LMFDB - Embedded newform 99.14.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,14,Mod(1,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("99.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	99.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$106.158619662$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-140.000 q^{2} +11408.0 q^{4} -48740.0 q^{5} +487486. q^{7} -450240. q^{8} +O(q^{10})$

\(q-140.000 q^{2} +11408.0 q^{4} -48740.0 q^{5} +487486. q^{7} -450240. q^{8} +6.82360e6 q^{10} +1.77156e6 q^{11} -1.83883e7 q^{13} -6.82480e7 q^{14} -3.04207e7 q^{16} +9.62333e7 q^{17} -1.49547e7 q^{19} -5.56026e8 q^{20} -2.48019e8 q^{22} -1.53804e8 q^{23} +1.15488e9 q^{25} +2.57436e9 q^{26} +5.56124e9 q^{28} -5.21901e9 q^{29} +1.18381e9 q^{31} +7.94727e9 q^{32} -1.34727e10 q^{34} -2.37601e10 q^{35} -1.76722e10 q^{37} +2.09365e9 q^{38} +2.19447e10 q^{40} +1.94617e10 q^{41} -3.41230e9 q^{43} +2.02100e10 q^{44} +2.15326e10 q^{46} +1.00328e11 q^{47} +1.40754e11 q^{49} -1.61684e11 q^{50} -2.09774e11 q^{52} -2.75469e11 q^{53} -8.63459e10 q^{55} -2.19486e11 q^{56} +7.30661e11 q^{58} +2.67677e11 q^{59} +5.63487e11 q^{61} -1.65734e11 q^{62} -8.63411e11 q^{64} +8.96246e11 q^{65} +1.08084e12 q^{67} +1.09783e12 q^{68} +3.32641e12 q^{70} +1.15056e12 q^{71} -3.45915e11 q^{73} +2.47411e12 q^{74} -1.70603e11 q^{76} +8.63611e11 q^{77} -2.00408e12 q^{79} +1.48271e12 q^{80} -2.72464e12 q^{82} +3.33673e12 q^{83} -4.69041e12 q^{85} +4.77723e11 q^{86} -7.97628e11 q^{88} +5.69624e12 q^{89} -8.96404e12 q^{91} -1.75460e12 q^{92} -1.40459e13 q^{94} +7.28890e11 q^{95} -6.55011e12 q^{97} -1.97055e13 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−140.000	−1.54680	−0.773398	−	0.633921i	$-0.781445\pi$
$2$	−140.000	−1.54680	−0.773398	+	0.633921i	$0.781445\pi$
$3$	0	0
$3$	0	0
$4$	11408.0	1.39258
$5$	−48740.0	−1.39502	−0.697510	−	0.716575i	$-0.745709\pi$
$5$	−48740.0	−1.39502	−0.697510	+	0.716575i	$0.745709\pi$
$6$	0	0
$7$	487486.	1.56612	0.783060	−	0.621947i	$-0.213658\pi$
$7$	487486.	1.56612	0.783060	+	0.621947i	$0.213658\pi$
$8$	−450240.	−0.607238
$9$	0	0
$10$	6.82360e6	2.15781
$11$	1.77156e6	0.301511
$11$	1.77156e6	0.301511
$12$	0	0
$13$	−1.83883e7	−1.05660	−0.528299	−	0.849058i	$-0.677170\pi$
$13$	−1.83883e7	−1.05660	−0.528299	+	0.849058i	$0.677170\pi$
$14$	−6.82480e7	−2.42247
$15$	0	0
$16$	−3.04207e7	−0.453304
$17$	9.62333e7	0.966957	0.483479	−	0.875356i	$-0.339373\pi$
$17$	9.62333e7	0.966957	0.483479	+	0.875356i	$0.339373\pi$
$18$	0	0
$19$	−1.49547e7	−0.0729252	−0.0364626	−	0.999335i	$-0.511609\pi$
$19$	−1.49547e7	−0.0729252	−0.0364626	+	0.999335i	$0.511609\pi$
$20$	−5.56026e8	−1.94267
$21$	0	0
$22$	−2.48019e8	−0.466377
$23$	−1.53804e8	−0.216640	−0.108320	−	0.994116i	$-0.534547\pi$
$23$	−1.53804e8	−0.216640	−0.108320	+	0.994116i	$0.534547\pi$
$24$	0	0
$25$	1.15488e9	0.946081
$26$	2.57436e9	1.63434
$27$	0	0
$28$	5.56124e9	2.18094
$29$	−5.21901e9	−1.62930	−0.814650	−	0.579953i	$-0.803071\pi$
$29$	−5.21901e9	−1.62930	−0.814650	+	0.579953i	$0.803071\pi$
$30$	0	0
$31$	1.18381e9	0.239570	0.119785	−	0.992800i	$-0.461780\pi$
$31$	1.18381e9	0.239570	0.119785	+	0.992800i	$0.461780\pi$
$32$	7.94727e9	1.30841
$33$	0	0
$34$	−1.34727e10	−1.49569
$35$	−2.37601e10	−2.18477
$36$	0	0
$37$	−1.76722e10	−1.13235	−0.566173	−	0.824286i	$-0.691577\pi$
$37$	−1.76722e10	−1.13235	−0.566173	+	0.824286i	$0.691577\pi$
$38$	2.09365e9	0.112800
$39$	0	0
$40$	2.19447e10	0.847110
$41$	1.94617e10	0.639862	0.319931	−	0.947441i	$-0.396340\pi$
$41$	1.94617e10	0.639862	0.319931	+	0.947441i	$0.396340\pi$
$42$	0	0
$43$	−3.41230e9	−0.0823195	−0.0411598	−	0.999153i	$-0.513105\pi$
$43$	−3.41230e9	−0.0823195	−0.0411598	+	0.999153i	$0.513105\pi$
$44$	2.02100e10	0.419878
$45$	0	0
$46$	2.15326e10	0.335097
$47$	1.00328e11	1.35764	0.678820	−	0.734304i	$-0.262491\pi$
$47$	1.00328e11	1.35764	0.678820	+	0.734304i	$0.262491\pi$
$48$	0	0
$49$	1.40754e11	1.45273
$50$	−1.61684e11	−1.46339
$51$	0	0
$52$	−2.09774e11	−1.47140
$53$	−2.75469e11	−1.70718	−0.853591	−	0.520944i	$-0.825580\pi$
$53$	−2.75469e11	−1.70718	−0.853591	+	0.520944i	$0.825580\pi$
$54$	0	0
$55$	−8.63459e10	−0.420614
$56$	−2.19486e11	−0.951008
$57$	0	0
$58$	7.30661e11	2.52020
$59$	2.67677e11	0.826176	0.413088	−	0.910691i	$-0.364450\pi$
$59$	2.67677e11	0.826176	0.413088	+	0.910691i	$0.364450\pi$
$60$	0	0
$61$	5.63487e11	1.40036	0.700180	−	0.713966i	$-0.253103\pi$
$61$	5.63487e11	1.40036	0.700180	+	0.713966i	$0.253103\pi$
$62$	−1.65734e11	−0.370565
$63$	0	0
$64$	−8.63411e11	−1.57054
$65$	8.96246e11	1.47398
$66$	0	0
$67$	1.08084e12	1.45974	0.729871	−	0.683585i	$-0.239580\pi$
$67$	1.08084e12	1.45974	0.729871	+	0.683585i	$0.239580\pi$
$68$	1.09783e12	1.34656
$69$	0	0
$70$	3.32641e12	3.37939
$71$	1.15056e12	1.06594	0.532968	−	0.846136i	$-0.321077\pi$
$71$	1.15056e12	1.06594	0.532968	+	0.846136i	$0.321077\pi$
$72$	0	0
$73$	−3.45915e11	−0.267529	−0.133764	−	0.991013i	$-0.542707\pi$
$73$	−3.45915e11	−0.267529	−0.133764	+	0.991013i	$0.542707\pi$
$74$	2.47411e12	1.75151
$75$	0	0
$76$	−1.70603e11	−0.101554
$77$	8.63611e11	0.472203
$78$	0	0
$79$	−2.00408e12	−0.927554	−0.463777	−	0.885952i	$-0.653506\pi$
$79$	−2.00408e12	−0.927554	−0.463777	+	0.885952i	$0.653506\pi$
$80$	1.48271e12	0.632369
$81$	0	0
$82$	−2.72464e12	−0.989737
$83$	3.33673e12	1.12025	0.560123	−	0.828409i	$-0.310754\pi$
$83$	3.33673e12	1.12025	0.560123	+	0.828409i	$0.310754\pi$
$84$	0	0
$85$	−4.69041e12	−1.34892
$86$	4.77723e11	0.127332
$87$	0	0
$88$	−7.97628e11	−0.183089
$89$	5.69624e12	1.21494	0.607468	−	0.794344i	$-0.292185\pi$
$89$	5.69624e12	1.21494	0.607468	+	0.794344i	$0.292185\pi$
$90$	0	0
$91$	−8.96404e12	−1.65476
$92$	−1.75460e12	−0.301688
$93$	0	0
$94$	−1.40459e13	−2.09999
$95$	7.28890e11	0.101732
$96$	0	0
$97$	−6.55011e12	−0.798422	−0.399211	−	0.916859i	$-0.630716\pi$
$97$	−6.55011e12	−0.798422	−0.399211	+	0.916859i	$0.630716\pi$
$98$	−1.97055e13	−2.24708
$99$	0	0
$100$	1.31749e13	1.31749
$101$	−2.00225e13	−1.87685	−0.938424	−	0.345487i	$-0.887714\pi$
$101$	−2.00225e13	−1.87685	−0.938424	+	0.345487i	$0.887714\pi$
$102$	0	0
$103$	8.50230e12	0.701608	0.350804	−	0.936449i	$-0.385908\pi$
$103$	8.50230e12	0.701608	0.350804	+	0.936449i	$0.385908\pi$
$104$	8.27915e12	0.641607
$105$	0	0
$106$	3.85657e13	2.64066
$107$	−2.60740e13	−1.67963	−0.839814	−	0.542875i	$-0.817336\pi$
$107$	−2.60740e13	−1.67963	−0.839814	+	0.542875i	$0.817336\pi$
$108$	0	0
$109$	−2.65871e12	−0.151844	−0.0759222	−	0.997114i	$-0.524190\pi$
$109$	−2.65871e12	−0.151844	−0.0759222	+	0.997114i	$0.524190\pi$
$110$	1.20884e13	0.650605
$111$	0	0
$112$	−1.48297e13	−0.709929
$113$	3.76049e13	1.69916	0.849580	−	0.527460i	$-0.176856\pi$
$113$	3.76049e13	1.69916	0.849580	+	0.527460i	$0.176856\pi$
$114$	0	0
$115$	7.49643e12	0.302217
$116$	−5.95385e13	−2.26893
$117$	0	0
$118$	−3.74748e13	−1.27793
$119$	4.69124e13	1.51437
$120$	0	0
$121$	3.13843e12	0.0909091
$122$	−7.88881e13	−2.16607
$123$	0	0
$124$	1.35049e13	0.333619
$125$	3.20800e12	0.0752176
$126$	0	0
$127$	−6.93279e13	−1.46617	−0.733084	−	0.680138i	$-0.761920\pi$
$127$	−6.93279e13	−1.46617	−0.733084	+	0.680138i	$0.761920\pi$
$128$	5.57735e13	1.12089
$129$	0	0
$130$	−1.25474e14	−2.27994
$131$	5.31970e13	0.919653	0.459827	−	0.888009i	$-0.347912\pi$
$131$	5.31970e13	0.919653	0.459827	+	0.888009i	$0.347912\pi$
$132$	0	0
$133$	−7.29018e12	−0.114210
$134$	−1.51318e14	−2.25792
$135$	0	0
$136$	−4.33281e13	−0.587173
$137$	−1.21037e14	−1.56399	−0.781994	−	0.623286i	$-0.785797\pi$
$137$	−1.21037e14	−1.56399	−0.781994	+	0.623286i	$0.785797\pi$
$138$	0	0
$139$	1.03707e14	1.21958	0.609791	−	0.792562i	$-0.291253\pi$
$139$	1.03707e14	1.21958	0.609791	+	0.792562i	$0.291253\pi$
$140$	−2.71055e14	−3.04246
$141$	0	0
$142$	−1.61079e14	−1.64878
$143$	−3.25760e13	−0.318576
$144$	0	0
$145$	2.54375e14	2.27291
$146$	4.84280e13	0.413812
$147$	0	0
$148$	−2.01604e14	−1.57688
$149$	2.94068e13	0.220159	0.110080	−	0.993923i	$-0.464889\pi$
$149$	2.94068e13	0.220159	0.110080	+	0.993923i	$0.464889\pi$
$150$	0	0
$151$	−4.86579e13	−0.334043	−0.167022	−	0.985953i	$-0.553415\pi$
$151$	−4.86579e13	−0.334043	−0.167022	+	0.985953i	$0.553415\pi$
$152$	6.73318e12	0.0442830
$153$	0	0
$154$	−1.20906e14	−0.730401
$155$	−5.76990e13	−0.334204
$156$	0	0
$157$	−2.31548e14	−1.23394	−0.616969	−	0.786988i	$-0.711640\pi$
$157$	−2.31548e14	−1.23394	−0.616969	+	0.786988i	$0.711640\pi$
$158$	2.80571e14	1.43474
$159$	0	0
$160$	−3.87350e14	−1.82526
$161$	−7.49775e13	−0.339283
$162$	0	0
$163$	1.44315e14	0.602688	0.301344	−	0.953516i	$-0.402565\pi$
$163$	1.44315e14	0.602688	0.301344	+	0.953516i	$0.402565\pi$
$164$	2.22020e14	0.891058
$165$	0	0
$166$	−4.67143e14	−1.73279
$167$	−4.17920e14	−1.49086	−0.745429	−	0.666585i	$-0.767756\pi$
$167$	−4.17920e14	−1.49086	−0.745429	+	0.666585i	$0.767756\pi$
$168$	0	0
$169$	3.52546e13	0.116400
$170$	6.56657e14	2.08651
$171$	0	0
$172$	−3.89276e13	−0.114636
$173$	−4.17435e14	−1.18383	−0.591914	−	0.806001i	$-0.701628\pi$
$173$	−4.17435e14	−1.18383	−0.591914	+	0.806001i	$0.701628\pi$
$174$	0	0
$175$	5.62990e14	1.48168
$176$	−5.38922e13	−0.136676
$177$	0	0
$178$	−7.97473e14	−1.87926
$179$	−4.89549e14	−1.11238	−0.556188	−	0.831056i	$-0.687737\pi$
$179$	−4.89549e14	−1.11238	−0.556188	+	0.831056i	$0.687737\pi$
$180$	0	0
$181$	3.82069e14	0.807664	0.403832	−	0.914833i	$-0.367678\pi$
$181$	3.82069e14	0.807664	0.403832	+	0.914833i	$0.367678\pi$
$182$	1.25497e15	2.55957
$183$	0	0
$184$	6.92489e13	0.131552
$185$	8.61343e14	1.57965
$186$	0	0
$187$	1.70483e14	0.291549
$188$	1.14454e15	1.89062
$189$	0	0
$190$	−1.02045e14	−0.157359
$191$	−2.81803e14	−0.419980	−0.209990	−	0.977704i	$-0.567343\pi$
$191$	−2.81803e14	−0.419980	−0.209990	+	0.977704i	$0.567343\pi$
$192$	0	0
$193$	6.26551e14	0.872638	0.436319	−	0.899792i	$-0.356282\pi$
$193$	6.26551e14	0.872638	0.436319	+	0.899792i	$0.356282\pi$
$194$	9.17016e14	1.23500
$195$	0	0
$196$	1.60572e15	2.02304
$197$	6.60082e14	0.804576	0.402288	−	0.915513i	$-0.368215\pi$
$197$	6.60082e14	0.804576	0.402288	+	0.915513i	$0.368215\pi$
$198$	0	0
$199$	−1.45047e15	−1.65564	−0.827818	−	0.560996i	$-0.810418\pi$
$199$	−1.45047e15	−1.65564	−0.827818	+	0.560996i	$0.810418\pi$
$200$	−5.19975e14	−0.574497
$201$	0	0
$202$	2.80315e15	2.90310
$203$	−2.54419e15	−2.55168
$204$	0	0
$205$	−9.48565e14	−0.892621
$206$	−1.19032e15	−1.08524
$207$	0	0
$208$	5.59386e14	0.478961
$209$	−2.64931e13	−0.0219878
$210$	0	0
$211$	−1.86139e15	−1.45212	−0.726059	−	0.687633i	$-0.758650\pi$
$211$	−1.86139e15	−1.45212	−0.726059	+	0.687633i	$0.758650\pi$
$212$	−3.14255e15	−2.37738
$213$	0	0
$214$	3.65036e15	2.59804
$215$	1.66316e14	0.114837
$216$	0	0
$217$	5.77092e14	0.375195
$218$	3.72219e14	0.234872
$219$	0	0
$220$	−9.85034e14	−0.585738
$221$	−1.76957e15	−1.02169
$222$	0	0
$223$	2.64472e15	1.44012	0.720059	−	0.693913i	$-0.244115\pi$
$223$	2.64472e15	1.44012	0.720059	+	0.693913i	$0.244115\pi$
$224$	3.87418e15	2.04912
$225$	0	0
$226$	−5.26468e15	−2.62825
$227$	−3.07427e15	−1.49133	−0.745666	−	0.666319i	$-0.767869\pi$
$227$	−3.07427e15	−1.49133	−0.745666	+	0.666319i	$0.767869\pi$
$228$	0	0
$229$	−2.98623e15	−1.36834	−0.684168	−	0.729324i	$-0.739835\pi$
$229$	−2.98623e15	−1.36834	−0.684168	+	0.729324i	$0.739835\pi$
$230$	−1.04950e15	−0.467467
$231$	0	0
$232$	2.34981e15	0.989374
$233$	1.86637e15	0.764159	0.382079	−	0.924130i	$-0.375208\pi$
$233$	1.86637e15	0.764159	0.382079	+	0.924130i	$0.375208\pi$
$234$	0	0
$235$	−4.88997e15	−1.89394
$236$	3.05366e15	1.15052
$237$	0	0
$238$	−6.56773e15	−2.34242
$239$	3.11970e14	0.108275	0.0541373	−	0.998534i	$-0.482759\pi$
$239$	3.11970e14	0.108275	0.0541373	+	0.998534i	$0.482759\pi$
$240$	0	0
$241$	5.25176e15	1.72661	0.863305	−	0.504683i	$-0.168391\pi$
$241$	5.25176e15	1.72661	0.863305	+	0.504683i	$0.168391\pi$
$242$	−4.39380e14	−0.140618
$243$	0	0
$244$	6.42826e15	1.95011
$245$	−6.86033e15	−2.02659
$246$	0	0
$247$	2.74991e14	0.0770527
$248$	−5.32999e14	−0.145476
$249$	0	0
$250$	−4.49120e14	−0.116346
$251$	2.46350e15	0.621833	0.310916	−	0.950437i	$-0.399364\pi$
$251$	2.46350e15	0.621833	0.310916	+	0.950437i	$0.399364\pi$
$252$	0	0
$253$	−2.72474e14	−0.0653193
$254$	9.70590e15	2.26786
$255$	0	0
$256$	−7.35229e14	−0.163254
$257$	−2.41514e15	−0.522851	−0.261425	−	0.965224i	$-0.584192\pi$
$257$	−2.41514e15	−0.522851	−0.261425	+	0.965224i	$0.584192\pi$
$258$	0	0
$259$	−8.61495e15	−1.77339
$260$	1.02244e16	2.05263
$261$	0	0
$262$	−7.44759e15	−1.42252
$263$	1.68025e15	0.313084	0.156542	−	0.987671i	$-0.449965\pi$
$263$	1.68025e15	0.313084	0.156542	+	0.987671i	$0.449965\pi$
$264$	0	0
$265$	1.34264e16	2.38155
$266$	1.02063e15	0.176659
$267$	0	0
$268$	1.23303e16	2.03281
$269$	5.87926e14	0.0946091	0.0473046	−	0.998881i	$-0.484937\pi$
$269$	5.87926e14	0.0946091	0.0473046	+	0.998881i	$0.484937\pi$
$270$	0	0
$271$	3.69154e14	0.0566119	0.0283059	−	0.999599i	$-0.490989\pi$
$271$	3.69154e14	0.0566119	0.0283059	+	0.999599i	$0.490989\pi$
$272$	−2.92749e15	−0.438326
$273$	0	0
$274$	1.69451e16	2.41917
$275$	2.04595e15	0.285254
$276$	0	0
$277$	3.44319e15	0.457976	0.228988	−	0.973429i	$-0.426458\pi$
$277$	3.44319e15	0.457976	0.228988	+	0.973429i	$0.426458\pi$
$278$	−1.45190e16	−1.88645
$279$	0	0
$280$	1.06977e16	1.32667
$281$	−1.73559e15	−0.210309	−0.105154	−	0.994456i	$-0.533534\pi$
$281$	−1.73559e15	−0.210309	−0.105154	+	0.994456i	$0.533534\pi$
$282$	0	0
$283$	1.72244e15	0.199311	0.0996556	−	0.995022i	$-0.468226\pi$
$283$	1.72244e15	0.199311	0.0996556	+	0.995022i	$0.468226\pi$
$284$	1.31256e16	1.48440
$285$	0	0
$286$	4.56064e15	0.492773
$287$	9.48733e15	1.00210
$288$	0	0
$289$	−6.43739e14	−0.0649941
$290$	−3.56124e16	−3.51572
$291$	0	0
$292$	−3.94619e15	−0.372554
$293$	9.32911e15	0.861392	0.430696	−	0.902497i	$-0.358268\pi$
$293$	9.32911e15	0.861392	0.430696	+	0.902497i	$0.358268\pi$
$294$	0	0
$295$	−1.30466e16	−1.15253
$296$	7.95673e15	0.687604
$297$	0	0
$298$	−4.11695e15	−0.340541
$299$	2.82820e15	0.228901
$300$	0	0
$301$	−1.66345e15	−0.128922
$302$	6.81210e15	0.516697
$303$	0	0
$304$	4.54932e14	0.0330573
$305$	−2.74643e16	−1.95353
$306$	0	0
$307$	−1.85795e16	−1.26658	−0.633292	−	0.773913i	$-0.718297\pi$
$307$	−1.85795e16	−1.26658	−0.633292	+	0.773913i	$0.718297\pi$
$308$	9.85208e15	0.657579
$309$	0	0
$310$	8.07786e15	0.516946
$311$	−1.10219e16	−0.690739	−0.345369	−	0.938467i	$-0.612246\pi$
$311$	−1.10219e16	−0.690739	−0.345369	+	0.938467i	$0.612246\pi$
$312$	0	0
$313$	2.44634e16	1.47055	0.735273	−	0.677771i	$-0.237054\pi$
$313$	2.44634e16	1.47055	0.735273	+	0.677771i	$0.237054\pi$
$314$	3.24167e16	1.90865
$315$	0	0
$316$	−2.28626e16	−1.29169
$317$	−7.28014e15	−0.402953	−0.201477	−	0.979493i	$-0.564574\pi$
$317$	−7.28014e15	−0.402953	−0.201477	+	0.979493i	$0.564574\pi$
$318$	0	0
$319$	−9.24580e15	−0.491253
$320$	4.20827e16	2.19093
$321$	0	0
$322$	1.04968e16	0.524802
$323$	−1.43913e15	−0.0705156
$324$	0	0
$325$	−2.12364e16	−0.999628
$326$	−2.02041e16	−0.932235
$327$	0	0
$328$	−8.76245e15	−0.388549
$329$	4.89084e16	2.12623
$330$	0	0
$331$	4.91941e15	0.205604	0.102802	−	0.994702i	$-0.467219\pi$
$331$	4.91941e15	0.205604	0.102802	+	0.994702i	$0.467219\pi$
$332$	3.80654e16	1.56003
$333$	0	0
$334$	5.85089e16	2.30605
$335$	−5.26803e16	−2.03637
$336$	0	0
$337$	−3.61707e15	−0.134512	−0.0672562	−	0.997736i	$-0.521424\pi$
$337$	−3.61707e15	−0.134512	−0.0672562	+	0.997736i	$0.521424\pi$
$338$	−4.93565e15	−0.180047
$339$	0	0
$340$	−5.35082e16	−1.87848
$341$	2.09719e15	0.0722329
$342$	0	0
$343$	2.13834e16	0.709030
$344$	1.53636e15	0.0499876
$345$	0	0
$346$	5.84408e16	1.83114
$347$	−2.03135e16	−0.624660	−0.312330	−	0.949974i	$-0.601110\pi$
$347$	−2.03135e16	−0.624660	−0.312330	+	0.949974i	$0.601110\pi$
$348$	0	0
$349$	−1.16091e16	−0.343902	−0.171951	−	0.985106i	$-0.555007\pi$
$349$	−1.16091e16	−0.343902	−0.171951	+	0.985106i	$0.555007\pi$
$350$	−7.88186e16	−2.29185
$351$	0	0
$352$	1.40791e16	0.394500
$353$	−1.93894e16	−0.533370	−0.266685	−	0.963784i	$-0.585928\pi$
$353$	−1.93894e16	−0.533370	−0.266685	+	0.963784i	$0.585928\pi$
$354$	0	0
$355$	−5.60784e16	−1.48700
$356$	6.49827e16	1.69189
$357$	0	0
$358$	6.85369e16	1.72062
$359$	1.45895e16	0.359689	0.179844	−	0.983695i	$-0.442441\pi$
$359$	1.45895e16	0.359689	0.179844	+	0.983695i	$0.442441\pi$
$360$	0	0
$361$	−4.18293e16	−0.994682
$362$	−5.34896e16	−1.24929
$363$	0	0
$364$	−1.02262e17	−2.30438
$365$	1.68599e16	0.373208
$366$	0	0
$367$	−5.04342e16	−1.07745	−0.538724	−	0.842482i	$-0.681093\pi$
$367$	−5.04342e16	−1.07745	−0.538724	+	0.842482i	$0.681093\pi$
$368$	4.67884e15	0.0982037
$369$	0	0
$370$	−1.20588e17	−2.44339
$371$	−1.34287e17	−2.67365
$372$	0	0
$373$	6.41403e15	0.123317	0.0616586	−	0.998097i	$-0.480361\pi$
$373$	6.41403e15	0.123317	0.0616586	+	0.998097i	$0.480361\pi$
$374$	−2.38676e16	−0.450966
$375$	0	0
$376$	−4.51716e16	−0.824411
$377$	9.59688e16	1.72152
$378$	0	0
$379$	6.85830e15	0.118867	0.0594335	−	0.998232i	$-0.481071\pi$
$379$	6.85830e15	0.118867	0.0594335	+	0.998232i	$0.481071\pi$
$380$	8.31517e15	0.141670
$381$	0	0
$382$	3.94524e16	0.649623
$383$	−5.27865e16	−0.854537	−0.427268	−	0.904125i	$-0.640524\pi$
$383$	−5.27865e16	−0.854537	−0.427268	+	0.904125i	$0.640524\pi$
$384$	0	0
$385$	−4.20924e16	−0.658732
$386$	−8.77171e16	−1.34979
$387$	0	0
$388$	−7.47237e16	−1.11187
$389$	−6.57216e16	−0.961692	−0.480846	−	0.876805i	$-0.659670\pi$
$389$	−6.57216e16	−0.961692	−0.480846	+	0.876805i	$0.659670\pi$
$390$	0	0
$391$	−1.48011e16	−0.209481
$392$	−6.33729e16	−0.882153
$393$	0	0
$394$	−9.24114e16	−1.24452
$395$	9.76789e16	1.29396
$396$	0	0
$397$	−1.04942e17	−1.34528	−0.672639	−	0.739971i	$-0.734839\pi$
$397$	−1.04942e17	−1.34528	−0.672639	+	0.739971i	$0.734839\pi$
$398$	2.03066e17	2.56093
$399$	0	0
$400$	−3.51324e16	−0.428863
$401$	−2.14759e16	−0.257936	−0.128968	−	0.991649i	$-0.541166\pi$
$401$	−2.14759e16	−0.257936	−0.128968	+	0.991649i	$0.541166\pi$
$402$	0	0
$403$	−2.17683e16	−0.253129
$404$	−2.28416e17	−2.61366
$405$	0	0
$406$	3.56187e17	3.94693
$407$	−3.13074e16	−0.341415
$408$	0	0
$409$	1.57661e17	1.66542	0.832708	−	0.553713i	$-0.186790\pi$
$409$	1.57661e17	1.66542	0.832708	+	0.553713i	$0.186790\pi$
$410$	1.32799e17	1.38070
$411$	0	0
$412$	9.69943e16	0.977044
$413$	1.30489e17	1.29389
$414$	0	0
$415$	−1.62632e17	−1.56277
$416$	−1.46137e17	−1.38246
$417$	0	0
$418$	3.70903e15	0.0340106
$419$	−8.20257e16	−0.740558	−0.370279	−	0.928921i	$-0.620738\pi$
$419$	−8.20257e16	−0.740558	−0.370279	+	0.928921i	$0.620738\pi$
$420$	0	0
$421$	−5.59695e16	−0.489912	−0.244956	−	0.969534i	$-0.578774\pi$
$421$	−5.59695e16	−0.489912	−0.244956	+	0.969534i	$0.578774\pi$
$422$	2.60595e17	2.24613
$423$	0	0
$424$	1.24027e17	1.03667
$425$	1.11138e17	0.914820
$426$	0	0
$427$	2.74692e17	2.19313
$428$	−2.97452e17	−2.33901
$429$	0	0
$430$	−2.32842e16	−0.177630
$431$	−1.77267e17	−1.33207	−0.666034	−	0.745921i	$-0.732009\pi$
$431$	−1.77267e17	−1.33207	−0.666034	+	0.745921i	$0.732009\pi$
$432$	0	0
$433$	−5.06598e16	−0.369396	−0.184698	−	0.982795i	$-0.559131\pi$
$433$	−5.06598e16	−0.369396	−0.184698	+	0.982795i	$0.559131\pi$
$434$	−8.07928e16	−0.580349
$435$	0	0
$436$	−3.03306e16	−0.211455
$437$	2.30009e15	0.0157985
$438$	0	0
$439$	−6.76669e16	−0.451187	−0.225594	−	0.974221i	$-0.572432\pi$
$439$	−6.76669e16	−0.451187	−0.225594	+	0.974221i	$0.572432\pi$
$440$	3.88764e16	0.255413
$441$	0	0
$442$	2.47739e17	1.58034
$443$	−1.70873e17	−1.07411	−0.537057	−	0.843546i	$-0.680464\pi$
$443$	−1.70873e17	−1.07411	−0.537057	+	0.843546i	$0.680464\pi$
$444$	0	0
$445$	−2.77635e17	−1.69486
$446$	−3.70261e17	−2.22757
$447$	0	0
$448$	−4.20901e17	−2.45965
$449$	−2.13667e14	−0.00123066	−0.000615329	−	1.00000i	$-0.500196\pi$
$449$	−2.13667e14	−0.00123066	−0.000615329		1.00000i	$0.500196\pi$
$450$	0	0
$451$	3.44777e16	0.192926
$452$	4.28996e17	2.36621
$453$	0	0
$454$	4.30398e17	2.30679
$455$	4.36907e17	2.30842
$456$	0	0
$457$	3.31395e17	1.70173	0.850864	−	0.525386i	$-0.176079\pi$
$457$	3.31395e17	1.70173	0.850864	+	0.525386i	$0.176079\pi$
$458$	4.18073e17	2.11654
$459$	0	0
$460$	8.55192e16	0.420860
$461$	2.65757e17	1.28952	0.644761	−	0.764384i	$-0.276957\pi$
$461$	2.65757e17	1.28952	0.644761	+	0.764384i	$0.276957\pi$
$462$	0	0
$463$	−4.27497e15	−0.0201677	−0.0100839	−	0.999949i	$-0.503210\pi$
$463$	−4.27497e15	−0.0201677	−0.0100839	+	0.999949i	$0.503210\pi$
$464$	1.58766e17	0.738569
$465$	0	0
$466$	−2.61291e17	−1.18200
$467$	2.56398e16	0.114381	0.0571907	−	0.998363i	$-0.481786\pi$
$467$	2.56398e16	0.114381	0.0571907	+	0.998363i	$0.481786\pi$
$468$	0	0
$469$	5.26896e17	2.28613
$470$	6.84596e17	2.92953
$471$	0	0
$472$	−1.20519e17	−0.501686
$473$	−6.04511e15	−0.0248203
$474$	0	0
$475$	−1.72709e16	−0.0689932
$476$	5.35176e17	2.10888
$477$	0	0
$478$	−4.36758e16	−0.167479
$479$	−3.69707e17	−1.39855	−0.699274	−	0.714854i	$-0.746493\pi$
$479$	−3.69707e17	−1.39855	−0.699274	+	0.714854i	$0.746493\pi$
$480$	0	0
$481$	3.24962e17	1.19644
$482$	−7.35246e17	−2.67071
$483$	0	0
$484$	3.58032e16	0.126598
$485$	3.19253e17	1.11382
$486$	0	0
$487$	−5.17795e17	−1.75881	−0.879406	−	0.476073i	$-0.842060\pi$
$487$	−5.17795e17	−1.75881	−0.879406	+	0.476073i	$0.842060\pi$
$488$	−2.53704e17	−0.850352
$489$	0	0
$490$	9.60446e17	3.13472
$491$	−1.72056e17	−0.554165	−0.277082	−	0.960846i	$-0.589368\pi$
$491$	−1.72056e17	−0.554165	−0.277082	+	0.960846i	$0.589368\pi$
$492$	0	0
$493$	−5.02242e17	−1.57546
$494$	−3.84987e16	−0.119185
$495$	0	0
$496$	−3.60124e16	−0.108598
$497$	5.60883e17	1.66938
$498$	0	0
$499$	1.31941e17	0.382584	0.191292	−	0.981533i	$-0.438732\pi$
$499$	1.31941e17	0.382584	0.191292	+	0.981533i	$0.438732\pi$
$500$	3.65969e16	0.104746
$501$	0	0
$502$	−3.44890e17	−0.961848
$503$	−2.26740e17	−0.624218	−0.312109	−	0.950046i	$-0.601035\pi$
$503$	−2.26740e17	−0.624218	−0.312109	+	0.950046i	$0.601035\pi$
$504$	0	0
$505$	9.75896e17	2.61824
$506$	3.81463e16	0.101036
$507$	0	0
$508$	−7.90892e17	−2.04175
$509$	8.67070e16	0.220998	0.110499	−	0.993876i	$-0.464755\pi$
$509$	8.67070e16	0.220998	0.110499	+	0.993876i	$0.464755\pi$
$510$	0	0
$511$	−1.68628e17	−0.418982
$512$	−3.53965e17	−0.868371
$513$	0	0
$514$	3.38120e17	0.808743
$515$	−4.14402e17	−0.978758
$516$	0	0
$517$	1.77737e17	0.409344
$518$	1.20609e18	2.74307
$519$	0	0
$520$	−4.03526e17	−0.895055
$521$	−5.57568e17	−1.22138	−0.610692	−	0.791868i	$-0.709109\pi$
$521$	−5.57568e17	−1.22138	−0.610692	+	0.791868i	$0.709109\pi$
$522$	0	0
$523$	−4.80021e17	−1.02565	−0.512826	−	0.858493i	$-0.671401\pi$
$523$	−4.80021e17	−1.02565	−0.512826	+	0.858493i	$0.671401\pi$
$524$	6.06872e17	1.28069
$525$	0	0
$526$	−2.35235e17	−0.484277
$527$	1.13922e17	0.231653
$528$	0	0
$529$	−4.80381e17	−0.953067
$530$	−1.87969e18	−3.68378
$531$	0	0
$532$	−8.31664e16	−0.159046
$533$	−3.57868e17	−0.676077
$534$	0	0
$535$	1.27085e18	2.34311
$536$	−4.86639e17	−0.886412
$537$	0	0
$538$	−8.23097e16	−0.146341
$539$	2.49354e17	0.438015
$540$	0	0
$541$	−3.07367e17	−0.527078	−0.263539	−	0.964649i	$-0.584890\pi$
$541$	−3.07367e17	−0.527078	−0.263539	+	0.964649i	$0.584890\pi$
$542$	−5.16816e16	−0.0875670
$543$	0	0
$544$	7.64792e17	1.26517
$545$	1.29585e17	0.211826
$546$	0	0
$547$	6.25426e17	0.998294	0.499147	−	0.866517i	$-0.333647\pi$
$547$	6.25426e17	0.998294	0.499147	+	0.866517i	$0.333647\pi$
$548$	−1.38079e18	−2.17798
$549$	0	0
$550$	−2.86433e17	−0.441230
$551$	7.80485e16	0.118817
$552$	0	0
$553$	−9.76961e17	−1.45266
$554$	−4.82047e17	−0.708396
$555$	0	0
$556$	1.18309e18	1.69836
$557$	−5.97923e17	−0.848372	−0.424186	−	0.905575i	$-0.639440\pi$
$557$	−5.97923e17	−0.848372	−0.424186	+	0.905575i	$0.639440\pi$
$558$	0	0
$559$	6.27465e16	0.0869787
$560$	7.22799e17	0.990365
$561$	0	0
$562$	2.42983e17	0.325305
$563$	9.48274e16	0.125496	0.0627479	−	0.998029i	$-0.480014\pi$
$563$	9.48274e16	0.125496	0.0627479	+	0.998029i	$0.480014\pi$
$564$	0	0
$565$	−1.83286e18	−2.37036
$566$	−2.41141e17	−0.308294
$567$	0	0
$568$	−5.18029e17	−0.647277
$569$	−7.42364e17	−0.917038	−0.458519	−	0.888685i	$-0.651620\pi$
$569$	−7.42364e17	−0.917038	−0.458519	+	0.888685i	$0.651620\pi$
$570$	0	0
$571$	9.72970e17	1.17480	0.587401	−	0.809296i	$-0.300151\pi$
$571$	9.72970e17	1.17480	0.587401	+	0.809296i	$0.300151\pi$
$572$	−3.71627e17	−0.443642
$573$	0	0
$574$	−1.32823e18	−1.55005
$575$	−1.77626e17	−0.204959
$576$	0	0
$577$	−4.88742e17	−0.551362	−0.275681	−	0.961249i	$-0.588903\pi$
$577$	−4.88742e17	−0.551362	−0.275681	+	0.961249i	$0.588903\pi$
$578$	9.01234e16	0.100533
$579$	0	0
$580$	2.90191e18	3.16520
$581$	1.62661e18	1.75444
$582$	0	0
$583$	−4.88010e17	−0.514735
$584$	1.55745e17	0.162454
$585$	0	0
$586$	−1.30608e18	−1.33240
$587$	−1.09582e18	−1.10558	−0.552792	−	0.833320i	$-0.686437\pi$
$587$	−1.09582e18	−1.10558	−0.552792	+	0.833320i	$0.686437\pi$
$588$	0	0
$589$	−1.77035e16	−0.0174707
$590$	1.82652e18	1.78273
$591$	0	0
$592$	5.37601e17	0.513298
$593$	1.82087e18	1.71959	0.859794	−	0.510641i	$-0.170592\pi$
$593$	1.82087e18	1.71959	0.859794	+	0.510641i	$0.170592\pi$
$594$	0	0
$595$	−2.28651e18	−2.11258
$596$	3.35473e17	0.306589
$597$	0	0
$598$	−3.95948e17	−0.354063
$599$	−5.79052e17	−0.512204	−0.256102	−	0.966650i	$-0.582438\pi$
$599$	−5.79052e17	−0.512204	−0.256102	+	0.966650i	$0.582438\pi$
$600$	0	0
$601$	−1.68040e18	−1.45455	−0.727273	−	0.686348i	$-0.759213\pi$
$601$	−1.68040e18	−1.45455	−0.727273	+	0.686348i	$0.759213\pi$
$602$	2.32883e17	0.199416
$603$	0	0
$604$	−5.55089e17	−0.465182
$605$	−1.52967e17	−0.126820
$606$	0	0
$607$	−2.18412e17	−0.177235	−0.0886176	−	0.996066i	$-0.528245\pi$
$607$	−2.18412e17	−0.177235	−0.0886176	+	0.996066i	$0.528245\pi$
$608$	−1.18849e17	−0.0954159
$609$	0	0
$610$	3.84501e18	3.02171
$611$	−1.84486e18	−1.43448
$612$	0	0
$613$	−8.91819e16	−0.0678865	−0.0339433	−	0.999424i	$-0.510807\pi$
$613$	−8.91819e16	−0.0678865	−0.0339433	+	0.999424i	$0.510807\pi$
$614$	2.60113e18	1.95915
$615$	0	0
$616$	−3.88832e17	−0.286740
$617$	−1.19832e18	−0.874419	−0.437210	−	0.899360i	$-0.644033\pi$
$617$	−1.19832e18	−0.874419	−0.437210	+	0.899360i	$0.644033\pi$
$618$	0	0
$619$	2.57248e18	1.83807	0.919037	−	0.394170i	$-0.128968\pi$
$619$	2.57248e18	1.83807	0.919037	+	0.394170i	$0.128968\pi$
$620$	−6.58230e17	−0.465406
$621$	0	0
$622$	1.54307e18	1.06843
$623$	2.77684e18	1.90273
$624$	0	0
$625$	−1.56613e18	−1.05101
$626$	−3.42488e18	−2.27463
$627$	0	0
$628$	−2.64150e18	−1.71835
$629$	−1.70065e18	−1.09493
$630$	0	0
$631$	1.23798e18	0.780767	0.390383	−	0.920652i	$-0.372342\pi$
$631$	1.23798e18	0.780767	0.390383	+	0.920652i	$0.372342\pi$
$632$	9.02317e17	0.563246
$633$	0	0
$634$	1.01922e18	0.623286
$635$	3.37904e18	2.04533
$636$	0	0
$637$	−2.58822e18	−1.53495
$638$	1.29441e18	0.759868
$639$	0	0
$640$	−2.71840e18	−1.56366
$641$	3.15860e17	0.179853	0.0899264	−	0.995948i	$-0.471337\pi$
$641$	3.15860e17	0.179853	0.0899264	+	0.995948i	$0.471337\pi$
$642$	0	0
$643$	1.62866e18	0.908782	0.454391	−	0.890802i	$-0.349857\pi$
$643$	1.62866e18	0.908782	0.454391	+	0.890802i	$0.349857\pi$
$644$	−8.55343e17	−0.472479
$645$	0	0
$646$	2.01479e17	0.109073
$647$	1.20409e18	0.645327	0.322664	−	0.946514i	$-0.395422\pi$
$647$	1.20409e18	0.645327	0.322664	+	0.946514i	$0.395422\pi$
$648$	0	0
$649$	4.74206e17	0.249102
$650$	2.97309e18	1.54622
$651$	0	0
$652$	1.64635e18	0.839290
$653$	2.58301e18	1.30374	0.651869	−	0.758332i	$-0.273985\pi$
$653$	2.58301e18	1.30374	0.651869	+	0.758332i	$0.273985\pi$
$654$	0	0
$655$	−2.59282e18	−1.28293
$656$	−5.92040e17	−0.290052
$657$	0	0
$658$	−6.84717e18	−3.28884
$659$	−2.90720e18	−1.38267	−0.691337	−	0.722532i	$-0.742978\pi$
$659$	−2.90720e18	−1.38267	−0.691337	+	0.722532i	$0.742978\pi$
$660$	0	0
$661$	−3.29270e18	−1.53547	−0.767737	−	0.640765i	$-0.778617\pi$
$661$	−3.29270e18	−1.53547	−0.767737	+	0.640765i	$0.778617\pi$
$662$	−6.88717e17	−0.318027
$663$	0	0
$664$	−1.50233e18	−0.680257
$665$	3.55324e17	0.159325
$666$	0	0
$667$	8.02707e17	0.352971
$668$	−4.76764e18	−2.07614
$669$	0	0
$670$	7.37524e18	3.14985
$671$	9.98251e17	0.422224
$672$	0	0
$673$	−2.98149e18	−1.23690	−0.618451	−	0.785823i	$-0.712240\pi$
$673$	−2.98149e18	−1.23690	−0.618451	+	0.785823i	$0.712240\pi$
$674$	5.06390e17	0.208063
$675$	0	0
$676$	4.02185e17	0.162096
$677$	6.19017e17	0.247102	0.123551	−	0.992338i	$-0.460572\pi$
$677$	6.19017e17	0.247102	0.123551	+	0.992338i	$0.460572\pi$
$678$	0	0
$679$	−3.19309e18	−1.25042
$680$	2.11181e18	0.819119
$681$	0	0
$682$	−2.93607e17	−0.111730
$683$	−1.07700e18	−0.405960	−0.202980	−	0.979183i	$-0.565063\pi$
$683$	−1.07700e18	−0.405960	−0.202980	+	0.979183i	$0.565063\pi$
$684$	0	0
$685$	5.89933e18	2.18180
$686$	−2.99367e18	−1.09672
$687$	0	0
$688$	1.03805e17	0.0373158
$689$	5.06541e18	1.80381
$690$	0	0
$691$	−4.77336e17	−0.166808	−0.0834039	−	0.996516i	$-0.526579\pi$
$691$	−4.77336e17	−0.166808	−0.0834039	+	0.996516i	$0.526579\pi$
$692$	−4.76209e18	−1.64857
$693$	0	0
$694$	2.84390e18	0.966222
$695$	−5.05467e18	−1.70134
$696$	0	0
$697$	1.87287e18	0.618719
$698$	1.62528e18	0.531946
$699$	0	0
$700$	6.42259e18	2.06335
$701$	−4.37219e18	−1.39166	−0.695828	−	0.718208i	$-0.744962\pi$
$701$	−4.37219e18	−1.39166	−0.695828	+	0.718208i	$0.744962\pi$
$702$	0	0
$703$	2.64282e17	0.0825767
$704$	−1.52959e18	−0.473534
$705$	0	0
$706$	2.71451e18	0.825014
$707$	−9.76068e18	−2.93937
$708$	0	0
$709$	−2.41723e18	−0.714689	−0.357344	−	0.933973i	$-0.616318\pi$
$709$	−2.41723e18	−0.714689	−0.357344	+	0.933973i	$0.616318\pi$
$710$	7.85098e18	2.30009
$711$	0	0
$712$	−2.56467e18	−0.737755
$713$	−1.82075e17	−0.0519002
$714$	0	0
$715$	1.58775e18	0.444420
$716$	−5.58478e18	−1.54907
$717$	0	0
$718$	−2.04253e18	−0.556365
$719$	1.88829e18	0.509719	0.254860	−	0.966978i	$-0.417971\pi$
$719$	1.88829e18	0.509719	0.254860	+	0.966978i	$0.417971\pi$
$720$	0	0
$721$	4.14475e18	1.09880
$722$	5.85611e18	1.53857
$723$	0	0
$724$	4.35864e18	1.12474
$725$	−6.02735e18	−1.54145
$726$	0	0
$727$	−5.58551e17	−0.140310	−0.0701551	−	0.997536i	$-0.522349\pi$
$727$	−5.58551e17	−0.140310	−0.0701551	+	0.997536i	$0.522349\pi$
$728$	4.03597e18	1.00483
$729$	0	0
$730$	−2.36038e18	−0.577276
$731$	−3.28377e17	−0.0795994
$732$	0	0
$733$	−1.54585e18	−0.368122	−0.184061	−	0.982915i	$-0.558924\pi$
$733$	−1.54585e18	−0.368122	−0.184061	+	0.982915i	$0.558924\pi$
$734$	7.06079e18	1.66659
$735$	0	0
$736$	−1.22232e18	−0.283453
$737$	1.91478e18	0.440129
$738$	0	0
$739$	−6.42538e18	−1.45114	−0.725571	−	0.688147i	$-0.758424\pi$
$739$	−6.42538e18	−1.45114	−0.725571	+	0.688147i	$0.758424\pi$
$740$	9.82620e18	2.19978
$741$	0	0
$742$	1.88002e19	4.13559
$743$	−4.38566e18	−0.956330	−0.478165	−	0.878270i	$-0.658698\pi$
$743$	−4.38566e18	−0.956330	−0.478165	+	0.878270i	$0.658698\pi$
$744$	0	0
$745$	−1.43329e18	−0.307127
$746$	−8.97965e17	−0.190747
$747$	0	0
$748$	1.94487e18	0.406004
$749$	−1.27107e19	−2.63050
$750$	0	0
$751$	1.75685e18	0.357334	0.178667	−	0.983910i	$-0.442821\pi$
$751$	1.75685e18	0.357334	0.178667	+	0.983910i	$0.442821\pi$
$752$	−3.05204e18	−0.615424
$753$	0	0
$754$	−1.34356e19	−2.66283
$755$	2.37158e18	0.465997
$756$	0	0
$757$	−1.97367e18	−0.381199	−0.190600	−	0.981668i	$-0.561043\pi$
$757$	−1.97367e18	−0.381199	−0.190600	+	0.981668i	$0.561043\pi$
$758$	−9.60161e17	−0.183863
$759$	0	0
$760$	−3.28175e17	−0.0617757
$761$	−1.91433e18	−0.357286	−0.178643	−	0.983914i	$-0.557171\pi$
$761$	−1.91433e18	−0.357286	−0.178643	+	0.983914i	$0.557171\pi$
$762$	0	0
$763$	−1.29608e18	−0.237806
$764$	−3.21481e18	−0.584855
$765$	0	0
$766$	7.39011e18	1.32179
$767$	−4.92212e18	−0.872936
$768$	0	0
$769$	−9.69949e18	−1.69133	−0.845664	−	0.533716i	$-0.820795\pi$
$769$	−9.69949e18	−1.69133	−0.845664	+	0.533716i	$0.820795\pi$
$770$	5.89294e18	1.01892
$771$	0	0
$772$	7.14769e18	1.21522
$773$	1.83115e18	0.308714	0.154357	−	0.988015i	$-0.450669\pi$
$773$	1.83115e18	0.308714	0.154357	+	0.988015i	$0.450669\pi$
$774$	0	0
$775$	1.36717e18	0.226652
$776$	2.94912e18	0.484833
$777$	0	0
$778$	9.20103e18	1.48754
$779$	−2.91044e17	−0.0466621
$780$	0	0
$781$	2.03829e18	0.321392
$782$	2.07215e18	0.324025
$783$	0	0
$784$	−4.28183e18	−0.658529
$785$	1.12856e19	1.72137
$786$	0	0
$787$	4.83945e17	0.0726039	0.0363019	−	0.999341i	$-0.488442\pi$
$787$	4.83945e17	0.0726039	0.0363019	+	0.999341i	$0.488442\pi$
$788$	7.53021e18	1.12044
$789$	0	0
$790$	−1.36750e19	−2.00149
$791$	1.83318e19	2.66109
$792$	0	0
$793$	−1.03616e19	−1.47962
$794$	1.46919e19	2.08087
$795$	0	0
$796$	−1.65470e19	−2.30560
$797$	1.28612e19	1.77747	0.888734	−	0.458423i	$-0.151585\pi$
$797$	1.28612e19	1.77747	0.888734	+	0.458423i	$0.151585\pi$
$798$	0	0
$799$	9.65486e18	1.31278
$800$	9.17818e18	1.23786
$801$	0	0
$802$	3.00662e18	0.398975
$803$	−6.12809e17	−0.0806629
$804$	0	0
$805$	3.65440e18	0.473307
$806$	3.04756e18	0.391539
$807$	0	0
$808$	9.01492e18	1.13969
$809$	−6.97044e18	−0.874168	−0.437084	−	0.899421i	$-0.643989\pi$
$809$	−6.97044e18	−0.874168	−0.437084	+	0.899421i	$0.643989\pi$
$810$	0	0
$811$	1.21111e19	1.49468	0.747338	−	0.664444i	$-0.231332\pi$
$811$	1.21111e19	1.49468	0.747338	+	0.664444i	$0.231332\pi$
$812$	−2.90242e19	−3.55341
$813$	0	0
$814$	4.38303e18	0.528100
$815$	−7.03392e18	−0.840762
$816$	0	0
$817$	5.10298e16	0.00600317
$818$	−2.20725e19	−2.57606
$819$	0	0
$820$	−1.08212e19	−1.24304
$821$	−1.13387e19	−1.29220	−0.646102	−	0.763251i	$-0.723602\pi$
$821$	−1.13387e19	−1.29220	−0.646102	+	0.763251i	$0.723602\pi$
$822$	0	0
$823$	−4.21754e17	−0.0473108	−0.0236554	−	0.999720i	$-0.507530\pi$
$823$	−4.21754e17	−0.0473108	−0.0236554	+	0.999720i	$0.507530\pi$
$824$	−3.82808e18	−0.426043
$825$	0	0
$826$	−1.82684e19	−2.00139
$827$	−9.62297e18	−1.04598	−0.522990	−	0.852339i	$-0.675183\pi$
$827$	−9.62297e18	−1.04598	−0.522990	+	0.852339i	$0.675183\pi$
$828$	0	0
$829$	−1.01074e19	−1.08152	−0.540759	−	0.841178i	$-0.681863\pi$
$829$	−1.01074e19	−1.08152	−0.540759	+	0.841178i	$0.681863\pi$
$830$	2.27685e19	2.41728
$831$	0	0
$832$	1.58767e19	1.65943
$833$	1.35452e19	1.40473
$834$	0	0
$835$	2.03694e19	2.07978
$836$	−3.02233e17	−0.0306197
$837$	0	0
$838$	1.14836e19	1.14549
$839$	9.83113e17	0.0973085	0.0486543	−	0.998816i	$-0.484507\pi$
$839$	9.83113e17	0.0973085	0.0486543	+	0.998816i	$0.484507\pi$
$840$	0	0
$841$	1.69774e19	1.65462
$842$	7.83573e18	0.757794
$843$	0	0
$844$	−2.12348e19	−2.02219
$845$	−1.71831e18	−0.162380
$846$	0	0
$847$	1.52994e18	0.142374
$848$	8.37997e18	0.773873
$849$	0	0
$850$	−1.55594e19	−1.41504
$851$	2.71806e18	0.245311
$852$	0	0
$853$	1.20347e19	1.06971	0.534854	−	0.844944i	$-0.320367\pi$
$853$	1.20347e19	1.06971	0.534854	+	0.844944i	$0.320367\pi$
$854$	−3.84569e19	−3.39233
$855$	0	0
$856$	1.17396e19	1.01993
$857$	5.60320e18	0.483127	0.241563	−	0.970385i	$-0.422340\pi$
$857$	5.60320e18	0.483127	0.241563	+	0.970385i	$0.422340\pi$
$858$	0	0
$859$	1.16060e17	0.00985656	0.00492828	−	0.999988i	$-0.498431\pi$
$859$	1.16060e17	0.00985656	0.00492828	+	0.999988i	$0.498431\pi$
$860$	1.89733e18	0.159920
$861$	0	0
$862$	2.48174e19	2.06044
$863$	1.14438e18	0.0942978	0.0471489	−	0.998888i	$-0.484986\pi$
$863$	1.14438e18	0.0942978	0.0471489	+	0.998888i	$0.484986\pi$
$864$	0	0
$865$	2.03458e19	1.65146
$866$	7.09237e18	0.571380
$867$	0	0
$868$	6.58346e18	0.522488
$869$	−3.55035e18	−0.279668
$870$	0	0
$871$	−1.98749e19	−1.54236
$872$	1.19706e18	0.0922057
$873$	0	0
$874$	−3.22013e17	−0.0244371
$875$	1.56386e18	0.117800
$876$	0	0
$877$	5.25918e17	0.0390320	0.0195160	−	0.999810i	$-0.493787\pi$
$877$	5.25918e17	0.0390320	0.0195160	+	0.999810i	$0.493787\pi$
$878$	9.47337e18	0.697895
$879$	0	0
$880$	2.62671e18	0.190666
$881$	1.02154e19	0.736056	0.368028	−	0.929815i	$-0.380033\pi$
$881$	1.02154e19	0.736056	0.368028	+	0.929815i	$0.380033\pi$
$882$	0	0
$883$	−1.67904e19	−1.19211	−0.596055	−	0.802943i	$-0.703266\pi$
$883$	−1.67904e19	−1.19211	−0.596055	+	0.802943i	$0.703266\pi$
$884$	−2.01872e19	−1.42278
$885$	0	0
$886$	2.39223e19	1.66143
$887$	9.98165e18	0.688175	0.344087	−	0.938938i	$-0.388188\pi$
$887$	9.98165e18	0.688175	0.344087	+	0.938938i	$0.388188\pi$
$888$	0	0
$889$	−3.37964e19	−2.29619
$890$	3.88688e19	2.62160
$891$	0	0
$892$	3.01710e19	2.00548
$893$	−1.50037e18	−0.0990063
$894$	0	0
$895$	2.38606e19	1.55179
$896$	2.71888e19	1.75545
$897$	0	0
$898$	2.99134e16	0.00190358
$899$	−6.17833e18	−0.390331
$900$	0	0
$901$	−2.65093e19	−1.65077
$902$	−4.82687e18	−0.298417
$903$	0	0
$904$	−1.69312e19	−1.03179
$905$	−1.86220e19	−1.12671
$906$	0	0
$907$	−1.90931e19	−1.13875	−0.569377	−	0.822076i	$-0.692816\pi$
$907$	−1.90931e19	−1.13875	−0.569377	+	0.822076i	$0.692816\pi$
$908$	−3.50713e19	−2.07680
$909$	0	0
$910$	−6.11670e19	−3.57066
$911$	−2.12403e19	−1.23109	−0.615547	−	0.788100i	$-0.711065\pi$
$911$	−2.12403e19	−1.23109	−0.615547	+	0.788100i	$0.711065\pi$
$912$	0	0
$913$	5.91122e18	0.337767
$914$	−4.63953e19	−2.63223
$915$	0	0
$916$	−3.40669e19	−1.90552
$917$	2.59328e19	1.44029
$918$	0	0
$919$	2.14539e19	1.17478	0.587388	−	0.809305i	$-0.300156\pi$
$919$	2.14539e19	1.17478	0.587388	+	0.809305i	$0.300156\pi$
$920$	−3.37519e18	−0.183517
$921$	0	0
$922$	−3.72060e19	−1.99463
$923$	−2.11569e19	−1.12627
$924$	0	0
$925$	−2.04093e19	−1.07129
$926$	5.98496e17	0.0311953
$927$	0	0
$928$	−4.14769e19	−2.13179
$929$	−6.27434e17	−0.0320233	−0.0160116	−	0.999872i	$-0.505097\pi$
$929$	−6.27434e17	−0.0320233	−0.0160116	+	0.999872i	$0.505097\pi$
$930$	0	0
$931$	−2.10492e18	−0.105941
$932$	2.12915e19	1.06415
$933$	0	0
$934$	−3.58957e18	−0.176925
$935$	−8.30935e18	−0.406716
$936$	0	0
$937$	1.14580e19	0.553098	0.276549	−	0.961000i	$-0.410809\pi$
$937$	1.14580e19	0.553098	0.276549	+	0.961000i	$0.410809\pi$
$938$	−7.37654e19	−3.53618
$939$	0	0
$940$	−5.57848e19	−2.63745
$941$	−8.37033e18	−0.393016	−0.196508	−	0.980502i	$-0.562960\pi$
$941$	−8.37033e18	−0.393016	−0.196508	+	0.980502i	$0.562960\pi$
$942$	0	0
$943$	−2.99330e18	−0.138620
$944$	−8.14293e18	−0.374509
$945$	0	0
$946$	8.46315e17	0.0383919
$947$	1.66309e19	0.749275	0.374637	−	0.927171i	$-0.377767\pi$
$947$	1.66309e19	0.749275	0.374637	+	0.927171i	$0.377767\pi$
$948$	0	0
$949$	6.36078e18	0.282670
$950$	2.41793e18	0.106718
$951$	0	0
$952$	−2.11218e19	−0.919584
$953$	2.54297e19	1.09961	0.549803	−	0.835294i	$-0.314703\pi$
$953$	2.54297e19	1.09961	0.549803	+	0.835294i	$0.314703\pi$
$954$	0	0
$955$	1.37351e19	0.585880
$956$	3.55895e18	0.150781
$957$	0	0
$958$	5.17590e19	2.16327
$959$	−5.90037e19	−2.44939
$960$	0	0
$961$	−2.30161e19	−0.942606
$962$	−4.54947e19	−1.85064
$963$	0	0
$964$	5.99121e19	2.40444
$965$	−3.05381e19	−1.21735
$966$	0	0
$967$	5.78322e18	0.227456	0.113728	−	0.993512i	$-0.463721\pi$
$967$	5.78322e18	0.227456	0.113728	+	0.993512i	$0.463721\pi$
$968$	−1.41305e18	−0.0552035
$969$	0	0
$970$	−4.46954e19	−1.72284
$971$	4.12182e19	1.57821	0.789104	−	0.614259i	$-0.210545\pi$
$971$	4.12182e19	1.57821	0.789104	+	0.614259i	$0.210545\pi$
$972$	0	0
$973$	5.05556e19	1.91001
$974$	7.24912e19	2.72052
$975$	0	0
$976$	−1.71417e19	−0.634789
$977$	4.33217e19	1.59364	0.796822	−	0.604215i	$-0.206513\pi$
$977$	4.33217e19	1.59364	0.796822	+	0.604215i	$0.206513\pi$
$978$	0	0
$979$	1.00912e19	0.366317
$980$	−7.82626e19	−2.82218
$981$	0	0
$982$	2.40878e19	0.857180
$983$	2.52492e19	0.892584	0.446292	−	0.894887i	$-0.352744\pi$
$983$	2.52492e19	0.892584	0.446292	+	0.894887i	$0.352744\pi$
$984$	0	0
$985$	−3.21724e19	−1.12240
$986$	7.03139e19	2.43692
$987$	0	0
$988$	3.13709e18	0.107302
$989$	5.24827e17	0.0178337
$990$	0	0
$991$	1.90400e19	0.638539	0.319269	−	0.947664i	$-0.396562\pi$
$991$	1.90400e19	0.638539	0.319269	+	0.947664i	$0.396562\pi$
$992$	9.40807e18	0.313455
$993$	0	0
$994$	−7.85236e19	−2.58219
$995$	7.06961e19	2.30965
$996$	0	0
$997$	3.63643e19	1.17262	0.586309	−	0.810087i	$-0.300580\pi$
$997$	3.63643e19	1.17262	0.586309	+	0.810087i	$0.300580\pi$
$998$	−1.84717e19	−0.591779
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.14.a.a.1.1		1
3.2	odd	2		33.14.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.14.a.a.1.1	✓	1	3.2	odd	2
99.14.a.a.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	99.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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