LMFDB - Embedded newform 22.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,10,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	22.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:	$11.3307883956$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+16.0000 q^{2} +201.000 q^{3} +256.000 q^{4} +2349.00 q^{5} +3216.00 q^{6} -8806.00 q^{7} +4096.00 q^{8} +20718.0 q^{9} +O(q^{10})$

\(q+16.0000 q^{2} +201.000 q^{3} +256.000 q^{4} +2349.00 q^{5} +3216.00 q^{6} -8806.00 q^{7} +4096.00 q^{8} +20718.0 q^{9} +37584.0 q^{10} -14641.0 q^{11} +51456.0 q^{12} -131068. q^{13} -140896. q^{14} +472149. q^{15} +65536.0 q^{16} -55698.0 q^{17} +331488. q^{18} +1.04182e6 q^{19} +601344. q^{20} -1.77001e6 q^{21} -234256. q^{22} -662139. q^{23} +823296. q^{24} +3.56468e6 q^{25} -2.09709e6 q^{26} +208035. q^{27} -2.25434e6 q^{28} -4.81934e6 q^{29} +7.55438e6 q^{30} -180115. q^{31} +1.04858e6 q^{32} -2.94284e6 q^{33} -891168. q^{34} -2.06853e7 q^{35} +5.30381e6 q^{36} -7.80302e6 q^{37} +1.66692e7 q^{38} -2.63447e7 q^{39} +9.62150e6 q^{40} -5.92774e6 q^{41} -2.83201e7 q^{42} -5.92916e6 q^{43} -3.74810e6 q^{44} +4.86666e7 q^{45} -1.05942e7 q^{46} +6.15762e7 q^{47} +1.31727e7 q^{48} +3.71920e7 q^{49} +5.70348e7 q^{50} -1.11953e7 q^{51} -3.35534e7 q^{52} +7.34951e6 q^{53} +3.32856e6 q^{54} -3.43917e7 q^{55} -3.60694e7 q^{56} +2.09407e8 q^{57} -7.71095e7 q^{58} -1.13902e8 q^{59} +1.20870e8 q^{60} -1.38143e7 q^{61} -2.88184e6 q^{62} -1.82443e8 q^{63} +1.67772e7 q^{64} -3.07879e8 q^{65} -4.70855e7 q^{66} +3.09981e8 q^{67} -1.42587e7 q^{68} -1.33090e8 q^{69} -3.30965e8 q^{70} +4.27526e7 q^{71} +8.48609e7 q^{72} +1.42018e8 q^{73} -1.24848e8 q^{74} +7.16500e8 q^{75} +2.66707e8 q^{76} +1.28929e8 q^{77} -4.21515e8 q^{78} -3.25376e8 q^{79} +1.53944e8 q^{80} -3.65977e8 q^{81} -9.48438e7 q^{82} +2.53503e8 q^{83} -4.53122e8 q^{84} -1.30835e8 q^{85} -9.48666e7 q^{86} -9.68688e8 q^{87} -5.99695e7 q^{88} -9.94228e8 q^{89} +7.78665e8 q^{90} +1.15418e9 q^{91} -1.69508e8 q^{92} -3.62031e7 q^{93} +9.85219e8 q^{94} +2.44724e9 q^{95} +2.10764e8 q^{96} -3.52091e8 q^{97} +5.95072e8 q^{98} -3.03332e8 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	201.000	1.43268	0.716342	−	0.697749i	$-0.245815\pi$
$3$	201.000	1.43268	0.716342	+	0.697749i	$0.245815\pi$
$4$	256.000	0.500000
$5$	2349.00	1.68081	0.840404	−	0.541961i	$-0.182318\pi$
$5$	2349.00	1.68081	0.840404	+	0.541961i	$0.182318\pi$
$6$	3216.00	1.01306
$7$	−8806.00	−1.38624	−0.693119	−	0.720824i	$-0.743764\pi$
$7$	−8806.00	−1.38624	−0.693119	+	0.720824i	$0.743764\pi$
$8$	4096.00	0.353553
$9$	20718.0	1.05258
$10$	37584.0	1.18851
$11$	−14641.0	−0.301511
$11$	−14641.0	−0.301511
$12$	51456.0	0.716342
$13$	−131068.	−1.27277	−0.636387	−	0.771370i	$-0.719572\pi$
$13$	−131068.	−1.27277	−0.636387	+	0.771370i	$0.719572\pi$
$14$	−140896.	−0.980218
$15$	472149.	2.40807
$16$	65536.0	0.250000
$17$	−55698.0	−0.161741	−0.0808704	−	0.996725i	$-0.525770\pi$
$17$	−55698.0	−0.161741	−0.0808704	+	0.996725i	$0.525770\pi$
$18$	331488.	0.744289
$19$	1.04182e6	1.83402	0.917008	−	0.398869i	$-0.130597\pi$
$19$	1.04182e6	1.83402	0.917008	+	0.398869i	$0.130597\pi$
$20$	601344.	0.840404
$21$	−1.77001e6	−1.98604
$22$	−234256.	−0.213201
$23$	−662139.	−0.493371	−0.246686	−	0.969096i	$-0.579342\pi$
$23$	−662139.	−0.493371	−0.246686	+	0.969096i	$0.579342\pi$
$24$	823296.	0.506530
$25$	3.56468e6	1.82511
$26$	−2.09709e6	−0.899988
$27$	208035.	0.0753355
$28$	−2.25434e6	−0.693119
$29$	−4.81934e6	−1.26531	−0.632655	−	0.774434i	$-0.718035\pi$
$29$	−4.81934e6	−1.26531	−0.632655	+	0.774434i	$0.718035\pi$
$30$	7.55438e6	1.70276
$31$	−180115.	−0.0350286	−0.0175143	−	0.999847i	$-0.505575\pi$
$31$	−180115.	−0.0350286	−0.0175143	+	0.999847i	$0.505575\pi$
$32$	1.04858e6	0.176777
$33$	−2.94284e6	−0.431970
$34$	−891168.	−0.114368
$35$	−2.06853e7	−2.33000
$36$	5.30381e6	0.526292
$37$	−7.80302e6	−0.684471	−0.342236	−	0.939614i	$-0.611184\pi$
$37$	−7.80302e6	−0.684471	−0.342236	+	0.939614i	$0.611184\pi$
$38$	1.66692e7	1.29685
$39$	−2.63447e7	−1.82348
$40$	9.62150e6	0.594255
$41$	−5.92774e6	−0.327613	−0.163807	−	0.986492i	$-0.552377\pi$
$41$	−5.92774e6	−0.327613	−0.163807	+	0.986492i	$0.552377\pi$
$42$	−2.83201e7	−1.40434
$43$	−5.92916e6	−0.264475	−0.132238	−	0.991218i	$-0.542216\pi$
$43$	−5.92916e6	−0.264475	−0.132238	+	0.991218i	$0.542216\pi$
$44$	−3.74810e6	−0.150756
$45$	4.86666e7	1.76919
$46$	−1.05942e7	−0.348866
$47$	6.15762e7	1.84065	0.920327	−	0.391149i	$-0.127922\pi$
$47$	6.15762e7	1.84065	0.920327	+	0.391149i	$0.127922\pi$
$48$	1.31727e7	0.358171
$49$	3.71920e7	0.921653
$50$	5.70348e7	1.29055
$51$	−1.11953e7	−0.231723
$52$	−3.35534e7	−0.636387
$53$	7.34951e6	0.127943	0.0639716	−	0.997952i	$-0.479623\pi$
$53$	7.34951e6	0.127943	0.0639716	+	0.997952i	$0.479623\pi$
$54$	3.32856e6	0.0532702
$55$	−3.43917e7	−0.506783
$56$	−3.60694e7	−0.490109
$57$	2.09407e8	2.62757
$58$	−7.71095e7	−0.894709
$59$	−1.13902e8	−1.22376	−0.611881	−	0.790950i	$-0.709587\pi$
$59$	−1.13902e8	−1.22376	−0.611881	+	0.790950i	$0.709587\pi$
$60$	1.20870e8	1.20403
$61$	−1.38143e7	−0.127745	−0.0638724	−	0.997958i	$-0.520345\pi$
$61$	−1.38143e7	−0.127745	−0.0638724	+	0.997958i	$0.520345\pi$
$62$	−2.88184e6	−0.0247689
$63$	−1.82443e8	−1.45913
$64$	1.67772e7	0.125000
$65$	−3.07879e8	−2.13929
$66$	−4.70855e7	−0.305449
$67$	3.09981e8	1.87931	0.939655	−	0.342124i	$-0.111146\pi$
$67$	3.09981e8	1.87931	0.939655	+	0.342124i	$0.111146\pi$
$68$	−1.42587e7	−0.0808704
$69$	−1.33090e8	−0.706845
$70$	−3.30965e8	−1.64756
$71$	4.27526e7	0.199664	0.0998321	−	0.995004i	$-0.468169\pi$
$71$	4.27526e7	0.199664	0.0998321	+	0.995004i	$0.468169\pi$
$72$	8.48609e7	0.372144
$73$	1.42018e8	0.585318	0.292659	−	0.956217i	$-0.405460\pi$
$73$	1.42018e8	0.585318	0.292659	+	0.956217i	$0.405460\pi$
$74$	−1.24848e8	−0.483994
$75$	7.16500e8	2.61481
$76$	2.66707e8	0.917008
$77$	1.28929e8	0.417966
$78$	−4.21515e8	−1.28940
$79$	−3.25376e8	−0.939862	−0.469931	−	0.882703i	$-0.655721\pi$
$79$	−3.25376e8	−0.939862	−0.469931	+	0.882703i	$0.655721\pi$
$80$	1.53944e8	0.420202
$81$	−3.65977e8	−0.944652
$82$	−9.48438e7	−0.231658
$83$	2.53503e8	0.586316	0.293158	−	0.956064i	$-0.405294\pi$
$83$	2.53503e8	0.586316	0.293158	+	0.956064i	$0.405294\pi$
$84$	−4.53122e8	−0.993020
$85$	−1.30835e8	−0.271855
$86$	−9.48666e7	−0.187012
$87$	−9.68688e8	−1.81279
$88$	−5.99695e7	−0.106600
$89$	−9.94228e8	−1.67970	−0.839848	−	0.542821i	$-0.817356\pi$
$89$	−9.94228e8	−1.67970	−0.839848	+	0.542821i	$0.817356\pi$
$90$	7.78665e8	1.25101
$91$	1.15418e9	1.76437
$92$	−1.69508e8	−0.246686
$93$	−3.62031e7	−0.0501849
$94$	9.85219e8	1.30154
$95$	2.44724e9	3.08263
$96$	2.10764e8	0.253265
$97$	−3.52091e8	−0.403815	−0.201907	−	0.979405i	$-0.564714\pi$
$97$	−3.52091e8	−0.403815	−0.201907	+	0.979405i	$0.564714\pi$
$98$	5.95072e8	0.651707
$99$	−3.03332e8	−0.317366
$100$	9.12557e8	0.912557
$101$	6.88270e8	0.658131	0.329066	−	0.944307i	$-0.393266\pi$
$101$	6.88270e8	0.658131	0.329066	+	0.944307i	$0.393266\pi$
$102$	−1.79125e8	−0.163853
$103$	−3.83601e8	−0.335824	−0.167912	−	0.985802i	$-0.553702\pi$
$103$	−3.83601e8	−0.335824	−0.167912	+	0.985802i	$0.553702\pi$
$104$	−5.36855e8	−0.449994
$105$	−4.15774e9	−3.33815
$106$	1.17592e8	0.0904695
$107$	1.09202e9	0.805386	0.402693	−	0.915335i	$-0.368074\pi$
$107$	1.09202e9	0.805386	0.402693	+	0.915335i	$0.368074\pi$
$108$	5.32570e7	0.0376677
$109$	2.57677e9	1.74846	0.874231	−	0.485511i	$-0.161366\pi$
$109$	2.57677e9	1.74846	0.874231	+	0.485511i	$0.161366\pi$
$110$	−5.50267e8	−0.358349
$111$	−1.56841e9	−0.980631
$112$	−5.77110e8	−0.346559
$113$	4.58506e7	0.0264540	0.0132270	−	0.999913i	$-0.495790\pi$
$113$	4.58506e7	0.0264540	0.0132270	+	0.999913i	$0.495790\pi$
$114$	3.35051e9	1.85797
$115$	−1.55536e9	−0.829262
$116$	−1.23375e9	−0.632655
$117$	−2.71547e9	−1.33970
$118$	−1.82243e9	−0.865330
$119$	4.90477e8	0.224211
$120$	1.93392e9	0.851380
$121$	2.14359e8	0.0909091
$122$	−2.21028e8	−0.0903292
$123$	−1.19147e9	−0.469366
$124$	−4.61094e7	−0.0175143
$125$	3.78553e9	1.38686
$126$	−2.91908e9	−1.03176
$127$	1.48624e8	0.0506959	0.0253479	−	0.999679i	$-0.491931\pi$
$127$	1.48624e8	0.0506959	0.0253479	+	0.999679i	$0.491931\pi$
$128$	2.68435e8	0.0883883
$129$	−1.19176e9	−0.378910
$130$	−4.92606e9	−1.51271
$131$	1.38776e9	0.411711	0.205855	−	0.978582i	$-0.434002\pi$
$131$	1.38776e9	0.411711	0.205855	+	0.978582i	$0.434002\pi$
$132$	−7.53367e8	−0.215985
$133$	−9.17430e9	−2.54238
$134$	4.95969e9	1.32887
$135$	4.88674e8	0.126624
$136$	−2.28139e8	−0.0571840
$137$	6.00034e9	1.45524	0.727618	−	0.685983i	$-0.240628\pi$
$137$	6.00034e9	1.45524	0.727618	+	0.685983i	$0.240628\pi$
$138$	−2.12944e9	−0.499815
$139$	1.49373e9	0.339395	0.169697	−	0.985496i	$-0.445721\pi$
$139$	1.49373e9	0.339395	0.169697	+	0.985496i	$0.445721\pi$
$140$	−5.29544e9	−1.16500
$141$	1.23768e10	2.63708
$142$	6.84042e8	0.141184
$143$	1.91897e9	0.383756
$144$	1.35777e9	0.263146
$145$	−1.13206e10	−2.12674
$146$	2.27229e9	0.413882
$147$	7.47560e9	1.32044
$148$	−1.99757e9	−0.342236
$149$	1.92475e9	0.319916	0.159958	−	0.987124i	$-0.448864\pi$
$149$	1.92475e9	0.319916	0.159958	+	0.987124i	$0.448864\pi$
$150$	1.14640e10	1.84895
$151$	−1.26046e9	−0.197303	−0.0986516	−	0.995122i	$-0.531453\pi$
$151$	−1.26046e9	−0.197303	−0.0986516	+	0.995122i	$0.531453\pi$
$152$	4.26731e9	0.648423
$153$	−1.15395e9	−0.170246
$154$	2.06286e9	0.295547
$155$	−4.23090e8	−0.0588763
$156$	−6.74424e9	−0.911742
$157$	−3.69405e9	−0.485238	−0.242619	−	0.970122i	$-0.578006\pi$
$157$	−3.69405e9	−0.485238	−0.242619	+	0.970122i	$0.578006\pi$
$158$	−5.20602e9	−0.664583
$159$	1.47725e9	0.183302
$160$	2.46311e9	0.297128
$161$	5.83080e9	0.683930
$162$	−5.85564e9	−0.667970
$163$	1.63111e10	1.80984	0.904919	−	0.425583i	$-0.139931\pi$
$163$	1.63111e10	1.80984	0.904919	+	0.425583i	$0.139931\pi$
$164$	−1.51750e9	−0.163807
$165$	−6.91273e9	−0.726059
$166$	4.05605e9	0.414588
$167$	4.30760e9	0.428560	0.214280	−	0.976772i	$-0.431260\pi$
$167$	4.30760e9	0.428560	0.214280	+	0.976772i	$0.431260\pi$
$168$	−7.24994e9	−0.702171
$169$	6.57432e9	0.619956
$170$	−2.09335e9	−0.192231
$171$	2.15845e10	1.93046
$172$	−1.51787e9	−0.132238
$173$	−9.59874e9	−0.814717	−0.407359	−	0.913268i	$-0.633550\pi$
$173$	−9.59874e9	−0.814717	−0.407359	+	0.913268i	$0.633550\pi$
$174$	−1.54990e10	−1.28184
$175$	−3.13905e10	−2.53004
$176$	−9.59513e8	−0.0753778
$177$	−2.28943e10	−1.75326
$178$	−1.59076e10	−1.18772
$179$	4.17227e9	0.303762	0.151881	−	0.988399i	$-0.451467\pi$
$179$	4.17227e9	0.303762	0.151881	+	0.988399i	$0.451467\pi$
$180$	1.24586e10	0.884595
$181$	−1.63012e10	−1.12893	−0.564463	−	0.825458i	$-0.690917\pi$
$181$	−1.63012e10	−1.12893	−0.564463	+	0.825458i	$0.690917\pi$
$182$	1.84670e10	1.24760
$183$	−2.77667e9	−0.183018
$184$	−2.71212e9	−0.174433
$185$	−1.83293e10	−1.15046
$186$	−5.79250e8	−0.0354861
$187$	8.15474e8	0.0487667
$188$	1.57635e10	0.920327
$189$	−1.83196e9	−0.104433
$190$	3.91559e10	2.17975
$191$	1.70247e10	0.925612	0.462806	−	0.886460i	$-0.346843\pi$
$191$	1.70247e10	0.925612	0.462806	+	0.886460i	$0.346843\pi$
$192$	3.37222e9	0.179086
$193$	4.77165e9	0.247549	0.123774	−	0.992310i	$-0.460500\pi$
$193$	4.77165e9	0.247549	0.123774	+	0.992310i	$0.460500\pi$
$194$	−5.63346e9	−0.285540
$195$	−6.18836e10	−3.06493
$196$	9.52116e9	0.460827
$197$	−1.31057e10	−0.619959	−0.309979	−	0.950743i	$-0.600322\pi$
$197$	−1.31057e10	−0.619959	−0.309979	+	0.950743i	$0.600322\pi$
$198$	−4.85332e9	−0.224412
$199$	2.34216e10	1.05871	0.529355	−	0.848401i	$-0.322434\pi$
$199$	2.34216e10	1.05871	0.529355	+	0.848401i	$0.322434\pi$
$200$	1.46009e10	0.645275
$201$	6.23062e10	2.69246
$202$	1.10123e10	0.465369
$203$	4.24391e10	1.75402
$204$	−2.86600e9	−0.115862
$205$	−1.39243e10	−0.550655
$206$	−6.13761e9	−0.237464
$207$	−1.37182e10	−0.519314
$208$	−8.58967e9	−0.318194
$209$	−1.52533e10	−0.552977
$210$	−6.65239e10	−2.36043
$211$	−3.58111e10	−1.24379	−0.621895	−	0.783101i	$-0.713637\pi$
$211$	−3.58111e10	−1.24379	−0.621895	+	0.783101i	$0.713637\pi$
$212$	1.88148e9	0.0639716
$213$	8.59328e9	0.286056
$214$	1.74723e10	0.569494
$215$	−1.39276e10	−0.444532
$216$	8.52111e8	0.0266351
$217$	1.58609e9	0.0485579
$218$	4.12283e10	1.23635
$219$	2.85457e10	0.838575
$220$	−8.80428e9	−0.253391
$221$	7.30023e9	0.205860
$222$	−2.50945e10	−0.693411
$223$	−3.58004e10	−0.969429	−0.484714	−	0.874672i	$-0.661076\pi$
$223$	−3.58004e10	−0.969429	−0.484714	+	0.874672i	$0.661076\pi$
$224$	−9.23376e9	−0.245054
$225$	7.38530e10	1.92108
$226$	7.33609e8	0.0187058
$227$	5.56032e10	1.38990	0.694949	−	0.719059i	$-0.255427\pi$
$227$	5.56032e10	1.38990	0.694949	+	0.719059i	$0.255427\pi$
$228$	5.36081e10	1.31378
$229$	−4.24510e10	−1.02006	−0.510032	−	0.860155i	$-0.670367\pi$
$229$	−4.24510e10	−1.02006	−0.510032	+	0.860155i	$0.670367\pi$
$230$	−2.48858e10	−0.586377
$231$	2.59147e10	0.598813
$232$	−1.97400e10	−0.447355
$233$	4.57899e10	1.01781	0.508907	−	0.860822i	$-0.330050\pi$
$233$	4.57899e10	1.01781	0.508907	+	0.860822i	$0.330050\pi$
$234$	−4.34475e10	−0.947312
$235$	1.44642e11	3.09379
$236$	−2.91589e10	−0.611881
$237$	−6.54007e10	−1.34653
$238$	7.84763e9	0.158541
$239$	−9.66351e10	−1.91577	−0.957887	−	0.287145i	$-0.907294\pi$
$239$	−9.66351e10	−1.91577	−0.957887	+	0.287145i	$0.907294\pi$
$240$	3.09428e10	0.602017
$241$	1.42603e10	0.272303	0.136152	−	0.990688i	$-0.456527\pi$
$241$	1.42603e10	0.272303	0.136152	+	0.990688i	$0.456527\pi$
$242$	3.42974e9	0.0642824
$243$	−7.76562e10	−1.42872
$244$	−3.53645e9	−0.0638724
$245$	8.73641e10	1.54912
$246$	−1.90636e10	−0.331892
$247$	−1.36550e11	−2.33429
$248$	−7.37751e8	−0.0123845
$249$	5.09541e10	0.840005
$250$	6.05685e10	0.980657
$251$	4.38989e10	0.698107	0.349053	−	0.937103i	$-0.386503\pi$
$251$	4.38989e10	0.698107	0.349053	+	0.937103i	$0.386503\pi$
$252$	−4.67053e10	−0.729565
$253$	9.69438e9	0.148757
$254$	2.37799e9	0.0358474
$255$	−2.62978e10	−0.389482
$256$	4.29497e9	0.0625000
$257$	−1.05393e11	−1.50699	−0.753497	−	0.657452i	$-0.771634\pi$
$257$	−1.05393e11	−1.50699	−0.753497	+	0.657452i	$0.771634\pi$
$258$	−1.90682e10	−0.267930
$259$	6.87134e10	0.948839
$260$	−7.88170e10	−1.06964
$261$	−9.98472e10	−1.33184
$262$	2.22041e10	0.291123
$263$	−8.81095e8	−0.0113559	−0.00567796	−	0.999984i	$-0.501807\pi$
$263$	−8.81095e8	−0.0113559	−0.00567796	+	0.999984i	$0.501807\pi$
$264$	−1.20539e10	−0.152725
$265$	1.72640e10	0.215048
$266$	−1.46789e11	−1.79773
$267$	−1.99840e11	−2.40647
$268$	7.93551e10	0.939655
$269$	−7.04017e10	−0.819782	−0.409891	−	0.912135i	$-0.634433\pi$
$269$	−7.04017e10	−0.819782	−0.409891	+	0.912135i	$0.634433\pi$
$270$	7.81879e9	0.0895370
$271$	1.98306e10	0.223344	0.111672	−	0.993745i	$-0.464379\pi$
$271$	1.98306e10	0.223344	0.111672	+	0.993745i	$0.464379\pi$
$272$	−3.65022e9	−0.0404352
$273$	2.31991e11	2.52778
$274$	9.60054e10	1.02901
$275$	−5.21904e10	−0.550293
$276$	−3.40710e10	−0.353423
$277$	1.56911e11	1.60138	0.800689	−	0.599080i	$-0.204467\pi$
$277$	1.56911e11	1.60138	0.800689	+	0.599080i	$0.204467\pi$
$278$	2.38996e10	0.239988
$279$	−3.73162e9	−0.0368705
$280$	−8.47270e10	−0.823779
$281$	−1.17120e11	−1.12060	−0.560300	−	0.828289i	$-0.689314\pi$
$281$	−1.17120e11	−1.12060	−0.560300	+	0.828289i	$0.689314\pi$
$282$	1.98029e11	1.86469
$283$	2.85801e10	0.264865	0.132433	−	0.991192i	$-0.457721\pi$
$283$	2.85801e10	0.264865	0.132433	+	0.991192i	$0.457721\pi$
$284$	1.09447e10	0.0998321
$285$	4.91896e11	4.41643
$286$	3.07035e10	0.271357
$287$	5.21996e10	0.454150
$288$	2.17244e10	0.186072
$289$	−1.15486e11	−0.973840
$290$	−1.81130e11	−1.50383
$291$	−7.07703e10	−0.578539
$292$	3.63567e10	0.292659
$293$	5.33249e9	0.0422694	0.0211347	−	0.999777i	$-0.493272\pi$
$293$	5.33249e9	0.0422694	0.0211347	+	0.999777i	$0.493272\pi$
$294$	1.19610e11	0.933690
$295$	−2.67556e11	−2.05691
$296$	−3.19612e10	−0.241997
$297$	−3.04584e9	−0.0227145
$298$	3.07960e10	0.226215
$299$	8.67852e10	0.627951
$300$	1.83424e11	1.30741
$301$	5.22122e10	0.366626
$302$	−2.01674e10	−0.139514
$303$	1.38342e11	0.942894
$304$	6.82770e10	0.458504
$305$	−3.24497e10	−0.214714
$306$	−1.84632e10	−0.120382
$307$	−2.51695e11	−1.61715	−0.808576	−	0.588391i	$-0.799762\pi$
$307$	−2.51695e11	−1.61715	−0.808576	+	0.588391i	$0.799762\pi$
$308$	3.30057e10	0.208983
$309$	−7.71038e10	−0.481130
$310$	−6.76944e9	−0.0416318
$311$	4.28397e10	0.259672	0.129836	−	0.991536i	$-0.458555\pi$
$311$	4.28397e10	0.259672	0.129836	+	0.991536i	$0.458555\pi$
$312$	−1.07908e11	−0.644699
$313$	2.77976e11	1.63703	0.818516	−	0.574483i	$-0.194797\pi$
$313$	2.77976e11	1.63703	0.818516	+	0.574483i	$0.194797\pi$
$314$	−5.91049e10	−0.343115
$315$	−4.28558e11	−2.45252
$316$	−8.32964e10	−0.469931
$317$	−1.63568e11	−0.909771	−0.454885	−	0.890550i	$-0.650320\pi$
$317$	−1.63568e11	−0.909771	−0.454885	+	0.890550i	$0.650320\pi$
$318$	2.36360e10	0.129614
$319$	7.05600e10	0.381505
$320$	3.94097e10	0.210101
$321$	2.19496e11	1.15386
$322$	9.32927e10	0.483611
$323$	−5.80275e10	−0.296635
$324$	−9.36902e10	−0.472326
$325$	−4.67215e11	−2.32296
$326$	2.60978e11	1.27975
$327$	5.17930e11	2.50499
$328$	−2.42800e10	−0.115829
$329$	−5.42240e11	−2.55158
$330$	−1.10604e11	−0.513401
$331$	−1.14079e11	−0.522373	−0.261187	−	0.965288i	$-0.584114\pi$
$331$	−1.14079e11	−0.522373	−0.261187	+	0.965288i	$0.584114\pi$
$332$	6.48968e10	0.293158
$333$	−1.61663e11	−0.720463
$334$	6.89216e10	0.303038
$335$	7.28145e11	3.15876
$336$	−1.15999e11	−0.496510
$337$	−2.95496e11	−1.24801	−0.624003	−	0.781422i	$-0.714495\pi$
$337$	−2.95496e11	−1.24801	−0.624003	+	0.781422i	$0.714495\pi$
$338$	1.05189e11	0.438375
$339$	9.21597e9	0.0379003
$340$	−3.34937e10	−0.135928
$341$	2.63706e9	0.0105615
$342$	3.45352e11	1.36504
$343$	2.78409e10	0.108607
$344$	−2.42858e10	−0.0935062
$345$	−3.12628e11	−1.18807
$346$	−1.53580e11	−0.576092
$347$	2.36035e11	0.873965	0.436982	−	0.899470i	$-0.356047\pi$
$347$	2.36035e11	0.873965	0.436982	+	0.899470i	$0.356047\pi$
$348$	−2.47984e11	−0.906395
$349$	−2.53444e11	−0.914466	−0.457233	−	0.889347i	$-0.651159\pi$
$349$	−2.53444e11	−0.914466	−0.457233	+	0.889347i	$0.651159\pi$
$350$	−5.02249e11	−1.78901
$351$	−2.72667e10	−0.0958851
$352$	−1.53522e10	−0.0533002
$353$	8.59537e10	0.294631	0.147315	−	0.989090i	$-0.452937\pi$
$353$	8.59537e10	0.294631	0.147315	+	0.989090i	$0.452937\pi$
$354$	−3.66309e11	−1.23974
$355$	1.00426e11	0.335597
$356$	−2.54522e11	−0.839848
$357$	9.85858e10	0.321224
$358$	6.67563e10	0.214792
$359$	−1.02076e11	−0.324340	−0.162170	−	0.986763i	$-0.551849\pi$
$359$	−1.02076e11	−0.324340	−0.162170	+	0.986763i	$0.551849\pi$
$360$	1.99338e11	0.625503
$361$	7.62710e11	2.36362
$362$	−2.60819e11	−0.798272
$363$	4.30861e10	0.130244
$364$	2.95471e11	0.882184
$365$	3.33601e11	0.983806
$366$	−4.44267e10	−0.129413
$367$	−1.34359e11	−0.386607	−0.193304	−	0.981139i	$-0.561920\pi$
$367$	−1.34359e11	−0.386607	−0.193304	+	0.981139i	$0.561920\pi$
$368$	−4.33939e10	−0.123343
$369$	−1.22811e11	−0.344840
$370$	−2.93269e11	−0.813501
$371$	−6.47198e10	−0.177360
$372$	−9.26800e9	−0.0250924
$373$	5.00742e11	1.33944	0.669722	−	0.742612i	$-0.266413\pi$
$373$	5.00742e11	1.33944	0.669722	+	0.742612i	$0.266413\pi$
$374$	1.30476e10	0.0344832
$375$	7.60892e11	1.98693
$376$	2.52216e11	0.650770
$377$	6.31662e11	1.61045
$378$	−2.93113e10	−0.0738451
$379$	2.34637e11	0.584143	0.292072	−	0.956396i	$-0.405655\pi$
$379$	2.34637e11	0.584143	0.292072	+	0.956396i	$0.405655\pi$
$380$	6.26495e11	1.54131
$381$	2.98735e10	0.0726312
$382$	2.72395e11	0.654506
$383$	−4.64289e11	−1.10254	−0.551270	−	0.834327i	$-0.685857\pi$
$383$	−4.64289e11	−1.10254	−0.551270	+	0.834327i	$0.685857\pi$
$384$	5.39555e10	0.126633
$385$	3.02853e11	0.702521
$386$	7.63464e10	0.175043
$387$	−1.22840e11	−0.278382
$388$	−9.01353e10	−0.201907
$389$	−8.73777e11	−1.93476	−0.967381	−	0.253326i	$-0.918475\pi$
$389$	−8.73777e11	−1.93476	−0.967381	+	0.253326i	$0.918475\pi$
$390$	−9.90138e11	−2.16723
$391$	3.68798e10	0.0797982
$392$	1.52339e11	0.325854
$393$	2.78939e11	0.589851
$394$	−2.09691e11	−0.438377
$395$	−7.64309e11	−1.57973
$396$	−7.76531e10	−0.158683
$397$	9.36834e10	0.189280	0.0946401	−	0.995512i	$-0.469830\pi$
$397$	9.36834e10	0.189280	0.0946401	+	0.995512i	$0.469830\pi$
$398$	3.74745e11	0.748621
$399$	−1.84403e12	−3.64243
$400$	2.33615e11	0.456279
$401$	−2.36886e11	−0.457499	−0.228750	−	0.973485i	$-0.573464\pi$
$401$	−2.36886e11	−0.457499	−0.228750	+	0.973485i	$0.573464\pi$
$402$	9.96899e11	1.90385
$403$	2.36073e10	0.0445835
$404$	1.76197e11	0.329066
$405$	−8.59681e11	−1.58778
$406$	6.79026e11	1.24028
$407$	1.14244e11	0.206376
$408$	−4.58559e10	−0.0819266
$409$	−5.49313e11	−0.970656	−0.485328	−	0.874332i	$-0.661300\pi$
$409$	−5.49313e11	−0.970656	−0.485328	+	0.874332i	$0.661300\pi$
$410$	−2.22788e11	−0.389372
$411$	1.20607e12	2.08489
$412$	−9.82018e10	−0.167912
$413$	1.00302e12	1.69642
$414$	−2.19491e11	−0.367211
$415$	5.95478e11	0.985484
$416$	−1.37435e11	−0.224997
$417$	3.00239e11	0.486245
$418$	−2.44054e11	−0.391014
$419$	2.37197e11	0.375964	0.187982	−	0.982173i	$-0.439805\pi$
$419$	2.37197e11	0.375964	0.187982	+	0.982173i	$0.439805\pi$
$420$	−1.06438e12	−1.66908
$421$	−6.30625e11	−0.978367	−0.489184	−	0.872181i	$-0.662705\pi$
$421$	−6.30625e11	−0.978367	−0.489184	+	0.872181i	$0.662705\pi$
$422$	−5.72978e11	−0.879492
$423$	1.27574e12	1.93744
$424$	3.01036e10	0.0452348
$425$	−1.98545e11	−0.295195
$426$	1.37492e11	0.202272
$427$	1.21648e11	0.177085
$428$	2.79557e11	0.402693
$429$	3.85712e11	0.549801
$430$	−2.22842e11	−0.314332
$431$	1.52381e11	0.212708	0.106354	−	0.994328i	$-0.466082\pi$
$431$	1.52381e11	0.212708	0.106354	+	0.994328i	$0.466082\pi$
$432$	1.36338e10	0.0188339
$433$	−7.40697e11	−1.01262	−0.506308	−	0.862353i	$-0.668990\pi$
$433$	−7.40697e11	−1.01262	−0.506308	+	0.862353i	$0.668990\pi$
$434$	2.53775e10	0.0343356
$435$	−2.27545e12	−3.04695
$436$	6.59653e11	0.874231
$437$	−6.89832e11	−0.904851
$438$	4.56731e11	0.592962
$439$	−4.51581e11	−0.580291	−0.290145	−	0.956983i	$-0.593704\pi$
$439$	−4.51581e11	−0.580291	−0.290145	+	0.956983i	$0.593704\pi$
$440$	−1.40868e11	−0.179175
$441$	7.70544e11	0.970117
$442$	1.16804e11	0.145565
$443$	−2.76648e11	−0.341280	−0.170640	−	0.985333i	$-0.554583\pi$
$443$	−2.76648e11	−0.341280	−0.170640	+	0.985333i	$0.554583\pi$
$444$	−4.01512e11	−0.490316
$445$	−2.33544e12	−2.82325
$446$	−5.72806e11	−0.685490
$447$	3.86875e11	0.458339
$448$	−1.47740e11	−0.173280
$449$	1.29935e12	1.50876	0.754378	−	0.656440i	$-0.227939\pi$
$449$	1.29935e12	1.50876	0.754378	+	0.656440i	$0.227939\pi$
$450$	1.18165e12	1.35841
$451$	8.67880e10	0.0987791
$452$	1.17378e10	0.0132270
$453$	−2.53353e11	−0.282673
$454$	8.89651e11	0.982807
$455$	2.71118e12	2.96556
$456$	8.57730e11	0.928985
$457$	−1.32625e12	−1.42233	−0.711166	−	0.703024i	$-0.751833\pi$
$457$	−1.32625e12	−1.42233	−0.711166	+	0.703024i	$0.751833\pi$
$458$	−6.79215e11	−0.721295
$459$	−1.15871e10	−0.0121848
$460$	−3.98173e11	−0.414631
$461$	2.22504e11	0.229448	0.114724	−	0.993397i	$-0.463402\pi$
$461$	2.22504e11	0.229448	0.114724	+	0.993397i	$0.463402\pi$
$462$	4.14635e11	0.423425
$463$	−1.54466e12	−1.56213	−0.781066	−	0.624449i	$-0.785324\pi$
$463$	−1.54466e12	−1.56213	−0.781066	+	0.624449i	$0.785324\pi$
$464$	−3.15841e11	−0.316327
$465$	−8.50411e10	−0.0843511
$466$	7.32639e11	0.719703
$467$	1.02788e11	0.100003	0.0500017	−	0.998749i	$-0.484077\pi$
$467$	1.02788e11	0.100003	0.0500017	+	0.998749i	$0.484077\pi$
$468$	−6.95160e11	−0.669851
$469$	−2.72969e12	−2.60517
$470$	2.31428e12	2.18764
$471$	−7.42505e11	−0.695193
$472$	−4.66542e11	−0.432665
$473$	8.68089e10	0.0797423
$474$	−1.04641e12	−0.952137
$475$	3.71377e12	3.34729
$476$	1.25562e11	0.112106
$477$	1.52267e11	0.134671
$478$	−1.54616e12	−1.35466
$479$	−7.12999e11	−0.618841	−0.309420	−	0.950925i	$-0.600135\pi$
$479$	−7.12999e11	−0.618841	−0.309420	+	0.950925i	$0.600135\pi$
$480$	4.95084e11	0.425690
$481$	1.02273e12	0.871178
$482$	2.28165e11	0.192547
$483$	1.17199e12	0.979855
$484$	5.48759e10	0.0454545
$485$	−8.27062e11	−0.678735
$486$	−1.24250e12	−1.01026
$487$	2.24737e12	1.81048	0.905241	−	0.424899i	$-0.139690\pi$
$487$	2.24737e12	1.81048	0.905241	+	0.424899i	$0.139690\pi$
$488$	−5.65832e10	−0.0451646
$489$	3.27854e12	2.59293
$490$	1.39783e12	1.09539
$491$	1.43130e12	1.11139	0.555694	−	0.831387i	$-0.312453\pi$
$491$	1.43130e12	1.11139	0.555694	+	0.831387i	$0.312453\pi$
$492$	−3.05018e11	−0.234683
$493$	2.68428e11	0.204652
$494$	−2.18480e12	−1.65059
$495$	−7.12527e11	−0.533431
$496$	−1.18040e10	−0.00875714
$497$	−3.76480e11	−0.276782
$498$	8.15265e11	0.593973
$499$	−8.45721e11	−0.610625	−0.305312	−	0.952252i	$-0.598761\pi$
$499$	−8.45721e11	−0.610625	−0.305312	+	0.952252i	$0.598761\pi$
$500$	9.69097e11	0.693429
$501$	8.65828e11	0.613991
$502$	7.02382e11	0.493636
$503$	−1.12790e12	−0.785622	−0.392811	−	0.919619i	$-0.628497\pi$
$503$	−1.12790e12	−0.785622	−0.392811	+	0.919619i	$0.628497\pi$
$504$	−7.47285e11	−0.515880
$505$	1.61675e12	1.10619
$506$	1.55110e11	0.105187
$507$	1.32144e12	0.888201
$508$	3.80478e10	0.0253479
$509$	7.94997e11	0.524971	0.262485	−	0.964936i	$-0.415458\pi$
$509$	7.94997e11	0.524971	0.262485	+	0.964936i	$0.415458\pi$
$510$	−4.20764e11	−0.275406
$511$	−1.25061e12	−0.811389
$512$	6.87195e10	0.0441942
$513$	2.16736e11	0.138166
$514$	−1.68628e12	−1.06561
$515$	−9.01078e11	−0.564456
$516$	−3.05091e11	−0.189455
$517$	−9.01537e11	−0.554978
$518$	1.09942e12	0.670931
$519$	−1.92935e12	−1.16723
$520$	−1.26107e12	−0.756353
$521$	6.59850e11	0.392351	0.196176	−	0.980569i	$-0.437148\pi$
$521$	6.59850e11	0.392351	0.196176	+	0.980569i	$0.437148\pi$
$522$	−1.59755e12	−0.941756
$523$	4.57365e11	0.267304	0.133652	−	0.991028i	$-0.457330\pi$
$523$	4.57365e11	0.267304	0.133652	+	0.991028i	$0.457330\pi$
$524$	3.55265e11	0.205855
$525$	−6.30950e12	−3.62475
$526$	−1.40975e10	−0.00802984
$527$	1.00320e10	0.00566555
$528$	−1.92862e11	−0.107993
$529$	−1.36272e12	−0.756585
$530$	2.76224e11	0.152062
$531$	−2.35982e12	−1.28811
$532$	−2.34862e12	−1.27119
$533$	7.76937e11	0.416978
$534$	−3.19744e12	−1.70163
$535$	2.56516e12	1.35370
$536$	1.26968e12	0.664436
$537$	8.38625e11	0.435195
$538$	−1.12643e12	−0.579673
$539$	−5.44528e11	−0.277889
$540$	1.25101e11	0.0633122
$541$	1.51397e12	0.759852	0.379926	−	0.925017i	$-0.375949\pi$
$541$	1.51397e12	0.759852	0.379926	+	0.925017i	$0.375949\pi$
$542$	3.17289e11	0.157928
$543$	−3.27654e12	−1.61740
$544$	−5.84036e10	−0.0285920
$545$	6.05283e12	2.93883
$546$	3.71186e12	1.78741
$547$	1.54206e12	0.736476	0.368238	−	0.929732i	$-0.379961\pi$
$547$	1.54206e12	0.736476	0.368238	+	0.929732i	$0.379961\pi$
$548$	1.53609e12	0.727618
$549$	−2.86204e11	−0.134462
$550$	−8.35047e11	−0.389116
$551$	−5.02091e12	−2.32060
$552$	−5.45136e11	−0.249908
$553$	2.86526e12	1.30287
$554$	2.51057e12	1.13235
$555$	−3.68419e12	−1.64825
$556$	3.82394e11	0.169697
$557$	−6.33279e11	−0.278770	−0.139385	−	0.990238i	$-0.544513\pi$
$557$	−6.33279e11	−0.278770	−0.139385	+	0.990238i	$0.544513\pi$
$558$	−5.97060e10	−0.0260714
$559$	7.77123e11	0.336618
$560$	−1.35563e12	−0.582499
$561$	1.63910e11	0.0698672
$562$	−1.87391e12	−0.792384
$563$	3.67443e12	1.54136	0.770678	−	0.637225i	$-0.219918\pi$
$563$	3.67443e12	1.54136	0.770678	+	0.637225i	$0.219918\pi$
$564$	3.16846e12	1.31854
$565$	1.07703e11	0.0444641
$566$	4.57281e11	0.187288
$567$	3.22280e12	1.30951
$568$	1.75115e11	0.0705920
$569$	−3.72900e12	−1.49138	−0.745688	−	0.666295i	$-0.767879\pi$
$569$	−3.72900e12	−1.49138	−0.745688	+	0.666295i	$0.767879\pi$
$570$	7.87034e12	3.12289
$571$	−3.86174e12	−1.52027	−0.760135	−	0.649766i	$-0.774867\pi$
$571$	−3.86174e12	−1.52027	−0.760135	+	0.649766i	$0.774867\pi$
$572$	4.91255e11	0.191878
$573$	3.42196e12	1.32611
$574$	8.35194e11	0.321132
$575$	−2.36031e12	−0.900459
$576$	3.47590e11	0.131573
$577$	4.56854e12	1.71588	0.857939	−	0.513752i	$-0.171745\pi$
$577$	4.56854e12	1.71588	0.857939	+	0.513752i	$0.171745\pi$
$578$	−1.84777e12	−0.688609
$579$	9.59101e11	0.354659
$580$	−2.89808e12	−1.06337
$581$	−2.23235e12	−0.812773
$582$	−1.13232e12	−0.409089
$583$	−1.07604e11	−0.0385763
$584$	5.81707e11	0.206941
$585$	−6.37863e12	−2.25178
$586$	8.53199e10	0.0298890
$587$	−2.58810e12	−0.899724	−0.449862	−	0.893098i	$-0.648527\pi$
$587$	−2.58810e12	−0.899724	−0.449862	+	0.893098i	$0.648527\pi$
$588$	1.91375e12	0.660219
$589$	−1.87648e11	−0.0642429
$590$	−4.28089e12	−1.45445
$591$	−2.63425e12	−0.888205
$592$	−5.11379e11	−0.171118
$593$	4.61703e12	1.53326	0.766631	−	0.642087i	$-0.221931\pi$
$593$	4.61703e12	1.53326	0.766631	+	0.642087i	$0.221931\pi$
$594$	−4.87334e10	−0.0160616
$595$	1.15213e12	0.376856
$596$	4.92736e11	0.159958
$597$	4.70773e12	1.51680
$598$	1.38856e12	0.444028
$599$	3.37095e11	0.106987	0.0534936	−	0.998568i	$-0.482964\pi$
$599$	3.37095e11	0.106987	0.0534936	+	0.998568i	$0.482964\pi$
$600$	2.93478e12	0.924476
$601$	−1.84897e12	−0.578089	−0.289045	−	0.957316i	$-0.593338\pi$
$601$	−1.84897e12	−0.578089	−0.289045	+	0.957316i	$0.593338\pi$
$602$	8.35395e11	0.259243
$603$	6.42218e12	1.97813
$604$	−3.22679e11	−0.0986516
$605$	5.03529e11	0.152801
$606$	2.21348e12	0.666727
$607$	−4.29602e12	−1.28445	−0.642225	−	0.766516i	$-0.721989\pi$
$607$	−4.29602e12	−1.28445	−0.642225	+	0.766516i	$0.721989\pi$
$608$	1.09243e12	0.324211
$609$	8.53027e12	2.51296
$610$	−5.19195e11	−0.151826
$611$	−8.07067e12	−2.34274
$612$	−2.95411e11	−0.0851228
$613$	1.91087e12	0.546585	0.273293	−	0.961931i	$-0.411887\pi$
$613$	1.91087e12	0.546585	0.273293	+	0.961931i	$0.411887\pi$
$614$	−4.02711e12	−1.14350
$615$	−2.79877e12	−0.788914
$616$	5.28092e11	0.147773
$617$	−3.39102e12	−0.941992	−0.470996	−	0.882135i	$-0.656105\pi$
$617$	−3.39102e12	−0.941992	−0.470996	+	0.882135i	$0.656105\pi$
$618$	−1.23366e12	−0.340210
$619$	−1.85635e12	−0.508220	−0.254110	−	0.967175i	$-0.581782\pi$
$619$	−1.85635e12	−0.508220	−0.254110	+	0.967175i	$0.581782\pi$
$620$	−1.08311e11	−0.0294381
$621$	−1.37748e11	−0.0371684
$622$	6.85435e11	0.183616
$623$	8.75517e12	2.32846
$624$	−1.72652e12	−0.455871
$625$	1.92996e12	0.505927
$626$	4.44761e12	1.15756
$627$	−3.06592e12	−0.792241
$628$	−9.45678e11	−0.242619
$629$	4.34613e11	0.110707
$630$	−6.85693e12	−1.73419
$631$	2.69381e12	0.676448	0.338224	−	0.941066i	$-0.390174\pi$
$631$	2.69381e12	0.676448	0.338224	+	0.941066i	$0.390174\pi$
$632$	−1.33274e12	−0.332291
$633$	−7.19804e12	−1.78196
$634$	−2.61709e12	−0.643305
$635$	3.49118e11	0.0852100
$636$	3.78177e11	0.0916511
$637$	−4.87468e12	−1.17306
$638$	1.12896e12	0.269765
$639$	8.85749e11	0.210163
$640$	6.30555e11	0.148564
$641$	−5.23535e10	−0.0122486	−0.00612428	−	0.999981i	$-0.501949\pi$
$641$	−5.23535e10	−0.0122486	−0.00612428	+	0.999981i	$0.501949\pi$
$642$	3.51194e12	0.815905
$643$	6.75276e12	1.55787	0.778936	−	0.627103i	$-0.215759\pi$
$643$	6.75276e12	1.55787	0.778936	+	0.627103i	$0.215759\pi$
$644$	1.49268e12	0.341965
$645$	−2.79945e12	−0.636874
$646$	−9.28440e11	−0.209753
$647$	−7.21753e12	−1.61927	−0.809635	−	0.586934i	$-0.800335\pi$
$647$	−7.21753e12	−1.61927	−0.809635	+	0.586934i	$0.800335\pi$
$648$	−1.49904e12	−0.333985
$649$	1.66764e12	0.368978
$650$	−7.47544e12	−1.64258
$651$	3.18805e11	0.0695681
$652$	4.17565e12	0.904919
$653$	6.78616e12	1.46054	0.730272	−	0.683156i	$-0.239393\pi$
$653$	6.78616e12	1.46054	0.730272	+	0.683156i	$0.239393\pi$
$654$	8.28688e12	1.77130
$655$	3.25984e12	0.692006
$656$	−3.88480e11	−0.0819033
$657$	2.94234e12	0.616096
$658$	−8.67584e12	−1.80424
$659$	2.82859e12	0.584233	0.292116	−	0.956383i	$-0.405641\pi$
$659$	2.82859e12	0.584233	0.292116	+	0.956383i	$0.405641\pi$
$660$	−1.76966e12	−0.363030
$661$	−6.85418e12	−1.39653	−0.698263	−	0.715841i	$-0.746043\pi$
$661$	−6.85418e12	−1.39653	−0.698263	+	0.715841i	$0.746043\pi$
$662$	−1.82527e12	−0.369374
$663$	1.46735e12	0.294932
$664$	1.03835e12	0.207294
$665$	−2.15504e13	−4.27325
$666$	−2.58661e12	−0.509444
$667$	3.19108e12	0.624268
$668$	1.10275e12	0.214280
$669$	−7.19588e12	−1.38889
$670$	1.16503e13	2.23358
$671$	2.02255e11	0.0385165
$672$	−1.85599e12	−0.351086
$673$	−3.75425e12	−0.705433	−0.352717	−	0.935730i	$-0.614742\pi$
$673$	−3.75425e12	−0.705433	−0.352717	+	0.935730i	$0.614742\pi$
$674$	−4.72793e12	−0.882473
$675$	7.41577e11	0.137496
$676$	1.68303e12	0.309978
$677$	2.31949e12	0.424369	0.212184	−	0.977230i	$-0.431942\pi$
$677$	2.31949e12	0.424369	0.212184	+	0.977230i	$0.431942\pi$
$678$	1.47456e11	0.0267995
$679$	3.10051e12	0.559783
$680$	−5.35899e11	−0.0961153
$681$	1.11762e13	1.99129
$682$	4.21930e10	0.00746811
$683$	−5.85311e12	−1.02918	−0.514592	−	0.857435i	$-0.672057\pi$
$683$	−5.85311e12	−1.02918	−0.514592	+	0.857435i	$0.672057\pi$
$684$	5.52563e12	0.965228
$685$	1.40948e13	2.44597
$686$	4.45454e11	0.0767970
$687$	−8.53264e12	−1.46143
$688$	−3.88574e11	−0.0661188
$689$	−9.63286e11	−0.162843
$690$	−5.00205e12	−0.840093
$691$	7.64843e12	1.27621	0.638104	−	0.769950i	$-0.279719\pi$
$691$	7.64843e12	1.27621	0.638104	+	0.769950i	$0.279719\pi$
$692$	−2.45728e12	−0.407359
$693$	2.67114e12	0.439944
$694$	3.77656e12	0.617987
$695$	3.50877e12	0.570457
$696$	−3.96775e12	−0.640918
$697$	3.30163e11	0.0529884
$698$	−4.05510e12	−0.646625
$699$	9.20378e12	1.45821
$700$	−8.03598e12	−1.26502
$701$	1.19373e13	1.86713	0.933566	−	0.358405i	$-0.116679\pi$
$701$	1.19373e13	1.86713	0.933566	+	0.358405i	$0.116679\pi$
$702$	−4.36268e11	−0.0678010
$703$	−8.12938e12	−1.25533
$704$	−2.45635e11	−0.0376889
$705$	2.90731e13	4.43242
$706$	1.37526e12	0.208335
$707$	−6.06090e12	−0.912326
$708$	−5.86094e12	−0.876632
$709$	2.78229e11	0.0413519	0.0206759	−	0.999786i	$-0.493418\pi$
$709$	2.78229e11	0.0413519	0.0206759	+	0.999786i	$0.493418\pi$
$710$	1.60681e12	0.237303
$711$	−6.74115e12	−0.989283
$712$	−4.07236e12	−0.593862
$713$	1.19261e11	0.0172821
$714$	1.57737e12	0.227139
$715$	4.50765e12	0.645020
$716$	1.06810e12	0.151881
$717$	−1.94237e13	−2.74470
$718$	−1.63322e12	−0.229343
$719$	7.71632e12	1.07679	0.538394	−	0.842693i	$-0.319031\pi$
$719$	7.71632e12	1.07679	0.538394	+	0.842693i	$0.319031\pi$
$720$	3.18941e12	0.442298
$721$	3.37799e12	0.465532
$722$	1.22034e13	1.67133
$723$	2.86632e12	0.390124
$724$	−4.17310e12	−0.564463
$725$	−1.71794e13	−2.30934
$726$	6.89378e11	0.0920964
$727$	2.79239e12	0.370741	0.185371	−	0.982669i	$-0.440651\pi$
$727$	2.79239e12	0.370741	0.185371	+	0.982669i	$0.440651\pi$
$728$	4.72754e12	0.623798
$729$	−8.40536e12	−1.10226
$730$	5.33762e12	0.695656
$731$	3.30242e11	0.0427764
$732$	−7.10827e11	−0.0915090
$733$	−3.53447e12	−0.452227	−0.226114	−	0.974101i	$-0.572602\pi$
$733$	−3.53447e12	−0.452227	−0.226114	+	0.974101i	$0.572602\pi$
$734$	−2.14975e12	−0.273373
$735$	1.75602e13	2.21940
$736$	−6.94303e11	−0.0872166
$737$	−4.53843e12	−0.566633
$738$	−1.96497e12	−0.243839
$739$	6.91730e11	0.0853172	0.0426586	−	0.999090i	$-0.486417\pi$
$739$	6.91730e11	0.0853172	0.0426586	+	0.999090i	$0.486417\pi$
$740$	−4.69230e12	−0.575232
$741$	−2.74465e13	−3.34430
$742$	−1.03552e12	−0.125412
$743$	−2.93102e12	−0.352833	−0.176417	−	0.984316i	$-0.556451\pi$
$743$	−2.93102e12	−0.352833	−0.176417	+	0.984316i	$0.556451\pi$
$744$	−1.48288e11	−0.0177430
$745$	4.52124e12	0.537717
$746$	8.01187e12	0.947129
$747$	5.25207e12	0.617146
$748$	2.08761e11	0.0243833
$749$	−9.61634e12	−1.11646
$750$	1.21743e13	1.40497
$751$	1.85963e12	0.213328	0.106664	−	0.994295i	$-0.465983\pi$
$751$	1.85963e12	0.213328	0.106664	+	0.994295i	$0.465983\pi$
$752$	4.03546e12	0.460164
$753$	8.82368e12	1.00017
$754$	1.01066e13	1.13876
$755$	−2.96083e12	−0.331629
$756$	−4.68981e11	−0.0522164
$757$	−1.85704e12	−0.205536	−0.102768	−	0.994705i	$-0.532770\pi$
$757$	−1.85704e12	−0.205536	−0.102768	+	0.994705i	$0.532770\pi$
$758$	3.75418e12	0.413052
$759$	1.94857e12	0.213122
$760$	1.00239e13	1.08987
$761$	8.46037e12	0.914447	0.457223	−	0.889352i	$-0.348844\pi$
$761$	8.46037e12	0.914447	0.457223	+	0.889352i	$0.348844\pi$
$762$	4.77975e11	0.0513580
$763$	−2.26910e13	−2.42378
$764$	4.35832e12	0.462806
$765$	−2.71063e12	−0.286150
$766$	−7.42863e12	−0.779613
$767$	1.49289e13	1.55757
$768$	8.63288e11	0.0895428
$769$	−1.82185e12	−0.187864	−0.0939319	−	0.995579i	$-0.529944\pi$
$769$	−1.82185e12	−0.187864	−0.0939319	+	0.995579i	$0.529944\pi$
$770$	4.84565e12	0.496757
$771$	−2.11839e13	−2.15905
$772$	1.22154e12	0.123774
$773$	−9.95350e12	−1.00269	−0.501347	−	0.865246i	$-0.667162\pi$
$773$	−9.95350e12	−1.00269	−0.501347	+	0.865246i	$0.667162\pi$
$774$	−1.96545e12	−0.196846
$775$	−6.42052e11	−0.0639311
$776$	−1.44216e12	−0.142770
$777$	1.38114e13	1.35939
$778$	−1.39804e13	−1.36808
$779$	−6.17566e12	−0.600848
$780$	−1.58422e13	−1.53246
$781$	−6.25941e11	−0.0602010
$782$	5.90077e11	0.0564259
$783$	−1.00259e12	−0.0953227
$784$	2.43742e12	0.230413
$785$	−8.67733e12	−0.815592
$786$	4.46302e12	0.417088
$787$	−4.01205e12	−0.372803	−0.186402	−	0.982474i	$-0.559683\pi$
$787$	−4.01205e12	−0.372803	−0.186402	+	0.982474i	$0.559683\pi$
$788$	−3.35506e12	−0.309979
$789$	−1.77100e11	−0.0162694
$790$	−1.22289e13	−1.11704
$791$	−4.03760e11	−0.0366716
$792$	−1.24245e12	−0.112206
$793$	1.81061e12	0.162590
$794$	1.49893e12	0.133841
$795$	3.47007e12	0.308096
$796$	5.99592e12	0.529355
$797$	3.93014e12	0.345021	0.172511	−	0.985008i	$-0.444812\pi$
$797$	3.93014e12	0.345021	0.172511	+	0.985008i	$0.444812\pi$
$798$	−2.95046e13	−2.57559
$799$	−3.42967e12	−0.297709
$800$	3.73783e12	0.322638
$801$	−2.05984e13	−1.76802
$802$	−3.79018e12	−0.323501
$803$	−2.07929e12	−0.176480
$804$	1.59504e13	1.34623
$805$	1.36965e13	1.14955
$806$	3.77717e11	0.0315253
$807$	−1.41508e13	−1.17449
$808$	2.81915e12	0.232685
$809$	5.61164e12	0.460597	0.230299	−	0.973120i	$-0.426030\pi$
$809$	5.61164e12	0.460597	0.230299	+	0.973120i	$0.426030\pi$
$810$	−1.37549e13	−1.12273
$811$	−4.65110e12	−0.377539	−0.188770	−	0.982021i	$-0.560450\pi$
$811$	−4.65110e12	−0.377539	−0.188770	+	0.982021i	$0.560450\pi$
$812$	1.08644e13	0.877010
$813$	3.98595e12	0.319981
$814$	1.82791e12	0.145930
$815$	3.83149e13	3.04199
$816$	−7.33695e11	−0.0579308
$817$	−6.17714e12	−0.485052
$818$	−8.78901e12	−0.686357
$819$	2.39124e13	1.85714
$820$	−3.56461e12	−0.275327
$821$	1.27809e13	0.981784	0.490892	−	0.871220i	$-0.336671\pi$
$821$	1.27809e13	0.981784	0.490892	+	0.871220i	$0.336671\pi$
$822$	1.92971e13	1.47424
$823$	−1.78551e13	−1.35663	−0.678317	−	0.734770i	$-0.737290\pi$
$823$	−1.78551e13	−1.35663	−0.678317	+	0.734770i	$0.737290\pi$
$824$	−1.57123e12	−0.118732
$825$	−1.04903e13	−0.788395
$826$	1.60483e13	1.19955
$827$	2.57926e12	0.191744	0.0958718	−	0.995394i	$-0.469436\pi$
$827$	2.57926e12	0.191744	0.0958718	+	0.995394i	$0.469436\pi$
$828$	−3.51186e12	−0.259657
$829$	1.69538e12	0.124673	0.0623363	−	0.998055i	$-0.480145\pi$
$829$	1.69538e12	0.124673	0.0623363	+	0.998055i	$0.480145\pi$
$830$	9.52765e12	0.696842
$831$	3.15391e13	2.29427
$832$	−2.19896e12	−0.159097
$833$	−2.07152e12	−0.149069
$834$	4.80383e12	0.343827
$835$	1.01186e13	0.720327
$836$	−3.90486e12	−0.276488
$837$	−3.74702e10	−0.00263889
$838$	3.79515e12	0.265846
$839$	1.11453e13	0.776539	0.388269	−	0.921546i	$-0.373073\pi$
$839$	1.11453e13	0.776539	0.388269	+	0.921546i	$0.373073\pi$
$840$	−1.70301e13	−1.18021
$841$	8.71893e12	0.601009
$842$	−1.00900e13	−0.691810
$843$	−2.35410e13	−1.60547
$844$	−9.16765e12	−0.621895
$845$	1.54431e13	1.04203
$846$	2.04118e13	1.36998
$847$	−1.88764e12	−0.126022
$848$	4.81658e11	0.0319858
$849$	5.74460e12	0.379468
$850$	−3.17673e12	−0.208735
$851$	5.16669e12	0.337699
$852$	2.19988e12	0.143028
$853$	−1.24913e13	−0.807864	−0.403932	−	0.914789i	$-0.632357\pi$
$853$	−1.24913e13	−0.807864	−0.403932	+	0.914789i	$0.632357\pi$
$854$	1.94637e12	0.125218
$855$	5.07020e13	3.24472
$856$	4.47292e12	0.284747
$857$	2.53810e13	1.60729	0.803645	−	0.595109i	$-0.202891\pi$
$857$	2.53810e13	1.60729	0.803645	+	0.595109i	$0.202891\pi$
$858$	6.17140e12	0.388768
$859$	4.08357e12	0.255900	0.127950	−	0.991781i	$-0.459160\pi$
$859$	4.08357e12	0.255900	0.127950	+	0.991781i	$0.459160\pi$
$860$	−3.56547e12	−0.222266
$861$	1.04921e13	0.650653
$862$	2.43810e12	0.150407
$863$	−2.27820e13	−1.39812	−0.699059	−	0.715064i	$-0.746397\pi$
$863$	−2.27820e13	−1.39812	−0.699059	+	0.715064i	$0.746397\pi$
$864$	2.18141e11	0.0133176
$865$	−2.25474e13	−1.36938
$866$	−1.18512e13	−0.716028
$867$	−2.32126e13	−1.39520
$868$	4.06040e11	0.0242789
$869$	4.76384e12	0.283379
$870$	−3.64072e13	−2.15452
$871$	−4.06286e13	−2.39194
$872$	1.05544e13	0.618174
$873$	−7.29462e12	−0.425049
$874$	−1.10373e13	−0.639826
$875$	−3.33354e13	−1.92251
$876$	7.30770e12	0.419288
$877$	1.64072e12	0.0936561	0.0468281	−	0.998903i	$-0.485089\pi$
$877$	1.64072e12	0.0936561	0.0468281	+	0.998903i	$0.485089\pi$
$878$	−7.22530e12	−0.410328
$879$	1.07183e12	0.0605587
$880$	−2.25390e12	−0.126696
$881$	5.64204e12	0.315533	0.157766	−	0.987476i	$-0.449571\pi$
$881$	5.64204e12	0.315533	0.157766	+	0.987476i	$0.449571\pi$
$882$	1.23287e13	0.685976
$883$	1.86226e13	1.03090	0.515452	−	0.856919i	$-0.327624\pi$
$883$	1.86226e13	1.03090	0.515452	+	0.856919i	$0.327624\pi$
$884$	1.86886e12	0.102930
$885$	−5.37787e13	−2.94690
$886$	−4.42636e12	−0.241321
$887$	6.54696e12	0.355127	0.177563	−	0.984109i	$-0.443179\pi$
$887$	6.54696e12	0.355127	0.177563	+	0.984109i	$0.443179\pi$
$888$	−6.42420e12	−0.346705
$889$	−1.30878e12	−0.0702765
$890$	−3.73671e13	−1.99634
$891$	5.35827e12	0.284823
$892$	−9.16490e12	−0.484714
$893$	6.41515e13	3.37579
$894$	6.19000e12	0.324094
$895$	9.80065e12	0.510565
$896$	−2.36384e12	−0.122527
$897$	1.74438e13	0.899655
$898$	2.07897e13	1.06685
$899$	8.68036e11	0.0443220
$900$	1.89064e13	0.960542
$901$	−4.09353e11	−0.0206936
$902$	1.38861e12	0.0698474
$903$	1.04947e13	0.525259
$904$	1.87804e11	0.00935291
$905$	−3.82915e13	−1.89751
$906$	−4.05365e12	−0.199880
$907$	−2.63878e13	−1.29470	−0.647352	−	0.762191i	$-0.724124\pi$
$907$	−2.63878e13	−1.29470	−0.647352	+	0.762191i	$0.724124\pi$
$908$	1.42344e13	0.694949
$909$	1.42596e13	0.692738
$910$	4.33789e13	2.09697
$911$	2.94650e12	0.141734	0.0708670	−	0.997486i	$-0.477423\pi$
$911$	2.94650e12	0.141734	0.0708670	+	0.997486i	$0.477423\pi$
$912$	1.37237e13	0.656891
$913$	−3.71154e12	−0.176781
$914$	−2.12199e13	−1.00574
$915$	−6.52239e12	−0.307618
$916$	−1.08674e13	−0.510032
$917$	−1.22206e13	−0.570728
$918$	−1.85394e11	−0.00861596
$919$	−2.75354e13	−1.27342	−0.636710	−	0.771103i	$-0.719705\pi$
$919$	−2.75354e13	−1.27342	−0.636710	+	0.771103i	$0.719705\pi$
$920$	−6.37077e12	−0.293188
$921$	−5.05906e13	−2.31687
$922$	3.56007e12	0.162244
$923$	−5.60350e12	−0.254128
$924$	6.63415e12	0.299407
$925$	−2.78153e13	−1.24924
$926$	−2.47145e13	−1.10459
$927$	−7.94744e12	−0.353483
$928$	−5.05345e12	−0.223677
$929$	2.27772e13	1.00330	0.501648	−	0.865072i	$-0.332727\pi$
$929$	2.27772e13	1.00330	0.501648	+	0.865072i	$0.332727\pi$
$930$	−1.36066e12	−0.0596452
$931$	3.87475e13	1.69033
$932$	1.17222e13	0.508907
$933$	8.61077e12	0.372027
$934$	1.64460e12	0.0707130
$935$	1.91555e12	0.0819674
$936$	−1.11226e13	−0.473656
$937$	−7.19897e12	−0.305100	−0.152550	−	0.988296i	$-0.548749\pi$
$937$	−7.19897e12	−0.305100	−0.152550	+	0.988296i	$0.548749\pi$
$938$	−4.36751e13	−1.84213
$939$	5.58731e13	2.34535
$940$	3.70285e13	1.54689
$941$	3.01086e13	1.25180	0.625902	−	0.779901i	$-0.284731\pi$
$941$	3.01086e13	1.25180	0.625902	+	0.779901i	$0.284731\pi$
$942$	−1.18801e13	−0.491575
$943$	3.92499e12	0.161635
$944$	−7.46468e12	−0.305940
$945$	−4.30327e12	−0.175531
$946$	1.38894e12	0.0563863
$947$	1.41930e13	0.573456	0.286728	−	0.958012i	$-0.407432\pi$
$947$	1.41930e13	0.573456	0.286728	+	0.958012i	$0.407432\pi$
$948$	−1.67426e13	−0.673263
$949$	−1.86141e13	−0.744977
$950$	5.94202e13	2.36689
$951$	−3.28772e13	−1.30341
$952$	2.00899e12	0.0792706
$953$	2.63286e13	1.03397	0.516986	−	0.855994i	$-0.327054\pi$
$953$	2.63286e13	1.03397	0.516986	+	0.855994i	$0.327054\pi$
$954$	2.43628e12	0.0952267
$955$	3.99910e13	1.55578
$956$	−2.47386e13	−0.957887
$957$	1.41826e13	0.546577
$958$	−1.14080e13	−0.437586
$959$	−5.28390e13	−2.01730
$960$	7.92135e12	0.301008
$961$	−2.64072e13	−0.998773
$962$	1.63636e13	0.616016
$963$	2.26245e13	0.847736
$964$	3.65064e12	0.136152
$965$	1.12086e13	0.416082
$966$	1.87518e13	0.692862
$967$	2.57448e13	0.946825	0.473413	−	0.880841i	$-0.343022\pi$
$967$	2.57448e13	0.946825	0.473413	+	0.880841i	$0.343022\pi$
$968$	8.78014e11	0.0321412
$969$	−1.16635e13	−0.424984
$970$	−1.32330e13	−0.479938
$971$	8.56655e12	0.309257	0.154629	−	0.987973i	$-0.450582\pi$
$971$	8.56655e12	0.309257	0.154629	+	0.987973i	$0.450582\pi$
$972$	−1.98800e13	−0.714361
$973$	−1.31538e13	−0.470481
$974$	3.59579e13	1.28020
$975$	−9.39102e13	−3.32807
$976$	−9.05331e11	−0.0319362
$977$	−1.41299e13	−0.496152	−0.248076	−	0.968741i	$-0.579798\pi$
$977$	−1.41299e13	−0.496152	−0.248076	+	0.968741i	$0.579798\pi$
$978$	5.24566e13	1.83348
$979$	1.45565e13	0.506448
$980$	2.23652e13	0.774561
$981$	5.33855e13	1.84040
$982$	2.29009e13	0.785869
$983$	−3.37139e13	−1.15164	−0.575822	−	0.817575i	$-0.695318\pi$
$983$	−3.37139e13	−1.15164	−0.575822	+	0.817575i	$0.695318\pi$
$984$	−4.88028e12	−0.165946
$985$	−3.07853e13	−1.04203
$986$	4.29485e12	0.144711
$987$	−1.08990e14	−3.65561
$988$	−3.49567e13	−1.16714
$989$	3.92593e12	0.130485
$990$	−1.14004e13	−0.377193
$991$	−2.70722e13	−0.891644	−0.445822	−	0.895122i	$-0.647089\pi$
$991$	−2.70722e13	−0.891644	−0.445822	+	0.895122i	$0.647089\pi$
$992$	−1.88864e11	−0.00619223
$993$	−2.29299e13	−0.748396
$994$	−6.02367e12	−0.195714
$995$	5.50172e13	1.77949
$996$	1.30442e13	0.420003
$997$	4.38778e13	1.40643	0.703213	−	0.710979i	$-0.251748\pi$
$997$	4.38778e13	1.40643	0.703213	+	0.710979i	$0.251748\pi$
$998$	−1.35315e13	−0.431777
$999$	−1.62330e12	−0.0515650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.10.a.c.1.1	✓	1
3.2	odd	2		198.10.a.a.1.1		1
4.3	odd	2		176.10.a.a.1.1		1
11.10	odd	2		242.10.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.10.a.c.1.1	✓	1	1.1	even	1	trivial
176.10.a.a.1.1		1	4.3	odd	2
198.10.a.a.1.1		1	3.2	odd	2
242.10.a.d.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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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