LMFDB - Embedded newform 1610.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1610,4,Mod(1,1610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1610, 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("1610.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1610 = 2 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1610.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:	$94.9930751092$
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	$\chi$	$=$	1610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -5.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +10.0000 q^{6} -7.00000 q^{7} -8.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -5.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} +10.0000 q^{6} -7.00000 q^{7} -8.00000 q^{8} -2.00000 q^{9} -10.0000 q^{10} -50.0000 q^{11} -20.0000 q^{12} -33.0000 q^{13} +14.0000 q^{14} -25.0000 q^{15} +16.0000 q^{16} +98.0000 q^{17} +4.00000 q^{18} -18.0000 q^{19} +20.0000 q^{20} +35.0000 q^{21} +100.000 q^{22} -23.0000 q^{23} +40.0000 q^{24} +25.0000 q^{25} +66.0000 q^{26} +145.000 q^{27} -28.0000 q^{28} +285.000 q^{29} +50.0000 q^{30} +69.0000 q^{31} -32.0000 q^{32} +250.000 q^{33} -196.000 q^{34} -35.0000 q^{35} -8.00000 q^{36} -132.000 q^{37} +36.0000 q^{38} +165.000 q^{39} -40.0000 q^{40} -87.0000 q^{41} -70.0000 q^{42} +138.000 q^{43} -200.000 q^{44} -10.0000 q^{45} +46.0000 q^{46} -565.000 q^{47} -80.0000 q^{48} +49.0000 q^{49} -50.0000 q^{50} -490.000 q^{51} -132.000 q^{52} +380.000 q^{53} -290.000 q^{54} -250.000 q^{55} +56.0000 q^{56} +90.0000 q^{57} -570.000 q^{58} -180.000 q^{59} -100.000 q^{60} +700.000 q^{61} -138.000 q^{62} +14.0000 q^{63} +64.0000 q^{64} -165.000 q^{65} -500.000 q^{66} +76.0000 q^{67} +392.000 q^{68} +115.000 q^{69} +70.0000 q^{70} -861.000 q^{71} +16.0000 q^{72} +505.000 q^{73} +264.000 q^{74} -125.000 q^{75} -72.0000 q^{76} +350.000 q^{77} -330.000 q^{78} +962.000 q^{79} +80.0000 q^{80} -671.000 q^{81} +174.000 q^{82} +406.000 q^{83} +140.000 q^{84} +490.000 q^{85} -276.000 q^{86} -1425.00 q^{87} +400.000 q^{88} -530.000 q^{89} +20.0000 q^{90} +231.000 q^{91} -92.0000 q^{92} -345.000 q^{93} +1130.00 q^{94} -90.0000 q^{95} +160.000 q^{96} -742.000 q^{97} -98.0000 q^{98} +100.000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−5.00000	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$3$	−5.00000	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	10.0000	0.680414
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	−2.00000	−0.0740741
$10$	−10.0000	−0.316228
$11$	−50.0000	−1.37051	−0.685253	−	0.728305i	$-0.740308\pi$
$11$	−50.0000	−1.37051	−0.685253	+	0.728305i	$0.740308\pi$
$12$	−20.0000	−0.481125
$13$	−33.0000	−0.704043	−0.352021	−	0.935992i	$-0.614506\pi$
$13$	−33.0000	−0.704043	−0.352021	+	0.935992i	$0.614506\pi$
$14$	14.0000	0.267261
$15$	−25.0000	−0.430331
$16$	16.0000	0.250000
$17$	98.0000	1.39815	0.699073	−	0.715050i	$-0.253596\pi$
$17$	98.0000	1.39815	0.699073	+	0.715050i	$0.253596\pi$
$18$	4.00000	0.0523783
$19$	−18.0000	−0.217341	−0.108671	−	0.994078i	$-0.534659\pi$
$19$	−18.0000	−0.217341	−0.108671	+	0.994078i	$0.534659\pi$
$20$	20.0000	0.223607
$21$	35.0000	0.363696
$22$	100.000	0.969094
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	40.0000	0.340207
$25$	25.0000	0.200000
$26$	66.0000	0.497833
$27$	145.000	1.03353
$28$	−28.0000	−0.188982
$29$	285.000	1.82494	0.912468	−	0.409147i	$-0.134174\pi$
$29$	285.000	1.82494	0.912468	+	0.409147i	$0.134174\pi$
$30$	50.0000	0.304290
$31$	69.0000	0.399767	0.199883	−	0.979820i	$-0.435944\pi$
$31$	69.0000	0.399767	0.199883	+	0.979820i	$0.435944\pi$
$32$	−32.0000	−0.176777
$33$	250.000	1.31877
$34$	−196.000	−0.988639
$35$	−35.0000	−0.169031
$36$	−8.00000	−0.0370370
$37$	−132.000	−0.586504	−0.293252	−	0.956035i	$-0.594738\pi$
$37$	−132.000	−0.586504	−0.293252	+	0.956035i	$0.594738\pi$
$38$	36.0000	0.153683
$39$	165.000	0.677465
$40$	−40.0000	−0.158114
$41$	−87.0000	−0.331393	−0.165697	−	0.986177i	$-0.552987\pi$
$41$	−87.0000	−0.331393	−0.165697	+	0.986177i	$0.552987\pi$
$42$	−70.0000	−0.257172
$43$	138.000	0.489414	0.244707	−	0.969597i	$-0.421308\pi$
$43$	138.000	0.489414	0.244707	+	0.969597i	$0.421308\pi$
$44$	−200.000	−0.685253
$45$	−10.0000	−0.0331269
$46$	46.0000	0.147442
$47$	−565.000	−1.75348	−0.876742	−	0.480962i	$-0.840288\pi$
$47$	−565.000	−1.75348	−0.876742	+	0.480962i	$0.840288\pi$
$48$	−80.0000	−0.240563
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	−490.000	−1.34537
$52$	−132.000	−0.352021
$53$	380.000	0.984849	0.492425	−	0.870355i	$-0.336111\pi$
$53$	380.000	0.984849	0.492425	+	0.870355i	$0.336111\pi$
$54$	−290.000	−0.730815
$55$	−250.000	−0.612909
$56$	56.0000	0.133631
$57$	90.0000	0.209137
$58$	−570.000	−1.29043
$59$	−180.000	−0.397187	−0.198593	−	0.980082i	$-0.563637\pi$
$59$	−180.000	−0.397187	−0.198593	+	0.980082i	$0.563637\pi$
$60$	−100.000	−0.215166
$61$	700.000	1.46928	0.734638	−	0.678459i	$-0.237352\pi$
$61$	700.000	1.46928	0.734638	+	0.678459i	$0.237352\pi$
$62$	−138.000	−0.282678
$63$	14.0000	0.0279974
$64$	64.0000	0.125000
$65$	−165.000	−0.314857
$66$	−500.000	−0.932511
$67$	76.0000	0.138580	0.0692901	−	0.997597i	$-0.477927\pi$
$67$	76.0000	0.138580	0.0692901	+	0.997597i	$0.477927\pi$
$68$	392.000	0.699073
$69$	115.000	0.200643
$70$	70.0000	0.119523
$71$	−861.000	−1.43918	−0.719591	−	0.694398i	$-0.755671\pi$
$71$	−861.000	−1.43918	−0.719591	+	0.694398i	$0.755671\pi$
$72$	16.0000	0.0261891
$73$	505.000	0.809668	0.404834	−	0.914390i	$-0.367329\pi$
$73$	505.000	0.809668	0.404834	+	0.914390i	$0.367329\pi$
$74$	264.000	0.414721
$75$	−125.000	−0.192450
$76$	−72.0000	−0.108671
$77$	350.000	0.518003
$78$	−330.000	−0.479040
$79$	962.000	1.37004	0.685022	−	0.728522i	$-0.259793\pi$
$79$	962.000	1.37004	0.685022	+	0.728522i	$0.259793\pi$
$80$	80.0000	0.111803
$81$	−671.000	−0.920439
$82$	174.000	0.234330
$83$	406.000	0.536919	0.268460	−	0.963291i	$-0.413485\pi$
$83$	406.000	0.536919	0.268460	+	0.963291i	$0.413485\pi$
$84$	140.000	0.181848
$85$	490.000	0.625270
$86$	−276.000	−0.346068
$87$	−1425.00	−1.75605
$88$	400.000	0.484547
$89$	−530.000	−0.631235	−0.315617	−	0.948887i	$-0.602212\pi$
$89$	−530.000	−0.631235	−0.315617	+	0.948887i	$0.602212\pi$
$90$	20.0000	0.0234243
$91$	231.000	0.266103
$92$	−92.0000	−0.104257
$93$	−345.000	−0.384676
$94$	1130.00	1.23990
$95$	−90.0000	−0.0971979
$96$	160.000	0.170103
$97$	−742.000	−0.776687	−0.388344	−	0.921515i	$-0.626953\pi$
$97$	−742.000	−0.776687	−0.388344	+	0.921515i	$0.626953\pi$
$98$	−98.0000	−0.101015
$99$	100.000	0.101519
$100$	100.000	0.100000
$101$	−830.000	−0.817704	−0.408852	−	0.912601i	$-0.634071\pi$
$101$	−830.000	−0.817704	−0.408852	+	0.912601i	$0.634071\pi$
$102$	980.000	0.951318
$103$	488.000	0.466836	0.233418	−	0.972377i	$-0.425009\pi$
$103$	488.000	0.466836	0.233418	+	0.972377i	$0.425009\pi$
$104$	264.000	0.248917
$105$	175.000	0.162650
$106$	−760.000	−0.696394
$107$	1910.00	1.72567	0.862835	−	0.505486i	$-0.168687\pi$
$107$	1910.00	1.72567	0.862835	+	0.505486i	$0.168687\pi$
$108$	580.000	0.516764
$109$	306.000	0.268894	0.134447	−	0.990921i	$-0.457074\pi$
$109$	306.000	0.268894	0.134447	+	0.990921i	$0.457074\pi$
$110$	500.000	0.433392
$111$	660.000	0.564364
$112$	−112.000	−0.0944911
$113$	180.000	0.149849	0.0749247	−	0.997189i	$-0.476128\pi$
$113$	180.000	0.149849	0.0749247	+	0.997189i	$0.476128\pi$
$114$	−180.000	−0.147882
$115$	−115.000	−0.0932505
$116$	1140.00	0.912468
$117$	66.0000	0.0521513
$118$	360.000	0.280853
$119$	−686.000	−0.528450
$120$	200.000	0.152145
$121$	1169.00	0.878287
$122$	−1400.00	−1.03893
$123$	435.000	0.318883
$124$	276.000	0.199883
$125$	125.000	0.0894427
$126$	−28.0000	−0.0197971
$127$	−1289.00	−0.900632	−0.450316	−	0.892869i	$-0.648689\pi$
$127$	−1289.00	−0.900632	−0.450316	+	0.892869i	$0.648689\pi$
$128$	−128.000	−0.0883883
$129$	−690.000	−0.470939
$130$	330.000	0.222638
$131$	−519.000	−0.346147	−0.173073	−	0.984909i	$-0.555370\pi$
$131$	−519.000	−0.346147	−0.173073	+	0.984909i	$0.555370\pi$
$132$	1000.00	0.659385
$133$	126.000	0.0821473
$134$	−152.000	−0.0979910
$135$	725.000	0.462208
$136$	−784.000	−0.494319
$137$	1350.00	0.841885	0.420943	−	0.907087i	$-0.361699\pi$
$137$	1350.00	0.841885	0.420943	+	0.907087i	$0.361699\pi$
$138$	−230.000	−0.141876
$139$	−1137.00	−0.693806	−0.346903	−	0.937901i	$-0.612767\pi$
$139$	−1137.00	−0.693806	−0.346903	+	0.937901i	$0.612767\pi$
$140$	−140.000	−0.0845154
$141$	2825.00	1.68729
$142$	1722.00	1.01766
$143$	1650.00	0.964895
$144$	−32.0000	−0.0185185
$145$	1425.00	0.816137
$146$	−1010.00	−0.572522
$147$	−245.000	−0.137464
$148$	−528.000	−0.293252
$149$	−308.000	−0.169345	−0.0846723	−	0.996409i	$-0.526984\pi$
$149$	−308.000	−0.169345	−0.0846723	+	0.996409i	$0.526984\pi$
$150$	250.000	0.136083
$151$	−657.000	−0.354079	−0.177039	−	0.984204i	$-0.556652\pi$
$151$	−657.000	−0.354079	−0.177039	+	0.984204i	$0.556652\pi$
$152$	144.000	0.0768417
$153$	−196.000	−0.103566
$154$	−700.000	−0.366283
$155$	345.000	0.178781
$156$	660.000	0.338733
$157$	1174.00	0.596786	0.298393	−	0.954443i	$-0.403549\pi$
$157$	1174.00	0.596786	0.298393	+	0.954443i	$0.403549\pi$
$158$	−1924.00	−0.968767
$159$	−1900.00	−0.947672
$160$	−160.000	−0.0790569
$161$	161.000	0.0788110
$162$	1342.00	0.650849
$163$	235.000	0.112924	0.0564620	−	0.998405i	$-0.482018\pi$
$163$	235.000	0.112924	0.0564620	+	0.998405i	$0.482018\pi$
$164$	−348.000	−0.165697
$165$	1250.00	0.589772
$166$	−812.000	−0.379659
$167$	2272.00	1.05277	0.526385	−	0.850246i	$-0.323547\pi$
$167$	2272.00	1.05277	0.526385	+	0.850246i	$0.323547\pi$
$168$	−280.000	−0.128586
$169$	−1108.00	−0.504324
$170$	−980.000	−0.442133
$171$	36.0000	0.0160993
$172$	552.000	0.244707
$173$	1302.00	0.572192	0.286096	−	0.958201i	$-0.407642\pi$
$173$	1302.00	0.572192	0.286096	+	0.958201i	$0.407642\pi$
$174$	2850.00	1.24171
$175$	−175.000	−0.0755929
$176$	−800.000	−0.342627
$177$	900.000	0.382193
$178$	1060.00	0.446350
$179$	−2915.00	−1.21719	−0.608596	−	0.793480i	$-0.708267\pi$
$179$	−2915.00	−1.21719	−0.608596	+	0.793480i	$0.708267\pi$
$180$	−40.0000	−0.0165635
$181$	−3962.00	−1.62703	−0.813517	−	0.581541i	$-0.802450\pi$
$181$	−3962.00	−1.62703	−0.813517	+	0.581541i	$0.802450\pi$
$182$	−462.000	−0.188163
$183$	−3500.00	−1.41381
$184$	184.000	0.0737210
$185$	−660.000	−0.262293
$186$	690.000	0.272007
$187$	−4900.00	−1.91617
$188$	−2260.00	−0.876742
$189$	−1015.00	−0.390637
$190$	180.000	0.0687293
$191$	−2106.00	−0.797826	−0.398913	−	0.916989i	$-0.630612\pi$
$191$	−2106.00	−0.797826	−0.398913	+	0.916989i	$0.630612\pi$
$192$	−320.000	−0.120281
$193$	−485.000	−0.180886	−0.0904432	−	0.995902i	$-0.528828\pi$
$193$	−485.000	−0.180886	−0.0904432	+	0.995902i	$0.528828\pi$
$194$	1484.00	0.549201
$195$	825.000	0.302972
$196$	196.000	0.0714286
$197$	4627.00	1.67340	0.836701	−	0.547660i	$-0.184481\pi$
$197$	4627.00	1.67340	0.836701	+	0.547660i	$0.184481\pi$
$198$	−200.000	−0.0717848
$199$	−1394.00	−0.496573	−0.248287	−	0.968687i	$-0.579867\pi$
$199$	−1394.00	−0.496573	−0.248287	+	0.968687i	$0.579867\pi$
$200$	−200.000	−0.0707107
$201$	−380.000	−0.133349
$202$	1660.00	0.578204
$203$	−1995.00	−0.689761
$204$	−1960.00	−0.672684
$205$	−435.000	−0.148204
$206$	−976.000	−0.330103
$207$	46.0000	0.0154455
$208$	−528.000	−0.176011
$209$	900.000	0.297867
$210$	−350.000	−0.115011
$211$	−972.000	−0.317134	−0.158567	−	0.987348i	$-0.550687\pi$
$211$	−972.000	−0.317134	−0.158567	+	0.987348i	$0.550687\pi$
$212$	1520.00	0.492425
$213$	4305.00	1.38485
$214$	−3820.00	−1.22023
$215$	690.000	0.218873
$216$	−1160.00	−0.365407
$217$	−483.000	−0.151098
$218$	−612.000	−0.190137
$219$	−2525.00	−0.779104
$220$	−1000.00	−0.306454
$221$	−3234.00	−0.984355
$222$	−1320.00	−0.399066
$223$	−3296.00	−0.989760	−0.494880	−	0.868961i	$-0.664788\pi$
$223$	−3296.00	−0.989760	−0.494880	+	0.868961i	$0.664788\pi$
$224$	224.000	0.0668153
$225$	−50.0000	−0.0148148
$226$	−360.000	−0.105959
$227$	344.000	0.100582	0.0502909	−	0.998735i	$-0.483985\pi$
$227$	344.000	0.100582	0.0502909	+	0.998735i	$0.483985\pi$
$228$	360.000	0.104568
$229$	−5976.00	−1.72448	−0.862238	−	0.506503i	$-0.830938\pi$
$229$	−5976.00	−1.72448	−0.862238	+	0.506503i	$0.830938\pi$
$230$	230.000	0.0659380
$231$	−1750.00	−0.498448
$232$	−2280.00	−0.645213
$233$	−2839.00	−0.798236	−0.399118	−	0.916899i	$-0.630684\pi$
$233$	−2839.00	−0.798236	−0.399118	+	0.916899i	$0.630684\pi$
$234$	−132.000	−0.0368765
$235$	−2825.00	−0.784182
$236$	−720.000	−0.198593
$237$	−4810.00	−1.31833
$238$	1372.00	0.373670
$239$	−1845.00	−0.499344	−0.249672	−	0.968331i	$-0.580323\pi$
$239$	−1845.00	−0.499344	−0.249672	+	0.968331i	$0.580323\pi$
$240$	−400.000	−0.107583
$241$	4372.00	1.16857	0.584285	−	0.811549i	$-0.301375\pi$
$241$	4372.00	1.16857	0.584285	+	0.811549i	$0.301375\pi$
$242$	−2338.00	−0.621043
$243$	−560.000	−0.147835
$244$	2800.00	0.734638
$245$	245.000	0.0638877
$246$	−870.000	−0.225484
$247$	594.000	0.153017
$248$	−552.000	−0.141339
$249$	−2030.00	−0.516651
$250$	−250.000	−0.0632456
$251$	−4784.00	−1.20304	−0.601521	−	0.798857i	$-0.705438\pi$
$251$	−4784.00	−1.20304	−0.601521	+	0.798857i	$0.705438\pi$
$252$	56.0000	0.0139987
$253$	1150.00	0.285770
$254$	2578.00	0.636843
$255$	−2450.00	−0.601666
$256$	256.000	0.0625000
$257$	2863.00	0.694899	0.347449	−	0.937699i	$-0.387048\pi$
$257$	2863.00	0.694899	0.347449	+	0.937699i	$0.387048\pi$
$258$	1380.00	0.333004
$259$	924.000	0.221678
$260$	−660.000	−0.157429
$261$	−570.000	−0.135181
$262$	1038.00	0.244763
$263$	7908.00	1.85410	0.927050	−	0.374938i	$-0.122336\pi$
$263$	7908.00	1.85410	0.927050	+	0.374938i	$0.122336\pi$
$264$	−2000.00	−0.466256
$265$	1900.00	0.440438
$266$	−252.000	−0.0580869
$267$	2650.00	0.607406
$268$	304.000	0.0692901
$269$	−3381.00	−0.766332	−0.383166	−	0.923680i	$-0.625166\pi$
$269$	−3381.00	−0.766332	−0.383166	+	0.923680i	$0.625166\pi$
$270$	−1450.00	−0.326830
$271$	−1900.00	−0.425892	−0.212946	−	0.977064i	$-0.568306\pi$
$271$	−1900.00	−0.425892	−0.212946	+	0.977064i	$0.568306\pi$
$272$	1568.00	0.349537
$273$	−1155.00	−0.256058
$274$	−2700.00	−0.595303
$275$	−1250.00	−0.274101
$276$	460.000	0.100322
$277$	−2041.00	−0.442714	−0.221357	−	0.975193i	$-0.571049\pi$
$277$	−2041.00	−0.442714	−0.221357	+	0.975193i	$0.571049\pi$
$278$	2274.00	0.490595
$279$	−138.000	−0.0296123
$280$	280.000	0.0597614
$281$	−5158.00	−1.09502	−0.547510	−	0.836799i	$-0.684424\pi$
$281$	−5158.00	−1.09502	−0.547510	+	0.836799i	$0.684424\pi$
$282$	−5650.00	−1.19309
$283$	6492.00	1.36364	0.681819	−	0.731521i	$-0.261189\pi$
$283$	6492.00	1.36364	0.681819	+	0.731521i	$0.261189\pi$
$284$	−3444.00	−0.719591
$285$	450.000	0.0935288
$286$	−3300.00	−0.682284
$287$	609.000	0.125255
$288$	64.0000	0.0130946
$289$	4691.00	0.954814
$290$	−2850.00	−0.577096
$291$	3710.00	0.747368
$292$	2020.00	0.404834
$293$	−5118.00	−1.02047	−0.510233	−	0.860036i	$-0.670441\pi$
$293$	−5118.00	−1.02047	−0.510233	+	0.860036i	$0.670441\pi$
$294$	490.000	0.0972020
$295$	−900.000	−0.177627
$296$	1056.00	0.207361
$297$	−7250.00	−1.41646
$298$	616.000	0.119745
$299$	759.000	0.146803
$300$	−500.000	−0.0962250
$301$	−966.000	−0.184981
$302$	1314.00	0.250372
$303$	4150.00	0.786836
$304$	−288.000	−0.0543353
$305$	3500.00	0.657080
$306$	392.000	0.0732325
$307$	−7212.00	−1.34075	−0.670376	−	0.742022i	$-0.733867\pi$
$307$	−7212.00	−1.34075	−0.670376	+	0.742022i	$0.733867\pi$
$308$	1400.00	0.259001
$309$	−2440.00	−0.449213
$310$	−690.000	−0.126417
$311$	8189.00	1.49310	0.746552	−	0.665327i	$-0.231708\pi$
$311$	8189.00	1.49310	0.746552	+	0.665327i	$0.231708\pi$
$312$	−1320.00	−0.239520
$313$	3130.00	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	3130.00	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−2348.00	−0.421991
$315$	70.0000	0.0125208
$316$	3848.00	0.685022
$317$	1718.00	0.304393	0.152196	−	0.988350i	$-0.451365\pi$
$317$	1718.00	0.304393	0.152196	+	0.988350i	$0.451365\pi$
$318$	3800.00	0.670105
$319$	−14250.0	−2.50109
$320$	320.000	0.0559017
$321$	−9550.00	−1.66053
$322$	−322.000	−0.0557278
$323$	−1764.00	−0.303875
$324$	−2684.00	−0.460219
$325$	−825.000	−0.140809
$326$	−470.000	−0.0798494
$327$	−1530.00	−0.258744
$328$	696.000	0.117165
$329$	3955.00	0.662754
$330$	−2500.00	−0.417032
$331$	−6007.00	−0.997506	−0.498753	−	0.866744i	$-0.666209\pi$
$331$	−6007.00	−0.997506	−0.498753	+	0.866744i	$0.666209\pi$
$332$	1624.00	0.268460
$333$	264.000	0.0434448
$334$	−4544.00	−0.744421
$335$	380.000	0.0619750
$336$	560.000	0.0909241
$337$	−3996.00	−0.645923	−0.322961	−	0.946412i	$-0.604678\pi$
$337$	−3996.00	−0.645923	−0.322961	+	0.946412i	$0.604678\pi$
$338$	2216.00	0.356611
$339$	−900.000	−0.144193
$340$	1960.00	0.312635
$341$	−3450.00	−0.547883
$342$	−72.0000	−0.0113840
$343$	−343.000	−0.0539949
$344$	−1104.00	−0.173034
$345$	575.000	0.0897303
$346$	−2604.00	−0.404601
$347$	−8488.00	−1.31314	−0.656570	−	0.754265i	$-0.727993\pi$
$347$	−8488.00	−1.31314	−0.656570	+	0.754265i	$0.727993\pi$
$348$	−5700.00	−0.878023
$349$	−7601.00	−1.16582	−0.582911	−	0.812536i	$-0.698087\pi$
$349$	−7601.00	−1.16582	−0.582911	+	0.812536i	$0.698087\pi$
$350$	350.000	0.0534522
$351$	−4785.00	−0.727648
$352$	1600.00	0.242274
$353$	445.000	0.0670962	0.0335481	−	0.999437i	$-0.489319\pi$
$353$	445.000	0.0670962	0.0335481	+	0.999437i	$0.489319\pi$
$354$	−1800.00	−0.270251
$355$	−4305.00	−0.643622
$356$	−2120.00	−0.315617
$357$	3430.00	0.508501
$358$	5830.00	0.860685
$359$	6266.00	0.921189	0.460594	−	0.887611i	$-0.347636\pi$
$359$	6266.00	0.921189	0.460594	+	0.887611i	$0.347636\pi$
$360$	80.0000	0.0117121
$361$	−6535.00	−0.952763
$362$	7924.00	1.15049
$363$	−5845.00	−0.845132
$364$	924.000	0.133052
$365$	2525.00	0.362095
$366$	7000.00	0.999715
$367$	4486.00	0.638058	0.319029	−	0.947745i	$-0.396643\pi$
$367$	4486.00	0.638058	0.319029	+	0.947745i	$0.396643\pi$
$368$	−368.000	−0.0521286
$369$	174.000	0.0245476
$370$	1320.00	0.185469
$371$	−2660.00	−0.372238
$372$	−1380.00	−0.192338
$373$	5392.00	0.748491	0.374246	−	0.927330i	$-0.377902\pi$
$373$	5392.00	0.748491	0.374246	+	0.927330i	$0.377902\pi$
$374$	9800.00	1.35494
$375$	−625.000	−0.0860663
$376$	4520.00	0.619950
$377$	−9405.00	−1.28483
$378$	2030.00	0.276222
$379$	−7414.00	−1.00483	−0.502416	−	0.864626i	$-0.667556\pi$
$379$	−7414.00	−1.00483	−0.502416	+	0.864626i	$0.667556\pi$
$380$	−360.000	−0.0485990
$381$	6445.00	0.866633
$382$	4212.00	0.564148
$383$	−12324.0	−1.64420	−0.822098	−	0.569346i	$-0.807196\pi$
$383$	−12324.0	−1.64420	−0.822098	+	0.569346i	$0.807196\pi$
$384$	640.000	0.0850517
$385$	1750.00	0.231658
$386$	970.000	0.127906
$387$	−276.000	−0.0362529
$388$	−2968.00	−0.388344
$389$	−8016.00	−1.04480	−0.522400	−	0.852700i	$-0.674963\pi$
$389$	−8016.00	−1.04480	−0.522400	+	0.852700i	$0.674963\pi$
$390$	−1650.00	−0.214233
$391$	−2254.00	−0.291534
$392$	−392.000	−0.0505076
$393$	2595.00	0.333080
$394$	−9254.00	−1.18327
$395$	4810.00	0.612702
$396$	400.000	0.0507595
$397$	19.0000	0.00240197	0.00120099	−	0.999999i	$-0.499618\pi$
$397$	19.0000	0.00240197	0.00120099	+	0.999999i	$0.499618\pi$
$398$	2788.00	0.351130
$399$	−630.000	−0.0790462
$400$	400.000	0.0500000
$401$	−5680.00	−0.707346	−0.353673	−	0.935369i	$-0.615067\pi$
$401$	−5680.00	−0.707346	−0.353673	+	0.935369i	$0.615067\pi$
$402$	760.000	0.0942919
$403$	−2277.00	−0.281453
$404$	−3320.00	−0.408852
$405$	−3355.00	−0.411633
$406$	3990.00	0.487735
$407$	6600.00	0.803808
$408$	3920.00	0.475659
$409$	10807.0	1.30653	0.653266	−	0.757128i	$-0.273398\pi$
$409$	10807.0	1.30653	0.653266	+	0.757128i	$0.273398\pi$
$410$	870.000	0.104796
$411$	−6750.00	−0.810104
$412$	1952.00	0.233418
$413$	1260.00	0.150122
$414$	−92.0000	−0.0109216
$415$	2030.00	0.240118
$416$	1056.00	0.124458
$417$	5685.00	0.667615
$418$	−1800.00	−0.210624
$419$	890.000	0.103769	0.0518847	−	0.998653i	$-0.483477\pi$
$419$	890.000	0.103769	0.0518847	+	0.998653i	$0.483477\pi$
$420$	700.000	0.0813250
$421$	6720.00	0.777940	0.388970	−	0.921250i	$-0.372831\pi$
$421$	6720.00	0.777940	0.388970	+	0.921250i	$0.372831\pi$
$422$	1944.00	0.224247
$423$	1130.00	0.129888
$424$	−3040.00	−0.348197
$425$	2450.00	0.279629
$426$	−8610.00	−0.979239
$427$	−4900.00	−0.555334
$428$	7640.00	0.862835
$429$	−8250.00	−0.928470
$430$	−1380.00	−0.154766
$431$	2724.00	0.304433	0.152216	−	0.988347i	$-0.451359\pi$
$431$	2724.00	0.304433	0.152216	+	0.988347i	$0.451359\pi$
$432$	2320.00	0.258382
$433$	8576.00	0.951816	0.475908	−	0.879495i	$-0.342120\pi$
$433$	8576.00	0.951816	0.475908	+	0.879495i	$0.342120\pi$
$434$	966.000	0.106842
$435$	−7125.00	−0.785328
$436$	1224.00	0.134447
$437$	414.000	0.0453188
$438$	5050.00	0.550909
$439$	191.000	0.0207652	0.0103826	−	0.999946i	$-0.496695\pi$
$439$	191.000	0.0207652	0.0103826	+	0.999946i	$0.496695\pi$
$440$	2000.00	0.216696
$441$	−98.0000	−0.0105820
$442$	6468.00	0.696044
$443$	−12311.0	−1.32035	−0.660173	−	0.751114i	$-0.729517\pi$
$443$	−12311.0	−1.32035	−0.660173	+	0.751114i	$0.729517\pi$
$444$	2640.00	0.282182
$445$	−2650.00	−0.282297
$446$	6592.00	0.699866
$447$	1540.00	0.162952
$448$	−448.000	−0.0472456
$449$	3330.00	0.350005	0.175003	−	0.984568i	$-0.444007\pi$
$449$	3330.00	0.350005	0.175003	+	0.984568i	$0.444007\pi$
$450$	100.000	0.0104757
$451$	4350.00	0.454176
$452$	720.000	0.0749247
$453$	3285.00	0.340713
$454$	−688.000	−0.0711221
$455$	1155.00	0.119005
$456$	−720.000	−0.0739410
$457$	−12954.0	−1.32596	−0.662979	−	0.748638i	$-0.730708\pi$
$457$	−12954.0	−1.32596	−0.662979	+	0.748638i	$0.730708\pi$
$458$	11952.0	1.21939
$459$	14210.0	1.44502
$460$	−460.000	−0.0466252
$461$	2123.00	0.214486	0.107243	−	0.994233i	$-0.465798\pi$
$461$	2123.00	0.214486	0.107243	+	0.994233i	$0.465798\pi$
$462$	3500.00	0.352456
$463$	−13184.0	−1.32335	−0.661677	−	0.749789i	$-0.730155\pi$
$463$	−13184.0	−1.32335	−0.661677	+	0.749789i	$0.730155\pi$
$464$	4560.00	0.456234
$465$	−1725.00	−0.172032
$466$	5678.00	0.564438
$467$	−19010.0	−1.88368	−0.941839	−	0.336064i	$-0.890904\pi$
$467$	−19010.0	−1.88368	−0.941839	+	0.336064i	$0.890904\pi$
$468$	264.000	0.0260757
$469$	−532.000	−0.0523784
$470$	5650.00	0.554500
$471$	−5870.00	−0.574258
$472$	1440.00	0.140427
$473$	−6900.00	−0.670745
$474$	9620.00	0.932197
$475$	−450.000	−0.0434682
$476$	−2744.00	−0.264225
$477$	−760.000	−0.0729518
$478$	3690.00	0.353089
$479$	2784.00	0.265562	0.132781	−	0.991145i	$-0.457609\pi$
$479$	2784.00	0.265562	0.132781	+	0.991145i	$0.457609\pi$
$480$	800.000	0.0760726
$481$	4356.00	0.412924
$482$	−8744.00	−0.826303
$483$	−805.000	−0.0758360
$484$	4676.00	0.439144
$485$	−3710.00	−0.347345
$486$	1120.00	0.104535
$487$	−2549.00	−0.237179	−0.118590	−	0.992943i	$-0.537837\pi$
$487$	−2549.00	−0.237179	−0.118590	+	0.992943i	$0.537837\pi$
$488$	−5600.00	−0.519467
$489$	−1175.00	−0.108661
$490$	−490.000	−0.0451754
$491$	13377.0	1.22952	0.614761	−	0.788713i	$-0.289252\pi$
$491$	13377.0	1.22952	0.614761	+	0.788713i	$0.289252\pi$
$492$	1740.00	0.159442
$493$	27930.0	2.55153
$494$	−1188.00	−0.108200
$495$	500.000	0.0454007
$496$	1104.00	0.0999417
$497$	6027.00	0.543960
$498$	4060.00	0.365327
$499$	−8813.00	−0.790629	−0.395315	−	0.918546i	$-0.629364\pi$
$499$	−8813.00	−0.790629	−0.395315	+	0.918546i	$0.629364\pi$
$500$	500.000	0.0447214
$501$	−11360.0	−1.01303
$502$	9568.00	0.850679
$503$	16068.0	1.42433	0.712164	−	0.702013i	$-0.247715\pi$
$503$	16068.0	1.42433	0.712164	+	0.702013i	$0.247715\pi$
$504$	−112.000	−0.00989856
$505$	−4150.00	−0.365688
$506$	−2300.00	−0.202070
$507$	5540.00	0.485286
$508$	−5156.00	−0.450316
$509$	−10705.0	−0.932202	−0.466101	−	0.884732i	$-0.654342\pi$
$509$	−10705.0	−0.932202	−0.466101	+	0.884732i	$0.654342\pi$
$510$	4900.00	0.425442
$511$	−3535.00	−0.306026
$512$	−512.000	−0.0441942
$513$	−2610.00	−0.224628
$514$	−5726.00	−0.491368
$515$	2440.00	0.208775
$516$	−2760.00	−0.235469
$517$	28250.0	2.40316
$518$	−1848.00	−0.156750
$519$	−6510.00	−0.550592
$520$	1320.00	0.111319
$521$	9780.00	0.822398	0.411199	−	0.911546i	$-0.365110\pi$
$521$	9780.00	0.822398	0.411199	+	0.911546i	$0.365110\pi$
$522$	1140.00	0.0955871
$523$	−11922.0	−0.996774	−0.498387	−	0.866955i	$-0.666074\pi$
$523$	−11922.0	−0.996774	−0.498387	+	0.866955i	$0.666074\pi$
$524$	−2076.00	−0.173073
$525$	875.000	0.0727393
$526$	−15816.0	−1.31105
$527$	6762.00	0.558932
$528$	4000.00	0.329693
$529$	529.000	0.0434783
$530$	−3800.00	−0.311437
$531$	360.000	0.0294212
$532$	504.000	0.0410736
$533$	2871.00	0.233315
$534$	−5300.00	−0.429501
$535$	9550.00	0.771743
$536$	−608.000	−0.0489955
$537$	14575.0	1.17124
$538$	6762.00	0.541878
$539$	−2450.00	−0.195787
$540$	2900.00	0.231104
$541$	3521.00	0.279814	0.139907	−	0.990165i	$-0.455320\pi$
$541$	3521.00	0.279814	0.139907	+	0.990165i	$0.455320\pi$
$542$	3800.00	0.301151
$543$	19810.0	1.56561
$544$	−3136.00	−0.247160
$545$	1530.00	0.120253
$546$	2310.00	0.181060
$547$	−2129.00	−0.166416	−0.0832079	−	0.996532i	$-0.526517\pi$
$547$	−2129.00	−0.166416	−0.0832079	+	0.996532i	$0.526517\pi$
$548$	5400.00	0.420943
$549$	−1400.00	−0.108835
$550$	2500.00	0.193819
$551$	−5130.00	−0.396634
$552$	−920.000	−0.0709380
$553$	−6734.00	−0.517828
$554$	4082.00	0.313046
$555$	3300.00	0.252391
$556$	−4548.00	−0.346903
$557$	−6888.00	−0.523975	−0.261987	−	0.965071i	$-0.584378\pi$
$557$	−6888.00	−0.523975	−0.261987	+	0.965071i	$0.584378\pi$
$558$	276.000	0.0209391
$559$	−4554.00	−0.344568
$560$	−560.000	−0.0422577
$561$	24500.0	1.84383
$562$	10316.0	0.774296
$563$	3690.00	0.276226	0.138113	−	0.990417i	$-0.455896\pi$
$563$	3690.00	0.276226	0.138113	+	0.990417i	$0.455896\pi$
$564$	11300.0	0.843645
$565$	900.000	0.0670147
$566$	−12984.0	−0.964237
$567$	4697.00	0.347893
$568$	6888.00	0.508828
$569$	3134.00	0.230904	0.115452	−	0.993313i	$-0.463168\pi$
$569$	3134.00	0.230904	0.115452	+	0.993313i	$0.463168\pi$
$570$	−900.000	−0.0661348
$571$	8572.00	0.628243	0.314122	−	0.949383i	$-0.398290\pi$
$571$	8572.00	0.628243	0.314122	+	0.949383i	$0.398290\pi$
$572$	6600.00	0.482447
$573$	10530.0	0.767709
$574$	−1218.00	−0.0885685
$575$	−575.000	−0.0417029
$576$	−128.000	−0.00925926
$577$	4245.00	0.306277	0.153138	−	0.988205i	$-0.451062\pi$
$577$	4245.00	0.306277	0.153138	+	0.988205i	$0.451062\pi$
$578$	−9382.00	−0.675155
$579$	2425.00	0.174058
$580$	5700.00	0.408068
$581$	−2842.00	−0.202936
$582$	−7420.00	−0.528469
$583$	−19000.0	−1.34974
$584$	−4040.00	−0.286261
$585$	330.000	0.0233228
$586$	10236.0	0.721579
$587$	17043.0	1.19836	0.599182	−	0.800613i	$-0.295493\pi$
$587$	17043.0	1.19836	0.599182	+	0.800613i	$0.295493\pi$
$588$	−980.000	−0.0687322
$589$	−1242.00	−0.0868858
$590$	1800.00	0.125601
$591$	−23135.0	−1.61023
$592$	−2112.00	−0.146626
$593$	−6322.00	−0.437797	−0.218898	−	0.975748i	$-0.570246\pi$
$593$	−6322.00	−0.437797	−0.218898	+	0.975748i	$0.570246\pi$
$594$	14500.0	1.00159
$595$	−3430.00	−0.236330
$596$	−1232.00	−0.0846723
$597$	6970.00	0.477828
$598$	−1518.00	−0.103805
$599$	−12880.0	−0.878569	−0.439284	−	0.898348i	$-0.644768\pi$
$599$	−12880.0	−0.878569	−0.439284	+	0.898348i	$0.644768\pi$
$600$	1000.00	0.0680414
$601$	7031.00	0.477205	0.238603	−	0.971117i	$-0.423311\pi$
$601$	7031.00	0.477205	0.238603	+	0.971117i	$0.423311\pi$
$602$	1932.00	0.130801
$603$	−152.000	−0.0102652
$604$	−2628.00	−0.177039
$605$	5845.00	0.392782
$606$	−8300.00	−0.556377
$607$	−17784.0	−1.18918	−0.594588	−	0.804030i	$-0.702685\pi$
$607$	−17784.0	−1.18918	−0.594588	+	0.804030i	$0.702685\pi$
$608$	576.000	0.0384209
$609$	9975.00	0.663723
$610$	−7000.00	−0.464626
$611$	18645.0	1.23453
$612$	−784.000	−0.0517832
$613$	−12080.0	−0.795932	−0.397966	−	0.917400i	$-0.630284\pi$
$613$	−12080.0	−0.795932	−0.397966	+	0.917400i	$0.630284\pi$
$614$	14424.0	0.948054
$615$	2175.00	0.142609
$616$	−2800.00	−0.183142
$617$	15306.0	0.998698	0.499349	−	0.866401i	$-0.333573\pi$
$617$	15306.0	0.998698	0.499349	+	0.866401i	$0.333573\pi$
$618$	4880.00	0.317641
$619$	−20362.0	−1.32216	−0.661081	−	0.750315i	$-0.729902\pi$
$619$	−20362.0	−1.32216	−0.661081	+	0.750315i	$0.729902\pi$
$620$	1380.00	0.0893905
$621$	−3335.00	−0.215506
$622$	−16378.0	−1.05578
$623$	3710.00	0.238584
$624$	2640.00	0.169366
$625$	625.000	0.0400000
$626$	−6260.00	−0.399680
$627$	−4500.00	−0.286623
$628$	4696.00	0.298393
$629$	−12936.0	−0.820019
$630$	−140.000	−0.00885355
$631$	−6890.00	−0.434686	−0.217343	−	0.976095i	$-0.569739\pi$
$631$	−6890.00	−0.434686	−0.217343	+	0.976095i	$0.569739\pi$
$632$	−7696.00	−0.484384
$633$	4860.00	0.305162
$634$	−3436.00	−0.215238
$635$	−6445.00	−0.402775
$636$	−7600.00	−0.473836
$637$	−1617.00	−0.100578
$638$	28500.0	1.76854
$639$	1722.00	0.106606
$640$	−640.000	−0.0395285
$641$	−11562.0	−0.712436	−0.356218	−	0.934403i	$-0.615934\pi$
$641$	−11562.0	−0.712436	−0.356218	+	0.934403i	$0.615934\pi$
$642$	19100.0	1.17417
$643$	−13622.0	−0.835458	−0.417729	−	0.908572i	$-0.637174\pi$
$643$	−13622.0	−0.835458	−0.417729	+	0.908572i	$0.637174\pi$
$644$	644.000	0.0394055
$645$	−3450.00	−0.210610
$646$	3528.00	0.214872
$647$	687.000	0.0417446	0.0208723	−	0.999782i	$-0.493356\pi$
$647$	687.000	0.0417446	0.0208723	+	0.999782i	$0.493356\pi$
$648$	5368.00	0.325424
$649$	9000.00	0.544347
$650$	1650.00	0.0995667
$651$	2415.00	0.145394
$652$	940.000	0.0564620
$653$	−17123.0	−1.02615	−0.513074	−	0.858344i	$-0.671493\pi$
$653$	−17123.0	−1.02615	−0.513074	+	0.858344i	$0.671493\pi$
$654$	3060.00	0.182959
$655$	−2595.00	−0.154802
$656$	−1392.00	−0.0828483
$657$	−1010.00	−0.0599754
$658$	−7910.00	−0.468638
$659$	7080.00	0.418509	0.209255	−	0.977861i	$-0.432896\pi$
$659$	7080.00	0.418509	0.209255	+	0.977861i	$0.432896\pi$
$660$	5000.00	0.294886
$661$	2848.00	0.167586	0.0837930	−	0.996483i	$-0.473297\pi$
$661$	2848.00	0.167586	0.0837930	+	0.996483i	$0.473297\pi$
$662$	12014.0	0.705343
$663$	16170.0	0.947196
$664$	−3248.00	−0.189830
$665$	630.000	0.0367374
$666$	−528.000	−0.0307201
$667$	−6555.00	−0.380526
$668$	9088.00	0.526385
$669$	16480.0	0.952397
$670$	−760.000	−0.0438229
$671$	−35000.0	−2.01365
$672$	−1120.00	−0.0642931
$673$	−31427.0	−1.80003	−0.900016	−	0.435856i	$-0.856446\pi$
$673$	−31427.0	−1.80003	−0.900016	+	0.435856i	$0.856446\pi$
$674$	7992.00	0.456736
$675$	3625.00	0.206706
$676$	−4432.00	−0.252162
$677$	−12560.0	−0.713028	−0.356514	−	0.934290i	$-0.616035\pi$
$677$	−12560.0	−0.713028	−0.356514	+	0.934290i	$0.616035\pi$
$678$	1800.00	0.101960
$679$	5194.00	0.293560
$680$	−3920.00	−0.221066
$681$	−1720.00	−0.0967849
$682$	6900.00	0.387412
$683$	3971.00	0.222469	0.111234	−	0.993794i	$-0.464520\pi$
$683$	3971.00	0.222469	0.111234	+	0.993794i	$0.464520\pi$
$684$	144.000	0.00804967
$685$	6750.00	0.376503
$686$	686.000	0.0381802
$687$	29880.0	1.65938
$688$	2208.00	0.122354
$689$	−12540.0	−0.693376
$690$	−1150.00	−0.0634489
$691$	8428.00	0.463989	0.231994	−	0.972717i	$-0.425475\pi$
$691$	8428.00	0.463989	0.231994	+	0.972717i	$0.425475\pi$
$692$	5208.00	0.286096
$693$	−700.000	−0.0383706
$694$	16976.0	0.928530
$695$	−5685.00	−0.310280
$696$	11400.0	0.620856
$697$	−8526.00	−0.463336
$698$	15202.0	0.824361
$699$	14195.0	0.768103
$700$	−700.000	−0.0377964
$701$	4458.00	0.240194	0.120097	−	0.992762i	$-0.461679\pi$
$701$	4458.00	0.240194	0.120097	+	0.992762i	$0.461679\pi$
$702$	9570.00	0.514525
$703$	2376.00	0.127472
$704$	−3200.00	−0.171313
$705$	14125.0	0.754579
$706$	−890.000	−0.0474442
$707$	5810.00	0.309063
$708$	3600.00	0.191096
$709$	−28204.0	−1.49397	−0.746984	−	0.664842i	$-0.768499\pi$
$709$	−28204.0	−1.49397	−0.746984	+	0.664842i	$0.768499\pi$
$710$	8610.00	0.455109
$711$	−1924.00	−0.101485
$712$	4240.00	0.223175
$713$	−1587.00	−0.0833571
$714$	−6860.00	−0.359564
$715$	8250.00	0.431514
$716$	−11660.0	−0.608596
$717$	9225.00	0.480494
$718$	−12532.0	−0.651379
$719$	30392.0	1.57640	0.788199	−	0.615420i	$-0.211014\pi$
$719$	30392.0	1.57640	0.788199	+	0.615420i	$0.211014\pi$
$720$	−160.000	−0.00828173
$721$	−3416.00	−0.176447
$722$	13070.0	0.673705
$723$	−21860.0	−1.12446
$724$	−15848.0	−0.813517
$725$	7125.00	0.364987
$726$	11690.0	0.597599
$727$	−16622.0	−0.847972	−0.423986	−	0.905669i	$-0.639369\pi$
$727$	−16622.0	−0.847972	−0.423986	+	0.905669i	$0.639369\pi$
$728$	−1848.00	−0.0940816
$729$	20917.0	1.06269
$730$	−5050.00	−0.256040
$731$	13524.0	0.684273
$732$	−14000.0	−0.706906
$733$	3218.00	0.162155	0.0810775	−	0.996708i	$-0.474164\pi$
$733$	3218.00	0.162155	0.0810775	+	0.996708i	$0.474164\pi$
$734$	−8972.00	−0.451175
$735$	−1225.00	−0.0614759
$736$	736.000	0.0368605
$737$	−3800.00	−0.189925
$738$	−348.000	−0.0173578
$739$	−28963.0	−1.44171	−0.720853	−	0.693088i	$-0.756250\pi$
$739$	−28963.0	−1.44171	−0.720853	+	0.693088i	$0.756250\pi$
$740$	−2640.00	−0.131146
$741$	−2970.00	−0.147241
$742$	5320.00	0.263212
$743$	−1118.00	−0.0552025	−0.0276012	−	0.999619i	$-0.508787\pi$
$743$	−1118.00	−0.0552025	−0.0276012	+	0.999619i	$0.508787\pi$
$744$	2760.00	0.136003
$745$	−1540.00	−0.0757332
$746$	−10784.0	−0.529263
$747$	−812.000	−0.0397718
$748$	−19600.0	−0.958084
$749$	−13370.0	−0.652242
$750$	1250.00	0.0608581
$751$	21278.0	1.03388	0.516941	−	0.856021i	$-0.327071\pi$
$751$	21278.0	1.03388	0.516941	+	0.856021i	$0.327071\pi$
$752$	−9040.00	−0.438371
$753$	23920.0	1.15763
$754$	18810.0	0.908514
$755$	−3285.00	−0.158349
$756$	−4060.00	−0.195318
$757$	−7306.00	−0.350781	−0.175390	−	0.984499i	$-0.556119\pi$
$757$	−7306.00	−0.350781	−0.175390	+	0.984499i	$0.556119\pi$
$758$	14828.0	0.710524
$759$	−5750.00	−0.274983
$760$	720.000	0.0343647
$761$	38907.0	1.85332	0.926661	−	0.375899i	$-0.122666\pi$
$761$	38907.0	1.85332	0.926661	+	0.375899i	$0.122666\pi$
$762$	−12890.0	−0.612802
$763$	−2142.00	−0.101633
$764$	−8424.00	−0.398913
$765$	−980.000	−0.0463163
$766$	24648.0	1.16262
$767$	5940.00	0.279636
$768$	−1280.00	−0.0601407
$769$	2558.00	0.119953	0.0599765	−	0.998200i	$-0.480897\pi$
$769$	2558.00	0.119953	0.0599765	+	0.998200i	$0.480897\pi$
$770$	−3500.00	−0.163807
$771$	−14315.0	−0.668667
$772$	−1940.00	−0.0904432
$773$	22696.0	1.05604	0.528020	−	0.849232i	$-0.322935\pi$
$773$	22696.0	1.05604	0.528020	+	0.849232i	$0.322935\pi$
$774$	552.000	0.0256347
$775$	1725.00	0.0799533
$776$	5936.00	0.274600
$777$	−4620.00	−0.213310
$778$	16032.0	0.738785
$779$	1566.00	0.0720254
$780$	3300.00	0.151486
$781$	43050.0	1.97241
$782$	4508.00	0.206145
$783$	41325.0	1.88612
$784$	784.000	0.0357143
$785$	5870.00	0.266891
$786$	−5190.00	−0.235523
$787$	38456.0	1.74181	0.870907	−	0.491447i	$-0.163532\pi$
$787$	38456.0	1.74181	0.870907	+	0.491447i	$0.163532\pi$
$788$	18508.0	0.836701
$789$	−39540.0	−1.78411
$790$	−9620.00	−0.433246
$791$	−1260.00	−0.0566377
$792$	−800.000	−0.0358924
$793$	−23100.0	−1.03443
$794$	−38.0000	−0.00169845
$795$	−9500.00	−0.423812
$796$	−5576.00	−0.248287
$797$	4562.00	0.202753	0.101377	−	0.994848i	$-0.467675\pi$
$797$	4562.00	0.202753	0.101377	+	0.994848i	$0.467675\pi$
$798$	1260.00	0.0558941
$799$	−55370.0	−2.45163
$800$	−800.000	−0.0353553
$801$	1060.00	0.0467581
$802$	11360.0	0.500169
$803$	−25250.0	−1.10966
$804$	−1520.00	−0.0666745
$805$	805.000	0.0352454
$806$	4554.00	0.199017
$807$	16905.0	0.737403
$808$	6640.00	0.289102
$809$	17690.0	0.768785	0.384393	−	0.923170i	$-0.374411\pi$
$809$	17690.0	0.768785	0.384393	+	0.923170i	$0.374411\pi$
$810$	6710.00	0.291068
$811$	−22551.0	−0.976415	−0.488208	−	0.872728i	$-0.662349\pi$
$811$	−22551.0	−0.976415	−0.488208	+	0.872728i	$0.662349\pi$
$812$	−7980.00	−0.344881
$813$	9500.00	0.409815
$814$	−13200.0	−0.568378
$815$	1175.00	0.0505012
$816$	−7840.00	−0.336342
$817$	−2484.00	−0.106370
$818$	−21614.0	−0.923858
$819$	−462.000	−0.0197113
$820$	−1740.00	−0.0741018
$821$	14190.0	0.603209	0.301604	−	0.953433i	$-0.402478\pi$
$821$	14190.0	0.603209	0.301604	+	0.953433i	$0.402478\pi$
$822$	13500.0	0.572830
$823$	12037.0	0.509822	0.254911	−	0.966965i	$-0.417954\pi$
$823$	12037.0	0.509822	0.254911	+	0.966965i	$0.417954\pi$
$824$	−3904.00	−0.165051
$825$	6250.00	0.263754
$826$	−2520.00	−0.106153
$827$	−31716.0	−1.33358	−0.666792	−	0.745244i	$-0.732333\pi$
$827$	−31716.0	−1.33358	−0.666792	+	0.745244i	$0.732333\pi$
$828$	184.000	0.00772276
$829$	−11950.0	−0.500652	−0.250326	−	0.968162i	$-0.580538\pi$
$829$	−11950.0	−0.500652	−0.250326	+	0.968162i	$0.580538\pi$
$830$	−4060.00	−0.169789
$831$	10205.0	0.426002
$832$	−2112.00	−0.0880053
$833$	4802.00	0.199735
$834$	−11370.0	−0.472075
$835$	11360.0	0.470813
$836$	3600.00	0.148934
$837$	10005.0	0.413170
$838$	−1780.00	−0.0733760
$839$	−29442.0	−1.21150	−0.605751	−	0.795654i	$-0.707127\pi$
$839$	−29442.0	−1.21150	−0.605751	+	0.795654i	$0.707127\pi$
$840$	−1400.00	−0.0575055
$841$	56836.0	2.33039
$842$	−13440.0	−0.550087
$843$	25790.0	1.05368
$844$	−3888.00	−0.158567
$845$	−5540.00	−0.225541
$846$	−2260.00	−0.0918444
$847$	−8183.00	−0.331961
$848$	6080.00	0.246212
$849$	−32460.0	−1.31216
$850$	−4900.00	−0.197728
$851$	3036.00	0.122295
$852$	17220.0	0.692427
$853$	33562.0	1.34718	0.673588	−	0.739107i	$-0.264752\pi$
$853$	33562.0	1.34718	0.673588	+	0.739107i	$0.264752\pi$
$854$	9800.00	0.392680
$855$	180.000	0.00719985
$856$	−15280.0	−0.610116
$857$	38559.0	1.53693	0.768466	−	0.639891i	$-0.221020\pi$
$857$	38559.0	1.53693	0.768466	+	0.639891i	$0.221020\pi$
$858$	16500.0	0.656528
$859$	40933.0	1.62586	0.812931	−	0.582360i	$-0.197870\pi$
$859$	40933.0	1.62586	0.812931	+	0.582360i	$0.197870\pi$
$860$	2760.00	0.109436
$861$	−3045.00	−0.120527
$862$	−5448.00	−0.215266
$863$	−29645.0	−1.16933	−0.584663	−	0.811277i	$-0.698773\pi$
$863$	−29645.0	−1.16933	−0.584663	+	0.811277i	$0.698773\pi$
$864$	−4640.00	−0.182704
$865$	6510.00	0.255892
$866$	−17152.0	−0.673035
$867$	−23455.0	−0.918770
$868$	−1932.00	−0.0755488
$869$	−48100.0	−1.87765
$870$	14250.0	0.555311
$871$	−2508.00	−0.0975664
$872$	−2448.00	−0.0950685
$873$	1484.00	0.0575324
$874$	−828.000	−0.0320452
$875$	−875.000	−0.0338062
$876$	−10100.0	−0.389552
$877$	−13014.0	−0.501085	−0.250543	−	0.968106i	$-0.580609\pi$
$877$	−13014.0	−0.501085	−0.250543	+	0.968106i	$0.580609\pi$
$878$	−382.000	−0.0146832
$879$	25590.0	0.981945
$880$	−4000.00	−0.153227
$881$	46212.0	1.76722	0.883611	−	0.468223i	$-0.155105\pi$
$881$	46212.0	1.76722	0.883611	+	0.468223i	$0.155105\pi$
$882$	196.000	0.00748261
$883$	−15060.0	−0.573963	−0.286982	−	0.957936i	$-0.592652\pi$
$883$	−15060.0	−0.573963	−0.286982	+	0.957936i	$0.592652\pi$
$884$	−12936.0	−0.492177
$885$	4500.00	0.170922
$886$	24622.0	0.933626
$887$	−1185.00	−0.0448573	−0.0224286	−	0.999748i	$-0.507140\pi$
$887$	−1185.00	−0.0448573	−0.0224286	+	0.999748i	$0.507140\pi$
$888$	−5280.00	−0.199533
$889$	9023.00	0.340407
$890$	5300.00	0.199614
$891$	33550.0	1.26147
$892$	−13184.0	−0.494880
$893$	10170.0	0.381104
$894$	−3080.00	−0.115224
$895$	−14575.0	−0.544345
$896$	896.000	0.0334077
$897$	−3795.00	−0.141261
$898$	−6660.00	−0.247491
$899$	19665.0	0.729549
$900$	−200.000	−0.00740741
$901$	37240.0	1.37696
$902$	−8700.00	−0.321151
$903$	4830.00	0.177998
$904$	−1440.00	−0.0529797
$905$	−19810.0	−0.727632
$906$	−6570.00	−0.240920
$907$	−48350.0	−1.77005	−0.885025	−	0.465543i	$-0.845859\pi$
$907$	−48350.0	−1.77005	−0.885025	+	0.465543i	$0.845859\pi$
$908$	1376.00	0.0502909
$909$	1660.00	0.0605707
$910$	−2310.00	−0.0841492
$911$	21056.0	0.765770	0.382885	−	0.923796i	$-0.374931\pi$
$911$	21056.0	0.765770	0.382885	+	0.923796i	$0.374931\pi$
$912$	1440.00	0.0522842
$913$	−20300.0	−0.735851
$914$	25908.0	0.937594
$915$	−17500.0	−0.632276
$916$	−23904.0	−0.862238
$917$	3633.00	0.130831
$918$	−28420.0	−1.02179
$919$	29718.0	1.06671	0.533355	−	0.845892i	$-0.320931\pi$
$919$	29718.0	1.06671	0.533355	+	0.845892i	$0.320931\pi$
$920$	920.000	0.0329690
$921$	36060.0	1.29014
$922$	−4246.00	−0.151664
$923$	28413.0	1.01325
$924$	−7000.00	−0.249224
$925$	−3300.00	−0.117301
$926$	26368.0	0.935752
$927$	−976.000	−0.0345804
$928$	−9120.00	−0.322606
$929$	−25335.0	−0.894741	−0.447370	−	0.894349i	$-0.647639\pi$
$929$	−25335.0	−0.894741	−0.447370	+	0.894349i	$0.647639\pi$
$930$	3450.00	0.121645
$931$	−882.000	−0.0310487
$932$	−11356.0	−0.399118
$933$	−40945.0	−1.43674
$934$	38020.0	1.33196
$935$	−24500.0	−0.856937
$936$	−528.000	−0.0184383
$937$	16360.0	0.570393	0.285196	−	0.958469i	$-0.407941\pi$
$937$	16360.0	0.570393	0.285196	+	0.958469i	$0.407941\pi$
$938$	1064.00	0.0370371
$939$	−15650.0	−0.543896
$940$	−11300.0	−0.392091
$941$	−8316.00	−0.288091	−0.144046	−	0.989571i	$-0.546011\pi$
$941$	−8316.00	−0.288091	−0.144046	+	0.989571i	$0.546011\pi$
$942$	11740.0	0.406061
$943$	2001.00	0.0691002
$944$	−2880.00	−0.0992966
$945$	−5075.00	−0.174698
$946$	13800.0	0.474288
$947$	−7111.00	−0.244009	−0.122004	−	0.992530i	$-0.538932\pi$
$947$	−7111.00	−0.244009	−0.122004	+	0.992530i	$0.538932\pi$
$948$	−19240.0	−0.659163
$949$	−16665.0	−0.570041
$950$	900.000	0.0307367
$951$	−8590.00	−0.292902
$952$	5488.00	0.186835
$953$	43126.0	1.46588	0.732942	−	0.680291i	$-0.238146\pi$
$953$	43126.0	1.46588	0.732942	+	0.680291i	$0.238146\pi$
$954$	1520.00	0.0515847
$955$	−10530.0	−0.356799
$956$	−7380.00	−0.249672
$957$	71250.0	2.40667
$958$	−5568.00	−0.187781
$959$	−9450.00	−0.318203
$960$	−1600.00	−0.0537914
$961$	−25030.0	−0.840187
$962$	−8712.00	−0.291981
$963$	−3820.00	−0.127827
$964$	17488.0	0.584285
$965$	−2425.00	−0.0808948
$966$	1610.00	0.0536241
$967$	−31805.0	−1.05768	−0.528842	−	0.848720i	$-0.677373\pi$
$967$	−31805.0	−1.05768	−0.528842	+	0.848720i	$0.677373\pi$
$968$	−9352.00	−0.310521
$969$	8820.00	0.292404
$970$	7420.00	0.245610
$971$	17904.0	0.591727	0.295863	−	0.955230i	$-0.404393\pi$
$971$	17904.0	0.591727	0.295863	+	0.955230i	$0.404393\pi$
$972$	−2240.00	−0.0739177
$973$	7959.00	0.262234
$974$	5098.00	0.167711
$975$	4125.00	0.135493
$976$	11200.0	0.367319
$977$	27940.0	0.914923	0.457462	−	0.889229i	$-0.348759\pi$
$977$	27940.0	0.914923	0.457462	+	0.889229i	$0.348759\pi$
$978$	2350.00	0.0768351
$979$	26500.0	0.865111
$980$	980.000	0.0319438
$981$	−612.000	−0.0199181
$982$	−26754.0	−0.869404
$983$	16140.0	0.523689	0.261844	−	0.965110i	$-0.415669\pi$
$983$	16140.0	0.523689	0.261844	+	0.965110i	$0.415669\pi$
$984$	−3480.00	−0.112742
$985$	23135.0	0.748368
$986$	−55860.0	−1.80420
$987$	−19775.0	−0.637736
$988$	2376.00	0.0765087
$989$	−3174.00	−0.102050
$990$	−1000.00	−0.0321031
$991$	26424.0	0.847009	0.423505	−	0.905894i	$-0.360800\pi$
$991$	26424.0	0.847009	0.423505	+	0.905894i	$0.360800\pi$
$992$	−2208.00	−0.0706694
$993$	30035.0	0.959851
$994$	−12054.0	−0.384637
$995$	−6970.00	−0.222074
$996$	−8120.00	−0.258325
$997$	27878.0	0.885562	0.442781	−	0.896630i	$-0.353992\pi$
$997$	27878.0	0.885562	0.442781	+	0.896630i	$0.353992\pi$
$998$	17626.0	0.559059
$999$	−19140.0	−0.606169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1610.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1610.4.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:	\( N \)	\(=\)	\( 1610 = 2 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1610.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more