Properties

Label 245.6.a.b.1.1
Level $245$
Weight $6$
Character 245.1
Self dual yes
Analytic conductor $39.294$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(39.2940358542\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 5)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 245.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +4.00000 q^{3} -28.0000 q^{4} -25.0000 q^{5} +8.00000 q^{6} -120.000 q^{8} -227.000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +4.00000 q^{3} -28.0000 q^{4} -25.0000 q^{5} +8.00000 q^{6} -120.000 q^{8} -227.000 q^{9} -50.0000 q^{10} -148.000 q^{11} -112.000 q^{12} -286.000 q^{13} -100.000 q^{15} +656.000 q^{16} +1678.00 q^{17} -454.000 q^{18} -1060.00 q^{19} +700.000 q^{20} -296.000 q^{22} +2976.00 q^{23} -480.000 q^{24} +625.000 q^{25} -572.000 q^{26} -1880.00 q^{27} -3410.00 q^{29} -200.000 q^{30} +2448.00 q^{31} +5152.00 q^{32} -592.000 q^{33} +3356.00 q^{34} +6356.00 q^{36} +182.000 q^{37} -2120.00 q^{38} -1144.00 q^{39} +3000.00 q^{40} +9398.00 q^{41} -1244.00 q^{43} +4144.00 q^{44} +5675.00 q^{45} +5952.00 q^{46} +12088.0 q^{47} +2624.00 q^{48} +1250.00 q^{50} +6712.00 q^{51} +8008.00 q^{52} +23846.0 q^{53} -3760.00 q^{54} +3700.00 q^{55} -4240.00 q^{57} -6820.00 q^{58} +20020.0 q^{59} +2800.00 q^{60} -32302.0 q^{61} +4896.00 q^{62} -10688.0 q^{64} +7150.00 q^{65} -1184.00 q^{66} +60972.0 q^{67} -46984.0 q^{68} +11904.0 q^{69} -32648.0 q^{71} +27240.0 q^{72} +38774.0 q^{73} +364.000 q^{74} +2500.00 q^{75} +29680.0 q^{76} -2288.00 q^{78} -33360.0 q^{79} -16400.0 q^{80} +47641.0 q^{81} +18796.0 q^{82} -16716.0 q^{83} -41950.0 q^{85} -2488.00 q^{86} -13640.0 q^{87} +17760.0 q^{88} -101370. q^{89} +11350.0 q^{90} -83328.0 q^{92} +9792.00 q^{93} +24176.0 q^{94} +26500.0 q^{95} +20608.0 q^{96} +119038. q^{97} +33596.0 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.353553 0.176777 0.984251i \(-0.443433\pi\)
0.176777 + 0.984251i \(0.443433\pi\)
\(3\) 4.00000 0.256600 0.128300 0.991735i \(-0.459048\pi\)
0.128300 + 0.991735i \(0.459048\pi\)
\(4\) −28.0000 −0.875000
\(5\) −25.0000 −0.447214
\(6\) 8.00000 0.0907218
\(7\) 0 0
\(8\) −120.000 −0.662913
\(9\) −227.000 −0.934156
\(10\) −50.0000 −0.158114
\(11\) −148.000 −0.368791 −0.184395 0.982852i \(-0.559033\pi\)
−0.184395 + 0.982852i \(0.559033\pi\)
\(12\) −112.000 −0.224525
\(13\) −286.000 −0.469362 −0.234681 0.972072i \(-0.575405\pi\)
−0.234681 + 0.972072i \(0.575405\pi\)
\(14\) 0 0
\(15\) −100.000 −0.114755
\(16\) 656.000 0.640625
\(17\) 1678.00 1.40822 0.704109 0.710092i \(-0.251347\pi\)
0.704109 + 0.710092i \(0.251347\pi\)
\(18\) −454.000 −0.330274
\(19\) −1060.00 −0.673631 −0.336815 0.941571i \(-0.609350\pi\)
−0.336815 + 0.941571i \(0.609350\pi\)
\(20\) 700.000 0.391312
\(21\) 0 0
\(22\) −296.000 −0.130387
\(23\) 2976.00 1.17304 0.586521 0.809934i \(-0.300497\pi\)
0.586521 + 0.809934i \(0.300497\pi\)
\(24\) −480.000 −0.170103
\(25\) 625.000 0.200000
\(26\) −572.000 −0.165944
\(27\) −1880.00 −0.496305
\(28\) 0 0
\(29\) −3410.00 −0.752938 −0.376469 0.926429i \(-0.622862\pi\)
−0.376469 + 0.926429i \(0.622862\pi\)
\(30\) −200.000 −0.0405720
\(31\) 2448.00 0.457517 0.228758 0.973483i \(-0.426533\pi\)
0.228758 + 0.973483i \(0.426533\pi\)
\(32\) 5152.00 0.889408
\(33\) −592.000 −0.0946317
\(34\) 3356.00 0.497880
\(35\) 0 0
\(36\) 6356.00 0.817387
\(37\) 182.000 0.0218558 0.0109279 0.999940i \(-0.496521\pi\)
0.0109279 + 0.999940i \(0.496521\pi\)
\(38\) −2120.00 −0.238164
\(39\) −1144.00 −0.120438
\(40\) 3000.00 0.296464
\(41\) 9398.00 0.873124 0.436562 0.899674i \(-0.356196\pi\)
0.436562 + 0.899674i \(0.356196\pi\)
\(42\) 0 0
\(43\) −1244.00 −0.102600 −0.0513002 0.998683i \(-0.516337\pi\)
−0.0513002 + 0.998683i \(0.516337\pi\)
\(44\) 4144.00 0.322692
\(45\) 5675.00 0.417767
\(46\) 5952.00 0.414733
\(47\) 12088.0 0.798196 0.399098 0.916908i \(-0.369323\pi\)
0.399098 + 0.916908i \(0.369323\pi\)
\(48\) 2624.00 0.164384
\(49\) 0 0
\(50\) 1250.00 0.0707107
\(51\) 6712.00 0.361349
\(52\) 8008.00 0.410691
\(53\) 23846.0 1.16607 0.583037 0.812446i \(-0.301864\pi\)
0.583037 + 0.812446i \(0.301864\pi\)
\(54\) −3760.00 −0.175470
\(55\) 3700.00 0.164928
\(56\) 0 0
\(57\) −4240.00 −0.172854
\(58\) −6820.00 −0.266204
\(59\) 20020.0 0.748745 0.374373 0.927278i \(-0.377858\pi\)
0.374373 + 0.927278i \(0.377858\pi\)
\(60\) 2800.00 0.100411
\(61\) −32302.0 −1.11149 −0.555744 0.831353i \(-0.687567\pi\)
−0.555744 + 0.831353i \(0.687567\pi\)
\(62\) 4896.00 0.161757
\(63\) 0 0
\(64\) −10688.0 −0.326172
\(65\) 7150.00 0.209905
\(66\) −1184.00 −0.0334574
\(67\) 60972.0 1.65937 0.829685 0.558231i \(-0.188520\pi\)
0.829685 + 0.558231i \(0.188520\pi\)
\(68\) −46984.0 −1.23219
\(69\) 11904.0 0.301003
\(70\) 0 0
\(71\) −32648.0 −0.768618 −0.384309 0.923204i \(-0.625560\pi\)
−0.384309 + 0.923204i \(0.625560\pi\)
\(72\) 27240.0 0.619264
\(73\) 38774.0 0.851596 0.425798 0.904818i \(-0.359993\pi\)
0.425798 + 0.904818i \(0.359993\pi\)
\(74\) 364.000 0.00772720
\(75\) 2500.00 0.0513200
\(76\) 29680.0 0.589427
\(77\) 0 0
\(78\) −2288.00 −0.0425814
\(79\) −33360.0 −0.601393 −0.300696 0.953720i \(-0.597219\pi\)
−0.300696 + 0.953720i \(0.597219\pi\)
\(80\) −16400.0 −0.286496
\(81\) 47641.0 0.806805
\(82\) 18796.0 0.308696
\(83\) −16716.0 −0.266340 −0.133170 0.991093i \(-0.542516\pi\)
−0.133170 + 0.991093i \(0.542516\pi\)
\(84\) 0 0
\(85\) −41950.0 −0.629774
\(86\) −2488.00 −0.0362747
\(87\) −13640.0 −0.193204
\(88\) 17760.0 0.244476
\(89\) −101370. −1.35655 −0.678273 0.734810i \(-0.737271\pi\)
−0.678273 + 0.734810i \(0.737271\pi\)
\(90\) 11350.0 0.147703
\(91\) 0 0
\(92\) −83328.0 −1.02641
\(93\) 9792.00 0.117399
\(94\) 24176.0 0.282205
\(95\) 26500.0 0.301257
\(96\) 20608.0 0.228222
\(97\) 119038. 1.28457 0.642283 0.766468i \(-0.277987\pi\)
0.642283 + 0.766468i \(0.277987\pi\)
\(98\) 0 0
\(99\) 33596.0 0.344508
\(100\) −17500.0 −0.175000
\(101\) 89898.0 0.876893 0.438446 0.898757i \(-0.355529\pi\)
0.438446 + 0.898757i \(0.355529\pi\)
\(102\) 13424.0 0.127756
\(103\) 19504.0 0.181147 0.0905734 0.995890i \(-0.471130\pi\)
0.0905734 + 0.995890i \(0.471130\pi\)
\(104\) 34320.0 0.311146
\(105\) 0 0
\(106\) 47692.0 0.412269
\(107\) 158292. 1.33659 0.668297 0.743895i \(-0.267024\pi\)
0.668297 + 0.743895i \(0.267024\pi\)
\(108\) 52640.0 0.434267
\(109\) 36830.0 0.296917 0.148459 0.988919i \(-0.452569\pi\)
0.148459 + 0.988919i \(0.452569\pi\)
\(110\) 7400.00 0.0583109
\(111\) 728.000 0.00560821
\(112\) 0 0
\(113\) 11186.0 0.0824098 0.0412049 0.999151i \(-0.486880\pi\)
0.0412049 + 0.999151i \(0.486880\pi\)
\(114\) −8480.00 −0.0611130
\(115\) −74400.0 −0.524600
\(116\) 95480.0 0.658821
\(117\) 64922.0 0.438457
\(118\) 40040.0 0.264721
\(119\) 0 0
\(120\) 12000.0 0.0760726
\(121\) −139147. −0.863993
\(122\) −64604.0 −0.392970
\(123\) 37592.0 0.224044
\(124\) −68544.0 −0.400327
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) 70552.0 0.388150 0.194075 0.980987i \(-0.437829\pi\)
0.194075 + 0.980987i \(0.437829\pi\)
\(128\) −186240. −1.00473
\(129\) −4976.00 −0.0263273
\(130\) 14300.0 0.0742126
\(131\) −76452.0 −0.389234 −0.194617 0.980879i \(-0.562346\pi\)
−0.194617 + 0.980879i \(0.562346\pi\)
\(132\) 16576.0 0.0828028
\(133\) 0 0
\(134\) 121944. 0.586676
\(135\) 47000.0 0.221954
\(136\) −201360. −0.933525
\(137\) −144918. −0.659661 −0.329831 0.944040i \(-0.606992\pi\)
−0.329831 + 0.944040i \(0.606992\pi\)
\(138\) 23808.0 0.106420
\(139\) −112220. −0.492644 −0.246322 0.969188i \(-0.579222\pi\)
−0.246322 + 0.969188i \(0.579222\pi\)
\(140\) 0 0
\(141\) 48352.0 0.204817
\(142\) −65296.0 −0.271748
\(143\) 42328.0 0.173096
\(144\) −148912. −0.598444
\(145\) 85250.0 0.336724
\(146\) 77548.0 0.301085
\(147\) 0 0
\(148\) −5096.00 −0.0191238
\(149\) 403750. 1.48986 0.744932 0.667140i \(-0.232482\pi\)
0.744932 + 0.667140i \(0.232482\pi\)
\(150\) 5000.00 0.0181444
\(151\) −446648. −1.59413 −0.797064 0.603895i \(-0.793615\pi\)
−0.797064 + 0.603895i \(0.793615\pi\)
\(152\) 127200. 0.446558
\(153\) −380906. −1.31550
\(154\) 0 0
\(155\) −61200.0 −0.204608
\(156\) 32032.0 0.105383
\(157\) 262258. 0.849141 0.424570 0.905395i \(-0.360425\pi\)
0.424570 + 0.905395i \(0.360425\pi\)
\(158\) −66720.0 −0.212625
\(159\) 95384.0 0.299215
\(160\) −128800. −0.397755
\(161\) 0 0
\(162\) 95282.0 0.285248
\(163\) −154564. −0.455658 −0.227829 0.973701i \(-0.573163\pi\)
−0.227829 + 0.973701i \(0.573163\pi\)
\(164\) −263144. −0.763983
\(165\) 14800.0 0.0423206
\(166\) −33432.0 −0.0941656
\(167\) −396672. −1.10063 −0.550314 0.834958i \(-0.685492\pi\)
−0.550314 + 0.834958i \(0.685492\pi\)
\(168\) 0 0
\(169\) −289497. −0.779700
\(170\) −83900.0 −0.222659
\(171\) 240620. 0.629276
\(172\) 34832.0 0.0897754
\(173\) 573474. 1.45680 0.728398 0.685155i \(-0.240265\pi\)
0.728398 + 0.685155i \(0.240265\pi\)
\(174\) −27280.0 −0.0683079
\(175\) 0 0
\(176\) −97088.0 −0.236257
\(177\) 80080.0 0.192128
\(178\) −202740. −0.479611
\(179\) −594460. −1.38672 −0.693362 0.720589i \(-0.743871\pi\)
−0.693362 + 0.720589i \(0.743871\pi\)
\(180\) −158900. −0.365547
\(181\) 107098. 0.242988 0.121494 0.992592i \(-0.461231\pi\)
0.121494 + 0.992592i \(0.461231\pi\)
\(182\) 0 0
\(183\) −129208. −0.285208
\(184\) −357120. −0.777624
\(185\) −4550.00 −0.00977422
\(186\) 19584.0 0.0415068
\(187\) −248344. −0.519337
\(188\) −338464. −0.698422
\(189\) 0 0
\(190\) 53000.0 0.106510
\(191\) 469552. 0.931323 0.465661 0.884963i \(-0.345816\pi\)
0.465661 + 0.884963i \(0.345816\pi\)
\(192\) −42752.0 −0.0836957
\(193\) 52706.0 0.101851 0.0509257 0.998702i \(-0.483783\pi\)
0.0509257 + 0.998702i \(0.483783\pi\)
\(194\) 238076. 0.454163
\(195\) 28600.0 0.0538616
\(196\) 0 0
\(197\) 455862. 0.836889 0.418444 0.908242i \(-0.362575\pi\)
0.418444 + 0.908242i \(0.362575\pi\)
\(198\) 67192.0 0.121802
\(199\) −865000. −1.54840 −0.774200 0.632940i \(-0.781848\pi\)
−0.774200 + 0.632940i \(0.781848\pi\)
\(200\) −75000.0 −0.132583
\(201\) 243888. 0.425795
\(202\) 179796. 0.310028
\(203\) 0 0
\(204\) −187936. −0.316180
\(205\) −234950. −0.390473
\(206\) 39008.0 0.0640451
\(207\) −675552. −1.09580
\(208\) −187616. −0.300685
\(209\) 156880. 0.248429
\(210\) 0 0
\(211\) 1.10565e6 1.70967 0.854835 0.518900i \(-0.173658\pi\)
0.854835 + 0.518900i \(0.173658\pi\)
\(212\) −667688. −1.02031
\(213\) −130592. −0.197228
\(214\) 316584. 0.472557
\(215\) 31100.0 0.0458843
\(216\) 225600. 0.329007
\(217\) 0 0
\(218\) 73660.0 0.104976
\(219\) 155096. 0.218520
\(220\) −103600. −0.144312
\(221\) −479908. −0.660963
\(222\) 1456.00 0.00198280
\(223\) −1.12158e6 −1.51031 −0.755156 0.655545i \(-0.772439\pi\)
−0.755156 + 0.655545i \(0.772439\pi\)
\(224\) 0 0
\(225\) −141875. −0.186831
\(226\) 22372.0 0.0291363
\(227\) 23348.0 0.0300736 0.0150368 0.999887i \(-0.495213\pi\)
0.0150368 + 0.999887i \(0.495213\pi\)
\(228\) 118720. 0.151247
\(229\) 596010. 0.751043 0.375522 0.926814i \(-0.377464\pi\)
0.375522 + 0.926814i \(0.377464\pi\)
\(230\) −148800. −0.185474
\(231\) 0 0
\(232\) 409200. 0.499132
\(233\) −485334. −0.585667 −0.292834 0.956163i \(-0.594598\pi\)
−0.292834 + 0.956163i \(0.594598\pi\)
\(234\) 129844. 0.155018
\(235\) −302200. −0.356964
\(236\) −560560. −0.655152
\(237\) −133440. −0.154317
\(238\) 0 0
\(239\) −48880.0 −0.0553524 −0.0276762 0.999617i \(-0.508811\pi\)
−0.0276762 + 0.999617i \(0.508811\pi\)
\(240\) −65600.0 −0.0735150
\(241\) 110798. 0.122882 0.0614411 0.998111i \(-0.480430\pi\)
0.0614411 + 0.998111i \(0.480430\pi\)
\(242\) −278294. −0.305468
\(243\) 647404. 0.703331
\(244\) 904456. 0.972552
\(245\) 0 0
\(246\) 75184.0 0.0792114
\(247\) 303160. 0.316176
\(248\) −293760. −0.303294
\(249\) −66864.0 −0.0683430
\(250\) −31250.0 −0.0316228
\(251\) 1.64375e6 1.64684 0.823419 0.567434i \(-0.192064\pi\)
0.823419 + 0.567434i \(0.192064\pi\)
\(252\) 0 0
\(253\) −440448. −0.432607
\(254\) 141104. 0.137232
\(255\) −167800. −0.161600
\(256\) −30464.0 −0.0290527
\(257\) −1.30624e6 −1.23365 −0.616823 0.787102i \(-0.711581\pi\)
−0.616823 + 0.787102i \(0.711581\pi\)
\(258\) −9952.00 −0.00930810
\(259\) 0 0
\(260\) −200200. −0.183667
\(261\) 774070. 0.703362
\(262\) −152904. −0.137615
\(263\) 2.12834e6 1.89736 0.948682 0.316231i \(-0.102417\pi\)
0.948682 + 0.316231i \(0.102417\pi\)
\(264\) 71040.0 0.0627326
\(265\) −596150. −0.521484
\(266\) 0 0
\(267\) −405480. −0.348090
\(268\) −1.70722e6 −1.45195
\(269\) 1.44109e6 1.21426 0.607128 0.794604i \(-0.292321\pi\)
0.607128 + 0.794604i \(0.292321\pi\)
\(270\) 94000.0 0.0784727
\(271\) 93248.0 0.0771288 0.0385644 0.999256i \(-0.487722\pi\)
0.0385644 + 0.999256i \(0.487722\pi\)
\(272\) 1.10077e6 0.902139
\(273\) 0 0
\(274\) −289836. −0.233225
\(275\) −92500.0 −0.0737581
\(276\) −333312. −0.263377
\(277\) −110298. −0.0863711 −0.0431855 0.999067i \(-0.513751\pi\)
−0.0431855 + 0.999067i \(0.513751\pi\)
\(278\) −224440. −0.174176
\(279\) −555696. −0.427392
\(280\) 0 0
\(281\) −192198. −0.145205 −0.0726027 0.997361i \(-0.523131\pi\)
−0.0726027 + 0.997361i \(0.523131\pi\)
\(282\) 96704.0 0.0724139
\(283\) 331884. 0.246332 0.123166 0.992386i \(-0.460695\pi\)
0.123166 + 0.992386i \(0.460695\pi\)
\(284\) 914144. 0.672541
\(285\) 106000. 0.0773025
\(286\) 84656.0 0.0611988
\(287\) 0 0
\(288\) −1.16950e6 −0.830846
\(289\) 1.39583e6 0.983076
\(290\) 170500. 0.119050
\(291\) 476152. 0.329620
\(292\) −1.08567e6 −0.745146
\(293\) −2.19481e6 −1.49358 −0.746788 0.665063i \(-0.768405\pi\)
−0.746788 + 0.665063i \(0.768405\pi\)
\(294\) 0 0
\(295\) −500500. −0.334849
\(296\) −21840.0 −0.0144885
\(297\) 278240. 0.183033
\(298\) 807500. 0.526747
\(299\) −851136. −0.550581
\(300\) −70000.0 −0.0449050
\(301\) 0 0
\(302\) −893296. −0.563609
\(303\) 359592. 0.225011
\(304\) −695360. −0.431545
\(305\) 807550. 0.497073
\(306\) −761812. −0.465098
\(307\) 2.37751e6 1.43971 0.719857 0.694123i \(-0.244207\pi\)
0.719857 + 0.694123i \(0.244207\pi\)
\(308\) 0 0
\(309\) 78016.0 0.0464823
\(310\) −122400. −0.0723398
\(311\) 2.37305e6 1.39125 0.695626 0.718405i \(-0.255127\pi\)
0.695626 + 0.718405i \(0.255127\pi\)
\(312\) 137280. 0.0798400
\(313\) 1.42941e6 0.824702 0.412351 0.911025i \(-0.364708\pi\)
0.412351 + 0.911025i \(0.364708\pi\)
\(314\) 524516. 0.300217
\(315\) 0 0
\(316\) 934080. 0.526219
\(317\) 2.12462e6 1.18750 0.593750 0.804650i \(-0.297647\pi\)
0.593750 + 0.804650i \(0.297647\pi\)
\(318\) 190768. 0.105788
\(319\) 504680. 0.277677
\(320\) 267200. 0.145868
\(321\) 633168. 0.342970
\(322\) 0 0
\(323\) −1.77868e6 −0.948618
\(324\) −1.33395e6 −0.705954
\(325\) −178750. −0.0938723
\(326\) −309128. −0.161100
\(327\) 147320. 0.0761890
\(328\) −1.12776e6 −0.578805
\(329\) 0 0
\(330\) 29600.0 0.0149626
\(331\) 3.09985e6 1.55515 0.777573 0.628793i \(-0.216451\pi\)
0.777573 + 0.628793i \(0.216451\pi\)
\(332\) 468048. 0.233048
\(333\) −41314.0 −0.0204168
\(334\) −793344. −0.389131
\(335\) −1.52430e6 −0.742093
\(336\) 0 0
\(337\) 2.40008e6 1.15120 0.575601 0.817731i \(-0.304768\pi\)
0.575601 + 0.817731i \(0.304768\pi\)
\(338\) −578994. −0.275665
\(339\) 44744.0 0.0211464
\(340\) 1.17460e6 0.551052
\(341\) −362304. −0.168728
\(342\) 481240. 0.222483
\(343\) 0 0
\(344\) 149280. 0.0680151
\(345\) −297600. −0.134612
\(346\) 1.14695e6 0.515055
\(347\) 1.77741e6 0.792436 0.396218 0.918156i \(-0.370322\pi\)
0.396218 + 0.918156i \(0.370322\pi\)
\(348\) 381920. 0.169054
\(349\) 2.14805e6 0.944019 0.472010 0.881593i \(-0.343529\pi\)
0.472010 + 0.881593i \(0.343529\pi\)
\(350\) 0 0
\(351\) 537680. 0.232946
\(352\) −762496. −0.328005
\(353\) 661854. 0.282700 0.141350 0.989960i \(-0.454856\pi\)
0.141350 + 0.989960i \(0.454856\pi\)
\(354\) 160160. 0.0679275
\(355\) 816200. 0.343737
\(356\) 2.83836e6 1.18698
\(357\) 0 0
\(358\) −1.18892e6 −0.490281
\(359\) −259320. −0.106194 −0.0530970 0.998589i \(-0.516909\pi\)
−0.0530970 + 0.998589i \(0.516909\pi\)
\(360\) −681000. −0.276943
\(361\) −1.35250e6 −0.546222
\(362\) 214196. 0.0859093
\(363\) −556588. −0.221701
\(364\) 0 0
\(365\) −969350. −0.380845
\(366\) −258416. −0.100836
\(367\) 1.49993e6 0.581307 0.290653 0.956828i \(-0.406127\pi\)
0.290653 + 0.956828i \(0.406127\pi\)
\(368\) 1.95226e6 0.751480
\(369\) −2.13335e6 −0.815634
\(370\) −9100.00 −0.00345571
\(371\) 0 0
\(372\) −274176. −0.102724
\(373\) −2.23807e6 −0.832918 −0.416459 0.909154i \(-0.636729\pi\)
−0.416459 + 0.909154i \(0.636729\pi\)
\(374\) −496688. −0.183614
\(375\) −62500.0 −0.0229510
\(376\) −1.45056e6 −0.529135
\(377\) 975260. 0.353400
\(378\) 0 0
\(379\) 3.15934e6 1.12979 0.564896 0.825162i \(-0.308916\pi\)
0.564896 + 0.825162i \(0.308916\pi\)
\(380\) −742000. −0.263600
\(381\) 282208. 0.0995994
\(382\) 939104. 0.329272
\(383\) −342216. −0.119207 −0.0596037 0.998222i \(-0.518984\pi\)
−0.0596037 + 0.998222i \(0.518984\pi\)
\(384\) −744960. −0.257813
\(385\) 0 0
\(386\) 105412. 0.0360099
\(387\) 282388. 0.0958449
\(388\) −3.33306e6 −1.12399
\(389\) 88470.0 0.0296430 0.0148215 0.999890i \(-0.495282\pi\)
0.0148215 + 0.999890i \(0.495282\pi\)
\(390\) 57200.0 0.0190430
\(391\) 4.99373e6 1.65190
\(392\) 0 0
\(393\) −305808. −0.0998775
\(394\) 911724. 0.295885
\(395\) 834000. 0.268951
\(396\) −940688. −0.301445
\(397\) 5.45674e6 1.73763 0.868814 0.495138i \(-0.164883\pi\)
0.868814 + 0.495138i \(0.164883\pi\)
\(398\) −1.73000e6 −0.547442
\(399\) 0 0
\(400\) 410000. 0.128125
\(401\) 4.04680e6 1.25676 0.628378 0.777908i \(-0.283719\pi\)
0.628378 + 0.777908i \(0.283719\pi\)
\(402\) 487776. 0.150541
\(403\) −700128. −0.214741
\(404\) −2.51714e6 −0.767281
\(405\) −1.19102e6 −0.360814
\(406\) 0 0
\(407\) −26936.0 −0.00806022
\(408\) −805440. −0.239543
\(409\) 2.71207e6 0.801664 0.400832 0.916151i \(-0.368721\pi\)
0.400832 + 0.916151i \(0.368721\pi\)
\(410\) −469900. −0.138053
\(411\) −579672. −0.169269
\(412\) −546112. −0.158503
\(413\) 0 0
\(414\) −1.35110e6 −0.387425
\(415\) 417900. 0.119111
\(416\) −1.47347e6 −0.417454
\(417\) −448880. −0.126413
\(418\) 313760. 0.0878328
\(419\) −3.71746e6 −1.03445 −0.517227 0.855848i \(-0.673036\pi\)
−0.517227 + 0.855848i \(0.673036\pi\)
\(420\) 0 0
\(421\) 3.55250e6 0.976853 0.488426 0.872605i \(-0.337571\pi\)
0.488426 + 0.872605i \(0.337571\pi\)
\(422\) 2.21130e6 0.604460
\(423\) −2.74398e6 −0.745640
\(424\) −2.86152e6 −0.773005
\(425\) 1.04875e6 0.281643
\(426\) −261184. −0.0697305
\(427\) 0 0
\(428\) −4.43218e6 −1.16952
\(429\) 169312. 0.0444165
\(430\) 62200.0 0.0162226
\(431\) −4.06205e6 −1.05330 −0.526650 0.850082i \(-0.676552\pi\)
−0.526650 + 0.850082i \(0.676552\pi\)
\(432\) −1.23328e6 −0.317945
\(433\) −7.26287e6 −1.86161 −0.930804 0.365518i \(-0.880892\pi\)
−0.930804 + 0.365518i \(0.880892\pi\)
\(434\) 0 0
\(435\) 341000. 0.0864035
\(436\) −1.03124e6 −0.259803
\(437\) −3.15456e6 −0.790197
\(438\) 310192. 0.0772583
\(439\) 5.41028e6 1.33986 0.669928 0.742426i \(-0.266325\pi\)
0.669928 + 0.742426i \(0.266325\pi\)
\(440\) −444000. −0.109333
\(441\) 0 0
\(442\) −959816. −0.233686
\(443\) −6.51524e6 −1.57733 −0.788663 0.614826i \(-0.789226\pi\)
−0.788663 + 0.614826i \(0.789226\pi\)
\(444\) −20384.0 −0.00490718
\(445\) 2.53425e6 0.606666
\(446\) −2.24315e6 −0.533976
\(447\) 1.61500e6 0.382299
\(448\) 0 0
\(449\) −509950. −0.119375 −0.0596873 0.998217i \(-0.519010\pi\)
−0.0596873 + 0.998217i \(0.519010\pi\)
\(450\) −283750. −0.0660548
\(451\) −1.39090e6 −0.322000
\(452\) −313208. −0.0721085
\(453\) −1.78659e6 −0.409053
\(454\) 46696.0 0.0106326
\(455\) 0 0
\(456\) 508800. 0.114587
\(457\) 1.22084e6 0.273444 0.136722 0.990609i \(-0.456343\pi\)
0.136722 + 0.990609i \(0.456343\pi\)
\(458\) 1.19202e6 0.265534
\(459\) −3.15464e6 −0.698905
\(460\) 2.08320e6 0.459025
\(461\) 4.07210e6 0.892413 0.446207 0.894930i \(-0.352775\pi\)
0.446207 + 0.894930i \(0.352775\pi\)
\(462\) 0 0
\(463\) 2.02294e6 0.438561 0.219280 0.975662i \(-0.429629\pi\)
0.219280 + 0.975662i \(0.429629\pi\)
\(464\) −2.23696e6 −0.482351
\(465\) −244800. −0.0525024
\(466\) −970668. −0.207065
\(467\) −3.25097e6 −0.689797 −0.344898 0.938640i \(-0.612087\pi\)
−0.344898 + 0.938640i \(0.612087\pi\)
\(468\) −1.81782e6 −0.383650
\(469\) 0 0
\(470\) −604400. −0.126206
\(471\) 1.04903e6 0.217890
\(472\) −2.40240e6 −0.496353
\(473\) 184112. 0.0378381
\(474\) −266880. −0.0545595
\(475\) −662500. −0.134726
\(476\) 0 0
\(477\) −5.41304e6 −1.08929
\(478\) −97760.0 −0.0195700
\(479\) 3.27936e6 0.653056 0.326528 0.945188i \(-0.394121\pi\)
0.326528 + 0.945188i \(0.394121\pi\)
\(480\) −515200. −0.102064
\(481\) −52052.0 −0.0102583
\(482\) 221596. 0.0434455
\(483\) 0 0
\(484\) 3.89612e6 0.755994
\(485\) −2.97595e6 −0.574475
\(486\) 1.29481e6 0.248665
\(487\) −8.53197e6 −1.63015 −0.815074 0.579357i \(-0.803304\pi\)
−0.815074 + 0.579357i \(0.803304\pi\)
\(488\) 3.87624e6 0.736819
\(489\) −618256. −0.116922
\(490\) 0 0
\(491\) 1.51265e6 0.283162 0.141581 0.989927i \(-0.454781\pi\)
0.141581 + 0.989927i \(0.454781\pi\)
\(492\) −1.05258e6 −0.196038
\(493\) −5.72198e6 −1.06030
\(494\) 606320. 0.111785
\(495\) −839900. −0.154069
\(496\) 1.60589e6 0.293097
\(497\) 0 0
\(498\) −133728. −0.0241629
\(499\) −6.49190e6 −1.16713 −0.583567 0.812065i \(-0.698343\pi\)
−0.583567 + 0.812065i \(0.698343\pi\)
\(500\) 437500. 0.0782624
\(501\) −1.58669e6 −0.282421
\(502\) 3.28750e6 0.582245
\(503\) −8.61770e6 −1.51870 −0.759349 0.650684i \(-0.774482\pi\)
−0.759349 + 0.650684i \(0.774482\pi\)
\(504\) 0 0
\(505\) −2.24745e6 −0.392158
\(506\) −880896. −0.152950
\(507\) −1.15799e6 −0.200071
\(508\) −1.97546e6 −0.339632
\(509\) −2.67323e6 −0.457343 −0.228671 0.973504i \(-0.573438\pi\)
−0.228671 + 0.973504i \(0.573438\pi\)
\(510\) −335600. −0.0571342
\(511\) 0 0
\(512\) 5.89875e6 0.994455
\(513\) 1.99280e6 0.334326
\(514\) −2.61248e6 −0.436160
\(515\) −487600. −0.0810113
\(516\) 139328. 0.0230364
\(517\) −1.78902e6 −0.294367
\(518\) 0 0
\(519\) 2.29390e6 0.373814
\(520\) −858000. −0.139149
\(521\) −6.18500e6 −0.998264 −0.499132 0.866526i \(-0.666348\pi\)
−0.499132 + 0.866526i \(0.666348\pi\)
\(522\) 1.54814e6 0.248676
\(523\) 6.89452e6 1.10217 0.551087 0.834448i \(-0.314213\pi\)
0.551087 + 0.834448i \(0.314213\pi\)
\(524\) 2.14066e6 0.340580
\(525\) 0 0
\(526\) 4.25667e6 0.670820
\(527\) 4.10774e6 0.644283
\(528\) −388352. −0.0606235
\(529\) 2.42023e6 0.376026
\(530\) −1.19230e6 −0.184372
\(531\) −4.54454e6 −0.699445
\(532\) 0 0
\(533\) −2.68783e6 −0.409811
\(534\) −810960. −0.123068
\(535\) −3.95730e6 −0.597743
\(536\) −7.31664e6 −1.10002
\(537\) −2.37784e6 −0.355834
\(538\) 2.88218e6 0.429304
\(539\) 0 0
\(540\) −1.31600e6 −0.194210
\(541\) 155502. 0.0228425 0.0114212 0.999935i \(-0.496364\pi\)
0.0114212 + 0.999935i \(0.496364\pi\)
\(542\) 186496. 0.0272691
\(543\) 428392. 0.0623508
\(544\) 8.64506e6 1.25248
\(545\) −920750. −0.132785
\(546\) 0 0
\(547\) 1.26544e7 1.80831 0.904157 0.427201i \(-0.140500\pi\)
0.904157 + 0.427201i \(0.140500\pi\)
\(548\) 4.05770e6 0.577204
\(549\) 7.33255e6 1.03830
\(550\) −185000. −0.0260774
\(551\) 3.61460e6 0.507202
\(552\) −1.42848e6 −0.199538
\(553\) 0 0
\(554\) −220596. −0.0305368
\(555\) −18200.0 −0.00250807
\(556\) 3.14216e6 0.431064
\(557\) −7.07786e6 −0.966638 −0.483319 0.875444i \(-0.660569\pi\)
−0.483319 + 0.875444i \(0.660569\pi\)
\(558\) −1.11139e6 −0.151106
\(559\) 355784. 0.0481567
\(560\) 0 0
\(561\) −993376. −0.133262
\(562\) −384396. −0.0513379
\(563\) −846636. −0.112571 −0.0562854 0.998415i \(-0.517926\pi\)
−0.0562854 + 0.998415i \(0.517926\pi\)
\(564\) −1.35386e6 −0.179215
\(565\) −279650. −0.0368548
\(566\) 663768. 0.0870914
\(567\) 0 0
\(568\) 3.91776e6 0.509527
\(569\) 4.96041e6 0.642299 0.321149 0.947029i \(-0.395931\pi\)
0.321149 + 0.947029i \(0.395931\pi\)
\(570\) 212000. 0.0273306
\(571\) 8.96505e6 1.15070 0.575351 0.817907i \(-0.304866\pi\)
0.575351 + 0.817907i \(0.304866\pi\)
\(572\) −1.18518e6 −0.151459
\(573\) 1.87821e6 0.238978
\(574\) 0 0
\(575\) 1.86000e6 0.234608
\(576\) 2.42618e6 0.304696
\(577\) 2.86080e6 0.357724 0.178862 0.983874i \(-0.442758\pi\)
0.178862 + 0.983874i \(0.442758\pi\)
\(578\) 2.79165e6 0.347570
\(579\) 210824. 0.0261351
\(580\) −2.38700e6 −0.294634
\(581\) 0 0
\(582\) 952304. 0.116538
\(583\) −3.52921e6 −0.430037
\(584\) −4.65288e6 −0.564534
\(585\) −1.62305e6 −0.196084
\(586\) −4.38961e6 −0.528059
\(587\) 6.74027e6 0.807387 0.403694 0.914894i \(-0.367726\pi\)
0.403694 + 0.914894i \(0.367726\pi\)
\(588\) 0 0
\(589\) −2.59488e6 −0.308197
\(590\) −1.00100e6 −0.118387
\(591\) 1.82345e6 0.214746
\(592\) 119392. 0.0140014
\(593\) 1.78609e6 0.208578 0.104289 0.994547i \(-0.466743\pi\)
0.104289 + 0.994547i \(0.466743\pi\)
\(594\) 556480. 0.0647118
\(595\) 0 0
\(596\) −1.13050e7 −1.30363
\(597\) −3.46000e6 −0.397320
\(598\) −1.70227e6 −0.194660
\(599\) 4.94620e6 0.563254 0.281627 0.959524i \(-0.409126\pi\)
0.281627 + 0.959524i \(0.409126\pi\)
\(600\) −300000. −0.0340207
\(601\) 4.58100e6 0.517337 0.258669 0.965966i \(-0.416716\pi\)
0.258669 + 0.965966i \(0.416716\pi\)
\(602\) 0 0
\(603\) −1.38406e7 −1.55011
\(604\) 1.25061e7 1.39486
\(605\) 3.47868e6 0.386390
\(606\) 719184. 0.0795533
\(607\) −7.07999e6 −0.779940 −0.389970 0.920828i \(-0.627515\pi\)
−0.389970 + 0.920828i \(0.627515\pi\)
\(608\) −5.46112e6 −0.599132
\(609\) 0 0
\(610\) 1.61510e6 0.175742
\(611\) −3.45717e6 −0.374643
\(612\) 1.06654e7 1.15106
\(613\) 5.09609e6 0.547754 0.273877 0.961765i \(-0.411694\pi\)
0.273877 + 0.961765i \(0.411694\pi\)
\(614\) 4.75502e6 0.509016
\(615\) −939800. −0.100195
\(616\) 0 0
\(617\) −1.30003e7 −1.37480 −0.687400 0.726279i \(-0.741248\pi\)
−0.687400 + 0.726279i \(0.741248\pi\)
\(618\) 156032. 0.0164340
\(619\) −4.84406e6 −0.508139 −0.254070 0.967186i \(-0.581769\pi\)
−0.254070 + 0.967186i \(0.581769\pi\)
\(620\) 1.71360e6 0.179032
\(621\) −5.59488e6 −0.582186
\(622\) 4.74610e6 0.491882
\(623\) 0 0
\(624\) −750464. −0.0771558
\(625\) 390625. 0.0400000
\(626\) 2.85883e6 0.291576
\(627\) 627520. 0.0637468
\(628\) −7.34322e6 −0.742998
\(629\) 305396. 0.0307777
\(630\) 0 0
\(631\) 6.22775e6 0.622670 0.311335 0.950300i \(-0.399224\pi\)
0.311335 + 0.950300i \(0.399224\pi\)
\(632\) 4.00320e6 0.398671
\(633\) 4.42261e6 0.438702
\(634\) 4.24924e6 0.419845
\(635\) −1.76380e6 −0.173586
\(636\) −2.67075e6 −0.261813
\(637\) 0 0
\(638\) 1.00936e6 0.0981735
\(639\) 7.41110e6 0.718010
\(640\) 4.65600e6 0.449328
\(641\) 1.53280e6 0.147347 0.0736734 0.997282i \(-0.476528\pi\)
0.0736734 + 0.997282i \(0.476528\pi\)
\(642\) 1.26634e6 0.121258
\(643\) 1.74382e7 1.66332 0.831659 0.555287i \(-0.187391\pi\)
0.831659 + 0.555287i \(0.187391\pi\)
\(644\) 0 0
\(645\) 124400. 0.0117739
\(646\) −3.55736e6 −0.335387
\(647\) 4.25469e6 0.399583 0.199792 0.979838i \(-0.435974\pi\)
0.199792 + 0.979838i \(0.435974\pi\)
\(648\) −5.71692e6 −0.534841
\(649\) −2.96296e6 −0.276130
\(650\) −357500. −0.0331889
\(651\) 0 0
\(652\) 4.32779e6 0.398701
\(653\) 3.01085e6 0.276316 0.138158 0.990410i \(-0.455882\pi\)
0.138158 + 0.990410i \(0.455882\pi\)
\(654\) 294640. 0.0269369
\(655\) 1.91130e6 0.174071
\(656\) 6.16509e6 0.559345
\(657\) −8.80170e6 −0.795524
\(658\) 0 0
\(659\) −8.11462e6 −0.727871 −0.363936 0.931424i \(-0.618567\pi\)
−0.363936 + 0.931424i \(0.618567\pi\)
\(660\) −414400. −0.0370305
\(661\) −2.47370e6 −0.220213 −0.110107 0.993920i \(-0.535119\pi\)
−0.110107 + 0.993920i \(0.535119\pi\)
\(662\) 6.19970e6 0.549827
\(663\) −1.91963e6 −0.169603
\(664\) 2.00592e6 0.176560
\(665\) 0 0
\(666\) −82628.0 −0.00721841
\(667\) −1.01482e7 −0.883228
\(668\) 1.11068e7 0.963049
\(669\) −4.48630e6 −0.387546
\(670\) −3.04860e6 −0.262370
\(671\) 4.78070e6 0.409907
\(672\) 0 0
\(673\) 5.77063e6 0.491117 0.245559 0.969382i \(-0.421029\pi\)
0.245559 + 0.969382i \(0.421029\pi\)
\(674\) 4.80016e6 0.407011
\(675\) −1.17500e6 −0.0992610
\(676\) 8.10592e6 0.682237
\(677\) −1.67197e7 −1.40203 −0.701014 0.713147i \(-0.747269\pi\)
−0.701014 + 0.713147i \(0.747269\pi\)
\(678\) 89488.0 0.00747637
\(679\) 0 0
\(680\) 5.03400e6 0.417485
\(681\) 93392.0 0.00771688
\(682\) −724608. −0.0596544
\(683\) 7.14532e6 0.586097 0.293049 0.956098i \(-0.405330\pi\)
0.293049 + 0.956098i \(0.405330\pi\)
\(684\) −6.73736e6 −0.550617
\(685\) 3.62295e6 0.295009
\(686\) 0 0
\(687\) 2.38404e6 0.192718
\(688\) −816064. −0.0657284
\(689\) −6.81996e6 −0.547310
\(690\) −595200. −0.0475927
\(691\) 8.78395e6 0.699833 0.349917 0.936781i \(-0.386210\pi\)
0.349917 + 0.936781i \(0.386210\pi\)
\(692\) −1.60573e7 −1.27470
\(693\) 0 0
\(694\) 3.55482e6 0.280169
\(695\) 2.80550e6 0.220317
\(696\) 1.63680e6 0.128077
\(697\) 1.57698e7 1.22955
\(698\) 4.29610e6 0.333761
\(699\) −1.94134e6 −0.150282
\(700\) 0 0
\(701\) −1.60141e7 −1.23086 −0.615428 0.788193i \(-0.711017\pi\)
−0.615428 + 0.788193i \(0.711017\pi\)
\(702\) 1.07536e6 0.0823590
\(703\) −192920. −0.0147228
\(704\) 1.58182e6 0.120289
\(705\) −1.20880e6 −0.0915971
\(706\) 1.32371e6 0.0999495
\(707\) 0 0
\(708\) −2.24224e6 −0.168112
\(709\) −1.91354e7 −1.42962 −0.714811 0.699318i \(-0.753487\pi\)
−0.714811 + 0.699318i \(0.753487\pi\)
\(710\) 1.63240e6 0.121529
\(711\) 7.57272e6 0.561795
\(712\) 1.21644e7 0.899271
\(713\) 7.28525e6 0.536686
\(714\) 0 0
\(715\) −1.05820e6 −0.0774110
\(716\) 1.66449e7 1.21338
\(717\) −195520. −0.0142034
\(718\) −518640. −0.0375452
\(719\) −1.02934e7 −0.742566 −0.371283 0.928520i \(-0.621082\pi\)
−0.371283 + 0.928520i \(0.621082\pi\)
\(720\) 3.72280e6 0.267632
\(721\) 0 0
\(722\) −2.70500e6 −0.193119
\(723\) 443192. 0.0315316
\(724\) −2.99874e6 −0.212615
\(725\) −2.13125e6 −0.150588
\(726\) −1.11318e6 −0.0783831
\(727\) 1.93264e7 1.35618 0.678088 0.734981i \(-0.262809\pi\)
0.678088 + 0.734981i \(0.262809\pi\)
\(728\) 0 0
\(729\) −8.98715e6 −0.626330
\(730\) −1.93870e6 −0.134649
\(731\) −2.08743e6 −0.144484
\(732\) 3.61782e6 0.249557
\(733\) −5.26197e6 −0.361733 −0.180866 0.983508i \(-0.557890\pi\)
−0.180866 + 0.983508i \(0.557890\pi\)
\(734\) 2.99986e6 0.205523
\(735\) 0 0
\(736\) 1.53324e7 1.04331
\(737\) −9.02386e6 −0.611961
\(738\) −4.26669e6 −0.288370
\(739\) 2.82944e7 1.90585 0.952927 0.303199i \(-0.0980548\pi\)
0.952927 + 0.303199i \(0.0980548\pi\)
\(740\) 127400. 0.00855244
\(741\) 1.21264e6 0.0811309
\(742\) 0 0
\(743\) 2.09863e7 1.39464 0.697321 0.716759i \(-0.254375\pi\)
0.697321 + 0.716759i \(0.254375\pi\)
\(744\) −1.17504e6 −0.0778252
\(745\) −1.00938e7 −0.666288
\(746\) −4.47615e6 −0.294481
\(747\) 3.79453e6 0.248804
\(748\) 6.95363e6 0.454420
\(749\) 0 0
\(750\) −125000. −0.00811441
\(751\) −1.89668e7 −1.22714 −0.613572 0.789639i \(-0.710268\pi\)
−0.613572 + 0.789639i \(0.710268\pi\)
\(752\) 7.92973e6 0.511345
\(753\) 6.57499e6 0.422579
\(754\) 1.95052e6 0.124946
\(755\) 1.11662e7 0.712915
\(756\) 0 0
\(757\) −1.08257e7 −0.686617 −0.343309 0.939223i \(-0.611548\pi\)
−0.343309 + 0.939223i \(0.611548\pi\)
\(758\) 6.31868e6 0.399442
\(759\) −1.76179e6 −0.111007
\(760\) −3.18000e6 −0.199707
\(761\) −1.90534e7 −1.19264 −0.596322 0.802745i \(-0.703372\pi\)
−0.596322 + 0.802745i \(0.703372\pi\)
\(762\) 564416. 0.0352137
\(763\) 0 0
\(764\) −1.31475e7 −0.814908
\(765\) 9.52265e6 0.588307
\(766\) −684432. −0.0421462
\(767\) −5.72572e6 −0.351432
\(768\) −121856. −0.00745494
\(769\) 1.57826e7 0.962415 0.481208 0.876607i \(-0.340198\pi\)
0.481208 + 0.876607i \(0.340198\pi\)
\(770\) 0 0
\(771\) −5.22497e6 −0.316554
\(772\) −1.47577e6 −0.0891199
\(773\) 2.44049e7 1.46902 0.734510 0.678598i \(-0.237412\pi\)
0.734510 + 0.678598i \(0.237412\pi\)
\(774\) 564776. 0.0338863
\(775\) 1.53000e6 0.0915034
\(776\) −1.42846e7 −0.851555
\(777\) 0 0
\(778\) 176940. 0.0104804
\(779\) −9.96188e6 −0.588163
\(780\) −800800. −0.0471289
\(781\) 4.83190e6 0.283459
\(782\) 9.98746e6 0.584034
\(783\) 6.41080e6 0.373687
\(784\) 0 0
\(785\) −6.55645e6 −0.379747
\(786\) −611616. −0.0353120
\(787\) −3.37607e7 −1.94301 −0.971505 0.237019i \(-0.923830\pi\)
−0.971505 + 0.237019i \(0.923830\pi\)
\(788\) −1.27641e7 −0.732278
\(789\) 8.51334e6 0.486864
\(790\) 1.66800e6 0.0950886
\(791\) 0 0
\(792\) −4.03152e6 −0.228379
\(793\) 9.23837e6 0.521690
\(794\) 1.09135e7 0.614344
\(795\) −2.38460e6 −0.133813
\(796\) 2.42200e7 1.35485
\(797\) −2.19885e7 −1.22617 −0.613083 0.790019i \(-0.710071\pi\)
−0.613083 + 0.790019i \(0.710071\pi\)
\(798\) 0 0
\(799\) 2.02837e7 1.12403
\(800\) 3.22000e6 0.177882
\(801\) 2.30110e7 1.26723
\(802\) 8.09360e6 0.444330
\(803\) −5.73855e6 −0.314061
\(804\) −6.82886e6 −0.372570
\(805\) 0 0
\(806\) −1.40026e6 −0.0759224
\(807\) 5.76436e6 0.311578
\(808\) −1.07878e7 −0.581303
\(809\) −2.93597e7 −1.57717 −0.788587 0.614923i \(-0.789187\pi\)
−0.788587 + 0.614923i \(0.789187\pi\)
\(810\) −2.38205e6 −0.127567
\(811\) −3.17703e7 −1.69617 −0.848083 0.529863i \(-0.822243\pi\)
−0.848083 + 0.529863i \(0.822243\pi\)
\(812\) 0 0
\(813\) 372992. 0.0197912
\(814\) −53872.0 −0.00284972
\(815\) 3.86410e6 0.203777
\(816\) 4.40307e6 0.231489
\(817\) 1.31864e6 0.0691148
\(818\) 5.42414e6 0.283431
\(819\) 0 0
\(820\) 6.57860e6 0.341664
\(821\) −2.71430e6 −0.140540 −0.0702699 0.997528i \(-0.522386\pi\)
−0.0702699 + 0.997528i \(0.522386\pi\)
\(822\) −1.15934e6 −0.0598457
\(823\) −1.25866e7 −0.647753 −0.323877 0.946099i \(-0.604986\pi\)
−0.323877 + 0.946099i \(0.604986\pi\)
\(824\) −2.34048e6 −0.120084
\(825\) −370000. −0.0189263
\(826\) 0 0
\(827\) −8.72355e6 −0.443537 −0.221768 0.975099i \(-0.571183\pi\)
−0.221768 + 0.975099i \(0.571183\pi\)
\(828\) 1.89155e7 0.958829
\(829\) 1.06178e7 0.536597 0.268299 0.963336i \(-0.413539\pi\)
0.268299 + 0.963336i \(0.413539\pi\)
\(830\) 835800. 0.0421121
\(831\) −441192. −0.0221628
\(832\) 3.05677e6 0.153093
\(833\) 0 0
\(834\) −897760. −0.0446936
\(835\) 9.91680e6 0.492216
\(836\) −4.39264e6 −0.217375
\(837\) −4.60224e6 −0.227068
\(838\) −7.43492e6 −0.365735
\(839\) −1.67765e7 −0.822805 −0.411403 0.911454i \(-0.634961\pi\)
−0.411403 + 0.911454i \(0.634961\pi\)
\(840\) 0 0
\(841\) −8.88305e6 −0.433084
\(842\) 7.10500e6 0.345370
\(843\) −768792. −0.0372597
\(844\) −3.09583e7 −1.49596
\(845\) 7.23742e6 0.348692
\(846\) −5.48795e6 −0.263624
\(847\) 0 0
\(848\) 1.56430e7 0.747016
\(849\) 1.32754e6 0.0632087
\(850\) 2.09750e6 0.0995760
\(851\) 541632. 0.0256378
\(852\) 3.65658e6 0.172574
\(853\) 2.20186e7 1.03613 0.518067 0.855340i \(-0.326652\pi\)
0.518067 + 0.855340i \(0.326652\pi\)
\(854\) 0 0
\(855\) −6.01550e6 −0.281421
\(856\) −1.89950e7 −0.886045
\(857\) −3.16676e7 −1.47287 −0.736434 0.676510i \(-0.763492\pi\)
−0.736434 + 0.676510i \(0.763492\pi\)
\(858\) 338624. 0.0157036
\(859\) −1.58064e7 −0.730886 −0.365443 0.930834i \(-0.619082\pi\)
−0.365443 + 0.930834i \(0.619082\pi\)
\(860\) −870800. −0.0401488
\(861\) 0 0
\(862\) −8.12410e6 −0.372398
\(863\) −1.44287e7 −0.659476 −0.329738 0.944072i \(-0.606960\pi\)
−0.329738 + 0.944072i \(0.606960\pi\)
\(864\) −9.68576e6 −0.441417
\(865\) −1.43368e7 −0.651499
\(866\) −1.45257e7 −0.658178
\(867\) 5.58331e6 0.252257
\(868\) 0 0
\(869\) 4.93728e6 0.221788
\(870\) 682000. 0.0305482
\(871\) −1.74380e7 −0.778845
\(872\) −4.41960e6 −0.196830
\(873\) −2.70216e7 −1.19999
\(874\) −6.30912e6 −0.279377
\(875\) 0 0
\(876\) −4.34269e6 −0.191205
\(877\) 247902. 0.0108838 0.00544191 0.999985i \(-0.498268\pi\)
0.00544191 + 0.999985i \(0.498268\pi\)
\(878\) 1.08206e7 0.473711
\(879\) −8.77922e6 −0.383252
\(880\) 2.42720e6 0.105657
\(881\) −4.10268e7 −1.78085 −0.890426 0.455128i \(-0.849594\pi\)
−0.890426 + 0.455128i \(0.849594\pi\)
\(882\) 0 0
\(883\) 4.18015e7 1.80422 0.902112 0.431503i \(-0.142016\pi\)
0.902112 + 0.431503i \(0.142016\pi\)
\(884\) 1.34374e7 0.578343
\(885\) −2.00200e6 −0.0859223
\(886\) −1.30305e7 −0.557669
\(887\) 2.10476e7 0.898241 0.449120 0.893471i \(-0.351737\pi\)
0.449120 + 0.893471i \(0.351737\pi\)
\(888\) −87360.0 −0.00371775
\(889\) 0 0
\(890\) 5.06850e6 0.214489
\(891\) −7.05087e6 −0.297542
\(892\) 3.14041e7 1.32152
\(893\) −1.28133e7 −0.537690
\(894\) 3.23000e6 0.135163
\(895\) 1.48615e7 0.620162
\(896\) 0 0
\(897\) −3.40454e6 −0.141279
\(898\) −1.01990e6 −0.0422053
\(899\) −8.34768e6 −0.344482
\(900\) 3.97250e6 0.163477
\(901\) 4.00136e7 1.64208
\(902\) −2.78181e6 −0.113844
\(903\) 0 0
\(904\) −1.34232e6 −0.0546305
\(905\) −2.67745e6 −0.108668
\(906\) −3.57318e6 −0.144622
\(907\) 7.48309e6 0.302039 0.151019 0.988531i \(-0.451744\pi\)
0.151019 + 0.988531i \(0.451744\pi\)
\(908\) −653744. −0.0263144
\(909\) −2.04068e7 −0.819155
\(910\) 0 0
\(911\) −6.63165e6 −0.264744 −0.132372 0.991200i \(-0.542259\pi\)
−0.132372 + 0.991200i \(0.542259\pi\)
\(912\) −2.78144e6 −0.110734
\(913\) 2.47397e6 0.0982239
\(914\) 2.44168e6 0.0966772
\(915\) 3.23020e6 0.127549
\(916\) −1.66883e7 −0.657163
\(917\) 0 0
\(918\) −6.30928e6 −0.247100
\(919\) −1.68976e7 −0.659990 −0.329995 0.943983i \(-0.607047\pi\)
−0.329995 + 0.943983i \(0.607047\pi\)
\(920\) 8.92800e6 0.347764
\(921\) 9.51003e6 0.369431
\(922\) 8.14420e6 0.315516
\(923\) 9.33733e6 0.360760
\(924\) 0 0
\(925\) 113750. 0.00437116
\(926\) 4.04587e6 0.155055
\(927\) −4.42741e6 −0.169219
\(928\) −1.75683e7 −0.669669
\(929\) 1.28653e7 0.489081 0.244541 0.969639i \(-0.421363\pi\)
0.244541 + 0.969639i \(0.421363\pi\)
\(930\) −489600. −0.0185624
\(931\) 0 0
\(932\) 1.35894e7 0.512459
\(933\) 9.49219e6 0.356995
\(934\) −6.50194e6 −0.243880
\(935\) 6.20860e6 0.232255
\(936\) −7.79064e6 −0.290659
\(937\) −1.06887e7 −0.397718 −0.198859 0.980028i \(-0.563724\pi\)
−0.198859 + 0.980028i \(0.563724\pi\)
\(938\) 0 0
\(939\) 5.71766e6 0.211619
\(940\) 8.46160e6 0.312344
\(941\) −2.82455e7 −1.03986 −0.519930 0.854209i \(-0.674042\pi\)
−0.519930 + 0.854209i \(0.674042\pi\)
\(942\) 2.09806e6 0.0770356
\(943\) 2.79684e7 1.02421
\(944\) 1.31331e7 0.479665
\(945\) 0 0
\(946\) 368224. 0.0133778
\(947\) −1.70892e7 −0.619222 −0.309611 0.950863i \(-0.600199\pi\)
−0.309611 + 0.950863i \(0.600199\pi\)
\(948\) 3.73632e6 0.135028
\(949\) −1.10894e7 −0.399706
\(950\) −1.32500e6 −0.0476329
\(951\) 8.49849e6 0.304713
\(952\) 0 0
\(953\) 2.22259e7 0.792735 0.396367 0.918092i \(-0.370271\pi\)
0.396367 + 0.918092i \(0.370271\pi\)
\(954\) −1.08261e7 −0.385124
\(955\) −1.17388e7 −0.416500
\(956\) 1.36864e6 0.0484333
\(957\) 2.01872e6 0.0712519
\(958\) 6.55872e6 0.230890
\(959\) 0 0
\(960\) 1.06880e6 0.0374299
\(961\) −2.26364e7 −0.790678
\(962\) −104104. −0.00362685
\(963\) −3.59323e7 −1.24859
\(964\) −3.10234e6 −0.107522
\(965\) −1.31765e6 −0.0455493
\(966\) 0 0
\(967\) 2.41551e7 0.830696 0.415348 0.909663i \(-0.363660\pi\)
0.415348 + 0.909663i \(0.363660\pi\)
\(968\) 1.66976e7 0.572752
\(969\) −7.11472e6 −0.243416
\(970\) −5.95190e6 −0.203108
\(971\) 5.48313e7 1.86630 0.933149 0.359491i \(-0.117050\pi\)
0.933149 + 0.359491i \(0.117050\pi\)
\(972\) −1.81273e7 −0.615415
\(973\) 0 0
\(974\) −1.70639e7 −0.576344
\(975\) −715000. −0.0240877
\(976\) −2.11901e7 −0.712047
\(977\) −1.56612e7 −0.524915 −0.262457 0.964944i \(-0.584533\pi\)
−0.262457 + 0.964944i \(0.584533\pi\)
\(978\) −1.23651e6 −0.0413382
\(979\) 1.50028e7 0.500281
\(980\) 0 0
\(981\) −8.36041e6 −0.277367
\(982\) 3.02530e6 0.100113
\(983\) 1.63420e7 0.539412 0.269706 0.962943i \(-0.413073\pi\)
0.269706 + 0.962943i \(0.413073\pi\)
\(984\) −4.51104e6 −0.148521
\(985\) −1.13966e7 −0.374268
\(986\) −1.14440e7 −0.374873
\(987\) 0 0
\(988\) −8.48848e6 −0.276654
\(989\) −3.70214e6 −0.120355
\(990\) −1.67980e6 −0.0544715
\(991\) 1.37576e7 0.444997 0.222498 0.974933i \(-0.428579\pi\)
0.222498 + 0.974933i \(0.428579\pi\)
\(992\) 1.26121e7 0.406919
\(993\) 1.23994e7 0.399050
\(994\) 0 0
\(995\) 2.16250e7 0.692466
\(996\) 1.87219e6 0.0598001
\(997\) 1.29097e7 0.411320 0.205660 0.978624i \(-0.434066\pi\)
0.205660 + 0.978624i \(0.434066\pi\)
\(998\) −1.29838e7 −0.412644
\(999\) −342160. −0.0108471
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 245.6.a.b.1.1 1
7.6 odd 2 5.6.a.a.1.1 1
21.20 even 2 45.6.a.b.1.1 1
28.27 even 2 80.6.a.e.1.1 1
35.13 even 4 25.6.b.a.24.1 2
35.27 even 4 25.6.b.a.24.2 2
35.34 odd 2 25.6.a.a.1.1 1
56.13 odd 2 320.6.a.j.1.1 1
56.27 even 2 320.6.a.g.1.1 1
77.76 even 2 605.6.a.a.1.1 1
84.83 odd 2 720.6.a.a.1.1 1
91.90 odd 2 845.6.a.b.1.1 1
105.62 odd 4 225.6.b.e.199.1 2
105.83 odd 4 225.6.b.e.199.2 2
105.104 even 2 225.6.a.f.1.1 1
140.27 odd 4 400.6.c.j.49.1 2
140.83 odd 4 400.6.c.j.49.2 2
140.139 even 2 400.6.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5.6.a.a.1.1 1 7.6 odd 2
25.6.a.a.1.1 1 35.34 odd 2
25.6.b.a.24.1 2 35.13 even 4
25.6.b.a.24.2 2 35.27 even 4
45.6.a.b.1.1 1 21.20 even 2
80.6.a.e.1.1 1 28.27 even 2
225.6.a.f.1.1 1 105.104 even 2
225.6.b.e.199.1 2 105.62 odd 4
225.6.b.e.199.2 2 105.83 odd 4
245.6.a.b.1.1 1 1.1 even 1 trivial
320.6.a.g.1.1 1 56.27 even 2
320.6.a.j.1.1 1 56.13 odd 2
400.6.a.g.1.1 1 140.139 even 2
400.6.c.j.49.1 2 140.27 odd 4
400.6.c.j.49.2 2 140.83 odd 4
605.6.a.a.1.1 1 77.76 even 2
720.6.a.a.1.1 1 84.83 odd 2
845.6.a.b.1.1 1 91.90 odd 2