Properties

Label 280.6.a.e.1.2
Level $280$
Weight $6$
Character 280.1
Self dual yes
Analytic conductor $44.907$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(44.9074695476\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 463 x - 1890\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-4.24759\) of defining polynomial
Character \(\chi\) \(=\) 280.1

$q$-expansion

\(f(q)\) \(=\) \(q+6.24759 q^{3} -25.0000 q^{5} +49.0000 q^{7} -203.968 q^{9} +O(q^{10})\) \(q+6.24759 q^{3} -25.0000 q^{5} +49.0000 q^{7} -203.968 q^{9} +89.4628 q^{11} +459.250 q^{13} -156.190 q^{15} +701.108 q^{17} -396.470 q^{19} +306.132 q^{21} -4316.18 q^{23} +625.000 q^{25} -2792.47 q^{27} -1437.19 q^{29} +3669.99 q^{31} +558.927 q^{33} -1225.00 q^{35} -3166.84 q^{37} +2869.21 q^{39} -6353.05 q^{41} -15510.1 q^{43} +5099.19 q^{45} -3995.07 q^{47} +2401.00 q^{49} +4380.24 q^{51} -24472.8 q^{53} -2236.57 q^{55} -2476.98 q^{57} -2395.32 q^{59} -21052.6 q^{61} -9994.41 q^{63} -11481.3 q^{65} +853.274 q^{67} -26965.7 q^{69} -1378.74 q^{71} +12248.5 q^{73} +3904.75 q^{75} +4383.68 q^{77} -51047.4 q^{79} +32117.9 q^{81} +17615.6 q^{83} -17527.7 q^{85} -8978.99 q^{87} -18346.0 q^{89} +22503.3 q^{91} +22928.6 q^{93} +9911.74 q^{95} -103460. q^{97} -18247.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 6 q^{3} - 75 q^{5} + 147 q^{7} + 209 q^{9} + O(q^{10}) \) \( 3 q + 6 q^{3} - 75 q^{5} + 147 q^{7} + 209 q^{9} - 578 q^{11} + 80 q^{13} - 150 q^{15} - 1244 q^{17} + 944 q^{19} + 294 q^{21} + 1096 q^{23} + 1875 q^{25} - 3006 q^{27} + 1868 q^{29} - 6620 q^{31} + 2662 q^{33} - 3675 q^{35} - 4058 q^{37} - 20910 q^{39} - 9602 q^{41} - 12340 q^{43} - 5225 q^{45} - 41026 q^{47} + 7203 q^{49} + 10006 q^{51} - 37610 q^{53} + 14450 q^{55} - 95456 q^{57} - 37664 q^{59} - 8386 q^{61} + 10241 q^{63} - 2000 q^{65} + 69340 q^{67} - 37712 q^{69} - 34016 q^{71} - 45314 q^{73} + 3750 q^{75} - 28322 q^{77} + 1382 q^{79} - 101005 q^{81} - 10128 q^{83} + 31100 q^{85} - 41510 q^{87} - 222810 q^{89} + 3920 q^{91} - 174292 q^{93} - 23600 q^{95} - 159476 q^{97} - 156568 q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 6.24759 0.400783 0.200392 0.979716i \(-0.435779\pi\)
0.200392 + 0.979716i \(0.435779\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) −203.968 −0.839373
\(10\) 0 0
\(11\) 89.4628 0.222926 0.111463 0.993769i \(-0.464446\pi\)
0.111463 + 0.993769i \(0.464446\pi\)
\(12\) 0 0
\(13\) 459.250 0.753687 0.376843 0.926277i \(-0.377009\pi\)
0.376843 + 0.926277i \(0.377009\pi\)
\(14\) 0 0
\(15\) −156.190 −0.179236
\(16\) 0 0
\(17\) 701.108 0.588387 0.294193 0.955746i \(-0.404949\pi\)
0.294193 + 0.955746i \(0.404949\pi\)
\(18\) 0 0
\(19\) −396.470 −0.251957 −0.125978 0.992033i \(-0.540207\pi\)
−0.125978 + 0.992033i \(0.540207\pi\)
\(20\) 0 0
\(21\) 306.132 0.151482
\(22\) 0 0
\(23\) −4316.18 −1.70130 −0.850649 0.525735i \(-0.823790\pi\)
−0.850649 + 0.525735i \(0.823790\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) −2792.47 −0.737190
\(28\) 0 0
\(29\) −1437.19 −0.317336 −0.158668 0.987332i \(-0.550720\pi\)
−0.158668 + 0.987332i \(0.550720\pi\)
\(30\) 0 0
\(31\) 3669.99 0.685899 0.342950 0.939354i \(-0.388574\pi\)
0.342950 + 0.939354i \(0.388574\pi\)
\(32\) 0 0
\(33\) 558.927 0.0893450
\(34\) 0 0
\(35\) −1225.00 −0.169031
\(36\) 0 0
\(37\) −3166.84 −0.380295 −0.190148 0.981755i \(-0.560897\pi\)
−0.190148 + 0.981755i \(0.560897\pi\)
\(38\) 0 0
\(39\) 2869.21 0.302065
\(40\) 0 0
\(41\) −6353.05 −0.590232 −0.295116 0.955461i \(-0.595358\pi\)
−0.295116 + 0.955461i \(0.595358\pi\)
\(42\) 0 0
\(43\) −15510.1 −1.27921 −0.639606 0.768703i \(-0.720902\pi\)
−0.639606 + 0.768703i \(0.720902\pi\)
\(44\) 0 0
\(45\) 5099.19 0.375379
\(46\) 0 0
\(47\) −3995.07 −0.263803 −0.131902 0.991263i \(-0.542108\pi\)
−0.131902 + 0.991263i \(0.542108\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 4380.24 0.235816
\(52\) 0 0
\(53\) −24472.8 −1.19673 −0.598363 0.801225i \(-0.704182\pi\)
−0.598363 + 0.801225i \(0.704182\pi\)
\(54\) 0 0
\(55\) −2236.57 −0.0996955
\(56\) 0 0
\(57\) −2476.98 −0.100980
\(58\) 0 0
\(59\) −2395.32 −0.0895848 −0.0447924 0.998996i \(-0.514263\pi\)
−0.0447924 + 0.998996i \(0.514263\pi\)
\(60\) 0 0
\(61\) −21052.6 −0.724404 −0.362202 0.932100i \(-0.617975\pi\)
−0.362202 + 0.932100i \(0.617975\pi\)
\(62\) 0 0
\(63\) −9994.41 −0.317253
\(64\) 0 0
\(65\) −11481.3 −0.337059
\(66\) 0 0
\(67\) 853.274 0.0232221 0.0116111 0.999933i \(-0.496304\pi\)
0.0116111 + 0.999933i \(0.496304\pi\)
\(68\) 0 0
\(69\) −26965.7 −0.681851
\(70\) 0 0
\(71\) −1378.74 −0.0324591 −0.0162295 0.999868i \(-0.505166\pi\)
−0.0162295 + 0.999868i \(0.505166\pi\)
\(72\) 0 0
\(73\) 12248.5 0.269014 0.134507 0.990913i \(-0.457055\pi\)
0.134507 + 0.990913i \(0.457055\pi\)
\(74\) 0 0
\(75\) 3904.75 0.0801566
\(76\) 0 0
\(77\) 4383.68 0.0842581
\(78\) 0 0
\(79\) −51047.4 −0.920250 −0.460125 0.887854i \(-0.652195\pi\)
−0.460125 + 0.887854i \(0.652195\pi\)
\(80\) 0 0
\(81\) 32117.9 0.543919
\(82\) 0 0
\(83\) 17615.6 0.280674 0.140337 0.990104i \(-0.455181\pi\)
0.140337 + 0.990104i \(0.455181\pi\)
\(84\) 0 0
\(85\) −17527.7 −0.263135
\(86\) 0 0
\(87\) −8978.99 −0.127183
\(88\) 0 0
\(89\) −18346.0 −0.245508 −0.122754 0.992437i \(-0.539173\pi\)
−0.122754 + 0.992437i \(0.539173\pi\)
\(90\) 0 0
\(91\) 22503.3 0.284867
\(92\) 0 0
\(93\) 22928.6 0.274897
\(94\) 0 0
\(95\) 9911.74 0.112678
\(96\) 0 0
\(97\) −103460. −1.11646 −0.558231 0.829686i \(-0.688520\pi\)
−0.558231 + 0.829686i \(0.688520\pi\)
\(98\) 0 0
\(99\) −18247.5 −0.187118
\(100\) 0 0
\(101\) −155074. −1.51264 −0.756320 0.654202i \(-0.773005\pi\)
−0.756320 + 0.654202i \(0.773005\pi\)
\(102\) 0 0
\(103\) −36262.5 −0.336794 −0.168397 0.985719i \(-0.553859\pi\)
−0.168397 + 0.985719i \(0.553859\pi\)
\(104\) 0 0
\(105\) −7653.30 −0.0677447
\(106\) 0 0
\(107\) −116698. −0.985378 −0.492689 0.870205i \(-0.663986\pi\)
−0.492689 + 0.870205i \(0.663986\pi\)
\(108\) 0 0
\(109\) 6940.27 0.0559513 0.0279756 0.999609i \(-0.491094\pi\)
0.0279756 + 0.999609i \(0.491094\pi\)
\(110\) 0 0
\(111\) −19785.1 −0.152416
\(112\) 0 0
\(113\) −244790. −1.80342 −0.901711 0.432339i \(-0.857688\pi\)
−0.901711 + 0.432339i \(0.857688\pi\)
\(114\) 0 0
\(115\) 107905. 0.760843
\(116\) 0 0
\(117\) −93672.2 −0.632624
\(118\) 0 0
\(119\) 34354.3 0.222389
\(120\) 0 0
\(121\) −153047. −0.950304
\(122\) 0 0
\(123\) −39691.3 −0.236555
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 173950. 0.957008 0.478504 0.878085i \(-0.341179\pi\)
0.478504 + 0.878085i \(0.341179\pi\)
\(128\) 0 0
\(129\) −96900.6 −0.512687
\(130\) 0 0
\(131\) −133105. −0.677667 −0.338833 0.940846i \(-0.610032\pi\)
−0.338833 + 0.940846i \(0.610032\pi\)
\(132\) 0 0
\(133\) −19427.0 −0.0952307
\(134\) 0 0
\(135\) 69811.8 0.329681
\(136\) 0 0
\(137\) 154448. 0.703039 0.351520 0.936180i \(-0.385665\pi\)
0.351520 + 0.936180i \(0.385665\pi\)
\(138\) 0 0
\(139\) 219692. 0.964443 0.482221 0.876049i \(-0.339830\pi\)
0.482221 + 0.876049i \(0.339830\pi\)
\(140\) 0 0
\(141\) −24959.6 −0.105728
\(142\) 0 0
\(143\) 41085.8 0.168016
\(144\) 0 0
\(145\) 35929.8 0.141917
\(146\) 0 0
\(147\) 15000.5 0.0572547
\(148\) 0 0
\(149\) 259928. 0.959152 0.479576 0.877500i \(-0.340790\pi\)
0.479576 + 0.877500i \(0.340790\pi\)
\(150\) 0 0
\(151\) 125854. 0.449186 0.224593 0.974453i \(-0.427895\pi\)
0.224593 + 0.974453i \(0.427895\pi\)
\(152\) 0 0
\(153\) −143003. −0.493876
\(154\) 0 0
\(155\) −91749.7 −0.306743
\(156\) 0 0
\(157\) −19697.3 −0.0637760 −0.0318880 0.999491i \(-0.510152\pi\)
−0.0318880 + 0.999491i \(0.510152\pi\)
\(158\) 0 0
\(159\) −152896. −0.479628
\(160\) 0 0
\(161\) −211493. −0.643030
\(162\) 0 0
\(163\) 490838. 1.44700 0.723501 0.690324i \(-0.242532\pi\)
0.723501 + 0.690324i \(0.242532\pi\)
\(164\) 0 0
\(165\) −13973.2 −0.0399563
\(166\) 0 0
\(167\) 593431. 1.64657 0.823283 0.567632i \(-0.192140\pi\)
0.823283 + 0.567632i \(0.192140\pi\)
\(168\) 0 0
\(169\) −160382. −0.431956
\(170\) 0 0
\(171\) 80866.9 0.211486
\(172\) 0 0
\(173\) 75225.1 0.191094 0.0955472 0.995425i \(-0.469540\pi\)
0.0955472 + 0.995425i \(0.469540\pi\)
\(174\) 0 0
\(175\) 30625.0 0.0755929
\(176\) 0 0
\(177\) −14965.0 −0.0359041
\(178\) 0 0
\(179\) 210903. 0.491984 0.245992 0.969272i \(-0.420886\pi\)
0.245992 + 0.969272i \(0.420886\pi\)
\(180\) 0 0
\(181\) 347613. 0.788677 0.394339 0.918965i \(-0.370974\pi\)
0.394339 + 0.918965i \(0.370974\pi\)
\(182\) 0 0
\(183\) −131528. −0.290329
\(184\) 0 0
\(185\) 79170.9 0.170073
\(186\) 0 0
\(187\) 62723.1 0.131167
\(188\) 0 0
\(189\) −136831. −0.278632
\(190\) 0 0
\(191\) 181647. 0.360284 0.180142 0.983641i \(-0.442344\pi\)
0.180142 + 0.983641i \(0.442344\pi\)
\(192\) 0 0
\(193\) −468479. −0.905309 −0.452655 0.891686i \(-0.649523\pi\)
−0.452655 + 0.891686i \(0.649523\pi\)
\(194\) 0 0
\(195\) −71730.2 −0.135088
\(196\) 0 0
\(197\) 301806. 0.554066 0.277033 0.960860i \(-0.410649\pi\)
0.277033 + 0.960860i \(0.410649\pi\)
\(198\) 0 0
\(199\) −34553.3 −0.0618525 −0.0309262 0.999522i \(-0.509846\pi\)
−0.0309262 + 0.999522i \(0.509846\pi\)
\(200\) 0 0
\(201\) 5330.91 0.00930703
\(202\) 0 0
\(203\) −70422.4 −0.119942
\(204\) 0 0
\(205\) 158826. 0.263960
\(206\) 0 0
\(207\) 880361. 1.42802
\(208\) 0 0
\(209\) −35469.3 −0.0561677
\(210\) 0 0
\(211\) 538344. 0.832442 0.416221 0.909263i \(-0.363354\pi\)
0.416221 + 0.909263i \(0.363354\pi\)
\(212\) 0 0
\(213\) −8613.79 −0.0130090
\(214\) 0 0
\(215\) 387752. 0.572081
\(216\) 0 0
\(217\) 179829. 0.259245
\(218\) 0 0
\(219\) 76523.5 0.107816
\(220\) 0 0
\(221\) 321984. 0.443459
\(222\) 0 0
\(223\) 243135. 0.327404 0.163702 0.986510i \(-0.447656\pi\)
0.163702 + 0.986510i \(0.447656\pi\)
\(224\) 0 0
\(225\) −127480. −0.167875
\(226\) 0 0
\(227\) 341415. 0.439762 0.219881 0.975527i \(-0.429433\pi\)
0.219881 + 0.975527i \(0.429433\pi\)
\(228\) 0 0
\(229\) −113641. −0.143201 −0.0716004 0.997433i \(-0.522811\pi\)
−0.0716004 + 0.997433i \(0.522811\pi\)
\(230\) 0 0
\(231\) 27387.4 0.0337692
\(232\) 0 0
\(233\) −1.10838e6 −1.33751 −0.668756 0.743482i \(-0.733173\pi\)
−0.668756 + 0.743482i \(0.733173\pi\)
\(234\) 0 0
\(235\) 99876.9 0.117976
\(236\) 0 0
\(237\) −318923. −0.368821
\(238\) 0 0
\(239\) 274846. 0.311240 0.155620 0.987817i \(-0.450263\pi\)
0.155620 + 0.987817i \(0.450263\pi\)
\(240\) 0 0
\(241\) 1.32322e6 1.46754 0.733770 0.679397i \(-0.237759\pi\)
0.733770 + 0.679397i \(0.237759\pi\)
\(242\) 0 0
\(243\) 879230. 0.955184
\(244\) 0 0
\(245\) −60025.0 −0.0638877
\(246\) 0 0
\(247\) −182079. −0.189896
\(248\) 0 0
\(249\) 110055. 0.112489
\(250\) 0 0
\(251\) −1.56166e6 −1.56460 −0.782298 0.622905i \(-0.785953\pi\)
−0.782298 + 0.622905i \(0.785953\pi\)
\(252\) 0 0
\(253\) −386138. −0.379263
\(254\) 0 0
\(255\) −109506. −0.105460
\(256\) 0 0
\(257\) 1.19597e6 1.12950 0.564750 0.825262i \(-0.308972\pi\)
0.564750 + 0.825262i \(0.308972\pi\)
\(258\) 0 0
\(259\) −155175. −0.143738
\(260\) 0 0
\(261\) 293140. 0.266363
\(262\) 0 0
\(263\) 1.54763e6 1.37968 0.689839 0.723962i \(-0.257681\pi\)
0.689839 + 0.723962i \(0.257681\pi\)
\(264\) 0 0
\(265\) 611821. 0.535192
\(266\) 0 0
\(267\) −114618. −0.0983956
\(268\) 0 0
\(269\) −1.04788e6 −0.882941 −0.441470 0.897276i \(-0.645543\pi\)
−0.441470 + 0.897276i \(0.645543\pi\)
\(270\) 0 0
\(271\) 842735. 0.697056 0.348528 0.937298i \(-0.386682\pi\)
0.348528 + 0.937298i \(0.386682\pi\)
\(272\) 0 0
\(273\) 140591. 0.114170
\(274\) 0 0
\(275\) 55914.2 0.0445852
\(276\) 0 0
\(277\) 660555. 0.517261 0.258630 0.965976i \(-0.416729\pi\)
0.258630 + 0.965976i \(0.416729\pi\)
\(278\) 0 0
\(279\) −748558. −0.575725
\(280\) 0 0
\(281\) −1.46200e6 −1.10454 −0.552272 0.833664i \(-0.686239\pi\)
−0.552272 + 0.833664i \(0.686239\pi\)
\(282\) 0 0
\(283\) −1.68634e6 −1.25164 −0.625819 0.779968i \(-0.715235\pi\)
−0.625819 + 0.779968i \(0.715235\pi\)
\(284\) 0 0
\(285\) 61924.5 0.0451596
\(286\) 0 0
\(287\) −311299. −0.223087
\(288\) 0 0
\(289\) −928304. −0.653801
\(290\) 0 0
\(291\) −646377. −0.447459
\(292\) 0 0
\(293\) 1.03667e6 0.705458 0.352729 0.935725i \(-0.385254\pi\)
0.352729 + 0.935725i \(0.385254\pi\)
\(294\) 0 0
\(295\) 59883.1 0.0400635
\(296\) 0 0
\(297\) −249822. −0.164339
\(298\) 0 0
\(299\) −1.98221e6 −1.28225
\(300\) 0 0
\(301\) −759993. −0.483497
\(302\) 0 0
\(303\) −968839. −0.606241
\(304\) 0 0
\(305\) 526315. 0.323963
\(306\) 0 0
\(307\) 1.33764e6 0.810013 0.405006 0.914314i \(-0.367269\pi\)
0.405006 + 0.914314i \(0.367269\pi\)
\(308\) 0 0
\(309\) −226553. −0.134981
\(310\) 0 0
\(311\) 443660. 0.260105 0.130053 0.991507i \(-0.458485\pi\)
0.130053 + 0.991507i \(0.458485\pi\)
\(312\) 0 0
\(313\) 242889. 0.140135 0.0700677 0.997542i \(-0.477678\pi\)
0.0700677 + 0.997542i \(0.477678\pi\)
\(314\) 0 0
\(315\) 249860. 0.141880
\(316\) 0 0
\(317\) 546897. 0.305673 0.152837 0.988251i \(-0.451159\pi\)
0.152837 + 0.988251i \(0.451159\pi\)
\(318\) 0 0
\(319\) −128575. −0.0707425
\(320\) 0 0
\(321\) −729080. −0.394923
\(322\) 0 0
\(323\) −277968. −0.148248
\(324\) 0 0
\(325\) 287031. 0.150737
\(326\) 0 0
\(327\) 43360.0 0.0224243
\(328\) 0 0
\(329\) −195759. −0.0997083
\(330\) 0 0
\(331\) 518092. 0.259918 0.129959 0.991519i \(-0.458515\pi\)
0.129959 + 0.991519i \(0.458515\pi\)
\(332\) 0 0
\(333\) 645932. 0.319210
\(334\) 0 0
\(335\) −21331.9 −0.0103852
\(336\) 0 0
\(337\) 1.93329e6 0.927303 0.463651 0.886018i \(-0.346539\pi\)
0.463651 + 0.886018i \(0.346539\pi\)
\(338\) 0 0
\(339\) −1.52935e6 −0.722782
\(340\) 0 0
\(341\) 328327. 0.152905
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 674144. 0.304933
\(346\) 0 0
\(347\) 2.20916e6 0.984925 0.492463 0.870334i \(-0.336097\pi\)
0.492463 + 0.870334i \(0.336097\pi\)
\(348\) 0 0
\(349\) −2.05917e6 −0.904957 −0.452479 0.891775i \(-0.649460\pi\)
−0.452479 + 0.891775i \(0.649460\pi\)
\(350\) 0 0
\(351\) −1.28244e6 −0.555610
\(352\) 0 0
\(353\) −3.62255e6 −1.54731 −0.773655 0.633607i \(-0.781574\pi\)
−0.773655 + 0.633607i \(0.781574\pi\)
\(354\) 0 0
\(355\) 34468.4 0.0145161
\(356\) 0 0
\(357\) 214632. 0.0891299
\(358\) 0 0
\(359\) −3.42481e6 −1.40249 −0.701247 0.712919i \(-0.747373\pi\)
−0.701247 + 0.712919i \(0.747373\pi\)
\(360\) 0 0
\(361\) −2.31891e6 −0.936518
\(362\) 0 0
\(363\) −956178. −0.380866
\(364\) 0 0
\(365\) −306212. −0.120307
\(366\) 0 0
\(367\) −2.57705e6 −0.998751 −0.499375 0.866386i \(-0.666437\pi\)
−0.499375 + 0.866386i \(0.666437\pi\)
\(368\) 0 0
\(369\) 1.29582e6 0.495424
\(370\) 0 0
\(371\) −1.19917e6 −0.452320
\(372\) 0 0
\(373\) −647873. −0.241111 −0.120556 0.992707i \(-0.538468\pi\)
−0.120556 + 0.992707i \(0.538468\pi\)
\(374\) 0 0
\(375\) −97618.6 −0.0358471
\(376\) 0 0
\(377\) −660030. −0.239172
\(378\) 0 0
\(379\) −3.07292e6 −1.09889 −0.549443 0.835531i \(-0.685160\pi\)
−0.549443 + 0.835531i \(0.685160\pi\)
\(380\) 0 0
\(381\) 1.08677e6 0.383553
\(382\) 0 0
\(383\) −1.50940e6 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(384\) 0 0
\(385\) −109592. −0.0376814
\(386\) 0 0
\(387\) 3.16355e6 1.07374
\(388\) 0 0
\(389\) 1.06421e6 0.356576 0.178288 0.983978i \(-0.442944\pi\)
0.178288 + 0.983978i \(0.442944\pi\)
\(390\) 0 0
\(391\) −3.02611e6 −1.00102
\(392\) 0 0
\(393\) −831586. −0.271597
\(394\) 0 0
\(395\) 1.27619e6 0.411548
\(396\) 0 0
\(397\) 4.99307e6 1.58998 0.794990 0.606622i \(-0.207476\pi\)
0.794990 + 0.606622i \(0.207476\pi\)
\(398\) 0 0
\(399\) −121372. −0.0381669
\(400\) 0 0
\(401\) 2.28925e6 0.710939 0.355470 0.934688i \(-0.384321\pi\)
0.355470 + 0.934688i \(0.384321\pi\)
\(402\) 0 0
\(403\) 1.68544e6 0.516953
\(404\) 0 0
\(405\) −802948. −0.243248
\(406\) 0 0
\(407\) −283314. −0.0847777
\(408\) 0 0
\(409\) −2.34946e6 −0.694479 −0.347239 0.937777i \(-0.612881\pi\)
−0.347239 + 0.937777i \(0.612881\pi\)
\(410\) 0 0
\(411\) 964925. 0.281766
\(412\) 0 0
\(413\) −117371. −0.0338599
\(414\) 0 0
\(415\) −440390. −0.125521
\(416\) 0 0
\(417\) 1.37254e6 0.386533
\(418\) 0 0
\(419\) −6.91433e6 −1.92405 −0.962023 0.272969i \(-0.911994\pi\)
−0.962023 + 0.272969i \(0.911994\pi\)
\(420\) 0 0
\(421\) −910368. −0.250329 −0.125165 0.992136i \(-0.539946\pi\)
−0.125165 + 0.992136i \(0.539946\pi\)
\(422\) 0 0
\(423\) 814866. 0.221429
\(424\) 0 0
\(425\) 438193. 0.117677
\(426\) 0 0
\(427\) −1.03158e6 −0.273799
\(428\) 0 0
\(429\) 256687. 0.0673381
\(430\) 0 0
\(431\) 2.71383e6 0.703704 0.351852 0.936056i \(-0.385552\pi\)
0.351852 + 0.936056i \(0.385552\pi\)
\(432\) 0 0
\(433\) −5.02281e6 −1.28744 −0.643720 0.765261i \(-0.722610\pi\)
−0.643720 + 0.765261i \(0.722610\pi\)
\(434\) 0 0
\(435\) 224475. 0.0568780
\(436\) 0 0
\(437\) 1.71124e6 0.428653
\(438\) 0 0
\(439\) −1.26405e6 −0.313041 −0.156521 0.987675i \(-0.550028\pi\)
−0.156521 + 0.987675i \(0.550028\pi\)
\(440\) 0 0
\(441\) −489726. −0.119910
\(442\) 0 0
\(443\) 1.63750e6 0.396435 0.198217 0.980158i \(-0.436485\pi\)
0.198217 + 0.980158i \(0.436485\pi\)
\(444\) 0 0
\(445\) 458650. 0.109795
\(446\) 0 0
\(447\) 1.62392e6 0.384412
\(448\) 0 0
\(449\) −4.63732e6 −1.08555 −0.542777 0.839877i \(-0.682627\pi\)
−0.542777 + 0.839877i \(0.682627\pi\)
\(450\) 0 0
\(451\) −568361. −0.131578
\(452\) 0 0
\(453\) 786287. 0.180026
\(454\) 0 0
\(455\) −562581. −0.127396
\(456\) 0 0
\(457\) 5.25976e6 1.17808 0.589040 0.808104i \(-0.299506\pi\)
0.589040 + 0.808104i \(0.299506\pi\)
\(458\) 0 0
\(459\) −1.95782e6 −0.433753
\(460\) 0 0
\(461\) 3.52812e6 0.773199 0.386599 0.922248i \(-0.373650\pi\)
0.386599 + 0.922248i \(0.373650\pi\)
\(462\) 0 0
\(463\) 402711. 0.0873054 0.0436527 0.999047i \(-0.486101\pi\)
0.0436527 + 0.999047i \(0.486101\pi\)
\(464\) 0 0
\(465\) −573214. −0.122938
\(466\) 0 0
\(467\) −4.65025e6 −0.986697 −0.493348 0.869832i \(-0.664227\pi\)
−0.493348 + 0.869832i \(0.664227\pi\)
\(468\) 0 0
\(469\) 41810.4 0.00877713
\(470\) 0 0
\(471\) −123061. −0.0255604
\(472\) 0 0
\(473\) −1.38757e6 −0.285170
\(474\) 0 0
\(475\) −247793. −0.0503913
\(476\) 0 0
\(477\) 4.99167e6 1.00450
\(478\) 0 0
\(479\) −7.54178e6 −1.50188 −0.750940 0.660371i \(-0.770399\pi\)
−0.750940 + 0.660371i \(0.770399\pi\)
\(480\) 0 0
\(481\) −1.45437e6 −0.286624
\(482\) 0 0
\(483\) −1.32132e6 −0.257716
\(484\) 0 0
\(485\) 2.58650e6 0.499297
\(486\) 0 0
\(487\) 8.68725e6 1.65982 0.829908 0.557900i \(-0.188393\pi\)
0.829908 + 0.557900i \(0.188393\pi\)
\(488\) 0 0
\(489\) 3.06655e6 0.579934
\(490\) 0 0
\(491\) −4.24852e6 −0.795306 −0.397653 0.917536i \(-0.630175\pi\)
−0.397653 + 0.917536i \(0.630175\pi\)
\(492\) 0 0
\(493\) −1.00763e6 −0.186716
\(494\) 0 0
\(495\) 456188. 0.0836817
\(496\) 0 0
\(497\) −67558.2 −0.0122684
\(498\) 0 0
\(499\) 5.49814e6 0.988473 0.494236 0.869328i \(-0.335448\pi\)
0.494236 + 0.869328i \(0.335448\pi\)
\(500\) 0 0
\(501\) 3.70751e6 0.659916
\(502\) 0 0
\(503\) −9.46196e6 −1.66748 −0.833741 0.552156i \(-0.813805\pi\)
−0.833741 + 0.552156i \(0.813805\pi\)
\(504\) 0 0
\(505\) 3.87685e6 0.676473
\(506\) 0 0
\(507\) −1.00200e6 −0.173121
\(508\) 0 0
\(509\) 5.87612e6 1.00530 0.502651 0.864489i \(-0.332358\pi\)
0.502651 + 0.864489i \(0.332358\pi\)
\(510\) 0 0
\(511\) 600175. 0.101678
\(512\) 0 0
\(513\) 1.10713e6 0.185740
\(514\) 0 0
\(515\) 906562. 0.150619
\(516\) 0 0
\(517\) −357410. −0.0588086
\(518\) 0 0
\(519\) 469976. 0.0765874
\(520\) 0 0
\(521\) −1.08233e7 −1.74689 −0.873443 0.486926i \(-0.838118\pi\)
−0.873443 + 0.486926i \(0.838118\pi\)
\(522\) 0 0
\(523\) 3.75209e6 0.599818 0.299909 0.953968i \(-0.403044\pi\)
0.299909 + 0.953968i \(0.403044\pi\)
\(524\) 0 0
\(525\) 191333. 0.0302964
\(526\) 0 0
\(527\) 2.57306e6 0.403574
\(528\) 0 0
\(529\) 1.21931e7 1.89441
\(530\) 0 0
\(531\) 488568. 0.0751950
\(532\) 0 0
\(533\) −2.91764e6 −0.444850
\(534\) 0 0
\(535\) 2.91744e6 0.440674
\(536\) 0 0
\(537\) 1.31764e6 0.197179
\(538\) 0 0
\(539\) 214800. 0.0318466
\(540\) 0 0
\(541\) 5.78772e6 0.850187 0.425093 0.905150i \(-0.360241\pi\)
0.425093 + 0.905150i \(0.360241\pi\)
\(542\) 0 0
\(543\) 2.17174e6 0.316089
\(544\) 0 0
\(545\) −173507. −0.0250222
\(546\) 0 0
\(547\) 8.05012e6 1.15036 0.575180 0.818027i \(-0.304932\pi\)
0.575180 + 0.818027i \(0.304932\pi\)
\(548\) 0 0
\(549\) 4.29405e6 0.608045
\(550\) 0 0
\(551\) 569803. 0.0799550
\(552\) 0 0
\(553\) −2.50132e6 −0.347822
\(554\) 0 0
\(555\) 494627. 0.0681625
\(556\) 0 0
\(557\) 1.13985e7 1.55671 0.778356 0.627824i \(-0.216054\pi\)
0.778356 + 0.627824i \(0.216054\pi\)
\(558\) 0 0
\(559\) −7.12300e6 −0.964125
\(560\) 0 0
\(561\) 391868. 0.0525694
\(562\) 0 0
\(563\) 9.73011e6 1.29374 0.646870 0.762601i \(-0.276078\pi\)
0.646870 + 0.762601i \(0.276078\pi\)
\(564\) 0 0
\(565\) 6.11975e6 0.806515
\(566\) 0 0
\(567\) 1.57378e6 0.205582
\(568\) 0 0
\(569\) −5.09214e6 −0.659355 −0.329678 0.944094i \(-0.606940\pi\)
−0.329678 + 0.944094i \(0.606940\pi\)
\(570\) 0 0
\(571\) 1.25025e7 1.60475 0.802376 0.596818i \(-0.203569\pi\)
0.802376 + 0.596818i \(0.203569\pi\)
\(572\) 0 0
\(573\) 1.13486e6 0.144396
\(574\) 0 0
\(575\) −2.69761e6 −0.340259
\(576\) 0 0
\(577\) −1.02876e7 −1.28640 −0.643198 0.765700i \(-0.722393\pi\)
−0.643198 + 0.765700i \(0.722393\pi\)
\(578\) 0 0
\(579\) −2.92687e6 −0.362833
\(580\) 0 0
\(581\) 863164. 0.106085
\(582\) 0 0
\(583\) −2.18941e6 −0.266781
\(584\) 0 0
\(585\) 2.34180e6 0.282918
\(586\) 0 0
\(587\) 411635. 0.0493079 0.0246540 0.999696i \(-0.492152\pi\)
0.0246540 + 0.999696i \(0.492152\pi\)
\(588\) 0 0
\(589\) −1.45504e6 −0.172817
\(590\) 0 0
\(591\) 1.88556e6 0.222061
\(592\) 0 0
\(593\) 1.85606e6 0.216748 0.108374 0.994110i \(-0.465436\pi\)
0.108374 + 0.994110i \(0.465436\pi\)
\(594\) 0 0
\(595\) −858858. −0.0994555
\(596\) 0 0
\(597\) −215875. −0.0247894
\(598\) 0 0
\(599\) −7.01077e6 −0.798359 −0.399180 0.916873i \(-0.630705\pi\)
−0.399180 + 0.916873i \(0.630705\pi\)
\(600\) 0 0
\(601\) −8.82536e6 −0.996658 −0.498329 0.866988i \(-0.666053\pi\)
−0.498329 + 0.866988i \(0.666053\pi\)
\(602\) 0 0
\(603\) −174040. −0.0194920
\(604\) 0 0
\(605\) 3.82619e6 0.424989
\(606\) 0 0
\(607\) 1.49962e7 1.65200 0.826000 0.563671i \(-0.190611\pi\)
0.826000 + 0.563671i \(0.190611\pi\)
\(608\) 0 0
\(609\) −439970. −0.0480707
\(610\) 0 0
\(611\) −1.83474e6 −0.198825
\(612\) 0 0
\(613\) 1.68954e7 1.81601 0.908004 0.418961i \(-0.137606\pi\)
0.908004 + 0.418961i \(0.137606\pi\)
\(614\) 0 0
\(615\) 992281. 0.105791
\(616\) 0 0
\(617\) −1.61632e7 −1.70928 −0.854642 0.519218i \(-0.826223\pi\)
−0.854642 + 0.519218i \(0.826223\pi\)
\(618\) 0 0
\(619\) −3.57039e6 −0.374532 −0.187266 0.982309i \(-0.559963\pi\)
−0.187266 + 0.982309i \(0.559963\pi\)
\(620\) 0 0
\(621\) 1.20528e7 1.25418
\(622\) 0 0
\(623\) −898954. −0.0927934
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −221598. −0.0225111
\(628\) 0 0
\(629\) −2.22029e6 −0.223761
\(630\) 0 0
\(631\) 5.52777e6 0.552684 0.276342 0.961059i \(-0.410878\pi\)
0.276342 + 0.961059i \(0.410878\pi\)
\(632\) 0 0
\(633\) 3.36336e6 0.333629
\(634\) 0 0
\(635\) −4.34876e6 −0.427987
\(636\) 0 0
\(637\) 1.10266e6 0.107670
\(638\) 0 0
\(639\) 281218. 0.0272452
\(640\) 0 0
\(641\) −4.42446e6 −0.425320 −0.212660 0.977126i \(-0.568213\pi\)
−0.212660 + 0.977126i \(0.568213\pi\)
\(642\) 0 0
\(643\) −3.13757e6 −0.299272 −0.149636 0.988741i \(-0.547810\pi\)
−0.149636 + 0.988741i \(0.547810\pi\)
\(644\) 0 0
\(645\) 2.42251e6 0.229280
\(646\) 0 0
\(647\) 9.66818e6 0.907996 0.453998 0.891003i \(-0.349997\pi\)
0.453998 + 0.891003i \(0.349997\pi\)
\(648\) 0 0
\(649\) −214292. −0.0199708
\(650\) 0 0
\(651\) 1.12350e6 0.103901
\(652\) 0 0
\(653\) −1.38904e7 −1.27477 −0.637386 0.770545i \(-0.719984\pi\)
−0.637386 + 0.770545i \(0.719984\pi\)
\(654\) 0 0
\(655\) 3.32762e6 0.303062
\(656\) 0 0
\(657\) −2.49829e6 −0.225803
\(658\) 0 0
\(659\) 6.78274e6 0.608403 0.304202 0.952608i \(-0.401610\pi\)
0.304202 + 0.952608i \(0.401610\pi\)
\(660\) 0 0
\(661\) −1.96423e7 −1.74860 −0.874298 0.485390i \(-0.838677\pi\)
−0.874298 + 0.485390i \(0.838677\pi\)
\(662\) 0 0
\(663\) 2.01163e6 0.177731
\(664\) 0 0
\(665\) 485675. 0.0425885
\(666\) 0 0
\(667\) 6.20318e6 0.539883
\(668\) 0 0
\(669\) 1.51901e6 0.131218
\(670\) 0 0
\(671\) −1.88342e6 −0.161489
\(672\) 0 0
\(673\) −2.14538e7 −1.82586 −0.912930 0.408116i \(-0.866186\pi\)
−0.912930 + 0.408116i \(0.866186\pi\)
\(674\) 0 0
\(675\) −1.74529e6 −0.147438
\(676\) 0 0
\(677\) 6.25982e6 0.524917 0.262458 0.964943i \(-0.415467\pi\)
0.262458 + 0.964943i \(0.415467\pi\)
\(678\) 0 0
\(679\) −5.06955e6 −0.421983
\(680\) 0 0
\(681\) 2.13302e6 0.176249
\(682\) 0 0
\(683\) 6.24086e6 0.511909 0.255954 0.966689i \(-0.417610\pi\)
0.255954 + 0.966689i \(0.417610\pi\)
\(684\) 0 0
\(685\) −3.86119e6 −0.314409
\(686\) 0 0
\(687\) −709982. −0.0573925
\(688\) 0 0
\(689\) −1.12392e7 −0.901957
\(690\) 0 0
\(691\) −1.94232e6 −0.154748 −0.0773740 0.997002i \(-0.524654\pi\)
−0.0773740 + 0.997002i \(0.524654\pi\)
\(692\) 0 0
\(693\) −894128. −0.0707240
\(694\) 0 0
\(695\) −5.49229e6 −0.431312
\(696\) 0 0
\(697\) −4.45418e6 −0.347284
\(698\) 0 0
\(699\) −6.92469e6 −0.536052
\(700\) 0 0
\(701\) −1.06388e7 −0.817707 −0.408854 0.912600i \(-0.634071\pi\)
−0.408854 + 0.912600i \(0.634071\pi\)
\(702\) 0 0
\(703\) 1.25555e6 0.0958180
\(704\) 0 0
\(705\) 623990. 0.0472830
\(706\) 0 0
\(707\) −7.59863e6 −0.571724
\(708\) 0 0
\(709\) 1.81481e7 1.35586 0.677930 0.735126i \(-0.262877\pi\)
0.677930 + 0.735126i \(0.262877\pi\)
\(710\) 0 0
\(711\) 1.04120e7 0.772433
\(712\) 0 0
\(713\) −1.58403e7 −1.16692
\(714\) 0 0
\(715\) −1.02714e6 −0.0751392
\(716\) 0 0
\(717\) 1.71713e6 0.124740
\(718\) 0 0
\(719\) 9.37540e6 0.676344 0.338172 0.941084i \(-0.390191\pi\)
0.338172 + 0.941084i \(0.390191\pi\)
\(720\) 0 0
\(721\) −1.77686e6 −0.127296
\(722\) 0 0
\(723\) 8.26695e6 0.588166
\(724\) 0 0
\(725\) −898245. −0.0634672
\(726\) 0 0
\(727\) −5.67290e6 −0.398079 −0.199040 0.979991i \(-0.563782\pi\)
−0.199040 + 0.979991i \(0.563782\pi\)
\(728\) 0 0
\(729\) −2.31158e6 −0.161098
\(730\) 0 0
\(731\) −1.08742e7 −0.752671
\(732\) 0 0
\(733\) −1.16816e7 −0.803051 −0.401526 0.915848i \(-0.631520\pi\)
−0.401526 + 0.915848i \(0.631520\pi\)
\(734\) 0 0
\(735\) −375012. −0.0256051
\(736\) 0 0
\(737\) 76336.3 0.00517681
\(738\) 0 0
\(739\) 9.25981e6 0.623722 0.311861 0.950128i \(-0.399048\pi\)
0.311861 + 0.950128i \(0.399048\pi\)
\(740\) 0 0
\(741\) −1.13755e6 −0.0761073
\(742\) 0 0
\(743\) 1.02603e7 0.681850 0.340925 0.940090i \(-0.389260\pi\)
0.340925 + 0.940090i \(0.389260\pi\)
\(744\) 0 0
\(745\) −6.49820e6 −0.428946
\(746\) 0 0
\(747\) −3.59301e6 −0.235590
\(748\) 0 0
\(749\) −5.71819e6 −0.372438
\(750\) 0 0
\(751\) 2.31032e6 0.149476 0.0747381 0.997203i \(-0.476188\pi\)
0.0747381 + 0.997203i \(0.476188\pi\)
\(752\) 0 0
\(753\) −9.75661e6 −0.627064
\(754\) 0 0
\(755\) −3.14636e6 −0.200882
\(756\) 0 0
\(757\) −1.33223e7 −0.844967 −0.422483 0.906371i \(-0.638842\pi\)
−0.422483 + 0.906371i \(0.638842\pi\)
\(758\) 0 0
\(759\) −2.41243e6 −0.152002
\(760\) 0 0
\(761\) −1.32578e7 −0.829868 −0.414934 0.909852i \(-0.636195\pi\)
−0.414934 + 0.909852i \(0.636195\pi\)
\(762\) 0 0
\(763\) 340073. 0.0211476
\(764\) 0 0
\(765\) 3.57508e6 0.220868
\(766\) 0 0
\(767\) −1.10005e6 −0.0675189
\(768\) 0 0
\(769\) 1.26945e7 0.774103 0.387051 0.922058i \(-0.373494\pi\)
0.387051 + 0.922058i \(0.373494\pi\)
\(770\) 0 0
\(771\) 7.47192e6 0.452685
\(772\) 0 0
\(773\) −2.79823e7 −1.68436 −0.842179 0.539198i \(-0.818727\pi\)
−0.842179 + 0.539198i \(0.818727\pi\)
\(774\) 0 0
\(775\) 2.29374e6 0.137180
\(776\) 0 0
\(777\) −969470. −0.0576079
\(778\) 0 0
\(779\) 2.51879e6 0.148713
\(780\) 0 0
\(781\) −123346. −0.00723597
\(782\) 0 0
\(783\) 4.01332e6 0.233937
\(784\) 0 0
\(785\) 492432. 0.0285215
\(786\) 0 0
\(787\) 2.95888e6 0.170290 0.0851452 0.996369i \(-0.472865\pi\)
0.0851452 + 0.996369i \(0.472865\pi\)
\(788\) 0 0
\(789\) 9.66897e6 0.552952
\(790\) 0 0
\(791\) −1.19947e7 −0.681630
\(792\) 0 0
\(793\) −9.66841e6 −0.545974
\(794\) 0 0
\(795\) 3.82241e6 0.214496
\(796\) 0 0
\(797\) −2.52840e6 −0.140994 −0.0704969 0.997512i \(-0.522458\pi\)
−0.0704969 + 0.997512i \(0.522458\pi\)
\(798\) 0 0
\(799\) −2.80098e6 −0.155218
\(800\) 0 0
\(801\) 3.74199e6 0.206073
\(802\) 0 0
\(803\) 1.09578e6 0.0599702
\(804\) 0 0
\(805\) 5.28732e6 0.287572
\(806\) 0 0
\(807\) −6.54674e6 −0.353868
\(808\) 0 0
\(809\) −1.96696e6 −0.105663 −0.0528316 0.998603i \(-0.516825\pi\)
−0.0528316 + 0.998603i \(0.516825\pi\)
\(810\) 0 0
\(811\) 2.25136e7 1.20197 0.600984 0.799261i \(-0.294776\pi\)
0.600984 + 0.799261i \(0.294776\pi\)
\(812\) 0 0
\(813\) 5.26506e6 0.279368
\(814\) 0 0
\(815\) −1.22709e7 −0.647119
\(816\) 0 0
\(817\) 6.14927e6 0.322306
\(818\) 0 0
\(819\) −4.58994e6 −0.239110
\(820\) 0 0
\(821\) 5.29690e6 0.274261 0.137131 0.990553i \(-0.456212\pi\)
0.137131 + 0.990553i \(0.456212\pi\)
\(822\) 0 0
\(823\) 2.52150e7 1.29765 0.648827 0.760936i \(-0.275260\pi\)
0.648827 + 0.760936i \(0.275260\pi\)
\(824\) 0 0
\(825\) 349329. 0.0178690
\(826\) 0 0
\(827\) −1.85137e7 −0.941305 −0.470652 0.882319i \(-0.655981\pi\)
−0.470652 + 0.882319i \(0.655981\pi\)
\(828\) 0 0
\(829\) 1.58266e7 0.799837 0.399918 0.916551i \(-0.369038\pi\)
0.399918 + 0.916551i \(0.369038\pi\)
\(830\) 0 0
\(831\) 4.12688e6 0.207309
\(832\) 0 0
\(833\) 1.68336e6 0.0840552
\(834\) 0 0
\(835\) −1.48358e7 −0.736366
\(836\) 0 0
\(837\) −1.02483e7 −0.505638
\(838\) 0 0
\(839\) −3.93063e7 −1.92778 −0.963890 0.266300i \(-0.914199\pi\)
−0.963890 + 0.266300i \(0.914199\pi\)
\(840\) 0 0
\(841\) −1.84456e7 −0.899298
\(842\) 0 0
\(843\) −9.13401e6 −0.442683
\(844\) 0 0
\(845\) 4.00956e6 0.193177
\(846\) 0 0
\(847\) −7.49932e6 −0.359181
\(848\) 0 0
\(849\) −1.05356e7 −0.501635
\(850\) 0 0
\(851\) 1.36686e7 0.646996
\(852\) 0 0
\(853\) 2.96226e7 1.39396 0.696979 0.717091i \(-0.254527\pi\)
0.696979 + 0.717091i \(0.254527\pi\)
\(854\) 0 0
\(855\) −2.02167e6 −0.0945792
\(856\) 0 0
\(857\) −7.86894e6 −0.365986 −0.182993 0.983114i \(-0.558579\pi\)
−0.182993 + 0.983114i \(0.558579\pi\)
\(858\) 0 0
\(859\) −1.38750e7 −0.641581 −0.320790 0.947150i \(-0.603948\pi\)
−0.320790 + 0.947150i \(0.603948\pi\)
\(860\) 0 0
\(861\) −1.94487e6 −0.0894094
\(862\) 0 0
\(863\) −8.53024e6 −0.389883 −0.194941 0.980815i \(-0.562452\pi\)
−0.194941 + 0.980815i \(0.562452\pi\)
\(864\) 0 0
\(865\) −1.88063e6 −0.0854600
\(866\) 0 0
\(867\) −5.79967e6 −0.262033
\(868\) 0 0
\(869\) −4.56684e6 −0.205148
\(870\) 0 0
\(871\) 391866. 0.0175022
\(872\) 0 0
\(873\) 2.11025e7 0.937128
\(874\) 0 0
\(875\) −765625. −0.0338062
\(876\) 0 0
\(877\) 4.02539e6 0.176729 0.0883647 0.996088i \(-0.471836\pi\)
0.0883647 + 0.996088i \(0.471836\pi\)
\(878\) 0 0
\(879\) 6.47669e6 0.282736
\(880\) 0 0
\(881\) −1.20511e7 −0.523102 −0.261551 0.965190i \(-0.584234\pi\)
−0.261551 + 0.965190i \(0.584234\pi\)
\(882\) 0 0
\(883\) 2.00355e7 0.864765 0.432383 0.901690i \(-0.357673\pi\)
0.432383 + 0.901690i \(0.357673\pi\)
\(884\) 0 0
\(885\) 374125. 0.0160568
\(886\) 0 0
\(887\) −2.87782e7 −1.22816 −0.614079 0.789244i \(-0.710473\pi\)
−0.614079 + 0.789244i \(0.710473\pi\)
\(888\) 0 0
\(889\) 8.52356e6 0.361715
\(890\) 0 0
\(891\) 2.87336e6 0.121254
\(892\) 0 0
\(893\) 1.58393e6 0.0664670
\(894\) 0 0
\(895\) −5.27259e6 −0.220022
\(896\) 0 0
\(897\) −1.23840e7 −0.513902
\(898\) 0 0
\(899\) −5.27447e6 −0.217661
\(900\) 0 0
\(901\) −1.71581e7 −0.704138
\(902\) 0 0
\(903\) −4.74813e6 −0.193777
\(904\) 0 0
\(905\) −8.69032e6 −0.352707
\(906\) 0 0
\(907\) 1.23149e7 0.497066 0.248533 0.968623i \(-0.420052\pi\)
0.248533 + 0.968623i \(0.420052\pi\)
\(908\) 0 0
\(909\) 3.16301e7 1.26967
\(910\) 0 0
\(911\) 2.38428e7 0.951836 0.475918 0.879490i \(-0.342116\pi\)
0.475918 + 0.879490i \(0.342116\pi\)
\(912\) 0 0
\(913\) 1.57594e6 0.0625695
\(914\) 0 0
\(915\) 3.28820e6 0.129839
\(916\) 0 0
\(917\) −6.52214e6 −0.256134
\(918\) 0 0
\(919\) −6.18286e6 −0.241491 −0.120745 0.992684i \(-0.538528\pi\)
−0.120745 + 0.992684i \(0.538528\pi\)
\(920\) 0 0
\(921\) 8.35700e6 0.324640
\(922\) 0 0
\(923\) −633186. −0.0244640
\(924\) 0 0
\(925\) −1.97927e6 −0.0760591
\(926\) 0 0
\(927\) 7.39637e6 0.282696
\(928\) 0 0
\(929\) 2.03934e7 0.775267 0.387633 0.921814i \(-0.373293\pi\)
0.387633 + 0.921814i \(0.373293\pi\)
\(930\) 0 0
\(931\) −951924. −0.0359938
\(932\) 0 0
\(933\) 2.77181e6 0.104246
\(934\) 0 0
\(935\) −1.56808e6 −0.0586595
\(936\) 0 0
\(937\) −3.22222e7 −1.19896 −0.599481 0.800389i \(-0.704626\pi\)
−0.599481 + 0.800389i \(0.704626\pi\)
\(938\) 0 0
\(939\) 1.51747e6 0.0561639
\(940\) 0 0
\(941\) −4.01203e6 −0.147703 −0.0738517 0.997269i \(-0.523529\pi\)
−0.0738517 + 0.997269i \(0.523529\pi\)
\(942\) 0 0
\(943\) 2.74209e7 1.00416
\(944\) 0 0
\(945\) 3.42078e6 0.124608
\(946\) 0 0
\(947\) −3.07238e7 −1.11327 −0.556635 0.830757i \(-0.687908\pi\)
−0.556635 + 0.830757i \(0.687908\pi\)
\(948\) 0 0
\(949\) 5.62511e6 0.202752
\(950\) 0 0
\(951\) 3.41679e6 0.122509
\(952\) 0 0
\(953\) −3.10153e7 −1.10622 −0.553112 0.833107i \(-0.686560\pi\)
−0.553112 + 0.833107i \(0.686560\pi\)
\(954\) 0 0
\(955\) −4.54118e6 −0.161124
\(956\) 0 0
\(957\) −803285. −0.0283524
\(958\) 0 0
\(959\) 7.56793e6 0.265724
\(960\) 0 0
\(961\) −1.51604e7 −0.529542
\(962\) 0 0
\(963\) 2.38026e7 0.827100
\(964\) 0 0
\(965\) 1.17120e7 0.404867
\(966\) 0 0
\(967\) 2.39410e7 0.823335 0.411668 0.911334i \(-0.364946\pi\)
0.411668 + 0.911334i \(0.364946\pi\)
\(968\) 0 0
\(969\) −1.73663e6 −0.0594153
\(970\) 0 0
\(971\) −7.44188e6 −0.253300 −0.126650 0.991947i \(-0.540422\pi\)
−0.126650 + 0.991947i \(0.540422\pi\)
\(972\) 0 0
\(973\) 1.07649e7 0.364525
\(974\) 0 0
\(975\) 1.79325e6 0.0604130
\(976\) 0 0
\(977\) −1.26312e7 −0.423359 −0.211680 0.977339i \(-0.567893\pi\)
−0.211680 + 0.977339i \(0.567893\pi\)
\(978\) 0 0
\(979\) −1.64128e6 −0.0547302
\(980\) 0 0
\(981\) −1.41559e6 −0.0469640
\(982\) 0 0
\(983\) 3.11593e7 1.02850 0.514249 0.857641i \(-0.328071\pi\)
0.514249 + 0.857641i \(0.328071\pi\)
\(984\) 0 0
\(985\) −7.54514e6 −0.247786
\(986\) 0 0
\(987\) −1.22302e6 −0.0399614
\(988\) 0 0
\(989\) 6.69443e7 2.17632
\(990\) 0 0
\(991\) −2.08229e7 −0.673530 −0.336765 0.941589i \(-0.609333\pi\)
−0.336765 + 0.941589i \(0.609333\pi\)
\(992\) 0 0
\(993\) 3.23683e6 0.104171
\(994\) 0 0
\(995\) 863833. 0.0276613
\(996\) 0 0
\(997\) −1.04553e7 −0.333118 −0.166559 0.986031i \(-0.553266\pi\)
−0.166559 + 0.986031i \(0.553266\pi\)
\(998\) 0 0
\(999\) 8.84330e6 0.280350
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 280.6.a.e.1.2 3
4.3 odd 2 560.6.a.s.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.e.1.2 3 1.1 even 1 trivial
560.6.a.s.1.2 3 4.3 odd 2