Properties

Label 400.6.a.w.1.1
Level $400$
Weight $6$
Character 400.1
Self dual yes
Analytic conductor $64.154$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 400.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.1535279252\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{241}) \)
Defining polynomial: \(x^{2} - x - 60\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 25)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(8.26209\) of defining polynomial
Character \(\chi\) \(=\) 400.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.52417 q^{3} +68.9517 q^{7} -212.483 q^{9} +O(q^{10})\) \(q-5.52417 q^{3} +68.9517 q^{7} -212.483 q^{9} +486.104 q^{11} +428.387 q^{13} -1800.64 q^{17} +1046.65 q^{19} -380.901 q^{21} +686.855 q^{23} +2516.17 q^{27} -1339.03 q^{29} -7990.30 q^{31} -2685.33 q^{33} +1970.64 q^{37} -2366.48 q^{39} +10772.2 q^{41} +15017.7 q^{43} +895.337 q^{47} -12052.7 q^{49} +9947.07 q^{51} +19327.1 q^{53} -5781.90 q^{57} -21193.7 q^{59} -27722.2 q^{61} -14651.1 q^{63} -7719.33 q^{67} -3794.31 q^{69} +51410.1 q^{71} +43776.4 q^{73} +33517.7 q^{77} +6225.68 q^{79} +37733.7 q^{81} +52949.9 q^{83} +7397.05 q^{87} +44631.2 q^{89} +29538.0 q^{91} +44139.8 q^{93} +148018. q^{97} -103289. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 20q^{3} + 200q^{7} + 196q^{9} + O(q^{10}) \) \( 2q + 20q^{3} + 200q^{7} + 196q^{9} + 196q^{11} + 360q^{13} - 1490q^{17} + 3180q^{19} + 2964q^{21} + 1560q^{23} + 6740q^{27} - 3920q^{29} + 1096q^{31} - 10090q^{33} - 2020q^{37} - 4112q^{39} + 27754q^{41} - 3000q^{43} + 25760q^{47} - 11686q^{49} + 17876q^{51} + 26980q^{53} + 48670q^{57} - 11960q^{59} - 24396q^{61} + 38880q^{63} - 40060q^{67} + 18492q^{69} + 87296q^{71} + 70290q^{73} - 4500q^{77} - 65480q^{79} + 46282q^{81} + 92580q^{83} - 58480q^{87} - 72810q^{89} + 20576q^{91} + 276060q^{93} + 126140q^{97} - 221792q^{99} + O(q^{100}) \)

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
\(3\) −5.52417 −0.354376 −0.177188 0.984177i \(-0.556700\pi\)
−0.177188 + 0.984177i \(0.556700\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 68.9517 0.531863 0.265931 0.963992i \(-0.414321\pi\)
0.265931 + 0.963992i \(0.414321\pi\)
\(8\) 0 0
\(9\) −212.483 −0.874418
\(10\) 0 0
\(11\) 486.104 1.21129 0.605645 0.795735i \(-0.292915\pi\)
0.605645 + 0.795735i \(0.292915\pi\)
\(12\) 0 0
\(13\) 428.387 0.703036 0.351518 0.936181i \(-0.385666\pi\)
0.351518 + 0.936181i \(0.385666\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1800.64 −1.51114 −0.755571 0.655066i \(-0.772641\pi\)
−0.755571 + 0.655066i \(0.772641\pi\)
\(18\) 0 0
\(19\) 1046.65 0.665149 0.332575 0.943077i \(-0.392083\pi\)
0.332575 + 0.943077i \(0.392083\pi\)
\(20\) 0 0
\(21\) −380.901 −0.188479
\(22\) 0 0
\(23\) 686.855 0.270736 0.135368 0.990795i \(-0.456778\pi\)
0.135368 + 0.990795i \(0.456778\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 2516.17 0.664249
\(28\) 0 0
\(29\) −1339.03 −0.295663 −0.147831 0.989013i \(-0.547229\pi\)
−0.147831 + 0.989013i \(0.547229\pi\)
\(30\) 0 0
\(31\) −7990.30 −1.49334 −0.746670 0.665195i \(-0.768349\pi\)
−0.746670 + 0.665195i \(0.768349\pi\)
\(32\) 0 0
\(33\) −2685.33 −0.429252
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1970.64 0.236648 0.118324 0.992975i \(-0.462248\pi\)
0.118324 + 0.992975i \(0.462248\pi\)
\(38\) 0 0
\(39\) −2366.48 −0.249139
\(40\) 0 0
\(41\) 10772.2 1.00079 0.500395 0.865797i \(-0.333188\pi\)
0.500395 + 0.865797i \(0.333188\pi\)
\(42\) 0 0
\(43\) 15017.7 1.23861 0.619303 0.785152i \(-0.287415\pi\)
0.619303 + 0.785152i \(0.287415\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 895.337 0.0591210 0.0295605 0.999563i \(-0.490589\pi\)
0.0295605 + 0.999563i \(0.490589\pi\)
\(48\) 0 0
\(49\) −12052.7 −0.717122
\(50\) 0 0
\(51\) 9947.07 0.535513
\(52\) 0 0
\(53\) 19327.1 0.945098 0.472549 0.881304i \(-0.343334\pi\)
0.472549 + 0.881304i \(0.343334\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −5781.90 −0.235713
\(58\) 0 0
\(59\) −21193.7 −0.792641 −0.396321 0.918112i \(-0.629713\pi\)
−0.396321 + 0.918112i \(0.629713\pi\)
\(60\) 0 0
\(61\) −27722.2 −0.953900 −0.476950 0.878931i \(-0.658258\pi\)
−0.476950 + 0.878931i \(0.658258\pi\)
\(62\) 0 0
\(63\) −14651.1 −0.465070
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7719.33 −0.210084 −0.105042 0.994468i \(-0.533498\pi\)
−0.105042 + 0.994468i \(0.533498\pi\)
\(68\) 0 0
\(69\) −3794.31 −0.0959422
\(70\) 0 0
\(71\) 51410.1 1.21033 0.605163 0.796101i \(-0.293108\pi\)
0.605163 + 0.796101i \(0.293108\pi\)
\(72\) 0 0
\(73\) 43776.4 0.961465 0.480732 0.876867i \(-0.340371\pi\)
0.480732 + 0.876867i \(0.340371\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 33517.7 0.644240
\(78\) 0 0
\(79\) 6225.68 0.112233 0.0561163 0.998424i \(-0.482128\pi\)
0.0561163 + 0.998424i \(0.482128\pi\)
\(80\) 0 0
\(81\) 37733.7 0.639024
\(82\) 0 0
\(83\) 52949.9 0.843664 0.421832 0.906674i \(-0.361387\pi\)
0.421832 + 0.906674i \(0.361387\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 7397.05 0.104776
\(88\) 0 0
\(89\) 44631.2 0.597260 0.298630 0.954369i \(-0.403470\pi\)
0.298630 + 0.954369i \(0.403470\pi\)
\(90\) 0 0
\(91\) 29538.0 0.373919
\(92\) 0 0
\(93\) 44139.8 0.529204
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 148018. 1.59730 0.798649 0.601797i \(-0.205548\pi\)
0.798649 + 0.601797i \(0.205548\pi\)
\(98\) 0 0
\(99\) −103289. −1.05917
\(100\) 0 0
\(101\) 148476. 1.44828 0.724141 0.689652i \(-0.242237\pi\)
0.724141 + 0.689652i \(0.242237\pi\)
\(102\) 0 0
\(103\) 188391. 1.74972 0.874859 0.484378i \(-0.160954\pi\)
0.874859 + 0.484378i \(0.160954\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 67887.7 0.573234 0.286617 0.958045i \(-0.407469\pi\)
0.286617 + 0.958045i \(0.407469\pi\)
\(108\) 0 0
\(109\) −219292. −1.76790 −0.883949 0.467582i \(-0.845125\pi\)
−0.883949 + 0.467582i \(0.845125\pi\)
\(110\) 0 0
\(111\) −10886.2 −0.0838625
\(112\) 0 0
\(113\) 80783.9 0.595153 0.297577 0.954698i \(-0.403822\pi\)
0.297577 + 0.954698i \(0.403822\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −91025.1 −0.614747
\(118\) 0 0
\(119\) −124157. −0.803721
\(120\) 0 0
\(121\) 75246.5 0.467221
\(122\) 0 0
\(123\) −59507.3 −0.354656
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 161301. 0.887417 0.443708 0.896171i \(-0.353663\pi\)
0.443708 + 0.896171i \(0.353663\pi\)
\(128\) 0 0
\(129\) −82960.5 −0.438932
\(130\) 0 0
\(131\) 193006. 0.982636 0.491318 0.870980i \(-0.336515\pi\)
0.491318 + 0.870980i \(0.336515\pi\)
\(132\) 0 0
\(133\) 72168.5 0.353768
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −250340. −1.13954 −0.569768 0.821806i \(-0.692967\pi\)
−0.569768 + 0.821806i \(0.692967\pi\)
\(138\) 0 0
\(139\) 218650. 0.959871 0.479935 0.877304i \(-0.340660\pi\)
0.479935 + 0.877304i \(0.340660\pi\)
\(140\) 0 0
\(141\) −4946.00 −0.0209511
\(142\) 0 0
\(143\) 208241. 0.851580
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 66581.1 0.254131
\(148\) 0 0
\(149\) −38740.0 −0.142953 −0.0714766 0.997442i \(-0.522771\pi\)
−0.0714766 + 0.997442i \(0.522771\pi\)
\(150\) 0 0
\(151\) 154945. 0.553013 0.276507 0.961012i \(-0.410823\pi\)
0.276507 + 0.961012i \(0.410823\pi\)
\(152\) 0 0
\(153\) 382607. 1.32137
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 344442. 1.11523 0.557617 0.830098i \(-0.311716\pi\)
0.557617 + 0.830098i \(0.311716\pi\)
\(158\) 0 0
\(159\) −106766. −0.334920
\(160\) 0 0
\(161\) 47359.8 0.143994
\(162\) 0 0
\(163\) 366203. 1.07957 0.539787 0.841801i \(-0.318505\pi\)
0.539787 + 0.841801i \(0.318505\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 249272. 0.691644 0.345822 0.938300i \(-0.387600\pi\)
0.345822 + 0.938300i \(0.387600\pi\)
\(168\) 0 0
\(169\) −187778. −0.505740
\(170\) 0 0
\(171\) −222397. −0.581618
\(172\) 0 0
\(173\) 61460.1 0.156127 0.0780635 0.996948i \(-0.475126\pi\)
0.0780635 + 0.996948i \(0.475126\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 117078. 0.280893
\(178\) 0 0
\(179\) −606803. −1.41552 −0.707759 0.706454i \(-0.750294\pi\)
−0.707759 + 0.706454i \(0.750294\pi\)
\(180\) 0 0
\(181\) 153684. 0.348685 0.174343 0.984685i \(-0.444220\pi\)
0.174343 + 0.984685i \(0.444220\pi\)
\(182\) 0 0
\(183\) 153142. 0.338039
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −875301. −1.83043
\(188\) 0 0
\(189\) 173494. 0.353289
\(190\) 0 0
\(191\) −182315. −0.361608 −0.180804 0.983519i \(-0.557870\pi\)
−0.180804 + 0.983519i \(0.557870\pi\)
\(192\) 0 0
\(193\) 102080. 0.197265 0.0986323 0.995124i \(-0.468553\pi\)
0.0986323 + 0.995124i \(0.468553\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 404656. 0.742882 0.371441 0.928456i \(-0.378864\pi\)
0.371441 + 0.928456i \(0.378864\pi\)
\(198\) 0 0
\(199\) 167297. 0.299472 0.149736 0.988726i \(-0.452158\pi\)
0.149736 + 0.988726i \(0.452158\pi\)
\(200\) 0 0
\(201\) 42642.9 0.0744487
\(202\) 0 0
\(203\) −92328.5 −0.157252
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −145945. −0.236736
\(208\) 0 0
\(209\) 508783. 0.805688
\(210\) 0 0
\(211\) 460778. 0.712502 0.356251 0.934390i \(-0.384055\pi\)
0.356251 + 0.934390i \(0.384055\pi\)
\(212\) 0 0
\(213\) −283998. −0.428911
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −550944. −0.794252
\(218\) 0 0
\(219\) −241829. −0.340720
\(220\) 0 0
\(221\) −771372. −1.06239
\(222\) 0 0
\(223\) −1.08298e6 −1.45834 −0.729172 0.684330i \(-0.760095\pi\)
−0.729172 + 0.684330i \(0.760095\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 412201. 0.530938 0.265469 0.964119i \(-0.414473\pi\)
0.265469 + 0.964119i \(0.414473\pi\)
\(228\) 0 0
\(229\) −433163. −0.545836 −0.272918 0.962037i \(-0.587989\pi\)
−0.272918 + 0.962037i \(0.587989\pi\)
\(230\) 0 0
\(231\) −185158. −0.228303
\(232\) 0 0
\(233\) −760097. −0.917232 −0.458616 0.888635i \(-0.651655\pi\)
−0.458616 + 0.888635i \(0.651655\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −34391.7 −0.0397725
\(238\) 0 0
\(239\) 988624. 1.11953 0.559766 0.828651i \(-0.310891\pi\)
0.559766 + 0.828651i \(0.310891\pi\)
\(240\) 0 0
\(241\) −358878. −0.398020 −0.199010 0.979997i \(-0.563773\pi\)
−0.199010 + 0.979997i \(0.563773\pi\)
\(242\) 0 0
\(243\) −819877. −0.890703
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 448373. 0.467624
\(248\) 0 0
\(249\) −292504. −0.298974
\(250\) 0 0
\(251\) 851049. 0.852649 0.426324 0.904570i \(-0.359808\pi\)
0.426324 + 0.904570i \(0.359808\pi\)
\(252\) 0 0
\(253\) 333883. 0.327939
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 76358.4 0.0721147 0.0360574 0.999350i \(-0.488520\pi\)
0.0360574 + 0.999350i \(0.488520\pi\)
\(258\) 0 0
\(259\) 135879. 0.125864
\(260\) 0 0
\(261\) 284522. 0.258533
\(262\) 0 0
\(263\) 1.19420e6 1.06460 0.532301 0.846555i \(-0.321327\pi\)
0.532301 + 0.846555i \(0.321327\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −246551. −0.211655
\(268\) 0 0
\(269\) 1.02930e6 0.867286 0.433643 0.901085i \(-0.357228\pi\)
0.433643 + 0.901085i \(0.357228\pi\)
\(270\) 0 0
\(271\) −2.12144e6 −1.75472 −0.877359 0.479834i \(-0.840697\pi\)
−0.877359 + 0.479834i \(0.840697\pi\)
\(272\) 0 0
\(273\) −163173. −0.132508
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.85145e6 −1.44982 −0.724908 0.688845i \(-0.758118\pi\)
−0.724908 + 0.688845i \(0.758118\pi\)
\(278\) 0 0
\(279\) 1.69781e6 1.30580
\(280\) 0 0
\(281\) 90653.2 0.0684884 0.0342442 0.999413i \(-0.489098\pi\)
0.0342442 + 0.999413i \(0.489098\pi\)
\(282\) 0 0
\(283\) −929308. −0.689753 −0.344877 0.938648i \(-0.612079\pi\)
−0.344877 + 0.938648i \(0.612079\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 742759. 0.532283
\(288\) 0 0
\(289\) 1.82246e6 1.28355
\(290\) 0 0
\(291\) −817679. −0.566044
\(292\) 0 0
\(293\) −2.72733e6 −1.85596 −0.927979 0.372632i \(-0.878455\pi\)
−0.927979 + 0.372632i \(0.878455\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 1.22312e6 0.804597
\(298\) 0 0
\(299\) 294240. 0.190337
\(300\) 0 0
\(301\) 1.03550e6 0.658768
\(302\) 0 0
\(303\) −820208. −0.513236
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −2.29648e6 −1.39064 −0.695322 0.718698i \(-0.744738\pi\)
−0.695322 + 0.718698i \(0.744738\pi\)
\(308\) 0 0
\(309\) −1.04071e6 −0.620058
\(310\) 0 0
\(311\) −984847. −0.577388 −0.288694 0.957421i \(-0.593221\pi\)
−0.288694 + 0.957421i \(0.593221\pi\)
\(312\) 0 0
\(313\) −2.06650e6 −1.19227 −0.596135 0.802884i \(-0.703298\pi\)
−0.596135 + 0.802884i \(0.703298\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.14349e6 −0.639125 −0.319563 0.947565i \(-0.603536\pi\)
−0.319563 + 0.947565i \(0.603536\pi\)
\(318\) 0 0
\(319\) −650910. −0.358133
\(320\) 0 0
\(321\) −375024. −0.203140
\(322\) 0 0
\(323\) −1.88465e6 −1.00514
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.21141e6 0.626501
\(328\) 0 0
\(329\) 61735.0 0.0314443
\(330\) 0 0
\(331\) −205230. −0.102961 −0.0514804 0.998674i \(-0.516394\pi\)
−0.0514804 + 0.998674i \(0.516394\pi\)
\(332\) 0 0
\(333\) −418729. −0.206929
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −488213. −0.234172 −0.117086 0.993122i \(-0.537355\pi\)
−0.117086 + 0.993122i \(0.537355\pi\)
\(338\) 0 0
\(339\) −446265. −0.210908
\(340\) 0 0
\(341\) −3.88412e6 −1.80887
\(342\) 0 0
\(343\) −1.98992e6 −0.913273
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.82809e6 −1.70670 −0.853351 0.521336i \(-0.825434\pi\)
−0.853351 + 0.521336i \(0.825434\pi\)
\(348\) 0 0
\(349\) 1.45476e6 0.639333 0.319667 0.947530i \(-0.396429\pi\)
0.319667 + 0.947530i \(0.396429\pi\)
\(350\) 0 0
\(351\) 1.07789e6 0.466991
\(352\) 0 0
\(353\) 778492. 0.332520 0.166260 0.986082i \(-0.446831\pi\)
0.166260 + 0.986082i \(0.446831\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 685867. 0.284819
\(358\) 0 0
\(359\) 2.12510e6 0.870247 0.435124 0.900371i \(-0.356705\pi\)
0.435124 + 0.900371i \(0.356705\pi\)
\(360\) 0 0
\(361\) −1.38061e6 −0.557577
\(362\) 0 0
\(363\) −415675. −0.165572
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.10801e6 1.59208 0.796042 0.605242i \(-0.206923\pi\)
0.796042 + 0.605242i \(0.206923\pi\)
\(368\) 0 0
\(369\) −2.28891e6 −0.875109
\(370\) 0 0
\(371\) 1.33263e6 0.502662
\(372\) 0 0
\(373\) 4.54570e6 1.69172 0.845860 0.533405i \(-0.179088\pi\)
0.845860 + 0.533405i \(0.179088\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −573624. −0.207861
\(378\) 0 0
\(379\) −1.40554e6 −0.502626 −0.251313 0.967906i \(-0.580862\pi\)
−0.251313 + 0.967906i \(0.580862\pi\)
\(380\) 0 0
\(381\) −891054. −0.314479
\(382\) 0 0
\(383\) 4.64417e6 1.61775 0.808874 0.587982i \(-0.200078\pi\)
0.808874 + 0.587982i \(0.200078\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.19102e6 −1.08306
\(388\) 0 0
\(389\) 3.53606e6 1.18480 0.592400 0.805644i \(-0.298181\pi\)
0.592400 + 0.805644i \(0.298181\pi\)
\(390\) 0 0
\(391\) −1.23678e6 −0.409120
\(392\) 0 0
\(393\) −1.06620e6 −0.348223
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 2.95611e6 0.941336 0.470668 0.882310i \(-0.344013\pi\)
0.470668 + 0.882310i \(0.344013\pi\)
\(398\) 0 0
\(399\) −398671. −0.125367
\(400\) 0 0
\(401\) −799254. −0.248213 −0.124106 0.992269i \(-0.539606\pi\)
−0.124106 + 0.992269i \(0.539606\pi\)
\(402\) 0 0
\(403\) −3.42294e6 −1.04987
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 957937. 0.286649
\(408\) 0 0
\(409\) 898422. 0.265566 0.132783 0.991145i \(-0.457609\pi\)
0.132783 + 0.991145i \(0.457609\pi\)
\(410\) 0 0
\(411\) 1.38292e6 0.403824
\(412\) 0 0
\(413\) −1.46134e6 −0.421576
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.20786e6 −0.340155
\(418\) 0 0
\(419\) −2.31259e6 −0.643523 −0.321761 0.946821i \(-0.604275\pi\)
−0.321761 + 0.946821i \(0.604275\pi\)
\(420\) 0 0
\(421\) 4.43296e6 1.21896 0.609478 0.792803i \(-0.291379\pi\)
0.609478 + 0.792803i \(0.291379\pi\)
\(422\) 0 0
\(423\) −190244. −0.0516965
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −1.91149e6 −0.507344
\(428\) 0 0
\(429\) −1.15036e6 −0.301780
\(430\) 0 0
\(431\) −5.97999e6 −1.55063 −0.775314 0.631576i \(-0.782408\pi\)
−0.775314 + 0.631576i \(0.782408\pi\)
\(432\) 0 0
\(433\) −2.06419e6 −0.529089 −0.264545 0.964373i \(-0.585222\pi\)
−0.264545 + 0.964373i \(0.585222\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 718899. 0.180080
\(438\) 0 0
\(439\) 4.09148e6 1.01326 0.506628 0.862165i \(-0.330892\pi\)
0.506628 + 0.862165i \(0.330892\pi\)
\(440\) 0 0
\(441\) 2.56099e6 0.627064
\(442\) 0 0
\(443\) 2.75822e6 0.667759 0.333879 0.942616i \(-0.391642\pi\)
0.333879 + 0.942616i \(0.391642\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 214006. 0.0506592
\(448\) 0 0
\(449\) −3.76648e6 −0.881698 −0.440849 0.897581i \(-0.645323\pi\)
−0.440849 + 0.897581i \(0.645323\pi\)
\(450\) 0 0
\(451\) 5.23640e6 1.21225
\(452\) 0 0
\(453\) −855944. −0.195975
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −480604. −0.107646 −0.0538229 0.998550i \(-0.517141\pi\)
−0.0538229 + 0.998550i \(0.517141\pi\)
\(458\) 0 0
\(459\) −4.53073e6 −1.00377
\(460\) 0 0
\(461\) 4.52514e6 0.991699 0.495849 0.868409i \(-0.334857\pi\)
0.495849 + 0.868409i \(0.334857\pi\)
\(462\) 0 0
\(463\) 7.39975e6 1.60422 0.802111 0.597175i \(-0.203710\pi\)
0.802111 + 0.597175i \(0.203710\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.84711e6 0.391923 0.195962 0.980612i \(-0.437217\pi\)
0.195962 + 0.980612i \(0.437217\pi\)
\(468\) 0 0
\(469\) −532261. −0.111736
\(470\) 0 0
\(471\) −1.90276e6 −0.395212
\(472\) 0 0
\(473\) 7.30018e6 1.50031
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.10669e6 −0.826410
\(478\) 0 0
\(479\) 3.05088e6 0.607555 0.303778 0.952743i \(-0.401752\pi\)
0.303778 + 0.952743i \(0.401752\pi\)
\(480\) 0 0
\(481\) 844197. 0.166372
\(482\) 0 0
\(483\) −261624. −0.0510281
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 7.28136e6 1.39120 0.695601 0.718429i \(-0.255138\pi\)
0.695601 + 0.718429i \(0.255138\pi\)
\(488\) 0 0
\(489\) −2.02297e6 −0.382575
\(490\) 0 0
\(491\) 6.60475e6 1.23638 0.618191 0.786028i \(-0.287866\pi\)
0.618191 + 0.786028i \(0.287866\pi\)
\(492\) 0 0
\(493\) 2.41112e6 0.446788
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.54481e6 0.643727
\(498\) 0 0
\(499\) −4.87006e6 −0.875555 −0.437777 0.899083i \(-0.644234\pi\)
−0.437777 + 0.899083i \(0.644234\pi\)
\(500\) 0 0
\(501\) −1.37702e6 −0.245102
\(502\) 0 0
\(503\) −1.16752e6 −0.205753 −0.102876 0.994694i \(-0.532805\pi\)
−0.102876 + 0.994694i \(0.532805\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.03732e6 0.179222
\(508\) 0 0
\(509\) −7.41468e6 −1.26852 −0.634261 0.773119i \(-0.718695\pi\)
−0.634261 + 0.773119i \(0.718695\pi\)
\(510\) 0 0
\(511\) 3.01846e6 0.511367
\(512\) 0 0
\(513\) 2.63356e6 0.441824
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 435227. 0.0716127
\(518\) 0 0
\(519\) −339516. −0.0553277
\(520\) 0 0
\(521\) −811897. −0.131041 −0.0655204 0.997851i \(-0.520871\pi\)
−0.0655204 + 0.997851i \(0.520871\pi\)
\(522\) 0 0
\(523\) 5.06828e6 0.810226 0.405113 0.914267i \(-0.367232\pi\)
0.405113 + 0.914267i \(0.367232\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.43877e7 2.25665
\(528\) 0 0
\(529\) −5.96457e6 −0.926702
\(530\) 0 0
\(531\) 4.50331e6 0.693099
\(532\) 0 0
\(533\) 4.61465e6 0.703592
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 3.35209e6 0.501626
\(538\) 0 0
\(539\) −5.85886e6 −0.868642
\(540\) 0 0
\(541\) 1.52830e6 0.224499 0.112250 0.993680i \(-0.464194\pi\)
0.112250 + 0.993680i \(0.464194\pi\)
\(542\) 0 0
\(543\) −848980. −0.123566
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.23234e7 −1.76101 −0.880506 0.474036i \(-0.842797\pi\)
−0.880506 + 0.474036i \(0.842797\pi\)
\(548\) 0 0
\(549\) 5.89050e6 0.834107
\(550\) 0 0
\(551\) −1.40150e6 −0.196660
\(552\) 0 0
\(553\) 429271. 0.0596923
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4.08606e6 0.558042 0.279021 0.960285i \(-0.409990\pi\)
0.279021 + 0.960285i \(0.409990\pi\)
\(558\) 0 0
\(559\) 6.43339e6 0.870784
\(560\) 0 0
\(561\) 4.83531e6 0.648661
\(562\) 0 0
\(563\) 24160.3 0.00321241 0.00160621 0.999999i \(-0.499489\pi\)
0.00160621 + 0.999999i \(0.499489\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.60180e6 0.339873
\(568\) 0 0
\(569\) 1.42000e7 1.83869 0.919344 0.393454i \(-0.128720\pi\)
0.919344 + 0.393454i \(0.128720\pi\)
\(570\) 0 0
\(571\) 767642. 0.0985300 0.0492650 0.998786i \(-0.484312\pi\)
0.0492650 + 0.998786i \(0.484312\pi\)
\(572\) 0 0
\(573\) 1.00714e6 0.128145
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.51488e6 0.189426 0.0947129 0.995505i \(-0.469807\pi\)
0.0947129 + 0.995505i \(0.469807\pi\)
\(578\) 0 0
\(579\) −563910. −0.0699059
\(580\) 0 0
\(581\) 3.65098e6 0.448714
\(582\) 0 0
\(583\) 9.39498e6 1.14479
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.28973e7 −1.54491 −0.772455 0.635070i \(-0.780971\pi\)
−0.772455 + 0.635070i \(0.780971\pi\)
\(588\) 0 0
\(589\) −8.36307e6 −0.993294
\(590\) 0 0
\(591\) −2.23539e6 −0.263260
\(592\) 0 0
\(593\) 5.43125e6 0.634254 0.317127 0.948383i \(-0.397282\pi\)
0.317127 + 0.948383i \(0.397282\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −924180. −0.106126
\(598\) 0 0
\(599\) −3.92217e6 −0.446642 −0.223321 0.974745i \(-0.571690\pi\)
−0.223321 + 0.974745i \(0.571690\pi\)
\(600\) 0 0
\(601\) −5.64824e6 −0.637863 −0.318931 0.947778i \(-0.603324\pi\)
−0.318931 + 0.947778i \(0.603324\pi\)
\(602\) 0 0
\(603\) 1.64023e6 0.183701
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −1.07148e7 −1.18035 −0.590177 0.807274i \(-0.700942\pi\)
−0.590177 + 0.807274i \(0.700942\pi\)
\(608\) 0 0
\(609\) 510039. 0.0557263
\(610\) 0 0
\(611\) 383551. 0.0415642
\(612\) 0 0
\(613\) −4.08748e6 −0.439344 −0.219672 0.975574i \(-0.570499\pi\)
−0.219672 + 0.975574i \(0.570499\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.83395e6 0.828453 0.414227 0.910174i \(-0.364052\pi\)
0.414227 + 0.910174i \(0.364052\pi\)
\(618\) 0 0
\(619\) −1.23423e7 −1.29470 −0.647352 0.762191i \(-0.724124\pi\)
−0.647352 + 0.762191i \(0.724124\pi\)
\(620\) 0 0
\(621\) 1.72824e6 0.179836
\(622\) 0 0
\(623\) 3.07739e6 0.317660
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.81061e6 −0.285516
\(628\) 0 0
\(629\) −3.54842e6 −0.357609
\(630\) 0 0
\(631\) 1.31578e6 0.131556 0.0657780 0.997834i \(-0.479047\pi\)
0.0657780 + 0.997834i \(0.479047\pi\)
\(632\) 0 0
\(633\) −2.54542e6 −0.252494
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.16320e6 −0.504163
\(638\) 0 0
\(639\) −1.09238e7 −1.05833
\(640\) 0 0
\(641\) 6.55744e6 0.630360 0.315180 0.949032i \(-0.397935\pi\)
0.315180 + 0.949032i \(0.397935\pi\)
\(642\) 0 0
\(643\) −4.69954e6 −0.448258 −0.224129 0.974559i \(-0.571954\pi\)
−0.224129 + 0.974559i \(0.571954\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.05827e7 1.93305 0.966523 0.256580i \(-0.0825956\pi\)
0.966523 + 0.256580i \(0.0825956\pi\)
\(648\) 0 0
\(649\) −1.03023e7 −0.960117
\(650\) 0 0
\(651\) 3.04351e6 0.281464
\(652\) 0 0
\(653\) 1.42466e7 1.30746 0.653731 0.756727i \(-0.273203\pi\)
0.653731 + 0.756727i \(0.273203\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −9.30177e6 −0.840722
\(658\) 0 0
\(659\) 1.35369e7 1.21425 0.607123 0.794608i \(-0.292324\pi\)
0.607123 + 0.794608i \(0.292324\pi\)
\(660\) 0 0
\(661\) −1.30443e7 −1.16122 −0.580612 0.814180i \(-0.697187\pi\)
−0.580612 + 0.814180i \(0.697187\pi\)
\(662\) 0 0
\(663\) 4.26119e6 0.376485
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −919721. −0.0800464
\(668\) 0 0
\(669\) 5.98260e6 0.516802
\(670\) 0 0
\(671\) −1.34759e7 −1.15545
\(672\) 0 0
\(673\) −4.75951e6 −0.405065 −0.202532 0.979276i \(-0.564917\pi\)
−0.202532 + 0.979276i \(0.564917\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.51397e7 1.26954 0.634770 0.772701i \(-0.281095\pi\)
0.634770 + 0.772701i \(0.281095\pi\)
\(678\) 0 0
\(679\) 1.02061e7 0.849543
\(680\) 0 0
\(681\) −2.27707e6 −0.188152
\(682\) 0 0
\(683\) −2.34145e7 −1.92058 −0.960292 0.278998i \(-0.909998\pi\)
−0.960292 + 0.278998i \(0.909998\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 2.39287e6 0.193431
\(688\) 0 0
\(689\) 8.27947e6 0.664438
\(690\) 0 0
\(691\) 1.62194e7 1.29223 0.646113 0.763242i \(-0.276394\pi\)
0.646113 + 0.763242i \(0.276394\pi\)
\(692\) 0 0
\(693\) −7.12196e6 −0.563334
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.93968e7 −1.51234
\(698\) 0 0
\(699\) 4.19891e6 0.325045
\(700\) 0 0
\(701\) −1.89605e7 −1.45732 −0.728659 0.684876i \(-0.759856\pi\)
−0.728659 + 0.684876i \(0.759856\pi\)
\(702\) 0 0
\(703\) 2.06258e6 0.157406
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.02377e7 0.770287
\(708\) 0 0
\(709\) 128325. 0.00958732 0.00479366 0.999989i \(-0.498474\pi\)
0.00479366 + 0.999989i \(0.498474\pi\)
\(710\) 0 0
\(711\) −1.32285e6 −0.0981382
\(712\) 0 0
\(713\) −5.48817e6 −0.404300
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −5.46133e6 −0.396735
\(718\) 0 0
\(719\) 2.41874e7 1.74489 0.872444 0.488714i \(-0.162534\pi\)
0.872444 + 0.488714i \(0.162534\pi\)
\(720\) 0 0
\(721\) 1.29899e7 0.930610
\(722\) 0 0
\(723\) 1.98251e6 0.141049
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −513307. −0.0360198 −0.0180099 0.999838i \(-0.505733\pi\)
−0.0180099 + 0.999838i \(0.505733\pi\)
\(728\) 0 0
\(729\) −4.64015e6 −0.323380
\(730\) 0 0
\(731\) −2.70416e7 −1.87171
\(732\) 0 0
\(733\) −1.64153e7 −1.12847 −0.564234 0.825615i \(-0.690828\pi\)
−0.564234 + 0.825615i \(0.690828\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.75240e6 −0.254472
\(738\) 0 0
\(739\) −1.16112e7 −0.782109 −0.391054 0.920368i \(-0.627890\pi\)
−0.391054 + 0.920368i \(0.627890\pi\)
\(740\) 0 0
\(741\) −2.47689e6 −0.165715
\(742\) 0 0
\(743\) −5.72590e6 −0.380515 −0.190257 0.981734i \(-0.560932\pi\)
−0.190257 + 0.981734i \(0.560932\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.12510e7 −0.737715
\(748\) 0 0
\(749\) 4.68097e6 0.304882
\(750\) 0 0
\(751\) −1.15324e7 −0.746137 −0.373069 0.927804i \(-0.621694\pi\)
−0.373069 + 0.927804i \(0.621694\pi\)
\(752\) 0 0
\(753\) −4.70134e6 −0.302158
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −8.63293e6 −0.547544 −0.273772 0.961795i \(-0.588271\pi\)
−0.273772 + 0.961795i \(0.588271\pi\)
\(758\) 0 0
\(759\) −1.84443e6 −0.116214
\(760\) 0 0
\(761\) −3.52622e6 −0.220723 −0.110361 0.993892i \(-0.535201\pi\)
−0.110361 + 0.993892i \(0.535201\pi\)
\(762\) 0 0
\(763\) −1.51206e7 −0.940280
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −9.07910e6 −0.557255
\(768\) 0 0
\(769\) 1.40471e7 0.856585 0.428293 0.903640i \(-0.359115\pi\)
0.428293 + 0.903640i \(0.359115\pi\)
\(770\) 0 0
\(771\) −421817. −0.0255557
\(772\) 0 0
\(773\) −2.44760e7 −1.47330 −0.736651 0.676274i \(-0.763594\pi\)
−0.736651 + 0.676274i \(0.763594\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −750619. −0.0446033
\(778\) 0 0
\(779\) 1.12747e7 0.665675
\(780\) 0 0
\(781\) 2.49907e7 1.46606
\(782\) 0 0
\(783\) −3.36924e6 −0.196393
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −4.35977e6 −0.250915 −0.125458 0.992099i \(-0.540040\pi\)
−0.125458 + 0.992099i \(0.540040\pi\)
\(788\) 0 0
\(789\) −6.59697e6 −0.377270
\(790\) 0 0
\(791\) 5.57019e6 0.316540
\(792\) 0 0
\(793\) −1.18758e7 −0.670626
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.06887e7 0.596044 0.298022 0.954559i \(-0.403673\pi\)
0.298022 + 0.954559i \(0.403673\pi\)
\(798\) 0 0
\(799\) −1.61218e6 −0.0893403
\(800\) 0 0
\(801\) −9.48339e6 −0.522255
\(802\) 0 0
\(803\) 2.12799e7 1.16461
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −5.68605e6 −0.307345
\(808\) 0 0
\(809\) 9.12014e6 0.489926 0.244963 0.969532i \(-0.421224\pi\)
0.244963 + 0.969532i \(0.421224\pi\)
\(810\) 0 0
\(811\) −5.22575e6 −0.278995 −0.139497 0.990222i \(-0.544549\pi\)
−0.139497 + 0.990222i \(0.544549\pi\)
\(812\) 0 0
\(813\) 1.17192e7 0.621830
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.57184e7 0.823857
\(818\) 0 0
\(819\) −6.27633e6 −0.326961
\(820\) 0 0
\(821\) 9.00437e6 0.466225 0.233112 0.972450i \(-0.425109\pi\)
0.233112 + 0.972450i \(0.425109\pi\)
\(822\) 0 0
\(823\) −2.78867e7 −1.43515 −0.717574 0.696482i \(-0.754748\pi\)
−0.717574 + 0.696482i \(0.754748\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −6.64309e6 −0.337758 −0.168879 0.985637i \(-0.554015\pi\)
−0.168879 + 0.985637i \(0.554015\pi\)
\(828\) 0 0
\(829\) 2.17030e7 1.09682 0.548408 0.836211i \(-0.315234\pi\)
0.548408 + 0.836211i \(0.315234\pi\)
\(830\) 0 0
\(831\) 1.02277e7 0.513780
\(832\) 0 0
\(833\) 2.17026e7 1.08367
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2.01049e7 −0.991949
\(838\) 0 0
\(839\) 1.01238e7 0.496520 0.248260 0.968693i \(-0.420141\pi\)
0.248260 + 0.968693i \(0.420141\pi\)
\(840\) 0 0
\(841\) −1.87181e7 −0.912584
\(842\) 0 0
\(843\) −500784. −0.0242707
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 5.18837e6 0.248498
\(848\) 0 0
\(849\) 5.13366e6 0.244432
\(850\) 0 0
\(851\) 1.35354e6 0.0640691
\(852\) 0 0
\(853\) −1.46326e7 −0.688573 −0.344286 0.938865i \(-0.611879\pi\)
−0.344286 + 0.938865i \(0.611879\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 5.52218e6 0.256838 0.128419 0.991720i \(-0.459010\pi\)
0.128419 + 0.991720i \(0.459010\pi\)
\(858\) 0 0
\(859\) 3.02260e6 0.139765 0.0698824 0.997555i \(-0.477738\pi\)
0.0698824 + 0.997555i \(0.477738\pi\)
\(860\) 0 0
\(861\) −4.10313e6 −0.188628
\(862\) 0 0
\(863\) −3.06818e7 −1.40234 −0.701172 0.712992i \(-0.747339\pi\)
−0.701172 + 0.712992i \(0.747339\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.00676e7 −0.454860
\(868\) 0 0
\(869\) 3.02633e6 0.135946
\(870\) 0 0
\(871\) −3.30686e6 −0.147697
\(872\) 0 0
\(873\) −3.14514e7 −1.39671
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 5.17607e6 0.227249 0.113624 0.993524i \(-0.463754\pi\)
0.113624 + 0.993524i \(0.463754\pi\)
\(878\) 0 0
\(879\) 1.50662e7 0.657707
\(880\) 0 0
\(881\) −4.25937e7 −1.84887 −0.924433 0.381345i \(-0.875461\pi\)
−0.924433 + 0.381345i \(0.875461\pi\)
\(882\) 0 0
\(883\) −1.72076e7 −0.742709 −0.371354 0.928491i \(-0.621107\pi\)
−0.371354 + 0.928491i \(0.621107\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.53773e6 0.108302 0.0541510 0.998533i \(-0.482755\pi\)
0.0541510 + 0.998533i \(0.482755\pi\)
\(888\) 0 0
\(889\) 1.11220e7 0.471984
\(890\) 0 0
\(891\) 1.83425e7 0.774043
\(892\) 0 0
\(893\) 937108. 0.0393243
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.62543e6 −0.0674508
\(898\) 0 0
\(899\) 1.06993e7 0.441525
\(900\) 0 0
\(901\) −3.48012e7 −1.42818
\(902\) 0 0
\(903\) −5.72026e6 −0.233452
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 2.60899e7 1.05306 0.526531 0.850156i \(-0.323492\pi\)
0.526531 + 0.850156i \(0.323492\pi\)
\(908\) 0 0
\(909\) −3.15487e7 −1.26640
\(910\) 0 0
\(911\) −1.44818e7 −0.578130 −0.289065 0.957309i \(-0.593344\pi\)
−0.289065 + 0.957309i \(0.593344\pi\)
\(912\) 0 0
\(913\) 2.57392e7 1.02192
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.33081e7 0.522627
\(918\) 0 0
\(919\) −4.61041e7 −1.80074 −0.900369 0.435127i \(-0.856704\pi\)
−0.900369 + 0.435127i \(0.856704\pi\)
\(920\) 0 0
\(921\) 1.26861e7 0.492811
\(922\) 0 0
\(923\) 2.20234e7 0.850903
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −4.00301e7 −1.52998
\(928\) 0 0
\(929\) −1.81557e7 −0.690197 −0.345098 0.938567i \(-0.612154\pi\)
−0.345098 + 0.938567i \(0.612154\pi\)
\(930\) 0 0
\(931\) −1.26150e7 −0.476993
\(932\) 0 0
\(933\) 5.44047e6 0.204612
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1.78946e7 −0.665844 −0.332922 0.942954i \(-0.608035\pi\)
−0.332922 + 0.942954i \(0.608035\pi\)
\(938\) 0 0
\(939\) 1.14157e7 0.422512
\(940\) 0 0
\(941\) −3.04463e6 −0.112088 −0.0560441 0.998428i \(-0.517849\pi\)
−0.0560441 + 0.998428i \(0.517849\pi\)
\(942\) 0 0
\(943\) 7.39891e6 0.270950
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.17110e7 1.14904 0.574519 0.818491i \(-0.305189\pi\)
0.574519 + 0.818491i \(0.305189\pi\)
\(948\) 0 0
\(949\) 1.87532e7 0.675944
\(950\) 0 0
\(951\) 6.31686e6 0.226491
\(952\) 0 0
\(953\) −1.01913e7 −0.363494 −0.181747 0.983345i \(-0.558175\pi\)
−0.181747 + 0.983345i \(0.558175\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 3.59574e6 0.126914
\(958\) 0 0
\(959\) −1.72613e7 −0.606077
\(960\) 0 0
\(961\) 3.52157e7 1.23006
\(962\) 0 0
\(963\) −1.44250e7 −0.501246
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −3.21125e7 −1.10435 −0.552177 0.833727i \(-0.686203\pi\)
−0.552177 + 0.833727i \(0.686203\pi\)
\(968\) 0 0
\(969\) 1.04111e7 0.356196
\(970\) 0 0
\(971\) −2.29867e7 −0.782399 −0.391200 0.920306i \(-0.627940\pi\)
−0.391200 + 0.920306i \(0.627940\pi\)
\(972\) 0 0
\(973\) 1.50763e7 0.510519
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.47331e7 0.828978 0.414489 0.910054i \(-0.363960\pi\)
0.414489 + 0.910054i \(0.363960\pi\)
\(978\) 0 0
\(979\) 2.16954e7 0.723455
\(980\) 0 0
\(981\) 4.65960e7 1.54588
\(982\) 0 0
\(983\) 5.57031e7 1.83863 0.919317 0.393518i \(-0.128742\pi\)
0.919317 + 0.393518i \(0.128742\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −341035. −0.0111431
\(988\) 0 0
\(989\) 1.03150e7 0.335335
\(990\) 0 0
\(991\) 6.86029e6 0.221901 0.110950 0.993826i \(-0.464611\pi\)
0.110950 + 0.993826i \(0.464611\pi\)
\(992\) 0 0
\(993\) 1.13373e6 0.0364868
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −6.03725e7 −1.92354 −0.961771 0.273856i \(-0.911701\pi\)
−0.961771 + 0.273856i \(0.911701\pi\)
\(998\) 0 0
\(999\) 4.95847e6 0.157193
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 400.6.a.w.1.1 2
4.3 odd 2 25.6.a.b.1.1 2
5.2 odd 4 400.6.c.n.49.3 4
5.3 odd 4 400.6.c.n.49.2 4
5.4 even 2 400.6.a.o.1.2 2
12.11 even 2 225.6.a.s.1.2 2
20.3 even 4 25.6.b.b.24.4 4
20.7 even 4 25.6.b.b.24.1 4
20.19 odd 2 25.6.a.d.1.2 yes 2
60.23 odd 4 225.6.b.i.199.1 4
60.47 odd 4 225.6.b.i.199.4 4
60.59 even 2 225.6.a.l.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.6.a.b.1.1 2 4.3 odd 2
25.6.a.d.1.2 yes 2 20.19 odd 2
25.6.b.b.24.1 4 20.7 even 4
25.6.b.b.24.4 4 20.3 even 4
225.6.a.l.1.1 2 60.59 even 2
225.6.a.s.1.2 2 12.11 even 2
225.6.b.i.199.1 4 60.23 odd 4
225.6.b.i.199.4 4 60.47 odd 4
400.6.a.o.1.2 2 5.4 even 2
400.6.a.w.1.1 2 1.1 even 1 trivial
400.6.c.n.49.2 4 5.3 odd 4
400.6.c.n.49.3 4 5.2 odd 4