LMFDB - Embedded newform 798.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,4,Mod(1,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, 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("798.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	798.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:	$47.0835241846$
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	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.0000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -10.0000 q^{5} -6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -20.0000 q^{10} +8.00000 q^{11} -12.0000 q^{12} -50.0000 q^{13} +14.0000 q^{14} +30.0000 q^{15} +16.0000 q^{16} +114.000 q^{17} +18.0000 q^{18} +19.0000 q^{19} -40.0000 q^{20} -21.0000 q^{21} +16.0000 q^{22} -148.000 q^{23} -24.0000 q^{24} -25.0000 q^{25} -100.000 q^{26} -27.0000 q^{27} +28.0000 q^{28} -30.0000 q^{29} +60.0000 q^{30} +304.000 q^{31} +32.0000 q^{32} -24.0000 q^{33} +228.000 q^{34} -70.0000 q^{35} +36.0000 q^{36} -274.000 q^{37} +38.0000 q^{38} +150.000 q^{39} -80.0000 q^{40} -202.000 q^{41} -42.0000 q^{42} -116.000 q^{43} +32.0000 q^{44} -90.0000 q^{45} -296.000 q^{46} -324.000 q^{47} -48.0000 q^{48} +49.0000 q^{49} -50.0000 q^{50} -342.000 q^{51} -200.000 q^{52} -550.000 q^{53} -54.0000 q^{54} -80.0000 q^{55} +56.0000 q^{56} -57.0000 q^{57} -60.0000 q^{58} +628.000 q^{59} +120.000 q^{60} -58.0000 q^{61} +608.000 q^{62} +63.0000 q^{63} +64.0000 q^{64} +500.000 q^{65} -48.0000 q^{66} -756.000 q^{67} +456.000 q^{68} +444.000 q^{69} -140.000 q^{70} -216.000 q^{71} +72.0000 q^{72} -278.000 q^{73} -548.000 q^{74} +75.0000 q^{75} +76.0000 q^{76} +56.0000 q^{77} +300.000 q^{78} -952.000 q^{79} -160.000 q^{80} +81.0000 q^{81} -404.000 q^{82} -1184.00 q^{83} -84.0000 q^{84} -1140.00 q^{85} -232.000 q^{86} +90.0000 q^{87} +64.0000 q^{88} +1542.00 q^{89} -180.000 q^{90} -350.000 q^{91} -592.000 q^{92} -912.000 q^{93} -648.000 q^{94} -190.000 q^{95} -96.0000 q^{96} -870.000 q^{97} +98.0000 q^{98} +72.0000 q^{99} +O(q^{100})\)

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
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−10.0000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−10.0000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−20.0000	−0.632456
$11$	8.00000	0.219281	0.109640	−	0.993971i	$-0.465030\pi$
$11$	8.00000	0.219281	0.109640	+	0.993971i	$0.465030\pi$
$12$	−12.0000	−0.288675
$13$	−50.0000	−1.06673	−0.533366	−	0.845885i	$-0.679073\pi$
$13$	−50.0000	−1.06673	−0.533366	+	0.845885i	$0.679073\pi$
$14$	14.0000	0.267261
$15$	30.0000	0.516398
$16$	16.0000	0.250000
$17$	114.000	1.62642	0.813208	−	0.581974i	$-0.197719\pi$
$17$	114.000	1.62642	0.813208	+	0.581974i	$0.197719\pi$
$18$	18.0000	0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−40.0000	−0.447214
$21$	−21.0000	−0.218218
$22$	16.0000	0.155055
$23$	−148.000	−1.34174	−0.670872	−	0.741573i	$-0.734080\pi$
$23$	−148.000	−1.34174	−0.670872	+	0.741573i	$0.734080\pi$
$24$	−24.0000	−0.204124
$25$	−25.0000	−0.200000
$26$	−100.000	−0.754293
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−30.0000	−0.192099	−0.0960493	−	0.995377i	$-0.530621\pi$
$29$	−30.0000	−0.192099	−0.0960493	+	0.995377i	$0.530621\pi$
$30$	60.0000	0.365148
$31$	304.000	1.76129	0.880645	−	0.473776i	$-0.157109\pi$
$31$	304.000	1.76129	0.880645	+	0.473776i	$0.157109\pi$
$32$	32.0000	0.176777
$33$	−24.0000	−0.126602
$34$	228.000	1.15005
$35$	−70.0000	−0.338062
$36$	36.0000	0.166667
$37$	−274.000	−1.21744	−0.608721	−	0.793385i	$-0.708317\pi$
$37$	−274.000	−1.21744	−0.608721	+	0.793385i	$0.708317\pi$
$38$	38.0000	0.162221
$39$	150.000	0.615878
$40$	−80.0000	−0.316228
$41$	−202.000	−0.769441	−0.384721	−	0.923033i	$-0.625702\pi$
$41$	−202.000	−0.769441	−0.384721	+	0.923033i	$0.625702\pi$
$42$	−42.0000	−0.154303
$43$	−116.000	−0.411391	−0.205696	−	0.978616i	$-0.565946\pi$
$43$	−116.000	−0.411391	−0.205696	+	0.978616i	$0.565946\pi$
$44$	32.0000	0.109640
$45$	−90.0000	−0.298142
$46$	−296.000	−0.948757
$47$	−324.000	−1.00554	−0.502769	−	0.864421i	$-0.667685\pi$
$47$	−324.000	−1.00554	−0.502769	+	0.864421i	$0.667685\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	−342.000	−0.939011
$52$	−200.000	−0.533366
$53$	−550.000	−1.42544	−0.712720	−	0.701449i	$-0.752537\pi$
$53$	−550.000	−1.42544	−0.712720	+	0.701449i	$0.752537\pi$
$54$	−54.0000	−0.136083
$55$	−80.0000	−0.196131
$56$	56.0000	0.133631
$57$	−57.0000	−0.132453
$58$	−60.0000	−0.135834
$59$	628.000	1.38574	0.692870	−	0.721063i	$-0.256346\pi$
$59$	628.000	1.38574	0.692870	+	0.721063i	$0.256346\pi$
$60$	120.000	0.258199
$61$	−58.0000	−0.121740	−0.0608700	−	0.998146i	$-0.519388\pi$
$61$	−58.0000	−0.121740	−0.0608700	+	0.998146i	$0.519388\pi$
$62$	608.000	1.24542
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	500.000	0.954113
$66$	−48.0000	−0.0895211
$67$	−756.000	−1.37851	−0.689254	−	0.724519i	$-0.742062\pi$
$67$	−756.000	−1.37851	−0.689254	+	0.724519i	$0.742062\pi$
$68$	456.000	0.813208
$69$	444.000	0.774657
$70$	−140.000	−0.239046
$71$	−216.000	−0.361049	−0.180525	−	0.983570i	$-0.557780\pi$
$71$	−216.000	−0.361049	−0.180525	+	0.983570i	$0.557780\pi$
$72$	72.0000	0.117851
$73$	−278.000	−0.445718	−0.222859	−	0.974851i	$-0.571539\pi$
$73$	−278.000	−0.445718	−0.222859	+	0.974851i	$0.571539\pi$
$74$	−548.000	−0.860861
$75$	75.0000	0.115470
$76$	76.0000	0.114708
$77$	56.0000	0.0828804
$78$	300.000	0.435491
$79$	−952.000	−1.35580	−0.677901	−	0.735153i	$-0.737110\pi$
$79$	−952.000	−1.35580	−0.677901	+	0.735153i	$0.737110\pi$
$80$	−160.000	−0.223607
$81$	81.0000	0.111111
$82$	−404.000	−0.544077
$83$	−1184.00	−1.56579	−0.782897	−	0.622151i	$-0.786259\pi$
$83$	−1184.00	−1.56579	−0.782897	+	0.622151i	$0.786259\pi$
$84$	−84.0000	−0.109109
$85$	−1140.00	−1.45471
$86$	−232.000	−0.290898
$87$	90.0000	0.110908
$88$	64.0000	0.0775275
$89$	1542.00	1.83654	0.918268	−	0.395960i	$-0.129588\pi$
$89$	1542.00	1.83654	0.918268	+	0.395960i	$0.129588\pi$
$90$	−180.000	−0.210819
$91$	−350.000	−0.403186
$92$	−592.000	−0.670872
$93$	−912.000	−1.01688
$94$	−648.000	−0.711022
$95$	−190.000	−0.205196
$96$	−96.0000	−0.102062
$97$	−870.000	−0.910671	−0.455336	−	0.890320i	$-0.650481\pi$
$97$	−870.000	−0.910671	−0.455336	+	0.890320i	$0.650481\pi$
$98$	98.0000	0.101015
$99$	72.0000	0.0730937
$100$	−100.000	−0.100000
$101$	−594.000	−0.585200	−0.292600	−	0.956235i	$-0.594520\pi$
$101$	−594.000	−0.585200	−0.292600	+	0.956235i	$0.594520\pi$
$102$	−684.000	−0.663981
$103$	−288.000	−0.275510	−0.137755	−	0.990466i	$-0.543989\pi$
$103$	−288.000	−0.275510	−0.137755	+	0.990466i	$0.543989\pi$
$104$	−400.000	−0.377146
$105$	210.000	0.195180
$106$	−1100.00	−1.00794
$107$	−276.000	−0.249364	−0.124682	−	0.992197i	$-0.539791\pi$
$107$	−276.000	−0.249364	−0.124682	+	0.992197i	$0.539791\pi$
$108$	−108.000	−0.0962250
$109$	−1714.00	−1.50616	−0.753080	−	0.657929i	$-0.771433\pi$
$109$	−1714.00	−1.50616	−0.753080	+	0.657929i	$0.771433\pi$
$110$	−160.000	−0.138685
$111$	822.000	0.702890
$112$	112.000	0.0944911
$113$	−730.000	−0.607722	−0.303861	−	0.952716i	$-0.598276\pi$
$113$	−730.000	−0.607722	−0.303861	+	0.952716i	$0.598276\pi$
$114$	−114.000	−0.0936586
$115$	1480.00	1.20009
$116$	−120.000	−0.0960493
$117$	−450.000	−0.355577
$118$	1256.00	0.979866
$119$	798.000	0.614727
$120$	240.000	0.182574
$121$	−1267.00	−0.951916
$122$	−116.000	−0.0860832
$123$	606.000	0.444237
$124$	1216.00	0.880645
$125$	1500.00	1.07331
$126$	126.000	0.0890871
$127$	784.000	0.547785	0.273893	−	0.961760i	$-0.411689\pi$
$127$	784.000	0.547785	0.273893	+	0.961760i	$0.411689\pi$
$128$	128.000	0.0883883
$129$	348.000	0.237517
$130$	1000.00	0.674660
$131$	−120.000	−0.0800340	−0.0400170	−	0.999199i	$-0.512741\pi$
$131$	−120.000	−0.0800340	−0.0400170	+	0.999199i	$0.512741\pi$
$132$	−96.0000	−0.0633010
$133$	133.000	0.0867110
$134$	−1512.00	−0.974753
$135$	270.000	0.172133
$136$	912.000	0.575025
$137$	−30.0000	−0.0187086	−0.00935428	−	0.999956i	$-0.502978\pi$
$137$	−30.0000	−0.0187086	−0.00935428	+	0.999956i	$0.502978\pi$
$138$	888.000	0.547765
$139$	1140.00	0.695637	0.347818	−	0.937562i	$-0.386923\pi$
$139$	1140.00	0.695637	0.347818	+	0.937562i	$0.386923\pi$
$140$	−280.000	−0.169031
$141$	972.000	0.580547
$142$	−432.000	−0.255300
$143$	−400.000	−0.233914
$144$	144.000	0.0833333
$145$	300.000	0.171818
$146$	−556.000	−0.315170
$147$	−147.000	−0.0824786
$148$	−1096.00	−0.608721
$149$	406.000	0.223227	0.111613	−	0.993752i	$-0.464398\pi$
$149$	406.000	0.223227	0.111613	+	0.993752i	$0.464398\pi$
$150$	150.000	0.0816497
$151$	2320.00	1.25032	0.625162	−	0.780495i	$-0.285033\pi$
$151$	2320.00	1.25032	0.625162	+	0.780495i	$0.285033\pi$
$152$	152.000	0.0811107
$153$	1026.00	0.542138
$154$	112.000	0.0586053
$155$	−3040.00	−1.57535
$156$	600.000	0.307939
$157$	−3194.00	−1.62362	−0.811812	−	0.583919i	$-0.801519\pi$
$157$	−3194.00	−1.62362	−0.811812	+	0.583919i	$0.801519\pi$
$158$	−1904.00	−0.958697
$159$	1650.00	0.822978
$160$	−320.000	−0.158114
$161$	−1036.00	−0.507132
$162$	162.000	0.0785674
$163$	−4.00000	−0.00192211	−0.000961056	−	1.00000i	$-0.500306\pi$
$163$	−4.00000	−0.00192211	−0.000961056		1.00000i	$0.500306\pi$
$164$	−808.000	−0.384721
$165$	240.000	0.113236
$166$	−2368.00	−1.10718
$167$	−632.000	−0.292848	−0.146424	−	0.989222i	$-0.546776\pi$
$167$	−632.000	−0.292848	−0.146424	+	0.989222i	$0.546776\pi$
$168$	−168.000	−0.0771517
$169$	303.000	0.137915
$170$	−2280.00	−1.02864
$171$	171.000	0.0764719
$172$	−464.000	−0.205696
$173$	3682.00	1.61813	0.809067	−	0.587716i	$-0.199973\pi$
$173$	3682.00	1.61813	0.809067	+	0.587716i	$0.199973\pi$
$174$	180.000	0.0784239
$175$	−175.000	−0.0755929
$176$	128.000	0.0548202
$177$	−1884.00	−0.800057
$178$	3084.00	1.29863
$179$	2196.00	0.916965	0.458483	−	0.888703i	$-0.348393\pi$
$179$	2196.00	0.916965	0.458483	+	0.888703i	$0.348393\pi$
$180$	−360.000	−0.149071
$181$	−3802.00	−1.56133	−0.780664	−	0.624951i	$-0.785119\pi$
$181$	−3802.00	−1.56133	−0.780664	+	0.624951i	$0.785119\pi$
$182$	−700.000	−0.285096
$183$	174.000	0.0702866
$184$	−1184.00	−0.474378
$185$	2740.00	1.08891
$186$	−1824.00	−0.719044
$187$	912.000	0.356642
$188$	−1296.00	−0.502769
$189$	−189.000	−0.0727393
$190$	−380.000	−0.145095
$191$	1852.00	0.701602	0.350801	−	0.936450i	$-0.385909\pi$
$191$	1852.00	0.701602	0.350801	+	0.936450i	$0.385909\pi$
$192$	−192.000	−0.0721688
$193$	4242.00	1.58210	0.791051	−	0.611750i	$-0.209534\pi$
$193$	4242.00	1.58210	0.791051	+	0.611750i	$0.209534\pi$
$194$	−1740.00	−0.643942
$195$	−1500.00	−0.550858
$196$	196.000	0.0714286
$197$	670.000	0.242312	0.121156	−	0.992633i	$-0.461340\pi$
$197$	670.000	0.242312	0.121156	+	0.992633i	$0.461340\pi$
$198$	144.000	0.0516850
$199$	−4672.00	−1.66427	−0.832134	−	0.554575i	$-0.812881\pi$
$199$	−4672.00	−1.66427	−0.832134	+	0.554575i	$0.812881\pi$
$200$	−200.000	−0.0707107
$201$	2268.00	0.795883
$202$	−1188.00	−0.413799
$203$	−210.000	−0.0726065
$204$	−1368.00	−0.469506
$205$	2020.00	0.688209
$206$	−576.000	−0.194815
$207$	−1332.00	−0.447248
$208$	−800.000	−0.266683
$209$	152.000	0.0503065
$210$	420.000	0.138013
$211$	1852.00	0.604251	0.302125	−	0.953268i	$-0.402304\pi$
$211$	1852.00	0.604251	0.302125	+	0.953268i	$0.402304\pi$
$212$	−2200.00	−0.712720
$213$	648.000	0.208452
$214$	−552.000	−0.176327
$215$	1160.00	0.367960
$216$	−216.000	−0.0680414
$217$	2128.00	0.665705
$218$	−3428.00	−1.06502
$219$	834.000	0.257336
$220$	−320.000	−0.0980654
$221$	−5700.00	−1.73495
$222$	1644.00	0.497018
$223$	4312.00	1.29486	0.647428	−	0.762127i	$-0.275845\pi$
$223$	4312.00	1.29486	0.647428	+	0.762127i	$0.275845\pi$
$224$	224.000	0.0668153
$225$	−225.000	−0.0666667
$226$	−1460.00	−0.429725
$227$	1476.00	0.431566	0.215783	−	0.976441i	$-0.430770\pi$
$227$	1476.00	0.431566	0.215783	+	0.976441i	$0.430770\pi$
$228$	−228.000	−0.0662266
$229$	−3042.00	−0.877821	−0.438911	−	0.898531i	$-0.644635\pi$
$229$	−3042.00	−0.877821	−0.438911	+	0.898531i	$0.644635\pi$
$230$	2960.00	0.848594
$231$	−168.000	−0.0478510
$232$	−240.000	−0.0679171
$233$	938.000	0.263736	0.131868	−	0.991267i	$-0.457903\pi$
$233$	938.000	0.263736	0.131868	+	0.991267i	$0.457903\pi$
$234$	−900.000	−0.251431
$235$	3240.00	0.899380
$236$	2512.00	0.692870
$237$	2856.00	0.782773
$238$	1596.00	0.434678
$239$	812.000	0.219765	0.109883	−	0.993945i	$-0.464952\pi$
$239$	812.000	0.219765	0.109883	+	0.993945i	$0.464952\pi$
$240$	480.000	0.129099
$241$	842.000	0.225054	0.112527	−	0.993649i	$-0.464106\pi$
$241$	842.000	0.225054	0.112527	+	0.993649i	$0.464106\pi$
$242$	−2534.00	−0.673106
$243$	−243.000	−0.0641500
$244$	−232.000	−0.0608700
$245$	−490.000	−0.127775
$246$	1212.00	0.314123
$247$	−950.000	−0.244725
$248$	2432.00	0.622710
$249$	3552.00	0.904011
$250$	3000.00	0.758947
$251$	−3288.00	−0.826840	−0.413420	−	0.910541i	$-0.635666\pi$
$251$	−3288.00	−0.826840	−0.413420	+	0.910541i	$0.635666\pi$
$252$	252.000	0.0629941
$253$	−1184.00	−0.294219
$254$	1568.00	0.387343
$255$	3420.00	0.839877
$256$	256.000	0.0625000
$257$	−2522.00	−0.612132	−0.306066	−	0.952010i	$-0.599013\pi$
$257$	−2522.00	−0.612132	−0.306066	+	0.952010i	$0.599013\pi$
$258$	696.000	0.167950
$259$	−1918.00	−0.460150
$260$	2000.00	0.477057
$261$	−270.000	−0.0640329
$262$	−240.000	−0.0565926
$263$	−3228.00	−0.756833	−0.378416	−	0.925635i	$-0.623531\pi$
$263$	−3228.00	−0.756833	−0.378416	+	0.925635i	$0.623531\pi$
$264$	−192.000	−0.0447605
$265$	5500.00	1.27495
$266$	266.000	0.0613139
$267$	−4626.00	−1.06032
$268$	−3024.00	−0.689254
$269$	8434.00	1.91164	0.955818	−	0.293959i	$-0.0949730\pi$
$269$	8434.00	1.91164	0.955818	+	0.293959i	$0.0949730\pi$
$270$	540.000	0.121716
$271$	−7400.00	−1.65874	−0.829369	−	0.558701i	$-0.811300\pi$
$271$	−7400.00	−1.65874	−0.829369	+	0.558701i	$0.811300\pi$
$272$	1824.00	0.406604
$273$	1050.00	0.232780
$274$	−60.0000	−0.0132290
$275$	−200.000	−0.0438562
$276$	1776.00	0.387328
$277$	−1442.00	−0.312785	−0.156392	−	0.987695i	$-0.549986\pi$
$277$	−1442.00	−0.312785	−0.156392	+	0.987695i	$0.549986\pi$
$278$	2280.00	0.491890
$279$	2736.00	0.587097
$280$	−560.000	−0.119523
$281$	6262.00	1.32939	0.664697	−	0.747113i	$-0.268561\pi$
$281$	6262.00	1.32939	0.664697	+	0.747113i	$0.268561\pi$
$282$	1944.00	0.410509
$283$	−3796.00	−0.797346	−0.398673	−	0.917093i	$-0.630529\pi$
$283$	−3796.00	−0.797346	−0.398673	+	0.917093i	$0.630529\pi$
$284$	−864.000	−0.180525
$285$	570.000	0.118470
$286$	−800.000	−0.165402
$287$	−1414.00	−0.290822
$288$	288.000	0.0589256
$289$	8083.00	1.64523
$290$	600.000	0.121494
$291$	2610.00	0.525776
$292$	−1112.00	−0.222859
$293$	−5046.00	−1.00611	−0.503055	−	0.864254i	$-0.667791\pi$
$293$	−5046.00	−1.00611	−0.503055	+	0.864254i	$0.667791\pi$
$294$	−294.000	−0.0583212
$295$	−6280.00	−1.23944
$296$	−2192.00	−0.430430
$297$	−216.000	−0.0422006
$298$	812.000	0.157845
$299$	7400.00	1.43128
$300$	300.000	0.0577350
$301$	−812.000	−0.155491
$302$	4640.00	0.884113
$303$	1782.00	0.337865
$304$	304.000	0.0573539
$305$	580.000	0.108888
$306$	2052.00	0.383350
$307$	244.000	0.0453610	0.0226805	−	0.999743i	$-0.492780\pi$
$307$	244.000	0.0453610	0.0226805	+	0.999743i	$0.492780\pi$
$308$	224.000	0.0414402
$309$	864.000	0.159066
$310$	−6080.00	−1.11394
$311$	−8028.00	−1.46375	−0.731875	−	0.681439i	$-0.761354\pi$
$311$	−8028.00	−1.46375	−0.731875	+	0.681439i	$0.761354\pi$
$312$	1200.00	0.217746
$313$	9178.00	1.65742	0.828708	−	0.559681i	$-0.189076\pi$
$313$	9178.00	1.65742	0.828708	+	0.559681i	$0.189076\pi$
$314$	−6388.00	−1.14808
$315$	−630.000	−0.112687
$316$	−3808.00	−0.677901
$317$	1514.00	0.268248	0.134124	−	0.990965i	$-0.457178\pi$
$317$	1514.00	0.268248	0.134124	+	0.990965i	$0.457178\pi$
$318$	3300.00	0.581933
$319$	−240.000	−0.0421236
$320$	−640.000	−0.111803
$321$	828.000	0.143970
$322$	−2072.00	−0.358596
$323$	2166.00	0.373125
$324$	324.000	0.0555556
$325$	1250.00	0.213346
$326$	−8.00000	−0.00135914
$327$	5142.00	0.869582
$328$	−1616.00	−0.272039
$329$	−2268.00	−0.380057
$330$	480.000	0.0800701
$331$	−2196.00	−0.364662	−0.182331	−	0.983237i	$-0.558364\pi$
$331$	−2196.00	−0.364662	−0.182331	+	0.983237i	$0.558364\pi$
$332$	−4736.00	−0.782897
$333$	−2466.00	−0.405814
$334$	−1264.00	−0.207075
$335$	7560.00	1.23298
$336$	−336.000	−0.0545545
$337$	7594.00	1.22751	0.613756	−	0.789496i	$-0.289658\pi$
$337$	7594.00	1.22751	0.613756	+	0.789496i	$0.289658\pi$
$338$	606.000	0.0975209
$339$	2190.00	0.350869
$340$	−4560.00	−0.727355
$341$	2432.00	0.386218
$342$	342.000	0.0540738
$343$	343.000	0.0539949
$344$	−928.000	−0.145449
$345$	−4440.00	−0.692874
$346$	7364.00	1.14419
$347$	4632.00	0.716596	0.358298	−	0.933607i	$-0.383357\pi$
$347$	4632.00	0.716596	0.358298	+	0.933607i	$0.383357\pi$
$348$	360.000	0.0554541
$349$	1798.00	0.275773	0.137886	−	0.990448i	$-0.455969\pi$
$349$	1798.00	0.275773	0.137886	+	0.990448i	$0.455969\pi$
$350$	−350.000	−0.0534522
$351$	1350.00	0.205293
$352$	256.000	0.0387638
$353$	3666.00	0.552752	0.276376	−	0.961050i	$-0.410866\pi$
$353$	3666.00	0.552752	0.276376	+	0.961050i	$0.410866\pi$
$354$	−3768.00	−0.565726
$355$	2160.00	0.322932
$356$	6168.00	0.918268
$357$	−2394.00	−0.354913
$358$	4392.00	0.648392
$359$	12004.0	1.76475	0.882377	−	0.470543i	$-0.155942\pi$
$359$	12004.0	1.76475	0.882377	+	0.470543i	$0.155942\pi$
$360$	−720.000	−0.105409
$361$	361.000	0.0526316
$362$	−7604.00	−1.10403
$363$	3801.00	0.549589
$364$	−1400.00	−0.201593
$365$	2780.00	0.398663
$366$	348.000	0.0497001
$367$	120.000	0.0170680	0.00853399	−	0.999964i	$-0.497284\pi$
$367$	120.000	0.0170680	0.00853399	+	0.999964i	$0.497284\pi$
$368$	−2368.00	−0.335436
$369$	−1818.00	−0.256480
$370$	5480.00	0.769977
$371$	−3850.00	−0.538766
$372$	−3648.00	−0.508441
$373$	−7954.00	−1.10414	−0.552068	−	0.833799i	$-0.686161\pi$
$373$	−7954.00	−1.10414	−0.552068	+	0.833799i	$0.686161\pi$
$374$	1824.00	0.252184
$375$	−4500.00	−0.619677
$376$	−2592.00	−0.355511
$377$	1500.00	0.204918
$378$	−378.000	−0.0514344
$379$	−11268.0	−1.52717	−0.763586	−	0.645706i	$-0.776563\pi$
$379$	−11268.0	−1.52717	−0.763586	+	0.645706i	$0.776563\pi$
$380$	−760.000	−0.102598
$381$	−2352.00	−0.316264
$382$	3704.00	0.496108
$383$	1224.00	0.163299	0.0816494	−	0.996661i	$-0.473981\pi$
$383$	1224.00	0.163299	0.0816494	+	0.996661i	$0.473981\pi$
$384$	−384.000	−0.0510310
$385$	−560.000	−0.0741305
$386$	8484.00	1.11872
$387$	−1044.00	−0.137130
$388$	−3480.00	−0.455336
$389$	7038.00	0.917328	0.458664	−	0.888610i	$-0.348328\pi$
$389$	7038.00	0.917328	0.458664	+	0.888610i	$0.348328\pi$
$390$	−3000.00	−0.389515
$391$	−16872.0	−2.18223
$392$	392.000	0.0505076
$393$	360.000	0.0462076
$394$	1340.00	0.171341
$395$	9520.00	1.21267
$396$	288.000	0.0365468
$397$	13110.0	1.65736	0.828680	−	0.559722i	$-0.189092\pi$
$397$	13110.0	1.65736	0.828680	+	0.559722i	$0.189092\pi$
$398$	−9344.00	−1.17682
$399$	−399.000	−0.0500626
$400$	−400.000	−0.0500000
$401$	−4346.00	−0.541219	−0.270610	−	0.962689i	$-0.587225\pi$
$401$	−4346.00	−0.541219	−0.270610	+	0.962689i	$0.587225\pi$
$402$	4536.00	0.562774
$403$	−15200.0	−1.87882
$404$	−2376.00	−0.292600
$405$	−810.000	−0.0993808
$406$	−420.000	−0.0513405
$407$	−2192.00	−0.266962
$408$	−2736.00	−0.331991
$409$	−14734.0	−1.78129	−0.890647	−	0.454695i	$-0.849748\pi$
$409$	−14734.0	−1.78129	−0.890647	+	0.454695i	$0.849748\pi$
$410$	4040.00	0.486638
$411$	90.0000	0.0108014
$412$	−1152.00	−0.137755
$413$	4396.00	0.523760
$414$	−2664.00	−0.316252
$415$	11840.0	1.40049
$416$	−1600.00	−0.188573
$417$	−3420.00	−0.401626
$418$	304.000	0.0355721
$419$	7528.00	0.877725	0.438863	−	0.898554i	$-0.355381\pi$
$419$	7528.00	0.877725	0.438863	+	0.898554i	$0.355381\pi$
$420$	840.000	0.0975900
$421$	−11018.0	−1.27550	−0.637749	−	0.770244i	$-0.720134\pi$
$421$	−11018.0	−1.27550	−0.637749	+	0.770244i	$0.720134\pi$
$422$	3704.00	0.427270
$423$	−2916.00	−0.335179
$424$	−4400.00	−0.503969
$425$	−2850.00	−0.325283
$426$	1296.00	0.147398
$427$	−406.000	−0.0460134
$428$	−1104.00	−0.124682
$429$	1200.00	0.135050
$430$	2320.00	0.260187
$431$	−2448.00	−0.273587	−0.136794	−	0.990600i	$-0.543680\pi$
$431$	−2448.00	−0.273587	−0.136794	+	0.990600i	$0.543680\pi$
$432$	−432.000	−0.0481125
$433$	−46.0000	−0.00510536	−0.00255268	−	0.999997i	$-0.500813\pi$
$433$	−46.0000	−0.00510536	−0.00255268	+	0.999997i	$0.500813\pi$
$434$	4256.00	0.470725
$435$	−900.000	−0.0991993
$436$	−6856.00	−0.753080
$437$	−2812.00	−0.307817
$438$	1668.00	0.181964
$439$	16672.0	1.81255	0.906277	−	0.422684i	$-0.138912\pi$
$439$	16672.0	1.81255	0.906277	+	0.422684i	$0.138912\pi$
$440$	−640.000	−0.0693427
$441$	441.000	0.0476190
$442$	−11400.0	−1.22679
$443$	−4232.00	−0.453879	−0.226939	−	0.973909i	$-0.572872\pi$
$443$	−4232.00	−0.453879	−0.226939	+	0.973909i	$0.572872\pi$
$444$	3288.00	0.351445
$445$	−15420.0	−1.64265
$446$	8624.00	0.915601
$447$	−1218.00	−0.128880
$448$	448.000	0.0472456
$449$	11150.0	1.17194	0.585970	−	0.810333i	$-0.300714\pi$
$449$	11150.0	1.17194	0.585970	+	0.810333i	$0.300714\pi$
$450$	−450.000	−0.0471405
$451$	−1616.00	−0.168724
$452$	−2920.00	−0.303861
$453$	−6960.00	−0.721875
$454$	2952.00	0.305163
$455$	3500.00	0.360621
$456$	−456.000	−0.0468293
$457$	2538.00	0.259787	0.129893	−	0.991528i	$-0.458536\pi$
$457$	2538.00	0.259787	0.129893	+	0.991528i	$0.458536\pi$
$458$	−6084.00	−0.620713
$459$	−3078.00	−0.313004
$460$	5920.00	0.600047
$461$	7078.00	0.715087	0.357544	−	0.933896i	$-0.383614\pi$
$461$	7078.00	0.715087	0.357544	+	0.933896i	$0.383614\pi$
$462$	−336.000	−0.0338358
$463$	−11432.0	−1.14749	−0.573747	−	0.819032i	$-0.694511\pi$
$463$	−11432.0	−1.14749	−0.573747	+	0.819032i	$0.694511\pi$
$464$	−480.000	−0.0480247
$465$	9120.00	0.909527
$466$	1876.00	0.186489
$467$	9984.00	0.989303	0.494651	−	0.869091i	$-0.335296\pi$
$467$	9984.00	0.989303	0.494651	+	0.869091i	$0.335296\pi$
$468$	−1800.00	−0.177789
$469$	−5292.00	−0.521027
$470$	6480.00	0.635958
$471$	9582.00	0.937400
$472$	5024.00	0.489933
$473$	−928.000	−0.0902103
$474$	5712.00	0.553504
$475$	−475.000	−0.0458831
$476$	3192.00	0.307364
$477$	−4950.00	−0.475147
$478$	1624.00	0.155398
$479$	−9276.00	−0.884825	−0.442413	−	0.896812i	$-0.645877\pi$
$479$	−9276.00	−0.884825	−0.442413	+	0.896812i	$0.645877\pi$
$480$	960.000	0.0912871
$481$	13700.0	1.29868
$482$	1684.00	0.159137
$483$	3108.00	0.292793
$484$	−5068.00	−0.475958
$485$	8700.00	0.814529
$486$	−486.000	−0.0453609
$487$	−19240.0	−1.79024	−0.895121	−	0.445824i	$-0.852911\pi$
$487$	−19240.0	−1.79024	−0.895121	+	0.445824i	$0.852911\pi$
$488$	−464.000	−0.0430416
$489$	12.0000	0.00110973
$490$	−980.000	−0.0903508
$491$	−11384.0	−1.04634	−0.523170	−	0.852228i	$-0.675251\pi$
$491$	−11384.0	−1.04634	−0.523170	+	0.852228i	$0.675251\pi$
$492$	2424.00	0.222119
$493$	−3420.00	−0.312432
$494$	−1900.00	−0.173047
$495$	−720.000	−0.0653770
$496$	4864.00	0.440323
$497$	−1512.00	−0.136464
$498$	7104.00	0.639233
$499$	6204.00	0.556572	0.278286	−	0.960498i	$-0.410234\pi$
$499$	6204.00	0.556572	0.278286	+	0.960498i	$0.410234\pi$
$500$	6000.00	0.536656
$501$	1896.00	0.169076
$502$	−6576.00	−0.584664
$503$	−17332.0	−1.53637	−0.768187	−	0.640226i	$-0.778841\pi$
$503$	−17332.0	−1.53637	−0.768187	+	0.640226i	$0.778841\pi$
$504$	504.000	0.0445435
$505$	5940.00	0.523419
$506$	−2368.00	−0.208044
$507$	−909.000	−0.0796255
$508$	3136.00	0.273893
$509$	4930.00	0.429309	0.214655	−	0.976690i	$-0.431137\pi$
$509$	4930.00	0.429309	0.214655	+	0.976690i	$0.431137\pi$
$510$	6840.00	0.593883
$511$	−1946.00	−0.168466
$512$	512.000	0.0441942
$513$	−513.000	−0.0441511
$514$	−5044.00	−0.432843
$515$	2880.00	0.246423
$516$	1392.00	0.118758
$517$	−2592.00	−0.220495
$518$	−3836.00	−0.325375
$519$	−11046.0	−0.934230
$520$	4000.00	0.337330
$521$	21014.0	1.76706	0.883532	−	0.468371i	$-0.155159\pi$
$521$	21014.0	1.76706	0.883532	+	0.468371i	$0.155159\pi$
$522$	−540.000	−0.0452781
$523$	−4828.00	−0.403659	−0.201830	−	0.979421i	$-0.564689\pi$
$523$	−4828.00	−0.403659	−0.201830	+	0.979421i	$0.564689\pi$
$524$	−480.000	−0.0400170
$525$	525.000	0.0436436
$526$	−6456.00	−0.535162
$527$	34656.0	2.86459
$528$	−384.000	−0.0316505
$529$	9737.00	0.800279
$530$	11000.0	0.901527
$531$	5652.00	0.461913
$532$	532.000	0.0433555
$533$	10100.0	0.820787
$534$	−9252.00	−0.749763
$535$	2760.00	0.223038
$536$	−6048.00	−0.487377
$537$	−6588.00	−0.529410
$538$	16868.0	1.35173
$539$	392.000	0.0313259
$540$	1080.00	0.0860663
$541$	16038.0	1.27454	0.637271	−	0.770640i	$-0.280063\pi$
$541$	16038.0	1.27454	0.637271	+	0.770640i	$0.280063\pi$
$542$	−14800.0	−1.17290
$543$	11406.0	0.901433
$544$	3648.00	0.287512
$545$	17140.0	1.34715
$546$	2100.00	0.164600
$547$	−14524.0	−1.13529	−0.567643	−	0.823275i	$-0.692145\pi$
$547$	−14524.0	−1.13529	−0.567643	+	0.823275i	$0.692145\pi$
$548$	−120.000	−0.00935428
$549$	−522.000	−0.0405800
$550$	−400.000	−0.0310110
$551$	−570.000	−0.0440704
$552$	3552.00	0.273883
$553$	−6664.00	−0.512445
$554$	−2884.00	−0.221172
$555$	−8220.00	−0.628684
$556$	4560.00	0.347818
$557$	−12322.0	−0.937343	−0.468671	−	0.883373i	$-0.655267\pi$
$557$	−12322.0	−0.937343	−0.468671	+	0.883373i	$0.655267\pi$
$558$	5472.00	0.415140
$559$	5800.00	0.438844
$560$	−1120.00	−0.0845154
$561$	−2736.00	−0.205907
$562$	12524.0	0.940023
$563$	−11100.0	−0.830922	−0.415461	−	0.909611i	$-0.636380\pi$
$563$	−11100.0	−0.830922	−0.415461	+	0.909611i	$0.636380\pi$
$564$	3888.00	0.290274
$565$	7300.00	0.543563
$566$	−7592.00	−0.563808
$567$	567.000	0.0419961
$568$	−1728.00	−0.127650
$569$	−9418.00	−0.693889	−0.346945	−	0.937886i	$-0.612781\pi$
$569$	−9418.00	−0.693889	−0.346945	+	0.937886i	$0.612781\pi$
$570$	1140.00	0.0837708
$571$	−16452.0	−1.20577	−0.602885	−	0.797828i	$-0.705982\pi$
$571$	−16452.0	−1.20577	−0.602885	+	0.797828i	$0.705982\pi$
$572$	−1600.00	−0.116957
$573$	−5556.00	−0.405070
$574$	−2828.00	−0.205642
$575$	3700.00	0.268349
$576$	576.000	0.0416667
$577$	16658.0	1.20187	0.600937	−	0.799296i	$-0.294794\pi$
$577$	16658.0	1.20187	0.600937	+	0.799296i	$0.294794\pi$
$578$	16166.0	1.16335
$579$	−12726.0	−0.913427
$580$	1200.00	0.0859091
$581$	−8288.00	−0.591814
$582$	5220.00	0.371780
$583$	−4400.00	−0.312572
$584$	−2224.00	−0.157585
$585$	4500.00	0.318038
$586$	−10092.0	−0.711428
$587$	−5544.00	−0.389822	−0.194911	−	0.980821i	$-0.562442\pi$
$587$	−5544.00	−0.389822	−0.194911	+	0.980821i	$0.562442\pi$
$588$	−588.000	−0.0412393
$589$	5776.00	0.404068
$590$	−12560.0	−0.876419
$591$	−2010.00	−0.139899
$592$	−4384.00	−0.304360
$593$	14058.0	0.973512	0.486756	−	0.873538i	$-0.338180\pi$
$593$	14058.0	0.973512	0.486756	+	0.873538i	$0.338180\pi$
$594$	−432.000	−0.0298404
$595$	−7980.00	−0.549829
$596$	1624.00	0.111613
$597$	14016.0	0.960865
$598$	14800.0	1.01207
$599$	4720.00	0.321960	0.160980	−	0.986958i	$-0.448535\pi$
$599$	4720.00	0.321960	0.160980	+	0.986958i	$0.448535\pi$
$600$	600.000	0.0408248
$601$	−3558.00	−0.241487	−0.120744	−	0.992684i	$-0.538528\pi$
$601$	−3558.00	−0.241487	−0.120744	+	0.992684i	$0.538528\pi$
$602$	−1624.00	−0.109949
$603$	−6804.00	−0.459503
$604$	9280.00	0.625162
$605$	12670.0	0.851419
$606$	3564.00	0.238907
$607$	−23744.0	−1.58771	−0.793854	−	0.608108i	$-0.791929\pi$
$607$	−23744.0	−1.58771	−0.793854	+	0.608108i	$0.791929\pi$
$608$	608.000	0.0405554
$609$	630.000	0.0419194
$610$	1160.00	0.0769951
$611$	16200.0	1.07264
$612$	4104.00	0.271069
$613$	16062.0	1.05830	0.529150	−	0.848528i	$-0.322511\pi$
$613$	16062.0	1.05830	0.529150	+	0.848528i	$0.322511\pi$
$614$	488.000	0.0320750
$615$	−6060.00	−0.397338
$616$	448.000	0.0293027
$617$	14498.0	0.945977	0.472988	−	0.881069i	$-0.343175\pi$
$617$	14498.0	0.945977	0.472988	+	0.881069i	$0.343175\pi$
$618$	1728.00	0.112476
$619$	−6764.00	−0.439205	−0.219603	−	0.975589i	$-0.570476\pi$
$619$	−6764.00	−0.439205	−0.219603	+	0.975589i	$0.570476\pi$
$620$	−12160.0	−0.787673
$621$	3996.00	0.258219
$622$	−16056.0	−1.03503
$623$	10794.0	0.694145
$624$	2400.00	0.153969
$625$	−11875.0	−0.760000
$626$	18356.0	1.17197
$627$	−456.000	−0.0290445
$628$	−12776.0	−0.811812
$629$	−31236.0	−1.98006
$630$	−1260.00	−0.0796819
$631$	15016.0	0.947349	0.473675	−	0.880700i	$-0.342927\pi$
$631$	15016.0	0.947349	0.473675	+	0.880700i	$0.342927\pi$
$632$	−7616.00	−0.479348
$633$	−5556.00	−0.348864
$634$	3028.00	0.189680
$635$	−7840.00	−0.489954
$636$	6600.00	0.411489
$637$	−2450.00	−0.152390
$638$	−480.000	−0.0297859
$639$	−1944.00	−0.120350
$640$	−1280.00	−0.0790569
$641$	−18906.0	−1.16496	−0.582482	−	0.812844i	$-0.697918\pi$
$641$	−18906.0	−1.16496	−0.582482	+	0.812844i	$0.697918\pi$
$642$	1656.00	0.101802
$643$	−29532.0	−1.81124	−0.905621	−	0.424088i	$-0.860595\pi$
$643$	−29532.0	−1.81124	−0.905621	+	0.424088i	$0.860595\pi$
$644$	−4144.00	−0.253566
$645$	−3480.00	−0.212442
$646$	4332.00	0.263839
$647$	3636.00	0.220936	0.110468	−	0.993880i	$-0.464765\pi$
$647$	3636.00	0.220936	0.110468	+	0.993880i	$0.464765\pi$
$648$	648.000	0.0392837
$649$	5024.00	0.303866
$650$	2500.00	0.150859
$651$	−6384.00	−0.384345
$652$	−16.0000	−0.000961056 0
$653$	12126.0	0.726688	0.363344	−	0.931655i	$-0.381635\pi$
$653$	12126.0	0.726688	0.363344	+	0.931655i	$0.381635\pi$
$654$	10284.0	0.614887
$655$	1200.00	0.0715845
$656$	−3232.00	−0.192360
$657$	−2502.00	−0.148573
$658$	−4536.00	−0.268741
$659$	−4580.00	−0.270731	−0.135365	−	0.990796i	$-0.543221\pi$
$659$	−4580.00	−0.270731	−0.135365	+	0.990796i	$0.543221\pi$
$660$	960.000	0.0566181
$661$	−18178.0	−1.06966	−0.534828	−	0.844961i	$-0.679623\pi$
$661$	−18178.0	−1.06966	−0.534828	+	0.844961i	$0.679623\pi$
$662$	−4392.00	−0.257855
$663$	17100.0	1.00167
$664$	−9472.00	−0.553592
$665$	−1330.00	−0.0775567
$666$	−4932.00	−0.286954
$667$	4440.00	0.257747
$668$	−2528.00	−0.146424
$669$	−12936.0	−0.747585
$670$	15120.0	0.871846
$671$	−464.000	−0.0266953
$672$	−672.000	−0.0385758
$673$	10802.0	0.618702	0.309351	−	0.950948i	$-0.399888\pi$
$673$	10802.0	0.618702	0.309351	+	0.950948i	$0.399888\pi$
$674$	15188.0	0.867982
$675$	675.000	0.0384900
$676$	1212.00	0.0689577
$677$	11186.0	0.635026	0.317513	−	0.948254i	$-0.397152\pi$
$677$	11186.0	0.635026	0.317513	+	0.948254i	$0.397152\pi$
$678$	4380.00	0.248102
$679$	−6090.00	−0.344201
$680$	−9120.00	−0.514318
$681$	−4428.00	−0.249165
$682$	4864.00	0.273097
$683$	−29940.0	−1.67734	−0.838669	−	0.544641i	$-0.816666\pi$
$683$	−29940.0	−1.67734	−0.838669	+	0.544641i	$0.816666\pi$
$684$	684.000	0.0382360
$685$	300.000	0.0167334
$686$	686.000	0.0381802
$687$	9126.00	0.506810
$688$	−1856.00	−0.102848
$689$	27500.0	1.52056
$690$	−8880.00	−0.489936
$691$	−17036.0	−0.937887	−0.468944	−	0.883228i	$-0.655365\pi$
$691$	−17036.0	−0.937887	−0.468944	+	0.883228i	$0.655365\pi$
$692$	14728.0	0.809067
$693$	504.000	0.0276268
$694$	9264.00	0.506710
$695$	−11400.0	−0.622197
$696$	720.000	0.0392120
$697$	−23028.0	−1.25143
$698$	3596.00	0.195001
$699$	−2814.00	−0.152268
$700$	−700.000	−0.0377964
$701$	−15762.0	−0.849248	−0.424624	−	0.905370i	$-0.639594\pi$
$701$	−15762.0	−0.849248	−0.424624	+	0.905370i	$0.639594\pi$
$702$	2700.00	0.145164
$703$	−5206.00	−0.279300
$704$	512.000	0.0274101
$705$	−9720.00	−0.519257
$706$	7332.00	0.390855
$707$	−4158.00	−0.221185
$708$	−7536.00	−0.400029
$709$	−16210.0	−0.858645	−0.429323	−	0.903151i	$-0.641248\pi$
$709$	−16210.0	−0.858645	−0.429323	+	0.903151i	$0.641248\pi$
$710$	4320.00	0.228347
$711$	−8568.00	−0.451934
$712$	12336.0	0.649313
$713$	−44992.0	−2.36320
$714$	−4788.00	−0.250961
$715$	4000.00	0.209219
$716$	8784.00	0.458483
$717$	−2436.00	−0.126882
$718$	24008.0	1.24787
$719$	3916.00	0.203118	0.101559	−	0.994829i	$-0.467617\pi$
$719$	3916.00	0.203118	0.101559	+	0.994829i	$0.467617\pi$
$720$	−1440.00	−0.0745356
$721$	−2016.00	−0.104133
$722$	722.000	0.0372161
$723$	−2526.00	−0.129935
$724$	−15208.0	−0.780664
$725$	750.000	0.0384197
$726$	7602.00	0.388618
$727$	−25520.0	−1.30190	−0.650952	−	0.759119i	$-0.725630\pi$
$727$	−25520.0	−1.30190	−0.650952	+	0.759119i	$0.725630\pi$
$728$	−2800.00	−0.142548
$729$	729.000	0.0370370
$730$	5560.00	0.281897
$731$	−13224.0	−0.669093
$732$	696.000	0.0351433
$733$	16726.0	0.842823	0.421411	−	0.906870i	$-0.361535\pi$
$733$	16726.0	0.842823	0.421411	+	0.906870i	$0.361535\pi$
$734$	240.000	0.0120689
$735$	1470.00	0.0737711
$736$	−4736.00	−0.237189
$737$	−6048.00	−0.302281
$738$	−3636.00	−0.181359
$739$	3436.00	0.171036	0.0855178	−	0.996337i	$-0.472746\pi$
$739$	3436.00	0.171036	0.0855178	+	0.996337i	$0.472746\pi$
$740$	10960.0	0.544456
$741$	2850.00	0.141292
$742$	−7700.00	−0.380965
$743$	24664.0	1.21781	0.608906	−	0.793242i	$-0.291609\pi$
$743$	24664.0	1.21781	0.608906	+	0.793242i	$0.291609\pi$
$744$	−7296.00	−0.359522
$745$	−4060.00	−0.199660
$746$	−15908.0	−0.780742
$747$	−10656.0	−0.521931
$748$	3648.00	0.178321
$749$	−1932.00	−0.0942507
$750$	−9000.00	−0.438178
$751$	−29208.0	−1.41919	−0.709597	−	0.704608i	$-0.751123\pi$
$751$	−29208.0	−1.41919	−0.709597	+	0.704608i	$0.751123\pi$
$752$	−5184.00	−0.251384
$753$	9864.00	0.477376
$754$	3000.00	0.144899
$755$	−23200.0	−1.11832
$756$	−756.000	−0.0363696
$757$	20686.0	0.993191	0.496595	−	0.867982i	$-0.334583\pi$
$757$	20686.0	0.993191	0.496595	+	0.867982i	$0.334583\pi$
$758$	−22536.0	−1.07987
$759$	3552.00	0.169867
$760$	−1520.00	−0.0725476
$761$	−40182.0	−1.91406	−0.957028	−	0.289996i	$-0.906346\pi$
$761$	−40182.0	−1.91406	−0.957028	+	0.289996i	$0.906346\pi$
$762$	−4704.00	−0.223632
$763$	−11998.0	−0.569275
$764$	7408.00	0.350801
$765$	−10260.0	−0.484903
$766$	2448.00	0.115470
$767$	−31400.0	−1.47821
$768$	−768.000	−0.0360844
$769$	−4686.00	−0.219742	−0.109871	−	0.993946i	$-0.535044\pi$
$769$	−4686.00	−0.219742	−0.109871	+	0.993946i	$0.535044\pi$
$770$	−1120.00	−0.0524182
$771$	7566.00	0.353415
$772$	16968.0	0.791051
$773$	31114.0	1.44773	0.723863	−	0.689943i	$-0.242365\pi$
$773$	31114.0	1.44773	0.723863	+	0.689943i	$0.242365\pi$
$774$	−2088.00	−0.0969659
$775$	−7600.00	−0.352258
$776$	−6960.00	−0.321971
$777$	5754.00	0.265667
$778$	14076.0	0.648649
$779$	−3838.00	−0.176522
$780$	−6000.00	−0.275429
$781$	−1728.00	−0.0791712
$782$	−33744.0	−1.54307
$783$	810.000	0.0369694
$784$	784.000	0.0357143
$785$	31940.0	1.45221
$786$	720.000	0.0326737
$787$	25708.0	1.16441	0.582205	−	0.813042i	$-0.302190\pi$
$787$	25708.0	1.16441	0.582205	+	0.813042i	$0.302190\pi$
$788$	2680.00	0.121156
$789$	9684.00	0.436958
$790$	19040.0	0.857485
$791$	−5110.00	−0.229697
$792$	576.000	0.0258425
$793$	2900.00	0.129864
$794$	26220.0	1.17193
$795$	−16500.0	−0.736094
$796$	−18688.0	−0.832134
$797$	−41326.0	−1.83669	−0.918345	−	0.395781i	$-0.870474\pi$
$797$	−41326.0	−1.83669	−0.918345	+	0.395781i	$0.870474\pi$
$798$	−798.000	−0.0353996
$799$	−36936.0	−1.63542
$800$	−800.000	−0.0353553
$801$	13878.0	0.612179
$802$	−8692.00	−0.382700
$803$	−2224.00	−0.0977376
$804$	9072.00	0.397941
$805$	10360.0	0.453593
$806$	−30400.0	−1.32853
$807$	−25302.0	−1.10368
$808$	−4752.00	−0.206899
$809$	−34086.0	−1.48133	−0.740667	−	0.671872i	$-0.765491\pi$
$809$	−34086.0	−1.48133	−0.740667	+	0.671872i	$0.765491\pi$
$810$	−1620.00	−0.0702728
$811$	15564.0	0.673891	0.336946	−	0.941524i	$-0.390606\pi$
$811$	15564.0	0.673891	0.336946	+	0.941524i	$0.390606\pi$
$812$	−840.000	−0.0363032
$813$	22200.0	0.957673
$814$	−4384.00	−0.188770
$815$	40.0000	0.00171919
$816$	−5472.00	−0.234753
$817$	−2204.00	−0.0943797
$818$	−29468.0	−1.25957
$819$	−3150.00	−0.134395
$820$	8080.00	0.344105
$821$	−16074.0	−0.683297	−0.341648	−	0.939828i	$-0.610985\pi$
$821$	−16074.0	−0.683297	−0.341648	+	0.939828i	$0.610985\pi$
$822$	180.000	0.00763774
$823$	−22840.0	−0.967378	−0.483689	−	0.875240i	$-0.660703\pi$
$823$	−22840.0	−0.967378	−0.483689	+	0.875240i	$0.660703\pi$
$824$	−2304.00	−0.0974073
$825$	600.000	0.0253204
$826$	8792.00	0.370354
$827$	−32628.0	−1.37193	−0.685965	−	0.727634i	$-0.740620\pi$
$827$	−32628.0	−1.37193	−0.685965	+	0.727634i	$0.740620\pi$
$828$	−5328.00	−0.223624
$829$	27326.0	1.14484	0.572419	−	0.819961i	$-0.306005\pi$
$829$	27326.0	1.14484	0.572419	+	0.819961i	$0.306005\pi$
$830$	23680.0	0.990295
$831$	4326.00	0.180586
$832$	−3200.00	−0.133341
$833$	5586.00	0.232345
$834$	−6840.00	−0.283993
$835$	6320.00	0.261931
$836$	608.000	0.0251533
$837$	−8208.00	−0.338961
$838$	15056.0	0.620645
$839$	26400.0	1.08633	0.543164	−	0.839627i	$-0.317226\pi$
$839$	26400.0	1.08633	0.543164	+	0.839627i	$0.317226\pi$
$840$	1680.00	0.0690066
$841$	−23489.0	−0.963098
$842$	−22036.0	−0.901913
$843$	−18786.0	−0.767526
$844$	7408.00	0.302125
$845$	−3030.00	−0.123355
$846$	−5832.00	−0.237007
$847$	−8869.00	−0.359790
$848$	−8800.00	−0.356360
$849$	11388.0	0.460348
$850$	−5700.00	−0.230010
$851$	40552.0	1.63350
$852$	2592.00	0.104226
$853$	20078.0	0.805929	0.402965	−	0.915216i	$-0.367980\pi$
$853$	20078.0	0.805929	0.402965	+	0.915216i	$0.367980\pi$
$854$	−812.000	−0.0325364
$855$	−1710.00	−0.0683986
$856$	−2208.00	−0.0881634
$857$	24214.0	0.965151	0.482576	−	0.875854i	$-0.339701\pi$
$857$	24214.0	0.965151	0.482576	+	0.875854i	$0.339701\pi$
$858$	2400.00	0.0954949
$859$	34708.0	1.37860	0.689302	−	0.724474i	$-0.257917\pi$
$859$	34708.0	1.37860	0.689302	+	0.724474i	$0.257917\pi$
$860$	4640.00	0.183980
$861$	4242.00	0.167906
$862$	−4896.00	−0.193455
$863$	11072.0	0.436727	0.218363	−	0.975868i	$-0.429928\pi$
$863$	11072.0	0.436727	0.218363	+	0.975868i	$0.429928\pi$
$864$	−864.000	−0.0340207
$865$	−36820.0	−1.44730
$866$	−92.0000	−0.00361003
$867$	−24249.0	−0.949872
$868$	8512.00	0.332853
$869$	−7616.00	−0.297302
$870$	−1800.00	−0.0701445
$871$	37800.0	1.47050
$872$	−13712.0	−0.532508
$873$	−7830.00	−0.303557
$874$	−5624.00	−0.217660
$875$	10500.0	0.405674
$876$	3336.00	0.128668
$877$	−8314.00	−0.320118	−0.160059	−	0.987107i	$-0.551169\pi$
$877$	−8314.00	−0.320118	−0.160059	+	0.987107i	$0.551169\pi$
$878$	33344.0	1.28167
$879$	15138.0	0.580878
$880$	−1280.00	−0.0490327
$881$	−7710.00	−0.294843	−0.147421	−	0.989074i	$-0.547097\pi$
$881$	−7710.00	−0.294843	−0.147421	+	0.989074i	$0.547097\pi$
$882$	882.000	0.0336718
$883$	−37748.0	−1.43864	−0.719321	−	0.694678i	$-0.755547\pi$
$883$	−37748.0	−1.43864	−0.719321	+	0.694678i	$0.755547\pi$
$884$	−22800.0	−0.867474
$885$	18840.0	0.715593
$886$	−8464.00	−0.320941
$887$	−45624.0	−1.72706	−0.863531	−	0.504296i	$-0.831752\pi$
$887$	−45624.0	−1.72706	−0.863531	+	0.504296i	$0.831752\pi$
$888$	6576.00	0.248509
$889$	5488.00	0.207043
$890$	−30840.0	−1.16153
$891$	648.000	0.0243646
$892$	17248.0	0.647428
$893$	−6156.00	−0.230686
$894$	−2436.00	−0.0911320
$895$	−21960.0	−0.820158
$896$	896.000	0.0334077
$897$	−22200.0	−0.826351
$898$	22300.0	0.828687
$899$	−9120.00	−0.338342
$900$	−900.000	−0.0333333
$901$	−62700.0	−2.31836
$902$	−3232.00	−0.119306
$903$	2436.00	0.0897730
$904$	−5840.00	−0.214862
$905$	38020.0	1.39649
$906$	−13920.0	−0.510443
$907$	11732.0	0.429498	0.214749	−	0.976669i	$-0.431107\pi$
$907$	11732.0	0.429498	0.214749	+	0.976669i	$0.431107\pi$
$908$	5904.00	0.215783
$909$	−5346.00	−0.195067
$910$	7000.00	0.254998
$911$	18696.0	0.679941	0.339970	−	0.940436i	$-0.389583\pi$
$911$	18696.0	0.679941	0.339970	+	0.940436i	$0.389583\pi$
$912$	−912.000	−0.0331133
$913$	−9472.00	−0.343349
$914$	5076.00	0.183697
$915$	−1740.00	−0.0628663
$916$	−12168.0	−0.438911
$917$	−840.000	−0.0302500
$918$	−6156.00	−0.221327
$919$	37512.0	1.34647	0.673235	−	0.739428i	$-0.264904\pi$
$919$	37512.0	1.34647	0.673235	+	0.739428i	$0.264904\pi$
$920$	11840.0	0.424297
$921$	−732.000	−0.0261892
$922$	14156.0	0.505643
$923$	10800.0	0.385142
$924$	−672.000	−0.0239255
$925$	6850.00	0.243488
$926$	−22864.0	−0.811401
$927$	−2592.00	−0.0918365
$928$	−960.000	−0.0339586
$929$	−14838.0	−0.524025	−0.262012	−	0.965065i	$-0.584386\pi$
$929$	−14838.0	−0.524025	−0.262012	+	0.965065i	$0.584386\pi$
$930$	18240.0	0.643132
$931$	931.000	0.0327737
$932$	3752.00	0.131868
$933$	24084.0	0.845096
$934$	19968.0	0.699543
$935$	−9120.00	−0.318990
$936$	−3600.00	−0.125715
$937$	45754.0	1.59522	0.797608	−	0.603176i	$-0.206098\pi$
$937$	45754.0	1.59522	0.797608	+	0.603176i	$0.206098\pi$
$938$	−10584.0	−0.368422
$939$	−27534.0	−0.956910
$940$	12960.0	0.449690
$941$	28018.0	0.970628	0.485314	−	0.874340i	$-0.338705\pi$
$941$	28018.0	0.970628	0.485314	+	0.874340i	$0.338705\pi$
$942$	19164.0	0.662842
$943$	29896.0	1.03239
$944$	10048.0	0.346435
$945$	1890.00	0.0650600
$946$	−1856.00	−0.0637883
$947$	14064.0	0.482596	0.241298	−	0.970451i	$-0.422427\pi$
$947$	14064.0	0.482596	0.241298	+	0.970451i	$0.422427\pi$
$948$	11424.0	0.391386
$949$	13900.0	0.475462
$950$	−950.000	−0.0324443
$951$	−4542.00	−0.154873
$952$	6384.00	0.217339
$953$	−12218.0	−0.415299	−0.207649	−	0.978203i	$-0.566581\pi$
$953$	−12218.0	−0.415299	−0.207649	+	0.978203i	$0.566581\pi$
$954$	−9900.00	−0.335979
$955$	−18520.0	−0.627532
$956$	3248.00	0.109883
$957$	720.000	0.0243201
$958$	−18552.0	−0.625666
$959$	−210.000	−0.00707117
$960$	1920.00	0.0645497
$961$	62625.0	2.10214
$962$	27400.0	0.918307
$963$	−2484.00	−0.0831213
$964$	3368.00	0.112527
$965$	−42420.0	−1.41508
$966$	6216.00	0.207036
$967$	23256.0	0.773384	0.386692	−	0.922209i	$-0.373618\pi$
$967$	23256.0	0.773384	0.386692	+	0.922209i	$0.373618\pi$
$968$	−10136.0	−0.336553
$969$	−6498.00	−0.215424
$970$	17400.0	0.575959
$971$	15836.0	0.523379	0.261690	−	0.965152i	$-0.415720\pi$
$971$	15836.0	0.523379	0.261690	+	0.965152i	$0.415720\pi$
$972$	−972.000	−0.0320750
$973$	7980.00	0.262926
$974$	−38480.0	−1.26589
$975$	−3750.00	−0.123176
$976$	−928.000	−0.0304350
$977$	33718.0	1.10413	0.552065	−	0.833801i	$-0.313840\pi$
$977$	33718.0	1.10413	0.552065	+	0.833801i	$0.313840\pi$
$978$	24.0000	0.000784699 0
$979$	12336.0	0.402717
$980$	−1960.00	−0.0638877
$981$	−15426.0	−0.502053
$982$	−22768.0	−0.739874
$983$	59832.0	1.94135	0.970674	−	0.240401i	$-0.0772789\pi$
$983$	59832.0	1.94135	0.970674	+	0.240401i	$0.0772789\pi$
$984$	4848.00	0.157062
$985$	−6700.00	−0.216731
$986$	−6840.00	−0.220923
$987$	6804.00	0.219426
$988$	−3800.00	−0.122362
$989$	17168.0	0.551982
$990$	−1440.00	−0.0462285
$991$	−6304.00	−0.202072	−0.101036	−	0.994883i	$-0.532216\pi$
$991$	−6304.00	−0.202072	−0.101036	+	0.994883i	$0.532216\pi$
$992$	9728.00	0.311355
$993$	6588.00	0.210538
$994$	−3024.00	−0.0964944
$995$	46720.0	1.48857
$996$	14208.0	0.452006
$997$	−23266.0	−0.739059	−0.369529	−	0.929219i	$-0.620481\pi$
$997$	−23266.0	−0.739059	−0.369529	+	0.929219i	$0.620481\pi$
$998$	12408.0	0.393555
$999$	7398.00	0.234297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.b.1.1	✓	1
3.2	odd	2		2394.4.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.b.1.1	✓	1	1.1	even	1	trivial
2394.4.a.c.1.1		1	3.2	odd	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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