LMFDB - Embedded newform 704.6.a.i.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:	$1$
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)

$f(q)$

$=$

$q+21.0000 q^{3} -81.0000 q^{5} +98.0000 q^{7} +198.000 q^{9} +O(q^{10})$

$q+21.0000 q^{3} -81.0000 q^{5} +98.0000 q^{7} +198.000 q^{9} -121.000 q^{11} -824.000 q^{13} -1701.00 q^{15} +978.000 q^{17} +2140.00 q^{19} +2058.00 q^{21} +3699.00 q^{23} +3436.00 q^{25} -945.000 q^{27} -3480.00 q^{29} -7813.00 q^{31} -2541.00 q^{33} -7938.00 q^{35} +13597.0 q^{37} -17304.0 q^{39} +6492.00 q^{41} -14234.0 q^{43} -16038.0 q^{45} -20352.0 q^{47} -7203.00 q^{49} +20538.0 q^{51} +366.000 q^{53} +9801.00 q^{55} +44940.0 q^{57} -9825.00 q^{59} -26132.0 q^{61} +19404.0 q^{63} +66744.0 q^{65} -17093.0 q^{67} +77679.0 q^{69} -23583.0 q^{71} -35176.0 q^{73} +72156.0 q^{75} -11858.0 q^{77} -42490.0 q^{79} -67959.0 q^{81} -22674.0 q^{83} -79218.0 q^{85} -73080.0 q^{87} -17145.0 q^{89} -80752.0 q^{91} -164073. q^{93} -173340. q^{95} -30727.0 q^{97} -23958.0 q^{99} +O(q^{100})$

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
$3$	21.0000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	21.0000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	0	0
$5$	−81.0000	−1.44897	−0.724486	−	0.689289i	$-0.757923\pi$
$5$	−81.0000	−1.44897	−0.724486	+	0.689289i	$0.757923\pi$
$6$	0	0
$7$	98.0000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	98.0000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	0	0
$9$	198.000	0.814815
$10$	0	0
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	0	0
$13$	−824.000	−1.35229	−0.676143	−	0.736770i	$-0.736350\pi$
$13$	−824.000	−1.35229	−0.676143	+	0.736770i	$0.736350\pi$
$14$	0	0
$15$	−1701.00	−1.95198
$16$	0	0
$17$	978.000	0.820761	0.410380	−	0.911914i	$-0.365396\pi$
$17$	978.000	0.820761	0.410380	+	0.911914i	$0.365396\pi$
$18$	0	0
$19$	2140.00	1.35997	0.679986	−	0.733225i	$-0.261986\pi$
$19$	2140.00	1.35997	0.679986	+	0.733225i	$0.261986\pi$
$20$	0	0
$21$	2058.00	1.01835
$22$	0	0
$23$	3699.00	1.45802	0.729012	−	0.684501i	$-0.239980\pi$
$23$	3699.00	1.45802	0.729012	+	0.684501i	$0.239980\pi$
$24$	0	0
$25$	3436.00	1.09952
$26$	0	0
$27$	−945.000	−0.249472
$28$	0	0
$29$	−3480.00	−0.768395	−0.384197	−	0.923251i	$-0.625522\pi$
$29$	−3480.00	−0.768395	−0.384197	+	0.923251i	$0.625522\pi$
$30$	0	0
$31$	−7813.00	−1.46020	−0.730102	−	0.683338i	$-0.760528\pi$
$31$	−7813.00	−1.46020	−0.730102	+	0.683338i	$0.760528\pi$
$32$	0	0
$33$	−2541.00	−0.406181
$34$	0	0
$35$	−7938.00	−1.09532
$36$	0	0
$37$	13597.0	1.63282	0.816411	−	0.577471i	$-0.195961\pi$
$37$	13597.0	1.63282	0.816411	+	0.577471i	$0.195961\pi$
$38$	0	0
$39$	−17304.0	−1.82173
$40$	0	0
$41$	6492.00	0.603141	0.301571	−	0.953444i	$-0.402489\pi$
$41$	6492.00	0.603141	0.301571	+	0.953444i	$0.402489\pi$
$42$	0	0
$43$	−14234.0	−1.17397	−0.586983	−	0.809599i	$-0.699685\pi$
$43$	−14234.0	−1.17397	−0.586983	+	0.809599i	$0.699685\pi$
$44$	0	0
$45$	−16038.0	−1.18064
$46$	0	0
$47$	−20352.0	−1.34389	−0.671943	−	0.740603i	$-0.734540\pi$
$47$	−20352.0	−1.34389	−0.671943	+	0.740603i	$0.734540\pi$
$48$	0	0
$49$	−7203.00	−0.428571
$50$	0	0
$51$	20538.0	1.10569
$52$	0	0
$53$	366.000	0.0178975	0.00894873	−	0.999960i	$-0.497151\pi$
$53$	366.000	0.0178975	0.00894873	+	0.999960i	$0.497151\pi$
$54$	0	0
$55$	9801.00	0.436882
$56$	0	0
$57$	44940.0	1.83209
$58$	0	0
$59$	−9825.00	−0.367454	−0.183727	−	0.982977i	$-0.558816\pi$
$59$	−9825.00	−0.367454	−0.183727	+	0.982977i	$0.558816\pi$
$60$	0	0
$61$	−26132.0	−0.899183	−0.449591	−	0.893234i	$-0.648430\pi$
$61$	−26132.0	−0.899183	−0.449591	+	0.893234i	$0.648430\pi$
$62$	0	0
$63$	19404.0	0.615942
$64$	0	0
$65$	66744.0	1.95943
$66$	0	0
$67$	−17093.0	−0.465191	−0.232595	−	0.972574i	$-0.574722\pi$
$67$	−17093.0	−0.465191	−0.232595	+	0.972574i	$0.574722\pi$
$68$	0	0
$69$	77679.0	1.96418
$70$	0	0
$71$	−23583.0	−0.555205	−0.277602	−	0.960696i	$-0.589540\pi$
$71$	−23583.0	−0.555205	−0.277602	+	0.960696i	$0.589540\pi$
$72$	0	0
$73$	−35176.0	−0.772573	−0.386286	−	0.922379i	$-0.626242\pi$
$73$	−35176.0	−0.772573	−0.386286	+	0.922379i	$0.626242\pi$
$74$	0	0
$75$	72156.0	1.48122
$76$	0	0
$77$	−11858.0	−0.227921
$78$	0	0
$79$	−42490.0	−0.765983	−0.382991	−	0.923752i	$-0.625106\pi$
$79$	−42490.0	−0.765983	−0.382991	+	0.923752i	$0.625106\pi$
$80$	0	0
$81$	−67959.0	−1.15089
$82$	0	0
$83$	−22674.0	−0.361271	−0.180635	−	0.983550i	$-0.557815\pi$
$83$	−22674.0	−0.361271	−0.180635	+	0.983550i	$0.557815\pi$
$84$	0	0
$85$	−79218.0	−1.18926
$86$	0	0
$87$	−73080.0	−1.03514
$88$	0	0
$89$	−17145.0	−0.229436	−0.114718	−	0.993398i	$-0.536597\pi$
$89$	−17145.0	−0.229436	−0.114718	+	0.993398i	$0.536597\pi$
$90$	0	0
$91$	−80752.0	−1.02223
$92$	0	0
$93$	−164073.	−1.96711
$94$	0	0
$95$	−173340.	−1.97056
$96$	0	0
$97$	−30727.0	−0.331582	−0.165791	−	0.986161i	$-0.553018\pi$
$97$	−30727.0	−0.331582	−0.165791	+	0.986161i	$0.553018\pi$
$98$	0	0
$99$	−23958.0	−0.245676
$100$	0	0
$101$	−138102.	−1.34709	−0.673545	−	0.739146i	$-0.735229\pi$
$101$	−138102.	−1.34709	−0.673545	+	0.739146i	$0.735229\pi$
$102$	0	0
$103$	11864.0	0.110189	0.0550945	−	0.998481i	$-0.482454\pi$
$103$	11864.0	0.110189	0.0550945	+	0.998481i	$0.482454\pi$
$104$	0	0
$105$	−166698.	−1.47556
$106$	0	0
$107$	−16998.0	−0.143529	−0.0717643	−	0.997422i	$-0.522863\pi$
$107$	−16998.0	−0.143529	−0.0717643	+	0.997422i	$0.522863\pi$
$108$	0	0
$109$	221830.	1.78836	0.894178	−	0.447711i	$-0.147761\pi$
$109$	221830.	1.78836	0.894178	+	0.447711i	$0.147761\pi$
$110$	0	0
$111$	285537.	2.19966
$112$	0	0
$113$	−196671.	−1.44892	−0.724460	−	0.689317i	$-0.757911\pi$
$113$	−196671.	−1.44892	−0.724460	+	0.689317i	$0.757911\pi$
$114$	0	0
$115$	−299619.	−2.11264
$116$	0	0
$117$	−163152.	−1.10186
$118$	0	0
$119$	95844.0	0.620437
$120$	0	0
$121$	14641.0	0.0909091
$122$	0	0
$123$	136332.	0.812522
$124$	0	0
$125$	−25191.0	−0.144202
$126$	0	0
$127$	120548.	0.663209	0.331605	−	0.943418i	$-0.392410\pi$
$127$	120548.	0.663209	0.331605	+	0.943418i	$0.392410\pi$
$128$	0	0
$129$	−298914.	−1.58151
$130$	0	0
$131$	−68442.0	−0.348453	−0.174227	−	0.984706i	$-0.555743\pi$
$131$	−68442.0	−0.348453	−0.174227	+	0.984706i	$0.555743\pi$
$132$	0	0
$133$	209720.	1.02804
$134$	0	0
$135$	76545.0	0.361478
$136$	0	0
$137$	−373647.	−1.70083	−0.850413	−	0.526115i	$-0.823648\pi$
$137$	−373647.	−1.70083	−0.850413	+	0.526115i	$0.823648\pi$
$138$	0	0
$139$	60610.0	0.266077	0.133038	−	0.991111i	$-0.457527\pi$
$139$	60610.0	0.266077	0.133038	+	0.991111i	$0.457527\pi$
$140$	0	0
$141$	−427392.	−1.81042
$142$	0	0
$143$	99704.0	0.407730
$144$	0	0
$145$	281880.	1.11338
$146$	0	0
$147$	−151263.	−0.577350
$148$	0	0
$149$	438030.	1.61636	0.808180	−	0.588935i	$-0.200453\pi$
$149$	438030.	1.61636	0.808180	+	0.588935i	$0.200453\pi$
$150$	0	0
$151$	−239398.	−0.854433	−0.427217	−	0.904149i	$-0.640506\pi$
$151$	−239398.	−0.854433	−0.427217	+	0.904149i	$0.640506\pi$
$152$	0	0
$153$	193644.	0.668768
$154$	0	0
$155$	632853.	2.11580
$156$	0	0
$157$	−62153.0	−0.201239	−0.100620	−	0.994925i	$-0.532083\pi$
$157$	−62153.0	−0.201239	−0.100620	+	0.994925i	$0.532083\pi$
$158$	0	0
$159$	7686.00	0.0241106
$160$	0	0
$161$	362502.	1.10216
$162$	0	0
$163$	−298724.	−0.880645	−0.440323	−	0.897840i	$-0.645136\pi$
$163$	−298724.	−0.880645	−0.440323	+	0.897840i	$0.645136\pi$
$164$	0	0
$165$	205821.	0.588545
$166$	0	0
$167$	82728.0	0.229542	0.114771	−	0.993392i	$-0.463387\pi$
$167$	82728.0	0.229542	0.114771	+	0.993392i	$0.463387\pi$
$168$	0	0
$169$	307683.	0.828680
$170$	0	0
$171$	423720.	1.10812
$172$	0	0
$173$	−135834.	−0.345059	−0.172529	−	0.985004i	$-0.555194\pi$
$173$	−135834.	−0.345059	−0.172529	+	0.985004i	$0.555194\pi$
$174$	0	0
$175$	336728.	0.831159
$176$	0	0
$177$	−206325.	−0.495015
$178$	0	0
$179$	−112725.	−0.262959	−0.131479	−	0.991319i	$-0.541973\pi$
$179$	−112725.	−0.262959	−0.131479	+	0.991319i	$0.541973\pi$
$180$	0	0
$181$	−593807.	−1.34725	−0.673626	−	0.739072i	$-0.735264\pi$
$181$	−593807.	−1.34725	−0.673626	+	0.739072i	$0.735264\pi$
$182$	0	0
$183$	−548772.	−1.21133
$184$	0	0
$185$	−1.10136e6	−2.36591
$186$	0	0
$187$	−118338.	−0.247469
$188$	0	0
$189$	−92610.0	−0.188583
$190$	0	0
$191$	652557.	1.29430	0.647150	−	0.762363i	$-0.275961\pi$
$191$	652557.	1.29430	0.647150	+	0.762363i	$0.275961\pi$
$192$	0	0
$193$	402164.	0.777159	0.388580	−	0.921415i	$-0.372966\pi$
$193$	402164.	0.777159	0.388580	+	0.921415i	$0.372966\pi$
$194$	0	0
$195$	1.40162e6	2.63964
$196$	0	0
$197$	268482.	0.492890	0.246445	−	0.969157i	$-0.420738\pi$
$197$	268482.	0.492890	0.246445	+	0.969157i	$0.420738\pi$
$198$	0	0
$199$	−581200.	−1.04038	−0.520191	−	0.854050i	$-0.674139\pi$
$199$	−581200.	−1.04038	−0.520191	+	0.854050i	$0.674139\pi$
$200$	0	0
$201$	−358953.	−0.626682
$202$	0	0
$203$	−341040.	−0.580852
$204$	0	0
$205$	−525852.	−0.873934
$206$	0	0
$207$	732402.	1.18802
$208$	0	0
$209$	−258940.	−0.410047
$210$	0	0
$211$	183988.	0.284501	0.142250	−	0.989831i	$-0.454566\pi$
$211$	183988.	0.284501	0.142250	+	0.989831i	$0.454566\pi$
$212$	0	0
$213$	−495243.	−0.747944
$214$	0	0
$215$	1.15295e6	1.70105
$216$	0	0
$217$	−765674.	−1.10381
$218$	0	0
$219$	−738696.	−1.04077
$220$	0	0
$221$	−805872.	−1.10990
$222$	0	0
$223$	631679.	0.850617	0.425309	−	0.905048i	$-0.360166\pi$
$223$	631679.	0.850617	0.425309	+	0.905048i	$0.360166\pi$
$224$	0	0
$225$	680328.	0.895905
$226$	0	0
$227$	−1398.00	−0.00180070	−0.000900352	−	1.00000i	$-0.500287\pi$
$227$	−1398.00	−0.00180070	−0.000900352		1.00000i	$0.500287\pi$
$228$	0	0
$229$	−206135.	−0.259754	−0.129877	−	0.991530i	$-0.541458\pi$
$229$	−206135.	−0.259754	−0.129877	+	0.991530i	$0.541458\pi$
$230$	0	0
$231$	−249018.	−0.307044
$232$	0	0
$233$	640704.	0.773157	0.386578	−	0.922257i	$-0.373657\pi$
$233$	640704.	0.773157	0.386578	+	0.922257i	$0.373657\pi$
$234$	0	0
$235$	1.64851e6	1.94725
$236$	0	0
$237$	−892290.	−1.03189
$238$	0	0
$239$	128250.	0.145232	0.0726161	−	0.997360i	$-0.476865\pi$
$239$	128250.	0.145232	0.0726161	+	0.997360i	$0.476865\pi$
$240$	0	0
$241$	−1.69749e6	−1.88263	−0.941313	−	0.337535i	$-0.890407\pi$
$241$	−1.69749e6	−1.88263	−0.941313	+	0.337535i	$0.890407\pi$
$242$	0	0
$243$	−1.19750e6	−1.30095
$244$	0	0
$245$	583443.	0.620988
$246$	0	0
$247$	−1.76336e6	−1.83907
$248$	0	0
$249$	−476154.	−0.486686
$250$	0	0
$251$	325323.	0.325935	0.162967	−	0.986631i	$-0.447893\pi$
$251$	325323.	0.325935	0.162967	+	0.986631i	$0.447893\pi$
$252$	0	0
$253$	−447579.	−0.439611
$254$	0	0
$255$	−1.66358e6	−1.60211
$256$	0	0
$257$	1.64948e6	1.55781	0.778904	−	0.627144i	$-0.215776\pi$
$257$	1.64948e6	1.55781	0.778904	+	0.627144i	$0.215776\pi$
$258$	0	0
$259$	1.33251e6	1.23430
$260$	0	0
$261$	−689040.	−0.626099
$262$	0	0
$263$	−1.37653e6	−1.22714	−0.613571	−	0.789639i	$-0.710268\pi$
$263$	−1.37653e6	−1.22714	−0.613571	+	0.789639i	$0.710268\pi$
$264$	0	0
$265$	−29646.0	−0.0259329
$266$	0	0
$267$	−360045.	−0.309085
$268$	0	0
$269$	−75450.0	−0.0635739	−0.0317869	−	0.999495i	$-0.510120\pi$
$269$	−75450.0	−0.0635739	−0.0317869	+	0.999495i	$0.510120\pi$
$270$	0	0
$271$	−360568.	−0.298239	−0.149119	−	0.988819i	$-0.547644\pi$
$271$	−360568.	−0.298239	−0.149119	+	0.988819i	$0.547644\pi$
$272$	0	0
$273$	−1.69579e6	−1.37710
$274$	0	0
$275$	−415756.	−0.331518
$276$	0	0
$277$	418522.	0.327732	0.163866	−	0.986483i	$-0.447604\pi$
$277$	418522.	0.327732	0.163866	+	0.986483i	$0.447604\pi$
$278$	0	0
$279$	−1.54697e6	−1.18980
$280$	0	0
$281$	−794298.	−0.600092	−0.300046	−	0.953925i	$-0.597002\pi$
$281$	−794298.	−0.600092	−0.300046	+	0.953925i	$0.597002\pi$
$282$	0	0
$283$	−1.80796e6	−1.34191	−0.670955	−	0.741498i	$-0.734116\pi$
$283$	−1.80796e6	−1.34191	−0.670955	+	0.741498i	$0.734116\pi$
$284$	0	0
$285$	−3.64014e6	−2.65464
$286$	0	0
$287$	636216.	0.455932
$288$	0	0
$289$	−463373.	−0.326352
$290$	0	0
$291$	−645267.	−0.446691
$292$	0	0
$293$	875436.	0.595738	0.297869	−	0.954607i	$-0.403724\pi$
$293$	875436.	0.595738	0.297869	+	0.954607i	$0.403724\pi$
$294$	0	0
$295$	795825.	0.532430
$296$	0	0
$297$	114345.	0.0752187
$298$	0	0
$299$	−3.04798e6	−1.97167
$300$	0	0
$301$	−1.39493e6	−0.887436
$302$	0	0
$303$	−2.90014e6	−1.81473
$304$	0	0
$305$	2.11669e6	1.30289
$306$	0	0
$307$	−137468.	−0.0832445	−0.0416223	−	0.999133i	$-0.513253\pi$
$307$	−137468.	−0.0832445	−0.0416223	+	0.999133i	$0.513253\pi$
$308$	0	0
$309$	249144.	0.148441
$310$	0	0
$311$	1.22629e6	0.718940	0.359470	−	0.933157i	$-0.382957\pi$
$311$	1.22629e6	0.718940	0.359470	+	0.933157i	$0.382957\pi$
$312$	0	0
$313$	−3.13692e6	−1.80985	−0.904925	−	0.425570i	$-0.860073\pi$
$313$	−3.13692e6	−1.80985	−0.904925	+	0.425570i	$0.860073\pi$
$314$	0	0
$315$	−1.57172e6	−0.892483
$316$	0	0
$317$	1.69119e6	0.945243	0.472622	−	0.881266i	$-0.343308\pi$
$317$	1.69119e6	0.945243	0.472622	+	0.881266i	$0.343308\pi$
$318$	0	0
$319$	421080.	0.231680
$320$	0	0
$321$	−356958.	−0.193355
$322$	0	0
$323$	2.09292e6	1.11621
$324$	0	0
$325$	−2.83126e6	−1.48687
$326$	0	0
$327$	4.65843e6	2.40919
$328$	0	0
$329$	−1.99450e6	−1.01588
$330$	0	0
$331$	2.13901e6	1.07311	0.536554	−	0.843866i	$-0.319726\pi$
$331$	2.13901e6	1.07311	0.536554	+	0.843866i	$0.319726\pi$
$332$	0	0
$333$	2.69221e6	1.33045
$334$	0	0
$335$	1.38453e6	0.674049
$336$	0	0
$337$	553598.	0.265534	0.132767	−	0.991147i	$-0.457614\pi$
$337$	553598.	0.265534	0.132767	+	0.991147i	$0.457614\pi$
$338$	0	0
$339$	−4.13009e6	−1.95191
$340$	0	0
$341$	945373.	0.440268
$342$	0	0
$343$	−2.35298e6	−1.07990
$344$	0	0
$345$	−6.29200e6	−2.84604
$346$	0	0
$347$	−167208.	−0.0745475	−0.0372738	−	0.999305i	$-0.511867\pi$
$347$	−167208.	−0.0745475	−0.0372738	+	0.999305i	$0.511867\pi$
$348$	0	0
$349$	−469490.	−0.206330	−0.103165	−	0.994664i	$-0.532897\pi$
$349$	−469490.	−0.206330	−0.103165	+	0.994664i	$0.532897\pi$
$350$	0	0
$351$	778680.	0.337358
$352$	0	0
$353$	2.82154e6	1.20517	0.602586	−	0.798054i	$-0.294137\pi$
$353$	2.82154e6	1.20517	0.602586	+	0.798054i	$0.294137\pi$
$354$	0	0
$355$	1.91022e6	0.804476
$356$	0	0
$357$	2.01272e6	0.835822
$358$	0	0
$359$	1.95696e6	0.801394	0.400697	−	0.916211i	$-0.368768\pi$
$359$	1.95696e6	0.801394	0.400697	+	0.916211i	$0.368768\pi$
$360$	0	0
$361$	2.10350e6	0.849522
$362$	0	0
$363$	307461.	0.122468
$364$	0	0
$365$	2.84926e6	1.11944
$366$	0	0
$367$	−2.28592e6	−0.885922	−0.442961	−	0.896541i	$-0.646072\pi$
$367$	−2.28592e6	−0.885922	−0.442961	+	0.896541i	$0.646072\pi$
$368$	0	0
$369$	1.28542e6	0.491448
$370$	0	0
$371$	35868.0	0.0135292
$372$	0	0
$373$	−583274.	−0.217070	−0.108535	−	0.994093i	$-0.534616\pi$
$373$	−583274.	−0.217070	−0.108535	+	0.994093i	$0.534616\pi$
$374$	0	0
$375$	−529011.	−0.194261
$376$	0	0
$377$	2.86752e6	1.03909
$378$	0	0
$379$	−2.83629e6	−1.01427	−0.507135	−	0.861867i	$-0.669295\pi$
$379$	−2.83629e6	−1.01427	−0.507135	+	0.861867i	$0.669295\pi$
$380$	0	0
$381$	2.53151e6	0.893443
$382$	0	0
$383$	−3.52202e6	−1.22686	−0.613430	−	0.789749i	$-0.710211\pi$
$383$	−3.52202e6	−1.22686	−0.613430	+	0.789749i	$0.710211\pi$
$384$	0	0
$385$	960498.	0.330251
$386$	0	0
$387$	−2.81833e6	−0.956566
$388$	0	0
$389$	1.81358e6	0.607661	0.303831	−	0.952726i	$-0.401734\pi$
$389$	1.81358e6	0.607661	0.303831	+	0.952726i	$0.401734\pi$
$390$	0	0
$391$	3.61762e6	1.19669
$392$	0	0
$393$	−1.43728e6	−0.469419
$394$	0	0
$395$	3.44169e6	1.10989
$396$	0	0
$397$	−3.42076e6	−1.08930	−0.544648	−	0.838665i	$-0.683337\pi$
$397$	−3.42076e6	−1.08930	−0.544648	+	0.838665i	$0.683337\pi$
$398$	0	0
$399$	4.40412e6	1.38493
$400$	0	0
$401$	398442.	0.123738	0.0618692	−	0.998084i	$-0.480294\pi$
$401$	398442.	0.123738	0.0618692	+	0.998084i	$0.480294\pi$
$402$	0	0
$403$	6.43791e6	1.97461
$404$	0	0
$405$	5.50468e6	1.66761
$406$	0	0
$407$	−1.64524e6	−0.492314
$408$	0	0
$409$	1.40957e6	0.416657	0.208328	−	0.978059i	$-0.433198\pi$
$409$	1.40957e6	0.416657	0.208328	+	0.978059i	$0.433198\pi$
$410$	0	0
$411$	−7.84659e6	−2.29127
$412$	0	0
$413$	−962850.	−0.277769
$414$	0	0
$415$	1.83659e6	0.523471
$416$	0	0
$417$	1.27281e6	0.358446
$418$	0	0
$419$	1.86618e6	0.519300	0.259650	−	0.965703i	$-0.416393\pi$
$419$	1.86618e6	0.519300	0.259650	+	0.965703i	$0.416393\pi$
$420$	0	0
$421$	−2.07774e6	−0.571329	−0.285665	−	0.958330i	$-0.592214\pi$
$421$	−2.07774e6	−0.571329	−0.285665	+	0.958330i	$0.592214\pi$
$422$	0	0
$423$	−4.02970e6	−1.09502
$424$	0	0
$425$	3.36041e6	0.902443
$426$	0	0
$427$	−2.56094e6	−0.679718
$428$	0	0
$429$	2.09378e6	0.549273
$430$	0	0
$431$	−6.28436e6	−1.62955	−0.814775	−	0.579777i	$-0.803140\pi$
$431$	−6.28436e6	−1.62955	−0.814775	+	0.579777i	$0.803140\pi$
$432$	0	0
$433$	3.26559e6	0.837031	0.418516	−	0.908210i	$-0.362550\pi$
$433$	3.26559e6	0.837031	0.418516	+	0.908210i	$0.362550\pi$
$434$	0	0
$435$	5.91948e6	1.49989
$436$	0	0
$437$	7.91586e6	1.98287
$438$	0	0
$439$	−2.64568e6	−0.655203	−0.327602	−	0.944816i	$-0.606240\pi$
$439$	−2.64568e6	−0.655203	−0.327602	+	0.944816i	$0.606240\pi$
$440$	0	0
$441$	−1.42619e6	−0.349206
$442$	0	0
$443$	5.63531e6	1.36430	0.682148	−	0.731214i	$-0.261046\pi$
$443$	5.63531e6	1.36430	0.682148	+	0.731214i	$0.261046\pi$
$444$	0	0
$445$	1.38874e6	0.332447
$446$	0	0
$447$	9.19863e6	2.17748
$448$	0	0
$449$	−370005.	−0.0866147	−0.0433074	−	0.999062i	$-0.513789\pi$
$449$	−370005.	−0.0866147	−0.0433074	+	0.999062i	$0.513789\pi$
$450$	0	0
$451$	−785532.	−0.181854
$452$	0	0
$453$	−5.02736e6	−1.15105
$454$	0	0
$455$	6.54091e6	1.48119
$456$	0	0
$457$	3.31891e6	0.743369	0.371685	−	0.928359i	$-0.378780\pi$
$457$	3.31891e6	0.743369	0.371685	+	0.928359i	$0.378780\pi$
$458$	0	0
$459$	−924210.	−0.204757
$460$	0	0
$461$	−8.77021e6	−1.92202	−0.961010	−	0.276515i	$-0.910821\pi$
$461$	−8.77021e6	−1.92202	−0.961010	+	0.276515i	$0.910821\pi$
$462$	0	0
$463$	224249.	0.0486159	0.0243079	−	0.999705i	$-0.492262\pi$
$463$	224249.	0.0486159	0.0243079	+	0.999705i	$0.492262\pi$
$464$	0	0
$465$	1.32899e7	2.85029
$466$	0	0
$467$	2.55573e6	0.542278	0.271139	−	0.962540i	$-0.412600\pi$
$467$	2.55573e6	0.542278	0.271139	+	0.962540i	$0.412600\pi$
$468$	0	0
$469$	−1.67511e6	−0.351651
$470$	0	0
$471$	−1.30521e6	−0.271100
$472$	0	0
$473$	1.72231e6	0.353964
$474$	0	0
$475$	7.35304e6	1.49532
$476$	0	0
$477$	72468.0	0.0145831
$478$	0	0
$479$	5.36664e6	1.06872	0.534360	−	0.845257i	$-0.320553\pi$
$479$	5.36664e6	1.06872	0.534360	+	0.845257i	$0.320553\pi$
$480$	0	0
$481$	−1.12039e7	−2.20804
$482$	0	0
$483$	7.61254e6	1.48478
$484$	0	0
$485$	2.48889e6	0.480453
$486$	0	0
$487$	−8.17528e6	−1.56200	−0.780998	−	0.624533i	$-0.785289\pi$
$487$	−8.17528e6	−1.56200	−0.780998	+	0.624533i	$0.785289\pi$
$488$	0	0
$489$	−6.27320e6	−1.18636
$490$	0	0
$491$	−3.78007e6	−0.707614	−0.353807	−	0.935318i	$-0.615113\pi$
$491$	−3.78007e6	−0.707614	−0.353807	+	0.935318i	$0.615113\pi$
$492$	0	0
$493$	−3.40344e6	−0.630668
$494$	0	0
$495$	1.94060e6	0.355978
$496$	0	0
$497$	−2.31113e6	−0.419695
$498$	0	0
$499$	−3.98186e6	−0.715871	−0.357935	−	0.933746i	$-0.616519\pi$
$499$	−3.98186e6	−0.715871	−0.357935	+	0.933746i	$0.616519\pi$
$500$	0	0
$501$	1.73729e6	0.309227
$502$	0	0
$503$	1.04569e7	1.84281	0.921406	−	0.388601i	$-0.127042\pi$
$503$	1.04569e7	1.84281	0.921406	+	0.388601i	$0.127042\pi$
$504$	0	0
$505$	1.11863e7	1.95190
$506$	0	0
$507$	6.46134e6	1.11636
$508$	0	0
$509$	6.05507e6	1.03592	0.517958	−	0.855406i	$-0.326692\pi$
$509$	6.05507e6	1.03592	0.517958	+	0.855406i	$0.326692\pi$
$510$	0	0
$511$	−3.44725e6	−0.584010
$512$	0	0
$513$	−2.02230e6	−0.339275
$514$	0	0
$515$	−960984.	−0.159661
$516$	0	0
$517$	2.46259e6	0.405197
$518$	0	0
$519$	−2.85251e6	−0.464846
$520$	0	0
$521$	1.05053e7	1.69556	0.847780	−	0.530348i	$-0.177939\pi$
$521$	1.05053e7	1.69556	0.847780	+	0.530348i	$0.177939\pi$
$522$	0	0
$523$	−6.49492e6	−1.03829	−0.519146	−	0.854685i	$-0.673750\pi$
$523$	−6.49492e6	−1.03829	−0.519146	+	0.854685i	$0.673750\pi$
$524$	0	0
$525$	7.07129e6	1.11970
$526$	0	0
$527$	−7.64111e6	−1.19848
$528$	0	0
$529$	7.24626e6	1.12583
$530$	0	0
$531$	−1.94535e6	−0.299407
$532$	0	0
$533$	−5.34941e6	−0.815620
$534$	0	0
$535$	1.37684e6	0.207969
$536$	0	0
$537$	−2.36722e6	−0.354245
$538$	0	0
$539$	871563.	0.129219
$540$	0	0
$541$	−5.66349e6	−0.831938	−0.415969	−	0.909379i	$-0.636558\pi$
$541$	−5.66349e6	−0.831938	−0.415969	+	0.909379i	$0.636558\pi$
$542$	0	0
$543$	−1.24699e7	−1.81495
$544$	0	0
$545$	−1.79682e7	−2.59128
$546$	0	0
$547$	1.33609e7	1.90927	0.954636	−	0.297775i	$-0.0962446\pi$
$547$	1.33609e7	1.90927	0.954636	+	0.297775i	$0.0962446\pi$
$548$	0	0
$549$	−5.17414e6	−0.732668
$550$	0	0
$551$	−7.44720e6	−1.04499
$552$	0	0
$553$	−4.16402e6	−0.579029
$554$	0	0
$555$	−2.31285e7	−3.18724
$556$	0	0
$557$	1.00947e7	1.37866	0.689330	−	0.724447i	$-0.257905\pi$
$557$	1.00947e7	1.37866	0.689330	+	0.724447i	$0.257905\pi$
$558$	0	0
$559$	1.17288e7	1.58754
$560$	0	0
$561$	−2.48510e6	−0.333378
$562$	0	0
$563$	−5.58692e6	−0.742851	−0.371426	−	0.928463i	$-0.621131\pi$
$563$	−5.58692e6	−0.742851	−0.371426	+	0.928463i	$0.621131\pi$
$564$	0	0
$565$	1.59304e7	2.09944
$566$	0	0
$567$	−6.65998e6	−0.869992
$568$	0	0
$569$	2.20884e6	0.286012	0.143006	−	0.989722i	$-0.454323\pi$
$569$	2.20884e6	0.286012	0.143006	+	0.989722i	$0.454323\pi$
$570$	0	0
$571$	1.05324e7	1.35188	0.675940	−	0.736957i	$-0.263738\pi$
$571$	1.05324e7	1.35188	0.675940	+	0.736957i	$0.263738\pi$
$572$	0	0
$573$	1.37037e7	1.74362
$574$	0	0
$575$	1.27098e7	1.60313
$576$	0	0
$577$	1.84319e6	0.230479	0.115239	−	0.993338i	$-0.463236\pi$
$577$	1.84319e6	0.230479	0.115239	+	0.993338i	$0.463236\pi$
$578$	0	0
$579$	8.44544e6	1.04695
$580$	0	0
$581$	−2.22205e6	−0.273095
$582$	0	0
$583$	−44286.0	−0.00539629
$584$	0	0
$585$	1.32153e7	1.59657
$586$	0	0
$587$	−1.16959e7	−1.40100	−0.700501	−	0.713652i	$-0.747040\pi$
$587$	−1.16959e7	−1.40100	−0.700501	+	0.713652i	$0.747040\pi$
$588$	0	0
$589$	−1.67198e7	−1.98584
$590$	0	0
$591$	5.63812e6	0.663996
$592$	0	0
$593$	5.81252e6	0.678778	0.339389	−	0.940646i	$-0.389780\pi$
$593$	5.81252e6	0.678778	0.339389	+	0.940646i	$0.389780\pi$
$594$	0	0
$595$	−7.76336e6	−0.898996
$596$	0	0
$597$	−1.22052e7	−1.40155
$598$	0	0
$599$	7.85604e6	0.894616	0.447308	−	0.894380i	$-0.352383\pi$
$599$	7.85604e6	0.894616	0.447308	+	0.894380i	$0.352383\pi$
$600$	0	0
$601$	1.09429e7	1.23579	0.617895	−	0.786261i	$-0.287986\pi$
$601$	1.09429e7	1.23579	0.617895	+	0.786261i	$0.287986\pi$
$602$	0	0
$603$	−3.38441e6	−0.379045
$604$	0	0
$605$	−1.18592e6	−0.131725
$606$	0	0
$607$	185018.	0.0203818	0.0101909	−	0.999948i	$-0.496756\pi$
$607$	185018.	0.0203818	0.0101909	+	0.999948i	$0.496756\pi$
$608$	0	0
$609$	−7.16184e6	−0.782495
$610$	0	0
$611$	1.67700e7	1.81732
$612$	0	0
$613$	−1.77449e7	−1.90731	−0.953655	−	0.300901i	$-0.902713\pi$
$613$	−1.77449e7	−1.90731	−0.953655	+	0.300901i	$0.902713\pi$
$614$	0	0
$615$	−1.10429e7	−1.17732
$616$	0	0
$617$	1.53912e7	1.62765	0.813823	−	0.581113i	$-0.197382\pi$
$617$	1.53912e7	1.62765	0.813823	+	0.581113i	$0.197382\pi$
$618$	0	0
$619$	1.75502e7	1.84101	0.920504	−	0.390734i	$-0.127779\pi$
$619$	1.75502e7	1.84101	0.920504	+	0.390734i	$0.127779\pi$
$620$	0	0
$621$	−3.49556e6	−0.363737
$622$	0	0
$623$	−1.68021e6	−0.173438
$624$	0	0
$625$	−8.69703e6	−0.890576
$626$	0	0
$627$	−5.43774e6	−0.552395
$628$	0	0
$629$	1.32979e7	1.34016
$630$	0	0
$631$	−5.64613e6	−0.564518	−0.282259	−	0.959338i	$-0.591084\pi$
$631$	−5.64613e6	−0.564518	−0.282259	+	0.959338i	$0.591084\pi$
$632$	0	0
$633$	3.86375e6	0.383265
$634$	0	0
$635$	−9.76439e6	−0.960972
$636$	0	0
$637$	5.93527e6	0.579552
$638$	0	0
$639$	−4.66943e6	−0.452389
$640$	0	0
$641$	−4.46307e6	−0.429031	−0.214516	−	0.976721i	$-0.568817\pi$
$641$	−4.46307e6	−0.429031	−0.214516	+	0.976721i	$0.568817\pi$
$642$	0	0
$643$	3.24099e6	0.309137	0.154568	−	0.987982i	$-0.450601\pi$
$643$	3.24099e6	0.309137	0.154568	+	0.987982i	$0.450601\pi$
$644$	0	0
$645$	2.42120e7	2.29156
$646$	0	0
$647$	1.01885e7	0.956858	0.478429	−	0.878126i	$-0.341206\pi$
$647$	1.01885e7	0.956858	0.478429	+	0.878126i	$0.341206\pi$
$648$	0	0
$649$	1.18882e6	0.110791
$650$	0	0
$651$	−1.60792e7	−1.48700
$652$	0	0
$653$	4.66760e6	0.428362	0.214181	−	0.976794i	$-0.431292\pi$
$653$	4.66760e6	0.428362	0.214181	+	0.976794i	$0.431292\pi$
$654$	0	0
$655$	5.54380e6	0.504899
$656$	0	0
$657$	−6.96485e6	−0.629504
$658$	0	0
$659$	−1.29177e6	−0.115870	−0.0579351	−	0.998320i	$-0.518452\pi$
$659$	−1.29177e6	−0.115870	−0.0579351	+	0.998320i	$0.518452\pi$
$660$	0	0
$661$	1.15658e7	1.02960	0.514802	−	0.857309i	$-0.327865\pi$
$661$	1.15658e7	1.02960	0.514802	+	0.857309i	$0.327865\pi$
$662$	0	0
$663$	−1.69233e7	−1.49521
$664$	0	0
$665$	−1.69873e7	−1.48960
$666$	0	0
$667$	−1.28725e7	−1.12034
$668$	0	0
$669$	1.32653e7	1.14591
$670$	0	0
$671$	3.16197e6	0.271114
$672$	0	0
$673$	1.47706e7	1.25707	0.628535	−	0.777781i	$-0.283655\pi$
$673$	1.47706e7	1.25707	0.628535	+	0.777781i	$0.283655\pi$
$674$	0	0
$675$	−3.24702e6	−0.274300
$676$	0	0
$677$	3.09022e6	0.259130	0.129565	−	0.991571i	$-0.458642\pi$
$677$	3.09022e6	0.259130	0.129565	+	0.991571i	$0.458642\pi$
$678$	0	0
$679$	−3.01125e6	−0.250652
$680$	0	0
$681$	−29358.0	−0.00242582
$682$	0	0
$683$	−1.47394e7	−1.20900	−0.604502	−	0.796604i	$-0.706628\pi$
$683$	−1.47394e7	−1.20900	−0.604502	+	0.796604i	$0.706628\pi$
$684$	0	0
$685$	3.02654e7	2.46445
$686$	0	0
$687$	−4.32884e6	−0.349928
$688$	0	0
$689$	−301584.	−0.0242025
$690$	0	0
$691$	−2.36276e6	−0.188245	−0.0941226	−	0.995561i	$-0.530005\pi$
$691$	−2.36276e6	−0.188245	−0.0941226	+	0.995561i	$0.530005\pi$
$692$	0	0
$693$	−2.34788e6	−0.185714
$694$	0	0
$695$	−4.90941e6	−0.385538
$696$	0	0
$697$	6.34918e6	0.495034
$698$	0	0
$699$	1.34548e7	1.04156
$700$	0	0
$701$	1.78888e7	1.37495	0.687473	−	0.726210i	$-0.258720\pi$
$701$	1.78888e7	1.37495	0.687473	+	0.726210i	$0.258720\pi$
$702$	0	0
$703$	2.90976e7	2.22059
$704$	0	0
$705$	3.46188e7	2.62324
$706$	0	0
$707$	−1.35340e7	−1.01830
$708$	0	0
$709$	−1.22735e7	−0.916962	−0.458481	−	0.888704i	$-0.651606\pi$
$709$	−1.22735e7	−0.916962	−0.458481	+	0.888704i	$0.651606\pi$
$710$	0	0
$711$	−8.41302e6	−0.624134
$712$	0	0
$713$	−2.89003e7	−2.12901
$714$	0	0
$715$	−8.07602e6	−0.590789
$716$	0	0
$717$	2.69325e6	0.195650
$718$	0	0
$719$	−7.35232e6	−0.530399	−0.265199	−	0.964194i	$-0.585438\pi$
$719$	−7.35232e6	−0.530399	−0.265199	+	0.964194i	$0.585438\pi$
$720$	0	0
$721$	1.16267e6	0.0832950
$722$	0	0
$723$	−3.56472e7	−2.53618
$724$	0	0
$725$	−1.19573e7	−0.844865
$726$	0	0
$727$	−3.16762e6	−0.222278	−0.111139	−	0.993805i	$-0.535450\pi$
$727$	−3.16762e6	−0.222278	−0.111139	+	0.993805i	$0.535450\pi$
$728$	0	0
$729$	−8.63355e6	−0.601687
$730$	0	0
$731$	−1.39209e7	−0.963546
$732$	0	0
$733$	−857924.	−0.0589778	−0.0294889	−	0.999565i	$-0.509388\pi$
$733$	−857924.	−0.0589778	−0.0294889	+	0.999565i	$0.509388\pi$
$734$	0	0
$735$	1.22523e7	0.836564
$736$	0	0
$737$	2.06825e6	0.140260
$738$	0	0
$739$	1.93551e7	1.30372	0.651860	−	0.758339i	$-0.273989\pi$
$739$	1.93551e7	1.30372	0.651860	+	0.758339i	$0.273989\pi$
$740$	0	0
$741$	−3.70306e7	−2.47751
$742$	0	0
$743$	−2.80305e7	−1.86277	−0.931383	−	0.364040i	$-0.881397\pi$
$743$	−2.80305e7	−1.86277	−0.931383	+	0.364040i	$0.881397\pi$
$744$	0	0
$745$	−3.54804e7	−2.34206
$746$	0	0
$747$	−4.48945e6	−0.294369
$748$	0	0
$749$	−1.66580e6	−0.108497
$750$	0	0
$751$	2.57014e7	1.66287	0.831434	−	0.555624i	$-0.187521\pi$
$751$	2.57014e7	1.66287	0.831434	+	0.555624i	$0.187521\pi$
$752$	0	0
$753$	6.83178e6	0.439083
$754$	0	0
$755$	1.93912e7	1.23805
$756$	0	0
$757$	1.17223e7	0.743489	0.371745	−	0.928335i	$-0.378760\pi$
$757$	1.17223e7	0.743489	0.371745	+	0.928335i	$0.378760\pi$
$758$	0	0
$759$	−9.39916e6	−0.592222
$760$	0	0
$761$	5.77783e6	0.361662	0.180831	−	0.983514i	$-0.442121\pi$
$761$	5.77783e6	0.361662	0.180831	+	0.983514i	$0.442121\pi$
$762$	0	0
$763$	2.17393e7	1.35187
$764$	0	0
$765$	−1.56852e7	−0.969026
$766$	0	0
$767$	8.09580e6	0.496903
$768$	0	0
$769$	−2.04989e7	−1.25001	−0.625007	−	0.780619i	$-0.714904\pi$
$769$	−2.04989e7	−1.25001	−0.625007	+	0.780619i	$0.714904\pi$
$770$	0	0
$771$	3.46390e7	2.09860
$772$	0	0
$773$	−1.50298e7	−0.904697	−0.452348	−	0.891841i	$-0.649414\pi$
$773$	−1.50298e7	−0.904697	−0.452348	+	0.891841i	$0.649414\pi$
$774$	0	0
$775$	−2.68455e7	−1.60552
$776$	0	0
$777$	2.79826e7	1.66278
$778$	0	0
$779$	1.38929e7	0.820255
$780$	0	0
$781$	2.85354e6	0.167401
$782$	0	0
$783$	3.28860e6	0.191693
$784$	0	0
$785$	5.03439e6	0.291590
$786$	0	0
$787$	−2.05325e7	−1.18169	−0.590847	−	0.806784i	$-0.701206\pi$
$787$	−2.05325e7	−1.18169	−0.590847	+	0.806784i	$0.701206\pi$
$788$	0	0
$789$	−2.89070e7	−1.65315
$790$	0	0
$791$	−1.92738e7	−1.09528
$792$	0	0
$793$	2.15328e7	1.21595
$794$	0	0
$795$	−622566.	−0.0349355
$796$	0	0
$797$	1.76247e6	0.0982823	0.0491411	−	0.998792i	$-0.484352\pi$
$797$	1.76247e6	0.0982823	0.0491411	+	0.998792i	$0.484352\pi$
$798$	0	0
$799$	−1.99043e7	−1.10301
$800$	0	0
$801$	−3.39471e6	−0.186948
$802$	0	0
$803$	4.25630e6	0.232939
$804$	0	0
$805$	−2.93627e7	−1.59700
$806$	0	0
$807$	−1.58445e6	−0.0856436
$808$	0	0
$809$	2.00289e7	1.07593	0.537967	−	0.842966i	$-0.319192\pi$
$809$	2.00289e7	1.07593	0.537967	+	0.842966i	$0.319192\pi$
$810$	0	0
$811$	2.55409e7	1.36359	0.681796	−	0.731542i	$-0.261199\pi$
$811$	2.55409e7	1.36359	0.681796	+	0.731542i	$0.261199\pi$
$812$	0	0
$813$	−7.57193e6	−0.401772
$814$	0	0
$815$	2.41966e7	1.27603
$816$	0	0
$817$	−3.04608e7	−1.59656
$818$	0	0
$819$	−1.59889e7	−0.832930
$820$	0	0
$821$	6.73166e6	0.348549	0.174275	−	0.984697i	$-0.444242\pi$
$821$	6.73166e6	0.348549	0.174275	+	0.984697i	$0.444242\pi$
$822$	0	0
$823$	1.44880e7	0.745606	0.372803	−	0.927911i	$-0.378397\pi$
$823$	1.44880e7	0.745606	0.372803	+	0.927911i	$0.378397\pi$
$824$	0	0
$825$	−8.73088e6	−0.446604
$826$	0	0
$827$	4.15879e6	0.211448	0.105724	−	0.994396i	$-0.466284\pi$
$827$	4.15879e6	0.211448	0.105724	+	0.994396i	$0.466284\pi$
$828$	0	0
$829$	−1.02525e7	−0.518136	−0.259068	−	0.965859i	$-0.583415\pi$
$829$	−1.02525e7	−0.518136	−0.259068	+	0.965859i	$0.583415\pi$
$830$	0	0
$831$	8.78896e6	0.441504
$832$	0	0
$833$	−7.04453e6	−0.351755
$834$	0	0
$835$	−6.70097e6	−0.332599
$836$	0	0
$837$	7.38328e6	0.364281
$838$	0	0
$839$	3.07705e7	1.50914	0.754571	−	0.656218i	$-0.227845\pi$
$839$	3.07705e7	1.50914	0.754571	+	0.656218i	$0.227845\pi$
$840$	0	0
$841$	−8.40075e6	−0.409570
$842$	0	0
$843$	−1.66803e7	−0.808414
$844$	0	0
$845$	−2.49223e7	−1.20073
$846$	0	0
$847$	1.43482e6	0.0687208
$848$	0	0
$849$	−3.79672e7	−1.80776
$850$	0	0
$851$	5.02953e7	2.38069
$852$	0	0
$853$	−4.19232e7	−1.97280	−0.986398	−	0.164377i	$-0.947439\pi$
$853$	−4.19232e7	−1.97280	−0.986398	+	0.164377i	$0.947439\pi$
$854$	0	0
$855$	−3.43213e7	−1.60564
$856$	0	0
$857$	−1.87686e7	−0.872929	−0.436464	−	0.899722i	$-0.643769\pi$
$857$	−1.87686e7	−0.872929	−0.436464	+	0.899722i	$0.643769\pi$
$858$	0	0
$859$	3.95520e7	1.82888	0.914441	−	0.404720i	$-0.132631\pi$
$859$	3.95520e7	1.82888	0.914441	+	0.404720i	$0.132631\pi$
$860$	0	0
$861$	1.33605e7	0.614209
$862$	0	0
$863$	1.50569e7	0.688191	0.344095	−	0.938935i	$-0.388186\pi$
$863$	1.50569e7	0.688191	0.344095	+	0.938935i	$0.388186\pi$
$864$	0	0
$865$	1.10026e7	0.499981
$866$	0	0
$867$	−9.73083e6	−0.439645
$868$	0	0
$869$	5.14129e6	0.230952
$870$	0	0
$871$	1.40846e7	0.629072
$872$	0	0
$873$	−6.08395e6	−0.270178
$874$	0	0
$875$	−2.46872e6	−0.109006
$876$	0	0
$877$	−1.58591e7	−0.696272	−0.348136	−	0.937444i	$-0.613185\pi$
$877$	−1.58591e7	−0.696272	−0.348136	+	0.937444i	$0.613185\pi$
$878$	0	0
$879$	1.83842e7	0.802549
$880$	0	0
$881$	−2.29142e7	−0.994640	−0.497320	−	0.867567i	$-0.665682\pi$
$881$	−2.29142e7	−0.994640	−0.497320	+	0.867567i	$0.665682\pi$
$882$	0	0
$883$	−1.06073e7	−0.457830	−0.228915	−	0.973446i	$-0.573518\pi$
$883$	−1.06073e7	−0.457830	−0.228915	+	0.973446i	$0.573518\pi$
$884$	0	0
$885$	1.67123e7	0.717263
$886$	0	0
$887$	2.28527e7	0.975278	0.487639	−	0.873045i	$-0.337858\pi$
$887$	2.28527e7	0.975278	0.487639	+	0.873045i	$0.337858\pi$
$888$	0	0
$889$	1.18137e7	0.501339
$890$	0	0
$891$	8.22304e6	0.347007
$892$	0	0
$893$	−4.35533e7	−1.82765
$894$	0	0
$895$	9.13072e6	0.381020
$896$	0	0
$897$	−6.40075e7	−2.65613
$898$	0	0
$899$	2.71892e7	1.12201
$900$	0	0
$901$	357948.	0.0146895
$902$	0	0
$903$	−2.92936e7	−1.19551
$904$	0	0
$905$	4.80984e7	1.95213
$906$	0	0
$907$	3.21947e7	1.29947	0.649736	−	0.760160i	$-0.274880\pi$
$907$	3.21947e7	1.29947	0.649736	+	0.760160i	$0.274880\pi$
$908$	0	0
$909$	−2.73442e7	−1.09763
$910$	0	0
$911$	2.02254e7	0.807424	0.403712	−	0.914886i	$-0.367720\pi$
$911$	2.02254e7	0.807424	0.403712	+	0.914886i	$0.367720\pi$
$912$	0	0
$913$	2.74355e6	0.108927
$914$	0	0
$915$	4.44505e7	1.75519
$916$	0	0
$917$	−6.70732e6	−0.263406
$918$	0	0
$919$	−2.30019e7	−0.898411	−0.449206	−	0.893428i	$-0.648293\pi$
$919$	−2.30019e7	−0.898411	−0.449206	+	0.893428i	$0.648293\pi$
$920$	0	0
$921$	−2.88683e6	−0.112143
$922$	0	0
$923$	1.94324e7	0.750796
$924$	0	0
$925$	4.67193e7	1.79532
$926$	0	0
$927$	2.34907e6	0.0897836
$928$	0	0
$929$	−1.64913e7	−0.626924	−0.313462	−	0.949601i	$-0.601489\pi$
$929$	−1.64913e7	−0.626924	−0.313462	+	0.949601i	$0.601489\pi$
$930$	0	0
$931$	−1.54144e7	−0.582845
$932$	0	0
$933$	2.57521e7	0.968521
$934$	0	0
$935$	9.58538e6	0.358575
$936$	0	0
$937$	−4.99402e7	−1.85824	−0.929119	−	0.369780i	$-0.879433\pi$
$937$	−4.99402e7	−1.85824	−0.929119	+	0.369780i	$0.879433\pi$
$938$	0	0
$939$	−6.58753e7	−2.43814
$940$	0	0
$941$	−4.21000e6	−0.154992	−0.0774958	−	0.996993i	$-0.524692\pi$
$941$	−4.21000e6	−0.154992	−0.0774958	+	0.996993i	$0.524692\pi$
$942$	0	0
$943$	2.40139e7	0.879394
$944$	0	0
$945$	7.50141e6	0.273252
$946$	0	0
$947$	−2.76066e7	−1.00032	−0.500159	−	0.865933i	$-0.666725\pi$
$947$	−2.76066e7	−1.00032	−0.500159	+	0.865933i	$0.666725\pi$
$948$	0	0
$949$	2.89850e7	1.04474
$950$	0	0
$951$	3.55149e7	1.27338
$952$	0	0
$953$	1.69297e7	0.603832	0.301916	−	0.953335i	$-0.402374\pi$
$953$	1.69297e7	0.603832	0.301916	+	0.953335i	$0.402374\pi$
$954$	0	0
$955$	−5.28571e7	−1.87540
$956$	0	0
$957$	8.84268e6	0.312107
$958$	0	0
$959$	−3.66174e7	−1.28570
$960$	0	0
$961$	3.24138e7	1.13220
$962$	0	0
$963$	−3.36560e6	−0.116949
$964$	0	0
$965$	−3.25753e7	−1.12608
$966$	0	0
$967$	1.08793e6	0.0374140	0.0187070	−	0.999825i	$-0.494045\pi$
$967$	1.08793e6	0.0374140	0.0187070	+	0.999825i	$0.494045\pi$
$968$	0	0
$969$	4.39513e7	1.50370
$970$	0	0
$971$	−7.15335e6	−0.243479	−0.121739	−	0.992562i	$-0.538847\pi$
$971$	−7.15335e6	−0.243479	−0.121739	+	0.992562i	$0.538847\pi$
$972$	0	0
$973$	5.93978e6	0.201135
$974$	0	0
$975$	−5.94565e7	−2.00303
$976$	0	0
$977$	−7.88535e6	−0.264292	−0.132146	−	0.991230i	$-0.542187\pi$
$977$	−7.88535e6	−0.264292	−0.132146	+	0.991230i	$0.542187\pi$
$978$	0	0
$979$	2.07454e6	0.0691777
$980$	0	0
$981$	4.39223e7	1.45718
$982$	0	0
$983$	7.58842e6	0.250477	0.125238	−	0.992127i	$-0.460030\pi$
$983$	7.58842e6	0.250477	0.125238	+	0.992127i	$0.460030\pi$
$984$	0	0
$985$	−2.17470e7	−0.714183
$986$	0	0
$987$	−4.18844e7	−1.36855
$988$	0	0
$989$	−5.26516e7	−1.71167
$990$	0	0
$991$	8.80935e6	0.284944	0.142472	−	0.989799i	$-0.454495\pi$
$991$	8.80935e6	0.284944	0.142472	+	0.989799i	$0.454495\pi$
$992$	0	0
$993$	4.49193e7	1.44564
$994$	0	0
$995$	4.70772e7	1.50748
$996$	0	0
$997$	−3.53833e7	−1.12735	−0.563677	−	0.825995i	$-0.690614\pi$
$997$	−3.53833e7	−1.12735	−0.563677	+	0.825995i	$0.690614\pi$
$998$	0	0
$999$	−1.28492e7	−0.407344

Twists

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

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

Related objects

Downloads

Learn more