Properties

Label 570.6.a.m.1.3
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(91.4187772934\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 39154 x^{2} - 3172892 x - 35506440\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-89.1990\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +197.010 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} -36.0000 q^{6} +197.010 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} +380.119 q^{11} +144.000 q^{12} -672.422 q^{13} -788.042 q^{14} +225.000 q^{15} +256.000 q^{16} -583.456 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1773.09 q^{21} -1520.48 q^{22} +4671.99 q^{23} -576.000 q^{24} +625.000 q^{25} +2689.69 q^{26} +729.000 q^{27} +3152.17 q^{28} +1268.92 q^{29} -900.000 q^{30} +47.9332 q^{31} -1024.00 q^{32} +3421.07 q^{33} +2333.82 q^{34} +4925.26 q^{35} +1296.00 q^{36} +8030.61 q^{37} -1444.00 q^{38} -6051.80 q^{39} -1600.00 q^{40} -3803.90 q^{41} -7092.37 q^{42} +7360.67 q^{43} +6081.91 q^{44} +2025.00 q^{45} -18688.0 q^{46} -12592.8 q^{47} +2304.00 q^{48} +22006.1 q^{49} -2500.00 q^{50} -5251.10 q^{51} -10758.8 q^{52} +7812.71 q^{53} -2916.00 q^{54} +9502.98 q^{55} -12608.7 q^{56} +3249.00 q^{57} -5075.67 q^{58} -17688.7 q^{59} +3600.00 q^{60} +2738.26 q^{61} -191.733 q^{62} +15957.8 q^{63} +4096.00 q^{64} -16810.6 q^{65} -13684.3 q^{66} +14579.3 q^{67} -9335.29 q^{68} +42047.9 q^{69} -19701.0 q^{70} -3576.29 q^{71} -5184.00 q^{72} +29838.9 q^{73} -32122.4 q^{74} +5625.00 q^{75} +5776.00 q^{76} +74887.4 q^{77} +24207.2 q^{78} +28741.8 q^{79} +6400.00 q^{80} +6561.00 q^{81} +15215.6 q^{82} -98445.4 q^{83} +28369.5 q^{84} -14586.4 q^{85} -29442.7 q^{86} +11420.3 q^{87} -24327.6 q^{88} +29985.9 q^{89} -8100.00 q^{90} -132474. q^{91} +74751.9 q^{92} +431.399 q^{93} +50371.3 q^{94} +9025.00 q^{95} -9216.00 q^{96} +2993.04 q^{97} -88024.4 q^{98} +30789.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} + 36q^{3} + 64q^{4} + 100q^{5} - 144q^{6} + 268q^{7} - 256q^{8} + 324q^{9} - 400q^{10} + 338q^{11} + 576q^{12} + 1302q^{13} - 1072q^{14} + 900q^{15} + 1024q^{16} + 542q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 2412q^{21} - 1352q^{22} - 88q^{23} - 2304q^{24} + 2500q^{25} - 5208q^{26} + 2916q^{27} + 4288q^{28} + 5014q^{29} - 3600q^{30} + 4962q^{31} - 4096q^{32} + 3042q^{33} - 2168q^{34} + 6700q^{35} + 5184q^{36} + 8022q^{37} - 5776q^{38} + 11718q^{39} - 6400q^{40} + 2764q^{41} - 9648q^{42} + 25346q^{43} + 5408q^{44} + 8100q^{45} + 352q^{46} + 10008q^{47} + 9216q^{48} + 37248q^{49} - 10000q^{50} + 4878q^{51} + 20832q^{52} - 224q^{53} - 11664q^{54} + 8450q^{55} - 17152q^{56} + 12996q^{57} - 20056q^{58} + 29654q^{59} + 14400q^{60} + 27276q^{61} - 19848q^{62} + 21708q^{63} + 16384q^{64} + 32550q^{65} - 12168q^{66} + 26024q^{67} + 8672q^{68} - 792q^{69} - 26800q^{70} - 26940q^{71} - 20736q^{72} - 60916q^{73} - 32088q^{74} + 22500q^{75} + 23104q^{76} - 21228q^{77} - 46872q^{78} + 34902q^{79} + 25600q^{80} + 26244q^{81} - 11056q^{82} - 48430q^{83} + 38592q^{84} + 13550q^{85} - 101384q^{86} + 45126q^{87} - 21632q^{88} - 38348q^{89} - 32400q^{90} + 69280q^{91} - 1408q^{92} + 44658q^{93} - 40032q^{94} + 36100q^{95} - 36864q^{96} + 45942q^{97} - 148992q^{98} + 27378q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 −0.707107
\(3\) 9.00000 0.577350
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) −36.0000 −0.408248
\(7\) 197.010 1.51965 0.759826 0.650127i \(-0.225284\pi\)
0.759826 + 0.650127i \(0.225284\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) 380.119 0.947192 0.473596 0.880742i \(-0.342956\pi\)
0.473596 + 0.880742i \(0.342956\pi\)
\(12\) 144.000 0.288675
\(13\) −672.422 −1.10353 −0.551764 0.834000i \(-0.686045\pi\)
−0.551764 + 0.834000i \(0.686045\pi\)
\(14\) −788.042 −1.07456
\(15\) 225.000 0.258199
\(16\) 256.000 0.250000
\(17\) −583.456 −0.489650 −0.244825 0.969567i \(-0.578730\pi\)
−0.244825 + 0.969567i \(0.578730\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) 1773.09 0.877371
\(22\) −1520.48 −0.669766
\(23\) 4671.99 1.84155 0.920773 0.390099i \(-0.127559\pi\)
0.920773 + 0.390099i \(0.127559\pi\)
\(24\) −576.000 −0.204124
\(25\) 625.000 0.200000
\(26\) 2689.69 0.780313
\(27\) 729.000 0.192450
\(28\) 3152.17 0.759826
\(29\) 1268.92 0.280181 0.140090 0.990139i \(-0.455261\pi\)
0.140090 + 0.990139i \(0.455261\pi\)
\(30\) −900.000 −0.182574
\(31\) 47.9332 0.00895844 0.00447922 0.999990i \(-0.498574\pi\)
0.00447922 + 0.999990i \(0.498574\pi\)
\(32\) −1024.00 −0.176777
\(33\) 3421.07 0.546862
\(34\) 2333.82 0.346235
\(35\) 4925.26 0.679609
\(36\) 1296.00 0.166667
\(37\) 8030.61 0.964371 0.482185 0.876069i \(-0.339843\pi\)
0.482185 + 0.876069i \(0.339843\pi\)
\(38\) −1444.00 −0.162221
\(39\) −6051.80 −0.637123
\(40\) −1600.00 −0.158114
\(41\) −3803.90 −0.353402 −0.176701 0.984265i \(-0.556543\pi\)
−0.176701 + 0.984265i \(0.556543\pi\)
\(42\) −7092.37 −0.620395
\(43\) 7360.67 0.607081 0.303540 0.952819i \(-0.401831\pi\)
0.303540 + 0.952819i \(0.401831\pi\)
\(44\) 6081.91 0.473596
\(45\) 2025.00 0.149071
\(46\) −18688.0 −1.30217
\(47\) −12592.8 −0.831531 −0.415766 0.909472i \(-0.636486\pi\)
−0.415766 + 0.909472i \(0.636486\pi\)
\(48\) 2304.00 0.144338
\(49\) 22006.1 1.30934
\(50\) −2500.00 −0.141421
\(51\) −5251.10 −0.282699
\(52\) −10758.8 −0.551764
\(53\) 7812.71 0.382043 0.191021 0.981586i \(-0.438820\pi\)
0.191021 + 0.981586i \(0.438820\pi\)
\(54\) −2916.00 −0.136083
\(55\) 9502.98 0.423597
\(56\) −12608.7 −0.537278
\(57\) 3249.00 0.132453
\(58\) −5075.67 −0.198118
\(59\) −17688.7 −0.661555 −0.330777 0.943709i \(-0.607311\pi\)
−0.330777 + 0.943709i \(0.607311\pi\)
\(60\) 3600.00 0.129099
\(61\) 2738.26 0.0942216 0.0471108 0.998890i \(-0.484999\pi\)
0.0471108 + 0.998890i \(0.484999\pi\)
\(62\) −191.733 −0.00633457
\(63\) 15957.8 0.506551
\(64\) 4096.00 0.125000
\(65\) −16810.6 −0.493513
\(66\) −13684.3 −0.386690
\(67\) 14579.3 0.396779 0.198390 0.980123i \(-0.436429\pi\)
0.198390 + 0.980123i \(0.436429\pi\)
\(68\) −9335.29 −0.244825
\(69\) 42047.9 1.06322
\(70\) −19701.0 −0.480556
\(71\) −3576.29 −0.0841951 −0.0420975 0.999114i \(-0.513404\pi\)
−0.0420975 + 0.999114i \(0.513404\pi\)
\(72\) −5184.00 −0.117851
\(73\) 29838.9 0.655354 0.327677 0.944790i \(-0.393734\pi\)
0.327677 + 0.944790i \(0.393734\pi\)
\(74\) −32122.4 −0.681913
\(75\) 5625.00 0.115470
\(76\) 5776.00 0.114708
\(77\) 74887.4 1.43940
\(78\) 24207.2 0.450514
\(79\) 28741.8 0.518139 0.259070 0.965859i \(-0.416584\pi\)
0.259070 + 0.965859i \(0.416584\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) 15215.6 0.249893
\(83\) −98445.4 −1.56856 −0.784278 0.620409i \(-0.786967\pi\)
−0.784278 + 0.620409i \(0.786967\pi\)
\(84\) 28369.5 0.438686
\(85\) −14586.4 −0.218978
\(86\) −29442.7 −0.429271
\(87\) 11420.3 0.161763
\(88\) −24327.6 −0.334883
\(89\) 29985.9 0.401276 0.200638 0.979665i \(-0.435699\pi\)
0.200638 + 0.979665i \(0.435699\pi\)
\(90\) −8100.00 −0.105409
\(91\) −132474. −1.67698
\(92\) 74751.9 0.920773
\(93\) 431.399 0.00517216
\(94\) 50371.3 0.587981
\(95\) 9025.00 0.102598
\(96\) −9216.00 −0.102062
\(97\) 2993.04 0.0322986 0.0161493 0.999870i \(-0.494859\pi\)
0.0161493 + 0.999870i \(0.494859\pi\)
\(98\) −88024.4 −0.925844
\(99\) 30789.7 0.315731
\(100\) 10000.0 0.100000
\(101\) −32061.9 −0.312742 −0.156371 0.987698i \(-0.549980\pi\)
−0.156371 + 0.987698i \(0.549980\pi\)
\(102\) 21004.4 0.199899
\(103\) −123950. −1.15121 −0.575604 0.817729i \(-0.695233\pi\)
−0.575604 + 0.817729i \(0.695233\pi\)
\(104\) 43035.0 0.390156
\(105\) 44327.3 0.392372
\(106\) −31250.8 −0.270145
\(107\) −150037. −1.26689 −0.633444 0.773789i \(-0.718359\pi\)
−0.633444 + 0.773789i \(0.718359\pi\)
\(108\) 11664.0 0.0962250
\(109\) 158769. 1.27997 0.639983 0.768389i \(-0.278941\pi\)
0.639983 + 0.768389i \(0.278941\pi\)
\(110\) −38011.9 −0.299528
\(111\) 72275.5 0.556780
\(112\) 50434.7 0.379913
\(113\) −17144.7 −0.126309 −0.0631545 0.998004i \(-0.520116\pi\)
−0.0631545 + 0.998004i \(0.520116\pi\)
\(114\) −12996.0 −0.0936586
\(115\) 116800. 0.823564
\(116\) 20302.7 0.140090
\(117\) −54466.2 −0.367843
\(118\) 70754.8 0.467790
\(119\) −114947. −0.744097
\(120\) −14400.0 −0.0912871
\(121\) −16560.4 −0.102827
\(122\) −10953.1 −0.0666248
\(123\) −34235.1 −0.204037
\(124\) 766.931 0.00447922
\(125\) 15625.0 0.0894427
\(126\) −63831.4 −0.358185
\(127\) −28136.2 −0.154795 −0.0773973 0.997000i \(-0.524661\pi\)
−0.0773973 + 0.997000i \(0.524661\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 66246.1 0.350498
\(130\) 67242.2 0.348966
\(131\) 130615. 0.664989 0.332495 0.943105i \(-0.392110\pi\)
0.332495 + 0.943105i \(0.392110\pi\)
\(132\) 54737.2 0.273431
\(133\) 71120.8 0.348632
\(134\) −58317.1 −0.280565
\(135\) 18225.0 0.0860663
\(136\) 37341.2 0.173117
\(137\) 37242.5 0.169526 0.0847632 0.996401i \(-0.472987\pi\)
0.0847632 + 0.996401i \(0.472987\pi\)
\(138\) −168192. −0.751808
\(139\) 119642. 0.525227 0.262614 0.964901i \(-0.415416\pi\)
0.262614 + 0.964901i \(0.415416\pi\)
\(140\) 78804.2 0.339804
\(141\) −113335. −0.480085
\(142\) 14305.2 0.0595349
\(143\) −255601. −1.04525
\(144\) 20736.0 0.0833333
\(145\) 31723.0 0.125301
\(146\) −119356. −0.463405
\(147\) 198055. 0.755948
\(148\) 128490. 0.482185
\(149\) −30423.0 −0.112263 −0.0561314 0.998423i \(-0.517877\pi\)
−0.0561314 + 0.998423i \(0.517877\pi\)
\(150\) −22500.0 −0.0816497
\(151\) 460120. 1.64221 0.821105 0.570777i \(-0.193358\pi\)
0.821105 + 0.570777i \(0.193358\pi\)
\(152\) −23104.0 −0.0811107
\(153\) −47259.9 −0.163217
\(154\) −299550. −1.01781
\(155\) 1198.33 0.00400634
\(156\) −96828.8 −0.318561
\(157\) 313042. 1.01357 0.506785 0.862072i \(-0.330834\pi\)
0.506785 + 0.862072i \(0.330834\pi\)
\(158\) −114967. −0.366380
\(159\) 70314.4 0.220573
\(160\) −25600.0 −0.0790569
\(161\) 920431. 2.79851
\(162\) −26244.0 −0.0785674
\(163\) 134478. 0.396443 0.198221 0.980157i \(-0.436483\pi\)
0.198221 + 0.980157i \(0.436483\pi\)
\(164\) −60862.4 −0.176701
\(165\) 85526.8 0.244564
\(166\) 393782. 1.10914
\(167\) −275829. −0.765329 −0.382664 0.923887i \(-0.624993\pi\)
−0.382664 + 0.923887i \(0.624993\pi\)
\(168\) −113478. −0.310198
\(169\) 80858.6 0.217776
\(170\) 58345.6 0.154841
\(171\) 29241.0 0.0764719
\(172\) 117771. 0.303540
\(173\) 405849. 1.03098 0.515489 0.856896i \(-0.327610\pi\)
0.515489 + 0.856896i \(0.327610\pi\)
\(174\) −45681.1 −0.114383
\(175\) 123131. 0.303930
\(176\) 97310.5 0.236798
\(177\) −159198. −0.381949
\(178\) −119944. −0.283745
\(179\) −240843. −0.561824 −0.280912 0.959733i \(-0.590637\pi\)
−0.280912 + 0.959733i \(0.590637\pi\)
\(180\) 32400.0 0.0745356
\(181\) −825228. −1.87231 −0.936154 0.351590i \(-0.885641\pi\)
−0.936154 + 0.351590i \(0.885641\pi\)
\(182\) 529897. 1.18580
\(183\) 24644.4 0.0543989
\(184\) −299007. −0.651085
\(185\) 200765. 0.431280
\(186\) −1725.60 −0.00365727
\(187\) −221783. −0.463792
\(188\) −201485. −0.415766
\(189\) 143621. 0.292457
\(190\) −36100.0 −0.0725476
\(191\) 806960. 1.60055 0.800274 0.599634i \(-0.204687\pi\)
0.800274 + 0.599634i \(0.204687\pi\)
\(192\) 36864.0 0.0721688
\(193\) 777842. 1.50314 0.751568 0.659656i \(-0.229298\pi\)
0.751568 + 0.659656i \(0.229298\pi\)
\(194\) −11972.2 −0.0228385
\(195\) −151295. −0.284930
\(196\) 352098. 0.654671
\(197\) 13324.1 0.0244608 0.0122304 0.999925i \(-0.496107\pi\)
0.0122304 + 0.999925i \(0.496107\pi\)
\(198\) −123159. −0.223255
\(199\) −73064.3 −0.130789 −0.0653947 0.997859i \(-0.520831\pi\)
−0.0653947 + 0.997859i \(0.520831\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 131213. 0.229081
\(202\) 128248. 0.221142
\(203\) 249990. 0.425777
\(204\) −84017.6 −0.141350
\(205\) −95097.5 −0.158046
\(206\) 495800. 0.814027
\(207\) 378431. 0.613849
\(208\) −172140. −0.275882
\(209\) 137223. 0.217301
\(210\) −177309. −0.277449
\(211\) −272445. −0.421281 −0.210641 0.977564i \(-0.567555\pi\)
−0.210641 + 0.977564i \(0.567555\pi\)
\(212\) 125003. 0.191021
\(213\) −32186.6 −0.0486100
\(214\) 600147. 0.895825
\(215\) 184017. 0.271495
\(216\) −46656.0 −0.0680414
\(217\) 9443.34 0.0136137
\(218\) −635075. −0.905073
\(219\) 268550. 0.378369
\(220\) 152048. 0.211799
\(221\) 392329. 0.540343
\(222\) −289102. −0.393703
\(223\) 280747. 0.378054 0.189027 0.981972i \(-0.439467\pi\)
0.189027 + 0.981972i \(0.439467\pi\)
\(224\) −201739. −0.268639
\(225\) 50625.0 0.0666667
\(226\) 68578.8 0.0893139
\(227\) 1.38523e6 1.78425 0.892125 0.451788i \(-0.149214\pi\)
0.892125 + 0.451788i \(0.149214\pi\)
\(228\) 51984.0 0.0662266
\(229\) 1.41899e6 1.78810 0.894048 0.447971i \(-0.147853\pi\)
0.894048 + 0.447971i \(0.147853\pi\)
\(230\) −467199. −0.582348
\(231\) 673987. 0.831039
\(232\) −81210.8 −0.0990589
\(233\) 1.31529e6 1.58720 0.793600 0.608440i \(-0.208204\pi\)
0.793600 + 0.608440i \(0.208204\pi\)
\(234\) 217865. 0.260104
\(235\) −314821. −0.371872
\(236\) −283019. −0.330777
\(237\) 258676. 0.299148
\(238\) 459787. 0.526156
\(239\) −774779. −0.877371 −0.438686 0.898641i \(-0.644556\pi\)
−0.438686 + 0.898641i \(0.644556\pi\)
\(240\) 57600.0 0.0645497
\(241\) 17548.8 0.0194628 0.00973140 0.999953i \(-0.496902\pi\)
0.00973140 + 0.999953i \(0.496902\pi\)
\(242\) 66241.7 0.0727098
\(243\) 59049.0 0.0641500
\(244\) 43812.2 0.0471108
\(245\) 550152. 0.585555
\(246\) 136940. 0.144276
\(247\) −242744. −0.253167
\(248\) −3067.73 −0.00316729
\(249\) −886009. −0.905607
\(250\) −62500.0 −0.0632456
\(251\) −44645.5 −0.0447295 −0.0223647 0.999750i \(-0.507120\pi\)
−0.0223647 + 0.999750i \(0.507120\pi\)
\(252\) 255325. 0.253275
\(253\) 1.77591e6 1.74430
\(254\) 112545. 0.109456
\(255\) −131278. −0.126427
\(256\) 65536.0 0.0625000
\(257\) −1.01057e6 −0.954407 −0.477203 0.878793i \(-0.658349\pi\)
−0.477203 + 0.878793i \(0.658349\pi\)
\(258\) −264984. −0.247840
\(259\) 1.58211e6 1.46551
\(260\) −268969. −0.246757
\(261\) 102782. 0.0933936
\(262\) −522460. −0.470218
\(263\) 750727. 0.669257 0.334628 0.942350i \(-0.391389\pi\)
0.334628 + 0.942350i \(0.391389\pi\)
\(264\) −218949. −0.193345
\(265\) 195318. 0.170855
\(266\) −284483. −0.246520
\(267\) 269873. 0.231677
\(268\) 233268. 0.198390
\(269\) −2.14837e6 −1.81021 −0.905104 0.425191i \(-0.860207\pi\)
−0.905104 + 0.425191i \(0.860207\pi\)
\(270\) −72900.0 −0.0608581
\(271\) 1.19832e6 0.991177 0.495589 0.868557i \(-0.334952\pi\)
0.495589 + 0.868557i \(0.334952\pi\)
\(272\) −149365. −0.122412
\(273\) −1.19227e6 −0.968204
\(274\) −148970. −0.119873
\(275\) 237574. 0.189438
\(276\) 672767. 0.531608
\(277\) 2.21742e6 1.73639 0.868197 0.496219i \(-0.165279\pi\)
0.868197 + 0.496219i \(0.165279\pi\)
\(278\) −478569. −0.371392
\(279\) 3882.59 0.00298615
\(280\) −315217. −0.240278
\(281\) −1.82310e6 −1.37735 −0.688675 0.725070i \(-0.741808\pi\)
−0.688675 + 0.725070i \(0.741808\pi\)
\(282\) 453342. 0.339471
\(283\) 1.10885e6 0.823013 0.411506 0.911407i \(-0.365003\pi\)
0.411506 + 0.911407i \(0.365003\pi\)
\(284\) −57220.6 −0.0420975
\(285\) 81225.0 0.0592349
\(286\) 1.02240e6 0.739106
\(287\) −749408. −0.537049
\(288\) −82944.0 −0.0589256
\(289\) −1.07944e6 −0.760243
\(290\) −126892. −0.0886010
\(291\) 26937.4 0.0186476
\(292\) 477422. 0.327677
\(293\) 668940. 0.455217 0.227608 0.973753i \(-0.426909\pi\)
0.227608 + 0.973753i \(0.426909\pi\)
\(294\) −792219. −0.534536
\(295\) −442217. −0.295856
\(296\) −513959. −0.340957
\(297\) 277107. 0.182287
\(298\) 121692. 0.0793818
\(299\) −3.14155e6 −2.03220
\(300\) 90000.0 0.0577350
\(301\) 1.45013e6 0.922551
\(302\) −1.84048e6 −1.16122
\(303\) −288557. −0.180562
\(304\) 92416.0 0.0573539
\(305\) 68456.6 0.0421372
\(306\) 189040. 0.115412
\(307\) −2.30928e6 −1.39840 −0.699198 0.714928i \(-0.746460\pi\)
−0.699198 + 0.714928i \(0.746460\pi\)
\(308\) 1.19820e6 0.719701
\(309\) −1.11555e6 −0.664650
\(310\) −4793.32 −0.00283291
\(311\) −2.32274e6 −1.36176 −0.680880 0.732395i \(-0.738402\pi\)
−0.680880 + 0.732395i \(0.738402\pi\)
\(312\) 387315. 0.225257
\(313\) 303022. 0.174829 0.0874145 0.996172i \(-0.472140\pi\)
0.0874145 + 0.996172i \(0.472140\pi\)
\(314\) −1.25217e6 −0.716702
\(315\) 398946. 0.226536
\(316\) 459869. 0.259070
\(317\) −1.71217e6 −0.956968 −0.478484 0.878096i \(-0.658814\pi\)
−0.478484 + 0.878096i \(0.658814\pi\)
\(318\) −281258. −0.155968
\(319\) 482340. 0.265385
\(320\) 102400. 0.0559017
\(321\) −1.35033e6 −0.731438
\(322\) −3.68172e6 −1.97884
\(323\) −210628. −0.112333
\(324\) 104976. 0.0555556
\(325\) −420264. −0.220706
\(326\) −537910. −0.280327
\(327\) 1.42892e6 0.738989
\(328\) 243450. 0.124947
\(329\) −2.48092e6 −1.26364
\(330\) −342107. −0.172933
\(331\) 1.19409e6 0.599054 0.299527 0.954088i \(-0.403171\pi\)
0.299527 + 0.954088i \(0.403171\pi\)
\(332\) −1.57513e6 −0.784278
\(333\) 650479. 0.321457
\(334\) 1.10331e6 0.541169
\(335\) 364482. 0.177445
\(336\) 453912. 0.219343
\(337\) 202322. 0.0970440 0.0485220 0.998822i \(-0.484549\pi\)
0.0485220 + 0.998822i \(0.484549\pi\)
\(338\) −323435. −0.153991
\(339\) −154302. −0.0729245
\(340\) −233382. −0.109489
\(341\) 18220.3 0.00848536
\(342\) −116964. −0.0540738
\(343\) 1.02428e6 0.470091
\(344\) −471083. −0.214635
\(345\) 1.05120e6 0.475485
\(346\) −1.62340e6 −0.729011
\(347\) −896143. −0.399534 −0.199767 0.979843i \(-0.564019\pi\)
−0.199767 + 0.979843i \(0.564019\pi\)
\(348\) 182724. 0.0808813
\(349\) 735417. 0.323199 0.161600 0.986856i \(-0.448335\pi\)
0.161600 + 0.986856i \(0.448335\pi\)
\(350\) −492526. −0.214911
\(351\) −490196. −0.212374
\(352\) −389242. −0.167441
\(353\) 2.19963e6 0.939533 0.469767 0.882791i \(-0.344338\pi\)
0.469767 + 0.882791i \(0.344338\pi\)
\(354\) 636793. 0.270079
\(355\) −89407.2 −0.0376532
\(356\) 479775. 0.200638
\(357\) −1.03452e6 −0.429605
\(358\) 963370. 0.397270
\(359\) −1.06446e6 −0.435907 −0.217954 0.975959i \(-0.569938\pi\)
−0.217954 + 0.975959i \(0.569938\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) 3.30091e6 1.32392
\(363\) −149044. −0.0593673
\(364\) −2.11959e6 −0.838490
\(365\) 745973. 0.293083
\(366\) −98577.5 −0.0384658
\(367\) 1.26262e6 0.489337 0.244668 0.969607i \(-0.421321\pi\)
0.244668 + 0.969607i \(0.421321\pi\)
\(368\) 1.19603e6 0.460386
\(369\) −308116. −0.117801
\(370\) −803061. −0.304961
\(371\) 1.53919e6 0.580572
\(372\) 6902.38 0.00258608
\(373\) 4.98592e6 1.85555 0.927776 0.373138i \(-0.121718\pi\)
0.927776 + 0.373138i \(0.121718\pi\)
\(374\) 887131. 0.327951
\(375\) 140625. 0.0516398
\(376\) 805941. 0.293991
\(377\) −853249. −0.309188
\(378\) −574482. −0.206798
\(379\) −256131. −0.0915935 −0.0457968 0.998951i \(-0.514583\pi\)
−0.0457968 + 0.998951i \(0.514583\pi\)
\(380\) 144400. 0.0512989
\(381\) −253226. −0.0893707
\(382\) −3.22784e6 −1.13176
\(383\) 571433. 0.199053 0.0995263 0.995035i \(-0.468267\pi\)
0.0995263 + 0.995035i \(0.468267\pi\)
\(384\) −147456. −0.0510310
\(385\) 1.87219e6 0.643720
\(386\) −3.11137e6 −1.06288
\(387\) 596214. 0.202360
\(388\) 47888.6 0.0161493
\(389\) −4.73099e6 −1.58518 −0.792589 0.609756i \(-0.791268\pi\)
−0.792589 + 0.609756i \(0.791268\pi\)
\(390\) 605180. 0.201476
\(391\) −2.72590e6 −0.901713
\(392\) −1.40839e6 −0.462922
\(393\) 1.17553e6 0.383932
\(394\) −53296.2 −0.0172964
\(395\) 718545. 0.231719
\(396\) 492634. 0.157865
\(397\) −2.84731e6 −0.906690 −0.453345 0.891335i \(-0.649769\pi\)
−0.453345 + 0.891335i \(0.649769\pi\)
\(398\) 292257. 0.0924820
\(399\) 640087. 0.201283
\(400\) 160000. 0.0500000
\(401\) −1.20188e6 −0.373251 −0.186626 0.982431i \(-0.559755\pi\)
−0.186626 + 0.982431i \(0.559755\pi\)
\(402\) −524854. −0.161984
\(403\) −32231.4 −0.00988589
\(404\) −512991. −0.156371
\(405\) 164025. 0.0496904
\(406\) −999960. −0.301070
\(407\) 3.05259e6 0.913445
\(408\) 336071. 0.0999494
\(409\) −5.15592e6 −1.52405 −0.762023 0.647550i \(-0.775794\pi\)
−0.762023 + 0.647550i \(0.775794\pi\)
\(410\) 380390. 0.111756
\(411\) 335182. 0.0978761
\(412\) −1.98320e6 −0.575604
\(413\) −3.48486e6 −1.00533
\(414\) −1.51373e6 −0.434056
\(415\) −2.46114e6 −0.701480
\(416\) 688560. 0.195078
\(417\) 1.07678e6 0.303240
\(418\) −548892. −0.153655
\(419\) −2.53122e6 −0.704361 −0.352181 0.935932i \(-0.614560\pi\)
−0.352181 + 0.935932i \(0.614560\pi\)
\(420\) 709237. 0.196186
\(421\) 1.19341e6 0.328160 0.164080 0.986447i \(-0.447534\pi\)
0.164080 + 0.986447i \(0.447534\pi\)
\(422\) 1.08978e6 0.297891
\(423\) −1.02002e6 −0.277177
\(424\) −500014. −0.135073
\(425\) −364660. −0.0979300
\(426\) 128746. 0.0343725
\(427\) 539466. 0.143184
\(428\) −2.40059e6 −0.633444
\(429\) −2.30041e6 −0.603478
\(430\) −736067. −0.191976
\(431\) −1.85560e6 −0.481161 −0.240580 0.970629i \(-0.577338\pi\)
−0.240580 + 0.970629i \(0.577338\pi\)
\(432\) 186624. 0.0481125
\(433\) −4.55220e6 −1.16681 −0.583407 0.812180i \(-0.698281\pi\)
−0.583407 + 0.812180i \(0.698281\pi\)
\(434\) −37773.4 −0.00962634
\(435\) 285507. 0.0723424
\(436\) 2.54030e6 0.639983
\(437\) 1.68659e6 0.422480
\(438\) −1.07420e6 −0.267547
\(439\) −683362. −0.169235 −0.0846174 0.996414i \(-0.526967\pi\)
−0.0846174 + 0.996414i \(0.526967\pi\)
\(440\) −608191. −0.149764
\(441\) 1.78249e6 0.436447
\(442\) −1.56931e6 −0.382080
\(443\) 4.03950e6 0.977955 0.488977 0.872296i \(-0.337370\pi\)
0.488977 + 0.872296i \(0.337370\pi\)
\(444\) 1.15641e6 0.278390
\(445\) 749649. 0.179456
\(446\) −1.12299e6 −0.267324
\(447\) −273807. −0.0648149
\(448\) 806955. 0.189956
\(449\) −7.41760e6 −1.73639 −0.868196 0.496222i \(-0.834720\pi\)
−0.868196 + 0.496222i \(0.834720\pi\)
\(450\) −202500. −0.0471405
\(451\) −1.44594e6 −0.334740
\(452\) −274315. −0.0631545
\(453\) 4.14108e6 0.948130
\(454\) −5.54090e6 −1.26166
\(455\) −3.31185e6 −0.749968
\(456\) −207936. −0.0468293
\(457\) 8.28004e6 1.85456 0.927282 0.374363i \(-0.122139\pi\)
0.927282 + 0.374363i \(0.122139\pi\)
\(458\) −5.67596e6 −1.26437
\(459\) −425339. −0.0942332
\(460\) 1.86880e6 0.411782
\(461\) −6.39517e6 −1.40152 −0.700761 0.713396i \(-0.747156\pi\)
−0.700761 + 0.713396i \(0.747156\pi\)
\(462\) −2.69595e6 −0.587633
\(463\) −6.26670e6 −1.35858 −0.679292 0.733868i \(-0.737713\pi\)
−0.679292 + 0.733868i \(0.737713\pi\)
\(464\) 324843. 0.0700452
\(465\) 10785.0 0.00231306
\(466\) −5.26116e6 −1.12232
\(467\) −7.64352e6 −1.62181 −0.810907 0.585174i \(-0.801026\pi\)
−0.810907 + 0.585174i \(0.801026\pi\)
\(468\) −871459. −0.183921
\(469\) 2.87227e6 0.602966
\(470\) 1.25928e6 0.262953
\(471\) 2.81738e6 0.585185
\(472\) 1.13208e6 0.233895
\(473\) 2.79793e6 0.575022
\(474\) −1.03471e6 −0.211529
\(475\) 225625. 0.0458831
\(476\) −1.83915e6 −0.372049
\(477\) 632830. 0.127348
\(478\) 3.09912e6 0.620395
\(479\) 525106. 0.104570 0.0522852 0.998632i \(-0.483350\pi\)
0.0522852 + 0.998632i \(0.483350\pi\)
\(480\) −230400. −0.0456435
\(481\) −5.39996e6 −1.06421
\(482\) −70195.3 −0.0137623
\(483\) 8.28388e6 1.61572
\(484\) −264967. −0.0514136
\(485\) 74826.0 0.0144444
\(486\) −236196. −0.0453609
\(487\) −5.32536e6 −1.01748 −0.508741 0.860920i \(-0.669889\pi\)
−0.508741 + 0.860920i \(0.669889\pi\)
\(488\) −175249. −0.0333124
\(489\) 1.21030e6 0.228886
\(490\) −2.20061e6 −0.414050
\(491\) 6.94802e6 1.30064 0.650320 0.759660i \(-0.274635\pi\)
0.650320 + 0.759660i \(0.274635\pi\)
\(492\) −547762. −0.102019
\(493\) −740358. −0.137191
\(494\) 970978. 0.179016
\(495\) 769741. 0.141199
\(496\) 12270.9 0.00223961
\(497\) −704566. −0.127947
\(498\) 3.54403e6 0.640361
\(499\) 3.40412e6 0.612002 0.306001 0.952031i \(-0.401009\pi\)
0.306001 + 0.952031i \(0.401009\pi\)
\(500\) 250000. 0.0447214
\(501\) −2.48246e6 −0.441863
\(502\) 178582. 0.0316285
\(503\) 1.06481e6 0.187651 0.0938254 0.995589i \(-0.470090\pi\)
0.0938254 + 0.995589i \(0.470090\pi\)
\(504\) −1.02130e6 −0.179093
\(505\) −801548. −0.139862
\(506\) −7.10365e6 −1.23340
\(507\) 727728. 0.125733
\(508\) −450179. −0.0773973
\(509\) 8.70053e6 1.48851 0.744254 0.667897i \(-0.232805\pi\)
0.744254 + 0.667897i \(0.232805\pi\)
\(510\) 525110. 0.0893974
\(511\) 5.87857e6 0.995909
\(512\) −262144. −0.0441942
\(513\) 263169. 0.0441511
\(514\) 4.04228e6 0.674867
\(515\) −3.09875e6 −0.514836
\(516\) 1.05994e6 0.175249
\(517\) −4.78677e6 −0.787620
\(518\) −6.32845e6 −1.03627
\(519\) 3.65264e6 0.595235
\(520\) 1.07588e6 0.174483
\(521\) 7.51485e6 1.21290 0.606451 0.795121i \(-0.292593\pi\)
0.606451 + 0.795121i \(0.292593\pi\)
\(522\) −411129. −0.0660393
\(523\) −2.40784e6 −0.384922 −0.192461 0.981305i \(-0.561647\pi\)
−0.192461 + 0.981305i \(0.561647\pi\)
\(524\) 2.08984e6 0.332495
\(525\) 1.10818e6 0.175474
\(526\) −3.00291e6 −0.473236
\(527\) −27966.9 −0.00438650
\(528\) 875795. 0.136715
\(529\) 1.53912e7 2.39129
\(530\) −781271. −0.120813
\(531\) −1.43278e6 −0.220518
\(532\) 1.13793e6 0.174316
\(533\) 2.55783e6 0.389990
\(534\) −1.07949e6 −0.163820
\(535\) −3.75092e6 −0.566569
\(536\) −933073. −0.140283
\(537\) −2.16758e6 −0.324369
\(538\) 8.59348e6 1.28001
\(539\) 8.36494e6 1.24020
\(540\) 291600. 0.0430331
\(541\) −687897. −0.101049 −0.0505243 0.998723i \(-0.516089\pi\)
−0.0505243 + 0.998723i \(0.516089\pi\)
\(542\) −4.79330e6 −0.700868
\(543\) −7.42705e6 −1.08098
\(544\) 597459. 0.0865587
\(545\) 3.96922e6 0.572419
\(546\) 4.76907e6 0.684624
\(547\) −9.97003e6 −1.42472 −0.712358 0.701817i \(-0.752373\pi\)
−0.712358 + 0.701817i \(0.752373\pi\)
\(548\) 595880. 0.0847632
\(549\) 221799. 0.0314072
\(550\) −950298. −0.133953
\(551\) 458079. 0.0642779
\(552\) −2.69107e6 −0.375904
\(553\) 5.66244e6 0.787391
\(554\) −8.86968e6 −1.22782
\(555\) 1.80689e6 0.249000
\(556\) 1.91427e6 0.262614
\(557\) 8.72289e6 1.19130 0.595652 0.803243i \(-0.296894\pi\)
0.595652 + 0.803243i \(0.296894\pi\)
\(558\) −15530.4 −0.00211152
\(559\) −4.94948e6 −0.669931
\(560\) 1.26087e6 0.169902
\(561\) −1.99604e6 −0.267771
\(562\) 7.29240e6 0.973934
\(563\) 933880. 0.124171 0.0620855 0.998071i \(-0.480225\pi\)
0.0620855 + 0.998071i \(0.480225\pi\)
\(564\) −1.81337e6 −0.240042
\(565\) −428618. −0.0564871
\(566\) −4.43540e6 −0.581958
\(567\) 1.29259e6 0.168850
\(568\) 228882. 0.0297674
\(569\) −44406.4 −0.00574997 −0.00287498 0.999996i \(-0.500915\pi\)
−0.00287498 + 0.999996i \(0.500915\pi\)
\(570\) −324900. −0.0418854
\(571\) 4.47973e6 0.574992 0.287496 0.957782i \(-0.407177\pi\)
0.287496 + 0.957782i \(0.407177\pi\)
\(572\) −4.08961e6 −0.522627
\(573\) 7.26264e6 0.924077
\(574\) 2.99763e6 0.379751
\(575\) 2.91999e6 0.368309
\(576\) 331776. 0.0416667
\(577\) −2.00312e6 −0.250477 −0.125238 0.992127i \(-0.539970\pi\)
−0.125238 + 0.992127i \(0.539970\pi\)
\(578\) 4.31775e6 0.537573
\(579\) 7.00058e6 0.867835
\(580\) 507567. 0.0626504
\(581\) −1.93948e7 −2.38366
\(582\) −107749. −0.0131858
\(583\) 2.96976e6 0.361868
\(584\) −1.90969e6 −0.231703
\(585\) −1.36165e6 −0.164504
\(586\) −2.67576e6 −0.321887
\(587\) 4.22612e6 0.506228 0.253114 0.967436i \(-0.418545\pi\)
0.253114 + 0.967436i \(0.418545\pi\)
\(588\) 3.16888e6 0.377974
\(589\) 17303.9 0.00205521
\(590\) 1.76887e6 0.209202
\(591\) 119917. 0.0141225
\(592\) 2.05584e6 0.241093
\(593\) −1.64563e7 −1.92174 −0.960869 0.277002i \(-0.910659\pi\)
−0.960869 + 0.277002i \(0.910659\pi\)
\(594\) −1.10843e6 −0.128897
\(595\) −2.87367e6 −0.332770
\(596\) −486767. −0.0561314
\(597\) −657578. −0.0755112
\(598\) 1.25662e7 1.43698
\(599\) −2.74490e6 −0.312579 −0.156289 0.987711i \(-0.549953\pi\)
−0.156289 + 0.987711i \(0.549953\pi\)
\(600\) −360000. −0.0408248
\(601\) 6.48955e6 0.732873 0.366436 0.930443i \(-0.380578\pi\)
0.366436 + 0.930443i \(0.380578\pi\)
\(602\) −5.80052e6 −0.652342
\(603\) 1.18092e6 0.132260
\(604\) 7.36192e6 0.821105
\(605\) −414011. −0.0459857
\(606\) 1.15423e6 0.127676
\(607\) 7.23071e6 0.796543 0.398271 0.917268i \(-0.369610\pi\)
0.398271 + 0.917268i \(0.369610\pi\)
\(608\) −369664. −0.0405554
\(609\) 2.24991e6 0.245823
\(610\) −273826. −0.0297955
\(611\) 8.46769e6 0.917618
\(612\) −756159. −0.0816083
\(613\) −3.87455e6 −0.416457 −0.208228 0.978080i \(-0.566770\pi\)
−0.208228 + 0.978080i \(0.566770\pi\)
\(614\) 9.23711e6 0.988816
\(615\) −855878. −0.0912481
\(616\) −4.79280e6 −0.508905
\(617\) 8.73449e6 0.923686 0.461843 0.886962i \(-0.347188\pi\)
0.461843 + 0.886962i \(0.347188\pi\)
\(618\) 4.46220e6 0.469979
\(619\) −2.90336e6 −0.304561 −0.152280 0.988337i \(-0.548662\pi\)
−0.152280 + 0.988337i \(0.548662\pi\)
\(620\) 19173.3 0.00200317
\(621\) 3.40588e6 0.354406
\(622\) 9.29098e6 0.962910
\(623\) 5.90754e6 0.609799
\(624\) −1.54926e6 −0.159281
\(625\) 390625. 0.0400000
\(626\) −1.21209e6 −0.123623
\(627\) 1.23501e6 0.125459
\(628\) 5.00868e6 0.506785
\(629\) −4.68550e6 −0.472204
\(630\) −1.59578e6 −0.160185
\(631\) 153939. 0.0153913 0.00769566 0.999970i \(-0.497550\pi\)
0.00769566 + 0.999970i \(0.497550\pi\)
\(632\) −1.83948e6 −0.183190
\(633\) −2.45200e6 −0.243227
\(634\) 6.84866e6 0.676679
\(635\) −703405. −0.0692263
\(636\) 1.12503e6 0.110286
\(637\) −1.47974e7 −1.44490
\(638\) −1.92936e6 −0.187656
\(639\) −289679. −0.0280650
\(640\) −409600. −0.0395285
\(641\) −1.27540e7 −1.22603 −0.613014 0.790072i \(-0.710043\pi\)
−0.613014 + 0.790072i \(0.710043\pi\)
\(642\) 5.40132e6 0.517205
\(643\) 1.25557e7 1.19760 0.598802 0.800897i \(-0.295643\pi\)
0.598802 + 0.800897i \(0.295643\pi\)
\(644\) 1.47269e7 1.39925
\(645\) 1.65615e6 0.156748
\(646\) 842510. 0.0794317
\(647\) −1.36613e7 −1.28301 −0.641506 0.767118i \(-0.721690\pi\)
−0.641506 + 0.767118i \(0.721690\pi\)
\(648\) −419904. −0.0392837
\(649\) −6.72381e6 −0.626620
\(650\) 1.68106e6 0.156063
\(651\) 84990.1 0.00785988
\(652\) 2.15164e6 0.198221
\(653\) 3.83364e6 0.351827 0.175913 0.984406i \(-0.443712\pi\)
0.175913 + 0.984406i \(0.443712\pi\)
\(654\) −5.71567e6 −0.522544
\(655\) 3.26537e6 0.297392
\(656\) −973799. −0.0883506
\(657\) 2.41695e6 0.218451
\(658\) 9.92367e6 0.893527
\(659\) −1.15676e7 −1.03760 −0.518798 0.854897i \(-0.673620\pi\)
−0.518798 + 0.854897i \(0.673620\pi\)
\(660\) 1.36843e6 0.122282
\(661\) 2.87611e6 0.256036 0.128018 0.991772i \(-0.459138\pi\)
0.128018 + 0.991772i \(0.459138\pi\)
\(662\) −4.77635e6 −0.423595
\(663\) 3.53096e6 0.311967
\(664\) 6.30051e6 0.554569
\(665\) 1.77802e6 0.155913
\(666\) −2.60192e6 −0.227304
\(667\) 5.92838e6 0.515966
\(668\) −4.41326e6 −0.382664
\(669\) 2.52673e6 0.218270
\(670\) −1.45793e6 −0.125473
\(671\) 1.04087e6 0.0892460
\(672\) −1.81565e6 −0.155099
\(673\) 1.14921e7 0.978054 0.489027 0.872269i \(-0.337352\pi\)
0.489027 + 0.872269i \(0.337352\pi\)
\(674\) −809288. −0.0686205
\(675\) 455625. 0.0384900
\(676\) 1.29374e6 0.108888
\(677\) −5.02640e6 −0.421488 −0.210744 0.977541i \(-0.567589\pi\)
−0.210744 + 0.977541i \(0.567589\pi\)
\(678\) 617210. 0.0515654
\(679\) 589660. 0.0490826
\(680\) 933529. 0.0774204
\(681\) 1.24670e7 1.03014
\(682\) −72881.3 −0.00600006
\(683\) 5.62673e6 0.461535 0.230767 0.973009i \(-0.425876\pi\)
0.230767 + 0.973009i \(0.425876\pi\)
\(684\) 467856. 0.0382360
\(685\) 931062. 0.0758145
\(686\) −4.09710e6 −0.332404
\(687\) 1.27709e7 1.03236
\(688\) 1.88433e6 0.151770
\(689\) −5.25344e6 −0.421595
\(690\) −4.20479e6 −0.336219
\(691\) −1.42173e7 −1.13272 −0.566361 0.824157i \(-0.691649\pi\)
−0.566361 + 0.824157i \(0.691649\pi\)
\(692\) 6.49359e6 0.515489
\(693\) 6.06588e6 0.479801
\(694\) 3.58457e6 0.282513
\(695\) 2.99105e6 0.234889
\(696\) −730897. −0.0571917
\(697\) 2.21941e6 0.173043
\(698\) −2.94167e6 −0.228536
\(699\) 1.18376e7 0.916371
\(700\) 1.97010e6 0.151965
\(701\) 2.45934e6 0.189027 0.0945133 0.995524i \(-0.469871\pi\)
0.0945133 + 0.995524i \(0.469871\pi\)
\(702\) 1.96078e6 0.150171
\(703\) 2.89905e6 0.221242
\(704\) 1.55697e6 0.118399
\(705\) −2.83339e6 −0.214700
\(706\) −8.79850e6 −0.664350
\(707\) −6.31653e6 −0.475259
\(708\) −2.54717e6 −0.190974
\(709\) −7.06855e6 −0.528099 −0.264049 0.964509i \(-0.585058\pi\)
−0.264049 + 0.964509i \(0.585058\pi\)
\(710\) 357629. 0.0266248
\(711\) 2.32809e6 0.172713
\(712\) −1.91910e6 −0.141872
\(713\) 223944. 0.0164974
\(714\) 4.13809e6 0.303776
\(715\) −6.39001e6 −0.467452
\(716\) −3.85348e6 −0.280912
\(717\) −6.97302e6 −0.506550
\(718\) 4.25785e6 0.308233
\(719\) −7.42345e6 −0.535530 −0.267765 0.963484i \(-0.586285\pi\)
−0.267765 + 0.963484i \(0.586285\pi\)
\(720\) 518400. 0.0372678
\(721\) −2.44195e7 −1.74944
\(722\) −521284. −0.0372161
\(723\) 157939. 0.0112369
\(724\) −1.32036e7 −0.936154
\(725\) 793074. 0.0560362
\(726\) 596175. 0.0419790
\(727\) −1.16530e7 −0.817715 −0.408857 0.912598i \(-0.634073\pi\)
−0.408857 + 0.912598i \(0.634073\pi\)
\(728\) 8.47835e6 0.592902
\(729\) 531441. 0.0370370
\(730\) −2.98389e6 −0.207241
\(731\) −4.29463e6 −0.297257
\(732\) 394310. 0.0271994
\(733\) −1.69274e7 −1.16367 −0.581835 0.813307i \(-0.697665\pi\)
−0.581835 + 0.813307i \(0.697665\pi\)
\(734\) −5.05048e6 −0.346013
\(735\) 4.95137e6 0.338070
\(736\) −4.78412e6 −0.325542
\(737\) 5.54186e6 0.375826
\(738\) 1.23246e6 0.0832978
\(739\) −2.47308e7 −1.66582 −0.832909 0.553410i \(-0.813326\pi\)
−0.832909 + 0.553410i \(0.813326\pi\)
\(740\) 3.21224e6 0.215640
\(741\) −2.18470e6 −0.146166
\(742\) −6.15674e6 −0.410527
\(743\) −1.97993e6 −0.131576 −0.0657881 0.997834i \(-0.520956\pi\)
−0.0657881 + 0.997834i \(0.520956\pi\)
\(744\) −27609.5 −0.00182863
\(745\) −760574. −0.0502054
\(746\) −1.99437e7 −1.31207
\(747\) −7.97408e6 −0.522852
\(748\) −3.54852e6 −0.231896
\(749\) −2.95588e7 −1.92523
\(750\) −562500. −0.0365148
\(751\) −4.54219e6 −0.293877 −0.146938 0.989146i \(-0.546942\pi\)
−0.146938 + 0.989146i \(0.546942\pi\)
\(752\) −3.22376e6 −0.207883
\(753\) −401810. −0.0258246
\(754\) 3.41299e6 0.218629
\(755\) 1.15030e7 0.734419
\(756\) 2.29793e6 0.146229
\(757\) 2.98125e7 1.89086 0.945428 0.325830i \(-0.105644\pi\)
0.945428 + 0.325830i \(0.105644\pi\)
\(758\) 1.02453e6 0.0647664
\(759\) 1.59832e7 1.00707
\(760\) −577600. −0.0362738
\(761\) −5.98609e6 −0.374698 −0.187349 0.982293i \(-0.559990\pi\)
−0.187349 + 0.982293i \(0.559990\pi\)
\(762\) 1.01290e6 0.0631946
\(763\) 3.12791e7 1.94510
\(764\) 1.29114e7 0.800274
\(765\) −1.18150e6 −0.0729927
\(766\) −2.28573e6 −0.140752
\(767\) 1.18943e7 0.730045
\(768\) 589824. 0.0360844
\(769\) −1.84407e7 −1.12450 −0.562251 0.826966i \(-0.690065\pi\)
−0.562251 + 0.826966i \(0.690065\pi\)
\(770\) −7.48874e6 −0.455179
\(771\) −9.09513e6 −0.551027
\(772\) 1.24455e7 0.751568
\(773\) 1.39741e7 0.841153 0.420577 0.907257i \(-0.361828\pi\)
0.420577 + 0.907257i \(0.361828\pi\)
\(774\) −2.38486e6 −0.143090
\(775\) 29958.3 0.00179169
\(776\) −191555. −0.0114193
\(777\) 1.42390e7 0.846111
\(778\) 1.89240e7 1.12089
\(779\) −1.37321e6 −0.0810761
\(780\) −2.42072e6 −0.142465
\(781\) −1.35942e6 −0.0797489
\(782\) 1.09036e7 0.637607
\(783\) 925041. 0.0539208
\(784\) 5.63356e6 0.327335
\(785\) 7.82606e6 0.453282
\(786\) −4.70214e6 −0.271481
\(787\) 2.51310e6 0.144635 0.0723174 0.997382i \(-0.476961\pi\)
0.0723174 + 0.997382i \(0.476961\pi\)
\(788\) 213185. 0.0122304
\(789\) 6.75654e6 0.386396
\(790\) −2.87418e6 −0.163850
\(791\) −3.37769e6 −0.191946
\(792\) −1.97054e6 −0.111628
\(793\) −1.84127e6 −0.103976
\(794\) 1.13892e7 0.641127
\(795\) 1.75786e6 0.0986431
\(796\) −1.16903e6 −0.0653947
\(797\) −3.19909e7 −1.78394 −0.891970 0.452095i \(-0.850677\pi\)
−0.891970 + 0.452095i \(0.850677\pi\)
\(798\) −2.56035e6 −0.142328
\(799\) 7.34736e6 0.407159
\(800\) −640000. −0.0353553
\(801\) 2.42886e6 0.133759
\(802\) 4.80753e6 0.263928
\(803\) 1.13423e7 0.620746
\(804\) 2.09941e6 0.114540
\(805\) 2.30108e7 1.25153
\(806\) 128925. 0.00699038
\(807\) −1.93353e7 −1.04512
\(808\) 2.05196e6 0.110571
\(809\) 6.22287e6 0.334287 0.167144 0.985933i \(-0.446546\pi\)
0.167144 + 0.985933i \(0.446546\pi\)
\(810\) −656100. −0.0351364
\(811\) −2.01280e7 −1.07460 −0.537302 0.843390i \(-0.680556\pi\)
−0.537302 + 0.843390i \(0.680556\pi\)
\(812\) 3.99984e6 0.212889
\(813\) 1.07849e7 0.572256
\(814\) −1.22104e7 −0.645903
\(815\) 3.36194e6 0.177295
\(816\) −1.34428e6 −0.0706749
\(817\) 2.65720e6 0.139274
\(818\) 2.06237e7 1.07766
\(819\) −1.07304e7 −0.558993
\(820\) −1.52156e6 −0.0790232
\(821\) 1.59487e7 0.825786 0.412893 0.910780i \(-0.364518\pi\)
0.412893 + 0.910780i \(0.364518\pi\)
\(822\) −1.34073e6 −0.0692089
\(823\) −3.13818e6 −0.161502 −0.0807509 0.996734i \(-0.525732\pi\)
−0.0807509 + 0.996734i \(0.525732\pi\)
\(824\) 7.93281e6 0.407014
\(825\) 2.13817e6 0.109372
\(826\) 1.39394e7 0.710878
\(827\) 1.60959e7 0.818376 0.409188 0.912450i \(-0.365812\pi\)
0.409188 + 0.912450i \(0.365812\pi\)
\(828\) 6.05490e6 0.306924
\(829\) 2.79234e7 1.41118 0.705590 0.708620i \(-0.250682\pi\)
0.705590 + 0.708620i \(0.250682\pi\)
\(830\) 9.84454e6 0.496021
\(831\) 1.99568e7 1.00251
\(832\) −2.75424e6 −0.137941
\(833\) −1.28396e7 −0.641119
\(834\) −4.30712e6 −0.214423
\(835\) −6.89572e6 −0.342266
\(836\) 2.19557e6 0.108650
\(837\) 34943.3 0.00172405
\(838\) 1.01249e7 0.498059
\(839\) −3.54083e7 −1.73660 −0.868300 0.496039i \(-0.834787\pi\)
−0.868300 + 0.496039i \(0.834787\pi\)
\(840\) −2.83695e6 −0.138725
\(841\) −1.89010e7 −0.921499
\(842\) −4.77365e6 −0.232044
\(843\) −1.64079e7 −0.795214
\(844\) −4.35911e6 −0.210641
\(845\) 2.02147e6 0.0973923
\(846\) 4.08007e6 0.195994
\(847\) −3.26258e6 −0.156262
\(848\) 2.00005e6 0.0955107
\(849\) 9.97965e6 0.475167
\(850\) 1.45864e6 0.0692469
\(851\) 3.75189e7 1.77593
\(852\) −514985. −0.0243050
\(853\) −1.34191e7 −0.631469 −0.315735 0.948848i \(-0.602251\pi\)
−0.315735 + 0.948848i \(0.602251\pi\)
\(854\) −2.15787e6 −0.101246
\(855\) 731025. 0.0341993
\(856\) 9.60235e6 0.447912
\(857\) −1.94060e6 −0.0902579 −0.0451289 0.998981i \(-0.514370\pi\)
−0.0451289 + 0.998981i \(0.514370\pi\)
\(858\) 9.20162e6 0.426723
\(859\) −3.62803e7 −1.67760 −0.838800 0.544440i \(-0.816742\pi\)
−0.838800 + 0.544440i \(0.816742\pi\)
\(860\) 2.94427e6 0.135747
\(861\) −6.74467e6 −0.310065
\(862\) 7.42238e6 0.340232
\(863\) 3.68747e7 1.68539 0.842696 0.538389i \(-0.180967\pi\)
0.842696 + 0.538389i \(0.180967\pi\)
\(864\) −746496. −0.0340207
\(865\) 1.01462e7 0.461067
\(866\) 1.82088e7 0.825063
\(867\) −9.71493e6 −0.438927
\(868\) 151093. 0.00680685
\(869\) 1.09253e7 0.490777
\(870\) −1.14203e6 −0.0511538
\(871\) −9.80343e6 −0.437857
\(872\) −1.01612e7 −0.452537
\(873\) 242436. 0.0107662
\(874\) −6.74636e6 −0.298738
\(875\) 3.07829e6 0.135922
\(876\) 4.29680e6 0.189184
\(877\) 2.48608e7 1.09148 0.545741 0.837954i \(-0.316248\pi\)
0.545741 + 0.837954i \(0.316248\pi\)
\(878\) 2.73345e6 0.119667
\(879\) 6.02046e6 0.262819
\(880\) 2.43276e6 0.105899
\(881\) 2.32562e7 1.00948 0.504740 0.863271i \(-0.331588\pi\)
0.504740 + 0.863271i \(0.331588\pi\)
\(882\) −7.12997e6 −0.308615
\(883\) 3.73212e7 1.61084 0.805422 0.592702i \(-0.201939\pi\)
0.805422 + 0.592702i \(0.201939\pi\)
\(884\) 6.27726e6 0.270171
\(885\) −3.97996e6 −0.170813
\(886\) −1.61580e7 −0.691518
\(887\) 1.50942e7 0.644173 0.322086 0.946710i \(-0.395616\pi\)
0.322086 + 0.946710i \(0.395616\pi\)
\(888\) −4.62563e6 −0.196851
\(889\) −5.54312e6 −0.235234
\(890\) −2.99859e6 −0.126894
\(891\) 2.49396e6 0.105244
\(892\) 4.49196e6 0.189027
\(893\) −4.54601e6 −0.190766
\(894\) 1.09523e6 0.0458311
\(895\) −6.02106e6 −0.251255
\(896\) −3.22782e6 −0.134319
\(897\) −2.82740e7 −1.17329
\(898\) 2.96704e7 1.22781
\(899\) 60823.3 0.00250998
\(900\) 810000. 0.0333333
\(901\) −4.55837e6 −0.187067
\(902\) 5.78374e6 0.236697
\(903\) 1.30512e7 0.532635
\(904\) 1.09726e6 0.0446570
\(905\) −2.06307e7 −0.837322
\(906\) −1.65643e7 −0.670429
\(907\) −1.39715e7 −0.563931 −0.281965 0.959425i \(-0.590986\pi\)
−0.281965 + 0.959425i \(0.590986\pi\)
\(908\) 2.21636e7 0.892125
\(909\) −2.59702e6 −0.104247
\(910\) 1.32474e7 0.530307
\(911\) −3.92485e7 −1.56685 −0.783425 0.621486i \(-0.786529\pi\)
−0.783425 + 0.621486i \(0.786529\pi\)
\(912\) 831744. 0.0331133
\(913\) −3.74210e7 −1.48572
\(914\) −3.31202e7 −1.31138
\(915\) 616109. 0.0243279
\(916\) 2.27038e7 0.894048
\(917\) 2.57325e7 1.01055
\(918\) 1.70136e6 0.0666329
\(919\) 8.24119e6 0.321885 0.160943 0.986964i \(-0.448547\pi\)
0.160943 + 0.986964i \(0.448547\pi\)
\(920\) −7.47519e6 −0.291174
\(921\) −2.07835e7 −0.807365
\(922\) 2.55807e7 0.991025
\(923\) 2.40478e6 0.0929117
\(924\) 1.07838e7 0.415520
\(925\) 5.01913e6 0.192874
\(926\) 2.50668e7 0.960664
\(927\) −1.00400e7 −0.383736
\(928\) −1.29937e6 −0.0495295
\(929\) −3.19115e7 −1.21313 −0.606566 0.795033i \(-0.707453\pi\)
−0.606566 + 0.795033i \(0.707453\pi\)
\(930\) −43139.9 −0.00163558
\(931\) 7.94420e6 0.300383
\(932\) 2.10446e7 0.793600
\(933\) −2.09047e7 −0.786212
\(934\) 3.05741e7 1.14680
\(935\) −5.54457e6 −0.207414
\(936\) 3.48584e6 0.130052
\(937\) −4.28942e7 −1.59606 −0.798031 0.602616i \(-0.794125\pi\)
−0.798031 + 0.602616i \(0.794125\pi\)
\(938\) −1.14891e7 −0.426361
\(939\) 2.72720e6 0.100938
\(940\) −5.03713e6 −0.185936
\(941\) −1.31571e7 −0.484380 −0.242190 0.970229i \(-0.577866\pi\)
−0.242190 + 0.970229i \(0.577866\pi\)
\(942\) −1.12695e7 −0.413788
\(943\) −1.77718e7 −0.650807
\(944\) −4.52831e6 −0.165389
\(945\) 3.59051e6 0.130791
\(946\) −1.11917e7 −0.406602
\(947\) −4.81781e7 −1.74572 −0.872861 0.487969i \(-0.837738\pi\)
−0.872861 + 0.487969i \(0.837738\pi\)
\(948\) 4.13882e6 0.149574
\(949\) −2.00643e7 −0.723202
\(950\) −902500. −0.0324443
\(951\) −1.54095e7 −0.552506
\(952\) 7.35660e6 0.263078
\(953\) 2.65269e7 0.946137 0.473068 0.881026i \(-0.343146\pi\)
0.473068 + 0.881026i \(0.343146\pi\)
\(954\) −2.53132e6 −0.0900484
\(955\) 2.01740e7 0.715787
\(956\) −1.23965e7 −0.438686
\(957\) 4.34106e6 0.153220
\(958\) −2.10043e6 −0.0739424
\(959\) 7.33716e6 0.257621
\(960\) 921600. 0.0322749
\(961\) −2.86269e7 −0.999920
\(962\) 2.15998e7 0.752511
\(963\) −1.21530e7 −0.422296
\(964\) 280781. 0.00973140
\(965\) 1.94460e7 0.672222
\(966\) −3.31355e7 −1.14249
\(967\) −2.31096e7 −0.794741 −0.397370 0.917658i \(-0.630077\pi\)
−0.397370 + 0.917658i \(0.630077\pi\)
\(968\) 1.05987e6 0.0363549
\(969\) −1.89565e6 −0.0648557
\(970\) −299304. −0.0102137
\(971\) 1.09900e7 0.374069 0.187034 0.982353i \(-0.440112\pi\)
0.187034 + 0.982353i \(0.440112\pi\)
\(972\) 944784. 0.0320750
\(973\) 2.35707e7 0.798162
\(974\) 2.13015e7 0.719469
\(975\) −3.78237e6 −0.127425
\(976\) 700995. 0.0235554
\(977\) 3.16949e6 0.106231 0.0531157 0.998588i \(-0.483085\pi\)
0.0531157 + 0.998588i \(0.483085\pi\)
\(978\) −4.84119e6 −0.161847
\(979\) 1.13982e7 0.380085
\(980\) 8.80244e6 0.292778
\(981\) 1.28603e7 0.426656
\(982\) −2.77921e7 −0.919692
\(983\) −4.25969e6 −0.140603 −0.0703015 0.997526i \(-0.522396\pi\)
−0.0703015 + 0.997526i \(0.522396\pi\)
\(984\) 2.19105e6 0.0721380
\(985\) 333101. 0.0109392
\(986\) 2.96143e6 0.0970084
\(987\) −2.23283e7 −0.729561
\(988\) −3.88391e6 −0.126583
\(989\) 3.43890e7 1.11797
\(990\) −3.07897e6 −0.0998428
\(991\) −1.78313e6 −0.0576764 −0.0288382 0.999584i \(-0.509181\pi\)
−0.0288382 + 0.999584i \(0.509181\pi\)
\(992\) −49083.6 −0.00158364
\(993\) 1.07468e7 0.345864
\(994\) 2.81826e6 0.0904723
\(995\) −1.82661e6 −0.0584908
\(996\) −1.41761e7 −0.452803
\(997\) −2.23417e6 −0.0711833 −0.0355916 0.999366i \(-0.511332\pi\)
−0.0355916 + 0.999366i \(0.511332\pi\)
\(998\) −1.36165e7 −0.432751
\(999\) 5.85431e6 0.185593
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 570.6.a.m.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.m.1.3 4 1.1 even 1 trivial