LMFDB - Embedded newform 259.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [259,2,Mod(1,259)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(259, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("259.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 259 = 7 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	259.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:	$2.06812541235$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	259.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{4} +4.00000 q^{5} +1.00000 q^{7} -3.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{4} +4.00000 q^{5} +1.00000 q^{7} -3.00000 q^{8} -3.00000 q^{9} +4.00000 q^{10} +4.00000 q^{11} +4.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -3.00000 q^{18} -6.00000 q^{19} -4.00000 q^{20} +4.00000 q^{22} -4.00000 q^{23} +11.0000 q^{25} +4.00000 q^{26} -1.00000 q^{28} -6.00000 q^{29} +2.00000 q^{31} +5.00000 q^{32} +4.00000 q^{35} +3.00000 q^{36} -1.00000 q^{37} -6.00000 q^{38} -12.0000 q^{40} -6.00000 q^{41} -4.00000 q^{43} -4.00000 q^{44} -12.0000 q^{45} -4.00000 q^{46} -12.0000 q^{47} +1.00000 q^{49} +11.0000 q^{50} -4.00000 q^{52} +10.0000 q^{53} +16.0000 q^{55} -3.00000 q^{56} -6.00000 q^{58} -10.0000 q^{59} -8.00000 q^{61} +2.00000 q^{62} -3.00000 q^{63} +7.00000 q^{64} +16.0000 q^{65} -4.00000 q^{67} +4.00000 q^{70} +9.00000 q^{72} +2.00000 q^{73} -1.00000 q^{74} +6.00000 q^{76} +4.00000 q^{77} +4.00000 q^{79} -4.00000 q^{80} +9.00000 q^{81} -6.00000 q^{82} -4.00000 q^{86} -12.0000 q^{88} +16.0000 q^{89} -12.0000 q^{90} +4.00000 q^{91} +4.00000 q^{92} -12.0000 q^{94} -24.0000 q^{95} +4.00000 q^{97} +1.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	−1.00000	−0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.00000	−1.06066
$9$	−3.00000	−1.00000
$10$	4.00000	1.26491
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	0	0
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−3.00000	−0.707107
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	−4.00000	−0.894427
$21$	0	0
$22$	4.00000	0.852803
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	4.00000	0.784465
$27$	0	0
$28$	−1.00000	−0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	0	0
$35$	4.00000	0.676123
$36$	3.00000	0.500000
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−6.00000	−0.973329
$39$	0	0
$40$	−12.0000	−1.89737
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−4.00000	−0.603023
$45$	−12.0000	−1.78885
$46$	−4.00000	−0.589768
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	11.0000	1.55563
$51$	0	0
$52$	−4.00000	−0.554700
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	0	0
$55$	16.0000	2.15744
$56$	−3.00000	−0.400892
$57$	0	0
$58$	−6.00000	−0.787839
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	−8.00000	−1.02430	−0.512148	−	0.858898i	$-0.671150\pi$
$61$	−8.00000	−1.02430	−0.512148	+	0.858898i	$0.671150\pi$
$62$	2.00000	0.254000
$63$	−3.00000	−0.377964
$64$	7.00000	0.875000
$65$	16.0000	1.98456
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	0	0
$69$	0	0
$70$	4.00000	0.478091
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	9.00000	1.06066
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−1.00000	−0.116248
$75$	0	0
$76$	6.00000	0.688247
$77$	4.00000	0.455842
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	−4.00000	−0.447214
$81$	9.00000	1.00000
$82$	−6.00000	−0.662589
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	−12.0000	−1.27920
$89$	16.0000	1.69600	0.847998	−	0.529999i	$-0.177808\pi$
$89$	16.0000	1.69600	0.847998	+	0.529999i	$0.177808\pi$
$90$	−12.0000	−1.26491
$91$	4.00000	0.419314
$92$	4.00000	0.417029
$93$	0	0
$94$	−12.0000	−1.23771
$95$	−24.0000	−2.46235
$96$	0	0
$97$	4.00000	0.406138	0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000	0.406138	0.203069	+	0.979164i	$0.434908\pi$
$98$	1.00000	0.101015
$99$	−12.0000	−1.20605
$100$	−11.0000	−1.10000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	−12.0000	−1.17670
$105$	0	0
$106$	10.0000	0.971286
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	16.0000	1.52554
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	0	0
$115$	−16.0000	−1.49201
$116$	6.00000	0.557086
$117$	−12.0000	−1.10940
$118$	−10.0000	−0.920575
$119$	0	0
$120$	0	0
$121$	5.00000	0.454545
$122$	−8.00000	−0.724286
$123$	0	0
$124$	−2.00000	−0.179605
$125$	24.0000	2.14663
$126$	−3.00000	−0.267261
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−3.00000	−0.265165
$129$	0	0
$130$	16.0000	1.40329
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	−6.00000	−0.520266
$134$	−4.00000	−0.345547
$135$	0	0
$136$	0	0
$137$	18.0000	1.53784	0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000	1.53784	0.768922	+	0.639343i	$0.220793\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−4.00000	−0.338062
$141$	0	0
$142$	0	0
$143$	16.0000	1.33799
$144$	3.00000	0.250000
$145$	−24.0000	−1.99309
$146$	2.00000	0.165521
$147$	0	0
$148$	1.00000	0.0821995
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	18.0000	1.45999
$153$	0	0
$154$	4.00000	0.322329
$155$	8.00000	0.642575
$156$	0	0
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	4.00000	0.318223
$159$	0	0
$160$	20.0000	1.58114
$161$	−4.00000	−0.315244
$162$	9.00000	0.707107
$163$	−24.0000	−1.87983	−0.939913	−	0.341415i	$-0.889094\pi$
$163$	−24.0000	−1.87983	−0.939913	+	0.341415i	$0.889094\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	0	0
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	18.0000	1.37649
$172$	4.00000	0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	11.0000	0.831522
$176$	−4.00000	−0.301511
$177$	0	0
$178$	16.0000	1.19925
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	12.0000	0.894427
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	4.00000	0.296500
$183$	0	0
$184$	12.0000	0.884652
$185$	−4.00000	−0.294086
$186$	0	0
$187$	0	0
$188$	12.0000	0.875190
$189$	0	0
$190$	−24.0000	−1.74114
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	0	0
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	4.00000	0.287183
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	−12.0000	−0.852803
$199$	14.0000	0.992434	0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000	0.992434	0.496217	+	0.868199i	$0.334722\pi$
$200$	−33.0000	−2.33345
$201$	0	0
$202$	6.00000	0.422159
$203$	−6.00000	−0.421117
$204$	0	0
$205$	−24.0000	−1.67623
$206$	6.00000	0.418040
$207$	12.0000	0.834058
$208$	−4.00000	−0.277350
$209$	−24.0000	−1.66011
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	−10.0000	−0.686803
$213$	0	0
$214$	12.0000	0.820303
$215$	−16.0000	−1.09119
$216$	0	0
$217$	2.00000	0.135769
$218$	2.00000	0.135457
$219$	0	0
$220$	−16.0000	−1.07872
$221$	0	0
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	5.00000	0.334077
$225$	−33.0000	−2.20000
$226$	18.0000	1.19734
$227$	−10.0000	−0.663723	−0.331862	−	0.943328i	$-0.607677\pi$
$227$	−10.0000	−0.663723	−0.331862	+	0.943328i	$0.607677\pi$
$228$	0	0
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	−16.0000	−1.05501
$231$	0	0
$232$	18.0000	1.18176
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	−12.0000	−0.784465
$235$	−48.0000	−3.13117
$236$	10.0000	0.650945
$237$	0	0
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	−4.00000	−0.257663	−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000	−0.257663	−0.128831	+	0.991667i	$0.541123\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	8.00000	0.512148
$245$	4.00000	0.255551
$246$	0	0
$247$	−24.0000	−1.52708
$248$	−6.00000	−0.381000
$249$	0	0
$250$	24.0000	1.51789
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	3.00000	0.188982
$253$	−16.0000	−1.00591
$254$	−8.00000	−0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−24.0000	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$257$	−24.0000	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$258$	0	0
$259$	−1.00000	−0.0621370
$260$	−16.0000	−0.992278
$261$	18.0000	1.11417
$262$	18.0000	1.11204
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	40.0000	2.45718
$266$	−6.00000	−0.367884
$267$	0	0
$268$	4.00000	0.244339
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	0	0
$273$	0	0
$274$	18.0000	1.08742
$275$	44.0000	2.65330
$276$	0	0
$277$	30.0000	1.80253	0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000	1.80253	0.901263	+	0.433273i	$0.142641\pi$
$278$	4.00000	0.239904
$279$	−6.00000	−0.359211
$280$	−12.0000	−0.717137
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	0	0
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	0	0
$285$	0	0
$286$	16.0000	0.946100
$287$	−6.00000	−0.354169
$288$	−15.0000	−0.883883
$289$	−17.0000	−1.00000
$290$	−24.0000	−1.40933
$291$	0	0
$292$	−2.00000	−0.117041
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	−40.0000	−2.32889
$296$	3.00000	0.174371
$297$	0	0
$298$	−14.0000	−0.810998
$299$	−16.0000	−0.925304
$300$	0	0
$301$	−4.00000	−0.230556
$302$	−8.00000	−0.460348
$303$	0	0
$304$	6.00000	0.344124
$305$	−32.0000	−1.83231
$306$	0	0
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	−4.00000	−0.227921
$309$	0	0
$310$	8.00000	0.454369
$311$	30.0000	1.70114	0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000	1.70114	0.850572	+	0.525859i	$0.176256\pi$
$312$	0	0
$313$	−20.0000	−1.13047	−0.565233	−	0.824931i	$-0.691214\pi$
$313$	−20.0000	−1.13047	−0.565233	+	0.824931i	$0.691214\pi$
$314$	−10.0000	−0.564333
$315$	−12.0000	−0.676123
$316$	−4.00000	−0.225018
$317$	34.0000	1.90963	0.954815	−	0.297200i	$-0.0960529\pi$
$317$	34.0000	1.90963	0.954815	+	0.297200i	$0.0960529\pi$
$318$	0	0
$319$	−24.0000	−1.34374
$320$	28.0000	1.56525
$321$	0	0
$322$	−4.00000	−0.222911
$323$	0	0
$324$	−9.00000	−0.500000
$325$	44.0000	2.44068
$326$	−24.0000	−1.32924
$327$	0	0
$328$	18.0000	0.993884
$329$	−12.0000	−0.661581
$330$	0	0
$331$	16.0000	0.879440	0.439720	−	0.898135i	$-0.355078\pi$
$331$	16.0000	0.879440	0.439720	+	0.898135i	$0.355078\pi$
$332$	0	0
$333$	3.00000	0.164399
$334$	−6.00000	−0.328305
$335$	−16.0000	−0.874173
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	3.00000	0.163178
$339$	0	0
$340$	0	0
$341$	8.00000	0.433224
$342$	18.0000	0.973329
$343$	1.00000	0.0539949
$344$	12.0000	0.646997
$345$	0	0
$346$	−6.00000	−0.322562
$347$	8.00000	0.429463	0.214731	−	0.976673i	$-0.431112\pi$
$347$	8.00000	0.429463	0.214731	+	0.976673i	$0.431112\pi$
$348$	0	0
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	11.0000	0.587975
$351$	0	0
$352$	20.0000	1.06600
$353$	−4.00000	−0.212899	−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000	−0.212899	−0.106449	+	0.994318i	$0.533948\pi$
$354$	0	0
$355$	0	0
$356$	−16.0000	−0.847998
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	36.0000	1.89737
$361$	17.0000	0.894737
$362$	−22.0000	−1.15629
$363$	0	0
$364$	−4.00000	−0.209657
$365$	8.00000	0.418739
$366$	0	0
$367$	20.0000	1.04399	0.521996	−	0.852948i	$-0.325188\pi$
$367$	20.0000	1.04399	0.521996	+	0.852948i	$0.325188\pi$
$368$	4.00000	0.208514
$369$	18.0000	0.937043
$370$	−4.00000	−0.207950
$371$	10.0000	0.519174
$372$	0	0
$373$	−22.0000	−1.13912	−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000	−1.13912	−0.569558	+	0.821951i	$0.692886\pi$
$374$	0	0
$375$	0	0
$376$	36.0000	1.85656
$377$	−24.0000	−1.23606
$378$	0	0
$379$	36.0000	1.84920	0.924598	−	0.380945i	$-0.124401\pi$
$379$	36.0000	1.84920	0.924598	+	0.380945i	$0.124401\pi$
$380$	24.0000	1.23117
$381$	0	0
$382$	−16.0000	−0.818631
$383$	−34.0000	−1.73732	−0.868659	−	0.495410i	$-0.835018\pi$
$383$	−34.0000	−1.73732	−0.868659	+	0.495410i	$0.835018\pi$
$384$	0	0
$385$	16.0000	0.815436
$386$	10.0000	0.508987
$387$	12.0000	0.609994
$388$	−4.00000	−0.203069
$389$	34.0000	1.72387	0.861934	−	0.507020i	$-0.169253\pi$
$389$	34.0000	1.72387	0.861934	+	0.507020i	$0.169253\pi$
$390$	0	0
$391$	0	0
$392$	−3.00000	−0.151523
$393$	0	0
$394$	6.00000	0.302276
$395$	16.0000	0.805047
$396$	12.0000	0.603023
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	14.0000	0.701757
$399$	0	0
$400$	−11.0000	−0.550000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	8.00000	0.398508
$404$	−6.00000	−0.298511
$405$	36.0000	1.78885
$406$	−6.00000	−0.297775
$407$	−4.00000	−0.198273
$408$	0	0
$409$	−16.0000	−0.791149	−0.395575	−	0.918434i	$-0.629455\pi$
$409$	−16.0000	−0.791149	−0.395575	+	0.918434i	$0.629455\pi$
$410$	−24.0000	−1.18528
$411$	0	0
$412$	−6.00000	−0.295599
$413$	−10.0000	−0.492068
$414$	12.0000	0.589768
$415$	0	0
$416$	20.0000	0.980581
$417$	0	0
$418$	−24.0000	−1.17388
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	0	0
$421$	6.00000	0.292422	0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000	0.292422	0.146211	+	0.989253i	$0.453292\pi$
$422$	20.0000	0.973585
$423$	36.0000	1.75038
$424$	−30.0000	−1.45693
$425$	0	0
$426$	0	0
$427$	−8.00000	−0.387147
$428$	−12.0000	−0.580042
$429$	0	0
$430$	−16.0000	−0.771589
$431$	−12.0000	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$432$	0	0
$433$	−18.0000	−0.865025	−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000	−0.865025	−0.432512	+	0.901628i	$0.642373\pi$
$434$	2.00000	0.0960031
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	24.0000	1.14808
$438$	0	0
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	−48.0000	−2.28831
$441$	−3.00000	−0.142857
$442$	0	0
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	0	0
$445$	64.0000	3.03389
$446$	−8.00000	−0.378811
$447$	0	0
$448$	7.00000	0.330719
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−33.0000	−1.55563
$451$	−24.0000	−1.13012
$452$	−18.0000	−0.846649
$453$	0	0
$454$	−10.0000	−0.469323
$455$	16.0000	0.750092
$456$	0	0
$457$	−6.00000	−0.280668	−0.140334	−	0.990104i	$-0.544818\pi$
$457$	−6.00000	−0.280668	−0.140334	+	0.990104i	$0.544818\pi$
$458$	22.0000	1.02799
$459$	0	0
$460$	16.0000	0.746004
$461$	36.0000	1.67669	0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000	1.67669	0.838344	+	0.545142i	$0.183524\pi$
$462$	0	0
$463$	−28.0000	−1.30127	−0.650635	−	0.759390i	$-0.725497\pi$
$463$	−28.0000	−1.30127	−0.650635	+	0.759390i	$0.725497\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	6.00000	0.277945
$467$	−14.0000	−0.647843	−0.323921	−	0.946084i	$-0.605001\pi$
$467$	−14.0000	−0.647843	−0.323921	+	0.946084i	$0.605001\pi$
$468$	12.0000	0.554700
$469$	−4.00000	−0.184703
$470$	−48.0000	−2.21407
$471$	0	0
$472$	30.0000	1.38086
$473$	−16.0000	−0.735681
$474$	0	0
$475$	−66.0000	−3.02829
$476$	0	0
$477$	−30.0000	−1.37361
$478$	24.0000	1.09773
$479$	−34.0000	−1.55350	−0.776750	−	0.629809i	$-0.783133\pi$
$479$	−34.0000	−1.55350	−0.776750	+	0.629809i	$0.783133\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	−4.00000	−0.182195
$483$	0	0
$484$	−5.00000	−0.227273
$485$	16.0000	0.726523
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	24.0000	1.08643
$489$	0	0
$490$	4.00000	0.180702
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	0	0
$493$	0	0
$494$	−24.0000	−1.07981
$495$	−48.0000	−2.15744
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	0	0
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	−24.0000	−1.07331
$501$	0	0
$502$	−2.00000	−0.0892644
$503$	10.0000	0.445878	0.222939	−	0.974832i	$-0.428435\pi$
$503$	10.0000	0.445878	0.222939	+	0.974832i	$0.428435\pi$
$504$	9.00000	0.400892
$505$	24.0000	1.06799
$506$	−16.0000	−0.711287
$507$	0	0
$508$	8.00000	0.354943
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	−11.0000	−0.486136
$513$	0	0
$514$	−24.0000	−1.05859
$515$	24.0000	1.05757
$516$	0	0
$517$	−48.0000	−2.11104
$518$	−1.00000	−0.0439375
$519$	0	0
$520$	−48.0000	−2.10494
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	18.0000	0.787839
$523$	−10.0000	−0.437269	−0.218635	−	0.975807i	$-0.570160\pi$
$523$	−10.0000	−0.437269	−0.218635	+	0.975807i	$0.570160\pi$
$524$	−18.0000	−0.786334
$525$	0	0
$526$	16.0000	0.697633
$527$	0	0
$528$	0	0
$529$	−7.00000	−0.304348
$530$	40.0000	1.73749
$531$	30.0000	1.30189
$532$	6.00000	0.260133
$533$	−24.0000	−1.03956
$534$	0	0
$535$	48.0000	2.07522
$536$	12.0000	0.518321
$537$	0	0
$538$	6.00000	0.258678
$539$	4.00000	0.172292
$540$	0	0
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	8.00000	0.343629
$543$	0	0
$544$	0	0
$545$	8.00000	0.342682
$546$	0	0
$547$	−16.0000	−0.684111	−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000	−0.684111	−0.342055	+	0.939680i	$0.611123\pi$
$548$	−18.0000	−0.768922
$549$	24.0000	1.02430
$550$	44.0000	1.87617
$551$	36.0000	1.53365
$552$	0	0
$553$	4.00000	0.170097
$554$	30.0000	1.27458
$555$	0	0
$556$	−4.00000	−0.169638
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	−6.00000	−0.254000
$559$	−16.0000	−0.676728
$560$	−4.00000	−0.169031
$561$	0	0
$562$	−18.0000	−0.759284
$563$	−30.0000	−1.26435	−0.632175	−	0.774826i	$-0.717837\pi$
$563$	−30.0000	−1.26435	−0.632175	+	0.774826i	$0.717837\pi$
$564$	0	0
$565$	72.0000	3.02906
$566$	−26.0000	−1.09286
$567$	9.00000	0.377964
$568$	0	0
$569$	6.00000	0.251533	0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000	0.251533	0.125767	+	0.992060i	$0.459861\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	−16.0000	−0.668994
$573$	0	0
$574$	−6.00000	−0.250435
$575$	−44.0000	−1.83493
$576$	−21.0000	−0.875000
$577$	12.0000	0.499567	0.249783	−	0.968302i	$-0.419641\pi$
$577$	12.0000	0.499567	0.249783	+	0.968302i	$0.419641\pi$
$578$	−17.0000	−0.707107
$579$	0	0
$580$	24.0000	0.996546
$581$	0	0
$582$	0	0
$583$	40.0000	1.65663
$584$	−6.00000	−0.248282
$585$	−48.0000	−1.98456
$586$	−14.0000	−0.578335
$587$	10.0000	0.412744	0.206372	−	0.978474i	$-0.433834\pi$
$587$	10.0000	0.412744	0.206372	+	0.978474i	$0.433834\pi$
$588$	0	0
$589$	−12.0000	−0.494451
$590$	−40.0000	−1.64677
$591$	0	0
$592$	1.00000	0.0410997
$593$	10.0000	0.410651	0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000	0.410651	0.205325	+	0.978694i	$0.434175\pi$
$594$	0	0
$595$	0	0
$596$	14.0000	0.573462
$597$	0	0
$598$	−16.0000	−0.654289
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	0	0
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	−4.00000	−0.163028
$603$	12.0000	0.488678
$604$	8.00000	0.325515
$605$	20.0000	0.813116
$606$	0	0
$607$	22.0000	0.892952	0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000	0.892952	0.446476	+	0.894795i	$0.352679\pi$
$608$	−30.0000	−1.21666
$609$	0	0
$610$	−32.0000	−1.29564
$611$	−48.0000	−1.94187
$612$	0	0
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	−12.0000	−0.483494
$617$	2.00000	0.0805170	0.0402585	−	0.999189i	$-0.487182\pi$
$617$	2.00000	0.0805170	0.0402585	+	0.999189i	$0.487182\pi$
$618$	0	0
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−8.00000	−0.321288
$621$	0	0
$622$	30.0000	1.20289
$623$	16.0000	0.641026
$624$	0	0
$625$	41.0000	1.64000
$626$	−20.0000	−0.799361
$627$	0	0
$628$	10.0000	0.399043
$629$	0	0
$630$	−12.0000	−0.478091
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	−12.0000	−0.477334
$633$	0	0
$634$	34.0000	1.35031
$635$	−32.0000	−1.26988
$636$	0	0
$637$	4.00000	0.158486
$638$	−24.0000	−0.950169
$639$	0	0
$640$	−12.0000	−0.474342
$641$	−34.0000	−1.34292	−0.671460	−	0.741041i	$-0.734332\pi$
$641$	−34.0000	−1.34292	−0.671460	+	0.741041i	$0.734332\pi$
$642$	0	0
$643$	50.0000	1.97181	0.985904	−	0.167313i	$-0.0535092\pi$
$643$	50.0000	1.97181	0.985904	+	0.167313i	$0.0535092\pi$
$644$	4.00000	0.157622
$645$	0	0
$646$	0	0
$647$	10.0000	0.393141	0.196570	−	0.980490i	$-0.437020\pi$
$647$	10.0000	0.393141	0.196570	+	0.980490i	$0.437020\pi$
$648$	−27.0000	−1.06066
$649$	−40.0000	−1.57014
$650$	44.0000	1.72582
$651$	0	0
$652$	24.0000	0.939913
$653$	−30.0000	−1.17399	−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000	−1.17399	−0.586995	+	0.809590i	$0.699689\pi$
$654$	0	0
$655$	72.0000	2.81327
$656$	6.00000	0.234261
$657$	−6.00000	−0.234082
$658$	−12.0000	−0.467809
$659$	12.0000	0.467454	0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000	0.467454	0.233727	+	0.972302i	$0.424908\pi$
$660$	0	0
$661$	−28.0000	−1.08907	−0.544537	−	0.838737i	$-0.683295\pi$
$661$	−28.0000	−1.08907	−0.544537	+	0.838737i	$0.683295\pi$
$662$	16.0000	0.621858
$663$	0	0
$664$	0	0
$665$	−24.0000	−0.930680
$666$	3.00000	0.116248
$667$	24.0000	0.929284
$668$	6.00000	0.232147
$669$	0	0
$670$	−16.0000	−0.618134
$671$	−32.0000	−1.23535
$672$	0	0
$673$	−30.0000	−1.15642	−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000	−1.15642	−0.578208	+	0.815890i	$0.696248\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	−3.00000	−0.115385
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	0	0
$679$	4.00000	0.153506
$680$	0	0
$681$	0	0
$682$	8.00000	0.306336
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−18.0000	−0.688247
$685$	72.0000	2.75098
$686$	1.00000	0.0381802
$687$	0	0
$688$	4.00000	0.152499
$689$	40.0000	1.52388
$690$	0	0
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	6.00000	0.228086
$693$	−12.0000	−0.455842
$694$	8.00000	0.303676
$695$	16.0000	0.606915
$696$	0	0
$697$	0	0
$698$	18.0000	0.681310
$699$	0	0
$700$	−11.0000	−0.415761
$701$	42.0000	1.58632	0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000	1.58632	0.793159	+	0.609015i	$0.208435\pi$
$702$	0	0
$703$	6.00000	0.226294
$704$	28.0000	1.05529
$705$	0	0
$706$	−4.00000	−0.150542
$707$	6.00000	0.225653
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	0	0
$711$	−12.0000	−0.450035
$712$	−48.0000	−1.79888
$713$	−8.00000	−0.299602
$714$	0	0
$715$	64.0000	2.39346
$716$	0	0
$717$	0	0
$718$	0	0
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	12.0000	0.447214
$721$	6.00000	0.223452
$722$	17.0000	0.632674
$723$	0	0
$724$	22.0000	0.817624
$725$	−66.0000	−2.45118
$726$	0	0
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	−12.0000	−0.444750
$729$	−27.0000	−1.00000
$730$	8.00000	0.296093
$731$	0	0
$732$	0	0
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	20.0000	0.738213
$735$	0	0
$736$	−20.0000	−0.737210
$737$	−16.0000	−0.589368
$738$	18.0000	0.662589
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	10.0000	0.367112
$743$	48.0000	1.76095	0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000	1.76095	0.880475	+	0.474093i	$0.157224\pi$
$744$	0	0
$745$	−56.0000	−2.05168
$746$	−22.0000	−0.805477
$747$	0	0
$748$	0	0
$749$	12.0000	0.438470
$750$	0	0
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	−24.0000	−0.874028
$755$	−32.0000	−1.16460
$756$	0	0
$757$	−14.0000	−0.508839	−0.254419	−	0.967094i	$-0.581884\pi$
$757$	−14.0000	−0.508839	−0.254419	+	0.967094i	$0.581884\pi$
$758$	36.0000	1.30758
$759$	0	0
$760$	72.0000	2.61171
$761$	−2.00000	−0.0724999	−0.0362500	−	0.999343i	$-0.511541\pi$
$761$	−2.00000	−0.0724999	−0.0362500	+	0.999343i	$0.511541\pi$
$762$	0	0
$763$	2.00000	0.0724049
$764$	16.0000	0.578860
$765$	0	0
$766$	−34.0000	−1.22847
$767$	−40.0000	−1.44432
$768$	0	0
$769$	20.0000	0.721218	0.360609	−	0.932717i	$-0.382569\pi$
$769$	20.0000	0.721218	0.360609	+	0.932717i	$0.382569\pi$
$770$	16.0000	0.576600
$771$	0	0
$772$	−10.0000	−0.359908
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	12.0000	0.431331
$775$	22.0000	0.790263
$776$	−12.0000	−0.430775
$777$	0	0
$778$	34.0000	1.21896
$779$	36.0000	1.28983
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−1.00000	−0.0357143
$785$	−40.0000	−1.42766
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	16.0000	0.569254
$791$	18.0000	0.640006
$792$	36.0000	1.27920
$793$	−32.0000	−1.13635
$794$	−2.00000	−0.0709773
$795$	0	0
$796$	−14.0000	−0.496217
$797$	−8.00000	−0.283375	−0.141687	−	0.989911i	$-0.545253\pi$
$797$	−8.00000	−0.283375	−0.141687	+	0.989911i	$0.545253\pi$
$798$	0	0
$799$	0	0
$800$	55.0000	1.94454
$801$	−48.0000	−1.69600
$802$	30.0000	1.05934
$803$	8.00000	0.282314
$804$	0	0
$805$	−16.0000	−0.563926
$806$	8.00000	0.281788
$807$	0	0
$808$	−18.0000	−0.633238
$809$	2.00000	0.0703163	0.0351581	−	0.999382i	$-0.488807\pi$
$809$	2.00000	0.0703163	0.0351581	+	0.999382i	$0.488807\pi$
$810$	36.0000	1.26491
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	−4.00000	−0.140200
$815$	−96.0000	−3.36273
$816$	0	0
$817$	24.0000	0.839654
$818$	−16.0000	−0.559427
$819$	−12.0000	−0.419314
$820$	24.0000	0.838116
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	0	0
$823$	−16.0000	−0.557725	−0.278862	−	0.960331i	$-0.589957\pi$
$823$	−16.0000	−0.557725	−0.278862	+	0.960331i	$0.589957\pi$
$824$	−18.0000	−0.627060
$825$	0	0
$826$	−10.0000	−0.347945
$827$	−32.0000	−1.11275	−0.556375	−	0.830932i	$-0.687808\pi$
$827$	−32.0000	−1.11275	−0.556375	+	0.830932i	$0.687808\pi$
$828$	−12.0000	−0.417029
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	0	0
$831$	0	0
$832$	28.0000	0.970725
$833$	0	0
$834$	0	0
$835$	−24.0000	−0.830554
$836$	24.0000	0.830057
$837$	0	0
$838$	4.00000	0.138178
$839$	8.00000	0.276191	0.138095	−	0.990419i	$-0.455902\pi$
$839$	8.00000	0.276191	0.138095	+	0.990419i	$0.455902\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	6.00000	0.206774
$843$	0	0
$844$	−20.0000	−0.688428
$845$	12.0000	0.412813
$846$	36.0000	1.23771
$847$	5.00000	0.171802
$848$	−10.0000	−0.343401
$849$	0	0
$850$	0	0
$851$	4.00000	0.137118
$852$	0	0
$853$	8.00000	0.273915	0.136957	−	0.990577i	$-0.456268\pi$
$853$	8.00000	0.273915	0.136957	+	0.990577i	$0.456268\pi$
$854$	−8.00000	−0.273754
$855$	72.0000	2.46235
$856$	−36.0000	−1.23045
$857$	−24.0000	−0.819824	−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000	−0.819824	−0.409912	+	0.912125i	$0.634441\pi$
$858$	0	0
$859$	−26.0000	−0.887109	−0.443554	−	0.896248i	$-0.646283\pi$
$859$	−26.0000	−0.887109	−0.443554	+	0.896248i	$0.646283\pi$
$860$	16.0000	0.545595
$861$	0	0
$862$	−12.0000	−0.408722
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	−24.0000	−0.816024
$866$	−18.0000	−0.611665
$867$	0	0
$868$	−2.00000	−0.0678844
$869$	16.0000	0.542763
$870$	0	0
$871$	−16.0000	−0.542139
$872$	−6.00000	−0.203186
$873$	−12.0000	−0.406138
$874$	24.0000	0.811812
$875$	24.0000	0.811348
$876$	0	0
$877$	14.0000	0.472746	0.236373	−	0.971662i	$-0.424041\pi$
$877$	14.0000	0.472746	0.236373	+	0.971662i	$0.424041\pi$
$878$	−14.0000	−0.472477
$879$	0	0
$880$	−16.0000	−0.539360
$881$	22.0000	0.741199	0.370599	−	0.928793i	$-0.379152\pi$
$881$	22.0000	0.741199	0.370599	+	0.928793i	$0.379152\pi$
$882$	−3.00000	−0.101015
$883$	−48.0000	−1.61533	−0.807664	−	0.589643i	$-0.799269\pi$
$883$	−48.0000	−1.61533	−0.807664	+	0.589643i	$0.799269\pi$
$884$	0	0
$885$	0	0
$886$	4.00000	0.134383
$887$	28.0000	0.940148	0.470074	−	0.882627i	$-0.344227\pi$
$887$	28.0000	0.940148	0.470074	+	0.882627i	$0.344227\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	64.0000	2.14528
$891$	36.0000	1.20605
$892$	8.00000	0.267860
$893$	72.0000	2.40939
$894$	0	0
$895$	0	0
$896$	−3.00000	−0.100223
$897$	0	0
$898$	−6.00000	−0.200223
$899$	−12.0000	−0.400222
$900$	33.0000	1.10000
$901$	0	0
$902$	−24.0000	−0.799113
$903$	0	0
$904$	−54.0000	−1.79601
$905$	−88.0000	−2.92522
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	10.0000	0.331862
$909$	−18.0000	−0.597022
$910$	16.0000	0.530395
$911$	32.0000	1.06021	0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000	1.06021	0.530104	+	0.847933i	$0.322153\pi$
$912$	0	0
$913$	0	0
$914$	−6.00000	−0.198462
$915$	0	0
$916$	−22.0000	−0.726900
$917$	18.0000	0.594412
$918$	0	0
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	48.0000	1.58251
$921$	0	0
$922$	36.0000	1.18560
$923$	0	0
$924$	0	0
$925$	−11.0000	−0.361678
$926$	−28.0000	−0.920137
$927$	−18.0000	−0.591198
$928$	−30.0000	−0.984798
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	−6.00000	−0.196537
$933$	0	0
$934$	−14.0000	−0.458094
$935$	0	0
$936$	36.0000	1.17670
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−4.00000	−0.130605
$939$	0	0
$940$	48.0000	1.56559
$941$	−46.0000	−1.49956	−0.749779	−	0.661689i	$-0.769840\pi$
$941$	−46.0000	−1.49956	−0.749779	+	0.661689i	$0.769840\pi$
$942$	0	0
$943$	24.0000	0.781548
$944$	10.0000	0.325472
$945$	0	0
$946$	−16.0000	−0.520205
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	8.00000	0.259691
$950$	−66.0000	−2.14132
$951$	0	0
$952$	0	0
$953$	22.0000	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$954$	−30.0000	−0.971286
$955$	−64.0000	−2.07099
$956$	−24.0000	−0.776215
$957$	0	0
$958$	−34.0000	−1.09849
$959$	18.0000	0.581250
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−4.00000	−0.128965
$963$	−36.0000	−1.16008
$964$	4.00000	0.128831
$965$	40.0000	1.28765
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	−15.0000	−0.482118
$969$	0	0
$970$	16.0000	0.513729
$971$	−8.00000	−0.256732	−0.128366	−	0.991727i	$-0.540973\pi$
$971$	−8.00000	−0.256732	−0.128366	+	0.991727i	$0.540973\pi$
$972$	0	0
$973$	4.00000	0.128234
$974$	0	0
$975$	0	0
$976$	8.00000	0.256074
$977$	22.0000	0.703842	0.351921	−	0.936030i	$-0.385529\pi$
$977$	22.0000	0.703842	0.351921	+	0.936030i	$0.385529\pi$
$978$	0	0
$979$	64.0000	2.04545
$980$	−4.00000	−0.127775
$981$	−6.00000	−0.191565
$982$	20.0000	0.638226
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	24.0000	0.764704
$986$	0	0
$987$	0	0
$988$	24.0000	0.763542
$989$	16.0000	0.508770
$990$	−48.0000	−1.52554
$991$	−24.0000	−0.762385	−0.381193	−	0.924496i	$-0.624487\pi$
$991$	−24.0000	−0.762385	−0.381193	+	0.924496i	$0.624487\pi$
$992$	10.0000	0.317500
$993$	0	0
$994$	0	0
$995$	56.0000	1.77532
$996$	0	0
$997$	24.0000	0.760088	0.380044	−	0.924968i	$-0.375909\pi$
$997$	24.0000	0.760088	0.380044	+	0.924968i	$0.375909\pi$
$998$	24.0000	0.759707
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	259.2.a.a.1.1	✓	1
3.2	odd	2		2331.2.a.a.1.1		1
4.3	odd	2		4144.2.a.f.1.1		1
5.4	even	2		6475.2.a.a.1.1		1
7.6	odd	2		1813.2.a.c.1.1		1
37.36	even	2		9583.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
259.2.a.a.1.1	✓	1	1.1	even	1	trivial
1813.2.a.c.1.1		1	7.6	odd	2
2331.2.a.a.1.1		1	3.2	odd	2
4144.2.a.f.1.1		1	4.3	odd	2
6475.2.a.a.1.1		1	5.4	even	2
9583.2.a.a.1.1		1	37.36	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:	\( N \)	\(=\)	\( 259 = 7 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	259.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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