LMFDB - Embedded newform 950.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,6,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("950.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	950.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:	$152.364628822$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{2} +14.0000 q^{3} +16.0000 q^{4} -56.0000 q^{6} +121.000 q^{7} -64.0000 q^{8} -47.0000 q^{9} +O(q^{10})$

\(q-4.00000 q^{2} +14.0000 q^{3} +16.0000 q^{4} -56.0000 q^{6} +121.000 q^{7} -64.0000 q^{8} -47.0000 q^{9} -381.000 q^{11} +224.000 q^{12} +100.000 q^{13} -484.000 q^{14} +256.000 q^{16} -933.000 q^{17} +188.000 q^{18} +361.000 q^{19} +1694.00 q^{21} +1524.00 q^{22} +552.000 q^{23} -896.000 q^{24} -400.000 q^{26} -4060.00 q^{27} +1936.00 q^{28} +2394.00 q^{29} -4024.00 q^{31} -1024.00 q^{32} -5334.00 q^{33} +3732.00 q^{34} -752.000 q^{36} -9182.00 q^{37} -1444.00 q^{38} +1400.00 q^{39} -2250.00 q^{41} -6776.00 q^{42} +23377.0 q^{43} -6096.00 q^{44} -2208.00 q^{46} +26595.0 q^{47} +3584.00 q^{48} -2166.00 q^{49} -13062.0 q^{51} +1600.00 q^{52} +16008.0 q^{53} +16240.0 q^{54} -7744.00 q^{56} +5054.00 q^{57} -9576.00 q^{58} -126.000 q^{59} +21335.0 q^{61} +16096.0 q^{62} -5687.00 q^{63} +4096.00 q^{64} +21336.0 q^{66} +51760.0 q^{67} -14928.0 q^{68} +7728.00 q^{69} +8574.00 q^{71} +3008.00 q^{72} -11153.0 q^{73} +36728.0 q^{74} +5776.00 q^{76} -46101.0 q^{77} -5600.00 q^{78} -1660.00 q^{79} -45419.0 q^{81} +9000.00 q^{82} -95964.0 q^{83} +27104.0 q^{84} -93508.0 q^{86} +33516.0 q^{87} +24384.0 q^{88} +118848. q^{89} +12100.0 q^{91} +8832.00 q^{92} -56336.0 q^{93} -106380. q^{94} -14336.0 q^{96} +153760. q^{97} +8664.00 q^{98} +17907.0 q^{99} +O(q^{100})\)

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	14.0000	0.898100	0.449050	−	0.893507i	$-0.351762\pi$
$3$	14.0000	0.898100	0.449050	+	0.893507i	$0.351762\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	−56.0000	−0.635053
$7$	121.000	0.933341	0.466670	−	0.884431i	$-0.345453\pi$
$7$	121.000	0.933341	0.466670	+	0.884431i	$0.345453\pi$
$8$	−64.0000	−0.353553
$9$	−47.0000	−0.193416
$10$	0	0
$11$	−381.000	−0.949387	−0.474693	−	0.880151i	$-0.657441\pi$
$11$	−381.000	−0.949387	−0.474693	+	0.880151i	$0.657441\pi$
$12$	224.000	0.449050
$13$	100.000	0.164112	0.0820562	−	0.996628i	$-0.473851\pi$
$13$	100.000	0.164112	0.0820562	+	0.996628i	$0.473851\pi$
$14$	−484.000	−0.659972
$15$	0	0
$16$	256.000	0.250000
$17$	−933.000	−0.782996	−0.391498	−	0.920179i	$-0.628043\pi$
$17$	−933.000	−0.782996	−0.391498	+	0.920179i	$0.628043\pi$
$18$	188.000	0.136766
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	0	0
$21$	1694.00	0.838234
$22$	1524.00	0.671318
$23$	552.000	0.217580	0.108790	−	0.994065i	$-0.465302\pi$
$23$	552.000	0.217580	0.108790	+	0.994065i	$0.465302\pi$
$24$	−896.000	−0.317526
$25$	0	0
$26$	−400.000	−0.116045
$27$	−4060.00	−1.07181
$28$	1936.00	0.466670
$29$	2394.00	0.528602	0.264301	−	0.964440i	$-0.414859\pi$
$29$	2394.00	0.528602	0.264301	+	0.964440i	$0.414859\pi$
$30$	0	0
$31$	−4024.00	−0.752062	−0.376031	−	0.926607i	$-0.622711\pi$
$31$	−4024.00	−0.752062	−0.376031	+	0.926607i	$0.622711\pi$
$32$	−1024.00	−0.176777
$33$	−5334.00	−0.852645
$34$	3732.00	0.553662
$35$	0	0
$36$	−752.000	−0.0967078
$37$	−9182.00	−1.10264	−0.551319	−	0.834295i	$-0.685875\pi$
$37$	−9182.00	−1.10264	−0.551319	+	0.834295i	$0.685875\pi$
$38$	−1444.00	−0.162221
$39$	1400.00	0.147389
$40$	0	0
$41$	−2250.00	−0.209037	−0.104518	−	0.994523i	$-0.533330\pi$
$41$	−2250.00	−0.209037	−0.104518	+	0.994523i	$0.533330\pi$
$42$	−6776.00	−0.592721
$43$	23377.0	1.92805	0.964024	−	0.265817i	$-0.0856416\pi$
$43$	23377.0	1.92805	0.964024	+	0.265817i	$0.0856416\pi$
$44$	−6096.00	−0.474693
$45$	0	0
$46$	−2208.00	−0.153852
$47$	26595.0	1.75612	0.878062	−	0.478546i	$-0.158836\pi$
$47$	26595.0	1.75612	0.878062	+	0.478546i	$0.158836\pi$
$48$	3584.00	0.224525
$49$	−2166.00	−0.128875
$50$	0	0
$51$	−13062.0	−0.703209
$52$	1600.00	0.0820562
$53$	16008.0	0.782794	0.391397	−	0.920222i	$-0.371992\pi$
$53$	16008.0	0.782794	0.391397	+	0.920222i	$0.371992\pi$
$54$	16240.0	0.757882
$55$	0	0
$56$	−7744.00	−0.329986
$57$	5054.00	0.206038
$58$	−9576.00	−0.373778
$59$	−126.000	−0.00471238	−0.00235619	−	0.999997i	$-0.500750\pi$
$59$	−126.000	−0.00471238	−0.00235619	+	0.999997i	$0.500750\pi$
$60$	0	0
$61$	21335.0	0.734122	0.367061	−	0.930197i	$-0.380364\pi$
$61$	21335.0	0.734122	0.367061	+	0.930197i	$0.380364\pi$
$62$	16096.0	0.531788
$63$	−5687.00	−0.180523
$64$	4096.00	0.125000
$65$	0	0
$66$	21336.0	0.602911
$67$	51760.0	1.40866	0.704332	−	0.709871i	$-0.251247\pi$
$67$	51760.0	1.40866	0.704332	+	0.709871i	$0.251247\pi$
$68$	−14928.0	−0.391498
$69$	7728.00	0.195409
$70$	0	0
$71$	8574.00	0.201854	0.100927	−	0.994894i	$-0.467819\pi$
$71$	8574.00	0.201854	0.100927	+	0.994894i	$0.467819\pi$
$72$	3008.00	0.0683828
$73$	−11153.0	−0.244954	−0.122477	−	0.992471i	$-0.539084\pi$
$73$	−11153.0	−0.244954	−0.122477	+	0.992471i	$0.539084\pi$
$74$	36728.0	0.779683
$75$	0	0
$76$	5776.00	0.114708
$77$	−46101.0	−0.886102
$78$	−5600.00	−0.104220
$79$	−1660.00	−0.0299254	−0.0149627	−	0.999888i	$-0.504763\pi$
$79$	−1660.00	−0.0299254	−0.0149627	+	0.999888i	$0.504763\pi$
$80$	0	0
$81$	−45419.0	−0.769175
$82$	9000.00	0.147811
$83$	−95964.0	−1.52902	−0.764510	−	0.644612i	$-0.777019\pi$
$83$	−95964.0	−1.52902	−0.764510	+	0.644612i	$0.777019\pi$
$84$	27104.0	0.419117
$85$	0	0
$86$	−93508.0	−1.36334
$87$	33516.0	0.474738
$88$	24384.0	0.335659
$89$	118848.	1.59044	0.795219	−	0.606322i	$-0.207356\pi$
$89$	118848.	1.59044	0.795219	+	0.606322i	$0.207356\pi$
$90$	0	0
$91$	12100.0	0.153173
$92$	8832.00	0.108790
$93$	−56336.0	−0.675427
$94$	−106380.	−1.24177
$95$	0	0
$96$	−14336.0	−0.158763
$97$	153760.	1.65926	0.829629	−	0.558315i	$-0.188552\pi$
$97$	153760.	1.65926	0.829629	+	0.558315i	$0.188552\pi$
$98$	8664.00	0.0911283
$99$	17907.0	0.183626
$100$	0	0
$101$	153198.	1.49434	0.747170	−	0.664633i	$-0.231412\pi$
$101$	153198.	1.49434	0.747170	+	0.664633i	$0.231412\pi$
$102$	52248.0	0.497244
$103$	44506.0	0.413357	0.206679	−	0.978409i	$-0.433735\pi$
$103$	44506.0	0.413357	0.206679	+	0.978409i	$0.433735\pi$
$104$	−6400.00	−0.0580225
$105$	0	0
$106$	−64032.0	−0.553519
$107$	122634.	1.03550	0.517752	−	0.855531i	$-0.326769\pi$
$107$	122634.	1.03550	0.517752	+	0.855531i	$0.326769\pi$
$108$	−64960.0	−0.535904
$109$	54956.0	0.443046	0.221523	−	0.975155i	$-0.428897\pi$
$109$	54956.0	0.443046	0.221523	+	0.975155i	$0.428897\pi$
$110$	0	0
$111$	−128548.	−0.990280
$112$	30976.0	0.233335
$113$	−101586.	−0.748407	−0.374203	−	0.927347i	$-0.622084\pi$
$113$	−101586.	−0.748407	−0.374203	+	0.927347i	$0.622084\pi$
$114$	−20216.0	−0.145691
$115$	0	0
$116$	38304.0	0.264301
$117$	−4700.00	−0.0317419
$118$	504.000	0.00333216
$119$	−112893.	−0.730802
$120$	0	0
$121$	−15890.0	−0.0986644
$122$	−85340.0	−0.519102
$123$	−31500.0	−0.187736
$124$	−64384.0	−0.376031
$125$	0	0
$126$	22748.0	0.127649
$127$	309778.	1.70428	0.852141	−	0.523313i	$-0.175304\pi$
$127$	309778.	1.70428	0.852141	+	0.523313i	$0.175304\pi$
$128$	−16384.0	−0.0883883
$129$	327278.	1.73158
$130$	0	0
$131$	−2295.00	−0.0116843	−0.00584217	−	0.999983i	$-0.501860\pi$
$131$	−2295.00	−0.0116843	−0.00584217	+	0.999983i	$0.501860\pi$
$132$	−85344.0	−0.426322
$133$	43681.0	0.214123
$134$	−207040.	−0.996076
$135$	0	0
$136$	59712.0	0.276831
$137$	−89181.0	−0.405948	−0.202974	−	0.979184i	$-0.565061\pi$
$137$	−89181.0	−0.405948	−0.202974	+	0.979184i	$0.565061\pi$
$138$	−30912.0	−0.138175
$139$	189971.	0.833970	0.416985	−	0.908913i	$-0.363087\pi$
$139$	189971.	0.833970	0.416985	+	0.908913i	$0.363087\pi$
$140$	0	0
$141$	372330.	1.57718
$142$	−34296.0	−0.142732
$143$	−38100.0	−0.155806
$144$	−12032.0	−0.0483539
$145$	0	0
$146$	44612.0	0.173209
$147$	−30324.0	−0.115743
$148$	−146912.	−0.551319
$149$	−435915.	−1.60856	−0.804278	−	0.594253i	$-0.797448\pi$
$149$	−435915.	−1.60856	−0.804278	+	0.594253i	$0.797448\pi$
$150$	0	0
$151$	−316570.	−1.12987	−0.564934	−	0.825136i	$-0.691098\pi$
$151$	−316570.	−1.12987	−0.564934	+	0.825136i	$0.691098\pi$
$152$	−23104.0	−0.0811107
$153$	43851.0	0.151444
$154$	184404.	0.626568
$155$	0	0
$156$	22400.0	0.0736947
$157$	445042.	1.44096	0.720480	−	0.693476i	$-0.243922\pi$
$157$	445042.	1.44096	0.720480	+	0.693476i	$0.243922\pi$
$158$	6640.00	0.0211605
$159$	224112.	0.703027
$160$	0	0
$161$	66792.0	0.203077
$162$	181676.	0.543889
$163$	−349580.	−1.03057	−0.515285	−	0.857019i	$-0.672314\pi$
$163$	−349580.	−1.03057	−0.515285	+	0.857019i	$0.672314\pi$
$164$	−36000.0	−0.104518
$165$	0	0
$166$	383856.	1.08118
$167$	−277962.	−0.771248	−0.385624	−	0.922656i	$-0.626014\pi$
$167$	−277962.	−0.771248	−0.385624	+	0.922656i	$0.626014\pi$
$168$	−108416.	−0.296360
$169$	−361293.	−0.973067
$170$	0	0
$171$	−16967.0	−0.0443726
$172$	374032.	0.964024
$173$	−526566.	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$173$	−526566.	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$174$	−134064.	−0.335691
$175$	0	0
$176$	−97536.0	−0.237347
$177$	−1764.00	−0.00423219
$178$	−475392.	−1.12461
$179$	−150750.	−0.351661	−0.175831	−	0.984420i	$-0.556261\pi$
$179$	−150750.	−0.351661	−0.175831	+	0.984420i	$0.556261\pi$
$180$	0	0
$181$	−186118.	−0.422272	−0.211136	−	0.977457i	$-0.567716\pi$
$181$	−186118.	−0.422272	−0.211136	+	0.977457i	$0.567716\pi$
$182$	−48400.0	−0.108310
$183$	298690.	0.659315
$184$	−35328.0	−0.0769262
$185$	0	0
$186$	225344.	0.477599
$187$	355473.	0.743366
$188$	425520.	0.878062
$189$	−491260.	−1.00036
$190$	0	0
$191$	7683.00	0.0152387	0.00761934	−	0.999971i	$-0.497575\pi$
$191$	7683.00	0.0152387	0.00761934	+	0.999971i	$0.497575\pi$
$192$	57344.0	0.112263
$193$	993736.	1.92034	0.960169	−	0.279419i	$-0.0901420\pi$
$193$	993736.	1.92034	0.960169	+	0.279419i	$0.0901420\pi$
$194$	−615040.	−1.17327
$195$	0	0
$196$	−34656.0	−0.0644374
$197$	−430290.	−0.789943	−0.394971	−	0.918693i	$-0.629246\pi$
$197$	−430290.	−0.789943	−0.394971	+	0.918693i	$0.629246\pi$
$198$	−71628.0	−0.129843
$199$	511211.	0.915098	0.457549	−	0.889184i	$-0.348727\pi$
$199$	511211.	0.915098	0.457549	+	0.889184i	$0.348727\pi$
$200$	0	0
$201$	724640.	1.26512
$202$	−612792.	−1.05666
$203$	289674.	0.493366
$204$	−208992.	−0.351604
$205$	0	0
$206$	−178024.	−0.292288
$207$	−25944.0	−0.0420834
$208$	25600.0	0.0410281
$209$	−137541.	−0.217804
$210$	0	0
$211$	1.27439e6	1.97059	0.985295	−	0.170863i	$-0.0546554\pi$
$211$	1.27439e6	1.97059	0.985295	+	0.170863i	$0.0546554\pi$
$212$	256128.	0.391397
$213$	120036.	0.181285
$214$	−490536.	−0.732211
$215$	0	0
$216$	259840.	0.378941
$217$	−486904.	−0.701930
$218$	−219824.	−0.313281
$219$	−156142.	−0.219993
$220$	0	0
$221$	−93300.0	−0.128499
$222$	514192.	0.700233
$223$	−678146.	−0.913190	−0.456595	−	0.889675i	$-0.650931\pi$
$223$	−678146.	−0.913190	−0.456595	+	0.889675i	$0.650931\pi$
$224$	−123904.	−0.164993
$225$	0	0
$226$	406344.	0.529204
$227$	54300.0	0.0699415	0.0349708	−	0.999388i	$-0.488866\pi$
$227$	54300.0	0.0699415	0.0349708	+	0.999388i	$0.488866\pi$
$228$	80864.0	0.103019
$229$	1.15781e6	1.45898	0.729491	−	0.683991i	$-0.239757\pi$
$229$	1.15781e6	1.45898	0.729491	+	0.683991i	$0.239757\pi$
$230$	0	0
$231$	−645414.	−0.795808
$232$	−153216.	−0.186889
$233$	−282939.	−0.341431	−0.170716	−	0.985320i	$-0.554608\pi$
$233$	−282939.	−0.341431	−0.170716	+	0.985320i	$0.554608\pi$
$234$	18800.0	0.0224449
$235$	0	0
$236$	−2016.00	−0.00235619
$237$	−23240.0	−0.0268760
$238$	451572.	0.516755
$239$	1.42024e6	1.60830	0.804149	−	0.594427i	$-0.202621\pi$
$239$	1.42024e6	1.60830	0.804149	+	0.594427i	$0.202621\pi$
$240$	0	0
$241$	−1.02998e6	−1.14232	−0.571159	−	0.820839i	$-0.693506\pi$
$241$	−1.02998e6	−1.14232	−0.571159	+	0.820839i	$0.693506\pi$
$242$	63560.0	0.0697663
$243$	350714.	0.381011
$244$	341360.	0.367061
$245$	0	0
$246$	126000.	0.132749
$247$	36100.0	0.0376500
$248$	257536.	0.265894
$249$	−1.34350e6	−1.37321
$250$	0	0
$251$	−968379.	−0.970200	−0.485100	−	0.874459i	$-0.661217\pi$
$251$	−968379.	−0.970200	−0.485100	+	0.874459i	$0.661217\pi$
$252$	−90992.0	−0.0902614
$253$	−210312.	−0.206568
$254$	−1.23911e6	−1.20511
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.93721e6	1.82955	0.914773	−	0.403968i	$-0.132369\pi$
$257$	1.93721e6	1.82955	0.914773	+	0.403968i	$0.132369\pi$
$258$	−1.30911e6	−1.22441
$259$	−1.11102e6	−1.02914
$260$	0	0
$261$	−112518.	−0.102240
$262$	9180.00	0.00826208
$263$	1.31531e6	1.17257	0.586285	−	0.810105i	$-0.300590\pi$
$263$	1.31531e6	1.17257	0.586285	+	0.810105i	$0.300590\pi$
$264$	341376.	0.301455
$265$	0	0
$266$	−174724.	−0.151408
$267$	1.66387e6	1.42837
$268$	828160.	0.704332
$269$	−2.08672e6	−1.75826	−0.879129	−	0.476584i	$-0.841875\pi$
$269$	−2.08672e6	−1.75826	−0.879129	+	0.476584i	$0.841875\pi$
$270$	0	0
$271$	613856.	0.507742	0.253871	−	0.967238i	$-0.418296\pi$
$271$	613856.	0.507742	0.253871	+	0.967238i	$0.418296\pi$
$272$	−238848.	−0.195749
$273$	169400.	0.137565
$274$	356724.	0.287049
$275$	0	0
$276$	123648.	0.0977045
$277$	−163013.	−0.127651	−0.0638253	−	0.997961i	$-0.520330\pi$
$277$	−163013.	−0.127651	−0.0638253	+	0.997961i	$0.520330\pi$
$278$	−759884.	−0.589706
$279$	189128.	0.145461
$280$	0	0
$281$	−194490.	−0.146937	−0.0734686	−	0.997298i	$-0.523407\pi$
$281$	−194490.	−0.146937	−0.0734686	+	0.997298i	$0.523407\pi$
$282$	−1.48932e6	−1.11523
$283$	362197.	0.268831	0.134415	−	0.990925i	$-0.457084\pi$
$283$	362197.	0.268831	0.134415	+	0.990925i	$0.457084\pi$
$284$	137184.	0.100927
$285$	0	0
$286$	152400.	0.110172
$287$	−272250.	−0.195103
$288$	48128.0	0.0341914
$289$	−549368.	−0.386918
$290$	0	0
$291$	2.15264e6	1.49018
$292$	−178448.	−0.122477
$293$	−1.95164e6	−1.32810	−0.664051	−	0.747687i	$-0.731164\pi$
$293$	−1.95164e6	−1.32810	−0.664051	+	0.747687i	$0.731164\pi$
$294$	121296.	0.0818424
$295$	0	0
$296$	587648.	0.389841
$297$	1.54686e6	1.01756
$298$	1.74366e6	1.13742
$299$	55200.0	0.0357076
$300$	0	0
$301$	2.82862e6	1.79953
$302$	1.26628e6	0.798937
$303$	2.14477e6	1.34207
$304$	92416.0	0.0573539
$305$	0	0
$306$	−175404.	−0.107087
$307$	1.82536e6	1.10536	0.552679	−	0.833395i	$-0.313606\pi$
$307$	1.82536e6	1.10536	0.552679	+	0.833395i	$0.313606\pi$
$308$	−737616.	−0.443051
$309$	623084.	0.371236
$310$	0	0
$311$	688989.	0.403935	0.201967	−	0.979392i	$-0.435266\pi$
$311$	688989.	0.403935	0.201967	+	0.979392i	$0.435266\pi$
$312$	−89600.0	−0.0521101
$313$	1.62459e6	0.937312	0.468656	−	0.883381i	$-0.344738\pi$
$313$	1.62459e6	0.937312	0.468656	+	0.883381i	$0.344738\pi$
$314$	−1.78017e6	−1.01891
$315$	0	0
$316$	−26560.0	−0.0149627
$317$	−1.40665e6	−0.786207	−0.393103	−	0.919494i	$-0.628599\pi$
$317$	−1.40665e6	−0.786207	−0.393103	+	0.919494i	$0.628599\pi$
$318$	−896448.	−0.497115
$319$	−912114.	−0.501848
$320$	0	0
$321$	1.71688e6	0.929986
$322$	−267168.	−0.143597
$323$	−336813.	−0.179632
$324$	−726704.	−0.384587
$325$	0	0
$326$	1.39832e6	0.728723
$327$	769384.	0.397900
$328$	144000.	0.0739057
$329$	3.21800e6	1.63906
$330$	0	0
$331$	2.42506e6	1.21662	0.608308	−	0.793701i	$-0.291849\pi$
$331$	2.42506e6	1.21662	0.608308	+	0.793701i	$0.291849\pi$
$332$	−1.53542e6	−0.764510
$333$	431554.	0.213267
$334$	1.11185e6	0.545355
$335$	0	0
$336$	433664.	0.209558
$337$	2.05782e6	0.987037	0.493519	−	0.869735i	$-0.335711\pi$
$337$	2.05782e6	0.987037	0.493519	+	0.869735i	$0.335711\pi$
$338$	1.44517e6	0.688062
$339$	−1.42220e6	−0.672145
$340$	0	0
$341$	1.53314e6	0.713998
$342$	67868.0	0.0313762
$343$	−2.29573e6	−1.05363
$344$	−1.49613e6	−0.681668
$345$	0	0
$346$	2.10626e6	0.945851
$347$	1.95915e6	0.873461	0.436730	−	0.899592i	$-0.356136\pi$
$347$	1.95915e6	0.873461	0.436730	+	0.899592i	$0.356136\pi$
$348$	536256.	0.237369
$349$	2.12491e6	0.933847	0.466924	−	0.884298i	$-0.345362\pi$
$349$	2.12491e6	0.933847	0.466924	+	0.884298i	$0.345362\pi$
$350$	0	0
$351$	−406000.	−0.175897
$352$	390144.	0.167829
$353$	4.28979e6	1.83231	0.916156	−	0.400823i	$-0.131276\pi$
$353$	4.28979e6	1.83231	0.916156	+	0.400823i	$0.131276\pi$
$354$	7056.00	0.00299261
$355$	0	0
$356$	1.90157e6	0.795219
$357$	−1.58050e6	−0.656333
$358$	603000.	0.248662
$359$	1.53239e6	0.627529	0.313764	−	0.949501i	$-0.398410\pi$
$359$	1.53239e6	0.627529	0.313764	+	0.949501i	$0.398410\pi$
$360$	0	0
$361$	130321.	0.0526316
$362$	744472.	0.298591
$363$	−222460.	−0.0886105
$364$	193600.	0.0765864
$365$	0	0
$366$	−1.19476e6	−0.466206
$367$	2.19921e6	0.852317	0.426158	−	0.904649i	$-0.359867\pi$
$367$	2.19921e6	0.852317	0.426158	+	0.904649i	$0.359867\pi$
$368$	141312.	0.0543951
$369$	105750.	0.0404310
$370$	0	0
$371$	1.93697e6	0.730613
$372$	−901376.	−0.337714
$373$	−1.18855e6	−0.442328	−0.221164	−	0.975237i	$-0.570986\pi$
$373$	−1.18855e6	−0.442328	−0.221164	+	0.975237i	$0.570986\pi$
$374$	−1.42189e6	−0.525639
$375$	0	0
$376$	−1.70208e6	−0.620884
$377$	239400.	0.0867503
$378$	1.96504e6	0.707362
$379$	−1.32224e6	−0.472839	−0.236419	−	0.971651i	$-0.575974\pi$
$379$	−1.32224e6	−0.472839	−0.236419	+	0.971651i	$0.575974\pi$
$380$	0	0
$381$	4.33689e6	1.53062
$382$	−30732.0	−0.0107754
$383$	216432.	0.0753919	0.0376959	−	0.999289i	$-0.487998\pi$
$383$	216432.	0.0753919	0.0376959	+	0.999289i	$0.487998\pi$
$384$	−229376.	−0.0793816
$385$	0	0
$386$	−3.97494e6	−1.35788
$387$	−1.09872e6	−0.372914
$388$	2.46016e6	0.829629
$389$	2.08770e6	0.699511	0.349756	−	0.936841i	$-0.386265\pi$
$389$	2.08770e6	0.699511	0.349756	+	0.936841i	$0.386265\pi$
$390$	0	0
$391$	−515016.	−0.170364
$392$	138624.	0.0455641
$393$	−32130.0	−0.0104937
$394$	1.72116e6	0.558574
$395$	0	0
$396$	286512.	0.0918131
$397$	3.31410e6	1.05533	0.527665	−	0.849452i	$-0.323067\pi$
$397$	3.31410e6	1.05533	0.527665	+	0.849452i	$0.323067\pi$
$398$	−2.04484e6	−0.647072
$399$	611534.	0.192304
$400$	0	0
$401$	2.00772e6	0.623508	0.311754	−	0.950163i	$-0.399083\pi$
$401$	2.00772e6	0.623508	0.311754	+	0.950163i	$0.399083\pi$
$402$	−2.89856e6	−0.894576
$403$	−402400.	−0.123423
$404$	2.45117e6	0.747170
$405$	0	0
$406$	−1.15870e6	−0.348863
$407$	3.49834e6	1.04683
$408$	835968.	0.248622
$409$	465992.	0.137743	0.0688716	−	0.997626i	$-0.478060\pi$
$409$	465992.	0.137743	0.0688716	+	0.997626i	$0.478060\pi$
$410$	0	0
$411$	−1.24853e6	−0.364583
$412$	712096.	0.206679
$413$	−15246.0	−0.00439826
$414$	103776.	0.0297575
$415$	0	0
$416$	−102400.	−0.0290113
$417$	2.65959e6	0.748989
$418$	550164.	0.154011
$419$	−108132.	−0.0300898	−0.0150449	−	0.999887i	$-0.504789\pi$
$419$	−108132.	−0.0300898	−0.0150449	+	0.999887i	$0.504789\pi$
$420$	0	0
$421$	−1.49739e6	−0.411746	−0.205873	−	0.978579i	$-0.566003\pi$
$421$	−1.49739e6	−0.411746	−0.205873	+	0.978579i	$0.566003\pi$
$422$	−5.09756e6	−1.39342
$423$	−1.24997e6	−0.339662
$424$	−1.02451e6	−0.276759
$425$	0	0
$426$	−480144.	−0.128188
$427$	2.58153e6	0.685186
$428$	1.96214e6	0.517752
$429$	−533400.	−0.139930
$430$	0	0
$431$	3.77098e6	0.977824	0.488912	−	0.872333i	$-0.337394\pi$
$431$	3.77098e6	0.977824	0.488912	+	0.872333i	$0.337394\pi$
$432$	−1.03936e6	−0.267952
$433$	−3.87162e6	−0.992369	−0.496185	−	0.868217i	$-0.665266\pi$
$433$	−3.87162e6	−0.992369	−0.496185	+	0.868217i	$0.665266\pi$
$434$	1.94762e6	0.496340
$435$	0	0
$436$	879296.	0.221523
$437$	199272.	0.0499163
$438$	624568.	0.155559
$439$	−155758.	−0.0385735	−0.0192868	−	0.999814i	$-0.506140\pi$
$439$	−155758.	−0.0385735	−0.0192868	+	0.999814i	$0.506140\pi$
$440$	0	0
$441$	101802.	0.0249264
$442$	373200.	0.0908628
$443$	7.49688e6	1.81498	0.907489	−	0.420076i	$-0.137996\pi$
$443$	7.49688e6	1.81498	0.907489	+	0.420076i	$0.137996\pi$
$444$	−2.05677e6	−0.495140
$445$	0	0
$446$	2.71258e6	0.645723
$447$	−6.10281e6	−1.44464
$448$	495616.	0.116668
$449$	−1.53641e6	−0.359659	−0.179829	−	0.983698i	$-0.557555\pi$
$449$	−1.53641e6	−0.359659	−0.179829	+	0.983698i	$0.557555\pi$
$450$	0	0
$451$	857250.	0.198457
$452$	−1.62538e6	−0.374203
$453$	−4.43198e6	−1.01473
$454$	−217200.	−0.0494561
$455$	0	0
$456$	−323456.	−0.0728456
$457$	−1.78379e6	−0.399533	−0.199766	−	0.979844i	$-0.564018\pi$
$457$	−1.78379e6	−0.399533	−0.199766	+	0.979844i	$0.564018\pi$
$458$	−4.63125e6	−1.03166
$459$	3.78798e6	0.839220
$460$	0	0
$461$	396273.	0.0868445	0.0434222	−	0.999057i	$-0.486174\pi$
$461$	396273.	0.0868445	0.0434222	+	0.999057i	$0.486174\pi$
$462$	2.58166e6	0.562721
$463$	−85121.0	−0.0184537	−0.00922687	−	0.999957i	$-0.502937\pi$
$463$	−85121.0	−0.0184537	−0.00922687	+	0.999957i	$0.502937\pi$
$464$	612864.	0.132151
$465$	0	0
$466$	1.13176e6	0.241428
$467$	6.23883e6	1.32376	0.661882	−	0.749608i	$-0.269758\pi$
$467$	6.23883e6	1.32376	0.661882	+	0.749608i	$0.269758\pi$
$468$	−75200.0	−0.0158710
$469$	6.26296e6	1.31476
$470$	0	0
$471$	6.23059e6	1.29413
$472$	8064.00	0.00166608
$473$	−8.90664e6	−1.83046
$474$	92960.0	0.0190042
$475$	0	0
$476$	−1.80629e6	−0.365401
$477$	−752376.	−0.151405
$478$	−5.68096e6	−1.13724
$479$	−5.82908e6	−1.16081	−0.580406	−	0.814328i	$-0.697106\pi$
$479$	−5.82908e6	−1.16081	−0.580406	+	0.814328i	$0.697106\pi$
$480$	0	0
$481$	−918200.	−0.180957
$482$	4.11993e6	0.807741
$483$	935088.	0.182383
$484$	−254240.	−0.0493322
$485$	0	0
$486$	−1.40286e6	−0.269415
$487$	1.01250e7	1.93452	0.967258	−	0.253793i	$-0.0816783\pi$
$487$	1.01250e7	1.93452	0.967258	+	0.253793i	$0.0816783\pi$
$488$	−1.36544e6	−0.259551
$489$	−4.89412e6	−0.925555
$490$	0	0
$491$	−8.53312e6	−1.59736	−0.798682	−	0.601753i	$-0.794469\pi$
$491$	−8.53312e6	−1.59736	−0.798682	+	0.601753i	$0.794469\pi$
$492$	−504000.	−0.0938680
$493$	−2.23360e6	−0.413893
$494$	−144400.	−0.0266226
$495$	0	0
$496$	−1.03014e6	−0.188016
$497$	1.03745e6	0.188399
$498$	5.37398e6	0.971008
$499$	9.88702e6	1.77752	0.888759	−	0.458374i	$-0.151568\pi$
$499$	9.88702e6	1.77752	0.888759	+	0.458374i	$0.151568\pi$
$500$	0	0
$501$	−3.89147e6	−0.692658
$502$	3.87352e6	0.686035
$503$	−729804.	−0.128613	−0.0643067	−	0.997930i	$-0.520484\pi$
$503$	−729804.	−0.128613	−0.0643067	+	0.997930i	$0.520484\pi$
$504$	363968.	0.0638244
$505$	0	0
$506$	841248.	0.146066
$507$	−5.05810e6	−0.873912
$508$	4.95645e6	0.852141
$509$	−6.26628e6	−1.07205	−0.536025	−	0.844202i	$-0.680075\pi$
$509$	−6.26628e6	−1.07205	−0.536025	+	0.844202i	$0.680075\pi$
$510$	0	0
$511$	−1.34951e6	−0.228626
$512$	−262144.	−0.0441942
$513$	−1.46566e6	−0.245889
$514$	−7.74883e6	−1.29368
$515$	0	0
$516$	5.23645e6	0.865790
$517$	−1.01327e7	−1.66724
$518$	4.44409e6	0.727710
$519$	−7.37192e6	−1.20133
$520$	0	0
$521$	−6.24352e6	−1.00771	−0.503854	−	0.863789i	$-0.668085\pi$
$521$	−6.24352e6	−1.00771	−0.503854	+	0.863789i	$0.668085\pi$
$522$	450072.	0.0722946
$523$	−8.15433e6	−1.30357	−0.651784	−	0.758404i	$-0.725979\pi$
$523$	−8.15433e6	−1.30357	−0.651784	+	0.758404i	$0.725979\pi$
$524$	−36720.0	−0.00584217
$525$	0	0
$526$	−5.26124e6	−0.829133
$527$	3.75439e6	0.588861
$528$	−1.36550e6	−0.213161
$529$	−6.13164e6	−0.952659
$530$	0	0
$531$	5922.00	0.000911448 0
$532$	698896.	0.107062
$533$	−225000.	−0.0343056
$534$	−6.65549e6	−1.01001
$535$	0	0
$536$	−3.31264e6	−0.498038
$537$	−2.11050e6	−0.315827
$538$	8.34686e6	1.24328
$539$	825246.	0.122352
$540$	0	0
$541$	−6.93571e6	−1.01882	−0.509411	−	0.860524i	$-0.670137\pi$
$541$	−6.93571e6	−1.01882	−0.509411	+	0.860524i	$0.670137\pi$
$542$	−2.45542e6	−0.359028
$543$	−2.60565e6	−0.379242
$544$	955392.	0.138415
$545$	0	0
$546$	−677600.	−0.0972729
$547$	6.74360e6	0.963659	0.481829	−	0.876265i	$-0.339973\pi$
$547$	6.74360e6	0.963659	0.481829	+	0.876265i	$0.339973\pi$
$548$	−1.42690e6	−0.202974
$549$	−1.00274e6	−0.141991
$550$	0	0
$551$	864234.	0.121270
$552$	−494592.	−0.0690875
$553$	−200860.	−0.0279306
$554$	652052.	0.0902626
$555$	0	0
$556$	3.03954e6	0.416985
$557$	−9.47731e6	−1.29434	−0.647168	−	0.762347i	$-0.724047\pi$
$557$	−9.47731e6	−1.29434	−0.647168	+	0.762347i	$0.724047\pi$
$558$	−756512.	−0.102856
$559$	2.33770e6	0.316417
$560$	0	0
$561$	4.97662e6	0.667617
$562$	777960.	0.103900
$563$	3.42670e6	0.455623	0.227811	−	0.973705i	$-0.426843\pi$
$563$	3.42670e6	0.455623	0.227811	+	0.973705i	$0.426843\pi$
$564$	5.95728e6	0.788588
$565$	0	0
$566$	−1.44879e6	−0.190092
$567$	−5.49570e6	−0.717902
$568$	−548736.	−0.0713662
$569$	1.00682e7	1.30368	0.651841	−	0.758355i	$-0.273997\pi$
$569$	1.00682e7	1.30368	0.651841	+	0.758355i	$0.273997\pi$
$570$	0	0
$571$	9.87672e6	1.26772	0.633858	−	0.773449i	$-0.281470\pi$
$571$	9.87672e6	1.26772	0.633858	+	0.773449i	$0.281470\pi$
$572$	−609600.	−0.0779031
$573$	107562.	0.0136859
$574$	1.08900e6	0.137958
$575$	0	0
$576$	−192512.	−0.0241770
$577$	5.53139e6	0.691663	0.345832	−	0.938297i	$-0.387597\pi$
$577$	5.53139e6	0.691663	0.345832	+	0.938297i	$0.387597\pi$
$578$	2.19747e6	0.273592
$579$	1.39123e7	1.72466
$580$	0	0
$581$	−1.16116e7	−1.42710
$582$	−8.61056e6	−1.05372
$583$	−6.09905e6	−0.743174
$584$	713792.	0.0866043
$585$	0	0
$586$	7.80658e6	0.939110
$587$	335067.	0.0401362	0.0200681	−	0.999799i	$-0.493612\pi$
$587$	335067.	0.0401362	0.0200681	+	0.999799i	$0.493612\pi$
$588$	−485184.	−0.0578713
$589$	−1.45266e6	−0.172535
$590$	0	0
$591$	−6.02406e6	−0.709448
$592$	−2.35059e6	−0.275660
$593$	−8.54859e6	−0.998292	−0.499146	−	0.866518i	$-0.666353\pi$
$593$	−8.54859e6	−0.998292	−0.499146	+	0.866518i	$0.666353\pi$
$594$	−6.18744e6	−0.719523
$595$	0	0
$596$	−6.97464e6	−0.804278
$597$	7.15695e6	0.821850
$598$	−220800.	−0.0252491
$599$	−2.26826e6	−0.258301	−0.129151	−	0.991625i	$-0.541225\pi$
$599$	−2.26826e6	−0.258301	−0.129151	+	0.991625i	$0.541225\pi$
$600$	0	0
$601$	−1.01940e6	−0.115122	−0.0575609	−	0.998342i	$-0.518332\pi$
$601$	−1.01940e6	−0.115122	−0.0575609	+	0.998342i	$0.518332\pi$
$602$	−1.13145e7	−1.27246
$603$	−2.43272e6	−0.272458
$604$	−5.06512e6	−0.564934
$605$	0	0
$606$	−8.57909e6	−0.948985
$607$	−7.55389e6	−0.832145	−0.416072	−	0.909332i	$-0.636594\pi$
$607$	−7.55389e6	−0.832145	−0.416072	+	0.909332i	$0.636594\pi$
$608$	−369664.	−0.0405554
$609$	4.05544e6	0.443092
$610$	0	0
$611$	2.65950e6	0.288202
$612$	701616.	0.0757218
$613$	−8.38112e6	−0.900846	−0.450423	−	0.892815i	$-0.648727\pi$
$613$	−8.38112e6	−0.900846	−0.450423	+	0.892815i	$0.648727\pi$
$614$	−7.30144e6	−0.781605
$615$	0	0
$616$	2.95046e6	0.313284
$617$	1.27110e7	1.34421	0.672104	−	0.740457i	$-0.265391\pi$
$617$	1.27110e7	1.34421	0.672104	+	0.740457i	$0.265391\pi$
$618$	−2.49234e6	−0.262504
$619$	−4.29862e6	−0.450923	−0.225462	−	0.974252i	$-0.572389\pi$
$619$	−4.29862e6	−0.450923	−0.225462	+	0.974252i	$0.572389\pi$
$620$	0	0
$621$	−2.24112e6	−0.233204
$622$	−2.75596e6	−0.285625
$623$	1.43806e7	1.48442
$624$	358400.	0.0368474
$625$	0	0
$626$	−6.49838e6	−0.662779
$627$	−1.92557e6	−0.195610
$628$	7.12067e6	0.720480
$629$	8.56681e6	0.863361
$630$	0	0
$631$	771779.	0.0771649	0.0385824	−	0.999255i	$-0.487716\pi$
$631$	771779.	0.0771649	0.0385824	+	0.999255i	$0.487716\pi$
$632$	106240.	0.0105802
$633$	1.78415e7	1.76979
$634$	5.62658e6	0.555932
$635$	0	0
$636$	3.58579e6	0.351514
$637$	−216600.	−0.0211500
$638$	3.64846e6	0.354860
$639$	−402978.	−0.0390417
$640$	0	0
$641$	−6.05234e6	−0.581806	−0.290903	−	0.956752i	$-0.593956\pi$
$641$	−6.05234e6	−0.581806	−0.290903	+	0.956752i	$0.593956\pi$
$642$	−6.86750e6	−0.657599
$643$	−3.90956e6	−0.372907	−0.186454	−	0.982464i	$-0.559699\pi$
$643$	−3.90956e6	−0.372907	−0.186454	+	0.982464i	$0.559699\pi$
$644$	1.06867e6	0.101538
$645$	0	0
$646$	1.34725e6	0.127019
$647$	−1.85962e7	−1.74648	−0.873239	−	0.487292i	$-0.837985\pi$
$647$	−1.85962e7	−1.74648	−0.873239	+	0.487292i	$0.837985\pi$
$648$	2.90682e6	0.271944
$649$	48006.0	0.00447387
$650$	0	0
$651$	−6.81666e6	−0.630404
$652$	−5.59328e6	−0.515285
$653$	5.71847e6	0.524804	0.262402	−	0.964959i	$-0.415485\pi$
$653$	5.71847e6	0.524804	0.262402	+	0.964959i	$0.415485\pi$
$654$	−3.07754e6	−0.281358
$655$	0	0
$656$	−576000.	−0.0522592
$657$	524191.	0.0473779
$658$	−1.28720e7	−1.15899
$659$	−9.62991e6	−0.863791	−0.431896	−	0.901924i	$-0.642155\pi$
$659$	−9.62991e6	−0.863791	−0.431896	+	0.901924i	$0.642155\pi$
$660$	0	0
$661$	−1.18896e7	−1.05843	−0.529215	−	0.848488i	$-0.677514\pi$
$661$	−1.18896e7	−1.05843	−0.529215	+	0.848488i	$0.677514\pi$
$662$	−9.70026e6	−0.860277
$663$	−1.30620e6	−0.115405
$664$	6.14170e6	0.540590
$665$	0	0
$666$	−1.72622e6	−0.150803
$667$	1.32149e6	0.115013
$668$	−4.44739e6	−0.385624
$669$	−9.49404e6	−0.820136
$670$	0	0
$671$	−8.12864e6	−0.696966
$672$	−1.73466e6	−0.148180
$673$	4.78115e6	0.406906	0.203453	−	0.979085i	$-0.434784\pi$
$673$	4.78115e6	0.406906	0.203453	+	0.979085i	$0.434784\pi$
$674$	−8.23130e6	−0.697941
$675$	0	0
$676$	−5.78069e6	−0.486534
$677$	−2.04491e7	−1.71476	−0.857379	−	0.514685i	$-0.827909\pi$
$677$	−2.04491e7	−1.71476	−0.857379	+	0.514685i	$0.827909\pi$
$678$	5.68882e6	0.475278
$679$	1.86050e7	1.54865
$680$	0	0
$681$	760200.	0.0628145
$682$	−6.13258e6	−0.504873
$683$	−5.60056e6	−0.459388	−0.229694	−	0.973263i	$-0.573772\pi$
$683$	−5.60056e6	−0.459388	−0.229694	+	0.973263i	$0.573772\pi$
$684$	−271472.	−0.0221863
$685$	0	0
$686$	9.18293e6	0.745025
$687$	1.62094e7	1.31031
$688$	5.98451e6	0.482012
$689$	1.60080e6	0.128466
$690$	0	0
$691$	−1.15825e7	−0.922796	−0.461398	−	0.887193i	$-0.652652\pi$
$691$	−1.15825e7	−0.922796	−0.461398	+	0.887193i	$0.652652\pi$
$692$	−8.42506e6	−0.668817
$693$	2.16675e6	0.171386
$694$	−7.83659e6	−0.617630
$695$	0	0
$696$	−2.14502e6	−0.167845
$697$	2.09925e6	0.163675
$698$	−8.49962e6	−0.660330
$699$	−3.96115e6	−0.306639
$700$	0	0
$701$	−773058.	−0.0594179	−0.0297089	−	0.999559i	$-0.509458\pi$
$701$	−773058.	−0.0594179	−0.0297089	+	0.999559i	$0.509458\pi$
$702$	1.62400e6	0.124378
$703$	−3.31470e6	−0.252963
$704$	−1.56058e6	−0.118673
$705$	0	0
$706$	−1.71592e7	−1.29564
$707$	1.85370e7	1.39473
$708$	−28224.0	−0.00211610
$709$	2.19381e7	1.63902	0.819508	−	0.573068i	$-0.194247\pi$
$709$	2.19381e7	1.63902	0.819508	+	0.573068i	$0.194247\pi$
$710$	0	0
$711$	78020.0	0.00578805
$712$	−7.60627e6	−0.562305
$713$	−2.22125e6	−0.163634
$714$	6.32201e6	0.464098
$715$	0	0
$716$	−2.41200e6	−0.175831
$717$	1.98833e7	1.44441
$718$	−6.12956e6	−0.443730
$719$	934359.	0.0674049	0.0337025	−	0.999432i	$-0.489270\pi$
$719$	934359.	0.0674049	0.0337025	+	0.999432i	$0.489270\pi$
$720$	0	0
$721$	5.38523e6	0.385803
$722$	−521284.	−0.0372161
$723$	−1.44197e7	−1.02592
$724$	−2.97789e6	−0.211136
$725$	0	0
$726$	889840.	0.0626571
$727$	−8.42717e6	−0.591352	−0.295676	−	0.955288i	$-0.595545\pi$
$727$	−8.42717e6	−0.591352	−0.295676	+	0.955288i	$0.595545\pi$
$728$	−774400.	−0.0541548
$729$	1.59468e7	1.11136
$730$	0	0
$731$	−2.18107e7	−1.50965
$732$	4.77904e6	0.329658
$733$	−1.75092e7	−1.20367	−0.601834	−	0.798622i	$-0.705563\pi$
$733$	−1.75092e7	−1.20367	−0.601834	+	0.798622i	$0.705563\pi$
$734$	−8.79683e6	−0.602679
$735$	0	0
$736$	−565248.	−0.0384631
$737$	−1.97206e7	−1.33737
$738$	−423000.	−0.0285890
$739$	−436741.	−0.0294180	−0.0147090	−	0.999892i	$-0.504682\pi$
$739$	−436741.	−0.0294180	−0.0147090	+	0.999892i	$0.504682\pi$
$740$	0	0
$741$	505400.	0.0338135
$742$	−7.74787e6	−0.516622
$743$	5.44936e6	0.362137	0.181069	−	0.983470i	$-0.442044\pi$
$743$	5.44936e6	0.362137	0.181069	+	0.983470i	$0.442044\pi$
$744$	3.60550e6	0.238800
$745$	0	0
$746$	4.75419e6	0.312773
$747$	4.51031e6	0.295736
$748$	5.68757e6	0.371683
$749$	1.48387e7	0.966477
$750$	0	0
$751$	9.63980e6	0.623689	0.311845	−	0.950133i	$-0.399053\pi$
$751$	9.63980e6	0.623689	0.311845	+	0.950133i	$0.399053\pi$
$752$	6.80832e6	0.439031
$753$	−1.35573e7	−0.871337
$754$	−957600.	−0.0613417
$755$	0	0
$756$	−7.86016e6	−0.500181
$757$	−1.59059e7	−1.00883	−0.504417	−	0.863460i	$-0.668292\pi$
$757$	−1.59059e7	−1.00883	−0.504417	+	0.863460i	$0.668292\pi$
$758$	5.28897e6	0.334347
$759$	−2.94437e6	−0.185519
$760$	0	0
$761$	−5.98955e6	−0.374915	−0.187457	−	0.982273i	$-0.560025\pi$
$761$	−5.98955e6	−0.374915	−0.187457	+	0.982273i	$0.560025\pi$
$762$	−1.73476e7	−1.08231
$763$	6.64968e6	0.413513
$764$	122928.	0.00761934
$765$	0	0
$766$	−865728.	−0.0533101
$767$	−12600.0	−0.000773361 0
$768$	917504.	0.0561313
$769$	3.49006e6	0.212822	0.106411	−	0.994322i	$-0.466064\pi$
$769$	3.49006e6	0.212822	0.106411	+	0.994322i	$0.466064\pi$
$770$	0	0
$771$	2.71209e7	1.64312
$772$	1.58998e7	0.960169
$773$	1.69009e7	1.01733	0.508663	−	0.860966i	$-0.330140\pi$
$773$	1.69009e7	1.01733	0.508663	+	0.860966i	$0.330140\pi$
$774$	4.39488e6	0.263690
$775$	0	0
$776$	−9.84064e6	−0.586636
$777$	−1.55543e7	−0.924268
$778$	−8.35081e6	−0.494629
$779$	−812250.	−0.0479563
$780$	0	0
$781$	−3.26669e6	−0.191638
$782$	2.06006e6	0.120466
$783$	−9.71964e6	−0.566560
$784$	−554496.	−0.0322187
$785$	0	0
$786$	128520.	0.00742018
$787$	1.49349e7	0.859540	0.429770	−	0.902938i	$-0.358595\pi$
$787$	1.49349e7	0.859540	0.429770	+	0.902938i	$0.358595\pi$
$788$	−6.88464e6	−0.394971
$789$	1.84144e7	1.05309
$790$	0	0
$791$	−1.22919e7	−0.698519
$792$	−1.14605e6	−0.0649217
$793$	2.13350e6	0.120479
$794$	−1.32564e7	−0.746232
$795$	0	0
$796$	8.17938e6	0.457549
$797$	951504.	0.0530597	0.0265299	−	0.999648i	$-0.491554\pi$
$797$	951504.	0.0530597	0.0265299	+	0.999648i	$0.491554\pi$
$798$	−2.44614e6	−0.135979
$799$	−2.48131e7	−1.37504
$800$	0	0
$801$	−5.58586e6	−0.307616
$802$	−8.03088e6	−0.440887
$803$	4.24929e6	0.232556
$804$	1.15942e7	0.632561
$805$	0	0
$806$	1.60960e6	0.0872731
$807$	−2.92140e7	−1.57909
$808$	−9.80467e6	−0.528329
$809$	1.77090e7	0.951314	0.475657	−	0.879631i	$-0.342210\pi$
$809$	1.77090e7	0.951314	0.475657	+	0.879631i	$0.342210\pi$
$810$	0	0
$811$	3.94242e6	0.210480	0.105240	−	0.994447i	$-0.466439\pi$
$811$	3.94242e6	0.210480	0.105240	+	0.994447i	$0.466439\pi$
$812$	4.63478e6	0.246683
$813$	8.59398e6	0.456004
$814$	−1.39934e7	−0.740221
$815$	0	0
$816$	−3.34387e6	−0.175802
$817$	8.43910e6	0.442324
$818$	−1.86397e6	−0.0973992
$819$	−568700.	−0.0296260
$820$	0	0
$821$	−3.66993e7	−1.90020	−0.950100	−	0.311945i	$-0.899019\pi$
$821$	−3.66993e7	−1.90020	−0.950100	+	0.311945i	$0.899019\pi$
$822$	4.99414e6	0.257799
$823$	−6.51679e6	−0.335378	−0.167689	−	0.985840i	$-0.553630\pi$
$823$	−6.51679e6	−0.335378	−0.167689	+	0.985840i	$0.553630\pi$
$824$	−2.84838e6	−0.146144
$825$	0	0
$826$	60984.0	0.00311004
$827$	2.68822e7	1.36679	0.683395	−	0.730049i	$-0.260503\pi$
$827$	2.68822e7	1.36679	0.683395	+	0.730049i	$0.260503\pi$
$828$	−415104.	−0.0210417
$829$	−1.20484e7	−0.608897	−0.304449	−	0.952529i	$-0.598472\pi$
$829$	−1.20484e7	−0.608897	−0.304449	+	0.952529i	$0.598472\pi$
$830$	0	0
$831$	−2.28218e6	−0.114643
$832$	409600.	0.0205141
$833$	2.02088e6	0.100908
$834$	−1.06384e7	−0.529615
$835$	0	0
$836$	−2.20066e6	−0.108902
$837$	1.63374e7	0.806066
$838$	432528.	0.0212767
$839$	1.80665e7	0.886073	0.443037	−	0.896503i	$-0.353901\pi$
$839$	1.80665e7	0.886073	0.443037	+	0.896503i	$0.353901\pi$
$840$	0	0
$841$	−1.47799e7	−0.720579
$842$	5.98955e6	0.291148
$843$	−2.72286e6	−0.131964
$844$	2.03902e7	0.985295
$845$	0	0
$846$	4.99986e6	0.240177
$847$	−1.92269e6	−0.0920875
$848$	4.09805e6	0.195698
$849$	5.07076e6	0.241437
$850$	0	0
$851$	−5.06846e6	−0.239912
$852$	1.92058e6	0.0906426
$853$	2.46483e7	1.15988	0.579941	−	0.814658i	$-0.303075\pi$
$853$	2.46483e7	1.15988	0.579941	+	0.814658i	$0.303075\pi$
$854$	−1.03261e7	−0.484499
$855$	0	0
$856$	−7.84858e6	−0.366106
$857$	−3.15037e7	−1.46524	−0.732622	−	0.680636i	$-0.761704\pi$
$857$	−3.15037e7	−1.46524	−0.732622	+	0.680636i	$0.761704\pi$
$858$	2.13360e6	0.0989452
$859$	−1.38352e7	−0.639737	−0.319868	−	0.947462i	$-0.603639\pi$
$859$	−1.38352e7	−0.639737	−0.319868	+	0.947462i	$0.603639\pi$
$860$	0	0
$861$	−3.81150e6	−0.175222
$862$	−1.50839e7	−0.691426
$863$	−2.35818e7	−1.07783	−0.538914	−	0.842361i	$-0.681165\pi$
$863$	−2.35818e7	−1.07783	−0.538914	+	0.842361i	$0.681165\pi$
$864$	4.15744e6	0.189471
$865$	0	0
$866$	1.54865e7	0.701711
$867$	−7.69115e6	−0.347491
$868$	−7.79046e6	−0.350965
$869$	632460.	0.0284108
$870$	0	0
$871$	5.17600e6	0.231179
$872$	−3.51718e6	−0.156640
$873$	−7.22672e6	−0.320927
$874$	−797088.	−0.0352962
$875$	0	0
$876$	−2.49827e6	−0.109997
$877$	1.82530e7	0.801373	0.400687	−	0.916215i	$-0.368772\pi$
$877$	1.82530e7	0.801373	0.400687	+	0.916215i	$0.368772\pi$
$878$	623032.	0.0272756
$879$	−2.73230e7	−1.19277
$880$	0	0
$881$	2.63474e7	1.14366	0.571832	−	0.820371i	$-0.306233\pi$
$881$	2.63474e7	1.14366	0.571832	+	0.820371i	$0.306233\pi$
$882$	−407208.	−0.0176256
$883$	−1.25210e7	−0.540427	−0.270213	−	0.962800i	$-0.587094\pi$
$883$	−1.25210e7	−0.540427	−0.270213	+	0.962800i	$0.587094\pi$
$884$	−1.49280e6	−0.0642497
$885$	0	0
$886$	−2.99875e7	−1.28338
$887$	3.13534e6	0.133806	0.0669030	−	0.997759i	$-0.478688\pi$
$887$	3.13534e6	0.133806	0.0669030	+	0.997759i	$0.478688\pi$
$888$	8.22707e6	0.350117
$889$	3.74831e7	1.59068
$890$	0	0
$891$	1.73046e7	0.730244
$892$	−1.08503e7	−0.456595
$893$	9.60080e6	0.402883
$894$	2.44112e7	1.02152
$895$	0	0
$896$	−1.98246e6	−0.0824965
$897$	772800.	0.0320690
$898$	6.14563e6	0.254317
$899$	−9.63346e6	−0.397542
$900$	0	0
$901$	−1.49355e7	−0.612924
$902$	−3.42900e6	−0.140330
$903$	3.96006e7	1.61615
$904$	6.50150e6	0.264602
$905$	0	0
$906$	1.77279e7	0.717525
$907$	2.60067e7	1.04970	0.524852	−	0.851193i	$-0.324121\pi$
$907$	2.60067e7	1.04970	0.524852	+	0.851193i	$0.324121\pi$
$908$	868800.	0.0349708
$909$	−7.20031e6	−0.289029
$910$	0	0
$911$	−1.31626e6	−0.0525468	−0.0262734	−	0.999655i	$-0.508364\pi$
$911$	−1.31626e6	−0.0525468	−0.0262734	+	0.999655i	$0.508364\pi$
$912$	1.29382e6	0.0515096
$913$	3.65623e7	1.45163
$914$	7.13515e6	0.282512
$915$	0	0
$916$	1.85250e7	0.729491
$917$	−277695.	−0.0109055
$918$	−1.51519e7	−0.593418
$919$	3.45812e7	1.35068	0.675338	−	0.737508i	$-0.263998\pi$
$919$	3.45812e7	1.35068	0.675338	+	0.737508i	$0.263998\pi$
$920$	0	0
$921$	2.55550e7	0.992722
$922$	−1.58509e6	−0.0614083
$923$	857400.	0.0331268
$924$	−1.03266e7	−0.397904
$925$	0	0
$926$	340484.	0.0130488
$927$	−2.09178e6	−0.0799497
$928$	−2.45146e6	−0.0934446
$929$	1.05033e7	0.399289	0.199644	−	0.979868i	$-0.436021\pi$
$929$	1.05033e7	0.399289	0.199644	+	0.979868i	$0.436021\pi$
$930$	0	0
$931$	−781926.	−0.0295659
$932$	−4.52702e6	−0.170716
$933$	9.64585e6	0.362774
$934$	−2.49553e7	−0.936043
$935$	0	0
$936$	300800.	0.0112225
$937$	−1.97665e7	−0.735497	−0.367749	−	0.929925i	$-0.619871\pi$
$937$	−1.97665e7	−0.735497	−0.367749	+	0.929925i	$0.619871\pi$
$938$	−2.50518e7	−0.929678
$939$	2.27443e7	0.841800
$940$	0	0
$941$	2.32092e7	0.854449	0.427225	−	0.904146i	$-0.359491\pi$
$941$	2.32092e7	0.854449	0.427225	+	0.904146i	$0.359491\pi$
$942$	−2.49224e7	−0.915086
$943$	−1.24200e6	−0.0454823
$944$	−32256.0	−0.00117810
$945$	0	0
$946$	3.56265e7	1.29433
$947$	4.28615e6	0.155307	0.0776537	−	0.996980i	$-0.475257\pi$
$947$	4.28615e6	0.155307	0.0776537	+	0.996980i	$0.475257\pi$
$948$	−371840.	−0.0134380
$949$	−1.11530e6	−0.0402000
$950$	0	0
$951$	−1.96930e7	−0.706092
$952$	7.22515e6	0.258377
$953$	−5.20118e7	−1.85511	−0.927555	−	0.373688i	$-0.878093\pi$
$953$	−5.20118e7	−1.85511	−0.927555	+	0.373688i	$0.878093\pi$
$954$	3.00950e6	0.107059
$955$	0	0
$956$	2.27238e7	0.804149
$957$	−1.27696e7	−0.450710
$958$	2.33163e7	0.820817
$959$	−1.07909e7	−0.378888
$960$	0	0
$961$	−1.24366e7	−0.434403
$962$	3.67280e6	0.127956
$963$	−5.76380e6	−0.200283
$964$	−1.64797e7	−0.571159
$965$	0	0
$966$	−3.74035e6	−0.128964
$967$	1.64670e7	0.566301	0.283151	−	0.959075i	$-0.408620\pi$
$967$	1.64670e7	0.566301	0.283151	+	0.959075i	$0.408620\pi$
$968$	1.01696e6	0.0348831
$969$	−4.71538e6	−0.161327
$970$	0	0
$971$	2.14039e7	0.728527	0.364263	−	0.931296i	$-0.381321\pi$
$971$	2.14039e7	0.728527	0.364263	+	0.931296i	$0.381321\pi$
$972$	5.61142e6	0.190505
$973$	2.29865e7	0.778378
$974$	−4.05000e7	−1.36791
$975$	0	0
$976$	5.46176e6	0.183530
$977$	−7.37087e6	−0.247049	−0.123524	−	0.992342i	$-0.539420\pi$
$977$	−7.37087e6	−0.247049	−0.123524	+	0.992342i	$0.539420\pi$
$978$	1.95765e7	0.654467
$979$	−4.52811e7	−1.50994
$980$	0	0
$981$	−2.58293e6	−0.0856920
$982$	3.41325e7	1.12951
$983$	−3.78457e7	−1.24920	−0.624600	−	0.780944i	$-0.714738\pi$
$983$	−3.78457e7	−1.24920	−0.624600	+	0.780944i	$0.714738\pi$
$984$	2.01600e6	0.0663747
$985$	0	0
$986$	8.93441e6	0.292667
$987$	4.50519e7	1.47204
$988$	577600.	0.0188250
$989$	1.29041e7	0.419505
$990$	0	0
$991$	−4.00548e7	−1.29560	−0.647798	−	0.761812i	$-0.724310\pi$
$991$	−4.00548e7	−1.29560	−0.647798	+	0.761812i	$0.724310\pi$
$992$	4.12058e6	0.132947
$993$	3.39509e7	1.09264
$994$	−4.14982e6	−0.133218
$995$	0	0
$996$	−2.14959e7	−0.686607
$997$	3.52370e7	1.12269	0.561347	−	0.827580i	$-0.310283\pi$
$997$	3.52370e7	1.12269	0.561347	+	0.827580i	$0.310283\pi$
$998$	−3.95481e7	−1.25690
$999$	3.72789e7	1.18182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.6.a.a.1.1		1
5.4	even	2		38.6.a.b.1.1	✓	1
15.14	odd	2		342.6.a.b.1.1		1
20.19	odd	2		304.6.a.e.1.1		1
95.94	odd	2		722.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.a.b.1.1	✓	1	5.4	even	2
304.6.a.e.1.1		1	20.19	odd	2
342.6.a.b.1.1		1	15.14	odd	2
722.6.a.a.1.1		1	95.94	odd	2
950.6.a.a.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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