LMFDB - Embedded newform 10.6.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [10,6,Mod(1,10)] 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("10.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [1,-4,-26] 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:	$1.60383819813$
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	$\chi$	$=$	10.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-4.00000 q^{2} -26.0000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +104.000 q^{6} -22.0000 q^{7} -64.0000 q^{8} +433.000 q^{9} +100.000 q^{10} -768.000 q^{11} -416.000 q^{12} -46.0000 q^{13} +88.0000 q^{14} +650.000 q^{15} +256.000 q^{16} +378.000 q^{17} -1732.00 q^{18} +1100.00 q^{19} -400.000 q^{20} +572.000 q^{21} +3072.00 q^{22} -1986.00 q^{23} +1664.00 q^{24} +625.000 q^{25} +184.000 q^{26} -4940.00 q^{27} -352.000 q^{28} -5610.00 q^{29} -2600.00 q^{30} -3988.00 q^{31} -1024.00 q^{32} +19968.0 q^{33} -1512.00 q^{34} +550.000 q^{35} +6928.00 q^{36} -142.000 q^{37} -4400.00 q^{38} +1196.00 q^{39} +1600.00 q^{40} +1542.00 q^{41} -2288.00 q^{42} -5026.00 q^{43} -12288.0 q^{44} -10825.0 q^{45} +7944.00 q^{46} +24738.0 q^{47} -6656.00 q^{48} -16323.0 q^{49} -2500.00 q^{50} -9828.00 q^{51} -736.000 q^{52} -14166.0 q^{53} +19760.0 q^{54} +19200.0 q^{55} +1408.00 q^{56} -28600.0 q^{57} +22440.0 q^{58} +28380.0 q^{59} +10400.0 q^{60} +5522.00 q^{61} +15952.0 q^{62} -9526.00 q^{63} +4096.00 q^{64} +1150.00 q^{65} -79872.0 q^{66} -24742.0 q^{67} +6048.00 q^{68} +51636.0 q^{69} -2200.00 q^{70} +42372.0 q^{71} -27712.0 q^{72} -52126.0 q^{73} +568.000 q^{74} -16250.0 q^{75} +17600.0 q^{76} +16896.0 q^{77} -4784.00 q^{78} -39640.0 q^{79} -6400.00 q^{80} +23221.0 q^{81} -6168.00 q^{82} -59826.0 q^{83} +9152.00 q^{84} -9450.00 q^{85} +20104.0 q^{86} +145860. q^{87} +49152.0 q^{88} +57690.0 q^{89} +43300.0 q^{90} +1012.00 q^{91} -31776.0 q^{92} +103688. q^{93} -98952.0 q^{94} -27500.0 q^{95} +26624.0 q^{96} -144382. q^{97} +65292.0 q^{98} -332544. q^{99} +O(q^{100})\)

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
$3$	−26.0000	−1.66790	−0.833950	−	0.551839i	$-0.813926\pi$
$3$	−26.0000	−1.66790	−0.833950	+	0.551839i	$0.813926\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	104.000	1.17938
$7$	−22.0000	−0.169698	−0.0848492	−	0.996394i	$-0.527041\pi$
$7$	−22.0000	−0.169698	−0.0848492	+	0.996394i	$0.527041\pi$
$8$	−64.0000	−0.353553
$9$	433.000	1.78189
$10$	100.000	0.316228
$11$	−768.000	−1.91372	−0.956862	−	0.290541i	$-0.906165\pi$
$11$	−768.000	−1.91372	−0.956862	+	0.290541i	$0.906165\pi$
$12$	−416.000	−0.833950
$13$	−46.0000	−0.0754917	−0.0377459	−	0.999287i	$-0.512018\pi$
$13$	−46.0000	−0.0754917	−0.0377459	+	0.999287i	$0.512018\pi$
$14$	88.0000	0.119995
$15$	650.000	0.745908
$16$	256.000	0.250000
$17$	378.000	0.317227	0.158613	−	0.987341i	$-0.449298\pi$
$17$	378.000	0.317227	0.158613	+	0.987341i	$0.449298\pi$
$18$	−1732.00	−1.25999
$19$	1100.00	0.699051	0.349525	−	0.936927i	$-0.386343\pi$
$19$	1100.00	0.699051	0.349525	+	0.936927i	$0.386343\pi$
$20$	−400.000	−0.223607
$21$	572.000	0.283040
$22$	3072.00	1.35321
$23$	−1986.00	−0.782816	−0.391408	−	0.920217i	$-0.628012\pi$
$23$	−1986.00	−0.782816	−0.391408	+	0.920217i	$0.628012\pi$
$24$	1664.00	0.589692
$25$	625.000	0.200000
$26$	184.000	0.0533807
$27$	−4940.00	−1.30412
$28$	−352.000	−0.0848492
$29$	−5610.00	−1.23870	−0.619352	−	0.785113i	$-0.712605\pi$
$29$	−5610.00	−1.23870	−0.619352	+	0.785113i	$0.712605\pi$
$30$	−2600.00	−0.527437
$31$	−3988.00	−0.745334	−0.372667	−	0.927965i	$-0.621557\pi$
$31$	−3988.00	−0.745334	−0.372667	+	0.927965i	$0.621557\pi$
$32$	−1024.00	−0.176777
$33$	19968.0	3.19190
$34$	−1512.00	−0.224313
$35$	550.000	0.0758914
$36$	6928.00	0.890947
$37$	−142.000	−0.0170523	−0.00852617	−	0.999964i	$-0.502714\pi$
$37$	−142.000	−0.0170523	−0.00852617	+	0.999964i	$0.502714\pi$
$38$	−4400.00	−0.494303
$39$	1196.00	0.125913
$40$	1600.00	0.158114
$41$	1542.00	0.143260	0.0716300	−	0.997431i	$-0.477180\pi$
$41$	1542.00	0.143260	0.0716300	+	0.997431i	$0.477180\pi$
$42$	−2288.00	−0.200139
$43$	−5026.00	−0.414526	−0.207263	−	0.978285i	$-0.566456\pi$
$43$	−5026.00	−0.414526	−0.207263	+	0.978285i	$0.566456\pi$
$44$	−12288.0	−0.956862
$45$	−10825.0	−0.796887
$46$	7944.00	0.553534
$47$	24738.0	1.63350	0.816752	−	0.576990i	$-0.195773\pi$
$47$	24738.0	1.63350	0.816752	+	0.576990i	$0.195773\pi$
$48$	−6656.00	−0.416975
$49$	−16323.0	−0.971202
$50$	−2500.00	−0.141421
$51$	−9828.00	−0.529102
$52$	−736.000	−0.0377459
$53$	−14166.0	−0.692720	−0.346360	−	0.938102i	$-0.612582\pi$
$53$	−14166.0	−0.692720	−0.346360	+	0.938102i	$0.612582\pi$
$54$	19760.0	0.922152
$55$	19200.0	0.855844
$56$	1408.00	0.0599974
$57$	−28600.0	−1.16595
$58$	22440.0	0.875897
$59$	28380.0	1.06141	0.530704	−	0.847557i	$-0.321928\pi$
$59$	28380.0	1.06141	0.530704	+	0.847557i	$0.321928\pi$
$60$	10400.0	0.372954
$61$	5522.00	0.190008	0.0950040	−	0.995477i	$-0.469714\pi$
$61$	5522.00	0.190008	0.0950040	+	0.995477i	$0.469714\pi$
$62$	15952.0	0.527031
$63$	−9526.00	−0.302384
$64$	4096.00	0.125000
$65$	1150.00	0.0337609
$66$	−79872.0	−2.25702
$67$	−24742.0	−0.673361	−0.336680	−	0.941619i	$-0.609304\pi$
$67$	−24742.0	−0.673361	−0.336680	+	0.941619i	$0.609304\pi$
$68$	6048.00	0.158613
$69$	51636.0	1.30566
$70$	−2200.00	−0.0536633
$71$	42372.0	0.997546	0.498773	−	0.866733i	$-0.333784\pi$
$71$	42372.0	0.997546	0.498773	+	0.866733i	$0.333784\pi$
$72$	−27712.0	−0.629994
$73$	−52126.0	−1.14485	−0.572423	−	0.819958i	$-0.693997\pi$
$73$	−52126.0	−1.14485	−0.572423	+	0.819958i	$0.693997\pi$
$74$	568.000	0.0120578
$75$	−16250.0	−0.333580
$76$	17600.0	0.349525
$77$	16896.0	0.324756
$78$	−4784.00	−0.0890337
$79$	−39640.0	−0.714605	−0.357302	−	0.933989i	$-0.616303\pi$
$79$	−39640.0	−0.714605	−0.357302	+	0.933989i	$0.616303\pi$
$80$	−6400.00	−0.111803
$81$	23221.0	0.393250
$82$	−6168.00	−0.101300
$83$	−59826.0	−0.953223	−0.476612	−	0.879114i	$-0.658135\pi$
$83$	−59826.0	−0.953223	−0.476612	+	0.879114i	$0.658135\pi$
$84$	9152.00	0.141520
$85$	−9450.00	−0.141868
$86$	20104.0	0.293114
$87$	145860.	2.06604
$88$	49152.0	0.676604
$89$	57690.0	0.772015	0.386007	−	0.922496i	$-0.373854\pi$
$89$	57690.0	0.772015	0.386007	+	0.922496i	$0.373854\pi$
$90$	43300.0	0.563484
$91$	1012.00	0.0128108
$92$	−31776.0	−0.391408
$93$	103688.	1.24314
$94$	−98952.0	−1.15506
$95$	−27500.0	−0.312625
$96$	26624.0	0.294846
$97$	−144382.	−1.55806	−0.779029	−	0.626988i	$-0.784288\pi$
$97$	−144382.	−1.55806	−0.779029	+	0.626988i	$0.784288\pi$
$98$	65292.0	0.686744
$99$	−332544.	−3.41005
$100$	10000.0	0.100000
$101$	−141258.	−1.37787	−0.688937	−	0.724821i	$-0.741922\pi$
$101$	−141258.	−1.37787	−0.688937	+	0.724821i	$0.741922\pi$
$102$	39312.0	0.374132
$103$	139814.	1.29855	0.649273	−	0.760555i	$-0.275073\pi$
$103$	139814.	1.29855	0.649273	+	0.760555i	$0.275073\pi$
$104$	2944.00	0.0266904
$105$	−14300.0	−0.126579
$106$	56664.0	0.489827
$107$	86418.0	0.729701	0.364850	−	0.931066i	$-0.381120\pi$
$107$	86418.0	0.729701	0.364850	+	0.931066i	$0.381120\pi$
$108$	−79040.0	−0.652060
$109$	218450.	1.76111	0.880554	−	0.473947i	$-0.157171\pi$
$109$	218450.	1.76111	0.880554	+	0.473947i	$0.157171\pi$
$110$	−76800.0	−0.605173
$111$	3692.00	0.0284416
$112$	−5632.00	−0.0424246
$113$	−28806.0	−0.212220	−0.106110	−	0.994354i	$-0.533840\pi$
$113$	−28806.0	−0.212220	−0.106110	+	0.994354i	$0.533840\pi$
$114$	114400.	0.824449
$115$	49650.0	0.350086
$116$	−89760.0	−0.619352
$117$	−19918.0	−0.134518
$118$	−113520.	−0.750529
$119$	−8316.00	−0.0538328
$120$	−41600.0	−0.263718
$121$	428773.	2.66234
$122$	−22088.0	−0.134356
$123$	−40092.0	−0.238943
$124$	−63808.0	−0.372667
$125$	−15625.0	−0.0894427
$126$	38104.0	0.213818
$127$	−216502.	−1.19111	−0.595556	−	0.803314i	$-0.703068\pi$
$127$	−216502.	−1.19111	−0.595556	+	0.803314i	$0.703068\pi$
$128$	−16384.0	−0.0883883
$129$	130676.	0.691388
$130$	−4600.00	−0.0238726
$131$	−244608.	−1.24535	−0.622676	−	0.782479i	$-0.713955\pi$
$131$	−244608.	−1.24535	−0.622676	+	0.782479i	$0.713955\pi$
$132$	319488.	1.59595
$133$	−24200.0	−0.118628
$134$	98968.0	0.476138
$135$	123500.	0.583220
$136$	−24192.0	−0.112157
$137$	−239502.	−1.09020	−0.545102	−	0.838370i	$-0.683509\pi$
$137$	−239502.	−1.09020	−0.545102	+	0.838370i	$0.683509\pi$
$138$	−206544.	−0.923241
$139$	30860.0	0.135475	0.0677375	−	0.997703i	$-0.478422\pi$
$139$	30860.0	0.135475	0.0677375	+	0.997703i	$0.478422\pi$
$140$	8800.00	0.0379457
$141$	−643188.	−2.72452
$142$	−169488.	−0.705372
$143$	35328.0	0.144470
$144$	110848.	0.445473
$145$	140250.	0.553966
$146$	208504.	0.809529
$147$	424398.	1.61987
$148$	−2272.00	−0.00852617
$149$	−100950.	−0.372512	−0.186256	−	0.982501i	$-0.559635\pi$
$149$	−100950.	−0.372512	−0.186256	+	0.982501i	$0.559635\pi$
$150$	65000.0	0.235877
$151$	12452.0	0.0444423	0.0222212	−	0.999753i	$-0.492926\pi$
$151$	12452.0	0.0444423	0.0222212	+	0.999753i	$0.492926\pi$
$152$	−70400.0	−0.247152
$153$	163674.	0.565264
$154$	−67584.0	−0.229637
$155$	99700.0	0.333323
$156$	19136.0	0.0629564
$157$	−6022.00	−0.0194981	−0.00974903	−	0.999952i	$-0.503103\pi$
$157$	−6022.00	−0.0194981	−0.00974903	+	0.999952i	$0.503103\pi$
$158$	158560.	0.505302
$159$	368316.	1.15539
$160$	25600.0	0.0790569
$161$	43692.0	0.132843
$162$	−92884.0	−0.278070
$163$	−500866.	−1.47656	−0.738282	−	0.674492i	$-0.764363\pi$
$163$	−500866.	−1.47656	−0.738282	+	0.674492i	$0.764363\pi$
$164$	24672.0	0.0716300
$165$	−499200.	−1.42746
$166$	239304.	0.674031
$167$	555258.	1.54065	0.770324	−	0.637652i	$-0.220094\pi$
$167$	555258.	1.54065	0.770324	+	0.637652i	$0.220094\pi$
$168$	−36608.0	−0.100070
$169$	−369177.	−0.994301
$170$	37800.0	0.100316
$171$	476300.	1.24563
$172$	−80416.0	−0.207263
$173$	417354.	1.06020	0.530102	−	0.847934i	$-0.322154\pi$
$173$	417354.	1.06020	0.530102	+	0.847934i	$0.322154\pi$
$174$	−583440.	−1.46091
$175$	−13750.0	−0.0339397
$176$	−196608.	−0.478431
$177$	−737880.	−1.77032
$178$	−230760.	−0.545897
$179$	−52380.0	−0.122189	−0.0610946	−	0.998132i	$-0.519459\pi$
$179$	−52380.0	−0.122189	−0.0610946	+	0.998132i	$0.519459\pi$
$180$	−173200.	−0.398443
$181$	546662.	1.24029	0.620144	−	0.784488i	$-0.287074\pi$
$181$	546662.	1.24029	0.620144	+	0.784488i	$0.287074\pi$
$182$	−4048.00	−0.00905862
$183$	−143572.	−0.316914
$184$	127104.	0.276767
$185$	3550.00	0.00762604
$186$	−414752.	−0.879035
$187$	−290304.	−0.607084
$188$	395808.	0.816752
$189$	108680.	0.221307
$190$	110000.	0.221059
$191$	−452028.	−0.896565	−0.448283	−	0.893892i	$-0.647964\pi$
$191$	−452028.	−0.896565	−0.448283	+	0.893892i	$0.647964\pi$
$192$	−106496.	−0.208488
$193$	485594.	0.938383	0.469191	−	0.883097i	$-0.344545\pi$
$193$	485594.	0.938383	0.469191	+	0.883097i	$0.344545\pi$
$194$	577528.	1.10171
$195$	−29900.0	−0.0563099
$196$	−261168.	−0.485601
$197$	1.01018e6	1.85452	0.927262	−	0.374414i	$-0.122156\pi$
$197$	1.01018e6	1.85452	0.927262	+	0.374414i	$0.122156\pi$
$198$	1.33018e6	2.41127
$199$	−807640.	−1.44572	−0.722862	−	0.690993i	$-0.757174\pi$
$199$	−807640.	−1.44572	−0.722862	+	0.690993i	$0.757174\pi$
$200$	−40000.0	−0.0707107
$201$	643292.	1.12310
$202$	565032.	0.974304
$203$	123420.	0.210206
$204$	−157248.	−0.264551
$205$	−38550.0	−0.0640678
$206$	−559256.	−0.918211
$207$	−859938.	−1.39489
$208$	−11776.0	−0.0188729
$209$	−844800.	−1.33779
$210$	57200.0	0.0895051
$211$	149552.	0.231252	0.115626	−	0.993293i	$-0.463113\pi$
$211$	149552.	0.231252	0.115626	+	0.993293i	$0.463113\pi$
$212$	−226656.	−0.346360
$213$	−1.10167e6	−1.66381
$214$	−345672.	−0.515976
$215$	125650.	0.185381
$216$	316160.	0.461076
$217$	87736.0	0.126482
$218$	−873800.	−1.24529
$219$	1.35528e6	1.90949
$220$	307200.	0.427922
$221$	−17388.0	−0.0239480
$222$	−14768.0	−0.0201113
$223$	−443506.	−0.597224	−0.298612	−	0.954375i	$-0.596524\pi$
$223$	−443506.	−0.597224	−0.298612	+	0.954375i	$0.596524\pi$
$224$	22528.0	0.0299987
$225$	270625.	0.356379
$226$	115224.	0.150062
$227$	420018.	0.541007	0.270504	−	0.962719i	$-0.412810\pi$
$227$	420018.	0.541007	0.270504	+	0.962719i	$0.412810\pi$
$228$	−457600.	−0.582974
$229$	1.05875e6	1.33415	0.667075	−	0.744990i	$-0.267546\pi$
$229$	1.05875e6	1.33415	0.667075	+	0.744990i	$0.267546\pi$
$230$	−198600.	−0.247548
$231$	−439296.	−0.541661
$232$	359040.	0.437948
$233$	−1.27345e6	−1.53671	−0.768353	−	0.640026i	$-0.778923\pi$
$233$	−1.27345e6	−1.53671	−0.768353	+	0.640026i	$0.778923\pi$
$234$	79672.0	0.0951187
$235$	−618450.	−0.730525
$236$	454080.	0.530704
$237$	1.03064e6	1.19189
$238$	33264.0	0.0380655
$239$	−370680.	−0.419763	−0.209882	−	0.977727i	$-0.567308\pi$
$239$	−370680.	−0.419763	−0.209882	+	0.977727i	$0.567308\pi$
$240$	166400.	0.186477
$241$	−561298.	−0.622517	−0.311258	−	0.950325i	$-0.600750\pi$
$241$	−561298.	−0.622517	−0.311258	+	0.950325i	$0.600750\pi$
$242$	−1.71509e6	−1.88256
$243$	596674.	0.648219
$244$	88352.0	0.0950040
$245$	408075.	0.434335
$246$	160368.	0.168958
$247$	−50600.0	−0.0527726
$248$	255232.	0.263515
$249$	1.55548e6	1.58988
$250$	62500.0	0.0632456
$251$	577152.	0.578237	0.289119	−	0.957293i	$-0.406638\pi$
$251$	577152.	0.578237	0.289119	+	0.957293i	$0.406638\pi$
$252$	−152416.	−0.151192
$253$	1.52525e6	1.49809
$254$	866008.	0.842243
$255$	245700.	0.236622
$256$	65536.0	0.0625000
$257$	−651462.	−0.615257	−0.307628	−	0.951507i	$-0.599535\pi$
$257$	−651462.	−0.615257	−0.307628	+	0.951507i	$0.599535\pi$
$258$	−522704.	−0.488885
$259$	3124.00	0.00289375
$260$	18400.0	0.0168805
$261$	−2.42913e6	−2.20724
$262$	978432.	0.880597
$263$	917574.	0.817997	0.408999	−	0.912535i	$-0.365878\pi$
$263$	917574.	0.817997	0.408999	+	0.912535i	$0.365878\pi$
$264$	−1.27795e6	−1.12851
$265$	354150.	0.309794
$266$	96800.0	0.0838825
$267$	−1.49994e6	−1.28764
$268$	−395872.	−0.336680
$269$	−735390.	−0.619637	−0.309818	−	0.950796i	$-0.600268\pi$
$269$	−735390.	−0.619637	−0.309818	+	0.950796i	$0.600268\pi$
$270$	−494000.	−0.412399
$271$	−1.12131e6	−0.927474	−0.463737	−	0.885973i	$-0.653492\pi$
$271$	−1.12131e6	−0.927474	−0.463737	+	0.885973i	$0.653492\pi$
$272$	96768.0	0.0793066
$273$	−26312.0	−0.0213672
$274$	958008.	0.770891
$275$	−480000.	−0.382745
$276$	826176.	0.652830
$277$	−1.66034e6	−1.30016	−0.650082	−	0.759864i	$-0.725265\pi$
$277$	−1.66034e6	−1.30016	−0.650082	+	0.759864i	$0.725265\pi$
$278$	−123440.	−0.0957952
$279$	−1.72680e6	−1.32811
$280$	−35200.0	−0.0268317
$281$	1.45210e6	1.09706	0.548531	−	0.836130i	$-0.315187\pi$
$281$	1.45210e6	1.09706	0.548531	+	0.836130i	$0.315187\pi$
$282$	2.57275e6	1.92653
$283$	309014.	0.229357	0.114679	−	0.993403i	$-0.463416\pi$
$283$	309014.	0.229357	0.114679	+	0.993403i	$0.463416\pi$
$284$	677952.	0.498773
$285$	715000.	0.521427
$286$	−141312.	−0.102156
$287$	−33924.0	−0.0243110
$288$	−443392.	−0.314997
$289$	−1.27697e6	−0.899367
$290$	−561000.	−0.391713
$291$	3.75393e6	2.59869
$292$	−834016.	−0.572423
$293$	−1.59301e6	−1.08405	−0.542024	−	0.840363i	$-0.682342\pi$
$293$	−1.59301e6	−1.08405	−0.542024	+	0.840363i	$0.682342\pi$
$294$	−1.69759e6	−1.14542
$295$	−709500.	−0.474676
$296$	9088.00	0.00602891
$297$	3.79392e6	2.49573
$298$	403800.	0.263406
$299$	91356.0	0.0590961
$300$	−260000.	−0.166790
$301$	110572.	0.0703443
$302$	−49808.0	−0.0314255
$303$	3.67271e6	2.29816
$304$	281600.	0.174763
$305$	−138050.	−0.0849741
$306$	−654696.	−0.399702
$307$	1.24726e6	0.755284	0.377642	−	0.925952i	$-0.376735\pi$
$307$	1.24726e6	0.755284	0.377642	+	0.925952i	$0.376735\pi$
$308$	270336.	0.162378
$309$	−3.63516e6	−2.16585
$310$	−398800.	−0.235695
$311$	−665988.	−0.390450	−0.195225	−	0.980758i	$-0.562544\pi$
$311$	−665988.	−0.390450	−0.195225	+	0.980758i	$0.562544\pi$
$312$	−76544.0	−0.0445169
$313$	−591286.	−0.341143	−0.170572	−	0.985345i	$-0.554561\pi$
$313$	−591286.	−0.341143	−0.170572	+	0.985345i	$0.554561\pi$
$314$	24088.0	0.0137872
$315$	238150.	0.135230
$316$	−634240.	−0.357302
$317$	−516342.	−0.288595	−0.144298	−	0.989534i	$-0.546092\pi$
$317$	−516342.	−0.288595	−0.144298	+	0.989534i	$0.546092\pi$
$318$	−1.47326e6	−0.816983
$319$	4.30848e6	2.37054
$320$	−102400.	−0.0559017
$321$	−2.24687e6	−1.21707
$322$	−174768.	−0.0939339
$323$	415800.	0.221757
$324$	371536.	0.196625
$325$	−28750.0	−0.0150983
$326$	2.00346e6	1.04409
$327$	−5.67970e6	−2.93735
$328$	−98688.0	−0.0506500
$329$	−544236.	−0.277203
$330$	1.99680e6	1.00937
$331$	−3.29577e6	−1.65343	−0.826717	−	0.562619i	$-0.809794\pi$
$331$	−3.29577e6	−1.65343	−0.826717	+	0.562619i	$0.809794\pi$
$332$	−957216.	−0.476612
$333$	−61486.0	−0.0303854
$334$	−2.22103e6	−1.08940
$335$	618550.	0.301136
$336$	146432.	0.0707600
$337$	1.91098e6	0.916602	0.458301	−	0.888797i	$-0.348458\pi$
$337$	1.91098e6	0.916602	0.458301	+	0.888797i	$0.348458\pi$
$338$	1.47671e6	0.703077
$339$	748956.	0.353962
$340$	−151200.	−0.0709340
$341$	3.06278e6	1.42636
$342$	−1.90520e6	−0.880796
$343$	728860.	0.334510
$344$	321664.	0.146557
$345$	−1.29090e6	−0.583909
$346$	−1.66942e6	−0.749677
$347$	2.42006e6	1.07895	0.539476	−	0.842001i	$-0.318622\pi$
$347$	2.42006e6	1.07895	0.539476	+	0.842001i	$0.318622\pi$
$348$	2.33376e6	1.03302
$349$	2.50727e6	1.10189	0.550944	−	0.834542i	$-0.314268\pi$
$349$	2.50727e6	1.10189	0.550944	+	0.834542i	$0.314268\pi$
$350$	55000.0	0.0239990
$351$	227240.	0.0984503
$352$	786432.	0.338302
$353$	−413166.	−0.176477	−0.0882384	−	0.996099i	$-0.528124\pi$
$353$	−413166.	−0.176477	−0.0882384	+	0.996099i	$0.528124\pi$
$354$	2.95152e6	1.25181
$355$	−1.05930e6	−0.446116
$356$	923040.	0.386007
$357$	216216.	0.0897878
$358$	209520.	0.0864008
$359$	1.73772e6	0.711613	0.355806	−	0.934560i	$-0.384206\pi$
$359$	1.73772e6	0.711613	0.355806	+	0.934560i	$0.384206\pi$
$360$	692800.	0.281742
$361$	−1.26610e6	−0.511328
$362$	−2.18665e6	−0.877016
$363$	−1.11481e7	−4.44052
$364$	16192.0	0.00640541
$365$	1.30315e6	0.511991
$366$	574288.	0.224092
$367$	1.16098e6	0.449944	0.224972	−	0.974365i	$-0.427771\pi$
$367$	1.16098e6	0.449944	0.224972	+	0.974365i	$0.427771\pi$
$368$	−508416.	−0.195704
$369$	667686.	0.255274
$370$	−14200.0	−0.00539242
$371$	311652.	0.117553
$372$	1.65901e6	0.621572
$373$	343754.	0.127931	0.0639655	−	0.997952i	$-0.479625\pi$
$373$	343754.	0.127931	0.0639655	+	0.997952i	$0.479625\pi$
$374$	1.16122e6	0.429273
$375$	406250.	0.149182
$376$	−1.58323e6	−0.577531
$377$	258060.	0.0935120
$378$	−434720.	−0.156488
$379$	573140.	0.204957	0.102478	−	0.994735i	$-0.467323\pi$
$379$	573140.	0.204957	0.102478	+	0.994735i	$0.467323\pi$
$380$	−440000.	−0.156312
$381$	5.62905e6	1.98666
$382$	1.80811e6	0.633967
$383$	−2.88055e6	−1.00341	−0.501704	−	0.865039i	$-0.667293\pi$
$383$	−2.88055e6	−1.00341	−0.501704	+	0.865039i	$0.667293\pi$
$384$	425984.	0.147423
$385$	−422400.	−0.145235
$386$	−1.94238e6	−0.663537
$387$	−2.17626e6	−0.738640
$388$	−2.31011e6	−0.779029
$389$	−3.08559e6	−1.03387	−0.516933	−	0.856026i	$-0.672926\pi$
$389$	−3.08559e6	−1.03387	−0.516933	+	0.856026i	$0.672926\pi$
$390$	119600.	0.0398171
$391$	−750708.	−0.248330
$392$	1.04467e6	0.343372
$393$	6.35981e6	2.07712
$394$	−4.04071e6	−1.31135
$395$	991000.	0.319581
$396$	−5.32070e6	−1.70503
$397$	885458.	0.281963	0.140981	−	0.990012i	$-0.454974\pi$
$397$	885458.	0.281963	0.140981	+	0.990012i	$0.454974\pi$
$398$	3.23056e6	1.02228
$399$	629200.	0.197859
$400$	160000.	0.0500000
$401$	−3.75344e6	−1.16565	−0.582825	−	0.812598i	$-0.698053\pi$
$401$	−3.75344e6	−1.16565	−0.582825	+	0.812598i	$0.698053\pi$
$402$	−2.57317e6	−0.794151
$403$	183448.	0.0562666
$404$	−2.26013e6	−0.688937
$405$	−580525.	−0.175867
$406$	−493680.	−0.148638
$407$	109056.	0.0326335
$408$	628992.	0.187066
$409$	−1.94653e6	−0.575377	−0.287689	−	0.957724i	$-0.592887\pi$
$409$	−1.94653e6	−0.575377	−0.287689	+	0.957724i	$0.592887\pi$
$410$	154200.	0.0453028
$411$	6.22705e6	1.81835
$412$	2.23702e6	0.649273
$413$	−624360.	−0.180119
$414$	3.43975e6	0.986339
$415$	1.49565e6	0.426295
$416$	47104.0	0.0133452
$417$	−802360.	−0.225959
$418$	3.37920e6	0.945961
$419$	−2.99166e6	−0.832486	−0.416243	−	0.909253i	$-0.636654\pi$
$419$	−2.99166e6	−0.832486	−0.416243	+	0.909253i	$0.636654\pi$
$420$	−228800.	−0.0632897
$421$	3.96660e6	1.09072	0.545360	−	0.838202i	$-0.316393\pi$
$421$	3.96660e6	1.09072	0.545360	+	0.838202i	$0.316393\pi$
$422$	−598208.	−0.163520
$423$	1.07116e7	2.91073
$424$	906624.	0.244913
$425$	236250.	0.0634453
$426$	4.40669e6	1.17649
$427$	−121484.	−0.0322440
$428$	1.38269e6	0.364850
$429$	−918528.	−0.240962
$430$	−502600.	−0.131085
$431$	−5.17115e6	−1.34089	−0.670446	−	0.741958i	$-0.733897\pi$
$431$	−5.17115e6	−1.34089	−0.670446	+	0.741958i	$0.733897\pi$
$432$	−1.26464e6	−0.326030
$433$	−4.53485e6	−1.16237	−0.581183	−	0.813773i	$-0.697410\pi$
$433$	−4.53485e6	−1.16237	−0.581183	+	0.813773i	$0.697410\pi$
$434$	−350944.	−0.0894362
$435$	−3.64650e6	−0.923960
$436$	3.49520e6	0.880554
$437$	−2.18460e6	−0.547228
$438$	−5.42110e6	−1.35021
$439$	−1.08220e6	−0.268007	−0.134004	−	0.990981i	$-0.542783\pi$
$439$	−1.08220e6	−0.268007	−0.134004	+	0.990981i	$0.542783\pi$
$440$	−1.22880e6	−0.302586
$441$	−7.06786e6	−1.73058
$442$	69552.0	0.0169338
$443$	−1.08079e6	−0.261656	−0.130828	−	0.991405i	$-0.541764\pi$
$443$	−1.08079e6	−0.261656	−0.130828	+	0.991405i	$0.541764\pi$
$444$	59072.0	0.0142208
$445$	−1.44225e6	−0.345255
$446$	1.77402e6	0.422301
$447$	2.62470e6	0.621314
$448$	−90112.0	−0.0212123
$449$	2.61783e6	0.612810	0.306405	−	0.951901i	$-0.400874\pi$
$449$	2.61783e6	0.612810	0.306405	+	0.951901i	$0.400874\pi$
$450$	−1.08250e6	−0.251998
$451$	−1.18426e6	−0.274160
$452$	−460896.	−0.106110
$453$	−323752.	−0.0741254
$454$	−1.68007e6	−0.382550
$455$	−25300.0	−0.00572917
$456$	1.83040e6	0.412225
$457$	1.59046e6	0.356231	0.178115	−	0.984010i	$-0.443000\pi$
$457$	1.59046e6	0.356231	0.178115	+	0.984010i	$0.443000\pi$
$458$	−4.23500e6	−0.943387
$459$	−1.86732e6	−0.413701
$460$	794400.	0.175043
$461$	4.25470e6	0.932431	0.466216	−	0.884671i	$-0.345617\pi$
$461$	4.25470e6	0.932431	0.466216	+	0.884671i	$0.345617\pi$
$462$	1.75718e6	0.383012
$463$	3.26605e6	0.708061	0.354031	−	0.935234i	$-0.384811\pi$
$463$	3.26605e6	0.708061	0.354031	+	0.935234i	$0.384811\pi$
$464$	−1.43616e6	−0.309676
$465$	−2.59220e6	−0.555950
$466$	5.09378e6	1.08662
$467$	−601542.	−0.127636	−0.0638181	−	0.997962i	$-0.520328\pi$
$467$	−601542.	−0.127636	−0.0638181	+	0.997962i	$0.520328\pi$
$468$	−318688.	−0.0672591
$469$	544324.	0.114268
$470$	2.47380e6	0.516559
$471$	156572.	0.0325208
$472$	−1.81632e6	−0.375264
$473$	3.85997e6	0.793288
$474$	−4.12256e6	−0.842793
$475$	687500.	0.139810
$476$	−133056.	−0.0269164
$477$	−6.13388e6	−1.23435
$478$	1.48272e6	0.296817
$479$	−4.57932e6	−0.911931	−0.455966	−	0.889997i	$-0.650706\pi$
$479$	−4.57932e6	−0.911931	−0.455966	+	0.889997i	$0.650706\pi$
$480$	−665600.	−0.131859
$481$	6532.00	0.00128731
$482$	2.24519e6	0.440186
$483$	−1.13599e6	−0.221568
$484$	6.86037e6	1.33117
$485$	3.60955e6	0.696785
$486$	−2.38670e6	−0.458360
$487$	7.05226e6	1.34743	0.673714	−	0.738992i	$-0.264698\pi$
$487$	7.05226e6	1.34743	0.673714	+	0.738992i	$0.264698\pi$
$488$	−353408.	−0.0671780
$489$	1.30225e7	2.46276
$490$	−1.63230e6	−0.307121
$491$	−2.62349e6	−0.491106	−0.245553	−	0.969383i	$-0.578970\pi$
$491$	−2.62349e6	−0.491106	−0.245553	+	0.969383i	$0.578970\pi$
$492$	−641472.	−0.119472
$493$	−2.12058e6	−0.392950
$494$	202400.	0.0373158
$495$	8.31360e6	1.52502
$496$	−1.02093e6	−0.186333
$497$	−932184.	−0.169282
$498$	−6.22190e6	−1.12422
$499$	−3.61234e6	−0.649437	−0.324719	−	0.945811i	$-0.605270\pi$
$499$	−3.61234e6	−0.649437	−0.324719	+	0.945811i	$0.605270\pi$
$500$	−250000.	−0.0447214
$501$	−1.44367e7	−2.56965
$502$	−2.30861e6	−0.408875
$503$	9.15629e6	1.61361	0.806807	−	0.590815i	$-0.201194\pi$
$503$	9.15629e6	1.61361	0.806807	+	0.590815i	$0.201194\pi$
$504$	609664.	0.106909
$505$	3.53145e6	0.616204
$506$	−6.10099e6	−1.05931
$507$	9.59860e6	1.65840
$508$	−3.46403e6	−0.595556
$509$	7.26159e6	1.24233	0.621165	−	0.783679i	$-0.286660\pi$
$509$	7.26159e6	1.24233	0.621165	+	0.783679i	$0.286660\pi$
$510$	−982800.	−0.167317
$511$	1.14677e6	0.194279
$512$	−262144.	−0.0441942
$513$	−5.43400e6	−0.911646
$514$	2.60585e6	0.435052
$515$	−3.49535e6	−0.580728
$516$	2.09082e6	0.345694
$517$	−1.89988e7	−3.12608
$518$	−12496.0	−0.00204619
$519$	−1.08512e7	−1.76831
$520$	−73600.0	−0.0119363
$521$	5.81020e6	0.937771	0.468886	−	0.883259i	$-0.344656\pi$
$521$	5.81020e6	0.937771	0.468886	+	0.883259i	$0.344656\pi$
$522$	9.71652e6	1.56075
$523$	−8.17067e6	−1.30618	−0.653090	−	0.757280i	$-0.726528\pi$
$523$	−8.17067e6	−1.30618	−0.653090	+	0.757280i	$0.726528\pi$
$524$	−3.91373e6	−0.622676
$525$	357500.	0.0566080
$526$	−3.67030e6	−0.578411
$527$	−1.50746e6	−0.236440
$528$	5.11181e6	0.797976
$529$	−2.49215e6	−0.387199
$530$	−1.41660e6	−0.219057
$531$	1.22885e7	1.89132
$532$	−387200.	−0.0593139
$533$	−70932.0	−0.0108149
$534$	5.99976e6	0.910502
$535$	−2.16045e6	−0.326332
$536$	1.58349e6	0.238069
$537$	1.36188e6	0.203800
$538$	2.94156e6	0.438149
$539$	1.25361e7	1.85861
$540$	1.97600e6	0.291610
$541$	−817378.	−0.120069	−0.0600343	−	0.998196i	$-0.519121\pi$
$541$	−817378.	−0.120069	−0.0600343	+	0.998196i	$0.519121\pi$
$542$	4.48523e6	0.655823
$543$	−1.42132e7	−2.06868
$544$	−387072.	−0.0560783
$545$	−5.46125e6	−0.787591
$546$	105248.	0.0151089
$547$	−3.50750e6	−0.501221	−0.250611	−	0.968088i	$-0.580631\pi$
$547$	−3.50750e6	−0.501221	−0.250611	+	0.968088i	$0.580631\pi$
$548$	−3.83203e6	−0.545102
$549$	2.39103e6	0.338574
$550$	1.92000e6	0.270642
$551$	−6.17100e6	−0.865918
$552$	−3.30470e6	−0.461620
$553$	872080.	0.121267
$554$	6.64137e6	0.919355
$555$	−92300.0	−0.0127195
$556$	493760.	0.0677375
$557$	9.61490e6	1.31313	0.656563	−	0.754271i	$-0.272009\pi$
$557$	9.61490e6	1.31313	0.656563	+	0.754271i	$0.272009\pi$
$558$	6.90722e6	0.939112
$559$	231196.	0.0312933
$560$	140800.	0.0189729
$561$	7.54790e6	1.01256
$562$	−5.80841e6	−0.775740
$563$	2.01941e6	0.268506	0.134253	−	0.990947i	$-0.457136\pi$
$563$	2.01941e6	0.268506	0.134253	+	0.990947i	$0.457136\pi$
$564$	−1.02910e7	−1.36226
$565$	720150.	0.0949078
$566$	−1.23606e6	−0.162180
$567$	−510862.	−0.0667338
$568$	−2.71181e6	−0.352686
$569$	1.37859e6	0.178507	0.0892533	−	0.996009i	$-0.471552\pi$
$569$	1.37859e6	0.178507	0.0892533	+	0.996009i	$0.471552\pi$
$570$	−2.86000e6	−0.368705
$571$	8.54295e6	1.09652	0.548261	−	0.836307i	$-0.315290\pi$
$571$	8.54295e6	1.09652	0.548261	+	0.836307i	$0.315290\pi$
$572$	565248.	0.0722352
$573$	1.17527e7	1.49538
$574$	135696.	0.0171905
$575$	−1.24125e6	−0.156563
$576$	1.77357e6	0.222737
$577$	−2.31458e6	−0.289423	−0.144711	−	0.989474i	$-0.546225\pi$
$577$	−2.31458e6	−0.289423	−0.144711	+	0.989474i	$0.546225\pi$
$578$	5.10789e6	0.635949
$579$	−1.26254e7	−1.56513
$580$	2.24400e6	0.276983
$581$	1.31617e6	0.161760
$582$	−1.50157e7	−1.83755
$583$	1.08795e7	1.32568
$584$	3.33606e6	0.404764
$585$	497950.	0.0601584
$586$	6.37202e6	0.766537
$587$	928338.	0.111202	0.0556008	−	0.998453i	$-0.482293\pi$
$587$	928338.	0.111202	0.0556008	+	0.998453i	$0.482293\pi$
$588$	6.79037e6	0.809935
$589$	−4.38680e6	−0.521026
$590$	2.83800e6	0.335647
$591$	−2.62646e7	−3.09316
$592$	−36352.0	−0.00426309
$593$	−909486.	−0.106209	−0.0531043	−	0.998589i	$-0.516912\pi$
$593$	−909486.	−0.106209	−0.0531043	+	0.998589i	$0.516912\pi$
$594$	−1.51757e7	−1.76475
$595$	207900.	0.0240748
$596$	−1.61520e6	−0.186256
$597$	2.09986e7	2.41132
$598$	−365424.	−0.0417873
$599$	−8.51136e6	−0.969241	−0.484621	−	0.874724i	$-0.661042\pi$
$599$	−8.51136e6	−0.969241	−0.484621	+	0.874724i	$0.661042\pi$
$600$	1.04000e6	0.117938
$601$	6.12498e6	0.691701	0.345851	−	0.938290i	$-0.387590\pi$
$601$	6.12498e6	0.691701	0.345851	+	0.938290i	$0.387590\pi$
$602$	−442288.	−0.0497409
$603$	−1.07133e7	−1.19986
$604$	199232.	0.0222212
$605$	−1.07193e7	−1.19064
$606$	−1.46908e7	−1.62504
$607$	−4.51646e6	−0.497538	−0.248769	−	0.968563i	$-0.580026\pi$
$607$	−4.51646e6	−0.497538	−0.248769	+	0.968563i	$0.580026\pi$
$608$	−1.12640e6	−0.123576
$609$	−3.20892e6	−0.350603
$610$	552200.	0.0600858
$611$	−1.13795e6	−0.123316
$612$	2.61878e6	0.282632
$613$	9.63979e6	1.03614	0.518068	−	0.855340i	$-0.326651\pi$
$613$	9.63979e6	1.03614	0.518068	+	0.855340i	$0.326651\pi$
$614$	−4.98903e6	−0.534067
$615$	1.00230e6	0.106859
$616$	−1.08134e6	−0.114819
$617$	−9.92650e6	−1.04974	−0.524872	−	0.851181i	$-0.675887\pi$
$617$	−9.92650e6	−1.04974	−0.524872	+	0.851181i	$0.675887\pi$
$618$	1.45407e7	1.53149
$619$	7.63322e6	0.800721	0.400360	−	0.916358i	$-0.368885\pi$
$619$	7.63322e6	0.800721	0.400360	+	0.916358i	$0.368885\pi$
$620$	1.59520e6	0.166662
$621$	9.81084e6	1.02089
$622$	2.66395e6	0.276090
$623$	−1.26918e6	−0.131010
$624$	306176.	0.0314782
$625$	390625.	0.0400000
$626$	2.36514e6	0.241225
$627$	2.19648e7	2.23130
$628$	−96352.0	−0.00974903
$629$	−53676.0	−0.00540946
$630$	−952600.	−0.0956223
$631$	1.80314e7	1.80284	0.901418	−	0.432949i	$-0.142527\pi$
$631$	1.80314e7	1.80284	0.901418	+	0.432949i	$0.142527\pi$
$632$	2.53696e6	0.252651
$633$	−3.88835e6	−0.385706
$634$	2.06537e6	0.204068
$635$	5.41255e6	0.532681
$636$	5.89306e6	0.577694
$637$	750858.	0.0733178
$638$	−1.72339e7	−1.67623
$639$	1.83471e7	1.77752
$640$	409600.	0.0395285
$641$	9.30190e6	0.894184	0.447092	−	0.894488i	$-0.352460\pi$
$641$	9.30190e6	0.894184	0.447092	+	0.894488i	$0.352460\pi$
$642$	8.98747e6	0.860597
$643$	−1.38332e7	−1.31946	−0.659730	−	0.751503i	$-0.729329\pi$
$643$	−1.38332e7	−1.31946	−0.659730	+	0.751503i	$0.729329\pi$
$644$	699072.	0.0664213
$645$	−3.26690e6	−0.309198
$646$	−1.66320e6	−0.156806
$647$	−1.48997e7	−1.39932	−0.699658	−	0.714478i	$-0.746664\pi$
$647$	−1.48997e7	−1.39932	−0.699658	+	0.714478i	$0.746664\pi$
$648$	−1.48614e6	−0.139035
$649$	−2.17958e7	−2.03124
$650$	115000.	0.0106761
$651$	−2.28114e6	−0.210959
$652$	−8.01386e6	−0.738282
$653$	−1.93306e7	−1.77403	−0.887016	−	0.461738i	$-0.847226\pi$
$653$	−1.93306e7	−1.77403	−0.887016	+	0.461738i	$0.847226\pi$
$654$	2.27188e7	2.07702
$655$	6.11520e6	0.556939
$656$	394752.	0.0358150
$657$	−2.25706e7	−2.03999
$658$	2.17694e6	0.196012
$659$	−4.06110e6	−0.364276	−0.182138	−	0.983273i	$-0.558302\pi$
$659$	−4.06110e6	−0.364276	−0.182138	+	0.983273i	$0.558302\pi$
$660$	−7.98720e6	−0.713731
$661$	−1.35152e7	−1.20315	−0.601575	−	0.798816i	$-0.705460\pi$
$661$	−1.35152e7	−1.20315	−0.601575	+	0.798816i	$0.705460\pi$
$662$	1.31831e7	1.16915
$663$	452088.	0.0399429
$664$	3.82886e6	0.337015
$665$	605000.	0.0530519
$666$	245944.	0.0214858
$667$	1.11415e7	0.969678
$668$	8.88413e6	0.770324
$669$	1.15312e7	0.996111
$670$	−2.47420e6	−0.212935
$671$	−4.24090e6	−0.363623
$672$	−585728.	−0.0500349
$673$	1.43520e7	1.22144	0.610722	−	0.791845i	$-0.290879\pi$
$673$	1.43520e7	1.22144	0.610722	+	0.791845i	$0.290879\pi$
$674$	−7.64391e6	−0.648136
$675$	−3.08750e6	−0.260824
$676$	−5.90683e6	−0.497150
$677$	1.89530e6	0.158930	0.0794650	−	0.996838i	$-0.474679\pi$
$677$	1.89530e6	0.158930	0.0794650	+	0.996838i	$0.474679\pi$
$678$	−2.99582e6	−0.250289
$679$	3.17640e6	0.264400
$680$	604800.	0.0501579
$681$	−1.09205e7	−0.902347
$682$	−1.22511e7	−1.00859
$683$	2.91641e6	0.239220	0.119610	−	0.992821i	$-0.461836\pi$
$683$	2.91641e6	0.239220	0.119610	+	0.992821i	$0.461836\pi$
$684$	7.62080e6	0.622817
$685$	5.98755e6	0.487554
$686$	−2.91544e6	−0.236534
$687$	−2.75275e7	−2.22523
$688$	−1.28666e6	−0.103631
$689$	651636.	0.0522946
$690$	5.16360e6	0.412886
$691$	1.44278e7	1.14949	0.574743	−	0.818334i	$-0.305102\pi$
$691$	1.44278e7	1.14949	0.574743	+	0.818334i	$0.305102\pi$
$692$	6.67766e6	0.530102
$693$	7.31597e6	0.578680
$694$	−9.68023e6	−0.762934
$695$	−771500.	−0.0605862
$696$	−9.33504e6	−0.730454
$697$	582876.	0.0454458
$698$	−1.00291e7	−0.779153
$699$	3.31096e7	2.56307
$700$	−220000.	−0.0169698
$701$	−1.58679e7	−1.21962	−0.609811	−	0.792547i	$-0.708754\pi$
$701$	−1.58679e7	−1.21962	−0.609811	+	0.792547i	$0.708754\pi$
$702$	−908960.	−0.0696149
$703$	−156200.	−0.0119205
$704$	−3.14573e6	−0.239216
$705$	1.60797e7	1.21844
$706$	1.65266e6	0.124788
$707$	3.10768e6	0.233823
$708$	−1.18061e7	−0.885162
$709$	−301810.	−0.0225485	−0.0112743	−	0.999936i	$-0.503589\pi$
$709$	−301810.	−0.0225485	−0.0112743	+	0.999936i	$0.503589\pi$
$710$	4.23720e6	0.315452
$711$	−1.71641e7	−1.27335
$712$	−3.69216e6	−0.272948
$713$	7.92017e6	0.583459
$714$	−864864.	−0.0634896
$715$	−883200.	−0.0646091
$716$	−838080.	−0.0610946
$717$	9.63768e6	0.700123
$718$	−6.95088e6	−0.503186
$719$	2.12677e7	1.53426	0.767130	−	0.641492i	$-0.221684\pi$
$719$	2.12677e7	1.53426	0.767130	+	0.641492i	$0.221684\pi$
$720$	−2.77120e6	−0.199222
$721$	−3.07591e6	−0.220361
$722$	5.06440e6	0.361564
$723$	1.45937e7	1.03830
$724$	8.74659e6	0.620144
$725$	−3.50625e6	−0.247741
$726$	4.45924e7	3.13992
$727$	1.55009e7	1.08773	0.543863	−	0.839174i	$-0.316961\pi$
$727$	1.55009e7	1.08773	0.543863	+	0.839174i	$0.316961\pi$
$728$	−64768.0	−0.00452931
$729$	−2.11562e7	−1.47441
$730$	−5.21260e6	−0.362032
$731$	−1.89983e6	−0.131499
$732$	−2.29715e6	−0.158457
$733$	−1.21850e7	−0.837653	−0.418827	−	0.908066i	$-0.637559\pi$
$733$	−1.21850e7	−0.837653	−0.418827	+	0.908066i	$0.637559\pi$
$734$	−4.64391e6	−0.318159
$735$	−1.06100e7	−0.724428
$736$	2.03366e6	0.138384
$737$	1.90019e7	1.28863
$738$	−2.67074e6	−0.180506
$739$	−2.90282e7	−1.95528	−0.977641	−	0.210282i	$-0.932562\pi$
$739$	−2.90282e7	−1.95528	−0.977641	+	0.210282i	$0.932562\pi$
$740$	56800.0	0.00381302
$741$	1.31560e6	0.0880194
$742$	−1.24661e6	−0.0831228
$743$	1.61145e7	1.07089	0.535445	−	0.844570i	$-0.320144\pi$
$743$	1.61145e7	1.07089	0.535445	+	0.844570i	$0.320144\pi$
$744$	−6.63603e6	−0.439517
$745$	2.52375e6	0.166593
$746$	−1.37502e6	−0.0904609
$747$	−2.59047e7	−1.69854
$748$	−4.64486e6	−0.303542
$749$	−1.90120e6	−0.123829
$750$	−1.62500e6	−0.105487
$751$	−2.92431e6	−0.189201	−0.0946005	−	0.995515i	$-0.530157\pi$
$751$	−2.92431e6	−0.189201	−0.0946005	+	0.995515i	$0.530157\pi$
$752$	6.33293e6	0.408376
$753$	−1.50060e7	−0.964442
$754$	−1.03224e6	−0.0661230
$755$	−311300.	−0.0198752
$756$	1.73888e6	0.110653
$757$	2.60325e7	1.65111	0.825557	−	0.564319i	$-0.190861\pi$
$757$	2.60325e7	1.65111	0.825557	+	0.564319i	$0.190861\pi$
$758$	−2.29256e6	−0.144926
$759$	−3.96564e7	−2.49867
$760$	1.76000e6	0.110530
$761$	1.63263e7	1.02194	0.510970	−	0.859598i	$-0.329286\pi$
$761$	1.63263e7	1.02194	0.510970	+	0.859598i	$0.329286\pi$
$762$	−2.25162e7	−1.40478
$763$	−4.80590e6	−0.298857
$764$	−7.23245e6	−0.448283
$765$	−4.09185e6	−0.252794
$766$	1.15222e7	0.709517
$767$	−1.30548e6	−0.0801275
$768$	−1.70394e6	−0.104244
$769$	2.58132e7	1.57408	0.787040	−	0.616902i	$-0.211612\pi$
$769$	2.58132e7	1.57408	0.787040	+	0.616902i	$0.211612\pi$
$770$	1.68960e6	0.102697
$771$	1.69380e7	1.02619
$772$	7.76950e6	0.469191
$773$	−1.90592e7	−1.14725	−0.573624	−	0.819119i	$-0.694463\pi$
$773$	−1.90592e7	−1.14725	−0.573624	+	0.819119i	$0.694463\pi$
$774$	8.70503e6	0.522298
$775$	−2.49250e6	−0.149067
$776$	9.24045e6	0.550857
$777$	−81224.0	−0.00482649
$778$	1.23424e7	0.731054
$779$	1.69620e6	0.100146
$780$	−478400.	−0.0281549
$781$	−3.25417e7	−1.90903
$782$	3.00283e6	0.175596
$783$	2.77134e7	1.61542
$784$	−4.17869e6	−0.242801
$785$	150550.	0.00871980
$786$	−2.54392e7	−1.46875
$787$	−1.73411e7	−0.998021	−0.499011	−	0.866596i	$-0.666303\pi$
$787$	−1.73411e7	−0.998021	−0.499011	+	0.866596i	$0.666303\pi$
$788$	1.61628e7	0.927262
$789$	−2.38569e7	−1.36434
$790$	−3.96400e6	−0.225978
$791$	633732.	0.0360134
$792$	2.12828e7	1.20564
$793$	−254012.	−0.0143440
$794$	−3.54183e6	−0.199378
$795$	−9.20790e6	−0.516705
$796$	−1.29222e7	−0.722862
$797$	−2.58169e7	−1.43965	−0.719827	−	0.694153i	$-0.755779\pi$
$797$	−2.58169e7	−1.43965	−0.719827	+	0.694153i	$0.755779\pi$
$798$	−2.51680e6	−0.139908
$799$	9.35096e6	0.518190
$800$	−640000.	−0.0353553
$801$	2.49798e7	1.37565
$802$	1.50138e7	0.824239
$803$	4.00328e7	2.19092
$804$	1.02927e7	0.561549
$805$	−1.09230e6	−0.0594090
$806$	−733792.	−0.0397865
$807$	1.91201e7	1.03349
$808$	9.04051e6	0.487152
$809$	8.88489e6	0.477288	0.238644	−	0.971107i	$-0.423297\pi$
$809$	8.88489e6	0.477288	0.238644	+	0.971107i	$0.423297\pi$
$810$	2.32210e6	0.124356
$811$	−2.46396e7	−1.31547	−0.657735	−	0.753249i	$-0.728485\pi$
$811$	−2.46396e7	−1.31547	−0.657735	+	0.753249i	$0.728485\pi$
$812$	1.97472e6	0.105103
$813$	2.91540e7	1.54693
$814$	−436224.	−0.0230754
$815$	1.25216e7	0.660340
$816$	−2.51597e6	−0.132276
$817$	−5.52860e6	−0.289774
$818$	7.78612e6	0.406853
$819$	438196.	0.0228275
$820$	−616800.	−0.0320339
$821$	1.13768e7	0.589062	0.294531	−	0.955642i	$-0.404837\pi$
$821$	1.13768e7	0.589062	0.294531	+	0.955642i	$0.404837\pi$
$822$	−2.49082e7	−1.28577
$823$	−1.30783e7	−0.673057	−0.336529	−	0.941673i	$-0.609253\pi$
$823$	−1.30783e7	−0.673057	−0.336529	+	0.941673i	$0.609253\pi$
$824$	−8.94810e6	−0.459106
$825$	1.24800e7	0.638381
$826$	2.49744e6	0.127363
$827$	−3.57188e7	−1.81607	−0.908037	−	0.418891i	$-0.862419\pi$
$827$	−3.57188e7	−1.81607	−0.908037	+	0.418891i	$0.862419\pi$
$828$	−1.37590e7	−0.697447
$829$	1.61880e7	0.818103	0.409052	−	0.912511i	$-0.365860\pi$
$829$	1.61880e7	0.818103	0.409052	+	0.912511i	$0.365860\pi$
$830$	−5.98260e6	−0.301436
$831$	4.31689e7	2.16854
$832$	−188416.	−0.00943647
$833$	−6.17009e6	−0.308091
$834$	3.20944e6	0.159777
$835$	−1.38814e7	−0.688999
$836$	−1.35168e7	−0.668895
$837$	1.97007e7	0.972005
$838$	1.19666e7	0.588657
$839$	−2.55497e7	−1.25309	−0.626543	−	0.779387i	$-0.715531\pi$
$839$	−2.55497e7	−1.25309	−0.626543	+	0.779387i	$0.715531\pi$
$840$	915200.	0.0447526
$841$	1.09610e7	0.534390
$842$	−1.58664e7	−0.771256
$843$	−3.77547e7	−1.82979
$844$	2.39283e6	0.115626
$845$	9.22942e6	0.444665
$846$	−4.28462e7	−2.05820
$847$	−9.43301e6	−0.451795
$848$	−3.62650e6	−0.173180
$849$	−8.03436e6	−0.382545
$850$	−945000.	−0.0448626
$851$	282012.	0.0133488
$852$	−1.76268e7	−0.831904
$853$	−2.22953e7	−1.04916	−0.524579	−	0.851362i	$-0.675777\pi$
$853$	−2.22953e7	−1.04916	−0.524579	+	0.851362i	$0.675777\pi$
$854$	485936.	0.0228000
$855$	−1.19075e7	−0.557064
$856$	−5.53075e6	−0.257988
$857$	1.96872e7	0.915656	0.457828	−	0.889041i	$-0.348628\pi$
$857$	1.96872e7	0.915656	0.457828	+	0.889041i	$0.348628\pi$
$858$	3.67411e6	0.170386
$859$	6.77582e6	0.313313	0.156657	−	0.987653i	$-0.449928\pi$
$859$	6.77582e6	0.313313	0.156657	+	0.987653i	$0.449928\pi$
$860$	2.01040e6	0.0926907
$861$	882024.	0.0405483
$862$	2.06846e7	0.948154
$863$	−2.63804e7	−1.20574	−0.602871	−	0.797839i	$-0.705977\pi$
$863$	−2.63804e7	−1.20574	−0.602871	+	0.797839i	$0.705977\pi$
$864$	5.05856e6	0.230538
$865$	−1.04338e7	−0.474138
$866$	1.81394e7	0.821917
$867$	3.32013e7	1.50006
$868$	1.40378e6	0.0632410
$869$	3.04435e7	1.36756
$870$	1.45860e7	0.653338
$871$	1.13813e6	0.0508332
$872$	−1.39808e7	−0.622645
$873$	−6.25174e7	−2.77629
$874$	8.73840e6	0.386949
$875$	343750.	0.0151783
$876$	2.16844e7	0.954745
$877$	2.95161e7	1.29587	0.647934	−	0.761697i	$-0.275633\pi$
$877$	2.95161e7	1.29587	0.647934	+	0.761697i	$0.275633\pi$
$878$	4.32880e6	0.189510
$879$	4.14182e7	1.80808
$880$	4.91520e6	0.213961
$881$	−1.48565e7	−0.644877	−0.322438	−	0.946590i	$-0.604502\pi$
$881$	−1.48565e7	−0.644877	−0.322438	+	0.946590i	$0.604502\pi$
$882$	2.82714e7	1.22370
$883$	−1.45340e7	−0.627313	−0.313656	−	0.949537i	$-0.601554\pi$
$883$	−1.45340e7	−0.627313	−0.313656	+	0.949537i	$0.601554\pi$
$884$	−278208.	−0.0119740
$885$	1.84470e7	0.791713
$886$	4.32314e6	0.185019
$887$	−1.72028e7	−0.734160	−0.367080	−	0.930189i	$-0.619642\pi$
$887$	−1.72028e7	−0.734160	−0.367080	+	0.930189i	$0.619642\pi$
$888$	−236288.	−0.0100556
$889$	4.76304e6	0.202130
$890$	5.76900e6	0.244132
$891$	−1.78337e7	−0.752572
$892$	−7.09610e6	−0.298612
$893$	2.72118e7	1.14190
$894$	−1.04988e7	−0.439335
$895$	1.30950e6	0.0546447
$896$	360448.	0.0149994
$897$	−2.37526e6	−0.0985665
$898$	−1.04713e7	−0.433322
$899$	2.23727e7	0.923249
$900$	4.33000e6	0.178189
$901$	−5.35475e6	−0.219749
$902$	4.73702e6	0.193860
$903$	−2.87487e6	−0.117327
$904$	1.84358e6	0.0750312
$905$	−1.36666e7	−0.554674
$906$	1.29501e6	0.0524146
$907$	−3.44434e7	−1.39023	−0.695116	−	0.718897i	$-0.744647\pi$
$907$	−3.44434e7	−1.39023	−0.695116	+	0.718897i	$0.744647\pi$
$908$	6.72029e6	0.270504
$909$	−6.11647e7	−2.45522
$910$	101200.	0.00405114
$911$	−983748.	−0.0392724	−0.0196362	−	0.999807i	$-0.506251\pi$
$911$	−983748.	−0.0392724	−0.0196362	+	0.999807i	$0.506251\pi$
$912$	−7.32160e6	−0.291487
$913$	4.59464e7	1.82421
$914$	−6.36183e6	−0.251893
$915$	3.58930e6	0.141728
$916$	1.69400e7	0.667075
$917$	5.38138e6	0.211334
$918$	7.46928e6	0.292531
$919$	3.08857e7	1.20634	0.603168	−	0.797614i	$-0.293905\pi$
$919$	3.08857e7	1.20634	0.603168	+	0.797614i	$0.293905\pi$
$920$	−3.17760e6	−0.123774
$921$	−3.24287e7	−1.25974
$922$	−1.70188e7	−0.659328
$923$	−1.94911e6	−0.0753065
$924$	−7.02874e6	−0.270830
$925$	−88750.0	−0.00341047
$926$	−1.30642e7	−0.500675
$927$	6.05395e7	2.31387
$928$	5.74464e6	0.218974
$929$	−3.20874e7	−1.21982	−0.609909	−	0.792472i	$-0.708794\pi$
$929$	−3.20874e7	−1.21982	−0.609909	+	0.792472i	$0.708794\pi$
$930$	1.03688e7	0.393116
$931$	−1.79553e7	−0.678920
$932$	−2.03751e7	−0.768353
$933$	1.73157e7	0.651232
$934$	2.40617e6	0.0902524
$935$	7.25760e6	0.271496
$936$	1.27475e6	0.0475594
$937$	1.52520e7	0.567515	0.283757	−	0.958896i	$-0.408419\pi$
$937$	1.52520e7	0.567515	0.283757	+	0.958896i	$0.408419\pi$
$938$	−2.17730e6	−0.0807998
$939$	1.53734e7	0.568993
$940$	−9.89520e6	−0.365262
$941$	3.48166e6	0.128178	0.0640889	−	0.997944i	$-0.479586\pi$
$941$	3.48166e6	0.128178	0.0640889	+	0.997944i	$0.479586\pi$
$942$	−626288.	−0.0229957
$943$	−3.06241e6	−0.112146
$944$	7.26528e6	0.265352
$945$	−2.71700e6	−0.0989715
$946$	−1.54399e7	−0.560939
$947$	−2.54010e7	−0.920398	−0.460199	−	0.887816i	$-0.652222\pi$
$947$	−2.54010e7	−0.920398	−0.460199	+	0.887816i	$0.652222\pi$
$948$	1.64902e7	0.595945
$949$	2.39780e6	0.0864265
$950$	−2.75000e6	−0.0988607
$951$	1.34249e7	0.481348
$952$	532224.	0.0190328
$953$	−4.97352e7	−1.77391	−0.886955	−	0.461856i	$-0.847184\pi$
$953$	−4.97352e7	−1.77391	−0.886955	+	0.461856i	$0.847184\pi$
$954$	2.45355e7	0.872819
$955$	1.13007e7	0.400956
$956$	−5.93088e6	−0.209882
$957$	−1.12020e8	−3.95383
$958$	1.83173e7	0.644833
$959$	5.26904e6	0.185006
$960$	2.66240e6	0.0932385
$961$	−1.27250e7	−0.444477
$962$	−26128.0	−0.000910266 0
$963$	3.74190e7	1.30025
$964$	−8.98077e6	−0.311258
$965$	−1.21398e7	−0.419658
$966$	4.54397e6	0.156672
$967$	3.05173e7	1.04949	0.524747	−	0.851258i	$-0.324160\pi$
$967$	3.05173e7	1.04949	0.524747	+	0.851258i	$0.324160\pi$
$968$	−2.74415e7	−0.941280
$969$	−1.08108e7	−0.369869
$970$	−1.44382e7	−0.492701
$971$	3.19854e7	1.08869	0.544344	−	0.838862i	$-0.316779\pi$
$971$	3.19854e7	1.08869	0.544344	+	0.838862i	$0.316779\pi$
$972$	9.54678e6	0.324109
$973$	−678920.	−0.0229899
$974$	−2.82090e7	−0.952776
$975$	747500.	0.0251825
$976$	1.41363e6	0.0475020
$977$	2.90786e6	0.0974623	0.0487312	−	0.998812i	$-0.484482\pi$
$977$	2.90786e6	0.0974623	0.0487312	+	0.998812i	$0.484482\pi$
$978$	−5.20901e7	−1.74144
$979$	−4.43059e7	−1.47742
$980$	6.52920e6	0.217167
$981$	9.45888e7	3.13810
$982$	1.04940e7	0.347264
$983$	3.49621e7	1.15402	0.577010	−	0.816737i	$-0.304219\pi$
$983$	3.49621e7	1.15402	0.577010	+	0.816737i	$0.304219\pi$
$984$	2.56589e6	0.0844792
$985$	−2.52544e7	−0.829368
$986$	8.48232e6	0.277858
$987$	1.41501e7	0.462347
$988$	−809600.	−0.0263863
$989$	9.98164e6	0.324497
$990$	−3.32544e7	−1.07835
$991$	3.00465e6	0.0971874	0.0485937	−	0.998819i	$-0.484526\pi$
$991$	3.00465e6	0.0971874	0.0485937	+	0.998819i	$0.484526\pi$
$992$	4.08371e6	0.131758
$993$	8.56900e7	2.75776
$994$	3.72874e6	0.119700
$995$	2.01910e7	0.646547
$996$	2.48876e7	0.794941
$997$	3.20789e7	1.02207	0.511035	−	0.859560i	$-0.329262\pi$
$997$	3.20789e7	1.02207	0.511035	+	0.859560i	$0.329262\pi$
$998$	1.44494e7	0.459222
$999$	701480.	0.0222383

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.6.a.a.1.1	✓	1	1.1	even	1	trivial
50.6.a.g.1.1		1	5.4	even	2
50.6.b.d.49.1		2	5.2	odd	4
50.6.b.d.49.2		2	5.3	odd	4
80.6.a.h.1.1		1	4.3	odd	2
90.6.a.f.1.1		1	3.2	odd	2
320.6.a.a.1.1		1	8.3	odd	2
320.6.a.p.1.1		1	8.5	even	2
400.6.a.a.1.1		1	20.19	odd	2
400.6.c.a.49.1		2	20.7	even	4
400.6.c.a.49.2		2	20.3	even	4
450.6.a.h.1.1		1	15.14	odd	2
450.6.c.o.199.1		2	15.8	even	4
450.6.c.o.199.2		2	15.2	even	4
490.6.a.j.1.1		1	7.6	odd	2
720.6.a.r.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 $\F_{q}$
Belyi maps

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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