LMFDB - Embedded newform 912.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,6,Mod(1,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, 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("912.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	912.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:	$146.270043669$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	912.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-9.00000 q^{3} -54.0000 q^{5} -104.000 q^{7} +81.0000 q^{9} +330.000 q^{11} -46.0000 q^{13} +486.000 q^{15} -618.000 q^{17} -361.000 q^{19} +936.000 q^{21} +402.000 q^{23} -209.000 q^{25} -729.000 q^{27} -2628.00 q^{29} +2368.00 q^{31} -2970.00 q^{33} +5616.00 q^{35} -12130.0 q^{37} +414.000 q^{39} -18864.0 q^{41} +10408.0 q^{43} -4374.00 q^{45} +4770.00 q^{47} -5991.00 q^{49} +5562.00 q^{51} -19452.0 q^{53} -17820.0 q^{55} +3249.00 q^{57} -30528.0 q^{59} +11138.0 q^{61} -8424.00 q^{63} +2484.00 q^{65} -49508.0 q^{67} -3618.00 q^{69} -7572.00 q^{71} +2342.00 q^{73} +1881.00 q^{75} -34320.0 q^{77} -22424.0 q^{79} +6561.00 q^{81} +46734.0 q^{83} +33372.0 q^{85} +23652.0 q^{87} -70104.0 q^{89} +4784.00 q^{91} -21312.0 q^{93} +19494.0 q^{95} +105710. q^{97} +26730.0 q^{99} +O(q^{100})$

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
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	0	0
$5$	−54.0000	−0.965981	−0.482991	−	0.875625i	$-0.660450\pi$
$5$	−54.0000	−0.965981	−0.482991	+	0.875625i	$0.660450\pi$
$6$	0	0
$7$	−104.000	−0.802210	−0.401105	−	0.916032i	$-0.631374\pi$
$7$	−104.000	−0.802210	−0.401105	+	0.916032i	$0.631374\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	330.000	0.822304	0.411152	−	0.911567i	$-0.365127\pi$
$11$	330.000	0.822304	0.411152	+	0.911567i	$0.365127\pi$
$12$	0	0
$13$	−46.0000	−0.0754917	−0.0377459	−	0.999287i	$-0.512018\pi$
$13$	−46.0000	−0.0754917	−0.0377459	+	0.999287i	$0.512018\pi$
$14$	0	0
$15$	486.000	0.557710
$16$	0	0
$17$	−618.000	−0.518640	−0.259320	−	0.965791i	$-0.583498\pi$
$17$	−618.000	−0.518640	−0.259320	+	0.965791i	$0.583498\pi$
$18$	0	0
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	0	0
$21$	936.000	0.463156
$22$	0	0
$23$	402.000	0.158455	0.0792276	−	0.996857i	$-0.474755\pi$
$23$	402.000	0.158455	0.0792276	+	0.996857i	$0.474755\pi$
$24$	0	0
$25$	−209.000	−0.0668800
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	−2628.00	−0.580270	−0.290135	−	0.956986i	$-0.593700\pi$
$29$	−2628.00	−0.580270	−0.290135	+	0.956986i	$0.593700\pi$
$30$	0	0
$31$	2368.00	0.442565	0.221283	−	0.975210i	$-0.428976\pi$
$31$	2368.00	0.442565	0.221283	+	0.975210i	$0.428976\pi$
$32$	0	0
$33$	−2970.00	−0.474757
$34$	0	0
$35$	5616.00	0.774920
$36$	0	0
$37$	−12130.0	−1.45665	−0.728327	−	0.685230i	$-0.759702\pi$
$37$	−12130.0	−1.45665	−0.728327	+	0.685230i	$0.759702\pi$
$38$	0	0
$39$	414.000	0.0435852
$40$	0	0
$41$	−18864.0	−1.75257	−0.876283	−	0.481798i	$-0.839984\pi$
$41$	−18864.0	−1.75257	−0.876283	+	0.481798i	$0.839984\pi$
$42$	0	0
$43$	10408.0	0.858413	0.429206	−	0.903206i	$-0.358793\pi$
$43$	10408.0	0.858413	0.429206	+	0.903206i	$0.358793\pi$
$44$	0	0
$45$	−4374.00	−0.321994
$46$	0	0
$47$	4770.00	0.314973	0.157487	−	0.987521i	$-0.449661\pi$
$47$	4770.00	0.314973	0.157487	+	0.987521i	$0.449661\pi$
$48$	0	0
$49$	−5991.00	−0.356459
$50$	0	0
$51$	5562.00	0.299437
$52$	0	0
$53$	−19452.0	−0.951206	−0.475603	−	0.879660i	$-0.657770\pi$
$53$	−19452.0	−0.951206	−0.475603	+	0.879660i	$0.657770\pi$
$54$	0	0
$55$	−17820.0	−0.794330
$56$	0	0
$57$	3249.00	0.132453
$58$	0	0
$59$	−30528.0	−1.14174	−0.570871	−	0.821039i	$-0.693395\pi$
$59$	−30528.0	−1.14174	−0.570871	+	0.821039i	$0.693395\pi$
$60$	0	0
$61$	11138.0	0.383250	0.191625	−	0.981468i	$-0.438624\pi$
$61$	11138.0	0.383250	0.191625	+	0.981468i	$0.438624\pi$
$62$	0	0
$63$	−8424.00	−0.267403
$64$	0	0
$65$	2484.00	0.0729236
$66$	0	0
$67$	−49508.0	−1.34737	−0.673687	−	0.739016i	$-0.735291\pi$
$67$	−49508.0	−1.34737	−0.673687	+	0.739016i	$0.735291\pi$
$68$	0	0
$69$	−3618.00	−0.0914841
$70$	0	0
$71$	−7572.00	−0.178264	−0.0891322	−	0.996020i	$-0.528409\pi$
$71$	−7572.00	−0.178264	−0.0891322	+	0.996020i	$0.528409\pi$
$72$	0	0
$73$	2342.00	0.0514375	0.0257187	−	0.999669i	$-0.491813\pi$
$73$	2342.00	0.0514375	0.0257187	+	0.999669i	$0.491813\pi$
$74$	0	0
$75$	1881.00	0.0386132
$76$	0	0
$77$	−34320.0	−0.659660
$78$	0	0
$79$	−22424.0	−0.404246	−0.202123	−	0.979360i	$-0.564784\pi$
$79$	−22424.0	−0.404246	−0.202123	+	0.979360i	$0.564784\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	46734.0	0.744625	0.372313	−	0.928107i	$-0.378565\pi$
$83$	46734.0	0.744625	0.372313	+	0.928107i	$0.378565\pi$
$84$	0	0
$85$	33372.0	0.500997
$86$	0	0
$87$	23652.0	0.335019
$88$	0	0
$89$	−70104.0	−0.938140	−0.469070	−	0.883161i	$-0.655411\pi$
$89$	−70104.0	−0.938140	−0.469070	+	0.883161i	$0.655411\pi$
$90$	0	0
$91$	4784.00	0.0605603
$92$	0	0
$93$	−21312.0	−0.255515
$94$	0	0
$95$	19494.0	0.221611
$96$	0	0
$97$	105710.	1.14074	0.570370	−	0.821388i	$-0.306800\pi$
$97$	105710.	1.14074	0.570370	+	0.821388i	$0.306800\pi$
$98$	0	0
$99$	26730.0	0.274101
$100$	0	0
$101$	124542.	1.21482	0.607411	−	0.794388i	$-0.292208\pi$
$101$	124542.	1.21482	0.607411	+	0.794388i	$0.292208\pi$
$102$	0	0
$103$	−6488.00	−0.0602584	−0.0301292	−	0.999546i	$-0.509592\pi$
$103$	−6488.00	−0.0602584	−0.0301292	+	0.999546i	$0.509592\pi$
$104$	0	0
$105$	−50544.0	−0.447400
$106$	0	0
$107$	−50040.0	−0.422530	−0.211265	−	0.977429i	$-0.567758\pi$
$107$	−50040.0	−0.422530	−0.211265	+	0.977429i	$0.567758\pi$
$108$	0	0
$109$	88706.0	0.715133	0.357566	−	0.933888i	$-0.383607\pi$
$109$	88706.0	0.715133	0.357566	+	0.933888i	$0.383607\pi$
$110$	0	0
$111$	109170.	0.841000
$112$	0	0
$113$	−156792.	−1.15512	−0.577561	−	0.816348i	$-0.695995\pi$
$113$	−156792.	−1.15512	−0.577561	+	0.816348i	$0.695995\pi$
$114$	0	0
$115$	−21708.0	−0.153065
$116$	0	0
$117$	−3726.00	−0.0251639
$118$	0	0
$119$	64272.0	0.416059
$120$	0	0
$121$	−52151.0	−0.323817
$122$	0	0
$123$	169776.	1.01184
$124$	0	0
$125$	180036.	1.03059
$126$	0	0
$127$	211768.	1.16507	0.582534	−	0.812807i	$-0.302061\pi$
$127$	211768.	1.16507	0.582534	+	0.812807i	$0.302061\pi$
$128$	0	0
$129$	−93672.0	−0.495605
$130$	0	0
$131$	4410.00	0.0224523	0.0112261	−	0.999937i	$-0.496427\pi$
$131$	4410.00	0.0224523	0.0112261	+	0.999937i	$0.496427\pi$
$132$	0	0
$133$	37544.0	0.184040
$134$	0	0
$135$	39366.0	0.185903
$136$	0	0
$137$	205974.	0.937586	0.468793	−	0.883308i	$-0.344689\pi$
$137$	205974.	0.937586	0.468793	+	0.883308i	$0.344689\pi$
$138$	0	0
$139$	−315908.	−1.38683	−0.693416	−	0.720538i	$-0.743895\pi$
$139$	−315908.	−1.38683	−0.693416	+	0.720538i	$0.743895\pi$
$140$	0	0
$141$	−42930.0	−0.181850
$142$	0	0
$143$	−15180.0	−0.0620771
$144$	0	0
$145$	141912.	0.560530
$146$	0	0
$147$	53919.0	0.205801
$148$	0	0
$149$	211158.	0.779187	0.389594	−	0.920987i	$-0.372615\pi$
$149$	211158.	0.779187	0.389594	+	0.920987i	$0.372615\pi$
$150$	0	0
$151$	118120.	0.421581	0.210791	−	0.977531i	$-0.432396\pi$
$151$	118120.	0.421581	0.210791	+	0.977531i	$0.432396\pi$
$152$	0	0
$153$	−50058.0	−0.172880
$154$	0	0
$155$	−127872.	−0.427510
$156$	0	0
$157$	−163990.	−0.530968	−0.265484	−	0.964115i	$-0.585532\pi$
$157$	−163990.	−0.530968	−0.265484	+	0.964115i	$0.585532\pi$
$158$	0	0
$159$	175068.	0.549179
$160$	0	0
$161$	−41808.0	−0.127114
$162$	0	0
$163$	−26948.0	−0.0794433	−0.0397217	−	0.999211i	$-0.512647\pi$
$163$	−26948.0	−0.0794433	−0.0397217	+	0.999211i	$0.512647\pi$
$164$	0	0
$165$	160380.	0.458607
$166$	0	0
$167$	−5808.00	−0.0161152	−0.00805759	−	0.999968i	$-0.502565\pi$
$167$	−5808.00	−0.0161152	−0.00805759	+	0.999968i	$0.502565\pi$
$168$	0	0
$169$	−369177.	−0.994301
$170$	0	0
$171$	−29241.0	−0.0764719
$172$	0	0
$173$	37104.0	0.0942552	0.0471276	−	0.998889i	$-0.484993\pi$
$173$	37104.0	0.0942552	0.0471276	+	0.998889i	$0.484993\pi$
$174$	0	0
$175$	21736.0	0.0536518
$176$	0	0
$177$	274752.	0.659186
$178$	0	0
$179$	−198360.	−0.462723	−0.231362	−	0.972868i	$-0.574318\pi$
$179$	−198360.	−0.462723	−0.231362	+	0.972868i	$0.574318\pi$
$180$	0	0
$181$	−276838.	−0.628101	−0.314050	−	0.949406i	$-0.601686\pi$
$181$	−276838.	−0.628101	−0.314050	+	0.949406i	$0.601686\pi$
$182$	0	0
$183$	−100242.	−0.221270
$184$	0	0
$185$	655020.	1.40710
$186$	0	0
$187$	−203940.	−0.426480
$188$	0	0
$189$	75816.0	0.154385
$190$	0	0
$191$	531222.	1.05364	0.526820	−	0.849977i	$-0.323384\pi$
$191$	531222.	1.05364	0.526820	+	0.849977i	$0.323384\pi$
$192$	0	0
$193$	−245062.	−0.473568	−0.236784	−	0.971562i	$-0.576093\pi$
$193$	−245062.	−0.473568	−0.236784	+	0.971562i	$0.576093\pi$
$194$	0	0
$195$	−22356.0	−0.0421025
$196$	0	0
$197$	219906.	0.403712	0.201856	−	0.979415i	$-0.435303\pi$
$197$	219906.	0.403712	0.201856	+	0.979415i	$0.435303\pi$
$198$	0	0
$199$	1.01820e6	1.82265	0.911323	−	0.411693i	$-0.135062\pi$
$199$	1.01820e6	1.82265	0.911323	+	0.411693i	$0.135062\pi$
$200$	0	0
$201$	445572.	0.777907
$202$	0	0
$203$	273312.	0.465499
$204$	0	0
$205$	1.01866e6	1.69295
$206$	0	0
$207$	32562.0	0.0528184
$208$	0	0
$209$	−119130.	−0.188649
$210$	0	0
$211$	−105020.	−0.162392	−0.0811962	−	0.996698i	$-0.525874\pi$
$211$	−105020.	−0.162392	−0.0811962	+	0.996698i	$0.525874\pi$
$212$	0	0
$213$	68148.0	0.102921
$214$	0	0
$215$	−562032.	−0.829211
$216$	0	0
$217$	−246272.	−0.355031
$218$	0	0
$219$	−21078.0	−0.0296974
$220$	0	0
$221$	28428.0	0.0391531
$222$	0	0
$223$	−988304.	−1.33085	−0.665424	−	0.746466i	$-0.731749\pi$
$223$	−988304.	−1.33085	−0.665424	+	0.746466i	$0.731749\pi$
$224$	0	0
$225$	−16929.0	−0.0222933
$226$	0	0
$227$	515940.	0.664561	0.332280	−	0.943181i	$-0.392182\pi$
$227$	515940.	0.664561	0.332280	+	0.943181i	$0.392182\pi$
$228$	0	0
$229$	−277354.	−0.349499	−0.174749	−	0.984613i	$-0.555912\pi$
$229$	−277354.	−0.349499	−0.174749	+	0.984613i	$0.555912\pi$
$230$	0	0
$231$	308880.	0.380855
$232$	0	0
$233$	1.54151e6	1.86019	0.930096	−	0.367317i	$-0.119724\pi$
$233$	1.54151e6	1.86019	0.930096	+	0.367317i	$0.119724\pi$
$234$	0	0
$235$	−257580.	−0.304258
$236$	0	0
$237$	201816.	0.233391
$238$	0	0
$239$	314310.	0.355929	0.177965	−	0.984037i	$-0.443049\pi$
$239$	314310.	0.355929	0.177965	+	0.984037i	$0.443049\pi$
$240$	0	0
$241$	24566.0	0.0272453	0.0136227	−	0.999907i	$-0.495664\pi$
$241$	24566.0	0.0272453	0.0136227	+	0.999907i	$0.495664\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	323514.	0.344332
$246$	0	0
$247$	16606.0	0.0173190
$248$	0	0
$249$	−420606.	−0.429910
$250$	0	0
$251$	−661290.	−0.662533	−0.331267	−	0.943537i	$-0.607476\pi$
$251$	−661290.	−0.662533	−0.331267	+	0.943537i	$0.607476\pi$
$252$	0	0
$253$	132660.	0.130298
$254$	0	0
$255$	−300348.	−0.289251
$256$	0	0
$257$	1.05035e6	0.991974	0.495987	−	0.868330i	$-0.334806\pi$
$257$	1.05035e6	0.991974	0.495987	+	0.868330i	$0.334806\pi$
$258$	0	0
$259$	1.26152e6	1.16854
$260$	0	0
$261$	−212868.	−0.193423
$262$	0	0
$263$	465510.	0.414992	0.207496	−	0.978236i	$-0.433469\pi$
$263$	465510.	0.414992	0.207496	+	0.978236i	$0.433469\pi$
$264$	0	0
$265$	1.05041e6	0.918847
$266$	0	0
$267$	630936.	0.541636
$268$	0	0
$269$	−317112.	−0.267197	−0.133599	−	0.991036i	$-0.542653\pi$
$269$	−317112.	−0.267197	−0.133599	+	0.991036i	$0.542653\pi$
$270$	0	0
$271$	1.48901e6	1.23162	0.615808	−	0.787897i	$-0.288830\pi$
$271$	1.48901e6	1.23162	0.615808	+	0.787897i	$0.288830\pi$
$272$	0	0
$273$	−43056.0	−0.0349645
$274$	0	0
$275$	−68970.0	−0.0549957
$276$	0	0
$277$	−1.54028e6	−1.20615	−0.603074	−	0.797685i	$-0.706058\pi$
$277$	−1.54028e6	−1.20615	−0.603074	+	0.797685i	$0.706058\pi$
$278$	0	0
$279$	191808.	0.147522
$280$	0	0
$281$	1.99595e6	1.50794	0.753969	−	0.656910i	$-0.228137\pi$
$281$	1.99595e6	1.50794	0.753969	+	0.656910i	$0.228137\pi$
$282$	0	0
$283$	946936.	0.702837	0.351418	−	0.936219i	$-0.385699\pi$
$283$	946936.	0.702837	0.351418	+	0.936219i	$0.385699\pi$
$284$	0	0
$285$	−175446.	−0.127947
$286$	0	0
$287$	1.96186e6	1.40593
$288$	0	0
$289$	−1.03793e6	−0.731012
$290$	0	0
$291$	−951390.	−0.658607
$292$	0	0
$293$	2.18170e6	1.48465	0.742327	−	0.670038i	$-0.233722\pi$
$293$	2.18170e6	1.48465	0.742327	+	0.670038i	$0.233722\pi$
$294$	0	0
$295$	1.64851e6	1.10290
$296$	0	0
$297$	−240570.	−0.158252
$298$	0	0
$299$	−18492.0	−0.0119621
$300$	0	0
$301$	−1.08243e6	−0.688628
$302$	0	0
$303$	−1.12088e6	−0.701377
$304$	0	0
$305$	−601452.	−0.370213
$306$	0	0
$307$	2.50414e6	1.51640	0.758198	−	0.652024i	$-0.226080\pi$
$307$	2.50414e6	1.51640	0.758198	+	0.652024i	$0.226080\pi$
$308$	0	0
$309$	58392.0	0.0347902
$310$	0	0
$311$	785658.	0.460609	0.230305	−	0.973119i	$-0.426028\pi$
$311$	785658.	0.460609	0.230305	+	0.973119i	$0.426028\pi$
$312$	0	0
$313$	364334.	0.210203	0.105101	−	0.994462i	$-0.466483\pi$
$313$	364334.	0.210203	0.105101	+	0.994462i	$0.466483\pi$
$314$	0	0
$315$	454896.	0.258307
$316$	0	0
$317$	−1.46938e6	−0.821268	−0.410634	−	0.911800i	$-0.634693\pi$
$317$	−1.46938e6	−0.821268	−0.410634	+	0.911800i	$0.634693\pi$
$318$	0	0
$319$	−867240.	−0.477158
$320$	0	0
$321$	450360.	0.243948
$322$	0	0
$323$	223098.	0.118984
$324$	0	0
$325$	9614.00	0.00504889
$326$	0	0
$327$	−798354.	−0.412882
$328$	0	0
$329$	−496080.	−0.252675
$330$	0	0
$331$	−1.67414e6	−0.839889	−0.419944	−	0.907550i	$-0.637950\pi$
$331$	−1.67414e6	−0.839889	−0.419944	+	0.907550i	$0.637950\pi$
$332$	0	0
$333$	−982530.	−0.485551
$334$	0	0
$335$	2.67343e6	1.30154
$336$	0	0
$337$	3.02010e6	1.44859	0.724297	−	0.689488i	$-0.242164\pi$
$337$	3.02010e6	1.44859	0.724297	+	0.689488i	$0.242164\pi$
$338$	0	0
$339$	1.41113e6	0.666910
$340$	0	0
$341$	781440.	0.363923
$342$	0	0
$343$	2.37099e6	1.08817
$344$	0	0
$345$	195372.	0.0883720
$346$	0	0
$347$	−2.79531e6	−1.24625	−0.623127	−	0.782121i	$-0.714138\pi$
$347$	−2.79531e6	−1.24625	−0.623127	+	0.782121i	$0.714138\pi$
$348$	0	0
$349$	−3.92975e6	−1.72703	−0.863517	−	0.504320i	$-0.831743\pi$
$349$	−3.92975e6	−1.72703	−0.863517	+	0.504320i	$0.831743\pi$
$350$	0	0
$351$	33534.0	0.0145284
$352$	0	0
$353$	−1.56554e6	−0.668693	−0.334347	−	0.942450i	$-0.608516\pi$
$353$	−1.56554e6	−0.668693	−0.334347	+	0.942450i	$0.608516\pi$
$354$	0	0
$355$	408888.	0.172200
$356$	0	0
$357$	−578448.	−0.240211
$358$	0	0
$359$	2.19680e6	0.899609	0.449805	−	0.893127i	$-0.351494\pi$
$359$	2.19680e6	0.899609	0.449805	+	0.893127i	$0.351494\pi$
$360$	0	0
$361$	130321.	0.0526316
$362$	0	0
$363$	469359.	0.186956
$364$	0	0
$365$	−126468.	−0.0496877
$366$	0	0
$367$	4.24772e6	1.64623	0.823115	−	0.567875i	$-0.192234\pi$
$367$	4.24772e6	1.64623	0.823115	+	0.567875i	$0.192234\pi$
$368$	0	0
$369$	−1.52798e6	−0.584188
$370$	0	0
$371$	2.02301e6	0.763067
$372$	0	0
$373$	4.24597e6	1.58018	0.790088	−	0.612994i	$-0.210035\pi$
$373$	4.24597e6	1.58018	0.790088	+	0.612994i	$0.210035\pi$
$374$	0	0
$375$	−1.62032e6	−0.595009
$376$	0	0
$377$	120888.	0.0438056
$378$	0	0
$379$	−3.06794e6	−1.09711	−0.548553	−	0.836116i	$-0.684821\pi$
$379$	−3.06794e6	−1.09711	−0.548553	+	0.836116i	$0.684821\pi$
$380$	0	0
$381$	−1.90591e6	−0.672652
$382$	0	0
$383$	−5.23012e6	−1.82186	−0.910929	−	0.412564i	$-0.864633\pi$
$383$	−5.23012e6	−1.82186	−0.910929	+	0.412564i	$0.864633\pi$
$384$	0	0
$385$	1.85328e6	0.637220
$386$	0	0
$387$	843048.	0.286138
$388$	0	0
$389$	−3.36209e6	−1.12651	−0.563256	−	0.826282i	$-0.690452\pi$
$389$	−3.36209e6	−1.12651	−0.563256	+	0.826282i	$0.690452\pi$
$390$	0	0
$391$	−248436.	−0.0821812
$392$	0	0
$393$	−39690.0	−0.0129628
$394$	0	0
$395$	1.21090e6	0.390494
$396$	0	0
$397$	2.92432e6	0.931211	0.465606	−	0.884992i	$-0.345836\pi$
$397$	2.92432e6	0.931211	0.465606	+	0.884992i	$0.345836\pi$
$398$	0	0
$399$	−337896.	−0.106255
$400$	0	0
$401$	5.80702e6	1.80340	0.901700	−	0.432362i	$-0.142320\pi$
$401$	5.80702e6	1.80340	0.901700	+	0.432362i	$0.142320\pi$
$402$	0	0
$403$	−108928.	−0.0334100
$404$	0	0
$405$	−354294.	−0.107331
$406$	0	0
$407$	−4.00290e6	−1.19781
$408$	0	0
$409$	1.80028e6	0.532147	0.266073	−	0.963953i	$-0.414274\pi$
$409$	1.80028e6	0.532147	0.266073	+	0.963953i	$0.414274\pi$
$410$	0	0
$411$	−1.85377e6	−0.541315
$412$	0	0
$413$	3.17491e6	0.915918
$414$	0	0
$415$	−2.52364e6	−0.719294
$416$	0	0
$417$	2.84317e6	0.800687
$418$	0	0
$419$	1.38477e6	0.385339	0.192669	−	0.981264i	$-0.438286\pi$
$419$	1.38477e6	0.385339	0.192669	+	0.981264i	$0.438286\pi$
$420$	0	0
$421$	−315598.	−0.0867819	−0.0433909	−	0.999058i	$-0.513816\pi$
$421$	−315598.	−0.0867819	−0.0433909	+	0.999058i	$0.513816\pi$
$422$	0	0
$423$	386370.	0.104991
$424$	0	0
$425$	129162.	0.0346867
$426$	0	0
$427$	−1.15835e6	−0.307447
$428$	0	0
$429$	136620.	0.0358403
$430$	0	0
$431$	6.52696e6	1.69246	0.846228	−	0.532821i	$-0.178868\pi$
$431$	6.52696e6	1.69246	0.846228	+	0.532821i	$0.178868\pi$
$432$	0	0
$433$	2.63139e6	0.674473	0.337237	−	0.941420i	$-0.390508\pi$
$433$	2.63139e6	0.674473	0.337237	+	0.941420i	$0.390508\pi$
$434$	0	0
$435$	−1.27721e6	−0.323622
$436$	0	0
$437$	−145122.	−0.0363521
$438$	0	0
$439$	−3.09445e6	−0.766341	−0.383170	−	0.923678i	$-0.625168\pi$
$439$	−3.09445e6	−0.766341	−0.383170	+	0.923678i	$0.625168\pi$
$440$	0	0
$441$	−485271.	−0.118820
$442$	0	0
$443$	−985086.	−0.238487	−0.119244	−	0.992865i	$-0.538047\pi$
$443$	−985086.	−0.238487	−0.119244	+	0.992865i	$0.538047\pi$
$444$	0	0
$445$	3.78562e6	0.906226
$446$	0	0
$447$	−1.90042e6	−0.449864
$448$	0	0
$449$	−2.91582e6	−0.682566	−0.341283	−	0.939961i	$-0.610862\pi$
$449$	−2.91582e6	−0.682566	−0.341283	+	0.939961i	$0.610862\pi$
$450$	0	0
$451$	−6.22512e6	−1.44114
$452$	0	0
$453$	−1.06308e6	−0.243400
$454$	0	0
$455$	−258336.	−0.0585001
$456$	0	0
$457$	−3.54721e6	−0.794505	−0.397252	−	0.917709i	$-0.630036\pi$
$457$	−3.54721e6	−0.794505	−0.397252	+	0.917709i	$0.630036\pi$
$458$	0	0
$459$	450522.	0.0998124
$460$	0	0
$461$	4.57057e6	1.00165	0.500827	−	0.865547i	$-0.333029\pi$
$461$	4.57057e6	1.00165	0.500827	+	0.865547i	$0.333029\pi$
$462$	0	0
$463$	−5.91304e6	−1.28191	−0.640957	−	0.767577i	$-0.721462\pi$
$463$	−5.91304e6	−1.28191	−0.640957	+	0.767577i	$0.721462\pi$
$464$	0	0
$465$	1.15085e6	0.246823
$466$	0	0
$467$	3.73808e6	0.793152	0.396576	−	0.918002i	$-0.370198\pi$
$467$	3.73808e6	0.793152	0.396576	+	0.918002i	$0.370198\pi$
$468$	0	0
$469$	5.14883e6	1.08088
$470$	0	0
$471$	1.47591e6	0.306554
$472$	0	0
$473$	3.43464e6	0.705876
$474$	0	0
$475$	75449.0	0.0153433
$476$	0	0
$477$	−1.57561e6	−0.317069
$478$	0	0
$479$	3.79193e6	0.755130	0.377565	−	0.925983i	$-0.376761\pi$
$479$	3.79193e6	0.755130	0.377565	+	0.925983i	$0.376761\pi$
$480$	0	0
$481$	557980.	0.109965
$482$	0	0
$483$	376272.	0.0733895
$484$	0	0
$485$	−5.70834e6	−1.10193
$486$	0	0
$487$	−2.78559e6	−0.532225	−0.266112	−	0.963942i	$-0.585739\pi$
$487$	−2.78559e6	−0.532225	−0.266112	+	0.963942i	$0.585739\pi$
$488$	0	0
$489$	242532.	0.0458666
$490$	0	0
$491$	−1.70523e6	−0.319212	−0.159606	−	0.987181i	$-0.551022\pi$
$491$	−1.70523e6	−0.319212	−0.159606	+	0.987181i	$0.551022\pi$
$492$	0	0
$493$	1.62410e6	0.300952
$494$	0	0
$495$	−1.44342e6	−0.264777
$496$	0	0
$497$	787488.	0.143006
$498$	0	0
$499$	−3.60026e6	−0.647266	−0.323633	−	0.946183i	$-0.604904\pi$
$499$	−3.60026e6	−0.647266	−0.323633	+	0.946183i	$0.604904\pi$
$500$	0	0
$501$	52272.0	0.00930411
$502$	0	0
$503$	8.68129e6	1.52990	0.764952	−	0.644087i	$-0.222763\pi$
$503$	8.68129e6	1.52990	0.764952	+	0.644087i	$0.222763\pi$
$504$	0	0
$505$	−6.72527e6	−1.17349
$506$	0	0
$507$	3.32259e6	0.574060
$508$	0	0
$509$	−1.09767e7	−1.87792	−0.938962	−	0.344022i	$-0.888211\pi$
$509$	−1.09767e7	−1.87792	−0.938962	+	0.344022i	$0.888211\pi$
$510$	0	0
$511$	−243568.	−0.0412637
$512$	0	0
$513$	263169.	0.0441511
$514$	0	0
$515$	350352.	0.0582085
$516$	0	0
$517$	1.57410e6	0.259004
$518$	0	0
$519$	−333936.	−0.0544183
$520$	0	0
$521$	−9.09036e6	−1.46719	−0.733596	−	0.679586i	$-0.762159\pi$
$521$	−9.09036e6	−1.46719	−0.733596	+	0.679586i	$0.762159\pi$
$522$	0	0
$523$	−8.46276e6	−1.35287	−0.676437	−	0.736500i	$-0.736477\pi$
$523$	−8.46276e6	−1.35287	−0.676437	+	0.736500i	$0.736477\pi$
$524$	0	0
$525$	−195624.	−0.0309759
$526$	0	0
$527$	−1.46342e6	−0.229532
$528$	0	0
$529$	−6.27474e6	−0.974892
$530$	0	0
$531$	−2.47277e6	−0.380581
$532$	0	0
$533$	867744.	0.132304
$534$	0	0
$535$	2.70216e6	0.408156
$536$	0	0
$537$	1.78524e6	0.267154
$538$	0	0
$539$	−1.97703e6	−0.293117
$540$	0	0
$541$	−8.03851e6	−1.18082	−0.590408	−	0.807105i	$-0.701033\pi$
$541$	−8.03851e6	−1.18082	−0.590408	+	0.807105i	$0.701033\pi$
$542$	0	0
$543$	2.49154e6	0.362634
$544$	0	0
$545$	−4.79012e6	−0.690805
$546$	0	0
$547$	1.32779e7	1.89741	0.948704	−	0.316167i	$-0.102396\pi$
$547$	1.32779e7	1.89741	0.948704	+	0.316167i	$0.102396\pi$
$548$	0	0
$549$	902178.	0.127750
$550$	0	0
$551$	948708.	0.133123
$552$	0	0
$553$	2.33210e6	0.324290
$554$	0	0
$555$	−5.89518e6	−0.812390
$556$	0	0
$557$	−9.11080e6	−1.24428	−0.622141	−	0.782905i	$-0.713737\pi$
$557$	−9.11080e6	−1.24428	−0.622141	+	0.782905i	$0.713737\pi$
$558$	0	0
$559$	−478768.	−0.0648031
$560$	0	0
$561$	1.83546e6	0.246228
$562$	0	0
$563$	5.07313e6	0.674536	0.337268	−	0.941409i	$-0.390497\pi$
$563$	5.07313e6	0.674536	0.337268	+	0.941409i	$0.390497\pi$
$564$	0	0
$565$	8.46677e6	1.11583
$566$	0	0
$567$	−682344.	−0.0891345
$568$	0	0
$569$	2.30192e6	0.298065	0.149032	−	0.988832i	$-0.452384\pi$
$569$	2.30192e6	0.298065	0.149032	+	0.988832i	$0.452384\pi$
$570$	0	0
$571$	1.14948e7	1.47540	0.737702	−	0.675127i	$-0.235911\pi$
$571$	1.14948e7	1.47540	0.737702	+	0.675127i	$0.235911\pi$
$572$	0	0
$573$	−4.78100e6	−0.608320
$574$	0	0
$575$	−84018.0	−0.0105975
$576$	0	0
$577$	308198.	0.0385381	0.0192690	−	0.999814i	$-0.493866\pi$
$577$	308198.	0.0385381	0.0192690	+	0.999814i	$0.493866\pi$
$578$	0	0
$579$	2.20556e6	0.273415
$580$	0	0
$581$	−4.86034e6	−0.597346
$582$	0	0
$583$	−6.41916e6	−0.782180
$584$	0	0
$585$	201204.	0.0243079
$586$	0	0
$587$	−5.02053e6	−0.601387	−0.300694	−	0.953721i	$-0.597218\pi$
$587$	−5.02053e6	−0.601387	−0.300694	+	0.953721i	$0.597218\pi$
$588$	0	0
$589$	−854848.	−0.101531
$590$	0	0
$591$	−1.97915e6	−0.233083
$592$	0	0
$593$	1.70294e7	1.98867	0.994335	−	0.106288i	$-0.0338967\pi$
$593$	1.70294e7	1.98867	0.994335	+	0.106288i	$0.0338967\pi$
$594$	0	0
$595$	−3.47069e6	−0.401905
$596$	0	0
$597$	−9.16384e6	−1.05230
$598$	0	0
$599$	−2.86572e6	−0.326337	−0.163169	−	0.986598i	$-0.552171\pi$
$599$	−2.86572e6	−0.326337	−0.163169	+	0.986598i	$0.552171\pi$
$600$	0	0
$601$	−1.03461e7	−1.16840	−0.584200	−	0.811609i	$-0.698592\pi$
$601$	−1.03461e7	−1.16840	−0.584200	+	0.811609i	$0.698592\pi$
$602$	0	0
$603$	−4.01015e6	−0.449125
$604$	0	0
$605$	2.81615e6	0.312801
$606$	0	0
$607$	−3.56084e6	−0.392266	−0.196133	−	0.980577i	$-0.562838\pi$
$607$	−3.56084e6	−0.392266	−0.196133	+	0.980577i	$0.562838\pi$
$608$	0	0
$609$	−2.45981e6	−0.268756
$610$	0	0
$611$	−219420.	−0.0237779
$612$	0	0
$613$	7.56115e6	0.812712	0.406356	−	0.913715i	$-0.366799\pi$
$613$	7.56115e6	0.812712	0.406356	+	0.913715i	$0.366799\pi$
$614$	0	0
$615$	−9.16790e6	−0.977422
$616$	0	0
$617$	5.03233e6	0.532177	0.266088	−	0.963949i	$-0.414269\pi$
$617$	5.03233e6	0.532177	0.266088	+	0.963949i	$0.414269\pi$
$618$	0	0
$619$	5.87528e6	0.616313	0.308157	−	0.951336i	$-0.400288\pi$
$619$	5.87528e6	0.616313	0.308157	+	0.951336i	$0.400288\pi$
$620$	0	0
$621$	−293058.	−0.0304947
$622$	0	0
$623$	7.29082e6	0.752586
$624$	0	0
$625$	−9.06882e6	−0.928647
$626$	0	0
$627$	1.07217e6	0.108917
$628$	0	0
$629$	7.49634e6	0.755479
$630$	0	0
$631$	4.33809e6	0.433735	0.216868	−	0.976201i	$-0.430416\pi$
$631$	4.33809e6	0.433735	0.216868	+	0.976201i	$0.430416\pi$
$632$	0	0
$633$	945180.	0.0937573
$634$	0	0
$635$	−1.14355e7	−1.12543
$636$	0	0
$637$	275586.	0.0269097
$638$	0	0
$639$	−613332.	−0.0594215
$640$	0	0
$641$	1.35603e7	1.30354	0.651769	−	0.758417i	$-0.274027\pi$
$641$	1.35603e7	1.30354	0.651769	+	0.758417i	$0.274027\pi$
$642$	0	0
$643$	−6.02612e6	−0.574792	−0.287396	−	0.957812i	$-0.592789\pi$
$643$	−6.02612e6	−0.574792	−0.287396	+	0.957812i	$0.592789\pi$
$644$	0	0
$645$	5.05829e6	0.478745
$646$	0	0
$647$	8.69474e6	0.816574	0.408287	−	0.912854i	$-0.366126\pi$
$647$	8.69474e6	0.816574	0.408287	+	0.912854i	$0.366126\pi$
$648$	0	0
$649$	−1.00742e7	−0.938859
$650$	0	0
$651$	2.21645e6	0.204977
$652$	0	0
$653$	−1.09929e6	−0.100886	−0.0504428	−	0.998727i	$-0.516063\pi$
$653$	−1.09929e6	−0.100886	−0.0504428	+	0.998727i	$0.516063\pi$
$654$	0	0
$655$	−238140.	−0.0216885
$656$	0	0
$657$	189702.	0.0171458
$658$	0	0
$659$	3.94808e6	0.354138	0.177069	−	0.984198i	$-0.443338\pi$
$659$	3.94808e6	0.354138	0.177069	+	0.984198i	$0.443338\pi$
$660$	0	0
$661$	−1.96958e7	−1.75335	−0.876676	−	0.481082i	$-0.840244\pi$
$661$	−1.96958e7	−1.75335	−0.876676	+	0.481082i	$0.840244\pi$
$662$	0	0
$663$	−255852.	−0.0226050
$664$	0	0
$665$	−2.02738e6	−0.177779
$666$	0	0
$667$	−1.05646e6	−0.0919468
$668$	0	0
$669$	8.89474e6	0.768365
$670$	0	0
$671$	3.67554e6	0.315148
$672$	0	0
$673$	−2.06650e7	−1.75873	−0.879363	−	0.476151i	$-0.842031\pi$
$673$	−2.06650e7	−1.75873	−0.879363	+	0.476151i	$0.842031\pi$
$674$	0	0
$675$	152361.	0.0128711
$676$	0	0
$677$	1.64591e7	1.38018	0.690090	−	0.723724i	$-0.257571\pi$
$677$	1.64591e7	1.38018	0.690090	+	0.723724i	$0.257571\pi$
$678$	0	0
$679$	−1.09938e7	−0.915114
$680$	0	0
$681$	−4.64346e6	−0.383684
$682$	0	0
$683$	876672.	0.0719094	0.0359547	−	0.999353i	$-0.488553\pi$
$683$	876672.	0.0719094	0.0359547	+	0.999353i	$0.488553\pi$
$684$	0	0
$685$	−1.11226e7	−0.905690
$686$	0	0
$687$	2.49619e6	0.201783
$688$	0	0
$689$	894792.	0.0718082
$690$	0	0
$691$	−1.64070e7	−1.30717	−0.653586	−	0.756852i	$-0.726736\pi$
$691$	−1.64070e7	−1.30717	−0.653586	+	0.756852i	$0.726736\pi$
$692$	0	0
$693$	−2.77992e6	−0.219887
$694$	0	0
$695$	1.70590e7	1.33965
$696$	0	0
$697$	1.16580e7	0.908951
$698$	0	0
$699$	−1.38736e7	−1.07398
$700$	0	0
$701$	1.03676e6	0.0796861	0.0398430	−	0.999206i	$-0.487314\pi$
$701$	1.03676e6	0.0796861	0.0398430	+	0.999206i	$0.487314\pi$
$702$	0	0
$703$	4.37893e6	0.334179
$704$	0	0
$705$	2.31822e6	0.175664
$706$	0	0
$707$	−1.29524e7	−0.974542
$708$	0	0
$709$	−2.00637e6	−0.149898	−0.0749491	−	0.997187i	$-0.523879\pi$
$709$	−2.00637e6	−0.149898	−0.0749491	+	0.997187i	$0.523879\pi$
$710$	0	0
$711$	−1.81634e6	−0.134749
$712$	0	0
$713$	951936.	0.0701268
$714$	0	0
$715$	819720.	0.0599654
$716$	0	0
$717$	−2.82879e6	−0.205496
$718$	0	0
$719$	8.95036e6	0.645682	0.322841	−	0.946453i	$-0.395362\pi$
$719$	8.95036e6	0.645682	0.322841	+	0.946453i	$0.395362\pi$
$720$	0	0
$721$	674752.	0.0483399
$722$	0	0
$723$	−221094.	−0.0157301
$724$	0	0
$725$	549252.	0.0388085
$726$	0	0
$727$	614668.	0.0431325	0.0215662	−	0.999767i	$-0.493135\pi$
$727$	614668.	0.0431325	0.0215662	+	0.999767i	$0.493135\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−6.43214e6	−0.445207
$732$	0	0
$733$	−8.47041e6	−0.582297	−0.291149	−	0.956678i	$-0.594037\pi$
$733$	−8.47041e6	−0.582297	−0.291149	+	0.956678i	$0.594037\pi$
$734$	0	0
$735$	−2.91163e6	−0.198800
$736$	0	0
$737$	−1.63376e7	−1.10795
$738$	0	0
$739$	9.40491e6	0.633495	0.316748	−	0.948510i	$-0.397409\pi$
$739$	9.40491e6	0.633495	0.316748	+	0.948510i	$0.397409\pi$
$740$	0	0
$741$	−149454.	−0.00999913
$742$	0	0
$743$	−2.73198e7	−1.81554	−0.907769	−	0.419471i	$-0.862216\pi$
$743$	−2.73198e7	−1.81554	−0.907769	+	0.419471i	$0.862216\pi$
$744$	0	0
$745$	−1.14025e7	−0.752680
$746$	0	0
$747$	3.78545e6	0.248208
$748$	0	0
$749$	5.20416e6	0.338958
$750$	0	0
$751$	1.07808e7	0.697509	0.348755	−	0.937214i	$-0.386605\pi$
$751$	1.07808e7	0.697509	0.348755	+	0.937214i	$0.386605\pi$
$752$	0	0
$753$	5.95161e6	0.382514
$754$	0	0
$755$	−6.37848e6	−0.407239
$756$	0	0
$757$	−543058.	−0.0344434	−0.0172217	−	0.999852i	$-0.505482\pi$
$757$	−543058.	−0.0344434	−0.0172217	+	0.999852i	$0.505482\pi$
$758$	0	0
$759$	−1.19394e6	−0.0752277
$760$	0	0
$761$	9.07913e6	0.568307	0.284153	−	0.958779i	$-0.408288\pi$
$761$	9.07913e6	0.568307	0.284153	+	0.958779i	$0.408288\pi$
$762$	0	0
$763$	−9.22542e6	−0.573687
$764$	0	0
$765$	2.70313e6	0.166999
$766$	0	0
$767$	1.40429e6	0.0861922
$768$	0	0
$769$	5.14583e6	0.313790	0.156895	−	0.987615i	$-0.449852\pi$
$769$	5.14583e6	0.313790	0.156895	+	0.987615i	$0.449852\pi$
$770$	0	0
$771$	−9.45313e6	−0.572717
$772$	0	0
$773$	7.50322e6	0.451647	0.225823	−	0.974168i	$-0.427493\pi$
$773$	7.50322e6	0.451647	0.225823	+	0.974168i	$0.427493\pi$
$774$	0	0
$775$	−494912.	−0.0295988
$776$	0	0
$777$	−1.13537e7	−0.674659
$778$	0	0
$779$	6.80990e6	0.402066
$780$	0	0
$781$	−2.49876e6	−0.146588
$782$	0	0
$783$	1.91581e6	0.111673
$784$	0	0
$785$	8.85546e6	0.512905
$786$	0	0
$787$	−1.48747e7	−0.856076	−0.428038	−	0.903761i	$-0.640795\pi$
$787$	−1.48747e7	−0.856076	−0.428038	+	0.903761i	$0.640795\pi$
$788$	0	0
$789$	−4.18959e6	−0.239596
$790$	0	0
$791$	1.63064e7	0.926651
$792$	0	0
$793$	−512348.	−0.0289322
$794$	0	0
$795$	−9.45367e6	−0.530497
$796$	0	0
$797$	2.77279e7	1.54622	0.773109	−	0.634273i	$-0.218701\pi$
$797$	2.77279e7	1.54622	0.773109	+	0.634273i	$0.218701\pi$
$798$	0	0
$799$	−2.94786e6	−0.163358
$800$	0	0
$801$	−5.67842e6	−0.312713
$802$	0	0
$803$	772860.	0.0422972
$804$	0	0
$805$	2.25763e6	0.122790
$806$	0	0
$807$	2.85401e6	0.154266
$808$	0	0
$809$	−3.46147e7	−1.85947	−0.929735	−	0.368229i	$-0.879964\pi$
$809$	−3.46147e7	−1.85947	−0.929735	+	0.368229i	$0.879964\pi$
$810$	0	0
$811$	−1.42801e7	−0.762392	−0.381196	−	0.924494i	$-0.624488\pi$
$811$	−1.42801e7	−0.762392	−0.381196	+	0.924494i	$0.624488\pi$
$812$	0	0
$813$	−1.34011e7	−0.711073
$814$	0	0
$815$	1.45519e6	0.0767408
$816$	0	0
$817$	−3.75729e6	−0.196933
$818$	0	0
$819$	387504.	0.0201868
$820$	0	0
$821$	3.69632e6	0.191387	0.0956933	−	0.995411i	$-0.469493\pi$
$821$	3.69632e6	0.191387	0.0956933	+	0.995411i	$0.469493\pi$
$822$	0	0
$823$	−2.05703e7	−1.05862	−0.529310	−	0.848428i	$-0.677549\pi$
$823$	−2.05703e7	−1.05862	−0.529310	+	0.848428i	$0.677549\pi$
$824$	0	0
$825$	620730.	0.0317518
$826$	0	0
$827$	2.42257e7	1.23172	0.615860	−	0.787856i	$-0.288809\pi$
$827$	2.42257e7	1.23172	0.615860	+	0.787856i	$0.288809\pi$
$828$	0	0
$829$	−1.93936e7	−0.980102	−0.490051	−	0.871694i	$-0.663022\pi$
$829$	−1.93936e7	−0.980102	−0.490051	+	0.871694i	$0.663022\pi$
$830$	0	0
$831$	1.38625e7	0.696370
$832$	0	0
$833$	3.70244e6	0.184874
$834$	0	0
$835$	313632.	0.0155670
$836$	0	0
$837$	−1.72627e6	−0.0851718
$838$	0	0
$839$	3.44560e7	1.68990	0.844949	−	0.534847i	$-0.179631\pi$
$839$	3.44560e7	1.68990	0.844949	+	0.534847i	$0.179631\pi$
$840$	0	0
$841$	−1.36048e7	−0.663286
$842$	0	0
$843$	−1.79635e7	−0.870608
$844$	0	0
$845$	1.99356e7	0.960476
$846$	0	0
$847$	5.42370e6	0.259769
$848$	0	0
$849$	−8.52242e6	−0.405783
$850$	0	0
$851$	−4.87626e6	−0.230814
$852$	0	0
$853$	1.43023e7	0.673029	0.336514	−	0.941678i	$-0.390752\pi$
$853$	1.43023e7	0.673029	0.336514	+	0.941678i	$0.390752\pi$
$854$	0	0
$855$	1.57901e6	0.0738704
$856$	0	0
$857$	1.96706e7	0.914882	0.457441	−	0.889240i	$-0.348766\pi$
$857$	1.96706e7	0.914882	0.457441	+	0.889240i	$0.348766\pi$
$858$	0	0
$859$	−9.60088e6	−0.443944	−0.221972	−	0.975053i	$-0.571249\pi$
$859$	−9.60088e6	−0.443944	−0.221972	+	0.975053i	$0.571249\pi$
$860$	0	0
$861$	−1.76567e7	−0.811712
$862$	0	0
$863$	−1.46481e7	−0.669508	−0.334754	−	0.942306i	$-0.608653\pi$
$863$	−1.46481e7	−0.669508	−0.334754	+	0.942306i	$0.608653\pi$
$864$	0	0
$865$	−2.00362e6	−0.0910488
$866$	0	0
$867$	9.34140e6	0.422050
$868$	0	0
$869$	−7.39992e6	−0.332413
$870$	0	0
$871$	2.27737e6	0.101716
$872$	0	0
$873$	8.56251e6	0.380247
$874$	0	0
$875$	−1.87237e7	−0.826747
$876$	0	0
$877$	−1.17035e7	−0.513825	−0.256913	−	0.966435i	$-0.582705\pi$
$877$	−1.17035e7	−0.513825	−0.256913	+	0.966435i	$0.582705\pi$
$878$	0	0
$879$	−1.96353e7	−0.857165
$880$	0	0
$881$	−4.52787e7	−1.96541	−0.982706	−	0.185171i	$-0.940716\pi$
$881$	−4.52787e7	−1.96541	−0.982706	+	0.185171i	$0.940716\pi$
$882$	0	0
$883$	−2.59473e7	−1.11993	−0.559965	−	0.828517i	$-0.689185\pi$
$883$	−2.59473e7	−1.11993	−0.559965	+	0.828517i	$0.689185\pi$
$884$	0	0
$885$	−1.48366e7	−0.636761
$886$	0	0
$887$	2.07015e7	0.883473	0.441737	−	0.897145i	$-0.354363\pi$
$887$	2.07015e7	0.883473	0.441737	+	0.897145i	$0.354363\pi$
$888$	0	0
$889$	−2.20239e7	−0.934629
$890$	0	0
$891$	2.16513e6	0.0913671
$892$	0	0
$893$	−1.72197e6	−0.0722598
$894$	0	0
$895$	1.07114e7	0.446982
$896$	0	0
$897$	166428.	0.00690630
$898$	0	0
$899$	−6.22310e6	−0.256808
$900$	0	0
$901$	1.20213e7	0.493334
$902$	0	0
$903$	9.74189e6	0.397579
$904$	0	0
$905$	1.49493e7	0.606734
$906$	0	0
$907$	−4.76595e7	−1.92367	−0.961836	−	0.273628i	$-0.911776\pi$
$907$	−4.76595e7	−1.92367	−0.961836	+	0.273628i	$0.911776\pi$
$908$	0	0
$909$	1.00879e7	0.404940
$910$	0	0
$911$	387816.	0.0154821	0.00774105	−	0.999970i	$-0.497536\pi$
$911$	387816.	0.0154821	0.00774105	+	0.999970i	$0.497536\pi$
$912$	0	0
$913$	1.54222e7	0.612308
$914$	0	0
$915$	5.41307e6	0.213742
$916$	0	0
$917$	−458640.	−0.0180114
$918$	0	0
$919$	−3.45269e7	−1.34855	−0.674277	−	0.738479i	$-0.735545\pi$
$919$	−3.45269e7	−1.34855	−0.674277	+	0.738479i	$0.735545\pi$
$920$	0	0
$921$	−2.25373e7	−0.875492
$922$	0	0
$923$	348312.	0.0134575
$924$	0	0
$925$	2.53517e6	0.0974210
$926$	0	0
$927$	−525528.	−0.0200861
$928$	0	0
$929$	3.96164e7	1.50604	0.753018	−	0.657999i	$-0.228597\pi$
$929$	3.96164e7	1.50604	0.753018	+	0.657999i	$0.228597\pi$
$930$	0	0
$931$	2.16275e6	0.0817772
$932$	0	0
$933$	−7.07092e6	−0.265933
$934$	0	0
$935$	1.10128e7	0.411971
$936$	0	0
$937$	−1.42780e7	−0.531272	−0.265636	−	0.964073i	$-0.585582\pi$
$937$	−1.42780e7	−0.531272	−0.265636	+	0.964073i	$0.585582\pi$
$938$	0	0
$939$	−3.27901e6	−0.121361
$940$	0	0
$941$	−2.33088e6	−0.0858116	−0.0429058	−	0.999079i	$-0.513662\pi$
$941$	−2.33088e6	−0.0858116	−0.0429058	+	0.999079i	$0.513662\pi$
$942$	0	0
$943$	−7.58333e6	−0.277703
$944$	0	0
$945$	−4.09406e6	−0.149133
$946$	0	0
$947$	2.93987e7	1.06526	0.532628	−	0.846350i	$-0.321205\pi$
$947$	2.93987e7	1.06526	0.532628	+	0.846350i	$0.321205\pi$
$948$	0	0
$949$	−107732.	−0.00388311
$950$	0	0
$951$	1.32244e7	0.474159
$952$	0	0
$953$	−2.26835e7	−0.809055	−0.404528	−	0.914526i	$-0.632564\pi$
$953$	−2.26835e7	−0.809055	−0.404528	+	0.914526i	$0.632564\pi$
$954$	0	0
$955$	−2.86860e7	−1.01780
$956$	0	0
$957$	7.80516e6	0.275488
$958$	0	0
$959$	−2.14213e7	−0.752141
$960$	0	0
$961$	−2.30217e7	−0.804136
$962$	0	0
$963$	−4.05324e6	−0.140843
$964$	0	0
$965$	1.32333e7	0.457458
$966$	0	0
$967$	2.50637e7	0.861944	0.430972	−	0.902365i	$-0.358171\pi$
$967$	2.50637e7	0.861944	0.430972	+	0.902365i	$0.358171\pi$
$968$	0	0
$969$	−2.00788e6	−0.0686956
$970$	0	0
$971$	−2.93328e7	−0.998402	−0.499201	−	0.866486i	$-0.666373\pi$
$971$	−2.93328e7	−0.998402	−0.499201	+	0.866486i	$0.666373\pi$
$972$	0	0
$973$	3.28544e7	1.11253
$974$	0	0
$975$	−86526.0	−0.00291498
$976$	0	0
$977$	4.53306e7	1.51934	0.759670	−	0.650309i	$-0.225361\pi$
$977$	4.53306e7	1.51934	0.759670	+	0.650309i	$0.225361\pi$
$978$	0	0
$979$	−2.31343e7	−0.771436
$980$	0	0
$981$	7.18519e6	0.238378
$982$	0	0
$983$	2.13167e7	0.703615	0.351808	−	0.936072i	$-0.385567\pi$
$983$	2.13167e7	0.703615	0.351808	+	0.936072i	$0.385567\pi$
$984$	0	0
$985$	−1.18749e7	−0.389978
$986$	0	0
$987$	4.46472e6	0.145882
$988$	0	0
$989$	4.18402e6	0.136020
$990$	0	0
$991$	3.14104e7	1.01599	0.507996	−	0.861360i	$-0.330387\pi$
$991$	3.14104e7	1.01599	0.507996	+	0.861360i	$0.330387\pi$
$992$	0	0
$993$	1.50673e7	0.484910
$994$	0	0
$995$	−5.49830e7	−1.76064
$996$	0	0
$997$	9.54091e6	0.303985	0.151992	−	0.988382i	$-0.451431\pi$
$997$	9.54091e6	0.303985	0.151992	+	0.988382i	$0.451431\pi$
$998$	0	0
$999$	8.84277e6	0.280333

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.6.a.c.1.1		1
4.3	odd	2		114.6.a.a.1.1	✓	1
12.11	even	2		342.6.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.6.a.a.1.1	✓	1	4.3	odd	2
342.6.a.f.1.1		1	12.11	even	2
912.6.a.c.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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	912.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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