LMFDB - Embedded newform 847.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,6,Mod(1,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("847.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	847.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:	$135.845095382$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	847.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -6.00000 q^{3} -28.0000 q^{4} -74.0000 q^{5} -12.0000 q^{6} +49.0000 q^{7} -120.000 q^{8} -207.000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -6.00000 q^{3} -28.0000 q^{4} -74.0000 q^{5} -12.0000 q^{6} +49.0000 q^{7} -120.000 q^{8} -207.000 q^{9} -148.000 q^{10} +168.000 q^{12} -364.000 q^{13} +98.0000 q^{14} +444.000 q^{15} +656.000 q^{16} -148.000 q^{17} -414.000 q^{18} +1320.00 q^{19} +2072.00 q^{20} -294.000 q^{21} -436.000 q^{23} +720.000 q^{24} +2351.00 q^{25} -728.000 q^{26} +2700.00 q^{27} -1372.00 q^{28} -2970.00 q^{29} +888.000 q^{30} +8842.00 q^{31} +5152.00 q^{32} -296.000 q^{34} -3626.00 q^{35} +5796.00 q^{36} +138.000 q^{37} +2640.00 q^{38} +2184.00 q^{39} +8880.00 q^{40} -532.000 q^{41} -588.000 q^{42} +20676.0 q^{43} +15318.0 q^{45} -872.000 q^{46} -11722.0 q^{47} -3936.00 q^{48} +2401.00 q^{49} +4702.00 q^{50} +888.000 q^{51} +10192.0 q^{52} +5274.00 q^{53} +5400.00 q^{54} -5880.00 q^{56} -7920.00 q^{57} -5940.00 q^{58} -27670.0 q^{59} -12432.0 q^{60} -19512.0 q^{61} +17684.0 q^{62} -10143.0 q^{63} -10688.0 q^{64} +26936.0 q^{65} +64088.0 q^{67} +4144.00 q^{68} +2616.00 q^{69} -7252.00 q^{70} -3708.00 q^{71} +24840.0 q^{72} +24296.0 q^{73} +276.000 q^{74} -14106.0 q^{75} -36960.0 q^{76} +4368.00 q^{78} +2200.00 q^{79} -48544.0 q^{80} +34101.0 q^{81} -1064.00 q^{82} -74424.0 q^{83} +8232.00 q^{84} +10952.0 q^{85} +41352.0 q^{86} +17820.0 q^{87} +34170.0 q^{89} +30636.0 q^{90} -17836.0 q^{91} +12208.0 q^{92} -53052.0 q^{93} -23444.0 q^{94} -97680.0 q^{95} -30912.0 q^{96} +151718. q^{97} +4802.00 q^{98} +O(q^{100})\)

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 $

$2$	2.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	2.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	−6.00000	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$3$	−6.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	−28.0000	−0.875000
$5$	−74.0000	−1.32375	−0.661876	−	0.749613i	$-0.730240\pi$
$5$	−74.0000	−1.32375	−0.661876	+	0.749613i	$0.730240\pi$
$6$	−12.0000	−0.136083
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−120.000	−0.662913
$9$	−207.000	−0.851852
$10$	−148.000	−0.468017
$11$	0	0
$11$	0	0
$12$	168.000	0.336788
$13$	−364.000	−0.597369	−0.298685	−	0.954352i	$-0.596548\pi$
$13$	−364.000	−0.597369	−0.298685	+	0.954352i	$0.596548\pi$
$14$	98.0000	0.133631
$15$	444.000	0.509512
$16$	656.000	0.640625
$17$	−148.000	−0.124205	−0.0621025	−	0.998070i	$-0.519781\pi$
$17$	−148.000	−0.124205	−0.0621025	+	0.998070i	$0.519781\pi$
$18$	−414.000	−0.301175
$19$	1320.00	0.838861	0.419430	−	0.907787i	$-0.362230\pi$
$19$	1320.00	0.838861	0.419430	+	0.907787i	$0.362230\pi$
$20$	2072.00	1.15828
$21$	−294.000	−0.145479
$22$	0	0
$23$	−436.000	−0.171857	−0.0859284	−	0.996301i	$-0.527386\pi$
$23$	−436.000	−0.171857	−0.0859284	+	0.996301i	$0.527386\pi$
$24$	720.000	0.255155
$25$	2351.00	0.752320
$26$	−728.000	−0.211202
$27$	2700.00	0.712778
$28$	−1372.00	−0.330719
$29$	−2970.00	−0.655785	−0.327892	−	0.944715i	$-0.606338\pi$
$29$	−2970.00	−0.655785	−0.327892	+	0.944715i	$0.606338\pi$
$30$	888.000	0.180140
$31$	8842.00	1.65252	0.826259	−	0.563290i	$-0.190465\pi$
$31$	8842.00	1.65252	0.826259	+	0.563290i	$0.190465\pi$
$32$	5152.00	0.889408
$33$	0	0
$34$	−296.000	−0.0439131
$35$	−3626.00	−0.500331
$36$	5796.00	0.745370
$37$	138.000	0.0165720	0.00828600	−	0.999966i	$-0.497362\pi$
$37$	138.000	0.0165720	0.00828600	+	0.999966i	$0.497362\pi$
$38$	2640.00	0.296582
$39$	2184.00	0.229928
$40$	8880.00	0.877532
$41$	−532.000	−0.0494256	−0.0247128	−	0.999695i	$-0.507867\pi$
$41$	−532.000	−0.0494256	−0.0247128	+	0.999695i	$0.507867\pi$
$42$	−588.000	−0.0514344
$43$	20676.0	1.70528	0.852639	−	0.522500i	$-0.175000\pi$
$43$	20676.0	1.70528	0.852639	+	0.522500i	$0.175000\pi$
$44$	0	0
$45$	15318.0	1.12764
$46$	−872.000	−0.0607606
$47$	−11722.0	−0.774029	−0.387014	−	0.922074i	$-0.626494\pi$
$47$	−11722.0	−0.774029	−0.387014	+	0.922074i	$0.626494\pi$
$48$	−3936.00	−0.246577
$49$	2401.00	0.142857
$50$	4702.00	0.265985
$51$	888.000	0.0478066
$52$	10192.0	0.522698
$53$	5274.00	0.257899	0.128950	−	0.991651i	$-0.458839\pi$
$53$	5274.00	0.257899	0.128950	+	0.991651i	$0.458839\pi$
$54$	5400.00	0.252005
$55$	0	0
$56$	−5880.00	−0.250557
$57$	−7920.00	−0.322878
$58$	−5940.00	−0.231855
$59$	−27670.0	−1.03485	−0.517427	−	0.855727i	$-0.673110\pi$
$59$	−27670.0	−1.03485	−0.517427	+	0.855727i	$0.673110\pi$
$60$	−12432.0	−0.445823
$61$	−19512.0	−0.671394	−0.335697	−	0.941970i	$-0.608972\pi$
$61$	−19512.0	−0.671394	−0.335697	+	0.941970i	$0.608972\pi$
$62$	17684.0	0.584253
$63$	−10143.0	−0.321970
$64$	−10688.0	−0.326172
$65$	26936.0	0.790769
$66$	0	0
$67$	64088.0	1.74417	0.872087	−	0.489351i	$-0.162766\pi$
$67$	64088.0	1.74417	0.872087	+	0.489351i	$0.162766\pi$
$68$	4144.00	0.108679
$69$	2616.00	0.0661477
$70$	−7252.00	−0.176894
$71$	−3708.00	−0.0872959	−0.0436480	−	0.999047i	$-0.513898\pi$
$71$	−3708.00	−0.0872959	−0.0436480	+	0.999047i	$0.513898\pi$
$72$	24840.0	0.564703
$73$	24296.0	0.533615	0.266807	−	0.963750i	$-0.414031\pi$
$73$	24296.0	0.533615	0.266807	+	0.963750i	$0.414031\pi$
$74$	276.000	0.00585908
$75$	−14106.0	−0.289568
$76$	−36960.0	−0.734003
$77$	0	0
$78$	4368.00	0.0812917
$79$	2200.00	0.0396602	0.0198301	−	0.999803i	$-0.493687\pi$
$79$	2200.00	0.0396602	0.0198301	+	0.999803i	$0.493687\pi$
$80$	−48544.0	−0.848029
$81$	34101.0	0.577503
$82$	−1064.00	−0.0174746
$83$	−74424.0	−1.18582	−0.592909	−	0.805270i	$-0.702020\pi$
$83$	−74424.0	−1.18582	−0.592909	+	0.805270i	$0.702020\pi$
$84$	8232.00	0.127294
$85$	10952.0	0.164417
$86$	41352.0	0.602907
$87$	17820.0	0.252412
$88$	0	0
$89$	34170.0	0.457267	0.228634	−	0.973513i	$-0.426574\pi$
$89$	34170.0	0.457267	0.228634	+	0.973513i	$0.426574\pi$
$90$	30636.0	0.398681
$91$	−17836.0	−0.225784
$92$	12208.0	0.150375
$93$	−53052.0	−0.636055
$94$	−23444.0	−0.273660
$95$	−97680.0	−1.11044
$96$	−30912.0	−0.342333
$97$	151718.	1.63722	0.818611	−	0.574348i	$-0.194744\pi$
$97$	151718.	1.63722	0.818611	+	0.574348i	$0.194744\pi$
$98$	4802.00	0.0505076
$99$	0	0
$100$	−65828.0	−0.658280
$101$	−116852.	−1.13981	−0.569905	−	0.821710i	$-0.693020\pi$
$101$	−116852.	−1.13981	−0.569905	+	0.821710i	$0.693020\pi$
$102$	1776.00	0.0169022
$103$	103694.	0.963076	0.481538	−	0.876425i	$-0.340078\pi$
$103$	103694.	0.963076	0.481538	+	0.876425i	$0.340078\pi$
$104$	43680.0	0.396004
$105$	21756.0	0.192578
$106$	10548.0	0.0911812
$107$	97092.0	0.819830	0.409915	−	0.912124i	$-0.365558\pi$
$107$	97092.0	0.819830	0.409915	+	0.912124i	$0.365558\pi$
$108$	−75600.0	−0.623681
$109$	−52930.0	−0.426713	−0.213356	−	0.976974i	$-0.568440\pi$
$109$	−52930.0	−0.426713	−0.213356	+	0.976974i	$0.568440\pi$
$110$	0	0
$111$	−828.000	−0.00637856
$112$	32144.0	0.242133
$113$	−80526.0	−0.593253	−0.296627	−	0.954994i	$-0.595862\pi$
$113$	−80526.0	−0.593253	−0.296627	+	0.954994i	$0.595862\pi$
$114$	−15840.0	−0.114155
$115$	32264.0	0.227496
$116$	83160.0	0.573812
$117$	75348.0	0.508870
$118$	−55340.0	−0.365876
$119$	−7252.00	−0.0469451
$120$	−53280.0	−0.337762
$121$	0	0
$122$	−39024.0	−0.237373
$123$	3192.00	0.0190239
$124$	−247576.	−1.44595
$125$	57276.0	0.327867
$126$	−20286.0	−0.113833
$127$	−221048.	−1.21612	−0.608061	−	0.793890i	$-0.708052\pi$
$127$	−221048.	−1.21612	−0.608061	+	0.793890i	$0.708052\pi$
$128$	−186240.	−1.00473
$129$	−124056.	−0.656362
$130$	53872.0	0.279579
$131$	−37572.0	−0.191287	−0.0956436	−	0.995416i	$-0.530491\pi$
$131$	−37572.0	−0.191287	−0.0956436	+	0.995416i	$0.530491\pi$
$132$	0	0
$133$	64680.0	0.317060
$134$	128176.	0.616658
$135$	−199800.	−0.943542
$136$	17760.0	0.0823371
$137$	−290602.	−1.32281	−0.661405	−	0.750029i	$-0.730039\pi$
$137$	−290602.	−1.32281	−0.661405	+	0.750029i	$0.730039\pi$
$138$	5232.00	0.0233868
$139$	−367360.	−1.61270	−0.806352	−	0.591435i	$-0.798561\pi$
$139$	−367360.	−1.61270	−0.806352	+	0.591435i	$0.798561\pi$
$140$	101528.	0.437790
$141$	70332.0	0.297924
$142$	−7416.00	−0.0308638
$143$	0	0
$144$	−135792.	−0.545718
$145$	219780.	0.868097
$146$	48592.0	0.188661
$147$	−14406.0	−0.0549857
$148$	−3864.00	−0.0145005
$149$	462730.	1.70751	0.853753	−	0.520679i	$-0.174321\pi$
$149$	462730.	1.70751	0.853753	+	0.520679i	$0.174321\pi$
$150$	−28212.0	−0.102378
$151$	7648.00	0.0272964	0.0136482	−	0.999907i	$-0.495656\pi$
$151$	7648.00	0.0272964	0.0136482	+	0.999907i	$0.495656\pi$
$152$	−158400.	−0.556091
$153$	30636.0	0.105804
$154$	0	0
$155$	−654308.	−2.18752
$156$	−61152.0	−0.201187
$157$	−161482.	−0.522847	−0.261424	−	0.965224i	$-0.584192\pi$
$157$	−161482.	−0.522847	−0.261424	+	0.965224i	$0.584192\pi$
$158$	4400.00	0.0140220
$159$	−31644.0	−0.0992656
$160$	−381248.	−1.17736
$161$	−21364.0	−0.0649558
$162$	68202.0	0.204178
$163$	179464.	0.529064	0.264532	−	0.964377i	$-0.414782\pi$
$163$	179464.	0.529064	0.264532	+	0.964377i	$0.414782\pi$
$164$	14896.0	0.0432474
$165$	0	0
$166$	−148848.	−0.419250
$167$	−316848.	−0.879144	−0.439572	−	0.898207i	$-0.644870\pi$
$167$	−316848.	−0.879144	−0.439572	+	0.898207i	$0.644870\pi$
$168$	35280.0	0.0964396
$169$	−238797.	−0.643150
$170$	21904.0	0.0581301
$171$	−273240.	−0.714585
$172$	−578928.	−1.49212
$173$	175116.	0.444847	0.222423	−	0.974950i	$-0.428603\pi$
$173$	175116.	0.444847	0.222423	+	0.974950i	$0.428603\pi$
$174$	35640.0	0.0892410
$175$	115199.	0.284350
$176$	0	0
$177$	166020.	0.398316
$178$	68340.0	0.161668
$179$	−69780.0	−0.162779	−0.0813895	−	0.996682i	$-0.525936\pi$
$179$	−69780.0	−0.162779	−0.0813895	+	0.996682i	$0.525936\pi$
$180$	−428904.	−0.986686
$181$	−78638.0	−0.178417	−0.0892085	−	0.996013i	$-0.528434\pi$
$181$	−78638.0	−0.178417	−0.0892085	+	0.996013i	$0.528434\pi$
$182$	−35672.0	−0.0798268
$183$	117072.	0.258420
$184$	52320.0	0.113926
$185$	−10212.0	−0.0219372
$186$	−106104.	−0.224879
$187$	0	0
$188$	328216.	0.677275
$189$	132300.	0.269405
$190$	−195360.	−0.392601
$191$	−927208.	−1.83905	−0.919525	−	0.393030i	$-0.871427\pi$
$191$	−927208.	−1.83905	−0.919525	+	0.393030i	$0.871427\pi$
$192$	64128.0	0.125544
$193$	−877474.	−1.69567	−0.847834	−	0.530261i	$-0.822094\pi$
$193$	−877474.	−1.69567	−0.847834	+	0.530261i	$0.822094\pi$
$194$	303436.	0.578846
$195$	−161616.	−0.304367
$196$	−67228.0	−0.125000
$197$	744602.	1.36697	0.683484	−	0.729965i	$-0.260464\pi$
$197$	744602.	1.36697	0.683484	+	0.729965i	$0.260464\pi$
$198$	0	0
$199$	1.07931e6	1.93203	0.966014	−	0.258489i	$-0.0832246\pi$
$199$	1.07931e6	1.93203	0.966014	+	0.258489i	$0.0832246\pi$
$200$	−282120.	−0.498722
$201$	−384528.	−0.671333
$202$	−233704.	−0.402984
$203$	−145530.	−0.247863
$204$	−24864.0	−0.0418307
$205$	39368.0	0.0654273
$206$	207388.	0.340499
$207$	90252.0	0.146397
$208$	−238784.	−0.382690
$209$	0	0
$210$	43512.0	0.0680865
$211$	−728772.	−1.12690	−0.563450	−	0.826150i	$-0.690526\pi$
$211$	−728772.	−1.12690	−0.563450	+	0.826150i	$0.690526\pi$
$212$	−147672.	−0.225662
$213$	22248.0	0.0336002
$214$	194184.	0.289854
$215$	−1.53002e6	−2.25737
$216$	−324000.	−0.472510
$217$	433258.	0.624593
$218$	−105860.	−0.150866
$219$	−145776.	−0.205388
$220$	0	0
$221$	53872.0	0.0741963
$222$	−1656.00	−0.00225516
$223$	38374.0	0.0516743	0.0258372	−	0.999666i	$-0.491775\pi$
$223$	38374.0	0.0516743	0.0258372	+	0.999666i	$0.491775\pi$
$224$	252448.	0.336165
$225$	−486657.	−0.640865
$226$	−161052.	−0.209747
$227$	−323268.	−0.416388	−0.208194	−	0.978088i	$-0.566759\pi$
$227$	−323268.	−0.416388	−0.208194	+	0.978088i	$0.566759\pi$
$228$	221760.	0.282518
$229$	813690.	1.02535	0.512673	−	0.858584i	$-0.328655\pi$
$229$	813690.	1.02535	0.512673	+	0.858584i	$0.328655\pi$
$230$	64528.0	0.0804320
$231$	0	0
$232$	356400.	0.434728
$233$	−1.10801e6	−1.33707	−0.668537	−	0.743679i	$-0.733079\pi$
$233$	−1.10801e6	−1.33707	−0.668537	+	0.743679i	$0.733079\pi$
$234$	150696.	0.179913
$235$	867428.	1.02462
$236$	774760.	0.905497
$237$	−13200.0	−0.0152652
$238$	−14504.0	−0.0165976
$239$	1.31352e6	1.48745	0.743724	−	0.668487i	$-0.233058\pi$
$239$	1.31352e6	1.48745	0.743724	+	0.668487i	$0.233058\pi$
$240$	291264.	0.326406
$241$	1.05607e6	1.17125	0.585625	−	0.810582i	$-0.300849\pi$
$241$	1.05607e6	1.17125	0.585625	+	0.810582i	$0.300849\pi$
$242$	0	0
$243$	−860706.	−0.935059
$244$	546336.	0.587469
$245$	−177674.	−0.189107
$246$	6384.00	0.00672597
$247$	−480480.	−0.501110
$248$	−1.06104e6	−1.09548
$249$	446544.	0.456421
$250$	114552.	0.115918
$251$	1.68914e6	1.69232	0.846159	−	0.532931i	$-0.178909\pi$
$251$	1.68914e6	1.69232	0.846159	+	0.532931i	$0.178909\pi$
$252$	284004.	0.281724
$253$	0	0
$254$	−442096.	−0.429964
$255$	−65712.0	−0.0632840
$256$	−30464.0	−0.0290527
$257$	641938.	0.606262	0.303131	−	0.952949i	$-0.401968\pi$
$257$	641938.	0.606262	0.303131	+	0.952949i	$0.401968\pi$
$258$	−248112.	−0.232059
$259$	6762.00	0.00626363
$260$	−754208.	−0.691923
$261$	614790.	0.558632
$262$	−75144.0	−0.0676303
$263$	1.10150e6	0.981959	0.490980	−	0.871171i	$-0.336639\pi$
$263$	1.10150e6	0.981959	0.490980	+	0.871171i	$0.336639\pi$
$264$	0	0
$265$	−390276.	−0.341395
$266$	129360.	0.112097
$267$	−205020.	−0.176002
$268$	−1.79446e6	−1.52615
$269$	−2.15147e6	−1.81282	−0.906410	−	0.422399i	$-0.861188\pi$
$269$	−2.15147e6	−1.81282	−0.906410	+	0.422399i	$0.861188\pi$
$270$	−399600.	−0.333592
$271$	1.08327e6	0.896010	0.448005	−	0.894031i	$-0.352135\pi$
$271$	1.08327e6	0.896010	0.448005	+	0.894031i	$0.352135\pi$
$272$	−97088.0	−0.0795689
$273$	107016.	0.0869045
$274$	−581204.	−0.467684
$275$	0	0
$276$	−73248.0	−0.0578793
$277$	2.22372e6	1.74133	0.870665	−	0.491877i	$-0.163689\pi$
$277$	2.22372e6	1.74133	0.870665	+	0.491877i	$0.163689\pi$
$278$	−734720.	−0.570177
$279$	−1.83029e6	−1.40770
$280$	435120.	0.331676
$281$	153018.	0.115605	0.0578025	−	0.998328i	$-0.481591\pi$
$281$	153018.	0.115605	0.0578025	+	0.998328i	$0.481591\pi$
$282$	140664.	0.105332
$283$	−715324.	−0.530929	−0.265465	−	0.964121i	$-0.585525\pi$
$283$	−715324.	−0.530929	−0.265465	+	0.964121i	$0.585525\pi$
$284$	103824.	0.0763839
$285$	586080.	0.427410
$286$	0	0
$287$	−26068.0	−0.0186811
$288$	−1.06646e6	−0.757644
$289$	−1.39795e6	−0.984573
$290$	439560.	0.306919
$291$	−910308.	−0.630167
$292$	−680288.	−0.466913
$293$	−347424.	−0.236424	−0.118212	−	0.992988i	$-0.537716\pi$
$293$	−347424.	−0.236424	−0.118212	+	0.992988i	$0.537716\pi$
$294$	−28812.0	−0.0194404
$295$	2.04758e6	1.36989
$296$	−16560.0	−0.0109858
$297$	0	0
$298$	925460.	0.603694
$299$	158704.	0.102662
$300$	394968.	0.253372
$301$	1.01312e6	0.644535
$302$	15296.0	0.00965074
$303$	701112.	0.438713
$304$	865920.	0.537395
$305$	1.44389e6	0.888759
$306$	61272.0	0.0374075
$307$	−2.64043e6	−1.59893	−0.799463	−	0.600715i	$-0.794883\pi$
$307$	−2.64043e6	−1.59893	−0.799463	+	0.600715i	$0.794883\pi$
$308$	0	0
$309$	−622164.	−0.370688
$310$	−1.30862e6	−0.773407
$311$	−947778.	−0.555656	−0.277828	−	0.960631i	$-0.589614\pi$
$311$	−947778.	−0.555656	−0.277828	+	0.960631i	$0.589614\pi$
$312$	−262080.	−0.152422
$313$	−248686.	−0.143480	−0.0717399	−	0.997423i	$-0.522855\pi$
$313$	−248686.	−0.143480	−0.0717399	+	0.997423i	$0.522855\pi$
$314$	−322964.	−0.184854
$315$	750582.	0.426208
$316$	−61600.0	−0.0347027
$317$	2.60904e6	1.45825	0.729125	−	0.684380i	$-0.239927\pi$
$317$	2.60904e6	1.45825	0.729125	+	0.684380i	$0.239927\pi$
$318$	−63288.0	−0.0350957
$319$	0	0
$320$	790912.	0.431771
$321$	−582552.	−0.315553
$322$	−42728.0	−0.0229653
$323$	−195360.	−0.104191
$324$	−954828.	−0.505316
$325$	−855764.	−0.449413
$326$	358928.	0.187052
$327$	317580.	0.164242
$328$	63840.0	0.0327649
$329$	−574378.	−0.292555
$330$	0	0
$331$	152332.	0.0764225	0.0382112	−	0.999270i	$-0.487834\pi$
$331$	152332.	0.0764225	0.0382112	+	0.999270i	$0.487834\pi$
$332$	2.08387e6	1.03759
$333$	−28566.0	−0.0141169
$334$	−633696.	−0.310824
$335$	−4.74251e6	−2.30885
$336$	−192864.	−0.0931972
$337$	−206558.	−0.0990757	−0.0495379	−	0.998772i	$-0.515775\pi$
$337$	−206558.	−0.0990757	−0.0495379	+	0.998772i	$0.515775\pi$
$338$	−477594.	−0.227388
$339$	483156.	0.228343
$340$	−306656.	−0.143865
$341$	0	0
$342$	−546480.	−0.252644
$343$	117649.	0.0539949
$344$	−2.48112e6	−1.13045
$345$	−193584.	−0.0875632
$346$	350232.	0.157277
$347$	−2.01807e6	−0.899730	−0.449865	−	0.893097i	$-0.648528\pi$
$347$	−2.01807e6	−0.899730	−0.449865	+	0.893097i	$0.648528\pi$
$348$	−498960.	−0.220860
$349$	580440.	0.255090	0.127545	−	0.991833i	$-0.459290\pi$
$349$	580440.	0.255090	0.127545	+	0.991833i	$0.459290\pi$
$350$	230398.	0.100533
$351$	−982800.	−0.425792
$352$	0	0
$353$	572034.	0.244335	0.122167	−	0.992510i	$-0.461016\pi$
$353$	572034.	0.244335	0.122167	+	0.992510i	$0.461016\pi$
$354$	332040.	0.140826
$355$	274392.	0.115558
$356$	−956760.	−0.400109
$357$	43512.0	0.0180692
$358$	−139560.	−0.0575511
$359$	−4.56544e6	−1.86959	−0.934795	−	0.355187i	$-0.884417\pi$
$359$	−4.56544e6	−1.86959	−0.934795	+	0.355187i	$0.884417\pi$
$360$	−1.83816e6	−0.747527
$361$	−733699.	−0.296312
$362$	−157276.	−0.0630799
$363$	0	0
$364$	499408.	0.197561
$365$	−1.79790e6	−0.706373
$366$	234144.	0.0913651
$367$	924358.	0.358241	0.179120	−	0.983827i	$-0.442675\pi$
$367$	924358.	0.358241	0.179120	+	0.983827i	$0.442675\pi$
$368$	−286016.	−0.110096
$369$	110124.	0.0421033
$370$	−20424.0	−0.00775598
$371$	258426.	0.0974768
$372$	1.48546e6	0.556548
$373$	−4.92021e6	−1.83110	−0.915550	−	0.402205i	$-0.868244\pi$
$373$	−4.92021e6	−1.83110	−0.915550	+	0.402205i	$0.868244\pi$
$374$	0	0
$375$	−343656.	−0.126196
$376$	1.40664e6	0.513113
$377$	1.08108e6	0.391746
$378$	264600.	0.0952490
$379$	3.97540e6	1.42162	0.710809	−	0.703385i	$-0.248329\pi$
$379$	3.97540e6	1.42162	0.710809	+	0.703385i	$0.248329\pi$
$380$	2.73504e6	0.971638
$381$	1.32629e6	0.468086
$382$	−1.85442e6	−0.650203
$383$	−982846.	−0.342364	−0.171182	−	0.985239i	$-0.554759\pi$
$383$	−982846.	−0.342364	−0.171182	+	0.985239i	$0.554759\pi$
$384$	1.11744e6	0.386720
$385$	0	0
$386$	−1.75495e6	−0.599509
$387$	−4.27993e6	−1.45264
$388$	−4.24810e6	−1.43257
$389$	−744090.	−0.249317	−0.124658	−	0.992200i	$-0.539783\pi$
$389$	−744090.	−0.249317	−0.124658	+	0.992200i	$0.539783\pi$
$390$	−323232.	−0.107610
$391$	64528.0	0.0213455
$392$	−288120.	−0.0947018
$393$	225432.	0.0736265
$394$	1.48920e6	0.483296
$395$	−162800.	−0.0525003
$396$	0	0
$397$	5.73024e6	1.82472	0.912360	−	0.409388i	$-0.134258\pi$
$397$	5.73024e6	1.82472	0.912360	+	0.409388i	$0.134258\pi$
$398$	2.15862e6	0.683075
$399$	−388080.	−0.122036
$400$	1.54226e6	0.481955
$401$	4.26756e6	1.32531	0.662657	−	0.748923i	$-0.269429\pi$
$401$	4.26756e6	1.32531	0.662657	+	0.748923i	$0.269429\pi$
$402$	−769056.	−0.237352
$403$	−3.21849e6	−0.987164
$404$	3.27186e6	0.997334
$405$	−2.52347e6	−0.764471
$406$	−291060.	−0.0876330
$407$	0	0
$408$	−106560.	−0.0316916
$409$	5.81772e6	1.71967	0.859834	−	0.510574i	$-0.170567\pi$
$409$	5.81772e6	1.71967	0.859834	+	0.510574i	$0.170567\pi$
$410$	78736.0	0.0231320
$411$	1.74361e6	0.509149
$412$	−2.90343e6	−0.842692
$413$	−1.35583e6	−0.391138
$414$	180504.	0.0517590
$415$	5.50738e6	1.56973
$416$	−1.87533e6	−0.531305
$417$	2.20416e6	0.620730
$418$	0	0
$419$	−4.38823e6	−1.22111	−0.610554	−	0.791974i	$-0.709053\pi$
$419$	−4.38823e6	−1.22111	−0.610554	+	0.791974i	$0.709053\pi$
$420$	−609168.	−0.168505
$421$	−1.48456e6	−0.408218	−0.204109	−	0.978948i	$-0.565430\pi$
$421$	−1.48456e6	−0.408218	−0.204109	+	0.978948i	$0.565430\pi$
$422$	−1.45754e6	−0.398419
$423$	2.42645e6	0.659358
$424$	−632880.	−0.170965
$425$	−347948.	−0.0934420
$426$	44496.0	0.0118795
$427$	−956088.	−0.253763
$428$	−2.71858e6	−0.717352
$429$	0	0
$430$	−3.06005e6	−0.798100
$431$	206448.	0.0535325	0.0267662	−	0.999642i	$-0.491479\pi$
$431$	206448.	0.0535325	0.0267662	+	0.999642i	$0.491479\pi$
$432$	1.77120e6	0.456623
$433$	−5.67867e6	−1.45555	−0.727774	−	0.685817i	$-0.759445\pi$
$433$	−5.67867e6	−1.45555	−0.727774	+	0.685817i	$0.759445\pi$
$434$	866516.	0.220827
$435$	−1.31868e6	−0.334131
$436$	1.48204e6	0.373374
$437$	−575520.	−0.144164
$438$	−291552.	−0.0726157
$439$	4.43666e6	1.09874	0.549370	−	0.835579i	$-0.314868\pi$
$439$	4.43666e6	1.09874	0.549370	+	0.835579i	$0.314868\pi$
$440$	0	0
$441$	−497007.	−0.121693
$442$	107744.	0.0262324
$443$	6.17328e6	1.49454	0.747269	−	0.664522i	$-0.231365\pi$
$443$	6.17328e6	1.49454	0.747269	+	0.664522i	$0.231365\pi$
$444$	23184.0	0.00558124
$445$	−2.52858e6	−0.605308
$446$	76748.0	0.0182696
$447$	−2.77638e6	−0.657219
$448$	−523712.	−0.123281
$449$	−4.93105e6	−1.15431	−0.577156	−	0.816634i	$-0.695838\pi$
$449$	−4.93105e6	−1.15431	−0.577156	+	0.816634i	$0.695838\pi$
$450$	−973314.	−0.226580
$451$	0	0
$452$	2.25473e6	0.519096
$453$	−45888.0	−0.0105064
$454$	−646536.	−0.147215
$455$	1.31986e6	0.298883
$456$	950400.	0.214040
$457$	4.15030e6	0.929585	0.464793	−	0.885420i	$-0.346129\pi$
$457$	4.15030e6	0.929585	0.464793	+	0.885420i	$0.346129\pi$
$458$	1.62738e6	0.362514
$459$	−399600.	−0.0885307
$460$	−903392.	−0.199059
$461$	4.40345e6	0.965029	0.482515	−	0.875888i	$-0.339723\pi$
$461$	4.40345e6	0.965029	0.482515	+	0.875888i	$0.339723\pi$
$462$	0	0
$463$	6.82728e6	1.48012	0.740058	−	0.672544i	$-0.234798\pi$
$463$	6.82728e6	1.48012	0.740058	+	0.672544i	$0.234798\pi$
$464$	−1.94832e6	−0.420112
$465$	3.92585e6	0.841979
$466$	−2.21603e6	−0.472727
$467$	6.88244e6	1.46033	0.730163	−	0.683272i	$-0.239444\pi$
$467$	6.88244e6	1.46033	0.730163	+	0.683272i	$0.239444\pi$
$468$	−2.10974e6	−0.445261
$469$	3.14031e6	0.659236
$470$	1.73486e6	0.362259
$471$	968892.	0.201244
$472$	3.32040e6	0.686018
$473$	0	0
$474$	−26400.0	−0.00539707
$475$	3.10332e6	0.631092
$476$	203056.	0.0410770
$477$	−1.09172e6	−0.219692
$478$	2.62704e6	0.525892
$479$	−5.02430e6	−1.00055	−0.500273	−	0.865868i	$-0.666767\pi$
$479$	−5.02430e6	−1.00055	−0.500273	+	0.865868i	$0.666767\pi$
$480$	2.28749e6	0.453164
$481$	−50232.0	−0.00989960
$482$	2.11214e6	0.414099
$483$	128184.	0.0250015
$484$	0	0
$485$	−1.12271e7	−2.16728
$486$	−1.72141e6	−0.330593
$487$	−4.51601e6	−0.862845	−0.431422	−	0.902150i	$-0.641988\pi$
$487$	−4.51601e6	−0.862845	−0.431422	+	0.902150i	$0.641988\pi$
$488$	2.34144e6	0.445075
$489$	−1.07678e6	−0.203637
$490$	−355348.	−0.0668596
$491$	−5.55737e6	−1.04032	−0.520159	−	0.854070i	$-0.674127\pi$
$491$	−5.55737e6	−1.04032	−0.520159	+	0.854070i	$0.674127\pi$
$492$	−89376.0	−0.0166459
$493$	439560.	0.0814518
$494$	−960960.	−0.177169
$495$	0	0
$496$	5.80035e6	1.05864
$497$	−181692.	−0.0329947
$498$	893088.	0.161369
$499$	−3.49744e6	−0.628780	−0.314390	−	0.949294i	$-0.601800\pi$
$499$	−3.49744e6	−0.628780	−0.314390	+	0.949294i	$0.601800\pi$
$500$	−1.60373e6	−0.286884
$501$	1.90109e6	0.338383
$502$	3.37828e6	0.598325
$503$	−4.61280e6	−0.812915	−0.406457	−	0.913670i	$-0.633236\pi$
$503$	−4.61280e6	−0.812915	−0.406457	+	0.913670i	$0.633236\pi$
$504$	1.21716e6	0.213438
$505$	8.64705e6	1.50883
$506$	0	0
$507$	1.43278e6	0.247548
$508$	6.18934e6	1.06411
$509$	7.41609e6	1.26876	0.634382	−	0.773020i	$-0.281255\pi$
$509$	7.41609e6	1.26876	0.634382	+	0.773020i	$0.281255\pi$
$510$	−131424.	−0.0223743
$511$	1.19050e6	0.201687
$512$	5.89875e6	0.994455
$513$	3.56400e6	0.597922
$514$	1.28388e6	0.214346
$515$	−7.67336e6	−1.27487
$516$	3.47357e6	0.574317
$517$	0	0
$518$	13524.0	0.00221453
$519$	−1.05070e6	−0.171222
$520$	−3.23232e6	−0.524211
$521$	9.75970e6	1.57522	0.787612	−	0.616172i	$-0.211317\pi$
$521$	9.75970e6	1.57522	0.787612	+	0.616172i	$0.211317\pi$
$522$	1.22958e6	0.197506
$523$	−1.66084e6	−0.265506	−0.132753	−	0.991149i	$-0.542382\pi$
$523$	−1.66084e6	−0.265506	−0.132753	+	0.991149i	$0.542382\pi$
$524$	1.05202e6	0.167376
$525$	−691194.	−0.109446
$526$	2.20299e6	0.347175
$527$	−1.30862e6	−0.205251
$528$	0	0
$529$	−6.24625e6	−0.970465
$530$	−780552.	−0.120701
$531$	5.72769e6	0.881542
$532$	−1.81104e6	−0.277427
$533$	193648.	0.0295253
$534$	−410040.	−0.0622262
$535$	−7.18481e6	−1.08525
$536$	−7.69056e6	−1.15623
$537$	418680.	0.0626537
$538$	−4.30294e6	−0.640929
$539$	0	0
$540$	5.59440e6	0.825599
$541$	−6.97250e6	−1.02423	−0.512113	−	0.858918i	$-0.671137\pi$
$541$	−6.97250e6	−1.02423	−0.512113	+	0.858918i	$0.671137\pi$
$542$	2.16654e6	0.316787
$543$	471828.	0.0686727
$544$	−762496.	−0.110469
$545$	3.91682e6	0.564862
$546$	214032.	0.0307254
$547$	−3.08503e6	−0.440850	−0.220425	−	0.975404i	$-0.570744\pi$
$547$	−3.08503e6	−0.440850	−0.220425	+	0.975404i	$0.570744\pi$
$548$	8.13686e6	1.15746
$549$	4.03898e6	0.571928
$550$	0	0
$551$	−3.92040e6	−0.550112
$552$	−313920.	−0.0438502
$553$	107800.	0.0149901
$554$	4.44744e6	0.615653
$555$	61272.0	0.00844364
$556$	1.02861e7	1.41112
$557$	3.29052e6	0.449394	0.224697	−	0.974429i	$-0.427861\pi$
$557$	3.29052e6	0.449394	0.224697	+	0.974429i	$0.427861\pi$
$558$	−3.66059e6	−0.497697
$559$	−7.52606e6	−1.01868
$560$	−2.37866e6	−0.320525
$561$	0	0
$562$	306036.	0.0408725
$563$	−5.45754e6	−0.725648	−0.362824	−	0.931858i	$-0.618187\pi$
$563$	−5.45754e6	−0.725648	−0.362824	+	0.931858i	$0.618187\pi$
$564$	−1.96930e6	−0.260683
$565$	5.95892e6	0.785320
$566$	−1.43065e6	−0.187712
$567$	1.67095e6	0.218276
$568$	444960.	0.0578696
$569$	−7.28571e6	−0.943390	−0.471695	−	0.881762i	$-0.656358\pi$
$569$	−7.28571e6	−0.943390	−0.471695	+	0.881762i	$0.656358\pi$
$570$	1.17216e6	0.151112
$571$	−1.07129e7	−1.37504	−0.687519	−	0.726166i	$-0.741300\pi$
$571$	−1.07129e7	−1.37504	−0.687519	+	0.726166i	$0.741300\pi$
$572$	0	0
$573$	5.56325e6	0.707851
$574$	−52136.0	−0.00660477
$575$	−1.02504e6	−0.129291
$576$	2.21242e6	0.277850
$577$	4.22024e6	0.527713	0.263856	−	0.964562i	$-0.415006\pi$
$577$	4.22024e6	0.527713	0.263856	+	0.964562i	$0.415006\pi$
$578$	−2.79591e6	−0.348099
$579$	5.26484e6	0.652663
$580$	−6.15384e6	−0.759585
$581$	−3.64678e6	−0.448197
$582$	−1.82062e6	−0.222798
$583$	0	0
$584$	−2.91552e6	−0.353740
$585$	−5.57575e6	−0.673618
$586$	−694848.	−0.0835884
$587$	−6.24180e6	−0.747678	−0.373839	−	0.927494i	$-0.621959\pi$
$587$	−6.24180e6	−0.747678	−0.373839	+	0.927494i	$0.621959\pi$
$588$	403368.	0.0481125
$589$	1.16714e7	1.38623
$590$	4.09516e6	0.484329
$591$	−4.46761e6	−0.526147
$592$	90528.0	0.0106164
$593$	−493664.	−0.0576494	−0.0288247	−	0.999584i	$-0.509176\pi$
$593$	−493664.	−0.0576494	−0.0288247	+	0.999584i	$0.509176\pi$
$594$	0	0
$595$	536648.	0.0621437
$596$	−1.29564e7	−1.49407
$597$	−6.47586e6	−0.743638
$598$	317408.	0.0362965
$599$	−8.28890e6	−0.943908	−0.471954	−	0.881623i	$-0.656451\pi$
$599$	−8.28890e6	−0.943908	−0.471954	+	0.881623i	$0.656451\pi$
$600$	1.69272e6	0.191958
$601$	−80612.0	−0.00910361	−0.00455180	−	0.999990i	$-0.501449\pi$
$601$	−80612.0	−0.00910361	−0.00455180	+	0.999990i	$0.501449\pi$
$602$	2.02625e6	0.227877
$603$	−1.32662e7	−1.48578
$604$	−214144.	−0.0238844
$605$	0	0
$606$	1.40222e6	0.155109
$607$	−914168.	−0.100706	−0.0503529	−	0.998731i	$-0.516035\pi$
$607$	−914168.	−0.100706	−0.0503529	+	0.998731i	$0.516035\pi$
$608$	6.80064e6	0.746089
$609$	873180.	0.0954027
$610$	2.88778e6	0.314224
$611$	4.26681e6	0.462381
$612$	−857808.	−0.0925788
$613$	−9.97327e6	−1.07198	−0.535990	−	0.844224i	$-0.680061\pi$
$613$	−9.97327e6	−1.07198	−0.535990	+	0.844224i	$0.680061\pi$
$614$	−5.28086e6	−0.565306
$615$	−236208.	−0.0251830
$616$	0	0
$617$	−4.60636e6	−0.487130	−0.243565	−	0.969885i	$-0.578317\pi$
$617$	−4.60636e6	−0.487130	−0.243565	+	0.969885i	$0.578317\pi$
$618$	−1.24433e6	−0.131058
$619$	2.51711e6	0.264044	0.132022	−	0.991247i	$-0.457853\pi$
$619$	2.51711e6	0.264044	0.132022	+	0.991247i	$0.457853\pi$
$620$	1.83206e7	1.91408
$621$	−1.17720e6	−0.122496
$622$	−1.89556e6	−0.196454
$623$	1.67433e6	0.172831
$624$	1.43270e6	0.147297
$625$	−1.15853e7	−1.18633
$626$	−497372.	−0.0507277
$627$	0	0
$628$	4.52150e6	0.457492
$629$	−20424.0	−0.00205833
$630$	1.50116e6	0.150687
$631$	−2.02153e6	−0.202119	−0.101059	−	0.994880i	$-0.532223\pi$
$631$	−2.02153e6	−0.202119	−0.101059	+	0.994880i	$0.532223\pi$
$632$	−264000.	−0.0262912
$633$	4.37263e6	0.433744
$634$	5.21808e6	0.515570
$635$	1.63576e7	1.60984
$636$	886032.	0.0868574
$637$	−873964.	−0.0853385
$638$	0	0
$639$	767556.	0.0743632
$640$	1.37818e7	1.33001
$641$	1.55870e7	1.49837	0.749183	−	0.662363i	$-0.230446\pi$
$641$	1.55870e7	1.49837	0.749183	+	0.662363i	$0.230446\pi$
$642$	−1.16510e6	−0.111565
$643$	−5.88755e6	−0.561574	−0.280787	−	0.959770i	$-0.590595\pi$
$643$	−5.88755e6	−0.561574	−0.280787	+	0.959770i	$0.590595\pi$
$644$	598192.	0.0568363
$645$	9.18014e6	0.868861
$646$	−390720.	−0.0368370
$647$	5.58958e6	0.524950	0.262475	−	0.964939i	$-0.415461\pi$
$647$	5.58958e6	0.524950	0.262475	+	0.964939i	$0.415461\pi$
$648$	−4.09212e6	−0.382834
$649$	0	0
$650$	−1.71153e6	−0.158891
$651$	−2.59955e6	−0.240406
$652$	−5.02499e6	−0.462931
$653$	1.76227e7	1.61730	0.808648	−	0.588293i	$-0.200200\pi$
$653$	1.76227e7	1.61730	0.808648	+	0.588293i	$0.200200\pi$
$654$	635160.	0.0580683
$655$	2.78033e6	0.253217
$656$	−348992.	−0.0316633
$657$	−5.02927e6	−0.454561
$658$	−1.14876e6	−0.103434
$659$	9.75566e6	0.875071	0.437535	−	0.899201i	$-0.355851\pi$
$659$	9.75566e6	0.875071	0.437535	+	0.899201i	$0.355851\pi$
$660$	0	0
$661$	−9.79522e6	−0.871988	−0.435994	−	0.899950i	$-0.643603\pi$
$661$	−9.79522e6	−0.871988	−0.435994	+	0.899950i	$0.643603\pi$
$662$	304664.	0.0270194
$663$	−323232.	−0.0285582
$664$	8.93088e6	0.786093
$665$	−4.78632e6	−0.419708
$666$	−57132.0	−0.00499107
$667$	1.29492e6	0.112701
$668$	8.87174e6	0.769251
$669$	−230244.	−0.0198895
$670$	−9.48502e6	−0.816303
$671$	0	0
$672$	−1.51469e6	−0.129390
$673$	4.72727e6	0.402321	0.201160	−	0.979558i	$-0.435529\pi$
$673$	4.72727e6	0.402321	0.201160	+	0.979558i	$0.435529\pi$
$674$	−413116.	−0.0350286
$675$	6.34770e6	0.536237
$676$	6.68632e6	0.562756
$677$	1.93989e7	1.62669	0.813344	−	0.581783i	$-0.197645\pi$
$677$	1.93989e7	1.62669	0.813344	+	0.581783i	$0.197645\pi$
$678$	966312.	0.0807315
$679$	7.43418e6	0.618812
$680$	−1.31424e6	−0.108994
$681$	1.93961e6	0.160268
$682$	0	0
$683$	−6.22004e6	−0.510201	−0.255100	−	0.966915i	$-0.582109\pi$
$683$	−6.22004e6	−0.510201	−0.255100	+	0.966915i	$0.582109\pi$
$684$	7.65072e6	0.625262
$685$	2.15045e7	1.75107
$686$	235298.	0.0190901
$687$	−4.88214e6	−0.394656
$688$	1.35635e7	1.09244
$689$	−1.91974e6	−0.154061
$690$	−387168.	−0.0309583
$691$	6.04140e6	0.481330	0.240665	−	0.970608i	$-0.422635\pi$
$691$	6.04140e6	0.481330	0.240665	+	0.970608i	$0.422635\pi$
$692$	−4.90325e6	−0.389241
$693$	0	0
$694$	−4.03614e6	−0.318103
$695$	2.71846e7	2.13482
$696$	−2.13840e6	−0.167327
$697$	78736.0	0.00613891
$698$	1.16088e6	0.0901880
$699$	6.64808e6	0.514640
$700$	−3.22557e6	−0.248806
$701$	−3.97068e6	−0.305190	−0.152595	−	0.988289i	$-0.548763\pi$
$701$	−3.97068e6	−0.305190	−0.152595	+	0.988289i	$0.548763\pi$
$702$	−1.96560e6	−0.150540
$703$	182160.	0.0139016
$704$	0	0
$705$	−5.20457e6	−0.394377
$706$	1.14407e6	0.0863853
$707$	−5.72575e6	−0.430808
$708$	−4.64856e6	−0.348526
$709$	5.15939e6	0.385463	0.192732	−	0.981252i	$-0.438265\pi$
$709$	5.15939e6	0.385463	0.192732	+	0.981252i	$0.438265\pi$
$710$	548784.	0.0408560
$711$	−455400.	−0.0337846
$712$	−4.10040e6	−0.303128
$713$	−3.85511e6	−0.283997
$714$	87024.0	0.00638842
$715$	0	0
$716$	1.95384e6	0.142432
$717$	−7.88112e6	−0.572519
$718$	−9.13088e6	−0.661000
$719$	−1.26734e7	−0.914259	−0.457129	−	0.889400i	$-0.651122\pi$
$719$	−1.26734e7	−0.914259	−0.457129	+	0.889400i	$0.651122\pi$
$720$	1.00486e7	0.722395
$721$	5.08101e6	0.364009
$722$	−1.46740e6	−0.104762
$723$	−6.33641e6	−0.450814
$724$	2.20186e6	0.156115
$725$	−6.98247e6	−0.493360
$726$	0	0
$727$	1.32783e7	0.931762	0.465881	−	0.884847i	$-0.345737\pi$
$727$	1.32783e7	0.931762	0.465881	+	0.884847i	$0.345737\pi$
$728$	2.14032e6	0.149675
$729$	−3.12231e6	−0.217599
$730$	−3.59581e6	−0.249741
$731$	−3.06005e6	−0.211804
$732$	−3.27802e6	−0.226117
$733$	−3.84050e6	−0.264015	−0.132007	−	0.991249i	$-0.542142\pi$
$733$	−3.84050e6	−0.264015	−0.132007	+	0.991249i	$0.542142\pi$
$734$	1.84872e6	0.126657
$735$	1.06604e6	0.0727875
$736$	−2.24627e6	−0.152851
$737$	0	0
$738$	220248.	0.0148858
$739$	−1.19394e7	−0.804215	−0.402107	−	0.915592i	$-0.631722\pi$
$739$	−1.19394e7	−0.804215	−0.402107	+	0.915592i	$0.631722\pi$
$740$	285936.	0.0191951
$741$	2.88288e6	0.192877
$742$	516852.	0.0344633
$743$	−2.53631e7	−1.68551	−0.842754	−	0.538298i	$-0.819067\pi$
$743$	−2.53631e7	−1.68551	−0.842754	+	0.538298i	$0.819067\pi$
$744$	6.36624e6	0.421649
$745$	−3.42420e7	−2.26031
$746$	−9.84043e6	−0.647391
$747$	1.54058e7	1.01014
$748$	0	0
$749$	4.75751e6	0.309867
$750$	−687312.	−0.0446170
$751$	1.43903e7	0.931046	0.465523	−	0.885036i	$-0.345866\pi$
$751$	1.43903e7	0.931046	0.465523	+	0.885036i	$0.345866\pi$
$752$	−7.68963e6	−0.495862
$753$	−1.01349e7	−0.651373
$754$	2.16216e6	0.138503
$755$	−565952.	−0.0361337
$756$	−3.70440e6	−0.235729
$757$	−1.85431e7	−1.17609	−0.588047	−	0.808827i	$-0.700103\pi$
$757$	−1.85431e7	−1.17609	−0.588047	+	0.808827i	$0.700103\pi$
$758$	7.95080e6	0.502618
$759$	0	0
$760$	1.17216e7	0.736127
$761$	−6.43123e6	−0.402562	−0.201281	−	0.979534i	$-0.564510\pi$
$761$	−6.43123e6	−0.402562	−0.201281	+	0.979534i	$0.564510\pi$
$762$	2.65258e6	0.165493
$763$	−2.59357e6	−0.161282
$764$	2.59618e7	1.60917
$765$	−2.26706e6	−0.140059
$766$	−1.96569e6	−0.121044
$767$	1.00719e7	0.618190
$768$	182784.	0.0111824
$769$	−1.48249e7	−0.904014	−0.452007	−	0.892014i	$-0.649292\pi$
$769$	−1.48249e7	−0.904014	−0.452007	+	0.892014i	$0.649292\pi$
$770$	0	0
$771$	−3.85163e6	−0.233350
$772$	2.45693e7	1.48371
$773$	1.96325e7	1.18175	0.590876	−	0.806762i	$-0.298782\pi$
$773$	1.96325e7	1.18175	0.590876	+	0.806762i	$0.298782\pi$
$774$	−8.55986e6	−0.513588
$775$	2.07875e7	1.24322
$776$	−1.82062e7	−1.08534
$777$	−40572.0	−0.00241087
$778$	−1.48818e6	−0.0881468
$779$	−702240.	−0.0414612
$780$	4.52525e6	0.266321
$781$	0	0
$782$	129056.	0.00754677
$783$	−8.01900e6	−0.467429
$784$	1.57506e6	0.0915179
$785$	1.19497e7	0.692120
$786$	450864.	0.0260309
$787$	9.48639e6	0.545964	0.272982	−	0.962019i	$-0.411990\pi$
$787$	9.48639e6	0.545964	0.272982	+	0.962019i	$0.411990\pi$
$788$	−2.08489e7	−1.19610
$789$	−6.60898e6	−0.377956
$790$	−325600.	−0.0185617
$791$	−3.94577e6	−0.224229
$792$	0	0
$793$	7.10237e6	0.401070
$794$	1.14605e7	0.645136
$795$	2.34166e6	0.131403
$796$	−3.02207e7	−1.69052
$797$	3.32326e7	1.85318	0.926592	−	0.376068i	$-0.122724\pi$
$797$	3.32326e7	1.85318	0.926592	+	0.376068i	$0.122724\pi$
$798$	−776160.	−0.0431463
$799$	1.73486e6	0.0961383
$800$	1.21124e7	0.669119
$801$	−7.07319e6	−0.389524
$802$	8.53512e6	0.468569
$803$	0	0
$804$	1.07668e7	0.587416
$805$	1.58094e6	0.0859854
$806$	−6.43698e6	−0.349015
$807$	1.29088e7	0.697755
$808$	1.40222e7	0.755595
$809$	2.75792e7	1.48153	0.740764	−	0.671766i	$-0.234464\pi$
$809$	2.75792e7	1.48153	0.740764	+	0.671766i	$0.234464\pi$
$810$	−5.04695e6	−0.270281
$811$	7.76107e6	0.414352	0.207176	−	0.978304i	$-0.433573\pi$
$811$	7.76107e6	0.414352	0.207176	+	0.978304i	$0.433573\pi$
$812$	4.07484e6	0.216880
$813$	−6.49961e6	−0.344874
$814$	0	0
$815$	−1.32803e7	−0.700350
$816$	582528.	0.0306261
$817$	2.72923e7	1.43049
$818$	1.16354e7	0.607994
$819$	3.69205e6	0.192335
$820$	−1.10230e6	−0.0572488
$821$	1.60578e7	0.831434	0.415717	−	0.909494i	$-0.363531\pi$
$821$	1.60578e7	0.831434	0.415717	+	0.909494i	$0.363531\pi$
$822$	3.48722e6	0.180012
$823$	1.04666e6	0.0538651	0.0269326	−	0.999637i	$-0.491426\pi$
$823$	1.04666e6	0.0538651	0.0269326	+	0.999637i	$0.491426\pi$
$824$	−1.24433e7	−0.638435
$825$	0	0
$826$	−2.71166e6	−0.138288
$827$	−8.91799e6	−0.453423	−0.226711	−	0.973962i	$-0.572797\pi$
$827$	−8.91799e6	−0.453423	−0.226711	+	0.973962i	$0.572797\pi$
$828$	−2.52706e6	−0.128097
$829$	−2.53821e7	−1.28275	−0.641374	−	0.767229i	$-0.721635\pi$
$829$	−2.53821e7	−1.28275	−0.641374	+	0.767229i	$0.721635\pi$
$830$	1.10148e7	0.554983
$831$	−1.33423e7	−0.670238
$832$	3.89043e6	0.194845
$833$	−355348.	−0.0177436
$834$	4.40832e6	0.219461
$835$	2.34468e7	1.16377
$836$	0	0
$837$	2.38734e7	1.17788
$838$	−8.77646e6	−0.431727
$839$	−3.10636e7	−1.52351	−0.761757	−	0.647863i	$-0.775663\pi$
$839$	−3.10636e7	−1.52351	−0.761757	+	0.647863i	$0.775663\pi$
$840$	−2.61072e6	−0.127662
$841$	−1.16902e7	−0.569946
$842$	−2.96912e6	−0.144327
$843$	−918108.	−0.0444964
$844$	2.04056e7	0.986038
$845$	1.76710e7	0.851371
$846$	4.85291e6	0.233118
$847$	0	0
$848$	3.45974e6	0.165217
$849$	4.29194e6	0.204355
$850$	−695896.	−0.0330367
$851$	−60168.0	−0.00284801
$852$	−622944.	−0.0294002
$853$	−2.24337e7	−1.05567	−0.527835	−	0.849347i	$-0.676996\pi$
$853$	−2.24337e7	−1.05567	−0.527835	+	0.849347i	$0.676996\pi$
$854$	−1.91218e6	−0.0897187
$855$	2.02198e7	0.945934
$856$	−1.16510e7	−0.543476
$857$	−4.76449e6	−0.221597	−0.110799	−	0.993843i	$-0.535341\pi$
$857$	−4.76449e6	−0.221597	−0.110799	+	0.993843i	$0.535341\pi$
$858$	0	0
$859$	468030.	0.0216417	0.0108208	−	0.999941i	$-0.496556\pi$
$859$	468030.	0.0216417	0.0108208	+	0.999941i	$0.496556\pi$
$860$	4.28407e7	1.97520
$861$	156408.	0.00719037
$862$	412896.	0.0189266
$863$	−1.20487e7	−0.550697	−0.275349	−	0.961344i	$-0.588793\pi$
$863$	−1.20487e7	−0.550697	−0.275349	+	0.961344i	$0.588793\pi$
$864$	1.39104e7	0.633950
$865$	−1.29586e7	−0.588867
$866$	−1.13573e7	−0.514614
$867$	8.38772e6	0.378962
$868$	−1.21312e7	−0.546519
$869$	0	0
$870$	−2.63736e6	−0.118133
$871$	−2.33280e7	−1.04192
$872$	6.35160e6	0.282873
$873$	−3.14056e7	−1.39467
$874$	−1.15104e6	−0.0509697
$875$	2.80652e6	0.123922
$876$	4.08173e6	0.179715
$877$	−3.61718e6	−0.158807	−0.0794037	−	0.996843i	$-0.525302\pi$
$877$	−3.61718e6	−0.158807	−0.0794037	+	0.996843i	$0.525302\pi$
$878$	8.87332e6	0.388463
$879$	2.08454e6	0.0909995
$880$	0	0
$881$	−2.27025e7	−0.985448	−0.492724	−	0.870186i	$-0.663999\pi$
$881$	−2.27025e7	−0.985448	−0.492724	+	0.870186i	$0.663999\pi$
$882$	−994014.	−0.0430250
$883$	2.41926e7	1.04419	0.522097	−	0.852886i	$-0.325150\pi$
$883$	2.41926e7	1.04419	0.522097	+	0.852886i	$0.325150\pi$
$884$	−1.50842e6	−0.0649218
$885$	−1.22855e7	−0.527271
$886$	1.23466e7	0.528399
$887$	4.06125e7	1.73321	0.866604	−	0.498997i	$-0.166298\pi$
$887$	4.06125e7	1.73321	0.866604	+	0.498997i	$0.166298\pi$
$888$	99360.0	0.00422843
$889$	−1.08314e7	−0.459651
$890$	−5.05716e6	−0.214009
$891$	0	0
$892$	−1.07447e6	−0.0452150
$893$	−1.54730e7	−0.649302
$894$	−5.55276e6	−0.232362
$895$	5.16372e6	0.215479
$896$	−9.12576e6	−0.379751
$897$	−952224.	−0.0395146
$898$	−9.86210e6	−0.408111
$899$	−2.62607e7	−1.08370
$900$	1.36264e7	0.560757
$901$	−780552.	−0.0320324
$902$	0	0
$903$	−6.07874e6	−0.248082
$904$	9.66312e6	0.393275
$905$	5.81921e6	0.236180
$906$	−91776.0	−0.00371457
$907$	−1.98235e7	−0.800132	−0.400066	−	0.916486i	$-0.631013\pi$
$907$	−1.98235e7	−0.800132	−0.400066	+	0.916486i	$0.631013\pi$
$908$	9.05150e6	0.364339
$909$	2.41884e7	0.970950
$910$	2.63973e6	0.105671
$911$	−2.21209e7	−0.883094	−0.441547	−	0.897238i	$-0.645570\pi$
$911$	−2.21209e7	−0.883094	−0.441547	+	0.897238i	$0.645570\pi$
$912$	−5.19552e6	−0.206844
$913$	0	0
$914$	8.30060e6	0.328658
$915$	−8.66333e6	−0.342083
$916$	−2.27833e7	−0.897177
$917$	−1.84103e6	−0.0722998
$918$	−799200.	−0.0313003
$919$	−4.42949e7	−1.73008	−0.865038	−	0.501706i	$-0.832706\pi$
$919$	−4.42949e7	−1.73008	−0.865038	+	0.501706i	$0.832706\pi$
$920$	−3.87168e6	−0.150810
$921$	1.58426e7	0.615427
$922$	8.80690e6	0.341189
$923$	1.34971e6	0.0521479
$924$	0	0
$925$	324438.	0.0124674
$926$	1.36546e7	0.523300
$927$	−2.14647e7	−0.820398
$928$	−1.53014e7	−0.583260
$929$	1.13166e7	0.430207	0.215104	−	0.976591i	$-0.430991\pi$
$929$	1.13166e7	0.430207	0.215104	+	0.976591i	$0.430991\pi$
$930$	7.85170e6	0.297684
$931$	3.16932e6	0.119837
$932$	3.10244e7	1.16994
$933$	5.68667e6	0.213872
$934$	1.37649e7	0.516304
$935$	0	0
$936$	−9.04176e6	−0.337337
$937$	−3.37578e7	−1.25610	−0.628052	−	0.778172i	$-0.716147\pi$
$937$	−3.37578e7	−1.25610	−0.628052	+	0.778172i	$0.716147\pi$
$938$	6.28062e6	0.233075
$939$	1.49212e6	0.0552254
$940$	−2.42880e7	−0.896544
$941$	3.30036e7	1.21503	0.607516	−	0.794307i	$-0.292166\pi$
$941$	3.30036e7	1.21503	0.607516	+	0.794307i	$0.292166\pi$
$942$	1.93778e6	0.0711505
$943$	231952.	0.00849413
$944$	−1.81515e7	−0.662953
$945$	−9.79020e6	−0.356625
$946$	0	0
$947$	1.92599e7	0.697876	0.348938	−	0.937146i	$-0.386542\pi$
$947$	1.92599e7	0.697876	0.348938	+	0.937146i	$0.386542\pi$
$948$	369600.	0.0133571
$949$	−8.84374e6	−0.318765
$950$	6.20664e6	0.223125
$951$	−1.56542e7	−0.561281
$952$	870240.	0.0311205
$953$	−1.18503e7	−0.422665	−0.211332	−	0.977414i	$-0.567780\pi$
$953$	−1.18503e7	−0.422665	−0.211332	+	0.977414i	$0.567780\pi$
$954$	−2.18344e6	−0.0776729
$955$	6.86134e7	2.43445
$956$	−3.67786e7	−1.30152
$957$	0	0
$958$	−1.00486e7	−0.353746
$959$	−1.42395e7	−0.499975
$960$	−4.74547e6	−0.166189
$961$	4.95518e7	1.73082
$962$	−100464.	−0.00350004
$963$	−2.00980e7	−0.698374
$964$	−2.95699e7	−1.02484
$965$	6.49331e7	2.24465
$966$	256368.	0.00883936
$967$	1.44196e7	0.495892	0.247946	−	0.968774i	$-0.420245\pi$
$967$	1.44196e7	0.495892	0.247946	+	0.968774i	$0.420245\pi$
$968$	0	0
$969$	1.17216e6	0.0401031
$970$	−2.24543e7	−0.766248
$971$	−1.37494e7	−0.467990	−0.233995	−	0.972238i	$-0.575180\pi$
$971$	−1.37494e7	−0.467990	−0.233995	+	0.972238i	$0.575180\pi$
$972$	2.40998e7	0.818177
$973$	−1.80006e7	−0.609545
$974$	−9.03202e6	−0.305062
$975$	5.13458e6	0.172979
$976$	−1.27999e7	−0.430112
$977$	−9.18802e6	−0.307954	−0.153977	−	0.988074i	$-0.549208\pi$
$977$	−9.18802e6	−0.307954	−0.153977	+	0.988074i	$0.549208\pi$
$978$	−2.15357e6	−0.0719965
$979$	0	0
$980$	4.97487e6	0.165469
$981$	1.09565e7	0.363496
$982$	−1.11147e7	−0.367808
$983$	−3.43732e7	−1.13458	−0.567292	−	0.823517i	$-0.692009\pi$
$983$	−3.43732e7	−1.13458	−0.567292	+	0.823517i	$0.692009\pi$
$984$	−383040.	−0.0126112
$985$	−5.51005e7	−1.80953
$986$	879120.	0.0287976
$987$	3.44627e6	0.112605
$988$	1.34534e7	0.438471
$989$	−9.01474e6	−0.293064
$990$	0	0
$991$	−4.32179e7	−1.39791	−0.698956	−	0.715164i	$-0.746352\pi$
$991$	−4.32179e7	−1.39791	−0.698956	+	0.715164i	$0.746352\pi$
$992$	4.55540e7	1.46976
$993$	−913992.	−0.0294150
$994$	−363384.	−0.0116654
$995$	−7.98689e7	−2.55753
$996$	−1.25032e7	−0.399369
$997$	−2.54793e7	−0.811801	−0.405901	−	0.913917i	$-0.633042\pi$
$997$	−2.54793e7	−0.811801	−0.405901	+	0.913917i	$0.633042\pi$
$998$	−6.99488e6	−0.222307
$999$	372600.	0.0118122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.6.a.a.1.1		1
11.10	odd	2		77.6.a.a.1.1	✓	1
33.32	even	2		693.6.a.a.1.1		1
77.76	even	2		539.6.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.6.a.a.1.1	✓	1	11.10	odd	2
539.6.a.d.1.1		1	77.76	even	2
693.6.a.a.1.1		1	33.32	even	2
847.6.a.a.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	847.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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