	$0.538623\pi$
$758$	−6392.00	−0.306290
$759$	0	0
$760$	0	0
$761$	29574.0	1.40875	0.704374	−	0.709829i	$-0.251228\pi$
$761$	29574.0	1.40875	0.704374	+	0.709829i	$0.251228\pi$
$762$	4656.00	0.221351
$763$	11158.0	0.529419
$764$	3168.00	0.150019
$765$	0	0
$766$	16296.0	0.768666
$767$	15288.0	0.719710
$768$	−768.000	−0.0360844
$769$	−8206.00	−0.384806	−0.192403	−	0.981316i	$-0.561628\pi$
$769$	−8206.00	−0.384806	−0.192403	+	0.981316i	$0.561628\pi$
$770$	0	0
$771$	−16650.0	−0.777737
$772$	856.000	0.0399069
$773$	−30786.0	−1.43247	−0.716233	−	0.697862i	$-0.754135\pi$
$773$	−30786.0	−1.43247	−0.716233	+	0.697862i	$0.754135\pi$
$774$	−4464.00	−0.207306
$775$	0	0
$776$	−880.000	−0.0407090
$777$	−8610.00	−0.397532
$778$	708.000	0.0326260
$779$	16008.0	0.736259
$780$	0	0
$781$	0	0
$782$	0	0
$783$	162.000	0.00739388
$784$	784.000	0.0357143
$785$	0	0
$786$	−3528.00	−0.160101
$787$	−19532.0	−0.884677	−0.442338	−	0.896848i	$-0.645851\pi$
$787$	−19532.0	−0.884677	−0.442338	+	0.896848i	$0.645851\pi$
$788$	−11064.0	−0.500176
$789$	13104.0	0.591273
$790$	0	0
$791$	5166.00	0.232215
$792$	0	0
$793$	−16900.0	−0.756793
$794$	−19828.0	−0.886233
$795$	0	0
$796$	−8080.00	−0.359784
$797$	−12546.0	−0.557594	−0.278797	−	0.960350i	$-0.589936\pi$
$797$	−12546.0	−0.557594	−0.278797	+	0.960350i	$0.589936\pi$
$798$	3864.00	0.171409
$799$	7560.00	0.334735
$800$	0	0
$801$	−7506.00	−0.331100
$802$	10980.0	0.483438
$803$	0	0
$804$	1824.00	0.0800094
$805$	0	0
$806$	208.000	0.00908993
$807$	306.000	0.0133478
$808$	−10992.0	−0.478586
$809$	9570.00	0.415900	0.207950	−	0.978139i	$-0.433321\pi$
$809$	9570.00	0.415900	0.207950	+	0.978139i	$0.433321\pi$
$810$	0	0
$811$	1964.00	0.0850374	0.0425187	−	0.999096i	$-0.486462\pi$
$811$	1964.00	0.0850374	0.0425187	+	0.999096i	$0.486462\pi$
$812$	168.000	0.00726065
$813$	−24540.0	−1.05862
$814$	0	0
$815$	0	0
$816$	864.000	0.0370662
$817$	−22816.0	−0.977027
$818$	−12332.0	−0.527113
$819$	1638.00	0.0698857
$820$	0	0
$821$	37122.0	1.57803	0.789017	−	0.614371i	$-0.210590\pi$
$821$	37122.0	1.57803	0.789017	+	0.614371i	$0.210590\pi$
$822$	7452.00	0.316202
$823$	−36536.0	−1.54747	−0.773733	−	0.633512i	$-0.781613\pi$
$823$	−36536.0	−1.54747	−0.773733	+	0.633512i	$0.781613\pi$
$824$	−9472.00	−0.400452
$825$	0	0
$826$	8232.00	0.346765
$827$	32412.0	1.36285	0.681424	−	0.731889i	$-0.261361\pi$
$827$	32412.0	1.36285	0.681424	+	0.731889i	$0.261361\pi$
$828$	0	0
$829$	−23686.0	−0.992339	−0.496169	−	0.868226i	$-0.665260\pi$
$829$	−23686.0	−0.992339	−0.496169	+	0.868226i	$0.665260\pi$
$830$	0	0
$831$	10230.0	0.427045
$832$	−1664.00	−0.0693375
$833$	−882.000	−0.0366861
$834$	4344.00	0.180360
$835$	0	0
$836$	0	0
$837$	108.000	0.00446001
$838$	12264.0	0.505552
$839$	25680.0	1.05670	0.528350	−	0.849026i	$-0.322811\pi$
$839$	25680.0	1.05670	0.528350	+	0.849026i	$0.322811\pi$
$840$	0	0
$841$	−24353.0	−0.998524
$842$	−6404.00	−0.262110
$843$	−15174.0	−0.619953
$844$	1424.00	0.0580759
$845$	0	0
$846$	−7560.00	−0.307232
$847$	9317.00	0.377964
$848$	−1632.00	−0.0660886
$849$	−16716.0	−0.675726
$850$	0	0
$851$	0	0
$852$	2016.00	0.0810646
$853$	29662.0	1.19063	0.595315	−	0.803492i	$-0.297027\pi$
$853$	29662.0	1.19063	0.595315	+	0.803492i	$0.297027\pi$
$854$	−9100.00	−0.364632
$855$	0	0
$856$	2208.00	0.0881634
$857$	−17418.0	−0.694268	−0.347134	−	0.937816i	$-0.612845\pi$
$857$	−17418.0	−0.694268	−0.347134	+	0.937816i	$0.612845\pi$
$858$	0	0
$859$	−22420.0	−0.890524	−0.445262	−	0.895400i	$-0.646890\pi$
$859$	−22420.0	−0.890524	−0.445262	+	0.895400i	$0.646890\pi$
$860$	0	0
$861$	3654.00	0.144632
$862$	−11424.0	−0.451396
$863$	−37008.0	−1.45975	−0.729877	−	0.683579i	$-0.760422\pi$
$863$	−37008.0	−1.45975	−0.729877	+	0.683579i	$0.760422\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	18980.0	0.744765
$867$	13767.0	0.539275
$868$	112.000	0.00437964
$869$	0	0
$870$	0	0
$871$	3952.00	0.153741
$872$	−12752.0	−0.495226
$873$	−990.000	−0.0383808
$874$	0	0
$875$	0	0
$876$	−7320.00	−0.282329
$877$	37222.0	1.43318	0.716589	−	0.697495i	$-0.245702\pi$
$877$	37222.0	1.43318	0.716589	+	0.697495i	$0.245702\pi$
$878$	23656.0	0.909284
$879$	−17370.0	−0.666525
$880$	0	0
$881$	48270.0	1.84592	0.922961	−	0.384893i	$-0.125762\pi$
$881$	48270.0	1.84592	0.922961	+	0.384893i	$0.125762\pi$
$882$	882.000	0.0336718
$883$	−35192.0	−1.34123	−0.670614	−	0.741806i	$-0.733969\pi$
$883$	−35192.0	−1.34123	−0.670614	+	0.741806i	$0.733969\pi$
$884$	1872.00	0.0712242
$885$	0	0
$886$	−14328.0	−0.543294
$887$	−50148.0	−1.89831	−0.949157	−	0.314802i	$-0.898062\pi$
$887$	−50148.0	−1.89831	−0.949157	+	0.314802i	$0.898062\pi$
$888$	9840.00	0.371857
$889$	5432.00	0.204931
$890$	0	0
$891$	0	0
$892$	8704.00	0.326717
$893$	−38640.0	−1.44797
$894$	9396.00	0.351509
$895$	0	0
$896$	−896.000	−0.0334077
$897$	0	0
$898$	15444.0	0.573912
$899$	24.0000	0.000890372 0
$900$	0	0
$901$	1836.00	0.0678868
$902$	0	0
$903$	−5208.00	−0.191928
$904$	−5904.00	−0.217217
$905$	0	0
$906$	−7248.00	−0.265782
$907$	18976.0	0.694694	0.347347	−	0.937737i	$-0.387083\pi$
$907$	18976.0	0.694694	0.347347	+	0.937737i	$0.387083\pi$
$908$	6864.00	0.250870
$909$	−12366.0	−0.451215
$910$	0	0
$911$	−52968.0	−1.92635	−0.963177	−	0.268869i	$-0.913350\pi$
$911$	−52968.0	−1.92635	−0.963177	+	0.268869i	$0.913350\pi$
$912$	−4416.00	−0.160338
$913$	0	0
$914$	−26788.0	−0.969440
$915$	0	0
$916$	−22936.0	−0.827322
$917$	−4116.00	−0.148225
$918$	972.000	0.0349464
$919$	−4792.00	−0.172006	−0.0860030	−	0.996295i	$-0.527409\pi$
$919$	−4792.00	−0.172006	−0.0860030	+	0.996295i	$0.527409\pi$
$920$	0	0
$921$	10356.0	0.370512
$922$	17364.0	0.620231
$923$	4368.00	0.155769
$924$	0	0
$925$	0	0
$926$	13280.0	0.471283
$927$	−10656.0	−0.377550
$928$	−192.000	−0.00679171
$929$	−32370.0	−1.14319	−0.571596	−	0.820535i	$-0.693676\pi$
$929$	−32370.0	−1.14319	−0.571596	+	0.820535i	$0.693676\pi$
$930$	0	0
$931$	4508.00	0.158694
$932$	−7080.00	−0.248834
$933$	11088.0	0.389073
$934$	6744.00	0.236264
$935$	0	0
$936$	−1872.00	−0.0653720
$937$	−4286.00	−0.149432	−0.0747159	−	0.997205i	$-0.523805\pi$
$937$	−4286.00	−0.149432	−0.0747159	+	0.997205i	$0.523805\pi$
$938$	2128.00	0.0740743
$939$	−21054.0	−0.731705
$940$	0	0
$941$	−18678.0	−0.647062	−0.323531	−	0.946218i	$-0.604870\pi$
$941$	−18678.0	−0.647062	−0.323531	+	0.946218i	$0.604870\pi$
$942$	−14244.0	−0.492669
$943$	0	0
$944$	−9408.00	−0.324369
$945$	0	0
$946$	0	0
$947$	21012.0	0.721012	0.360506	−	0.932757i	$-0.382604\pi$
$947$	21012.0	0.721012	0.360506	+	0.932757i	$0.382604\pi$
$948$	12576.0	0.430854
$949$	−15860.0	−0.542505
$950$	0	0
$951$	28458.0	0.970362
$952$	1008.00	0.0343167
$953$	−21930.0	−0.745417	−0.372708	−	0.927948i	$-0.621571\pi$
$953$	−21930.0	−0.745417	−0.372708	+	0.927948i	$0.621571\pi$
$954$	−1836.00	−0.0623089
$955$	0	0
$956$	24288.0	0.821684
$957$	0	0
$958$	28080.0	0.946998
$959$	8694.00	0.292747
$960$	0	0
$961$	−29775.0	−0.999463
$962$	21320.0	0.714537
$963$	2484.00	0.0831213
$964$	−16216.0	−0.541787
$965$	0	0
$966$	0	0
$967$	49144.0	1.63430	0.817148	−	0.576428i	$-0.195554\pi$
$967$	49144.0	1.63430	0.817148	+	0.576428i	$0.195554\pi$
$968$	−10648.0	−0.353553
$969$	4968.00	0.164701
$970$	0	0
$971$	−52884.0	−1.74781	−0.873907	−	0.486092i	$-0.838422\pi$
$971$	−52884.0	−1.74781	−0.873907	+	0.486092i	$0.838422\pi$
$972$	−972.000	−0.0320750
$973$	5068.00	0.166981
$974$	−37408.0	−1.23063
$975$	0	0
$976$	10400.0	0.341082
$977$	−22722.0	−0.744054	−0.372027	−	0.928222i	$-0.621337\pi$
$977$	−22722.0	−0.744054	−0.372027	+	0.928222i	$0.621337\pi$
$978$	−2400.00	−0.0784699
$979$	0	0
$980$	0	0
$981$	−14346.0	−0.466904
$982$	−32880.0	−1.06848
$983$	−11772.0	−0.381962	−0.190981	−	0.981594i	$-0.561167\pi$
$983$	−11772.0	−0.381962	−0.190981	+	0.981594i	$0.561167\pi$
$984$	−4176.00	−0.135291
$985$	0	0
$986$	216.000	0.00697651
$987$	−8820.00	−0.284441
$988$	−9568.00	−0.308096
$989$	0	0
$990$	0	0
$991$	17408.0	0.558005	0.279003	−	0.960290i	$-0.409996\pi$
$991$	17408.0	0.558005	0.279003	+	0.960290i	$0.409996\pi$
$992$	−128.000	−0.00409678
$993$	−17556.0	−0.561050
$994$	2352.00	0.0750512
$995$	0	0
$996$	−8208.00	−0.261125
$997$	24478.0	0.777559	0.388779	−	0.921331i	$-0.372897\pi$
$997$	24478.0	0.777559	0.388779	+	0.921331i	$0.372897\pi$
$998$	−11720.0	−0.371734
$999$	11070.0	0.350590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.4.a.n.1.1		1
5.2	odd	4		1050.4.g.d.799.2		2
5.3	odd	4		1050.4.g.d.799.1		2
5.4	even	2		210.4.a.e.1.1	✓	1
15.14	odd	2		630.4.a.w.1.1		1
20.19	odd	2		1680.4.a.a.1.1		1
35.34	odd	2		1470.4.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.e.1.1	✓	1	5.4	even	2
630.4.a.w.1.1		1	15.14	odd	2
1050.4.a.n.1.1		1	1.1	even	1	trivial
1050.4.g.d.799.1		2	5.3	odd	4
1050.4.g.d.799.2		2	5.2	odd	4
1470.4.a.g.1.1		1	35.34	odd	2
1680.4.a.a.1.1		1	20.19	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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