LMFDB - Embedded newform 150.6.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,6,Mod(1,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, 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("150.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	150.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:	$24.0575729719$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -36.0000 q^{6} -164.000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -36.0000 q^{6} -164.000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +720.000 q^{11} -144.000 q^{12} -698.000 q^{13} -656.000 q^{14} +256.000 q^{16} +2226.00 q^{17} +324.000 q^{18} +356.000 q^{19} +1476.00 q^{21} +2880.00 q^{22} +1800.00 q^{23} -576.000 q^{24} -2792.00 q^{26} -729.000 q^{27} -2624.00 q^{28} +714.000 q^{29} +848.000 q^{31} +1024.00 q^{32} -6480.00 q^{33} +8904.00 q^{34} +1296.00 q^{36} +11302.0 q^{37} +1424.00 q^{38} +6282.00 q^{39} +9354.00 q^{41} +5904.00 q^{42} +5956.00 q^{43} +11520.0 q^{44} +7200.00 q^{46} +11160.0 q^{47} -2304.00 q^{48} +10089.0 q^{49} -20034.0 q^{51} -11168.0 q^{52} -14106.0 q^{53} -2916.00 q^{54} -10496.0 q^{56} -3204.00 q^{57} +2856.00 q^{58} +7920.00 q^{59} -13450.0 q^{61} +3392.00 q^{62} -13284.0 q^{63} +4096.00 q^{64} -25920.0 q^{66} +65476.0 q^{67} +35616.0 q^{68} -16200.0 q^{69} +34560.0 q^{71} +5184.00 q^{72} -86258.0 q^{73} +45208.0 q^{74} +5696.00 q^{76} -118080. q^{77} +25128.0 q^{78} -108832. q^{79} +6561.00 q^{81} +37416.0 q^{82} -10668.0 q^{83} +23616.0 q^{84} +23824.0 q^{86} -6426.00 q^{87} +46080.0 q^{88} +10818.0 q^{89} +114472. q^{91} +28800.0 q^{92} -7632.00 q^{93} +44640.0 q^{94} -9216.00 q^{96} -4418.00 q^{97} +40356.0 q^{98} +58320.0 q^{99} +O(q^{100})\)

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
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	−36.0000	−0.408248
$7$	−164.000	−1.26502	−0.632512	−	0.774551i	$-0.717976\pi$
$7$	−164.000	−1.26502	−0.632512	+	0.774551i	$0.717976\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	0	0
$11$	720.000	1.79412	0.897059	−	0.441912i	$-0.145700\pi$
$11$	720.000	1.79412	0.897059	+	0.441912i	$0.145700\pi$
$12$	−144.000	−0.288675
$13$	−698.000	−1.14551	−0.572753	−	0.819728i	$-0.694124\pi$
$13$	−698.000	−1.14551	−0.572753	+	0.819728i	$0.694124\pi$
$14$	−656.000	−0.894507
$15$	0	0
$16$	256.000	0.250000
$17$	2226.00	1.86811	0.934056	−	0.357127i	$-0.116244\pi$
$17$	2226.00	1.86811	0.934056	+	0.357127i	$0.116244\pi$
$18$	324.000	0.235702
$19$	356.000	0.226238	0.113119	−	0.993581i	$-0.463916\pi$
$19$	356.000	0.226238	0.113119	+	0.993581i	$0.463916\pi$
$20$	0	0
$21$	1476.00	0.730362
$22$	2880.00	1.26863
$23$	1800.00	0.709501	0.354750	−	0.934961i	$-0.384566\pi$
$23$	1800.00	0.709501	0.354750	+	0.934961i	$0.384566\pi$
$24$	−576.000	−0.204124
$25$	0	0
$26$	−2792.00	−0.809994
$27$	−729.000	−0.192450
$28$	−2624.00	−0.632512
$29$	714.000	0.157653	0.0788267	−	0.996888i	$-0.474883\pi$
$29$	714.000	0.157653	0.0788267	+	0.996888i	$0.474883\pi$
$30$	0	0
$31$	848.000	0.158486	0.0792431	−	0.996855i	$-0.474750\pi$
$31$	848.000	0.158486	0.0792431	+	0.996855i	$0.474750\pi$
$32$	1024.00	0.176777
$33$	−6480.00	−1.03583
$34$	8904.00	1.32095
$35$	0	0
$36$	1296.00	0.166667
$37$	11302.0	1.35722	0.678611	−	0.734498i	$-0.262582\pi$
$37$	11302.0	1.35722	0.678611	+	0.734498i	$0.262582\pi$
$38$	1424.00	0.159975
$39$	6282.00	0.661358
$40$	0	0
$41$	9354.00	0.869036	0.434518	−	0.900663i	$-0.356919\pi$
$41$	9354.00	0.869036	0.434518	+	0.900663i	$0.356919\pi$
$42$	5904.00	0.516444
$43$	5956.00	0.491228	0.245614	−	0.969368i	$-0.421010\pi$
$43$	5956.00	0.491228	0.245614	+	0.969368i	$0.421010\pi$
$44$	11520.0	0.897059
$45$	0	0
$46$	7200.00	0.501693
$47$	11160.0	0.736919	0.368459	−	0.929644i	$-0.379885\pi$
$47$	11160.0	0.736919	0.368459	+	0.929644i	$0.379885\pi$
$48$	−2304.00	−0.144338
$49$	10089.0	0.600286
$50$	0	0
$51$	−20034.0	−1.07855
$52$	−11168.0	−0.572753
$53$	−14106.0	−0.689786	−0.344893	−	0.938642i	$-0.612085\pi$
$53$	−14106.0	−0.689786	−0.344893	+	0.938642i	$0.612085\pi$
$54$	−2916.00	−0.136083
$55$	0	0
$56$	−10496.0	−0.447254
$57$	−3204.00	−0.130619
$58$	2856.00	0.111478
$59$	7920.00	0.296207	0.148103	−	0.988972i	$-0.452683\pi$
$59$	7920.00	0.296207	0.148103	+	0.988972i	$0.452683\pi$
$60$	0	0
$61$	−13450.0	−0.462805	−0.231402	−	0.972858i	$-0.574331\pi$
$61$	−13450.0	−0.462805	−0.231402	+	0.972858i	$0.574331\pi$
$62$	3392.00	0.112067
$63$	−13284.0	−0.421675
$64$	4096.00	0.125000
$65$	0	0
$66$	−25920.0	−0.732445
$67$	65476.0	1.78195	0.890974	−	0.454054i	$-0.150023\pi$
$67$	65476.0	1.78195	0.890974	+	0.454054i	$0.150023\pi$
$68$	35616.0	0.934056
$69$	−16200.0	−0.409631
$70$	0	0
$71$	34560.0	0.813632	0.406816	−	0.913510i	$-0.366639\pi$
$71$	34560.0	0.813632	0.406816	+	0.913510i	$0.366639\pi$
$72$	5184.00	0.117851
$73$	−86258.0	−1.89449	−0.947245	−	0.320511i	$-0.896145\pi$
$73$	−86258.0	−1.89449	−0.947245	+	0.320511i	$0.896145\pi$
$74$	45208.0	0.959701
$75$	0	0
$76$	5696.00	0.113119
$77$	−118080.	−2.26960
$78$	25128.0	0.467651
$79$	−108832.	−1.96195	−0.980977	−	0.194123i	$-0.937814\pi$
$79$	−108832.	−1.96195	−0.980977	+	0.194123i	$0.937814\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	37416.0	0.614501
$83$	−10668.0	−0.169976	−0.0849880	−	0.996382i	$-0.527085\pi$
$83$	−10668.0	−0.169976	−0.0849880	+	0.996382i	$0.527085\pi$
$84$	23616.0	0.365181
$85$	0	0
$86$	23824.0	0.347351
$87$	−6426.00	−0.0910212
$88$	46080.0	0.634316
$89$	10818.0	0.144768	0.0723839	−	0.997377i	$-0.476939\pi$
$89$	10818.0	0.144768	0.0723839	+	0.997377i	$0.476939\pi$
$90$	0	0
$91$	114472.	1.44909
$92$	28800.0	0.354750
$93$	−7632.00	−0.0915021
$94$	44640.0	0.521080
$95$	0	0
$96$	−9216.00	−0.102062
$97$	−4418.00	−0.0476756	−0.0238378	−	0.999716i	$-0.507589\pi$
$97$	−4418.00	−0.0476756	−0.0238378	+	0.999716i	$0.507589\pi$
$98$	40356.0	0.424466
$99$	58320.0	0.598039
$100$	0	0
$101$	−102942.	−1.00413	−0.502064	−	0.864830i	$-0.667426\pi$
$101$	−102942.	−1.00413	−0.502064	+	0.864830i	$0.667426\pi$
$102$	−80136.0	−0.762653
$103$	69436.0	0.644899	0.322449	−	0.946587i	$-0.395494\pi$
$103$	69436.0	0.644899	0.322449	+	0.946587i	$0.395494\pi$
$104$	−44672.0	−0.404997
$105$	0	0
$106$	−56424.0	−0.487752
$107$	−17412.0	−0.147024	−0.0735122	−	0.997294i	$-0.523421\pi$
$107$	−17412.0	−0.147024	−0.0735122	+	0.997294i	$0.523421\pi$
$108$	−11664.0	−0.0962250
$109$	−203770.	−1.64276	−0.821380	−	0.570382i	$-0.806795\pi$
$109$	−203770.	−1.64276	−0.821380	+	0.570382i	$0.806795\pi$
$110$	0	0
$111$	−101718.	−0.783593
$112$	−41984.0	−0.316256
$113$	212202.	1.56334	0.781670	−	0.623692i	$-0.214368\pi$
$113$	212202.	1.56334	0.781670	+	0.623692i	$0.214368\pi$
$114$	−12816.0	−0.0923614
$115$	0	0
$116$	11424.0	0.0788267
$117$	−56538.0	−0.381835
$118$	31680.0	0.209450
$119$	−365064.	−2.36321
$120$	0	0
$121$	357349.	2.21886
$122$	−53800.0	−0.327252
$123$	−84186.0	−0.501738
$124$	13568.0	0.0792431
$125$	0	0
$126$	−53136.0	−0.298169
$127$	−6140.00	−0.0337800	−0.0168900	−	0.999857i	$-0.505377\pi$
$127$	−6140.00	−0.0337800	−0.0168900	+	0.999857i	$0.505377\pi$
$128$	16384.0	0.0883883
$129$	−53604.0	−0.283611
$130$	0	0
$131$	−205920.	−1.04838	−0.524192	−	0.851600i	$-0.675633\pi$
$131$	−205920.	−1.04838	−0.524192	+	0.851600i	$0.675633\pi$
$132$	−103680.	−0.517917
$133$	−58384.0	−0.286197
$134$	261904.	1.26003
$135$	0	0
$136$	142464.	0.660477
$137$	−230334.	−1.04847	−0.524236	−	0.851573i	$-0.675649\pi$
$137$	−230334.	−1.04847	−0.524236	+	0.851573i	$0.675649\pi$
$138$	−64800.0	−0.289653
$139$	260756.	1.14471	0.572357	−	0.820004i	$-0.306029\pi$
$139$	260756.	1.14471	0.572357	+	0.820004i	$0.306029\pi$
$140$	0	0
$141$	−100440.	−0.425460
$142$	138240.	0.575324
$143$	−502560.	−2.05517
$144$	20736.0	0.0833333
$145$	0	0
$146$	−345032.	−1.33961
$147$	−90801.0	−0.346575
$148$	180832.	0.678611
$149$	−29526.0	−0.108953	−0.0544765	−	0.998515i	$-0.517349\pi$
$149$	−29526.0	−0.108953	−0.0544765	+	0.998515i	$0.517349\pi$
$150$	0	0
$151$	125168.	0.446736	0.223368	−	0.974734i	$-0.428295\pi$
$151$	125168.	0.446736	0.223368	+	0.974734i	$0.428295\pi$
$152$	22784.0	0.0799873
$153$	180306.	0.622704
$154$	−472320.	−1.60485
$155$	0	0
$156$	100512.	0.330679
$157$	43222.0	0.139944	0.0699722	−	0.997549i	$-0.477709\pi$
$157$	43222.0	0.139944	0.0699722	+	0.997549i	$0.477709\pi$
$158$	−435328.	−1.38731
$159$	126954.	0.398248
$160$	0	0
$161$	−295200.	−0.897536
$162$	26244.0	0.0785674
$163$	293476.	0.865174	0.432587	−	0.901592i	$-0.357601\pi$
$163$	293476.	0.865174	0.432587	+	0.901592i	$0.357601\pi$
$164$	149664.	0.434518
$165$	0	0
$166$	−42672.0	−0.120191
$167$	−322200.	−0.893993	−0.446997	−	0.894536i	$-0.647506\pi$
$167$	−322200.	−0.893993	−0.446997	+	0.894536i	$0.647506\pi$
$168$	94464.0	0.258222
$169$	115911.	0.312182
$170$	0	0
$171$	28836.0	0.0754127
$172$	95296.0	0.245614
$173$	261918.	0.665350	0.332675	−	0.943042i	$-0.392049\pi$
$173$	261918.	0.665350	0.332675	+	0.943042i	$0.392049\pi$
$174$	−25704.0	−0.0643617
$175$	0	0
$176$	184320.	0.448529
$177$	−71280.0	−0.171015
$178$	43272.0	0.102366
$179$	623544.	1.45457	0.727285	−	0.686336i	$-0.240782\pi$
$179$	623544.	1.45457	0.727285	+	0.686336i	$0.240782\pi$
$180$	0	0
$181$	−61186.0	−0.138821	−0.0694106	−	0.997588i	$-0.522112\pi$
$181$	−61186.0	−0.138821	−0.0694106	+	0.997588i	$0.522112\pi$
$182$	457888.	1.02466
$183$	121050.	0.267200
$184$	115200.	0.250846
$185$	0	0
$186$	−30528.0	−0.0647017
$187$	1.60272e6	3.35161
$188$	178560.	0.368459
$189$	119556.	0.243454
$190$	0	0
$191$	737256.	1.46229	0.731147	−	0.682220i	$-0.238985\pi$
$191$	737256.	1.46229	0.731147	+	0.682220i	$0.238985\pi$
$192$	−36864.0	−0.0721688
$193$	−539162.	−1.04190	−0.520950	−	0.853587i	$-0.674422\pi$
$193$	−539162.	−1.04190	−0.520950	+	0.853587i	$0.674422\pi$
$194$	−17672.0	−0.0337118
$195$	0	0
$196$	161424.	0.300143
$197$	651174.	1.19545	0.597725	−	0.801701i	$-0.296071\pi$
$197$	651174.	1.19545	0.597725	+	0.801701i	$0.296071\pi$
$198$	233280.	0.422877
$199$	157328.	0.281626	0.140813	−	0.990036i	$-0.455028\pi$
$199$	157328.	0.281626	0.140813	+	0.990036i	$0.455028\pi$
$200$	0	0
$201$	−589284.	−1.02881
$202$	−411768.	−0.710026
$203$	−117096.	−0.199435
$204$	−320544.	−0.539277
$205$	0	0
$206$	277744.	0.456012
$207$	145800.	0.236500
$208$	−178688.	−0.286376
$209$	256320.	0.405898
$210$	0	0
$211$	707180.	1.09351	0.546756	−	0.837292i	$-0.315862\pi$
$211$	707180.	1.09351	0.546756	+	0.837292i	$0.315862\pi$
$212$	−225696.	−0.344893
$213$	−311040.	−0.469750
$214$	−69648.0	−0.103962
$215$	0	0
$216$	−46656.0	−0.0680414
$217$	−139072.	−0.200489
$218$	−815080.	−1.16161
$219$	776322.	1.09378
$220$	0	0
$221$	−1.55375e6	−2.13993
$222$	−406872.	−0.554084
$223$	530740.	0.714693	0.357347	−	0.933972i	$-0.383681\pi$
$223$	530740.	0.714693	0.357347	+	0.933972i	$0.383681\pi$
$224$	−167936.	−0.223627
$225$	0	0
$226$	848808.	1.10545
$227$	−120372.	−0.155046	−0.0775230	−	0.996991i	$-0.524701\pi$
$227$	−120372.	−0.155046	−0.0775230	+	0.996991i	$0.524701\pi$
$228$	−51264.0	−0.0653094
$229$	772310.	0.973202	0.486601	−	0.873624i	$-0.338237\pi$
$229$	772310.	0.973202	0.486601	+	0.873624i	$0.338237\pi$
$230$	0	0
$231$	1.06272e6	1.31035
$232$	45696.0	0.0557389
$233$	−8838.00	−0.0106651	−0.00533254	−	0.999986i	$-0.501697\pi$
$233$	−8838.00	−0.0106651	−0.00533254	+	0.999986i	$0.501697\pi$
$234$	−226152.	−0.269998
$235$	0	0
$236$	126720.	0.148103
$237$	979488.	1.13273
$238$	−1.46026e6	−1.67104
$239$	−775416.	−0.878092	−0.439046	−	0.898465i	$-0.644683\pi$
$239$	−775416.	−0.878092	−0.439046	+	0.898465i	$0.644683\pi$
$240$	0	0
$241$	−373438.	−0.414167	−0.207084	−	0.978323i	$-0.566397\pi$
$241$	−373438.	−0.414167	−0.207084	+	0.978323i	$0.566397\pi$
$242$	1.42940e6	1.56897
$243$	−59049.0	−0.0641500
$244$	−215200.	−0.231402
$245$	0	0
$246$	−336744.	−0.354782
$247$	−248488.	−0.259157
$248$	54272.0	0.0560334
$249$	96012.0	0.0981357
$250$	0	0
$251$	71976.0	0.0721113	0.0360557	−	0.999350i	$-0.488521\pi$
$251$	71976.0	0.0721113	0.0360557	+	0.999350i	$0.488521\pi$
$252$	−212544.	−0.210837
$253$	1.29600e6	1.27293
$254$	−24560.0	−0.0238860
$255$	0	0
$256$	65536.0	0.0625000
$257$	−1.59356e6	−1.50500	−0.752498	−	0.658595i	$-0.771151\pi$
$257$	−1.59356e6	−1.50500	−0.752498	+	0.658595i	$0.771151\pi$
$258$	−214416.	−0.200543
$259$	−1.85353e6	−1.71692
$260$	0	0
$261$	57834.0	0.0525511
$262$	−823680.	−0.741319
$263$	2.05452e6	1.83156	0.915780	−	0.401681i	$-0.131574\pi$
$263$	2.05452e6	1.83156	0.915780	+	0.401681i	$0.131574\pi$
$264$	−414720.	−0.366223
$265$	0	0
$266$	−233536.	−0.202372
$267$	−97362.0	−0.0835817
$268$	1.04762e6	0.890974
$269$	−258486.	−0.217799	−0.108900	−	0.994053i	$-0.534733\pi$
$269$	−258486.	−0.217799	−0.108900	+	0.994053i	$0.534733\pi$
$270$	0	0
$271$	−1.98398e6	−1.64102	−0.820509	−	0.571634i	$-0.806310\pi$
$271$	−1.98398e6	−1.64102	−0.820509	+	0.571634i	$0.806310\pi$
$272$	569856.	0.467028
$273$	−1.03025e6	−0.836633
$274$	−921336.	−0.741381
$275$	0	0
$276$	−259200.	−0.204815
$277$	−1.61326e6	−1.26329	−0.631647	−	0.775256i	$-0.717621\pi$
$277$	−1.61326e6	−1.26329	−0.631647	+	0.775256i	$0.717621\pi$
$278$	1.04302e6	0.809436
$279$	68688.0	0.0528288
$280$	0	0
$281$	1.37882e6	1.04170	0.520848	−	0.853649i	$-0.325616\pi$
$281$	1.37882e6	1.04170	0.520848	+	0.853649i	$0.325616\pi$
$282$	−401760.	−0.300846
$283$	−1.45831e6	−1.08239	−0.541194	−	0.840898i	$-0.682028\pi$
$283$	−1.45831e6	−1.08239	−0.541194	+	0.840898i	$0.682028\pi$
$284$	552960.	0.406816
$285$	0	0
$286$	−2.01024e6	−1.45322
$287$	−1.53406e6	−1.09935
$288$	82944.0	0.0589256
$289$	3.53522e6	2.48984
$290$	0	0
$291$	39762.0	0.0275255
$292$	−1.38013e6	−0.947245
$293$	988134.	0.672430	0.336215	−	0.941785i	$-0.390853\pi$
$293$	988134.	0.672430	0.336215	+	0.941785i	$0.390853\pi$
$294$	−363204.	−0.245066
$295$	0	0
$296$	723328.	0.479851
$297$	−524880.	−0.345278
$298$	−118104.	−0.0770414
$299$	−1.25640e6	−0.812737
$300$	0	0
$301$	−976784.	−0.621416
$302$	500672.	0.315890
$303$	926478.	0.579734
$304$	91136.0	0.0565596
$305$	0	0
$306$	721224.	0.440318
$307$	393820.	0.238480	0.119240	−	0.992865i	$-0.461954\pi$
$307$	393820.	0.238480	0.119240	+	0.992865i	$0.461954\pi$
$308$	−1.88928e6	−1.13480
$309$	−624924.	−0.372333
$310$	0	0
$311$	1.55448e6	0.911348	0.455674	−	0.890147i	$-0.349398\pi$
$311$	1.55448e6	0.911348	0.455674	+	0.890147i	$0.349398\pi$
$312$	402048.	0.233825
$313$	−1.76050e6	−1.01572	−0.507861	−	0.861439i	$-0.669564\pi$
$313$	−1.76050e6	−1.01572	−0.507861	+	0.861439i	$0.669564\pi$
$314$	172888.	0.0989557
$315$	0	0
$316$	−1.74131e6	−0.980977
$317$	−2.37112e6	−1.32527	−0.662637	−	0.748941i	$-0.730563\pi$
$317$	−2.37112e6	−1.32527	−0.662637	+	0.748941i	$0.730563\pi$
$318$	507816.	0.281604
$319$	514080.	0.282849
$320$	0	0
$321$	156708.	0.0848845
$322$	−1.18080e6	−0.634653
$323$	792456.	0.422638
$324$	104976.	0.0555556
$325$	0	0
$326$	1.17390e6	0.611771
$327$	1.83393e6	0.948448
$328$	598656.	0.307251
$329$	−1.83024e6	−0.932220
$330$	0	0
$331$	−980068.	−0.491684	−0.245842	−	0.969310i	$-0.579064\pi$
$331$	−980068.	−0.491684	−0.245842	+	0.969310i	$0.579064\pi$
$332$	−170688.	−0.0849880
$333$	915462.	0.452407
$334$	−1.28880e6	−0.632149
$335$	0	0
$336$	377856.	0.182590
$337$	−905834.	−0.434484	−0.217242	−	0.976118i	$-0.569706\pi$
$337$	−905834.	−0.434484	−0.217242	+	0.976118i	$0.569706\pi$
$338$	463644.	0.220746
$339$	−1.90982e6	−0.902595
$340$	0	0
$341$	610560.	0.284343
$342$	115344.	0.0533249
$343$	1.10175e6	0.505648
$344$	381184.	0.173675
$345$	0	0
$346$	1.04767e6	0.470473
$347$	2.95069e6	1.31553	0.657764	−	0.753224i	$-0.271502\pi$
$347$	2.95069e6	1.31553	0.657764	+	0.753224i	$0.271502\pi$
$348$	−102816.	−0.0455106
$349$	−2.15761e6	−0.948221	−0.474110	−	0.880465i	$-0.657230\pi$
$349$	−2.15761e6	−0.948221	−0.474110	+	0.880465i	$0.657230\pi$
$350$	0	0
$351$	508842.	0.220453
$352$	737280.	0.317158
$353$	−1.28873e6	−0.550461	−0.275230	−	0.961378i	$-0.588754\pi$
$353$	−1.28873e6	−0.550461	−0.275230	+	0.961378i	$0.588754\pi$
$354$	−285120.	−0.120926
$355$	0	0
$356$	173088.	0.0723839
$357$	3.28558e6	1.36440
$358$	2.49418e6	1.02854
$359$	−2.26946e6	−0.929367	−0.464683	−	0.885477i	$-0.653832\pi$
$359$	−2.26946e6	−0.929367	−0.464683	+	0.885477i	$0.653832\pi$
$360$	0	0
$361$	−2.34936e6	−0.948816
$362$	−244744.	−0.0981614
$363$	−3.21614e6	−1.28106
$364$	1.83155e6	0.724546
$365$	0	0
$366$	484200.	0.188939
$367$	−1.04659e6	−0.405612	−0.202806	−	0.979219i	$-0.565006\pi$
$367$	−1.04659e6	−0.405612	−0.202806	+	0.979219i	$0.565006\pi$
$368$	460800.	0.177375
$369$	757674.	0.289679
$370$	0	0
$371$	2.31338e6	0.872595
$372$	−122112.	−0.0457510
$373$	−1.79827e6	−0.669243	−0.334621	−	0.942353i	$-0.608608\pi$
$373$	−1.79827e6	−0.669243	−0.334621	+	0.942353i	$0.608608\pi$
$374$	6.41088e6	2.36995
$375$	0	0
$376$	714240.	0.260540
$377$	−498372.	−0.180593
$378$	478224.	0.172148
$379$	−2.18412e6	−0.781051	−0.390525	−	0.920592i	$-0.627707\pi$
$379$	−2.18412e6	−0.781051	−0.390525	+	0.920592i	$0.627707\pi$
$380$	0	0
$381$	55260.0	0.0195029
$382$	2.94902e6	1.03400
$383$	−1.78452e6	−0.621619	−0.310810	−	0.950472i	$-0.600600\pi$
$383$	−1.78452e6	−0.621619	−0.310810	+	0.950472i	$0.600600\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	−2.15665e6	−0.736734
$387$	482436.	0.163743
$388$	−70688.0	−0.0238378
$389$	−1.10953e6	−0.371761	−0.185880	−	0.982572i	$-0.559514\pi$
$389$	−1.10953e6	−0.371761	−0.185880	+	0.982572i	$0.559514\pi$
$390$	0	0
$391$	4.00680e6	1.32543
$392$	645696.	0.212233
$393$	1.85328e6	0.605285
$394$	2.60470e6	0.845311
$395$	0	0
$396$	933120.	0.299020
$397$	−3.89568e6	−1.24053	−0.620265	−	0.784392i	$-0.712975\pi$
$397$	−3.89568e6	−1.24053	−0.620265	+	0.784392i	$0.712975\pi$
$398$	629312.	0.199140
$399$	525456.	0.165236
$400$	0	0
$401$	−1.20673e6	−0.374755	−0.187378	−	0.982288i	$-0.559999\pi$
$401$	−1.20673e6	−0.374755	−0.187378	+	0.982288i	$0.559999\pi$
$402$	−2.35714e6	−0.727477
$403$	−591904.	−0.181547
$404$	−1.64707e6	−0.502064
$405$	0	0
$406$	−468384.	−0.141022
$407$	8.13744e6	2.43502
$408$	−1.28218e6	−0.381327
$409$	5.61363e6	1.65934	0.829670	−	0.558255i	$-0.188529\pi$
$409$	5.61363e6	1.65934	0.829670	+	0.558255i	$0.188529\pi$
$410$	0	0
$411$	2.07301e6	0.605335
$412$	1.11098e6	0.322449
$413$	−1.29888e6	−0.374709
$414$	583200.	0.167231
$415$	0	0
$416$	−714752.	−0.202499
$417$	−2.34680e6	−0.660901
$418$	1.02528e6	0.287013
$419$	1.15056e6	0.320165	0.160083	−	0.987104i	$-0.448824\pi$
$419$	1.15056e6	0.320165	0.160083	+	0.987104i	$0.448824\pi$
$420$	0	0
$421$	−3.83089e6	−1.05340	−0.526701	−	0.850050i	$-0.676571\pi$
$421$	−3.83089e6	−1.05340	−0.526701	+	0.850050i	$0.676571\pi$
$422$	2.82872e6	0.773230
$423$	903960.	0.245640
$424$	−902784.	−0.243876
$425$	0	0
$426$	−1.24416e6	−0.332164
$427$	2.20580e6	0.585459
$428$	−278592.	−0.0735122
$429$	4.52304e6	1.18655
$430$	0	0
$431$	155520.	0.0403267	0.0201634	−	0.999797i	$-0.493581\pi$
$431$	155520.	0.0403267	0.0201634	+	0.999797i	$0.493581\pi$
$432$	−186624.	−0.0481125
$433$	−4.14391e6	−1.06216	−0.531081	−	0.847321i	$-0.678214\pi$
$433$	−4.14391e6	−1.06216	−0.531081	+	0.847321i	$0.678214\pi$
$434$	−556288.	−0.141767
$435$	0	0
$436$	−3.26032e6	−0.821380
$437$	640800.	0.160516
$438$	3.10529e6	0.773422
$439$	6.23653e6	1.54448	0.772239	−	0.635332i	$-0.219137\pi$
$439$	6.23653e6	1.54448	0.772239	+	0.635332i	$0.219137\pi$
$440$	0	0
$441$	817209.	0.200095
$442$	−6.21499e6	−1.51316
$443$	−4.52507e6	−1.09551	−0.547754	−	0.836639i	$-0.684517\pi$
$443$	−4.52507e6	−1.09551	−0.547754	+	0.836639i	$0.684517\pi$
$444$	−1.62749e6	−0.391796
$445$	0	0
$446$	2.12296e6	0.505364
$447$	265734.	0.0629040
$448$	−671744.	−0.158128
$449$	2.56463e6	0.600357	0.300178	−	0.953883i	$-0.402954\pi$
$449$	2.56463e6	0.600357	0.300178	+	0.953883i	$0.402954\pi$
$450$	0	0
$451$	6.73488e6	1.55915
$452$	3.39523e6	0.781670
$453$	−1.12651e6	−0.257923
$454$	−481488.	−0.109634
$455$	0	0
$456$	−205056.	−0.0461807
$457$	5.53409e6	1.23953	0.619763	−	0.784789i	$-0.287229\pi$
$457$	5.53409e6	1.23953	0.619763	+	0.784789i	$0.287229\pi$
$458$	3.08924e6	0.688158
$459$	−1.62275e6	−0.359518
$460$	0	0
$461$	−7.19211e6	−1.57617	−0.788087	−	0.615564i	$-0.788928\pi$
$461$	−7.19211e6	−1.57617	−0.788087	+	0.615564i	$0.788928\pi$
$462$	4.25088e6	0.926561
$463$	1.13936e6	0.247006	0.123503	−	0.992344i	$-0.460587\pi$
$463$	1.13936e6	0.247006	0.123503	+	0.992344i	$0.460587\pi$
$464$	182784.	0.0394133
$465$	0	0
$466$	−35352.0	−0.00754135
$467$	−7.36168e6	−1.56201	−0.781006	−	0.624523i	$-0.785293\pi$
$467$	−7.36168e6	−1.56201	−0.781006	+	0.624523i	$0.785293\pi$
$468$	−904608.	−0.190918
$469$	−1.07381e7	−2.25421
$470$	0	0
$471$	−388998.	−0.0807970
$472$	506880.	0.104725
$473$	4.28832e6	0.881321
$474$	3.91795e6	0.800964
$475$	0	0
$476$	−5.84102e6	−1.18160
$477$	−1.14259e6	−0.229929
$478$	−3.10166e6	−0.620905
$479$	−1.36226e6	−0.271283	−0.135641	−	0.990758i	$-0.543310\pi$
$479$	−1.36226e6	−0.271283	−0.135641	+	0.990758i	$0.543310\pi$
$480$	0	0
$481$	−7.88880e6	−1.55471
$482$	−1.49375e6	−0.292861
$483$	2.65680e6	0.518192
$484$	5.71758e6	1.10943
$485$	0	0
$486$	−236196.	−0.0453609
$487$	−606428.	−0.115866	−0.0579331	−	0.998320i	$-0.518451\pi$
$487$	−606428.	−0.115866	−0.0579331	+	0.998320i	$0.518451\pi$
$488$	−860800.	−0.163626
$489$	−2.64128e6	−0.499509
$490$	0	0
$491$	−5.84278e6	−1.09374	−0.546872	−	0.837216i	$-0.684181\pi$
$491$	−5.84278e6	−1.09374	−0.546872	+	0.837216i	$0.684181\pi$
$492$	−1.34698e6	−0.250869
$493$	1.58936e6	0.294514
$494$	−993952.	−0.183252
$495$	0	0
$496$	217088.	0.0396216
$497$	−5.66784e6	−1.02926
$498$	384048.	0.0693924
$499$	−1.15044e6	−0.206830	−0.103415	−	0.994638i	$-0.532977\pi$
$499$	−1.15044e6	−0.206830	−0.103415	+	0.994638i	$0.532977\pi$
$500$	0	0
$501$	2.89980e6	0.516147
$502$	287904.	0.0509904
$503$	869664.	0.153261	0.0766305	−	0.997060i	$-0.475584\pi$
$503$	869664.	0.153261	0.0766305	+	0.997060i	$0.475584\pi$
$504$	−850176.	−0.149085
$505$	0	0
$506$	5.18400e6	0.900096
$507$	−1.04320e6	−0.180238
$508$	−98240.0	−0.0168900
$509$	1.43495e6	0.245495	0.122748	−	0.992438i	$-0.460829\pi$
$509$	1.43495e6	0.245495	0.122748	+	0.992438i	$0.460829\pi$
$510$	0	0
$511$	1.41463e7	2.39657
$512$	262144.	0.0441942
$513$	−259524.	−0.0435396
$514$	−6.37423e6	−1.06419
$515$	0	0
$516$	−857664.	−0.141805
$517$	8.03520e6	1.32212
$518$	−7.41411e6	−1.21404
$519$	−2.35726e6	−0.384140
$520$	0	0
$521$	1.04371e7	1.68456	0.842281	−	0.539038i	$-0.181212\pi$
$521$	1.04371e7	1.68456	0.842281	+	0.539038i	$0.181212\pi$
$522$	231336.	0.0371593
$523$	7.75942e6	1.24044	0.620219	−	0.784429i	$-0.287044\pi$
$523$	7.75942e6	1.24044	0.620219	+	0.784429i	$0.287044\pi$
$524$	−3.29472e6	−0.524192
$525$	0	0
$526$	8.21808e6	1.29511
$527$	1.88765e6	0.296070
$528$	−1.65888e6	−0.258958
$529$	−3.19634e6	−0.496609
$530$	0	0
$531$	641520.	0.0987356
$532$	−934144.	−0.143098
$533$	−6.52909e6	−0.995485
$534$	−389448.	−0.0591012
$535$	0	0
$536$	4.19046e6	0.630014
$537$	−5.61190e6	−0.839796
$538$	−1.03394e6	−0.154007
$539$	7.26408e6	1.07698
$540$	0	0
$541$	−1.10233e6	−0.161927	−0.0809633	−	0.996717i	$-0.525800\pi$
$541$	−1.10233e6	−0.161927	−0.0809633	+	0.996717i	$0.525800\pi$
$542$	−7.93590e6	−1.16037
$543$	550674.	0.0801484
$544$	2.27942e6	0.330239
$545$	0	0
$546$	−4.12099e6	−0.591589
$547$	−2.48263e6	−0.354767	−0.177384	−	0.984142i	$-0.556763\pi$
$547$	−2.48263e6	−0.354767	−0.177384	+	0.984142i	$0.556763\pi$
$548$	−3.68534e6	−0.524236
$549$	−1.08945e6	−0.154268
$550$	0	0
$551$	254184.	0.0356672
$552$	−1.03680e6	−0.144826
$553$	1.78484e7	2.48192
$554$	−6.45303e6	−0.893284
$555$	0	0
$556$	4.17210e6	0.572357
$557$	−5.73568e6	−0.783334	−0.391667	−	0.920107i	$-0.628102\pi$
$557$	−5.73568e6	−0.783334	−0.391667	+	0.920107i	$0.628102\pi$
$558$	274752.	0.0373556
$559$	−4.15729e6	−0.562705
$560$	0	0
$561$	−1.44245e7	−1.93505
$562$	5.51527e6	0.736591
$563$	−517092.	−0.0687538	−0.0343769	−	0.999409i	$-0.510945\pi$
$563$	−517092.	−0.0687538	−0.0343769	+	0.999409i	$0.510945\pi$
$564$	−1.60704e6	−0.212730
$565$	0	0
$566$	−5.83323e6	−0.765364
$567$	−1.07600e6	−0.140558
$568$	2.21184e6	0.287662
$569$	−6.72766e6	−0.871131	−0.435566	−	0.900157i	$-0.643452\pi$
$569$	−6.72766e6	−0.871131	−0.435566	+	0.900157i	$0.643452\pi$
$570$	0	0
$571$	−1.03290e7	−1.32577	−0.662883	−	0.748723i	$-0.730668\pi$
$571$	−1.03290e7	−1.32577	−0.662883	+	0.748723i	$0.730668\pi$
$572$	−8.04096e6	−1.02759
$573$	−6.63530e6	−0.844256
$574$	−6.13622e6	−0.777359
$575$	0	0
$576$	331776.	0.0416667
$577$	−9.25834e6	−1.15769	−0.578847	−	0.815436i	$-0.696497\pi$
$577$	−9.25834e6	−1.15769	−0.578847	+	0.815436i	$0.696497\pi$
$578$	1.41409e7	1.76058
$579$	4.85246e6	0.601541
$580$	0	0
$581$	1.74955e6	0.215024
$582$	159048.	0.0194635
$583$	−1.01563e7	−1.23756
$584$	−5.52051e6	−0.669803
$585$	0	0
$586$	3.95254e6	0.475479
$587$	9.57155e6	1.14653	0.573267	−	0.819369i	$-0.305676\pi$
$587$	9.57155e6	1.14653	0.573267	+	0.819369i	$0.305676\pi$
$588$	−1.45282e6	−0.173288
$589$	301888.	0.0358557
$590$	0	0
$591$	−5.86057e6	−0.690193
$592$	2.89331e6	0.339306
$593$	1.12388e7	1.31245	0.656226	−	0.754564i	$-0.272152\pi$
$593$	1.12388e7	1.31245	0.656226	+	0.754564i	$0.272152\pi$
$594$	−2.09952e6	−0.244148
$595$	0	0
$596$	−472416.	−0.0544765
$597$	−1.41595e6	−0.162597
$598$	−5.02560e6	−0.574692
$599$	3.72670e6	0.424382	0.212191	−	0.977228i	$-0.431940\pi$
$599$	3.72670e6	0.424382	0.212191	+	0.977228i	$0.431940\pi$
$600$	0	0
$601$	6.74734e6	0.761985	0.380992	−	0.924578i	$-0.375582\pi$
$601$	6.74734e6	0.761985	0.380992	+	0.924578i	$0.375582\pi$
$602$	−3.90714e6	−0.439407
$603$	5.30356e6	0.593983
$604$	2.00269e6	0.223368
$605$	0	0
$606$	3.70591e6	0.409934
$607$	6.83384e6	0.752823	0.376411	−	0.926453i	$-0.377158\pi$
$607$	6.83384e6	0.752823	0.376411	+	0.926453i	$0.377158\pi$
$608$	364544.	0.0399936
$609$	1.05386e6	0.115144
$610$	0	0
$611$	−7.78968e6	−0.844144
$612$	2.88490e6	0.311352
$613$	433222.	0.0465650	0.0232825	−	0.999729i	$-0.492588\pi$
$613$	433222.	0.0465650	0.0232825	+	0.999729i	$0.492588\pi$
$614$	1.57528e6	0.168631
$615$	0	0
$616$	−7.55712e6	−0.802425
$617$	5.17569e6	0.547338	0.273669	−	0.961824i	$-0.411763\pi$
$617$	5.17569e6	0.547338	0.273669	+	0.961824i	$0.411763\pi$
$618$	−2.49970e6	−0.263279
$619$	−151996.	−0.0159443	−0.00797215	−	0.999968i	$-0.502538\pi$
$619$	−151996.	−0.0159443	−0.00797215	+	0.999968i	$0.502538\pi$
$620$	0	0
$621$	−1.31220e6	−0.136544
$622$	6.21792e6	0.644420
$623$	−1.77415e6	−0.183135
$624$	1.60819e6	0.165339
$625$	0	0
$626$	−7.04199e6	−0.718224
$627$	−2.30688e6	−0.234345
$628$	691552.	0.0699722
$629$	2.51583e7	2.53544
$630$	0	0
$631$	1.05635e7	1.05617	0.528086	−	0.849191i	$-0.322910\pi$
$631$	1.05635e7	1.05617	0.528086	+	0.849191i	$0.322910\pi$
$632$	−6.96525e6	−0.693656
$633$	−6.36462e6	−0.631340
$634$	−9.48449e6	−0.937110
$635$	0	0
$636$	2.03126e6	0.199124
$637$	−7.04212e6	−0.687630
$638$	2.05632e6	0.200004
$639$	2.79936e6	0.271211
$640$	0	0
$641$	−5.53755e6	−0.532320	−0.266160	−	0.963929i	$-0.585755\pi$
$641$	−5.53755e6	−0.532320	−0.266160	+	0.963929i	$0.585755\pi$
$642$	626832.	0.0600224
$643$	−8.89132e6	−0.848084	−0.424042	−	0.905642i	$-0.639389\pi$
$643$	−8.89132e6	−0.848084	−0.424042	+	0.905642i	$0.639389\pi$
$644$	−4.72320e6	−0.448768
$645$	0	0
$646$	3.16982e6	0.298850
$647$	−2.29474e6	−0.215512	−0.107756	−	0.994177i	$-0.534367\pi$
$647$	−2.29474e6	−0.215512	−0.107756	+	0.994177i	$0.534367\pi$
$648$	419904.	0.0392837
$649$	5.70240e6	0.531430
$650$	0	0
$651$	1.25165e6	0.115752
$652$	4.69562e6	0.432587
$653$	1.36338e7	1.25122	0.625608	−	0.780137i	$-0.284851\pi$
$653$	1.36338e7	1.25122	0.625608	+	0.780137i	$0.284851\pi$
$654$	7.33572e6	0.670654
$655$	0	0
$656$	2.39462e6	0.217259
$657$	−6.98690e6	−0.631497
$658$	−7.32096e6	−0.659179
$659$	−1.31234e7	−1.17715	−0.588576	−	0.808442i	$-0.700311\pi$
$659$	−1.31234e7	−1.17715	−0.588576	+	0.808442i	$0.700311\pi$
$660$	0	0
$661$	1.78522e7	1.58923	0.794616	−	0.607112i	$-0.207672\pi$
$661$	1.78522e7	1.58923	0.794616	+	0.607112i	$0.207672\pi$
$662$	−3.92027e6	−0.347673
$663$	1.39837e7	1.23549
$664$	−682752.	−0.0600956
$665$	0	0
$666$	3.66185e6	0.319900
$667$	1.28520e6	0.111855
$668$	−5.15520e6	−0.446997
$669$	−4.77666e6	−0.412628
$670$	0	0
$671$	−9.68400e6	−0.830326
$672$	1.51142e6	0.129111
$673$	−1.32471e7	−1.12741	−0.563707	−	0.825975i	$-0.690625\pi$
$673$	−1.32471e7	−1.12741	−0.563707	+	0.825975i	$0.690625\pi$
$674$	−3.62334e6	−0.307227
$675$	0	0
$676$	1.85458e6	0.156091
$677$	−1.04491e7	−0.876205	−0.438103	−	0.898925i	$-0.644349\pi$
$677$	−1.04491e7	−0.876205	−0.438103	+	0.898925i	$0.644349\pi$
$678$	−7.63927e6	−0.638231
$679$	724552.	0.0603108
$680$	0	0
$681$	1.08335e6	0.0895159
$682$	2.44224e6	0.201061
$683$	613308.	0.0503068	0.0251534	−	0.999684i	$-0.491993\pi$
$683$	613308.	0.0503068	0.0251534	+	0.999684i	$0.491993\pi$
$684$	461376.	0.0377064
$685$	0	0
$686$	4.40701e6	0.357547
$687$	−6.95079e6	−0.561878
$688$	1.52474e6	0.122807
$689$	9.84599e6	0.790153
$690$	0	0
$691$	−2.13992e7	−1.70491	−0.852457	−	0.522798i	$-0.824888\pi$
$691$	−2.13992e7	−1.70491	−0.852457	+	0.522798i	$0.824888\pi$
$692$	4.19069e6	0.332675
$693$	−9.56448e6	−0.756534
$694$	1.18028e7	0.930219
$695$	0	0
$696$	−411264.	−0.0321809
$697$	2.08220e7	1.62346
$698$	−8.63044e6	−0.670493
$699$	79542.0	0.00615749
$700$	0	0
$701$	1.09778e7	0.843765	0.421883	−	0.906650i	$-0.361369\pi$
$701$	1.09778e7	0.843765	0.421883	+	0.906650i	$0.361369\pi$
$702$	2.03537e6	0.155884
$703$	4.02351e6	0.307056
$704$	2.94912e6	0.224265
$705$	0	0
$706$	−5.15494e6	−0.389235
$707$	1.68825e7	1.27025
$708$	−1.14048e6	−0.0855076
$709$	1.69732e6	0.126808	0.0634041	−	0.997988i	$-0.479804\pi$
$709$	1.69732e6	0.126808	0.0634041	+	0.997988i	$0.479804\pi$
$710$	0	0
$711$	−8.81539e6	−0.653985
$712$	692352.	0.0511831
$713$	1.52640e6	0.112446
$714$	1.31423e7	0.964775
$715$	0	0
$716$	9.97670e6	0.727285
$717$	6.97874e6	0.506967
$718$	−9.07786e6	−0.657162
$719$	3.71304e6	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$719$	3.71304e6	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$720$	0	0
$721$	−1.13875e7	−0.815813
$722$	−9.39745e6	−0.670914
$723$	3.36094e6	0.239120
$724$	−978976.	−0.0694106
$725$	0	0
$726$	−1.28646e7	−0.905844
$727$	−1.38067e6	−0.0968843	−0.0484421	−	0.998826i	$-0.515426\pi$
$727$	−1.38067e6	−0.0968843	−0.0484421	+	0.998826i	$0.515426\pi$
$728$	7.32621e6	0.512331
$729$	531441.	0.0370370
$730$	0	0
$731$	1.32581e7	0.917670
$732$	1.93680e6	0.133600
$733$	−1.38156e7	−0.949751	−0.474876	−	0.880053i	$-0.657507\pi$
$733$	−1.38156e7	−0.949751	−0.474876	+	0.880053i	$0.657507\pi$
$734$	−4.18635e6	−0.286811
$735$	0	0
$736$	1.84320e6	0.125423
$737$	4.71427e7	3.19702
$738$	3.03070e6	0.204834
$739$	4.59463e6	0.309485	0.154742	−	0.987955i	$-0.450545\pi$
$739$	4.59463e6	0.309485	0.154742	+	0.987955i	$0.450545\pi$
$740$	0	0
$741$	2.23639e6	0.149624
$742$	9.25354e6	0.617018
$743$	−8.51174e6	−0.565648	−0.282824	−	0.959172i	$-0.591271\pi$
$743$	−8.51174e6	−0.565648	−0.282824	+	0.959172i	$0.591271\pi$
$744$	−488448.	−0.0323509
$745$	0	0
$746$	−7.19310e6	−0.473226
$747$	−864108.	−0.0566587
$748$	2.56435e7	1.67581
$749$	2.85557e6	0.185989
$750$	0	0
$751$	1.71224e7	1.10781	0.553904	−	0.832580i	$-0.313137\pi$
$751$	1.71224e7	1.10781	0.553904	+	0.832580i	$0.313137\pi$
$752$	2.85696e6	0.184230
$753$	−647784.	−0.0416335
$754$	−1.99349e6	−0.127698
$755$	0	0
$756$	1.91290e6	0.121727
$757$	1.22018e6	0.0773900	0.0386950	−	0.999251i	$-0.487680\pi$
$757$	1.22018e6	0.0773900	0.0386950	+	0.999251i	$0.487680\pi$
$758$	−8.73650e6	−0.552286
$759$	−1.16640e7	−0.734925
$760$	0	0
$761$	1.20327e7	0.753182	0.376591	−	0.926380i	$-0.377096\pi$
$761$	1.20327e7	0.753182	0.376591	+	0.926380i	$0.377096\pi$
$762$	221040.	0.0137906
$763$	3.34183e7	2.07813
$764$	1.17961e7	0.731147
$765$	0	0
$766$	−7.13808e6	−0.439551
$767$	−5.52816e6	−0.339307
$768$	−589824.	−0.0360844
$769$	−1.88952e7	−1.15222	−0.576110	−	0.817372i	$-0.695430\pi$
$769$	−1.88952e7	−1.15222	−0.576110	+	0.817372i	$0.695430\pi$
$770$	0	0
$771$	1.43420e7	0.868909
$772$	−8.62659e6	−0.520950
$773$	−1.72115e7	−1.03602	−0.518012	−	0.855373i	$-0.673328\pi$
$773$	−1.72115e7	−1.03602	−0.518012	+	0.855373i	$0.673328\pi$
$774$	1.92974e6	0.115784
$775$	0	0
$776$	−282752.	−0.0168559
$777$	1.66818e7	0.991263
$778$	−4.43810e6	−0.262875
$779$	3.33002e6	0.196609
$780$	0	0
$781$	2.48832e7	1.45975
$782$	1.60272e7	0.937218
$783$	−520506.	−0.0303404
$784$	2.58278e6	0.150071
$785$	0	0
$786$	7.41312e6	0.428001
$787$	−1.32970e7	−0.765274	−0.382637	−	0.923899i	$-0.624984\pi$
$787$	−1.32970e7	−0.765274	−0.382637	+	0.923899i	$0.624984\pi$
$788$	1.04188e7	0.597725
$789$	−1.84907e7	−1.05745
$790$	0	0
$791$	−3.48011e7	−1.97766
$792$	3.73248e6	0.211439
$793$	9.38810e6	0.530145
$794$	−1.55827e7	−0.877187
$795$	0	0
$796$	2.51725e6	0.140813
$797$	−2.15632e7	−1.20245	−0.601227	−	0.799078i	$-0.705321\pi$
$797$	−2.15632e7	−1.20245	−0.601227	+	0.799078i	$0.705321\pi$
$798$	2.10182e6	0.116839
$799$	2.48422e7	1.37665
$800$	0	0
$801$	876258.	0.0482559
$802$	−4.82690e6	−0.264992
$803$	−6.21058e7	−3.39894
$804$	−9.42854e6	−0.514404
$805$	0	0
$806$	−2.36762e6	−0.128373
$807$	2.32637e6	0.125746
$808$	−6.58829e6	−0.355013
$809$	2.65355e7	1.42547	0.712733	−	0.701436i	$-0.247457\pi$
$809$	2.65355e7	1.42547	0.712733	+	0.701436i	$0.247457\pi$
$810$	0	0
$811$	−1.40015e7	−0.747518	−0.373759	−	0.927526i	$-0.621931\pi$
$811$	−1.40015e7	−0.747518	−0.373759	+	0.927526i	$0.621931\pi$
$812$	−1.87354e6	−0.0997176
$813$	1.78558e7	0.947442
$814$	3.25498e7	1.72182
$815$	0	0
$816$	−5.12870e6	−0.269639
$817$	2.12034e6	0.111135
$818$	2.24545e7	1.17333
$819$	9.27223e6	0.483030
$820$	0	0
$821$	1.32286e7	0.684944	0.342472	−	0.939528i	$-0.388736\pi$
$821$	1.32286e7	0.684944	0.342472	+	0.939528i	$0.388736\pi$
$822$	8.29202e6	0.428037
$823$	7.25818e6	0.373532	0.186766	−	0.982404i	$-0.440199\pi$
$823$	7.25818e6	0.373532	0.186766	+	0.982404i	$0.440199\pi$
$824$	4.44390e6	0.228006
$825$	0	0
$826$	−5.19552e6	−0.264959
$827$	−1.84527e7	−0.938204	−0.469102	−	0.883144i	$-0.655422\pi$
$827$	−1.84527e7	−0.938204	−0.469102	+	0.883144i	$0.655422\pi$
$828$	2.33280e6	0.118250
$829$	−2.43640e7	−1.23130	−0.615649	−	0.788021i	$-0.711106\pi$
$829$	−2.43640e7	−1.23130	−0.615649	+	0.788021i	$0.711106\pi$
$830$	0	0
$831$	1.45193e7	0.729363
$832$	−2.85901e6	−0.143188
$833$	2.24581e7	1.12140
$834$	−9.38722e6	−0.467328
$835$	0	0
$836$	4.10112e6	0.202949
$837$	−618192.	−0.0305007
$838$	4.60224e6	0.226391
$839$	−1.55793e7	−0.764089	−0.382045	−	0.924144i	$-0.624780\pi$
$839$	−1.55793e7	−0.764089	−0.382045	+	0.924144i	$0.624780\pi$
$840$	0	0
$841$	−2.00014e7	−0.975145
$842$	−1.53236e7	−0.744868
$843$	−1.24094e7	−0.601424
$844$	1.13149e7	0.546756
$845$	0	0
$846$	3.61584e6	0.173693
$847$	−5.86052e7	−2.80691
$848$	−3.61114e6	−0.172446
$849$	1.31248e7	0.624917
$850$	0	0
$851$	2.03436e7	0.962950
$852$	−4.97664e6	−0.234875
$853$	−3.08062e7	−1.44966	−0.724829	−	0.688929i	$-0.758081\pi$
$853$	−3.08062e7	−1.44966	−0.724829	+	0.688929i	$0.758081\pi$
$854$	8.82320e6	0.413982
$855$	0	0
$856$	−1.11437e6	−0.0519810
$857$	2.02084e6	0.0939897	0.0469949	−	0.998895i	$-0.485036\pi$
$857$	2.02084e6	0.0939897	0.0469949	+	0.998895i	$0.485036\pi$
$858$	1.80922e7	0.839020
$859$	−2.24790e7	−1.03943	−0.519714	−	0.854340i	$-0.673961\pi$
$859$	−2.24790e7	−1.03943	−0.519714	+	0.854340i	$0.673961\pi$
$860$	0	0
$861$	1.38065e7	0.634711
$862$	622080.	0.0285153
$863$	9.20942e6	0.420926	0.210463	−	0.977602i	$-0.432503\pi$
$863$	9.20942e6	0.420926	0.210463	+	0.977602i	$0.432503\pi$
$864$	−746496.	−0.0340207
$865$	0	0
$866$	−1.65757e7	−0.751062
$867$	−3.18170e7	−1.43751
$868$	−2.22515e6	−0.100244
$869$	−7.83590e7	−3.51998
$870$	0	0
$871$	−4.57022e7	−2.04123
$872$	−1.30413e7	−0.580803
$873$	−357858.	−0.0158919
$874$	2.56320e6	0.113502
$875$	0	0
$876$	1.24212e7	0.546892
$877$	5.36258e6	0.235437	0.117719	−	0.993047i	$-0.462442\pi$
$877$	5.36258e6	0.235437	0.117719	+	0.993047i	$0.462442\pi$
$878$	2.49461e7	1.09211
$879$	−8.89321e6	−0.388227
$880$	0	0
$881$	1.38347e7	0.600525	0.300263	−	0.953857i	$-0.402926\pi$
$881$	1.38347e7	0.600525	0.300263	+	0.953857i	$0.402926\pi$
$882$	3.26884e6	0.141489
$883$	1.66004e6	0.0716499	0.0358250	−	0.999358i	$-0.488594\pi$
$883$	1.66004e6	0.0716499	0.0358250	+	0.999358i	$0.488594\pi$
$884$	−2.48600e7	−1.06997
$885$	0	0
$886$	−1.81003e7	−0.774642
$887$	8.10612e6	0.345943	0.172971	−	0.984927i	$-0.444663\pi$
$887$	8.10612e6	0.345943	0.172971	+	0.984927i	$0.444663\pi$
$888$	−6.50995e6	−0.277042
$889$	1.00696e6	0.0427325
$890$	0	0
$891$	4.72392e6	0.199346
$892$	8.49184e6	0.357347
$893$	3.97296e6	0.166719
$894$	1.06294e6	0.0444799
$895$	0	0
$896$	−2.68698e6	−0.111813
$897$	1.13076e7	0.469234
$898$	1.02585e7	0.424516
$899$	605472.	0.0249859
$900$	0	0
$901$	−3.14000e7	−1.28860
$902$	2.69395e7	1.10249
$903$	8.79106e6	0.358775
$904$	1.35809e7	0.552724
$905$	0	0
$906$	−4.50605e6	−0.182379
$907$	−4.05360e6	−0.163615	−0.0818073	−	0.996648i	$-0.526069\pi$
$907$	−4.05360e6	−0.163615	−0.0818073	+	0.996648i	$0.526069\pi$
$908$	−1.92595e6	−0.0775230
$909$	−8.33830e6	−0.334709
$910$	0	0
$911$	−1.38233e7	−0.551844	−0.275922	−	0.961180i	$-0.588983\pi$
$911$	−1.38233e7	−0.551844	−0.275922	+	0.961180i	$0.588983\pi$
$912$	−820224.	−0.0326547
$913$	−7.68096e6	−0.304957
$914$	2.21363e7	0.876477
$915$	0	0
$916$	1.23570e7	0.486601
$917$	3.37709e7	1.32623
$918$	−6.49102e6	−0.254218
$919$	−3.78443e7	−1.47813	−0.739063	−	0.673636i	$-0.764732\pi$
$919$	−3.78443e7	−1.47813	−0.739063	+	0.673636i	$0.764732\pi$
$920$	0	0
$921$	−3.54438e6	−0.137686
$922$	−2.87684e7	−1.11452
$923$	−2.41229e7	−0.932019
$924$	1.70035e7	0.655177
$925$	0	0
$926$	4.55742e6	0.174659
$927$	5.62432e6	0.214966
$928$	731136.	0.0278694
$929$	−2.72822e7	−1.03715	−0.518574	−	0.855033i	$-0.673537\pi$
$929$	−2.72822e7	−1.03715	−0.518574	+	0.855033i	$0.673537\pi$
$930$	0	0
$931$	3.59168e6	0.135808
$932$	−141408.	−0.00533254
$933$	−1.39903e7	−0.526167
$934$	−2.94467e7	−1.10451
$935$	0	0
$936$	−3.61843e6	−0.134999
$937$	−4.32666e7	−1.60992	−0.804958	−	0.593332i	$-0.797812\pi$
$937$	−4.32666e7	−1.60992	−0.804958	+	0.593332i	$0.797812\pi$
$938$	−4.29523e7	−1.59397
$939$	1.58445e7	0.586427
$940$	0	0
$941$	8.50106e6	0.312967	0.156484	−	0.987681i	$-0.449984\pi$
$941$	8.50106e6	0.312967	0.156484	+	0.987681i	$0.449984\pi$
$942$	−1.55599e6	−0.0571321
$943$	1.68372e7	0.616582
$944$	2.02752e6	0.0740517
$945$	0	0
$946$	1.71533e7	0.623188
$947$	−7.10456e6	−0.257432	−0.128716	−	0.991681i	$-0.541086\pi$
$947$	−7.10456e6	−0.257432	−0.128716	+	0.991681i	$0.541086\pi$
$948$	1.56718e7	0.566367
$949$	6.02081e7	2.17015
$950$	0	0
$951$	2.13401e7	0.765147
$952$	−2.33641e7	−0.835520
$953$	5.39741e7	1.92510	0.962551	−	0.271102i	$-0.0873882\pi$
$953$	5.39741e7	1.92510	0.962551	+	0.271102i	$0.0873882\pi$
$954$	−4.57034e6	−0.162584
$955$	0	0
$956$	−1.24067e7	−0.439046
$957$	−4.62672e6	−0.163303
$958$	−5.44906e6	−0.191826
$959$	3.77748e7	1.32634
$960$	0	0
$961$	−2.79100e7	−0.974882
$962$	−3.15552e7	−1.09934
$963$	−1.41037e6	−0.0490081
$964$	−5.97501e6	−0.207084
$965$	0	0
$966$	1.06272e7	0.366417
$967$	−3.64583e7	−1.25381	−0.626903	−	0.779097i	$-0.715678\pi$
$967$	−3.64583e7	−1.25381	−0.626903	+	0.779097i	$0.715678\pi$
$968$	2.28703e7	0.784484
$969$	−7.13210e6	−0.244010
$970$	0	0
$971$	−5.20286e7	−1.77090	−0.885450	−	0.464734i	$-0.846150\pi$
$971$	−5.20286e7	−1.77090	−0.885450	+	0.464734i	$0.846150\pi$
$972$	−944784.	−0.0320750
$973$	−4.27640e7	−1.44809
$974$	−2.42571e6	−0.0819298
$975$	0	0
$976$	−3.44320e6	−0.115701
$977$	−127902.	−0.00428688	−0.00214344	−	0.999998i	$-0.500682\pi$
$977$	−127902.	−0.00428688	−0.00214344	+	0.999998i	$0.500682\pi$
$978$	−1.05651e7	−0.353206
$979$	7.78896e6	0.259730
$980$	0	0
$981$	−1.65054e7	−0.547587
$982$	−2.33711e7	−0.773393
$983$	1.57667e7	0.520422	0.260211	−	0.965552i	$-0.416208\pi$
$983$	1.57667e7	0.520422	0.260211	+	0.965552i	$0.416208\pi$
$984$	−5.38790e6	−0.177391
$985$	0	0
$986$	6.35746e6	0.208253
$987$	1.64722e7	0.538217
$988$	−3.97581e6	−0.129579
$989$	1.07208e7	0.348527
$990$	0	0
$991$	2.99415e7	0.968479	0.484239	−	0.874936i	$-0.339096\pi$
$991$	2.99415e7	0.968479	0.484239	+	0.874936i	$0.339096\pi$
$992$	868352.	0.0280167
$993$	8.82061e6	0.283874
$994$	−2.26714e7	−0.727799
$995$	0	0
$996$	1.53619e6	0.0490679
$997$	5.07440e7	1.61676	0.808382	−	0.588659i	$-0.200344\pi$
$997$	5.07440e7	1.61676	0.808382	+	0.588659i	$0.200344\pi$
$998$	−4.60178e6	−0.146251
$999$	−8.23916e6	−0.261198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.6.a.h.1.1		1
3.2	odd	2		450.6.a.b.1.1		1
5.2	odd	4		150.6.c.d.49.2		2
5.3	odd	4		150.6.c.d.49.1		2
5.4	even	2		30.6.a.a.1.1	✓	1
15.2	even	4		450.6.c.b.199.1		2
15.8	even	4		450.6.c.b.199.2		2
15.14	odd	2		90.6.a.g.1.1		1
20.19	odd	2		240.6.a.a.1.1		1
40.19	odd	2		960.6.a.u.1.1		1
40.29	even	2		960.6.a.n.1.1		1
60.59	even	2		720.6.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.6.a.a.1.1	✓	1	5.4	even	2
90.6.a.g.1.1		1	15.14	odd	2
150.6.a.h.1.1		1	1.1	even	1	trivial
150.6.c.d.49.1		2	5.3	odd	4
150.6.c.d.49.2		2	5.2	odd	4
240.6.a.a.1.1		1	20.19	odd	2
450.6.a.b.1.1		1	3.2	odd	2
450.6.c.b.199.1		2	15.2	even	4
450.6.c.b.199.2		2	15.8	even	4
720.6.a.m.1.1		1	60.59	even	2
960.6.a.n.1.1		1	40.29	even	2
960.6.a.u.1.1		1	40.19	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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