LMFDB - Embedded newform 99.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,6,Mod(1,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, 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("99.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	99.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:	$15.8779981615$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -31.0000 q^{4} +92.0000 q^{5} -26.0000 q^{7} +63.0000 q^{8} +O(q^{10})$

\(q-1.00000 q^{2} -31.0000 q^{4} +92.0000 q^{5} -26.0000 q^{7} +63.0000 q^{8} -92.0000 q^{10} -121.000 q^{11} -692.000 q^{13} +26.0000 q^{14} +929.000 q^{16} +1442.00 q^{17} +2160.00 q^{19} -2852.00 q^{20} +121.000 q^{22} +1582.00 q^{23} +5339.00 q^{25} +692.000 q^{26} +806.000 q^{28} +5526.00 q^{29} +4792.00 q^{31} -2945.00 q^{32} -1442.00 q^{34} -2392.00 q^{35} -10194.0 q^{37} -2160.00 q^{38} +5796.00 q^{40} +10622.0 q^{41} +8580.00 q^{43} +3751.00 q^{44} -1582.00 q^{46} +2362.00 q^{47} -16131.0 q^{49} -5339.00 q^{50} +21452.0 q^{52} +30804.0 q^{53} -11132.0 q^{55} -1638.00 q^{56} -5526.00 q^{58} -6416.00 q^{59} +42096.0 q^{61} -4792.00 q^{62} -26783.0 q^{64} -63664.0 q^{65} -28444.0 q^{67} -44702.0 q^{68} +2392.00 q^{70} -45690.0 q^{71} -18374.0 q^{73} +10194.0 q^{74} -66960.0 q^{76} +3146.00 q^{77} -105214. q^{79} +85468.0 q^{80} -10622.0 q^{82} -62292.0 q^{83} +132664. q^{85} -8580.00 q^{86} -7623.00 q^{88} +72246.0 q^{89} +17992.0 q^{91} -49042.0 q^{92} -2362.00 q^{94} +198720. q^{95} +79262.0 q^{97} +16131.0 q^{98} +O(q^{100})\)

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 $

$2$	−1.00000	−0.176777	−0.0883883	−	0.996086i	$-0.528172\pi$
$2$	−1.00000	−0.176777	−0.0883883	+	0.996086i	$0.528172\pi$
$3$	0	0
$3$	0	0
$4$	−31.0000	−0.968750
$5$	92.0000	1.64575	0.822873	−	0.568225i	$-0.192370\pi$
$5$	92.0000	1.64575	0.822873	+	0.568225i	$0.192370\pi$
$6$	0	0
$7$	−26.0000	−0.200553	−0.100276	−	0.994960i	$-0.531973\pi$
$7$	−26.0000	−0.200553	−0.100276	+	0.994960i	$0.531973\pi$
$8$	63.0000	0.348029
$9$	0	0
$10$	−92.0000	−0.290930
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	0	0
$13$	−692.000	−1.13566	−0.567829	−	0.823146i	$-0.692217\pi$
$13$	−692.000	−1.13566	−0.567829	+	0.823146i	$0.692217\pi$
$14$	26.0000	0.0354530
$15$	0	0
$16$	929.000	0.907227
$17$	1442.00	1.21016	0.605080	−	0.796165i	$-0.293141\pi$
$17$	1442.00	1.21016	0.605080	+	0.796165i	$0.293141\pi$
$18$	0	0
$19$	2160.00	1.37268	0.686341	−	0.727280i	$-0.259216\pi$
$19$	2160.00	1.37268	0.686341	+	0.727280i	$0.259216\pi$
$20$	−2852.00	−1.59432
$21$	0	0
$22$	121.000	0.0533002
$23$	1582.00	0.623572	0.311786	−	0.950152i	$-0.399073\pi$
$23$	1582.00	0.623572	0.311786	+	0.950152i	$0.399073\pi$
$24$	0	0
$25$	5339.00	1.70848
$26$	692.000	0.200758
$27$	0	0
$28$	806.000	0.194285
$29$	5526.00	1.22016	0.610079	−	0.792341i	$-0.291138\pi$
$29$	5526.00	1.22016	0.610079	+	0.792341i	$0.291138\pi$
$30$	0	0
$31$	4792.00	0.895597	0.447798	−	0.894135i	$-0.352208\pi$
$31$	4792.00	0.895597	0.447798	+	0.894135i	$0.352208\pi$
$32$	−2945.00	−0.508406
$33$	0	0
$34$	−1442.00	−0.213928
$35$	−2392.00	−0.330059
$36$	0	0
$37$	−10194.0	−1.22417	−0.612083	−	0.790794i	$-0.709668\pi$
$37$	−10194.0	−1.22417	−0.612083	+	0.790794i	$0.709668\pi$
$38$	−2160.00	−0.242658
$39$	0	0
$40$	5796.00	0.572768
$41$	10622.0	0.986840	0.493420	−	0.869791i	$-0.335747\pi$
$41$	10622.0	0.986840	0.493420	+	0.869791i	$0.335747\pi$
$42$	0	0
$43$	8580.00	0.707646	0.353823	−	0.935312i	$-0.384881\pi$
$43$	8580.00	0.707646	0.353823	+	0.935312i	$0.384881\pi$
$44$	3751.00	0.292089
$45$	0	0
$46$	−1582.00	−0.110233
$47$	2362.00	0.155968	0.0779840	−	0.996955i	$-0.475152\pi$
$47$	2362.00	0.155968	0.0779840	+	0.996955i	$0.475152\pi$
$48$	0	0
$49$	−16131.0	−0.959779
$50$	−5339.00	−0.302019
$51$	0	0
$52$	21452.0	1.10017
$53$	30804.0	1.50632	0.753160	−	0.657837i	$-0.228528\pi$
$53$	30804.0	1.50632	0.753160	+	0.657837i	$0.228528\pi$
$54$	0	0
$55$	−11132.0	−0.496211
$56$	−1638.00	−0.0697981
$57$	0	0
$58$	−5526.00	−0.215695
$59$	−6416.00	−0.239957	−0.119979	−	0.992776i	$-0.538283\pi$
$59$	−6416.00	−0.239957	−0.119979	+	0.992776i	$0.538283\pi$
$60$	0	0
$61$	42096.0	1.44849	0.724246	−	0.689541i	$-0.242188\pi$
$61$	42096.0	1.44849	0.724246	+	0.689541i	$0.242188\pi$
$62$	−4792.00	−0.158321
$63$	0	0
$64$	−26783.0	−0.817352
$65$	−63664.0	−1.86901
$66$	0	0
$67$	−28444.0	−0.774112	−0.387056	−	0.922056i	$-0.626508\pi$
$67$	−28444.0	−0.774112	−0.387056	+	0.922056i	$0.626508\pi$
$68$	−44702.0	−1.17234
$69$	0	0
$70$	2392.00	0.0583467
$71$	−45690.0	−1.07566	−0.537830	−	0.843053i	$-0.680756\pi$
$71$	−45690.0	−1.07566	−0.537830	+	0.843053i	$0.680756\pi$
$72$	0	0
$73$	−18374.0	−0.403549	−0.201775	−	0.979432i	$-0.564671\pi$
$73$	−18374.0	−0.403549	−0.201775	+	0.979432i	$0.564671\pi$
$74$	10194.0	0.216404
$75$	0	0
$76$	−66960.0	−1.32979
$77$	3146.00	0.0604689
$78$	0	0
$79$	−105214.	−1.89673	−0.948366	−	0.317179i	$-0.897264\pi$
$79$	−105214.	−1.89673	−0.948366	+	0.317179i	$0.897264\pi$
$80$	85468.0	1.49306
$81$	0	0
$82$	−10622.0	−0.174450
$83$	−62292.0	−0.992515	−0.496257	−	0.868175i	$-0.665293\pi$
$83$	−62292.0	−0.992515	−0.496257	+	0.868175i	$0.665293\pi$
$84$	0	0
$85$	132664.	1.99162
$86$	−8580.00	−0.125095
$87$	0	0
$88$	−7623.00	−0.104935
$89$	72246.0	0.966805	0.483402	−	0.875398i	$-0.339401\pi$
$89$	72246.0	0.966805	0.483402	+	0.875398i	$0.339401\pi$
$90$	0	0
$91$	17992.0	0.227759
$92$	−49042.0	−0.604086
$93$	0	0
$94$	−2362.00	−0.0275715
$95$	198720.	2.25908
$96$	0	0
$97$	79262.0	0.855334	0.427667	−	0.903936i	$-0.359336\pi$
$97$	79262.0	0.855334	0.427667	+	0.903936i	$0.359336\pi$
$98$	16131.0	0.169667
$99$	0	0
$100$	−165509.	−1.65509
$101$	24958.0	0.243448	0.121724	−	0.992564i	$-0.461158\pi$
$101$	24958.0	0.243448	0.121724	+	0.992564i	$0.461158\pi$
$102$	0	0
$103$	−56812.0	−0.527651	−0.263826	−	0.964570i	$-0.584984\pi$
$103$	−56812.0	−0.527651	−0.263826	+	0.964570i	$0.584984\pi$
$104$	−43596.0	−0.395242
$105$	0	0
$106$	−30804.0	−0.266282
$107$	12492.0	0.105481	0.0527403	−	0.998608i	$-0.483204\pi$
$107$	12492.0	0.105481	0.0527403	+	0.998608i	$0.483204\pi$
$108$	0	0
$109$	198748.	1.60227	0.801137	−	0.598482i	$-0.204229\pi$
$109$	198748.	1.60227	0.801137	+	0.598482i	$0.204229\pi$
$110$	11132.0	0.0877186
$111$	0	0
$112$	−24154.0	−0.181947
$113$	−166554.	−1.22704	−0.613520	−	0.789679i	$-0.710247\pi$
$113$	−166554.	−1.22704	−0.613520	+	0.789679i	$0.710247\pi$
$114$	0	0
$115$	145544.	1.02624
$116$	−171306.	−1.18203
$117$	0	0
$118$	6416.00	0.0424189
$119$	−37492.0	−0.242701
$120$	0	0
$121$	14641.0	0.0909091
$122$	−42096.0	−0.256060
$123$	0	0
$124$	−148552.	−0.867609
$125$	203688.	1.16598
$126$	0	0
$127$	304226.	1.67374	0.836868	−	0.547405i	$-0.184384\pi$
$127$	304226.	1.67374	0.836868	+	0.547405i	$0.184384\pi$
$128$	121023.	0.652894
$129$	0	0
$130$	63664.0	0.330397
$131$	−274428.	−1.39717	−0.698586	−	0.715526i	$-0.746187\pi$
$131$	−274428.	−1.39717	−0.698586	+	0.715526i	$0.746187\pi$
$132$	0	0
$133$	−56160.0	−0.275295
$134$	28444.0	0.136845
$135$	0	0
$136$	90846.0	0.421171
$137$	245458.	1.11732	0.558658	−	0.829398i	$-0.311317\pi$
$137$	245458.	1.11732	0.558658	+	0.829398i	$0.311317\pi$
$138$	0	0
$139$	−59888.0	−0.262907	−0.131454	−	0.991322i	$-0.541964\pi$
$139$	−59888.0	−0.262907	−0.131454	+	0.991322i	$0.541964\pi$
$140$	74152.0	0.319744
$141$	0	0
$142$	45690.0	0.190152
$143$	83732.0	0.342414
$144$	0	0
$145$	508392.	2.00807
$146$	18374.0	0.0713381
$147$	0	0
$148$	316014.	1.18591
$149$	−72038.0	−0.265825	−0.132913	−	0.991128i	$-0.542433\pi$
$149$	−72038.0	−0.265825	−0.132913	+	0.991128i	$0.542433\pi$
$150$	0	0
$151$	−323110.	−1.15321	−0.576605	−	0.817023i	$-0.695623\pi$
$151$	−323110.	−1.15321	−0.576605	+	0.817023i	$0.695623\pi$
$152$	136080.	0.477733
$153$	0	0
$154$	−3146.00	−0.0106895
$155$	440864.	1.47393
$156$	0	0
$157$	−318766.	−1.03210	−0.516051	−	0.856558i	$-0.672599\pi$
$157$	−318766.	−1.03210	−0.516051	+	0.856558i	$0.672599\pi$
$158$	105214.	0.335298
$159$	0	0
$160$	−270940.	−0.836707
$161$	−41132.0	−0.125059
$162$	0	0
$163$	−431996.	−1.27353	−0.636767	−	0.771056i	$-0.719729\pi$
$163$	−431996.	−1.27353	−0.636767	+	0.771056i	$0.719729\pi$
$164$	−329282.	−0.956001
$165$	0	0
$166$	62292.0	0.175454
$167$	251580.	0.698047	0.349024	−	0.937114i	$-0.386513\pi$
$167$	251580.	0.698047	0.349024	+	0.937114i	$0.386513\pi$
$168$	0	0
$169$	107571.	0.289720
$170$	−132664.	−0.352071
$171$	0	0
$172$	−265980.	−0.685532
$173$	−476634.	−1.21079	−0.605396	−	0.795924i	$-0.706985\pi$
$173$	−476634.	−1.21079	−0.605396	+	0.795924i	$0.706985\pi$
$174$	0	0
$175$	−138814.	−0.342640
$176$	−112409.	−0.273539
$177$	0	0
$178$	−72246.0	−0.170909
$179$	−90192.0	−0.210395	−0.105198	−	0.994451i	$-0.533547\pi$
$179$	−90192.0	−0.210395	−0.105198	+	0.994451i	$0.533547\pi$
$180$	0	0
$181$	248002.	0.562676	0.281338	−	0.959609i	$-0.409222\pi$
$181$	248002.	0.562676	0.281338	+	0.959609i	$0.409222\pi$
$182$	−17992.0	−0.0402625
$183$	0	0
$184$	99666.0	0.217021
$185$	−937848.	−2.01467
$186$	0	0
$187$	−174482.	−0.364877
$188$	−73222.0	−0.151094
$189$	0	0
$190$	−198720.	−0.399354
$191$	156802.	0.311006	0.155503	−	0.987835i	$-0.450300\pi$
$191$	156802.	0.311006	0.155503	+	0.987835i	$0.450300\pi$
$192$	0	0
$193$	−431234.	−0.833335	−0.416668	−	0.909059i	$-0.636802\pi$
$193$	−431234.	−0.833335	−0.416668	+	0.909059i	$0.636802\pi$
$194$	−79262.0	−0.151203
$195$	0	0
$196$	500061.	0.929786
$197$	864974.	1.58795	0.793976	−	0.607949i	$-0.208007\pi$
$197$	864974.	1.58795	0.793976	+	0.607949i	$0.208007\pi$
$198$	0	0
$199$	−480060.	−0.859336	−0.429668	−	0.902987i	$-0.641369\pi$
$199$	−480060.	−0.859336	−0.429668	+	0.902987i	$0.641369\pi$
$200$	336357.	0.594601
$201$	0	0
$202$	−24958.0	−0.0430359
$203$	−143676.	−0.244706
$204$	0	0
$205$	977224.	1.62409
$206$	56812.0	0.0932765
$207$	0	0
$208$	−642868.	−1.03030
$209$	−261360.	−0.413879
$210$	0	0
$211$	525900.	0.813199	0.406600	−	0.913606i	$-0.366714\pi$
$211$	525900.	0.813199	0.406600	+	0.913606i	$0.366714\pi$
$212$	−954924.	−1.45925
$213$	0	0
$214$	−12492.0	−0.0186465
$215$	789360.	1.16461
$216$	0	0
$217$	−124592.	−0.179614
$218$	−198748.	−0.283245
$219$	0	0
$220$	345092.	0.480705
$221$	−997864.	−1.37433
$222$	0	0
$223$	−245264.	−0.330272	−0.165136	−	0.986271i	$-0.552806\pi$
$223$	−245264.	−0.330272	−0.165136	+	0.986271i	$0.552806\pi$
$224$	76570.0	0.101962
$225$	0	0
$226$	166554.	0.216912
$227$	799308.	1.02955	0.514777	−	0.857324i	$-0.327875\pi$
$227$	799308.	1.02955	0.514777	+	0.857324i	$0.327875\pi$
$228$	0	0
$229$	−1.53989e6	−1.94045	−0.970224	−	0.242208i	$-0.922128\pi$
$229$	−1.53989e6	−1.94045	−0.970224	+	0.242208i	$0.922128\pi$
$230$	−145544.	−0.181416
$231$	0	0
$232$	348138.	0.424650
$233$	721830.	0.871054	0.435527	−	0.900176i	$-0.356562\pi$
$233$	721830.	0.871054	0.435527	+	0.900176i	$0.356562\pi$
$234$	0	0
$235$	217304.	0.256684
$236$	198896.	0.232459
$237$	0	0
$238$	37492.0	0.0429038
$239$	638436.	0.722974	0.361487	−	0.932377i	$-0.382269\pi$
$239$	638436.	0.722974	0.361487	+	0.932377i	$0.382269\pi$
$240$	0	0
$241$	220990.	0.245092	0.122546	−	0.992463i	$-0.460894\pi$
$241$	220990.	0.245092	0.122546	+	0.992463i	$0.460894\pi$
$242$	−14641.0	−0.0160706
$243$	0	0
$244$	−1.30498e6	−1.40323
$245$	−1.48405e6	−1.57955
$246$	0	0
$247$	−1.49472e6	−1.55890
$248$	301896.	0.311694
$249$	0	0
$250$	−203688.	−0.206118
$251$	−627304.	−0.628483	−0.314242	−	0.949343i	$-0.601750\pi$
$251$	−627304.	−0.628483	−0.314242	+	0.949343i	$0.601750\pi$
$252$	0	0
$253$	−191422.	−0.188014
$254$	−304226.	−0.295878
$255$	0	0
$256$	736033.	0.701936
$257$	468014.	0.442004	0.221002	−	0.975273i	$-0.429067\pi$
$257$	468014.	0.442004	0.221002	+	0.975273i	$0.429067\pi$
$258$	0	0
$259$	265044.	0.245510
$260$	1.97358e6	1.81060
$261$	0	0
$262$	274428.	0.246988
$263$	−1.54510e6	−1.37743	−0.688713	−	0.725034i	$-0.741824\pi$
$263$	−1.54510e6	−1.37743	−0.688713	+	0.725034i	$0.741824\pi$
$264$	0	0
$265$	2.83397e6	2.47902
$266$	56160.0	0.0486657
$267$	0	0
$268$	881764.	0.749921
$269$	1.07457e6	0.905430	0.452715	−	0.891655i	$-0.350456\pi$
$269$	1.07457e6	0.905430	0.452715	+	0.891655i	$0.350456\pi$
$270$	0	0
$271$	1.58723e6	1.31285	0.656427	−	0.754389i	$-0.272067\pi$
$271$	1.58723e6	1.31285	0.656427	+	0.754389i	$0.272067\pi$
$272$	1.33962e6	1.09789
$273$	0	0
$274$	−245458.	−0.197515
$275$	−646019.	−0.515126
$276$	0	0
$277$	692704.	0.542436	0.271218	−	0.962518i	$-0.412574\pi$
$277$	692704.	0.542436	0.271218	+	0.962518i	$0.412574\pi$
$278$	59888.0	0.0464759
$279$	0	0
$280$	−150696.	−0.114870
$281$	567018.	0.428382	0.214191	−	0.976792i	$-0.431289\pi$
$281$	567018.	0.428382	0.214191	+	0.976792i	$0.431289\pi$
$282$	0	0
$283$	714916.	0.530626	0.265313	−	0.964162i	$-0.414525\pi$
$283$	714916.	0.530626	0.265313	+	0.964162i	$0.414525\pi$
$284$	1.41639e6	1.04205
$285$	0	0
$286$	−83732.0	−0.0605308
$287$	−276172.	−0.197913
$288$	0	0
$289$	659507.	0.464488
$290$	−508392.	−0.354980
$291$	0	0
$292$	569594.	0.390938
$293$	−2.14409e6	−1.45907	−0.729533	−	0.683946i	$-0.760262\pi$
$293$	−2.14409e6	−1.45907	−0.729533	+	0.683946i	$0.760262\pi$
$294$	0	0
$295$	−590272.	−0.394909
$296$	−642222.	−0.426045
$297$	0	0
$298$	72038.0	0.0469917
$299$	−1.09474e6	−0.708165
$300$	0	0
$301$	−223080.	−0.141920
$302$	323110.	0.203860
$303$	0	0
$304$	2.00664e6	1.24533
$305$	3.87283e6	2.38385
$306$	0	0
$307$	−588808.	−0.356556	−0.178278	−	0.983980i	$-0.557053\pi$
$307$	−588808.	−0.356556	−0.178278	+	0.983980i	$0.557053\pi$
$308$	−97526.0	−0.0585792
$309$	0	0
$310$	−440864.	−0.260556
$311$	−2.51827e6	−1.47639	−0.738194	−	0.674588i	$-0.764321\pi$
$311$	−2.51827e6	−1.47639	−0.738194	+	0.674588i	$0.764321\pi$
$312$	0	0
$313$	−2.23562e6	−1.28985	−0.644923	−	0.764248i	$-0.723110\pi$
$313$	−2.23562e6	−1.28985	−0.644923	+	0.764248i	$0.723110\pi$
$314$	318766.	0.182452
$315$	0	0
$316$	3.26163e6	1.83746
$317$	−1.06079e6	−0.592901	−0.296450	−	0.955048i	$-0.595803\pi$
$317$	−1.06079e6	−0.592901	−0.296450	+	0.955048i	$0.595803\pi$
$318$	0	0
$319$	−668646.	−0.367891
$320$	−2.46404e6	−1.34515
$321$	0	0
$322$	41132.0	0.0221075
$323$	3.11472e6	1.66116
$324$	0	0
$325$	−3.69459e6	−1.94025
$326$	431996.	0.225131
$327$	0	0
$328$	669186.	0.343449
$329$	−61412.0	−0.0312798
$330$	0	0
$331$	−2.34566e6	−1.17678	−0.588390	−	0.808577i	$-0.700238\pi$
$331$	−2.34566e6	−1.17678	−0.588390	+	0.808577i	$0.700238\pi$
$332$	1.93105e6	0.961499
$333$	0	0
$334$	−251580.	−0.123399
$335$	−2.61685e6	−1.27399
$336$	0	0
$337$	839978.	0.402896	0.201448	−	0.979499i	$-0.435435\pi$
$337$	839978.	0.402896	0.201448	+	0.979499i	$0.435435\pi$
$338$	−107571.	−0.0512157
$339$	0	0
$340$	−4.11258e6	−1.92938
$341$	−579832.	−0.270033
$342$	0	0
$343$	856388.	0.393039
$344$	540540.	0.246281
$345$	0	0
$346$	476634.	0.214040
$347$	2.02560e6	0.903086	0.451543	−	0.892249i	$-0.350874\pi$
$347$	2.02560e6	0.903086	0.451543	+	0.892249i	$0.350874\pi$
$348$	0	0
$349$	−378924.	−0.166528	−0.0832642	−	0.996528i	$-0.526535\pi$
$349$	−378924.	−0.166528	−0.0832642	+	0.996528i	$0.526535\pi$
$350$	138814.	0.0605708
$351$	0	0
$352$	356345.	0.153290
$353$	1.98730e6	0.848842	0.424421	−	0.905465i	$-0.360478\pi$
$353$	1.98730e6	0.848842	0.424421	+	0.905465i	$0.360478\pi$
$354$	0	0
$355$	−4.20348e6	−1.77026
$356$	−2.23963e6	−0.936592
$357$	0	0
$358$	90192.0	0.0371929
$359$	3.43975e6	1.40861	0.704305	−	0.709898i	$-0.251259\pi$
$359$	3.43975e6	1.40861	0.704305	+	0.709898i	$0.251259\pi$
$360$	0	0
$361$	2.18950e6	0.884254
$362$	−248002.	−0.0994681
$363$	0	0
$364$	−557752.	−0.220642
$365$	−1.69041e6	−0.664140
$366$	0	0
$367$	−1.79679e6	−0.696358	−0.348179	−	0.937428i	$-0.613200\pi$
$367$	−1.79679e6	−0.696358	−0.348179	+	0.937428i	$0.613200\pi$
$368$	1.46968e6	0.565721
$369$	0	0
$370$	937848.	0.356146
$371$	−800904.	−0.302096
$372$	0	0
$373$	−1.43541e6	−0.534201	−0.267100	−	0.963669i	$-0.586066\pi$
$373$	−1.43541e6	−0.534201	−0.267100	+	0.963669i	$0.586066\pi$
$374$	174482.	0.0645018
$375$	0	0
$376$	148806.	0.0542814
$377$	−3.82399e6	−1.38568
$378$	0	0
$379$	2.66235e6	0.952065	0.476033	−	0.879428i	$-0.342074\pi$
$379$	2.66235e6	0.952065	0.476033	+	0.879428i	$0.342074\pi$
$380$	−6.16032e6	−2.18849
$381$	0	0
$382$	−156802.	−0.0549785
$383$	−2.04091e6	−0.710932	−0.355466	−	0.934689i	$-0.615678\pi$
$383$	−2.04091e6	−0.710932	−0.355466	+	0.934689i	$0.615678\pi$
$384$	0	0
$385$	289432.	0.0995164
$386$	431234.	0.147314
$387$	0	0
$388$	−2.45712e6	−0.828605
$389$	4.29947e6	1.44059	0.720296	−	0.693667i	$-0.244006\pi$
$389$	4.29947e6	1.44059	0.720296	+	0.693667i	$0.244006\pi$
$390$	0	0
$391$	2.28124e6	0.754623
$392$	−1.01625e6	−0.334031
$393$	0	0
$394$	−864974.	−0.280713
$395$	−9.67969e6	−3.12154
$396$	0	0
$397$	728818.	0.232083	0.116041	−	0.993244i	$-0.462979\pi$
$397$	728818.	0.232083	0.116041	+	0.993244i	$0.462979\pi$
$398$	480060.	0.151911
$399$	0	0
$400$	4.95993e6	1.54998
$401$	5.92515e6	1.84009	0.920044	−	0.391814i	$-0.128152\pi$
$401$	5.92515e6	1.84009	0.920044	+	0.391814i	$0.128152\pi$
$402$	0	0
$403$	−3.31606e6	−1.01709
$404$	−773698.	−0.235840
$405$	0	0
$406$	143676.	0.0432583
$407$	1.23347e6	0.369100
$408$	0	0
$409$	1.38212e6	0.408542	0.204271	−	0.978914i	$-0.434518\pi$
$409$	1.38212e6	0.408542	0.204271	+	0.978914i	$0.434518\pi$
$410$	−977224.	−0.287101
$411$	0	0
$412$	1.76117e6	0.511162
$413$	166816.	0.0481241
$414$	0	0
$415$	−5.73086e6	−1.63343
$416$	2.03794e6	0.577375
$417$	0	0
$418$	261360.	0.0731642
$419$	−5.47794e6	−1.52434	−0.762170	−	0.647377i	$-0.775866\pi$
$419$	−5.47794e6	−1.52434	−0.762170	+	0.647377i	$0.775866\pi$
$420$	0	0
$421$	1.02873e6	0.282877	0.141439	−	0.989947i	$-0.454827\pi$
$421$	1.02873e6	0.282877	0.141439	+	0.989947i	$0.454827\pi$
$422$	−525900.	−0.143755
$423$	0	0
$424$	1.94065e6	0.524243
$425$	7.69884e6	2.06753
$426$	0	0
$427$	−1.09450e6	−0.290499
$428$	−387252.	−0.102184
$429$	0	0
$430$	−789360.	−0.205875
$431$	5.14310e6	1.33362	0.666810	−	0.745228i	$-0.267659\pi$
$431$	5.14310e6	1.33362	0.666810	+	0.745228i	$0.267659\pi$
$432$	0	0
$433$	412954.	0.105848	0.0529239	−	0.998599i	$-0.483146\pi$
$433$	412954.	0.105848	0.0529239	+	0.998599i	$0.483146\pi$
$434$	124592.	0.0317516
$435$	0	0
$436$	−6.16119e6	−1.55220
$437$	3.41712e6	0.855966
$438$	0	0
$439$	5.96365e6	1.47690	0.738450	−	0.674309i	$-0.235558\pi$
$439$	5.96365e6	1.47690	0.738450	+	0.674309i	$0.235558\pi$
$440$	−701316.	−0.172696
$441$	0	0
$442$	997864.	0.242949
$443$	−2.18433e6	−0.528821	−0.264410	−	0.964410i	$-0.585177\pi$
$443$	−2.18433e6	−0.528821	−0.264410	+	0.964410i	$0.585177\pi$
$444$	0	0
$445$	6.64663e6	1.59112
$446$	245264.	0.0583844
$447$	0	0
$448$	696358.	0.163922
$449$	7858.00	0.00183948	0.000919742	−	1.00000i	$-0.499707\pi$
$449$	7858.00	0.00183948	0.000919742		1.00000i	$0.499707\pi$
$450$	0	0
$451$	−1.28526e6	−0.297543
$452$	5.16317e6	1.18870
$453$	0	0
$454$	−799308.	−0.182001
$455$	1.65526e6	0.374834
$456$	0	0
$457$	−899922.	−0.201565	−0.100782	−	0.994908i	$-0.532135\pi$
$457$	−899922.	−0.201565	−0.100782	+	0.994908i	$0.532135\pi$
$458$	1.53989e6	0.343026
$459$	0	0
$460$	−4.51186e6	−0.994172
$461$	−1.13619e6	−0.249000	−0.124500	−	0.992220i	$-0.539733\pi$
$461$	−1.13619e6	−0.249000	−0.124500	+	0.992220i	$0.539733\pi$
$462$	0	0
$463$	−7.38964e6	−1.60203	−0.801016	−	0.598643i	$-0.795707\pi$
$463$	−7.38964e6	−1.60203	−0.801016	+	0.598643i	$0.795707\pi$
$464$	5.13365e6	1.10696
$465$	0	0
$466$	−721830.	−0.153982
$467$	−4.20851e6	−0.892968	−0.446484	−	0.894792i	$-0.647324\pi$
$467$	−4.20851e6	−0.892968	−0.446484	+	0.894792i	$0.647324\pi$
$468$	0	0
$469$	739544.	0.155250
$470$	−217304.	−0.0453757
$471$	0	0
$472$	−404208.	−0.0835122
$473$	−1.03818e6	−0.213363
$474$	0	0
$475$	1.15322e7	2.34520
$476$	1.16225e6	0.235116
$477$	0	0
$478$	−638436.	−0.127805
$479$	−7.39441e6	−1.47253	−0.736266	−	0.676692i	$-0.763413\pi$
$479$	−7.39441e6	−1.47253	−0.736266	+	0.676692i	$0.763413\pi$
$480$	0	0
$481$	7.05425e6	1.39023
$482$	−220990.	−0.0433266
$483$	0	0
$484$	−453871.	−0.0880682
$485$	7.29210e6	1.40766
$486$	0	0
$487$	−3.81644e6	−0.729181	−0.364591	−	0.931168i	$-0.618791\pi$
$487$	−3.81644e6	−0.729181	−0.364591	+	0.931168i	$0.618791\pi$
$488$	2.65205e6	0.504118
$489$	0	0
$490$	1.48405e6	0.279228
$491$	−1.69716e6	−0.317702	−0.158851	−	0.987303i	$-0.550779\pi$
$491$	−1.69716e6	−0.317702	−0.158851	+	0.987303i	$0.550779\pi$
$492$	0	0
$493$	7.96849e6	1.47659
$494$	1.49472e6	0.275577
$495$	0	0
$496$	4.45177e6	0.812509
$497$	1.18794e6	0.215727
$498$	0	0
$499$	6.95160e6	1.24978	0.624889	−	0.780713i	$-0.285144\pi$
$499$	6.95160e6	1.24978	0.624889	+	0.780713i	$0.285144\pi$
$500$	−6.31433e6	−1.12954
$501$	0	0
$502$	627304.	0.111101
$503$	−6.01023e6	−1.05918	−0.529591	−	0.848253i	$-0.677655\pi$
$503$	−6.01023e6	−1.05918	−0.529591	+	0.848253i	$0.677655\pi$
$504$	0	0
$505$	2.29614e6	0.400654
$506$	191422.	0.0332365
$507$	0	0
$508$	−9.43101e6	−1.62143
$509$	−624660.	−0.106868	−0.0534342	−	0.998571i	$-0.517017\pi$
$509$	−624660.	−0.106868	−0.0534342	+	0.998571i	$0.517017\pi$
$510$	0	0
$511$	477724.	0.0809328
$512$	−4.60877e6	−0.776980
$513$	0	0
$514$	−468014.	−0.0781360
$515$	−5.22670e6	−0.868380
$516$	0	0
$517$	−285802.	−0.0470261
$518$	−265044.	−0.0434004
$519$	0	0
$520$	−4.01083e6	−0.650468
$521$	647490.	0.104505	0.0522527	−	0.998634i	$-0.483360\pi$
$521$	647490.	0.104505	0.0522527	+	0.998634i	$0.483360\pi$
$522$	0	0
$523$	−114676.	−0.0183324	−0.00916618	−	0.999958i	$-0.502918\pi$
$523$	−114676.	−0.0183324	−0.00916618	+	0.999958i	$0.502918\pi$
$524$	8.50727e6	1.35351
$525$	0	0
$526$	1.54510e6	0.243497
$527$	6.91006e6	1.08382
$528$	0	0
$529$	−3.93362e6	−0.611157
$530$	−2.83397e6	−0.438233
$531$	0	0
$532$	1.74096e6	0.266692
$533$	−7.35042e6	−1.12071
$534$	0	0
$535$	1.14926e6	0.173594
$536$	−1.79197e6	−0.269413
$537$	0	0
$538$	−1.07457e6	−0.160059
$539$	1.95185e6	0.289384
$540$	0	0
$541$	−2.12404e6	−0.312011	−0.156006	−	0.987756i	$-0.549862\pi$
$541$	−2.12404e6	−0.312011	−0.156006	+	0.987756i	$0.549862\pi$
$542$	−1.58723e6	−0.232082
$543$	0	0
$544$	−4.24669e6	−0.615252
$545$	1.82848e7	2.63693
$546$	0	0
$547$	1.22672e7	1.75299	0.876494	−	0.481413i	$-0.159876\pi$
$547$	1.22672e7	1.75299	0.876494	+	0.481413i	$0.159876\pi$
$548$	−7.60920e6	−1.08240
$549$	0	0
$550$	646019.	0.0910623
$551$	1.19362e7	1.67489
$552$	0	0
$553$	2.73556e6	0.380394
$554$	−692704.	−0.0958900
$555$	0	0
$556$	1.85653e6	0.254692
$557$	−1.10980e7	−1.51568	−0.757839	−	0.652442i	$-0.773745\pi$
$557$	−1.10980e7	−1.51568	−0.757839	+	0.652442i	$0.773745\pi$
$558$	0	0
$559$	−5.93736e6	−0.803644
$560$	−2.22217e6	−0.299438
$561$	0	0
$562$	−567018.	−0.0757279
$563$	−4.61984e6	−0.614265	−0.307132	−	0.951667i	$-0.599369\pi$
$563$	−4.61984e6	−0.614265	−0.307132	+	0.951667i	$0.599369\pi$
$564$	0	0
$565$	−1.53230e7	−2.01940
$566$	−714916.	−0.0938024
$567$	0	0
$568$	−2.87847e6	−0.374361
$569$	−1.01716e7	−1.31707	−0.658537	−	0.752548i	$-0.728824\pi$
$569$	−1.01716e7	−1.31707	−0.658537	+	0.752548i	$0.728824\pi$
$570$	0	0
$571$	−9.36866e6	−1.20251	−0.601253	−	0.799059i	$-0.705331\pi$
$571$	−9.36866e6	−1.20251	−0.601253	+	0.799059i	$0.705331\pi$
$572$	−2.59569e6	−0.331713
$573$	0	0
$574$	276172.	0.0349865
$575$	8.44630e6	1.06536
$576$	0	0
$577$	−6.14973e6	−0.768983	−0.384491	−	0.923129i	$-0.625623\pi$
$577$	−6.14973e6	−0.768983	−0.384491	+	0.923129i	$0.625623\pi$
$578$	−659507.	−0.0821107
$579$	0	0
$580$	−1.57602e7	−1.94532
$581$	1.61959e6	0.199051
$582$	0	0
$583$	−3.72728e6	−0.454173
$584$	−1.15756e6	−0.140447
$585$	0	0
$586$	2.14409e6	0.257929
$587$	−1.04649e6	−0.125354	−0.0626771	−	0.998034i	$-0.519964\pi$
$587$	−1.04649e6	−0.125354	−0.0626771	+	0.998034i	$0.519964\pi$
$588$	0	0
$589$	1.03507e7	1.22937
$590$	590272.	0.0698107
$591$	0	0
$592$	−9.47023e6	−1.11060
$593$	3.31784e6	0.387453	0.193726	−	0.981056i	$-0.437943\pi$
$593$	3.31784e6	0.387453	0.193726	+	0.981056i	$0.437943\pi$
$594$	0	0
$595$	−3.44926e6	−0.399424
$596$	2.23318e6	0.257518
$597$	0	0
$598$	1.09474e6	0.125187
$599$	1.73991e7	1.98134	0.990670	−	0.136280i	$-0.0435146\pi$
$599$	1.73991e7	1.98134	0.990670	+	0.136280i	$0.0435146\pi$
$600$	0	0
$601$	7.13163e6	0.805383	0.402691	−	0.915336i	$-0.368075\pi$
$601$	7.13163e6	0.805383	0.402691	+	0.915336i	$0.368075\pi$
$602$	223080.	0.0250882
$603$	0	0
$604$	1.00164e7	1.11717
$605$	1.34697e6	0.149613
$606$	0	0
$607$	−9.64617e6	−1.06263	−0.531317	−	0.847173i	$-0.678303\pi$
$607$	−9.64617e6	−1.06263	−0.531317	+	0.847173i	$0.678303\pi$
$608$	−6.36120e6	−0.697879
$609$	0	0
$610$	−3.87283e6	−0.421409
$611$	−1.63450e6	−0.177126
$612$	0	0
$613$	3.68170e6	0.395729	0.197864	−	0.980229i	$-0.436599\pi$
$613$	3.68170e6	0.395729	0.197864	+	0.980229i	$0.436599\pi$
$614$	588808.	0.0630308
$615$	0	0
$616$	198198.	0.0210449
$617$	−1.83190e7	−1.93727	−0.968635	−	0.248489i	$-0.920066\pi$
$617$	−1.83190e7	−1.93727	−0.968635	+	0.248489i	$0.920066\pi$
$618$	0	0
$619$	1.09660e6	0.115033	0.0575166	−	0.998345i	$-0.481682\pi$
$619$	1.09660e6	0.115033	0.0575166	+	0.998345i	$0.481682\pi$
$620$	−1.36668e7	−1.42786
$621$	0	0
$622$	2.51827e6	0.260991
$623$	−1.87840e6	−0.193895
$624$	0	0
$625$	2.05492e6	0.210424
$626$	2.23562e6	0.228015
$627$	0	0
$628$	9.88175e6	0.999849
$629$	−1.46997e7	−1.48144
$630$	0	0
$631$	−9.58030e6	−0.957869	−0.478934	−	0.877851i	$-0.658977\pi$
$631$	−9.58030e6	−0.957869	−0.478934	+	0.877851i	$0.658977\pi$
$632$	−6.62848e6	−0.660118
$633$	0	0
$634$	1.06079e6	0.104811
$635$	2.79888e7	2.75454
$636$	0	0
$637$	1.11627e7	1.08998
$638$	668646.	0.0650346
$639$	0	0
$640$	1.11341e7	1.07450
$641$	1.18062e7	1.13492	0.567462	−	0.823400i	$-0.307925\pi$
$641$	1.18062e7	1.13492	0.567462	+	0.823400i	$0.307925\pi$
$642$	0	0
$643$	−5.88298e6	−0.561138	−0.280569	−	0.959834i	$-0.590523\pi$
$643$	−5.88298e6	−0.561138	−0.280569	+	0.959834i	$0.590523\pi$
$644$	1.27509e6	0.121151
$645$	0	0
$646$	−3.11472e6	−0.293655
$647$	3.62822e6	0.340748	0.170374	−	0.985379i	$-0.445502\pi$
$647$	3.62822e6	0.340748	0.170374	+	0.985379i	$0.445502\pi$
$648$	0	0
$649$	776336.	0.0723499
$650$	3.69459e6	0.342991
$651$	0	0
$652$	1.33919e7	1.23374
$653$	5.70795e6	0.523838	0.261919	−	0.965090i	$-0.415645\pi$
$653$	5.70795e6	0.523838	0.261919	+	0.965090i	$0.415645\pi$
$654$	0	0
$655$	−2.52474e7	−2.29939
$656$	9.86784e6	0.895287
$657$	0	0
$658$	61412.0	0.00552953
$659$	−1.08205e7	−0.970588	−0.485294	−	0.874351i	$-0.661287\pi$
$659$	−1.08205e7	−0.970588	−0.485294	+	0.874351i	$0.661287\pi$
$660$	0	0
$661$	1.14311e7	1.01762	0.508809	−	0.860879i	$-0.330086\pi$
$661$	1.14311e7	1.01762	0.508809	+	0.860879i	$0.330086\pi$
$662$	2.34566e6	0.208027
$663$	0	0
$664$	−3.92440e6	−0.345424
$665$	−5.16672e6	−0.453065
$666$	0	0
$667$	8.74213e6	0.760857
$668$	−7.79898e6	−0.676233
$669$	0	0
$670$	2.61685e6	0.225212
$671$	−5.09362e6	−0.436737
$672$	0	0
$673$	−2.03858e7	−1.73496	−0.867482	−	0.497468i	$-0.834263\pi$
$673$	−2.03858e7	−1.73496	−0.867482	+	0.497468i	$0.834263\pi$
$674$	−839978.	−0.0712227
$675$	0	0
$676$	−3.33470e6	−0.280666
$677$	−6.09278e6	−0.510909	−0.255455	−	0.966821i	$-0.582225\pi$
$677$	−6.09278e6	−0.510909	−0.255455	+	0.966821i	$0.582225\pi$
$678$	0	0
$679$	−2.06081e6	−0.171539
$680$	8.35783e6	0.693141
$681$	0	0
$682$	579832.	0.0477355
$683$	−1.44978e7	−1.18918	−0.594592	−	0.804027i	$-0.702686\pi$
$683$	−1.44978e7	−1.18918	−0.594592	+	0.804027i	$0.702686\pi$
$684$	0	0
$685$	2.25821e7	1.83882
$686$	−856388.	−0.0694801
$687$	0	0
$688$	7.97082e6	0.641995
$689$	−2.13164e7	−1.71067
$690$	0	0
$691$	9.87069e6	0.786416	0.393208	−	0.919449i	$-0.371365\pi$
$691$	9.87069e6	0.786416	0.393208	+	0.919449i	$0.371365\pi$
$692$	1.47757e7	1.17296
$693$	0	0
$694$	−2.02560e6	−0.159645
$695$	−5.50970e6	−0.432679
$696$	0	0
$697$	1.53169e7	1.19423
$698$	378924.	0.0294384
$699$	0	0
$700$	4.30323e6	0.331933
$701$	−6.35411e6	−0.488382	−0.244191	−	0.969727i	$-0.578522\pi$
$701$	−6.35411e6	−0.488382	−0.244191	+	0.969727i	$0.578522\pi$
$702$	0	0
$703$	−2.20190e7	−1.68039
$704$	3.24074e6	0.246441
$705$	0	0
$706$	−1.98730e6	−0.150056
$707$	−648908.	−0.0488241
$708$	0	0
$709$	−411382.	−0.0307348	−0.0153674	−	0.999882i	$-0.504892\pi$
$709$	−411382.	−0.0307348	−0.0153674	+	0.999882i	$0.504892\pi$
$710$	4.20348e6	0.312941
$711$	0	0
$712$	4.55150e6	0.336476
$713$	7.58094e6	0.558470
$714$	0	0
$715$	7.70334e6	0.563526
$716$	2.79595e6	0.203820
$717$	0	0
$718$	−3.43975e6	−0.249009
$719$	−6.29795e6	−0.454336	−0.227168	−	0.973856i	$-0.572947\pi$
$719$	−6.29795e6	−0.454336	−0.227168	+	0.973856i	$0.572947\pi$
$720$	0	0
$721$	1.47711e6	0.105822
$722$	−2.18950e6	−0.156316
$723$	0	0
$724$	−7.68806e6	−0.545093
$725$	2.95033e7	2.08461
$726$	0	0
$727$	1.14699e7	0.804866	0.402433	−	0.915449i	$-0.368165\pi$
$727$	1.14699e7	0.804866	0.402433	+	0.915449i	$0.368165\pi$
$728$	1.13350e6	0.0792668
$729$	0	0
$730$	1.69041e6	0.117404
$731$	1.23724e7	0.856365
$732$	0	0
$733$	−1.87547e7	−1.28929	−0.644646	−	0.764481i	$-0.722995\pi$
$733$	−1.87547e7	−1.28929	−0.644646	+	0.764481i	$0.722995\pi$
$734$	1.79679e6	0.123100
$735$	0	0
$736$	−4.65899e6	−0.317028
$737$	3.44172e6	0.233403
$738$	0	0
$739$	2.79727e6	0.188418	0.0942091	−	0.995552i	$-0.469968\pi$
$739$	2.79727e6	0.188418	0.0942091	+	0.995552i	$0.469968\pi$
$740$	2.90733e7	1.95171
$741$	0	0
$742$	800904.	0.0534036
$743$	2.25651e7	1.49956	0.749781	−	0.661686i	$-0.230159\pi$
$743$	2.25651e7	1.49956	0.749781	+	0.661686i	$0.230159\pi$
$744$	0	0
$745$	−6.62750e6	−0.437481
$746$	1.43541e6	0.0944342
$747$	0	0
$748$	5.40894e6	0.353475
$749$	−324792.	−0.0211544
$750$	0	0
$751$	−7.49233e6	−0.484749	−0.242375	−	0.970183i	$-0.577926\pi$
$751$	−7.49233e6	−0.484749	−0.242375	+	0.970183i	$0.577926\pi$
$752$	2.19430e6	0.141498
$753$	0	0
$754$	3.82399e6	0.244956
$755$	−2.97261e7	−1.89789
$756$	0	0
$757$	2.88492e7	1.82976	0.914880	−	0.403727i	$-0.132285\pi$
$757$	2.88492e7	1.82976	0.914880	+	0.403727i	$0.132285\pi$
$758$	−2.66235e6	−0.168303
$759$	0	0
$760$	1.25194e7	0.786227
$761$	9.56279e6	0.598581	0.299291	−	0.954162i	$-0.403250\pi$
$761$	9.56279e6	0.598581	0.299291	+	0.954162i	$0.403250\pi$
$762$	0	0
$763$	−5.16745e6	−0.321340
$764$	−4.86086e6	−0.301287
$765$	0	0
$766$	2.04091e6	0.125676
$767$	4.43987e6	0.272510
$768$	0	0
$769$	−744898.	−0.0454235	−0.0227118	−	0.999742i	$-0.507230\pi$
$769$	−744898.	−0.0454235	−0.0227118	+	0.999742i	$0.507230\pi$
$770$	−289432.	−0.0175922
$771$	0	0
$772$	1.33683e7	0.807293
$773$	−6.07336e6	−0.365578	−0.182789	−	0.983152i	$-0.558513\pi$
$773$	−6.07336e6	−0.365578	−0.182789	+	0.983152i	$0.558513\pi$
$774$	0	0
$775$	2.55845e7	1.53011
$776$	4.99351e6	0.297681
$777$	0	0
$778$	−4.29947e6	−0.254663
$779$	2.29435e7	1.35462
$780$	0	0
$781$	5.52849e6	0.324324
$782$	−2.28124e6	−0.133400
$783$	0	0
$784$	−1.49857e7	−0.870737
$785$	−2.93265e7	−1.69858
$786$	0	0
$787$	−1.47512e7	−0.848966	−0.424483	−	0.905436i	$-0.639544\pi$
$787$	−1.47512e7	−0.848966	−0.424483	+	0.905436i	$0.639544\pi$
$788$	−2.68142e7	−1.53833
$789$	0	0
$790$	9.67969e6	0.551815
$791$	4.33040e6	0.246086
$792$	0	0
$793$	−2.91304e7	−1.64499
$794$	−728818.	−0.0410268
$795$	0	0
$796$	1.48819e7	0.832481
$797$	2.78359e7	1.55224	0.776121	−	0.630584i	$-0.217185\pi$
$797$	2.78359e7	1.55224	0.776121	+	0.630584i	$0.217185\pi$
$798$	0	0
$799$	3.40600e6	0.188746
$800$	−1.57234e7	−0.868601
$801$	0	0
$802$	−5.92515e6	−0.325285
$803$	2.22325e6	0.121675
$804$	0	0
$805$	−3.78414e6	−0.205815
$806$	3.31606e6	0.179798
$807$	0	0
$808$	1.57235e6	0.0847270
$809$	−2.54767e7	−1.36859	−0.684293	−	0.729207i	$-0.739889\pi$
$809$	−2.54767e7	−1.36859	−0.684293	+	0.729207i	$0.739889\pi$
$810$	0	0
$811$	−1.91915e7	−1.02460	−0.512302	−	0.858805i	$-0.671207\pi$
$811$	−1.91915e7	−1.02460	−0.512302	+	0.858805i	$0.671207\pi$
$812$	4.45396e6	0.237059
$813$	0	0
$814$	−1.23347e6	−0.0652483
$815$	−3.97436e7	−2.09591
$816$	0	0
$817$	1.85328e7	0.971373
$818$	−1.38212e6	−0.0722207
$819$	0	0
$820$	−3.02939e7	−1.57333
$821$	−3.27107e6	−0.169368	−0.0846840	−	0.996408i	$-0.526988\pi$
$821$	−3.27107e6	−0.169368	−0.0846840	+	0.996408i	$0.526988\pi$
$822$	0	0
$823$	−3.19195e7	−1.64269	−0.821347	−	0.570430i	$-0.806777\pi$
$823$	−3.19195e7	−1.64269	−0.821347	+	0.570430i	$0.806777\pi$
$824$	−3.57916e6	−0.183638
$825$	0	0
$826$	−166816.	−0.00850722
$827$	−2.45556e7	−1.24850	−0.624248	−	0.781226i	$-0.714595\pi$
$827$	−2.45556e7	−1.24850	−0.624248	+	0.781226i	$0.714595\pi$
$828$	0	0
$829$	−1.40969e7	−0.712421	−0.356211	−	0.934406i	$-0.615931\pi$
$829$	−1.40969e7	−0.712421	−0.356211	+	0.934406i	$0.615931\pi$
$830$	5.73086e6	0.288752
$831$	0	0
$832$	1.85338e7	0.928233
$833$	−2.32609e7	−1.16149
$834$	0	0
$835$	2.31454e7	1.14881
$836$	8.10216e6	0.400945
$837$	0	0
$838$	5.47794e6	0.269468
$839$	3.01443e6	0.147843	0.0739213	−	0.997264i	$-0.476449\pi$
$839$	3.01443e6	0.147843	0.0739213	+	0.997264i	$0.476449\pi$
$840$	0	0
$841$	1.00255e7	0.488784
$842$	−1.02873e6	−0.0500061
$843$	0	0
$844$	−1.63029e7	−0.787787
$845$	9.89653e6	0.476806
$846$	0	0
$847$	−380666.	−0.0182321
$848$	2.86169e7	1.36657
$849$	0	0
$850$	−7.69884e6	−0.365492
$851$	−1.61269e7	−0.763356
$852$	0	0
$853$	−1.67201e7	−0.786806	−0.393403	−	0.919366i	$-0.628702\pi$
$853$	−1.67201e7	−0.786806	−0.393403	+	0.919366i	$0.628702\pi$
$854$	1.09450e6	0.0513534
$855$	0	0
$856$	786996.	0.0367103
$857$	9.15871e6	0.425973	0.212987	−	0.977055i	$-0.431681\pi$
$857$	9.15871e6	0.425973	0.212987	+	0.977055i	$0.431681\pi$
$858$	0	0
$859$	1.51068e7	0.698536	0.349268	−	0.937023i	$-0.386430\pi$
$859$	1.51068e7	0.698536	0.349268	+	0.937023i	$0.386430\pi$
$860$	−2.44702e7	−1.12821
$861$	0	0
$862$	−5.14310e6	−0.235753
$863$	−5.11568e6	−0.233817	−0.116909	−	0.993143i	$-0.537298\pi$
$863$	−5.11568e6	−0.233817	−0.116909	+	0.993143i	$0.537298\pi$
$864$	0	0
$865$	−4.38503e7	−1.99266
$866$	−412954.	−0.0187114
$867$	0	0
$868$	3.86235e6	0.174001
$869$	1.27309e7	0.571886
$870$	0	0
$871$	1.96832e7	0.879127
$872$	1.25211e7	0.557638
$873$	0	0
$874$	−3.41712e6	−0.151315
$875$	−5.29589e6	−0.233840
$876$	0	0
$877$	−1.26998e7	−0.557568	−0.278784	−	0.960354i	$-0.589931\pi$
$877$	−1.26998e7	−0.557568	−0.278784	+	0.960354i	$0.589931\pi$
$878$	−5.96365e6	−0.261081
$879$	0	0
$880$	−1.03416e7	−0.450176
$881$	8.38173e6	0.363826	0.181913	−	0.983315i	$-0.441771\pi$
$881$	8.38173e6	0.363826	0.181913	+	0.983315i	$0.441771\pi$
$882$	0	0
$883$	−1.69529e7	−0.731715	−0.365858	−	0.930671i	$-0.619224\pi$
$883$	−1.69529e7	−0.731715	−0.365858	+	0.930671i	$0.619224\pi$
$884$	3.09338e7	1.33138
$885$	0	0
$886$	2.18433e6	0.0934832
$887$	1.05143e7	0.448717	0.224359	−	0.974507i	$-0.427971\pi$
$887$	1.05143e7	0.448717	0.224359	+	0.974507i	$0.427971\pi$
$888$	0	0
$889$	−7.90988e6	−0.335672
$890$	−6.64663e6	−0.281272
$891$	0	0
$892$	7.60318e6	0.319951
$893$	5.10192e6	0.214094
$894$	0	0
$895$	−8.29766e6	−0.346257
$896$	−3.14660e6	−0.130940
$897$	0	0
$898$	−7858.00	−0.000325178 0
$899$	2.64806e7	1.09277
$900$	0	0
$901$	4.44194e7	1.82289
$902$	1.28526e6	0.0525987
$903$	0	0
$904$	−1.04929e7	−0.427046
$905$	2.28162e7	0.926023
$906$	0	0
$907$	−1.53747e7	−0.620569	−0.310284	−	0.950644i	$-0.600424\pi$
$907$	−1.53747e7	−0.620569	−0.310284	+	0.950644i	$0.600424\pi$
$908$	−2.47785e7	−0.997381
$909$	0	0
$910$	−1.65526e6	−0.0662619
$911$	−1.25424e7	−0.500708	−0.250354	−	0.968154i	$-0.580547\pi$
$911$	−1.25424e7	−0.500708	−0.250354	+	0.968154i	$0.580547\pi$
$912$	0	0
$913$	7.53733e6	0.299255
$914$	899922.	0.0356319
$915$	0	0
$916$	4.77367e7	1.87981
$917$	7.13513e6	0.280207
$918$	0	0
$919$	3.31432e7	1.29451	0.647256	−	0.762273i	$-0.275916\pi$
$919$	3.31432e7	1.29451	0.647256	+	0.762273i	$0.275916\pi$
$920$	9.16927e6	0.357162
$921$	0	0
$922$	1.13619e6	0.0440173
$923$	3.16175e7	1.22158
$924$	0	0
$925$	−5.44258e7	−2.09146
$926$	7.38964e6	0.283202
$927$	0	0
$928$	−1.62741e7	−0.620335
$929$	−3.10442e7	−1.18016	−0.590080	−	0.807345i	$-0.700904\pi$
$929$	−3.10442e7	−1.18016	−0.590080	+	0.807345i	$0.700904\pi$
$930$	0	0
$931$	−3.48430e7	−1.31747
$932$	−2.23767e7	−0.843834
$933$	0	0
$934$	4.20851e6	0.157856
$935$	−1.60523e7	−0.600495
$936$	0	0
$937$	−3.10737e7	−1.15623	−0.578115	−	0.815955i	$-0.696212\pi$
$937$	−3.10737e7	−1.15623	−0.578115	+	0.815955i	$0.696212\pi$
$938$	−739544.	−0.0274446
$939$	0	0
$940$	−6.73642e6	−0.248662
$941$	2.50349e7	0.921664	0.460832	−	0.887488i	$-0.347551\pi$
$941$	2.50349e7	0.921664	0.460832	+	0.887488i	$0.347551\pi$
$942$	0	0
$943$	1.68040e7	0.615366
$944$	−5.96046e6	−0.217696
$945$	0	0
$946$	1.03818e6	0.0377177
$947$	5.37383e6	0.194719	0.0973596	−	0.995249i	$-0.468960\pi$
$947$	5.37383e6	0.194719	0.0973596	+	0.995249i	$0.468960\pi$
$948$	0	0
$949$	1.27148e7	0.458294
$950$	−1.15322e7	−0.414576
$951$	0	0
$952$	−2.36200e6	−0.0844669
$953$	−7.26908e6	−0.259267	−0.129634	−	0.991562i	$-0.541380\pi$
$953$	−7.26908e6	−0.259267	−0.129634	+	0.991562i	$0.541380\pi$
$954$	0	0
$955$	1.44258e7	0.511836
$956$	−1.97915e7	−0.700381
$957$	0	0
$958$	7.39441e6	0.260309
$959$	−6.38191e6	−0.224080
$960$	0	0
$961$	−5.66589e6	−0.197906
$962$	−7.05425e6	−0.245761
$963$	0	0
$964$	−6.85069e6	−0.237433
$965$	−3.96735e7	−1.37146
$966$	0	0
$967$	−2.54428e7	−0.874983	−0.437491	−	0.899223i	$-0.644133\pi$
$967$	−2.54428e7	−0.874983	−0.437491	+	0.899223i	$0.644133\pi$
$968$	922383.	0.0316390
$969$	0	0
$970$	−7.29210e6	−0.248842
$971$	−9.88213e6	−0.336358	−0.168179	−	0.985756i	$-0.553789\pi$
$971$	−9.88213e6	−0.336358	−0.168179	+	0.985756i	$0.553789\pi$
$972$	0	0
$973$	1.55709e6	0.0527268
$974$	3.81644e6	0.128902
$975$	0	0
$976$	3.91072e7	1.31411
$977$	−2.22197e6	−0.0744736	−0.0372368	−	0.999306i	$-0.511856\pi$
$977$	−2.22197e6	−0.0744736	−0.0372368	+	0.999306i	$0.511856\pi$
$978$	0	0
$979$	−8.74177e6	−0.291503
$980$	4.60056e7	1.53019
$981$	0	0
$982$	1.69716e6	0.0561623
$983$	−2.53706e7	−0.837428	−0.418714	−	0.908118i	$-0.637519\pi$
$983$	−2.53706e7	−0.837428	−0.418714	+	0.908118i	$0.637519\pi$
$984$	0	0
$985$	7.95776e7	2.61337
$986$	−7.96849e6	−0.261026
$987$	0	0
$988$	4.63363e7	1.51018
$989$	1.35736e7	0.441269
$990$	0	0
$991$	3.24132e7	1.04843	0.524214	−	0.851587i	$-0.324359\pi$
$991$	3.24132e7	1.04843	0.524214	+	0.851587i	$0.324359\pi$
$992$	−1.41124e7	−0.455327
$993$	0	0
$994$	−1.18794e6	−0.0381354
$995$	−4.41655e7	−1.41425
$996$	0	0
$997$	−1.55048e6	−0.0494000	−0.0247000	−	0.999695i	$-0.507863\pi$
$997$	−1.55048e6	−0.0494000	−0.0247000	+	0.999695i	$0.507863\pi$
$998$	−6.95160e6	−0.220932
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.6.a.a.1.1		1
3.2	odd	2		33.6.a.b.1.1	✓	1
11.10	odd	2		1089.6.a.h.1.1		1
12.11	even	2		528.6.a.a.1.1		1
15.14	odd	2		825.6.a.a.1.1		1
33.32	even	2		363.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.a.b.1.1	✓	1	3.2	odd	2
99.6.a.a.1.1		1	1.1	even	1	trivial
363.6.a.b.1.1		1	33.32	even	2
528.6.a.a.1.1		1	12.11	even	2
825.6.a.a.1.1		1	15.14	odd	2
1089.6.a.h.1.1		1	11.10	odd	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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	99.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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