LMFDB - Embedded newform 1925.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,4,Mod(1,1925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1925.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1925.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:	$113.578676761$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{2} -4.00000 q^{3} +1.00000 q^{4} +12.0000 q^{6} -7.00000 q^{7} +21.0000 q^{8} -11.0000 q^{9} +O(q^{10})$

\(q-3.00000 q^{2} -4.00000 q^{3} +1.00000 q^{4} +12.0000 q^{6} -7.00000 q^{7} +21.0000 q^{8} -11.0000 q^{9} +11.0000 q^{11} -4.00000 q^{12} -38.0000 q^{13} +21.0000 q^{14} -71.0000 q^{16} +48.0000 q^{17} +33.0000 q^{18} -70.0000 q^{19} +28.0000 q^{21} -33.0000 q^{22} -12.0000 q^{23} -84.0000 q^{24} +114.000 q^{26} +152.000 q^{27} -7.00000 q^{28} +126.000 q^{29} -70.0000 q^{31} +45.0000 q^{32} -44.0000 q^{33} -144.000 q^{34} -11.0000 q^{36} +358.000 q^{37} +210.000 q^{38} +152.000 q^{39} -216.000 q^{41} -84.0000 q^{42} -344.000 q^{43} +11.0000 q^{44} +36.0000 q^{46} -390.000 q^{47} +284.000 q^{48} +49.0000 q^{49} -192.000 q^{51} -38.0000 q^{52} -438.000 q^{53} -456.000 q^{54} -147.000 q^{56} +280.000 q^{57} -378.000 q^{58} -552.000 q^{59} +830.000 q^{61} +210.000 q^{62} +77.0000 q^{63} +433.000 q^{64} +132.000 q^{66} +196.000 q^{67} +48.0000 q^{68} +48.0000 q^{69} +648.000 q^{71} -231.000 q^{72} +16.0000 q^{73} -1074.00 q^{74} -70.0000 q^{76} -77.0000 q^{77} -456.000 q^{78} +1352.00 q^{79} -311.000 q^{81} +648.000 q^{82} -90.0000 q^{83} +28.0000 q^{84} +1032.00 q^{86} -504.000 q^{87} +231.000 q^{88} +1146.00 q^{89} +266.000 q^{91} -12.0000 q^{92} +280.000 q^{93} +1170.00 q^{94} -180.000 q^{96} +70.0000 q^{97} -147.000 q^{98} -121.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−3.00000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	−4.00000	−0.769800	−0.384900	−	0.922958i	$-0.625764\pi$
$3$	−4.00000	−0.769800	−0.384900	+	0.922958i	$0.625764\pi$
$4$	1.00000	0.125000
$5$	0	0
$5$	0	0
$6$	12.0000	0.816497
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	21.0000	0.928078
$9$	−11.0000	−0.407407
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−4.00000	−0.0962250
$13$	−38.0000	−0.810716	−0.405358	−	0.914158i	$-0.632853\pi$
$13$	−38.0000	−0.810716	−0.405358	+	0.914158i	$0.632853\pi$
$14$	21.0000	0.400892
$15$	0	0
$16$	−71.0000	−1.10938
$17$	48.0000	0.684806	0.342403	−	0.939553i	$-0.388759\pi$
$17$	48.0000	0.684806	0.342403	+	0.939553i	$0.388759\pi$
$18$	33.0000	0.432121
$19$	−70.0000	−0.845216	−0.422608	−	0.906313i	$-0.638885\pi$
$19$	−70.0000	−0.845216	−0.422608	+	0.906313i	$0.638885\pi$
$20$	0	0
$21$	28.0000	0.290957
$22$	−33.0000	−0.319801
$23$	−12.0000	−0.108790	−0.0543951	−	0.998519i	$-0.517323\pi$
$23$	−12.0000	−0.108790	−0.0543951	+	0.998519i	$0.517323\pi$
$24$	−84.0000	−0.714435
$25$	0	0
$26$	114.000	0.859894
$27$	152.000	1.08342
$28$	−7.00000	−0.0472456
$29$	126.000	0.806814	0.403407	−	0.915021i	$-0.367826\pi$
$29$	126.000	0.806814	0.403407	+	0.915021i	$0.367826\pi$
$30$	0	0
$31$	−70.0000	−0.405560	−0.202780	−	0.979224i	$-0.564998\pi$
$31$	−70.0000	−0.405560	−0.202780	+	0.979224i	$0.564998\pi$
$32$	45.0000	0.248592
$33$	−44.0000	−0.232104
$34$	−144.000	−0.726347
$35$	0	0
$36$	−11.0000	−0.0509259
$37$	358.000	1.59067	0.795336	−	0.606169i	$-0.207295\pi$
$37$	358.000	1.59067	0.795336	+	0.606169i	$0.207295\pi$
$38$	210.000	0.896487
$39$	152.000	0.624089
$40$	0	0
$41$	−216.000	−0.822769	−0.411385	−	0.911462i	$-0.634955\pi$
$41$	−216.000	−0.822769	−0.411385	+	0.911462i	$0.634955\pi$
$42$	−84.0000	−0.308607
$43$	−344.000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−344.000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	11.0000	0.0376889
$45$	0	0
$46$	36.0000	0.115389
$47$	−390.000	−1.21037	−0.605185	−	0.796085i	$-0.706901\pi$
$47$	−390.000	−1.21037	−0.605185	+	0.796085i	$0.706901\pi$
$48$	284.000	0.853997
$49$	49.0000	0.142857
$50$	0	0
$51$	−192.000	−0.527164
$52$	−38.0000	−0.101339
$53$	−438.000	−1.13517	−0.567584	−	0.823315i	$-0.692122\pi$
$53$	−438.000	−1.13517	−0.567584	+	0.823315i	$0.692122\pi$
$54$	−456.000	−1.14914
$55$	0	0
$56$	−147.000	−0.350780
$57$	280.000	0.650647
$58$	−378.000	−0.855756
$59$	−552.000	−1.21804	−0.609019	−	0.793155i	$-0.708437\pi$
$59$	−552.000	−1.21804	−0.609019	+	0.793155i	$0.708437\pi$
$60$	0	0
$61$	830.000	1.74214	0.871071	−	0.491158i	$-0.163426\pi$
$61$	830.000	1.74214	0.871071	+	0.491158i	$0.163426\pi$
$62$	210.000	0.430162
$63$	77.0000	0.153986
$64$	433.000	0.845703
$65$	0	0
$66$	132.000	0.246183
$67$	196.000	0.357391	0.178696	−	0.983904i	$-0.442812\pi$
$67$	196.000	0.357391	0.178696	+	0.983904i	$0.442812\pi$
$68$	48.0000	0.0856008
$69$	48.0000	0.0837467
$70$	0	0
$71$	648.000	1.08315	0.541574	−	0.840653i	$-0.317829\pi$
$71$	648.000	1.08315	0.541574	+	0.840653i	$0.317829\pi$
$72$	−231.000	−0.378106
$73$	16.0000	0.0256529	0.0128264	−	0.999918i	$-0.495917\pi$
$73$	16.0000	0.0256529	0.0128264	+	0.999918i	$0.495917\pi$
$74$	−1074.00	−1.68716
$75$	0	0
$76$	−70.0000	−0.105652
$77$	−77.0000	−0.113961
$78$	−456.000	−0.661947
$79$	1352.00	1.92547	0.962733	−	0.270452i	$-0.0871732\pi$
$79$	1352.00	1.92547	0.962733	+	0.270452i	$0.0871732\pi$
$80$	0	0
$81$	−311.000	−0.426612
$82$	648.000	0.872678
$83$	−90.0000	−0.119021	−0.0595107	−	0.998228i	$-0.518954\pi$
$83$	−90.0000	−0.119021	−0.0595107	+	0.998228i	$0.518954\pi$
$84$	28.0000	0.0363696
$85$	0	0
$86$	1032.00	1.29399
$87$	−504.000	−0.621086
$88$	231.000	0.279826
$89$	1146.00	1.36490	0.682448	−	0.730934i	$-0.260915\pi$
$89$	1146.00	1.36490	0.682448	+	0.730934i	$0.260915\pi$
$90$	0	0
$91$	266.000	0.306422
$92$	−12.0000	−0.0135988
$93$	280.000	0.312201
$94$	1170.00	1.28379
$95$	0	0
$96$	−180.000	−0.191366
$97$	70.0000	0.0732724	0.0366362	−	0.999329i	$-0.488336\pi$
$97$	70.0000	0.0732724	0.0366362	+	0.999329i	$0.488336\pi$
$98$	−147.000	−0.151523
$99$	−121.000	−0.122838
$100$	0	0
$101$	−1254.00	−1.23542	−0.617711	−	0.786405i	$-0.711940\pi$
$101$	−1254.00	−1.23542	−0.617711	+	0.786405i	$0.711940\pi$
$102$	576.000	0.559142
$103$	682.000	0.652422	0.326211	−	0.945297i	$-0.394228\pi$
$103$	682.000	0.652422	0.326211	+	0.945297i	$0.394228\pi$
$104$	−798.000	−0.752407
$105$	0	0
$106$	1314.00	1.20403
$107$	384.000	0.346941	0.173470	−	0.984839i	$-0.444502\pi$
$107$	384.000	0.346941	0.173470	+	0.984839i	$0.444502\pi$
$108$	152.000	0.135428
$109$	−646.000	−0.567666	−0.283833	−	0.958874i	$-0.591606\pi$
$109$	−646.000	−0.567666	−0.283833	+	0.958874i	$0.591606\pi$
$110$	0	0
$111$	−1432.00	−1.22450
$112$	497.000	0.419304
$113$	1314.00	1.09390	0.546950	−	0.837165i	$-0.315789\pi$
$113$	1314.00	1.09390	0.546950	+	0.837165i	$0.315789\pi$
$114$	−840.000	−0.690116
$115$	0	0
$116$	126.000	0.100852
$117$	418.000	0.330292
$118$	1656.00	1.29193
$119$	−336.000	−0.258833
$120$	0	0
$121$	121.000	0.0909091
$122$	−2490.00	−1.84782
$123$	864.000	0.633368
$124$	−70.0000	−0.0506950
$125$	0	0
$126$	−231.000	−0.163326
$127$	−344.000	−0.240355	−0.120177	−	0.992752i	$-0.538346\pi$
$127$	−344.000	−0.240355	−0.120177	+	0.992752i	$0.538346\pi$
$128$	−1659.00	−1.14560
$129$	1376.00	0.939148
$130$	0	0
$131$	−258.000	−0.172073	−0.0860365	−	0.996292i	$-0.527420\pi$
$131$	−258.000	−0.172073	−0.0860365	+	0.996292i	$0.527420\pi$
$132$	−44.0000	−0.0290129
$133$	490.000	0.319462
$134$	−588.000	−0.379071
$135$	0	0
$136$	1008.00	0.635554
$137$	2730.00	1.70248	0.851240	−	0.524777i	$-0.175851\pi$
$137$	2730.00	1.70248	0.851240	+	0.524777i	$0.175851\pi$
$138$	−144.000	−0.0888268
$139$	1838.00	1.12156	0.560781	−	0.827964i	$-0.310501\pi$
$139$	1838.00	1.12156	0.560781	+	0.827964i	$0.310501\pi$
$140$	0	0
$141$	1560.00	0.931743
$142$	−1944.00	−1.14885
$143$	−418.000	−0.244440
$144$	781.000	0.451968
$145$	0	0
$146$	−48.0000	−0.0272090
$147$	−196.000	−0.109971
$148$	358.000	0.198834
$149$	−510.000	−0.280408	−0.140204	−	0.990123i	$-0.544776\pi$
$149$	−510.000	−0.280408	−0.140204	+	0.990123i	$0.544776\pi$
$150$	0	0
$151$	2864.00	1.54350	0.771752	−	0.635924i	$-0.219381\pi$
$151$	2864.00	1.54350	0.771752	+	0.635924i	$0.219381\pi$
$152$	−1470.00	−0.784426
$153$	−528.000	−0.278995
$154$	231.000	0.120873
$155$	0	0
$156$	152.000	0.0780112
$157$	2968.00	1.50874	0.754370	−	0.656449i	$-0.227942\pi$
$157$	2968.00	1.50874	0.754370	+	0.656449i	$0.227942\pi$
$158$	−4056.00	−2.04227
$159$	1752.00	0.873853
$160$	0	0
$161$	84.0000	0.0411188
$162$	933.000	0.452490
$163$	−1604.00	−0.770767	−0.385383	−	0.922757i	$-0.625931\pi$
$163$	−1604.00	−0.770767	−0.385383	+	0.922757i	$0.625931\pi$
$164$	−216.000	−0.102846
$165$	0	0
$166$	270.000	0.126241
$167$	−180.000	−0.0834061	−0.0417030	−	0.999130i	$-0.513278\pi$
$167$	−180.000	−0.0834061	−0.0417030	+	0.999130i	$0.513278\pi$
$168$	588.000	0.270031
$169$	−753.000	−0.342740
$170$	0	0
$171$	770.000	0.344347
$172$	−344.000	−0.152499
$173$	1626.00	0.714581	0.357290	−	0.933993i	$-0.383701\pi$
$173$	1626.00	0.714581	0.357290	+	0.933993i	$0.383701\pi$
$174$	1512.00	0.658761
$175$	0	0
$176$	−781.000	−0.334489
$177$	2208.00	0.937647
$178$	−3438.00	−1.44769
$179$	−3252.00	−1.35791	−0.678955	−	0.734180i	$-0.737567\pi$
$179$	−3252.00	−1.35791	−0.678955	+	0.734180i	$0.737567\pi$
$180$	0	0
$181$	1820.00	0.747401	0.373700	−	0.927549i	$-0.378089\pi$
$181$	1820.00	0.747401	0.373700	+	0.927549i	$0.378089\pi$
$182$	−798.000	−0.325009
$183$	−3320.00	−1.34110
$184$	−252.000	−0.100966
$185$	0	0
$186$	−840.000	−0.331139
$187$	528.000	0.206477
$188$	−390.000	−0.151296
$189$	−1064.00	−0.409495
$190$	0	0
$191$	−1212.00	−0.459148	−0.229574	−	0.973291i	$-0.573733\pi$
$191$	−1212.00	−0.459148	−0.229574	+	0.973291i	$0.573733\pi$
$192$	−1732.00	−0.651023
$193$	−2522.00	−0.940609	−0.470304	−	0.882504i	$-0.655856\pi$
$193$	−2522.00	−0.940609	−0.470304	+	0.882504i	$0.655856\pi$
$194$	−210.000	−0.0777171
$195$	0	0
$196$	49.0000	0.0178571
$197$	3474.00	1.25641	0.628204	−	0.778049i	$-0.283790\pi$
$197$	3474.00	1.25641	0.628204	+	0.778049i	$0.283790\pi$
$198$	363.000	0.130289
$199$	−2842.00	−1.01238	−0.506191	−	0.862421i	$-0.668947\pi$
$199$	−2842.00	−1.01238	−0.506191	+	0.862421i	$0.668947\pi$
$200$	0	0
$201$	−784.000	−0.275120
$202$	3762.00	1.31036
$203$	−882.000	−0.304947
$204$	−192.000	−0.0658955
$205$	0	0
$206$	−2046.00	−0.691998
$207$	132.000	0.0443219
$208$	2698.00	0.899388
$209$	−770.000	−0.254842
$210$	0	0
$211$	5528.00	1.80362	0.901809	−	0.432136i	$-0.142240\pi$
$211$	5528.00	1.80362	0.901809	+	0.432136i	$0.142240\pi$
$212$	−438.000	−0.141896
$213$	−2592.00	−0.833807
$214$	−1152.00	−0.367986
$215$	0	0
$216$	3192.00	1.00550
$217$	490.000	0.153287
$218$	1938.00	0.602101
$219$	−64.0000	−0.0197476
$220$	0	0
$221$	−1824.00	−0.555183
$222$	4296.00	1.29878
$223$	−4034.00	−1.21137	−0.605687	−	0.795703i	$-0.707102\pi$
$223$	−4034.00	−1.21137	−0.605687	+	0.795703i	$0.707102\pi$
$224$	−315.000	−0.0939590
$225$	0	0
$226$	−3942.00	−1.16026
$227$	−726.000	−0.212275	−0.106137	−	0.994351i	$-0.533848\pi$
$227$	−726.000	−0.212275	−0.106137	+	0.994351i	$0.533848\pi$
$228$	280.000	0.0813309
$229$	−2788.00	−0.804525	−0.402263	−	0.915524i	$-0.631776\pi$
$229$	−2788.00	−0.804525	−0.402263	+	0.915524i	$0.631776\pi$
$230$	0	0
$231$	308.000	0.0877269
$232$	2646.00	0.748786
$233$	−2694.00	−0.757467	−0.378733	−	0.925506i	$-0.623640\pi$
$233$	−2694.00	−0.757467	−0.378733	+	0.925506i	$0.623640\pi$
$234$	−1254.00	−0.350327
$235$	0	0
$236$	−552.000	−0.152255
$237$	−5408.00	−1.48223
$238$	1008.00	0.274533
$239$	6480.00	1.75379	0.876896	−	0.480680i	$-0.159610\pi$
$239$	6480.00	1.75379	0.876896	+	0.480680i	$0.159610\pi$
$240$	0	0
$241$	−2320.00	−0.620101	−0.310050	−	0.950720i	$-0.600346\pi$
$241$	−2320.00	−0.620101	−0.310050	+	0.950720i	$0.600346\pi$
$242$	−363.000	−0.0964237
$243$	−2860.00	−0.755017
$244$	830.000	0.217768
$245$	0	0
$246$	−2592.00	−0.671788
$247$	2660.00	0.685230
$248$	−1470.00	−0.376392
$249$	360.000	0.0916228
$250$	0	0
$251$	2088.00	0.525073	0.262537	−	0.964922i	$-0.415441\pi$
$251$	2088.00	0.525073	0.262537	+	0.964922i	$0.415441\pi$
$252$	77.0000	0.0192482
$253$	−132.000	−0.0328015
$254$	1032.00	0.254935
$255$	0	0
$256$	1513.00	0.369385
$257$	4182.00	1.01504	0.507521	−	0.861639i	$-0.330562\pi$
$257$	4182.00	1.01504	0.507521	+	0.861639i	$0.330562\pi$
$258$	−4128.00	−0.996116
$259$	−2506.00	−0.601217
$260$	0	0
$261$	−1386.00	−0.328702
$262$	774.000	0.182511
$263$	−3696.00	−0.866559	−0.433280	−	0.901260i	$-0.642644\pi$
$263$	−3696.00	−0.866559	−0.433280	+	0.901260i	$0.642644\pi$
$264$	−924.000	−0.215410
$265$	0	0
$266$	−1470.00	−0.338840
$267$	−4584.00	−1.05070
$268$	196.000	0.0446739
$269$	−6060.00	−1.37355	−0.686775	−	0.726870i	$-0.740974\pi$
$269$	−6060.00	−1.37355	−0.686775	+	0.726870i	$0.740974\pi$
$270$	0	0
$271$	−8764.00	−1.96448	−0.982242	−	0.187619i	$-0.939923\pi$
$271$	−8764.00	−1.96448	−0.982242	+	0.187619i	$0.939923\pi$
$272$	−3408.00	−0.759707
$273$	−1064.00	−0.235884
$274$	−8190.00	−1.80575
$275$	0	0
$276$	48.0000	0.0104683
$277$	−5186.00	−1.12490	−0.562449	−	0.826832i	$-0.690141\pi$
$277$	−5186.00	−1.12490	−0.562449	+	0.826832i	$0.690141\pi$
$278$	−5514.00	−1.18960
$279$	770.000	0.165228
$280$	0	0
$281$	3006.00	0.638160	0.319080	−	0.947728i	$-0.396626\pi$
$281$	3006.00	0.638160	0.319080	+	0.947728i	$0.396626\pi$
$282$	−4680.00	−0.988262
$283$	3922.00	0.823812	0.411906	−	0.911226i	$-0.364863\pi$
$283$	3922.00	0.823812	0.411906	+	0.911226i	$0.364863\pi$
$284$	648.000	0.135393
$285$	0	0
$286$	1254.00	0.259268
$287$	1512.00	0.310977
$288$	−495.000	−0.101278
$289$	−2609.00	−0.531040
$290$	0	0
$291$	−280.000	−0.0564051
$292$	16.0000	0.00320661
$293$	5778.00	1.15206	0.576031	−	0.817428i	$-0.304601\pi$
$293$	5778.00	1.15206	0.576031	+	0.817428i	$0.304601\pi$
$294$	588.000	0.116642
$295$	0	0
$296$	7518.00	1.47627
$297$	1672.00	0.326664
$298$	1530.00	0.297418
$299$	456.000	0.0881979
$300$	0	0
$301$	2408.00	0.461112
$302$	−8592.00	−1.63713
$303$	5016.00	0.951029
$304$	4970.00	0.937661
$305$	0	0
$306$	1584.00	0.295919
$307$	610.000	0.113402	0.0567012	−	0.998391i	$-0.481942\pi$
$307$	610.000	0.113402	0.0567012	+	0.998391i	$0.481942\pi$
$308$	−77.0000	−0.0142451
$309$	−2728.00	−0.502235
$310$	0	0
$311$	6882.00	1.25480	0.627399	−	0.778698i	$-0.284119\pi$
$311$	6882.00	1.25480	0.627399	+	0.778698i	$0.284119\pi$
$312$	3192.00	0.579203
$313$	−10334.0	−1.86617	−0.933087	−	0.359652i	$-0.882895\pi$
$313$	−10334.0	−1.86617	−0.933087	+	0.359652i	$0.882895\pi$
$314$	−8904.00	−1.60026
$315$	0	0
$316$	1352.00	0.240683
$317$	−5934.00	−1.05138	−0.525689	−	0.850677i	$-0.676192\pi$
$317$	−5934.00	−1.05138	−0.525689	+	0.850677i	$0.676192\pi$
$318$	−5256.00	−0.926861
$319$	1386.00	0.243264
$320$	0	0
$321$	−1536.00	−0.267075
$322$	−252.000	−0.0436131
$323$	−3360.00	−0.578809
$324$	−311.000	−0.0533265
$325$	0	0
$326$	4812.00	0.817522
$327$	2584.00	0.436989
$328$	−4536.00	−0.763594
$329$	2730.00	0.457477
$330$	0	0
$331$	−3220.00	−0.534705	−0.267352	−	0.963599i	$-0.586149\pi$
$331$	−3220.00	−0.534705	−0.267352	+	0.963599i	$0.586149\pi$
$332$	−90.0000	−0.0148777
$333$	−3938.00	−0.648051
$334$	540.000	0.0884655
$335$	0	0
$336$	−1988.00	−0.322781
$337$	6658.00	1.07621	0.538107	−	0.842876i	$-0.319139\pi$
$337$	6658.00	1.07621	0.538107	+	0.842876i	$0.319139\pi$
$338$	2259.00	0.363531
$339$	−5256.00	−0.842085
$340$	0	0
$341$	−770.000	−0.122281
$342$	−2310.00	−0.365235
$343$	−343.000	−0.0539949
$344$	−7224.00	−1.13224
$345$	0	0
$346$	−4878.00	−0.757927
$347$	6888.00	1.06561	0.532806	−	0.846238i	$-0.321138\pi$
$347$	6888.00	1.06561	0.532806	+	0.846238i	$0.321138\pi$
$348$	−504.000	−0.0776357
$349$	−6190.00	−0.949407	−0.474704	−	0.880146i	$-0.657445\pi$
$349$	−6190.00	−0.949407	−0.474704	+	0.880146i	$0.657445\pi$
$350$	0	0
$351$	−5776.00	−0.878348
$352$	495.000	0.0749534
$353$	3990.00	0.601604	0.300802	−	0.953687i	$-0.402746\pi$
$353$	3990.00	0.601604	0.300802	+	0.953687i	$0.402746\pi$
$354$	−6624.00	−0.994524
$355$	0	0
$356$	1146.00	0.170612
$357$	1344.00	0.199249
$358$	9756.00	1.44028
$359$	−7656.00	−1.12554	−0.562769	−	0.826614i	$-0.690264\pi$
$359$	−7656.00	−1.12554	−0.562769	+	0.826614i	$0.690264\pi$
$360$	0	0
$361$	−1959.00	−0.285610
$362$	−5460.00	−0.792738
$363$	−484.000	−0.0699819
$364$	266.000	0.0383027
$365$	0	0
$366$	9960.00	1.42245
$367$	−8426.00	−1.19846	−0.599228	−	0.800578i	$-0.704526\pi$
$367$	−8426.00	−1.19846	−0.599228	+	0.800578i	$0.704526\pi$
$368$	852.000	0.120689
$369$	2376.00	0.335202
$370$	0	0
$371$	3066.00	0.429053
$372$	280.000	0.0390251
$373$	−11918.0	−1.65440	−0.827199	−	0.561909i	$-0.810067\pi$
$373$	−11918.0	−1.65440	−0.827199	+	0.561909i	$0.810067\pi$
$374$	−1584.00	−0.219002
$375$	0	0
$376$	−8190.00	−1.12332
$377$	−4788.00	−0.654097
$378$	3192.00	0.434335
$379$	3908.00	0.529658	0.264829	−	0.964295i	$-0.414684\pi$
$379$	3908.00	0.529658	0.264829	+	0.964295i	$0.414684\pi$
$380$	0	0
$381$	1376.00	0.185025
$382$	3636.00	0.487000
$383$	3246.00	0.433062	0.216531	−	0.976276i	$-0.430526\pi$
$383$	3246.00	0.433062	0.216531	+	0.976276i	$0.430526\pi$
$384$	6636.00	0.881880
$385$	0	0
$386$	7566.00	0.997666
$387$	3784.00	0.497032
$388$	70.0000	0.00915905
$389$	−8166.00	−1.06435	−0.532176	−	0.846634i	$-0.678625\pi$
$389$	−8166.00	−1.06435	−0.532176	+	0.846634i	$0.678625\pi$
$390$	0	0
$391$	−576.000	−0.0745002
$392$	1029.00	0.132583
$393$	1032.00	0.132462
$394$	−10422.0	−1.33262
$395$	0	0
$396$	−121.000	−0.0153547
$397$	2824.00	0.357009	0.178504	−	0.983939i	$-0.442874\pi$
$397$	2824.00	0.357009	0.178504	+	0.983939i	$0.442874\pi$
$398$	8526.00	1.07379
$399$	−1960.00	−0.245922
$400$	0	0
$401$	−10482.0	−1.30535	−0.652676	−	0.757637i	$-0.726354\pi$
$401$	−10482.0	−1.30535	−0.652676	+	0.757637i	$0.726354\pi$
$402$	2352.00	0.291809
$403$	2660.00	0.328794
$404$	−1254.00	−0.154428
$405$	0	0
$406$	2646.00	0.323445
$407$	3938.00	0.479605
$408$	−4032.00	−0.489249
$409$	8156.00	0.986035	0.493017	−	0.870019i	$-0.335894\pi$
$409$	8156.00	0.986035	0.493017	+	0.870019i	$0.335894\pi$
$410$	0	0
$411$	−10920.0	−1.31057
$412$	682.000	0.0815527
$413$	3864.00	0.460375
$414$	−396.000	−0.0470105
$415$	0	0
$416$	−1710.00	−0.201538
$417$	−7352.00	−0.863379
$418$	2310.00	0.270301
$419$	−11052.0	−1.28861	−0.644303	−	0.764771i	$-0.722852\pi$
$419$	−11052.0	−1.28861	−0.644303	+	0.764771i	$0.722852\pi$
$420$	0	0
$421$	5006.00	0.579519	0.289760	−	0.957099i	$-0.406425\pi$
$421$	5006.00	0.579519	0.289760	+	0.957099i	$0.406425\pi$
$422$	−16584.0	−1.91302
$423$	4290.00	0.493113
$424$	−9198.00	−1.05352
$425$	0	0
$426$	7776.00	0.884386
$427$	−5810.00	−0.658467
$428$	384.000	0.0433676
$429$	1672.00	0.188170
$430$	0	0
$431$	−9480.00	−1.05948	−0.529740	−	0.848160i	$-0.677710\pi$
$431$	−9480.00	−1.05948	−0.529740	+	0.848160i	$0.677710\pi$
$432$	−10792.0	−1.20192
$433$	1942.00	0.215535	0.107767	−	0.994176i	$-0.465630\pi$
$433$	1942.00	0.215535	0.107767	+	0.994176i	$0.465630\pi$
$434$	−1470.00	−0.162586
$435$	0	0
$436$	−646.000	−0.0709582
$437$	840.000	0.0919511
$438$	192.000	0.0209455
$439$	−13660.0	−1.48509	−0.742547	−	0.669794i	$-0.766382\pi$
$439$	−13660.0	−1.48509	−0.742547	+	0.669794i	$0.766382\pi$
$440$	0	0
$441$	−539.000	−0.0582011
$442$	5472.00	0.588861
$443$	−3828.00	−0.410550	−0.205275	−	0.978704i	$-0.565809\pi$
$443$	−3828.00	−0.410550	−0.205275	+	0.978704i	$0.565809\pi$
$444$	−1432.00	−0.153062
$445$	0	0
$446$	12102.0	1.28486
$447$	2040.00	0.215858
$448$	−3031.00	−0.319646
$449$	18270.0	1.92030	0.960150	−	0.279486i	$-0.0901639\pi$
$449$	18270.0	1.92030	0.960150	+	0.279486i	$0.0901639\pi$
$450$	0	0
$451$	−2376.00	−0.248074
$452$	1314.00	0.136738
$453$	−11456.0	−1.18819
$454$	2178.00	0.225151
$455$	0	0
$456$	5880.00	0.603851
$457$	−10154.0	−1.03935	−0.519676	−	0.854363i	$-0.673947\pi$
$457$	−10154.0	−1.03935	−0.519676	+	0.854363i	$0.673947\pi$
$458$	8364.00	0.853328
$459$	7296.00	0.741935
$460$	0	0
$461$	−17190.0	−1.73670	−0.868349	−	0.495953i	$-0.834819\pi$
$461$	−17190.0	−1.73670	−0.868349	+	0.495953i	$0.834819\pi$
$462$	−924.000	−0.0930484
$463$	−4448.00	−0.446471	−0.223236	−	0.974765i	$-0.571662\pi$
$463$	−4448.00	−0.446471	−0.223236	+	0.974765i	$0.571662\pi$
$464$	−8946.00	−0.895060
$465$	0	0
$466$	8082.00	0.803415
$467$	−11100.0	−1.09989	−0.549943	−	0.835202i	$-0.685351\pi$
$467$	−11100.0	−1.09989	−0.549943	+	0.835202i	$0.685351\pi$
$468$	418.000	0.0412864
$469$	−1372.00	−0.135081
$470$	0	0
$471$	−11872.0	−1.16143
$472$	−11592.0	−1.13043
$473$	−3784.00	−0.367840
$474$	16224.0	1.57214
$475$	0	0
$476$	−336.000	−0.0323541
$477$	4818.00	0.462476
$478$	−19440.0	−1.86018
$479$	−15816.0	−1.50867	−0.754333	−	0.656491i	$-0.772040\pi$
$479$	−15816.0	−1.50867	−0.754333	+	0.656491i	$0.772040\pi$
$480$	0	0
$481$	−13604.0	−1.28958
$482$	6960.00	0.657716
$483$	−336.000	−0.0316533
$484$	121.000	0.0113636
$485$	0	0
$486$	8580.00	0.800816
$487$	1924.00	0.179024	0.0895121	−	0.995986i	$-0.471469\pi$
$487$	1924.00	0.179024	0.0895121	+	0.995986i	$0.471469\pi$
$488$	17430.0	1.61684
$489$	6416.00	0.593337
$490$	0	0
$491$	13068.0	1.20112	0.600561	−	0.799579i	$-0.294944\pi$
$491$	13068.0	1.20112	0.600561	+	0.799579i	$0.294944\pi$
$492$	864.000	0.0791710
$493$	6048.00	0.552512
$494$	−7980.00	−0.726796
$495$	0	0
$496$	4970.00	0.449919
$497$	−4536.00	−0.409391
$498$	−1080.00	−0.0971806
$499$	17876.0	1.60369	0.801843	−	0.597534i	$-0.203853\pi$
$499$	17876.0	1.60369	0.801843	+	0.597534i	$0.203853\pi$
$500$	0	0
$501$	720.000	0.0642060
$502$	−6264.00	−0.556924
$503$	3852.00	0.341456	0.170728	−	0.985318i	$-0.445388\pi$
$503$	3852.00	0.341456	0.170728	+	0.985318i	$0.445388\pi$
$504$	1617.00	0.142911
$505$	0	0
$506$	396.000	0.0347912
$507$	3012.00	0.263841
$508$	−344.000	−0.0300444
$509$	15132.0	1.31771	0.658855	−	0.752270i	$-0.271041\pi$
$509$	15132.0	1.31771	0.658855	+	0.752270i	$0.271041\pi$
$510$	0	0
$511$	−112.000	−0.00969587
$512$	8733.00	0.753804
$513$	−10640.0	−0.915726
$514$	−12546.0	−1.07662
$515$	0	0
$516$	1376.00	0.117393
$517$	−4290.00	−0.364940
$518$	7518.00	0.637687
$519$	−6504.00	−0.550085
$520$	0	0
$521$	−3054.00	−0.256810	−0.128405	−	0.991722i	$-0.540986\pi$
$521$	−3054.00	−0.256810	−0.128405	+	0.991722i	$0.540986\pi$
$522$	4158.00	0.348641
$523$	11770.0	0.984065	0.492033	−	0.870577i	$-0.336254\pi$
$523$	11770.0	0.984065	0.492033	+	0.870577i	$0.336254\pi$
$524$	−258.000	−0.0215091
$525$	0	0
$526$	11088.0	0.919125
$527$	−3360.00	−0.277730
$528$	3124.00	0.257490
$529$	−12023.0	−0.988165
$530$	0	0
$531$	6072.00	0.496238
$532$	490.000	0.0399327
$533$	8208.00	0.667032
$534$	13752.0	1.11443
$535$	0	0
$536$	4116.00	0.331687
$537$	13008.0	1.04532
$538$	18180.0	1.45687
$539$	539.000	0.0430730
$540$	0	0
$541$	10694.0	0.849854	0.424927	−	0.905228i	$-0.360300\pi$
$541$	10694.0	0.849854	0.424927	+	0.905228i	$0.360300\pi$
$542$	26292.0	2.08365
$543$	−7280.00	−0.575349
$544$	2160.00	0.170238
$545$	0	0
$546$	3192.00	0.250192
$547$	−5636.00	−0.440545	−0.220272	−	0.975438i	$-0.570695\pi$
$547$	−5636.00	−0.440545	−0.220272	+	0.975438i	$0.570695\pi$
$548$	2730.00	0.212810
$549$	−9130.00	−0.709761
$550$	0	0
$551$	−8820.00	−0.681932
$552$	1008.00	0.0777234
$553$	−9464.00	−0.727758
$554$	15558.0	1.19313
$555$	0	0
$556$	1838.00	0.140195
$557$	−15126.0	−1.15064	−0.575322	−	0.817927i	$-0.695123\pi$
$557$	−15126.0	−1.15064	−0.575322	+	0.817927i	$0.695123\pi$
$558$	−2310.00	−0.175251
$559$	13072.0	0.989064
$560$	0	0
$561$	−2112.00	−0.158946
$562$	−9018.00	−0.676871
$563$	−3246.00	−0.242989	−0.121494	−	0.992592i	$-0.538769\pi$
$563$	−3246.00	−0.242989	−0.121494	+	0.992592i	$0.538769\pi$
$564$	1560.00	0.116468
$565$	0	0
$566$	−11766.0	−0.873784
$567$	2177.00	0.161244
$568$	13608.0	1.00524
$569$	−1050.00	−0.0773608	−0.0386804	−	0.999252i	$-0.512315\pi$
$569$	−1050.00	−0.0773608	−0.0386804	+	0.999252i	$0.512315\pi$
$570$	0	0
$571$	6860.00	0.502771	0.251385	−	0.967887i	$-0.419114\pi$
$571$	6860.00	0.502771	0.251385	+	0.967887i	$0.419114\pi$
$572$	−418.000	−0.0305550
$573$	4848.00	0.353452
$574$	−4536.00	−0.329841
$575$	0	0
$576$	−4763.00	−0.344546
$577$	12634.0	0.911543	0.455771	−	0.890097i	$-0.349363\pi$
$577$	12634.0	0.911543	0.455771	+	0.890097i	$0.349363\pi$
$578$	7827.00	0.563253
$579$	10088.0	0.724081
$580$	0	0
$581$	630.000	0.0449859
$582$	840.000	0.0598267
$583$	−4818.00	−0.342266
$584$	336.000	0.0238078
$585$	0	0
$586$	−17334.0	−1.22195
$587$	−18144.0	−1.27578	−0.637890	−	0.770127i	$-0.720193\pi$
$587$	−18144.0	−1.27578	−0.637890	+	0.770127i	$0.720193\pi$
$588$	−196.000	−0.0137464
$589$	4900.00	0.342786
$590$	0	0
$591$	−13896.0	−0.967183
$592$	−25418.0	−1.76465
$593$	10896.0	0.754545	0.377272	−	0.926102i	$-0.376862\pi$
$593$	10896.0	0.754545	0.377272	+	0.926102i	$0.376862\pi$
$594$	−5016.00	−0.346480
$595$	0	0
$596$	−510.000	−0.0350510
$597$	11368.0	0.779332
$598$	−1368.00	−0.0935480
$599$	−20280.0	−1.38334	−0.691668	−	0.722216i	$-0.743124\pi$
$599$	−20280.0	−1.38334	−0.691668	+	0.722216i	$0.743124\pi$
$600$	0	0
$601$	12332.0	0.836993	0.418496	−	0.908218i	$-0.362557\pi$
$601$	12332.0	0.836993	0.418496	+	0.908218i	$0.362557\pi$
$602$	−7224.00	−0.489083
$603$	−2156.00	−0.145604
$604$	2864.00	0.192938
$605$	0	0
$606$	−15048.0	−1.00872
$607$	−21800.0	−1.45772	−0.728859	−	0.684664i	$-0.759949\pi$
$607$	−21800.0	−1.45772	−0.728859	+	0.684664i	$0.759949\pi$
$608$	−3150.00	−0.210114
$609$	3528.00	0.234748
$610$	0	0
$611$	14820.0	0.981265
$612$	−528.000	−0.0348744
$613$	−18542.0	−1.22170	−0.610852	−	0.791745i	$-0.709173\pi$
$613$	−18542.0	−1.22170	−0.610852	+	0.791745i	$0.709173\pi$
$614$	−1830.00	−0.120281
$615$	0	0
$616$	−1617.00	−0.105764
$617$	−10098.0	−0.658882	−0.329441	−	0.944176i	$-0.606860\pi$
$617$	−10098.0	−0.658882	−0.329441	+	0.944176i	$0.606860\pi$
$618$	8184.00	0.532700
$619$	−124.000	−0.00805167	−0.00402583	−	0.999992i	$-0.501281\pi$
$619$	−124.000	−0.00805167	−0.00402583	+	0.999992i	$0.501281\pi$
$620$	0	0
$621$	−1824.00	−0.117866
$622$	−20646.0	−1.33092
$623$	−8022.00	−0.515882
$624$	−10792.0	−0.692349
$625$	0	0
$626$	31002.0	1.97938
$627$	3080.00	0.196178
$628$	2968.00	0.188593
$629$	17184.0	1.08930
$630$	0	0
$631$	−14308.0	−0.902682	−0.451341	−	0.892351i	$-0.649054\pi$
$631$	−14308.0	−0.902682	−0.451341	+	0.892351i	$0.649054\pi$
$632$	28392.0	1.78698
$633$	−22112.0	−1.38843
$634$	17802.0	1.11515
$635$	0	0
$636$	1752.00	0.109232
$637$	−1862.00	−0.115817
$638$	−4158.00	−0.258020
$639$	−7128.00	−0.441282
$640$	0	0
$641$	−678.000	−0.0417775	−0.0208888	−	0.999782i	$-0.506650\pi$
$641$	−678.000	−0.0417775	−0.0208888	+	0.999782i	$0.506650\pi$
$642$	4608.00	0.283276
$643$	−17408.0	−1.06766	−0.533829	−	0.845592i	$-0.679248\pi$
$643$	−17408.0	−1.06766	−0.533829	+	0.845592i	$0.679248\pi$
$644$	84.0000	0.00513985
$645$	0	0
$646$	10080.0	0.613920
$647$	28686.0	1.74306	0.871532	−	0.490338i	$-0.163127\pi$
$647$	28686.0	1.74306	0.871532	+	0.490338i	$0.163127\pi$
$648$	−6531.00	−0.395929
$649$	−6072.00	−0.367252
$650$	0	0
$651$	−1960.00	−0.118001
$652$	−1604.00	−0.0963458
$653$	−9858.00	−0.590771	−0.295385	−	0.955378i	$-0.595448\pi$
$653$	−9858.00	−0.590771	−0.295385	+	0.955378i	$0.595448\pi$
$654$	−7752.00	−0.463497
$655$	0	0
$656$	15336.0	0.912759
$657$	−176.000	−0.0104512
$658$	−8190.00	−0.485227
$659$	−22824.0	−1.34916	−0.674580	−	0.738201i	$-0.735675\pi$
$659$	−22824.0	−1.34916	−0.674580	+	0.738201i	$0.735675\pi$
$660$	0	0
$661$	24212.0	1.42472	0.712358	−	0.701816i	$-0.247627\pi$
$661$	24212.0	1.42472	0.712358	+	0.701816i	$0.247627\pi$
$662$	9660.00	0.567140
$663$	7296.00	0.427380
$664$	−1890.00	−0.110461
$665$	0	0
$666$	11814.0	0.687362
$667$	−1512.00	−0.0877734
$668$	−180.000	−0.0104258
$669$	16136.0	0.932517
$670$	0	0
$671$	9130.00	0.525275
$672$	1260.00	0.0723297
$673$	17458.0	0.999935	0.499968	−	0.866044i	$-0.333345\pi$
$673$	17458.0	0.999935	0.499968	+	0.866044i	$0.333345\pi$
$674$	−19974.0	−1.14150
$675$	0	0
$676$	−753.000	−0.0428425
$677$	−14574.0	−0.827362	−0.413681	−	0.910422i	$-0.635757\pi$
$677$	−14574.0	−0.827362	−0.413681	+	0.910422i	$0.635757\pi$
$678$	15768.0	0.893166
$679$	−490.000	−0.0276944
$680$	0	0
$681$	2904.00	0.163409
$682$	2310.00	0.129699
$683$	27588.0	1.54557	0.772786	−	0.634667i	$-0.218863\pi$
$683$	27588.0	1.54557	0.772786	+	0.634667i	$0.218863\pi$
$684$	770.000	0.0430434
$685$	0	0
$686$	1029.00	0.0572703
$687$	11152.0	0.619324
$688$	24424.0	1.35342
$689$	16644.0	0.920299
$690$	0	0
$691$	10424.0	0.573875	0.286938	−	0.957949i	$-0.407363\pi$
$691$	10424.0	0.573875	0.286938	+	0.957949i	$0.407363\pi$
$692$	1626.00	0.0893226
$693$	847.000	0.0464284
$694$	−20664.0	−1.13025
$695$	0	0
$696$	−10584.0	−0.576416
$697$	−10368.0	−0.563438
$698$	18570.0	1.00700
$699$	10776.0	0.583098
$700$	0	0
$701$	3978.00	0.214332	0.107166	−	0.994241i	$-0.465822\pi$
$701$	3978.00	0.214332	0.107166	+	0.994241i	$0.465822\pi$
$702$	17328.0	0.931629
$703$	−25060.0	−1.34446
$704$	4763.00	0.254989
$705$	0	0
$706$	−11970.0	−0.638098
$707$	8778.00	0.466946
$708$	2208.00	0.117206
$709$	18794.0	0.995520	0.497760	−	0.867315i	$-0.334156\pi$
$709$	18794.0	0.995520	0.497760	+	0.867315i	$0.334156\pi$
$710$	0	0
$711$	−14872.0	−0.784449
$712$	24066.0	1.26673
$713$	840.000	0.0441210
$714$	−4032.00	−0.211336
$715$	0	0
$716$	−3252.00	−0.169739
$717$	−25920.0	−1.35007
$718$	22968.0	1.19381
$719$	33906.0	1.75867	0.879333	−	0.476208i	$-0.157989\pi$
$719$	33906.0	1.75867	0.879333	+	0.476208i	$0.157989\pi$
$720$	0	0
$721$	−4774.00	−0.246592
$722$	5877.00	0.302935
$723$	9280.00	0.477354
$724$	1820.00	0.0934251
$725$	0	0
$726$	1452.00	0.0742270
$727$	2446.00	0.124783	0.0623914	−	0.998052i	$-0.480127\pi$
$727$	2446.00	0.124783	0.0623914	+	0.998052i	$0.480127\pi$
$728$	5586.00	0.284383
$729$	19837.0	1.00782
$730$	0	0
$731$	−16512.0	−0.835456
$732$	−3320.00	−0.167638
$733$	20410.0	1.02846	0.514230	−	0.857653i	$-0.328078\pi$
$733$	20410.0	1.02846	0.514230	+	0.857653i	$0.328078\pi$
$734$	25278.0	1.27116
$735$	0	0
$736$	−540.000	−0.0270444
$737$	2156.00	0.107758
$738$	−7128.00	−0.355536
$739$	14564.0	0.724960	0.362480	−	0.931992i	$-0.381930\pi$
$739$	14564.0	0.724960	0.362480	+	0.931992i	$0.381930\pi$
$740$	0	0
$741$	−10640.0	−0.527490
$742$	−9198.00	−0.455080
$743$	7416.00	0.366173	0.183087	−	0.983097i	$-0.441391\pi$
$743$	7416.00	0.366173	0.183087	+	0.983097i	$0.441391\pi$
$744$	5880.00	0.289746
$745$	0	0
$746$	35754.0	1.75475
$747$	990.000	0.0484902
$748$	528.000	0.0258096
$749$	−2688.00	−0.131131
$750$	0	0
$751$	−17980.0	−0.873635	−0.436817	−	0.899550i	$-0.643894\pi$
$751$	−17980.0	−0.873635	−0.436817	+	0.899550i	$0.643894\pi$
$752$	27690.0	1.34275
$753$	−8352.00	−0.404202
$754$	14364.0	0.693775
$755$	0	0
$756$	−1064.00	−0.0511869
$757$	−3170.00	−0.152200	−0.0761001	−	0.997100i	$-0.524247\pi$
$757$	−3170.00	−0.152200	−0.0761001	+	0.997100i	$0.524247\pi$
$758$	−11724.0	−0.561787
$759$	528.000	0.0252506
$760$	0	0
$761$	−27492.0	−1.30957	−0.654786	−	0.755814i	$-0.727241\pi$
$761$	−27492.0	−1.30957	−0.654786	+	0.755814i	$0.727241\pi$
$762$	−4128.00	−0.196249
$763$	4522.00	0.214558
$764$	−1212.00	−0.0573935
$765$	0	0
$766$	−9738.00	−0.459332
$767$	20976.0	0.987483
$768$	−6052.00	−0.284353
$769$	2108.00	0.0988510	0.0494255	−	0.998778i	$-0.484261\pi$
$769$	2108.00	0.0988510	0.0494255	+	0.998778i	$0.484261\pi$
$770$	0	0
$771$	−16728.0	−0.781380
$772$	−2522.00	−0.117576
$773$	−32280.0	−1.50198	−0.750990	−	0.660313i	$-0.770423\pi$
$773$	−32280.0	−1.50198	−0.750990	+	0.660313i	$0.770423\pi$
$774$	−11352.0	−0.527182
$775$	0	0
$776$	1470.00	0.0680025
$777$	10024.0	0.462817
$778$	24498.0	1.12891
$779$	15120.0	0.695417
$780$	0	0
$781$	7128.00	0.326581
$782$	1728.00	0.0790194
$783$	19152.0	0.874121
$784$	−3479.00	−0.158482
$785$	0	0
$786$	−3096.00	−0.140497
$787$	−9578.00	−0.433823	−0.216912	−	0.976191i	$-0.569598\pi$
$787$	−9578.00	−0.433823	−0.216912	+	0.976191i	$0.569598\pi$
$788$	3474.00	0.157051
$789$	14784.0	0.667078
$790$	0	0
$791$	−9198.00	−0.413455
$792$	−2541.00	−0.114003
$793$	−31540.0	−1.41238
$794$	−8472.00	−0.378665
$795$	0	0
$796$	−2842.00	−0.126548
$797$	−11952.0	−0.531194	−0.265597	−	0.964084i	$-0.585569\pi$
$797$	−11952.0	−0.531194	−0.265597	+	0.964084i	$0.585569\pi$
$798$	5880.00	0.260839
$799$	−18720.0	−0.828869
$800$	0	0
$801$	−12606.0	−0.556069
$802$	31446.0	1.38453
$803$	176.000	0.00773463
$804$	−784.000	−0.0343900
$805$	0	0
$806$	−7980.00	−0.348739
$807$	24240.0	1.05736
$808$	−26334.0	−1.14657
$809$	−9030.00	−0.392433	−0.196216	−	0.980561i	$-0.562865\pi$
$809$	−9030.00	−0.392433	−0.196216	+	0.980561i	$0.562865\pi$
$810$	0	0
$811$	−37762.0	−1.63502	−0.817511	−	0.575913i	$-0.804647\pi$
$811$	−37762.0	−1.63502	−0.817511	+	0.575913i	$0.804647\pi$
$812$	−882.000	−0.0381184
$813$	35056.0	1.51226
$814$	−11814.0	−0.508698
$815$	0	0
$816$	13632.0	0.584823
$817$	24080.0	1.03115
$818$	−24468.0	−1.04585
$819$	−2926.00	−0.124838
$820$	0	0
$821$	−14334.0	−0.609330	−0.304665	−	0.952460i	$-0.598545\pi$
$821$	−14334.0	−0.609330	−0.304665	+	0.952460i	$0.598545\pi$
$822$	32760.0	1.39007
$823$	−13988.0	−0.592456	−0.296228	−	0.955117i	$-0.595729\pi$
$823$	−13988.0	−0.592456	−0.296228	+	0.955117i	$0.595729\pi$
$824$	14322.0	0.605498
$825$	0	0
$826$	−11592.0	−0.488302
$827$	22284.0	0.936990	0.468495	−	0.883466i	$-0.344796\pi$
$827$	22284.0	0.936990	0.468495	+	0.883466i	$0.344796\pi$
$828$	132.000	0.00554024
$829$	−12868.0	−0.539112	−0.269556	−	0.962985i	$-0.586877\pi$
$829$	−12868.0	−0.539112	−0.269556	+	0.962985i	$0.586877\pi$
$830$	0	0
$831$	20744.0	0.865946
$832$	−16454.0	−0.685625
$833$	2352.00	0.0978295
$834$	22056.0	0.915752
$835$	0	0
$836$	−770.000	−0.0318553
$837$	−10640.0	−0.439393
$838$	33156.0	1.36677
$839$	2826.00	0.116286	0.0581432	−	0.998308i	$-0.481482\pi$
$839$	2826.00	0.116286	0.0581432	+	0.998308i	$0.481482\pi$
$840$	0	0
$841$	−8513.00	−0.349051
$842$	−15018.0	−0.614673
$843$	−12024.0	−0.491256
$844$	5528.00	0.225452
$845$	0	0
$846$	−12870.0	−0.523026
$847$	−847.000	−0.0343604
$848$	31098.0	1.25933
$849$	−15688.0	−0.634171
$850$	0	0
$851$	−4296.00	−0.173049
$852$	−2592.00	−0.104226
$853$	17962.0	0.720993	0.360497	−	0.932761i	$-0.382607\pi$
$853$	17962.0	0.720993	0.360497	+	0.932761i	$0.382607\pi$
$854$	17430.0	0.698410
$855$	0	0
$856$	8064.00	0.321988
$857$	−47148.0	−1.87928	−0.939641	−	0.342161i	$-0.888841\pi$
$857$	−47148.0	−1.87928	−0.939641	+	0.342161i	$0.888841\pi$
$858$	−5016.00	−0.199584
$859$	34904.0	1.38639	0.693195	−	0.720750i	$-0.256202\pi$
$859$	34904.0	1.38639	0.693195	+	0.720750i	$0.256202\pi$
$860$	0	0
$861$	−6048.00	−0.239391
$862$	28440.0	1.12375
$863$	44052.0	1.73760	0.868799	−	0.495164i	$-0.164892\pi$
$863$	44052.0	1.73760	0.868799	+	0.495164i	$0.164892\pi$
$864$	6840.00	0.269330
$865$	0	0
$866$	−5826.00	−0.228609
$867$	10436.0	0.408795
$868$	490.000	0.0191609
$869$	14872.0	0.580550
$870$	0	0
$871$	−7448.00	−0.289743
$872$	−13566.0	−0.526838
$873$	−770.000	−0.0298517
$874$	−2520.00	−0.0975289
$875$	0	0
$876$	−64.0000	−0.00246845
$877$	36214.0	1.39437	0.697184	−	0.716893i	$-0.254436\pi$
$877$	36214.0	1.39437	0.697184	+	0.716893i	$0.254436\pi$
$878$	40980.0	1.57518
$879$	−23112.0	−0.886858
$880$	0	0
$881$	17046.0	0.651866	0.325933	−	0.945393i	$-0.394322\pi$
$881$	17046.0	0.651866	0.325933	+	0.945393i	$0.394322\pi$
$882$	1617.00	0.0617315
$883$	−41276.0	−1.57310	−0.786550	−	0.617526i	$-0.788135\pi$
$883$	−41276.0	−1.57310	−0.786550	+	0.617526i	$0.788135\pi$
$884$	−1824.00	−0.0693979
$885$	0	0
$886$	11484.0	0.435454
$887$	−6456.00	−0.244387	−0.122193	−	0.992506i	$-0.538993\pi$
$887$	−6456.00	−0.244387	−0.122193	+	0.992506i	$0.538993\pi$
$888$	−30072.0	−1.13643
$889$	2408.00	0.0908456
$890$	0	0
$891$	−3421.00	−0.128628
$892$	−4034.00	−0.151422
$893$	27300.0	1.02302
$894$	−6120.00	−0.228952
$895$	0	0
$896$	11613.0	0.432995
$897$	−1824.00	−0.0678947
$898$	−54810.0	−2.03679
$899$	−8820.00	−0.327212
$900$	0	0
$901$	−21024.0	−0.777371
$902$	7128.00	0.263122
$903$	−9632.00	−0.354964
$904$	27594.0	1.01522
$905$	0	0
$906$	34368.0	1.26027
$907$	11500.0	0.421005	0.210502	−	0.977593i	$-0.432490\pi$
$907$	11500.0	0.421005	0.210502	+	0.977593i	$0.432490\pi$
$908$	−726.000	−0.0265343
$909$	13794.0	0.503320
$910$	0	0
$911$	27396.0	0.996345	0.498172	−	0.867078i	$-0.334005\pi$
$911$	27396.0	0.996345	0.498172	+	0.867078i	$0.334005\pi$
$912$	−19880.0	−0.721812
$913$	−990.000	−0.0358863
$914$	30462.0	1.10240
$915$	0	0
$916$	−2788.00	−0.100566
$917$	1806.00	0.0650375
$918$	−21888.0	−0.786941
$919$	8840.00	0.317307	0.158653	−	0.987334i	$-0.449285\pi$
$919$	8840.00	0.317307	0.158653	+	0.987334i	$0.449285\pi$
$920$	0	0
$921$	−2440.00	−0.0872972
$922$	51570.0	1.84205
$923$	−24624.0	−0.878124
$924$	308.000	0.0109659
$925$	0	0
$926$	13344.0	0.473554
$927$	−7502.00	−0.265802
$928$	5670.00	0.200568
$929$	2874.00	0.101499	0.0507497	−	0.998711i	$-0.483839\pi$
$929$	2874.00	0.101499	0.0507497	+	0.998711i	$0.483839\pi$
$930$	0	0
$931$	−3430.00	−0.120745
$932$	−2694.00	−0.0946834
$933$	−27528.0	−0.965945
$934$	33300.0	1.16661
$935$	0	0
$936$	8778.00	0.306536
$937$	−7832.00	−0.273063	−0.136532	−	0.990636i	$-0.543596\pi$
$937$	−7832.00	−0.273063	−0.136532	+	0.990636i	$0.543596\pi$
$938$	4116.00	0.143275
$939$	41336.0	1.43658
$940$	0	0
$941$	16926.0	0.586368	0.293184	−	0.956056i	$-0.405285\pi$
$941$	16926.0	0.586368	0.293184	+	0.956056i	$0.405285\pi$
$942$	35616.0	1.23188
$943$	2592.00	0.0895092
$944$	39192.0	1.35126
$945$	0	0
$946$	11352.0	0.390154
$947$	17988.0	0.617245	0.308623	−	0.951185i	$-0.400132\pi$
$947$	17988.0	0.617245	0.308623	+	0.951185i	$0.400132\pi$
$948$	−5408.00	−0.185278
$949$	−608.000	−0.0207972
$950$	0	0
$951$	23736.0	0.809351
$952$	−7056.00	−0.240217
$953$	29142.0	0.990558	0.495279	−	0.868734i	$-0.335066\pi$
$953$	29142.0	0.990558	0.495279	+	0.868734i	$0.335066\pi$
$954$	−14454.0	−0.490530
$955$	0	0
$956$	6480.00	0.219224
$957$	−5544.00	−0.187264
$958$	47448.0	1.60018
$959$	−19110.0	−0.643477
$960$	0	0
$961$	−24891.0	−0.835521
$962$	40812.0	1.36781
$963$	−4224.00	−0.141346
$964$	−2320.00	−0.0775126
$965$	0	0
$966$	1008.00	0.0335734
$967$	−31160.0	−1.03623	−0.518117	−	0.855310i	$-0.673367\pi$
$967$	−31160.0	−1.03623	−0.518117	+	0.855310i	$0.673367\pi$
$968$	2541.00	0.0843707
$969$	13440.0	0.445568
$970$	0	0
$971$	−33036.0	−1.09184	−0.545920	−	0.837838i	$-0.683820\pi$
$971$	−33036.0	−1.09184	−0.545920	+	0.837838i	$0.683820\pi$
$972$	−2860.00	−0.0943771
$973$	−12866.0	−0.423911
$974$	−5772.00	−0.189884
$975$	0	0
$976$	−58930.0	−1.93269
$977$	−12786.0	−0.418690	−0.209345	−	0.977842i	$-0.567133\pi$
$977$	−12786.0	−0.418690	−0.209345	+	0.977842i	$0.567133\pi$
$978$	−19248.0	−0.629328
$979$	12606.0	0.411532
$980$	0	0
$981$	7106.00	0.231271
$982$	−39204.0	−1.27398
$983$	−24918.0	−0.808505	−0.404253	−	0.914647i	$-0.632468\pi$
$983$	−24918.0	−0.808505	−0.404253	+	0.914647i	$0.632468\pi$
$984$	18144.0	0.587815
$985$	0	0
$986$	−18144.0	−0.586027
$987$	−10920.0	−0.352166
$988$	2660.00	0.0856537
$989$	4128.00	0.132723
$990$	0	0
$991$	−7648.00	−0.245153	−0.122577	−	0.992459i	$-0.539116\pi$
$991$	−7648.00	−0.245153	−0.122577	+	0.992459i	$0.539116\pi$
$992$	−3150.00	−0.100819
$993$	12880.0	0.411616
$994$	13608.0	0.434225
$995$	0	0
$996$	360.000	0.0114528
$997$	31750.0	1.00856	0.504279	−	0.863541i	$-0.331758\pi$
$997$	31750.0	1.00856	0.504279	+	0.863541i	$0.331758\pi$
$998$	−53628.0	−1.70097
$999$	54416.0	1.72337

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.4.a.a.1.1		1
5.4	even	2		77.4.a.a.1.1	✓	1
15.14	odd	2		693.4.a.b.1.1		1
20.19	odd	2		1232.4.a.d.1.1		1
35.34	odd	2		539.4.a.a.1.1		1
55.54	odd	2		847.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.4.a.a.1.1	✓	1	5.4	even	2
539.4.a.a.1.1		1	35.34	odd	2
693.4.a.b.1.1		1	15.14	odd	2
847.4.a.a.1.1		1	55.54	odd	2
1232.4.a.d.1.1		1	20.19	odd	2
1925.4.a.a.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:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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