LMFDB - Embedded newform 1610.4.a.d.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)

$f(q)$

$=$

$q-2.00000 q^{2} +8.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -16.0000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +37.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +8.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -16.0000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +37.0000 q^{9} -10.0000 q^{10} -50.0000 q^{11} +32.0000 q^{12} +84.0000 q^{13} +14.0000 q^{14} +40.0000 q^{15} +16.0000 q^{16} -58.0000 q^{17} -74.0000 q^{18} -96.0000 q^{19} +20.0000 q^{20} -56.0000 q^{21} +100.000 q^{22} -23.0000 q^{23} -64.0000 q^{24} +25.0000 q^{25} -168.000 q^{26} +80.0000 q^{27} -28.0000 q^{28} -118.000 q^{29} -80.0000 q^{30} -126.000 q^{31} -32.0000 q^{32} -400.000 q^{33} +116.000 q^{34} -35.0000 q^{35} +148.000 q^{36} -236.000 q^{37} +192.000 q^{38} +672.000 q^{39} -40.0000 q^{40} +30.0000 q^{41} +112.000 q^{42} -148.000 q^{43} -200.000 q^{44} +185.000 q^{45} +46.0000 q^{46} -240.000 q^{47} +128.000 q^{48} +49.0000 q^{49} -50.0000 q^{50} -464.000 q^{51} +336.000 q^{52} +120.000 q^{53} -160.000 q^{54} -250.000 q^{55} +56.0000 q^{56} -768.000 q^{57} +236.000 q^{58} +834.000 q^{59} +160.000 q^{60} +154.000 q^{61} +252.000 q^{62} -259.000 q^{63} +64.0000 q^{64} +420.000 q^{65} +800.000 q^{66} -496.000 q^{67} -232.000 q^{68} -184.000 q^{69} +70.0000 q^{70} -224.000 q^{71} -296.000 q^{72} -1068.00 q^{73} +472.000 q^{74} +200.000 q^{75} -384.000 q^{76} +350.000 q^{77} -1344.00 q^{78} -442.000 q^{79} +80.0000 q^{80} -359.000 q^{81} -60.0000 q^{82} +380.000 q^{83} -224.000 q^{84} -290.000 q^{85} +296.000 q^{86} -944.000 q^{87} +400.000 q^{88} +1030.00 q^{89} -370.000 q^{90} -588.000 q^{91} -92.0000 q^{92} -1008.00 q^{93} +480.000 q^{94} -480.000 q^{95} -256.000 q^{96} -846.000 q^{97} -98.0000 q^{98} -1850.00 q^{99} +O(q^{100})\)

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
$3$	8.00000	1.53960	0.769800	−	0.638285i	$-0.220356\pi$
$3$	8.00000	1.53960	0.769800	+	0.638285i	$0.220356\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−16.0000	−1.08866
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	37.0000	1.37037
$10$	−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	$0.740308\pi$
$12$	32.0000	0.769800
$13$	84.0000	1.79211	0.896054	−	0.443945i	$-0.146421\pi$
$13$	84.0000	1.79211	0.896054	+	0.443945i	$0.146421\pi$
$14$	14.0000	0.267261
$15$	40.0000	0.688530
$16$	16.0000	0.250000
$17$	−58.0000	−0.827474	−0.413737	−	0.910396i	$-0.635777\pi$
$17$	−58.0000	−0.827474	−0.413737	+	0.910396i	$0.635777\pi$
$18$	−74.0000	−0.968998
$19$	−96.0000	−1.15915	−0.579577	−	0.814918i	$-0.696782\pi$
$19$	−96.0000	−1.15915	−0.579577	+	0.814918i	$0.696782\pi$
$20$	20.0000	0.223607
$21$	−56.0000	−0.581914
$22$	100.000	0.969094
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−64.0000	−0.544331
$25$	25.0000	0.200000
$26$	−168.000	−1.26721
$27$	80.0000	0.570222
$28$	−28.0000	−0.188982
$29$	−118.000	−0.755588	−0.377794	−	0.925890i	$-0.623317\pi$
$29$	−118.000	−0.755588	−0.377794	+	0.925890i	$0.623317\pi$
$30$	−80.0000	−0.486864
$31$	−126.000	−0.730009	−0.365004	−	0.931006i	$-0.618932\pi$
$31$	−126.000	−0.730009	−0.365004	+	0.931006i	$0.618932\pi$
$32$	−32.0000	−0.176777
$33$	−400.000	−2.11003
$34$	116.000	0.585113
$35$	−35.0000	−0.169031
$36$	148.000	0.685185
$37$	−236.000	−1.04860	−0.524299	−	0.851534i	$-0.675673\pi$
$37$	−236.000	−1.04860	−0.524299	+	0.851534i	$0.675673\pi$
$38$	192.000	0.819645
$39$	672.000	2.75913
$40$	−40.0000	−0.158114
$41$	30.0000	0.114273	0.0571367	−	0.998366i	$-0.481803\pi$
$41$	30.0000	0.114273	0.0571367	+	0.998366i	$0.481803\pi$
$42$	112.000	0.411476
$43$	−148.000	−0.524879	−0.262439	−	0.964948i	$-0.584527\pi$
$43$	−148.000	−0.524879	−0.262439	+	0.964948i	$0.584527\pi$
$44$	−200.000	−0.685253
$45$	185.000	0.612848
$46$	46.0000	0.147442
$47$	−240.000	−0.744843	−0.372421	−	0.928064i	$-0.621472\pi$
$47$	−240.000	−0.744843	−0.372421	+	0.928064i	$0.621472\pi$
$48$	128.000	0.384900
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	−464.000	−1.27398
$52$	336.000	0.896054
$53$	120.000	0.311005	0.155503	−	0.987835i	$-0.450300\pi$
$53$	120.000	0.311005	0.155503	+	0.987835i	$0.450300\pi$
$54$	−160.000	−0.403208
$55$	−250.000	−0.612909
$56$	56.0000	0.133631
$57$	−768.000	−1.78463
$58$	236.000	0.534281
$59$	834.000	1.84030	0.920149	−	0.391569i	$-0.128068\pi$
$59$	834.000	1.84030	0.920149	+	0.391569i	$0.128068\pi$
$60$	160.000	0.344265
$61$	154.000	0.323241	0.161620	−	0.986853i	$-0.448328\pi$
$61$	154.000	0.323241	0.161620	+	0.986853i	$0.448328\pi$
$62$	252.000	0.516194
$63$	−259.000	−0.517951
$64$	64.0000	0.125000
$65$	420.000	0.801455
$66$	800.000	1.49202
$67$	−496.000	−0.904419	−0.452209	−	0.891912i	$-0.649364\pi$
$67$	−496.000	−0.904419	−0.452209	+	0.891912i	$0.649364\pi$
$68$	−232.000	−0.413737
$69$	−184.000	−0.321029
$70$	70.0000	0.119523
$71$	−224.000	−0.374421	−0.187211	−	0.982320i	$-0.559945\pi$
$71$	−224.000	−0.374421	−0.187211	+	0.982320i	$0.559945\pi$
$72$	−296.000	−0.484499
$73$	−1068.00	−1.71233	−0.856164	−	0.516704i	$-0.827159\pi$
$73$	−1068.00	−1.71233	−0.856164	+	0.516704i	$0.827159\pi$
$74$	472.000	0.741471
$75$	200.000	0.307920
$76$	−384.000	−0.579577
$77$	350.000	0.518003
$78$	−1344.00	−1.95100
$79$	−442.000	−0.629480	−0.314740	−	0.949178i	$-0.601917\pi$
$79$	−442.000	−0.629480	−0.314740	+	0.949178i	$0.601917\pi$
$80$	80.0000	0.111803
$81$	−359.000	−0.492455
$82$	−60.0000	−0.0808036
$83$	380.000	0.502535	0.251268	−	0.967918i	$-0.419153\pi$
$83$	380.000	0.502535	0.251268	+	0.967918i	$0.419153\pi$
$84$	−224.000	−0.290957
$85$	−290.000	−0.370058
$86$	296.000	0.371145
$87$	−944.000	−1.16330
$88$	400.000	0.484547
$89$	1030.00	1.22674	0.613370	−	0.789796i	$-0.289814\pi$
$89$	1030.00	1.22674	0.613370	+	0.789796i	$0.289814\pi$
$90$	−370.000	−0.433349
$91$	−588.000	−0.677353
$92$	−92.0000	−0.104257
$93$	−1008.00	−1.12392
$94$	480.000	0.526683
$95$	−480.000	−0.518389
$96$	−256.000	−0.272166
$97$	−846.000	−0.885549	−0.442775	−	0.896633i	$-0.646006\pi$
$97$	−846.000	−0.885549	−0.442775	+	0.896633i	$0.646006\pi$
$98$	−98.0000	−0.101015
$99$	−1850.00	−1.87810
$100$	100.000	0.100000
$101$	−258.000	−0.254178	−0.127089	−	0.991891i	$-0.540563\pi$
$101$	−258.000	−0.254178	−0.127089	+	0.991891i	$0.540563\pi$
$102$	928.000	0.900840
$103$	−656.000	−0.627550	−0.313775	−	0.949497i	$-0.601594\pi$
$103$	−656.000	−0.627550	−0.313775	+	0.949497i	$0.601594\pi$
$104$	−672.000	−0.633606
$105$	−280.000	−0.260240
$106$	−240.000	−0.219914
$107$	1104.00	0.997455	0.498728	−	0.866759i	$-0.333801\pi$
$107$	1104.00	0.997455	0.498728	+	0.866759i	$0.333801\pi$
$108$	320.000	0.285111
$109$	−682.000	−0.599300	−0.299650	−	0.954049i	$-0.596870\pi$
$109$	−682.000	−0.599300	−0.299650	+	0.954049i	$0.596870\pi$
$110$	500.000	0.433392
$111$	−1888.00	−1.61442
$112$	−112.000	−0.0944911
$113$	−756.000	−0.629367	−0.314684	−	0.949197i	$-0.601898\pi$
$113$	−756.000	−0.629367	−0.314684	+	0.949197i	$0.601898\pi$
$114$	1536.00	1.26193
$115$	−115.000	−0.0932505
$116$	−472.000	−0.377794
$117$	3108.00	2.45585
$118$	−1668.00	−1.30129
$119$	406.000	0.312756
$120$	−320.000	−0.243432
$121$	1169.00	0.878287
$122$	−308.000	−0.228566
$123$	240.000	0.175936
$124$	−504.000	−0.365004
$125$	125.000	0.0894427
$126$	518.000	0.366247
$127$	−1224.00	−0.855216	−0.427608	−	0.903964i	$-0.640644\pi$
$127$	−1224.00	−0.855216	−0.427608	+	0.903964i	$0.640644\pi$
$128$	−128.000	−0.0883883
$129$	−1184.00	−0.808104
$130$	−840.000	−0.566714
$131$	−870.000	−0.580246	−0.290123	−	0.956989i	$-0.593696\pi$
$131$	−870.000	−0.580246	−0.290123	+	0.956989i	$0.593696\pi$
$132$	−1600.00	−1.05502
$133$	672.000	0.438119
$134$	992.000	0.639521
$135$	400.000	0.255011
$136$	464.000	0.292556
$137$	3040.00	1.89580	0.947900	−	0.318567i	$-0.103201\pi$
$137$	3040.00	1.89580	0.947900	+	0.318567i	$0.103201\pi$
$138$	368.000	0.227002
$139$	1502.00	0.916532	0.458266	−	0.888815i	$-0.348471\pi$
$139$	1502.00	0.916532	0.458266	+	0.888815i	$0.348471\pi$
$140$	−140.000	−0.0845154
$141$	−1920.00	−1.14676
$142$	448.000	0.264756
$143$	−4200.00	−2.45610
$144$	592.000	0.342593
$145$	−590.000	−0.337909
$146$	2136.00	1.21080
$147$	392.000	0.219943
$148$	−944.000	−0.524299
$149$	−2570.00	−1.41304	−0.706519	−	0.707694i	$-0.749735\pi$
$149$	−2570.00	−1.41304	−0.706519	+	0.707694i	$0.749735\pi$
$150$	−400.000	−0.217732
$151$	−1476.00	−0.795465	−0.397732	−	0.917501i	$-0.630203\pi$
$151$	−1476.00	−0.795465	−0.397732	+	0.917501i	$0.630203\pi$
$152$	768.000	0.409823
$153$	−2146.00	−1.13395
$154$	−700.000	−0.366283
$155$	−630.000	−0.326470
$156$	2688.00	1.37957
$157$	1538.00	0.781820	0.390910	−	0.920429i	$-0.372160\pi$
$157$	1538.00	0.781820	0.390910	+	0.920429i	$0.372160\pi$
$158$	884.000	0.445109
$159$	960.000	0.478824
$160$	−160.000	−0.0790569
$161$	161.000	0.0788110
$162$	718.000	0.348219
$163$	−3652.00	−1.75489	−0.877444	−	0.479679i	$-0.840753\pi$
$163$	−3652.00	−1.75489	−0.877444	+	0.479679i	$0.840753\pi$
$164$	120.000	0.0571367
$165$	−2000.00	−0.943635
$166$	−760.000	−0.355346
$167$	−3240.00	−1.50131	−0.750655	−	0.660695i	$-0.770262\pi$
$167$	−3240.00	−1.50131	−0.750655	+	0.660695i	$0.770262\pi$
$168$	448.000	0.205738
$169$	4859.00	2.21165
$170$	580.000	0.261670
$171$	−3552.00	−1.58847
$172$	−592.000	−0.262439
$173$	2628.00	1.15493	0.577466	−	0.816415i	$-0.304042\pi$
$173$	2628.00	1.15493	0.577466	+	0.816415i	$0.304042\pi$
$174$	1888.00	0.822580
$175$	−175.000	−0.0755929
$176$	−800.000	−0.342627
$177$	6672.00	2.83332
$178$	−2060.00	−0.867436
$179$	2428.00	1.01384	0.506920	−	0.861993i	$-0.330784\pi$
$179$	2428.00	1.01384	0.506920	+	0.861993i	$0.330784\pi$
$180$	740.000	0.306424
$181$	−114.000	−0.0468152	−0.0234076	−	0.999726i	$-0.507452\pi$
$181$	−114.000	−0.0468152	−0.0234076	+	0.999726i	$0.507452\pi$
$182$	1176.00	0.478961
$183$	1232.00	0.497662
$184$	184.000	0.0737210
$185$	−1180.00	−0.468948
$186$	2016.00	0.794733
$187$	2900.00	1.13406
$188$	−960.000	−0.372421
$189$	−560.000	−0.215524
$190$	960.000	0.366556
$191$	−390.000	−0.147746	−0.0738728	−	0.997268i	$-0.523536\pi$
$191$	−390.000	−0.147746	−0.0738728	+	0.997268i	$0.523536\pi$
$192$	512.000	0.192450
$193$	3142.00	1.17185	0.585923	−	0.810367i	$-0.300732\pi$
$193$	3142.00	1.17185	0.585923	+	0.810367i	$0.300732\pi$
$194$	1692.00	0.626178
$195$	3360.00	1.23392
$196$	196.000	0.0714286
$197$	5394.00	1.95079	0.975397	−	0.220454i	$-0.0707538\pi$
$197$	5394.00	1.95079	0.975397	+	0.220454i	$0.0707538\pi$
$198$	3700.00	1.32802
$199$	556.000	0.198059	0.0990296	−	0.995084i	$-0.468426\pi$
$199$	556.000	0.198059	0.0990296	+	0.995084i	$0.468426\pi$
$200$	−200.000	−0.0707107
$201$	−3968.00	−1.39244
$202$	516.000	0.179731
$203$	826.000	0.285585
$204$	−1856.00	−0.636990
$205$	150.000	0.0511047
$206$	1312.00	0.443745
$207$	−851.000	−0.285742
$208$	1344.00	0.448027
$209$	4800.00	1.58863
$210$	560.000	0.184017
$211$	−920.000	−0.300168	−0.150084	−	0.988673i	$-0.547954\pi$
$211$	−920.000	−0.300168	−0.150084	+	0.988673i	$0.547954\pi$
$212$	480.000	0.155503
$213$	−1792.00	−0.576459
$214$	−2208.00	−0.705307
$215$	−740.000	−0.234733
$216$	−640.000	−0.201604
$217$	882.000	0.275917
$218$	1364.00	0.423769
$219$	−8544.00	−2.63630
$220$	−1000.00	−0.306454
$221$	−4872.00	−1.48292
$222$	3776.00	1.14157
$223$	1592.00	0.478064	0.239032	−	0.971012i	$-0.423170\pi$
$223$	1592.00	0.478064	0.239032	+	0.971012i	$0.423170\pi$
$224$	224.000	0.0668153
$225$	925.000	0.274074
$226$	1512.00	0.445030
$227$	−4596.00	−1.34382	−0.671910	−	0.740633i	$-0.734526\pi$
$227$	−4596.00	−1.34382	−0.671910	+	0.740633i	$0.734526\pi$
$228$	−3072.00	−0.892317
$229$	−1790.00	−0.516535	−0.258268	−	0.966073i	$-0.583152\pi$
$229$	−1790.00	−0.516535	−0.258268	+	0.966073i	$0.583152\pi$
$230$	230.000	0.0659380
$231$	2800.00	0.797517
$232$	944.000	0.267141
$233$	502.000	0.141146	0.0705732	−	0.997507i	$-0.477517\pi$
$233$	502.000	0.141146	0.0705732	+	0.997507i	$0.477517\pi$
$234$	−6216.00	−1.73655
$235$	−1200.00	−0.333104
$236$	3336.00	0.920149
$237$	−3536.00	−0.969147
$238$	−812.000	−0.221152
$239$	3160.00	0.855244	0.427622	−	0.903958i	$-0.359351\pi$
$239$	3160.00	0.855244	0.427622	+	0.903958i	$0.359351\pi$
$240$	640.000	0.172133
$241$	−1478.00	−0.395047	−0.197524	−	0.980298i	$-0.563290\pi$
$241$	−1478.00	−0.395047	−0.197524	+	0.980298i	$0.563290\pi$
$242$	−2338.00	−0.621043
$243$	−5032.00	−1.32841
$244$	616.000	0.161620
$245$	245.000	0.0638877
$246$	−480.000	−0.124405
$247$	−8064.00	−2.07733
$248$	1008.00	0.258097
$249$	3040.00	0.773704
$250$	−250.000	−0.0632456
$251$	−3432.00	−0.863051	−0.431526	−	0.902101i	$-0.642025\pi$
$251$	−3432.00	−0.863051	−0.431526	+	0.902101i	$0.642025\pi$
$252$	−1036.00	−0.258976
$253$	1150.00	0.285770
$254$	2448.00	0.604729
$255$	−2320.00	−0.569741
$256$	256.000	0.0625000
$257$	68.0000	0.0165048	0.00825238	−	0.999966i	$-0.497373\pi$
$257$	68.0000	0.0165048	0.00825238	+	0.999966i	$0.497373\pi$
$258$	2368.00	0.571416
$259$	1652.00	0.396333
$260$	1680.00	0.400728
$261$	−4366.00	−1.03544
$262$	1740.00	0.410296
$263$	−4364.00	−1.02318	−0.511589	−	0.859230i	$-0.670943\pi$
$263$	−4364.00	−1.02318	−0.511589	+	0.859230i	$0.670943\pi$
$264$	3200.00	0.746009
$265$	600.000	0.139086
$266$	−1344.00	−0.309797
$267$	8240.00	1.88869
$268$	−1984.00	−0.452209
$269$	5862.00	1.32867	0.664335	−	0.747435i	$-0.268715\pi$
$269$	5862.00	1.32867	0.664335	+	0.747435i	$0.268715\pi$
$270$	−800.000	−0.180320
$271$	−2758.00	−0.618216	−0.309108	−	0.951027i	$-0.600030\pi$
$271$	−2758.00	−0.618216	−0.309108	+	0.951027i	$0.600030\pi$
$272$	−928.000	−0.206869
$273$	−4704.00	−1.04285
$274$	−6080.00	−1.34053
$275$	−1250.00	−0.274101
$276$	−736.000	−0.160514
$277$	−4342.00	−0.941825	−0.470912	−	0.882180i	$-0.656075\pi$
$277$	−4342.00	−0.941825	−0.470912	+	0.882180i	$0.656075\pi$
$278$	−3004.00	−0.648086
$279$	−4662.00	−1.00038
$280$	280.000	0.0597614
$281$	3110.00	0.660239	0.330119	−	0.943939i	$-0.392911\pi$
$281$	3110.00	0.660239	0.330119	+	0.943939i	$0.392911\pi$
$282$	3840.00	0.810882
$283$	6284.00	1.31995	0.659974	−	0.751289i	$-0.270567\pi$
$283$	6284.00	1.31995	0.659974	+	0.751289i	$0.270567\pi$
$284$	−896.000	−0.187211
$285$	−3840.00	−0.798112
$286$	8400.00	1.73672
$287$	−210.000	−0.0431913
$288$	−1184.00	−0.242250
$289$	−1549.00	−0.315286
$290$	1180.00	0.238938
$291$	−6768.00	−1.36339
$292$	−4272.00	−0.856164
$293$	−3922.00	−0.781999	−0.390999	−	0.920391i	$-0.627871\pi$
$293$	−3922.00	−0.781999	−0.390999	+	0.920391i	$0.627871\pi$
$294$	−784.000	−0.155523
$295$	4170.00	0.823006
$296$	1888.00	0.370736
$297$	−4000.00	−0.781493
$298$	5140.00	0.999168
$299$	−1932.00	−0.373680
$300$	800.000	0.153960
$301$	1036.00	0.198386
$302$	2952.00	0.562479
$303$	−2064.00	−0.391332
$304$	−1536.00	−0.289788
$305$	770.000	0.144558
$306$	4292.00	0.801821
$307$	−296.000	−0.0550281	−0.0275140	−	0.999621i	$-0.508759\pi$
$307$	−296.000	−0.0550281	−0.0275140	+	0.999621i	$0.508759\pi$
$308$	1400.00	0.259001
$309$	−5248.00	−0.966176
$310$	1260.00	0.230849
$311$	7942.00	1.44807	0.724035	−	0.689764i	$-0.242286\pi$
$311$	7942.00	1.44807	0.724035	+	0.689764i	$0.242286\pi$
$312$	−5376.00	−0.975500
$313$	−3058.00	−0.552231	−0.276116	−	0.961124i	$-0.589047\pi$
$313$	−3058.00	−0.552231	−0.276116	+	0.961124i	$0.589047\pi$
$314$	−3076.00	−0.552830
$315$	−1295.00	−0.231635
$316$	−1768.00	−0.314740
$317$	2186.00	0.387312	0.193656	−	0.981069i	$-0.437965\pi$
$317$	2186.00	0.387312	0.193656	+	0.981069i	$0.437965\pi$
$318$	−1920.00	−0.338579
$319$	5900.00	1.03554
$320$	320.000	0.0559017
$321$	8832.00	1.53568
$322$	−322.000	−0.0557278
$323$	5568.00	0.959170
$324$	−1436.00	−0.246228
$325$	2100.00	0.358422
$326$	7304.00	1.24089
$327$	−5456.00	−0.922683
$328$	−240.000	−0.0404018
$329$	1680.00	0.281524
$330$	4000.00	0.667251
$331$	428.000	0.0710725	0.0355363	−	0.999368i	$-0.488686\pi$
$331$	428.000	0.0710725	0.0355363	+	0.999368i	$0.488686\pi$
$332$	1520.00	0.251268
$333$	−8732.00	−1.43697
$334$	6480.00	1.06159
$335$	−2480.00	−0.404468
$336$	−896.000	−0.145479
$337$	−3892.00	−0.629112	−0.314556	−	0.949239i	$-0.601856\pi$
$337$	−3892.00	−0.629112	−0.314556	+	0.949239i	$0.601856\pi$
$338$	−9718.00	−1.56387
$339$	−6048.00	−0.968974
$340$	−1160.00	−0.185029
$341$	6300.00	1.00048
$342$	7104.00	1.12322
$343$	−343.000	−0.0539949
$344$	1184.00	0.185573
$345$	−920.000	−0.143569
$346$	−5256.00	−0.816660
$347$	3940.00	0.609540	0.304770	−	0.952426i	$-0.401420\pi$
$347$	3940.00	0.609540	0.304770	+	0.952426i	$0.401420\pi$
$348$	−3776.00	−0.581652
$349$	186.000	0.0285282	0.0142641	−	0.999898i	$-0.495459\pi$
$349$	186.000	0.0285282	0.0142641	+	0.999898i	$0.495459\pi$
$350$	350.000	0.0534522
$351$	6720.00	1.02190
$352$	1600.00	0.242274
$353$	−11320.0	−1.70681	−0.853403	−	0.521251i	$-0.825466\pi$
$353$	−11320.0	−1.70681	−0.853403	+	0.521251i	$0.825466\pi$
$354$	−13344.0	−2.00346
$355$	−1120.00	−0.167446
$356$	4120.00	0.613370
$357$	3248.00	0.481519
$358$	−4856.00	−0.716893
$359$	−7722.00	−1.13524	−0.567621	−	0.823290i	$-0.692136\pi$
$359$	−7722.00	−1.13524	−0.567621	+	0.823290i	$0.692136\pi$
$360$	−1480.00	−0.216675
$361$	2357.00	0.343636
$362$	228.000	0.0331034
$363$	9352.00	1.35221
$364$	−2352.00	−0.338677
$365$	−5340.00	−0.765776
$366$	−2464.00	−0.351900
$367$	−2144.00	−0.304948	−0.152474	−	0.988307i	$-0.548724\pi$
$367$	−2144.00	−0.304948	−0.152474	+	0.988307i	$0.548724\pi$
$368$	−368.000	−0.0521286
$369$	1110.00	0.156597
$370$	2360.00	0.331596
$371$	−840.000	−0.117549
$372$	−4032.00	−0.561961
$373$	1076.00	0.149365	0.0746825	−	0.997207i	$-0.476206\pi$
$373$	1076.00	0.149365	0.0746825	+	0.997207i	$0.476206\pi$
$374$	−5800.00	−0.801901
$375$	1000.00	0.137706
$376$	1920.00	0.263342
$377$	−9912.00	−1.35410
$378$	1120.00	0.152398
$379$	8914.00	1.20813	0.604065	−	0.796935i	$-0.293547\pi$
$379$	8914.00	1.20813	0.604065	+	0.796935i	$0.293547\pi$
$380$	−1920.00	−0.259195
$381$	−9792.00	−1.31669
$382$	780.000	0.104472
$383$	8112.00	1.08226	0.541128	−	0.840940i	$-0.317998\pi$
$383$	8112.00	1.08226	0.541128	+	0.840940i	$0.317998\pi$
$384$	−1024.00	−0.136083
$385$	1750.00	0.231658
$386$	−6284.00	−0.828620
$387$	−5476.00	−0.719278
$388$	−3384.00	−0.442775
$389$	−3986.00	−0.519533	−0.259766	−	0.965671i	$-0.583646\pi$
$389$	−3986.00	−0.519533	−0.259766	+	0.965671i	$0.583646\pi$
$390$	−6720.00	−0.872514
$391$	1334.00	0.172540
$392$	−392.000	−0.0505076
$393$	−6960.00	−0.893347
$394$	−10788.0	−1.37942
$395$	−2210.00	−0.281512
$396$	−7400.00	−0.939050
$397$	−3712.00	−0.469269	−0.234635	−	0.972084i	$-0.575389\pi$
$397$	−3712.00	−0.469269	−0.234635	+	0.972084i	$0.575389\pi$
$398$	−1112.00	−0.140049
$399$	5376.00	0.674528
$400$	400.000	0.0500000
$401$	−13350.0	−1.66251	−0.831256	−	0.555890i	$-0.812378\pi$
$401$	−13350.0	−1.66251	−0.831256	+	0.555890i	$0.812378\pi$
$402$	7936.00	0.984606
$403$	−10584.0	−1.30825
$404$	−1032.00	−0.127089
$405$	−1795.00	−0.220233
$406$	−1652.00	−0.201939
$407$	11800.0	1.43711
$408$	3712.00	0.450420
$409$	−11878.0	−1.43601	−0.718006	−	0.696036i	$-0.754945\pi$
$409$	−11878.0	−1.43601	−0.718006	+	0.696036i	$0.754945\pi$
$410$	−300.000	−0.0361364
$411$	24320.0	2.91878
$412$	−2624.00	−0.313775
$413$	−5838.00	−0.695567
$414$	1702.00	0.202050
$415$	1900.00	0.224741
$416$	−2688.00	−0.316803
$417$	12016.0	1.41109
$418$	−9600.00	−1.12333
$419$	−14996.0	−1.74845	−0.874227	−	0.485517i	$-0.838631\pi$
$419$	−14996.0	−1.74845	−0.874227	+	0.485517i	$0.838631\pi$
$420$	−1120.00	−0.130120
$421$	4146.00	0.479961	0.239981	−	0.970778i	$-0.422859\pi$
$421$	4146.00	0.479961	0.239981	+	0.970778i	$0.422859\pi$
$422$	1840.00	0.212251
$423$	−8880.00	−1.02071
$424$	−960.000	−0.109957
$425$	−1450.00	−0.165495
$426$	3584.00	0.407618
$427$	−1078.00	−0.122173
$428$	4416.00	0.498728
$429$	−33600.0	−3.78141
$430$	1480.00	0.165981
$431$	−13578.0	−1.51747	−0.758735	−	0.651400i	$-0.774182\pi$
$431$	−13578.0	−1.51747	−0.758735	+	0.651400i	$0.774182\pi$
$432$	1280.00	0.142556
$433$	9018.00	1.00087	0.500436	−	0.865774i	$-0.333173\pi$
$433$	9018.00	1.00087	0.500436	+	0.865774i	$0.333173\pi$
$434$	−1764.00	−0.195103
$435$	−4720.00	−0.520245
$436$	−2728.00	−0.299650
$437$	2208.00	0.241700
$438$	17088.0	1.86415
$439$	−5074.00	−0.551637	−0.275819	−	0.961210i	$-0.588949\pi$
$439$	−5074.00	−0.551637	−0.275819	+	0.961210i	$0.588949\pi$
$440$	2000.00	0.216696
$441$	1813.00	0.195767
$442$	9744.00	1.04859
$443$	364.000	0.0390387	0.0195194	−	0.999809i	$-0.493786\pi$
$443$	364.000	0.0390387	0.0195194	+	0.999809i	$0.493786\pi$
$444$	−7552.00	−0.807212
$445$	5150.00	0.548614
$446$	−3184.00	−0.338042
$447$	−20560.0	−2.17551
$448$	−448.000	−0.0472456
$449$	10454.0	1.09879	0.549393	−	0.835564i	$-0.314859\pi$
$449$	10454.0	1.09879	0.549393	+	0.835564i	$0.314859\pi$
$450$	−1850.00	−0.193800
$451$	−1500.00	−0.156613
$452$	−3024.00	−0.314684
$453$	−11808.0	−1.22470
$454$	9192.00	0.950225
$455$	−2940.00	−0.302922
$456$	6144.00	0.630963
$457$	3192.00	0.326730	0.163365	−	0.986566i	$-0.447765\pi$
$457$	3192.00	0.326730	0.163365	+	0.986566i	$0.447765\pi$
$458$	3580.00	0.365245
$459$	−4640.00	−0.471845
$460$	−460.000	−0.0466252
$461$	15422.0	1.55808	0.779039	−	0.626975i	$-0.215707\pi$
$461$	15422.0	1.55808	0.779039	+	0.626975i	$0.215707\pi$
$462$	−5600.00	−0.563930
$463$	−4032.00	−0.404715	−0.202357	−	0.979312i	$-0.564860\pi$
$463$	−4032.00	−0.404715	−0.202357	+	0.979312i	$0.564860\pi$
$464$	−1888.00	−0.188897
$465$	−5040.00	−0.502633
$466$	−1004.00	−0.0998056
$467$	−15708.0	−1.55649	−0.778244	−	0.627962i	$-0.783889\pi$
$467$	−15708.0	−1.55649	−0.778244	+	0.627962i	$0.783889\pi$
$468$	12432.0	1.22793
$469$	3472.00	0.341838
$470$	2400.00	0.235540
$471$	12304.0	1.20369
$472$	−6672.00	−0.650643
$473$	7400.00	0.719350
$474$	7072.00	0.685291
$475$	−2400.00	−0.231831
$476$	1624.00	0.156378
$477$	4440.00	0.426192
$478$	−6320.00	−0.604749
$479$	−10684.0	−1.01913	−0.509566	−	0.860431i	$-0.670194\pi$
$479$	−10684.0	−1.01913	−0.509566	+	0.860431i	$0.670194\pi$
$480$	−1280.00	−0.121716
$481$	−19824.0	−1.87920
$482$	2956.00	0.279340
$483$	1288.00	0.121338
$484$	4676.00	0.439144
$485$	−4230.00	−0.396030
$486$	10064.0	0.939326
$487$	13896.0	1.29299	0.646497	−	0.762917i	$-0.276233\pi$
$487$	13896.0	1.29299	0.646497	+	0.762917i	$0.276233\pi$
$488$	−1232.00	−0.114283
$489$	−29216.0	−2.70183
$490$	−490.000	−0.0451754
$491$	1404.00	0.129046	0.0645230	−	0.997916i	$-0.479447\pi$
$491$	1404.00	0.129046	0.0645230	+	0.997916i	$0.479447\pi$
$492$	960.000	0.0879678
$493$	6844.00	0.625230
$494$	16128.0	1.46889
$495$	−9250.00	−0.839912
$496$	−2016.00	−0.182502
$497$	1568.00	0.141518
$498$	−6080.00	−0.547091
$499$	−20344.0	−1.82510	−0.912548	−	0.408970i	$-0.865888\pi$
$499$	−20344.0	−1.82510	−0.912548	+	0.408970i	$0.865888\pi$
$500$	500.000	0.0447214
$501$	−25920.0	−2.31142
$502$	6864.00	0.610270
$503$	−6968.00	−0.617670	−0.308835	−	0.951116i	$-0.599939\pi$
$503$	−6968.00	−0.617670	−0.308835	+	0.951116i	$0.599939\pi$
$504$	2072.00	0.183123
$505$	−1290.00	−0.113672
$506$	−2300.00	−0.202070
$507$	38872.0	3.40506
$508$	−4896.00	−0.427608
$509$	−8534.00	−0.743149	−0.371575	−	0.928403i	$-0.621182\pi$
$509$	−8534.00	−0.743149	−0.371575	+	0.928403i	$0.621182\pi$
$510$	4640.00	0.402868
$511$	7476.00	0.647199
$512$	−512.000	−0.0441942
$513$	−7680.00	−0.660975
$514$	−136.000	−0.0116706
$515$	−3280.00	−0.280649
$516$	−4736.00	−0.404052
$517$	12000.0	1.02081
$518$	−3304.00	−0.280250
$519$	21024.0	1.77813
$520$	−3360.00	−0.283357
$521$	13550.0	1.13942	0.569709	−	0.821847i	$-0.307056\pi$
$521$	13550.0	1.13942	0.569709	+	0.821847i	$0.307056\pi$
$522$	8732.00	0.732163
$523$	1468.00	0.122736	0.0613682	−	0.998115i	$-0.480454\pi$
$523$	1468.00	0.122736	0.0613682	+	0.998115i	$0.480454\pi$
$524$	−3480.00	−0.290123
$525$	−1400.00	−0.116383
$526$	8728.00	0.723496
$527$	7308.00	0.604064
$528$	−6400.00	−0.527508
$529$	529.000	0.0434783
$530$	−1200.00	−0.0983484
$531$	30858.0	2.52189
$532$	2688.00	0.219059
$533$	2520.00	0.204790
$534$	−16480.0	−1.33550
$535$	5520.00	0.446076
$536$	3968.00	0.319760
$537$	19424.0	1.56091
$538$	−11724.0	−0.939512
$539$	−2450.00	−0.195787
$540$	1600.00	0.127506
$541$	4730.00	0.375894	0.187947	−	0.982179i	$-0.439817\pi$
$541$	4730.00	0.375894	0.187947	+	0.982179i	$0.439817\pi$
$542$	5516.00	0.437145
$543$	−912.000	−0.0720767
$544$	1856.00	0.146278
$545$	−3410.00	−0.268015
$546$	9408.00	0.737409
$547$	12132.0	0.948312	0.474156	−	0.880441i	$-0.342753\pi$
$547$	12132.0	0.948312	0.474156	+	0.880441i	$0.342753\pi$
$548$	12160.0	0.947900
$549$	5698.00	0.442959
$550$	2500.00	0.193819
$551$	11328.0	0.875842
$552$	1472.00	0.113501
$553$	3094.00	0.237921
$554$	8684.00	0.665971
$555$	−9440.00	−0.721992
$556$	6008.00	0.458266
$557$	3512.00	0.267160	0.133580	−	0.991038i	$-0.457353\pi$
$557$	3512.00	0.267160	0.133580	+	0.991038i	$0.457353\pi$
$558$	9324.00	0.707377
$559$	−12432.0	−0.940640
$560$	−560.000	−0.0422577
$561$	23200.0	1.74600
$562$	−6220.00	−0.466859
$563$	−10012.0	−0.749477	−0.374738	−	0.927131i	$-0.622267\pi$
$563$	−10012.0	−0.749477	−0.374738	+	0.927131i	$0.622267\pi$
$564$	−7680.00	−0.573380
$565$	−3780.00	−0.281462
$566$	−12568.0	−0.933344
$567$	2513.00	0.186131
$568$	1792.00	0.132378
$569$	25338.0	1.86683	0.933413	−	0.358803i	$-0.116815\pi$
$569$	25338.0	1.86683	0.933413	+	0.358803i	$0.116815\pi$
$570$	7680.00	0.564351
$571$	−3726.00	−0.273079	−0.136540	−	0.990635i	$-0.543598\pi$
$571$	−3726.00	−0.273079	−0.136540	+	0.990635i	$0.543598\pi$
$572$	−16800.0	−1.22805
$573$	−3120.00	−0.227469
$574$	420.000	0.0305409
$575$	−575.000	−0.0417029
$576$	2368.00	0.171296
$577$	−17452.0	−1.25916	−0.629581	−	0.776935i	$-0.716773\pi$
$577$	−17452.0	−1.25916	−0.629581	+	0.776935i	$0.716773\pi$
$578$	3098.00	0.222941
$579$	25136.0	1.80417
$580$	−2360.00	−0.168955
$581$	−2660.00	−0.189940
$582$	13536.0	0.964064
$583$	−6000.00	−0.426234
$584$	8544.00	0.605399
$585$	15540.0	1.09829
$586$	7844.00	0.552957
$587$	27248.0	1.91592	0.957960	−	0.286901i	$-0.0926251\pi$
$587$	27248.0	1.91592	0.957960	+	0.286901i	$0.0926251\pi$
$588$	1568.00	0.109971
$589$	12096.0	0.846192
$590$	−8340.00	−0.581953
$591$	43152.0	3.00345
$592$	−3776.00	−0.262150
$593$	25944.0	1.79661	0.898307	−	0.439368i	$-0.144798\pi$
$593$	25944.0	1.79661	0.898307	+	0.439368i	$0.144798\pi$
$594$	8000.00	0.552599
$595$	2030.00	0.139869
$596$	−10280.0	−0.706519
$597$	4448.00	0.304932
$598$	3864.00	0.264232
$599$	24924.0	1.70011	0.850056	−	0.526692i	$-0.176568\pi$
$599$	24924.0	1.70011	0.850056	+	0.526692i	$0.176568\pi$
$600$	−1600.00	−0.108866
$601$	−6034.00	−0.409537	−0.204769	−	0.978810i	$-0.565644\pi$
$601$	−6034.00	−0.409537	−0.204769	+	0.978810i	$0.565644\pi$
$602$	−2072.00	−0.140280
$603$	−18352.0	−1.23939
$604$	−5904.00	−0.397732
$605$	5845.00	0.392782
$606$	4128.00	0.276714
$607$	7540.00	0.504183	0.252092	−	0.967703i	$-0.418882\pi$
$607$	7540.00	0.504183	0.252092	+	0.967703i	$0.418882\pi$
$608$	3072.00	0.204911
$609$	6608.00	0.439687
$610$	−1540.00	−0.102218
$611$	−20160.0	−1.33484
$612$	−8584.00	−0.566973
$613$	3728.00	0.245632	0.122816	−	0.992429i	$-0.460807\pi$
$613$	3728.00	0.245632	0.122816	+	0.992429i	$0.460807\pi$
$614$	592.000	0.0389107
$615$	1200.00	0.0786808
$616$	−2800.00	−0.183142
$617$	−5780.00	−0.377138	−0.188569	−	0.982060i	$-0.560385\pi$
$617$	−5780.00	−0.377138	−0.188569	+	0.982060i	$0.560385\pi$
$618$	10496.0	0.683189
$619$	−7128.00	−0.462841	−0.231420	−	0.972854i	$-0.574337\pi$
$619$	−7128.00	−0.462841	−0.231420	+	0.972854i	$0.574337\pi$
$620$	−2520.00	−0.163235
$621$	−1840.00	−0.118900
$622$	−15884.0	−1.02394
$623$	−7210.00	−0.463664
$624$	10752.0	0.689783
$625$	625.000	0.0400000
$626$	6116.00	0.390486
$627$	38400.0	2.44585
$628$	6152.00	0.390910
$629$	13688.0	0.867689
$630$	2590.00	0.163791
$631$	29198.0	1.84208	0.921041	−	0.389465i	$-0.127340\pi$
$631$	29198.0	1.84208	0.921041	+	0.389465i	$0.127340\pi$
$632$	3536.00	0.222555
$633$	−7360.00	−0.462139
$634$	−4372.00	−0.273871
$635$	−6120.00	−0.382464
$636$	3840.00	0.239412
$637$	4116.00	0.256015
$638$	−11800.0	−0.732236
$639$	−8288.00	−0.513096
$640$	−640.000	−0.0395285
$641$	2686.00	0.165508	0.0827540	−	0.996570i	$-0.473628\pi$
$641$	2686.00	0.165508	0.0827540	+	0.996570i	$0.473628\pi$
$642$	−17664.0	−1.08589
$643$	−9124.00	−0.559589	−0.279794	−	0.960060i	$-0.590266\pi$
$643$	−9124.00	−0.559589	−0.279794	+	0.960060i	$0.590266\pi$
$644$	644.000	0.0394055
$645$	−5920.00	−0.361395
$646$	−11136.0	−0.678235
$647$	−29460.0	−1.79010	−0.895048	−	0.445970i	$-0.852859\pi$
$647$	−29460.0	−1.79010	−0.895048	+	0.445970i	$0.852859\pi$
$648$	2872.00	0.174109
$649$	−41700.0	−2.52214
$650$	−4200.00	−0.253442
$651$	7056.00	0.424803
$652$	−14608.0	−0.877444
$653$	−3590.00	−0.215142	−0.107571	−	0.994197i	$-0.534307\pi$
$653$	−3590.00	−0.215142	−0.107571	+	0.994197i	$0.534307\pi$
$654$	10912.0	0.652436
$655$	−4350.00	−0.259494
$656$	480.000	0.0285684
$657$	−39516.0	−2.34652
$658$	−3360.00	−0.199068
$659$	12930.0	0.764312	0.382156	−	0.924098i	$-0.375182\pi$
$659$	12930.0	0.764312	0.382156	+	0.924098i	$0.375182\pi$
$660$	−8000.00	−0.471818
$661$	−19434.0	−1.14356	−0.571781	−	0.820406i	$-0.693747\pi$
$661$	−19434.0	−1.14356	−0.571781	+	0.820406i	$0.693747\pi$
$662$	−856.000	−0.0502559
$663$	−38976.0	−2.28311
$664$	−3040.00	−0.177673
$665$	3360.00	0.195933
$666$	17464.0	1.01609
$667$	2714.00	0.157551
$668$	−12960.0	−0.750655
$669$	12736.0	0.736027
$670$	4960.00	0.286002
$671$	−7700.00	−0.443003
$672$	1792.00	0.102869
$673$	25110.0	1.43822	0.719108	−	0.694898i	$-0.244551\pi$
$673$	25110.0	1.43822	0.719108	+	0.694898i	$0.244551\pi$
$674$	7784.00	0.444849
$675$	2000.00	0.114044
$676$	19436.0	1.10583
$677$	−17422.0	−0.989043	−0.494521	−	0.869166i	$-0.664657\pi$
$677$	−17422.0	−0.989043	−0.494521	+	0.869166i	$0.664657\pi$
$678$	12096.0	0.685168
$679$	5922.00	0.334706
$680$	2320.00	0.130835
$681$	−36768.0	−2.06895
$682$	−12600.0	−0.707447
$683$	17868.0	1.00102	0.500512	−	0.865729i	$-0.333145\pi$
$683$	17868.0	1.00102	0.500512	+	0.865729i	$0.333145\pi$
$684$	−14208.0	−0.794235
$685$	15200.0	0.847828
$686$	686.000	0.0381802
$687$	−14320.0	−0.795258
$688$	−2368.00	−0.131220
$689$	10080.0	0.557355
$690$	1840.00	0.101518
$691$	30814.0	1.69641	0.848205	−	0.529668i	$-0.177683\pi$
$691$	30814.0	1.69641	0.848205	+	0.529668i	$0.177683\pi$
$692$	10512.0	0.577466
$693$	12950.0	0.709855
$694$	−7880.00	−0.431010
$695$	7510.00	0.409886
$696$	7552.00	0.411290
$697$	−1740.00	−0.0945584
$698$	−372.000	−0.0201725
$699$	4016.00	0.217309
$700$	−700.000	−0.0377964
$701$	21618.0	1.16477	0.582383	−	0.812915i	$-0.302121\pi$
$701$	21618.0	1.16477	0.582383	+	0.812915i	$0.302121\pi$
$702$	−13440.0	−0.722593
$703$	22656.0	1.21549
$704$	−3200.00	−0.171313
$705$	−9600.00	−0.512847
$706$	22640.0	1.20689
$707$	1806.00	0.0960702
$708$	26688.0	1.41666
$709$	−7430.00	−0.393568	−0.196784	−	0.980447i	$-0.563050\pi$
$709$	−7430.00	−0.393568	−0.196784	+	0.980447i	$0.563050\pi$
$710$	2240.00	0.118402
$711$	−16354.0	−0.862620
$712$	−8240.00	−0.433718
$713$	2898.00	0.152217
$714$	−6496.00	−0.340486
$715$	−21000.0	−1.09840
$716$	9712.00	0.506920
$717$	25280.0	1.31673
$718$	15444.0	0.802737
$719$	1818.00	0.0942976	0.0471488	−	0.998888i	$-0.484987\pi$
$719$	1818.00	0.0942976	0.0471488	+	0.998888i	$0.484987\pi$
$720$	2960.00	0.153212
$721$	4592.00	0.237191
$722$	−4714.00	−0.242987
$723$	−11824.0	−0.608215
$724$	−456.000	−0.0234076
$725$	−2950.00	−0.151118
$726$	−18704.0	−0.956158
$727$	27032.0	1.37904	0.689520	−	0.724267i	$-0.257822\pi$
$727$	27032.0	1.37904	0.689520	+	0.724267i	$0.257822\pi$
$728$	4704.00	0.239481
$729$	−30563.0	−1.55276
$730$	10680.0	0.541486
$731$	8584.00	0.434324
$732$	4928.00	0.248831
$733$	−786.000	−0.0396065	−0.0198033	−	0.999804i	$-0.506304\pi$
$733$	−786.000	−0.0396065	−0.0198033	+	0.999804i	$0.506304\pi$
$734$	4288.00	0.215631
$735$	1960.00	0.0983615
$736$	736.000	0.0368605
$737$	24800.0	1.23951
$738$	−2220.00	−0.110731
$739$	1392.00	0.0692903	0.0346452	−	0.999400i	$-0.488970\pi$
$739$	1392.00	0.0692903	0.0346452	+	0.999400i	$0.488970\pi$
$740$	−4720.00	−0.234474
$741$	−64512.0	−3.19826
$742$	1680.00	0.0831196
$743$	−23504.0	−1.16054	−0.580268	−	0.814426i	$-0.697052\pi$
$743$	−23504.0	−1.16054	−0.580268	+	0.814426i	$0.697052\pi$
$744$	8064.00	0.397366
$745$	−12850.0	−0.631930
$746$	−2152.00	−0.105617
$747$	14060.0	0.688659
$748$	11600.0	0.567029
$749$	−7728.00	−0.377003
$750$	−2000.00	−0.0973729
$751$	29182.0	1.41793	0.708966	−	0.705243i	$-0.249162\pi$
$751$	29182.0	1.41793	0.708966	+	0.705243i	$0.249162\pi$
$752$	−3840.00	−0.186211
$753$	−27456.0	−1.32875
$754$	19824.0	0.957490
$755$	−7380.00	−0.355743
$756$	−2240.00	−0.107762
$757$	15496.0	0.744005	0.372002	−	0.928232i	$-0.378671\pi$
$757$	15496.0	0.744005	0.372002	+	0.928232i	$0.378671\pi$
$758$	−17828.0	−0.854277
$759$	9200.00	0.439972
$760$	3840.00	0.183278
$761$	−29278.0	−1.39465	−0.697324	−	0.716756i	$-0.745626\pi$
$761$	−29278.0	−1.39465	−0.697324	+	0.716756i	$0.745626\pi$
$762$	19584.0	0.931041
$763$	4774.00	0.226514
$764$	−1560.00	−0.0738728
$765$	−10730.0	−0.507116
$766$	−16224.0	−0.765270
$767$	70056.0	3.29801
$768$	2048.00	0.0962250
$769$	−28278.0	−1.32605	−0.663024	−	0.748598i	$-0.730727\pi$
$769$	−28278.0	−1.32605	−0.663024	+	0.748598i	$0.730727\pi$
$770$	−3500.00	−0.163807
$771$	544.000	0.0254107
$772$	12568.0	0.585923
$773$	36762.0	1.71053	0.855263	−	0.518193i	$-0.173395\pi$
$773$	36762.0	1.71053	0.855263	+	0.518193i	$0.173395\pi$
$774$	10952.0	0.508607
$775$	−3150.00	−0.146002
$776$	6768.00	0.313089
$777$	13216.0	0.610195
$778$	7972.00	0.367365
$779$	−2880.00	−0.132460
$780$	13440.0	0.616961
$781$	11200.0	0.513147
$782$	−2668.00	−0.122004
$783$	−9440.00	−0.430853
$784$	784.000	0.0357143
$785$	7690.00	0.349641
$786$	13920.0	0.631692
$787$	−21292.0	−0.964394	−0.482197	−	0.876063i	$-0.660161\pi$
$787$	−21292.0	−0.964394	−0.482197	+	0.876063i	$0.660161\pi$
$788$	21576.0	0.975397
$789$	−34912.0	−1.57529
$790$	4420.00	0.199059
$791$	5292.00	0.237878
$792$	14800.0	0.664009
$793$	12936.0	0.579282
$794$	7424.00	0.331824
$795$	4800.00	0.214136
$796$	2224.00	0.0990296
$797$	−25546.0	−1.13536	−0.567682	−	0.823248i	$-0.692160\pi$
$797$	−25546.0	−1.13536	−0.567682	+	0.823248i	$0.692160\pi$
$798$	−10752.0	−0.476963
$799$	13920.0	0.616338
$800$	−800.000	−0.0353553
$801$	38110.0	1.68109
$802$	26700.0	1.17557
$803$	53400.0	2.34676
$804$	−15872.0	−0.696222
$805$	805.000	0.0352454
$806$	21168.0	0.925076
$807$	46896.0	2.04562
$808$	2064.00	0.0898654
$809$	11970.0	0.520201	0.260101	−	0.965582i	$-0.416244\pi$
$809$	11970.0	0.520201	0.260101	+	0.965582i	$0.416244\pi$
$810$	3590.00	0.155728
$811$	−26594.0	−1.15147	−0.575735	−	0.817637i	$-0.695284\pi$
$811$	−26594.0	−1.15147	−0.575735	+	0.817637i	$0.695284\pi$
$812$	3304.00	0.142793
$813$	−22064.0	−0.951806
$814$	−23600.0	−1.01619
$815$	−18260.0	−0.784810
$816$	−7424.00	−0.318495
$817$	14208.0	0.608415
$818$	23756.0	1.01541
$819$	−21756.0	−0.928225
$820$	600.000	0.0255523
$821$	−21586.0	−0.917609	−0.458804	−	0.888537i	$-0.651722\pi$
$821$	−21586.0	−0.917609	−0.458804	+	0.888537i	$0.651722\pi$
$822$	−48640.0	−2.06389
$823$	28352.0	1.20084	0.600418	−	0.799686i	$-0.295001\pi$
$823$	28352.0	1.20084	0.600418	+	0.799686i	$0.295001\pi$
$824$	5248.00	0.221872
$825$	−10000.0	−0.422006
$826$	11676.0	0.491840
$827$	36872.0	1.55038	0.775190	−	0.631728i	$-0.217654\pi$
$827$	36872.0	1.55038	0.775190	+	0.631728i	$0.217654\pi$
$828$	−3404.00	−0.142871
$829$	−36026.0	−1.50933	−0.754665	−	0.656110i	$-0.772201\pi$
$829$	−36026.0	−1.50933	−0.754665	+	0.656110i	$0.772201\pi$
$830$	−3800.00	−0.158916
$831$	−34736.0	−1.45003
$832$	5376.00	0.224014
$833$	−2842.00	−0.118211
$834$	−24032.0	−0.997794
$835$	−16200.0	−0.671406
$836$	19200.0	0.794313
$837$	−10080.0	−0.416267
$838$	29992.0	1.23634
$839$	−33836.0	−1.39231	−0.696155	−	0.717891i	$-0.745107\pi$
$839$	−33836.0	−1.39231	−0.696155	+	0.717891i	$0.745107\pi$
$840$	2240.00	0.0920087
$841$	−10465.0	−0.429087
$842$	−8292.00	−0.339384
$843$	24880.0	1.01650
$844$	−3680.00	−0.150084
$845$	24295.0	0.989081
$846$	17760.0	0.721751
$847$	−8183.00	−0.331961
$848$	1920.00	0.0777513
$849$	50272.0	2.03219
$850$	2900.00	0.117023
$851$	5428.00	0.218648
$852$	−7168.00	−0.288230
$853$	6704.00	0.269098	0.134549	−	0.990907i	$-0.457041\pi$
$853$	6704.00	0.269098	0.134549	+	0.990907i	$0.457041\pi$
$854$	2156.00	0.0863897
$855$	−17760.0	−0.710385
$856$	−8832.00	−0.352654
$857$	7944.00	0.316642	0.158321	−	0.987388i	$-0.449392\pi$
$857$	7944.00	0.316642	0.158321	+	0.987388i	$0.449392\pi$
$858$	67200.0	2.67386
$859$	31326.0	1.24427	0.622136	−	0.782909i	$-0.286265\pi$
$859$	31326.0	1.24427	0.622136	+	0.782909i	$0.286265\pi$
$860$	−2960.00	−0.117366
$861$	−1680.00	−0.0664974
$862$	27156.0	1.07301
$863$	20808.0	0.820756	0.410378	−	0.911915i	$-0.365397\pi$
$863$	20808.0	0.820756	0.410378	+	0.911915i	$0.365397\pi$
$864$	−2560.00	−0.100802
$865$	13140.0	0.516501
$866$	−18036.0	−0.707723
$867$	−12392.0	−0.485415
$868$	3528.00	0.137959
$869$	22100.0	0.862706
$870$	9440.00	0.367869
$871$	−41664.0	−1.62082
$872$	5456.00	0.211885
$873$	−31302.0	−1.21353
$874$	−4416.00	−0.170908
$875$	−875.000	−0.0338062
$876$	−34176.0	−1.31815
$877$	46318.0	1.78341	0.891703	−	0.452620i	$-0.149511\pi$
$877$	46318.0	1.78341	0.891703	+	0.452620i	$0.149511\pi$
$878$	10148.0	0.390067
$879$	−31376.0	−1.20397
$880$	−4000.00	−0.153227
$881$	322.000	0.0123138	0.00615690	−	0.999981i	$-0.498040\pi$
$881$	322.000	0.0123138	0.00615690	+	0.999981i	$0.498040\pi$
$882$	−3626.00	−0.138428
$883$	32676.0	1.24534	0.622670	−	0.782485i	$-0.286048\pi$
$883$	32676.0	1.24534	0.622670	+	0.782485i	$0.286048\pi$
$884$	−19488.0	−0.741462
$885$	33360.0	1.26710
$886$	−728.000	−0.0276046
$887$	−50364.0	−1.90649	−0.953246	−	0.302197i	$-0.902280\pi$
$887$	−50364.0	−1.90649	−0.953246	+	0.302197i	$0.902280\pi$
$888$	15104.0	0.570785
$889$	8568.00	0.323241
$890$	−10300.0	−0.387929
$891$	17950.0	0.674913
$892$	6368.00	0.239032
$893$	23040.0	0.863387
$894$	41120.0	1.53832
$895$	12140.0	0.453403
$896$	896.000	0.0334077
$897$	−15456.0	−0.575319
$898$	−20908.0	−0.776959
$899$	14868.0	0.551586
$900$	3700.00	0.137037
$901$	−6960.00	−0.257349
$902$	3000.00	0.110742
$903$	8288.00	0.305435
$904$	6048.00	0.222515
$905$	−570.000	−0.0209364
$906$	23616.0	0.865992
$907$	12516.0	0.458200	0.229100	−	0.973403i	$-0.426422\pi$
$907$	12516.0	0.458200	0.229100	+	0.973403i	$0.426422\pi$
$908$	−18384.0	−0.671910
$909$	−9546.00	−0.348318
$910$	5880.00	0.214198
$911$	46614.0	1.69527	0.847635	−	0.530580i	$-0.178026\pi$
$911$	46614.0	1.69527	0.847635	+	0.530580i	$0.178026\pi$
$912$	−12288.0	−0.446158
$913$	−19000.0	−0.688728
$914$	−6384.00	−0.231033
$915$	6160.00	0.222561
$916$	−7160.00	−0.258268
$917$	6090.00	0.219312
$918$	9280.00	0.333644
$919$	−41990.0	−1.50721	−0.753603	−	0.657330i	$-0.771686\pi$
$919$	−41990.0	−1.50721	−0.753603	+	0.657330i	$0.771686\pi$
$920$	920.000	0.0329690
$921$	−2368.00	−0.0847212
$922$	−30844.0	−1.10173
$923$	−18816.0	−0.671003
$924$	11200.0	0.398759
$925$	−5900.00	−0.209720
$926$	8064.00	0.286177
$927$	−24272.0	−0.859975
$928$	3776.00	0.133570
$929$	37650.0	1.32966	0.664831	−	0.746994i	$-0.268503\pi$
$929$	37650.0	1.32966	0.664831	+	0.746994i	$0.268503\pi$
$930$	10080.0	0.355415
$931$	−4704.00	−0.165593
$932$	2008.00	0.0705732
$933$	63536.0	2.22945
$934$	31416.0	1.10060
$935$	14500.0	0.507167
$936$	−24864.0	−0.868275
$937$	24498.0	0.854125	0.427062	−	0.904222i	$-0.359548\pi$
$937$	24498.0	0.854125	0.427062	+	0.904222i	$0.359548\pi$
$938$	−6944.00	−0.241716
$939$	−24464.0	−0.850216
$940$	−4800.00	−0.166552
$941$	10898.0	0.377539	0.188770	−	0.982021i	$-0.439550\pi$
$941$	10898.0	0.377539	0.188770	+	0.982021i	$0.439550\pi$
$942$	−24608.0	−0.851138
$943$	−690.000	−0.0238277
$944$	13344.0	0.460074
$945$	−2800.00	−0.0963852
$946$	−14800.0	−0.508657
$947$	884.000	0.0303338	0.0151669	−	0.999885i	$-0.495172\pi$
$947$	884.000	0.0303338	0.0151669	+	0.999885i	$0.495172\pi$
$948$	−14144.0	−0.484574
$949$	−89712.0	−3.06868
$950$	4800.00	0.163929
$951$	17488.0	0.596306
$952$	−3248.00	−0.110576
$953$	16424.0	0.558264	0.279132	−	0.960253i	$-0.409953\pi$
$953$	16424.0	0.558264	0.279132	+	0.960253i	$0.409953\pi$
$954$	−8880.00	−0.301363
$955$	−1950.00	−0.0660738
$956$	12640.0	0.427622
$957$	47200.0	1.59431
$958$	21368.0	0.720635
$959$	−21280.0	−0.716545
$960$	2560.00	0.0860663
$961$	−13915.0	−0.467087
$962$	39648.0	1.32880
$963$	40848.0	1.36688
$964$	−5912.00	−0.197524
$965$	15710.0	0.524065
$966$	−2576.00	−0.0857986
$967$	−38552.0	−1.28206	−0.641028	−	0.767517i	$-0.721492\pi$
$967$	−38552.0	−1.28206	−0.641028	+	0.767517i	$0.721492\pi$
$968$	−9352.00	−0.310521
$969$	44544.0	1.47674
$970$	8460.00	0.280035
$971$	−47200.0	−1.55996	−0.779979	−	0.625805i	$-0.784771\pi$
$971$	−47200.0	−1.55996	−0.779979	+	0.625805i	$0.784771\pi$
$972$	−20128.0	−0.664204
$973$	−10514.0	−0.346417
$974$	−27792.0	−0.914285
$975$	16800.0	0.551826
$976$	2464.00	0.0808102
$977$	16812.0	0.550526	0.275263	−	0.961369i	$-0.411235\pi$
$977$	16812.0	0.550526	0.275263	+	0.961369i	$0.411235\pi$
$978$	58432.0	1.91048
$979$	−51500.0	−1.68125
$980$	980.000	0.0319438
$981$	−25234.0	−0.821264
$982$	−2808.00	−0.0912494
$983$	4752.00	0.154186	0.0770932	−	0.997024i	$-0.475436\pi$
$983$	4752.00	0.154186	0.0770932	+	0.997024i	$0.475436\pi$
$984$	−1920.00	−0.0622026
$985$	26970.0	0.872422
$986$	−13688.0	−0.442104
$987$	13440.0	0.433435
$988$	−32256.0	−1.03866
$989$	3404.00	0.109445
$990$	18500.0	0.593908
$991$	−26252.0	−0.841496	−0.420748	−	0.907178i	$-0.638232\pi$
$991$	−26252.0	−0.841496	−0.420748	+	0.907178i	$0.638232\pi$
$992$	4032.00	0.129049
$993$	3424.00	0.109423
$994$	−3136.00	−0.100068
$995$	2780.00	0.0885748
$996$	12160.0	0.386852
$997$	−4076.00	−0.129477	−0.0647383	−	0.997902i	$-0.520621\pi$
$997$	−4076.00	−0.129477	−0.0647383	+	0.997902i	$0.520621\pi$
$998$	40688.0	1.29054
$999$	−18880.0	−0.597935

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1610.4.a.d.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

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