Properties

Label 570.6.a.j.1.1
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $1$
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: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - 25872 x^{2} - 1407374 x - 6356280\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-4.97007\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -177.358 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +36.0000 q^{6} -177.358 q^{7} -64.0000 q^{8} +81.0000 q^{9} -100.000 q^{10} -464.803 q^{11} -144.000 q^{12} +535.413 q^{13} +709.432 q^{14} -225.000 q^{15} +256.000 q^{16} +173.676 q^{17} -324.000 q^{18} +361.000 q^{19} +400.000 q^{20} +1596.22 q^{21} +1859.21 q^{22} +2051.32 q^{23} +576.000 q^{24} +625.000 q^{25} -2141.65 q^{26} -729.000 q^{27} -2837.73 q^{28} +6005.28 q^{29} +900.000 q^{30} -7404.30 q^{31} -1024.00 q^{32} +4183.23 q^{33} -694.704 q^{34} -4433.95 q^{35} +1296.00 q^{36} -1709.29 q^{37} -1444.00 q^{38} -4818.72 q^{39} -1600.00 q^{40} -731.943 q^{41} -6384.89 q^{42} +24127.7 q^{43} -7436.85 q^{44} +2025.00 q^{45} -8205.27 q^{46} -22819.3 q^{47} -2304.00 q^{48} +14648.8 q^{49} -2500.00 q^{50} -1563.08 q^{51} +8566.61 q^{52} -5428.32 q^{53} +2916.00 q^{54} -11620.1 q^{55} +11350.9 q^{56} -3249.00 q^{57} -24021.1 q^{58} +16791.6 q^{59} -3600.00 q^{60} +51053.5 q^{61} +29617.2 q^{62} -14366.0 q^{63} +4096.00 q^{64} +13385.3 q^{65} -16732.9 q^{66} -59420.7 q^{67} +2778.82 q^{68} -18461.9 q^{69} +17735.8 q^{70} +5792.90 q^{71} -5184.00 q^{72} -56301.8 q^{73} +6837.17 q^{74} -5625.00 q^{75} +5776.00 q^{76} +82436.5 q^{77} +19274.9 q^{78} +71932.4 q^{79} +6400.00 q^{80} +6561.00 q^{81} +2927.77 q^{82} +83624.9 q^{83} +25539.5 q^{84} +4341.90 q^{85} -96510.7 q^{86} -54047.5 q^{87} +29747.4 q^{88} +125338. q^{89} -8100.00 q^{90} -94959.7 q^{91} +32821.1 q^{92} +66638.7 q^{93} +91277.1 q^{94} +9025.00 q^{95} +9216.00 q^{96} +19704.2 q^{97} -58595.4 q^{98} -37649.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} + O(q^{10}) \) \( 4q - 16q^{2} - 36q^{3} + 64q^{4} + 100q^{5} + 144q^{6} - 108q^{7} - 256q^{8} + 324q^{9} - 400q^{10} - 246q^{11} - 576q^{12} + 640q^{13} + 432q^{14} - 900q^{15} + 1024q^{16} - 612q^{17} - 1296q^{18} + 1444q^{19} + 1600q^{20} + 972q^{21} + 984q^{22} - 1242q^{23} + 2304q^{24} + 2500q^{25} - 2560q^{26} - 2916q^{27} - 1728q^{28} - 6230q^{29} + 3600q^{30} - 11360q^{31} - 4096q^{32} + 2214q^{33} + 2448q^{34} - 2700q^{35} + 5184q^{36} - 4792q^{37} - 5776q^{38} - 5760q^{39} - 6400q^{40} + 9170q^{41} - 3888q^{42} - 11412q^{43} - 3936q^{44} + 8100q^{45} + 4968q^{46} - 29858q^{47} - 9216q^{48} + 31092q^{49} - 10000q^{50} + 5508q^{51} + 10240q^{52} + 27498q^{53} + 11664q^{54} - 6150q^{55} + 6912q^{56} - 12996q^{57} + 24920q^{58} + 54984q^{59} - 14400q^{60} + 20868q^{61} + 45440q^{62} - 8748q^{63} + 16384q^{64} + 16000q^{65} - 8856q^{66} - 20244q^{67} - 9792q^{68} + 11178q^{69} + 10800q^{70} + 86864q^{71} - 20736q^{72} - 3728q^{73} + 19168q^{74} - 22500q^{75} + 23104q^{76} + 18796q^{77} + 23040q^{78} + 164192q^{79} + 25600q^{80} + 26244q^{81} - 36680q^{82} - 60506q^{83} + 15552q^{84} - 15300q^{85} + 45648q^{86} + 56070q^{87} + 15744q^{88} + 113798q^{89} - 32400q^{90} + 159528q^{91} - 19872q^{92} + 102240q^{93} + 119432q^{94} + 36100q^{95} + 36864q^{96} + 79440q^{97} - 124368q^{98} - 19926q^{99} + O(q^{100}) \)

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
\(7\) −177.358 −1.36806 −0.684031 0.729453i \(-0.739775\pi\)
−0.684031 + 0.729453i \(0.739775\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) −100.000 −0.316228
\(11\) −464.803 −1.15821 −0.579105 0.815253i \(-0.696598\pi\)
−0.579105 + 0.815253i \(0.696598\pi\)
\(12\) −144.000 −0.288675
\(13\) 535.413 0.878680 0.439340 0.898321i \(-0.355212\pi\)
0.439340 + 0.898321i \(0.355212\pi\)
\(14\) 709.432 0.967365
\(15\) −225.000 −0.258199
\(16\) 256.000 0.250000
\(17\) 173.676 0.145753 0.0728765 0.997341i \(-0.476782\pi\)
0.0728765 + 0.997341i \(0.476782\pi\)
\(18\) −324.000 −0.235702
\(19\) 361.000 0.229416
\(20\) 400.000 0.223607
\(21\) 1596.22 0.789851
\(22\) 1859.21 0.818978
\(23\) 2051.32 0.808562 0.404281 0.914635i \(-0.367522\pi\)
0.404281 + 0.914635i \(0.367522\pi\)
\(24\) 576.000 0.204124
\(25\) 625.000 0.200000
\(26\) −2141.65 −0.621320
\(27\) −729.000 −0.192450
\(28\) −2837.73 −0.684031
\(29\) 6005.28 1.32598 0.662992 0.748627i \(-0.269287\pi\)
0.662992 + 0.748627i \(0.269287\pi\)
\(30\) 900.000 0.182574
\(31\) −7404.30 −1.38382 −0.691911 0.721983i \(-0.743231\pi\)
−0.691911 + 0.721983i \(0.743231\pi\)
\(32\) −1024.00 −0.176777
\(33\) 4183.23 0.668693
\(34\) −694.704 −0.103063
\(35\) −4433.95 −0.611816
\(36\) 1296.00 0.166667
\(37\) −1709.29 −0.205264 −0.102632 0.994719i \(-0.532726\pi\)
−0.102632 + 0.994719i \(0.532726\pi\)
\(38\) −1444.00 −0.162221
\(39\) −4818.72 −0.507306
\(40\) −1600.00 −0.158114
\(41\) −731.943 −0.0680013 −0.0340007 0.999422i \(-0.510825\pi\)
−0.0340007 + 0.999422i \(0.510825\pi\)
\(42\) −6384.89 −0.558509
\(43\) 24127.7 1.98996 0.994980 0.100070i \(-0.0319068\pi\)
0.994980 + 0.100070i \(0.0319068\pi\)
\(44\) −7436.85 −0.579105
\(45\) 2025.00 0.149071
\(46\) −8205.27 −0.571739
\(47\) −22819.3 −1.50681 −0.753403 0.657560i \(-0.771589\pi\)
−0.753403 + 0.657560i \(0.771589\pi\)
\(48\) −2304.00 −0.144338
\(49\) 14648.8 0.871592
\(50\) −2500.00 −0.141421
\(51\) −1563.08 −0.0841505
\(52\) 8566.61 0.439340
\(53\) −5428.32 −0.265446 −0.132723 0.991153i \(-0.542372\pi\)
−0.132723 + 0.991153i \(0.542372\pi\)
\(54\) 2916.00 0.136083
\(55\) −11620.1 −0.517967
\(56\) 11350.9 0.483683
\(57\) −3249.00 −0.132453
\(58\) −24021.1 −0.937612
\(59\) 16791.6 0.628003 0.314001 0.949423i \(-0.398330\pi\)
0.314001 + 0.949423i \(0.398330\pi\)
\(60\) −3600.00 −0.129099
\(61\) 51053.5 1.75671 0.878357 0.478005i \(-0.158640\pi\)
0.878357 + 0.478005i \(0.158640\pi\)
\(62\) 29617.2 0.978509
\(63\) −14366.0 −0.456020
\(64\) 4096.00 0.125000
\(65\) 13385.3 0.392957
\(66\) −16732.9 −0.472837
\(67\) −59420.7 −1.61715 −0.808576 0.588391i \(-0.799762\pi\)
−0.808576 + 0.588391i \(0.799762\pi\)
\(68\) 2778.82 0.0728765
\(69\) −18461.9 −0.466823
\(70\) 17735.8 0.432619
\(71\) 5792.90 0.136380 0.0681900 0.997672i \(-0.478278\pi\)
0.0681900 + 0.997672i \(0.478278\pi\)
\(72\) −5184.00 −0.117851
\(73\) −56301.8 −1.23656 −0.618280 0.785958i \(-0.712170\pi\)
−0.618280 + 0.785958i \(0.712170\pi\)
\(74\) 6837.17 0.145143
\(75\) −5625.00 −0.115470
\(76\) 5776.00 0.114708
\(77\) 82436.5 1.58450
\(78\) 19274.9 0.358719
\(79\) 71932.4 1.29675 0.648376 0.761321i \(-0.275449\pi\)
0.648376 + 0.761321i \(0.275449\pi\)
\(80\) 6400.00 0.111803
\(81\) 6561.00 0.111111
\(82\) 2927.77 0.0480842
\(83\) 83624.9 1.33242 0.666209 0.745766i \(-0.267916\pi\)
0.666209 + 0.745766i \(0.267916\pi\)
\(84\) 25539.5 0.394925
\(85\) 4341.90 0.0651827
\(86\) −96510.7 −1.40711
\(87\) −54047.5 −0.765557
\(88\) 29747.4 0.409489
\(89\) 125338. 1.67729 0.838647 0.544675i \(-0.183347\pi\)
0.838647 + 0.544675i \(0.183347\pi\)
\(90\) −8100.00 −0.105409
\(91\) −94959.7 −1.20209
\(92\) 32821.1 0.404281
\(93\) 66638.7 0.798950
\(94\) 91277.1 1.06547
\(95\) 9025.00 0.102598
\(96\) 9216.00 0.102062
\(97\) 19704.2 0.212633 0.106316 0.994332i \(-0.466094\pi\)
0.106316 + 0.994332i \(0.466094\pi\)
\(98\) −58595.4 −0.616308
\(99\) −37649.1 −0.386070
\(100\) 10000.0 0.100000
\(101\) −70891.2 −0.691495 −0.345747 0.938328i \(-0.612375\pi\)
−0.345747 + 0.938328i \(0.612375\pi\)
\(102\) 6252.34 0.0595034
\(103\) −11519.4 −0.106989 −0.0534944 0.998568i \(-0.517036\pi\)
−0.0534944 + 0.998568i \(0.517036\pi\)
\(104\) −34266.4 −0.310660
\(105\) 39905.5 0.353232
\(106\) 21713.3 0.187698
\(107\) −24983.5 −0.210957 −0.105479 0.994422i \(-0.533637\pi\)
−0.105479 + 0.994422i \(0.533637\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 84410.5 0.680504 0.340252 0.940334i \(-0.389488\pi\)
0.340252 + 0.940334i \(0.389488\pi\)
\(110\) 46480.3 0.366258
\(111\) 15383.6 0.118509
\(112\) −45403.6 −0.342015
\(113\) −204453. −1.50625 −0.753126 0.657877i \(-0.771455\pi\)
−0.753126 + 0.657877i \(0.771455\pi\)
\(114\) 12996.0 0.0936586
\(115\) 51282.9 0.361600
\(116\) 96084.4 0.662992
\(117\) 43368.5 0.292893
\(118\) −67166.3 −0.444065
\(119\) −30802.8 −0.199399
\(120\) 14400.0 0.0912871
\(121\) 54991.1 0.341451
\(122\) −204214. −1.24218
\(123\) 6587.48 0.0392606
\(124\) −118469. −0.691911
\(125\) 15625.0 0.0894427
\(126\) 57464.0 0.322455
\(127\) −330032. −1.81571 −0.907857 0.419280i \(-0.862282\pi\)
−0.907857 + 0.419280i \(0.862282\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −217149. −1.14890
\(130\) −53541.3 −0.277863
\(131\) −234542. −1.19411 −0.597053 0.802202i \(-0.703662\pi\)
−0.597053 + 0.802202i \(0.703662\pi\)
\(132\) 66931.7 0.334347
\(133\) −64026.2 −0.313855
\(134\) 237683. 1.14350
\(135\) −18225.0 −0.0860663
\(136\) −11115.3 −0.0515315
\(137\) −221612. −1.00877 −0.504385 0.863479i \(-0.668281\pi\)
−0.504385 + 0.863479i \(0.668281\pi\)
\(138\) 73847.4 0.330094
\(139\) −85413.0 −0.374962 −0.187481 0.982268i \(-0.560032\pi\)
−0.187481 + 0.982268i \(0.560032\pi\)
\(140\) −70943.2 −0.305908
\(141\) 205373. 0.869954
\(142\) −23171.6 −0.0964352
\(143\) −248862. −1.01770
\(144\) 20736.0 0.0833333
\(145\) 150132. 0.592998
\(146\) 225207. 0.874380
\(147\) −131840. −0.503214
\(148\) −27348.7 −0.102632
\(149\) 456176. 1.68332 0.841661 0.540007i \(-0.181578\pi\)
0.841661 + 0.540007i \(0.181578\pi\)
\(150\) 22500.0 0.0816497
\(151\) 8751.42 0.0312346 0.0156173 0.999878i \(-0.495029\pi\)
0.0156173 + 0.999878i \(0.495029\pi\)
\(152\) −23104.0 −0.0811107
\(153\) 14067.8 0.0485843
\(154\) −329746. −1.12041
\(155\) −185108. −0.618864
\(156\) −77099.5 −0.253653
\(157\) −86034.8 −0.278564 −0.139282 0.990253i \(-0.544479\pi\)
−0.139282 + 0.990253i \(0.544479\pi\)
\(158\) −287730. −0.916942
\(159\) 48854.9 0.153255
\(160\) −25600.0 −0.0790569
\(161\) −363817. −1.10616
\(162\) −26244.0 −0.0785674
\(163\) 281927. 0.831127 0.415563 0.909564i \(-0.363584\pi\)
0.415563 + 0.909564i \(0.363584\pi\)
\(164\) −11711.1 −0.0340007
\(165\) 104581. 0.299049
\(166\) −334499. −0.942161
\(167\) −467561. −1.29732 −0.648660 0.761078i \(-0.724670\pi\)
−0.648660 + 0.761078i \(0.724670\pi\)
\(168\) −102158. −0.279254
\(169\) −84625.9 −0.227922
\(170\) −17367.6 −0.0460911
\(171\) 29241.0 0.0764719
\(172\) 386043. 0.994980
\(173\) −518177. −1.31632 −0.658162 0.752876i \(-0.728666\pi\)
−0.658162 + 0.752876i \(0.728666\pi\)
\(174\) 216190. 0.541330
\(175\) −110849. −0.273612
\(176\) −118990. −0.289553
\(177\) −151124. −0.362577
\(178\) −501354. −1.18603
\(179\) −740069. −1.72639 −0.863196 0.504869i \(-0.831541\pi\)
−0.863196 + 0.504869i \(0.831541\pi\)
\(180\) 32400.0 0.0745356
\(181\) 797442. 1.80927 0.904633 0.426190i \(-0.140145\pi\)
0.904633 + 0.426190i \(0.140145\pi\)
\(182\) 379839. 0.850004
\(183\) −459482. −1.01424
\(184\) −131284. −0.285870
\(185\) −42732.3 −0.0917968
\(186\) −266555. −0.564943
\(187\) −80725.2 −0.168813
\(188\) −365108. −0.753403
\(189\) 129294. 0.263284
\(190\) −36100.0 −0.0725476
\(191\) −677830. −1.34443 −0.672214 0.740357i \(-0.734656\pi\)
−0.672214 + 0.740357i \(0.734656\pi\)
\(192\) −36864.0 −0.0721688
\(193\) −599323. −1.15816 −0.579079 0.815271i \(-0.696588\pi\)
−0.579079 + 0.815271i \(0.696588\pi\)
\(194\) −78816.9 −0.150354
\(195\) −120468. −0.226874
\(196\) 234381. 0.435796
\(197\) −913469. −1.67698 −0.838490 0.544916i \(-0.816561\pi\)
−0.838490 + 0.544916i \(0.816561\pi\)
\(198\) 150596. 0.272993
\(199\) −777236. −1.39130 −0.695650 0.718381i \(-0.744883\pi\)
−0.695650 + 0.718381i \(0.744883\pi\)
\(200\) −40000.0 −0.0707107
\(201\) 534787. 0.933664
\(202\) 283565. 0.488961
\(203\) −1.06508e6 −1.81403
\(204\) −25009.3 −0.0420753
\(205\) −18298.6 −0.0304111
\(206\) 46077.8 0.0756525
\(207\) 166157. 0.269521
\(208\) 137066. 0.219670
\(209\) −167794. −0.265712
\(210\) −159622. −0.249773
\(211\) 438515. 0.678076 0.339038 0.940773i \(-0.389898\pi\)
0.339038 + 0.940773i \(0.389898\pi\)
\(212\) −86853.1 −0.132723
\(213\) −52136.1 −0.0787390
\(214\) 99934.1 0.149169
\(215\) 603192. 0.889937
\(216\) 46656.0 0.0680414
\(217\) 1.31321e6 1.89315
\(218\) −337642. −0.481189
\(219\) 506716. 0.713928
\(220\) −185921. −0.258984
\(221\) 92988.4 0.128070
\(222\) −61534.6 −0.0837986
\(223\) 253681. 0.341607 0.170803 0.985305i \(-0.445364\pi\)
0.170803 + 0.985305i \(0.445364\pi\)
\(224\) 181615. 0.241841
\(225\) 50625.0 0.0666667
\(226\) 817812. 1.06508
\(227\) −436025. −0.561625 −0.280813 0.959763i \(-0.590604\pi\)
−0.280813 + 0.959763i \(0.590604\pi\)
\(228\) −51984.0 −0.0662266
\(229\) 1.00535e6 1.26685 0.633427 0.773802i \(-0.281647\pi\)
0.633427 + 0.773802i \(0.281647\pi\)
\(230\) −205132. −0.255690
\(231\) −741929. −0.914813
\(232\) −384338. −0.468806
\(233\) 1.26085e6 1.52151 0.760755 0.649039i \(-0.224829\pi\)
0.760755 + 0.649039i \(0.224829\pi\)
\(234\) −173474. −0.207107
\(235\) −570482. −0.673864
\(236\) 268665. 0.314001
\(237\) −647391. −0.748680
\(238\) 123211. 0.140996
\(239\) −783233. −0.886944 −0.443472 0.896288i \(-0.646253\pi\)
−0.443472 + 0.896288i \(0.646253\pi\)
\(240\) −57600.0 −0.0645497
\(241\) 683254. 0.757773 0.378887 0.925443i \(-0.376307\pi\)
0.378887 + 0.925443i \(0.376307\pi\)
\(242\) −219964. −0.241443
\(243\) −59049.0 −0.0641500
\(244\) 816857. 0.878357
\(245\) 366221. 0.389788
\(246\) −26349.9 −0.0277614
\(247\) 193284. 0.201583
\(248\) 473875. 0.489255
\(249\) −752624. −0.769271
\(250\) −62500.0 −0.0632456
\(251\) −159091. −0.159390 −0.0796952 0.996819i \(-0.525395\pi\)
−0.0796952 + 0.996819i \(0.525395\pi\)
\(252\) −229856. −0.228010
\(253\) −953459. −0.936485
\(254\) 1.32013e6 1.28390
\(255\) −39077.1 −0.0376333
\(256\) 65536.0 0.0625000
\(257\) −1.38427e6 −1.30734 −0.653670 0.756780i \(-0.726771\pi\)
−0.653670 + 0.756780i \(0.726771\pi\)
\(258\) 868597. 0.812398
\(259\) 303157. 0.280813
\(260\) 214165. 0.196479
\(261\) 486427. 0.441994
\(262\) 938170. 0.844361
\(263\) 538976. 0.480486 0.240243 0.970713i \(-0.422773\pi\)
0.240243 + 0.970713i \(0.422773\pi\)
\(264\) −267727. −0.236419
\(265\) −135708. −0.118711
\(266\) 256105. 0.221929
\(267\) −1.12805e6 −0.968386
\(268\) −950732. −0.808576
\(269\) −302609. −0.254977 −0.127489 0.991840i \(-0.540692\pi\)
−0.127489 + 0.991840i \(0.540692\pi\)
\(270\) 72900.0 0.0608581
\(271\) 806768. 0.667306 0.333653 0.942696i \(-0.391719\pi\)
0.333653 + 0.942696i \(0.391719\pi\)
\(272\) 44461.1 0.0364383
\(273\) 854638. 0.694026
\(274\) 886449. 0.713308
\(275\) −290502. −0.231642
\(276\) −295390. −0.233412
\(277\) −1.52143e6 −1.19139 −0.595694 0.803211i \(-0.703123\pi\)
−0.595694 + 0.803211i \(0.703123\pi\)
\(278\) 341652. 0.265138
\(279\) −599749. −0.461274
\(280\) 283773. 0.216309
\(281\) −2.17452e6 −1.64285 −0.821425 0.570316i \(-0.806821\pi\)
−0.821425 + 0.570316i \(0.806821\pi\)
\(282\) −821494. −0.615151
\(283\) 1.21558e6 0.902230 0.451115 0.892466i \(-0.351026\pi\)
0.451115 + 0.892466i \(0.351026\pi\)
\(284\) 92686.5 0.0681900
\(285\) −81225.0 −0.0592349
\(286\) 995447. 0.719620
\(287\) 129816. 0.0930300
\(288\) −82944.0 −0.0589256
\(289\) −1.38969e6 −0.978756
\(290\) −600528. −0.419313
\(291\) −177338. −0.122764
\(292\) −900829. −0.618280
\(293\) −649268. −0.441830 −0.220915 0.975293i \(-0.570904\pi\)
−0.220915 + 0.975293i \(0.570904\pi\)
\(294\) 527358. 0.355826
\(295\) 419789. 0.280851
\(296\) 109395. 0.0725717
\(297\) 338842. 0.222898
\(298\) −1.82471e6 −1.19029
\(299\) 1.09830e6 0.710467
\(300\) −90000.0 −0.0577350
\(301\) −4.27924e6 −2.72239
\(302\) −35005.7 −0.0220862
\(303\) 638021. 0.399235
\(304\) 92416.0 0.0573539
\(305\) 1.27634e6 0.785627
\(306\) −56271.0 −0.0343543
\(307\) 2.24128e6 1.35722 0.678610 0.734499i \(-0.262583\pi\)
0.678610 + 0.734499i \(0.262583\pi\)
\(308\) 1.31898e6 0.792251
\(309\) 103675. 0.0617700
\(310\) 740430. 0.437603
\(311\) −2.11332e6 −1.23898 −0.619490 0.785005i \(-0.712661\pi\)
−0.619490 + 0.785005i \(0.712661\pi\)
\(312\) 308398. 0.179360
\(313\) −135006. −0.0778920 −0.0389460 0.999241i \(-0.512400\pi\)
−0.0389460 + 0.999241i \(0.512400\pi\)
\(314\) 344139. 0.196974
\(315\) −359150. −0.203939
\(316\) 1.15092e6 0.648376
\(317\) −2.91526e6 −1.62941 −0.814704 0.579877i \(-0.803101\pi\)
−0.814704 + 0.579877i \(0.803101\pi\)
\(318\) −195420. −0.108368
\(319\) −2.79127e6 −1.53577
\(320\) 102400. 0.0559017
\(321\) 224852. 0.121796
\(322\) 1.45527e6 0.782175
\(323\) 62697.0 0.0334380
\(324\) 104976. 0.0555556
\(325\) 334633. 0.175736
\(326\) −1.12771e6 −0.587695
\(327\) −759695. −0.392889
\(328\) 46844.3 0.0240421
\(329\) 4.04718e6 2.06140
\(330\) −418323. −0.211459
\(331\) −1.07282e6 −0.538214 −0.269107 0.963110i \(-0.586729\pi\)
−0.269107 + 0.963110i \(0.586729\pi\)
\(332\) 1.33800e6 0.666209
\(333\) −138453. −0.0684213
\(334\) 1.87024e6 0.917344
\(335\) −1.48552e6 −0.723213
\(336\) 408633. 0.197463
\(337\) 2.79253e6 1.33944 0.669720 0.742613i \(-0.266414\pi\)
0.669720 + 0.742613i \(0.266414\pi\)
\(338\) 338504. 0.161165
\(339\) 1.84008e6 0.869634
\(340\) 69470.4 0.0325914
\(341\) 3.44154e6 1.60276
\(342\) −116964. −0.0540738
\(343\) 382767. 0.175671
\(344\) −1.54417e6 −0.703557
\(345\) −461546. −0.208770
\(346\) 2.07271e6 0.930782
\(347\) 551516. 0.245886 0.122943 0.992414i \(-0.460767\pi\)
0.122943 + 0.992414i \(0.460767\pi\)
\(348\) −864760. −0.382778
\(349\) −3.04968e6 −1.34027 −0.670133 0.742241i \(-0.733763\pi\)
−0.670133 + 0.742241i \(0.733763\pi\)
\(350\) 443395. 0.193473
\(351\) −390316. −0.169102
\(352\) 475959. 0.204745
\(353\) −2.24249e6 −0.957842 −0.478921 0.877858i \(-0.658972\pi\)
−0.478921 + 0.877858i \(0.658972\pi\)
\(354\) 604497. 0.256381
\(355\) 144823. 0.0609910
\(356\) 2.00541e6 0.838647
\(357\) 277225. 0.115123
\(358\) 2.96027e6 1.22074
\(359\) −3.29132e6 −1.34782 −0.673912 0.738811i \(-0.735387\pi\)
−0.673912 + 0.738811i \(0.735387\pi\)
\(360\) −129600. −0.0527046
\(361\) 130321. 0.0526316
\(362\) −3.18977e6 −1.27934
\(363\) −494920. −0.197137
\(364\) −1.51936e6 −0.601044
\(365\) −1.40755e6 −0.553006
\(366\) 1.83793e6 0.717176
\(367\) 280146. 0.108572 0.0542862 0.998525i \(-0.482712\pi\)
0.0542862 + 0.998525i \(0.482712\pi\)
\(368\) 525137. 0.202140
\(369\) −59287.4 −0.0226671
\(370\) 170929. 0.0649101
\(371\) 962756. 0.363146
\(372\) 1.06622e6 0.399475
\(373\) 2.44113e6 0.908488 0.454244 0.890877i \(-0.349909\pi\)
0.454244 + 0.890877i \(0.349909\pi\)
\(374\) 322901. 0.119369
\(375\) −140625. −0.0516398
\(376\) 1.46043e6 0.532736
\(377\) 3.21530e6 1.16511
\(378\) −517176. −0.186170
\(379\) 1.08801e6 0.389078 0.194539 0.980895i \(-0.437679\pi\)
0.194539 + 0.980895i \(0.437679\pi\)
\(380\) 144400. 0.0512989
\(381\) 2.97029e6 1.04830
\(382\) 2.71132e6 0.950654
\(383\) 351536. 0.122454 0.0612270 0.998124i \(-0.480499\pi\)
0.0612270 + 0.998124i \(0.480499\pi\)
\(384\) 147456. 0.0510310
\(385\) 2.06091e6 0.708611
\(386\) 2.39729e6 0.818942
\(387\) 1.95434e6 0.663320
\(388\) 315268. 0.106316
\(389\) 2.45203e6 0.821582 0.410791 0.911729i \(-0.365253\pi\)
0.410791 + 0.911729i \(0.365253\pi\)
\(390\) 481872. 0.160424
\(391\) 356265. 0.117850
\(392\) −937526. −0.308154
\(393\) 2.11088e6 0.689418
\(394\) 3.65387e6 1.18580
\(395\) 1.79831e6 0.579925
\(396\) −602385. −0.193035
\(397\) 3.67908e6 1.17156 0.585778 0.810472i \(-0.300789\pi\)
0.585778 + 0.810472i \(0.300789\pi\)
\(398\) 3.10895e6 0.983797
\(399\) 576236. 0.181204
\(400\) 160000. 0.0500000
\(401\) −4.33449e6 −1.34610 −0.673049 0.739598i \(-0.735016\pi\)
−0.673049 + 0.739598i \(0.735016\pi\)
\(402\) −2.13915e6 −0.660200
\(403\) −3.96436e6 −1.21594
\(404\) −1.13426e6 −0.345747
\(405\) 164025. 0.0496904
\(406\) 4.26033e6 1.28271
\(407\) 794485. 0.237739
\(408\) 100037. 0.0297517
\(409\) −1.34530e6 −0.397658 −0.198829 0.980034i \(-0.563714\pi\)
−0.198829 + 0.980034i \(0.563714\pi\)
\(410\) 73194.3 0.0215039
\(411\) 1.99451e6 0.582414
\(412\) −184311. −0.0534944
\(413\) −2.97812e6 −0.859146
\(414\) −664627. −0.190580
\(415\) 2.09062e6 0.595875
\(416\) −548263. −0.155330
\(417\) 768717. 0.216484
\(418\) 671176. 0.187887
\(419\) 3.05787e6 0.850911 0.425455 0.904979i \(-0.360114\pi\)
0.425455 + 0.904979i \(0.360114\pi\)
\(420\) 638489. 0.176616
\(421\) −3.38663e6 −0.931243 −0.465621 0.884984i \(-0.654169\pi\)
−0.465621 + 0.884984i \(0.654169\pi\)
\(422\) −1.75406e6 −0.479472
\(423\) −1.84836e6 −0.502268
\(424\) 347413. 0.0938492
\(425\) 108548. 0.0291506
\(426\) 208545. 0.0556769
\(427\) −9.05475e6 −2.40329
\(428\) −399737. −0.105479
\(429\) 2.23976e6 0.587567
\(430\) −2.41277e6 −0.629281
\(431\) 3.91738e6 1.01579 0.507893 0.861420i \(-0.330425\pi\)
0.507893 + 0.861420i \(0.330425\pi\)
\(432\) −186624. −0.0481125
\(433\) −724664. −0.185745 −0.0928724 0.995678i \(-0.529605\pi\)
−0.0928724 + 0.995678i \(0.529605\pi\)
\(434\) −5.25285e6 −1.33866
\(435\) −1.35119e6 −0.342367
\(436\) 1.35057e6 0.340252
\(437\) 740525. 0.185497
\(438\) −2.02687e6 −0.504823
\(439\) 524470. 0.129885 0.0649426 0.997889i \(-0.479314\pi\)
0.0649426 + 0.997889i \(0.479314\pi\)
\(440\) 743685. 0.183129
\(441\) 1.18656e6 0.290531
\(442\) −371954. −0.0905593
\(443\) −4.67976e6 −1.13296 −0.566480 0.824076i \(-0.691695\pi\)
−0.566480 + 0.824076i \(0.691695\pi\)
\(444\) 246138. 0.0592545
\(445\) 3.13346e6 0.750109
\(446\) −1.01473e6 −0.241552
\(447\) −4.10559e6 −0.971866
\(448\) −726458. −0.171008
\(449\) 5.36687e6 1.25634 0.628168 0.778078i \(-0.283805\pi\)
0.628168 + 0.778078i \(0.283805\pi\)
\(450\) −202500. −0.0471405
\(451\) 340209. 0.0787598
\(452\) −3.27125e6 −0.753126
\(453\) −78762.8 −0.0180333
\(454\) 1.74410e6 0.397129
\(455\) −2.37399e6 −0.537590
\(456\) 207936. 0.0468293
\(457\) 3.69159e6 0.826842 0.413421 0.910540i \(-0.364334\pi\)
0.413421 + 0.910540i \(0.364334\pi\)
\(458\) −4.02138e6 −0.895802
\(459\) −126610. −0.0280502
\(460\) 820527. 0.180800
\(461\) −4.24028e6 −0.929272 −0.464636 0.885502i \(-0.653815\pi\)
−0.464636 + 0.885502i \(0.653815\pi\)
\(462\) 2.96772e6 0.646871
\(463\) 2.98697e6 0.647557 0.323779 0.946133i \(-0.395047\pi\)
0.323779 + 0.946133i \(0.395047\pi\)
\(464\) 1.53735e6 0.331496
\(465\) 1.66597e6 0.357301
\(466\) −5.04341e6 −1.07587
\(467\) 3.91149e6 0.829947 0.414974 0.909833i \(-0.363791\pi\)
0.414974 + 0.909833i \(0.363791\pi\)
\(468\) 693895. 0.146447
\(469\) 1.05387e7 2.21236
\(470\) 2.28193e6 0.476494
\(471\) 774313. 0.160829
\(472\) −1.07466e6 −0.222032
\(473\) −1.12146e7 −2.30479
\(474\) 2.58957e6 0.529397
\(475\) 225625. 0.0458831
\(476\) −492845. −0.0996995
\(477\) −439694. −0.0884819
\(478\) 3.13293e6 0.627164
\(479\) −4.07717e6 −0.811933 −0.405966 0.913888i \(-0.633065\pi\)
−0.405966 + 0.913888i \(0.633065\pi\)
\(480\) 230400. 0.0456435
\(481\) −915178. −0.180361
\(482\) −2.73301e6 −0.535827
\(483\) 3.27436e6 0.638643
\(484\) 879857. 0.170726
\(485\) 492606. 0.0950923
\(486\) 236196. 0.0453609
\(487\) 4.37454e6 0.835815 0.417907 0.908490i \(-0.362764\pi\)
0.417907 + 0.908490i \(0.362764\pi\)
\(488\) −3.26743e6 −0.621092
\(489\) −2.53734e6 −0.479851
\(490\) −1.46488e6 −0.275621
\(491\) 8.45256e6 1.58228 0.791142 0.611632i \(-0.209487\pi\)
0.791142 + 0.611632i \(0.209487\pi\)
\(492\) 105400. 0.0196303
\(493\) 1.04297e6 0.193266
\(494\) −773136. −0.142541
\(495\) −941227. −0.172656
\(496\) −1.89550e6 −0.345955
\(497\) −1.02742e6 −0.186576
\(498\) 3.01049e6 0.543957
\(499\) 462733. 0.0831916 0.0415958 0.999135i \(-0.486756\pi\)
0.0415958 + 0.999135i \(0.486756\pi\)
\(500\) 250000. 0.0447214
\(501\) 4.20805e6 0.749008
\(502\) 636365. 0.112706
\(503\) −4.52443e6 −0.797341 −0.398671 0.917094i \(-0.630528\pi\)
−0.398671 + 0.917094i \(0.630528\pi\)
\(504\) 919424. 0.161228
\(505\) −1.77228e6 −0.309246
\(506\) 3.81383e6 0.662195
\(507\) 761633. 0.131591
\(508\) −5.28052e6 −0.907857
\(509\) −3.31915e6 −0.567848 −0.283924 0.958847i \(-0.591636\pi\)
−0.283924 + 0.958847i \(0.591636\pi\)
\(510\) 156308. 0.0266107
\(511\) 9.98557e6 1.69169
\(512\) −262144. −0.0441942
\(513\) −263169. −0.0441511
\(514\) 5.53708e6 0.924428
\(515\) −287986. −0.0478468
\(516\) −3.47439e6 −0.574452
\(517\) 1.06065e7 1.74520
\(518\) −1.21263e6 −0.198565
\(519\) 4.66360e6 0.759981
\(520\) −856661. −0.138931
\(521\) 1.17275e7 1.89282 0.946412 0.322962i \(-0.104679\pi\)
0.946412 + 0.322962i \(0.104679\pi\)
\(522\) −1.94571e6 −0.312537
\(523\) −1.06231e7 −1.69823 −0.849115 0.528208i \(-0.822864\pi\)
−0.849115 + 0.528208i \(0.822864\pi\)
\(524\) −3.75268e6 −0.597053
\(525\) 997638. 0.157970
\(526\) −2.15591e6 −0.339755
\(527\) −1.28595e6 −0.201696
\(528\) 1.07091e6 0.167173
\(529\) −2.22844e6 −0.346228
\(530\) 542832. 0.0839413
\(531\) 1.36012e6 0.209334
\(532\) −1.02442e6 −0.156927
\(533\) −391892. −0.0597514
\(534\) 4.51218e6 0.684752
\(535\) −624588. −0.0943429
\(536\) 3.80293e6 0.571750
\(537\) 6.66062e6 0.996733
\(538\) 1.21044e6 0.180296
\(539\) −6.80883e6 −1.00949
\(540\) −291600. −0.0430331
\(541\) 3.79848e6 0.557977 0.278989 0.960294i \(-0.410001\pi\)
0.278989 + 0.960294i \(0.410001\pi\)
\(542\) −3.22707e6 −0.471857
\(543\) −7.17698e6 −1.04458
\(544\) −177844. −0.0257657
\(545\) 2.11026e6 0.304330
\(546\) −3.41855e6 −0.490750
\(547\) 4.14052e6 0.591680 0.295840 0.955238i \(-0.404401\pi\)
0.295840 + 0.955238i \(0.404401\pi\)
\(548\) −3.54579e6 −0.504385
\(549\) 4.13534e6 0.585572
\(550\) 1.16201e6 0.163796
\(551\) 2.16790e6 0.304201
\(552\) 1.18156e6 0.165047
\(553\) −1.27578e7 −1.77404
\(554\) 6.08573e6 0.842439
\(555\) 384591. 0.0529989
\(556\) −1.36661e6 −0.187481
\(557\) −1.49034e6 −0.203539 −0.101769 0.994808i \(-0.532450\pi\)
−0.101769 + 0.994808i \(0.532450\pi\)
\(558\) 2.39899e6 0.326170
\(559\) 1.29183e7 1.74854
\(560\) −1.13509e6 −0.152954
\(561\) 726527. 0.0974640
\(562\) 8.69809e6 1.16167
\(563\) 206889. 0.0275085 0.0137542 0.999905i \(-0.495622\pi\)
0.0137542 + 0.999905i \(0.495622\pi\)
\(564\) 3.28597e6 0.434977
\(565\) −5.11132e6 −0.673616
\(566\) −4.86232e6 −0.637973
\(567\) −1.16365e6 −0.152007
\(568\) −370746. −0.0482176
\(569\) −882672. −0.114293 −0.0571464 0.998366i \(-0.518200\pi\)
−0.0571464 + 0.998366i \(0.518200\pi\)
\(570\) 324900. 0.0418854
\(571\) −7.73644e6 −0.993004 −0.496502 0.868036i \(-0.665382\pi\)
−0.496502 + 0.868036i \(0.665382\pi\)
\(572\) −3.98179e6 −0.508848
\(573\) 6.10047e6 0.776206
\(574\) −519263. −0.0657821
\(575\) 1.28207e6 0.161712
\(576\) 331776. 0.0416667
\(577\) −1.12065e7 −1.40130 −0.700651 0.713504i \(-0.747107\pi\)
−0.700651 + 0.713504i \(0.747107\pi\)
\(578\) 5.55877e6 0.692085
\(579\) 5.39391e6 0.668663
\(580\) 2.40211e6 0.296499
\(581\) −1.48315e7 −1.82283
\(582\) 709352. 0.0868070
\(583\) 2.52310e6 0.307442
\(584\) 3.60332e6 0.437190
\(585\) 1.08421e6 0.130986
\(586\) 2.59707e6 0.312421
\(587\) 3.40837e6 0.408274 0.204137 0.978942i \(-0.434561\pi\)
0.204137 + 0.978942i \(0.434561\pi\)
\(588\) −2.10943e6 −0.251607
\(589\) −2.67295e6 −0.317470
\(590\) −1.67916e6 −0.198592
\(591\) 8.22122e6 0.968205
\(592\) −437579. −0.0513159
\(593\) −9.87756e6 −1.15349 −0.576744 0.816925i \(-0.695677\pi\)
−0.576744 + 0.816925i \(0.695677\pi\)
\(594\) −1.35537e6 −0.157612
\(595\) −770070. −0.0891740
\(596\) 7.29882e6 0.841661
\(597\) 6.99513e6 0.803267
\(598\) −4.39321e6 −0.502376
\(599\) 2.77791e6 0.316338 0.158169 0.987412i \(-0.449441\pi\)
0.158169 + 0.987412i \(0.449441\pi\)
\(600\) 360000. 0.0408248
\(601\) −1.59740e7 −1.80396 −0.901982 0.431774i \(-0.857888\pi\)
−0.901982 + 0.431774i \(0.857888\pi\)
\(602\) 1.71169e7 1.92502
\(603\) −4.81308e6 −0.539051
\(604\) 140023. 0.0156173
\(605\) 1.37478e6 0.152702
\(606\) −2.55208e6 −0.282302
\(607\) 7.53030e6 0.829546 0.414773 0.909925i \(-0.363861\pi\)
0.414773 + 0.909925i \(0.363861\pi\)
\(608\) −369664. −0.0405554
\(609\) 9.58575e6 1.04733
\(610\) −5.10535e6 −0.555522
\(611\) −1.22177e7 −1.32400
\(612\) 225084. 0.0242922
\(613\) −1.49828e7 −1.61043 −0.805216 0.592982i \(-0.797951\pi\)
−0.805216 + 0.592982i \(0.797951\pi\)
\(614\) −8.96512e6 −0.959699
\(615\) 164687. 0.0175579
\(616\) −5.27594e6 −0.560206
\(617\) −436190. −0.0461278 −0.0230639 0.999734i \(-0.507342\pi\)
−0.0230639 + 0.999734i \(0.507342\pi\)
\(618\) −414700. −0.0436780
\(619\) −1.31886e7 −1.38348 −0.691738 0.722149i \(-0.743155\pi\)
−0.691738 + 0.722149i \(0.743155\pi\)
\(620\) −2.96172e6 −0.309432
\(621\) −1.49541e6 −0.155608
\(622\) 8.45328e6 0.876091
\(623\) −2.22298e7 −2.29464
\(624\) −1.23359e6 −0.126826
\(625\) 390625. 0.0400000
\(626\) 540025. 0.0550780
\(627\) 1.51015e6 0.153409
\(628\) −1.37656e6 −0.139282
\(629\) −296863. −0.0299178
\(630\) 1.43660e6 0.144206
\(631\) 3.98839e6 0.398772 0.199386 0.979921i \(-0.436105\pi\)
0.199386 + 0.979921i \(0.436105\pi\)
\(632\) −4.60367e6 −0.458471
\(633\) −3.94664e6 −0.391487
\(634\) 1.16611e7 1.15217
\(635\) −8.25081e6 −0.812012
\(636\) 781678. 0.0766276
\(637\) 7.84318e6 0.765850
\(638\) 1.11651e7 1.08595
\(639\) 469225. 0.0454600
\(640\) −409600. −0.0395285
\(641\) 1.58226e7 1.52101 0.760507 0.649330i \(-0.224951\pi\)
0.760507 + 0.649330i \(0.224951\pi\)
\(642\) −899407. −0.0861229
\(643\) 5.61190e6 0.535282 0.267641 0.963519i \(-0.413756\pi\)
0.267641 + 0.963519i \(0.413756\pi\)
\(644\) −5.82108e6 −0.553081
\(645\) −5.42873e6 −0.513806
\(646\) −250788. −0.0236443
\(647\) −1.53830e7 −1.44471 −0.722353 0.691525i \(-0.756939\pi\)
−0.722353 + 0.691525i \(0.756939\pi\)
\(648\) −419904. −0.0392837
\(649\) −7.80478e6 −0.727359
\(650\) −1.33853e6 −0.124264
\(651\) −1.18189e7 −1.09301
\(652\) 4.51083e6 0.415563
\(653\) 1.30815e6 0.120053 0.0600265 0.998197i \(-0.480881\pi\)
0.0600265 + 0.998197i \(0.480881\pi\)
\(654\) 3.03878e6 0.277814
\(655\) −5.86356e6 −0.534021
\(656\) −187377. −0.0170003
\(657\) −4.56045e6 −0.412187
\(658\) −1.61887e7 −1.45763
\(659\) 1.79181e7 1.60723 0.803615 0.595149i \(-0.202907\pi\)
0.803615 + 0.595149i \(0.202907\pi\)
\(660\) 1.67329e6 0.149524
\(661\) 1.24925e7 1.11210 0.556051 0.831148i \(-0.312316\pi\)
0.556051 + 0.831148i \(0.312316\pi\)
\(662\) 4.29126e6 0.380575
\(663\) −836895. −0.0739414
\(664\) −5.35199e6 −0.471081
\(665\) −1.60066e6 −0.140360
\(666\) 553811. 0.0483811
\(667\) 1.23187e7 1.07214
\(668\) −7.48098e6 −0.648660
\(669\) −2.28313e6 −0.197227
\(670\) 5.94207e6 0.511389
\(671\) −2.37298e7 −2.03465
\(672\) −1.63453e6 −0.139627
\(673\) 1.18467e7 1.00823 0.504116 0.863636i \(-0.331818\pi\)
0.504116 + 0.863636i \(0.331818\pi\)
\(674\) −1.11701e7 −0.947127
\(675\) −455625. −0.0384900
\(676\) −1.35401e6 −0.113961
\(677\) 5.95235e6 0.499134 0.249567 0.968358i \(-0.419712\pi\)
0.249567 + 0.968358i \(0.419712\pi\)
\(678\) −7.36031e6 −0.614924
\(679\) −3.49470e6 −0.290895
\(680\) −277882. −0.0230456
\(681\) 3.92423e6 0.324255
\(682\) −1.37662e7 −1.13332
\(683\) −9.89319e6 −0.811493 −0.405746 0.913986i \(-0.632988\pi\)
−0.405746 + 0.913986i \(0.632988\pi\)
\(684\) 467856. 0.0382360
\(685\) −5.54030e6 −0.451136
\(686\) −1.53107e6 −0.124218
\(687\) −9.04811e6 −0.731419
\(688\) 6.17669e6 0.497490
\(689\) −2.90639e6 −0.233242
\(690\) 1.84619e6 0.147622
\(691\) −1.31393e7 −1.04683 −0.523415 0.852078i \(-0.675342\pi\)
−0.523415 + 0.852078i \(0.675342\pi\)
\(692\) −8.29084e6 −0.658162
\(693\) 6.67736e6 0.528168
\(694\) −2.20606e6 −0.173868
\(695\) −2.13533e6 −0.167688
\(696\) 3.45904e6 0.270665
\(697\) −127121. −0.00991140
\(698\) 1.21987e7 0.947711
\(699\) −1.13477e7 −0.878444
\(700\) −1.77358e6 −0.136806
\(701\) 2.64964e6 0.203654 0.101827 0.994802i \(-0.467531\pi\)
0.101827 + 0.994802i \(0.467531\pi\)
\(702\) 1.56126e6 0.119573
\(703\) −617055. −0.0470907
\(704\) −1.90383e6 −0.144776
\(705\) 5.13434e6 0.389055
\(706\) 8.96996e6 0.677297
\(707\) 1.25731e7 0.946007
\(708\) −2.41799e6 −0.181289
\(709\) 2.06464e6 0.154251 0.0771257 0.997021i \(-0.475426\pi\)
0.0771257 + 0.997021i \(0.475426\pi\)
\(710\) −579290. −0.0431271
\(711\) 5.82652e6 0.432250
\(712\) −8.02166e6 −0.593013
\(713\) −1.51886e7 −1.11890
\(714\) −1.10890e6 −0.0814043
\(715\) −6.22154e6 −0.455127
\(716\) −1.18411e7 −0.863196
\(717\) 7.04909e6 0.512077
\(718\) 1.31653e7 0.953056
\(719\) −1.64668e7 −1.18792 −0.593960 0.804494i \(-0.702436\pi\)
−0.593960 + 0.804494i \(0.702436\pi\)
\(720\) 518400. 0.0372678
\(721\) 2.04306e6 0.146367
\(722\) −521284. −0.0372161
\(723\) −6.14928e6 −0.437501
\(724\) 1.27591e7 0.904633
\(725\) 3.75330e6 0.265197
\(726\) 1.97968e6 0.139397
\(727\) −1.12187e7 −0.787236 −0.393618 0.919274i \(-0.628777\pi\)
−0.393618 + 0.919274i \(0.628777\pi\)
\(728\) 6.07742e6 0.425002
\(729\) 531441. 0.0370370
\(730\) 5.63018e6 0.391035
\(731\) 4.19040e6 0.290043
\(732\) −7.35171e6 −0.507120
\(733\) −2.06322e7 −1.41836 −0.709180 0.705028i \(-0.750935\pi\)
−0.709180 + 0.705028i \(0.750935\pi\)
\(734\) −1.12058e6 −0.0767722
\(735\) −3.29599e6 −0.225044
\(736\) −2.10055e6 −0.142935
\(737\) 2.76190e7 1.87300
\(738\) 237149. 0.0160281
\(739\) 2.05403e7 1.38356 0.691778 0.722111i \(-0.256828\pi\)
0.691778 + 0.722111i \(0.256828\pi\)
\(740\) −683717. −0.0458984
\(741\) −1.73956e6 −0.116384
\(742\) −3.85102e6 −0.256783
\(743\) −1.03955e7 −0.690833 −0.345416 0.938449i \(-0.612262\pi\)
−0.345416 + 0.938449i \(0.612262\pi\)
\(744\) −4.26488e6 −0.282471
\(745\) 1.14044e7 0.752804
\(746\) −9.76453e6 −0.642398
\(747\) 6.77361e6 0.444139
\(748\) −1.29160e6 −0.0844063
\(749\) 4.43103e6 0.288602
\(750\) 562500. 0.0365148
\(751\) 6.76123e6 0.437447 0.218724 0.975787i \(-0.429811\pi\)
0.218724 + 0.975787i \(0.429811\pi\)
\(752\) −5.84173e6 −0.376701
\(753\) 1.43182e6 0.0920241
\(754\) −1.28612e7 −0.823860
\(755\) 218786. 0.0139685
\(756\) 2.06870e6 0.131642
\(757\) −1.29976e7 −0.824373 −0.412187 0.911099i \(-0.635235\pi\)
−0.412187 + 0.911099i \(0.635235\pi\)
\(758\) −4.35206e6 −0.275120
\(759\) 8.58113e6 0.540680
\(760\) −577600. −0.0362738
\(761\) −1.17498e7 −0.735479 −0.367739 0.929929i \(-0.619868\pi\)
−0.367739 + 0.929929i \(0.619868\pi\)
\(762\) −1.18812e7 −0.741262
\(763\) −1.49709e7 −0.930971
\(764\) −1.08453e7 −0.672214
\(765\) 351694. 0.0217276
\(766\) −1.40615e6 −0.0865881
\(767\) 8.99043e6 0.551813
\(768\) −589824. −0.0360844
\(769\) −2.24427e7 −1.36855 −0.684273 0.729226i \(-0.739880\pi\)
−0.684273 + 0.729226i \(0.739880\pi\)
\(770\) −8.24365e6 −0.501064
\(771\) 1.24584e7 0.754793
\(772\) −9.58918e6 −0.579079
\(773\) 1.07423e7 0.646620 0.323310 0.946293i \(-0.395204\pi\)
0.323310 + 0.946293i \(0.395204\pi\)
\(774\) −7.81737e6 −0.469038
\(775\) −4.62769e6 −0.276764
\(776\) −1.26107e6 −0.0751770
\(777\) −2.72841e6 −0.162128
\(778\) −9.80810e6 −0.580946
\(779\) −264231. −0.0156006
\(780\) −1.92749e6 −0.113437
\(781\) −2.69256e6 −0.157957
\(782\) −1.42506e6 −0.0833327
\(783\) −4.37785e6 −0.255186
\(784\) 3.75010e6 0.217898
\(785\) −2.15087e6 −0.124578
\(786\) −8.44353e6 −0.487492
\(787\) −1.26423e7 −0.727593 −0.363797 0.931478i \(-0.618520\pi\)
−0.363797 + 0.931478i \(0.618520\pi\)
\(788\) −1.46155e7 −0.838490
\(789\) −4.85079e6 −0.277408
\(790\) −7.19324e6 −0.410069
\(791\) 3.62614e7 2.06064
\(792\) 2.40954e6 0.136496
\(793\) 2.73347e7 1.54359
\(794\) −1.47163e7 −0.828415
\(795\) 1.22137e6 0.0685378
\(796\) −1.24358e7 −0.695650
\(797\) 1.20769e7 0.673456 0.336728 0.941602i \(-0.390680\pi\)
0.336728 + 0.941602i \(0.390680\pi\)
\(798\) −2.30494e6 −0.128131
\(799\) −3.96316e6 −0.219621
\(800\) −640000. −0.0353553
\(801\) 1.01524e7 0.559098
\(802\) 1.73379e7 0.951835
\(803\) 2.61693e7 1.43220
\(804\) 8.55659e6 0.466832
\(805\) −9.09543e6 −0.494691
\(806\) 1.58574e7 0.859796
\(807\) 2.72348e6 0.147211
\(808\) 4.53704e6 0.244480
\(809\) −1.74362e7 −0.936657 −0.468329 0.883554i \(-0.655144\pi\)
−0.468329 + 0.883554i \(0.655144\pi\)
\(810\) −656100. −0.0351364
\(811\) 1.82230e7 0.972897 0.486448 0.873709i \(-0.338292\pi\)
0.486448 + 0.873709i \(0.338292\pi\)
\(812\) −1.70413e7 −0.907013
\(813\) −7.26091e6 −0.385270
\(814\) −3.17794e6 −0.168107
\(815\) 7.04817e6 0.371691
\(816\) −400150. −0.0210376
\(817\) 8.71009e6 0.456528
\(818\) 5.38119e6 0.281187
\(819\) −7.69174e6 −0.400696
\(820\) −292777. −0.0152056
\(821\) 3.45896e7 1.79097 0.895484 0.445093i \(-0.146829\pi\)
0.895484 + 0.445093i \(0.146829\pi\)
\(822\) −7.97804e6 −0.411829
\(823\) 1.24813e7 0.642333 0.321166 0.947023i \(-0.395925\pi\)
0.321166 + 0.947023i \(0.395925\pi\)
\(824\) 737244. 0.0378263
\(825\) 2.61452e6 0.133739
\(826\) 1.19125e7 0.607508
\(827\) 1.56510e7 0.795752 0.397876 0.917439i \(-0.369747\pi\)
0.397876 + 0.917439i \(0.369747\pi\)
\(828\) 2.65851e6 0.134760
\(829\) 2.15080e7 1.08696 0.543479 0.839423i \(-0.317107\pi\)
0.543479 + 0.839423i \(0.317107\pi\)
\(830\) −8.36249e6 −0.421347
\(831\) 1.36929e7 0.687849
\(832\) 2.19305e6 0.109835
\(833\) 2.54415e6 0.127037
\(834\) −3.07487e6 −0.153078
\(835\) −1.16890e7 −0.580179
\(836\) −2.68470e6 −0.132856
\(837\) 5.39774e6 0.266317
\(838\) −1.22315e7 −0.601685
\(839\) 1.95321e7 0.957950 0.478975 0.877828i \(-0.341008\pi\)
0.478975 + 0.877828i \(0.341008\pi\)
\(840\) −2.55395e6 −0.124886
\(841\) 1.55522e7 0.758231
\(842\) 1.35465e7 0.658488
\(843\) 1.95707e7 0.948500
\(844\) 7.01624e6 0.339038
\(845\) −2.11565e6 −0.101930
\(846\) 7.39344e6 0.355157
\(847\) −9.75310e6 −0.467126
\(848\) −1.38965e6 −0.0663614
\(849\) −1.09402e7 −0.520903
\(850\) −434190. −0.0206126
\(851\) −3.50630e6 −0.165968
\(852\) −834178. −0.0393695
\(853\) −9.33840e6 −0.439440 −0.219720 0.975563i \(-0.570514\pi\)
−0.219720 + 0.975563i \(0.570514\pi\)
\(854\) 3.62190e7 1.69938
\(855\) 731025. 0.0341993
\(856\) 1.59895e6 0.0745846
\(857\) 2.01622e7 0.937749 0.468875 0.883265i \(-0.344660\pi\)
0.468875 + 0.883265i \(0.344660\pi\)
\(858\) −8.95902e6 −0.415473
\(859\) −3.58234e7 −1.65647 −0.828237 0.560379i \(-0.810656\pi\)
−0.828237 + 0.560379i \(0.810656\pi\)
\(860\) 9.65107e6 0.444969
\(861\) −1.16834e6 −0.0537109
\(862\) −1.56695e7 −0.718269
\(863\) −3.67297e7 −1.67877 −0.839383 0.543541i \(-0.817083\pi\)
−0.839383 + 0.543541i \(0.817083\pi\)
\(864\) 746496. 0.0340207
\(865\) −1.29544e7 −0.588678
\(866\) 2.89866e6 0.131341
\(867\) 1.25072e7 0.565085
\(868\) 2.10114e7 0.946576
\(869\) −3.34344e7 −1.50191
\(870\) 5.40475e6 0.242090
\(871\) −3.18146e7 −1.42096
\(872\) −5.40227e6 −0.240594
\(873\) 1.59604e6 0.0708776
\(874\) −2.96210e6 −0.131166
\(875\) −2.77122e6 −0.122363
\(876\) 8.10746e6 0.356964
\(877\) 5.68096e6 0.249415 0.124708 0.992194i \(-0.460201\pi\)
0.124708 + 0.992194i \(0.460201\pi\)
\(878\) −2.09788e6 −0.0918427
\(879\) 5.84342e6 0.255091
\(880\) −2.97474e6 −0.129492
\(881\) −3.73234e7 −1.62010 −0.810050 0.586361i \(-0.800560\pi\)
−0.810050 + 0.586361i \(0.800560\pi\)
\(882\) −4.74622e6 −0.205436
\(883\) 2.77655e7 1.19840 0.599202 0.800598i \(-0.295485\pi\)
0.599202 + 0.800598i \(0.295485\pi\)
\(884\) 1.48781e6 0.0640351
\(885\) −3.77810e6 −0.162150
\(886\) 1.87190e7 0.801123
\(887\) 1.11088e7 0.474085 0.237043 0.971499i \(-0.423822\pi\)
0.237043 + 0.971499i \(0.423822\pi\)
\(888\) −984553. −0.0418993
\(889\) 5.85339e7 2.48401
\(890\) −1.25338e7 −0.530407
\(891\) −3.04957e6 −0.128690
\(892\) 4.05890e6 0.170803
\(893\) −8.23776e6 −0.345685
\(894\) 1.64223e7 0.687213
\(895\) −1.85017e7 −0.772066
\(896\) 2.90583e6 0.120921
\(897\) −9.88471e6 −0.410188
\(898\) −2.14675e7 −0.888363
\(899\) −4.44649e7 −1.83492
\(900\) 810000. 0.0333333
\(901\) −942769. −0.0386895
\(902\) −1.36084e6 −0.0556916
\(903\) 3.85131e7 1.57177
\(904\) 1.30850e7 0.532540
\(905\) 1.99360e7 0.809129
\(906\) 315051. 0.0127515
\(907\) −798853. −0.0322440 −0.0161220 0.999870i \(-0.505132\pi\)
−0.0161220 + 0.999870i \(0.505132\pi\)
\(908\) −6.97640e6 −0.280813
\(909\) −5.74219e6 −0.230498
\(910\) 9.49597e6 0.380133
\(911\) −1.70870e7 −0.682133 −0.341066 0.940039i \(-0.610788\pi\)
−0.341066 + 0.940039i \(0.610788\pi\)
\(912\) −831744. −0.0331133
\(913\) −3.88691e7 −1.54322
\(914\) −1.47663e7 −0.584666
\(915\) −1.14870e7 −0.453582
\(916\) 1.60855e7 0.633427
\(917\) 4.15980e7 1.63361
\(918\) 506439. 0.0198345
\(919\) 9.93460e6 0.388027 0.194013 0.980999i \(-0.437850\pi\)
0.194013 + 0.980999i \(0.437850\pi\)
\(920\) −3.28211e6 −0.127845
\(921\) −2.01715e7 −0.783591
\(922\) 1.69611e7 0.657094
\(923\) 3.10160e6 0.119834
\(924\) −1.18709e7 −0.457407
\(925\) −1.06831e6 −0.0410528
\(926\) −1.19479e7 −0.457892
\(927\) −933075. −0.0356629
\(928\) −6.14940e6 −0.234403
\(929\) 1.68971e7 0.642353 0.321177 0.947019i \(-0.395922\pi\)
0.321177 + 0.947019i \(0.395922\pi\)
\(930\) −6.66387e6 −0.252650
\(931\) 5.28823e6 0.199957
\(932\) 2.01737e7 0.760755
\(933\) 1.90199e7 0.715325
\(934\) −1.56460e7 −0.586861
\(935\) −2.01813e6 −0.0754953
\(936\) −2.77558e6 −0.103553
\(937\) 1.89292e7 0.704342 0.352171 0.935936i \(-0.385444\pi\)
0.352171 + 0.935936i \(0.385444\pi\)
\(938\) −4.21550e7 −1.56438
\(939\) 1.21506e6 0.0449710
\(940\) −9.12771e6 −0.336932
\(941\) −8.72232e6 −0.321113 −0.160557 0.987027i \(-0.551329\pi\)
−0.160557 + 0.987027i \(0.551329\pi\)
\(942\) −3.09725e6 −0.113723
\(943\) −1.50145e6 −0.0549833
\(944\) 4.29864e6 0.157001
\(945\) 3.23235e6 0.117744
\(946\) 4.48585e7 1.62973
\(947\) −1.03850e7 −0.376298 −0.188149 0.982141i \(-0.560249\pi\)
−0.188149 + 0.982141i \(0.560249\pi\)
\(948\) −1.03583e7 −0.374340
\(949\) −3.01447e7 −1.08654
\(950\) −902500. −0.0324443
\(951\) 2.62374e7 0.940739
\(952\) 1.97138e6 0.0704982
\(953\) 3.97021e7 1.41606 0.708029 0.706183i \(-0.249585\pi\)
0.708029 + 0.706183i \(0.249585\pi\)
\(954\) 1.75878e6 0.0625662
\(955\) −1.69457e7 −0.601246
\(956\) −1.25317e7 −0.443472
\(957\) 2.51214e7 0.886676
\(958\) 1.63087e7 0.574123
\(959\) 3.93047e7 1.38006
\(960\) −921600. −0.0322749
\(961\) 2.61946e7 0.914962
\(962\) 3.66071e6 0.127535
\(963\) −2.02367e6 −0.0703191
\(964\) 1.09321e7 0.378887
\(965\) −1.49831e7 −0.517944
\(966\) −1.30974e7 −0.451589
\(967\) −3.61663e7 −1.24376 −0.621882 0.783111i \(-0.713631\pi\)
−0.621882 + 0.783111i \(0.713631\pi\)
\(968\) −3.51943e6 −0.120721
\(969\) −564273. −0.0193055
\(970\) −1.97042e6 −0.0672404
\(971\) 4.93115e7 1.67842 0.839209 0.543809i \(-0.183018\pi\)
0.839209 + 0.543809i \(0.183018\pi\)
\(972\) −944784. −0.0320750
\(973\) 1.51487e7 0.512971
\(974\) −1.74982e7 −0.591010
\(975\) −3.01170e6 −0.101461
\(976\) 1.30697e7 0.439179
\(977\) −2.54182e7 −0.851939 −0.425970 0.904737i \(-0.640067\pi\)
−0.425970 + 0.904737i \(0.640067\pi\)
\(978\) 1.01494e7 0.339306
\(979\) −5.82577e7 −1.94266
\(980\) 5.85954e6 0.194894
\(981\) 6.83725e6 0.226835
\(982\) −3.38103e7 −1.11884
\(983\) −3.29336e7 −1.08706 −0.543532 0.839388i \(-0.682913\pi\)
−0.543532 + 0.839388i \(0.682913\pi\)
\(984\) −421599. −0.0138807
\(985\) −2.28367e7 −0.749969
\(986\) −4.17189e6 −0.136660
\(987\) −3.64246e7 −1.19015
\(988\) 3.09255e6 0.100791
\(989\) 4.94935e7 1.60901
\(990\) 3.76491e6 0.122086
\(991\) −3.13422e7 −1.01378 −0.506892 0.862010i \(-0.669206\pi\)
−0.506892 + 0.862010i \(0.669206\pi\)
\(992\) 7.58201e6 0.244627
\(993\) 9.65534e6 0.310738
\(994\) 4.10967e6 0.131929
\(995\) −1.94309e7 −0.622208
\(996\) −1.20420e7 −0.384636
\(997\) −1.23943e7 −0.394897 −0.197448 0.980313i \(-0.563266\pi\)
−0.197448 + 0.980313i \(0.563266\pi\)
\(998\) −1.85093e6 −0.0588253
\(999\) 1.24607e6 0.0395030
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.j.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.j.1.1 4 1.1 even 1 trivial