LMFDB - Embedded newform 1083.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1083,6,Mod(1,1083)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1083, 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("1083.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1083 = 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1083.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:	$173.695676857$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1083.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -9.00000 q^{3} -28.0000 q^{4} -98.0000 q^{5} -18.0000 q^{6} +240.000 q^{7} -120.000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -9.00000 q^{3} -28.0000 q^{4} -98.0000 q^{5} -18.0000 q^{6} +240.000 q^{7} -120.000 q^{8} +81.0000 q^{9} -196.000 q^{10} +336.000 q^{11} +252.000 q^{12} -342.000 q^{13} +480.000 q^{14} +882.000 q^{15} +656.000 q^{16} -6.00000 q^{17} +162.000 q^{18} +2744.00 q^{20} -2160.00 q^{21} +672.000 q^{22} +2836.00 q^{23} +1080.00 q^{24} +6479.00 q^{25} -684.000 q^{26} -729.000 q^{27} -6720.00 q^{28} +5902.00 q^{29} +1764.00 q^{30} -2744.00 q^{31} +5152.00 q^{32} -3024.00 q^{33} -12.0000 q^{34} -23520.0 q^{35} -2268.00 q^{36} -13670.0 q^{37} +3078.00 q^{39} +11760.0 q^{40} -10990.0 q^{41} -4320.00 q^{42} -4996.00 q^{43} -9408.00 q^{44} -7938.00 q^{45} +5672.00 q^{46} -17124.0 q^{47} -5904.00 q^{48} +40793.0 q^{49} +12958.0 q^{50} +54.0000 q^{51} +9576.00 q^{52} +4470.00 q^{53} -1458.00 q^{54} -32928.0 q^{55} -28800.0 q^{56} +11804.0 q^{58} -26292.0 q^{59} -24696.0 q^{60} +29134.0 q^{61} -5488.00 q^{62} +19440.0 q^{63} -10688.0 q^{64} +33516.0 q^{65} -6048.00 q^{66} +42052.0 q^{67} +168.000 q^{68} -25524.0 q^{69} -47040.0 q^{70} +26112.0 q^{71} -9720.00 q^{72} -49046.0 q^{73} -27340.0 q^{74} -58311.0 q^{75} +80640.0 q^{77} +6156.00 q^{78} -79056.0 q^{79} -64288.0 q^{80} +6561.00 q^{81} -21980.0 q^{82} +9472.00 q^{83} +60480.0 q^{84} +588.000 q^{85} -9992.00 q^{86} -53118.0 q^{87} -40320.0 q^{88} -82894.0 q^{89} -15876.0 q^{90} -82080.0 q^{91} -79408.0 q^{92} +24696.0 q^{93} -34248.0 q^{94} -46368.0 q^{96} -39850.0 q^{97} +81586.0 q^{98} +27216.0 q^{99} +O(q^{100})\)

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 $

$2$	2.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	2.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−28.0000	−0.875000
$5$	−98.0000	−1.75308	−0.876539	−	0.481331i	$-0.840153\pi$
$5$	−98.0000	−1.75308	−0.876539	+	0.481331i	$0.840153\pi$
$6$	−18.0000	−0.204124
$7$	240.000	1.85125	0.925627	−	0.378436i	$-0.123538\pi$
$7$	240.000	1.85125	0.925627	+	0.378436i	$0.123538\pi$
$8$	−120.000	−0.662913
$9$	81.0000	0.333333
$10$	−196.000	−0.619806
$11$	336.000	0.837255	0.418627	−	0.908158i	$-0.362511\pi$
$11$	336.000	0.837255	0.418627	+	0.908158i	$0.362511\pi$
$12$	252.000	0.505181
$13$	−342.000	−0.561265	−0.280632	−	0.959815i	$-0.590544\pi$
$13$	−342.000	−0.561265	−0.280632	+	0.959815i	$0.590544\pi$
$14$	480.000	0.654517
$15$	882.000	1.01214
$16$	656.000	0.640625
$17$	−6.00000	−0.00503534	−0.00251767	−	0.999997i	$-0.500801\pi$
$17$	−6.00000	−0.00503534	−0.00251767	+	0.999997i	$0.500801\pi$
$18$	162.000	0.117851
$19$	0	0
$19$	0	0
$20$	2744.00	1.53394
$21$	−2160.00	−1.06882
$22$	672.000	0.296014
$23$	2836.00	1.11786	0.558929	−	0.829216i	$-0.311212\pi$
$23$	2836.00	1.11786	0.558929	+	0.829216i	$0.311212\pi$
$24$	1080.00	0.382733
$25$	6479.00	2.07328
$26$	−684.000	−0.198437
$27$	−729.000	−0.192450
$28$	−6720.00	−1.61985
$29$	5902.00	1.30318	0.651590	−	0.758572i	$-0.274102\pi$
$29$	5902.00	1.30318	0.651590	+	0.758572i	$0.274102\pi$
$30$	1764.00	0.357845
$31$	−2744.00	−0.512838	−0.256419	−	0.966566i	$-0.582543\pi$
$31$	−2744.00	−0.512838	−0.256419	+	0.966566i	$0.582543\pi$
$32$	5152.00	0.889408
$33$	−3024.00	−0.483389
$34$	−12.0000	−0.00178026
$35$	−23520.0	−3.24539
$36$	−2268.00	−0.291667
$37$	−13670.0	−1.64159	−0.820794	−	0.571224i	$-0.806469\pi$
$37$	−13670.0	−1.64159	−0.820794	+	0.571224i	$0.806469\pi$
$38$	0	0
$39$	3078.00	0.324046
$40$	11760.0	1.16214
$41$	−10990.0	−1.02103	−0.510514	−	0.859869i	$-0.670545\pi$
$41$	−10990.0	−1.02103	−0.510514	+	0.859869i	$0.670545\pi$
$42$	−4320.00	−0.377886
$43$	−4996.00	−0.412051	−0.206026	−	0.978547i	$-0.566053\pi$
$43$	−4996.00	−0.412051	−0.206026	+	0.978547i	$0.566053\pi$
$44$	−9408.00	−0.732598
$45$	−7938.00	−0.584359
$46$	5672.00	0.395222
$47$	−17124.0	−1.13073	−0.565367	−	0.824839i	$-0.691266\pi$
$47$	−17124.0	−1.13073	−0.565367	+	0.824839i	$0.691266\pi$
$48$	−5904.00	−0.369865
$49$	40793.0	2.42714
$50$	12958.0	0.733015
$51$	54.0000	0.00290716
$52$	9576.00	0.491107
$53$	4470.00	0.218584	0.109292	−	0.994010i	$-0.465142\pi$
$53$	4470.00	0.218584	0.109292	+	0.994010i	$0.465142\pi$
$54$	−1458.00	−0.0680414
$55$	−32928.0	−1.46777
$56$	−28800.0	−1.22722
$57$	0	0
$58$	11804.0	0.460743
$59$	−26292.0	−0.983317	−0.491659	−	0.870788i	$-0.663609\pi$
$59$	−26292.0	−0.983317	−0.491659	+	0.870788i	$0.663609\pi$
$60$	−24696.0	−0.885622
$61$	29134.0	1.00248	0.501240	−	0.865308i	$-0.332877\pi$
$61$	29134.0	1.00248	0.501240	+	0.865308i	$0.332877\pi$
$62$	−5488.00	−0.181315
$63$	19440.0	0.617085
$64$	−10688.0	−0.326172
$65$	33516.0	0.983940
$66$	−6048.00	−0.170904
$67$	42052.0	1.14446	0.572229	−	0.820094i	$-0.306079\pi$
$67$	42052.0	1.14446	0.572229	+	0.820094i	$0.306079\pi$
$68$	168.000	0.00440592
$69$	−25524.0	−0.645396
$70$	−47040.0	−1.14742
$71$	26112.0	0.614744	0.307372	−	0.951589i	$-0.400550\pi$
$71$	26112.0	0.614744	0.307372	+	0.951589i	$0.400550\pi$
$72$	−9720.00	−0.220971
$73$	−49046.0	−1.07720	−0.538600	−	0.842562i	$-0.681047\pi$
$73$	−49046.0	−1.07720	−0.538600	+	0.842562i	$0.681047\pi$
$74$	−27340.0	−0.580389
$75$	−58311.0	−1.19701
$76$	0	0
$77$	80640.0	1.54997
$78$	6156.00	0.114568
$79$	−79056.0	−1.42517	−0.712586	−	0.701585i	$-0.752476\pi$
$79$	−79056.0	−1.42517	−0.712586	+	0.701585i	$0.752476\pi$
$80$	−64288.0	−1.12307
$81$	6561.00	0.111111
$82$	−21980.0	−0.360988
$83$	9472.00	0.150920	0.0754599	−	0.997149i	$-0.475958\pi$
$83$	9472.00	0.150920	0.0754599	+	0.997149i	$0.475958\pi$
$84$	60480.0	0.935220
$85$	588.000	0.00882734
$86$	−9992.00	−0.145682
$87$	−53118.0	−0.752391
$88$	−40320.0	−0.555027
$89$	−82894.0	−1.10930	−0.554649	−	0.832085i	$-0.687147\pi$
$89$	−82894.0	−1.10930	−0.554649	+	0.832085i	$0.687147\pi$
$90$	−15876.0	−0.206602
$91$	−82080.0	−1.03904
$92$	−79408.0	−0.978126
$93$	24696.0	0.296087
$94$	−34248.0	−0.399775
$95$	0	0
$96$	−46368.0	−0.513500
$97$	−39850.0	−0.430030	−0.215015	−	0.976611i	$-0.568980\pi$
$97$	−39850.0	−0.430030	−0.215015	+	0.976611i	$0.568980\pi$
$98$	81586.0	0.858125
$99$	27216.0	0.279085
$100$	−181412.	−1.81412
$101$	99542.0	0.970964	0.485482	−	0.874247i	$-0.338644\pi$
$101$	99542.0	0.970964	0.485482	+	0.874247i	$0.338644\pi$
$102$	108.000	0.00102783
$103$	−69368.0	−0.644267	−0.322134	−	0.946694i	$-0.604400\pi$
$103$	−69368.0	−0.644267	−0.322134	+	0.946694i	$0.604400\pi$
$104$	41040.0	0.372069
$105$	211680.	1.87373
$106$	8940.00	0.0772810
$107$	110204.	0.930546	0.465273	−	0.885167i	$-0.345956\pi$
$107$	110204.	0.930546	0.465273	+	0.885167i	$0.345956\pi$
$108$	20412.0	0.168394
$109$	217786.	1.75575	0.877877	−	0.478886i	$-0.158959\pi$
$109$	217786.	1.75575	0.877877	+	0.478886i	$0.158959\pi$
$110$	−65856.0	−0.518936
$111$	123030.	0.947771
$112$	157440.	1.18596
$113$	84618.0	0.623400	0.311700	−	0.950181i	$-0.399102\pi$
$113$	84618.0	0.623400	0.311700	+	0.950181i	$0.399102\pi$
$114$	0	0
$115$	−277928.	−1.95969
$116$	−165256.	−1.14028
$117$	−27702.0	−0.187088
$118$	−52584.0	−0.347655
$119$	−1440.00	−0.00932170
$120$	−105840.	−0.670960
$121$	−48155.0	−0.299005
$122$	58268.0	0.354430
$123$	98910.0	0.589491
$124$	76832.0	0.448733
$125$	−328692.	−1.88154
$126$	38880.0	0.218172
$127$	−89608.0	−0.492989	−0.246495	−	0.969144i	$-0.579279\pi$
$127$	−89608.0	−0.492989	−0.246495	+	0.969144i	$0.579279\pi$
$128$	−186240.	−1.00473
$129$	44964.0	0.237898
$130$	67032.0	0.347875
$131$	255992.	1.30331	0.651656	−	0.758515i	$-0.274075\pi$
$131$	255992.	1.30331	0.651656	+	0.758515i	$0.274075\pi$
$132$	84672.0	0.422966
$133$	0	0
$134$	84104.0	0.404627
$135$	71442.0	0.337380
$136$	720.000	0.00333799
$137$	50226.0	0.228627	0.114313	−	0.993445i	$-0.463533\pi$
$137$	50226.0	0.228627	0.114313	+	0.993445i	$0.463533\pi$
$138$	−51048.0	−0.228182
$139$	−242108.	−1.06285	−0.531425	−	0.847105i	$-0.678343\pi$
$139$	−242108.	−1.06285	−0.531425	+	0.847105i	$0.678343\pi$
$140$	658560.	2.83972
$141$	154116.	0.652830
$142$	52224.0	0.217345
$143$	−114912.	−0.469921
$144$	53136.0	0.213542
$145$	−578396.	−2.28457
$146$	−98092.0	−0.380848
$147$	−367137.	−1.40131
$148$	382760.	1.43639
$149$	−352506.	−1.30077	−0.650385	−	0.759604i	$-0.725393\pi$
$149$	−352506.	−1.30077	−0.650385	+	0.759604i	$0.725393\pi$
$150$	−116622.	−0.423207
$151$	272120.	0.971221	0.485611	−	0.874175i	$-0.338597\pi$
$151$	272120.	0.971221	0.485611	+	0.874175i	$0.338597\pi$
$152$	0	0
$153$	−486.000	−0.00167845
$154$	161280.	0.547998
$155$	268912.	0.899044
$156$	−86184.0	−0.283541
$157$	124942.	0.404538	0.202269	−	0.979330i	$-0.435168\pi$
$157$	124942.	0.404538	0.202269	+	0.979330i	$0.435168\pi$
$158$	−158112.	−0.503874
$159$	−40230.0	−0.126199
$160$	−504896.	−1.55920
$161$	680640.	2.06944
$162$	13122.0	0.0392837
$163$	−28900.0	−0.0851979	−0.0425989	−	0.999092i	$-0.513564\pi$
$163$	−28900.0	−0.0851979	−0.0425989	+	0.999092i	$0.513564\pi$
$164$	307720.	0.893400
$165$	296352.	0.847419
$166$	18944.0	0.0533582
$167$	−370200.	−1.02718	−0.513588	−	0.858037i	$-0.671684\pi$
$167$	−370200.	−1.02718	−0.513588	+	0.858037i	$0.671684\pi$
$168$	259200.	0.708536
$169$	−254329.	−0.684982
$170$	1176.00	0.00312094
$171$	0	0
$172$	139888.	0.360545
$173$	277414.	0.704714	0.352357	−	0.935866i	$-0.385380\pi$
$173$	277414.	0.704714	0.352357	+	0.935866i	$0.385380\pi$
$174$	−106236.	−0.266010
$175$	1.55496e6	3.83817
$176$	220416.	0.536366
$177$	236628.	0.567718
$178$	−165788.	−0.392196
$179$	439108.	1.02433	0.512164	−	0.858888i	$-0.328844\pi$
$179$	439108.	1.02433	0.512164	+	0.858888i	$0.328844\pi$
$180$	222264.	0.511314
$181$	−25406.0	−0.0576421	−0.0288211	−	0.999585i	$-0.509175\pi$
$181$	−25406.0	−0.0576421	−0.0288211	+	0.999585i	$0.509175\pi$
$182$	−164160.	−0.367357
$183$	−262206.	−0.578782
$184$	−340320.	−0.741042
$185$	1.33966e6	2.87783
$186$	49392.0	0.104683
$187$	−2016.00	−0.00421586
$188$	479472.	0.989393
$189$	−174960.	−0.356274
$190$	0	0
$191$	640644.	1.27067	0.635336	−	0.772236i	$-0.280862\pi$
$191$	640644.	1.27067	0.635336	+	0.772236i	$0.280862\pi$
$192$	96192.0	0.188315
$193$	224846.	0.434502	0.217251	−	0.976116i	$-0.430291\pi$
$193$	224846.	0.434502	0.217251	+	0.976116i	$0.430291\pi$
$194$	−79700.0	−0.152039
$195$	−301644.	−0.568078
$196$	−1.14220e6	−2.12375
$197$	325438.	0.597452	0.298726	−	0.954339i	$-0.403438\pi$
$197$	325438.	0.597452	0.298726	+	0.954339i	$0.403438\pi$
$198$	54432.0	0.0986714
$199$	−983576.	−1.76066	−0.880329	−	0.474363i	$-0.842679\pi$
$199$	−983576.	−1.76066	−0.880329	+	0.474363i	$0.842679\pi$
$200$	−777480.	−1.37440
$201$	−378468.	−0.660753
$202$	199084.	0.343287
$203$	1.41648e6	2.41252
$204$	−1512.00	−0.00254376
$205$	1.07702e6	1.78994
$206$	−138736.	−0.227783
$207$	229716.	0.372619
$208$	−224352.	−0.359560
$209$	0	0
$210$	423360.	0.662463
$211$	866308.	1.33957	0.669786	−	0.742554i	$-0.266386\pi$
$211$	866308.	1.33957	0.669786	+	0.742554i	$0.266386\pi$
$212$	−125160.	−0.191261
$213$	−235008.	−0.354923
$214$	220408.	0.328998
$215$	489608.	0.722358
$216$	87480.0	0.127578
$217$	−658560.	−0.949393
$218$	435572.	0.620753
$219$	441414.	0.621922
$220$	921984.	1.28430
$221$	2052.00	0.00282616
$222$	246060.	0.335088
$223$	76928.0	0.103591	0.0517955	−	0.998658i	$-0.483506\pi$
$223$	76928.0	0.103591	0.0517955	+	0.998658i	$0.483506\pi$
$224$	1.23648e6	1.64652
$225$	524799.	0.691093
$226$	169236.	0.220405
$227$	969612.	1.24892	0.624458	−	0.781058i	$-0.285320\pi$
$227$	969612.	1.24892	0.624458	+	0.781058i	$0.285320\pi$
$228$	0	0
$229$	840150.	1.05869	0.529344	−	0.848407i	$-0.322438\pi$
$229$	840150.	1.05869	0.529344	+	0.848407i	$0.322438\pi$
$230$	−555856.	−0.692856
$231$	−725760.	−0.894876
$232$	−708240.	−0.863894
$233$	575914.	0.694973	0.347486	−	0.937685i	$-0.387035\pi$
$233$	575914.	0.694973	0.347486	+	0.937685i	$0.387035\pi$
$234$	−55404.0	−0.0661457
$235$	1.67815e6	1.98226
$236$	736176.	0.860402
$237$	711504.	0.822823
$238$	−2880.00	−0.00329572
$239$	−352188.	−0.398823	−0.199411	−	0.979916i	$-0.563903\pi$
$239$	−352188.	−0.398823	−0.199411	+	0.979916i	$0.563903\pi$
$240$	578592.	0.648402
$241$	−451290.	−0.500510	−0.250255	−	0.968180i	$-0.580515\pi$
$241$	−451290.	−0.500510	−0.250255	+	0.968180i	$0.580515\pi$
$242$	−96310.0	−0.105714
$243$	−59049.0	−0.0641500
$244$	−815752.	−0.877170
$245$	−3.99771e6	−4.25497
$246$	197820.	0.208417
$247$	0	0
$248$	329280.	0.339967
$249$	−85248.0	−0.0871336
$250$	−657384.	−0.665226
$251$	145752.	0.146026	0.0730130	−	0.997331i	$-0.476739\pi$
$251$	145752.	0.146026	0.0730130	+	0.997331i	$0.476739\pi$
$252$	−544320.	−0.539949
$253$	952896.	0.935932
$254$	−179216.	−0.174298
$255$	−5292.00	−0.00509647
$256$	−30464.0	−0.0290527
$257$	1.87818e6	1.77380	0.886899	−	0.461964i	$-0.152855\pi$
$257$	1.87818e6	1.77380	0.886899	+	0.461964i	$0.152855\pi$
$258$	89928.0	0.0841096
$259$	−3.28080e6	−3.03900
$260$	−938448.	−0.860948
$261$	478062.	0.434393
$262$	511984.	0.460790
$263$	895068.	0.797933	0.398967	−	0.916965i	$-0.369369\pi$
$263$	895068.	0.797933	0.398967	+	0.916965i	$0.369369\pi$
$264$	362880.	0.320445
$265$	−438060.	−0.383194
$266$	0	0
$267$	746046.	0.640453
$268$	−1.17746e6	−1.00140
$269$	−1.27291e6	−1.07255	−0.536273	−	0.844045i	$-0.680168\pi$
$269$	−1.27291e6	−1.07255	−0.536273	+	0.844045i	$0.680168\pi$
$270$	142884.	0.119282
$271$	306672.	0.253659	0.126830	−	0.991925i	$-0.459520\pi$
$271$	306672.	0.253659	0.126830	+	0.991925i	$0.459520\pi$
$272$	−3936.00	−0.00322577
$273$	738720.	0.599892
$274$	100452.	0.0808318
$275$	2.17694e6	1.73586
$276$	714672.	0.564721
$277$	−192026.	−0.150370	−0.0751849	−	0.997170i	$-0.523955\pi$
$277$	−192026.	−0.150370	−0.0751849	+	0.997170i	$0.523955\pi$
$278$	−484216.	−0.375774
$279$	−222264.	−0.170946
$280$	2.82240e6	2.15141
$281$	−1.00055e6	−0.755915	−0.377958	−	0.925823i	$-0.623373\pi$
$281$	−1.00055e6	−0.755915	−0.377958	+	0.925823i	$0.623373\pi$
$282$	308232.	0.230810
$283$	−1.26847e6	−0.941485	−0.470743	−	0.882271i	$-0.656014\pi$
$283$	−1.26847e6	−0.941485	−0.470743	+	0.882271i	$0.656014\pi$
$284$	−731136.	−0.537901
$285$	0	0
$286$	−229824.	−0.166142
$287$	−2.63760e6	−1.89018
$288$	417312.	0.296469
$289$	−1.41982e6	−0.999975
$290$	−1.15679e6	−0.807719
$291$	358650.	0.248278
$292$	1.37329e6	0.942550
$293$	1.52560e6	1.03818	0.519088	−	0.854721i	$-0.326272\pi$
$293$	1.52560e6	1.03818	0.519088	+	0.854721i	$0.326272\pi$
$294$	−734274.	−0.495439
$295$	2.57662e6	1.72383
$296$	1.64040e6	1.08823
$297$	−244944.	−0.161130
$298$	−705012.	−0.459892
$299$	−969912.	−0.627414
$300$	1.63271e6	1.04738
$301$	−1.19904e6	−0.762812
$302$	544240.	0.343379
$303$	−895878.	−0.560586
$304$	0	0
$305$	−2.85513e6	−1.75742
$306$	−972.000	−0.000593421 0
$307$	1.19665e6	0.724639	0.362320	−	0.932054i	$-0.381985\pi$
$307$	1.19665e6	0.724639	0.362320	+	0.932054i	$0.381985\pi$
$308$	−2.25792e6	−1.35623
$309$	624312.	0.371968
$310$	537824.	0.317860
$311$	2.37144e6	1.39031	0.695155	−	0.718859i	$-0.255336\pi$
$311$	2.37144e6	1.39031	0.695155	+	0.718859i	$0.255336\pi$
$312$	−369360.	−0.214814
$313$	353738.	0.204090	0.102045	−	0.994780i	$-0.467461\pi$
$313$	353738.	0.204090	0.102045	+	0.994780i	$0.467461\pi$
$314$	249884.	0.143026
$315$	−1.90512e6	−1.08180
$316$	2.21357e6	1.24703
$317$	−2.70427e6	−1.51148	−0.755738	−	0.654874i	$-0.772722\pi$
$317$	−2.70427e6	−1.51148	−0.755738	+	0.654874i	$0.772722\pi$
$318$	−80460.0	−0.0446182
$319$	1.98307e6	1.09109
$320$	1.04742e6	0.571805
$321$	−991836.	−0.537251
$322$	1.36128e6	0.731657
$323$	0	0
$324$	−183708.	−0.0972222
$325$	−2.21582e6	−1.16366
$326$	−57800.0	−0.0301220
$327$	−1.96007e6	−1.01369
$328$	1.31880e6	0.676853
$329$	−4.10976e6	−2.09328
$330$	592704.	0.299608
$331$	327444.	0.164273	0.0821367	−	0.996621i	$-0.473826\pi$
$331$	327444.	0.164273	0.0821367	+	0.996621i	$0.473826\pi$
$332$	−265216.	−0.132055
$333$	−1.10727e6	−0.547196
$334$	−740400.	−0.363162
$335$	−4.12110e6	−2.00632
$336$	−1.41696e6	−0.684714
$337$	−367946.	−0.176486	−0.0882428	−	0.996099i	$-0.528125\pi$
$337$	−367946.	−0.176486	−0.0882428	+	0.996099i	$0.528125\pi$
$338$	−508658.	−0.242178
$339$	−761562.	−0.359920
$340$	−16464.0	−0.00772393
$341$	−921984.	−0.429376
$342$	0	0
$343$	5.75664e6	2.64201
$344$	599520.	0.273154
$345$	2.50135e6	1.13143
$346$	554828.	0.249154
$347$	566160.	0.252415	0.126208	−	0.992004i	$-0.459719\pi$
$347$	566160.	0.252415	0.126208	+	0.992004i	$0.459719\pi$
$348$	1.48730e6	0.658342
$349$	−4.50687e6	−1.98067	−0.990333	−	0.138713i	$-0.955703\pi$
$349$	−4.50687e6	−1.98067	−0.990333	+	0.138713i	$0.955703\pi$
$350$	3.10992e6	1.35700
$351$	249318.	0.108015
$352$	1.73107e6	0.744661
$353$	−1.09778e6	−0.468899	−0.234450	−	0.972128i	$-0.575329\pi$
$353$	−1.09778e6	−0.468899	−0.234450	+	0.972128i	$0.575329\pi$
$354$	473256.	0.200719
$355$	−2.55898e6	−1.07769
$356$	2.32103e6	0.970635
$357$	12960.0	0.00538189
$358$	878216.	0.362154
$359$	−1.95223e6	−0.799456	−0.399728	−	0.916634i	$-0.630895\pi$
$359$	−1.95223e6	−0.799456	−0.399728	+	0.916634i	$0.630895\pi$
$360$	952560.	0.387379
$361$	0	0
$362$	−50812.0	−0.0203796
$363$	433395.	0.172630
$364$	2.29824e6	0.909163
$365$	4.80651e6	1.88842
$366$	−524412.	−0.204630
$367$	1.49163e6	0.578091	0.289046	−	0.957315i	$-0.406662\pi$
$367$	1.49163e6	0.578091	0.289046	+	0.957315i	$0.406662\pi$
$368$	1.86042e6	0.716128
$369$	−890190.	−0.340343
$370$	2.67932e6	1.01747
$371$	1.07280e6	0.404654
$372$	−691488.	−0.259076
$373$	−1.48305e6	−0.551928	−0.275964	−	0.961168i	$-0.588997\pi$
$373$	−1.48305e6	−0.551928	−0.275964	+	0.961168i	$0.588997\pi$
$374$	−4032.00	−0.00149053
$375$	2.95823e6	1.08631
$376$	2.05488e6	0.749578
$377$	−2.01848e6	−0.731429
$378$	−349920.	−0.125962
$379$	2.79436e6	0.999272	0.499636	−	0.866235i	$-0.333467\pi$
$379$	2.79436e6	0.999272	0.499636	+	0.866235i	$0.333467\pi$
$380$	0	0
$381$	806472.	0.284627
$382$	1.28129e6	0.449250
$383$	−2.06910e6	−0.720748	−0.360374	−	0.932808i	$-0.617351\pi$
$383$	−2.06910e6	−0.720748	−0.360374	+	0.932808i	$0.617351\pi$
$384$	1.67616e6	0.580079
$385$	−7.90272e6	−2.71722
$386$	449692.	0.153620
$387$	−404676.	−0.137350
$388$	1.11580e6	0.376276
$389$	4.61696e6	1.54697	0.773485	−	0.633815i	$-0.218512\pi$
$389$	4.61696e6	1.54697	0.773485	+	0.633815i	$0.218512\pi$
$390$	−603288.	−0.200846
$391$	−17016.0	−0.00562880
$392$	−4.89516e6	−1.60898
$393$	−2.30393e6	−0.752467
$394$	650876.	0.211231
$395$	7.74749e6	2.49844
$396$	−762048.	−0.244199
$397$	875870.	0.278910	0.139455	−	0.990228i	$-0.455465\pi$
$397$	875870.	0.278910	0.139455	+	0.990228i	$0.455465\pi$
$398$	−1.96715e6	−0.622487
$399$	0	0
$400$	4.25022e6	1.32820
$401$	3.36615e6	1.04538	0.522689	−	0.852524i	$-0.324929\pi$
$401$	3.36615e6	1.04538	0.522689	+	0.852524i	$0.324929\pi$
$402$	−756936.	−0.233611
$403$	938448.	0.287838
$404$	−2.78718e6	−0.849593
$405$	−642978.	−0.194786
$406$	2.83296e6	0.852954
$407$	−4.59312e6	−1.37443
$408$	−6480.00	−0.00192719
$409$	−6.58655e6	−1.94693	−0.973463	−	0.228844i	$-0.926505\pi$
$409$	−6.58655e6	−1.94693	−0.973463	+	0.228844i	$0.926505\pi$
$410$	2.15404e6	0.632840
$411$	−452034.	−0.131998
$412$	1.94230e6	0.563734
$413$	−6.31008e6	−1.82037
$414$	459432.	0.131741
$415$	−928256.	−0.264574
$416$	−1.76198e6	−0.499193
$417$	2.17897e6	0.613637
$418$	0	0
$419$	−1.06775e6	−0.297122	−0.148561	−	0.988903i	$-0.547464\pi$
$419$	−1.06775e6	−0.297122	−0.148561	+	0.988903i	$0.547464\pi$
$420$	−5.92704e6	−1.63951
$421$	−3.60621e6	−0.991620	−0.495810	−	0.868431i	$-0.665129\pi$
$421$	−3.60621e6	−0.991620	−0.495810	+	0.868431i	$0.665129\pi$
$422$	1.73262e6	0.473610
$423$	−1.38704e6	−0.376911
$424$	−536400.	−0.144902
$425$	−38874.0	−0.0104397
$426$	−470016.	−0.125484
$427$	6.99216e6	1.85584
$428$	−3.08571e6	−0.814228
$429$	1.03421e6	0.271309
$430$	979216.	0.255392
$431$	−1.05310e6	−0.273071	−0.136535	−	0.990635i	$-0.543597\pi$
$431$	−1.05310e6	−0.273071	−0.136535	+	0.990635i	$0.543597\pi$
$432$	−478224.	−0.123288
$433$	3.45697e6	0.886087	0.443044	−	0.896500i	$-0.353899\pi$
$433$	3.45697e6	0.886087	0.443044	+	0.896500i	$0.353899\pi$
$434$	−1.31712e6	−0.335661
$435$	5.20556e6	1.31900
$436$	−6.09801e6	−1.53628
$437$	0	0
$438$	882828.	0.219883
$439$	5.88610e6	1.45769	0.728847	−	0.684676i	$-0.240056\pi$
$439$	5.88610e6	1.45769	0.728847	+	0.684676i	$0.240056\pi$
$440$	3.95136e6	0.973005
$441$	3.30423e6	0.809048
$442$	4104.00	0.000999198 0
$443$	−4.80216e6	−1.16259	−0.581296	−	0.813692i	$-0.697454\pi$
$443$	−4.80216e6	−1.16259	−0.581296	+	0.813692i	$0.697454\pi$
$444$	−3.44484e6	−0.829300
$445$	8.12361e6	1.94468
$446$	153856.	0.0366250
$447$	3.17255e6	0.751000
$448$	−2.56512e6	−0.603827
$449$	3.17967e6	0.744330	0.372165	−	0.928167i	$-0.378616\pi$
$449$	3.17967e6	0.744330	0.372165	+	0.928167i	$0.378616\pi$
$450$	1.04960e6	0.244338
$451$	−3.69264e6	−0.854861
$452$	−2.36930e6	−0.545475
$453$	−2.44908e6	−0.560735
$454$	1.93922e6	0.441559
$455$	8.04384e6	1.82152
$456$	0	0
$457$	483546.	0.108305	0.0541523	−	0.998533i	$-0.482754\pi$
$457$	483546.	0.108305	0.0541523	+	0.998533i	$0.482754\pi$
$458$	1.68030e6	0.374303
$459$	4374.00	0.000969052 0
$460$	7.78198e6	1.71473
$461$	707982.	0.155156	0.0775782	−	0.996986i	$-0.475281\pi$
$461$	707982.	0.155156	0.0775782	+	0.996986i	$0.475281\pi$
$462$	−1.45152e6	−0.316387
$463$	8.24091e6	1.78658	0.893291	−	0.449479i	$-0.148390\pi$
$463$	8.24091e6	1.78658	0.893291	+	0.449479i	$0.148390\pi$
$464$	3.87171e6	0.834849
$465$	−2.42021e6	−0.519063
$466$	1.15183e6	0.245710
$467$	2.13640e6	0.453305	0.226652	−	0.973976i	$-0.427222\pi$
$467$	2.13640e6	0.453305	0.226652	+	0.973976i	$0.427222\pi$
$468$	775656.	0.163702
$469$	1.00925e7	2.11868
$470$	3.35630e6	0.700836
$471$	−1.12448e6	−0.233560
$472$	3.15504e6	0.651853
$473$	−1.67866e6	−0.344992
$474$	1.42301e6	0.290912
$475$	0	0
$476$	40320.0	0.00815649
$477$	362070.	0.0728612
$478$	−704376.	−0.141005
$479$	1.20736e6	0.240436	0.120218	−	0.992748i	$-0.461641\pi$
$479$	1.20736e6	0.240436	0.120218	+	0.992748i	$0.461641\pi$
$480$	4.54406e6	0.900205
$481$	4.67514e6	0.921365
$482$	−902580.	−0.176957
$483$	−6.12576e6	−1.19479
$484$	1.34834e6	0.261629
$485$	3.90530e6	0.753876
$486$	−118098.	−0.0226805
$487$	8.77970e6	1.67748	0.838739	−	0.544533i	$-0.183293\pi$
$487$	8.77970e6	1.67748	0.838739	+	0.544533i	$0.183293\pi$
$488$	−3.49608e6	−0.664556
$489$	260100.	0.0491890
$490$	−7.99543e6	−1.50436
$491$	4.23400e6	0.792587	0.396294	−	0.918124i	$-0.370296\pi$
$491$	4.23400e6	0.792587	0.396294	+	0.918124i	$0.370296\pi$
$492$	−2.76948e6	−0.515805
$493$	−35412.0	−0.00656195
$494$	0	0
$495$	−2.66717e6	−0.489257
$496$	−1.80006e6	−0.328537
$497$	6.26688e6	1.13805
$498$	−170496.	−0.0308064
$499$	−1.73450e6	−0.311834	−0.155917	−	0.987770i	$-0.549833\pi$
$499$	−1.73450e6	−0.311834	−0.155917	+	0.987770i	$0.549833\pi$
$500$	9.20338e6	1.64635
$501$	3.33180e6	0.593041
$502$	291504.	0.0516280
$503$	−4.72352e6	−0.832427	−0.416214	−	0.909267i	$-0.636643\pi$
$503$	−4.72352e6	−0.832427	−0.416214	+	0.909267i	$0.636643\pi$
$504$	−2.33280e6	−0.409073
$505$	−9.75512e6	−1.70217
$506$	1.90579e6	0.330902
$507$	2.28896e6	0.395475
$508$	2.50902e6	0.431366
$509$	2.49741e6	0.427264	0.213632	−	0.976914i	$-0.431471\pi$
$509$	2.49741e6	0.427264	0.213632	+	0.976914i	$0.431471\pi$
$510$	−10584.0	−0.00180187
$511$	−1.17710e7	−1.99417
$512$	5.89875e6	0.994455
$513$	0	0
$514$	3.75636e6	0.627132
$515$	6.79806e6	1.12945
$516$	−1.25899e6	−0.208161
$517$	−5.75366e6	−0.946713
$518$	−6.56160e6	−1.07445
$519$	−2.49673e6	−0.406867
$520$	−4.02192e6	−0.652266
$521$	−2.86413e6	−0.462272	−0.231136	−	0.972921i	$-0.574244\pi$
$521$	−2.86413e6	−0.462272	−0.231136	+	0.972921i	$0.574244\pi$
$522$	956124.	0.153581
$523$	−2.46228e6	−0.393625	−0.196812	−	0.980441i	$-0.563059\pi$
$523$	−2.46228e6	−0.393625	−0.196812	+	0.980441i	$0.563059\pi$
$524$	−7.16778e6	−1.14040
$525$	−1.39946e7	−2.21597
$526$	1.79014e6	0.282112
$527$	16464.0	0.00258231
$528$	−1.98374e6	−0.309671
$529$	1.60655e6	0.249606
$530$	−876120.	−0.135480
$531$	−2.12965e6	−0.327772
$532$	0	0
$533$	3.75858e6	0.573067
$534$	1.49209e6	0.226434
$535$	−1.08000e7	−1.63132
$536$	−5.04624e6	−0.758675
$537$	−3.95197e6	−0.591396
$538$	−2.54581e6	−0.379202
$539$	1.37064e7	2.03214
$540$	−2.00038e6	−0.295207
$541$	6.88192e6	1.01092	0.505459	−	0.862850i	$-0.331323\pi$
$541$	6.88192e6	1.01092	0.505459	+	0.862850i	$0.331323\pi$
$542$	613344.	0.0896821
$543$	228654.	0.0332797
$544$	−30912.0	−0.00447847
$545$	−2.13430e7	−3.07797
$546$	1.47744e6	0.212094
$547$	4.99680e6	0.714041	0.357021	−	0.934097i	$-0.383793\pi$
$547$	4.99680e6	0.714041	0.357021	+	0.934097i	$0.383793\pi$
$548$	−1.40633e6	−0.200048
$549$	2.35985e6	0.334160
$550$	4.35389e6	0.613720
$551$	0	0
$552$	3.06288e6	0.427841
$553$	−1.89734e7	−2.63836
$554$	−384052.	−0.0531638
$555$	−1.20569e7	−1.66152
$556$	6.77902e6	0.929994
$557$	−8.42887e6	−1.15115	−0.575574	−	0.817750i	$-0.695221\pi$
$557$	−8.42887e6	−1.15115	−0.575574	+	0.817750i	$0.695221\pi$
$558$	−444528.	−0.0604385
$559$	1.70863e6	0.231270
$560$	−1.54291e7	−2.07908
$561$	18144.0	0.00243403
$562$	−2.00110e6	−0.267256
$563$	1.01781e7	1.35330	0.676652	−	0.736303i	$-0.263430\pi$
$563$	1.01781e7	1.35330	0.676652	+	0.736303i	$0.263430\pi$
$564$	−4.31525e6	−0.571226
$565$	−8.29256e6	−1.09287
$566$	−2.53694e6	−0.332865
$567$	1.57464e6	0.205695
$568$	−3.13344e6	−0.407522
$569$	−1.13792e7	−1.47344	−0.736719	−	0.676199i	$-0.763626\pi$
$569$	−1.13792e7	−1.47344	−0.736719	+	0.676199i	$0.763626\pi$
$570$	0	0
$571$	−7.57426e6	−0.972187	−0.486094	−	0.873907i	$-0.661579\pi$
$571$	−7.57426e6	−0.972187	−0.486094	+	0.873907i	$0.661579\pi$
$572$	3.21754e6	0.411181
$573$	−5.76580e6	−0.733623
$574$	−5.27520e6	−0.668281
$575$	1.83744e7	2.31763
$576$	−865728.	−0.108724
$577$	−6.06488e6	−0.758372	−0.379186	−	0.925320i	$-0.623796\pi$
$577$	−6.06488e6	−0.758372	−0.379186	+	0.925320i	$0.623796\pi$
$578$	−2.83964e6	−0.353544
$579$	−2.02361e6	−0.250860
$580$	1.61951e7	1.99900
$581$	2.27328e6	0.279391
$582$	717300.	0.0877796
$583$	1.50192e6	0.183010
$584$	5.88552e6	0.714090
$585$	2.71480e6	0.327980
$586$	3.05120e6	0.367051
$587$	1.62011e7	1.94066	0.970330	−	0.241783i	$-0.0777323\pi$
$587$	1.62011e7	1.94066	0.970330	+	0.241783i	$0.0777323\pi$
$588$	1.02798e7	1.22615
$589$	0	0
$590$	5.15323e6	0.609466
$591$	−2.92894e6	−0.344939
$592$	−8.96752e6	−1.05164
$593$	9.92291e6	1.15878	0.579392	−	0.815049i	$-0.303290\pi$
$593$	9.92291e6	1.15878	0.579392	+	0.815049i	$0.303290\pi$
$594$	−489888.	−0.0569680
$595$	141120.	0.0163417
$596$	9.87017e6	1.13817
$597$	8.85218e6	1.01652
$598$	−1.93982e6	−0.221824
$599$	9.55020e6	1.08754	0.543770	−	0.839234i	$-0.316996\pi$
$599$	9.55020e6	1.08754	0.543770	+	0.839234i	$0.316996\pi$
$600$	6.99732e6	0.793512
$601$	−1.57009e6	−0.177312	−0.0886560	−	0.996062i	$-0.528257\pi$
$601$	−1.57009e6	−0.177312	−0.0886560	+	0.996062i	$0.528257\pi$
$602$	−2.39808e6	−0.269695
$603$	3.40621e6	0.381486
$604$	−7.61936e6	−0.849818
$605$	4.71919e6	0.524178
$606$	−1.79176e6	−0.198197
$607$	−8.83870e6	−0.973680	−0.486840	−	0.873491i	$-0.661851\pi$
$607$	−8.83870e6	−0.973680	−0.486840	+	0.873491i	$0.661851\pi$
$608$	0	0
$609$	−1.27483e7	−1.39287
$610$	−5.71026e6	−0.621343
$611$	5.85641e6	0.634641
$612$	13608.0	0.00146864
$613$	−4.94068e6	−0.531050	−0.265525	−	0.964104i	$-0.585545\pi$
$613$	−4.94068e6	−0.531050	−0.265525	+	0.964104i	$0.585545\pi$
$614$	2.39330e6	0.256199
$615$	−9.69318e6	−1.03342
$616$	−9.67680e6	−1.02750
$617$	−5.44608e6	−0.575932	−0.287966	−	0.957641i	$-0.592979\pi$
$617$	−5.44608e6	−0.575932	−0.287966	+	0.957641i	$0.592979\pi$
$618$	1.24862e6	0.131511
$619$	9.25648e6	0.971000	0.485500	−	0.874237i	$-0.338637\pi$
$619$	9.25648e6	0.971000	0.485500	+	0.874237i	$0.338637\pi$
$620$	−7.52954e6	−0.786663
$621$	−2.06744e6	−0.215132
$622$	4.74289e6	0.491549
$623$	−1.98946e7	−2.05359
$624$	2.01917e6	0.207592
$625$	1.19649e7	1.22521
$626$	707476.	0.0721566
$627$	0	0
$628$	−3.49838e6	−0.353971
$629$	82020.0	0.00826596
$630$	−3.81024e6	−0.382473
$631$	−1.84220e7	−1.84189	−0.920944	−	0.389694i	$-0.872581\pi$
$631$	−1.84220e7	−1.84189	−0.920944	+	0.389694i	$0.872581\pi$
$632$	9.48672e6	0.944764
$633$	−7.79677e6	−0.773402
$634$	−5.40853e6	−0.534387
$635$	8.78158e6	0.864248
$636$	1.12644e6	0.110424
$637$	−1.39512e7	−1.36227
$638$	3.96614e6	0.385760
$639$	2.11507e6	0.204915
$640$	1.82515e7	1.76136
$641$	1.83640e7	1.76532	0.882660	−	0.470013i	$-0.155751\pi$
$641$	1.83640e7	1.76532	0.882660	+	0.470013i	$0.155751\pi$
$642$	−1.98367e6	−0.189947
$643$	5.30824e6	0.506318	0.253159	−	0.967425i	$-0.418530\pi$
$643$	5.30824e6	0.506318	0.253159	+	0.967425i	$0.418530\pi$
$644$	−1.90579e7	−1.81076
$645$	−4.40647e6	−0.417053
$646$	0	0
$647$	−3.32276e6	−0.312060	−0.156030	−	0.987752i	$-0.549870\pi$
$647$	−3.32276e6	−0.312060	−0.156030	+	0.987752i	$0.549870\pi$
$648$	−787320.	−0.0736570
$649$	−8.83411e6	−0.823287
$650$	−4.43164e6	−0.411416
$651$	5.92704e6	0.548132
$652$	809200.	0.0745482
$653$	−5.81096e6	−0.533292	−0.266646	−	0.963795i	$-0.585915\pi$
$653$	−5.81096e6	−0.533292	−0.266646	+	0.963795i	$0.585915\pi$
$654$	−3.92015e6	−0.358392
$655$	−2.50872e7	−2.28481
$656$	−7.20944e6	−0.654097
$657$	−3.97273e6	−0.359067
$658$	−8.21952e6	−0.740085
$659$	1.60066e7	1.43577	0.717886	−	0.696160i	$-0.245110\pi$
$659$	1.60066e7	1.43577	0.717886	+	0.696160i	$0.245110\pi$
$660$	−8.29786e6	−0.741491
$661$	1.27998e7	1.13946	0.569731	−	0.821831i	$-0.307047\pi$
$661$	1.27998e7	1.13946	0.569731	+	0.821831i	$0.307047\pi$
$662$	654888.	0.0580794
$663$	−18468.0	−0.00163168
$664$	−1.13664e6	−0.100047
$665$	0	0
$666$	−2.21454e6	−0.193463
$667$	1.67381e7	1.45677
$668$	1.03656e7	0.898780
$669$	−692352.	−0.0598083
$670$	−8.24219e6	−0.709342
$671$	9.78902e6	0.839331
$672$	−1.11283e7	−0.950619
$673$	−9.83823e6	−0.837296	−0.418648	−	0.908149i	$-0.637496\pi$
$673$	−9.83823e6	−0.837296	−0.418648	+	0.908149i	$0.637496\pi$
$674$	−735892.	−0.0623971
$675$	−4.72319e6	−0.399003
$676$	7.12121e6	0.599359
$677$	8.54417e6	0.716470	0.358235	−	0.933631i	$-0.383379\pi$
$677$	8.54417e6	0.716470	0.358235	+	0.933631i	$0.383379\pi$
$678$	−1.52312e6	−0.127251
$679$	−9.56400e6	−0.796095
$680$	−70560.0	−0.00585176
$681$	−8.72651e6	−0.721062
$682$	−1.84397e6	−0.151807
$683$	1.00816e7	0.826947	0.413473	−	0.910516i	$-0.364315\pi$
$683$	1.00816e7	0.826947	0.413473	+	0.910516i	$0.364315\pi$
$684$	0	0
$685$	−4.92215e6	−0.400800
$686$	1.15133e7	0.934090
$687$	−7.56135e6	−0.611234
$688$	−3.27738e6	−0.263970
$689$	−1.52874e6	−0.122683
$690$	5.00270e6	0.400020
$691$	−7.71320e6	−0.614525	−0.307262	−	0.951625i	$-0.599413\pi$
$691$	−7.71320e6	−0.614525	−0.307262	+	0.951625i	$0.599413\pi$
$692$	−7.76759e6	−0.616625
$693$	6.53184e6	0.516657
$694$	1.13232e6	0.0892422
$695$	2.37266e7	1.86326
$696$	6.37416e6	0.498769
$697$	65940.0	0.00514123
$698$	−9.01373e6	−0.700271
$699$	−5.18323e6	−0.401243
$700$	−4.35389e7	−3.35840
$701$	4.92440e6	0.378493	0.189247	−	0.981930i	$-0.439395\pi$
$701$	4.92440e6	0.378493	0.189247	+	0.981930i	$0.439395\pi$
$702$	498636.	0.0381892
$703$	0	0
$704$	−3.59117e6	−0.273089
$705$	−1.51034e7	−1.14446
$706$	−2.19556e6	−0.165781
$707$	2.38901e7	1.79750
$708$	−6.62558e6	−0.496754
$709$	5.35468e6	0.400053	0.200027	−	0.979790i	$-0.435897\pi$
$709$	5.35468e6	0.400053	0.200027	+	0.979790i	$0.435897\pi$
$710$	−5.11795e6	−0.381022
$711$	−6.40354e6	−0.475057
$712$	9.94728e6	0.735367
$713$	−7.78198e6	−0.573280
$714$	25920.0	0.00190278
$715$	1.12614e7	0.823809
$716$	−1.22950e7	−0.896286
$717$	3.16969e6	0.230260
$718$	−3.90446e6	−0.282650
$719$	9.39507e6	0.677763	0.338881	−	0.940829i	$-0.389951\pi$
$719$	9.39507e6	0.677763	0.338881	+	0.940829i	$0.389951\pi$
$720$	−5.20733e6	−0.374355
$721$	−1.66483e7	−1.19270
$722$	0	0
$723$	4.06161e6	0.288970
$724$	711368.	0.0504368
$725$	3.82391e7	2.70186
$726$	866790.	0.0610341
$727$	6.83055e6	0.479314	0.239657	−	0.970858i	$-0.422965\pi$
$727$	6.83055e6	0.479314	0.239657	+	0.970858i	$0.422965\pi$
$728$	9.84960e6	0.688795
$729$	531441.	0.0370370
$730$	9.61302e6	0.667656
$731$	29976.0	0.00207482
$732$	7.34177e6	0.506434
$733$	1.29536e7	0.890491	0.445245	−	0.895409i	$-0.353116\pi$
$733$	1.29536e7	0.890491	0.445245	+	0.895409i	$0.353116\pi$
$734$	2.98326e6	0.204386
$735$	3.59794e7	2.45661
$736$	1.46111e7	0.994232
$737$	1.41295e7	0.958202
$738$	−1.78038e6	−0.120329
$739$	1.15292e7	0.776582	0.388291	−	0.921537i	$-0.373066\pi$
$739$	1.15292e7	0.776582	0.388291	+	0.921537i	$0.373066\pi$
$740$	−3.75105e7	−2.51810
$741$	0	0
$742$	2.14560e6	0.143067
$743$	−3.20131e6	−0.212743	−0.106372	−	0.994326i	$-0.533923\pi$
$743$	−3.20131e6	−0.212743	−0.106372	+	0.994326i	$0.533923\pi$
$744$	−2.96352e6	−0.196280
$745$	3.45456e7	2.28035
$746$	−2.96609e6	−0.195136
$747$	767232.	0.0503066
$748$	56448.0	0.00368888
$749$	2.64490e7	1.72268
$750$	5.91646e6	0.384068
$751$	−5.52822e6	−0.357673	−0.178836	−	0.983879i	$-0.557233\pi$
$751$	−5.52822e6	−0.357673	−0.178836	+	0.983879i	$0.557233\pi$
$752$	−1.12333e7	−0.724377
$753$	−1.31177e6	−0.0843082
$754$	−4.03697e6	−0.258599
$755$	−2.66678e7	−1.70263
$756$	4.89888e6	0.311740
$757$	1.62708e7	1.03198	0.515989	−	0.856595i	$-0.327425\pi$
$757$	1.62708e7	1.03198	0.515989	+	0.856595i	$0.327425\pi$
$758$	5.58871e6	0.353296
$759$	−8.57606e6	−0.540360
$760$	0	0
$761$	−8.40043e6	−0.525823	−0.262912	−	0.964820i	$-0.584683\pi$
$761$	−8.40043e6	−0.525823	−0.262912	+	0.964820i	$0.584683\pi$
$762$	1.61294e6	0.100631
$763$	5.22686e7	3.25035
$764$	−1.79380e7	−1.11184
$765$	47628.0	0.00294245
$766$	−4.13819e6	−0.254823
$767$	8.99186e6	0.551901
$768$	274176.	0.0167736
$769$	7.66543e6	0.467434	0.233717	−	0.972305i	$-0.424911\pi$
$769$	7.66543e6	0.467434	0.233717	+	0.972305i	$0.424911\pi$
$770$	−1.58054e7	−0.960682
$771$	−1.69036e7	−1.02410
$772$	−6.29569e6	−0.380189
$773$	2.59829e7	1.56401	0.782004	−	0.623273i	$-0.214198\pi$
$773$	2.59829e7	1.56401	0.782004	+	0.623273i	$0.214198\pi$
$774$	−809352.	−0.0485607
$775$	−1.77784e7	−1.06326
$776$	4.78200e6	0.285072
$777$	2.95272e7	1.75457
$778$	9.23392e6	0.546937
$779$	0	0
$780$	8.44603e6	0.497068
$781$	8.77363e6	0.514697
$782$	−34032.0	−0.00199008
$783$	−4.30256e6	−0.250797
$784$	2.67602e7	1.55489
$785$	−1.22443e7	−0.709186
$786$	−4.60786e6	−0.266037
$787$	−2.59845e7	−1.49547	−0.747734	−	0.663999i	$-0.768858\pi$
$787$	−2.59845e7	−1.49547	−0.747734	+	0.663999i	$0.768858\pi$
$788$	−9.11226e6	−0.522770
$789$	−8.05561e6	−0.460687
$790$	1.54950e7	0.883330
$791$	2.03083e7	1.15407
$792$	−3.26592e6	−0.185009
$793$	−9.96383e6	−0.562656
$794$	1.75174e6	0.0986094
$795$	3.94254e6	0.221237
$796$	2.75401e7	1.54058
$797$	−2.12011e7	−1.18226	−0.591129	−	0.806577i	$-0.701317\pi$
$797$	−2.12011e7	−1.18226	−0.591129	+	0.806577i	$0.701317\pi$
$798$	0	0
$799$	102744.	0.00569363
$800$	3.33798e7	1.84399
$801$	−6.71441e6	−0.369766
$802$	6.73231e6	0.369597
$803$	−1.64795e7	−0.901891
$804$	1.05971e7	0.578159
$805$	−6.67027e7	−3.62789
$806$	1.87690e6	0.101766
$807$	1.14562e7	0.619234
$808$	−1.19450e7	−0.643664
$809$	−1.06374e7	−0.571429	−0.285714	−	0.958315i	$-0.592231\pi$
$809$	−1.06374e7	−0.571429	−0.285714	+	0.958315i	$0.592231\pi$
$810$	−1.28596e6	−0.0688674
$811$	1.19205e7	0.636416	0.318208	−	0.948021i	$-0.396919\pi$
$811$	1.19205e7	0.636416	0.318208	+	0.948021i	$0.396919\pi$
$812$	−3.96614e7	−2.11095
$813$	−2.76005e6	−0.146450
$814$	−9.18624e6	−0.485933
$815$	2.83220e6	0.149358
$816$	35424.0	0.00186240
$817$	0	0
$818$	−1.31731e7	−0.688342
$819$	−6.64848e6	−0.346348
$820$	−3.01566e7	−1.56620
$821$	8.14431e6	0.421693	0.210847	−	0.977519i	$-0.432378\pi$
$821$	8.14431e6	0.421693	0.210847	+	0.977519i	$0.432378\pi$
$822$	−904068.	−0.0466683
$823$	−9.57675e6	−0.492854	−0.246427	−	0.969161i	$-0.579257\pi$
$823$	−9.57675e6	−0.492854	−0.246427	+	0.969161i	$0.579257\pi$
$824$	8.32416e6	0.427093
$825$	−1.95925e7	−1.00220
$826$	−1.26202e7	−0.643598
$827$	2.95107e6	0.150043	0.0750214	−	0.997182i	$-0.476097\pi$
$827$	2.95107e6	0.150043	0.0750214	+	0.997182i	$0.476097\pi$
$828$	−6.43205e6	−0.326042
$829$	−8.79546e6	−0.444501	−0.222250	−	0.974990i	$-0.571340\pi$
$829$	−8.79546e6	−0.444501	−0.222250	+	0.974990i	$0.571340\pi$
$830$	−1.85651e6	−0.0935411
$831$	1.72823e6	0.0868160
$832$	3.65530e6	0.183069
$833$	−244758.	−0.0122215
$834$	4.35794e6	0.216953
$835$	3.62796e7	1.80072
$836$	0	0
$837$	2.00038e6	0.0986956
$838$	−2.13550e6	−0.105049
$839$	1.46842e6	0.0720185	0.0360093	−	0.999351i	$-0.488535\pi$
$839$	1.46842e6	0.0720185	0.0360093	+	0.999351i	$0.488535\pi$
$840$	−2.54016e7	−1.24212
$841$	1.43225e7	0.698277
$842$	−7.21241e6	−0.350591
$843$	9.00495e6	0.436428
$844$	−2.42566e7	−1.17213
$845$	2.49242e7	1.20083
$846$	−2.77409e6	−0.133258
$847$	−1.15572e7	−0.553534
$848$	2.93232e6	0.140030
$849$	1.14162e7	0.543567
$850$	−77748.0	−0.00369098
$851$	−3.87681e7	−1.83506
$852$	6.58022e6	0.310557
$853$	2.37789e7	1.11897	0.559486	−	0.828840i	$-0.310999\pi$
$853$	2.37789e7	1.11897	0.559486	+	0.828840i	$0.310999\pi$
$854$	1.39843e7	0.656140
$855$	0	0
$856$	−1.32245e7	−0.616871
$857$	4.09013e7	1.90233	0.951163	−	0.308688i	$-0.0998900\pi$
$857$	4.09013e7	1.90233	0.951163	+	0.308688i	$0.0998900\pi$
$858$	2.06842e6	0.0959223
$859$	−7.99731e6	−0.369795	−0.184897	−	0.982758i	$-0.559195\pi$
$859$	−7.99731e6	−0.369795	−0.184897	+	0.982758i	$0.559195\pi$
$860$	−1.37090e7	−0.632063
$861$	2.37384e7	1.09130
$862$	−2.10619e6	−0.0965450
$863$	4.40634e6	0.201396	0.100698	−	0.994917i	$-0.467892\pi$
$863$	4.40634e6	0.201396	0.100698	+	0.994917i	$0.467892\pi$
$864$	−3.75581e6	−0.171167
$865$	−2.71866e7	−1.23542
$866$	6.91395e6	0.313279
$867$	1.27784e7	0.577336
$868$	1.84397e7	0.830719
$869$	−2.65628e7	−1.19323
$870$	1.04111e7	0.466337
$871$	−1.43818e7	−0.642344
$872$	−2.61343e7	−1.16391
$873$	−3.22785e6	−0.143343
$874$	0	0
$875$	−7.88861e7	−3.48321
$876$	−1.23596e7	−0.544182
$877$	2.55057e7	1.11980	0.559898	−	0.828561i	$-0.310840\pi$
$877$	2.55057e7	1.11980	0.559898	+	0.828561i	$0.310840\pi$
$878$	1.17722e7	0.515373
$879$	−1.37304e7	−0.599391
$880$	−2.16008e7	−0.940292
$881$	−3.50822e7	−1.52281	−0.761407	−	0.648274i	$-0.775491\pi$
$881$	−3.50822e7	−1.52281	−0.761407	+	0.648274i	$0.775491\pi$
$882$	6.60847e6	0.286042
$883$	−2.47814e7	−1.06961	−0.534803	−	0.844977i	$-0.679614\pi$
$883$	−2.47814e7	−1.06961	−0.534803	+	0.844977i	$0.679614\pi$
$884$	−57456.0	−0.00247289
$885$	−2.31895e7	−0.995254
$886$	−9.60432e6	−0.411038
$887$	6.85463e6	0.292533	0.146267	−	0.989245i	$-0.453274\pi$
$887$	6.85463e6	0.292533	0.146267	+	0.989245i	$0.453274\pi$
$888$	−1.47636e7	−0.628290
$889$	−2.15059e7	−0.912649
$890$	1.62472e7	0.687550
$891$	2.20450e6	0.0930283
$892$	−2.15398e6	−0.0906422
$893$	0	0
$894$	6.34511e6	0.265519
$895$	−4.30326e7	−1.79573
$896$	−4.46976e7	−1.86001
$897$	8.72921e6	0.362238
$898$	6.35933e6	0.263160
$899$	−1.61951e7	−0.668319
$900$	−1.46944e7	−0.604707
$901$	−26820.0	−0.00110064
$902$	−7.38528e6	−0.302239
$903$	1.07914e7	0.440410
$904$	−1.01542e7	−0.413260
$905$	2.48979e6	0.101051
$906$	−4.89816e6	−0.198250
$907$	3.64392e7	1.47079	0.735395	−	0.677639i	$-0.236997\pi$
$907$	3.64392e7	1.47079	0.735395	+	0.677639i	$0.236997\pi$
$908$	−2.71491e7	−1.09280
$909$	8.06290e6	0.323655
$910$	1.60877e7	0.644006
$911$	2.83123e7	1.13026	0.565132	−	0.825001i	$-0.308825\pi$
$911$	2.83123e7	1.13026	0.565132	+	0.825001i	$0.308825\pi$
$912$	0	0
$913$	3.18259e6	0.126358
$914$	967092.	0.0382915
$915$	2.56962e7	1.01465
$916$	−2.35242e7	−0.926352
$917$	6.14381e7	2.41276
$918$	8748.00	0.000342612 0
$919$	−3.75587e6	−0.146697	−0.0733486	−	0.997306i	$-0.523369\pi$
$919$	−3.75587e6	−0.146697	−0.0733486	+	0.997306i	$0.523369\pi$
$920$	3.33514e7	1.29910
$921$	−1.07699e7	−0.418371
$922$	1.41596e6	0.0548561
$923$	−8.93030e6	−0.345034
$924$	2.03213e7	0.783017
$925$	−8.85679e7	−3.40347
$926$	1.64818e7	0.631652
$927$	−5.61881e6	−0.214756
$928$	3.04071e7	1.15906
$929$	−5.55366e6	−0.211125	−0.105563	−	0.994413i	$-0.533664\pi$
$929$	−5.55366e6	−0.211125	−0.105563	+	0.994413i	$0.533664\pi$
$930$	−4.84042e6	−0.183517
$931$	0	0
$932$	−1.61256e7	−0.608101
$933$	−2.13430e7	−0.802696
$934$	4.27280e6	0.160267
$935$	197568.	0.00739073
$936$	3.32424e6	0.124023
$937$	2.46166e7	0.915965	0.457982	−	0.888961i	$-0.348572\pi$
$937$	2.46166e7	0.915965	0.457982	+	0.888961i	$0.348572\pi$
$938$	2.01850e7	0.749067
$939$	−3.18364e6	−0.117831
$940$	−4.69883e7	−1.73448
$941$	3.89956e7	1.43563	0.717813	−	0.696236i	$-0.245143\pi$
$941$	3.89956e7	1.43563	0.717813	+	0.696236i	$0.245143\pi$
$942$	−2.24896e6	−0.0825760
$943$	−3.11676e7	−1.14137
$944$	−1.72476e7	−0.629938
$945$	1.71461e7	0.624576
$946$	−3.35731e6	−0.121973
$947$	2.16559e7	0.784696	0.392348	−	0.919817i	$-0.371663\pi$
$947$	2.16559e7	0.784696	0.392348	+	0.919817i	$0.371663\pi$
$948$	−1.99221e7	−0.719970
$949$	1.67737e7	0.604594
$950$	0	0
$951$	2.43384e7	0.872651
$952$	172800.	0.00617947
$953$	1.94047e7	0.692109	0.346054	−	0.938214i	$-0.387521\pi$
$953$	1.94047e7	0.692109	0.346054	+	0.938214i	$0.387521\pi$
$954$	724140.	0.0257603
$955$	−6.27831e7	−2.22759
$956$	9.86126e6	0.348970
$957$	−1.78476e7	−0.629943
$958$	2.41473e6	0.0850070
$959$	1.20542e7	0.423246
$960$	−9.42682e6	−0.330131
$961$	−2.10996e7	−0.736998
$962$	9.35028e6	0.325752
$963$	8.92652e6	0.310182
$964$	1.26361e7	0.437947
$965$	−2.20349e7	−0.761716
$966$	−1.22515e7	−0.422423
$967$	7.26789e6	0.249944	0.124972	−	0.992160i	$-0.460116\pi$
$967$	7.26789e6	0.249944	0.124972	+	0.992160i	$0.460116\pi$
$968$	5.77860e6	0.198214
$969$	0	0
$970$	7.81060e6	0.266536
$971$	2.43391e7	0.828431	0.414216	−	0.910179i	$-0.364056\pi$
$971$	2.43391e7	0.828431	0.414216	+	0.910179i	$0.364056\pi$
$972$	1.65337e6	0.0561313
$973$	−5.81059e7	−1.96761
$974$	1.75594e7	0.593078
$975$	1.99424e7	0.671839
$976$	1.91119e7	0.642213
$977$	3.09415e7	1.03706	0.518531	−	0.855059i	$-0.326479\pi$
$977$	3.09415e7	1.03706	0.518531	+	0.855059i	$0.326479\pi$
$978$	520200.	0.0173909
$979$	−2.78524e7	−0.928765
$980$	1.11936e8	3.72310
$981$	1.76407e7	0.585251
$982$	8.46800e6	0.280222
$983$	−3.53169e7	−1.16573	−0.582865	−	0.812569i	$-0.698069\pi$
$983$	−3.53169e7	−1.16573	−0.582865	+	0.812569i	$0.698069\pi$
$984$	−1.18692e7	−0.390781
$985$	−3.18929e7	−1.04738
$986$	−70824.0	−0.00232000
$987$	3.69878e7	1.20855
$988$	0	0
$989$	−1.41687e7	−0.460615
$990$	−5.33434e6	−0.172979
$991$	−4.96000e7	−1.60434	−0.802172	−	0.597092i	$-0.796323\pi$
$991$	−4.96000e7	−1.60434	−0.802172	+	0.597092i	$0.796323\pi$
$992$	−1.41371e7	−0.456122
$993$	−2.94700e6	−0.0948432
$994$	1.25338e7	0.402361
$995$	9.63904e7	3.08657
$996$	2.38694e6	0.0762419
$997$	−5.33551e7	−1.69996	−0.849978	−	0.526818i	$-0.823385\pi$
$997$	−5.33551e7	−1.69996	−0.849978	+	0.526818i	$0.823385\pi$
$998$	−3.46900e6	−0.110250
$999$	9.96543e6	0.315924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1083.6.a.b.1.1		1
19.18	odd	2		57.6.a.a.1.1	✓	1
57.56	even	2		171.6.a.c.1.1		1
76.75	even	2		912.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.6.a.a.1.1	✓	1	19.18	odd	2
171.6.a.c.1.1		1	57.56	even	2
912.6.a.a.1.1		1	76.75	even	2
1083.6.a.b.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:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1083.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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