LMFDB - Embedded newform 10.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,6,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	10.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:	$1.60383819813$
Analytic rank:	$0$
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	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} +6.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +24.0000 q^{6} -118.000 q^{7} +64.0000 q^{8} -207.000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} +6.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +24.0000 q^{6} -118.000 q^{7} +64.0000 q^{8} -207.000 q^{9} -100.000 q^{10} +192.000 q^{11} +96.0000 q^{12} +1106.00 q^{13} -472.000 q^{14} -150.000 q^{15} +256.000 q^{16} +762.000 q^{17} -828.000 q^{18} -2740.00 q^{19} -400.000 q^{20} -708.000 q^{21} +768.000 q^{22} +1566.00 q^{23} +384.000 q^{24} +625.000 q^{25} +4424.00 q^{26} -2700.00 q^{27} -1888.00 q^{28} +5910.00 q^{29} -600.000 q^{30} -6868.00 q^{31} +1024.00 q^{32} +1152.00 q^{33} +3048.00 q^{34} +2950.00 q^{35} -3312.00 q^{36} -5518.00 q^{37} -10960.0 q^{38} +6636.00 q^{39} -1600.00 q^{40} -378.000 q^{41} -2832.00 q^{42} -2434.00 q^{43} +3072.00 q^{44} +5175.00 q^{45} +6264.00 q^{46} +13122.0 q^{47} +1536.00 q^{48} -2883.00 q^{49} +2500.00 q^{50} +4572.00 q^{51} +17696.0 q^{52} -9174.00 q^{53} -10800.0 q^{54} -4800.00 q^{55} -7552.00 q^{56} -16440.0 q^{57} +23640.0 q^{58} -34980.0 q^{59} -2400.00 q^{60} -9838.00 q^{61} -27472.0 q^{62} +24426.0 q^{63} +4096.00 q^{64} -27650.0 q^{65} +4608.00 q^{66} +33722.0 q^{67} +12192.0 q^{68} +9396.00 q^{69} +11800.0 q^{70} +70212.0 q^{71} -13248.0 q^{72} +21986.0 q^{73} -22072.0 q^{74} +3750.00 q^{75} -43840.0 q^{76} -22656.0 q^{77} +26544.0 q^{78} +4520.00 q^{79} -6400.00 q^{80} +34101.0 q^{81} -1512.00 q^{82} -109074. q^{83} -11328.0 q^{84} -19050.0 q^{85} -9736.00 q^{86} +35460.0 q^{87} +12288.0 q^{88} +38490.0 q^{89} +20700.0 q^{90} -130508. q^{91} +25056.0 q^{92} -41208.0 q^{93} +52488.0 q^{94} +68500.0 q^{95} +6144.00 q^{96} -1918.00 q^{97} -11532.0 q^{98} -39744.0 q^{99} +O(q^{100})\)

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
$3$	6.00000	0.384900	0.192450	−	0.981307i	$-0.438357\pi$
$3$	6.00000	0.384900	0.192450	+	0.981307i	$0.438357\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	24.0000	0.272166
$7$	−118.000	−0.910200	−0.455100	−	0.890440i	$-0.650397\pi$
$7$	−118.000	−0.910200	−0.455100	+	0.890440i	$0.650397\pi$
$8$	64.0000	0.353553
$9$	−207.000	−0.851852
$10$	−100.000	−0.316228
$11$	192.000	0.478431	0.239216	−	0.970966i	$-0.423110\pi$
$11$	192.000	0.478431	0.239216	+	0.970966i	$0.423110\pi$
$12$	96.0000	0.192450
$13$	1106.00	1.81508	0.907542	−	0.419961i	$-0.137956\pi$
$13$	1106.00	1.81508	0.907542	+	0.419961i	$0.137956\pi$
$14$	−472.000	−0.643609
$15$	−150.000	−0.172133
$16$	256.000	0.250000
$17$	762.000	0.639488	0.319744	−	0.947504i	$-0.396403\pi$
$17$	762.000	0.639488	0.319744	+	0.947504i	$0.396403\pi$
$18$	−828.000	−0.602350
$19$	−2740.00	−1.74127	−0.870636	−	0.491928i	$-0.836292\pi$
$19$	−2740.00	−1.74127	−0.870636	+	0.491928i	$0.836292\pi$
$20$	−400.000	−0.223607
$21$	−708.000	−0.350336
$22$	768.000	0.338302
$23$	1566.00	0.617266	0.308633	−	0.951181i	$-0.400129\pi$
$23$	1566.00	0.617266	0.308633	+	0.951181i	$0.400129\pi$
$24$	384.000	0.136083
$25$	625.000	0.200000
$26$	4424.00	1.28346
$27$	−2700.00	−0.712778
$28$	−1888.00	−0.455100
$29$	5910.00	1.30495	0.652473	−	0.757812i	$-0.273732\pi$
$29$	5910.00	1.30495	0.652473	+	0.757812i	$0.273732\pi$
$30$	−600.000	−0.121716
$31$	−6868.00	−1.28359	−0.641795	−	0.766877i	$-0.721810\pi$
$31$	−6868.00	−1.28359	−0.641795	+	0.766877i	$0.721810\pi$
$32$	1024.00	0.176777
$33$	1152.00	0.184148
$34$	3048.00	0.452187
$35$	2950.00	0.407054
$36$	−3312.00	−0.425926
$37$	−5518.00	−0.662640	−0.331320	−	0.943519i	$-0.607494\pi$
$37$	−5518.00	−0.662640	−0.331320	+	0.943519i	$0.607494\pi$
$38$	−10960.0	−1.23127
$39$	6636.00	0.698626
$40$	−1600.00	−0.158114
$41$	−378.000	−0.0351182	−0.0175591	−	0.999846i	$-0.505590\pi$
$41$	−378.000	−0.0351182	−0.0175591	+	0.999846i	$0.505590\pi$
$42$	−2832.00	−0.247725
$43$	−2434.00	−0.200747	−0.100374	−	0.994950i	$-0.532004\pi$
$43$	−2434.00	−0.200747	−0.100374	+	0.994950i	$0.532004\pi$
$44$	3072.00	0.239216
$45$	5175.00	0.380960
$46$	6264.00	0.436473
$47$	13122.0	0.866474	0.433237	−	0.901280i	$-0.357371\pi$
$47$	13122.0	0.866474	0.433237	+	0.901280i	$0.357371\pi$
$48$	1536.00	0.0962250
$49$	−2883.00	−0.171536
$50$	2500.00	0.141421
$51$	4572.00	0.246139
$52$	17696.0	0.907542
$53$	−9174.00	−0.448610	−0.224305	−	0.974519i	$-0.572011\pi$
$53$	−9174.00	−0.448610	−0.224305	+	0.974519i	$0.572011\pi$
$54$	−10800.0	−0.504010
$55$	−4800.00	−0.213961
$56$	−7552.00	−0.321804
$57$	−16440.0	−0.670216
$58$	23640.0	0.922736
$59$	−34980.0	−1.30825	−0.654124	−	0.756388i	$-0.726962\pi$
$59$	−34980.0	−1.30825	−0.654124	+	0.756388i	$0.726962\pi$
$60$	−2400.00	−0.0860663
$61$	−9838.00	−0.338518	−0.169259	−	0.985572i	$-0.554137\pi$
$61$	−9838.00	−0.338518	−0.169259	+	0.985572i	$0.554137\pi$
$62$	−27472.0	−0.907635
$63$	24426.0	0.775356
$64$	4096.00	0.125000
$65$	−27650.0	−0.811730
$66$	4608.00	0.130212
$67$	33722.0	0.917754	0.458877	−	0.888500i	$-0.348252\pi$
$67$	33722.0	0.917754	0.458877	+	0.888500i	$0.348252\pi$
$68$	12192.0	0.319744
$69$	9396.00	0.237586
$70$	11800.0	0.287831
$71$	70212.0	1.65297	0.826486	−	0.562957i	$-0.190336\pi$
$71$	70212.0	1.65297	0.826486	+	0.562957i	$0.190336\pi$
$72$	−13248.0	−0.301175
$73$	21986.0	0.482880	0.241440	−	0.970416i	$-0.422380\pi$
$73$	21986.0	0.482880	0.241440	+	0.970416i	$0.422380\pi$
$74$	−22072.0	−0.468557
$75$	3750.00	0.0769800
$76$	−43840.0	−0.870636
$77$	−22656.0	−0.435468
$78$	26544.0	0.494003
$79$	4520.00	0.0814837	0.0407418	−	0.999170i	$-0.487028\pi$
$79$	4520.00	0.0814837	0.0407418	+	0.999170i	$0.487028\pi$
$80$	−6400.00	−0.111803
$81$	34101.0	0.577503
$82$	−1512.00	−0.0248323
$83$	−109074.	−1.73790	−0.868952	−	0.494896i	$-0.835206\pi$
$83$	−109074.	−1.73790	−0.868952	+	0.494896i	$0.835206\pi$
$84$	−11328.0	−0.175168
$85$	−19050.0	−0.285988
$86$	−9736.00	−0.141950
$87$	35460.0	0.502274
$88$	12288.0	0.169151
$89$	38490.0	0.515078	0.257539	−	0.966268i	$-0.417088\pi$
$89$	38490.0	0.515078	0.257539	+	0.966268i	$0.417088\pi$
$90$	20700.0	0.269379
$91$	−130508.	−1.65209
$92$	25056.0	0.308633
$93$	−41208.0	−0.494054
$94$	52488.0	0.612689
$95$	68500.0	0.778720
$96$	6144.00	0.0680414
$97$	−1918.00	−0.0206976	−0.0103488	−	0.999946i	$-0.503294\pi$
$97$	−1918.00	−0.0206976	−0.0103488	+	0.999946i	$0.503294\pi$
$98$	−11532.0	−0.121294
$99$	−39744.0	−0.407553
$100$	10000.0	0.100000
$101$	77622.0	0.757149	0.378575	−	0.925571i	$-0.376414\pi$
$101$	77622.0	0.757149	0.378575	+	0.925571i	$0.376414\pi$
$102$	18288.0	0.174047
$103$	−46714.0	−0.433864	−0.216932	−	0.976187i	$-0.569605\pi$
$103$	−46714.0	−0.433864	−0.216932	+	0.976187i	$0.569605\pi$
$104$	70784.0	0.641729
$105$	17700.0	0.156675
$106$	−36696.0	−0.317215
$107$	−1038.00	−0.00876472	−0.00438236	−	0.999990i	$-0.501395\pi$
$107$	−1038.00	−0.00876472	−0.00438236	+	0.999990i	$0.501395\pi$
$108$	−43200.0	−0.356389
$109$	206930.	1.66823	0.834117	−	0.551587i	$-0.185977\pi$
$109$	206930.	1.66823	0.834117	+	0.551587i	$0.185977\pi$
$110$	−19200.0	−0.151293
$111$	−33108.0	−0.255050
$112$	−30208.0	−0.227550
$113$	139386.	1.02689	0.513444	−	0.858123i	$-0.328369\pi$
$113$	139386.	1.02689	0.513444	+	0.858123i	$0.328369\pi$
$114$	−65760.0	−0.473914
$115$	−39150.0	−0.276050
$116$	94560.0	0.652473
$117$	−228942.	−1.54618
$118$	−139920.	−0.925070
$119$	−89916.0	−0.582062
$120$	−9600.00	−0.0608581
$121$	−124187.	−0.771104
$122$	−39352.0	−0.239369
$123$	−2268.00	−0.0135170
$124$	−109888.	−0.641795
$125$	−15625.0	−0.0894427
$126$	97704.0	0.548259
$127$	299882.	1.64984	0.824919	−	0.565252i	$-0.191221\pi$
$127$	299882.	1.64984	0.824919	+	0.565252i	$0.191221\pi$
$128$	16384.0	0.0883883
$129$	−14604.0	−0.0772676
$130$	−110600.	−0.573980
$131$	7872.00	0.0400781	0.0200390	−	0.999799i	$-0.493621\pi$
$131$	7872.00	0.0400781	0.0200390	+	0.999799i	$0.493621\pi$
$132$	18432.0	0.0920741
$133$	323320.	1.58491
$134$	134888.	0.648950
$135$	67500.0	0.318764
$136$	48768.0	0.226093
$137$	−164238.	−0.747605	−0.373803	−	0.927508i	$-0.621946\pi$
$137$	−164238.	−0.747605	−0.373803	+	0.927508i	$0.621946\pi$
$138$	37584.0	0.167998
$139$	−282100.	−1.23841	−0.619207	−	0.785228i	$-0.712546\pi$
$139$	−282100.	−1.23841	−0.619207	+	0.785228i	$0.712546\pi$
$140$	47200.0	0.203527
$141$	78732.0	0.333506
$142$	280848.	1.16883
$143$	212352.	0.868393
$144$	−52992.0	−0.212963
$145$	−147750.	−0.583590
$146$	87944.0	0.341448
$147$	−17298.0	−0.0660241
$148$	−88288.0	−0.331320
$149$	−388950.	−1.43525	−0.717626	−	0.696429i	$-0.754771\pi$
$149$	−388950.	−1.43525	−0.717626	+	0.696429i	$0.754771\pi$
$150$	15000.0	0.0544331
$151$	−97948.0	−0.349585	−0.174793	−	0.984605i	$-0.555926\pi$
$151$	−97948.0	−0.349585	−0.174793	+	0.984605i	$0.555926\pi$
$152$	−175360.	−0.615633
$153$	−157734.	−0.544749
$154$	−90624.0	−0.307923
$155$	171700.	0.574039
$156$	106176.	0.349313
$157$	−3718.00	−0.0120382	−0.00601908	−	0.999982i	$-0.501916\pi$
$157$	−3718.00	−0.0120382	−0.00601908	+	0.999982i	$0.501916\pi$
$158$	18080.0	0.0576177
$159$	−55044.0	−0.172670
$160$	−25600.0	−0.0790569
$161$	−184788.	−0.561835
$162$	136404.	0.408357
$163$	−43234.0	−0.127455	−0.0637274	−	0.997967i	$-0.520299\pi$
$163$	−43234.0	−0.127455	−0.0637274	+	0.997967i	$0.520299\pi$
$164$	−6048.00	−0.0175591
$165$	−28800.0	−0.0823536
$166$	−436296.	−1.22888
$167$	186522.	0.517534	0.258767	−	0.965940i	$-0.416684\pi$
$167$	186522.	0.517534	0.258767	+	0.965940i	$0.416684\pi$
$168$	−45312.0	−0.123863
$169$	851943.	2.29453
$170$	−76200.0	−0.202224
$171$	567180.	1.48331
$172$	−38944.0	−0.100374
$173$	−374454.	−0.951225	−0.475612	−	0.879655i	$-0.657774\pi$
$173$	−374454.	−0.951225	−0.475612	+	0.879655i	$0.657774\pi$
$174$	141840.	0.355161
$175$	−73750.0	−0.182040
$176$	49152.0	0.119608
$177$	−209880.	−0.503545
$178$	153960.	0.364215
$179$	272100.	0.634740	0.317370	−	0.948302i	$-0.397200\pi$
$179$	272100.	0.634740	0.317370	+	0.948302i	$0.397200\pi$
$180$	82800.0	0.190480
$181$	−75418.0	−0.171111	−0.0855556	−	0.996333i	$-0.527267\pi$
$181$	−75418.0	−0.171111	−0.0855556	+	0.996333i	$0.527267\pi$
$182$	−522032.	−1.16820
$183$	−59028.0	−0.130296
$184$	100224.	0.218236
$185$	137950.	0.296341
$186$	−164832.	−0.349349
$187$	146304.	0.305951
$188$	209952.	0.433237
$189$	318600.	0.648771
$190$	274000.	0.550638
$191$	−356988.	−0.708060	−0.354030	−	0.935234i	$-0.615189\pi$
$191$	−356988.	−0.708060	−0.354030	+	0.935234i	$0.615189\pi$
$192$	24576.0	0.0481125
$193$	−438694.	−0.847751	−0.423876	−	0.905720i	$-0.639331\pi$
$193$	−438694.	−0.847751	−0.423876	+	0.905720i	$0.639331\pi$
$194$	−7672.00	−0.0146354
$195$	−165900.	−0.312435
$196$	−46128.0	−0.0857678
$197$	−156798.	−0.287856	−0.143928	−	0.989588i	$-0.545973\pi$
$197$	−156798.	−0.287856	−0.143928	+	0.989588i	$0.545973\pi$
$198$	−158976.	−0.288183
$199$	−162520.	−0.290920	−0.145460	−	0.989364i	$-0.546466\pi$
$199$	−162520.	−0.290920	−0.145460	+	0.989364i	$0.546466\pi$
$200$	40000.0	0.0707107
$201$	202332.	0.353244
$202$	310488.	0.535385
$203$	−697380.	−1.18776
$204$	73152.0	0.123070
$205$	9450.00	0.0157053
$206$	−186856.	−0.306788
$207$	−324162.	−0.525819
$208$	283136.	0.453771
$209$	−526080.	−0.833079
$210$	70800.0	0.110786
$211$	−181648.	−0.280882	−0.140441	−	0.990089i	$-0.544852\pi$
$211$	−181648.	−0.280882	−0.140441	+	0.990089i	$0.544852\pi$
$212$	−146784.	−0.224305
$213$	421272.	0.636229
$214$	−4152.00	−0.00619759
$215$	60850.0	0.0897769
$216$	−172800.	−0.252005
$217$	810424.	1.16832
$218$	827720.	1.17962
$219$	131916.	0.185861
$220$	−76800.0	−0.106980
$221$	842772.	1.16073
$222$	−132432.	−0.180348
$223$	−288274.	−0.388189	−0.194095	−	0.980983i	$-0.562177\pi$
$223$	−288274.	−0.388189	−0.194095	+	0.980983i	$0.562177\pi$
$224$	−120832.	−0.160902
$225$	−129375.	−0.170370
$226$	557544.	0.726119
$227$	1.12552e6	1.44974	0.724869	−	0.688887i	$-0.241900\pi$
$227$	1.12552e6	1.44974	0.724869	+	0.688887i	$0.241900\pi$
$228$	−263040.	−0.335108
$229$	−415810.	−0.523970	−0.261985	−	0.965072i	$-0.584377\pi$
$229$	−415810.	−0.523970	−0.261985	+	0.965072i	$0.584377\pi$
$230$	−156600.	−0.195197
$231$	−135936.	−0.167612
$232$	378240.	0.461368
$233$	770586.	0.929889	0.464945	−	0.885340i	$-0.346074\pi$
$233$	770586.	0.929889	0.464945	+	0.885340i	$0.346074\pi$
$234$	−915768.	−1.09332
$235$	−328050.	−0.387499
$236$	−559680.	−0.654124
$237$	27120.0	0.0313631
$238$	−359664.	−0.411580
$239$	−595320.	−0.674149	−0.337074	−	0.941478i	$-0.609437\pi$
$239$	−595320.	−0.674149	−0.337074	+	0.941478i	$0.609437\pi$
$240$	−38400.0	−0.0430331
$241$	273902.	0.303775	0.151888	−	0.988398i	$-0.451465\pi$
$241$	273902.	0.303775	0.151888	+	0.988398i	$0.451465\pi$
$242$	−496748.	−0.545253
$243$	860706.	0.935059
$244$	−157408.	−0.169259
$245$	72075.0	0.0767131
$246$	−9072.00	−0.00955796
$247$	−3.03044e6	−3.16055
$248$	−439552.	−0.453817
$249$	−654444.	−0.668920
$250$	−62500.0	−0.0632456
$251$	850752.	0.852351	0.426176	−	0.904640i	$-0.359861\pi$
$251$	850752.	0.852351	0.426176	+	0.904640i	$0.359861\pi$
$252$	390816.	0.387678
$253$	300672.	0.295319
$254$	1.19953e6	1.16661
$255$	−114300.	−0.110077
$256$	65536.0	0.0625000
$257$	825402.	0.779530	0.389765	−	0.920914i	$-0.372556\pi$
$257$	825402.	0.779530	0.389765	+	0.920914i	$0.372556\pi$
$258$	−58416.0	−0.0546365
$259$	651124.	0.603135
$260$	−442400.	−0.405865
$261$	−1.22337e6	−1.11162
$262$	31488.0	0.0283395
$263$	1.36465e6	1.21655	0.608276	−	0.793726i	$-0.291861\pi$
$263$	1.36465e6	1.21655	0.608276	+	0.793726i	$0.291861\pi$
$264$	73728.0	0.0651062
$265$	229350.	0.200625
$266$	1.29328e6	1.12070
$267$	230940.	0.198254
$268$	539552.	0.458877
$269$	−113310.	−0.0954745	−0.0477373	−	0.998860i	$-0.515201\pi$
$269$	−113310.	−0.0954745	−0.0477373	+	0.998860i	$0.515201\pi$
$270$	270000.	0.225400
$271$	−849628.	−0.702758	−0.351379	−	0.936233i	$-0.614287\pi$
$271$	−849628.	−0.702758	−0.351379	+	0.936233i	$0.614287\pi$
$272$	195072.	0.159872
$273$	−783048.	−0.635890
$274$	−656952.	−0.528637
$275$	120000.	0.0956862
$276$	150336.	0.118793
$277$	438602.	0.343456	0.171728	−	0.985144i	$-0.445065\pi$
$277$	438602.	0.343456	0.171728	+	0.985144i	$0.445065\pi$
$278$	−1.12840e6	−0.875691
$279$	1.42168e6	1.09343
$280$	188800.	0.143915
$281$	−1.45670e6	−1.10053	−0.550267	−	0.834989i	$-0.685474\pi$
$281$	−1.45670e6	−1.10053	−0.550267	+	0.834989i	$0.685474\pi$
$282$	314928.	0.235824
$283$	−120394.	−0.0893591	−0.0446795	−	0.999001i	$-0.514227\pi$
$283$	−120394.	−0.0893591	−0.0446795	+	0.999001i	$0.514227\pi$
$284$	1.12339e6	0.826486
$285$	411000.	0.299730
$286$	849408.	0.614047
$287$	44604.0	0.0319646
$288$	−211968.	−0.150588
$289$	−839213.	−0.591055
$290$	−591000.	−0.412660
$291$	−11508.0	−0.00796650
$292$	351776.	0.241440
$293$	−2.64209e6	−1.79796	−0.898978	−	0.437993i	$-0.855689\pi$
$293$	−2.64209e6	−1.79796	−0.898978	+	0.437993i	$0.855689\pi$
$294$	−69192.0	−0.0466861
$295$	874500.	0.585066
$296$	−353152.	−0.234278
$297$	−518400.	−0.341015
$298$	−1.55580e6	−1.01488
$299$	1.73200e6	1.12039
$300$	60000.0	0.0384900
$301$	287212.	0.182720
$302$	−391792.	−0.247194
$303$	465732.	0.291427
$304$	−701440.	−0.435318
$305$	245950.	0.151390
$306$	−630936.	−0.385196
$307$	−1.44756e6	−0.876577	−0.438288	−	0.898834i	$-0.644415\pi$
$307$	−1.44756e6	−0.876577	−0.438288	+	0.898834i	$0.644415\pi$
$308$	−362496.	−0.217734
$309$	−280284.	−0.166994
$310$	686800.	0.405907
$311$	−928068.	−0.544100	−0.272050	−	0.962283i	$-0.587702\pi$
$311$	−928068.	−0.544100	−0.272050	+	0.962283i	$0.587702\pi$
$312$	424704.	0.247002
$313$	2.29563e6	1.32446	0.662232	−	0.749299i	$-0.269609\pi$
$313$	2.29563e6	1.32446	0.662232	+	0.749299i	$0.269609\pi$
$314$	−14872.0	−0.00851227
$315$	−610650.	−0.346750
$316$	72320.0	0.0407418
$317$	2.73652e6	1.52950	0.764752	−	0.644324i	$-0.222861\pi$
$317$	2.73652e6	1.52950	0.764752	+	0.644324i	$0.222861\pi$
$318$	−220176.	−0.122096
$319$	1.13472e6	0.624327
$320$	−102400.	−0.0559017
$321$	−6228.00	−0.00337354
$322$	−739152.	−0.397278
$323$	−2.08788e6	−1.11352
$324$	545616.	0.288752
$325$	691250.	0.363017
$326$	−172936.	−0.0901242
$327$	1.24158e6	0.642104
$328$	−24192.0	−0.0124162
$329$	−1.54840e6	−0.788665
$330$	−115200.	−0.0582328
$331$	3.81879e6	1.91583	0.957913	−	0.287059i	$-0.0926776\pi$
$331$	3.81879e6	1.91583	0.957913	+	0.287059i	$0.0926776\pi$
$332$	−1.74518e6	−0.868952
$333$	1.14223e6	0.564471
$334$	746088.	0.365952
$335$	−843050.	−0.410432
$336$	−181248.	−0.0875841
$337$	−2.21088e6	−1.06045	−0.530225	−	0.847857i	$-0.677892\pi$
$337$	−2.21088e6	−1.06045	−0.530225	+	0.847857i	$0.677892\pi$
$338$	3.40777e6	1.62248
$339$	836316.	0.395249
$340$	−304800.	−0.142994
$341$	−1.31866e6	−0.614109
$342$	2.26872e6	1.04886
$343$	2.32342e6	1.06633
$344$	−155776.	−0.0709748
$345$	−234900.	−0.106252
$346$	−1.49782e6	−0.672618
$347$	−2.32724e6	−1.03757	−0.518785	−	0.854905i	$-0.673615\pi$
$347$	−2.32724e6	−1.03757	−0.518785	+	0.854905i	$0.673615\pi$
$348$	567360.	0.251137
$349$	−311290.	−0.136805	−0.0684024	−	0.997658i	$-0.521790\pi$
$349$	−311290.	−0.136805	−0.0684024	+	0.997658i	$0.521790\pi$
$350$	−295000.	−0.128722
$351$	−2.98620e6	−1.29375
$352$	196608.	0.0845755
$353$	−3.08657e6	−1.31838	−0.659189	−	0.751977i	$-0.729100\pi$
$353$	−3.08657e6	−1.31838	−0.659189	+	0.751977i	$0.729100\pi$
$354$	−839520.	−0.356060
$355$	−1.75530e6	−0.739232
$356$	615840.	0.257539
$357$	−539496.	−0.224036
$358$	1.08840e6	0.448829
$359$	−3.53076e6	−1.44588	−0.722940	−	0.690911i	$-0.757210\pi$
$359$	−3.53076e6	−1.44588	−0.722940	+	0.690911i	$0.757210\pi$
$360$	331200.	0.134690
$361$	5.03150e6	2.03203
$362$	−301672.	−0.120994
$363$	−745122.	−0.296798
$364$	−2.08813e6	−0.826045
$365$	−549650.	−0.215950
$366$	−236112.	−0.0921330
$367$	35762.0	0.0138598	0.00692989	−	0.999976i	$-0.497794\pi$
$367$	35762.0	0.0138598	0.00692989	+	0.999976i	$0.497794\pi$
$368$	400896.	0.154316
$369$	78246.0	0.0299155
$370$	551800.	0.209545
$371$	1.08253e6	0.408325
$372$	−659328.	−0.247027
$373$	−1.71525e6	−0.638346	−0.319173	−	0.947696i	$-0.603405\pi$
$373$	−1.71525e6	−0.638346	−0.319173	+	0.947696i	$0.603405\pi$
$374$	585216.	0.216340
$375$	−93750.0	−0.0344265
$376$	839808.	0.306345
$377$	6.53646e6	2.36859
$378$	1.27440e6	0.458750
$379$	−3.10174e6	−1.10919	−0.554597	−	0.832119i	$-0.687127\pi$
$379$	−3.10174e6	−1.10919	−0.554597	+	0.832119i	$0.687127\pi$
$380$	1.09600e6	0.389360
$381$	1.79929e6	0.635023
$382$	−1.42795e6	−0.500674
$383$	5.31949e6	1.85299	0.926494	−	0.376309i	$-0.122807\pi$
$383$	5.31949e6	1.85299	0.926494	+	0.376309i	$0.122807\pi$
$384$	98304.0	0.0340207
$385$	566400.	0.194747
$386$	−1.75478e6	−0.599451
$387$	503838.	0.171007
$388$	−30688.0	−0.0103488
$389$	1.16145e6	0.389158	0.194579	−	0.980887i	$-0.437666\pi$
$389$	1.16145e6	0.389158	0.194579	+	0.980887i	$0.437666\pi$
$390$	−663600.	−0.220925
$391$	1.19329e6	0.394734
$392$	−184512.	−0.0606470
$393$	47232.0	0.0154261
$394$	−627192.	−0.203545
$395$	−113000.	−0.0364406
$396$	−635904.	−0.203776
$397$	628562.	0.200157	0.100079	−	0.994980i	$-0.468091\pi$
$397$	628562.	0.200157	0.100079	+	0.994980i	$0.468091\pi$
$398$	−650080.	−0.205712
$399$	1.93992e6	0.610031
$400$	160000.	0.0500000
$401$	−2.72432e6	−0.846052	−0.423026	−	0.906118i	$-0.639032\pi$
$401$	−2.72432e6	−0.846052	−0.423026	+	0.906118i	$0.639032\pi$
$402$	809328.	0.249781
$403$	−7.59601e6	−2.32982
$404$	1.24195e6	0.378575
$405$	−852525.	−0.258267
$406$	−2.78952e6	−0.839875
$407$	−1.05946e6	−0.317027
$408$	292608.	0.0870233
$409$	1.78019e6	0.526209	0.263104	−	0.964767i	$-0.415254\pi$
$409$	1.78019e6	0.526209	0.263104	+	0.964767i	$0.415254\pi$
$410$	37800.0	0.0111053
$411$	−985428.	−0.287753
$412$	−747424.	−0.216932
$413$	4.12764e6	1.19077
$414$	−1.29665e6	−0.371810
$415$	2.72685e6	0.777215
$416$	1.13254e6	0.320865
$417$	−1.69260e6	−0.476666
$418$	−2.10432e6	−0.589076
$419$	650580.	0.181036	0.0905181	−	0.995895i	$-0.471148\pi$
$419$	650580.	0.181036	0.0905181	+	0.995895i	$0.471148\pi$
$420$	283200.	0.0783376
$421$	−3.54060e6	−0.973579	−0.486790	−	0.873519i	$-0.661832\pi$
$421$	−3.54060e6	−0.973579	−0.486790	+	0.873519i	$0.661832\pi$
$422$	−726592.	−0.198614
$423$	−2.71625e6	−0.738107
$424$	−587136.	−0.158608
$425$	476250.	0.127898
$426$	1.68509e6	0.449882
$427$	1.16088e6	0.308119
$428$	−16608.0	−0.00438236
$429$	1.27411e6	0.334245
$430$	243400.	0.0634818
$431$	−548748.	−0.142292	−0.0711459	−	0.997466i	$-0.522666\pi$
$431$	−548748.	−0.142292	−0.0711459	+	0.997466i	$0.522666\pi$
$432$	−691200.	−0.178195
$433$	−1.49241e6	−0.382534	−0.191267	−	0.981538i	$-0.561260\pi$
$433$	−1.49241e6	−0.382534	−0.191267	+	0.981538i	$0.561260\pi$
$434$	3.24170e6	0.826129
$435$	−886500.	−0.224624
$436$	3.31088e6	0.834117
$437$	−4.29084e6	−1.07483
$438$	527664.	0.131423
$439$	4.86212e6	1.20411	0.602053	−	0.798456i	$-0.294350\pi$
$439$	4.86212e6	1.20411	0.602053	+	0.798456i	$0.294350\pi$
$440$	−307200.	−0.0756466
$441$	596781.	0.146123
$442$	3.37109e6	0.820757
$443$	−1.86155e6	−0.450678	−0.225339	−	0.974280i	$-0.572349\pi$
$443$	−1.86155e6	−0.450678	−0.225339	+	0.974280i	$0.572349\pi$
$444$	−529728.	−0.127525
$445$	−962250.	−0.230350
$446$	−1.15310e6	−0.274491
$447$	−2.33370e6	−0.552429
$448$	−483328.	−0.113775
$449$	3.73719e6	0.874841	0.437421	−	0.899257i	$-0.355892\pi$
$449$	3.73719e6	0.874841	0.437421	+	0.899257i	$0.355892\pi$
$450$	−517500.	−0.120470
$451$	−72576.0	−0.0168016
$452$	2.23018e6	0.513444
$453$	−587688.	−0.134555
$454$	4.50209e6	1.02512
$455$	3.26270e6	0.738837
$456$	−1.05216e6	−0.236957
$457$	−6.48276e6	−1.45201	−0.726005	−	0.687690i	$-0.758625\pi$
$457$	−6.48276e6	−1.45201	−0.726005	+	0.687690i	$0.758625\pi$
$458$	−1.66324e6	−0.370503
$459$	−2.05740e6	−0.455813
$460$	−626400.	−0.138025
$461$	1.50910e6	0.330724	0.165362	−	0.986233i	$-0.447121\pi$
$461$	1.50910e6	0.330724	0.165362	+	0.986233i	$0.447121\pi$
$462$	−543744.	−0.118519
$463$	8.68401e6	1.88264	0.941321	−	0.337513i	$-0.109586\pi$
$463$	8.68401e6	1.88264	0.941321	+	0.337513i	$0.109586\pi$
$464$	1.51296e6	0.326236
$465$	1.03020e6	0.220948
$466$	3.08234e6	0.657531
$467$	6.96412e6	1.47766	0.738829	−	0.673893i	$-0.235379\pi$
$467$	6.96412e6	1.47766	0.738829	+	0.673893i	$0.235379\pi$
$468$	−3.66307e6	−0.773091
$469$	−3.97920e6	−0.835340
$470$	−1.31220e6	−0.274003
$471$	−22308.0	−0.00463349
$472$	−2.23872e6	−0.462535
$473$	−467328.	−0.0960437
$474$	108480.	0.0221771
$475$	−1.71250e6	−0.348254
$476$	−1.43866e6	−0.291031
$477$	1.89902e6	0.382149
$478$	−2.38128e6	−0.476695
$479$	−5.51052e6	−1.09737	−0.548686	−	0.836029i	$-0.684872\pi$
$479$	−5.51052e6	−1.09737	−0.548686	+	0.836029i	$0.684872\pi$
$480$	−153600.	−0.0304290
$481$	−6.10291e6	−1.20275
$482$	1.09561e6	0.214802
$483$	−1.10873e6	−0.216251
$484$	−1.98699e6	−0.385552
$485$	47950.0	0.00925623
$486$	3.44282e6	0.661187
$487$	5.51808e6	1.05430	0.527152	−	0.849771i	$-0.323260\pi$
$487$	5.51808e6	1.05430	0.527152	+	0.849771i	$0.323260\pi$
$488$	−629632.	−0.119684
$489$	−259404.	−0.0490574
$490$	288300.	0.0542443
$491$	−1.51277e6	−0.283184	−0.141592	−	0.989925i	$-0.545222\pi$
$491$	−1.51277e6	−0.283184	−0.141592	+	0.989925i	$0.545222\pi$
$492$	−36288.0	−0.00675850
$493$	4.50342e6	0.834498
$494$	−1.21218e7	−2.23485
$495$	993600.	0.182263
$496$	−1.75821e6	−0.320897
$497$	−8.28502e6	−1.50454
$498$	−2.61778e6	−0.472998
$499$	−1.93042e6	−0.347057	−0.173528	−	0.984829i	$-0.555517\pi$
$499$	−1.93042e6	−0.347057	−0.173528	+	0.984829i	$0.555517\pi$
$500$	−250000.	−0.0447214
$501$	1.11913e6	0.199199
$502$	3.40301e6	0.602703
$503$	6.73105e6	1.18621	0.593106	−	0.805124i	$-0.297901\pi$
$503$	6.73105e6	1.18621	0.593106	+	0.805124i	$0.297901\pi$
$504$	1.56326e6	0.274130
$505$	−1.94055e6	−0.338607
$506$	1.20269e6	0.208822
$507$	5.11166e6	0.883165
$508$	4.79811e6	0.824919
$509$	−556650.	−0.0952331	−0.0476165	−	0.998866i	$-0.515163\pi$
$509$	−556650.	−0.0952331	−0.0476165	+	0.998866i	$0.515163\pi$
$510$	−457200.	−0.0778360
$511$	−2.59435e6	−0.439517
$512$	262144.	0.0441942
$513$	7.39800e6	1.24114
$514$	3.30161e6	0.551211
$515$	1.16785e6	0.194030
$516$	−233664.	−0.0386338
$517$	2.51942e6	0.414548
$518$	2.60450e6	0.426481
$519$	−2.24672e6	−0.366127
$520$	−1.76960e6	−0.286990
$521$	1.01110e7	1.63192	0.815962	−	0.578106i	$-0.196208\pi$
$521$	1.01110e7	1.63192	0.815962	+	0.578106i	$0.196208\pi$
$522$	−4.89348e6	−0.786034
$523$	−7.03719e6	−1.12498	−0.562491	−	0.826804i	$-0.690157\pi$
$523$	−7.03719e6	−1.12498	−0.562491	+	0.826804i	$0.690157\pi$
$524$	125952.	0.0200390
$525$	−442500.	−0.0700672
$526$	5.45858e6	0.860232
$527$	−5.23342e6	−0.820840
$528$	294912.	0.0460371
$529$	−3.98399e6	−0.618983
$530$	917400.	0.141863
$531$	7.24086e6	1.11443
$532$	5.17312e6	0.792453
$533$	−418068.	−0.0637425
$534$	923760.	0.140186
$535$	25950.0	0.00391970
$536$	2.15821e6	0.324475
$537$	1.63260e6	0.244312
$538$	−453240.	−0.0675107
$539$	−553536.	−0.0820680
$540$	1.08000e6	0.159382
$541$	−4.23114e6	−0.621533	−0.310766	−	0.950486i	$-0.600586\pi$
$541$	−4.23114e6	−0.621533	−0.310766	+	0.950486i	$0.600586\pi$
$542$	−3.39851e6	−0.496925
$543$	−452508.	−0.0658608
$544$	780288.	0.113047
$545$	−5.17325e6	−0.746057
$546$	−3.13219e6	−0.449642
$547$	4.44024e6	0.634510	0.317255	−	0.948340i	$-0.397239\pi$
$547$	4.44024e6	0.634510	0.317255	+	0.948340i	$0.397239\pi$
$548$	−2.62781e6	−0.373803
$549$	2.03647e6	0.288367
$550$	480000.	0.0676604
$551$	−1.61934e7	−2.27227
$552$	601344.	0.0839992
$553$	−533360.	−0.0741665
$554$	1.75441e6	0.242860
$555$	827700.	0.114062
$556$	−4.51360e6	−0.619207
$557$	−9.01448e6	−1.23113	−0.615563	−	0.788088i	$-0.711071\pi$
$557$	−9.01448e6	−1.23113	−0.615563	+	0.788088i	$0.711071\pi$
$558$	5.68670e6	0.773170
$559$	−2.69200e6	−0.364373
$560$	755200.	0.101763
$561$	877824.	0.117761
$562$	−5.82679e6	−0.778196
$563$	−9.81287e6	−1.30474	−0.652372	−	0.757899i	$-0.726226\pi$
$563$	−9.81287e6	−1.30474	−0.652372	+	0.757899i	$0.726226\pi$
$564$	1.25971e6	0.166753
$565$	−3.48465e6	−0.459238
$566$	−481576.	−0.0631864
$567$	−4.02392e6	−0.525644
$568$	4.49357e6	0.584414
$569$	1.33152e7	1.72412	0.862061	−	0.506804i	$-0.169173\pi$
$569$	1.33152e7	1.72412	0.862061	+	0.506804i	$0.169173\pi$
$570$	1.64400e6	0.211941
$571$	9.95895e6	1.27827	0.639136	−	0.769094i	$-0.279292\pi$
$571$	9.95895e6	1.27827	0.639136	+	0.769094i	$0.279292\pi$
$572$	3.39763e6	0.434196
$573$	−2.14193e6	−0.272533
$574$	178416.	0.0226024
$575$	978750.	0.123453
$576$	−847872.	−0.106481
$577$	4.50372e6	0.563160	0.281580	−	0.959538i	$-0.409141\pi$
$577$	4.50372e6	0.563160	0.281580	+	0.959538i	$0.409141\pi$
$578$	−3.35685e6	−0.417939
$579$	−2.63216e6	−0.326300
$580$	−2.36400e6	−0.291795
$581$	1.28707e7	1.58184
$582$	−46032.0	−0.00563316
$583$	−1.76141e6	−0.214629
$584$	1.40710e6	0.170724
$585$	5.72355e6	0.691474
$586$	−1.05684e7	−1.27135
$587$	625842.	0.0749669	0.0374834	−	0.999297i	$-0.488066\pi$
$587$	625842.	0.0749669	0.0374834	+	0.999297i	$0.488066\pi$
$588$	−276768.	−0.0330121
$589$	1.88183e7	2.23508
$590$	3.49800e6	0.413704
$591$	−940788.	−0.110796
$592$	−1.41261e6	−0.165660
$593$	−2.50385e6	−0.292397	−0.146198	−	0.989255i	$-0.546704\pi$
$593$	−2.50385e6	−0.292397	−0.146198	+	0.989255i	$0.546704\pi$
$594$	−2.07360e6	−0.241134
$595$	2.24790e6	0.260306
$596$	−6.22320e6	−0.717626
$597$	−975120.	−0.111975
$598$	6.92798e6	0.792235
$599$	−756480.	−0.0861451	−0.0430725	−	0.999072i	$-0.513715\pi$
$599$	−756480.	−0.0861451	−0.0430725	+	0.999072i	$0.513715\pi$
$600$	240000.	0.0272166
$601$	−1.38565e7	−1.56483	−0.782413	−	0.622760i	$-0.786011\pi$
$601$	−1.38565e7	−1.56483	−0.782413	+	0.622760i	$0.786011\pi$
$602$	1.14885e6	0.129203
$603$	−6.98045e6	−0.781791
$604$	−1.56717e6	−0.174793
$605$	3.10468e6	0.344848
$606$	1.86293e6	0.206070
$607$	1.13772e7	1.25333	0.626663	−	0.779291i	$-0.284420\pi$
$607$	1.13772e7	1.25333	0.626663	+	0.779291i	$0.284420\pi$
$608$	−2.80576e6	−0.307816
$609$	−4.18428e6	−0.457170
$610$	983800.	0.107049
$611$	1.45129e7	1.57272
$612$	−2.52374e6	−0.272375
$613$	−7.00161e6	−0.752570	−0.376285	−	0.926504i	$-0.622799\pi$
$613$	−7.00161e6	−0.752570	−0.376285	+	0.926504i	$0.622799\pi$
$614$	−5.79023e6	−0.619833
$615$	56700.0	0.00604499
$616$	−1.44998e6	−0.153961
$617$	7.90300e6	0.835755	0.417878	−	0.908503i	$-0.362774\pi$
$617$	7.90300e6	0.835755	0.417878	+	0.908503i	$0.362774\pi$
$618$	−1.12114e6	−0.118083
$619$	4.02362e6	0.422076	0.211038	−	0.977478i	$-0.432316\pi$
$619$	4.02362e6	0.422076	0.211038	+	0.977478i	$0.432316\pi$
$620$	2.74720e6	0.287019
$621$	−4.22820e6	−0.439974
$622$	−3.71227e6	−0.384737
$623$	−4.54182e6	−0.468824
$624$	1.69882e6	0.174657
$625$	390625.	0.0400000
$626$	9.18250e6	0.936538
$627$	−3.15648e6	−0.320652
$628$	−59488.0	−0.00601908
$629$	−4.20472e6	−0.423750
$630$	−2.44260e6	−0.245189
$631$	−1.00227e7	−1.00210	−0.501049	−	0.865419i	$-0.667052\pi$
$631$	−1.00227e7	−1.00210	−0.501049	+	0.865419i	$0.667052\pi$
$632$	289280.	0.0288088
$633$	−1.08989e6	−0.108112
$634$	1.09461e7	1.08152
$635$	−7.49705e6	−0.737830
$636$	−880704.	−0.0863351
$637$	−3.18860e6	−0.311352
$638$	4.53888e6	0.441466
$639$	−1.45339e7	−1.40809
$640$	−409600.	−0.0395285
$641$	6.37390e6	0.612718	0.306359	−	0.951916i	$-0.400889\pi$
$641$	6.37390e6	0.612718	0.306359	+	0.951916i	$0.400889\pi$
$642$	−24912.0	−0.00238545
$643$	5.00457e6	0.477352	0.238676	−	0.971099i	$-0.423287\pi$
$643$	5.00457e6	0.477352	0.238676	+	0.971099i	$0.423287\pi$
$644$	−2.95661e6	−0.280918
$645$	365100.	0.0345551
$646$	−8.35152e6	−0.787380
$647$	−8.71928e6	−0.818879	−0.409440	−	0.912337i	$-0.634276\pi$
$647$	−8.71928e6	−0.818879	−0.409440	+	0.912337i	$0.634276\pi$
$648$	2.18246e6	0.204178
$649$	−6.71616e6	−0.625906
$650$	2.76500e6	0.256692
$651$	4.86254e6	0.449688
$652$	−691744.	−0.0637274
$653$	−1.58477e6	−0.145440	−0.0727201	−	0.997352i	$-0.523168\pi$
$653$	−1.58477e6	−0.145440	−0.0727201	+	0.997352i	$0.523168\pi$
$654$	4.96632e6	0.454036
$655$	−196800.	−0.0179235
$656$	−96768.0	−0.00877955
$657$	−4.55110e6	−0.411342
$658$	−6.19358e6	−0.557670
$659$	1.26410e7	1.13388	0.566940	−	0.823759i	$-0.308127\pi$
$659$	1.26410e7	1.13388	0.566940	+	0.823759i	$0.308127\pi$
$660$	−460800.	−0.0411768
$661$	−3.61572e6	−0.321878	−0.160939	−	0.986964i	$-0.551452\pi$
$661$	−3.61572e6	−0.321878	−0.160939	+	0.986964i	$0.551452\pi$
$662$	1.52752e7	1.35469
$663$	5.05663e6	0.446763
$664$	−6.98074e6	−0.614442
$665$	−8.08300e6	−0.708791
$666$	4.56890e6	0.399141
$667$	9.25506e6	0.805498
$668$	2.98435e6	0.258767
$669$	−1.72964e6	−0.149414
$670$	−3.37220e6	−0.290219
$671$	−1.88890e6	−0.161958
$672$	−724992.	−0.0619313
$673$	1.11313e7	0.947349	0.473675	−	0.880700i	$-0.342927\pi$
$673$	1.11313e7	0.947349	0.473675	+	0.880700i	$0.342927\pi$
$674$	−8.84351e6	−0.749851
$675$	−1.68750e6	−0.142556
$676$	1.36311e7	1.14727
$677$	−235518.	−0.0197493	−0.00987467	−	0.999951i	$-0.503143\pi$
$677$	−235518.	−0.0197493	−0.00987467	+	0.999951i	$0.503143\pi$
$678$	3.34526e6	0.279483
$679$	226324.	0.0188389
$680$	−1.21920e6	−0.101112
$681$	6.75313e6	0.558004
$682$	−5.27462e6	−0.434241
$683$	2.05830e7	1.68833	0.844164	−	0.536084i	$-0.180097\pi$
$683$	2.05830e7	1.68833	0.844164	+	0.536084i	$0.180097\pi$
$684$	9.07488e6	0.741653
$685$	4.10595e6	0.334339
$686$	9.29368e6	0.754011
$687$	−2.49486e6	−0.201676
$688$	−623104.	−0.0501868
$689$	−1.01464e7	−0.814265
$690$	−939600.	−0.0751312
$691$	−9.54825e6	−0.760727	−0.380363	−	0.924837i	$-0.624201\pi$
$691$	−9.54825e6	−0.760727	−0.380363	+	0.924837i	$0.624201\pi$
$692$	−5.99126e6	−0.475612
$693$	4.68979e6	0.370954
$694$	−9.30895e6	−0.733672
$695$	7.05250e6	0.553836
$696$	2.26944e6	0.177581
$697$	−288036.	−0.0224577
$698$	−1.24516e6	−0.0967357
$699$	4.62352e6	0.357915
$700$	−1.18000e6	−0.0910200
$701$	1.29304e6	0.0993843	0.0496921	−	0.998765i	$-0.484176\pi$
$701$	1.29304e6	0.0993843	0.0496921	+	0.998765i	$0.484176\pi$
$702$	−1.19448e7	−0.914821
$703$	1.51193e7	1.15384
$704$	786432.	0.0598039
$705$	−1.96830e6	−0.149148
$706$	−1.23463e7	−0.932234
$707$	−9.15940e6	−0.689157
$708$	−3.35808e6	−0.251772
$709$	−2.12720e7	−1.58926	−0.794628	−	0.607097i	$-0.792334\pi$
$709$	−2.12720e7	−1.58926	−0.794628	+	0.607097i	$0.792334\pi$
$710$	−7.02120e6	−0.522716
$711$	−935640.	−0.0694120
$712$	2.46336e6	0.182108
$713$	−1.07553e7	−0.792316
$714$	−2.15798e6	−0.158417
$715$	−5.30880e6	−0.388357
$716$	4.35360e6	0.317370
$717$	−3.57192e6	−0.259480
$718$	−1.41230e7	−1.02239
$719$	8.31732e6	0.600014	0.300007	−	0.953937i	$-0.403011\pi$
$719$	8.31732e6	0.600014	0.300007	+	0.953937i	$0.403011\pi$
$720$	1.32480e6	0.0952399
$721$	5.51225e6	0.394903
$722$	2.01260e7	1.43686
$723$	1.64341e6	0.116923
$724$	−1.20669e6	−0.0855556
$725$	3.69375e6	0.260989
$726$	−2.98049e6	−0.209868
$727$	−4.36740e6	−0.306469	−0.153235	−	0.988190i	$-0.548969\pi$
$727$	−4.36740e6	−0.306469	−0.153235	+	0.988190i	$0.548969\pi$
$728$	−8.35251e6	−0.584102
$729$	−3.12231e6	−0.217599
$730$	−2.19860e6	−0.152700
$731$	−1.85471e6	−0.128375
$732$	−944448.	−0.0651479
$733$	−4.05645e6	−0.278860	−0.139430	−	0.990232i	$-0.544527\pi$
$733$	−4.05645e6	−0.278860	−0.139430	+	0.990232i	$0.544527\pi$
$734$	143048.	0.00980035
$735$	432450.	0.0295269
$736$	1.60358e6	0.109118
$737$	6.47462e6	0.439082
$738$	312984.	0.0211535
$739$	768260.	0.0517484	0.0258742	−	0.999665i	$-0.491763\pi$
$739$	768260.	0.0517484	0.0258742	+	0.999665i	$0.491763\pi$
$740$	2.20720e6	0.148171
$741$	−1.81826e7	−1.21650
$742$	4.33013e6	0.288729
$743$	6.18781e6	0.411211	0.205605	−	0.978635i	$-0.434084\pi$
$743$	6.18781e6	0.411211	0.205605	+	0.978635i	$0.434084\pi$
$744$	−2.63731e6	−0.174674
$745$	9.72375e6	0.641864
$746$	−6.86102e6	−0.451379
$747$	2.25783e7	1.48044
$748$	2.34086e6	0.152976
$749$	122484.	0.00797765
$750$	−375000.	−0.0243432
$751$	1.81698e7	1.17557	0.587787	−	0.809016i	$-0.299999\pi$
$751$	1.81698e7	1.17557	0.587787	+	0.809016i	$0.299999\pi$
$752$	3.35923e6	0.216618
$753$	5.10451e6	0.328070
$754$	2.61458e7	1.67484
$755$	2.44870e6	0.156339
$756$	5.09760e6	0.324385
$757$	1.93494e7	1.22724	0.613618	−	0.789603i	$-0.289714\pi$
$757$	1.93494e7	1.22724	0.613618	+	0.789603i	$0.289714\pi$
$758$	−1.24070e7	−0.784318
$759$	1.80403e6	0.113668
$760$	4.38400e6	0.275319
$761$	−3.01992e7	−1.89031	−0.945155	−	0.326621i	$-0.894090\pi$
$761$	−3.01992e7	−1.89031	−0.945155	+	0.326621i	$0.894090\pi$
$762$	7.19717e6	0.449029
$763$	−2.44177e7	−1.51843
$764$	−5.71181e6	−0.354030
$765$	3.94335e6	0.243619
$766$	2.12779e7	1.31026
$767$	−3.86879e7	−2.37458
$768$	393216.	0.0240563
$769$	2.15854e7	1.31627	0.658134	−	0.752901i	$-0.271346\pi$
$769$	2.15854e7	1.31627	0.658134	+	0.752901i	$0.271346\pi$
$770$	2.26560e6	0.137707
$771$	4.95241e6	0.300041
$772$	−7.01910e6	−0.423876
$773$	3.90895e6	0.235294	0.117647	−	0.993055i	$-0.462465\pi$
$773$	3.90895e6	0.235294	0.117647	+	0.993055i	$0.462465\pi$
$774$	2.01535e6	0.120920
$775$	−4.29250e6	−0.256718
$776$	−122752.	−0.00731769
$777$	3.90674e6	0.232147
$778$	4.64580e6	0.275177
$779$	1.03572e6	0.0611503
$780$	−2.65440e6	−0.156218
$781$	1.34807e7	0.790833
$782$	4.77317e6	0.279119
$783$	−1.59570e7	−0.930137
$784$	−738048.	−0.0428839
$785$	92950.0	0.00538363
$786$	188928.	0.0109079
$787$	−2.65082e7	−1.52561	−0.762806	−	0.646628i	$-0.776179\pi$
$787$	−2.65082e7	−1.52561	−0.762806	+	0.646628i	$0.776179\pi$
$788$	−2.50877e6	−0.143928
$789$	8.18788e6	0.468251
$790$	−452000.	−0.0257674
$791$	−1.64475e7	−0.934674
$792$	−2.54362e6	−0.144092
$793$	−1.08808e7	−0.614439
$794$	2.51425e6	0.141533
$795$	1.37610e6	0.0772204
$796$	−2.60032e6	−0.145460
$797$	1.07940e7	0.601919	0.300960	−	0.953637i	$-0.402693\pi$
$797$	1.07940e7	0.601919	0.300960	+	0.953637i	$0.402693\pi$
$798$	7.75968e6	0.431357
$799$	9.99896e6	0.554100
$800$	640000.	0.0353553
$801$	−7.96743e6	−0.438770
$802$	−1.08973e7	−0.598249
$803$	4.22131e6	0.231025
$804$	3.23731e6	0.176622
$805$	4.61970e6	0.251260
$806$	−3.03840e7	−1.64743
$807$	−679860.	−0.0367482
$808$	4.96781e6	0.267693
$809$	−1.11446e7	−0.598675	−0.299338	−	0.954147i	$-0.596766\pi$
$809$	−1.11446e7	−0.598675	−0.299338	+	0.954147i	$0.596766\pi$
$810$	−3.41010e6	−0.182623
$811$	−1.14866e7	−0.613253	−0.306626	−	0.951830i	$-0.599200\pi$
$811$	−1.14866e7	−0.613253	−0.306626	+	0.951830i	$0.599200\pi$
$812$	−1.11581e7	−0.593881
$813$	−5.09777e6	−0.270492
$814$	−4.23782e6	−0.224172
$815$	1.08085e6	0.0569995
$816$	1.17043e6	0.0615348
$817$	6.66916e6	0.349555
$818$	7.12076e6	0.372086
$819$	2.70152e7	1.40734
$820$	151200.	0.00785267
$821$	3.04347e7	1.57584	0.787918	−	0.615781i	$-0.211159\pi$
$821$	3.04347e7	1.57584	0.787918	+	0.615781i	$0.211159\pi$
$822$	−3.94171e6	−0.203472
$823$	4.09773e6	0.210884	0.105442	−	0.994425i	$-0.466374\pi$
$823$	4.09773e6	0.210884	0.105442	+	0.994425i	$0.466374\pi$
$824$	−2.98970e6	−0.153394
$825$	720000.	0.0368297
$826$	1.65106e7	0.841999
$827$	−1.70652e7	−0.867654	−0.433827	−	0.900996i	$-0.642837\pi$
$827$	−1.70652e7	−0.867654	−0.433827	+	0.900996i	$0.642837\pi$
$828$	−5.18659e6	−0.262909
$829$	−2.47617e7	−1.25139	−0.625697	−	0.780066i	$-0.715185\pi$
$829$	−2.47617e7	−1.25139	−0.625697	+	0.780066i	$0.715185\pi$
$830$	1.09074e7	0.549574
$831$	2.63161e6	0.132196
$832$	4.53018e6	0.226886
$833$	−2.19685e6	−0.109695
$834$	−6.77040e6	−0.337054
$835$	−4.66305e6	−0.231448
$836$	−8.41728e6	−0.416539
$837$	1.85436e7	0.914914
$838$	2.60232e6	0.128012
$839$	3.16529e7	1.55242	0.776208	−	0.630476i	$-0.217140\pi$
$839$	3.16529e7	1.55242	0.776208	+	0.630476i	$0.217140\pi$
$840$	1.13280e6	0.0553930
$841$	1.44170e7	0.702884
$842$	−1.41624e7	−0.688425
$843$	−8.74019e6	−0.423596
$844$	−2.90637e6	−0.140441
$845$	−2.12986e7	−1.02615
$846$	−1.08650e7	−0.521921
$847$	1.46541e7	0.701859
$848$	−2.34854e6	−0.112153
$849$	−722364.	−0.0343943
$850$	1.90500e6	0.0904373
$851$	−8.64119e6	−0.409025
$852$	6.74035e6	0.318115
$853$	2.82671e7	1.33017	0.665087	−	0.746765i	$-0.268394\pi$
$853$	2.82671e7	1.33017	0.665087	+	0.746765i	$0.268394\pi$
$854$	4.64354e6	0.217873
$855$	−1.41795e7	−0.663354
$856$	−66432.0	−0.00309880
$857$	2.60870e7	1.21331	0.606655	−	0.794966i	$-0.292511\pi$
$857$	2.60870e7	1.21331	0.606655	+	0.794966i	$0.292511\pi$
$858$	5.09645e6	0.236347
$859$	−3.38111e7	−1.56342	−0.781710	−	0.623642i	$-0.785652\pi$
$859$	−3.38111e7	−1.56342	−0.781710	+	0.623642i	$0.785652\pi$
$860$	973600.	0.0448884
$861$	267624.	0.0123032
$862$	−2.19499e6	−0.100615
$863$	2.22817e7	1.01841	0.509204	−	0.860646i	$-0.329940\pi$
$863$	2.22817e7	1.01841	0.509204	+	0.860646i	$0.329940\pi$
$864$	−2.76480e6	−0.126003
$865$	9.36135e6	0.425401
$866$	−5.96966e6	−0.270492
$867$	−5.03528e6	−0.227497
$868$	1.29668e7	0.584162
$869$	867840.	0.0389843
$870$	−3.54600e6	−0.158833
$871$	3.72965e7	1.66580
$872$	1.32435e7	0.589810
$873$	397026.	0.0176313
$874$	−1.71634e7	−0.760018
$875$	1.84375e6	0.0814108
$876$	2.11066e6	0.0929303
$877$	−3.46748e7	−1.52235	−0.761177	−	0.648545i	$-0.775378\pi$
$877$	−3.46748e7	−1.52235	−0.761177	+	0.648545i	$0.775378\pi$
$878$	1.94485e7	0.851431
$879$	−1.58526e7	−0.692034
$880$	−1.22880e6	−0.0534902
$881$	1.42603e7	0.618998	0.309499	−	0.950900i	$-0.399839\pi$
$881$	1.42603e7	0.618998	0.309499	+	0.950900i	$0.399839\pi$
$882$	2.38712e6	0.103325
$883$	−3.75177e7	−1.61933	−0.809663	−	0.586895i	$-0.800350\pi$
$883$	−3.75177e7	−1.61933	−0.809663	+	0.586895i	$0.800350\pi$
$884$	1.34844e7	0.580363
$885$	5.24700e6	0.225192
$886$	−7.44622e6	−0.318677
$887$	4.07657e7	1.73975	0.869873	−	0.493275i	$-0.164200\pi$
$887$	4.07657e7	1.73975	0.869873	+	0.493275i	$0.164200\pi$
$888$	−2.11891e6	−0.0901738
$889$	−3.53861e7	−1.50168
$890$	−3.84900e6	−0.162882
$891$	6.54739e6	0.276296
$892$	−4.61238e6	−0.194095
$893$	−3.59543e7	−1.50877
$894$	−9.33480e6	−0.390626
$895$	−6.80250e6	−0.283864
$896$	−1.93331e6	−0.0804511
$897$	1.03920e7	0.431238
$898$	1.49488e7	0.618606
$899$	−4.05899e7	−1.67501
$900$	−2.07000e6	−0.0851852
$901$	−6.99059e6	−0.286881
$902$	−290304.	−0.0118806
$903$	1.72327e6	0.0703290
$904$	8.92070e6	0.363060
$905$	1.88545e6	0.0765233
$906$	−2.35075e6	−0.0951451
$907$	−3.57116e7	−1.44142	−0.720712	−	0.693235i	$-0.756185\pi$
$907$	−3.57116e7	−1.44142	−0.720712	+	0.693235i	$0.756185\pi$
$908$	1.80084e7	0.724869
$909$	−1.60678e7	−0.644979
$910$	1.30508e7	0.522437
$911$	−2.11389e7	−0.843893	−0.421947	−	0.906621i	$-0.638653\pi$
$911$	−2.11389e7	−0.843893	−0.421947	+	0.906621i	$0.638653\pi$
$912$	−4.20864e6	−0.167554
$913$	−2.09422e7	−0.831468
$914$	−2.59310e7	−1.02673
$915$	1.47570e6	0.0582700
$916$	−6.65296e6	−0.261985
$917$	−928896.	−0.0364791
$918$	−8.22960e6	−0.322309
$919$	1.85996e7	0.726465	0.363233	−	0.931698i	$-0.381673\pi$
$919$	1.85996e7	0.726465	0.363233	+	0.931698i	$0.381673\pi$
$920$	−2.50560e6	−0.0975983
$921$	−8.68535e6	−0.337395
$922$	6.03641e6	0.233857
$923$	7.76545e7	3.00028
$924$	−2.17498e6	−0.0838059
$925$	−3.44875e6	−0.132528
$926$	3.47360e7	1.33123
$927$	9.66980e6	0.369588
$928$	6.05184e6	0.230684
$929$	4.45110e7	1.69211	0.846055	−	0.533096i	$-0.178972\pi$
$929$	4.45110e7	1.69211	0.846055	+	0.533096i	$0.178972\pi$
$930$	4.12080e6	0.156234
$931$	7.89942e6	0.298690
$932$	1.23294e7	0.464945
$933$	−5.56841e6	−0.209424
$934$	2.78565e7	1.04486
$935$	−3.65760e6	−0.136826
$936$	−1.46523e7	−0.546658
$937$	−2.19419e7	−0.816441	−0.408221	−	0.912883i	$-0.633851\pi$
$937$	−2.19419e7	−0.816441	−0.408221	+	0.912883i	$0.633851\pi$
$938$	−1.59168e7	−0.590675
$939$	1.37738e7	0.509787
$940$	−5.24880e6	−0.193749
$941$	−7.77722e6	−0.286319	−0.143160	−	0.989700i	$-0.545726\pi$
$941$	−7.77722e6	−0.286319	−0.143160	+	0.989700i	$0.545726\pi$
$942$	−89232.0	−0.00327637
$943$	−591948.	−0.0216773
$944$	−8.95488e6	−0.327062
$945$	−7.96500e6	−0.290139
$946$	−1.86931e6	−0.0679132
$947$	3.17199e7	1.14936	0.574681	−	0.818378i	$-0.305126\pi$
$947$	3.17199e7	1.14936	0.574681	+	0.818378i	$0.305126\pi$
$948$	433920.	0.0156815
$949$	2.43165e7	0.876468
$950$	−6.85000e6	−0.246253
$951$	1.64191e7	0.588707
$952$	−5.75462e6	−0.205790
$953$	−5.60285e6	−0.199838	−0.0999188	−	0.994996i	$-0.531858\pi$
$953$	−5.60285e6	−0.199838	−0.0999188	+	0.994996i	$0.531858\pi$
$954$	7.59607e6	0.270220
$955$	8.92470e6	0.316654
$956$	−9.52512e6	−0.337074
$957$	6.80832e6	0.240304
$958$	−2.20421e7	−0.775959
$959$	1.93801e7	0.680470
$960$	−614400.	−0.0215166
$961$	1.85403e7	0.647601
$962$	−2.44116e7	−0.850470
$963$	214866.	0.00746624
$964$	4.38243e6	0.151888
$965$	1.09674e7	0.379126
$966$	−4.43491e6	−0.152912
$967$	−2.03532e7	−0.699949	−0.349975	−	0.936759i	$-0.613810\pi$
$967$	−2.03532e7	−0.699949	−0.349975	+	0.936759i	$0.613810\pi$
$968$	−7.94797e6	−0.272626
$969$	−1.25273e7	−0.428595
$970$	191800.	0.00654514
$971$	−2.34306e7	−0.797510	−0.398755	−	0.917057i	$-0.630558\pi$
$971$	−2.34306e7	−0.797510	−0.398755	+	0.917057i	$0.630558\pi$
$972$	1.37713e7	0.467530
$973$	3.32878e7	1.12721
$974$	2.20723e7	0.745505
$975$	4.14750e6	0.139725
$976$	−2.51853e6	−0.0846296
$977$	−4.30412e7	−1.44261	−0.721303	−	0.692619i	$-0.756457\pi$
$977$	−4.30412e7	−1.44261	−0.721303	+	0.692619i	$0.756457\pi$
$978$	−1.03762e6	−0.0346888
$979$	7.39008e6	0.246429
$980$	1.15320e6	0.0383565
$981$	−4.28345e7	−1.42109
$982$	−6.05107e6	−0.200241
$983$	−4.75003e7	−1.56788	−0.783940	−	0.620837i	$-0.786793\pi$
$983$	−4.75003e7	−1.56788	−0.783940	+	0.620837i	$0.786793\pi$
$984$	−145152.	−0.00477898
$985$	3.91995e6	0.128733
$986$	1.80137e7	0.590079
$987$	−9.29038e6	−0.303557
$988$	−4.84870e7	−1.58028
$989$	−3.81164e6	−0.123914
$990$	3.97440e6	0.128879
$991$	2.09231e7	0.676770	0.338385	−	0.941008i	$-0.390119\pi$
$991$	2.09231e7	0.676770	0.338385	+	0.941008i	$0.390119\pi$
$992$	−7.03283e6	−0.226909
$993$	2.29128e7	0.737402
$994$	−3.31401e7	−1.06387
$995$	4.06300e6	0.130104
$996$	−1.04711e7	−0.334460
$997$	2.96332e7	0.944148	0.472074	−	0.881559i	$-0.343505\pi$
$997$	2.96332e7	0.944148	0.472074	+	0.881559i	$0.343505\pi$
$998$	−7.72168e6	−0.245406
$999$	1.48986e7	0.472315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.6.a.c.1.1	✓	1
3.2	odd	2		90.6.a.b.1.1		1
4.3	odd	2		80.6.a.c.1.1		1
5.2	odd	4		50.6.b.b.49.2		2
5.3	odd	4		50.6.b.b.49.1		2
5.4	even	2		50.6.a.b.1.1		1
7.6	odd	2		490.6.a.k.1.1		1
8.3	odd	2		320.6.a.k.1.1		1
8.5	even	2		320.6.a.f.1.1		1
12.11	even	2		720.6.a.v.1.1		1
15.2	even	4		450.6.c.f.199.1		2
15.8	even	4		450.6.c.f.199.2		2
15.14	odd	2		450.6.a.u.1.1		1
20.3	even	4		400.6.c.i.49.1		2
20.7	even	4		400.6.c.i.49.2		2
20.19	odd	2		400.6.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.6.a.c.1.1	✓	1	1.1	even	1	trivial
50.6.a.b.1.1		1	5.4	even	2
50.6.b.b.49.1		2	5.3	odd	4
50.6.b.b.49.2		2	5.2	odd	4
80.6.a.c.1.1		1	4.3	odd	2
90.6.a.b.1.1		1	3.2	odd	2
320.6.a.f.1.1		1	8.5	even	2
320.6.a.k.1.1		1	8.3	odd	2
400.6.a.i.1.1		1	20.19	odd	2
400.6.c.i.49.1		2	20.3	even	4
400.6.c.i.49.2		2	20.7	even	4
450.6.a.u.1.1		1	15.14	odd	2
450.6.c.f.199.1		2	15.2	even	4
450.6.c.f.199.2		2	15.8	even	4
490.6.a.k.1.1		1	7.6	odd	2
720.6.a.v.1.1		1	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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