LMFDB - Embedded newform 64.14.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,14,Mod(1,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, 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("64.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	64.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:	$68.6277945292$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 4)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-468.000 q^{3} -56214.0 q^{5} +333032. q^{7} -1.37530e6 q^{9} +O(q^{10})$

$q-468.000 q^{3} -56214.0 q^{5} +333032. q^{7} -1.37530e6 q^{9} +6.39738e6 q^{11} -1.51997e7 q^{13} +2.63082e7 q^{15} +4.31142e7 q^{17} +3.65115e8 q^{19} -1.55859e8 q^{21} -5.72268e7 q^{23} +1.93931e9 q^{25} +1.38978e9 q^{27} +4.64190e7 q^{29} -5.68219e9 q^{31} -2.99397e9 q^{33} -1.87211e10 q^{35} +1.88719e9 q^{37} +7.11348e9 q^{39} -7.33680e9 q^{41} +2.68867e10 q^{43} +7.73111e10 q^{45} +1.01840e11 q^{47} +1.40213e10 q^{49} -2.01774e10 q^{51} -2.78732e11 q^{53} -3.59622e11 q^{55} -1.70874e11 q^{57} -5.95739e10 q^{59} +2.74845e10 q^{61} -4.58019e11 q^{63} +8.54438e11 q^{65} -7.84410e11 q^{67} +2.67822e10 q^{69} -3.60365e11 q^{71} -1.59264e12 q^{73} -9.07597e11 q^{75} +2.13053e12 q^{77} -2.31612e10 q^{79} +1.54225e12 q^{81} -2.05016e12 q^{83} -2.42362e12 q^{85} -2.17241e10 q^{87} -3.48539e12 q^{89} -5.06200e12 q^{91} +2.65926e12 q^{93} -2.05246e13 q^{95} +6.70667e12 q^{97} -8.79831e12 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−468.000	−0.370645	−0.185322	−	0.982678i	$-0.559333\pi$
$3$	−468.000	−0.370645	−0.185322	+	0.982678i	$0.559333\pi$
$4$	0	0
$5$	−56214.0	−1.60894	−0.804469	−	0.593994i	$-0.797550\pi$
$5$	−56214.0	−1.60894	−0.804469	+	0.593994i	$0.797550\pi$
$6$	0	0
$7$	333032.	1.06991	0.534957	−	0.844879i	$-0.320328\pi$
$7$	333032.	1.06991	0.534957	+	0.844879i	$0.320328\pi$
$8$	0	0
$9$	−1.37530e6	−0.862623
$10$	0	0
$11$	6.39738e6	1.08880	0.544402	−	0.838824i	$-0.316757\pi$
$11$	6.39738e6	1.08880	0.544402	+	0.838824i	$0.316757\pi$
$12$	0	0
$13$	−1.51997e7	−0.873382	−0.436691	−	0.899611i	$-0.643850\pi$
$13$	−1.51997e7	−0.873382	−0.436691	+	0.899611i	$0.643850\pi$
$14$	0	0
$15$	2.63082e7	0.596344
$16$	0	0
$17$	4.31142e7	0.433214	0.216607	−	0.976259i	$-0.430501\pi$
$17$	4.31142e7	0.433214	0.216607	+	0.976259i	$0.430501\pi$
$18$	0	0
$19$	3.65115e8	1.78046	0.890229	−	0.455513i	$-0.150544\pi$
$19$	3.65115e8	1.78046	0.890229	+	0.455513i	$0.150544\pi$
$20$	0	0
$21$	−1.55859e8	−0.396558
$22$	0	0
$23$	−5.72268e7	−0.0806062	−0.0403031	−	0.999187i	$-0.512832\pi$
$23$	−5.72268e7	−0.0806062	−0.0403031	+	0.999187i	$0.512832\pi$
$24$	0	0
$25$	1.93931e9	1.58868
$26$	0	0
$27$	1.38978e9	0.690371
$28$	0	0
$29$	4.64190e7	0.0144913	0.00724567	−	0.999974i	$-0.497694\pi$
$29$	4.64190e7	0.0144913	0.00724567	+	0.999974i	$0.497694\pi$
$30$	0	0
$31$	−5.68219e9	−1.14991	−0.574956	−	0.818185i	$-0.694981\pi$
$31$	−5.68219e9	−1.14991	−0.574956	+	0.818185i	$0.694981\pi$
$32$	0	0
$33$	−2.99397e9	−0.403559
$34$	0	0
$35$	−1.87211e10	−1.72143
$36$	0	0
$37$	1.88719e9	0.120921	0.0604607	−	0.998171i	$-0.480743\pi$
$37$	1.88719e9	0.120921	0.0604607	+	0.998171i	$0.480743\pi$
$38$	0	0
$39$	7.11348e9	0.323714
$40$	0	0
$41$	−7.33680e9	−0.241219	−0.120610	−	0.992700i	$-0.538485\pi$
$41$	−7.33680e9	−0.241219	−0.120610	+	0.992700i	$0.538485\pi$
$42$	0	0
$43$	2.68867e10	0.648623	0.324311	−	0.945950i	$-0.394867\pi$
$43$	2.68867e10	0.648623	0.324311	+	0.945950i	$0.394867\pi$
$44$	0	0
$45$	7.73111e10	1.38791
$46$	0	0
$47$	1.01840e11	1.37810	0.689051	−	0.724712i	$-0.258027\pi$
$47$	1.01840e11	1.37810	0.689051	+	0.724712i	$0.258027\pi$
$48$	0	0
$49$	1.40213e10	0.144715
$50$	0	0
$51$	−2.01774e10	−0.160568
$52$	0	0
$53$	−2.78732e11	−1.72740	−0.863701	−	0.504004i	$-0.831860\pi$
$53$	−2.78732e11	−1.72740	−0.863701	+	0.504004i	$0.831860\pi$
$54$	0	0
$55$	−3.59622e11	−1.75182
$56$	0	0
$57$	−1.70874e11	−0.659917
$58$	0	0
$59$	−5.95739e10	−0.183873	−0.0919366	−	0.995765i	$-0.529306\pi$
$59$	−5.95739e10	−0.183873	−0.0919366	+	0.995765i	$0.529306\pi$
$60$	0	0
$61$	2.74845e10	0.0683036	0.0341518	−	0.999417i	$-0.489127\pi$
$61$	2.74845e10	0.0683036	0.0341518	+	0.999417i	$0.489127\pi$
$62$	0	0
$63$	−4.58019e11	−0.922932
$64$	0	0
$65$	8.54438e11	1.40522
$66$	0	0
$67$	−7.84410e11	−1.05939	−0.529696	−	0.848187i	$-0.677694\pi$
$67$	−7.84410e11	−1.05939	−0.529696	+	0.848187i	$0.677694\pi$
$68$	0	0
$69$	2.67822e10	0.0298763
$70$	0	0
$71$	−3.60365e11	−0.333859	−0.166930	−	0.985969i	$-0.553385\pi$
$71$	−3.60365e11	−0.333859	−0.166930	+	0.985969i	$0.553385\pi$
$72$	0	0
$73$	−1.59264e12	−1.23174	−0.615868	−	0.787849i	$-0.711195\pi$
$73$	−1.59264e12	−1.23174	−0.615868	+	0.787849i	$0.711195\pi$
$74$	0	0
$75$	−9.07597e11	−0.588837
$76$	0	0
$77$	2.13053e12	1.16493
$78$	0	0
$79$	−2.31612e10	−0.0107198	−0.00535988	−	0.999986i	$-0.501706\pi$
$79$	−2.31612e10	−0.0107198	−0.00535988	+	0.999986i	$0.501706\pi$
$80$	0	0
$81$	1.54225e12	0.606740
$82$	0	0
$83$	−2.05016e12	−0.688303	−0.344152	−	0.938914i	$-0.611833\pi$
$83$	−2.05016e12	−0.688303	−0.344152	+	0.938914i	$0.611833\pi$
$84$	0	0
$85$	−2.42362e12	−0.697014
$86$	0	0
$87$	−2.17241e10	−0.00537114
$88$	0	0
$89$	−3.48539e12	−0.743390	−0.371695	−	0.928355i	$-0.621223\pi$
$89$	−3.48539e12	−0.743390	−0.371695	+	0.928355i	$0.621223\pi$
$90$	0	0
$91$	−5.06200e12	−0.934444
$92$	0	0
$93$	2.65926e12	0.426209
$94$	0	0
$95$	−2.05246e13	−2.86465
$96$	0	0
$97$	6.70667e12	0.817505	0.408753	−	0.912645i	$-0.365964\pi$
$97$	6.70667e12	0.817505	0.408753	+	0.912645i	$0.365964\pi$
$98$	0	0
$99$	−8.79831e12	−0.939227
$100$	0	0
$101$	−1.06537e13	−0.998649	−0.499325	−	0.866415i	$-0.666418\pi$
$101$	−1.06537e13	−0.998649	−0.499325	+	0.866415i	$0.666418\pi$
$102$	0	0
$103$	−1.09245e13	−0.901484	−0.450742	−	0.892654i	$-0.648841\pi$
$103$	−1.09245e13	−0.901484	−0.450742	+	0.892654i	$0.648841\pi$
$104$	0	0
$105$	8.76146e12	0.638037
$106$	0	0
$107$	−1.25876e13	−0.810862	−0.405431	−	0.914126i	$-0.632879\pi$
$107$	−1.25876e13	−0.810862	−0.405431	+	0.914126i	$0.632879\pi$
$108$	0	0
$109$	4.36642e11	0.0249375	0.0124688	−	0.999922i	$-0.496031\pi$
$109$	4.36642e11	0.0249375	0.0124688	+	0.999922i	$0.496031\pi$
$110$	0	0
$111$	−8.83203e11	−0.0448189
$112$	0	0
$113$	−3.18312e13	−1.43828	−0.719139	−	0.694866i	$-0.755464\pi$
$113$	−3.18312e13	−1.43828	−0.719139	+	0.694866i	$0.755464\pi$
$114$	0	0
$115$	3.21695e12	0.129691
$116$	0	0
$117$	2.09042e13	0.753399
$118$	0	0
$119$	1.43584e13	0.463501
$120$	0	0
$121$	6.40376e12	0.185494
$122$	0	0
$123$	3.43362e12	0.0894066
$124$	0	0
$125$	−4.03958e13	−0.947155
$126$	0	0
$127$	3.94077e13	0.833406	0.416703	−	0.909043i	$-0.363185\pi$
$127$	3.94077e13	0.833406	0.416703	+	0.909043i	$0.363185\pi$
$128$	0	0
$129$	−1.25830e13	−0.240409
$130$	0	0
$131$	−7.37440e13	−1.27486	−0.637431	−	0.770507i	$-0.720003\pi$
$131$	−7.37440e13	−1.27486	−0.637431	+	0.770507i	$0.720003\pi$
$132$	0	0
$133$	1.21595e14	1.90494
$134$	0	0
$135$	−7.81253e13	−1.11076
$136$	0	0
$137$	8.54100e13	1.10363	0.551817	−	0.833965i	$-0.313935\pi$
$137$	8.54100e13	1.10363	0.551817	+	0.833965i	$0.313935\pi$
$138$	0	0
$139$	7.97827e13	0.938237	0.469119	−	0.883135i	$-0.344572\pi$
$139$	7.97827e13	0.938237	0.469119	+	0.883135i	$0.344572\pi$
$140$	0	0
$141$	−4.76610e13	−0.510786
$142$	0	0
$143$	−9.72385e13	−0.950942
$144$	0	0
$145$	−2.60940e12	−0.0233157
$146$	0	0
$147$	−6.56197e12	−0.0536379
$148$	0	0
$149$	−1.89341e14	−1.41753	−0.708766	−	0.705443i	$-0.750748\pi$
$149$	−1.89341e14	−1.41753	−0.708766	+	0.705443i	$0.750748\pi$
$150$	0	0
$151$	2.83932e14	1.94923	0.974617	−	0.223879i	$-0.0718722\pi$
$151$	2.83932e14	1.94923	0.974617	+	0.223879i	$0.0718722\pi$
$152$	0	0
$153$	−5.92949e13	−0.373700
$154$	0	0
$155$	3.19418e14	1.85014
$156$	0	0
$157$	−2.74932e13	−0.146513	−0.0732567	−	0.997313i	$-0.523339\pi$
$157$	−2.74932e13	−0.146513	−0.0732567	+	0.997313i	$0.523339\pi$
$158$	0	0
$159$	1.30447e14	0.640252
$160$	0	0
$161$	−1.90584e13	−0.0862417
$162$	0	0
$163$	3.74652e14	1.56462	0.782309	−	0.622890i	$-0.214042\pi$
$163$	3.74652e14	1.56462	0.782309	+	0.622890i	$0.214042\pi$
$164$	0	0
$165$	1.68303e14	0.649302
$166$	0	0
$167$	1.26477e14	0.451183	0.225592	−	0.974222i	$-0.427569\pi$
$167$	1.26477e14	0.451183	0.225592	+	0.974222i	$0.427569\pi$
$168$	0	0
$169$	−7.18429e13	−0.237203
$170$	0	0
$171$	−5.02143e14	−1.53586
$172$	0	0
$173$	3.62732e14	1.02869	0.514347	−	0.857582i	$-0.328034\pi$
$173$	3.62732e14	1.02869	0.514347	+	0.857582i	$0.328034\pi$
$174$	0	0
$175$	6.45853e14	1.69975
$176$	0	0
$177$	2.78806e13	0.0681516
$178$	0	0
$179$	3.17214e14	0.720789	0.360394	−	0.932800i	$-0.382642\pi$
$179$	3.17214e14	0.720789	0.360394	+	0.932800i	$0.382642\pi$
$180$	0	0
$181$	−4.55669e14	−0.963249	−0.481625	−	0.876378i	$-0.659953\pi$
$181$	−4.55669e14	−0.963249	−0.481625	+	0.876378i	$0.659953\pi$
$182$	0	0
$183$	−1.28627e13	−0.0253164
$184$	0	0
$185$	−1.06086e14	−0.194555
$186$	0	0
$187$	2.75818e14	0.471685
$188$	0	0
$189$	4.62842e14	0.738637
$190$	0	0
$191$	−9.66030e14	−1.43971	−0.719853	−	0.694127i	$-0.755791\pi$
$191$	−9.66030e14	−1.43971	−0.719853	+	0.694127i	$0.755791\pi$
$192$	0	0
$193$	−1.82063e14	−0.253571	−0.126785	−	0.991930i	$-0.540466\pi$
$193$	−1.82063e14	−0.253571	−0.126785	+	0.991930i	$0.540466\pi$
$194$	0	0
$195$	−3.99877e14	−0.520837
$196$	0	0
$197$	−8.62598e14	−1.05142	−0.525712	−	0.850663i	$-0.676201\pi$
$197$	−8.62598e14	−1.05142	−0.525712	+	0.850663i	$0.676201\pi$
$198$	0	0
$199$	3.24819e14	0.370764	0.185382	−	0.982667i	$-0.440648\pi$
$199$	3.24819e14	0.370764	0.185382	+	0.982667i	$0.440648\pi$
$200$	0	0
$201$	3.67104e14	0.392658
$202$	0	0
$203$	1.54590e13	0.0155045
$204$	0	0
$205$	4.12431e14	0.388107
$206$	0	0
$207$	7.87040e13	0.0695328
$208$	0	0
$209$	2.33578e15	1.93857
$210$	0	0
$211$	7.03123e14	0.548523	0.274262	−	0.961655i	$-0.411567\pi$
$211$	7.03123e14	0.548523	0.274262	+	0.961655i	$0.411567\pi$
$212$	0	0
$213$	1.68651e14	0.123743
$214$	0	0
$215$	−1.51141e15	−1.04359
$216$	0	0
$217$	−1.89235e15	−1.23031
$218$	0	0
$219$	7.45353e14	0.456536
$220$	0	0
$221$	−6.55325e14	−0.378361
$222$	0	0
$223$	1.50865e15	0.821499	0.410749	−	0.911748i	$-0.365267\pi$
$223$	1.50865e15	0.821499	0.410749	+	0.911748i	$0.365267\pi$
$224$	0	0
$225$	−2.66713e15	−1.37043
$226$	0	0
$227$	−2.50306e15	−1.21424	−0.607118	−	0.794611i	$-0.707675\pi$
$227$	−2.50306e15	−1.21424	−0.607118	+	0.794611i	$0.707675\pi$
$228$	0	0
$229$	1.22112e15	0.559534	0.279767	−	0.960068i	$-0.409743\pi$
$229$	1.22112e15	0.559534	0.279767	+	0.960068i	$0.409743\pi$
$230$	0	0
$231$	−9.97089e14	−0.431774
$232$	0	0
$233$	3.53791e15	1.44855	0.724274	−	0.689512i	$-0.242175\pi$
$233$	3.53791e15	1.44855	0.724274	+	0.689512i	$0.242175\pi$
$234$	0	0
$235$	−5.72482e15	−2.21728
$236$	0	0
$237$	1.08394e13	0.00397322
$238$	0	0
$239$	−3.11280e15	−1.08035	−0.540175	−	0.841553i	$-0.681642\pi$
$239$	−3.11280e15	−1.08035	−0.540175	+	0.841553i	$0.681642\pi$
$240$	0	0
$241$	−4.57091e15	−1.50277	−0.751385	−	0.659864i	$-0.770614\pi$
$241$	−4.57091e15	−1.50277	−0.751385	+	0.659864i	$0.770614\pi$
$242$	0	0
$243$	−2.93754e15	−0.915256
$244$	0	0
$245$	−7.88194e14	−0.232838
$246$	0	0
$247$	−5.54966e15	−1.55502
$248$	0	0
$249$	9.59474e14	0.255116
$250$	0	0
$251$	1.66332e15	0.419852	0.209926	−	0.977717i	$-0.432678\pi$
$251$	1.66332e15	0.419852	0.209926	+	0.977717i	$0.432678\pi$
$252$	0	0
$253$	−3.66102e14	−0.0877644
$254$	0	0
$255$	1.13425e15	0.258345
$256$	0	0
$257$	−3.74052e15	−0.809780	−0.404890	−	0.914365i	$-0.632690\pi$
$257$	−3.74052e15	−0.809780	−0.404890	+	0.914365i	$0.632690\pi$
$258$	0	0
$259$	6.28493e14	0.129375
$260$	0	0
$261$	−6.38400e13	−0.0125006
$262$	0	0
$263$	2.50616e15	0.466978	0.233489	−	0.972359i	$-0.424986\pi$
$263$	2.50616e15	0.466978	0.233489	+	0.972359i	$0.424986\pi$
$264$	0	0
$265$	1.56686e16	2.77928
$266$	0	0
$267$	1.63116e15	0.275533
$268$	0	0
$269$	8.11300e13	0.0130554	0.00652772	−	0.999979i	$-0.497922\pi$
$269$	8.11300e13	0.0130554	0.00652772	+	0.999979i	$0.497922\pi$
$270$	0	0
$271$	−2.29141e15	−0.351400	−0.175700	−	0.984444i	$-0.556219\pi$
$271$	−2.29141e15	−0.351400	−0.175700	+	0.984444i	$0.556219\pi$
$272$	0	0
$273$	2.36902e15	0.346347
$274$	0	0
$275$	1.24065e16	1.72976
$276$	0	0
$277$	−9.98960e14	−0.132871	−0.0664354	−	0.997791i	$-0.521163\pi$
$277$	−9.98960e14	−0.132871	−0.0664354	+	0.997791i	$0.521163\pi$
$278$	0	0
$279$	7.81470e15	0.991940
$280$	0	0
$281$	−1.17580e16	−1.42476	−0.712381	−	0.701793i	$-0.752383\pi$
$281$	−1.17580e16	−1.42476	−0.712381	+	0.701793i	$0.752383\pi$
$282$	0	0
$283$	−3.81237e15	−0.441147	−0.220574	−	0.975370i	$-0.570793\pi$
$283$	−3.81237e15	−0.441147	−0.220574	+	0.975370i	$0.570793\pi$
$284$	0	0
$285$	9.60551e15	1.06177
$286$	0	0
$287$	−2.44339e15	−0.258084
$288$	0	0
$289$	−8.04574e15	−0.812326
$290$	0	0
$291$	−3.13872e15	−0.303004
$292$	0	0
$293$	−1.89831e16	−1.75278	−0.876389	−	0.481603i	$-0.840055\pi$
$293$	−1.89831e16	−1.75278	−0.876389	+	0.481603i	$0.840055\pi$
$294$	0	0
$295$	3.34889e15	0.295841
$296$	0	0
$297$	8.89097e15	0.751679
$298$	0	0
$299$	8.69833e14	0.0704001
$300$	0	0
$301$	8.95412e15	0.693970
$302$	0	0
$303$	4.98595e15	0.370144
$304$	0	0
$305$	−1.54501e15	−0.109896
$306$	0	0
$307$	−1.52021e16	−1.03634	−0.518172	−	0.855276i	$-0.673387\pi$
$307$	−1.52021e16	−1.03634	−0.518172	+	0.855276i	$0.673387\pi$
$308$	0	0
$309$	5.11265e15	0.334130
$310$	0	0
$311$	1.96486e16	1.23137	0.615687	−	0.787991i	$-0.288879\pi$
$311$	1.96486e16	1.23137	0.615687	+	0.787991i	$0.288879\pi$
$312$	0	0
$313$	−1.99943e16	−1.20190	−0.600948	−	0.799288i	$-0.705210\pi$
$313$	−1.99943e16	−1.20190	−0.600948	+	0.799288i	$0.705210\pi$
$314$	0	0
$315$	2.57471e16	1.48494
$316$	0	0
$317$	2.44565e16	1.35366	0.676828	−	0.736141i	$-0.263354\pi$
$317$	2.44565e16	1.35366	0.676828	+	0.736141i	$0.263354\pi$
$318$	0	0
$319$	2.96960e14	0.0157782
$320$	0	0
$321$	5.89098e15	0.300542
$322$	0	0
$323$	1.57417e16	0.771319
$324$	0	0
$325$	−2.94770e16	−1.38753
$326$	0	0
$327$	−2.04348e14	−0.00924295
$328$	0	0
$329$	3.39159e16	1.47445
$330$	0	0
$331$	3.39924e16	1.42069	0.710347	−	0.703852i	$-0.248538\pi$
$331$	3.39924e16	1.42069	0.710347	+	0.703852i	$0.248538\pi$
$332$	0	0
$333$	−2.59544e15	−0.104310
$334$	0	0
$335$	4.40948e16	1.70450
$336$	0	0
$337$	−2.88718e15	−0.107369	−0.0536846	−	0.998558i	$-0.517097\pi$
$337$	−2.88718e15	−0.107369	−0.0536846	+	0.998558i	$0.517097\pi$
$338$	0	0
$339$	1.48970e16	0.533090
$340$	0	0
$341$	−3.63511e16	−1.25203
$342$	0	0
$343$	−2.75976e16	−0.915081
$344$	0	0
$345$	−1.50553e15	−0.0480691
$346$	0	0
$347$	−3.36011e16	−1.03327	−0.516633	−	0.856207i	$-0.672815\pi$
$347$	−3.36011e16	−1.03327	−0.516633	+	0.856207i	$0.672815\pi$
$348$	0	0
$349$	1.90527e16	0.564405	0.282203	−	0.959355i	$-0.408935\pi$
$349$	1.90527e16	0.564405	0.282203	+	0.959355i	$0.408935\pi$
$350$	0	0
$351$	−2.11243e16	−0.602958
$352$	0	0
$353$	−6.85474e16	−1.88562	−0.942812	−	0.333324i	$-0.891830\pi$
$353$	−6.85474e16	−1.88562	−0.942812	+	0.333324i	$0.891830\pi$
$354$	0	0
$355$	2.02576e16	0.537159
$356$	0	0
$357$	−6.71973e15	−0.171794
$358$	0	0
$359$	−1.15154e16	−0.283900	−0.141950	−	0.989874i	$-0.545337\pi$
$359$	−1.15154e16	−0.283900	−0.141950	+	0.989874i	$0.545337\pi$
$360$	0	0
$361$	9.12563e16	2.17003
$362$	0	0
$363$	−2.99696e15	−0.0687524
$364$	0	0
$365$	8.95284e16	1.98179
$366$	0	0
$367$	−9.43079e14	−0.0201474	−0.0100737	−	0.999949i	$-0.503207\pi$
$367$	−9.43079e14	−0.0201474	−0.0100737	+	0.999949i	$0.503207\pi$
$368$	0	0
$369$	1.00903e16	0.208081
$370$	0	0
$371$	−9.28266e16	−1.84817
$372$	0	0
$373$	−2.74345e16	−0.527459	−0.263730	−	0.964597i	$-0.584953\pi$
$373$	−2.74345e16	−0.527459	−0.263730	+	0.964597i	$0.584953\pi$
$374$	0	0
$375$	1.89052e16	0.351058
$376$	0	0
$377$	−7.05557e14	−0.0126565
$378$	0	0
$379$	−6.51327e16	−1.12887	−0.564435	−	0.825478i	$-0.690906\pi$
$379$	−6.51327e16	−1.12887	−0.564435	+	0.825478i	$0.690906\pi$
$380$	0	0
$381$	−1.84428e16	−0.308897
$382$	0	0
$383$	−8.78344e16	−1.42191	−0.710956	−	0.703236i	$-0.751738\pi$
$383$	−8.78344e16	−1.42191	−0.710956	+	0.703236i	$0.751738\pi$
$384$	0	0
$385$	−1.19766e17	−1.87429
$386$	0	0
$387$	−3.69772e16	−0.559517
$388$	0	0
$389$	4.09282e16	0.598895	0.299448	−	0.954113i	$-0.403198\pi$
$389$	4.09282e16	0.598895	0.299448	+	0.954113i	$0.403198\pi$
$390$	0	0
$391$	−2.46729e15	−0.0349197
$392$	0	0
$393$	3.45122e16	0.472521
$394$	0	0
$395$	1.30198e15	0.0172474
$396$	0	0
$397$	−2.53776e16	−0.325321	−0.162661	−	0.986682i	$-0.552008\pi$
$397$	−2.53776e16	−0.325321	−0.162661	+	0.986682i	$0.552008\pi$
$398$	0	0
$399$	−5.69065e16	−0.706055
$400$	0	0
$401$	−8.11985e16	−0.975235	−0.487618	−	0.873057i	$-0.662134\pi$
$401$	−8.11985e16	−0.975235	−0.487618	+	0.873057i	$0.662134\pi$
$402$	0	0
$403$	8.63678e16	1.00431
$404$	0	0
$405$	−8.66962e16	−0.976208
$406$	0	0
$407$	1.20730e16	0.131660
$408$	0	0
$409$	1.56903e17	1.65741	0.828705	−	0.559686i	$-0.189078\pi$
$409$	1.56903e17	1.65741	0.828705	+	0.559686i	$0.189078\pi$
$410$	0	0
$411$	−3.99719e16	−0.409056
$412$	0	0
$413$	−1.98400e16	−0.196728
$414$	0	0
$415$	1.15248e17	1.10744
$416$	0	0
$417$	−3.73383e16	−0.347753
$418$	0	0
$419$	1.91659e16	0.173036	0.0865182	−	0.996250i	$-0.472426\pi$
$419$	1.91659e16	0.173036	0.0865182	+	0.996250i	$0.472426\pi$
$420$	0	0
$421$	−2.20629e16	−0.193120	−0.0965602	−	0.995327i	$-0.530784\pi$
$421$	−2.20629e16	−0.193120	−0.0965602	+	0.995327i	$0.530784\pi$
$422$	0	0
$423$	−1.40060e17	−1.18878
$424$	0	0
$425$	8.36118e16	0.688240
$426$	0	0
$427$	9.15321e15	0.0730789
$428$	0	0
$429$	4.55076e16	0.352462
$430$	0	0
$431$	−1.36347e17	−1.02457	−0.512286	−	0.858815i	$-0.671201\pi$
$431$	−1.36347e17	−1.02457	−0.512286	+	0.858815i	$0.671201\pi$
$432$	0	0
$433$	−4.34949e16	−0.317152	−0.158576	−	0.987347i	$-0.550690\pi$
$433$	−4.34949e16	−0.317152	−0.158576	+	0.987347i	$0.550690\pi$
$434$	0	0
$435$	1.22120e15	0.00864183
$436$	0	0
$437$	−2.08944e16	−0.143516
$438$	0	0
$439$	−2.08498e17	−1.39021	−0.695107	−	0.718906i	$-0.744643\pi$
$439$	−2.08498e17	−1.39021	−0.695107	+	0.718906i	$0.744643\pi$
$440$	0	0
$441$	−1.92835e16	−0.124835
$442$	0	0
$443$	−2.49283e17	−1.56700	−0.783498	−	0.621395i	$-0.786566\pi$
$443$	−2.49283e17	−1.56700	−0.783498	+	0.621395i	$0.786566\pi$
$444$	0	0
$445$	1.95928e17	1.19607
$446$	0	0
$447$	8.86114e16	0.525401
$448$	0	0
$449$	1.45110e17	0.835787	0.417894	−	0.908496i	$-0.362768\pi$
$449$	1.45110e17	0.835787	0.417894	+	0.908496i	$0.362768\pi$
$450$	0	0
$451$	−4.69363e16	−0.262640
$452$	0	0
$453$	−1.32880e17	−0.722473
$454$	0	0
$455$	2.84555e17	1.50346
$456$	0	0
$457$	−1.98127e17	−1.01739	−0.508696	−	0.860946i	$-0.669872\pi$
$457$	−1.98127e17	−1.01739	−0.508696	+	0.860946i	$0.669872\pi$
$458$	0	0
$459$	5.99194e16	0.299078
$460$	0	0
$461$	2.30382e17	1.11787	0.558937	−	0.829210i	$-0.311210\pi$
$461$	2.30382e17	1.11787	0.558937	+	0.829210i	$0.311210\pi$
$462$	0	0
$463$	3.64296e17	1.71861	0.859307	−	0.511460i	$-0.170895\pi$
$463$	3.64296e17	1.71861	0.859307	+	0.511460i	$0.170895\pi$
$464$	0	0
$465$	−1.49488e17	−0.685743
$466$	0	0
$467$	2.17175e16	0.0968835	0.0484417	−	0.998826i	$-0.484574\pi$
$467$	2.17175e16	0.0968835	0.0484417	+	0.998826i	$0.484574\pi$
$468$	0	0
$469$	−2.61234e17	−1.13346
$470$	0	0
$471$	1.28668e16	0.0543044
$472$	0	0
$473$	1.72004e17	0.706223
$474$	0	0
$475$	7.08072e17	2.82858
$476$	0	0
$477$	3.83340e17	1.49010
$478$	0	0
$479$	−1.98719e17	−0.751724	−0.375862	−	0.926676i	$-0.622653\pi$
$479$	−1.98719e17	−0.751724	−0.375862	+	0.926676i	$0.622653\pi$
$480$	0	0
$481$	−2.86847e16	−0.105611
$482$	0	0
$483$	8.91931e15	0.0319650
$484$	0	0
$485$	−3.77009e17	−1.31532
$486$	0	0
$487$	4.71598e17	1.60189	0.800947	−	0.598736i	$-0.204330\pi$
$487$	4.71598e17	1.60189	0.800947	+	0.598736i	$0.204330\pi$
$488$	0	0
$489$	−1.75337e17	−0.579917
$490$	0	0
$491$	1.14636e17	0.369226	0.184613	−	0.982811i	$-0.440897\pi$
$491$	1.14636e17	0.369226	0.184613	+	0.982811i	$0.440897\pi$
$492$	0	0
$493$	2.00132e15	0.00627785
$494$	0	0
$495$	4.94588e17	1.51116
$496$	0	0
$497$	−1.20013e17	−0.357201
$498$	0	0
$499$	−1.28794e16	−0.0373457	−0.0186729	−	0.999826i	$-0.505944\pi$
$499$	−1.28794e16	−0.0373457	−0.0186729	+	0.999826i	$0.505944\pi$
$500$	0	0
$501$	−5.91910e16	−0.167229
$502$	0	0
$503$	−2.72812e17	−0.751055	−0.375528	−	0.926811i	$-0.622538\pi$
$503$	−2.72812e17	−0.751055	−0.375528	+	0.926811i	$0.622538\pi$
$504$	0	0
$505$	5.98889e17	1.60677
$506$	0	0
$507$	3.36225e16	0.0879181
$508$	0	0
$509$	−4.08824e17	−1.04201	−0.521004	−	0.853554i	$-0.674442\pi$
$509$	−4.08824e17	−1.04201	−0.521004	+	0.853554i	$0.674442\pi$
$510$	0	0
$511$	−5.30399e17	−1.31785
$512$	0	0
$513$	5.07431e17	1.22918
$514$	0	0
$515$	6.14108e17	1.45043
$516$	0	0
$517$	6.51508e17	1.50048
$518$	0	0
$519$	−1.69759e17	−0.381280
$520$	0	0
$521$	−4.68976e17	−1.02732	−0.513659	−	0.857994i	$-0.671710\pi$
$521$	−4.68976e17	−1.02732	−0.513659	+	0.857994i	$0.671710\pi$
$522$	0	0
$523$	−6.12359e17	−1.30841	−0.654207	−	0.756316i	$-0.726997\pi$
$523$	−6.12359e17	−1.30841	−0.654207	+	0.756316i	$0.726997\pi$
$524$	0	0
$525$	−3.02259e17	−0.630005
$526$	0	0
$527$	−2.44983e17	−0.498158
$528$	0	0
$529$	−5.00761e17	−0.993503
$530$	0	0
$531$	8.19320e16	0.158613
$532$	0	0
$533$	1.11518e17	0.210677
$534$	0	0
$535$	7.07597e17	1.30463
$536$	0	0
$537$	−1.48456e17	−0.267156
$538$	0	0
$539$	8.96996e16	0.157566
$540$	0	0
$541$	−4.68270e17	−0.802998	−0.401499	−	0.915859i	$-0.631511\pi$
$541$	−4.68270e17	−0.802998	−0.401499	+	0.915859i	$0.631511\pi$
$542$	0	0
$543$	2.13253e17	0.357023
$544$	0	0
$545$	−2.45454e16	−0.0401229
$546$	0	0
$547$	−1.11611e18	−1.78151	−0.890756	−	0.454482i	$-0.849824\pi$
$547$	−1.11611e18	−1.78151	−0.890756	+	0.454482i	$0.849824\pi$
$548$	0	0
$549$	−3.77994e16	−0.0589202
$550$	0	0
$551$	1.69483e16	0.0258012
$552$	0	0
$553$	−7.71342e15	−0.0114692
$554$	0	0
$555$	4.96484e16	0.0721108
$556$	0	0
$557$	2.78973e17	0.395825	0.197913	−	0.980220i	$-0.436584\pi$
$557$	2.78973e17	0.395825	0.197913	+	0.980220i	$0.436584\pi$
$558$	0	0
$559$	−4.08671e17	−0.566496
$560$	0	0
$561$	−1.29083e17	−0.174827
$562$	0	0
$563$	4.97446e17	0.658327	0.329163	−	0.944273i	$-0.393233\pi$
$563$	4.97446e17	0.658327	0.329163	+	0.944273i	$0.393233\pi$
$564$	0	0
$565$	1.78936e18	2.31410
$566$	0	0
$567$	5.13619e17	0.649160
$568$	0	0
$569$	1.15654e18	1.42866	0.714330	−	0.699809i	$-0.246731\pi$
$569$	1.15654e18	1.42866	0.714330	+	0.699809i	$0.246731\pi$
$570$	0	0
$571$	−8.80150e16	−0.106273	−0.0531364	−	0.998587i	$-0.516922\pi$
$571$	−8.80150e16	−0.106273	−0.0531364	+	0.998587i	$0.516922\pi$
$572$	0	0
$573$	4.52102e17	0.533619
$574$	0	0
$575$	−1.10981e17	−0.128058
$576$	0	0
$577$	−1.54048e17	−0.173786	−0.0868928	−	0.996218i	$-0.527694\pi$
$577$	−1.54048e17	−0.173786	−0.0868928	+	0.996218i	$0.527694\pi$
$578$	0	0
$579$	8.52055e16	0.0939847
$580$	0	0
$581$	−6.82768e17	−0.736425
$582$	0	0
$583$	−1.78315e18	−1.88080
$584$	0	0
$585$	−1.17511e18	−1.21217
$586$	0	0
$587$	−1.46111e18	−1.47413	−0.737066	−	0.675821i	$-0.763789\pi$
$587$	−1.46111e18	−1.47413	−0.737066	+	0.675821i	$0.763789\pi$
$588$	0	0
$589$	−2.07465e18	−2.04737
$590$	0	0
$591$	4.03696e17	0.389705
$592$	0	0
$593$	1.32372e18	1.25009	0.625043	−	0.780591i	$-0.285082\pi$
$593$	1.32372e18	1.25009	0.625043	+	0.780591i	$0.285082\pi$
$594$	0	0
$595$	−8.07143e17	−0.745745
$596$	0	0
$597$	−1.52016e17	−0.137422
$598$	0	0
$599$	−1.54325e18	−1.36509	−0.682546	−	0.730842i	$-0.739127\pi$
$599$	−1.54325e18	−1.36509	−0.682546	+	0.730842i	$0.739127\pi$
$600$	0	0
$601$	2.66564e17	0.230737	0.115369	−	0.993323i	$-0.463195\pi$
$601$	2.66564e17	0.230737	0.115369	+	0.993323i	$0.463195\pi$
$602$	0	0
$603$	1.07880e18	0.913856
$604$	0	0
$605$	−3.59981e17	−0.298449
$606$	0	0
$607$	−1.03281e18	−0.838099	−0.419049	−	0.907963i	$-0.637637\pi$
$607$	−1.03281e18	−0.838099	−0.419049	+	0.907963i	$0.637637\pi$
$608$	0	0
$609$	−7.23482e15	−0.00574666
$610$	0	0
$611$	−1.54794e18	−1.20361
$612$	0	0
$613$	4.51541e17	0.343720	0.171860	−	0.985121i	$-0.445022\pi$
$613$	4.51541e17	0.343720	0.171860	+	0.985121i	$0.445022\pi$
$614$	0	0
$615$	−1.93018e17	−0.143850
$616$	0	0
$617$	−1.86870e18	−1.36360	−0.681798	−	0.731541i	$-0.738802\pi$
$617$	−1.86870e18	−1.36360	−0.681798	+	0.731541i	$0.738802\pi$
$618$	0	0
$619$	1.23724e18	0.884024	0.442012	−	0.897009i	$-0.354265\pi$
$619$	1.23724e18	0.884024	0.442012	+	0.897009i	$0.354265\pi$
$620$	0	0
$621$	−7.95329e16	−0.0556482
$622$	0	0
$623$	−1.16075e18	−0.795363
$624$	0	0
$625$	−9.65128e16	−0.0647687
$626$	0	0
$627$	−1.09315e18	−0.718521
$628$	0	0
$629$	8.13645e16	0.0523848
$630$	0	0
$631$	6.02949e17	0.380268	0.190134	−	0.981758i	$-0.439108\pi$
$631$	6.02949e17	0.380268	0.190134	+	0.981758i	$0.439108\pi$
$632$	0	0
$633$	−3.29061e17	−0.203307
$634$	0	0
$635$	−2.21526e18	−1.34090
$636$	0	0
$637$	−2.13120e17	−0.126392
$638$	0	0
$639$	4.95610e17	0.287995
$640$	0	0
$641$	2.68783e18	1.53047	0.765236	−	0.643750i	$-0.222622\pi$
$641$	2.68783e18	1.53047	0.765236	+	0.643750i	$0.222622\pi$
$642$	0	0
$643$	1.92261e18	1.07280	0.536400	−	0.843964i	$-0.319784\pi$
$643$	1.92261e18	1.07280	0.536400	+	0.843964i	$0.319784\pi$
$644$	0	0
$645$	7.07339e17	0.386803
$646$	0	0
$647$	1.54829e18	0.829805	0.414902	−	0.909866i	$-0.363816\pi$
$647$	1.54829e18	0.829805	0.414902	+	0.909866i	$0.363816\pi$
$648$	0	0
$649$	−3.81117e17	−0.200202
$650$	0	0
$651$	8.85620e17	0.456006
$652$	0	0
$653$	2.11868e18	1.06937	0.534687	−	0.845050i	$-0.320430\pi$
$653$	2.11868e18	1.06937	0.534687	+	0.845050i	$0.320430\pi$
$654$	0	0
$655$	4.14545e18	2.05118
$656$	0	0
$657$	2.19035e18	1.06252
$658$	0	0
$659$	1.71376e18	0.815069	0.407534	−	0.913190i	$-0.366389\pi$
$659$	1.71376e18	0.815069	0.407534	+	0.913190i	$0.366389\pi$
$660$	0	0
$661$	3.39226e17	0.158190	0.0790951	−	0.996867i	$-0.474797\pi$
$661$	3.39226e17	0.158190	0.0790951	+	0.996867i	$0.474797\pi$
$662$	0	0
$663$	3.06692e17	0.140238
$664$	0	0
$665$	−6.83535e18	−3.06493
$666$	0	0
$667$	−2.65641e15	−0.00116809
$668$	0	0
$669$	−7.06048e17	−0.304484
$670$	0	0
$671$	1.75829e17	0.0743692
$672$	0	0
$673$	1.99607e16	0.00828089	0.00414045	−	0.999991i	$-0.498682\pi$
$673$	1.99607e16	0.00828089	0.00414045	+	0.999991i	$0.498682\pi$
$674$	0	0
$675$	2.69522e18	1.09678
$676$	0	0
$677$	3.26744e18	1.30431	0.652157	−	0.758084i	$-0.273864\pi$
$677$	3.26744e18	1.30431	0.652157	+	0.758084i	$0.273864\pi$
$678$	0	0
$679$	2.23353e18	0.874660
$680$	0	0
$681$	1.17143e18	0.450050
$682$	0	0
$683$	−9.80130e17	−0.369444	−0.184722	−	0.982791i	$-0.559139\pi$
$683$	−9.80130e17	−0.369444	−0.184722	+	0.982791i	$0.559139\pi$
$684$	0	0
$685$	−4.80124e18	−1.77568
$686$	0	0
$687$	−5.71483e17	−0.207388
$688$	0	0
$689$	4.23665e18	1.50868
$690$	0	0
$691$	2.72145e18	0.951028	0.475514	−	0.879708i	$-0.342262\pi$
$691$	2.72145e18	0.951028	0.475514	+	0.879708i	$0.342262\pi$
$692$	0	0
$693$	−2.93012e18	−1.00489
$694$	0	0
$695$	−4.48491e18	−1.50957
$696$	0	0
$697$	−3.16320e17	−0.104499
$698$	0	0
$699$	−1.65574e18	−0.536897
$700$	0	0
$701$	−5.87143e17	−0.186886	−0.0934430	−	0.995625i	$-0.529787\pi$
$701$	−5.87143e17	−0.186886	−0.0934430	+	0.995625i	$0.529787\pi$
$702$	0	0
$703$	6.89041e17	0.215296
$704$	0	0
$705$	2.67922e18	0.821824
$706$	0	0
$707$	−3.54804e18	−1.06847
$708$	0	0
$709$	3.67804e18	1.08747	0.543733	−	0.839258i	$-0.317010\pi$
$709$	3.67804e18	1.08747	0.543733	+	0.839258i	$0.317010\pi$
$710$	0	0
$711$	3.18536e16	0.00924710
$712$	0	0
$713$	3.25173e17	0.0926901
$714$	0	0
$715$	5.46617e18	1.53001
$716$	0	0
$717$	1.45679e18	0.400426
$718$	0	0
$719$	−2.24609e18	−0.606302	−0.303151	−	0.952942i	$-0.598039\pi$
$719$	−2.24609e18	−0.606302	−0.303151	+	0.952942i	$0.598039\pi$
$720$	0	0
$721$	−3.63820e18	−0.964510
$722$	0	0
$723$	2.13919e18	0.556993
$724$	0	0
$725$	9.00209e16	0.0230222
$726$	0	0
$727$	6.28082e18	1.57777	0.788883	−	0.614543i	$-0.210660\pi$
$727$	6.28082e18	1.57777	0.788883	+	0.614543i	$0.210660\pi$
$728$	0	0
$729$	−1.08408e18	−0.267506
$730$	0	0
$731$	1.15920e18	0.280992
$732$	0	0
$733$	−5.84068e18	−1.39087	−0.695436	−	0.718588i	$-0.744789\pi$
$733$	−5.84068e18	−1.39087	−0.695436	+	0.718588i	$0.744789\pi$
$734$	0	0
$735$	3.68875e17	0.0863000
$736$	0	0
$737$	−5.01817e18	−1.15347
$738$	0	0
$739$	6.40249e18	1.44597	0.722986	−	0.690862i	$-0.242769\pi$
$739$	6.40249e18	1.44597	0.722986	+	0.690862i	$0.242769\pi$
$740$	0	0
$741$	2.59724e18	0.576360
$742$	0	0
$743$	6.61717e18	1.44293	0.721465	−	0.692451i	$-0.243469\pi$
$743$	6.61717e18	1.44293	0.721465	+	0.692451i	$0.243469\pi$
$744$	0	0
$745$	1.06436e19	2.28072
$746$	0	0
$747$	2.81958e18	0.593746
$748$	0	0
$749$	−4.19206e18	−0.867553
$750$	0	0
$751$	1.09760e18	0.223246	0.111623	−	0.993751i	$-0.464395\pi$
$751$	1.09760e18	0.223246	0.111623	+	0.993751i	$0.464395\pi$
$752$	0	0
$753$	−7.78432e17	−0.155616
$754$	0	0
$755$	−1.59609e19	−3.13620
$756$	0	0
$757$	8.91699e18	1.72225	0.861123	−	0.508397i	$-0.169762\pi$
$757$	8.91699e18	1.72225	0.861123	+	0.508397i	$0.169762\pi$
$758$	0	0
$759$	1.71336e17	0.0325294
$760$	0	0
$761$	−8.55167e18	−1.59606	−0.798032	−	0.602614i	$-0.794126\pi$
$761$	−8.55167e18	−1.59606	−0.798032	+	0.602614i	$0.794126\pi$
$762$	0	0
$763$	1.45416e17	0.0266810
$764$	0	0
$765$	3.33320e18	0.601260
$766$	0	0
$767$	9.05509e17	0.160592
$768$	0	0
$769$	−3.40420e18	−0.593600	−0.296800	−	0.954940i	$-0.595920\pi$
$769$	−3.40420e18	−0.593600	−0.296800	+	0.954940i	$0.595920\pi$
$770$	0	0
$771$	1.75056e18	0.300141
$772$	0	0
$773$	−4.27187e18	−0.720197	−0.360098	−	0.932914i	$-0.617257\pi$
$773$	−4.27187e18	−0.720197	−0.360098	+	0.932914i	$0.617257\pi$
$774$	0	0
$775$	−1.10195e19	−1.82685
$776$	0	0
$777$	−2.94135e17	−0.0479523
$778$	0	0
$779$	−2.67878e18	−0.429481
$780$	0	0
$781$	−2.30539e18	−0.363507
$782$	0	0
$783$	6.45123e16	0.0100044
$784$	0	0
$785$	1.54550e18	0.235731
$786$	0	0
$787$	2.01020e18	0.301581	0.150790	−	0.988566i	$-0.451818\pi$
$787$	2.01020e18	0.301581	0.150790	+	0.988566i	$0.451818\pi$
$788$	0	0
$789$	−1.17288e18	−0.173083
$790$	0	0
$791$	−1.06008e19	−1.53883
$792$	0	0
$793$	−4.17757e17	−0.0596551
$794$	0	0
$795$	−7.33292e18	−1.03013
$796$	0	0
$797$	1.68131e18	0.232364	0.116182	−	0.993228i	$-0.462934\pi$
$797$	1.68131e18	0.232364	0.116182	+	0.993228i	$0.462934\pi$
$798$	0	0
$799$	4.39074e18	0.597013
$800$	0	0
$801$	4.79346e18	0.641265
$802$	0	0
$803$	−1.01887e19	−1.34112
$804$	0	0
$805$	1.07135e18	0.138758
$806$	0	0
$807$	−3.79688e16	−0.00483893
$808$	0	0
$809$	8.89742e18	1.11583	0.557916	−	0.829898i	$-0.311601\pi$
$809$	8.89742e18	1.11583	0.557916	+	0.829898i	$0.311601\pi$
$810$	0	0
$811$	−7.39152e18	−0.912217	−0.456108	−	0.889924i	$-0.650757\pi$
$811$	−7.39152e18	−0.912217	−0.456108	+	0.889924i	$0.650757\pi$
$812$	0	0
$813$	1.07238e18	0.130245
$814$	0	0
$815$	−2.10607e19	−2.51738
$816$	0	0
$817$	9.81674e18	1.15485
$818$	0	0
$819$	6.96176e18	0.806072
$820$	0	0
$821$	−4.72575e18	−0.538568	−0.269284	−	0.963061i	$-0.586787\pi$
$821$	−4.72575e18	−0.538568	−0.269284	+	0.963061i	$0.586787\pi$
$822$	0	0
$823$	2.48090e18	0.278298	0.139149	−	0.990271i	$-0.455563\pi$
$823$	2.48090e18	0.278298	0.139149	+	0.990271i	$0.455563\pi$
$824$	0	0
$825$	−5.80625e18	−0.641128
$826$	0	0
$827$	1.02026e19	1.10898	0.554492	−	0.832189i	$-0.312913\pi$
$827$	1.02026e19	1.10898	0.554492	+	0.832189i	$0.312913\pi$
$828$	0	0
$829$	7.91603e18	0.847038	0.423519	−	0.905887i	$-0.360795\pi$
$829$	7.91603e18	0.847038	0.423519	+	0.905887i	$0.360795\pi$
$830$	0	0
$831$	4.67513e17	0.0492479
$832$	0	0
$833$	6.04517e17	0.0626926
$834$	0	0
$835$	−7.10975e18	−0.725926
$836$	0	0
$837$	−7.89701e18	−0.793866
$838$	0	0
$839$	−1.37076e19	−1.35678	−0.678389	−	0.734703i	$-0.737322\pi$
$839$	−1.37076e19	−1.35678	−0.678389	+	0.734703i	$0.737322\pi$
$840$	0	0
$841$	−1.02585e19	−0.999790
$842$	0	0
$843$	5.50275e18	0.528081
$844$	0	0
$845$	4.03858e18	0.381645
$846$	0	0
$847$	2.13266e18	0.198463
$848$	0	0
$849$	1.78419e18	0.163509
$850$	0	0
$851$	−1.07998e17	−0.00974702
$852$	0	0
$853$	−9.04601e18	−0.804060	−0.402030	−	0.915627i	$-0.631695\pi$
$853$	−9.04601e18	−0.804060	−0.402030	+	0.915627i	$0.631695\pi$
$854$	0	0
$855$	2.82275e19	2.47111
$856$	0	0
$857$	5.96941e18	0.514703	0.257351	−	0.966318i	$-0.417150\pi$
$857$	5.96941e18	0.514703	0.257351	+	0.966318i	$0.417150\pi$
$858$	0	0
$859$	−1.03550e19	−0.879417	−0.439709	−	0.898140i	$-0.644918\pi$
$859$	−1.03550e19	−0.879417	−0.439709	+	0.898140i	$0.644918\pi$
$860$	0	0
$861$	1.14351e18	0.0956573
$862$	0	0
$863$	−3.95923e18	−0.326242	−0.163121	−	0.986606i	$-0.552156\pi$
$863$	−3.95923e18	−0.326242	−0.163121	+	0.986606i	$0.552156\pi$
$864$	0	0
$865$	−2.03906e19	−1.65511
$866$	0	0
$867$	3.76541e18	0.301084
$868$	0	0
$869$	−1.48171e17	−0.0116717
$870$	0	0
$871$	1.19228e19	0.925255
$872$	0	0
$873$	−9.22367e18	−0.705198
$874$	0	0
$875$	−1.34531e19	−1.01337
$876$	0	0
$877$	−4.38403e18	−0.325369	−0.162685	−	0.986678i	$-0.552015\pi$
$877$	−4.38403e18	−0.325369	−0.162685	+	0.986678i	$0.552015\pi$
$878$	0	0
$879$	8.88408e18	0.649658
$880$	0	0
$881$	−4.00058e18	−0.288257	−0.144129	−	0.989559i	$-0.546038\pi$
$881$	−4.00058e18	−0.288257	−0.144129	+	0.989559i	$0.546038\pi$
$882$	0	0
$883$	9.47450e18	0.672685	0.336343	−	0.941740i	$-0.390810\pi$
$883$	9.47450e18	0.672685	0.336343	+	0.941740i	$0.390810\pi$
$884$	0	0
$885$	−1.56728e18	−0.109652
$886$	0	0
$887$	−1.22101e19	−0.841816	−0.420908	−	0.907103i	$-0.638289\pi$
$887$	−1.22101e19	−0.841816	−0.420908	+	0.907103i	$0.638289\pi$
$888$	0	0
$889$	1.31240e19	0.891673
$890$	0	0
$891$	9.86637e18	0.660621
$892$	0	0
$893$	3.71833e19	2.45365
$894$	0	0
$895$	−1.78319e19	−1.15970
$896$	0	0
$897$	−4.07082e17	−0.0260934
$898$	0	0
$899$	−2.63761e17	−0.0166638
$900$	0	0
$901$	−1.20173e19	−0.748335
$902$	0	0
$903$	−4.19053e18	−0.257216
$904$	0	0
$905$	2.56150e19	1.54981
$906$	0	0
$907$	−3.27305e18	−0.195211	−0.0976057	−	0.995225i	$-0.531118\pi$
$907$	−3.27305e18	−0.195211	−0.0976057	+	0.995225i	$0.531118\pi$
$908$	0	0
$909$	1.46521e19	0.861457
$910$	0	0
$911$	2.50694e19	1.45303	0.726514	−	0.687151i	$-0.241139\pi$
$911$	2.50694e19	1.45303	0.726514	+	0.687151i	$0.241139\pi$
$912$	0	0
$913$	−1.31156e19	−0.749427
$914$	0	0
$915$	7.23066e17	0.0407325
$916$	0	0
$917$	−2.45591e19	−1.36399
$918$	0	0
$919$	5.26547e18	0.288328	0.144164	−	0.989554i	$-0.453951\pi$
$919$	5.26547e18	0.288328	0.144164	+	0.989554i	$0.453951\pi$
$920$	0	0
$921$	7.11458e18	0.384115
$922$	0	0
$923$	5.47746e18	0.291587
$924$	0	0
$925$	3.65984e18	0.192106
$926$	0	0
$927$	1.50244e19	0.777641
$928$	0	0
$929$	1.82719e18	0.0932572	0.0466286	−	0.998912i	$-0.485152\pi$
$929$	1.82719e18	0.0932572	0.0466286	+	0.998912i	$0.485152\pi$
$930$	0	0
$931$	5.11939e18	0.257659
$932$	0	0
$933$	−9.19556e18	−0.456402
$934$	0	0
$935$	−1.55048e19	−0.758912
$936$	0	0
$937$	3.72615e16	0.00179867	0.000899337	−	1.00000i	$-0.499714\pi$
$937$	3.72615e16	0.00179867	0.000899337		1.00000i	$0.499714\pi$
$938$	0	0
$939$	9.35731e18	0.445476
$940$	0	0
$941$	−4.08755e19	−1.91925	−0.959623	−	0.281289i	$-0.909238\pi$
$941$	−4.08755e19	−1.91925	−0.959623	+	0.281289i	$0.909238\pi$
$942$	0	0
$943$	4.19862e17	0.0194438
$944$	0	0
$945$	−2.60182e19	−1.18842
$946$	0	0
$947$	2.50489e19	1.12853	0.564267	−	0.825593i	$-0.309159\pi$
$947$	2.50489e19	1.12853	0.564267	+	0.825593i	$0.309159\pi$
$948$	0	0
$949$	2.42076e19	1.07578
$950$	0	0
$951$	−1.14456e19	−0.501725
$952$	0	0
$953$	2.88981e19	1.24958	0.624791	−	0.780792i	$-0.285184\pi$
$953$	2.88981e19	1.24958	0.624791	+	0.780792i	$0.285184\pi$
$954$	0	0
$955$	5.43044e19	2.31640
$956$	0	0
$957$	−1.38977e17	−0.00584812
$958$	0	0
$959$	2.84443e19	1.18079
$960$	0	0
$961$	7.86969e18	0.322296
$962$	0	0
$963$	1.73117e19	0.699468
$964$	0	0
$965$	1.02345e19	0.407980
$966$	0	0
$967$	3.95693e19	1.55627	0.778137	−	0.628094i	$-0.216165\pi$
$967$	3.95693e19	1.55627	0.778137	+	0.628094i	$0.216165\pi$
$968$	0	0
$969$	−7.36710e18	−0.285885
$970$	0	0
$971$	−1.53855e19	−0.589096	−0.294548	−	0.955637i	$-0.595169\pi$
$971$	−1.53855e19	−0.589096	−0.294548	+	0.955637i	$0.595169\pi$
$972$	0	0
$973$	2.65702e19	1.00383
$974$	0	0
$975$	1.37952e19	0.514280
$976$	0	0
$977$	−2.00465e19	−0.737435	−0.368717	−	0.929542i	$-0.620203\pi$
$977$	−2.00465e19	−0.737435	−0.368717	+	0.929542i	$0.620203\pi$
$978$	0	0
$979$	−2.22974e19	−0.809406
$980$	0	0
$981$	−6.00513e17	−0.0215117
$982$	0	0
$983$	−5.84007e18	−0.206452	−0.103226	−	0.994658i	$-0.532917\pi$
$983$	−5.84007e18	−0.206452	−0.103226	+	0.994658i	$0.532917\pi$
$984$	0	0
$985$	4.84901e19	1.69168
$986$	0	0
$987$	−1.58727e19	−0.546497
$988$	0	0
$989$	−1.53864e18	−0.0522830
$990$	0	0
$991$	3.21687e19	1.07883	0.539417	−	0.842039i	$-0.318645\pi$
$991$	3.21687e19	1.07883	0.539417	+	0.842039i	$0.318645\pi$
$992$	0	0
$993$	−1.59085e19	−0.526572
$994$	0	0
$995$	−1.82594e19	−0.596536
$996$	0	0
$997$	−2.94173e18	−0.0948604	−0.0474302	−	0.998875i	$-0.515103\pi$
$997$	−2.94173e18	−0.0948604	−0.0474302	+	0.998875i	$0.515103\pi$
$998$	0	0
$999$	2.62278e18	0.0834807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.14.a.c.1.1		1
4.3	odd	2		64.14.a.g.1.1		1
8.3	odd	2		16.14.a.b.1.1		1
8.5	even	2		4.14.a.a.1.1	✓	1
24.5	odd	2		36.14.a.a.1.1		1
24.11	even	2		144.14.a.a.1.1		1
40.13	odd	4		100.14.c.a.49.2		2
40.29	even	2		100.14.a.a.1.1		1
40.37	odd	4		100.14.c.a.49.1		2
56.5	odd	6		196.14.e.b.165.1		2
56.13	odd	2		196.14.a.a.1.1		1
56.37	even	6		196.14.e.a.165.1		2
56.45	odd	6		196.14.e.b.177.1		2
56.53	even	6		196.14.e.a.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.14.a.a.1.1	✓	1	8.5	even	2
16.14.a.b.1.1		1	8.3	odd	2
36.14.a.a.1.1		1	24.5	odd	2
64.14.a.c.1.1		1	1.1	even	1	trivial
64.14.a.g.1.1		1	4.3	odd	2
100.14.a.a.1.1		1	40.29	even	2
100.14.c.a.49.1		2	40.37	odd	4
100.14.c.a.49.2		2	40.13	odd	4
144.14.a.a.1.1		1	24.11	even	2
196.14.a.a.1.1		1	56.13	odd	2
196.14.e.a.165.1		2	56.37	even	6
196.14.e.a.177.1		2	56.53	even	6
196.14.e.b.165.1		2	56.5	odd	6
196.14.e.b.177.1		2	56.45	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more