LMFDB - Embedded newform 560.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,6,Mod(1,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, 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("560.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	560.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:	$89.8149390953$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	560.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-11.0000 q^{3} -25.0000 q^{5} +49.0000 q^{7} -122.000 q^{9} +O(q^{10})$

$q-11.0000 q^{3} -25.0000 q^{5} +49.0000 q^{7} -122.000 q^{9} -83.0000 q^{11} -83.0000 q^{13} +275.000 q^{15} -177.000 q^{17} +2082.00 q^{19} -539.000 q^{21} +3170.00 q^{23} +625.000 q^{25} +4015.00 q^{27} -8681.00 q^{29} -1636.00 q^{31} +913.000 q^{33} -1225.00 q^{35} +4298.00 q^{37} +913.000 q^{39} +2356.00 q^{41} -8738.00 q^{43} +3050.00 q^{45} +3641.00 q^{47} +2401.00 q^{49} +1947.00 q^{51} +33268.0 q^{53} +2075.00 q^{55} -22902.0 q^{57} +30968.0 q^{59} +4560.00 q^{61} -5978.00 q^{63} +2075.00 q^{65} -37788.0 q^{67} -34870.0 q^{69} +59304.0 q^{71} -8910.00 q^{73} -6875.00 q^{75} -4067.00 q^{77} -27589.0 q^{79} -14519.0 q^{81} -67676.0 q^{83} +4425.00 q^{85} +95491.0 q^{87} +10700.0 q^{89} -4067.00 q^{91} +17996.0 q^{93} -52050.0 q^{95} +65075.0 q^{97} +10126.0 q^{99} +O(q^{100})$

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
$3$	−11.0000	−0.705650	−0.352825	−	0.935689i	$-0.614779\pi$
$3$	−11.0000	−0.705650	−0.352825	+	0.935689i	$0.614779\pi$
$4$	0	0
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	0	0
$9$	−122.000	−0.502058
$10$	0	0
$11$	−83.0000	−0.206822	−0.103411	−	0.994639i	$-0.532976\pi$
$11$	−83.0000	−0.206822	−0.103411	+	0.994639i	$0.532976\pi$
$12$	0	0
$13$	−83.0000	−0.136213	−0.0681067	−	0.997678i	$-0.521696\pi$
$13$	−83.0000	−0.136213	−0.0681067	+	0.997678i	$0.521696\pi$
$14$	0	0
$15$	275.000	0.315576
$16$	0	0
$17$	−177.000	−0.148543	−0.0742713	−	0.997238i	$-0.523663\pi$
$17$	−177.000	−0.148543	−0.0742713	+	0.997238i	$0.523663\pi$
$18$	0	0
$19$	2082.00	1.32311	0.661556	−	0.749896i	$-0.269896\pi$
$19$	2082.00	1.32311	0.661556	+	0.749896i	$0.269896\pi$
$20$	0	0
$21$	−539.000	−0.266711
$22$	0	0
$23$	3170.00	1.24951	0.624755	−	0.780821i	$-0.285199\pi$
$23$	3170.00	1.24951	0.624755	+	0.780821i	$0.285199\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	4015.00	1.05993
$28$	0	0
$29$	−8681.00	−1.91679	−0.958395	−	0.285444i	$-0.907859\pi$
$29$	−8681.00	−1.91679	−0.958395	+	0.285444i	$0.907859\pi$
$30$	0	0
$31$	−1636.00	−0.305759	−0.152879	−	0.988245i	$-0.548855\pi$
$31$	−1636.00	−0.305759	−0.152879	+	0.988245i	$0.548855\pi$
$32$	0	0
$33$	913.000	0.145944
$34$	0	0
$35$	−1225.00	−0.169031
$36$	0	0
$37$	4298.00	0.516134	0.258067	−	0.966127i	$-0.416915\pi$
$37$	4298.00	0.516134	0.258067	+	0.966127i	$0.416915\pi$
$38$	0	0
$39$	913.000	0.0961190
$40$	0	0
$41$	2356.00	0.218885	0.109442	−	0.993993i	$-0.465093\pi$
$41$	2356.00	0.218885	0.109442	+	0.993993i	$0.465093\pi$
$42$	0	0
$43$	−8738.00	−0.720677	−0.360339	−	0.932822i	$-0.617339\pi$
$43$	−8738.00	−0.720677	−0.360339	+	0.932822i	$0.617339\pi$
$44$	0	0
$45$	3050.00	0.224527
$46$	0	0
$47$	3641.00	0.240423	0.120212	−	0.992748i	$-0.461643\pi$
$47$	3641.00	0.240423	0.120212	+	0.992748i	$0.461643\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	0	0
$51$	1947.00	0.104819
$52$	0	0
$53$	33268.0	1.62681	0.813405	−	0.581697i	$-0.197611\pi$
$53$	33268.0	1.62681	0.813405	+	0.581697i	$0.197611\pi$
$54$	0	0
$55$	2075.00	0.0924935
$56$	0	0
$57$	−22902.0	−0.933655
$58$	0	0
$59$	30968.0	1.15820	0.579099	−	0.815257i	$-0.303404\pi$
$59$	30968.0	1.15820	0.579099	+	0.815257i	$0.303404\pi$
$60$	0	0
$61$	4560.00	0.156906	0.0784531	−	0.996918i	$-0.475002\pi$
$61$	4560.00	0.156906	0.0784531	+	0.996918i	$0.475002\pi$
$62$	0	0
$63$	−5978.00	−0.189760
$64$	0	0
$65$	2075.00	0.0609165
$66$	0	0
$67$	−37788.0	−1.02841	−0.514206	−	0.857667i	$-0.671913\pi$
$67$	−37788.0	−1.02841	−0.514206	+	0.857667i	$0.671913\pi$
$68$	0	0
$69$	−34870.0	−0.881717
$70$	0	0
$71$	59304.0	1.39617	0.698085	−	0.716015i	$-0.254036\pi$
$71$	59304.0	1.39617	0.698085	+	0.716015i	$0.254036\pi$
$72$	0	0
$73$	−8910.00	−0.195691	−0.0978454	−	0.995202i	$-0.531195\pi$
$73$	−8910.00	−0.195691	−0.0978454	+	0.995202i	$0.531195\pi$
$74$	0	0
$75$	−6875.00	−0.141130
$76$	0	0
$77$	−4067.00	−0.0781713
$78$	0	0
$79$	−27589.0	−0.497357	−0.248678	−	0.968586i	$-0.579996\pi$
$79$	−27589.0	−0.497357	−0.248678	+	0.968586i	$0.579996\pi$
$80$	0	0
$81$	−14519.0	−0.245881
$82$	0	0
$83$	−67676.0	−1.07830	−0.539150	−	0.842210i	$-0.681254\pi$
$83$	−67676.0	−1.07830	−0.539150	+	0.842210i	$0.681254\pi$
$84$	0	0
$85$	4425.00	0.0664303
$86$	0	0
$87$	95491.0	1.35258
$88$	0	0
$89$	10700.0	0.143189	0.0715944	−	0.997434i	$-0.477191\pi$
$89$	10700.0	0.143189	0.0715944	+	0.997434i	$0.477191\pi$
$90$	0	0
$91$	−4067.00	−0.0514838
$92$	0	0
$93$	17996.0	0.215759
$94$	0	0
$95$	−52050.0	−0.591714
$96$	0	0
$97$	65075.0	0.702239	0.351119	−	0.936331i	$-0.385801\pi$
$97$	65075.0	0.702239	0.351119	+	0.936331i	$0.385801\pi$
$98$	0	0
$99$	10126.0	0.103836
$100$	0	0
$101$	−149250.	−1.45583	−0.727915	−	0.685667i	$-0.759511\pi$
$101$	−149250.	−1.45583	−0.727915	+	0.685667i	$0.759511\pi$
$102$	0	0
$103$	−194315.	−1.80473	−0.902367	−	0.430968i	$-0.858172\pi$
$103$	−194315.	−1.80473	−0.902367	+	0.430968i	$0.858172\pi$
$104$	0	0
$105$	13475.0	0.119277
$106$	0	0
$107$	−40538.0	−0.342297	−0.171148	−	0.985245i	$-0.554748\pi$
$107$	−40538.0	−0.342297	−0.171148	+	0.985245i	$0.554748\pi$
$108$	0	0
$109$	−87651.0	−0.706628	−0.353314	−	0.935505i	$-0.614945\pi$
$109$	−87651.0	−0.706628	−0.353314	+	0.935505i	$0.614945\pi$
$110$	0	0
$111$	−47278.0	−0.364210
$112$	0	0
$113$	−76314.0	−0.562222	−0.281111	−	0.959675i	$-0.590703\pi$
$113$	−76314.0	−0.562222	−0.281111	+	0.959675i	$0.590703\pi$
$114$	0	0
$115$	−79250.0	−0.558798
$116$	0	0
$117$	10126.0	0.0683870
$118$	0	0
$119$	−8673.00	−0.0561438
$120$	0	0
$121$	−154162.	−0.957225
$122$	0	0
$123$	−25916.0	−0.154456
$124$	0	0
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	183128.	1.00750	0.503750	−	0.863849i	$-0.331953\pi$
$127$	183128.	1.00750	0.503750	+	0.863849i	$0.331953\pi$
$128$	0	0
$129$	96118.0	0.508546
$130$	0	0
$131$	−216190.	−1.10067	−0.550335	−	0.834944i	$-0.685500\pi$
$131$	−216190.	−1.10067	−0.550335	+	0.834944i	$0.685500\pi$
$132$	0	0
$133$	102018.	0.500089
$134$	0	0
$135$	−100375.	−0.474014
$136$	0	0
$137$	−119844.	−0.545525	−0.272763	−	0.962081i	$-0.587937\pi$
$137$	−119844.	−0.545525	−0.272763	+	0.962081i	$0.587937\pi$
$138$	0	0
$139$	−259298.	−1.13831	−0.569157	−	0.822229i	$-0.692730\pi$
$139$	−259298.	−1.13831	−0.569157	+	0.822229i	$0.692730\pi$
$140$	0	0
$141$	−40051.0	−0.169655
$142$	0	0
$143$	6889.00	0.0281719
$144$	0	0
$145$	217025.	0.857215
$146$	0	0
$147$	−26411.0	−0.100807
$148$	0	0
$149$	−88518.0	−0.326637	−0.163319	−	0.986573i	$-0.552220\pi$
$149$	−88518.0	−0.326637	−0.163319	+	0.986573i	$0.552220\pi$
$150$	0	0
$151$	−115053.	−0.410635	−0.205317	−	0.978695i	$-0.565823\pi$
$151$	−115053.	−0.410635	−0.205317	+	0.978695i	$0.565823\pi$
$152$	0	0
$153$	21594.0	0.0745769
$154$	0	0
$155$	40900.0	0.136740
$156$	0	0
$157$	−324370.	−1.05025	−0.525124	−	0.851026i	$-0.675981\pi$
$157$	−324370.	−1.05025	−0.525124	+	0.851026i	$0.675981\pi$
$158$	0	0
$159$	−365948.	−1.14796
$160$	0	0
$161$	155330.	0.472270
$162$	0	0
$163$	−236470.	−0.697119	−0.348560	−	0.937287i	$-0.613329\pi$
$163$	−236470.	−0.697119	−0.348560	+	0.937287i	$0.613329\pi$
$164$	0	0
$165$	−22825.0	−0.0652681
$166$	0	0
$167$	332853.	0.923552	0.461776	−	0.886997i	$-0.347212\pi$
$167$	332853.	0.923552	0.461776	+	0.886997i	$0.347212\pi$
$168$	0	0
$169$	−364404.	−0.981446
$170$	0	0
$171$	−254004.	−0.664279
$172$	0	0
$173$	−435681.	−1.10676	−0.553380	−	0.832929i	$-0.686662\pi$
$173$	−435681.	−1.10676	−0.553380	+	0.832929i	$0.686662\pi$
$174$	0	0
$175$	30625.0	0.0755929
$176$	0	0
$177$	−340648.	−0.817283
$178$	0	0
$179$	727852.	1.69789	0.848947	−	0.528478i	$-0.177237\pi$
$179$	727852.	1.69789	0.848947	+	0.528478i	$0.177237\pi$
$180$	0	0
$181$	287292.	0.651819	0.325910	−	0.945401i	$-0.394330\pi$
$181$	287292.	0.651819	0.325910	+	0.945401i	$0.394330\pi$
$182$	0	0
$183$	−50160.0	−0.110721
$184$	0	0
$185$	−107450.	−0.230822
$186$	0	0
$187$	14691.0	0.0307218
$188$	0	0
$189$	196735.	0.400615
$190$	0	0
$191$	454581.	0.901629	0.450814	−	0.892618i	$-0.351134\pi$
$191$	454581.	0.901629	0.450814	+	0.892618i	$0.351134\pi$
$192$	0	0
$193$	−398780.	−0.770620	−0.385310	−	0.922787i	$-0.625905\pi$
$193$	−398780.	−0.770620	−0.385310	+	0.922787i	$0.625905\pi$
$194$	0	0
$195$	−22825.0	−0.0429857
$196$	0	0
$197$	−959776.	−1.76199	−0.880997	−	0.473122i	$-0.843127\pi$
$197$	−959776.	−1.76199	−0.880997	+	0.473122i	$0.843127\pi$
$198$	0	0
$199$	−342024.	−0.612243	−0.306122	−	0.951992i	$-0.599031\pi$
$199$	−342024.	−0.612243	−0.306122	+	0.951992i	$0.599031\pi$
$200$	0	0
$201$	415668.	0.725699
$202$	0	0
$203$	−425369.	−0.724479
$204$	0	0
$205$	−58900.0	−0.0978883
$206$	0	0
$207$	−386740.	−0.627326
$208$	0	0
$209$	−172806.	−0.273649
$210$	0	0
$211$	255043.	0.394373	0.197187	−	0.980366i	$-0.436820\pi$
$211$	255043.	0.394373	0.197187	+	0.980366i	$0.436820\pi$
$212$	0	0
$213$	−652344.	−0.985207
$214$	0	0
$215$	218450.	0.322297
$216$	0	0
$217$	−80164.0	−0.115566
$218$	0	0
$219$	98010.0	0.138089
$220$	0	0
$221$	14691.0	0.0202335
$222$	0	0
$223$	198381.	0.267139	0.133570	−	0.991039i	$-0.457356\pi$
$223$	198381.	0.267139	0.133570	+	0.991039i	$0.457356\pi$
$224$	0	0
$225$	−76250.0	−0.100412
$226$	0	0
$227$	−544967.	−0.701949	−0.350975	−	0.936385i	$-0.614150\pi$
$227$	−544967.	−0.701949	−0.350975	+	0.936385i	$0.614150\pi$
$228$	0	0
$229$	−1.45584e6	−1.83454	−0.917268	−	0.398271i	$-0.869610\pi$
$229$	−1.45584e6	−1.83454	−0.917268	+	0.398271i	$0.869610\pi$
$230$	0	0
$231$	44737.0	0.0551616
$232$	0	0
$233$	−65544.0	−0.0790939	−0.0395470	−	0.999218i	$-0.512591\pi$
$233$	−65544.0	−0.0790939	−0.0395470	+	0.999218i	$0.512591\pi$
$234$	0	0
$235$	−91025.0	−0.107520
$236$	0	0
$237$	303479.	0.350960
$238$	0	0
$239$	621207.	0.703464	0.351732	−	0.936101i	$-0.385593\pi$
$239$	621207.	0.703464	0.351732	+	0.936101i	$0.385593\pi$
$240$	0	0
$241$	1.02763e6	1.13971	0.569855	−	0.821745i	$-0.306999\pi$
$241$	1.02763e6	1.13971	0.569855	+	0.821745i	$0.306999\pi$
$242$	0	0
$243$	−815936.	−0.886422
$244$	0	0
$245$	−60025.0	−0.0638877
$246$	0	0
$247$	−172806.	−0.180226
$248$	0	0
$249$	744436.	0.760902
$250$	0	0
$251$	−1.79275e6	−1.79612	−0.898060	−	0.439873i	$-0.855024\pi$
$251$	−1.79275e6	−1.79612	−0.898060	+	0.439873i	$0.855024\pi$
$252$	0	0
$253$	−263110.	−0.258426
$254$	0	0
$255$	−48675.0	−0.0468765
$256$	0	0
$257$	1.15843e6	1.09405	0.547025	−	0.837116i	$-0.315760\pi$
$257$	1.15843e6	1.09405	0.547025	+	0.837116i	$0.315760\pi$
$258$	0	0
$259$	210602.	0.195080
$260$	0	0
$261$	1.05908e6	0.962340
$262$	0	0
$263$	639534.	0.570130	0.285065	−	0.958508i	$-0.407985\pi$
$263$	639534.	0.570130	0.285065	+	0.958508i	$0.407985\pi$
$264$	0	0
$265$	−831700.	−0.727532
$266$	0	0
$267$	−117700.	−0.101041
$268$	0	0
$269$	2.19619e6	1.85050	0.925252	−	0.379353i	$-0.123853\pi$
$269$	2.19619e6	1.85050	0.925252	+	0.379353i	$0.123853\pi$
$270$	0	0
$271$	−1.38063e6	−1.14197	−0.570985	−	0.820960i	$-0.693439\pi$
$271$	−1.38063e6	−1.14197	−0.570985	+	0.820960i	$0.693439\pi$
$272$	0	0
$273$	44737.0	0.0363296
$274$	0	0
$275$	−51875.0	−0.0413644
$276$	0	0
$277$	2.12298e6	1.66244	0.831222	−	0.555941i	$-0.187642\pi$
$277$	2.12298e6	1.66244	0.831222	+	0.555941i	$0.187642\pi$
$278$	0	0
$279$	199592.	0.153509
$280$	0	0
$281$	1.19699e6	0.904323	0.452162	−	0.891936i	$-0.350653\pi$
$281$	1.19699e6	0.904323	0.452162	+	0.891936i	$0.350653\pi$
$282$	0	0
$283$	−281449.	−0.208898	−0.104449	−	0.994530i	$-0.533308\pi$
$283$	−281449.	−0.208898	−0.104449	+	0.994530i	$0.533308\pi$
$284$	0	0
$285$	572550.	0.417543
$286$	0	0
$287$	115444.	0.0827307
$288$	0	0
$289$	−1.38853e6	−0.977935
$290$	0	0
$291$	−715825.	−0.495535
$292$	0	0
$293$	−2.71466e6	−1.84734	−0.923669	−	0.383190i	$-0.874825\pi$
$293$	−2.71466e6	−1.84734	−0.923669	+	0.383190i	$0.874825\pi$
$294$	0	0
$295$	−774200.	−0.517962
$296$	0	0
$297$	−333245.	−0.219216
$298$	0	0
$299$	−263110.	−0.170200
$300$	0	0
$301$	−428162.	−0.272390
$302$	0	0
$303$	1.64175e6	1.02731
$304$	0	0
$305$	−114000.	−0.0701706
$306$	0	0
$307$	2.68381e6	1.62519	0.812597	−	0.582826i	$-0.198053\pi$
$307$	2.68381e6	1.62519	0.812597	+	0.582826i	$0.198053\pi$
$308$	0	0
$309$	2.13746e6	1.27351
$310$	0	0
$311$	−25542.0	−0.0149746	−0.00748728	−	0.999972i	$-0.502383\pi$
$311$	−25542.0	−0.0149746	−0.00748728	+	0.999972i	$0.502383\pi$
$312$	0	0
$313$	−975975.	−0.563090	−0.281545	−	0.959548i	$-0.590847\pi$
$313$	−975975.	−0.563090	−0.281545	+	0.959548i	$0.590847\pi$
$314$	0	0
$315$	149450.	0.0848632
$316$	0	0
$317$	−1.45540e6	−0.813457	−0.406729	−	0.913549i	$-0.633331\pi$
$317$	−1.45540e6	−0.813457	−0.406729	+	0.913549i	$0.633331\pi$
$318$	0	0
$319$	720523.	0.396434
$320$	0	0
$321$	445918.	0.241542
$322$	0	0
$323$	−368514.	−0.196539
$324$	0	0
$325$	−51875.0	−0.0272427
$326$	0	0
$327$	964161.	0.498632
$328$	0	0
$329$	178409.	0.0908714
$330$	0	0
$331$	2.98186e6	1.49595	0.747975	−	0.663727i	$-0.231026\pi$
$331$	2.98186e6	1.49595	0.747975	+	0.663727i	$0.231026\pi$
$332$	0	0
$333$	−524356.	−0.259129
$334$	0	0
$335$	944700.	0.459920
$336$	0	0
$337$	−928698.	−0.445451	−0.222725	−	0.974881i	$-0.571495\pi$
$337$	−928698.	−0.445451	−0.222725	+	0.974881i	$0.571495\pi$
$338$	0	0
$339$	839454.	0.396732
$340$	0	0
$341$	135788.	0.0632376
$342$	0	0
$343$	117649.	0.0539949
$344$	0	0
$345$	871750.	0.394316
$346$	0	0
$347$	−1.75435e6	−0.782156	−0.391078	−	0.920357i	$-0.627898\pi$
$347$	−1.75435e6	−0.782156	−0.391078	+	0.920357i	$0.627898\pi$
$348$	0	0
$349$	−1.78606e6	−0.784934	−0.392467	−	0.919766i	$-0.628378\pi$
$349$	−1.78606e6	−0.784934	−0.392467	+	0.919766i	$0.628378\pi$
$350$	0	0
$351$	−333245.	−0.144376
$352$	0	0
$353$	1.23308e6	0.526687	0.263344	−	0.964702i	$-0.415175\pi$
$353$	1.23308e6	0.526687	0.263344	+	0.964702i	$0.415175\pi$
$354$	0	0
$355$	−1.48260e6	−0.624386
$356$	0	0
$357$	95403.0	0.0396179
$358$	0	0
$359$	1.69914e6	0.695812	0.347906	−	0.937529i	$-0.386893\pi$
$359$	1.69914e6	0.695812	0.347906	+	0.937529i	$0.386893\pi$
$360$	0	0
$361$	1.85862e6	0.750626
$362$	0	0
$363$	1.69578e6	0.675466
$364$	0	0
$365$	222750.	0.0875156
$366$	0	0
$367$	−1.82938e6	−0.708989	−0.354494	−	0.935058i	$-0.615347\pi$
$367$	−1.82938e6	−0.708989	−0.354494	+	0.935058i	$0.615347\pi$
$368$	0	0
$369$	−287432.	−0.109893
$370$	0	0
$371$	1.63013e6	0.614877
$372$	0	0
$373$	−1.03316e6	−0.384501	−0.192250	−	0.981346i	$-0.561579\pi$
$373$	−1.03316e6	−0.384501	−0.192250	+	0.981346i	$0.561579\pi$
$374$	0	0
$375$	171875.	0.0631153
$376$	0	0
$377$	720523.	0.261093
$378$	0	0
$379$	−1.25601e6	−0.449155	−0.224577	−	0.974456i	$-0.572100\pi$
$379$	−1.25601e6	−0.449155	−0.224577	+	0.974456i	$0.572100\pi$
$380$	0	0
$381$	−2.01441e6	−0.710943
$382$	0	0
$383$	−3.64322e6	−1.26908	−0.634539	−	0.772891i	$-0.718810\pi$
$383$	−3.64322e6	−1.26908	−0.634539	+	0.772891i	$0.718810\pi$
$384$	0	0
$385$	101675.	0.0349593
$386$	0	0
$387$	1.06604e6	0.361822
$388$	0	0
$389$	3.67368e6	1.23091	0.615457	−	0.788171i	$-0.288972\pi$
$389$	3.67368e6	1.23091	0.615457	+	0.788171i	$0.288972\pi$
$390$	0	0
$391$	−561090.	−0.185605
$392$	0	0
$393$	2.37809e6	0.776689
$394$	0	0
$395$	689725.	0.222425
$396$	0	0
$397$	−5.64367e6	−1.79716	−0.898578	−	0.438815i	$-0.855398\pi$
$397$	−5.64367e6	−1.79716	−0.898578	+	0.438815i	$0.855398\pi$
$398$	0	0
$399$	−1.12220e6	−0.352888
$400$	0	0
$401$	−4.22249e6	−1.31132	−0.655658	−	0.755058i	$-0.727609\pi$
$401$	−4.22249e6	−1.31132	−0.655658	+	0.755058i	$0.727609\pi$
$402$	0	0
$403$	135788.	0.0416484
$404$	0	0
$405$	362975.	0.109961
$406$	0	0
$407$	−356734.	−0.106748
$408$	0	0
$409$	606470.	0.179267	0.0896336	−	0.995975i	$-0.471430\pi$
$409$	606470.	0.179267	0.0896336	+	0.995975i	$0.471430\pi$
$410$	0	0
$411$	1.31828e6	0.384950
$412$	0	0
$413$	1.51743e6	0.437758
$414$	0	0
$415$	1.69190e6	0.482230
$416$	0	0
$417$	2.85228e6	0.803252
$418$	0	0
$419$	726668.	0.202209	0.101105	−	0.994876i	$-0.467762\pi$
$419$	726668.	0.202209	0.101105	+	0.994876i	$0.467762\pi$
$420$	0	0
$421$	−149315.	−0.0410580	−0.0205290	−	0.999789i	$-0.506535\pi$
$421$	−149315.	−0.0410580	−0.0205290	+	0.999789i	$0.506535\pi$
$422$	0	0
$423$	−444202.	−0.120706
$424$	0	0
$425$	−110625.	−0.0297085
$426$	0	0
$427$	223440.	0.0593050
$428$	0	0
$429$	−75779.0	−0.0198795
$430$	0	0
$431$	5.70872e6	1.48029	0.740143	−	0.672449i	$-0.234758\pi$
$431$	5.70872e6	1.48029	0.740143	+	0.672449i	$0.234758\pi$
$432$	0	0
$433$	−1.66009e6	−0.425513	−0.212757	−	0.977105i	$-0.568244\pi$
$433$	−1.66009e6	−0.425513	−0.212757	+	0.977105i	$0.568244\pi$
$434$	0	0
$435$	−2.38728e6	−0.604894
$436$	0	0
$437$	6.59994e6	1.65324
$438$	0	0
$439$	6.06987e6	1.50321	0.751603	−	0.659616i	$-0.229281\pi$
$439$	6.06987e6	1.50321	0.751603	+	0.659616i	$0.229281\pi$
$440$	0	0
$441$	−292922.	−0.0717225
$442$	0	0
$443$	−6.52331e6	−1.57928	−0.789639	−	0.613572i	$-0.789732\pi$
$443$	−6.52331e6	−1.57928	−0.789639	+	0.613572i	$0.789732\pi$
$444$	0	0
$445$	−267500.	−0.0640359
$446$	0	0
$447$	973698.	0.230492
$448$	0	0
$449$	7.47982e6	1.75096	0.875478	−	0.483259i	$-0.160547\pi$
$449$	7.47982e6	1.75096	0.875478	+	0.483259i	$0.160547\pi$
$450$	0	0
$451$	−195548.	−0.0452702
$452$	0	0
$453$	1.26558e6	0.289764
$454$	0	0
$455$	101675.	0.0230243
$456$	0	0
$457$	6.18223e6	1.38470	0.692349	−	0.721563i	$-0.256576\pi$
$457$	6.18223e6	1.38470	0.692349	+	0.721563i	$0.256576\pi$
$458$	0	0
$459$	−710655.	−0.157444
$460$	0	0
$461$	−1.01935e6	−0.223394	−0.111697	−	0.993742i	$-0.535629\pi$
$461$	−1.01935e6	−0.223394	−0.111697	+	0.993742i	$0.535629\pi$
$462$	0	0
$463$	−1.30513e6	−0.282944	−0.141472	−	0.989942i	$-0.545184\pi$
$463$	−1.30513e6	−0.282944	−0.141472	+	0.989942i	$0.545184\pi$
$464$	0	0
$465$	−449900.	−0.0964903
$466$	0	0
$467$	2.73130e6	0.579531	0.289766	−	0.957098i	$-0.406423\pi$
$467$	2.73130e6	0.579531	0.289766	+	0.957098i	$0.406423\pi$
$468$	0	0
$469$	−1.85161e6	−0.388703
$470$	0	0
$471$	3.56807e6	0.741107
$472$	0	0
$473$	725254.	0.149052
$474$	0	0
$475$	1.30125e6	0.264622
$476$	0	0
$477$	−4.05870e6	−0.816753
$478$	0	0
$479$	322322.	0.0641876	0.0320938	−	0.999485i	$-0.489782\pi$
$479$	322322.	0.0641876	0.0320938	+	0.999485i	$0.489782\pi$
$480$	0	0
$481$	−356734.	−0.0703043
$482$	0	0
$483$	−1.70863e6	−0.333258
$484$	0	0
$485$	−1.62688e6	−0.314051
$486$	0	0
$487$	2.87469e6	0.549249	0.274624	−	0.961552i	$-0.411446\pi$
$487$	2.87469e6	0.549249	0.274624	+	0.961552i	$0.411446\pi$
$488$	0	0
$489$	2.60117e6	0.491922
$490$	0	0
$491$	5.97817e6	1.11909	0.559544	−	0.828801i	$-0.310976\pi$
$491$	5.97817e6	1.11909	0.559544	+	0.828801i	$0.310976\pi$
$492$	0	0
$493$	1.53654e6	0.284725
$494$	0	0
$495$	−253150.	−0.0464371
$496$	0	0
$497$	2.90590e6	0.527702
$498$	0	0
$499$	4.91507e6	0.883647	0.441823	−	0.897102i	$-0.354332\pi$
$499$	4.91507e6	0.883647	0.441823	+	0.897102i	$0.354332\pi$
$500$	0	0
$501$	−3.66138e6	−0.651705
$502$	0	0
$503$	−6.65935e6	−1.17358	−0.586789	−	0.809740i	$-0.699608\pi$
$503$	−6.65935e6	−1.17358	−0.586789	+	0.809740i	$0.699608\pi$
$504$	0	0
$505$	3.73125e6	0.651067
$506$	0	0
$507$	4.00844e6	0.692558
$508$	0	0
$509$	−1.11240e6	−0.190312	−0.0951559	−	0.995462i	$-0.530335\pi$
$509$	−1.11240e6	−0.190312	−0.0951559	+	0.995462i	$0.530335\pi$
$510$	0	0
$511$	−436590.	−0.0739642
$512$	0	0
$513$	8.35923e6	1.40240
$514$	0	0
$515$	4.85788e6	0.807102
$516$	0	0
$517$	−302203.	−0.0497247
$518$	0	0
$519$	4.79249e6	0.780985
$520$	0	0
$521$	2.31725e6	0.374007	0.187003	−	0.982359i	$-0.440122\pi$
$521$	2.31725e6	0.374007	0.187003	+	0.982359i	$0.440122\pi$
$522$	0	0
$523$	−269108.	−0.0430202	−0.0215101	−	0.999769i	$-0.506847\pi$
$523$	−269108.	−0.0430202	−0.0215101	+	0.999769i	$0.506847\pi$
$524$	0	0
$525$	−336875.	−0.0533422
$526$	0	0
$527$	289572.	0.0454182
$528$	0	0
$529$	3.61256e6	0.561275
$530$	0	0
$531$	−3.77810e6	−0.581483
$532$	0	0
$533$	−195548.	−0.0298150
$534$	0	0
$535$	1.01345e6	0.153080
$536$	0	0
$537$	−8.00637e6	−1.19812
$538$	0	0
$539$	−199283.	−0.0295460
$540$	0	0
$541$	−1.13145e7	−1.66205	−0.831024	−	0.556236i	$-0.812245\pi$
$541$	−1.13145e7	−1.66205	−0.831024	+	0.556236i	$0.812245\pi$
$542$	0	0
$543$	−3.16021e6	−0.459956
$544$	0	0
$545$	2.19128e6	0.316013
$546$	0	0
$547$	920240.	0.131502	0.0657511	−	0.997836i	$-0.479056\pi$
$547$	920240.	0.131502	0.0657511	+	0.997836i	$0.479056\pi$
$548$	0	0
$549$	−556320.	−0.0787760
$550$	0	0
$551$	−1.80738e7	−2.53613
$552$	0	0
$553$	−1.35186e6	−0.187983
$554$	0	0
$555$	1.18195e6	0.162880
$556$	0	0
$557$	217416.	0.0296930	0.0148465	−	0.999890i	$-0.495274\pi$
$557$	217416.	0.0296930	0.0148465	+	0.999890i	$0.495274\pi$
$558$	0	0
$559$	725254.	0.0981659
$560$	0	0
$561$	−161601.	−0.0216789
$562$	0	0
$563$	7.58971e6	1.00915	0.504573	−	0.863369i	$-0.331650\pi$
$563$	7.58971e6	1.00915	0.504573	+	0.863369i	$0.331650\pi$
$564$	0	0
$565$	1.90785e6	0.251433
$566$	0	0
$567$	−711431.	−0.0929341
$568$	0	0
$569$	1.06524e7	1.37933	0.689664	−	0.724130i	$-0.257758\pi$
$569$	1.06524e7	1.37933	0.689664	+	0.724130i	$0.257758\pi$
$570$	0	0
$571$	4.60492e6	0.591061	0.295530	−	0.955333i	$-0.404504\pi$
$571$	4.60492e6	0.591061	0.295530	+	0.955333i	$0.404504\pi$
$572$	0	0
$573$	−5.00039e6	−0.636235
$574$	0	0
$575$	1.98125e6	0.249902
$576$	0	0
$577$	1.08802e7	1.36049	0.680246	−	0.732983i	$-0.261873\pi$
$577$	1.08802e7	1.36049	0.680246	+	0.732983i	$0.261873\pi$
$578$	0	0
$579$	4.38658e6	0.543788
$580$	0	0
$581$	−3.31612e6	−0.407559
$582$	0	0
$583$	−2.76124e6	−0.336460
$584$	0	0
$585$	−253150.	−0.0305836
$586$	0	0
$587$	−1.61205e7	−1.93100	−0.965500	−	0.260403i	$-0.916145\pi$
$587$	−1.61205e7	−1.93100	−0.965500	+	0.260403i	$0.916145\pi$
$588$	0	0
$589$	−3.40615e6	−0.404553
$590$	0	0
$591$	1.05575e7	1.24335
$592$	0	0
$593$	5.91061e6	0.690233	0.345117	−	0.938560i	$-0.387839\pi$
$593$	5.91061e6	0.690233	0.345117	+	0.938560i	$0.387839\pi$
$594$	0	0
$595$	216825.	0.0251083
$596$	0	0
$597$	3.76226e6	0.432030
$598$	0	0
$599$	−1.66052e7	−1.89094	−0.945471	−	0.325707i	$-0.894398\pi$
$599$	−1.66052e7	−1.89094	−0.945471	+	0.325707i	$0.894398\pi$
$600$	0	0
$601$	6.63144e6	0.748896	0.374448	−	0.927248i	$-0.377832\pi$
$601$	6.63144e6	0.748896	0.374448	+	0.927248i	$0.377832\pi$
$602$	0	0
$603$	4.61014e6	0.516322
$604$	0	0
$605$	3.85405e6	0.428084
$606$	0	0
$607$	−7.31847e6	−0.806211	−0.403105	−	0.915154i	$-0.632069\pi$
$607$	−7.31847e6	−0.806211	−0.403105	+	0.915154i	$0.632069\pi$
$608$	0	0
$609$	4.67906e6	0.511229
$610$	0	0
$611$	−302203.	−0.0327488
$612$	0	0
$613$	−1.26540e7	−1.36012	−0.680061	−	0.733155i	$-0.738047\pi$
$613$	−1.26540e7	−1.36012	−0.680061	+	0.733155i	$0.738047\pi$
$614$	0	0
$615$	647900.	0.0690749
$616$	0	0
$617$	−6.39256e6	−0.676023	−0.338012	−	0.941142i	$-0.609754\pi$
$617$	−6.39256e6	−0.676023	−0.338012	+	0.941142i	$0.609754\pi$
$618$	0	0
$619$	7.70898e6	0.808668	0.404334	−	0.914611i	$-0.367503\pi$
$619$	7.70898e6	0.808668	0.404334	+	0.914611i	$0.367503\pi$
$620$	0	0
$621$	1.27276e7	1.32439
$622$	0	0
$623$	524300.	0.0541202
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	1.90087e6	0.193100
$628$	0	0
$629$	−760746.	−0.0766678
$630$	0	0
$631$	−1.16280e7	−1.16260	−0.581302	−	0.813688i	$-0.697457\pi$
$631$	−1.16280e7	−1.16260	−0.581302	+	0.813688i	$0.697457\pi$
$632$	0	0
$633$	−2.80547e6	−0.278289
$634$	0	0
$635$	−4.57820e6	−0.450568
$636$	0	0
$637$	−199283.	−0.0194591
$638$	0	0
$639$	−7.23509e6	−0.700957
$640$	0	0
$641$	−1.15719e7	−1.11239	−0.556197	−	0.831051i	$-0.687740\pi$
$641$	−1.15719e7	−1.11239	−0.556197	+	0.831051i	$0.687740\pi$
$642$	0	0
$643$	4.51688e6	0.430836	0.215418	−	0.976522i	$-0.430889\pi$
$643$	4.51688e6	0.430836	0.215418	+	0.976522i	$0.430889\pi$
$644$	0	0
$645$	−2.40295e6	−0.227429
$646$	0	0
$647$	−6.71774e6	−0.630902	−0.315451	−	0.948942i	$-0.602156\pi$
$647$	−6.71774e6	−0.630902	−0.315451	+	0.948942i	$0.602156\pi$
$648$	0	0
$649$	−2.57034e6	−0.239541
$650$	0	0
$651$	881804.	0.0815492
$652$	0	0
$653$	−1.26522e7	−1.16114	−0.580569	−	0.814211i	$-0.697170\pi$
$653$	−1.26522e7	−1.16114	−0.580569	+	0.814211i	$0.697170\pi$
$654$	0	0
$655$	5.40475e6	0.492235
$656$	0	0
$657$	1.08702e6	0.0982481
$658$	0	0
$659$	1.20321e7	1.07927	0.539633	−	0.841900i	$-0.318563\pi$
$659$	1.20321e7	1.07927	0.539633	+	0.841900i	$0.318563\pi$
$660$	0	0
$661$	−2.14150e7	−1.90640	−0.953199	−	0.302343i	$-0.902231\pi$
$661$	−2.14150e7	−1.90640	−0.953199	+	0.302343i	$0.902231\pi$
$662$	0	0
$663$	−161601.	−0.0142778
$664$	0	0
$665$	−2.55045e6	−0.223647
$666$	0	0
$667$	−2.75188e7	−2.39505
$668$	0	0
$669$	−2.18219e6	−0.188507
$670$	0	0
$671$	−378480.	−0.0324516
$672$	0	0
$673$	−2.18091e7	−1.85610	−0.928048	−	0.372462i	$-0.878514\pi$
$673$	−2.18091e7	−1.85610	−0.928048	+	0.372462i	$0.878514\pi$
$674$	0	0
$675$	2.50938e6	0.211985
$676$	0	0
$677$	−1.71852e7	−1.44106	−0.720531	−	0.693423i	$-0.756102\pi$
$677$	−1.71852e7	−1.44106	−0.720531	+	0.693423i	$0.756102\pi$
$678$	0	0
$679$	3.18867e6	0.265421
$680$	0	0
$681$	5.99464e6	0.495331
$682$	0	0
$683$	−2.63085e6	−0.215796	−0.107898	−	0.994162i	$-0.534412\pi$
$683$	−2.63085e6	−0.215796	−0.107898	+	0.994162i	$0.534412\pi$
$684$	0	0
$685$	2.99610e6	0.243966
$686$	0	0
$687$	1.60143e7	1.29454
$688$	0	0
$689$	−2.76124e6	−0.221593
$690$	0	0
$691$	−1.29911e7	−1.03503	−0.517513	−	0.855675i	$-0.673142\pi$
$691$	−1.29911e7	−1.03503	−0.517513	+	0.855675i	$0.673142\pi$
$692$	0	0
$693$	496174.	0.0392465
$694$	0	0
$695$	6.48245e6	0.509070
$696$	0	0
$697$	−417012.	−0.0325137
$698$	0	0
$699$	720984.	0.0558127
$700$	0	0
$701$	−9.03664e6	−0.694564	−0.347282	−	0.937761i	$-0.612895\pi$
$701$	−9.03664e6	−0.694564	−0.347282	+	0.937761i	$0.612895\pi$
$702$	0	0
$703$	8.94844e6	0.682903
$704$	0	0
$705$	1.00127e6	0.0758718
$706$	0	0
$707$	−7.31325e6	−0.550252
$708$	0	0
$709$	1.41423e7	1.05658	0.528292	−	0.849063i	$-0.322833\pi$
$709$	1.41423e7	1.05658	0.528292	+	0.849063i	$0.322833\pi$
$710$	0	0
$711$	3.36586e6	0.249702
$712$	0	0
$713$	−5.18612e6	−0.382049
$714$	0	0
$715$	−172225.	−0.0125989
$716$	0	0
$717$	−6.83328e6	−0.496399
$718$	0	0
$719$	−6.27347e6	−0.452570	−0.226285	−	0.974061i	$-0.572658\pi$
$719$	−6.27347e6	−0.452570	−0.226285	+	0.974061i	$0.572658\pi$
$720$	0	0
$721$	−9.52144e6	−0.682125
$722$	0	0
$723$	−1.13039e7	−0.804236
$724$	0	0
$725$	−5.42562e6	−0.383358
$726$	0	0
$727$	5.20530e6	0.365267	0.182633	−	0.983181i	$-0.441538\pi$
$727$	5.20530e6	0.365267	0.182633	+	0.983181i	$0.441538\pi$
$728$	0	0
$729$	1.25034e7	0.871384
$730$	0	0
$731$	1.54663e6	0.107051
$732$	0	0
$733$	−2.80490e7	−1.92822	−0.964111	−	0.265499i	$-0.914463\pi$
$733$	−2.80490e7	−1.92822	−0.964111	+	0.265499i	$0.914463\pi$
$734$	0	0
$735$	660275.	0.0450823
$736$	0	0
$737$	3.13640e6	0.212698
$738$	0	0
$739$	4.42340e6	0.297952	0.148976	−	0.988841i	$-0.452402\pi$
$739$	4.42340e6	0.297952	0.148976	+	0.988841i	$0.452402\pi$
$740$	0	0
$741$	1.90087e6	0.127176
$742$	0	0
$743$	2.08246e7	1.38390	0.691950	−	0.721945i	$-0.256752\pi$
$743$	2.08246e7	1.38390	0.691950	+	0.721945i	$0.256752\pi$
$744$	0	0
$745$	2.21295e6	0.146077
$746$	0	0
$747$	8.25647e6	0.541369
$748$	0	0
$749$	−1.98636e6	−0.129376
$750$	0	0
$751$	−2.13899e7	−1.38391	−0.691957	−	0.721939i	$-0.743251\pi$
$751$	−2.13899e7	−1.38391	−0.691957	+	0.721939i	$0.743251\pi$
$752$	0	0
$753$	1.97202e7	1.26743
$754$	0	0
$755$	2.87632e6	0.183641
$756$	0	0
$757$	1.99739e7	1.26685	0.633423	−	0.773806i	$-0.281649\pi$
$757$	1.99739e7	1.26685	0.633423	+	0.773806i	$0.281649\pi$
$758$	0	0
$759$	2.89421e6	0.182358
$760$	0	0
$761$	1.52078e7	0.951932	0.475966	−	0.879464i	$-0.342098\pi$
$761$	1.52078e7	0.951932	0.475966	+	0.879464i	$0.342098\pi$
$762$	0	0
$763$	−4.29490e6	−0.267080
$764$	0	0
$765$	−539850.	−0.0333518
$766$	0	0
$767$	−2.57034e6	−0.157762
$768$	0	0
$769$	−1.75417e7	−1.06969	−0.534843	−	0.844951i	$-0.679629\pi$
$769$	−1.75417e7	−1.06969	−0.534843	+	0.844951i	$0.679629\pi$
$770$	0	0
$771$	−1.27427e7	−0.772016
$772$	0	0
$773$	−2.01261e7	−1.21146	−0.605732	−	0.795669i	$-0.707119\pi$
$773$	−2.01261e7	−1.21146	−0.605732	+	0.795669i	$0.707119\pi$
$774$	0	0
$775$	−1.02250e6	−0.0611518
$776$	0	0
$777$	−2.31662e6	−0.137658
$778$	0	0
$779$	4.90519e6	0.289609
$780$	0	0
$781$	−4.92223e6	−0.288758
$782$	0	0
$783$	−3.48542e7	−2.03166
$784$	0	0
$785$	8.10925e6	0.469685
$786$	0	0
$787$	−2.41718e7	−1.39114	−0.695571	−	0.718458i	$-0.744848\pi$
$787$	−2.41718e7	−1.39114	−0.695571	+	0.718458i	$0.744848\pi$
$788$	0	0
$789$	−7.03487e6	−0.402313
$790$	0	0
$791$	−3.73939e6	−0.212500
$792$	0	0
$793$	−378480.	−0.0213727
$794$	0	0
$795$	9.14870e6	0.513383
$796$	0	0
$797$	−2.67019e7	−1.48901	−0.744503	−	0.667619i	$-0.767313\pi$
$797$	−2.67019e7	−1.48901	−0.744503	+	0.667619i	$0.767313\pi$
$798$	0	0
$799$	−644457.	−0.0357131
$800$	0	0
$801$	−1.30540e6	−0.0718890
$802$	0	0
$803$	739530.	0.0404731
$804$	0	0
$805$	−3.88325e6	−0.211206
$806$	0	0
$807$	−2.41581e7	−1.30581
$808$	0	0
$809$	2.15124e7	1.15562	0.577812	−	0.816170i	$-0.303907\pi$
$809$	2.15124e7	1.15562	0.577812	+	0.816170i	$0.303907\pi$
$810$	0	0
$811$	−3.50935e7	−1.87359	−0.936794	−	0.349882i	$-0.886222\pi$
$811$	−3.50935e7	−1.87359	−0.936794	+	0.349882i	$0.886222\pi$
$812$	0	0
$813$	1.51870e7	0.805832
$814$	0	0
$815$	5.91175e6	0.311761
$816$	0	0
$817$	−1.81925e7	−0.953537
$818$	0	0
$819$	496174.	0.0258478
$820$	0	0
$821$	−1.26329e7	−0.654100	−0.327050	−	0.945007i	$-0.606055\pi$
$821$	−1.26329e7	−0.654100	−0.327050	+	0.945007i	$0.606055\pi$
$822$	0	0
$823$	−1.55348e7	−0.799475	−0.399737	−	0.916630i	$-0.630899\pi$
$823$	−1.55348e7	−0.799475	−0.399737	+	0.916630i	$0.630899\pi$
$824$	0	0
$825$	570625.	0.0291888
$826$	0	0
$827$	3.89597e7	1.98085	0.990426	−	0.138043i	$-0.0440813\pi$
$827$	3.89597e7	1.98085	0.990426	+	0.138043i	$0.0440813\pi$
$828$	0	0
$829$	1.35099e7	0.682757	0.341379	−	0.939926i	$-0.389106\pi$
$829$	1.35099e7	0.682757	0.341379	+	0.939926i	$0.389106\pi$
$830$	0	0
$831$	−2.33528e7	−1.17310
$832$	0	0
$833$	−424977.	−0.0212204
$834$	0	0
$835$	−8.32132e6	−0.413025
$836$	0	0
$837$	−6.56854e6	−0.324082
$838$	0	0
$839$	250486.	0.0122851	0.00614255	−	0.999981i	$-0.498045\pi$
$839$	250486.	0.0122851	0.00614255	+	0.999981i	$0.498045\pi$
$840$	0	0
$841$	5.48486e7	2.67409
$842$	0	0
$843$	−1.31669e7	−0.638136
$844$	0	0
$845$	9.11010e6	0.438916
$846$	0	0
$847$	−7.55394e6	−0.361797
$848$	0	0
$849$	3.09594e6	0.147409
$850$	0	0
$851$	1.36247e7	0.644914
$852$	0	0
$853$	2.87228e7	1.35162	0.675809	−	0.737077i	$-0.263794\pi$
$853$	2.87228e7	1.35162	0.675809	+	0.737077i	$0.263794\pi$
$854$	0	0
$855$	6.35010e6	0.297074
$856$	0	0
$857$	1.61269e7	0.750066	0.375033	−	0.927011i	$-0.377631\pi$
$857$	1.61269e7	0.750066	0.375033	+	0.927011i	$0.377631\pi$
$858$	0	0
$859$	4.03773e7	1.86704	0.933521	−	0.358523i	$-0.116719\pi$
$859$	4.03773e7	1.86704	0.933521	+	0.358523i	$0.116719\pi$
$860$	0	0
$861$	−1.26988e6	−0.0583789
$862$	0	0
$863$	2.57025e7	1.17476	0.587378	−	0.809312i	$-0.300160\pi$
$863$	2.57025e7	1.17476	0.587378	+	0.809312i	$0.300160\pi$
$864$	0	0
$865$	1.08920e7	0.494958
$866$	0	0
$867$	1.52738e7	0.690080
$868$	0	0
$869$	2.28989e6	0.102864
$870$	0	0
$871$	3.13640e6	0.140083
$872$	0	0
$873$	−7.93915e6	−0.352564
$874$	0	0
$875$	−765625.	−0.0338062
$876$	0	0
$877$	−1.75541e7	−0.770689	−0.385344	−	0.922773i	$-0.625917\pi$
$877$	−1.75541e7	−0.770689	−0.385344	+	0.922773i	$0.625917\pi$
$878$	0	0
$879$	2.98613e7	1.30358
$880$	0	0
$881$	−2.13350e7	−0.926088	−0.463044	−	0.886335i	$-0.653243\pi$
$881$	−2.13350e7	−0.926088	−0.463044	+	0.886335i	$0.653243\pi$
$882$	0	0
$883$	−3.95442e7	−1.70679	−0.853397	−	0.521261i	$-0.825462\pi$
$883$	−3.95442e7	−1.70679	−0.853397	+	0.521261i	$0.825462\pi$
$884$	0	0
$885$	8.51620e6	0.365500
$886$	0	0
$887$	3.42741e7	1.46271	0.731353	−	0.681999i	$-0.238889\pi$
$887$	3.42741e7	1.46271	0.731353	+	0.681999i	$0.238889\pi$
$888$	0	0
$889$	8.97327e6	0.380800
$890$	0	0
$891$	1.20508e6	0.0508535
$892$	0	0
$893$	7.58056e6	0.318107
$894$	0	0
$895$	−1.81963e7	−0.759321
$896$	0	0
$897$	2.89421e6	0.120102
$898$	0	0
$899$	1.42021e7	0.586076
$900$	0	0
$901$	−5.88844e6	−0.241651
$902$	0	0
$903$	4.70978e6	0.192212
$904$	0	0
$905$	−7.18230e6	−0.291502
$906$	0	0
$907$	−3.72968e7	−1.50541	−0.752703	−	0.658361i	$-0.771250\pi$
$907$	−3.72968e7	−1.50541	−0.752703	+	0.658361i	$0.771250\pi$
$908$	0	0
$909$	1.82085e7	0.730911
$910$	0	0
$911$	−2.83311e7	−1.13101	−0.565505	−	0.824745i	$-0.691319\pi$
$911$	−2.83311e7	−1.13101	−0.565505	+	0.824745i	$0.691319\pi$
$912$	0	0
$913$	5.61711e6	0.223016
$914$	0	0
$915$	1.25400e6	0.0495159
$916$	0	0
$917$	−1.05933e7	−0.416014
$918$	0	0
$919$	9.27364e6	0.362211	0.181105	−	0.983464i	$-0.442032\pi$
$919$	9.27364e6	0.362211	0.181105	+	0.983464i	$0.442032\pi$
$920$	0	0
$921$	−2.95219e7	−1.14682
$922$	0	0
$923$	−4.92223e6	−0.190177
$924$	0	0
$925$	2.68625e6	0.103227
$926$	0	0
$927$	2.37064e7	0.906081
$928$	0	0
$929$	1.39068e7	0.528674	0.264337	−	0.964430i	$-0.414847\pi$
$929$	1.39068e7	0.528674	0.264337	+	0.964430i	$0.414847\pi$
$930$	0	0
$931$	4.99888e6	0.189016
$932$	0	0
$933$	280962.	0.0105668
$934$	0	0
$935$	−367275.	−0.0137392
$936$	0	0
$937$	−1.93922e6	−0.0721570	−0.0360785	−	0.999349i	$-0.511487\pi$
$937$	−1.93922e6	−0.0721570	−0.0360785	+	0.999349i	$0.511487\pi$
$938$	0	0
$939$	1.07357e7	0.397345
$940$	0	0
$941$	−2.44080e7	−0.898582	−0.449291	−	0.893385i	$-0.648323\pi$
$941$	−2.44080e7	−0.898582	−0.449291	+	0.893385i	$0.648323\pi$
$942$	0	0
$943$	7.46852e6	0.273499
$944$	0	0
$945$	−4.91838e6	−0.179160
$946$	0	0
$947$	−36592.0	−0.00132590	−0.000662951	−	1.00000i	$-0.500211\pi$
$947$	−36592.0	−0.00132590	−0.000662951		1.00000i	$0.500211\pi$
$948$	0	0
$949$	739530.	0.0266557
$950$	0	0
$951$	1.60094e7	0.574016
$952$	0	0
$953$	2.75598e7	0.982978	0.491489	−	0.870884i	$-0.336453\pi$
$953$	2.75598e7	0.982978	0.491489	+	0.870884i	$0.336453\pi$
$954$	0	0
$955$	−1.13645e7	−0.403221
$956$	0	0
$957$	−7.92575e6	−0.279744
$958$	0	0
$959$	−5.87236e6	−0.206189
$960$	0	0
$961$	−2.59527e7	−0.906512
$962$	0	0
$963$	4.94564e6	0.171853
$964$	0	0
$965$	9.96950e6	0.344632
$966$	0	0
$967$	1.42984e7	0.491725	0.245863	−	0.969305i	$-0.420929\pi$
$967$	1.42984e7	0.491725	0.245863	+	0.969305i	$0.420929\pi$
$968$	0	0
$969$	4.05365e6	0.138687
$970$	0	0
$971$	−2.29801e7	−0.782176	−0.391088	−	0.920353i	$-0.627901\pi$
$971$	−2.29801e7	−0.782176	−0.391088	+	0.920353i	$0.627901\pi$
$972$	0	0
$973$	−1.27056e7	−0.430242
$974$	0	0
$975$	570625.	0.0192238
$976$	0	0
$977$	−2.07391e7	−0.695111	−0.347556	−	0.937659i	$-0.612988\pi$
$977$	−2.07391e7	−0.695111	−0.347556	+	0.937659i	$0.612988\pi$
$978$	0	0
$979$	−888100.	−0.0296146
$980$	0	0
$981$	1.06934e7	0.354768
$982$	0	0
$983$	−2.95326e7	−0.974807	−0.487403	−	0.873177i	$-0.662056\pi$
$983$	−2.95326e7	−0.974807	−0.487403	+	0.873177i	$0.662056\pi$
$984$	0	0
$985$	2.39944e7	0.787987
$986$	0	0
$987$	−1.96250e6	−0.0641234
$988$	0	0
$989$	−2.76995e7	−0.900493
$990$	0	0
$991$	3.56883e7	1.15436	0.577181	−	0.816616i	$-0.304153\pi$
$991$	3.56883e7	1.15436	0.577181	+	0.816616i	$0.304153\pi$
$992$	0	0
$993$	−3.28005e7	−1.05562
$994$	0	0
$995$	8.55060e6	0.273803
$996$	0	0
$997$	3.48937e7	1.11176	0.555878	−	0.831264i	$-0.312382\pi$
$997$	3.48937e7	1.11176	0.555878	+	0.831264i	$0.312382\pi$
$998$	0	0
$999$	1.72565e7	0.547064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.6.a.a.1.1		1
4.3	odd	2		70.6.a.d.1.1	✓	1
12.11	even	2		630.6.a.l.1.1		1
20.3	even	4		350.6.c.c.99.2		2
20.7	even	4		350.6.c.c.99.1		2
20.19	odd	2		350.6.a.h.1.1		1
28.27	even	2		490.6.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.d.1.1	✓	1	4.3	odd	2
350.6.a.h.1.1		1	20.19	odd	2
350.6.c.c.99.1		2	20.7	even	4
350.6.c.c.99.2		2	20.3	even	4
490.6.a.c.1.1		1	28.27	even	2
560.6.a.a.1.1		1	1.1	even	1	trivial
630.6.a.l.1.1		1	12.11	even	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	560.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more