LMFDB - Embedded newform 363.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,4,Mod(1,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("363.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	363.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:	$21.4176933321$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	363.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -4.00000 q^{5} -3.00000 q^{6} +26.0000 q^{7} -15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} -4.00000 q^{5} -3.00000 q^{6} +26.0000 q^{7} -15.0000 q^{8} +9.00000 q^{9} -4.00000 q^{10} +21.0000 q^{12} +32.0000 q^{13} +26.0000 q^{14} +12.0000 q^{15} +41.0000 q^{16} -74.0000 q^{17} +9.00000 q^{18} +60.0000 q^{19} +28.0000 q^{20} -78.0000 q^{21} -182.000 q^{23} +45.0000 q^{24} -109.000 q^{25} +32.0000 q^{26} -27.0000 q^{27} -182.000 q^{28} +90.0000 q^{29} +12.0000 q^{30} -8.00000 q^{31} +161.000 q^{32} -74.0000 q^{34} -104.000 q^{35} -63.0000 q^{36} -66.0000 q^{37} +60.0000 q^{38} -96.0000 q^{39} +60.0000 q^{40} -422.000 q^{41} -78.0000 q^{42} -408.000 q^{43} -36.0000 q^{45} -182.000 q^{46} -506.000 q^{47} -123.000 q^{48} +333.000 q^{49} -109.000 q^{50} +222.000 q^{51} -224.000 q^{52} +348.000 q^{53} -27.0000 q^{54} -390.000 q^{56} -180.000 q^{57} +90.0000 q^{58} -200.000 q^{59} -84.0000 q^{60} -132.000 q^{61} -8.00000 q^{62} +234.000 q^{63} -167.000 q^{64} -128.000 q^{65} -1036.00 q^{67} +518.000 q^{68} +546.000 q^{69} -104.000 q^{70} +762.000 q^{71} -135.000 q^{72} +542.000 q^{73} -66.0000 q^{74} +327.000 q^{75} -420.000 q^{76} -96.0000 q^{78} +550.000 q^{79} -164.000 q^{80} +81.0000 q^{81} -422.000 q^{82} +132.000 q^{83} +546.000 q^{84} +296.000 q^{85} -408.000 q^{86} -270.000 q^{87} +570.000 q^{89} -36.0000 q^{90} +832.000 q^{91} +1274.00 q^{92} +24.0000 q^{93} -506.000 q^{94} -240.000 q^{95} -483.000 q^{96} +14.0000 q^{97} +333.000 q^{98} +O(q^{100})\)

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	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.00000	−0.875000
$5$	−4.00000	−0.357771	−0.178885	−	0.983870i	$-0.557249\pi$
$5$	−4.00000	−0.357771	−0.178885	+	0.983870i	$0.557249\pi$
$6$	−3.00000	−0.204124
$7$	26.0000	1.40387	0.701934	−	0.712242i	$-0.252320\pi$
$7$	26.0000	1.40387	0.701934	+	0.712242i	$0.252320\pi$
$8$	−15.0000	−0.662913
$9$	9.00000	0.333333
$10$	−4.00000	−0.126491
$11$	0	0
$11$	0	0
$12$	21.0000	0.505181
$13$	32.0000	0.682708	0.341354	−	0.939935i	$-0.389115\pi$
$13$	32.0000	0.682708	0.341354	+	0.939935i	$0.389115\pi$
$14$	26.0000	0.496342
$15$	12.0000	0.206559
$16$	41.0000	0.640625
$17$	−74.0000	−1.05574	−0.527872	−	0.849324i	$-0.677010\pi$
$17$	−74.0000	−1.05574	−0.527872	+	0.849324i	$0.677010\pi$
$18$	9.00000	0.117851
$19$	60.0000	0.724471	0.362235	−	0.932087i	$-0.382014\pi$
$19$	60.0000	0.724471	0.362235	+	0.932087i	$0.382014\pi$
$20$	28.0000	0.313050
$21$	−78.0000	−0.810524
$22$	0	0
$23$	−182.000	−1.64998	−0.824992	−	0.565145i	$-0.808820\pi$
$23$	−182.000	−1.64998	−0.824992	+	0.565145i	$0.808820\pi$
$24$	45.0000	0.382733
$25$	−109.000	−0.872000
$26$	32.0000	0.241374
$27$	−27.0000	−0.192450
$28$	−182.000	−1.22838
$29$	90.0000	0.576296	0.288148	−	0.957586i	$-0.406961\pi$
$29$	90.0000	0.576296	0.288148	+	0.957586i	$0.406961\pi$
$30$	12.0000	0.0730297
$31$	−8.00000	−0.0463498	−0.0231749	−	0.999731i	$-0.507377\pi$
$31$	−8.00000	−0.0463498	−0.0231749	+	0.999731i	$0.507377\pi$
$32$	161.000	0.889408
$33$	0	0
$34$	−74.0000	−0.373262
$35$	−104.000	−0.502263
$36$	−63.0000	−0.291667
$37$	−66.0000	−0.293252	−0.146626	−	0.989192i	$-0.546841\pi$
$37$	−66.0000	−0.293252	−0.146626	+	0.989192i	$0.546841\pi$
$38$	60.0000	0.256139
$39$	−96.0000	−0.394162
$40$	60.0000	0.237171
$41$	−422.000	−1.60745	−0.803724	−	0.595003i	$-0.797151\pi$
$41$	−422.000	−1.60745	−0.803724	+	0.595003i	$0.797151\pi$
$42$	−78.0000	−0.286563
$43$	−408.000	−1.44696	−0.723482	−	0.690344i	$-0.757459\pi$
$43$	−408.000	−1.44696	−0.723482	+	0.690344i	$0.757459\pi$
$44$	0	0
$45$	−36.0000	−0.119257
$46$	−182.000	−0.583357
$47$	−506.000	−1.57038	−0.785188	−	0.619257i	$-0.787434\pi$
$47$	−506.000	−1.57038	−0.785188	+	0.619257i	$0.787434\pi$
$48$	−123.000	−0.369865
$49$	333.000	0.970845
$50$	−109.000	−0.308299
$51$	222.000	0.609534
$52$	−224.000	−0.597369
$53$	348.000	0.901915	0.450957	−	0.892546i	$-0.351083\pi$
$53$	348.000	0.901915	0.450957	+	0.892546i	$0.351083\pi$
$54$	−27.0000	−0.0680414
$55$	0	0
$56$	−390.000	−0.930642
$57$	−180.000	−0.418273
$58$	90.0000	0.203751
$59$	−200.000	−0.441318	−0.220659	−	0.975351i	$-0.570821\pi$
$59$	−200.000	−0.441318	−0.220659	+	0.975351i	$0.570821\pi$
$60$	−84.0000	−0.180739
$61$	−132.000	−0.277063	−0.138532	−	0.990358i	$-0.544238\pi$
$61$	−132.000	−0.277063	−0.138532	+	0.990358i	$0.544238\pi$
$62$	−8.00000	−0.0163871
$63$	234.000	0.467956
$64$	−167.000	−0.326172
$65$	−128.000	−0.244253
$66$	0	0
$67$	−1036.00	−1.88907	−0.944534	−	0.328414i	$-0.893486\pi$
$67$	−1036.00	−1.88907	−0.944534	+	0.328414i	$0.893486\pi$
$68$	518.000	0.923775
$69$	546.000	0.952618
$70$	−104.000	−0.177577
$71$	762.000	1.27370	0.636850	−	0.770987i	$-0.280237\pi$
$71$	762.000	1.27370	0.636850	+	0.770987i	$0.280237\pi$
$72$	−135.000	−0.220971
$73$	542.000	0.868990	0.434495	−	0.900674i	$-0.356927\pi$
$73$	542.000	0.868990	0.434495	+	0.900674i	$0.356927\pi$
$74$	−66.0000	−0.103680
$75$	327.000	0.503449
$76$	−420.000	−0.633912
$77$	0	0
$78$	−96.0000	−0.139357
$79$	550.000	0.783289	0.391645	−	0.920117i	$-0.371906\pi$
$79$	550.000	0.783289	0.391645	+	0.920117i	$0.371906\pi$
$80$	−164.000	−0.229197
$81$	81.0000	0.111111
$82$	−422.000	−0.568318
$83$	132.000	0.174565	0.0872824	−	0.996184i	$-0.472182\pi$
$83$	132.000	0.174565	0.0872824	+	0.996184i	$0.472182\pi$
$84$	546.000	0.709208
$85$	296.000	0.377714
$86$	−408.000	−0.511579
$87$	−270.000	−0.332725
$88$	0	0
$89$	570.000	0.678875	0.339438	−	0.940629i	$-0.389763\pi$
$89$	570.000	0.678875	0.339438	+	0.940629i	$0.389763\pi$
$90$	−36.0000	−0.0421637
$91$	832.000	0.958432
$92$	1274.00	1.44374
$93$	24.0000	0.0267600
$94$	−506.000	−0.555212
$95$	−240.000	−0.259195
$96$	−483.000	−0.513500
$97$	14.0000	0.0146545	0.00732724	−	0.999973i	$-0.497668\pi$
$97$	14.0000	0.0146545	0.00732724	+	0.999973i	$0.497668\pi$
$98$	333.000	0.343246
$99$	0	0
$100$	763.000	0.763000
$101$	−1702.00	−1.67679	−0.838393	−	0.545067i	$-0.816504\pi$
$101$	−1702.00	−1.67679	−0.838393	+	0.545067i	$0.816504\pi$
$102$	222.000	0.215503
$103$	−1132.00	−1.08291	−0.541453	−	0.840731i	$-0.682126\pi$
$103$	−1132.00	−1.08291	−0.541453	+	0.840731i	$0.682126\pi$
$104$	−480.000	−0.452576
$105$	312.000	0.289982
$106$	348.000	0.318875
$107$	−564.000	−0.509570	−0.254785	−	0.966998i	$-0.582005\pi$
$107$	−564.000	−0.509570	−0.254785	+	0.966998i	$0.582005\pi$
$108$	189.000	0.168394
$109$	320.000	0.281197	0.140598	−	0.990067i	$-0.455097\pi$
$109$	320.000	0.281197	0.140598	+	0.990067i	$0.455097\pi$
$110$	0	0
$111$	198.000	0.169309
$112$	1066.00	0.899353
$113$	−2142.00	−1.78321	−0.891604	−	0.452817i	$-0.850419\pi$
$113$	−2142.00	−1.78321	−0.891604	+	0.452817i	$0.850419\pi$
$114$	−180.000	−0.147882
$115$	728.000	0.590316
$116$	−630.000	−0.504259
$117$	288.000	0.227569
$118$	−200.000	−0.156030
$119$	−1924.00	−1.48212
$120$	−180.000	−0.136931
$121$	0	0
$122$	−132.000	−0.0979567
$123$	1266.00	0.928060
$124$	56.0000	0.0405560
$125$	936.000	0.669747
$126$	234.000	0.165447
$127$	1606.00	1.12212	0.561061	−	0.827775i	$-0.310393\pi$
$127$	1606.00	1.12212	0.561061	+	0.827775i	$0.310393\pi$
$128$	−1455.00	−1.00473
$129$	1224.00	0.835405
$130$	−128.000	−0.0863565
$131$	1908.00	1.27254	0.636270	−	0.771466i	$-0.280476\pi$
$131$	1908.00	1.27254	0.636270	+	0.771466i	$0.280476\pi$
$132$	0	0
$133$	1560.00	1.01706
$134$	−1036.00	−0.667886
$135$	108.000	0.0688530
$136$	1110.00	0.699866
$137$	−2186.00	−1.36323	−0.681615	−	0.731711i	$-0.738722\pi$
$137$	−2186.00	−1.36323	−0.681615	+	0.731711i	$0.738722\pi$
$138$	546.000	0.336801
$139$	−2740.00	−1.67197	−0.835985	−	0.548753i	$-0.815103\pi$
$139$	−2740.00	−1.67197	−0.835985	+	0.548753i	$0.815103\pi$
$140$	728.000	0.439480
$141$	1518.00	0.906657
$142$	762.000	0.450321
$143$	0	0
$144$	369.000	0.213542
$145$	−360.000	−0.206182
$146$	542.000	0.307235
$147$	−999.000	−0.560518
$148$	462.000	0.256596
$149$	1310.00	0.720264	0.360132	−	0.932901i	$-0.382732\pi$
$149$	1310.00	0.720264	0.360132	+	0.932901i	$0.382732\pi$
$150$	327.000	0.177996
$151$	1198.00	0.645641	0.322821	−	0.946460i	$-0.395369\pi$
$151$	1198.00	0.645641	0.322821	+	0.946460i	$0.395369\pi$
$152$	−900.000	−0.480261
$153$	−666.000	−0.351914
$154$	0	0
$155$	32.0000	0.0165826
$156$	672.000	0.344891
$157$	2114.00	1.07462	0.537311	−	0.843384i	$-0.319440\pi$
$157$	2114.00	1.07462	0.537311	+	0.843384i	$0.319440\pi$
$158$	550.000	0.276934
$159$	−1044.00	−0.520721
$160$	−644.000	−0.318204
$161$	−4732.00	−2.31636
$162$	81.0000	0.0392837
$163$	3868.00	1.85868	0.929341	−	0.369223i	$-0.120376\pi$
$163$	3868.00	1.85868	0.929341	+	0.369223i	$0.120376\pi$
$164$	2954.00	1.40652
$165$	0	0
$166$	132.000	0.0617180
$167$	−2004.00	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−2004.00	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	1170.00	0.537306
$169$	−1173.00	−0.533910
$170$	296.000	0.133542
$171$	540.000	0.241490
$172$	2856.00	1.26609
$173$	−678.000	−0.297962	−0.148981	−	0.988840i	$-0.547599\pi$
$173$	−678.000	−0.297962	−0.148981	+	0.988840i	$0.547599\pi$
$174$	−270.000	−0.117636
$175$	−2834.00	−1.22417
$176$	0	0
$177$	600.000	0.254795
$178$	570.000	0.240019
$179$	−1680.00	−0.701503	−0.350752	−	0.936469i	$-0.614074\pi$
$179$	−1680.00	−0.701503	−0.350752	+	0.936469i	$0.614074\pi$
$180$	252.000	0.104350
$181$	−4358.00	−1.78966	−0.894828	−	0.446412i	$-0.852702\pi$
$181$	−4358.00	−1.78966	−0.894828	+	0.446412i	$0.852702\pi$
$182$	832.000	0.338857
$183$	396.000	0.159963
$184$	2730.00	1.09379
$185$	264.000	0.104917
$186$	24.0000	0.00946110
$187$	0	0
$188$	3542.00	1.37408
$189$	−702.000	−0.270175
$190$	−240.000	−0.0916391
$191$	−1778.00	−0.673568	−0.336784	−	0.941582i	$-0.609339\pi$
$191$	−1778.00	−0.673568	−0.336784	+	0.941582i	$0.609339\pi$
$192$	501.000	0.188315
$193$	3962.00	1.47767	0.738837	−	0.673884i	$-0.235375\pi$
$193$	3962.00	1.47767	0.738837	+	0.673884i	$0.235375\pi$
$194$	14.0000	0.00518114
$195$	384.000	0.141020
$196$	−2331.00	−0.849490
$197$	−374.000	−0.135261	−0.0676304	−	0.997710i	$-0.521544\pi$
$197$	−374.000	−0.135261	−0.0676304	+	0.997710i	$0.521544\pi$
$198$	0	0
$199$	2100.00	0.748066	0.374033	−	0.927415i	$-0.377975\pi$
$199$	2100.00	0.748066	0.374033	+	0.927415i	$0.377975\pi$
$200$	1635.00	0.578060
$201$	3108.00	1.09065
$202$	−1702.00	−0.592833
$203$	2340.00	0.809043
$204$	−1554.00	−0.533342
$205$	1688.00	0.575098
$206$	−1132.00	−0.382865
$207$	−1638.00	−0.549995
$208$	1312.00	0.437360
$209$	0	0
$210$	312.000	0.102524
$211$	−2232.00	−0.728233	−0.364117	−	0.931353i	$-0.618629\pi$
$211$	−2232.00	−0.728233	−0.364117	+	0.931353i	$0.618629\pi$
$212$	−2436.00	−0.789175
$213$	−2286.00	−0.735372
$214$	−564.000	−0.180160
$215$	1632.00	0.517681
$216$	405.000	0.127578
$217$	−208.000	−0.0650689
$218$	320.000	0.0994180
$219$	−1626.00	−0.501712
$220$	0	0
$221$	−2368.00	−0.720764
$222$	198.000	0.0598599
$223$	2128.00	0.639020	0.319510	−	0.947583i	$-0.396482\pi$
$223$	2128.00	0.639020	0.319510	+	0.947583i	$0.396482\pi$
$224$	4186.00	1.24861
$225$	−981.000	−0.290667
$226$	−2142.00	−0.630459
$227$	−2964.00	−0.866641	−0.433321	−	0.901240i	$-0.642658\pi$
$227$	−2964.00	−0.866641	−0.433321	+	0.901240i	$0.642658\pi$
$228$	1260.00	0.365989
$229$	−2550.00	−0.735846	−0.367923	−	0.929856i	$-0.619931\pi$
$229$	−2550.00	−0.735846	−0.367923	+	0.929856i	$0.619931\pi$
$230$	728.000	0.208708
$231$	0	0
$232$	−1350.00	−0.382034
$233$	3042.00	0.855314	0.427657	−	0.903941i	$-0.359339\pi$
$233$	3042.00	0.855314	0.427657	+	0.903941i	$0.359339\pi$
$234$	288.000	0.0804579
$235$	2024.00	0.561835
$236$	1400.00	0.386154
$237$	−1650.00	−0.452232
$238$	−1924.00	−0.524010
$239$	−2700.00	−0.730747	−0.365373	−	0.930861i	$-0.619059\pi$
$239$	−2700.00	−0.730747	−0.365373	+	0.930861i	$0.619059\pi$
$240$	492.000	0.132327
$241$	578.000	0.154491	0.0772453	−	0.997012i	$-0.475388\pi$
$241$	578.000	0.154491	0.0772453	+	0.997012i	$0.475388\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	924.000	0.242430
$245$	−1332.00	−0.347340
$246$	1266.00	0.328119
$247$	1920.00	0.494602
$248$	120.000	0.0307258
$249$	−396.000	−0.100785
$250$	936.000	0.236791
$251$	3752.00	0.943522	0.471761	−	0.881726i	$-0.343618\pi$
$251$	3752.00	0.943522	0.471761	+	0.881726i	$0.343618\pi$
$252$	−1638.00	−0.409462
$253$	0	0
$254$	1606.00	0.396730
$255$	−888.000	−0.218073
$256$	−119.000	−0.0290527
$257$	674.000	0.163591	0.0817957	−	0.996649i	$-0.473935\pi$
$257$	674.000	0.163591	0.0817957	+	0.996649i	$0.473935\pi$
$258$	1224.00	0.295360
$259$	−1716.00	−0.411687
$260$	896.000	0.213721
$261$	810.000	0.192099
$262$	1908.00	0.449911
$263$	4352.00	1.02036	0.510182	−	0.860066i	$-0.329578\pi$
$263$	4352.00	1.02036	0.510182	+	0.860066i	$0.329578\pi$
$264$	0	0
$265$	−1392.00	−0.322679
$266$	1560.00	0.359585
$267$	−1710.00	−0.391949
$268$	7252.00	1.65293
$269$	500.000	0.113329	0.0566646	−	0.998393i	$-0.481953\pi$
$269$	500.000	0.113329	0.0566646	+	0.998393i	$0.481953\pi$
$270$	108.000	0.0243432
$271$	6538.00	1.46552	0.732759	−	0.680489i	$-0.238232\pi$
$271$	6538.00	1.46552	0.732759	+	0.680489i	$0.238232\pi$
$272$	−3034.00	−0.676336
$273$	−2496.00	−0.553351
$274$	−2186.00	−0.481975
$275$	0	0
$276$	−3822.00	−0.833541
$277$	−124.000	−0.0268969	−0.0134484	−	0.999910i	$-0.504281\pi$
$277$	−124.000	−0.0268969	−0.0134484	+	0.999910i	$0.504281\pi$
$278$	−2740.00	−0.591131
$279$	−72.0000	−0.0154499
$280$	1560.00	0.332957
$281$	−3642.00	−0.773180	−0.386590	−	0.922252i	$-0.626347\pi$
$281$	−3642.00	−0.773180	−0.386590	+	0.922252i	$0.626347\pi$
$282$	1518.00	0.320552
$283$	−4648.00	−0.976307	−0.488154	−	0.872758i	$-0.662329\pi$
$283$	−4648.00	−0.976307	−0.488154	+	0.872758i	$0.662329\pi$
$284$	−5334.00	−1.11449
$285$	720.000	0.149646
$286$	0	0
$287$	−10972.0	−2.25664
$288$	1449.00	0.296469
$289$	563.000	0.114594
$290$	−360.000	−0.0728963
$291$	−42.0000	−0.00846077
$292$	−3794.00	−0.760367
$293$	3102.00	0.618501	0.309250	−	0.950981i	$-0.399922\pi$
$293$	3102.00	0.618501	0.309250	+	0.950981i	$0.399922\pi$
$294$	−999.000	−0.198173
$295$	800.000	0.157891
$296$	990.000	0.194401
$297$	0	0
$298$	1310.00	0.254652
$299$	−5824.00	−1.12646
$300$	−2289.00	−0.440518
$301$	−10608.0	−2.03135
$302$	1198.00	0.228269
$303$	5106.00	0.968093
$304$	2460.00	0.464114
$305$	528.000	0.0991252
$306$	−666.000	−0.124421
$307$	−1244.00	−0.231267	−0.115633	−	0.993292i	$-0.536890\pi$
$307$	−1244.00	−0.231267	−0.115633	+	0.993292i	$0.536890\pi$
$308$	0	0
$309$	3396.00	0.625216
$310$	32.0000	0.00586283
$311$	2082.00	0.379612	0.189806	−	0.981822i	$-0.439214\pi$
$311$	2082.00	0.379612	0.189806	+	0.981822i	$0.439214\pi$
$312$	1440.00	0.261295
$313$	2378.00	0.429433	0.214716	−	0.976676i	$-0.431117\pi$
$313$	2378.00	0.429433	0.214716	+	0.976676i	$0.431117\pi$
$314$	2114.00	0.379936
$315$	−936.000	−0.167421
$316$	−3850.00	−0.685378
$317$	−496.000	−0.0878806	−0.0439403	−	0.999034i	$-0.513991\pi$
$317$	−496.000	−0.0878806	−0.0439403	+	0.999034i	$0.513991\pi$
$318$	−1044.00	−0.184103
$319$	0	0
$320$	668.000	0.116695
$321$	1692.00	0.294200
$322$	−4732.00	−0.818957
$323$	−4440.00	−0.764855
$324$	−567.000	−0.0972222
$325$	−3488.00	−0.595321
$326$	3868.00	0.657143
$327$	−960.000	−0.162349
$328$	6330.00	1.06560
$329$	−13156.0	−2.20460
$330$	0	0
$331$	−2708.00	−0.449683	−0.224842	−	0.974395i	$-0.572186\pi$
$331$	−2708.00	−0.449683	−0.224842	+	0.974395i	$0.572186\pi$
$332$	−924.000	−0.152744
$333$	−594.000	−0.0977507
$334$	−2004.00	−0.328305
$335$	4144.00	0.675853
$336$	−3198.00	−0.519242
$337$	−4034.00	−0.652065	−0.326033	−	0.945359i	$-0.605712\pi$
$337$	−4034.00	−0.652065	−0.326033	+	0.945359i	$0.605712\pi$
$338$	−1173.00	−0.188766
$339$	6426.00	1.02954
$340$	−2072.00	−0.330500
$341$	0	0
$342$	540.000	0.0853797
$343$	−260.000	−0.0409291
$344$	6120.00	0.959210
$345$	−2184.00	−0.340819
$346$	−678.000	−0.105345
$347$	−11084.0	−1.71476	−0.857378	−	0.514687i	$-0.827908\pi$
$347$	−11084.0	−1.71476	−0.857378	+	0.514687i	$0.827908\pi$
$348$	1890.00	0.291134
$349$	3120.00	0.478538	0.239269	−	0.970953i	$-0.423092\pi$
$349$	3120.00	0.478538	0.239269	+	0.970953i	$0.423092\pi$
$350$	−2834.00	−0.432810
$351$	−864.000	−0.131387
$352$	0	0
$353$	−5622.00	−0.847674	−0.423837	−	0.905739i	$-0.639317\pi$
$353$	−5622.00	−0.847674	−0.423837	+	0.905739i	$0.639317\pi$
$354$	600.000	0.0900837
$355$	−3048.00	−0.455693
$356$	−3990.00	−0.594016
$357$	5772.00	0.855705
$358$	−1680.00	−0.248019
$359$	8500.00	1.24962	0.624809	−	0.780778i	$-0.285177\pi$
$359$	8500.00	1.24962	0.624809	+	0.780778i	$0.285177\pi$
$360$	540.000	0.0790569
$361$	−3259.00	−0.475142
$362$	−4358.00	−0.632739
$363$	0	0
$364$	−5824.00	−0.838628
$365$	−2168.00	−0.310899
$366$	396.000	0.0565553
$367$	7144.00	1.01611	0.508057	−	0.861324i	$-0.330364\pi$
$367$	7144.00	1.01611	0.508057	+	0.861324i	$0.330364\pi$
$368$	−7462.00	−1.05702
$369$	−3798.00	−0.535816
$370$	264.000	0.0370938
$371$	9048.00	1.26617
$372$	−168.000	−0.0234150
$373$	632.000	0.0877312	0.0438656	−	0.999037i	$-0.486033\pi$
$373$	632.000	0.0877312	0.0438656	+	0.999037i	$0.486033\pi$
$374$	0	0
$375$	−2808.00	−0.386679
$376$	7590.00	1.04102
$377$	2880.00	0.393442
$378$	−702.000	−0.0955211
$379$	−4220.00	−0.571944	−0.285972	−	0.958238i	$-0.592316\pi$
$379$	−4220.00	−0.571944	−0.285972	+	0.958238i	$0.592316\pi$
$380$	1680.00	0.226795
$381$	−4818.00	−0.647857
$382$	−1778.00	−0.238142
$383$	8458.00	1.12842	0.564208	−	0.825632i	$-0.309181\pi$
$383$	8458.00	1.12842	0.564208	+	0.825632i	$0.309181\pi$
$384$	4365.00	0.580079
$385$	0	0
$386$	3962.00	0.522437
$387$	−3672.00	−0.482321
$388$	−98.0000	−0.0128227
$389$	1740.00	0.226790	0.113395	−	0.993550i	$-0.463827\pi$
$389$	1740.00	0.226790	0.113395	+	0.993550i	$0.463827\pi$
$390$	384.000	0.0498579
$391$	13468.0	1.74196
$392$	−4995.00	−0.643586
$393$	−5724.00	−0.734701
$394$	−374.000	−0.0478219
$395$	−2200.00	−0.280238
$396$	0	0
$397$	−5126.00	−0.648027	−0.324013	−	0.946053i	$-0.605032\pi$
$397$	−5126.00	−0.648027	−0.324013	+	0.946053i	$0.605032\pi$
$398$	2100.00	0.264481
$399$	−4680.00	−0.587201
$400$	−4469.00	−0.558625
$401$	−3098.00	−0.385802	−0.192901	−	0.981218i	$-0.561790\pi$
$401$	−3098.00	−0.385802	−0.192901	+	0.981218i	$0.561790\pi$
$402$	3108.00	0.385604
$403$	−256.000	−0.0316433
$404$	11914.0	1.46719
$405$	−324.000	−0.0397523
$406$	2340.00	0.286040
$407$	0	0
$408$	−3330.00	−0.404068
$409$	−6390.00	−0.772531	−0.386265	−	0.922388i	$-0.626235\pi$
$409$	−6390.00	−0.772531	−0.386265	+	0.922388i	$0.626235\pi$
$410$	1688.00	0.203328
$411$	6558.00	0.787062
$412$	7924.00	0.947542
$413$	−5200.00	−0.619553
$414$	−1638.00	−0.194452
$415$	−528.000	−0.0624542
$416$	5152.00	0.607206
$417$	8220.00	0.965312
$418$	0	0
$419$	9760.00	1.13796	0.568982	−	0.822350i	$-0.307337\pi$
$419$	9760.00	1.13796	0.568982	+	0.822350i	$0.307337\pi$
$420$	−2184.00	−0.253734
$421$	−5138.00	−0.594800	−0.297400	−	0.954753i	$-0.596119\pi$
$421$	−5138.00	−0.594800	−0.297400	+	0.954753i	$0.596119\pi$
$422$	−2232.00	−0.257469
$423$	−4554.00	−0.523459
$424$	−5220.00	−0.597891
$425$	8066.00	0.920608
$426$	−2286.00	−0.259993
$427$	−3432.00	−0.388960
$428$	3948.00	0.445873
$429$	0	0
$430$	1632.00	0.183028
$431$	7008.00	0.783210	0.391605	−	0.920133i	$-0.371920\pi$
$431$	7008.00	0.783210	0.391605	+	0.920133i	$0.371920\pi$
$432$	−1107.00	−0.123288
$433$	5578.00	0.619080	0.309540	−	0.950886i	$-0.399825\pi$
$433$	5578.00	0.619080	0.309540	+	0.950886i	$0.399825\pi$
$434$	−208.000	−0.0230053
$435$	1080.00	0.119039
$436$	−2240.00	−0.246047
$437$	−10920.0	−1.19536
$438$	−1626.00	−0.177382
$439$	10430.0	1.13393	0.566967	−	0.823741i	$-0.308117\pi$
$439$	10430.0	1.13393	0.566967	+	0.823741i	$0.308117\pi$
$440$	0	0
$441$	2997.00	0.323615
$442$	−2368.00	−0.254829
$443$	−4432.00	−0.475329	−0.237664	−	0.971347i	$-0.576382\pi$
$443$	−4432.00	−0.475329	−0.237664	+	0.971347i	$0.576382\pi$
$444$	−1386.00	−0.148146
$445$	−2280.00	−0.242882
$446$	2128.00	0.225928
$447$	−3930.00	−0.415845
$448$	−4342.00	−0.457902
$449$	−6290.00	−0.661121	−0.330561	−	0.943785i	$-0.607238\pi$
$449$	−6290.00	−0.661121	−0.330561	+	0.943785i	$0.607238\pi$
$450$	−981.000	−0.102766
$451$	0	0
$452$	14994.0	1.56031
$453$	−3594.00	−0.372761
$454$	−2964.00	−0.306404
$455$	−3328.00	−0.342899
$456$	2700.00	0.277279
$457$	−3054.00	−0.312604	−0.156302	−	0.987709i	$-0.549957\pi$
$457$	−3054.00	−0.312604	−0.156302	+	0.987709i	$0.549957\pi$
$458$	−2550.00	−0.260161
$459$	1998.00	0.203178
$460$	−5096.00	−0.516527
$461$	−12882.0	−1.30146	−0.650732	−	0.759308i	$-0.725538\pi$
$461$	−12882.0	−1.30146	−0.650732	+	0.759308i	$0.725538\pi$
$462$	0	0
$463$	6148.00	0.617110	0.308555	−	0.951207i	$-0.400155\pi$
$463$	6148.00	0.617110	0.308555	+	0.951207i	$0.400155\pi$
$464$	3690.00	0.369190
$465$	−96.0000	−0.00957396
$466$	3042.00	0.302399
$467$	5124.00	0.507731	0.253866	−	0.967240i	$-0.418298\pi$
$467$	5124.00	0.507731	0.253866	+	0.967240i	$0.418298\pi$
$468$	−2016.00	−0.199123
$469$	−26936.0	−2.65200
$470$	2024.00	0.198639
$471$	−6342.00	−0.620433
$472$	3000.00	0.292555
$473$	0	0
$474$	−1650.00	−0.159888
$475$	−6540.00	−0.631738
$476$	13468.0	1.29686
$477$	3132.00	0.300638
$478$	−2700.00	−0.258358
$479$	16520.0	1.57582	0.787910	−	0.615790i	$-0.211163\pi$
$479$	16520.0	1.57582	0.787910	+	0.615790i	$0.211163\pi$
$480$	1932.00	0.183715
$481$	−2112.00	−0.200206
$482$	578.000	0.0546207
$483$	14196.0	1.33735
$484$	0	0
$485$	−56.0000	−0.00524295
$486$	−243.000	−0.0226805
$487$	524.000	0.0487571	0.0243785	−	0.999703i	$-0.492239\pi$
$487$	524.000	0.0487571	0.0243785	+	0.999703i	$0.492239\pi$
$488$	1980.00	0.183669
$489$	−11604.0	−1.07311
$490$	−1332.00	−0.122803
$491$	15028.0	1.38127	0.690636	−	0.723203i	$-0.257331\pi$
$491$	15028.0	1.38127	0.690636	+	0.723203i	$0.257331\pi$
$492$	−8862.00	−0.812052
$493$	−6660.00	−0.608421
$494$	1920.00	0.174868
$495$	0	0
$496$	−328.000	−0.0296928
$497$	19812.0	1.78811
$498$	−396.000	−0.0356329
$499$	9020.00	0.809200	0.404600	−	0.914494i	$-0.367411\pi$
$499$	9020.00	0.809200	0.404600	+	0.914494i	$0.367411\pi$
$500$	−6552.00	−0.586029
$501$	6012.00	0.536120
$502$	3752.00	0.333586
$503$	14812.0	1.31299	0.656495	−	0.754330i	$-0.272038\pi$
$503$	14812.0	1.31299	0.656495	+	0.754330i	$0.272038\pi$
$504$	−3510.00	−0.310214
$505$	6808.00	0.599905
$506$	0	0
$507$	3519.00	0.308253
$508$	−11242.0	−0.981856
$509$	12660.0	1.10245	0.551223	−	0.834358i	$-0.314161\pi$
$509$	12660.0	1.10245	0.551223	+	0.834358i	$0.314161\pi$
$510$	−888.000	−0.0771006
$511$	14092.0	1.21995
$512$	11521.0	0.994455
$513$	−1620.00	−0.139424
$514$	674.000	0.0578383
$515$	4528.00	0.387432
$516$	−8568.00	−0.730979
$517$	0	0
$518$	−1716.00	−0.145553
$519$	2034.00	0.172028
$520$	1920.00	0.161918
$521$	−3738.00	−0.314328	−0.157164	−	0.987573i	$-0.550235\pi$
$521$	−3738.00	−0.314328	−0.157164	+	0.987573i	$0.550235\pi$
$522$	810.000	0.0679171
$523$	6352.00	0.531078	0.265539	−	0.964100i	$-0.414450\pi$
$523$	6352.00	0.531078	0.265539	+	0.964100i	$0.414450\pi$
$524$	−13356.0	−1.11347
$525$	8502.00	0.706777
$526$	4352.00	0.360753
$527$	592.000	0.0489334
$528$	0	0
$529$	20957.0	1.72245
$530$	−1392.00	−0.114084
$531$	−1800.00	−0.147106
$532$	−10920.0	−0.889929
$533$	−13504.0	−1.09742
$534$	−1710.00	−0.138575
$535$	2256.00	0.182309
$536$	15540.0	1.25229
$537$	5040.00	0.405013
$538$	500.000	0.0400679
$539$	0	0
$540$	−756.000	−0.0602464
$541$	24728.0	1.96514	0.982569	−	0.185898i	$-0.0595193\pi$
$541$	24728.0	1.96514	0.982569	+	0.185898i	$0.0595193\pi$
$542$	6538.00	0.518139
$543$	13074.0	1.03326
$544$	−11914.0	−0.938986
$545$	−1280.00	−0.100604
$546$	−2496.00	−0.195639
$547$	22756.0	1.77875	0.889375	−	0.457178i	$-0.151140\pi$
$547$	22756.0	1.77875	0.889375	+	0.457178i	$0.151140\pi$
$548$	15302.0	1.19283
$549$	−1188.00	−0.0923545
$550$	0	0
$551$	5400.00	0.417509
$552$	−8190.00	−0.631503
$553$	14300.0	1.09963
$554$	−124.000	−0.00950949
$555$	−792.000	−0.0605739
$556$	19180.0	1.46297
$557$	9526.00	0.724649	0.362325	−	0.932052i	$-0.381983\pi$
$557$	9526.00	0.724649	0.362325	+	0.932052i	$0.381983\pi$
$558$	−72.0000	−0.00546237
$559$	−13056.0	−0.987853
$560$	−4264.00	−0.321762
$561$	0	0
$562$	−3642.00	−0.273360
$563$	−12068.0	−0.903385	−0.451692	−	0.892174i	$-0.649180\pi$
$563$	−12068.0	−0.903385	−0.451692	+	0.892174i	$0.649180\pi$
$564$	−10626.0	−0.793325
$565$	8568.00	0.637980
$566$	−4648.00	−0.345177
$567$	2106.00	0.155985
$568$	−11430.0	−0.844352
$569$	−15090.0	−1.11179	−0.555893	−	0.831254i	$-0.687623\pi$
$569$	−15090.0	−1.11179	−0.555893	+	0.831254i	$0.687623\pi$
$570$	720.000	0.0529079
$571$	−4412.00	−0.323356	−0.161678	−	0.986844i	$-0.551691\pi$
$571$	−4412.00	−0.323356	−0.161678	+	0.986844i	$0.551691\pi$
$572$	0	0
$573$	5334.00	0.388885
$574$	−10972.0	−0.797844
$575$	19838.0	1.43879
$576$	−1503.00	−0.108724
$577$	−3906.00	−0.281818	−0.140909	−	0.990023i	$-0.545002\pi$
$577$	−3906.00	−0.281818	−0.140909	+	0.990023i	$0.545002\pi$
$578$	563.000	0.0405151
$579$	−11886.0	−0.853135
$580$	2520.00	0.180409
$581$	3432.00	0.245066
$582$	−42.0000	−0.00299133
$583$	0	0
$584$	−8130.00	−0.576065
$585$	−1152.00	−0.0814177
$586$	3102.00	0.218673
$587$	−12016.0	−0.844895	−0.422448	−	0.906387i	$-0.638829\pi$
$587$	−12016.0	−0.844895	−0.422448	+	0.906387i	$0.638829\pi$
$588$	6993.00	0.490453
$589$	−480.000	−0.0335790
$590$	800.000	0.0558228
$591$	1122.00	0.0780929
$592$	−2706.00	−0.187865
$593$	11342.0	0.785430	0.392715	−	0.919660i	$-0.371536\pi$
$593$	11342.0	0.785430	0.392715	+	0.919660i	$0.371536\pi$
$594$	0	0
$595$	7696.00	0.530261
$596$	−9170.00	−0.630231
$597$	−6300.00	−0.431896
$598$	−5824.00	−0.398263
$599$	20690.0	1.41130	0.705651	−	0.708559i	$-0.250654\pi$
$599$	20690.0	1.41130	0.705651	+	0.708559i	$0.250654\pi$
$600$	−4905.00	−0.333743
$601$	598.000	0.0405872	0.0202936	−	0.999794i	$-0.493540\pi$
$601$	598.000	0.0405872	0.0202936	+	0.999794i	$0.493540\pi$
$602$	−10608.0	−0.718189
$603$	−9324.00	−0.629689
$604$	−8386.00	−0.564936
$605$	0	0
$606$	5106.00	0.342272
$607$	166.000	0.0111001	0.00555003	−	0.999985i	$-0.498233\pi$
$607$	166.000	0.0111001	0.00555003	+	0.999985i	$0.498233\pi$
$608$	9660.00	0.644350
$609$	−7020.00	−0.467101
$610$	528.000	0.0350461
$611$	−16192.0	−1.07211
$612$	4662.00	0.307925
$613$	−20108.0	−1.32488	−0.662442	−	0.749113i	$-0.730480\pi$
$613$	−20108.0	−1.32488	−0.662442	+	0.749113i	$0.730480\pi$
$614$	−1244.00	−0.0817651
$615$	−5064.00	−0.332033
$616$	0	0
$617$	−2286.00	−0.149159	−0.0745793	−	0.997215i	$-0.523761\pi$
$617$	−2286.00	−0.149159	−0.0745793	+	0.997215i	$0.523761\pi$
$618$	3396.00	0.221047
$619$	−25660.0	−1.66618	−0.833088	−	0.553141i	$-0.813429\pi$
$619$	−25660.0	−1.66618	−0.833088	+	0.553141i	$0.813429\pi$
$620$	−224.000	−0.0145098
$621$	4914.00	0.317539
$622$	2082.00	0.134213
$623$	14820.0	0.953051
$624$	−3936.00	−0.252510
$625$	9881.00	0.632384
$626$	2378.00	0.151827
$627$	0	0
$628$	−14798.0	−0.940294
$629$	4884.00	0.309599
$630$	−936.000	−0.0591923
$631$	−11408.0	−0.719723	−0.359862	−	0.933006i	$-0.617176\pi$
$631$	−11408.0	−0.719723	−0.359862	+	0.933006i	$0.617176\pi$
$632$	−8250.00	−0.519252
$633$	6696.00	0.420446
$634$	−496.000	−0.0310705
$635$	−6424.00	−0.401462
$636$	7308.00	0.455631
$637$	10656.0	0.662804
$638$	0	0
$639$	6858.00	0.424567
$640$	5820.00	0.359462
$641$	−3378.00	−0.208148	−0.104074	−	0.994570i	$-0.533188\pi$
$641$	−3378.00	−0.208148	−0.104074	+	0.994570i	$0.533188\pi$
$642$	1692.00	0.104015
$643$	−11212.0	−0.687649	−0.343824	−	0.939034i	$-0.611722\pi$
$643$	−11212.0	−0.687649	−0.343824	+	0.939034i	$0.611722\pi$
$644$	33124.0	2.02681
$645$	−4896.00	−0.298883
$646$	−4440.00	−0.270417
$647$	−86.0000	−0.00522567	−0.00261284	−	0.999997i	$-0.500832\pi$
$647$	−86.0000	−0.00522567	−0.00261284	+	0.999997i	$0.500832\pi$
$648$	−1215.00	−0.0736570
$649$	0	0
$650$	−3488.00	−0.210478
$651$	624.000	0.0375676
$652$	−27076.0	−1.62635
$653$	−4432.00	−0.265601	−0.132801	−	0.991143i	$-0.542397\pi$
$653$	−4432.00	−0.265601	−0.132801	+	0.991143i	$0.542397\pi$
$654$	−960.000	−0.0573990
$655$	−7632.00	−0.455278
$656$	−17302.0	−1.02977
$657$	4878.00	0.289663
$658$	−13156.0	−0.779444
$659$	−4580.00	−0.270731	−0.135365	−	0.990796i	$-0.543221\pi$
$659$	−4580.00	−0.270731	−0.135365	+	0.990796i	$0.543221\pi$
$660$	0	0
$661$	4282.00	0.251967	0.125984	−	0.992032i	$-0.459791\pi$
$661$	4282.00	0.251967	0.125984	+	0.992032i	$0.459791\pi$
$662$	−2708.00	−0.158987
$663$	7104.00	0.416133
$664$	−1980.00	−0.115721
$665$	−6240.00	−0.363875
$666$	−594.000	−0.0345601
$667$	−16380.0	−0.950879
$668$	14028.0	0.812514
$669$	−6384.00	−0.368938
$670$	4144.00	0.238950
$671$	0	0
$672$	−12558.0	−0.720886
$673$	−8438.00	−0.483300	−0.241650	−	0.970363i	$-0.577689\pi$
$673$	−8438.00	−0.483300	−0.241650	+	0.970363i	$0.577689\pi$
$674$	−4034.00	−0.230540
$675$	2943.00	0.167816
$676$	8211.00	0.467171
$677$	−34494.0	−1.95822	−0.979108	−	0.203341i	$-0.934820\pi$
$677$	−34494.0	−1.95822	−0.979108	+	0.203341i	$0.934820\pi$
$678$	6426.00	0.363996
$679$	364.000	0.0205730
$680$	−4440.00	−0.250392
$681$	8892.00	0.500356
$682$	0	0
$683$	−13712.0	−0.768192	−0.384096	−	0.923293i	$-0.625487\pi$
$683$	−13712.0	−0.768192	−0.384096	+	0.923293i	$0.625487\pi$
$684$	−3780.00	−0.211304
$685$	8744.00	0.487724
$686$	−260.000	−0.0144706
$687$	7650.00	0.424841
$688$	−16728.0	−0.926961
$689$	11136.0	0.615744
$690$	−2184.00	−0.120498
$691$	11372.0	0.626066	0.313033	−	0.949742i	$-0.398655\pi$
$691$	11372.0	0.626066	0.313033	+	0.949742i	$0.398655\pi$
$692$	4746.00	0.260717
$693$	0	0
$694$	−11084.0	−0.606258
$695$	10960.0	0.598182
$696$	4050.00	0.220567
$697$	31228.0	1.69705
$698$	3120.00	0.169189
$699$	−9126.00	−0.493815
$700$	19838.0	1.07115
$701$	6398.00	0.344721	0.172360	−	0.985034i	$-0.444861\pi$
$701$	6398.00	0.344721	0.172360	+	0.985034i	$0.444861\pi$
$702$	−864.000	−0.0464524
$703$	−3960.00	−0.212453
$704$	0	0
$705$	−6072.00	−0.324376
$706$	−5622.00	−0.299698
$707$	−44252.0	−2.35399
$708$	−4200.00	−0.222946
$709$	−5830.00	−0.308816	−0.154408	−	0.988007i	$-0.549347\pi$
$709$	−5830.00	−0.308816	−0.154408	+	0.988007i	$0.549347\pi$
$710$	−3048.00	−0.161112
$711$	4950.00	0.261096
$712$	−8550.00	−0.450035
$713$	1456.00	0.0764763
$714$	5772.00	0.302537
$715$	0	0
$716$	11760.0	0.613815
$717$	8100.00	0.421897
$718$	8500.00	0.441807
$719$	34530.0	1.79103	0.895516	−	0.445030i	$-0.146807\pi$
$719$	34530.0	1.79103	0.895516	+	0.445030i	$0.146807\pi$
$720$	−1476.00	−0.0763990
$721$	−29432.0	−1.52026
$722$	−3259.00	−0.167988
$723$	−1734.00	−0.0891952
$724$	30506.0	1.56595
$725$	−9810.00	−0.502530
$726$	0	0
$727$	−17316.0	−0.883377	−0.441688	−	0.897169i	$-0.645620\pi$
$727$	−17316.0	−0.883377	−0.441688	+	0.897169i	$0.645620\pi$
$728$	−12480.0	−0.635357
$729$	729.000	0.0370370
$730$	−2168.00	−0.109920
$731$	30192.0	1.52762
$732$	−2772.00	−0.139967
$733$	27072.0	1.36416	0.682079	−	0.731279i	$-0.261076\pi$
$733$	27072.0	1.36416	0.682079	+	0.731279i	$0.261076\pi$
$734$	7144.00	0.359250
$735$	3996.00	0.200537
$736$	−29302.0	−1.46751
$737$	0	0
$738$	−3798.00	−0.189439
$739$	17320.0	0.862147	0.431073	−	0.902317i	$-0.358135\pi$
$739$	17320.0	0.862147	0.431073	+	0.902317i	$0.358135\pi$
$740$	−1848.00	−0.0918025
$741$	−5760.00	−0.285559
$742$	9048.00	0.447658
$743$	−14588.0	−0.720299	−0.360149	−	0.932895i	$-0.617274\pi$
$743$	−14588.0	−0.720299	−0.360149	+	0.932895i	$0.617274\pi$
$744$	−360.000	−0.0177396
$745$	−5240.00	−0.257690
$746$	632.000	0.0310176
$747$	1188.00	0.0581883
$748$	0	0
$749$	−14664.0	−0.715368
$750$	−2808.00	−0.136712
$751$	26152.0	1.27071	0.635353	−	0.772222i	$-0.280855\pi$
$751$	26152.0	1.27071	0.635353	+	0.772222i	$0.280855\pi$
$752$	−20746.0	−1.00602
$753$	−11256.0	−0.544743
$754$	2880.00	0.139103
$755$	−4792.00	−0.230992
$756$	4914.00	0.236403
$757$	−1066.00	−0.0511815	−0.0255908	−	0.999673i	$-0.508147\pi$
$757$	−1066.00	−0.0511815	−0.0255908	+	0.999673i	$0.508147\pi$
$758$	−4220.00	−0.202213
$759$	0	0
$760$	3600.00	0.171823
$761$	37518.0	1.78716	0.893578	−	0.448907i	$-0.148187\pi$
$761$	37518.0	1.78716	0.893578	+	0.448907i	$0.148187\pi$
$762$	−4818.00	−0.229052
$763$	8320.00	0.394763
$764$	12446.0	0.589372
$765$	2664.00	0.125905
$766$	8458.00	0.398956
$767$	−6400.00	−0.301292
$768$	357.000	0.0167736
$769$	17290.0	0.810785	0.405392	−	0.914143i	$-0.367135\pi$
$769$	17290.0	0.810785	0.405392	+	0.914143i	$0.367135\pi$
$770$	0	0
$771$	−2022.00	−0.0944495
$772$	−27734.0	−1.29296
$773$	−17172.0	−0.799009	−0.399504	−	0.916731i	$-0.630818\pi$
$773$	−17172.0	−0.799009	−0.399504	+	0.916731i	$0.630818\pi$
$774$	−3672.00	−0.170526
$775$	872.000	0.0404170
$776$	−210.000	−0.00971464
$777$	5148.00	0.237688
$778$	1740.00	0.0801825
$779$	−25320.0	−1.16455
$780$	−2688.00	−0.123392
$781$	0	0
$782$	13468.0	0.615876
$783$	−2430.00	−0.110908
$784$	13653.0	0.621948
$785$	−8456.00	−0.384468
$786$	−5724.00	−0.259756
$787$	9536.00	0.431921	0.215960	−	0.976402i	$-0.430712\pi$
$787$	9536.00	0.431921	0.215960	+	0.976402i	$0.430712\pi$
$788$	2618.00	0.118353
$789$	−13056.0	−0.589108
$790$	−2200.00	−0.0990791
$791$	−55692.0	−2.50339
$792$	0	0
$793$	−4224.00	−0.189153
$794$	−5126.00	−0.229112
$795$	4176.00	0.186299
$796$	−14700.0	−0.654557
$797$	−20516.0	−0.911812	−0.455906	−	0.890028i	$-0.650685\pi$
$797$	−20516.0	−0.911812	−0.455906	+	0.890028i	$0.650685\pi$
$798$	−4680.00	−0.207607
$799$	37444.0	1.65791
$800$	−17549.0	−0.775564
$801$	5130.00	0.226292
$802$	−3098.00	−0.136402
$803$	0	0
$804$	−21756.0	−0.954322
$805$	18928.0	0.828726
$806$	−256.000	−0.0111876
$807$	−1500.00	−0.0654306
$808$	25530.0	1.11156
$809$	−22470.0	−0.976518	−0.488259	−	0.872699i	$-0.662368\pi$
$809$	−22470.0	−0.976518	−0.488259	+	0.872699i	$0.662368\pi$
$810$	−324.000	−0.0140546
$811$	3368.00	0.145828	0.0729140	−	0.997338i	$-0.476770\pi$
$811$	3368.00	0.145828	0.0729140	+	0.997338i	$0.476770\pi$
$812$	−16380.0	−0.707913
$813$	−19614.0	−0.846117
$814$	0	0
$815$	−15472.0	−0.664982
$816$	9102.00	0.390483
$817$	−24480.0	−1.04828
$818$	−6390.00	−0.273131
$819$	7488.00	0.319477
$820$	−11816.0	−0.503211
$821$	10738.0	0.456466	0.228233	−	0.973607i	$-0.426705\pi$
$821$	10738.0	0.456466	0.228233	+	0.973607i	$0.426705\pi$
$822$	6558.00	0.278268
$823$	−15912.0	−0.673946	−0.336973	−	0.941514i	$-0.609403\pi$
$823$	−15912.0	−0.673946	−0.336973	+	0.941514i	$0.609403\pi$
$824$	16980.0	0.717872
$825$	0	0
$826$	−5200.00	−0.219045
$827$	−22924.0	−0.963900	−0.481950	−	0.876199i	$-0.660071\pi$
$827$	−22924.0	−0.963900	−0.481950	+	0.876199i	$0.660071\pi$
$828$	11466.0	0.481245
$829$	−41690.0	−1.74663	−0.873313	−	0.487159i	$-0.838033\pi$
$829$	−41690.0	−1.74663	−0.873313	+	0.487159i	$0.838033\pi$
$830$	−528.000	−0.0220809
$831$	372.000	0.0155289
$832$	−5344.00	−0.222680
$833$	−24642.0	−1.02496
$834$	8220.00	0.341289
$835$	8016.00	0.332222
$836$	0	0
$837$	216.000	0.00892001
$838$	9760.00	0.402331
$839$	−16450.0	−0.676898	−0.338449	−	0.940985i	$-0.609902\pi$
$839$	−16450.0	−0.676898	−0.338449	+	0.940985i	$0.609902\pi$
$840$	−4680.00	−0.192233
$841$	−16289.0	−0.667883
$842$	−5138.00	−0.210294
$843$	10926.0	0.446396
$844$	15624.0	0.637204
$845$	4692.00	0.191017
$846$	−4554.00	−0.185071
$847$	0	0
$848$	14268.0	0.577789
$849$	13944.0	0.563671
$850$	8066.00	0.325484
$851$	12012.0	0.483861
$852$	16002.0	0.643450
$853$	30892.0	1.24000	0.620001	−	0.784601i	$-0.287132\pi$
$853$	30892.0	1.24000	0.620001	+	0.784601i	$0.287132\pi$
$854$	−3432.00	−0.137518
$855$	−2160.00	−0.0863982
$856$	8460.00	0.337800
$857$	38906.0	1.55076	0.775381	−	0.631493i	$-0.217558\pi$
$857$	38906.0	1.55076	0.775381	+	0.631493i	$0.217558\pi$
$858$	0	0
$859$	−1020.00	−0.0405145	−0.0202572	−	0.999795i	$-0.506449\pi$
$859$	−1020.00	−0.0405145	−0.0202572	+	0.999795i	$0.506449\pi$
$860$	−11424.0	−0.452971
$861$	32916.0	1.30287
$862$	7008.00	0.276907
$863$	15078.0	0.594741	0.297370	−	0.954762i	$-0.403890\pi$
$863$	15078.0	0.594741	0.297370	+	0.954762i	$0.403890\pi$
$864$	−4347.00	−0.171167
$865$	2712.00	0.106602
$866$	5578.00	0.218878
$867$	−1689.00	−0.0661608
$868$	1456.00	0.0569353
$869$	0	0
$870$	1080.00	0.0420867
$871$	−33152.0	−1.28968
$872$	−4800.00	−0.186409
$873$	126.000	0.00488483
$874$	−10920.0	−0.422625
$875$	24336.0	0.940237
$876$	11382.0	0.438998
$877$	−22704.0	−0.874184	−0.437092	−	0.899417i	$-0.643992\pi$
$877$	−22704.0	−0.874184	−0.437092	+	0.899417i	$0.643992\pi$
$878$	10430.0	0.400906
$879$	−9306.00	−0.357092
$880$	0	0
$881$	−19358.0	−0.740281	−0.370141	−	0.928976i	$-0.620690\pi$
$881$	−19358.0	−0.740281	−0.370141	+	0.928976i	$0.620690\pi$
$882$	2997.00	0.114415
$883$	−11252.0	−0.428833	−0.214417	−	0.976742i	$-0.568785\pi$
$883$	−11252.0	−0.428833	−0.214417	+	0.976742i	$0.568785\pi$
$884$	16576.0	0.630669
$885$	−2400.00	−0.0911583
$886$	−4432.00	−0.168054
$887$	−43684.0	−1.65362	−0.826812	−	0.562478i	$-0.809848\pi$
$887$	−43684.0	−1.65362	−0.826812	+	0.562478i	$0.809848\pi$
$888$	−2970.00	−0.112237
$889$	41756.0	1.57531
$890$	−2280.00	−0.0858717
$891$	0	0
$892$	−14896.0	−0.559142
$893$	−30360.0	−1.13769
$894$	−3930.00	−0.147023
$895$	6720.00	0.250977
$896$	−37830.0	−1.41050
$897$	17472.0	0.650360
$898$	−6290.00	−0.233742
$899$	−720.000	−0.0267112
$900$	6867.00	0.254333
$901$	−25752.0	−0.952190
$902$	0	0
$903$	31824.0	1.17280
$904$	32130.0	1.18211
$905$	17432.0	0.640287
$906$	−3594.00	−0.131791
$907$	45804.0	1.67684	0.838422	−	0.545022i	$-0.183479\pi$
$907$	45804.0	1.67684	0.838422	+	0.545022i	$0.183479\pi$
$908$	20748.0	0.758311
$909$	−15318.0	−0.558928
$910$	−3328.00	−0.121233
$911$	−15318.0	−0.557089	−0.278544	−	0.960423i	$-0.589852\pi$
$911$	−15318.0	−0.557089	−0.278544	+	0.960423i	$0.589852\pi$
$912$	−7380.00	−0.267956
$913$	0	0
$914$	−3054.00	−0.110522
$915$	−1584.00	−0.0572300
$916$	17850.0	0.643865
$917$	49608.0	1.78648
$918$	1998.00	0.0718342
$919$	−11350.0	−0.407401	−0.203701	−	0.979033i	$-0.565297\pi$
$919$	−11350.0	−0.407401	−0.203701	+	0.979033i	$0.565297\pi$
$920$	−10920.0	−0.391328
$921$	3732.00	0.133522
$922$	−12882.0	−0.460137
$923$	24384.0	0.869566
$924$	0	0
$925$	7194.00	0.255716
$926$	6148.00	0.218181
$927$	−10188.0	−0.360969
$928$	14490.0	0.512562
$929$	33030.0	1.16650	0.583250	−	0.812292i	$-0.301781\pi$
$929$	33030.0	1.16650	0.583250	+	0.812292i	$0.301781\pi$
$930$	−96.0000	−0.00338491
$931$	19980.0	0.703349
$932$	−21294.0	−0.748399
$933$	−6246.00	−0.219169
$934$	5124.00	0.179510
$935$	0	0
$936$	−4320.00	−0.150859
$937$	10006.0	0.348860	0.174430	−	0.984670i	$-0.444192\pi$
$937$	10006.0	0.348860	0.174430	+	0.984670i	$0.444192\pi$
$938$	−26936.0	−0.937624
$939$	−7134.00	−0.247933
$940$	−14168.0	−0.491606
$941$	−2622.00	−0.0908340	−0.0454170	−	0.998968i	$-0.514462\pi$
$941$	−2622.00	−0.0908340	−0.0454170	+	0.998968i	$0.514462\pi$
$942$	−6342.00	−0.219356
$943$	76804.0	2.65226
$944$	−8200.00	−0.282720
$945$	2808.00	0.0966606
$946$	0	0
$947$	−39876.0	−1.36832	−0.684158	−	0.729334i	$-0.739830\pi$
$947$	−39876.0	−1.36832	−0.684158	+	0.729334i	$0.739830\pi$
$948$	11550.0	0.395703
$949$	17344.0	0.593267
$950$	−6540.00	−0.223353
$951$	1488.00	0.0507379
$952$	28860.0	0.982519
$953$	−38918.0	−1.32285	−0.661426	−	0.750011i	$-0.730048\pi$
$953$	−38918.0	−1.32285	−0.661426	+	0.750011i	$0.730048\pi$
$954$	3132.00	0.106292
$955$	7112.00	0.240983
$956$	18900.0	0.639403
$957$	0	0
$958$	16520.0	0.557137
$959$	−56836.0	−1.91380
$960$	−2004.00	−0.0673738
$961$	−29727.0	−0.997852
$962$	−2112.00	−0.0707834
$963$	−5076.00	−0.169857
$964$	−4046.00	−0.135179
$965$	−15848.0	−0.528669
$966$	14196.0	0.472825
$967$	−1114.00	−0.0370464	−0.0185232	−	0.999828i	$-0.505896\pi$
$967$	−1114.00	−0.0370464	−0.0185232	+	0.999828i	$0.505896\pi$
$968$	0	0
$969$	13320.0	0.441589
$970$	−56.0000	−0.00185366
$971$	−1688.00	−0.0557884	−0.0278942	−	0.999611i	$-0.508880\pi$
$971$	−1688.00	−0.0557884	−0.0278942	+	0.999611i	$0.508880\pi$
$972$	1701.00	0.0561313
$973$	−71240.0	−2.34722
$974$	524.000	0.0172382
$975$	10464.0	0.343709
$976$	−5412.00	−0.177494
$977$	−41826.0	−1.36963	−0.684817	−	0.728715i	$-0.740118\pi$
$977$	−41826.0	−1.36963	−0.684817	+	0.728715i	$0.740118\pi$
$978$	−11604.0	−0.379402
$979$	0	0
$980$	9324.00	0.303923
$981$	2880.00	0.0937322
$982$	15028.0	0.488353
$983$	978.000	0.0317328	0.0158664	−	0.999874i	$-0.494949\pi$
$983$	978.000	0.0317328	0.0158664	+	0.999874i	$0.494949\pi$
$984$	−18990.0	−0.615223
$985$	1496.00	0.0483924
$986$	−6660.00	−0.215109
$987$	39468.0	1.27283
$988$	−13440.0	−0.432777
$989$	74256.0	2.38747
$990$	0	0
$991$	47272.0	1.51528	0.757641	−	0.652671i	$-0.226352\pi$
$991$	47272.0	1.51528	0.757641	+	0.652671i	$0.226352\pi$
$992$	−1288.00	−0.0412238
$993$	8124.00	0.259625
$994$	19812.0	0.632192
$995$	−8400.00	−0.267636
$996$	2772.00	0.0881869
$997$	−51104.0	−1.62335	−0.811675	−	0.584109i	$-0.801444\pi$
$997$	−51104.0	−1.62335	−0.811675	+	0.584109i	$0.801444\pi$
$998$	9020.00	0.286095
$999$	1782.00	0.0564364

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.4.a.d.1.1		1
3.2	odd	2		1089.4.a.e.1.1		1
11.10	odd	2		33.4.a.b.1.1	✓	1
33.32	even	2		99.4.a.a.1.1		1
44.43	even	2		528.4.a.h.1.1		1
55.32	even	4		825.4.c.f.199.1		2
55.43	even	4		825.4.c.f.199.2		2
55.54	odd	2		825.4.a.f.1.1		1
77.76	even	2		1617.4.a.d.1.1		1
88.21	odd	2		2112.4.a.u.1.1		1
88.43	even	2		2112.4.a.h.1.1		1
132.131	odd	2		1584.4.a.l.1.1		1
165.164	even	2		2475.4.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.4.a.b.1.1	✓	1	11.10	odd	2
99.4.a.a.1.1		1	33.32	even	2
363.4.a.d.1.1		1	1.1	even	1	trivial
528.4.a.h.1.1		1	44.43	even	2
825.4.a.f.1.1		1	55.54	odd	2
825.4.c.f.199.1		2	55.32	even	4
825.4.c.f.199.2		2	55.43	even	4
1089.4.a.e.1.1		1	3.2	odd	2
1584.4.a.l.1.1		1	132.131	odd	2
1617.4.a.d.1.1		1	77.76	even	2
2112.4.a.h.1.1		1	88.43	even	2
2112.4.a.u.1.1		1	88.21	odd	2
2475.4.a.e.1.1		1	165.164	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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