LMFDB - Embedded newform 64.6.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,6,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, 6, names="a")

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

chi := DirichletCharacter("64.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 6 $
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:	$10.2645644680$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 8)
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)

$f(q)$

$=$

$q+20.0000 q^{3} +74.0000 q^{5} +24.0000 q^{7} +157.000 q^{9} +O(q^{10})$

$q+20.0000 q^{3} +74.0000 q^{5} +24.0000 q^{7} +157.000 q^{9} +124.000 q^{11} -478.000 q^{13} +1480.00 q^{15} -1198.00 q^{17} +3044.00 q^{19} +480.000 q^{21} -184.000 q^{23} +2351.00 q^{25} -1720.00 q^{27} +3282.00 q^{29} +5728.00 q^{31} +2480.00 q^{33} +1776.00 q^{35} -10326.0 q^{37} -9560.00 q^{39} -8886.00 q^{41} -9188.00 q^{43} +11618.0 q^{45} -23664.0 q^{47} -16231.0 q^{49} -23960.0 q^{51} -11686.0 q^{53} +9176.00 q^{55} +60880.0 q^{57} +16876.0 q^{59} +18482.0 q^{61} +3768.00 q^{63} -35372.0 q^{65} -15532.0 q^{67} -3680.00 q^{69} +31960.0 q^{71} -4886.00 q^{73} +47020.0 q^{75} +2976.00 q^{77} -44560.0 q^{79} -72551.0 q^{81} +67364.0 q^{83} -88652.0 q^{85} +65640.0 q^{87} +71994.0 q^{89} -11472.0 q^{91} +114560. q^{93} +225256. q^{95} +48866.0 q^{97} +19468.0 q^{99} +O(q^{100})$

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
$3$	20.0000	1.28300	0.641500	−	0.767123i	$-0.278312\pi$
$3$	20.0000	1.28300	0.641500	+	0.767123i	$0.278312\pi$
$4$	0	0
$5$	74.0000	1.32375	0.661876	−	0.749613i	$-0.269760\pi$
$5$	74.0000	1.32375	0.661876	+	0.749613i	$0.269760\pi$
$6$	0	0
$7$	24.0000	0.185125	0.0925627	−	0.995707i	$-0.470494\pi$
$7$	24.0000	0.185125	0.0925627	+	0.995707i	$0.470494\pi$
$8$	0	0
$9$	157.000	0.646091
$10$	0	0
$11$	124.000	0.308987	0.154493	−	0.987994i	$-0.450625\pi$
$11$	124.000	0.308987	0.154493	+	0.987994i	$0.450625\pi$
$12$	0	0
$13$	−478.000	−0.784458	−0.392229	−	0.919868i	$-0.628296\pi$
$13$	−478.000	−0.784458	−0.392229	+	0.919868i	$0.628296\pi$
$14$	0	0
$15$	1480.00	1.69837
$16$	0	0
$17$	−1198.00	−1.00539	−0.502695	−	0.864464i	$-0.667658\pi$
$17$	−1198.00	−1.00539	−0.502695	+	0.864464i	$0.667658\pi$
$18$	0	0
$19$	3044.00	1.93446	0.967232	−	0.253894i	$-0.0817115\pi$
$19$	3044.00	1.93446	0.967232	+	0.253894i	$0.0817115\pi$
$20$	0	0
$21$	480.000	0.237516
$22$	0	0
$23$	−184.000	−0.0725268	−0.0362634	−	0.999342i	$-0.511546\pi$
$23$	−184.000	−0.0725268	−0.0362634	+	0.999342i	$0.511546\pi$
$24$	0	0
$25$	2351.00	0.752320
$26$	0	0
$27$	−1720.00	−0.454066
$28$	0	0
$29$	3282.00	0.724676	0.362338	−	0.932047i	$-0.381979\pi$
$29$	3282.00	0.724676	0.362338	+	0.932047i	$0.381979\pi$
$30$	0	0
$31$	5728.00	1.07053	0.535265	−	0.844684i	$-0.320212\pi$
$31$	5728.00	1.07053	0.535265	+	0.844684i	$0.320212\pi$
$32$	0	0
$33$	2480.00	0.396430
$34$	0	0
$35$	1776.00	0.245060
$36$	0	0
$37$	−10326.0	−1.24002	−0.620009	−	0.784595i	$-0.712871\pi$
$37$	−10326.0	−1.24002	−0.620009	+	0.784595i	$0.712871\pi$
$38$	0	0
$39$	−9560.00	−1.00646
$40$	0	0
$41$	−8886.00	−0.825556	−0.412778	−	0.910832i	$-0.635442\pi$
$41$	−8886.00	−0.825556	−0.412778	+	0.910832i	$0.635442\pi$
$42$	0	0
$43$	−9188.00	−0.757792	−0.378896	−	0.925439i	$-0.623696\pi$
$43$	−9188.00	−0.757792	−0.378896	+	0.925439i	$0.623696\pi$
$44$	0	0
$45$	11618.0	0.855264
$46$	0	0
$47$	−23664.0	−1.56258	−0.781292	−	0.624165i	$-0.785439\pi$
$47$	−23664.0	−1.56258	−0.781292	+	0.624165i	$0.785439\pi$
$48$	0	0
$49$	−16231.0	−0.965729
$50$	0	0
$51$	−23960.0	−1.28992
$52$	0	0
$53$	−11686.0	−0.571447	−0.285724	−	0.958312i	$-0.592234\pi$
$53$	−11686.0	−0.571447	−0.285724	+	0.958312i	$0.592234\pi$
$54$	0	0
$55$	9176.00	0.409022
$56$	0	0
$57$	60880.0	2.48192
$58$	0	0
$59$	16876.0	0.631160	0.315580	−	0.948899i	$-0.397801\pi$
$59$	16876.0	0.631160	0.315580	+	0.948899i	$0.397801\pi$
$60$	0	0
$61$	18482.0	0.635952	0.317976	−	0.948099i	$-0.396997\pi$
$61$	18482.0	0.635952	0.317976	+	0.948099i	$0.396997\pi$
$62$	0	0
$63$	3768.00	0.119608
$64$	0	0
$65$	−35372.0	−1.03843
$66$	0	0
$67$	−15532.0	−0.422708	−0.211354	−	0.977410i	$-0.567787\pi$
$67$	−15532.0	−0.422708	−0.211354	+	0.977410i	$0.567787\pi$
$68$	0	0
$69$	−3680.00	−0.0930519
$70$	0	0
$71$	31960.0	0.752421	0.376210	−	0.926534i	$-0.377227\pi$
$71$	31960.0	0.752421	0.376210	+	0.926534i	$0.377227\pi$
$72$	0	0
$73$	−4886.00	−0.107312	−0.0536558	−	0.998559i	$-0.517087\pi$
$73$	−4886.00	−0.107312	−0.0536558	+	0.998559i	$0.517087\pi$
$74$	0	0
$75$	47020.0	0.965227
$76$	0	0
$77$	2976.00	0.0572013
$78$	0	0
$79$	−44560.0	−0.803299	−0.401650	−	0.915793i	$-0.631563\pi$
$79$	−44560.0	−0.803299	−0.401650	+	0.915793i	$0.631563\pi$
$80$	0	0
$81$	−72551.0	−1.22866
$82$	0	0
$83$	67364.0	1.07333	0.536664	−	0.843796i	$-0.319684\pi$
$83$	67364.0	1.07333	0.536664	+	0.843796i	$0.319684\pi$
$84$	0	0
$85$	−88652.0	−1.33089
$86$	0	0
$87$	65640.0	0.929759
$88$	0	0
$89$	71994.0	0.963432	0.481716	−	0.876327i	$-0.340014\pi$
$89$	71994.0	0.963432	0.481716	+	0.876327i	$0.340014\pi$
$90$	0	0
$91$	−11472.0	−0.145223
$92$	0	0
$93$	114560.	1.37349
$94$	0	0
$95$	225256.	2.56075
$96$	0	0
$97$	48866.0	0.527324	0.263662	−	0.964615i	$-0.415070\pi$
$97$	48866.0	0.527324	0.263662	+	0.964615i	$0.415070\pi$
$98$	0	0
$99$	19468.0	0.199633
$100$	0	0
$101$	−51606.0	−0.503381	−0.251690	−	0.967808i	$-0.580986\pi$
$101$	−51606.0	−0.503381	−0.251690	+	0.967808i	$0.580986\pi$
$102$	0	0
$103$	−180424.	−1.67572	−0.837860	−	0.545886i	$-0.816193\pi$
$103$	−180424.	−1.67572	−0.837860	+	0.545886i	$0.816193\pi$
$104$	0	0
$105$	35520.0	0.314412
$106$	0	0
$107$	−65700.0	−0.554761	−0.277381	−	0.960760i	$-0.589466\pi$
$107$	−65700.0	−0.554761	−0.277381	+	0.960760i	$0.589466\pi$
$108$	0	0
$109$	112706.	0.908617	0.454308	−	0.890844i	$-0.349886\pi$
$109$	112706.	0.908617	0.454308	+	0.890844i	$0.349886\pi$
$110$	0	0
$111$	−206520.	−1.59094
$112$	0	0
$113$	−23502.0	−0.173145	−0.0865723	−	0.996246i	$-0.527591\pi$
$113$	−23502.0	−0.173145	−0.0865723	+	0.996246i	$0.527591\pi$
$114$	0	0
$115$	−13616.0	−0.0960075
$116$	0	0
$117$	−75046.0	−0.506831
$118$	0	0
$119$	−28752.0	−0.186123
$120$	0	0
$121$	−145675.	−0.904527
$122$	0	0
$123$	−177720.	−1.05919
$124$	0	0
$125$	−57276.0	−0.327867
$126$	0	0
$127$	94592.0	0.520409	0.260205	−	0.965553i	$-0.416210\pi$
$127$	94592.0	0.520409	0.260205	+	0.965553i	$0.416210\pi$
$128$	0	0
$129$	−183760.	−0.972247
$130$	0	0
$131$	70292.0	0.357872	0.178936	−	0.983861i	$-0.442735\pi$
$131$	70292.0	0.357872	0.178936	+	0.983861i	$0.442735\pi$
$132$	0	0
$133$	73056.0	0.358119
$134$	0	0
$135$	−127280.	−0.601071
$136$	0	0
$137$	277290.	1.26221	0.631107	−	0.775696i	$-0.282601\pi$
$137$	277290.	1.26221	0.631107	+	0.775696i	$0.282601\pi$
$138$	0	0
$139$	−130308.	−0.572050	−0.286025	−	0.958222i	$-0.592334\pi$
$139$	−130308.	−0.572050	−0.286025	+	0.958222i	$0.592334\pi$
$140$	0	0
$141$	−473280.	−2.00480
$142$	0	0
$143$	−59272.0	−0.242387
$144$	0	0
$145$	242868.	0.959291
$146$	0	0
$147$	−324620.	−1.23903
$148$	0	0
$149$	401530.	1.48167	0.740836	−	0.671685i	$-0.234429\pi$
$149$	401530.	1.48167	0.740836	+	0.671685i	$0.234429\pi$
$150$	0	0
$151$	75976.0	0.271165	0.135583	−	0.990766i	$-0.456709\pi$
$151$	75976.0	0.271165	0.135583	+	0.990766i	$0.456709\pi$
$152$	0	0
$153$	−188086.	−0.649573
$154$	0	0
$155$	423872.	1.41712
$156$	0	0
$157$	394322.	1.27674	0.638369	−	0.769730i	$-0.279609\pi$
$157$	394322.	1.27674	0.638369	+	0.769730i	$0.279609\pi$
$158$	0	0
$159$	−233720.	−0.733167
$160$	0	0
$161$	−4416.00	−0.0134265
$162$	0	0
$163$	−11724.0	−0.0345626	−0.0172813	−	0.999851i	$-0.505501\pi$
$163$	−11724.0	−0.0345626	−0.0172813	+	0.999851i	$0.505501\pi$
$164$	0	0
$165$	183520.	0.524775
$166$	0	0
$167$	551928.	1.53141	0.765705	−	0.643192i	$-0.222390\pi$
$167$	551928.	1.53141	0.765705	+	0.643192i	$0.222390\pi$
$168$	0	0
$169$	−142809.	−0.384626
$170$	0	0
$171$	477908.	1.24984
$172$	0	0
$173$	−432894.	−1.09968	−0.549840	−	0.835270i	$-0.685311\pi$
$173$	−432894.	−1.09968	−0.549840	+	0.835270i	$0.685311\pi$
$174$	0	0
$175$	56424.0	0.139274
$176$	0	0
$177$	337520.	0.809779
$178$	0	0
$179$	559620.	1.30545	0.652726	−	0.757594i	$-0.273625\pi$
$179$	559620.	1.30545	0.652726	+	0.757594i	$0.273625\pi$
$180$	0	0
$181$	−604710.	−1.37199	−0.685995	−	0.727607i	$-0.740633\pi$
$181$	−604710.	−1.37199	−0.685995	+	0.727607i	$0.740633\pi$
$182$	0	0
$183$	369640.	0.815927
$184$	0	0
$185$	−764124.	−1.64148
$186$	0	0
$187$	−148552.	−0.310652
$188$	0	0
$189$	−41280.0	−0.0840592
$190$	0	0
$191$	409152.	0.811524	0.405762	−	0.913979i	$-0.367006\pi$
$191$	409152.	0.811524	0.405762	+	0.913979i	$0.367006\pi$
$192$	0	0
$193$	540866.	1.04519	0.522596	−	0.852580i	$-0.324963\pi$
$193$	540866.	1.04519	0.522596	+	0.852580i	$0.324963\pi$
$194$	0	0
$195$	−707440.	−1.33230
$196$	0	0
$197$	629898.	1.15639	0.578195	−	0.815898i	$-0.303757\pi$
$197$	629898.	1.15639	0.578195	+	0.815898i	$0.303757\pi$
$198$	0	0
$199$	−283048.	−0.506673	−0.253336	−	0.967378i	$-0.581528\pi$
$199$	−283048.	−0.506673	−0.253336	+	0.967378i	$0.581528\pi$
$200$	0	0
$201$	−310640.	−0.542335
$202$	0	0
$203$	78768.0	0.134156
$204$	0	0
$205$	−657564.	−1.09283
$206$	0	0
$207$	−28888.0	−0.0468588
$208$	0	0
$209$	377456.	0.597724
$210$	0	0
$211$	142756.	0.220744	0.110372	−	0.993890i	$-0.464796\pi$
$211$	142756.	0.220744	0.110372	+	0.993890i	$0.464796\pi$
$212$	0	0
$213$	639200.	0.965357
$214$	0	0
$215$	−679912.	−1.00313
$216$	0	0
$217$	137472.	0.198182
$218$	0	0
$219$	−97720.0	−0.137681
$220$	0	0
$221$	572644.	0.788686
$222$	0	0
$223$	−889696.	−1.19806	−0.599031	−	0.800726i	$-0.704447\pi$
$223$	−889696.	−1.19806	−0.599031	+	0.800726i	$0.704447\pi$
$224$	0	0
$225$	369107.	0.486067
$226$	0	0
$227$	1.14316e6	1.47245	0.736226	−	0.676736i	$-0.236606\pi$
$227$	1.14316e6	1.47245	0.736226	+	0.676736i	$0.236606\pi$
$228$	0	0
$229$	695786.	0.876773	0.438386	−	0.898787i	$-0.355550\pi$
$229$	695786.	0.876773	0.438386	+	0.898787i	$0.355550\pi$
$230$	0	0
$231$	59520.0	0.0733893
$232$	0	0
$233$	−347126.	−0.418887	−0.209444	−	0.977821i	$-0.567165\pi$
$233$	−347126.	−0.418887	−0.209444	+	0.977821i	$0.567165\pi$
$234$	0	0
$235$	−1.75114e6	−2.06847
$236$	0	0
$237$	−891200.	−1.03063
$238$	0	0
$239$	1.64296e6	1.86051	0.930255	−	0.366912i	$-0.119585\pi$
$239$	1.64296e6	1.86051	0.930255	+	0.366912i	$0.119585\pi$
$240$	0	0
$241$	−1.16744e6	−1.29477	−0.647383	−	0.762165i	$-0.724137\pi$
$241$	−1.16744e6	−1.29477	−0.647383	+	0.762165i	$0.724137\pi$
$242$	0	0
$243$	−1.03306e6	−1.12230
$244$	0	0
$245$	−1.20109e6	−1.27839
$246$	0	0
$247$	−1.45503e6	−1.51751
$248$	0	0
$249$	1.34728e6	1.37708
$250$	0	0
$251$	−790612.	−0.792098	−0.396049	−	0.918229i	$-0.629619\pi$
$251$	−790612.	−0.792098	−0.396049	+	0.918229i	$0.629619\pi$
$252$	0	0
$253$	−22816.0	−0.0224098
$254$	0	0
$255$	−1.77304e6	−1.70753
$256$	0	0
$257$	−129790.	−0.122577	−0.0612884	−	0.998120i	$-0.519521\pi$
$257$	−129790.	−0.122577	−0.0612884	+	0.998120i	$0.519521\pi$
$258$	0	0
$259$	−247824.	−0.229559
$260$	0	0
$261$	515274.	0.468206
$262$	0	0
$263$	−70888.0	−0.0631951	−0.0315975	−	0.999501i	$-0.510059\pi$
$263$	−70888.0	−0.0631951	−0.0315975	+	0.999501i	$0.510059\pi$
$264$	0	0
$265$	−864764.	−0.756455
$266$	0	0
$267$	1.43988e6	1.23608
$268$	0	0
$269$	−1.79017e6	−1.50839	−0.754197	−	0.656649i	$-0.771973\pi$
$269$	−1.79017e6	−1.50839	−0.754197	+	0.656649i	$0.771973\pi$
$270$	0	0
$271$	1.77362e6	1.46702	0.733511	−	0.679678i	$-0.237880\pi$
$271$	1.77362e6	1.46702	0.733511	+	0.679678i	$0.237880\pi$
$272$	0	0
$273$	−229440.	−0.186321
$274$	0	0
$275$	291524.	0.232457
$276$	0	0
$277$	275450.	0.215697	0.107848	−	0.994167i	$-0.465604\pi$
$277$	275450.	0.215697	0.107848	+	0.994167i	$0.465604\pi$
$278$	0	0
$279$	899296.	0.691659
$280$	0	0
$281$	594170.	0.448895	0.224448	−	0.974486i	$-0.427942\pi$
$281$	594170.	0.448895	0.224448	+	0.974486i	$0.427942\pi$
$282$	0	0
$283$	1.09243e6	0.810824	0.405412	−	0.914134i	$-0.367128\pi$
$283$	1.09243e6	0.810824	0.405412	+	0.914134i	$0.367128\pi$
$284$	0	0
$285$	4.50512e6	3.28545
$286$	0	0
$287$	−213264.	−0.152831
$288$	0	0
$289$	15347.0	0.0108088
$290$	0	0
$291$	977320.	0.676557
$292$	0	0
$293$	−333654.	−0.227053	−0.113527	−	0.993535i	$-0.536215\pi$
$293$	−333654.	−0.227053	−0.113527	+	0.993535i	$0.536215\pi$
$294$	0	0
$295$	1.24882e6	0.835500
$296$	0	0
$297$	−213280.	−0.140300
$298$	0	0
$299$	87952.0	0.0568942
$300$	0	0
$301$	−220512.	−0.140287
$302$	0	0
$303$	−1.03212e6	−0.645838
$304$	0	0
$305$	1.36767e6	0.841843
$306$	0	0
$307$	1.05997e6	0.641872	0.320936	−	0.947101i	$-0.396003\pi$
$307$	1.05997e6	0.641872	0.320936	+	0.947101i	$0.396003\pi$
$308$	0	0
$309$	−3.60848e6	−2.14995
$310$	0	0
$311$	1.33649e6	0.783545	0.391773	−	0.920062i	$-0.371862\pi$
$311$	1.33649e6	0.783545	0.391773	+	0.920062i	$0.371862\pi$
$312$	0	0
$313$	1.64419e6	0.948615	0.474308	−	0.880359i	$-0.342698\pi$
$313$	1.64419e6	0.948615	0.474308	+	0.880359i	$0.342698\pi$
$314$	0	0
$315$	278832.	0.158331
$316$	0	0
$317$	1.72370e6	0.963414	0.481707	−	0.876332i	$-0.340017\pi$
$317$	1.72370e6	0.963414	0.481707	+	0.876332i	$0.340017\pi$
$318$	0	0
$319$	406968.	0.223915
$320$	0	0
$321$	−1.31400e6	−0.711759
$322$	0	0
$323$	−3.64671e6	−1.94489
$324$	0	0
$325$	−1.12378e6	−0.590163
$326$	0	0
$327$	2.25412e6	1.16576
$328$	0	0
$329$	−567936.	−0.289274
$330$	0	0
$331$	2.74963e6	1.37944	0.689722	−	0.724074i	$-0.257733\pi$
$331$	2.74963e6	1.37944	0.689722	+	0.724074i	$0.257733\pi$
$332$	0	0
$333$	−1.62118e6	−0.801164
$334$	0	0
$335$	−1.14937e6	−0.559561
$336$	0	0
$337$	−3.41489e6	−1.63796	−0.818978	−	0.573824i	$-0.805459\pi$
$337$	−3.41489e6	−1.63796	−0.818978	+	0.573824i	$0.805459\pi$
$338$	0	0
$339$	−470040.	−0.222145
$340$	0	0
$341$	710272.	0.330780
$342$	0	0
$343$	−792912.	−0.363906
$344$	0	0
$345$	−272320.	−0.123178
$346$	0	0
$347$	730764.	0.325802	0.162901	−	0.986642i	$-0.447915\pi$
$347$	730764.	0.325802	0.162901	+	0.986642i	$0.447915\pi$
$348$	0	0
$349$	2.29749e6	1.00969	0.504847	−	0.863209i	$-0.331549\pi$
$349$	2.29749e6	1.00969	0.504847	+	0.863209i	$0.331549\pi$
$350$	0	0
$351$	822160.	0.356196
$352$	0	0
$353$	−1.17072e6	−0.500052	−0.250026	−	0.968239i	$-0.580439\pi$
$353$	−1.17072e6	−0.500052	−0.250026	+	0.968239i	$0.580439\pi$
$354$	0	0
$355$	2.36504e6	0.996019
$356$	0	0
$357$	−575040.	−0.238796
$358$	0	0
$359$	−3.88654e6	−1.59157	−0.795787	−	0.605577i	$-0.792942\pi$
$359$	−3.88654e6	−1.59157	−0.795787	+	0.605577i	$0.792942\pi$
$360$	0	0
$361$	6.78984e6	2.74215
$362$	0	0
$363$	−2.91350e6	−1.16051
$364$	0	0
$365$	−361564.	−0.142054
$366$	0	0
$367$	−933040.	−0.361606	−0.180803	−	0.983519i	$-0.557870\pi$
$367$	−933040.	−0.361606	−0.180803	+	0.983519i	$0.557870\pi$
$368$	0	0
$369$	−1.39510e6	−0.533384
$370$	0	0
$371$	−280464.	−0.105789
$372$	0	0
$373$	392218.	0.145967	0.0729836	−	0.997333i	$-0.476748\pi$
$373$	392218.	0.145967	0.0729836	+	0.997333i	$0.476748\pi$
$374$	0	0
$375$	−1.14552e6	−0.420653
$376$	0	0
$377$	−1.56880e6	−0.568477
$378$	0	0
$379$	−4.72930e6	−1.69122	−0.845608	−	0.533805i	$-0.820762\pi$
$379$	−4.72930e6	−1.69122	−0.845608	+	0.533805i	$0.820762\pi$
$380$	0	0
$381$	1.89184e6	0.667686
$382$	0	0
$383$	−1.89734e6	−0.660920	−0.330460	−	0.943820i	$-0.607204\pi$
$383$	−1.89734e6	−0.660920	−0.330460	+	0.943820i	$0.607204\pi$
$384$	0	0
$385$	220224.	0.0757204
$386$	0	0
$387$	−1.44252e6	−0.489602
$388$	0	0
$389$	3.72295e6	1.24742	0.623711	−	0.781655i	$-0.285624\pi$
$389$	3.72295e6	1.24742	0.623711	+	0.781655i	$0.285624\pi$
$390$	0	0
$391$	220432.	0.0729177
$392$	0	0
$393$	1.40584e6	0.459150
$394$	0	0
$395$	−3.29744e6	−1.06337
$396$	0	0
$397$	−3.33808e6	−1.06297	−0.531484	−	0.847068i	$-0.678365\pi$
$397$	−3.33808e6	−1.06297	−0.531484	+	0.847068i	$0.678365\pi$
$398$	0	0
$399$	1.46112e6	0.459466
$400$	0	0
$401$	4.27490e6	1.32759	0.663796	−	0.747913i	$-0.268944\pi$
$401$	4.27490e6	1.32759	0.663796	+	0.747913i	$0.268944\pi$
$402$	0	0
$403$	−2.73798e6	−0.839785
$404$	0	0
$405$	−5.36877e6	−1.62644
$406$	0	0
$407$	−1.28042e6	−0.383149
$408$	0	0
$409$	−2.57319e6	−0.760613	−0.380306	−	0.924861i	$-0.624181\pi$
$409$	−2.57319e6	−0.760613	−0.380306	+	0.924861i	$0.624181\pi$
$410$	0	0
$411$	5.54580e6	1.61942
$412$	0	0
$413$	405024.	0.116844
$414$	0	0
$415$	4.98494e6	1.42082
$416$	0	0
$417$	−2.60616e6	−0.733941
$418$	0	0
$419$	5.26828e6	1.46600	0.732999	−	0.680230i	$-0.238120\pi$
$419$	5.26828e6	1.46600	0.732999	+	0.680230i	$0.238120\pi$
$420$	0	0
$421$	973354.	0.267649	0.133824	−	0.991005i	$-0.457274\pi$
$421$	973354.	0.267649	0.133824	+	0.991005i	$0.457274\pi$
$422$	0	0
$423$	−3.71525e6	−1.00957
$424$	0	0
$425$	−2.81650e6	−0.756375
$426$	0	0
$427$	443568.	0.117731
$428$	0	0
$429$	−1.18544e6	−0.310983
$430$	0	0
$431$	−3.55736e6	−0.922433	−0.461216	−	0.887288i	$-0.652587\pi$
$431$	−3.55736e6	−0.922433	−0.461216	+	0.887288i	$0.652587\pi$
$432$	0	0
$433$	−1.95496e6	−0.501092	−0.250546	−	0.968105i	$-0.580610\pi$
$433$	−1.95496e6	−0.501092	−0.250546	+	0.968105i	$0.580610\pi$
$434$	0	0
$435$	4.85736e6	1.23077
$436$	0	0
$437$	−560096.	−0.140300
$438$	0	0
$439$	3.29681e6	0.816455	0.408228	−	0.912880i	$-0.366147\pi$
$439$	3.29681e6	0.816455	0.408228	+	0.912880i	$0.366147\pi$
$440$	0	0
$441$	−2.54827e6	−0.623948
$442$	0	0
$443$	−5.05820e6	−1.22458	−0.612289	−	0.790634i	$-0.709751\pi$
$443$	−5.05820e6	−1.22458	−0.612289	+	0.790634i	$0.709751\pi$
$444$	0	0
$445$	5.32756e6	1.27535
$446$	0	0
$447$	8.03060e6	1.90099
$448$	0	0
$449$	2.12730e6	0.497981	0.248990	−	0.968506i	$-0.419901\pi$
$449$	2.12730e6	0.497981	0.248990	+	0.968506i	$0.419901\pi$
$450$	0	0
$451$	−1.10186e6	−0.255086
$452$	0	0
$453$	1.51952e6	0.347905
$454$	0	0
$455$	−848928.	−0.192239
$456$	0	0
$457$	289130.	0.0647594	0.0323797	−	0.999476i	$-0.489691\pi$
$457$	289130.	0.0647594	0.0323797	+	0.999476i	$0.489691\pi$
$458$	0	0
$459$	2.06056e6	0.456513
$460$	0	0
$461$	−2.66870e6	−0.584854	−0.292427	−	0.956288i	$-0.594463\pi$
$461$	−2.66870e6	−0.584854	−0.292427	+	0.956288i	$0.594463\pi$
$462$	0	0
$463$	−7.58619e6	−1.64464	−0.822321	−	0.569024i	$-0.807321\pi$
$463$	−7.58619e6	−1.64464	−0.822321	+	0.569024i	$0.807321\pi$
$464$	0	0
$465$	8.47744e6	1.81816
$466$	0	0
$467$	−1.41961e6	−0.301216	−0.150608	−	0.988594i	$-0.548123\pi$
$467$	−1.41961e6	−0.301216	−0.150608	+	0.988594i	$0.548123\pi$
$468$	0	0
$469$	−372768.	−0.0782540
$470$	0	0
$471$	7.88644e6	1.63806
$472$	0	0
$473$	−1.13931e6	−0.234148
$474$	0	0
$475$	7.15644e6	1.45534
$476$	0	0
$477$	−1.83470e6	−0.369207
$478$	0	0
$479$	1.88406e6	0.375195	0.187597	−	0.982246i	$-0.439930\pi$
$479$	1.88406e6	0.375195	0.187597	+	0.982246i	$0.439930\pi$
$480$	0	0
$481$	4.93583e6	0.972741
$482$	0	0
$483$	−88320.0	−0.0172263
$484$	0	0
$485$	3.61608e6	0.698046
$486$	0	0
$487$	6.01388e6	1.14903	0.574516	−	0.818493i	$-0.305190\pi$
$487$	6.01388e6	1.14903	0.574516	+	0.818493i	$0.305190\pi$
$488$	0	0
$489$	−234480.	−0.0443439
$490$	0	0
$491$	4.29232e6	0.803504	0.401752	−	0.915749i	$-0.368401\pi$
$491$	4.29232e6	0.803504	0.401752	+	0.915749i	$0.368401\pi$
$492$	0	0
$493$	−3.93184e6	−0.728581
$494$	0	0
$495$	1.44063e6	0.264265
$496$	0	0
$497$	767040.	0.139292
$498$	0	0
$499$	1.34509e6	0.241825	0.120912	−	0.992663i	$-0.461418\pi$
$499$	1.34509e6	0.241825	0.120912	+	0.992663i	$0.461418\pi$
$500$	0	0
$501$	1.10386e7	1.96480
$502$	0	0
$503$	−202008.	−0.0355999	−0.0177999	−	0.999842i	$-0.505666\pi$
$503$	−202008.	−0.0355999	−0.0177999	+	0.999842i	$0.505666\pi$
$504$	0	0
$505$	−3.81884e6	−0.666352
$506$	0	0
$507$	−2.85618e6	−0.493476
$508$	0	0
$509$	−9.78344e6	−1.67377	−0.836887	−	0.547375i	$-0.815627\pi$
$509$	−9.78344e6	−1.67377	−0.836887	+	0.547375i	$0.815627\pi$
$510$	0	0
$511$	−117264.	−0.0198661
$512$	0	0
$513$	−5.23568e6	−0.878374
$514$	0	0
$515$	−1.33514e7	−2.21824
$516$	0	0
$517$	−2.93434e6	−0.482818
$518$	0	0
$519$	−8.65788e6	−1.41089
$520$	0	0
$521$	−1.04830e7	−1.69197	−0.845985	−	0.533207i	$-0.820987\pi$
$521$	−1.04830e7	−1.69197	−0.845985	+	0.533207i	$0.820987\pi$
$522$	0	0
$523$	6.21017e6	0.992772	0.496386	−	0.868102i	$-0.334660\pi$
$523$	6.21017e6	0.992772	0.496386	+	0.868102i	$0.334660\pi$
$524$	0	0
$525$	1.12848e6	0.178688
$526$	0	0
$527$	−6.86214e6	−1.07630
$528$	0	0
$529$	−6.40249e6	−0.994740
$530$	0	0
$531$	2.64953e6	0.407787
$532$	0	0
$533$	4.24751e6	0.647614
$534$	0	0
$535$	−4.86180e6	−0.734366
$536$	0	0
$537$	1.11924e7	1.67489
$538$	0	0
$539$	−2.01264e6	−0.298397
$540$	0	0
$541$	−5.08088e6	−0.746355	−0.373178	−	0.927760i	$-0.621732\pi$
$541$	−5.08088e6	−0.746355	−0.373178	+	0.927760i	$0.621732\pi$
$542$	0	0
$543$	−1.20942e7	−1.76026
$544$	0	0
$545$	8.34024e6	1.20278
$546$	0	0
$547$	3.34687e6	0.478267	0.239133	−	0.970987i	$-0.423137\pi$
$547$	3.34687e6	0.478267	0.239133	+	0.970987i	$0.423137\pi$
$548$	0	0
$549$	2.90167e6	0.410883
$550$	0	0
$551$	9.99041e6	1.40186
$552$	0	0
$553$	−1.06944e6	−0.148711
$554$	0	0
$555$	−1.52825e7	−2.10601
$556$	0	0
$557$	−7.00377e6	−0.956520	−0.478260	−	0.878218i	$-0.658732\pi$
$557$	−7.00377e6	−0.956520	−0.478260	+	0.878218i	$0.658732\pi$
$558$	0	0
$559$	4.39186e6	0.594456
$560$	0	0
$561$	−2.97104e6	−0.398567
$562$	0	0
$563$	−1.29819e7	−1.72610	−0.863052	−	0.505116i	$-0.831450\pi$
$563$	−1.29819e7	−1.72610	−0.863052	+	0.505116i	$0.831450\pi$
$564$	0	0
$565$	−1.73915e6	−0.229200
$566$	0	0
$567$	−1.74122e6	−0.227456
$568$	0	0
$569$	1.89942e6	0.245946	0.122973	−	0.992410i	$-0.460757\pi$
$569$	1.89942e6	0.245946	0.122973	+	0.992410i	$0.460757\pi$
$570$	0	0
$571$	−1.66300e6	−0.213452	−0.106726	−	0.994288i	$-0.534037\pi$
$571$	−1.66300e6	−0.213452	−0.106726	+	0.994288i	$0.534037\pi$
$572$	0	0
$573$	8.18304e6	1.04119
$574$	0	0
$575$	−432584.	−0.0545633
$576$	0	0
$577$	8.77344e6	1.09706	0.548530	−	0.836131i	$-0.315188\pi$
$577$	8.77344e6	1.09706	0.548530	+	0.836131i	$0.315188\pi$
$578$	0	0
$579$	1.08173e7	1.34098
$580$	0	0
$581$	1.61674e6	0.198700
$582$	0	0
$583$	−1.44906e6	−0.176570
$584$	0	0
$585$	−5.55340e6	−0.670918
$586$	0	0
$587$	5.18393e6	0.620961	0.310480	−	0.950580i	$-0.399510\pi$
$587$	5.18393e6	0.620961	0.310480	+	0.950580i	$0.399510\pi$
$588$	0	0
$589$	1.74360e7	2.07090
$590$	0	0
$591$	1.25980e7	1.48365
$592$	0	0
$593$	8.49858e6	0.992452	0.496226	−	0.868193i	$-0.334719\pi$
$593$	8.49858e6	0.992452	0.496226	+	0.868193i	$0.334719\pi$
$594$	0	0
$595$	−2.12765e6	−0.246381
$596$	0	0
$597$	−5.66096e6	−0.650061
$598$	0	0
$599$	−1.12471e7	−1.28078	−0.640388	−	0.768051i	$-0.721227\pi$
$599$	−1.12471e7	−1.28078	−0.640388	+	0.768051i	$0.721227\pi$
$600$	0	0
$601$	−3.46439e6	−0.391238	−0.195619	−	0.980680i	$-0.562672\pi$
$601$	−3.46439e6	−0.391238	−0.195619	+	0.980680i	$0.562672\pi$
$602$	0	0
$603$	−2.43852e6	−0.273108
$604$	0	0
$605$	−1.07799e7	−1.19737
$606$	0	0
$607$	999712.	0.110129	0.0550647	−	0.998483i	$-0.482463\pi$
$607$	999712.	0.110129	0.0550647	+	0.998483i	$0.482463\pi$
$608$	0	0
$609$	1.57536e6	0.172122
$610$	0	0
$611$	1.13114e7	1.22578
$612$	0	0
$613$	−9.81340e6	−1.05480	−0.527398	−	0.849619i	$-0.676832\pi$
$613$	−9.81340e6	−1.05480	−0.527398	+	0.849619i	$0.676832\pi$
$614$	0	0
$615$	−1.31513e7	−1.40210
$616$	0	0
$617$	−5.34745e6	−0.565501	−0.282751	−	0.959193i	$-0.591247\pi$
$617$	−5.34745e6	−0.565501	−0.282751	+	0.959193i	$0.591247\pi$
$618$	0	0
$619$	−6.82768e6	−0.716221	−0.358110	−	0.933679i	$-0.616579\pi$
$619$	−6.82768e6	−0.716221	−0.358110	+	0.933679i	$0.616579\pi$
$620$	0	0
$621$	316480.	0.0329319
$622$	0	0
$623$	1.72786e6	0.178356
$624$	0	0
$625$	−1.15853e7	−1.18633
$626$	0	0
$627$	7.54912e6	0.766880
$628$	0	0
$629$	1.23705e7	1.24670
$630$	0	0
$631$	3.60970e6	0.360909	0.180455	−	0.983583i	$-0.442243\pi$
$631$	3.60970e6	0.360909	0.180455	+	0.983583i	$0.442243\pi$
$632$	0	0
$633$	2.85512e6	0.283214
$634$	0	0
$635$	6.99981e6	0.688893
$636$	0	0
$637$	7.75842e6	0.757573
$638$	0	0
$639$	5.01772e6	0.486132
$640$	0	0
$641$	−1.33853e7	−1.28672	−0.643361	−	0.765563i	$-0.722460\pi$
$641$	−1.33853e7	−1.28672	−0.643361	+	0.765563i	$0.722460\pi$
$642$	0	0
$643$	−9.91115e6	−0.945358	−0.472679	−	0.881235i	$-0.656713\pi$
$643$	−9.91115e6	−0.945358	−0.472679	+	0.881235i	$0.656713\pi$
$644$	0	0
$645$	−1.35982e7	−1.28701
$646$	0	0
$647$	1.78359e7	1.67508	0.837539	−	0.546378i	$-0.183994\pi$
$647$	1.78359e7	1.67508	0.837539	+	0.546378i	$0.183994\pi$
$648$	0	0
$649$	2.09262e6	0.195020
$650$	0	0
$651$	2.74944e6	0.254268
$652$	0	0
$653$	4.32323e6	0.396758	0.198379	−	0.980125i	$-0.436432\pi$
$653$	4.32323e6	0.396758	0.198379	+	0.980125i	$0.436432\pi$
$654$	0	0
$655$	5.20161e6	0.473734
$656$	0	0
$657$	−767102.	−0.0693330
$658$	0	0
$659$	1.97858e7	1.77476	0.887382	−	0.461035i	$-0.152522\pi$
$659$	1.97858e7	1.77476	0.887382	+	0.461035i	$0.152522\pi$
$660$	0	0
$661$	−1.57772e7	−1.40451	−0.702255	−	0.711925i	$-0.747824\pi$
$661$	−1.57772e7	−1.40451	−0.702255	+	0.711925i	$0.747824\pi$
$662$	0	0
$663$	1.14529e7	1.01188
$664$	0	0
$665$	5.40614e6	0.474060
$666$	0	0
$667$	−603888.	−0.0525584
$668$	0	0
$669$	−1.77939e7	−1.53711
$670$	0	0
$671$	2.29177e6	0.196501
$672$	0	0
$673$	6.78762e6	0.577670	0.288835	−	0.957379i	$-0.406732\pi$
$673$	6.78762e6	0.577670	0.288835	+	0.957379i	$0.406732\pi$
$674$	0	0
$675$	−4.04372e6	−0.341603
$676$	0	0
$677$	1.49942e7	1.25734	0.628669	−	0.777673i	$-0.283600\pi$
$677$	1.49942e7	1.25734	0.628669	+	0.777673i	$0.283600\pi$
$678$	0	0
$679$	1.17278e6	0.0976211
$680$	0	0
$681$	2.28631e7	1.88916
$682$	0	0
$683$	1.15580e7	0.948053	0.474026	−	0.880511i	$-0.342800\pi$
$683$	1.15580e7	0.948053	0.474026	+	0.880511i	$0.342800\pi$
$684$	0	0
$685$	2.05195e7	1.67086
$686$	0	0
$687$	1.39157e7	1.12490
$688$	0	0
$689$	5.58591e6	0.448276
$690$	0	0
$691$	−220156.	−0.0175402	−0.00877012	−	0.999962i	$-0.502792\pi$
$691$	−220156.	−0.0175402	−0.00877012	+	0.999962i	$0.502792\pi$
$692$	0	0
$693$	467232.	0.0369572
$694$	0	0
$695$	−9.64279e6	−0.757253
$696$	0	0
$697$	1.06454e7	0.830006
$698$	0	0
$699$	−6.94252e6	−0.537433
$700$	0	0
$701$	−4.78933e6	−0.368111	−0.184056	−	0.982916i	$-0.558923\pi$
$701$	−4.78933e6	−0.368111	−0.184056	+	0.982916i	$0.558923\pi$
$702$	0	0
$703$	−3.14323e7	−2.39877
$704$	0	0
$705$	−3.50227e7	−2.65385
$706$	0	0
$707$	−1.23854e6	−0.0931886
$708$	0	0
$709$	−4.26892e6	−0.318935	−0.159468	−	0.987203i	$-0.550978\pi$
$709$	−4.26892e6	−0.318935	−0.159468	+	0.987203i	$0.550978\pi$
$710$	0	0
$711$	−6.99592e6	−0.519004
$712$	0	0
$713$	−1.05395e6	−0.0776421
$714$	0	0
$715$	−4.38613e6	−0.320860
$716$	0	0
$717$	3.28592e7	2.38704
$718$	0	0
$719$	1.61960e7	1.16838	0.584190	−	0.811617i	$-0.301412\pi$
$719$	1.61960e7	1.16838	0.584190	+	0.811617i	$0.301412\pi$
$720$	0	0
$721$	−4.33018e6	−0.310218
$722$	0	0
$723$	−2.33488e7	−1.66119
$724$	0	0
$725$	7.71598e6	0.545188
$726$	0	0
$727$	−6.53426e6	−0.458522	−0.229261	−	0.973365i	$-0.573631\pi$
$727$	−6.53426e6	−0.458522	−0.229261	+	0.973365i	$0.573631\pi$
$728$	0	0
$729$	−3.03131e6	−0.211257
$730$	0	0
$731$	1.10072e7	0.761876
$732$	0	0
$733$	−1.31617e7	−0.904800	−0.452400	−	0.891815i	$-0.649432\pi$
$733$	−1.31617e7	−0.904800	−0.452400	+	0.891815i	$0.649432\pi$
$734$	0	0
$735$	−2.40219e7	−1.64017
$736$	0	0
$737$	−1.92597e6	−0.130611
$738$	0	0
$739$	−1.42348e7	−0.958825	−0.479412	−	0.877590i	$-0.659150\pi$
$739$	−1.42348e7	−0.958825	−0.479412	+	0.877590i	$0.659150\pi$
$740$	0	0
$741$	−2.91006e7	−1.94696
$742$	0	0
$743$	2.15835e7	1.43434	0.717168	−	0.696901i	$-0.245438\pi$
$743$	2.15835e7	1.43434	0.717168	+	0.696901i	$0.245438\pi$
$744$	0	0
$745$	2.97132e7	1.96137
$746$	0	0
$747$	1.05761e7	0.693467
$748$	0	0
$749$	−1.57680e6	−0.102700
$750$	0	0
$751$	−1.86594e7	−1.20725	−0.603625	−	0.797268i	$-0.706278\pi$
$751$	−1.86594e7	−1.20725	−0.603625	+	0.797268i	$0.706278\pi$
$752$	0	0
$753$	−1.58122e7	−1.01626
$754$	0	0
$755$	5.62222e6	0.358956
$756$	0	0
$757$	2.56681e6	0.162800	0.0813999	−	0.996682i	$-0.474061\pi$
$757$	2.56681e6	0.162800	0.0813999	+	0.996682i	$0.474061\pi$
$758$	0	0
$759$	−456320.	−0.0287518
$760$	0	0
$761$	−2.59586e7	−1.62487	−0.812436	−	0.583051i	$-0.801859\pi$
$761$	−2.59586e7	−1.62487	−0.812436	+	0.583051i	$0.801859\pi$
$762$	0	0
$763$	2.70494e6	0.168208
$764$	0	0
$765$	−1.39184e7	−0.859874
$766$	0	0
$767$	−8.06673e6	−0.495118
$768$	0	0
$769$	5.53267e6	0.337380	0.168690	−	0.985669i	$-0.446046\pi$
$769$	5.53267e6	0.337380	0.168690	+	0.985669i	$0.446046\pi$
$770$	0	0
$771$	−2.59580e6	−0.157266
$772$	0	0
$773$	−8.32940e6	−0.501378	−0.250689	−	0.968068i	$-0.580657\pi$
$773$	−8.32940e6	−0.501378	−0.250689	+	0.968068i	$0.580657\pi$
$774$	0	0
$775$	1.34665e7	0.805381
$776$	0	0
$777$	−4.95648e6	−0.294524
$778$	0	0
$779$	−2.70490e7	−1.59701
$780$	0	0
$781$	3.96304e6	0.232488
$782$	0	0
$783$	−5.64504e6	−0.329051
$784$	0	0
$785$	2.91798e7	1.69009
$786$	0	0
$787$	−1.36523e7	−0.785719	−0.392860	−	0.919598i	$-0.628514\pi$
$787$	−1.36523e7	−0.785719	−0.392860	+	0.919598i	$0.628514\pi$
$788$	0	0
$789$	−1.41776e6	−0.0810793
$790$	0	0
$791$	−564048.	−0.0320535
$792$	0	0
$793$	−8.83440e6	−0.498877
$794$	0	0
$795$	−1.72953e7	−0.970532
$796$	0	0
$797$	8.54626e6	0.476574	0.238287	−	0.971195i	$-0.423414\pi$
$797$	8.54626e6	0.476574	0.238287	+	0.971195i	$0.423414\pi$
$798$	0	0
$799$	2.83495e7	1.57101
$800$	0	0
$801$	1.13031e7	0.622465
$802$	0	0
$803$	−605864.	−0.0331578
$804$	0	0
$805$	−326784.	−0.0177734
$806$	0	0
$807$	−3.58035e7	−1.93527
$808$	0	0
$809$	7.58484e6	0.407451	0.203725	−	0.979028i	$-0.434695\pi$
$809$	7.58484e6	0.407451	0.203725	+	0.979028i	$0.434695\pi$
$810$	0	0
$811$	6.18473e6	0.330194	0.165097	−	0.986277i	$-0.447206\pi$
$811$	6.18473e6	0.330194	0.165097	+	0.986277i	$0.447206\pi$
$812$	0	0
$813$	3.54723e7	1.88219
$814$	0	0
$815$	−867576.	−0.0457524
$816$	0	0
$817$	−2.79683e7	−1.46592
$818$	0	0
$819$	−1.80110e6	−0.0938273
$820$	0	0
$821$	2.78102e6	0.143995	0.0719973	−	0.997405i	$-0.477063\pi$
$821$	2.78102e6	0.143995	0.0719973	+	0.997405i	$0.477063\pi$
$822$	0	0
$823$	−1.63895e7	−0.843461	−0.421731	−	0.906721i	$-0.638577\pi$
$823$	−1.63895e7	−0.843461	−0.421731	+	0.906721i	$0.638577\pi$
$824$	0	0
$825$	5.83048e6	0.298242
$826$	0	0
$827$	2.29511e7	1.16692	0.583459	−	0.812142i	$-0.301699\pi$
$827$	2.29511e7	1.16692	0.583459	+	0.812142i	$0.301699\pi$
$828$	0	0
$829$	3.50136e6	0.176950	0.0884750	−	0.996078i	$-0.471801\pi$
$829$	3.50136e6	0.176950	0.0884750	+	0.996078i	$0.471801\pi$
$830$	0	0
$831$	5.50900e6	0.276739
$832$	0	0
$833$	1.94447e7	0.970934
$834$	0	0
$835$	4.08427e7	2.02721
$836$	0	0
$837$	−9.85216e6	−0.486091
$838$	0	0
$839$	−5.29668e6	−0.259776	−0.129888	−	0.991529i	$-0.541462\pi$
$839$	−5.29668e6	−0.259776	−0.129888	+	0.991529i	$0.541462\pi$
$840$	0	0
$841$	−9.73962e6	−0.474845
$842$	0	0
$843$	1.18834e7	0.575933
$844$	0	0
$845$	−1.05679e7	−0.509150
$846$	0	0
$847$	−3.49620e6	−0.167451
$848$	0	0
$849$	2.18486e7	1.04029
$850$	0	0
$851$	1.89998e6	0.0899344
$852$	0	0
$853$	2.02948e7	0.955021	0.477511	−	0.878626i	$-0.341539\pi$
$853$	2.02948e7	0.955021	0.477511	+	0.878626i	$0.341539\pi$
$854$	0	0
$855$	3.53652e7	1.65448
$856$	0	0
$857$	−4.82785e6	−0.224544	−0.112272	−	0.993678i	$-0.535813\pi$
$857$	−4.82785e6	−0.224544	−0.112272	+	0.993678i	$0.535813\pi$
$858$	0	0
$859$	−1.30210e7	−0.602092	−0.301046	−	0.953610i	$-0.597336\pi$
$859$	−1.30210e7	−0.602092	−0.301046	+	0.953610i	$0.597336\pi$
$860$	0	0
$861$	−4.26528e6	−0.196083
$862$	0	0
$863$	3.92387e7	1.79344	0.896721	−	0.442596i	$-0.145942\pi$
$863$	3.92387e7	1.79344	0.896721	+	0.442596i	$0.145942\pi$
$864$	0	0
$865$	−3.20342e7	−1.45570
$866$	0	0
$867$	306940.	0.0138677
$868$	0	0
$869$	−5.52544e6	−0.248209
$870$	0	0
$871$	7.42430e6	0.331596
$872$	0	0
$873$	7.67196e6	0.340699
$874$	0	0
$875$	−1.37462e6	−0.0606965
$876$	0	0
$877$	−1.34622e7	−0.591041	−0.295520	−	0.955336i	$-0.595493\pi$
$877$	−1.34622e7	−0.591041	−0.295520	+	0.955336i	$0.595493\pi$
$878$	0	0
$879$	−6.67308e6	−0.291309
$880$	0	0
$881$	−917710.	−0.0398351	−0.0199175	−	0.999802i	$-0.506340\pi$
$881$	−917710.	−0.0398351	−0.0199175	+	0.999802i	$0.506340\pi$
$882$	0	0
$883$	2.45488e7	1.05957	0.529784	−	0.848133i	$-0.322273\pi$
$883$	2.45488e7	1.05957	0.529784	+	0.848133i	$0.322273\pi$
$884$	0	0
$885$	2.49765e7	1.07195
$886$	0	0
$887$	1.61463e7	0.689070	0.344535	−	0.938773i	$-0.388037\pi$
$887$	1.61463e7	0.689070	0.344535	+	0.938773i	$0.388037\pi$
$888$	0	0
$889$	2.27021e6	0.0963410
$890$	0	0
$891$	−8.99632e6	−0.379639
$892$	0	0
$893$	−7.20332e7	−3.02276
$894$	0	0
$895$	4.14119e7	1.72809
$896$	0	0
$897$	1.75904e6	0.0729953
$898$	0	0
$899$	1.87993e7	0.775787
$900$	0	0
$901$	1.39998e7	0.574527
$902$	0	0
$903$	−4.41024e6	−0.179988
$904$	0	0
$905$	−4.47485e7	−1.81617
$906$	0	0
$907$	−2.03361e7	−0.820824	−0.410412	−	0.911900i	$-0.634615\pi$
$907$	−2.03361e7	−0.820824	−0.410412	+	0.911900i	$0.634615\pi$
$908$	0	0
$909$	−8.10214e6	−0.325230
$910$	0	0
$911$	−1.07726e7	−0.430054	−0.215027	−	0.976608i	$-0.568984\pi$
$911$	−1.07726e7	−0.430054	−0.215027	+	0.976608i	$0.568984\pi$
$912$	0	0
$913$	8.35314e6	0.331644
$914$	0	0
$915$	2.73534e7	1.08009
$916$	0	0
$917$	1.68701e6	0.0662512
$918$	0	0
$919$	−4.18566e7	−1.63484	−0.817419	−	0.576043i	$-0.804596\pi$
$919$	−4.18566e7	−1.63484	−0.817419	+	0.576043i	$0.804596\pi$
$920$	0	0
$921$	2.11994e7	0.823522
$922$	0	0
$923$	−1.52769e7	−0.590242
$924$	0	0
$925$	−2.42764e7	−0.932890
$926$	0	0
$927$	−2.83266e7	−1.08267
$928$	0	0
$929$	2.99845e7	1.13988	0.569939	−	0.821687i	$-0.306967\pi$
$929$	2.99845e7	1.13988	0.569939	+	0.821687i	$0.306967\pi$
$930$	0	0
$931$	−4.94072e7	−1.86817
$932$	0	0
$933$	2.67298e7	1.00529
$934$	0	0
$935$	−1.09928e7	−0.411227
$936$	0	0
$937$	1.42402e7	0.529867	0.264934	−	0.964267i	$-0.414650\pi$
$937$	1.42402e7	0.529867	0.264934	+	0.964267i	$0.414650\pi$
$938$	0	0
$939$	3.28837e7	1.21707
$940$	0	0
$941$	4.14546e7	1.52615	0.763077	−	0.646307i	$-0.223687\pi$
$941$	4.14546e7	1.52615	0.763077	+	0.646307i	$0.223687\pi$
$942$	0	0
$943$	1.63502e6	0.0598749
$944$	0	0
$945$	−3.05472e6	−0.111274
$946$	0	0
$947$	−1.54079e7	−0.558300	−0.279150	−	0.960248i	$-0.590053\pi$
$947$	−1.54079e7	−0.558300	−0.279150	+	0.960248i	$0.590053\pi$
$948$	0	0
$949$	2.33551e6	0.0841813
$950$	0	0
$951$	3.44740e7	1.23606
$952$	0	0
$953$	−2.06328e7	−0.735912	−0.367956	−	0.929843i	$-0.619942\pi$
$953$	−2.06328e7	−0.735912	−0.367956	+	0.929843i	$0.619942\pi$
$954$	0	0
$955$	3.02772e7	1.07426
$956$	0	0
$957$	8.13936e6	0.287283
$958$	0	0
$959$	6.65496e6	0.233668
$960$	0	0
$961$	4.18083e6	0.146034
$962$	0	0
$963$	−1.03149e7	−0.358426
$964$	0	0
$965$	4.00241e7	1.38358
$966$	0	0
$967$	−1.18724e7	−0.408294	−0.204147	−	0.978940i	$-0.565442\pi$
$967$	−1.18724e7	−0.408294	−0.204147	+	0.978940i	$0.565442\pi$
$968$	0	0
$969$	−7.29342e7	−2.49530
$970$	0	0
$971$	1.53222e6	0.0521523	0.0260761	−	0.999660i	$-0.491699\pi$
$971$	1.53222e6	0.0521523	0.0260761	+	0.999660i	$0.491699\pi$
$972$	0	0
$973$	−3.12739e6	−0.105901
$974$	0	0
$975$	−2.24756e7	−0.757180
$976$	0	0
$977$	1.74321e7	0.584269	0.292135	−	0.956377i	$-0.405635\pi$
$977$	1.74321e7	0.584269	0.292135	+	0.956377i	$0.405635\pi$
$978$	0	0
$979$	8.92726e6	0.297688
$980$	0	0
$981$	1.76948e7	0.587049
$982$	0	0
$983$	−2.23270e6	−0.0736963	−0.0368482	−	0.999321i	$-0.511732\pi$
$983$	−2.23270e6	−0.0736963	−0.0368482	+	0.999321i	$0.511732\pi$
$984$	0	0
$985$	4.66125e7	1.53078
$986$	0	0
$987$	−1.13587e7	−0.371139
$988$	0	0
$989$	1.69059e6	0.0549602
$990$	0	0
$991$	−2.22501e7	−0.719693	−0.359847	−	0.933011i	$-0.617171\pi$
$991$	−2.22501e7	−0.719693	−0.359847	+	0.933011i	$0.617171\pi$
$992$	0	0
$993$	5.49926e7	1.76983
$994$	0	0
$995$	−2.09456e7	−0.670709
$996$	0	0
$997$	−5.32662e7	−1.69712	−0.848562	−	0.529095i	$-0.822531\pi$
$997$	−5.32662e7	−1.69712	−0.848562	+	0.529095i	$0.822531\pi$
$998$	0	0
$999$	1.77607e7	0.563050

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.6.a.g.1.1		1
3.2	odd	2		576.6.a.h.1.1		1
4.3	odd	2		64.6.a.a.1.1		1
8.3	odd	2		8.6.a.a.1.1	✓	1
8.5	even	2		16.6.a.a.1.1		1
12.11	even	2		576.6.a.g.1.1		1
16.3	odd	4		256.6.b.f.129.1		2
16.5	even	4		256.6.b.d.129.1		2
16.11	odd	4		256.6.b.f.129.2		2
16.13	even	4		256.6.b.d.129.2		2
24.5	odd	2		144.6.a.k.1.1		1
24.11	even	2		72.6.a.f.1.1		1
40.3	even	4		200.6.c.a.49.2		2
40.13	odd	4		400.6.c.d.49.1		2
40.19	odd	2		200.6.a.a.1.1		1
40.27	even	4		200.6.c.a.49.1		2
40.29	even	2		400.6.a.l.1.1		1
40.37	odd	4		400.6.c.d.49.2		2
56.3	even	6		392.6.i.e.177.1		2
56.11	odd	6		392.6.i.b.177.1		2
56.13	odd	2		784.6.a.l.1.1		1
56.19	even	6		392.6.i.e.361.1		2
56.27	even	2		392.6.a.b.1.1		1
56.51	odd	6		392.6.i.b.361.1		2
88.43	even	2		968.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.6.a.a.1.1	✓	1	8.3	odd	2
16.6.a.a.1.1		1	8.5	even	2
64.6.a.a.1.1		1	4.3	odd	2
64.6.a.g.1.1		1	1.1	even	1	trivial
72.6.a.f.1.1		1	24.11	even	2
144.6.a.k.1.1		1	24.5	odd	2
200.6.a.a.1.1		1	40.19	odd	2
200.6.c.a.49.1		2	40.27	even	4
200.6.c.a.49.2		2	40.3	even	4
256.6.b.d.129.1		2	16.5	even	4
256.6.b.d.129.2		2	16.13	even	4
256.6.b.f.129.1		2	16.3	odd	4
256.6.b.f.129.2		2	16.11	odd	4
392.6.a.b.1.1		1	56.27	even	2
392.6.i.b.177.1		2	56.11	odd	6
392.6.i.b.361.1		2	56.51	odd	6
392.6.i.e.177.1		2	56.3	even	6
392.6.i.e.361.1		2	56.19	even	6
400.6.a.l.1.1		1	40.29	even	2
400.6.c.d.49.1		2	40.13	odd	4
400.6.c.d.49.2		2	40.37	odd	4
576.6.a.g.1.1		1	12.11	even	2
576.6.a.h.1.1		1	3.2	odd	2
784.6.a.l.1.1		1	56.13	odd	2
968.6.a.a.1.1		1	88.43	even	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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