Properties

Label 324.6.a.d.1.1
Level 324
Weight 6
Character 324.1
Self dual yes
Analytic conductor 51.964
Analytic rank 1
Dimension 5
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 324.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.9643576194\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial: \(x^{5} - 2 x^{4} - 110 x^{3} + 39 x^{2} + 2214 x - 1944\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{7} \)
Twist minimal: no (minimal twist has level 36)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-7.49663\) of defining polynomial
Character \(\chi\) \(=\) 324.1

$q$-expansion

\(f(q)\) \(=\) \(q-110.399 q^{5} +101.745 q^{7} +O(q^{10})\) \(q-110.399 q^{5} +101.745 q^{7} +150.312 q^{11} +635.424 q^{13} -1498.54 q^{17} +1437.69 q^{19} +1264.11 q^{23} +9063.00 q^{25} +2777.50 q^{29} -6968.68 q^{31} -11232.5 q^{35} -7950.71 q^{37} +2027.53 q^{41} -12523.3 q^{43} +6482.34 q^{47} -6455.01 q^{49} -9827.54 q^{53} -16594.3 q^{55} -47087.9 q^{59} +8337.84 q^{61} -70150.3 q^{65} -7260.89 q^{67} -3582.33 q^{71} +58077.5 q^{73} +15293.5 q^{77} -63742.8 q^{79} -82846.5 q^{83} +165438. q^{85} +3861.51 q^{89} +64651.0 q^{91} -158720. q^{95} +69277.2 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5q - 21q^{5} - 29q^{7} + O(q^{10}) \) \( 5q - 21q^{5} - 29q^{7} + 177q^{11} + 181q^{13} - 1140q^{17} - 416q^{19} + 399q^{23} + 4778q^{25} - 6033q^{29} - 2759q^{31} - 18573q^{35} - 7586q^{37} - 18435q^{41} - 1469q^{43} - 25155q^{47} + 4056q^{49} - 58422q^{53} + 7389q^{55} - 90537q^{59} - 1403q^{61} - 148407q^{65} - 13907q^{67} - 114684q^{71} + 7600q^{73} - 211983q^{77} - 29993q^{79} - 228951q^{83} + 49662q^{85} - 299166q^{89} + 62465q^{91} - 394764q^{95} - 40541q^{97} + O(q^{100}) \)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −110.399 −1.97488 −0.987441 0.157988i \(-0.949499\pi\)
−0.987441 + 0.157988i \(0.949499\pi\)
\(6\) 0 0
\(7\) 101.745 0.784814 0.392407 0.919792i \(-0.371642\pi\)
0.392407 + 0.919792i \(0.371642\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 150.312 0.374552 0.187276 0.982307i \(-0.440034\pi\)
0.187276 + 0.982307i \(0.440034\pi\)
\(12\) 0 0
\(13\) 635.424 1.04281 0.521405 0.853309i \(-0.325408\pi\)
0.521405 + 0.853309i \(0.325408\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1498.54 −1.25761 −0.628806 0.777562i \(-0.716456\pi\)
−0.628806 + 0.777562i \(0.716456\pi\)
\(18\) 0 0
\(19\) 1437.69 0.913651 0.456825 0.889556i \(-0.348986\pi\)
0.456825 + 0.889556i \(0.348986\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1264.11 0.498269 0.249134 0.968469i \(-0.419854\pi\)
0.249134 + 0.968469i \(0.419854\pi\)
\(24\) 0 0
\(25\) 9063.00 2.90016
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2777.50 0.613280 0.306640 0.951826i \(-0.400795\pi\)
0.306640 + 0.951826i \(0.400795\pi\)
\(30\) 0 0
\(31\) −6968.68 −1.30241 −0.651203 0.758904i \(-0.725735\pi\)
−0.651203 + 0.758904i \(0.725735\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −11232.5 −1.54992
\(36\) 0 0
\(37\) −7950.71 −0.954776 −0.477388 0.878693i \(-0.658416\pi\)
−0.477388 + 0.878693i \(0.658416\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2027.53 0.188369 0.0941843 0.995555i \(-0.469976\pi\)
0.0941843 + 0.995555i \(0.469976\pi\)
\(42\) 0 0
\(43\) −12523.3 −1.03288 −0.516438 0.856325i \(-0.672742\pi\)
−0.516438 + 0.856325i \(0.672742\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6482.34 0.428043 0.214021 0.976829i \(-0.431344\pi\)
0.214021 + 0.976829i \(0.431344\pi\)
\(48\) 0 0
\(49\) −6455.01 −0.384067
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9827.54 −0.480568 −0.240284 0.970703i \(-0.577241\pi\)
−0.240284 + 0.970703i \(0.577241\pi\)
\(54\) 0 0
\(55\) −16594.3 −0.739696
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −47087.9 −1.76108 −0.880541 0.473970i \(-0.842821\pi\)
−0.880541 + 0.473970i \(0.842821\pi\)
\(60\) 0 0
\(61\) 8337.84 0.286899 0.143450 0.989658i \(-0.454181\pi\)
0.143450 + 0.989658i \(0.454181\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −70150.3 −2.05943
\(66\) 0 0
\(67\) −7260.89 −0.197607 −0.0988036 0.995107i \(-0.531502\pi\)
−0.0988036 + 0.995107i \(0.531502\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3582.33 −0.0843372 −0.0421686 0.999111i \(-0.513427\pi\)
−0.0421686 + 0.999111i \(0.513427\pi\)
\(72\) 0 0
\(73\) 58077.5 1.27556 0.637780 0.770218i \(-0.279853\pi\)
0.637780 + 0.770218i \(0.279853\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 15293.5 0.293954
\(78\) 0 0
\(79\) −63742.8 −1.14912 −0.574558 0.818464i \(-0.694826\pi\)
−0.574558 + 0.818464i \(0.694826\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −82846.5 −1.32002 −0.660008 0.751259i \(-0.729447\pi\)
−0.660008 + 0.751259i \(0.729447\pi\)
\(84\) 0 0
\(85\) 165438. 2.48363
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3861.51 0.0516752 0.0258376 0.999666i \(-0.491775\pi\)
0.0258376 + 0.999666i \(0.491775\pi\)
\(90\) 0 0
\(91\) 64651.0 0.818412
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −158720. −1.80435
\(96\) 0 0
\(97\) 69277.2 0.747585 0.373793 0.927512i \(-0.378057\pi\)
0.373793 + 0.927512i \(0.378057\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 25445.7 0.248205 0.124103 0.992269i \(-0.460395\pi\)
0.124103 + 0.992269i \(0.460395\pi\)
\(102\) 0 0
\(103\) −63387.8 −0.588725 −0.294363 0.955694i \(-0.595107\pi\)
−0.294363 + 0.955694i \(0.595107\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 61158.9 0.516417 0.258208 0.966089i \(-0.416868\pi\)
0.258208 + 0.966089i \(0.416868\pi\)
\(108\) 0 0
\(109\) −124036. −0.999957 −0.499979 0.866038i \(-0.666659\pi\)
−0.499979 + 0.866038i \(0.666659\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −117437. −0.865185 −0.432592 0.901590i \(-0.642401\pi\)
−0.432592 + 0.901590i \(0.642401\pi\)
\(114\) 0 0
\(115\) −139556. −0.984022
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −152469. −0.986991
\(120\) 0 0
\(121\) −138457. −0.859711
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −655551. −3.75259
\(126\) 0 0
\(127\) −29838.6 −0.164161 −0.0820803 0.996626i \(-0.526156\pi\)
−0.0820803 + 0.996626i \(0.526156\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 172058. 0.875983 0.437992 0.898979i \(-0.355690\pi\)
0.437992 + 0.898979i \(0.355690\pi\)
\(132\) 0 0
\(133\) 146277. 0.717046
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −190361. −0.866518 −0.433259 0.901270i \(-0.642636\pi\)
−0.433259 + 0.901270i \(0.642636\pi\)
\(138\) 0 0
\(139\) −337063. −1.47970 −0.739852 0.672770i \(-0.765104\pi\)
−0.739852 + 0.672770i \(0.765104\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 95511.9 0.390586
\(144\) 0 0
\(145\) −306634. −1.21115
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 55098.7 0.203318 0.101659 0.994819i \(-0.467585\pi\)
0.101659 + 0.994819i \(0.467585\pi\)
\(150\) 0 0
\(151\) 334064. 1.19230 0.596152 0.802872i \(-0.296696\pi\)
0.596152 + 0.802872i \(0.296696\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 769337. 2.57210
\(156\) 0 0
\(157\) −120107. −0.388882 −0.194441 0.980914i \(-0.562289\pi\)
−0.194441 + 0.980914i \(0.562289\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 128616. 0.391048
\(162\) 0 0
\(163\) 367083. 1.08217 0.541085 0.840968i \(-0.318014\pi\)
0.541085 + 0.840968i \(0.318014\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −589448. −1.63552 −0.817758 0.575563i \(-0.804783\pi\)
−0.817758 + 0.575563i \(0.804783\pi\)
\(168\) 0 0
\(169\) 32470.6 0.0874527
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −436457. −1.10873 −0.554366 0.832273i \(-0.687039\pi\)
−0.554366 + 0.832273i \(0.687039\pi\)
\(174\) 0 0
\(175\) 922112. 2.27609
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −241064. −0.562341 −0.281171 0.959658i \(-0.590723\pi\)
−0.281171 + 0.959658i \(0.590723\pi\)
\(180\) 0 0
\(181\) 27128.8 0.0615510 0.0307755 0.999526i \(-0.490202\pi\)
0.0307755 + 0.999526i \(0.490202\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 877752. 1.88557
\(186\) 0 0
\(187\) −225249. −0.471041
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 56072.5 0.111216 0.0556079 0.998453i \(-0.482290\pi\)
0.0556079 + 0.998453i \(0.482290\pi\)
\(192\) 0 0
\(193\) 354483. 0.685019 0.342510 0.939514i \(-0.388723\pi\)
0.342510 + 0.939514i \(0.388723\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 816895. 1.49969 0.749844 0.661615i \(-0.230129\pi\)
0.749844 + 0.661615i \(0.230129\pi\)
\(198\) 0 0
\(199\) 860396. 1.54016 0.770079 0.637948i \(-0.220217\pi\)
0.770079 + 0.637948i \(0.220217\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 282596. 0.481310
\(204\) 0 0
\(205\) −223838. −0.372006
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 216102. 0.342210
\(210\) 0 0
\(211\) −387171. −0.598683 −0.299341 0.954146i \(-0.596767\pi\)
−0.299341 + 0.954146i \(0.596767\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.38256e6 2.03981
\(216\) 0 0
\(217\) −709026. −1.02215
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −952209. −1.31145
\(222\) 0 0
\(223\) −294994. −0.397238 −0.198619 0.980077i \(-0.563646\pi\)
−0.198619 + 0.980077i \(0.563646\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −687980. −0.886158 −0.443079 0.896483i \(-0.646114\pi\)
−0.443079 + 0.896483i \(0.646114\pi\)
\(228\) 0 0
\(229\) −1.08647e6 −1.36908 −0.684538 0.728977i \(-0.739996\pi\)
−0.684538 + 0.728977i \(0.739996\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −168058. −0.202801 −0.101400 0.994846i \(-0.532332\pi\)
−0.101400 + 0.994846i \(0.532332\pi\)
\(234\) 0 0
\(235\) −715646. −0.845334
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.54628e6 1.75102 0.875512 0.483197i \(-0.160524\pi\)
0.875512 + 0.483197i \(0.160524\pi\)
\(240\) 0 0
\(241\) −1.15373e6 −1.27956 −0.639782 0.768557i \(-0.720975\pi\)
−0.639782 + 0.768557i \(0.720975\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 712629. 0.758487
\(246\) 0 0
\(247\) 913541. 0.952764
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 586711. 0.587814 0.293907 0.955834i \(-0.405044\pi\)
0.293907 + 0.955834i \(0.405044\pi\)
\(252\) 0 0
\(253\) 190010. 0.186628
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −108342. −0.102321 −0.0511604 0.998690i \(-0.516292\pi\)
−0.0511604 + 0.998690i \(0.516292\pi\)
\(258\) 0 0
\(259\) −808942. −0.749321
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.73671e6 1.54823 0.774117 0.633042i \(-0.218194\pi\)
0.774117 + 0.633042i \(0.218194\pi\)
\(264\) 0 0
\(265\) 1.08495e6 0.949065
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18297.3 −0.0154172 −0.00770860 0.999970i \(-0.502454\pi\)
−0.00770860 + 0.999970i \(0.502454\pi\)
\(270\) 0 0
\(271\) 7105.09 0.00587688 0.00293844 0.999996i \(-0.499065\pi\)
0.00293844 + 0.999996i \(0.499065\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.36228e6 1.08626
\(276\) 0 0
\(277\) 710403. 0.556296 0.278148 0.960538i \(-0.410280\pi\)
0.278148 + 0.960538i \(0.410280\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.02845e6 0.776991 0.388496 0.921451i \(-0.372995\pi\)
0.388496 + 0.921451i \(0.372995\pi\)
\(282\) 0 0
\(283\) −1.84463e6 −1.36913 −0.684564 0.728953i \(-0.740007\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 206291. 0.147834
\(288\) 0 0
\(289\) 825769. 0.581586
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −940972. −0.640336 −0.320168 0.947361i \(-0.603739\pi\)
−0.320168 + 0.947361i \(0.603739\pi\)
\(294\) 0 0
\(295\) 5.19847e6 3.47793
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 803243. 0.519600
\(300\) 0 0
\(301\) −1.27418e6 −0.810615
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −920492. −0.566592
\(306\) 0 0
\(307\) −2.93094e6 −1.77485 −0.887425 0.460952i \(-0.847508\pi\)
−0.887425 + 0.460952i \(0.847508\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.28251e6 1.33817 0.669086 0.743185i \(-0.266686\pi\)
0.669086 + 0.743185i \(0.266686\pi\)
\(312\) 0 0
\(313\) 802648. 0.463089 0.231544 0.972824i \(-0.425622\pi\)
0.231544 + 0.972824i \(0.425622\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.11196e6 −0.621502 −0.310751 0.950491i \(-0.600581\pi\)
−0.310751 + 0.950491i \(0.600581\pi\)
\(318\) 0 0
\(319\) 417491. 0.229705
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.15443e6 −1.14902
\(324\) 0 0
\(325\) 5.75885e6 3.02432
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 659544. 0.335934
\(330\) 0 0
\(331\) −1.22658e6 −0.615355 −0.307678 0.951491i \(-0.599552\pi\)
−0.307678 + 0.951491i \(0.599552\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 801597. 0.390251
\(336\) 0 0
\(337\) 2.30128e6 1.10381 0.551907 0.833906i \(-0.313900\pi\)
0.551907 + 0.833906i \(0.313900\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.04748e6 −0.487818
\(342\) 0 0
\(343\) −2.36679e6 −1.08624
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.61930e6 −0.721945 −0.360973 0.932576i \(-0.617555\pi\)
−0.360973 + 0.932576i \(0.617555\pi\)
\(348\) 0 0
\(349\) −278614. −0.122445 −0.0612223 0.998124i \(-0.519500\pi\)
−0.0612223 + 0.998124i \(0.519500\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.36993e6 −1.43941 −0.719704 0.694281i \(-0.755723\pi\)
−0.719704 + 0.694281i \(0.755723\pi\)
\(354\) 0 0
\(355\) 395486. 0.166556
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −272571. −0.111621 −0.0558103 0.998441i \(-0.517774\pi\)
−0.0558103 + 0.998441i \(0.517774\pi\)
\(360\) 0 0
\(361\) −409156. −0.165242
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.41172e6 −2.51908
\(366\) 0 0
\(367\) −3.95765e6 −1.53381 −0.766906 0.641759i \(-0.778205\pi\)
−0.766906 + 0.641759i \(0.778205\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −999900. −0.377157
\(372\) 0 0
\(373\) −1.92388e6 −0.715987 −0.357994 0.933724i \(-0.616539\pi\)
−0.357994 + 0.933724i \(0.616539\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.76489e6 0.639534
\(378\) 0 0
\(379\) −3.11015e6 −1.11220 −0.556101 0.831115i \(-0.687703\pi\)
−0.556101 + 0.831115i \(0.687703\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.83421e6 0.987269 0.493634 0.869670i \(-0.335668\pi\)
0.493634 + 0.869670i \(0.335668\pi\)
\(384\) 0 0
\(385\) −1.68839e6 −0.580524
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.05383e6 0.688162 0.344081 0.938940i \(-0.388190\pi\)
0.344081 + 0.938940i \(0.388190\pi\)
\(390\) 0 0
\(391\) −1.89431e6 −0.626628
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 7.03716e6 2.26937
\(396\) 0 0
\(397\) −3.82167e6 −1.21696 −0.608480 0.793569i \(-0.708220\pi\)
−0.608480 + 0.793569i \(0.708220\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.31729e6 −1.65131 −0.825656 0.564173i \(-0.809195\pi\)
−0.825656 + 0.564173i \(0.809195\pi\)
\(402\) 0 0
\(403\) −4.42807e6 −1.35816
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.19509e6 −0.357613
\(408\) 0 0
\(409\) 3.15843e6 0.933605 0.466803 0.884362i \(-0.345406\pi\)
0.466803 + 0.884362i \(0.345406\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.79095e6 −1.38212
\(414\) 0 0
\(415\) 9.14620e6 2.60688
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.61564e6 1.00612 0.503060 0.864251i \(-0.332207\pi\)
0.503060 + 0.864251i \(0.332207\pi\)
\(420\) 0 0
\(421\) 1.02889e6 0.282920 0.141460 0.989944i \(-0.454820\pi\)
0.141460 + 0.989944i \(0.454820\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.35813e7 −3.64727
\(426\) 0 0
\(427\) 848331. 0.225162
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.21668e6 −1.61200 −0.806001 0.591914i \(-0.798372\pi\)
−0.806001 + 0.591914i \(0.798372\pi\)
\(432\) 0 0
\(433\) −598070. −0.153297 −0.0766483 0.997058i \(-0.524422\pi\)
−0.0766483 + 0.997058i \(0.524422\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.81739e6 0.455244
\(438\) 0 0
\(439\) −493097. −0.122115 −0.0610577 0.998134i \(-0.519447\pi\)
−0.0610577 + 0.998134i \(0.519447\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 195512. 0.0473329 0.0236665 0.999720i \(-0.492466\pi\)
0.0236665 + 0.999720i \(0.492466\pi\)
\(444\) 0 0
\(445\) −426308. −0.102053
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.51225e6 0.354004 0.177002 0.984210i \(-0.443360\pi\)
0.177002 + 0.984210i \(0.443360\pi\)
\(450\) 0 0
\(451\) 304763. 0.0705538
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7.13743e6 −1.61627
\(456\) 0 0
\(457\) 2.56472e6 0.574445 0.287223 0.957864i \(-0.407268\pi\)
0.287223 + 0.957864i \(0.407268\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5.36673e6 1.17613 0.588067 0.808812i \(-0.299889\pi\)
0.588067 + 0.808812i \(0.299889\pi\)
\(462\) 0 0
\(463\) 5.50215e6 1.19283 0.596417 0.802675i \(-0.296591\pi\)
0.596417 + 0.802675i \(0.296591\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −964114. −0.204567 −0.102284 0.994755i \(-0.532615\pi\)
−0.102284 + 0.994755i \(0.532615\pi\)
\(468\) 0 0
\(469\) −738757. −0.155085
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.88240e6 −0.386865
\(474\) 0 0
\(475\) 1.30298e7 2.64973
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 562534. 0.112024 0.0560118 0.998430i \(-0.482162\pi\)
0.0560118 + 0.998430i \(0.482162\pi\)
\(480\) 0 0
\(481\) −5.05207e6 −0.995650
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.64815e6 −1.47639
\(486\) 0 0
\(487\) 3.14185e6 0.600292 0.300146 0.953893i \(-0.402965\pi\)
0.300146 + 0.953893i \(0.402965\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.73361e6 −1.07331 −0.536654 0.843802i \(-0.680312\pi\)
−0.536654 + 0.843802i \(0.680312\pi\)
\(492\) 0 0
\(493\) −4.16219e6 −0.771267
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −364483. −0.0661890
\(498\) 0 0
\(499\) 1.71562e6 0.308439 0.154220 0.988037i \(-0.450714\pi\)
0.154220 + 0.988037i \(0.450714\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.15229e6 0.907989 0.453995 0.891004i \(-0.349999\pi\)
0.453995 + 0.891004i \(0.349999\pi\)
\(504\) 0 0
\(505\) −2.80919e6 −0.490176
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.04256e6 0.178364 0.0891819 0.996015i \(-0.471575\pi\)
0.0891819 + 0.996015i \(0.471575\pi\)
\(510\) 0 0
\(511\) 5.90908e6 1.00108
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 6.99796e6 1.16266
\(516\) 0 0
\(517\) 974374. 0.160324
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.52239e6 −1.53692 −0.768461 0.639897i \(-0.778977\pi\)
−0.768461 + 0.639897i \(0.778977\pi\)
\(522\) 0 0
\(523\) −2.97573e6 −0.475706 −0.237853 0.971301i \(-0.576444\pi\)
−0.237853 + 0.971301i \(0.576444\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.04429e7 1.63792
\(528\) 0 0
\(529\) −4.83838e6 −0.751728
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.28834e6 0.196433
\(534\) 0 0
\(535\) −6.75190e6 −1.01986
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −970266. −0.143853
\(540\) 0 0
\(541\) 1.80579e6 0.265261 0.132631 0.991166i \(-0.457658\pi\)
0.132631 + 0.991166i \(0.457658\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.36935e7 1.97480
\(546\) 0 0
\(547\) −9.36973e6 −1.33893 −0.669466 0.742843i \(-0.733477\pi\)
−0.669466 + 0.742843i \(0.733477\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.99317e6 0.560323
\(552\) 0 0
\(553\) −6.48550e6 −0.901842
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.53733e6 −0.483101 −0.241550 0.970388i \(-0.577656\pi\)
−0.241550 + 0.970388i \(0.577656\pi\)
\(558\) 0 0
\(559\) −7.95761e6 −1.07709
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −2.78060e6 −0.369716 −0.184858 0.982765i \(-0.559182\pi\)
−0.184858 + 0.982765i \(0.559182\pi\)
\(564\) 0 0
\(565\) 1.29650e7 1.70864
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −7.35293e6 −0.952094 −0.476047 0.879420i \(-0.657931\pi\)
−0.476047 + 0.879420i \(0.657931\pi\)
\(570\) 0 0
\(571\) −5.75171e6 −0.738255 −0.369128 0.929379i \(-0.620343\pi\)
−0.369128 + 0.929379i \(0.620343\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.14566e7 1.44506
\(576\) 0 0
\(577\) −1.30488e7 −1.63167 −0.815835 0.578285i \(-0.803722\pi\)
−0.815835 + 0.578285i \(0.803722\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −8.42920e6 −1.03597
\(582\) 0 0
\(583\) −1.47720e6 −0.179998
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.24724e6 −0.149401 −0.0747005 0.997206i \(-0.523800\pi\)
−0.0747005 + 0.997206i \(0.523800\pi\)
\(588\) 0 0
\(589\) −1.00188e7 −1.18994
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.32769e7 1.55045 0.775226 0.631684i \(-0.217636\pi\)
0.775226 + 0.631684i \(0.217636\pi\)
\(594\) 0 0
\(595\) 1.68324e7 1.94919
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.04914e6 −0.461101 −0.230551 0.973060i \(-0.574053\pi\)
−0.230551 + 0.973060i \(0.574053\pi\)
\(600\) 0 0
\(601\) −6.83714e6 −0.772126 −0.386063 0.922472i \(-0.626165\pi\)
−0.386063 + 0.922472i \(0.626165\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.52856e7 1.69783
\(606\) 0 0
\(607\) 696200. 0.0766941 0.0383471 0.999264i \(-0.487791\pi\)
0.0383471 + 0.999264i \(0.487791\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.11904e6 0.446367
\(612\) 0 0
\(613\) −1.42785e6 −0.153473 −0.0767363 0.997051i \(-0.524450\pi\)
−0.0767363 + 0.997051i \(0.524450\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.50335e7 1.58982 0.794908 0.606730i \(-0.207519\pi\)
0.794908 + 0.606730i \(0.207519\pi\)
\(618\) 0 0
\(619\) −7.16303e6 −0.751398 −0.375699 0.926742i \(-0.622597\pi\)
−0.375699 + 0.926742i \(0.622597\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 392889. 0.0405555
\(624\) 0 0
\(625\) 4.40504e7 4.51076
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.19145e7 1.20074
\(630\) 0 0
\(631\) 1.38021e7 1.37998 0.689989 0.723820i \(-0.257615\pi\)
0.689989 + 0.723820i \(0.257615\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.29416e6 0.324198
\(636\) 0 0
\(637\) −4.10167e6 −0.400509
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.04659e6 0.388995 0.194497 0.980903i \(-0.437692\pi\)
0.194497 + 0.980903i \(0.437692\pi\)
\(642\) 0 0
\(643\) 1.08876e7 1.03850 0.519249 0.854623i \(-0.326212\pi\)
0.519249 + 0.854623i \(0.326212\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.45797e6 0.794339 0.397169 0.917745i \(-0.369993\pi\)
0.397169 + 0.917745i \(0.369993\pi\)
\(648\) 0 0
\(649\) −7.07788e6 −0.659617
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.95548e6 −0.454782 −0.227391 0.973804i \(-0.573020\pi\)
−0.227391 + 0.973804i \(0.573020\pi\)
\(654\) 0 0
\(655\) −1.89950e7 −1.72996
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.67430e7 −1.50183 −0.750915 0.660398i \(-0.770387\pi\)
−0.750915 + 0.660398i \(0.770387\pi\)
\(660\) 0 0
\(661\) −1.50798e7 −1.34243 −0.671217 0.741260i \(-0.734228\pi\)
−0.671217 + 0.741260i \(0.734228\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.61489e7 −1.41608
\(666\) 0 0
\(667\) 3.51105e6 0.305578
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.25328e6 0.107459
\(672\) 0 0
\(673\) 1.41419e7 1.20357 0.601784 0.798659i \(-0.294457\pi\)
0.601784 + 0.798659i \(0.294457\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.45879e7 −1.22327 −0.611635 0.791140i \(-0.709488\pi\)
−0.611635 + 0.791140i \(0.709488\pi\)
\(678\) 0 0
\(679\) 7.04859e6 0.586715
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.10096e7 0.903065 0.451532 0.892255i \(-0.350878\pi\)
0.451532 + 0.892255i \(0.350878\pi\)
\(684\) 0 0
\(685\) 2.10158e7 1.71127
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.24465e6 −0.501141
\(690\) 0 0
\(691\) 1.10359e7 0.879247 0.439623 0.898182i \(-0.355112\pi\)
0.439623 + 0.898182i \(0.355112\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.72116e7 2.92224
\(696\) 0 0
\(697\) −3.03834e6 −0.236894
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.51294e7 1.93146 0.965732 0.259542i \(-0.0835717\pi\)
0.965732 + 0.259542i \(0.0835717\pi\)
\(702\) 0 0
\(703\) −1.14306e7 −0.872332
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.58896e6 0.194795
\(708\) 0 0
\(709\) 1.25301e7 0.936137 0.468068 0.883692i \(-0.344950\pi\)
0.468068 + 0.883692i \(0.344950\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.80915e6 −0.648948
\(714\) 0 0
\(715\) −1.05444e7 −0.771362
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.72246e6 0.124258 0.0621292 0.998068i \(-0.480211\pi\)
0.0621292 + 0.998068i \(0.480211\pi\)
\(720\) 0 0
\(721\) −6.44937e6 −0.462040
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.51724e7 1.77861
\(726\) 0 0
\(727\) 6.98849e6 0.490397 0.245198 0.969473i \(-0.421147\pi\)
0.245198 + 0.969473i \(0.421147\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.87667e7 1.29896
\(732\) 0 0
\(733\) −5.92609e6 −0.407388 −0.203694 0.979035i \(-0.565295\pi\)
−0.203694 + 0.979035i \(0.565295\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.09140e6 −0.0740142
\(738\) 0 0
\(739\) −1.06632e7 −0.718254 −0.359127 0.933289i \(-0.616925\pi\)
−0.359127 + 0.933289i \(0.616925\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.84986e7 1.22933 0.614664 0.788789i \(-0.289292\pi\)
0.614664 + 0.788789i \(0.289292\pi\)
\(744\) 0 0
\(745\) −6.08286e6 −0.401529
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 6.22259e6 0.405291
\(750\) 0 0
\(751\) −2.61247e7 −1.69025 −0.845127 0.534566i \(-0.820475\pi\)
−0.845127 + 0.534566i \(0.820475\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.68804e7 −2.35466
\(756\) 0 0
\(757\) 2.49174e7 1.58039 0.790193 0.612858i \(-0.209980\pi\)
0.790193 + 0.612858i \(0.209980\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.12439e7 −0.703808 −0.351904 0.936036i \(-0.614466\pi\)
−0.351904 + 0.936036i \(0.614466\pi\)
\(762\) 0 0
\(763\) −1.26200e7 −0.784781
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.99208e7 −1.83647
\(768\) 0 0
\(769\) 8.67461e6 0.528974 0.264487 0.964389i \(-0.414797\pi\)
0.264487 + 0.964389i \(0.414797\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.17066e7 −1.30660 −0.653300 0.757099i \(-0.726616\pi\)
−0.653300 + 0.757099i \(0.726616\pi\)
\(774\) 0 0
\(775\) −6.31571e7 −3.77718
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.91496e6 0.172103
\(780\) 0 0
\(781\) −538467. −0.0315887
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.32597e7 0.767997
\(786\) 0 0
\(787\) 7.86429e6 0.452609 0.226304 0.974057i \(-0.427336\pi\)
0.226304 + 0.974057i \(0.427336\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.19486e7 −0.679009
\(792\) 0 0
\(793\) 5.29807e6 0.299181
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.89618e7 −1.05739 −0.528693 0.848813i \(-0.677318\pi\)
−0.528693 + 0.848813i \(0.677318\pi\)
\(798\) 0 0
\(799\) −9.71406e6 −0.538312
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.72975e6 0.477764
\(804\) 0 0
\(805\) −1.41991e7 −0.772274
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 2.09408e7 1.12492 0.562459 0.826825i \(-0.309855\pi\)
0.562459 + 0.826825i \(0.309855\pi\)
\(810\) 0 0
\(811\) 3.21466e7 1.71626 0.858130 0.513432i \(-0.171626\pi\)
0.858130 + 0.513432i \(0.171626\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −4.05257e7 −2.13716
\(816\) 0 0
\(817\) −1.80046e7 −0.943687
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.97605e7 1.54093 0.770463 0.637485i \(-0.220025\pi\)
0.770463 + 0.637485i \(0.220025\pi\)
\(822\) 0 0
\(823\) −1.65220e7 −0.850284 −0.425142 0.905127i \(-0.639776\pi\)
−0.425142 + 0.905127i \(0.639776\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.49588e7 −1.26900 −0.634498 0.772925i \(-0.718793\pi\)
−0.634498 + 0.772925i \(0.718793\pi\)
\(828\) 0 0
\(829\) −2.92909e7 −1.48029 −0.740145 0.672447i \(-0.765243\pi\)
−0.740145 + 0.672447i \(0.765243\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 9.67311e6 0.483007
\(834\) 0 0
\(835\) 6.50747e7 3.22995
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −3.74835e7 −1.83838 −0.919189 0.393817i \(-0.871155\pi\)
−0.919189 + 0.393817i \(0.871155\pi\)
\(840\) 0 0
\(841\) −1.27967e7 −0.623888
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.58473e6 −0.172709
\(846\) 0 0
\(847\) −1.40873e7 −0.674713
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.00505e7 −0.475735
\(852\) 0 0
\(853\) 1.48271e7 0.697726 0.348863 0.937174i \(-0.386568\pi\)
0.348863 + 0.937174i \(0.386568\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −5.32370e6 −0.247606 −0.123803 0.992307i \(-0.539509\pi\)
−0.123803 + 0.992307i \(0.539509\pi\)
\(858\) 0 0
\(859\) 2.68868e7 1.24324 0.621621 0.783318i \(-0.286474\pi\)
0.621621 + 0.783318i \(0.286474\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 2.21441e6 0.101212 0.0506060 0.998719i \(-0.483885\pi\)
0.0506060 + 0.998719i \(0.483885\pi\)
\(864\) 0 0
\(865\) 4.81846e7 2.18961
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −9.58131e6 −0.430403
\(870\) 0 0
\(871\) −4.61374e6 −0.206067
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6.66988e7 −2.94509
\(876\) 0 0
\(877\) 3.24646e7 1.42531 0.712657 0.701513i \(-0.247492\pi\)
0.712657 + 0.701513i \(0.247492\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −7.78418e6 −0.337888 −0.168944 0.985626i \(-0.554036\pi\)
−0.168944 + 0.985626i \(0.554036\pi\)
\(882\) 0 0
\(883\) 1.71890e7 0.741906 0.370953 0.928652i \(-0.379031\pi\)
0.370953 + 0.928652i \(0.379031\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 3.63433e7 1.55101 0.775506 0.631340i \(-0.217495\pi\)
0.775506 + 0.631340i \(0.217495\pi\)
\(888\) 0 0
\(889\) −3.03592e6 −0.128836
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 9.31958e6 0.391082
\(894\) 0 0
\(895\) 2.66133e7 1.11056
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.93555e7 −0.798739
\(900\) 0 0
\(901\) 1.47270e7 0.604368
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.99500e6 −0.121556
\(906\) 0 0
\(907\) −8.78418e6 −0.354555 −0.177277 0.984161i \(-0.556729\pi\)
−0.177277 + 0.984161i \(0.556729\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.67006e6 0.146513 0.0732566 0.997313i \(-0.476661\pi\)
0.0732566 + 0.997313i \(0.476661\pi\)
\(912\) 0 0
\(913\) −1.24528e7 −0.494414
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.75060e7 0.687484
\(918\) 0 0
\(919\) 3.38118e7 1.32063 0.660313 0.750990i \(-0.270424\pi\)
0.660313 + 0.750990i \(0.270424\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.27630e6 −0.0879477
\(924\) 0 0
\(925\) −7.20572e7 −2.76900
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1.17835e7 0.447954 0.223977 0.974594i \(-0.428096\pi\)
0.223977 + 0.974594i \(0.428096\pi\)
\(930\) 0 0
\(931\) −9.28029e6 −0.350903
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.48673e7 0.930250
\(936\) 0 0
\(937\) −3.78550e7 −1.40856 −0.704278 0.709924i \(-0.748729\pi\)
−0.704278 + 0.709924i \(0.748729\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.56271e7 −1.67977 −0.839884 0.542766i \(-0.817377\pi\)
−0.839884 + 0.542766i \(0.817377\pi\)
\(942\) 0 0
\(943\) 2.56302e6 0.0938582
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.15884e7 −1.50694 −0.753472 0.657480i \(-0.771622\pi\)
−0.753472 + 0.657480i \(0.771622\pi\)
\(948\) 0 0
\(949\) 3.69039e7 1.33017
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 5.40042e7 1.92617 0.963087 0.269190i \(-0.0867560\pi\)
0.963087 + 0.269190i \(0.0867560\pi\)
\(954\) 0 0
\(955\) −6.19036e6 −0.219638
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.93683e7 −0.680055
\(960\) 0 0
\(961\) 1.99334e7 0.696261
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3.91347e7 −1.35283
\(966\) 0 0
\(967\) 1.72935e7 0.594724 0.297362 0.954765i \(-0.403893\pi\)
0.297362 + 0.954765i \(0.403893\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.55169e7 −1.54926 −0.774630 0.632415i \(-0.782064\pi\)
−0.774630 + 0.632415i \(0.782064\pi\)
\(972\) 0 0
\(973\) −3.42944e7 −1.16129
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.59652e6 −0.221095 −0.110547 0.993871i \(-0.535260\pi\)
−0.110547 + 0.993871i \(0.535260\pi\)
\(978\) 0 0
\(979\) 580432. 0.0193551
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 3.69457e7 1.21950 0.609748 0.792595i \(-0.291271\pi\)
0.609748 + 0.792595i \(0.291271\pi\)
\(984\) 0 0
\(985\) −9.01846e7 −2.96171
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.58308e7 −0.514649
\(990\) 0 0
\(991\) −7.56015e6 −0.244538 −0.122269 0.992497i \(-0.539017\pi\)
−0.122269 + 0.992497i \(0.539017\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −9.49870e7 −3.04163
\(996\) 0 0
\(997\) −1.56153e7 −0.497521 −0.248761 0.968565i \(-0.580023\pi\)
−0.248761 + 0.968565i \(0.580023\pi\)
\(998\) 0 0
\(999\) 0 0
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 324.6.a.d.1.1 5
3.2 odd 2 324.6.a.e.1.5 5
9.2 odd 6 36.6.e.a.13.5 10
9.4 even 3 108.6.e.a.73.5 10
9.5 odd 6 36.6.e.a.25.5 yes 10
9.7 even 3 108.6.e.a.37.5 10
36.7 odd 6 432.6.i.d.145.5 10
36.11 even 6 144.6.i.d.49.1 10
36.23 even 6 144.6.i.d.97.1 10
36.31 odd 6 432.6.i.d.289.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.6.e.a.13.5 10 9.2 odd 6
36.6.e.a.25.5 yes 10 9.5 odd 6
108.6.e.a.37.5 10 9.7 even 3
108.6.e.a.73.5 10 9.4 even 3
144.6.i.d.49.1 10 36.11 even 6
144.6.i.d.97.1 10 36.23 even 6
324.6.a.d.1.1 5 1.1 even 1 trivial
324.6.a.e.1.5 5 3.2 odd 2
432.6.i.d.145.5 10 36.7 odd 6
432.6.i.d.289.5 10 36.31 odd 6