LMFDB - Embedded newform 570.6.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,6,Mod(1,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("570.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	570.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:	$91.4187772934$
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	$\chi$	$=$	570.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -82.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$

\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} -36.0000 q^{6} -82.0000 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +228.000 q^{11} +144.000 q^{12} -232.000 q^{13} +328.000 q^{14} -225.000 q^{15} +256.000 q^{16} -546.000 q^{17} -324.000 q^{18} +361.000 q^{19} -400.000 q^{20} -738.000 q^{21} -912.000 q^{22} +2622.00 q^{23} -576.000 q^{24} +625.000 q^{25} +928.000 q^{26} +729.000 q^{27} -1312.00 q^{28} -3222.00 q^{29} +900.000 q^{30} +5408.00 q^{31} -1024.00 q^{32} +2052.00 q^{33} +2184.00 q^{34} +2050.00 q^{35} +1296.00 q^{36} -112.000 q^{37} -1444.00 q^{38} -2088.00 q^{39} +1600.00 q^{40} -8946.00 q^{41} +2952.00 q^{42} +10730.0 q^{43} +3648.00 q^{44} -2025.00 q^{45} -10488.0 q^{46} +14478.0 q^{47} +2304.00 q^{48} -10083.0 q^{49} -2500.00 q^{50} -4914.00 q^{51} -3712.00 q^{52} +1044.00 q^{53} -2916.00 q^{54} -5700.00 q^{55} +5248.00 q^{56} +3249.00 q^{57} +12888.0 q^{58} -46284.0 q^{59} -3600.00 q^{60} -44506.0 q^{61} -21632.0 q^{62} -6642.00 q^{63} +4096.00 q^{64} +5800.00 q^{65} -8208.00 q^{66} +21260.0 q^{67} -8736.00 q^{68} +23598.0 q^{69} -8200.00 q^{70} +61560.0 q^{71} -5184.00 q^{72} -87154.0 q^{73} +448.000 q^{74} +5625.00 q^{75} +5776.00 q^{76} -18696.0 q^{77} +8352.00 q^{78} -57688.0 q^{79} -6400.00 q^{80} +6561.00 q^{81} +35784.0 q^{82} -36690.0 q^{83} -11808.0 q^{84} +13650.0 q^{85} -42920.0 q^{86} -28998.0 q^{87} -14592.0 q^{88} +92190.0 q^{89} +8100.00 q^{90} +19024.0 q^{91} +41952.0 q^{92} +48672.0 q^{93} -57912.0 q^{94} -9025.00 q^{95} -9216.00 q^{96} +114692. q^{97} +40332.0 q^{98} +18468.0 q^{99} +O(q^{100})\)

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−36.0000	−0.408248
$7$	−82.0000	−0.632512	−0.316256	−	0.948674i	$-0.602426\pi$
$7$	−82.0000	−0.632512	−0.316256	+	0.948674i	$0.602426\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	100.000	0.316228
$11$	228.000	0.568137	0.284069	−	0.958804i	$-0.408316\pi$
$11$	228.000	0.568137	0.284069	+	0.958804i	$0.408316\pi$
$12$	144.000	0.288675
$13$	−232.000	−0.380741	−0.190370	−	0.981712i	$-0.560969\pi$
$13$	−232.000	−0.380741	−0.190370	+	0.981712i	$0.560969\pi$
$14$	328.000	0.447254
$15$	−225.000	−0.258199
$16$	256.000	0.250000
$17$	−546.000	−0.458216	−0.229108	−	0.973401i	$-0.573581\pi$
$17$	−546.000	−0.458216	−0.229108	+	0.973401i	$0.573581\pi$
$18$	−324.000	−0.235702
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−400.000	−0.223607
$21$	−738.000	−0.365181
$22$	−912.000	−0.401734
$23$	2622.00	1.03351	0.516753	−	0.856134i	$-0.327141\pi$
$23$	2622.00	1.03351	0.516753	+	0.856134i	$0.327141\pi$
$24$	−576.000	−0.204124
$25$	625.000	0.200000
$26$	928.000	0.269225
$27$	729.000	0.192450
$28$	−1312.00	−0.316256
$29$	−3222.00	−0.711427	−0.355714	−	0.934595i	$-0.615762\pi$
$29$	−3222.00	−0.711427	−0.355714	+	0.934595i	$0.615762\pi$
$30$	900.000	0.182574
$31$	5408.00	1.01072	0.505362	−	0.862908i	$-0.331359\pi$
$31$	5408.00	1.01072	0.505362	+	0.862908i	$0.331359\pi$
$32$	−1024.00	−0.176777
$33$	2052.00	0.328014
$34$	2184.00	0.324008
$35$	2050.00	0.282868
$36$	1296.00	0.166667
$37$	−112.000	−0.0134497	−0.00672487	−	0.999977i	$-0.502141\pi$
$37$	−112.000	−0.0134497	−0.00672487	+	0.999977i	$0.502141\pi$
$38$	−1444.00	−0.162221
$39$	−2088.00	−0.219821
$40$	1600.00	0.158114
$41$	−8946.00	−0.831131	−0.415565	−	0.909563i	$-0.636416\pi$
$41$	−8946.00	−0.831131	−0.415565	+	0.909563i	$0.636416\pi$
$42$	2952.00	0.258222
$43$	10730.0	0.884970	0.442485	−	0.896776i	$-0.354097\pi$
$43$	10730.0	0.884970	0.442485	+	0.896776i	$0.354097\pi$
$44$	3648.00	0.284069
$45$	−2025.00	−0.149071
$46$	−10488.0	−0.730799
$47$	14478.0	0.956013	0.478007	−	0.878356i	$-0.341359\pi$
$47$	14478.0	0.956013	0.478007	+	0.878356i	$0.341359\pi$
$48$	2304.00	0.144338
$49$	−10083.0	−0.599929
$50$	−2500.00	−0.141421
$51$	−4914.00	−0.264551
$52$	−3712.00	−0.190370
$53$	1044.00	0.0510518	0.0255259	−	0.999674i	$-0.491874\pi$
$53$	1044.00	0.0510518	0.0255259	+	0.999674i	$0.491874\pi$
$54$	−2916.00	−0.136083
$55$	−5700.00	−0.254079
$56$	5248.00	0.223627
$57$	3249.00	0.132453
$58$	12888.0	0.503055
$59$	−46284.0	−1.73102	−0.865508	−	0.500896i	$-0.833004\pi$
$59$	−46284.0	−1.73102	−0.865508	+	0.500896i	$0.833004\pi$
$60$	−3600.00	−0.129099
$61$	−44506.0	−1.53142	−0.765709	−	0.643187i	$-0.777612\pi$
$61$	−44506.0	−1.53142	−0.765709	+	0.643187i	$0.777612\pi$
$62$	−21632.0	−0.714690
$63$	−6642.00	−0.210837
$64$	4096.00	0.125000
$65$	5800.00	0.170273
$66$	−8208.00	−0.231941
$67$	21260.0	0.578597	0.289299	−	0.957239i	$-0.406578\pi$
$67$	21260.0	0.578597	0.289299	+	0.957239i	$0.406578\pi$
$68$	−8736.00	−0.229108
$69$	23598.0	0.596695
$70$	−8200.00	−0.200018
$71$	61560.0	1.44928	0.724641	−	0.689127i	$-0.242006\pi$
$71$	61560.0	1.44928	0.724641	+	0.689127i	$0.242006\pi$
$72$	−5184.00	−0.117851
$73$	−87154.0	−1.91417	−0.957084	−	0.289810i	$-0.906408\pi$
$73$	−87154.0	−1.91417	−0.957084	+	0.289810i	$0.906408\pi$
$74$	448.000	0.00951040
$75$	5625.00	0.115470
$76$	5776.00	0.114708
$77$	−18696.0	−0.359354
$78$	8352.00	0.155437
$79$	−57688.0	−1.03996	−0.519981	−	0.854178i	$-0.674061\pi$
$79$	−57688.0	−1.03996	−0.519981	+	0.854178i	$0.674061\pi$
$80$	−6400.00	−0.111803
$81$	6561.00	0.111111
$82$	35784.0	0.587698
$83$	−36690.0	−0.584591	−0.292296	−	0.956328i	$-0.594419\pi$
$83$	−36690.0	−0.584591	−0.292296	+	0.956328i	$0.594419\pi$
$84$	−11808.0	−0.182590
$85$	13650.0	0.204920
$86$	−42920.0	−0.625768
$87$	−28998.0	−0.410743
$88$	−14592.0	−0.200867
$89$	92190.0	1.23370	0.616849	−	0.787082i	$-0.288409\pi$
$89$	92190.0	1.23370	0.616849	+	0.787082i	$0.288409\pi$
$90$	8100.00	0.105409
$91$	19024.0	0.240823
$92$	41952.0	0.516753
$93$	48672.0	0.583542
$94$	−57912.0	−0.676003
$95$	−9025.00	−0.102598
$96$	−9216.00	−0.102062
$97$	114692.	1.23767	0.618833	−	0.785522i	$-0.287606\pi$
$97$	114692.	1.23767	0.618833	+	0.785522i	$0.287606\pi$
$98$	40332.0	0.424214
$99$	18468.0	0.189379
$100$	10000.0	0.100000
$101$	−90894.0	−0.886608	−0.443304	−	0.896371i	$-0.646194\pi$
$101$	−90894.0	−0.886608	−0.443304	+	0.896371i	$0.646194\pi$
$102$	19656.0	0.187066
$103$	119672.	1.11147	0.555737	−	0.831358i	$-0.312436\pi$
$103$	119672.	1.11147	0.555737	+	0.831358i	$0.312436\pi$
$104$	14848.0	0.134612
$105$	18450.0	0.163314
$106$	−4176.00	−0.0360991
$107$	79440.0	0.670780	0.335390	−	0.942079i	$-0.391132\pi$
$107$	79440.0	0.670780	0.335390	+	0.942079i	$0.391132\pi$
$108$	11664.0	0.0962250
$109$	−145258.	−1.17105	−0.585523	−	0.810656i	$-0.699111\pi$
$109$	−145258.	−1.17105	−0.585523	+	0.810656i	$0.699111\pi$
$110$	22800.0	0.179661
$111$	−1008.00	−0.00776521
$112$	−20992.0	−0.158128
$113$	−14724.0	−0.108475	−0.0542375	−	0.998528i	$-0.517273\pi$
$113$	−14724.0	−0.108475	−0.0542375	+	0.998528i	$0.517273\pi$
$114$	−12996.0	−0.0936586
$115$	−65550.0	−0.462198
$116$	−51552.0	−0.355714
$117$	−18792.0	−0.126914
$118$	185136.	1.22401
$119$	44772.0	0.289827
$120$	14400.0	0.0912871
$121$	−109067.	−0.677220
$122$	178024.	1.08288
$123$	−80514.0	−0.479853
$124$	86528.0	0.505362
$125$	−15625.0	−0.0894427
$126$	26568.0	0.149085
$127$	−333376.	−1.83411	−0.917054	−	0.398762i	$-0.869440\pi$
$127$	−333376.	−1.83411	−0.917054	+	0.398762i	$0.869440\pi$
$128$	−16384.0	−0.0883883
$129$	96570.0	0.510938
$130$	−23200.0	−0.120401
$131$	310080.	1.57869	0.789343	−	0.613953i	$-0.210422\pi$
$131$	310080.	1.57869	0.789343	+	0.613953i	$0.210422\pi$
$132$	32832.0	0.164007
$133$	−29602.0	−0.145108
$134$	−85040.0	−0.409130
$135$	−18225.0	−0.0860663
$136$	34944.0	0.162004
$137$	43758.0	0.199185	0.0995924	−	0.995028i	$-0.468246\pi$
$137$	43758.0	0.199185	0.0995924	+	0.995028i	$0.468246\pi$
$138$	−94392.0	−0.421927
$139$	−233464.	−1.02490	−0.512452	−	0.858716i	$-0.671263\pi$
$139$	−233464.	−1.02490	−0.512452	+	0.858716i	$0.671263\pi$
$140$	32800.0	0.141434
$141$	130302.	0.551955
$142$	−246240.	−1.02480
$143$	−52896.0	−0.216313
$144$	20736.0	0.0833333
$145$	80550.0	0.318160
$146$	348616.	1.35352
$147$	−90747.0	−0.346369
$148$	−1792.00	−0.00672487
$149$	−208218.	−0.768339	−0.384169	−	0.923263i	$-0.625512\pi$
$149$	−208218.	−0.768339	−0.384169	+	0.923263i	$0.625512\pi$
$150$	−22500.0	−0.0816497
$151$	−373000.	−1.33127	−0.665635	−	0.746277i	$-0.731839\pi$
$151$	−373000.	−1.33127	−0.665635	+	0.746277i	$0.731839\pi$
$152$	−23104.0	−0.0811107
$153$	−44226.0	−0.152739
$154$	74784.0	0.254101
$155$	−135200.	−0.452009
$156$	−33408.0	−0.109910
$157$	−14314.0	−0.0463460	−0.0231730	−	0.999731i	$-0.507377\pi$
$157$	−14314.0	−0.0463460	−0.0231730	+	0.999731i	$0.507377\pi$
$158$	230752.	0.735365
$159$	9396.00	0.0294748
$160$	25600.0	0.0790569
$161$	−215004.	−0.653705
$162$	−26244.0	−0.0785674
$163$	−153358.	−0.452103	−0.226052	−	0.974115i	$-0.572582\pi$
$163$	−153358.	−0.452103	−0.226052	+	0.974115i	$0.572582\pi$
$164$	−143136.	−0.415565
$165$	−51300.0	−0.146692
$166$	146760.	0.413369
$167$	−15732.0	−0.0436509	−0.0218254	−	0.999762i	$-0.506948\pi$
$167$	−15732.0	−0.0436509	−0.0218254	+	0.999762i	$0.506948\pi$
$168$	47232.0	0.129111
$169$	−317469.	−0.855036
$170$	−54600.0	−0.144901
$171$	29241.0	0.0764719
$172$	171680.	0.442485
$173$	−518172.	−1.31631	−0.658156	−	0.752882i	$-0.728663\pi$
$173$	−518172.	−1.31631	−0.658156	+	0.752882i	$0.728663\pi$
$174$	115992.	0.290439
$175$	−51250.0	−0.126502
$176$	58368.0	0.142034
$177$	−416556.	−0.999402
$178$	−368760.	−0.872356
$179$	−779820.	−1.81912	−0.909561	−	0.415571i	$-0.863582\pi$
$179$	−779820.	−1.81912	−0.909561	+	0.415571i	$0.863582\pi$
$180$	−32400.0	−0.0745356
$181$	35030.0	0.0794774	0.0397387	−	0.999210i	$-0.487347\pi$
$181$	35030.0	0.0794774	0.0397387	+	0.999210i	$0.487347\pi$
$182$	−76096.0	−0.170288
$183$	−400554.	−0.884165
$184$	−167808.	−0.365400
$185$	2800.00	0.00601490
$186$	−194688.	−0.412626
$187$	−124488.	−0.260330
$188$	231648.	0.478007
$189$	−59778.0	−0.121727
$190$	36100.0	0.0725476
$191$	898068.	1.78125	0.890627	−	0.454735i	$-0.150266\pi$
$191$	898068.	1.78125	0.890627	+	0.454735i	$0.150266\pi$
$192$	36864.0	0.0721688
$193$	−651100.	−1.25821	−0.629107	−	0.777319i	$-0.716579\pi$
$193$	−651100.	−1.25821	−0.629107	+	0.777319i	$0.716579\pi$
$194$	−458768.	−0.875163
$195$	52200.0	0.0983069
$196$	−161328.	−0.299964
$197$	−51366.0	−0.0942997	−0.0471498	−	0.998888i	$-0.515014\pi$
$197$	−51366.0	−0.0942997	−0.0471498	+	0.998888i	$0.515014\pi$
$198$	−73872.0	−0.133911
$199$	231992.	0.415279	0.207640	−	0.978205i	$-0.433422\pi$
$199$	231992.	0.415279	0.207640	+	0.978205i	$0.433422\pi$
$200$	−40000.0	−0.0707107
$201$	191340.	0.334053
$202$	363576.	0.626927
$203$	264204.	0.449986
$204$	−78624.0	−0.132276
$205$	223650.	0.371693
$206$	−478688.	−0.785931
$207$	212382.	0.344502
$208$	−59392.0	−0.0951852
$209$	82308.0	0.130340
$210$	−73800.0	−0.115480
$211$	−301108.	−0.465603	−0.232802	−	0.972524i	$-0.574789\pi$
$211$	−301108.	−0.465603	−0.232802	+	0.972524i	$0.574789\pi$
$212$	16704.0	0.0255259
$213$	554040.	0.836743
$214$	−317760.	−0.474313
$215$	−268250.	−0.395771
$216$	−46656.0	−0.0680414
$217$	−443456.	−0.639295
$218$	581032.	0.828054
$219$	−784386.	−1.10515
$220$	−91200.0	−0.127039
$221$	126672.	0.174462
$222$	4032.00	0.00549083
$223$	−994720.	−1.33949	−0.669744	−	0.742592i	$-0.733596\pi$
$223$	−994720.	−1.33949	−0.669744	+	0.742592i	$0.733596\pi$
$224$	83968.0	0.111813
$225$	50625.0	0.0666667
$226$	58896.0	0.0767034
$227$	−662352.	−0.853148	−0.426574	−	0.904453i	$-0.640280\pi$
$227$	−662352.	−0.853148	−0.426574	+	0.904453i	$0.640280\pi$
$228$	51984.0	0.0662266
$229$	−1.22916e6	−1.54888	−0.774442	−	0.632645i	$-0.781969\pi$
$229$	−1.22916e6	−1.54888	−0.774442	+	0.632645i	$0.781969\pi$
$230$	262200.	0.326823
$231$	−168264.	−0.207473
$232$	206208.	0.251528
$233$	−558366.	−0.673797	−0.336899	−	0.941541i	$-0.609378\pi$
$233$	−558366.	−0.673797	−0.336899	+	0.941541i	$0.609378\pi$
$234$	75168.0	0.0897415
$235$	−361950.	−0.427542
$236$	−740544.	−0.865508
$237$	−519192.	−0.600423
$238$	−179088.	−0.204939
$239$	−290760.	−0.329261	−0.164630	−	0.986355i	$-0.552643\pi$
$239$	−290760.	−0.329261	−0.164630	+	0.986355i	$0.552643\pi$
$240$	−57600.0	−0.0645497
$241$	1.34303e6	1.48951	0.744754	−	0.667339i	$-0.232567\pi$
$241$	1.34303e6	1.48951	0.744754	+	0.667339i	$0.232567\pi$
$242$	436268.	0.478867
$243$	59049.0	0.0641500
$244$	−712096.	−0.765709
$245$	252075.	0.268296
$246$	322056.	0.339308
$247$	−83752.0	−0.0873480
$248$	−346112.	−0.357345
$249$	−330210.	−0.337514
$250$	62500.0	0.0632456
$251$	−1.34878e6	−1.35131	−0.675656	−	0.737217i	$-0.736139\pi$
$251$	−1.34878e6	−1.35131	−0.675656	+	0.737217i	$0.736139\pi$
$252$	−106272.	−0.105419
$253$	597816.	0.587173
$254$	1.33350e6	1.29691
$255$	122850.	0.118311
$256$	65536.0	0.0625000
$257$	−111696.	−0.105488	−0.0527442	−	0.998608i	$-0.516797\pi$
$257$	−111696.	−0.105488	−0.0527442	+	0.998608i	$0.516797\pi$
$258$	−386280.	−0.361288
$259$	9184.00	0.00850712
$260$	92800.0	0.0851363
$261$	−260982.	−0.237142
$262$	−1.24032e6	−1.11630
$263$	1.82845e6	1.63002	0.815010	−	0.579447i	$-0.196732\pi$
$263$	1.82845e6	1.63002	0.815010	+	0.579447i	$0.196732\pi$
$264$	−131328.	−0.115970
$265$	−26100.0	−0.0228310
$266$	118408.	0.102607
$267$	829710.	0.712276
$268$	340160.	0.289299
$269$	−70050.0	−0.0590238	−0.0295119	−	0.999564i	$-0.509395\pi$
$269$	−70050.0	−0.0590238	−0.0295119	+	0.999564i	$0.509395\pi$
$270$	72900.0	0.0608581
$271$	−2.04100e6	−1.68818	−0.844092	−	0.536198i	$-0.819860\pi$
$271$	−2.04100e6	−1.68818	−0.844092	+	0.536198i	$0.819860\pi$
$272$	−139776.	−0.114554
$273$	171216.	0.139039
$274$	−175032.	−0.140845
$275$	142500.	0.113627
$276$	377568.	0.298348
$277$	−1.31327e6	−1.02838	−0.514190	−	0.857677i	$-0.671907\pi$
$277$	−1.31327e6	−1.02838	−0.514190	+	0.857677i	$0.671907\pi$
$278$	933856.	0.724716
$279$	438048.	0.336908
$280$	−131200.	−0.100009
$281$	−1.48228e6	−1.11986	−0.559932	−	0.828539i	$-0.689173\pi$
$281$	−1.48228e6	−1.11986	−0.559932	+	0.828539i	$0.689173\pi$
$282$	−521208.	−0.390291
$283$	−607618.	−0.450988	−0.225494	−	0.974245i	$-0.572400\pi$
$283$	−607618.	−0.450988	−0.225494	+	0.974245i	$0.572400\pi$
$284$	984960.	0.724641
$285$	−81225.0	−0.0592349
$286$	211584.	0.152956
$287$	733572.	0.525700
$288$	−82944.0	−0.0589256
$289$	−1.12174e6	−0.790038
$290$	−322200.	−0.224973
$291$	1.03223e6	0.714567
$292$	−1.39446e6	−0.957084
$293$	741300.	0.504458	0.252229	−	0.967668i	$-0.418836\pi$
$293$	741300.	0.504458	0.252229	+	0.967668i	$0.418836\pi$
$294$	362988.	0.244920
$295$	1.15710e6	0.774133
$296$	7168.00	0.00475520
$297$	166212.	0.109338
$298$	832872.	0.543297
$299$	−608304.	−0.393498
$300$	90000.0	0.0577350
$301$	−879860.	−0.559754
$302$	1.49200e6	0.941351
$303$	−818046.	−0.511884
$304$	92416.0	0.0573539
$305$	1.11265e6	0.684871
$306$	176904.	0.108003
$307$	2.59018e6	1.56850	0.784250	−	0.620445i	$-0.213048\pi$
$307$	2.59018e6	1.56850	0.784250	+	0.620445i	$0.213048\pi$
$308$	−299136.	−0.179677
$309$	1.07705e6	0.641710
$310$	540800.	0.319619
$311$	2.64115e6	1.54843	0.774217	−	0.632921i	$-0.218144\pi$
$311$	2.64115e6	1.54843	0.774217	+	0.632921i	$0.218144\pi$
$312$	133632.	0.0777184
$313$	−2.37818e6	−1.37210	−0.686048	−	0.727557i	$-0.740656\pi$
$313$	−2.37818e6	−1.37210	−0.686048	+	0.727557i	$0.740656\pi$
$314$	57256.0	0.0327715
$315$	166050.	0.0942893
$316$	−923008.	−0.519981
$317$	−2.16079e6	−1.20772	−0.603858	−	0.797092i	$-0.706371\pi$
$317$	−2.16079e6	−1.20772	−0.603858	+	0.797092i	$0.706371\pi$
$318$	−37584.0	−0.0208418
$319$	−734616.	−0.404188
$320$	−102400.	−0.0559017
$321$	714960.	0.387275
$322$	860016.	0.462239
$323$	−197106.	−0.105122
$324$	104976.	0.0555556
$325$	−145000.	−0.0761482
$326$	613432.	0.319685
$327$	−1.30732e6	−0.676104
$328$	572544.	0.293849
$329$	−1.18720e6	−0.604690
$330$	205200.	0.103727
$331$	2.20502e6	1.10622	0.553111	−	0.833107i	$-0.313440\pi$
$331$	2.20502e6	1.10622	0.553111	+	0.833107i	$0.313440\pi$
$332$	−587040.	−0.292296
$333$	−9072.00	−0.00448324
$334$	62928.0	0.0308658
$335$	−531500.	−0.258756
$336$	−188928.	−0.0912952
$337$	2.35099e6	1.12765	0.563827	−	0.825893i	$-0.309329\pi$
$337$	2.35099e6	1.12765	0.563827	+	0.825893i	$0.309329\pi$
$338$	1.26988e6	0.604602
$339$	−132516.	−0.0626281
$340$	218400.	0.102460
$341$	1.23302e6	0.574230
$342$	−116964.	−0.0540738
$343$	2.20498e6	1.01197
$344$	−686720.	−0.312884
$345$	−589950.	−0.266850
$346$	2.07269e6	0.930773
$347$	−1.31218e6	−0.585020	−0.292510	−	0.956263i	$-0.594490\pi$
$347$	−1.31218e6	−0.585020	−0.292510	+	0.956263i	$0.594490\pi$
$348$	−463968.	−0.205371
$349$	2.38485e6	1.04809	0.524043	−	0.851692i	$-0.324423\pi$
$349$	2.38485e6	1.04809	0.524043	+	0.851692i	$0.324423\pi$
$350$	205000.	0.0894507
$351$	−169128.	−0.0732736
$352$	−233472.	−0.100433
$353$	1.61953e6	0.691753	0.345877	−	0.938280i	$-0.387582\pi$
$353$	1.61953e6	0.691753	0.345877	+	0.938280i	$0.387582\pi$
$354$	1.66622e6	0.706684
$355$	−1.53900e6	−0.648138
$356$	1.47504e6	0.616849
$357$	402948.	0.167332
$358$	3.11928e6	1.28631
$359$	−513780.	−0.210398	−0.105199	−	0.994451i	$-0.533548\pi$
$359$	−513780.	−0.210398	−0.105199	+	0.994451i	$0.533548\pi$
$360$	129600.	0.0527046
$361$	130321.	0.0526316
$362$	−140120.	−0.0561990
$363$	−981603.	−0.390993
$364$	304384.	0.120412
$365$	2.17885e6	0.856042
$366$	1.60222e6	0.625199
$367$	−1.59606e6	−0.618562	−0.309281	−	0.950971i	$-0.600088\pi$
$367$	−1.59606e6	−0.618562	−0.309281	+	0.950971i	$0.600088\pi$
$368$	671232.	0.258377
$369$	−724626.	−0.277044
$370$	−11200.0	−0.00425318
$371$	−85608.0	−0.0322909
$372$	778752.	0.291771
$373$	1.31649e6	0.489944	0.244972	−	0.969530i	$-0.421221\pi$
$373$	1.31649e6	0.489944	0.244972	+	0.969530i	$0.421221\pi$
$374$	497952.	0.184081
$375$	−140625.	−0.0516398
$376$	−926592.	−0.338002
$377$	747504.	0.270870
$378$	239112.	0.0860740
$379$	−928420.	−0.332006	−0.166003	−	0.986125i	$-0.553086\pi$
$379$	−928420.	−0.332006	−0.166003	+	0.986125i	$0.553086\pi$
$380$	−144400.	−0.0512989
$381$	−3.00038e6	−1.05892
$382$	−3.59227e6	−1.25954
$383$	3.36551e6	1.17234	0.586170	−	0.810188i	$-0.300635\pi$
$383$	3.36551e6	1.17234	0.586170	+	0.810188i	$0.300635\pi$
$384$	−147456.	−0.0510310
$385$	467400.	0.160708
$386$	2.60440e6	0.889691
$387$	869130.	0.294990
$388$	1.83507e6	0.618833
$389$	−223926.	−0.0750292	−0.0375146	−	0.999296i	$-0.511944\pi$
$389$	−223926.	−0.0750292	−0.0375146	+	0.999296i	$0.511944\pi$
$390$	−208800.	−0.0695135
$391$	−1.43161e6	−0.473569
$392$	645312.	0.212107
$393$	2.79072e6	0.911454
$394$	205464.	0.0666799
$395$	1.44220e6	0.465085
$396$	295488.	0.0946895
$397$	4.21096e6	1.34093	0.670463	−	0.741943i	$-0.266096\pi$
$397$	4.21096e6	1.34093	0.670463	+	0.741943i	$0.266096\pi$
$398$	−927968.	−0.293647
$399$	−266418.	−0.0837783
$400$	160000.	0.0500000
$401$	−586326.	−0.182087	−0.0910433	−	0.995847i	$-0.529020\pi$
$401$	−586326.	−0.182087	−0.0910433	+	0.995847i	$0.529020\pi$
$402$	−765360.	−0.236211
$403$	−1.25466e6	−0.384824
$404$	−1.45430e6	−0.443304
$405$	−164025.	−0.0496904
$406$	−1.05682e6	−0.318188
$407$	−25536.0	−0.00764129
$408$	314496.	0.0935330
$409$	−3.16329e6	−0.935042	−0.467521	−	0.883982i	$-0.654853\pi$
$409$	−3.16329e6	−0.935042	−0.467521	+	0.883982i	$0.654853\pi$
$410$	−894600.	−0.262827
$411$	393822.	0.114999
$412$	1.91475e6	0.555737
$413$	3.79529e6	1.09489
$414$	−849528.	−0.243600
$415$	917250.	0.261437
$416$	237568.	0.0673061
$417$	−2.10118e6	−0.591728
$418$	−329232.	−0.0921640
$419$	891252.	0.248008	0.124004	−	0.992282i	$-0.460426\pi$
$419$	891252.	0.248008	0.124004	+	0.992282i	$0.460426\pi$
$420$	295200.	0.0816569
$421$	−2.41879e6	−0.665109	−0.332555	−	0.943084i	$-0.607911\pi$
$421$	−2.41879e6	−0.665109	−0.332555	+	0.943084i	$0.607911\pi$
$422$	1.20443e6	0.329231
$423$	1.17272e6	0.318671
$424$	−66816.0	−0.0180495
$425$	−341250.	−0.0916432
$426$	−2.21616e6	−0.591667
$427$	3.64949e6	0.968641
$428$	1.27104e6	0.335390
$429$	−476064.	−0.124888
$430$	1.07300e6	0.279852
$431$	5.81309e6	1.50735	0.753674	−	0.657248i	$-0.228280\pi$
$431$	5.81309e6	1.50735	0.753674	+	0.657248i	$0.228280\pi$
$432$	186624.	0.0481125
$433$	288836.	0.0740341	0.0370170	−	0.999315i	$-0.488214\pi$
$433$	288836.	0.0740341	0.0370170	+	0.999315i	$0.488214\pi$
$434$	1.77382e6	0.452050
$435$	724950.	0.183690
$436$	−2.32413e6	−0.585523
$437$	946542.	0.237103
$438$	3.13754e6	0.781456
$439$	−2.38348e6	−0.590269	−0.295135	−	0.955456i	$-0.595365\pi$
$439$	−2.38348e6	−0.590269	−0.295135	+	0.955456i	$0.595365\pi$
$440$	364800.	0.0898304
$441$	−816723.	−0.199976
$442$	−506688.	−0.123363
$443$	2.12072e6	0.513421	0.256710	−	0.966488i	$-0.417361\pi$
$443$	2.12072e6	0.513421	0.256710	+	0.966488i	$0.417361\pi$
$444$	−16128.0	−0.00388260
$445$	−2.30475e6	−0.551726
$446$	3.97888e6	0.947161
$447$	−1.87396e6	−0.443600
$448$	−335872.	−0.0790640
$449$	−423918.	−0.0992353	−0.0496176	−	0.998768i	$-0.515800\pi$
$449$	−423918.	−0.0992353	−0.0496176	+	0.998768i	$0.515800\pi$
$450$	−202500.	−0.0471405
$451$	−2.03969e6	−0.472196
$452$	−235584.	−0.0542375
$453$	−3.35700e6	−0.768610
$454$	2.64941e6	0.603267
$455$	−475600.	−0.107699
$456$	−207936.	−0.0468293
$457$	−4.82810e6	−1.08140	−0.540699	−	0.841216i	$-0.681840\pi$
$457$	−4.82810e6	−1.08140	−0.540699	+	0.841216i	$0.681840\pi$
$458$	4.91663e6	1.09523
$459$	−398034.	−0.0881837
$460$	−1.04880e6	−0.231099
$461$	−1.58512e6	−0.347384	−0.173692	−	0.984800i	$-0.555570\pi$
$461$	−1.58512e6	−0.347384	−0.173692	+	0.984800i	$0.555570\pi$
$462$	673056.	0.146705
$463$	3.02229e6	0.655214	0.327607	−	0.944814i	$-0.393758\pi$
$463$	3.02229e6	0.655214	0.327607	+	0.944814i	$0.393758\pi$
$464$	−824832.	−0.177857
$465$	−1.21680e6	−0.260968
$466$	2.23346e6	0.476447
$467$	7.79267e6	1.65346	0.826731	−	0.562597i	$-0.190198\pi$
$467$	7.79267e6	1.65346	0.826731	+	0.562597i	$0.190198\pi$
$468$	−300672.	−0.0634568
$469$	−1.74332e6	−0.365970
$470$	1.44780e6	0.302318
$471$	−128826.	−0.0267579
$472$	2.96218e6	0.612006
$473$	2.44644e6	0.502784
$474$	2.07677e6	0.424563
$475$	225625.	0.0458831
$476$	716352.	0.144914
$477$	84564.0	0.0170173
$478$	1.16304e6	0.232822
$479$	7.28809e6	1.45136	0.725680	−	0.688033i	$-0.241525\pi$
$479$	7.28809e6	1.45136	0.725680	+	0.688033i	$0.241525\pi$
$480$	230400.	0.0456435
$481$	25984.0	0.00512086
$482$	−5.37212e6	−1.05324
$483$	−1.93504e6	−0.377417
$484$	−1.74507e6	−0.338610
$485$	−2.86730e6	−0.553501
$486$	−236196.	−0.0453609
$487$	−4.30738e6	−0.822983	−0.411491	−	0.911414i	$-0.634992\pi$
$487$	−4.30738e6	−0.822983	−0.411491	+	0.911414i	$0.634992\pi$
$488$	2.84838e6	0.541438
$489$	−1.38022e6	−0.261022
$490$	−1.00830e6	−0.189714
$491$	2.56157e6	0.479515	0.239757	−	0.970833i	$-0.422932\pi$
$491$	2.56157e6	0.479515	0.239757	+	0.970833i	$0.422932\pi$
$492$	−1.28822e6	−0.239927
$493$	1.75921e6	0.325987
$494$	335008.	0.0617643
$495$	−461700.	−0.0846929
$496$	1.38445e6	0.252681
$497$	−5.04792e6	−0.916688
$498$	1.32084e6	0.238658
$499$	−8.51294e6	−1.53048	−0.765241	−	0.643744i	$-0.777380\pi$
$499$	−8.51294e6	−1.53048	−0.765241	+	0.643744i	$0.777380\pi$
$500$	−250000.	−0.0447214
$501$	−141588.	−0.0252018
$502$	5.39510e6	0.955522
$503$	2.69861e6	0.475577	0.237788	−	0.971317i	$-0.423577\pi$
$503$	2.69861e6	0.475577	0.237788	+	0.971317i	$0.423577\pi$
$504$	425088.	0.0745423
$505$	2.27235e6	0.396503
$506$	−2.39126e6	−0.415194
$507$	−2.85722e6	−0.493655
$508$	−5.33402e6	−0.917054
$509$	640698.	0.109612	0.0548061	−	0.998497i	$-0.482546\pi$
$509$	640698.	0.109612	0.0548061	+	0.998497i	$0.482546\pi$
$510$	−491400.	−0.0836584
$511$	7.14663e6	1.21073
$512$	−262144.	−0.0441942
$513$	263169.	0.0441511
$514$	446784.	0.0745916
$515$	−2.99180e6	−0.497066
$516$	1.54512e6	0.255469
$517$	3.30098e6	0.543147
$518$	−36736.0	−0.00601544
$519$	−4.66355e6	−0.759973
$520$	−371200.	−0.0602004
$521$	−3.04527e6	−0.491509	−0.245755	−	0.969332i	$-0.579036\pi$
$521$	−3.04527e6	−0.491509	−0.245755	+	0.969332i	$0.579036\pi$
$522$	1.04393e6	0.167685
$523$	8.36276e6	1.33689	0.668445	−	0.743762i	$-0.266960\pi$
$523$	8.36276e6	1.33689	0.668445	+	0.743762i	$0.266960\pi$
$524$	4.96128e6	0.789343
$525$	−461250.	−0.0730362
$526$	−7.31378e6	−1.15260
$527$	−2.95277e6	−0.463130
$528$	525312.	0.0820035
$529$	438541.	0.0681351
$530$	104400.	0.0161440
$531$	−3.74900e6	−0.577005
$532$	−473632.	−0.0725541
$533$	2.07547e6	0.316445
$534$	−3.31884e6	−0.503655
$535$	−1.98600e6	−0.299982
$536$	−1.36064e6	−0.204565
$537$	−7.01838e6	−1.05027
$538$	280200.	0.0417362
$539$	−2.29892e6	−0.340842
$540$	−291600.	−0.0430331
$541$	−3.91656e6	−0.575323	−0.287661	−	0.957732i	$-0.592878\pi$
$541$	−3.91656e6	−0.575323	−0.287661	+	0.957732i	$0.592878\pi$
$542$	8.16400e6	1.19373
$543$	315270.	0.0458863
$544$	559104.	0.0810019
$545$	3.63145e6	0.523708
$546$	−684864.	−0.0983157
$547$	−8.15966e6	−1.16601	−0.583007	−	0.812467i	$-0.698124\pi$
$547$	−8.15966e6	−1.16601	−0.583007	+	0.812467i	$0.698124\pi$
$548$	700128.	0.0995924
$549$	−3.60499e6	−0.510473
$550$	−570000.	−0.0803467
$551$	−1.16314e6	−0.163213
$552$	−1.51027e6	−0.210964
$553$	4.73042e6	0.657789
$554$	5.25306e6	0.727174
$555$	25200.0	0.00347271
$556$	−3.73542e6	−0.512452
$557$	1.38009e7	1.88482	0.942410	−	0.334459i	$-0.108554\pi$
$557$	1.38009e7	1.88482	0.942410	+	0.334459i	$0.108554\pi$
$558$	−1.75219e6	−0.238230
$559$	−2.48936e6	−0.336944
$560$	524800.	0.0707170
$561$	−1.12039e6	−0.150301
$562$	5.92913e6	0.791863
$563$	7.36495e6	0.979262	0.489631	−	0.871930i	$-0.337131\pi$
$563$	7.36495e6	0.979262	0.489631	+	0.871930i	$0.337131\pi$
$564$	2.08483e6	0.275977
$565$	368100.	0.0485115
$566$	2.43047e6	0.318896
$567$	−538002.	−0.0702791
$568$	−3.93984e6	−0.512398
$569$	−3.50389e6	−0.453701	−0.226850	−	0.973930i	$-0.572843\pi$
$569$	−3.50389e6	−0.453701	−0.226850	+	0.973930i	$0.572843\pi$
$570$	324900.	0.0418854
$571$	−3.85956e6	−0.495391	−0.247695	−	0.968838i	$-0.579673\pi$
$571$	−3.85956e6	−0.495391	−0.247695	+	0.968838i	$0.579673\pi$
$572$	−846336.	−0.108157
$573$	8.08261e6	1.02841
$574$	−2.93429e6	−0.371726
$575$	1.63875e6	0.206701
$576$	331776.	0.0416667
$577$	−1.04040e7	−1.30095	−0.650475	−	0.759528i	$-0.725430\pi$
$577$	−1.04040e7	−1.30095	−0.650475	+	0.759528i	$0.725430\pi$
$578$	4.48696e6	0.558641
$579$	−5.85990e6	−0.726430
$580$	1.28880e6	0.159080
$581$	3.00858e6	0.369761
$582$	−4.12891e6	−0.505275
$583$	238032.	0.0290044
$584$	5.57786e6	0.676761
$585$	469800.	0.0567575
$586$	−2.96520e6	−0.356706
$587$	−3.21063e6	−0.384587	−0.192294	−	0.981337i	$-0.561593\pi$
$587$	−3.21063e6	−0.384587	−0.192294	+	0.981337i	$0.561593\pi$
$588$	−1.45195e6	−0.173184
$589$	1.95229e6	0.231876
$590$	−4.62840e6	−0.547395
$591$	−462294.	−0.0544439
$592$	−28672.0	−0.00336243
$593$	−9.20285e6	−1.07470	−0.537348	−	0.843360i	$-0.680574\pi$
$593$	−9.20285e6	−1.07470	−0.537348	+	0.843360i	$0.680574\pi$
$594$	−664848.	−0.0773137
$595$	−1.11930e6	−0.129615
$596$	−3.33149e6	−0.384169
$597$	2.08793e6	0.239762
$598$	2.43322e6	0.278245
$599$	−1.33404e7	−1.51915	−0.759577	−	0.650417i	$-0.774594\pi$
$599$	−1.33404e7	−1.51915	−0.759577	+	0.650417i	$0.774594\pi$
$600$	−360000.	−0.0408248
$601$	1.83136e6	0.206817	0.103409	−	0.994639i	$-0.467025\pi$
$601$	1.83136e6	0.206817	0.103409	+	0.994639i	$0.467025\pi$
$602$	3.51944e6	0.395806
$603$	1.72206e6	0.192866
$604$	−5.96800e6	−0.665635
$605$	2.72668e6	0.302862
$606$	3.27218e6	0.361956
$607$	1.33681e7	1.47264	0.736322	−	0.676631i	$-0.236561\pi$
$607$	1.33681e7	1.47264	0.736322	+	0.676631i	$0.236561\pi$
$608$	−369664.	−0.0405554
$609$	2.37784e6	0.259800
$610$	−4.45060e6	−0.484277
$611$	−3.35890e6	−0.363993
$612$	−707616.	−0.0763693
$613$	1.48957e6	0.160107	0.0800536	−	0.996791i	$-0.474491\pi$
$613$	1.48957e6	0.160107	0.0800536	+	0.996791i	$0.474491\pi$
$614$	−1.03607e7	−1.10910
$615$	2.01285e6	0.214597
$616$	1.19654e6	0.127051
$617$	−1.16903e7	−1.23627	−0.618135	−	0.786072i	$-0.712112\pi$
$617$	−1.16903e7	−1.23627	−0.618135	+	0.786072i	$0.712112\pi$
$618$	−4.30819e6	−0.453758
$619$	1.27471e7	1.33716	0.668582	−	0.743638i	$-0.266901\pi$
$619$	1.27471e7	1.33716	0.668582	+	0.743638i	$0.266901\pi$
$620$	−2.16320e6	−0.226005
$621$	1.91144e6	0.198898
$622$	−1.05646e7	−1.09491
$623$	−7.55958e6	−0.780329
$624$	−534528.	−0.0549552
$625$	390625.	0.0400000
$626$	9.51273e6	0.970218
$627$	740772.	0.0752516
$628$	−229024.	−0.0231730
$629$	61152.0	0.00616288
$630$	−664200.	−0.0666726
$631$	995960.	0.0995792	0.0497896	−	0.998760i	$-0.484145\pi$
$631$	995960.	0.0995792	0.0497896	+	0.998760i	$0.484145\pi$
$632$	3.69203e6	0.367682
$633$	−2.70997e6	−0.268816
$634$	8.64317e6	0.853984
$635$	8.33440e6	0.820238
$636$	150336.	0.0147374
$637$	2.33926e6	0.228417
$638$	2.93846e6	0.285804
$639$	4.98636e6	0.483094
$640$	409600.	0.0395285
$641$	−5.45246e6	−0.524140	−0.262070	−	0.965049i	$-0.584405\pi$
$641$	−5.45246e6	−0.524140	−0.262070	+	0.965049i	$0.584405\pi$
$642$	−2.85984e6	−0.273845
$643$	−6.82791e6	−0.651269	−0.325635	−	0.945496i	$-0.605578\pi$
$643$	−6.82791e6	−0.651269	−0.325635	+	0.945496i	$0.605578\pi$
$644$	−3.44006e6	−0.326853
$645$	−2.41425e6	−0.228498
$646$	788424.	0.0743325
$647$	−6.56991e6	−0.617019	−0.308510	−	0.951221i	$-0.599830\pi$
$647$	−6.56991e6	−0.617019	−0.308510	+	0.951221i	$0.599830\pi$
$648$	−419904.	−0.0392837
$649$	−1.05528e7	−0.983454
$650$	580000.	0.0538449
$651$	−3.99110e6	−0.369097
$652$	−2.45373e6	−0.226052
$653$	6.70659e6	0.615487	0.307743	−	0.951469i	$-0.400426\pi$
$653$	6.70659e6	0.615487	0.307743	+	0.951469i	$0.400426\pi$
$654$	5.22929e6	0.478077
$655$	−7.75200e6	−0.706009
$656$	−2.29018e6	−0.207783
$657$	−7.05947e6	−0.638056
$658$	4.74878e6	0.427580
$659$	1.44822e7	1.29904	0.649519	−	0.760345i	$-0.274970\pi$
$659$	1.44822e7	1.29904	0.649519	+	0.760345i	$0.274970\pi$
$660$	−820800.	−0.0733462
$661$	−1.68549e6	−0.150046	−0.0750229	−	0.997182i	$-0.523903\pi$
$661$	−1.68549e6	−0.150046	−0.0750229	+	0.997182i	$0.523903\pi$
$662$	−8.82008e6	−0.782218
$663$	1.14005e6	0.100725
$664$	2.34816e6	0.206684
$665$	740050.	0.0648944
$666$	36288.0	0.00317013
$667$	−8.44808e6	−0.735265
$668$	−251712.	−0.0218254
$669$	−8.95248e6	−0.773354
$670$	2.12600e6	0.182968
$671$	−1.01474e7	−0.870056
$672$	755712.	0.0645555
$673$	2.11851e7	1.80299	0.901496	−	0.432788i	$-0.142470\pi$
$673$	2.11851e7	1.80299	0.901496	+	0.432788i	$0.142470\pi$
$674$	−9.40395e6	−0.797371
$675$	455625.	0.0384900
$676$	−5.07950e6	−0.427518
$677$	1.06647e7	0.894291	0.447146	−	0.894461i	$-0.352441\pi$
$677$	1.06647e7	0.894291	0.447146	+	0.894461i	$0.352441\pi$
$678$	530064.	0.0442847
$679$	−9.40474e6	−0.782839
$680$	−873600.	−0.0724503
$681$	−5.96117e6	−0.492565
$682$	−4.93210e6	−0.406042
$683$	−4.72075e6	−0.387221	−0.193611	−	0.981078i	$-0.562020\pi$
$683$	−4.72075e6	−0.387221	−0.193611	+	0.981078i	$0.562020\pi$
$684$	467856.	0.0382360
$685$	−1.09395e6	−0.0890781
$686$	−8.81992e6	−0.715574
$687$	−1.10624e7	−0.894249
$688$	2.74688e6	0.221243
$689$	−242208.	−0.0194375
$690$	2.35980e6	0.188692
$691$	−1.32373e7	−1.05464	−0.527322	−	0.849666i	$-0.676804\pi$
$691$	−1.32373e7	−1.05464	−0.527322	+	0.849666i	$0.676804\pi$
$692$	−8.29075e6	−0.658156
$693$	−1.51438e6	−0.119785
$694$	5.24873e6	0.413671
$695$	5.83660e6	0.458351
$696$	1.85587e6	0.145219
$697$	4.88452e6	0.380837
$698$	−9.53938e6	−0.741108
$699$	−5.02529e6	−0.389017
$700$	−820000.	−0.0632512
$701$	619566.	0.0476203	0.0238102	−	0.999716i	$-0.492420\pi$
$701$	619566.	0.0476203	0.0238102	+	0.999716i	$0.492420\pi$
$702$	676512.	0.0518123
$703$	−40432.0	−0.00308558
$704$	933888.	0.0710171
$705$	−3.25755e6	−0.246842
$706$	−6.47810e6	−0.489143
$707$	7.45331e6	0.560790
$708$	−6.66490e6	−0.499701
$709$	1.33253e7	0.995544	0.497772	−	0.867308i	$-0.334152\pi$
$709$	1.33253e7	0.995544	0.497772	+	0.867308i	$0.334152\pi$
$710$	6.15600e6	0.458303
$711$	−4.67273e6	−0.346654
$712$	−5.90016e6	−0.436178
$713$	1.41798e7	1.04459
$714$	−1.61179e6	−0.118321
$715$	1.32240e6	0.0967381
$716$	−1.24771e7	−0.909561
$717$	−2.61684e6	−0.190099
$718$	2.05512e6	0.148774
$719$	−1.23690e6	−0.0892303	−0.0446152	−	0.999004i	$-0.514206\pi$
$719$	−1.23690e6	−0.0892303	−0.0446152	+	0.999004i	$0.514206\pi$
$720$	−518400.	−0.0372678
$721$	−9.81310e6	−0.703021
$722$	−521284.	−0.0372161
$723$	1.20873e7	0.859968
$724$	560480.	0.0397387
$725$	−2.01375e6	−0.142285
$726$	3.92641e6	0.276474
$727$	2.50908e7	1.76067	0.880337	−	0.474350i	$-0.157317\pi$
$727$	2.50908e7	1.76067	0.880337	+	0.474350i	$0.157317\pi$
$728$	−1.21754e6	−0.0851439
$729$	531441.	0.0370370
$730$	−8.71540e6	−0.605313
$731$	−5.85858e6	−0.405508
$732$	−6.40886e6	−0.442083
$733$	1.20731e7	0.829965	0.414983	−	0.909829i	$-0.363788\pi$
$733$	1.20731e7	0.829965	0.414983	+	0.909829i	$0.363788\pi$
$734$	6.38423e6	0.437390
$735$	2.26868e6	0.154901
$736$	−2.68493e6	−0.182700
$737$	4.84728e6	0.328722
$738$	2.89850e6	0.195899
$739$	−1.07274e7	−0.722574	−0.361287	−	0.932455i	$-0.617663\pi$
$739$	−1.07274e7	−0.722574	−0.361287	+	0.932455i	$0.617663\pi$
$740$	44800.0	0.00300745
$741$	−753768.	−0.0504304
$742$	342432.	0.0228331
$743$	6.61168e6	0.439379	0.219690	−	0.975570i	$-0.429496\pi$
$743$	6.61168e6	0.439379	0.219690	+	0.975570i	$0.429496\pi$
$744$	−3.11501e6	−0.206313
$745$	5.20545e6	0.343611
$746$	−5.26597e6	−0.346442
$747$	−2.97189e6	−0.194864
$748$	−1.99181e6	−0.130165
$749$	−6.51408e6	−0.424276
$750$	562500.	0.0365148
$751$	−6.72726e6	−0.435250	−0.217625	−	0.976032i	$-0.569831\pi$
$751$	−6.72726e6	−0.435250	−0.217625	+	0.976032i	$0.569831\pi$
$752$	3.70637e6	0.239003
$753$	−1.21390e7	−0.780180
$754$	−2.99002e6	−0.191534
$755$	9.32500e6	0.595362
$756$	−956448.	−0.0608635
$757$	8.43435e6	0.534948	0.267474	−	0.963565i	$-0.413811\pi$
$757$	8.43435e6	0.534948	0.267474	+	0.963565i	$0.413811\pi$
$758$	3.71368e6	0.234764
$759$	5.38034e6	0.339005
$760$	577600.	0.0362738
$761$	−4.98110e6	−0.311791	−0.155895	−	0.987774i	$-0.549826\pi$
$761$	−4.98110e6	−0.311791	−0.155895	+	0.987774i	$0.549826\pi$
$762$	1.20015e7	0.748772
$763$	1.19112e7	0.740700
$764$	1.43691e7	0.890627
$765$	1.10565e6	0.0683068
$766$	−1.34620e7	−0.828970
$767$	1.07379e7	0.659068
$768$	589824.	0.0360844
$769$	2.59761e7	1.58401	0.792006	−	0.610513i	$-0.209037\pi$
$769$	2.59761e7	1.58401	0.792006	+	0.610513i	$0.209037\pi$
$770$	−1.86960e6	−0.113638
$771$	−1.00526e6	−0.0609038
$772$	−1.04176e7	−0.629107
$773$	−2.34415e6	−0.141103	−0.0705516	−	0.997508i	$-0.522476\pi$
$773$	−2.34415e6	−0.141103	−0.0705516	+	0.997508i	$0.522476\pi$
$774$	−3.47652e6	−0.208589
$775$	3.38000e6	0.202145
$776$	−7.34029e6	−0.437581
$777$	82656.0	0.00491159
$778$	895704.	0.0530537
$779$	−3.22951e6	−0.190674
$780$	835200.	0.0491534
$781$	1.40357e7	0.823391
$782$	5.72645e6	0.334864
$783$	−2.34884e6	−0.136914
$784$	−2.58125e6	−0.149982
$785$	357850.	0.0207265
$786$	−1.11629e7	−0.644496
$787$	−3.39905e7	−1.95623	−0.978117	−	0.208057i	$-0.933286\pi$
$787$	−3.39905e7	−1.95623	−0.978117	+	0.208057i	$0.933286\pi$
$788$	−821856.	−0.0471498
$789$	1.64560e7	0.941092
$790$	−5.76880e6	−0.328865
$791$	1.20737e6	0.0686117
$792$	−1.18195e6	−0.0669556
$793$	1.03254e7	0.583074
$794$	−1.68438e7	−0.948177
$795$	−234900.	−0.0131815
$796$	3.71187e6	0.207640
$797$	−1.34788e7	−0.751633	−0.375817	−	0.926694i	$-0.622638\pi$
$797$	−1.34788e7	−0.751633	−0.375817	+	0.926694i	$0.622638\pi$
$798$	1.06567e6	0.0592402
$799$	−7.90499e6	−0.438061
$800$	−640000.	−0.0353553
$801$	7.46739e6	0.411233
$802$	2.34530e6	0.128755
$803$	−1.98711e7	−1.08751
$804$	3.06144e6	0.167027
$805$	5.37510e6	0.292346
$806$	5.01862e6	0.272112
$807$	−630450.	−0.0340774
$808$	5.81722e6	0.313463
$809$	2.49339e7	1.33943	0.669714	−	0.742619i	$-0.266417\pi$
$809$	2.49339e7	1.33943	0.669714	+	0.742619i	$0.266417\pi$
$810$	656100.	0.0351364
$811$	7.06596e6	0.377241	0.188620	−	0.982050i	$-0.439598\pi$
$811$	7.06596e6	0.377241	0.188620	+	0.982050i	$0.439598\pi$
$812$	4.22726e6	0.224993
$813$	−1.83690e7	−0.974673
$814$	102144.	0.00540321
$815$	3.83395e6	0.202187
$816$	−1.25798e6	−0.0661378
$817$	3.87353e6	0.203026
$818$	1.26532e7	0.661175
$819$	1.54094e6	0.0802744
$820$	3.57840e6	0.185846
$821$	−1.08711e7	−0.562879	−0.281440	−	0.959579i	$-0.590812\pi$
$821$	−1.08711e7	−0.562879	−0.281440	+	0.959579i	$0.590812\pi$
$822$	−1.57529e6	−0.0813168
$823$	1.49090e7	0.767271	0.383635	−	0.923485i	$-0.374672\pi$
$823$	1.49090e7	0.767271	0.383635	+	0.923485i	$0.374672\pi$
$824$	−7.65901e6	−0.392966
$825$	1.28250e6	0.0656028
$826$	−1.51812e7	−0.774203
$827$	−3.40481e7	−1.73113	−0.865564	−	0.500799i	$-0.833040\pi$
$827$	−3.40481e7	−1.73113	−0.865564	+	0.500799i	$0.833040\pi$
$828$	3.39811e6	0.172251
$829$	1.30544e7	0.659737	0.329868	−	0.944027i	$-0.392996\pi$
$829$	1.30544e7	0.659737	0.329868	+	0.944027i	$0.392996\pi$
$830$	−3.66900e6	−0.184864
$831$	−1.18194e7	−0.593735
$832$	−950272.	−0.0475926
$833$	5.50532e6	0.274897
$834$	8.40470e6	0.418415
$835$	393300.	0.0195213
$836$	1.31693e6	0.0651698
$837$	3.94243e6	0.194514
$838$	−3.56501e6	−0.175368
$839$	−1.06437e7	−0.522022	−0.261011	−	0.965336i	$-0.584056\pi$
$839$	−1.06437e7	−0.522022	−0.261011	+	0.965336i	$0.584056\pi$
$840$	−1.18080e6	−0.0577402
$841$	−1.01299e7	−0.493871
$842$	9.67516e6	0.470303
$843$	−1.33405e7	−0.646553
$844$	−4.81773e6	−0.232802
$845$	7.93672e6	0.382384
$846$	−4.69087e6	−0.225334
$847$	8.94349e6	0.428350
$848$	267264.	0.0127629
$849$	−5.46856e6	−0.260378
$850$	1.36500e6	0.0648015
$851$	−293664.	−0.0139004
$852$	8.86464e6	0.418372
$853$	3.58967e7	1.68920	0.844602	−	0.535395i	$-0.179837\pi$
$853$	3.58967e7	1.68920	0.844602	+	0.535395i	$0.179837\pi$
$854$	−1.45980e7	−0.684932
$855$	−731025.	−0.0341993
$856$	−5.08416e6	−0.237156
$857$	3.03144e7	1.40993	0.704963	−	0.709244i	$-0.250964\pi$
$857$	3.03144e7	1.40993	0.704963	+	0.709244i	$0.250964\pi$
$858$	1.90426e6	0.0883094
$859$	−2.70069e7	−1.24880	−0.624398	−	0.781106i	$-0.714656\pi$
$859$	−2.70069e7	−1.24880	−0.624398	+	0.781106i	$0.714656\pi$
$860$	−4.29200e6	−0.197885
$861$	6.60215e6	0.303513
$862$	−2.32524e7	−1.06586
$863$	8.96809e6	0.409895	0.204948	−	0.978773i	$-0.434298\pi$
$863$	8.96809e6	0.409895	0.204948	+	0.978773i	$0.434298\pi$
$864$	−746496.	−0.0340207
$865$	1.29543e7	0.588672
$866$	−1.15534e6	−0.0523500
$867$	−1.00957e7	−0.456129
$868$	−7.09530e6	−0.319647
$869$	−1.31529e7	−0.590841
$870$	−2.89980e6	−0.129888
$871$	−4.93232e6	−0.220296
$872$	9.29651e6	0.414027
$873$	9.29005e6	0.412556
$874$	−3.78617e6	−0.167657
$875$	1.28125e6	0.0565736
$876$	−1.25502e7	−0.552573
$877$	−1.29465e7	−0.568398	−0.284199	−	0.958765i	$-0.591728\pi$
$877$	−1.29465e7	−0.568398	−0.284199	+	0.958765i	$0.591728\pi$
$878$	9.53392e6	0.417383
$879$	6.67170e6	0.291249
$880$	−1.45920e6	−0.0635197
$881$	−2.61260e7	−1.13405	−0.567026	−	0.823700i	$-0.691906\pi$
$881$	−2.61260e7	−1.13405	−0.567026	+	0.823700i	$0.691906\pi$
$882$	3.26689e6	0.141405
$883$	1.03213e7	0.445483	0.222742	−	0.974877i	$-0.428499\pi$
$883$	1.03213e7	0.445483	0.222742	+	0.974877i	$0.428499\pi$
$884$	2.02675e6	0.0872308
$885$	1.04139e7	0.446946
$886$	−8.48287e6	−0.363043
$887$	2.43723e7	1.04013	0.520065	−	0.854127i	$-0.325908\pi$
$887$	2.43723e7	1.04013	0.520065	+	0.854127i	$0.325908\pi$
$888$	64512.0	0.00274542
$889$	2.73368e7	1.16010
$890$	9.21900e6	0.390130
$891$	1.49591e6	0.0631263
$892$	−1.59155e7	−0.669744
$893$	5.22656e6	0.219324
$894$	7.49585e6	0.313673
$895$	1.94955e7	0.813536
$896$	1.34349e6	0.0559067
$897$	−5.47474e6	−0.227186
$898$	1.69567e6	0.0701699
$899$	−1.74246e7	−0.719056
$900$	810000.	0.0333333
$901$	−570024.	−0.0233927
$902$	8.15875e6	0.333893
$903$	−7.91874e6	−0.323174
$904$	942336.	0.0383517
$905$	−875750.	−0.0355434
$906$	1.34280e7	0.543489
$907$	−2.81949e6	−0.113803	−0.0569013	−	0.998380i	$-0.518122\pi$
$907$	−2.81949e6	−0.113803	−0.0569013	+	0.998380i	$0.518122\pi$
$908$	−1.05976e7	−0.426574
$909$	−7.36241e6	−0.295536
$910$	1.90240e6	0.0761550
$911$	2.66568e7	1.06417	0.532086	−	0.846690i	$-0.321408\pi$
$911$	2.66568e7	1.06417	0.532086	+	0.846690i	$0.321408\pi$
$912$	831744.	0.0331133
$913$	−8.36532e6	−0.332128
$914$	1.93124e7	0.764665
$915$	1.00138e7	0.395411
$916$	−1.96665e7	−0.774442
$917$	−2.54266e7	−0.998537
$918$	1.59214e6	0.0623553
$919$	−2.78150e7	−1.08640	−0.543200	−	0.839603i	$-0.682787\pi$
$919$	−2.78150e7	−1.08640	−0.543200	+	0.839603i	$0.682787\pi$
$920$	4.19520e6	0.163412
$921$	2.33117e7	0.905574
$922$	6.34049e6	0.245638
$923$	−1.42819e7	−0.551801
$924$	−2.69222e6	−0.103736
$925$	−70000.0	−0.00268995
$926$	−1.20891e7	−0.463306
$927$	9.69343e6	0.370491
$928$	3.29933e6	0.125764
$929$	−885690.	−0.0336699	−0.0168350	−	0.999858i	$-0.505359\pi$
$929$	−885690.	−0.0336699	−0.0168350	+	0.999858i	$0.505359\pi$
$930$	4.86720e6	0.184532
$931$	−3.63996e6	−0.137633
$932$	−8.93386e6	−0.336899
$933$	2.37704e7	0.893988
$934$	−3.11707e7	−1.16917
$935$	3.11220e6	0.116423
$936$	1.20269e6	0.0448708
$937$	3.76480e6	0.140085	0.0700427	−	0.997544i	$-0.477686\pi$
$937$	3.76480e6	0.140085	0.0700427	+	0.997544i	$0.477686\pi$
$938$	6.97328e6	0.258780
$939$	−2.14036e7	−0.792180
$940$	−5.79120e6	−0.213771
$941$	−6.80275e6	−0.250444	−0.125222	−	0.992129i	$-0.539964\pi$
$941$	−6.80275e6	−0.250444	−0.125222	+	0.992129i	$0.539964\pi$
$942$	515304.	0.0189207
$943$	−2.34564e7	−0.858979
$944$	−1.18487e7	−0.432754
$945$	1.49445e6	0.0544380
$946$	−9.78576e6	−0.355522
$947$	−1.04449e7	−0.378469	−0.189235	−	0.981932i	$-0.560601\pi$
$947$	−1.04449e7	−0.378469	−0.189235	+	0.981932i	$0.560601\pi$
$948$	−8.30707e6	−0.300211
$949$	2.02197e7	0.728802
$950$	−902500.	−0.0324443
$951$	−1.94471e7	−0.697275
$952$	−2.86541e6	−0.102469
$953$	−3.13840e7	−1.11938	−0.559689	−	0.828703i	$-0.689079\pi$
$953$	−3.13840e7	−1.11938	−0.559689	+	0.828703i	$0.689079\pi$
$954$	−338256.	−0.0120330
$955$	−2.24517e7	−0.796601
$956$	−4.65216e6	−0.164630
$957$	−6.61154e6	−0.233358
$958$	−2.91524e7	−1.02627
$959$	−3.58816e6	−0.125987
$960$	−921600.	−0.0322749
$961$	617313.	0.0215624
$962$	−103936.	−0.00362100
$963$	6.43464e6	0.223593
$964$	2.14885e7	0.744754
$965$	1.62775e7	0.562690
$966$	7.74014e6	0.266874
$967$	1.94676e6	0.0669494	0.0334747	−	0.999440i	$-0.489343\pi$
$967$	1.94676e6	0.0669494	0.0334747	+	0.999440i	$0.489343\pi$
$968$	6.98029e6	0.239434
$969$	−1.77395e6	−0.0606922
$970$	1.14692e7	0.391385
$971$	−1.82511e7	−0.621213	−0.310606	−	0.950539i	$-0.600532\pi$
$971$	−1.82511e7	−0.621213	−0.310606	+	0.950539i	$0.600532\pi$
$972$	944784.	0.0320750
$973$	1.91440e7	0.648264
$974$	1.72295e7	0.581937
$975$	−1.30500e6	−0.0439642
$976$	−1.13935e7	−0.382855
$977$	4.05343e7	1.35858	0.679292	−	0.733868i	$-0.262287\pi$
$977$	4.05343e7	1.35858	0.679292	+	0.733868i	$0.262287\pi$
$978$	5.52089e6	0.184570
$979$	2.10193e7	0.700909
$980$	4.03320e6	0.134148
$981$	−1.17659e7	−0.390349
$982$	−1.02463e7	−0.339068
$983$	1.07799e7	0.355821	0.177911	−	0.984047i	$-0.443066\pi$
$983$	1.07799e7	0.355821	0.177911	+	0.984047i	$0.443066\pi$
$984$	5.15290e6	0.169654
$985$	1.28415e6	0.0421721
$986$	−7.03685e6	−0.230508
$987$	−1.06848e7	−0.349118
$988$	−1.34003e6	−0.0436740
$989$	2.81341e7	0.914622
$990$	1.84680e6	0.0598869
$991$	−2.36290e7	−0.764295	−0.382148	−	0.924101i	$-0.624815\pi$
$991$	−2.36290e7	−0.764295	−0.382148	+	0.924101i	$0.624815\pi$
$992$	−5.53779e6	−0.178672
$993$	1.98452e7	0.638678
$994$	2.01917e7	0.648196
$995$	−5.79980e6	−0.185719
$996$	−5.28336e6	−0.168757
$997$	−3.52951e7	−1.12454	−0.562272	−	0.826952i	$-0.690073\pi$
$997$	−3.52951e7	−1.12454	−0.562272	+	0.826952i	$0.690073\pi$
$998$	3.40517e7	1.08221
$999$	−81648.0	−0.00258840

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.6.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.6.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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	570.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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