Properties

Label 605.6.a.a.1.1
Level $605$
Weight $6$
Character 605.1
Self dual yes
Analytic conductor $97.032$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 605.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(97.0322109869\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 605.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} -4.00000 q^{3} -28.0000 q^{4} +25.0000 q^{5} +8.00000 q^{6} -192.000 q^{7} +120.000 q^{8} -227.000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -4.00000 q^{3} -28.0000 q^{4} +25.0000 q^{5} +8.00000 q^{6} -192.000 q^{7} +120.000 q^{8} -227.000 q^{9} -50.0000 q^{10} +112.000 q^{12} -286.000 q^{13} +384.000 q^{14} -100.000 q^{15} +656.000 q^{16} +1678.00 q^{17} +454.000 q^{18} -1060.00 q^{19} -700.000 q^{20} +768.000 q^{21} +2976.00 q^{23} -480.000 q^{24} +625.000 q^{25} +572.000 q^{26} +1880.00 q^{27} +5376.00 q^{28} +3410.00 q^{29} +200.000 q^{30} -2448.00 q^{31} -5152.00 q^{32} -3356.00 q^{34} -4800.00 q^{35} +6356.00 q^{36} +182.000 q^{37} +2120.00 q^{38} +1144.00 q^{39} +3000.00 q^{40} +9398.00 q^{41} -1536.00 q^{42} +1244.00 q^{43} -5675.00 q^{45} -5952.00 q^{46} -12088.0 q^{47} -2624.00 q^{48} +20057.0 q^{49} -1250.00 q^{50} -6712.00 q^{51} +8008.00 q^{52} +23846.0 q^{53} -3760.00 q^{54} -23040.0 q^{56} +4240.00 q^{57} -6820.00 q^{58} -20020.0 q^{59} +2800.00 q^{60} -32302.0 q^{61} +4896.00 q^{62} +43584.0 q^{63} -10688.0 q^{64} -7150.00 q^{65} +60972.0 q^{67} -46984.0 q^{68} -11904.0 q^{69} +9600.00 q^{70} -32648.0 q^{71} -27240.0 q^{72} +38774.0 q^{73} -364.000 q^{74} -2500.00 q^{75} +29680.0 q^{76} -2288.00 q^{78} +33360.0 q^{79} +16400.0 q^{80} +47641.0 q^{81} -18796.0 q^{82} -16716.0 q^{83} -21504.0 q^{84} +41950.0 q^{85} -2488.00 q^{86} -13640.0 q^{87} +101370. q^{89} +11350.0 q^{90} +54912.0 q^{91} -83328.0 q^{92} +9792.00 q^{93} +24176.0 q^{94} -26500.0 q^{95} +20608.0 q^{96} -119038. q^{97} -40114.0 q^{98} +O(q^{100})\)

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 \(-0.556567\pi\)
−0.176777 + 0.984251i \(0.556567\pi\)
\(3\) −4.00000 −0.256600 −0.128300 0.991735i \(-0.540952\pi\)
−0.128300 + 0.991735i \(0.540952\pi\)
\(4\) −28.0000 −0.875000
\(5\) 25.0000 0.447214
\(6\) 8.00000 0.0907218
\(7\) −192.000 −1.48100 −0.740502 0.672054i \(-0.765412\pi\)
−0.740502 + 0.672054i \(0.765412\pi\)
\(8\) 120.000 0.662913
\(9\) −227.000 −0.934156
\(10\) −50.0000 −0.158114
\(11\) 0 0
\(12\) 112.000 0.224525
\(13\) −286.000 −0.469362 −0.234681 0.972072i \(-0.575405\pi\)
−0.234681 + 0.972072i \(0.575405\pi\)
\(14\) 384.000 0.523614
\(15\) −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
\(21\) 768.000 0.380026
\(22\) 0 0
\(23\) 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
\(28\) 5376.00 1.29588
\(29\) 3410.00 0.752938 0.376469 0.926429i \(-0.377138\pi\)
0.376469 + 0.926429i \(0.377138\pi\)
\(30\) 200.000 0.0405720
\(31\) −2448.00 −0.457517 −0.228758 0.973483i \(-0.573467\pi\)
−0.228758 + 0.973483i \(0.573467\pi\)
\(32\) −5152.00 −0.889408
\(33\) 0 0
\(34\) −3356.00 −0.497880
\(35\) −4800.00 −0.662325
\(36\) 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 \(0.356196\pi\)
\(42\) −1536.00 −0.134359
\(43\) 1244.00 0.102600 0.0513002 0.998683i \(-0.483663\pi\)
0.0513002 + 0.998683i \(0.483663\pi\)
\(44\) 0 0
\(45\) −5675.00 −0.417767
\(46\) −5952.00 −0.414733
\(47\) −12088.0 −0.798196 −0.399098 0.916908i \(-0.630677\pi\)
−0.399098 + 0.916908i \(0.630677\pi\)
\(48\) −2624.00 −0.164384
\(49\) 20057.0 1.19337
\(50\) −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
\(55\) 0 0
\(56\) −23040.0 −0.981776
\(57\) 4240.00 0.172854
\(58\) −6820.00 −0.266204
\(59\) −20020.0 −0.748745 −0.374373 0.927278i \(-0.622142\pi\)
−0.374373 + 0.927278i \(0.622142\pi\)
\(60\) 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
\(63\) 43584.0 1.38349
\(64\) −10688.0 −0.326172
\(65\) −7150.00 −0.209905
\(66\) 0 0
\(67\) 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
\(70\) 9600.00 0.234167
\(71\) −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 \(-0.402781\pi\)
0.300696 + 0.953720i \(0.402781\pi\)
\(80\) 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 \(0.542516\pi\)
\(84\) −21504.0 −0.332522
\(85\) 41950.0 0.629774
\(86\) −2488.00 −0.0362747
\(87\) −13640.0 −0.193204
\(88\) 0 0
\(89\) 101370. 1.35655 0.678273 0.734810i \(-0.262729\pi\)
0.678273 + 0.734810i \(0.262729\pi\)
\(90\) 11350.0 0.147703
\(91\) 54912.0 0.695126
\(92\) −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 \(-0.722013\pi\)
−0.642283 + 0.766468i \(0.722013\pi\)
\(98\) −40114.0 −0.421921
\(99\) 0 0
\(100\) −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 \(-0.528870\pi\)
−0.0905734 + 0.995890i \(0.528870\pi\)
\(104\) −34320.0 −0.311146
\(105\) 19200.0 0.169953
\(106\) −47692.0 −0.412269
\(107\) −158292. −1.33659 −0.668297 0.743895i \(-0.732976\pi\)
−0.668297 + 0.743895i \(0.732976\pi\)
\(108\) −52640.0 −0.434267
\(109\) −36830.0 −0.296917 −0.148459 0.988919i \(-0.547431\pi\)
−0.148459 + 0.988919i \(0.547431\pi\)
\(110\) 0 0
\(111\) −728.000 −0.00560821
\(112\) −125952. −0.948768
\(113\) 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
\(119\) −322176. −2.08557
\(120\) −12000.0 −0.0760726
\(121\) 0 0
\(122\) 64604.0 0.392970
\(123\) −37592.0 −0.224044
\(124\) 68544.0 0.400327
\(125\) 15625.0 0.0894427
\(126\) −87168.0 −0.489137
\(127\) −70552.0 −0.388150 −0.194075 0.980987i \(-0.562171\pi\)
−0.194075 + 0.980987i \(0.562171\pi\)
\(128\) 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 \(0.562346\pi\)
\(132\) 0 0
\(133\) 203520. 0.997650
\(134\) −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 \(0.579222\pi\)
\(140\) 134400. 0.579534
\(141\) 48352.0 0.204817
\(142\) 65296.0 0.271748
\(143\) 0 0
\(144\) −148912. −0.598444
\(145\) 85250.0 0.336724
\(146\) −77548.0 −0.301085
\(147\) −80228.0 −0.306219
\(148\) −5096.00 −0.0191238
\(149\) −403750. −1.48986 −0.744932 0.667140i \(-0.767518\pi\)
−0.744932 + 0.667140i \(0.767518\pi\)
\(150\) 5000.00 0.0181444
\(151\) 446648. 1.59413 0.797064 0.603895i \(-0.206385\pi\)
0.797064 + 0.603895i \(0.206385\pi\)
\(152\) −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 \(-0.639575\pi\)
−0.424570 + 0.905395i \(0.639575\pi\)
\(158\) −66720.0 −0.212625
\(159\) −95384.0 −0.299215
\(160\) −128800. −0.397755
\(161\) −571392. −1.73728
\(162\) −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
\(165\) 0 0
\(166\) 33432.0 0.0941656
\(167\) −396672. −1.10063 −0.550314 0.834958i \(-0.685492\pi\)
−0.550314 + 0.834958i \(0.685492\pi\)
\(168\) 92160.0 0.251924
\(169\) −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
\(175\) −120000. −0.296201
\(176\) 0 0
\(177\) 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 \(-0.538769\pi\)
−0.121494 + 0.992592i \(0.538769\pi\)
\(182\) −109824. −0.245764
\(183\) 129208. 0.285208
\(184\) 357120. 0.777624
\(185\) 4550.00 0.00977422
\(186\) −19584.0 −0.0415068
\(187\) 0 0
\(188\) 338464. 0.698422
\(189\) −360960. −0.735029
\(190\) 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 \(-0.516217\pi\)
−0.0509257 + 0.998702i \(0.516217\pi\)
\(194\) 238076. 0.454163
\(195\) 28600.0 0.0538616
\(196\) −561596. −1.04420
\(197\) −455862. −0.836889 −0.418444 0.908242i \(-0.637425\pi\)
−0.418444 + 0.908242i \(0.637425\pi\)
\(198\) 0 0
\(199\) 865000. 1.54840 0.774200 0.632940i \(-0.218152\pi\)
0.774200 + 0.632940i \(0.218152\pi\)
\(200\) 75000.0 0.132583
\(201\) −243888. −0.425795
\(202\) −179796. −0.310028
\(203\) −654720. −1.11510
\(204\) 187936. 0.316180
\(205\) 234950. 0.390473
\(206\) 39008.0 0.0640451
\(207\) −675552. −1.09580
\(208\) −187616. −0.300685
\(209\) 0 0
\(210\) −38400.0 −0.0600873
\(211\) −1.10565e6 −1.70967 −0.854835 0.518900i \(-0.826342\pi\)
−0.854835 + 0.518900i \(0.826342\pi\)
\(212\) −667688. −1.02031
\(213\) 130592. 0.197228
\(214\) 316584. 0.472557
\(215\) 31100.0 0.0458843
\(216\) 225600. 0.329007
\(217\) 470016. 0.677584
\(218\) 73660.0 0.104976
\(219\) −155096. −0.218520
\(220\) 0 0
\(221\) −479908. −0.660963
\(222\) 1456.00 0.00198280
\(223\) 1.12158e6 1.51031 0.755156 0.655545i \(-0.227561\pi\)
0.755156 + 0.655545i \(0.227561\pi\)
\(224\) 989184. 1.31722
\(225\) −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 \(-0.622536\pi\)
−0.375522 + 0.926814i \(0.622536\pi\)
\(230\) −148800. −0.185474
\(231\) 0 0
\(232\) 409200. 0.499132
\(233\) 485334. 0.585667 0.292834 0.956163i \(-0.405402\pi\)
0.292834 + 0.956163i \(0.405402\pi\)
\(234\) −129844. −0.155018
\(235\) −302200. −0.356964
\(236\) 560560. 0.655152
\(237\) −133440. −0.154317
\(238\) 644352. 0.737362
\(239\) 48880.0 0.0553524 0.0276762 0.999617i \(-0.491189\pi\)
0.0276762 + 0.999617i \(0.491189\pi\)
\(240\) −65600.0 −0.0735150
\(241\) 110798. 0.122882 0.0614411 0.998111i \(-0.480430\pi\)
0.0614411 + 0.998111i \(0.480430\pi\)
\(242\) 0 0
\(243\) −647404. −0.703331
\(244\) 904456. 0.972552
\(245\) 501425. 0.533692
\(246\) 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 \(-0.807936\pi\)
−0.823419 + 0.567434i \(0.807936\pi\)
\(252\) −1.22035e6 −1.21055
\(253\) 0 0
\(254\) 141104. 0.137232
\(255\) −167800. −0.161600
\(256\) −30464.0 −0.0290527
\(257\) 1.30624e6 1.23365 0.616823 0.787102i \(-0.288419\pi\)
0.616823 + 0.787102i \(0.288419\pi\)
\(258\) 9952.00 0.00930810
\(259\) −34944.0 −0.0323685
\(260\) 200200. 0.183667
\(261\) −774070. −0.703362
\(262\) 152904. 0.137615
\(263\) −2.12834e6 −1.89736 −0.948682 0.316231i \(-0.897583\pi\)
−0.948682 + 0.316231i \(0.897583\pi\)
\(264\) 0 0
\(265\) 596150. 0.521484
\(266\) −407040. −0.352722
\(267\) −405480. −0.348090
\(268\) −1.70722e6 −1.45195
\(269\) −1.44109e6 −1.21426 −0.607128 0.794604i \(-0.707679\pi\)
−0.607128 + 0.794604i \(0.707679\pi\)
\(270\) −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
\(273\) −219648. −0.178370
\(274\) 289836. 0.233225
\(275\) 0 0
\(276\) 333312. 0.263377
\(277\) 110298. 0.0863711 0.0431855 0.999067i \(-0.486249\pi\)
0.0431855 + 0.999067i \(0.486249\pi\)
\(278\) 224440. 0.174176
\(279\) 555696. 0.427392
\(280\) −576000. −0.439064
\(281\) 192198. 0.145205 0.0726027 0.997361i \(-0.476869\pi\)
0.0726027 + 0.997361i \(0.476869\pi\)
\(282\) −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
\(286\) 0 0
\(287\) −1.80442e6 −1.29310
\(288\) 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 \(0.768405\pi\)
\(294\) 160456. 0.108265
\(295\) −500500. −0.334849
\(296\) 21840.0 0.0144885
\(297\) 0 0
\(298\) 807500. 0.526747
\(299\) −851136. −0.550581
\(300\) 70000.0 0.0449050
\(301\) −238848. −0.151952
\(302\) −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 \(-0.744873\pi\)
−0.695626 + 0.718405i \(0.744873\pi\)
\(312\) 137280. 0.0798400
\(313\) −1.42941e6 −0.824702 −0.412351 0.911025i \(-0.635292\pi\)
−0.412351 + 0.911025i \(0.635292\pi\)
\(314\) 524516. 0.300217
\(315\) 1.08960e6 0.618715
\(316\) −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
\(319\) 0 0
\(320\) −267200. −0.145868
\(321\) 633168. 0.342970
\(322\) 1.14278e6 0.614221
\(323\) −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
\(329\) 2.32090e6 1.18213
\(330\) 0 0
\(331\) 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
\(336\) 503808. 0.243454
\(337\) −2.40008e6 −1.15120 −0.575601 0.817731i \(-0.695232\pi\)
−0.575601 + 0.817731i \(0.695232\pi\)
\(338\) 578994. 0.275665
\(339\) −44744.0 −0.0211464
\(340\) −1.17460e6 −0.551052
\(341\) 0 0
\(342\) −481240. −0.222483
\(343\) −624000. −0.286384
\(344\) 149280. 0.0680151
\(345\) −297600. −0.134612
\(346\) −1.14695e6 −0.515055
\(347\) −1.77741e6 −0.792436 −0.396218 0.918156i \(-0.629678\pi\)
−0.396218 + 0.918156i \(0.629678\pi\)
\(348\) 381920. 0.169054
\(349\) 2.14805e6 0.944019 0.472010 0.881593i \(-0.343529\pi\)
0.472010 + 0.881593i \(0.343529\pi\)
\(350\) 240000. 0.104723
\(351\) −537680. −0.232946
\(352\) 0 0
\(353\) −661854. −0.282700 −0.141350 0.989960i \(-0.545144\pi\)
−0.141350 + 0.989960i \(0.545144\pi\)
\(354\) −160160. −0.0679275
\(355\) −816200. −0.343737
\(356\) −2.83836e6 −1.18698
\(357\) 1.28870e6 0.535159
\(358\) 1.18892e6 0.490281
\(359\) 259320. 0.106194 0.0530970 0.998589i \(-0.483091\pi\)
0.0530970 + 0.998589i \(0.483091\pi\)
\(360\) −681000. −0.276943
\(361\) −1.35250e6 −0.546222
\(362\) 214196. 0.0859093
\(363\) 0 0
\(364\) −1.53754e6 −0.608236
\(365\) 969350. 0.380845
\(366\) −258416. −0.100836
\(367\) −1.49993e6 −0.581307 −0.290653 0.956828i \(-0.593873\pi\)
−0.290653 + 0.956828i \(0.593873\pi\)
\(368\) 1.95226e6 0.751480
\(369\) −2.13335e6 −0.815634
\(370\) −9100.00 −0.00345571
\(371\) −4.57843e6 −1.72696
\(372\) −274176. −0.102724
\(373\) 2.23807e6 0.832918 0.416459 0.909154i \(-0.363271\pi\)
0.416459 + 0.909154i \(0.363271\pi\)
\(374\) 0 0
\(375\) −62500.0 −0.0229510
\(376\) −1.45056e6 −0.529135
\(377\) −975260. −0.353400
\(378\) 721920. 0.259872
\(379\) 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 \(-0.481016\pi\)
0.0596037 + 0.998222i \(0.481016\pi\)
\(384\) −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
\(392\) 2.40684e6 0.791101
\(393\) 305808. 0.0998775
\(394\) 911724. 0.295885
\(395\) 834000. 0.268951
\(396\) 0 0
\(397\) −5.45674e6 −1.73763 −0.868814 0.495138i \(-0.835117\pi\)
−0.868814 + 0.495138i \(0.835117\pi\)
\(398\) −1.73000e6 −0.547442
\(399\) −814080. −0.255997
\(400\) 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
\(406\) 1.30944e6 0.394249
\(407\) 0 0
\(408\) −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
\(413\) 3.84384e6 1.10889
\(414\) 1.35110e6 0.387425
\(415\) −417900. −0.119111
\(416\) 1.47347e6 0.417454
\(417\) 448880. 0.126413
\(418\) 0 0
\(419\) 3.71746e6 1.03445 0.517227 0.855848i \(-0.326964\pi\)
0.517227 + 0.855848i \(0.326964\pi\)
\(420\) −537600. −0.148709
\(421\) 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
\(427\) 6.20198e6 1.64612
\(428\) 4.43218e6 1.16952
\(429\) 0 0
\(430\) −62200.0 −0.0162226
\(431\) 4.06205e6 1.05330 0.526650 0.850082i \(-0.323448\pi\)
0.526650 + 0.850082i \(0.323448\pi\)
\(432\) 1.23328e6 0.317945
\(433\) 7.26287e6 1.86161 0.930804 0.365518i \(-0.119108\pi\)
0.930804 + 0.365518i \(0.119108\pi\)
\(434\) −940032. −0.239562
\(435\) −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 \(0.266325\pi\)
\(440\) 0 0
\(441\) −4.55294e6 −1.11480
\(442\) 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
\(448\) 2.05210e6 0.483062
\(449\) −509950. −0.119375 −0.0596873 0.998217i \(-0.519010\pi\)
−0.0596873 + 0.998217i \(0.519010\pi\)
\(450\) 283750. 0.0660548
\(451\) 0 0
\(452\) −313208. −0.0721085
\(453\) −1.78659e6 −0.409053
\(454\) −46696.0 −0.0106326
\(455\) 1.37280e6 0.310870
\(456\) 508800. 0.114587
\(457\) −1.22084e6 −0.273444 −0.136722 0.990609i \(-0.543657\pi\)
−0.136722 + 0.990609i \(0.543657\pi\)
\(458\) 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 \(-0.387913\pi\)
0.344898 + 0.938640i \(0.387913\pi\)
\(468\) −1.81782e6 −0.383650
\(469\) −1.17066e7 −2.45753
\(470\) 604400. 0.126206
\(471\) 1.04903e6 0.217890
\(472\) −2.40240e6 −0.496353
\(473\) 0 0
\(474\) 266880. 0.0545595
\(475\) −662500. −0.134726
\(476\) 9.02093e6 1.82488
\(477\) −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
\(483\) 2.28557e6 0.445786
\(484\) 0 0
\(485\) −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
\(490\) −1.00285e6 −0.188689
\(491\) −1.51265e6 −0.283162 −0.141581 0.989927i \(-0.545219\pi\)
−0.141581 + 0.989927i \(0.545219\pi\)
\(492\) 1.05258e6 0.196038
\(493\) 5.72198e6 1.06030
\(494\) −606320. −0.111785
\(495\) 0 0
\(496\) −1.60589e6 −0.293097
\(497\) 6.26842e6 1.13833
\(498\) −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 \(0.774482\pi\)
\(504\) 5.23008e6 0.917132
\(505\) 2.24745e6 0.392158
\(506\) 0 0
\(507\) 1.15799e6 0.200071
\(508\) 1.97546e6 0.339632
\(509\) 2.67323e6 0.457343 0.228671 0.973504i \(-0.426562\pi\)
0.228671 + 0.973504i \(0.426562\pi\)
\(510\) 335600. 0.0571342
\(511\) −7.44461e6 −1.26122
\(512\) −5.89875e6 −0.994455
\(513\) −1.99280e6 −0.334326
\(514\) −2.61248e6 −0.436160
\(515\) −487600. −0.0810113
\(516\) 139328. 0.0230364
\(517\) 0 0
\(518\) 69888.0 0.0114440
\(519\) −2.29390e6 −0.373814
\(520\) −858000. −0.139149
\(521\) 6.18500e6 0.998264 0.499132 0.866526i \(-0.333652\pi\)
0.499132 + 0.866526i \(0.333652\pi\)
\(522\) 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
\(525\) 480000. 0.0760051
\(526\) 4.25667e6 0.670820
\(527\) −4.10774e6 −0.644283
\(528\) 0 0
\(529\) 2.42023e6 0.376026
\(530\) −1.19230e6 −0.184372
\(531\) 4.54454e6 0.699445
\(532\) −5.69856e6 −0.872943
\(533\) −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 \(-0.503636\pi\)
−0.0114212 + 0.999935i \(0.503636\pi\)
\(542\) −186496. −0.0272691
\(543\) 428392. 0.0623508
\(544\) −8.64506e6 −1.25248
\(545\) −920750. −0.132785
\(546\) 439296. 0.0630631
\(547\) −1.26544e7 −1.80831 −0.904157 0.427201i \(-0.859500\pi\)
−0.904157 + 0.427201i \(0.859500\pi\)
\(548\) 4.05770e6 0.577204
\(549\) 7.33255e6 1.03830
\(550\) 0 0
\(551\) −3.61460e6 −0.507202
\(552\) −1.42848e6 −0.199538
\(553\) −6.40512e6 −0.890665
\(554\) −220596. −0.0305368
\(555\) −18200.0 −0.00250807
\(556\) 3.14216e6 0.431064
\(557\) 7.07786e6 0.966638 0.483319 0.875444i \(-0.339431\pi\)
0.483319 + 0.875444i \(0.339431\pi\)
\(558\) −1.11139e6 −0.151106
\(559\) −355784. −0.0481567
\(560\) −3.14880e6 −0.424302
\(561\) 0 0
\(562\) −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
\(567\) −9.14707e6 −1.19488
\(568\) −3.91776e6 −0.509527
\(569\) −4.96041e6 −0.642299 −0.321149 0.947029i \(-0.604069\pi\)
−0.321149 + 0.947029i \(0.604069\pi\)
\(570\) −212000. −0.0273306
\(571\) −8.96505e6 −1.15070 −0.575351 0.817907i \(-0.695134\pi\)
−0.575351 + 0.817907i \(0.695134\pi\)
\(572\) 0 0
\(573\) −1.87821e6 −0.238978
\(574\) 3.60883e6 0.457180
\(575\) 1.86000e6 0.234608
\(576\) 2.42618e6 0.304696
\(577\) −2.86080e6 −0.357724 −0.178862 0.983874i \(-0.557242\pi\)
−0.178862 + 0.983874i \(0.557242\pi\)
\(578\) −2.79165e6 −0.347570
\(579\) 210824. 0.0261351
\(580\) −2.38700e6 −0.294634
\(581\) 3.20947e6 0.394451
\(582\) −952304. −0.116538
\(583\) 0 0
\(584\) 4.65288e6 0.564534
\(585\) 1.62305e6 0.196084
\(586\) 4.38961e6 0.528059
\(587\) −6.74027e6 −0.807387 −0.403694 0.914894i \(-0.632274\pi\)
−0.403694 + 0.914894i \(0.632274\pi\)
\(588\) 2.24638e6 0.267942
\(589\) 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 \(0.466743\pi\)
\(594\) 0 0
\(595\) −8.05440e6 −0.932697
\(596\) 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 \(0.416716\pi\)
\(602\) 477696. 0.0537230
\(603\) −1.38406e7 −1.55011
\(604\) −1.25061e7 −1.39486
\(605\) 0 0
\(606\) 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
\(609\) 2.61888e6 0.286136
\(610\) 1.61510e6 0.175742
\(611\) 3.45717e6 0.374643
\(612\) 1.06654e7 1.15106
\(613\) −5.09609e6 −0.547754 −0.273877 0.961765i \(-0.588306\pi\)
−0.273877 + 0.961765i \(0.588306\pi\)
\(614\) −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 \(-0.418231\pi\)
0.254070 + 0.967186i \(0.418231\pi\)
\(620\) 1.71360e6 0.179032
\(621\) 5.59488e6 0.582186
\(622\) 4.74610e6 0.491882
\(623\) −1.94630e7 −2.00905
\(624\) 750464. 0.0771558
\(625\) 390625. 0.0400000
\(626\) 2.85883e6 0.291576
\(627\) 0 0
\(628\) 7.34322e6 0.742998
\(629\) 305396. 0.0307777
\(630\) −2.17920e6 −0.218749
\(631\) 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
\(637\) −5.73630e6 −0.560123
\(638\) 0 0
\(639\) 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 \(-0.812609\pi\)
−0.831659 + 0.555287i \(0.812609\pi\)
\(644\) 1.59990e7 1.52012
\(645\) −124400. −0.0117739
\(646\) 3.55736e6 0.335387
\(647\) −4.25469e6 −0.399583 −0.199792 0.979838i \(-0.564026\pi\)
−0.199792 + 0.979838i \(0.564026\pi\)
\(648\) 5.71692e6 0.534841
\(649\) 0 0
\(650\) 357500. 0.0331889
\(651\) −1.88006e6 −0.173868
\(652\) 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
\(658\) −4.64179e6 −0.417947
\(659\) 8.11462e6 0.727871 0.363936 0.931424i \(-0.381433\pi\)
0.363936 + 0.931424i \(0.381433\pi\)
\(660\) 0 0
\(661\) 2.47370e6 0.220213 0.110107 0.993920i \(-0.464881\pi\)
0.110107 + 0.993920i \(0.464881\pi\)
\(662\) −6.19970e6 −0.549827
\(663\) 1.91963e6 0.169603
\(664\) −2.00592e6 −0.176560
\(665\) 5.08800e6 0.446162
\(666\) 82628.0 0.00721841
\(667\) 1.01482e7 0.883228
\(668\) 1.11068e7 0.963049
\(669\) −4.48630e6 −0.387546
\(670\) −3.04860e6 −0.262370
\(671\) 0 0
\(672\) −3.95674e6 −0.337998
\(673\) −5.77063e6 −0.491117 −0.245559 0.969382i \(-0.578971\pi\)
−0.245559 + 0.969382i \(0.578971\pi\)
\(674\) 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
\(679\) 2.28553e7 1.90245
\(680\) 5.03400e6 0.417485
\(681\) −93392.0 −0.00771688
\(682\) 0 0
\(683\) 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
\(686\) 1.24800e6 0.101252
\(687\) 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 \(-0.613790\pi\)
−0.349917 + 0.936781i \(0.613790\pi\)
\(692\) −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
\(700\) 3.36000e6 0.259176
\(701\) 1.60141e7 1.23086 0.615428 0.788193i \(-0.288983\pi\)
0.615428 + 0.788193i \(0.288983\pi\)
\(702\) 1.07536e6 0.0823590
\(703\) −192920. −0.0147228
\(704\) 0 0
\(705\) 1.20880e6 0.0915971
\(706\) 1.32371e6 0.0999495
\(707\) −1.72604e7 −1.29868
\(708\) −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
\(714\) −2.57741e6 −0.189207
\(715\) 0 0
\(716\) 1.66449e7 1.21338
\(717\) −195520. −0.0142034
\(718\) −518640. −0.0375452
\(719\) 1.02934e7 0.742566 0.371283 0.928520i \(-0.378918\pi\)
0.371283 + 0.928520i \(0.378918\pi\)
\(720\) −3.72280e6 −0.267632
\(721\) 3.74477e6 0.268279
\(722\) 2.70500e6 0.193119
\(723\) −443192. −0.0315316
\(724\) 2.99874e6 0.212615
\(725\) 2.13125e6 0.150588
\(726\) 0 0
\(727\) −1.93264e7 −1.35618 −0.678088 0.734981i \(-0.737191\pi\)
−0.678088 + 0.734981i \(0.737191\pi\)
\(728\) 6.58944e6 0.460808
\(729\) −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
\(735\) −2.00570e6 −0.136945
\(736\) −1.53324e7 −1.04331
\(737\) 0 0
\(738\) 4.26669e6 0.288370
\(739\) −2.82944e7 −1.90585 −0.952927 0.303199i \(-0.901945\pi\)
−0.952927 + 0.303199i \(0.901945\pi\)
\(740\) −127400. −0.00855244
\(741\) −1.21264e6 −0.0811309
\(742\) 9.15686e6 0.610572
\(743\) −2.09863e7 −1.39464 −0.697321 0.716759i \(-0.745625\pi\)
−0.697321 + 0.716759i \(0.745625\pi\)
\(744\) 1.17504e6 0.0778252
\(745\) −1.00938e7 −0.666288
\(746\) −4.47615e6 −0.294481
\(747\) 3.79453e6 0.248804
\(748\) 0 0
\(749\) 3.03921e7 1.97950
\(750\) 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
\(756\) 1.01069e7 0.643151
\(757\) −1.08257e7 −0.686617 −0.343309 0.939223i \(-0.611548\pi\)
−0.343309 + 0.939223i \(0.611548\pi\)
\(758\) −6.31868e6 −0.399442
\(759\) 0 0
\(760\) −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
\(763\) 7.07136e6 0.439736
\(764\) −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 \(-0.762588\pi\)
−0.734510 + 0.678598i \(0.762588\pi\)
\(774\) 564776. 0.0338863
\(775\) −1.53000e6 −0.0915034
\(776\) −1.42846e7 −0.851555
\(777\) 139776. 0.00830577
\(778\) −176940. −0.0104804
\(779\) −9.96188e6 −0.588163
\(780\) −800800. −0.0471289
\(781\) 0 0
\(782\) −9.98746e6 −0.584034
\(783\) 6.41080e6 0.373687
\(784\) 1.31574e7 0.764504
\(785\) −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
\(791\) −2.14771e6 −0.122049
\(792\) 0 0
\(793\) 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 \(-0.289929\pi\)
0.613083 + 0.790019i \(0.289929\pi\)
\(798\) 1.62816e6 0.0905086
\(799\) −2.02837e7 −1.12403
\(800\) −3.22000e6 −0.177882
\(801\) −2.30110e7 −1.26723
\(802\) −8.09360e6 −0.444330
\(803\) 0 0
\(804\) 6.82886e6 0.372570
\(805\) −1.42848e7 −0.776935
\(806\) −1.40026e6 −0.0759224
\(807\) 5.76436e6 0.311578
\(808\) 1.07878e7 0.581303
\(809\) 2.93597e7 1.57717 0.788587 0.614923i \(-0.210813\pi\)
0.788587 + 0.614923i \(0.210813\pi\)
\(810\) −2.38205e6 −0.127567
\(811\) −3.17703e7 −1.69617 −0.848083 0.529863i \(-0.822243\pi\)
−0.848083 + 0.529863i \(0.822243\pi\)
\(812\) 1.83322e7 0.975716
\(813\) −372992. −0.0197912
\(814\) 0 0
\(815\) −3.86410e6 −0.203777
\(816\) −4.40307e6 −0.231489
\(817\) −1.31864e6 −0.0691148
\(818\) −5.42414e6 −0.283431
\(819\) −1.24650e7 −0.649357
\(820\) −6.57860e6 −0.341664
\(821\) 2.71430e6 0.140540 0.0702699 0.997528i \(-0.477614\pi\)
0.0702699 + 0.997528i \(0.477614\pi\)
\(822\) −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
\(825\) 0 0
\(826\) −7.68768e6 −0.392053
\(827\) 8.72355e6 0.443537 0.221768 0.975099i \(-0.428817\pi\)
0.221768 + 0.975099i \(0.428817\pi\)
\(828\) 1.89155e7 0.958829
\(829\) −1.06178e7 −0.536597 −0.268299 0.963336i \(-0.586461\pi\)
−0.268299 + 0.963336i \(0.586461\pi\)
\(830\) 835800. 0.0421121
\(831\) −441192. −0.0221628
\(832\) 3.05677e6 0.153093
\(833\) 3.36556e7 1.68053
\(834\) −897760. −0.0446936
\(835\) −9.91680e6 −0.492216
\(836\) 0 0
\(837\) −4.60224e6 −0.227068
\(838\) −7.43492e6 −0.365735
\(839\) 1.67765e7 0.822805 0.411403 0.911454i \(-0.365039\pi\)
0.411403 + 0.911454i \(0.365039\pi\)
\(840\) 2.30400e6 0.112664
\(841\) −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 \(0.326652\pi\)
\(854\) −1.24040e7 −0.581991
\(855\) 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 \(0.763492\pi\)
\(858\) 0 0
\(859\) 1.58064e7 0.730886 0.365443 0.930834i \(-0.380918\pi\)
0.365443 + 0.930834i \(0.380918\pi\)
\(860\) −870800. −0.0401488
\(861\) 7.21766e6 0.331809
\(862\) −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
\(868\) −1.31604e7 −0.592886
\(869\) 0 0
\(870\) 682000. 0.0305482
\(871\) −1.74380e7 −0.778845
\(872\) −4.41960e6 −0.196830
\(873\) 2.70216e7 1.19999
\(874\) 6.30912e6 0.279377
\(875\) −3.00000e6 −0.132465
\(876\) 4.34269e6 0.191205
\(877\) −247902. −0.0108838 −0.00544191 0.999985i \(-0.501732\pi\)
−0.00544191 + 0.999985i \(0.501732\pi\)
\(878\) −1.08206e7 −0.473711
\(879\) 8.77922e6 0.383252
\(880\) 0 0
\(881\) 4.10268e7 1.78085 0.890426 0.455128i \(-0.150406\pi\)
0.890426 + 0.455128i \(0.150406\pi\)
\(882\) 9.10588e6 0.394140
\(883\) 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
\(889\) 1.35460e7 0.574852
\(890\) −5.06850e6 −0.214489
\(891\) 0 0
\(892\) −3.14041e7 −1.32152
\(893\) 1.28133e7 0.537690
\(894\) −3.23000e6 −0.135163
\(895\) −1.48615e7 −0.620162
\(896\) −3.57581e7 −1.48800
\(897\) 3.40454e6 0.141279
\(898\) 1.01990e6 0.0422053
\(899\) −8.34768e6 −0.344482
\(900\) 3.97250e6 0.163477
\(901\) 4.00136e7 1.64208
\(902\) 0 0
\(903\) 955392. 0.0389908
\(904\) 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
\(910\) −2.74560e6 −0.109909
\(911\) −6.63165e6 −0.264744 −0.132372 0.991200i \(-0.542259\pi\)
−0.132372 + 0.991200i \(0.542259\pi\)
\(912\) 2.78144e6 0.110734
\(913\) 0 0
\(914\) 2.44168e6 0.0966772
\(915\) 3.23020e6 0.127549
\(916\) 1.66883e7 0.657163
\(917\) 1.46788e7 0.576457
\(918\) −6.30928e6 −0.247100
\(919\) 1.68976e7 0.659990 0.329995 0.943983i \(-0.392953\pi\)
0.329995 + 0.943983i \(0.392953\pi\)
\(920\) 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 \(-0.578637\pi\)
−0.244541 + 0.969639i \(0.578637\pi\)
\(930\) −489600. −0.0185624
\(931\) −2.12604e7 −0.803892
\(932\) −1.35894e7 −0.512459
\(933\) 9.49219e6 0.356995
\(934\) −6.50194e6 −0.243880
\(935\) 0 0
\(936\) 7.79064e6 0.290659
\(937\) −1.06887e7 −0.397718 −0.198859 0.980028i \(-0.563724\pi\)
−0.198859 + 0.980028i \(0.563724\pi\)
\(938\) 2.34132e7 0.868870
\(939\) 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
\(945\) −9.02400e6 −0.328715
\(946\) 0 0
\(947\) −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
\(952\) −3.86611e7 −1.38255
\(953\) −2.22259e7 −0.792735 −0.396367 0.918092i \(-0.629729\pi\)
−0.396367 + 0.918092i \(0.629729\pi\)
\(954\) 1.08261e7 0.385124
\(955\) 1.17388e7 0.416500
\(956\) −1.36864e6 −0.0484333
\(957\) 0 0
\(958\) −6.55872e6 −0.230890
\(959\) 2.78243e7 0.976961
\(960\) 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
\(966\) −4.57114e6 −0.157609
\(967\) −2.41551e7 −0.830696 −0.415348 0.909663i \(-0.636340\pi\)
−0.415348 + 0.909663i \(0.636340\pi\)
\(968\) 0 0
\(969\) 7.11472e6 0.243416
\(970\) 5.95190e6 0.203108
\(971\) −5.48313e7 −1.86630 −0.933149 0.359491i \(-0.882950\pi\)
−0.933149 + 0.359491i \(0.882950\pi\)
\(972\) 1.81273e7 0.615415
\(973\) 2.15462e7 0.729608
\(974\) 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
\(979\) 0 0
\(980\) −1.40399e7 −0.466981
\(981\) 8.36041e6 0.277367
\(982\) 3.02530e6 0.100113
\(983\) −1.63420e7 −0.539412 −0.269706 0.962943i \(-0.586927\pi\)
−0.269706 + 0.962943i \(0.586927\pi\)
\(984\) −4.51104e6 −0.148521
\(985\) −1.13966e7 −0.374268
\(986\) −1.14440e7 −0.374873
\(987\) −9.28358e6 −0.303335
\(988\) −8.48848e6 −0.276654
\(989\) 3.70214e6 0.120355
\(990\) 0 0
\(991\) 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
\(994\) −1.25368e7 −0.402459
\(995\) 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 605.6.a.a.1.1 1
11.10 odd 2 5.6.a.a.1.1 1
33.32 even 2 45.6.a.b.1.1 1
44.43 even 2 80.6.a.e.1.1 1
55.32 even 4 25.6.b.a.24.2 2
55.43 even 4 25.6.b.a.24.1 2
55.54 odd 2 25.6.a.a.1.1 1
77.76 even 2 245.6.a.b.1.1 1
88.21 odd 2 320.6.a.j.1.1 1
88.43 even 2 320.6.a.g.1.1 1
132.131 odd 2 720.6.a.a.1.1 1
143.142 odd 2 845.6.a.b.1.1 1
165.32 odd 4 225.6.b.e.199.1 2
165.98 odd 4 225.6.b.e.199.2 2
165.164 even 2 225.6.a.f.1.1 1
220.43 odd 4 400.6.c.j.49.2 2
220.87 odd 4 400.6.c.j.49.1 2
220.219 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 11.10 odd 2
25.6.a.a.1.1 1 55.54 odd 2
25.6.b.a.24.1 2 55.43 even 4
25.6.b.a.24.2 2 55.32 even 4
45.6.a.b.1.1 1 33.32 even 2
80.6.a.e.1.1 1 44.43 even 2
225.6.a.f.1.1 1 165.164 even 2
225.6.b.e.199.1 2 165.32 odd 4
225.6.b.e.199.2 2 165.98 odd 4
245.6.a.b.1.1 1 77.76 even 2
320.6.a.g.1.1 1 88.43 even 2
320.6.a.j.1.1 1 88.21 odd 2
400.6.a.g.1.1 1 220.219 even 2
400.6.c.j.49.1 2 220.87 odd 4
400.6.c.j.49.2 2 220.43 odd 4
605.6.a.a.1.1 1 1.1 even 1 trivial
720.6.a.a.1.1 1 132.131 odd 2
845.6.a.b.1.1 1 143.142 odd 2