Properties

Label 320.6.a.v.1.1
Level 320
Weight 6
Character 320.1
Self dual yes
Analytic conductor 51.323
Analytic rank 1
Dimension 2
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 320.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.3228223402\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{70}) \)
Defining polynomial: \(x^{2} - 70\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 160)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-8.36660\) of defining polynomial
Character \(\chi\) \(=\) 320.1

$q$-expansion

\(f(q)\) \(=\) \(q-12.7332 q^{3} -25.0000 q^{5} -68.7332 q^{7} -80.8656 q^{9} +O(q^{10})\) \(q-12.7332 q^{3} -25.0000 q^{5} -68.7332 q^{7} -80.8656 q^{9} +327.332 q^{11} +719.328 q^{13} +318.330 q^{15} -379.328 q^{17} +1029.33 q^{19} +875.194 q^{21} +779.120 q^{23} +625.000 q^{25} +4123.85 q^{27} -1392.66 q^{29} -2744.68 q^{31} -4167.98 q^{33} +1718.33 q^{35} -12640.6 q^{37} -9159.35 q^{39} +8210.43 q^{41} +22524.5 q^{43} +2021.64 q^{45} -7739.18 q^{47} -12082.7 q^{49} +4830.06 q^{51} +2401.86 q^{53} -8183.30 q^{55} -13106.6 q^{57} +15734.7 q^{59} -32082.1 q^{61} +5558.15 q^{63} -17983.2 q^{65} +9009.07 q^{67} -9920.70 q^{69} -43832.3 q^{71} -65837.5 q^{73} -7958.25 q^{75} -22498.6 q^{77} -39601.3 q^{79} -32859.4 q^{81} -63101.4 q^{83} +9483.20 q^{85} +17733.0 q^{87} +34510.9 q^{89} -49441.7 q^{91} +34948.6 q^{93} -25733.2 q^{95} -14081.3 q^{97} -26469.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 8q^{3} - 50q^{5} - 104q^{7} + 106q^{9} + O(q^{10}) \) \( 2q + 8q^{3} - 50q^{5} - 104q^{7} + 106q^{9} + 320q^{11} + 100q^{13} - 200q^{15} + 580q^{17} + 720q^{19} + 144q^{21} - 1688q^{23} + 1250q^{25} + 2960q^{27} - 108q^{29} - 9840q^{31} - 4320q^{33} + 2600q^{35} - 6540q^{37} - 22000q^{39} - 10620q^{41} + 25672q^{43} - 2650q^{45} - 28296q^{47} - 27646q^{49} + 24720q^{51} - 31340q^{53} - 8000q^{55} - 19520q^{57} + 30800q^{59} - 24540q^{61} - 1032q^{63} - 2500q^{65} + 34584q^{67} - 61072q^{69} + 12400q^{71} - 7180q^{73} + 5000q^{75} - 22240q^{77} - 71840q^{79} - 102398q^{81} - 31928q^{83} - 14500q^{85} + 44368q^{87} - 40748q^{89} - 27600q^{91} - 112160q^{93} - 18000q^{95} - 190140q^{97} - 27840q^{99} + O(q^{100}) \)

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
\(3\) −12.7332 −0.816835 −0.408418 0.912795i \(-0.633919\pi\)
−0.408418 + 0.912795i \(0.633919\pi\)
\(4\) 0 0
\(5\) −25.0000 −0.447214
\(6\) 0 0
\(7\) −68.7332 −0.530178 −0.265089 0.964224i \(-0.585401\pi\)
−0.265089 + 0.964224i \(0.585401\pi\)
\(8\) 0 0
\(9\) −80.8656 −0.332780
\(10\) 0 0
\(11\) 327.332 0.815655 0.407828 0.913059i \(-0.366286\pi\)
0.407828 + 0.913059i \(0.366286\pi\)
\(12\) 0 0
\(13\) 719.328 1.18051 0.590254 0.807218i \(-0.299028\pi\)
0.590254 + 0.807218i \(0.299028\pi\)
\(14\) 0 0
\(15\) 318.330 0.365300
\(16\) 0 0
\(17\) −379.328 −0.318341 −0.159171 0.987251i \(-0.550882\pi\)
−0.159171 + 0.987251i \(0.550882\pi\)
\(18\) 0 0
\(19\) 1029.33 0.654139 0.327069 0.945000i \(-0.393939\pi\)
0.327069 + 0.945000i \(0.393939\pi\)
\(20\) 0 0
\(21\) 875.194 0.433068
\(22\) 0 0
\(23\) 779.120 0.307104 0.153552 0.988141i \(-0.450929\pi\)
0.153552 + 0.988141i \(0.450929\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 4123.85 1.08866
\(28\) 0 0
\(29\) −1392.66 −0.307503 −0.153751 0.988110i \(-0.549135\pi\)
−0.153751 + 0.988110i \(0.549135\pi\)
\(30\) 0 0
\(31\) −2744.68 −0.512965 −0.256483 0.966549i \(-0.582564\pi\)
−0.256483 + 0.966549i \(0.582564\pi\)
\(32\) 0 0
\(33\) −4167.98 −0.666256
\(34\) 0 0
\(35\) 1718.33 0.237103
\(36\) 0 0
\(37\) −12640.6 −1.51797 −0.758985 0.651108i \(-0.774304\pi\)
−0.758985 + 0.651108i \(0.774304\pi\)
\(38\) 0 0
\(39\) −9159.35 −0.964280
\(40\) 0 0
\(41\) 8210.43 0.762792 0.381396 0.924412i \(-0.375443\pi\)
0.381396 + 0.924412i \(0.375443\pi\)
\(42\) 0 0
\(43\) 22524.5 1.85774 0.928869 0.370408i \(-0.120782\pi\)
0.928869 + 0.370408i \(0.120782\pi\)
\(44\) 0 0
\(45\) 2021.64 0.148824
\(46\) 0 0
\(47\) −7739.18 −0.511035 −0.255517 0.966804i \(-0.582246\pi\)
−0.255517 + 0.966804i \(0.582246\pi\)
\(48\) 0 0
\(49\) −12082.7 −0.718912
\(50\) 0 0
\(51\) 4830.06 0.260032
\(52\) 0 0
\(53\) 2401.86 0.117451 0.0587256 0.998274i \(-0.481296\pi\)
0.0587256 + 0.998274i \(0.481296\pi\)
\(54\) 0 0
\(55\) −8183.30 −0.364772
\(56\) 0 0
\(57\) −13106.6 −0.534323
\(58\) 0 0
\(59\) 15734.7 0.588474 0.294237 0.955732i \(-0.404934\pi\)
0.294237 + 0.955732i \(0.404934\pi\)
\(60\) 0 0
\(61\) −32082.1 −1.10392 −0.551961 0.833870i \(-0.686120\pi\)
−0.551961 + 0.833870i \(0.686120\pi\)
\(62\) 0 0
\(63\) 5558.15 0.176433
\(64\) 0 0
\(65\) −17983.2 −0.527939
\(66\) 0 0
\(67\) 9009.07 0.245184 0.122592 0.992457i \(-0.460879\pi\)
0.122592 + 0.992457i \(0.460879\pi\)
\(68\) 0 0
\(69\) −9920.70 −0.250853
\(70\) 0 0
\(71\) −43832.3 −1.03192 −0.515962 0.856611i \(-0.672566\pi\)
−0.515962 + 0.856611i \(0.672566\pi\)
\(72\) 0 0
\(73\) −65837.5 −1.44599 −0.722997 0.690852i \(-0.757236\pi\)
−0.722997 + 0.690852i \(0.757236\pi\)
\(74\) 0 0
\(75\) −7958.25 −0.163367
\(76\) 0 0
\(77\) −22498.6 −0.432442
\(78\) 0 0
\(79\) −39601.3 −0.713907 −0.356954 0.934122i \(-0.616185\pi\)
−0.356954 + 0.934122i \(0.616185\pi\)
\(80\) 0 0
\(81\) −32859.4 −0.556477
\(82\) 0 0
\(83\) −63101.4 −1.00541 −0.502706 0.864458i \(-0.667662\pi\)
−0.502706 + 0.864458i \(0.667662\pi\)
\(84\) 0 0
\(85\) 9483.20 0.142366
\(86\) 0 0
\(87\) 17733.0 0.251179
\(88\) 0 0
\(89\) 34510.9 0.461829 0.230915 0.972974i \(-0.425828\pi\)
0.230915 + 0.972974i \(0.425828\pi\)
\(90\) 0 0
\(91\) −49441.7 −0.625879
\(92\) 0 0
\(93\) 34948.6 0.419008
\(94\) 0 0
\(95\) −25733.2 −0.292540
\(96\) 0 0
\(97\) −14081.3 −0.151955 −0.0759773 0.997110i \(-0.524208\pi\)
−0.0759773 + 0.997110i \(0.524208\pi\)
\(98\) 0 0
\(99\) −26469.9 −0.271434
\(100\) 0 0
\(101\) −184018. −1.79497 −0.897485 0.441044i \(-0.854608\pi\)
−0.897485 + 0.441044i \(0.854608\pi\)
\(102\) 0 0
\(103\) 70168.0 0.651697 0.325849 0.945422i \(-0.394350\pi\)
0.325849 + 0.945422i \(0.394350\pi\)
\(104\) 0 0
\(105\) −21879.8 −0.193674
\(106\) 0 0
\(107\) 7952.89 0.0671530 0.0335765 0.999436i \(-0.489310\pi\)
0.0335765 + 0.999436i \(0.489310\pi\)
\(108\) 0 0
\(109\) −168681. −1.35988 −0.679939 0.733269i \(-0.737994\pi\)
−0.679939 + 0.733269i \(0.737994\pi\)
\(110\) 0 0
\(111\) 160955. 1.23993
\(112\) 0 0
\(113\) −61891.3 −0.455967 −0.227984 0.973665i \(-0.573213\pi\)
−0.227984 + 0.973665i \(0.573213\pi\)
\(114\) 0 0
\(115\) −19478.0 −0.137341
\(116\) 0 0
\(117\) −58168.9 −0.392849
\(118\) 0 0
\(119\) 26072.4 0.168777
\(120\) 0 0
\(121\) −53904.8 −0.334706
\(122\) 0 0
\(123\) −104545. −0.623075
\(124\) 0 0
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 358695. 1.97340 0.986702 0.162538i \(-0.0519681\pi\)
0.986702 + 0.162538i \(0.0519681\pi\)
\(128\) 0 0
\(129\) −286809. −1.51747
\(130\) 0 0
\(131\) −312592. −1.59148 −0.795738 0.605641i \(-0.792917\pi\)
−0.795738 + 0.605641i \(0.792917\pi\)
\(132\) 0 0
\(133\) −70749.0 −0.346810
\(134\) 0 0
\(135\) −103096. −0.486864
\(136\) 0 0
\(137\) −33573.9 −0.152827 −0.0764135 0.997076i \(-0.524347\pi\)
−0.0764135 + 0.997076i \(0.524347\pi\)
\(138\) 0 0
\(139\) 342175. 1.50214 0.751072 0.660220i \(-0.229537\pi\)
0.751072 + 0.660220i \(0.229537\pi\)
\(140\) 0 0
\(141\) 98544.6 0.417431
\(142\) 0 0
\(143\) 235459. 0.962887
\(144\) 0 0
\(145\) 34816.4 0.137519
\(146\) 0 0
\(147\) 153852. 0.587232
\(148\) 0 0
\(149\) 239318. 0.883099 0.441549 0.897237i \(-0.354429\pi\)
0.441549 + 0.897237i \(0.354429\pi\)
\(150\) 0 0
\(151\) −169513. −0.605007 −0.302503 0.953148i \(-0.597822\pi\)
−0.302503 + 0.953148i \(0.597822\pi\)
\(152\) 0 0
\(153\) 30674.6 0.105938
\(154\) 0 0
\(155\) 68617.1 0.229405
\(156\) 0 0
\(157\) −186382. −0.603469 −0.301735 0.953392i \(-0.597566\pi\)
−0.301735 + 0.953392i \(0.597566\pi\)
\(158\) 0 0
\(159\) −30583.3 −0.0959383
\(160\) 0 0
\(161\) −53551.4 −0.162820
\(162\) 0 0
\(163\) −403058. −1.18822 −0.594112 0.804382i \(-0.702496\pi\)
−0.594112 + 0.804382i \(0.702496\pi\)
\(164\) 0 0
\(165\) 104200. 0.297959
\(166\) 0 0
\(167\) −167631. −0.465119 −0.232560 0.972582i \(-0.574710\pi\)
−0.232560 + 0.972582i \(0.574710\pi\)
\(168\) 0 0
\(169\) 146140. 0.393597
\(170\) 0 0
\(171\) −83237.2 −0.217684
\(172\) 0 0
\(173\) −84080.4 −0.213589 −0.106795 0.994281i \(-0.534059\pi\)
−0.106795 + 0.994281i \(0.534059\pi\)
\(174\) 0 0
\(175\) −42958.3 −0.106036
\(176\) 0 0
\(177\) −200353. −0.480686
\(178\) 0 0
\(179\) 741698. 1.73019 0.865096 0.501607i \(-0.167257\pi\)
0.865096 + 0.501607i \(0.167257\pi\)
\(180\) 0 0
\(181\) 343670. 0.779732 0.389866 0.920872i \(-0.372521\pi\)
0.389866 + 0.920872i \(0.372521\pi\)
\(182\) 0 0
\(183\) 408508. 0.901722
\(184\) 0 0
\(185\) 316015. 0.678857
\(186\) 0 0
\(187\) −124166. −0.259657
\(188\) 0 0
\(189\) −283445. −0.577184
\(190\) 0 0
\(191\) −631035. −1.25161 −0.625806 0.779978i \(-0.715230\pi\)
−0.625806 + 0.779978i \(0.715230\pi\)
\(192\) 0 0
\(193\) 847791. 1.63831 0.819154 0.573574i \(-0.194444\pi\)
0.819154 + 0.573574i \(0.194444\pi\)
\(194\) 0 0
\(195\) 228984. 0.431239
\(196\) 0 0
\(197\) 397282. 0.729346 0.364673 0.931136i \(-0.381181\pi\)
0.364673 + 0.931136i \(0.381181\pi\)
\(198\) 0 0
\(199\) −896038. −1.60396 −0.801980 0.597350i \(-0.796220\pi\)
−0.801980 + 0.597350i \(0.796220\pi\)
\(200\) 0 0
\(201\) −114714. −0.200275
\(202\) 0 0
\(203\) 95721.7 0.163031
\(204\) 0 0
\(205\) −205261. −0.341131
\(206\) 0 0
\(207\) −63004.0 −0.102198
\(208\) 0 0
\(209\) 336932. 0.533552
\(210\) 0 0
\(211\) −876761. −1.35574 −0.677868 0.735184i \(-0.737096\pi\)
−0.677868 + 0.735184i \(0.737096\pi\)
\(212\) 0 0
\(213\) 558125. 0.842913
\(214\) 0 0
\(215\) −563113. −0.830806
\(216\) 0 0
\(217\) 188651. 0.271963
\(218\) 0 0
\(219\) 838322. 1.18114
\(220\) 0 0
\(221\) −272861. −0.375804
\(222\) 0 0
\(223\) −54891.1 −0.0739162 −0.0369581 0.999317i \(-0.511767\pi\)
−0.0369581 + 0.999317i \(0.511767\pi\)
\(224\) 0 0
\(225\) −50541.0 −0.0665561
\(226\) 0 0
\(227\) 803329. 1.03473 0.517367 0.855764i \(-0.326912\pi\)
0.517367 + 0.855764i \(0.326912\pi\)
\(228\) 0 0
\(229\) 589546. 0.742898 0.371449 0.928453i \(-0.378861\pi\)
0.371449 + 0.928453i \(0.378861\pi\)
\(230\) 0 0
\(231\) 286479. 0.353234
\(232\) 0 0
\(233\) 1.02048e6 1.23144 0.615720 0.787965i \(-0.288865\pi\)
0.615720 + 0.787965i \(0.288865\pi\)
\(234\) 0 0
\(235\) 193480. 0.228542
\(236\) 0 0
\(237\) 504251. 0.583145
\(238\) 0 0
\(239\) −1.65512e6 −1.87428 −0.937139 0.348956i \(-0.886536\pi\)
−0.937139 + 0.348956i \(0.886536\pi\)
\(240\) 0 0
\(241\) −1.19028e6 −1.32010 −0.660049 0.751223i \(-0.729464\pi\)
−0.660049 + 0.751223i \(0.729464\pi\)
\(242\) 0 0
\(243\) −583689. −0.634112
\(244\) 0 0
\(245\) 302069. 0.321507
\(246\) 0 0
\(247\) 740424. 0.772215
\(248\) 0 0
\(249\) 803483. 0.821256
\(250\) 0 0
\(251\) −23776.0 −0.0238207 −0.0119104 0.999929i \(-0.503791\pi\)
−0.0119104 + 0.999929i \(0.503791\pi\)
\(252\) 0 0
\(253\) 255031. 0.250491
\(254\) 0 0
\(255\) −120751. −0.116290
\(256\) 0 0
\(257\) −341681. −0.322692 −0.161346 0.986898i \(-0.551584\pi\)
−0.161346 + 0.986898i \(0.551584\pi\)
\(258\) 0 0
\(259\) 868828. 0.804794
\(260\) 0 0
\(261\) 112618. 0.102331
\(262\) 0 0
\(263\) 1.09120e6 0.972782 0.486391 0.873741i \(-0.338313\pi\)
0.486391 + 0.873741i \(0.338313\pi\)
\(264\) 0 0
\(265\) −60046.4 −0.0525258
\(266\) 0 0
\(267\) −439434. −0.377238
\(268\) 0 0
\(269\) 922907. 0.777638 0.388819 0.921314i \(-0.372883\pi\)
0.388819 + 0.921314i \(0.372883\pi\)
\(270\) 0 0
\(271\) 1.34302e6 1.11086 0.555430 0.831564i \(-0.312554\pi\)
0.555430 + 0.831564i \(0.312554\pi\)
\(272\) 0 0
\(273\) 629551. 0.511240
\(274\) 0 0
\(275\) 204583. 0.163131
\(276\) 0 0
\(277\) 247543. 0.193843 0.0969217 0.995292i \(-0.469100\pi\)
0.0969217 + 0.995292i \(0.469100\pi\)
\(278\) 0 0
\(279\) 221951. 0.170705
\(280\) 0 0
\(281\) 1.03588e6 0.782604 0.391302 0.920262i \(-0.372025\pi\)
0.391302 + 0.920262i \(0.372025\pi\)
\(282\) 0 0
\(283\) −2.39427e6 −1.77708 −0.888542 0.458795i \(-0.848281\pi\)
−0.888542 + 0.458795i \(0.848281\pi\)
\(284\) 0 0
\(285\) 327666. 0.238957
\(286\) 0 0
\(287\) −564329. −0.404415
\(288\) 0 0
\(289\) −1.27597e6 −0.898659
\(290\) 0 0
\(291\) 179300. 0.124122
\(292\) 0 0
\(293\) 2.44817e6 1.66599 0.832995 0.553280i \(-0.186624\pi\)
0.832995 + 0.553280i \(0.186624\pi\)
\(294\) 0 0
\(295\) −393367. −0.263174
\(296\) 0 0
\(297\) 1.34987e6 0.887973
\(298\) 0 0
\(299\) 560443. 0.362538
\(300\) 0 0
\(301\) −1.54818e6 −0.984931
\(302\) 0 0
\(303\) 2.34314e6 1.46620
\(304\) 0 0
\(305\) 802053. 0.493689
\(306\) 0 0
\(307\) −939476. −0.568905 −0.284453 0.958690i \(-0.591812\pi\)
−0.284453 + 0.958690i \(0.591812\pi\)
\(308\) 0 0
\(309\) −893463. −0.532329
\(310\) 0 0
\(311\) 1.13941e6 0.668004 0.334002 0.942572i \(-0.391601\pi\)
0.334002 + 0.942572i \(0.391601\pi\)
\(312\) 0 0
\(313\) 1.51692e6 0.875191 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(314\) 0 0
\(315\) −138954. −0.0789031
\(316\) 0 0
\(317\) −2.73484e6 −1.52857 −0.764284 0.644880i \(-0.776907\pi\)
−0.764284 + 0.644880i \(0.776907\pi\)
\(318\) 0 0
\(319\) −455861. −0.250816
\(320\) 0 0
\(321\) −101266. −0.0548530
\(322\) 0 0
\(323\) −390453. −0.208239
\(324\) 0 0
\(325\) 449580. 0.236101
\(326\) 0 0
\(327\) 2.14785e6 1.11080
\(328\) 0 0
\(329\) 531939. 0.270939
\(330\) 0 0
\(331\) 122807. 0.0616104 0.0308052 0.999525i \(-0.490193\pi\)
0.0308052 + 0.999525i \(0.490193\pi\)
\(332\) 0 0
\(333\) 1.02219e6 0.505150
\(334\) 0 0
\(335\) −225227. −0.109650
\(336\) 0 0
\(337\) −1.65582e6 −0.794217 −0.397108 0.917772i \(-0.629986\pi\)
−0.397108 + 0.917772i \(0.629986\pi\)
\(338\) 0 0
\(339\) 788075. 0.372450
\(340\) 0 0
\(341\) −898423. −0.418403
\(342\) 0 0
\(343\) 1.98568e6 0.911329
\(344\) 0 0
\(345\) 248017. 0.112185
\(346\) 0 0
\(347\) −1.63896e6 −0.730711 −0.365355 0.930868i \(-0.619052\pi\)
−0.365355 + 0.930868i \(0.619052\pi\)
\(348\) 0 0
\(349\) −2.07756e6 −0.913040 −0.456520 0.889713i \(-0.650904\pi\)
−0.456520 + 0.889713i \(0.650904\pi\)
\(350\) 0 0
\(351\) 2.96640e6 1.28517
\(352\) 0 0
\(353\) −3.87344e6 −1.65447 −0.827236 0.561854i \(-0.810088\pi\)
−0.827236 + 0.561854i \(0.810088\pi\)
\(354\) 0 0
\(355\) 1.09581e6 0.461491
\(356\) 0 0
\(357\) −331985. −0.137863
\(358\) 0 0
\(359\) −3.16016e6 −1.29411 −0.647057 0.762441i \(-0.724001\pi\)
−0.647057 + 0.762441i \(0.724001\pi\)
\(360\) 0 0
\(361\) −1.41658e6 −0.572103
\(362\) 0 0
\(363\) 686380. 0.273400
\(364\) 0 0
\(365\) 1.64594e6 0.646668
\(366\) 0 0
\(367\) −1.76875e6 −0.685491 −0.342745 0.939428i \(-0.611357\pi\)
−0.342745 + 0.939428i \(0.611357\pi\)
\(368\) 0 0
\(369\) −663941. −0.253842
\(370\) 0 0
\(371\) −165087. −0.0622700
\(372\) 0 0
\(373\) 3.86744e6 1.43930 0.719651 0.694336i \(-0.244302\pi\)
0.719651 + 0.694336i \(0.244302\pi\)
\(374\) 0 0
\(375\) 198956. 0.0730600
\(376\) 0 0
\(377\) −1.00178e6 −0.363009
\(378\) 0 0
\(379\) −5.06193e6 −1.81016 −0.905082 0.425236i \(-0.860191\pi\)
−0.905082 + 0.425236i \(0.860191\pi\)
\(380\) 0 0
\(381\) −4.56734e6 −1.61195
\(382\) 0 0
\(383\) −4.23524e6 −1.47530 −0.737652 0.675181i \(-0.764065\pi\)
−0.737652 + 0.675181i \(0.764065\pi\)
\(384\) 0 0
\(385\) 562464. 0.193394
\(386\) 0 0
\(387\) −1.82146e6 −0.618219
\(388\) 0 0
\(389\) 390940. 0.130989 0.0654947 0.997853i \(-0.479137\pi\)
0.0654947 + 0.997853i \(0.479137\pi\)
\(390\) 0 0
\(391\) −295542. −0.0977637
\(392\) 0 0
\(393\) 3.98030e6 1.29997
\(394\) 0 0
\(395\) 990033. 0.319269
\(396\) 0 0
\(397\) −3.36908e6 −1.07284 −0.536421 0.843951i \(-0.680224\pi\)
−0.536421 + 0.843951i \(0.680224\pi\)
\(398\) 0 0
\(399\) 900861. 0.283286
\(400\) 0 0
\(401\) −5.51542e6 −1.71284 −0.856422 0.516277i \(-0.827318\pi\)
−0.856422 + 0.516277i \(0.827318\pi\)
\(402\) 0 0
\(403\) −1.97433e6 −0.605559
\(404\) 0 0
\(405\) 821485. 0.248864
\(406\) 0 0
\(407\) −4.13767e6 −1.23814
\(408\) 0 0
\(409\) −3.29662e6 −0.974453 −0.487227 0.873276i \(-0.661991\pi\)
−0.487227 + 0.873276i \(0.661991\pi\)
\(410\) 0 0
\(411\) 427503. 0.124834
\(412\) 0 0
\(413\) −1.08149e6 −0.311996
\(414\) 0 0
\(415\) 1.57754e6 0.449634
\(416\) 0 0
\(417\) −4.35699e6 −1.22700
\(418\) 0 0
\(419\) 6.88088e6 1.91474 0.957368 0.288870i \(-0.0932795\pi\)
0.957368 + 0.288870i \(0.0932795\pi\)
\(420\) 0 0
\(421\) −3.04971e6 −0.838596 −0.419298 0.907849i \(-0.637724\pi\)
−0.419298 + 0.907849i \(0.637724\pi\)
\(422\) 0 0
\(423\) 625834. 0.170062
\(424\) 0 0
\(425\) −237080. −0.0636682
\(426\) 0 0
\(427\) 2.20511e6 0.585275
\(428\) 0 0
\(429\) −2.99815e6 −0.786520
\(430\) 0 0
\(431\) −6.20632e6 −1.60931 −0.804657 0.593740i \(-0.797651\pi\)
−0.804657 + 0.593740i \(0.797651\pi\)
\(432\) 0 0
\(433\) 1.87723e6 0.481169 0.240585 0.970628i \(-0.422661\pi\)
0.240585 + 0.970628i \(0.422661\pi\)
\(434\) 0 0
\(435\) −443324. −0.112331
\(436\) 0 0
\(437\) 801971. 0.200888
\(438\) 0 0
\(439\) −1.85883e6 −0.460341 −0.230170 0.973150i \(-0.573928\pi\)
−0.230170 + 0.973150i \(0.573928\pi\)
\(440\) 0 0
\(441\) 977079. 0.239240
\(442\) 0 0
\(443\) 4.39604e6 1.06427 0.532136 0.846659i \(-0.321390\pi\)
0.532136 + 0.846659i \(0.321390\pi\)
\(444\) 0 0
\(445\) −862772. −0.206536
\(446\) 0 0
\(447\) −3.04728e6 −0.721346
\(448\) 0 0
\(449\) −984885. −0.230552 −0.115276 0.993333i \(-0.536775\pi\)
−0.115276 + 0.993333i \(0.536775\pi\)
\(450\) 0 0
\(451\) 2.68754e6 0.622175
\(452\) 0 0
\(453\) 2.15844e6 0.494191
\(454\) 0 0
\(455\) 1.23604e6 0.279901
\(456\) 0 0
\(457\) −696014. −0.155893 −0.0779466 0.996958i \(-0.524836\pi\)
−0.0779466 + 0.996958i \(0.524836\pi\)
\(458\) 0 0
\(459\) −1.56429e6 −0.346566
\(460\) 0 0
\(461\) −6.03623e6 −1.32286 −0.661430 0.750007i \(-0.730050\pi\)
−0.661430 + 0.750007i \(0.730050\pi\)
\(462\) 0 0
\(463\) −2.07793e6 −0.450483 −0.225241 0.974303i \(-0.572317\pi\)
−0.225241 + 0.974303i \(0.572317\pi\)
\(464\) 0 0
\(465\) −873715. −0.187386
\(466\) 0 0
\(467\) 1.81361e6 0.384816 0.192408 0.981315i \(-0.438370\pi\)
0.192408 + 0.981315i \(0.438370\pi\)
\(468\) 0 0
\(469\) −619222. −0.129991
\(470\) 0 0
\(471\) 2.37324e6 0.492935
\(472\) 0 0
\(473\) 7.37300e6 1.51527
\(474\) 0 0
\(475\) 643330. 0.130828
\(476\) 0 0
\(477\) −194228. −0.0390854
\(478\) 0 0
\(479\) 6.10687e6 1.21613 0.608065 0.793887i \(-0.291946\pi\)
0.608065 + 0.793887i \(0.291946\pi\)
\(480\) 0 0
\(481\) −9.09273e6 −1.79197
\(482\) 0 0
\(483\) 681881. 0.132997
\(484\) 0 0
\(485\) 352033. 0.0679561
\(486\) 0 0
\(487\) 1.32848e6 0.253823 0.126912 0.991914i \(-0.459494\pi\)
0.126912 + 0.991914i \(0.459494\pi\)
\(488\) 0 0
\(489\) 5.13222e6 0.970583
\(490\) 0 0
\(491\) 8.72480e6 1.63325 0.816623 0.577171i \(-0.195843\pi\)
0.816623 + 0.577171i \(0.195843\pi\)
\(492\) 0 0
\(493\) 528273. 0.0978907
\(494\) 0 0
\(495\) 661748. 0.121389
\(496\) 0 0
\(497\) 3.01273e6 0.547104
\(498\) 0 0
\(499\) −5.20143e6 −0.935129 −0.467564 0.883959i \(-0.654868\pi\)
−0.467564 + 0.883959i \(0.654868\pi\)
\(500\) 0 0
\(501\) 2.13448e6 0.379926
\(502\) 0 0
\(503\) −6.44189e6 −1.13525 −0.567627 0.823286i \(-0.692139\pi\)
−0.567627 + 0.823286i \(0.692139\pi\)
\(504\) 0 0
\(505\) 4.60045e6 0.802735
\(506\) 0 0
\(507\) −1.86083e6 −0.321504
\(508\) 0 0
\(509\) 2.31511e6 0.396075 0.198038 0.980194i \(-0.436543\pi\)
0.198038 + 0.980194i \(0.436543\pi\)
\(510\) 0 0
\(511\) 4.52522e6 0.766633
\(512\) 0 0
\(513\) 4.24479e6 0.712136
\(514\) 0 0
\(515\) −1.75420e6 −0.291448
\(516\) 0 0
\(517\) −2.53328e6 −0.416828
\(518\) 0 0
\(519\) 1.07061e6 0.174467
\(520\) 0 0
\(521\) −9.65617e6 −1.55851 −0.779257 0.626705i \(-0.784403\pi\)
−0.779257 + 0.626705i \(0.784403\pi\)
\(522\) 0 0
\(523\) 6.40583e6 1.02405 0.512025 0.858970i \(-0.328895\pi\)
0.512025 + 0.858970i \(0.328895\pi\)
\(524\) 0 0
\(525\) 546996. 0.0866136
\(526\) 0 0
\(527\) 1.04114e6 0.163298
\(528\) 0 0
\(529\) −5.82931e6 −0.905687
\(530\) 0 0
\(531\) −1.27239e6 −0.195833
\(532\) 0 0
\(533\) 5.90599e6 0.900481
\(534\) 0 0
\(535\) −198822. −0.0300317
\(536\) 0 0
\(537\) −9.44418e6 −1.41328
\(538\) 0 0
\(539\) −3.95507e6 −0.586384
\(540\) 0 0
\(541\) −1.32300e6 −0.194342 −0.0971709 0.995268i \(-0.530979\pi\)
−0.0971709 + 0.995268i \(0.530979\pi\)
\(542\) 0 0
\(543\) −4.37602e6 −0.636912
\(544\) 0 0
\(545\) 4.21702e6 0.608156
\(546\) 0 0
\(547\) −4.68044e6 −0.668834 −0.334417 0.942425i \(-0.608539\pi\)
−0.334417 + 0.942425i \(0.608539\pi\)
\(548\) 0 0
\(549\) 2.59434e6 0.367363
\(550\) 0 0
\(551\) −1.43350e6 −0.201149
\(552\) 0 0
\(553\) 2.72192e6 0.378498
\(554\) 0 0
\(555\) −4.02388e6 −0.554514
\(556\) 0 0
\(557\) −7.58860e6 −1.03639 −0.518195 0.855262i \(-0.673396\pi\)
−0.518195 + 0.855262i \(0.673396\pi\)
\(558\) 0 0
\(559\) 1.62025e7 2.19307
\(560\) 0 0
\(561\) 1.58103e6 0.212097
\(562\) 0 0
\(563\) 399946. 0.0531777 0.0265889 0.999646i \(-0.491536\pi\)
0.0265889 + 0.999646i \(0.491536\pi\)
\(564\) 0 0
\(565\) 1.54728e6 0.203915
\(566\) 0 0
\(567\) 2.25853e6 0.295032
\(568\) 0 0
\(569\) 1.57419e6 0.203834 0.101917 0.994793i \(-0.467502\pi\)
0.101917 + 0.994793i \(0.467502\pi\)
\(570\) 0 0
\(571\) −3.11290e6 −0.399554 −0.199777 0.979841i \(-0.564022\pi\)
−0.199777 + 0.979841i \(0.564022\pi\)
\(572\) 0 0
\(573\) 8.03509e6 1.02236
\(574\) 0 0
\(575\) 486950. 0.0614207
\(576\) 0 0
\(577\) −5.57621e6 −0.697267 −0.348634 0.937259i \(-0.613354\pi\)
−0.348634 + 0.937259i \(0.613354\pi\)
\(578\) 0 0
\(579\) −1.07951e7 −1.33823
\(580\) 0 0
\(581\) 4.33716e6 0.533047
\(582\) 0 0
\(583\) 786205. 0.0957997
\(584\) 0 0
\(585\) 1.45422e6 0.175688
\(586\) 0 0
\(587\) 1.11890e7 1.34028 0.670138 0.742236i \(-0.266235\pi\)
0.670138 + 0.742236i \(0.266235\pi\)
\(588\) 0 0
\(589\) −2.82518e6 −0.335551
\(590\) 0 0
\(591\) −5.05868e6 −0.595756
\(592\) 0 0
\(593\) 1.44707e7 1.68987 0.844934 0.534871i \(-0.179640\pi\)
0.844934 + 0.534871i \(0.179640\pi\)
\(594\) 0 0
\(595\) −651811. −0.0754795
\(596\) 0 0
\(597\) 1.14094e7 1.31017
\(598\) 0 0
\(599\) 2.32734e6 0.265028 0.132514 0.991181i \(-0.457695\pi\)
0.132514 + 0.991181i \(0.457695\pi\)
\(600\) 0 0
\(601\) 4.28568e6 0.483987 0.241993 0.970278i \(-0.422199\pi\)
0.241993 + 0.970278i \(0.422199\pi\)
\(602\) 0 0
\(603\) −728524. −0.0815925
\(604\) 0 0
\(605\) 1.34762e6 0.149685
\(606\) 0 0
\(607\) 1.04310e7 1.14909 0.574547 0.818471i \(-0.305178\pi\)
0.574547 + 0.818471i \(0.305178\pi\)
\(608\) 0 0
\(609\) −1.21884e6 −0.133170
\(610\) 0 0
\(611\) −5.56701e6 −0.603280
\(612\) 0 0
\(613\) −3.52495e6 −0.378880 −0.189440 0.981892i \(-0.560667\pi\)
−0.189440 + 0.981892i \(0.560667\pi\)
\(614\) 0 0
\(615\) 2.61363e6 0.278648
\(616\) 0 0
\(617\) 1.16178e7 1.22861 0.614303 0.789070i \(-0.289437\pi\)
0.614303 + 0.789070i \(0.289437\pi\)
\(618\) 0 0
\(619\) −1.04132e7 −1.09234 −0.546171 0.837673i \(-0.683915\pi\)
−0.546171 + 0.837673i \(0.683915\pi\)
\(620\) 0 0
\(621\) 3.21297e6 0.334332
\(622\) 0 0
\(623\) −2.37204e6 −0.244851
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) −4.29022e6 −0.435824
\(628\) 0 0
\(629\) 4.79493e6 0.483232
\(630\) 0 0
\(631\) −6.57325e6 −0.657214 −0.328607 0.944467i \(-0.606579\pi\)
−0.328607 + 0.944467i \(0.606579\pi\)
\(632\) 0 0
\(633\) 1.11640e7 1.10741
\(634\) 0 0
\(635\) −8.96738e6 −0.882533
\(636\) 0 0
\(637\) −8.69146e6 −0.848680
\(638\) 0 0
\(639\) 3.54452e6 0.343404
\(640\) 0 0
\(641\) 7.21768e6 0.693829 0.346914 0.937897i \(-0.387229\pi\)
0.346914 + 0.937897i \(0.387229\pi\)
\(642\) 0 0
\(643\) −989729. −0.0944036 −0.0472018 0.998885i \(-0.515030\pi\)
−0.0472018 + 0.998885i \(0.515030\pi\)
\(644\) 0 0
\(645\) 7.17023e6 0.678631
\(646\) 0 0
\(647\) −4.31383e6 −0.405138 −0.202569 0.979268i \(-0.564929\pi\)
−0.202569 + 0.979268i \(0.564929\pi\)
\(648\) 0 0
\(649\) 5.15046e6 0.479992
\(650\) 0 0
\(651\) −2.40213e6 −0.222149
\(652\) 0 0
\(653\) 1.49637e7 1.37327 0.686633 0.727004i \(-0.259088\pi\)
0.686633 + 0.727004i \(0.259088\pi\)
\(654\) 0 0
\(655\) 7.81481e6 0.711730
\(656\) 0 0
\(657\) 5.32399e6 0.481198
\(658\) 0 0
\(659\) −4.42210e6 −0.396657 −0.198328 0.980136i \(-0.563551\pi\)
−0.198328 + 0.980136i \(0.563551\pi\)
\(660\) 0 0
\(661\) −1.57925e7 −1.40587 −0.702937 0.711252i \(-0.748128\pi\)
−0.702937 + 0.711252i \(0.748128\pi\)
\(662\) 0 0
\(663\) 3.47440e6 0.306970
\(664\) 0 0
\(665\) 1.76873e6 0.155098
\(666\) 0 0
\(667\) −1.08505e6 −0.0944352
\(668\) 0 0
\(669\) 698939. 0.0603773
\(670\) 0 0
\(671\) −1.05015e7 −0.900420
\(672\) 0 0
\(673\) −5.60799e6 −0.477276 −0.238638 0.971109i \(-0.576701\pi\)
−0.238638 + 0.971109i \(0.576701\pi\)
\(674\) 0 0
\(675\) 2.57740e6 0.217732
\(676\) 0 0
\(677\) 7.01232e6 0.588017 0.294009 0.955803i \(-0.405011\pi\)
0.294009 + 0.955803i \(0.405011\pi\)
\(678\) 0 0
\(679\) 967853. 0.0805629
\(680\) 0 0
\(681\) −1.02289e7 −0.845207
\(682\) 0 0
\(683\) 2.16662e7 1.77718 0.888590 0.458703i \(-0.151686\pi\)
0.888590 + 0.458703i \(0.151686\pi\)
\(684\) 0 0
\(685\) 839347. 0.0683463
\(686\) 0 0
\(687\) −7.50681e6 −0.606825
\(688\) 0 0
\(689\) 1.72772e6 0.138652
\(690\) 0 0
\(691\) 4.20276e6 0.334842 0.167421 0.985885i \(-0.446456\pi\)
0.167421 + 0.985885i \(0.446456\pi\)
\(692\) 0 0
\(693\) 1.81936e6 0.143908
\(694\) 0 0
\(695\) −8.55439e6 −0.671780
\(696\) 0 0
\(697\) −3.11444e6 −0.242828
\(698\) 0 0
\(699\) −1.29939e7 −1.00588
\(700\) 0 0
\(701\) 1.50989e6 0.116051 0.0580256 0.998315i \(-0.481519\pi\)
0.0580256 + 0.998315i \(0.481519\pi\)
\(702\) 0 0
\(703\) −1.30113e7 −0.992963
\(704\) 0 0
\(705\) −2.46361e6 −0.186681
\(706\) 0 0
\(707\) 1.26482e7 0.951653
\(708\) 0 0
\(709\) −2.08359e6 −0.155667 −0.0778336 0.996966i \(-0.524800\pi\)
−0.0778336 + 0.996966i \(0.524800\pi\)
\(710\) 0 0
\(711\) 3.20238e6 0.237574
\(712\) 0 0
\(713\) −2.13844e6 −0.157534
\(714\) 0 0
\(715\) −5.88648e6 −0.430616
\(716\) 0 0
\(717\) 2.10749e7 1.53098
\(718\) 0 0
\(719\) 1.03357e7 0.745618 0.372809 0.927908i \(-0.378395\pi\)
0.372809 + 0.927908i \(0.378395\pi\)
\(720\) 0 0
\(721\) −4.82287e6 −0.345515
\(722\) 0 0
\(723\) 1.51561e7 1.07830
\(724\) 0 0
\(725\) −870410. −0.0615005
\(726\) 0 0
\(727\) 3.39227e6 0.238042 0.119021 0.992892i \(-0.462024\pi\)
0.119021 + 0.992892i \(0.462024\pi\)
\(728\) 0 0
\(729\) 1.54171e7 1.07444
\(730\) 0 0
\(731\) −8.54418e6 −0.591394
\(732\) 0 0
\(733\) 1.99922e7 1.37436 0.687180 0.726487i \(-0.258848\pi\)
0.687180 + 0.726487i \(0.258848\pi\)
\(734\) 0 0
\(735\) −3.84630e6 −0.262618
\(736\) 0 0
\(737\) 2.94896e6 0.199986
\(738\) 0 0
\(739\) 2.37515e7 1.59986 0.799928 0.600096i \(-0.204871\pi\)
0.799928 + 0.600096i \(0.204871\pi\)
\(740\) 0 0
\(741\) −9.42797e6 −0.630773
\(742\) 0 0
\(743\) 768079. 0.0510427 0.0255214 0.999674i \(-0.491875\pi\)
0.0255214 + 0.999674i \(0.491875\pi\)
\(744\) 0 0
\(745\) −5.98294e6 −0.394934
\(746\) 0 0
\(747\) 5.10273e6 0.334581
\(748\) 0 0
\(749\) −546628. −0.0356030
\(750\) 0 0
\(751\) −2.34656e7 −1.51821 −0.759105 0.650968i \(-0.774363\pi\)
−0.759105 + 0.650968i \(0.774363\pi\)
\(752\) 0 0
\(753\) 302745. 0.0194576
\(754\) 0 0
\(755\) 4.23782e6 0.270567
\(756\) 0 0
\(757\) −2.58118e7 −1.63711 −0.818557 0.574425i \(-0.805226\pi\)
−0.818557 + 0.574425i \(0.805226\pi\)
\(758\) 0 0
\(759\) −3.24736e6 −0.204610
\(760\) 0 0
\(761\) 1.19501e7 0.748013 0.374006 0.927426i \(-0.377984\pi\)
0.374006 + 0.927426i \(0.377984\pi\)
\(762\) 0 0
\(763\) 1.15940e7 0.720977
\(764\) 0 0
\(765\) −766865. −0.0473767
\(766\) 0 0
\(767\) 1.13184e7 0.694698
\(768\) 0 0
\(769\) −1.61907e7 −0.987302 −0.493651 0.869660i \(-0.664338\pi\)
−0.493651 + 0.869660i \(0.664338\pi\)
\(770\) 0 0
\(771\) 4.35070e6 0.263586
\(772\) 0 0
\(773\) 1.40818e7 0.847637 0.423818 0.905747i \(-0.360689\pi\)
0.423818 + 0.905747i \(0.360689\pi\)
\(774\) 0 0
\(775\) −1.71543e6 −0.102593
\(776\) 0 0
\(777\) −1.10630e7 −0.657384
\(778\) 0 0
\(779\) 8.45122e6 0.498972
\(780\) 0 0
\(781\) −1.43477e7 −0.841695
\(782\) 0 0
\(783\) −5.74310e6 −0.334766
\(784\) 0 0
\(785\) 4.65955e6 0.269880
\(786\) 0 0
\(787\) 4.41819e6 0.254277 0.127139 0.991885i \(-0.459421\pi\)
0.127139 + 0.991885i \(0.459421\pi\)
\(788\) 0 0
\(789\) −1.38945e7 −0.794602
\(790\) 0 0
\(791\) 4.25399e6 0.241744
\(792\) 0 0
\(793\) −2.30776e7 −1.30319
\(794\) 0 0
\(795\) 764583. 0.0429049
\(796\) 0 0
\(797\) −6.04472e6 −0.337078 −0.168539 0.985695i \(-0.553905\pi\)
−0.168539 + 0.985695i \(0.553905\pi\)
\(798\) 0 0
\(799\) 2.93569e6 0.162683
\(800\) 0 0
\(801\) −2.79074e6 −0.153688
\(802\) 0 0
\(803\) −2.15507e7 −1.17943
\(804\) 0 0
\(805\) 1.33879e6 0.0728151
\(806\) 0 0
\(807\) −1.17516e7 −0.635202
\(808\) 0 0
\(809\) −1.71556e7 −0.921583 −0.460791 0.887509i \(-0.652434\pi\)
−0.460791 + 0.887509i \(0.652434\pi\)
\(810\) 0 0
\(811\) 1.83020e7 0.977114 0.488557 0.872532i \(-0.337523\pi\)
0.488557 + 0.872532i \(0.337523\pi\)
\(812\) 0 0
\(813\) −1.71009e7 −0.907389
\(814\) 0 0
\(815\) 1.00764e7 0.531390
\(816\) 0 0
\(817\) 2.31851e7 1.21522
\(818\) 0 0
\(819\) 3.99813e6 0.208280
\(820\) 0 0
\(821\) 77887.9 0.00403285 0.00201643 0.999998i \(-0.499358\pi\)
0.00201643 + 0.999998i \(0.499358\pi\)
\(822\) 0 0
\(823\) 423648. 0.0218025 0.0109012 0.999941i \(-0.496530\pi\)
0.0109012 + 0.999941i \(0.496530\pi\)
\(824\) 0 0
\(825\) −2.60499e6 −0.133251
\(826\) 0 0
\(827\) 5.18956e6 0.263856 0.131928 0.991259i \(-0.457883\pi\)
0.131928 + 0.991259i \(0.457883\pi\)
\(828\) 0 0
\(829\) 2.08613e7 1.05428 0.527139 0.849779i \(-0.323265\pi\)
0.527139 + 0.849779i \(0.323265\pi\)
\(830\) 0 0
\(831\) −3.15201e6 −0.158338
\(832\) 0 0
\(833\) 4.58332e6 0.228859
\(834\) 0 0
\(835\) 4.19079e6 0.208008
\(836\) 0 0
\(837\) −1.13187e7 −0.558446
\(838\) 0 0
\(839\) 8.18798e6 0.401580 0.200790 0.979634i \(-0.435649\pi\)
0.200790 + 0.979634i \(0.435649\pi\)
\(840\) 0 0
\(841\) −1.85717e7 −0.905442
\(842\) 0 0
\(843\) −1.31900e7 −0.639258
\(844\) 0 0
\(845\) −3.65350e6 −0.176022
\(846\) 0 0
\(847\) 3.70505e6 0.177454
\(848\) 0 0
\(849\) 3.04868e7 1.45158
\(850\) 0 0
\(851\) −9.84854e6 −0.466174
\(852\) 0 0
\(853\) −3.11924e7 −1.46783 −0.733915 0.679241i \(-0.762309\pi\)
−0.733915 + 0.679241i \(0.762309\pi\)
\(854\) 0 0
\(855\) 2.08093e6 0.0973514
\(856\) 0 0
\(857\) −1.88654e7 −0.877433 −0.438716 0.898626i \(-0.644567\pi\)
−0.438716 + 0.898626i \(0.644567\pi\)
\(858\) 0 0
\(859\) 1.30703e7 0.604369 0.302184 0.953249i \(-0.402284\pi\)
0.302184 + 0.953249i \(0.402284\pi\)
\(860\) 0 0
\(861\) 7.18571e6 0.330341
\(862\) 0 0
\(863\) −5.58115e6 −0.255092 −0.127546 0.991833i \(-0.540710\pi\)
−0.127546 + 0.991833i \(0.540710\pi\)
\(864\) 0 0
\(865\) 2.10201e6 0.0955201
\(866\) 0 0
\(867\) 1.62471e7 0.734056
\(868\) 0 0
\(869\) −1.29628e7 −0.582302
\(870\) 0 0
\(871\) 6.48047e6 0.289442
\(872\) 0 0
\(873\) 1.13869e6 0.0505675
\(874\) 0 0
\(875\) 1.07396e6 0.0474205
\(876\) 0 0
\(877\) −2.17437e7 −0.954629 −0.477315 0.878732i \(-0.658390\pi\)
−0.477315 + 0.878732i \(0.658390\pi\)
\(878\) 0 0
\(879\) −3.11730e7 −1.36084
\(880\) 0 0
\(881\) 2.26789e7 0.984425 0.492212 0.870475i \(-0.336188\pi\)
0.492212 + 0.870475i \(0.336188\pi\)
\(882\) 0 0
\(883\) −2.34145e7 −1.01061 −0.505304 0.862942i \(-0.668619\pi\)
−0.505304 + 0.862942i \(0.668619\pi\)
\(884\) 0 0
\(885\) 5.00882e6 0.214970
\(886\) 0 0
\(887\) 1.56731e7 0.668875 0.334437 0.942418i \(-0.391454\pi\)
0.334437 + 0.942418i \(0.391454\pi\)
\(888\) 0 0
\(889\) −2.46543e7 −1.04626
\(890\) 0 0
\(891\) −1.07559e7 −0.453894
\(892\) 0 0
\(893\) −7.96616e6 −0.334288
\(894\) 0 0
\(895\) −1.85424e7 −0.773765
\(896\) 0 0
\(897\) −7.13624e6 −0.296134
\(898\) 0 0
\(899\) 3.82240e6 0.157738
\(900\) 0 0
\(901\) −911092. −0.0373895
\(902\) 0 0
\(903\) 1.97133e7 0.804527
\(904\) 0 0
\(905\) −8.59175e6 −0.348707
\(906\) 0 0
\(907\) −3.67553e7 −1.48355 −0.741775 0.670649i \(-0.766016\pi\)
−0.741775 + 0.670649i \(0.766016\pi\)
\(908\) 0 0
\(909\) 1.48807e7 0.597331
\(910\) 0 0
\(911\) 2.11183e7 0.843067 0.421534 0.906813i \(-0.361492\pi\)
0.421534 + 0.906813i \(0.361492\pi\)
\(912\) 0 0
\(913\) −2.06551e7 −0.820070
\(914\) 0 0
\(915\) −1.02127e7 −0.403262
\(916\) 0 0
\(917\) 2.14855e7 0.843765
\(918\) 0 0
\(919\) −7.27922e6 −0.284312 −0.142156 0.989844i \(-0.545404\pi\)
−0.142156 + 0.989844i \(0.545404\pi\)
\(920\) 0 0
\(921\) 1.19625e7 0.464702
\(922\) 0 0
\(923\) −3.15298e7 −1.21819
\(924\) 0 0
\(925\) −7.90037e6 −0.303594
\(926\) 0 0
\(927\) −5.67418e6 −0.216872
\(928\) 0 0
\(929\) −3.41165e7 −1.29696 −0.648478 0.761234i \(-0.724594\pi\)
−0.648478 + 0.761234i \(0.724594\pi\)
\(930\) 0 0
\(931\) −1.24371e7 −0.470268
\(932\) 0 0
\(933\) −1.45083e7 −0.545649
\(934\) 0 0
\(935\) 3.10416e6 0.116122
\(936\) 0 0
\(937\) −4.73880e7 −1.76327 −0.881637 0.471929i \(-0.843558\pi\)
−0.881637 + 0.471929i \(0.843558\pi\)
\(938\) 0 0
\(939\) −1.93153e7 −0.714887
\(940\) 0 0
\(941\) 3.97476e7 1.46331 0.731656 0.681674i \(-0.238748\pi\)
0.731656 + 0.681674i \(0.238748\pi\)
\(942\) 0 0
\(943\) 6.39691e6 0.234256
\(944\) 0 0
\(945\) 7.08613e6 0.258125
\(946\) 0 0
\(947\) −2.76410e7 −1.00156 −0.500782 0.865573i \(-0.666954\pi\)
−0.500782 + 0.865573i \(0.666954\pi\)
\(948\) 0 0
\(949\) −4.73588e7 −1.70701
\(950\) 0 0
\(951\) 3.48233e7 1.24859
\(952\) 0 0
\(953\) −5.22977e6 −0.186531 −0.0932654 0.995641i \(-0.529731\pi\)
−0.0932654 + 0.995641i \(0.529731\pi\)
\(954\) 0 0
\(955\) 1.57759e7 0.559738
\(956\) 0 0
\(957\) 5.80457e6 0.204876
\(958\) 0 0
\(959\) 2.30764e6 0.0810255
\(960\) 0 0
\(961\) −2.10959e7 −0.736866
\(962\) 0 0
\(963\) −643115. −0.0223472
\(964\) 0 0
\(965\) −2.11948e7 −0.732673
\(966\) 0 0
\(967\) −1.76477e7 −0.606905 −0.303453 0.952847i \(-0.598139\pi\)
−0.303453 + 0.952847i \(0.598139\pi\)
\(968\) 0 0
\(969\) 4.97172e6 0.170097
\(970\) 0 0
\(971\) −3.66934e7 −1.24893 −0.624467 0.781051i \(-0.714684\pi\)
−0.624467 + 0.781051i \(0.714684\pi\)
\(972\) 0 0
\(973\) −2.35188e7 −0.796404
\(974\) 0 0
\(975\) −5.72459e6 −0.192856
\(976\) 0 0
\(977\) 3.16023e7 1.05921 0.529605 0.848244i \(-0.322340\pi\)
0.529605 + 0.848244i \(0.322340\pi\)
\(978\) 0 0
\(979\) 1.12965e7 0.376693
\(980\) 0 0
\(981\) 1.36405e7 0.452540
\(982\) 0 0
\(983\) 3.73829e7 1.23393 0.616963 0.786992i \(-0.288363\pi\)
0.616963 + 0.786992i \(0.288363\pi\)
\(984\) 0 0
\(985\) −9.93206e6 −0.326174
\(986\) 0 0
\(987\) −6.77328e6 −0.221313
\(988\) 0 0
\(989\) 1.75493e7 0.570518
\(990\) 0 0
\(991\) 2.84243e7 0.919401 0.459701 0.888074i \(-0.347957\pi\)
0.459701 + 0.888074i \(0.347957\pi\)
\(992\) 0 0
\(993\) −1.56373e6 −0.0503256
\(994\) 0 0
\(995\) 2.24010e7 0.717313
\(996\) 0 0
\(997\) 1.70600e7 0.543553 0.271776 0.962360i \(-0.412389\pi\)
0.271776 + 0.962360i \(0.412389\pi\)
\(998\) 0 0
\(999\) −5.21279e7 −1.65256
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 320.6.a.v.1.1 2
4.3 odd 2 320.6.a.r.1.2 2
8.3 odd 2 160.6.a.e.1.1 yes 2
8.5 even 2 160.6.a.a.1.2 2
40.3 even 4 800.6.c.g.449.2 4
40.13 odd 4 800.6.c.f.449.3 4
40.19 odd 2 800.6.a.g.1.2 2
40.27 even 4 800.6.c.g.449.3 4
40.29 even 2 800.6.a.l.1.1 2
40.37 odd 4 800.6.c.f.449.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.6.a.a.1.2 2 8.5 even 2
160.6.a.e.1.1 yes 2 8.3 odd 2
320.6.a.r.1.2 2 4.3 odd 2
320.6.a.v.1.1 2 1.1 even 1 trivial
800.6.a.g.1.2 2 40.19 odd 2
800.6.a.l.1.1 2 40.29 even 2
800.6.c.f.449.2 4 40.37 odd 4
800.6.c.f.449.3 4 40.13 odd 4
800.6.c.g.449.2 4 40.3 even 4
800.6.c.g.449.3 4 40.27 even 4