LMFDB - Embedded newform 8015.2.a.b.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)

$f(q)$

$=$

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

\(q-1.00000 q^{2} -2.00000 q^{3} -1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{6} +1.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +3.00000 q^{11} +2.00000 q^{12} -7.00000 q^{13} -1.00000 q^{14} -2.00000 q^{15} -1.00000 q^{16} +6.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -1.00000 q^{20} -2.00000 q^{21} -3.00000 q^{22} -6.00000 q^{24} +1.00000 q^{25} +7.00000 q^{26} +4.00000 q^{27} -1.00000 q^{28} +2.00000 q^{30} -9.00000 q^{31} -5.00000 q^{32} -6.00000 q^{33} -6.00000 q^{34} +1.00000 q^{35} -1.00000 q^{36} -1.00000 q^{37} -4.00000 q^{38} +14.0000 q^{39} +3.00000 q^{40} -5.00000 q^{41} +2.00000 q^{42} +1.00000 q^{43} -3.00000 q^{44} +1.00000 q^{45} +5.00000 q^{47} +2.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -12.0000 q^{51} +7.00000 q^{52} -5.00000 q^{53} -4.00000 q^{54} +3.00000 q^{55} +3.00000 q^{56} -8.00000 q^{57} -12.0000 q^{59} +2.00000 q^{60} +14.0000 q^{61} +9.00000 q^{62} +1.00000 q^{63} +7.00000 q^{64} -7.00000 q^{65} +6.00000 q^{66} -6.00000 q^{68} -1.00000 q^{70} -3.00000 q^{71} +3.00000 q^{72} -2.00000 q^{73} +1.00000 q^{74} -2.00000 q^{75} -4.00000 q^{76} +3.00000 q^{77} -14.0000 q^{78} -12.0000 q^{79} -1.00000 q^{80} -11.0000 q^{81} +5.00000 q^{82} -2.00000 q^{83} +2.00000 q^{84} +6.00000 q^{85} -1.00000 q^{86} +9.00000 q^{88} -5.00000 q^{89} -1.00000 q^{90} -7.00000 q^{91} +18.0000 q^{93} -5.00000 q^{94} +4.00000 q^{95} +10.0000 q^{96} -2.00000 q^{97} -1.00000 q^{98} +3.00000 q^{99} +O(q^{100})\)

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	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.00000	0.816497
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.00000	1.06066
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	2.00000	0.577350
$13$	−7.00000	−1.94145	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−7.00000	−1.94145	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−1.00000	−0.267261
$15$	−2.00000	−0.516398
$16$	−1.00000	−0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−1.00000	−0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−1.00000	−0.223607
$21$	−2.00000	−0.436436
$22$	−3.00000	−0.639602
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−6.00000	−1.22474
$25$	1.00000	0.200000
$26$	7.00000	1.37281
$27$	4.00000	0.769800
$28$	−1.00000	−0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	2.00000	0.365148
$31$	−9.00000	−1.61645	−0.808224	−	0.588875i	$-0.799571\pi$
$31$	−9.00000	−1.61645	−0.808224	+	0.588875i	$0.799571\pi$
$32$	−5.00000	−0.883883
$33$	−6.00000	−1.04447
$34$	−6.00000	−1.02899
$35$	1.00000	0.169031
$36$	−1.00000	−0.166667
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−4.00000	−0.648886
$39$	14.0000	2.24179
$40$	3.00000	0.474342
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	2.00000	0.308607
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	−3.00000	−0.452267
$45$	1.00000	0.149071
$46$	0	0
$47$	5.00000	0.729325	0.364662	−	0.931140i	$-0.381184\pi$
$47$	5.00000	0.729325	0.364662	+	0.931140i	$0.381184\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−12.0000	−1.68034
$52$	7.00000	0.970725
$53$	−5.00000	−0.686803	−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000	−0.686803	−0.343401	+	0.939189i	$0.611579\pi$
$54$	−4.00000	−0.544331
$55$	3.00000	0.404520
$56$	3.00000	0.400892
$57$	−8.00000	−1.05963
$58$	0	0
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	2.00000	0.258199
$61$	14.0000	1.79252	0.896258	−	0.443533i	$-0.146275\pi$
$61$	14.0000	1.79252	0.896258	+	0.443533i	$0.146275\pi$
$62$	9.00000	1.14300
$63$	1.00000	0.125988
$64$	7.00000	0.875000
$65$	−7.00000	−0.868243
$66$	6.00000	0.738549
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−6.00000	−0.727607
$69$	0	0
$70$	−1.00000	−0.119523
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	3.00000	0.353553
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	1.00000	0.116248
$75$	−2.00000	−0.230940
$76$	−4.00000	−0.458831
$77$	3.00000	0.341882
$78$	−14.0000	−1.58519
$79$	−12.0000	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$80$	−1.00000	−0.111803
$81$	−11.0000	−1.22222
$82$	5.00000	0.552158
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	2.00000	0.218218
$85$	6.00000	0.650791
$86$	−1.00000	−0.107833
$87$	0	0
$88$	9.00000	0.959403
$89$	−5.00000	−0.529999	−0.264999	−	0.964249i	$-0.585372\pi$
$89$	−5.00000	−0.529999	−0.264999	+	0.964249i	$0.585372\pi$
$90$	−1.00000	−0.105409
$91$	−7.00000	−0.733799
$92$	0	0
$93$	18.0000	1.86651
$94$	−5.00000	−0.515711
$95$	4.00000	0.410391
$96$	10.0000	1.02062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.00000	−0.101015
$99$	3.00000	0.301511
$100$	−1.00000	−0.100000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	12.0000	1.18818
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	−21.0000	−2.05922
$105$	−2.00000	−0.195180
$106$	5.00000	0.485643
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−4.00000	−0.384900
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−3.00000	−0.286039
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	8.00000	0.749269
$115$	0	0
$116$	0	0
$117$	−7.00000	−0.647150
$118$	12.0000	1.10469
$119$	6.00000	0.550019
$120$	−6.00000	−0.547723
$121$	−2.00000	−0.181818
$122$	−14.0000	−1.26750
$123$	10.0000	0.901670
$124$	9.00000	0.808224
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	−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
$129$	−2.00000	−0.176090
$130$	7.00000	0.613941
$131$	−15.0000	−1.31056	−0.655278	−	0.755388i	$-0.727449\pi$
$131$	−15.0000	−1.31056	−0.655278	+	0.755388i	$0.727449\pi$
$132$	6.00000	0.522233
$133$	4.00000	0.346844
$134$	0	0
$135$	4.00000	0.344265
$136$	18.0000	1.54349
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	−11.0000	−0.933008	−0.466504	−	0.884519i	$-0.654487\pi$
$139$	−11.0000	−0.933008	−0.466504	+	0.884519i	$0.654487\pi$
$140$	−1.00000	−0.0845154
$141$	−10.0000	−0.842152
$142$	3.00000	0.251754
$143$	−21.0000	−1.75611
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	2.00000	0.165521
$147$	−2.00000	−0.164957
$148$	1.00000	0.0821995
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	2.00000	0.163299
$151$	19.0000	1.54620	0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000	1.54620	0.773099	+	0.634285i	$0.218706\pi$
$152$	12.0000	0.973329
$153$	6.00000	0.485071
$154$	−3.00000	−0.241747
$155$	−9.00000	−0.722897
$156$	−14.0000	−1.12090
$157$	13.0000	1.03751	0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000	1.03751	0.518756	+	0.854922i	$0.326395\pi$
$158$	12.0000	0.954669
$159$	10.0000	0.793052
$160$	−5.00000	−0.395285
$161$	0	0
$162$	11.0000	0.864242
$163$	0	0		−	1.00000i	$-0.5\pi$
$163$	0	0			1.00000i	$0.5\pi$
$164$	5.00000	0.390434
$165$	−6.00000	−0.467099
$166$	2.00000	0.155230
$167$	20.0000	1.54765	0.773823	−	0.633402i	$-0.218342\pi$
$167$	20.0000	1.54765	0.773823	+	0.633402i	$0.218342\pi$
$168$	−6.00000	−0.462910
$169$	36.0000	2.76923
$170$	−6.00000	−0.460179
$171$	4.00000	0.305888
$172$	−1.00000	−0.0762493
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	−3.00000	−0.226134
$177$	24.0000	1.80395
$178$	5.00000	0.374766
$179$	2.00000	0.149487	0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000	0.149487	0.0747435	+	0.997203i	$0.476186\pi$
$180$	−1.00000	−0.0745356
$181$	−12.0000	−0.891953	−0.445976	−	0.895045i	$-0.647144\pi$
$181$	−12.0000	−0.891953	−0.445976	+	0.895045i	$0.647144\pi$
$182$	7.00000	0.518875
$183$	−28.0000	−2.06982
$184$	0	0
$185$	−1.00000	−0.0735215
$186$	−18.0000	−1.31982
$187$	18.0000	1.31629
$188$	−5.00000	−0.364662
$189$	4.00000	0.290957
$190$	−4.00000	−0.290191
$191$	−26.0000	−1.88129	−0.940647	−	0.339387i	$-0.889781\pi$
$191$	−26.0000	−1.88129	−0.940647	+	0.339387i	$0.889781\pi$
$192$	−14.0000	−1.01036
$193$	5.00000	0.359908	0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000	0.359908	0.179954	+	0.983675i	$0.442405\pi$
$194$	2.00000	0.143592
$195$	14.0000	1.00256
$196$	−1.00000	−0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	−3.00000	−0.213201
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	3.00000	0.212132
$201$	0	0
$202$	−14.0000	−0.985037
$203$	0	0
$204$	12.0000	0.840168
$205$	−5.00000	−0.349215
$206$	0	0
$207$	0	0
$208$	7.00000	0.485363
$209$	12.0000	0.830057
$210$	2.00000	0.138013
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	5.00000	0.343401
$213$	6.00000	0.411113
$214$	−4.00000	−0.273434
$215$	1.00000	0.0681994
$216$	12.0000	0.816497
$217$	−9.00000	−0.610960
$218$	−2.00000	−0.135457
$219$	4.00000	0.270295
$220$	−3.00000	−0.202260
$221$	−42.0000	−2.82523
$222$	−2.00000	−0.134231
$223$	13.0000	0.870544	0.435272	−	0.900299i	$-0.356652\pi$
$223$	13.0000	0.870544	0.435272	+	0.900299i	$0.356652\pi$
$224$	−5.00000	−0.334077
$225$	1.00000	0.0666667
$226$	6.00000	0.399114
$227$	−7.00000	−0.464606	−0.232303	−	0.972643i	$-0.574626\pi$
$227$	−7.00000	−0.464606	−0.232303	+	0.972643i	$0.574626\pi$
$228$	8.00000	0.529813
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	0	0
$231$	−6.00000	−0.394771
$232$	0	0
$233$	15.0000	0.982683	0.491341	−	0.870967i	$-0.336507\pi$
$233$	15.0000	0.982683	0.491341	+	0.870967i	$0.336507\pi$
$234$	7.00000	0.457604
$235$	5.00000	0.326164
$236$	12.0000	0.781133
$237$	24.0000	1.55897
$238$	−6.00000	−0.388922
$239$	−2.00000	−0.129369	−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000	−0.129369	−0.0646846	+	0.997906i	$0.520604\pi$
$240$	2.00000	0.129099
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	2.00000	0.128565
$243$	10.0000	0.641500
$244$	−14.0000	−0.896258
$245$	1.00000	0.0638877
$246$	−10.0000	−0.637577
$247$	−28.0000	−1.78160
$248$	−27.0000	−1.71450
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	−5.00000	−0.315597	−0.157799	−	0.987471i	$-0.550440\pi$
$251$	−5.00000	−0.315597	−0.157799	+	0.987471i	$0.550440\pi$
$252$	−1.00000	−0.0629941
$253$	0	0
$254$	8.00000	0.501965
$255$	−12.0000	−0.751469
$256$	−17.0000	−1.06250
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	2.00000	0.124515
$259$	−1.00000	−0.0621370
$260$	7.00000	0.434122
$261$	0	0
$262$	15.0000	0.926703
$263$	−14.0000	−0.863277	−0.431638	−	0.902047i	$-0.642064\pi$
$263$	−14.0000	−0.863277	−0.431638	+	0.902047i	$0.642064\pi$
$264$	−18.0000	−1.10782
$265$	−5.00000	−0.307148
$266$	−4.00000	−0.245256
$267$	10.0000	0.611990
$268$	0	0
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	−4.00000	−0.243432
$271$	28.0000	1.70088	0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000	1.70088	0.850439	+	0.526073i	$0.176336\pi$
$272$	−6.00000	−0.363803
$273$	14.0000	0.847319
$274$	−12.0000	−0.724947
$275$	3.00000	0.180907
$276$	0	0
$277$	11.0000	0.660926	0.330463	−	0.943819i	$-0.392795\pi$
$277$	11.0000	0.660926	0.330463	+	0.943819i	$0.392795\pi$
$278$	11.0000	0.659736
$279$	−9.00000	−0.538816
$280$	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
$283$	5.00000	0.297219	0.148610	−	0.988896i	$-0.452520\pi$
$283$	5.00000	0.297219	0.148610	+	0.988896i	$0.452520\pi$
$284$	3.00000	0.178017
$285$	−8.00000	−0.473879
$286$	21.0000	1.24176
$287$	−5.00000	−0.295141
$288$	−5.00000	−0.294628
$289$	19.0000	1.11765
$290$	0	0
$291$	4.00000	0.234484
$292$	2.00000	0.117041
$293$	2.00000	0.116841	0.0584206	−	0.998292i	$-0.481394\pi$
$293$	2.00000	0.116841	0.0584206	+	0.998292i	$0.481394\pi$
$294$	2.00000	0.116642
$295$	−12.0000	−0.698667
$296$	−3.00000	−0.174371
$297$	12.0000	0.696311
$298$	9.00000	0.521356
$299$	0	0
$300$	2.00000	0.115470
$301$	1.00000	0.0576390
$302$	−19.0000	−1.09333
$303$	−28.0000	−1.60856
$304$	−4.00000	−0.229416
$305$	14.0000	0.801638
$306$	−6.00000	−0.342997
$307$	22.0000	1.25561	0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000	1.25561	0.627803	+	0.778372i	$0.283954\pi$
$308$	−3.00000	−0.170941
$309$	0	0
$310$	9.00000	0.511166
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	42.0000	2.37778
$313$	19.0000	1.07394	0.536972	−	0.843600i	$-0.319568\pi$
$313$	19.0000	1.07394	0.536972	+	0.843600i	$0.319568\pi$
$314$	−13.0000	−0.733632
$315$	1.00000	0.0563436
$316$	12.0000	0.675053
$317$	16.0000	0.898650	0.449325	−	0.893368i	$-0.351665\pi$
$317$	16.0000	0.898650	0.449325	+	0.893368i	$0.351665\pi$
$318$	−10.0000	−0.560772
$319$	0	0
$320$	7.00000	0.391312
$321$	−8.00000	−0.446516
$322$	0	0
$323$	24.0000	1.33540
$324$	11.0000	0.611111
$325$	−7.00000	−0.388290
$326$	0	0
$327$	−4.00000	−0.221201
$328$	−15.0000	−0.828236
$329$	5.00000	0.275659
$330$	6.00000	0.330289
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	2.00000	0.109764
$333$	−1.00000	−0.0547997
$334$	−20.0000	−1.09435
$335$	0	0
$336$	2.00000	0.109109
$337$	25.0000	1.36184	0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000	1.36184	0.680918	+	0.732359i	$0.261581\pi$
$338$	−36.0000	−1.95814
$339$	12.0000	0.651751
$340$	−6.00000	−0.325396
$341$	−27.0000	−1.46213
$342$	−4.00000	−0.216295
$343$	1.00000	0.0539949
$344$	3.00000	0.161749
$345$	0	0
$346$	0	0
$347$	−11.0000	−0.590511	−0.295255	−	0.955418i	$-0.595405\pi$
$347$	−11.0000	−0.590511	−0.295255	+	0.955418i	$0.595405\pi$
$348$	0	0
$349$	21.0000	1.12410	0.562052	−	0.827102i	$-0.310012\pi$
$349$	21.0000	1.12410	0.562052	+	0.827102i	$0.310012\pi$
$350$	−1.00000	−0.0534522
$351$	−28.0000	−1.49453
$352$	−15.0000	−0.799503
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	−24.0000	−1.27559
$355$	−3.00000	−0.159223
$356$	5.00000	0.264999
$357$	−12.0000	−0.635107
$358$	−2.00000	−0.105703
$359$	17.0000	0.897226	0.448613	−	0.893726i	$-0.351918\pi$
$359$	17.0000	0.897226	0.448613	+	0.893726i	$0.351918\pi$
$360$	3.00000	0.158114
$361$	−3.00000	−0.157895
$362$	12.0000	0.630706
$363$	4.00000	0.209946
$364$	7.00000	0.366900
$365$	−2.00000	−0.104685
$366$	28.0000	1.46358
$367$	−6.00000	−0.313197	−0.156599	−	0.987662i	$-0.550053\pi$
$367$	−6.00000	−0.313197	−0.156599	+	0.987662i	$0.550053\pi$
$368$	0	0
$369$	−5.00000	−0.260290
$370$	1.00000	0.0519875
$371$	−5.00000	−0.259587
$372$	−18.0000	−0.933257
$373$	−37.0000	−1.91579	−0.957894	−	0.287123i	$-0.907301\pi$
$373$	−37.0000	−1.91579	−0.957894	+	0.287123i	$0.907301\pi$
$374$	−18.0000	−0.930758
$375$	−2.00000	−0.103280
$376$	15.0000	0.773566
$377$	0	0
$378$	−4.00000	−0.205738
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	−4.00000	−0.205196
$381$	16.0000	0.819705
$382$	26.0000	1.33028
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	−6.00000	−0.306186
$385$	3.00000	0.152894
$386$	−5.00000	−0.254493
$387$	1.00000	0.0508329
$388$	2.00000	0.101535
$389$	−20.0000	−1.01404	−0.507020	−	0.861934i	$-0.669253\pi$
$389$	−20.0000	−1.01404	−0.507020	+	0.861934i	$0.669253\pi$
$390$	−14.0000	−0.708918
$391$	0	0
$392$	3.00000	0.151523
$393$	30.0000	1.51330
$394$	10.0000	0.503793
$395$	−12.0000	−0.603786
$396$	−3.00000	−0.150756
$397$	−38.0000	−1.90717	−0.953583	−	0.301131i	$-0.902636\pi$
$397$	−38.0000	−1.90717	−0.953583	+	0.301131i	$0.902636\pi$
$398$	−20.0000	−1.00251
$399$	−8.00000	−0.400501
$400$	−1.00000	−0.0500000
$401$	−10.0000	−0.499376	−0.249688	−	0.968326i	$-0.580328\pi$
$401$	−10.0000	−0.499376	−0.249688	+	0.968326i	$0.580328\pi$
$402$	0	0
$403$	63.0000	3.13825
$404$	−14.0000	−0.696526
$405$	−11.0000	−0.546594
$406$	0	0
$407$	−3.00000	−0.148704
$408$	−36.0000	−1.78227
$409$	−32.0000	−1.58230	−0.791149	−	0.611623i	$-0.790517\pi$
$409$	−32.0000	−1.58230	−0.791149	+	0.611623i	$0.790517\pi$
$410$	5.00000	0.246932
$411$	−24.0000	−1.18383
$412$	0	0
$413$	−12.0000	−0.590481
$414$	0	0
$415$	−2.00000	−0.0981761
$416$	35.0000	1.71602
$417$	22.0000	1.07734
$418$	−12.0000	−0.586939
$419$	15.0000	0.732798	0.366399	−	0.930458i	$-0.380591\pi$
$419$	15.0000	0.732798	0.366399	+	0.930458i	$0.380591\pi$
$420$	2.00000	0.0975900
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	4.00000	0.194717
$423$	5.00000	0.243108
$424$	−15.0000	−0.728464
$425$	6.00000	0.291043
$426$	−6.00000	−0.290701
$427$	14.0000	0.677507
$428$	−4.00000	−0.193347
$429$	42.0000	2.02778
$430$	−1.00000	−0.0482243
$431$	4.00000	0.192673	0.0963366	−	0.995349i	$-0.469287\pi$
$431$	4.00000	0.192673	0.0963366	+	0.995349i	$0.469287\pi$
$432$	−4.00000	−0.192450
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	9.00000	0.432014
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	0	0
$438$	−4.00000	−0.191127
$439$	−6.00000	−0.286364	−0.143182	−	0.989696i	$-0.545733\pi$
$439$	−6.00000	−0.286364	−0.143182	+	0.989696i	$0.545733\pi$
$440$	9.00000	0.429058
$441$	1.00000	0.0476190
$442$	42.0000	1.99774
$443$	8.00000	0.380091	0.190046	−	0.981775i	$-0.439136\pi$
$443$	8.00000	0.380091	0.190046	+	0.981775i	$0.439136\pi$
$444$	−2.00000	−0.0949158
$445$	−5.00000	−0.237023
$446$	−13.0000	−0.615568
$447$	18.0000	0.851371
$448$	7.00000	0.330719
$449$	7.00000	0.330350	0.165175	−	0.986264i	$-0.447181\pi$
$449$	7.00000	0.330350	0.165175	+	0.986264i	$0.447181\pi$
$450$	−1.00000	−0.0471405
$451$	−15.0000	−0.706322
$452$	6.00000	0.282216
$453$	−38.0000	−1.78540
$454$	7.00000	0.328526
$455$	−7.00000	−0.328165
$456$	−24.0000	−1.12390
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	1.00000	0.0467269
$459$	24.0000	1.12022
$460$	0	0
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	6.00000	0.279145
$463$	13.0000	0.604161	0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000	0.604161	0.302081	+	0.953282i	$0.402319\pi$
$464$	0	0
$465$	18.0000	0.834730
$466$	−15.0000	−0.694862
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	7.00000	0.323575
$469$	0	0
$470$	−5.00000	−0.230633
$471$	−26.0000	−1.19802
$472$	−36.0000	−1.65703
$473$	3.00000	0.137940
$474$	−24.0000	−1.10236
$475$	4.00000	0.183533
$476$	−6.00000	−0.275010
$477$	−5.00000	−0.228934
$478$	2.00000	0.0914779
$479$	−33.0000	−1.50781	−0.753904	−	0.656984i	$-0.771832\pi$
$479$	−33.0000	−1.50781	−0.753904	+	0.656984i	$0.771832\pi$
$480$	10.0000	0.456435
$481$	7.00000	0.319173
$482$	−4.00000	−0.182195
$483$	0	0
$484$	2.00000	0.0909091
$485$	−2.00000	−0.0908153
$486$	−10.0000	−0.453609
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	42.0000	1.90125
$489$	0	0
$490$	−1.00000	−0.0451754
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	−10.0000	−0.450835
$493$	0	0
$494$	28.0000	1.25978
$495$	3.00000	0.134840
$496$	9.00000	0.404112
$497$	−3.00000	−0.134568
$498$	−4.00000	−0.179244
$499$	−10.0000	−0.447661	−0.223831	−	0.974628i	$-0.571856\pi$
$499$	−10.0000	−0.447661	−0.223831	+	0.974628i	$0.571856\pi$
$500$	−1.00000	−0.0447214
$501$	−40.0000	−1.78707
$502$	5.00000	0.223161
$503$	−40.0000	−1.78351	−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000	−1.78351	−0.891756	+	0.452517i	$0.850526\pi$
$504$	3.00000	0.133631
$505$	14.0000	0.622992
$506$	0	0
$507$	−72.0000	−3.19763
$508$	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	$0.485887\pi$
$510$	12.0000	0.531369
$511$	−2.00000	−0.0884748
$512$	11.0000	0.486136
$513$	16.0000	0.706417
$514$	18.0000	0.793946
$515$	0	0
$516$	2.00000	0.0880451
$517$	15.0000	0.659699
$518$	1.00000	0.0439375
$519$	0	0
$520$	−21.0000	−0.920911
$521$	−39.0000	−1.70862	−0.854311	−	0.519763i	$-0.826020\pi$
$521$	−39.0000	−1.70862	−0.854311	+	0.519763i	$0.826020\pi$
$522$	0	0
$523$	−21.0000	−0.918266	−0.459133	−	0.888368i	$-0.651840\pi$
$523$	−21.0000	−0.918266	−0.459133	+	0.888368i	$0.651840\pi$
$524$	15.0000	0.655278
$525$	−2.00000	−0.0872872
$526$	14.0000	0.610429
$527$	−54.0000	−2.35228
$528$	6.00000	0.261116
$529$	−23.0000	−1.00000
$530$	5.00000	0.217186
$531$	−12.0000	−0.520756
$532$	−4.00000	−0.173422
$533$	35.0000	1.51602
$534$	−10.0000	−0.432742
$535$	4.00000	0.172935
$536$	0	0
$537$	−4.00000	−0.172613
$538$	−14.0000	−0.603583
$539$	3.00000	0.129219
$540$	−4.00000	−0.172133
$541$	−43.0000	−1.84871	−0.924357	−	0.381528i	$-0.875398\pi$
$541$	−43.0000	−1.84871	−0.924357	+	0.381528i	$0.875398\pi$
$542$	−28.0000	−1.20270
$543$	24.0000	1.02994
$544$	−30.0000	−1.28624
$545$	2.00000	0.0856706
$546$	−14.0000	−0.599145
$547$	−2.00000	−0.0855138	−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000	−0.0855138	−0.0427569	+	0.999086i	$0.513614\pi$
$548$	−12.0000	−0.512615
$549$	14.0000	0.597505
$550$	−3.00000	−0.127920
$551$	0	0
$552$	0	0
$553$	−12.0000	−0.510292
$554$	−11.0000	−0.467345
$555$	2.00000	0.0848953
$556$	11.0000	0.466504
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	9.00000	0.381000
$559$	−7.00000	−0.296068
$560$	−1.00000	−0.0422577
$561$	−36.0000	−1.51992
$562$	20.0000	0.843649
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	10.0000	0.421076
$565$	−6.00000	−0.252422
$566$	−5.00000	−0.210166
$567$	−11.0000	−0.461957
$568$	−9.00000	−0.377632
$569$	−45.0000	−1.88650	−0.943249	−	0.332086i	$-0.892248\pi$
$569$	−45.0000	−1.88650	−0.943249	+	0.332086i	$0.892248\pi$
$570$	8.00000	0.335083
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	21.0000	0.878054
$573$	52.0000	2.17233
$574$	5.00000	0.208696
$575$	0	0
$576$	7.00000	0.291667
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	−19.0000	−0.790296
$579$	−10.0000	−0.415586
$580$	0	0
$581$	−2.00000	−0.0829740
$582$	−4.00000	−0.165805
$583$	−15.0000	−0.621237
$584$	−6.00000	−0.248282
$585$	−7.00000	−0.289414
$586$	−2.00000	−0.0826192
$587$	−8.00000	−0.330195	−0.165098	−	0.986277i	$-0.552794\pi$
$587$	−8.00000	−0.330195	−0.165098	+	0.986277i	$0.552794\pi$
$588$	2.00000	0.0824786
$589$	−36.0000	−1.48335
$590$	12.0000	0.494032
$591$	20.0000	0.822690
$592$	1.00000	0.0410997
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	−12.0000	−0.492366
$595$	6.00000	0.245976
$596$	9.00000	0.368654
$597$	−40.0000	−1.63709
$598$	0	0
$599$	30.0000	1.22577	0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000	1.22577	0.612883	+	0.790173i	$0.290010\pi$
$600$	−6.00000	−0.244949
$601$	−38.0000	−1.55005	−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000	−1.55005	−0.775026	+	0.631929i	$0.782263\pi$
$602$	−1.00000	−0.0407570
$603$	0	0
$604$	−19.0000	−0.773099
$605$	−2.00000	−0.0813116
$606$	28.0000	1.13742
$607$	−26.0000	−1.05531	−0.527654	−	0.849460i	$-0.676928\pi$
$607$	−26.0000	−1.05531	−0.527654	+	0.849460i	$0.676928\pi$
$608$	−20.0000	−0.811107
$609$	0	0
$610$	−14.0000	−0.566843
$611$	−35.0000	−1.41595
$612$	−6.00000	−0.242536
$613$	−30.0000	−1.21169	−0.605844	−	0.795583i	$-0.707165\pi$
$613$	−30.0000	−1.21169	−0.605844	+	0.795583i	$0.707165\pi$
$614$	−22.0000	−0.887848
$615$	10.0000	0.403239
$616$	9.00000	0.362620
$617$	17.0000	0.684394	0.342197	−	0.939628i	$-0.388829\pi$
$617$	17.0000	0.684394	0.342197	+	0.939628i	$0.388829\pi$
$618$	0	0
$619$	6.00000	0.241160	0.120580	−	0.992704i	$-0.461525\pi$
$619$	6.00000	0.241160	0.120580	+	0.992704i	$0.461525\pi$
$620$	9.00000	0.361449
$621$	0	0
$622$	−16.0000	−0.641542
$623$	−5.00000	−0.200321
$624$	−14.0000	−0.560449
$625$	1.00000	0.0400000
$626$	−19.0000	−0.759393
$627$	−24.0000	−0.958468
$628$	−13.0000	−0.518756
$629$	−6.00000	−0.239236
$630$	−1.00000	−0.0398410
$631$	27.0000	1.07485	0.537427	−	0.843311i	$-0.319397\pi$
$631$	27.0000	1.07485	0.537427	+	0.843311i	$0.319397\pi$
$632$	−36.0000	−1.43200
$633$	8.00000	0.317971
$634$	−16.0000	−0.635441
$635$	−8.00000	−0.317470
$636$	−10.0000	−0.396526
$637$	−7.00000	−0.277350
$638$	0	0
$639$	−3.00000	−0.118678
$640$	3.00000	0.118585
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	8.00000	0.315735
$643$	−18.0000	−0.709851	−0.354925	−	0.934895i	$-0.615494\pi$
$643$	−18.0000	−0.709851	−0.354925	+	0.934895i	$0.615494\pi$
$644$	0	0
$645$	−2.00000	−0.0787499
$646$	−24.0000	−0.944267
$647$	−21.0000	−0.825595	−0.412798	−	0.910823i	$-0.635448\pi$
$647$	−21.0000	−0.825595	−0.412798	+	0.910823i	$0.635448\pi$
$648$	−33.0000	−1.29636
$649$	−36.0000	−1.41312
$650$	7.00000	0.274563
$651$	18.0000	0.705476
$652$	0	0
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	4.00000	0.156412
$655$	−15.0000	−0.586098
$656$	5.00000	0.195217
$657$	−2.00000	−0.0780274
$658$	−5.00000	−0.194920
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	6.00000	0.233550
$661$	20.0000	0.777910	0.388955	−	0.921257i	$-0.372836\pi$
$661$	20.0000	0.777910	0.388955	+	0.921257i	$0.372836\pi$
$662$	8.00000	0.310929
$663$	84.0000	3.26229
$664$	−6.00000	−0.232845
$665$	4.00000	0.155113
$666$	1.00000	0.0387492
$667$	0	0
$668$	−20.0000	−0.773823
$669$	−26.0000	−1.00522
$670$	0	0
$671$	42.0000	1.62139
$672$	10.0000	0.385758
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	−25.0000	−0.962964
$675$	4.00000	0.153960
$676$	−36.0000	−1.38462
$677$	38.0000	1.46046	0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000	1.46046	0.730229	+	0.683202i	$0.239413\pi$
$678$	−12.0000	−0.460857
$679$	−2.00000	−0.0767530
$680$	18.0000	0.690268
$681$	14.0000	0.536481
$682$	27.0000	1.03388
$683$	33.0000	1.26271	0.631355	−	0.775494i	$-0.282499\pi$
$683$	33.0000	1.26271	0.631355	+	0.775494i	$0.282499\pi$
$684$	−4.00000	−0.152944
$685$	12.0000	0.458496
$686$	−1.00000	−0.0381802
$687$	2.00000	0.0763048
$688$	−1.00000	−0.0381246
$689$	35.0000	1.33339
$690$	0	0
$691$	−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
$693$	3.00000	0.113961
$694$	11.0000	0.417554
$695$	−11.0000	−0.417254
$696$	0	0
$697$	−30.0000	−1.13633
$698$	−21.0000	−0.794862
$699$	−30.0000	−1.13470
$700$	−1.00000	−0.0377964
$701$	−33.0000	−1.24639	−0.623196	−	0.782065i	$-0.714166\pi$
$701$	−33.0000	−1.24639	−0.623196	+	0.782065i	$0.714166\pi$
$702$	28.0000	1.05679
$703$	−4.00000	−0.150863
$704$	21.0000	0.791467
$705$	−10.0000	−0.376622
$706$	−14.0000	−0.526897
$707$	14.0000	0.526524
$708$	−24.0000	−0.901975
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	3.00000	0.112588
$711$	−12.0000	−0.450035
$712$	−15.0000	−0.562149
$713$	0	0
$714$	12.0000	0.449089
$715$	−21.0000	−0.785355
$716$	−2.00000	−0.0747435
$717$	4.00000	0.149383
$718$	−17.0000	−0.634434
$719$	−15.0000	−0.559406	−0.279703	−	0.960087i	$-0.590236\pi$
$719$	−15.0000	−0.559406	−0.279703	+	0.960087i	$0.590236\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	3.00000	0.111648
$723$	−8.00000	−0.297523
$724$	12.0000	0.445976
$725$	0	0
$726$	−4.00000	−0.148454
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	−21.0000	−0.778312
$729$	13.0000	0.481481
$730$	2.00000	0.0740233
$731$	6.00000	0.221918
$732$	28.0000	1.03491
$733$	−8.00000	−0.295487	−0.147743	−	0.989026i	$-0.547201\pi$
$733$	−8.00000	−0.295487	−0.147743	+	0.989026i	$0.547201\pi$
$734$	6.00000	0.221464
$735$	−2.00000	−0.0737711
$736$	0	0
$737$	0	0
$738$	5.00000	0.184053
$739$	18.0000	0.662141	0.331070	−	0.943606i	$-0.392590\pi$
$739$	18.0000	0.662141	0.331070	+	0.943606i	$0.392590\pi$
$740$	1.00000	0.0367607
$741$	56.0000	2.05721
$742$	5.00000	0.183556
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	54.0000	1.97974
$745$	−9.00000	−0.329734
$746$	37.0000	1.35467
$747$	−2.00000	−0.0731762
$748$	−18.0000	−0.658145
$749$	4.00000	0.146157
$750$	2.00000	0.0730297
$751$	−23.0000	−0.839282	−0.419641	−	0.907690i	$-0.637844\pi$
$751$	−23.0000	−0.839282	−0.419641	+	0.907690i	$0.637844\pi$
$752$	−5.00000	−0.182331
$753$	10.0000	0.364420
$754$	0	0
$755$	19.0000	0.691481
$756$	−4.00000	−0.145479
$757$	21.0000	0.763258	0.381629	−	0.924316i	$-0.375363\pi$
$757$	21.0000	0.763258	0.381629	+	0.924316i	$0.375363\pi$
$758$	28.0000	1.01701
$759$	0	0
$760$	12.0000	0.435286
$761$	27.0000	0.978749	0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000	0.978749	0.489375	+	0.872074i	$0.337225\pi$
$762$	−16.0000	−0.579619
$763$	2.00000	0.0724049
$764$	26.0000	0.940647
$765$	6.00000	0.216930
$766$	6.00000	0.216789
$767$	84.0000	3.03306
$768$	34.0000	1.22687
$769$	10.0000	0.360609	0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000	0.360609	0.180305	+	0.983611i	$0.442292\pi$
$770$	−3.00000	−0.108112
$771$	36.0000	1.29651
$772$	−5.00000	−0.179954
$773$	27.0000	0.971123	0.485561	−	0.874203i	$-0.338615\pi$
$773$	27.0000	0.971123	0.485561	+	0.874203i	$0.338615\pi$
$774$	−1.00000	−0.0359443
$775$	−9.00000	−0.323290
$776$	−6.00000	−0.215387
$777$	2.00000	0.0717496
$778$	20.0000	0.717035
$779$	−20.0000	−0.716574
$780$	−14.0000	−0.501280
$781$	−9.00000	−0.322045
$782$	0	0
$783$	0	0
$784$	−1.00000	−0.0357143
$785$	13.0000	0.463990
$786$	−30.0000	−1.07006
$787$	14.0000	0.499046	0.249523	−	0.968369i	$-0.419726\pi$
$787$	14.0000	0.499046	0.249523	+	0.968369i	$0.419726\pi$
$788$	10.0000	0.356235
$789$	28.0000	0.996826
$790$	12.0000	0.426941
$791$	−6.00000	−0.213335
$792$	9.00000	0.319801
$793$	−98.0000	−3.48008
$794$	38.0000	1.34857
$795$	10.0000	0.354663
$796$	−20.0000	−0.708881
$797$	−3.00000	−0.106265	−0.0531327	−	0.998587i	$-0.516921\pi$
$797$	−3.00000	−0.106265	−0.0531327	+	0.998587i	$0.516921\pi$
$798$	8.00000	0.283197
$799$	30.0000	1.06132
$800$	−5.00000	−0.176777
$801$	−5.00000	−0.176666
$802$	10.0000	0.353112
$803$	−6.00000	−0.211735
$804$	0	0
$805$	0	0
$806$	−63.0000	−2.21908
$807$	−28.0000	−0.985647
$808$	42.0000	1.47755
$809$	−16.0000	−0.562530	−0.281265	−	0.959630i	$-0.590754\pi$
$809$	−16.0000	−0.562530	−0.281265	+	0.959630i	$0.590754\pi$
$810$	11.0000	0.386501
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	0	0
$813$	−56.0000	−1.96401
$814$	3.00000	0.105150
$815$	0	0
$816$	12.0000	0.420084
$817$	4.00000	0.139942
$818$	32.0000	1.11885
$819$	−7.00000	−0.244600
$820$	5.00000	0.174608
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	24.0000	0.837096
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	0	0
$825$	−6.00000	−0.208893
$826$	12.0000	0.417533
$827$	−20.0000	−0.695468	−0.347734	−	0.937593i	$-0.613049\pi$
$827$	−20.0000	−0.695468	−0.347734	+	0.937593i	$0.613049\pi$
$828$	0	0
$829$	−6.00000	−0.208389	−0.104194	−	0.994557i	$-0.533226\pi$
$829$	−6.00000	−0.208389	−0.104194	+	0.994557i	$0.533226\pi$
$830$	2.00000	0.0694210
$831$	−22.0000	−0.763172
$832$	−49.0000	−1.69877
$833$	6.00000	0.207888
$834$	−22.0000	−0.761798
$835$	20.0000	0.692129
$836$	−12.0000	−0.415029
$837$	−36.0000	−1.24434
$838$	−15.0000	−0.518166
$839$	−11.0000	−0.379762	−0.189881	−	0.981807i	$-0.560810\pi$
$839$	−11.0000	−0.379762	−0.189881	+	0.981807i	$0.560810\pi$
$840$	−6.00000	−0.207020
$841$	−29.0000	−1.00000
$842$	26.0000	0.896019
$843$	40.0000	1.37767
$844$	4.00000	0.137686
$845$	36.0000	1.23844
$846$	−5.00000	−0.171904
$847$	−2.00000	−0.0687208
$848$	5.00000	0.171701
$849$	−10.0000	−0.343199
$850$	−6.00000	−0.205798
$851$	0	0
$852$	−6.00000	−0.205557
$853$	43.0000	1.47229	0.736146	−	0.676823i	$-0.236644\pi$
$853$	43.0000	1.47229	0.736146	+	0.676823i	$0.236644\pi$
$854$	−14.0000	−0.479070
$855$	4.00000	0.136797
$856$	12.0000	0.410152
$857$	−3.00000	−0.102478	−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000	−0.102478	−0.0512390	+	0.998686i	$0.516317\pi$
$858$	−42.0000	−1.43386
$859$	−2.00000	−0.0682391	−0.0341196	−	0.999418i	$-0.510863\pi$
$859$	−2.00000	−0.0682391	−0.0341196	+	0.999418i	$0.510863\pi$
$860$	−1.00000	−0.0340997
$861$	10.0000	0.340799
$862$	−4.00000	−0.136241
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	−20.0000	−0.680414
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	−38.0000	−1.29055
$868$	9.00000	0.305480
$869$	−36.0000	−1.22122
$870$	0	0
$871$	0	0
$872$	6.00000	0.203186
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	1.00000	0.0338062
$876$	−4.00000	−0.135147
$877$	14.0000	0.472746	0.236373	−	0.971662i	$-0.424041\pi$
$877$	14.0000	0.472746	0.236373	+	0.971662i	$0.424041\pi$
$878$	6.00000	0.202490
$879$	−4.00000	−0.134917
$880$	−3.00000	−0.101130
$881$	−17.0000	−0.572745	−0.286372	−	0.958118i	$-0.592449\pi$
$881$	−17.0000	−0.572745	−0.286372	+	0.958118i	$0.592449\pi$
$882$	−1.00000	−0.0336718
$883$	−21.0000	−0.706706	−0.353353	−	0.935490i	$-0.614959\pi$
$883$	−21.0000	−0.706706	−0.353353	+	0.935490i	$0.614959\pi$
$884$	42.0000	1.41261
$885$	24.0000	0.806751
$886$	−8.00000	−0.268765
$887$	13.0000	0.436497	0.218249	−	0.975893i	$-0.429966\pi$
$887$	13.0000	0.436497	0.218249	+	0.975893i	$0.429966\pi$
$888$	6.00000	0.201347
$889$	−8.00000	−0.268311
$890$	5.00000	0.167600
$891$	−33.0000	−1.10554
$892$	−13.0000	−0.435272
$893$	20.0000	0.669274
$894$	−18.0000	−0.602010
$895$	2.00000	0.0668526
$896$	3.00000	0.100223
$897$	0	0
$898$	−7.00000	−0.233593
$899$	0	0
$900$	−1.00000	−0.0333333
$901$	−30.0000	−0.999445
$902$	15.0000	0.499445
$903$	−2.00000	−0.0665558
$904$	−18.0000	−0.598671
$905$	−12.0000	−0.398893
$906$	38.0000	1.26247
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	7.00000	0.232303
$909$	14.0000	0.464351
$910$	7.00000	0.232048
$911$	37.0000	1.22586	0.612932	−	0.790135i	$-0.289990\pi$
$911$	37.0000	1.22586	0.612932	+	0.790135i	$0.289990\pi$
$912$	8.00000	0.264906
$913$	−6.00000	−0.198571
$914$	34.0000	1.12462
$915$	−28.0000	−0.925651
$916$	1.00000	0.0330409
$917$	−15.0000	−0.495344
$918$	−24.0000	−0.792118
$919$	−35.0000	−1.15454	−0.577272	−	0.816552i	$-0.695883\pi$
$919$	−35.0000	−1.15454	−0.577272	+	0.816552i	$0.695883\pi$
$920$	0	0
$921$	−44.0000	−1.44985
$922$	30.0000	0.987997
$923$	21.0000	0.691223
$924$	6.00000	0.197386
$925$	−1.00000	−0.0328798
$926$	−13.0000	−0.427207
$927$	0	0
$928$	0	0
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	−18.0000	−0.590243
$931$	4.00000	0.131095
$932$	−15.0000	−0.491341
$933$	−32.0000	−1.04763
$934$	36.0000	1.17796
$935$	18.0000	0.588663
$936$	−21.0000	−0.686406
$937$	15.0000	0.490029	0.245014	−	0.969519i	$-0.421207\pi$
$937$	15.0000	0.490029	0.245014	+	0.969519i	$0.421207\pi$
$938$	0	0
$939$	−38.0000	−1.24008
$940$	−5.00000	−0.163082
$941$	−28.0000	−0.912774	−0.456387	−	0.889781i	$-0.650857\pi$
$941$	−28.0000	−0.912774	−0.456387	+	0.889781i	$0.650857\pi$
$942$	26.0000	0.847126
$943$	0	0
$944$	12.0000	0.390567
$945$	4.00000	0.130120
$946$	−3.00000	−0.0975384
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	−24.0000	−0.779484
$949$	14.0000	0.454459
$950$	−4.00000	−0.129777
$951$	−32.0000	−1.03767
$952$	18.0000	0.583383
$953$	38.0000	1.23094	0.615470	−	0.788160i	$-0.288966\pi$
$953$	38.0000	1.23094	0.615470	+	0.788160i	$0.288966\pi$
$954$	5.00000	0.161881
$955$	−26.0000	−0.841340
$956$	2.00000	0.0646846
$957$	0	0
$958$	33.0000	1.06618
$959$	12.0000	0.387500
$960$	−14.0000	−0.451848
$961$	50.0000	1.61290
$962$	−7.00000	−0.225689
$963$	4.00000	0.128898
$964$	−4.00000	−0.128831
$965$	5.00000	0.160956
$966$	0	0
$967$	−53.0000	−1.70437	−0.852183	−	0.523245i	$-0.824721\pi$
$967$	−53.0000	−1.70437	−0.852183	+	0.523245i	$0.824721\pi$
$968$	−6.00000	−0.192847
$969$	−48.0000	−1.54198
$970$	2.00000	0.0642161
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	−10.0000	−0.320750
$973$	−11.0000	−0.352644
$974$	8.00000	0.256337
$975$	14.0000	0.448359
$976$	−14.0000	−0.448129
$977$	−37.0000	−1.18373	−0.591867	−	0.806035i	$-0.701609\pi$
$977$	−37.0000	−1.18373	−0.591867	+	0.806035i	$0.701609\pi$
$978$	0	0
$979$	−15.0000	−0.479402
$980$	−1.00000	−0.0319438
$981$	2.00000	0.0638551
$982$	0	0
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	30.0000	0.956365
$985$	−10.0000	−0.318626
$986$	0	0
$987$	−10.0000	−0.318304
$988$	28.0000	0.890799
$989$	0	0
$990$	−3.00000	−0.0953463
$991$	35.0000	1.11181	0.555906	−	0.831245i	$-0.312372\pi$
$991$	35.0000	1.11181	0.555906	+	0.831245i	$0.312372\pi$
$992$	45.0000	1.42875
$993$	16.0000	0.507745
$994$	3.00000	0.0951542
$995$	20.0000	0.634043
$996$	−4.00000	−0.126745
$997$	32.0000	1.01345	0.506725	−	0.862108i	$-0.330856\pi$
$997$	32.0000	1.01345	0.506725	+	0.862108i	$0.330856\pi$
$998$	10.0000	0.316544
$999$	−4.00000	−0.126554

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.b.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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