LMFDB - Embedded newform 9.22.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,22,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 22, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	9.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:	$25.1529609858$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2844.00 q^{2} +5.99118e6 q^{4} -3.10995e6 q^{5} +3.63304e8 q^{7} +1.10746e10 q^{8} +O(q^{10})$

\(q+2844.00 q^{2} +5.99118e6 q^{4} -3.10995e6 q^{5} +3.63304e8 q^{7} +1.10746e10 q^{8} -8.84470e9 q^{10} -1.45818e10 q^{11} +1.13351e11 q^{13} +1.03324e12 q^{14} +1.89318e13 q^{16} +8.58939e12 q^{17} -2.92029e13 q^{19} -1.86323e13 q^{20} -4.14707e13 q^{22} +1.55899e14 q^{23} -4.67165e14 q^{25} +3.22370e14 q^{26} +2.17662e15 q^{28} -2.40079e15 q^{29} +2.23982e15 q^{31} +3.06169e16 q^{32} +2.44282e16 q^{34} -1.12986e15 q^{35} -3.07851e16 q^{37} -8.30532e16 q^{38} -3.44415e16 q^{40} +1.03208e17 q^{41} -1.65557e17 q^{43} -8.73624e16 q^{44} +4.43377e17 q^{46} +6.65872e16 q^{47} -4.26556e17 q^{49} -1.32862e18 q^{50} +6.79105e17 q^{52} -4.35423e17 q^{53} +4.53488e16 q^{55} +4.02346e18 q^{56} -6.82784e18 q^{58} -5.53437e18 q^{59} -7.17621e18 q^{61} +6.37005e18 q^{62} +4.73716e19 q^{64} -3.52515e17 q^{65} -1.57554e19 q^{67} +5.14606e19 q^{68} -3.21331e18 q^{70} -2.64579e19 q^{71} +1.34712e19 q^{73} -8.75527e19 q^{74} -1.74960e20 q^{76} -5.29764e18 q^{77} -1.68861e19 q^{79} -5.88770e19 q^{80} +2.93522e20 q^{82} +1.70688e20 q^{83} -2.67126e19 q^{85} -4.70845e20 q^{86} -1.61488e20 q^{88} +3.12592e20 q^{89} +4.11808e19 q^{91} +9.34021e20 q^{92} +1.89374e20 q^{94} +9.08197e19 q^{95} +9.49015e20 q^{97} -1.21313e21 q^{98} +O(q^{100})\)

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 $

$2$	2844.00	1.96388	0.981939	−	0.189196i	$-0.0605882\pi$
$2$	2844.00	1.96388	0.981939	+	0.189196i	$0.0605882\pi$
$3$	0	0
$3$	0	0
$4$	5.99118e6	2.85682
$5$	−3.10995e6	−0.142419	−0.0712096	−	0.997461i	$-0.522686\pi$
$5$	−3.10995e6	−0.142419	−0.0712096	+	0.997461i	$0.522686\pi$
$6$	0	0
$7$	3.63304e8	0.486117	0.243058	−	0.970012i	$-0.421849\pi$
$7$	3.63304e8	0.486117	0.243058	+	0.970012i	$0.421849\pi$
$8$	1.10746e10	3.64657
$9$	0	0
$10$	−8.84470e9	−0.279694
$11$	−1.45818e10	−0.169508	−0.0847538	−	0.996402i	$-0.527010\pi$
$11$	−1.45818e10	−0.169508	−0.0847538	+	0.996402i	$0.527010\pi$
$12$	0	0
$13$	1.13351e11	0.228044	0.114022	−	0.993478i	$-0.463627\pi$
$13$	1.13351e11	0.228044	0.114022	+	0.993478i	$0.463627\pi$
$14$	1.03324e12	0.954674
$15$	0	0
$16$	1.89318e13	4.30460
$17$	8.58939e12	1.03335	0.516676	−	0.856181i	$-0.327169\pi$
$17$	8.58939e12	1.03335	0.516676	+	0.856181i	$0.327169\pi$
$18$	0	0
$19$	−2.92029e13	−1.09273	−0.546366	−	0.837546i	$-0.683989\pi$
$19$	−2.92029e13	−1.09273	−0.546366	+	0.837546i	$0.683989\pi$
$20$	−1.86323e13	−0.406866
$21$	0	0
$22$	−4.14707e13	−0.332892
$23$	1.55899e14	0.784696	0.392348	−	0.919817i	$-0.371663\pi$
$23$	1.55899e14	0.784696	0.392348	+	0.919817i	$0.371663\pi$
$24$	0	0
$25$	−4.67165e14	−0.979717
$26$	3.22370e14	0.447851
$27$	0	0
$28$	2.17662e15	1.38875
$29$	−2.40079e15	−1.05968	−0.529840	−	0.848097i	$-0.677748\pi$
$29$	−2.40079e15	−1.05968	−0.529840	+	0.848097i	$0.677748\pi$
$30$	0	0
$31$	2.23982e15	0.490812	0.245406	−	0.969420i	$-0.421079\pi$
$31$	2.23982e15	0.490812	0.245406	+	0.969420i	$0.421079\pi$
$32$	3.06169e16	4.80714
$33$	0	0
$34$	2.44282e16	2.02938
$35$	−1.12986e15	−0.0692323
$36$	0	0
$37$	−3.07851e16	−1.05250	−0.526250	−	0.850330i	$-0.676402\pi$
$37$	−3.07851e16	−1.05250	−0.526250	+	0.850330i	$0.676402\pi$
$38$	−8.30532e16	−2.14599
$39$	0	0
$40$	−3.44415e16	−0.519341
$41$	1.03208e17	1.20083	0.600414	−	0.799689i	$-0.295002\pi$
$41$	1.03208e17	1.20083	0.600414	+	0.799689i	$0.295002\pi$
$42$	0	0
$43$	−1.65557e17	−1.16823	−0.584117	−	0.811670i	$-0.698559\pi$
$43$	−1.65557e17	−1.16823	−0.584117	+	0.811670i	$0.698559\pi$
$44$	−8.73624e16	−0.484252
$45$	0	0
$46$	4.43377e17	1.54105
$47$	6.65872e16	0.184656	0.0923280	−	0.995729i	$-0.470569\pi$
$47$	6.65872e16	0.184656	0.0923280	+	0.995729i	$0.470569\pi$
$48$	0	0
$49$	−4.26556e17	−0.763690
$50$	−1.32862e18	−1.92404
$51$	0	0
$52$	6.79105e17	0.651482
$53$	−4.35423e17	−0.341991	−0.170995	−	0.985272i	$-0.554698\pi$
$53$	−4.35423e17	−0.341991	−0.170995	+	0.985272i	$0.554698\pi$
$54$	0	0
$55$	4.53488e16	0.0241411
$56$	4.02346e18	1.77266
$57$	0	0
$58$	−6.82784e18	−2.08108
$59$	−5.53437e18	−1.40968	−0.704842	−	0.709364i	$-0.748982\pi$
$59$	−5.53437e18	−1.40968	−0.704842	+	0.709364i	$0.748982\pi$
$60$	0	0
$61$	−7.17621e18	−1.28805	−0.644023	−	0.765006i	$-0.722736\pi$
$61$	−7.17621e18	−1.28805	−0.644023	+	0.765006i	$0.722736\pi$
$62$	6.37005e18	0.963896
$63$	0	0
$64$	4.73716e19	5.13604
$65$	−3.52515e17	−0.0324779
$66$	0	0
$67$	−1.57554e19	−1.05595	−0.527977	−	0.849258i	$-0.677049\pi$
$67$	−1.57554e19	−1.05595	−0.527977	+	0.849258i	$0.677049\pi$
$68$	5.14606e19	2.95210
$69$	0	0
$70$	−3.21331e18	−0.135964
$71$	−2.64579e19	−0.964588	−0.482294	−	0.876009i	$-0.660196\pi$
$71$	−2.64579e19	−0.964588	−0.482294	+	0.876009i	$0.660196\pi$
$72$	0	0
$73$	1.34712e19	0.366875	0.183437	−	0.983031i	$-0.441278\pi$
$73$	1.34712e19	0.366875	0.183437	+	0.983031i	$0.441278\pi$
$74$	−8.75527e19	−2.06698
$75$	0	0
$76$	−1.74960e20	−3.12174
$77$	−5.29764e18	−0.0824005
$78$	0	0
$79$	−1.68861e19	−0.200653	−0.100326	−	0.994955i	$-0.531989\pi$
$79$	−1.68861e19	−0.200653	−0.100326	+	0.994955i	$0.531989\pi$
$80$	−5.88770e19	−0.613057
$81$	0	0
$82$	2.93522e20	2.35828
$83$	1.70688e20	1.20749	0.603744	−	0.797178i	$-0.293675\pi$
$83$	1.70688e20	1.20749	0.603744	+	0.797178i	$0.293675\pi$
$84$	0	0
$85$	−2.67126e19	−0.147169
$86$	−4.70845e20	−2.29427
$87$	0	0
$88$	−1.61488e20	−0.618121
$89$	3.12592e20	1.06263	0.531317	−	0.847173i	$-0.321697\pi$
$89$	3.12592e20	1.06263	0.531317	+	0.847173i	$0.321697\pi$
$90$	0	0
$91$	4.11808e19	0.110856
$92$	9.34021e20	2.24174
$93$	0	0
$94$	1.89374e20	0.362642
$95$	9.08197e19	0.155626
$96$	0	0
$97$	9.49015e20	1.30668	0.653341	−	0.757064i	$-0.273367\pi$
$97$	9.49015e20	1.30668	0.653341	+	0.757064i	$0.273367\pi$
$98$	−1.21313e21	−1.49980
$99$	0	0
$100$	−2.79887e21	−2.79887
$101$	−1.44798e20	−0.130433	−0.0652166	−	0.997871i	$-0.520774\pi$
$101$	−1.44798e20	−0.130433	−0.0652166	+	0.997871i	$0.520774\pi$
$102$	0	0
$103$	2.19627e21	1.61025	0.805127	−	0.593102i	$-0.202097\pi$
$103$	2.19627e21	1.61025	0.805127	+	0.593102i	$0.202097\pi$
$104$	1.25532e21	0.831579
$105$	0	0
$106$	−1.23834e21	−0.671629
$107$	1.63087e20	0.0801473	0.0400737	−	0.999197i	$-0.487241\pi$
$107$	1.63087e20	0.0801473	0.0400737	+	0.999197i	$0.487241\pi$
$108$	0	0
$109$	2.24852e20	0.0909743	0.0454871	−	0.998965i	$-0.485516\pi$
$109$	2.24852e20	0.0909743	0.0454871	+	0.998965i	$0.485516\pi$
$110$	1.28972e20	0.0474102
$111$	0	0
$112$	6.87800e21	2.09254
$113$	4.24118e21	1.17534	0.587670	−	0.809101i	$-0.300045\pi$
$113$	4.24118e21	1.17534	0.587670	+	0.809101i	$0.300045\pi$
$114$	0	0
$115$	−4.84839e20	−0.111756
$116$	−1.43836e22	−3.02732
$117$	0	0
$118$	−1.57397e22	−2.76845
$119$	3.12056e21	0.502330
$120$	0	0
$121$	−7.18762e21	−0.971267
$122$	−2.04091e22	−2.52957
$123$	0	0
$124$	1.34192e22	1.40216
$125$	2.93580e21	0.281950
$126$	0	0
$127$	1.66312e21	0.135202	0.0676012	−	0.997712i	$-0.478465\pi$
$127$	1.66312e21	0.135202	0.0676012	+	0.997712i	$0.478465\pi$
$128$	7.05165e22	5.27942
$129$	0	0
$130$	−1.00255e21	−0.0637826
$131$	−6.40663e21	−0.376081	−0.188040	−	0.982161i	$-0.560214\pi$
$131$	−6.40663e21	−0.376081	−0.188040	+	0.982161i	$0.560214\pi$
$132$	0	0
$133$	−1.06095e22	−0.531196
$134$	−4.48085e22	−2.07377
$135$	0	0
$136$	9.51243e22	3.76819
$137$	1.98314e22	0.727423	0.363711	−	0.931512i	$-0.381509\pi$
$137$	1.98314e22	0.727423	0.363711	+	0.931512i	$0.381509\pi$
$138$	0	0
$139$	−5.20143e21	−0.163858	−0.0819290	−	0.996638i	$-0.526108\pi$
$139$	−5.20143e21	−0.163858	−0.0819290	+	0.996638i	$0.526108\pi$
$140$	−6.76918e21	−0.197784
$141$	0	0
$142$	−7.52461e22	−1.89433
$143$	−1.65286e21	−0.0386552
$144$	0	0
$145$	7.46633e21	0.150919
$146$	3.83122e22	0.720498
$147$	0	0
$148$	−1.84439e23	−3.00680
$149$	7.47631e22	1.13562	0.567808	−	0.823161i	$-0.307792\pi$
$149$	7.47631e22	1.13562	0.567808	+	0.823161i	$0.307792\pi$
$150$	0	0
$151$	1.11044e23	1.46635	0.733174	−	0.680042i	$-0.238038\pi$
$151$	1.11044e23	1.46635	0.733174	+	0.680042i	$0.238038\pi$
$152$	−3.23412e23	−3.98472
$153$	0	0
$154$	−1.50665e22	−0.161824
$155$	−6.96573e21	−0.0699011
$156$	0	0
$157$	4.36563e22	0.382913	0.191457	−	0.981501i	$-0.438679\pi$
$157$	4.36563e22	0.382913	0.191457	+	0.981501i	$0.438679\pi$
$158$	−4.80241e22	−0.394058
$159$	0	0
$160$	−9.52171e22	−0.684628
$161$	5.66388e22	0.381454
$162$	0	0
$163$	2.85661e23	1.68998	0.844989	−	0.534783i	$-0.179607\pi$
$163$	2.85661e23	1.68998	0.844989	+	0.534783i	$0.179607\pi$
$164$	6.18336e23	3.43055
$165$	0	0
$166$	4.85437e23	2.37136
$167$	−2.66950e23	−1.22435	−0.612177	−	0.790720i	$-0.709706\pi$
$167$	−2.66950e23	−1.22435	−0.612177	+	0.790720i	$0.709706\pi$
$168$	0	0
$169$	−2.34216e23	−0.947996
$170$	−7.59706e22	−0.289022
$171$	0	0
$172$	−9.91884e23	−3.33743
$173$	2.28496e23	0.723425	0.361713	−	0.932290i	$-0.382192\pi$
$173$	2.28496e23	0.723425	0.361713	+	0.932290i	$0.382192\pi$
$174$	0	0
$175$	−1.69723e23	−0.476257
$176$	−2.76061e23	−0.729661
$177$	0	0
$178$	8.89013e23	2.08688
$179$	1.29151e22	0.0285852	0.0142926	−	0.999898i	$-0.495450\pi$
$179$	1.29151e22	0.0285852	0.0142926	+	0.999898i	$0.495450\pi$
$180$	0	0
$181$	−8.75338e23	−1.72405	−0.862026	−	0.506863i	$-0.830805\pi$
$181$	−8.75338e23	−1.72405	−0.862026	+	0.506863i	$0.830805\pi$
$182$	1.17118e23	0.217708
$183$	0	0
$184$	1.72653e24	2.86145
$185$	9.57400e22	0.149896
$186$	0	0
$187$	−1.25249e23	−0.175161
$188$	3.98936e23	0.527529
$189$	0	0
$190$	2.58291e23	0.305631
$191$	−1.33961e24	−1.50013	−0.750066	−	0.661363i	$-0.769978\pi$
$191$	−1.33961e24	−1.50013	−0.750066	+	0.661363i	$0.769978\pi$
$192$	0	0
$193$	−2.13970e23	−0.214783	−0.107392	−	0.994217i	$-0.534250\pi$
$193$	−2.13970e23	−0.214783	−0.107392	+	0.994217i	$0.534250\pi$
$194$	2.69900e24	2.56616
$195$	0	0
$196$	−2.55558e24	−2.18173
$197$	−1.42895e24	−1.15644	−0.578220	−	0.815881i	$-0.696252\pi$
$197$	−1.42895e24	−1.15644	−0.578220	+	0.815881i	$0.696252\pi$
$198$	0	0
$199$	7.45856e23	0.542872	0.271436	−	0.962456i	$-0.412501\pi$
$199$	7.45856e23	0.542872	0.271436	+	0.962456i	$0.412501\pi$
$200$	−5.17368e24	−3.57260
$201$	0	0
$202$	−4.11805e23	−0.256155
$203$	−8.72216e23	−0.515129
$204$	0	0
$205$	−3.20970e23	−0.171021
$206$	6.24619e24	3.16234
$207$	0	0
$208$	2.14594e24	0.981639
$209$	4.25832e23	0.185226
$210$	0	0
$211$	−2.65090e24	−1.04334	−0.521671	−	0.853147i	$-0.674691\pi$
$211$	−2.65090e24	−1.04334	−0.521671	+	0.853147i	$0.674691\pi$
$212$	−2.60870e24	−0.977006
$213$	0	0
$214$	4.63819e23	0.157400
$215$	5.14875e23	0.166379
$216$	0	0
$217$	8.13736e23	0.238592
$218$	6.39479e23	0.178662
$219$	0	0
$220$	2.71693e23	0.0689668
$221$	9.73614e23	0.235650
$222$	0	0
$223$	3.97174e24	0.874539	0.437270	−	0.899330i	$-0.355946\pi$
$223$	3.97174e24	0.874539	0.437270	+	0.899330i	$0.355946\pi$
$224$	1.11232e25	2.33683
$225$	0	0
$226$	1.20619e25	2.30823
$227$	2.14690e24	0.392229	0.196114	−	0.980581i	$-0.437168\pi$
$227$	2.14690e24	0.392229	0.196114	+	0.980581i	$0.437168\pi$
$228$	0	0
$229$	3.66024e24	0.609869	0.304934	−	0.952373i	$-0.401365\pi$
$229$	3.66024e24	0.609869	0.304934	+	0.952373i	$0.401365\pi$
$230$	−1.37888e24	−0.219475
$231$	0	0
$232$	−2.65878e25	−3.86420
$233$	2.90921e24	0.404145	0.202073	−	0.979371i	$-0.435232\pi$
$233$	2.90921e24	0.404145	0.202073	+	0.979371i	$0.435232\pi$
$234$	0	0
$235$	−2.07083e23	−0.0262985
$236$	−3.31574e25	−4.02721
$237$	0	0
$238$	8.87487e24	0.986516
$239$	4.80224e24	0.510818	0.255409	−	0.966833i	$-0.417790\pi$
$239$	4.80224e24	0.510818	0.255409	+	0.966833i	$0.417790\pi$
$240$	0	0
$241$	7.86263e24	0.766282	0.383141	−	0.923690i	$-0.374842\pi$
$241$	7.86263e24	0.766282	0.383141	+	0.923690i	$0.374842\pi$
$242$	−2.04416e25	−1.90745
$243$	0	0
$244$	−4.29940e25	−3.67972
$245$	1.32657e24	0.108764
$246$	0	0
$247$	−3.31018e24	−0.249191
$248$	2.48052e25	1.78978
$249$	0	0
$250$	8.34942e24	0.553715
$251$	1.99525e25	1.26889	0.634443	−	0.772969i	$-0.281229\pi$
$251$	1.99525e25	1.26889	0.634443	+	0.772969i	$0.281229\pi$
$252$	0	0
$253$	−2.27330e24	−0.133012
$254$	4.72991e24	0.265521
$255$	0	0
$256$	1.01203e26	5.23210
$257$	−1.33580e25	−0.662894	−0.331447	−	0.943474i	$-0.607537\pi$
$257$	−1.33580e25	−0.662894	−0.331447	+	0.943474i	$0.607537\pi$
$258$	0	0
$259$	−1.11843e25	−0.511638
$260$	−2.11198e24	−0.0927834
$261$	0	0
$262$	−1.82204e25	−0.738576
$263$	5.83637e24	0.227304	0.113652	−	0.993521i	$-0.463745\pi$
$263$	5.83637e24	0.227304	0.113652	+	0.993521i	$0.463745\pi$
$264$	0	0
$265$	1.35414e24	0.0487060
$266$	−3.01735e25	−1.04320
$267$	0	0
$268$	−9.43938e25	−3.01667
$269$	−5.35297e25	−1.64511	−0.822557	−	0.568683i	$-0.807453\pi$
$269$	−5.35297e25	−1.64511	−0.822557	+	0.568683i	$0.807453\pi$
$270$	0	0
$271$	−1.04403e25	−0.296849	−0.148425	−	0.988924i	$-0.547420\pi$
$271$	−1.04403e25	−0.296849	−0.148425	+	0.988924i	$0.547420\pi$
$272$	1.62613e26	4.44817
$273$	0	0
$274$	5.64004e25	1.42857
$275$	6.81213e24	0.166069
$276$	0	0
$277$	3.14884e25	0.711399	0.355699	−	0.934600i	$-0.384243\pi$
$277$	3.14884e25	0.711399	0.355699	+	0.934600i	$0.384243\pi$
$278$	−1.47929e25	−0.321797
$279$	0	0
$280$	−1.25127e25	−0.252460
$281$	1.15887e25	0.225225	0.112613	−	0.993639i	$-0.464078\pi$
$281$	1.15887e25	0.225225	0.112613	+	0.993639i	$0.464078\pi$
$282$	0	0
$283$	−4.80399e25	−0.866652	−0.433326	−	0.901237i	$-0.642660\pi$
$283$	−4.80399e25	−0.866652	−0.433326	+	0.901237i	$0.642660\pi$
$284$	−1.58514e26	−2.75565
$285$	0	0
$286$	−4.70074e24	−0.0759142
$287$	3.74957e25	0.583743
$288$	0	0
$289$	4.68568e24	0.0678180
$290$	2.12343e25	0.296386
$291$	0	0
$292$	8.07087e25	1.04809
$293$	7.96714e25	0.998142	0.499071	−	0.866561i	$-0.333675\pi$
$293$	7.96714e25	0.998142	0.499071	+	0.866561i	$0.333675\pi$
$294$	0	0
$295$	1.72116e25	0.200766
$296$	−3.40933e26	−3.83801
$297$	0	0
$298$	2.12626e26	2.23021
$299$	1.76713e25	0.178946
$300$	0	0
$301$	−6.01476e25	−0.567898
$302$	3.15809e26	2.87973
$303$	0	0
$304$	−5.52865e26	−4.70377
$305$	2.23176e25	0.183442
$306$	0	0
$307$	1.51498e26	1.16266	0.581332	−	0.813666i	$-0.302532\pi$
$307$	1.51498e26	1.16266	0.581332	+	0.813666i	$0.302532\pi$
$308$	−3.17391e25	−0.235403
$309$	0	0
$310$	−1.98105e25	−0.137277
$311$	−1.41406e26	−0.947292	−0.473646	−	0.880715i	$-0.657062\pi$
$311$	−1.41406e26	−0.947292	−0.473646	+	0.880715i	$0.657062\pi$
$312$	0	0
$313$	4.99598e25	0.312899	0.156450	−	0.987686i	$-0.449995\pi$
$313$	4.99598e25	0.312899	0.156450	+	0.987686i	$0.449995\pi$
$314$	1.24158e26	0.751995
$315$	0	0
$316$	−1.01168e26	−0.573229
$317$	−1.81535e26	−0.995033	−0.497517	−	0.867454i	$-0.665755\pi$
$317$	−1.81535e26	−0.995033	−0.497517	+	0.867454i	$0.665755\pi$
$318$	0	0
$319$	3.50079e25	0.179624
$320$	−1.47323e26	−0.731470
$321$	0	0
$322$	1.61081e26	0.749130
$323$	−2.50835e26	−1.12918
$324$	0	0
$325$	−5.29536e25	−0.223419
$326$	8.12420e26	3.31891
$327$	0	0
$328$	1.14299e27	4.37890
$329$	2.41914e25	0.0897644
$330$	0	0
$331$	1.44090e26	0.501695	0.250848	−	0.968027i	$-0.419291\pi$
$331$	1.44090e26	0.501695	0.250848	+	0.968027i	$0.419291\pi$
$332$	1.02262e27	3.44958
$333$	0	0
$334$	−7.59206e26	−2.40448
$335$	4.89987e25	0.150388
$336$	0	0
$337$	−3.63051e26	−1.04678	−0.523388	−	0.852095i	$-0.675332\pi$
$337$	−3.63051e26	−1.04678	−0.523388	+	0.852095i	$0.675332\pi$
$338$	−6.66111e26	−1.86175
$339$	0	0
$340$	−1.60040e26	−0.420436
$341$	−3.26607e25	−0.0831964
$342$	0	0
$343$	−3.57891e26	−0.857360
$344$	−1.83349e27	−4.26004
$345$	0	0
$346$	6.49841e26	1.42072
$347$	7.09622e25	0.150511	0.0752554	−	0.997164i	$-0.476023\pi$
$347$	7.09622e25	0.150511	0.0752554	+	0.997164i	$0.476023\pi$
$348$	0	0
$349$	−7.03939e26	−1.40562	−0.702810	−	0.711378i	$-0.748072\pi$
$349$	−7.03939e26	−1.40562	−0.702810	+	0.711378i	$0.748072\pi$
$350$	−4.82692e26	−0.935311
$351$	0	0
$352$	−4.46451e26	−0.814846
$353$	1.08085e26	0.191483	0.0957414	−	0.995406i	$-0.469478\pi$
$353$	1.08085e26	0.191483	0.0957414	+	0.995406i	$0.469478\pi$
$354$	0	0
$355$	8.22826e25	0.137376
$356$	1.87280e27	3.03575
$357$	0	0
$358$	3.67305e25	0.0561378
$359$	1.67492e26	0.248601	0.124301	−	0.992245i	$-0.460331\pi$
$359$	1.67492e26	0.248601	0.124301	+	0.992245i	$0.460331\pi$
$360$	0	0
$361$	1.38602e26	0.194064
$362$	−2.48946e27	−3.38583
$363$	0	0
$364$	2.46722e26	0.316696
$365$	−4.18949e25	−0.0522500
$366$	0	0
$367$	9.83667e26	1.15839	0.579194	−	0.815190i	$-0.303367\pi$
$367$	9.83667e26	1.15839	0.579194	+	0.815190i	$0.303367\pi$
$368$	2.95146e27	3.37780
$369$	0	0
$370$	2.72285e26	0.294378
$371$	−1.58191e26	−0.166248
$372$	0	0
$373$	1.00058e26	0.0993824	0.0496912	−	0.998765i	$-0.484176\pi$
$373$	1.00058e26	0.0993824	0.0496912	+	0.998765i	$0.484176\pi$
$374$	−3.56208e26	−0.343995
$375$	0	0
$376$	7.37429e26	0.673360
$377$	−2.72131e26	−0.241654
$378$	0	0
$379$	9.23905e25	0.0776096	0.0388048	−	0.999247i	$-0.487645\pi$
$379$	9.23905e25	0.0776096	0.0388048	+	0.999247i	$0.487645\pi$
$380$	5.44117e26	0.444595
$381$	0	0
$382$	−3.80986e27	−2.94608
$383$	2.13677e27	1.60757	0.803786	−	0.594919i	$-0.202816\pi$
$383$	2.13677e27	1.60757	0.803786	+	0.594919i	$0.202816\pi$
$384$	0	0
$385$	1.64754e25	0.0117354
$386$	−6.08530e26	−0.421809
$387$	0	0
$388$	5.68572e27	3.73295
$389$	1.25581e27	0.802516	0.401258	−	0.915965i	$-0.368573\pi$
$389$	1.25581e27	0.802516	0.401258	+	0.915965i	$0.368573\pi$
$390$	0	0
$391$	1.33908e27	0.810868
$392$	−4.72395e27	−2.78485
$393$	0	0
$394$	−4.06394e27	−2.27111
$395$	5.25150e25	0.0285768
$396$	0	0
$397$	1.78165e27	0.919439	0.459719	−	0.888064i	$-0.347950\pi$
$397$	1.78165e27	0.919439	0.459719	+	0.888064i	$0.347950\pi$
$398$	2.12121e27	1.06614
$399$	0	0
$400$	−8.84429e27	−4.21729
$401$	−1.40181e27	−0.651141	−0.325570	−	0.945518i	$-0.605556\pi$
$401$	−1.40181e27	−0.651141	−0.325570	+	0.945518i	$0.605556\pi$
$402$	0	0
$403$	2.53885e26	0.111927
$404$	−8.67511e26	−0.372624
$405$	0	0
$406$	−2.48058e27	−1.01165
$407$	4.48903e26	0.178407
$408$	0	0
$409$	2.17493e27	0.821015	0.410507	−	0.911857i	$-0.365352\pi$
$409$	2.17493e27	0.821015	0.410507	+	0.911857i	$0.365352\pi$
$410$	−9.12840e26	−0.335864
$411$	0	0
$412$	1.31582e28	4.60021
$413$	−2.01066e27	−0.685271
$414$	0	0
$415$	−5.30831e26	−0.171969
$416$	3.47045e27	1.09624
$417$	0	0
$418$	1.21107e27	0.363762
$419$	6.07636e27	1.77990	0.889952	−	0.456055i	$-0.150738\pi$
$419$	6.07636e27	1.77990	0.889952	+	0.456055i	$0.150738\pi$
$420$	0	0
$421$	−1.89993e27	−0.529389	−0.264695	−	0.964332i	$-0.585271\pi$
$421$	−1.89993e27	−0.529389	−0.264695	+	0.964332i	$0.585271\pi$
$422$	−7.53915e27	−2.04900
$423$	0	0
$424$	−4.82214e27	−1.24709
$425$	−4.01267e27	−1.01239
$426$	0	0
$427$	−2.60714e27	−0.626141
$428$	9.77083e26	0.228966
$429$	0	0
$430$	1.46430e27	0.326748
$431$	8.08572e24	0.00176079	0.000880395	−	1.00000i	$-0.499720\pi$
$431$	8.08572e24	0.00176079	0.000880395		1.00000i	$0.499720\pi$
$432$	0	0
$433$	−5.60439e27	−1.16253	−0.581267	−	0.813713i	$-0.697443\pi$
$433$	−5.60439e27	−1.16253	−0.581267	+	0.813713i	$0.697443\pi$
$434$	2.31426e27	0.468566
$435$	0	0
$436$	1.34713e27	0.259897
$437$	−4.55272e27	−0.857463
$438$	0	0
$439$	−8.51110e27	−1.52795	−0.763973	−	0.645248i	$-0.776754\pi$
$439$	−8.51110e27	−1.52795	−0.763973	+	0.645248i	$0.776754\pi$
$440$	5.02221e26	0.0880322
$441$	0	0
$442$	2.76896e27	0.462789
$443$	6.63134e27	1.08234	0.541168	−	0.840915i	$-0.317982\pi$
$443$	6.63134e27	1.08234	0.541168	+	0.840915i	$0.317982\pi$
$444$	0	0
$445$	−9.72147e26	−0.151339
$446$	1.12956e28	1.71749
$447$	0	0
$448$	1.72103e28	2.49671
$449$	−1.30394e28	−1.84787	−0.923933	−	0.382555i	$-0.875044\pi$
$449$	−1.30394e28	−1.84787	−0.923933	+	0.382555i	$0.875044\pi$
$450$	0	0
$451$	−1.50496e27	−0.203549
$452$	2.54097e28	3.35773
$453$	0	0
$454$	6.10577e27	0.770289
$455$	−1.28070e26	−0.0157880
$456$	0	0
$457$	4.72949e27	0.556793	0.278397	−	0.960466i	$-0.410197\pi$
$457$	4.72949e27	0.556793	0.278397	+	0.960466i	$0.410197\pi$
$458$	1.04097e28	1.19771
$459$	0	0
$460$	−2.90476e27	−0.319266
$461$	−4.92722e27	−0.529349	−0.264675	−	0.964338i	$-0.585265\pi$
$461$	−4.92722e27	−0.529349	−0.264675	+	0.964338i	$0.585265\pi$
$462$	0	0
$463$	1.20207e28	1.23404	0.617021	−	0.786947i	$-0.288339\pi$
$463$	1.20207e28	1.23404	0.617021	+	0.786947i	$0.288339\pi$
$464$	−4.54513e28	−4.56150
$465$	0	0
$466$	8.27379e27	0.793693
$467$	−1.09969e28	−1.03144	−0.515719	−	0.856758i	$-0.672475\pi$
$467$	−1.09969e28	−1.03144	−0.515719	+	0.856758i	$0.672475\pi$
$468$	0	0
$469$	−5.72402e27	−0.513317
$470$	−5.88944e26	−0.0516471
$471$	0	0
$472$	−6.12910e28	−5.14051
$473$	2.41413e27	0.198024
$474$	0	0
$475$	1.36426e28	1.07057
$476$	1.86958e28	1.43507
$477$	0	0
$478$	1.36576e28	1.00318
$479$	1.32717e28	0.953684	0.476842	−	0.878989i	$-0.341781\pi$
$479$	1.32717e28	0.953684	0.476842	+	0.878989i	$0.341781\pi$
$480$	0	0
$481$	−3.48951e27	−0.240017
$482$	2.23613e28	1.50489
$483$	0	0
$484$	−4.30624e28	−2.77473
$485$	−2.95139e27	−0.186096
$486$	0	0
$487$	2.62576e28	1.58563	0.792813	−	0.609466i	$-0.208616\pi$
$487$	2.62576e28	1.58563	0.792813	+	0.609466i	$0.208616\pi$
$488$	−7.94738e28	−4.69695
$489$	0	0
$490$	3.77276e27	0.213600
$491$	2.54066e28	1.40796	0.703982	−	0.710218i	$-0.251404\pi$
$491$	2.54066e28	1.40796	0.703982	+	0.710218i	$0.251404\pi$
$492$	0	0
$493$	−2.06213e28	−1.09502
$494$	−9.41414e27	−0.489382
$495$	0	0
$496$	4.24039e28	2.11275
$497$	−9.61224e27	−0.468903
$498$	0	0
$499$	−1.30048e28	−0.608204	−0.304102	−	0.952640i	$-0.598356\pi$
$499$	−1.30048e28	−0.608204	−0.304102	+	0.952640i	$0.598356\pi$
$500$	1.75889e28	0.805479
$501$	0	0
$502$	5.67449e28	2.49194
$503$	−1.34993e27	−0.0580559	−0.0290280	−	0.999579i	$-0.509241\pi$
$503$	−1.34993e27	−0.0580559	−0.0290280	+	0.999579i	$0.509241\pi$
$504$	0	0
$505$	4.50314e26	0.0185762
$506$	−6.46525e27	−0.261219
$507$	0	0
$508$	9.96406e27	0.386249
$509$	4.04902e28	1.53749	0.768746	−	0.639554i	$-0.220881\pi$
$509$	4.04902e28	1.53749	0.768746	+	0.639554i	$0.220881\pi$
$510$	0	0
$511$	4.89416e27	0.178344
$512$	1.39939e29	4.99579
$513$	0	0
$514$	−3.79902e28	−1.30184
$515$	−6.83028e27	−0.229331
$516$	0	0
$517$	−9.70964e26	−0.0313006
$518$	−3.18083e28	−1.00479
$519$	0	0
$520$	−3.90398e27	−0.118433
$521$	−5.40378e28	−1.60658	−0.803289	−	0.595590i	$-0.796918\pi$
$521$	−5.40378e28	−1.60658	−0.803289	+	0.595590i	$0.796918\pi$
$522$	0	0
$523$	1.54066e28	0.439988	0.219994	−	0.975501i	$-0.429396\pi$
$523$	1.54066e28	0.439988	0.219994	+	0.975501i	$0.429396\pi$
$524$	−3.83833e28	−1.07439
$525$	0	0
$526$	1.65986e28	0.446398
$527$	1.92387e28	0.507182
$528$	0	0
$529$	−1.51670e28	−0.384252
$530$	3.85118e27	0.0956528
$531$	0	0
$532$	−6.35637e28	−1.51753
$533$	1.16987e28	0.273842
$534$	0	0
$535$	−5.07192e26	−0.0114145
$536$	−1.74486e29	−3.85061
$537$	0	0
$538$	−1.52238e29	−3.23080
$539$	6.21997e27	0.129451
$540$	0	0
$541$	−7.54478e28	−1.51034	−0.755171	−	0.655528i	$-0.772446\pi$
$541$	−7.54478e28	−1.51034	−0.755171	+	0.655528i	$0.772446\pi$
$542$	−2.96923e28	−0.582976
$543$	0	0
$544$	2.62981e29	4.96747
$545$	−6.99279e26	−0.0129565
$546$	0	0
$547$	7.90524e28	1.40944	0.704722	−	0.709483i	$-0.251072\pi$
$547$	7.90524e28	1.40944	0.704722	+	0.709483i	$0.251072\pi$
$548$	1.18813e29	2.07812
$549$	0	0
$550$	1.93737e28	0.326140
$551$	7.01101e28	1.15795
$552$	0	0
$553$	−6.13480e27	−0.0975408
$554$	8.95531e28	1.39710
$555$	0	0
$556$	−3.11627e28	−0.468113
$557$	−1.17729e29	−1.73541	−0.867707	−	0.497075i	$-0.834407\pi$
$557$	−1.17729e29	−1.73541	−0.867707	+	0.497075i	$0.834407\pi$
$558$	0	0
$559$	−1.87660e28	−0.266409
$560$	−2.13902e28	−0.298017
$561$	0	0
$562$	3.29582e28	0.442315
$563$	9.20807e28	1.21291	0.606457	−	0.795116i	$-0.292590\pi$
$563$	9.20807e28	1.21291	0.606457	+	0.795116i	$0.292590\pi$
$564$	0	0
$565$	−1.31899e28	−0.167391
$566$	−1.36626e29	−1.70200
$567$	0	0
$568$	−2.93011e29	−3.51744
$569$	2.71795e27	0.0320304	0.0160152	−	0.999872i	$-0.494902\pi$
$569$	2.71795e27	0.0320304	0.0160152	+	0.999872i	$0.494902\pi$
$570$	0	0
$571$	1.28086e28	0.145487	0.0727434	−	0.997351i	$-0.476825\pi$
$571$	1.28086e28	0.145487	0.0727434	+	0.997351i	$0.476825\pi$
$572$	−9.90260e27	−0.110431
$573$	0	0
$574$	1.06638e29	1.14640
$575$	−7.28307e28	−0.768780
$576$	0	0
$577$	1.49329e29	1.51984	0.759922	−	0.650015i	$-0.225237\pi$
$577$	1.49329e29	1.51984	0.759922	+	0.650015i	$0.225237\pi$
$578$	1.33261e28	0.133186
$579$	0	0
$580$	4.47322e28	0.431148
$581$	6.20116e28	0.586980
$582$	0	0
$583$	6.34926e27	0.0579700
$584$	1.49189e29	1.33783
$585$	0	0
$586$	2.26586e29	1.96023
$587$	−2.62975e28	−0.223468	−0.111734	−	0.993738i	$-0.535640\pi$
$587$	−2.62975e28	−0.223468	−0.111734	+	0.993738i	$0.535640\pi$
$588$	0	0
$589$	−6.54093e28	−0.536326
$590$	4.89498e28	0.394280
$591$	0	0
$592$	−5.82817e29	−4.53059
$593$	−1.92294e29	−1.46856	−0.734278	−	0.678849i	$-0.762479\pi$
$593$	−1.92294e29	−1.46856	−0.734278	+	0.678849i	$0.762479\pi$
$594$	0	0
$595$	−9.70478e27	−0.0715414
$596$	4.47919e29	3.24425
$597$	0	0
$598$	5.02572e28	0.351427
$599$	2.45874e29	1.68940	0.844699	−	0.535242i	$-0.179780\pi$
$599$	2.45874e29	1.68940	0.844699	+	0.535242i	$0.179780\pi$
$600$	0	0
$601$	7.47252e28	0.495776	0.247888	−	0.968789i	$-0.420264\pi$
$601$	7.47252e28	0.495776	0.247888	+	0.968789i	$0.420264\pi$
$602$	−1.71060e29	−1.11528
$603$	0	0
$604$	6.65285e29	4.18909
$605$	2.23531e28	0.138327
$606$	0	0
$607$	−1.23466e29	−0.738016	−0.369008	−	0.929426i	$-0.620302\pi$
$607$	−1.23466e29	−0.738016	−0.369008	+	0.929426i	$0.620302\pi$
$608$	−8.94104e29	−5.25291
$609$	0	0
$610$	6.34714e28	0.360259
$611$	7.54771e27	0.0421098
$612$	0	0
$613$	−1.59244e29	−0.858476	−0.429238	−	0.903191i	$-0.641218\pi$
$613$	−1.59244e29	−0.858476	−0.429238	+	0.903191i	$0.641218\pi$
$614$	4.30861e29	2.28333
$615$	0	0
$616$	−5.86694e28	−0.300479
$617$	−1.23256e29	−0.620602	−0.310301	−	0.950638i	$-0.600430\pi$
$617$	−1.23256e29	−0.620602	−0.310301	+	0.950638i	$0.600430\pi$
$618$	0	0
$619$	−5.18990e28	−0.252585	−0.126292	−	0.991993i	$-0.540308\pi$
$619$	−5.18990e28	−0.252585	−0.126292	+	0.991993i	$0.540308\pi$
$620$	−4.17330e28	−0.199695
$621$	0	0
$622$	−4.02159e29	−1.86037
$623$	1.13566e29	0.516564
$624$	0	0
$625$	2.13632e29	0.939562
$626$	1.42086e29	0.614497
$627$	0	0
$628$	2.61553e29	1.09391
$629$	−2.64425e29	−1.08760
$630$	0	0
$631$	−2.05208e28	−0.0816366	−0.0408183	−	0.999167i	$-0.512996\pi$
$631$	−2.05208e28	−0.0816366	−0.0408183	+	0.999167i	$0.512996\pi$
$632$	−1.87008e29	−0.731694
$633$	0	0
$634$	−5.16285e29	−1.95412
$635$	−5.17222e27	−0.0192554
$636$	0	0
$637$	−4.83505e28	−0.174155
$638$	9.95625e28	0.352759
$639$	0	0
$640$	−2.19303e29	−0.751890
$641$	−5.14342e29	−1.73477	−0.867386	−	0.497636i	$-0.834202\pi$
$641$	−5.14342e29	−1.73477	−0.867386	+	0.497636i	$0.834202\pi$
$642$	0	0
$643$	−8.85766e28	−0.289137	−0.144569	−	0.989495i	$-0.546179\pi$
$643$	−8.85766e28	−0.289137	−0.144569	+	0.989495i	$0.546179\pi$
$644$	3.39333e29	1.08975
$645$	0	0
$646$	−7.13376e29	−2.21757
$647$	−5.46916e29	−1.67273	−0.836364	−	0.548174i	$-0.815323\pi$
$647$	−5.46916e29	−1.67273	−0.836364	+	0.548174i	$0.815323\pi$
$648$	0	0
$649$	8.07012e28	0.238952
$650$	−1.50600e29	−0.438768
$651$	0	0
$652$	1.71145e30	4.82796
$653$	5.66153e29	1.57161	0.785806	−	0.618473i	$-0.212248\pi$
$653$	5.66153e29	1.57161	0.785806	+	0.618473i	$0.212248\pi$
$654$	0	0
$655$	1.99243e28	0.0535611
$656$	1.95391e30	5.16908
$657$	0	0
$658$	6.88003e28	0.176286
$659$	1.48653e29	0.374867	0.187434	−	0.982277i	$-0.439983\pi$
$659$	1.48653e29	0.374867	0.187434	+	0.982277i	$0.439983\pi$
$660$	0	0
$661$	−4.04669e29	−0.988517	−0.494259	−	0.869315i	$-0.664560\pi$
$661$	−4.04669e29	−0.988517	−0.494259	+	0.869315i	$0.664560\pi$
$662$	4.09792e29	0.985268
$663$	0	0
$664$	1.89031e30	4.40319
$665$	3.29951e28	0.0756524
$666$	0	0
$667$	−3.74281e29	−0.831527
$668$	−1.59935e30	−3.49776
$669$	0	0
$670$	1.39352e29	0.295344
$671$	1.04642e29	0.218334
$672$	0	0
$673$	−1.54590e29	−0.312625	−0.156313	−	0.987708i	$-0.549961\pi$
$673$	−1.54590e29	−0.312625	−0.156313	+	0.987708i	$0.549961\pi$
$674$	−1.03252e30	−2.05574
$675$	0	0
$676$	−1.40323e30	−2.70825
$677$	9.88421e29	1.87828	0.939142	−	0.343530i	$-0.111623\pi$
$677$	9.88421e29	1.87828	0.939142	+	0.343530i	$0.111623\pi$
$678$	0	0
$679$	3.44781e29	0.635200
$680$	−2.95832e29	−0.536662
$681$	0	0
$682$	−9.28870e28	−0.163388
$683$	1.41169e29	0.244524	0.122262	−	0.992498i	$-0.460985\pi$
$683$	1.41169e29	0.244524	0.122262	+	0.992498i	$0.460985\pi$
$684$	0	0
$685$	−6.16746e28	−0.103599
$686$	−1.01784e30	−1.68375
$687$	0	0
$688$	−3.13430e30	−5.02877
$689$	−4.93555e28	−0.0779891
$690$	0	0
$691$	7.11585e29	1.09070	0.545352	−	0.838207i	$-0.316396\pi$
$691$	7.11585e29	1.09070	0.545352	+	0.838207i	$0.316396\pi$
$692$	1.36896e30	2.06669
$693$	0	0
$694$	2.01817e29	0.295585
$695$	1.61762e28	0.0233365
$696$	0	0
$697$	8.86490e29	1.24088
$698$	−2.00200e30	−2.76047
$699$	0	0
$700$	−1.01684e30	−1.36058
$701$	8.80754e29	1.16096	0.580478	−	0.814276i	$-0.302866\pi$
$701$	8.80754e29	1.16096	0.580478	+	0.814276i	$0.302866\pi$
$702$	0	0
$703$	8.99015e29	1.15010
$704$	−6.90765e29	−0.870597
$705$	0	0
$706$	3.07393e29	0.376049
$707$	−5.26057e28	−0.0634058
$708$	0	0
$709$	−2.79000e29	−0.326452	−0.163226	−	0.986589i	$-0.552190\pi$
$709$	−2.79000e29	−0.326452	−0.163226	+	0.986589i	$0.552190\pi$
$710$	2.34012e29	0.269789
$711$	0	0
$712$	3.46185e30	3.87496
$713$	3.49186e29	0.385139
$714$	0	0
$715$	5.14032e27	0.00550524
$716$	7.73767e28	0.0816626
$717$	0	0
$718$	4.76349e29	0.488223
$719$	−1.21404e30	−1.22625	−0.613124	−	0.789987i	$-0.710087\pi$
$719$	−1.21404e30	−1.22625	−0.613124	+	0.789987i	$0.710087\pi$
$720$	0	0
$721$	7.97913e29	0.782772
$722$	3.94185e29	0.381118
$723$	0	0
$724$	−5.24431e30	−4.92531
$725$	1.12157e30	1.03819
$726$	0	0
$727$	−6.54831e29	−0.588868	−0.294434	−	0.955672i	$-0.595131\pi$
$727$	−6.54831e29	−0.588868	−0.294434	+	0.955672i	$0.595131\pi$
$728$	4.56062e29	0.404245
$729$	0	0
$730$	−1.19149e29	−0.102613
$731$	−1.42204e30	−1.20720
$732$	0	0
$733$	2.20665e29	0.182029	0.0910147	−	0.995850i	$-0.470989\pi$
$733$	2.20665e29	0.182029	0.0910147	+	0.995850i	$0.470989\pi$
$734$	2.79755e30	2.27493
$735$	0	0
$736$	4.77315e30	3.77214
$737$	2.29743e29	0.178992
$738$	0	0
$739$	−4.07297e29	−0.308422	−0.154211	−	0.988038i	$-0.549283\pi$
$739$	−4.07297e29	−0.308422	−0.154211	+	0.988038i	$0.549283\pi$
$740$	5.73596e29	0.428226
$741$	0	0
$742$	−4.49895e29	−0.326490
$743$	−3.97218e29	−0.284214	−0.142107	−	0.989851i	$-0.545388\pi$
$743$	−3.97218e29	−0.284214	−0.142107	+	0.989851i	$0.545388\pi$
$744$	0	0
$745$	−2.32509e29	−0.161733
$746$	2.84565e29	0.195175
$747$	0	0
$748$	−7.50390e29	−0.500403
$749$	5.92500e28	0.0389610
$750$	0	0
$751$	−1.86890e30	−1.19500	−0.597498	−	0.801871i	$-0.703838\pi$
$751$	−1.86890e30	−1.19500	−0.597498	+	0.801871i	$0.703838\pi$
$752$	1.26062e30	0.794869
$753$	0	0
$754$	−7.73941e29	−0.474579
$755$	−3.45341e29	−0.208836
$756$	0	0
$757$	−2.99103e30	−1.75919	−0.879597	−	0.475720i	$-0.842188\pi$
$757$	−2.99103e30	−1.75919	−0.879597	+	0.475720i	$0.842188\pi$
$758$	2.62759e29	0.152416
$759$	0	0
$760$	1.00579e30	0.567501
$761$	−1.51341e30	−0.842206	−0.421103	−	0.907013i	$-0.638357\pi$
$761$	−1.51341e30	−0.842206	−0.421103	+	0.907013i	$0.638357\pi$
$762$	0	0
$763$	8.16896e28	0.0442241
$764$	−8.02588e30	−4.28561
$765$	0	0
$766$	6.07697e30	3.15707
$767$	−6.27325e29	−0.321470
$768$	0	0
$769$	2.53401e30	1.26352	0.631759	−	0.775165i	$-0.282333\pi$
$769$	2.53401e30	1.26352	0.631759	+	0.775165i	$0.282333\pi$
$770$	4.68560e28	0.0230469
$771$	0	0
$772$	−1.28193e30	−0.613598
$773$	1.69545e30	0.800571	0.400285	−	0.916390i	$-0.368911\pi$
$773$	1.69545e30	0.800571	0.400285	+	0.916390i	$0.368911\pi$
$774$	0	0
$775$	−1.04637e30	−0.480857
$776$	1.05100e31	4.76490
$777$	0	0
$778$	3.57153e30	1.57604
$779$	−3.01396e30	−1.31218
$780$	0	0
$781$	3.85804e29	0.163505
$782$	3.80834e30	1.59245
$783$	0	0
$784$	−8.07548e30	−3.28738
$785$	−1.35769e29	−0.0545342
$786$	0	0
$787$	−1.87332e30	−0.732616	−0.366308	−	0.930494i	$-0.619378\pi$
$787$	−1.87332e30	−0.732616	−0.366308	+	0.930494i	$0.619378\pi$
$788$	−8.56113e30	−3.30374
$789$	0	0
$790$	1.49353e29	0.0561214
$791$	1.54084e30	0.571353
$792$	0	0
$793$	−8.13429e29	−0.293732
$794$	5.06702e30	1.80567
$795$	0	0
$796$	4.46856e30	1.55089
$797$	7.79664e29	0.267051	0.133526	−	0.991045i	$-0.457370\pi$
$797$	7.79664e29	0.267051	0.133526	+	0.991045i	$0.457370\pi$
$798$	0	0
$799$	5.71944e29	0.190815
$800$	−1.43032e31	−4.70963
$801$	0	0
$802$	−3.98676e30	−1.27876
$803$	−1.96436e29	−0.0621880
$804$	0	0
$805$	−1.76144e29	−0.0543264
$806$	7.22050e29	0.219811
$807$	0	0
$808$	−1.60358e30	−0.475633
$809$	−8.82262e29	−0.258308	−0.129154	−	0.991625i	$-0.541226\pi$
$809$	−8.82262e29	−0.258308	−0.129154	+	0.991625i	$0.541226\pi$
$810$	0	0
$811$	−2.06044e30	−0.587815	−0.293907	−	0.955834i	$-0.594956\pi$
$811$	−2.06044e30	−0.587815	−0.293907	+	0.955834i	$0.594956\pi$
$812$	−5.22561e30	−1.47163
$813$	0	0
$814$	1.27668e30	0.350369
$815$	−8.88392e29	−0.240685
$816$	0	0
$817$	4.83476e30	1.27657
$818$	6.18551e30	1.61237
$819$	0	0
$820$	−1.92299e30	−0.488576
$821$	1.83846e30	0.461160	0.230580	−	0.973053i	$-0.425938\pi$
$821$	1.83846e30	0.461160	0.230580	+	0.973053i	$0.425938\pi$
$822$	0	0
$823$	7.73766e29	0.189196	0.0945979	−	0.995516i	$-0.469843\pi$
$823$	7.73766e29	0.189196	0.0945979	+	0.995516i	$0.469843\pi$
$824$	2.43229e31	5.87190
$825$	0	0
$826$	−5.71831e30	−1.34579
$827$	4.59989e30	1.06891	0.534453	−	0.845198i	$-0.320518\pi$
$827$	4.59989e30	1.06891	0.534453	+	0.845198i	$0.320518\pi$
$828$	0	0
$829$	7.93000e30	1.79660	0.898298	−	0.439386i	$-0.144804\pi$
$829$	7.93000e30	1.79660	0.898298	+	0.439386i	$0.144804\pi$
$830$	−1.50968e30	−0.337727
$831$	0	0
$832$	5.36961e30	1.17124
$833$	−3.66386e30	−0.789162
$834$	0	0
$835$	8.30202e29	0.174372
$836$	2.55124e30	0.529158
$837$	0	0
$838$	1.72812e31	3.49551
$839$	−4.84033e30	−0.966884	−0.483442	−	0.875376i	$-0.660614\pi$
$839$	−4.84033e30	−0.966884	−0.483442	+	0.875376i	$0.660614\pi$
$840$	0	0
$841$	6.30944e29	0.122923
$842$	−5.40340e30	−1.03966
$843$	0	0
$844$	−1.58820e31	−2.98064
$845$	7.28400e29	0.135013
$846$	0	0
$847$	−2.61129e30	−0.472149
$848$	−8.24334e30	−1.47213
$849$	0	0
$850$	−1.14120e31	−1.98822
$851$	−4.79937e30	−0.825893
$852$	0	0
$853$	2.96903e30	0.498483	0.249242	−	0.968441i	$-0.419819\pi$
$853$	2.96903e30	0.498483	0.249242	+	0.968441i	$0.419819\pi$
$854$	−7.41472e30	−1.22967
$855$	0	0
$856$	1.80612e30	0.292263
$857$	3.70009e30	0.591444	0.295722	−	0.955274i	$-0.404440\pi$
$857$	3.70009e30	0.591444	0.295722	+	0.955274i	$0.404440\pi$
$858$	0	0
$859$	7.75385e29	0.120945	0.0604726	−	0.998170i	$-0.480739\pi$
$859$	7.75385e29	0.120945	0.0604726	+	0.998170i	$0.480739\pi$
$860$	3.08471e30	0.475314
$861$	0	0
$862$	2.29958e28	0.00345798
$863$	1.29544e31	1.92443	0.962217	−	0.272283i	$-0.0877786\pi$
$863$	1.29544e31	1.92443	0.962217	+	0.272283i	$0.0877786\pi$
$864$	0	0
$865$	−7.10610e29	−0.103030
$866$	−1.59389e31	−2.28307
$867$	0	0
$868$	4.87524e30	0.681615
$869$	2.46231e29	0.0340122
$870$	0	0
$871$	−1.78589e30	−0.240805
$872$	2.49015e30	0.331744
$873$	0	0
$874$	−1.29479e31	−1.68395
$875$	1.06659e30	0.137060
$876$	0	0
$877$	−1.57355e31	−1.97417	−0.987083	−	0.160207i	$-0.948784\pi$
$877$	−1.57355e31	−1.97417	−0.987083	+	0.160207i	$0.948784\pi$
$878$	−2.42056e31	−3.00070
$879$	0	0
$880$	8.58535e29	0.103918
$881$	1.47526e31	1.76450	0.882252	−	0.470778i	$-0.156027\pi$
$881$	1.47526e31	1.76450	0.882252	+	0.470778i	$0.156027\pi$
$882$	0	0
$883$	−5.64453e30	−0.659235	−0.329617	−	0.944115i	$-0.606920\pi$
$883$	−5.64453e30	−0.659235	−0.329617	+	0.944115i	$0.606920\pi$
$884$	5.83310e30	0.673210
$885$	0	0
$886$	1.88595e31	2.12558
$887$	−5.89300e30	−0.656354	−0.328177	−	0.944616i	$-0.606434\pi$
$887$	−5.89300e30	−0.656354	−0.328177	+	0.944616i	$0.606434\pi$
$888$	0	0
$889$	6.04218e29	0.0657242
$890$	−2.76479e30	−0.297212
$891$	0	0
$892$	2.37954e31	2.49840
$893$	−1.94454e30	−0.201780
$894$	0	0
$895$	−4.01653e28	−0.00407107
$896$	2.56189e31	2.56641
$897$	0	0
$898$	−3.70840e31	−3.62898
$899$	−5.37734e30	−0.520104
$900$	0	0
$901$	−3.74002e30	−0.353397
$902$	−4.28009e30	−0.399746
$903$	0	0
$904$	4.69695e31	4.28596
$905$	2.72226e30	0.245538
$906$	0	0
$907$	8.32782e30	0.733931	0.366965	−	0.930235i	$-0.380397\pi$
$907$	8.32782e30	0.733931	0.366965	+	0.930235i	$0.380397\pi$
$908$	1.28624e31	1.12053
$909$	0	0
$910$	−3.64232e29	−0.0310058
$911$	−1.08086e31	−0.909548	−0.454774	−	0.890607i	$-0.650280\pi$
$911$	−1.08086e31	−0.909548	−0.454774	+	0.890607i	$0.650280\pi$
$912$	0	0
$913$	−2.48894e30	−0.204678
$914$	1.34507e31	1.09347
$915$	0	0
$916$	2.19291e31	1.74229
$917$	−2.32755e30	−0.182819
$918$	0	0
$919$	6.55205e30	0.502996	0.251498	−	0.967858i	$-0.419077\pi$
$919$	6.55205e30	0.502996	0.251498	+	0.967858i	$0.419077\pi$
$920$	−5.36941e30	−0.407525
$921$	0	0
$922$	−1.40130e31	−1.03958
$923$	−2.99902e30	−0.219969
$924$	0	0
$925$	1.43817e31	1.03115
$926$	3.41869e31	2.42351
$927$	0	0
$928$	−7.35047e31	−5.09403
$929$	−1.04036e31	−0.712883	−0.356442	−	0.934318i	$-0.616010\pi$
$929$	−1.04036e31	−0.712883	−0.356442	+	0.934318i	$0.616010\pi$
$930$	0	0
$931$	1.24567e31	0.834509
$932$	1.74296e31	1.15457
$933$	0	0
$934$	−3.12752e31	−2.02562
$935$	3.89518e29	0.0249463
$936$	0	0
$937$	−2.09831e31	−1.31402	−0.657012	−	0.753880i	$-0.728180\pi$
$937$	−2.09831e31	−1.31402	−0.657012	+	0.753880i	$0.728180\pi$
$938$	−1.62791e31	−1.00809
$939$	0	0
$940$	−1.24067e30	−0.0751302
$941$	−2.20967e31	−1.32323	−0.661617	−	0.749842i	$-0.730130\pi$
$941$	−2.20967e31	−1.32323	−0.661617	+	0.749842i	$0.730130\pi$
$942$	0	0
$943$	1.60900e31	0.942286
$944$	−1.04776e32	−6.06812
$945$	0	0
$946$	6.86578e30	0.388896
$947$	2.59604e31	1.45424	0.727121	−	0.686509i	$-0.240858\pi$
$947$	2.59604e31	1.45424	0.727121	+	0.686509i	$0.240858\pi$
$948$	0	0
$949$	1.52698e30	0.0836637
$950$	3.87996e31	2.10247
$951$	0	0
$952$	3.45590e31	1.83178
$953$	2.94729e31	1.54507	0.772535	−	0.634973i	$-0.218989\pi$
$953$	2.94729e31	1.54507	0.772535	+	0.634973i	$0.218989\pi$
$954$	0	0
$955$	4.16613e30	0.213648
$956$	2.87711e31	1.45931
$957$	0	0
$958$	3.77448e31	1.87292
$959$	7.20482e30	0.353612
$960$	0	0
$961$	−1.58087e31	−0.759103
$962$	−9.92417e30	−0.471364
$963$	0	0
$964$	4.71064e31	2.18913
$965$	6.65436e29	0.0305893
$966$	0	0
$967$	6.98077e30	0.313997	0.156998	−	0.987599i	$-0.449818\pi$
$967$	6.98077e30	0.313997	0.156998	+	0.987599i	$0.449818\pi$
$968$	−7.96002e31	−3.54179
$969$	0	0
$970$	−8.39375e30	−0.365471
$971$	1.30234e30	0.0560946	0.0280473	−	0.999607i	$-0.491071\pi$
$971$	1.30234e30	0.0560946	0.0280473	+	0.999607i	$0.491071\pi$
$972$	0	0
$973$	−1.88970e30	−0.0796541
$974$	7.46765e31	3.11398
$975$	0	0
$976$	−1.35859e32	−5.54452
$977$	−3.06599e31	−1.23788	−0.618939	−	0.785439i	$-0.712437\pi$
$977$	−3.06599e31	−1.23788	−0.618939	+	0.785439i	$0.712437\pi$
$978$	0	0
$979$	−4.55817e30	−0.180124
$980$	7.94771e30	0.310719
$981$	0	0
$982$	7.22564e31	2.76507
$983$	−8.31325e30	−0.314745	−0.157373	−	0.987539i	$-0.550302\pi$
$983$	−8.31325e30	−0.314745	−0.157373	+	0.987539i	$0.550302\pi$
$984$	0	0
$985$	4.44398e30	0.164699
$986$	−5.86470e31	−2.15049
$987$	0	0
$988$	−1.98319e31	−0.711895
$989$	−2.58102e31	−0.916708
$990$	0	0
$991$	−1.32568e31	−0.460962	−0.230481	−	0.973077i	$-0.574030\pi$
$991$	−1.32568e31	−0.460962	−0.230481	+	0.973077i	$0.574030\pi$
$992$	6.85764e31	2.35940
$993$	0	0
$994$	−2.73372e31	−0.920868
$995$	−2.31958e30	−0.0773154
$996$	0	0
$997$	3.42048e31	1.11632	0.558159	−	0.829734i	$-0.311508\pi$
$997$	3.42048e31	1.11632	0.558159	+	0.829734i	$0.311508\pi$
$998$	−3.69857e31	−1.19444
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.22.a.d.1.1		1
3.2	odd	2		3.22.a.a.1.1	✓	1
12.11	even	2		48.22.a.e.1.1		1
15.2	even	4		75.22.b.a.49.1		2
15.8	even	4		75.22.b.a.49.2		2
15.14	odd	2		75.22.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.a.1.1	✓	1	3.2	odd	2
9.22.a.d.1.1		1	1.1	even	1	trivial
48.22.a.e.1.1		1	12.11	even	2
75.22.a.c.1.1		1	15.14	odd	2
75.22.b.a.49.1		2	15.2	even	4
75.22.b.a.49.2		2	15.8	even	4

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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