LMFDB - Embedded newform 1045.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,4,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1045.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:	$61.6569959560$
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	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-5.00000 q^{2} -1.00000 q^{3} +17.0000 q^{4} -5.00000 q^{5} +5.00000 q^{6} -2.00000 q^{7} -45.0000 q^{8} -26.0000 q^{9} +O(q^{10})$

\(q-5.00000 q^{2} -1.00000 q^{3} +17.0000 q^{4} -5.00000 q^{5} +5.00000 q^{6} -2.00000 q^{7} -45.0000 q^{8} -26.0000 q^{9} +25.0000 q^{10} -11.0000 q^{11} -17.0000 q^{12} -7.00000 q^{13} +10.0000 q^{14} +5.00000 q^{15} +89.0000 q^{16} +14.0000 q^{17} +130.000 q^{18} +19.0000 q^{19} -85.0000 q^{20} +2.00000 q^{21} +55.0000 q^{22} +55.0000 q^{23} +45.0000 q^{24} +25.0000 q^{25} +35.0000 q^{26} +53.0000 q^{27} -34.0000 q^{28} -26.0000 q^{29} -25.0000 q^{30} +261.000 q^{31} -85.0000 q^{32} +11.0000 q^{33} -70.0000 q^{34} +10.0000 q^{35} -442.000 q^{36} -126.000 q^{37} -95.0000 q^{38} +7.00000 q^{39} +225.000 q^{40} -381.000 q^{41} -10.0000 q^{42} +387.000 q^{43} -187.000 q^{44} +130.000 q^{45} -275.000 q^{46} +189.000 q^{47} -89.0000 q^{48} -339.000 q^{49} -125.000 q^{50} -14.0000 q^{51} -119.000 q^{52} -404.000 q^{53} -265.000 q^{54} +55.0000 q^{55} +90.0000 q^{56} -19.0000 q^{57} +130.000 q^{58} +746.000 q^{59} +85.0000 q^{60} +79.0000 q^{61} -1305.00 q^{62} +52.0000 q^{63} -287.000 q^{64} +35.0000 q^{65} -55.0000 q^{66} +537.000 q^{67} +238.000 q^{68} -55.0000 q^{69} -50.0000 q^{70} -824.000 q^{71} +1170.00 q^{72} +169.000 q^{73} +630.000 q^{74} -25.0000 q^{75} +323.000 q^{76} +22.0000 q^{77} -35.0000 q^{78} -338.000 q^{79} -445.000 q^{80} +649.000 q^{81} +1905.00 q^{82} +601.000 q^{83} +34.0000 q^{84} -70.0000 q^{85} -1935.00 q^{86} +26.0000 q^{87} +495.000 q^{88} -762.000 q^{89} -650.000 q^{90} +14.0000 q^{91} +935.000 q^{92} -261.000 q^{93} -945.000 q^{94} -95.0000 q^{95} +85.0000 q^{96} +866.000 q^{97} +1695.00 q^{98} +286.000 q^{99} +O(q^{100})\)

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 $

$2$	−5.00000	−1.76777	−0.883883	−	0.467707i	$-0.845080\pi$
$2$	−5.00000	−1.76777	−0.883883	+	0.467707i	$0.845080\pi$
$3$	−1.00000	−0.192450	−0.0962250	−	0.995360i	$-0.530677\pi$
$3$	−1.00000	−0.192450	−0.0962250	+	0.995360i	$0.530677\pi$
$4$	17.0000	2.12500
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	5.00000	0.340207
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	−45.0000	−1.98874
$9$	−26.0000	−0.962963
$10$	25.0000	0.790569
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−17.0000	−0.408956
$13$	−7.00000	−0.149342	−0.0746712	−	0.997208i	$-0.523791\pi$
$13$	−7.00000	−0.149342	−0.0746712	+	0.997208i	$0.523791\pi$
$14$	10.0000	0.190901
$15$	5.00000	0.0860663
$16$	89.0000	1.39062
$17$	14.0000	0.199735	0.0998676	−	0.995001i	$-0.468158\pi$
$17$	14.0000	0.199735	0.0998676	+	0.995001i	$0.468158\pi$
$18$	130.000	1.70229
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−85.0000	−0.950329
$21$	2.00000	0.0207827
$22$	55.0000	0.533002
$23$	55.0000	0.498621	0.249311	−	0.968424i	$-0.419796\pi$
$23$	55.0000	0.498621	0.249311	+	0.968424i	$0.419796\pi$
$24$	45.0000	0.382733
$25$	25.0000	0.200000
$26$	35.0000	0.264002
$27$	53.0000	0.377772
$28$	−34.0000	−0.229478
$29$	−26.0000	−0.166485	−0.0832427	−	0.996529i	$-0.526528\pi$
$29$	−26.0000	−0.166485	−0.0832427	+	0.996529i	$0.526528\pi$
$30$	−25.0000	−0.152145
$31$	261.000	1.51216	0.756080	−	0.654479i	$-0.227112\pi$
$31$	261.000	1.51216	0.756080	+	0.654479i	$0.227112\pi$
$32$	−85.0000	−0.469563
$33$	11.0000	0.0580259
$34$	−70.0000	−0.353085
$35$	10.0000	0.0482945
$36$	−442.000	−2.04630
$37$	−126.000	−0.559845	−0.279923	−	0.960023i	$-0.590309\pi$
$37$	−126.000	−0.559845	−0.279923	+	0.960023i	$0.590309\pi$
$38$	−95.0000	−0.405554
$39$	7.00000	0.0287410
$40$	225.000	0.889391
$41$	−381.000	−1.45127	−0.725637	−	0.688078i	$-0.758455\pi$
$41$	−381.000	−1.45127	−0.725637	+	0.688078i	$0.758455\pi$
$42$	−10.0000	−0.0367389
$43$	387.000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	387.000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	−187.000	−0.640712
$45$	130.000	0.430650
$46$	−275.000	−0.881446
$47$	189.000	0.586563	0.293282	−	0.956026i	$-0.405253\pi$
$47$	189.000	0.586563	0.293282	+	0.956026i	$0.405253\pi$
$48$	−89.0000	−0.267626
$49$	−339.000	−0.988338
$50$	−125.000	−0.353553
$51$	−14.0000	−0.0384391
$52$	−119.000	−0.317353
$53$	−404.000	−1.04705	−0.523525	−	0.852010i	$-0.675383\pi$
$53$	−404.000	−1.04705	−0.523525	+	0.852010i	$0.675383\pi$
$54$	−265.000	−0.667814
$55$	55.0000	0.134840
$56$	90.0000	0.214763
$57$	−19.0000	−0.0441511
$58$	130.000	0.294308
$59$	746.000	1.64612	0.823059	−	0.567956i	$-0.192266\pi$
$59$	746.000	1.64612	0.823059	+	0.567956i	$0.192266\pi$
$60$	85.0000	0.182891
$61$	79.0000	0.165818	0.0829091	−	0.996557i	$-0.473579\pi$
$61$	79.0000	0.165818	0.0829091	+	0.996557i	$0.473579\pi$
$62$	−1305.00	−2.67315
$63$	52.0000	0.103990
$64$	−287.000	−0.560547
$65$	35.0000	0.0667879
$66$	−55.0000	−0.102576
$67$	537.000	0.979179	0.489589	−	0.871953i	$-0.337147\pi$
$67$	537.000	0.979179	0.489589	+	0.871953i	$0.337147\pi$
$68$	238.000	0.424437
$69$	−55.0000	−0.0959597
$70$	−50.0000	−0.0853735
$71$	−824.000	−1.37734	−0.688668	−	0.725077i	$-0.741804\pi$
$71$	−824.000	−1.37734	−0.688668	+	0.725077i	$0.741804\pi$
$72$	1170.00	1.91508
$73$	169.000	0.270958	0.135479	−	0.990780i	$-0.456743\pi$
$73$	169.000	0.270958	0.135479	+	0.990780i	$0.456743\pi$
$74$	630.000	0.989676
$75$	−25.0000	−0.0384900
$76$	323.000	0.487508
$77$	22.0000	0.0325602
$78$	−35.0000	−0.0508073
$79$	−338.000	−0.481367	−0.240683	−	0.970604i	$-0.577372\pi$
$79$	−338.000	−0.481367	−0.240683	+	0.970604i	$0.577372\pi$
$80$	−445.000	−0.621906
$81$	649.000	0.890261
$82$	1905.00	2.56551
$83$	601.000	0.794799	0.397400	−	0.917646i	$-0.369913\pi$
$83$	601.000	0.794799	0.397400	+	0.917646i	$0.369913\pi$
$84$	34.0000	0.0441631
$85$	−70.0000	−0.0893243
$86$	−1935.00	−2.42624
$87$	26.0000	0.0320401
$88$	495.000	0.599627
$89$	−762.000	−0.907549	−0.453774	−	0.891117i	$-0.649923\pi$
$89$	−762.000	−0.907549	−0.453774	+	0.891117i	$0.649923\pi$
$90$	−650.000	−0.761289
$91$	14.0000	0.0161275
$92$	935.000	1.05957
$93$	−261.000	−0.291015
$94$	−945.000	−1.03691
$95$	−95.0000	−0.102598
$96$	85.0000	0.0903675
$97$	866.000	0.906484	0.453242	−	0.891387i	$-0.350267\pi$
$97$	866.000	0.906484	0.453242	+	0.891387i	$0.350267\pi$
$98$	1695.00	1.74715
$99$	286.000	0.290344
$100$	425.000	0.425000
$101$	1006.00	0.991096	0.495548	−	0.868580i	$-0.334967\pi$
$101$	1006.00	0.991096	0.495548	+	0.868580i	$0.334967\pi$
$102$	70.0000	0.0679513
$103$	2002.00	1.91517	0.957587	−	0.288144i	$-0.0930383\pi$
$103$	2002.00	1.91517	0.957587	+	0.288144i	$0.0930383\pi$
$104$	315.000	0.297003
$105$	−10.0000	−0.00929429
$106$	2020.00	1.85094
$107$	1144.00	1.03359	0.516797	−	0.856108i	$-0.327124\pi$
$107$	1144.00	1.03359	0.516797	+	0.856108i	$0.327124\pi$
$108$	901.000	0.802766
$109$	766.000	0.673115	0.336557	−	0.941663i	$-0.390737\pi$
$109$	766.000	0.673115	0.336557	+	0.941663i	$0.390737\pi$
$110$	−275.000	−0.238366
$111$	126.000	0.107742
$112$	−178.000	−0.150173
$113$	−2042.00	−1.69996	−0.849979	−	0.526817i	$-0.823385\pi$
$113$	−2042.00	−1.69996	−0.849979	+	0.526817i	$0.823385\pi$
$114$	95.0000	0.0780488
$115$	−275.000	−0.222990
$116$	−442.000	−0.353782
$117$	182.000	0.143811
$118$	−3730.00	−2.90995
$119$	−28.0000	−0.0215694
$120$	−225.000	−0.171163
$121$	121.000	0.0909091
$122$	−395.000	−0.293128
$123$	381.000	0.279298
$124$	4437.00	3.21334
$125$	−125.000	−0.0894427
$126$	−260.000	−0.183830
$127$	−171.000	−0.119479	−0.0597394	−	0.998214i	$-0.519027\pi$
$127$	−171.000	−0.119479	−0.0597394	+	0.998214i	$0.519027\pi$
$128$	2115.00	1.46048
$129$	−387.000	−0.264135
$130$	−175.000	−0.118066
$131$	−1900.00	−1.26720	−0.633602	−	0.773659i	$-0.718424\pi$
$131$	−1900.00	−1.26720	−0.633602	+	0.773659i	$0.718424\pi$
$132$	187.000	0.123305
$133$	−38.0000	−0.0247746
$134$	−2685.00	−1.73096
$135$	−265.000	−0.168945
$136$	−630.000	−0.397221
$137$	324.000	0.202052	0.101026	−	0.994884i	$-0.467787\pi$
$137$	324.000	0.202052	0.101026	+	0.994884i	$0.467787\pi$
$138$	275.000	0.169634
$139$	178.000	0.108617	0.0543085	−	0.998524i	$-0.482705\pi$
$139$	178.000	0.108617	0.0543085	+	0.998524i	$0.482705\pi$
$140$	170.000	0.102626
$141$	−189.000	−0.112884
$142$	4120.00	2.43481
$143$	77.0000	0.0450284
$144$	−2314.00	−1.33912
$145$	130.000	0.0744546
$146$	−845.000	−0.478991
$147$	339.000	0.190206
$148$	−2142.00	−1.18967
$149$	−1491.00	−0.819782	−0.409891	−	0.912135i	$-0.634433\pi$
$149$	−1491.00	−0.819782	−0.409891	+	0.912135i	$0.634433\pi$
$150$	125.000	0.0680414
$151$	−860.000	−0.463482	−0.231741	−	0.972778i	$-0.574442\pi$
$151$	−860.000	−0.463482	−0.231741	+	0.972778i	$0.574442\pi$
$152$	−855.000	−0.456248
$153$	−364.000	−0.192338
$154$	−110.000	−0.0575588
$155$	−1305.00	−0.676259
$156$	119.000	0.0610745
$157$	1733.00	0.880946	0.440473	−	0.897766i	$-0.354811\pi$
$157$	1733.00	0.880946	0.440473	+	0.897766i	$0.354811\pi$
$158$	1690.00	0.850944
$159$	404.000	0.201505
$160$	425.000	0.209995
$161$	−110.000	−0.0538461
$162$	−3245.00	−1.57377
$163$	−3980.00	−1.91250	−0.956250	−	0.292549i	$-0.905496\pi$
$163$	−3980.00	−1.91250	−0.956250	+	0.292549i	$0.905496\pi$
$164$	−6477.00	−3.08396
$165$	−55.0000	−0.0259500
$166$	−3005.00	−1.40502
$167$	1059.00	0.490706	0.245353	−	0.969434i	$-0.421096\pi$
$167$	1059.00	0.490706	0.245353	+	0.969434i	$0.421096\pi$
$168$	−90.0000	−0.0413313
$169$	−2148.00	−0.977697
$170$	350.000	0.157905
$171$	−494.000	−0.220919
$172$	6579.00	2.91654
$173$	971.000	0.426727	0.213363	−	0.976973i	$-0.431558\pi$
$173$	971.000	0.426727	0.213363	+	0.976973i	$0.431558\pi$
$174$	−130.000	−0.0566395
$175$	−50.0000	−0.0215980
$176$	−979.000	−0.419289
$177$	−746.000	−0.316795
$178$	3810.00	1.60433
$179$	−2202.00	−0.919470	−0.459735	−	0.888056i	$-0.652056\pi$
$179$	−2202.00	−0.919470	−0.459735	+	0.888056i	$0.652056\pi$
$180$	2210.00	0.915132
$181$	1097.00	0.450494	0.225247	−	0.974302i	$-0.427681\pi$
$181$	1097.00	0.450494	0.225247	+	0.974302i	$0.427681\pi$
$182$	−70.0000	−0.0285096
$183$	−79.0000	−0.0319117
$184$	−2475.00	−0.991627
$185$	630.000	0.250370
$186$	1305.00	0.514448
$187$	−154.000	−0.0602224
$188$	3213.00	1.24645
$189$	−106.000	−0.0407956
$190$	475.000	0.181369
$191$	−3022.00	−1.14484	−0.572419	−	0.819961i	$-0.693995\pi$
$191$	−3022.00	−1.14484	−0.572419	+	0.819961i	$0.693995\pi$
$192$	287.000	0.107877
$193$	658.000	0.245409	0.122704	−	0.992443i	$-0.460843\pi$
$193$	658.000	0.245409	0.122704	+	0.992443i	$0.460843\pi$
$194$	−4330.00	−1.60245
$195$	−35.0000	−0.0128533
$196$	−5763.00	−2.10022
$197$	426.000	0.154067	0.0770336	−	0.997028i	$-0.475455\pi$
$197$	426.000	0.154067	0.0770336	+	0.997028i	$0.475455\pi$
$198$	−1430.00	−0.513261
$199$	−1276.00	−0.454539	−0.227269	−	0.973832i	$-0.572980\pi$
$199$	−1276.00	−0.454539	−0.227269	+	0.973832i	$0.572980\pi$
$200$	−1125.00	−0.397748
$201$	−537.000	−0.188443
$202$	−5030.00	−1.75203
$203$	52.0000	0.0179787
$204$	−238.000	−0.0816830
$205$	1905.00	0.649029
$206$	−10010.0	−3.38558
$207$	−1430.00	−0.480154
$208$	−623.000	−0.207679
$209$	−209.000	−0.0691714
$210$	50.0000	0.0164301
$211$	4489.00	1.46462	0.732312	−	0.680970i	$-0.238441\pi$
$211$	4489.00	1.46462	0.732312	+	0.680970i	$0.238441\pi$
$212$	−6868.00	−2.22498
$213$	824.000	0.265068
$214$	−5720.00	−1.82715
$215$	−1935.00	−0.613795
$216$	−2385.00	−0.751290
$217$	−522.000	−0.163298
$218$	−3830.00	−1.18991
$219$	−169.000	−0.0521459
$220$	935.000	0.286535
$221$	−98.0000	−0.0298289
$222$	−630.000	−0.190463
$223$	−750.000	−0.225218	−0.112609	−	0.993639i	$-0.535921\pi$
$223$	−750.000	−0.225218	−0.112609	+	0.993639i	$0.535921\pi$
$224$	170.000	0.0507080
$225$	−650.000	−0.192593
$226$	10210.0	3.00513
$227$	−2016.00	−0.589456	−0.294728	−	0.955581i	$-0.595229\pi$
$227$	−2016.00	−0.589456	−0.294728	+	0.955581i	$0.595229\pi$
$228$	−323.000	−0.0938210
$229$	−6680.00	−1.92763	−0.963814	−	0.266576i	$-0.914108\pi$
$229$	−6680.00	−1.92763	−0.963814	+	0.266576i	$0.914108\pi$
$230$	1375.00	0.394195
$231$	−22.0000	−0.00626621
$232$	1170.00	0.331096
$233$	−6423.00	−1.80594	−0.902972	−	0.429700i	$-0.858619\pi$
$233$	−6423.00	−1.80594	−0.902972	+	0.429700i	$0.858619\pi$
$234$	−910.000	−0.254225
$235$	−945.000	−0.262319
$236$	12682.0	3.49800
$237$	338.000	0.0926391
$238$	140.000	0.0381296
$239$	−5440.00	−1.47232	−0.736160	−	0.676808i	$-0.763363\pi$
$239$	−5440.00	−1.47232	−0.736160	+	0.676808i	$0.763363\pi$
$240$	445.000	0.119686
$241$	−155.000	−0.0414292	−0.0207146	−	0.999785i	$-0.506594\pi$
$241$	−155.000	−0.0414292	−0.0207146	+	0.999785i	$0.506594\pi$
$242$	−605.000	−0.160706
$243$	−2080.00	−0.549103
$244$	1343.00	0.352364
$245$	1695.00	0.441998
$246$	−1905.00	−0.493733
$247$	−133.000	−0.0342615
$248$	−11745.0	−3.00729
$249$	−601.000	−0.152959
$250$	625.000	0.158114
$251$	−6609.00	−1.66198	−0.830989	−	0.556289i	$-0.812225\pi$
$251$	−6609.00	−1.66198	−0.830989	+	0.556289i	$0.812225\pi$
$252$	884.000	0.220979
$253$	−605.000	−0.150340
$254$	855.000	0.211211
$255$	70.0000	0.0171905
$256$	−8279.00	−2.02124
$257$	−2505.00	−0.608006	−0.304003	−	0.952671i	$-0.598323\pi$
$257$	−2505.00	−0.608006	−0.304003	+	0.952671i	$0.598323\pi$
$258$	1935.00	0.466930
$259$	252.000	0.0604576
$260$	595.000	0.141924
$261$	676.000	0.160319
$262$	9500.00	2.24012
$263$	442.000	0.103631	0.0518154	−	0.998657i	$-0.483499\pi$
$263$	442.000	0.103631	0.0518154	+	0.998657i	$0.483499\pi$
$264$	−495.000	−0.115398
$265$	2020.00	0.468255
$266$	190.000	0.0437957
$267$	762.000	0.174658
$268$	9129.00	2.08076
$269$	1226.00	0.277883	0.138942	−	0.990301i	$-0.455630\pi$
$269$	1226.00	0.277883	0.138942	+	0.990301i	$0.455630\pi$
$270$	1325.00	0.298655
$271$	8264.00	1.85241	0.926203	−	0.377024i	$-0.123053\pi$
$271$	8264.00	1.85241	0.926203	+	0.377024i	$0.123053\pi$
$272$	1246.00	0.277757
$273$	−14.0000	−0.00310373
$274$	−1620.00	−0.357182
$275$	−275.000	−0.0603023
$276$	−935.000	−0.203914
$277$	−8128.00	−1.76305	−0.881524	−	0.472140i	$-0.843482\pi$
$277$	−8128.00	−1.76305	−0.881524	+	0.472140i	$0.843482\pi$
$278$	−890.000	−0.192010
$279$	−6786.00	−1.45615
$280$	−450.000	−0.0960452
$281$	886.000	0.188094	0.0940468	−	0.995568i	$-0.470020\pi$
$281$	886.000	0.188094	0.0940468	+	0.995568i	$0.470020\pi$
$282$	945.000	0.199553
$283$	5621.00	1.18068	0.590342	−	0.807153i	$-0.298993\pi$
$283$	5621.00	1.18068	0.590342	+	0.807153i	$0.298993\pi$
$284$	−14008.0	−2.92684
$285$	95.0000	0.0197450
$286$	−385.000	−0.0795997
$287$	762.000	0.156723
$288$	2210.00	0.452172
$289$	−4717.00	−0.960106
$290$	−650.000	−0.131618
$291$	−866.000	−0.174453
$292$	2873.00	0.575786
$293$	−386.000	−0.0769637	−0.0384818	−	0.999259i	$-0.512252\pi$
$293$	−386.000	−0.0769637	−0.0384818	+	0.999259i	$0.512252\pi$
$294$	−1695.00	−0.336239
$295$	−3730.00	−0.736166
$296$	5670.00	1.11339
$297$	−583.000	−0.113903
$298$	7455.00	1.44918
$299$	−385.000	−0.0744653
$300$	−425.000	−0.0817913
$301$	−774.000	−0.148215
$302$	4300.00	0.819328
$303$	−1006.00	−0.190737
$304$	1691.00	0.319031
$305$	−395.000	−0.0741562
$306$	1820.00	0.340008
$307$	2480.00	0.461046	0.230523	−	0.973067i	$-0.425956\pi$
$307$	2480.00	0.461046	0.230523	+	0.973067i	$0.425956\pi$
$308$	374.000	0.0691903
$309$	−2002.00	−0.368575
$310$	6525.00	1.19547
$311$	8242.00	1.50277	0.751384	−	0.659865i	$-0.229387\pi$
$311$	8242.00	1.50277	0.751384	+	0.659865i	$0.229387\pi$
$312$	−315.000	−0.0571582
$313$	−510.000	−0.0920987	−0.0460494	−	0.998939i	$-0.514663\pi$
$313$	−510.000	−0.0920987	−0.0460494	+	0.998939i	$0.514663\pi$
$314$	−8665.00	−1.55731
$315$	−260.000	−0.0465058
$316$	−5746.00	−1.02290
$317$	−8748.00	−1.54996	−0.774979	−	0.631987i	$-0.782240\pi$
$317$	−8748.00	−1.54996	−0.774979	+	0.631987i	$0.782240\pi$
$318$	−2020.00	−0.356214
$319$	286.000	0.0501973
$320$	1435.00	0.250684
$321$	−1144.00	−0.198915
$322$	550.000	0.0951873
$323$	266.000	0.0458224
$324$	11033.0	1.89180
$325$	−175.000	−0.0298685
$326$	19900.0	3.38086
$327$	−766.000	−0.129541
$328$	17145.0	2.88620
$329$	−378.000	−0.0633429
$330$	275.000	0.0458735
$331$	6742.00	1.11956	0.559779	−	0.828642i	$-0.310886\pi$
$331$	6742.00	1.11956	0.559779	+	0.828642i	$0.310886\pi$
$332$	10217.0	1.68895
$333$	3276.00	0.539110
$334$	−5295.00	−0.867454
$335$	−2685.00	−0.437902
$336$	178.000	0.0289009
$337$	2244.00	0.362725	0.181363	−	0.983416i	$-0.441949\pi$
$337$	2244.00	0.362725	0.181363	+	0.983416i	$0.441949\pi$
$338$	10740.0	1.72834
$339$	2042.00	0.327157
$340$	−1190.00	−0.189814
$341$	−2871.00	−0.455934
$342$	2470.00	0.390533
$343$	1364.00	0.214720
$344$	−17415.0	−2.72952
$345$	275.000	0.0429145
$346$	−4855.00	−0.754354
$347$	−1623.00	−0.251087	−0.125544	−	0.992088i	$-0.540067\pi$
$347$	−1623.00	−0.251087	−0.125544	+	0.992088i	$0.540067\pi$
$348$	442.000	0.0680853
$349$	−8637.00	−1.32472	−0.662361	−	0.749185i	$-0.730445\pi$
$349$	−8637.00	−1.32472	−0.662361	+	0.749185i	$0.730445\pi$
$350$	250.000	0.0381802
$351$	−371.000	−0.0564174
$352$	935.000	0.141579
$353$	−68.0000	−0.0102529	−0.00512645	−	0.999987i	$-0.501632\pi$
$353$	−68.0000	−0.0102529	−0.00512645	+	0.999987i	$0.501632\pi$
$354$	3730.00	0.560021
$355$	4120.00	0.615963
$356$	−12954.0	−1.92854
$357$	28.0000	0.00415103
$358$	11010.0	1.62541
$359$	9785.00	1.43853	0.719265	−	0.694735i	$-0.244479\pi$
$359$	9785.00	1.43853	0.719265	+	0.694735i	$0.244479\pi$
$360$	−5850.00	−0.856450
$361$	361.000	0.0526316
$362$	−5485.00	−0.796368
$363$	−121.000	−0.0174955
$364$	238.000	0.0342709
$365$	−845.000	−0.121176
$366$	395.000	0.0564125
$367$	−9159.00	−1.30271	−0.651357	−	0.758772i	$-0.725800\pi$
$367$	−9159.00	−1.30271	−0.651357	+	0.758772i	$0.725800\pi$
$368$	4895.00	0.693395
$369$	9906.00	1.39752
$370$	−3150.00	−0.442596
$371$	808.000	0.113071
$372$	−4437.00	−0.618408
$373$	2773.00	0.384934	0.192467	−	0.981303i	$-0.438351\pi$
$373$	2773.00	0.384934	0.192467	+	0.981303i	$0.438351\pi$
$374$	770.000	0.106459
$375$	125.000	0.0172133
$376$	−8505.00	−1.16652
$377$	182.000	0.0248633
$378$	530.000	0.0721171
$379$	−8326.00	−1.12844	−0.564219	−	0.825625i	$-0.690823\pi$
$379$	−8326.00	−1.12844	−0.564219	+	0.825625i	$0.690823\pi$
$380$	−1615.00	−0.218020
$381$	171.000	0.0229937
$382$	15110.0	2.02381
$383$	−6644.00	−0.886404	−0.443202	−	0.896422i	$-0.646157\pi$
$383$	−6644.00	−0.886404	−0.443202	+	0.896422i	$0.646157\pi$
$384$	−2115.00	−0.281069
$385$	−110.000	−0.0145613
$386$	−3290.00	−0.433825
$387$	−10062.0	−1.32165
$388$	14722.0	1.92628
$389$	−8880.00	−1.15741	−0.578707	−	0.815536i	$-0.696442\pi$
$389$	−8880.00	−1.15741	−0.578707	+	0.815536i	$0.696442\pi$
$390$	175.000	0.0227217
$391$	770.000	0.0995923
$392$	15255.0	1.96555
$393$	1900.00	0.243874
$394$	−2130.00	−0.272355
$395$	1690.00	0.215274
$396$	4862.00	0.616982
$397$	−3094.00	−0.391142	−0.195571	−	0.980690i	$-0.562656\pi$
$397$	−3094.00	−0.391142	−0.195571	+	0.980690i	$0.562656\pi$
$398$	6380.00	0.803519
$399$	38.0000	0.00476787
$400$	2225.00	0.278125
$401$	−6008.00	−0.748193	−0.374096	−	0.927390i	$-0.622047\pi$
$401$	−6008.00	−0.748193	−0.374096	+	0.927390i	$0.622047\pi$
$402$	2685.00	0.333123
$403$	−1827.00	−0.225830
$404$	17102.0	2.10608
$405$	−3245.00	−0.398137
$406$	−260.000	−0.0317822
$407$	1386.00	0.168800
$408$	630.000	0.0764452
$409$	−5761.00	−0.696487	−0.348243	−	0.937404i	$-0.613222\pi$
$409$	−5761.00	−0.696487	−0.348243	+	0.937404i	$0.613222\pi$
$410$	−9525.00	−1.14733
$411$	−324.000	−0.0388850
$412$	34034.0	4.06974
$413$	−1492.00	−0.177764
$414$	7150.00	0.848800
$415$	−3005.00	−0.355445
$416$	595.000	0.0701257
$417$	−178.000	−0.0209034
$418$	1045.00	0.122279
$419$	−5063.00	−0.590319	−0.295160	−	0.955448i	$-0.595373\pi$
$419$	−5063.00	−0.590319	−0.295160	+	0.955448i	$0.595373\pi$
$420$	−170.000	−0.0197504
$421$	−8537.00	−0.988285	−0.494142	−	0.869381i	$-0.664518\pi$
$421$	−8537.00	−0.988285	−0.494142	+	0.869381i	$0.664518\pi$
$422$	−22445.0	−2.58911
$423$	−4914.00	−0.564839
$424$	18180.0	2.08231
$425$	350.000	0.0399470
$426$	−4120.00	−0.468579
$427$	−158.000	−0.0179067
$428$	19448.0	2.19639
$429$	−77.0000	−0.00866572
$430$	9675.00	1.08505
$431$	5936.00	0.663404	0.331702	−	0.943384i	$-0.392377\pi$
$431$	5936.00	0.663404	0.331702	+	0.943384i	$0.392377\pi$
$432$	4717.00	0.525340
$433$	5441.00	0.603875	0.301937	−	0.953328i	$-0.402367\pi$
$433$	5441.00	0.603875	0.301937	+	0.953328i	$0.402367\pi$
$434$	2610.00	0.288673
$435$	−130.000	−0.0143288
$436$	13022.0	1.43037
$437$	1045.00	0.114392
$438$	845.000	0.0921819
$439$	11500.0	1.25026	0.625131	−	0.780520i	$-0.285046\pi$
$439$	11500.0	1.25026	0.625131	+	0.780520i	$0.285046\pi$
$440$	−2475.00	−0.268161
$441$	8814.00	0.951733
$442$	490.000	0.0527306
$443$	3226.00	0.345986	0.172993	−	0.984923i	$-0.444656\pi$
$443$	3226.00	0.345986	0.172993	+	0.984923i	$0.444656\pi$
$444$	2142.00	0.228952
$445$	3810.00	0.405868
$446$	3750.00	0.398134
$447$	1491.00	0.157767
$448$	574.000	0.0605334
$449$	16350.0	1.71849	0.859247	−	0.511560i	$-0.170932\pi$
$449$	16350.0	1.71849	0.859247	+	0.511560i	$0.170932\pi$
$450$	3250.00	0.340459
$451$	4191.00	0.437575
$452$	−34714.0	−3.61241
$453$	860.000	0.0891972
$454$	10080.0	1.04202
$455$	−70.0000	−0.00721242
$456$	855.000	0.0878049
$457$	11851.0	1.21306	0.606528	−	0.795062i	$-0.292562\pi$
$457$	11851.0	1.21306	0.606528	+	0.795062i	$0.292562\pi$
$458$	33400.0	3.40760
$459$	742.000	0.0754545
$460$	−4675.00	−0.473854
$461$	−9891.00	−0.999284	−0.499642	−	0.866232i	$-0.666535\pi$
$461$	−9891.00	−0.999284	−0.499642	+	0.866232i	$0.666535\pi$
$462$	110.000	0.0110772
$463$	−17088.0	−1.71522	−0.857610	−	0.514301i	$-0.828051\pi$
$463$	−17088.0	−1.71522	−0.857610	+	0.514301i	$0.828051\pi$
$464$	−2314.00	−0.231519
$465$	1305.00	0.130146
$466$	32115.0	3.19249
$467$	4716.00	0.467303	0.233651	−	0.972320i	$-0.424933\pi$
$467$	4716.00	0.467303	0.233651	+	0.972320i	$0.424933\pi$
$468$	3094.00	0.305599
$469$	−1074.00	−0.105741
$470$	4725.00	0.463719
$471$	−1733.00	−0.169538
$472$	−33570.0	−3.27370
$473$	−4257.00	−0.413820
$474$	−1690.00	−0.163764
$475$	475.000	0.0458831
$476$	−476.000	−0.0458349
$477$	10504.0	1.00827
$478$	27200.0	2.60272
$479$	327.000	0.0311921	0.0155960	−	0.999878i	$-0.495035\pi$
$479$	327.000	0.0311921	0.0155960	+	0.999878i	$0.495035\pi$
$480$	−425.000	−0.0404136
$481$	882.000	0.0836086
$482$	775.000	0.0732371
$483$	110.000	0.0103627
$484$	2057.00	0.193182
$485$	−4330.00	−0.405392
$486$	10400.0	0.970686
$487$	14.0000	0.00130267	0.000651335	−	1.00000i	$-0.499793\pi$
$487$	14.0000	0.00130267	0.000651335		1.00000i	$0.499793\pi$
$488$	−3555.00	−0.329769
$489$	3980.00	0.368061
$490$	−8475.00	−0.781350
$491$	18382.0	1.68955	0.844774	−	0.535123i	$-0.179735\pi$
$491$	18382.0	1.68955	0.844774	+	0.535123i	$0.179735\pi$
$492$	6477.00	0.593508
$493$	−364.000	−0.0332530
$494$	665.000	0.0605663
$495$	−1430.00	−0.129846
$496$	23229.0	2.10285
$497$	1648.00	0.148738
$498$	3005.00	0.270396
$499$	−745.000	−0.0668352	−0.0334176	−	0.999441i	$-0.510639\pi$
$499$	−745.000	−0.0668352	−0.0334176	+	0.999441i	$0.510639\pi$
$500$	−2125.00	−0.190066
$501$	−1059.00	−0.0944364
$502$	33045.0	2.93799
$503$	−3504.00	−0.310608	−0.155304	−	0.987867i	$-0.549636\pi$
$503$	−3504.00	−0.310608	−0.155304	+	0.987867i	$0.549636\pi$
$504$	−2340.00	−0.206809
$505$	−5030.00	−0.443232
$506$	3025.00	0.265766
$507$	2148.00	0.188158
$508$	−2907.00	−0.253892
$509$	−8085.00	−0.704050	−0.352025	−	0.935991i	$-0.614507\pi$
$509$	−8085.00	−0.704050	−0.352025	+	0.935991i	$0.614507\pi$
$510$	−350.000	−0.0303887
$511$	−338.000	−0.0292607
$512$	24475.0	2.11260
$513$	1007.00	0.0866669
$514$	12525.0	1.07481
$515$	−10010.0	−0.856492
$516$	−6579.00	−0.561287
$517$	−2079.00	−0.176856
$518$	−1260.00	−0.106875
$519$	−971.000	−0.0821236
$520$	−1575.00	−0.132824
$521$	3600.00	0.302723	0.151362	−	0.988478i	$-0.451634\pi$
$521$	3600.00	0.302723	0.151362	+	0.988478i	$0.451634\pi$
$522$	−3380.00	−0.283407
$523$	−4086.00	−0.341622	−0.170811	−	0.985304i	$-0.554639\pi$
$523$	−4086.00	−0.341622	−0.170811	+	0.985304i	$0.554639\pi$
$524$	−32300.0	−2.69281
$525$	50.0000	0.00415653
$526$	−2210.00	−0.183195
$527$	3654.00	0.302032
$528$	979.000	0.0806922
$529$	−9142.00	−0.751377
$530$	−10100.0	−0.827766
$531$	−19396.0	−1.58515
$532$	−646.000	−0.0526460
$533$	2667.00	0.216737
$534$	−3810.00	−0.308754
$535$	−5720.00	−0.462238
$536$	−24165.0	−1.94733
$537$	2202.00	0.176952
$538$	−6130.00	−0.491232
$539$	3729.00	0.297995
$540$	−4505.00	−0.359008
$541$	105.000	0.00834437	0.00417218	−	0.999991i	$-0.498672\pi$
$541$	105.000	0.00834437	0.00417218	+	0.999991i	$0.498672\pi$
$542$	−41320.0	−3.27462
$543$	−1097.00	−0.0866976
$544$	−1190.00	−0.0937883
$545$	−3830.00	−0.301026
$546$	70.0000	0.00548667
$547$	−2486.00	−0.194321	−0.0971606	−	0.995269i	$-0.530976\pi$
$547$	−2486.00	−0.194321	−0.0971606	+	0.995269i	$0.530976\pi$
$548$	5508.00	0.429361
$549$	−2054.00	−0.159677
$550$	1375.00	0.106600
$551$	−494.000	−0.0381944
$552$	2475.00	0.190839
$553$	676.000	0.0519827
$554$	40640.0	3.11666
$555$	−630.000	−0.0481838
$556$	3026.00	0.230811
$557$	−18568.0	−1.41248	−0.706240	−	0.707972i	$-0.749610\pi$
$557$	−18568.0	−1.41248	−0.706240	+	0.707972i	$0.749610\pi$
$558$	33930.0	2.57414
$559$	−2709.00	−0.204970
$560$	890.000	0.0671596
$561$	154.000	0.0115898
$562$	−4430.00	−0.332506
$563$	−5682.00	−0.425342	−0.212671	−	0.977124i	$-0.568216\pi$
$563$	−5682.00	−0.425342	−0.212671	+	0.977124i	$0.568216\pi$
$564$	−3213.00	−0.239879
$565$	10210.0	0.760244
$566$	−28105.0	−2.08718
$567$	−1298.00	−0.0961391
$568$	37080.0	2.73916
$569$	12474.0	0.919046	0.459523	−	0.888166i	$-0.348020\pi$
$569$	12474.0	0.919046	0.459523	+	0.888166i	$0.348020\pi$
$570$	−475.000	−0.0349045
$571$	−19574.0	−1.43458	−0.717291	−	0.696774i	$-0.754618\pi$
$571$	−19574.0	−1.43458	−0.717291	+	0.696774i	$0.754618\pi$
$572$	1309.00	0.0956854
$573$	3022.00	0.220324
$574$	−3810.00	−0.277049
$575$	1375.00	0.0997243
$576$	7462.00	0.539786
$577$	−12278.0	−0.885858	−0.442929	−	0.896557i	$-0.646061\pi$
$577$	−12278.0	−0.885858	−0.442929	+	0.896557i	$0.646061\pi$
$578$	23585.0	1.69724
$579$	−658.000	−0.0472289
$580$	2210.00	0.158216
$581$	−1202.00	−0.0858302
$582$	4330.00	0.308392
$583$	4444.00	0.315698
$584$	−7605.00	−0.538865
$585$	−910.000	−0.0643143
$586$	1930.00	0.136054
$587$	1710.00	0.120237	0.0601186	−	0.998191i	$-0.480852\pi$
$587$	1710.00	0.120237	0.0601186	+	0.998191i	$0.480852\pi$
$588$	5763.00	0.404187
$589$	4959.00	0.346913
$590$	18650.0	1.30137
$591$	−426.000	−0.0296503
$592$	−11214.0	−0.778535
$593$	−18701.0	−1.29504	−0.647519	−	0.762049i	$-0.724194\pi$
$593$	−18701.0	−1.29504	−0.647519	+	0.762049i	$0.724194\pi$
$594$	2915.00	0.201353
$595$	140.000	0.00964612
$596$	−25347.0	−1.74204
$597$	1276.00	0.0874761
$598$	1925.00	0.131637
$599$	−6279.00	−0.428302	−0.214151	−	0.976801i	$-0.568698\pi$
$599$	−6279.00	−0.428302	−0.214151	+	0.976801i	$0.568698\pi$
$600$	1125.00	0.0765466
$601$	−6349.00	−0.430917	−0.215458	−	0.976513i	$-0.569125\pi$
$601$	−6349.00	−0.430917	−0.215458	+	0.976513i	$0.569125\pi$
$602$	3870.00	0.262009
$603$	−13962.0	−0.942913
$604$	−14620.0	−0.984900
$605$	−605.000	−0.0406558
$606$	5030.00	0.337178
$607$	−22731.0	−1.51997	−0.759986	−	0.649940i	$-0.774794\pi$
$607$	−22731.0	−1.51997	−0.759986	+	0.649940i	$0.774794\pi$
$608$	−1615.00	−0.107725
$609$	−52.0000	−0.00346001
$610$	1975.00	0.131091
$611$	−1323.00	−0.0875988
$612$	−6188.00	−0.408717
$613$	−20648.0	−1.36046	−0.680232	−	0.732997i	$-0.738121\pi$
$613$	−20648.0	−1.36046	−0.680232	+	0.732997i	$0.738121\pi$
$614$	−12400.0	−0.815022
$615$	−1905.00	−0.124906
$616$	−990.000	−0.0647536
$617$	−9092.00	−0.593242	−0.296621	−	0.954995i	$-0.595860\pi$
$617$	−9092.00	−0.593242	−0.296621	+	0.954995i	$0.595860\pi$
$618$	10010.0	0.651555
$619$	4531.00	0.294210	0.147105	−	0.989121i	$-0.453004\pi$
$619$	4531.00	0.294210	0.147105	+	0.989121i	$0.453004\pi$
$620$	−22185.0	−1.43705
$621$	2915.00	0.188365
$622$	−41210.0	−2.65654
$623$	1524.00	0.0980061
$624$	623.000	0.0399679
$625$	625.000	0.0400000
$626$	2550.00	0.162809
$627$	209.000	0.0133121
$628$	29461.0	1.87201
$629$	−1764.00	−0.111821
$630$	1300.00	0.0822115
$631$	−10714.0	−0.675939	−0.337970	−	0.941157i	$-0.609740\pi$
$631$	−10714.0	−0.675939	−0.337970	+	0.941157i	$0.609740\pi$
$632$	15210.0	0.957312
$633$	−4489.00	−0.281867
$634$	43740.0	2.73996
$635$	855.000	0.0534325
$636$	6868.00	0.428198
$637$	2373.00	0.147601
$638$	−1430.00	−0.0887371
$639$	21424.0	1.32632
$640$	−10575.0	−0.653146
$641$	−11700.0	−0.720939	−0.360470	−	0.932771i	$-0.617384\pi$
$641$	−11700.0	−0.720939	−0.360470	+	0.932771i	$0.617384\pi$
$642$	5720.00	0.351636
$643$	25296.0	1.55144	0.775721	−	0.631076i	$-0.217387\pi$
$643$	25296.0	1.55144	0.775721	+	0.631076i	$0.217387\pi$
$644$	−1870.00	−0.114423
$645$	1935.00	0.118125
$646$	−1330.00	−0.0810033
$647$	18044.0	1.09642	0.548209	−	0.836341i	$-0.315310\pi$
$647$	18044.0	1.09642	0.548209	+	0.836341i	$0.315310\pi$
$648$	−29205.0	−1.77049
$649$	−8206.00	−0.496323
$650$	875.000	0.0528005
$651$	522.000	0.0314267
$652$	−67660.0	−4.06406
$653$	−3877.00	−0.232341	−0.116171	−	0.993229i	$-0.537062\pi$
$653$	−3877.00	−0.232341	−0.116171	+	0.993229i	$0.537062\pi$
$654$	3830.00	0.228998
$655$	9500.00	0.566711
$656$	−33909.0	−2.01818
$657$	−4394.00	−0.260923
$658$	1890.00	0.111975
$659$	−16215.0	−0.958493	−0.479246	−	0.877680i	$-0.659090\pi$
$659$	−16215.0	−0.958493	−0.479246	+	0.877680i	$0.659090\pi$
$660$	−935.000	−0.0551437
$661$	4517.00	0.265796	0.132898	−	0.991130i	$-0.457572\pi$
$661$	4517.00	0.265796	0.132898	+	0.991130i	$0.457572\pi$
$662$	−33710.0	−1.97912
$663$	98.0000	0.00574058
$664$	−27045.0	−1.58065
$665$	190.000	0.0110795
$666$	−16380.0	−0.953021
$667$	−1430.00	−0.0830132
$668$	18003.0	1.04275
$669$	750.000	0.0433433
$670$	13425.0	0.774109
$671$	−869.000	−0.0499961
$672$	−170.000	−0.00975877
$673$	33090.0	1.89528	0.947642	−	0.319335i	$-0.103460\pi$
$673$	33090.0	1.89528	0.947642	+	0.319335i	$0.103460\pi$
$674$	−11220.0	−0.641214
$675$	1325.00	0.0755545
$676$	−36516.0	−2.07761
$677$	−26169.0	−1.48561	−0.742804	−	0.669509i	$-0.766504\pi$
$677$	−26169.0	−1.48561	−0.742804	+	0.669509i	$0.766504\pi$
$678$	−10210.0	−0.578337
$679$	−1732.00	−0.0978911
$680$	3150.00	0.177643
$681$	2016.00	0.113441
$682$	14355.0	0.805984
$683$	5043.00	0.282526	0.141263	−	0.989972i	$-0.454884\pi$
$683$	5043.00	0.282526	0.141263	+	0.989972i	$0.454884\pi$
$684$	−8398.00	−0.469453
$685$	−1620.00	−0.0903606
$686$	−6820.00	−0.379576
$687$	6680.00	0.370972
$688$	34443.0	1.90861
$689$	2828.00	0.156369
$690$	−1375.00	−0.0758628
$691$	−6333.00	−0.348652	−0.174326	−	0.984688i	$-0.555775\pi$
$691$	−6333.00	−0.348652	−0.174326	+	0.984688i	$0.555775\pi$
$692$	16507.0	0.906795
$693$	−572.000	−0.0313542
$694$	8115.00	0.443863
$695$	−890.000	−0.0485750
$696$	−1170.00	−0.0637194
$697$	−5334.00	−0.289870
$698$	43185.0	2.34180
$699$	6423.00	0.347554
$700$	−850.000	−0.0458957
$701$	27261.0	1.46881	0.734404	−	0.678713i	$-0.237462\pi$
$701$	27261.0	1.46881	0.734404	+	0.678713i	$0.237462\pi$
$702$	1855.00	0.0997329
$703$	−2394.00	−0.128437
$704$	3157.00	0.169011
$705$	945.000	0.0504833
$706$	340.000	0.0181247
$707$	−2012.00	−0.107028
$708$	−12682.0	−0.673190
$709$	19844.0	1.05114	0.525569	−	0.850751i	$-0.323852\pi$
$709$	19844.0	1.05114	0.525569	+	0.850751i	$0.323852\pi$
$710$	−20600.0	−1.08888
$711$	8788.00	0.463538
$712$	34290.0	1.80488
$713$	14355.0	0.753996
$714$	−140.000	−0.00733805
$715$	−385.000	−0.0201373
$716$	−37434.0	−1.95387
$717$	5440.00	0.283348
$718$	−48925.0	−2.54299
$719$	−28410.0	−1.47359	−0.736797	−	0.676114i	$-0.763663\pi$
$719$	−28410.0	−1.47359	−0.736797	+	0.676114i	$0.763663\pi$
$720$	11570.0	0.598873
$721$	−4004.00	−0.206819
$722$	−1805.00	−0.0930404
$723$	155.000	0.00797305
$724$	18649.0	0.957299
$725$	−650.000	−0.0332971
$726$	605.000	0.0309279
$727$	−25323.0	−1.29185	−0.645927	−	0.763399i	$-0.723529\pi$
$727$	−25323.0	−1.29185	−0.645927	+	0.763399i	$0.723529\pi$
$728$	−630.000	−0.0320733
$729$	−15443.0	−0.784586
$730$	4225.00	0.214211
$731$	5418.00	0.274134
$732$	−1343.00	−0.0678124
$733$	20104.0	1.01304	0.506520	−	0.862228i	$-0.330932\pi$
$733$	20104.0	1.01304	0.506520	+	0.862228i	$0.330932\pi$
$734$	45795.0	2.30289
$735$	−1695.00	−0.0850626
$736$	−4675.00	−0.234134
$737$	−5907.00	−0.295234
$738$	−49530.0	−2.47049
$739$	9704.00	0.483041	0.241521	−	0.970396i	$-0.422354\pi$
$739$	9704.00	0.483041	0.241521	+	0.970396i	$0.422354\pi$
$740$	10710.0	0.532037
$741$	133.000	0.00659363
$742$	−4040.00	−0.199883
$743$	413.000	0.0203923	0.0101962	−	0.999948i	$-0.496754\pi$
$743$	413.000	0.0203923	0.0101962	+	0.999948i	$0.496754\pi$
$744$	11745.0	0.578753
$745$	7455.00	0.366618
$746$	−13865.0	−0.680474
$747$	−15626.0	−0.765362
$748$	−2618.00	−0.127973
$749$	−2288.00	−0.111618
$750$	−625.000	−0.0304290
$751$	5572.00	0.270739	0.135370	−	0.990795i	$-0.456778\pi$
$751$	5572.00	0.270739	0.135370	+	0.990795i	$0.456778\pi$
$752$	16821.0	0.815690
$753$	6609.00	0.319848
$754$	−910.000	−0.0439526
$755$	4300.00	0.207276
$756$	−1802.00	−0.0866906
$757$	−17915.0	−0.860148	−0.430074	−	0.902794i	$-0.641512\pi$
$757$	−17915.0	−0.860148	−0.430074	+	0.902794i	$0.641512\pi$
$758$	41630.0	1.99481
$759$	605.000	0.0289329
$760$	4275.00	0.204040
$761$	33118.0	1.57756	0.788782	−	0.614673i	$-0.210712\pi$
$761$	33118.0	1.57756	0.788782	+	0.614673i	$0.210712\pi$
$762$	−855.000	−0.0406475
$763$	−1532.00	−0.0726895
$764$	−51374.0	−2.43278
$765$	1820.00	0.0860160
$766$	33220.0	1.56695
$767$	−5222.00	−0.245835
$768$	8279.00	0.388988
$769$	−21758.0	−1.02030	−0.510152	−	0.860084i	$-0.670411\pi$
$769$	−21758.0	−1.02030	−0.510152	+	0.860084i	$0.670411\pi$
$770$	550.000	0.0257411
$771$	2505.00	0.117011
$772$	11186.0	0.521493
$773$	13222.0	0.615216	0.307608	−	0.951513i	$-0.400471\pi$
$773$	13222.0	0.615216	0.307608	+	0.951513i	$0.400471\pi$
$774$	50310.0	2.33638
$775$	6525.00	0.302432
$776$	−38970.0	−1.80276
$777$	−252.000	−0.0116351
$778$	44400.0	2.04604
$779$	−7239.00	−0.332945
$780$	−595.000	−0.0273134
$781$	9064.00	0.415282
$782$	−3850.00	−0.176056
$783$	−1378.00	−0.0628936
$784$	−30171.0	−1.37441
$785$	−8665.00	−0.393971
$786$	−9500.00	−0.431112
$787$	13862.0	0.627861	0.313931	−	0.949446i	$-0.398354\pi$
$787$	13862.0	0.627861	0.313931	+	0.949446i	$0.398354\pi$
$788$	7242.00	0.327393
$789$	−442.000	−0.0199437
$790$	−8450.00	−0.380554
$791$	4084.00	0.183578
$792$	−12870.0	−0.577419
$793$	−553.000	−0.0247637
$794$	15470.0	0.691448
$795$	−2020.00	−0.0901157
$796$	−21692.0	−0.965895
$797$	−4274.00	−0.189953	−0.0949767	−	0.995479i	$-0.530278\pi$
$797$	−4274.00	−0.189953	−0.0949767	+	0.995479i	$0.530278\pi$
$798$	−190.000	−0.00842848
$799$	2646.00	0.117157
$800$	−2125.00	−0.0939126
$801$	19812.0	0.873936
$802$	30040.0	1.32263
$803$	−1859.00	−0.0816970
$804$	−9129.00	−0.400442
$805$	550.000	0.0240807
$806$	9135.00	0.399214
$807$	−1226.00	−0.0534786
$808$	−45270.0	−1.97103
$809$	−23656.0	−1.02806	−0.514030	−	0.857772i	$-0.671848\pi$
$809$	−23656.0	−1.02806	−0.514030	+	0.857772i	$0.671848\pi$
$810$	16225.0	0.703813
$811$	−35621.0	−1.54232	−0.771161	−	0.636641i	$-0.780323\pi$
$811$	−35621.0	−1.54232	−0.771161	+	0.636641i	$0.780323\pi$
$812$	884.000	0.0382048
$813$	−8264.00	−0.356496
$814$	−6930.00	−0.298398
$815$	19900.0	0.855296
$816$	−1246.00	−0.0534543
$817$	7353.00	0.314870
$818$	28805.0	1.23123
$819$	−364.000	−0.0155301
$820$	32385.0	1.37919
$821$	38723.0	1.64609	0.823046	−	0.567974i	$-0.192273\pi$
$821$	38723.0	1.64609	0.823046	+	0.567974i	$0.192273\pi$
$822$	1620.00	0.0687396
$823$	17768.0	0.752556	0.376278	−	0.926507i	$-0.377204\pi$
$823$	17768.0	0.752556	0.376278	+	0.926507i	$0.377204\pi$
$824$	−90090.0	−3.80878
$825$	275.000	0.0116052
$826$	7460.00	0.314245
$827$	−31116.0	−1.30835	−0.654177	−	0.756341i	$-0.726985\pi$
$827$	−31116.0	−1.30835	−0.654177	+	0.756341i	$0.726985\pi$
$828$	−24310.0	−1.02033
$829$	24931.0	1.04450	0.522249	−	0.852793i	$-0.325093\pi$
$829$	24931.0	1.04450	0.522249	+	0.852793i	$0.325093\pi$
$830$	15025.0	0.628344
$831$	8128.00	0.339299
$832$	2009.00	0.0837134
$833$	−4746.00	−0.197406
$834$	890.000	0.0369523
$835$	−5295.00	−0.219450
$836$	−3553.00	−0.146989
$837$	13833.0	0.571253
$838$	25315.0	1.04355
$839$	10697.0	0.440169	0.220084	−	0.975481i	$-0.429367\pi$
$839$	10697.0	0.440169	0.220084	+	0.975481i	$0.429367\pi$
$840$	450.000	0.0184839
$841$	−23713.0	−0.972283
$842$	42685.0	1.74706
$843$	−886.000	−0.0361986
$844$	76313.0	3.11232
$845$	10740.0	0.437239
$846$	24570.0	0.998504
$847$	−242.000	−0.00981726
$848$	−35956.0	−1.45605
$849$	−5621.00	−0.227223
$850$	−1750.00	−0.0706171
$851$	−6930.00	−0.279151
$852$	14008.0	0.563270
$853$	4338.00	0.174127	0.0870635	−	0.996203i	$-0.472252\pi$
$853$	4338.00	0.174127	0.0870635	+	0.996203i	$0.472252\pi$
$854$	790.000	0.0316549
$855$	2470.00	0.0987979
$856$	−51480.0	−2.05555
$857$	19186.0	0.764739	0.382369	−	0.924010i	$-0.375108\pi$
$857$	19186.0	0.764739	0.382369	+	0.924010i	$0.375108\pi$
$858$	385.000	0.0153190
$859$	−37956.0	−1.50762	−0.753808	−	0.657095i	$-0.771785\pi$
$859$	−37956.0	−1.50762	−0.753808	+	0.657095i	$0.771785\pi$
$860$	−32895.0	−1.30431
$861$	−762.000	−0.0301613
$862$	−29680.0	−1.17274
$863$	−28396.0	−1.12006	−0.560030	−	0.828473i	$-0.689210\pi$
$863$	−28396.0	−1.12006	−0.560030	+	0.828473i	$0.689210\pi$
$864$	−4505.00	−0.177388
$865$	−4855.00	−0.190838
$866$	−27205.0	−1.06751
$867$	4717.00	0.184772
$868$	−8874.00	−0.347008
$869$	3718.00	0.145138
$870$	650.000	0.0253300
$871$	−3759.00	−0.146233
$872$	−34470.0	−1.33865
$873$	−22516.0	−0.872911
$874$	−5225.00	−0.202218
$875$	250.000	0.00965891
$876$	−2873.00	−0.110810
$877$	49966.0	1.92387	0.961934	−	0.273282i	$-0.0881094\pi$
$877$	49966.0	1.92387	0.961934	+	0.273282i	$0.0881094\pi$
$878$	−57500.0	−2.21017
$879$	386.000	0.0148117
$880$	4895.00	0.187512
$881$	38733.0	1.48121	0.740606	−	0.671939i	$-0.234538\pi$
$881$	38733.0	1.48121	0.740606	+	0.671939i	$0.234538\pi$
$882$	−44070.0	−1.68244
$883$	45426.0	1.73126	0.865632	−	0.500680i	$-0.166917\pi$
$883$	45426.0	1.73126	0.865632	+	0.500680i	$0.166917\pi$
$884$	−1666.00	−0.0633865
$885$	3730.00	0.141675
$886$	−16130.0	−0.611623
$887$	29496.0	1.11655	0.558274	−	0.829656i	$-0.311464\pi$
$887$	29496.0	1.11655	0.558274	+	0.829656i	$0.311464\pi$
$888$	−5670.00	−0.214271
$889$	342.000	0.0129025
$890$	−19050.0	−0.717480
$891$	−7139.00	−0.268424
$892$	−12750.0	−0.478589
$893$	3591.00	0.134567
$894$	−7455.00	−0.278895
$895$	11010.0	0.411200
$896$	−4230.00	−0.157717
$897$	385.000	0.0143309
$898$	−81750.0	−3.03790
$899$	−6786.00	−0.251753
$900$	−11050.0	−0.409259
$901$	−5656.00	−0.209133
$902$	−20955.0	−0.773531
$903$	774.000	0.0285239
$904$	91890.0	3.38077
$905$	−5485.00	−0.201467
$906$	−4300.00	−0.157680
$907$	17796.0	0.651496	0.325748	−	0.945457i	$-0.394384\pi$
$907$	17796.0	0.651496	0.325748	+	0.945457i	$0.394384\pi$
$908$	−34272.0	−1.25260
$909$	−26156.0	−0.954389
$910$	350.000	0.0127499
$911$	−8661.00	−0.314985	−0.157493	−	0.987520i	$-0.550341\pi$
$911$	−8661.00	−0.314985	−0.157493	+	0.987520i	$0.550341\pi$
$912$	−1691.00	−0.0613976
$913$	−6611.00	−0.239641
$914$	−59255.0	−2.14440
$915$	395.000	0.0142714
$916$	−113560.	−4.09621
$917$	3800.00	0.136845
$918$	−3710.00	−0.133386
$919$	40505.0	1.45390	0.726951	−	0.686689i	$-0.240937\pi$
$919$	40505.0	1.45390	0.726951	+	0.686689i	$0.240937\pi$
$920$	12375.0	0.443469
$921$	−2480.00	−0.0887283
$922$	49455.0	1.76650
$923$	5768.00	0.205695
$924$	−374.000	−0.0133157
$925$	−3150.00	−0.111969
$926$	85440.0	3.03211
$927$	−52052.0	−1.84424
$928$	2210.00	0.0781754
$929$	563.000	0.0198831	0.00994157	−	0.999951i	$-0.496835\pi$
$929$	563.000	0.0198831	0.00994157	+	0.999951i	$0.496835\pi$
$930$	−6525.00	−0.230068
$931$	−6441.00	−0.226740
$932$	−109191.	−3.83763
$933$	−8242.00	−0.289208
$934$	−23580.0	−0.826083
$935$	770.000	0.0269323
$936$	−8190.00	−0.286003
$937$	41626.0	1.45129	0.725647	−	0.688067i	$-0.241541\pi$
$937$	41626.0	1.45129	0.725647	+	0.688067i	$0.241541\pi$
$938$	5370.00	0.186926
$939$	510.000	0.0177244
$940$	−16065.0	−0.557428
$941$	−17508.0	−0.606530	−0.303265	−	0.952906i	$-0.598077\pi$
$941$	−17508.0	−0.606530	−0.303265	+	0.952906i	$0.598077\pi$
$942$	8665.00	0.299704
$943$	−20955.0	−0.723636
$944$	66394.0	2.28913
$945$	530.000	0.0182443
$946$	21285.0	0.731538
$947$	5208.00	0.178709	0.0893544	−	0.996000i	$-0.471520\pi$
$947$	5208.00	0.178709	0.0893544	+	0.996000i	$0.471520\pi$
$948$	5746.00	0.196858
$949$	−1183.00	−0.0404655
$950$	−2375.00	−0.0811107
$951$	8748.00	0.298290
$952$	1260.00	0.0428958
$953$	−1334.00	−0.0453437	−0.0226718	−	0.999743i	$-0.507217\pi$
$953$	−1334.00	−0.0453437	−0.0226718	+	0.999743i	$0.507217\pi$
$954$	−52520.0	−1.78239
$955$	15110.0	0.511988
$956$	−92480.0	−3.12868
$957$	−286.000	−0.00966047
$958$	−1635.00	−0.0551403
$959$	−648.000	−0.0218196
$960$	−1435.00	−0.0482442
$961$	38330.0	1.28663
$962$	−4410.00	−0.147801
$963$	−29744.0	−0.995314
$964$	−2635.00	−0.0880370
$965$	−3290.00	−0.109750
$966$	−550.000	−0.0183188
$967$	−46050.0	−1.53140	−0.765702	−	0.643195i	$-0.777608\pi$
$967$	−46050.0	−1.53140	−0.765702	+	0.643195i	$0.777608\pi$
$968$	−5445.00	−0.180794
$969$	−266.000	−0.00881853
$970$	21650.0	0.716639
$971$	44770.0	1.47965	0.739824	−	0.672801i	$-0.234909\pi$
$971$	44770.0	1.47965	0.739824	+	0.672801i	$0.234909\pi$
$972$	−35360.0	−1.16684
$973$	−356.000	−0.0117295
$974$	−70.0000	−0.00230282
$975$	175.000	0.00574819
$976$	7031.00	0.230591
$977$	17023.0	0.557435	0.278718	−	0.960373i	$-0.410091\pi$
$977$	17023.0	0.557435	0.278718	+	0.960373i	$0.410091\pi$
$978$	−19900.0	−0.650646
$979$	8382.00	0.273636
$980$	28815.0	0.939246
$981$	−19916.0	−0.648184
$982$	−91910.0	−2.98673
$983$	−1698.00	−0.0550944	−0.0275472	−	0.999621i	$-0.508770\pi$
$983$	−1698.00	−0.0550944	−0.0275472	+	0.999621i	$0.508770\pi$
$984$	−17145.0	−0.555450
$985$	−2130.00	−0.0689010
$986$	1820.00	0.0587836
$987$	378.000	0.0121903
$988$	−2261.00	−0.0728057
$989$	21285.0	0.684351
$990$	7150.00	0.229537
$991$	46096.0	1.47759	0.738793	−	0.673932i	$-0.235396\pi$
$991$	46096.0	1.47759	0.738793	+	0.673932i	$0.235396\pi$
$992$	−22185.0	−0.710055
$993$	−6742.00	−0.215459
$994$	−8240.00	−0.262935
$995$	6380.00	0.203276
$996$	−10217.0	−0.325038
$997$	−15636.0	−0.496687	−0.248344	−	0.968672i	$-0.579886\pi$
$997$	−15636.0	−0.496687	−0.248344	+	0.968672i	$0.579886\pi$
$998$	3725.00	0.118149
$999$	−6678.00	−0.211494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.4.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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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