LMFDB - Embedded newform 912.6.a.d.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:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
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)

$f(q)$

$=$

$q-9.00000 q^{3} +6.00000 q^{5} +176.000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q-9.00000 q^{3} +6.00000 q^{5} +176.000 q^{7} +81.0000 q^{9} +496.000 q^{11} -178.000 q^{13} -54.0000 q^{15} +202.000 q^{17} +361.000 q^{19} -1584.00 q^{21} -4396.00 q^{23} -3089.00 q^{25} -729.000 q^{27} -5902.00 q^{29} -5760.00 q^{31} -4464.00 q^{33} +1056.00 q^{35} -3906.00 q^{37} +1602.00 q^{39} +15774.0 q^{41} +7492.00 q^{43} +486.000 q^{45} +7452.00 q^{47} +14169.0 q^{49} -1818.00 q^{51} -29014.0 q^{53} +2976.00 q^{55} -3249.00 q^{57} -13604.0 q^{59} -12466.0 q^{61} +14256.0 q^{63} -1068.00 q^{65} -43436.0 q^{67} +39564.0 q^{69} -28800.0 q^{71} +80746.0 q^{73} +27801.0 q^{75} +87296.0 q^{77} -76456.0 q^{79} +6561.00 q^{81} +56880.0 q^{83} +1212.00 q^{85} +53118.0 q^{87} -103266. q^{89} -31328.0 q^{91} +51840.0 q^{93} +2166.00 q^{95} +82490.0 q^{97} +40176.0 q^{99} +O(q^{100})$

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
$5$	6.00000	0.107331	0.0536656	−	0.998559i	$-0.482909\pi$
$5$	6.00000	0.107331	0.0536656	+	0.998559i	$0.482909\pi$
$6$	0	0
$7$	176.000	1.35759	0.678793	−	0.734329i	$-0.262503\pi$
$7$	176.000	1.35759	0.678793	+	0.734329i	$0.262503\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	496.000	1.23595	0.617974	−	0.786199i	$-0.287954\pi$
$11$	496.000	1.23595	0.617974	+	0.786199i	$0.287954\pi$
$12$	0	0
$13$	−178.000	−0.292120	−0.146060	−	0.989276i	$-0.546659\pi$
$13$	−178.000	−0.292120	−0.146060	+	0.989276i	$0.546659\pi$
$14$	0	0
$15$	−54.0000	−0.0619677
$16$	0	0
$17$	202.000	0.169523	0.0847616	−	0.996401i	$-0.472987\pi$
$17$	202.000	0.169523	0.0847616	+	0.996401i	$0.472987\pi$
$18$	0	0
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	0	0
$21$	−1584.00	−0.783803
$22$	0	0
$23$	−4396.00	−1.73276	−0.866379	−	0.499386i	$-0.833559\pi$
$23$	−4396.00	−1.73276	−0.866379	+	0.499386i	$0.833559\pi$
$24$	0	0
$25$	−3089.00	−0.988480
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	−5902.00	−1.30318	−0.651590	−	0.758572i	$-0.725898\pi$
$29$	−5902.00	−1.30318	−0.651590	+	0.758572i	$0.725898\pi$
$30$	0	0
$31$	−5760.00	−1.07651	−0.538255	−	0.842782i	$-0.680916\pi$
$31$	−5760.00	−1.07651	−0.538255	+	0.842782i	$0.680916\pi$
$32$	0	0
$33$	−4464.00	−0.713575
$34$	0	0
$35$	1056.00	0.145711
$36$	0	0
$37$	−3906.00	−0.469059	−0.234530	−	0.972109i	$-0.575355\pi$
$37$	−3906.00	−0.469059	−0.234530	+	0.972109i	$0.575355\pi$
$38$	0	0
$39$	1602.00	0.168656
$40$	0	0
$41$	15774.0	1.46549	0.732744	−	0.680505i	$-0.238239\pi$
$41$	15774.0	1.46549	0.732744	+	0.680505i	$0.238239\pi$
$42$	0	0
$43$	7492.00	0.617912	0.308956	−	0.951076i	$-0.400020\pi$
$43$	7492.00	0.617912	0.308956	+	0.951076i	$0.400020\pi$
$44$	0	0
$45$	486.000	0.0357771
$46$	0	0
$47$	7452.00	0.492071	0.246036	−	0.969261i	$-0.420872\pi$
$47$	7452.00	0.492071	0.246036	+	0.969261i	$0.420872\pi$
$48$	0	0
$49$	14169.0	0.843042
$50$	0	0
$51$	−1818.00	−0.0978742
$52$	0	0
$53$	−29014.0	−1.41879	−0.709395	−	0.704811i	$-0.751032\pi$
$53$	−29014.0	−1.41879	−0.709395	+	0.704811i	$0.751032\pi$
$54$	0	0
$55$	2976.00	0.132656
$56$	0	0
$57$	−3249.00	−0.132453
$58$	0	0
$59$	−13604.0	−0.508788	−0.254394	−	0.967101i	$-0.581876\pi$
$59$	−13604.0	−0.508788	−0.254394	+	0.967101i	$0.581876\pi$
$60$	0	0
$61$	−12466.0	−0.428946	−0.214473	−	0.976730i	$-0.568803\pi$
$61$	−12466.0	−0.428946	−0.214473	+	0.976730i	$0.568803\pi$
$62$	0	0
$63$	14256.0	0.452529
$64$	0	0
$65$	−1068.00	−0.0313536
$66$	0	0
$67$	−43436.0	−1.18212	−0.591062	−	0.806626i	$-0.701291\pi$
$67$	−43436.0	−1.18212	−0.591062	+	0.806626i	$0.701291\pi$
$68$	0	0
$69$	39564.0	1.00041
$70$	0	0
$71$	−28800.0	−0.678026	−0.339013	−	0.940782i	$-0.610093\pi$
$71$	−28800.0	−0.678026	−0.339013	+	0.940782i	$0.610093\pi$
$72$	0	0
$73$	80746.0	1.77343	0.886715	−	0.462317i	$-0.152982\pi$
$73$	80746.0	1.77343	0.886715	+	0.462317i	$0.152982\pi$
$74$	0	0
$75$	27801.0	0.570699
$76$	0	0
$77$	87296.0	1.67791
$78$	0	0
$79$	−76456.0	−1.37830	−0.689150	−	0.724619i	$-0.742016\pi$
$79$	−76456.0	−1.37830	−0.689150	+	0.724619i	$0.742016\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	56880.0	0.906284	0.453142	−	0.891438i	$-0.350303\pi$
$83$	56880.0	0.906284	0.453142	+	0.891438i	$0.350303\pi$
$84$	0	0
$85$	1212.00	0.0181951
$86$	0	0
$87$	53118.0	0.752391
$88$	0	0
$89$	−103266.	−1.38192	−0.690959	−	0.722894i	$-0.742812\pi$
$89$	−103266.	−1.38192	−0.690959	+	0.722894i	$0.742812\pi$
$90$	0	0
$91$	−31328.0	−0.396579
$92$	0	0
$93$	51840.0	0.621524
$94$	0	0
$95$	2166.00	0.0246235
$96$	0	0
$97$	82490.0	0.890168	0.445084	−	0.895489i	$-0.353174\pi$
$97$	82490.0	0.890168	0.445084	+	0.895489i	$0.353174\pi$
$98$	0	0
$99$	40176.0	0.411982
$100$	0	0
$101$	47230.0	0.460696	0.230348	−	0.973108i	$-0.426014\pi$
$101$	47230.0	0.460696	0.230348	+	0.973108i	$0.426014\pi$
$102$	0	0
$103$	−157456.	−1.46240	−0.731200	−	0.682163i	$-0.761039\pi$
$103$	−157456.	−1.46240	−0.731200	+	0.682163i	$0.761039\pi$
$104$	0	0
$105$	−9504.00	−0.0841266
$106$	0	0
$107$	62988.0	0.531861	0.265931	−	0.963992i	$-0.414321\pi$
$107$	62988.0	0.531861	0.265931	+	0.963992i	$0.414321\pi$
$108$	0	0
$109$	38158.0	0.307623	0.153812	−	0.988100i	$-0.450845\pi$
$109$	38158.0	0.307623	0.153812	+	0.988100i	$0.450845\pi$
$110$	0	0
$111$	35154.0	0.270812
$112$	0	0
$113$	9190.00	0.0677048	0.0338524	−	0.999427i	$-0.489222\pi$
$113$	9190.00	0.0677048	0.0338524	+	0.999427i	$0.489222\pi$
$114$	0	0
$115$	−26376.0	−0.185979
$116$	0	0
$117$	−14418.0	−0.0973734
$118$	0	0
$119$	35552.0	0.230142
$120$	0	0
$121$	84965.0	0.527566
$122$	0	0
$123$	−141966.	−0.846100
$124$	0	0
$125$	−37284.0	−0.213426
$126$	0	0
$127$	70448.0	0.387578	0.193789	−	0.981043i	$-0.437922\pi$
$127$	70448.0	0.387578	0.193789	+	0.981043i	$0.437922\pi$
$128$	0	0
$129$	−67428.0	−0.356752
$130$	0	0
$131$	−101864.	−0.518612	−0.259306	−	0.965795i	$-0.583494\pi$
$131$	−101864.	−0.518612	−0.259306	+	0.965795i	$0.583494\pi$
$132$	0	0
$133$	63536.0	0.311452
$134$	0	0
$135$	−4374.00	−0.0206559
$136$	0	0
$137$	−432126.	−1.96702	−0.983510	−	0.180851i	$-0.942115\pi$
$137$	−432126.	−1.96702	−0.983510	+	0.180851i	$0.942115\pi$
$138$	0	0
$139$	376684.	1.65364	0.826818	−	0.562469i	$-0.190148\pi$
$139$	376684.	1.65364	0.826818	+	0.562469i	$0.190148\pi$
$140$	0	0
$141$	−67068.0	−0.284098
$142$	0	0
$143$	−88288.0	−0.361045
$144$	0	0
$145$	−35412.0	−0.139872
$146$	0	0
$147$	−127521.	−0.486730
$148$	0	0
$149$	−283554.	−1.04633	−0.523167	−	0.852230i	$-0.675249\pi$
$149$	−283554.	−1.04633	−0.523167	+	0.852230i	$0.675249\pi$
$150$	0	0
$151$	79200.0	0.282672	0.141336	−	0.989962i	$-0.454860\pi$
$151$	79200.0	0.282672	0.141336	+	0.989962i	$0.454860\pi$
$152$	0	0
$153$	16362.0	0.0565077
$154$	0	0
$155$	−34560.0	−0.115543
$156$	0	0
$157$	−129858.	−0.420455	−0.210228	−	0.977652i	$-0.567420\pi$
$157$	−129858.	−0.420455	−0.210228	+	0.977652i	$0.567420\pi$
$158$	0	0
$159$	261126.	0.819138
$160$	0	0
$161$	−773696.	−2.35237
$162$	0	0
$163$	−57420.0	−0.169276	−0.0846378	−	0.996412i	$-0.526973\pi$
$163$	−57420.0	−0.169276	−0.0846378	+	0.996412i	$0.526973\pi$
$164$	0	0
$165$	−26784.0	−0.0765889
$166$	0	0
$167$	254008.	0.704784	0.352392	−	0.935852i	$-0.385368\pi$
$167$	254008.	0.704784	0.352392	+	0.935852i	$0.385368\pi$
$168$	0	0
$169$	−339609.	−0.914666
$170$	0	0
$171$	29241.0	0.0764719
$172$	0	0
$173$	−177366.	−0.450563	−0.225281	−	0.974294i	$-0.572330\pi$
$173$	−177366.	−0.450563	−0.225281	+	0.974294i	$0.572330\pi$
$174$	0	0
$175$	−543664.	−1.34195
$176$	0	0
$177$	122436.	0.293749
$178$	0	0
$179$	25188.0	0.0587572	0.0293786	−	0.999568i	$-0.490647\pi$
$179$	25188.0	0.0587572	0.0293786	+	0.999568i	$0.490647\pi$
$180$	0	0
$181$	729382.	1.65485	0.827425	−	0.561576i	$-0.189805\pi$
$181$	729382.	1.65485	0.827425	+	0.561576i	$0.189805\pi$
$182$	0	0
$183$	112194.	0.247652
$184$	0	0
$185$	−23436.0	−0.0503447
$186$	0	0
$187$	100192.	0.209522
$188$	0	0
$189$	−128304.	−0.261268
$190$	0	0
$191$	285060.	0.565396	0.282698	−	0.959209i	$-0.408771\pi$
$191$	285060.	0.565396	0.282698	+	0.959209i	$0.408771\pi$
$192$	0	0
$193$	−457598.	−0.884282	−0.442141	−	0.896946i	$-0.645781\pi$
$193$	−457598.	−0.884282	−0.442141	+	0.896946i	$0.645781\pi$
$194$	0	0
$195$	9612.00	0.0181020
$196$	0	0
$197$	−291178.	−0.534556	−0.267278	−	0.963620i	$-0.586124\pi$
$197$	−291178.	−0.534556	−0.267278	+	0.963620i	$0.586124\pi$
$198$	0	0
$199$	−364680.	−0.652799	−0.326399	−	0.945232i	$-0.605835\pi$
$199$	−364680.	−0.652799	−0.326399	+	0.945232i	$0.605835\pi$
$200$	0	0
$201$	390924.	0.682499
$202$	0	0
$203$	−1.03875e6	−1.76918
$204$	0	0
$205$	94644.0	0.157293
$206$	0	0
$207$	−356076.	−0.577586
$208$	0	0
$209$	179056.	0.283546
$210$	0	0
$211$	452388.	0.699528	0.349764	−	0.936838i	$-0.386262\pi$
$211$	452388.	0.699528	0.349764	+	0.936838i	$0.386262\pi$
$212$	0	0
$213$	259200.	0.391459
$214$	0	0
$215$	44952.0	0.0663213
$216$	0	0
$217$	−1.01376e6	−1.46146
$218$	0	0
$219$	−726714.	−1.02389
$220$	0	0
$221$	−35956.0	−0.0495211
$222$	0	0
$223$	−940296.	−1.26620	−0.633100	−	0.774070i	$-0.718218\pi$
$223$	−940296.	−1.26620	−0.633100	+	0.774070i	$0.718218\pi$
$224$	0	0
$225$	−250209.	−0.329493
$226$	0	0
$227$	−796308.	−1.02569	−0.512845	−	0.858481i	$-0.671409\pi$
$227$	−796308.	−1.02569	−0.512845	+	0.858481i	$0.671409\pi$
$228$	0	0
$229$	153334.	0.193219	0.0966095	−	0.995322i	$-0.469200\pi$
$229$	153334.	0.193219	0.0966095	+	0.995322i	$0.469200\pi$
$230$	0	0
$231$	−785664.	−0.968739
$232$	0	0
$233$	246858.	0.297891	0.148946	−	0.988845i	$-0.452412\pi$
$233$	246858.	0.297891	0.148946	+	0.988845i	$0.452412\pi$
$234$	0	0
$235$	44712.0	0.0528147
$236$	0	0
$237$	688104.	0.795762
$238$	0	0
$239$	−105516.	−0.119488	−0.0597439	−	0.998214i	$-0.519028\pi$
$239$	−105516.	−0.119488	−0.0597439	+	0.998214i	$0.519028\pi$
$240$	0	0
$241$	41738.0	0.0462902	0.0231451	−	0.999732i	$-0.492632\pi$
$241$	41738.0	0.0462902	0.0231451	+	0.999732i	$0.492632\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	85014.0	0.0904847
$246$	0	0
$247$	−64258.0	−0.0670170
$248$	0	0
$249$	−511920.	−0.523243
$250$	0	0
$251$	362392.	0.363073	0.181537	−	0.983384i	$-0.441893\pi$
$251$	362392.	0.363073	0.181537	+	0.983384i	$0.441893\pi$
$252$	0	0
$253$	−2.18042e6	−2.14160
$254$	0	0
$255$	−10908.0	−0.0105050
$256$	0	0
$257$	−1.16120e6	−1.09667	−0.548334	−	0.836260i	$-0.684738\pi$
$257$	−1.16120e6	−1.09667	−0.548334	+	0.836260i	$0.684738\pi$
$258$	0	0
$259$	−687456.	−0.636789
$260$	0	0
$261$	−478062.	−0.434393
$262$	0	0
$263$	−1.35860e6	−1.21116	−0.605579	−	0.795785i	$-0.707059\pi$
$263$	−1.35860e6	−1.21116	−0.605579	+	0.795785i	$0.707059\pi$
$264$	0	0
$265$	−174084.	−0.152280
$266$	0	0
$267$	929394.	0.797851
$268$	0	0
$269$	2.19871e6	1.85263	0.926314	−	0.376753i	$-0.122960\pi$
$269$	2.19871e6	1.85263	0.926314	+	0.376753i	$0.122960\pi$
$270$	0	0
$271$	512016.	0.423507	0.211753	−	0.977323i	$-0.432083\pi$
$271$	512016.	0.423507	0.211753	+	0.977323i	$0.432083\pi$
$272$	0	0
$273$	281952.	0.228965
$274$	0	0
$275$	−1.53214e6	−1.22171
$276$	0	0
$277$	857542.	0.671515	0.335758	−	0.941948i	$-0.391008\pi$
$277$	857542.	0.671515	0.335758	+	0.941948i	$0.391008\pi$
$278$	0	0
$279$	−466560.	−0.358837
$280$	0	0
$281$	−375370.	−0.283592	−0.141796	−	0.989896i	$-0.545288\pi$
$281$	−375370.	−0.283592	−0.141796	+	0.989896i	$0.545288\pi$
$282$	0	0
$283$	−2204.00	−0.00163586	−0.000817929	−	1.00000i	$-0.500260\pi$
$283$	−2204.00	−0.00163586	−0.000817929		1.00000i	$0.500260\pi$
$284$	0	0
$285$	−19494.0	−0.0142164
$286$	0	0
$287$	2.77622e6	1.98953
$288$	0	0
$289$	−1.37905e6	−0.971262
$290$	0	0
$291$	−742410.	−0.513939
$292$	0	0
$293$	−605198.	−0.411840	−0.205920	−	0.978569i	$-0.566019\pi$
$293$	−605198.	−0.411840	−0.205920	+	0.978569i	$0.566019\pi$
$294$	0	0
$295$	−81624.0	−0.0546088
$296$	0	0
$297$	−361584.	−0.237858
$298$	0	0
$299$	782488.	0.506174
$300$	0	0
$301$	1.31859e6	0.838869
$302$	0	0
$303$	−425070.	−0.265983
$304$	0	0
$305$	−74796.0	−0.0460393
$306$	0	0
$307$	1.25593e6	0.760537	0.380268	−	0.924876i	$-0.375832\pi$
$307$	1.25593e6	0.760537	0.380268	+	0.924876i	$0.375832\pi$
$308$	0	0
$309$	1.41710e6	0.844317
$310$	0	0
$311$	824580.	0.483428	0.241714	−	0.970348i	$-0.422290\pi$
$311$	824580.	0.483428	0.241714	+	0.970348i	$0.422290\pi$
$312$	0	0
$313$	−1.23455e6	−0.712275	−0.356138	−	0.934434i	$-0.615907\pi$
$313$	−1.23455e6	−0.712275	−0.356138	+	0.934434i	$0.615907\pi$
$314$	0	0
$315$	85536.0	0.0485705
$316$	0	0
$317$	−1.19428e6	−0.667509	−0.333755	−	0.942660i	$-0.608316\pi$
$317$	−1.19428e6	−0.667509	−0.333755	+	0.942660i	$0.608316\pi$
$318$	0	0
$319$	−2.92739e6	−1.61066
$320$	0	0
$321$	−566892.	−0.307070
$322$	0	0
$323$	72922.0	0.0388913
$324$	0	0
$325$	549842.	0.288755
$326$	0	0
$327$	−343422.	−0.177606
$328$	0	0
$329$	1.31155e6	0.668030
$330$	0	0
$331$	−1.99113e6	−0.998919	−0.499459	−	0.866337i	$-0.666468\pi$
$331$	−1.99113e6	−0.998919	−0.499459	+	0.866337i	$0.666468\pi$
$332$	0	0
$333$	−316386.	−0.156353
$334$	0	0
$335$	−260616.	−0.126879
$336$	0	0
$337$	6442.00	0.00308991	0.00154496	−	0.999999i	$-0.499508\pi$
$337$	6442.00	0.00308991	0.00154496	+	0.999999i	$0.499508\pi$
$338$	0	0
$339$	−82710.0	−0.0390894
$340$	0	0
$341$	−2.85696e6	−1.33051
$342$	0	0
$343$	−464288.	−0.213085
$344$	0	0
$345$	237384.	0.107375
$346$	0	0
$347$	1.66693e6	0.743179	0.371589	−	0.928397i	$-0.378813\pi$
$347$	1.66693e6	0.743179	0.371589	+	0.928397i	$0.378813\pi$
$348$	0	0
$349$	−3.89805e6	−1.71310	−0.856552	−	0.516060i	$-0.827398\pi$
$349$	−3.89805e6	−1.71310	−0.856552	+	0.516060i	$0.827398\pi$
$350$	0	0
$351$	129762.	0.0562186
$352$	0	0
$353$	407306.	0.173974	0.0869869	−	0.996209i	$-0.472276\pi$
$353$	407306.	0.173974	0.0869869	+	0.996209i	$0.472276\pi$
$354$	0	0
$355$	−172800.	−0.0727734
$356$	0	0
$357$	−319968.	−0.132873
$358$	0	0
$359$	−2.59413e6	−1.06232	−0.531161	−	0.847271i	$-0.678244\pi$
$359$	−2.59413e6	−1.06232	−0.531161	+	0.847271i	$0.678244\pi$
$360$	0	0
$361$	130321.	0.0526316
$362$	0	0
$363$	−764685.	−0.304590
$364$	0	0
$365$	484476.	0.190344
$366$	0	0
$367$	761840.	0.295256	0.147628	−	0.989043i	$-0.452836\pi$
$367$	761840.	0.295256	0.147628	+	0.989043i	$0.452836\pi$
$368$	0	0
$369$	1.27769e6	0.488496
$370$	0	0
$371$	−5.10646e6	−1.92613
$372$	0	0
$373$	−837506.	−0.311685	−0.155842	−	0.987782i	$-0.549809\pi$
$373$	−837506.	−0.311685	−0.155842	+	0.987782i	$0.549809\pi$
$374$	0	0
$375$	335556.	0.123222
$376$	0	0
$377$	1.05056e6	0.380685
$378$	0	0
$379$	623876.	0.223100	0.111550	−	0.993759i	$-0.464418\pi$
$379$	623876.	0.223100	0.111550	+	0.993759i	$0.464418\pi$
$380$	0	0
$381$	−634032.	−0.223768
$382$	0	0
$383$	−97672.0	−0.0340230	−0.0170115	−	0.999855i	$-0.505415\pi$
$383$	−97672.0	−0.0340230	−0.0170115	+	0.999855i	$0.505415\pi$
$384$	0	0
$385$	523776.	0.180092
$386$	0	0
$387$	606852.	0.205971
$388$	0	0
$389$	−2.23487e6	−0.748823	−0.374411	−	0.927263i	$-0.622155\pi$
$389$	−2.23487e6	−0.748823	−0.374411	+	0.927263i	$0.622155\pi$
$390$	0	0
$391$	−887992.	−0.293743
$392$	0	0
$393$	916776.	0.299421
$394$	0	0
$395$	−458736.	−0.147935
$396$	0	0
$397$	4.93416e6	1.57122	0.785610	−	0.618723i	$-0.212349\pi$
$397$	4.93416e6	1.57122	0.785610	+	0.618723i	$0.212349\pi$
$398$	0	0
$399$	−571824.	−0.179817
$400$	0	0
$401$	−3.73411e6	−1.15965	−0.579823	−	0.814742i	$-0.696878\pi$
$401$	−3.73411e6	−1.15965	−0.579823	+	0.814742i	$0.696878\pi$
$402$	0	0
$403$	1.02528e6	0.314470
$404$	0	0
$405$	39366.0	0.0119257
$406$	0	0
$407$	−1.93738e6	−0.579733
$408$	0	0
$409$	−2.46083e6	−0.727400	−0.363700	−	0.931516i	$-0.618487\pi$
$409$	−2.46083e6	−0.727400	−0.363700	+	0.931516i	$0.618487\pi$
$410$	0	0
$411$	3.88913e6	1.13566
$412$	0	0
$413$	−2.39430e6	−0.690723
$414$	0	0
$415$	341280.	0.0972726
$416$	0	0
$417$	−3.39016e6	−0.954728
$418$	0	0
$419$	437512.	0.121746	0.0608730	−	0.998146i	$-0.480612\pi$
$419$	437512.	0.121746	0.0608730	+	0.998146i	$0.480612\pi$
$420$	0	0
$421$	2.91013e6	0.800217	0.400108	−	0.916468i	$-0.368972\pi$
$421$	2.91013e6	0.800217	0.400108	+	0.916468i	$0.368972\pi$
$422$	0	0
$423$	603612.	0.164024
$424$	0	0
$425$	−623978.	−0.167570
$426$	0	0
$427$	−2.19402e6	−0.582331
$428$	0	0
$429$	794592.	0.208450
$430$	0	0
$431$	4.64881e6	1.20545	0.602724	−	0.797950i	$-0.294082\pi$
$431$	4.64881e6	1.20545	0.602724	+	0.797950i	$0.294082\pi$
$432$	0	0
$433$	6.90871e6	1.77083	0.885415	−	0.464801i	$-0.153874\pi$
$433$	6.90871e6	1.77083	0.885415	+	0.464801i	$0.153874\pi$
$434$	0	0
$435$	318708.	0.0807551
$436$	0	0
$437$	−1.58696e6	−0.397522
$438$	0	0
$439$	−6.25621e6	−1.54935	−0.774676	−	0.632359i	$-0.782087\pi$
$439$	−6.25621e6	−1.54935	−0.774676	+	0.632359i	$0.782087\pi$
$440$	0	0
$441$	1.14769e6	0.281014
$442$	0	0
$443$	−2.14088e6	−0.518302	−0.259151	−	0.965837i	$-0.583443\pi$
$443$	−2.14088e6	−0.518302	−0.259151	+	0.965837i	$0.583443\pi$
$444$	0	0
$445$	−619596.	−0.148323
$446$	0	0
$447$	2.55199e6	0.604101
$448$	0	0
$449$	4.92089e6	1.15194	0.575968	−	0.817472i	$-0.304625\pi$
$449$	4.92089e6	1.15194	0.575968	+	0.817472i	$0.304625\pi$
$450$	0	0
$451$	7.82390e6	1.81127
$452$	0	0
$453$	−712800.	−0.163201
$454$	0	0
$455$	−187968.	−0.0425653
$456$	0	0
$457$	3.94009e6	0.882502	0.441251	−	0.897384i	$-0.354535\pi$
$457$	3.94009e6	0.882502	0.441251	+	0.897384i	$0.354535\pi$
$458$	0	0
$459$	−147258.	−0.0326247
$460$	0	0
$461$	−2.25945e6	−0.495166	−0.247583	−	0.968867i	$-0.579636\pi$
$461$	−2.25945e6	−0.495166	−0.247583	+	0.968867i	$0.579636\pi$
$462$	0	0
$463$	3.31806e6	0.719337	0.359668	−	0.933080i	$-0.382890\pi$
$463$	3.31806e6	0.719337	0.359668	+	0.933080i	$0.382890\pi$
$464$	0	0
$465$	311040.	0.0667089
$466$	0	0
$467$	−3.63171e6	−0.770583	−0.385291	−	0.922795i	$-0.625899\pi$
$467$	−3.63171e6	−0.770583	−0.385291	+	0.922795i	$0.625899\pi$
$468$	0	0
$469$	−7.64474e6	−1.60483
$470$	0	0
$471$	1.16872e6	0.242750
$472$	0	0
$473$	3.71603e6	0.763707
$474$	0	0
$475$	−1.11513e6	−0.226773
$476$	0	0
$477$	−2.35013e6	−0.472930
$478$	0	0
$479$	1.45764e6	0.290275	0.145138	−	0.989411i	$-0.453637\pi$
$479$	1.45764e6	0.290275	0.145138	+	0.989411i	$0.453637\pi$
$480$	0	0
$481$	695268.	0.137022
$482$	0	0
$483$	6.96326e6	1.35814
$484$	0	0
$485$	494940.	0.0955429
$486$	0	0
$487$	−6.73825e6	−1.28743	−0.643716	−	0.765264i	$-0.722608\pi$
$487$	−6.73825e6	−1.28743	−0.643716	+	0.765264i	$0.722608\pi$
$488$	0	0
$489$	516780.	0.0977313
$490$	0	0
$491$	−3.47875e6	−0.651208	−0.325604	−	0.945506i	$-0.605568\pi$
$491$	−3.47875e6	−0.651208	−0.325604	+	0.945506i	$0.605568\pi$
$492$	0	0
$493$	−1.19220e6	−0.220919
$494$	0	0
$495$	241056.	0.0442186
$496$	0	0
$497$	−5.06880e6	−0.920480
$498$	0	0
$499$	9.39514e6	1.68909	0.844543	−	0.535487i	$-0.179872\pi$
$499$	9.39514e6	1.68909	0.844543	+	0.535487i	$0.179872\pi$
$500$	0	0
$501$	−2.28607e6	−0.406907
$502$	0	0
$503$	−9.43514e6	−1.66276	−0.831378	−	0.555708i	$-0.812447\pi$
$503$	−9.43514e6	−1.66276	−0.831378	+	0.555708i	$0.812447\pi$
$504$	0	0
$505$	283380.	0.0494471
$506$	0	0
$507$	3.05648e6	0.528083
$508$	0	0
$509$	6.92644e6	1.18499	0.592496	−	0.805573i	$-0.298142\pi$
$509$	6.92644e6	1.18499	0.592496	+	0.805573i	$0.298142\pi$
$510$	0	0
$511$	1.42113e7	2.40758
$512$	0	0
$513$	−263169.	−0.0441511
$514$	0	0
$515$	−944736.	−0.156961
$516$	0	0
$517$	3.69619e6	0.608174
$518$	0	0
$519$	1.59629e6	0.260132
$520$	0	0
$521$	−6.53061e6	−1.05405	−0.527023	−	0.849851i	$-0.676692\pi$
$521$	−6.53061e6	−1.05405	−0.527023	+	0.849851i	$0.676692\pi$
$522$	0	0
$523$	1.80276e6	0.288194	0.144097	−	0.989564i	$-0.453972\pi$
$523$	1.80276e6	0.288194	0.144097	+	0.989564i	$0.453972\pi$
$524$	0	0
$525$	4.89298e6	0.774774
$526$	0	0
$527$	−1.16352e6	−0.182493
$528$	0	0
$529$	1.28885e7	2.00245
$530$	0	0
$531$	−1.10192e6	−0.169596
$532$	0	0
$533$	−2.80777e6	−0.428099
$534$	0	0
$535$	377928.	0.0570853
$536$	0	0
$537$	−226692.	−0.0339235
$538$	0	0
$539$	7.02782e6	1.04196
$540$	0	0
$541$	1.03740e7	1.52389	0.761946	−	0.647640i	$-0.224244\pi$
$541$	1.03740e7	1.52389	0.761946	+	0.647640i	$0.224244\pi$
$542$	0	0
$543$	−6.56444e6	−0.955428
$544$	0	0
$545$	228948.	0.0330176
$546$	0	0
$547$	8.14488e6	1.16390	0.581951	−	0.813224i	$-0.302290\pi$
$547$	8.14488e6	1.16390	0.581951	+	0.813224i	$0.302290\pi$
$548$	0	0
$549$	−1.00975e6	−0.142982
$550$	0	0
$551$	−2.13062e6	−0.298970
$552$	0	0
$553$	−1.34563e7	−1.87116
$554$	0	0
$555$	210924.	0.0290666
$556$	0	0
$557$	−5.47163e6	−0.747271	−0.373636	−	0.927576i	$-0.621889\pi$
$557$	−5.47163e6	−0.747271	−0.373636	+	0.927576i	$0.621889\pi$
$558$	0	0
$559$	−1.33358e6	−0.180505
$560$	0	0
$561$	−901728.	−0.120967
$562$	0	0
$563$	−6.41428e6	−0.852858	−0.426429	−	0.904521i	$-0.640229\pi$
$563$	−6.41428e6	−0.852858	−0.426429	+	0.904521i	$0.640229\pi$
$564$	0	0
$565$	55140.0	0.00726684
$566$	0	0
$567$	1.15474e6	0.150843
$568$	0	0
$569$	−1.25705e7	−1.62769	−0.813847	−	0.581080i	$-0.802631\pi$
$569$	−1.25705e7	−1.62769	−0.813847	+	0.581080i	$0.802631\pi$
$570$	0	0
$571$	7.51477e6	0.964552	0.482276	−	0.876019i	$-0.339810\pi$
$571$	7.51477e6	0.964552	0.482276	+	0.876019i	$0.339810\pi$
$572$	0	0
$573$	−2.56554e6	−0.326432
$574$	0	0
$575$	1.35792e7	1.71280
$576$	0	0
$577$	1.96226e6	0.245367	0.122684	−	0.992446i	$-0.460850\pi$
$577$	1.96226e6	0.245367	0.122684	+	0.992446i	$0.460850\pi$
$578$	0	0
$579$	4.11838e6	0.510541
$580$	0	0
$581$	1.00109e7	1.23036
$582$	0	0
$583$	−1.43909e7	−1.75355
$584$	0	0
$585$	−86508.0	−0.0104512
$586$	0	0
$587$	−7.03206e6	−0.842339	−0.421170	−	0.906982i	$-0.638380\pi$
$587$	−7.03206e6	−0.842339	−0.421170	+	0.906982i	$0.638380\pi$
$588$	0	0
$589$	−2.07936e6	−0.246968
$590$	0	0
$591$	2.62060e6	0.308626
$592$	0	0
$593$	−4.68493e6	−0.547099	−0.273550	−	0.961858i	$-0.588198\pi$
$593$	−4.68493e6	−0.547099	−0.273550	+	0.961858i	$0.588198\pi$
$594$	0	0
$595$	213312.	0.0247015
$596$	0	0
$597$	3.28212e6	0.376893
$598$	0	0
$599$	−5.00460e6	−0.569905	−0.284952	−	0.958542i	$-0.591978\pi$
$599$	−5.00460e6	−0.569905	−0.284952	+	0.958542i	$0.591978\pi$
$600$	0	0
$601$	−1.20527e7	−1.36112	−0.680561	−	0.732692i	$-0.738264\pi$
$601$	−1.20527e7	−1.36112	−0.680561	+	0.732692i	$0.738264\pi$
$602$	0	0
$603$	−3.51832e6	−0.394041
$604$	0	0
$605$	509790.	0.0566243
$606$	0	0
$607$	9.62474e6	1.06027	0.530136	−	0.847913i	$-0.322141\pi$
$607$	9.62474e6	1.06027	0.530136	+	0.847913i	$0.322141\pi$
$608$	0	0
$609$	9.34877e6	1.02144
$610$	0	0
$611$	−1.32646e6	−0.143744
$612$	0	0
$613$	2.45060e6	0.263403	0.131702	−	0.991289i	$-0.457956\pi$
$613$	2.45060e6	0.263403	0.131702	+	0.991289i	$0.457956\pi$
$614$	0	0
$615$	−851796.	−0.0908130
$616$	0	0
$617$	4.17808e6	0.441839	0.220920	−	0.975292i	$-0.429094\pi$
$617$	4.17808e6	0.441839	0.220920	+	0.975292i	$0.429094\pi$
$618$	0	0
$619$	−1.80615e7	−1.89465	−0.947323	−	0.320279i	$-0.896223\pi$
$619$	−1.80615e7	−1.89465	−0.947323	+	0.320279i	$0.896223\pi$
$620$	0	0
$621$	3.20468e6	0.333470
$622$	0	0
$623$	−1.81748e7	−1.87607
$624$	0	0
$625$	9.42942e6	0.965573
$626$	0	0
$627$	−1.61150e6	−0.163705
$628$	0	0
$629$	−789012.	−0.0795165
$630$	0	0
$631$	−1.35029e7	−1.35006	−0.675030	−	0.737790i	$-0.735869\pi$
$631$	−1.35029e7	−1.35006	−0.675030	+	0.737790i	$0.735869\pi$
$632$	0	0
$633$	−4.07149e6	−0.403873
$634$	0	0
$635$	422688.	0.0415993
$636$	0	0
$637$	−2.52208e6	−0.246269
$638$	0	0
$639$	−2.33280e6	−0.226009
$640$	0	0
$641$	−8.29497e6	−0.797388	−0.398694	−	0.917084i	$-0.630536\pi$
$641$	−8.29497e6	−0.797388	−0.398694	+	0.917084i	$0.630536\pi$
$642$	0	0
$643$	7.22854e6	0.689482	0.344741	−	0.938698i	$-0.387967\pi$
$643$	7.22854e6	0.689482	0.344741	+	0.938698i	$0.387967\pi$
$644$	0	0
$645$	−404568.	−0.0382906
$646$	0	0
$647$	−6.59915e6	−0.619765	−0.309883	−	0.950775i	$-0.600290\pi$
$647$	−6.59915e6	−0.619765	−0.309883	+	0.950775i	$0.600290\pi$
$648$	0	0
$649$	−6.74758e6	−0.628835
$650$	0	0
$651$	9.12384e6	0.843772
$652$	0	0
$653$	1.68576e7	1.54708	0.773540	−	0.633747i	$-0.218484\pi$
$653$	1.68576e7	1.54708	0.773540	+	0.633747i	$0.218484\pi$
$654$	0	0
$655$	−611184.	−0.0556633
$656$	0	0
$657$	6.54043e6	0.591143
$658$	0	0
$659$	2.13425e6	0.191440	0.0957199	−	0.995408i	$-0.469485\pi$
$659$	2.13425e6	0.191440	0.0957199	+	0.995408i	$0.469485\pi$
$660$	0	0
$661$	1.65547e7	1.47373	0.736865	−	0.676040i	$-0.236305\pi$
$661$	1.65547e7	1.47373	0.736865	+	0.676040i	$0.236305\pi$
$662$	0	0
$663$	323604.	0.0285910
$664$	0	0
$665$	381216.	0.0334285
$666$	0	0
$667$	2.59452e7	2.25810
$668$	0	0
$669$	8.46266e6	0.731041
$670$	0	0
$671$	−6.18314e6	−0.530155
$672$	0	0
$673$	−704670.	−0.0599719	−0.0299860	−	0.999550i	$-0.509546\pi$
$673$	−704670.	−0.0599719	−0.0299860	+	0.999550i	$0.509546\pi$
$674$	0	0
$675$	2.25188e6	0.190233
$676$	0	0
$677$	6.83619e6	0.573248	0.286624	−	0.958043i	$-0.407467\pi$
$677$	6.83619e6	0.573248	0.286624	+	0.958043i	$0.407467\pi$
$678$	0	0
$679$	1.45182e7	1.20848
$680$	0	0
$681$	7.16677e6	0.592183
$682$	0	0
$683$	−1.24211e7	−1.01884	−0.509422	−	0.860517i	$-0.670141\pi$
$683$	−1.24211e7	−1.01884	−0.509422	+	0.860517i	$0.670141\pi$
$684$	0	0
$685$	−2.59276e6	−0.211123
$686$	0	0
$687$	−1.38001e6	−0.111555
$688$	0	0
$689$	5.16449e6	0.414457
$690$	0	0
$691$	8.00772e6	0.637990	0.318995	−	0.947756i	$-0.396655\pi$
$691$	8.00772e6	0.637990	0.318995	+	0.947756i	$0.396655\pi$
$692$	0	0
$693$	7.07098e6	0.559302
$694$	0	0
$695$	2.26010e6	0.177487
$696$	0	0
$697$	3.18635e6	0.248434
$698$	0	0
$699$	−2.22172e6	−0.171987
$700$	0	0
$701$	−1.18657e7	−0.912005	−0.456003	−	0.889978i	$-0.650719\pi$
$701$	−1.18657e7	−0.912005	−0.456003	+	0.889978i	$0.650719\pi$
$702$	0	0
$703$	−1.41007e6	−0.107610
$704$	0	0
$705$	−402408.	−0.0304926
$706$	0	0
$707$	8.31248e6	0.625435
$708$	0	0
$709$	8.30329e6	0.620347	0.310173	−	0.950680i	$-0.399613\pi$
$709$	8.30329e6	0.620347	0.310173	+	0.950680i	$0.399613\pi$
$710$	0	0
$711$	−6.19294e6	−0.459433
$712$	0	0
$713$	2.53210e7	1.86533
$714$	0	0
$715$	−529728.	−0.0387514
$716$	0	0
$717$	949644.	0.0689863
$718$	0	0
$719$	1.18495e7	0.854828	0.427414	−	0.904056i	$-0.359425\pi$
$719$	1.18495e7	0.854828	0.427414	+	0.904056i	$0.359425\pi$
$720$	0	0
$721$	−2.77123e7	−1.98533
$722$	0	0
$723$	−375642.	−0.0267257
$724$	0	0
$725$	1.82313e7	1.28817
$726$	0	0
$727$	−4.81482e6	−0.337866	−0.168933	−	0.985628i	$-0.554032\pi$
$727$	−4.81482e6	−0.337866	−0.168933	+	0.985628i	$0.554032\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	1.51338e6	0.104750
$732$	0	0
$733$	1.10193e6	0.0757523	0.0378761	−	0.999282i	$-0.487941\pi$
$733$	1.10193e6	0.0757523	0.0378761	+	0.999282i	$0.487941\pi$
$734$	0	0
$735$	−765126.	−0.0522414
$736$	0	0
$737$	−2.15443e7	−1.46104
$738$	0	0
$739$	−2.45211e7	−1.65169	−0.825845	−	0.563898i	$-0.809301\pi$
$739$	−2.45211e7	−1.65169	−0.825845	+	0.563898i	$0.809301\pi$
$740$	0	0
$741$	578322.	0.0386923
$742$	0	0
$743$	8.14072e6	0.540992	0.270496	−	0.962721i	$-0.412812\pi$
$743$	8.14072e6	0.540992	0.270496	+	0.962721i	$0.412812\pi$
$744$	0	0
$745$	−1.70132e6	−0.112304
$746$	0	0
$747$	4.60728e6	0.302095
$748$	0	0
$749$	1.10859e7	0.722048
$750$	0	0
$751$	−1.07734e6	−0.0697030	−0.0348515	−	0.999393i	$-0.511096\pi$
$751$	−1.07734e6	−0.0697030	−0.0348515	+	0.999393i	$0.511096\pi$
$752$	0	0
$753$	−3.26153e6	−0.209620
$754$	0	0
$755$	475200.	0.0303395
$756$	0	0
$757$	1.90412e7	1.20769	0.603843	−	0.797103i	$-0.293635\pi$
$757$	1.90412e7	1.20769	0.603843	+	0.797103i	$0.293635\pi$
$758$	0	0
$759$	1.96237e7	1.23645
$760$	0	0
$761$	2.74948e7	1.72103	0.860515	−	0.509426i	$-0.170142\pi$
$761$	2.74948e7	1.72103	0.860515	+	0.509426i	$0.170142\pi$
$762$	0	0
$763$	6.71581e6	0.417625
$764$	0	0
$765$	98172.0	0.00606505
$766$	0	0
$767$	2.42151e6	0.148627
$768$	0	0
$769$	2.51266e7	1.53221	0.766105	−	0.642716i	$-0.222192\pi$
$769$	2.51266e7	1.53221	0.766105	+	0.642716i	$0.222192\pi$
$770$	0	0
$771$	1.04508e7	0.633161
$772$	0	0
$773$	−1.50927e7	−0.908483	−0.454242	−	0.890879i	$-0.650090\pi$
$773$	−1.50927e7	−0.908483	−0.454242	+	0.890879i	$0.650090\pi$
$774$	0	0
$775$	1.77926e7	1.06411
$776$	0	0
$777$	6.18710e6	0.367650
$778$	0	0
$779$	5.69441e6	0.336206
$780$	0	0
$781$	−1.42848e7	−0.838005
$782$	0	0
$783$	4.30256e6	0.250797
$784$	0	0
$785$	−779148.	−0.0451280
$786$	0	0
$787$	2.71612e7	1.56319	0.781596	−	0.623785i	$-0.214406\pi$
$787$	2.71612e7	1.56319	0.781596	+	0.623785i	$0.214406\pi$
$788$	0	0
$789$	1.22274e7	0.699263
$790$	0	0
$791$	1.61744e6	0.0919151
$792$	0	0
$793$	2.21895e6	0.125304
$794$	0	0
$795$	1.56676e6	0.0879192
$796$	0	0
$797$	−2.12149e7	−1.18303	−0.591515	−	0.806294i	$-0.701470\pi$
$797$	−2.12149e7	−1.18303	−0.591515	+	0.806294i	$0.701470\pi$
$798$	0	0
$799$	1.50530e6	0.0834175
$800$	0	0
$801$	−8.36455e6	−0.460639
$802$	0	0
$803$	4.00500e7	2.19187
$804$	0	0
$805$	−4.64218e6	−0.252483
$806$	0	0
$807$	−1.97884e7	−1.06961
$808$	0	0
$809$	−6.93973e6	−0.372796	−0.186398	−	0.982474i	$-0.559681\pi$
$809$	−6.93973e6	−0.372796	−0.186398	+	0.982474i	$0.559681\pi$
$810$	0	0
$811$	−2.52867e6	−0.135002	−0.0675009	−	0.997719i	$-0.521503\pi$
$811$	−2.52867e6	−0.135002	−0.0675009	+	0.997719i	$0.521503\pi$
$812$	0	0
$813$	−4.60814e6	−0.244512
$814$	0	0
$815$	−344520.	−0.0181686
$816$	0	0
$817$	2.70461e6	0.141759
$818$	0	0
$819$	−2.53757e6	−0.132193
$820$	0	0
$821$	−2.31034e7	−1.19624	−0.598120	−	0.801406i	$-0.704085\pi$
$821$	−2.31034e7	−1.19624	−0.598120	+	0.801406i	$0.704085\pi$
$822$	0	0
$823$	−103360.	−0.00531928	−0.00265964	−	0.999996i	$-0.500847\pi$
$823$	−103360.	−0.00531928	−0.00265964	+	0.999996i	$0.500847\pi$
$824$	0	0
$825$	1.37893e7	0.705354
$826$	0	0
$827$	−3.23111e6	−0.164281	−0.0821406	−	0.996621i	$-0.526176\pi$
$827$	−3.23111e6	−0.164281	−0.0821406	+	0.996621i	$0.526176\pi$
$828$	0	0
$829$	−1.24466e7	−0.629022	−0.314511	−	0.949254i	$-0.601841\pi$
$829$	−1.24466e7	−0.629022	−0.314511	+	0.949254i	$0.601841\pi$
$830$	0	0
$831$	−7.71788e6	−0.387700
$832$	0	0
$833$	2.86214e6	0.142915
$834$	0	0
$835$	1.52405e6	0.0756454
$836$	0	0
$837$	4.19904e6	0.207175
$838$	0	0
$839$	−1.20780e7	−0.592366	−0.296183	−	0.955131i	$-0.595714\pi$
$839$	−1.20780e7	−0.592366	−0.296183	+	0.955131i	$0.595714\pi$
$840$	0	0
$841$	1.43225e7	0.698277
$842$	0	0
$843$	3.37833e6	0.163732
$844$	0	0
$845$	−2.03765e6	−0.0981722
$846$	0	0
$847$	1.49538e7	0.716216
$848$	0	0
$849$	19836.0	0.000944463 0
$850$	0	0
$851$	1.71708e7	0.812767
$852$	0	0
$853$	−7.24764e6	−0.341055	−0.170527	−	0.985353i	$-0.554547\pi$
$853$	−7.24764e6	−0.341055	−0.170527	+	0.985353i	$0.554547\pi$
$854$	0	0
$855$	175446.	0.00820783
$856$	0	0
$857$	2.29801e6	0.106881	0.0534405	−	0.998571i	$-0.482981\pi$
$857$	2.29801e6	0.106881	0.0534405	+	0.998571i	$0.482981\pi$
$858$	0	0
$859$	1.60848e7	0.743758	0.371879	−	0.928281i	$-0.378714\pi$
$859$	1.60848e7	0.743758	0.371879	+	0.928281i	$0.378714\pi$
$860$	0	0
$861$	−2.49860e7	−1.14865
$862$	0	0
$863$	−6.42193e6	−0.293521	−0.146760	−	0.989172i	$-0.546885\pi$
$863$	−6.42193e6	−0.293521	−0.146760	+	0.989172i	$0.546885\pi$
$864$	0	0
$865$	−1.06420e6	−0.0483595
$866$	0	0
$867$	1.24115e7	0.560758
$868$	0	0
$869$	−3.79222e7	−1.70351
$870$	0	0
$871$	7.73161e6	0.345322
$872$	0	0
$873$	6.68169e6	0.296723
$874$	0	0
$875$	−6.56198e6	−0.289744
$876$	0	0
$877$	2.82068e7	1.23838	0.619192	−	0.785240i	$-0.287460\pi$
$877$	2.82068e7	1.23838	0.619192	+	0.785240i	$0.287460\pi$
$878$	0	0
$879$	5.44678e6	0.237776
$880$	0	0
$881$	−3.93965e7	−1.71009	−0.855043	−	0.518557i	$-0.826470\pi$
$881$	−3.93965e7	−1.71009	−0.855043	+	0.518557i	$0.826470\pi$
$882$	0	0
$883$	−3.38638e7	−1.46162	−0.730809	−	0.682582i	$-0.760857\pi$
$883$	−3.38638e7	−1.46162	−0.730809	+	0.682582i	$0.760857\pi$
$884$	0	0
$885$	734616.	0.0315284
$886$	0	0
$887$	−2.08861e7	−0.891351	−0.445675	−	0.895195i	$-0.647036\pi$
$887$	−2.08861e7	−0.891351	−0.445675	+	0.895195i	$0.647036\pi$
$888$	0	0
$889$	1.23988e7	0.526171
$890$	0	0
$891$	3.25426e6	0.137327
$892$	0	0
$893$	2.69017e6	0.112889
$894$	0	0
$895$	151128.	0.00630648
$896$	0	0
$897$	−7.04239e6	−0.292240
$898$	0	0
$899$	3.39955e7	1.40289
$900$	0	0
$901$	−5.86083e6	−0.240518
$902$	0	0
$903$	−1.18673e7	−0.484321
$904$	0	0
$905$	4.37629e6	0.177617
$906$	0	0
$907$	3.63949e7	1.46900	0.734501	−	0.678608i	$-0.237416\pi$
$907$	3.63949e7	1.46900	0.734501	+	0.678608i	$0.237416\pi$
$908$	0	0
$909$	3.82563e6	0.153565
$910$	0	0
$911$	−1.83331e6	−0.0731881	−0.0365940	−	0.999330i	$-0.511651\pi$
$911$	−1.83331e6	−0.0731881	−0.0365940	+	0.999330i	$0.511651\pi$
$912$	0	0
$913$	2.82125e7	1.12012
$914$	0	0
$915$	673164.	0.0265808
$916$	0	0
$917$	−1.79281e7	−0.704061
$918$	0	0
$919$	1.62178e7	0.633436	0.316718	−	0.948520i	$-0.397419\pi$
$919$	1.62178e7	0.633436	0.316718	+	0.948520i	$0.397419\pi$
$920$	0	0
$921$	−1.13034e7	−0.439096
$922$	0	0
$923$	5.12640e6	0.198065
$924$	0	0
$925$	1.20656e7	0.463656
$926$	0	0
$927$	−1.27539e7	−0.487467
$928$	0	0
$929$	2.06857e7	0.786379	0.393189	−	0.919457i	$-0.371372\pi$
$929$	2.06857e7	0.786379	0.393189	+	0.919457i	$0.371372\pi$
$930$	0	0
$931$	5.11501e6	0.193407
$932$	0	0
$933$	−7.42122e6	−0.279107
$934$	0	0
$935$	601152.	0.0224882
$936$	0	0
$937$	7.79438e6	0.290023	0.145012	−	0.989430i	$-0.453678\pi$
$937$	7.79438e6	0.290023	0.145012	+	0.989430i	$0.453678\pi$
$938$	0	0
$939$	1.11110e7	0.411232
$940$	0	0
$941$	−2.20151e7	−0.810487	−0.405243	−	0.914209i	$-0.632813\pi$
$941$	−2.20151e7	−0.810487	−0.405243	+	0.914209i	$0.632813\pi$
$942$	0	0
$943$	−6.93425e7	−2.53934
$944$	0	0
$945$	−769824.	−0.0280422
$946$	0	0
$947$	−3.67660e6	−0.133221	−0.0666103	−	0.997779i	$-0.521218\pi$
$947$	−3.67660e6	−0.133221	−0.0666103	+	0.997779i	$0.521218\pi$
$948$	0	0
$949$	−1.43728e7	−0.518055
$950$	0	0
$951$	1.07485e7	0.385387
$952$	0	0
$953$	−6.27011e6	−0.223636	−0.111818	−	0.993729i	$-0.535667\pi$
$953$	−6.27011e6	−0.223636	−0.111818	+	0.993729i	$0.535667\pi$
$954$	0	0
$955$	1.71036e6	0.0606847
$956$	0	0
$957$	2.63465e7	0.929916
$958$	0	0
$959$	−7.60542e7	−2.67040
$960$	0	0
$961$	4.54845e6	0.158875
$962$	0	0
$963$	5.10203e6	0.177287
$964$	0	0
$965$	−2.74559e6	−0.0949111
$966$	0	0
$967$	−3.19646e7	−1.09927	−0.549633	−	0.835406i	$-0.685232\pi$
$967$	−3.19646e7	−1.09927	−0.549633	+	0.835406i	$0.685232\pi$
$968$	0	0
$969$	−656298.	−0.0224539
$970$	0	0
$971$	3.00150e7	1.02162	0.510811	−	0.859693i	$-0.329345\pi$
$971$	3.00150e7	1.02162	0.510811	+	0.859693i	$0.329345\pi$
$972$	0	0
$973$	6.62964e7	2.24496
$974$	0	0
$975$	−4.94858e6	−0.166713
$976$	0	0
$977$	2.19294e7	0.735006	0.367503	−	0.930022i	$-0.380213\pi$
$977$	2.19294e7	0.735006	0.367503	+	0.930022i	$0.380213\pi$
$978$	0	0
$979$	−5.12199e7	−1.70798
$980$	0	0
$981$	3.09080e6	0.102541
$982$	0	0
$983$	−3.32485e7	−1.09746	−0.548730	−	0.836000i	$-0.684888\pi$
$983$	−3.32485e7	−1.09746	−0.548730	+	0.836000i	$0.684888\pi$
$984$	0	0
$985$	−1.74707e6	−0.0573745
$986$	0	0
$987$	−1.18040e7	−0.385687
$988$	0	0
$989$	−3.29348e7	−1.07069
$990$	0	0
$991$	5.46424e7	1.76744	0.883722	−	0.468012i	$-0.155030\pi$
$991$	5.46424e7	1.76744	0.883722	+	0.468012i	$0.155030\pi$
$992$	0	0
$993$	1.79202e7	0.576726
$994$	0	0
$995$	−2.18808e6	−0.0700657
$996$	0	0
$997$	−2.89095e7	−0.921090	−0.460545	−	0.887636i	$-0.652346\pi$
$997$	−2.89095e7	−0.921090	−0.460545	+	0.887636i	$0.652346\pi$
$998$	0	0
$999$	2.84747e6	0.0902705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.6.a.d.1.1		1
4.3	odd	2		57.6.a.b.1.1	✓	1
12.11	even	2		171.6.a.a.1.1		1
76.75	even	2		1083.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.6.a.b.1.1	✓	1	4.3	odd	2
171.6.a.a.1.1		1	12.11	even	2
912.6.a.d.1.1		1	1.1	even	1	trivial
1083.6.a.a.1.1		1	76.75	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	912.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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