LMFDB - Embedded newform 162.7.b.a.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(161,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.161");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			161.3
Root			$1.93185i$ of defining polynomial
Character	$\chi$	$=$	162.161
Dual form			162.7.b.a.161.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.65685i q^{2} -32.0000 q^{4} -208.528i q^{5} +4.19615 q^{7} -181.019i q^{8} +O(q^{10})$	\(q+5.65685i q^{2} -32.0000 q^{4} -208.528i q^{5} +4.19615 q^{7} -181.019i q^{8} +1179.62 q^{10} +2261.95i q^{11} +2840.01 q^{13} +23.7370i q^{14} +1024.00 q^{16} -1965.86i q^{17} -281.295 q^{19} +6672.91i q^{20} -12795.5 q^{22} -16744.3i q^{23} -27859.1 q^{25} +16065.5i q^{26} -134.277 q^{28} -37114.1i q^{29} -24708.3 q^{31} +5792.62i q^{32} +11120.6 q^{34} -875.017i q^{35} -17016.7 q^{37} -1591.25i q^{38} -37747.7 q^{40} -116236. i q^{41} -30662.9 q^{43} -72382.5i q^{44} +94720.0 q^{46} +77666.6i q^{47} -117631. q^{49} -157595. i q^{50} -90880.2 q^{52} -138657. i q^{53} +471682. q^{55} -759.585i q^{56} +209949. q^{58} +152958. i q^{59} -16138.1 q^{61} -139771. i q^{62} -32768.0 q^{64} -592222. i q^{65} -474667. q^{67} +62907.4i q^{68} +4949.85 q^{70} +150338. i q^{71} +331690. q^{73} -96261.2i q^{74} +9001.45 q^{76} +9491.50i q^{77} -896112. q^{79} -213533. i q^{80} +657529. q^{82} -945090. i q^{83} -409937. q^{85} -173455. i q^{86} +409457. q^{88} -790302. i q^{89} +11917.1 q^{91} +535817. i q^{92} -439349. q^{94} +58658.1i q^{95} +1.39268e6 q^{97} -665424. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 128 q^{4} - 4 q^{7}+O(q^{10}) $ 4 * q - 128 * q^4 - 4 * q^7	$ 4 q - 128 q^{4} - 4 q^{7} + 2640 q^{10} + 3836 q^{13} + 4096 q^{16} + 10244 q^{19} - 27072 q^{22} - 25700 q^{25} + 128 q^{28} - 40096 q^{31} + 60528 q^{34} - 20200 q^{37} - 84480 q^{40} + 184940 q^{43} + 162720 q^{46} - 470484 q^{49} - 122752 q^{52} + 949860 q^{55} + 24624 q^{58} + 609056 q^{61} - 131072 q^{64} - 2008972 q^{67} + 8160 q^{70} + 525824 q^{73} - 327808 q^{76} - 848716 q^{79} + 705792 q^{82} - 987840 q^{85} + 866304 q^{88} + 35260 q^{91} - 1965408 q^{94} + 3621728 q^{97}+O(q^{100}) $ 4 * q - 128 * q^4 - 4 * q^7 + 2640 * q^10 + 3836 * q^13 + 4096 * q^16 + 10244 * q^19 - 27072 * q^22 - 25700 * q^25 + 128 * q^28 - 40096 * q^31 + 60528 * q^34 - 20200 * q^37 - 84480 * q^40 + 184940 * q^43 + 162720 * q^46 - 470484 * q^49 - 122752 * q^52 + 949860 * q^55 + 24624 * q^58 + 609056 * q^61 - 131072 * q^64 - 2008972 * q^67 + 8160 * q^70 + 525824 * q^73 - 327808 * q^76 - 848716 * q^79 + 705792 * q^82 - 987840 * q^85 + 866304 * q^88 + 35260 * q^91 - 1965408 * q^94 + 3621728 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$-1$

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 $

$2$	5.65685i	0.707107i
$2$	5.65685i	0.707107i
$3$	0	0
$3$	0	0
$4$	−32.0000	−0.500000
$5$	− 208.528i	− 1.66823i	−0.551592	−	0.834114i	$-0.685980\pi$
$5$	− 208.528i	− 1.66823i	0.551592	−	0.834114i	$-0.314020\pi$
$6$	0	0
$7$	4.19615	0.0122337	0.00611684	−	0.999981i	$-0.498053\pi$
$7$	4.19615	0.0122337	0.00611684	+	0.999981i	$0.498053\pi$
$8$	− 181.019i	− 0.353553i
$9$	0	0
$10$	1179.62	1.17962
$11$	2261.95i	1.69944i	0.527235	+	0.849719i	$0.323229\pi$
$11$	2261.95i	1.69944i	−0.527235	+	0.849719i	$0.676771\pi$
$12$	0	0
$13$	2840.01	1.29268	0.646338	−	0.763052i	$-0.276300\pi$
$13$	2840.01	1.29268	0.646338	+	0.763052i	$0.276300\pi$
$14$	23.7370i	0.00865052i
$15$	0	0
$16$	1024.00	0.250000
$17$	− 1965.86i	− 0.400134i	−0.979782	−	0.200067i	$-0.935884\pi$
$17$	− 1965.86i	− 0.400134i	0.979782	−	0.200067i	$-0.0641160\pi$
$18$	0	0
$19$	−281.295	−0.0410111	−0.0205056	−	0.999790i	$-0.506528\pi$
$19$	−281.295	−0.0410111	−0.0205056	+	0.999790i	$0.506528\pi$
$20$	6672.91i	0.834114i
$21$	0	0
$22$	−12795.5	−1.20168
$23$	− 16744.3i	− 1.37620i	−0.725614	−	0.688102i	$-0.758444\pi$
$23$	− 16744.3i	− 1.37620i	0.725614	−	0.688102i	$-0.241556\pi$
$24$	0	0
$25$	−27859.1	−1.78298
$26$	16065.5i	0.914059i
$27$	0	0
$28$	−134.277	−0.00611684
$29$	− 37114.1i	− 1.52176i	−0.648895	−	0.760878i	$-0.724769\pi$
$29$	− 37114.1i	− 1.52176i	0.648895	−	0.760878i	$-0.275231\pi$
$30$	0	0
$31$	−24708.3	−0.829389	−0.414694	−	0.909961i	$-0.636112\pi$
$31$	−24708.3	−0.829389	−0.414694	+	0.909961i	$0.636112\pi$
$32$	5792.62i	0.176777i
$33$	0	0
$34$	11120.6	0.282937
$35$	− 875.017i	− 0.0204086i
$36$	0	0
$37$	−17016.7	−0.335947	−0.167974	−	0.985791i	$-0.553722\pi$
$37$	−17016.7	−0.335947	−0.167974	+	0.985791i	$0.553722\pi$
$38$	− 1591.25i	− 0.0289993i
$39$	0	0
$40$	−37747.7	−0.589808
$41$	− 116236.i	− 1.68651i	−0.537516	−	0.843253i	$-0.680637\pi$
$41$	− 116236.i	− 1.68651i	0.537516	−	0.843253i	$-0.319363\pi$
$42$	0	0
$43$	−30662.9	−0.385662	−0.192831	−	0.981232i	$-0.561767\pi$
$43$	−30662.9	−0.385662	−0.192831	+	0.981232i	$0.561767\pi$
$44$	− 72382.5i	− 0.849719i
$45$	0	0
$46$	94720.0	0.973124
$47$	77666.6i	0.748068i	0.927415	+	0.374034i	$0.122026\pi$
$47$	77666.6i	0.748068i	−0.927415	+	0.374034i	$0.877974\pi$
$48$	0	0
$49$	−117631.	−0.999850
$50$	− 157595.i	− 1.26076i
$51$	0	0
$52$	−90880.2	−0.646338
$53$	− 138657.i	− 0.931354i	−0.884955	−	0.465677i	$-0.845811\pi$
$53$	− 138657.i	− 0.931354i	0.884955	−	0.465677i	$-0.154189\pi$
$54$	0	0
$55$	471682.	2.83505
$56$	− 759.585i	− 0.00432526i
$57$	0	0
$58$	209949.	1.07604
$59$	152958.i	0.744758i	0.928081	+	0.372379i	$0.121458\pi$
$59$	152958.i	0.744758i	−0.928081	+	0.372379i	$0.878542\pi$
$60$	0	0
$61$	−16138.1	−0.0710989	−0.0355495	−	0.999368i	$-0.511318\pi$
$61$	−16138.1	−0.0710989	−0.0355495	+	0.999368i	$0.511318\pi$
$62$	− 139771.i	− 0.586467i
$63$	0	0
$64$	−32768.0	−0.125000
$65$	− 592222.i	− 2.15648i
$66$	0	0
$67$	−474667.	−1.57821	−0.789105	−	0.614259i	$-0.789455\pi$
$67$	−474667.	−1.57821	−0.789105	+	0.614259i	$0.789455\pi$
$68$	62907.4i	0.200067i
$69$	0	0
$70$	4949.85	0.0144310
$71$	150338.i	0.420043i	0.977697	+	0.210021i	$0.0673534\pi$
$71$	150338.i	0.420043i	−0.977697	+	0.210021i	$0.932647\pi$
$72$	0	0
$73$	331690.	0.852636	0.426318	−	0.904573i	$-0.359811\pi$
$73$	331690.	0.852636	0.426318	+	0.904573i	$0.359811\pi$
$74$	− 96261.2i	− 0.237551i
$75$	0	0
$76$	9001.45	0.0205056
$77$	9491.50i	0.0207904i
$78$	0	0
$79$	−896112.	−1.81753	−0.908764	−	0.417310i	$-0.862973\pi$
$79$	−896112.	−1.81753	−0.908764	+	0.417310i	$0.862973\pi$
$80$	− 213533.i	− 0.417057i
$81$	0	0
$82$	657529.	1.19254
$83$	− 945090.i	− 1.65287i	−0.563032	−	0.826435i	$-0.690365\pi$
$83$	− 945090.i	− 1.65287i	0.563032	−	0.826435i	$-0.309635\pi$
$84$	0	0
$85$	−409937.	−0.667514
$86$	− 173455.i	− 0.272704i
$87$	0	0
$88$	409457.	0.600842
$89$	− 790302.i	− 1.12105i	−0.828139	−	0.560523i	$-0.810600\pi$
$89$	− 790302.i	− 1.12105i	0.828139	−	0.560523i	$-0.189400\pi$
$90$	0	0
$91$	11917.1	0.0158142
$92$	535817.i	0.688102i
$93$	0	0
$94$	−439349.	−0.528964
$95$	58658.1i	0.0684159i
$96$	0	0
$97$	1.39268e6	1.52593	0.762965	−	0.646440i	$-0.223743\pi$
$97$	1.39268e6	1.52593	0.762965	+	0.646440i	$0.223743\pi$
$98$	− 665424.i	− 0.707001i
$99$	0	0
$100$	891492.	0.891492
$101$	− 131552.i	− 0.127683i	−0.997960	−	0.0638414i	$-0.979665\pi$
$101$	− 131552.i	− 0.127683i	0.997960	−	0.0638414i	$-0.0203352\pi$
$102$	0	0
$103$	1.93461e6	1.77044	0.885221	−	0.465171i	$-0.154007\pi$
$103$	1.93461e6	1.77044	0.885221	+	0.465171i	$0.154007\pi$
$104$	− 514096.i	− 0.457030i
$105$	0	0
$106$	784364.	0.658567
$107$	621916.i	0.507669i	0.967248	+	0.253834i	$0.0816918\pi$
$107$	621916.i	0.507669i	−0.967248	+	0.253834i	$0.918308\pi$
$108$	0	0
$109$	−1.34578e6	−1.03919	−0.519594	−	0.854413i	$-0.673917\pi$
$109$	−1.34578e6	−1.03919	−0.519594	+	0.854413i	$0.673917\pi$
$110$	2.66823e6i	2.00468i
$111$	0	0
$112$	4296.86	0.00305842
$113$	− 1.23932e6i	− 0.858914i	−0.903087	−	0.429457i	$-0.858705\pi$
$113$	− 1.23932e6i	− 0.858914i	0.903087	−	0.429457i	$-0.141295\pi$
$114$	0	0
$115$	−3.49166e6	−2.29582
$116$	1.18765e6i	0.760878i
$117$	0	0
$118$	−865259.	−0.526623
$119$	− 8249.04i	− 0.00489511i
$120$	0	0
$121$	−3.34487e6	−1.88809
$122$	− 91290.9i	− 0.0502745i
$123$	0	0
$124$	790666.	0.414694
$125$	2.55116e6i	1.30620i
$126$	0	0
$127$	−1.65297e6	−0.806962	−0.403481	−	0.914988i	$-0.632200\pi$
$127$	−1.65297e6	−0.806962	−0.403481	+	0.914988i	$0.632200\pi$
$128$	− 185364.i	− 0.0883883i
$129$	0	0
$130$	3.35012e6	1.52486
$131$	2.66126e6i	1.18379i	0.806017	+	0.591893i	$0.201619\pi$
$131$	2.66126e6i	1.18379i	−0.806017	+	0.591893i	$0.798381\pi$
$132$	0	0
$133$	−1180.36	−0.000501717 0
$134$	− 2.68512e6i	− 1.11596i
$135$	0	0
$136$	−355858.	−0.141469
$137$	− 2.61015e6i	− 1.01509i	−0.861626	−	0.507544i	$-0.830553\pi$
$137$	− 2.61015e6i	− 1.01509i	0.861626	−	0.507544i	$-0.169447\pi$
$138$	0	0
$139$	−701321.	−0.261139	−0.130570	−	0.991439i	$-0.541681\pi$
$139$	−701321.	−0.261139	−0.130570	+	0.991439i	$0.541681\pi$
$140$	28000.6i	0.0102043i
$141$	0	0
$142$	−850440.	−0.297015
$143$	6.42396e6i	2.19682i
$144$	0	0
$145$	−7.73935e6	−2.53864
$146$	1.87632e6i	0.602904i
$147$	0	0
$148$	544536.	0.167974
$149$	4.73344e6i	1.43093i	0.698650	+	0.715464i	$0.253785\pi$
$149$	4.73344e6i	1.43093i	−0.698650	+	0.715464i	$0.746215\pi$
$150$	0	0
$151$	3.73729e6	1.08549	0.542746	−	0.839897i	$-0.317385\pi$
$151$	3.73729e6	1.08549	0.542746	+	0.839897i	$0.317385\pi$
$152$	50919.9i	0.0144996i
$153$	0	0
$154$	−53692.0	−0.0147010
$155$	5.15239e6i	1.38361i
$156$	0	0
$157$	3.20662e6	0.828607	0.414303	−	0.910139i	$-0.364025\pi$
$157$	3.20662e6	0.828607	0.414303	+	0.910139i	$0.364025\pi$
$158$	− 5.06918e6i	− 1.28519i
$159$	0	0
$160$	1.20793e6	0.294904
$161$	− 70261.6i	− 0.0168361i
$162$	0	0
$163$	−964418.	−0.222691	−0.111345	−	0.993782i	$-0.535516\pi$
$163$	−964418.	−0.222691	−0.111345	+	0.993782i	$0.535516\pi$
$164$	3.71954e6i	0.843253i
$165$	0	0
$166$	5.34624e6	1.16876
$167$	1.03499e6i	0.222222i	0.993808	+	0.111111i	$0.0354410\pi$
$167$	1.03499e6i	0.222222i	−0.993808	+	0.111111i	$0.964559\pi$
$168$	0	0
$169$	3.23883e6	0.671009
$170$	− 2.31896e6i	− 0.472004i
$171$	0	0
$172$	981212.	0.192831
$173$	− 648596.i	− 0.125267i	−0.998037	−	0.0626334i	$-0.980050\pi$
$173$	− 648596.i	− 0.125267i	0.998037	−	0.0626334i	$-0.0199499\pi$
$174$	0	0
$175$	−116901.	−0.0218125
$176$	2.31624e6i	0.424860i
$177$	0	0
$178$	4.47063e6	0.792699
$179$	− 4.65189e6i	− 0.811092i	−0.914075	−	0.405546i	$-0.867081\pi$
$179$	− 4.65189e6i	− 0.811092i	0.914075	−	0.405546i	$-0.132919\pi$
$180$	0	0
$181$	3.43720e6	0.579654	0.289827	−	0.957079i	$-0.406402\pi$
$181$	3.43720e6	0.579654	0.289827	+	0.957079i	$0.406402\pi$
$182$	67413.3i	0.0111823i
$183$	0	0
$184$	−3.03104e6	−0.486562
$185$	3.54847e6i	0.560437i
$186$	0	0
$187$	4.44668e6	0.680003
$188$	− 2.48533e6i	− 0.374034i
$189$	0	0
$190$	−331820.	−0.0483774
$191$	− 1.17509e7i	− 1.68644i	−0.537565	−	0.843222i	$-0.680656\pi$
$191$	− 1.17509e7i	− 1.68644i	0.537565	−	0.843222i	$-0.319344\pi$
$192$	0	0
$193$	6.95599e6	0.967581	0.483790	−	0.875184i	$-0.339260\pi$
$193$	6.95599e6	0.967581	0.483790	+	0.875184i	$0.339260\pi$
$194$	7.87816e6i	1.07900i
$195$	0	0
$196$	3.76420e6	0.499925
$197$	− 409645.i	− 0.0535807i	−0.999641	−	0.0267904i	$-0.991471\pi$
$197$	− 409645.i	− 0.0535807i	0.999641	−	0.0267904i	$-0.00852866\pi$
$198$	0	0
$199$	−3.24847e6	−0.412212	−0.206106	−	0.978530i	$-0.566079\pi$
$199$	−3.24847e6	−0.412212	−0.206106	+	0.978530i	$0.566079\pi$
$200$	5.04304e6i	0.630380i
$201$	0	0
$202$	744169.	0.0902854
$203$	− 155736.i	− 0.0186167i
$204$	0	0
$205$	−2.42385e7	−2.81348
$206$	1.09438e7i	1.25189i
$207$	0	0
$208$	2.90817e6	0.323169
$209$	− 636277.i	− 0.0696959i
$210$	0	0
$211$	−4.99487e6	−0.531712	−0.265856	−	0.964013i	$-0.585655\pi$
$211$	−4.99487e6	−0.531712	−0.265856	+	0.964013i	$0.585655\pi$
$212$	4.43703e6i	0.465677i
$213$	0	0
$214$	−3.51809e6	−0.358976
$215$	6.39408e6i	0.643373i
$216$	0	0
$217$	−103680.	−0.0101465
$218$	− 7.61287e6i	− 0.734817i
$219$	0	0
$220$	−1.50938e7	−1.41753
$221$	− 5.58305e6i	− 0.517243i
$222$	0	0
$223$	5.68924e6	0.513027	0.256513	−	0.966541i	$-0.417426\pi$
$223$	5.68924e6	0.513027	0.256513	+	0.966541i	$0.417426\pi$
$224$	24306.7i	0.00216263i
$225$	0	0
$226$	7.01068e6	0.607344
$227$	− 1.16064e7i	− 0.992246i	−0.868252	−	0.496123i	$-0.834757\pi$
$227$	− 1.16064e7i	− 0.992246i	0.868252	−	0.496123i	$-0.165243\pi$
$228$	0	0
$229$	−3.45690e6	−0.287859	−0.143930	−	0.989588i	$-0.545974\pi$
$229$	−3.45690e6	−0.287859	−0.143930	+	0.989588i	$0.545974\pi$
$230$	− 1.97518e7i	− 1.62339i
$231$	0	0
$232$	−6.71837e6	−0.538022
$233$	− 1.27739e7i	− 1.00985i	−0.863164	−	0.504924i	$-0.831520\pi$
$233$	− 1.27739e7i	− 1.00985i	0.863164	−	0.504924i	$-0.168480\pi$
$234$	0	0
$235$	1.61957e7	1.24795
$236$	− 4.89464e6i	− 0.372379i
$237$	0	0
$238$	46663.6	0.00346137
$239$	− 1.29231e7i	− 0.946617i	−0.880897	−	0.473309i	$-0.843060\pi$
$239$	− 1.29231e7i	− 0.946617i	0.880897	−	0.473309i	$-0.156940\pi$
$240$	0	0
$241$	7.28032e6	0.520115	0.260057	−	0.965593i	$-0.416259\pi$
$241$	7.28032e6	0.520115	0.260057	+	0.965593i	$0.416259\pi$
$242$	− 1.89214e7i	− 1.33508i
$243$	0	0
$244$	516419.	0.0355495
$245$	2.45295e7i	1.66798i
$246$	0	0
$247$	−798881.	−0.0530141
$248$	4.47268e6i	0.293233i
$249$	0	0
$250$	−1.44316e7	−0.923620
$251$	− 1.71927e7i	− 1.08723i	−0.839334	−	0.543616i	$-0.817055\pi$
$251$	− 1.71927e7i	− 1.08723i	0.839334	−	0.543616i	$-0.182945\pi$
$252$	0	0
$253$	3.78748e7	2.33878
$254$	− 9.35059e6i	− 0.570608i
$255$	0	0
$256$	1.04858e6	0.0625000
$257$	− 8.01111e6i	− 0.471947i	−0.971759	−	0.235974i	$-0.924172\pi$
$257$	− 8.01111e6i	− 0.471947i	0.971759	−	0.235974i	$-0.0758279\pi$
$258$	0	0
$259$	−71404.8	−0.00410987
$260$	1.89511e7i	1.07824i
$261$	0	0
$262$	−1.50543e7	−0.837062
$263$	1.68209e7i	0.924661i	0.886708	+	0.462331i	$0.152987\pi$
$263$	1.68209e7i	0.924661i	−0.886708	+	0.462331i	$0.847013\pi$
$264$	0	0
$265$	−2.89140e7	−1.55371
$266$	− 6677.11i	0 0.000354768i
$267$	0	0
$268$	1.51893e7	0.789105
$269$	− 3.33514e6i	− 0.171339i	−0.996324	−	0.0856697i	$-0.972697\pi$
$269$	− 3.33514e6i	− 0.171339i	0.996324	−	0.0856697i	$-0.0273030\pi$
$270$	0	0
$271$	−1.47048e7	−0.738840	−0.369420	−	0.929263i	$-0.620444\pi$
$271$	−1.47048e7	−0.738840	−0.369420	+	0.929263i	$0.620444\pi$
$272$	− 2.01304e6i	− 0.100033i
$273$	0	0
$274$	1.47652e7	0.717776
$275$	− 6.30160e7i	− 3.03007i
$276$	0	0
$277$	−1.09201e7	−0.513790	−0.256895	−	0.966439i	$-0.582699\pi$
$277$	−1.09201e7	−0.513790	−0.256895	+	0.966439i	$0.582699\pi$
$278$	− 3.96727e6i	− 0.184653i
$279$	0	0
$280$	−158395.	−0.00721552
$281$	1.86747e7i	0.841654i	0.907141	+	0.420827i	$0.138260\pi$
$281$	1.86747e7i	0.841654i	−0.907141	+	0.420827i	$0.861740\pi$
$282$	0	0
$283$	−1.46255e7	−0.645284	−0.322642	−	0.946521i	$-0.604571\pi$
$283$	−1.46255e7	−0.645284	−0.322642	+	0.946521i	$0.604571\pi$
$284$	− 4.81081e6i	− 0.210021i
$285$	0	0
$286$	−3.63394e7	−1.55339
$287$	− 487743.i	− 0.0206322i
$288$	0	0
$289$	2.02730e7	0.839893
$290$	− 4.37804e7i	− 1.79509i
$291$	0	0
$292$	−1.06141e7	−0.426318
$293$	4.78429e7i	1.90202i	0.309162	+	0.951010i	$0.399952\pi$
$293$	4.78429e7i	1.90202i	−0.309162	+	0.951010i	$0.600048\pi$
$294$	0	0
$295$	3.18960e7	1.24243
$296$	3.08036e6i	0.118775i
$297$	0	0
$298$	−2.67764e7	−1.01182
$299$	− 4.75539e7i	− 1.77899i
$300$	0	0
$301$	−128666.	−0.00471807
$302$	2.11413e7i	0.767558i
$303$	0	0
$304$	−288046.	−0.0102528
$305$	3.36525e6i	0.118609i
$306$	0	0
$307$	4.24782e7	1.46808	0.734042	−	0.679104i	$-0.237631\pi$
$307$	4.24782e7	1.46808	0.734042	+	0.679104i	$0.237631\pi$
$308$	− 303728.i	− 0.0103952i
$309$	0	0
$310$	−2.91463e7	−0.978360
$311$	3.09996e7i	1.03056i	0.857021	+	0.515282i	$0.172313\pi$
$311$	3.09996e7i	1.03056i	−0.857021	+	0.515282i	$0.827687\pi$
$312$	0	0
$313$	−2.97828e7	−0.971254	−0.485627	−	0.874166i	$-0.661409\pi$
$313$	−2.97828e7	−0.971254	−0.485627	+	0.874166i	$0.661409\pi$
$314$	1.81394e7i	0.585913i
$315$	0	0
$316$	2.86756e7	0.908764
$317$	− 2.17911e6i	− 0.0684072i	−0.999415	−	0.0342036i	$-0.989111\pi$
$317$	− 2.17911e6i	− 0.0684072i	0.999415	−	0.0342036i	$-0.0108895\pi$
$318$	0	0
$319$	8.39504e7	2.58613
$320$	6.83306e6i	0.208528i
$321$	0	0
$322$	397459.	0.0119049
$323$	552987.i	0.0164099i
$324$	0	0
$325$	−7.91201e7	−2.30482
$326$	− 5.45557e6i	− 0.157466i
$327$	0	0
$328$	−2.10409e7	−0.596270
$329$	325901.i	0.00915162i
$330$	0	0
$331$	1.33671e7	0.368598	0.184299	−	0.982870i	$-0.440999\pi$
$331$	1.33671e7	0.368598	0.184299	+	0.982870i	$0.440999\pi$
$332$	3.02429e7i	0.826435i
$333$	0	0
$334$	−5.85480e6	−0.157135
$335$	9.89816e7i	2.63281i
$336$	0	0
$337$	4.45488e7	1.16398	0.581991	−	0.813195i	$-0.302274\pi$
$337$	4.45488e7	1.16398	0.581991	+	0.813195i	$0.302274\pi$
$338$	1.83216e7i	0.474475i
$339$	0	0
$340$	1.31180e7	0.333757
$341$	− 5.58891e7i	− 1.40950i
$342$	0	0
$343$	−987272.	−0.0244655
$344$	5.55057e6i	0.136352i
$345$	0	0
$346$	3.66902e6	0.0885771
$347$	2.08986e7i	0.500182i	0.968222	+	0.250091i	$0.0804605\pi$
$347$	2.08986e7i	0.500182i	−0.968222	+	0.250091i	$0.919540\pi$
$348$	0	0
$349$	6.45154e7	1.51770	0.758852	−	0.651263i	$-0.225761\pi$
$349$	6.45154e7	1.51770	0.758852	+	0.651263i	$0.225761\pi$
$350$	− 661293.i	− 0.0154237i
$351$	0	0
$352$	−1.31026e7	−0.300421
$353$	4.20921e6i	0.0956923i	0.998855	+	0.0478461i	$0.0152357\pi$
$353$	4.20921e6i	0.0956923i	−0.998855	+	0.0478461i	$0.984764\pi$
$354$	0	0
$355$	3.13497e7	0.700727
$356$	2.52897e7i	0.560523i
$357$	0	0
$358$	2.63151e7	0.573529
$359$	5.61320e7i	1.21319i	0.795012	+	0.606593i	$0.207464\pi$
$359$	5.61320e7i	1.21319i	−0.795012	+	0.606593i	$0.792536\pi$
$360$	0	0
$361$	−4.69668e7	−0.998318
$362$	1.94437e7i	0.409877i
$363$	0	0
$364$	−381347.	−0.00790709
$365$	− 6.91668e7i	− 1.42239i
$366$	0	0
$367$	3.35103e7	0.677922	0.338961	−	0.940800i	$-0.389925\pi$
$367$	3.35103e7	0.677922	0.338961	+	0.940800i	$0.389925\pi$
$368$	− 1.71461e7i	− 0.344051i
$369$	0	0
$370$	−2.00732e7	−0.396289
$371$	− 581827.i	− 0.0113939i
$372$	0	0
$373$	2.22777e7	0.429283	0.214642	−	0.976693i	$-0.431142\pi$
$373$	2.22777e7	0.429283	0.214642	+	0.976693i	$0.431142\pi$
$374$	2.51542e7i	0.480835i
$375$	0	0
$376$	1.40592e7	0.264482
$377$	− 1.05404e8i	− 1.96714i
$378$	0	0
$379$	7.72205e7	1.41845	0.709226	−	0.704981i	$-0.249044\pi$
$379$	7.72205e7	1.41845	0.709226	+	0.704981i	$0.249044\pi$
$380$	− 1.87706e6i	− 0.0342080i
$381$	0	0
$382$	6.64733e7	1.19250
$383$	3.32594e7i	0.591996i	0.955189	+	0.295998i	$0.0956521\pi$
$383$	3.32594e7i	0.591996i	−0.955189	+	0.295998i	$0.904348\pi$
$384$	0	0
$385$	1.97925e6	0.0346831
$386$	3.93490e7i	0.684183i
$387$	0	0
$388$	−4.45656e7	−0.762965
$389$	1.50959e7i	0.256454i	0.991745	+	0.128227i	$0.0409286\pi$
$389$	1.50959e7i	0.256454i	−0.991745	+	0.128227i	$0.959071\pi$
$390$	0	0
$391$	−3.29169e7	−0.550666
$392$	2.12936e7i	0.353500i
$393$	0	0
$394$	2.31730e6	0.0378873
$395$	1.86865e8i	3.03205i
$396$	0	0
$397$	−8.91350e7	−1.42455	−0.712273	−	0.701902i	$-0.752334\pi$
$397$	−8.91350e7	−1.42455	−0.712273	+	0.701902i	$0.752334\pi$
$398$	− 1.83761e7i	− 0.291478i
$399$	0	0
$400$	−2.85277e7	−0.445746
$401$	1.12043e8i	1.73761i	0.495158	+	0.868803i	$0.335110\pi$
$401$	1.12043e8i	1.73761i	−0.495158	+	0.868803i	$0.664890\pi$
$402$	0	0
$403$	−7.01718e7	−1.07213
$404$	4.20966e6i	0.0638414i
$405$	0	0
$406$	880978.	0.0131640
$407$	− 3.84911e7i	− 0.570922i
$408$	0	0
$409$	−6.67941e7	−0.976266	−0.488133	−	0.872769i	$-0.662322\pi$
$409$	−6.67941e7	−0.976266	−0.488133	+	0.872769i	$0.662322\pi$
$410$	− 1.37113e8i	− 1.98943i
$411$	0	0
$412$	−6.19075e7	−0.885221
$413$	641833.i	0.00911113i
$414$	0	0
$415$	−1.97078e8	−2.75736
$416$	1.64511e7i	0.228515i
$417$	0	0
$418$	3.59933e6	0.0492824
$419$	− 4.73571e7i	− 0.643789i	−0.946776	−	0.321894i	$-0.895680\pi$
$419$	− 4.73571e7i	− 0.643789i	0.946776	−	0.321894i	$-0.104320\pi$
$420$	0	0
$421$	6.61569e7	0.886602	0.443301	−	0.896373i	$-0.353807\pi$
$421$	6.61569e7	0.886602	0.443301	+	0.896373i	$0.353807\pi$
$422$	− 2.82552e7i	− 0.375977i
$423$	0	0
$424$	−2.50996e7	−0.329283
$425$	5.47671e7i	0.713432i
$426$	0	0
$427$	−67717.9	−0.000869801 0
$428$	− 1.99013e7i	− 0.253834i
$429$	0	0
$430$	−3.61704e7	−0.454933
$431$	9.06666e7i	1.13244i	0.824254	+	0.566221i	$0.191595\pi$
$431$	9.06666e7i	1.13244i	−0.824254	+	0.566221i	$0.808405\pi$
$432$	0	0
$433$	−699414.	−0.00861530	−0.00430765	−	0.999991i	$-0.501371\pi$
$433$	−699414.	−0.00861530	−0.00430765	+	0.999991i	$0.501371\pi$
$434$	− 586502.i	− 0.00717464i
$435$	0	0
$436$	4.30649e7	0.519594
$437$	4.71009e6i	0.0564397i
$438$	0	0
$439$	−2.57296e7	−0.304116	−0.152058	−	0.988372i	$-0.548590\pi$
$439$	−2.57296e7	−0.304116	−0.152058	+	0.988372i	$0.548590\pi$
$440$	− 8.53835e7i	− 1.00234i
$441$	0	0
$442$	3.15825e7	0.365746
$443$	− 165578.i	− 0.00190455i	−1.00000		0.000952273i	$-0.999697\pi$
$443$	− 165578.i	− 0.00190455i	1.00000		0.000952273i	$-0.000303118\pi$
$444$	0	0
$445$	−1.64801e8	−1.87016
$446$	3.21832e7i	0.362765i
$447$	0	0
$448$	−137500.	−0.00152921
$449$	4.30456e7i	0.475542i	0.971321	+	0.237771i	$0.0764169\pi$
$449$	4.30456e7i	0.475542i	−0.971321	+	0.237771i	$0.923583\pi$
$450$	0	0
$451$	2.62920e8	2.86611
$452$	3.96584e7i	0.429457i
$453$	0	0
$454$	6.56556e7	0.701624
$455$	− 2.48506e6i	− 0.0263816i
$456$	0	0
$457$	−1.35491e8	−1.41959	−0.709793	−	0.704411i	$-0.751211\pi$
$457$	−1.35491e8	−1.41959	−0.709793	+	0.704411i	$0.751211\pi$
$458$	− 1.95552e7i	− 0.203547i
$459$	0	0
$460$	1.11733e8	1.14791
$461$	− 3.20349e7i	− 0.326980i	−0.986545	−	0.163490i	$-0.947725\pi$
$461$	− 3.20349e7i	− 0.326980i	0.986545	−	0.163490i	$-0.0522751\pi$
$462$	0	0
$463$	1.29333e8	1.30306	0.651532	−	0.758621i	$-0.274127\pi$
$463$	1.29333e8	1.30306	0.651532	+	0.758621i	$0.274127\pi$
$464$	− 3.80048e7i	− 0.380439i
$465$	0	0
$466$	7.22602e7	0.714071
$467$	− 8.49294e7i	− 0.833887i	−0.908932	−	0.416944i	$-0.863101\pi$
$467$	− 8.49294e7i	− 0.833887i	0.908932	−	0.416944i	$-0.136899\pi$
$468$	0	0
$469$	−1.99178e6	−0.0193073
$470$	9.16168e7i	0.882432i
$471$	0	0
$472$	2.76883e7	0.263312
$473$	− 6.93579e7i	− 0.655410i
$474$	0	0
$475$	7.83664e6	0.0731222
$476$	263969.i	0.00244755i
$477$	0	0
$478$	7.31043e7	0.669360
$479$	− 1.15719e8i	− 1.05292i	−0.850199	−	0.526461i	$-0.823518\pi$
$479$	− 1.15719e8i	− 1.05292i	0.850199	−	0.526461i	$-0.176482\pi$
$480$	0	0
$481$	−4.83277e7	−0.434271
$482$	4.11837e7i	0.367777i
$483$	0	0
$484$	1.07036e8	0.944046
$485$	− 2.90412e8i	− 2.54560i
$486$	0	0
$487$	4.52839e7	0.392064	0.196032	−	0.980597i	$-0.437194\pi$
$487$	4.52839e7	0.392064	0.196032	+	0.980597i	$0.437194\pi$
$488$	2.92131e6i	0.0251373i
$489$	0	0
$490$	−1.38760e8	−1.17944
$491$	− 2.04312e8i	− 1.72603i	−0.505175	−	0.863017i	$-0.668572\pi$
$491$	− 2.04312e8i	− 1.72603i	0.505175	−	0.863017i	$-0.331428\pi$
$492$	0	0
$493$	−7.29611e7	−0.608906
$494$	− 4.51915e6i	− 0.0374866i
$495$	0	0
$496$	−2.53013e7	−0.207347
$497$	630841.i	0.00513867i
$498$	0	0
$499$	−2.92990e7	−0.235804	−0.117902	−	0.993025i	$-0.537617\pi$
$499$	−2.92990e7	−0.235804	−0.117902	+	0.993025i	$0.537617\pi$
$500$	− 8.16373e7i	− 0.653098i
$501$	0	0
$502$	9.72564e7	0.768789
$503$	1.64834e8i	1.29522i	0.761973	+	0.647609i	$0.224231\pi$
$503$	1.64834e8i	1.29522i	−0.761973	+	0.647609i	$0.775769\pi$
$504$	0	0
$505$	−2.74323e7	−0.213004
$506$	2.14252e8i	1.65376i
$507$	0	0
$508$	5.28949e7	0.403481
$509$	1.67339e8i	1.26895i	0.772944	+	0.634474i	$0.218783\pi$
$509$	1.67339e8i	1.26895i	−0.772944	+	0.634474i	$0.781217\pi$
$510$	0	0
$511$	1.39182e6	0.0104309
$512$	5.93164e6i	0.0441942i
$513$	0	0
$514$	4.53177e7	0.333717
$515$	− 4.03421e8i	− 2.95350i
$516$	0	0
$517$	−1.75678e8	−1.27130
$518$	− 403927.i	− 0.00290612i
$519$	0	0
$520$	−1.07204e8	−0.762430
$521$	6.01419e7i	0.425270i	0.977132	+	0.212635i	$0.0682045\pi$
$521$	6.01419e7i	0.425270i	−0.977132	+	0.212635i	$0.931796\pi$
$522$	0	0
$523$	1.09251e8	0.763698	0.381849	−	0.924225i	$-0.375287\pi$
$523$	1.09251e8	0.763698	0.381849	+	0.924225i	$0.375287\pi$
$524$	− 8.51602e7i	− 0.591893i
$525$	0	0
$526$	−9.51535e7	−0.653834
$527$	4.85731e7i	0.331867i
$528$	0	0
$529$	−1.32335e8	−0.893940
$530$	− 1.63562e8i	− 1.09864i
$531$	0	0
$532$	37771.5	0.000250859 0
$533$	− 3.30110e8i	− 2.18011i
$534$	0	0
$535$	1.29687e8	0.846907
$536$	8.59239e7i	0.557981i
$537$	0	0
$538$	1.88664e7	0.121155
$539$	− 2.66077e8i	− 1.69918i
$540$	0	0
$541$	4.52159e7	0.285561	0.142781	−	0.989754i	$-0.454396\pi$
$541$	4.52159e7	0.285561	0.142781	+	0.989754i	$0.454396\pi$
$542$	− 8.31827e7i	− 0.522439i
$543$	0	0
$544$	1.13875e7	0.0707343
$545$	2.80633e8i	1.73360i
$546$	0	0
$547$	5.11451e7	0.312494	0.156247	−	0.987718i	$-0.450060\pi$
$547$	5.11451e7	0.312494	0.156247	+	0.987718i	$0.450060\pi$
$548$	8.35248e7i	0.507544i
$549$	0	0
$550$	3.56473e8	2.14258
$551$	1.04400e7i	0.0624089i
$552$	0	0
$553$	−3.76022e6	−0.0222351
$554$	− 6.17732e7i	− 0.363304i
$555$	0	0
$556$	2.24423e7	0.130570
$557$	2.43306e7i	0.140795i	0.997519	+	0.0703974i	$0.0224267\pi$
$557$	2.43306e7i	0.140795i	−0.997519	+	0.0703974i	$0.977573\pi$
$558$	0	0
$559$	−8.70827e7	−0.498536
$560$	− 896018.i	− 0.00510214i
$561$	0	0
$562$	−1.05640e8	−0.595139
$563$	− 1.44398e8i	− 0.809166i	−0.914501	−	0.404583i	$-0.867417\pi$
$563$	− 1.44398e8i	− 0.809166i	0.914501	−	0.404583i	$-0.132583\pi$
$564$	0	0
$565$	−2.58434e8	−1.43286
$566$	− 8.27342e7i	− 0.456284i
$567$	0	0
$568$	2.72141e7	0.148508
$569$	8.31553e7i	0.451391i	0.974198	+	0.225696i	$0.0724655\pi$
$569$	8.31553e7i	0.451391i	−0.974198	+	0.225696i	$0.927534\pi$
$570$	0	0
$571$	−2.26080e8	−1.21438	−0.607188	−	0.794558i	$-0.707703\pi$
$571$	−2.26080e8	−1.21438	−0.607188	+	0.794558i	$0.707703\pi$
$572$	− 2.05567e8i	− 1.09841i
$573$	0	0
$574$	2.75909e6	0.0145892
$575$	4.66481e8i	2.45375i
$576$	0	0
$577$	4.11006e7	0.213954	0.106977	−	0.994261i	$-0.465883\pi$
$577$	4.11006e7	0.213954	0.106977	+	0.994261i	$0.465883\pi$
$578$	1.14681e8i	0.593894i
$579$	0	0
$580$	2.47659e8	1.26932
$581$	− 3.96574e6i	− 0.0202207i
$582$	0	0
$583$	3.13636e8	1.58278
$584$	− 6.00423e7i	− 0.301452i
$585$	0	0
$586$	−2.70640e8	−1.34493
$587$	1.14693e8i	0.567052i	0.958965	+	0.283526i	$0.0915042\pi$
$587$	1.14693e8i	0.567052i	−0.958965	+	0.283526i	$0.908496\pi$
$588$	0	0
$589$	6.95034e6	0.0340142
$590$	1.80431e8i	0.878528i
$591$	0	0
$592$	−1.74251e7	−0.0839868
$593$	− 2.90487e8i	− 1.39304i	−0.717539	−	0.696518i	$-0.754731\pi$
$593$	− 2.90487e8i	− 1.39304i	0.717539	−	0.696518i	$-0.245269\pi$
$594$	0	0
$595$	−1.72016e6	−0.00816616
$596$	− 1.51470e8i	− 0.715464i
$597$	0	0
$598$	2.69005e8	1.25793
$599$	− 3.57152e8i	− 1.66178i	−0.556439	−	0.830888i	$-0.687833\pi$
$599$	− 3.57152e8i	− 1.66178i	0.556439	−	0.830888i	$-0.312167\pi$
$600$	0	0
$601$	−8.40094e7	−0.386994	−0.193497	−	0.981101i	$-0.561983\pi$
$601$	−8.40094e7	−0.386994	−0.193497	+	0.981101i	$0.561983\pi$
$602$	− 727845.i	− 0.00333618i
$603$	0	0
$604$	−1.19593e8	−0.542746
$605$	6.97500e8i	3.14977i
$606$	0	0
$607$	5.16287e7	0.230847	0.115424	−	0.993316i	$-0.463177\pi$
$607$	5.16287e7	0.230847	0.115424	+	0.993316i	$0.463177\pi$
$608$	− 1.62944e6i	− 0.00724981i
$609$	0	0
$610$	−1.90368e7	−0.0838694
$611$	2.20574e8i	0.967009i
$612$	0	0
$613$	4.44326e7	0.192895	0.0964473	−	0.995338i	$-0.469252\pi$
$613$	4.44326e7	0.192895	0.0964473	+	0.995338i	$0.469252\pi$
$614$	2.40293e8i	1.03809i
$615$	0	0
$616$	1.71814e6	0.00735051
$617$	1.65408e8i	0.704208i	0.935961	+	0.352104i	$0.114534\pi$
$617$	1.65408e8i	0.704208i	−0.935961	+	0.352104i	$0.885466\pi$
$618$	0	0
$619$	2.68162e8	1.13064	0.565320	−	0.824871i	$-0.308753\pi$
$619$	2.68162e8	1.13064	0.565320	+	0.824871i	$0.308753\pi$
$620$	− 1.64876e8i	− 0.691805i
$621$	0	0
$622$	−1.75360e8	−0.728718
$623$	− 3.31623e6i	− 0.0137145i
$624$	0	0
$625$	9.66915e7	0.396049
$626$	− 1.68477e8i	− 0.686780i
$627$	0	0
$628$	−1.02612e8	−0.414303
$629$	3.34525e7i	0.134424i
$630$	0	0
$631$	1.13998e8	0.453741	0.226871	−	0.973925i	$-0.427151\pi$
$631$	1.13998e8	0.453741	0.226871	+	0.973925i	$0.427151\pi$
$632$	1.62214e8i	0.642593i
$633$	0	0
$634$	1.23269e7	0.0483712
$635$	3.44691e8i	1.34620i
$636$	0	0
$637$	−3.34074e8	−1.29248
$638$	4.74895e8i	1.82867i
$639$	0	0
$640$	−3.86536e7	−0.147452
$641$	− 3.65639e7i	− 0.138828i	−0.997588	−	0.0694142i	$-0.977887\pi$
$641$	− 3.65639e7i	− 0.138828i	0.997588	−	0.0694142i	$-0.0221130\pi$
$642$	0	0
$643$	−2.82268e8	−1.06177	−0.530883	−	0.847445i	$-0.678140\pi$
$643$	−2.82268e8	−1.06177	−0.530883	+	0.847445i	$0.678140\pi$
$644$	2.24837e6i	0.00841803i
$645$	0	0
$646$	−3.12817e6	−0.0116036
$647$	− 1.45187e8i	− 0.536062i	−0.963410	−	0.268031i	$-0.913627\pi$
$647$	− 1.45187e8i	− 0.536062i	0.963410	−	0.268031i	$-0.0863729\pi$
$648$	0	0
$649$	−3.45983e8	−1.26567
$650$	− 4.47571e8i	− 1.62975i
$651$	0	0
$652$	3.08614e7	0.111345
$653$	− 9.91905e7i	− 0.356230i	−0.984010	−	0.178115i	$-0.943000\pi$
$653$	− 9.91905e7i	− 0.356230i	0.984010	−	0.178115i	$-0.0569999\pi$
$654$	0	0
$655$	5.54948e8	1.97482
$656$	− 1.19025e8i	− 0.421627i
$657$	0	0
$658$	−1.84357e6	−0.00647117
$659$	− 1.69578e8i	− 0.592535i	−0.955105	−	0.296268i	$-0.904258\pi$
$659$	− 1.69578e8i	− 0.592535i	0.955105	−	0.296268i	$-0.0957420\pi$
$660$	0	0
$661$	5.38050e8	1.86302	0.931511	−	0.363713i	$-0.118491\pi$
$661$	5.38050e8	1.86302	0.931511	+	0.363713i	$0.118491\pi$
$662$	7.56157e7i	0.260638i
$663$	0	0
$664$	−1.71080e8	−0.584378
$665$	246138.i	0 0.000836978i
$666$	0	0
$667$	−6.21449e8	−2.09425
$668$	− 3.31198e7i	− 0.111111i
$669$	0	0
$670$	−5.59924e8	−1.86168
$671$	− 3.65036e7i	− 0.120828i
$672$	0	0
$673$	−3.85365e7	−0.126423	−0.0632116	−	0.998000i	$-0.520134\pi$
$673$	−3.85365e7	−0.126423	−0.0632116	+	0.998000i	$0.520134\pi$
$674$	2.52006e8i	0.823060i
$675$	0	0
$676$	−1.03643e8	−0.335504
$677$	1.90802e8i	0.614916i	0.951562	+	0.307458i	$0.0994784\pi$
$677$	1.90802e8i	0.614916i	−0.951562	+	0.307458i	$0.900522\pi$
$678$	0	0
$679$	5.84388e6	0.0186677
$680$	7.42066e7i	0.236002i
$681$	0	0
$682$	3.16156e8	0.996664
$683$	5.45896e8i	1.71336i	0.515850	+	0.856679i	$0.327476\pi$
$683$	5.45896e8i	1.71336i	−0.515850	+	0.856679i	$0.672524\pi$
$684$	0	0
$685$	−5.44291e8	−1.69340
$686$	− 5.58486e6i	− 0.0172997i
$687$	0	0
$688$	−3.13988e7	−0.0964156
$689$	− 3.93788e8i	− 1.20394i
$690$	0	0
$691$	−1.70447e8	−0.516601	−0.258301	−	0.966065i	$-0.583162\pi$
$691$	−1.70447e8	−0.516601	−0.258301	+	0.966065i	$0.583162\pi$
$692$	2.07551e7i	0.0626334i
$693$	0	0
$694$	−1.18220e8	−0.353682
$695$	1.46245e8i	0.435640i
$696$	0	0
$697$	−2.28503e8	−0.674828
$698$	3.64954e8i	1.07318i
$699$	0	0
$700$	3.74084e6	0.0109062
$701$	8.02305e7i	0.232909i	0.993196	+	0.116454i	$0.0371529\pi$
$701$	8.02305e7i	0.232909i	−0.993196	+	0.116454i	$0.962847\pi$
$702$	0	0
$703$	4.78673e6	0.0137776
$704$	− 7.41197e7i	− 0.212430i
$705$	0	0
$706$	−2.38109e7	−0.0676647
$707$	− 552011.i	− 0.00156203i
$708$	0	0
$709$	4.01132e8	1.12551	0.562754	−	0.826625i	$-0.309742\pi$
$709$	4.01132e8	1.12551	0.562754	+	0.826625i	$0.309742\pi$
$710$	1.77341e8i	0.495489i
$711$	0	0
$712$	−1.43060e8	−0.396349
$713$	4.13723e8i	1.14141i
$714$	0	0
$715$	1.33958e9	3.66480
$716$	1.48860e8i	0.405546i
$717$	0	0
$718$	−3.17531e8	−0.857852
$719$	1.02302e8i	0.275232i	0.990486	+	0.137616i	$0.0439439\pi$
$719$	1.02302e8i	0.275232i	−0.990486	+	0.137616i	$0.956056\pi$
$720$	0	0
$721$	8.11792e6	0.0216590
$722$	− 2.65684e8i	− 0.705917i
$723$	0	0
$724$	−1.09990e8	−0.289827
$725$	1.03397e9i	2.71327i
$726$	0	0
$727$	−5.87675e8	−1.52944	−0.764722	−	0.644360i	$-0.777124\pi$
$727$	−5.87675e8	−1.52944	−0.764722	+	0.644360i	$0.777124\pi$
$728$	− 2.15723e6i	− 0.00559115i
$729$	0	0
$730$	3.91266e8	1.00578
$731$	6.02788e7i	0.154317i
$732$	0	0
$733$	−1.12015e8	−0.284424	−0.142212	−	0.989836i	$-0.545421\pi$
$733$	−1.12015e8	−0.284424	−0.142212	+	0.989836i	$0.545421\pi$
$734$	1.89563e8i	0.479363i
$735$	0	0
$736$	9.69933e7	0.243281
$737$	− 1.07367e9i	− 2.68207i
$738$	0	0
$739$	6.86968e8	1.70217	0.851086	−	0.525027i	$-0.175945\pi$
$739$	6.86968e8	1.70217	0.851086	+	0.525027i	$0.175945\pi$
$740$	− 1.13551e8i	− 0.280218i
$741$	0	0
$742$	3.29131e6	0.00805670
$743$	− 5.57615e8i	− 1.35946i	−0.733460	−	0.679732i	$-0.762096\pi$
$743$	− 5.57615e8i	− 1.35946i	0.733460	−	0.679732i	$-0.237904\pi$
$744$	0	0
$745$	9.87057e8	2.38711
$746$	1.26022e8i	0.303549i
$747$	0	0
$748$	−1.42294e8	−0.340001
$749$	2.60966e6i	0.00621066i
$750$	0	0
$751$	4.04996e8	0.956160	0.478080	−	0.878316i	$-0.341333\pi$
$751$	4.04996e8	0.956160	0.478080	+	0.878316i	$0.341333\pi$
$752$	7.95306e7i	0.187017i
$753$	0	0
$754$	5.96257e8	1.39098
$755$	− 7.79332e8i	− 1.81085i
$756$	0	0
$757$	6.51769e8	1.50247	0.751235	−	0.660035i	$-0.229458\pi$
$757$	6.51769e8	1.50247	0.751235	+	0.660035i	$0.229458\pi$
$758$	4.36825e8i	1.00300i
$759$	0	0
$760$	1.06182e7	0.0241887
$761$	− 3.11208e8i	− 0.706149i	−0.935595	−	0.353074i	$-0.885136\pi$
$761$	− 3.11208e8i	− 0.706149i	0.935595	−	0.353074i	$-0.114864\pi$
$762$	0	0
$763$	−5.64709e6	−0.0127131
$764$	3.76030e8i	0.843222i
$765$	0	0
$766$	−1.88144e8	−0.418604
$767$	4.34401e8i	0.962730i
$768$	0	0
$769$	−4.37211e8	−0.961417	−0.480708	−	0.876880i	$-0.659620\pi$
$769$	−4.37211e8	−0.961417	−0.480708	+	0.876880i	$0.659620\pi$
$770$	1.11963e7i	0.0245247i
$771$	0	0
$772$	−2.22592e8	−0.483790
$773$	5.41906e7i	0.117324i	0.998278	+	0.0586619i	$0.0186834\pi$
$773$	5.41906e7i	0.117324i	−0.998278	+	0.0586619i	$0.981317\pi$
$774$	0	0
$775$	6.88352e8	1.47879
$776$	− 2.52101e8i	− 0.539498i
$777$	0	0
$778$	−8.53951e7	−0.181340
$779$	3.26966e7i	0.0691656i
$780$	0	0
$781$	−3.40057e8	−0.713837
$782$	− 1.86206e8i	− 0.389380i
$783$	0	0
$784$	−1.20455e8	−0.249963
$785$	− 6.68671e8i	− 1.38230i
$786$	0	0
$787$	−4.02320e7	−0.0825367	−0.0412684	−	0.999148i	$-0.513140\pi$
$787$	−4.02320e7	−0.0825367	−0.0412684	+	0.999148i	$0.513140\pi$
$788$	1.31086e7i	0.0267904i
$789$	0	0
$790$	−1.05707e9	−2.14398
$791$	− 5.20039e6i	− 0.0105077i
$792$	0	0
$793$	−4.58323e7	−0.0919078
$794$	− 5.04223e8i	− 1.00731i
$795$	0	0
$796$	1.03951e8	0.206106
$797$	− 8.94029e7i	− 0.176594i	−0.996094	−	0.0882972i	$-0.971857\pi$
$797$	− 8.94029e7i	− 0.176594i	0.996094	−	0.0882972i	$-0.0281425\pi$
$798$	0	0
$799$	1.52682e8	0.299327
$800$	− 1.61377e8i	− 0.315190i
$801$	0	0
$802$	−6.33810e8	−1.22867
$803$	7.50266e8i	1.44900i
$804$	0	0
$805$	−1.46515e7	−0.0280864
$806$	− 3.96952e8i	− 0.758111i
$807$	0	0
$808$	−2.38134e7	−0.0451427
$809$	7.82985e8i	1.47879i	0.673270	+	0.739397i	$0.264889\pi$
$809$	7.82985e8i	1.47879i	−0.673270	+	0.739397i	$0.735111\pi$
$810$	0	0
$811$	−6.76238e6	−0.0126776	−0.00633880	−	0.999980i	$-0.502018\pi$
$811$	−6.76238e6	−0.0126776	−0.00633880	+	0.999980i	$0.502018\pi$
$812$	4.98357e6i	0.00930834i
$813$	0	0
$814$	2.17738e8	0.403703
$815$	2.01109e8i	0.371499i
$816$	0	0
$817$	8.62532e6	0.0158165
$818$	− 3.77844e8i	− 0.690324i
$819$	0	0
$820$	7.75631e8	1.40674
$821$	− 2.93295e7i	− 0.0530000i	−0.999649	−	0.0265000i	$-0.991564\pi$
$821$	− 2.93295e7i	− 0.0530000i	0.999649	−	0.0265000i	$-0.00843619\pi$
$822$	0	0
$823$	−8.90952e8	−1.59829	−0.799144	−	0.601140i	$-0.794713\pi$
$823$	−8.90952e8	−1.59829	−0.799144	+	0.601140i	$0.794713\pi$
$824$	− 3.50202e8i	− 0.625946i
$825$	0	0
$826$	−3.63076e6	−0.00644254
$827$	4.36886e8i	0.772417i	0.922411	+	0.386209i	$0.126216\pi$
$827$	4.36886e8i	0.772417i	−0.922411	+	0.386209i	$0.873784\pi$
$828$	0	0
$829$	2.08489e8	0.365948	0.182974	−	0.983118i	$-0.441428\pi$
$829$	2.08489e8	0.365948	0.182974	+	0.983118i	$0.441428\pi$
$830$	− 1.11484e9i	− 1.94975i
$831$	0	0
$832$	−9.30614e7	−0.161584
$833$	2.31247e8i	0.400074i
$834$	0	0
$835$	2.15825e8	0.370718
$836$	2.03609e7i	0.0348480i
$837$	0	0
$838$	2.67892e8	0.455227
$839$	− 1.11428e9i	− 1.88672i	−0.331767	−	0.943361i	$-0.607645\pi$
$839$	− 1.11428e9i	− 1.88672i	0.331767	−	0.943361i	$-0.392355\pi$
$840$	0	0
$841$	−7.82634e8	−1.31574
$842$	3.74240e8i	0.626922i
$843$	0	0
$844$	1.59836e8	0.265856
$845$	− 6.75389e8i	− 1.11940i
$846$	0	0
$847$	−1.40356e7	−0.0230983
$848$	− 1.41985e8i	− 0.232839i
$849$	0	0
$850$	−3.09809e8	−0.504473
$851$	2.84933e8i	0.462332i
$852$	0	0
$853$	−7.03808e7	−0.113399	−0.0566993	−	0.998391i	$-0.518058\pi$
$853$	−7.03808e7	−0.113399	−0.0566993	+	0.998391i	$0.518058\pi$
$854$	− 383071.i	0 0.000615043i
$855$	0	0
$856$	1.12579e8	0.179488
$857$	− 1.58916e8i	− 0.252479i	−0.992000	−	0.126240i	$-0.959709\pi$
$857$	− 1.58916e8i	− 0.252479i	0.992000	−	0.126240i	$-0.0402908\pi$
$858$	0	0
$859$	3.14241e8	0.495774	0.247887	−	0.968789i	$-0.420264\pi$
$859$	3.14241e8	0.495774	0.247887	+	0.968789i	$0.420264\pi$
$860$	− 2.04611e8i	− 0.321686i
$861$	0	0
$862$	−5.12888e8	−0.800757
$863$	− 3.90351e8i	− 0.607328i	−0.952779	−	0.303664i	$-0.901790\pi$
$863$	− 3.90351e8i	− 0.607328i	0.952779	−	0.303664i	$-0.0982101\pi$
$864$	0	0
$865$	−1.35251e8	−0.208974
$866$	− 3.95648e6i	− 0.00609194i
$867$	0	0
$868$	3.31776e6	0.00507324
$869$	− 2.02696e9i	− 3.08878i
$870$	0	0
$871$	−1.34806e9	−2.04011
$872$	2.43612e8i	0.367408i
$873$	0	0
$874$	−2.66443e7	−0.0399089
$875$	1.07051e7i	0.0159796i
$876$	0	0
$877$	−1.15579e9	−1.71349	−0.856745	−	0.515741i	$-0.827517\pi$
$877$	−1.15579e9	−1.71349	−0.856745	+	0.515741i	$0.827517\pi$
$878$	− 1.45549e8i	− 0.215043i
$879$	0	0
$880$	4.83002e8	0.708763
$881$	− 7.82859e8i	− 1.14487i	−0.819951	−	0.572434i	$-0.805999\pi$
$881$	− 7.82859e8i	− 1.14487i	0.819951	−	0.572434i	$-0.194001\pi$
$882$	0	0
$883$	1.01047e9	1.46772	0.733860	−	0.679300i	$-0.237717\pi$
$883$	1.01047e9	1.46772	0.733860	+	0.679300i	$0.237717\pi$
$884$	1.78658e8i	0.258622i
$885$	0	0
$886$	936650.	0.00134672
$887$	− 3.28343e8i	− 0.470498i	−0.971935	−	0.235249i	$-0.924410\pi$
$887$	− 3.28343e8i	− 0.470498i	0.971935	−	0.235249i	$-0.0755905\pi$
$888$	0	0
$889$	−6.93610e6	−0.00987211
$890$	− 9.32253e8i	− 1.32240i
$891$	0	0
$892$	−1.82056e8	−0.256513
$893$	− 2.18473e7i	− 0.0306791i
$894$	0	0
$895$	−9.70051e8	−1.35309
$896$	− 777815.i	− 0.00108131i
$897$	0	0
$898$	−2.43502e8	−0.336259
$899$	9.17028e8i	1.26213i
$900$	0	0
$901$	−2.72580e8	−0.372666
$902$	1.48730e9i	2.02665i
$903$	0	0
$904$	−2.24342e8	−0.303672
$905$	− 7.16753e8i	− 0.966994i
$906$	0	0
$907$	2.15438e8	0.288736	0.144368	−	0.989524i	$-0.453885\pi$
$907$	2.15438e8	0.288736	0.144368	+	0.989524i	$0.453885\pi$
$908$	3.71404e8i	0.496123i
$909$	0	0
$910$	1.40576e7	0.0186546
$911$	7.52234e8i	0.994942i	0.867481	+	0.497471i	$0.165738\pi$
$911$	7.52234e8i	0.994942i	−0.867481	+	0.497471i	$0.834262\pi$
$912$	0	0
$913$	2.13775e9	2.80895
$914$	− 7.66452e8i	− 1.00380i
$915$	0	0
$916$	1.10621e8	0.143930
$917$	1.11670e7i	0.0144820i
$918$	0	0
$919$	6.81968e8	0.878653	0.439327	−	0.898327i	$-0.355217\pi$
$919$	6.81968e8	0.878653	0.439327	+	0.898327i	$0.355217\pi$
$920$	6.32058e8i	0.811696i
$921$	0	0
$922$	1.81217e8	0.231210
$923$	4.26961e8i	0.542979i
$924$	0	0
$925$	4.74072e8	0.598989
$926$	7.31617e8i	0.921406i
$927$	0	0
$928$	2.14988e8	0.269011
$929$	1.11639e8i	0.139242i	0.997574	+	0.0696208i	$0.0221789\pi$
$929$	1.11639e8i	0.139242i	−0.997574	+	0.0696208i	$0.977821\pi$
$930$	0	0
$931$	3.30892e7	0.0410050
$932$	4.08765e8i	0.504924i
$933$	0	0
$934$	4.80433e8	0.589647
$935$	− 9.27259e8i	− 1.13440i
$936$	0	0
$937$	7.66443e8	0.931668	0.465834	−	0.884872i	$-0.345754\pi$
$937$	7.66443e8	0.931668	0.465834	+	0.884872i	$0.345754\pi$
$938$	− 1.12672e7i	− 0.0136523i
$939$	0	0
$940$	−5.18263e8	−0.623974
$941$	5.32996e8i	0.639669i	0.947473	+	0.319834i	$0.103627\pi$
$941$	5.32996e8i	0.639669i	−0.947473	+	0.319834i	$0.896373\pi$
$942$	0	0
$943$	−1.94628e9	−2.32098
$944$	1.56629e8i	0.186189i
$945$	0	0
$946$	3.92348e8	0.463445
$947$	3.13628e7i	0.0369288i	0.999830	+	0.0184644i	$0.00587773\pi$
$947$	3.13628e7i	0.0369288i	−0.999830	+	0.0184644i	$0.994122\pi$
$948$	0	0
$949$	9.42001e8	1.10218
$950$	4.43308e7i	0.0517052i
$951$	0	0
$952$	−1.49324e6	−0.00173068
$953$	6.21244e8i	0.717767i	0.933382	+	0.358883i	$0.116842\pi$
$953$	6.21244e8i	0.717767i	−0.933382	+	0.358883i	$0.883158\pi$
$954$	0	0
$955$	−2.45040e9	−2.81337
$956$	4.13541e8i	0.473309i
$957$	0	0
$958$	6.54603e8	0.744529
$959$	− 1.09526e7i	− 0.0124183i
$960$	0	0
$961$	−2.77002e8	−0.312114
$962$	− 2.73383e8i	− 0.307076i
$963$	0	0
$964$	−2.32970e8	−0.260057
$965$	− 1.45052e9i	− 1.61415i
$966$	0	0
$967$	−6.29984e8	−0.696707	−0.348354	−	0.937363i	$-0.613259\pi$
$967$	−6.29984e8	−0.696707	−0.348354	+	0.937363i	$0.613259\pi$
$968$	6.05486e8i	0.667541i
$969$	0	0
$970$	1.64282e9	1.80001
$971$	1.38333e8i	0.151101i	0.997142	+	0.0755507i	$0.0240715\pi$
$971$	1.38333e8i	0.151101i	−0.997142	+	0.0755507i	$0.975929\pi$
$972$	0	0
$973$	−2.94285e6	−0.00319470
$974$	2.56165e8i	0.277231i
$975$	0	0
$976$	−1.65254e7	−0.0177747
$977$	8.23975e8i	0.883549i	0.897126	+	0.441774i	$0.145651\pi$
$977$	8.23975e8i	0.883549i	−0.897126	+	0.441774i	$0.854349\pi$
$978$	0	0
$979$	1.78763e9	1.90515
$980$	− 7.84944e8i	− 0.833989i
$981$	0	0
$982$	1.15576e9	1.22049
$983$	− 1.28601e9i	− 1.35389i	−0.736032	−	0.676947i	$-0.763303\pi$
$983$	− 1.28601e9i	− 1.35389i	0.736032	−	0.676947i	$-0.236697\pi$
$984$	0	0
$985$	−8.54226e7	−0.0893849
$986$	− 4.12730e8i	− 0.430562i
$987$	0	0
$988$	2.55642e7	0.0265070
$989$	5.13428e8i	0.530751i
$990$	0	0
$991$	−1.70244e8	−0.174924	−0.0874621	−	0.996168i	$-0.527876\pi$
$991$	−1.70244e8	−0.174924	−0.0874621	+	0.996168i	$0.527876\pi$
$992$	− 1.43126e8i	− 0.146617i
$993$	0	0
$994$	−3.56858e6	−0.00363359
$995$	6.77399e8i	0.687663i
$996$	0	0
$997$	−7.01078e8	−0.707426	−0.353713	−	0.935354i	$-0.615081\pi$
$997$	−7.01078e8	−0.707426	−0.353713	+	0.935354i	$0.615081\pi$
$998$	− 1.65740e8i	− 0.166738i
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.b.a.161.3	yes	4
3.2	odd	2	inner	162.7.b.a.161.2	✓	4
9.2	odd	6		162.7.d.f.53.1		8
9.4	even	3		162.7.d.f.107.1		8
9.5	odd	6		162.7.d.f.107.4		8
9.7	even	3		162.7.d.f.53.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.a.161.2	✓	4	3.2	odd	2	inner
162.7.b.a.161.3	yes	4	1.1	even	1	trivial
162.7.d.f.53.1		8	9.2	odd	6
162.7.d.f.53.4		8	9.7	even	3
162.7.d.f.107.1		8	9.4	even	3
162.7.d.f.107.4		8	9.5	odd	6

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.65685i q^{2} -32.0000 q^{4} -208.528i q^{5} +4.19615 q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+5.65685i q^{2} -32.0000 q^{4} -208.528i q^{5} +4.19615 q^{7} -181.019i q^{8} +1179.62 q^{10} +2261.95i q^{11} +2840.01 q^{13} +23.7370i q^{14} +1024.00 q^{16} -1965.86i q^{17} -281.295 q^{19} +6672.91i q^{20} -12795.5 q^{22} -16744.3i q^{23} -27859.1 q^{25} +16065.5i q^{26} -134.277 q^{28} -37114.1i q^{29} -24708.3 q^{31} +5792.62i q^{32} +11120.6 q^{34} -875.017i q^{35} -17016.7 q^{37} -1591.25i q^{38} -37747.7 q^{40} -116236. i q^{41} -30662.9 q^{43} -72382.5i q^{44} +94720.0 q^{46} +77666.6i q^{47} -117631. q^{49} -157595. i q^{50} -90880.2 q^{52} -138657. i q^{53} +471682. q^{55} -759.585i q^{56} +209949. q^{58} +152958. i q^{59} -16138.1 q^{61} -139771. i q^{62} -32768.0 q^{64} -592222. i q^{65} -474667. q^{67} +62907.4i q^{68} +4949.85 q^{70} +150338. i q^{71} +331690. q^{73} -96261.2i q^{74} +9001.45 q^{76} +9491.50i q^{77} -896112. q^{79} -213533. i q^{80} +657529. q^{82} -945090. i q^{83} -409937. q^{85} -173455. i q^{86} +409457. q^{88} -790302. i q^{89} +11917.1 q^{91} +535817. i q^{92} -439349. q^{94} +58658.1i q^{95} +1.39268e6 q^{97} -665424. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 128 q^{4} - 4 q^{7}+O(q^{10}) \) 4 * q - 128 * q^4 - 4 * q^7	\( 4 q - 128 q^{4} - 4 q^{7} + 2640 q^{10} + 3836 q^{13} + 4096 q^{16} + 10244 q^{19} - 27072 q^{22} - 25700 q^{25} + 128 q^{28} - 40096 q^{31} + 60528 q^{34} - 20200 q^{37} - 84480 q^{40} + 184940 q^{43} + 162720 q^{46} - 470484 q^{49} - 122752 q^{52} + 949860 q^{55} + 24624 q^{58} + 609056 q^{61} - 131072 q^{64} - 2008972 q^{67} + 8160 q^{70} + 525824 q^{73} - 327808 q^{76} - 848716 q^{79} + 705792 q^{82} - 987840 q^{85} + 866304 q^{88} + 35260 q^{91} - 1965408 q^{94} + 3621728 q^{97}+O(q^{100}) \) 4 * q - 128 * q^4 - 4 * q^7 + 2640 * q^10 + 3836 * q^13 + 4096 * q^16 + 10244 * q^19 - 27072 * q^22 - 25700 * q^25 + 128 * q^28 - 40096 * q^31 + 60528 * q^34 - 20200 * q^37 - 84480 * q^40 + 184940 * q^43 + 162720 * q^46 - 470484 * q^49 - 122752 * q^52 + 949860 * q^55 + 24624 * q^58 + 609056 * q^61 - 131072 * q^64 - 2008972 * q^67 + 8160 * q^70 + 525824 * q^73 - 327808 * q^76 - 848716 * q^79 + 705792 * q^82 - 987840 * q^85 + 866304 * q^88 + 35260 * q^91 - 1965408 * q^94 + 3621728 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more