LMFDB - Embedded newform 1050.6.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,6,Mod(1,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1050.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1050.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$168.403010804$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -36.0000 q^{6} +49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -36.0000 q^{6} +49.0000 q^{7} +64.0000 q^{8} +81.0000 q^{9} +664.000 q^{11} -144.000 q^{12} -318.000 q^{13} +196.000 q^{14} +256.000 q^{16} -1582.00 q^{17} +324.000 q^{18} +236.000 q^{19} -441.000 q^{21} +2656.00 q^{22} -2212.00 q^{23} -576.000 q^{24} -1272.00 q^{26} -729.000 q^{27} +784.000 q^{28} -4954.00 q^{29} -7128.00 q^{31} +1024.00 q^{32} -5976.00 q^{33} -6328.00 q^{34} +1296.00 q^{36} -4358.00 q^{37} +944.000 q^{38} +2862.00 q^{39} +10542.0 q^{41} -1764.00 q^{42} +8452.00 q^{43} +10624.0 q^{44} -8848.00 q^{46} -5352.00 q^{47} -2304.00 q^{48} +2401.00 q^{49} +14238.0 q^{51} -5088.00 q^{52} +33354.0 q^{53} -2916.00 q^{54} +3136.00 q^{56} -2124.00 q^{57} -19816.0 q^{58} -15436.0 q^{59} -36762.0 q^{61} -28512.0 q^{62} +3969.00 q^{63} +4096.00 q^{64} -23904.0 q^{66} -40972.0 q^{67} -25312.0 q^{68} +19908.0 q^{69} -9092.00 q^{71} +5184.00 q^{72} +73454.0 q^{73} -17432.0 q^{74} +3776.00 q^{76} +32536.0 q^{77} +11448.0 q^{78} +89400.0 q^{79} +6561.00 q^{81} +42168.0 q^{82} +6428.00 q^{83} -7056.00 q^{84} +33808.0 q^{86} +44586.0 q^{87} +42496.0 q^{88} -122658. q^{89} -15582.0 q^{91} -35392.0 q^{92} +64152.0 q^{93} -21408.0 q^{94} -9216.00 q^{96} -21370.0 q^{97} +9604.00 q^{98} +53784.0 q^{99} +O(q^{100})\)

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
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	0	0
$11$	664.000	1.65457	0.827287	−	0.561779i	$-0.189883\pi$
$11$	664.000	1.65457	0.827287	+	0.561779i	$0.189883\pi$
$12$	−144.000	−0.288675
$13$	−318.000	−0.521878	−0.260939	−	0.965355i	$-0.584032\pi$
$13$	−318.000	−0.521878	−0.260939	+	0.965355i	$0.584032\pi$
$14$	196.000	0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	−1582.00	−1.32765	−0.663826	−	0.747887i	$-0.731068\pi$
$17$	−1582.00	−1.32765	−0.663826	+	0.747887i	$0.731068\pi$
$18$	324.000	0.235702
$19$	236.000	0.149978	0.0749891	−	0.997184i	$-0.476108\pi$
$19$	236.000	0.149978	0.0749891	+	0.997184i	$0.476108\pi$
$20$	0	0
$21$	−441.000	−0.218218
$22$	2656.00	1.16996
$23$	−2212.00	−0.871898	−0.435949	−	0.899971i	$-0.643587\pi$
$23$	−2212.00	−0.871898	−0.435949	+	0.899971i	$0.643587\pi$
$24$	−576.000	−0.204124
$25$	0	0
$26$	−1272.00	−0.369023
$27$	−729.000	−0.192450
$28$	784.000	0.188982
$29$	−4954.00	−1.09386	−0.546929	−	0.837179i	$-0.684203\pi$
$29$	−4954.00	−1.09386	−0.546929	+	0.837179i	$0.684203\pi$
$30$	0	0
$31$	−7128.00	−1.33218	−0.666091	−	0.745871i	$-0.732034\pi$
$31$	−7128.00	−1.33218	−0.666091	+	0.745871i	$0.732034\pi$
$32$	1024.00	0.176777
$33$	−5976.00	−0.955269
$34$	−6328.00	−0.938792
$35$	0	0
$36$	1296.00	0.166667
$37$	−4358.00	−0.523339	−0.261669	−	0.965158i	$-0.584273\pi$
$37$	−4358.00	−0.523339	−0.261669	+	0.965158i	$0.584273\pi$
$38$	944.000	0.106051
$39$	2862.00	0.301306
$40$	0	0
$41$	10542.0	0.979407	0.489704	−	0.871889i	$-0.337105\pi$
$41$	10542.0	0.979407	0.489704	+	0.871889i	$0.337105\pi$
$42$	−1764.00	−0.154303
$43$	8452.00	0.697089	0.348545	−	0.937292i	$-0.386676\pi$
$43$	8452.00	0.697089	0.348545	+	0.937292i	$0.386676\pi$
$44$	10624.0	0.827287
$45$	0	0
$46$	−8848.00	−0.616525
$47$	−5352.00	−0.353404	−0.176702	−	0.984264i	$-0.556543\pi$
$47$	−5352.00	−0.353404	−0.176702	+	0.984264i	$0.556543\pi$
$48$	−2304.00	−0.144338
$49$	2401.00	0.142857
$50$	0	0
$51$	14238.0	0.766520
$52$	−5088.00	−0.260939
$53$	33354.0	1.63102	0.815508	−	0.578746i	$-0.196458\pi$
$53$	33354.0	1.63102	0.815508	+	0.578746i	$0.196458\pi$
$54$	−2916.00	−0.136083
$55$	0	0
$56$	3136.00	0.133631
$57$	−2124.00	−0.0865899
$58$	−19816.0	−0.773475
$59$	−15436.0	−0.577304	−0.288652	−	0.957434i	$-0.593207\pi$
$59$	−15436.0	−0.577304	−0.288652	+	0.957434i	$0.593207\pi$
$60$	0	0
$61$	−36762.0	−1.26495	−0.632477	−	0.774579i	$-0.717962\pi$
$61$	−36762.0	−1.26495	−0.632477	+	0.774579i	$0.717962\pi$
$62$	−28512.0	−0.941995
$63$	3969.00	0.125988
$64$	4096.00	0.125000
$65$	0	0
$66$	−23904.0	−0.675477
$67$	−40972.0	−1.11506	−0.557532	−	0.830155i	$-0.688252\pi$
$67$	−40972.0	−1.11506	−0.557532	+	0.830155i	$0.688252\pi$
$68$	−25312.0	−0.663826
$69$	19908.0	0.503390
$70$	0	0
$71$	−9092.00	−0.214049	−0.107025	−	0.994256i	$-0.534132\pi$
$71$	−9092.00	−0.214049	−0.107025	+	0.994256i	$0.534132\pi$
$72$	5184.00	0.117851
$73$	73454.0	1.61327	0.806637	−	0.591047i	$-0.201285\pi$
$73$	73454.0	1.61327	0.806637	+	0.591047i	$0.201285\pi$
$74$	−17432.0	−0.370056
$75$	0	0
$76$	3776.00	0.0749891
$77$	32536.0	0.625370
$78$	11448.0	0.213056
$79$	89400.0	1.61165	0.805823	−	0.592156i	$-0.201723\pi$
$79$	89400.0	1.61165	0.805823	+	0.592156i	$0.201723\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	42168.0	0.692546
$83$	6428.00	0.102419	0.0512095	−	0.998688i	$-0.483692\pi$
$83$	6428.00	0.102419	0.0512095	+	0.998688i	$0.483692\pi$
$84$	−7056.00	−0.109109
$85$	0	0
$86$	33808.0	0.492916
$87$	44586.0	0.631539
$88$	42496.0	0.584980
$89$	−122658.	−1.64142	−0.820712	−	0.571342i	$-0.806423\pi$
$89$	−122658.	−1.64142	−0.820712	+	0.571342i	$0.806423\pi$
$90$	0	0
$91$	−15582.0	−0.197251
$92$	−35392.0	−0.435949
$93$	64152.0	0.769135
$94$	−21408.0	−0.249894
$95$	0	0
$96$	−9216.00	−0.102062
$97$	−21370.0	−0.230608	−0.115304	−	0.993330i	$-0.536784\pi$
$97$	−21370.0	−0.230608	−0.115304	+	0.993330i	$0.536784\pi$
$98$	9604.00	0.101015
$99$	53784.0	0.551525
$100$	0	0
$101$	−36814.0	−0.359095	−0.179548	−	0.983749i	$-0.557463\pi$
$101$	−36814.0	−0.359095	−0.179548	+	0.983749i	$0.557463\pi$
$102$	56952.0	0.542012
$103$	−104528.	−0.970822	−0.485411	−	0.874286i	$-0.661330\pi$
$103$	−104528.	−0.970822	−0.485411	+	0.874286i	$0.661330\pi$
$104$	−20352.0	−0.184512
$105$	0	0
$106$	133416.	1.15330
$107$	−214440.	−1.81070	−0.905350	−	0.424667i	$-0.860391\pi$
$107$	−214440.	−1.81070	−0.905350	+	0.424667i	$0.860391\pi$
$108$	−11664.0	−0.0962250
$109$	28798.0	0.232165	0.116082	−	0.993240i	$-0.462966\pi$
$109$	28798.0	0.232165	0.116082	+	0.993240i	$0.462966\pi$
$110$	0	0
$111$	39222.0	0.302150
$112$	12544.0	0.0944911
$113$	56014.0	0.412668	0.206334	−	0.978482i	$-0.433847\pi$
$113$	56014.0	0.412668	0.206334	+	0.978482i	$0.433847\pi$
$114$	−8496.00	−0.0612283
$115$	0	0
$116$	−79264.0	−0.546929
$117$	−25758.0	−0.173959
$118$	−61744.0	−0.408216
$119$	−77518.0	−0.501805
$120$	0	0
$121$	279845.	1.73762
$122$	−147048.	−0.894457
$123$	−94878.0	−0.565461
$124$	−114048.	−0.666091
$125$	0	0
$126$	15876.0	0.0890871
$127$	−185400.	−1.02000	−0.510000	−	0.860174i	$-0.670355\pi$
$127$	−185400.	−1.02000	−0.510000	+	0.860174i	$0.670355\pi$
$128$	16384.0	0.0883883
$129$	−76068.0	−0.402465
$130$	0	0
$131$	64532.0	0.328547	0.164273	−	0.986415i	$-0.447472\pi$
$131$	64532.0	0.328547	0.164273	+	0.986415i	$0.447472\pi$
$132$	−95616.0	−0.477635
$133$	11564.0	0.0566864
$134$	−163888.	−0.788470
$135$	0	0
$136$	−101248.	−0.469396
$137$	−152930.	−0.696131	−0.348066	−	0.937470i	$-0.613161\pi$
$137$	−152930.	−0.696131	−0.348066	+	0.937470i	$0.613161\pi$
$138$	79632.0	0.355951
$139$	−343460.	−1.50778	−0.753892	−	0.656998i	$-0.771826\pi$
$139$	−343460.	−1.50778	−0.753892	+	0.656998i	$0.771826\pi$
$140$	0	0
$141$	48168.0	0.204038
$142$	−36368.0	−0.151356
$143$	−211152.	−0.863486
$144$	20736.0	0.0833333
$145$	0	0
$146$	293816.	1.14076
$147$	−21609.0	−0.0824786
$148$	−69728.0	−0.261669
$149$	−174858.	−0.645238	−0.322619	−	0.946529i	$-0.604563\pi$
$149$	−174858.	−0.645238	−0.322619	+	0.946529i	$0.604563\pi$
$150$	0	0
$151$	−452552.	−1.61520	−0.807600	−	0.589731i	$-0.799234\pi$
$151$	−452552.	−1.61520	−0.807600	+	0.589731i	$0.799234\pi$
$152$	15104.0	0.0530253
$153$	−128142.	−0.442551
$154$	130144.	0.442204
$155$	0	0
$156$	45792.0	0.150653
$157$	499066.	1.61588	0.807940	−	0.589265i	$-0.200583\pi$
$157$	499066.	1.61588	0.807940	+	0.589265i	$0.200583\pi$
$158$	357600.	1.13961
$159$	−300186.	−0.941668
$160$	0	0
$161$	−108388.	−0.329546
$162$	26244.0	0.0785674
$163$	475588.	1.40204	0.701022	−	0.713139i	$-0.252727\pi$
$163$	475588.	1.40204	0.701022	+	0.713139i	$0.252727\pi$
$164$	168672.	0.489704
$165$	0	0
$166$	25712.0	0.0724212
$167$	−120224.	−0.333580	−0.166790	−	0.985992i	$-0.553340\pi$
$167$	−120224.	−0.333580	−0.166790	+	0.985992i	$0.553340\pi$
$168$	−28224.0	−0.0771517
$169$	−270169.	−0.727644
$170$	0	0
$171$	19116.0	0.0499927
$172$	135232.	0.348545
$173$	−508874.	−1.29269	−0.646346	−	0.763045i	$-0.723704\pi$
$173$	−508874.	−1.29269	−0.646346	+	0.763045i	$0.723704\pi$
$174$	178344.	0.446566
$175$	0	0
$176$	169984.	0.413644
$177$	138924.	0.333307
$178$	−490632.	−1.16066
$179$	487560.	1.13735	0.568677	−	0.822561i	$-0.307456\pi$
$179$	487560.	1.13735	0.568677	+	0.822561i	$0.307456\pi$
$180$	0	0
$181$	−544410.	−1.23518	−0.617589	−	0.786501i	$-0.711891\pi$
$181$	−544410.	−1.23518	−0.617589	+	0.786501i	$0.711891\pi$
$182$	−62328.0	−0.139478
$183$	330858.	0.730321
$184$	−141568.	−0.308262
$185$	0	0
$186$	256608.	0.543861
$187$	−1.05045e6	−2.19670
$188$	−85632.0	−0.176702
$189$	−35721.0	−0.0727393
$190$	0	0
$191$	376404.	0.746570	0.373285	−	0.927717i	$-0.378231\pi$
$191$	376404.	0.746570	0.373285	+	0.927717i	$0.378231\pi$
$192$	−36864.0	−0.0721688
$193$	−844946.	−1.63281	−0.816405	−	0.577480i	$-0.804036\pi$
$193$	−844946.	−1.63281	−0.816405	+	0.577480i	$0.804036\pi$
$194$	−85480.0	−0.163065
$195$	0	0
$196$	38416.0	0.0714286
$197$	492794.	0.904690	0.452345	−	0.891843i	$-0.350588\pi$
$197$	492794.	0.904690	0.452345	+	0.891843i	$0.350588\pi$
$198$	215136.	0.389987
$199$	−914776.	−1.63750	−0.818751	−	0.574148i	$-0.805333\pi$
$199$	−914776.	−1.63750	−0.818751	+	0.574148i	$0.805333\pi$
$200$	0	0
$201$	368748.	0.643783
$202$	−147256.	−0.253919
$203$	−242746.	−0.413440
$204$	227808.	0.383260
$205$	0	0
$206$	−418112.	−0.686475
$207$	−179172.	−0.290633
$208$	−81408.0	−0.130469
$209$	156704.	0.248150
$210$	0	0
$211$	311780.	0.482106	0.241053	−	0.970512i	$-0.422507\pi$
$211$	311780.	0.482106	0.241053	+	0.970512i	$0.422507\pi$
$212$	533664.	0.815508
$213$	81828.0	0.123581
$214$	−857760.	−1.28036
$215$	0	0
$216$	−46656.0	−0.0680414
$217$	−349272.	−0.503517
$218$	115192.	0.164165
$219$	−661086.	−0.931425
$220$	0	0
$221$	503076.	0.692872
$222$	156888.	0.213652
$223$	1.28776e6	1.73409	0.867047	−	0.498226i	$-0.166015\pi$
$223$	1.28776e6	1.73409	0.867047	+	0.498226i	$0.166015\pi$
$224$	50176.0	0.0668153
$225$	0	0
$226$	224056.	0.291800
$227$	−1.28905e6	−1.66037	−0.830187	−	0.557485i	$-0.811766\pi$
$227$	−1.28905e6	−1.66037	−0.830187	+	0.557485i	$0.811766\pi$
$228$	−33984.0	−0.0432950
$229$	678214.	0.854630	0.427315	−	0.904103i	$-0.359460\pi$
$229$	678214.	0.854630	0.427315	+	0.904103i	$0.359460\pi$
$230$	0	0
$231$	−292824.	−0.361058
$232$	−317056.	−0.386737
$233$	1.11731e6	1.34829	0.674146	−	0.738598i	$-0.264512\pi$
$233$	1.11731e6	1.34829	0.674146	+	0.738598i	$0.264512\pi$
$234$	−103032.	−0.123008
$235$	0	0
$236$	−246976.	−0.288652
$237$	−804600.	−0.930485
$238$	−310072.	−0.354830
$239$	−1.26196e6	−1.42906	−0.714528	−	0.699606i	$-0.753359\pi$
$239$	−1.26196e6	−1.42906	−0.714528	+	0.699606i	$0.753359\pi$
$240$	0	0
$241$	948218.	1.05164	0.525818	−	0.850597i	$-0.323759\pi$
$241$	948218.	1.05164	0.525818	+	0.850597i	$0.323759\pi$
$242$	1.11938e6	1.22868
$243$	−59049.0	−0.0641500
$244$	−588192.	−0.632477
$245$	0	0
$246$	−379512.	−0.399841
$247$	−75048.0	−0.0782703
$248$	−456192.	−0.470997
$249$	−57852.0	−0.0591317
$250$	0	0
$251$	−486396.	−0.487310	−0.243655	−	0.969862i	$-0.578347\pi$
$251$	−486396.	−0.487310	−0.243655	+	0.969862i	$0.578347\pi$
$252$	63504.0	0.0629941
$253$	−1.46877e6	−1.44262
$254$	−741600.	−0.721249
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.03910e6	0.981349	0.490675	−	0.871343i	$-0.336750\pi$
$257$	1.03910e6	0.981349	0.490675	+	0.871343i	$0.336750\pi$
$258$	−304272.	−0.284585
$259$	−213542.	−0.197803
$260$	0	0
$261$	−401274.	−0.364619
$262$	258128.	0.232317
$263$	−1.35104e6	−1.20443	−0.602213	−	0.798335i	$-0.705714\pi$
$263$	−1.35104e6	−1.20443	−0.602213	+	0.798335i	$0.705714\pi$
$264$	−382464.	−0.337739
$265$	0	0
$266$	46256.0	0.0400833
$267$	1.10392e6	0.947677
$268$	−655552.	−0.557532
$269$	−1.11811e6	−0.942115	−0.471057	−	0.882103i	$-0.656128\pi$
$269$	−1.11811e6	−0.942115	−0.471057	+	0.882103i	$0.656128\pi$
$270$	0	0
$271$	−190104.	−0.157242	−0.0786209	−	0.996905i	$-0.525052\pi$
$271$	−190104.	−0.157242	−0.0786209	+	0.996905i	$0.525052\pi$
$272$	−404992.	−0.331913
$273$	140238.	0.113883
$274$	−611720.	−0.492239
$275$	0	0
$276$	318528.	0.251695
$277$	200506.	0.157010	0.0785051	−	0.996914i	$-0.474985\pi$
$277$	200506.	0.157010	0.0785051	+	0.996914i	$0.474985\pi$
$278$	−1.37384e6	−1.06616
$279$	−577368.	−0.444061
$280$	0	0
$281$	1.09237e6	0.825285	0.412643	−	0.910893i	$-0.364606\pi$
$281$	1.09237e6	0.825285	0.412643	+	0.910893i	$0.364606\pi$
$282$	192672.	0.144277
$283$	−1.81258e6	−1.34534	−0.672669	−	0.739944i	$-0.734852\pi$
$283$	−1.81258e6	−1.34534	−0.672669	+	0.739944i	$0.734852\pi$
$284$	−145472.	−0.107025
$285$	0	0
$286$	−844608.	−0.610577
$287$	516558.	0.370181
$288$	82944.0	0.0589256
$289$	1.08287e6	0.762659
$290$	0	0
$291$	192330.	0.133142
$292$	1.17526e6	0.806637
$293$	−2.10031e6	−1.42927	−0.714634	−	0.699499i	$-0.753407\pi$
$293$	−2.10031e6	−1.42927	−0.714634	+	0.699499i	$0.753407\pi$
$294$	−86436.0	−0.0583212
$295$	0	0
$296$	−278912.	−0.185028
$297$	−484056.	−0.318423
$298$	−699432.	−0.456252
$299$	703416.	0.455024
$300$	0	0
$301$	414148.	0.263475
$302$	−1.81021e6	−1.14212
$303$	331326.	0.207324
$304$	60416.0	0.0374945
$305$	0	0
$306$	−512568.	−0.312931
$307$	1.64104e6	0.993743	0.496872	−	0.867824i	$-0.334482\pi$
$307$	1.64104e6	0.993743	0.496872	+	0.867824i	$0.334482\pi$
$308$	520576.	0.312685
$309$	940752.	0.560504
$310$	0	0
$311$	−945232.	−0.554163	−0.277081	−	0.960846i	$-0.589367\pi$
$311$	−945232.	−0.554163	−0.277081	+	0.960846i	$0.589367\pi$
$312$	183168.	0.106528
$313$	−415354.	−0.239639	−0.119820	−	0.992796i	$-0.538232\pi$
$313$	−415354.	−0.239639	−0.119820	+	0.992796i	$0.538232\pi$
$314$	1.99626e6	1.14260
$315$	0	0
$316$	1.43040e6	0.805823
$317$	−1.18481e6	−0.662220	−0.331110	−	0.943592i	$-0.607423\pi$
$317$	−1.18481e6	−0.662220	−0.331110	+	0.943592i	$0.607423\pi$
$318$	−1.20074e6	−0.665860
$319$	−3.28946e6	−1.80987
$320$	0	0
$321$	1.92996e6	1.04541
$322$	−433552.	−0.233024
$323$	−373352.	−0.199119
$324$	104976.	0.0555556
$325$	0	0
$326$	1.90235e6	0.991395
$327$	−259182.	−0.134040
$328$	674688.	0.346273
$329$	−262248.	−0.133574
$330$	0	0
$331$	1.37155e6	0.688083	0.344042	−	0.938954i	$-0.388204\pi$
$331$	1.37155e6	0.688083	0.344042	+	0.938954i	$0.388204\pi$
$332$	102848.	0.0512095
$333$	−352998.	−0.174446
$334$	−480896.	−0.235877
$335$	0	0
$336$	−112896.	−0.0545545
$337$	−963522.	−0.462154	−0.231077	−	0.972935i	$-0.574225\pi$
$337$	−963522.	−0.462154	−0.231077	+	0.972935i	$0.574225\pi$
$338$	−1.08068e6	−0.514522
$339$	−504126.	−0.238254
$340$	0	0
$341$	−4.73299e6	−2.20419
$342$	76464.0	0.0353502
$343$	117649.	0.0539949
$344$	540928.	0.246458
$345$	0	0
$346$	−2.03550e6	−0.914071
$347$	−2.57731e6	−1.14906	−0.574531	−	0.818483i	$-0.694815\pi$
$347$	−2.57731e6	−1.14906	−0.574531	+	0.818483i	$0.694815\pi$
$348$	713376.	0.315770
$349$	−3.06751e6	−1.34810	−0.674051	−	0.738684i	$-0.735447\pi$
$349$	−3.06751e6	−1.34810	−0.674051	+	0.738684i	$0.735447\pi$
$350$	0	0
$351$	231822.	0.100435
$352$	679936.	0.292490
$353$	3.10144e6	1.32473	0.662364	−	0.749182i	$-0.269553\pi$
$353$	3.10144e6	1.32473	0.662364	+	0.749182i	$0.269553\pi$
$354$	555696.	0.235683
$355$	0	0
$356$	−1.96253e6	−0.820712
$357$	697662.	0.289717
$358$	1.95024e6	0.804230
$359$	−327508.	−0.134118	−0.0670588	−	0.997749i	$-0.521362\pi$
$359$	−327508.	−0.134118	−0.0670588	+	0.997749i	$0.521362\pi$
$360$	0	0
$361$	−2.42040e6	−0.977507
$362$	−2.17764e6	−0.873403
$363$	−2.51860e6	−1.00321
$364$	−249312.	−0.0986256
$365$	0	0
$366$	1.32343e6	0.516415
$367$	2.86739e6	1.11128	0.555638	−	0.831424i	$-0.312474\pi$
$367$	2.86739e6	1.11128	0.555638	+	0.831424i	$0.312474\pi$
$368$	−566272.	−0.217974
$369$	853902.	0.326469
$370$	0	0
$371$	1.63435e6	0.616466
$372$	1.02643e6	0.384568
$373$	−3.58029e6	−1.33244	−0.666218	−	0.745757i	$-0.732088\pi$
$373$	−3.58029e6	−1.33244	−0.666218	+	0.745757i	$0.732088\pi$
$374$	−4.20179e6	−1.55330
$375$	0	0
$376$	−342528.	−0.124947
$377$	1.57537e6	0.570860
$378$	−142884.	−0.0514344
$379$	1.64235e6	0.587310	0.293655	−	0.955912i	$-0.405128\pi$
$379$	1.64235e6	0.587310	0.293655	+	0.955912i	$0.405128\pi$
$380$	0	0
$381$	1.66860e6	0.588898
$382$	1.50562e6	0.527905
$383$	2.05698e6	0.716527	0.358263	−	0.933621i	$-0.383369\pi$
$383$	2.05698e6	0.716527	0.358263	+	0.933621i	$0.383369\pi$
$384$	−147456.	−0.0510310
$385$	0	0
$386$	−3.37978e6	−1.15457
$387$	684612.	0.232363
$388$	−341920.	−0.115304
$389$	616142.	0.206446	0.103223	−	0.994658i	$-0.467084\pi$
$389$	616142.	0.206446	0.103223	+	0.994658i	$0.467084\pi$
$390$	0	0
$391$	3.49938e6	1.15758
$392$	153664.	0.0505076
$393$	−580788.	−0.189686
$394$	1.97118e6	0.639713
$395$	0	0
$396$	860544.	0.275762
$397$	−2.19212e6	−0.698052	−0.349026	−	0.937113i	$-0.613487\pi$
$397$	−2.19212e6	−0.698052	−0.349026	+	0.937113i	$0.613487\pi$
$398$	−3.65910e6	−1.15789
$399$	−104076.	−0.0327279
$400$	0	0
$401$	3.28454e6	1.02003	0.510015	−	0.860165i	$-0.329640\pi$
$401$	3.28454e6	1.02003	0.510015	+	0.860165i	$0.329640\pi$
$402$	1.47499e6	0.455223
$403$	2.26670e6	0.695236
$404$	−589024.	−0.179548
$405$	0	0
$406$	−970984.	−0.292346
$407$	−2.89371e6	−0.865903
$408$	911232.	0.271006
$409$	−3.61219e6	−1.06773	−0.533866	−	0.845569i	$-0.679261\pi$
$409$	−3.61219e6	−1.06773	−0.533866	+	0.845569i	$0.679261\pi$
$410$	0	0
$411$	1.37637e6	0.401912
$412$	−1.67245e6	−0.485411
$413$	−756364.	−0.218200
$414$	−716688.	−0.205508
$415$	0	0
$416$	−325632.	−0.0922558
$417$	3.09114e6	0.870520
$418$	626816.	0.175469
$419$	5.41489e6	1.50680	0.753398	−	0.657564i	$-0.228413\pi$
$419$	5.41489e6	1.50680	0.753398	+	0.657564i	$0.228413\pi$
$420$	0	0
$421$	3.60629e6	0.991644	0.495822	−	0.868424i	$-0.334867\pi$
$421$	3.60629e6	0.991644	0.495822	+	0.868424i	$0.334867\pi$
$422$	1.24712e6	0.340900
$423$	−433512.	−0.117801
$424$	2.13466e6	0.576651
$425$	0	0
$426$	327312.	0.0873852
$427$	−1.80134e6	−0.478107
$428$	−3.43104e6	−0.905350
$429$	1.90037e6	0.498534
$430$	0	0
$431$	−2.78214e6	−0.721416	−0.360708	−	0.932679i	$-0.617465\pi$
$431$	−2.78214e6	−0.721416	−0.360708	+	0.932679i	$0.617465\pi$
$432$	−186624.	−0.0481125
$433$	−6.27619e6	−1.60871	−0.804353	−	0.594152i	$-0.797488\pi$
$433$	−6.27619e6	−1.60871	−0.804353	+	0.594152i	$0.797488\pi$
$434$	−1.39709e6	−0.356041
$435$	0	0
$436$	460768.	0.116082
$437$	−522032.	−0.130766
$438$	−2.64434e6	−0.658617
$439$	641592.	0.158890	0.0794452	−	0.996839i	$-0.474685\pi$
$439$	641592.	0.158890	0.0794452	+	0.996839i	$0.474685\pi$
$440$	0	0
$441$	194481.	0.0476190
$442$	2.01230e6	0.489934
$443$	−6.05546e6	−1.46601	−0.733006	−	0.680222i	$-0.761883\pi$
$443$	−6.05546e6	−1.46601	−0.733006	+	0.680222i	$0.761883\pi$
$444$	627552.	0.151075
$445$	0	0
$446$	5.15104e6	1.22619
$447$	1.57372e6	0.372528
$448$	200704.	0.0472456
$449$	−5.16681e6	−1.20950	−0.604752	−	0.796414i	$-0.706728\pi$
$449$	−5.16681e6	−1.20950	−0.604752	+	0.796414i	$0.706728\pi$
$450$	0	0
$451$	6.99989e6	1.62050
$452$	896224.	0.206334
$453$	4.07297e6	0.932536
$454$	−5.15621e6	−1.17406
$455$	0	0
$456$	−135936.	−0.0306142
$457$	227798.	0.0510222	0.0255111	−	0.999675i	$-0.491879\pi$
$457$	227798.	0.0510222	0.0255111	+	0.999675i	$0.491879\pi$
$458$	2.71286e6	0.604315
$459$	1.15328e6	0.255507
$460$	0	0
$461$	585146.	0.128237	0.0641183	−	0.997942i	$-0.479577\pi$
$461$	585146.	0.128237	0.0641183	+	0.997942i	$0.479577\pi$
$462$	−1.17130e6	−0.255306
$463$	3.41454e6	0.740251	0.370126	−	0.928982i	$-0.379315\pi$
$463$	3.41454e6	0.740251	0.370126	+	0.928982i	$0.379315\pi$
$464$	−1.26822e6	−0.273465
$465$	0	0
$466$	4.46924e6	0.953386
$467$	−716300.	−0.151986	−0.0759929	−	0.997108i	$-0.524213\pi$
$467$	−716300.	−0.151986	−0.0759929	+	0.997108i	$0.524213\pi$
$468$	−412128.	−0.0869796
$469$	−2.00763e6	−0.421455
$470$	0	0
$471$	−4.49159e6	−0.932928
$472$	−987904.	−0.204108
$473$	5.61213e6	1.15339
$474$	−3.21840e6	−0.657952
$475$	0	0
$476$	−1.24029e6	−0.250903
$477$	2.70167e6	0.543672
$478$	−5.04782e6	−1.01050
$479$	5.24092e6	1.04368	0.521842	−	0.853042i	$-0.325245\pi$
$479$	5.24092e6	1.04368	0.521842	+	0.853042i	$0.325245\pi$
$480$	0	0
$481$	1.38584e6	0.273119
$482$	3.79287e6	0.743619
$483$	975492.	0.190264
$484$	4.47752e6	0.868809
$485$	0	0
$486$	−236196.	−0.0453609
$487$	−1.11702e6	−0.213421	−0.106710	−	0.994290i	$-0.534032\pi$
$487$	−1.11702e6	−0.213421	−0.106710	+	0.994290i	$0.534032\pi$
$488$	−2.35277e6	−0.447229
$489$	−4.28029e6	−0.809471
$490$	0	0
$491$	1.34458e6	0.251699	0.125850	−	0.992049i	$-0.459834\pi$
$491$	1.34458e6	0.251699	0.125850	+	0.992049i	$0.459834\pi$
$492$	−1.51805e6	−0.282731
$493$	7.83723e6	1.45226
$494$	−300192.	−0.0553454
$495$	0	0
$496$	−1.82477e6	−0.333045
$497$	−445508.	−0.0809030
$498$	−231408.	−0.0418124
$499$	−6.54648e6	−1.17695	−0.588473	−	0.808517i	$-0.700271\pi$
$499$	−6.54648e6	−1.17695	−0.588473	+	0.808517i	$0.700271\pi$
$500$	0	0
$501$	1.08202e6	0.192592
$502$	−1.94558e6	−0.344580
$503$	8.22050e6	1.44870	0.724350	−	0.689432i	$-0.242140\pi$
$503$	8.22050e6	1.44870	0.724350	+	0.689432i	$0.242140\pi$
$504$	254016.	0.0445435
$505$	0	0
$506$	−5.87507e6	−1.02009
$507$	2.43152e6	0.420105
$508$	−2.96640e6	−0.510000
$509$	−5.11045e6	−0.874308	−0.437154	−	0.899387i	$-0.644013\pi$
$509$	−5.11045e6	−0.874308	−0.437154	+	0.899387i	$0.644013\pi$
$510$	0	0
$511$	3.59925e6	0.609760
$512$	262144.	0.0441942
$513$	−172044.	−0.0288633
$514$	4.15639e6	0.693919
$515$	0	0
$516$	−1.21709e6	−0.201232
$517$	−3.55373e6	−0.584733
$518$	−854168.	−0.139868
$519$	4.57987e6	0.746336
$520$	0	0
$521$	9.69999e6	1.56559	0.782793	−	0.622282i	$-0.213794\pi$
$521$	9.69999e6	1.56559	0.782793	+	0.622282i	$0.213794\pi$
$522$	−1.60510e6	−0.257825
$523$	3.17295e6	0.507234	0.253617	−	0.967305i	$-0.418380\pi$
$523$	3.17295e6	0.507234	0.253617	+	0.967305i	$0.418380\pi$
$524$	1.03251e6	0.164273
$525$	0	0
$526$	−5.40418e6	−0.851658
$527$	1.12765e7	1.76867
$528$	−1.52986e6	−0.238817
$529$	−1.54340e6	−0.239794
$530$	0	0
$531$	−1.25032e6	−0.192435
$532$	185024.	0.0283432
$533$	−3.35236e6	−0.511131
$534$	4.41569e6	0.670109
$535$	0	0
$536$	−2.62221e6	−0.394235
$537$	−4.38804e6	−0.656651
$538$	−4.47244e6	−0.666176
$539$	1.59426e6	0.236368
$540$	0	0
$541$	−6.62575e6	−0.973289	−0.486644	−	0.873600i	$-0.661779\pi$
$541$	−6.62575e6	−0.973289	−0.486644	+	0.873600i	$0.661779\pi$
$542$	−760416.	−0.111187
$543$	4.89969e6	0.713131
$544$	−1.61997e6	−0.234698
$545$	0	0
$546$	560952.	0.0805275
$547$	−3.84707e6	−0.549745	−0.274873	−	0.961481i	$-0.588636\pi$
$547$	−3.84707e6	−0.549745	−0.274873	+	0.961481i	$0.588636\pi$
$548$	−2.44688e6	−0.348066
$549$	−2.97772e6	−0.421651
$550$	0	0
$551$	−1.16914e6	−0.164055
$552$	1.27411e6	0.177975
$553$	4.38060e6	0.609145
$554$	802024.	0.111023
$555$	0	0
$556$	−5.49536e6	−0.753892
$557$	−5.00176e6	−0.683101	−0.341550	−	0.939863i	$-0.610952\pi$
$557$	−5.00176e6	−0.683101	−0.341550	+	0.939863i	$0.610952\pi$
$558$	−2.30947e6	−0.313998
$559$	−2.68774e6	−0.363795
$560$	0	0
$561$	9.45403e6	1.26826
$562$	4.36948e6	0.583565
$563$	−2.27772e6	−0.302852	−0.151426	−	0.988469i	$-0.548386\pi$
$563$	−2.27772e6	−0.302852	−0.151426	+	0.988469i	$0.548386\pi$
$564$	770688.	0.102019
$565$	0	0
$566$	−7.25032e6	−0.951297
$567$	321489.	0.0419961
$568$	−581888.	−0.0756778
$569$	8.86979e6	1.14850	0.574252	−	0.818678i	$-0.305293\pi$
$569$	8.86979e6	1.14850	0.574252	+	0.818678i	$0.305293\pi$
$570$	0	0
$571$	1.40102e7	1.79826	0.899132	−	0.437678i	$-0.144199\pi$
$571$	1.40102e7	1.79826	0.899132	+	0.437678i	$0.144199\pi$
$572$	−3.37843e6	−0.431743
$573$	−3.38764e6	−0.431033
$574$	2.06623e6	0.261758
$575$	0	0
$576$	331776.	0.0416667
$577$	−8.75327e6	−1.09454	−0.547269	−	0.836957i	$-0.684332\pi$
$577$	−8.75327e6	−1.09454	−0.547269	+	0.836957i	$0.684332\pi$
$578$	4.33147e6	0.539281
$579$	7.60451e6	0.942703
$580$	0	0
$581$	314972.	0.0387108
$582$	769320.	0.0941455
$583$	2.21471e7	2.69864
$584$	4.70106e6	0.570379
$585$	0	0
$586$	−8.40122e6	−1.01064
$587$	1.06117e7	1.27113	0.635564	−	0.772048i	$-0.280768\pi$
$587$	1.06117e7	1.27113	0.635564	+	0.772048i	$0.280768\pi$
$588$	−345744.	−0.0412393
$589$	−1.68221e6	−0.199798
$590$	0	0
$591$	−4.43515e6	−0.522323
$592$	−1.11565e6	−0.130835
$593$	−1.88552e6	−0.220188	−0.110094	−	0.993921i	$-0.535115\pi$
$593$	−1.88552e6	−0.220188	−0.110094	+	0.993921i	$0.535115\pi$
$594$	−1.93622e6	−0.225159
$595$	0	0
$596$	−2.79773e6	−0.322619
$597$	8.23298e6	0.945413
$598$	2.81366e6	0.321751
$599$	1.27256e7	1.44915	0.724573	−	0.689198i	$-0.242037\pi$
$599$	1.27256e7	1.44915	0.724573	+	0.689198i	$0.242037\pi$
$600$	0	0
$601$	7.18846e6	0.811801	0.405900	−	0.913917i	$-0.366958\pi$
$601$	7.18846e6	0.811801	0.405900	+	0.913917i	$0.366958\pi$
$602$	1.65659e6	0.186305
$603$	−3.31873e6	−0.371688
$604$	−7.24083e6	−0.807600
$605$	0	0
$606$	1.32530e6	0.146600
$607$	−1.08494e7	−1.19519	−0.597593	−	0.801800i	$-0.703876\pi$
$607$	−1.08494e7	−1.19519	−0.597593	+	0.801800i	$0.703876\pi$
$608$	241664.	0.0265126
$609$	2.18471e6	0.238699
$610$	0	0
$611$	1.70194e6	0.184434
$612$	−2.05027e6	−0.221275
$613$	4.90511e6	0.527227	0.263614	−	0.964628i	$-0.415086\pi$
$613$	4.90511e6	0.527227	0.263614	+	0.964628i	$0.415086\pi$
$614$	6.56418e6	0.702683
$615$	0	0
$616$	2.08230e6	0.221102
$617$	−2.58445e6	−0.273310	−0.136655	−	0.990619i	$-0.543635\pi$
$617$	−2.58445e6	−0.273310	−0.136655	+	0.990619i	$0.543635\pi$
$618$	3.76301e6	0.396336
$619$	−4.99336e6	−0.523801	−0.261901	−	0.965095i	$-0.584349\pi$
$619$	−4.99336e6	−0.523801	−0.261901	+	0.965095i	$0.584349\pi$
$620$	0	0
$621$	1.61255e6	0.167797
$622$	−3.78093e6	−0.391852
$623$	−6.01024e6	−0.620400
$624$	732672.	0.0753266
$625$	0	0
$626$	−1.66142e6	−0.169450
$627$	−1.41034e6	−0.143269
$628$	7.98506e6	0.807940
$629$	6.89436e6	0.694812
$630$	0	0
$631$	−1.18219e7	−1.18199	−0.590997	−	0.806674i	$-0.701265\pi$
$631$	−1.18219e7	−1.18199	−0.590997	+	0.806674i	$0.701265\pi$
$632$	5.72160e6	0.569803
$633$	−2.80602e6	−0.278344
$634$	−4.73926e6	−0.468260
$635$	0	0
$636$	−4.80298e6	−0.470834
$637$	−763518.	−0.0745540
$638$	−1.31578e7	−1.27977
$639$	−736452.	−0.0713497
$640$	0	0
$641$	−5.47007e6	−0.525833	−0.262916	−	0.964819i	$-0.584684\pi$
$641$	−5.47007e6	−0.525833	−0.262916	+	0.964819i	$0.584684\pi$
$642$	7.71984e6	0.739215
$643$	−9.64934e6	−0.920386	−0.460193	−	0.887819i	$-0.652220\pi$
$643$	−9.64934e6	−0.920386	−0.460193	+	0.887819i	$0.652220\pi$
$644$	−1.73421e6	−0.164773
$645$	0	0
$646$	−1.49341e6	−0.140798
$647$	−292368.	−0.0274580	−0.0137290	−	0.999906i	$-0.504370\pi$
$647$	−292368.	−0.0274580	−0.0137290	+	0.999906i	$0.504370\pi$
$648$	419904.	0.0392837
$649$	−1.02495e7	−0.955193
$650$	0	0
$651$	3.14345e6	0.290706
$652$	7.60941e6	0.701022
$653$	−6.94081e6	−0.636982	−0.318491	−	0.947926i	$-0.603176\pi$
$653$	−6.94081e6	−0.636982	−0.318491	+	0.947926i	$0.603176\pi$
$654$	−1.03673e6	−0.0947808
$655$	0	0
$656$	2.69875e6	0.244852
$657$	5.94977e6	0.537758
$658$	−1.04899e6	−0.0944512
$659$	−1.32912e7	−1.19221	−0.596104	−	0.802908i	$-0.703285\pi$
$659$	−1.32912e7	−1.19221	−0.596104	+	0.802908i	$0.703285\pi$
$660$	0	0
$661$	2.05219e6	0.182690	0.0913448	−	0.995819i	$-0.470883\pi$
$661$	2.05219e6	0.182690	0.0913448	+	0.995819i	$0.470883\pi$
$662$	5.48619e6	0.486548
$663$	−4.52768e6	−0.400030
$664$	411392.	0.0362106
$665$	0	0
$666$	−1.41199e6	−0.123352
$667$	1.09582e7	0.953732
$668$	−1.92358e6	−0.166790
$669$	−1.15898e7	−1.00118
$670$	0	0
$671$	−2.44100e7	−2.09296
$672$	−451584.	−0.0385758
$673$	1.57039e7	1.33650	0.668252	−	0.743935i	$-0.267043\pi$
$673$	1.57039e7	1.33650	0.668252	+	0.743935i	$0.267043\pi$
$674$	−3.85409e6	−0.326792
$675$	0	0
$676$	−4.32270e6	−0.363822
$677$	969534.	0.0813002	0.0406501	−	0.999173i	$-0.487057\pi$
$677$	969534.	0.0813002	0.0406501	+	0.999173i	$0.487057\pi$
$678$	−2.01650e6	−0.168471
$679$	−1.04713e6	−0.0871618
$680$	0	0
$681$	1.16015e7	0.958617
$682$	−1.89320e7	−1.55860
$683$	1.49908e7	1.22962	0.614812	−	0.788673i	$-0.289232\pi$
$683$	1.49908e7	1.22962	0.614812	+	0.788673i	$0.289232\pi$
$684$	305856.	0.0249964
$685$	0	0
$686$	470596.	0.0381802
$687$	−6.10393e6	−0.493421
$688$	2.16371e6	0.174272
$689$	−1.06066e7	−0.851191
$690$	0	0
$691$	−7.16038e6	−0.570481	−0.285240	−	0.958456i	$-0.592073\pi$
$691$	−7.16038e6	−0.570481	−0.285240	+	0.958456i	$0.592073\pi$
$692$	−8.14198e6	−0.646346
$693$	2.63542e6	0.208457
$694$	−1.03092e7	−0.812509
$695$	0	0
$696$	2.85350e6	0.223283
$697$	−1.66774e7	−1.30031
$698$	−1.22701e7	−0.953253
$699$	−1.00558e7	−0.778437
$700$	0	0
$701$	−91834.0	−0.00705844	−0.00352922	−	0.999994i	$-0.501123\pi$
$701$	−91834.0	−0.00705844	−0.00352922	+	0.999994i	$0.501123\pi$
$702$	927288.	0.0710186
$703$	−1.02849e6	−0.0784894
$704$	2.71974e6	0.206822
$705$	0	0
$706$	1.24058e7	0.936725
$707$	−1.80389e6	−0.135725
$708$	2.22278e6	0.166653
$709$	2.20981e7	1.65097	0.825487	−	0.564422i	$-0.190901\pi$
$709$	2.20981e7	1.65097	0.825487	+	0.564422i	$0.190901\pi$
$710$	0	0
$711$	7.24140e6	0.537216
$712$	−7.85011e6	−0.580331
$713$	1.57671e7	1.16153
$714$	2.79065e6	0.204861
$715$	0	0
$716$	7.80096e6	0.568677
$717$	1.13576e7	0.825066
$718$	−1.31003e6	−0.0948355
$719$	1.58388e7	1.14262	0.571308	−	0.820736i	$-0.306436\pi$
$719$	1.58388e7	1.14262	0.571308	+	0.820736i	$0.306436\pi$
$720$	0	0
$721$	−5.12187e6	−0.366936
$722$	−9.68161e6	−0.691202
$723$	−8.53396e6	−0.607163
$724$	−8.71056e6	−0.617589
$725$	0	0
$726$	−1.00744e7	−0.709379
$727$	−6.31418e6	−0.443078	−0.221539	−	0.975151i	$-0.571108\pi$
$727$	−6.31418e6	−0.443078	−0.221539	+	0.975151i	$0.571108\pi$
$728$	−997248.	−0.0697388
$729$	531441.	0.0370370
$730$	0	0
$731$	−1.33711e7	−0.925492
$732$	5.29373e6	0.365161
$733$	−6.93003e6	−0.476404	−0.238202	−	0.971216i	$-0.576558\pi$
$733$	−6.93003e6	−0.476404	−0.238202	+	0.971216i	$0.576558\pi$
$734$	1.14696e7	0.785791
$735$	0	0
$736$	−2.26509e6	−0.154131
$737$	−2.72054e7	−1.84496
$738$	3.41561e6	0.230849
$739$	1.42331e7	0.958714	0.479357	−	0.877620i	$-0.340870\pi$
$739$	1.42331e7	0.958714	0.479357	+	0.877620i	$0.340870\pi$
$740$	0	0
$741$	675432.	0.0451894
$742$	6.53738e6	0.435907
$743$	5.94460e6	0.395048	0.197524	−	0.980298i	$-0.436710\pi$
$743$	5.94460e6	0.395048	0.197524	+	0.980298i	$0.436710\pi$
$744$	4.10573e6	0.271930
$745$	0	0
$746$	−1.43212e7	−0.942175
$747$	520668.	0.0341397
$748$	−1.68072e7	−1.09835
$749$	−1.05076e7	−0.684380
$750$	0	0
$751$	−682752.	−0.0441736	−0.0220868	−	0.999756i	$-0.507031\pi$
$751$	−682752.	−0.0441736	−0.0220868	+	0.999756i	$0.507031\pi$
$752$	−1.37011e6	−0.0883510
$753$	4.37756e6	0.281349
$754$	6.30149e6	0.403659
$755$	0	0
$756$	−571536.	−0.0363696
$757$	−1.46333e7	−0.928116	−0.464058	−	0.885805i	$-0.653607\pi$
$757$	−1.46333e7	−0.928116	−0.464058	+	0.885805i	$0.653607\pi$
$758$	6.56939e6	0.415291
$759$	1.32189e7	0.832897
$760$	0	0
$761$	−1.16367e7	−0.728399	−0.364200	−	0.931321i	$-0.618657\pi$
$761$	−1.16367e7	−0.728399	−0.364200	+	0.931321i	$0.618657\pi$
$762$	6.67440e6	0.416414
$763$	1.41110e6	0.0877500
$764$	6.02246e6	0.373285
$765$	0	0
$766$	8.22790e6	0.506661
$767$	4.90865e6	0.301282
$768$	−589824.	−0.0360844
$769$	1.91472e7	1.16759	0.583793	−	0.811902i	$-0.301568\pi$
$769$	1.91472e7	1.16759	0.583793	+	0.811902i	$0.301568\pi$
$770$	0	0
$771$	−9.35188e6	−0.566582
$772$	−1.35191e7	−0.816405
$773$	5.39261e6	0.324601	0.162301	−	0.986741i	$-0.448109\pi$
$773$	5.39261e6	0.324601	0.162301	+	0.986741i	$0.448109\pi$
$774$	2.73845e6	0.164305
$775$	0	0
$776$	−1.36768e6	−0.0815324
$777$	1.92188e6	0.114202
$778$	2.46457e6	0.145979
$779$	2.48791e6	0.146890
$780$	0	0
$781$	−6.03709e6	−0.354160
$782$	1.39975e7	0.818530
$783$	3.61147e6	0.210513
$784$	614656.	0.0357143
$785$	0	0
$786$	−2.32315e6	−0.134129
$787$	−3.04348e6	−0.175159	−0.0875796	−	0.996158i	$-0.527913\pi$
$787$	−3.04348e6	−0.175159	−0.0875796	+	0.996158i	$0.527913\pi$
$788$	7.88470e6	0.452345
$789$	1.21594e7	0.695376
$790$	0	0
$791$	2.74469e6	0.155974
$792$	3.44218e6	0.194993
$793$	1.16903e7	0.660151
$794$	−8.76847e6	−0.493597
$795$	0	0
$796$	−1.46364e7	−0.818751
$797$	−2.29652e7	−1.28063	−0.640316	−	0.768111i	$-0.721197\pi$
$797$	−2.29652e7	−1.28063	−0.640316	+	0.768111i	$0.721197\pi$
$798$	−416304.	−0.0231421
$799$	8.46686e6	0.469197
$800$	0	0
$801$	−9.93530e6	−0.547141
$802$	1.31382e7	0.721271
$803$	4.87735e7	2.66928
$804$	5.89997e6	0.321892
$805$	0	0
$806$	9.06682e6	0.491606
$807$	1.00630e7	0.543930
$808$	−2.35610e6	−0.126959
$809$	1.90787e7	1.02489	0.512445	−	0.858720i	$-0.328740\pi$
$809$	1.90787e7	1.02489	0.512445	+	0.858720i	$0.328740\pi$
$810$	0	0
$811$	1.09414e7	0.584147	0.292074	−	0.956396i	$-0.405655\pi$
$811$	1.09414e7	0.584147	0.292074	+	0.956396i	$0.405655\pi$
$812$	−3.88394e6	−0.206720
$813$	1.71094e6	0.0907836
$814$	−1.15748e7	−0.612286
$815$	0	0
$816$	3.64493e6	0.191630
$817$	1.99467e6	0.104548
$818$	−1.44488e7	−0.755001
$819$	−1.26214e6	−0.0657504
$820$	0	0
$821$	2.12594e7	1.10076	0.550380	−	0.834914i	$-0.314483\pi$
$821$	2.12594e7	1.10076	0.550380	+	0.834914i	$0.314483\pi$
$822$	5.50548e6	0.284194
$823$	1.42256e7	0.732103	0.366052	−	0.930595i	$-0.380709\pi$
$823$	1.42256e7	0.732103	0.366052	+	0.930595i	$0.380709\pi$
$824$	−6.68979e6	−0.343237
$825$	0	0
$826$	−3.02546e6	−0.154291
$827$	−2.76103e6	−0.140381	−0.0701904	−	0.997534i	$-0.522361\pi$
$827$	−2.76103e6	−0.140381	−0.0701904	+	0.997534i	$0.522361\pi$
$828$	−2.86675e6	−0.145316
$829$	−3.82147e7	−1.93127	−0.965637	−	0.259895i	$-0.916312\pi$
$829$	−3.82147e7	−1.93127	−0.965637	+	0.259895i	$0.916312\pi$
$830$	0	0
$831$	−1.80455e6	−0.0906499
$832$	−1.30253e6	−0.0652347
$833$	−3.79838e6	−0.189665
$834$	1.23646e7	0.615550
$835$	0	0
$836$	2.50726e6	0.124075
$837$	5.19631e6	0.256378
$838$	2.16596e7	1.06547
$839$	1.06044e7	0.520094	0.260047	−	0.965596i	$-0.416262\pi$
$839$	1.06044e7	0.520094	0.260047	+	0.965596i	$0.416262\pi$
$840$	0	0
$841$	4.03097e6	0.196526
$842$	1.44252e7	0.701198
$843$	−9.83133e6	−0.476479
$844$	4.98848e6	0.241053
$845$	0	0
$846$	−1.73405e6	−0.0832981
$847$	1.37124e7	0.656758
$848$	8.53862e6	0.407754
$849$	1.63132e7	0.776731
$850$	0	0
$851$	9.63990e6	0.456298
$852$	1.30925e6	0.0617907
$853$	4.07009e7	1.91527	0.957637	−	0.287977i	$-0.0929826\pi$
$853$	4.07009e7	1.91527	0.957637	+	0.287977i	$0.0929826\pi$
$854$	−7.20535e6	−0.338073
$855$	0	0
$856$	−1.37242e7	−0.640179
$857$	3.10120e7	1.44237	0.721187	−	0.692741i	$-0.243597\pi$
$857$	3.10120e7	1.44237	0.721187	+	0.692741i	$0.243597\pi$
$858$	7.60147e6	0.352517
$859$	1.09104e7	0.504495	0.252247	−	0.967663i	$-0.418830\pi$
$859$	1.09104e7	0.504495	0.252247	+	0.967663i	$0.418830\pi$
$860$	0	0
$861$	−4.64902e6	−0.213724
$862$	−1.11286e7	−0.510118
$863$	−1.04089e7	−0.475751	−0.237875	−	0.971296i	$-0.576451\pi$
$863$	−1.04089e7	−0.475751	−0.237875	+	0.971296i	$0.576451\pi$
$864$	−746496.	−0.0340207
$865$	0	0
$866$	−2.51048e7	−1.13753
$867$	−9.74580e6	−0.440321
$868$	−5.58835e6	−0.251759
$869$	5.93616e7	2.66659
$870$	0	0
$871$	1.30291e7	0.581928
$872$	1.84307e6	0.0820826
$873$	−1.73097e6	−0.0768695
$874$	−2.08813e6	−0.0924652
$875$	0	0
$876$	−1.05774e7	−0.465712
$877$	−1.64064e7	−0.720299	−0.360150	−	0.932895i	$-0.617274\pi$
$877$	−1.64064e7	−0.720299	−0.360150	+	0.932895i	$0.617274\pi$
$878$	2.56637e6	0.112352
$879$	1.89028e7	0.825188
$880$	0	0
$881$	1.48577e7	0.644927	0.322464	−	0.946582i	$-0.395489\pi$
$881$	1.48577e7	0.644927	0.322464	+	0.946582i	$0.395489\pi$
$882$	777924.	0.0336718
$883$	2.72018e7	1.17407	0.587037	−	0.809560i	$-0.300294\pi$
$883$	2.72018e7	1.17407	0.587037	+	0.809560i	$0.300294\pi$
$884$	8.04922e6	0.346436
$885$	0	0
$886$	−2.42218e7	−1.03663
$887$	−2.71242e7	−1.15757	−0.578785	−	0.815480i	$-0.696473\pi$
$887$	−2.71242e7	−1.15757	−0.578785	+	0.815480i	$0.696473\pi$
$888$	2.51021e6	0.106826
$889$	−9.08460e6	−0.385524
$890$	0	0
$891$	4.35650e6	0.183842
$892$	2.06042e7	0.867047
$893$	−1.26307e6	−0.0530029
$894$	6.29489e6	0.263417
$895$	0	0
$896$	802816.	0.0334077
$897$	−6.33074e6	−0.262708
$898$	−2.06673e7	−0.855248
$899$	3.53121e7	1.45722
$900$	0	0
$901$	−5.27660e7	−2.16542
$902$	2.79996e7	1.14587
$903$	−3.72733e6	−0.152117
$904$	3.58490e6	0.145900
$905$	0	0
$906$	1.62919e7	0.659402
$907$	8.42269e6	0.339964	0.169982	−	0.985447i	$-0.445629\pi$
$907$	8.42269e6	0.339964	0.169982	+	0.985447i	$0.445629\pi$
$908$	−2.06248e7	−0.830187
$909$	−2.98193e6	−0.119698
$910$	0	0
$911$	3.08637e7	1.23212	0.616060	−	0.787700i	$-0.288728\pi$
$911$	3.08637e7	1.23212	0.616060	+	0.787700i	$0.288728\pi$
$912$	−543744.	−0.0216475
$913$	4.26819e6	0.169460
$914$	911192.	0.0360782
$915$	0	0
$916$	1.08514e7	0.427315
$917$	3.16207e6	0.124179
$918$	4.61311e6	0.180671
$919$	4.93895e6	0.192906	0.0964531	−	0.995338i	$-0.469250\pi$
$919$	4.93895e6	0.192906	0.0964531	+	0.995338i	$0.469250\pi$
$920$	0	0
$921$	−1.47694e7	−0.573738
$922$	2.34058e6	0.0906770
$923$	2.89126e6	0.111707
$924$	−4.68518e6	−0.180529
$925$	0	0
$926$	1.36581e7	0.523437
$927$	−8.46677e6	−0.323607
$928$	−5.07290e6	−0.193369
$929$	5.62575e6	0.213866	0.106933	−	0.994266i	$-0.465897\pi$
$929$	5.62575e6	0.213866	0.106933	+	0.994266i	$0.465897\pi$
$930$	0	0
$931$	566636.	0.0214255
$932$	1.78770e7	0.674146
$933$	8.50709e6	0.319946
$934$	−2.86520e6	−0.107470
$935$	0	0
$936$	−1.64851e6	−0.0615039
$937$	−2.60073e7	−0.967714	−0.483857	−	0.875147i	$-0.660764\pi$
$937$	−2.60073e7	−0.967714	−0.483857	+	0.875147i	$0.660764\pi$
$938$	−8.03051e6	−0.298014
$939$	3.73819e6	0.138356
$940$	0	0
$941$	3.02160e6	0.111241	0.0556203	−	0.998452i	$-0.482286\pi$
$941$	3.02160e6	0.111241	0.0556203	+	0.998452i	$0.482286\pi$
$942$	−1.79664e7	−0.659680
$943$	−2.33189e7	−0.853943
$944$	−3.95162e6	−0.144326
$945$	0	0
$946$	2.24485e7	0.815567
$947$	3.48282e7	1.26199	0.630995	−	0.775787i	$-0.282647\pi$
$947$	3.48282e7	1.26199	0.630995	+	0.775787i	$0.282647\pi$
$948$	−1.28736e7	−0.465242
$949$	−2.33584e7	−0.841932
$950$	0	0
$951$	1.06633e7	0.382333
$952$	−4.96115e6	−0.177415
$953$	9.39009e6	0.334917	0.167459	−	0.985879i	$-0.446444\pi$
$953$	9.39009e6	0.334917	0.167459	+	0.985879i	$0.446444\pi$
$954$	1.08067e7	0.384434
$955$	0	0
$956$	−2.01913e7	−0.714528
$957$	2.96051e7	1.04493
$958$	2.09637e7	0.737996
$959$	−7.49357e6	−0.263113
$960$	0	0
$961$	2.21792e7	0.774708
$962$	5.54338e6	0.193124
$963$	−1.73696e7	−0.603566
$964$	1.51715e7	0.525818
$965$	0	0
$966$	3.90197e6	0.134537
$967$	−1.44768e7	−0.497860	−0.248930	−	0.968521i	$-0.580079\pi$
$967$	−1.44768e7	−0.497860	−0.248930	+	0.968521i	$0.580079\pi$
$968$	1.79101e7	0.614340
$969$	3.36017e6	0.114961
$970$	0	0
$971$	9.24976e6	0.314834	0.157417	−	0.987532i	$-0.449683\pi$
$971$	9.24976e6	0.314834	0.157417	+	0.987532i	$0.449683\pi$
$972$	−944784.	−0.0320750
$973$	−1.68295e7	−0.569889
$974$	−4.46806e6	−0.150911
$975$	0	0
$976$	−9.41107e6	−0.316238
$977$	4.97780e7	1.66840	0.834202	−	0.551459i	$-0.185929\pi$
$977$	4.97780e7	1.66840	0.834202	+	0.551459i	$0.185929\pi$
$978$	−1.71212e7	−0.572382
$979$	−8.14449e7	−2.71586
$980$	0	0
$981$	2.33264e6	0.0773882
$982$	5.37830e6	0.177978
$983$	8.95601e6	0.295618	0.147809	−	0.989016i	$-0.452778\pi$
$983$	8.95601e6	0.295618	0.147809	+	0.989016i	$0.452778\pi$
$984$	−6.07219e6	−0.199921
$985$	0	0
$986$	3.13489e7	1.02690
$987$	2.36023e6	0.0771191
$988$	−1.20077e6	−0.0391351
$989$	−1.86958e7	−0.607790
$990$	0	0
$991$	2.62400e7	0.848751	0.424376	−	0.905486i	$-0.360494\pi$
$991$	2.62400e7	0.848751	0.424376	+	0.905486i	$0.360494\pi$
$992$	−7.29907e6	−0.235499
$993$	−1.23439e7	−0.397265
$994$	−1.78203e6	−0.0572070
$995$	0	0
$996$	−925632.	−0.0295658
$997$	−2.80506e7	−0.893727	−0.446863	−	0.894602i	$-0.647459\pi$
$997$	−2.80506e7	−0.893727	−0.446863	+	0.894602i	$0.647459\pi$
$998$	−2.61859e7	−0.832226
$999$	3.17698e6	0.100717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.6.a.k.1.1		1
5.2	odd	4		1050.6.g.i.799.2		2
5.3	odd	4		1050.6.g.i.799.1		2
5.4	even	2		42.6.a.d.1.1	✓	1
15.14	odd	2		126.6.a.i.1.1		1
20.19	odd	2		336.6.a.h.1.1		1
35.4	even	6		294.6.e.i.79.1		2
35.9	even	6		294.6.e.i.67.1		2
35.19	odd	6		294.6.e.p.67.1		2
35.24	odd	6		294.6.e.p.79.1		2
35.34	odd	2		294.6.a.b.1.1		1
60.59	even	2		1008.6.a.j.1.1		1
105.104	even	2		882.6.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.6.a.d.1.1	✓	1	5.4	even	2
126.6.a.i.1.1		1	15.14	odd	2
294.6.a.b.1.1		1	35.34	odd	2
294.6.e.i.67.1		2	35.9	even	6
294.6.e.i.79.1		2	35.4	even	6
294.6.e.p.67.1		2	35.19	odd	6
294.6.e.p.79.1		2	35.24	odd	6
336.6.a.h.1.1		1	20.19	odd	2
882.6.a.s.1.1		1	105.104	even	2
1008.6.a.j.1.1		1	60.59	even	2
1050.6.a.k.1.1		1	1.1	even	1	trivial
1050.6.g.i.799.1		2	5.3	odd	4
1050.6.g.i.799.2		2	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1050.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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