LMFDB - Embedded newform 8015.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
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	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +5.00000 q^{13} -1.00000 q^{14} +1.00000 q^{15} -1.00000 q^{16} +2.00000 q^{18} -8.00000 q^{19} -1.00000 q^{20} +1.00000 q^{21} +6.00000 q^{23} +3.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} -5.00000 q^{27} -1.00000 q^{28} -1.00000 q^{30} -5.00000 q^{32} +1.00000 q^{35} +2.00000 q^{36} +2.00000 q^{37} +8.00000 q^{38} +5.00000 q^{39} +3.00000 q^{40} -8.00000 q^{41} -1.00000 q^{42} -8.00000 q^{43} -2.00000 q^{45} -6.00000 q^{46} -10.0000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -5.00000 q^{52} -2.00000 q^{53} +5.00000 q^{54} +3.00000 q^{56} -8.00000 q^{57} +3.00000 q^{59} -1.00000 q^{60} +5.00000 q^{61} -2.00000 q^{63} +7.00000 q^{64} +5.00000 q^{65} -6.00000 q^{67} +6.00000 q^{69} -1.00000 q^{70} -6.00000 q^{71} -6.00000 q^{72} -11.0000 q^{73} -2.00000 q^{74} +1.00000 q^{75} +8.00000 q^{76} -5.00000 q^{78} +3.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +8.00000 q^{82} +7.00000 q^{83} -1.00000 q^{84} +8.00000 q^{86} +10.0000 q^{89} +2.00000 q^{90} +5.00000 q^{91} -6.00000 q^{92} +10.0000 q^{94} -8.00000 q^{95} -5.00000 q^{96} -8.00000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.00000	1.06066
$9$	−2.00000	−0.666667
$10$	−1.00000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−1.00000	−0.288675
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	−1.00000	−0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	2.00000	0.471405
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−1.00000	−0.223607
$21$	1.00000	0.218218
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	3.00000	0.612372
$25$	1.00000	0.200000
$26$	−5.00000	−0.980581
$27$	−5.00000	−0.962250
$28$	−1.00000	−0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	−1.00000	−0.182574
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	0	0
$35$	1.00000	0.169031
$36$	2.00000	0.333333
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	8.00000	1.29777
$39$	5.00000	0.800641
$40$	3.00000	0.474342
$41$	−8.00000	−1.24939	−0.624695	−	0.780869i	$-0.714777\pi$
$41$	−8.00000	−1.24939	−0.624695	+	0.780869i	$0.714777\pi$
$42$	−1.00000	−0.154303
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	−2.00000	−0.298142
$46$	−6.00000	−0.884652
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0	0
$52$	−5.00000	−0.693375
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	3.00000	0.400892
$57$	−8.00000	−1.05963
$58$	0	0
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	−1.00000	−0.129099
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	0	0
$63$	−2.00000	−0.251976
$64$	7.00000	0.875000
$65$	5.00000	0.620174
$66$	0	0
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	0	0
$69$	6.00000	0.722315
$70$	−1.00000	−0.119523
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	−6.00000	−0.707107
$73$	−11.0000	−1.28745	−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000	−1.28745	−0.643726	+	0.765256i	$0.722612\pi$
$74$	−2.00000	−0.232495
$75$	1.00000	0.115470
$76$	8.00000	0.917663
$77$	0	0
$78$	−5.00000	−0.566139
$79$	3.00000	0.337526	0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000	0.337526	0.168763	+	0.985657i	$0.446023\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	8.00000	0.883452
$83$	7.00000	0.768350	0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000	0.768350	0.384175	+	0.923260i	$0.374486\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	8.00000	0.862662
$87$	0	0
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	2.00000	0.210819
$91$	5.00000	0.524142
$92$	−6.00000	−0.625543
$93$	0	0
$94$	10.0000	1.03142
$95$	−8.00000	−0.820783
$96$	−5.00000	−0.510310
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	3.00000	0.295599	0.147799	−	0.989017i	$-0.452781\pi$
$103$	3.00000	0.295599	0.147799	+	0.989017i	$0.452781\pi$
$104$	15.0000	1.47087
$105$	1.00000	0.0975900
$106$	2.00000	0.194257
$107$	−8.00000	−0.773389	−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000	−0.773389	−0.386695	+	0.922208i	$0.626383\pi$
$108$	5.00000	0.481125
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	3.00000	0.282216	0.141108	−	0.989994i	$-0.454933\pi$
$113$	3.00000	0.282216	0.141108	+	0.989994i	$0.454933\pi$
$114$	8.00000	0.749269
$115$	6.00000	0.559503
$116$	0	0
$117$	−10.0000	−0.924500
$118$	−3.00000	−0.276172
$119$	0	0
$120$	3.00000	0.273861
$121$	−11.0000	−1.00000
$122$	−5.00000	−0.452679
$123$	−8.00000	−0.721336
$124$	0	0
$125$	1.00000	0.0894427
$126$	2.00000	0.178174
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	3.00000	0.265165
$129$	−8.00000	−0.704361
$130$	−5.00000	−0.438529
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	−8.00000	−0.693688
$134$	6.00000	0.518321
$135$	−5.00000	−0.430331
$136$	0	0
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	−6.00000	−0.510754
$139$	19.0000	1.61156	0.805779	−	0.592216i	$-0.201747\pi$
$139$	19.0000	1.61156	0.805779	+	0.592216i	$0.201747\pi$
$140$	−1.00000	−0.0845154
$141$	−10.0000	−0.842152
$142$	6.00000	0.503509
$143$	0	0
$144$	2.00000	0.166667
$145$	0	0
$146$	11.0000	0.910366
$147$	1.00000	0.0824786
$148$	−2.00000	−0.164399
$149$	−15.0000	−1.22885	−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000	−1.22885	−0.614424	+	0.788976i	$0.710612\pi$
$150$	−1.00000	−0.0816497
$151$	10.0000	0.813788	0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000	0.813788	0.406894	+	0.913475i	$0.366612\pi$
$152$	−24.0000	−1.94666
$153$	0	0
$154$	0	0
$155$	0	0
$156$	−5.00000	−0.400320
$157$	−11.0000	−0.877896	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−11.0000	−0.877896	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−3.00000	−0.238667
$159$	−2.00000	−0.158610
$160$	−5.00000	−0.395285
$161$	6.00000	0.472866
$162$	−1.00000	−0.0785674
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	−7.00000	−0.543305
$167$	20.0000	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$168$	3.00000	0.231455
$169$	12.0000	0.923077
$170$	0	0
$171$	16.0000	1.22355
$172$	8.00000	0.609994
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	0	0
$177$	3.00000	0.225494
$178$	−10.0000	−0.749532
$179$	5.00000	0.373718	0.186859	−	0.982387i	$-0.440169\pi$
$179$	5.00000	0.373718	0.186859	+	0.982387i	$0.440169\pi$
$180$	2.00000	0.149071
$181$	9.00000	0.668965	0.334482	−	0.942402i	$-0.391439\pi$
$181$	9.00000	0.668965	0.334482	+	0.942402i	$0.391439\pi$
$182$	−5.00000	−0.370625
$183$	5.00000	0.369611
$184$	18.0000	1.32698
$185$	2.00000	0.147043
$186$	0	0
$187$	0	0
$188$	10.0000	0.729325
$189$	−5.00000	−0.363696
$190$	8.00000	0.580381
$191$	−17.0000	−1.23008	−0.615038	−	0.788497i	$-0.710860\pi$
$191$	−17.0000	−1.23008	−0.615038	+	0.788497i	$0.710860\pi$
$192$	7.00000	0.505181
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	8.00000	0.574367
$195$	5.00000	0.358057
$196$	−1.00000	−0.0714286
$197$	−13.0000	−0.926212	−0.463106	−	0.886303i	$-0.653265\pi$
$197$	−13.0000	−0.926212	−0.463106	+	0.886303i	$0.653265\pi$
$198$	0	0
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	3.00000	0.212132
$201$	−6.00000	−0.423207
$202$	10.0000	0.703598
$203$	0	0
$204$	0	0
$205$	−8.00000	−0.558744
$206$	−3.00000	−0.209020
$207$	−12.0000	−0.834058
$208$	−5.00000	−0.346688
$209$	0	0
$210$	−1.00000	−0.0690066
$211$	17.0000	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$211$	17.0000	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$212$	2.00000	0.137361
$213$	−6.00000	−0.411113
$214$	8.00000	0.546869
$215$	−8.00000	−0.545595
$216$	−15.0000	−1.02062
$217$	0	0
$218$	−2.00000	−0.135457
$219$	−11.0000	−0.743311
$220$	0	0
$221$	0	0
$222$	−2.00000	−0.134231
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	−5.00000	−0.334077
$225$	−2.00000	−0.133333
$226$	−3.00000	−0.199557
$227$	−16.0000	−1.06196	−0.530979	−	0.847385i	$-0.678176\pi$
$227$	−16.0000	−1.06196	−0.530979	+	0.847385i	$0.678176\pi$
$228$	8.00000	0.529813
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−6.00000	−0.395628
$231$	0	0
$232$	0	0
$233$	12.0000	0.786146	0.393073	−	0.919507i	$-0.371412\pi$
$233$	12.0000	0.786146	0.393073	+	0.919507i	$0.371412\pi$
$234$	10.0000	0.653720
$235$	−10.0000	−0.652328
$236$	−3.00000	−0.195283
$237$	3.00000	0.194871
$238$	0	0
$239$	1.00000	0.0646846	0.0323423	−	0.999477i	$-0.489703\pi$
$239$	1.00000	0.0646846	0.0323423	+	0.999477i	$0.489703\pi$
$240$	−1.00000	−0.0645497
$241$	7.00000	0.450910	0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000	0.450910	0.225455	+	0.974254i	$0.427613\pi$
$242$	11.0000	0.707107
$243$	16.0000	1.02640
$244$	−5.00000	−0.320092
$245$	1.00000	0.0638877
$246$	8.00000	0.510061
$247$	−40.0000	−2.54514
$248$	0	0
$249$	7.00000	0.443607
$250$	−1.00000	−0.0632456
$251$	13.0000	0.820553	0.410276	−	0.911961i	$-0.365432\pi$
$251$	13.0000	0.820553	0.410276	+	0.911961i	$0.365432\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	−4.00000	−0.250982
$255$	0	0
$256$	−17.0000	−1.06250
$257$	3.00000	0.187135	0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000	0.187135	0.0935674	+	0.995613i	$0.470173\pi$
$258$	8.00000	0.498058
$259$	2.00000	0.124274
$260$	−5.00000	−0.310087
$261$	0	0
$262$	12.0000	0.741362
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	0	0
$265$	−2.00000	−0.122859
$266$	8.00000	0.490511
$267$	10.0000	0.611990
$268$	6.00000	0.366508
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	5.00000	0.304290
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	0	0
$273$	5.00000	0.302614
$274$	6.00000	0.362473
$275$	0	0
$276$	−6.00000	−0.361158
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−19.0000	−1.13954
$279$	0	0
$280$	3.00000	0.179284
$281$	−20.0000	−1.19310	−0.596550	−	0.802576i	$-0.703462\pi$
$281$	−20.0000	−1.19310	−0.596550	+	0.802576i	$0.703462\pi$
$282$	10.0000	0.595491
$283$	−22.0000	−1.30776	−0.653882	−	0.756596i	$-0.726861\pi$
$283$	−22.0000	−1.30776	−0.653882	+	0.756596i	$0.726861\pi$
$284$	6.00000	0.356034
$285$	−8.00000	−0.473879
$286$	0	0
$287$	−8.00000	−0.472225
$288$	10.0000	0.589256
$289$	−17.0000	−1.00000
$290$	0	0
$291$	−8.00000	−0.468968
$292$	11.0000	0.643726
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	−1.00000	−0.0583212
$295$	3.00000	0.174667
$296$	6.00000	0.348743
$297$	0	0
$298$	15.0000	0.868927
$299$	30.0000	1.73494
$300$	−1.00000	−0.0577350
$301$	−8.00000	−0.461112
$302$	−10.0000	−0.575435
$303$	−10.0000	−0.574485
$304$	8.00000	0.458831
$305$	5.00000	0.286299
$306$	0	0
$307$	19.0000	1.08439	0.542194	−	0.840254i	$-0.317594\pi$
$307$	19.0000	1.08439	0.542194	+	0.840254i	$0.317594\pi$
$308$	0	0
$309$	3.00000	0.170664
$310$	0	0
$311$	−20.0000	−1.13410	−0.567048	−	0.823685i	$-0.691915\pi$
$311$	−20.0000	−1.13410	−0.567048	+	0.823685i	$0.691915\pi$
$312$	15.0000	0.849208
$313$	−23.0000	−1.30004	−0.650018	−	0.759918i	$-0.725239\pi$
$313$	−23.0000	−1.30004	−0.650018	+	0.759918i	$0.725239\pi$
$314$	11.0000	0.620766
$315$	−2.00000	−0.112687
$316$	−3.00000	−0.168763
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	2.00000	0.112154
$319$	0	0
$320$	7.00000	0.391312
$321$	−8.00000	−0.446516
$322$	−6.00000	−0.334367
$323$	0	0
$324$	−1.00000	−0.0555556
$325$	5.00000	0.277350
$326$	12.0000	0.664619
$327$	2.00000	0.110600
$328$	−24.0000	−1.32518
$329$	−10.0000	−0.551318
$330$	0	0
$331$	−5.00000	−0.274825	−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000	−0.274825	−0.137412	+	0.990514i	$0.543879\pi$
$332$	−7.00000	−0.384175
$333$	−4.00000	−0.219199
$334$	−20.0000	−1.09435
$335$	−6.00000	−0.327815
$336$	−1.00000	−0.0545545
$337$	28.0000	1.52526	0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000	1.52526	0.762629	+	0.646837i	$0.223908\pi$
$338$	−12.0000	−0.652714
$339$	3.00000	0.162938
$340$	0	0
$341$	0	0
$342$	−16.0000	−0.865181
$343$	1.00000	0.0539949
$344$	−24.0000	−1.29399
$345$	6.00000	0.323029
$346$	0	0
$347$	31.0000	1.66417	0.832084	−	0.554650i	$-0.187148\pi$
$347$	31.0000	1.66417	0.832084	+	0.554650i	$0.187148\pi$
$348$	0	0
$349$	−18.0000	−0.963518	−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000	−0.963518	−0.481759	+	0.876304i	$0.660002\pi$
$350$	−1.00000	−0.0534522
$351$	−25.0000	−1.33440
$352$	0	0
$353$	−19.0000	−1.01127	−0.505634	−	0.862748i	$-0.668741\pi$
$353$	−19.0000	−1.01127	−0.505634	+	0.862748i	$0.668741\pi$
$354$	−3.00000	−0.159448
$355$	−6.00000	−0.318447
$356$	−10.0000	−0.529999
$357$	0	0
$358$	−5.00000	−0.264258
$359$	−34.0000	−1.79445	−0.897226	−	0.441572i	$-0.854421\pi$
$359$	−34.0000	−1.79445	−0.897226	+	0.441572i	$0.854421\pi$
$360$	−6.00000	−0.316228
$361$	45.0000	2.36842
$362$	−9.00000	−0.473029
$363$	−11.0000	−0.577350
$364$	−5.00000	−0.262071
$365$	−11.0000	−0.575766
$366$	−5.00000	−0.261354
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	−6.00000	−0.312772
$369$	16.0000	0.832927
$370$	−2.00000	−0.103975
$371$	−2.00000	−0.103835
$372$	0	0
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−30.0000	−1.54713
$377$	0	0
$378$	5.00000	0.257172
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	8.00000	0.410391
$381$	4.00000	0.204926
$382$	17.0000	0.869796
$383$	21.0000	1.07305	0.536525	−	0.843884i	$-0.319737\pi$
$383$	21.0000	1.07305	0.536525	+	0.843884i	$0.319737\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	22.0000	1.11977
$387$	16.0000	0.813326
$388$	8.00000	0.406138
$389$	−8.00000	−0.405616	−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000	−0.405616	−0.202808	+	0.979219i	$0.565007\pi$
$390$	−5.00000	−0.253185
$391$	0	0
$392$	3.00000	0.151523
$393$	−12.0000	−0.605320
$394$	13.0000	0.654931
$395$	3.00000	0.150946
$396$	0	0
$397$	−20.0000	−1.00377	−0.501886	−	0.864934i	$-0.667360\pi$
$397$	−20.0000	−1.00377	−0.501886	+	0.864934i	$0.667360\pi$
$398$	−11.0000	−0.551380
$399$	−8.00000	−0.400501
$400$	−1.00000	−0.0500000
$401$	5.00000	0.249688	0.124844	−	0.992176i	$-0.460157\pi$
$401$	5.00000	0.249688	0.124844	+	0.992176i	$0.460157\pi$
$402$	6.00000	0.299253
$403$	0	0
$404$	10.0000	0.497519
$405$	1.00000	0.0496904
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−26.0000	−1.28562	−0.642809	−	0.766027i	$-0.722231\pi$
$409$	−26.0000	−1.28562	−0.642809	+	0.766027i	$0.722231\pi$
$410$	8.00000	0.395092
$411$	−6.00000	−0.295958
$412$	−3.00000	−0.147799
$413$	3.00000	0.147620
$414$	12.0000	0.589768
$415$	7.00000	0.343616
$416$	−25.0000	−1.22573
$417$	19.0000	0.930434
$418$	0	0
$419$	−21.0000	−1.02592	−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000	−1.02592	−0.512959	+	0.858413i	$0.671451\pi$
$420$	−1.00000	−0.0487950
$421$	−17.0000	−0.828529	−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000	−0.828529	−0.414265	+	0.910156i	$0.635961\pi$
$422$	−17.0000	−0.827547
$423$	20.0000	0.972433
$424$	−6.00000	−0.291386
$425$	0	0
$426$	6.00000	0.290701
$427$	5.00000	0.241967
$428$	8.00000	0.386695
$429$	0	0
$430$	8.00000	0.385794
$431$	10.0000	0.481683	0.240842	−	0.970564i	$-0.422577\pi$
$431$	10.0000	0.481683	0.240842	+	0.970564i	$0.422577\pi$
$432$	5.00000	0.240563
$433$	38.0000	1.82616	0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000	1.82616	0.913082	+	0.407777i	$0.133696\pi$
$434$	0	0
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	−48.0000	−2.29615
$438$	11.0000	0.525600
$439$	−6.00000	−0.286364	−0.143182	−	0.989696i	$-0.545733\pi$
$439$	−6.00000	−0.286364	−0.143182	+	0.989696i	$0.545733\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	0	0
$443$	−28.0000	−1.33032	−0.665160	−	0.746701i	$-0.731637\pi$
$443$	−28.0000	−1.33032	−0.665160	+	0.746701i	$0.731637\pi$
$444$	−2.00000	−0.0949158
$445$	10.0000	0.474045
$446$	−4.00000	−0.189405
$447$	−15.0000	−0.709476
$448$	7.00000	0.330719
$449$	−5.00000	−0.235965	−0.117982	−	0.993016i	$-0.537643\pi$
$449$	−5.00000	−0.235965	−0.117982	+	0.993016i	$0.537643\pi$
$450$	2.00000	0.0942809
$451$	0	0
$452$	−3.00000	−0.141108
$453$	10.0000	0.469841
$454$	16.0000	0.750917
$455$	5.00000	0.234404
$456$	−24.0000	−1.12390
$457$	−22.0000	−1.02912	−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000	−1.02912	−0.514558	+	0.857455i	$0.672044\pi$
$458$	1.00000	0.0467269
$459$	0	0
$460$	−6.00000	−0.279751
$461$	9.00000	0.419172	0.209586	−	0.977790i	$-0.432788\pi$
$461$	9.00000	0.419172	0.209586	+	0.977790i	$0.432788\pi$
$462$	0	0
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	0	0
$465$	0	0
$466$	−12.0000	−0.555889
$467$	−21.0000	−0.971764	−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000	−0.971764	−0.485882	+	0.874024i	$0.661502\pi$
$468$	10.0000	0.462250
$469$	−6.00000	−0.277054
$470$	10.0000	0.461266
$471$	−11.0000	−0.506853
$472$	9.00000	0.414259
$473$	0	0
$474$	−3.00000	−0.137795
$475$	−8.00000	−0.367065
$476$	0	0
$477$	4.00000	0.183147
$478$	−1.00000	−0.0457389
$479$	−21.0000	−0.959514	−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000	−0.959514	−0.479757	+	0.877401i	$0.659275\pi$
$480$	−5.00000	−0.228218
$481$	10.0000	0.455961
$482$	−7.00000	−0.318841
$483$	6.00000	0.273009
$484$	11.0000	0.500000
$485$	−8.00000	−0.363261
$486$	−16.0000	−0.725775
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	15.0000	0.679018
$489$	−12.0000	−0.542659
$490$	−1.00000	−0.0451754
$491$	42.0000	1.89543	0.947717	−	0.319113i	$-0.103385\pi$
$491$	42.0000	1.89543	0.947717	+	0.319113i	$0.103385\pi$
$492$	8.00000	0.360668
$493$	0	0
$494$	40.0000	1.79969
$495$	0	0
$496$	0	0
$497$	−6.00000	−0.269137
$498$	−7.00000	−0.313678
$499$	23.0000	1.02962	0.514811	−	0.857304i	$-0.327862\pi$
$499$	23.0000	1.02962	0.514811	+	0.857304i	$0.327862\pi$
$500$	−1.00000	−0.0447214
$501$	20.0000	0.893534
$502$	−13.0000	−0.580218
$503$	−13.0000	−0.579641	−0.289821	−	0.957081i	$-0.593596\pi$
$503$	−13.0000	−0.579641	−0.289821	+	0.957081i	$0.593596\pi$
$504$	−6.00000	−0.267261
$505$	−10.0000	−0.444994
$506$	0	0
$507$	12.0000	0.532939
$508$	−4.00000	−0.177471
$509$	29.0000	1.28540	0.642701	−	0.766117i	$-0.277814\pi$
$509$	29.0000	1.28540	0.642701	+	0.766117i	$0.277814\pi$
$510$	0	0
$511$	−11.0000	−0.486611
$512$	11.0000	0.486136
$513$	40.0000	1.76604
$514$	−3.00000	−0.132324
$515$	3.00000	0.132196
$516$	8.00000	0.352180
$517$	0	0
$518$	−2.00000	−0.0878750
$519$	0	0
$520$	15.0000	0.657794
$521$	30.0000	1.31432	0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000	1.31432	0.657162	+	0.753749i	$0.271757\pi$
$522$	0	0
$523$	−6.00000	−0.262362	−0.131181	−	0.991358i	$-0.541877\pi$
$523$	−6.00000	−0.262362	−0.131181	+	0.991358i	$0.541877\pi$
$524$	12.0000	0.524222
$525$	1.00000	0.0436436
$526$	−28.0000	−1.22086
$527$	0	0
$528$	0	0
$529$	13.0000	0.565217
$530$	2.00000	0.0868744
$531$	−6.00000	−0.260378
$532$	8.00000	0.346844
$533$	−40.0000	−1.73259
$534$	−10.0000	−0.432742
$535$	−8.00000	−0.345870
$536$	−18.0000	−0.777482
$537$	5.00000	0.215766
$538$	4.00000	0.172452
$539$	0	0
$540$	5.00000	0.215166
$541$	−13.0000	−0.558914	−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000	−0.558914	−0.279457	+	0.960158i	$0.590154\pi$
$542$	20.0000	0.859074
$543$	9.00000	0.386227
$544$	0	0
$545$	2.00000	0.0856706
$546$	−5.00000	−0.213980
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	6.00000	0.256307
$549$	−10.0000	−0.426790
$550$	0	0
$551$	0	0
$552$	18.0000	0.766131
$553$	3.00000	0.127573
$554$	10.0000	0.424859
$555$	2.00000	0.0848953
$556$	−19.0000	−0.805779
$557$	24.0000	1.01691	0.508456	−	0.861088i	$-0.330216\pi$
$557$	24.0000	1.01691	0.508456	+	0.861088i	$0.330216\pi$
$558$	0	0
$559$	−40.0000	−1.69182
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	20.0000	0.843649
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	10.0000	0.421076
$565$	3.00000	0.126211
$566$	22.0000	0.924729
$567$	1.00000	0.0419961
$568$	−18.0000	−0.755263
$569$	−27.0000	−1.13190	−0.565949	−	0.824440i	$-0.691490\pi$
$569$	−27.0000	−1.13190	−0.565949	+	0.824440i	$0.691490\pi$
$570$	8.00000	0.335083
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	0	0
$573$	−17.0000	−0.710185
$574$	8.00000	0.333914
$575$	6.00000	0.250217
$576$	−14.0000	−0.583333
$577$	−34.0000	−1.41544	−0.707719	−	0.706494i	$-0.750276\pi$
$577$	−34.0000	−1.41544	−0.707719	+	0.706494i	$0.750276\pi$
$578$	17.0000	0.707107
$579$	−22.0000	−0.914289
$580$	0	0
$581$	7.00000	0.290409
$582$	8.00000	0.331611
$583$	0	0
$584$	−33.0000	−1.36555
$585$	−10.0000	−0.413449
$586$	−2.00000	−0.0826192
$587$	−23.0000	−0.949312	−0.474656	−	0.880172i	$-0.657427\pi$
$587$	−23.0000	−0.949312	−0.474656	+	0.880172i	$0.657427\pi$
$588$	−1.00000	−0.0412393
$589$	0	0
$590$	−3.00000	−0.123508
$591$	−13.0000	−0.534749
$592$	−2.00000	−0.0821995
$593$	−10.0000	−0.410651	−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000	−0.410651	−0.205325	+	0.978694i	$0.565825\pi$
$594$	0	0
$595$	0	0
$596$	15.0000	0.614424
$597$	11.0000	0.450200
$598$	−30.0000	−1.22679
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	3.00000	0.122474
$601$	40.0000	1.63163	0.815817	−	0.578310i	$-0.196288\pi$
$601$	40.0000	1.63163	0.815817	+	0.578310i	$0.196288\pi$
$602$	8.00000	0.326056
$603$	12.0000	0.488678
$604$	−10.0000	−0.406894
$605$	−11.0000	−0.447214
$606$	10.0000	0.406222
$607$	−35.0000	−1.42061	−0.710303	−	0.703896i	$-0.751442\pi$
$607$	−35.0000	−1.42061	−0.710303	+	0.703896i	$0.751442\pi$
$608$	40.0000	1.62221
$609$	0	0
$610$	−5.00000	−0.202444
$611$	−50.0000	−2.02278
$612$	0	0
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	−19.0000	−0.766778
$615$	−8.00000	−0.322591
$616$	0	0
$617$	−34.0000	−1.36879	−0.684394	−	0.729112i	$-0.739933\pi$
$617$	−34.0000	−1.36879	−0.684394	+	0.729112i	$0.739933\pi$
$618$	−3.00000	−0.120678
$619$	6.00000	0.241160	0.120580	−	0.992704i	$-0.461525\pi$
$619$	6.00000	0.241160	0.120580	+	0.992704i	$0.461525\pi$
$620$	0	0
$621$	−30.0000	−1.20386
$622$	20.0000	0.801927
$623$	10.0000	0.400642
$624$	−5.00000	−0.200160
$625$	1.00000	0.0400000
$626$	23.0000	0.919265
$627$	0	0
$628$	11.0000	0.438948
$629$	0	0
$630$	2.00000	0.0796819
$631$	6.00000	0.238856	0.119428	−	0.992843i	$-0.461894\pi$
$631$	6.00000	0.238856	0.119428	+	0.992843i	$0.461894\pi$
$632$	9.00000	0.358001
$633$	17.0000	0.675689
$634$	2.00000	0.0794301
$635$	4.00000	0.158735
$636$	2.00000	0.0793052
$637$	5.00000	0.198107
$638$	0	0
$639$	12.0000	0.474713
$640$	3.00000	0.118585
$641$	−15.0000	−0.592464	−0.296232	−	0.955116i	$-0.595730\pi$
$641$	−15.0000	−0.592464	−0.296232	+	0.955116i	$0.595730\pi$
$642$	8.00000	0.315735
$643$	−45.0000	−1.77463	−0.887313	−	0.461167i	$-0.847431\pi$
$643$	−45.0000	−1.77463	−0.887313	+	0.461167i	$0.847431\pi$
$644$	−6.00000	−0.236433
$645$	−8.00000	−0.315000
$646$	0	0
$647$	−18.0000	−0.707653	−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000	−0.707653	−0.353827	+	0.935311i	$0.615120\pi$
$648$	3.00000	0.117851
$649$	0	0
$650$	−5.00000	−0.196116
$651$	0	0
$652$	12.0000	0.469956
$653$	−3.00000	−0.117399	−0.0586995	−	0.998276i	$-0.518695\pi$
$653$	−3.00000	−0.117399	−0.0586995	+	0.998276i	$0.518695\pi$
$654$	−2.00000	−0.0782062
$655$	−12.0000	−0.468879
$656$	8.00000	0.312348
$657$	22.0000	0.858302
$658$	10.0000	0.389841
$659$	15.0000	0.584317	0.292159	−	0.956370i	$-0.405627\pi$
$659$	15.0000	0.584317	0.292159	+	0.956370i	$0.405627\pi$
$660$	0	0
$661$	−25.0000	−0.972387	−0.486194	−	0.873851i	$-0.661615\pi$
$661$	−25.0000	−0.972387	−0.486194	+	0.873851i	$0.661615\pi$
$662$	5.00000	0.194331
$663$	0	0
$664$	21.0000	0.814958
$665$	−8.00000	−0.310227
$666$	4.00000	0.154997
$667$	0	0
$668$	−20.0000	−0.773823
$669$	4.00000	0.154649
$670$	6.00000	0.231800
$671$	0	0
$672$	−5.00000	−0.192879
$673$	−16.0000	−0.616755	−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000	−0.616755	−0.308377	+	0.951264i	$0.599786\pi$
$674$	−28.0000	−1.07852
$675$	−5.00000	−0.192450
$676$	−12.0000	−0.461538
$677$	−34.0000	−1.30673	−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000	−1.30673	−0.653363	+	0.757045i	$0.726642\pi$
$678$	−3.00000	−0.115214
$679$	−8.00000	−0.307012
$680$	0	0
$681$	−16.0000	−0.613121
$682$	0	0
$683$	−12.0000	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	−16.0000	−0.611775
$685$	−6.00000	−0.229248
$686$	−1.00000	−0.0381802
$687$	−1.00000	−0.0381524
$688$	8.00000	0.304997
$689$	−10.0000	−0.380970
$690$	−6.00000	−0.228416
$691$	−14.0000	−0.532585	−0.266293	−	0.963892i	$-0.585799\pi$
$691$	−14.0000	−0.532585	−0.266293	+	0.963892i	$0.585799\pi$
$692$	0	0
$693$	0	0
$694$	−31.0000	−1.17674
$695$	19.0000	0.720711
$696$	0	0
$697$	0	0
$698$	18.0000	0.681310
$699$	12.0000	0.453882
$700$	−1.00000	−0.0377964
$701$	−27.0000	−1.01978	−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000	−1.01978	−0.509888	+	0.860241i	$0.670313\pi$
$702$	25.0000	0.943564
$703$	−16.0000	−0.603451
$704$	0	0
$705$	−10.0000	−0.376622
$706$	19.0000	0.715074
$707$	−10.0000	−0.376089
$708$	−3.00000	−0.112747
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	6.00000	0.225176
$711$	−6.00000	−0.225018
$712$	30.0000	1.12430
$713$	0	0
$714$	0	0
$715$	0	0
$716$	−5.00000	−0.186859
$717$	1.00000	0.0373457
$718$	34.0000	1.26887
$719$	24.0000	0.895049	0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000	0.895049	0.447524	+	0.894272i	$0.352306\pi$
$720$	2.00000	0.0745356
$721$	3.00000	0.111726
$722$	−45.0000	−1.67473
$723$	7.00000	0.260333
$724$	−9.00000	−0.334482
$725$	0	0
$726$	11.0000	0.408248
$727$	52.0000	1.92857	0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000	1.92857	0.964287	+	0.264861i	$0.0853260\pi$
$728$	15.0000	0.555937
$729$	13.0000	0.481481
$730$	11.0000	0.407128
$731$	0	0
$732$	−5.00000	−0.184805
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	−12.0000	−0.442928
$735$	1.00000	0.0368856
$736$	−30.0000	−1.10581
$737$	0	0
$738$	−16.0000	−0.588968
$739$	45.0000	1.65535	0.827676	−	0.561206i	$-0.189663\pi$
$739$	45.0000	1.65535	0.827676	+	0.561206i	$0.189663\pi$
$740$	−2.00000	−0.0735215
$741$	−40.0000	−1.46944
$742$	2.00000	0.0734223
$743$	−9.00000	−0.330178	−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000	−0.330178	−0.165089	+	0.986279i	$0.552791\pi$
$744$	0	0
$745$	−15.0000	−0.549557
$746$	−14.0000	−0.512576
$747$	−14.0000	−0.512233
$748$	0	0
$749$	−8.00000	−0.292314
$750$	−1.00000	−0.0365148
$751$	46.0000	1.67856	0.839282	−	0.543696i	$-0.182976\pi$
$751$	46.0000	1.67856	0.839282	+	0.543696i	$0.182976\pi$
$752$	10.0000	0.364662
$753$	13.0000	0.473746
$754$	0	0
$755$	10.0000	0.363937
$756$	5.00000	0.181848
$757$	−48.0000	−1.74459	−0.872295	−	0.488980i	$-0.837369\pi$
$757$	−48.0000	−1.74459	−0.872295	+	0.488980i	$0.837369\pi$
$758$	4.00000	0.145287
$759$	0	0
$760$	−24.0000	−0.870572
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	−4.00000	−0.144905
$763$	2.00000	0.0724049
$764$	17.0000	0.615038
$765$	0	0
$766$	−21.0000	−0.758761
$767$	15.0000	0.541619
$768$	−17.0000	−0.613435
$769$	19.0000	0.685158	0.342579	−	0.939489i	$-0.388700\pi$
$769$	19.0000	0.685158	0.342579	+	0.939489i	$0.388700\pi$
$770$	0	0
$771$	3.00000	0.108042
$772$	22.0000	0.791797
$773$	15.0000	0.539513	0.269756	−	0.962929i	$-0.413057\pi$
$773$	15.0000	0.539513	0.269756	+	0.962929i	$0.413057\pi$
$774$	−16.0000	−0.575108
$775$	0	0
$776$	−24.0000	−0.861550
$777$	2.00000	0.0717496
$778$	8.00000	0.286814
$779$	64.0000	2.29304
$780$	−5.00000	−0.179029
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−1.00000	−0.0357143
$785$	−11.0000	−0.392607
$786$	12.0000	0.428026
$787$	−1.00000	−0.0356462	−0.0178231	−	0.999841i	$-0.505674\pi$
$787$	−1.00000	−0.0356462	−0.0178231	+	0.999841i	$0.505674\pi$
$788$	13.0000	0.463106
$789$	28.0000	0.996826
$790$	−3.00000	−0.106735
$791$	3.00000	0.106668
$792$	0	0
$793$	25.0000	0.887776
$794$	20.0000	0.709773
$795$	−2.00000	−0.0709327
$796$	−11.0000	−0.389885
$797$	39.0000	1.38145	0.690725	−	0.723117i	$-0.257291\pi$
$797$	39.0000	1.38145	0.690725	+	0.723117i	$0.257291\pi$
$798$	8.00000	0.283197
$799$	0	0
$800$	−5.00000	−0.176777
$801$	−20.0000	−0.706665
$802$	−5.00000	−0.176556
$803$	0	0
$804$	6.00000	0.211604
$805$	6.00000	0.211472
$806$	0	0
$807$	−4.00000	−0.140807
$808$	−30.0000	−1.05540
$809$	8.00000	0.281265	0.140633	−	0.990062i	$-0.455086\pi$
$809$	8.00000	0.281265	0.140633	+	0.990062i	$0.455086\pi$
$810$	−1.00000	−0.0351364
$811$	25.0000	0.877869	0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000	0.877869	0.438934	+	0.898519i	$0.355356\pi$
$812$	0	0
$813$	−20.0000	−0.701431
$814$	0	0
$815$	−12.0000	−0.420342
$816$	0	0
$817$	64.0000	2.23908
$818$	26.0000	0.909069
$819$	−10.0000	−0.349428
$820$	8.00000	0.279372
$821$	3.00000	0.104701	0.0523504	−	0.998629i	$-0.483329\pi$
$821$	3.00000	0.104701	0.0523504	+	0.998629i	$0.483329\pi$
$822$	6.00000	0.209274
$823$	−44.0000	−1.53374	−0.766872	−	0.641800i	$-0.778188\pi$
$823$	−44.0000	−1.53374	−0.766872	+	0.641800i	$0.778188\pi$
$824$	9.00000	0.313530
$825$	0	0
$826$	−3.00000	−0.104383
$827$	16.0000	0.556375	0.278187	−	0.960527i	$-0.410266\pi$
$827$	16.0000	0.556375	0.278187	+	0.960527i	$0.410266\pi$
$828$	12.0000	0.417029
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	−7.00000	−0.242974
$831$	−10.0000	−0.346896
$832$	35.0000	1.21341
$833$	0	0
$834$	−19.0000	−0.657916
$835$	20.0000	0.692129
$836$	0	0
$837$	0	0
$838$	21.0000	0.725433
$839$	−5.00000	−0.172619	−0.0863096	−	0.996268i	$-0.527507\pi$
$839$	−5.00000	−0.172619	−0.0863096	+	0.996268i	$0.527507\pi$
$840$	3.00000	0.103510
$841$	−29.0000	−1.00000
$842$	17.0000	0.585859
$843$	−20.0000	−0.688837
$844$	−17.0000	−0.585164
$845$	12.0000	0.412813
$846$	−20.0000	−0.687614
$847$	−11.0000	−0.377964
$848$	2.00000	0.0686803
$849$	−22.0000	−0.755038
$850$	0	0
$851$	12.0000	0.411355
$852$	6.00000	0.205557
$853$	−35.0000	−1.19838	−0.599189	−	0.800608i	$-0.704510\pi$
$853$	−35.0000	−1.19838	−0.599189	+	0.800608i	$0.704510\pi$
$854$	−5.00000	−0.171096
$855$	16.0000	0.547188
$856$	−24.0000	−0.820303
$857$	3.00000	0.102478	0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000	0.102478	0.0512390	+	0.998686i	$0.483683\pi$
$858$	0	0
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	8.00000	0.272798
$861$	−8.00000	−0.272639
$862$	−10.0000	−0.340601
$863$	9.00000	0.306364	0.153182	−	0.988198i	$-0.451048\pi$
$863$	9.00000	0.306364	0.153182	+	0.988198i	$0.451048\pi$
$864$	25.0000	0.850517
$865$	0	0
$866$	−38.0000	−1.29129
$867$	−17.0000	−0.577350
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−30.0000	−1.01651
$872$	6.00000	0.203186
$873$	16.0000	0.541518
$874$	48.0000	1.62362
$875$	1.00000	0.0338062
$876$	11.0000	0.371656
$877$	35.0000	1.18187	0.590933	−	0.806721i	$-0.298760\pi$
$877$	35.0000	1.18187	0.590933	+	0.806721i	$0.298760\pi$
$878$	6.00000	0.202490
$879$	2.00000	0.0674583
$880$	0	0
$881$	40.0000	1.34763	0.673817	−	0.738898i	$-0.264654\pi$
$881$	40.0000	1.34763	0.673817	+	0.738898i	$0.264654\pi$
$882$	2.00000	0.0673435
$883$	51.0000	1.71629	0.858143	−	0.513410i	$-0.171618\pi$
$883$	51.0000	1.71629	0.858143	+	0.513410i	$0.171618\pi$
$884$	0	0
$885$	3.00000	0.100844
$886$	28.0000	0.940678
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	6.00000	0.201347
$889$	4.00000	0.134156
$890$	−10.0000	−0.335201
$891$	0	0
$892$	−4.00000	−0.133930
$893$	80.0000	2.67710
$894$	15.0000	0.501675
$895$	5.00000	0.167132
$896$	3.00000	0.100223
$897$	30.0000	1.00167
$898$	5.00000	0.166852
$899$	0	0
$900$	2.00000	0.0666667
$901$	0	0
$902$	0	0
$903$	−8.00000	−0.266223
$904$	9.00000	0.299336
$905$	9.00000	0.299170
$906$	−10.0000	−0.332228
$907$	3.00000	0.0996134	0.0498067	−	0.998759i	$-0.484139\pi$
$907$	3.00000	0.0996134	0.0498067	+	0.998759i	$0.484139\pi$
$908$	16.0000	0.530979
$909$	20.0000	0.663358
$910$	−5.00000	−0.165748
$911$	−56.0000	−1.85536	−0.927681	−	0.373373i	$-0.878201\pi$
$911$	−56.0000	−1.85536	−0.927681	+	0.373373i	$0.878201\pi$
$912$	8.00000	0.264906
$913$	0	0
$914$	22.0000	0.727695
$915$	5.00000	0.165295
$916$	1.00000	0.0330409
$917$	−12.0000	−0.396275
$918$	0	0
$919$	22.0000	0.725713	0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000	0.725713	0.362857	+	0.931845i	$0.381802\pi$
$920$	18.0000	0.593442
$921$	19.0000	0.626071
$922$	−9.00000	−0.296399
$923$	−30.0000	−0.987462
$924$	0	0
$925$	2.00000	0.0657596
$926$	−4.00000	−0.131448
$927$	−6.00000	−0.197066
$928$	0	0
$929$	−36.0000	−1.18112	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000	−1.18112	−0.590561	+	0.806993i	$0.701093\pi$
$930$	0	0
$931$	−8.00000	−0.262189
$932$	−12.0000	−0.393073
$933$	−20.0000	−0.654771
$934$	21.0000	0.687141
$935$	0	0
$936$	−30.0000	−0.980581
$937$	−42.0000	−1.37208	−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000	−1.37208	−0.686040	+	0.727564i	$0.740653\pi$
$938$	6.00000	0.195907
$939$	−23.0000	−0.750577
$940$	10.0000	0.326164
$941$	5.00000	0.162995	0.0814977	−	0.996674i	$-0.474030\pi$
$941$	5.00000	0.162995	0.0814977	+	0.996674i	$0.474030\pi$
$942$	11.0000	0.358399
$943$	−48.0000	−1.56310
$944$	−3.00000	−0.0976417
$945$	−5.00000	−0.162650
$946$	0	0
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	−3.00000	−0.0974355
$949$	−55.0000	−1.78538
$950$	8.00000	0.259554
$951$	−2.00000	−0.0648544
$952$	0	0
$953$	−46.0000	−1.49009	−0.745043	−	0.667016i	$-0.767571\pi$
$953$	−46.0000	−1.49009	−0.745043	+	0.667016i	$0.767571\pi$
$954$	−4.00000	−0.129505
$955$	−17.0000	−0.550107
$956$	−1.00000	−0.0323423
$957$	0	0
$958$	21.0000	0.678479
$959$	−6.00000	−0.193750
$960$	7.00000	0.225924
$961$	−31.0000	−1.00000
$962$	−10.0000	−0.322413
$963$	16.0000	0.515593
$964$	−7.00000	−0.225455
$965$	−22.0000	−0.708205
$966$	−6.00000	−0.193047
$967$	−32.0000	−1.02905	−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000	−1.02905	−0.514525	+	0.857475i	$0.672032\pi$
$968$	−33.0000	−1.06066
$969$	0	0
$970$	8.00000	0.256865
$971$	−42.0000	−1.34784	−0.673922	−	0.738802i	$-0.735392\pi$
$971$	−42.0000	−1.34784	−0.673922	+	0.738802i	$0.735392\pi$
$972$	−16.0000	−0.513200
$973$	19.0000	0.609112
$974$	32.0000	1.02535
$975$	5.00000	0.160128
$976$	−5.00000	−0.160046
$977$	38.0000	1.21573	0.607864	−	0.794041i	$-0.292027\pi$
$977$	38.0000	1.21573	0.607864	+	0.794041i	$0.292027\pi$
$978$	12.0000	0.383718
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−4.00000	−0.127710
$982$	−42.0000	−1.34027
$983$	42.0000	1.33959	0.669796	−	0.742545i	$-0.266382\pi$
$983$	42.0000	1.33959	0.669796	+	0.742545i	$0.266382\pi$
$984$	−24.0000	−0.765092
$985$	−13.0000	−0.414214
$986$	0	0
$987$	−10.0000	−0.318304
$988$	40.0000	1.27257
$989$	−48.0000	−1.52631
$990$	0	0
$991$	2.00000	0.0635321	0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000	0.0635321	0.0317660	+	0.999495i	$0.489887\pi$
$992$	0	0
$993$	−5.00000	−0.158670
$994$	6.00000	0.190308
$995$	11.0000	0.348723
$996$	−7.00000	−0.221803
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	−23.0000	−0.728052
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.c.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.c.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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