LMFDB - Embedded newform 560.6.a.f.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:	$0$
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)

$f(q)$

$=$

$q+11.0000 q^{3} -25.0000 q^{5} -49.0000 q^{7} -122.000 q^{9} +267.000 q^{11} -1087.00 q^{13} -275.000 q^{15} -513.000 q^{17} +802.000 q^{19} -539.000 q^{21} +1290.00 q^{23} +625.000 q^{25} -4015.00 q^{27} +1779.00 q^{29} +2584.00 q^{31} +2937.00 q^{33} +1225.00 q^{35} +13862.0 q^{37} -11957.0 q^{39} -11904.0 q^{41} +598.000 q^{43} +3050.00 q^{45} +17019.0 q^{47} +2401.00 q^{49} -5643.00 q^{51} +27852.0 q^{53} -6675.00 q^{55} +8822.00 q^{57} -30912.0 q^{59} -1780.00 q^{61} +5978.00 q^{63} +27175.0 q^{65} -25052.0 q^{67} +14190.0 q^{69} +51984.0 q^{71} +47690.0 q^{73} +6875.00 q^{75} -13083.0 q^{77} +102121. q^{79} -14519.0 q^{81} +83676.0 q^{83} +12825.0 q^{85} +19569.0 q^{87} -32400.0 q^{89} +53263.0 q^{91} +28424.0 q^{93} -20050.0 q^{95} -148645. q^{97} -32574.0 q^{99} +O(q^{100})$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0
$2$	0	0
$3$	11.0000	0.705650	0.352825	−	0.935689i	$-0.385221\pi$
$3$	11.0000	0.705650	0.352825	+	0.935689i	$0.385221\pi$
$4$	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
$11$	267.000	0.665318	0.332659	−	0.943047i	$-0.392054\pi$
$11$	267.000	0.665318	0.332659	+	0.943047i	$0.392054\pi$
$12$	0	0
$13$	−1087.00	−1.78390	−0.891951	−	0.452131i	$-0.850664\pi$
$13$	−1087.00	−1.78390	−0.891951	+	0.452131i	$0.850664\pi$
$14$	0	0
$15$	−275.000	−0.315576
$16$	0	0
$17$	−513.000	−0.430522	−0.215261	−	0.976557i	$-0.569060\pi$
$17$	−513.000	−0.430522	−0.215261	+	0.976557i	$0.569060\pi$
$18$	0	0
$19$	802.000	0.509672	0.254836	−	0.966984i	$-0.417979\pi$
$19$	802.000	0.509672	0.254836	+	0.966984i	$0.417979\pi$
$20$	0	0
$21$	−539.000	−0.266711
$22$	0	0
$23$	1290.00	0.508476	0.254238	−	0.967142i	$-0.418175\pi$
$23$	1290.00	0.508476	0.254238	+	0.967142i	$0.418175\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	−4015.00	−1.05993
$28$	0	0
$29$	1779.00	0.392809	0.196404	−	0.980523i	$-0.437074\pi$
$29$	1779.00	0.392809	0.196404	+	0.980523i	$0.437074\pi$
$30$	0	0
$31$	2584.00	0.482935	0.241467	−	0.970409i	$-0.422371\pi$
$31$	2584.00	0.482935	0.241467	+	0.970409i	$0.422371\pi$
$32$	0	0
$33$	2937.00	0.469482
$34$	0	0
$35$	1225.00	0.169031
$36$	0	0
$37$	13862.0	1.66464	0.832322	−	0.554292i	$-0.187011\pi$
$37$	13862.0	1.66464	0.832322	+	0.554292i	$0.187011\pi$
$38$	0	0
$39$	−11957.0	−1.25881
$40$	0	0
$41$	−11904.0	−1.10594	−0.552972	−	0.833200i	$-0.686506\pi$
$41$	−11904.0	−1.10594	−0.552972	+	0.833200i	$0.686506\pi$
$42$	0	0
$43$	598.000	0.0493208	0.0246604	−	0.999696i	$-0.492150\pi$
$43$	598.000	0.0493208	0.0246604	+	0.999696i	$0.492150\pi$
$44$	0	0
$45$	3050.00	0.224527
$46$	0	0
$47$	17019.0	1.12380	0.561900	−	0.827205i	$-0.310070\pi$
$47$	17019.0	1.12380	0.561900	+	0.827205i	$0.310070\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	0	0
$51$	−5643.00	−0.303798
$52$	0	0
$53$	27852.0	1.36197	0.680984	−	0.732299i	$-0.261552\pi$
$53$	27852.0	1.36197	0.680984	+	0.732299i	$0.261552\pi$
$54$	0	0
$55$	−6675.00	−0.297539
$56$	0	0
$57$	8822.00	0.359650
$58$	0	0
$59$	−30912.0	−1.15610	−0.578052	−	0.816000i	$-0.696187\pi$
$59$	−30912.0	−1.15610	−0.578052	+	0.816000i	$0.696187\pi$
$60$	0	0
$61$	−1780.00	−0.0612485	−0.0306242	−	0.999531i	$-0.509750\pi$
$61$	−1780.00	−0.0612485	−0.0306242	+	0.999531i	$0.509750\pi$
$62$	0	0
$63$	5978.00	0.189760
$64$	0	0
$65$	27175.0	0.797786
$66$	0	0
$67$	−25052.0	−0.681797	−0.340899	−	0.940100i	$-0.610731\pi$
$67$	−25052.0	−0.681797	−0.340899	+	0.940100i	$0.610731\pi$
$68$	0	0
$69$	14190.0	0.358806
$70$	0	0
$71$	51984.0	1.22384	0.611919	−	0.790921i	$-0.290398\pi$
$71$	51984.0	1.22384	0.611919	+	0.790921i	$0.290398\pi$
$72$	0	0
$73$	47690.0	1.04742	0.523709	−	0.851897i	$-0.324548\pi$
$73$	47690.0	1.04742	0.523709	+	0.851897i	$0.324548\pi$
$74$	0	0
$75$	6875.00	0.141130
$76$	0	0
$77$	−13083.0	−0.251467
$78$	0	0
$79$	102121.	1.84097	0.920486	−	0.390775i	$-0.127793\pi$
$79$	102121.	1.84097	0.920486	+	0.390775i	$0.127793\pi$
$80$	0	0
$81$	−14519.0	−0.245881
$82$	0	0
$83$	83676.0	1.33323	0.666616	−	0.745401i	$-0.267742\pi$
$83$	83676.0	1.33323	0.666616	+	0.745401i	$0.267742\pi$
$84$	0	0
$85$	12825.0	0.192535
$86$	0	0
$87$	19569.0	0.277185
$88$	0	0
$89$	−32400.0	−0.433581	−0.216790	−	0.976218i	$-0.569559\pi$
$89$	−32400.0	−0.433581	−0.216790	+	0.976218i	$0.569559\pi$
$90$	0	0
$91$	53263.0	0.674252
$92$	0	0
$93$	28424.0	0.340783
$94$	0	0
$95$	−20050.0	−0.227932
$96$	0	0
$97$	−148645.	−1.60406	−0.802031	−	0.597283i	$-0.796247\pi$
$97$	−148645.	−1.60406	−0.802031	+	0.597283i	$0.796247\pi$
$98$	0	0
$99$	−32574.0	−0.334028
$100$	0	0
$101$	−41310.0	−0.402951	−0.201475	−	0.979494i	$-0.564574\pi$
$101$	−41310.0	−0.402951	−0.201475	+	0.979494i	$0.564574\pi$
$102$	0	0
$103$	−108785.	−1.01036	−0.505180	−	0.863014i	$-0.668574\pi$
$103$	−108785.	−1.01036	−0.505180	+	0.863014i	$0.668574\pi$
$104$	0	0
$105$	13475.0	0.119277
$106$	0	0
$107$	106098.	0.895876	0.447938	−	0.894065i	$-0.352159\pi$
$107$	106098.	0.895876	0.447938	+	0.894065i	$0.352159\pi$
$108$	0	0
$109$	−124111.	−1.00056	−0.500281	−	0.865863i	$-0.666770\pi$
$109$	−124111.	−1.00056	−0.500281	+	0.865863i	$0.666770\pi$
$110$	0	0
$111$	152482.	1.17466
$112$	0	0
$113$	192834.	1.42065	0.710326	−	0.703873i	$-0.248548\pi$
$113$	192834.	1.42065	0.710326	+	0.703873i	$0.248548\pi$
$114$	0	0
$115$	−32250.0	−0.227397
$116$	0	0
$117$	132614.	0.895622
$118$	0	0
$119$	25137.0	0.162722
$120$	0	0
$121$	−89762.0	−0.557351
$122$	0	0
$123$	−130944.	−0.780410
$124$	0	0
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−99248.0	−0.546025	−0.273012	−	0.962010i	$-0.588020\pi$
$127$	−99248.0	−0.546025	−0.273012	+	0.962010i	$0.588020\pi$
$128$	0	0
$129$	6578.00	0.0348032
$130$	0	0
$131$	276810.	1.40930	0.704650	−	0.709555i	$-0.251104\pi$
$131$	276810.	1.40930	0.704650	+	0.709555i	$0.251104\pi$
$132$	0	0
$133$	−39298.0	−0.192638
$134$	0	0
$135$	100375.	0.474014
$136$	0	0
$137$	237744.	1.08220	0.541101	−	0.840958i	$-0.318008\pi$
$137$	237744.	1.08220	0.541101	+	0.840958i	$0.318008\pi$
$138$	0	0
$139$	−160478.	−0.704496	−0.352248	−	0.935907i	$-0.614583\pi$
$139$	−160478.	−0.704496	−0.352248	+	0.935907i	$0.614583\pi$
$140$	0	0
$141$	187209.	0.793011
$142$	0	0
$143$	−290229.	−1.18686
$144$	0	0
$145$	−44475.0	−0.175669
$146$	0	0
$147$	26411.0	0.100807
$148$	0	0
$149$	−99678.0	−0.367819	−0.183909	−	0.982943i	$-0.558875\pi$
$149$	−99678.0	−0.367819	−0.183909	+	0.982943i	$0.558875\pi$
$150$	0	0
$151$	206017.	0.735293	0.367647	−	0.929966i	$-0.380164\pi$
$151$	206017.	0.735293	0.367647	+	0.929966i	$0.380164\pi$
$152$	0	0
$153$	62586.0	0.216147
$154$	0	0
$155$	−64600.0	−0.215975
$156$	0	0
$157$	581150.	1.88165	0.940826	−	0.338891i	$-0.110052\pi$
$157$	581150.	1.88165	0.940826	+	0.338891i	$0.110052\pi$
$158$	0	0
$159$	306372.	0.961073
$160$	0	0
$161$	−63210.0	−0.192186
$162$	0	0
$163$	−346610.	−1.02181	−0.510907	−	0.859636i	$-0.670690\pi$
$163$	−346610.	−1.02181	−0.510907	+	0.859636i	$0.670690\pi$
$164$	0	0
$165$	−73425.0	−0.209959
$166$	0	0
$167$	448887.	1.24551	0.622753	−	0.782418i	$-0.286014\pi$
$167$	448887.	1.24551	0.622753	+	0.782418i	$0.286014\pi$
$168$	0	0
$169$	810276.	2.18231
$170$	0	0
$171$	−97844.0	−0.255884
$172$	0	0
$173$	−262509.	−0.666851	−0.333426	−	0.942776i	$-0.608205\pi$
$173$	−262509.	−0.666851	−0.333426	+	0.942776i	$0.608205\pi$
$174$	0	0
$175$	−30625.0	−0.0755929
$176$	0	0
$177$	−340032.	−0.815805
$178$	0	0
$179$	111012.	0.258963	0.129481	−	0.991582i	$-0.458669\pi$
$179$	111012.	0.258963	0.129481	+	0.991582i	$0.458669\pi$
$180$	0	0
$181$	112772.	0.255861	0.127931	−	0.991783i	$-0.459166\pi$
$181$	112772.	0.255861	0.127931	+	0.991783i	$0.459166\pi$
$182$	0	0
$183$	−19580.0	−0.0432200
$184$	0	0
$185$	−346550.	−0.744452
$186$	0	0
$187$	−136971.	−0.286434
$188$	0	0
$189$	196735.	0.400615
$190$	0	0
$191$	731991.	1.45185	0.725926	−	0.687773i	$-0.241411\pi$
$191$	731991.	1.45185	0.725926	+	0.687773i	$0.241411\pi$
$192$	0	0
$193$	−186040.	−0.359512	−0.179756	−	0.983711i	$-0.557531\pi$
$193$	−186040.	−0.359512	−0.179756	+	0.983711i	$0.557531\pi$
$194$	0	0
$195$	298925.	0.562958
$196$	0	0
$197$	121356.	0.222790	0.111395	−	0.993776i	$-0.464468\pi$
$197$	121356.	0.222790	0.111395	+	0.993776i	$0.464468\pi$
$198$	0	0
$199$	−648584.	−1.16100	−0.580502	−	0.814259i	$-0.697144\pi$
$199$	−648584.	−1.16100	−0.580502	+	0.814259i	$0.697144\pi$
$200$	0	0
$201$	−275572.	−0.481111
$202$	0	0
$203$	−87171.0	−0.148468
$204$	0	0
$205$	297600.	0.494593
$206$	0	0
$207$	−157380.	−0.255284
$208$	0	0
$209$	214134.	0.339094
$210$	0	0
$211$	149773.	0.231594	0.115797	−	0.993273i	$-0.463058\pi$
$211$	149773.	0.231594	0.115797	+	0.993273i	$0.463058\pi$
$212$	0	0
$213$	571824.	0.863601
$214$	0	0
$215$	−14950.0	−0.0220569
$216$	0	0
$217$	−126616.	−0.182532
$218$	0	0
$219$	524590.	0.739111
$220$	0	0
$221$	557631.	0.768009
$222$	0	0
$223$	1.10096e6	1.48255	0.741274	−	0.671202i	$-0.234222\pi$
$223$	1.10096e6	1.48255	0.741274	+	0.671202i	$0.234222\pi$
$224$	0	0
$225$	−76250.0	−0.100412
$226$	0	0
$227$	695127.	0.895364	0.447682	−	0.894193i	$-0.352250\pi$
$227$	695127.	0.895364	0.447682	+	0.894193i	$0.352250\pi$
$228$	0	0
$229$	463736.	0.584362	0.292181	−	0.956363i	$-0.405619\pi$
$229$	463736.	0.584362	0.292181	+	0.956363i	$0.405619\pi$
$230$	0	0
$231$	−143913.	−0.177448
$232$	0	0
$233$	−1.57654e6	−1.90245	−0.951227	−	0.308492i	$-0.900176\pi$
$233$	−1.57654e6	−1.90245	−0.951227	+	0.308492i	$0.900176\pi$
$234$	0	0
$235$	−425475.	−0.502579
$236$	0	0
$237$	1.12333e6	1.29908
$238$	0	0
$239$	512037.	0.579838	0.289919	−	0.957051i	$-0.406372\pi$
$239$	512037.	0.579838	0.289919	+	0.957051i	$0.406372\pi$
$240$	0	0
$241$	989330.	1.09723	0.548616	−	0.836074i	$-0.315155\pi$
$241$	989330.	1.09723	0.548616	+	0.836074i	$0.315155\pi$
$242$	0	0
$243$	815936.	0.886422
$244$	0	0
$245$	−60025.0	−0.0638877
$246$	0	0
$247$	−871774.	−0.909204
$248$	0	0
$249$	920436.	0.940795
$250$	0	0
$251$	61230.0	0.0613451	0.0306726	−	0.999529i	$-0.490235\pi$
$251$	61230.0	0.0613451	0.0306726	+	0.999529i	$0.490235\pi$
$252$	0	0
$253$	344430.	0.338298
$254$	0	0
$255$	141075.	0.135863
$256$	0	0
$257$	1.33887e6	1.26446	0.632231	−	0.774780i	$-0.282139\pi$
$257$	1.33887e6	1.26446	0.632231	+	0.774780i	$0.282139\pi$
$258$	0	0
$259$	−679238.	−0.629177
$260$	0	0
$261$	−217038.	−0.197213
$262$	0	0
$263$	1.65619e6	1.47645	0.738227	−	0.674553i	$-0.235663\pi$
$263$	1.65619e6	1.47645	0.738227	+	0.674553i	$0.235663\pi$
$264$	0	0
$265$	−696300.	−0.609090
$266$	0	0
$267$	−356400.	−0.305956
$268$	0	0
$269$	−750606.	−0.632457	−0.316229	−	0.948683i	$-0.602417\pi$
$269$	−750606.	−0.632457	−0.316229	+	0.948683i	$0.602417\pi$
$270$	0	0
$271$	557908.	0.461466	0.230733	−	0.973017i	$-0.425888\pi$
$271$	557908.	0.461466	0.230733	+	0.973017i	$0.425888\pi$
$272$	0	0
$273$	585893.	0.475786
$274$	0	0
$275$	166875.	0.133064
$276$	0	0
$277$	1.77256e6	1.38804	0.694018	−	0.719957i	$-0.255839\pi$
$277$	1.77256e6	1.38804	0.694018	+	0.719957i	$0.255839\pi$
$278$	0	0
$279$	−315248.	−0.242461
$280$	0	0
$281$	−1.09893e6	−0.830243	−0.415122	−	0.909766i	$-0.636261\pi$
$281$	−1.09893e6	−0.830243	−0.415122	+	0.909766i	$0.636261\pi$
$282$	0	0
$283$	320569.	0.237933	0.118967	−	0.992898i	$-0.462042\pi$
$283$	320569.	0.237933	0.118967	+	0.992898i	$0.462042\pi$
$284$	0	0
$285$	−220550.	−0.160840
$286$	0	0
$287$	583296.	0.418008
$288$	0	0
$289$	−1.15669e6	−0.814651
$290$	0	0
$291$	−1.63510e6	−1.13191
$292$	0	0
$293$	−1.62337e6	−1.10471	−0.552355	−	0.833609i	$-0.686271\pi$
$293$	−1.62337e6	−1.10471	−0.552355	+	0.833609i	$0.686271\pi$
$294$	0	0
$295$	772800.	0.517026
$296$	0	0
$297$	−1.07200e6	−0.705189
$298$	0	0
$299$	−1.40223e6	−0.907071
$300$	0	0
$301$	−29302.0	−0.0186415
$302$	0	0
$303$	−454410.	−0.284342
$304$	0	0
$305$	44500.0	0.0273912
$306$	0	0
$307$	−995087.	−0.602581	−0.301290	−	0.953532i	$-0.597417\pi$
$307$	−995087.	−0.602581	−0.301290	+	0.953532i	$0.597417\pi$
$308$	0	0
$309$	−1.19664e6	−0.712961
$310$	0	0
$311$	−1.34398e6	−0.787939	−0.393969	−	0.919124i	$-0.628898\pi$
$311$	−1.34398e6	−0.787939	−0.393969	+	0.919124i	$0.628898\pi$
$312$	0	0
$313$	1.91971e6	1.10758	0.553788	−	0.832658i	$-0.313182\pi$
$313$	1.91971e6	1.10758	0.553788	+	0.832658i	$0.313182\pi$
$314$	0	0
$315$	−149450.	−0.0848632
$316$	0	0
$317$	−1.91366e6	−1.06959	−0.534794	−	0.844983i	$-0.679611\pi$
$317$	−1.91366e6	−1.06959	−0.534794	+	0.844983i	$0.679611\pi$
$318$	0	0
$319$	474993.	0.261343
$320$	0	0
$321$	1.16708e6	0.632175
$322$	0	0
$323$	−411426.	−0.219425
$324$	0	0
$325$	−679375.	−0.356781
$326$	0	0
$327$	−1.36522e6	−0.706047
$328$	0	0
$329$	−833931.	−0.424757
$330$	0	0
$331$	2.25694e6	1.13227	0.566135	−	0.824313i	$-0.308438\pi$
$331$	2.25694e6	1.13227	0.566135	+	0.824313i	$0.308438\pi$
$332$	0	0
$333$	−1.69116e6	−0.835748
$334$	0	0
$335$	626300.	0.304909
$336$	0	0
$337$	−1.45016e6	−0.695571	−0.347786	−	0.937574i	$-0.613066\pi$
$337$	−1.45016e6	−0.695571	−0.347786	+	0.937574i	$0.613066\pi$
$338$	0	0
$339$	2.12117e6	1.00248
$340$	0	0
$341$	689928.	0.321305
$342$	0	0
$343$	−117649.	−0.0539949
$344$	0	0
$345$	−354750.	−0.160463
$346$	0	0
$347$	−856386.	−0.381809	−0.190904	−	0.981609i	$-0.561142\pi$
$347$	−856386.	−0.381809	−0.190904	+	0.981609i	$0.561142\pi$
$348$	0	0
$349$	−347602.	−0.152763	−0.0763816	−	0.997079i	$-0.524337\pi$
$349$	−347602.	−0.152763	−0.0763816	+	0.997079i	$0.524337\pi$
$350$	0	0
$351$	4.36430e6	1.89081
$352$	0	0
$353$	−2.21860e6	−0.947640	−0.473820	−	0.880622i	$-0.657125\pi$
$353$	−2.21860e6	−0.947640	−0.473820	+	0.880622i	$0.657125\pi$
$354$	0	0
$355$	−1.29960e6	−0.547317
$356$	0	0
$357$	276507.	0.114825
$358$	0	0
$359$	−2.94338e6	−1.20534	−0.602672	−	0.797989i	$-0.705897\pi$
$359$	−2.94338e6	−1.20534	−0.602672	+	0.797989i	$0.705897\pi$
$360$	0	0
$361$	−1.83290e6	−0.740235
$362$	0	0
$363$	−987382.	−0.393295
$364$	0	0
$365$	−1.19225e6	−0.468420
$366$	0	0
$367$	−2.33000e6	−0.903005	−0.451503	−	0.892270i	$-0.649112\pi$
$367$	−2.33000e6	−0.903005	−0.451503	+	0.892270i	$0.649112\pi$
$368$	0	0
$369$	1.45229e6	0.555248
$370$	0	0
$371$	−1.36475e6	−0.514775
$372$	0	0
$373$	1.69246e6	0.629865	0.314932	−	0.949114i	$-0.398018\pi$
$373$	1.69246e6	0.629865	0.314932	+	0.949114i	$0.398018\pi$
$374$	0	0
$375$	−171875.	−0.0631153
$376$	0	0
$377$	−1.93377e6	−0.700732
$378$	0	0
$379$	1.50075e6	0.536673	0.268337	−	0.963325i	$-0.413526\pi$
$379$	1.50075e6	0.536673	0.268337	+	0.963325i	$0.413526\pi$
$380$	0	0
$381$	−1.09173e6	−0.385303
$382$	0	0
$383$	−3.48522e6	−1.21404	−0.607020	−	0.794686i	$-0.707635\pi$
$383$	−3.48522e6	−1.21404	−0.607020	+	0.794686i	$0.707635\pi$
$384$	0	0
$385$	327075.	0.112459
$386$	0	0
$387$	−72956.0	−0.0247619
$388$	0	0
$389$	−3.60598e6	−1.20823	−0.604114	−	0.796898i	$-0.706473\pi$
$389$	−3.60598e6	−1.20823	−0.604114	+	0.796898i	$0.706473\pi$
$390$	0	0
$391$	−661770.	−0.218910
$392$	0	0
$393$	3.04491e6	0.994473
$394$	0	0
$395$	−2.55302e6	−0.823308
$396$	0	0
$397$	4.74380e6	1.51060	0.755302	−	0.655377i	$-0.227490\pi$
$397$	4.74380e6	1.51060	0.755302	+	0.655377i	$0.227490\pi$
$398$	0	0
$399$	−432278.	−0.135935
$400$	0	0
$401$	5.26539e6	1.63520	0.817598	−	0.575789i	$-0.195305\pi$
$401$	5.26539e6	1.63520	0.817598	+	0.575789i	$0.195305\pi$
$402$	0	0
$403$	−2.80881e6	−0.861508
$404$	0	0
$405$	362975.	0.109961
$406$	0	0
$407$	3.70115e6	1.10752
$408$	0	0
$409$	1.37015e6	0.405004	0.202502	−	0.979282i	$-0.435093\pi$
$409$	1.37015e6	0.405004	0.202502	+	0.979282i	$0.435093\pi$
$410$	0	0
$411$	2.61518e6	0.763656
$412$	0	0
$413$	1.51469e6	0.436966
$414$	0	0
$415$	−2.09190e6	−0.596239
$416$	0	0
$417$	−1.76526e6	−0.497128
$418$	0	0
$419$	−6.16429e6	−1.71533	−0.857666	−	0.514207i	$-0.828086\pi$
$419$	−6.16429e6	−1.71533	−0.857666	+	0.514207i	$0.828086\pi$
$420$	0	0
$421$	2.45358e6	0.674677	0.337338	−	0.941383i	$-0.390473\pi$
$421$	2.45358e6	0.674677	0.337338	+	0.941383i	$0.390473\pi$
$422$	0	0
$423$	−2.07632e6	−0.564213
$424$	0	0
$425$	−320625.	−0.0861043
$426$	0	0
$427$	87220.0	0.0231498
$428$	0	0
$429$	−3.19252e6	−0.837510
$430$	0	0
$431$	−7.66771e6	−1.98826	−0.994128	−	0.108207i	$-0.965489\pi$
$431$	−7.66771e6	−1.98826	−0.994128	+	0.108207i	$0.965489\pi$
$432$	0	0
$433$	−5.00285e6	−1.28232	−0.641161	−	0.767406i	$-0.721547\pi$
$433$	−5.00285e6	−1.28232	−0.641161	+	0.767406i	$0.721547\pi$
$434$	0	0
$435$	−489225.	−0.123961
$436$	0	0
$437$	1.03458e6	0.259156
$438$	0	0
$439$	−1.86363e6	−0.461527	−0.230764	−	0.973010i	$-0.574122\pi$
$439$	−1.86363e6	−0.461527	−0.230764	+	0.973010i	$0.574122\pi$
$440$	0	0
$441$	−292922.	−0.0717225
$442$	0	0
$443$	−2.60747e6	−0.631263	−0.315632	−	0.948882i	$-0.602216\pi$
$443$	−2.60747e6	−0.631263	−0.315632	+	0.948882i	$0.602216\pi$
$444$	0	0
$445$	810000.	0.193903
$446$	0	0
$447$	−1.09646e6	−0.259551
$448$	0	0
$449$	−4.78007e6	−1.11897	−0.559484	−	0.828841i	$-0.689001\pi$
$449$	−4.78007e6	−1.11897	−0.559484	+	0.828841i	$0.689001\pi$
$450$	0	0
$451$	−3.17837e6	−0.735805
$452$	0	0
$453$	2.26619e6	0.518860
$454$	0	0
$455$	−1.33157e6	−0.301535
$456$	0	0
$457$	−7.96757e6	−1.78458	−0.892289	−	0.451465i	$-0.850902\pi$
$457$	−7.96757e6	−1.78458	−0.892289	+	0.451465i	$0.850902\pi$
$458$	0	0
$459$	2.05969e6	0.456322
$460$	0	0
$461$	1.77665e6	0.389358	0.194679	−	0.980867i	$-0.437633\pi$
$461$	1.77665e6	0.389358	0.194679	+	0.980867i	$0.437633\pi$
$462$	0	0
$463$	998548.	0.216479	0.108240	−	0.994125i	$-0.465479\pi$
$463$	998548.	0.216479	0.108240	+	0.994125i	$0.465479\pi$
$464$	0	0
$465$	−710600.	−0.152403
$466$	0	0
$467$	5.08478e6	1.07890	0.539449	−	0.842019i	$-0.318633\pi$
$467$	5.08478e6	1.07890	0.539449	+	0.842019i	$0.318633\pi$
$468$	0	0
$469$	1.22755e6	0.257695
$470$	0	0
$471$	6.39265e6	1.32779
$472$	0	0
$473$	159666.	0.0328140
$474$	0	0
$475$	501250.	0.101934
$476$	0	0
$477$	−3.39794e6	−0.683786
$478$	0	0
$479$	−3.71936e6	−0.740678	−0.370339	−	0.928897i	$-0.620758\pi$
$479$	−3.71936e6	−0.740678	−0.370339	+	0.928897i	$0.620758\pi$
$480$	0	0
$481$	−1.50680e7	−2.96956
$482$	0	0
$483$	−695310.	−0.135616
$484$	0	0
$485$	3.71612e6	0.717358
$486$	0	0
$487$	9.12035e6	1.74256	0.871282	−	0.490782i	$-0.163289\pi$
$487$	9.12035e6	1.74256	0.871282	+	0.490782i	$0.163289\pi$
$488$	0	0
$489$	−3.81271e6	−0.721044
$490$	0	0
$491$	7.83774e6	1.46719	0.733596	−	0.679586i	$-0.237840\pi$
$491$	7.83774e6	1.46719	0.733596	+	0.679586i	$0.237840\pi$
$492$	0	0
$493$	−912627.	−0.169113
$494$	0	0
$495$	814350.	0.149382
$496$	0	0
$497$	−2.54722e6	−0.462567
$498$	0	0
$499$	96103.0	0.0172777	0.00863884	−	0.999963i	$-0.497250\pi$
$499$	96103.0	0.0172777	0.00863884	+	0.999963i	$0.497250\pi$
$500$	0	0
$501$	4.93776e6	0.878892
$502$	0	0
$503$	2.37577e6	0.418682	0.209341	−	0.977843i	$-0.432868\pi$
$503$	2.37577e6	0.418682	0.209341	+	0.977843i	$0.432868\pi$
$504$	0	0
$505$	1.03275e6	0.180205
$506$	0	0
$507$	8.91304e6	1.53995
$508$	0	0
$509$	5.91484e6	1.01193	0.505963	−	0.862555i	$-0.331137\pi$
$509$	5.91484e6	1.01193	0.505963	+	0.862555i	$0.331137\pi$
$510$	0	0
$511$	−2.33681e6	−0.395887
$512$	0	0
$513$	−3.22003e6	−0.540215
$514$	0	0
$515$	2.71963e6	0.451847
$516$	0	0
$517$	4.54407e6	0.747685
$518$	0	0
$519$	−2.88760e6	−0.470564
$520$	0	0
$521$	1.46099e6	0.235806	0.117903	−	0.993025i	$-0.462383\pi$
$521$	1.46099e6	0.235806	0.117903	+	0.993025i	$0.462383\pi$
$522$	0	0
$523$	2.90691e6	0.464705	0.232352	−	0.972632i	$-0.425358\pi$
$523$	2.90691e6	0.464705	0.232352	+	0.972632i	$0.425358\pi$
$524$	0	0
$525$	−336875.	−0.0533422
$526$	0	0
$527$	−1.32559e6	−0.207914
$528$	0	0
$529$	−4.77224e6	−0.741453
$530$	0	0
$531$	3.77126e6	0.580431
$532$	0	0
$533$	1.29396e7	1.97290
$534$	0	0
$535$	−2.65245e6	−0.400648
$536$	0	0
$537$	1.22113e6	0.182737
$538$	0	0
$539$	641067.	0.0950455
$540$	0	0
$541$	5.28092e6	0.775741	0.387870	−	0.921714i	$-0.373211\pi$
$541$	5.28092e6	0.775741	0.387870	+	0.921714i	$0.373211\pi$
$542$	0	0
$543$	1.24049e6	0.180549
$544$	0	0
$545$	3.10278e6	0.447465
$546$	0	0
$547$	−1.31999e7	−1.88626	−0.943132	−	0.332419i	$-0.892135\pi$
$547$	−1.31999e7	−1.88626	−0.943132	+	0.332419i	$0.892135\pi$
$548$	0	0
$549$	217160.	0.0307503
$550$	0	0
$551$	1.42676e6	0.200203
$552$	0	0
$553$	−5.00393e6	−0.695822
$554$	0	0
$555$	−3.81205e6	−0.525323
$556$	0	0
$557$	−1.39920e7	−1.91091	−0.955457	−	0.295131i	$-0.904637\pi$
$557$	−1.39920e7	−1.91091	−0.955457	+	0.295131i	$0.904637\pi$
$558$	0	0
$559$	−650026.	−0.0879835
$560$	0	0
$561$	−1.50668e6	−0.202122
$562$	0	0
$563$	5.12689e6	0.681684	0.340842	−	0.940121i	$-0.389288\pi$
$563$	5.12689e6	0.681684	0.340842	+	0.940121i	$0.389288\pi$
$564$	0	0
$565$	−4.82085e6	−0.635335
$566$	0	0
$567$	711431.	0.0929341
$568$	0	0
$569$	−8.29102e6	−1.07356	−0.536781	−	0.843721i	$-0.680360\pi$
$569$	−8.29102e6	−1.07356	−0.536781	+	0.843721i	$0.680360\pi$
$570$	0	0
$571$	−6.21372e6	−0.797556	−0.398778	−	0.917048i	$-0.630566\pi$
$571$	−6.21372e6	−0.797556	−0.398778	+	0.917048i	$0.630566\pi$
$572$	0	0
$573$	8.05190e6	1.02450
$574$	0	0
$575$	806250.	0.101695
$576$	0	0
$577$	1.14818e7	1.43572	0.717861	−	0.696186i	$-0.245121\pi$
$577$	1.14818e7	1.43572	0.717861	+	0.696186i	$0.245121\pi$
$578$	0	0
$579$	−2.04644e6	−0.253690
$580$	0	0
$581$	−4.10012e6	−0.503914
$582$	0	0
$583$	7.43648e6	0.906142
$584$	0	0
$585$	−3.31535e6	−0.400534
$586$	0	0
$587$	−641856.	−0.0768851	−0.0384426	−	0.999261i	$-0.512240\pi$
$587$	−641856.	−0.0768851	−0.0384426	+	0.999261i	$0.512240\pi$
$588$	0	0
$589$	2.07237e6	0.246138
$590$	0	0
$591$	1.33492e6	0.157212
$592$	0	0
$593$	−2.80572e6	−0.327648	−0.163824	−	0.986490i	$-0.552383\pi$
$593$	−2.80572e6	−0.327648	−0.163824	+	0.986490i	$0.552383\pi$
$594$	0	0
$595$	−628425.	−0.0727715
$596$	0	0
$597$	−7.13442e6	−0.819263
$598$	0	0
$599$	−7.74415e6	−0.881874	−0.440937	−	0.897538i	$-0.645354\pi$
$599$	−7.74415e6	−0.881874	−0.440937	+	0.897538i	$0.645354\pi$
$600$	0	0
$601$	2.88868e6	0.326222	0.163111	−	0.986608i	$-0.447847\pi$
$601$	2.88868e6	0.326222	0.163111	+	0.986608i	$0.447847\pi$
$602$	0	0
$603$	3.05634e6	0.342302
$604$	0	0
$605$	2.24405e6	0.249255
$606$	0	0
$607$	−1.22095e7	−1.34501	−0.672504	−	0.740093i	$-0.734781\pi$
$607$	−1.22095e7	−1.34501	−0.672504	+	0.740093i	$0.734781\pi$
$608$	0	0
$609$	−958881.	−0.104766
$610$	0	0
$611$	−1.84997e7	−2.00475
$612$	0	0
$613$	1.51667e7	1.63019	0.815096	−	0.579326i	$-0.196684\pi$
$613$	1.51667e7	1.63019	0.815096	+	0.579326i	$0.196684\pi$
$614$	0	0
$615$	3.27360e6	0.349010
$616$	0	0
$617$	1.53927e7	1.62780	0.813899	−	0.581006i	$-0.197341\pi$
$617$	1.53927e7	1.62780	0.813899	+	0.581006i	$0.197341\pi$
$618$	0	0
$619$	1.40843e7	1.47744	0.738720	−	0.674013i	$-0.235431\pi$
$619$	1.40843e7	1.47744	0.738720	+	0.674013i	$0.235431\pi$
$620$	0	0
$621$	−5.17935e6	−0.538947
$622$	0	0
$623$	1.58760e6	0.163878
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	2.35547e6	0.239282
$628$	0	0
$629$	−7.11121e6	−0.716666
$630$	0	0
$631$	−1.56178e7	−1.56152	−0.780760	−	0.624831i	$-0.785168\pi$
$631$	−1.56178e7	−1.56152	−0.780760	+	0.624831i	$0.785168\pi$
$632$	0	0
$633$	1.64750e6	0.163424
$634$	0	0
$635$	2.48120e6	0.244190
$636$	0	0
$637$	−2.60989e6	−0.254843
$638$	0	0
$639$	−6.34205e6	−0.614437
$640$	0	0
$641$	4.04157e6	0.388513	0.194256	−	0.980951i	$-0.437771\pi$
$641$	4.04157e6	0.388513	0.194256	+	0.980951i	$0.437771\pi$
$642$	0	0
$643$	1.71035e7	1.63139	0.815693	−	0.578485i	$-0.196356\pi$
$643$	1.71035e7	1.63139	0.815693	+	0.578485i	$0.196356\pi$
$644$	0	0
$645$	−164450.	−0.0155645
$646$	0	0
$647$	8.83546e6	0.829790	0.414895	−	0.909869i	$-0.363818\pi$
$647$	8.83546e6	0.829790	0.414895	+	0.909869i	$0.363818\pi$
$648$	0	0
$649$	−8.25350e6	−0.769178
$650$	0	0
$651$	−1.39278e6	−0.128804
$652$	0	0
$653$	9.36125e6	0.859115	0.429557	−	0.903040i	$-0.358670\pi$
$653$	9.36125e6	0.859115	0.429557	+	0.903040i	$0.358670\pi$
$654$	0	0
$655$	−6.92025e6	−0.630258
$656$	0	0
$657$	−5.81818e6	−0.525864
$658$	0	0
$659$	366111.	0.0328397	0.0164199	−	0.999865i	$-0.494773\pi$
$659$	366111.	0.0328397	0.0164199	+	0.999865i	$0.494773\pi$
$660$	0	0
$661$	2.05164e7	1.82640	0.913202	−	0.407508i	$-0.133602\pi$
$661$	2.05164e7	1.82640	0.913202	+	0.407508i	$0.133602\pi$
$662$	0	0
$663$	6.13394e6	0.541946
$664$	0	0
$665$	982450.	0.0861502
$666$	0	0
$667$	2.29491e6	0.199734
$668$	0	0
$669$	1.21105e7	1.04616
$670$	0	0
$671$	−475260.	−0.0407498
$672$	0	0
$673$	7.48189e6	0.636757	0.318378	−	0.947964i	$-0.396862\pi$
$673$	7.48189e6	0.636757	0.318378	+	0.947964i	$0.396862\pi$
$674$	0	0
$675$	−2.50938e6	−0.211985
$676$	0	0
$677$	1.21459e7	1.01849	0.509247	−	0.860621i	$-0.329924\pi$
$677$	1.21459e7	1.01849	0.509247	+	0.860621i	$0.329924\pi$
$678$	0	0
$679$	7.28360e6	0.606278
$680$	0	0
$681$	7.64640e6	0.631814
$682$	0	0
$683$	1.15232e7	0.945197	0.472599	−	0.881278i	$-0.343316\pi$
$683$	1.15232e7	0.945197	0.472599	+	0.881278i	$0.343316\pi$
$684$	0	0
$685$	−5.94360e6	−0.483975
$686$	0	0
$687$	5.10110e6	0.412355
$688$	0	0
$689$	−3.02751e7	−2.42962
$690$	0	0
$691$	1.71185e7	1.36386	0.681931	−	0.731417i	$-0.261141\pi$
$691$	1.71185e7	1.36386	0.681931	+	0.731417i	$0.261141\pi$
$692$	0	0
$693$	1.59613e6	0.126251
$694$	0	0
$695$	4.01195e6	0.315060
$696$	0	0
$697$	6.10675e6	0.476133
$698$	0	0
$699$	−1.73419e7	−1.34247
$700$	0	0
$701$	9.72758e6	0.747669	0.373835	−	0.927495i	$-0.378043\pi$
$701$	9.72758e6	0.747669	0.373835	+	0.927495i	$0.378043\pi$
$702$	0	0
$703$	1.11173e7	0.848422
$704$	0	0
$705$	−4.68022e6	−0.354645
$706$	0	0
$707$	2.02419e6	0.152301
$708$	0	0
$709$	−673813.	−0.0503412	−0.0251706	−	0.999683i	$-0.508013\pi$
$709$	−673813.	−0.0503412	−0.0251706	+	0.999683i	$0.508013\pi$
$710$	0	0
$711$	−1.24588e7	−0.924274
$712$	0	0
$713$	3.33336e6	0.245560
$714$	0	0
$715$	7.25572e6	0.530781
$716$	0	0
$717$	5.63241e6	0.409163
$718$	0	0
$719$	−2.77719e6	−0.200347	−0.100174	−	0.994970i	$-0.531940\pi$
$719$	−2.77719e6	−0.200347	−0.100174	+	0.994970i	$0.531940\pi$
$720$	0	0
$721$	5.33046e6	0.381880
$722$	0	0
$723$	1.08826e7	0.774262
$724$	0	0
$725$	1.11188e6	0.0785617
$726$	0	0
$727$	−1.16385e7	−0.816700	−0.408350	−	0.912825i	$-0.633896\pi$
$727$	−1.16385e7	−0.816700	−0.408350	+	0.912825i	$0.633896\pi$
$728$	0	0
$729$	1.25034e7	0.871384
$730$	0	0
$731$	−306774.	−0.0212337
$732$	0	0
$733$	−1.32013e7	−0.907522	−0.453761	−	0.891123i	$-0.649918\pi$
$733$	−1.32013e7	−0.907522	−0.453761	+	0.891123i	$0.649918\pi$
$734$	0	0
$735$	−660275.	−0.0450823
$736$	0	0
$737$	−6.68888e6	−0.453612
$738$	0	0
$739$	−3.25476e6	−0.219234	−0.109617	−	0.993974i	$-0.534962\pi$
$739$	−3.25476e6	−0.219234	−0.109617	+	0.993974i	$0.534962\pi$
$740$	0	0
$741$	−9.58951e6	−0.641580
$742$	0	0
$743$	7.61596e6	0.506119	0.253059	−	0.967451i	$-0.418563\pi$
$743$	7.61596e6	0.506119	0.253059	+	0.967451i	$0.418563\pi$
$744$	0	0
$745$	2.49195e6	0.164493
$746$	0	0
$747$	−1.02085e7	−0.669359
$748$	0	0
$749$	−5.19880e6	−0.338609
$750$	0	0
$751$	−655199.	−0.0423910	−0.0211955	−	0.999775i	$-0.506747\pi$
$751$	−655199.	−0.0423910	−0.0211955	+	0.999775i	$0.506747\pi$
$752$	0	0
$753$	673530.	0.0432882
$754$	0	0
$755$	−5.15042e6	−0.328833
$756$	0	0
$757$	1.85111e7	1.17406	0.587032	−	0.809564i	$-0.300296\pi$
$757$	1.85111e7	1.17406	0.587032	+	0.809564i	$0.300296\pi$
$758$	0	0
$759$	3.78873e6	0.238720
$760$	0	0
$761$	−1.85291e7	−1.15983	−0.579914	−	0.814678i	$-0.696914\pi$
$761$	−1.85291e7	−1.15983	−0.579914	+	0.814678i	$0.696914\pi$
$762$	0	0
$763$	6.08144e6	0.378177
$764$	0	0
$765$	−1.56465e6	−0.0966637
$766$	0	0
$767$	3.36013e7	2.06238
$768$	0	0
$769$	−1.48414e7	−0.905024	−0.452512	−	0.891758i	$-0.649472\pi$
$769$	−1.48414e7	−0.905024	−0.452512	+	0.891758i	$0.649472\pi$
$770$	0	0
$771$	1.47276e7	0.892268
$772$	0	0
$773$	3.93042e6	0.236586	0.118293	−	0.992979i	$-0.462258\pi$
$773$	3.93042e6	0.236586	0.118293	+	0.992979i	$0.462258\pi$
$774$	0	0
$775$	1.61500e6	0.0965869
$776$	0	0
$777$	−7.47162e6	−0.443979
$778$	0	0
$779$	−9.54701e6	−0.563668
$780$	0	0
$781$	1.38797e7	0.814242
$782$	0	0
$783$	−7.14269e6	−0.416349
$784$	0	0
$785$	−1.45288e7	−0.841500
$786$	0	0
$787$	−1.17824e7	−0.678105	−0.339053	−	0.940767i	$-0.610107\pi$
$787$	−1.17824e7	−0.678105	−0.339053	+	0.940767i	$0.610107\pi$
$788$	0	0
$789$	1.82180e7	1.04186
$790$	0	0
$791$	−9.44887e6	−0.536956
$792$	0	0
$793$	1.93486e6	0.109261
$794$	0	0
$795$	−7.65930e6	−0.429805
$796$	0	0
$797$	−5.40952e6	−0.301657	−0.150828	−	0.988560i	$-0.548194\pi$
$797$	−5.40952e6	−0.301657	−0.150828	+	0.988560i	$0.548194\pi$
$798$	0	0
$799$	−8.73075e6	−0.483821
$800$	0	0
$801$	3.95280e6	0.217683
$802$	0	0
$803$	1.27332e7	0.696867
$804$	0	0
$805$	1.58025e6	0.0859481
$806$	0	0
$807$	−8.25667e6	−0.446294
$808$	0	0
$809$	−7.12264e6	−0.382622	−0.191311	−	0.981529i	$-0.561274\pi$
$809$	−7.12264e6	−0.382622	−0.191311	+	0.981529i	$0.561274\pi$
$810$	0	0
$811$	3.03045e7	1.61791	0.808956	−	0.587869i	$-0.200033\pi$
$811$	3.03045e7	1.61791	0.808956	+	0.587869i	$0.200033\pi$
$812$	0	0
$813$	6.13699e6	0.325633
$814$	0	0
$815$	8.66525e6	0.456969
$816$	0	0
$817$	479596.	0.0251374
$818$	0	0
$819$	−6.49809e6	−0.338513
$820$	0	0
$821$	2.82181e7	1.46106	0.730532	−	0.682878i	$-0.239272\pi$
$821$	2.82181e7	1.46106	0.730532	+	0.682878i	$0.239272\pi$
$822$	0	0
$823$	2.64534e7	1.36139	0.680694	−	0.732567i	$-0.261678\pi$
$823$	2.64534e7	1.36139	0.680694	+	0.732567i	$0.261678\pi$
$824$	0	0
$825$	1.83563e6	0.0938964
$826$	0	0
$827$	−4.44481e6	−0.225990	−0.112995	−	0.993596i	$-0.536044\pi$
$827$	−4.44481e6	−0.225990	−0.112995	+	0.993596i	$0.536044\pi$
$828$	0	0
$829$	−2.80386e6	−0.141700	−0.0708501	−	0.997487i	$-0.522571\pi$
$829$	−2.80386e6	−0.141700	−0.0708501	+	0.997487i	$0.522571\pi$
$830$	0	0
$831$	1.94981e7	0.979469
$832$	0	0
$833$	−1.23171e6	−0.0615031
$834$	0	0
$835$	−1.12222e7	−0.557007
$836$	0	0
$837$	−1.03748e7	−0.511876
$838$	0	0
$839$	−2.59804e7	−1.27421	−0.637104	−	0.770778i	$-0.719868\pi$
$839$	−2.59804e7	−1.27421	−0.637104	+	0.770778i	$0.719868\pi$
$840$	0	0
$841$	−1.73463e7	−0.845701
$842$	0	0
$843$	−1.20883e7	−0.585862
$844$	0	0
$845$	−2.02569e7	−0.975958
$846$	0	0
$847$	4.39834e6	0.210659
$848$	0	0
$849$	3.52626e6	0.167898
$850$	0	0
$851$	1.78820e7	0.846431
$852$	0	0
$853$	1.18392e7	0.557121	0.278560	−	0.960419i	$-0.410143\pi$
$853$	1.18392e7	0.557121	0.278560	+	0.960419i	$0.410143\pi$
$854$	0	0
$855$	2.44610e6	0.114435
$856$	0	0
$857$	−2.99283e6	−0.139197	−0.0695985	−	0.997575i	$-0.522172\pi$
$857$	−2.99283e6	−0.139197	−0.0695985	+	0.997575i	$0.522172\pi$
$858$	0	0
$859$	−2.80980e7	−1.29925	−0.649626	−	0.760254i	$-0.725074\pi$
$859$	−2.80980e7	−1.29925	−0.649626	+	0.760254i	$0.725074\pi$
$860$	0	0
$861$	6.41626e6	0.294967
$862$	0	0
$863$	−1.15833e7	−0.529424	−0.264712	−	0.964328i	$-0.585277\pi$
$863$	−1.15833e7	−0.529424	−0.264712	+	0.964328i	$0.585277\pi$
$864$	0	0
$865$	6.56272e6	0.298225
$866$	0	0
$867$	−1.27236e7	−0.574859
$868$	0	0
$869$	2.72663e7	1.22483
$870$	0	0
$871$	2.72315e7	1.21626
$872$	0	0
$873$	1.81347e7	0.805331
$874$	0	0
$875$	765625.	0.0338062
$876$	0	0
$877$	4.12538e7	1.81119	0.905596	−	0.424141i	$-0.139424\pi$
$877$	4.12538e7	1.81119	0.905596	+	0.424141i	$0.139424\pi$
$878$	0	0
$879$	−1.78571e7	−0.779539
$880$	0	0
$881$	−1.32541e7	−0.575321	−0.287661	−	0.957732i	$-0.592877\pi$
$881$	−1.32541e7	−0.575321	−0.287661	+	0.957732i	$0.592877\pi$
$882$	0	0
$883$	3.19208e7	1.37776	0.688878	−	0.724877i	$-0.258103\pi$
$883$	3.19208e7	1.37776	0.688878	+	0.724877i	$0.258103\pi$
$884$	0	0
$885$	8.50080e6	0.364839
$886$	0	0
$887$	−1.74303e7	−0.743866	−0.371933	−	0.928260i	$-0.621305\pi$
$887$	−1.74303e7	−0.743866	−0.371933	+	0.928260i	$0.621305\pi$
$888$	0	0
$889$	4.86315e6	0.206378
$890$	0	0
$891$	−3.87657e6	−0.163589
$892$	0	0
$893$	1.36492e7	0.572769
$894$	0	0
$895$	−2.77530e6	−0.115812
$896$	0	0
$897$	−1.54245e7	−0.640075
$898$	0	0
$899$	4.59694e6	0.189701
$900$	0	0
$901$	−1.42881e7	−0.586357
$902$	0	0
$903$	−322322.	−0.0131544
$904$	0	0
$905$	−2.81930e6	−0.114425
$906$	0	0
$907$	3.15066e7	1.27170	0.635848	−	0.771815i	$-0.280651\pi$
$907$	3.15066e7	1.27170	0.635848	+	0.771815i	$0.280651\pi$
$908$	0	0
$909$	5.03982e6	0.202304
$910$	0	0
$911$	4.91214e7	1.96099	0.980494	−	0.196548i	$-0.0629732\pi$
$911$	4.91214e7	1.96099	0.980494	+	0.196548i	$0.0629732\pi$
$912$	0	0
$913$	2.23415e7	0.887024
$914$	0	0
$915$	489500.	0.0193286
$916$	0	0
$917$	−1.35637e7	−0.532665
$918$	0	0
$919$	4.51238e7	1.76245	0.881226	−	0.472696i	$-0.156719\pi$
$919$	4.51238e7	1.76245	0.881226	+	0.472696i	$0.156719\pi$
$920$	0	0
$921$	−1.09460e7	−0.425211
$922$	0	0
$923$	−5.65066e7	−2.18321
$924$	0	0
$925$	8.66375e6	0.332929
$926$	0	0
$927$	1.32718e7	0.507259
$928$	0	0
$929$	−3.68196e7	−1.39972	−0.699858	−	0.714282i	$-0.746753\pi$
$929$	−3.68196e7	−1.39972	−0.699858	+	0.714282i	$0.746753\pi$
$930$	0	0
$931$	1.92560e6	0.0728102
$932$	0	0
$933$	−1.47838e7	−0.556009
$934$	0	0
$935$	3.42428e6	0.128097
$936$	0	0
$937$	1.71904e7	0.639641	0.319820	−	0.947478i	$-0.396377\pi$
$937$	1.71904e7	0.639641	0.319820	+	0.947478i	$0.396377\pi$
$938$	0	0
$939$	2.11168e7	0.781562
$940$	0	0
$941$	−8.10352e6	−0.298332	−0.149166	−	0.988812i	$-0.547659\pi$
$941$	−8.10352e6	−0.298332	−0.149166	+	0.988812i	$0.547659\pi$
$942$	0	0
$943$	−1.53562e7	−0.562346
$944$	0	0
$945$	−4.91838e6	−0.179160
$946$	0	0
$947$	−1.83337e7	−0.664317	−0.332158	−	0.943224i	$-0.607777\pi$
$947$	−1.83337e7	−0.664317	−0.332158	+	0.943224i	$0.607777\pi$
$948$	0	0
$949$	−5.18390e7	−1.86849
$950$	0	0
$951$	−2.10502e7	−0.754755
$952$	0	0
$953$	6.03035e6	0.215085	0.107542	−	0.994200i	$-0.465702\pi$
$953$	6.03035e6	0.215085	0.107542	+	0.994200i	$0.465702\pi$
$954$	0	0
$955$	−1.82998e7	−0.649288
$956$	0	0
$957$	5.22492e6	0.184417
$958$	0	0
$959$	−1.16495e7	−0.409034
$960$	0	0
$961$	−2.19521e7	−0.766774
$962$	0	0
$963$	−1.29440e7	−0.449781
$964$	0	0
$965$	4.65100e6	0.160779
$966$	0	0
$967$	3.09228e7	1.06344	0.531720	−	0.846920i	$-0.321546\pi$
$967$	3.09228e7	1.06344	0.531720	+	0.846920i	$0.321546\pi$
$968$	0	0
$969$	−4.52569e6	−0.154837
$970$	0	0
$971$	2.47924e6	0.0843859	0.0421929	−	0.999109i	$-0.486566\pi$
$971$	2.47924e6	0.0843859	0.0421929	+	0.999109i	$0.486566\pi$
$972$	0	0
$973$	7.86342e6	0.266274
$974$	0	0
$975$	−7.47312e6	−0.251762
$976$	0	0
$977$	−2.09758e6	−0.0703044	−0.0351522	−	0.999382i	$-0.511192\pi$
$977$	−2.09758e6	−0.0703044	−0.0351522	+	0.999382i	$0.511192\pi$
$978$	0	0
$979$	−8.65080e6	−0.288469
$980$	0	0
$981$	1.51415e7	0.502340
$982$	0	0
$983$	4.45491e7	1.47047	0.735233	−	0.677814i	$-0.237073\pi$
$983$	4.45491e7	1.47047	0.735233	+	0.677814i	$0.237073\pi$
$984$	0	0
$985$	−3.03390e6	−0.0996347
$986$	0	0
$987$	−9.17324e6	−0.299730
$988$	0	0
$989$	771420.	0.0250784
$990$	0	0
$991$	1.95104e7	0.631075	0.315538	−	0.948913i	$-0.397815\pi$
$991$	1.95104e7	0.631075	0.315538	+	0.948913i	$0.397815\pi$
$992$	0	0
$993$	2.48263e7	0.798987
$994$	0	0
$995$	1.62146e7	0.519217
$996$	0	0
$997$	−2.00678e7	−0.639385	−0.319692	−	0.947521i	$-0.603580\pi$
$997$	−2.00678e7	−0.639385	−0.319692	+	0.947521i	$0.603580\pi$
$998$	0	0
$999$	−5.56559e7	−1.76440

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.f.1.1	✓	1	4.3	odd	2
350.6.a.d.1.1		1	20.19	odd	2
350.6.c.b.99.1		2	20.3	even	4
350.6.c.b.99.2		2	20.7	even	4
490.6.a.l.1.1		1	28.27	even	2
560.6.a.f.1.1		1	1.1	even	1	trivial
630.6.a.e.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

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