LMFDB - Embedded newform 70.6.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,6,Mod(1,70)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("70.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	70.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-4,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.2268673869$
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	$\chi$	$=$	70.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-4.00000 q^{2} -3.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +12.0000 q^{6} +49.0000 q^{7} -64.0000 q^{8} -234.000 q^{9} +100.000 q^{10} +405.000 q^{11} -48.0000 q^{12} -391.000 q^{13} -196.000 q^{14} +75.0000 q^{15} +256.000 q^{16} +999.000 q^{17} +936.000 q^{18} +2342.00 q^{19} -400.000 q^{20} -147.000 q^{21} -1620.00 q^{22} +2430.00 q^{23} +192.000 q^{24} +625.000 q^{25} +1564.00 q^{26} +1431.00 q^{27} +784.000 q^{28} +8259.00 q^{29} -300.000 q^{30} +4016.00 q^{31} -1024.00 q^{32} -1215.00 q^{33} -3996.00 q^{34} -1225.00 q^{35} -3744.00 q^{36} -7042.00 q^{37} -9368.00 q^{38} +1173.00 q^{39} +1600.00 q^{40} +3336.00 q^{41} +588.000 q^{42} -23518.0 q^{43} +6480.00 q^{44} +5850.00 q^{45} -9720.00 q^{46} +10317.0 q^{47} -768.000 q^{48} +2401.00 q^{49} -2500.00 q^{50} -2997.00 q^{51} -6256.00 q^{52} +3084.00 q^{53} -5724.00 q^{54} -10125.0 q^{55} -3136.00 q^{56} -7026.00 q^{57} -33036.0 q^{58} -18816.0 q^{59} +1200.00 q^{60} +21668.0 q^{61} -16064.0 q^{62} -11466.0 q^{63} +4096.00 q^{64} +9775.00 q^{65} +4860.00 q^{66} +52124.0 q^{67} +15984.0 q^{68} -7290.00 q^{69} +4900.00 q^{70} -28560.0 q^{71} +14976.0 q^{72} -70342.0 q^{73} +28168.0 q^{74} -1875.00 q^{75} +37472.0 q^{76} +19845.0 q^{77} -4692.00 q^{78} +58823.0 q^{79} -6400.00 q^{80} +52569.0 q^{81} -13344.0 q^{82} +756.000 q^{83} -2352.00 q^{84} -24975.0 q^{85} +94072.0 q^{86} -24777.0 q^{87} -25920.0 q^{88} +135384. q^{89} -23400.0 q^{90} -19159.0 q^{91} +38880.0 q^{92} -12048.0 q^{93} -41268.0 q^{94} -58550.0 q^{95} +3072.00 q^{96} +110435. q^{97} -9604.00 q^{98} -94770.0 q^{99} +O(q^{100})\)

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
$3$	−3.00000	−0.192450	−0.0962250	−	0.995360i	$-0.530677\pi$
$3$	−3.00000	−0.192450	−0.0962250	+	0.995360i	$0.530677\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	12.0000	0.136083
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−64.0000	−0.353553
$9$	−234.000	−0.962963
$10$	100.000	0.316228
$11$	405.000	1.00919	0.504595	−	0.863356i	$-0.331642\pi$
$11$	405.000	1.00919	0.504595	+	0.863356i	$0.331642\pi$
$12$	−48.0000	−0.0962250
$13$	−391.000	−0.641680	−0.320840	−	0.947133i	$-0.603965\pi$
$13$	−391.000	−0.641680	−0.320840	+	0.947133i	$0.603965\pi$
$14$	−196.000	−0.267261
$15$	75.0000	0.0860663
$16$	256.000	0.250000
$17$	999.000	0.838384	0.419192	−	0.907898i	$-0.362313\pi$
$17$	999.000	0.838384	0.419192	+	0.907898i	$0.362313\pi$
$18$	936.000	0.680918
$19$	2342.00	1.48834	0.744171	−	0.667989i	$-0.232845\pi$
$19$	2342.00	1.48834	0.744171	+	0.667989i	$0.232845\pi$
$20$	−400.000	−0.223607
$21$	−147.000	−0.0727393
$22$	−1620.00	−0.713606
$23$	2430.00	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$23$	2430.00	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$24$	192.000	0.0680414
$25$	625.000	0.200000
$26$	1564.00	0.453736
$27$	1431.00	0.377772
$28$	784.000	0.188982
$29$	8259.00	1.82361	0.911806	−	0.410621i	$-0.134688\pi$
$29$	8259.00	1.82361	0.911806	+	0.410621i	$0.134688\pi$
$30$	−300.000	−0.0608581
$31$	4016.00	0.750567	0.375284	−	0.926910i	$-0.377545\pi$
$31$	4016.00	0.750567	0.375284	+	0.926910i	$0.377545\pi$
$32$	−1024.00	−0.176777
$33$	−1215.00	−0.194219
$34$	−3996.00	−0.592827
$35$	−1225.00	−0.169031
$36$	−3744.00	−0.481481
$37$	−7042.00	−0.845652	−0.422826	−	0.906211i	$-0.638962\pi$
$37$	−7042.00	−0.845652	−0.422826	+	0.906211i	$0.638962\pi$
$38$	−9368.00	−1.05242
$39$	1173.00	0.123491
$40$	1600.00	0.158114
$41$	3336.00	0.309932	0.154966	−	0.987920i	$-0.450473\pi$
$41$	3336.00	0.309932	0.154966	+	0.987920i	$0.450473\pi$
$42$	588.000	0.0514344
$43$	−23518.0	−1.93968	−0.969838	−	0.243750i	$-0.921622\pi$
$43$	−23518.0	−1.93968	−0.969838	+	0.243750i	$0.921622\pi$
$44$	6480.00	0.504595
$45$	5850.00	0.430650
$46$	−9720.00	−0.677285
$47$	10317.0	0.681254	0.340627	−	0.940199i	$-0.389361\pi$
$47$	10317.0	0.681254	0.340627	+	0.940199i	$0.389361\pi$
$48$	−768.000	−0.0481125
$49$	2401.00	0.142857
$50$	−2500.00	−0.141421
$51$	−2997.00	−0.161347
$52$	−6256.00	−0.320840
$53$	3084.00	0.150808	0.0754041	−	0.997153i	$-0.475975\pi$
$53$	3084.00	0.150808	0.0754041	+	0.997153i	$0.475975\pi$
$54$	−5724.00	−0.267125
$55$	−10125.0	−0.451324
$56$	−3136.00	−0.133631
$57$	−7026.00	−0.286432
$58$	−33036.0	−1.28949
$59$	−18816.0	−0.703716	−0.351858	−	0.936053i	$-0.614450\pi$
$59$	−18816.0	−0.703716	−0.351858	+	0.936053i	$0.614450\pi$
$60$	1200.00	0.0430331
$61$	21668.0	0.745580	0.372790	−	0.927916i	$-0.378401\pi$
$61$	21668.0	0.745580	0.372790	+	0.927916i	$0.378401\pi$
$62$	−16064.0	−0.530731
$63$	−11466.0	−0.363966
$64$	4096.00	0.125000
$65$	9775.00	0.286968
$66$	4860.00	0.137333
$67$	52124.0	1.41857	0.709285	−	0.704922i	$-0.249018\pi$
$67$	52124.0	1.41857	0.709285	+	0.704922i	$0.249018\pi$
$68$	15984.0	0.419192
$69$	−7290.00	−0.184334
$70$	4900.00	0.119523
$71$	−28560.0	−0.672376	−0.336188	−	0.941795i	$-0.609138\pi$
$71$	−28560.0	−0.672376	−0.336188	+	0.941795i	$0.609138\pi$
$72$	14976.0	0.340459
$73$	−70342.0	−1.54493	−0.772463	−	0.635060i	$-0.780975\pi$
$73$	−70342.0	−1.54493	−0.772463	+	0.635060i	$0.780975\pi$
$74$	28168.0	0.597966
$75$	−1875.00	−0.0384900
$76$	37472.0	0.744171
$77$	19845.0	0.381438
$78$	−4692.00	−0.0873216
$79$	58823.0	1.06042	0.530212	−	0.847865i	$-0.322112\pi$
$79$	58823.0	1.06042	0.530212	+	0.847865i	$0.322112\pi$
$80$	−6400.00	−0.111803
$81$	52569.0	0.890261
$82$	−13344.0	−0.219155
$83$	756.000	0.0120455	0.00602277	−	0.999982i	$-0.498083\pi$
$83$	756.000	0.0120455	0.00602277	+	0.999982i	$0.498083\pi$
$84$	−2352.00	−0.0363696
$85$	−24975.0	−0.374937
$86$	94072.0	1.37156
$87$	−24777.0	−0.350954
$88$	−25920.0	−0.356803
$89$	135384.	1.81173	0.905863	−	0.423572i	$-0.139224\pi$
$89$	135384.	1.81173	0.905863	+	0.423572i	$0.139224\pi$
$90$	−23400.0	−0.304516
$91$	−19159.0	−0.242532
$92$	38880.0	0.478913
$93$	−12048.0	−0.144447
$94$	−41268.0	−0.481719
$95$	−58550.0	−0.665607
$96$	3072.00	0.0340207
$97$	110435.	1.19173	0.595864	−	0.803085i	$-0.296810\pi$
$97$	110435.	1.19173	0.595864	+	0.803085i	$0.296810\pi$
$98$	−9604.00	−0.101015
$99$	−94770.0	−0.971813
$100$	10000.0	0.100000
$101$	33450.0	0.326282	0.163141	−	0.986603i	$-0.447838\pi$
$101$	33450.0	0.326282	0.163141	+	0.986603i	$0.447838\pi$
$102$	11988.0	0.114090
$103$	−110311.	−1.02453	−0.512266	−	0.858827i	$-0.671194\pi$
$103$	−110311.	−1.02453	−0.512266	+	0.858827i	$0.671194\pi$
$104$	25024.0	0.226868
$105$	3675.00	0.0325300
$106$	−12336.0	−0.106637
$107$	35358.0	0.298558	0.149279	−	0.988795i	$-0.452305\pi$
$107$	35358.0	0.298558	0.149279	+	0.988795i	$0.452305\pi$
$108$	22896.0	0.188886
$109$	−151183.	−1.21881	−0.609406	−	0.792858i	$-0.708592\pi$
$109$	−151183.	−1.21881	−0.609406	+	0.792858i	$0.708592\pi$
$110$	40500.0	0.319134
$111$	21126.0	0.162746
$112$	12544.0	0.0944911
$113$	−133686.	−0.984895	−0.492447	−	0.870342i	$-0.663898\pi$
$113$	−133686.	−0.984895	−0.492447	+	0.870342i	$0.663898\pi$
$114$	28104.0	0.202538
$115$	−60750.0	−0.428353
$116$	132144.	0.911806
$117$	91494.0	0.617914
$118$	75264.0	0.497602
$119$	48951.0	0.316880
$120$	−4800.00	−0.0304290
$121$	2974.00	0.0184662
$122$	−86672.0	−0.527205
$123$	−10008.0	−0.0596464
$124$	64256.0	0.375284
$125$	−15625.0	−0.0894427
$126$	45864.0	0.257363
$127$	−283984.	−1.56237	−0.781186	−	0.624298i	$-0.785385\pi$
$127$	−283984.	−1.56237	−0.781186	+	0.624298i	$0.785385\pi$
$128$	−16384.0	−0.0883883
$129$	70554.0	0.373291
$130$	−39100.0	−0.202917
$131$	261438.	1.33104	0.665519	−	0.746381i	$-0.268210\pi$
$131$	261438.	1.33104	0.665519	+	0.746381i	$0.268210\pi$
$132$	−19440.0	−0.0971094
$133$	114758.	0.562541
$134$	−208496.	−1.00308
$135$	−35775.0	−0.168945
$136$	−63936.0	−0.296414
$137$	39672.0	0.180585	0.0902927	−	0.995915i	$-0.471220\pi$
$137$	39672.0	0.180585	0.0902927	+	0.995915i	$0.471220\pi$
$138$	29160.0	0.130344
$139$	−182626.	−0.801725	−0.400863	−	0.916138i	$-0.631290\pi$
$139$	−182626.	−0.801725	−0.400863	+	0.916138i	$0.631290\pi$
$140$	−19600.0	−0.0845154
$141$	−30951.0	−0.131107
$142$	114240.	0.475442
$143$	−158355.	−0.647577
$144$	−59904.0	−0.240741
$145$	−206475.	−0.815544
$146$	281368.	1.09243
$147$	−7203.00	−0.0274929
$148$	−112672.	−0.422826
$149$	−12078.0	−0.0445686	−0.0222843	−	0.999752i	$-0.507094\pi$
$149$	−12078.0	−0.0445686	−0.0222843	+	0.999752i	$0.507094\pi$
$150$	7500.00	0.0272166
$151$	−208417.	−0.743859	−0.371930	−	0.928261i	$-0.621304\pi$
$151$	−208417.	−0.743859	−0.371930	+	0.928261i	$0.621304\pi$
$152$	−149888.	−0.526209
$153$	−233766.	−0.807333
$154$	−79380.0	−0.269718
$155$	−100400.	−0.335664
$156$	18768.0	0.0617457
$157$	364094.	1.17887	0.589433	−	0.807817i	$-0.299351\pi$
$157$	364094.	1.17887	0.589433	+	0.807817i	$0.299351\pi$
$158$	−235292.	−0.749833
$159$	−9252.00	−0.0290230
$160$	25600.0	0.0790569
$161$	119070.	0.362024
$162$	−210276.	−0.629509
$163$	626.000	0.00184546	0.000922731	−	1.00000i	$-0.499706\pi$
$163$	626.000	0.00184546	0.000922731		1.00000i	$0.499706\pi$
$164$	53376.0	0.154966
$165$	30375.0	0.0868573
$166$	−3024.00	−0.00851749
$167$	445617.	1.23643	0.618216	−	0.786008i	$-0.287856\pi$
$167$	445617.	1.23643	0.618216	+	0.786008i	$0.287856\pi$
$168$	9408.00	0.0257172
$169$	−218412.	−0.588247
$170$	99900.0	0.265120
$171$	−548028.	−1.43322
$172$	−376288.	−0.969838
$173$	643467.	1.63460	0.817299	−	0.576214i	$-0.195470\pi$
$173$	643467.	1.63460	0.817299	+	0.576214i	$0.195470\pi$
$174$	99108.0	0.248162
$175$	30625.0	0.0755929
$176$	103680.	0.252298
$177$	56448.0	0.135430
$178$	−541536.	−1.28108
$179$	245148.	0.571868	0.285934	−	0.958249i	$-0.407696\pi$
$179$	245148.	0.571868	0.285934	+	0.958249i	$0.407696\pi$
$180$	93600.0	0.215325
$181$	686180.	1.55683	0.778416	−	0.627749i	$-0.216024\pi$
$181$	686180.	1.55683	0.778416	+	0.627749i	$0.216024\pi$
$182$	76636.0	0.171496
$183$	−65004.0	−0.143487
$184$	−155520.	−0.338643
$185$	176050.	0.378187
$186$	48192.0	0.102139
$187$	404595.	0.846090
$188$	165072.	0.340627
$189$	70119.0	0.142785
$190$	234200.	0.470655
$191$	−527031.	−1.04533	−0.522664	−	0.852539i	$-0.675062\pi$
$191$	−527031.	−1.04533	−0.522664	+	0.852539i	$0.675062\pi$
$192$	−12288.0	−0.0240563
$193$	143216.	0.276757	0.138378	−	0.990379i	$-0.455811\pi$
$193$	143216.	0.276757	0.138378	+	0.990379i	$0.455811\pi$
$194$	−441740.	−0.842679
$195$	−29325.0	−0.0552270
$196$	38416.0	0.0714286
$197$	348468.	0.639731	0.319865	−	0.947463i	$-0.396362\pi$
$197$	348468.	0.639731	0.319865	+	0.947463i	$0.396362\pi$
$198$	379080.	0.687176
$199$	754520.	1.35064	0.675318	−	0.737527i	$-0.264007\pi$
$199$	754520.	1.35064	0.675318	+	0.737527i	$0.264007\pi$
$200$	−40000.0	−0.0707107
$201$	−156372.	−0.273004
$202$	−133800.	−0.230716
$203$	404691.	0.689261
$204$	−47952.0	−0.0806736
$205$	−83400.0	−0.138606
$206$	441244.	0.724454
$207$	−568620.	−0.922351
$208$	−100096.	−0.160420
$209$	948510.	1.50202
$210$	−14700.0	−0.0230022
$211$	−590749.	−0.913475	−0.456738	−	0.889601i	$-0.650982\pi$
$211$	−590749.	−0.913475	−0.456738	+	0.889601i	$0.650982\pi$
$212$	49344.0	0.0754041
$213$	85680.0	0.129399
$214$	−141432.	−0.211112
$215$	587950.	0.867450
$216$	−91584.0	−0.133563
$217$	196784.	0.283688
$218$	604732.	0.861830
$219$	211026.	0.297321
$220$	−162000.	−0.225662
$221$	−390609.	−0.537974
$222$	−84504.0	−0.115079
$223$	−396103.	−0.533391	−0.266696	−	0.963781i	$-0.585932\pi$
$223$	−396103.	−0.533391	−0.266696	+	0.963781i	$0.585932\pi$
$224$	−50176.0	−0.0668153
$225$	−146250.	−0.192593
$226$	534744.	0.696426
$227$	9537.00	0.0122842	0.00614210	−	0.999981i	$-0.498045\pi$
$227$	9537.00	0.0122842	0.00614210	+	0.999981i	$0.498045\pi$
$228$	−112416.	−0.143216
$229$	705056.	0.888454	0.444227	−	0.895914i	$-0.353478\pi$
$229$	705056.	0.888454	0.444227	+	0.895914i	$0.353478\pi$
$230$	243000.	0.302891
$231$	−59535.0	−0.0734078
$232$	−528576.	−0.644744
$233$	534216.	0.644655	0.322327	−	0.946628i	$-0.395535\pi$
$233$	534216.	0.644655	0.322327	+	0.946628i	$0.395535\pi$
$234$	−365976.	−0.436931
$235$	−257925.	−0.304666
$236$	−301056.	−0.351858
$237$	−176469.	−0.204079
$238$	−195804.	−0.224068
$239$	−901221.	−1.02056	−0.510278	−	0.860010i	$-0.670457\pi$
$239$	−901221.	−1.02056	−0.510278	+	0.860010i	$0.670457\pi$
$240$	19200.0	0.0215166
$241$	−952390.	−1.05626	−0.528132	−	0.849162i	$-0.677107\pi$
$241$	−952390.	−1.05626	−0.528132	+	0.849162i	$0.677107\pi$
$242$	−11896.0	−0.0130576
$243$	−505440.	−0.549103
$244$	346688.	0.372790
$245$	−60025.0	−0.0638877
$246$	40032.0	0.0421764
$247$	−915722.	−0.955039
$248$	−257024.	−0.265366
$249$	−2268.00	−0.00231817
$250$	62500.0	0.0632456
$251$	−1.10024e6	−1.10231	−0.551153	−	0.834404i	$-0.685812\pi$
$251$	−1.10024e6	−1.10231	−0.551153	+	0.834404i	$0.685812\pi$
$252$	−183456.	−0.181983
$253$	984150.	0.966629
$254$	1.13594e6	1.10476
$255$	74925.0	0.0721566
$256$	65536.0	0.0625000
$257$	−1.08230e6	−1.02215	−0.511074	−	0.859537i	$-0.670752\pi$
$257$	−1.08230e6	−1.02215	−0.511074	+	0.859537i	$0.670752\pi$
$258$	−282216.	−0.263957
$259$	−345058.	−0.319626
$260$	156400.	0.143484
$261$	−1.93261e6	−1.75607
$262$	−1.04575e6	−0.941186
$263$	82950.0	0.0739481	0.0369740	−	0.999316i	$-0.488228\pi$
$263$	82950.0	0.0739481	0.0369740	+	0.999316i	$0.488228\pi$
$264$	77760.0	0.0686667
$265$	−77100.0	−0.0674434
$266$	−459032.	−0.397776
$267$	−406152.	−0.348667
$268$	833984.	0.709285
$269$	−633822.	−0.534056	−0.267028	−	0.963689i	$-0.586042\pi$
$269$	−633822.	−0.534056	−0.267028	+	0.963689i	$0.586042\pi$
$270$	143100.	0.119462
$271$	−278956.	−0.230734	−0.115367	−	0.993323i	$-0.536804\pi$
$271$	−278956.	−0.230734	−0.115367	+	0.993323i	$0.536804\pi$
$272$	255744.	0.209596
$273$	57477.0	0.0466753
$274$	−158688.	−0.127693
$275$	253125.	0.201838
$276$	−116640.	−0.0921669
$277$	2.17523e6	1.70336	0.851679	−	0.524064i	$-0.175585\pi$
$277$	2.17523e6	1.70336	0.851679	+	0.524064i	$0.175585\pi$
$278$	730504.	0.566905
$279$	−939744.	−0.722768
$280$	78400.0	0.0597614
$281$	−692901.	−0.523486	−0.261743	−	0.965138i	$-0.584297\pi$
$281$	−692901.	−0.523486	−0.261743	+	0.965138i	$0.584297\pi$
$282$	123804.	0.0927069
$283$	1.04021e6	0.772065	0.386032	−	0.922485i	$-0.373845\pi$
$283$	1.04021e6	0.772065	0.386032	+	0.922485i	$0.373845\pi$
$284$	−456960.	−0.336188
$285$	175650.	0.128096
$286$	633420.	0.457906
$287$	163464.	0.117143
$288$	239616.	0.170229
$289$	−421856.	−0.297112
$290$	825900.	0.576677
$291$	−331305.	−0.229348
$292$	−1.12547e6	−0.772463
$293$	−1.08565e6	−0.738789	−0.369394	−	0.929273i	$-0.620435\pi$
$293$	−1.08565e6	−0.738789	−0.369394	+	0.929273i	$0.620435\pi$
$294$	28812.0	0.0194404
$295$	470400.	0.314711
$296$	450688.	0.298983
$297$	579555.	0.381244
$298$	48312.0	0.0315148
$299$	−950130.	−0.614618
$300$	−30000.0	−0.0192450
$301$	−1.15238e6	−0.733129
$302$	833668.	0.525988
$303$	−100350.	−0.0627929
$304$	599552.	0.372086
$305$	−541700.	−0.333434
$306$	935064.	0.570871
$307$	1463.00	0.000885928 0	0.000442964	−	1.00000i	$-0.499859\pi$
$307$	1463.00	0.000885928 0	0.000442964		1.00000i	$0.499859\pi$
$308$	317520.	0.190719
$309$	330933.	0.197171
$310$	401600.	0.237350
$311$	3.11977e6	1.82903	0.914515	−	0.404551i	$-0.132572\pi$
$311$	3.11977e6	1.82903	0.914515	+	0.404551i	$0.132572\pi$
$312$	−75072.0	−0.0436608
$313$	831425.	0.479692	0.239846	−	0.970811i	$-0.422903\pi$
$313$	831425.	0.479692	0.239846	+	0.970811i	$0.422903\pi$
$314$	−1.45638e6	−0.833584
$315$	286650.	0.162770
$316$	941168.	0.530212
$317$	−1.25851e6	−0.703408	−0.351704	−	0.936111i	$-0.614398\pi$
$317$	−1.25851e6	−0.703408	−0.351704	+	0.936111i	$0.614398\pi$
$318$	37008.0	0.0205224
$319$	3.34489e6	1.84037
$320$	−102400.	−0.0559017
$321$	−106074.	−0.0574575
$322$	−476280.	−0.255990
$323$	2.33966e6	1.24780
$324$	841104.	0.445130
$325$	−244375.	−0.128336
$326$	−2504.00	−0.00130494
$327$	453549.	0.234560
$328$	−213504.	−0.109578
$329$	505533.	0.257490
$330$	−121500.	−0.0614174
$331$	−2.30465e6	−1.15621	−0.578103	−	0.815964i	$-0.696207\pi$
$331$	−2.30465e6	−1.15621	−0.578103	+	0.815964i	$0.696207\pi$
$332$	12096.0	0.00602277
$333$	1.64783e6	0.814332
$334$	−1.78247e6	−0.874290
$335$	−1.30310e6	−0.634404
$336$	−37632.0	−0.0181848
$337$	769166.	0.368931	0.184466	−	0.982839i	$-0.440945\pi$
$337$	769166.	0.368931	0.184466	+	0.982839i	$0.440945\pi$
$338$	873648.	0.415953
$339$	401058.	0.189543
$340$	−399600.	−0.187468
$341$	1.62648e6	0.757465
$342$	2.19211e6	1.01344
$343$	117649.	0.0539949
$344$	1.50515e6	0.685779
$345$	182250.	0.0824365
$346$	−2.57387e6	−1.15584
$347$	382074.	0.170343	0.0851714	−	0.996366i	$-0.472856\pi$
$347$	382074.	0.170343	0.0851714	+	0.996366i	$0.472856\pi$
$348$	−396432.	−0.175477
$349$	−3.88710e6	−1.70829	−0.854146	−	0.520034i	$-0.825919\pi$
$349$	−3.88710e6	−1.70829	−0.854146	+	0.520034i	$0.825919\pi$
$350$	−122500.	−0.0534522
$351$	−559521.	−0.242409
$352$	−414720.	−0.178401
$353$	−366453.	−0.156524	−0.0782621	−	0.996933i	$-0.524937\pi$
$353$	−366453.	−0.156524	−0.0782621	+	0.996933i	$0.524937\pi$
$354$	−225792.	−0.0957636
$355$	714000.	0.300696
$356$	2.16614e6	0.905863
$357$	−146853.	−0.0609835
$358$	−980592.	−0.404372
$359$	−3.14858e6	−1.28937	−0.644687	−	0.764446i	$-0.723012\pi$
$359$	−3.14858e6	−1.28937	−0.644687	+	0.764446i	$0.723012\pi$
$360$	−374400.	−0.152258
$361$	3.00887e6	1.21516
$362$	−2.74472e6	−1.10085
$363$	−8922.00	−0.00355382
$364$	−306544.	−0.121266
$365$	1.75855e6	0.690912
$366$	260016.	0.101461
$367$	2.13740e6	0.828362	0.414181	−	0.910195i	$-0.364068\pi$
$367$	2.13740e6	0.828362	0.414181	+	0.910195i	$0.364068\pi$
$368$	622080.	0.239457
$369$	−780624.	−0.298453
$370$	−704200.	−0.267419
$371$	151116.	0.0570001
$372$	−192768.	−0.0722233
$373$	−205624.	−0.0765247	−0.0382624	−	0.999268i	$-0.512182\pi$
$373$	−205624.	−0.0765247	−0.0382624	+	0.999268i	$0.512182\pi$
$374$	−1.61838e6	−0.598276
$375$	46875.0	0.0172133
$376$	−660288.	−0.240860
$377$	−3.22927e6	−1.17018
$378$	−280476.	−0.100964
$379$	3.50536e6	1.25353	0.626766	−	0.779208i	$-0.284378\pi$
$379$	3.50536e6	1.25353	0.626766	+	0.779208i	$0.284378\pi$
$380$	−936800.	−0.332804
$381$	851952.	0.300679
$382$	2.10812e6	0.739159
$383$	1.12904e6	0.393291	0.196645	−	0.980475i	$-0.436995\pi$
$383$	1.12904e6	0.393291	0.196645	+	0.980475i	$0.436995\pi$
$384$	49152.0	0.0170103
$385$	−496125.	−0.170584
$386$	−572864.	−0.195697
$387$	5.50321e6	1.86784
$388$	1.76696e6	0.595864
$389$	−1.20003e6	−0.402084	−0.201042	−	0.979583i	$-0.564433\pi$
$389$	−1.20003e6	−0.402084	−0.201042	+	0.979583i	$0.564433\pi$
$390$	117300.	0.0390514
$391$	2.42757e6	0.803026
$392$	−153664.	−0.0505076
$393$	−784314.	−0.256158
$394$	−1.39387e6	−0.452358
$395$	−1.47058e6	−0.474236
$396$	−1.51632e6	−0.485907
$397$	−4.41836e6	−1.40697	−0.703486	−	0.710709i	$-0.748374\pi$
$397$	−4.41836e6	−1.40697	−0.703486	+	0.710709i	$0.748374\pi$
$398$	−3.01808e6	−0.955043
$399$	−344274.	−0.108261
$400$	160000.	0.0500000
$401$	−3.13278e6	−0.972903	−0.486451	−	0.873708i	$-0.661709\pi$
$401$	−3.13278e6	−0.972903	−0.486451	+	0.873708i	$0.661709\pi$
$402$	625488.	0.193043
$403$	−1.57026e6	−0.481624
$404$	535200.	0.163141
$405$	−1.31422e6	−0.398137
$406$	−1.61876e6	−0.487381
$407$	−2.85201e6	−0.853424
$408$	191808.	0.0570448
$409$	861494.	0.254650	0.127325	−	0.991861i	$-0.459361\pi$
$409$	861494.	0.254650	0.127325	+	0.991861i	$0.459361\pi$
$410$	333600.	0.0980091
$411$	−119016.	−0.0347537
$412$	−1.76498e6	−0.512266
$413$	−921984.	−0.265980
$414$	2.27448e6	0.652201
$415$	−18900.0	−0.00538693
$416$	400384.	0.113434
$417$	547878.	0.154292
$418$	−3.79404e6	−1.06209
$419$	4.65796e6	1.29617	0.648083	−	0.761570i	$-0.275571\pi$
$419$	4.65796e6	1.29617	0.648083	+	0.761570i	$0.275571\pi$
$420$	58800.0	0.0162650
$421$	6.99894e6	1.92454	0.962271	−	0.272093i	$-0.0877159\pi$
$421$	6.99894e6	1.92454	0.962271	+	0.272093i	$0.0877159\pi$
$422$	2.36300e6	0.645925
$423$	−2.41418e6	−0.656022
$424$	−197376.	−0.0533187
$425$	624375.	0.167677
$426$	−342720.	−0.0914988
$427$	1.06173e6	0.281803
$428$	565728.	0.149279
$429$	475065.	0.124626
$430$	−2.35180e6	−0.613379
$431$	−227091.	−0.0588853	−0.0294426	−	0.999566i	$-0.509373\pi$
$431$	−227091.	−0.0588853	−0.0294426	+	0.999566i	$0.509373\pi$
$432$	366336.	0.0944431
$433$	−7.09613e6	−1.81887	−0.909435	−	0.415846i	$-0.863485\pi$
$433$	−7.09613e6	−1.81887	−0.909435	+	0.415846i	$0.863485\pi$
$434$	−787136.	−0.200597
$435$	619425.	0.156952
$436$	−2.41893e6	−0.609406
$437$	5.69106e6	1.42557
$438$	−844104.	−0.210238
$439$	593258.	0.146920	0.0734602	−	0.997298i	$-0.476596\pi$
$439$	593258.	0.146920	0.0734602	+	0.997298i	$0.476596\pi$
$440$	648000.	0.159567
$441$	−561834.	−0.137566
$442$	1.56244e6	0.380405
$443$	−3.27692e6	−0.793334	−0.396667	−	0.917963i	$-0.629833\pi$
$443$	−3.27692e6	−0.793334	−0.396667	+	0.917963i	$0.629833\pi$
$444$	338016.	0.0813729
$445$	−3.38460e6	−0.810228
$446$	1.58441e6	0.377165
$447$	36234.0	0.00857724
$448$	200704.	0.0472456
$449$	−4.32930e6	−1.01345	−0.506724	−	0.862108i	$-0.669144\pi$
$449$	−4.32930e6	−1.01345	−0.506724	+	0.862108i	$0.669144\pi$
$450$	585000.	0.136184
$451$	1.35108e6	0.312781
$452$	−2.13898e6	−0.492447
$453$	625251.	0.143156
$454$	−38148.0	−0.00868625
$455$	478975.	0.108464
$456$	449664.	0.101269
$457$	−4.91638e6	−1.10117	−0.550586	−	0.834779i	$-0.685596\pi$
$457$	−4.91638e6	−1.10117	−0.550586	+	0.834779i	$0.685596\pi$
$458$	−2.82022e6	−0.628232
$459$	1.42957e6	0.316718
$460$	−972000.	−0.214176
$461$	7.02919e6	1.54047	0.770235	−	0.637761i	$-0.220139\pi$
$461$	7.02919e6	1.54047	0.770235	+	0.637761i	$0.220139\pi$
$462$	238140.	0.0519072
$463$	2.88559e6	0.625579	0.312789	−	0.949823i	$-0.398737\pi$
$463$	2.88559e6	0.625579	0.312789	+	0.949823i	$0.398737\pi$
$464$	2.11430e6	0.455903
$465$	301200.	0.0645985
$466$	−2.13686e6	−0.455840
$467$	−6.00583e6	−1.27433	−0.637163	−	0.770729i	$-0.719892\pi$
$467$	−6.00583e6	−1.27433	−0.637163	+	0.770729i	$0.719892\pi$
$468$	1.46390e6	0.308957
$469$	2.55408e6	0.536169
$470$	1.03170e6	0.215431
$471$	−1.09228e6	−0.226873
$472$	1.20422e6	0.248801
$473$	−9.52479e6	−1.95750
$474$	705876.	0.144305
$475$	1.46375e6	0.297669
$476$	783216.	0.158440
$477$	−721656.	−0.145223
$478$	3.60488e6	0.721642
$479$	941094.	0.187411	0.0937053	−	0.995600i	$-0.470129\pi$
$479$	941094.	0.187411	0.0937053	+	0.995600i	$0.470129\pi$
$480$	−76800.0	−0.0152145
$481$	2.75342e6	0.542638
$482$	3.80956e6	0.746891
$483$	−357210.	−0.0696716
$484$	47584.0	0.00923310
$485$	−2.76087e6	−0.532957
$486$	2.02176e6	0.388275
$487$	1.91121e6	0.365162	0.182581	−	0.983191i	$-0.441555\pi$
$487$	1.91121e6	0.365162	0.182581	+	0.983191i	$0.441555\pi$
$488$	−1.38675e6	−0.263602
$489$	−1878.00	−0.000355160 0
$490$	240100.	0.0451754
$491$	3.95490e6	0.740342	0.370171	−	0.928964i	$-0.379299\pi$
$491$	3.95490e6	0.740342	0.370171	+	0.928964i	$0.379299\pi$
$492$	−160128.	−0.0298232
$493$	8.25074e6	1.52889
$494$	3.66289e6	0.675315
$495$	2.36925e6	0.434608
$496$	1.02810e6	0.187642
$497$	−1.39944e6	−0.254134
$498$	9072.00	0.00163919
$499$	7.09708e6	1.27593	0.637967	−	0.770063i	$-0.279775\pi$
$499$	7.09708e6	1.27593	0.637967	+	0.770063i	$0.279775\pi$
$500$	−250000.	−0.0447214
$501$	−1.33685e6	−0.237952
$502$	4.40095e6	0.779448
$503$	−9.15982e6	−1.61424	−0.807118	−	0.590390i	$-0.798974\pi$
$503$	−9.15982e6	−1.61424	−0.807118	+	0.590390i	$0.798974\pi$
$504$	733824.	0.128681
$505$	−836250.	−0.145918
$506$	−3.93660e6	−0.683510
$507$	655236.	0.113208
$508$	−4.54374e6	−0.781186
$509$	−9.42509e6	−1.61247	−0.806234	−	0.591596i	$-0.798498\pi$
$509$	−9.42509e6	−1.61247	−0.806234	+	0.591596i	$0.798498\pi$
$510$	−299700.	−0.0510224
$511$	−3.44676e6	−0.583927
$512$	−262144.	−0.0441942
$513$	3.35140e6	0.562255
$514$	4.32919e6	0.722768
$515$	2.75778e6	0.458185
$516$	1.12886e6	0.186645
$517$	4.17838e6	0.687515
$518$	1.38023e6	0.226010
$519$	−1.93040e6	−0.314579
$520$	−625600.	−0.101458
$521$	−6.18917e6	−0.998938	−0.499469	−	0.866332i	$-0.666471\pi$
$521$	−6.18917e6	−0.998938	−0.499469	+	0.866332i	$0.666471\pi$
$522$	7.73042e6	1.24173
$523$	−3.81497e6	−0.609870	−0.304935	−	0.952373i	$-0.598635\pi$
$523$	−3.81497e6	−0.609870	−0.304935	+	0.952373i	$0.598635\pi$
$524$	4.18301e6	0.665519
$525$	−91875.0	−0.0145479
$526$	−331800.	−0.0522892
$527$	4.01198e6	0.629264
$528$	−311040.	−0.0485547
$529$	−531443.	−0.0825691
$530$	308400.	0.0476897
$531$	4.40294e6	0.677652
$532$	1.83613e6	0.281270
$533$	−1.30438e6	−0.198877
$534$	1.62461e6	0.246545
$535$	−883950.	−0.133519
$536$	−3.33594e6	−0.501540
$537$	−735444.	−0.110056
$538$	2.53529e6	0.377634
$539$	972405.	0.144170
$540$	−572400.	−0.0844725
$541$	6.30404e6	0.926032	0.463016	−	0.886350i	$-0.346767\pi$
$541$	6.30404e6	0.926032	0.463016	+	0.886350i	$0.346767\pi$
$542$	1.11582e6	0.163154
$543$	−2.05854e6	−0.299612
$544$	−1.02298e6	−0.148207
$545$	3.77957e6	0.545069
$546$	−229908.	−0.0330044
$547$	−8.48475e6	−1.21247	−0.606234	−	0.795286i	$-0.707321\pi$
$547$	−8.48475e6	−1.21247	−0.606234	+	0.795286i	$0.707321\pi$
$548$	634752.	0.0902927
$549$	−5.07031e6	−0.717966
$550$	−1.01250e6	−0.142721
$551$	1.93426e7	2.71416
$552$	466560.	0.0651718
$553$	2.88233e6	0.400802
$554$	−8.70092e6	−1.20446
$555$	−528150.	−0.0727821
$556$	−2.92202e6	−0.400863
$557$	6.87794e6	0.939335	0.469668	−	0.882843i	$-0.344374\pi$
$557$	6.87794e6	0.939335	0.469668	+	0.882843i	$0.344374\pi$
$558$	3.75898e6	0.511074
$559$	9.19554e6	1.24465
$560$	−313600.	−0.0422577
$561$	−1.21378e6	−0.162830
$562$	2.77160e6	0.370161
$563$	−1.02257e7	−1.35964	−0.679820	−	0.733379i	$-0.737942\pi$
$563$	−1.02257e7	−1.35964	−0.679820	+	0.733379i	$0.737942\pi$
$564$	−495216.	−0.0655537
$565$	3.34215e6	0.440458
$566$	−4.16083e6	−0.545932
$567$	2.57588e6	0.336487
$568$	1.82784e6	0.237721
$569$	−1.26751e7	−1.64123	−0.820614	−	0.571482i	$-0.806369\pi$
$569$	−1.26751e7	−1.64123	−0.820614	+	0.571482i	$0.806369\pi$
$570$	−702600.	−0.0905776
$571$	−6.67155e6	−0.856321	−0.428160	−	0.903703i	$-0.640838\pi$
$571$	−6.67155e6	−0.856321	−0.428160	+	0.903703i	$0.640838\pi$
$572$	−2.53368e6	−0.323789
$573$	1.58109e6	0.201174
$574$	−653856.	−0.0828328
$575$	1.51875e6	0.191565
$576$	−958464.	−0.120370
$577$	−3.36511e6	−0.420784	−0.210392	−	0.977617i	$-0.567474\pi$
$577$	−3.36511e6	−0.420784	−0.210392	+	0.977617i	$0.567474\pi$
$578$	1.68742e6	0.210090
$579$	−429648.	−0.0532619
$580$	−3.30360e6	−0.407772
$581$	37044.0	0.00455279
$582$	1.32522e6	0.162174
$583$	1.24902e6	0.152194
$584$	4.50189e6	0.546214
$585$	−2.28735e6	−0.276339
$586$	4.34260e6	0.522403
$587$	−1.10055e7	−1.31830	−0.659150	−	0.752012i	$-0.729084\pi$
$587$	−1.10055e7	−1.31830	−0.659150	+	0.752012i	$0.729084\pi$
$588$	−115248.	−0.0137464
$589$	9.40547e6	1.11710
$590$	−1.88160e6	−0.222534
$591$	−1.04540e6	−0.123116
$592$	−1.80275e6	−0.211413
$593$	1.40222e6	0.163749	0.0818747	−	0.996643i	$-0.473909\pi$
$593$	1.40222e6	0.163749	0.0818747	+	0.996643i	$0.473909\pi$
$594$	−2.31822e6	−0.269581
$595$	−1.22378e6	−0.141713
$596$	−193248.	−0.0222843
$597$	−2.26356e6	−0.259930
$598$	3.80052e6	0.434600
$599$	1.93034e6	0.219820	0.109910	−	0.993942i	$-0.464944\pi$
$599$	1.93034e6	0.219820	0.109910	+	0.993942i	$0.464944\pi$
$600$	120000.	0.0136083
$601$	−1.82271e6	−0.205841	−0.102921	−	0.994690i	$-0.532819\pi$
$601$	−1.82271e6	−0.205841	−0.102921	+	0.994690i	$0.532819\pi$
$602$	4.60953e6	0.518400
$603$	−1.21970e7	−1.36603
$604$	−3.33467e6	−0.371930
$605$	−74350.0	−0.00825834
$606$	401400.	0.0444013
$607$	−1.36917e7	−1.50830	−0.754148	−	0.656704i	$-0.771950\pi$
$607$	−1.36917e7	−1.50830	−0.754148	+	0.656704i	$0.771950\pi$
$608$	−2.39821e6	−0.263104
$609$	−1.21407e6	−0.132648
$610$	2.16680e6	0.235773
$611$	−4.03395e6	−0.437147
$612$	−3.74026e6	−0.403667
$613$	1.11975e7	1.20357	0.601785	−	0.798658i	$-0.294456\pi$
$613$	1.11975e7	1.20357	0.601785	+	0.798658i	$0.294456\pi$
$614$	−5852.00	−0.000626446 0
$615$	250200.	0.0266747
$616$	−1.27008e6	−0.134859
$617$	−1.37060e7	−1.44944	−0.724718	−	0.689045i	$-0.758030\pi$
$617$	−1.37060e7	−1.44944	−0.724718	+	0.689045i	$0.758030\pi$
$618$	−1.32373e6	−0.139421
$619$	−7.93359e6	−0.832230	−0.416115	−	0.909312i	$-0.636609\pi$
$619$	−7.93359e6	−0.832230	−0.416115	+	0.909312i	$0.636609\pi$
$620$	−1.60640e6	−0.167832
$621$	3.47733e6	0.361840
$622$	−1.24791e7	−1.29332
$623$	6.63382e6	0.684768
$624$	300288.	0.0308728
$625$	390625.	0.0400000
$626$	−3.32570e6	−0.339193
$627$	−2.84553e6	−0.289064
$628$	5.82550e6	0.589433
$629$	−7.03496e6	−0.708981
$630$	−1.14660e6	−0.115096
$631$	−1.31143e7	−1.31121	−0.655604	−	0.755105i	$-0.727586\pi$
$631$	−1.31143e7	−1.31121	−0.655604	+	0.755105i	$0.727586\pi$
$632$	−3.76467e6	−0.374916
$633$	1.77225e6	0.175798
$634$	5.03402e6	0.497384
$635$	7.09960e6	0.698714
$636$	−148032.	−0.0145115
$637$	−938791.	−0.0916685
$638$	−1.33796e7	−1.30134
$639$	6.68304e6	0.647473
$640$	409600.	0.0395285
$641$	−1.27270e7	−1.22344	−0.611719	−	0.791075i	$-0.709522\pi$
$641$	−1.27270e7	−1.22344	−0.611719	+	0.791075i	$0.709522\pi$
$642$	424296.	0.0406286
$643$	1.88399e7	1.79701	0.898505	−	0.438964i	$-0.144655\pi$
$643$	1.88399e7	1.79701	0.898505	+	0.438964i	$0.144655\pi$
$644$	1.90512e6	0.181012
$645$	−1.76385e6	−0.166941
$646$	−9.35863e6	−0.882330
$647$	−944688.	−0.0887213	−0.0443606	−	0.999016i	$-0.514125\pi$
$647$	−944688.	−0.0887213	−0.0443606	+	0.999016i	$0.514125\pi$
$648$	−3.36442e6	−0.314755
$649$	−7.62048e6	−0.710184
$650$	977500.	0.0907472
$651$	−590352.	−0.0545957
$652$	10016.0	0.000922731 0
$653$	2.01024e7	1.84486	0.922432	−	0.386158i	$-0.126198\pi$
$653$	2.01024e7	1.84486	0.922432	+	0.386158i	$0.126198\pi$
$654$	−1.81420e6	−0.165859
$655$	−6.53595e6	−0.595258
$656$	854016.	0.0774830
$657$	1.64600e7	1.48771
$658$	−2.02213e6	−0.182073
$659$	−1.97097e7	−1.76793	−0.883967	−	0.467549i	$-0.845137\pi$
$659$	−1.97097e7	−1.76793	−0.883967	+	0.467549i	$0.845137\pi$
$660$	486000.	0.0434287
$661$	−227080.	−0.0202151	−0.0101075	−	0.999949i	$-0.503217\pi$
$661$	−227080.	−0.0202151	−0.0101075	+	0.999949i	$0.503217\pi$
$662$	9.21861e6	0.817561
$663$	1.17183e6	0.103533
$664$	−48384.0	−0.00425874
$665$	−2.86895e6	−0.251576
$666$	−6.59131e6	−0.575819
$667$	2.00694e7	1.74670
$668$	7.12987e6	0.618216
$669$	1.18831e6	0.102651
$670$	5.21240e6	0.448591
$671$	8.77554e6	0.752433
$672$	150528.	0.0128586
$673$	1.93220e7	1.64443	0.822214	−	0.569178i	$-0.192739\pi$
$673$	1.93220e7	1.64443	0.822214	+	0.569178i	$0.192739\pi$
$674$	−3.07666e6	−0.260874
$675$	894375.	0.0755545
$676$	−3.49459e6	−0.294124
$677$	3.35334e6	0.281194	0.140597	−	0.990067i	$-0.455098\pi$
$677$	3.35334e6	0.281194	0.140597	+	0.990067i	$0.455098\pi$
$678$	−1.60423e6	−0.134027
$679$	5.41132e6	0.450431
$680$	1.59840e6	0.132560
$681$	−28611.0	−0.00236410
$682$	−6.50592e6	−0.535609
$683$	1.60555e7	1.31696	0.658481	−	0.752598i	$-0.271199\pi$
$683$	1.60555e7	1.31696	0.658481	+	0.752598i	$0.271199\pi$
$684$	−8.76845e6	−0.716609
$685$	−991800.	−0.0807603
$686$	−470596.	−0.0381802
$687$	−2.11517e6	−0.170983
$688$	−6.02061e6	−0.484919
$689$	−1.20584e6	−0.0967705
$690$	−729000.	−0.0582914
$691$	1.35824e7	1.08213	0.541066	−	0.840980i	$-0.318021\pi$
$691$	1.35824e7	1.08213	0.541066	+	0.840980i	$0.318021\pi$
$692$	1.02955e7	0.817299
$693$	−4.64373e6	−0.367311
$694$	−1.52830e6	−0.120451
$695$	4.56565e6	0.358542
$696$	1.58573e6	0.124081
$697$	3.33266e6	0.259842
$698$	1.55484e7	1.20794
$699$	−1.60265e6	−0.124064
$700$	490000.	0.0377964
$701$	2.05454e7	1.57913	0.789567	−	0.613664i	$-0.210305\pi$
$701$	2.05454e7	1.57913	0.789567	+	0.613664i	$0.210305\pi$
$702$	2.23808e6	0.171409
$703$	−1.64924e7	−1.25862
$704$	1.65888e6	0.126149
$705$	773775.	0.0586330
$706$	1.46581e6	0.110679
$707$	1.63905e6	0.123323
$708$	903168.	0.0677151
$709$	2.57278e7	1.92215	0.961075	−	0.276287i	$-0.0891040\pi$
$709$	2.57278e7	1.92215	0.961075	+	0.276287i	$0.0891040\pi$
$710$	−2.85600e6	−0.212624
$711$	−1.37646e7	−1.02115
$712$	−8.66458e6	−0.640542
$713$	9.75888e6	0.718913
$714$	587412.	0.0431218
$715$	3.95888e6	0.289605
$716$	3.92237e6	0.285934
$717$	2.70366e6	0.196406
$718$	1.25943e7	0.911726
$719$	7.04806e6	0.508449	0.254225	−	0.967145i	$-0.418180\pi$
$719$	7.04806e6	0.508449	0.254225	+	0.967145i	$0.418180\pi$
$720$	1.49760e6	0.107663
$721$	−5.40524e6	−0.387237
$722$	−1.20355e7	−0.859250
$723$	2.85717e6	0.203278
$724$	1.09789e7	0.778416
$725$	5.16187e6	0.364722
$726$	35688.0	0.00251293
$727$	−1.90997e7	−1.34027	−0.670134	−	0.742240i	$-0.733763\pi$
$727$	−1.90997e7	−1.34027	−0.670134	+	0.742240i	$0.733763\pi$
$728$	1.22618e6	0.0857481
$729$	−1.12579e7	−0.784586
$730$	−7.03420e6	−0.488548
$731$	−2.34945e7	−1.62619
$732$	−1.04006e6	−0.0717435
$733$	−2.30424e6	−0.158404	−0.0792021	−	0.996859i	$-0.525237\pi$
$733$	−2.30424e6	−0.158404	−0.0792021	+	0.996859i	$0.525237\pi$
$734$	−8.54959e6	−0.585740
$735$	180075.	0.0122952
$736$	−2.48832e6	−0.169321
$737$	2.11102e7	1.43161
$738$	3.12250e6	0.211038
$739$	3.62955e6	0.244479	0.122240	−	0.992501i	$-0.460992\pi$
$739$	3.62955e6	0.244479	0.122240	+	0.992501i	$0.460992\pi$
$740$	2.81680e6	0.189094
$741$	2.74717e6	0.183797
$742$	−604464.	−0.0403052
$743$	−9.73856e6	−0.647177	−0.323588	−	0.946198i	$-0.604889\pi$
$743$	−9.73856e6	−0.647177	−0.323588	+	0.946198i	$0.604889\pi$
$744$	771072.	0.0510696
$745$	301950.	0.0199317
$746$	822496.	0.0541111
$747$	−176904.	−0.0115994
$748$	6.47352e6	0.423045
$749$	1.73254e6	0.112844
$750$	−187500.	−0.0121716
$751$	−2.48272e7	−1.60630	−0.803152	−	0.595774i	$-0.796845\pi$
$751$	−2.48272e7	−1.60630	−0.803152	+	0.595774i	$0.796845\pi$
$752$	2.64115e6	0.170313
$753$	3.30071e6	0.212139
$754$	1.29171e7	0.827439
$755$	5.21043e6	0.332664
$756$	1.12190e6	0.0713923
$757$	−1.28400e7	−0.814376	−0.407188	−	0.913344i	$-0.633491\pi$
$757$	−1.28400e7	−0.814376	−0.407188	+	0.913344i	$0.633491\pi$
$758$	−1.40215e7	−0.886380
$759$	−2.95245e6	−0.186028
$760$	3.74720e6	0.235328
$761$	2.89560e7	1.81250	0.906249	−	0.422744i	$-0.138933\pi$
$761$	2.89560e7	1.81250	0.906249	+	0.422744i	$0.138933\pi$
$762$	−3.40781e6	−0.212612
$763$	−7.40797e6	−0.460668
$764$	−8.43250e6	−0.522664
$765$	5.84415e6	0.361050
$766$	−4.51618e6	−0.278099
$767$	7.35706e6	0.451560
$768$	−196608.	−0.0120281
$769$	−1.78116e7	−1.08614	−0.543071	−	0.839687i	$-0.682739\pi$
$769$	−1.78116e7	−1.08614	−0.543071	+	0.839687i	$0.682739\pi$
$770$	1.98450e6	0.120621
$771$	3.24689e6	0.196713
$772$	2.29146e6	0.138378
$773$	1.73536e7	1.04458	0.522290	−	0.852768i	$-0.325078\pi$
$773$	1.73536e7	1.04458	0.522290	+	0.852768i	$0.325078\pi$
$774$	−2.20128e7	−1.32076
$775$	2.51000e6	0.150113
$776$	−7.06784e6	−0.421340
$777$	1.03517e6	0.0615121
$778$	4.80011e6	0.284316
$779$	7.81291e6	0.461285
$780$	−469200.	−0.0276135
$781$	−1.15668e7	−0.678556
$782$	−9.71028e6	−0.567825
$783$	1.18186e7	0.688910
$784$	614656.	0.0357143
$785$	−9.10235e6	−0.527205
$786$	3.13726e6	0.181131
$787$	812177.	0.0467427	0.0233714	−	0.999727i	$-0.492560\pi$
$787$	812177.	0.0467427	0.0233714	+	0.999727i	$0.492560\pi$
$788$	5.57549e6	0.319865
$789$	−248850.	−0.0142313
$790$	5.88230e6	0.335335
$791$	−6.55061e6	−0.372255
$792$	6.06528e6	0.343588
$793$	−8.47219e6	−0.478424
$794$	1.76735e7	0.994879
$795$	231300.	0.0129795
$796$	1.20723e7	0.675318
$797$	−8.58201e6	−0.478568	−0.239284	−	0.970950i	$-0.576913\pi$
$797$	−8.58201e6	−0.478568	−0.239284	+	0.970950i	$0.576913\pi$
$798$	1.37710e6	0.0765521
$799$	1.03067e7	0.571152
$800$	−640000.	−0.0353553
$801$	−3.16799e7	−1.74462
$802$	1.25311e7	0.687946
$803$	−2.84885e7	−1.55912
$804$	−2.50195e6	−0.136502
$805$	−2.97675e6	−0.161902
$806$	6.28102e6	0.340559
$807$	1.90147e6	0.102779
$808$	−2.14080e6	−0.115358
$809$	−2.83000e6	−0.152025	−0.0760125	−	0.997107i	$-0.524219\pi$
$809$	−2.83000e6	−0.152025	−0.0760125	+	0.997107i	$0.524219\pi$
$810$	5.25690e6	0.281525
$811$	−1.06484e7	−0.568504	−0.284252	−	0.958750i	$-0.591745\pi$
$811$	−1.06484e7	−0.568504	−0.284252	+	0.958750i	$0.591745\pi$
$812$	6.47506e6	0.344630
$813$	836868.	0.0444049
$814$	1.14080e7	0.603462
$815$	−15650.0	−0.000825316 0
$816$	−767232.	−0.0403368
$817$	−5.50792e7	−2.88690
$818$	−3.44598e6	−0.180065
$819$	4.48321e6	0.233549
$820$	−1.33440e6	−0.0693029
$821$	−2.59970e7	−1.34606	−0.673032	−	0.739613i	$-0.735008\pi$
$821$	−2.59970e7	−1.34606	−0.673032	+	0.739613i	$0.735008\pi$
$822$	476064.	0.0245746
$823$	−2.03099e7	−1.04522	−0.522611	−	0.852571i	$-0.675042\pi$
$823$	−2.03099e7	−1.04522	−0.522611	+	0.852571i	$0.675042\pi$
$824$	7.05990e6	0.362227
$825$	−759375.	−0.0388438
$826$	3.68794e6	0.188076
$827$	1.68001e6	0.0854175	0.0427088	−	0.999088i	$-0.486401\pi$
$827$	1.68001e6	0.0854175	0.0427088	+	0.999088i	$0.486401\pi$
$828$	−9.09792e6	−0.461176
$829$	−6.71070e6	−0.339142	−0.169571	−	0.985518i	$-0.554238\pi$
$829$	−6.71070e6	−0.339142	−0.169571	+	0.985518i	$0.554238\pi$
$830$	75600.0	0.00380914
$831$	−6.52569e6	−0.327811
$832$	−1.60154e6	−0.0802100
$833$	2.39860e6	0.119769
$834$	−2.19151e6	−0.109101
$835$	−1.11404e7	−0.552950
$836$	1.51762e7	0.751011
$837$	5.74690e6	0.283543
$838$	−1.86318e7	−0.916527
$839$	2.60856e7	1.27937	0.639686	−	0.768637i	$-0.279065\pi$
$839$	2.60856e7	1.27937	0.639686	+	0.768637i	$0.279065\pi$
$840$	−235200.	−0.0115011
$841$	4.76999e7	2.32556
$842$	−2.79958e7	−1.36086
$843$	2.07870e6	0.100745
$844$	−9.45198e6	−0.456738
$845$	5.46030e6	0.263072
$846$	9.65671e6	0.463878
$847$	145726.	0.00697957
$848$	789504.	0.0377020
$849$	−3.12062e6	−0.148584
$850$	−2.49750e6	−0.118565
$851$	−1.71121e7	−0.809988
$852$	1.37088e6	0.0646994
$853$	9.54873e6	0.449338	0.224669	−	0.974435i	$-0.427870\pi$
$853$	9.54873e6	0.449338	0.224669	+	0.974435i	$0.427870\pi$
$854$	−4.24693e6	−0.199265
$855$	1.37007e7	0.640955
$856$	−2.26291e6	−0.105556
$857$	3.51377e7	1.63426	0.817130	−	0.576453i	$-0.195564\pi$
$857$	3.51377e7	1.63426	0.817130	+	0.576453i	$0.195564\pi$
$858$	−1.90026e6	−0.0881241
$859$	−1.60428e7	−0.741816	−0.370908	−	0.928670i	$-0.620953\pi$
$859$	−1.60428e7	−0.741816	−0.370908	+	0.928670i	$0.620953\pi$
$860$	9.40720e6	0.433725
$861$	−490392.	−0.0225442
$862$	908364.	0.0416382
$863$	−2.77776e7	−1.26960	−0.634802	−	0.772675i	$-0.718918\pi$
$863$	−2.77776e7	−1.26960	−0.634802	+	0.772675i	$0.718918\pi$
$864$	−1.46534e6	−0.0667814
$865$	−1.60867e7	−0.731015
$866$	2.83845e7	1.28614
$867$	1.26557e6	0.0571792
$868$	3.14854e6	0.141844
$869$	2.38233e7	1.07017
$870$	−2.47770e6	−0.110981
$871$	−2.03805e7	−0.910268
$872$	9.67571e6	0.430915
$873$	−2.58418e7	−1.14759
$874$	−2.27642e7	−1.00803
$875$	−765625.	−0.0338062
$876$	3.37642e6	0.148661
$877$	2.46748e7	1.08332	0.541658	−	0.840599i	$-0.317797\pi$
$877$	2.46748e7	1.08332	0.541658	+	0.840599i	$0.317797\pi$
$878$	−2.37303e6	−0.103888
$879$	3.25695e6	0.142180
$880$	−2.59200e6	−0.112831
$881$	−1.27792e7	−0.554707	−0.277353	−	0.960768i	$-0.589457\pi$
$881$	−1.27792e7	−0.554707	−0.277353	+	0.960768i	$0.589457\pi$
$882$	2.24734e6	0.0972739
$883$	−2.63417e7	−1.13695	−0.568476	−	0.822700i	$-0.692467\pi$
$883$	−2.63417e7	−1.13695	−0.568476	+	0.822700i	$0.692467\pi$
$884$	−6.24974e6	−0.268987
$885$	−1.41120e6	−0.0605662
$886$	1.31077e7	0.560972
$887$	2.60037e7	1.10975	0.554877	−	0.831932i	$-0.312765\pi$
$887$	2.60037e7	1.10975	0.554877	+	0.831932i	$0.312765\pi$
$888$	−1.35206e6	−0.0575393
$889$	−1.39152e7	−0.590521
$890$	1.35384e7	0.572918
$891$	2.12904e7	0.898443
$892$	−6.33765e6	−0.266696
$893$	2.41624e7	1.01394
$894$	−144936.	−0.00606502
$895$	−6.12870e6	−0.255747
$896$	−802816.	−0.0334077
$897$	2.85039e6	0.118283
$898$	1.73172e7	0.716616
$899$	3.31681e7	1.36874
$900$	−2.34000e6	−0.0962963
$901$	3.08092e6	0.126435
$902$	−5.40432e6	−0.221169
$903$	3.45715e6	0.141091
$904$	8.55590e6	0.348213
$905$	−1.71545e7	−0.696236
$906$	−2.50100e6	−0.101226
$907$	−4.11852e7	−1.66235	−0.831177	−	0.556008i	$-0.812332\pi$
$907$	−4.11852e7	−1.66235	−0.831177	+	0.556008i	$0.812332\pi$
$908$	152592.	0.00614210
$909$	−7.82730e6	−0.314197
$910$	−1.91590e6	−0.0766954
$911$	−7.92211e6	−0.316261	−0.158130	−	0.987418i	$-0.550547\pi$
$911$	−7.92211e6	−0.316261	−0.158130	+	0.987418i	$0.550547\pi$
$912$	−1.79866e6	−0.0716079
$913$	306180.	0.0121563
$914$	1.96655e7	0.778646
$915$	1.62510e6	0.0641693
$916$	1.12809e7	0.444227
$917$	1.28105e7	0.503085
$918$	−5.71828e6	−0.223954
$919$	1.59154e7	0.621624	0.310812	−	0.950471i	$-0.399399\pi$
$919$	1.59154e7	0.621624	0.310812	+	0.950471i	$0.399399\pi$
$920$	3.88800e6	0.151446
$921$	−4389.00	−0.000170497 0
$922$	−2.81168e7	−1.08928
$923$	1.11670e7	0.431450
$924$	−952560.	−0.0367039
$925$	−4.40125e6	−0.169130
$926$	−1.15424e7	−0.442351
$927$	2.58128e7	0.986587
$928$	−8.45722e6	−0.322372
$929$	−3.37148e7	−1.28169	−0.640843	−	0.767672i	$-0.721415\pi$
$929$	−3.37148e7	−1.28169	−0.640843	+	0.767672i	$0.721415\pi$
$930$	−1.20480e6	−0.0456781
$931$	5.62314e6	0.212620
$932$	8.54746e6	0.322327
$933$	−9.35930e6	−0.351997
$934$	2.40233e7	0.901085
$935$	−1.01149e7	−0.378383
$936$	−5.85562e6	−0.218466
$937$	−4.04362e7	−1.50460	−0.752300	−	0.658820i	$-0.771056\pi$
$937$	−4.04362e7	−1.50460	−0.752300	+	0.658820i	$0.771056\pi$
$938$	−1.02163e7	−0.379129
$939$	−2.49428e6	−0.0923167
$940$	−4.12680e6	−0.152333
$941$	3.62378e7	1.33410	0.667048	−	0.745015i	$-0.267557\pi$
$941$	3.62378e7	1.33410	0.667048	+	0.745015i	$0.267557\pi$
$942$	4.36913e6	0.160423
$943$	8.10648e6	0.296861
$944$	−4.81690e6	−0.175929
$945$	−1.75298e6	−0.0638552
$946$	3.80992e7	1.38416
$947$	2.94238e7	1.06616	0.533082	−	0.846064i	$-0.321034\pi$
$947$	2.94238e7	1.06616	0.533082	+	0.846064i	$0.321034\pi$
$948$	−2.82350e6	−0.102039
$949$	2.75037e7	0.991348
$950$	−5.85500e6	−0.210483
$951$	3.77552e6	0.135371
$952$	−3.13286e6	−0.112034
$953$	3.59497e7	1.28222	0.641110	−	0.767449i	$-0.278474\pi$
$953$	3.59497e7	1.28222	0.641110	+	0.767449i	$0.278474\pi$
$954$	2.88662e6	0.102688
$955$	1.31758e7	0.467485
$956$	−1.44195e7	−0.510278
$957$	−1.00347e7	−0.354180
$958$	−3.76438e6	−0.132519
$959$	1.94393e6	0.0682549
$960$	307200.	0.0107583
$961$	−1.25009e7	−0.436649
$962$	−1.10137e7	−0.383703
$963$	−8.27377e6	−0.287500
$964$	−1.52382e7	−0.528132
$965$	−3.58040e6	−0.123769
$966$	1.42884e6	0.0492653
$967$	1.19506e6	0.0410982	0.0205491	−	0.999789i	$-0.493459\pi$
$967$	1.19506e6	0.0410982	0.0205491	+	0.999789i	$0.493459\pi$
$968$	−190336.	−0.00652879
$969$	−7.01897e6	−0.240140
$970$	1.10435e7	0.376858
$971$	3.26221e7	1.11036	0.555180	−	0.831730i	$-0.312649\pi$
$971$	3.26221e7	1.11036	0.555180	+	0.831730i	$0.312649\pi$
$972$	−8.08704e6	−0.274552
$973$	−8.94867e6	−0.303024
$974$	−7.64482e6	−0.258208
$975$	733125.	0.0246983
$976$	5.54701e6	0.186395
$977$	5.36858e7	1.79938	0.899690	−	0.436529i	$-0.143792\pi$
$977$	5.36858e7	1.79938	0.899690	+	0.436529i	$0.143792\pi$
$978$	7512.00	0.000251136 0
$979$	5.48305e7	1.82838
$980$	−960400.	−0.0319438
$981$	3.53768e7	1.17367
$982$	−1.58196e7	−0.523501
$983$	−3.31124e7	−1.09297	−0.546484	−	0.837469i	$-0.684034\pi$
$983$	−3.31124e7	−1.09297	−0.546484	+	0.837469i	$0.684034\pi$
$984$	640512.	0.0210882
$985$	−8.71170e6	−0.286096
$986$	−3.30030e7	−1.08109
$987$	−1.51660e6	−0.0495539
$988$	−1.46516e7	−0.477520
$989$	−5.71487e7	−1.85787
$990$	−9.47700e6	−0.307314
$991$	−1.97082e7	−0.637475	−0.318738	−	0.947843i	$-0.603259\pi$
$991$	−1.97082e7	−0.637475	−0.318738	+	0.947843i	$0.603259\pi$
$992$	−4.11238e6	−0.132683
$993$	6.91396e6	0.222512
$994$	5.59776e6	0.179700
$995$	−1.88630e7	−0.604022
$996$	−36288.0	−0.00115908
$997$	3.31940e7	1.05760	0.528800	−	0.848747i	$-0.322642\pi$
$997$	3.31940e7	1.05760	0.528800	+	0.848747i	$0.322642\pi$
$998$	−2.83883e7	−0.902222
$999$	−1.00771e7	−0.319464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.6.a.c.1.1	✓	1
3.2	odd	2		630.6.a.n.1.1		1
4.3	odd	2		560.6.a.d.1.1		1
5.2	odd	4		350.6.c.e.99.1		2
5.3	odd	4		350.6.c.e.99.2		2
5.4	even	2		350.6.a.k.1.1		1
7.6	odd	2		490.6.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.c.1.1	✓	1	1.1	even	1	trivial
350.6.a.k.1.1		1	5.4	even	2
350.6.c.e.99.1		2	5.2	odd	4
350.6.c.e.99.2		2	5.3	odd	4
490.6.a.e.1.1		1	7.6	odd	2
560.6.a.d.1.1		1	4.3	odd	2
630.6.a.n.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	70.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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