LMFDB - Embedded newform 912.6.a.e.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)

$f(q)$

$=$

$q-9.00000 q^{3} +81.0000 q^{5} +247.000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q-9.00000 q^{3} +81.0000 q^{5} +247.000 q^{7} +81.0000 q^{9} +465.000 q^{11} -694.000 q^{13} -729.000 q^{15} +543.000 q^{17} -361.000 q^{19} -2223.00 q^{21} +2724.00 q^{23} +3436.00 q^{25} -729.000 q^{27} +342.000 q^{29} +9442.00 q^{31} -4185.00 q^{33} +20007.0 q^{35} +13088.0 q^{37} +6246.00 q^{39} -16272.0 q^{41} +391.000 q^{43} +6561.00 q^{45} +8523.00 q^{47} +44202.0 q^{49} -4887.00 q^{51} -10110.0 q^{53} +37665.0 q^{55} +3249.00 q^{57} +27144.0 q^{59} -48829.0 q^{61} +20007.0 q^{63} -56214.0 q^{65} -55448.0 q^{67} -24516.0 q^{69} -43212.0 q^{71} +37685.0 q^{73} -30924.0 q^{75} +114855. q^{77} +78016.0 q^{79} +6561.00 q^{81} -83892.0 q^{83} +43983.0 q^{85} -3078.00 q^{87} +25530.0 q^{89} -171418. q^{91} -84978.0 q^{93} -29241.0 q^{95} -76378.0 q^{97} +37665.0 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	0	0
$5$	81.0000	1.44897	0.724486	−	0.689289i	$-0.242077\pi$
$5$	81.0000	1.44897	0.724486	+	0.689289i	$0.242077\pi$
$6$	0	0
$7$	247.000	1.90525	0.952625	−	0.304148i	$-0.0983718\pi$
$7$	247.000	1.90525	0.952625	+	0.304148i	$0.0983718\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	465.000	1.15870	0.579350	−	0.815079i	$-0.303306\pi$
$11$	465.000	1.15870	0.579350	+	0.815079i	$0.303306\pi$
$12$	0	0
$13$	−694.000	−1.13894	−0.569470	−	0.822012i	$-0.692852\pi$
$13$	−694.000	−1.13894	−0.569470	+	0.822012i	$0.692852\pi$
$14$	0	0
$15$	−729.000	−0.836564
$16$	0	0
$17$	543.000	0.455698	0.227849	−	0.973696i	$-0.426831\pi$
$17$	543.000	0.455698	0.227849	+	0.973696i	$0.426831\pi$
$18$	0	0
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	0	0
$21$	−2223.00	−1.10000
$22$	0	0
$23$	2724.00	1.07371	0.536856	−	0.843674i	$-0.319612\pi$
$23$	2724.00	1.07371	0.536856	+	0.843674i	$0.319612\pi$
$24$	0	0
$25$	3436.00	1.09952
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	342.000	0.0755146	0.0377573	−	0.999287i	$-0.487979\pi$
$29$	342.000	0.0755146	0.0377573	+	0.999287i	$0.487979\pi$
$30$	0	0
$31$	9442.00	1.76465	0.882327	−	0.470636i	$-0.155976\pi$
$31$	9442.00	1.76465	0.882327	+	0.470636i	$0.155976\pi$
$32$	0	0
$33$	−4185.00	−0.668976
$34$	0	0
$35$	20007.0	2.76065
$36$	0	0
$37$	13088.0	1.57170	0.785849	−	0.618419i	$-0.212226\pi$
$37$	13088.0	1.57170	0.785849	+	0.618419i	$0.212226\pi$
$38$	0	0
$39$	6246.00	0.657568
$40$	0	0
$41$	−16272.0	−1.51175	−0.755877	−	0.654713i	$-0.772789\pi$
$41$	−16272.0	−1.51175	−0.755877	+	0.654713i	$0.772789\pi$
$42$	0	0
$43$	391.000	0.0322482	0.0161241	−	0.999870i	$-0.494867\pi$
$43$	391.000	0.0322482	0.0161241	+	0.999870i	$0.494867\pi$
$44$	0	0
$45$	6561.00	0.482991
$46$	0	0
$47$	8523.00	0.562792	0.281396	−	0.959592i	$-0.409203\pi$
$47$	8523.00	0.562792	0.281396	+	0.959592i	$0.409203\pi$
$48$	0	0
$49$	44202.0	2.62998
$50$	0	0
$51$	−4887.00	−0.263098
$52$	0	0
$53$	−10110.0	−0.494381	−0.247190	−	0.968967i	$-0.579507\pi$
$53$	−10110.0	−0.494381	−0.247190	+	0.968967i	$0.579507\pi$
$54$	0	0
$55$	37665.0	1.67892
$56$	0	0
$57$	3249.00	0.132453
$58$	0	0
$59$	27144.0	1.01518	0.507591	−	0.861598i	$-0.330536\pi$
$59$	27144.0	1.01518	0.507591	+	0.861598i	$0.330536\pi$
$60$	0	0
$61$	−48829.0	−1.68017	−0.840085	−	0.542455i	$-0.817495\pi$
$61$	−48829.0	−1.68017	−0.840085	+	0.542455i	$0.817495\pi$
$62$	0	0
$63$	20007.0	0.635083
$64$	0	0
$65$	−56214.0	−1.65029
$66$	0	0
$67$	−55448.0	−1.50903	−0.754517	−	0.656281i	$-0.772129\pi$
$67$	−55448.0	−1.50903	−0.754517	+	0.656281i	$0.772129\pi$
$68$	0	0
$69$	−24516.0	−0.619907
$70$	0	0
$71$	−43212.0	−1.01732	−0.508661	−	0.860967i	$-0.669859\pi$
$71$	−43212.0	−1.01732	−0.508661	+	0.860967i	$0.669859\pi$
$72$	0	0
$73$	37685.0	0.827678	0.413839	−	0.910350i	$-0.364188\pi$
$73$	37685.0	0.827678	0.413839	+	0.910350i	$0.364188\pi$
$74$	0	0
$75$	−30924.0	−0.634808
$76$	0	0
$77$	114855.	2.20761
$78$	0	0
$79$	78016.0	1.40642	0.703211	−	0.710981i	$-0.251749\pi$
$79$	78016.0	1.40642	0.703211	+	0.710981i	$0.251749\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	−83892.0	−1.33667	−0.668337	−	0.743859i	$-0.732993\pi$
$83$	−83892.0	−1.33667	−0.668337	+	0.743859i	$0.732993\pi$
$84$	0	0
$85$	43983.0	0.660294
$86$	0	0
$87$	−3078.00	−0.0435984
$88$	0	0
$89$	25530.0	0.341646	0.170823	−	0.985302i	$-0.445357\pi$
$89$	25530.0	0.341646	0.170823	+	0.985302i	$0.445357\pi$
$90$	0	0
$91$	−171418.	−2.16997
$92$	0	0
$93$	−84978.0	−1.01882
$94$	0	0
$95$	−29241.0	−0.332417
$96$	0	0
$97$	−76378.0	−0.824212	−0.412106	−	0.911136i	$-0.635207\pi$
$97$	−76378.0	−0.824212	−0.412106	+	0.911136i	$0.635207\pi$
$98$	0	0
$99$	37665.0	0.386234
$100$	0	0
$101$	−132606.	−1.29348	−0.646740	−	0.762711i	$-0.723868\pi$
$101$	−132606.	−1.29348	−0.646740	+	0.762711i	$0.723868\pi$
$102$	0	0
$103$	−67994.0	−0.631506	−0.315753	−	0.948841i	$-0.602257\pi$
$103$	−67994.0	−0.631506	−0.315753	+	0.948841i	$0.602257\pi$
$104$	0	0
$105$	−180063.	−1.59386
$106$	0	0
$107$	87606.0	0.739732	0.369866	−	0.929085i	$-0.379404\pi$
$107$	87606.0	0.739732	0.369866	+	0.929085i	$0.379404\pi$
$108$	0	0
$109$	75908.0	0.611958	0.305979	−	0.952038i	$-0.401016\pi$
$109$	75908.0	0.611958	0.305979	+	0.952038i	$0.401016\pi$
$110$	0	0
$111$	−117792.	−0.907420
$112$	0	0
$113$	50946.0	0.375331	0.187665	−	0.982233i	$-0.439908\pi$
$113$	50946.0	0.375331	0.187665	+	0.982233i	$0.439908\pi$
$114$	0	0
$115$	220644.	1.55578
$116$	0	0
$117$	−56214.0	−0.379647
$118$	0	0
$119$	134121.	0.868219
$120$	0	0
$121$	55174.0	0.342587
$122$	0	0
$123$	146448.	0.872812
$124$	0	0
$125$	25191.0	0.144202
$126$	0	0
$127$	−116282.	−0.639740	−0.319870	−	0.947462i	$-0.603639\pi$
$127$	−116282.	−0.639740	−0.319870	+	0.947462i	$0.603639\pi$
$128$	0	0
$129$	−3519.00	−0.0186185
$130$	0	0
$131$	172215.	0.876784	0.438392	−	0.898784i	$-0.355548\pi$
$131$	172215.	0.876784	0.438392	+	0.898784i	$0.355548\pi$
$132$	0	0
$133$	−89167.0	−0.437094
$134$	0	0
$135$	−59049.0	−0.278855
$136$	0	0
$137$	−10593.0	−0.0482189	−0.0241095	−	0.999709i	$-0.507675\pi$
$137$	−10593.0	−0.0482189	−0.0241095	+	0.999709i	$0.507675\pi$
$138$	0	0
$139$	240427.	1.05547	0.527735	−	0.849409i	$-0.323041\pi$
$139$	240427.	1.05547	0.527735	+	0.849409i	$0.323041\pi$
$140$	0	0
$141$	−76707.0	−0.324928
$142$	0	0
$143$	−322710.	−1.31969
$144$	0	0
$145$	27702.0	0.109419
$146$	0	0
$147$	−397818.	−1.51842
$148$	0	0
$149$	109935.	0.405668	0.202834	−	0.979213i	$-0.434985\pi$
$149$	109935.	0.405668	0.202834	+	0.979213i	$0.434985\pi$
$150$	0	0
$151$	−537008.	−1.91663	−0.958315	−	0.285713i	$-0.907770\pi$
$151$	−537008.	−1.91663	−0.958315	+	0.285713i	$0.907770\pi$
$152$	0	0
$153$	43983.0	0.151899
$154$	0	0
$155$	764802.	2.55694
$156$	0	0
$157$	158606.	0.513536	0.256768	−	0.966473i	$-0.417342\pi$
$157$	158606.	0.513536	0.256768	+	0.966473i	$0.417342\pi$
$158$	0	0
$159$	90990.0	0.285431
$160$	0	0
$161$	672828.	2.04569
$162$	0	0
$163$	−249968.	−0.736912	−0.368456	−	0.929645i	$-0.620113\pi$
$163$	−249968.	−0.736912	−0.368456	+	0.929645i	$0.620113\pi$
$164$	0	0
$165$	−338985.	−0.969328
$166$	0	0
$167$	−73038.0	−0.202655	−0.101328	−	0.994853i	$-0.532309\pi$
$167$	−73038.0	−0.202655	−0.101328	+	0.994853i	$0.532309\pi$
$168$	0	0
$169$	110343.	0.297186
$170$	0	0
$171$	−29241.0	−0.0764719
$172$	0	0
$173$	67182.0	0.170662	0.0853312	−	0.996353i	$-0.472805\pi$
$173$	67182.0	0.170662	0.0853312	+	0.996353i	$0.472805\pi$
$174$	0	0
$175$	848692.	2.09486
$176$	0	0
$177$	−244296.	−0.586115
$178$	0	0
$179$	−525330.	−1.22546	−0.612731	−	0.790292i	$-0.709929\pi$
$179$	−525330.	−1.22546	−0.612731	+	0.790292i	$0.709929\pi$
$180$	0	0
$181$	−74662.0	−0.169396	−0.0846980	−	0.996407i	$-0.526993\pi$
$181$	−74662.0	−0.169396	−0.0846980	+	0.996407i	$0.526993\pi$
$182$	0	0
$183$	439461.	0.970047
$184$	0	0
$185$	1.06013e6	2.27735
$186$	0	0
$187$	252495.	0.528018
$188$	0	0
$189$	−180063.	−0.366665
$190$	0	0
$191$	−404355.	−0.802009	−0.401005	−	0.916076i	$-0.631339\pi$
$191$	−404355.	−0.802009	−0.401005	+	0.916076i	$0.631339\pi$
$192$	0	0
$193$	835748.	1.61504	0.807518	−	0.589843i	$-0.200810\pi$
$193$	835748.	1.61504	0.807518	+	0.589843i	$0.200810\pi$
$194$	0	0
$195$	505926.	0.952797
$196$	0	0
$197$	−191682.	−0.351897	−0.175949	−	0.984399i	$-0.556299\pi$
$197$	−191682.	−0.351897	−0.175949	+	0.984399i	$0.556299\pi$
$198$	0	0
$199$	343231.	0.614404	0.307202	−	0.951644i	$-0.400607\pi$
$199$	343231.	0.614404	0.307202	+	0.951644i	$0.400607\pi$
$200$	0	0
$201$	499032.	0.871241
$202$	0	0
$203$	84474.0	0.143874
$204$	0	0
$205$	−1.31803e6	−2.19049
$206$	0	0
$207$	220644.	0.357904
$208$	0	0
$209$	−167865.	−0.265824
$210$	0	0
$211$	353116.	0.546023	0.273012	−	0.962011i	$-0.411980\pi$
$211$	353116.	0.546023	0.273012	+	0.962011i	$0.411980\pi$
$212$	0	0
$213$	388908.	0.587351
$214$	0	0
$215$	31671.0	0.0467268
$216$	0	0
$217$	2.33217e6	3.36211
$218$	0	0
$219$	−339165.	−0.477860
$220$	0	0
$221$	−376842.	−0.519013
$222$	0	0
$223$	443884.	0.597733	0.298867	−	0.954295i	$-0.403391\pi$
$223$	443884.	0.597733	0.298867	+	0.954295i	$0.403391\pi$
$224$	0	0
$225$	278316.	0.366507
$226$	0	0
$227$	110130.	0.141854	0.0709269	−	0.997482i	$-0.477404\pi$
$227$	110130.	0.141854	0.0709269	+	0.997482i	$0.477404\pi$
$228$	0	0
$229$	−543979.	−0.685478	−0.342739	−	0.939431i	$-0.611355\pi$
$229$	−543979.	−0.685478	−0.342739	+	0.939431i	$0.611355\pi$
$230$	0	0
$231$	−1.03369e6	−1.27457
$232$	0	0
$233$	−842991.	−1.01726	−0.508631	−	0.860984i	$-0.669848\pi$
$233$	−842991.	−1.01726	−0.508631	+	0.860984i	$0.669848\pi$
$234$	0	0
$235$	690363.	0.815470
$236$	0	0
$237$	−702144.	−0.811999
$238$	0	0
$239$	−1.08729e6	−1.23126	−0.615630	−	0.788036i	$-0.711098\pi$
$239$	−1.08729e6	−1.23126	−0.615630	+	0.788036i	$0.711098\pi$
$240$	0	0
$241$	392036.	0.434794	0.217397	−	0.976083i	$-0.430243\pi$
$241$	392036.	0.434794	0.217397	+	0.976083i	$0.430243\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	3.58036e6	3.81076
$246$	0	0
$247$	250534.	0.261291
$248$	0	0
$249$	755028.	0.771729
$250$	0	0
$251$	1.25925e6	1.26161	0.630807	−	0.775940i	$-0.282724\pi$
$251$	1.25925e6	1.26161	0.630807	+	0.775940i	$0.282724\pi$
$252$	0	0
$253$	1.26666e6	1.24411
$254$	0	0
$255$	−395847.	−0.381221
$256$	0	0
$257$	−22200.0	−0.0209662	−0.0104831	−	0.999945i	$-0.503337\pi$
$257$	−22200.0	−0.0209662	−0.0104831	+	0.999945i	$0.503337\pi$
$258$	0	0
$259$	3.23274e6	2.99448
$260$	0	0
$261$	27702.0	0.0251715
$262$	0	0
$263$	1.76991e6	1.57783	0.788917	−	0.614500i	$-0.210642\pi$
$263$	1.76991e6	1.57783	0.788917	+	0.614500i	$0.210642\pi$
$264$	0	0
$265$	−818910.	−0.716344
$266$	0	0
$267$	−229770.	−0.197249
$268$	0	0
$269$	333210.	0.280761	0.140381	−	0.990098i	$-0.455167\pi$
$269$	333210.	0.280761	0.140381	+	0.990098i	$0.455167\pi$
$270$	0	0
$271$	−1.21056e6	−1.00129	−0.500647	−	0.865652i	$-0.666905\pi$
$271$	−1.21056e6	−1.00129	−0.500647	+	0.865652i	$0.666905\pi$
$272$	0	0
$273$	1.54276e6	1.25283
$274$	0	0
$275$	1.59774e6	1.27401
$276$	0	0
$277$	51449.0	0.0402882	0.0201441	−	0.999797i	$-0.493588\pi$
$277$	51449.0	0.0402882	0.0201441	+	0.999797i	$0.493588\pi$
$278$	0	0
$279$	764802.	0.588218
$280$	0	0
$281$	1.57761e6	1.19188	0.595942	−	0.803028i	$-0.296779\pi$
$281$	1.57761e6	1.19188	0.595942	+	0.803028i	$0.296779\pi$
$282$	0	0
$283$	−833525.	−0.618661	−0.309330	−	0.950955i	$-0.600105\pi$
$283$	−833525.	−0.618661	−0.309330	+	0.950955i	$0.600105\pi$
$284$	0	0
$285$	263169.	0.191921
$286$	0	0
$287$	−4.01918e6	−2.88027
$288$	0	0
$289$	−1.12501e6	−0.792339
$290$	0	0
$291$	687402.	0.475859
$292$	0	0
$293$	−2.86547e6	−1.94996	−0.974982	−	0.222285i	$-0.928649\pi$
$293$	−2.86547e6	−1.94996	−0.974982	+	0.222285i	$0.928649\pi$
$294$	0	0
$295$	2.19866e6	1.47097
$296$	0	0
$297$	−338985.	−0.222992
$298$	0	0
$299$	−1.89046e6	−1.22289
$300$	0	0
$301$	96577.0	0.0614409
$302$	0	0
$303$	1.19345e6	0.746791
$304$	0	0
$305$	−3.95515e6	−2.43452
$306$	0	0
$307$	418228.	0.253260	0.126630	−	0.991950i	$-0.459584\pi$
$307$	418228.	0.253260	0.126630	+	0.991950i	$0.459584\pi$
$308$	0	0
$309$	611946.	0.364600
$310$	0	0
$311$	1.76735e6	1.03615	0.518074	−	0.855336i	$-0.326649\pi$
$311$	1.76735e6	1.03615	0.518074	+	0.855336i	$0.326649\pi$
$312$	0	0
$313$	−1.64835e6	−0.951020	−0.475510	−	0.879710i	$-0.657736\pi$
$313$	−1.64835e6	−0.951020	−0.475510	+	0.879710i	$0.657736\pi$
$314$	0	0
$315$	1.62057e6	0.920218
$316$	0	0
$317$	−1.94101e6	−1.08488	−0.542438	−	0.840096i	$-0.682499\pi$
$317$	−1.94101e6	−1.08488	−0.542438	+	0.840096i	$0.682499\pi$
$318$	0	0
$319$	159030.	0.0874989
$320$	0	0
$321$	−788454.	−0.427084
$322$	0	0
$323$	−196023.	−0.104544
$324$	0	0
$325$	−2.38458e6	−1.25229
$326$	0	0
$327$	−683172.	−0.353314
$328$	0	0
$329$	2.10518e6	1.07226
$330$	0	0
$331$	1.22566e6	0.614894	0.307447	−	0.951565i	$-0.400525\pi$
$331$	1.22566e6	0.614894	0.307447	+	0.951565i	$0.400525\pi$
$332$	0	0
$333$	1.06013e6	0.523899
$334$	0	0
$335$	−4.49129e6	−2.18655
$336$	0	0
$337$	−1.14470e6	−0.549057	−0.274529	−	0.961579i	$-0.588522\pi$
$337$	−1.14470e6	−0.549057	−0.274529	+	0.961579i	$0.588522\pi$
$338$	0	0
$339$	−458514.	−0.216697
$340$	0	0
$341$	4.39053e6	2.04471
$342$	0	0
$343$	6.76656e6	3.10551
$344$	0	0
$345$	−1.98580e6	−0.898229
$346$	0	0
$347$	3.51661e6	1.56784	0.783919	−	0.620863i	$-0.213218\pi$
$347$	3.51661e6	1.56784	0.783919	+	0.620863i	$0.213218\pi$
$348$	0	0
$349$	611789.	0.268867	0.134434	−	0.990923i	$-0.457078\pi$
$349$	611789.	0.268867	0.134434	+	0.990923i	$0.457078\pi$
$350$	0	0
$351$	505926.	0.219189
$352$	0	0
$353$	1.49043e6	0.636612	0.318306	−	0.947988i	$-0.396886\pi$
$353$	1.49043e6	0.636612	0.318306	+	0.947988i	$0.396886\pi$
$354$	0	0
$355$	−3.50017e6	−1.47407
$356$	0	0
$357$	−1.20709e6	−0.501267
$358$	0	0
$359$	1.79830e6	0.736423	0.368211	−	0.929742i	$-0.379970\pi$
$359$	1.79830e6	0.736423	0.368211	+	0.929742i	$0.379970\pi$
$360$	0	0
$361$	130321.	0.0526316
$362$	0	0
$363$	−496566.	−0.197793
$364$	0	0
$365$	3.05248e6	1.19928
$366$	0	0
$367$	453136.	0.175616	0.0878079	−	0.996137i	$-0.472014\pi$
$367$	453136.	0.175616	0.0878079	+	0.996137i	$0.472014\pi$
$368$	0	0
$369$	−1.31803e6	−0.503918
$370$	0	0
$371$	−2.49717e6	−0.941919
$372$	0	0
$373$	−2.01030e6	−0.748152	−0.374076	−	0.927398i	$-0.622040\pi$
$373$	−2.01030e6	−0.748152	−0.374076	+	0.927398i	$0.622040\pi$
$374$	0	0
$375$	−226719.	−0.0832549
$376$	0	0
$377$	−237348.	−0.0860067
$378$	0	0
$379$	−2.02633e6	−0.724624	−0.362312	−	0.932057i	$-0.618013\pi$
$379$	−2.02633e6	−0.724624	−0.362312	+	0.932057i	$0.618013\pi$
$380$	0	0
$381$	1.04654e6	0.369354
$382$	0	0
$383$	143910.	0.0501296	0.0250648	−	0.999686i	$-0.492021\pi$
$383$	143910.	0.0501296	0.0250648	+	0.999686i	$0.492021\pi$
$384$	0	0
$385$	9.30326e6	3.19877
$386$	0	0
$387$	31671.0	0.0107494
$388$	0	0
$389$	−4.49337e6	−1.50556	−0.752780	−	0.658273i	$-0.771287\pi$
$389$	−4.49337e6	−1.50556	−0.752780	+	0.658273i	$0.771287\pi$
$390$	0	0
$391$	1.47913e6	0.489289
$392$	0	0
$393$	−1.54994e6	−0.506212
$394$	0	0
$395$	6.31930e6	2.03787
$396$	0	0
$397$	4.70645e6	1.49871	0.749355	−	0.662169i	$-0.230364\pi$
$397$	4.70645e6	1.49871	0.749355	+	0.662169i	$0.230364\pi$
$398$	0	0
$399$	802503.	0.252356
$400$	0	0
$401$	−2.85534e6	−0.886741	−0.443371	−	0.896338i	$-0.646217\pi$
$401$	−2.85534e6	−0.886741	−0.443371	+	0.896338i	$0.646217\pi$
$402$	0	0
$403$	−6.55275e6	−2.00984
$404$	0	0
$405$	531441.	0.160997
$406$	0	0
$407$	6.08592e6	1.82113
$408$	0	0
$409$	−3.50069e6	−1.03477	−0.517386	−	0.855752i	$-0.673095\pi$
$409$	−3.50069e6	−1.03477	−0.517386	+	0.855752i	$0.673095\pi$
$410$	0	0
$411$	95337.0	0.0278392
$412$	0	0
$413$	6.70457e6	1.93417
$414$	0	0
$415$	−6.79525e6	−1.93680
$416$	0	0
$417$	−2.16384e6	−0.609376
$418$	0	0
$419$	5.67707e6	1.57975	0.789876	−	0.613266i	$-0.210145\pi$
$419$	5.67707e6	1.57975	0.789876	+	0.613266i	$0.210145\pi$
$420$	0	0
$421$	263714.	0.0725150	0.0362575	−	0.999342i	$-0.488456\pi$
$421$	263714.	0.0725150	0.0362575	+	0.999342i	$0.488456\pi$
$422$	0	0
$423$	690363.	0.187597
$424$	0	0
$425$	1.86575e6	0.501050
$426$	0	0
$427$	−1.20608e7	−3.20114
$428$	0	0
$429$	2.90439e6	0.761924
$430$	0	0
$431$	1.17097e6	0.303634	0.151817	−	0.988409i	$-0.451487\pi$
$431$	1.17097e6	0.303634	0.151817	+	0.988409i	$0.451487\pi$
$432$	0	0
$433$	5.82657e6	1.49346	0.746729	−	0.665129i	$-0.231623\pi$
$433$	5.82657e6	1.49346	0.746729	+	0.665129i	$0.231623\pi$
$434$	0	0
$435$	−249318.	−0.0631729
$436$	0	0
$437$	−983364.	−0.246326
$438$	0	0
$439$	892210.	0.220956	0.110478	−	0.993879i	$-0.464762\pi$
$439$	892210.	0.220956	0.110478	+	0.993879i	$0.464762\pi$
$440$	0	0
$441$	3.58036e6	0.876659
$442$	0	0
$443$	−2.33954e6	−0.566398	−0.283199	−	0.959061i	$-0.591396\pi$
$443$	−2.33954e6	−0.566398	−0.283199	+	0.959061i	$0.591396\pi$
$444$	0	0
$445$	2.06793e6	0.495035
$446$	0	0
$447$	−989415.	−0.234212
$448$	0	0
$449$	2.82784e6	0.661970	0.330985	−	0.943636i	$-0.392619\pi$
$449$	2.82784e6	0.661970	0.330985	+	0.943636i	$0.392619\pi$
$450$	0	0
$451$	−7.56648e6	−1.75167
$452$	0	0
$453$	4.83307e6	1.10657
$454$	0	0
$455$	−1.38849e7	−3.14422
$456$	0	0
$457$	287195.	0.0643260	0.0321630	−	0.999483i	$-0.489760\pi$
$457$	287195.	0.0643260	0.0321630	+	0.999483i	$0.489760\pi$
$458$	0	0
$459$	−395847.	−0.0876992
$460$	0	0
$461$	5.47137e6	1.19907	0.599534	−	0.800350i	$-0.295353\pi$
$461$	5.47137e6	1.19907	0.599534	+	0.800350i	$0.295353\pi$
$462$	0	0
$463$	−6.44627e6	−1.39751	−0.698756	−	0.715360i	$-0.746263\pi$
$463$	−6.44627e6	−1.39751	−0.698756	+	0.715360i	$0.746263\pi$
$464$	0	0
$465$	−6.88322e6	−1.47625
$466$	0	0
$467$	7.21695e6	1.53130	0.765652	−	0.643255i	$-0.222417\pi$
$467$	7.21695e6	1.53130	0.765652	+	0.643255i	$0.222417\pi$
$468$	0	0
$469$	−1.36957e7	−2.87509
$470$	0	0
$471$	−1.42745e6	−0.296490
$472$	0	0
$473$	181815.	0.0373660
$474$	0	0
$475$	−1.24040e6	−0.252247
$476$	0	0
$477$	−818910.	−0.164794
$478$	0	0
$479$	5.96484e6	1.18785	0.593923	−	0.804522i	$-0.297578\pi$
$479$	5.96484e6	1.18785	0.593923	+	0.804522i	$0.297578\pi$
$480$	0	0
$481$	−9.08307e6	−1.79007
$482$	0	0
$483$	−6.05545e6	−1.18108
$484$	0	0
$485$	−6.18662e6	−1.19426
$486$	0	0
$487$	5.30728e6	1.01403	0.507014	−	0.861938i	$-0.330749\pi$
$487$	5.30728e6	1.01403	0.507014	+	0.861938i	$0.330749\pi$
$488$	0	0
$489$	2.24971e6	0.425456
$490$	0	0
$491$	6.47410e6	1.21192	0.605962	−	0.795494i	$-0.292788\pi$
$491$	6.47410e6	1.21192	0.605962	+	0.795494i	$0.292788\pi$
$492$	0	0
$493$	185706.	0.0344119
$494$	0	0
$495$	3.05086e6	0.559642
$496$	0	0
$497$	−1.06734e7	−1.93825
$498$	0	0
$499$	−3.10316e6	−0.557896	−0.278948	−	0.960306i	$-0.589986\pi$
$499$	−3.10316e6	−0.557896	−0.278948	+	0.960306i	$0.589986\pi$
$500$	0	0
$501$	657342.	0.117003
$502$	0	0
$503$	9.26422e6	1.63263	0.816317	−	0.577604i	$-0.196012\pi$
$503$	9.26422e6	1.63263	0.816317	+	0.577604i	$0.196012\pi$
$504$	0	0
$505$	−1.07411e7	−1.87422
$506$	0	0
$507$	−993087.	−0.171580
$508$	0	0
$509$	3.70270e6	0.633467	0.316734	−	0.948514i	$-0.397414\pi$
$509$	3.70270e6	0.633467	0.316734	+	0.948514i	$0.397414\pi$
$510$	0	0
$511$	9.30820e6	1.57693
$512$	0	0
$513$	263169.	0.0441511
$514$	0	0
$515$	−5.50751e6	−0.915035
$516$	0	0
$517$	3.96320e6	0.652107
$518$	0	0
$519$	−604638.	−0.0985319
$520$	0	0
$521$	8.31762e6	1.34247	0.671235	−	0.741244i	$-0.265764\pi$
$521$	8.31762e6	1.34247	0.671235	+	0.741244i	$0.265764\pi$
$522$	0	0
$523$	−1.10321e7	−1.76362	−0.881810	−	0.471604i	$-0.843675\pi$
$523$	−1.10321e7	−1.76362	−0.881810	+	0.471604i	$0.843675\pi$
$524$	0	0
$525$	−7.63823e6	−1.20947
$526$	0	0
$527$	5.12701e6	0.804150
$528$	0	0
$529$	983833.	0.152856
$530$	0	0
$531$	2.19866e6	0.338394
$532$	0	0
$533$	1.12928e7	1.72180
$534$	0	0
$535$	7.09609e6	1.07185
$536$	0	0
$537$	4.72797e6	0.707520
$538$	0	0
$539$	2.05539e7	3.04735
$540$	0	0
$541$	−1.09731e7	−1.61189	−0.805947	−	0.591987i	$-0.798344\pi$
$541$	−1.09731e7	−1.61189	−0.805947	+	0.591987i	$0.798344\pi$
$542$	0	0
$543$	671958.	0.0978008
$544$	0	0
$545$	6.14855e6	0.886709
$546$	0	0
$547$	−1.71559e6	−0.245158	−0.122579	−	0.992459i	$-0.539116\pi$
$547$	−1.71559e6	−0.245158	−0.122579	+	0.992459i	$0.539116\pi$
$548$	0	0
$549$	−3.95515e6	−0.560057
$550$	0	0
$551$	−123462.	−0.0173242
$552$	0	0
$553$	1.92700e7	2.67959
$554$	0	0
$555$	−9.54115e6	−1.31483
$556$	0	0
$557$	582603.	0.0795673	0.0397837	−	0.999208i	$-0.487333\pi$
$557$	582603.	0.0795673	0.0397837	+	0.999208i	$0.487333\pi$
$558$	0	0
$559$	−271354.	−0.0367288
$560$	0	0
$561$	−2.27246e6	−0.304851
$562$	0	0
$563$	−8.98868e6	−1.19516	−0.597579	−	0.801810i	$-0.703870\pi$
$563$	−8.98868e6	−1.19516	−0.597579	+	0.801810i	$0.703870\pi$
$564$	0	0
$565$	4.12663e6	0.543844
$566$	0	0
$567$	1.62057e6	0.211694
$568$	0	0
$569$	−539826.	−0.0698993	−0.0349497	−	0.999389i	$-0.511127\pi$
$569$	−539826.	−0.0698993	−0.0349497	+	0.999389i	$0.511127\pi$
$570$	0	0
$571$	498448.	0.0639778	0.0319889	−	0.999488i	$-0.489816\pi$
$571$	498448.	0.0639778	0.0319889	+	0.999488i	$0.489816\pi$
$572$	0	0
$573$	3.63920e6	0.463040
$574$	0	0
$575$	9.35966e6	1.18057
$576$	0	0
$577$	1.95388e6	0.244319	0.122160	−	0.992510i	$-0.461018\pi$
$577$	1.95388e6	0.244319	0.122160	+	0.992510i	$0.461018\pi$
$578$	0	0
$579$	−7.52173e6	−0.932441
$580$	0	0
$581$	−2.07213e7	−2.54670
$582$	0	0
$583$	−4.70115e6	−0.572839
$584$	0	0
$585$	−4.55333e6	−0.550098
$586$	0	0
$587$	−2.34205e6	−0.280544	−0.140272	−	0.990113i	$-0.544798\pi$
$587$	−2.34205e6	−0.280544	−0.140272	+	0.990113i	$0.544798\pi$
$588$	0	0
$589$	−3.40856e6	−0.404840
$590$	0	0
$591$	1.72514e6	0.203168
$592$	0	0
$593$	−1.01216e7	−1.18198	−0.590992	−	0.806678i	$-0.701263\pi$
$593$	−1.01216e7	−1.18198	−0.590992	+	0.806678i	$0.701263\pi$
$594$	0	0
$595$	1.08638e7	1.25803
$596$	0	0
$597$	−3.08908e6	−0.354726
$598$	0	0
$599$	−3.41198e6	−0.388544	−0.194272	−	0.980948i	$-0.562234\pi$
$599$	−3.41198e6	−0.388544	−0.194272	+	0.980948i	$0.562234\pi$
$600$	0	0
$601$	1.03264e7	1.16617	0.583087	−	0.812410i	$-0.301845\pi$
$601$	1.03264e7	1.16617	0.583087	+	0.812410i	$0.301845\pi$
$602$	0	0
$603$	−4.49129e6	−0.503011
$604$	0	0
$605$	4.46909e6	0.496399
$606$	0	0
$607$	−1.59247e7	−1.75429	−0.877143	−	0.480229i	$-0.840554\pi$
$607$	−1.59247e7	−1.75429	−0.877143	+	0.480229i	$0.840554\pi$
$608$	0	0
$609$	−760266.	−0.0830658
$610$	0	0
$611$	−5.91496e6	−0.640987
$612$	0	0
$613$	−1.17105e6	−0.125871	−0.0629353	−	0.998018i	$-0.520046\pi$
$613$	−1.17105e6	−0.125871	−0.0629353	+	0.998018i	$0.520046\pi$
$614$	0	0
$615$	1.18623e7	1.26468
$616$	0	0
$617$	1.63844e7	1.73268	0.866338	−	0.499458i	$-0.166467\pi$
$617$	1.63844e7	1.73268	0.866338	+	0.499458i	$0.166467\pi$
$618$	0	0
$619$	1.63675e7	1.71694	0.858470	−	0.512864i	$-0.171415\pi$
$619$	1.63675e7	1.71694	0.858470	+	0.512864i	$0.171415\pi$
$620$	0	0
$621$	−1.98580e6	−0.206636
$622$	0	0
$623$	6.30591e6	0.650920
$624$	0	0
$625$	−8.69703e6	−0.890576
$626$	0	0
$627$	1.51078e6	0.153474
$628$	0	0
$629$	7.10678e6	0.716220
$630$	0	0
$631$	6.63506e6	0.663394	0.331697	−	0.943386i	$-0.392379\pi$
$631$	6.63506e6	0.663394	0.331697	+	0.943386i	$0.392379\pi$
$632$	0	0
$633$	−3.17804e6	−0.315247
$634$	0	0
$635$	−9.41884e6	−0.926965
$636$	0	0
$637$	−3.06762e7	−2.99539
$638$	0	0
$639$	−3.50017e6	−0.339107
$640$	0	0
$641$	−1.33964e7	−1.28778	−0.643890	−	0.765118i	$-0.722680\pi$
$641$	−1.33964e7	−1.28778	−0.643890	+	0.765118i	$0.722680\pi$
$642$	0	0
$643$	1.39471e7	1.33032	0.665161	−	0.746700i	$-0.268363\pi$
$643$	1.39471e7	1.33032	0.665161	+	0.746700i	$0.268363\pi$
$644$	0	0
$645$	−285039.	−0.0269777
$646$	0	0
$647$	−1.13734e6	−0.106814	−0.0534071	−	0.998573i	$-0.517008\pi$
$647$	−1.13734e6	−0.106814	−0.0534071	+	0.998573i	$0.517008\pi$
$648$	0	0
$649$	1.26220e7	1.17629
$650$	0	0
$651$	−2.09896e7	−1.94111
$652$	0	0
$653$	9.31890e6	0.855228	0.427614	−	0.903961i	$-0.359354\pi$
$653$	9.31890e6	0.855228	0.427614	+	0.903961i	$0.359354\pi$
$654$	0	0
$655$	1.39494e7	1.27044
$656$	0	0
$657$	3.05248e6	0.275893
$658$	0	0
$659$	1.39783e6	0.125383	0.0626916	−	0.998033i	$-0.480032\pi$
$659$	1.39783e6	0.125383	0.0626916	+	0.998033i	$0.480032\pi$
$660$	0	0
$661$	−3.23088e6	−0.287619	−0.143810	−	0.989605i	$-0.545935\pi$
$661$	−3.23088e6	−0.287619	−0.143810	+	0.989605i	$0.545935\pi$
$662$	0	0
$663$	3.39158e6	0.299653
$664$	0	0
$665$	−7.22253e6	−0.633337
$666$	0	0
$667$	931608.	0.0810809
$668$	0	0
$669$	−3.99496e6	−0.345101
$670$	0	0
$671$	−2.27055e7	−1.94681
$672$	0	0
$673$	1.26083e7	1.07305	0.536524	−	0.843885i	$-0.319737\pi$
$673$	1.26083e7	1.07305	0.536524	+	0.843885i	$0.319737\pi$
$674$	0	0
$675$	−2.50484e6	−0.211603
$676$	0	0
$677$	−2.55485e6	−0.214237	−0.107118	−	0.994246i	$-0.534162\pi$
$677$	−2.55485e6	−0.214237	−0.107118	+	0.994246i	$0.534162\pi$
$678$	0	0
$679$	−1.88654e7	−1.57033
$680$	0	0
$681$	−991170.	−0.0818993
$682$	0	0
$683$	−7.98629e6	−0.655079	−0.327539	−	0.944838i	$-0.606219\pi$
$683$	−7.98629e6	−0.655079	−0.327539	+	0.944838i	$0.606219\pi$
$684$	0	0
$685$	−858033.	−0.0698679
$686$	0	0
$687$	4.89581e6	0.395761
$688$	0	0
$689$	7.01634e6	0.563070
$690$	0	0
$691$	445657.	0.0355063	0.0177532	−	0.999842i	$-0.494349\pi$
$691$	445657.	0.0355063	0.0177532	+	0.999842i	$0.494349\pi$
$692$	0	0
$693$	9.30326e6	0.735871
$694$	0	0
$695$	1.94746e7	1.52935
$696$	0	0
$697$	−8.83570e6	−0.688904
$698$	0	0
$699$	7.58692e6	0.587317
$700$	0	0
$701$	−1.80137e7	−1.38455	−0.692273	−	0.721635i	$-0.743391\pi$
$701$	−1.80137e7	−1.38455	−0.692273	+	0.721635i	$0.743391\pi$
$702$	0	0
$703$	−4.72477e6	−0.360572
$704$	0	0
$705$	−6.21327e6	−0.470812
$706$	0	0
$707$	−3.27537e7	−2.46440
$708$	0	0
$709$	−1.46038e7	−1.09107	−0.545533	−	0.838090i	$-0.683673\pi$
$709$	−1.46038e7	−1.09107	−0.545533	+	0.838090i	$0.683673\pi$
$710$	0	0
$711$	6.31930e6	0.468808
$712$	0	0
$713$	2.57200e7	1.89473
$714$	0	0
$715$	−2.61395e7	−1.91220
$716$	0	0
$717$	9.78558e6	0.710868
$718$	0	0
$719$	1.77317e7	1.27917	0.639583	−	0.768722i	$-0.279107\pi$
$719$	1.77317e7	1.27917	0.639583	+	0.768722i	$0.279107\pi$
$720$	0	0
$721$	−1.67945e7	−1.20318
$722$	0	0
$723$	−3.52832e6	−0.251028
$724$	0	0
$725$	1.17511e6	0.0830298
$726$	0	0
$727$	−5.34167e6	−0.374836	−0.187418	−	0.982280i	$-0.560012\pi$
$727$	−5.34167e6	−0.374836	−0.187418	+	0.982280i	$0.560012\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	212313.	0.0146955
$732$	0	0
$733$	−251182.	−0.0172675	−0.00863373	−	0.999963i	$-0.502748\pi$
$733$	−251182.	−0.0172675	−0.00863373	+	0.999963i	$0.502748\pi$
$734$	0	0
$735$	−3.22233e7	−2.20014
$736$	0	0
$737$	−2.57833e7	−1.74852
$738$	0	0
$739$	−2.53900e7	−1.71022	−0.855108	−	0.518450i	$-0.826509\pi$
$739$	−2.53900e7	−1.71022	−0.855108	+	0.518450i	$0.826509\pi$
$740$	0	0
$741$	−2.25481e6	−0.150856
$742$	0	0
$743$	1.03864e7	0.690226	0.345113	−	0.938561i	$-0.387841\pi$
$743$	1.03864e7	0.690226	0.345113	+	0.938561i	$0.387841\pi$
$744$	0	0
$745$	8.90474e6	0.587801
$746$	0	0
$747$	−6.79525e6	−0.445558
$748$	0	0
$749$	2.16387e7	1.40937
$750$	0	0
$751$	−6.35473e6	−0.411147	−0.205573	−	0.978642i	$-0.565906\pi$
$751$	−6.35473e6	−0.411147	−0.205573	+	0.978642i	$0.565906\pi$
$752$	0	0
$753$	−1.13332e7	−0.728393
$754$	0	0
$755$	−4.34976e7	−2.77714
$756$	0	0
$757$	−1.96396e7	−1.24564	−0.622822	−	0.782364i	$-0.714014\pi$
$757$	−1.96396e7	−1.24564	−0.622822	+	0.782364i	$0.714014\pi$
$758$	0	0
$759$	−1.13999e7	−0.718287
$760$	0	0
$761$	−2.38787e7	−1.49468	−0.747342	−	0.664440i	$-0.768670\pi$
$761$	−2.38787e7	−1.49468	−0.747342	+	0.664440i	$0.768670\pi$
$762$	0	0
$763$	1.87493e7	1.16593
$764$	0	0
$765$	3.56262e6	0.220098
$766$	0	0
$767$	−1.88379e7	−1.15623
$768$	0	0
$769$	−8.58553e6	−0.523542	−0.261771	−	0.965130i	$-0.584306\pi$
$769$	−8.58553e6	−0.523542	−0.261771	+	0.965130i	$0.584306\pi$
$770$	0	0
$771$	199800.	0.0121049
$772$	0	0
$773$	−2.09415e7	−1.26055	−0.630274	−	0.776373i	$-0.717057\pi$
$773$	−2.09415e7	−1.26055	−0.630274	+	0.776373i	$0.717057\pi$
$774$	0	0
$775$	3.24427e7	1.94027
$776$	0	0
$777$	−2.90946e7	−1.72886
$778$	0	0
$779$	5.87419e6	0.346820
$780$	0	0
$781$	−2.00936e7	−1.17877
$782$	0	0
$783$	−249318.	−0.0145328
$784$	0	0
$785$	1.28471e7	0.744099
$786$	0	0
$787$	6.27868e6	0.361353	0.180676	−	0.983543i	$-0.442171\pi$
$787$	6.27868e6	0.361353	0.180676	+	0.983543i	$0.442171\pi$
$788$	0	0
$789$	−1.59292e7	−0.910962
$790$	0	0
$791$	1.25837e7	0.715098
$792$	0	0
$793$	3.38873e7	1.91361
$794$	0	0
$795$	7.37019e6	0.413581
$796$	0	0
$797$	−2.07776e7	−1.15864	−0.579322	−	0.815099i	$-0.696683\pi$
$797$	−2.07776e7	−1.15864	−0.579322	+	0.815099i	$0.696683\pi$
$798$	0	0
$799$	4.62799e6	0.256463
$800$	0	0
$801$	2.06793e6	0.113882
$802$	0	0
$803$	1.75235e7	0.959031
$804$	0	0
$805$	5.44991e7	2.96414
$806$	0	0
$807$	−2.99889e6	−0.162098
$808$	0	0
$809$	−1.98777e6	−0.106781	−0.0533905	−	0.998574i	$-0.517003\pi$
$809$	−1.98777e6	−0.106781	−0.0533905	+	0.998574i	$0.517003\pi$
$810$	0	0
$811$	7.95135e6	0.424511	0.212256	−	0.977214i	$-0.431919\pi$
$811$	7.95135e6	0.424511	0.212256	+	0.977214i	$0.431919\pi$
$812$	0	0
$813$	1.08950e7	0.578097
$814$	0	0
$815$	−2.02474e7	−1.06776
$816$	0	0
$817$	−141151.	−0.00739825
$818$	0	0
$819$	−1.38849e7	−0.723322
$820$	0	0
$821$	−1.83609e7	−0.950682	−0.475341	−	0.879802i	$-0.657675\pi$
$821$	−1.83609e7	−0.950682	−0.475341	+	0.879802i	$0.657675\pi$
$822$	0	0
$823$	2.41203e7	1.24132	0.620658	−	0.784081i	$-0.286865\pi$
$823$	2.41203e7	1.24132	0.620658	+	0.784081i	$0.286865\pi$
$824$	0	0
$825$	−1.43797e7	−0.735553
$826$	0	0
$827$	−2.72605e6	−0.138602	−0.0693011	−	0.997596i	$-0.522077\pi$
$827$	−2.72605e6	−0.138602	−0.0693011	+	0.997596i	$0.522077\pi$
$828$	0	0
$829$	−9.37985e6	−0.474034	−0.237017	−	0.971505i	$-0.576170\pi$
$829$	−9.37985e6	−0.474034	−0.237017	+	0.971505i	$0.576170\pi$
$830$	0	0
$831$	−463041.	−0.0232604
$832$	0	0
$833$	2.40017e7	1.19848
$834$	0	0
$835$	−5.91608e6	−0.293642
$836$	0	0
$837$	−6.88322e6	−0.339608
$838$	0	0
$839$	−9.77541e6	−0.479435	−0.239718	−	0.970843i	$-0.577055\pi$
$839$	−9.77541e6	−0.479435	−0.239718	+	0.970843i	$0.577055\pi$
$840$	0	0
$841$	−2.03942e7	−0.994298
$842$	0	0
$843$	−1.41985e7	−0.688134
$844$	0	0
$845$	8.93778e6	0.430614
$846$	0	0
$847$	1.36280e7	0.652714
$848$	0	0
$849$	7.50172e6	0.357184
$850$	0	0
$851$	3.56517e7	1.68755
$852$	0	0
$853$	6.31128e6	0.296992	0.148496	−	0.988913i	$-0.452557\pi$
$853$	6.31128e6	0.296992	0.148496	+	0.988913i	$0.452557\pi$
$854$	0	0
$855$	−2.36852e6	−0.110806
$856$	0	0
$857$	−5.14481e6	−0.239286	−0.119643	−	0.992817i	$-0.538175\pi$
$857$	−5.14481e6	−0.239286	−0.119643	+	0.992817i	$0.538175\pi$
$858$	0	0
$859$	−2.00958e7	−0.929226	−0.464613	−	0.885514i	$-0.653807\pi$
$859$	−2.00958e7	−0.929226	−0.464613	+	0.885514i	$0.653807\pi$
$860$	0	0
$861$	3.61727e7	1.66292
$862$	0	0
$863$	2.76609e7	1.26427	0.632133	−	0.774860i	$-0.282180\pi$
$863$	2.76609e7	1.26427	0.632133	+	0.774860i	$0.282180\pi$
$864$	0	0
$865$	5.44174e6	0.247285
$866$	0	0
$867$	1.01251e7	0.457457
$868$	0	0
$869$	3.62774e7	1.62962
$870$	0	0
$871$	3.84809e7	1.71870
$872$	0	0
$873$	−6.18662e6	−0.274737
$874$	0	0
$875$	6.22218e6	0.274740
$876$	0	0
$877$	−2.53036e7	−1.11092	−0.555460	−	0.831543i	$-0.687458\pi$
$877$	−2.53036e7	−1.11092	−0.555460	+	0.831543i	$0.687458\pi$
$878$	0	0
$879$	2.57892e7	1.12581
$880$	0	0
$881$	3.70933e7	1.61011	0.805056	−	0.593198i	$-0.202135\pi$
$881$	3.70933e7	1.61011	0.805056	+	0.593198i	$0.202135\pi$
$882$	0	0
$883$	−4.35101e7	−1.87797	−0.938985	−	0.343958i	$-0.888232\pi$
$883$	−4.35101e7	−1.87797	−0.938985	+	0.343958i	$0.888232\pi$
$884$	0	0
$885$	−1.97880e7	−0.849265
$886$	0	0
$887$	−2.37449e7	−1.01335	−0.506677	−	0.862136i	$-0.669126\pi$
$887$	−2.37449e7	−1.01335	−0.506677	+	0.862136i	$0.669126\pi$
$888$	0	0
$889$	−2.87217e7	−1.21886
$890$	0	0
$891$	3.05086e6	0.128745
$892$	0	0
$893$	−3.07680e6	−0.129113
$894$	0	0
$895$	−4.25517e7	−1.77566
$896$	0	0
$897$	1.70141e7	0.706038
$898$	0	0
$899$	3.22916e6	0.133257
$900$	0	0
$901$	−5.48973e6	−0.225288
$902$	0	0
$903$	−869193.	−0.0354729
$904$	0	0
$905$	−6.04762e6	−0.245450
$906$	0	0
$907$	2.01882e7	0.814855	0.407428	−	0.913238i	$-0.366426\pi$
$907$	2.01882e7	0.814855	0.407428	+	0.913238i	$0.366426\pi$
$908$	0	0
$909$	−1.07411e7	−0.431160
$910$	0	0
$911$	−8.39955e6	−0.335320	−0.167660	−	0.985845i	$-0.553621\pi$
$911$	−8.39955e6	−0.335320	−0.167660	+	0.985845i	$0.553621\pi$
$912$	0	0
$913$	−3.90098e7	−1.54880
$914$	0	0
$915$	3.55963e7	1.40557
$916$	0	0
$917$	4.25371e7	1.67049
$918$	0	0
$919$	−4.33552e7	−1.69337	−0.846686	−	0.532092i	$-0.821406\pi$
$919$	−4.33552e7	−1.69337	−0.846686	+	0.532092i	$0.821406\pi$
$920$	0	0
$921$	−3.76405e6	−0.146220
$922$	0	0
$923$	2.99891e7	1.15867
$924$	0	0
$925$	4.49704e7	1.72811
$926$	0	0
$927$	−5.50751e6	−0.210502
$928$	0	0
$929$	2.04854e7	0.778762	0.389381	−	0.921077i	$-0.372689\pi$
$929$	2.04854e7	0.778762	0.389381	+	0.921077i	$0.372689\pi$
$930$	0	0
$931$	−1.59569e7	−0.603358
$932$	0	0
$933$	−1.59062e7	−0.598220
$934$	0	0
$935$	2.04521e7	0.765083
$936$	0	0
$937$	1.70989e7	0.636237	0.318118	−	0.948051i	$-0.396949\pi$
$937$	1.70989e7	0.636237	0.318118	+	0.948051i	$0.396949\pi$
$938$	0	0
$939$	1.48352e7	0.549072
$940$	0	0
$941$	2.46405e6	0.0907142	0.0453571	−	0.998971i	$-0.485557\pi$
$941$	2.46405e6	0.0907142	0.0453571	+	0.998971i	$0.485557\pi$
$942$	0	0
$943$	−4.43249e7	−1.62319
$944$	0	0
$945$	−1.45851e7	−0.531288
$946$	0	0
$947$	−3.37152e7	−1.22166	−0.610831	−	0.791761i	$-0.709164\pi$
$947$	−3.37152e7	−1.22166	−0.610831	+	0.791761i	$0.709164\pi$
$948$	0	0
$949$	−2.61534e7	−0.942676
$950$	0	0
$951$	1.74691e7	0.626353
$952$	0	0
$953$	−1.19024e7	−0.424525	−0.212262	−	0.977213i	$-0.568083\pi$
$953$	−1.19024e7	−0.424525	−0.212262	+	0.977213i	$0.568083\pi$
$954$	0	0
$955$	−3.27528e7	−1.16209
$956$	0	0
$957$	−1.43127e6	−0.0505175
$958$	0	0
$959$	−2.61647e6	−0.0918691
$960$	0	0
$961$	6.05222e7	2.11401
$962$	0	0
$963$	7.09609e6	0.246577
$964$	0	0
$965$	6.76956e7	2.34014
$966$	0	0
$967$	−1.22453e7	−0.421119	−0.210559	−	0.977581i	$-0.567529\pi$
$967$	−1.22453e7	−0.421119	−0.210559	+	0.977581i	$0.567529\pi$
$968$	0	0
$969$	1.76421e6	0.0603587
$970$	0	0
$971$	1.19930e7	0.408205	0.204102	−	0.978950i	$-0.434572\pi$
$971$	1.19930e7	0.408205	0.204102	+	0.978950i	$0.434572\pi$
$972$	0	0
$973$	5.93855e7	2.01094
$974$	0	0
$975$	2.14613e7	0.723009
$976$	0	0
$977$	5.17458e7	1.73436	0.867179	−	0.497996i	$-0.165931\pi$
$977$	5.17458e7	1.73436	0.867179	+	0.497996i	$0.165931\pi$
$978$	0	0
$979$	1.18714e7	0.395865
$980$	0	0
$981$	6.14855e6	0.203986
$982$	0	0
$983$	5.48877e7	1.81172	0.905860	−	0.423577i	$-0.139226\pi$
$983$	5.48877e7	1.81172	0.905860	+	0.423577i	$0.139226\pi$
$984$	0	0
$985$	−1.55262e7	−0.509889
$986$	0	0
$987$	−1.89466e7	−0.619069
$988$	0	0
$989$	1.06508e6	0.0346253
$990$	0	0
$991$	9.62512e6	0.311331	0.155665	−	0.987810i	$-0.450248\pi$
$991$	9.62512e6	0.311331	0.155665	+	0.987810i	$0.450248\pi$
$992$	0	0
$993$	−1.10309e7	−0.355009
$994$	0	0
$995$	2.78017e7	0.890254
$996$	0	0
$997$	−1.67975e7	−0.535187	−0.267593	−	0.963532i	$-0.586228\pi$
$997$	−1.67975e7	−0.535187	−0.267593	+	0.963532i	$0.586228\pi$
$998$	0	0
$999$	−9.54115e6	−0.302473

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.6.a.b.1.1	✓	1	4.3	odd	2
342.6.a.d.1.1		1	12.11	even	2
912.6.a.e.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

Related objects

Downloads

Learn more