LMFDB - Embedded newform 176.6.a.e.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 22)
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)

$f(q)$

$=$

$q+29.0000 q^{3} -31.0000 q^{5} +230.000 q^{7} +598.000 q^{9} +O(q^{10})$

$q+29.0000 q^{3} -31.0000 q^{5} +230.000 q^{7} +598.000 q^{9} -121.000 q^{11} +112.000 q^{13} -899.000 q^{15} -1142.00 q^{17} +612.000 q^{19} +6670.00 q^{21} +1941.00 q^{23} -2164.00 q^{25} +10295.0 q^{27} +1192.00 q^{29} +1037.00 q^{31} -3509.00 q^{33} -7130.00 q^{35} +8083.00 q^{37} +3248.00 q^{39} -10444.0 q^{41} -58.0000 q^{43} -18538.0 q^{45} -8656.00 q^{47} +36093.0 q^{49} -33118.0 q^{51} -20318.0 q^{53} +3751.00 q^{55} +17748.0 q^{57} +21351.0 q^{59} +47044.0 q^{61} +137540. q^{63} -3472.00 q^{65} -48093.0 q^{67} +56289.0 q^{69} +24967.0 q^{71} -42288.0 q^{73} -62756.0 q^{75} -27830.0 q^{77} +72410.0 q^{79} +153241. q^{81} +15806.0 q^{83} +35402.0 q^{85} +34568.0 q^{87} -114761. q^{89} +25760.0 q^{91} +30073.0 q^{93} -18972.0 q^{95} -5159.00 q^{97} -72358.0 q^{99} +O(q^{100})$

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
$3$	29.0000	1.86035	0.930175	−	0.367115i	$-0.119655\pi$
$3$	29.0000	1.86035	0.930175	+	0.367115i	$0.119655\pi$
$4$	0	0
$5$	−31.0000	−0.554545	−0.277272	−	0.960791i	$-0.589430\pi$
$5$	−31.0000	−0.554545	−0.277272	+	0.960791i	$0.589430\pi$
$6$	0	0
$7$	230.000	1.77412	0.887059	−	0.461655i	$-0.152744\pi$
$7$	230.000	1.77412	0.887059	+	0.461655i	$0.152744\pi$
$8$	0	0
$9$	598.000	2.46091
$10$	0	0
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	0	0
$13$	112.000	0.183806	0.0919030	−	0.995768i	$-0.470705\pi$
$13$	112.000	0.183806	0.0919030	+	0.995768i	$0.470705\pi$
$14$	0	0
$15$	−899.000	−1.03165
$16$	0	0
$17$	−1142.00	−0.958393	−0.479197	−	0.877708i	$-0.659072\pi$
$17$	−1142.00	−0.958393	−0.479197	+	0.877708i	$0.659072\pi$
$18$	0	0
$19$	612.000	0.388926	0.194463	−	0.980910i	$-0.437704\pi$
$19$	612.000	0.388926	0.194463	+	0.980910i	$0.437704\pi$
$20$	0	0
$21$	6670.00	3.30048
$22$	0	0
$23$	1941.00	0.765078	0.382539	−	0.923939i	$-0.375050\pi$
$23$	1941.00	0.765078	0.382539	+	0.923939i	$0.375050\pi$
$24$	0	0
$25$	−2164.00	−0.692480
$26$	0	0
$27$	10295.0	2.71780
$28$	0	0
$29$	1192.00	0.263197	0.131599	−	0.991303i	$-0.457989\pi$
$29$	1192.00	0.263197	0.131599	+	0.991303i	$0.457989\pi$
$30$	0	0
$31$	1037.00	0.193809	0.0969046	−	0.995294i	$-0.469106\pi$
$31$	1037.00	0.193809	0.0969046	+	0.995294i	$0.469106\pi$
$32$	0	0
$33$	−3509.00	−0.560917
$34$	0	0
$35$	−7130.00	−0.983829
$36$	0	0
$37$	8083.00	0.970663	0.485331	−	0.874330i	$-0.338699\pi$
$37$	8083.00	0.970663	0.485331	+	0.874330i	$0.338699\pi$
$38$	0	0
$39$	3248.00	0.341944
$40$	0	0
$41$	−10444.0	−0.970303	−0.485151	−	0.874430i	$-0.661235\pi$
$41$	−10444.0	−0.970303	−0.485151	+	0.874430i	$0.661235\pi$
$42$	0	0
$43$	−58.0000	−0.00478362	−0.00239181	−	0.999997i	$-0.500761\pi$
$43$	−58.0000	−0.00478362	−0.00239181	+	0.999997i	$0.500761\pi$
$44$	0	0
$45$	−18538.0	−1.36468
$46$	0	0
$47$	−8656.00	−0.571574	−0.285787	−	0.958293i	$-0.592255\pi$
$47$	−8656.00	−0.571574	−0.285787	+	0.958293i	$0.592255\pi$
$48$	0	0
$49$	36093.0	2.14750
$50$	0	0
$51$	−33118.0	−1.78295
$52$	0	0
$53$	−20318.0	−0.993554	−0.496777	−	0.867878i	$-0.665483\pi$
$53$	−20318.0	−0.993554	−0.496777	+	0.867878i	$0.665483\pi$
$54$	0	0
$55$	3751.00	0.167202
$56$	0	0
$57$	17748.0	0.723540
$58$	0	0
$59$	21351.0	0.798524	0.399262	−	0.916837i	$-0.369266\pi$
$59$	21351.0	0.798524	0.399262	+	0.916837i	$0.369266\pi$
$60$	0	0
$61$	47044.0	1.61875	0.809375	−	0.587293i	$-0.199806\pi$
$61$	47044.0	1.61875	0.809375	+	0.587293i	$0.199806\pi$
$62$	0	0
$63$	137540.	4.36594
$64$	0	0
$65$	−3472.00	−0.101929
$66$	0	0
$67$	−48093.0	−1.30887	−0.654433	−	0.756120i	$-0.727092\pi$
$67$	−48093.0	−1.30887	−0.654433	+	0.756120i	$0.727092\pi$
$68$	0	0
$69$	56289.0	1.42331
$70$	0	0
$71$	24967.0	0.587788	0.293894	−	0.955838i	$-0.405049\pi$
$71$	24967.0	0.587788	0.293894	+	0.955838i	$0.405049\pi$
$72$	0	0
$73$	−42288.0	−0.928774	−0.464387	−	0.885632i	$-0.653725\pi$
$73$	−42288.0	−0.928774	−0.464387	+	0.885632i	$0.653725\pi$
$74$	0	0
$75$	−62756.0	−1.28826
$76$	0	0
$77$	−27830.0	−0.534917
$78$	0	0
$79$	72410.0	1.30536	0.652681	−	0.757633i	$-0.273644\pi$
$79$	72410.0	1.30536	0.652681	+	0.757633i	$0.273644\pi$
$80$	0	0
$81$	153241.	2.59515
$82$	0	0
$83$	15806.0	0.251841	0.125921	−	0.992040i	$-0.459812\pi$
$83$	15806.0	0.251841	0.125921	+	0.992040i	$0.459812\pi$
$84$	0	0
$85$	35402.0	0.531472
$86$	0	0
$87$	34568.0	0.489639
$88$	0	0
$89$	−114761.	−1.53575	−0.767873	−	0.640602i	$-0.778685\pi$
$89$	−114761.	−1.53575	−0.767873	+	0.640602i	$0.778685\pi$
$90$	0	0
$91$	25760.0	0.326094
$92$	0	0
$93$	30073.0	0.360553
$94$	0	0
$95$	−18972.0	−0.215677
$96$	0	0
$97$	−5159.00	−0.0556719	−0.0278360	−	0.999613i	$-0.508862\pi$
$97$	−5159.00	−0.0556719	−0.0278360	+	0.999613i	$0.508862\pi$
$98$	0	0
$99$	−72358.0	−0.741991
$100$	0	0
$101$	−61426.0	−0.599168	−0.299584	−	0.954070i	$-0.596848\pi$
$101$	−61426.0	−0.599168	−0.299584	+	0.954070i	$0.596848\pi$
$102$	0	0
$103$	−185896.	−1.72654	−0.863271	−	0.504741i	$-0.831588\pi$
$103$	−185896.	−1.72654	−0.863271	+	0.504741i	$0.831588\pi$
$104$	0	0
$105$	−206770.	−1.83027
$106$	0	0
$107$	23970.0	0.202399	0.101200	−	0.994866i	$-0.467732\pi$
$107$	23970.0	0.202399	0.101200	+	0.994866i	$0.467732\pi$
$108$	0	0
$109$	−56326.0	−0.454091	−0.227045	−	0.973884i	$-0.572907\pi$
$109$	−56326.0	−0.454091	−0.227045	+	0.973884i	$0.572907\pi$
$110$	0	0
$111$	234407.	1.80577
$112$	0	0
$113$	−261903.	−1.92950	−0.964749	−	0.263171i	$-0.915231\pi$
$113$	−261903.	−1.92950	−0.964749	+	0.263171i	$0.915231\pi$
$114$	0	0
$115$	−60171.0	−0.424270
$116$	0	0
$117$	66976.0	0.452329
$118$	0	0
$119$	−262660.	−1.70030
$120$	0	0
$121$	14641.0	0.0909091
$122$	0	0
$123$	−302876.	−1.80510
$124$	0	0
$125$	163959.	0.938556
$126$	0	0
$127$	−87404.0	−0.480864	−0.240432	−	0.970666i	$-0.577289\pi$
$127$	−87404.0	−0.480864	−0.240432	+	0.970666i	$0.577289\pi$
$128$	0	0
$129$	−1682.00	−0.00889922
$130$	0	0
$131$	−265122.	−1.34979	−0.674897	−	0.737912i	$-0.735812\pi$
$131$	−265122.	−1.34979	−0.674897	+	0.737912i	$0.735812\pi$
$132$	0	0
$133$	140760.	0.690002
$134$	0	0
$135$	−319145.	−1.50714
$136$	0	0
$137$	245857.	1.11913	0.559566	−	0.828786i	$-0.310968\pi$
$137$	245857.	1.11913	0.559566	+	0.828786i	$0.310968\pi$
$138$	0	0
$139$	363594.	1.59617	0.798086	−	0.602544i	$-0.205846\pi$
$139$	363594.	1.59617	0.798086	+	0.602544i	$0.205846\pi$
$140$	0	0
$141$	−251024.	−1.06333
$142$	0	0
$143$	−13552.0	−0.0554196
$144$	0	0
$145$	−36952.0	−0.145955
$146$	0	0
$147$	1.04670e6	3.99510
$148$	0	0
$149$	−55750.0	−0.205721	−0.102861	−	0.994696i	$-0.532800\pi$
$149$	−55750.0	−0.205721	−0.102861	+	0.994696i	$0.532800\pi$
$150$	0	0
$151$	−65642.0	−0.234282	−0.117141	−	0.993115i	$-0.537373\pi$
$151$	−65642.0	−0.234282	−0.117141	+	0.993115i	$0.537373\pi$
$152$	0	0
$153$	−682916.	−2.35852
$154$	0	0
$155$	−32147.0	−0.107476
$156$	0	0
$157$	−275367.	−0.891585	−0.445793	−	0.895136i	$-0.647078\pi$
$157$	−275367.	−0.891585	−0.445793	+	0.895136i	$0.647078\pi$
$158$	0	0
$159$	−589222.	−1.84836
$160$	0	0
$161$	446430.	1.35734
$162$	0	0
$163$	−291940.	−0.860646	−0.430323	−	0.902675i	$-0.641600\pi$
$163$	−291940.	−0.860646	−0.430323	+	0.902675i	$0.641600\pi$
$164$	0	0
$165$	108779.	0.311054
$166$	0	0
$167$	337344.	0.936013	0.468006	−	0.883725i	$-0.344972\pi$
$167$	337344.	0.936013	0.468006	+	0.883725i	$0.344972\pi$
$168$	0	0
$169$	−358749.	−0.966215
$170$	0	0
$171$	365976.	0.957111
$172$	0	0
$173$	−116742.	−0.296560	−0.148280	−	0.988945i	$-0.547374\pi$
$173$	−116742.	−0.296560	−0.148280	+	0.988945i	$0.547374\pi$
$174$	0	0
$175$	−497720.	−1.22854
$176$	0	0
$177$	619179.	1.48554
$178$	0	0
$179$	19107.0	0.0445718	0.0222859	−	0.999752i	$-0.492906\pi$
$179$	19107.0	0.0445718	0.0222859	+	0.999752i	$0.492906\pi$
$180$	0	0
$181$	−16177.0	−0.0367030	−0.0183515	−	0.999832i	$-0.505842\pi$
$181$	−16177.0	−0.0367030	−0.0183515	+	0.999832i	$0.505842\pi$
$182$	0	0
$183$	1.36428e6	3.01144
$184$	0	0
$185$	−250573.	−0.538276
$186$	0	0
$187$	138182.	0.288966
$188$	0	0
$189$	2.36785e6	4.82169
$190$	0	0
$191$	−685333.	−1.35931	−0.679655	−	0.733532i	$-0.737870\pi$
$191$	−685333.	−1.35931	−0.679655	+	0.733532i	$0.737870\pi$
$192$	0	0
$193$	−309292.	−0.597689	−0.298845	−	0.954302i	$-0.596601\pi$
$193$	−309292.	−0.597689	−0.298845	+	0.954302i	$0.596601\pi$
$194$	0	0
$195$	−100688.	−0.189623
$196$	0	0
$197$	−120930.	−0.222008	−0.111004	−	0.993820i	$-0.535407\pi$
$197$	−120930.	−0.222008	−0.111004	+	0.993820i	$0.535407\pi$
$198$	0	0
$199$	−915536.	−1.63886	−0.819432	−	0.573177i	$-0.805711\pi$
$199$	−915536.	−1.63886	−0.819432	+	0.573177i	$0.805711\pi$
$200$	0	0
$201$	−1.39470e6	−2.43495
$202$	0	0
$203$	274160.	0.466943
$204$	0	0
$205$	323764.	0.538076
$206$	0	0
$207$	1.16072e6	1.88279
$208$	0	0
$209$	−74052.0	−0.117266
$210$	0	0
$211$	134580.	0.208101	0.104051	−	0.994572i	$-0.466820\pi$
$211$	134580.	0.208101	0.104051	+	0.994572i	$0.466820\pi$
$212$	0	0
$213$	724043.	1.09349
$214$	0	0
$215$	1798.00	0.00265273
$216$	0	0
$217$	238510.	0.343841
$218$	0	0
$219$	−1.22635e6	−1.72785
$220$	0	0
$221$	−127904.	−0.176158
$222$	0	0
$223$	−468839.	−0.631337	−0.315669	−	0.948869i	$-0.602229\pi$
$223$	−468839.	−0.631337	−0.315669	+	0.948869i	$0.602229\pi$
$224$	0	0
$225$	−1.29407e6	−1.70413
$226$	0	0
$227$	−275022.	−0.354244	−0.177122	−	0.984189i	$-0.556679\pi$
$227$	−275022.	−0.354244	−0.177122	+	0.984189i	$0.556679\pi$
$228$	0	0
$229$	−642281.	−0.809350	−0.404675	−	0.914461i	$-0.632615\pi$
$229$	−642281.	−0.809350	−0.404675	+	0.914461i	$0.632615\pi$
$230$	0	0
$231$	−807070.	−0.995133
$232$	0	0
$233$	−1.50485e6	−1.81595	−0.907973	−	0.419029i	$-0.862371\pi$
$233$	−1.50485e6	−1.81595	−0.907973	+	0.419029i	$0.862371\pi$
$234$	0	0
$235$	268336.	0.316964
$236$	0	0
$237$	2.09989e6	2.42843
$238$	0	0
$239$	304694.	0.345040	0.172520	−	0.985006i	$-0.444809\pi$
$239$	304694.	0.345040	0.172520	+	0.985006i	$0.444809\pi$
$240$	0	0
$241$	1.27181e6	1.41052	0.705260	−	0.708949i	$-0.250830\pi$
$241$	1.27181e6	1.41052	0.705260	+	0.708949i	$0.250830\pi$
$242$	0	0
$243$	1.94230e6	2.11009
$244$	0	0
$245$	−1.11888e6	−1.19088
$246$	0	0
$247$	68544.0	0.0714870
$248$	0	0
$249$	458374.	0.468513
$250$	0	0
$251$	−629965.	−0.631149	−0.315575	−	0.948901i	$-0.602197\pi$
$251$	−629965.	−0.631149	−0.315575	+	0.948901i	$0.602197\pi$
$252$	0	0
$253$	−234861.	−0.230680
$254$	0	0
$255$	1.02666e6	0.988725
$256$	0	0
$257$	544086.	0.513848	0.256924	−	0.966432i	$-0.417291\pi$
$257$	544086.	0.513848	0.256924	+	0.966432i	$0.417291\pi$
$258$	0	0
$259$	1.85909e6	1.72207
$260$	0	0
$261$	712816.	0.647703
$262$	0	0
$263$	1.98933e6	1.77345	0.886724	−	0.462300i	$-0.152976\pi$
$263$	1.98933e6	1.77345	0.886724	+	0.462300i	$0.152976\pi$
$264$	0	0
$265$	629858.	0.550970
$266$	0	0
$267$	−3.32807e6	−2.85703
$268$	0	0
$269$	1.75446e6	1.47830	0.739149	−	0.673541i	$-0.235228\pi$
$269$	1.75446e6	1.47830	0.739149	+	0.673541i	$0.235228\pi$
$270$	0	0
$271$	1.65824e6	1.37159	0.685795	−	0.727795i	$-0.259455\pi$
$271$	1.65824e6	1.37159	0.685795	+	0.727795i	$0.259455\pi$
$272$	0	0
$273$	747040.	0.606649
$274$	0	0
$275$	261844.	0.208791
$276$	0	0
$277$	−42634.0	−0.0333854	−0.0166927	−	0.999861i	$-0.505314\pi$
$277$	−42634.0	−0.0333854	−0.0166927	+	0.999861i	$0.505314\pi$
$278$	0	0
$279$	620126.	0.476946
$280$	0	0
$281$	319510.	0.241390	0.120695	−	0.992690i	$-0.461488\pi$
$281$	319510.	0.241390	0.120695	+	0.992690i	$0.461488\pi$
$282$	0	0
$283$	2.02735e6	1.50474	0.752371	−	0.658739i	$-0.228910\pi$
$283$	2.02735e6	1.50474	0.752371	+	0.658739i	$0.228910\pi$
$284$	0	0
$285$	−550188.	−0.401235
$286$	0	0
$287$	−2.40212e6	−1.72143
$288$	0	0
$289$	−115693.	−0.0814821
$290$	0	0
$291$	−149611.	−0.103569
$292$	0	0
$293$	718844.	0.489177	0.244588	−	0.969627i	$-0.421347\pi$
$293$	718844.	0.489177	0.244588	+	0.969627i	$0.421347\pi$
$294$	0	0
$295$	−661881.	−0.442818
$296$	0	0
$297$	−1.24570e6	−0.819446
$298$	0	0
$299$	217392.	0.140626
$300$	0	0
$301$	−13340.0	−0.00848671
$302$	0	0
$303$	−1.78135e6	−1.11466
$304$	0	0
$305$	−1.45836e6	−0.897669
$306$	0	0
$307$	1.98142e6	1.19986	0.599930	−	0.800052i	$-0.295195\pi$
$307$	1.98142e6	1.19986	0.599930	+	0.800052i	$0.295195\pi$
$308$	0	0
$309$	−5.39098e6	−3.21197
$310$	0	0
$311$	1.51030e6	0.885446	0.442723	−	0.896658i	$-0.354012\pi$
$311$	1.51030e6	0.885446	0.442723	+	0.896658i	$0.354012\pi$
$312$	0	0
$313$	2.00092e6	1.15443	0.577216	−	0.816591i	$-0.304139\pi$
$313$	2.00092e6	1.15443	0.577216	+	0.816591i	$0.304139\pi$
$314$	0	0
$315$	−4.26374e6	−2.42111
$316$	0	0
$317$	−259331.	−0.144946	−0.0724730	−	0.997370i	$-0.523089\pi$
$317$	−259331.	−0.144946	−0.0724730	+	0.997370i	$0.523089\pi$
$318$	0	0
$319$	−144232.	−0.0793569
$320$	0	0
$321$	695130.	0.376533
$322$	0	0
$323$	−698904.	−0.372744
$324$	0	0
$325$	−242368.	−0.127282
$326$	0	0
$327$	−1.63345e6	−0.844768
$328$	0	0
$329$	−1.99088e6	−1.01404
$330$	0	0
$331$	−51203.0	−0.0256877	−0.0128439	−	0.999918i	$-0.504088\pi$
$331$	−51203.0	−0.0256877	−0.0128439	+	0.999918i	$0.504088\pi$
$332$	0	0
$333$	4.83363e6	2.38871
$334$	0	0
$335$	1.49088e6	0.725824
$336$	0	0
$337$	266870.	0.128004	0.0640022	−	0.997950i	$-0.479614\pi$
$337$	266870.	0.128004	0.0640022	+	0.997950i	$0.479614\pi$
$338$	0	0
$339$	−7.59519e6	−3.58954
$340$	0	0
$341$	−125477.	−0.0584357
$342$	0	0
$343$	4.43578e6	2.03580
$344$	0	0
$345$	−1.74496e6	−0.789292
$346$	0	0
$347$	−622800.	−0.277667	−0.138834	−	0.990316i	$-0.544335\pi$
$347$	−622800.	−0.277667	−0.138834	+	0.990316i	$0.544335\pi$
$348$	0	0
$349$	2.43649e6	1.07078	0.535391	−	0.844604i	$-0.320164\pi$
$349$	2.43649e6	1.07078	0.535391	+	0.844604i	$0.320164\pi$
$350$	0	0
$351$	1.15304e6	0.499547
$352$	0	0
$353$	1.55957e6	0.666144	0.333072	−	0.942901i	$-0.391915\pi$
$353$	1.55957e6	0.666144	0.333072	+	0.942901i	$0.391915\pi$
$354$	0	0
$355$	−773977.	−0.325955
$356$	0	0
$357$	−7.61714e6	−3.16316
$358$	0	0
$359$	−1.91961e6	−0.786098	−0.393049	−	0.919518i	$-0.628580\pi$
$359$	−1.91961e6	−0.786098	−0.393049	+	0.919518i	$0.628580\pi$
$360$	0	0
$361$	−2.10156e6	−0.848736
$362$	0	0
$363$	424589.	0.169123
$364$	0	0
$365$	1.31093e6	0.515047
$366$	0	0
$367$	−3.61225e6	−1.39995	−0.699975	−	0.714167i	$-0.746806\pi$
$367$	−3.61225e6	−1.39995	−0.699975	+	0.714167i	$0.746806\pi$
$368$	0	0
$369$	−6.24551e6	−2.38782
$370$	0	0
$371$	−4.67314e6	−1.76268
$372$	0	0
$373$	3.93968e6	1.46619	0.733093	−	0.680128i	$-0.238076\pi$
$373$	3.93968e6	1.46619	0.733093	+	0.680128i	$0.238076\pi$
$374$	0	0
$375$	4.75481e6	1.74604
$376$	0	0
$377$	133504.	0.0483772
$378$	0	0
$379$	2.18829e6	0.782540	0.391270	−	0.920276i	$-0.372036\pi$
$379$	2.18829e6	0.782540	0.391270	+	0.920276i	$0.372036\pi$
$380$	0	0
$381$	−2.53472e6	−0.894575
$382$	0	0
$383$	−768387.	−0.267660	−0.133830	−	0.991004i	$-0.542728\pi$
$383$	−768387.	−0.267660	−0.133830	+	0.991004i	$0.542728\pi$
$384$	0	0
$385$	862730.	0.296635
$386$	0	0
$387$	−34684.0	−0.0117720
$388$	0	0
$389$	324313.	0.108665	0.0543326	−	0.998523i	$-0.482697\pi$
$389$	324313.	0.108665	0.0543326	+	0.998523i	$0.482697\pi$
$390$	0	0
$391$	−2.21662e6	−0.733246
$392$	0	0
$393$	−7.68854e6	−2.51109
$394$	0	0
$395$	−2.24471e6	−0.723882
$396$	0	0
$397$	334758.	0.106599	0.0532997	−	0.998579i	$-0.483026\pi$
$397$	334758.	0.106599	0.0532997	+	0.998579i	$0.483026\pi$
$398$	0	0
$399$	4.08204e6	1.28365
$400$	0	0
$401$	−902022.	−0.280128	−0.140064	−	0.990142i	$-0.544731\pi$
$401$	−902022.	−0.280128	−0.140064	+	0.990142i	$0.544731\pi$
$402$	0	0
$403$	116144.	0.0356233
$404$	0	0
$405$	−4.75047e6	−1.43913
$406$	0	0
$407$	−978043.	−0.292666
$408$	0	0
$409$	−5.00457e6	−1.47931	−0.739654	−	0.672987i	$-0.765011\pi$
$409$	−5.00457e6	−1.47931	−0.739654	+	0.672987i	$0.765011\pi$
$410$	0	0
$411$	7.12985e6	2.08198
$412$	0	0
$413$	4.91073e6	1.41668
$414$	0	0
$415$	−489986.	−0.139657
$416$	0	0
$417$	1.05442e7	2.96944
$418$	0	0
$419$	3.00124e6	0.835151	0.417576	−	0.908642i	$-0.362880\pi$
$419$	3.00124e6	0.835151	0.417576	+	0.908642i	$0.362880\pi$
$420$	0	0
$421$	4.56224e6	1.25451	0.627253	−	0.778816i	$-0.284179\pi$
$421$	4.56224e6	1.25451	0.627253	+	0.778816i	$0.284179\pi$
$422$	0	0
$423$	−5.17629e6	−1.40659
$424$	0	0
$425$	2.47129e6	0.663668
$426$	0	0
$427$	1.08201e7	2.87185
$428$	0	0
$429$	−393008.	−0.103100
$430$	0	0
$431$	−4.89783e6	−1.27002	−0.635009	−	0.772504i	$-0.719004\pi$
$431$	−4.89783e6	−1.27002	−0.635009	+	0.772504i	$0.719004\pi$
$432$	0	0
$433$	6.72876e6	1.72471	0.862353	−	0.506307i	$-0.168990\pi$
$433$	6.72876e6	1.72471	0.862353	+	0.506307i	$0.168990\pi$
$434$	0	0
$435$	−1.07161e6	−0.271527
$436$	0	0
$437$	1.18789e6	0.297559
$438$	0	0
$439$	3.35034e6	0.829711	0.414856	−	0.909887i	$-0.363832\pi$
$439$	3.35034e6	0.829711	0.414856	+	0.909887i	$0.363832\pi$
$440$	0	0
$441$	2.15836e7	5.28479
$442$	0	0
$443$	7.12434e6	1.72479	0.862394	−	0.506238i	$-0.168964\pi$
$443$	7.12434e6	1.72479	0.862394	+	0.506238i	$0.168964\pi$
$444$	0	0
$445$	3.55759e6	0.851640
$446$	0	0
$447$	−1.61675e6	−0.382714
$448$	0	0
$449$	−2.70928e6	−0.634218	−0.317109	−	0.948389i	$-0.602712\pi$
$449$	−2.70928e6	−0.634218	−0.317109	+	0.948389i	$0.602712\pi$
$450$	0	0
$451$	1.26372e6	0.292557
$452$	0	0
$453$	−1.90362e6	−0.435847
$454$	0	0
$455$	−798560.	−0.180834
$456$	0	0
$457$	2.41361e6	0.540601	0.270301	−	0.962776i	$-0.412877\pi$
$457$	2.41361e6	0.540601	0.270301	+	0.962776i	$0.412877\pi$
$458$	0	0
$459$	−1.17569e7	−2.60472
$460$	0	0
$461$	−6.56065e6	−1.43779	−0.718894	−	0.695120i	$-0.755351\pi$
$461$	−6.56065e6	−1.43779	−0.718894	+	0.695120i	$0.755351\pi$
$462$	0	0
$463$	4.72421e6	1.02418	0.512090	−	0.858932i	$-0.328871\pi$
$463$	4.72421e6	1.02418	0.512090	+	0.858932i	$0.328871\pi$
$464$	0	0
$465$	−932263.	−0.199943
$466$	0	0
$467$	2.28444e6	0.484716	0.242358	−	0.970187i	$-0.422079\pi$
$467$	2.28444e6	0.484716	0.242358	+	0.970187i	$0.422079\pi$
$468$	0	0
$469$	−1.10614e7	−2.32208
$470$	0	0
$471$	−7.98564e6	−1.65866
$472$	0	0
$473$	7018.00	0.00144232
$474$	0	0
$475$	−1.32437e6	−0.269324
$476$	0	0
$477$	−1.21502e7	−2.44504
$478$	0	0
$479$	−951544.	−0.189492	−0.0947458	−	0.995501i	$-0.530204\pi$
$479$	−951544.	−0.189492	−0.0947458	+	0.995501i	$0.530204\pi$
$480$	0	0
$481$	905296.	0.178414
$482$	0	0
$483$	1.29465e7	2.52513
$484$	0	0
$485$	159929.	0.0308726
$486$	0	0
$487$	−3.51484e6	−0.671558	−0.335779	−	0.941941i	$-0.609000\pi$
$487$	−3.51484e6	−0.671558	−0.335779	+	0.941941i	$0.609000\pi$
$488$	0	0
$489$	−8.46626e6	−1.60110
$490$	0	0
$491$	5.78719e6	1.08334	0.541669	−	0.840592i	$-0.317793\pi$
$491$	5.78719e6	1.08334	0.541669	+	0.840592i	$0.317793\pi$
$492$	0	0
$493$	−1.36126e6	−0.252246
$494$	0	0
$495$	2.24310e6	0.411467
$496$	0	0
$497$	5.74241e6	1.04281
$498$	0	0
$499$	−1.02912e6	−0.185019	−0.0925095	−	0.995712i	$-0.529489\pi$
$499$	−1.02912e6	−0.185019	−0.0925095	+	0.995712i	$0.529489\pi$
$500$	0	0
$501$	9.78298e6	1.74131
$502$	0	0
$503$	727370.	0.128184	0.0640922	−	0.997944i	$-0.479585\pi$
$503$	727370.	0.128184	0.0640922	+	0.997944i	$0.479585\pi$
$504$	0	0
$505$	1.90421e6	0.332266
$506$	0	0
$507$	−1.04037e7	−1.79750
$508$	0	0
$509$	−1.94630e6	−0.332977	−0.166489	−	0.986043i	$-0.553243\pi$
$509$	−1.94630e6	−0.332977	−0.166489	+	0.986043i	$0.553243\pi$
$510$	0	0
$511$	−9.72624e6	−1.64776
$512$	0	0
$513$	6.30054e6	1.05702
$514$	0	0
$515$	5.76278e6	0.957445
$516$	0	0
$517$	1.04738e6	0.172336
$518$	0	0
$519$	−3.38552e6	−0.551705
$520$	0	0
$521$	−1.03133e7	−1.66457	−0.832286	−	0.554346i	$-0.812968\pi$
$521$	−1.03133e7	−1.66457	−0.832286	+	0.554346i	$0.812968\pi$
$522$	0	0
$523$	6.86840e6	1.09800	0.548998	−	0.835823i	$-0.315009\pi$
$523$	6.86840e6	1.09800	0.548998	+	0.835823i	$0.315009\pi$
$524$	0	0
$525$	−1.44339e7	−2.28552
$526$	0	0
$527$	−1.18425e6	−0.185746
$528$	0	0
$529$	−2.66886e6	−0.414655
$530$	0	0
$531$	1.27679e7	1.96509
$532$	0	0
$533$	−1.16973e6	−0.178347
$534$	0	0
$535$	−743070.	−0.112239
$536$	0	0
$537$	554103.	0.0829191
$538$	0	0
$539$	−4.36725e6	−0.647495
$540$	0	0
$541$	1.00545e7	1.47695	0.738476	−	0.674280i	$-0.235546\pi$
$541$	1.00545e7	1.47695	0.738476	+	0.674280i	$0.235546\pi$
$542$	0	0
$543$	−469133.	−0.0682805
$544$	0	0
$545$	1.74611e6	0.251814
$546$	0	0
$547$	−9.85725e6	−1.40860	−0.704299	−	0.709903i	$-0.748739\pi$
$547$	−9.85725e6	−1.40860	−0.704299	+	0.709903i	$0.748739\pi$
$548$	0	0
$549$	2.81323e7	3.98359
$550$	0	0
$551$	729504.	0.102364
$552$	0	0
$553$	1.66543e7	2.31587
$554$	0	0
$555$	−7.26662e6	−1.00138
$556$	0	0
$557$	−1.45892e7	−1.99247	−0.996237	−	0.0866757i	$-0.972376\pi$
$557$	−1.45892e7	−1.99247	−0.996237	+	0.0866757i	$0.972376\pi$
$558$	0	0
$559$	−6496.00	−0.000879258 0
$560$	0	0
$561$	4.00728e6	0.537579
$562$	0	0
$563$	1.02413e7	1.36171	0.680855	−	0.732418i	$-0.261608\pi$
$563$	1.02413e7	1.36171	0.680855	+	0.732418i	$0.261608\pi$
$564$	0	0
$565$	8.11899e6	1.06999
$566$	0	0
$567$	3.52454e7	4.60410
$568$	0	0
$569$	−751816.	−0.0973489	−0.0486744	−	0.998815i	$-0.515500\pi$
$569$	−751816.	−0.0973489	−0.0486744	+	0.998815i	$0.515500\pi$
$570$	0	0
$571$	7.01854e6	0.900858	0.450429	−	0.892812i	$-0.351271\pi$
$571$	7.01854e6	0.900858	0.450429	+	0.892812i	$0.351271\pi$
$572$	0	0
$573$	−1.98747e7	−2.52879
$574$	0	0
$575$	−4.20032e6	−0.529801
$576$	0	0
$577$	−3.36377e6	−0.420617	−0.210308	−	0.977635i	$-0.567447\pi$
$577$	−3.36377e6	−0.420617	−0.210308	+	0.977635i	$0.567447\pi$
$578$	0	0
$579$	−8.96947e6	−1.11191
$580$	0	0
$581$	3.63538e6	0.446796
$582$	0	0
$583$	2.45848e6	0.299568
$584$	0	0
$585$	−2.07626e6	−0.250837
$586$	0	0
$587$	−1.40585e7	−1.68401	−0.842006	−	0.539468i	$-0.818625\pi$
$587$	−1.40585e7	−1.68401	−0.842006	+	0.539468i	$0.818625\pi$
$588$	0	0
$589$	634644.	0.0753775
$590$	0	0
$591$	−3.50697e6	−0.413013
$592$	0	0
$593$	−5.39420e6	−0.629927	−0.314963	−	0.949104i	$-0.601992\pi$
$593$	−5.39420e6	−0.629927	−0.314963	+	0.949104i	$0.601992\pi$
$594$	0	0
$595$	8.14246e6	0.942895
$596$	0	0
$597$	−2.65505e7	−3.04886
$598$	0	0
$599$	1.20204e7	1.36883	0.684417	−	0.729090i	$-0.260057\pi$
$599$	1.20204e7	1.36883	0.684417	+	0.729090i	$0.260057\pi$
$600$	0	0
$601$	1.64636e6	0.185925	0.0929626	−	0.995670i	$-0.470366\pi$
$601$	1.64636e6	0.185925	0.0929626	+	0.995670i	$0.470366\pi$
$602$	0	0
$603$	−2.87596e7	−3.22099
$604$	0	0
$605$	−453871.	−0.0504132
$606$	0	0
$607$	−4.88451e6	−0.538083	−0.269041	−	0.963129i	$-0.586707\pi$
$607$	−4.88451e6	−0.538083	−0.269041	+	0.963129i	$0.586707\pi$
$608$	0	0
$609$	7.95064e6	0.868678
$610$	0	0
$611$	−969472.	−0.105059
$612$	0	0
$613$	3.49011e6	0.375136	0.187568	−	0.982252i	$-0.439940\pi$
$613$	3.49011e6	0.375136	0.187568	+	0.982252i	$0.439940\pi$
$614$	0	0
$615$	9.38916e6	1.00101
$616$	0	0
$617$	9.12072e6	0.964531	0.482266	−	0.876025i	$-0.339814\pi$
$617$	9.12072e6	0.964531	0.482266	+	0.876025i	$0.339814\pi$
$618$	0	0
$619$	−1.46635e7	−1.53820	−0.769098	−	0.639131i	$-0.779294\pi$
$619$	−1.46635e7	−1.53820	−0.769098	+	0.639131i	$0.779294\pi$
$620$	0	0
$621$	1.99826e7	2.07933
$622$	0	0
$623$	−2.63950e7	−2.72460
$624$	0	0
$625$	1.67977e6	0.172009
$626$	0	0
$627$	−2.14751e6	−0.218155
$628$	0	0
$629$	−9.23079e6	−0.930277
$630$	0	0
$631$	1.63870e7	1.63842	0.819212	−	0.573491i	$-0.194411\pi$
$631$	1.63870e7	1.63842	0.819212	+	0.573491i	$0.194411\pi$
$632$	0	0
$633$	3.90282e6	0.387141
$634$	0	0
$635$	2.70952e6	0.266660
$636$	0	0
$637$	4.04242e6	0.394723
$638$	0	0
$639$	1.49303e7	1.44649
$640$	0	0
$641$	−3.26835e6	−0.314184	−0.157092	−	0.987584i	$-0.550212\pi$
$641$	−3.26835e6	−0.314184	−0.157092	+	0.987584i	$0.550212\pi$
$642$	0	0
$643$	−8.32842e6	−0.794393	−0.397197	−	0.917734i	$-0.630017\pi$
$643$	−8.32842e6	−0.794393	−0.397197	+	0.917734i	$0.630017\pi$
$644$	0	0
$645$	52142.0	0.00493501
$646$	0	0
$647$	−2.49694e6	−0.234503	−0.117251	−	0.993102i	$-0.537408\pi$
$647$	−2.49694e6	−0.234503	−0.117251	+	0.993102i	$0.537408\pi$
$648$	0	0
$649$	−2.58347e6	−0.240764
$650$	0	0
$651$	6.91679e6	0.639664
$652$	0	0
$653$	−789105.	−0.0724189	−0.0362094	−	0.999344i	$-0.511528\pi$
$653$	−789105.	−0.0724189	−0.0362094	+	0.999344i	$0.511528\pi$
$654$	0	0
$655$	8.21878e6	0.748521
$656$	0	0
$657$	−2.52882e7	−2.28562
$658$	0	0
$659$	8.31393e6	0.745749	0.372874	−	0.927882i	$-0.378372\pi$
$659$	8.31393e6	0.745749	0.372874	+	0.927882i	$0.378372\pi$
$660$	0	0
$661$	−4.33517e6	−0.385925	−0.192962	−	0.981206i	$-0.561810\pi$
$661$	−4.33517e6	−0.385925	−0.192962	+	0.981206i	$0.561810\pi$
$662$	0	0
$663$	−3.70922e6	−0.327716
$664$	0	0
$665$	−4.36356e6	−0.382637
$666$	0	0
$667$	2.31367e6	0.201366
$668$	0	0
$669$	−1.35963e7	−1.17451
$670$	0	0
$671$	−5.69232e6	−0.488071
$672$	0	0
$673$	7.29313e6	0.620693	0.310346	−	0.950624i	$-0.399555\pi$
$673$	7.29313e6	0.620693	0.310346	+	0.950624i	$0.399555\pi$
$674$	0	0
$675$	−2.22784e7	−1.88202
$676$	0	0
$677$	1.55814e7	1.30658	0.653288	−	0.757109i	$-0.273389\pi$
$677$	1.55814e7	1.30658	0.653288	+	0.757109i	$0.273389\pi$
$678$	0	0
$679$	−1.18657e6	−0.0987686
$680$	0	0
$681$	−7.97564e6	−0.659019
$682$	0	0
$683$	2.16930e6	0.177938	0.0889690	−	0.996034i	$-0.471643\pi$
$683$	2.16930e6	0.177938	0.0889690	+	0.996034i	$0.471643\pi$
$684$	0	0
$685$	−7.62157e6	−0.620609
$686$	0	0
$687$	−1.86261e7	−1.50567
$688$	0	0
$689$	−2.27562e6	−0.182621
$690$	0	0
$691$	1.32195e7	1.05322	0.526610	−	0.850107i	$-0.323463\pi$
$691$	1.32195e7	1.05322	0.526610	+	0.850107i	$0.323463\pi$
$692$	0	0
$693$	−1.66423e7	−1.31638
$694$	0	0
$695$	−1.12714e7	−0.885149
$696$	0	0
$697$	1.19270e7	0.929932
$698$	0	0
$699$	−4.36406e7	−3.37830
$700$	0	0
$701$	−2.59395e7	−1.99373	−0.996866	−	0.0791122i	$-0.974791\pi$
$701$	−2.59395e7	−1.99373	−0.996866	+	0.0791122i	$0.974791\pi$
$702$	0	0
$703$	4.94680e6	0.377516
$704$	0	0
$705$	7.78174e6	0.589663
$706$	0	0
$707$	−1.41280e7	−1.06300
$708$	0	0
$709$	3.57531e6	0.267115	0.133557	−	0.991041i	$-0.457360\pi$
$709$	3.57531e6	0.267115	0.133557	+	0.991041i	$0.457360\pi$
$710$	0	0
$711$	4.33012e7	3.21237
$712$	0	0
$713$	2.01282e6	0.148279
$714$	0	0
$715$	420112.	0.0307326
$716$	0	0
$717$	8.83613e6	0.641895
$718$	0	0
$719$	1.95814e6	0.141261	0.0706304	−	0.997503i	$-0.477499\pi$
$719$	1.95814e6	0.141261	0.0706304	+	0.997503i	$0.477499\pi$
$720$	0	0
$721$	−4.27561e7	−3.06309
$722$	0	0
$723$	3.68824e7	2.62406
$724$	0	0
$725$	−2.57949e6	−0.182259
$726$	0	0
$727$	−1.55360e7	−1.09019	−0.545095	−	0.838374i	$-0.683507\pi$
$727$	−1.55360e7	−1.09019	−0.545095	+	0.838374i	$0.683507\pi$
$728$	0	0
$729$	1.90893e7	1.33036
$730$	0	0
$731$	66236.0	0.00458459
$732$	0	0
$733$	−1.46002e7	−1.00369	−0.501844	−	0.864958i	$-0.667345\pi$
$733$	−1.46002e7	−1.00369	−0.501844	+	0.864958i	$0.667345\pi$
$734$	0	0
$735$	−3.24476e7	−2.21546
$736$	0	0
$737$	5.81925e6	0.394638
$738$	0	0
$739$	2.06682e7	1.39217	0.696085	−	0.717959i	$-0.254923\pi$
$739$	2.06682e7	1.39217	0.696085	+	0.717959i	$0.254923\pi$
$740$	0	0
$741$	1.98778e6	0.132991
$742$	0	0
$743$	−1.17065e7	−0.777953	−0.388976	−	0.921248i	$-0.627171\pi$
$743$	−1.17065e7	−0.777953	−0.388976	+	0.921248i	$0.627171\pi$
$744$	0	0
$745$	1.72825e6	0.114082
$746$	0	0
$747$	9.45199e6	0.619757
$748$	0	0
$749$	5.51310e6	0.359080
$750$	0	0
$751$	1.27607e7	0.825610	0.412805	−	0.910819i	$-0.364549\pi$
$751$	1.27607e7	0.825610	0.412805	+	0.910819i	$0.364549\pi$
$752$	0	0
$753$	−1.82690e7	−1.17416
$754$	0	0
$755$	2.03490e6	0.129920
$756$	0	0
$757$	−1.40869e7	−0.893458	−0.446729	−	0.894669i	$-0.647411\pi$
$757$	−1.40869e7	−0.893458	−0.446729	+	0.894669i	$0.647411\pi$
$758$	0	0
$759$	−6.81097e6	−0.429145
$760$	0	0
$761$	2.33822e7	1.46360	0.731801	−	0.681518i	$-0.238680\pi$
$761$	2.33822e7	1.46360	0.731801	+	0.681518i	$0.238680\pi$
$762$	0	0
$763$	−1.29550e7	−0.805611
$764$	0	0
$765$	2.11704e7	1.30790
$766$	0	0
$767$	2.39131e6	0.146774
$768$	0	0
$769$	−1.09575e7	−0.668185	−0.334092	−	0.942540i	$-0.608430\pi$
$769$	−1.09575e7	−0.668185	−0.334092	+	0.942540i	$0.608430\pi$
$770$	0	0
$771$	1.57785e7	0.955938
$772$	0	0
$773$	1.69336e7	1.01930	0.509648	−	0.860383i	$-0.329776\pi$
$773$	1.69336e7	1.01930	0.509648	+	0.860383i	$0.329776\pi$
$774$	0	0
$775$	−2.24407e6	−0.134209
$776$	0	0
$777$	5.39136e7	3.20366
$778$	0	0
$779$	−6.39173e6	−0.377376
$780$	0	0
$781$	−3.02101e6	−0.177225
$782$	0	0
$783$	1.22716e7	0.715316
$784$	0	0
$785$	8.53638e6	0.494424
$786$	0	0
$787$	7.51655e6	0.432595	0.216298	−	0.976327i	$-0.430602\pi$
$787$	7.51655e6	0.432595	0.216298	+	0.976327i	$0.430602\pi$
$788$	0	0
$789$	5.76907e7	3.29923
$790$	0	0
$791$	−6.02377e7	−3.42316
$792$	0	0
$793$	5.26893e6	0.297536
$794$	0	0
$795$	1.82659e7	1.02500
$796$	0	0
$797$	3.93788e6	0.219592	0.109796	−	0.993954i	$-0.464980\pi$
$797$	3.93788e6	0.219592	0.109796	+	0.993954i	$0.464980\pi$
$798$	0	0
$799$	9.88515e6	0.547793
$800$	0	0
$801$	−6.86271e7	−3.77932
$802$	0	0
$803$	5.11685e6	0.280036
$804$	0	0
$805$	−1.38393e7	−0.752706
$806$	0	0
$807$	5.08793e7	2.75015
$808$	0	0
$809$	−1.73609e7	−0.932612	−0.466306	−	0.884624i	$-0.654415\pi$
$809$	−1.73609e7	−0.932612	−0.466306	+	0.884624i	$0.654415\pi$
$810$	0	0
$811$	−2.70850e7	−1.44603	−0.723014	−	0.690833i	$-0.757244\pi$
$811$	−2.70850e7	−1.44603	−0.723014	+	0.690833i	$0.757244\pi$
$812$	0	0
$813$	4.80890e7	2.55164
$814$	0	0
$815$	9.05014e6	0.477267
$816$	0	0
$817$	−35496.0	−0.00186048
$818$	0	0
$819$	1.54045e7	0.802486
$820$	0	0
$821$	3.59384e7	1.86080	0.930402	−	0.366540i	$-0.119458\pi$
$821$	3.59384e7	1.86080	0.930402	+	0.366540i	$0.119458\pi$
$822$	0	0
$823$	505509.	0.0260153	0.0130077	−	0.999915i	$-0.495859\pi$
$823$	505509.	0.0260153	0.0130077	+	0.999915i	$0.495859\pi$
$824$	0	0
$825$	7.59348e6	0.388424
$826$	0	0
$827$	2.99955e7	1.52508	0.762539	−	0.646942i	$-0.223952\pi$
$827$	2.99955e7	1.52508	0.762539	+	0.646942i	$0.223952\pi$
$828$	0	0
$829$	2.96942e7	1.50067	0.750334	−	0.661059i	$-0.229893\pi$
$829$	2.96942e7	1.50067	0.750334	+	0.661059i	$0.229893\pi$
$830$	0	0
$831$	−1.23639e6	−0.0621086
$832$	0	0
$833$	−4.12182e7	−2.05815
$834$	0	0
$835$	−1.04577e7	−0.519061
$836$	0	0
$837$	1.06759e7	0.526734
$838$	0	0
$839$	1.41371e7	0.693356	0.346678	−	0.937984i	$-0.387310\pi$
$839$	1.41371e7	0.693356	0.346678	+	0.937984i	$0.387310\pi$
$840$	0	0
$841$	−1.90903e7	−0.930727
$842$	0	0
$843$	9.26579e6	0.449069
$844$	0	0
$845$	1.11212e7	0.535810
$846$	0	0
$847$	3.36743e6	0.161284
$848$	0	0
$849$	5.87931e7	2.79935
$850$	0	0
$851$	1.56891e7	0.742633
$852$	0	0
$853$	−4.68539e6	−0.220482	−0.110241	−	0.993905i	$-0.535162\pi$
$853$	−4.68539e6	−0.220482	−0.110241	+	0.993905i	$0.535162\pi$
$854$	0	0
$855$	−1.13453e7	−0.530761
$856$	0	0
$857$	−4.12846e7	−1.92015	−0.960076	−	0.279740i	$-0.909752\pi$
$857$	−4.12846e7	−1.92015	−0.960076	+	0.279740i	$0.909752\pi$
$858$	0	0
$859$	3.54805e6	0.164062	0.0820308	−	0.996630i	$-0.473859\pi$
$859$	3.54805e6	0.164062	0.0820308	+	0.996630i	$0.473859\pi$
$860$	0	0
$861$	−6.96615e7	−3.20247
$862$	0	0
$863$	3.07605e7	1.40594	0.702970	−	0.711219i	$-0.251857\pi$
$863$	3.07605e7	1.40594	0.702970	+	0.711219i	$0.251857\pi$
$864$	0	0
$865$	3.61900e6	0.164456
$866$	0	0
$867$	−3.35510e6	−0.151585
$868$	0	0
$869$	−8.76161e6	−0.393581
$870$	0	0
$871$	−5.38642e6	−0.240577
$872$	0	0
$873$	−3.08508e6	−0.137003
$874$	0	0
$875$	3.77106e7	1.66511
$876$	0	0
$877$	3.05535e7	1.34141	0.670706	−	0.741723i	$-0.265991\pi$
$877$	3.05535e7	1.34141	0.670706	+	0.741723i	$0.265991\pi$
$878$	0	0
$879$	2.08465e7	0.910040
$880$	0	0
$881$	4.21018e7	1.82751	0.913757	−	0.406262i	$-0.133168\pi$
$881$	4.21018e7	1.82751	0.913757	+	0.406262i	$0.133168\pi$
$882$	0	0
$883$	−57164.0	−0.00246729	−0.00123365	−	0.999999i	$-0.500393\pi$
$883$	−57164.0	−0.00246729	−0.00123365	+	0.999999i	$0.500393\pi$
$884$	0	0
$885$	−1.91945e7	−0.823796
$886$	0	0
$887$	1.16106e7	0.495504	0.247752	−	0.968824i	$-0.420308\pi$
$887$	1.16106e7	0.495504	0.247752	+	0.968824i	$0.420308\pi$
$888$	0	0
$889$	−2.01029e7	−0.853109
$890$	0	0
$891$	−1.85422e7	−0.782467
$892$	0	0
$893$	−5.29747e6	−0.222300
$894$	0	0
$895$	−592317.	−0.0247170
$896$	0	0
$897$	6.30437e6	0.261614
$898$	0	0
$899$	1.23610e6	0.0510101
$900$	0	0
$901$	2.32032e7	0.952215
$902$	0	0
$903$	−386860.	−0.0157883
$904$	0	0
$905$	501487.	0.0203535
$906$	0	0
$907$	−2.09855e7	−0.847034	−0.423517	−	0.905888i	$-0.639205\pi$
$907$	−2.09855e7	−0.847034	−0.423517	+	0.905888i	$0.639205\pi$
$908$	0	0
$909$	−3.67327e7	−1.47450
$910$	0	0
$911$	−4.74125e7	−1.89277	−0.946383	−	0.323047i	$-0.895293\pi$
$911$	−4.74125e7	−1.89277	−0.946383	+	0.323047i	$0.895293\pi$
$912$	0	0
$913$	−1.91253e6	−0.0759330
$914$	0	0
$915$	−4.22926e7	−1.66998
$916$	0	0
$917$	−6.09781e7	−2.39470
$918$	0	0
$919$	−4.04326e7	−1.57922	−0.789610	−	0.613609i	$-0.789717\pi$
$919$	−4.04326e7	−1.57922	−0.789610	+	0.613609i	$0.789717\pi$
$920$	0	0
$921$	5.74612e7	2.23216
$922$	0	0
$923$	2.79630e6	0.108039
$924$	0	0
$925$	−1.74916e7	−0.672164
$926$	0	0
$927$	−1.11166e8	−4.24885
$928$	0	0
$929$	3.30757e7	1.25739	0.628694	−	0.777652i	$-0.283590\pi$
$929$	3.30757e7	1.25739	0.628694	+	0.777652i	$0.283590\pi$
$930$	0	0
$931$	2.20889e7	0.835219
$932$	0	0
$933$	4.37987e7	1.64724
$934$	0	0
$935$	−4.28364e6	−0.160245
$936$	0	0
$937$	−3.15132e7	−1.17258	−0.586292	−	0.810100i	$-0.699413\pi$
$937$	−3.15132e7	−1.17258	−0.586292	+	0.810100i	$0.699413\pi$
$938$	0	0
$939$	5.80267e7	2.14765
$940$	0	0
$941$	−9.54147e6	−0.351270	−0.175635	−	0.984455i	$-0.556198\pi$
$941$	−9.54147e6	−0.351270	−0.175635	+	0.984455i	$0.556198\pi$
$942$	0	0
$943$	−2.02718e7	−0.742358
$944$	0	0
$945$	−7.34034e7	−2.67385
$946$	0	0
$947$	−2.24208e7	−0.812410	−0.406205	−	0.913782i	$-0.633148\pi$
$947$	−2.24208e7	−0.812410	−0.406205	+	0.913782i	$0.633148\pi$
$948$	0	0
$949$	−4.73626e6	−0.170714
$950$	0	0
$951$	−7.52060e6	−0.269650
$952$	0	0
$953$	1.68985e7	0.602720	0.301360	−	0.953510i	$-0.402559\pi$
$953$	1.68985e7	0.602720	0.301360	+	0.953510i	$0.402559\pi$
$954$	0	0
$955$	2.12453e7	0.753798
$956$	0	0
$957$	−4.18273e6	−0.147632
$958$	0	0
$959$	5.65471e7	1.98547
$960$	0	0
$961$	−2.75538e7	−0.962438
$962$	0	0
$963$	1.43341e7	0.498085
$964$	0	0
$965$	9.58805e6	0.331445
$966$	0	0
$967$	3.06946e7	1.05559	0.527796	−	0.849371i	$-0.323018\pi$
$967$	3.06946e7	1.05559	0.527796	+	0.849371i	$0.323018\pi$
$968$	0	0
$969$	−2.02682e7	−0.693436
$970$	0	0
$971$	−3.35664e7	−1.14250	−0.571251	−	0.820776i	$-0.693542\pi$
$971$	−3.35664e7	−1.14250	−0.571251	+	0.820776i	$0.693542\pi$
$972$	0	0
$973$	8.36266e7	2.83180
$974$	0	0
$975$	−7.02867e6	−0.236789
$976$	0	0
$977$	2.47897e7	0.830873	0.415436	−	0.909622i	$-0.363629\pi$
$977$	2.47897e7	0.830873	0.415436	+	0.909622i	$0.363629\pi$
$978$	0	0
$979$	1.38861e7	0.463045
$980$	0	0
$981$	−3.36829e7	−1.11747
$982$	0	0
$983$	−5.22606e6	−0.172501	−0.0862503	−	0.996274i	$-0.527488\pi$
$983$	−5.22606e6	−0.172501	−0.0862503	+	0.996274i	$0.527488\pi$
$984$	0	0
$985$	3.74883e6	0.123113
$986$	0	0
$987$	−5.77355e7	−1.88647
$988$	0	0
$989$	−112578.	−0.00365985
$990$	0	0
$991$	−2.40826e7	−0.778967	−0.389484	−	0.921033i	$-0.627347\pi$
$991$	−2.40826e7	−0.778967	−0.389484	+	0.921033i	$0.627347\pi$
$992$	0	0
$993$	−1.48489e6	−0.0477882
$994$	0	0
$995$	2.83816e7	0.908823
$996$	0	0
$997$	−1.32606e7	−0.422499	−0.211249	−	0.977432i	$-0.567753\pi$
$997$	−1.32606e7	−0.422499	−0.211249	+	0.977432i	$0.567753\pi$
$998$	0	0
$999$	8.32145e7	2.63806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.6.a.e.1.1		1
4.3	odd	2		22.6.a.c.1.1	✓	1
8.3	odd	2		704.6.a.j.1.1		1
8.5	even	2		704.6.a.a.1.1		1
12.11	even	2		198.6.a.b.1.1		1
20.3	even	4		550.6.b.a.199.1		2
20.7	even	4		550.6.b.a.199.2		2
20.19	odd	2		550.6.a.c.1.1		1
28.27	even	2		1078.6.a.f.1.1		1
44.43	even	2		242.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.a.c.1.1	✓	1	4.3	odd	2
176.6.a.e.1.1		1	1.1	even	1	trivial
198.6.a.b.1.1		1	12.11	even	2
242.6.a.a.1.1		1	44.43	even	2
550.6.a.c.1.1		1	20.19	odd	2
550.6.b.a.199.1		2	20.3	even	4
550.6.b.a.199.2		2	20.7	even	4
704.6.a.a.1.1		1	8.5	even	2
704.6.a.j.1.1		1	8.3	odd	2
1078.6.a.f.1.1		1	28.27	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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	176.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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