LMFDB - Embedded newform 704.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,4,Mod(1,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("704.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	704.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:	$41.5373446440$
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	$\chi$	$=$	704.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-7.00000 q^{3} +19.0000 q^{5} -14.0000 q^{7} +22.0000 q^{9} +O(q^{10})$

$q-7.00000 q^{3} +19.0000 q^{5} -14.0000 q^{7} +22.0000 q^{9} +11.0000 q^{11} +72.0000 q^{13} -133.000 q^{15} -46.0000 q^{17} -20.0000 q^{19} +98.0000 q^{21} +107.000 q^{23} +236.000 q^{25} +35.0000 q^{27} -120.000 q^{29} -117.000 q^{31} -77.0000 q^{33} -266.000 q^{35} +201.000 q^{37} -504.000 q^{39} -228.000 q^{41} -242.000 q^{43} +418.000 q^{45} +96.0000 q^{47} -147.000 q^{49} +322.000 q^{51} -458.000 q^{53} +209.000 q^{55} +140.000 q^{57} +435.000 q^{59} +668.000 q^{61} -308.000 q^{63} +1368.00 q^{65} +439.000 q^{67} -749.000 q^{69} +1113.00 q^{71} -72.0000 q^{73} -1652.00 q^{75} -154.000 q^{77} +70.0000 q^{79} -839.000 q^{81} +358.000 q^{83} -874.000 q^{85} +840.000 q^{87} +895.000 q^{89} -1008.00 q^{91} +819.000 q^{93} -380.000 q^{95} +409.000 q^{97} +242.000 q^{99} +O(q^{100})$

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	−1.34715	−0.673575	−	0.739119i	$-0.735242\pi$
$3$	−7.00000	−1.34715	−0.673575	+	0.739119i	$0.735242\pi$
$4$	0	0
$5$	19.0000	1.69941	0.849706	−	0.527257i	$-0.176780\pi$
$5$	19.0000	1.69941	0.849706	+	0.527257i	$0.176780\pi$
$6$	0	0
$7$	−14.0000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−14.0000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	0	0
$9$	22.0000	0.814815
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0	0
$13$	72.0000	1.53609	0.768046	−	0.640394i	$-0.221229\pi$
$13$	72.0000	1.53609	0.768046	+	0.640394i	$0.221229\pi$
$14$	0	0
$15$	−133.000	−2.28936
$16$	0	0
$17$	−46.0000	−0.656273	−0.328136	−	0.944630i	$-0.606421\pi$
$17$	−46.0000	−0.656273	−0.328136	+	0.944630i	$0.606421\pi$
$18$	0	0
$19$	−20.0000	−0.241490	−0.120745	−	0.992684i	$-0.538528\pi$
$19$	−20.0000	−0.241490	−0.120745	+	0.992684i	$0.538528\pi$
$20$	0	0
$21$	98.0000	1.01835
$22$	0	0
$23$	107.000	0.970045	0.485023	−	0.874502i	$-0.338811\pi$
$23$	107.000	0.970045	0.485023	+	0.874502i	$0.338811\pi$
$24$	0	0
$25$	236.000	1.88800
$26$	0	0
$27$	35.0000	0.249472
$28$	0	0
$29$	−120.000	−0.768395	−0.384197	−	0.923251i	$-0.625522\pi$
$29$	−120.000	−0.768395	−0.384197	+	0.923251i	$0.625522\pi$
$30$	0	0
$31$	−117.000	−0.677865	−0.338933	−	0.940811i	$-0.610066\pi$
$31$	−117.000	−0.677865	−0.338933	+	0.940811i	$0.610066\pi$
$32$	0	0
$33$	−77.0000	−0.406181
$34$	0	0
$35$	−266.000	−1.28463
$36$	0	0
$37$	201.000	0.893086	0.446543	−	0.894762i	$-0.352655\pi$
$37$	201.000	0.893086	0.446543	+	0.894762i	$0.352655\pi$
$38$	0	0
$39$	−504.000	−2.06935
$40$	0	0
$41$	−228.000	−0.868478	−0.434239	−	0.900798i	$-0.642983\pi$
$41$	−228.000	−0.868478	−0.434239	+	0.900798i	$0.642983\pi$
$42$	0	0
$43$	−242.000	−0.858248	−0.429124	−	0.903246i	$-0.641178\pi$
$43$	−242.000	−0.858248	−0.429124	+	0.903246i	$0.641178\pi$
$44$	0	0
$45$	418.000	1.38471
$46$	0	0
$47$	96.0000	0.297937	0.148969	−	0.988842i	$-0.452405\pi$
$47$	96.0000	0.297937	0.148969	+	0.988842i	$0.452405\pi$
$48$	0	0
$49$	−147.000	−0.428571
$50$	0	0
$51$	322.000	0.884098
$52$	0	0
$53$	−458.000	−1.18700	−0.593501	−	0.804833i	$-0.702255\pi$
$53$	−458.000	−1.18700	−0.593501	+	0.804833i	$0.702255\pi$
$54$	0	0
$55$	209.000	0.512392
$56$	0	0
$57$	140.000	0.325324
$58$	0	0
$59$	435.000	0.959867	0.479934	−	0.877305i	$-0.340661\pi$
$59$	435.000	0.959867	0.479934	+	0.877305i	$0.340661\pi$
$60$	0	0
$61$	668.000	1.40211	0.701054	−	0.713108i	$-0.252713\pi$
$61$	668.000	1.40211	0.701054	+	0.713108i	$0.252713\pi$
$62$	0	0
$63$	−308.000	−0.615942
$64$	0	0
$65$	1368.00	2.61045
$66$	0	0
$67$	439.000	0.800483	0.400242	−	0.916410i	$-0.368926\pi$
$67$	439.000	0.800483	0.400242	+	0.916410i	$0.368926\pi$
$68$	0	0
$69$	−749.000	−1.30680
$70$	0	0
$71$	1113.00	1.86041	0.930203	−	0.367046i	$-0.119631\pi$
$71$	1113.00	1.86041	0.930203	+	0.367046i	$0.119631\pi$
$72$	0	0
$73$	−72.0000	−0.115438	−0.0577189	−	0.998333i	$-0.518383\pi$
$73$	−72.0000	−0.115438	−0.0577189	+	0.998333i	$0.518383\pi$
$74$	0	0
$75$	−1652.00	−2.54342
$76$	0	0
$77$	−154.000	−0.227921
$78$	0	0
$79$	70.0000	0.0996913	0.0498457	−	0.998757i	$-0.484127\pi$
$79$	70.0000	0.0996913	0.0498457	+	0.998757i	$0.484127\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	0	0
$83$	358.000	0.473441	0.236721	−	0.971578i	$-0.423927\pi$
$83$	358.000	0.473441	0.236721	+	0.971578i	$0.423927\pi$
$84$	0	0
$85$	−874.000	−1.11528
$86$	0	0
$87$	840.000	1.03514
$88$	0	0
$89$	895.000	1.06595	0.532976	−	0.846130i	$-0.321073\pi$
$89$	895.000	1.06595	0.532976	+	0.846130i	$0.321073\pi$
$90$	0	0
$91$	−1008.00	−1.16118
$92$	0	0
$93$	819.000	0.913186
$94$	0	0
$95$	−380.000	−0.410391
$96$	0	0
$97$	409.000	0.428120	0.214060	−	0.976820i	$-0.431331\pi$
$97$	409.000	0.428120	0.214060	+	0.976820i	$0.431331\pi$
$98$	0	0
$99$	242.000	0.245676
$100$	0	0
$101$	898.000	0.884696	0.442348	−	0.896843i	$-0.354146\pi$
$101$	898.000	0.884696	0.442348	+	0.896843i	$0.354146\pi$
$102$	0	0
$103$	312.000	0.298469	0.149234	−	0.988802i	$-0.452319\pi$
$103$	312.000	0.298469	0.149234	+	0.988802i	$0.452319\pi$
$104$	0	0
$105$	1862.00	1.73060
$106$	0	0
$107$	274.000	0.247557	0.123778	−	0.992310i	$-0.460499\pi$
$107$	274.000	0.247557	0.123778	+	0.992310i	$0.460499\pi$
$108$	0	0
$109$	1470.00	1.29175	0.645874	−	0.763444i	$-0.276493\pi$
$109$	1470.00	1.29175	0.645874	+	0.763444i	$0.276493\pi$
$110$	0	0
$111$	−1407.00	−1.20312
$112$	0	0
$113$	113.000	0.0940721	0.0470360	−	0.998893i	$-0.485022\pi$
$113$	113.000	0.0940721	0.0470360	+	0.998893i	$0.485022\pi$
$114$	0	0
$115$	2033.00	1.64851
$116$	0	0
$117$	1584.00	1.25163
$118$	0	0
$119$	644.000	0.496096
$120$	0	0
$121$	121.000	0.0909091
$122$	0	0
$123$	1596.00	1.16997
$124$	0	0
$125$	2109.00	1.50908
$126$	0	0
$127$	1476.00	1.03129	0.515645	−	0.856802i	$-0.327552\pi$
$127$	1476.00	1.03129	0.515645	+	0.856802i	$0.327552\pi$
$128$	0	0
$129$	1694.00	1.15619
$130$	0	0
$131$	1342.00	0.895046	0.447523	−	0.894272i	$-0.352306\pi$
$131$	1342.00	0.895046	0.447523	+	0.894272i	$0.352306\pi$
$132$	0	0
$133$	280.000	0.182549
$134$	0	0
$135$	665.000	0.423956
$136$	0	0
$137$	1769.00	1.10318	0.551591	−	0.834115i	$-0.314021\pi$
$137$	1769.00	1.10318	0.551591	+	0.834115i	$0.314021\pi$
$138$	0	0
$139$	−550.000	−0.335614	−0.167807	−	0.985820i	$-0.553669\pi$
$139$	−550.000	−0.335614	−0.167807	+	0.985820i	$0.553669\pi$
$140$	0	0
$141$	−672.000	−0.401366
$142$	0	0
$143$	792.000	0.463149
$144$	0	0
$145$	−2280.00	−1.30582
$146$	0	0
$147$	1029.00	0.577350
$148$	0	0
$149$	790.000	0.434358	0.217179	−	0.976132i	$-0.430314\pi$
$149$	790.000	0.434358	0.217179	+	0.976132i	$0.430314\pi$
$150$	0	0
$151$	−2902.00	−1.56398	−0.781991	−	0.623289i	$-0.785796\pi$
$151$	−2902.00	−1.56398	−0.781991	+	0.623289i	$0.785796\pi$
$152$	0	0
$153$	−1012.00	−0.534741
$154$	0	0
$155$	−2223.00	−1.15197
$156$	0	0
$157$	−749.000	−0.380743	−0.190372	−	0.981712i	$-0.560969\pi$
$157$	−749.000	−0.380743	−0.190372	+	0.981712i	$0.560969\pi$
$158$	0	0
$159$	3206.00	1.59907
$160$	0	0
$161$	−1498.00	−0.733285
$162$	0	0
$163$	1228.00	0.590088	0.295044	−	0.955484i	$-0.404666\pi$
$163$	1228.00	0.590088	0.295044	+	0.955484i	$0.404666\pi$
$164$	0	0
$165$	−1463.00	−0.690269
$166$	0	0
$167$	−2424.00	−1.12320	−0.561601	−	0.827408i	$-0.689814\pi$
$167$	−2424.00	−1.12320	−0.561601	+	0.827408i	$0.689814\pi$
$168$	0	0
$169$	2987.00	1.35958
$170$	0	0
$171$	−440.000	−0.196770
$172$	0	0
$173$	3742.00	1.64450	0.822251	−	0.569124i	$-0.192718\pi$
$173$	3742.00	1.64450	0.822251	+	0.569124i	$0.192718\pi$
$174$	0	0
$175$	−3304.00	−1.42719
$176$	0	0
$177$	−3045.00	−1.29309
$178$	0	0
$179$	−265.000	−0.110654	−0.0553269	−	0.998468i	$-0.517620\pi$
$179$	−265.000	−0.110654	−0.0553269	+	0.998468i	$0.517620\pi$
$180$	0	0
$181$	−67.0000	−0.0275142	−0.0137571	−	0.999905i	$-0.504379\pi$
$181$	−67.0000	−0.0275142	−0.0137571	+	0.999905i	$0.504379\pi$
$182$	0	0
$183$	−4676.00	−1.88885
$184$	0	0
$185$	3819.00	1.51772
$186$	0	0
$187$	−506.000	−0.197874
$188$	0	0
$189$	−490.000	−0.188583
$190$	0	0
$191$	3453.00	1.30812	0.654058	−	0.756444i	$-0.273065\pi$
$191$	3453.00	1.30812	0.654058	+	0.756444i	$0.273065\pi$
$192$	0	0
$193$	−4172.00	−1.55600	−0.777998	−	0.628267i	$-0.783765\pi$
$193$	−4172.00	−1.55600	−0.777998	+	0.628267i	$0.783765\pi$
$194$	0	0
$195$	−9576.00	−3.51667
$196$	0	0
$197$	2426.00	0.877388	0.438694	−	0.898637i	$-0.355441\pi$
$197$	2426.00	0.877388	0.438694	+	0.898637i	$0.355441\pi$
$198$	0	0
$199$	400.000	0.142489	0.0712443	−	0.997459i	$-0.477303\pi$
$199$	400.000	0.142489	0.0712443	+	0.997459i	$0.477303\pi$
$200$	0	0
$201$	−3073.00	−1.07837
$202$	0	0
$203$	1680.00	0.580852
$204$	0	0
$205$	−4332.00	−1.47590
$206$	0	0
$207$	2354.00	0.790407
$208$	0	0
$209$	−220.000	−0.0728120
$210$	0	0
$211$	3332.00	1.08713	0.543565	−	0.839367i	$-0.317074\pi$
$211$	3332.00	1.08713	0.543565	+	0.839367i	$0.317074\pi$
$212$	0	0
$213$	−7791.00	−2.50625
$214$	0	0
$215$	−4598.00	−1.45852
$216$	0	0
$217$	1638.00	0.512418
$218$	0	0
$219$	504.000	0.155512
$220$	0	0
$221$	−3312.00	−1.00810
$222$	0	0
$223$	−6033.00	−1.81166	−0.905829	−	0.423644i	$-0.860751\pi$
$223$	−6033.00	−1.81166	−0.905829	+	0.423644i	$0.860751\pi$
$224$	0	0
$225$	5192.00	1.53837
$226$	0	0
$227$	−5646.00	−1.65083	−0.825414	−	0.564527i	$-0.809059\pi$
$227$	−5646.00	−1.65083	−0.825414	+	0.564527i	$0.809059\pi$
$228$	0	0
$229$	4645.00	1.34039	0.670197	−	0.742183i	$-0.266210\pi$
$229$	4645.00	1.34039	0.670197	+	0.742183i	$0.266210\pi$
$230$	0	0
$231$	1078.00	0.307044
$232$	0	0
$233$	−2432.00	−0.683801	−0.341900	−	0.939736i	$-0.611071\pi$
$233$	−2432.00	−0.683801	−0.341900	+	0.939736i	$0.611071\pi$
$234$	0	0
$235$	1824.00	0.506318
$236$	0	0
$237$	−490.000	−0.134299
$238$	0	0
$239$	6010.00	1.62659	0.813294	−	0.581853i	$-0.197672\pi$
$239$	6010.00	1.62659	0.813294	+	0.581853i	$0.197672\pi$
$240$	0	0
$241$	−3728.00	−0.996438	−0.498219	−	0.867051i	$-0.666012\pi$
$241$	−3728.00	−0.996438	−0.498219	+	0.867051i	$0.666012\pi$
$242$	0	0
$243$	4928.00	1.30095
$244$	0	0
$245$	−2793.00	−0.728319
$246$	0	0
$247$	−1440.00	−0.370951
$248$	0	0
$249$	−2506.00	−0.637796
$250$	0	0
$251$	527.000	0.132526	0.0662628	−	0.997802i	$-0.478892\pi$
$251$	527.000	0.132526	0.0662628	+	0.997802i	$0.478892\pi$
$252$	0	0
$253$	1177.00	0.292480
$254$	0	0
$255$	6118.00	1.50245
$256$	0	0
$257$	−1786.00	−0.433493	−0.216746	−	0.976228i	$-0.569544\pi$
$257$	−1786.00	−0.433493	−0.216746	+	0.976228i	$0.569544\pi$
$258$	0	0
$259$	−2814.00	−0.675110
$260$	0	0
$261$	−2640.00	−0.626099
$262$	0	0
$263$	−3198.00	−0.749799	−0.374899	−	0.927065i	$-0.622323\pi$
$263$	−3198.00	−0.749799	−0.374899	+	0.927065i	$0.622323\pi$
$264$	0	0
$265$	−8702.00	−2.01721
$266$	0	0
$267$	−6265.00	−1.43600
$268$	0	0
$269$	1630.00	0.369453	0.184726	−	0.982790i	$-0.440860\pi$
$269$	1630.00	0.369453	0.184726	+	0.982790i	$0.440860\pi$
$270$	0	0
$271$	3688.00	0.826679	0.413340	−	0.910577i	$-0.364362\pi$
$271$	3688.00	0.826679	0.413340	+	0.910577i	$0.364362\pi$
$272$	0	0
$273$	7056.00	1.56428
$274$	0	0
$275$	2596.00	0.569253
$276$	0	0
$277$	−5294.00	−1.14832	−0.574162	−	0.818742i	$-0.694672\pi$
$277$	−5294.00	−1.14832	−0.574162	+	0.818742i	$0.694672\pi$
$278$	0	0
$279$	−2574.00	−0.552335
$280$	0	0
$281$	5942.00	1.26146	0.630730	−	0.776003i	$-0.282756\pi$
$281$	5942.00	1.26146	0.630730	+	0.776003i	$0.282756\pi$
$282$	0	0
$283$	−6572.00	−1.38044	−0.690221	−	0.723599i	$-0.742487\pi$
$283$	−6572.00	−1.38044	−0.690221	+	0.723599i	$0.742487\pi$
$284$	0	0
$285$	2660.00	0.552859
$286$	0	0
$287$	3192.00	0.656508
$288$	0	0
$289$	−2797.00	−0.569306
$290$	0	0
$291$	−2863.00	−0.576742
$292$	0	0
$293$	−5668.00	−1.13013	−0.565065	−	0.825046i	$-0.691149\pi$
$293$	−5668.00	−1.13013	−0.565065	+	0.825046i	$0.691149\pi$
$294$	0	0
$295$	8265.00	1.63121
$296$	0	0
$297$	385.000	0.0752187
$298$	0	0
$299$	7704.00	1.49008
$300$	0	0
$301$	3388.00	0.648774
$302$	0	0
$303$	−6286.00	−1.19182
$304$	0	0
$305$	12692.0	2.38276
$306$	0	0
$307$	9844.00	1.83005	0.915027	−	0.403392i	$-0.132169\pi$
$307$	9844.00	1.83005	0.915027	+	0.403392i	$0.132169\pi$
$308$	0	0
$309$	−2184.00	−0.402082
$310$	0	0
$311$	6068.00	1.10638	0.553191	−	0.833055i	$-0.313410\pi$
$311$	6068.00	1.10638	0.553191	+	0.833055i	$0.313410\pi$
$312$	0	0
$313$	3743.00	0.675932	0.337966	−	0.941158i	$-0.390261\pi$
$313$	3743.00	0.675932	0.337966	+	0.941158i	$0.390261\pi$
$314$	0	0
$315$	−5852.00	−1.04674
$316$	0	0
$317$	−6849.00	−1.21350	−0.606748	−	0.794894i	$-0.707526\pi$
$317$	−6849.00	−1.21350	−0.606748	+	0.794894i	$0.707526\pi$
$318$	0	0
$319$	−1320.00	−0.231680
$320$	0	0
$321$	−1918.00	−0.333496
$322$	0	0
$323$	920.000	0.158483
$324$	0	0
$325$	16992.0	2.90014
$326$	0	0
$327$	−10290.0	−1.74018
$328$	0	0
$329$	−1344.00	−0.225219
$330$	0	0
$331$	9617.00	1.59697	0.798487	−	0.602013i	$-0.205634\pi$
$331$	9617.00	1.59697	0.798487	+	0.602013i	$0.205634\pi$
$332$	0	0
$333$	4422.00	0.727700
$334$	0	0
$335$	8341.00	1.36035
$336$	0	0
$337$	−1026.00	−0.165845	−0.0829225	−	0.996556i	$-0.526425\pi$
$337$	−1026.00	−0.165845	−0.0829225	+	0.996556i	$0.526425\pi$
$338$	0	0
$339$	−791.000	−0.126729
$340$	0	0
$341$	−1287.00	−0.204384
$342$	0	0
$343$	6860.00	1.07990
$344$	0	0
$345$	−14231.0	−2.22079
$346$	0	0
$347$	−2536.00	−0.392333	−0.196167	−	0.980571i	$-0.562849\pi$
$347$	−2536.00	−0.392333	−0.196167	+	0.980571i	$0.562849\pi$
$348$	0	0
$349$	−7770.00	−1.19174	−0.595872	−	0.803080i	$-0.703193\pi$
$349$	−7770.00	−1.19174	−0.595872	+	0.803080i	$0.703193\pi$
$350$	0	0
$351$	2520.00	0.383213
$352$	0	0
$353$	−9597.00	−1.44702	−0.723508	−	0.690316i	$-0.757472\pi$
$353$	−9597.00	−1.44702	−0.723508	+	0.690316i	$0.757472\pi$
$354$	0	0
$355$	21147.0	3.16159
$356$	0	0
$357$	−4508.00	−0.668316
$358$	0	0
$359$	−5760.00	−0.846800	−0.423400	−	0.905943i	$-0.639163\pi$
$359$	−5760.00	−0.846800	−0.423400	+	0.905943i	$0.639163\pi$
$360$	0	0
$361$	−6459.00	−0.941682
$362$	0	0
$363$	−847.000	−0.122468
$364$	0	0
$365$	−1368.00	−0.196176
$366$	0	0
$367$	1891.00	0.268963	0.134481	−	0.990916i	$-0.457063\pi$
$367$	1891.00	0.268963	0.134481	+	0.990916i	$0.457063\pi$
$368$	0	0
$369$	−5016.00	−0.707649
$370$	0	0
$371$	6412.00	0.897290
$372$	0	0
$373$	11582.0	1.60776	0.803878	−	0.594794i	$-0.202766\pi$
$373$	11582.0	1.60776	0.803878	+	0.594794i	$0.202766\pi$
$374$	0	0
$375$	−14763.0	−2.03295
$376$	0	0
$377$	−8640.00	−1.18033
$378$	0	0
$379$	1925.00	0.260899	0.130449	−	0.991455i	$-0.458358\pi$
$379$	1925.00	0.260899	0.130449	+	0.991455i	$0.458358\pi$
$380$	0	0
$381$	−10332.0	−1.38930
$382$	0	0
$383$	3307.00	0.441201	0.220600	−	0.975364i	$-0.429198\pi$
$383$	3307.00	0.441201	0.220600	+	0.975364i	$0.429198\pi$
$384$	0	0
$385$	−2926.00	−0.387332
$386$	0	0
$387$	−5324.00	−0.699313
$388$	0	0
$389$	7275.00	0.948219	0.474109	−	0.880466i	$-0.342770\pi$
$389$	7275.00	0.948219	0.474109	+	0.880466i	$0.342770\pi$
$390$	0	0
$391$	−4922.00	−0.636614
$392$	0	0
$393$	−9394.00	−1.20576
$394$	0	0
$395$	1330.00	0.169417
$396$	0	0
$397$	−11374.0	−1.43790	−0.718948	−	0.695064i	$-0.755376\pi$
$397$	−11374.0	−1.43790	−0.718948	+	0.695064i	$0.755376\pi$
$398$	0	0
$399$	−1960.00	−0.245922
$400$	0	0
$401$	−4598.00	−0.572601	−0.286301	−	0.958140i	$-0.592426\pi$
$401$	−4598.00	−0.572601	−0.286301	+	0.958140i	$0.592426\pi$
$402$	0	0
$403$	−8424.00	−1.04126
$404$	0	0
$405$	−15941.0	−1.95584
$406$	0	0
$407$	2211.00	0.269276
$408$	0	0
$409$	9970.00	1.20534	0.602671	−	0.797990i	$-0.294103\pi$
$409$	9970.00	1.20534	0.602671	+	0.797990i	$0.294103\pi$
$410$	0	0
$411$	−12383.0	−1.48615
$412$	0	0
$413$	−6090.00	−0.725592
$414$	0	0
$415$	6802.00	0.804571
$416$	0	0
$417$	3850.00	0.452123
$418$	0	0
$419$	−8940.00	−1.04236	−0.521178	−	0.853448i	$-0.674507\pi$
$419$	−8940.00	−1.04236	−0.521178	+	0.853448i	$0.674507\pi$
$420$	0	0
$421$	−5462.00	−0.632308	−0.316154	−	0.948708i	$-0.602392\pi$
$421$	−5462.00	−0.632308	−0.316154	+	0.948708i	$0.602392\pi$
$422$	0	0
$423$	2112.00	0.242763
$424$	0	0
$425$	−10856.0	−1.23904
$426$	0	0
$427$	−9352.00	−1.05989
$428$	0	0
$429$	−5544.00	−0.623932
$430$	0	0
$431$	−3942.00	−0.440556	−0.220278	−	0.975437i	$-0.570696\pi$
$431$	−3942.00	−0.440556	−0.220278	+	0.975437i	$0.570696\pi$
$432$	0	0
$433$	12773.0	1.41762	0.708812	−	0.705397i	$-0.249231\pi$
$433$	12773.0	1.41762	0.708812	+	0.705397i	$0.249231\pi$
$434$	0	0
$435$	15960.0	1.75913
$436$	0	0
$437$	−2140.00	−0.234256
$438$	0	0
$439$	4880.00	0.530546	0.265273	−	0.964173i	$-0.414538\pi$
$439$	4880.00	0.530546	0.265273	+	0.964173i	$0.414538\pi$
$440$	0	0
$441$	−3234.00	−0.349206
$442$	0	0
$443$	−13277.0	−1.42395	−0.711974	−	0.702205i	$-0.752199\pi$
$443$	−13277.0	−1.42395	−0.711974	+	0.702205i	$0.752199\pi$
$444$	0	0
$445$	17005.0	1.81149
$446$	0	0
$447$	−5530.00	−0.585145
$448$	0	0
$449$	−4885.00	−0.513446	−0.256723	−	0.966485i	$-0.582643\pi$
$449$	−4885.00	−0.513446	−0.256723	+	0.966485i	$0.582643\pi$
$450$	0	0
$451$	−2508.00	−0.261856
$452$	0	0
$453$	20314.0	2.10692
$454$	0	0
$455$	−19152.0	−1.97332
$456$	0	0
$457$	17884.0	1.83059	0.915293	−	0.402788i	$-0.131959\pi$
$457$	17884.0	1.83059	0.915293	+	0.402788i	$0.131959\pi$
$458$	0	0
$459$	−1610.00	−0.163722
$460$	0	0
$461$	−4532.00	−0.457866	−0.228933	−	0.973442i	$-0.573524\pi$
$461$	−4532.00	−0.457866	−0.228933	+	0.973442i	$0.573524\pi$
$462$	0	0
$463$	1977.00	0.198443	0.0992214	−	0.995065i	$-0.468365\pi$
$463$	1977.00	0.198443	0.0992214	+	0.995065i	$0.468365\pi$
$464$	0	0
$465$	15561.0	1.55188
$466$	0	0
$467$	7179.00	0.711359	0.355679	−	0.934608i	$-0.384250\pi$
$467$	7179.00	0.711359	0.355679	+	0.934608i	$0.384250\pi$
$468$	0	0
$469$	−6146.00	−0.605109
$470$	0	0
$471$	5243.00	0.512919
$472$	0	0
$473$	−2662.00	−0.258771
$474$	0	0
$475$	−4720.00	−0.455934
$476$	0	0
$477$	−10076.0	−0.967187
$478$	0	0
$479$	3600.00	0.343399	0.171700	−	0.985149i	$-0.445074\pi$
$479$	3600.00	0.343399	0.171700	+	0.985149i	$0.445074\pi$
$480$	0	0
$481$	14472.0	1.37186
$482$	0	0
$483$	10486.0	0.987846
$484$	0	0
$485$	7771.00	0.727552
$486$	0	0
$487$	9691.00	0.901727	0.450864	−	0.892593i	$-0.351116\pi$
$487$	9691.00	0.901727	0.450864	+	0.892593i	$0.351116\pi$
$488$	0	0
$489$	−8596.00	−0.794938
$490$	0	0
$491$	14072.0	1.29340	0.646701	−	0.762744i	$-0.276148\pi$
$491$	14072.0	1.29340	0.646701	+	0.762744i	$0.276148\pi$
$492$	0	0
$493$	5520.00	0.504276
$494$	0	0
$495$	4598.00	0.417505
$496$	0	0
$497$	−15582.0	−1.40633
$498$	0	0
$499$	3980.00	0.357053	0.178526	−	0.983935i	$-0.442867\pi$
$499$	3980.00	0.357053	0.178526	+	0.983935i	$0.442867\pi$
$500$	0	0
$501$	16968.0	1.51312
$502$	0	0
$503$	2182.00	0.193421	0.0967103	−	0.995313i	$-0.469168\pi$
$503$	2182.00	0.193421	0.0967103	+	0.995313i	$0.469168\pi$
$504$	0	0
$505$	17062.0	1.50346
$506$	0	0
$507$	−20909.0	−1.83156
$508$	0	0
$509$	−15875.0	−1.38241	−0.691205	−	0.722658i	$-0.742920\pi$
$509$	−15875.0	−1.38241	−0.691205	+	0.722658i	$0.742920\pi$
$510$	0	0
$511$	1008.00	0.0872628
$512$	0	0
$513$	−700.000	−0.0602451
$514$	0	0
$515$	5928.00	0.507221
$516$	0	0
$517$	1056.00	0.0898314
$518$	0	0
$519$	−26194.0	−2.21539
$520$	0	0
$521$	6837.00	0.574922	0.287461	−	0.957792i	$-0.407189\pi$
$521$	6837.00	0.574922	0.287461	+	0.957792i	$0.407189\pi$
$522$	0	0
$523$	−17212.0	−1.43906	−0.719530	−	0.694462i	$-0.755643\pi$
$523$	−17212.0	−1.43906	−0.719530	+	0.694462i	$0.755643\pi$
$524$	0	0
$525$	23128.0	1.92265
$526$	0	0
$527$	5382.00	0.444865
$528$	0	0
$529$	−718.000	−0.0590121
$530$	0	0
$531$	9570.00	0.782114
$532$	0	0
$533$	−16416.0	−1.33406
$534$	0	0
$535$	5206.00	0.420701
$536$	0	0
$537$	1855.00	0.149067
$538$	0	0
$539$	−1617.00	−0.129219
$540$	0	0
$541$	22028.0	1.75057	0.875284	−	0.483609i	$-0.160674\pi$
$541$	22028.0	1.75057	0.875284	+	0.483609i	$0.160674\pi$
$542$	0	0
$543$	469.000	0.0370658
$544$	0	0
$545$	27930.0	2.19521
$546$	0	0
$547$	−19696.0	−1.53956	−0.769781	−	0.638308i	$-0.779634\pi$
$547$	−19696.0	−1.53956	−0.769781	+	0.638308i	$0.779634\pi$
$548$	0	0
$549$	14696.0	1.14246
$550$	0	0
$551$	2400.00	0.185560
$552$	0	0
$553$	−980.000	−0.0753596
$554$	0	0
$555$	−26733.0	−2.04460
$556$	0	0
$557$	11886.0	0.904176	0.452088	−	0.891973i	$-0.350679\pi$
$557$	11886.0	0.904176	0.452088	+	0.891973i	$0.350679\pi$
$558$	0	0
$559$	−17424.0	−1.31835
$560$	0	0
$561$	3542.00	0.266566
$562$	0	0
$563$	−12572.0	−0.941113	−0.470557	−	0.882370i	$-0.655947\pi$
$563$	−12572.0	−0.941113	−0.470557	+	0.882370i	$0.655947\pi$
$564$	0	0
$565$	2147.00	0.159867
$566$	0	0
$567$	11746.0	0.869992
$568$	0	0
$569$	−12920.0	−0.951906	−0.475953	−	0.879471i	$-0.657897\pi$
$569$	−12920.0	−0.951906	−0.475953	+	0.879471i	$0.657897\pi$
$570$	0	0
$571$	412.000	0.0301956	0.0150978	−	0.999886i	$-0.495194\pi$
$571$	412.000	0.0301956	0.0150978	+	0.999886i	$0.495194\pi$
$572$	0	0
$573$	−24171.0	−1.76223
$574$	0	0
$575$	25252.0	1.83145
$576$	0	0
$577$	22649.0	1.63413	0.817063	−	0.576549i	$-0.195601\pi$
$577$	22649.0	1.63413	0.817063	+	0.576549i	$0.195601\pi$
$578$	0	0
$579$	29204.0	2.09616
$580$	0	0
$581$	−5012.00	−0.357888
$582$	0	0
$583$	−5038.00	−0.357895
$584$	0	0
$585$	30096.0	2.12704
$586$	0	0
$587$	−24276.0	−1.70695	−0.853473	−	0.521136i	$-0.825508\pi$
$587$	−24276.0	−1.70695	−0.853473	+	0.521136i	$0.825508\pi$
$588$	0	0
$589$	2340.00	0.163698
$590$	0	0
$591$	−16982.0	−1.18197
$592$	0	0
$593$	−14292.0	−0.989717	−0.494858	−	0.868974i	$-0.664780\pi$
$593$	−14292.0	−0.989717	−0.494858	+	0.868974i	$0.664780\pi$
$594$	0	0
$595$	12236.0	0.843071
$596$	0	0
$597$	−2800.00	−0.191954
$598$	0	0
$599$	−18360.0	−1.25237	−0.626185	−	0.779675i	$-0.715384\pi$
$599$	−18360.0	−1.25237	−0.626185	+	0.779675i	$0.715384\pi$
$600$	0	0
$601$	−98.0000	−0.00665142	−0.00332571	−	0.999994i	$-0.501059\pi$
$601$	−98.0000	−0.00665142	−0.00332571	+	0.999994i	$0.501059\pi$
$602$	0	0
$603$	9658.00	0.652246
$604$	0	0
$605$	2299.00	0.154492
$606$	0	0
$607$	−22054.0	−1.47470	−0.737351	−	0.675510i	$-0.763924\pi$
$607$	−22054.0	−1.47470	−0.737351	+	0.675510i	$0.763924\pi$
$608$	0	0
$609$	−11760.0	−0.782495
$610$	0	0
$611$	6912.00	0.457659
$612$	0	0
$613$	−288.000	−0.0189759	−0.00948794	−	0.999955i	$-0.503020\pi$
$613$	−288.000	−0.0189759	−0.00948794	+	0.999955i	$0.503020\pi$
$614$	0	0
$615$	30324.0	1.98826
$616$	0	0
$617$	−5086.00	−0.331855	−0.165928	−	0.986138i	$-0.553062\pi$
$617$	−5086.00	−0.331855	−0.165928	+	0.986138i	$0.553062\pi$
$618$	0	0
$619$	27305.0	1.77299	0.886495	−	0.462738i	$-0.153133\pi$
$619$	27305.0	1.77299	0.886495	+	0.462738i	$0.153133\pi$
$620$	0	0
$621$	3745.00	0.241999
$622$	0	0
$623$	−12530.0	−0.805785
$624$	0	0
$625$	10571.0	0.676544
$626$	0	0
$627$	1540.00	0.0980888
$628$	0	0
$629$	−9246.00	−0.586108
$630$	0	0
$631$	−1117.00	−0.0704708	−0.0352354	−	0.999379i	$-0.511218\pi$
$631$	−1117.00	−0.0704708	−0.0352354	+	0.999379i	$0.511218\pi$
$632$	0	0
$633$	−23324.0	−1.46453
$634$	0	0
$635$	28044.0	1.75259
$636$	0	0
$637$	−10584.0	−0.658326
$638$	0	0
$639$	24486.0	1.51589
$640$	0	0
$641$	10047.0	0.619084	0.309542	−	0.950886i	$-0.399824\pi$
$641$	10047.0	0.619084	0.309542	+	0.950886i	$0.399824\pi$
$642$	0	0
$643$	−4597.00	−0.281941	−0.140970	−	0.990014i	$-0.545022\pi$
$643$	−4597.00	−0.281941	−0.140970	+	0.990014i	$0.545022\pi$
$644$	0	0
$645$	32186.0	1.96484
$646$	0	0
$647$	−1859.00	−0.112960	−0.0564798	−	0.998404i	$-0.517988\pi$
$647$	−1859.00	−0.112960	−0.0564798	+	0.998404i	$0.517988\pi$
$648$	0	0
$649$	4785.00	0.289411
$650$	0	0
$651$	−11466.0	−0.690304
$652$	0	0
$653$	837.000	0.0501598	0.0250799	−	0.999685i	$-0.492016\pi$
$653$	837.000	0.0501598	0.0250799	+	0.999685i	$0.492016\pi$
$654$	0	0
$655$	25498.0	1.52105
$656$	0	0
$657$	−1584.00	−0.0940605
$658$	0	0
$659$	−4770.00	−0.281962	−0.140981	−	0.990012i	$-0.545026\pi$
$659$	−4770.00	−0.281962	−0.140981	+	0.990012i	$0.545026\pi$
$660$	0	0
$661$	2343.00	0.137870	0.0689351	−	0.997621i	$-0.478040\pi$
$661$	2343.00	0.137870	0.0689351	+	0.997621i	$0.478040\pi$
$662$	0	0
$663$	23184.0	1.35806
$664$	0	0
$665$	5320.00	0.310227
$666$	0	0
$667$	−12840.0	−0.745377
$668$	0	0
$669$	42231.0	2.44058
$670$	0	0
$671$	7348.00	0.422752
$672$	0	0
$673$	−18802.0	−1.07692	−0.538458	−	0.842653i	$-0.680993\pi$
$673$	−18802.0	−1.07692	−0.538458	+	0.842653i	$0.680993\pi$
$674$	0	0
$675$	8260.00	0.471004
$676$	0	0
$677$	−874.000	−0.0496168	−0.0248084	−	0.999692i	$-0.507898\pi$
$677$	−874.000	−0.0496168	−0.0248084	+	0.999692i	$0.507898\pi$
$678$	0	0
$679$	−5726.00	−0.323628
$680$	0	0
$681$	39522.0	2.22392
$682$	0	0
$683$	30888.0	1.73045	0.865224	−	0.501385i	$-0.167176\pi$
$683$	30888.0	1.73045	0.865224	+	0.501385i	$0.167176\pi$
$684$	0	0
$685$	33611.0	1.87476
$686$	0	0
$687$	−32515.0	−1.80571
$688$	0	0
$689$	−32976.0	−1.82335
$690$	0	0
$691$	4647.00	0.255832	0.127916	−	0.991785i	$-0.459171\pi$
$691$	4647.00	0.255832	0.127916	+	0.991785i	$0.459171\pi$
$692$	0	0
$693$	−3388.00	−0.185714
$694$	0	0
$695$	−10450.0	−0.570347
$696$	0	0
$697$	10488.0	0.569959
$698$	0	0
$699$	17024.0	0.921183
$700$	0	0
$701$	7698.00	0.414764	0.207382	−	0.978260i	$-0.433506\pi$
$701$	7698.00	0.414764	0.207382	+	0.978260i	$0.433506\pi$
$702$	0	0
$703$	−4020.00	−0.215672
$704$	0	0
$705$	−12768.0	−0.682086
$706$	0	0
$707$	−12572.0	−0.668768
$708$	0	0
$709$	18285.0	0.968558	0.484279	−	0.874914i	$-0.339082\pi$
$709$	18285.0	0.968558	0.484279	+	0.874914i	$0.339082\pi$
$710$	0	0
$711$	1540.00	0.0812300
$712$	0	0
$713$	−12519.0	−0.657560
$714$	0	0
$715$	15048.0	0.787082
$716$	0	0
$717$	−42070.0	−2.19126
$718$	0	0
$719$	−19365.0	−1.00444	−0.502220	−	0.864740i	$-0.667483\pi$
$719$	−19365.0	−1.00444	−0.502220	+	0.864740i	$0.667483\pi$
$720$	0	0
$721$	−4368.00	−0.225621
$722$	0	0
$723$	26096.0	1.34235
$724$	0	0
$725$	−28320.0	−1.45073
$726$	0	0
$727$	−9.00000	−0.000459136 0	−0.000229568	−	1.00000i	$-0.500073\pi$
$727$	−9.00000	−0.000459136 0	−0.000229568		1.00000i	$0.500073\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	11132.0	0.563245
$732$	0	0
$733$	−25748.0	−1.29744	−0.648720	−	0.761027i	$-0.724696\pi$
$733$	−25748.0	−1.29744	−0.648720	+	0.761027i	$0.724696\pi$
$734$	0	0
$735$	19551.0	0.981156
$736$	0	0
$737$	4829.00	0.241355
$738$	0	0
$739$	−22690.0	−1.12945	−0.564726	−	0.825278i	$-0.691018\pi$
$739$	−22690.0	−1.12945	−0.564726	+	0.825278i	$0.691018\pi$
$740$	0	0
$741$	10080.0	0.499727
$742$	0	0
$743$	−3628.00	−0.179136	−0.0895682	−	0.995981i	$-0.528549\pi$
$743$	−3628.00	−0.179136	−0.0895682	+	0.995981i	$0.528549\pi$
$744$	0	0
$745$	15010.0	0.738153
$746$	0	0
$747$	7876.00	0.385767
$748$	0	0
$749$	−3836.00	−0.187135
$750$	0	0
$751$	33373.0	1.62157	0.810784	−	0.585345i	$-0.199041\pi$
$751$	33373.0	1.62157	0.810784	+	0.585345i	$0.199041\pi$
$752$	0	0
$753$	−3689.00	−0.178532
$754$	0	0
$755$	−55138.0	−2.65785
$756$	0	0
$757$	−11954.0	−0.573944	−0.286972	−	0.957939i	$-0.592649\pi$
$757$	−11954.0	−0.573944	−0.286972	+	0.957939i	$0.592649\pi$
$758$	0	0
$759$	−8239.00	−0.394014
$760$	0	0
$761$	−13368.0	−0.636780	−0.318390	−	0.947960i	$-0.603142\pi$
$761$	−13368.0	−0.636780	−0.318390	+	0.947960i	$0.603142\pi$
$762$	0	0
$763$	−20580.0	−0.976469
$764$	0	0
$765$	−19228.0	−0.908745
$766$	0	0
$767$	31320.0	1.47445
$768$	0	0
$769$	−37640.0	−1.76506	−0.882531	−	0.470254i	$-0.844162\pi$
$769$	−37640.0	−1.76506	−0.882531	+	0.470254i	$0.844162\pi$
$770$	0	0
$771$	12502.0	0.583980
$772$	0	0
$773$	17742.0	0.825531	0.412765	−	0.910837i	$-0.364563\pi$
$773$	17742.0	0.825531	0.412765	+	0.910837i	$0.364563\pi$
$774$	0	0
$775$	−27612.0	−1.27981
$776$	0	0
$777$	19698.0	0.909475
$778$	0	0
$779$	4560.00	0.209729
$780$	0	0
$781$	12243.0	0.560933
$782$	0	0
$783$	−4200.00	−0.191693
$784$	0	0
$785$	−14231.0	−0.647040
$786$	0	0
$787$	22744.0	1.03016	0.515080	−	0.857142i	$-0.327762\pi$
$787$	22744.0	1.03016	0.515080	+	0.857142i	$0.327762\pi$
$788$	0	0
$789$	22386.0	1.01009
$790$	0	0
$791$	−1582.00	−0.0711118
$792$	0	0
$793$	48096.0	2.15377
$794$	0	0
$795$	60914.0	2.71748
$796$	0	0
$797$	31311.0	1.39158	0.695792	−	0.718243i	$-0.255054\pi$
$797$	31311.0	1.39158	0.695792	+	0.718243i	$0.255054\pi$
$798$	0	0
$799$	−4416.00	−0.195528
$800$	0	0
$801$	19690.0	0.868554
$802$	0	0
$803$	−792.000	−0.0348058
$804$	0	0
$805$	−28462.0	−1.24615
$806$	0	0
$807$	−11410.0	−0.497709
$808$	0	0
$809$	3940.00	0.171227	0.0856137	−	0.996328i	$-0.472715\pi$
$809$	3940.00	0.171227	0.0856137	+	0.996328i	$0.472715\pi$
$810$	0	0
$811$	−19618.0	−0.849422	−0.424711	−	0.905329i	$-0.639624\pi$
$811$	−19618.0	−0.849422	−0.424711	+	0.905329i	$0.639624\pi$
$812$	0	0
$813$	−25816.0	−1.11366
$814$	0	0
$815$	23332.0	1.00280
$816$	0	0
$817$	4840.00	0.207258
$818$	0	0
$819$	−22176.0	−0.946144
$820$	0	0
$821$	−32062.0	−1.36294	−0.681469	−	0.731847i	$-0.738658\pi$
$821$	−32062.0	−1.36294	−0.681469	+	0.731847i	$0.738658\pi$
$822$	0	0
$823$	427.000	0.0180854	0.00904270	−	0.999959i	$-0.497122\pi$
$823$	427.000	0.0180854	0.00904270	+	0.999959i	$0.497122\pi$
$824$	0	0
$825$	−18172.0	−0.766870
$826$	0	0
$827$	−3256.00	−0.136907	−0.0684536	−	0.997654i	$-0.521807\pi$
$827$	−3256.00	−0.136907	−0.0684536	+	0.997654i	$0.521807\pi$
$828$	0	0
$829$	9155.00	0.383554	0.191777	−	0.981439i	$-0.438575\pi$
$829$	9155.00	0.383554	0.191777	+	0.981439i	$0.438575\pi$
$830$	0	0
$831$	37058.0	1.54696
$832$	0	0
$833$	6762.00	0.281260
$834$	0	0
$835$	−46056.0	−1.90878
$836$	0	0
$837$	−4095.00	−0.169109
$838$	0	0
$839$	−29265.0	−1.20422	−0.602110	−	0.798413i	$-0.705673\pi$
$839$	−29265.0	−1.20422	−0.602110	+	0.798413i	$0.705673\pi$
$840$	0	0
$841$	−9989.00	−0.409570
$842$	0	0
$843$	−41594.0	−1.69938
$844$	0	0
$845$	56753.0	2.31049
$846$	0	0
$847$	−1694.00	−0.0687208
$848$	0	0
$849$	46004.0	1.85966
$850$	0	0
$851$	21507.0	0.866334
$852$	0	0
$853$	−20598.0	−0.826802	−0.413401	−	0.910549i	$-0.635659\pi$
$853$	−20598.0	−0.826802	−0.413401	+	0.910549i	$0.635659\pi$
$854$	0	0
$855$	−8360.00	−0.334393
$856$	0	0
$857$	9944.00	0.396360	0.198180	−	0.980166i	$-0.436497\pi$
$857$	9944.00	0.396360	0.198180	+	0.980166i	$0.436497\pi$
$858$	0	0
$859$	−31745.0	−1.26091	−0.630457	−	0.776224i	$-0.717133\pi$
$859$	−31745.0	−1.26091	−0.630457	+	0.776224i	$0.717133\pi$
$860$	0	0
$861$	−22344.0	−0.884415
$862$	0	0
$863$	−28568.0	−1.12684	−0.563422	−	0.826169i	$-0.690515\pi$
$863$	−28568.0	−1.12684	−0.563422	+	0.826169i	$0.690515\pi$
$864$	0	0
$865$	71098.0	2.79469
$866$	0	0
$867$	19579.0	0.766941
$868$	0	0
$869$	770.000	0.0300581
$870$	0	0
$871$	31608.0	1.22962
$872$	0	0
$873$	8998.00	0.348839
$874$	0	0
$875$	−29526.0	−1.14076
$876$	0	0
$877$	33936.0	1.30666	0.653328	−	0.757075i	$-0.273372\pi$
$877$	33936.0	1.30666	0.653328	+	0.757075i	$0.273372\pi$
$878$	0	0
$879$	39676.0	1.52246
$880$	0	0
$881$	7117.00	0.272166	0.136083	−	0.990697i	$-0.456549\pi$
$881$	7117.00	0.272166	0.136083	+	0.990697i	$0.456549\pi$
$882$	0	0
$883$	−4172.00	−0.159002	−0.0795011	−	0.996835i	$-0.525333\pi$
$883$	−4172.00	−0.159002	−0.0795011	+	0.996835i	$0.525333\pi$
$884$	0	0
$885$	−57855.0	−2.19749
$886$	0	0
$887$	−9174.00	−0.347275	−0.173637	−	0.984810i	$-0.555552\pi$
$887$	−9174.00	−0.347275	−0.173637	+	0.984810i	$0.555552\pi$
$888$	0	0
$889$	−20664.0	−0.779582
$890$	0	0
$891$	−9229.00	−0.347007
$892$	0	0
$893$	−1920.00	−0.0719489
$894$	0	0
$895$	−5035.00	−0.188046
$896$	0	0
$897$	−53928.0	−2.00736
$898$	0	0
$899$	14040.0	0.520868
$900$	0	0
$901$	21068.0	0.778998
$902$	0	0
$903$	−23716.0	−0.873997
$904$	0	0
$905$	−1273.00	−0.0467580
$906$	0	0
$907$	−37316.0	−1.36611	−0.683053	−	0.730369i	$-0.739348\pi$
$907$	−37316.0	−1.36611	−0.683053	+	0.730369i	$0.739348\pi$
$908$	0	0
$909$	19756.0	0.720864
$910$	0	0
$911$	−34332.0	−1.24859	−0.624297	−	0.781187i	$-0.714615\pi$
$911$	−34332.0	−1.24859	−0.624297	+	0.781187i	$0.714615\pi$
$912$	0	0
$913$	3938.00	0.142748
$914$	0	0
$915$	−88844.0	−3.20994
$916$	0	0
$917$	−18788.0	−0.676592
$918$	0	0
$919$	−37670.0	−1.35214	−0.676071	−	0.736836i	$-0.736319\pi$
$919$	−37670.0	−1.35214	−0.676071	+	0.736836i	$0.736319\pi$
$920$	0	0
$921$	−68908.0	−2.46536
$922$	0	0
$923$	80136.0	2.85776
$924$	0	0
$925$	47436.0	1.68615
$926$	0	0
$927$	6864.00	0.243197
$928$	0	0
$929$	−34950.0	−1.23431	−0.617154	−	0.786842i	$-0.711714\pi$
$929$	−34950.0	−1.23431	−0.617154	+	0.786842i	$0.711714\pi$
$930$	0	0
$931$	2940.00	0.103496
$932$	0	0
$933$	−42476.0	−1.49046
$934$	0	0
$935$	−9614.00	−0.336269
$936$	0	0
$937$	17164.0	0.598424	0.299212	−	0.954187i	$-0.403276\pi$
$937$	17164.0	0.598424	0.299212	+	0.954187i	$0.403276\pi$
$938$	0	0
$939$	−26201.0	−0.910583
$940$	0	0
$941$	−6522.00	−0.225942	−0.112971	−	0.993598i	$-0.536037\pi$
$941$	−6522.00	−0.225942	−0.112971	+	0.993598i	$0.536037\pi$
$942$	0	0
$943$	−24396.0	−0.842463
$944$	0	0
$945$	−9310.00	−0.320481
$946$	0	0
$947$	−53901.0	−1.84957	−0.924787	−	0.380484i	$-0.875757\pi$
$947$	−53901.0	−1.84957	−0.924787	+	0.380484i	$0.875757\pi$
$948$	0	0
$949$	−5184.00	−0.177323
$950$	0	0
$951$	47943.0	1.63476
$952$	0	0
$953$	−15162.0	−0.515368	−0.257684	−	0.966229i	$-0.582959\pi$
$953$	−15162.0	−0.515368	−0.257684	+	0.966229i	$0.582959\pi$
$954$	0	0
$955$	65607.0	2.22303
$956$	0	0
$957$	9240.00	0.312107
$958$	0	0
$959$	−24766.0	−0.833927
$960$	0	0
$961$	−16102.0	−0.540499
$962$	0	0
$963$	6028.00	0.201713
$964$	0	0
$965$	−79268.0	−2.64428
$966$	0	0
$967$	−1864.00	−0.0619878	−0.0309939	−	0.999520i	$-0.509867\pi$
$967$	−1864.00	−0.0619878	−0.0309939	+	0.999520i	$0.509867\pi$
$968$	0	0
$969$	−6440.00	−0.213501
$970$	0	0
$971$	56937.0	1.88177	0.940883	−	0.338731i	$-0.109998\pi$
$971$	56937.0	1.88177	0.940883	+	0.338731i	$0.109998\pi$
$972$	0	0
$973$	7700.00	0.253701
$974$	0	0
$975$	−118944.	−3.90693
$976$	0	0
$977$	12269.0	0.401761	0.200880	−	0.979616i	$-0.435620\pi$
$977$	12269.0	0.401761	0.200880	+	0.979616i	$0.435620\pi$
$978$	0	0
$979$	9845.00	0.321397
$980$	0	0
$981$	32340.0	1.05253
$982$	0	0
$983$	9627.00	0.312364	0.156182	−	0.987728i	$-0.450081\pi$
$983$	9627.00	0.312364	0.156182	+	0.987728i	$0.450081\pi$
$984$	0	0
$985$	46094.0	1.49104
$986$	0	0
$987$	9408.00	0.303404
$988$	0	0
$989$	−25894.0	−0.832539
$990$	0	0
$991$	26728.0	0.856754	0.428377	−	0.903600i	$-0.359086\pi$
$991$	26728.0	0.856754	0.428377	+	0.903600i	$0.359086\pi$
$992$	0	0
$993$	−67319.0	−2.15136
$994$	0	0
$995$	7600.00	0.242147
$996$	0	0
$997$	15206.0	0.483028	0.241514	−	0.970397i	$-0.422356\pi$
$997$	15206.0	0.483028	0.241514	+	0.970397i	$0.422356\pi$
$998$	0	0
$999$	7035.00	0.222800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.4.a.b.1.1		1
4.3	odd	2		704.4.a.l.1.1		1
8.3	odd	2		22.4.a.a.1.1	✓	1
8.5	even	2		176.4.a.f.1.1		1
24.5	odd	2		1584.4.a.v.1.1		1
24.11	even	2		198.4.a.g.1.1		1
40.3	even	4		550.4.b.k.199.2		2
40.19	odd	2		550.4.a.n.1.1		1
40.27	even	4		550.4.b.k.199.1		2
56.27	even	2		1078.4.a.d.1.1		1
88.3	odd	10		242.4.c.l.9.1		4
88.19	even	10		242.4.c.e.9.1		4
88.21	odd	2		1936.4.a.n.1.1		1
88.27	odd	10		242.4.c.l.3.1		4
88.35	even	10		242.4.c.e.81.1		4
88.43	even	2		242.4.a.d.1.1		1
88.51	even	10		242.4.c.e.27.1		4
88.59	odd	10		242.4.c.l.27.1		4
88.75	odd	10		242.4.c.l.81.1		4
88.83	even	10		242.4.c.e.3.1		4
264.131	odd	2		2178.4.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.4.a.a.1.1	✓	1	8.3	odd	2
176.4.a.f.1.1		1	8.5	even	2
198.4.a.g.1.1		1	24.11	even	2
242.4.a.d.1.1		1	88.43	even	2
242.4.c.e.3.1		4	88.83	even	10
242.4.c.e.9.1		4	88.19	even	10
242.4.c.e.27.1		4	88.51	even	10
242.4.c.e.81.1		4	88.35	even	10
242.4.c.l.3.1		4	88.27	odd	10
242.4.c.l.9.1		4	88.3	odd	10
242.4.c.l.27.1		4	88.59	odd	10
242.4.c.l.81.1		4	88.75	odd	10
550.4.a.n.1.1		1	40.19	odd	2
550.4.b.k.199.1		2	40.27	even	4
550.4.b.k.199.2		2	40.3	even	4
704.4.a.b.1.1		1	1.1	even	1	trivial
704.4.a.l.1.1		1	4.3	odd	2
1078.4.a.d.1.1		1	56.27	even	2
1584.4.a.v.1.1		1	24.5	odd	2
1936.4.a.n.1.1		1	88.21	odd	2
2178.4.a.l.1.1		1	264.131	odd	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:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	704.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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