LMFDB - Embedded newform 1110.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,4,Mod(1,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, 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("1110.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1110.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:	$65.4921201064$
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	$\chi$	$=$	1110.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +1.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -5.00000 q^{5} -6.00000 q^{6} +1.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +10.0000 q^{10} -47.0000 q^{11} +12.0000 q^{12} +35.0000 q^{13} -2.00000 q^{14} -15.0000 q^{15} +16.0000 q^{16} +55.0000 q^{17} -18.0000 q^{18} -125.000 q^{19} -20.0000 q^{20} +3.00000 q^{21} +94.0000 q^{22} +213.000 q^{23} -24.0000 q^{24} +25.0000 q^{25} -70.0000 q^{26} +27.0000 q^{27} +4.00000 q^{28} +6.00000 q^{29} +30.0000 q^{30} -98.0000 q^{31} -32.0000 q^{32} -141.000 q^{33} -110.000 q^{34} -5.00000 q^{35} +36.0000 q^{36} -37.0000 q^{37} +250.000 q^{38} +105.000 q^{39} +40.0000 q^{40} -40.0000 q^{41} -6.00000 q^{42} -188.000 q^{43} -188.000 q^{44} -45.0000 q^{45} -426.000 q^{46} +304.000 q^{47} +48.0000 q^{48} -342.000 q^{49} -50.0000 q^{50} +165.000 q^{51} +140.000 q^{52} +341.000 q^{53} -54.0000 q^{54} +235.000 q^{55} -8.00000 q^{56} -375.000 q^{57} -12.0000 q^{58} -518.000 q^{59} -60.0000 q^{60} -382.000 q^{61} +196.000 q^{62} +9.00000 q^{63} +64.0000 q^{64} -175.000 q^{65} +282.000 q^{66} -578.000 q^{67} +220.000 q^{68} +639.000 q^{69} +10.0000 q^{70} +882.000 q^{71} -72.0000 q^{72} -713.000 q^{73} +74.0000 q^{74} +75.0000 q^{75} -500.000 q^{76} -47.0000 q^{77} -210.000 q^{78} +288.000 q^{79} -80.0000 q^{80} +81.0000 q^{81} +80.0000 q^{82} -849.000 q^{83} +12.0000 q^{84} -275.000 q^{85} +376.000 q^{86} +18.0000 q^{87} +376.000 q^{88} -1263.00 q^{89} +90.0000 q^{90} +35.0000 q^{91} +852.000 q^{92} -294.000 q^{93} -608.000 q^{94} +625.000 q^{95} -96.0000 q^{96} -1756.00 q^{97} +684.000 q^{98} -423.000 q^{99} +O(q^{100})\)

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
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−6.00000	−0.408248
$7$	1.00000	0.0539949	0.0269975	−	0.999636i	$-0.491405\pi$
$7$	1.00000	0.0539949	0.0269975	+	0.999636i	$0.491405\pi$
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	10.0000	0.316228
$11$	−47.0000	−1.28828	−0.644138	−	0.764909i	$-0.722784\pi$
$11$	−47.0000	−1.28828	−0.644138	+	0.764909i	$0.722784\pi$
$12$	12.0000	0.288675
$13$	35.0000	0.746712	0.373356	−	0.927688i	$-0.378207\pi$
$13$	35.0000	0.746712	0.373356	+	0.927688i	$0.378207\pi$
$14$	−2.00000	−0.0381802
$15$	−15.0000	−0.258199
$16$	16.0000	0.250000
$17$	55.0000	0.784674	0.392337	−	0.919822i	$-0.371667\pi$
$17$	55.0000	0.784674	0.392337	+	0.919822i	$0.371667\pi$
$18$	−18.0000	−0.235702
$19$	−125.000	−1.50931	−0.754657	−	0.656119i	$-0.772197\pi$
$19$	−125.000	−1.50931	−0.754657	+	0.656119i	$0.772197\pi$
$20$	−20.0000	−0.223607
$21$	3.00000	0.0311740
$22$	94.0000	0.910949
$23$	213.000	1.93102	0.965512	−	0.260357i	$-0.0838403\pi$
$23$	213.000	1.93102	0.965512	+	0.260357i	$0.0838403\pi$
$24$	−24.0000	−0.204124
$25$	25.0000	0.200000
$26$	−70.0000	−0.528005
$27$	27.0000	0.192450
$28$	4.00000	0.0269975
$29$	6.00000	0.0384197	0.0192099	−	0.999815i	$-0.493885\pi$
$29$	6.00000	0.0384197	0.0192099	+	0.999815i	$0.493885\pi$
$30$	30.0000	0.182574
$31$	−98.0000	−0.567785	−0.283892	−	0.958856i	$-0.591626\pi$
$31$	−98.0000	−0.567785	−0.283892	+	0.958856i	$0.591626\pi$
$32$	−32.0000	−0.176777
$33$	−141.000	−0.743786
$34$	−110.000	−0.554848
$35$	−5.00000	−0.0241473
$36$	36.0000	0.166667
$37$	−37.0000	−0.164399
$37$	−37.0000	−0.164399
$38$	250.000	1.06725
$39$	105.000	0.431114
$40$	40.0000	0.158114
$41$	−40.0000	−0.152365	−0.0761823	−	0.997094i	$-0.524273\pi$
$41$	−40.0000	−0.152365	−0.0761823	+	0.997094i	$0.524273\pi$
$42$	−6.00000	−0.0220433
$43$	−188.000	−0.666738	−0.333369	−	0.942796i	$-0.608185\pi$
$43$	−188.000	−0.666738	−0.333369	+	0.942796i	$0.608185\pi$
$44$	−188.000	−0.644138
$45$	−45.0000	−0.149071
$46$	−426.000	−1.36544
$47$	304.000	0.943467	0.471734	−	0.881741i	$-0.343628\pi$
$47$	304.000	0.943467	0.471734	+	0.881741i	$0.343628\pi$
$48$	48.0000	0.144338
$49$	−342.000	−0.997085
$50$	−50.0000	−0.141421
$51$	165.000	0.453032
$52$	140.000	0.373356
$53$	341.000	0.883773	0.441886	−	0.897071i	$-0.354309\pi$
$53$	341.000	0.883773	0.441886	+	0.897071i	$0.354309\pi$
$54$	−54.0000	−0.136083
$55$	235.000	0.576134
$56$	−8.00000	−0.0190901
$57$	−375.000	−0.871403
$58$	−12.0000	−0.0271668
$59$	−518.000	−1.14301	−0.571507	−	0.820597i	$-0.693641\pi$
$59$	−518.000	−1.14301	−0.571507	+	0.820597i	$0.693641\pi$
$60$	−60.0000	−0.129099
$61$	−382.000	−0.801805	−0.400902	−	0.916121i	$-0.631303\pi$
$61$	−382.000	−0.801805	−0.400902	+	0.916121i	$0.631303\pi$
$62$	196.000	0.401484
$63$	9.00000	0.0179983
$64$	64.0000	0.125000
$65$	−175.000	−0.333940
$66$	282.000	0.525936
$67$	−578.000	−1.05394	−0.526970	−	0.849884i	$-0.676672\pi$
$67$	−578.000	−1.05394	−0.526970	+	0.849884i	$0.676672\pi$
$68$	220.000	0.392337
$69$	639.000	1.11488
$70$	10.0000	0.0170747
$71$	882.000	1.47428	0.737142	−	0.675738i	$-0.236175\pi$
$71$	882.000	1.47428	0.737142	+	0.675738i	$0.236175\pi$
$72$	−72.0000	−0.117851
$73$	−713.000	−1.14316	−0.571578	−	0.820548i	$-0.693668\pi$
$73$	−713.000	−1.14316	−0.571578	+	0.820548i	$0.693668\pi$
$74$	74.0000	0.116248
$75$	75.0000	0.115470
$76$	−500.000	−0.754657
$77$	−47.0000	−0.0695604
$78$	−210.000	−0.304844
$79$	288.000	0.410159	0.205079	−	0.978745i	$-0.434255\pi$
$79$	288.000	0.410159	0.205079	+	0.978745i	$0.434255\pi$
$80$	−80.0000	−0.111803
$81$	81.0000	0.111111
$82$	80.0000	0.107738
$83$	−849.000	−1.12277	−0.561385	−	0.827555i	$-0.689731\pi$
$83$	−849.000	−1.12277	−0.561385	+	0.827555i	$0.689731\pi$
$84$	12.0000	0.0155870
$85$	−275.000	−0.350917
$86$	376.000	0.471455
$87$	18.0000	0.0221816
$88$	376.000	0.455474
$89$	−1263.00	−1.50424	−0.752122	−	0.659024i	$-0.770970\pi$
$89$	−1263.00	−1.50424	−0.752122	+	0.659024i	$0.770970\pi$
$90$	90.0000	0.105409
$91$	35.0000	0.0403186
$92$	852.000	0.965512
$93$	−294.000	−0.327811
$94$	−608.000	−0.667132
$95$	625.000	0.674986
$96$	−96.0000	−0.102062
$97$	−1756.00	−1.83809	−0.919045	−	0.394152i	$-0.871038\pi$
$97$	−1756.00	−1.83809	−0.919045	+	0.394152i	$0.871038\pi$
$98$	684.000	0.705045
$99$	−423.000	−0.429425
$100$	100.000	0.100000
$101$	98.0000	0.0965482	0.0482741	−	0.998834i	$-0.484628\pi$
$101$	98.0000	0.0965482	0.0482741	+	0.998834i	$0.484628\pi$
$102$	−330.000	−0.320342
$103$	1464.00	1.40051	0.700253	−	0.713894i	$-0.253070\pi$
$103$	1464.00	1.40051	0.700253	+	0.713894i	$0.253070\pi$
$104$	−280.000	−0.264002
$105$	−15.0000	−0.0139414
$106$	−682.000	−0.624922
$107$	−603.000	−0.544806	−0.272403	−	0.962183i	$-0.587818\pi$
$107$	−603.000	−0.544806	−0.272403	+	0.962183i	$0.587818\pi$
$108$	108.000	0.0962250
$109$	−617.000	−0.542182	−0.271091	−	0.962554i	$-0.587384\pi$
$109$	−617.000	−0.542182	−0.271091	+	0.962554i	$0.587384\pi$
$110$	−470.000	−0.407389
$111$	−111.000	−0.0949158
$112$	16.0000	0.0134987
$113$	70.0000	0.0582747	0.0291374	−	0.999575i	$-0.490724\pi$
$113$	70.0000	0.0582747	0.0291374	+	0.999575i	$0.490724\pi$
$114$	750.000	0.616175
$115$	−1065.00	−0.863581
$116$	24.0000	0.0192099
$117$	315.000	0.248904
$118$	1036.00	0.808233
$119$	55.0000	0.0423684
$120$	120.000	0.0912871
$121$	878.000	0.659654
$122$	764.000	0.566962
$123$	−120.000	−0.0879678
$124$	−392.000	−0.283892
$125$	−125.000	−0.0894427
$126$	−18.0000	−0.0127267
$127$	263.000	0.183760	0.0918798	−	0.995770i	$-0.470712\pi$
$127$	263.000	0.183760	0.0918798	+	0.995770i	$0.470712\pi$
$128$	−128.000	−0.0883883
$129$	−564.000	−0.384941
$130$	350.000	0.236131
$131$	1308.00	0.872370	0.436185	−	0.899857i	$-0.356329\pi$
$131$	1308.00	0.872370	0.436185	+	0.899857i	$0.356329\pi$
$132$	−564.000	−0.371893
$133$	−125.000	−0.0814953
$134$	1156.00	0.745248
$135$	−135.000	−0.0860663
$136$	−440.000	−0.277424
$137$	−522.000	−0.325529	−0.162764	−	0.986665i	$-0.552041\pi$
$137$	−522.000	−0.325529	−0.162764	+	0.986665i	$0.552041\pi$
$138$	−1278.00	−0.788338
$139$	2310.00	1.40958	0.704790	−	0.709416i	$-0.251041\pi$
$139$	2310.00	1.40958	0.704790	+	0.709416i	$0.251041\pi$
$140$	−20.0000	−0.0120736
$141$	912.000	0.544711
$142$	−1764.00	−1.04248
$143$	−1645.00	−0.961971
$144$	144.000	0.0833333
$145$	−30.0000	−0.0171818
$146$	1426.00	0.808333
$147$	−1026.00	−0.575667
$148$	−148.000	−0.0821995
$149$	−1158.00	−0.636692	−0.318346	−	0.947975i	$-0.603127\pi$
$149$	−1158.00	−0.636692	−0.318346	+	0.947975i	$0.603127\pi$
$150$	−150.000	−0.0816497
$151$	3045.00	1.64105	0.820525	−	0.571610i	$-0.193681\pi$
$151$	3045.00	1.64105	0.820525	+	0.571610i	$0.193681\pi$
$152$	1000.00	0.533623
$153$	495.000	0.261558
$154$	94.0000	0.0491866
$155$	490.000	0.253921
$156$	420.000	0.215557
$157$	−1972.00	−1.00244	−0.501219	−	0.865321i	$-0.667115\pi$
$157$	−1972.00	−1.00244	−0.501219	+	0.865321i	$0.667115\pi$
$158$	−576.000	−0.290026
$159$	1023.00	0.510246
$160$	160.000	0.0790569
$161$	213.000	0.104266
$162$	−162.000	−0.0785674
$163$	−1601.00	−0.769325	−0.384663	−	0.923057i	$-0.625682\pi$
$163$	−1601.00	−0.769325	−0.384663	+	0.923057i	$0.625682\pi$
$164$	−160.000	−0.0761823
$165$	705.000	0.332631
$166$	1698.00	0.793918
$167$	−2541.00	−1.17742	−0.588708	−	0.808346i	$-0.700363\pi$
$167$	−2541.00	−1.17742	−0.588708	+	0.808346i	$0.700363\pi$
$168$	−24.0000	−0.0110217
$169$	−972.000	−0.442421
$170$	550.000	0.248136
$171$	−1125.00	−0.503105
$172$	−752.000	−0.333369
$173$	−1629.00	−0.715899	−0.357950	−	0.933741i	$-0.616524\pi$
$173$	−1629.00	−0.715899	−0.357950	+	0.933741i	$0.616524\pi$
$174$	−36.0000	−0.0156848
$175$	25.0000	0.0107990
$176$	−752.000	−0.322069
$177$	−1554.00	−0.659920
$178$	2526.00	1.06366
$179$	−2640.00	−1.10236	−0.551181	−	0.834386i	$-0.685823\pi$
$179$	−2640.00	−1.10236	−0.551181	+	0.834386i	$0.685823\pi$
$180$	−180.000	−0.0745356
$181$	−4202.00	−1.72559	−0.862796	−	0.505552i	$-0.831289\pi$
$181$	−4202.00	−1.72559	−0.862796	+	0.505552i	$0.831289\pi$
$182$	−70.0000	−0.0285096
$183$	−1146.00	−0.462922
$184$	−1704.00	−0.682720
$185$	185.000	0.0735215
$186$	588.000	0.231797
$187$	−2585.00	−1.01088
$188$	1216.00	0.471734
$189$	27.0000	0.0103913
$190$	−1250.00	−0.477287
$191$	−2185.00	−0.827754	−0.413877	−	0.910333i	$-0.635826\pi$
$191$	−2185.00	−0.827754	−0.413877	+	0.910333i	$0.635826\pi$
$192$	192.000	0.0721688
$193$	2654.00	0.989840	0.494920	−	0.868939i	$-0.335197\pi$
$193$	2654.00	0.989840	0.494920	+	0.868939i	$0.335197\pi$
$194$	3512.00	1.29973
$195$	−525.000	−0.192800
$196$	−1368.00	−0.498542
$197$	−1329.00	−0.480646	−0.240323	−	0.970693i	$-0.577253\pi$
$197$	−1329.00	−0.480646	−0.240323	+	0.970693i	$0.577253\pi$
$198$	846.000	0.303650
$199$	−1480.00	−0.527208	−0.263604	−	0.964631i	$-0.584911\pi$
$199$	−1480.00	−0.527208	−0.263604	+	0.964631i	$0.584911\pi$
$200$	−200.000	−0.0707107
$201$	−1734.00	−0.608492
$202$	−196.000	−0.0682699
$203$	6.00000	0.00207447
$204$	660.000	0.226516
$205$	200.000	0.0681395
$206$	−2928.00	−0.990308
$207$	1917.00	0.643675
$208$	560.000	0.186678
$209$	5875.00	1.94441
$210$	30.0000	0.00985808
$211$	−278.000	−0.0907029	−0.0453514	−	0.998971i	$-0.514441\pi$
$211$	−278.000	−0.0907029	−0.0453514	+	0.998971i	$0.514441\pi$
$212$	1364.00	0.441886
$213$	2646.00	0.851178
$214$	1206.00	0.385236
$215$	940.000	0.298174
$216$	−216.000	−0.0680414
$217$	−98.0000	−0.0306575
$218$	1234.00	0.383381
$219$	−2139.00	−0.660001
$220$	940.000	0.288067
$221$	1925.00	0.585925
$222$	222.000	0.0671156
$223$	−4800.00	−1.44140	−0.720699	−	0.693248i	$-0.756179\pi$
$223$	−4800.00	−1.44140	−0.720699	+	0.693248i	$0.756179\pi$
$224$	−32.0000	−0.00954504
$225$	225.000	0.0666667
$226$	−140.000	−0.0412065
$227$	2840.00	0.830385	0.415193	−	0.909734i	$-0.363714\pi$
$227$	2840.00	0.830385	0.415193	+	0.909734i	$0.363714\pi$
$228$	−1500.00	−0.435701
$229$	1070.00	0.308767	0.154383	−	0.988011i	$-0.450661\pi$
$229$	1070.00	0.308767	0.154383	+	0.988011i	$0.450661\pi$
$230$	2130.00	0.610644
$231$	−141.000	−0.0401607
$232$	−48.0000	−0.0135834
$233$	3294.00	0.926168	0.463084	−	0.886314i	$-0.346743\pi$
$233$	3294.00	0.926168	0.463084	+	0.886314i	$0.346743\pi$
$234$	−630.000	−0.176002
$235$	−1520.00	−0.421931
$236$	−2072.00	−0.571507
$237$	864.000	0.236805
$238$	−110.000	−0.0299590
$239$	3492.00	0.945099	0.472550	−	0.881304i	$-0.343334\pi$
$239$	3492.00	0.945099	0.472550	+	0.881304i	$0.343334\pi$
$240$	−240.000	−0.0645497
$241$	−6642.00	−1.77531	−0.887653	−	0.460513i	$-0.847666\pi$
$241$	−6642.00	−1.77531	−0.887653	+	0.460513i	$0.847666\pi$
$242$	−1756.00	−0.466446
$243$	243.000	0.0641500
$244$	−1528.00	−0.400902
$245$	1710.00	0.445910
$246$	240.000	0.0622026
$247$	−4375.00	−1.12702
$248$	784.000	0.200742
$249$	−2547.00	−0.648231
$250$	250.000	0.0632456
$251$	−6518.00	−1.63909	−0.819547	−	0.573012i	$-0.805775\pi$
$251$	−6518.00	−1.63909	−0.819547	+	0.573012i	$0.805775\pi$
$252$	36.0000	0.00899915
$253$	−10011.0	−2.48769
$254$	−526.000	−0.129938
$255$	−825.000	−0.202602
$256$	256.000	0.0625000
$257$	4627.00	1.12305	0.561526	−	0.827459i	$-0.310214\pi$
$257$	4627.00	1.12305	0.561526	+	0.827459i	$0.310214\pi$
$258$	1128.00	0.272195
$259$	−37.0000	−0.00887671
$260$	−700.000	−0.166970
$261$	54.0000	0.0128066
$262$	−2616.00	−0.616859
$263$	−1380.00	−0.323553	−0.161777	−	0.986827i	$-0.551722\pi$
$263$	−1380.00	−0.323553	−0.161777	+	0.986827i	$0.551722\pi$
$264$	1128.00	0.262968
$265$	−1705.00	−0.395235
$266$	250.000	0.0576259
$267$	−3789.00	−0.868476
$268$	−2312.00	−0.526970
$269$	−8631.00	−1.95629	−0.978144	−	0.207930i	$-0.933327\pi$
$269$	−8631.00	−1.95629	−0.978144	+	0.207930i	$0.933327\pi$
$270$	270.000	0.0608581
$271$	−4060.00	−0.910064	−0.455032	−	0.890475i	$-0.650372\pi$
$271$	−4060.00	−0.910064	−0.455032	+	0.890475i	$0.650372\pi$
$272$	880.000	0.196169
$273$	105.000	0.0232780
$274$	1044.00	0.230184
$275$	−1175.00	−0.257655
$276$	2556.00	0.557439
$277$	3437.00	0.745521	0.372760	−	0.927928i	$-0.378411\pi$
$277$	3437.00	0.745521	0.372760	+	0.927928i	$0.378411\pi$
$278$	−4620.00	−0.996724
$279$	−882.000	−0.189262
$280$	40.0000	0.00853735
$281$	1149.00	0.243927	0.121964	−	0.992535i	$-0.461081\pi$
$281$	1149.00	0.243927	0.121964	+	0.992535i	$0.461081\pi$
$282$	−1824.00	−0.385169
$283$	219.000	0.0460007	0.0230004	−	0.999735i	$-0.492678\pi$
$283$	219.000	0.0460007	0.0230004	+	0.999735i	$0.492678\pi$
$284$	3528.00	0.737142
$285$	1875.00	0.389703
$286$	3290.00	0.680216
$287$	−40.0000	−0.00822692
$288$	−288.000	−0.0589256
$289$	−1888.00	−0.384287
$290$	60.0000	0.0121494
$291$	−5268.00	−1.06122
$292$	−2852.00	−0.571578
$293$	−2907.00	−0.579620	−0.289810	−	0.957084i	$-0.593592\pi$
$293$	−2907.00	−0.579620	−0.289810	+	0.957084i	$0.593592\pi$
$294$	2052.00	0.407058
$295$	2590.00	0.511172
$296$	296.000	0.0581238
$297$	−1269.00	−0.247929
$298$	2316.00	0.450209
$299$	7455.00	1.44192
$300$	300.000	0.0577350
$301$	−188.000	−0.0360005
$302$	−6090.00	−1.16040
$303$	294.000	0.0557421
$304$	−2000.00	−0.377329
$305$	1910.00	0.358578
$306$	−990.000	−0.184949
$307$	−7178.00	−1.33443	−0.667215	−	0.744865i	$-0.732514\pi$
$307$	−7178.00	−1.33443	−0.667215	+	0.744865i	$0.732514\pi$
$308$	−188.000	−0.0347802
$309$	4392.00	0.808583
$310$	−980.000	−0.179549
$311$	−1320.00	−0.240676	−0.120338	−	0.992733i	$-0.538398\pi$
$311$	−1320.00	−0.240676	−0.120338	+	0.992733i	$0.538398\pi$
$312$	−840.000	−0.152422
$313$	1152.00	0.208035	0.104017	−	0.994575i	$-0.466830\pi$
$313$	1152.00	0.208035	0.104017	+	0.994575i	$0.466830\pi$
$314$	3944.00	0.708831
$315$	−45.0000	−0.00804909
$316$	1152.00	0.205079
$317$	−1682.00	−0.298014	−0.149007	−	0.988836i	$-0.547608\pi$
$317$	−1682.00	−0.298014	−0.149007	+	0.988836i	$0.547608\pi$
$318$	−2046.00	−0.360799
$319$	−282.000	−0.0494952
$320$	−320.000	−0.0559017
$321$	−1809.00	−0.314544
$322$	−426.000	−0.0737269
$323$	−6875.00	−1.18432
$324$	324.000	0.0555556
$325$	875.000	0.149342
$326$	3202.00	0.543995
$327$	−1851.00	−0.313029
$328$	320.000	0.0538690
$329$	304.000	0.0509424
$330$	−1410.00	−0.235206
$331$	−10076.0	−1.67319	−0.836597	−	0.547819i	$-0.815458\pi$
$331$	−10076.0	−1.67319	−0.836597	+	0.547819i	$0.815458\pi$
$332$	−3396.00	−0.561385
$333$	−333.000	−0.0547997
$334$	5082.00	0.832559
$335$	2890.00	0.471336
$336$	48.0000	0.00779350
$337$	−1721.00	−0.278186	−0.139093	−	0.990279i	$-0.544419\pi$
$337$	−1721.00	−0.278186	−0.139093	+	0.990279i	$0.544419\pi$
$338$	1944.00	0.312839
$339$	210.000	0.0336449
$340$	−1100.00	−0.175458
$341$	4606.00	0.731463
$342$	2250.00	0.355749
$343$	−685.000	−0.107832
$344$	1504.00	0.235727
$345$	−3195.00	−0.498588
$346$	3258.00	0.506217
$347$	−4564.00	−0.706076	−0.353038	−	0.935609i	$-0.614851\pi$
$347$	−4564.00	−0.706076	−0.353038	+	0.935609i	$0.614851\pi$
$348$	72.0000	0.0110908
$349$	−4160.00	−0.638051	−0.319025	−	0.947746i	$-0.603356\pi$
$349$	−4160.00	−0.638051	−0.319025	+	0.947746i	$0.603356\pi$
$350$	−50.0000	−0.00763604
$351$	945.000	0.143705
$352$	1504.00	0.227737
$353$	10438.0	1.57382	0.786910	−	0.617067i	$-0.211679\pi$
$353$	10438.0	1.57382	0.786910	+	0.617067i	$0.211679\pi$
$354$	3108.00	0.466634
$355$	−4410.00	−0.659320
$356$	−5052.00	−0.752122
$357$	165.000	0.0244614
$358$	5280.00	0.779488
$359$	8572.00	1.26020	0.630101	−	0.776513i	$-0.283013\pi$
$359$	8572.00	1.26020	0.630101	+	0.776513i	$0.283013\pi$
$360$	360.000	0.0527046
$361$	8766.00	1.27803
$362$	8404.00	1.22018
$363$	2634.00	0.380852
$364$	140.000	0.0201593
$365$	3565.00	0.511235
$366$	2292.00	0.327335
$367$	−10015.0	−1.42447	−0.712233	−	0.701944i	$-0.752316\pi$
$367$	−10015.0	−1.42447	−0.712233	+	0.701944i	$0.752316\pi$
$368$	3408.00	0.482756
$369$	−360.000	−0.0507882
$370$	−370.000	−0.0519875
$371$	341.000	0.0477192
$372$	−1176.00	−0.163905
$373$	8718.00	1.21019	0.605095	−	0.796153i	$-0.293135\pi$
$373$	8718.00	1.21019	0.605095	+	0.796153i	$0.293135\pi$
$374$	5170.00	0.714798
$375$	−375.000	−0.0516398
$376$	−2432.00	−0.333566
$377$	210.000	0.0286885
$378$	−54.0000	−0.00734778
$379$	12986.0	1.76002	0.880008	−	0.474959i	$-0.157537\pi$
$379$	12986.0	1.76002	0.880008	+	0.474959i	$0.157537\pi$
$380$	2500.00	0.337493
$381$	789.000	0.106094
$382$	4370.00	0.585311
$383$	−1569.00	−0.209327	−0.104663	−	0.994508i	$-0.533377\pi$
$383$	−1569.00	−0.209327	−0.104663	+	0.994508i	$0.533377\pi$
$384$	−384.000	−0.0510310
$385$	235.000	0.0311083
$386$	−5308.00	−0.699923
$387$	−1692.00	−0.222246
$388$	−7024.00	−0.919045
$389$	−2046.00	−0.266674	−0.133337	−	0.991071i	$-0.542569\pi$
$389$	−2046.00	−0.266674	−0.133337	+	0.991071i	$0.542569\pi$
$390$	1050.00	0.136330
$391$	11715.0	1.51523
$392$	2736.00	0.352523
$393$	3924.00	0.503663
$394$	2658.00	0.339868
$395$	−1440.00	−0.183429
$396$	−1692.00	−0.214713
$397$	10228.0	1.29302	0.646510	−	0.762906i	$-0.276228\pi$
$397$	10228.0	1.29302	0.646510	+	0.762906i	$0.276228\pi$
$398$	2960.00	0.372792
$399$	−375.000	−0.0470513
$400$	400.000	0.0500000
$401$	−6927.00	−0.862638	−0.431319	−	0.902199i	$-0.641952\pi$
$401$	−6927.00	−0.862638	−0.431319	+	0.902199i	$0.641952\pi$
$402$	3468.00	0.430269
$403$	−3430.00	−0.423971
$404$	392.000	0.0482741
$405$	−405.000	−0.0496904
$406$	−12.0000	−0.00146687
$407$	1739.00	0.211791
$408$	−1320.00	−0.160171
$409$	4008.00	0.484555	0.242277	−	0.970207i	$-0.422106\pi$
$409$	4008.00	0.484555	0.242277	+	0.970207i	$0.422106\pi$
$410$	−400.000	−0.0481819
$411$	−1566.00	−0.187944
$412$	5856.00	0.700253
$413$	−518.000	−0.0617170
$414$	−3834.00	−0.455147
$415$	4245.00	0.502118
$416$	−1120.00	−0.132001
$417$	6930.00	0.813821
$418$	−11750.0	−1.37491
$419$	−9481.00	−1.10543	−0.552717	−	0.833369i	$-0.686409\pi$
$419$	−9481.00	−1.10543	−0.552717	+	0.833369i	$0.686409\pi$
$420$	−60.0000	−0.00697071
$421$	10930.0	1.26531	0.632655	−	0.774434i	$-0.281965\pi$
$421$	10930.0	1.26531	0.632655	+	0.774434i	$0.281965\pi$
$422$	556.000	0.0641366
$423$	2736.00	0.314489
$424$	−2728.00	−0.312461
$425$	1375.00	0.156935
$426$	−5292.00	−0.601874
$427$	−382.000	−0.0432934
$428$	−2412.00	−0.272403
$429$	−4935.00	−0.555394
$430$	−1880.00	−0.210841
$431$	14185.0	1.58531	0.792654	−	0.609672i	$-0.208699\pi$
$431$	14185.0	1.58531	0.792654	+	0.609672i	$0.208699\pi$
$432$	432.000	0.0481125
$433$	6293.00	0.698435	0.349217	−	0.937042i	$-0.386447\pi$
$433$	6293.00	0.698435	0.349217	+	0.937042i	$0.386447\pi$
$434$	196.000	0.0216781
$435$	−90.0000	−0.00991993
$436$	−2468.00	−0.271091
$437$	−26625.0	−2.91452
$438$	4278.00	0.466691
$439$	10996.0	1.19547	0.597734	−	0.801695i	$-0.296068\pi$
$439$	10996.0	1.19547	0.597734	+	0.801695i	$0.296068\pi$
$440$	−1880.00	−0.203694
$441$	−3078.00	−0.332362
$442$	−3850.00	−0.414312
$443$	11820.0	1.26769	0.633843	−	0.773462i	$-0.281476\pi$
$443$	11820.0	1.26769	0.633843	+	0.773462i	$0.281476\pi$
$444$	−444.000	−0.0474579
$445$	6315.00	0.672718
$446$	9600.00	1.01922
$447$	−3474.00	−0.367594
$448$	64.0000	0.00674937
$449$	9022.00	0.948273	0.474136	−	0.880451i	$-0.342760\pi$
$449$	9022.00	0.948273	0.474136	+	0.880451i	$0.342760\pi$
$450$	−450.000	−0.0471405
$451$	1880.00	0.196288
$452$	280.000	0.0291374
$453$	9135.00	0.947461
$454$	−5680.00	−0.587171
$455$	−175.000	−0.0180310
$456$	3000.00	0.308087
$457$	−16724.0	−1.71185	−0.855925	−	0.517099i	$-0.827012\pi$
$457$	−16724.0	−1.71185	−0.855925	+	0.517099i	$0.827012\pi$
$458$	−2140.00	−0.218331
$459$	1485.00	0.151011
$460$	−4260.00	−0.431790
$461$	−638.000	−0.0644569	−0.0322284	−	0.999481i	$-0.510260\pi$
$461$	−638.000	−0.0644569	−0.0322284	+	0.999481i	$0.510260\pi$
$462$	282.000	0.0283979
$463$	1868.00	0.187502	0.0937509	−	0.995596i	$-0.470114\pi$
$463$	1868.00	0.187502	0.0937509	+	0.995596i	$0.470114\pi$
$464$	96.0000	0.00960493
$465$	1470.00	0.146601
$466$	−6588.00	−0.654900
$467$	−2436.00	−0.241380	−0.120690	−	0.992690i	$-0.538511\pi$
$467$	−2436.00	−0.241380	−0.120690	+	0.992690i	$0.538511\pi$
$468$	1260.00	0.124452
$469$	−578.000	−0.0569074
$470$	3040.00	0.298351
$471$	−5916.00	−0.578758
$472$	4144.00	0.404117
$473$	8836.00	0.858942
$474$	−1728.00	−0.167447
$475$	−3125.00	−0.301863
$476$	220.000	0.0211842
$477$	3069.00	0.294591
$478$	−6984.00	−0.668286
$479$	14589.0	1.39163	0.695813	−	0.718223i	$-0.255044\pi$
$479$	14589.0	1.39163	0.695813	+	0.718223i	$0.255044\pi$
$480$	480.000	0.0456435
$481$	−1295.00	−0.122759
$482$	13284.0	1.25533
$483$	639.000	0.0601977
$484$	3512.00	0.329827
$485$	8780.00	0.822019
$486$	−486.000	−0.0453609
$487$	10206.0	0.949647	0.474823	−	0.880081i	$-0.342512\pi$
$487$	10206.0	0.949647	0.474823	+	0.880081i	$0.342512\pi$
$488$	3056.00	0.283481
$489$	−4803.00	−0.444170
$490$	−3420.00	−0.315306
$491$	19221.0	1.76666	0.883332	−	0.468749i	$-0.155295\pi$
$491$	19221.0	1.76666	0.883332	+	0.468749i	$0.155295\pi$
$492$	−480.000	−0.0439839
$493$	330.000	0.0301470
$494$	8750.00	0.796925
$495$	2115.00	0.192045
$496$	−1568.00	−0.141946
$497$	882.000	0.0796038
$498$	5094.00	0.458369
$499$	10757.0	0.965029	0.482514	−	0.875888i	$-0.339724\pi$
$499$	10757.0	0.965029	0.482514	+	0.875888i	$0.339724\pi$
$500$	−500.000	−0.0447214
$501$	−7623.00	−0.679781
$502$	13036.0	1.15901
$503$	13428.0	1.19031	0.595154	−	0.803612i	$-0.297091\pi$
$503$	13428.0	1.19031	0.595154	+	0.803612i	$0.297091\pi$
$504$	−72.0000	−0.00636336
$505$	−490.000	−0.0431777
$506$	20022.0	1.75906
$507$	−2916.00	−0.255432
$508$	1052.00	0.0918798
$509$	6207.00	0.540512	0.270256	−	0.962789i	$-0.412892\pi$
$509$	6207.00	0.540512	0.270256	+	0.962789i	$0.412892\pi$
$510$	1650.00	0.143261
$511$	−713.000	−0.0617246
$512$	−512.000	−0.0441942
$513$	−3375.00	−0.290468
$514$	−9254.00	−0.794118
$515$	−7320.00	−0.626326
$516$	−2256.00	−0.192471
$517$	−14288.0	−1.21545
$518$	74.0000	0.00627678
$519$	−4887.00	−0.413325
$520$	1400.00	0.118066
$521$	−9660.00	−0.812308	−0.406154	−	0.913805i	$-0.633130\pi$
$521$	−9660.00	−0.812308	−0.406154	+	0.913805i	$0.633130\pi$
$522$	−108.000	−0.00905562
$523$	−3732.00	−0.312025	−0.156012	−	0.987755i	$-0.549864\pi$
$523$	−3732.00	−0.312025	−0.156012	+	0.987755i	$0.549864\pi$
$524$	5232.00	0.436185
$525$	75.0000	0.00623480
$526$	2760.00	0.228787
$527$	−5390.00	−0.445526
$528$	−2256.00	−0.185947
$529$	33202.0	2.72886
$530$	3410.00	0.279473
$531$	−4662.00	−0.381005
$532$	−500.000	−0.0407476
$533$	−1400.00	−0.113772
$534$	7578.00	0.614105
$535$	3015.00	0.243645
$536$	4624.00	0.372624
$537$	−7920.00	−0.636449
$538$	17262.0	1.38330
$539$	16074.0	1.28452
$540$	−540.000	−0.0430331
$541$	−12991.0	−1.03240	−0.516198	−	0.856469i	$-0.672653\pi$
$541$	−12991.0	−1.03240	−0.516198	+	0.856469i	$0.672653\pi$
$542$	8120.00	0.643513
$543$	−12606.0	−0.996271
$544$	−1760.00	−0.138712
$545$	3085.00	0.242471
$546$	−210.000	−0.0164600
$547$	23635.0	1.84746	0.923729	−	0.383046i	$-0.125125\pi$
$547$	23635.0	1.84746	0.923729	+	0.383046i	$0.125125\pi$
$548$	−2088.00	−0.162764
$549$	−3438.00	−0.267268
$550$	2350.00	0.182190
$551$	−750.000	−0.0579874
$552$	−5112.00	−0.394169
$553$	288.000	0.0221465
$554$	−6874.00	−0.527163
$555$	555.000	0.0424476
$556$	9240.00	0.704790
$557$	19024.0	1.44717	0.723584	−	0.690236i	$-0.242493\pi$
$557$	19024.0	1.44717	0.723584	+	0.690236i	$0.242493\pi$
$558$	1764.00	0.133828
$559$	−6580.00	−0.497861
$560$	−80.0000	−0.00603682
$561$	−7755.00	−0.583630
$562$	−2298.00	−0.172483
$563$	6218.00	0.465466	0.232733	−	0.972541i	$-0.425233\pi$
$563$	6218.00	0.465466	0.232733	+	0.972541i	$0.425233\pi$
$564$	3648.00	0.272356
$565$	−350.000	−0.0260613
$566$	−438.000	−0.0325274
$567$	81.0000	0.00599944
$568$	−7056.00	−0.521238
$569$	−19137.0	−1.40996	−0.704978	−	0.709229i	$-0.749043\pi$
$569$	−19137.0	−1.40996	−0.704978	+	0.709229i	$0.749043\pi$
$570$	−3750.00	−0.275562
$571$	−20662.0	−1.51432	−0.757161	−	0.653228i	$-0.773414\pi$
$571$	−20662.0	−1.51432	−0.757161	+	0.653228i	$0.773414\pi$
$572$	−6580.00	−0.480985
$573$	−6555.00	−0.477904
$574$	80.0000	0.00581731
$575$	5325.00	0.386205
$576$	576.000	0.0416667
$577$	−4222.00	−0.304617	−0.152309	−	0.988333i	$-0.548671\pi$
$577$	−4222.00	−0.304617	−0.152309	+	0.988333i	$0.548671\pi$
$578$	3776.00	0.271732
$579$	7962.00	0.571484
$580$	−120.000	−0.00859091
$581$	−849.000	−0.0606238
$582$	10536.0	0.750397
$583$	−16027.0	−1.13854
$584$	5704.00	0.404166
$585$	−1575.00	−0.111313
$586$	5814.00	0.409853
$587$	−19744.0	−1.38828	−0.694141	−	0.719839i	$-0.744216\pi$
$587$	−19744.0	−1.38828	−0.694141	+	0.719839i	$0.744216\pi$
$588$	−4104.00	−0.287834
$589$	12250.0	0.856965
$590$	−5180.00	−0.361453
$591$	−3987.00	−0.277501
$592$	−592.000	−0.0410997
$593$	−4896.00	−0.339047	−0.169523	−	0.985526i	$-0.554223\pi$
$593$	−4896.00	−0.339047	−0.169523	+	0.985526i	$0.554223\pi$
$594$	2538.00	0.175312
$595$	−275.000	−0.0189477
$596$	−4632.00	−0.318346
$597$	−4440.00	−0.304384
$598$	−14910.0	−1.01959
$599$	5228.00	0.356612	0.178306	−	0.983975i	$-0.442938\pi$
$599$	5228.00	0.356612	0.178306	+	0.983975i	$0.442938\pi$
$600$	−600.000	−0.0408248
$601$	−12197.0	−0.827830	−0.413915	−	0.910315i	$-0.635839\pi$
$601$	−12197.0	−0.827830	−0.413915	+	0.910315i	$0.635839\pi$
$602$	376.000	0.0254562
$603$	−5202.00	−0.351313
$604$	12180.0	0.820525
$605$	−4390.00	−0.295006
$606$	−588.000	−0.0394156
$607$	6842.00	0.457509	0.228755	−	0.973484i	$-0.426535\pi$
$607$	6842.00	0.457509	0.228755	+	0.973484i	$0.426535\pi$
$608$	4000.00	0.266812
$609$	18.0000	0.00119770
$610$	−3820.00	−0.253553
$611$	10640.0	0.704498
$612$	1980.00	0.130779
$613$	−13086.0	−0.862216	−0.431108	−	0.902300i	$-0.641877\pi$
$613$	−13086.0	−0.862216	−0.431108	+	0.902300i	$0.641877\pi$
$614$	14356.0	0.943585
$615$	600.000	0.0393404
$616$	376.000	0.0245933
$617$	974.000	0.0635523	0.0317761	−	0.999495i	$-0.489884\pi$
$617$	974.000	0.0635523	0.0317761	+	0.999495i	$0.489884\pi$
$618$	−8784.00	−0.571755
$619$	2600.00	0.168825	0.0844126	−	0.996431i	$-0.473099\pi$
$619$	2600.00	0.168825	0.0844126	+	0.996431i	$0.473099\pi$
$620$	1960.00	0.126960
$621$	5751.00	0.371626
$622$	2640.00	0.170184
$623$	−1263.00	−0.0812216
$624$	1680.00	0.107779
$625$	625.000	0.0400000
$626$	−2304.00	−0.147103
$627$	17625.0	1.12261
$628$	−7888.00	−0.501219
$629$	−2035.00	−0.129000
$630$	90.0000	0.00569156
$631$	−11644.0	−0.734612	−0.367306	−	0.930100i	$-0.619720\pi$
$631$	−11644.0	−0.734612	−0.367306	+	0.930100i	$0.619720\pi$
$632$	−2304.00	−0.145013
$633$	−834.000	−0.0523673
$634$	3364.00	0.210728
$635$	−1315.00	−0.0821798
$636$	4092.00	0.255123
$637$	−11970.0	−0.744535
$638$	564.000	0.0349984
$639$	7938.00	0.491428
$640$	640.000	0.0395285
$641$	6144.00	0.378586	0.189293	−	0.981921i	$-0.439380\pi$
$641$	6144.00	0.378586	0.189293	+	0.981921i	$0.439380\pi$
$642$	3618.00	0.222416
$643$	12161.0	0.745852	0.372926	−	0.927861i	$-0.378354\pi$
$643$	12161.0	0.745852	0.372926	+	0.927861i	$0.378354\pi$
$644$	852.000	0.0521328
$645$	2820.00	0.172151
$646$	13750.0	0.837440
$647$	8989.00	0.546204	0.273102	−	0.961985i	$-0.411950\pi$
$647$	8989.00	0.546204	0.273102	+	0.961985i	$0.411950\pi$
$648$	−648.000	−0.0392837
$649$	24346.0	1.47252
$650$	−1750.00	−0.105601
$651$	−294.000	−0.0177001
$652$	−6404.00	−0.384663
$653$	−16216.0	−0.971793	−0.485897	−	0.874016i	$-0.661507\pi$
$653$	−16216.0	−0.971793	−0.485897	+	0.874016i	$0.661507\pi$
$654$	3702.00	0.221345
$655$	−6540.00	−0.390136
$656$	−640.000	−0.0380912
$657$	−6417.00	−0.381052
$658$	−608.000	−0.0360217
$659$	14484.0	0.856171	0.428085	−	0.903738i	$-0.359188\pi$
$659$	14484.0	0.856171	0.428085	+	0.903738i	$0.359188\pi$
$660$	2820.00	0.166316
$661$	11093.0	0.652750	0.326375	−	0.945240i	$-0.394173\pi$
$661$	11093.0	0.652750	0.326375	+	0.945240i	$0.394173\pi$
$662$	20152.0	1.18313
$663$	5775.00	0.338284
$664$	6792.00	0.396959
$665$	625.000	0.0364458
$666$	666.000	0.0387492
$667$	1278.00	0.0741894
$668$	−10164.0	−0.588708
$669$	−14400.0	−0.832192
$670$	−5780.00	−0.333285
$671$	17954.0	1.03295
$672$	−96.0000	−0.00551083
$673$	−29045.0	−1.66360	−0.831800	−	0.555076i	$-0.812689\pi$
$673$	−29045.0	−1.66360	−0.831800	+	0.555076i	$0.812689\pi$
$674$	3442.00	0.196708
$675$	675.000	0.0384900
$676$	−3888.00	−0.221211
$677$	4839.00	0.274709	0.137354	−	0.990522i	$-0.456140\pi$
$677$	4839.00	0.274709	0.137354	+	0.990522i	$0.456140\pi$
$678$	−420.000	−0.0237906
$679$	−1756.00	−0.0992476
$680$	2200.00	0.124068
$681$	8520.00	0.479423
$682$	−9212.00	−0.517222
$683$	2712.00	0.151935	0.0759676	−	0.997110i	$-0.475795\pi$
$683$	2712.00	0.151935	0.0759676	+	0.997110i	$0.475795\pi$
$684$	−4500.00	−0.251552
$685$	2610.00	0.145581
$686$	1370.00	0.0762490
$687$	3210.00	0.178267
$688$	−3008.00	−0.166684
$689$	11935.0	0.659923
$690$	6390.00	0.352555
$691$	−4818.00	−0.265247	−0.132623	−	0.991167i	$-0.542340\pi$
$691$	−4818.00	−0.265247	−0.132623	+	0.991167i	$0.542340\pi$
$692$	−6516.00	−0.357950
$693$	−423.000	−0.0231868
$694$	9128.00	0.499271
$695$	−11550.0	−0.630383
$696$	−144.000	−0.00784239
$697$	−2200.00	−0.119557
$698$	8320.00	0.451170
$699$	9882.00	0.534723
$700$	100.000	0.00539949
$701$	−2928.00	−0.157759	−0.0788795	−	0.996884i	$-0.525134\pi$
$701$	−2928.00	−0.157759	−0.0788795	+	0.996884i	$0.525134\pi$
$702$	−1890.00	−0.101615
$703$	4625.00	0.248130
$704$	−3008.00	−0.161034
$705$	−4560.00	−0.243602
$706$	−20876.0	−1.11286
$707$	98.0000	0.00521311
$708$	−6216.00	−0.329960
$709$	31433.0	1.66501	0.832504	−	0.554019i	$-0.186906\pi$
$709$	31433.0	1.66501	0.832504	+	0.554019i	$0.186906\pi$
$710$	8820.00	0.466209
$711$	2592.00	0.136720
$712$	10104.0	0.531831
$713$	−20874.0	−1.09641
$714$	−330.000	−0.0172968
$715$	8225.00	0.430206
$716$	−10560.0	−0.551181
$717$	10476.0	0.545653
$718$	−17144.0	−0.891098
$719$	−10958.0	−0.568379	−0.284189	−	0.958768i	$-0.591724\pi$
$719$	−10958.0	−0.568379	−0.284189	+	0.958768i	$0.591724\pi$
$720$	−720.000	−0.0372678
$721$	1464.00	0.0756203
$722$	−17532.0	−0.903703
$723$	−19926.0	−1.02497
$724$	−16808.0	−0.862796
$725$	150.000	0.00768395
$726$	−5268.00	−0.269303
$727$	29582.0	1.50913	0.754564	−	0.656227i	$-0.227849\pi$
$727$	29582.0	1.50913	0.754564	+	0.656227i	$0.227849\pi$
$728$	−280.000	−0.0142548
$729$	729.000	0.0370370
$730$	−7130.00	−0.361497
$731$	−10340.0	−0.523172
$732$	−4584.00	−0.231461
$733$	−17514.0	−0.882530	−0.441265	−	0.897377i	$-0.645470\pi$
$733$	−17514.0	−0.882530	−0.441265	+	0.897377i	$0.645470\pi$
$734$	20030.0	1.00725
$735$	5130.00	0.257446
$736$	−6816.00	−0.341360
$737$	27166.0	1.35776
$738$	720.000	0.0359127
$739$	−12826.0	−0.638447	−0.319223	−	0.947680i	$-0.603422\pi$
$739$	−12826.0	−0.638447	−0.319223	+	0.947680i	$0.603422\pi$
$740$	740.000	0.0367607
$741$	−13125.0	−0.650687
$742$	−682.000	−0.0337426
$743$	−31962.0	−1.57816	−0.789079	−	0.614291i	$-0.789442\pi$
$743$	−31962.0	−1.57816	−0.789079	+	0.614291i	$0.789442\pi$
$744$	2352.00	0.115899
$745$	5790.00	0.284737
$746$	−17436.0	−0.855734
$747$	−7641.00	−0.374256
$748$	−10340.0	−0.505438
$749$	−603.000	−0.0294167
$750$	750.000	0.0365148
$751$	9308.00	0.452269	0.226134	−	0.974096i	$-0.427391\pi$
$751$	9308.00	0.452269	0.226134	+	0.974096i	$0.427391\pi$
$752$	4864.00	0.235867
$753$	−19554.0	−0.946331
$754$	−420.000	−0.0202858
$755$	−15225.0	−0.733900
$756$	108.000	0.00519566
$757$	−33487.0	−1.60780	−0.803901	−	0.594763i	$-0.797246\pi$
$757$	−33487.0	−1.60780	−0.803901	+	0.594763i	$0.797246\pi$
$758$	−25972.0	−1.24452
$759$	−30033.0	−1.43627
$760$	−5000.00	−0.238644
$761$	1246.00	0.0593528	0.0296764	−	0.999560i	$-0.490552\pi$
$761$	1246.00	0.0593528	0.0296764	+	0.999560i	$0.490552\pi$
$762$	−1578.00	−0.0750196
$763$	−617.000	−0.0292751
$764$	−8740.00	−0.413877
$765$	−2475.00	−0.116972
$766$	3138.00	0.148016
$767$	−18130.0	−0.853502
$768$	768.000	0.0360844
$769$	−4670.00	−0.218992	−0.109496	−	0.993987i	$-0.534924\pi$
$769$	−4670.00	−0.218992	−0.109496	+	0.993987i	$0.534924\pi$
$770$	−470.000	−0.0219969
$771$	13881.0	0.648394
$772$	10616.0	0.494920
$773$	16347.0	0.760622	0.380311	−	0.924859i	$-0.375817\pi$
$773$	16347.0	0.760622	0.380311	+	0.924859i	$0.375817\pi$
$774$	3384.00	0.157152
$775$	−2450.00	−0.113557
$776$	14048.0	0.649863
$777$	−111.000	−0.00512497
$778$	4092.00	0.188567
$779$	5000.00	0.229966
$780$	−2100.00	−0.0964001
$781$	−41454.0	−1.89928
$782$	−23430.0	−1.07143
$783$	162.000	0.00739388
$784$	−5472.00	−0.249271
$785$	9860.00	0.448304
$786$	−7848.00	−0.356144
$787$	−16794.0	−0.760663	−0.380331	−	0.924850i	$-0.624190\pi$
$787$	−16794.0	−0.760663	−0.380331	+	0.924850i	$0.624190\pi$
$788$	−5316.00	−0.240323
$789$	−4140.00	−0.186803
$790$	2880.00	0.129704
$791$	70.0000	0.00314654
$792$	3384.00	0.151825
$793$	−13370.0	−0.598717
$794$	−20456.0	−0.914303
$795$	−5115.00	−0.228189
$796$	−5920.00	−0.263604
$797$	354.000	0.0157332	0.00786658	−	0.999969i	$-0.497496\pi$
$797$	354.000	0.0157332	0.00786658	+	0.999969i	$0.497496\pi$
$798$	750.000	0.0332703
$799$	16720.0	0.740314
$800$	−800.000	−0.0353553
$801$	−11367.0	−0.501415
$802$	13854.0	0.609977
$803$	33511.0	1.47270
$804$	−6936.00	−0.304246
$805$	−1065.00	−0.0466290
$806$	6860.00	0.299793
$807$	−25893.0	−1.12946
$808$	−784.000	−0.0341349
$809$	21309.0	0.926062	0.463031	−	0.886342i	$-0.346762\pi$
$809$	21309.0	0.926062	0.463031	+	0.886342i	$0.346762\pi$
$810$	810.000	0.0351364
$811$	38560.0	1.66957	0.834787	−	0.550573i	$-0.185591\pi$
$811$	38560.0	1.66957	0.834787	+	0.550573i	$0.185591\pi$
$812$	24.0000	0.00103724
$813$	−12180.0	−0.525426
$814$	−3478.00	−0.149759
$815$	8005.00	0.344053
$816$	2640.00	0.113258
$817$	23500.0	1.00632
$818$	−8016.00	−0.342632
$819$	315.000	0.0134395
$820$	800.000	0.0340698
$821$	20327.0	0.864089	0.432045	−	0.901852i	$-0.357792\pi$
$821$	20327.0	0.864089	0.432045	+	0.901852i	$0.357792\pi$
$822$	3132.00	0.132897
$823$	−23017.0	−0.974875	−0.487438	−	0.873158i	$-0.662068\pi$
$823$	−23017.0	−0.974875	−0.487438	+	0.873158i	$0.662068\pi$
$824$	−11712.0	−0.495154
$825$	−3525.00	−0.148757
$826$	1036.00	0.0436405
$827$	−34212.0	−1.43853	−0.719267	−	0.694734i	$-0.755522\pi$
$827$	−34212.0	−1.43853	−0.719267	+	0.694734i	$0.755522\pi$
$828$	7668.00	0.321837
$829$	−8357.00	−0.350121	−0.175061	−	0.984558i	$-0.556012\pi$
$829$	−8357.00	−0.350121	−0.175061	+	0.984558i	$0.556012\pi$
$830$	−8490.00	−0.355051
$831$	10311.0	0.430427
$832$	2240.00	0.0933390
$833$	−18810.0	−0.782386
$834$	−13860.0	−0.575459
$835$	12705.0	0.526556
$836$	23500.0	0.972206
$837$	−2646.00	−0.109270
$838$	18962.0	0.781660
$839$	−6526.00	−0.268537	−0.134268	−	0.990945i	$-0.542868\pi$
$839$	−6526.00	−0.268537	−0.134268	+	0.990945i	$0.542868\pi$
$840$	120.000	0.00492904
$841$	−24353.0	−0.998524
$842$	−21860.0	−0.894709
$843$	3447.00	0.140832
$844$	−1112.00	−0.0453514
$845$	4860.00	0.197857
$846$	−5472.00	−0.222377
$847$	878.000	0.0356180
$848$	5456.00	0.220943
$849$	657.000	0.0265585
$850$	−2750.00	−0.110970
$851$	−7881.00	−0.317459
$852$	10584.0	0.425589
$853$	41095.0	1.64955	0.824775	−	0.565461i	$-0.191302\pi$
$853$	41095.0	1.64955	0.824775	+	0.565461i	$0.191302\pi$
$854$	764.000	0.0306130
$855$	5625.00	0.224995
$856$	4824.00	0.192618
$857$	11333.0	0.451725	0.225862	−	0.974159i	$-0.427480\pi$
$857$	11333.0	0.451725	0.225862	+	0.974159i	$0.427480\pi$
$858$	9870.00	0.392723
$859$	39969.0	1.58757	0.793786	−	0.608197i	$-0.208107\pi$
$859$	39969.0	1.58757	0.793786	+	0.608197i	$0.208107\pi$
$860$	3760.00	0.149087
$861$	−120.000	−0.00474981
$862$	−28370.0	−1.12098
$863$	26268.0	1.03612	0.518061	−	0.855344i	$-0.326654\pi$
$863$	26268.0	1.03612	0.518061	+	0.855344i	$0.326654\pi$
$864$	−864.000	−0.0340207
$865$	8145.00	0.320160
$866$	−12586.0	−0.493868
$867$	−5664.00	−0.221868
$868$	−392.000	−0.0153287
$869$	−13536.0	−0.528397
$870$	180.000	0.00701445
$871$	−20230.0	−0.786989
$872$	4936.00	0.191690
$873$	−15804.0	−0.612697
$874$	53250.0	2.06088
$875$	−125.000	−0.00482945
$876$	−8556.00	−0.330001
$877$	−11524.0	−0.443715	−0.221857	−	0.975079i	$-0.571212\pi$
$877$	−11524.0	−0.443715	−0.221857	+	0.975079i	$0.571212\pi$
$878$	−21992.0	−0.845324
$879$	−8721.00	−0.334644
$880$	3760.00	0.144034
$881$	−39144.0	−1.49693	−0.748465	−	0.663175i	$-0.769209\pi$
$881$	−39144.0	−1.49693	−0.748465	+	0.663175i	$0.769209\pi$
$882$	6156.00	0.235015
$883$	25627.0	0.976690	0.488345	−	0.872651i	$-0.337601\pi$
$883$	25627.0	0.976690	0.488345	+	0.872651i	$0.337601\pi$
$884$	7700.00	0.292963
$885$	7770.00	0.295125
$886$	−23640.0	−0.896390
$887$	1358.00	0.0514061	0.0257030	−	0.999670i	$-0.491818\pi$
$887$	1358.00	0.0514061	0.0257030	+	0.999670i	$0.491818\pi$
$888$	888.000	0.0335578
$889$	263.000	0.00992209
$890$	−12630.0	−0.475684
$891$	−3807.00	−0.143142
$892$	−19200.0	−0.720699
$893$	−38000.0	−1.42399
$894$	6948.00	0.259928
$895$	13200.0	0.492991
$896$	−128.000	−0.00477252
$897$	22365.0	0.832492
$898$	−18044.0	−0.670530
$899$	−588.000	−0.0218141
$900$	900.000	0.0333333
$901$	18755.0	0.693474
$902$	−3760.00	−0.138796
$903$	−564.000	−0.0207849
$904$	−560.000	−0.0206032
$905$	21010.0	0.771708
$906$	−18270.0	−0.669956
$907$	25507.0	0.933788	0.466894	−	0.884313i	$-0.345373\pi$
$907$	25507.0	0.933788	0.466894	+	0.884313i	$0.345373\pi$
$908$	11360.0	0.415193
$909$	882.000	0.0321827
$910$	350.000	0.0127499
$911$	17640.0	0.641536	0.320768	−	0.947158i	$-0.396059\pi$
$911$	17640.0	0.641536	0.320768	+	0.947158i	$0.396059\pi$
$912$	−6000.00	−0.217851
$913$	39903.0	1.44644
$914$	33448.0	1.21046
$915$	5730.00	0.207025
$916$	4280.00	0.154383
$917$	1308.00	0.0471036
$918$	−2970.00	−0.106781
$919$	−15656.0	−0.561963	−0.280981	−	0.959713i	$-0.590660\pi$
$919$	−15656.0	−0.561963	−0.280981	+	0.959713i	$0.590660\pi$
$920$	8520.00	0.305322
$921$	−21534.0	−0.770434
$922$	1276.00	0.0455779
$923$	30870.0	1.10087
$924$	−564.000	−0.0200803
$925$	−925.000	−0.0328798
$926$	−3736.00	−0.132584
$927$	13176.0	0.466836
$928$	−192.000	−0.00679171
$929$	30690.0	1.08386	0.541930	−	0.840424i	$-0.317694\pi$
$929$	30690.0	1.08386	0.541930	+	0.840424i	$0.317694\pi$
$930$	−2940.00	−0.103663
$931$	42750.0	1.50491
$932$	13176.0	0.463084
$933$	−3960.00	−0.138955
$934$	4872.00	0.170682
$935$	12925.0	0.452078
$936$	−2520.00	−0.0880008
$937$	−37474.0	−1.30653	−0.653267	−	0.757128i	$-0.726602\pi$
$937$	−37474.0	−1.30653	−0.653267	+	0.757128i	$0.726602\pi$
$938$	1156.00	0.0402396
$939$	3456.00	0.120109
$940$	−6080.00	−0.210966
$941$	−3830.00	−0.132683	−0.0663414	−	0.997797i	$-0.521133\pi$
$941$	−3830.00	−0.132683	−0.0663414	+	0.997797i	$0.521133\pi$
$942$	11832.0	0.409244
$943$	−8520.00	−0.294220
$944$	−8288.00	−0.285754
$945$	−135.000	−0.00464714
$946$	−17672.0	−0.607364
$947$	−18916.0	−0.649089	−0.324545	−	0.945870i	$-0.605211\pi$
$947$	−18916.0	−0.649089	−0.324545	+	0.945870i	$0.605211\pi$
$948$	3456.00	0.118403
$949$	−24955.0	−0.853608
$950$	6250.00	0.213449
$951$	−5046.00	−0.172059
$952$	−440.000	−0.0149795
$953$	−24738.0	−0.840863	−0.420431	−	0.907324i	$-0.638121\pi$
$953$	−24738.0	−0.840863	−0.420431	+	0.907324i	$0.638121\pi$
$954$	−6138.00	−0.208307
$955$	10925.0	0.370183
$956$	13968.0	0.472550
$957$	−846.000	−0.0285761
$958$	−29178.0	−0.984028
$959$	−522.000	−0.0175769
$960$	−960.000	−0.0322749
$961$	−20187.0	−0.677621
$962$	2590.00	0.0868035
$963$	−5427.00	−0.181602
$964$	−26568.0	−0.887653
$965$	−13270.0	−0.442670
$966$	−1278.00	−0.0425662
$967$	−6854.00	−0.227932	−0.113966	−	0.993485i	$-0.536355\pi$
$967$	−6854.00	−0.227932	−0.113966	+	0.993485i	$0.536355\pi$
$968$	−7024.00	−0.233223
$969$	−20625.0	−0.683767
$970$	−17560.0	−0.581255
$971$	−45916.0	−1.51752	−0.758761	−	0.651369i	$-0.774195\pi$
$971$	−45916.0	−1.51752	−0.758761	+	0.651369i	$0.774195\pi$
$972$	972.000	0.0320750
$973$	2310.00	0.0761102
$974$	−20412.0	−0.671502
$975$	2625.00	0.0862229
$976$	−6112.00	−0.200451
$977$	11443.0	0.374712	0.187356	−	0.982292i	$-0.440008\pi$
$977$	11443.0	0.374712	0.187356	+	0.982292i	$0.440008\pi$
$978$	9606.00	0.314076
$979$	59361.0	1.93788
$980$	6840.00	0.222955
$981$	−5553.00	−0.180727
$982$	−38442.0	−1.24922
$983$	30042.0	0.974762	0.487381	−	0.873189i	$-0.337952\pi$
$983$	30042.0	0.974762	0.487381	+	0.873189i	$0.337952\pi$
$984$	960.000	0.0311013
$985$	6645.00	0.214952
$986$	−660.000	−0.0213171
$987$	912.000	0.0294116
$988$	−17500.0	−0.563511
$989$	−40044.0	−1.28749
$990$	−4230.00	−0.135796
$991$	−23648.0	−0.758026	−0.379013	−	0.925391i	$-0.623736\pi$
$991$	−23648.0	−0.758026	−0.379013	+	0.925391i	$0.623736\pi$
$992$	3136.00	0.100371
$993$	−30228.0	−0.966019
$994$	−1764.00	−0.0562884
$995$	7400.00	0.235775
$996$	−10188.0	−0.324116
$997$	34605.0	1.09925	0.549625	−	0.835412i	$-0.314771\pi$
$997$	34605.0	1.09925	0.549625	+	0.835412i	$0.314771\pi$
$998$	−21514.0	−0.682379
$999$	−999.000	−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.4.a.a.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1110.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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