LMFDB - Embedded newform 176.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,6,Mod(1,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("176.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	176.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:	$28.2275522871$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	176.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-7.00000 q^{3} -79.0000 q^{5} +50.0000 q^{7} -194.000 q^{9} +O(q^{10})$

$q-7.00000 q^{3} -79.0000 q^{5} +50.0000 q^{7} -194.000 q^{9} -121.000 q^{11} -380.000 q^{13} +553.000 q^{15} -1154.00 q^{17} +1824.00 q^{19} -350.000 q^{21} -3591.00 q^{23} +3116.00 q^{25} +3059.00 q^{27} +8032.00 q^{29} +2945.00 q^{31} +847.000 q^{33} -3950.00 q^{35} +6979.00 q^{37} +2660.00 q^{39} -520.000 q^{41} +2486.00 q^{43} +15326.0 q^{45} +6920.00 q^{47} -14307.0 q^{49} +8078.00 q^{51} -13718.0 q^{53} +9559.00 q^{55} -12768.0 q^{57} +31779.0 q^{59} +34156.0 q^{61} -9700.00 q^{63} +30020.0 q^{65} +61503.0 q^{67} +25137.0 q^{69} +14971.0 q^{71} -36444.0 q^{73} -21812.0 q^{75} -6050.00 q^{77} +28538.0 q^{79} +25729.0 q^{81} -77482.0 q^{83} +91166.0 q^{85} -56224.0 q^{87} +36271.0 q^{89} -19000.0 q^{91} -20615.0 q^{93} -144096. q^{95} -49799.0 q^{97} +23474.0 q^{99} +O(q^{100})$

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
$3$	−7.00000	−0.449050	−0.224525	−	0.974468i	$-0.572083\pi$
$3$	−7.00000	−0.449050	−0.224525	+	0.974468i	$0.572083\pi$
$4$	0	0
$5$	−79.0000	−1.41319	−0.706597	−	0.707616i	$-0.749771\pi$
$5$	−79.0000	−1.41319	−0.706597	+	0.707616i	$0.749771\pi$
$6$	0	0
$7$	50.0000	0.385678	0.192839	−	0.981230i	$-0.438230\pi$
$7$	50.0000	0.385678	0.192839	+	0.981230i	$0.438230\pi$
$8$	0	0
$9$	−194.000	−0.798354
$10$	0	0
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	0	0
$13$	−380.000	−0.623627	−0.311814	−	0.950143i	$-0.600936\pi$
$13$	−380.000	−0.623627	−0.311814	+	0.950143i	$0.600936\pi$
$14$	0	0
$15$	553.000	0.634595
$16$	0	0
$17$	−1154.00	−0.968464	−0.484232	−	0.874940i	$-0.660901\pi$
$17$	−1154.00	−0.968464	−0.484232	+	0.874940i	$0.660901\pi$
$18$	0	0
$19$	1824.00	1.15915	0.579577	−	0.814918i	$-0.303218\pi$
$19$	1824.00	1.15915	0.579577	+	0.814918i	$0.303218\pi$
$20$	0	0
$21$	−350.000	−0.173189
$22$	0	0
$23$	−3591.00	−1.41545	−0.707727	−	0.706486i	$-0.750279\pi$
$23$	−3591.00	−1.41545	−0.707727	+	0.706486i	$0.750279\pi$
$24$	0	0
$25$	3116.00	0.997120
$26$	0	0
$27$	3059.00	0.807551
$28$	0	0
$29$	8032.00	1.77349	0.886745	−	0.462259i	$-0.152961\pi$
$29$	8032.00	1.77349	0.886745	+	0.462259i	$0.152961\pi$
$30$	0	0
$31$	2945.00	0.550403	0.275202	−	0.961387i	$-0.411255\pi$
$31$	2945.00	0.550403	0.275202	+	0.961387i	$0.411255\pi$
$32$	0	0
$33$	847.000	0.135394
$34$	0	0
$35$	−3950.00	−0.545038
$36$	0	0
$37$	6979.00	0.838087	0.419043	−	0.907966i	$-0.362366\pi$
$37$	6979.00	0.838087	0.419043	+	0.907966i	$0.362366\pi$
$38$	0	0
$39$	2660.00	0.280040
$40$	0	0
$41$	−520.000	−0.0483107	−0.0241554	−	0.999708i	$-0.507690\pi$
$41$	−520.000	−0.0483107	−0.0241554	+	0.999708i	$0.507690\pi$
$42$	0	0
$43$	2486.00	0.205036	0.102518	−	0.994731i	$-0.467310\pi$
$43$	2486.00	0.205036	0.102518	+	0.994731i	$0.467310\pi$
$44$	0	0
$45$	15326.0	1.12823
$46$	0	0
$47$	6920.00	0.456942	0.228471	−	0.973551i	$-0.426627\pi$
$47$	6920.00	0.456942	0.228471	+	0.973551i	$0.426627\pi$
$48$	0	0
$49$	−14307.0	−0.851252
$50$	0	0
$51$	8078.00	0.434889
$52$	0	0
$53$	−13718.0	−0.670812	−0.335406	−	0.942074i	$-0.608874\pi$
$53$	−13718.0	−0.670812	−0.335406	+	0.942074i	$0.608874\pi$
$54$	0	0
$55$	9559.00	0.426094
$56$	0	0
$57$	−12768.0	−0.520518
$58$	0	0
$59$	31779.0	1.18853	0.594265	−	0.804269i	$-0.297443\pi$
$59$	31779.0	1.18853	0.594265	+	0.804269i	$0.297443\pi$
$60$	0	0
$61$	34156.0	1.17528	0.587641	−	0.809121i	$-0.300057\pi$
$61$	34156.0	1.17528	0.587641	+	0.809121i	$0.300057\pi$
$62$	0	0
$63$	−9700.00	−0.307908
$64$	0	0
$65$	30020.0	0.881307
$66$	0	0
$67$	61503.0	1.67382	0.836911	−	0.547339i	$-0.184359\pi$
$67$	61503.0	1.67382	0.836911	+	0.547339i	$0.184359\pi$
$68$	0	0
$69$	25137.0	0.635610
$70$	0	0
$71$	14971.0	0.352456	0.176228	−	0.984349i	$-0.443610\pi$
$71$	14971.0	0.352456	0.176228	+	0.984349i	$0.443610\pi$
$72$	0	0
$73$	−36444.0	−0.800422	−0.400211	−	0.916423i	$-0.631063\pi$
$73$	−36444.0	−0.800422	−0.400211	+	0.916423i	$0.631063\pi$
$74$	0	0
$75$	−21812.0	−0.447757
$76$	0	0
$77$	−6050.00	−0.116286
$78$	0	0
$79$	28538.0	0.514465	0.257232	−	0.966350i	$-0.417189\pi$
$79$	28538.0	0.514465	0.257232	+	0.966350i	$0.417189\pi$
$80$	0	0
$81$	25729.0	0.435723
$82$	0	0
$83$	−77482.0	−1.23454	−0.617271	−	0.786751i	$-0.711762\pi$
$83$	−77482.0	−1.23454	−0.617271	+	0.786751i	$0.711762\pi$
$84$	0	0
$85$	91166.0	1.36863
$86$	0	0
$87$	−56224.0	−0.796386
$88$	0	0
$89$	36271.0	0.485383	0.242691	−	0.970104i	$-0.421970\pi$
$89$	36271.0	0.485383	0.242691	+	0.970104i	$0.421970\pi$
$90$	0	0
$91$	−19000.0	−0.240519
$92$	0	0
$93$	−20615.0	−0.247159
$94$	0	0
$95$	−144096.	−1.63811
$96$	0	0
$97$	−49799.0	−0.537392	−0.268696	−	0.963225i	$-0.586593\pi$
$97$	−49799.0	−0.537392	−0.268696	+	0.963225i	$0.586593\pi$
$98$	0	0
$99$	23474.0	0.240713
$100$	0	0
$101$	−153406.	−1.49637	−0.748185	−	0.663490i	$-0.769074\pi$
$101$	−153406.	−1.49637	−0.748185	+	0.663490i	$0.769074\pi$
$102$	0	0
$103$	134720.	1.25124	0.625618	−	0.780130i	$-0.284847\pi$
$103$	134720.	1.25124	0.625618	+	0.780130i	$0.284847\pi$
$104$	0	0
$105$	27650.0	0.244750
$106$	0	0
$107$	−169218.	−1.42885	−0.714426	−	0.699711i	$-0.753312\pi$
$107$	−169218.	−1.42885	−0.714426	+	0.699711i	$0.753312\pi$
$108$	0	0
$109$	−233206.	−1.88007	−0.940034	−	0.341081i	$-0.889207\pi$
$109$	−233206.	−1.88007	−0.940034	+	0.341081i	$0.889207\pi$
$110$	0	0
$111$	−48853.0	−0.376343
$112$	0	0
$113$	94329.0	0.694943	0.347471	−	0.937691i	$-0.387040\pi$
$113$	94329.0	0.694943	0.347471	+	0.937691i	$0.387040\pi$
$114$	0	0
$115$	283689.	2.00031
$116$	0	0
$117$	73720.0	0.497875
$118$	0	0
$119$	−57700.0	−0.373515
$120$	0	0
$121$	14641.0	0.0909091
$122$	0	0
$123$	3640.00	0.0216939
$124$	0	0
$125$	711.000	0.00407000
$126$	0	0
$127$	259480.	1.42756	0.713780	−	0.700370i	$-0.246981\pi$
$127$	259480.	1.42756	0.713780	+	0.700370i	$0.246981\pi$
$128$	0	0
$129$	−17402.0	−0.0920714
$130$	0	0
$131$	85410.0	0.434841	0.217420	−	0.976078i	$-0.430236\pi$
$131$	85410.0	0.434841	0.217420	+	0.976078i	$0.430236\pi$
$132$	0	0
$133$	91200.0	0.447060
$134$	0	0
$135$	−241661.	−1.14123
$136$	0	0
$137$	−427703.	−1.94689	−0.973444	−	0.228926i	$-0.926479\pi$
$137$	−427703.	−1.94689	−0.973444	+	0.228926i	$0.926479\pi$
$138$	0	0
$139$	−309690.	−1.35953	−0.679767	−	0.733428i	$-0.737919\pi$
$139$	−309690.	−1.35953	−0.679767	+	0.733428i	$0.737919\pi$
$140$	0	0
$141$	−48440.0	−0.205190
$142$	0	0
$143$	45980.0	0.188031
$144$	0	0
$145$	−634528.	−2.50629
$146$	0	0
$147$	100149.	0.382255
$148$	0	0
$149$	449846.	1.65996	0.829981	−	0.557792i	$-0.188351\pi$
$149$	449846.	1.65996	0.829981	+	0.557792i	$0.188351\pi$
$150$	0	0
$151$	−405074.	−1.44575	−0.722873	−	0.690981i	$-0.757179\pi$
$151$	−405074.	−1.44575	−0.722873	+	0.690981i	$0.757179\pi$
$152$	0	0
$153$	223876.	0.773177
$154$	0	0
$155$	−232655.	−0.777827
$156$	0	0
$157$	339321.	1.09866	0.549328	−	0.835607i	$-0.314884\pi$
$157$	339321.	1.09866	0.549328	+	0.835607i	$0.314884\pi$
$158$	0	0
$159$	96026.0	0.301228
$160$	0	0
$161$	−179550.	−0.545910
$162$	0	0
$163$	−271396.	−0.800082	−0.400041	−	0.916497i	$-0.631004\pi$
$163$	−271396.	−0.800082	−0.400041	+	0.916497i	$0.631004\pi$
$164$	0	0
$165$	−66913.0	−0.191338
$166$	0	0
$167$	−72468.0	−0.201074	−0.100537	−	0.994933i	$-0.532056\pi$
$167$	−72468.0	−0.201074	−0.100537	+	0.994933i	$0.532056\pi$
$168$	0	0
$169$	−226893.	−0.611089
$170$	0	0
$171$	−353856.	−0.925414
$172$	0	0
$173$	479226.	1.21738	0.608689	−	0.793409i	$-0.291696\pi$
$173$	479226.	1.21738	0.608689	+	0.793409i	$0.291696\pi$
$174$	0	0
$175$	155800.	0.384567
$176$	0	0
$177$	−222453.	−0.533710
$178$	0	0
$179$	40935.0	0.0954910	0.0477455	−	0.998860i	$-0.484796\pi$
$179$	40935.0	0.0954910	0.0477455	+	0.998860i	$0.484796\pi$
$180$	0	0
$181$	−90169.0	−0.204579	−0.102289	−	0.994755i	$-0.532617\pi$
$181$	−90169.0	−0.204579	−0.102289	+	0.994755i	$0.532617\pi$
$182$	0	0
$183$	−239092.	−0.527761
$184$	0	0
$185$	−551341.	−1.18438
$186$	0	0
$187$	139634.	0.292003
$188$	0	0
$189$	152950.	0.311455
$190$	0	0
$191$	260375.	0.516435	0.258218	−	0.966087i	$-0.416865\pi$
$191$	260375.	0.516435	0.258218	+	0.966087i	$0.416865\pi$
$192$	0	0
$193$	524324.	1.01323	0.506613	−	0.862173i	$-0.330897\pi$
$193$	524324.	1.01323	0.506613	+	0.862173i	$0.330897\pi$
$194$	0	0
$195$	−210140.	−0.395751
$196$	0	0
$197$	759582.	1.39447	0.697235	−	0.716843i	$-0.254413\pi$
$197$	759582.	1.39447	0.697235	+	0.716843i	$0.254413\pi$
$198$	0	0
$199$	882736.	1.58015	0.790075	−	0.613011i	$-0.210042\pi$
$199$	882736.	1.58015	0.790075	+	0.613011i	$0.210042\pi$
$200$	0	0
$201$	−430521.	−0.751630
$202$	0	0
$203$	401600.	0.683996
$204$	0	0
$205$	41080.0	0.0682725
$206$	0	0
$207$	696654.	1.13003
$208$	0	0
$209$	−220704.	−0.349498
$210$	0	0
$211$	1.15285e6	1.78266	0.891328	−	0.453360i	$-0.149775\pi$
$211$	1.15285e6	1.78266	0.891328	+	0.453360i	$0.149775\pi$
$212$	0	0
$213$	−104797.	−0.158270
$214$	0	0
$215$	−196394.	−0.289756
$216$	0	0
$217$	147250.	0.212278
$218$	0	0
$219$	255108.	0.359430
$220$	0	0
$221$	438520.	0.603961
$222$	0	0
$223$	65893.0	0.0887314	0.0443657	−	0.999015i	$-0.485873\pi$
$223$	65893.0	0.0887314	0.0443657	+	0.999015i	$0.485873\pi$
$224$	0	0
$225$	−604504.	−0.796055
$226$	0	0
$227$	314526.	0.405128	0.202564	−	0.979269i	$-0.435073\pi$
$227$	314526.	0.405128	0.202564	+	0.979269i	$0.435073\pi$
$228$	0	0
$229$	1.03846e6	1.30859	0.654293	−	0.756241i	$-0.272966\pi$
$229$	1.03846e6	1.30859	0.654293	+	0.756241i	$0.272966\pi$
$230$	0	0
$231$	42350.0	0.0522184
$232$	0	0
$233$	509976.	0.615403	0.307702	−	0.951483i	$-0.400440\pi$
$233$	509976.	0.615403	0.307702	+	0.951483i	$0.400440\pi$
$234$	0	0
$235$	−546680.	−0.645749
$236$	0	0
$237$	−199766.	−0.231021
$238$	0	0
$239$	444494.	0.503351	0.251676	−	0.967812i	$-0.419018\pi$
$239$	444494.	0.503351	0.251676	+	0.967812i	$0.419018\pi$
$240$	0	0
$241$	−283464.	−0.314380	−0.157190	−	0.987568i	$-0.550244\pi$
$241$	−283464.	−0.314380	−0.157190	+	0.987568i	$0.550244\pi$
$242$	0	0
$243$	−923440.	−1.00321
$244$	0	0
$245$	1.13025e6	1.20299
$246$	0	0
$247$	−693120.	−0.722880
$248$	0	0
$249$	542374.	0.554371
$250$	0	0
$251$	773807.	0.775262	0.387631	−	0.921815i	$-0.373294\pi$
$251$	773807.	0.775262	0.387631	+	0.921815i	$0.373294\pi$
$252$	0	0
$253$	434511.	0.426775
$254$	0	0
$255$	−638162.	−0.614583
$256$	0	0
$257$	−387714.	−0.366167	−0.183083	−	0.983097i	$-0.558608\pi$
$257$	−387714.	−0.366167	−0.183083	+	0.983097i	$0.558608\pi$
$258$	0	0
$259$	348950.	0.323232
$260$	0	0
$261$	−1.55821e6	−1.41587
$262$	0	0
$263$	197602.	0.176158	0.0880789	−	0.996113i	$-0.471927\pi$
$263$	197602.	0.176158	0.0880789	+	0.996113i	$0.471927\pi$
$264$	0	0
$265$	1.08372e6	0.947989
$266$	0	0
$267$	−253897.	−0.217961
$268$	0	0
$269$	−262694.	−0.221345	−0.110672	−	0.993857i	$-0.535300\pi$
$269$	−262694.	−0.221345	−0.110672	+	0.993857i	$0.535300\pi$
$270$	0	0
$271$	159068.	0.131571	0.0657854	−	0.997834i	$-0.479045\pi$
$271$	159068.	0.131571	0.0657854	+	0.997834i	$0.479045\pi$
$272$	0	0
$273$	133000.	0.108005
$274$	0	0
$275$	−377036.	−0.300643
$276$	0	0
$277$	1.29385e6	1.01318	0.506589	−	0.862188i	$-0.330906\pi$
$277$	1.29385e6	1.01318	0.506589	+	0.862188i	$0.330906\pi$
$278$	0	0
$279$	−571330.	−0.439417
$280$	0	0
$281$	−1.78114e6	−1.34565	−0.672824	−	0.739802i	$-0.734919\pi$
$281$	−1.78114e6	−1.34565	−0.672824	+	0.739802i	$0.734919\pi$
$282$	0	0
$283$	−1.98279e6	−1.47167	−0.735835	−	0.677161i	$-0.763210\pi$
$283$	−1.98279e6	−1.47167	−0.735835	+	0.677161i	$0.763210\pi$
$284$	0	0
$285$	1.00867e6	0.735593
$286$	0	0
$287$	−26000.0	−0.0186324
$288$	0	0
$289$	−88141.0	−0.0620774
$290$	0	0
$291$	348593.	0.241316
$292$	0	0
$293$	578360.	0.393577	0.196788	−	0.980446i	$-0.436949\pi$
$293$	578360.	0.393577	0.196788	+	0.980446i	$0.436949\pi$
$294$	0	0
$295$	−2.51054e6	−1.67962
$296$	0	0
$297$	−370139.	−0.243486
$298$	0	0
$299$	1.36458e6	0.882716
$300$	0	0
$301$	124300.	0.0790779
$302$	0	0
$303$	1.07384e6	0.671945
$304$	0	0
$305$	−2.69832e6	−1.66090
$306$	0	0
$307$	3.07602e6	1.86270	0.931352	−	0.364120i	$-0.118630\pi$
$307$	3.07602e6	1.86270	0.931352	+	0.364120i	$0.118630\pi$
$308$	0	0
$309$	−943040.	−0.561868
$310$	0	0
$311$	3.13757e6	1.83947	0.919735	−	0.392540i	$-0.128403\pi$
$311$	3.13757e6	1.83947	0.919735	+	0.392540i	$0.128403\pi$
$312$	0	0
$313$	2.61784e6	1.51037	0.755183	−	0.655514i	$-0.227548\pi$
$313$	2.61784e6	1.51037	0.755183	+	0.655514i	$0.227548\pi$
$314$	0	0
$315$	766300.	0.435133
$316$	0	0
$317$	−2.49220e6	−1.39294	−0.696472	−	0.717584i	$-0.745248\pi$
$317$	−2.49220e6	−1.39294	−0.696472	+	0.717584i	$0.745248\pi$
$318$	0	0
$319$	−971872.	−0.534727
$320$	0	0
$321$	1.18453e6	0.641626
$322$	0	0
$323$	−2.10490e6	−1.12260
$324$	0	0
$325$	−1.18408e6	−0.621831
$326$	0	0
$327$	1.63244e6	0.844245
$328$	0	0
$329$	346000.	0.176233
$330$	0	0
$331$	2.70125e6	1.35517	0.677586	−	0.735443i	$-0.263026\pi$
$331$	2.70125e6	1.35517	0.677586	+	0.735443i	$0.263026\pi$
$332$	0	0
$333$	−1.35393e6	−0.669090
$334$	0	0
$335$	−4.85874e6	−2.36544
$336$	0	0
$337$	−1.42610e6	−0.684031	−0.342016	−	0.939694i	$-0.611110\pi$
$337$	−1.42610e6	−0.684031	−0.342016	+	0.939694i	$0.611110\pi$
$338$	0	0
$339$	−660303.	−0.312064
$340$	0	0
$341$	−356345.	−0.165953
$342$	0	0
$343$	−1.55570e6	−0.713987
$344$	0	0
$345$	−1.98582e6	−0.898241
$346$	0	0
$347$	−2.86374e6	−1.27676	−0.638381	−	0.769721i	$-0.720396\pi$
$347$	−2.86374e6	−1.27676	−0.638381	+	0.769721i	$0.720396\pi$
$348$	0	0
$349$	296350.	0.130239	0.0651195	−	0.997877i	$-0.479257\pi$
$349$	296350.	0.130239	0.0651195	+	0.997877i	$0.479257\pi$
$350$	0	0
$351$	−1.16242e6	−0.503611
$352$	0	0
$353$	−2.12114e6	−0.906010	−0.453005	−	0.891508i	$-0.649648\pi$
$353$	−2.12114e6	−0.906010	−0.453005	+	0.891508i	$0.649648\pi$
$354$	0	0
$355$	−1.18271e6	−0.498089
$356$	0	0
$357$	403900.	0.167727
$358$	0	0
$359$	3.47512e6	1.42310	0.711548	−	0.702638i	$-0.247994\pi$
$359$	3.47512e6	1.42310	0.711548	+	0.702638i	$0.247994\pi$
$360$	0	0
$361$	850877.	0.343636
$362$	0	0
$363$	−102487.	−0.0408227
$364$	0	0
$365$	2.87908e6	1.13115
$366$	0	0
$367$	−1.56190e6	−0.605322	−0.302661	−	0.953098i	$-0.597875\pi$
$367$	−1.56190e6	−0.605322	−0.302661	+	0.953098i	$0.597875\pi$
$368$	0	0
$369$	100880.	0.0385691
$370$	0	0
$371$	−685900.	−0.258718
$372$	0	0
$373$	1.93773e6	0.721144	0.360572	−	0.932731i	$-0.382581\pi$
$373$	1.93773e6	0.721144	0.360572	+	0.932731i	$0.382581\pi$
$374$	0	0
$375$	−4977.00	−0.00182764
$376$	0	0
$377$	−3.05216e6	−1.10600
$378$	0	0
$379$	−3.07495e6	−1.09961	−0.549806	−	0.835292i	$-0.685298\pi$
$379$	−3.07495e6	−1.09961	−0.549806	+	0.835292i	$0.685298\pi$
$380$	0	0
$381$	−1.81636e6	−0.641046
$382$	0	0
$383$	−4.31553e6	−1.50327	−0.751635	−	0.659579i	$-0.770734\pi$
$383$	−4.31553e6	−1.50327	−0.751635	+	0.659579i	$0.770734\pi$
$384$	0	0
$385$	477950.	0.164335
$386$	0	0
$387$	−482284.	−0.163691
$388$	0	0
$389$	2.36251e6	0.791590	0.395795	−	0.918339i	$-0.370469\pi$
$389$	2.36251e6	0.791590	0.395795	+	0.918339i	$0.370469\pi$
$390$	0	0
$391$	4.14401e6	1.37082
$392$	0	0
$393$	−597870.	−0.195265
$394$	0	0
$395$	−2.25450e6	−0.727039
$396$	0	0
$397$	1.77598e6	0.565539	0.282769	−	0.959188i	$-0.408747\pi$
$397$	1.77598e6	0.565539	0.282769	+	0.959188i	$0.408747\pi$
$398$	0	0
$399$	−638400.	−0.200752
$400$	0	0
$401$	1.56967e6	0.487468	0.243734	−	0.969842i	$-0.421628\pi$
$401$	1.56967e6	0.487468	0.243734	+	0.969842i	$0.421628\pi$
$402$	0	0
$403$	−1.11910e6	−0.343247
$404$	0	0
$405$	−2.03259e6	−0.615761
$406$	0	0
$407$	−844459.	−0.252693
$408$	0	0
$409$	1.29485e6	0.382746	0.191373	−	0.981517i	$-0.438706\pi$
$409$	1.29485e6	0.382746	0.191373	+	0.981517i	$0.438706\pi$
$410$	0	0
$411$	2.99392e6	0.874250
$412$	0	0
$413$	1.58895e6	0.458390
$414$	0	0
$415$	6.12108e6	1.74465
$416$	0	0
$417$	2.16783e6	0.610499
$418$	0	0
$419$	−272916.	−0.0759441	−0.0379720	−	0.999279i	$-0.512090\pi$
$419$	−272916.	−0.0759441	−0.0379720	+	0.999279i	$0.512090\pi$
$420$	0	0
$421$	−2.61801e6	−0.719890	−0.359945	−	0.932974i	$-0.617205\pi$
$421$	−2.61801e6	−0.719890	−0.359945	+	0.932974i	$0.617205\pi$
$422$	0	0
$423$	−1.34248e6	−0.364802
$424$	0	0
$425$	−3.59586e6	−0.965675
$426$	0	0
$427$	1.70780e6	0.453281
$428$	0	0
$429$	−321860.	−0.0844352
$430$	0	0
$431$	−2.81037e6	−0.728735	−0.364368	−	0.931255i	$-0.618715\pi$
$431$	−2.81037e6	−0.728735	−0.364368	+	0.931255i	$0.618715\pi$
$432$	0	0
$433$	5.98509e6	1.53409	0.767046	−	0.641593i	$-0.221726\pi$
$433$	5.98509e6	1.53409	0.767046	+	0.641593i	$0.221726\pi$
$434$	0	0
$435$	4.44170e6	1.12545
$436$	0	0
$437$	−6.54998e6	−1.64073
$438$	0	0
$439$	7.50486e6	1.85858	0.929290	−	0.369352i	$-0.120420\pi$
$439$	7.50486e6	1.85858	0.929290	+	0.369352i	$0.120420\pi$
$440$	0	0
$441$	2.77556e6	0.679601
$442$	0	0
$443$	−1.56806e6	−0.379624	−0.189812	−	0.981820i	$-0.560788\pi$
$443$	−1.56806e6	−0.379624	−0.189812	+	0.981820i	$0.560788\pi$
$444$	0	0
$445$	−2.86541e6	−0.685941
$446$	0	0
$447$	−3.14892e6	−0.745406
$448$	0	0
$449$	−4.04044e6	−0.945831	−0.472915	−	0.881108i	$-0.656798\pi$
$449$	−4.04044e6	−0.945831	−0.472915	+	0.881108i	$0.656798\pi$
$450$	0	0
$451$	62920.0	0.0145662
$452$	0	0
$453$	2.83552e6	0.649213
$454$	0	0
$455$	1.50100e6	0.339901
$456$	0	0
$457$	2.21132e6	0.495291	0.247645	−	0.968851i	$-0.420343\pi$
$457$	2.21132e6	0.495291	0.247645	+	0.968851i	$0.420343\pi$
$458$	0	0
$459$	−3.53009e6	−0.782084
$460$	0	0
$461$	−3.56735e6	−0.781795	−0.390898	−	0.920434i	$-0.627835\pi$
$461$	−3.56735e6	−0.781795	−0.390898	+	0.920434i	$0.627835\pi$
$462$	0	0
$463$	−747757.	−0.162109	−0.0810547	−	0.996710i	$-0.525829\pi$
$463$	−747757.	−0.162109	−0.0810547	+	0.996710i	$0.525829\pi$
$464$	0	0
$465$	1.62858e6	0.349283
$466$	0	0
$467$	5.44511e6	1.15535	0.577676	−	0.816266i	$-0.303960\pi$
$467$	5.44511e6	1.15535	0.577676	+	0.816266i	$0.303960\pi$
$468$	0	0
$469$	3.07515e6	0.645556
$470$	0	0
$471$	−2.37525e6	−0.493352
$472$	0	0
$473$	−300806.	−0.0618207
$474$	0	0
$475$	5.68358e6	1.15581
$476$	0	0
$477$	2.66129e6	0.535546
$478$	0	0
$479$	6.22046e6	1.23875	0.619375	−	0.785095i	$-0.287386\pi$
$479$	6.22046e6	1.23875	0.619375	+	0.785095i	$0.287386\pi$
$480$	0	0
$481$	−2.65202e6	−0.522654
$482$	0	0
$483$	1.25685e6	0.245141
$484$	0	0
$485$	3.93412e6	0.759440
$486$	0	0
$487$	3.34398e6	0.638913	0.319457	−	0.947601i	$-0.396500\pi$
$487$	3.34398e6	0.638913	0.319457	+	0.947601i	$0.396500\pi$
$488$	0	0
$489$	1.89977e6	0.359277
$490$	0	0
$491$	−5.58646e6	−1.04576	−0.522881	−	0.852406i	$-0.675143\pi$
$491$	−5.58646e6	−1.04576	−0.522881	+	0.852406i	$0.675143\pi$
$492$	0	0
$493$	−9.26893e6	−1.71756
$494$	0	0
$495$	−1.85445e6	−0.340174
$496$	0	0
$497$	748550.	0.135935
$498$	0	0
$499$	8.29348e6	1.49103	0.745514	−	0.666490i	$-0.232204\pi$
$499$	8.29348e6	1.49103	0.745514	+	0.666490i	$0.232204\pi$
$500$	0	0
$501$	507276.	0.0902922
$502$	0	0
$503$	−5.29951e6	−0.933933	−0.466967	−	0.884275i	$-0.654653\pi$
$503$	−5.29951e6	−0.933933	−0.466967	+	0.884275i	$0.654653\pi$
$504$	0	0
$505$	1.21191e7	2.11466
$506$	0	0
$507$	1.58825e6	0.274410
$508$	0	0
$509$	24415.0	0.00417698	0.00208849	−	0.999998i	$-0.499335\pi$
$509$	24415.0	0.00417698	0.00208849	+	0.999998i	$0.499335\pi$
$510$	0	0
$511$	−1.82220e6	−0.308705
$512$	0	0
$513$	5.57962e6	0.936076
$514$	0	0
$515$	−1.06429e7	−1.76824
$516$	0	0
$517$	−837320.	−0.137773
$518$	0	0
$519$	−3.35458e6	−0.546663
$520$	0	0
$521$	4.76275e6	0.768712	0.384356	−	0.923185i	$-0.374424\pi$
$521$	4.76275e6	0.768712	0.384356	+	0.923185i	$0.374424\pi$
$522$	0	0
$523$	−735248.	−0.117538	−0.0587692	−	0.998272i	$-0.518718\pi$
$523$	−735248.	−0.117538	−0.0587692	+	0.998272i	$0.518718\pi$
$524$	0	0
$525$	−1.09060e6	−0.172690
$526$	0	0
$527$	−3.39853e6	−0.533046
$528$	0	0
$529$	6.45894e6	1.00351
$530$	0	0
$531$	−6.16513e6	−0.948868
$532$	0	0
$533$	197600.	0.0301279
$534$	0	0
$535$	1.33682e7	2.01925
$536$	0	0
$537$	−286545.	−0.0428802
$538$	0	0
$539$	1.73115e6	0.256662
$540$	0	0
$541$	−3.19649e6	−0.469548	−0.234774	−	0.972050i	$-0.575435\pi$
$541$	−3.19649e6	−0.469548	−0.234774	+	0.972050i	$0.575435\pi$
$542$	0	0
$543$	631183.	0.0918662
$544$	0	0
$545$	1.84233e7	2.65690
$546$	0	0
$547$	−8.85902e6	−1.26595	−0.632976	−	0.774171i	$-0.718167\pi$
$547$	−8.85902e6	−1.26595	−0.632976	+	0.774171i	$0.718167\pi$
$548$	0	0
$549$	−6.62626e6	−0.938292
$550$	0	0
$551$	1.46504e7	2.05575
$552$	0	0
$553$	1.42690e6	0.198418
$554$	0	0
$555$	3.85939e6	0.531846
$556$	0	0
$557$	−1.74512e6	−0.238335	−0.119167	−	0.992874i	$-0.538023\pi$
$557$	−1.74512e6	−0.238335	−0.119167	+	0.992874i	$0.538023\pi$
$558$	0	0
$559$	−944680.	−0.127866
$560$	0	0
$561$	−977438.	−0.131124
$562$	0	0
$563$	1.32333e7	1.75953	0.879764	−	0.475410i	$-0.157700\pi$
$563$	1.32333e7	1.75953	0.879764	+	0.475410i	$0.157700\pi$
$564$	0	0
$565$	−7.45199e6	−0.982090
$566$	0	0
$567$	1.28645e6	0.168049
$568$	0	0
$569$	1.04156e7	1.34867	0.674335	−	0.738426i	$-0.264430\pi$
$569$	1.04156e7	1.34867	0.674335	+	0.738426i	$0.264430\pi$
$570$	0	0
$571$	2.48163e6	0.318527	0.159264	−	0.987236i	$-0.449088\pi$
$571$	2.48163e6	0.318527	0.159264	+	0.987236i	$0.449088\pi$
$572$	0	0
$573$	−1.82262e6	−0.231905
$574$	0	0
$575$	−1.11896e7	−1.41138
$576$	0	0
$577$	−1.31244e7	−1.64112	−0.820562	−	0.571557i	$-0.806339\pi$
$577$	−1.31244e7	−1.64112	−0.820562	+	0.571557i	$0.806339\pi$
$578$	0	0
$579$	−3.67027e6	−0.454989
$580$	0	0
$581$	−3.87410e6	−0.476135
$582$	0	0
$583$	1.65988e6	0.202258
$584$	0	0
$585$	−5.82388e6	−0.703595
$586$	0	0
$587$	4.86010e6	0.582170	0.291085	−	0.956697i	$-0.405984\pi$
$587$	4.86010e6	0.582170	0.291085	+	0.956697i	$0.405984\pi$
$588$	0	0
$589$	5.37168e6	0.638002
$590$	0	0
$591$	−5.31707e6	−0.626187
$592$	0	0
$593$	−1.58559e6	−0.185163	−0.0925814	−	0.995705i	$-0.529512\pi$
$593$	−1.58559e6	−0.185163	−0.0925814	+	0.995705i	$0.529512\pi$
$594$	0	0
$595$	4.55830e6	0.527850
$596$	0	0
$597$	−6.17915e6	−0.709566
$598$	0	0
$599$	−9.04294e6	−1.02978	−0.514888	−	0.857258i	$-0.672166\pi$
$599$	−9.04294e6	−1.02978	−0.514888	+	0.857258i	$0.672166\pi$
$600$	0	0
$601$	729186.	0.0823478	0.0411739	−	0.999152i	$-0.486890\pi$
$601$	729186.	0.0823478	0.0411739	+	0.999152i	$0.486890\pi$
$602$	0	0
$603$	−1.19316e7	−1.33630
$604$	0	0
$605$	−1.15664e6	−0.128472
$606$	0	0
$607$	3.91130e6	0.430873	0.215437	−	0.976518i	$-0.430883\pi$
$607$	3.91130e6	0.430873	0.215437	+	0.976518i	$0.430883\pi$
$608$	0	0
$609$	−2.81120e6	−0.307149
$610$	0	0
$611$	−2.62960e6	−0.284962
$612$	0	0
$613$	−5.52184e6	−0.593516	−0.296758	−	0.954953i	$-0.595906\pi$
$613$	−5.52184e6	−0.593516	−0.296758	+	0.954953i	$0.595906\pi$
$614$	0	0
$615$	−287560.	−0.0306578
$616$	0	0
$617$	−4.88539e6	−0.516638	−0.258319	−	0.966060i	$-0.583169\pi$
$617$	−4.88539e6	−0.516638	−0.258319	+	0.966060i	$0.583169\pi$
$618$	0	0
$619$	4.11150e6	0.431295	0.215647	−	0.976471i	$-0.430814\pi$
$619$	4.11150e6	0.431295	0.215647	+	0.976471i	$0.430814\pi$
$620$	0	0
$621$	−1.09849e7	−1.14305
$622$	0	0
$623$	1.81355e6	0.187202
$624$	0	0
$625$	−9.79367e6	−1.00287
$626$	0	0
$627$	1.54493e6	0.156942
$628$	0	0
$629$	−8.05377e6	−0.811657
$630$	0	0
$631$	−8.24910e6	−0.824771	−0.412385	−	0.911009i	$-0.635304\pi$
$631$	−8.24910e6	−0.824771	−0.412385	+	0.911009i	$0.635304\pi$
$632$	0	0
$633$	−8.06996e6	−0.800502
$634$	0	0
$635$	−2.04989e7	−2.01742
$636$	0	0
$637$	5.43666e6	0.530864
$638$	0	0
$639$	−2.90437e6	−0.281385
$640$	0	0
$641$	−4.29330e6	−0.412711	−0.206355	−	0.978477i	$-0.566160\pi$
$641$	−4.29330e6	−0.412711	−0.206355	+	0.978477i	$0.566160\pi$
$642$	0	0
$643$	1.63045e7	1.55518	0.777588	−	0.628774i	$-0.216443\pi$
$643$	1.63045e7	1.55518	0.777588	+	0.628774i	$0.216443\pi$
$644$	0	0
$645$	1.37476e6	0.130115
$646$	0	0
$647$	−4.42624e6	−0.415695	−0.207847	−	0.978161i	$-0.566646\pi$
$647$	−4.42624e6	−0.415695	−0.207847	+	0.978161i	$0.566646\pi$
$648$	0	0
$649$	−3.84526e6	−0.358355
$650$	0	0
$651$	−1.03075e6	−0.0953237
$652$	0	0
$653$	−6.27529e6	−0.575905	−0.287952	−	0.957645i	$-0.592975\pi$
$653$	−6.27529e6	−0.575905	−0.287952	+	0.957645i	$0.592975\pi$
$654$	0	0
$655$	−6.74739e6	−0.614515
$656$	0	0
$657$	7.07014e6	0.639020
$658$	0	0
$659$	1.09748e7	0.984422	0.492211	−	0.870476i	$-0.336189\pi$
$659$	1.09748e7	0.984422	0.492211	+	0.870476i	$0.336189\pi$
$660$	0	0
$661$	2.02025e7	1.79846	0.899229	−	0.437478i	$-0.144128\pi$
$661$	2.02025e7	1.79846	0.899229	+	0.437478i	$0.144128\pi$
$662$	0	0
$663$	−3.06964e6	−0.271209
$664$	0	0
$665$	−7.20480e6	−0.631783
$666$	0	0
$667$	−2.88429e7	−2.51029
$668$	0	0
$669$	−461251.	−0.0398448
$670$	0	0
$671$	−4.13288e6	−0.354361
$672$	0	0
$673$	1.14233e7	0.972200	0.486100	−	0.873903i	$-0.338419\pi$
$673$	1.14233e7	0.972200	0.486100	+	0.873903i	$0.338419\pi$
$674$	0	0
$675$	9.53184e6	0.805225
$676$	0	0
$677$	−2.43918e6	−0.204537	−0.102268	−	0.994757i	$-0.532610\pi$
$677$	−2.43918e6	−0.204537	−0.102268	+	0.994757i	$0.532610\pi$
$678$	0	0
$679$	−2.48995e6	−0.207260
$680$	0	0
$681$	−2.20168e6	−0.181923
$682$	0	0
$683$	−1.01384e6	−0.0831606	−0.0415803	−	0.999135i	$-0.513239\pi$
$683$	−1.01384e6	−0.0831606	−0.0415803	+	0.999135i	$0.513239\pi$
$684$	0	0
$685$	3.37885e7	2.75133
$686$	0	0
$687$	−7.26924e6	−0.587621
$688$	0	0
$689$	5.21284e6	0.418337
$690$	0	0
$691$	8.03186e6	0.639913	0.319957	−	0.947432i	$-0.396332\pi$
$691$	8.03186e6	0.639913	0.319957	+	0.947432i	$0.396332\pi$
$692$	0	0
$693$	1.17370e6	0.0928376
$694$	0	0
$695$	2.44655e7	1.92129
$696$	0	0
$697$	600080.	0.0467872
$698$	0	0
$699$	−3.56983e6	−0.276347
$700$	0	0
$701$	−259806.	−0.0199689	−0.00998445	−	0.999950i	$-0.503178\pi$
$701$	−259806.	−0.0199689	−0.00998445	+	0.999950i	$0.503178\pi$
$702$	0	0
$703$	1.27297e7	0.971471
$704$	0	0
$705$	3.82676e6	0.289974
$706$	0	0
$707$	−7.67030e6	−0.577117
$708$	0	0
$709$	−1.92848e7	−1.44079	−0.720393	−	0.693566i	$-0.756039\pi$
$709$	−1.92848e7	−1.44079	−0.720393	+	0.693566i	$0.756039\pi$
$710$	0	0
$711$	−5.53637e6	−0.410725
$712$	0	0
$713$	−1.05755e7	−0.779071
$714$	0	0
$715$	−3.63242e6	−0.265724
$716$	0	0
$717$	−3.11146e6	−0.226030
$718$	0	0
$719$	−926119.	−0.0668105	−0.0334052	−	0.999442i	$-0.510635\pi$
$719$	−926119.	−0.0668105	−0.0334052	+	0.999442i	$0.510635\pi$
$720$	0	0
$721$	6.73600e6	0.482574
$722$	0	0
$723$	1.98425e6	0.141173
$724$	0	0
$725$	2.50277e7	1.76838
$726$	0	0
$727$	−2.02599e7	−1.42168	−0.710840	−	0.703354i	$-0.751685\pi$
$727$	−2.02599e7	−1.42168	−0.710840	+	0.703354i	$0.751685\pi$
$728$	0	0
$729$	211933.	0.0147700
$730$	0	0
$731$	−2.86884e6	−0.198570
$732$	0	0
$733$	1.10982e7	0.762944	0.381472	−	0.924380i	$-0.375417\pi$
$733$	1.10982e7	0.762944	0.381472	+	0.924380i	$0.375417\pi$
$734$	0	0
$735$	−7.91177e6	−0.540201
$736$	0	0
$737$	−7.44186e6	−0.504676
$738$	0	0
$739$	−624962.	−0.0420962	−0.0210481	−	0.999778i	$-0.506700\pi$
$739$	−624962.	−0.0420962	−0.0210481	+	0.999778i	$0.506700\pi$
$740$	0	0
$741$	4.85184e6	0.324609
$742$	0	0
$743$	−46436.0	−0.00308591	−0.00154295	−	0.999999i	$-0.500491\pi$
$743$	−46436.0	−0.00308591	−0.00154295	+	0.999999i	$0.500491\pi$
$744$	0	0
$745$	−3.55378e7	−2.34585
$746$	0	0
$747$	1.50315e7	0.985601
$748$	0	0
$749$	−8.46090e6	−0.551077
$750$	0	0
$751$	6.12144e6	0.396053	0.198027	−	0.980197i	$-0.436547\pi$
$751$	6.12144e6	0.396053	0.198027	+	0.980197i	$0.436547\pi$
$752$	0	0
$753$	−5.41665e6	−0.348131
$754$	0	0
$755$	3.20008e7	2.04312
$756$	0	0
$757$	−3.26458e6	−0.207056	−0.103528	−	0.994627i	$-0.533013\pi$
$757$	−3.26458e6	−0.207056	−0.103528	+	0.994627i	$0.533013\pi$
$758$	0	0
$759$	−3.04158e6	−0.191644
$760$	0	0
$761$	1.60311e7	1.00346	0.501732	−	0.865023i	$-0.332696\pi$
$761$	1.60311e7	1.00346	0.501732	+	0.865023i	$0.332696\pi$
$762$	0	0
$763$	−1.16603e7	−0.725101
$764$	0	0
$765$	−1.76862e7	−1.09265
$766$	0	0
$767$	−1.20760e7	−0.741200
$768$	0	0
$769$	2.64617e7	1.61362	0.806811	−	0.590810i	$-0.201192\pi$
$769$	2.64617e7	1.61362	0.806811	+	0.590810i	$0.201192\pi$
$770$	0	0
$771$	2.71400e6	0.164427
$772$	0	0
$773$	−2.63836e7	−1.58813	−0.794063	−	0.607836i	$-0.792038\pi$
$773$	−2.63836e7	−1.58813	−0.794063	+	0.607836i	$0.792038\pi$
$774$	0	0
$775$	9.17662e6	0.548818
$776$	0	0
$777$	−2.44265e6	−0.145147
$778$	0	0
$779$	−948480.	−0.0559995
$780$	0	0
$781$	−1.81149e6	−0.106269
$782$	0	0
$783$	2.45699e7	1.43218
$784$	0	0
$785$	−2.68064e7	−1.55261
$786$	0	0
$787$	5.68115e6	0.326964	0.163482	−	0.986546i	$-0.447727\pi$
$787$	5.68115e6	0.326964	0.163482	+	0.986546i	$0.447727\pi$
$788$	0	0
$789$	−1.38321e6	−0.0791037
$790$	0	0
$791$	4.71645e6	0.268024
$792$	0	0
$793$	−1.29793e7	−0.732939
$794$	0	0
$795$	−7.58605e6	−0.425695
$796$	0	0
$797$	9.99383e6	0.557296	0.278648	−	0.960393i	$-0.410114\pi$
$797$	9.99383e6	0.557296	0.278648	+	0.960393i	$0.410114\pi$
$798$	0	0
$799$	−7.98568e6	−0.442532
$800$	0	0
$801$	−7.03657e6	−0.387507
$802$	0	0
$803$	4.40972e6	0.241336
$804$	0	0
$805$	1.41844e7	0.771477
$806$	0	0
$807$	1.83886e6	0.0993950
$808$	0	0
$809$	2.32455e7	1.24873	0.624364	−	0.781134i	$-0.285358\pi$
$809$	2.32455e7	1.24873	0.624364	+	0.781134i	$0.285358\pi$
$810$	0	0
$811$	−1.27367e7	−0.679991	−0.339995	−	0.940427i	$-0.610426\pi$
$811$	−1.27367e7	−0.679991	−0.339995	+	0.940427i	$0.610426\pi$
$812$	0	0
$813$	−1.11348e6	−0.0590819
$814$	0	0
$815$	2.14403e7	1.13067
$816$	0	0
$817$	4.53446e6	0.237668
$818$	0	0
$819$	3.68600e6	0.192020
$820$	0	0
$821$	−7.85748e6	−0.406842	−0.203421	−	0.979091i	$-0.565206\pi$
$821$	−7.85748e6	−0.406842	−0.203421	+	0.979091i	$0.565206\pi$
$822$	0	0
$823$	1.09499e7	0.563524	0.281762	−	0.959484i	$-0.409081\pi$
$823$	1.09499e7	0.563524	0.281762	+	0.959484i	$0.409081\pi$
$824$	0	0
$825$	2.63925e6	0.135004
$826$	0	0
$827$	−2.20638e7	−1.12180	−0.560901	−	0.827883i	$-0.689545\pi$
$827$	−2.20638e7	−1.12180	−0.560901	+	0.827883i	$0.689545\pi$
$828$	0	0
$829$	7.05255e6	0.356418	0.178209	−	0.983993i	$-0.442970\pi$
$829$	7.05255e6	0.356418	0.178209	+	0.983993i	$0.442970\pi$
$830$	0	0
$831$	−9.05698e6	−0.454968
$832$	0	0
$833$	1.65103e7	0.824407
$834$	0	0
$835$	5.72497e6	0.284156
$836$	0	0
$837$	9.00876e6	0.444479
$838$	0	0
$839$	2.26195e7	1.10937	0.554686	−	0.832060i	$-0.312838\pi$
$839$	2.26195e7	1.10937	0.554686	+	0.832060i	$0.312838\pi$
$840$	0	0
$841$	4.40019e7	2.14527
$842$	0	0
$843$	1.24680e7	0.604264
$844$	0	0
$845$	1.79245e7	0.863588
$846$	0	0
$847$	732050.	0.0350616
$848$	0	0
$849$	1.38795e7	0.660853
$850$	0	0
$851$	−2.50616e7	−1.18627
$852$	0	0
$853$	9.46645e6	0.445466	0.222733	−	0.974880i	$-0.428502\pi$
$853$	9.46645e6	0.445466	0.222733	+	0.974880i	$0.428502\pi$
$854$	0	0
$855$	2.79546e7	1.30779
$856$	0	0
$857$	941480.	0.0437884	0.0218942	−	0.999760i	$-0.493030\pi$
$857$	941480.	0.0437884	0.0218942	+	0.999760i	$0.493030\pi$
$858$	0	0
$859$	806423.	0.0372889	0.0186445	−	0.999826i	$-0.494065\pi$
$859$	806423.	0.0372889	0.0186445	+	0.999826i	$0.494065\pi$
$860$	0	0
$861$	182000.	0.00836688
$862$	0	0
$863$	−1.19485e7	−0.546119	−0.273059	−	0.961997i	$-0.588036\pi$
$863$	−1.19485e7	−0.546119	−0.273059	+	0.961997i	$0.588036\pi$
$864$	0	0
$865$	−3.78589e7	−1.72039
$866$	0	0
$867$	616987.	0.0278759
$868$	0	0
$869$	−3.45310e6	−0.155117
$870$	0	0
$871$	−2.33711e7	−1.04384
$872$	0	0
$873$	9.66101e6	0.429029
$874$	0	0
$875$	35550.0	0.00156971
$876$	0	0
$877$	7.84853e6	0.344580	0.172290	−	0.985046i	$-0.444883\pi$
$877$	7.84853e6	0.344580	0.172290	+	0.985046i	$0.444883\pi$
$878$	0	0
$879$	−4.04852e6	−0.176736
$880$	0	0
$881$	−1.73933e7	−0.754991	−0.377496	−	0.926011i	$-0.623215\pi$
$881$	−1.73933e7	−0.754991	−0.377496	+	0.926011i	$0.623215\pi$
$882$	0	0
$883$	4.31619e7	1.86294	0.931470	−	0.363818i	$-0.118527\pi$
$883$	4.31619e7	1.86294	0.931470	+	0.363818i	$0.118527\pi$
$884$	0	0
$885$	1.75738e7	0.754236
$886$	0	0
$887$	9.25652e6	0.395038	0.197519	−	0.980299i	$-0.436712\pi$
$887$	9.25652e6	0.395038	0.197519	+	0.980299i	$0.436712\pi$
$888$	0	0
$889$	1.29740e7	0.550579
$890$	0	0
$891$	−3.11321e6	−0.131375
$892$	0	0
$893$	1.26221e7	0.529666
$894$	0	0
$895$	−3.23386e6	−0.134947
$896$	0	0
$897$	−9.55206e6	−0.396384
$898$	0	0
$899$	2.36542e7	0.976135
$900$	0	0
$901$	1.58306e7	0.649658
$902$	0	0
$903$	−870100.	−0.0355099
$904$	0	0
$905$	7.12335e6	0.289110
$906$	0	0
$907$	−4.47293e7	−1.80540	−0.902700	−	0.430270i	$-0.858418\pi$
$907$	−4.47293e7	−1.80540	−0.902700	+	0.430270i	$0.858418\pi$
$908$	0	0
$909$	2.97608e7	1.19463
$910$	0	0
$911$	−2.57577e7	−1.02828	−0.514139	−	0.857707i	$-0.671888\pi$
$911$	−2.57577e7	−1.02828	−0.514139	+	0.857707i	$0.671888\pi$
$912$	0	0
$913$	9.37532e6	0.372228
$914$	0	0
$915$	1.88883e7	0.745829
$916$	0	0
$917$	4.27050e6	0.167709
$918$	0	0
$919$	3.63488e7	1.41972	0.709858	−	0.704344i	$-0.248759\pi$
$919$	3.63488e7	1.41972	0.709858	+	0.704344i	$0.248759\pi$
$920$	0	0
$921$	−2.15322e7	−0.836447
$922$	0	0
$923$	−5.68898e6	−0.219801
$924$	0	0
$925$	2.17466e7	0.835673
$926$	0	0
$927$	−2.61357e7	−0.998929
$928$	0	0
$929$	−3.96617e6	−0.150776	−0.0753880	−	0.997154i	$-0.524020\pi$
$929$	−3.96617e6	−0.150776	−0.0753880	+	0.997154i	$0.524020\pi$
$930$	0	0
$931$	−2.60960e7	−0.986732
$932$	0	0
$933$	−2.19630e7	−0.826014
$934$	0	0
$935$	−1.10311e7	−0.412657
$936$	0	0
$937$	−3.50528e7	−1.30429	−0.652145	−	0.758094i	$-0.726131\pi$
$937$	−3.50528e7	−1.30429	−0.652145	+	0.758094i	$0.726131\pi$
$938$	0	0
$939$	−1.83249e7	−0.678230
$940$	0	0
$941$	−1.40738e7	−0.518130	−0.259065	−	0.965860i	$-0.583414\pi$
$941$	−1.40738e7	−0.518130	−0.259065	+	0.965860i	$0.583414\pi$
$942$	0	0
$943$	1.86732e6	0.0683816
$944$	0	0
$945$	−1.20830e7	−0.440146
$946$	0	0
$947$	3.73759e7	1.35431	0.677153	−	0.735842i	$-0.263214\pi$
$947$	3.73759e7	1.35431	0.677153	+	0.735842i	$0.263214\pi$
$948$	0	0
$949$	1.38487e7	0.499165
$950$	0	0
$951$	1.74454e7	0.625502
$952$	0	0
$953$	−3.18424e7	−1.13572	−0.567862	−	0.823124i	$-0.692229\pi$
$953$	−3.18424e7	−1.13572	−0.567862	+	0.823124i	$0.692229\pi$
$954$	0	0
$955$	−2.05696e7	−0.729824
$956$	0	0
$957$	6.80310e6	0.240119
$958$	0	0
$959$	−2.13852e7	−0.750872
$960$	0	0
$961$	−1.99561e7	−0.697056
$962$	0	0
$963$	3.28283e7	1.14073
$964$	0	0
$965$	−4.14216e7	−1.43189
$966$	0	0
$967$	3.16276e7	1.08768	0.543838	−	0.839190i	$-0.316971\pi$
$967$	3.16276e7	1.08768	0.543838	+	0.839190i	$0.316971\pi$
$968$	0	0
$969$	1.47343e7	0.504103
$970$	0	0
$971$	2.73412e7	0.930614	0.465307	−	0.885149i	$-0.345944\pi$
$971$	2.73412e7	0.930614	0.465307	+	0.885149i	$0.345944\pi$
$972$	0	0
$973$	−1.54845e7	−0.524343
$974$	0	0
$975$	8.28856e6	0.279234
$976$	0	0
$977$	−5.81630e6	−0.194944	−0.0974721	−	0.995238i	$-0.531076\pi$
$977$	−5.81630e6	−0.194944	−0.0974721	+	0.995238i	$0.531076\pi$
$978$	0	0
$979$	−4.38879e6	−0.146348
$980$	0	0
$981$	4.52420e7	1.50096
$982$	0	0
$983$	3.81817e7	1.26029	0.630146	−	0.776476i	$-0.282995\pi$
$983$	3.81817e7	1.26029	0.630146	+	0.776476i	$0.282995\pi$
$984$	0	0
$985$	−6.00070e7	−1.97066
$986$	0	0
$987$	−2.42200e6	−0.0791373
$988$	0	0
$989$	−8.92723e6	−0.290219
$990$	0	0
$991$	−5.44564e6	−0.176143	−0.0880714	−	0.996114i	$-0.528070\pi$
$991$	−5.44564e6	−0.176143	−0.0880714	+	0.996114i	$0.528070\pi$
$992$	0	0
$993$	−1.89087e7	−0.608541
$994$	0	0
$995$	−6.97361e7	−2.23306
$996$	0	0
$997$	−3.77967e6	−0.120425	−0.0602125	−	0.998186i	$-0.519178\pi$
$997$	−3.77967e6	−0.120425	−0.0602125	+	0.998186i	$0.519178\pi$
$998$	0	0
$999$	2.13488e7	0.676798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.6.a.a.1.1		1
4.3	odd	2		44.6.a.a.1.1	✓	1
8.3	odd	2		704.6.a.d.1.1		1
8.5	even	2		704.6.a.g.1.1		1
12.11	even	2		396.6.a.e.1.1		1
20.3	even	4		1100.6.b.a.749.2		2
20.7	even	4		1100.6.b.a.749.1		2
20.19	odd	2		1100.6.a.a.1.1		1
44.43	even	2		484.6.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.6.a.a.1.1	✓	1	4.3	odd	2
176.6.a.a.1.1		1	1.1	even	1	trivial
396.6.a.e.1.1		1	12.11	even	2
484.6.a.b.1.1		1	44.43	even	2
704.6.a.d.1.1		1	8.3	odd	2
704.6.a.g.1.1		1	8.5	even	2
1100.6.a.a.1.1		1	20.19	odd	2
1100.6.b.a.749.1		2	20.7	even	4
1100.6.b.a.749.2		2	20.3	even	4

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	176.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more