LMFDB - Embedded newform 704.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,6,Mod(1,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, 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("704.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	704.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:	$112.910209148$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	704.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} +51.0000 q^{5} -166.000 q^{7} -242.000 q^{9} +O(q^{10})$

$q-1.00000 q^{3} +51.0000 q^{5} -166.000 q^{7} -242.000 q^{9} +121.000 q^{11} -692.000 q^{13} -51.0000 q^{15} -738.000 q^{17} -1424.00 q^{19} +166.000 q^{21} -1779.00 q^{23} -524.000 q^{25} +485.000 q^{27} +2064.00 q^{29} +6245.00 q^{31} -121.000 q^{33} -8466.00 q^{35} +14785.0 q^{37} +692.000 q^{39} +5304.00 q^{41} -17798.0 q^{43} -12342.0 q^{45} -17184.0 q^{47} +10749.0 q^{49} +738.000 q^{51} +30726.0 q^{53} +6171.00 q^{55} +1424.00 q^{57} +34989.0 q^{59} +45940.0 q^{61} +40172.0 q^{63} -35292.0 q^{65} -25343.0 q^{67} +1779.00 q^{69} +13311.0 q^{71} -53260.0 q^{73} +524.000 q^{75} -20086.0 q^{77} +77234.0 q^{79} +58321.0 q^{81} -55014.0 q^{83} -37638.0 q^{85} -2064.00 q^{87} +125415. q^{89} +114872. q^{91} -6245.00 q^{93} -72624.0 q^{95} -88807.0 q^{97} -29282.0 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−1.00000	−0.0641500	−0.0320750	−	0.999485i	$-0.510212\pi$
$3$	−1.00000	−0.0641500	−0.0320750	+	0.999485i	$0.510212\pi$
$4$	0	0
$5$	51.0000	0.912316	0.456158	−	0.889899i	$-0.349225\pi$
$5$	51.0000	0.912316	0.456158	+	0.889899i	$0.349225\pi$
$6$	0	0
$7$	−166.000	−1.28045	−0.640226	−	0.768187i	$-0.721159\pi$
$7$	−166.000	−1.28045	−0.640226	+	0.768187i	$0.721159\pi$
$8$	0	0
$9$	−242.000	−0.995885
$10$	0	0
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	0	0
$13$	−692.000	−1.13566	−0.567829	−	0.823146i	$-0.692217\pi$
$13$	−692.000	−1.13566	−0.567829	+	0.823146i	$0.692217\pi$
$14$	0	0
$15$	−51.0000	−0.0585251
$16$	0	0
$17$	−738.000	−0.619347	−0.309674	−	0.950843i	$-0.600220\pi$
$17$	−738.000	−0.619347	−0.309674	+	0.950843i	$0.600220\pi$
$18$	0	0
$19$	−1424.00	−0.904953	−0.452476	−	0.891776i	$-0.649459\pi$
$19$	−1424.00	−0.904953	−0.452476	+	0.891776i	$0.649459\pi$
$20$	0	0
$21$	166.000	0.0821410
$22$	0	0
$23$	−1779.00	−0.701223	−0.350612	−	0.936521i	$-0.614026\pi$
$23$	−1779.00	−0.701223	−0.350612	+	0.936521i	$0.614026\pi$
$24$	0	0
$25$	−524.000	−0.167680
$26$	0	0
$27$	485.000	0.128036
$28$	0	0
$29$	2064.00	0.455737	0.227869	−	0.973692i	$-0.426824\pi$
$29$	2064.00	0.455737	0.227869	+	0.973692i	$0.426824\pi$
$30$	0	0
$31$	6245.00	1.16715	0.583577	−	0.812058i	$-0.301653\pi$
$31$	6245.00	1.16715	0.583577	+	0.812058i	$0.301653\pi$
$32$	0	0
$33$	−121.000	−0.0193420
$34$	0	0
$35$	−8466.00	−1.16818
$36$	0	0
$37$	14785.0	1.77549	0.887743	−	0.460340i	$-0.152273\pi$
$37$	14785.0	1.77549	0.887743	+	0.460340i	$0.152273\pi$
$38$	0	0
$39$	692.000	0.0728525
$40$	0	0
$41$	5304.00	0.492770	0.246385	−	0.969172i	$-0.420757\pi$
$41$	5304.00	0.492770	0.246385	+	0.969172i	$0.420757\pi$
$42$	0	0
$43$	−17798.0	−1.46791	−0.733956	−	0.679197i	$-0.762328\pi$
$43$	−17798.0	−1.46791	−0.733956	+	0.679197i	$0.762328\pi$
$44$	0	0
$45$	−12342.0	−0.908561
$46$	0	0
$47$	−17184.0	−1.13470	−0.567348	−	0.823478i	$-0.692031\pi$
$47$	−17184.0	−1.13470	−0.567348	+	0.823478i	$0.692031\pi$
$48$	0	0
$49$	10749.0	0.639555
$50$	0	0
$51$	738.000	0.0397311
$52$	0	0
$53$	30726.0	1.50251	0.751253	−	0.660014i	$-0.229450\pi$
$53$	30726.0	1.50251	0.751253	+	0.660014i	$0.229450\pi$
$54$	0	0
$55$	6171.00	0.275074
$56$	0	0
$57$	1424.00	0.0580528
$58$	0	0
$59$	34989.0	1.30858	0.654292	−	0.756242i	$-0.272967\pi$
$59$	34989.0	1.30858	0.654292	+	0.756242i	$0.272967\pi$
$60$	0	0
$61$	45940.0	1.58076	0.790381	−	0.612616i	$-0.209883\pi$
$61$	45940.0	1.58076	0.790381	+	0.612616i	$0.209883\pi$
$62$	0	0
$63$	40172.0	1.27518
$64$	0	0
$65$	−35292.0	−1.03608
$66$	0	0
$67$	−25343.0	−0.689717	−0.344859	−	0.938655i	$-0.612073\pi$
$67$	−25343.0	−0.689717	−0.344859	+	0.938655i	$0.612073\pi$
$68$	0	0
$69$	1779.00	0.0449835
$70$	0	0
$71$	13311.0	0.313375	0.156688	−	0.987648i	$-0.449918\pi$
$71$	13311.0	0.313375	0.156688	+	0.987648i	$0.449918\pi$
$72$	0	0
$73$	−53260.0	−1.16975	−0.584876	−	0.811123i	$-0.698857\pi$
$73$	−53260.0	−1.16975	−0.584876	+	0.811123i	$0.698857\pi$
$74$	0	0
$75$	524.000	0.0107567
$76$	0	0
$77$	−20086.0	−0.386071
$78$	0	0
$79$	77234.0	1.39233	0.696163	−	0.717884i	$-0.254889\pi$
$79$	77234.0	1.39233	0.696163	+	0.717884i	$0.254889\pi$
$80$	0	0
$81$	58321.0	0.987671
$82$	0	0
$83$	−55014.0	−0.876553	−0.438276	−	0.898840i	$-0.644411\pi$
$83$	−55014.0	−0.876553	−0.438276	+	0.898840i	$0.644411\pi$
$84$	0	0
$85$	−37638.0	−0.565040
$86$	0	0
$87$	−2064.00	−0.0292356
$88$	0	0
$89$	125415.	1.67832	0.839159	−	0.543886i	$-0.183047\pi$
$89$	125415.	1.67832	0.839159	+	0.543886i	$0.183047\pi$
$90$	0	0
$91$	114872.	1.45416
$92$	0	0
$93$	−6245.00	−0.0748730
$94$	0	0
$95$	−72624.0	−0.825603
$96$	0	0
$97$	−88807.0	−0.958336	−0.479168	−	0.877723i	$-0.659062\pi$
$97$	−88807.0	−0.958336	−0.479168	+	0.877723i	$0.659062\pi$
$98$	0	0
$99$	−29282.0	−0.300271
$100$	0	0
$101$	−1482.00	−0.0144559	−0.00722794	−	0.999974i	$-0.502301\pi$
$101$	−1482.00	−0.0144559	−0.00722794	+	0.999974i	$0.502301\pi$
$102$	0	0
$103$	−117496.	−1.09126	−0.545632	−	0.838025i	$-0.683710\pi$
$103$	−117496.	−1.09126	−0.545632	+	0.838025i	$0.683710\pi$
$104$	0	0
$105$	8466.00	0.0749385
$106$	0	0
$107$	79362.0	0.670121	0.335060	−	0.942197i	$-0.391243\pi$
$107$	79362.0	0.670121	0.335060	+	0.942197i	$0.391243\pi$
$108$	0	0
$109$	−87842.0	−0.708167	−0.354084	−	0.935214i	$-0.615207\pi$
$109$	−87842.0	−0.708167	−0.354084	+	0.935214i	$0.615207\pi$
$110$	0	0
$111$	−14785.0	−0.113897
$112$	0	0
$113$	−47247.0	−0.348079	−0.174040	−	0.984739i	$-0.555682\pi$
$113$	−47247.0	−0.348079	−0.174040	+	0.984739i	$0.555682\pi$
$114$	0	0
$115$	−90729.0	−0.639737
$116$	0	0
$117$	167464.	1.13098
$118$	0	0
$119$	122508.	0.793044
$120$	0	0
$121$	14641.0	0.0909091
$122$	0	0
$123$	−5304.00	−0.0316112
$124$	0	0
$125$	−186099.	−1.06529
$126$	0	0
$127$	−239416.	−1.31718	−0.658588	−	0.752504i	$-0.728846\pi$
$127$	−239416.	−1.31718	−0.658588	+	0.752504i	$0.728846\pi$
$128$	0	0
$129$	17798.0	0.0941666
$130$	0	0
$131$	98142.0	0.499662	0.249831	−	0.968289i	$-0.419625\pi$
$131$	98142.0	0.499662	0.249831	+	0.968289i	$0.419625\pi$
$132$	0	0
$133$	236384.	1.15875
$134$	0	0
$135$	24735.0	0.116809
$136$	0	0
$137$	400137.	1.82141	0.910704	−	0.413059i	$-0.135540\pi$
$137$	400137.	1.82141	0.910704	+	0.413059i	$0.135540\pi$
$138$	0	0
$139$	−205766.	−0.903310	−0.451655	−	0.892193i	$-0.649166\pi$
$139$	−205766.	−0.903310	−0.451655	+	0.892193i	$0.649166\pi$
$140$	0	0
$141$	17184.0	0.0727908
$142$	0	0
$143$	−83732.0	−0.342414
$144$	0	0
$145$	105264.	0.415776
$146$	0	0
$147$	−10749.0	−0.0410275
$148$	0	0
$149$	−87726.0	−0.323715	−0.161857	−	0.986814i	$-0.551748\pi$
$149$	−87726.0	−0.323715	−0.161857	+	0.986814i	$0.551748\pi$
$150$	0	0
$151$	−432778.	−1.54462	−0.772312	−	0.635243i	$-0.780900\pi$
$151$	−432778.	−1.54462	−0.772312	+	0.635243i	$0.780900\pi$
$152$	0	0
$153$	178596.	0.616798
$154$	0	0
$155$	318495.	1.06481
$156$	0	0
$157$	34075.0	0.110328	0.0551641	−	0.998477i	$-0.482432\pi$
$157$	34075.0	0.110328	0.0551641	+	0.998477i	$0.482432\pi$
$158$	0	0
$159$	−30726.0	−0.0963858
$160$	0	0
$161$	295314.	0.897882
$162$	0	0
$163$	−45020.0	−0.132720	−0.0663600	−	0.997796i	$-0.521139\pi$
$163$	−45020.0	−0.132720	−0.0663600	+	0.997796i	$0.521139\pi$
$164$	0	0
$165$	−6171.00	−0.0176460
$166$	0	0
$167$	482556.	1.33893	0.669463	−	0.742845i	$-0.266524\pi$
$167$	482556.	1.33893	0.669463	+	0.742845i	$0.266524\pi$
$168$	0	0
$169$	107571.	0.289720
$170$	0	0
$171$	344608.	0.901229
$172$	0	0
$173$	766254.	1.94651	0.973257	−	0.229719i	$-0.0737808\pi$
$173$	766254.	1.94651	0.973257	+	0.229719i	$0.0737808\pi$
$174$	0	0
$175$	86984.0	0.214706
$176$	0	0
$177$	−34989.0	−0.0839457
$178$	0	0
$179$	−303399.	−0.707753	−0.353876	−	0.935292i	$-0.615137\pi$
$179$	−303399.	−0.707753	−0.353876	+	0.935292i	$0.615137\pi$
$180$	0	0
$181$	285181.	0.647030	0.323515	−	0.946223i	$-0.395135\pi$
$181$	285181.	0.647030	0.323515	+	0.946223i	$0.395135\pi$
$182$	0	0
$183$	−45940.0	−0.101406
$184$	0	0
$185$	754035.	1.61980
$186$	0	0
$187$	−89298.0	−0.186740
$188$	0	0
$189$	−80510.0	−0.163944
$190$	0	0
$191$	767067.	1.52142	0.760711	−	0.649090i	$-0.224850\pi$
$191$	767067.	1.52142	0.760711	+	0.649090i	$0.224850\pi$
$192$	0	0
$193$	411668.	0.795525	0.397763	−	0.917488i	$-0.369787\pi$
$193$	411668.	0.795525	0.397763	+	0.917488i	$0.369787\pi$
$194$	0	0
$195$	35292.0	0.0664645
$196$	0	0
$197$	759258.	1.39387	0.696937	−	0.717132i	$-0.254545\pi$
$197$	759258.	1.39387	0.696937	+	0.717132i	$0.254545\pi$
$198$	0	0
$199$	−46600.0	−0.0834167	−0.0417084	−	0.999130i	$-0.513280\pi$
$199$	−46600.0	−0.0834167	−0.0417084	+	0.999130i	$0.513280\pi$
$200$	0	0
$201$	25343.0	0.0442454
$202$	0	0
$203$	−342624.	−0.583549
$204$	0	0
$205$	270504.	0.449561
$206$	0	0
$207$	430518.	0.698338
$208$	0	0
$209$	−172304.	−0.272854
$210$	0	0
$211$	932428.	1.44181	0.720907	−	0.693032i	$-0.243726\pi$
$211$	932428.	1.44181	0.720907	+	0.693032i	$0.243726\pi$
$212$	0	0
$213$	−13311.0	−0.0201030
$214$	0	0
$215$	−907698.	−1.33920
$216$	0	0
$217$	−1.03667e6	−1.49448
$218$	0	0
$219$	53260.0	0.0750397
$220$	0	0
$221$	510696.	0.703367
$222$	0	0
$223$	169745.	0.228578	0.114289	−	0.993448i	$-0.463541\pi$
$223$	169745.	0.228578	0.114289	+	0.993448i	$0.463541\pi$
$224$	0	0
$225$	126808.	0.166990
$226$	0	0
$227$	−198078.	−0.255136	−0.127568	−	0.991830i	$-0.540717\pi$
$227$	−198078.	−0.255136	−0.127568	+	0.991830i	$0.540717\pi$
$228$	0	0
$229$	849997.	1.07110	0.535548	−	0.844505i	$-0.320105\pi$
$229$	849997.	1.07110	0.535548	+	0.844505i	$0.320105\pi$
$230$	0	0
$231$	20086.0	0.0247664
$232$	0	0
$233$	−401832.	−0.484903	−0.242451	−	0.970164i	$-0.577952\pi$
$233$	−401832.	−0.484903	−0.242451	+	0.970164i	$0.577952\pi$
$234$	0	0
$235$	−876384.	−1.03520
$236$	0	0
$237$	−77234.0	−0.0893177
$238$	0	0
$239$	855174.	0.968411	0.484206	−	0.874954i	$-0.339109\pi$
$239$	855174.	0.968411	0.484206	+	0.874954i	$0.339109\pi$
$240$	0	0
$241$	1.12546e6	1.24821	0.624107	−	0.781339i	$-0.285463\pi$
$241$	1.12546e6	1.24821	0.624107	+	0.781339i	$0.285463\pi$
$242$	0	0
$243$	−176176.	−0.191395
$244$	0	0
$245$	548199.	0.583476
$246$	0	0
$247$	985408.	1.02772
$248$	0	0
$249$	55014.0	0.0562309
$250$	0	0
$251$	1.19751e6	1.19976	0.599882	−	0.800088i	$-0.295214\pi$
$251$	1.19751e6	1.19976	0.599882	+	0.800088i	$0.295214\pi$
$252$	0	0
$253$	−215259.	−0.211427
$254$	0	0
$255$	37638.0	0.0362473
$256$	0	0
$257$	37758.0	0.0356596	0.0178298	−	0.999841i	$-0.494324\pi$
$257$	37758.0	0.0356596	0.0178298	+	0.999841i	$0.494324\pi$
$258$	0	0
$259$	−2.45431e6	−2.27342
$260$	0	0
$261$	−499488.	−0.453862
$262$	0	0
$263$	−631254.	−0.562749	−0.281375	−	0.959598i	$-0.590790\pi$
$263$	−631254.	−0.562749	−0.281375	+	0.959598i	$0.590790\pi$
$264$	0	0
$265$	1.56703e6	1.37076
$266$	0	0
$267$	−125415.	−0.107664
$268$	0	0
$269$	1.08034e6	0.910292	0.455146	−	0.890417i	$-0.349587\pi$
$269$	1.08034e6	0.910292	0.455146	+	0.890417i	$0.349587\pi$
$270$	0	0
$271$	−816100.	−0.675025	−0.337513	−	0.941321i	$-0.609586\pi$
$271$	−816100.	−0.675025	−0.337513	+	0.941321i	$0.609586\pi$
$272$	0	0
$273$	−114872.	−0.0932841
$274$	0	0
$275$	−63404.0	−0.0505574
$276$	0	0
$277$	−1.68820e6	−1.32198	−0.660989	−	0.750396i	$-0.729863\pi$
$277$	−1.68820e6	−1.32198	−0.660989	+	0.750396i	$0.729863\pi$
$278$	0	0
$279$	−1.51129e6	−1.16235
$280$	0	0
$281$	−879042.	−0.664116	−0.332058	−	0.943259i	$-0.607743\pi$
$281$	−879042.	−0.664116	−0.332058	+	0.943259i	$0.607743\pi$
$282$	0	0
$283$	−1.54027e6	−1.14322	−0.571611	−	0.820525i	$-0.693681\pi$
$283$	−1.54027e6	−1.14322	−0.571611	+	0.820525i	$0.693681\pi$
$284$	0	0
$285$	72624.0	0.0529624
$286$	0	0
$287$	−880464.	−0.630967
$288$	0	0
$289$	−875213.	−0.616409
$290$	0	0
$291$	88807.0	0.0614773
$292$	0	0
$293$	−720840.	−0.490535	−0.245267	−	0.969455i	$-0.578876\pi$
$293$	−720840.	−0.490535	−0.245267	+	0.969455i	$0.578876\pi$
$294$	0	0
$295$	1.78444e6	1.19384
$296$	0	0
$297$	58685.0	0.0386043
$298$	0	0
$299$	1.23107e6	0.796350
$300$	0	0
$301$	2.95447e6	1.87959
$302$	0	0
$303$	1482.00	0.000927346 0
$304$	0	0
$305$	2.34294e6	1.44215
$306$	0	0
$307$	1.03905e6	0.629201	0.314601	−	0.949224i	$-0.398129\pi$
$307$	1.03905e6	0.629201	0.314601	+	0.949224i	$0.398129\pi$
$308$	0	0
$309$	117496.	0.0700046
$310$	0	0
$311$	−1.25135e6	−0.733630	−0.366815	−	0.930294i	$-0.619552\pi$
$311$	−1.25135e6	−0.733630	−0.366815	+	0.930294i	$0.619552\pi$
$312$	0	0
$313$	−1.44336e6	−0.832749	−0.416375	−	0.909193i	$-0.636699\pi$
$313$	−1.44336e6	−0.832749	−0.416375	+	0.909193i	$0.636699\pi$
$314$	0	0
$315$	2.04877e6	1.16337
$316$	0	0
$317$	2.01208e6	1.12460	0.562298	−	0.826934i	$-0.309917\pi$
$317$	2.01208e6	1.12460	0.562298	+	0.826934i	$0.309917\pi$
$318$	0	0
$319$	249744.	0.137410
$320$	0	0
$321$	−79362.0	−0.0429883
$322$	0	0
$323$	1.05091e6	0.560480
$324$	0	0
$325$	362608.	0.190427
$326$	0	0
$327$	87842.0	0.0454290
$328$	0	0
$329$	2.85254e6	1.45292
$330$	0	0
$331$	−2.01734e6	−1.01207	−0.506033	−	0.862514i	$-0.668888\pi$
$331$	−2.01734e6	−1.01207	−0.506033	+	0.862514i	$0.668888\pi$
$332$	0	0
$333$	−3.57797e6	−1.76818
$334$	0	0
$335$	−1.29249e6	−0.629240
$336$	0	0
$337$	264122.	0.126686	0.0633432	−	0.997992i	$-0.479824\pi$
$337$	264122.	0.126686	0.0633432	+	0.997992i	$0.479824\pi$
$338$	0	0
$339$	47247.0	0.0223293
$340$	0	0
$341$	755645.	0.351910
$342$	0	0
$343$	1.00563e6	0.461532
$344$	0	0
$345$	90729.0	0.0410392
$346$	0	0
$347$	1.71049e6	0.762601	0.381300	−	0.924451i	$-0.375476\pi$
$347$	1.71049e6	0.762601	0.381300	+	0.924451i	$0.375476\pi$
$348$	0	0
$349$	−218822.	−0.0961673	−0.0480836	−	0.998843i	$-0.515311\pi$
$349$	−218822.	−0.0961673	−0.0480836	+	0.998843i	$0.515311\pi$
$350$	0	0
$351$	−335620.	−0.145405
$352$	0	0
$353$	3.68192e6	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$353$	3.68192e6	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$354$	0	0
$355$	678861.	0.285897
$356$	0	0
$357$	−122508.	−0.0508738
$358$	0	0
$359$	1.88528e6	0.772042	0.386021	−	0.922490i	$-0.373849\pi$
$359$	1.88528e6	0.772042	0.386021	+	0.922490i	$0.373849\pi$
$360$	0	0
$361$	−448323.	−0.181060
$362$	0	0
$363$	−14641.0	−0.00583182
$364$	0	0
$365$	−2.71626e6	−1.06718
$366$	0	0
$367$	−3.11666e6	−1.20788	−0.603940	−	0.797029i	$-0.706404\pi$
$367$	−3.11666e6	−1.20788	−0.603940	+	0.797029i	$0.706404\pi$
$368$	0	0
$369$	−1.28357e6	−0.490742
$370$	0	0
$371$	−5.10052e6	−1.92389
$372$	0	0
$373$	−1.39441e6	−0.518943	−0.259471	−	0.965751i	$-0.583548\pi$
$373$	−1.39441e6	−0.518943	−0.259471	+	0.965751i	$0.583548\pi$
$374$	0	0
$375$	186099.	0.0683386
$376$	0	0
$377$	−1.42829e6	−0.517562
$378$	0	0
$379$	4.26036e6	1.52352	0.761759	−	0.647860i	$-0.224336\pi$
$379$	4.26036e6	1.52352	0.761759	+	0.647860i	$0.224336\pi$
$380$	0	0
$381$	239416.	0.0844969
$382$	0	0
$383$	201765.	0.0702828	0.0351414	−	0.999382i	$-0.488812\pi$
$383$	201765.	0.0702828	0.0351414	+	0.999382i	$0.488812\pi$
$384$	0	0
$385$	−1.02439e6	−0.352218
$386$	0	0
$387$	4.30712e6	1.46187
$388$	0	0
$389$	−1.94882e6	−0.652977	−0.326489	−	0.945201i	$-0.605865\pi$
$389$	−1.94882e6	−0.652977	−0.326489	+	0.945201i	$0.605865\pi$
$390$	0	0
$391$	1.31290e6	0.434301
$392$	0	0
$393$	−98142.0	−0.0320534
$394$	0	0
$395$	3.93893e6	1.27024
$396$	0	0
$397$	1.46826e6	0.467548	0.233774	−	0.972291i	$-0.424892\pi$
$397$	1.46826e6	0.467548	0.233774	+	0.972291i	$0.424892\pi$
$398$	0	0
$399$	−236384.	−0.0743337
$400$	0	0
$401$	2.24618e6	0.697563	0.348781	−	0.937204i	$-0.386596\pi$
$401$	2.24618e6	0.697563	0.348781	+	0.937204i	$0.386596\pi$
$402$	0	0
$403$	−4.32154e6	−1.32549
$404$	0	0
$405$	2.97437e6	0.901068
$406$	0	0
$407$	1.78898e6	0.535329
$408$	0	0
$409$	−3.61488e6	−1.06853	−0.534263	−	0.845318i	$-0.679411\pi$
$409$	−3.61488e6	−1.06853	−0.534263	+	0.845318i	$0.679411\pi$
$410$	0	0
$411$	−400137.	−0.116843
$412$	0	0
$413$	−5.80817e6	−1.67558
$414$	0	0
$415$	−2.80571e6	−0.799693
$416$	0	0
$417$	205766.	0.0579473
$418$	0	0
$419$	3.81239e6	1.06087	0.530435	−	0.847726i	$-0.322029\pi$
$419$	3.81239e6	1.06087	0.530435	+	0.847726i	$0.322029\pi$
$420$	0	0
$421$	−1.97346e6	−0.542655	−0.271327	−	0.962487i	$-0.587463\pi$
$421$	−1.97346e6	−0.542655	−0.271327	+	0.962487i	$0.587463\pi$
$422$	0	0
$423$	4.15853e6	1.13003
$424$	0	0
$425$	386712.	0.103852
$426$	0	0
$427$	−7.62604e6	−2.02409
$428$	0	0
$429$	83732.0	0.0219659
$430$	0	0
$431$	−2.08359e6	−0.540280	−0.270140	−	0.962821i	$-0.587070\pi$
$431$	−2.08359e6	−0.540280	−0.270140	+	0.962821i	$0.587070\pi$
$432$	0	0
$433$	−72691.0	−0.0186321	−0.00931603	−	0.999957i	$-0.502965\pi$
$433$	−72691.0	−0.0186321	−0.00931603	+	0.999957i	$0.502965\pi$
$434$	0	0
$435$	−105264.	−0.0266721
$436$	0	0
$437$	2.53330e6	0.634574
$438$	0	0
$439$	594392.	0.147201	0.0736007	−	0.997288i	$-0.476551\pi$
$439$	594392.	0.147201	0.0736007	+	0.997288i	$0.476551\pi$
$440$	0	0
$441$	−2.60126e6	−0.636923
$442$	0	0
$443$	−4.56651e6	−1.10554	−0.552770	−	0.833334i	$-0.686429\pi$
$443$	−4.56651e6	−1.10554	−0.552770	+	0.833334i	$0.686429\pi$
$444$	0	0
$445$	6.39616e6	1.53116
$446$	0	0
$447$	87726.0	0.0207663
$448$	0	0
$449$	−5.44382e6	−1.27435	−0.637174	−	0.770720i	$-0.719897\pi$
$449$	−5.44382e6	−1.27435	−0.637174	+	0.770720i	$0.719897\pi$
$450$	0	0
$451$	641784.	0.148576
$452$	0	0
$453$	432778.	0.0990877
$454$	0	0
$455$	5.85847e6	1.32665
$456$	0	0
$457$	6.70312e6	1.50137	0.750683	−	0.660662i	$-0.229724\pi$
$457$	6.70312e6	1.50137	0.750683	+	0.660662i	$0.229724\pi$
$458$	0	0
$459$	−357930.	−0.0792988
$460$	0	0
$461$	1.25994e6	0.276120	0.138060	−	0.990424i	$-0.455913\pi$
$461$	1.25994e6	0.276120	0.138060	+	0.990424i	$0.455913\pi$
$462$	0	0
$463$	−5.02308e6	−1.08897	−0.544487	−	0.838769i	$-0.683276\pi$
$463$	−5.02308e6	−1.08897	−0.544487	+	0.838769i	$0.683276\pi$
$464$	0	0
$465$	−318495.	−0.0683078
$466$	0	0
$467$	2.35660e6	0.500028	0.250014	−	0.968242i	$-0.419565\pi$
$467$	2.35660e6	0.500028	0.250014	+	0.968242i	$0.419565\pi$
$468$	0	0
$469$	4.20694e6	0.883149
$470$	0	0
$471$	−34075.0	−0.00707756
$472$	0	0
$473$	−2.15356e6	−0.442592
$474$	0	0
$475$	746176.	0.151743
$476$	0	0
$477$	−7.43569e6	−1.49632
$478$	0	0
$479$	−6.72258e6	−1.33874	−0.669371	−	0.742928i	$-0.733437\pi$
$479$	−6.72258e6	−1.33874	−0.669371	+	0.742928i	$0.733437\pi$
$480$	0	0
$481$	−1.02312e7	−2.01634
$482$	0	0
$483$	−295314.	−0.0575992
$484$	0	0
$485$	−4.52916e6	−0.874305
$486$	0	0
$487$	1.96001e6	0.374487	0.187243	−	0.982314i	$-0.440045\pi$
$487$	1.96001e6	0.374487	0.187243	+	0.982314i	$0.440045\pi$
$488$	0	0
$489$	45020.0	0.00851399
$490$	0	0
$491$	579624.	0.108503	0.0542516	−	0.998527i	$-0.482723\pi$
$491$	579624.	0.108503	0.0542516	+	0.998527i	$0.482723\pi$
$492$	0	0
$493$	−1.52323e6	−0.282260
$494$	0	0
$495$	−1.49338e6	−0.273942
$496$	0	0
$497$	−2.20963e6	−0.401262
$498$	0	0
$499$	−1.36905e6	−0.246132	−0.123066	−	0.992398i	$-0.539273\pi$
$499$	−1.36905e6	−0.246132	−0.123066	+	0.992398i	$0.539273\pi$
$500$	0	0
$501$	−482556.	−0.0858921
$502$	0	0
$503$	1.83343e6	0.323105	0.161552	−	0.986864i	$-0.448350\pi$
$503$	1.83343e6	0.323105	0.161552	+	0.986864i	$0.448350\pi$
$504$	0	0
$505$	−75582.0	−0.0131883
$506$	0	0
$507$	−107571.	−0.0185855
$508$	0	0
$509$	1.71266e6	0.293006	0.146503	−	0.989210i	$-0.453198\pi$
$509$	1.71266e6	0.293006	0.146503	+	0.989210i	$0.453198\pi$
$510$	0	0
$511$	8.84116e6	1.49781
$512$	0	0
$513$	−690640.	−0.115867
$514$	0	0
$515$	−5.99230e6	−0.995578
$516$	0	0
$517$	−2.07926e6	−0.342124
$518$	0	0
$519$	−766254.	−0.124869
$520$	0	0
$521$	−789435.	−0.127415	−0.0637077	−	0.997969i	$-0.520293\pi$
$521$	−789435.	−0.127415	−0.0637077	+	0.997969i	$0.520293\pi$
$522$	0	0
$523$	−627392.	−0.100296	−0.0501481	−	0.998742i	$-0.515969\pi$
$523$	−627392.	−0.100296	−0.0501481	+	0.998742i	$0.515969\pi$
$524$	0	0
$525$	−86984.0	−0.0137734
$526$	0	0
$527$	−4.60881e6	−0.722873
$528$	0	0
$529$	−3.27150e6	−0.508286
$530$	0	0
$531$	−8.46734e6	−1.30320
$532$	0	0
$533$	−3.67037e6	−0.559618
$534$	0	0
$535$	4.04746e6	0.611362
$536$	0	0
$537$	303399.	0.0454024
$538$	0	0
$539$	1.30063e6	0.192833
$540$	0	0
$541$	−3.20895e6	−0.471379	−0.235689	−	0.971828i	$-0.575735\pi$
$541$	−3.20895e6	−0.471379	−0.235689	+	0.971828i	$0.575735\pi$
$542$	0	0
$543$	−285181.	−0.0415070
$544$	0	0
$545$	−4.47994e6	−0.646072
$546$	0	0
$547$	−3.42658e6	−0.489658	−0.244829	−	0.969566i	$-0.578732\pi$
$547$	−3.42658e6	−0.489658	−0.244829	+	0.969566i	$0.578732\pi$
$548$	0	0
$549$	−1.11175e7	−1.57426
$550$	0	0
$551$	−2.93914e6	−0.412421
$552$	0	0
$553$	−1.28208e7	−1.78280
$554$	0	0
$555$	−754035.	−0.103910
$556$	0	0
$557$	−1.05198e7	−1.43672	−0.718358	−	0.695674i	$-0.755106\pi$
$557$	−1.05198e7	−1.43672	−0.718358	+	0.695674i	$0.755106\pi$
$558$	0	0
$559$	1.23162e7	1.66705
$560$	0	0
$561$	89298.0	0.0119794
$562$	0	0
$563$	−5.47288e6	−0.727687	−0.363844	−	0.931460i	$-0.618536\pi$
$563$	−5.47288e6	−0.727687	−0.363844	+	0.931460i	$0.618536\pi$
$564$	0	0
$565$	−2.40960e6	−0.317558
$566$	0	0
$567$	−9.68129e6	−1.26466
$568$	0	0
$569$	−1.17787e7	−1.52516	−0.762580	−	0.646893i	$-0.776068\pi$
$569$	−1.17787e7	−1.52516	−0.762580	+	0.646893i	$0.776068\pi$
$570$	0	0
$571$	8.35628e6	1.07256	0.536281	−	0.844039i	$-0.319829\pi$
$571$	8.35628e6	1.07256	0.536281	+	0.844039i	$0.319829\pi$
$572$	0	0
$573$	−767067.	−0.0975993
$574$	0	0
$575$	932196.	0.117581
$576$	0	0
$577$	−1.37758e7	−1.72258	−0.861288	−	0.508117i	$-0.830342\pi$
$577$	−1.37758e7	−1.72258	−0.861288	+	0.508117i	$0.830342\pi$
$578$	0	0
$579$	−411668.	−0.0510330
$580$	0	0
$581$	9.13232e6	1.12238
$582$	0	0
$583$	3.71785e6	0.453023
$584$	0	0
$585$	8.54066e6	1.03182
$586$	0	0
$587$	1.27093e7	1.52239	0.761196	−	0.648522i	$-0.224612\pi$
$587$	1.27093e7	1.52239	0.761196	+	0.648522i	$0.224612\pi$
$588$	0	0
$589$	−8.89288e6	−1.05622
$590$	0	0
$591$	−759258.	−0.0894171
$592$	0	0
$593$	1.00825e6	0.117742	0.0588711	−	0.998266i	$-0.481250\pi$
$593$	1.00825e6	0.117742	0.0588711	+	0.998266i	$0.481250\pi$
$594$	0	0
$595$	6.24791e6	0.723506
$596$	0	0
$597$	46600.0	0.00535119
$598$	0	0
$599$	1.05100e7	1.19684	0.598421	−	0.801182i	$-0.295795\pi$
$599$	1.05100e7	1.19684	0.598421	+	0.801182i	$0.295795\pi$
$600$	0	0
$601$	−199390.	−0.0225173	−0.0112587	−	0.999937i	$-0.503584\pi$
$601$	−199390.	−0.0225173	−0.0112587	+	0.999937i	$0.503584\pi$
$602$	0	0
$603$	6.13301e6	0.686879
$604$	0	0
$605$	746691.	0.0829378
$606$	0	0
$607$	16190.0	0.00178351	0.000891754	−	1.00000i	$-0.499716\pi$
$607$	16190.0	0.00178351	0.000891754		1.00000i	$0.499716\pi$
$608$	0	0
$609$	342624.	0.0374347
$610$	0	0
$611$	1.18913e7	1.28863
$612$	0	0
$613$	1.15253e7	1.23880	0.619402	−	0.785074i	$-0.287375\pi$
$613$	1.15253e7	1.23880	0.619402	+	0.785074i	$0.287375\pi$
$614$	0	0
$615$	−270504.	−0.0288394
$616$	0	0
$617$	1.69974e7	1.79750	0.898751	−	0.438459i	$-0.144476\pi$
$617$	1.69974e7	1.79750	0.898751	+	0.438459i	$0.144476\pi$
$618$	0	0
$619$	1.84875e7	1.93933	0.969663	−	0.244445i	$-0.0786058\pi$
$619$	1.84875e7	1.93933	0.969663	+	0.244445i	$0.0786058\pi$
$620$	0	0
$621$	−862815.	−0.0897819
$622$	0	0
$623$	−2.08189e7	−2.14901
$624$	0	0
$625$	−7.85355e6	−0.804203
$626$	0	0
$627$	172304.	0.0175036
$628$	0	0
$629$	−1.09113e7	−1.09964
$630$	0	0
$631$	−4.54281e6	−0.454204	−0.227102	−	0.973871i	$-0.572925\pi$
$631$	−4.54281e6	−0.454204	−0.227102	+	0.973871i	$0.572925\pi$
$632$	0	0
$633$	−932428.	−0.0924924
$634$	0	0
$635$	−1.22102e7	−1.20168
$636$	0	0
$637$	−7.43831e6	−0.726316
$638$	0	0
$639$	−3.22126e6	−0.312086
$640$	0	0
$641$	1.84286e7	1.77153	0.885764	−	0.464136i	$-0.153635\pi$
$641$	1.84286e7	1.77153	0.885764	+	0.464136i	$0.153635\pi$
$642$	0	0
$643$	−9.66604e6	−0.921979	−0.460989	−	0.887406i	$-0.652505\pi$
$643$	−9.66604e6	−0.921979	−0.460989	+	0.887406i	$0.652505\pi$
$644$	0	0
$645$	907698.	0.0859097
$646$	0	0
$647$	−4.51430e6	−0.423965	−0.211982	−	0.977273i	$-0.567992\pi$
$647$	−4.51430e6	−0.423965	−0.211982	+	0.977273i	$0.567992\pi$
$648$	0	0
$649$	4.23367e6	0.394553
$650$	0	0
$651$	1.03667e6	0.0958712
$652$	0	0
$653$	5.37235e6	0.493039	0.246519	−	0.969138i	$-0.420713\pi$
$653$	5.37235e6	0.493039	0.246519	+	0.969138i	$0.420713\pi$
$654$	0	0
$655$	5.00524e6	0.455850
$656$	0	0
$657$	1.28889e7	1.16494
$658$	0	0
$659$	−9.87956e6	−0.886184	−0.443092	−	0.896476i	$-0.646119\pi$
$659$	−9.87956e6	−0.886184	−0.443092	+	0.896476i	$0.646119\pi$
$660$	0	0
$661$	−1.08052e7	−0.961898	−0.480949	−	0.876748i	$-0.659708\pi$
$661$	−1.08052e7	−0.961898	−0.480949	+	0.876748i	$0.659708\pi$
$662$	0	0
$663$	−510696.	−0.0451210
$664$	0	0
$665$	1.20556e7	1.05714
$666$	0	0
$667$	−3.67186e6	−0.319574
$668$	0	0
$669$	−169745.	−0.0146633
$670$	0	0
$671$	5.55874e6	0.476618
$672$	0	0
$673$	1.13275e7	0.964042	0.482021	−	0.876160i	$-0.339903\pi$
$673$	1.13275e7	0.964042	0.482021	+	0.876160i	$0.339903\pi$
$674$	0	0
$675$	−254140.	−0.0214691
$676$	0	0
$677$	1.20595e7	1.01125	0.505624	−	0.862754i	$-0.331262\pi$
$677$	1.20595e7	1.01125	0.505624	+	0.862754i	$0.331262\pi$
$678$	0	0
$679$	1.47420e7	1.22710
$680$	0	0
$681$	198078.	0.0163670
$682$	0	0
$683$	5.14166e6	0.421747	0.210873	−	0.977513i	$-0.432369\pi$
$683$	5.14166e6	0.421747	0.210873	+	0.977513i	$0.432369\pi$
$684$	0	0
$685$	2.04070e7	1.66170
$686$	0	0
$687$	−849997.	−0.0687109
$688$	0	0
$689$	−2.12624e7	−1.70633
$690$	0	0
$691$	−1.31243e7	−1.04563	−0.522817	−	0.852445i	$-0.675119\pi$
$691$	−1.31243e7	−1.04563	−0.522817	+	0.852445i	$0.675119\pi$
$692$	0	0
$693$	4.86081e6	0.384482
$694$	0	0
$695$	−1.04941e7	−0.824104
$696$	0	0
$697$	−3.91435e6	−0.305195
$698$	0	0
$699$	401832.	0.0311065
$700$	0	0
$701$	−3.65956e6	−0.281277	−0.140638	−	0.990061i	$-0.544916\pi$
$701$	−3.65956e6	−0.281277	−0.140638	+	0.990061i	$0.544916\pi$
$702$	0	0
$703$	−2.10538e7	−1.60673
$704$	0	0
$705$	876384.	0.0664082
$706$	0	0
$707$	246012.	0.0185101
$708$	0	0
$709$	−1.02252e7	−0.763935	−0.381968	−	0.924176i	$-0.624753\pi$
$709$	−1.02252e7	−0.763935	−0.381968	+	0.924176i	$0.624753\pi$
$710$	0	0
$711$	−1.86906e7	−1.38660
$712$	0	0
$713$	−1.11099e7	−0.818436
$714$	0	0
$715$	−4.27033e6	−0.312390
$716$	0	0
$717$	−855174.	−0.0621236
$718$	0	0
$719$	2.41683e7	1.74351	0.871753	−	0.489945i	$-0.162983\pi$
$719$	2.41683e7	1.74351	0.871753	+	0.489945i	$0.162983\pi$
$720$	0	0
$721$	1.95043e7	1.39731
$722$	0	0
$723$	−1.12546e6	−0.0800730
$724$	0	0
$725$	−1.08154e6	−0.0764181
$726$	0	0
$727$	1.68246e7	1.18062	0.590310	−	0.807177i	$-0.299006\pi$
$727$	1.68246e7	1.18062	0.590310	+	0.807177i	$0.299006\pi$
$728$	0	0
$729$	−1.39958e7	−0.975393
$730$	0	0
$731$	1.31349e7	0.909147
$732$	0	0
$733$	5.04168e6	0.346590	0.173295	−	0.984870i	$-0.444559\pi$
$733$	5.04168e6	0.346590	0.173295	+	0.984870i	$0.444559\pi$
$734$	0	0
$735$	−548199.	−0.0374300
$736$	0	0
$737$	−3.06650e6	−0.207958
$738$	0	0
$739$	6.26375e6	0.421913	0.210957	−	0.977495i	$-0.432342\pi$
$739$	6.26375e6	0.421913	0.210957	+	0.977495i	$0.432342\pi$
$740$	0	0
$741$	−985408.	−0.0659281
$742$	0	0
$743$	3.63976e6	0.241880	0.120940	−	0.992660i	$-0.461409\pi$
$743$	3.63976e6	0.241880	0.120940	+	0.992660i	$0.461409\pi$
$744$	0	0
$745$	−4.47403e6	−0.295330
$746$	0	0
$747$	1.33134e7	0.872945
$748$	0	0
$749$	−1.31741e7	−0.858057
$750$	0	0
$751$	−1.87370e7	−1.21227	−0.606135	−	0.795362i	$-0.707281\pi$
$751$	−1.87370e7	−1.21227	−0.606135	+	0.795362i	$0.707281\pi$
$752$	0	0
$753$	−1.19751e6	−0.0769649
$754$	0	0
$755$	−2.20717e7	−1.40918
$756$	0	0
$757$	−489242.	−0.0310302	−0.0155151	−	0.999880i	$-0.504939\pi$
$757$	−489242.	−0.0310302	−0.0155151	+	0.999880i	$0.504939\pi$
$758$	0	0
$759$	215259.	0.0135630
$760$	0	0
$761$	1.46969e7	0.919952	0.459976	−	0.887931i	$-0.347858\pi$
$761$	1.46969e7	0.919952	0.459976	+	0.887931i	$0.347858\pi$
$762$	0	0
$763$	1.45818e7	0.906774
$764$	0	0
$765$	9.10840e6	0.562715
$766$	0	0
$767$	−2.42124e7	−1.48610
$768$	0	0
$769$	2.42072e7	1.47615	0.738073	−	0.674721i	$-0.235736\pi$
$769$	2.42072e7	1.47615	0.738073	+	0.674721i	$0.235736\pi$
$770$	0	0
$771$	−37758.0	−0.00228756
$772$	0	0
$773$	−1.35260e7	−0.814181	−0.407091	−	0.913388i	$-0.633457\pi$
$773$	−1.35260e7	−0.814181	−0.407091	+	0.913388i	$0.633457\pi$
$774$	0	0
$775$	−3.27238e6	−0.195708
$776$	0	0
$777$	2.45431e6	0.145840
$778$	0	0
$779$	−7.55290e6	−0.445933
$780$	0	0
$781$	1.61063e6	0.0944862
$782$	0	0
$783$	1.00104e6	0.0583508
$784$	0	0
$785$	1.73782e6	0.100654
$786$	0	0
$787$	−1.42094e7	−0.817786	−0.408893	−	0.912582i	$-0.634085\pi$
$787$	−1.42094e7	−0.817786	−0.408893	+	0.912582i	$0.634085\pi$
$788$	0	0
$789$	631254.	0.0361004
$790$	0	0
$791$	7.84300e6	0.445698
$792$	0	0
$793$	−3.17905e7	−1.79521
$794$	0	0
$795$	−1.56703e6	−0.0879343
$796$	0	0
$797$	7.93333e6	0.442395	0.221197	−	0.975229i	$-0.429003\pi$
$797$	7.93333e6	0.442395	0.221197	+	0.975229i	$0.429003\pi$
$798$	0	0
$799$	1.26818e7	0.702771
$800$	0	0
$801$	−3.03504e7	−1.67141
$802$	0	0
$803$	−6.44446e6	−0.352694
$804$	0	0
$805$	1.50610e7	0.819152
$806$	0	0
$807$	−1.08034e6	−0.0583952
$808$	0	0
$809$	−1.04685e7	−0.562359	−0.281180	−	0.959655i	$-0.590726\pi$
$809$	−1.04685e7	−0.562359	−0.281180	+	0.959655i	$0.590726\pi$
$810$	0	0
$811$	−1.19147e7	−0.636110	−0.318055	−	0.948072i	$-0.603030\pi$
$811$	−1.19147e7	−0.636110	−0.318055	+	0.948072i	$0.603030\pi$
$812$	0	0
$813$	816100.	0.0433029
$814$	0	0
$815$	−2.29602e6	−0.121083
$816$	0	0
$817$	2.53444e7	1.32839
$818$	0	0
$819$	−2.77990e7	−1.44817
$820$	0	0
$821$	1.86112e6	0.0963645	0.0481822	−	0.998839i	$-0.484657\pi$
$821$	1.86112e6	0.0963645	0.0481822	+	0.998839i	$0.484657\pi$
$822$	0	0
$823$	2.30153e7	1.18445	0.592225	−	0.805773i	$-0.298250\pi$
$823$	2.30153e7	1.18445	0.592225	+	0.805773i	$0.298250\pi$
$824$	0	0
$825$	63404.0	0.00324326
$826$	0	0
$827$	1.68351e7	0.855959	0.427980	−	0.903788i	$-0.359225\pi$
$827$	1.68351e7	0.855959	0.427980	+	0.903788i	$0.359225\pi$
$828$	0	0
$829$	2.35299e7	1.18914	0.594570	−	0.804044i	$-0.297322\pi$
$829$	2.35299e7	1.18914	0.594570	+	0.804044i	$0.297322\pi$
$830$	0	0
$831$	1.68820e6	0.0848049
$832$	0	0
$833$	−7.93276e6	−0.396106
$834$	0	0
$835$	2.46104e7	1.22152
$836$	0	0
$837$	3.02882e6	0.149438
$838$	0	0
$839$	2.91549e7	1.42990	0.714952	−	0.699173i	$-0.246448\pi$
$839$	2.91549e7	1.42990	0.714952	+	0.699173i	$0.246448\pi$
$840$	0	0
$841$	−1.62511e7	−0.792303
$842$	0	0
$843$	879042.	0.0426030
$844$	0	0
$845$	5.48612e6	0.264316
$846$	0	0
$847$	−2.43041e6	−0.116405
$848$	0	0
$849$	1.54027e6	0.0733377
$850$	0	0
$851$	−2.63025e7	−1.24501
$852$	0	0
$853$	9.49052e6	0.446599	0.223299	−	0.974750i	$-0.428317\pi$
$853$	9.49052e6	0.446599	0.223299	+	0.974750i	$0.428317\pi$
$854$	0	0
$855$	1.75750e7	0.822205
$856$	0	0
$857$	−1.81553e6	−0.0844405	−0.0422203	−	0.999108i	$-0.513443\pi$
$857$	−1.81553e6	−0.0844405	−0.0422203	+	0.999108i	$0.513443\pi$
$858$	0	0
$859$	1.07812e7	0.498522	0.249261	−	0.968436i	$-0.419812\pi$
$859$	1.07812e7	0.498522	0.249261	+	0.968436i	$0.419812\pi$
$860$	0	0
$861$	880464.	0.0404766
$862$	0	0
$863$	−2.83355e7	−1.29510	−0.647550	−	0.762023i	$-0.724206\pi$
$863$	−2.83355e7	−1.29510	−0.647550	+	0.762023i	$0.724206\pi$
$864$	0	0
$865$	3.90790e7	1.77584
$866$	0	0
$867$	875213.	0.0395427
$868$	0	0
$869$	9.34531e6	0.419802
$870$	0	0
$871$	1.75374e7	0.783283
$872$	0	0
$873$	2.14913e7	0.954392
$874$	0	0
$875$	3.08924e7	1.36406
$876$	0	0
$877$	2.68919e7	1.18065	0.590326	−	0.807165i	$-0.298999\pi$
$877$	2.68919e7	1.18065	0.590326	+	0.807165i	$0.298999\pi$
$878$	0	0
$879$	720840.	0.0314678
$880$	0	0
$881$	−1.92132e7	−0.833989	−0.416995	−	0.908909i	$-0.636917\pi$
$881$	−1.92132e7	−0.833989	−0.416995	+	0.908909i	$0.636917\pi$
$882$	0	0
$883$	−1.15931e7	−0.500378	−0.250189	−	0.968197i	$-0.580493\pi$
$883$	−1.15931e7	−0.500378	−0.250189	+	0.968197i	$0.580493\pi$
$884$	0	0
$885$	−1.78444e6	−0.0765850
$886$	0	0
$887$	1.31857e7	0.562721	0.281361	−	0.959602i	$-0.409214\pi$
$887$	1.31857e7	0.562721	0.281361	+	0.959602i	$0.409214\pi$
$888$	0	0
$889$	3.97431e7	1.68658
$890$	0	0
$891$	7.05684e6	0.297794
$892$	0	0
$893$	2.44700e7	1.02685
$894$	0	0
$895$	−1.54733e7	−0.645694
$896$	0	0
$897$	−1.23107e6	−0.0510859
$898$	0	0
$899$	1.28897e7	0.531916
$900$	0	0
$901$	−2.26758e7	−0.930573
$902$	0	0
$903$	−2.95447e6	−0.120576
$904$	0	0
$905$	1.45442e7	0.590295
$906$	0	0
$907$	−2.98195e6	−0.120360	−0.0601800	−	0.998188i	$-0.519167\pi$
$907$	−2.98195e6	−0.120360	−0.0601800	+	0.998188i	$0.519167\pi$
$908$	0	0
$909$	358644.	0.0143964
$910$	0	0
$911$	2.96579e7	1.18398	0.591989	−	0.805946i	$-0.298343\pi$
$911$	2.96579e7	1.18398	0.591989	+	0.805946i	$0.298343\pi$
$912$	0	0
$913$	−6.65669e6	−0.264291
$914$	0	0
$915$	−2.34294e6	−0.0925142
$916$	0	0
$917$	−1.62916e7	−0.639793
$918$	0	0
$919$	3.18057e7	1.24227	0.621135	−	0.783704i	$-0.286672\pi$
$919$	3.18057e7	1.24227	0.621135	+	0.783704i	$0.286672\pi$
$920$	0	0
$921$	−1.03905e6	−0.0403633
$922$	0	0
$923$	−9.21121e6	−0.355887
$924$	0	0
$925$	−7.74734e6	−0.297713
$926$	0	0
$927$	2.84340e7	1.08677
$928$	0	0
$929$	−2.33444e7	−0.887451	−0.443725	−	0.896163i	$-0.646343\pi$
$929$	−2.33444e7	−0.887451	−0.443725	+	0.896163i	$0.646343\pi$
$930$	0	0
$931$	−1.53066e7	−0.578767
$932$	0	0
$933$	1.25135e6	0.0470624
$934$	0	0
$935$	−4.55420e6	−0.170366
$936$	0	0
$937$	2.07372e7	0.771616	0.385808	−	0.922579i	$-0.373923\pi$
$937$	2.07372e7	0.771616	0.385808	+	0.922579i	$0.373923\pi$
$938$	0	0
$939$	1.44336e6	0.0534209
$940$	0	0
$941$	−2.69193e7	−0.991036	−0.495518	−	0.868598i	$-0.665022\pi$
$941$	−2.69193e7	−0.991036	−0.495518	+	0.868598i	$0.665022\pi$
$942$	0	0
$943$	−9.43582e6	−0.345542
$944$	0	0
$945$	−4.10601e6	−0.149569
$946$	0	0
$947$	−1.01896e7	−0.369216	−0.184608	−	0.982812i	$-0.559102\pi$
$947$	−1.01896e7	−0.369216	−0.184608	+	0.982812i	$0.559102\pi$
$948$	0	0
$949$	3.68559e7	1.32844
$950$	0	0
$951$	−2.01208e6	−0.0721429
$952$	0	0
$953$	1.03924e7	0.370665	0.185333	−	0.982676i	$-0.440664\pi$
$953$	1.03924e7	0.370665	0.185333	+	0.982676i	$0.440664\pi$
$954$	0	0
$955$	3.91204e7	1.38802
$956$	0	0
$957$	−249744.	−0.00881486
$958$	0	0
$959$	−6.64227e7	−2.33222
$960$	0	0
$961$	1.03709e7	0.362249
$962$	0	0
$963$	−1.92056e7	−0.667363
$964$	0	0
$965$	2.09951e7	0.725770
$966$	0	0
$967$	−8.18877e6	−0.281613	−0.140806	−	0.990037i	$-0.544970\pi$
$967$	−8.18877e6	−0.281613	−0.140806	+	0.990037i	$0.544970\pi$
$968$	0	0
$969$	−1.05091e6	−0.0359548
$970$	0	0
$971$	1.73274e7	0.589775	0.294887	−	0.955532i	$-0.404718\pi$
$971$	1.73274e7	0.589775	0.294887	+	0.955532i	$0.404718\pi$
$972$	0	0
$973$	3.41572e7	1.15664
$974$	0	0
$975$	−362608.	−0.0122159
$976$	0	0
$977$	−438963.	−0.0147127	−0.00735634	−	0.999973i	$-0.502342\pi$
$977$	−438963.	−0.0147127	−0.00735634	+	0.999973i	$0.502342\pi$
$978$	0	0
$979$	1.51752e7	0.506032
$980$	0	0
$981$	2.12578e7	0.705253
$982$	0	0
$983$	−2.79124e7	−0.921326	−0.460663	−	0.887575i	$-0.652388\pi$
$983$	−2.79124e7	−0.921326	−0.460663	+	0.887575i	$0.652388\pi$
$984$	0	0
$985$	3.87222e7	1.27165
$986$	0	0
$987$	−2.85254e6	−0.0932051
$988$	0	0
$989$	3.16626e7	1.02933
$990$	0	0
$991$	−4.26846e7	−1.38066	−0.690331	−	0.723494i	$-0.742535\pi$
$991$	−4.26846e7	−1.38066	−0.690331	+	0.723494i	$0.742535\pi$
$992$	0	0
$993$	2.01734e6	0.0649240
$994$	0	0
$995$	−2.37660e6	−0.0761024
$996$	0	0
$997$	2.21044e7	0.704273	0.352137	−	0.935949i	$-0.385455\pi$
$997$	2.21044e7	0.704273	0.352137	+	0.935949i	$0.385455\pi$
$998$	0	0
$999$	7.17072e6	0.227326

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.6.a.e.1.1		1
4.3	odd	2		704.6.a.f.1.1		1
8.3	odd	2		176.6.a.b.1.1		1
8.5	even	2		22.6.a.b.1.1	✓	1
24.5	odd	2		198.6.a.i.1.1		1
40.13	odd	4		550.6.b.f.199.2		2
40.29	even	2		550.6.a.f.1.1		1
40.37	odd	4		550.6.b.f.199.1		2
56.13	odd	2		1078.6.a.a.1.1		1
88.21	odd	2		242.6.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.a.b.1.1	✓	1	8.5	even	2
176.6.a.b.1.1		1	8.3	odd	2
198.6.a.i.1.1		1	24.5	odd	2
242.6.a.d.1.1		1	88.21	odd	2
550.6.a.f.1.1		1	40.29	even	2
550.6.b.f.199.1		2	40.37	odd	4
550.6.b.f.199.2		2	40.13	odd	4
704.6.a.e.1.1		1	1.1	even	1	trivial
704.6.a.f.1.1		1	4.3	odd	2
1078.6.a.a.1.1		1	56.13	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:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	704.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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