LMFDB - Embedded newform 1682.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1682,4,Mod(1,1682)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1682, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1682.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1682 = 2 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1682.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:	$99.2412126297$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1682.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +7.00000 q^{3} +4.00000 q^{4} -15.0000 q^{5} -14.0000 q^{6} -18.0000 q^{7} -8.00000 q^{8} +22.0000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +7.00000 q^{3} +4.00000 q^{4} -15.0000 q^{5} -14.0000 q^{6} -18.0000 q^{7} -8.00000 q^{8} +22.0000 q^{9} +30.0000 q^{10} -27.0000 q^{11} +28.0000 q^{12} -57.0000 q^{13} +36.0000 q^{14} -105.000 q^{15} +16.0000 q^{16} +44.0000 q^{17} -44.0000 q^{18} -152.000 q^{19} -60.0000 q^{20} -126.000 q^{21} +54.0000 q^{22} -152.000 q^{23} -56.0000 q^{24} +100.000 q^{25} +114.000 q^{26} -35.0000 q^{27} -72.0000 q^{28} +210.000 q^{30} +173.000 q^{31} -32.0000 q^{32} -189.000 q^{33} -88.0000 q^{34} +270.000 q^{35} +88.0000 q^{36} +120.000 q^{37} +304.000 q^{38} -399.000 q^{39} +120.000 q^{40} +314.000 q^{41} +252.000 q^{42} -339.000 q^{43} -108.000 q^{44} -330.000 q^{45} +304.000 q^{46} +357.000 q^{47} +112.000 q^{48} -19.0000 q^{49} -200.000 q^{50} +308.000 q^{51} -228.000 q^{52} -59.0000 q^{53} +70.0000 q^{54} +405.000 q^{55} +144.000 q^{56} -1064.00 q^{57} -572.000 q^{59} -420.000 q^{60} +420.000 q^{61} -346.000 q^{62} -396.000 q^{63} +64.0000 q^{64} +855.000 q^{65} +378.000 q^{66} +660.000 q^{67} +176.000 q^{68} -1064.00 q^{69} -540.000 q^{70} +726.000 q^{71} -176.000 q^{72} -1004.00 q^{73} -240.000 q^{74} +700.000 q^{75} -608.000 q^{76} +486.000 q^{77} +798.000 q^{78} -361.000 q^{79} -240.000 q^{80} -839.000 q^{81} -628.000 q^{82} -168.000 q^{83} -504.000 q^{84} -660.000 q^{85} +678.000 q^{86} +216.000 q^{88} -58.0000 q^{89} +660.000 q^{90} +1026.00 q^{91} -608.000 q^{92} +1211.00 q^{93} -714.000 q^{94} +2280.00 q^{95} -224.000 q^{96} +1206.00 q^{97} +38.0000 q^{98} -594.000 q^{99} +O(q^{100})\)

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
$3$	7.00000	1.34715	0.673575	−	0.739119i	$-0.264758\pi$
$3$	7.00000	1.34715	0.673575	+	0.739119i	$0.264758\pi$
$4$	4.00000	0.500000
$5$	−15.0000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−15.0000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−14.0000	−0.952579
$7$	−18.0000	−0.971909	−0.485954	−	0.873984i	$-0.661528\pi$
$7$	−18.0000	−0.971909	−0.485954	+	0.873984i	$0.661528\pi$
$8$	−8.00000	−0.353553
$9$	22.0000	0.814815
$10$	30.0000	0.948683
$11$	−27.0000	−0.740073	−0.370037	−	0.929017i	$-0.620655\pi$
$11$	−27.0000	−0.740073	−0.370037	+	0.929017i	$0.620655\pi$
$12$	28.0000	0.673575
$13$	−57.0000	−1.21607	−0.608037	−	0.793909i	$-0.708043\pi$
$13$	−57.0000	−1.21607	−0.608037	+	0.793909i	$0.708043\pi$
$14$	36.0000	0.687243
$15$	−105.000	−1.80739
$16$	16.0000	0.250000
$17$	44.0000	0.627739	0.313870	−	0.949466i	$-0.398375\pi$
$17$	44.0000	0.627739	0.313870	+	0.949466i	$0.398375\pi$
$18$	−44.0000	−0.576161
$19$	−152.000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−152.000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	−60.0000	−0.670820
$21$	−126.000	−1.30931
$22$	54.0000	0.523311
$23$	−152.000	−1.37801	−0.689004	−	0.724757i	$-0.741952\pi$
$23$	−152.000	−1.37801	−0.689004	+	0.724757i	$0.741952\pi$
$24$	−56.0000	−0.476290
$25$	100.000	0.800000
$26$	114.000	0.859894
$27$	−35.0000	−0.249472
$28$	−72.0000	−0.485954
$29$	0	0
$29$	0	0
$30$	210.000	1.27802
$31$	173.000	1.00231	0.501157	−	0.865357i	$-0.332908\pi$
$31$	173.000	1.00231	0.501157	+	0.865357i	$0.332908\pi$
$32$	−32.0000	−0.176777
$33$	−189.000	−0.996990
$34$	−88.0000	−0.443879
$35$	270.000	1.30395
$36$	88.0000	0.407407
$37$	120.000	0.533186	0.266593	−	0.963809i	$-0.414102\pi$
$37$	120.000	0.533186	0.266593	+	0.963809i	$0.414102\pi$
$38$	304.000	1.29777
$39$	−399.000	−1.63823
$40$	120.000	0.474342
$41$	314.000	1.19606	0.598031	−	0.801473i	$-0.295950\pi$
$41$	314.000	1.19606	0.598031	+	0.801473i	$0.295950\pi$
$42$	252.000	0.925820
$43$	−339.000	−1.20226	−0.601128	−	0.799153i	$-0.705282\pi$
$43$	−339.000	−1.20226	−0.601128	+	0.799153i	$0.705282\pi$
$44$	−108.000	−0.370037
$45$	−330.000	−1.09319
$46$	304.000	0.974399
$47$	357.000	1.10795	0.553977	−	0.832532i	$-0.313110\pi$
$47$	357.000	1.10795	0.553977	+	0.832532i	$0.313110\pi$
$48$	112.000	0.336788
$49$	−19.0000	−0.0553936
$50$	−200.000	−0.565685
$51$	308.000	0.845659
$52$	−228.000	−0.608037
$53$	−59.0000	−0.152911	−0.0764554	−	0.997073i	$-0.524360\pi$
$53$	−59.0000	−0.152911	−0.0764554	+	0.997073i	$0.524360\pi$
$54$	70.0000	0.176404
$55$	405.000	0.992913
$56$	144.000	0.343622
$57$	−1064.00	−2.47246
$58$	0	0
$59$	−572.000	−1.26217	−0.631085	−	0.775713i	$-0.717390\pi$
$59$	−572.000	−1.26217	−0.631085	+	0.775713i	$0.717390\pi$
$60$	−420.000	−0.903696
$61$	420.000	0.881565	0.440783	−	0.897614i	$-0.354701\pi$
$61$	420.000	0.881565	0.440783	+	0.897614i	$0.354701\pi$
$62$	−346.000	−0.708743
$63$	−396.000	−0.791926
$64$	64.0000	0.125000
$65$	855.000	1.63153
$66$	378.000	0.704979
$67$	660.000	1.20346	0.601730	−	0.798699i	$-0.294478\pi$
$67$	660.000	1.20346	0.601730	+	0.798699i	$0.294478\pi$
$68$	176.000	0.313870
$69$	−1064.00	−1.85638
$70$	−540.000	−0.922033
$71$	726.000	1.21353	0.606763	−	0.794883i	$-0.292468\pi$
$71$	726.000	1.21353	0.606763	+	0.794883i	$0.292468\pi$
$72$	−176.000	−0.288081
$73$	−1004.00	−1.60972	−0.804858	−	0.593467i	$-0.797759\pi$
$73$	−1004.00	−1.60972	−0.804858	+	0.593467i	$0.797759\pi$
$74$	−240.000	−0.377019
$75$	700.000	1.07772
$76$	−608.000	−0.917663
$77$	486.000	0.719284
$78$	798.000	1.15841
$79$	−361.000	−0.514122	−0.257061	−	0.966395i	$-0.582754\pi$
$79$	−361.000	−0.514122	−0.257061	+	0.966395i	$0.582754\pi$
$80$	−240.000	−0.335410
$81$	−839.000	−1.15089
$82$	−628.000	−0.845744
$83$	−168.000	−0.222173	−0.111087	−	0.993811i	$-0.535433\pi$
$83$	−168.000	−0.222173	−0.111087	+	0.993811i	$0.535433\pi$
$84$	−504.000	−0.654654
$85$	−660.000	−0.842201
$86$	678.000	0.850123
$87$	0	0
$88$	216.000	0.261655
$89$	−58.0000	−0.0690785	−0.0345393	−	0.999403i	$-0.510996\pi$
$89$	−58.0000	−0.0690785	−0.0345393	+	0.999403i	$0.510996\pi$
$90$	660.000	0.773001
$91$	1026.00	1.18191
$92$	−608.000	−0.689004
$93$	1211.00	1.35027
$94$	−714.000	−0.783441
$95$	2280.00	2.46235
$96$	−224.000	−0.238145
$97$	1206.00	1.26238	0.631189	−	0.775629i	$-0.282567\pi$
$97$	1206.00	1.26238	0.631189	+	0.775629i	$0.282567\pi$
$98$	38.0000	0.0391692
$99$	−594.000	−0.603023
$100$	400.000	0.400000
$101$	−1440.00	−1.41867	−0.709333	−	0.704873i	$-0.751004\pi$
$101$	−1440.00	−1.41867	−0.709333	+	0.704873i	$0.751004\pi$
$102$	−616.000	−0.597971
$103$	1858.00	1.77742	0.888710	−	0.458471i	$-0.151603\pi$
$103$	1858.00	1.77742	0.888710	+	0.458471i	$0.151603\pi$
$104$	456.000	0.429947
$105$	1890.00	1.75662
$106$	118.000	0.108124
$107$	−1914.00	−1.72928	−0.864642	−	0.502389i	$-0.832455\pi$
$107$	−1914.00	−1.72928	−0.864642	+	0.502389i	$0.832455\pi$
$108$	−140.000	−0.124736
$109$	989.000	0.869074	0.434537	−	0.900654i	$-0.356912\pi$
$109$	989.000	0.869074	0.434537	+	0.900654i	$0.356912\pi$
$110$	−810.000	−0.702095
$111$	840.000	0.718282
$112$	−288.000	−0.242977
$113$	278.000	0.231434	0.115717	−	0.993282i	$-0.463083\pi$
$113$	278.000	0.231434	0.115717	+	0.993282i	$0.463083\pi$
$114$	2128.00	1.74829
$115$	2280.00	1.84879
$116$	0	0
$117$	−1254.00	−0.990875
$118$	1144.00	0.892489
$119$	−792.000	−0.610105
$120$	840.000	0.639010
$121$	−602.000	−0.452292
$122$	−840.000	−0.623361
$123$	2198.00	1.61128
$124$	692.000	0.501157
$125$	375.000	0.268328
$126$	792.000	0.559976
$127$	600.000	0.419224	0.209612	−	0.977785i	$-0.432780\pi$
$127$	600.000	0.419224	0.209612	+	0.977785i	$0.432780\pi$
$128$	−128.000	−0.0883883
$129$	−2373.00	−1.61962
$130$	−1710.00	−1.15367
$131$	1652.00	1.10180	0.550900	−	0.834571i	$-0.314284\pi$
$131$	1652.00	1.10180	0.550900	+	0.834571i	$0.314284\pi$
$132$	−756.000	−0.498495
$133$	2736.00	1.78377
$134$	−1320.00	−0.850975
$135$	525.000	0.334702
$136$	−352.000	−0.221939
$137$	1212.00	0.755826	0.377913	−	0.925841i	$-0.376642\pi$
$137$	1212.00	0.755826	0.377913	+	0.925841i	$0.376642\pi$
$138$	2128.00	1.31266
$139$	1328.00	0.810356	0.405178	−	0.914238i	$-0.367210\pi$
$139$	1328.00	0.810356	0.405178	+	0.914238i	$0.367210\pi$
$140$	1080.00	0.651976
$141$	2499.00	1.49258
$142$	−1452.00	−0.858092
$143$	1539.00	0.899984
$144$	352.000	0.203704
$145$	0	0
$146$	2008.00	1.13824
$147$	−133.000	−0.0746235
$148$	480.000	0.266593
$149$	−1777.00	−0.977030	−0.488515	−	0.872555i	$-0.662461\pi$
$149$	−1777.00	−0.977030	−0.488515	+	0.872555i	$0.662461\pi$
$150$	−1400.00	−0.762063
$151$	−1934.00	−1.04230	−0.521148	−	0.853466i	$-0.674496\pi$
$151$	−1934.00	−1.04230	−0.521148	+	0.853466i	$0.674496\pi$
$152$	1216.00	0.648886
$153$	968.000	0.511491
$154$	−972.000	−0.508610
$155$	−2595.00	−1.34474
$156$	−1596.00	−0.819117
$157$	−734.000	−0.373118	−0.186559	−	0.982444i	$-0.559734\pi$
$157$	−734.000	−0.373118	−0.186559	+	0.982444i	$0.559734\pi$
$158$	722.000	0.363539
$159$	−413.000	−0.205994
$160$	480.000	0.237171
$161$	2736.00	1.33930
$162$	1678.00	0.813803
$163$	3337.00	1.60352	0.801761	−	0.597645i	$-0.203897\pi$
$163$	3337.00	1.60352	0.801761	+	0.597645i	$0.203897\pi$
$164$	1256.00	0.598031
$165$	2835.00	1.33760
$166$	336.000	0.157100
$167$	−198.000	−0.0917467	−0.0458734	−	0.998947i	$-0.514607\pi$
$167$	−198.000	−0.0917467	−0.0458734	+	0.998947i	$0.514607\pi$
$168$	1008.00	0.462910
$169$	1052.00	0.478835
$170$	1320.00	0.595526
$171$	−3344.00	−1.49545
$172$	−1356.00	−0.601128
$173$	−2598.00	−1.14175	−0.570874	−	0.821038i	$-0.693395\pi$
$173$	−2598.00	−1.14175	−0.570874	+	0.821038i	$0.693395\pi$
$174$	0	0
$175$	−1800.00	−0.777527
$176$	−432.000	−0.185018
$177$	−4004.00	−1.70033
$178$	116.000	0.0488459
$179$	−1510.00	−0.630518	−0.315259	−	0.949006i	$-0.602091\pi$
$179$	−1510.00	−0.630518	−0.315259	+	0.949006i	$0.602091\pi$
$180$	−1320.00	−0.546594
$181$	−2865.00	−1.17654	−0.588270	−	0.808665i	$-0.700191\pi$
$181$	−2865.00	−1.17654	−0.588270	+	0.808665i	$0.700191\pi$
$182$	−2052.00	−0.835738
$183$	2940.00	1.18760
$184$	1216.00	0.487200
$185$	−1800.00	−0.715344
$186$	−2422.00	−0.954783
$187$	−1188.00	−0.464573
$188$	1428.00	0.553977
$189$	630.000	0.242464
$190$	−4560.00	−1.74114
$191$	1936.00	0.733424	0.366712	−	0.930334i	$-0.380483\pi$
$191$	1936.00	0.733424	0.366712	+	0.930334i	$0.380483\pi$
$192$	448.000	0.168394
$193$	−3850.00	−1.43590	−0.717951	−	0.696094i	$-0.754920\pi$
$193$	−3850.00	−1.43590	−0.717951	+	0.696094i	$0.754920\pi$
$194$	−2412.00	−0.892637
$195$	5985.00	2.19792
$196$	−76.0000	−0.0276968
$197$	3034.00	1.09728	0.548638	−	0.836060i	$-0.315146\pi$
$197$	3034.00	1.09728	0.548638	+	0.836060i	$0.315146\pi$
$198$	1188.00	0.426401
$199$	246.000	0.0876305	0.0438153	−	0.999040i	$-0.486049\pi$
$199$	246.000	0.0876305	0.0438153	+	0.999040i	$0.486049\pi$
$200$	−800.000	−0.282843
$201$	4620.00	1.62124
$202$	2880.00	1.00315
$203$	0	0
$204$	1232.00	0.422830
$205$	−4710.00	−1.60469
$206$	−3716.00	−1.25683
$207$	−3344.00	−1.12282
$208$	−912.000	−0.304018
$209$	4104.00	1.35828
$210$	−3780.00	−1.24212
$211$	1493.00	0.487120	0.243560	−	0.969886i	$-0.421685\pi$
$211$	1493.00	0.487120	0.243560	+	0.969886i	$0.421685\pi$
$212$	−236.000	−0.0764554
$213$	5082.00	1.63480
$214$	3828.00	1.22279
$215$	5085.00	1.61300
$216$	280.000	0.0882018
$217$	−3114.00	−0.974157
$218$	−1978.00	−0.614528
$219$	−7028.00	−2.16853
$220$	1620.00	0.496456
$221$	−2508.00	−0.763377
$222$	−1680.00	−0.507902
$223$	1402.00	0.421008	0.210504	−	0.977593i	$-0.432489\pi$
$223$	1402.00	0.421008	0.210504	+	0.977593i	$0.432489\pi$
$224$	576.000	0.171811
$225$	2200.00	0.651852
$226$	−556.000	−0.163649
$227$	1166.00	0.340926	0.170463	−	0.985364i	$-0.445474\pi$
$227$	1166.00	0.340926	0.170463	+	0.985364i	$0.445474\pi$
$228$	−4256.00	−1.23623
$229$	1466.00	0.423039	0.211520	−	0.977374i	$-0.432159\pi$
$229$	1466.00	0.423039	0.211520	+	0.977374i	$0.432159\pi$
$230$	−4560.00	−1.30729
$231$	3402.00	0.968983
$232$	0	0
$233$	847.000	0.238149	0.119075	−	0.992885i	$-0.462007\pi$
$233$	847.000	0.238149	0.119075	+	0.992885i	$0.462007\pi$
$234$	2508.00	0.700654
$235$	−5355.00	−1.48648
$236$	−2288.00	−0.631085
$237$	−2527.00	−0.692600
$238$	1584.00	0.431410
$239$	−444.000	−0.120167	−0.0600836	−	0.998193i	$-0.519137\pi$
$239$	−444.000	−0.120167	−0.0600836	+	0.998193i	$0.519137\pi$
$240$	−1680.00	−0.451848
$241$	5297.00	1.41581	0.707904	−	0.706309i	$-0.249641\pi$
$241$	5297.00	1.41581	0.707904	+	0.706309i	$0.249641\pi$
$242$	1204.00	0.319818
$243$	−4928.00	−1.30095
$244$	1680.00	0.440783
$245$	285.000	0.0743183
$246$	−4396.00	−1.13934
$247$	8664.00	2.23189
$248$	−1384.00	−0.354371
$249$	−1176.00	−0.299301
$250$	−750.000	−0.189737
$251$	−4061.00	−1.02123	−0.510614	−	0.859810i	$-0.670582\pi$
$251$	−4061.00	−1.02123	−0.510614	+	0.859810i	$0.670582\pi$
$252$	−1584.00	−0.395963
$253$	4104.00	1.01983
$254$	−1200.00	−0.296436
$255$	−4620.00	−1.13457
$256$	256.000	0.0625000
$257$	−6843.00	−1.66091	−0.830456	−	0.557084i	$-0.811920\pi$
$257$	−6843.00	−1.66091	−0.830456	+	0.557084i	$0.811920\pi$
$258$	4746.00	1.14524
$259$	−2160.00	−0.518208
$260$	3420.00	0.815767
$261$	0	0
$262$	−3304.00	−0.779091
$263$	−3191.00	−0.748158	−0.374079	−	0.927397i	$-0.622041\pi$
$263$	−3191.00	−0.748158	−0.374079	+	0.927397i	$0.622041\pi$
$264$	1512.00	0.352489
$265$	885.000	0.205151
$266$	−5472.00	−1.26132
$267$	−406.000	−0.0930592
$268$	2640.00	0.601730
$269$	−7436.00	−1.68543	−0.842715	−	0.538359i	$-0.819044\pi$
$269$	−7436.00	−1.68543	−0.842715	+	0.538359i	$0.819044\pi$
$270$	−1050.00	−0.236670
$271$	2755.00	0.617544	0.308772	−	0.951136i	$-0.400082\pi$
$271$	2755.00	0.617544	0.308772	+	0.951136i	$0.400082\pi$
$272$	704.000	0.156935
$273$	7182.00	1.59221
$274$	−2424.00	−0.534450
$275$	−2700.00	−0.592059
$276$	−4256.00	−0.928192
$277$	−2410.00	−0.522754	−0.261377	−	0.965237i	$-0.584177\pi$
$277$	−2410.00	−0.522754	−0.261377	+	0.965237i	$0.584177\pi$
$278$	−2656.00	−0.573008
$279$	3806.00	0.816700
$280$	−2160.00	−0.461017
$281$	2235.00	0.474480	0.237240	−	0.971451i	$-0.423757\pi$
$281$	2235.00	0.474480	0.237240	+	0.971451i	$0.423757\pi$
$282$	−4998.00	−1.05541
$283$	−1648.00	−0.346161	−0.173080	−	0.984908i	$-0.555372\pi$
$283$	−1648.00	−0.346161	−0.173080	+	0.984908i	$0.555372\pi$
$284$	2904.00	0.606763
$285$	15960.0	3.31715
$286$	−3078.00	−0.636384
$287$	−5652.00	−1.16246
$288$	−704.000	−0.144040
$289$	−2977.00	−0.605943
$290$	0	0
$291$	8442.00	1.70061
$292$	−4016.00	−0.804858
$293$	−2878.00	−0.573838	−0.286919	−	0.957955i	$-0.592631\pi$
$293$	−2878.00	−0.573838	−0.286919	+	0.957955i	$0.592631\pi$
$294$	266.000	0.0527668
$295$	8580.00	1.69338
$296$	−960.000	−0.188510
$297$	945.000	0.184628
$298$	3554.00	0.690865
$299$	8664.00	1.67576
$300$	2800.00	0.538860
$301$	6102.00	1.16848
$302$	3868.00	0.737015
$303$	−10080.0	−1.91116
$304$	−2432.00	−0.458831
$305$	−6300.00	−1.18274
$306$	−1936.00	−0.361679
$307$	−4903.00	−0.911495	−0.455748	−	0.890109i	$-0.650628\pi$
$307$	−4903.00	−0.911495	−0.455748	+	0.890109i	$0.650628\pi$
$308$	1944.00	0.359642
$309$	13006.0	2.39445
$310$	5190.00	0.950878
$311$	32.0000	0.00583458	0.00291729	−	0.999996i	$-0.499071\pi$
$311$	32.0000	0.00583458	0.00291729	+	0.999996i	$0.499071\pi$
$312$	3192.00	0.579203
$313$	−5455.00	−0.985095	−0.492548	−	0.870285i	$-0.663934\pi$
$313$	−5455.00	−0.985095	−0.492548	+	0.870285i	$0.663934\pi$
$314$	1468.00	0.263834
$315$	5940.00	1.06248
$316$	−1444.00	−0.257061
$317$	9552.00	1.69241	0.846205	−	0.532858i	$-0.178882\pi$
$317$	9552.00	1.69241	0.846205	+	0.532858i	$0.178882\pi$
$318$	826.000	0.145660
$319$	0	0
$320$	−960.000	−0.167705
$321$	−13398.0	−2.32961
$322$	−5472.00	−0.947027
$323$	−6688.00	−1.15211
$324$	−3356.00	−0.575446
$325$	−5700.00	−0.972859
$326$	−6674.00	−1.13386
$327$	6923.00	1.17077
$328$	−2512.00	−0.422872
$329$	−6426.00	−1.07683
$330$	−5670.00	−0.945828
$331$	2433.00	0.404017	0.202009	−	0.979384i	$-0.435253\pi$
$331$	2433.00	0.404017	0.202009	+	0.979384i	$0.435253\pi$
$332$	−672.000	−0.111087
$333$	2640.00	0.434448
$334$	396.000	0.0648747
$335$	−9900.00	−1.61461
$336$	−2016.00	−0.327327
$337$	7460.00	1.20585	0.602926	−	0.797797i	$-0.294001\pi$
$337$	7460.00	1.20585	0.602926	+	0.797797i	$0.294001\pi$
$338$	−2104.00	−0.338587
$339$	1946.00	0.311776
$340$	−2640.00	−0.421100
$341$	−4671.00	−0.741785
$342$	6688.00	1.05744
$343$	6516.00	1.02575
$344$	2712.00	0.425062
$345$	15960.0	2.49060
$346$	5196.00	0.807337
$347$	4002.00	0.619131	0.309566	−	0.950878i	$-0.399816\pi$
$347$	4002.00	0.619131	0.309566	+	0.950878i	$0.399816\pi$
$348$	0	0
$349$	−2167.00	−0.332369	−0.166185	−	0.986095i	$-0.553145\pi$
$349$	−2167.00	−0.332369	−0.166185	+	0.986095i	$0.553145\pi$
$350$	3600.00	0.549795
$351$	1995.00	0.303377
$352$	864.000	0.130828
$353$	−2354.00	−0.354931	−0.177466	−	0.984127i	$-0.556790\pi$
$353$	−2354.00	−0.354931	−0.177466	+	0.984127i	$0.556790\pi$
$354$	8008.00	1.20232
$355$	−10890.0	−1.62812
$356$	−232.000	−0.0345393
$357$	−5544.00	−0.821904
$358$	3020.00	0.445843
$359$	3471.00	0.510285	0.255143	−	0.966903i	$-0.417878\pi$
$359$	3471.00	0.510285	0.255143	+	0.966903i	$0.417878\pi$
$360$	2640.00	0.386501
$361$	16245.0	2.36842
$362$	5730.00	0.831940
$363$	−4214.00	−0.609305
$364$	4104.00	0.590956
$365$	15060.0	2.15966
$366$	−5880.00	−0.839761
$367$	10880.0	1.54750	0.773748	−	0.633493i	$-0.218379\pi$
$367$	10880.0	1.54750	0.773748	+	0.633493i	$0.218379\pi$
$368$	−2432.00	−0.344502
$369$	6908.00	0.974569
$370$	3600.00	0.505825
$371$	1062.00	0.148615
$372$	4844.00	0.675134
$373$	8827.00	1.22532	0.612661	−	0.790346i	$-0.290099\pi$
$373$	8827.00	1.22532	0.612661	+	0.790346i	$0.290099\pi$
$374$	2376.00	0.328503
$375$	2625.00	0.361478
$376$	−2856.00	−0.391721
$377$	0	0
$378$	−1260.00	−0.171448
$379$	876.000	0.118726	0.0593629	−	0.998236i	$-0.481093\pi$
$379$	876.000	0.118726	0.0593629	+	0.998236i	$0.481093\pi$
$380$	9120.00	1.23117
$381$	4200.00	0.564757
$382$	−3872.00	−0.518609
$383$	5446.00	0.726573	0.363287	−	0.931677i	$-0.381655\pi$
$383$	5446.00	0.726573	0.363287	+	0.931677i	$0.381655\pi$
$384$	−896.000	−0.119072
$385$	−7290.00	−0.965020
$386$	7700.00	1.01534
$387$	−7458.00	−0.979616
$388$	4824.00	0.631189
$389$	2216.00	0.288832	0.144416	−	0.989517i	$-0.453870\pi$
$389$	2216.00	0.288832	0.144416	+	0.989517i	$0.453870\pi$
$390$	−11970.0	−1.55417
$391$	−6688.00	−0.865030
$392$	152.000	0.0195846
$393$	11564.0	1.48429
$394$	−6068.00	−0.775892
$395$	5415.00	0.689768
$396$	−2376.00	−0.301511
$397$	6823.00	0.862561	0.431280	−	0.902218i	$-0.358062\pi$
$397$	6823.00	0.862561	0.431280	+	0.902218i	$0.358062\pi$
$398$	−492.000	−0.0619641
$399$	19152.0	2.40301
$400$	1600.00	0.200000
$401$	−5589.00	−0.696013	−0.348007	−	0.937492i	$-0.613141\pi$
$401$	−5589.00	−0.696013	−0.348007	+	0.937492i	$0.613141\pi$
$402$	−9240.00	−1.14639
$403$	−9861.00	−1.21889
$404$	−5760.00	−0.709333
$405$	12585.0	1.54408
$406$	0	0
$407$	−3240.00	−0.394597
$408$	−2464.00	−0.298986
$409$	8258.00	0.998366	0.499183	−	0.866496i	$-0.333633\pi$
$409$	8258.00	0.998366	0.499183	+	0.866496i	$0.333633\pi$
$410$	9420.00	1.13468
$411$	8484.00	1.01821
$412$	7432.00	0.888710
$413$	10296.0	1.22671
$414$	6688.00	0.793955
$415$	2520.00	0.298077
$416$	1824.00	0.214973
$417$	9296.00	1.09167
$418$	−8208.00	−0.960446
$419$	3946.00	0.460083	0.230041	−	0.973181i	$-0.426114\pi$
$419$	3946.00	0.460083	0.230041	+	0.973181i	$0.426114\pi$
$420$	7560.00	0.878310
$421$	−1380.00	−0.159756	−0.0798778	−	0.996805i	$-0.525453\pi$
$421$	−1380.00	−0.159756	−0.0798778	+	0.996805i	$0.525453\pi$
$422$	−2986.00	−0.344446
$423$	7854.00	0.902777
$424$	472.000	0.0540621
$425$	4400.00	0.502191
$426$	−10164.0	−1.15598
$427$	−7560.00	−0.856801
$428$	−7656.00	−0.864642
$429$	10773.0	1.21241
$430$	−10170.0	−1.14056
$431$	−5820.00	−0.650440	−0.325220	−	0.945638i	$-0.605438\pi$
$431$	−5820.00	−0.650440	−0.325220	+	0.945638i	$0.605438\pi$
$432$	−560.000	−0.0623681
$433$	14504.0	1.60974	0.804870	−	0.593451i	$-0.202235\pi$
$433$	14504.0	1.60974	0.804870	+	0.593451i	$0.202235\pi$
$434$	6228.00	0.688833
$435$	0	0
$436$	3956.00	0.434537
$437$	23104.0	2.52909
$438$	14056.0	1.53338
$439$	14912.0	1.62121	0.810605	−	0.585594i	$-0.199139\pi$
$439$	14912.0	1.62121	0.810605	+	0.585594i	$0.199139\pi$
$440$	−3240.00	−0.351048
$441$	−418.000	−0.0451355
$442$	5016.00	0.539789
$443$	−7180.00	−0.770050	−0.385025	−	0.922906i	$-0.625807\pi$
$443$	−7180.00	−0.770050	−0.385025	+	0.922906i	$0.625807\pi$
$444$	3360.00	0.359141
$445$	870.000	0.0926786
$446$	−2804.00	−0.297698
$447$	−12439.0	−1.31621
$448$	−1152.00	−0.121489
$449$	−1398.00	−0.146939	−0.0734696	−	0.997297i	$-0.523407\pi$
$449$	−1398.00	−0.146939	−0.0734696	+	0.997297i	$0.523407\pi$
$450$	−4400.00	−0.460929
$451$	−8478.00	−0.885174
$452$	1112.00	0.115717
$453$	−13538.0	−1.40413
$454$	−2332.00	−0.241071
$455$	−15390.0	−1.58570
$456$	8512.00	0.874147
$457$	−5658.00	−0.579147	−0.289573	−	0.957156i	$-0.593513\pi$
$457$	−5658.00	−0.579147	−0.289573	+	0.957156i	$0.593513\pi$
$458$	−2932.00	−0.299134
$459$	−1540.00	−0.156604
$460$	9120.00	0.924396
$461$	−11410.0	−1.15275	−0.576374	−	0.817186i	$-0.695533\pi$
$461$	−11410.0	−1.15275	−0.576374	+	0.817186i	$0.695533\pi$
$462$	−6804.00	−0.685175
$463$	−2560.00	−0.256962	−0.128481	−	0.991712i	$-0.541010\pi$
$463$	−2560.00	−0.256962	−0.128481	+	0.991712i	$0.541010\pi$
$464$	0	0
$465$	−18165.0	−1.81157
$466$	−1694.00	−0.168397
$467$	−10395.0	−1.03003	−0.515014	−	0.857182i	$-0.672213\pi$
$467$	−10395.0	−1.03003	−0.515014	+	0.857182i	$0.672213\pi$
$468$	−5016.00	−0.495437
$469$	−11880.0	−1.16965
$470$	10710.0	1.05110
$471$	−5138.00	−0.502647
$472$	4576.00	0.446245
$473$	9153.00	0.889758
$474$	5054.00	0.489742
$475$	−15200.0	−1.46826
$476$	−3168.00	−0.305053
$477$	−1298.00	−0.124594
$478$	888.000	0.0849711
$479$	5627.00	0.536752	0.268376	−	0.963314i	$-0.413513\pi$
$479$	5627.00	0.536752	0.268376	+	0.963314i	$0.413513\pi$
$480$	3360.00	0.319505
$481$	−6840.00	−0.648393
$482$	−10594.0	−1.00113
$483$	19152.0	1.80424
$484$	−2408.00	−0.226146
$485$	−18090.0	−1.69366
$486$	9856.00	0.919912
$487$	8738.00	0.813053	0.406526	−	0.913639i	$-0.366740\pi$
$487$	8738.00	0.813053	0.406526	+	0.913639i	$0.366740\pi$
$488$	−3360.00	−0.311680
$489$	23359.0	2.16019
$490$	−570.000	−0.0525510
$491$	−3177.00	−0.292008	−0.146004	−	0.989284i	$-0.546641\pi$
$491$	−3177.00	−0.292008	−0.146004	+	0.989284i	$0.546641\pi$
$492$	8792.00	0.805638
$493$	0	0
$494$	−17328.0	−1.57819
$495$	8910.00	0.809040
$496$	2768.00	0.250578
$497$	−13068.0	−1.17944
$498$	2352.00	0.211638
$499$	−5816.00	−0.521763	−0.260882	−	0.965371i	$-0.584013\pi$
$499$	−5816.00	−0.521763	−0.260882	+	0.965371i	$0.584013\pi$
$500$	1500.00	0.134164
$501$	−1386.00	−0.123597
$502$	8122.00	0.722117
$503$	2267.00	0.200955	0.100478	−	0.994939i	$-0.467963\pi$
$503$	2267.00	0.200955	0.100478	+	0.994939i	$0.467963\pi$
$504$	3168.00	0.279988
$505$	21600.0	1.90334
$506$	−8208.00	−0.721127
$507$	7364.00	0.645063
$508$	2400.00	0.209612
$509$	6481.00	0.564372	0.282186	−	0.959360i	$-0.408940\pi$
$509$	6481.00	0.564372	0.282186	+	0.959360i	$0.408940\pi$
$510$	9240.00	0.802263
$511$	18072.0	1.56450
$512$	−512.000	−0.0441942
$513$	5320.00	0.457863
$514$	13686.0	1.17444
$515$	−27870.0	−2.38466
$516$	−9492.00	−0.809810
$517$	−9639.00	−0.819967
$518$	4320.00	0.366428
$519$	−18186.0	−1.53811
$520$	−6840.00	−0.576834
$521$	−21357.0	−1.79591	−0.897953	−	0.440091i	$-0.854946\pi$
$521$	−21357.0	−1.79591	−0.897953	+	0.440091i	$0.854946\pi$
$522$	0	0
$523$	−6192.00	−0.517700	−0.258850	−	0.965917i	$-0.583344\pi$
$523$	−6192.00	−0.517700	−0.258850	+	0.965917i	$0.583344\pi$
$524$	6608.00	0.550900
$525$	−12600.0	−1.04745
$526$	6382.00	0.529027
$527$	7612.00	0.629192
$528$	−3024.00	−0.249248
$529$	10937.0	0.898907
$530$	−1770.00	−0.145064
$531$	−12584.0	−1.02844
$532$	10944.0	0.891885
$533$	−17898.0	−1.45450
$534$	812.000	0.0658028
$535$	28710.0	2.32008
$536$	−5280.00	−0.425487
$537$	−10570.0	−0.849403
$538$	14872.0	1.19178
$539$	513.000	0.0409953
$540$	2100.00	0.167351
$541$	19800.0	1.57351	0.786755	−	0.617266i	$-0.211760\pi$
$541$	19800.0	1.57351	0.786755	+	0.617266i	$0.211760\pi$
$542$	−5510.00	−0.436669
$543$	−20055.0	−1.58498
$544$	−1408.00	−0.110970
$545$	−14835.0	−1.16598
$546$	−14364.0	−1.12587
$547$	10526.0	0.822777	0.411389	−	0.911460i	$-0.365044\pi$
$547$	10526.0	0.822777	0.411389	+	0.911460i	$0.365044\pi$
$548$	4848.00	0.377913
$549$	9240.00	0.718313
$550$	5400.00	0.418649
$551$	0	0
$552$	8512.00	0.656331
$553$	6498.00	0.499680
$554$	4820.00	0.369643
$555$	−12600.0	−0.963676
$556$	5312.00	0.405178
$557$	−11834.0	−0.900220	−0.450110	−	0.892973i	$-0.648615\pi$
$557$	−11834.0	−0.900220	−0.450110	+	0.892973i	$0.648615\pi$
$558$	−7612.00	−0.577494
$559$	19323.0	1.46203
$560$	4320.00	0.325988
$561$	−8316.00	−0.625850
$562$	−4470.00	−0.335508
$563$	−21771.0	−1.62973	−0.814865	−	0.579650i	$-0.803189\pi$
$563$	−21771.0	−1.62973	−0.814865	+	0.579650i	$0.803189\pi$
$564$	9996.00	0.746290
$565$	−4170.00	−0.310501
$566$	3296.00	0.244772
$567$	15102.0	1.11856
$568$	−5808.00	−0.429046
$569$	−20778.0	−1.53086	−0.765430	−	0.643519i	$-0.777474\pi$
$569$	−20778.0	−1.53086	−0.765430	+	0.643519i	$0.777474\pi$
$570$	−31920.0	−2.34558
$571$	−5596.00	−0.410132	−0.205066	−	0.978748i	$-0.565741\pi$
$571$	−5596.00	−0.410132	−0.205066	+	0.978748i	$0.565741\pi$
$572$	6156.00	0.449992
$573$	13552.0	0.988033
$574$	11304.0	0.821986
$575$	−15200.0	−1.10241
$576$	1408.00	0.101852
$577$	14908.0	1.07561	0.537806	−	0.843069i	$-0.319253\pi$
$577$	14908.0	1.07561	0.537806	+	0.843069i	$0.319253\pi$
$578$	5954.00	0.428467
$579$	−26950.0	−1.93438
$580$	0	0
$581$	3024.00	0.215932
$582$	−16884.0	−1.20252
$583$	1593.00	0.113165
$584$	8032.00	0.569121
$585$	18810.0	1.32940
$586$	5756.00	0.405765
$587$	8136.00	0.572076	0.286038	−	0.958218i	$-0.407662\pi$
$587$	8136.00	0.572076	0.286038	+	0.958218i	$0.407662\pi$
$588$	−532.000	−0.0373118
$589$	−26296.0	−1.83957
$590$	−17160.0	−1.19740
$591$	21238.0	1.47820
$592$	1920.00	0.133296
$593$	−3521.00	−0.243828	−0.121914	−	0.992541i	$-0.538903\pi$
$593$	−3521.00	−0.243828	−0.121914	+	0.992541i	$0.538903\pi$
$594$	−1890.00	−0.130552
$595$	11880.0	0.818542
$596$	−7108.00	−0.488515
$597$	1722.00	0.118052
$598$	−17328.0	−1.18494
$599$	−7749.00	−0.528574	−0.264287	−	0.964444i	$-0.585137\pi$
$599$	−7749.00	−0.528574	−0.264287	+	0.964444i	$0.585137\pi$
$600$	−5600.00	−0.381032
$601$	−5054.00	−0.343023	−0.171512	−	0.985182i	$-0.554865\pi$
$601$	−5054.00	−0.343023	−0.171512	+	0.985182i	$0.554865\pi$
$602$	−12204.0	−0.826242
$603$	14520.0	0.980597
$604$	−7736.00	−0.521148
$605$	9030.00	0.606813
$606$	20160.0	1.35139
$607$	−27389.0	−1.83144	−0.915721	−	0.401815i	$-0.868380\pi$
$607$	−27389.0	−1.83144	−0.915721	+	0.401815i	$0.868380\pi$
$608$	4864.00	0.324443
$609$	0	0
$610$	12600.0	0.836326
$611$	−20349.0	−1.34735
$612$	3872.00	0.255746
$613$	−2375.00	−0.156485	−0.0782425	−	0.996934i	$-0.524931\pi$
$613$	−2375.00	−0.156485	−0.0782425	+	0.996934i	$0.524931\pi$
$614$	9806.00	0.644524
$615$	−32970.0	−2.16175
$616$	−3888.00	−0.254305
$617$	−3412.00	−0.222629	−0.111314	−	0.993785i	$-0.535506\pi$
$617$	−3412.00	−0.222629	−0.111314	+	0.993785i	$0.535506\pi$
$618$	−26012.0	−1.69313
$619$	−17659.0	−1.14665	−0.573324	−	0.819329i	$-0.694346\pi$
$619$	−17659.0	−1.14665	−0.573324	+	0.819329i	$0.694346\pi$
$620$	−10380.0	−0.672372
$621$	5320.00	0.343775
$622$	−64.0000	−0.00412567
$623$	1044.00	0.0671380
$624$	−6384.00	−0.409559
$625$	−18125.0	−1.16000
$626$	10910.0	0.696568
$627$	28728.0	1.82980
$628$	−2936.00	−0.186559
$629$	5280.00	0.334702
$630$	−11880.0	−0.751287
$631$	12742.0	0.803884	0.401942	−	0.915665i	$-0.368335\pi$
$631$	12742.0	0.803884	0.401942	+	0.915665i	$0.368335\pi$
$632$	2888.00	0.181770
$633$	10451.0	0.656224
$634$	−19104.0	−1.19671
$635$	−9000.00	−0.562447
$636$	−1652.00	−0.102997
$637$	1083.00	0.0673627
$638$	0	0
$639$	15972.0	0.988799
$640$	1920.00	0.118585
$641$	10988.0	0.677067	0.338533	−	0.940954i	$-0.390069\pi$
$641$	10988.0	0.677067	0.338533	+	0.940954i	$0.390069\pi$
$642$	26796.0	1.64728
$643$	−13190.0	−0.808962	−0.404481	−	0.914546i	$-0.632548\pi$
$643$	−13190.0	−0.808962	−0.404481	+	0.914546i	$0.632548\pi$
$644$	10944.0	0.669649
$645$	35595.0	2.17295
$646$	13376.0	0.814662
$647$	22924.0	1.39295	0.696473	−	0.717583i	$-0.254752\pi$
$647$	22924.0	1.39295	0.696473	+	0.717583i	$0.254752\pi$
$648$	6712.00	0.406902
$649$	15444.0	0.934099
$650$	11400.0	0.687915
$651$	−21798.0	−1.31234
$652$	13348.0	0.801761
$653$	10278.0	0.615941	0.307970	−	0.951396i	$-0.400350\pi$
$653$	10278.0	0.615941	0.307970	+	0.951396i	$0.400350\pi$
$654$	−13846.0	−0.827862
$655$	−24780.0	−1.47822
$656$	5024.00	0.299016
$657$	−22088.0	−1.31162
$658$	12852.0	0.761433
$659$	10607.0	0.626996	0.313498	−	0.949589i	$-0.398499\pi$
$659$	10607.0	0.626996	0.313498	+	0.949589i	$0.398499\pi$
$660$	11340.0	0.668801
$661$	−24698.0	−1.45331	−0.726657	−	0.687000i	$-0.758927\pi$
$661$	−24698.0	−1.45331	−0.726657	+	0.687000i	$0.758927\pi$
$662$	−4866.00	−0.285683
$663$	−17556.0	−1.02838
$664$	1344.00	0.0785502
$665$	−41040.0	−2.39318
$666$	−5280.00	−0.307201
$667$	0	0
$668$	−792.000	−0.0458734
$669$	9814.00	0.567162
$670$	19800.0	1.14170
$671$	−11340.0	−0.652423
$672$	4032.00	0.231455
$673$	16801.0	0.962305	0.481152	−	0.876637i	$-0.340218\pi$
$673$	16801.0	0.962305	0.481152	+	0.876637i	$0.340218\pi$
$674$	−14920.0	−0.852666
$675$	−3500.00	−0.199578
$676$	4208.00	0.239417
$677$	1258.00	0.0714163	0.0357082	−	0.999362i	$-0.488631\pi$
$677$	1258.00	0.0714163	0.0357082	+	0.999362i	$0.488631\pi$
$678$	−3892.00	−0.220459
$679$	−21708.0	−1.22692
$680$	5280.00	0.297763
$681$	8162.00	0.459278
$682$	9342.00	0.524522
$683$	−1256.00	−0.0703653	−0.0351827	−	0.999381i	$-0.511201\pi$
$683$	−1256.00	−0.0703653	−0.0351827	+	0.999381i	$0.511201\pi$
$684$	−13376.0	−0.747725
$685$	−18180.0	−1.01405
$686$	−13032.0	−0.725312
$687$	10262.0	0.569898
$688$	−5424.00	−0.300564
$689$	3363.00	0.185951
$690$	−31920.0	−1.76112
$691$	−15996.0	−0.880632	−0.440316	−	0.897843i	$-0.645134\pi$
$691$	−15996.0	−0.880632	−0.440316	+	0.897843i	$0.645134\pi$
$692$	−10392.0	−0.570874
$693$	10692.0	0.586083
$694$	−8004.00	−0.437792
$695$	−19920.0	−1.08721
$696$	0	0
$697$	13816.0	0.750815
$698$	4334.00	0.235021
$699$	5929.00	0.320823
$700$	−7200.00	−0.388763
$701$	−189.000	−0.0101832	−0.00509161	−	0.999987i	$-0.501621\pi$
$701$	−189.000	−0.0101832	−0.00509161	+	0.999987i	$0.501621\pi$
$702$	−3990.00	−0.214520
$703$	−18240.0	−0.978570
$704$	−1728.00	−0.0925092
$705$	−37485.0	−2.00251
$706$	4708.00	0.250974
$707$	25920.0	1.37881
$708$	−16016.0	−0.850167
$709$	2431.00	0.128770	0.0643851	−	0.997925i	$-0.479491\pi$
$709$	2431.00	0.128770	0.0643851	+	0.997925i	$0.479491\pi$
$710$	21780.0	1.15125
$711$	−7942.00	−0.418915
$712$	464.000	0.0244229
$713$	−26296.0	−1.38120
$714$	11088.0	0.581174
$715$	−23085.0	−1.20745
$716$	−6040.00	−0.315259
$717$	−3108.00	−0.161883
$718$	−6942.00	−0.360826
$719$	−3630.00	−0.188284	−0.0941420	−	0.995559i	$-0.530011\pi$
$719$	−3630.00	−0.188284	−0.0941420	+	0.995559i	$0.530011\pi$
$720$	−5280.00	−0.273297
$721$	−33444.0	−1.72749
$722$	−32490.0	−1.67473
$723$	37079.0	1.90731
$724$	−11460.0	−0.588270
$725$	0	0
$726$	8428.00	0.430844
$727$	1712.00	0.0873378	0.0436689	−	0.999046i	$-0.486095\pi$
$727$	1712.00	0.0873378	0.0436689	+	0.999046i	$0.486095\pi$
$728$	−8208.00	−0.417869
$729$	−11843.0	−0.601687
$730$	−30120.0	−1.52711
$731$	−14916.0	−0.754703
$732$	11760.0	0.593801
$733$	−26584.0	−1.33957	−0.669783	−	0.742557i	$-0.733613\pi$
$733$	−26584.0	−1.33957	−0.669783	+	0.742557i	$0.733613\pi$
$734$	−21760.0	−1.09425
$735$	1995.00	0.100118
$736$	4864.00	0.243600
$737$	−17820.0	−0.890649
$738$	−13816.0	−0.689125
$739$	−8125.00	−0.404442	−0.202221	−	0.979340i	$-0.564816\pi$
$739$	−8125.00	−0.404442	−0.202221	+	0.979340i	$0.564816\pi$
$740$	−7200.00	−0.357672
$741$	60648.0	3.00669
$742$	−2124.00	−0.105087
$743$	31804.0	1.57036	0.785179	−	0.619269i	$-0.212571\pi$
$743$	31804.0	1.57036	0.785179	+	0.619269i	$0.212571\pi$
$744$	−9688.00	−0.477392
$745$	26655.0	1.31082
$746$	−17654.0	−0.866433
$747$	−3696.00	−0.181030
$748$	−4752.00	−0.232287
$749$	34452.0	1.68071
$750$	−5250.00	−0.255604
$751$	37504.0	1.82229	0.911145	−	0.412085i	$-0.135199\pi$
$751$	37504.0	1.82229	0.911145	+	0.412085i	$0.135199\pi$
$752$	5712.00	0.276988
$753$	−28427.0	−1.37575
$754$	0	0
$755$	29010.0	1.39839
$756$	2520.00	0.121232
$757$	76.0000	0.00364897	0.00182448	−	0.999998i	$-0.499419\pi$
$757$	76.0000	0.00364897	0.00182448	+	0.999998i	$0.499419\pi$
$758$	−1752.00	−0.0839519
$759$	28728.0	1.37386
$760$	−18240.0	−0.870572
$761$	−23374.0	−1.11341	−0.556706	−	0.830709i	$-0.687935\pi$
$761$	−23374.0	−1.11341	−0.556706	+	0.830709i	$0.687935\pi$
$762$	−8400.00	−0.399344
$763$	−17802.0	−0.844660
$764$	7744.00	0.366712
$765$	−14520.0	−0.686238
$766$	−10892.0	−0.513765
$767$	32604.0	1.53489
$768$	1792.00	0.0841969
$769$	5448.00	0.255475	0.127737	−	0.991808i	$-0.459229\pi$
$769$	5448.00	0.255475	0.127737	+	0.991808i	$0.459229\pi$
$770$	14580.0	0.682372
$771$	−47901.0	−2.23750
$772$	−15400.0	−0.717951
$773$	16062.0	0.747361	0.373680	−	0.927558i	$-0.378096\pi$
$773$	16062.0	0.747361	0.373680	+	0.927558i	$0.378096\pi$
$774$	14916.0	0.692693
$775$	17300.0	0.801851
$776$	−9648.00	−0.446318
$777$	−15120.0	−0.698104
$778$	−4432.00	−0.204235
$779$	−47728.0	−2.19516
$780$	23940.0	1.09896
$781$	−19602.0	−0.898098
$782$	13376.0	0.611669
$783$	0	0
$784$	−304.000	−0.0138484
$785$	11010.0	0.500591
$786$	−23128.0	−1.04955
$787$	19182.0	0.868824	0.434412	−	0.900714i	$-0.356956\pi$
$787$	19182.0	0.868824	0.434412	+	0.900714i	$0.356956\pi$
$788$	12136.0	0.548638
$789$	−22337.0	−1.00788
$790$	−10830.0	−0.487739
$791$	−5004.00	−0.224933
$792$	4752.00	0.213201
$793$	−23940.0	−1.07205
$794$	−13646.0	−0.609922
$795$	6195.00	0.276370
$796$	984.000	0.0438153
$797$	−5556.00	−0.246931	−0.123465	−	0.992349i	$-0.539401\pi$
$797$	−5556.00	−0.246931	−0.123465	+	0.992349i	$0.539401\pi$
$798$	−38304.0	−1.69918
$799$	15708.0	0.695506
$800$	−3200.00	−0.141421
$801$	−1276.00	−0.0562862
$802$	11178.0	0.492156
$803$	27108.0	1.19131
$804$	18480.0	0.810621
$805$	−41040.0	−1.79686
$806$	19722.0	0.861883
$807$	−52052.0	−2.27053
$808$	11520.0	0.501574
$809$	−2616.00	−0.113688	−0.0568440	−	0.998383i	$-0.518104\pi$
$809$	−2616.00	−0.113688	−0.0568440	+	0.998383i	$0.518104\pi$
$810$	−25170.0	−1.09183
$811$	−9626.00	−0.416787	−0.208394	−	0.978045i	$-0.566824\pi$
$811$	−9626.00	−0.416787	−0.208394	+	0.978045i	$0.566824\pi$
$812$	0	0
$813$	19285.0	0.831924
$814$	6480.00	0.279022
$815$	−50055.0	−2.15135
$816$	4928.00	0.211415
$817$	51528.0	2.20653
$818$	−16516.0	−0.705952
$819$	22572.0	0.963040
$820$	−18840.0	−0.802343
$821$	16007.0	0.680448	0.340224	−	0.940344i	$-0.389497\pi$
$821$	16007.0	0.680448	0.340224	+	0.940344i	$0.389497\pi$
$822$	−16968.0	−0.719984
$823$	−23216.0	−0.983304	−0.491652	−	0.870792i	$-0.663607\pi$
$823$	−23216.0	−0.983304	−0.491652	+	0.870792i	$0.663607\pi$
$824$	−14864.0	−0.628413
$825$	−18900.0	−0.797592
$826$	−20592.0	−0.867418
$827$	46765.0	1.96636	0.983179	−	0.182644i	$-0.0584654\pi$
$827$	46765.0	1.96636	0.983179	+	0.182644i	$0.0584654\pi$
$828$	−13376.0	−0.561411
$829$	37820.0	1.58449	0.792245	−	0.610203i	$-0.208912\pi$
$829$	37820.0	1.58449	0.792245	+	0.610203i	$0.208912\pi$
$830$	−5040.00	−0.210772
$831$	−16870.0	−0.704228
$832$	−3648.00	−0.152009
$833$	−836.000	−0.0347727
$834$	−18592.0	−0.771928
$835$	2970.00	0.123091
$836$	16416.0	0.679138
$837$	−6055.00	−0.250049
$838$	−7892.00	−0.325328
$839$	−6747.00	−0.277631	−0.138815	−	0.990318i	$-0.544329\pi$
$839$	−6747.00	−0.277631	−0.138815	+	0.990318i	$0.544329\pi$
$840$	−15120.0	−0.621059
$841$	0	0
$842$	2760.00	0.112964
$843$	15645.0	0.639196
$844$	5972.00	0.243560
$845$	−15780.0	−0.642424
$846$	−15708.0	−0.638360
$847$	10836.0	0.439586
$848$	−944.000	−0.0382277
$849$	−11536.0	−0.466330
$850$	−8800.00	−0.355103
$851$	−18240.0	−0.734735
$852$	20328.0	0.817401
$853$	13274.0	0.532817	0.266409	−	0.963860i	$-0.414163\pi$
$853$	13274.0	0.532817	0.266409	+	0.963860i	$0.414163\pi$
$854$	15120.0	0.605850
$855$	50160.0	2.00636
$856$	15312.0	0.611394
$857$	39069.0	1.55726	0.778630	−	0.627483i	$-0.215915\pi$
$857$	39069.0	1.55726	0.778630	+	0.627483i	$0.215915\pi$
$858$	−21546.0	−0.857306
$859$	−35329.0	−1.40327	−0.701636	−	0.712536i	$-0.747547\pi$
$859$	−35329.0	−1.40327	−0.701636	+	0.712536i	$0.747547\pi$
$860$	20340.0	0.806498
$861$	−39564.0	−1.56601
$862$	11640.0	0.459930
$863$	−36378.0	−1.43490	−0.717452	−	0.696608i	$-0.754692\pi$
$863$	−36378.0	−1.43490	−0.717452	+	0.696608i	$0.754692\pi$
$864$	1120.00	0.0441009
$865$	38970.0	1.53181
$866$	−29008.0	−1.13826
$867$	−20839.0	−0.816297
$868$	−12456.0	−0.487079
$869$	9747.00	0.380488
$870$	0	0
$871$	−37620.0	−1.46350
$872$	−7912.00	−0.307264
$873$	26532.0	1.02860
$874$	−46208.0	−1.78834
$875$	−6750.00	−0.260790
$876$	−28112.0	−1.08427
$877$	−219.000	−0.00843227	−0.00421614	−	0.999991i	$-0.501342\pi$
$877$	−219.000	−0.00843227	−0.00421614	+	0.999991i	$0.501342\pi$
$878$	−29824.0	−1.14637
$879$	−20146.0	−0.773046
$880$	6480.00	0.248228
$881$	5598.00	0.214077	0.107038	−	0.994255i	$-0.465863\pi$
$881$	5598.00	0.214077	0.107038	+	0.994255i	$0.465863\pi$
$882$	836.000	0.0319156
$883$	5886.00	0.224326	0.112163	−	0.993690i	$-0.464222\pi$
$883$	5886.00	0.224326	0.112163	+	0.993690i	$0.464222\pi$
$884$	−10032.0	−0.381689
$885$	60060.0	2.28124
$886$	14360.0	0.544507
$887$	29673.0	1.12325	0.561624	−	0.827392i	$-0.310177\pi$
$887$	29673.0	1.12325	0.561624	+	0.827392i	$0.310177\pi$
$888$	−6720.00	−0.253951
$889$	−10800.0	−0.407447
$890$	−1740.00	−0.0655336
$891$	22653.0	0.851744
$892$	5608.00	0.210504
$893$	−54264.0	−2.03346
$894$	24878.0	0.930699
$895$	22650.0	0.845928
$896$	2304.00	0.0859054
$897$	60648.0	2.25750
$898$	2796.00	0.103902
$899$	0	0
$900$	8800.00	0.325926
$901$	−2596.00	−0.0959881
$902$	16956.0	0.625912
$903$	42714.0	1.57412
$904$	−2224.00	−0.0818243
$905$	42975.0	1.57849
$906$	27076.0	0.992870
$907$	−13668.0	−0.500373	−0.250187	−	0.968198i	$-0.580492\pi$
$907$	−13668.0	−0.500373	−0.250187	+	0.968198i	$0.580492\pi$
$908$	4664.00	0.170463
$909$	−31680.0	−1.15595
$910$	30780.0	1.12126
$911$	4963.00	0.180496	0.0902478	−	0.995919i	$-0.471234\pi$
$911$	4963.00	0.180496	0.0902478	+	0.995919i	$0.471234\pi$
$912$	−17024.0	−0.618115
$913$	4536.00	0.164425
$914$	11316.0	0.409519
$915$	−44100.0	−1.59333
$916$	5864.00	0.211520
$917$	−29736.0	−1.07085
$918$	3080.00	0.110735
$919$	9954.00	0.357293	0.178646	−	0.983913i	$-0.442828\pi$
$919$	9954.00	0.357293	0.178646	+	0.983913i	$0.442828\pi$
$920$	−18240.0	−0.653647
$921$	−34321.0	−1.22792
$922$	22820.0	0.815116
$923$	−41382.0	−1.47574
$924$	13608.0	0.484492
$925$	12000.0	0.426549
$926$	5120.00	0.181699
$927$	40876.0	1.44827
$928$	0	0
$929$	30930.0	1.09234	0.546168	−	0.837676i	$-0.316086\pi$
$929$	30930.0	1.09234	0.546168	+	0.837676i	$0.316086\pi$
$930$	36330.0	1.28098
$931$	2888.00	0.101665
$932$	3388.00	0.119075
$933$	224.000	0.00786005
$934$	20790.0	0.728340
$935$	17820.0	0.623290
$936$	10032.0	0.350327
$937$	−38770.0	−1.35172	−0.675859	−	0.737030i	$-0.736227\pi$
$937$	−38770.0	−1.35172	−0.675859	+	0.737030i	$0.736227\pi$
$938$	23760.0	0.827070
$939$	−38185.0	−1.32707
$940$	−21420.0	−0.743238
$941$	−30115.0	−1.04327	−0.521637	−	0.853167i	$-0.674678\pi$
$941$	−30115.0	−1.04327	−0.521637	+	0.853167i	$0.674678\pi$
$942$	10276.0	0.355425
$943$	−47728.0	−1.64818
$944$	−9152.00	−0.315543
$945$	−9450.00	−0.325300
$946$	−18306.0	−0.629154
$947$	−31319.0	−1.07469	−0.537345	−	0.843363i	$-0.680573\pi$
$947$	−31319.0	−1.07469	−0.537345	+	0.843363i	$0.680573\pi$
$948$	−10108.0	−0.346300
$949$	57228.0	1.95753
$950$	30400.0	1.03822
$951$	66864.0	2.27993
$952$	6336.00	0.215705
$953$	7623.00	0.259111	0.129556	−	0.991572i	$-0.458645\pi$
$953$	7623.00	0.259111	0.129556	+	0.991572i	$0.458645\pi$
$954$	2596.00	0.0881013
$955$	−29040.0	−0.983992
$956$	−1776.00	−0.0600836
$957$	0	0
$958$	−11254.0	−0.379541
$959$	−21816.0	−0.734594
$960$	−6720.00	−0.225924
$961$	138.000	0.00463227
$962$	13680.0	0.458483
$963$	−42108.0	−1.40905
$964$	21188.0	0.707904
$965$	57750.0	1.92646
$966$	−38304.0	−1.27579
$967$	6269.00	0.208477	0.104239	−	0.994552i	$-0.466759\pi$
$967$	6269.00	0.208477	0.104239	+	0.994552i	$0.466759\pi$
$968$	4816.00	0.159909
$969$	−46816.0	−1.55206
$970$	36180.0	1.19760
$971$	34020.0	1.12436	0.562180	−	0.827015i	$-0.309963\pi$
$971$	34020.0	1.12436	0.562180	+	0.827015i	$0.309963\pi$
$972$	−19712.0	−0.650476
$973$	−23904.0	−0.787592
$974$	−17476.0	−0.574915
$975$	−39900.0	−1.31059
$976$	6720.00	0.220391
$977$	−51291.0	−1.67957	−0.839787	−	0.542915i	$-0.817320\pi$
$977$	−51291.0	−1.67957	−0.839787	+	0.542915i	$0.817320\pi$
$978$	−46718.0	−1.52748
$979$	1566.00	0.0511232
$980$	1140.00	0.0371591
$981$	21758.0	0.708134
$982$	6354.00	0.206481
$983$	−38687.0	−1.25526	−0.627632	−	0.778511i	$-0.715976\pi$
$983$	−38687.0	−1.25526	−0.627632	+	0.778511i	$0.715976\pi$
$984$	−17584.0	−0.569672
$985$	−45510.0	−1.47215
$986$	0	0
$987$	−44982.0	−1.45065
$988$	34656.0	1.11595
$989$	51528.0	1.65672
$990$	−17820.0	−0.572078
$991$	−3158.00	−0.101228	−0.0506141	−	0.998718i	$-0.516118\pi$
$991$	−3158.00	−0.101228	−0.0506141	+	0.998718i	$0.516118\pi$
$992$	−5536.00	−0.177186
$993$	17031.0	0.544272
$994$	26136.0	0.833988
$995$	−3690.00	−0.117569
$996$	−4704.00	−0.149651
$997$	21944.0	0.697065	0.348532	−	0.937297i	$-0.386680\pi$
$997$	21944.0	0.697065	0.348532	+	0.937297i	$0.386680\pi$
$998$	11632.0	0.368942
$999$	−4200.00	−0.133015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1682.4.a.a.1.1		1
29.28	even	2		58.4.a.b.1.1	✓	1
87.86	odd	2		522.4.a.b.1.1		1
116.115	odd	2		464.4.a.b.1.1		1
145.144	even	2		1450.4.a.d.1.1		1
232.115	odd	2		1856.4.a.c.1.1		1
232.173	even	2		1856.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.a.b.1.1	✓	1	29.28	even	2
464.4.a.b.1.1		1	116.115	odd	2
522.4.a.b.1.1		1	87.86	odd	2
1450.4.a.d.1.1		1	145.144	even	2
1682.4.a.a.1.1		1	1.1	even	1	trivial
1856.4.a.c.1.1		1	232.115	odd	2
1856.4.a.f.1.1		1	232.173	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1682.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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