LMFDB - Embedded newform 960.6.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,6,Mod(1,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("960.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	960.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:	$153.968467020$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 120)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	960.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-9.00000 q^{3} -25.0000 q^{5} +80.0000 q^{7} +81.0000 q^{9} +684.000 q^{11} +978.000 q^{13} +225.000 q^{15} -862.000 q^{17} +916.000 q^{19} -720.000 q^{21} +1552.00 q^{23} +625.000 q^{25} -729.000 q^{27} +7314.00 q^{29} +9312.00 q^{31} -6156.00 q^{33} -2000.00 q^{35} +8826.00 q^{37} -8802.00 q^{39} -3286.00 q^{41} +7556.00 q^{43} -2025.00 q^{45} +5960.00 q^{47} -10407.0 q^{49} +7758.00 q^{51} +8698.00 q^{53} -17100.0 q^{55} -8244.00 q^{57} -42036.0 q^{59} -37518.0 q^{61} +6480.00 q^{63} -24450.0 q^{65} +29324.0 q^{67} -13968.0 q^{69} -84408.0 q^{71} -46550.0 q^{73} -5625.00 q^{75} +54720.0 q^{77} -26752.0 q^{79} +6561.00 q^{81} -7956.00 q^{83} +21550.0 q^{85} -65826.0 q^{87} +59674.0 q^{89} +78240.0 q^{91} -83808.0 q^{93} -22900.0 q^{95} +136898. q^{97} +55404.0 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	0	0
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	80.0000	0.617085	0.308542	−	0.951211i	$-0.400159\pi$
$7$	80.0000	0.617085	0.308542	+	0.951211i	$0.400159\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	684.000	1.70441	0.852206	−	0.523207i	$-0.175265\pi$
$11$	684.000	1.70441	0.852206	+	0.523207i	$0.175265\pi$
$12$	0	0
$13$	978.000	1.60502	0.802510	−	0.596639i	$-0.203497\pi$
$13$	978.000	1.60502	0.802510	+	0.596639i	$0.203497\pi$
$14$	0	0
$15$	225.000	0.258199
$16$	0	0
$17$	−862.000	−0.723411	−0.361705	−	0.932292i	$-0.617805\pi$
$17$	−862.000	−0.723411	−0.361705	+	0.932292i	$0.617805\pi$
$18$	0	0
$19$	916.000	0.582119	0.291059	−	0.956705i	$-0.405992\pi$
$19$	916.000	0.582119	0.291059	+	0.956705i	$0.405992\pi$
$20$	0	0
$21$	−720.000	−0.356274
$22$	0	0
$23$	1552.00	0.611747	0.305874	−	0.952072i	$-0.401051\pi$
$23$	1552.00	0.611747	0.305874	+	0.952072i	$0.401051\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	7314.00	1.61495	0.807477	−	0.589900i	$-0.200833\pi$
$29$	7314.00	1.61495	0.807477	+	0.589900i	$0.200833\pi$
$30$	0	0
$31$	9312.00	1.74036	0.870179	−	0.492735i	$-0.164003\pi$
$31$	9312.00	1.74036	0.870179	+	0.492735i	$0.164003\pi$
$32$	0	0
$33$	−6156.00	−0.984042
$34$	0	0
$35$	−2000.00	−0.275969
$36$	0	0
$37$	8826.00	1.05989	0.529944	−	0.848033i	$-0.322213\pi$
$37$	8826.00	1.05989	0.529944	+	0.848033i	$0.322213\pi$
$38$	0	0
$39$	−8802.00	−0.926659
$40$	0	0
$41$	−3286.00	−0.305287	−0.152643	−	0.988281i	$-0.548779\pi$
$41$	−3286.00	−0.305287	−0.152643	+	0.988281i	$0.548779\pi$
$42$	0	0
$43$	7556.00	0.623190	0.311595	−	0.950215i	$-0.399137\pi$
$43$	7556.00	0.623190	0.311595	+	0.950215i	$0.399137\pi$
$44$	0	0
$45$	−2025.00	−0.149071
$46$	0	0
$47$	5960.00	0.393552	0.196776	−	0.980449i	$-0.436953\pi$
$47$	5960.00	0.393552	0.196776	+	0.980449i	$0.436953\pi$
$48$	0	0
$49$	−10407.0	−0.619206
$50$	0	0
$51$	7758.00	0.417661
$52$	0	0
$53$	8698.00	0.425334	0.212667	−	0.977125i	$-0.431785\pi$
$53$	8698.00	0.425334	0.212667	+	0.977125i	$0.431785\pi$
$54$	0	0
$55$	−17100.0	−0.762236
$56$	0	0
$57$	−8244.00	−0.336086
$58$	0	0
$59$	−42036.0	−1.57214	−0.786070	−	0.618137i	$-0.787888\pi$
$59$	−42036.0	−1.57214	−0.786070	+	0.618137i	$0.787888\pi$
$60$	0	0
$61$	−37518.0	−1.29097	−0.645483	−	0.763774i	$-0.723344\pi$
$61$	−37518.0	−1.29097	−0.645483	+	0.763774i	$0.723344\pi$
$62$	0	0
$63$	6480.00	0.205695
$64$	0	0
$65$	−24450.0	−0.717787
$66$	0	0
$67$	29324.0	0.798061	0.399031	−	0.916938i	$-0.369347\pi$
$67$	29324.0	0.798061	0.399031	+	0.916938i	$0.369347\pi$
$68$	0	0
$69$	−13968.0	−0.353193
$70$	0	0
$71$	−84408.0	−1.98718	−0.993591	−	0.113033i	$-0.963943\pi$
$71$	−84408.0	−1.98718	−0.993591	+	0.113033i	$0.963943\pi$
$72$	0	0
$73$	−46550.0	−1.02238	−0.511190	−	0.859468i	$-0.670795\pi$
$73$	−46550.0	−1.02238	−0.511190	+	0.859468i	$0.670795\pi$
$74$	0	0
$75$	−5625.00	−0.115470
$76$	0	0
$77$	54720.0	1.05177
$78$	0	0
$79$	−26752.0	−0.482268	−0.241134	−	0.970492i	$-0.577519\pi$
$79$	−26752.0	−0.482268	−0.241134	+	0.970492i	$0.577519\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	−7956.00	−0.126765	−0.0633825	−	0.997989i	$-0.520189\pi$
$83$	−7956.00	−0.126765	−0.0633825	+	0.997989i	$0.520189\pi$
$84$	0	0
$85$	21550.0	0.323519
$86$	0	0
$87$	−65826.0	−0.932394
$88$	0	0
$89$	59674.0	0.798565	0.399282	−	0.916828i	$-0.369259\pi$
$89$	59674.0	0.798565	0.399282	+	0.916828i	$0.369259\pi$
$90$	0	0
$91$	78240.0	0.990434
$92$	0	0
$93$	−83808.0	−1.00480
$94$	0	0
$95$	−22900.0	−0.260331
$96$	0	0
$97$	136898.	1.47730	0.738648	−	0.674091i	$-0.235464\pi$
$97$	136898.	1.47730	0.738648	+	0.674091i	$0.235464\pi$
$98$	0	0
$99$	55404.0	0.568137
$100$	0	0
$101$	202858.	1.97874	0.989370	−	0.145421i	$-0.0464535\pi$
$101$	202858.	1.97874	0.989370	+	0.145421i	$0.0464535\pi$
$102$	0	0
$103$	8576.00	0.0796511	0.0398255	−	0.999207i	$-0.487320\pi$
$103$	8576.00	0.0796511	0.0398255	+	0.999207i	$0.487320\pi$
$104$	0	0
$105$	18000.0	0.159331
$106$	0	0
$107$	−19948.0	−0.168438	−0.0842190	−	0.996447i	$-0.526840\pi$
$107$	−19948.0	−0.168438	−0.0842190	+	0.996447i	$0.526840\pi$
$108$	0	0
$109$	−37598.0	−0.303109	−0.151554	−	0.988449i	$-0.548428\pi$
$109$	−37598.0	−0.303109	−0.151554	+	0.988449i	$0.548428\pi$
$110$	0	0
$111$	−79434.0	−0.611926
$112$	0	0
$113$	−191838.	−1.41331	−0.706657	−	0.707556i	$-0.749797\pi$
$113$	−191838.	−1.41331	−0.706657	+	0.707556i	$0.749797\pi$
$114$	0	0
$115$	−38800.0	−0.273582
$116$	0	0
$117$	79218.0	0.535007
$118$	0	0
$119$	−68960.0	−0.446406
$120$	0	0
$121$	306805.	1.90502
$122$	0	0
$123$	29574.0	0.176257
$124$	0	0
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−98888.0	−0.544044	−0.272022	−	0.962291i	$-0.587692\pi$
$127$	−98888.0	−0.544044	−0.272022	+	0.962291i	$0.587692\pi$
$128$	0	0
$129$	−68004.0	−0.359799
$130$	0	0
$131$	29636.0	0.150883	0.0754417	−	0.997150i	$-0.475963\pi$
$131$	29636.0	0.150883	0.0754417	+	0.997150i	$0.475963\pi$
$132$	0	0
$133$	73280.0	0.359217
$134$	0	0
$135$	18225.0	0.0860663
$136$	0	0
$137$	−4614.00	−0.0210028	−0.0105014	−	0.999945i	$-0.503343\pi$
$137$	−4614.00	−0.0210028	−0.0105014	+	0.999945i	$0.503343\pi$
$138$	0	0
$139$	−254292.	−1.11634	−0.558169	−	0.829727i	$-0.688496\pi$
$139$	−254292.	−1.11634	−0.558169	+	0.829727i	$0.688496\pi$
$140$	0	0
$141$	−53640.0	−0.227217
$142$	0	0
$143$	668952.	2.73561
$144$	0	0
$145$	−182850.	−0.722229
$146$	0	0
$147$	93663.0	0.357499
$148$	0	0
$149$	83226.0	0.307110	0.153555	−	0.988140i	$-0.450928\pi$
$149$	83226.0	0.307110	0.153555	+	0.988140i	$0.450928\pi$
$150$	0	0
$151$	212616.	0.758846	0.379423	−	0.925223i	$-0.376123\pi$
$151$	212616.	0.758846	0.379423	+	0.925223i	$0.376123\pi$
$152$	0	0
$153$	−69822.0	−0.241137
$154$	0	0
$155$	−232800.	−0.778312
$156$	0	0
$157$	−112702.	−0.364907	−0.182454	−	0.983214i	$-0.558404\pi$
$157$	−112702.	−0.364907	−0.182454	+	0.983214i	$0.558404\pi$
$158$	0	0
$159$	−78282.0	−0.245566
$160$	0	0
$161$	124160.	0.377500
$162$	0	0
$163$	−411172.	−1.21214	−0.606072	−	0.795409i	$-0.707256\pi$
$163$	−411172.	−1.21214	−0.606072	+	0.795409i	$0.707256\pi$
$164$	0	0
$165$	153900.	0.440077
$166$	0	0
$167$	−258896.	−0.718347	−0.359173	−	0.933271i	$-0.616941\pi$
$167$	−258896.	−0.718347	−0.359173	+	0.933271i	$0.616941\pi$
$168$	0	0
$169$	585191.	1.57609
$170$	0	0
$171$	74196.0	0.194040
$172$	0	0
$173$	397026.	1.00856	0.504282	−	0.863539i	$-0.331757\pi$
$173$	397026.	1.00856	0.504282	+	0.863539i	$0.331757\pi$
$174$	0	0
$175$	50000.0	0.123417
$176$	0	0
$177$	378324.	0.907676
$178$	0	0
$179$	−473468.	−1.10448	−0.552240	−	0.833685i	$-0.686227\pi$
$179$	−473468.	−1.10448	−0.552240	+	0.833685i	$0.686227\pi$
$180$	0	0
$181$	79834.0	0.181130	0.0905652	−	0.995891i	$-0.471133\pi$
$181$	79834.0	0.181130	0.0905652	+	0.995891i	$0.471133\pi$
$182$	0	0
$183$	337662.	0.745340
$184$	0	0
$185$	−220650.	−0.473996
$186$	0	0
$187$	−589608.	−1.23299
$188$	0	0
$189$	−58320.0	−0.118758
$190$	0	0
$191$	−397360.	−0.788135	−0.394068	−	0.919081i	$-0.628932\pi$
$191$	−397360.	−0.788135	−0.394068	+	0.919081i	$0.628932\pi$
$192$	0	0
$193$	777858.	1.50317	0.751583	−	0.659638i	$-0.229291\pi$
$193$	777858.	1.50317	0.751583	+	0.659638i	$0.229291\pi$
$194$	0	0
$195$	220050.	0.414414
$196$	0	0
$197$	−254678.	−0.467548	−0.233774	−	0.972291i	$-0.575108\pi$
$197$	−254678.	−0.467548	−0.233774	+	0.972291i	$0.575108\pi$
$198$	0	0
$199$	540264.	0.967104	0.483552	−	0.875316i	$-0.339346\pi$
$199$	540264.	0.967104	0.483552	+	0.875316i	$0.339346\pi$
$200$	0	0
$201$	−263916.	−0.460761
$202$	0	0
$203$	585120.	0.996563
$204$	0	0
$205$	82150.0	0.136528
$206$	0	0
$207$	125712.	0.203916
$208$	0	0
$209$	626544.	0.992169
$210$	0	0
$211$	1.05690e6	1.63428	0.817142	−	0.576436i	$-0.195557\pi$
$211$	1.05690e6	1.63428	0.817142	+	0.576436i	$0.195557\pi$
$212$	0	0
$213$	759672.	1.14730
$214$	0	0
$215$	−188900.	−0.278699
$216$	0	0
$217$	744960.	1.07395
$218$	0	0
$219$	418950.	0.590272
$220$	0	0
$221$	−843036.	−1.16109
$222$	0	0
$223$	1.09063e6	1.46864	0.734321	−	0.678802i	$-0.237501\pi$
$223$	1.09063e6	1.46864	0.734321	+	0.678802i	$0.237501\pi$
$224$	0	0
$225$	50625.0	0.0666667
$226$	0	0
$227$	−2772.00	−0.00357050	−0.00178525	−	0.999998i	$-0.500568\pi$
$227$	−2772.00	−0.00357050	−0.00178525	+	0.999998i	$0.500568\pi$
$228$	0	0
$229$	304458.	0.383653	0.191827	−	0.981429i	$-0.438559\pi$
$229$	304458.	0.383653	0.191827	+	0.981429i	$0.438559\pi$
$230$	0	0
$231$	−492480.	−0.607238
$232$	0	0
$233$	−329990.	−0.398209	−0.199104	−	0.979978i	$-0.563803\pi$
$233$	−329990.	−0.398209	−0.199104	+	0.979978i	$0.563803\pi$
$234$	0	0
$235$	−149000.	−0.176002
$236$	0	0
$237$	240768.	0.278438
$238$	0	0
$239$	−721584.	−0.817132	−0.408566	−	0.912729i	$-0.633971\pi$
$239$	−721584.	−0.817132	−0.408566	+	0.912729i	$0.633971\pi$
$240$	0	0
$241$	271538.	0.301154	0.150577	−	0.988598i	$-0.451887\pi$
$241$	271538.	0.301154	0.150577	+	0.988598i	$0.451887\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	260175.	0.276917
$246$	0	0
$247$	895848.	0.934312
$248$	0	0
$249$	71604.0	0.0731878
$250$	0	0
$251$	1.34534e6	1.34787	0.673935	−	0.738791i	$-0.264603\pi$
$251$	1.34534e6	1.34787	0.673935	+	0.738791i	$0.264603\pi$
$252$	0	0
$253$	1.06157e6	1.04267
$254$	0	0
$255$	−193950.	−0.186784
$256$	0	0
$257$	1.62290e6	1.53270	0.766352	−	0.642421i	$-0.222070\pi$
$257$	1.62290e6	1.53270	0.766352	+	0.642421i	$0.222070\pi$
$258$	0	0
$259$	706080.	0.654040
$260$	0	0
$261$	592434.	0.538318
$262$	0	0
$263$	−472128.	−0.420892	−0.210446	−	0.977606i	$-0.567492\pi$
$263$	−472128.	−0.420892	−0.210446	+	0.977606i	$0.567492\pi$
$264$	0	0
$265$	−217450.	−0.190215
$266$	0	0
$267$	−537066.	−0.461052
$268$	0	0
$269$	−2430.00	−0.00204751	−0.00102375	−	0.999999i	$-0.500326\pi$
$269$	−2430.00	−0.00204751	−0.00102375	+	0.999999i	$0.500326\pi$
$270$	0	0
$271$	−1.65157e6	−1.36607	−0.683035	−	0.730385i	$-0.739341\pi$
$271$	−1.65157e6	−1.36607	−0.683035	+	0.730385i	$0.739341\pi$
$272$	0	0
$273$	−704160.	−0.571827
$274$	0	0
$275$	427500.	0.340882
$276$	0	0
$277$	−2.21129e6	−1.73159	−0.865796	−	0.500397i	$-0.833187\pi$
$277$	−2.21129e6	−1.73159	−0.865796	+	0.500397i	$0.833187\pi$
$278$	0	0
$279$	754272.	0.580120
$280$	0	0
$281$	−423014.	−0.319587	−0.159793	−	0.987150i	$-0.551083\pi$
$281$	−423014.	−0.319587	−0.159793	+	0.987150i	$0.551083\pi$
$282$	0	0
$283$	−487052.	−0.361501	−0.180750	−	0.983529i	$-0.557853\pi$
$283$	−487052.	−0.361501	−0.180750	+	0.983529i	$0.557853\pi$
$284$	0	0
$285$	206100.	0.150302
$286$	0	0
$287$	−262880.	−0.188388
$288$	0	0
$289$	−676813.	−0.476677
$290$	0	0
$291$	−1.23208e6	−0.852918
$292$	0	0
$293$	1.02692e6	0.698825	0.349412	−	0.936969i	$-0.386381\pi$
$293$	1.02692e6	0.698825	0.349412	+	0.936969i	$0.386381\pi$
$294$	0	0
$295$	1.05090e6	0.703083
$296$	0	0
$297$	−498636.	−0.328014
$298$	0	0
$299$	1.51786e6	0.981867
$300$	0	0
$301$	604480.	0.384561
$302$	0	0
$303$	−1.82572e6	−1.14243
$304$	0	0
$305$	937950.	0.577338
$306$	0	0
$307$	−1.07133e6	−0.648751	−0.324376	−	0.945928i	$-0.605154\pi$
$307$	−1.07133e6	−0.648751	−0.324376	+	0.945928i	$0.605154\pi$
$308$	0	0
$309$	−77184.0	−0.0459866
$310$	0	0
$311$	−1.87422e6	−1.09880	−0.549400	−	0.835559i	$-0.685144\pi$
$311$	−1.87422e6	−1.09880	−0.549400	+	0.835559i	$0.685144\pi$
$312$	0	0
$313$	2.92883e6	1.68979	0.844895	−	0.534932i	$-0.179663\pi$
$313$	2.92883e6	1.68979	0.844895	+	0.534932i	$0.179663\pi$
$314$	0	0
$315$	−162000.	−0.0919896
$316$	0	0
$317$	2.94831e6	1.64788	0.823938	−	0.566680i	$-0.191773\pi$
$317$	2.94831e6	1.64788	0.823938	+	0.566680i	$0.191773\pi$
$318$	0	0
$319$	5.00278e6	2.75254
$320$	0	0
$321$	179532.	0.0972477
$322$	0	0
$323$	−789592.	−0.421111
$324$	0	0
$325$	611250.	0.321004
$326$	0	0
$327$	338382.	0.175000
$328$	0	0
$329$	476800.	0.242855
$330$	0	0
$331$	−856100.	−0.429491	−0.214746	−	0.976670i	$-0.568892\pi$
$331$	−856100.	−0.429491	−0.214746	+	0.976670i	$0.568892\pi$
$332$	0	0
$333$	714906.	0.353296
$334$	0	0
$335$	−733100.	−0.356904
$336$	0	0
$337$	−3.11272e6	−1.49302	−0.746509	−	0.665375i	$-0.768272\pi$
$337$	−3.11272e6	−1.49302	−0.746509	+	0.665375i	$0.768272\pi$
$338$	0	0
$339$	1.72654e6	0.815977
$340$	0	0
$341$	6.36941e6	2.96629
$342$	0	0
$343$	−2.17712e6	−0.999188
$344$	0	0
$345$	349200.	0.157952
$346$	0	0
$347$	−2.09651e6	−0.934701	−0.467351	−	0.884072i	$-0.654791\pi$
$347$	−2.09651e6	−0.934701	−0.467351	+	0.884072i	$0.654791\pi$
$348$	0	0
$349$	4.44677e6	1.95425	0.977127	−	0.212656i	$-0.0682113\pi$
$349$	4.44677e6	1.95425	0.977127	+	0.212656i	$0.0682113\pi$
$350$	0	0
$351$	−712962.	−0.308886
$352$	0	0
$353$	1.80434e6	0.770692	0.385346	−	0.922772i	$-0.374082\pi$
$353$	1.80434e6	0.770692	0.385346	+	0.922772i	$0.374082\pi$
$354$	0	0
$355$	2.11020e6	0.888695
$356$	0	0
$357$	620640.	0.257733
$358$	0	0
$359$	−2.84270e6	−1.16411	−0.582055	−	0.813149i	$-0.697751\pi$
$359$	−2.84270e6	−1.16411	−0.582055	+	0.813149i	$0.697751\pi$
$360$	0	0
$361$	−1.63704e6	−0.661138
$362$	0	0
$363$	−2.76124e6	−1.09986
$364$	0	0
$365$	1.16375e6	0.457222
$366$	0	0
$367$	−1.65561e6	−0.641641	−0.320821	−	0.947140i	$-0.603959\pi$
$367$	−1.65561e6	−0.641641	−0.320821	+	0.947140i	$0.603959\pi$
$368$	0	0
$369$	−266166.	−0.101762
$370$	0	0
$371$	695840.	0.262467
$372$	0	0
$373$	199690.	0.0743163	0.0371582	−	0.999309i	$-0.488169\pi$
$373$	199690.	0.0743163	0.0371582	+	0.999309i	$0.488169\pi$
$374$	0	0
$375$	140625.	0.0516398
$376$	0	0
$377$	7.15309e6	2.59203
$378$	0	0
$379$	−1.45610e6	−0.520707	−0.260353	−	0.965513i	$-0.583839\pi$
$379$	−1.45610e6	−0.520707	−0.260353	+	0.965513i	$0.583839\pi$
$380$	0	0
$381$	889992.	0.314104
$382$	0	0
$383$	4.62548e6	1.61124	0.805619	−	0.592434i	$-0.201833\pi$
$383$	4.62548e6	1.61124	0.805619	+	0.592434i	$0.201833\pi$
$384$	0	0
$385$	−1.36800e6	−0.470364
$386$	0	0
$387$	612036.	0.207730
$388$	0	0
$389$	−3.51068e6	−1.17630	−0.588149	−	0.808753i	$-0.700143\pi$
$389$	−3.51068e6	−1.17630	−0.588149	+	0.808753i	$0.700143\pi$
$390$	0	0
$391$	−1.33782e6	−0.442545
$392$	0	0
$393$	−266724.	−0.0871125
$394$	0	0
$395$	668800.	0.215677
$396$	0	0
$397$	−4.84773e6	−1.54370	−0.771848	−	0.635807i	$-0.780667\pi$
$397$	−4.84773e6	−1.54370	−0.771848	+	0.635807i	$0.780667\pi$
$398$	0	0
$399$	−659520.	−0.207394
$400$	0	0
$401$	−4.21515e6	−1.30904	−0.654519	−	0.756046i	$-0.727129\pi$
$401$	−4.21515e6	−1.30904	−0.654519	+	0.756046i	$0.727129\pi$
$402$	0	0
$403$	9.10714e6	2.79331
$404$	0	0
$405$	−164025.	−0.0496904
$406$	0	0
$407$	6.03698e6	1.80648
$408$	0	0
$409$	4.49535e6	1.32879	0.664394	−	0.747383i	$-0.268690\pi$
$409$	4.49535e6	1.32879	0.664394	+	0.747383i	$0.268690\pi$
$410$	0	0
$411$	41526.0	0.0121259
$412$	0	0
$413$	−3.36288e6	−0.970144
$414$	0	0
$415$	198900.	0.0566911
$416$	0	0
$417$	2.28863e6	0.644518
$418$	0	0
$419$	−4.44571e6	−1.23710	−0.618552	−	0.785744i	$-0.712280\pi$
$419$	−4.44571e6	−1.23710	−0.618552	+	0.785744i	$0.712280\pi$
$420$	0	0
$421$	4.87185e6	1.33964	0.669821	−	0.742523i	$-0.266371\pi$
$421$	4.87185e6	1.33964	0.669821	+	0.742523i	$0.266371\pi$
$422$	0	0
$423$	482760.	0.131184
$424$	0	0
$425$	−538750.	−0.144682
$426$	0	0
$427$	−3.00144e6	−0.796636
$428$	0	0
$429$	−6.02057e6	−1.57941
$430$	0	0
$431$	−549152.	−0.142397	−0.0711983	−	0.997462i	$-0.522682\pi$
$431$	−549152.	−0.142397	−0.0711983	+	0.997462i	$0.522682\pi$
$432$	0	0
$433$	2.37675e6	0.609206	0.304603	−	0.952479i	$-0.401476\pi$
$433$	2.37675e6	0.609206	0.304603	+	0.952479i	$0.401476\pi$
$434$	0	0
$435$	1.64565e6	0.416979
$436$	0	0
$437$	1.42163e6	0.356110
$438$	0	0
$439$	−1.31188e6	−0.324887	−0.162444	−	0.986718i	$-0.551938\pi$
$439$	−1.31188e6	−0.324887	−0.162444	+	0.986718i	$0.551938\pi$
$440$	0	0
$441$	−842967.	−0.206402
$442$	0	0
$443$	2.92914e6	0.709138	0.354569	−	0.935030i	$-0.384628\pi$
$443$	2.92914e6	0.709138	0.354569	+	0.935030i	$0.384628\pi$
$444$	0	0
$445$	−1.49185e6	−0.357129
$446$	0	0
$447$	−749034.	−0.177310
$448$	0	0
$449$	−4.30777e6	−1.00841	−0.504205	−	0.863584i	$-0.668214\pi$
$449$	−4.30777e6	−1.00841	−0.504205	+	0.863584i	$0.668214\pi$
$450$	0	0
$451$	−2.24762e6	−0.520334
$452$	0	0
$453$	−1.91354e6	−0.438120
$454$	0	0
$455$	−1.95600e6	−0.442935
$456$	0	0
$457$	4.48196e6	1.00387	0.501935	−	0.864905i	$-0.332622\pi$
$457$	4.48196e6	1.00387	0.501935	+	0.864905i	$0.332622\pi$
$458$	0	0
$459$	628398.	0.139220
$460$	0	0
$461$	95906.0	0.0210181	0.0105091	−	0.999945i	$-0.496655\pi$
$461$	95906.0	0.0210181	0.0105091	+	0.999945i	$0.496655\pi$
$462$	0	0
$463$	−7.24487e6	−1.57065	−0.785323	−	0.619086i	$-0.787503\pi$
$463$	−7.24487e6	−1.57065	−0.785323	+	0.619086i	$0.787503\pi$
$464$	0	0
$465$	2.09520e6	0.449359
$466$	0	0
$467$	−1.80528e6	−0.383048	−0.191524	−	0.981488i	$-0.561343\pi$
$467$	−1.80528e6	−0.383048	−0.191524	+	0.981488i	$0.561343\pi$
$468$	0	0
$469$	2.34592e6	0.492471
$470$	0	0
$471$	1.01432e6	0.210679
$472$	0	0
$473$	5.16830e6	1.06217
$474$	0	0
$475$	572500.	0.116424
$476$	0	0
$477$	704538.	0.141778
$478$	0	0
$479$	1.02682e6	0.204481	0.102241	−	0.994760i	$-0.467399\pi$
$479$	1.02682e6	0.204481	0.102241	+	0.994760i	$0.467399\pi$
$480$	0	0
$481$	8.63183e6	1.70114
$482$	0	0
$483$	−1.11744e6	−0.217950
$484$	0	0
$485$	−3.42245e6	−0.660667
$486$	0	0
$487$	6.43013e6	1.22856	0.614281	−	0.789087i	$-0.289446\pi$
$487$	6.43013e6	1.22856	0.614281	+	0.789087i	$0.289446\pi$
$488$	0	0
$489$	3.70055e6	0.699832
$490$	0	0
$491$	−6.89637e6	−1.29097	−0.645486	−	0.763772i	$-0.723345\pi$
$491$	−6.89637e6	−1.29097	−0.645486	+	0.763772i	$0.723345\pi$
$492$	0	0
$493$	−6.30467e6	−1.16827
$494$	0	0
$495$	−1.38510e6	−0.254079
$496$	0	0
$497$	−6.75264e6	−1.22626
$498$	0	0
$499$	−8.27403e6	−1.48753	−0.743765	−	0.668441i	$-0.766962\pi$
$499$	−8.27403e6	−1.48753	−0.743765	+	0.668441i	$0.766962\pi$
$500$	0	0
$501$	2.33006e6	0.414738
$502$	0	0
$503$	5.83070e6	1.02755	0.513773	−	0.857926i	$-0.328247\pi$
$503$	5.83070e6	1.02755	0.513773	+	0.857926i	$0.328247\pi$
$504$	0	0
$505$	−5.07145e6	−0.884919
$506$	0	0
$507$	−5.26672e6	−0.909956
$508$	0	0
$509$	−3.66421e6	−0.626881	−0.313441	−	0.949608i	$-0.601482\pi$
$509$	−3.66421e6	−0.626881	−0.313441	+	0.949608i	$0.601482\pi$
$510$	0	0
$511$	−3.72400e6	−0.630895
$512$	0	0
$513$	−667764.	−0.112029
$514$	0	0
$515$	−214400.	−0.0356210
$516$	0	0
$517$	4.07664e6	0.670774
$518$	0	0
$519$	−3.57323e6	−0.582295
$520$	0	0
$521$	−5.79381e6	−0.935126	−0.467563	−	0.883960i	$-0.654868\pi$
$521$	−5.79381e6	−0.935126	−0.467563	+	0.883960i	$0.654868\pi$
$522$	0	0
$523$	6.06676e6	0.969845	0.484922	−	0.874557i	$-0.338848\pi$
$523$	6.06676e6	0.969845	0.484922	+	0.874557i	$0.338848\pi$
$524$	0	0
$525$	−450000.	−0.0712548
$526$	0	0
$527$	−8.02694e6	−1.25899
$528$	0	0
$529$	−4.02764e6	−0.625765
$530$	0	0
$531$	−3.40492e6	−0.524047
$532$	0	0
$533$	−3.21371e6	−0.489991
$534$	0	0
$535$	498700.	0.0753277
$536$	0	0
$537$	4.26121e6	0.637672
$538$	0	0
$539$	−7.11839e6	−1.05538
$540$	0	0
$541$	2.19330e6	0.322184	0.161092	−	0.986939i	$-0.448498\pi$
$541$	2.19330e6	0.322184	0.161092	+	0.986939i	$0.448498\pi$
$542$	0	0
$543$	−718506.	−0.104576
$544$	0	0
$545$	939950.	0.135554
$546$	0	0
$547$	1.03263e7	1.47563	0.737814	−	0.675004i	$-0.235858\pi$
$547$	1.03263e7	1.47563	0.737814	+	0.675004i	$0.235858\pi$
$548$	0	0
$549$	−3.03896e6	−0.430322
$550$	0	0
$551$	6.69962e6	0.940094
$552$	0	0
$553$	−2.14016e6	−0.297600
$554$	0	0
$555$	1.98585e6	0.273662
$556$	0	0
$557$	4.01187e6	0.547910	0.273955	−	0.961742i	$-0.411668\pi$
$557$	4.01187e6	0.547910	0.273955	+	0.961742i	$0.411668\pi$
$558$	0	0
$559$	7.38977e6	1.00023
$560$	0	0
$561$	5.30647e6	0.711867
$562$	0	0
$563$	−9.59663e6	−1.27599	−0.637996	−	0.770040i	$-0.720236\pi$
$563$	−9.59663e6	−1.27599	−0.637996	+	0.770040i	$0.720236\pi$
$564$	0	0
$565$	4.79595e6	0.632053
$566$	0	0
$567$	524880.	0.0685650
$568$	0	0
$569$	6.76649e6	0.876159	0.438079	−	0.898936i	$-0.355659\pi$
$569$	6.76649e6	0.876159	0.438079	+	0.898936i	$0.355659\pi$
$570$	0	0
$571$	1.42954e7	1.83488	0.917439	−	0.397877i	$-0.130253\pi$
$571$	1.42954e7	1.83488	0.917439	+	0.397877i	$0.130253\pi$
$572$	0	0
$573$	3.57624e6	0.455030
$574$	0	0
$575$	970000.	0.122349
$576$	0	0
$577$	−1.38116e7	−1.72705	−0.863523	−	0.504309i	$-0.831747\pi$
$577$	−1.38116e7	−1.72705	−0.863523	+	0.504309i	$0.831747\pi$
$578$	0	0
$579$	−7.00072e6	−0.867854
$580$	0	0
$581$	−636480.	−0.0782248
$582$	0	0
$583$	5.94943e6	0.724943
$584$	0	0
$585$	−1.98045e6	−0.239262
$586$	0	0
$587$	−2.82424e6	−0.338303	−0.169151	−	0.985590i	$-0.554103\pi$
$587$	−2.82424e6	−0.338303	−0.169151	+	0.985590i	$0.554103\pi$
$588$	0	0
$589$	8.52979e6	1.01310
$590$	0	0
$591$	2.29210e6	0.269939
$592$	0	0
$593$	−6.72749e6	−0.785626	−0.392813	−	0.919618i	$-0.628498\pi$
$593$	−6.72749e6	−0.785626	−0.392813	+	0.919618i	$0.628498\pi$
$594$	0	0
$595$	1.72400e6	0.199639
$596$	0	0
$597$	−4.86238e6	−0.558358
$598$	0	0
$599$	−1.02563e7	−1.16795	−0.583977	−	0.811770i	$-0.698504\pi$
$599$	−1.02563e7	−1.16795	−0.583977	+	0.811770i	$0.698504\pi$
$600$	0	0
$601$	−6.93684e6	−0.783385	−0.391693	−	0.920096i	$-0.628110\pi$
$601$	−6.93684e6	−0.783385	−0.391693	+	0.920096i	$0.628110\pi$
$602$	0	0
$603$	2.37524e6	0.266020
$604$	0	0
$605$	−7.67012e6	−0.851950
$606$	0	0
$607$	6.04044e6	0.665422	0.332711	−	0.943029i	$-0.392037\pi$
$607$	6.04044e6	0.665422	0.332711	+	0.943029i	$0.392037\pi$
$608$	0	0
$609$	−5.26608e6	−0.575366
$610$	0	0
$611$	5.82888e6	0.631658
$612$	0	0
$613$	−5.65002e6	−0.607294	−0.303647	−	0.952785i	$-0.598204\pi$
$613$	−5.65002e6	−0.607294	−0.303647	+	0.952785i	$0.598204\pi$
$614$	0	0
$615$	−739350.	−0.0788247
$616$	0	0
$617$	−7.77818e6	−0.822555	−0.411278	−	0.911510i	$-0.634917\pi$
$617$	−7.77818e6	−0.822555	−0.411278	+	0.911510i	$0.634917\pi$
$618$	0	0
$619$	5.86584e6	0.615323	0.307662	−	0.951496i	$-0.400454\pi$
$619$	5.86584e6	0.615323	0.307662	+	0.951496i	$0.400454\pi$
$620$	0	0
$621$	−1.13141e6	−0.117731
$622$	0	0
$623$	4.77392e6	0.492782
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	−5.63890e6	−0.572829
$628$	0	0
$629$	−7.60801e6	−0.766734
$630$	0	0
$631$	4.14394e6	0.414324	0.207162	−	0.978307i	$-0.433577\pi$
$631$	4.14394e6	0.414324	0.207162	+	0.978307i	$0.433577\pi$
$632$	0	0
$633$	−9.51210e6	−0.943555
$634$	0	0
$635$	2.47220e6	0.243304
$636$	0	0
$637$	−1.01780e7	−0.993839
$638$	0	0
$639$	−6.83705e6	−0.662394
$640$	0	0
$641$	−8.41769e6	−0.809185	−0.404593	−	0.914497i	$-0.632587\pi$
$641$	−8.41769e6	−0.809185	−0.404593	+	0.914497i	$0.632587\pi$
$642$	0	0
$643$	1.79931e7	1.71625	0.858123	−	0.513444i	$-0.171630\pi$
$643$	1.79931e7	1.71625	0.858123	+	0.513444i	$0.171630\pi$
$644$	0	0
$645$	1.70010e6	0.160907
$646$	0	0
$647$	7.92533e6	0.744315	0.372157	−	0.928170i	$-0.378618\pi$
$647$	7.92533e6	0.744315	0.372157	+	0.928170i	$0.378618\pi$
$648$	0	0
$649$	−2.87526e7	−2.67957
$650$	0	0
$651$	−6.70464e6	−0.620045
$652$	0	0
$653$	1.53749e7	1.41101	0.705506	−	0.708704i	$-0.250720\pi$
$653$	1.53749e7	1.41101	0.705506	+	0.708704i	$0.250720\pi$
$654$	0	0
$655$	−740900.	−0.0674771
$656$	0	0
$657$	−3.77055e6	−0.340793
$658$	0	0
$659$	1.46609e7	1.31507	0.657534	−	0.753425i	$-0.271600\pi$
$659$	1.46609e7	1.31507	0.657534	+	0.753425i	$0.271600\pi$
$660$	0	0
$661$	3.32825e6	0.296287	0.148143	−	0.988966i	$-0.452670\pi$
$661$	3.32825e6	0.296287	0.148143	+	0.988966i	$0.452670\pi$
$662$	0	0
$663$	7.58732e6	0.670355
$664$	0	0
$665$	−1.83200e6	−0.160647
$666$	0	0
$667$	1.13513e7	0.987943
$668$	0	0
$669$	−9.81569e6	−0.847921
$670$	0	0
$671$	−2.56623e7	−2.20034
$672$	0	0
$673$	2.08463e7	1.77415	0.887077	−	0.461621i	$-0.152732\pi$
$673$	2.08463e7	1.77415	0.887077	+	0.461621i	$0.152732\pi$
$674$	0	0
$675$	−455625.	−0.0384900
$676$	0	0
$677$	−1.60880e7	−1.34906	−0.674530	−	0.738248i	$-0.735653\pi$
$677$	−1.60880e7	−1.34906	−0.674530	+	0.738248i	$0.735653\pi$
$678$	0	0
$679$	1.09518e7	0.911618
$680$	0	0
$681$	24948.0	0.00206143
$682$	0	0
$683$	3.93124e6	0.322461	0.161231	−	0.986917i	$-0.448454\pi$
$683$	3.93124e6	0.322461	0.161231	+	0.986917i	$0.448454\pi$
$684$	0	0
$685$	115350.	0.00939272
$686$	0	0
$687$	−2.74012e6	−0.221502
$688$	0	0
$689$	8.50664e6	0.682669
$690$	0	0
$691$	9.05300e6	0.721269	0.360634	−	0.932707i	$-0.382560\pi$
$691$	9.05300e6	0.721269	0.360634	+	0.932707i	$0.382560\pi$
$692$	0	0
$693$	4.43232e6	0.350589
$694$	0	0
$695$	6.35730e6	0.499242
$696$	0	0
$697$	2.83253e6	0.220848
$698$	0	0
$699$	2.96991e6	0.229906
$700$	0	0
$701$	−1.82887e7	−1.40568	−0.702842	−	0.711346i	$-0.748086\pi$
$701$	−1.82887e7	−1.40568	−0.702842	+	0.711346i	$0.748086\pi$
$702$	0	0
$703$	8.08462e6	0.616980
$704$	0	0
$705$	1.34100e6	0.101615
$706$	0	0
$707$	1.62286e7	1.22105
$708$	0	0
$709$	−1.05416e7	−0.787572	−0.393786	−	0.919202i	$-0.628835\pi$
$709$	−1.05416e7	−0.787572	−0.393786	+	0.919202i	$0.628835\pi$
$710$	0	0
$711$	−2.16691e6	−0.160756
$712$	0	0
$713$	1.44522e7	1.06466
$714$	0	0
$715$	−1.67238e7	−1.22340
$716$	0	0
$717$	6.49426e6	0.471771
$718$	0	0
$719$	−1.34280e7	−0.968703	−0.484352	−	0.874873i	$-0.660944\pi$
$719$	−1.34280e7	−0.968703	−0.484352	+	0.874873i	$0.660944\pi$
$720$	0	0
$721$	686080.	0.0491515
$722$	0	0
$723$	−2.44384e6	−0.173871
$724$	0	0
$725$	4.57125e6	0.322991
$726$	0	0
$727$	−9.97059e6	−0.699657	−0.349828	−	0.936814i	$-0.613760\pi$
$727$	−9.97059e6	−0.699657	−0.349828	+	0.936814i	$0.613760\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−6.51327e6	−0.450823
$732$	0	0
$733$	2.70572e7	1.86004	0.930020	−	0.367509i	$-0.119789\pi$
$733$	2.70572e7	1.86004	0.930020	+	0.367509i	$0.119789\pi$
$734$	0	0
$735$	−2.34158e6	−0.159878
$736$	0	0
$737$	2.00576e7	1.36022
$738$	0	0
$739$	4.87076e6	0.328084	0.164042	−	0.986453i	$-0.447547\pi$
$739$	4.87076e6	0.328084	0.164042	+	0.986453i	$0.447547\pi$
$740$	0	0
$741$	−8.06263e6	−0.539425
$742$	0	0
$743$	−144288.	−0.00958867	−0.00479433	−	0.999989i	$-0.501526\pi$
$743$	−144288.	−0.00958867	−0.00479433	+	0.999989i	$0.501526\pi$
$744$	0	0
$745$	−2.08065e6	−0.137344
$746$	0	0
$747$	−644436.	−0.0422550
$748$	0	0
$749$	−1.59584e6	−0.103941
$750$	0	0
$751$	8.74882e6	0.566043	0.283022	−	0.959114i	$-0.408663\pi$
$751$	8.74882e6	0.566043	0.283022	+	0.959114i	$0.408663\pi$
$752$	0	0
$753$	−1.21081e7	−0.778193
$754$	0	0
$755$	−5.31540e6	−0.339366
$756$	0	0
$757$	5.58062e6	0.353951	0.176975	−	0.984215i	$-0.443369\pi$
$757$	5.58062e6	0.353951	0.176975	+	0.984215i	$0.443369\pi$
$758$	0	0
$759$	−9.55411e6	−0.601985
$760$	0	0
$761$	273178.	0.0170995	0.00854976	−	0.999963i	$-0.497278\pi$
$761$	273178.	0.0170995	0.00854976	+	0.999963i	$0.497278\pi$
$762$	0	0
$763$	−3.00784e6	−0.187044
$764$	0	0
$765$	1.74555e6	0.107840
$766$	0	0
$767$	−4.11112e7	−2.52332
$768$	0	0
$769$	−2.16358e7	−1.31934	−0.659672	−	0.751554i	$-0.729305\pi$
$769$	−2.16358e7	−1.31934	−0.659672	+	0.751554i	$0.729305\pi$
$770$	0	0
$771$	−1.46061e7	−0.884907
$772$	0	0
$773$	−5.39836e6	−0.324947	−0.162474	−	0.986713i	$-0.551947\pi$
$773$	−5.39836e6	−0.324947	−0.162474	+	0.986713i	$0.551947\pi$
$774$	0	0
$775$	5.82000e6	0.348072
$776$	0	0
$777$	−6.35472e6	−0.377610
$778$	0	0
$779$	−3.00998e6	−0.177713
$780$	0	0
$781$	−5.77351e7	−3.38698
$782$	0	0
$783$	−5.33191e6	−0.310798
$784$	0	0
$785$	2.81755e6	0.163191
$786$	0	0
$787$	1.56497e7	0.900677	0.450338	−	0.892858i	$-0.351303\pi$
$787$	1.56497e7	0.900677	0.450338	+	0.892858i	$0.351303\pi$
$788$	0	0
$789$	4.24915e6	0.243002
$790$	0	0
$791$	−1.53470e7	−0.872134
$792$	0	0
$793$	−3.66926e7	−2.07203
$794$	0	0
$795$	1.95705e6	0.109821
$796$	0	0
$797$	2.43553e7	1.35815	0.679074	−	0.734069i	$-0.262381\pi$
$797$	2.43553e7	1.35815	0.679074	+	0.734069i	$0.262381\pi$
$798$	0	0
$799$	−5.13752e6	−0.284699
$800$	0	0
$801$	4.83359e6	0.266188
$802$	0	0
$803$	−3.18402e7	−1.74256
$804$	0	0
$805$	−3.10400e6	−0.168823
$806$	0	0
$807$	21870.0	0.00118213
$808$	0	0
$809$	−2.60329e7	−1.39846	−0.699231	−	0.714896i	$-0.746474\pi$
$809$	−2.60329e7	−1.39846	−0.699231	+	0.714896i	$0.746474\pi$
$810$	0	0
$811$	−2.63808e7	−1.40843	−0.704217	−	0.709985i	$-0.748702\pi$
$811$	−2.63808e7	−1.40843	−0.704217	+	0.709985i	$0.748702\pi$
$812$	0	0
$813$	1.48641e7	0.788701
$814$	0	0
$815$	1.02793e7	0.542088
$816$	0	0
$817$	6.92130e6	0.362771
$818$	0	0
$819$	6.33744e6	0.330145
$820$	0	0
$821$	7.46105e6	0.386315	0.193158	−	0.981168i	$-0.438127\pi$
$821$	7.46105e6	0.386315	0.193158	+	0.981168i	$0.438127\pi$
$822$	0	0
$823$	3.34734e6	0.172266	0.0861332	−	0.996284i	$-0.472549\pi$
$823$	3.34734e6	0.172266	0.0861332	+	0.996284i	$0.472549\pi$
$824$	0	0
$825$	−3.84750e6	−0.196808
$826$	0	0
$827$	−3.70089e7	−1.88167	−0.940833	−	0.338872i	$-0.889955\pi$
$827$	−3.70089e7	−1.88167	−0.940833	+	0.338872i	$0.889955\pi$
$828$	0	0
$829$	−2.35921e7	−1.19229	−0.596143	−	0.802878i	$-0.703301\pi$
$829$	−2.35921e7	−1.19229	−0.596143	+	0.802878i	$0.703301\pi$
$830$	0	0
$831$	1.99016e7	0.999735
$832$	0	0
$833$	8.97083e6	0.447940
$834$	0	0
$835$	6.47240e6	0.321254
$836$	0	0
$837$	−6.78845e6	−0.334932
$838$	0	0
$839$	3.54805e7	1.74014	0.870071	−	0.492926i	$-0.164073\pi$
$839$	3.54805e7	1.74014	0.870071	+	0.492926i	$0.164073\pi$
$840$	0	0
$841$	3.29834e7	1.60807
$842$	0	0
$843$	3.80713e6	0.184514
$844$	0	0
$845$	−1.46298e7	−0.704849
$846$	0	0
$847$	2.45444e7	1.17556
$848$	0	0
$849$	4.38347e6	0.208713
$850$	0	0
$851$	1.36980e7	0.648383
$852$	0	0
$853$	5.54993e6	0.261165	0.130582	−	0.991437i	$-0.458315\pi$
$853$	5.54993e6	0.261165	0.130582	+	0.991437i	$0.458315\pi$
$854$	0	0
$855$	−1.85490e6	−0.0867771
$856$	0	0
$857$	−2.21344e7	−1.02948	−0.514738	−	0.857348i	$-0.672111\pi$
$857$	−2.21344e7	−1.02948	−0.514738	+	0.857348i	$0.672111\pi$
$858$	0	0
$859$	−9.65533e6	−0.446462	−0.223231	−	0.974766i	$-0.571660\pi$
$859$	−9.65533e6	−0.446462	−0.223231	+	0.974766i	$0.571660\pi$
$860$	0	0
$861$	2.36592e6	0.108766
$862$	0	0
$863$	−1.43771e7	−0.657120	−0.328560	−	0.944483i	$-0.606563\pi$
$863$	−1.43771e7	−0.657120	−0.328560	+	0.944483i	$0.606563\pi$
$864$	0	0
$865$	−9.92565e6	−0.451044
$866$	0	0
$867$	6.09132e6	0.275210
$868$	0	0
$869$	−1.82984e7	−0.821983
$870$	0	0
$871$	2.86789e7	1.28090
$872$	0	0
$873$	1.10887e7	0.492432
$874$	0	0
$875$	−1.25000e6	−0.0551937
$876$	0	0
$877$	−9.01032e6	−0.395586	−0.197793	−	0.980244i	$-0.563377\pi$
$877$	−9.01032e6	−0.395586	−0.197793	+	0.980244i	$0.563377\pi$
$878$	0	0
$879$	−9.24230e6	−0.403467
$880$	0	0
$881$	−1.64420e7	−0.713700	−0.356850	−	0.934162i	$-0.616149\pi$
$881$	−1.64420e7	−0.713700	−0.356850	+	0.934162i	$0.616149\pi$
$882$	0	0
$883$	6.06516e6	0.261783	0.130891	−	0.991397i	$-0.458216\pi$
$883$	6.06516e6	0.261783	0.130891	+	0.991397i	$0.458216\pi$
$884$	0	0
$885$	−9.45810e6	−0.405925
$886$	0	0
$887$	−2.85746e7	−1.21947	−0.609735	−	0.792605i	$-0.708724\pi$
$887$	−2.85746e7	−1.21947	−0.609735	+	0.792605i	$0.708724\pi$
$888$	0	0
$889$	−7.91104e6	−0.335722
$890$	0	0
$891$	4.48772e6	0.189379
$892$	0	0
$893$	5.45936e6	0.229094
$894$	0	0
$895$	1.18367e7	0.493939
$896$	0	0
$897$	−1.36607e7	−0.566881
$898$	0	0
$899$	6.81080e7	2.81060
$900$	0	0
$901$	−7.49768e6	−0.307691
$902$	0	0
$903$	−5.44032e6	−0.222027
$904$	0	0
$905$	−1.99585e6	−0.0810040
$906$	0	0
$907$	−1.47466e7	−0.595215	−0.297607	−	0.954688i	$-0.596189\pi$
$907$	−1.47466e7	−0.595215	−0.297607	+	0.954688i	$0.596189\pi$
$908$	0	0
$909$	1.64315e7	0.659580
$910$	0	0
$911$	2.61222e6	0.104283	0.0521416	−	0.998640i	$-0.483395\pi$
$911$	2.61222e6	0.104283	0.0521416	+	0.998640i	$0.483395\pi$
$912$	0	0
$913$	−5.44190e6	−0.216060
$914$	0	0
$915$	−8.44155e6	−0.333326
$916$	0	0
$917$	2.37088e6	0.0931078
$918$	0	0
$919$	4.66079e7	1.82042	0.910208	−	0.414152i	$-0.135922\pi$
$919$	4.66079e7	1.82042	0.910208	+	0.414152i	$0.135922\pi$
$920$	0	0
$921$	9.64199e6	0.374557
$922$	0	0
$923$	−8.25510e7	−3.18947
$924$	0	0
$925$	5.51625e6	0.211977
$926$	0	0
$927$	694656.	0.0265504
$928$	0	0
$929$	−3.16320e7	−1.20251	−0.601254	−	0.799058i	$-0.705332\pi$
$929$	−3.16320e7	−1.20251	−0.601254	+	0.799058i	$0.705332\pi$
$930$	0	0
$931$	−9.53281e6	−0.360451
$932$	0	0
$933$	1.68679e7	0.634393
$934$	0	0
$935$	1.47402e7	0.551410
$936$	0	0
$937$	2.57021e7	0.956355	0.478177	−	0.878263i	$-0.341298\pi$
$937$	2.57021e7	0.956355	0.478177	+	0.878263i	$0.341298\pi$
$938$	0	0
$939$	−2.63594e7	−0.975601
$940$	0	0
$941$	7.01907e6	0.258408	0.129204	−	0.991618i	$-0.458758\pi$
$941$	7.01907e6	0.258408	0.129204	+	0.991618i	$0.458758\pi$
$942$	0	0
$943$	−5.09987e6	−0.186758
$944$	0	0
$945$	1.45800e6	0.0531102
$946$	0	0
$947$	3.38467e6	0.122643	0.0613213	−	0.998118i	$-0.480469\pi$
$947$	3.38467e6	0.122643	0.0613213	+	0.998118i	$0.480469\pi$
$948$	0	0
$949$	−4.55259e7	−1.64094
$950$	0	0
$951$	−2.65348e7	−0.951401
$952$	0	0
$953$	−9.74473e6	−0.347566	−0.173783	−	0.984784i	$-0.555599\pi$
$953$	−9.74473e6	−0.347566	−0.173783	+	0.984784i	$0.555599\pi$
$954$	0	0
$955$	9.93400e6	0.352465
$956$	0	0
$957$	−4.50250e7	−1.58918
$958$	0	0
$959$	−369120.	−0.0129605
$960$	0	0
$961$	5.80842e7	2.02885
$962$	0	0
$963$	−1.61579e6	−0.0561460
$964$	0	0
$965$	−1.94464e7	−0.672236
$966$	0	0
$967$	1.09405e7	0.376244	0.188122	−	0.982146i	$-0.439760\pi$
$967$	1.09405e7	0.376244	0.188122	+	0.982146i	$0.439760\pi$
$968$	0	0
$969$	7.10633e6	0.243128
$970$	0	0
$971$	−2.25329e7	−0.766953	−0.383476	−	0.923551i	$-0.625273\pi$
$971$	−2.25329e7	−0.766953	−0.383476	+	0.923551i	$0.625273\pi$
$972$	0	0
$973$	−2.03434e7	−0.688875
$974$	0	0
$975$	−5.50125e6	−0.185332
$976$	0	0
$977$	−2.79146e7	−0.935610	−0.467805	−	0.883832i	$-0.654955\pi$
$977$	−2.79146e7	−0.935610	−0.467805	+	0.883832i	$0.654955\pi$
$978$	0	0
$979$	4.08170e7	1.36108
$980$	0	0
$981$	−3.04544e6	−0.101036
$982$	0	0
$983$	3.07607e7	1.01534	0.507670	−	0.861551i	$-0.330507\pi$
$983$	3.07607e7	1.01534	0.507670	+	0.861551i	$0.330507\pi$
$984$	0	0
$985$	6.36695e6	0.209094
$986$	0	0
$987$	−4.29120e6	−0.140212
$988$	0	0
$989$	1.17269e7	0.381235
$990$	0	0
$991$	4.31296e6	0.139505	0.0697527	−	0.997564i	$-0.477779\pi$
$991$	4.31296e6	0.139505	0.0697527	+	0.997564i	$0.477779\pi$
$992$	0	0
$993$	7.70490e6	0.247967
$994$	0	0
$995$	−1.35066e7	−0.432502
$996$	0	0
$997$	2.85667e7	0.910170	0.455085	−	0.890448i	$-0.349609\pi$
$997$	2.85667e7	0.910170	0.455085	+	0.890448i	$0.349609\pi$
$998$	0	0
$999$	−6.43415e6	−0.203975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.6.a.f.1.1		1
4.3	odd	2		960.6.a.o.1.1		1
8.3	odd	2		120.6.a.c.1.1	✓	1
8.5	even	2		240.6.a.n.1.1		1
24.5	odd	2		720.6.a.g.1.1		1
24.11	even	2		360.6.a.c.1.1		1
40.3	even	4		600.6.f.i.49.1		2
40.19	odd	2		600.6.a.g.1.1		1
40.27	even	4		600.6.f.i.49.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.6.a.c.1.1	✓	1	8.3	odd	2
240.6.a.n.1.1		1	8.5	even	2
360.6.a.c.1.1		1	24.11	even	2
600.6.a.g.1.1		1	40.19	odd	2
600.6.f.i.49.1		2	40.3	even	4
600.6.f.i.49.2		2	40.27	even	4
720.6.a.g.1.1		1	24.5	odd	2
960.6.a.f.1.1		1	1.1	even	1	trivial
960.6.a.o.1.1		1	4.3	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	960.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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