LMFDB - Embedded newform 912.6.a.b.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 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)

$f(q)$

$=$

$q-9.00000 q^{3} -91.0000 q^{5} +33.0000 q^{7} +81.0000 q^{9} +O(q^{10})$

$q-9.00000 q^{3} -91.0000 q^{5} +33.0000 q^{7} +81.0000 q^{9} +91.0000 q^{11} -610.000 q^{13} +819.000 q^{15} -1833.00 q^{17} +361.000 q^{19} -297.000 q^{21} +3436.00 q^{23} +5156.00 q^{25} -729.000 q^{27} +3562.00 q^{29} -322.000 q^{31} -819.000 q^{33} -3003.00 q^{35} +7216.00 q^{37} +5490.00 q^{39} -13664.0 q^{41} +3701.00 q^{43} -7371.00 q^{45} -9203.00 q^{47} -15718.0 q^{49} +16497.0 q^{51} +29186.0 q^{53} -8281.00 q^{55} -3249.00 q^{57} +27804.0 q^{59} +43127.0 q^{61} +2673.00 q^{63} +55510.0 q^{65} +19428.0 q^{67} -30924.0 q^{69} -7040.00 q^{71} +37341.0 q^{73} -46404.0 q^{75} +3003.00 q^{77} +4972.00 q^{79} +6561.00 q^{81} +71196.0 q^{83} +166803. q^{85} -32058.0 q^{87} -3654.00 q^{89} -20130.0 q^{91} +2898.00 q^{93} -32851.0 q^{95} +62362.0 q^{97} +7371.00 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	0	0
$5$	−91.0000	−1.62786	−0.813929	−	0.580965i	$-0.802675\pi$
$5$	−91.0000	−1.62786	−0.813929	+	0.580965i	$0.802675\pi$
$6$	0	0
$7$	33.0000	0.254548	0.127274	−	0.991868i	$-0.459377\pi$
$7$	33.0000	0.254548	0.127274	+	0.991868i	$0.459377\pi$
$8$	0	0
$9$	81.0000	0.333333
$10$	0	0
$11$	91.0000	0.226756	0.113378	−	0.993552i	$-0.463833\pi$
$11$	91.0000	0.226756	0.113378	+	0.993552i	$0.463833\pi$
$12$	0	0
$13$	−610.000	−1.00109	−0.500543	−	0.865712i	$-0.666866\pi$
$13$	−610.000	−1.00109	−0.500543	+	0.865712i	$0.666866\pi$
$14$	0	0
$15$	819.000	0.939844
$16$	0	0
$17$	−1833.00	−1.53830	−0.769148	−	0.639070i	$-0.779319\pi$
$17$	−1833.00	−1.53830	−0.769148	+	0.639070i	$0.779319\pi$
$18$	0	0
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	0	0
$21$	−297.000	−0.146963
$22$	0	0
$23$	3436.00	1.35436	0.677179	−	0.735818i	$-0.263202\pi$
$23$	3436.00	1.35436	0.677179	+	0.735818i	$0.263202\pi$
$24$	0	0
$25$	5156.00	1.64992
$26$	0	0
$27$	−729.000	−0.192450
$28$	0	0
$29$	3562.00	0.786500	0.393250	−	0.919432i	$-0.371351\pi$
$29$	3562.00	0.786500	0.393250	+	0.919432i	$0.371351\pi$
$30$	0	0
$31$	−322.000	−0.0601799	−0.0300900	−	0.999547i	$-0.509579\pi$
$31$	−322.000	−0.0601799	−0.0300900	+	0.999547i	$0.509579\pi$
$32$	0	0
$33$	−819.000	−0.130918
$34$	0	0
$35$	−3003.00	−0.414367
$36$	0	0
$37$	7216.00	0.866547	0.433274	−	0.901262i	$-0.357358\pi$
$37$	7216.00	0.866547	0.433274	+	0.901262i	$0.357358\pi$
$38$	0	0
$39$	5490.00	0.577977
$40$	0	0
$41$	−13664.0	−1.26946	−0.634729	−	0.772735i	$-0.718888\pi$
$41$	−13664.0	−1.26946	−0.634729	+	0.772735i	$0.718888\pi$
$42$	0	0
$43$	3701.00	0.305245	0.152622	−	0.988285i	$-0.451228\pi$
$43$	3701.00	0.305245	0.152622	+	0.988285i	$0.451228\pi$
$44$	0	0
$45$	−7371.00	−0.542619
$46$	0	0
$47$	−9203.00	−0.607694	−0.303847	−	0.952721i	$-0.598271\pi$
$47$	−9203.00	−0.607694	−0.303847	+	0.952721i	$0.598271\pi$
$48$	0	0
$49$	−15718.0	−0.935206
$50$	0	0
$51$	16497.0	0.888136
$52$	0	0
$53$	29186.0	1.42720	0.713600	−	0.700553i	$-0.247063\pi$
$53$	29186.0	1.42720	0.713600	+	0.700553i	$0.247063\pi$
$54$	0	0
$55$	−8281.00	−0.369127
$56$	0	0
$57$	−3249.00	−0.132453
$58$	0	0
$59$	27804.0	1.03987	0.519933	−	0.854207i	$-0.325957\pi$
$59$	27804.0	1.03987	0.519933	+	0.854207i	$0.325957\pi$
$60$	0	0
$61$	43127.0	1.48397	0.741984	−	0.670417i	$-0.233885\pi$
$61$	43127.0	1.48397	0.741984	+	0.670417i	$0.233885\pi$
$62$	0	0
$63$	2673.00	0.0848492
$64$	0	0
$65$	55510.0	1.62963
$66$	0	0
$67$	19428.0	0.528739	0.264369	−	0.964422i	$-0.414836\pi$
$67$	19428.0	0.528739	0.264369	+	0.964422i	$0.414836\pi$
$68$	0	0
$69$	−30924.0	−0.781939
$70$	0	0
$71$	−7040.00	−0.165740	−0.0828699	−	0.996560i	$-0.526409\pi$
$71$	−7040.00	−0.165740	−0.0828699	+	0.996560i	$0.526409\pi$
$72$	0	0
$73$	37341.0	0.820123	0.410061	−	0.912058i	$-0.365507\pi$
$73$	37341.0	0.820123	0.410061	+	0.912058i	$0.365507\pi$
$74$	0	0
$75$	−46404.0	−0.952582
$76$	0	0
$77$	3003.00	0.0577203
$78$	0	0
$79$	4972.00	0.0896321	0.0448160	−	0.998995i	$-0.485730\pi$
$79$	4972.00	0.0896321	0.0448160	+	0.998995i	$0.485730\pi$
$80$	0	0
$81$	6561.00	0.111111
$82$	0	0
$83$	71196.0	1.13438	0.567192	−	0.823585i	$-0.308030\pi$
$83$	71196.0	1.13438	0.567192	+	0.823585i	$0.308030\pi$
$84$	0	0
$85$	166803.	2.50413
$86$	0	0
$87$	−32058.0	−0.454086
$88$	0	0
$89$	−3654.00	−0.0488983	−0.0244491	−	0.999701i	$-0.507783\pi$
$89$	−3654.00	−0.0488983	−0.0244491	+	0.999701i	$0.507783\pi$
$90$	0	0
$91$	−20130.0	−0.254824
$92$	0	0
$93$	2898.00	0.0347449
$94$	0	0
$95$	−32851.0	−0.373456
$96$	0	0
$97$	62362.0	0.672962	0.336481	−	0.941690i	$-0.390763\pi$
$97$	62362.0	0.672962	0.336481	+	0.941690i	$0.390763\pi$
$98$	0	0
$99$	7371.00	0.0755855
$100$	0	0
$101$	−171190.	−1.66984	−0.834920	−	0.550371i	$-0.814486\pi$
$101$	−171190.	−1.66984	−0.834920	+	0.550371i	$0.814486\pi$
$102$	0	0
$103$	−88590.0	−0.822795	−0.411397	−	0.911456i	$-0.634959\pi$
$103$	−88590.0	−0.822795	−0.411397	+	0.911456i	$0.634959\pi$
$104$	0	0
$105$	27027.0	0.239235
$106$	0	0
$107$	−117758.	−0.994331	−0.497165	−	0.867656i	$-0.665626\pi$
$107$	−117758.	−0.994331	−0.497165	+	0.867656i	$0.665626\pi$
$108$	0	0
$109$	82416.0	0.664424	0.332212	−	0.943205i	$-0.392205\pi$
$109$	82416.0	0.664424	0.332212	+	0.943205i	$0.392205\pi$
$110$	0	0
$111$	−64944.0	−0.500301
$112$	0	0
$113$	80414.0	0.592428	0.296214	−	0.955122i	$-0.404276\pi$
$113$	80414.0	0.592428	0.296214	+	0.955122i	$0.404276\pi$
$114$	0	0
$115$	−312676.	−2.20470
$116$	0	0
$117$	−49410.0	−0.333695
$118$	0	0
$119$	−60489.0	−0.391570
$120$	0	0
$121$	−152770.	−0.948582
$122$	0	0
$123$	122976.	0.732922
$124$	0	0
$125$	−184821.	−1.05798
$126$	0	0
$127$	138942.	0.764406	0.382203	−	0.924078i	$-0.375165\pi$
$127$	138942.	0.764406	0.382203	+	0.924078i	$0.375165\pi$
$128$	0	0
$129$	−33309.0	−0.176233
$130$	0	0
$131$	318813.	1.62315	0.811573	−	0.584251i	$-0.198611\pi$
$131$	318813.	1.62315	0.811573	+	0.584251i	$0.198611\pi$
$132$	0	0
$133$	11913.0	0.0583972
$134$	0	0
$135$	66339.0	0.313281
$136$	0	0
$137$	−363929.	−1.65659	−0.828295	−	0.560292i	$-0.810689\pi$
$137$	−363929.	−1.65659	−0.828295	+	0.560292i	$0.810689\pi$
$138$	0	0
$139$	309105.	1.35697	0.678483	−	0.734616i	$-0.262638\pi$
$139$	309105.	1.35697	0.678483	+	0.734616i	$0.262638\pi$
$140$	0	0
$141$	82827.0	0.350852
$142$	0	0
$143$	−55510.0	−0.227003
$144$	0	0
$145$	−324142.	−1.28031
$146$	0	0
$147$	141462.	0.539941
$148$	0	0
$149$	−436653.	−1.61128	−0.805640	−	0.592406i	$-0.798178\pi$
$149$	−436653.	−1.61128	−0.805640	+	0.592406i	$0.798178\pi$
$150$	0	0
$151$	−466100.	−1.66355	−0.831777	−	0.555110i	$-0.812676\pi$
$151$	−466100.	−1.66355	−0.831777	+	0.555110i	$0.812676\pi$
$152$	0	0
$153$	−148473.	−0.512766
$154$	0	0
$155$	29302.0	0.0979643
$156$	0	0
$157$	218686.	0.708063	0.354031	−	0.935234i	$-0.384811\pi$
$157$	218686.	0.708063	0.354031	+	0.935234i	$0.384811\pi$
$158$	0	0
$159$	−262674.	−0.823994
$160$	0	0
$161$	113388.	0.344749
$162$	0	0
$163$	279304.	0.823395	0.411697	−	0.911321i	$-0.364936\pi$
$163$	279304.	0.823395	0.411697	+	0.911321i	$0.364936\pi$
$164$	0	0
$165$	74529.0	0.213116
$166$	0	0
$167$	−457854.	−1.27039	−0.635193	−	0.772353i	$-0.719080\pi$
$167$	−457854.	−1.27039	−0.635193	+	0.772353i	$0.719080\pi$
$168$	0	0
$169$	807.000	0.00217349
$170$	0	0
$171$	29241.0	0.0764719
$172$	0	0
$173$	−733002.	−1.86204	−0.931022	−	0.364963i	$-0.881082\pi$
$173$	−733002.	−1.86204	−0.931022	+	0.364963i	$0.881082\pi$
$174$	0	0
$175$	170148.	0.419983
$176$	0	0
$177$	−250236.	−0.600367
$178$	0	0
$179$	247518.	0.577397	0.288698	−	0.957420i	$-0.406778\pi$
$179$	247518.	0.577397	0.288698	+	0.957420i	$0.406778\pi$
$180$	0	0
$181$	−189158.	−0.429169	−0.214584	−	0.976705i	$-0.568840\pi$
$181$	−189158.	−0.429169	−0.214584	+	0.976705i	$0.568840\pi$
$182$	0	0
$183$	−388143.	−0.856770
$184$	0	0
$185$	−656656.	−1.41062
$186$	0	0
$187$	−166803.	−0.348819
$188$	0	0
$189$	−24057.0	−0.0489877
$190$	0	0
$191$	−330733.	−0.655985	−0.327993	−	0.944680i	$-0.606372\pi$
$191$	−330733.	−0.655985	−0.327993	+	0.944680i	$0.606372\pi$
$192$	0	0
$193$	674472.	1.30338	0.651689	−	0.758486i	$-0.274061\pi$
$193$	674472.	1.30338	0.651689	+	0.758486i	$0.274061\pi$
$194$	0	0
$195$	−499590.	−0.940865
$196$	0	0
$197$	−942346.	−1.72999	−0.864997	−	0.501776i	$-0.832680\pi$
$197$	−942346.	−1.72999	−0.864997	+	0.501776i	$0.832680\pi$
$198$	0	0
$199$	429505.	0.768839	0.384420	−	0.923158i	$-0.374402\pi$
$199$	429505.	0.768839	0.384420	+	0.923158i	$0.374402\pi$
$200$	0	0
$201$	−174852.	−0.305267
$202$	0	0
$203$	117546.	0.200202
$204$	0	0
$205$	1.24342e6	2.06650
$206$	0	0
$207$	278316.	0.451453
$208$	0	0
$209$	32851.0	0.0520215
$210$	0	0
$211$	569088.	0.879981	0.439990	−	0.898002i	$-0.354982\pi$
$211$	569088.	0.879981	0.439990	+	0.898002i	$0.354982\pi$
$212$	0	0
$213$	63360.0	0.0956899
$214$	0	0
$215$	−336791.	−0.496895
$216$	0	0
$217$	−10626.0	−0.0153186
$218$	0	0
$219$	−336069.	−0.473498
$220$	0	0
$221$	1.11813e6	1.53997
$222$	0	0
$223$	−1.00132e6	−1.34838	−0.674190	−	0.738558i	$-0.735507\pi$
$223$	−1.00132e6	−1.34838	−0.674190	+	0.738558i	$0.735507\pi$
$224$	0	0
$225$	417636.	0.549973
$226$	0	0
$227$	−169582.	−0.218431	−0.109216	−	0.994018i	$-0.534834\pi$
$227$	−169582.	−0.218431	−0.109216	+	0.994018i	$0.534834\pi$
$228$	0	0
$229$	−405367.	−0.510810	−0.255405	−	0.966834i	$-0.582209\pi$
$229$	−405367.	−0.510810	−0.255405	+	0.966834i	$0.582209\pi$
$230$	0	0
$231$	−27027.0	−0.0333248
$232$	0	0
$233$	506649.	0.611389	0.305694	−	0.952130i	$-0.401111\pi$
$233$	506649.	0.611389	0.305694	+	0.952130i	$0.401111\pi$
$234$	0	0
$235$	837473.	0.989239
$236$	0	0
$237$	−44748.0	−0.0517491
$238$	0	0
$239$	−1.34766e6	−1.52611	−0.763053	−	0.646336i	$-0.776300\pi$
$239$	−1.34766e6	−1.52611	−0.763053	+	0.646336i	$0.776300\pi$
$240$	0	0
$241$	−840812.	−0.932516	−0.466258	−	0.884649i	$-0.654398\pi$
$241$	−840812.	−0.932516	−0.466258	+	0.884649i	$0.654398\pi$
$242$	0	0
$243$	−59049.0	−0.0641500
$244$	0	0
$245$	1.43034e6	1.52238
$246$	0	0
$247$	−220210.	−0.229665
$248$	0	0
$249$	−640764.	−0.654937
$250$	0	0
$251$	−1.08289e6	−1.08493	−0.542463	−	0.840079i	$-0.682508\pi$
$251$	−1.08289e6	−1.08493	−0.542463	+	0.840079i	$0.682508\pi$
$252$	0	0
$253$	312676.	0.307109
$254$	0	0
$255$	−1.50123e6	−1.44576
$256$	0	0
$257$	522416.	0.493382	0.246691	−	0.969094i	$-0.420657\pi$
$257$	522416.	0.493382	0.246691	+	0.969094i	$0.420657\pi$
$258$	0	0
$259$	238128.	0.220577
$260$	0	0
$261$	288522.	0.262167
$262$	0	0
$263$	1.08895e6	0.970774	0.485387	−	0.874299i	$-0.338679\pi$
$263$	1.08895e6	0.970774	0.485387	+	0.874299i	$0.338679\pi$
$264$	0	0
$265$	−2.65593e6	−2.32328
$266$	0	0
$267$	32886.0	0.0282314
$268$	0	0
$269$	−924702.	−0.779150	−0.389575	−	0.920995i	$-0.627378\pi$
$269$	−924702.	−0.779150	−0.389575	+	0.920995i	$0.627378\pi$
$270$	0	0
$271$	1.19270e6	0.986525	0.493262	−	0.869881i	$-0.335804\pi$
$271$	1.19270e6	0.986525	0.493262	+	0.869881i	$0.335804\pi$
$272$	0	0
$273$	181170.	0.147123
$274$	0	0
$275$	469196.	0.374130
$276$	0	0
$277$	−1.90691e6	−1.49324	−0.746621	−	0.665250i	$-0.768325\pi$
$277$	−1.90691e6	−1.49324	−0.746621	+	0.665250i	$0.768325\pi$
$278$	0	0
$279$	−26082.0	−0.0200600
$280$	0	0
$281$	19066.0	0.0144044	0.00720218	−	0.999974i	$-0.497707\pi$
$281$	19066.0	0.0144044	0.00720218	+	0.999974i	$0.497707\pi$
$282$	0	0
$283$	667833.	0.495680	0.247840	−	0.968801i	$-0.420279\pi$
$283$	667833.	0.495680	0.247840	+	0.968801i	$0.420279\pi$
$284$	0	0
$285$	295659.	0.215615
$286$	0	0
$287$	−450912.	−0.323137
$288$	0	0
$289$	1.94003e6	1.36636
$290$	0	0
$291$	−561258.	−0.388535
$292$	0	0
$293$	−1.43226e6	−0.974659	−0.487330	−	0.873218i	$-0.662029\pi$
$293$	−1.43226e6	−0.974659	−0.487330	+	0.873218i	$0.662029\pi$
$294$	0	0
$295$	−2.53016e6	−1.69275
$296$	0	0
$297$	−66339.0	−0.0436393
$298$	0	0
$299$	−2.09596e6	−1.35583
$300$	0	0
$301$	122133.	0.0776992
$302$	0	0
$303$	1.54071e6	0.964083
$304$	0	0
$305$	−3.92456e6	−2.41569
$306$	0	0
$307$	−3.08911e6	−1.87063	−0.935315	−	0.353817i	$-0.884884\pi$
$307$	−3.08911e6	−1.87063	−0.935315	+	0.353817i	$0.884884\pi$
$308$	0	0
$309$	797310.	0.475041
$310$	0	0
$311$	2.78248e6	1.63129	0.815645	−	0.578553i	$-0.196382\pi$
$311$	2.78248e6	1.63129	0.815645	+	0.578553i	$0.196382\pi$
$312$	0	0
$313$	−1.09383e6	−0.631089	−0.315544	−	0.948911i	$-0.602187\pi$
$313$	−1.09383e6	−0.631089	−0.315544	+	0.948911i	$0.602187\pi$
$314$	0	0
$315$	−243243.	−0.138122
$316$	0	0
$317$	1.55578e6	0.869559	0.434779	−	0.900537i	$-0.356826\pi$
$317$	1.55578e6	0.869559	0.434779	+	0.900537i	$0.356826\pi$
$318$	0	0
$319$	324142.	0.178344
$320$	0	0
$321$	1.05982e6	0.574077
$322$	0	0
$323$	−661713.	−0.352910
$324$	0	0
$325$	−3.14516e6	−1.65171
$326$	0	0
$327$	−741744.	−0.383605
$328$	0	0
$329$	−303699.	−0.154687
$330$	0	0
$331$	−35240.0	−0.0176793	−0.00883967	−	0.999961i	$-0.502814\pi$
$331$	−35240.0	−0.0176793	−0.00883967	+	0.999961i	$0.502814\pi$
$332$	0	0
$333$	584496.	0.288849
$334$	0	0
$335$	−1.76795e6	−0.860711
$336$	0	0
$337$	−1.64825e6	−0.790585	−0.395292	−	0.918555i	$-0.629357\pi$
$337$	−1.64825e6	−0.790585	−0.395292	+	0.918555i	$0.629357\pi$
$338$	0	0
$339$	−723726.	−0.342038
$340$	0	0
$341$	−29302.0	−0.0136462
$342$	0	0
$343$	−1.07332e6	−0.492602
$344$	0	0
$345$	2.81408e6	1.27289
$346$	0	0
$347$	3.74631e6	1.67024	0.835122	−	0.550065i	$-0.185397\pi$
$347$	3.74631e6	1.67024	0.835122	+	0.550065i	$0.185397\pi$
$348$	0	0
$349$	1.15723e6	0.508578	0.254289	−	0.967128i	$-0.418159\pi$
$349$	1.15723e6	0.508578	0.254289	+	0.967128i	$0.418159\pi$
$350$	0	0
$351$	444690.	0.192659
$352$	0	0
$353$	−648018.	−0.276790	−0.138395	−	0.990377i	$-0.544194\pi$
$353$	−648018.	−0.276790	−0.138395	+	0.990377i	$0.544194\pi$
$354$	0	0
$355$	640640.	0.269801
$356$	0	0
$357$	544401.	0.226073
$358$	0	0
$359$	−3.31969e6	−1.35944	−0.679722	−	0.733470i	$-0.737900\pi$
$359$	−3.31969e6	−1.35944	−0.679722	+	0.733470i	$0.737900\pi$
$360$	0	0
$361$	130321.	0.0526316
$362$	0	0
$363$	1.37493e6	0.547664
$364$	0	0
$365$	−3.39803e6	−1.33504
$366$	0	0
$367$	−3.30592e6	−1.28123	−0.640615	−	0.767862i	$-0.721321\pi$
$367$	−3.30592e6	−1.28123	−0.640615	+	0.767862i	$0.721321\pi$
$368$	0	0
$369$	−1.10678e6	−0.423153
$370$	0	0
$371$	963138.	0.363290
$372$	0	0
$373$	1.95786e6	0.728633	0.364316	−	0.931275i	$-0.381303\pi$
$373$	1.95786e6	0.728633	0.364316	+	0.931275i	$0.381303\pi$
$374$	0	0
$375$	1.66339e6	0.610823
$376$	0	0
$377$	−2.17282e6	−0.787355
$378$	0	0
$379$	1.12179e6	0.401156	0.200578	−	0.979678i	$-0.435718\pi$
$379$	1.12179e6	0.401156	0.200578	+	0.979678i	$0.435718\pi$
$380$	0	0
$381$	−1.25048e6	−0.441330
$382$	0	0
$383$	−1.03305e6	−0.359854	−0.179927	−	0.983680i	$-0.557586\pi$
$383$	−1.03305e6	−0.359854	−0.179927	+	0.983680i	$0.557586\pi$
$384$	0	0
$385$	−273273.	−0.0939604
$386$	0	0
$387$	299781.	0.101748
$388$	0	0
$389$	4.66876e6	1.56433	0.782164	−	0.623072i	$-0.214116\pi$
$389$	4.66876e6	1.56433	0.782164	+	0.623072i	$0.214116\pi$
$390$	0	0
$391$	−6.29819e6	−2.08341
$392$	0	0
$393$	−2.86932e6	−0.937124
$394$	0	0
$395$	−452452.	−0.145908
$396$	0	0
$397$	−3.00310e6	−0.956300	−0.478150	−	0.878278i	$-0.658692\pi$
$397$	−3.00310e6	−0.956300	−0.478150	+	0.878278i	$0.658692\pi$
$398$	0	0
$399$	−107217.	−0.0337156
$400$	0	0
$401$	3.94648e6	1.22560	0.612800	−	0.790238i	$-0.290043\pi$
$401$	3.94648e6	1.22560	0.612800	+	0.790238i	$0.290043\pi$
$402$	0	0
$403$	196420.	0.0602453
$404$	0	0
$405$	−597051.	−0.180873
$406$	0	0
$407$	656656.	0.196495
$408$	0	0
$409$	4.38003e6	1.29470	0.647350	−	0.762193i	$-0.275877\pi$
$409$	4.38003e6	1.29470	0.647350	+	0.762193i	$0.275877\pi$
$410$	0	0
$411$	3.27536e6	0.956433
$412$	0	0
$413$	917532.	0.264695
$414$	0	0
$415$	−6.47884e6	−1.84662
$416$	0	0
$417$	−2.78194e6	−0.783445
$418$	0	0
$419$	−872676.	−0.242839	−0.121419	−	0.992601i	$-0.538745\pi$
$419$	−872676.	−0.242839	−0.121419	+	0.992601i	$0.538745\pi$
$420$	0	0
$421$	−1.95854e6	−0.538552	−0.269276	−	0.963063i	$-0.586784\pi$
$421$	−1.95854e6	−0.538552	−0.269276	+	0.963063i	$0.586784\pi$
$422$	0	0
$423$	−745443.	−0.202565
$424$	0	0
$425$	−9.45095e6	−2.53807
$426$	0	0
$427$	1.42319e6	0.377740
$428$	0	0
$429$	499590.	0.131060
$430$	0	0
$431$	−90666.0	−0.0235099	−0.0117550	−	0.999931i	$-0.503742\pi$
$431$	−90666.0	−0.0235099	−0.0117550	+	0.999931i	$0.503742\pi$
$432$	0	0
$433$	3.50825e6	0.899230	0.449615	−	0.893222i	$-0.351561\pi$
$433$	3.50825e6	0.899230	0.449615	+	0.893222i	$0.351561\pi$
$434$	0	0
$435$	2.91728e6	0.739188
$436$	0	0
$437$	1.24040e6	0.310711
$438$	0	0
$439$	4.91970e6	1.21836	0.609182	−	0.793030i	$-0.291498\pi$
$439$	4.91970e6	1.21836	0.609182	+	0.793030i	$0.291498\pi$
$440$	0	0
$441$	−1.27316e6	−0.311735
$442$	0	0
$443$	−7.92687e6	−1.91908	−0.959539	−	0.281577i	$-0.909143\pi$
$443$	−7.92687e6	−1.91908	−0.959539	+	0.281577i	$0.909143\pi$
$444$	0	0
$445$	332514.	0.0795994
$446$	0	0
$447$	3.92988e6	0.930272
$448$	0	0
$449$	1.48280e6	0.347109	0.173554	−	0.984824i	$-0.444475\pi$
$449$	1.48280e6	0.347109	0.173554	+	0.984824i	$0.444475\pi$
$450$	0	0
$451$	−1.24342e6	−0.287858
$452$	0	0
$453$	4.19490e6	0.960453
$454$	0	0
$455$	1.83183e6	0.414817
$456$	0	0
$457$	1.72825e6	0.387094	0.193547	−	0.981091i	$-0.438001\pi$
$457$	1.72825e6	0.387094	0.193547	+	0.981091i	$0.438001\pi$
$458$	0	0
$459$	1.33626e6	0.296045
$460$	0	0
$461$	−552109.	−0.120996	−0.0604982	−	0.998168i	$-0.519269\pi$
$461$	−552109.	−0.120996	−0.0604982	+	0.998168i	$0.519269\pi$
$462$	0	0
$463$	5.54929e6	1.20305	0.601527	−	0.798853i	$-0.294559\pi$
$463$	5.54929e6	1.20305	0.601527	+	0.798853i	$0.294559\pi$
$464$	0	0
$465$	−263718.	−0.0565597
$466$	0	0
$467$	−2.05633e6	−0.436315	−0.218157	−	0.975914i	$-0.570005\pi$
$467$	−2.05633e6	−0.436315	−0.218157	+	0.975914i	$0.570005\pi$
$468$	0	0
$469$	641124.	0.134589
$470$	0	0
$471$	−1.96817e6	−0.408800
$472$	0	0
$473$	336791.	0.0692162
$474$	0	0
$475$	1.86132e6	0.378518
$476$	0	0
$477$	2.36407e6	0.475733
$478$	0	0
$479$	2.04279e6	0.406804	0.203402	−	0.979095i	$-0.434800\pi$
$479$	2.04279e6	0.406804	0.203402	+	0.979095i	$0.434800\pi$
$480$	0	0
$481$	−4.40176e6	−0.867488
$482$	0	0
$483$	−1.02049e6	−0.199041
$484$	0	0
$485$	−5.67494e6	−1.09549
$486$	0	0
$487$	6.58564e6	1.25828	0.629138	−	0.777294i	$-0.283408\pi$
$487$	6.58564e6	1.25828	0.629138	+	0.777294i	$0.283408\pi$
$488$	0	0
$489$	−2.51374e6	−0.475387
$490$	0	0
$491$	3.96714e6	0.742633	0.371316	−	0.928506i	$-0.378906\pi$
$491$	3.96714e6	0.742633	0.371316	+	0.928506i	$0.378906\pi$
$492$	0	0
$493$	−6.52915e6	−1.20987
$494$	0	0
$495$	−670761.	−0.123042
$496$	0	0
$497$	−232320.	−0.0421886
$498$	0	0
$499$	2.69611e6	0.484715	0.242357	−	0.970187i	$-0.422079\pi$
$499$	2.69611e6	0.484715	0.242357	+	0.970187i	$0.422079\pi$
$500$	0	0
$501$	4.12069e6	0.733458
$502$	0	0
$503$	−8.31756e6	−1.46580	−0.732902	−	0.680334i	$-0.761835\pi$
$503$	−8.31756e6	−1.46580	−0.732902	+	0.680334i	$0.761835\pi$
$504$	0	0
$505$	1.55783e7	2.71826
$506$	0	0
$507$	−7263.00	−0.00125486
$508$	0	0
$509$	1.00197e7	1.71420	0.857098	−	0.515153i	$-0.172265\pi$
$509$	1.00197e7	1.71420	0.857098	+	0.515153i	$0.172265\pi$
$510$	0	0
$511$	1.23225e6	0.208760
$512$	0	0
$513$	−263169.	−0.0441511
$514$	0	0
$515$	8.06169e6	1.33939
$516$	0	0
$517$	−837473.	−0.137798
$518$	0	0
$519$	6.59702e6	1.07505
$520$	0	0
$521$	−235936.	−0.0380803	−0.0190401	−	0.999819i	$-0.506061\pi$
$521$	−235936.	−0.0380803	−0.0190401	+	0.999819i	$0.506061\pi$
$522$	0	0
$523$	−914870.	−0.146253	−0.0731266	−	0.997323i	$-0.523298\pi$
$523$	−914870.	−0.146253	−0.0731266	+	0.997323i	$0.523298\pi$
$524$	0	0
$525$	−1.53133e6	−0.242477
$526$	0	0
$527$	590226.	0.0925746
$528$	0	0
$529$	5.36975e6	0.834286
$530$	0	0
$531$	2.25212e6	0.346622
$532$	0	0
$533$	8.33504e6	1.27084
$534$	0	0
$535$	1.07160e7	1.61863
$536$	0	0
$537$	−2.22766e6	−0.333360
$538$	0	0
$539$	−1.43034e6	−0.212064
$540$	0	0
$541$	−4.04192e6	−0.593738	−0.296869	−	0.954918i	$-0.595943\pi$
$541$	−4.04192e6	−0.593738	−0.296869	+	0.954918i	$0.595943\pi$
$542$	0	0
$543$	1.70242e6	0.247781
$544$	0	0
$545$	−7.49986e6	−1.08159
$546$	0	0
$547$	−8.18293e6	−1.16934	−0.584670	−	0.811271i	$-0.698776\pi$
$547$	−8.18293e6	−1.16934	−0.584670	+	0.811271i	$0.698776\pi$
$548$	0	0
$549$	3.49329e6	0.494656
$550$	0	0
$551$	1.28588e6	0.180436
$552$	0	0
$553$	164076.	0.0228156
$554$	0	0
$555$	5.90990e6	0.814419
$556$	0	0
$557$	−1.22357e7	−1.67105	−0.835527	−	0.549449i	$-0.814838\pi$
$557$	−1.22357e7	−1.67105	−0.835527	+	0.549449i	$0.814838\pi$
$558$	0	0
$559$	−2.25761e6	−0.305576
$560$	0	0
$561$	1.50123e6	0.201391
$562$	0	0
$563$	−1.07830e7	−1.43374	−0.716870	−	0.697207i	$-0.754426\pi$
$563$	−1.07830e7	−1.43374	−0.716870	+	0.697207i	$0.754426\pi$
$564$	0	0
$565$	−7.31767e6	−0.964388
$566$	0	0
$567$	216513.	0.0282831
$568$	0	0
$569$	1.10760e7	1.43418	0.717088	−	0.696982i	$-0.245474\pi$
$569$	1.10760e7	1.43418	0.717088	+	0.696982i	$0.245474\pi$
$570$	0	0
$571$	5.85570e6	0.751604	0.375802	−	0.926700i	$-0.377367\pi$
$571$	5.85570e6	0.751604	0.375802	+	0.926700i	$0.377367\pi$
$572$	0	0
$573$	2.97660e6	0.378733
$574$	0	0
$575$	1.77160e7	2.23458
$576$	0	0
$577$	−7.26541e6	−0.908491	−0.454246	−	0.890876i	$-0.650091\pi$
$577$	−7.26541e6	−0.908491	−0.454246	+	0.890876i	$0.650091\pi$
$578$	0	0
$579$	−6.07025e6	−0.752506
$580$	0	0
$581$	2.34947e6	0.288755
$582$	0	0
$583$	2.65593e6	0.323627
$584$	0	0
$585$	4.49631e6	0.543209
$586$	0	0
$587$	−1.19721e7	−1.43409	−0.717045	−	0.697027i	$-0.754506\pi$
$587$	−1.19721e7	−1.43409	−0.717045	+	0.697027i	$0.754506\pi$
$588$	0	0
$589$	−116242.	−0.0138062
$590$	0	0
$591$	8.48111e6	0.998813
$592$	0	0
$593$	−2.07789e6	−0.242653	−0.121326	−	0.992613i	$-0.538715\pi$
$593$	−2.07789e6	−0.242653	−0.121326	+	0.992613i	$0.538715\pi$
$594$	0	0
$595$	5.50450e6	0.637420
$596$	0	0
$597$	−3.86554e6	−0.443890
$598$	0	0
$599$	−1.05217e7	−1.19817	−0.599085	−	0.800686i	$-0.704469\pi$
$599$	−1.05217e7	−1.19817	−0.599085	+	0.800686i	$0.704469\pi$
$600$	0	0
$601$	3.58294e6	0.404626	0.202313	−	0.979321i	$-0.435154\pi$
$601$	3.58294e6	0.404626	0.202313	+	0.979321i	$0.435154\pi$
$602$	0	0
$603$	1.57367e6	0.176246
$604$	0	0
$605$	1.39021e7	1.54416
$606$	0	0
$607$	4.38625e6	0.483194	0.241597	−	0.970377i	$-0.422329\pi$
$607$	4.38625e6	0.483194	0.241597	+	0.970377i	$0.422329\pi$
$608$	0	0
$609$	−1.05791e6	−0.115587
$610$	0	0
$611$	5.61383e6	0.608354
$612$	0	0
$613$	3.85958e6	0.414848	0.207424	−	0.978251i	$-0.433492\pi$
$613$	3.85958e6	0.414848	0.207424	+	0.978251i	$0.433492\pi$
$614$	0	0
$615$	−1.11908e7	−1.19309
$616$	0	0
$617$	1.17256e7	1.24000	0.620000	−	0.784602i	$-0.287133\pi$
$617$	1.17256e7	1.24000	0.620000	+	0.784602i	$0.287133\pi$
$618$	0	0
$619$	−6.81869e6	−0.715277	−0.357639	−	0.933860i	$-0.616418\pi$
$619$	−6.81869e6	−0.715277	−0.357639	+	0.933860i	$0.616418\pi$
$620$	0	0
$621$	−2.50484e6	−0.260646
$622$	0	0
$623$	−120582.	−0.0124469
$624$	0	0
$625$	706211.	0.0723160
$626$	0	0
$627$	−295659.	−0.0300346
$628$	0	0
$629$	−1.32269e7	−1.33301
$630$	0	0
$631$	9.81980e6	0.981815	0.490907	−	0.871212i	$-0.336665\pi$
$631$	9.81980e6	0.981815	0.490907	+	0.871212i	$0.336665\pi$
$632$	0	0
$633$	−5.12179e6	−0.508057
$634$	0	0
$635$	−1.26437e7	−1.24434
$636$	0	0
$637$	9.58798e6	0.936221
$638$	0	0
$639$	−570240.	−0.0552466
$640$	0	0
$641$	−1.96019e7	−1.88432	−0.942158	−	0.335170i	$-0.891206\pi$
$641$	−1.96019e7	−1.88432	−0.942158	+	0.335170i	$0.891206\pi$
$642$	0	0
$643$	−1.23252e7	−1.17562	−0.587810	−	0.808999i	$-0.700010\pi$
$643$	−1.23252e7	−1.17562	−0.587810	+	0.808999i	$0.700010\pi$
$644$	0	0
$645$	3.03112e6	0.286882
$646$	0	0
$647$	−968621.	−0.0909689	−0.0454845	−	0.998965i	$-0.514483\pi$
$647$	−968621.	−0.0909689	−0.0454845	+	0.998965i	$0.514483\pi$
$648$	0	0
$649$	2.53016e6	0.235796
$650$	0	0
$651$	95634.0	0.00884423
$652$	0	0
$653$	−517653.	−0.0475068	−0.0237534	−	0.999718i	$-0.507562\pi$
$653$	−517653.	−0.0475068	−0.0237534	+	0.999718i	$0.507562\pi$
$654$	0	0
$655$	−2.90120e7	−2.64225
$656$	0	0
$657$	3.02462e6	0.273374
$658$	0	0
$659$	−7.30548e6	−0.655293	−0.327646	−	0.944800i	$-0.606255\pi$
$659$	−7.30548e6	−0.655293	−0.327646	+	0.944800i	$0.606255\pi$
$660$	0	0
$661$	−2.12076e7	−1.88794	−0.943971	−	0.330028i	$-0.892942\pi$
$661$	−2.12076e7	−1.88794	−0.943971	+	0.330028i	$0.892942\pi$
$662$	0	0
$663$	−1.00632e7	−0.889101
$664$	0	0
$665$	−1.08408e6	−0.0950623
$666$	0	0
$667$	1.22390e7	1.06520
$668$	0	0
$669$	9.01192e6	0.778488
$670$	0	0
$671$	3.92456e6	0.336499
$672$	0	0
$673$	−5.20143e6	−0.442675	−0.221337	−	0.975197i	$-0.571042\pi$
$673$	−5.20143e6	−0.442675	−0.221337	+	0.975197i	$0.571042\pi$
$674$	0	0
$675$	−3.75872e6	−0.317527
$676$	0	0
$677$	−8.90338e6	−0.746592	−0.373296	−	0.927712i	$-0.621772\pi$
$677$	−8.90338e6	−0.746592	−0.373296	+	0.927712i	$0.621772\pi$
$678$	0	0
$679$	2.05795e6	0.171301
$680$	0	0
$681$	1.52624e6	0.126111
$682$	0	0
$683$	1.40518e7	1.15260	0.576302	−	0.817237i	$-0.304495\pi$
$683$	1.40518e7	1.15260	0.576302	+	0.817237i	$0.304495\pi$
$684$	0	0
$685$	3.31175e7	2.69669
$686$	0	0
$687$	3.64830e6	0.294916
$688$	0	0
$689$	−1.78035e7	−1.42875
$690$	0	0
$691$	5.38920e6	0.429368	0.214684	−	0.976684i	$-0.431128\pi$
$691$	5.38920e6	0.429368	0.214684	+	0.976684i	$0.431128\pi$
$692$	0	0
$693$	243243.	0.0192401
$694$	0	0
$695$	−2.81286e7	−2.20895
$696$	0	0
$697$	2.50461e7	1.95280
$698$	0	0
$699$	−4.55984e6	−0.352985
$700$	0	0
$701$	2.30897e7	1.77469	0.887347	−	0.461103i	$-0.152546\pi$
$701$	2.30897e7	1.77469	0.887347	+	0.461103i	$0.152546\pi$
$702$	0	0
$703$	2.60498e6	0.198800
$704$	0	0
$705$	−7.53726e6	−0.571137
$706$	0	0
$707$	−5.64927e6	−0.425054
$708$	0	0
$709$	4.25355e6	0.317787	0.158893	−	0.987296i	$-0.449207\pi$
$709$	4.25355e6	0.317787	0.158893	+	0.987296i	$0.449207\pi$
$710$	0	0
$711$	402732.	0.0298774
$712$	0	0
$713$	−1.10639e6	−0.0815052
$714$	0	0
$715$	5.05141e6	0.369528
$716$	0	0
$717$	1.21289e7	0.881098
$718$	0	0
$719$	818051.	0.0590144	0.0295072	−	0.999565i	$-0.490606\pi$
$719$	818051.	0.0590144	0.0295072	+	0.999565i	$0.490606\pi$
$720$	0	0
$721$	−2.92347e6	−0.209440
$722$	0	0
$723$	7.56731e6	0.538388
$724$	0	0
$725$	1.83657e7	1.29766
$726$	0	0
$727$	2.45644e7	1.72373	0.861866	−	0.507136i	$-0.169296\pi$
$727$	2.45644e7	1.72373	0.861866	+	0.507136i	$0.169296\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	0	0
$731$	−6.78393e6	−0.469557
$732$	0	0
$733$	368658.	0.0253433	0.0126717	−	0.999920i	$-0.495966\pi$
$733$	368658.	0.0253433	0.0126717	+	0.999920i	$0.495966\pi$
$734$	0	0
$735$	−1.28730e7	−0.878947
$736$	0	0
$737$	1.76795e6	0.119895
$738$	0	0
$739$	2.64037e7	1.77850	0.889249	−	0.457424i	$-0.151228\pi$
$739$	2.64037e7	1.77850	0.889249	+	0.457424i	$0.151228\pi$
$740$	0	0
$741$	1.98189e6	0.132597
$742$	0	0
$743$	−2.77051e7	−1.84114	−0.920572	−	0.390574i	$-0.872277\pi$
$743$	−2.77051e7	−1.84114	−0.920572	+	0.390574i	$0.872277\pi$
$744$	0	0
$745$	3.97354e7	2.62293
$746$	0	0
$747$	5.76688e6	0.378128
$748$	0	0
$749$	−3.88601e6	−0.253104
$750$	0	0
$751$	2.72102e7	1.76048	0.880240	−	0.474528i	$-0.157381\pi$
$751$	2.72102e7	1.76048	0.880240	+	0.474528i	$0.157381\pi$
$752$	0	0
$753$	9.74602e6	0.626383
$754$	0	0
$755$	4.24151e7	2.70803
$756$	0	0
$757$	−1.40965e7	−0.894071	−0.447035	−	0.894516i	$-0.647520\pi$
$757$	−1.40965e7	−0.894071	−0.447035	+	0.894516i	$0.647520\pi$
$758$	0	0
$759$	−2.81408e6	−0.177310
$760$	0	0
$761$	3.58869e6	0.224633	0.112317	−	0.993672i	$-0.464173\pi$
$761$	3.58869e6	0.224633	0.112317	+	0.993672i	$0.464173\pi$
$762$	0	0
$763$	2.71973e6	0.169127
$764$	0	0
$765$	1.35110e7	0.834709
$766$	0	0
$767$	−1.69604e7	−1.04100
$768$	0	0
$769$	9.72717e6	0.593158	0.296579	−	0.955008i	$-0.404154\pi$
$769$	9.72717e6	0.593158	0.296579	+	0.955008i	$0.404154\pi$
$770$	0	0
$771$	−4.70174e6	−0.284854
$772$	0	0
$773$	−4.33598e6	−0.260999	−0.130500	−	0.991448i	$-0.541658\pi$
$773$	−4.33598e6	−0.260999	−0.130500	+	0.991448i	$0.541658\pi$
$774$	0	0
$775$	−1.66023e6	−0.0992921
$776$	0	0
$777$	−2.14315e6	−0.127350
$778$	0	0
$779$	−4.93270e6	−0.291234
$780$	0	0
$781$	−640640.	−0.0375826
$782$	0	0
$783$	−2.59670e6	−0.151362
$784$	0	0
$785$	−1.99004e7	−1.15263
$786$	0	0
$787$	3.07451e7	1.76946	0.884728	−	0.466108i	$-0.154344\pi$
$787$	3.07451e7	1.76946	0.884728	+	0.466108i	$0.154344\pi$
$788$	0	0
$789$	−9.80054e6	−0.560477
$790$	0	0
$791$	2.65366e6	0.150801
$792$	0	0
$793$	−2.63075e7	−1.48558
$794$	0	0
$795$	2.39033e7	1.34135
$796$	0	0
$797$	−2.49744e7	−1.39268	−0.696338	−	0.717714i	$-0.745189\pi$
$797$	−2.49744e7	−1.39268	−0.696338	+	0.717714i	$0.745189\pi$
$798$	0	0
$799$	1.68691e7	0.934813
$800$	0	0
$801$	−295974.	−0.0162994
$802$	0	0
$803$	3.39803e6	0.185968
$804$	0	0
$805$	−1.03183e7	−0.561201
$806$	0	0
$807$	8.32232e6	0.449842
$808$	0	0
$809$	−2.33716e7	−1.25550	−0.627750	−	0.778415i	$-0.716024\pi$
$809$	−2.33716e7	−1.25550	−0.627750	+	0.778415i	$0.716024\pi$
$810$	0	0
$811$	2.33591e7	1.24711	0.623554	−	0.781780i	$-0.285688\pi$
$811$	2.33591e7	1.24711	0.623554	+	0.781780i	$0.285688\pi$
$812$	0	0
$813$	−1.07343e7	−0.569570
$814$	0	0
$815$	−2.54167e7	−1.34037
$816$	0	0
$817$	1.33606e6	0.0700279
$818$	0	0
$819$	−1.63053e6	−0.0849413
$820$	0	0
$821$	−2.26403e7	−1.17226	−0.586131	−	0.810216i	$-0.699350\pi$
$821$	−2.26403e7	−1.17226	−0.586131	+	0.810216i	$0.699350\pi$
$822$	0	0
$823$	−2.62615e7	−1.35151	−0.675757	−	0.737125i	$-0.736183\pi$
$823$	−2.62615e7	−1.35151	−0.675757	+	0.737125i	$0.736183\pi$
$824$	0	0
$825$	−4.22276e6	−0.216004
$826$	0	0
$827$	1.54979e7	0.787969	0.393984	−	0.919117i	$-0.371096\pi$
$827$	1.54979e7	0.787969	0.393984	+	0.919117i	$0.371096\pi$
$828$	0	0
$829$	−6.51750e6	−0.329378	−0.164689	−	0.986346i	$-0.552662\pi$
$829$	−6.51750e6	−0.329378	−0.164689	+	0.986346i	$0.552662\pi$
$830$	0	0
$831$	1.71622e7	0.862123
$832$	0	0
$833$	2.88111e7	1.43862
$834$	0	0
$835$	4.16647e7	2.06801
$836$	0	0
$837$	234738.	0.0115816
$838$	0	0
$839$	−2.10515e7	−1.03247	−0.516236	−	0.856447i	$-0.672667\pi$
$839$	−2.10515e7	−1.03247	−0.516236	+	0.856447i	$0.672667\pi$
$840$	0	0
$841$	−7.82330e6	−0.381417
$842$	0	0
$843$	−171594.	−0.00831636
$844$	0	0
$845$	−73437.0	−0.00353812
$846$	0	0
$847$	−5.04141e6	−0.241459
$848$	0	0
$849$	−6.01050e6	−0.286181
$850$	0	0
$851$	2.47942e7	1.17362
$852$	0	0
$853$	2.92684e7	1.37729	0.688647	−	0.725097i	$-0.258205\pi$
$853$	2.92684e7	1.37729	0.688647	+	0.725097i	$0.258205\pi$
$854$	0	0
$855$	−2.66093e6	−0.124485
$856$	0	0
$857$	−1.40825e7	−0.654979	−0.327490	−	0.944855i	$-0.606203\pi$
$857$	−1.40825e7	−0.654979	−0.327490	+	0.944855i	$0.606203\pi$
$858$	0	0
$859$	1.08817e7	0.503167	0.251584	−	0.967836i	$-0.419049\pi$
$859$	1.08817e7	0.503167	0.251584	+	0.967836i	$0.419049\pi$
$860$	0	0
$861$	4.05821e6	0.186563
$862$	0	0
$863$	−7.83752e6	−0.358222	−0.179111	−	0.983829i	$-0.557322\pi$
$863$	−7.83752e6	−0.358222	−0.179111	+	0.983829i	$0.557322\pi$
$864$	0	0
$865$	6.67032e7	3.03114
$866$	0	0
$867$	−1.74603e7	−0.788867
$868$	0	0
$869$	452452.	0.0203246
$870$	0	0
$871$	−1.18511e7	−0.529313
$872$	0	0
$873$	5.05132e6	0.224321
$874$	0	0
$875$	−6.09909e6	−0.269305
$876$	0	0
$877$	−3.13170e6	−0.137493	−0.0687466	−	0.997634i	$-0.521900\pi$
$877$	−3.13170e6	−0.137493	−0.0687466	+	0.997634i	$0.521900\pi$
$878$	0	0
$879$	1.28903e7	0.562720
$880$	0	0
$881$	−1.85223e7	−0.803997	−0.401998	−	0.915640i	$-0.631684\pi$
$881$	−1.85223e7	−0.803997	−0.401998	+	0.915640i	$0.631684\pi$
$882$	0	0
$883$	−5.51096e6	−0.237862	−0.118931	−	0.992903i	$-0.537947\pi$
$883$	−5.51096e6	−0.237862	−0.118931	+	0.992903i	$0.537947\pi$
$884$	0	0
$885$	2.27715e7	0.977311
$886$	0	0
$887$	4.56817e7	1.94955	0.974773	−	0.223199i	$-0.0716499\pi$
$887$	4.56817e7	1.94955	0.974773	+	0.223199i	$0.0716499\pi$
$888$	0	0
$889$	4.58509e6	0.194578
$890$	0	0
$891$	597051.	0.0251952
$892$	0	0
$893$	−3.32228e6	−0.139415
$894$	0	0
$895$	−2.25241e7	−0.939919
$896$	0	0
$897$	1.88636e7	0.782788
$898$	0	0
$899$	−1.14696e6	−0.0473315
$900$	0	0
$901$	−5.34979e7	−2.19546
$902$	0	0
$903$	−1.09920e6	−0.0448597
$904$	0	0
$905$	1.72134e7	0.698626
$906$	0	0
$907$	−3.54419e7	−1.43054	−0.715269	−	0.698849i	$-0.753696\pi$
$907$	−3.54419e7	−1.43054	−0.715269	+	0.698849i	$0.753696\pi$
$908$	0	0
$909$	−1.38664e7	−0.556613
$910$	0	0
$911$	4.18553e7	1.67092	0.835458	−	0.549554i	$-0.185202\pi$
$911$	4.18553e7	1.67092	0.835458	+	0.549554i	$0.185202\pi$
$912$	0	0
$913$	6.47884e6	0.257229
$914$	0	0
$915$	3.53210e7	1.39470
$916$	0	0
$917$	1.05208e7	0.413168
$918$	0	0
$919$	−1.29489e7	−0.505758	−0.252879	−	0.967498i	$-0.581378\pi$
$919$	−1.29489e7	−0.505758	−0.252879	+	0.967498i	$0.581378\pi$
$920$	0	0
$921$	2.78020e7	1.08001
$922$	0	0
$923$	4.29440e6	0.165920
$924$	0	0
$925$	3.72057e7	1.42973
$926$	0	0
$927$	−7.17579e6	−0.274265
$928$	0	0
$929$	−3.42756e7	−1.30300	−0.651502	−	0.758647i	$-0.725861\pi$
$929$	−3.42756e7	−1.30300	−0.651502	+	0.758647i	$0.725861\pi$
$930$	0	0
$931$	−5.67420e6	−0.214551
$932$	0	0
$933$	−2.50423e7	−0.941826
$934$	0	0
$935$	1.51791e7	0.567827
$936$	0	0
$937$	3.81392e7	1.41913	0.709566	−	0.704639i	$-0.248891\pi$
$937$	3.81392e7	1.41913	0.709566	+	0.704639i	$0.248891\pi$
$938$	0	0
$939$	9.84451e6	0.364359
$940$	0	0
$941$	4.34881e7	1.60102	0.800510	−	0.599320i	$-0.204562\pi$
$941$	4.34881e7	1.60102	0.800510	+	0.599320i	$0.204562\pi$
$942$	0	0
$943$	−4.69495e7	−1.71930
$944$	0	0
$945$	2.18919e6	0.0797450
$946$	0	0
$947$	3.23771e7	1.17318	0.586588	−	0.809885i	$-0.300471\pi$
$947$	3.23771e7	1.17318	0.586588	+	0.809885i	$0.300471\pi$
$948$	0	0
$949$	−2.27780e7	−0.821013
$950$	0	0
$951$	−1.40020e7	−0.502040
$952$	0	0
$953$	4.12172e7	1.47010	0.735050	−	0.678013i	$-0.237159\pi$
$953$	4.12172e7	1.47010	0.735050	+	0.678013i	$0.237159\pi$
$954$	0	0
$955$	3.00967e7	1.06785
$956$	0	0
$957$	−2.91728e6	−0.102967
$958$	0	0
$959$	−1.20097e7	−0.421681
$960$	0	0
$961$	−2.85255e7	−0.996378
$962$	0	0
$963$	−9.53840e6	−0.331444
$964$	0	0
$965$	−6.13770e7	−2.12171
$966$	0	0
$967$	−3.40238e7	−1.17008	−0.585041	−	0.811003i	$-0.698922\pi$
$967$	−3.40238e7	−1.17008	−0.585041	+	0.811003i	$0.698922\pi$
$968$	0	0
$969$	5.95542e6	0.203752
$970$	0	0
$971$	4.03426e7	1.37314	0.686571	−	0.727063i	$-0.259115\pi$
$971$	4.03426e7	1.37314	0.686571	+	0.727063i	$0.259115\pi$
$972$	0	0
$973$	1.02005e7	0.345412
$974$	0	0
$975$	2.83064e7	0.953616
$976$	0	0
$977$	1.70401e7	0.571130	0.285565	−	0.958359i	$-0.407819\pi$
$977$	1.70401e7	0.571130	0.285565	+	0.958359i	$0.407819\pi$
$978$	0	0
$979$	−332514.	−0.0110880
$980$	0	0
$981$	6.67570e6	0.221475
$982$	0	0
$983$	−2.20796e7	−0.728799	−0.364399	−	0.931243i	$-0.618726\pi$
$983$	−2.20796e7	−0.728799	−0.364399	+	0.931243i	$0.618726\pi$
$984$	0	0
$985$	8.57535e7	2.81619
$986$	0	0
$987$	2.73329e6	0.0893085
$988$	0	0
$989$	1.27166e7	0.413411
$990$	0	0
$991$	1.70400e7	0.551171	0.275585	−	0.961277i	$-0.411128\pi$
$991$	1.70400e7	0.551171	0.275585	+	0.961277i	$0.411128\pi$
$992$	0	0
$993$	317160.	0.0102072
$994$	0	0
$995$	−3.90850e7	−1.25156
$996$	0	0
$997$	2.01866e7	0.643170	0.321585	−	0.946881i	$-0.395784\pi$
$997$	2.01866e7	0.643170	0.321585	+	0.946881i	$0.395784\pi$
$998$	0	0
$999$	−5.26046e6	−0.166767

Twists

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

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