LMFDB - Embedded newform 660.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [660,6,Mod(1,660)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(660, 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("660.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	660.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:	$105.853321077$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	660.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+9.00000 q^{3} -25.0000 q^{5} +188.000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q+9.00000 q^{3} -25.0000 q^{5} +188.000 q^{7} +81.0000 q^{9} +121.000 q^{11} +698.000 q^{13} -225.000 q^{15} +1890.00 q^{17} -2428.00 q^{19} +1692.00 q^{21} +2340.00 q^{23} +625.000 q^{25} +729.000 q^{27} +990.000 q^{29} +128.000 q^{31} +1089.00 q^{33} -4700.00 q^{35} -3202.00 q^{37} +6282.00 q^{39} +17370.0 q^{41} -6652.00 q^{43} -2025.00 q^{45} -25020.0 q^{47} +18537.0 q^{49} +17010.0 q^{51} -18246.0 q^{53} -3025.00 q^{55} -21852.0 q^{57} -8652.00 q^{59} +37682.0 q^{61} +15228.0 q^{63} -17450.0 q^{65} -18676.0 q^{67} +21060.0 q^{69} -2340.00 q^{71} +43058.0 q^{73} +5625.00 q^{75} +22748.0 q^{77} +65300.0 q^{79} +6561.00 q^{81} -55308.0 q^{83} -47250.0 q^{85} +8910.00 q^{87} -64806.0 q^{89} +131224. q^{91} +1152.00 q^{93} +60700.0 q^{95} +38306.0 q^{97} +9801.00 q^{99} +O(q^{100})$

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
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	0	0
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	0	0
$7$	188.000	1.45015	0.725075	−	0.688670i	$-0.241805\pi$
$7$	188.000	1.45015	0.725075	+	0.688670i	$0.241805\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	0	0
$13$	698.000	1.14551	0.572753	−	0.819728i	$-0.305876\pi$
$13$	698.000	1.14551	0.572753	+	0.819728i	$0.305876\pi$
$14$	0	0
$15$	−225.000	−0.258199
$16$	0	0
$17$	1890.00	1.58613	0.793066	−	0.609135i	$-0.208483\pi$
$17$	1890.00	1.58613	0.793066	+	0.609135i	$0.208483\pi$
$18$	0	0
$19$	−2428.00	−1.54300	−0.771498	−	0.636232i	$-0.780492\pi$
$19$	−2428.00	−1.54300	−0.771498	+	0.636232i	$0.780492\pi$
$20$	0	0
$21$	1692.00	0.837244
$22$	0	0
$23$	2340.00	0.922351	0.461176	−	0.887309i	$-0.347428\pi$
$23$	2340.00	0.922351	0.461176	+	0.887309i	$0.347428\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	0	0
$27$	729.000	0.192450
$28$	0	0
$29$	990.000	0.218595	0.109297	−	0.994009i	$-0.465140\pi$
$29$	990.000	0.218595	0.109297	+	0.994009i	$0.465140\pi$
$30$	0	0
$31$	128.000	0.0239225	0.0119612	−	0.999928i	$-0.496193\pi$
$31$	128.000	0.0239225	0.0119612	+	0.999928i	$0.496193\pi$
$32$	0	0
$33$	1089.00	0.174078
$34$	0	0
$35$	−4700.00	−0.648527
$36$	0	0
$37$	−3202.00	−0.384518	−0.192259	−	0.981344i	$-0.561581\pi$
$37$	−3202.00	−0.384518	−0.192259	+	0.981344i	$0.561581\pi$
$38$	0	0
$39$	6282.00	0.661358
$40$	0	0
$41$	17370.0	1.61376	0.806882	−	0.590712i	$-0.201153\pi$
$41$	17370.0	1.61376	0.806882	+	0.590712i	$0.201153\pi$
$42$	0	0
$43$	−6652.00	−0.548632	−0.274316	−	0.961640i	$-0.588451\pi$
$43$	−6652.00	−0.548632	−0.274316	+	0.961640i	$0.588451\pi$
$44$	0	0
$45$	−2025.00	−0.149071
$46$	0	0
$47$	−25020.0	−1.65212	−0.826062	−	0.563579i	$-0.809424\pi$
$47$	−25020.0	−1.65212	−0.826062	+	0.563579i	$0.809424\pi$
$48$	0	0
$49$	18537.0	1.10293
$50$	0	0
$51$	17010.0	0.915754
$52$	0	0
$53$	−18246.0	−0.892232	−0.446116	−	0.894975i	$-0.647193\pi$
$53$	−18246.0	−0.892232	−0.446116	+	0.894975i	$0.647193\pi$
$54$	0	0
$55$	−3025.00	−0.134840
$56$	0	0
$57$	−21852.0	−0.890849
$58$	0	0
$59$	−8652.00	−0.323584	−0.161792	−	0.986825i	$-0.551727\pi$
$59$	−8652.00	−0.323584	−0.161792	+	0.986825i	$0.551727\pi$
$60$	0	0
$61$	37682.0	1.29661	0.648305	−	0.761381i	$-0.275478\pi$
$61$	37682.0	1.29661	0.648305	+	0.761381i	$0.275478\pi$
$62$	0	0
$63$	15228.0	0.483383
$64$	0	0
$65$	−17450.0	−0.512285
$66$	0	0
$67$	−18676.0	−0.508273	−0.254136	−	0.967168i	$-0.581791\pi$
$67$	−18676.0	−0.508273	−0.254136	+	0.967168i	$0.581791\pi$
$68$	0	0
$69$	21060.0	0.532520
$70$	0	0
$71$	−2340.00	−0.0550896	−0.0275448	−	0.999621i	$-0.508769\pi$
$71$	−2340.00	−0.0550896	−0.0275448	+	0.999621i	$0.508769\pi$
$72$	0	0
$73$	43058.0	0.945685	0.472843	−	0.881147i	$-0.343228\pi$
$73$	43058.0	0.945685	0.472843	+	0.881147i	$0.343228\pi$
$74$	0	0
$75$	5625.00	0.115470
$76$	0	0
$77$	22748.0	0.437236
$78$	0	0
$79$	65300.0	1.17719	0.588593	−	0.808429i	$-0.299682\pi$
$79$	65300.0	1.17719	0.588593	+	0.808429i	$0.299682\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	−55308.0	−0.881237	−0.440618	−	0.897694i	$-0.645241\pi$
$83$	−55308.0	−0.881237	−0.440618	+	0.897694i	$0.645241\pi$
$84$	0	0
$85$	−47250.0	−0.709340
$86$	0	0
$87$	8910.00	0.126206
$88$	0	0
$89$	−64806.0	−0.867242	−0.433621	−	0.901095i	$-0.642764\pi$
$89$	−64806.0	−0.867242	−0.433621	+	0.901095i	$0.642764\pi$
$90$	0	0
$91$	131224.	1.66115
$92$	0	0
$93$	1152.00	0.0138116
$94$	0	0
$95$	60700.0	0.690049
$96$	0	0
$97$	38306.0	0.413369	0.206684	−	0.978408i	$-0.433733\pi$
$97$	38306.0	0.413369	0.206684	+	0.978408i	$0.433733\pi$
$98$	0	0
$99$	9801.00	0.100504
$100$	0	0
$101$	−169290.	−1.65131	−0.825654	−	0.564177i	$-0.809193\pi$
$101$	−169290.	−1.65131	−0.825654	+	0.564177i	$0.809193\pi$
$102$	0	0
$103$	147104.	1.36625	0.683127	−	0.730300i	$-0.260620\pi$
$103$	147104.	1.36625	0.683127	+	0.730300i	$0.260620\pi$
$104$	0	0
$105$	−42300.0	−0.374427
$106$	0	0
$107$	−48108.0	−0.406217	−0.203108	−	0.979156i	$-0.565104\pi$
$107$	−48108.0	−0.406217	−0.203108	+	0.979156i	$0.565104\pi$
$108$	0	0
$109$	75050.0	0.605041	0.302520	−	0.953143i	$-0.402172\pi$
$109$	75050.0	0.605041	0.302520	+	0.953143i	$0.402172\pi$
$110$	0	0
$111$	−28818.0	−0.222002
$112$	0	0
$113$	161034.	1.18637	0.593187	−	0.805065i	$-0.297870\pi$
$113$	161034.	1.18637	0.593187	+	0.805065i	$0.297870\pi$
$114$	0	0
$115$	−58500.0	−0.412488
$116$	0	0
$117$	56538.0	0.381835
$118$	0	0
$119$	355320.	2.30013
$120$	0	0
$121$	14641.0	0.0909091
$122$	0	0
$123$	156330.	0.931707
$124$	0	0
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	240428.	1.32274	0.661372	−	0.750058i	$-0.269975\pi$
$127$	240428.	1.32274	0.661372	+	0.750058i	$0.269975\pi$
$128$	0	0
$129$	−59868.0	−0.316753
$130$	0	0
$131$	248748.	1.26643	0.633215	−	0.773976i	$-0.281735\pi$
$131$	248748.	1.26643	0.633215	+	0.773976i	$0.281735\pi$
$132$	0	0
$133$	−456464.	−2.23757
$134$	0	0
$135$	−18225.0	−0.0860663
$136$	0	0
$137$	−23286.0	−0.105997	−0.0529985	−	0.998595i	$-0.516878\pi$
$137$	−23286.0	−0.105997	−0.0529985	+	0.998595i	$0.516878\pi$
$138$	0	0
$139$	367388.	1.61283	0.806414	−	0.591352i	$-0.201405\pi$
$139$	367388.	1.61283	0.806414	+	0.591352i	$0.201405\pi$
$140$	0	0
$141$	−225180.	−0.953854
$142$	0	0
$143$	84458.0	0.345383
$144$	0	0
$145$	−24750.0	−0.0977587
$146$	0	0
$147$	166833.	0.636779
$148$	0	0
$149$	1518.00	0.00560152	0.00280076	−	0.999996i	$-0.499108\pi$
$149$	1518.00	0.00560152	0.00280076	+	0.999996i	$0.499108\pi$
$150$	0	0
$151$	−85156.0	−0.303930	−0.151965	−	0.988386i	$-0.548560\pi$
$151$	−85156.0	−0.303930	−0.151965	+	0.988386i	$0.548560\pi$
$152$	0	0
$153$	153090.	0.528711
$154$	0	0
$155$	−3200.00	−0.0106984
$156$	0	0
$157$	−74674.0	−0.241780	−0.120890	−	0.992666i	$-0.538575\pi$
$157$	−74674.0	−0.241780	−0.120890	+	0.992666i	$0.538575\pi$
$158$	0	0
$159$	−164214.	−0.515131
$160$	0	0
$161$	439920.	1.33755
$162$	0	0
$163$	−159868.	−0.471295	−0.235647	−	0.971839i	$-0.575721\pi$
$163$	−159868.	−0.471295	−0.235647	+	0.971839i	$0.575721\pi$
$164$	0	0
$165$	−27225.0	−0.0778499
$166$	0	0
$167$	−522816.	−1.45063	−0.725317	−	0.688415i	$-0.758307\pi$
$167$	−522816.	−1.45063	−0.725317	+	0.688415i	$0.758307\pi$
$168$	0	0
$169$	115911.	0.312182
$170$	0	0
$171$	−196668.	−0.514332
$172$	0	0
$173$	77718.0	0.197427	0.0987135	−	0.995116i	$-0.468527\pi$
$173$	77718.0	0.197427	0.0987135	+	0.995116i	$0.468527\pi$
$174$	0	0
$175$	117500.	0.290030
$176$	0	0
$177$	−77868.0	−0.186821
$178$	0	0
$179$	−299892.	−0.699572	−0.349786	−	0.936830i	$-0.613746\pi$
$179$	−299892.	−0.699572	−0.349786	+	0.936830i	$0.613746\pi$
$180$	0	0
$181$	350.000	0.000794093 0	0.000397047	−	1.00000i	$-0.499874\pi$
$181$	350.000	0.000794093 0	0.000397047		1.00000i	$0.499874\pi$
$182$	0	0
$183$	339138.	0.748598
$184$	0	0
$185$	80050.0	0.171962
$186$	0	0
$187$	228690.	0.478237
$188$	0	0
$189$	137052.	0.279081
$190$	0	0
$191$	−437220.	−0.867195	−0.433597	−	0.901107i	$-0.642756\pi$
$191$	−437220.	−0.867195	−0.433597	+	0.901107i	$0.642756\pi$
$192$	0	0
$193$	584930.	1.13034	0.565172	−	0.824973i	$-0.308810\pi$
$193$	584930.	1.13034	0.565172	+	0.824973i	$0.308810\pi$
$194$	0	0
$195$	−157050.	−0.295768
$196$	0	0
$197$	−433218.	−0.795318	−0.397659	−	0.917533i	$-0.630177\pi$
$197$	−433218.	−0.795318	−0.397659	+	0.917533i	$0.630177\pi$
$198$	0	0
$199$	112304.	0.201031	0.100515	−	0.994936i	$-0.467951\pi$
$199$	112304.	0.201031	0.100515	+	0.994936i	$0.467951\pi$
$200$	0	0
$201$	−168084.	−0.293451
$202$	0	0
$203$	186120.	0.316995
$204$	0	0
$205$	−434250.	−0.721697
$206$	0	0
$207$	189540.	0.307450
$208$	0	0
$209$	−293788.	−0.465231
$210$	0	0
$211$	850508.	1.31514	0.657570	−	0.753393i	$-0.271584\pi$
$211$	850508.	1.31514	0.657570	+	0.753393i	$0.271584\pi$
$212$	0	0
$213$	−21060.0	−0.0318060
$214$	0	0
$215$	166300.	0.245356
$216$	0	0
$217$	24064.0	0.0346911
$218$	0	0
$219$	387522.	0.545992
$220$	0	0
$221$	1.31922e6	1.81692
$222$	0	0
$223$	−964000.	−1.29812	−0.649060	−	0.760737i	$-0.724838\pi$
$223$	−964000.	−1.29812	−0.649060	+	0.760737i	$0.724838\pi$
$224$	0	0
$225$	50625.0	0.0666667
$226$	0	0
$227$	509532.	0.656307	0.328153	−	0.944624i	$-0.393574\pi$
$227$	509532.	0.656307	0.328153	+	0.944624i	$0.393574\pi$
$228$	0	0
$229$	882302.	1.11180	0.555902	−	0.831248i	$-0.312373\pi$
$229$	882302.	1.11180	0.555902	+	0.831248i	$0.312373\pi$
$230$	0	0
$231$	204732.	0.252439
$232$	0	0
$233$	526458.	0.635293	0.317646	−	0.948209i	$-0.397108\pi$
$233$	526458.	0.635293	0.317646	+	0.948209i	$0.397108\pi$
$234$	0	0
$235$	625500.	0.738852
$236$	0	0
$237$	587700.	0.679649
$238$	0	0
$239$	1.07551e6	1.21792	0.608962	−	0.793199i	$-0.291586\pi$
$239$	1.07551e6	1.21792	0.608962	+	0.793199i	$0.291586\pi$
$240$	0	0
$241$	1.01705e6	1.12798	0.563988	−	0.825783i	$-0.309266\pi$
$241$	1.01705e6	1.12798	0.563988	+	0.825783i	$0.309266\pi$
$242$	0	0
$243$	59049.0	0.0641500
$244$	0	0
$245$	−463425.	−0.493247
$246$	0	0
$247$	−1.69474e6	−1.76751
$248$	0	0
$249$	−497772.	−0.508782
$250$	0	0
$251$	5412.00	0.00542217	0.00271109	−	0.999996i	$-0.499137\pi$
$251$	5412.00	0.00542217	0.00271109	+	0.999996i	$0.499137\pi$
$252$	0	0
$253$	283140.	0.278099
$254$	0	0
$255$	−425250.	−0.409538
$256$	0	0
$257$	−583398.	−0.550975	−0.275488	−	0.961305i	$-0.588839\pi$
$257$	−583398.	−0.550975	−0.275488	+	0.961305i	$0.588839\pi$
$258$	0	0
$259$	−601976.	−0.557609
$260$	0	0
$261$	80190.0	0.0728650
$262$	0	0
$263$	1.73628e6	1.54786	0.773928	−	0.633274i	$-0.218289\pi$
$263$	1.73628e6	1.54786	0.773928	+	0.633274i	$0.218289\pi$
$264$	0	0
$265$	456150.	0.399018
$266$	0	0
$267$	−583254.	−0.500702
$268$	0	0
$269$	−611790.	−0.515492	−0.257746	−	0.966213i	$-0.582980\pi$
$269$	−611790.	−0.515492	−0.257746	+	0.966213i	$0.582980\pi$
$270$	0	0
$271$	2.10681e6	1.74262	0.871310	−	0.490733i	$-0.163271\pi$
$271$	2.10681e6	1.74262	0.871310	+	0.490733i	$0.163271\pi$
$272$	0	0
$273$	1.18102e6	0.959067
$274$	0	0
$275$	75625.0	0.0603023
$276$	0	0
$277$	1.12222e6	0.878775	0.439388	−	0.898298i	$-0.355195\pi$
$277$	1.12222e6	0.878775	0.439388	+	0.898298i	$0.355195\pi$
$278$	0	0
$279$	10368.0	0.00797415
$280$	0	0
$281$	1.51065e6	1.14130	0.570648	−	0.821195i	$-0.306692\pi$
$281$	1.51065e6	1.14130	0.570648	+	0.821195i	$0.306692\pi$
$282$	0	0
$283$	−12076.0	−0.00896307	−0.00448154	−	0.999990i	$-0.501427\pi$
$283$	−12076.0	−0.00896307	−0.00448154	+	0.999990i	$0.501427\pi$
$284$	0	0
$285$	546300.	0.398400
$286$	0	0
$287$	3.26556e6	2.34020
$288$	0	0
$289$	2.15224e6	1.51582
$290$	0	0
$291$	344754.	0.238658
$292$	0	0
$293$	−673914.	−0.458601	−0.229301	−	0.973356i	$-0.573644\pi$
$293$	−673914.	−0.458601	−0.229301	+	0.973356i	$0.573644\pi$
$294$	0	0
$295$	216300.	0.144711
$296$	0	0
$297$	88209.0	0.0580259
$298$	0	0
$299$	1.63332e6	1.05656
$300$	0	0
$301$	−1.25058e6	−0.795598
$302$	0	0
$303$	−1.52361e6	−0.953383
$304$	0	0
$305$	−942050.	−0.579862
$306$	0	0
$307$	−189820.	−0.114947	−0.0574733	−	0.998347i	$-0.518304\pi$
$307$	−189820.	−0.114947	−0.0574733	+	0.998347i	$0.518304\pi$
$308$	0	0
$309$	1.32394e6	0.788807
$310$	0	0
$311$	−1.44124e6	−0.844956	−0.422478	−	0.906373i	$-0.638840\pi$
$311$	−1.44124e6	−0.844956	−0.422478	+	0.906373i	$0.638840\pi$
$312$	0	0
$313$	−908950.	−0.524420	−0.262210	−	0.965011i	$-0.584451\pi$
$313$	−908950.	−0.524420	−0.262210	+	0.965011i	$0.584451\pi$
$314$	0	0
$315$	−380700.	−0.216176
$316$	0	0
$317$	2.80924e6	1.57015	0.785075	−	0.619401i	$-0.212624\pi$
$317$	2.80924e6	1.57015	0.785075	+	0.619401i	$0.212624\pi$
$318$	0	0
$319$	119790.	0.0659089
$320$	0	0
$321$	−432972.	−0.234529
$322$	0	0
$323$	−4.58892e6	−2.44740
$324$	0	0
$325$	436250.	0.229101
$326$	0	0
$327$	675450.	0.349320
$328$	0	0
$329$	−4.70376e6	−2.39583
$330$	0	0
$331$	−1.92017e6	−0.963319	−0.481660	−	0.876358i	$-0.659966\pi$
$331$	−1.92017e6	−0.963319	−0.481660	+	0.876358i	$0.659966\pi$
$332$	0	0
$333$	−259362.	−0.128173
$334$	0	0
$335$	466900.	0.227307
$336$	0	0
$337$	−2.34857e6	−1.12649	−0.563246	−	0.826289i	$-0.690448\pi$
$337$	−2.34857e6	−1.12649	−0.563246	+	0.826289i	$0.690448\pi$
$338$	0	0
$339$	1.44931e6	0.684953
$340$	0	0
$341$	15488.0	0.00721289
$342$	0	0
$343$	325240.	0.149269
$344$	0	0
$345$	−526500.	−0.238150
$346$	0	0
$347$	1.80049e6	0.802726	0.401363	−	0.915919i	$-0.368537\pi$
$347$	1.80049e6	0.802726	0.401363	+	0.915919i	$0.368537\pi$
$348$	0	0
$349$	−4.04541e6	−1.77787	−0.888934	−	0.458036i	$-0.848553\pi$
$349$	−4.04541e6	−1.77787	−0.888934	+	0.458036i	$0.848553\pi$
$350$	0	0
$351$	508842.	0.220453
$352$	0	0
$353$	−1.26596e6	−0.540733	−0.270366	−	0.962758i	$-0.587145\pi$
$353$	−1.26596e6	−0.540733	−0.270366	+	0.962758i	$0.587145\pi$
$354$	0	0
$355$	58500.0	0.0246368
$356$	0	0
$357$	3.19788e6	1.32798
$358$	0	0
$359$	−3.40416e6	−1.39404	−0.697018	−	0.717054i	$-0.745490\pi$
$359$	−3.40416e6	−1.39404	−0.697018	+	0.717054i	$0.745490\pi$
$360$	0	0
$361$	3.41908e6	1.38084
$362$	0	0
$363$	131769.	0.0524864
$364$	0	0
$365$	−1.07645e6	−0.422923
$366$	0	0
$367$	2.68208e6	1.03946	0.519729	−	0.854331i	$-0.326033\pi$
$367$	2.68208e6	1.03946	0.519729	+	0.854331i	$0.326033\pi$
$368$	0	0
$369$	1.40697e6	0.537922
$370$	0	0
$371$	−3.43025e6	−1.29387
$372$	0	0
$373$	−1.43693e6	−0.534764	−0.267382	−	0.963591i	$-0.586159\pi$
$373$	−1.43693e6	−0.534764	−0.267382	+	0.963591i	$0.586159\pi$
$374$	0	0
$375$	−140625.	−0.0516398
$376$	0	0
$377$	691020.	0.250402
$378$	0	0
$379$	−4.04840e6	−1.44772	−0.723861	−	0.689946i	$-0.757634\pi$
$379$	−4.04840e6	−1.44772	−0.723861	+	0.689946i	$0.757634\pi$
$380$	0	0
$381$	2.16385e6	0.763687
$382$	0	0
$383$	−2.26304e6	−0.788308	−0.394154	−	0.919044i	$-0.628962\pi$
$383$	−2.26304e6	−0.788308	−0.394154	+	0.919044i	$0.628962\pi$
$384$	0	0
$385$	−568700.	−0.195538
$386$	0	0
$387$	−538812.	−0.182877
$388$	0	0
$389$	−3.67522e6	−1.23143	−0.615715	−	0.787969i	$-0.711133\pi$
$389$	−3.67522e6	−1.23143	−0.615715	+	0.787969i	$0.711133\pi$
$390$	0	0
$391$	4.42260e6	1.46297
$392$	0	0
$393$	2.23873e6	0.731174
$394$	0	0
$395$	−1.63250e6	−0.526454
$396$	0	0
$397$	−50722.0	−0.0161518	−0.00807588	−	0.999967i	$-0.502571\pi$
$397$	−50722.0	−0.0161518	−0.00807588	+	0.999967i	$0.502571\pi$
$398$	0	0
$399$	−4.10818e6	−1.29186
$400$	0	0
$401$	−2.92373e6	−0.907981	−0.453991	−	0.891006i	$-0.650000\pi$
$401$	−2.92373e6	−0.907981	−0.453991	+	0.891006i	$0.650000\pi$
$402$	0	0
$403$	89344.0	0.0274033
$404$	0	0
$405$	−164025.	−0.0496904
$406$	0	0
$407$	−387442.	−0.115937
$408$	0	0
$409$	6.01445e6	1.77782	0.888910	−	0.458082i	$-0.151464\pi$
$409$	6.01445e6	1.77782	0.888910	+	0.458082i	$0.151464\pi$
$410$	0	0
$411$	−209574.	−0.0611974
$412$	0	0
$413$	−1.62658e6	−0.469245
$414$	0	0
$415$	1.38270e6	0.394101
$416$	0	0
$417$	3.30649e6	0.931166
$418$	0	0
$419$	−4.35421e6	−1.21164	−0.605821	−	0.795601i	$-0.707155\pi$
$419$	−4.35421e6	−1.21164	−0.605821	+	0.795601i	$0.707155\pi$
$420$	0	0
$421$	2.53895e6	0.698150	0.349075	−	0.937095i	$-0.386496\pi$
$421$	2.53895e6	0.698150	0.349075	+	0.937095i	$0.386496\pi$
$422$	0	0
$423$	−2.02662e6	−0.550708
$424$	0	0
$425$	1.18125e6	0.317227
$426$	0	0
$427$	7.08422e6	1.88028
$428$	0	0
$429$	760122.	0.199407
$430$	0	0
$431$	−4.34069e6	−1.12555	−0.562776	−	0.826610i	$-0.690267\pi$
$431$	−4.34069e6	−1.12555	−0.562776	+	0.826610i	$0.690267\pi$
$432$	0	0
$433$	5.48467e6	1.40582	0.702912	−	0.711277i	$-0.251883\pi$
$433$	5.48467e6	1.40582	0.702912	+	0.711277i	$0.251883\pi$
$434$	0	0
$435$	−222750.	−0.0564410
$436$	0	0
$437$	−5.68152e6	−1.42318
$438$	0	0
$439$	−7.20039e6	−1.78318	−0.891589	−	0.452846i	$-0.850409\pi$
$439$	−7.20039e6	−1.78318	−0.891589	+	0.452846i	$0.850409\pi$
$440$	0	0
$441$	1.50150e6	0.367644
$442$	0	0
$443$	−1.83515e6	−0.444285	−0.222143	−	0.975014i	$-0.571305\pi$
$443$	−1.83515e6	−0.444285	−0.222143	+	0.975014i	$0.571305\pi$
$444$	0	0
$445$	1.62015e6	0.387842
$446$	0	0
$447$	13662.0	0.00323404
$448$	0	0
$449$	−1.24090e6	−0.290484	−0.145242	−	0.989396i	$-0.546396\pi$
$449$	−1.24090e6	−0.290484	−0.145242	+	0.989396i	$0.546396\pi$
$450$	0	0
$451$	2.10177e6	0.486568
$452$	0	0
$453$	−766404.	−0.175474
$454$	0	0
$455$	−3.28060e6	−0.742890
$456$	0	0
$457$	−8.50625e6	−1.90523	−0.952615	−	0.304178i	$-0.901618\pi$
$457$	−8.50625e6	−1.90523	−0.952615	+	0.304178i	$0.901618\pi$
$458$	0	0
$459$	1.37781e6	0.305251
$460$	0	0
$461$	−4.99891e6	−1.09553	−0.547763	−	0.836634i	$-0.684520\pi$
$461$	−4.99891e6	−1.09553	−0.547763	+	0.836634i	$0.684520\pi$
$462$	0	0
$463$	−5.77958e6	−1.25298	−0.626489	−	0.779430i	$-0.715509\pi$
$463$	−5.77958e6	−1.25298	−0.626489	+	0.779430i	$0.715509\pi$
$464$	0	0
$465$	−28800.0	−0.00617675
$466$	0	0
$467$	−2.07481e6	−0.440237	−0.220119	−	0.975473i	$-0.570644\pi$
$467$	−2.07481e6	−0.440237	−0.220119	+	0.975473i	$0.570644\pi$
$468$	0	0
$469$	−3.51109e6	−0.737071
$470$	0	0
$471$	−672066.	−0.139592
$472$	0	0
$473$	−804892.	−0.165419
$474$	0	0
$475$	−1.51750e6	−0.308599
$476$	0	0
$477$	−1.47793e6	−0.297411
$478$	0	0
$479$	4.62298e6	0.920625	0.460313	−	0.887757i	$-0.347737\pi$
$479$	4.62298e6	0.920625	0.460313	+	0.887757i	$0.347737\pi$
$480$	0	0
$481$	−2.23500e6	−0.440468
$482$	0	0
$483$	3.95928e6	0.772233
$484$	0	0
$485$	−957650.	−0.184864
$486$	0	0
$487$	−2.13501e6	−0.407922	−0.203961	−	0.978979i	$-0.565382\pi$
$487$	−2.13501e6	−0.407922	−0.203961	+	0.978979i	$0.565382\pi$
$488$	0	0
$489$	−1.43881e6	−0.272102
$490$	0	0
$491$	7.11198e6	1.33133	0.665667	−	0.746249i	$-0.268147\pi$
$491$	7.11198e6	1.33133	0.665667	+	0.746249i	$0.268147\pi$
$492$	0	0
$493$	1.87110e6	0.346721
$494$	0	0
$495$	−245025.	−0.0449467
$496$	0	0
$497$	−439920.	−0.0798882
$498$	0	0
$499$	−1.01274e7	−1.82074	−0.910370	−	0.413796i	$-0.864203\pi$
$499$	−1.01274e7	−1.82074	−0.910370	+	0.413796i	$0.864203\pi$
$500$	0	0
$501$	−4.70534e6	−0.837524
$502$	0	0
$503$	−201696.	−0.0355449	−0.0177725	−	0.999842i	$-0.505657\pi$
$503$	−201696.	−0.0355449	−0.0177725	+	0.999842i	$0.505657\pi$
$504$	0	0
$505$	4.23225e6	0.738487
$506$	0	0
$507$	1.04320e6	0.180238
$508$	0	0
$509$	6.97552e6	1.19339	0.596695	−	0.802468i	$-0.296480\pi$
$509$	6.97552e6	1.19339	0.596695	+	0.802468i	$0.296480\pi$
$510$	0	0
$511$	8.09490e6	1.37139
$512$	0	0
$513$	−1.77001e6	−0.296950
$514$	0	0
$515$	−3.67760e6	−0.611007
$516$	0	0
$517$	−3.02742e6	−0.498134
$518$	0	0
$519$	699462.	0.113984
$520$	0	0
$521$	−7.29267e6	−1.17704	−0.588521	−	0.808482i	$-0.700290\pi$
$521$	−7.29267e6	−1.17704	−0.588521	+	0.808482i	$0.700290\pi$
$522$	0	0
$523$	6.64293e6	1.06195	0.530977	−	0.847386i	$-0.321825\pi$
$523$	6.64293e6	1.06195	0.530977	+	0.847386i	$0.321825\pi$
$524$	0	0
$525$	1.05750e6	0.167449
$526$	0	0
$527$	241920.	0.0379442
$528$	0	0
$529$	−960743.	−0.149268
$530$	0	0
$531$	−700812.	−0.107861
$532$	0	0
$533$	1.21243e7	1.84858
$534$	0	0
$535$	1.20270e6	0.181666
$536$	0	0
$537$	−2.69903e6	−0.403898
$538$	0	0
$539$	2.24298e6	0.332547
$540$	0	0
$541$	−2.30853e6	−0.339112	−0.169556	−	0.985521i	$-0.554233\pi$
$541$	−2.30853e6	−0.339112	−0.169556	+	0.985521i	$0.554233\pi$
$542$	0	0
$543$	3150.00	0.000458470 0
$544$	0	0
$545$	−1.87625e6	−0.270582
$546$	0	0
$547$	−9.14552e6	−1.30689	−0.653446	−	0.756973i	$-0.726677\pi$
$547$	−9.14552e6	−1.30689	−0.653446	+	0.756973i	$0.726677\pi$
$548$	0	0
$549$	3.05224e6	0.432203
$550$	0	0
$551$	−2.40372e6	−0.337291
$552$	0	0
$553$	1.22764e7	1.70710
$554$	0	0
$555$	720450.	0.0992822
$556$	0	0
$557$	−2.03085e6	−0.277357	−0.138679	−	0.990337i	$-0.544286\pi$
$557$	−2.03085e6	−0.277357	−0.138679	+	0.990337i	$0.544286\pi$
$558$	0	0
$559$	−4.64310e6	−0.628461
$560$	0	0
$561$	2.05821e6	0.276110
$562$	0	0
$563$	−5.97176e6	−0.794020	−0.397010	−	0.917814i	$-0.629952\pi$
$563$	−5.97176e6	−0.794020	−0.397010	+	0.917814i	$0.629952\pi$
$564$	0	0
$565$	−4.02585e6	−0.530562
$566$	0	0
$567$	1.23347e6	0.161128
$568$	0	0
$569$	−4.40789e6	−0.570756	−0.285378	−	0.958415i	$-0.592119\pi$
$569$	−4.40789e6	−0.570756	−0.285378	+	0.958415i	$0.592119\pi$
$570$	0	0
$571$	6.84686e6	0.878823	0.439411	−	0.898286i	$-0.355187\pi$
$571$	6.84686e6	0.878823	0.439411	+	0.898286i	$0.355187\pi$
$572$	0	0
$573$	−3.93498e6	−0.500675
$574$	0	0
$575$	1.46250e6	0.184470
$576$	0	0
$577$	−1.13021e7	−1.41325	−0.706625	−	0.707589i	$-0.749783\pi$
$577$	−1.13021e7	−1.41325	−0.706625	+	0.707589i	$0.749783\pi$
$578$	0	0
$579$	5.26437e6	0.652604
$580$	0	0
$581$	−1.03979e7	−1.27793
$582$	0	0
$583$	−2.20777e6	−0.269018
$584$	0	0
$585$	−1.41345e6	−0.170762
$586$	0	0
$587$	−1.55865e7	−1.86704	−0.933521	−	0.358523i	$-0.883280\pi$
$587$	−1.55865e7	−1.86704	−0.933521	+	0.358523i	$0.883280\pi$
$588$	0	0
$589$	−310784.	−0.0369122
$590$	0	0
$591$	−3.89896e6	−0.459177
$592$	0	0
$593$	1.42591e6	0.166515	0.0832577	−	0.996528i	$-0.473468\pi$
$593$	1.42591e6	0.166515	0.0832577	+	0.996528i	$0.473468\pi$
$594$	0	0
$595$	−8.88300e6	−1.02865
$596$	0	0
$597$	1.01074e6	0.116065
$598$	0	0
$599$	1.85276e6	0.210986	0.105493	−	0.994420i	$-0.466358\pi$
$599$	1.85276e6	0.210986	0.105493	+	0.994420i	$0.466358\pi$
$600$	0	0
$601$	3.20211e6	0.361618	0.180809	−	0.983518i	$-0.442128\pi$
$601$	3.20211e6	0.361618	0.180809	+	0.983518i	$0.442128\pi$
$602$	0	0
$603$	−1.51276e6	−0.169424
$604$	0	0
$605$	−366025.	−0.0406558
$606$	0	0
$607$	−1.20352e7	−1.32581	−0.662905	−	0.748704i	$-0.730677\pi$
$607$	−1.20352e7	−1.32581	−0.662905	+	0.748704i	$0.730677\pi$
$608$	0	0
$609$	1.67508e6	0.183017
$610$	0	0
$611$	−1.74640e7	−1.89252
$612$	0	0
$613$	9.97567e6	1.07224	0.536119	−	0.844143i	$-0.319890\pi$
$613$	9.97567e6	1.07224	0.536119	+	0.844143i	$0.319890\pi$
$614$	0	0
$615$	−3.90825e6	−0.416672
$616$	0	0
$617$	2.81315e6	0.297496	0.148748	−	0.988875i	$-0.452476\pi$
$617$	2.81315e6	0.297496	0.148748	+	0.988875i	$0.452476\pi$
$618$	0	0
$619$	3.65553e6	0.383463	0.191732	−	0.981447i	$-0.438590\pi$
$619$	3.65553e6	0.383463	0.191732	+	0.981447i	$0.438590\pi$
$620$	0	0
$621$	1.70586e6	0.177507
$622$	0	0
$623$	−1.21835e7	−1.25763
$624$	0	0
$625$	390625.	0.0400000
$626$	0	0
$627$	−2.64409e6	−0.268601
$628$	0	0
$629$	−6.05178e6	−0.609897
$630$	0	0
$631$	8.85418e6	0.885269	0.442634	−	0.896702i	$-0.354044\pi$
$631$	8.85418e6	0.885269	0.442634	+	0.896702i	$0.354044\pi$
$632$	0	0
$633$	7.65457e6	0.759297
$634$	0	0
$635$	−6.01070e6	−0.591549
$636$	0	0
$637$	1.29388e7	1.26342
$638$	0	0
$639$	−189540.	−0.0183632
$640$	0	0
$641$	6.03969e6	0.580590	0.290295	−	0.956937i	$-0.406247\pi$
$641$	6.03969e6	0.580590	0.290295	+	0.956937i	$0.406247\pi$
$642$	0	0
$643$	−1.40178e7	−1.33706	−0.668531	−	0.743684i	$-0.733077\pi$
$643$	−1.40178e7	−1.33706	−0.668531	+	0.743684i	$0.733077\pi$
$644$	0	0
$645$	1.49670e6	0.141656
$646$	0	0
$647$	1.90558e7	1.78964	0.894821	−	0.446424i	$-0.147303\pi$
$647$	1.90558e7	1.78964	0.894821	+	0.446424i	$0.147303\pi$
$648$	0	0
$649$	−1.04689e6	−0.0975641
$650$	0	0
$651$	216576.	0.0200289
$652$	0	0
$653$	1.22124e7	1.12077	0.560387	−	0.828231i	$-0.310653\pi$
$653$	1.22124e7	1.12077	0.560387	+	0.828231i	$0.310653\pi$
$654$	0	0
$655$	−6.21870e6	−0.566365
$656$	0	0
$657$	3.48770e6	0.315228
$658$	0	0
$659$	4.36213e6	0.391278	0.195639	−	0.980676i	$-0.437322\pi$
$659$	4.36213e6	0.391278	0.195639	+	0.980676i	$0.437322\pi$
$660$	0	0
$661$	−9.70943e6	−0.864351	−0.432175	−	0.901790i	$-0.642254\pi$
$661$	−9.70943e6	−0.864351	−0.432175	+	0.901790i	$0.642254\pi$
$662$	0	0
$663$	1.18730e7	1.04900
$664$	0	0
$665$	1.14116e7	1.00067
$666$	0	0
$667$	2.31660e6	0.201621
$668$	0	0
$669$	−8.67600e6	−0.749470
$670$	0	0
$671$	4.55952e6	0.390943
$672$	0	0
$673$	1.67084e7	1.42199	0.710995	−	0.703197i	$-0.248245\pi$
$673$	1.67084e7	1.42199	0.710995	+	0.703197i	$0.248245\pi$
$674$	0	0
$675$	455625.	0.0384900
$676$	0	0
$677$	−7.03571e6	−0.589979	−0.294989	−	0.955501i	$-0.595316\pi$
$677$	−7.03571e6	−0.589979	−0.294989	+	0.955501i	$0.595316\pi$
$678$	0	0
$679$	7.20153e6	0.599446
$680$	0	0
$681$	4.58579e6	0.378919
$682$	0	0
$683$	−521148.	−0.0427474	−0.0213737	−	0.999772i	$-0.506804\pi$
$683$	−521148.	−0.0427474	−0.0213737	+	0.999772i	$0.506804\pi$
$684$	0	0
$685$	582150.	0.0474033
$686$	0	0
$687$	7.94072e6	0.641901
$688$	0	0
$689$	−1.27357e7	−1.02206
$690$	0	0
$691$	1.60093e7	1.27549	0.637744	−	0.770248i	$-0.279868\pi$
$691$	1.60093e7	1.27549	0.637744	+	0.770248i	$0.279868\pi$
$692$	0	0
$693$	1.84259e6	0.145745
$694$	0	0
$695$	−9.18470e6	−0.721278
$696$	0	0
$697$	3.28293e7	2.55964
$698$	0	0
$699$	4.73812e6	0.366786
$700$	0	0
$701$	1.84814e7	1.42050	0.710248	−	0.703952i	$-0.248583\pi$
$701$	1.84814e7	1.42050	0.710248	+	0.703952i	$0.248583\pi$
$702$	0	0
$703$	7.77446e6	0.593310
$704$	0	0
$705$	5.62950e6	0.426577
$706$	0	0
$707$	−3.18265e7	−2.39464
$708$	0	0
$709$	5.73270e6	0.428296	0.214148	−	0.976801i	$-0.431303\pi$
$709$	5.73270e6	0.428296	0.214148	+	0.976801i	$0.431303\pi$
$710$	0	0
$711$	5.28930e6	0.392396
$712$	0	0
$713$	299520.	0.0220649
$714$	0	0
$715$	−2.11145e6	−0.154460
$716$	0	0
$717$	9.67961e6	0.703169
$718$	0	0
$719$	−4.23808e6	−0.305736	−0.152868	−	0.988247i	$-0.548851\pi$
$719$	−4.23808e6	−0.305736	−0.152868	+	0.988247i	$0.548851\pi$
$720$	0	0
$721$	2.76556e7	1.98127
$722$	0	0
$723$	9.15345e6	0.651237
$724$	0	0
$725$	618750.	0.0437190
$726$	0	0
$727$	2.40063e7	1.68457	0.842284	−	0.539034i	$-0.181210\pi$
$727$	2.40063e7	1.68457	0.842284	+	0.539034i	$0.181210\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−1.25723e7	−0.870203
$732$	0	0
$733$	−2.15768e7	−1.48329	−0.741646	−	0.670791i	$-0.765955\pi$
$733$	−2.15768e7	−1.48329	−0.741646	+	0.670791i	$0.765955\pi$
$734$	0	0
$735$	−4.17082e6	−0.284776
$736$	0	0
$737$	−2.25980e6	−0.153250
$738$	0	0
$739$	−3.63576e6	−0.244898	−0.122449	−	0.992475i	$-0.539075\pi$
$739$	−3.63576e6	−0.244898	−0.122449	+	0.992475i	$0.539075\pi$
$740$	0	0
$741$	−1.52527e7	−1.02047
$742$	0	0
$743$	−2.55861e7	−1.70032	−0.850162	−	0.526522i	$-0.823496\pi$
$743$	−2.55861e7	−1.70032	−0.850162	+	0.526522i	$0.823496\pi$
$744$	0	0
$745$	−37950.0	−0.00250508
$746$	0	0
$747$	−4.47995e6	−0.293746
$748$	0	0
$749$	−9.04430e6	−0.589075
$750$	0	0
$751$	−1.06821e7	−0.691127	−0.345564	−	0.938395i	$-0.612312\pi$
$751$	−1.06821e7	−0.691127	−0.345564	+	0.938395i	$0.612312\pi$
$752$	0	0
$753$	48708.0	0.00313049
$754$	0	0
$755$	2.12890e6	0.135921
$756$	0	0
$757$	1.98831e7	1.26108	0.630541	−	0.776156i	$-0.282833\pi$
$757$	1.98831e7	1.26108	0.630541	+	0.776156i	$0.282833\pi$
$758$	0	0
$759$	2.54826e6	0.160561
$760$	0	0
$761$	7.78564e6	0.487341	0.243670	−	0.969858i	$-0.421648\pi$
$761$	7.78564e6	0.487341	0.243670	+	0.969858i	$0.421648\pi$
$762$	0	0
$763$	1.41094e7	0.877399
$764$	0	0
$765$	−3.82725e6	−0.236447
$766$	0	0
$767$	−6.03910e6	−0.370667
$768$	0	0
$769$	−1.85366e7	−1.13035	−0.565177	−	0.824970i	$-0.691192\pi$
$769$	−1.85366e7	−1.13035	−0.565177	+	0.824970i	$0.691192\pi$
$770$	0	0
$771$	−5.25058e6	−0.318106
$772$	0	0
$773$	2.39267e7	1.44024	0.720119	−	0.693851i	$-0.244087\pi$
$773$	2.39267e7	1.44024	0.720119	+	0.693851i	$0.244087\pi$
$774$	0	0
$775$	80000.0	0.00478449
$776$	0	0
$777$	−5.41778e6	−0.321936
$778$	0	0
$779$	−4.21744e7	−2.49003
$780$	0	0
$781$	−283140.	−0.0166102
$782$	0	0
$783$	721710.	0.0420686
$784$	0	0
$785$	1.86685e6	0.108127
$786$	0	0
$787$	−2.90401e7	−1.67132	−0.835662	−	0.549244i	$-0.814916\pi$
$787$	−2.90401e7	−1.67132	−0.835662	+	0.549244i	$0.814916\pi$
$788$	0	0
$789$	1.56265e7	0.893655
$790$	0	0
$791$	3.02744e7	1.72042
$792$	0	0
$793$	2.63020e7	1.48527
$794$	0	0
$795$	4.10535e6	0.230373
$796$	0	0
$797$	−1.39169e6	−0.0776065	−0.0388032	−	0.999247i	$-0.512355\pi$
$797$	−1.39169e6	−0.0776065	−0.0388032	+	0.999247i	$0.512355\pi$
$798$	0	0
$799$	−4.72878e7	−2.62049
$800$	0	0
$801$	−5.24929e6	−0.289081
$802$	0	0
$803$	5.21002e6	0.285135
$804$	0	0
$805$	−1.09980e7	−0.598169
$806$	0	0
$807$	−5.50611e6	−0.297619
$808$	0	0
$809$	−3.28839e7	−1.76649	−0.883247	−	0.468909i	$-0.844647\pi$
$809$	−3.28839e7	−1.76649	−0.883247	+	0.468909i	$0.844647\pi$
$810$	0	0
$811$	1.44206e7	0.769895	0.384948	−	0.922938i	$-0.374220\pi$
$811$	1.44206e7	0.769895	0.384948	+	0.922938i	$0.374220\pi$
$812$	0	0
$813$	1.89613e7	1.00610
$814$	0	0
$815$	3.99670e6	0.210769
$816$	0	0
$817$	1.61511e7	0.846537
$818$	0	0
$819$	1.06291e7	0.553718
$820$	0	0
$821$	1.58518e7	0.820767	0.410383	−	0.911913i	$-0.365395\pi$
$821$	1.58518e7	0.820767	0.410383	+	0.911913i	$0.365395\pi$
$822$	0	0
$823$	1.26517e7	0.651103	0.325551	−	0.945524i	$-0.394450\pi$
$823$	1.26517e7	0.651103	0.325551	+	0.945524i	$0.394450\pi$
$824$	0	0
$825$	680625.	0.0348155
$826$	0	0
$827$	−3.53133e7	−1.79546	−0.897729	−	0.440549i	$-0.854784\pi$
$827$	−3.53133e7	−1.79546	−0.897729	+	0.440549i	$0.854784\pi$
$828$	0	0
$829$	−1.28637e7	−0.650099	−0.325050	−	0.945697i	$-0.605381\pi$
$829$	−1.28637e7	−0.650099	−0.325050	+	0.945697i	$0.605381\pi$
$830$	0	0
$831$	1.01000e7	0.507361
$832$	0	0
$833$	3.50349e7	1.74940
$834$	0	0
$835$	1.30704e7	0.648743
$836$	0	0
$837$	93312.0	0.00460388
$838$	0	0
$839$	−4.76444e6	−0.233672	−0.116836	−	0.993151i	$-0.537275\pi$
$839$	−4.76444e6	−0.233672	−0.116836	+	0.993151i	$0.537275\pi$
$840$	0	0
$841$	−1.95310e7	−0.952216
$842$	0	0
$843$	1.35958e7	0.658927
$844$	0	0
$845$	−2.89777e6	−0.139612
$846$	0	0
$847$	2.75251e6	0.131832
$848$	0	0
$849$	−108684.	−0.00517483
$850$	0	0
$851$	−7.49268e6	−0.354661
$852$	0	0
$853$	−3.70508e7	−1.74351	−0.871756	−	0.489940i	$-0.837019\pi$
$853$	−3.70508e7	−1.74351	−0.871756	+	0.489940i	$0.837019\pi$
$854$	0	0
$855$	4.91670e6	0.230016
$856$	0	0
$857$	612282.	0.0284773	0.0142387	−	0.999899i	$-0.495468\pi$
$857$	612282.	0.0284773	0.0142387	+	0.999899i	$0.495468\pi$
$858$	0	0
$859$	2.15110e7	0.994666	0.497333	−	0.867560i	$-0.334313\pi$
$859$	2.15110e7	0.994666	0.497333	+	0.867560i	$0.334313\pi$
$860$	0	0
$861$	2.93900e7	1.35111
$862$	0	0
$863$	1.79713e7	0.821395	0.410698	−	0.911772i	$-0.365285\pi$
$863$	1.79713e7	0.821395	0.410698	+	0.911772i	$0.365285\pi$
$864$	0	0
$865$	−1.94295e6	−0.0882920
$866$	0	0
$867$	1.93702e7	0.875157
$868$	0	0
$869$	7.90130e6	0.354935
$870$	0	0
$871$	−1.30358e7	−0.582229
$872$	0	0
$873$	3.10279e6	0.137790
$874$	0	0
$875$	−2.93750e6	−0.129705
$876$	0	0
$877$	8.52348e6	0.374212	0.187106	−	0.982340i	$-0.440089\pi$
$877$	8.52348e6	0.374212	0.187106	+	0.982340i	$0.440089\pi$
$878$	0	0
$879$	−6.06523e6	−0.264774
$880$	0	0
$881$	−3.79568e6	−0.164759	−0.0823796	−	0.996601i	$-0.526252\pi$
$881$	−3.79568e6	−0.164759	−0.0823796	+	0.996601i	$0.526252\pi$
$882$	0	0
$883$	3.65570e7	1.57786	0.788931	−	0.614481i	$-0.210635\pi$
$883$	3.65570e7	1.57786	0.788931	+	0.614481i	$0.210635\pi$
$884$	0	0
$885$	1.94670e6	0.0835489
$886$	0	0
$887$	−1.52505e7	−0.650840	−0.325420	−	0.945570i	$-0.605506\pi$
$887$	−1.52505e7	−0.650840	−0.325420	+	0.945570i	$0.605506\pi$
$888$	0	0
$889$	4.52005e7	1.91818
$890$	0	0
$891$	793881.	0.0335013
$892$	0	0
$893$	6.07486e7	2.54922
$894$	0	0
$895$	7.49730e6	0.312858
$896$	0	0
$897$	1.46999e7	0.610004
$898$	0	0
$899$	126720.	0.00522933
$900$	0	0
$901$	−3.44849e7	−1.41520
$902$	0	0
$903$	−1.12552e7	−0.459339
$904$	0	0
$905$	−8750.00	−0.000355129 0
$906$	0	0
$907$	2.18551e7	0.882134	0.441067	−	0.897474i	$-0.354600\pi$
$907$	2.18551e7	0.882134	0.441067	+	0.897474i	$0.354600\pi$
$908$	0	0
$909$	−1.37125e7	−0.550436
$910$	0	0
$911$	−1.44376e7	−0.576369	−0.288184	−	0.957575i	$-0.593052\pi$
$911$	−1.44376e7	−0.576369	−0.288184	+	0.957575i	$0.593052\pi$
$912$	0	0
$913$	−6.69227e6	−0.265703
$914$	0	0
$915$	−8.47845e6	−0.334783
$916$	0	0
$917$	4.67646e7	1.83651
$918$	0	0
$919$	−1.94539e7	−0.759833	−0.379916	−	0.925021i	$-0.624047\pi$
$919$	−1.94539e7	−0.759833	−0.379916	+	0.925021i	$0.624047\pi$
$920$	0	0
$921$	−1.70838e6	−0.0663644
$922$	0	0
$923$	−1.63332e6	−0.0631055
$924$	0	0
$925$	−2.00125e6	−0.0769037
$926$	0	0
$927$	1.19154e7	0.455418
$928$	0	0
$929$	−3.91051e7	−1.48660	−0.743300	−	0.668958i	$-0.766741\pi$
$929$	−3.91051e7	−1.48660	−0.743300	+	0.668958i	$0.766741\pi$
$930$	0	0
$931$	−4.50078e7	−1.70182
$932$	0	0
$933$	−1.29711e7	−0.487836
$934$	0	0
$935$	−5.71725e6	−0.213874
$936$	0	0
$937$	−2.58129e6	−0.0960480	−0.0480240	−	0.998846i	$-0.515292\pi$
$937$	−2.58129e6	−0.0960480	−0.0480240	+	0.998846i	$0.515292\pi$
$938$	0	0
$939$	−8.18055e6	−0.302774
$940$	0	0
$941$	3.46880e7	1.27704	0.638522	−	0.769604i	$-0.279546\pi$
$941$	3.46880e7	1.27704	0.638522	+	0.769604i	$0.279546\pi$
$942$	0	0
$943$	4.06458e7	1.48846
$944$	0	0
$945$	−3.42630e6	−0.124809
$946$	0	0
$947$	−3.62410e7	−1.31318	−0.656591	−	0.754247i	$-0.728002\pi$
$947$	−3.62410e7	−1.31318	−0.656591	+	0.754247i	$0.728002\pi$
$948$	0	0
$949$	3.00545e7	1.08329
$950$	0	0
$951$	2.52832e7	0.906526
$952$	0	0
$953$	−1.60198e7	−0.571380	−0.285690	−	0.958322i	$-0.592223\pi$
$953$	−1.60198e7	−0.571380	−0.285690	+	0.958322i	$0.592223\pi$
$954$	0	0
$955$	1.09305e7	0.387821
$956$	0	0
$957$	1.07811e6	0.0380525
$958$	0	0
$959$	−4.37777e6	−0.153711
$960$	0	0
$961$	−2.86128e7	−0.999428
$962$	0	0
$963$	−3.89675e6	−0.135406
$964$	0	0
$965$	−1.46232e7	−0.505505
$966$	0	0
$967$	−1.64023e7	−0.564079	−0.282039	−	0.959403i	$-0.591011\pi$
$967$	−1.64023e7	−0.564079	−0.282039	+	0.959403i	$0.591011\pi$
$968$	0	0
$969$	−4.13003e7	−1.41300
$970$	0	0
$971$	2.45247e7	0.834748	0.417374	−	0.908735i	$-0.362951\pi$
$971$	2.45247e7	0.834748	0.417374	+	0.908735i	$0.362951\pi$
$972$	0	0
$973$	6.90689e7	2.33884
$974$	0	0
$975$	3.92625e6	0.132272
$976$	0	0
$977$	2.87179e7	0.962536	0.481268	−	0.876574i	$-0.340176\pi$
$977$	2.87179e7	0.962536	0.481268	+	0.876574i	$0.340176\pi$
$978$	0	0
$979$	−7.84153e6	−0.261483
$980$	0	0
$981$	6.07905e6	0.201680
$982$	0	0
$983$	−7.19622e6	−0.237531	−0.118766	−	0.992922i	$-0.537894\pi$
$983$	−7.19622e6	−0.237531	−0.118766	+	0.992922i	$0.537894\pi$
$984$	0	0
$985$	1.08304e7	0.355677
$986$	0	0
$987$	−4.23338e7	−1.38323
$988$	0	0
$989$	−1.55657e7	−0.506031
$990$	0	0
$991$	3.36560e7	1.08863	0.544313	−	0.838882i	$-0.316790\pi$
$991$	3.36560e7	1.08863	0.544313	+	0.838882i	$0.316790\pi$
$992$	0	0
$993$	−1.72815e7	−0.556173
$994$	0	0
$995$	−2.80760e6	−0.0899037
$996$	0	0
$997$	3.06471e7	0.976455	0.488227	−	0.872717i	$-0.337644\pi$
$997$	3.06471e7	0.976455	0.488227	+	0.872717i	$0.337644\pi$
$998$	0	0
$999$	−2.33426e6	−0.0740006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	660.6.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.6.a.a.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	660.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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