LMFDB - Embedded newform 1950.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,4,Mod(1,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, 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("1950.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1950.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:	$115.053724511$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -6.00000 q^{6} -2.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -12.0000 q^{12} -13.0000 q^{13} -4.00000 q^{14} +16.0000 q^{16} +60.0000 q^{17} +18.0000 q^{18} +50.0000 q^{19} +6.00000 q^{21} -210.000 q^{23} -24.0000 q^{24} -26.0000 q^{26} -27.0000 q^{27} -8.00000 q^{28} -228.000 q^{29} +116.000 q^{31} +32.0000 q^{32} +120.000 q^{34} +36.0000 q^{36} -386.000 q^{37} +100.000 q^{38} +39.0000 q^{39} +378.000 q^{41} +12.0000 q^{42} +4.00000 q^{43} -420.000 q^{46} +312.000 q^{47} -48.0000 q^{48} -339.000 q^{49} -180.000 q^{51} -52.0000 q^{52} +198.000 q^{53} -54.0000 q^{54} -16.0000 q^{56} -150.000 q^{57} -456.000 q^{58} +624.000 q^{59} +638.000 q^{61} +232.000 q^{62} -18.0000 q^{63} +64.0000 q^{64} -200.000 q^{67} +240.000 q^{68} +630.000 q^{69} -408.000 q^{71} +72.0000 q^{72} -1148.00 q^{73} -772.000 q^{74} +200.000 q^{76} +78.0000 q^{78} +824.000 q^{79} +81.0000 q^{81} +756.000 q^{82} -1332.00 q^{83} +24.0000 q^{84} +8.00000 q^{86} +684.000 q^{87} +54.0000 q^{89} +26.0000 q^{91} -840.000 q^{92} -348.000 q^{93} +624.000 q^{94} -96.0000 q^{96} +244.000 q^{97} -678.000 q^{98} +O(q^{100})\)

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 $

$2$	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
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	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
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−4.00000	−0.0763604
$15$	0	0
$16$	16.0000	0.250000
$17$	60.0000	0.856008	0.428004	−	0.903777i	$-0.359217\pi$
$17$	60.0000	0.856008	0.428004	+	0.903777i	$0.359217\pi$
$18$	18.0000	0.235702
$19$	50.0000	0.603726	0.301863	−	0.953351i	$-0.402392\pi$
$19$	50.0000	0.603726	0.301863	+	0.953351i	$0.402392\pi$
$20$	0	0
$21$	6.00000	0.0623480
$22$	0	0
$23$	−210.000	−1.90383	−0.951914	−	0.306367i	$-0.900887\pi$
$23$	−210.000	−1.90383	−0.951914	+	0.306367i	$0.900887\pi$
$24$	−24.0000	−0.204124
$25$	0	0
$26$	−26.0000	−0.196116
$27$	−27.0000	−0.192450
$28$	−8.00000	−0.0539949
$29$	−228.000	−1.45995	−0.729975	−	0.683474i	$-0.760468\pi$
$29$	−228.000	−1.45995	−0.729975	+	0.683474i	$0.760468\pi$
$30$	0	0
$31$	116.000	0.672071	0.336036	−	0.941849i	$-0.390914\pi$
$31$	116.000	0.672071	0.336036	+	0.941849i	$0.390914\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	120.000	0.605289
$35$	0	0
$36$	36.0000	0.166667
$37$	−386.000	−1.71508	−0.857541	−	0.514416i	$-0.828009\pi$
$37$	−386.000	−1.71508	−0.857541	+	0.514416i	$0.828009\pi$
$38$	100.000	0.426898
$39$	39.0000	0.160128
$40$	0	0
$41$	378.000	1.43985	0.719923	−	0.694054i	$-0.244177\pi$
$41$	378.000	1.43985	0.719923	+	0.694054i	$0.244177\pi$
$42$	12.0000	0.0440867
$43$	4.00000	0.0141859	0.00709296	−	0.999975i	$-0.497742\pi$
$43$	4.00000	0.0141859	0.00709296	+	0.999975i	$0.497742\pi$
$44$	0	0
$45$	0	0
$46$	−420.000	−1.34621
$47$	312.000	0.968295	0.484148	−	0.874986i	$-0.339130\pi$
$47$	312.000	0.968295	0.484148	+	0.874986i	$0.339130\pi$
$48$	−48.0000	−0.144338
$49$	−339.000	−0.988338
$50$	0	0
$51$	−180.000	−0.494217
$52$	−52.0000	−0.138675
$53$	198.000	0.513158	0.256579	−	0.966523i	$-0.417405\pi$
$53$	198.000	0.513158	0.256579	+	0.966523i	$0.417405\pi$
$54$	−54.0000	−0.136083
$55$	0	0
$56$	−16.0000	−0.0381802
$57$	−150.000	−0.348561
$58$	−456.000	−1.03234
$59$	624.000	1.37691	0.688457	−	0.725278i	$-0.258289\pi$
$59$	624.000	1.37691	0.688457	+	0.725278i	$0.258289\pi$
$60$	0	0
$61$	638.000	1.33914	0.669570	−	0.742749i	$-0.266478\pi$
$61$	638.000	1.33914	0.669570	+	0.742749i	$0.266478\pi$
$62$	232.000	0.475226
$63$	−18.0000	−0.0359966
$64$	64.0000	0.125000
$65$	0	0
$66$	0	0
$67$	−200.000	−0.364685	−0.182342	−	0.983235i	$-0.558368\pi$
$67$	−200.000	−0.364685	−0.182342	+	0.983235i	$0.558368\pi$
$68$	240.000	0.428004
$69$	630.000	1.09918
$70$	0	0
$71$	−408.000	−0.681982	−0.340991	−	0.940067i	$-0.610762\pi$
$71$	−408.000	−0.681982	−0.340991	+	0.940067i	$0.610762\pi$
$72$	72.0000	0.117851
$73$	−1148.00	−1.84059	−0.920296	−	0.391222i	$-0.872052\pi$
$73$	−1148.00	−1.84059	−0.920296	+	0.391222i	$0.872052\pi$
$74$	−772.000	−1.21275
$75$	0	0
$76$	200.000	0.301863
$77$	0	0
$78$	78.0000	0.113228
$79$	824.000	1.17351	0.586755	−	0.809765i	$-0.300405\pi$
$79$	824.000	1.17351	0.586755	+	0.809765i	$0.300405\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	756.000	1.01812
$83$	−1332.00	−1.76152	−0.880759	−	0.473565i	$-0.842967\pi$
$83$	−1332.00	−1.76152	−0.880759	+	0.473565i	$0.842967\pi$
$84$	24.0000	0.0311740
$85$	0	0
$86$	8.00000	0.0100310
$87$	684.000	0.842902
$88$	0	0
$89$	54.0000	0.0643145	0.0321572	−	0.999483i	$-0.489762\pi$
$89$	54.0000	0.0643145	0.0321572	+	0.999483i	$0.489762\pi$
$90$	0	0
$91$	26.0000	0.0299510
$92$	−840.000	−0.951914
$93$	−348.000	−0.388021
$94$	624.000	0.684688
$95$	0	0
$96$	−96.0000	−0.102062
$97$	244.000	0.255407	0.127703	−	0.991812i	$-0.459239\pi$
$97$	244.000	0.255407	0.127703	+	0.991812i	$0.459239\pi$
$98$	−678.000	−0.698861
$99$	0	0
$100$	0	0
$101$	−1512.00	−1.48960	−0.744800	−	0.667288i	$-0.767455\pi$
$101$	−1512.00	−1.48960	−0.744800	+	0.667288i	$0.767455\pi$
$102$	−360.000	−0.349464
$103$	−992.000	−0.948977	−0.474489	−	0.880262i	$-0.657367\pi$
$103$	−992.000	−0.948977	−0.474489	+	0.880262i	$0.657367\pi$
$104$	−104.000	−0.0980581
$105$	0	0
$106$	396.000	0.362858
$107$	−2148.00	−1.94070	−0.970350	−	0.241702i	$-0.922294\pi$
$107$	−2148.00	−1.94070	−0.970350	+	0.241702i	$0.922294\pi$
$108$	−108.000	−0.0962250
$109$	44.0000	0.0386645	0.0193323	−	0.999813i	$-0.493846\pi$
$109$	44.0000	0.0386645	0.0193323	+	0.999813i	$0.493846\pi$
$110$	0	0
$111$	1158.00	0.990203
$112$	−32.0000	−0.0269975
$113$	−144.000	−0.119879	−0.0599397	−	0.998202i	$-0.519091\pi$
$113$	−144.000	−0.119879	−0.0599397	+	0.998202i	$0.519091\pi$
$114$	−300.000	−0.246470
$115$	0	0
$116$	−912.000	−0.729975
$117$	−117.000	−0.0924500
$118$	1248.00	0.973625
$119$	−120.000	−0.0924402
$120$	0	0
$121$	−1331.00	−1.00000
$122$	1276.00	0.946915
$123$	−1134.00	−0.831295
$124$	464.000	0.336036
$125$	0	0
$126$	−36.0000	−0.0254535
$127$	−1856.00	−1.29680	−0.648399	−	0.761301i	$-0.724561\pi$
$127$	−1856.00	−1.29680	−0.648399	+	0.761301i	$0.724561\pi$
$128$	128.000	0.0883883
$129$	−12.0000	−0.00819024
$130$	0	0
$131$	−2202.00	−1.46862	−0.734312	−	0.678813i	$-0.762495\pi$
$131$	−2202.00	−1.46862	−0.734312	+	0.678813i	$0.762495\pi$
$132$	0	0
$133$	−100.000	−0.0651962
$134$	−400.000	−0.257871
$135$	0	0
$136$	480.000	0.302645
$137$	2454.00	1.53036	0.765180	−	0.643816i	$-0.222650\pi$
$137$	2454.00	1.53036	0.765180	+	0.643816i	$0.222650\pi$
$138$	1260.00	0.777234
$139$	392.000	0.239201	0.119601	−	0.992822i	$-0.461839\pi$
$139$	392.000	0.239201	0.119601	+	0.992822i	$0.461839\pi$
$140$	0	0
$141$	−936.000	−0.559046
$142$	−816.000	−0.482234
$143$	0	0
$144$	144.000	0.0833333
$145$	0	0
$146$	−2296.00	−1.30150
$147$	1017.00	0.570617
$148$	−1544.00	−0.857541
$149$	1542.00	0.847823	0.423911	−	0.905704i	$-0.360657\pi$
$149$	1542.00	0.847823	0.423911	+	0.905704i	$0.360657\pi$
$150$	0	0
$151$	−1156.00	−0.623006	−0.311503	−	0.950245i	$-0.600832\pi$
$151$	−1156.00	−0.623006	−0.311503	+	0.950245i	$0.600832\pi$
$152$	400.000	0.213449
$153$	540.000	0.285336
$154$	0	0
$155$	0	0
$156$	156.000	0.0800641
$157$	1750.00	0.889587	0.444794	−	0.895633i	$-0.353277\pi$
$157$	1750.00	0.889587	0.444794	+	0.895633i	$0.353277\pi$
$158$	1648.00	0.829796
$159$	−594.000	−0.296272
$160$	0	0
$161$	420.000	0.205594
$162$	162.000	0.0785674
$163$	2428.00	1.16672	0.583361	−	0.812213i	$-0.301737\pi$
$163$	2428.00	1.16672	0.583361	+	0.812213i	$0.301737\pi$
$164$	1512.00	0.719923
$165$	0	0
$166$	−2664.00	−1.24558
$167$	2892.00	1.34006	0.670029	−	0.742335i	$-0.266282\pi$
$167$	2892.00	1.34006	0.670029	+	0.742335i	$0.266282\pi$
$168$	48.0000	0.0220433
$169$	169.000	0.0769231
$170$	0	0
$171$	450.000	0.201242
$172$	16.0000	0.00709296
$173$	−138.000	−0.0606471	−0.0303235	−	0.999540i	$-0.509654\pi$
$173$	−138.000	−0.0606471	−0.0303235	+	0.999540i	$0.509654\pi$
$174$	1368.00	0.596022
$175$	0	0
$176$	0	0
$177$	−1872.00	−0.794961
$178$	108.000	0.0454772
$179$	−4182.00	−1.74624	−0.873121	−	0.487503i	$-0.837908\pi$
$179$	−4182.00	−1.74624	−0.873121	+	0.487503i	$0.837908\pi$
$180$	0	0
$181$	−2806.00	−1.15231	−0.576156	−	0.817340i	$-0.695448\pi$
$181$	−2806.00	−1.15231	−0.576156	+	0.817340i	$0.695448\pi$
$182$	52.0000	0.0211786
$183$	−1914.00	−0.773153
$184$	−1680.00	−0.673105
$185$	0	0
$186$	−696.000	−0.274372
$187$	0	0
$188$	1248.00	0.484148
$189$	54.0000	0.0207827
$190$	0	0
$191$	−552.000	−0.209117	−0.104558	−	0.994519i	$-0.533343\pi$
$191$	−552.000	−0.209117	−0.104558	+	0.994519i	$0.533343\pi$
$192$	−192.000	−0.0721688
$193$	−2720.00	−1.01446	−0.507228	−	0.861812i	$-0.669330\pi$
$193$	−2720.00	−1.01446	−0.507228	+	0.861812i	$0.669330\pi$
$194$	488.000	0.180600
$195$	0	0
$196$	−1356.00	−0.494169
$197$	−2718.00	−0.982992	−0.491496	−	0.870880i	$-0.663550\pi$
$197$	−2718.00	−0.982992	−0.491496	+	0.870880i	$0.663550\pi$
$198$	0	0
$199$	−448.000	−0.159587	−0.0797937	−	0.996811i	$-0.525426\pi$
$199$	−448.000	−0.159587	−0.0797937	+	0.996811i	$0.525426\pi$
$200$	0	0
$201$	600.000	0.210551
$202$	−3024.00	−1.05331
$203$	456.000	0.157660
$204$	−720.000	−0.247108
$205$	0	0
$206$	−1984.00	−0.671028
$207$	−1890.00	−0.634609
$208$	−208.000	−0.0693375
$209$	0	0
$210$	0	0
$211$	−3364.00	−1.09757	−0.548785	−	0.835963i	$-0.684909\pi$
$211$	−3364.00	−1.09757	−0.548785	+	0.835963i	$0.684909\pi$
$212$	792.000	0.256579
$213$	1224.00	0.393742
$214$	−4296.00	−1.37228
$215$	0	0
$216$	−216.000	−0.0680414
$217$	−232.000	−0.0725769
$218$	88.0000	0.0273400
$219$	3444.00	1.06267
$220$	0	0
$221$	−780.000	−0.237414
$222$	2316.00	0.700179
$223$	−2702.00	−0.811387	−0.405694	−	0.914009i	$-0.632970\pi$
$223$	−2702.00	−0.811387	−0.405694	+	0.914009i	$0.632970\pi$
$224$	−64.0000	−0.0190901
$225$	0	0
$226$	−288.000	−0.0847676
$227$	−1332.00	−0.389462	−0.194731	−	0.980857i	$-0.562383\pi$
$227$	−1332.00	−0.389462	−0.194731	+	0.980857i	$0.562383\pi$
$228$	−600.000	−0.174281
$229$	2972.00	0.857621	0.428811	−	0.903394i	$-0.358933\pi$
$229$	2972.00	0.857621	0.428811	+	0.903394i	$0.358933\pi$
$230$	0	0
$231$	0	0
$232$	−1824.00	−0.516170
$233$	3588.00	1.00883	0.504416	−	0.863461i	$-0.331708\pi$
$233$	3588.00	1.00883	0.504416	+	0.863461i	$0.331708\pi$
$234$	−234.000	−0.0653720
$235$	0	0
$236$	2496.00	0.688457
$237$	−2472.00	−0.677526
$238$	−240.000	−0.0653651
$239$	−5496.00	−1.48748	−0.743738	−	0.668471i	$-0.766949\pi$
$239$	−5496.00	−1.48748	−0.743738	+	0.668471i	$0.766949\pi$
$240$	0	0
$241$	−142.000	−0.0379545	−0.0189772	−	0.999820i	$-0.506041\pi$
$241$	−142.000	−0.0379545	−0.0189772	+	0.999820i	$0.506041\pi$
$242$	−2662.00	−0.707107
$243$	−243.000	−0.0641500
$244$	2552.00	0.669570
$245$	0	0
$246$	−2268.00	−0.587815
$247$	−650.000	−0.167443
$248$	928.000	0.237613
$249$	3996.00	1.01701
$250$	0	0
$251$	−2886.00	−0.725748	−0.362874	−	0.931838i	$-0.618204\pi$
$251$	−2886.00	−0.725748	−0.362874	+	0.931838i	$0.618204\pi$
$252$	−72.0000	−0.0179983
$253$	0	0
$254$	−3712.00	−0.916975
$255$	0	0
$256$	256.000	0.0625000
$257$	1704.00	0.413590	0.206795	−	0.978384i	$-0.433697\pi$
$257$	1704.00	0.413590	0.206795	+	0.978384i	$0.433697\pi$
$258$	−24.0000	−0.00579137
$259$	772.000	0.185211
$260$	0	0
$261$	−2052.00	−0.486650
$262$	−4404.00	−1.03847
$263$	−6702.00	−1.57134	−0.785671	−	0.618644i	$-0.787682\pi$
$263$	−6702.00	−1.57134	−0.785671	+	0.618644i	$0.787682\pi$
$264$	0	0
$265$	0	0
$266$	−200.000	−0.0461007
$267$	−162.000	−0.0371320
$268$	−800.000	−0.182342
$269$	3696.00	0.837729	0.418864	−	0.908049i	$-0.362428\pi$
$269$	3696.00	0.837729	0.418864	+	0.908049i	$0.362428\pi$
$270$	0	0
$271$	−6748.00	−1.51259	−0.756295	−	0.654231i	$-0.772992\pi$
$271$	−6748.00	−1.51259	−0.756295	+	0.654231i	$0.772992\pi$
$272$	960.000	0.214002
$273$	−78.0000	−0.0172922
$274$	4908.00	1.08213
$275$	0	0
$276$	2520.00	0.549588
$277$	−6338.00	−1.37478	−0.687389	−	0.726289i	$-0.741243\pi$
$277$	−6338.00	−1.37478	−0.687389	+	0.726289i	$0.741243\pi$
$278$	784.000	0.169141
$279$	1044.00	0.224024
$280$	0	0
$281$	−90.0000	−0.0191066	−0.00955329	−	0.999954i	$-0.503041\pi$
$281$	−90.0000	−0.0191066	−0.00955329	+	0.999954i	$0.503041\pi$
$282$	−1872.00	−0.395305
$283$	7444.00	1.56360	0.781802	−	0.623527i	$-0.214301\pi$
$283$	7444.00	1.56360	0.781802	+	0.623527i	$0.214301\pi$
$284$	−1632.00	−0.340991
$285$	0	0
$286$	0	0
$287$	−756.000	−0.155489
$288$	288.000	0.0589256
$289$	−1313.00	−0.267250
$290$	0	0
$291$	−732.000	−0.147459
$292$	−4592.00	−0.920296
$293$	−8382.00	−1.67127	−0.835634	−	0.549286i	$-0.814900\pi$
$293$	−8382.00	−1.67127	−0.835634	+	0.549286i	$0.814900\pi$
$294$	2034.00	0.403487
$295$	0	0
$296$	−3088.00	−0.606373
$297$	0	0
$298$	3084.00	0.599501
$299$	2730.00	0.528027
$300$	0	0
$301$	−8.00000	−0.00153193
$302$	−2312.00	−0.440532
$303$	4536.00	0.860021
$304$	800.000	0.150931
$305$	0	0
$306$	1080.00	0.201763
$307$	6544.00	1.21657	0.608283	−	0.793720i	$-0.291859\pi$
$307$	6544.00	1.21657	0.608283	+	0.793720i	$0.291859\pi$
$308$	0	0
$309$	2976.00	0.547892
$310$	0	0
$311$	4992.00	0.910194	0.455097	−	0.890442i	$-0.349605\pi$
$311$	4992.00	0.910194	0.455097	+	0.890442i	$0.349605\pi$
$312$	312.000	0.0566139
$313$	−902.000	−0.162888	−0.0814442	−	0.996678i	$-0.525953\pi$
$313$	−902.000	−0.162888	−0.0814442	+	0.996678i	$0.525953\pi$
$314$	3500.00	0.629033
$315$	0	0
$316$	3296.00	0.586755
$317$	−2010.00	−0.356129	−0.178064	−	0.984019i	$-0.556984\pi$
$317$	−2010.00	−0.356129	−0.178064	+	0.984019i	$0.556984\pi$
$318$	−1188.00	−0.209496
$319$	0	0
$320$	0	0
$321$	6444.00	1.12046
$322$	840.000	0.145377
$323$	3000.00	0.516794
$324$	324.000	0.0555556
$325$	0	0
$326$	4856.00	0.824997
$327$	−132.000	−0.0223230
$328$	3024.00	0.509062
$329$	−624.000	−0.104566
$330$	0	0
$331$	−1030.00	−0.171039	−0.0855195	−	0.996336i	$-0.527255\pi$
$331$	−1030.00	−0.171039	−0.0855195	+	0.996336i	$0.527255\pi$
$332$	−5328.00	−0.880759
$333$	−3474.00	−0.571694
$334$	5784.00	0.947564
$335$	0	0
$336$	96.0000	0.0155870
$337$	394.000	0.0636871	0.0318435	−	0.999493i	$-0.489862\pi$
$337$	394.000	0.0636871	0.0318435	+	0.999493i	$0.489862\pi$
$338$	338.000	0.0543928
$339$	432.000	0.0692124
$340$	0	0
$341$	0	0
$342$	900.000	0.142299
$343$	1364.00	0.214720
$344$	32.0000	0.00501548
$345$	0	0
$346$	−276.000	−0.0428840
$347$	−9792.00	−1.51488	−0.757438	−	0.652907i	$-0.773549\pi$
$347$	−9792.00	−1.51488	−0.757438	+	0.652907i	$0.773549\pi$
$348$	2736.00	0.421451
$349$	−5332.00	−0.817809	−0.408905	−	0.912577i	$-0.634089\pi$
$349$	−5332.00	−0.817809	−0.408905	+	0.912577i	$0.634089\pi$
$350$	0	0
$351$	351.000	0.0533761
$352$	0	0
$353$	1014.00	0.152889	0.0764444	−	0.997074i	$-0.475643\pi$
$353$	1014.00	0.152889	0.0764444	+	0.997074i	$0.475643\pi$
$354$	−3744.00	−0.562122
$355$	0	0
$356$	216.000	0.0321572
$357$	360.000	0.0533704
$358$	−8364.00	−1.23478
$359$	1128.00	0.165832	0.0829158	−	0.996557i	$-0.473577\pi$
$359$	1128.00	0.165832	0.0829158	+	0.996557i	$0.473577\pi$
$360$	0	0
$361$	−4359.00	−0.635515
$362$	−5612.00	−0.814807
$363$	3993.00	0.577350
$364$	104.000	0.0149755
$365$	0	0
$366$	−3828.00	−0.546702
$367$	4408.00	0.626964	0.313482	−	0.949594i	$-0.398504\pi$
$367$	4408.00	0.626964	0.313482	+	0.949594i	$0.398504\pi$
$368$	−3360.00	−0.475957
$369$	3402.00	0.479949
$370$	0	0
$371$	−396.000	−0.0554159
$372$	−1392.00	−0.194010
$373$	−12386.0	−1.71936	−0.859682	−	0.510830i	$-0.829338\pi$
$373$	−12386.0	−1.71936	−0.859682	+	0.510830i	$0.829338\pi$
$374$	0	0
$375$	0	0
$376$	2496.00	0.342344
$377$	2964.00	0.404917
$378$	108.000	0.0146956
$379$	4070.00	0.551614	0.275807	−	0.961213i	$-0.411055\pi$
$379$	4070.00	0.551614	0.275807	+	0.961213i	$0.411055\pi$
$380$	0	0
$381$	5568.00	0.748707
$382$	−1104.00	−0.147868
$383$	1500.00	0.200121	0.100061	−	0.994981i	$-0.468096\pi$
$383$	1500.00	0.200121	0.100061	+	0.994981i	$0.468096\pi$
$384$	−384.000	−0.0510310
$385$	0	0
$386$	−5440.00	−0.717328
$387$	36.0000	0.00472864
$388$	976.000	0.127703
$389$	768.000	0.100101	0.0500503	−	0.998747i	$-0.484062\pi$
$389$	768.000	0.100101	0.0500503	+	0.998747i	$0.484062\pi$
$390$	0	0
$391$	−12600.0	−1.62969
$392$	−2712.00	−0.349430
$393$	6606.00	0.847910
$394$	−5436.00	−0.695081
$395$	0	0
$396$	0	0
$397$	−5738.00	−0.725395	−0.362698	−	0.931907i	$-0.618144\pi$
$397$	−5738.00	−0.725395	−0.362698	+	0.931907i	$0.618144\pi$
$398$	−896.000	−0.112845
$399$	300.000	0.0376411
$400$	0	0
$401$	8970.00	1.11706	0.558529	−	0.829485i	$-0.311366\pi$
$401$	8970.00	1.11706	0.558529	+	0.829485i	$0.311366\pi$
$402$	1200.00	0.148882
$403$	−1508.00	−0.186399
$404$	−6048.00	−0.744800
$405$	0	0
$406$	912.000	0.111482
$407$	0	0
$408$	−1440.00	−0.174732
$409$	1334.00	0.161276	0.0806382	−	0.996743i	$-0.474304\pi$
$409$	1334.00	0.161276	0.0806382	+	0.996743i	$0.474304\pi$
$410$	0	0
$411$	−7362.00	−0.883554
$412$	−3968.00	−0.474489
$413$	−1248.00	−0.148693
$414$	−3780.00	−0.448736
$415$	0	0
$416$	−416.000	−0.0490290
$417$	−1176.00	−0.138103
$418$	0	0
$419$	−618.000	−0.0720556	−0.0360278	−	0.999351i	$-0.511470\pi$
$419$	−618.000	−0.0720556	−0.0360278	+	0.999351i	$0.511470\pi$
$420$	0	0
$421$	−13552.0	−1.56885	−0.784423	−	0.620226i	$-0.787041\pi$
$421$	−13552.0	−1.56885	−0.784423	+	0.620226i	$0.787041\pi$
$422$	−6728.00	−0.776099
$423$	2808.00	0.322765
$424$	1584.00	0.181429
$425$	0	0
$426$	2448.00	0.278418
$427$	−1276.00	−0.144614
$428$	−8592.00	−0.970350
$429$	0	0
$430$	0	0
$431$	3432.00	0.383558	0.191779	−	0.981438i	$-0.438574\pi$
$431$	3432.00	0.383558	0.191779	+	0.981438i	$0.438574\pi$
$432$	−432.000	−0.0481125
$433$	13402.0	1.48743	0.743717	−	0.668494i	$-0.233061\pi$
$433$	13402.0	1.48743	0.743717	+	0.668494i	$0.233061\pi$
$434$	−464.000	−0.0513196
$435$	0	0
$436$	176.000	0.0193323
$437$	−10500.0	−1.14939
$438$	6888.00	0.751419
$439$	−10624.0	−1.15502	−0.577512	−	0.816382i	$-0.695976\pi$
$439$	−10624.0	−1.15502	−0.577512	+	0.816382i	$0.695976\pi$
$440$	0	0
$441$	−3051.00	−0.329446
$442$	−1560.00	−0.167877
$443$	11424.0	1.22522	0.612608	−	0.790387i	$-0.290120\pi$
$443$	11424.0	1.22522	0.612608	+	0.790387i	$0.290120\pi$
$444$	4632.00	0.495101
$445$	0	0
$446$	−5404.00	−0.573737
$447$	−4626.00	−0.489491
$448$	−128.000	−0.0134987
$449$	4014.00	0.421898	0.210949	−	0.977497i	$-0.432345\pi$
$449$	4014.00	0.421898	0.210949	+	0.977497i	$0.432345\pi$
$450$	0	0
$451$	0	0
$452$	−576.000	−0.0599397
$453$	3468.00	0.359693
$454$	−2664.00	−0.275391
$455$	0	0
$456$	−1200.00	−0.123235
$457$	5164.00	0.528581	0.264291	−	0.964443i	$-0.414862\pi$
$457$	5164.00	0.528581	0.264291	+	0.964443i	$0.414862\pi$
$458$	5944.00	0.606430
$459$	−1620.00	−0.164739
$460$	0	0
$461$	13194.0	1.33298	0.666492	−	0.745512i	$-0.267795\pi$
$461$	13194.0	1.33298	0.666492	+	0.745512i	$0.267795\pi$
$462$	0	0
$463$	−2318.00	−0.232671	−0.116335	−	0.993210i	$-0.537115\pi$
$463$	−2318.00	−0.232671	−0.116335	+	0.993210i	$0.537115\pi$
$464$	−3648.00	−0.364987
$465$	0	0
$466$	7176.00	0.713351
$467$	12756.0	1.26398	0.631989	−	0.774978i	$-0.282239\pi$
$467$	12756.0	1.26398	0.631989	+	0.774978i	$0.282239\pi$
$468$	−468.000	−0.0462250
$469$	400.000	0.0393823
$470$	0	0
$471$	−5250.00	−0.513603
$472$	4992.00	0.486812
$473$	0	0
$474$	−4944.00	−0.479083
$475$	0	0
$476$	−480.000	−0.0462201
$477$	1782.00	0.171053
$478$	−10992.0	−1.05180
$479$	8616.00	0.821869	0.410934	−	0.911665i	$-0.365203\pi$
$479$	8616.00	0.821869	0.410934	+	0.911665i	$0.365203\pi$
$480$	0	0
$481$	5018.00	0.475678
$482$	−284.000	−0.0268379
$483$	−1260.00	−0.118700
$484$	−5324.00	−0.500000
$485$	0	0
$486$	−486.000	−0.0453609
$487$	10078.0	0.937737	0.468868	−	0.883268i	$-0.344662\pi$
$487$	10078.0	0.937737	0.468868	+	0.883268i	$0.344662\pi$
$488$	5104.00	0.473457
$489$	−7284.00	−0.673607
$490$	0	0
$491$	−4290.00	−0.394308	−0.197154	−	0.980373i	$-0.563170\pi$
$491$	−4290.00	−0.394308	−0.197154	+	0.980373i	$0.563170\pi$
$492$	−4536.00	−0.415648
$493$	−13680.0	−1.24973
$494$	−1300.00	−0.118400
$495$	0	0
$496$	1856.00	0.168018
$497$	816.000	0.0736471
$498$	7992.00	0.719137
$499$	3134.00	0.281157	0.140578	−	0.990070i	$-0.455104\pi$
$499$	3134.00	0.281157	0.140578	+	0.990070i	$0.455104\pi$
$500$	0	0
$501$	−8676.00	−0.773683
$502$	−5772.00	−0.513181
$503$	−19566.0	−1.73440	−0.867202	−	0.497957i	$-0.834084\pi$
$503$	−19566.0	−1.73440	−0.867202	+	0.497957i	$0.834084\pi$
$504$	−144.000	−0.0127267
$505$	0	0
$506$	0	0
$507$	−507.000	−0.0444116
$508$	−7424.00	−0.648399
$509$	11754.0	1.02355	0.511775	−	0.859120i	$-0.328988\pi$
$509$	11754.0	1.02355	0.511775	+	0.859120i	$0.328988\pi$
$510$	0	0
$511$	2296.00	0.198765
$512$	512.000	0.0441942
$513$	−1350.00	−0.116187
$514$	3408.00	0.292452
$515$	0	0
$516$	−48.0000	−0.00409512
$517$	0	0
$518$	1544.00	0.130964
$519$	414.000	0.0350146
$520$	0	0
$521$	18774.0	1.57870	0.789351	−	0.613942i	$-0.210417\pi$
$521$	18774.0	1.57870	0.789351	+	0.613942i	$0.210417\pi$
$522$	−4104.00	−0.344113
$523$	12316.0	1.02972	0.514858	−	0.857276i	$-0.327845\pi$
$523$	12316.0	1.02972	0.514858	+	0.857276i	$0.327845\pi$
$524$	−8808.00	−0.734312
$525$	0	0
$526$	−13404.0	−1.11111
$527$	6960.00	0.575299
$528$	0	0
$529$	31933.0	2.62456
$530$	0	0
$531$	5616.00	0.458971
$532$	−400.000	−0.0325981
$533$	−4914.00	−0.399341
$534$	−324.000	−0.0262563
$535$	0	0
$536$	−1600.00	−0.128936
$537$	12546.0	1.00819
$538$	7392.00	0.592364
$539$	0	0
$540$	0	0
$541$	2168.00	0.172291	0.0861457	−	0.996283i	$-0.472545\pi$
$541$	2168.00	0.172291	0.0861457	+	0.996283i	$0.472545\pi$
$542$	−13496.0	−1.06956
$543$	8418.00	0.665287
$544$	1920.00	0.151322
$545$	0	0
$546$	−156.000	−0.0122274
$547$	10156.0	0.793856	0.396928	−	0.917850i	$-0.370076\pi$
$547$	10156.0	0.793856	0.396928	+	0.917850i	$0.370076\pi$
$548$	9816.00	0.765180
$549$	5742.00	0.446380
$550$	0	0
$551$	−11400.0	−0.881409
$552$	5040.00	0.388617
$553$	−1648.00	−0.126727
$554$	−12676.0	−0.972115
$555$	0	0
$556$	1568.00	0.119601
$557$	16494.0	1.25471	0.627355	−	0.778734i	$-0.284138\pi$
$557$	16494.0	1.25471	0.627355	+	0.778734i	$0.284138\pi$
$558$	2088.00	0.158409
$559$	−52.0000	−0.00393446
$560$	0	0
$561$	0	0
$562$	−180.000	−0.0135104
$563$	168.000	0.0125761	0.00628806	−	0.999980i	$-0.497998\pi$
$563$	168.000	0.0125761	0.00628806	+	0.999980i	$0.497998\pi$
$564$	−3744.00	−0.279523
$565$	0	0
$566$	14888.0	1.10563
$567$	−162.000	−0.0119989
$568$	−3264.00	−0.241117
$569$	−14106.0	−1.03929	−0.519643	−	0.854383i	$-0.673935\pi$
$569$	−14106.0	−1.03929	−0.519643	+	0.854383i	$0.673935\pi$
$570$	0	0
$571$	−11632.0	−0.852511	−0.426256	−	0.904603i	$-0.640168\pi$
$571$	−11632.0	−0.852511	−0.426256	+	0.904603i	$0.640168\pi$
$572$	0	0
$573$	1656.00	0.120734
$574$	−1512.00	−0.109947
$575$	0	0
$576$	576.000	0.0416667
$577$	15736.0	1.13535	0.567676	−	0.823252i	$-0.307843\pi$
$577$	15736.0	1.13535	0.567676	+	0.823252i	$0.307843\pi$
$578$	−2626.00	−0.188974
$579$	8160.00	0.585696
$580$	0	0
$581$	2664.00	0.190226
$582$	−1464.00	−0.104269
$583$	0	0
$584$	−9184.00	−0.650748
$585$	0	0
$586$	−16764.0	−1.18177
$587$	−18540.0	−1.30362	−0.651812	−	0.758380i	$-0.725991\pi$
$587$	−18540.0	−1.30362	−0.651812	+	0.758380i	$0.725991\pi$
$588$	4068.00	0.285309
$589$	5800.00	0.405747
$590$	0	0
$591$	8154.00	0.567531
$592$	−6176.00	−0.428770
$593$	18426.0	1.27600	0.637998	−	0.770038i	$-0.279763\pi$
$593$	18426.0	1.27600	0.637998	+	0.770038i	$0.279763\pi$
$594$	0	0
$595$	0	0
$596$	6168.00	0.423911
$597$	1344.00	0.0921378
$598$	5460.00	0.373371
$599$	20424.0	1.39316	0.696579	−	0.717480i	$-0.254704\pi$
$599$	20424.0	1.39316	0.696579	+	0.717480i	$0.254704\pi$
$600$	0	0
$601$	2630.00	0.178502	0.0892512	−	0.996009i	$-0.471553\pi$
$601$	2630.00	0.178502	0.0892512	+	0.996009i	$0.471553\pi$
$602$	−16.0000	−0.00108324
$603$	−1800.00	−0.121562
$604$	−4624.00	−0.311503
$605$	0	0
$606$	9072.00	0.608127
$607$	−18296.0	−1.22341	−0.611707	−	0.791085i	$-0.709517\pi$
$607$	−18296.0	−1.22341	−0.611707	+	0.791085i	$0.709517\pi$
$608$	1600.00	0.106725
$609$	−1368.00	−0.0910249
$610$	0	0
$611$	−4056.00	−0.268557
$612$	2160.00	0.142668
$613$	166.000	0.0109375	0.00546874	−	0.999985i	$-0.498259\pi$
$613$	166.000	0.0109375	0.00546874	+	0.999985i	$0.498259\pi$
$614$	13088.0	0.860242
$615$	0	0
$616$	0	0
$617$	−23466.0	−1.53113	−0.765564	−	0.643360i	$-0.777540\pi$
$617$	−23466.0	−1.53113	−0.765564	+	0.643360i	$0.777540\pi$
$618$	5952.00	0.387418
$619$	2558.00	0.166098	0.0830490	−	0.996545i	$-0.473534\pi$
$619$	2558.00	0.166098	0.0830490	+	0.996545i	$0.473534\pi$
$620$	0	0
$621$	5670.00	0.366392
$622$	9984.00	0.643604
$623$	−108.000	−0.00694531
$624$	624.000	0.0400320
$625$	0	0
$626$	−1804.00	−0.115179
$627$	0	0
$628$	7000.00	0.444794
$629$	−23160.0	−1.46812
$630$	0	0
$631$	−1456.00	−0.0918581	−0.0459290	−	0.998945i	$-0.514625\pi$
$631$	−1456.00	−0.0918581	−0.0459290	+	0.998945i	$0.514625\pi$
$632$	6592.00	0.414898
$633$	10092.0	0.633682
$634$	−4020.00	−0.251821
$635$	0	0
$636$	−2376.00	−0.148136
$637$	4407.00	0.274116
$638$	0	0
$639$	−3672.00	−0.227327
$640$	0	0
$641$	17898.0	1.10285	0.551426	−	0.834224i	$-0.314084\pi$
$641$	17898.0	1.10285	0.551426	+	0.834224i	$0.314084\pi$
$642$	12888.0	0.792288
$643$	−16184.0	−0.992589	−0.496294	−	0.868154i	$-0.665306\pi$
$643$	−16184.0	−0.992589	−0.496294	+	0.868154i	$0.665306\pi$
$644$	1680.00	0.102797
$645$	0	0
$646$	6000.00	0.365429
$647$	22554.0	1.37046	0.685231	−	0.728326i	$-0.259701\pi$
$647$	22554.0	1.37046	0.685231	+	0.728326i	$0.259701\pi$
$648$	648.000	0.0392837
$649$	0	0
$650$	0	0
$651$	696.000	0.0419023
$652$	9712.00	0.583361
$653$	15234.0	0.912944	0.456472	−	0.889738i	$-0.349113\pi$
$653$	15234.0	0.912944	0.456472	+	0.889738i	$0.349113\pi$
$654$	−264.000	−0.0157847
$655$	0	0
$656$	6048.00	0.359961
$657$	−10332.0	−0.613531
$658$	−1248.00	−0.0739394
$659$	−954.000	−0.0563924	−0.0281962	−	0.999602i	$-0.508976\pi$
$659$	−954.000	−0.0563924	−0.0281962	+	0.999602i	$0.508976\pi$
$660$	0	0
$661$	11720.0	0.689645	0.344822	−	0.938668i	$-0.387939\pi$
$661$	11720.0	0.689645	0.344822	+	0.938668i	$0.387939\pi$
$662$	−2060.00	−0.120943
$663$	2340.00	0.137071
$664$	−10656.0	−0.622791
$665$	0	0
$666$	−6948.00	−0.404249
$667$	47880.0	2.77949
$668$	11568.0	0.670029
$669$	8106.00	0.468455
$670$	0	0
$671$	0	0
$672$	192.000	0.0110217
$673$	−10202.0	−0.584336	−0.292168	−	0.956367i	$-0.594377\pi$
$673$	−10202.0	−0.584336	−0.292168	+	0.956367i	$0.594377\pi$
$674$	788.000	0.0450336
$675$	0	0
$676$	676.000	0.0384615
$677$	13026.0	0.739483	0.369741	−	0.929135i	$-0.379446\pi$
$677$	13026.0	0.739483	0.369741	+	0.929135i	$0.379446\pi$
$678$	864.000	0.0489406
$679$	−488.000	−0.0275813
$680$	0	0
$681$	3996.00	0.224856
$682$	0	0
$683$	−16788.0	−0.940520	−0.470260	−	0.882528i	$-0.655840\pi$
$683$	−16788.0	−0.940520	−0.470260	+	0.882528i	$0.655840\pi$
$684$	1800.00	0.100621
$685$	0	0
$686$	2728.00	0.151830
$687$	−8916.00	−0.495148
$688$	64.0000	0.00354648
$689$	−2574.00	−0.142325
$690$	0	0
$691$	−33838.0	−1.86289	−0.931446	−	0.363880i	$-0.881452\pi$
$691$	−33838.0	−1.86289	−0.931446	+	0.363880i	$0.881452\pi$
$692$	−552.000	−0.0303235
$693$	0	0
$694$	−19584.0	−1.07118
$695$	0	0
$696$	5472.00	0.298011
$697$	22680.0	1.23252
$698$	−10664.0	−0.578278
$699$	−10764.0	−0.582449
$700$	0	0
$701$	30480.0	1.64224	0.821122	−	0.570752i	$-0.193348\pi$
$701$	30480.0	1.64224	0.821122	+	0.570752i	$0.193348\pi$
$702$	702.000	0.0377426
$703$	−19300.0	−1.03544
$704$	0	0
$705$	0	0
$706$	2028.00	0.108109
$707$	3024.00	0.160862
$708$	−7488.00	−0.397481
$709$	7796.00	0.412955	0.206477	−	0.978451i	$-0.433800\pi$
$709$	7796.00	0.412955	0.206477	+	0.978451i	$0.433800\pi$
$710$	0	0
$711$	7416.00	0.391170
$712$	432.000	0.0227386
$713$	−24360.0	−1.27951
$714$	720.000	0.0377385
$715$	0	0
$716$	−16728.0	−0.873121
$717$	16488.0	0.858794
$718$	2256.00	0.117261
$719$	4068.00	0.211003	0.105501	−	0.994419i	$-0.466355\pi$
$719$	4068.00	0.211003	0.105501	+	0.994419i	$0.466355\pi$
$720$	0	0
$721$	1984.00	0.102480
$722$	−8718.00	−0.449377
$723$	426.000	0.0219130
$724$	−11224.0	−0.576156
$725$	0	0
$726$	7986.00	0.408248
$727$	5044.00	0.257320	0.128660	−	0.991689i	$-0.458932\pi$
$727$	5044.00	0.257320	0.128660	+	0.991689i	$0.458932\pi$
$728$	208.000	0.0105893
$729$	729.000	0.0370370
$730$	0	0
$731$	240.000	0.0121433
$732$	−7656.00	−0.386576
$733$	−3530.00	−0.177877	−0.0889383	−	0.996037i	$-0.528347\pi$
$733$	−3530.00	−0.177877	−0.0889383	+	0.996037i	$0.528347\pi$
$734$	8816.00	0.443330
$735$	0	0
$736$	−6720.00	−0.336552
$737$	0	0
$738$	6804.00	0.339375
$739$	14942.0	0.743776	0.371888	−	0.928278i	$-0.378711\pi$
$739$	14942.0	0.743776	0.371888	+	0.928278i	$0.378711\pi$
$740$	0	0
$741$	1950.00	0.0966735
$742$	−792.000	−0.0391850
$743$	3252.00	0.160571	0.0802855	−	0.996772i	$-0.474417\pi$
$743$	3252.00	0.160571	0.0802855	+	0.996772i	$0.474417\pi$
$744$	−2784.00	−0.137186
$745$	0	0
$746$	−24772.0	−1.21577
$747$	−11988.0	−0.587173
$748$	0	0
$749$	4296.00	0.209576
$750$	0	0
$751$	−8920.00	−0.433416	−0.216708	−	0.976236i	$-0.569532\pi$
$751$	−8920.00	−0.433416	−0.216708	+	0.976236i	$0.569532\pi$
$752$	4992.00	0.242074
$753$	8658.00	0.419011
$754$	5928.00	0.286320
$755$	0	0
$756$	216.000	0.0103913
$757$	−1814.00	−0.0870950	−0.0435475	−	0.999051i	$-0.513866\pi$
$757$	−1814.00	−0.0870950	−0.0435475	+	0.999051i	$0.513866\pi$
$758$	8140.00	0.390050
$759$	0	0
$760$	0	0
$761$	−5958.00	−0.283807	−0.141904	−	0.989880i	$-0.545322\pi$
$761$	−5958.00	−0.283807	−0.141904	+	0.989880i	$0.545322\pi$
$762$	11136.0	0.529416
$763$	−88.0000	−0.00417538
$764$	−2208.00	−0.104558
$765$	0	0
$766$	3000.00	0.141507
$767$	−8112.00	−0.381887
$768$	−768.000	−0.0360844
$769$	3098.00	0.145275	0.0726377	−	0.997358i	$-0.476858\pi$
$769$	3098.00	0.145275	0.0726377	+	0.997358i	$0.476858\pi$
$770$	0	0
$771$	−5112.00	−0.238786
$772$	−10880.0	−0.507228
$773$	6882.00	0.320218	0.160109	−	0.987099i	$-0.448815\pi$
$773$	6882.00	0.320218	0.160109	+	0.987099i	$0.448815\pi$
$774$	72.0000	0.00334365
$775$	0	0
$776$	1952.00	0.0902999
$777$	−2316.00	−0.106932
$778$	1536.00	0.0707818
$779$	18900.0	0.869272
$780$	0	0
$781$	0	0
$782$	−25200.0	−1.15237
$783$	6156.00	0.280967
$784$	−5424.00	−0.247085
$785$	0	0
$786$	13212.0	0.599563
$787$	27460.0	1.24377	0.621883	−	0.783110i	$-0.286368\pi$
$787$	27460.0	1.24377	0.621883	+	0.783110i	$0.286368\pi$
$788$	−10872.0	−0.491496
$789$	20106.0	0.907215
$790$	0	0
$791$	288.000	0.0129458
$792$	0	0
$793$	−8294.00	−0.371411
$794$	−11476.0	−0.512932
$795$	0	0
$796$	−1792.00	−0.0797937
$797$	32814.0	1.45838	0.729192	−	0.684310i	$-0.239896\pi$
$797$	32814.0	1.45838	0.729192	+	0.684310i	$0.239896\pi$
$798$	600.000	0.0266163
$799$	18720.0	0.828869
$800$	0	0
$801$	486.000	0.0214382
$802$	17940.0	0.789880
$803$	0	0
$804$	2400.00	0.105275
$805$	0	0
$806$	−3016.00	−0.131804
$807$	−11088.0	−0.483663
$808$	−12096.0	−0.526653
$809$	18594.0	0.808072	0.404036	−	0.914743i	$-0.367607\pi$
$809$	18594.0	0.808072	0.404036	+	0.914743i	$0.367607\pi$
$810$	0	0
$811$	−3334.00	−0.144356	−0.0721779	−	0.997392i	$-0.522995\pi$
$811$	−3334.00	−0.144356	−0.0721779	+	0.997392i	$0.522995\pi$
$812$	1824.00	0.0788299
$813$	20244.0	0.873294
$814$	0	0
$815$	0	0
$816$	−2880.00	−0.123554
$817$	200.000	0.00856440
$818$	2668.00	0.114040
$819$	234.000	0.00998367
$820$	0	0
$821$	38094.0	1.61935	0.809677	−	0.586876i	$-0.199642\pi$
$821$	38094.0	1.61935	0.809677	+	0.586876i	$0.199642\pi$
$822$	−14724.0	−0.624767
$823$	−33104.0	−1.40211	−0.701053	−	0.713109i	$-0.747286\pi$
$823$	−33104.0	−1.40211	−0.701053	+	0.713109i	$0.747286\pi$
$824$	−7936.00	−0.335514
$825$	0	0
$826$	−2496.00	−0.105142
$827$	40068.0	1.68477	0.842383	−	0.538880i	$-0.181152\pi$
$827$	40068.0	1.68477	0.842383	+	0.538880i	$0.181152\pi$
$828$	−7560.00	−0.317305
$829$	14342.0	0.600866	0.300433	−	0.953803i	$-0.402869\pi$
$829$	14342.0	0.600866	0.300433	+	0.953803i	$0.402869\pi$
$830$	0	0
$831$	19014.0	0.793728
$832$	−832.000	−0.0346688
$833$	−20340.0	−0.846025
$834$	−2352.00	−0.0976536
$835$	0	0
$836$	0	0
$837$	−3132.00	−0.129340
$838$	−1236.00	−0.0509510
$839$	−22104.0	−0.909553	−0.454776	−	0.890606i	$-0.650281\pi$
$839$	−22104.0	−0.909553	−0.454776	+	0.890606i	$0.650281\pi$
$840$	0	0
$841$	27595.0	1.13145
$842$	−27104.0	−1.10934
$843$	270.000	0.0110312
$844$	−13456.0	−0.548785
$845$	0	0
$846$	5616.00	0.228229
$847$	2662.00	0.107990
$848$	3168.00	0.128290
$849$	−22332.0	−0.902747
$850$	0	0
$851$	81060.0	3.26522
$852$	4896.00	0.196871
$853$	−14474.0	−0.580985	−0.290493	−	0.956877i	$-0.593819\pi$
$853$	−14474.0	−0.580985	−0.290493	+	0.956877i	$0.593819\pi$
$854$	−2552.00	−0.102257
$855$	0	0
$856$	−17184.0	−0.686141
$857$	−23592.0	−0.940359	−0.470179	−	0.882571i	$-0.655811\pi$
$857$	−23592.0	−0.940359	−0.470179	+	0.882571i	$0.655811\pi$
$858$	0	0
$859$	−37996.0	−1.50920	−0.754602	−	0.656182i	$-0.772170\pi$
$859$	−37996.0	−1.50920	−0.754602	+	0.656182i	$0.772170\pi$
$860$	0	0
$861$	2268.00	0.0897715
$862$	6864.00	0.271217
$863$	34596.0	1.36461	0.682307	−	0.731066i	$-0.260977\pi$
$863$	34596.0	1.36461	0.682307	+	0.731066i	$0.260977\pi$
$864$	−864.000	−0.0340207
$865$	0	0
$866$	26804.0	1.05177
$867$	3939.00	0.154297
$868$	−928.000	−0.0362884
$869$	0	0
$870$	0	0
$871$	2600.00	0.101145
$872$	352.000	0.0136700
$873$	2196.00	0.0851356
$874$	−21000.0	−0.812741
$875$	0	0
$876$	13776.0	0.531333
$877$	−27590.0	−1.06231	−0.531156	−	0.847274i	$-0.678242\pi$
$877$	−27590.0	−1.06231	−0.531156	+	0.847274i	$0.678242\pi$
$878$	−21248.0	−0.816726
$879$	25146.0	0.964907
$880$	0	0
$881$	−43818.0	−1.67567	−0.837835	−	0.545923i	$-0.816179\pi$
$881$	−43818.0	−1.67567	−0.837835	+	0.545923i	$0.816179\pi$
$882$	−6102.00	−0.232954
$883$	−33524.0	−1.27766	−0.638829	−	0.769349i	$-0.720581\pi$
$883$	−33524.0	−1.27766	−0.638829	+	0.769349i	$0.720581\pi$
$884$	−3120.00	−0.118707
$885$	0	0
$886$	22848.0	0.866358
$887$	−30522.0	−1.15539	−0.577694	−	0.816254i	$-0.696047\pi$
$887$	−30522.0	−1.15539	−0.577694	+	0.816254i	$0.696047\pi$
$888$	9264.00	0.350090
$889$	3712.00	0.140041
$890$	0	0
$891$	0	0
$892$	−10808.0	−0.405694
$893$	15600.0	0.584585
$894$	−9252.00	−0.346122
$895$	0	0
$896$	−256.000	−0.00954504
$897$	−8190.00	−0.304856
$898$	8028.00	0.298327
$899$	−26448.0	−0.981190
$900$	0	0
$901$	11880.0	0.439268
$902$	0	0
$903$	24.0000	0.000884463 0
$904$	−1152.00	−0.0423838
$905$	0	0
$906$	6936.00	0.254341
$907$	−26540.0	−0.971606	−0.485803	−	0.874068i	$-0.661473\pi$
$907$	−26540.0	−0.971606	−0.485803	+	0.874068i	$0.661473\pi$
$908$	−5328.00	−0.194731
$909$	−13608.0	−0.496533
$910$	0	0
$911$	−24420.0	−0.888113	−0.444056	−	0.895999i	$-0.646461\pi$
$911$	−24420.0	−0.888113	−0.444056	+	0.895999i	$0.646461\pi$
$912$	−2400.00	−0.0871403
$913$	0	0
$914$	10328.0	0.373764
$915$	0	0
$916$	11888.0	0.428811
$917$	4404.00	0.158596
$918$	−3240.00	−0.116488
$919$	−36880.0	−1.32379	−0.661893	−	0.749599i	$-0.730247\pi$
$919$	−36880.0	−1.32379	−0.661893	+	0.749599i	$0.730247\pi$
$920$	0	0
$921$	−19632.0	−0.702385
$922$	26388.0	0.942562
$923$	5304.00	0.189148
$924$	0	0
$925$	0	0
$926$	−4636.00	−0.164523
$927$	−8928.00	−0.316326
$928$	−7296.00	−0.258085
$929$	−39858.0	−1.40764	−0.703821	−	0.710378i	$-0.748524\pi$
$929$	−39858.0	−1.40764	−0.703821	+	0.710378i	$0.748524\pi$
$930$	0	0
$931$	−16950.0	−0.596685
$932$	14352.0	0.504416
$933$	−14976.0	−0.525501
$934$	25512.0	0.893767
$935$	0	0
$936$	−936.000	−0.0326860
$937$	20182.0	0.703647	0.351823	−	0.936066i	$-0.385562\pi$
$937$	20182.0	0.703647	0.351823	+	0.936066i	$0.385562\pi$
$938$	800.000	0.0278475
$939$	2706.00	0.0940436
$940$	0	0
$941$	4998.00	0.173146	0.0865729	−	0.996246i	$-0.472408\pi$
$941$	4998.00	0.173146	0.0865729	+	0.996246i	$0.472408\pi$
$942$	−10500.0	−0.363172
$943$	−79380.0	−2.74122
$944$	9984.00	0.344228
$945$	0	0
$946$	0	0
$947$	5148.00	0.176650	0.0883250	−	0.996092i	$-0.471849\pi$
$947$	5148.00	0.176650	0.0883250	+	0.996092i	$0.471849\pi$
$948$	−9888.00	−0.338763
$949$	14924.0	0.510488
$950$	0	0
$951$	6030.00	0.205611
$952$	−960.000	−0.0326825
$953$	50268.0	1.70865	0.854323	−	0.519742i	$-0.173972\pi$
$953$	50268.0	1.70865	0.854323	+	0.519742i	$0.173972\pi$
$954$	3564.00	0.120953
$955$	0	0
$956$	−21984.0	−0.743738
$957$	0	0
$958$	17232.0	0.581149
$959$	−4908.00	−0.165263
$960$	0	0
$961$	−16335.0	−0.548320
$962$	10036.0	0.336355
$963$	−19332.0	−0.646900
$964$	−568.000	−0.0189772
$965$	0	0
$966$	−2520.00	−0.0839334
$967$	54766.0	1.82126	0.910629	−	0.413226i	$-0.135598\pi$
$967$	54766.0	1.82126	0.910629	+	0.413226i	$0.135598\pi$
$968$	−10648.0	−0.353553
$969$	−9000.00	−0.298371
$970$	0	0
$971$	34746.0	1.14835	0.574177	−	0.818731i	$-0.305322\pi$
$971$	34746.0	1.14835	0.574177	+	0.818731i	$0.305322\pi$
$972$	−972.000	−0.0320750
$973$	−784.000	−0.0258313
$974$	20156.0	0.663080
$975$	0	0
$976$	10208.0	0.334785
$977$	35466.0	1.16137	0.580685	−	0.814129i	$-0.302785\pi$
$977$	35466.0	1.16137	0.580685	+	0.814129i	$0.302785\pi$
$978$	−14568.0	−0.476312
$979$	0	0
$980$	0	0
$981$	396.000	0.0128882
$982$	−8580.00	−0.278818
$983$	16452.0	0.533812	0.266906	−	0.963723i	$-0.413999\pi$
$983$	16452.0	0.533812	0.266906	+	0.963723i	$0.413999\pi$
$984$	−9072.00	−0.293907
$985$	0	0
$986$	−27360.0	−0.883692
$987$	1872.00	0.0603712
$988$	−2600.00	−0.0837217
$989$	−840.000	−0.0270075
$990$	0	0
$991$	−59584.0	−1.90994	−0.954969	−	0.296706i	$-0.904112\pi$
$991$	−59584.0	−1.90994	−0.954969	+	0.296706i	$0.904112\pi$
$992$	3712.00	0.118807
$993$	3090.00	0.0987494
$994$	1632.00	0.0520764
$995$	0	0
$996$	15984.0	0.508506
$997$	−32042.0	−1.01783	−0.508917	−	0.860816i	$-0.669954\pi$
$997$	−32042.0	−1.01783	−0.508917	+	0.860816i	$0.669954\pi$
$998$	6268.00	0.198808
$999$	10422.0	0.330068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.4.a.j.1.1		1
5.4	even	2		390.4.a.d.1.1	✓	1
15.14	odd	2		1170.4.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.4.a.d.1.1	✓	1	5.4	even	2
1170.4.a.p.1.1		1	15.14	odd	2
1950.4.a.j.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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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