Properties

Label 245.6.a.i.1.1
Level $245$
Weight $6$
Character 245.1
Self dual yes
Analytic conductor $39.294$
Analytic rank $1$
Dimension $6$
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: \(1\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \( x^{6} - x^{5} - 109x^{4} + 41x^{3} + 2208x^{2} - 3204x + 560 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 35)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-8.17253\) of defining polynomial
Character \(\chi\) \(=\) 245.1

$q$-expansion

\(f(q)\) \(=\) \(q-9.17253 q^{2} +14.3258 q^{3} +52.1353 q^{4} -25.0000 q^{5} -131.404 q^{6} -184.691 q^{8} -37.7723 q^{9} +O(q^{10})\) \(q-9.17253 q^{2} +14.3258 q^{3} +52.1353 q^{4} -25.0000 q^{5} -131.404 q^{6} -184.691 q^{8} -37.7723 q^{9} +229.313 q^{10} +215.386 q^{11} +746.878 q^{12} +132.696 q^{13} -358.144 q^{15} +25.7572 q^{16} +441.638 q^{17} +346.467 q^{18} +519.002 q^{19} -1303.38 q^{20} -1975.63 q^{22} -4389.66 q^{23} -2645.84 q^{24} +625.000 q^{25} -1217.16 q^{26} -4022.28 q^{27} +7114.31 q^{29} +3285.09 q^{30} -10304.7 q^{31} +5673.86 q^{32} +3085.56 q^{33} -4050.94 q^{34} -1969.27 q^{36} +5568.08 q^{37} -4760.56 q^{38} +1900.98 q^{39} +4617.28 q^{40} +7246.54 q^{41} -184.308 q^{43} +11229.2 q^{44} +944.307 q^{45} +40264.3 q^{46} +16174.2 q^{47} +368.991 q^{48} -5732.83 q^{50} +6326.81 q^{51} +6918.16 q^{52} +7275.69 q^{53} +36894.5 q^{54} -5384.64 q^{55} +7435.11 q^{57} -65256.2 q^{58} -45301.7 q^{59} -18671.9 q^{60} -7369.70 q^{61} +94520.4 q^{62} -52867.9 q^{64} -3317.41 q^{65} -28302.4 q^{66} -64443.0 q^{67} +23024.9 q^{68} -62885.2 q^{69} -343.451 q^{71} +6976.21 q^{72} +45357.4 q^{73} -51073.4 q^{74} +8953.61 q^{75} +27058.3 q^{76} -17436.8 q^{78} -74587.6 q^{79} -643.929 q^{80} -48443.6 q^{81} -66469.1 q^{82} -54772.9 q^{83} -11041.0 q^{85} +1690.57 q^{86} +101918. q^{87} -39779.8 q^{88} -106839. q^{89} -8661.68 q^{90} -228856. q^{92} -147623. q^{93} -148358. q^{94} -12975.1 q^{95} +81282.4 q^{96} +19313.9 q^{97} -8135.60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 5 q^{2} + 20 q^{3} + 31 q^{4} - 150 q^{5} + 96 q^{6} - 135 q^{8} + 378 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 5 q^{2} + 20 q^{3} + 31 q^{4} - 150 q^{5} + 96 q^{6} - 135 q^{8} + 378 q^{9} + 125 q^{10} - 924 q^{11} + 370 q^{12} - 150 q^{13} - 500 q^{15} + 435 q^{16} + 1540 q^{17} + 195 q^{18} + 92 q^{19} - 775 q^{20} - 6855 q^{22} - 3920 q^{23} - 7200 q^{24} + 3750 q^{25} + 2635 q^{26} + 2060 q^{27} + 1264 q^{29} - 2400 q^{30} - 7160 q^{31} + 9105 q^{32} + 4460 q^{33} + 2166 q^{34} - 26375 q^{36} - 14170 q^{37} - 46215 q^{38} - 15376 q^{39} + 3375 q^{40} + 4098 q^{41} - 24460 q^{43} - 27873 q^{44} - 9450 q^{45} + 6815 q^{46} + 42940 q^{47} + 11610 q^{48} - 3125 q^{50} - 42008 q^{51} - 36115 q^{52} - 2450 q^{53} + 19566 q^{54} + 23100 q^{55} - 97100 q^{57} - 36110 q^{58} - 64600 q^{59} - 9250 q^{60} + 73620 q^{61} + 111440 q^{62} - 157997 q^{64} + 3750 q^{65} - 139138 q^{66} - 142620 q^{67} + 124330 q^{68} + 17344 q^{69} - 154256 q^{71} - 117495 q^{72} - 5120 q^{73} + 2785 q^{74} + 12500 q^{75} + 7775 q^{76} - 214090 q^{78} - 222504 q^{79} - 10875 q^{80} - 43986 q^{81} + 31665 q^{82} + 179580 q^{83} - 38500 q^{85} - 207160 q^{86} - 209300 q^{87} - 45145 q^{88} + 41648 q^{89} - 4875 q^{90} - 292185 q^{92} - 198520 q^{93} - 333699 q^{94} - 2300 q^{95} + 61824 q^{96} - 73980 q^{97} - 190772 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.17253 −1.62149 −0.810745 0.585400i \(-0.800937\pi\)
−0.810745 + 0.585400i \(0.800937\pi\)
\(3\) 14.3258 0.918999 0.459499 0.888178i \(-0.348029\pi\)
0.459499 + 0.888178i \(0.348029\pi\)
\(4\) 52.1353 1.62923
\(5\) −25.0000 −0.447214
\(6\) −131.404 −1.49015
\(7\) 0 0
\(8\) −184.691 −1.02028
\(9\) −37.7723 −0.155441
\(10\) 229.313 0.725152
\(11\) 215.386 0.536704 0.268352 0.963321i \(-0.413521\pi\)
0.268352 + 0.963321i \(0.413521\pi\)
\(12\) 746.878 1.49726
\(13\) 132.696 0.217771 0.108886 0.994054i \(-0.465272\pi\)
0.108886 + 0.994054i \(0.465272\pi\)
\(14\) 0 0
\(15\) −358.144 −0.410989
\(16\) 25.7572 0.0251535
\(17\) 441.638 0.370633 0.185317 0.982679i \(-0.440669\pi\)
0.185317 + 0.982679i \(0.440669\pi\)
\(18\) 346.467 0.252047
\(19\) 519.002 0.329826 0.164913 0.986308i \(-0.447266\pi\)
0.164913 + 0.986308i \(0.447266\pi\)
\(20\) −1303.38 −0.728612
\(21\) 0 0
\(22\) −1975.63 −0.870260
\(23\) −4389.66 −1.73026 −0.865129 0.501549i \(-0.832764\pi\)
−0.865129 + 0.501549i \(0.832764\pi\)
\(24\) −2645.84 −0.937640
\(25\) 625.000 0.200000
\(26\) −1217.16 −0.353114
\(27\) −4022.28 −1.06185
\(28\) 0 0
\(29\) 7114.31 1.57086 0.785430 0.618950i \(-0.212442\pi\)
0.785430 + 0.618950i \(0.212442\pi\)
\(30\) 3285.09 0.666414
\(31\) −10304.7 −1.92589 −0.962946 0.269693i \(-0.913078\pi\)
−0.962946 + 0.269693i \(0.913078\pi\)
\(32\) 5673.86 0.979499
\(33\) 3085.56 0.493230
\(34\) −4050.94 −0.600978
\(35\) 0 0
\(36\) −1969.27 −0.253249
\(37\) 5568.08 0.668654 0.334327 0.942457i \(-0.391491\pi\)
0.334327 + 0.942457i \(0.391491\pi\)
\(38\) −4760.56 −0.534810
\(39\) 1900.98 0.200132
\(40\) 4617.28 0.456285
\(41\) 7246.54 0.673242 0.336621 0.941640i \(-0.390716\pi\)
0.336621 + 0.941640i \(0.390716\pi\)
\(42\) 0 0
\(43\) −184.308 −0.0152010 −0.00760050 0.999971i \(-0.502419\pi\)
−0.00760050 + 0.999971i \(0.502419\pi\)
\(44\) 11229.2 0.874413
\(45\) 944.307 0.0695155
\(46\) 40264.3 2.80560
\(47\) 16174.2 1.06802 0.534008 0.845480i \(-0.320685\pi\)
0.534008 + 0.845480i \(0.320685\pi\)
\(48\) 368.991 0.0231160
\(49\) 0 0
\(50\) −5732.83 −0.324298
\(51\) 6326.81 0.340611
\(52\) 6918.16 0.354799
\(53\) 7275.69 0.355782 0.177891 0.984050i \(-0.443072\pi\)
0.177891 + 0.984050i \(0.443072\pi\)
\(54\) 36894.5 1.72178
\(55\) −5384.64 −0.240021
\(56\) 0 0
\(57\) 7435.11 0.303110
\(58\) −65256.2 −2.54713
\(59\) −45301.7 −1.69428 −0.847138 0.531373i \(-0.821676\pi\)
−0.847138 + 0.531373i \(0.821676\pi\)
\(60\) −18671.9 −0.669594
\(61\) −7369.70 −0.253586 −0.126793 0.991929i \(-0.540468\pi\)
−0.126793 + 0.991929i \(0.540468\pi\)
\(62\) 94520.4 3.12281
\(63\) 0 0
\(64\) −52867.9 −1.61340
\(65\) −3317.41 −0.0973903
\(66\) −28302.4 −0.799767
\(67\) −64443.0 −1.75383 −0.876917 0.480641i \(-0.840404\pi\)
−0.876917 + 0.480641i \(0.840404\pi\)
\(68\) 23024.9 0.603846
\(69\) −62885.2 −1.59011
\(70\) 0 0
\(71\) −343.451 −0.00808573 −0.00404286 0.999992i \(-0.501287\pi\)
−0.00404286 + 0.999992i \(0.501287\pi\)
\(72\) 6976.21 0.158595
\(73\) 45357.4 0.996187 0.498094 0.867123i \(-0.334034\pi\)
0.498094 + 0.867123i \(0.334034\pi\)
\(74\) −51073.4 −1.08421
\(75\) 8953.61 0.183800
\(76\) 27058.3 0.537362
\(77\) 0 0
\(78\) −17436.8 −0.324511
\(79\) −74587.6 −1.34462 −0.672309 0.740271i \(-0.734697\pi\)
−0.672309 + 0.740271i \(0.734697\pi\)
\(80\) −643.929 −0.0112490
\(81\) −48443.6 −0.820396
\(82\) −66469.1 −1.09165
\(83\) −54772.9 −0.872711 −0.436356 0.899774i \(-0.643731\pi\)
−0.436356 + 0.899774i \(0.643731\pi\)
\(84\) 0 0
\(85\) −11041.0 −0.165752
\(86\) 1690.57 0.0246483
\(87\) 101918. 1.44362
\(88\) −39779.8 −0.547591
\(89\) −106839. −1.42974 −0.714868 0.699260i \(-0.753513\pi\)
−0.714868 + 0.699260i \(0.753513\pi\)
\(90\) −8661.68 −0.112719
\(91\) 0 0
\(92\) −228856. −2.81898
\(93\) −147623. −1.76989
\(94\) −148358. −1.73178
\(95\) −12975.1 −0.147503
\(96\) 81282.4 0.900158
\(97\) 19313.9 0.208421 0.104210 0.994555i \(-0.466769\pi\)
0.104210 + 0.994555i \(0.466769\pi\)
\(98\) 0 0
\(99\) −8135.60 −0.0834261
\(100\) 32584.5 0.325845
\(101\) −24524.6 −0.239221 −0.119610 0.992821i \(-0.538165\pi\)
−0.119610 + 0.992821i \(0.538165\pi\)
\(102\) −58032.8 −0.552298
\(103\) −46312.7 −0.430137 −0.215069 0.976599i \(-0.568997\pi\)
−0.215069 + 0.976599i \(0.568997\pi\)
\(104\) −24507.9 −0.222189
\(105\) 0 0
\(106\) −66736.4 −0.576897
\(107\) 157154. 1.32699 0.663495 0.748181i \(-0.269073\pi\)
0.663495 + 0.748181i \(0.269073\pi\)
\(108\) −209703. −1.72999
\(109\) −141538. −1.14106 −0.570530 0.821277i \(-0.693262\pi\)
−0.570530 + 0.821277i \(0.693262\pi\)
\(110\) 49390.7 0.389192
\(111\) 79767.0 0.614492
\(112\) 0 0
\(113\) −157706. −1.16186 −0.580928 0.813955i \(-0.697310\pi\)
−0.580928 + 0.813955i \(0.697310\pi\)
\(114\) −68198.7 −0.491489
\(115\) 109741. 0.773795
\(116\) 370906. 2.55929
\(117\) −5012.25 −0.0338507
\(118\) 415531. 2.74725
\(119\) 0 0
\(120\) 66146.1 0.419325
\(121\) −114660. −0.711949
\(122\) 67598.8 0.411187
\(123\) 103812. 0.618709
\(124\) −537239. −3.13772
\(125\) −15625.0 −0.0894427
\(126\) 0 0
\(127\) −249665. −1.37356 −0.686782 0.726864i \(-0.740977\pi\)
−0.686782 + 0.726864i \(0.740977\pi\)
\(128\) 303369. 1.63661
\(129\) −2640.35 −0.0139697
\(130\) 30429.0 0.157917
\(131\) 216534. 1.10242 0.551210 0.834366i \(-0.314166\pi\)
0.551210 + 0.834366i \(0.314166\pi\)
\(132\) 160867. 0.803584
\(133\) 0 0
\(134\) 591105. 2.84382
\(135\) 100557. 0.474873
\(136\) −81566.7 −0.378151
\(137\) −58644.1 −0.266946 −0.133473 0.991052i \(-0.542613\pi\)
−0.133473 + 0.991052i \(0.542613\pi\)
\(138\) 576816. 2.57834
\(139\) −353961. −1.55388 −0.776941 0.629573i \(-0.783230\pi\)
−0.776941 + 0.629573i \(0.783230\pi\)
\(140\) 0 0
\(141\) 231708. 0.981505
\(142\) 3150.32 0.0131109
\(143\) 28580.9 0.116879
\(144\) −972.907 −0.00390989
\(145\) −177858. −0.702510
\(146\) −416042. −1.61531
\(147\) 0 0
\(148\) 290293. 1.08939
\(149\) 73724.4 0.272048 0.136024 0.990706i \(-0.456568\pi\)
0.136024 + 0.990706i \(0.456568\pi\)
\(150\) −82127.2 −0.298029
\(151\) −322597. −1.15138 −0.575689 0.817669i \(-0.695266\pi\)
−0.575689 + 0.817669i \(0.695266\pi\)
\(152\) −95855.2 −0.336517
\(153\) −16681.7 −0.0576118
\(154\) 0 0
\(155\) 257618. 0.861285
\(156\) 99108.0 0.326060
\(157\) 224924. 0.728261 0.364131 0.931348i \(-0.381366\pi\)
0.364131 + 0.931348i \(0.381366\pi\)
\(158\) 684156. 2.18028
\(159\) 104230. 0.326963
\(160\) −141847. −0.438045
\(161\) 0 0
\(162\) 444350. 1.33026
\(163\) −158217. −0.466427 −0.233214 0.972426i \(-0.574924\pi\)
−0.233214 + 0.972426i \(0.574924\pi\)
\(164\) 377800. 1.09686
\(165\) −77139.1 −0.220579
\(166\) 502406. 1.41509
\(167\) −316938. −0.879392 −0.439696 0.898147i \(-0.644914\pi\)
−0.439696 + 0.898147i \(0.644914\pi\)
\(168\) 0 0
\(169\) −353685. −0.952576
\(170\) 101273. 0.268765
\(171\) −19603.9 −0.0512687
\(172\) −9608.93 −0.0247659
\(173\) 360124. 0.914824 0.457412 0.889255i \(-0.348777\pi\)
0.457412 + 0.889255i \(0.348777\pi\)
\(174\) −934845. −2.34081
\(175\) 0 0
\(176\) 5547.72 0.0135000
\(177\) −648981. −1.55704
\(178\) 979986. 2.31830
\(179\) −440948. −1.02862 −0.514310 0.857604i \(-0.671952\pi\)
−0.514310 + 0.857604i \(0.671952\pi\)
\(180\) 49231.7 0.113257
\(181\) 19489.0 0.0442175 0.0221087 0.999756i \(-0.492962\pi\)
0.0221087 + 0.999756i \(0.492962\pi\)
\(182\) 0 0
\(183\) −105577. −0.233045
\(184\) 810731. 1.76536
\(185\) −139202. −0.299031
\(186\) 1.35408e6 2.86986
\(187\) 95122.5 0.198920
\(188\) 843245. 1.74004
\(189\) 0 0
\(190\) 119014. 0.239174
\(191\) −418719. −0.830499 −0.415250 0.909708i \(-0.636306\pi\)
−0.415250 + 0.909708i \(0.636306\pi\)
\(192\) −757373. −1.48271
\(193\) 4008.29 0.00774578 0.00387289 0.999993i \(-0.498767\pi\)
0.00387289 + 0.999993i \(0.498767\pi\)
\(194\) −177157. −0.337952
\(195\) −47524.5 −0.0895016
\(196\) 0 0
\(197\) 1.02060e6 1.87366 0.936830 0.349786i \(-0.113746\pi\)
0.936830 + 0.349786i \(0.113746\pi\)
\(198\) 74624.0 0.135274
\(199\) −157196. −0.281391 −0.140695 0.990053i \(-0.544934\pi\)
−0.140695 + 0.990053i \(0.544934\pi\)
\(200\) −115432. −0.204057
\(201\) −923195. −1.61177
\(202\) 224953. 0.387894
\(203\) 0 0
\(204\) 329850. 0.554933
\(205\) −181164. −0.301083
\(206\) 424804. 0.697463
\(207\) 165807. 0.268954
\(208\) 3417.88 0.00547771
\(209\) 111786. 0.177019
\(210\) 0 0
\(211\) −797769. −1.23359 −0.616795 0.787124i \(-0.711569\pi\)
−0.616795 + 0.787124i \(0.711569\pi\)
\(212\) 379320. 0.579650
\(213\) −4920.20 −0.00743077
\(214\) −1.44150e6 −2.15170
\(215\) 4607.69 0.00679810
\(216\) 742880. 1.08339
\(217\) 0 0
\(218\) 1.29827e6 1.85022
\(219\) 649780. 0.915495
\(220\) −280730. −0.391049
\(221\) 58603.8 0.0807133
\(222\) −731665. −0.996392
\(223\) 1.17028e6 1.57590 0.787951 0.615739i \(-0.211142\pi\)
0.787951 + 0.615739i \(0.211142\pi\)
\(224\) 0 0
\(225\) −23607.7 −0.0310883
\(226\) 1.44656e6 1.88394
\(227\) 419223. 0.539983 0.269991 0.962863i \(-0.412979\pi\)
0.269991 + 0.962863i \(0.412979\pi\)
\(228\) 387631. 0.493835
\(229\) −457265. −0.576208 −0.288104 0.957599i \(-0.593025\pi\)
−0.288104 + 0.957599i \(0.593025\pi\)
\(230\) −1.00661e6 −1.25470
\(231\) 0 0
\(232\) −1.31395e6 −1.60273
\(233\) −669972. −0.808475 −0.404237 0.914654i \(-0.632463\pi\)
−0.404237 + 0.914654i \(0.632463\pi\)
\(234\) 45975.0 0.0548886
\(235\) −404354. −0.477631
\(236\) −2.36181e6 −2.76036
\(237\) −1.06852e6 −1.23570
\(238\) 0 0
\(239\) −550244. −0.623104 −0.311552 0.950229i \(-0.600849\pi\)
−0.311552 + 0.950229i \(0.600849\pi\)
\(240\) −9224.78 −0.0103378
\(241\) 163023. 0.180804 0.0904018 0.995905i \(-0.471185\pi\)
0.0904018 + 0.995905i \(0.471185\pi\)
\(242\) 1.05172e6 1.15442
\(243\) 283422. 0.307906
\(244\) −384221. −0.413149
\(245\) 0 0
\(246\) −952221. −1.00323
\(247\) 68869.8 0.0718267
\(248\) 1.90319e6 1.96496
\(249\) −784664. −0.802020
\(250\) 143321. 0.145030
\(251\) 1.31883e6 1.32131 0.660654 0.750690i \(-0.270279\pi\)
0.660654 + 0.750690i \(0.270279\pi\)
\(252\) 0 0
\(253\) −945469. −0.928637
\(254\) 2.29006e6 2.22722
\(255\) −158170. −0.152326
\(256\) −1.09088e6 −1.04035
\(257\) −832987. −0.786693 −0.393347 0.919390i \(-0.628683\pi\)
−0.393347 + 0.919390i \(0.628683\pi\)
\(258\) 24218.7 0.0226517
\(259\) 0 0
\(260\) −172954. −0.158671
\(261\) −268724. −0.244177
\(262\) −1.98616e6 −1.78756
\(263\) −1.64512e6 −1.46659 −0.733296 0.679910i \(-0.762019\pi\)
−0.733296 + 0.679910i \(0.762019\pi\)
\(264\) −569877. −0.503235
\(265\) −181892. −0.159111
\(266\) 0 0
\(267\) −1.53055e6 −1.31392
\(268\) −3.35975e6 −2.85739
\(269\) 454521. 0.382978 0.191489 0.981495i \(-0.438668\pi\)
0.191489 + 0.981495i \(0.438668\pi\)
\(270\) −922362. −0.770002
\(271\) 831066. 0.687405 0.343702 0.939079i \(-0.388319\pi\)
0.343702 + 0.939079i \(0.388319\pi\)
\(272\) 11375.3 0.00932272
\(273\) 0 0
\(274\) 537915. 0.432850
\(275\) 134616. 0.107341
\(276\) −3.27854e6 −2.59064
\(277\) 1.30960e6 1.02551 0.512756 0.858534i \(-0.328625\pi\)
0.512756 + 0.858534i \(0.328625\pi\)
\(278\) 3.24671e6 2.51960
\(279\) 389233. 0.299364
\(280\) 0 0
\(281\) 175721. 0.132757 0.0663784 0.997795i \(-0.478856\pi\)
0.0663784 + 0.997795i \(0.478856\pi\)
\(282\) −2.12534e6 −1.59150
\(283\) 953011. 0.707346 0.353673 0.935369i \(-0.384933\pi\)
0.353673 + 0.935369i \(0.384933\pi\)
\(284\) −17905.9 −0.0131735
\(285\) −185878. −0.135555
\(286\) −262159. −0.189518
\(287\) 0 0
\(288\) −214315. −0.152255
\(289\) −1.22481e6 −0.862631
\(290\) 1.63140e6 1.13911
\(291\) 276686. 0.191538
\(292\) 2.36472e6 1.62302
\(293\) 275025. 0.187156 0.0935778 0.995612i \(-0.470170\pi\)
0.0935778 + 0.995612i \(0.470170\pi\)
\(294\) 0 0
\(295\) 1.13254e6 0.757703
\(296\) −1.02838e6 −0.682217
\(297\) −866341. −0.569899
\(298\) −676239. −0.441123
\(299\) −582492. −0.376801
\(300\) 466799. 0.299451
\(301\) 0 0
\(302\) 2.95903e6 1.86695
\(303\) −351334. −0.219843
\(304\) 13368.0 0.00829628
\(305\) 184242. 0.113407
\(306\) 153013. 0.0934169
\(307\) 473977. 0.287019 0.143510 0.989649i \(-0.454161\pi\)
0.143510 + 0.989649i \(0.454161\pi\)
\(308\) 0 0
\(309\) −663465. −0.395295
\(310\) −2.36301e6 −1.39656
\(311\) 3.10860e6 1.82248 0.911241 0.411873i \(-0.135125\pi\)
0.911241 + 0.411873i \(0.135125\pi\)
\(312\) −351094. −0.204191
\(313\) 1.51927e6 0.876544 0.438272 0.898842i \(-0.355591\pi\)
0.438272 + 0.898842i \(0.355591\pi\)
\(314\) −2.06312e6 −1.18087
\(315\) 0 0
\(316\) −3.88864e6 −2.19069
\(317\) 2.53235e6 1.41539 0.707695 0.706518i \(-0.249735\pi\)
0.707695 + 0.706518i \(0.249735\pi\)
\(318\) −956051. −0.530168
\(319\) 1.53232e6 0.843087
\(320\) 1.32170e6 0.721534
\(321\) 2.25136e6 1.21950
\(322\) 0 0
\(323\) 229211. 0.122245
\(324\) −2.52562e6 −1.33661
\(325\) 82935.3 0.0435543
\(326\) 1.45125e6 0.756307
\(327\) −2.02765e6 −1.04863
\(328\) −1.33837e6 −0.686899
\(329\) 0 0
\(330\) 707560. 0.357667
\(331\) 557600. 0.279739 0.139869 0.990170i \(-0.455332\pi\)
0.139869 + 0.990170i \(0.455332\pi\)
\(332\) −2.85560e6 −1.42184
\(333\) −210319. −0.103937
\(334\) 2.90712e6 1.42592
\(335\) 1.61107e6 0.784339
\(336\) 0 0
\(337\) 501783. 0.240681 0.120340 0.992733i \(-0.461601\pi\)
0.120340 + 0.992733i \(0.461601\pi\)
\(338\) 3.24418e6 1.54459
\(339\) −2.25926e6 −1.06774
\(340\) −575623. −0.270048
\(341\) −2.21949e6 −1.03363
\(342\) 179817. 0.0831316
\(343\) 0 0
\(344\) 34040.0 0.0155094
\(345\) 1.57213e6 0.711117
\(346\) −3.30325e6 −1.48338
\(347\) 283359. 0.126332 0.0631661 0.998003i \(-0.479880\pi\)
0.0631661 + 0.998003i \(0.479880\pi\)
\(348\) 5.31352e6 2.35198
\(349\) 569924. 0.250469 0.125234 0.992127i \(-0.460032\pi\)
0.125234 + 0.992127i \(0.460032\pi\)
\(350\) 0 0
\(351\) −533742. −0.231240
\(352\) 1.22207e6 0.525701
\(353\) −1.74073e6 −0.743522 −0.371761 0.928328i \(-0.621246\pi\)
−0.371761 + 0.928328i \(0.621246\pi\)
\(354\) 5.95280e6 2.52472
\(355\) 8586.28 0.00361605
\(356\) −5.57009e6 −2.32936
\(357\) 0 0
\(358\) 4.04461e6 1.66790
\(359\) 933824. 0.382410 0.191205 0.981550i \(-0.438761\pi\)
0.191205 + 0.981550i \(0.438761\pi\)
\(360\) −174405. −0.0709256
\(361\) −2.20674e6 −0.891215
\(362\) −178764. −0.0716982
\(363\) −1.64259e6 −0.654280
\(364\) 0 0
\(365\) −1.13394e6 −0.445509
\(366\) 968404. 0.377880
\(367\) 1.52484e6 0.590962 0.295481 0.955349i \(-0.404520\pi\)
0.295481 + 0.955349i \(0.404520\pi\)
\(368\) −113065. −0.0435220
\(369\) −273719. −0.104650
\(370\) 1.27683e6 0.484875
\(371\) 0 0
\(372\) −7.69637e6 −2.88356
\(373\) 2.28822e6 0.851579 0.425789 0.904822i \(-0.359996\pi\)
0.425789 + 0.904822i \(0.359996\pi\)
\(374\) −872514. −0.322547
\(375\) −223840. −0.0821977
\(376\) −2.98723e6 −1.08968
\(377\) 944044. 0.342089
\(378\) 0 0
\(379\) −210030. −0.0751074 −0.0375537 0.999295i \(-0.511957\pi\)
−0.0375537 + 0.999295i \(0.511957\pi\)
\(380\) −676458. −0.240316
\(381\) −3.57665e6 −1.26230
\(382\) 3.84071e6 1.34665
\(383\) −3.37503e6 −1.17566 −0.587828 0.808986i \(-0.700017\pi\)
−0.587828 + 0.808986i \(0.700017\pi\)
\(384\) 4.34599e6 1.50404
\(385\) 0 0
\(386\) −36766.1 −0.0125597
\(387\) 6961.72 0.00236287
\(388\) 1.00693e6 0.339564
\(389\) 1.98548e6 0.665259 0.332630 0.943058i \(-0.392064\pi\)
0.332630 + 0.943058i \(0.392064\pi\)
\(390\) 435920. 0.145126
\(391\) −1.93864e6 −0.641291
\(392\) 0 0
\(393\) 3.10201e6 1.01312
\(394\) −9.36150e6 −3.03812
\(395\) 1.86469e6 0.601331
\(396\) −424152. −0.135920
\(397\) 2.53409e6 0.806948 0.403474 0.914991i \(-0.367803\pi\)
0.403474 + 0.914991i \(0.367803\pi\)
\(398\) 1.44189e6 0.456272
\(399\) 0 0
\(400\) 16098.2 0.00503070
\(401\) 3.79055e6 1.17717 0.588587 0.808434i \(-0.299684\pi\)
0.588587 + 0.808434i \(0.299684\pi\)
\(402\) 8.46804e6 2.61347
\(403\) −1.36740e6 −0.419404
\(404\) −1.27860e6 −0.389745
\(405\) 1.21109e6 0.366892
\(406\) 0 0
\(407\) 1.19928e6 0.358869
\(408\) −1.16851e6 −0.347521
\(409\) −5.10159e6 −1.50798 −0.753992 0.656883i \(-0.771874\pi\)
−0.753992 + 0.656883i \(0.771874\pi\)
\(410\) 1.66173e6 0.488203
\(411\) −840122. −0.245323
\(412\) −2.41452e6 −0.700791
\(413\) 0 0
\(414\) −1.52087e6 −0.436106
\(415\) 1.36932e6 0.390288
\(416\) 752901. 0.213307
\(417\) −5.07076e6 −1.42802
\(418\) −1.02536e6 −0.287035
\(419\) 6.31053e6 1.75603 0.878013 0.478637i \(-0.158869\pi\)
0.878013 + 0.478637i \(0.158869\pi\)
\(420\) 0 0
\(421\) −3.26642e6 −0.898186 −0.449093 0.893485i \(-0.648253\pi\)
−0.449093 + 0.893485i \(0.648253\pi\)
\(422\) 7.31756e6 2.00025
\(423\) −610935. −0.166014
\(424\) −1.34376e6 −0.362999
\(425\) 276024. 0.0741267
\(426\) 45130.7 0.0120489
\(427\) 0 0
\(428\) 8.19329e6 2.16197
\(429\) 409443. 0.107411
\(430\) −42264.2 −0.0110230
\(431\) −2.31016e6 −0.599031 −0.299516 0.954091i \(-0.596825\pi\)
−0.299516 + 0.954091i \(0.596825\pi\)
\(432\) −103603. −0.0267092
\(433\) −3.81574e6 −0.978044 −0.489022 0.872271i \(-0.662646\pi\)
−0.489022 + 0.872271i \(0.662646\pi\)
\(434\) 0 0
\(435\) −2.54795e6 −0.645606
\(436\) −7.37915e6 −1.85905
\(437\) −2.27824e6 −0.570685
\(438\) −5.96012e6 −1.48446
\(439\) −673888. −0.166889 −0.0834443 0.996512i \(-0.526592\pi\)
−0.0834443 + 0.996512i \(0.526592\pi\)
\(440\) 994496. 0.244890
\(441\) 0 0
\(442\) −537545. −0.130876
\(443\) −4.84599e6 −1.17320 −0.586602 0.809875i \(-0.699535\pi\)
−0.586602 + 0.809875i \(0.699535\pi\)
\(444\) 4.15868e6 1.00115
\(445\) 2.67098e6 0.639397
\(446\) −1.07345e7 −2.55531
\(447\) 1.05616e6 0.250012
\(448\) 0 0
\(449\) 3.09732e6 0.725055 0.362527 0.931973i \(-0.381914\pi\)
0.362527 + 0.931973i \(0.381914\pi\)
\(450\) 216542. 0.0504093
\(451\) 1.56080e6 0.361332
\(452\) −8.22204e6 −1.89293
\(453\) −4.62145e6 −1.05812
\(454\) −3.84533e6 −0.875577
\(455\) 0 0
\(456\) −1.37320e6 −0.309258
\(457\) −6.58726e6 −1.47542 −0.737708 0.675120i \(-0.764092\pi\)
−0.737708 + 0.675120i \(0.764092\pi\)
\(458\) 4.19428e6 0.934315
\(459\) −1.77639e6 −0.393557
\(460\) 5.72140e6 1.26069
\(461\) −5.26481e6 −1.15380 −0.576900 0.816815i \(-0.695738\pi\)
−0.576900 + 0.816815i \(0.695738\pi\)
\(462\) 0 0
\(463\) −2.79127e6 −0.605131 −0.302565 0.953129i \(-0.597843\pi\)
−0.302565 + 0.953129i \(0.597843\pi\)
\(464\) 183244. 0.0395126
\(465\) 3.69058e6 0.791520
\(466\) 6.14533e6 1.31093
\(467\) −3.23304e6 −0.685992 −0.342996 0.939337i \(-0.611442\pi\)
−0.342996 + 0.939337i \(0.611442\pi\)
\(468\) −261315. −0.0551505
\(469\) 0 0
\(470\) 3.70895e6 0.774473
\(471\) 3.22221e6 0.669271
\(472\) 8.36682e6 1.72864
\(473\) −39697.2 −0.00815844
\(474\) 9.80107e6 2.00368
\(475\) 324376. 0.0659653
\(476\) 0 0
\(477\) −274819. −0.0553033
\(478\) 5.04713e6 1.01036
\(479\) 3.97758e6 0.792100 0.396050 0.918229i \(-0.370381\pi\)
0.396050 + 0.918229i \(0.370381\pi\)
\(480\) −2.03206e6 −0.402563
\(481\) 738864. 0.145614
\(482\) −1.49534e6 −0.293171
\(483\) 0 0
\(484\) −5.97783e6 −1.15993
\(485\) −482847. −0.0932085
\(486\) −2.59970e6 −0.499266
\(487\) 517375. 0.0988515 0.0494257 0.998778i \(-0.484261\pi\)
0.0494257 + 0.998778i \(0.484261\pi\)
\(488\) 1.36112e6 0.258730
\(489\) −2.26658e6 −0.428646
\(490\) 0 0
\(491\) −992388. −0.185771 −0.0928854 0.995677i \(-0.529609\pi\)
−0.0928854 + 0.995677i \(0.529609\pi\)
\(492\) 5.41228e6 1.00802
\(493\) 3.14195e6 0.582213
\(494\) −631710. −0.116466
\(495\) 203390. 0.0373093
\(496\) −265420. −0.0484429
\(497\) 0 0
\(498\) 7.19735e6 1.30047
\(499\) 2.95997e6 0.532153 0.266076 0.963952i \(-0.414273\pi\)
0.266076 + 0.963952i \(0.414273\pi\)
\(500\) −814613. −0.145722
\(501\) −4.54038e6 −0.808160
\(502\) −1.20970e7 −2.14249
\(503\) −2.55586e6 −0.450419 −0.225210 0.974310i \(-0.572307\pi\)
−0.225210 + 0.974310i \(0.572307\pi\)
\(504\) 0 0
\(505\) 613115. 0.106983
\(506\) 8.67234e6 1.50577
\(507\) −5.06681e6 −0.875416
\(508\) −1.30164e7 −2.23785
\(509\) −571600. −0.0977907 −0.0488953 0.998804i \(-0.515570\pi\)
−0.0488953 + 0.998804i \(0.515570\pi\)
\(510\) 1.45082e6 0.246995
\(511\) 0 0
\(512\) 298370. 0.0503015
\(513\) −2.08757e6 −0.350226
\(514\) 7.64060e6 1.27561
\(515\) 1.15782e6 0.192363
\(516\) −137655. −0.0227598
\(517\) 3.48368e6 0.573208
\(518\) 0 0
\(519\) 5.15906e6 0.840722
\(520\) 612697. 0.0993659
\(521\) 3.84947e6 0.621307 0.310653 0.950523i \(-0.399452\pi\)
0.310653 + 0.950523i \(0.399452\pi\)
\(522\) 2.46488e6 0.395930
\(523\) 3.34856e6 0.535308 0.267654 0.963515i \(-0.413752\pi\)
0.267654 + 0.963515i \(0.413752\pi\)
\(524\) 1.12890e7 1.79609
\(525\) 0 0
\(526\) 1.50899e7 2.37806
\(527\) −4.55096e6 −0.713800
\(528\) 79475.4 0.0124065
\(529\) 1.28327e7 1.99379
\(530\) 1.66841e6 0.257996
\(531\) 1.71115e6 0.263361
\(532\) 0 0
\(533\) 961591. 0.146613
\(534\) 1.40391e7 2.13052
\(535\) −3.92886e6 −0.593448
\(536\) 1.19021e7 1.78941
\(537\) −6.31692e6 −0.945301
\(538\) −4.16911e6 −0.620994
\(539\) 0 0
\(540\) 5.24256e6 0.773677
\(541\) 3.28206e6 0.482117 0.241059 0.970511i \(-0.422505\pi\)
0.241059 + 0.970511i \(0.422505\pi\)
\(542\) −7.62298e6 −1.11462
\(543\) 279196. 0.0406358
\(544\) 2.50579e6 0.363035
\(545\) 3.53846e6 0.510297
\(546\) 0 0
\(547\) 7.92785e6 1.13289 0.566444 0.824100i \(-0.308319\pi\)
0.566444 + 0.824100i \(0.308319\pi\)
\(548\) −3.05743e6 −0.434915
\(549\) 278370. 0.0394178
\(550\) −1.23477e6 −0.174052
\(551\) 3.69234e6 0.518111
\(552\) 1.16144e7 1.62236
\(553\) 0 0
\(554\) −1.20124e7 −1.66286
\(555\) −1.99418e6 −0.274809
\(556\) −1.84538e7 −2.53163
\(557\) 9.22341e6 1.25966 0.629830 0.776733i \(-0.283124\pi\)
0.629830 + 0.776733i \(0.283124\pi\)
\(558\) −3.57025e6 −0.485415
\(559\) −24457.0 −0.00331035
\(560\) 0 0
\(561\) 1.36270e6 0.182808
\(562\) −1.61180e6 −0.215264
\(563\) 1.16920e7 1.55460 0.777298 0.629132i \(-0.216590\pi\)
0.777298 + 0.629132i \(0.216590\pi\)
\(564\) 1.20801e7 1.59909
\(565\) 3.94265e6 0.519598
\(566\) −8.74152e6 −1.14695
\(567\) 0 0
\(568\) 63432.4 0.00824974
\(569\) 252494. 0.0326941 0.0163471 0.999866i \(-0.494796\pi\)
0.0163471 + 0.999866i \(0.494796\pi\)
\(570\) 1.70497e6 0.219801
\(571\) 4.62266e6 0.593337 0.296669 0.954981i \(-0.404124\pi\)
0.296669 + 0.954981i \(0.404124\pi\)
\(572\) 1.49007e6 0.190422
\(573\) −5.99847e6 −0.763228
\(574\) 0 0
\(575\) −2.74354e6 −0.346052
\(576\) 1.99694e6 0.250789
\(577\) −1.36752e7 −1.71000 −0.854999 0.518630i \(-0.826442\pi\)
−0.854999 + 0.518630i \(0.826442\pi\)
\(578\) 1.12346e7 1.39875
\(579\) 57421.8 0.00711836
\(580\) −9.27266e6 −1.14455
\(581\) 0 0
\(582\) −2.53791e6 −0.310577
\(583\) 1.56708e6 0.190950
\(584\) −8.37712e6 −1.01639
\(585\) 125306. 0.0151385
\(586\) −2.52267e6 −0.303471
\(587\) −1.08136e7 −1.29532 −0.647659 0.761930i \(-0.724252\pi\)
−0.647659 + 0.761930i \(0.724252\pi\)
\(588\) 0 0
\(589\) −5.34817e6 −0.635210
\(590\) −1.03883e7 −1.22861
\(591\) 1.46209e7 1.72189
\(592\) 143418. 0.0168190
\(593\) 5.20786e6 0.608166 0.304083 0.952645i \(-0.401650\pi\)
0.304083 + 0.952645i \(0.401650\pi\)
\(594\) 7.94654e6 0.924085
\(595\) 0 0
\(596\) 3.84364e6 0.443228
\(597\) −2.25196e6 −0.258598
\(598\) 5.34292e6 0.610979
\(599\) −1.43236e7 −1.63112 −0.815561 0.578671i \(-0.803572\pi\)
−0.815561 + 0.578671i \(0.803572\pi\)
\(600\) −1.65365e6 −0.187528
\(601\) 5.68832e6 0.642389 0.321194 0.947013i \(-0.395916\pi\)
0.321194 + 0.947013i \(0.395916\pi\)
\(602\) 0 0
\(603\) 2.43416e6 0.272619
\(604\) −1.68187e7 −1.87586
\(605\) 2.86650e6 0.318393
\(606\) 3.22262e6 0.356474
\(607\) 1.54940e7 1.70683 0.853417 0.521228i \(-0.174526\pi\)
0.853417 + 0.521228i \(0.174526\pi\)
\(608\) 2.94475e6 0.323064
\(609\) 0 0
\(610\) −1.68997e6 −0.183888
\(611\) 2.14626e6 0.232583
\(612\) −869704. −0.0938627
\(613\) −1.68053e7 −1.80632 −0.903161 0.429303i \(-0.858759\pi\)
−0.903161 + 0.429303i \(0.858759\pi\)
\(614\) −4.34756e6 −0.465399
\(615\) −2.59531e6 −0.276695
\(616\) 0 0
\(617\) −4.82924e6 −0.510700 −0.255350 0.966849i \(-0.582191\pi\)
−0.255350 + 0.966849i \(0.582191\pi\)
\(618\) 6.08565e6 0.640967
\(619\) −2.06396e6 −0.216508 −0.108254 0.994123i \(-0.534526\pi\)
−0.108254 + 0.994123i \(0.534526\pi\)
\(620\) 1.34310e7 1.40323
\(621\) 1.76564e7 1.83727
\(622\) −2.85137e7 −2.95514
\(623\) 0 0
\(624\) 48963.8 0.00503401
\(625\) 390625. 0.0400000
\(626\) −1.39355e7 −1.42131
\(627\) 1.60141e6 0.162680
\(628\) 1.17265e7 1.18650
\(629\) 2.45908e6 0.247825
\(630\) 0 0
\(631\) −1.37020e7 −1.36997 −0.684986 0.728556i \(-0.740192\pi\)
−0.684986 + 0.728556i \(0.740192\pi\)
\(632\) 1.37757e7 1.37189
\(633\) −1.14287e7 −1.13367
\(634\) −2.32281e7 −2.29504
\(635\) 6.24163e6 0.614276
\(636\) 5.43405e6 0.532698
\(637\) 0 0
\(638\) −1.40552e7 −1.36706
\(639\) 12972.9 0.00125686
\(640\) −7.58421e6 −0.731915
\(641\) 1.70359e6 0.163764 0.0818821 0.996642i \(-0.473907\pi\)
0.0818821 + 0.996642i \(0.473907\pi\)
\(642\) −2.06507e7 −1.97741
\(643\) −1.74387e7 −1.66336 −0.831682 0.555252i \(-0.812622\pi\)
−0.831682 + 0.555252i \(0.812622\pi\)
\(644\) 0 0
\(645\) 66008.8 0.00624744
\(646\) −2.10245e6 −0.198218
\(647\) −1.08759e7 −1.02142 −0.510712 0.859752i \(-0.670618\pi\)
−0.510712 + 0.859752i \(0.670618\pi\)
\(648\) 8.94711e6 0.837038
\(649\) −9.75732e6 −0.909325
\(650\) −760726. −0.0706228
\(651\) 0 0
\(652\) −8.24868e6 −0.759916
\(653\) −4.27466e6 −0.392300 −0.196150 0.980574i \(-0.562844\pi\)
−0.196150 + 0.980574i \(0.562844\pi\)
\(654\) 1.85987e7 1.70035
\(655\) −5.41334e6 −0.493018
\(656\) 186650. 0.0169344
\(657\) −1.71325e6 −0.154849
\(658\) 0 0
\(659\) 1.15036e7 1.03186 0.515931 0.856630i \(-0.327446\pi\)
0.515931 + 0.856630i \(0.327446\pi\)
\(660\) −4.02167e6 −0.359374
\(661\) 2.11275e7 1.88081 0.940403 0.340062i \(-0.110448\pi\)
0.940403 + 0.340062i \(0.110448\pi\)
\(662\) −5.11460e6 −0.453593
\(663\) 839545. 0.0741755
\(664\) 1.01161e7 0.890414
\(665\) 0 0
\(666\) 1.92916e6 0.168532
\(667\) −3.12294e7 −2.71800
\(668\) −1.65236e7 −1.43273
\(669\) 1.67652e7 1.44825
\(670\) −1.47776e7 −1.27180
\(671\) −1.58733e6 −0.136101
\(672\) 0 0
\(673\) 8.51341e6 0.724546 0.362273 0.932072i \(-0.382001\pi\)
0.362273 + 0.932072i \(0.382001\pi\)
\(674\) −4.60262e6 −0.390261
\(675\) −2.51392e6 −0.212370
\(676\) −1.84394e7 −1.55196
\(677\) 9.53112e6 0.799231 0.399616 0.916683i \(-0.369144\pi\)
0.399616 + 0.916683i \(0.369144\pi\)
\(678\) 2.07231e7 1.73133
\(679\) 0 0
\(680\) 2.03917e6 0.169114
\(681\) 6.00569e6 0.496244
\(682\) 2.03583e7 1.67603
\(683\) 2.84219e6 0.233132 0.116566 0.993183i \(-0.462811\pi\)
0.116566 + 0.993183i \(0.462811\pi\)
\(684\) −1.02205e6 −0.0835283
\(685\) 1.46610e6 0.119382
\(686\) 0 0
\(687\) −6.55067e6 −0.529534
\(688\) −4747.24 −0.000382358 0
\(689\) 965458. 0.0774792
\(690\) −1.44204e7 −1.15307
\(691\) −7.23494e6 −0.576421 −0.288210 0.957567i \(-0.593060\pi\)
−0.288210 + 0.957567i \(0.593060\pi\)
\(692\) 1.87752e7 1.49046
\(693\) 0 0
\(694\) −2.59912e6 −0.204846
\(695\) 8.84902e6 0.694917
\(696\) −1.88234e7 −1.47290
\(697\) 3.20035e6 0.249526
\(698\) −5.22764e6 −0.406132
\(699\) −9.59786e6 −0.742987
\(700\) 0 0
\(701\) −3.46129e6 −0.266038 −0.133019 0.991114i \(-0.542467\pi\)
−0.133019 + 0.991114i \(0.542467\pi\)
\(702\) 4.89576e6 0.374954
\(703\) 2.88985e6 0.220540
\(704\) −1.13870e7 −0.865918
\(705\) −5.79269e6 −0.438942
\(706\) 1.59669e7 1.20561
\(707\) 0 0
\(708\) −3.38348e7 −2.53677
\(709\) 1.40088e6 0.104661 0.0523306 0.998630i \(-0.483335\pi\)
0.0523306 + 0.998630i \(0.483335\pi\)
\(710\) −78757.9 −0.00586338
\(711\) 2.81734e6 0.209009
\(712\) 1.97323e7 1.45874
\(713\) 4.52342e7 3.33229
\(714\) 0 0
\(715\) −714522. −0.0522698
\(716\) −2.29890e7 −1.67586
\(717\) −7.88267e6 −0.572631
\(718\) −8.56553e6 −0.620073
\(719\) 5.86524e6 0.423120 0.211560 0.977365i \(-0.432146\pi\)
0.211560 + 0.977365i \(0.432146\pi\)
\(720\) 24322.7 0.00174856
\(721\) 0 0
\(722\) 2.02413e7 1.44509
\(723\) 2.33543e6 0.166158
\(724\) 1.01607e6 0.0720403
\(725\) 4.44644e6 0.314172
\(726\) 1.50667e7 1.06091
\(727\) 1.11670e7 0.783609 0.391804 0.920049i \(-0.371851\pi\)
0.391804 + 0.920049i \(0.371851\pi\)
\(728\) 0 0
\(729\) 1.58320e7 1.10336
\(730\) 1.04011e7 0.722387
\(731\) −81397.3 −0.00563400
\(732\) −5.50426e6 −0.379683
\(733\) 6.21665e6 0.427362 0.213681 0.976903i \(-0.431455\pi\)
0.213681 + 0.976903i \(0.431455\pi\)
\(734\) −1.39866e7 −0.958238
\(735\) 0 0
\(736\) −2.49063e7 −1.69479
\(737\) −1.38801e7 −0.941290
\(738\) 2.51069e6 0.169688
\(739\) −1.07075e7 −0.721236 −0.360618 0.932714i \(-0.617434\pi\)
−0.360618 + 0.932714i \(0.617434\pi\)
\(740\) −7.25733e6 −0.487189
\(741\) 986612. 0.0660087
\(742\) 0 0
\(743\) −7.87985e6 −0.523656 −0.261828 0.965115i \(-0.584325\pi\)
−0.261828 + 0.965115i \(0.584325\pi\)
\(744\) 2.72647e7 1.80579
\(745\) −1.84311e6 −0.121664
\(746\) −2.09887e7 −1.38083
\(747\) 2.06890e6 0.135656
\(748\) 4.95924e6 0.324086
\(749\) 0 0
\(750\) 2.05318e6 0.133283
\(751\) −9.79080e6 −0.633459 −0.316729 0.948516i \(-0.602585\pi\)
−0.316729 + 0.948516i \(0.602585\pi\)
\(752\) 416601. 0.0268643
\(753\) 1.88932e7 1.21428
\(754\) −8.65927e6 −0.554693
\(755\) 8.06493e6 0.514912
\(756\) 0 0
\(757\) 9.46073e6 0.600047 0.300023 0.953932i \(-0.403006\pi\)
0.300023 + 0.953932i \(0.403006\pi\)
\(758\) 1.92650e6 0.121786
\(759\) −1.35446e7 −0.853416
\(760\) 2.39638e6 0.150495
\(761\) −1.23890e7 −0.775488 −0.387744 0.921767i \(-0.626745\pi\)
−0.387744 + 0.921767i \(0.626745\pi\)
\(762\) 3.28069e7 2.04681
\(763\) 0 0
\(764\) −2.18300e7 −1.35307
\(765\) 417042. 0.0257648
\(766\) 3.09575e7 1.90631
\(767\) −6.01137e6 −0.368965
\(768\) −1.56278e7 −0.956078
\(769\) −2.81052e7 −1.71384 −0.856921 0.515447i \(-0.827626\pi\)
−0.856921 + 0.515447i \(0.827626\pi\)
\(770\) 0 0
\(771\) −1.19332e7 −0.722970
\(772\) 208973. 0.0126196
\(773\) −2.36299e7 −1.42237 −0.711187 0.703003i \(-0.751842\pi\)
−0.711187 + 0.703003i \(0.751842\pi\)
\(774\) −63856.6 −0.00383136
\(775\) −6.44045e6 −0.385179
\(776\) −3.56711e6 −0.212648
\(777\) 0 0
\(778\) −1.82119e7 −1.07871
\(779\) 3.76097e6 0.222053
\(780\) −2.47770e6 −0.145818
\(781\) −73974.4 −0.00433964
\(782\) 1.77822e7 1.03985
\(783\) −2.86157e7 −1.66802
\(784\) 0 0
\(785\) −5.62311e6 −0.325688
\(786\) −2.84533e7 −1.64277
\(787\) 1.10151e7 0.633946 0.316973 0.948435i \(-0.397333\pi\)
0.316973 + 0.948435i \(0.397333\pi\)
\(788\) 5.32093e7 3.05262
\(789\) −2.35677e7 −1.34780
\(790\) −1.71039e7 −0.975052
\(791\) 0 0
\(792\) 1.50257e6 0.0851183
\(793\) −977933. −0.0552238
\(794\) −2.32440e7 −1.30846
\(795\) −2.60575e6 −0.146223
\(796\) −8.19547e6 −0.458449
\(797\) −1.94131e7 −1.08256 −0.541278 0.840844i \(-0.682059\pi\)
−0.541278 + 0.840844i \(0.682059\pi\)
\(798\) 0 0
\(799\) 7.14313e6 0.395842
\(800\) 3.54616e6 0.195900
\(801\) 4.03556e6 0.222240
\(802\) −3.47689e7 −1.90878
\(803\) 9.76933e6 0.534658
\(804\) −4.81310e7 −2.62594
\(805\) 0 0
\(806\) 1.25425e7 0.680060
\(807\) 6.51137e6 0.351956
\(808\) 4.52948e6 0.244073
\(809\) −1.03581e7 −0.556427 −0.278213 0.960519i \(-0.589742\pi\)
−0.278213 + 0.960519i \(0.589742\pi\)
\(810\) −1.11088e7 −0.594912
\(811\) 1.22637e6 0.0654740 0.0327370 0.999464i \(-0.489578\pi\)
0.0327370 + 0.999464i \(0.489578\pi\)
\(812\) 0 0
\(813\) 1.19057e7 0.631724
\(814\) −1.10005e7 −0.581902
\(815\) 3.95542e6 0.208593
\(816\) 162961. 0.00856756
\(817\) −95656.1 −0.00501369
\(818\) 4.67944e7 2.44518
\(819\) 0 0
\(820\) −9.44501e6 −0.490533
\(821\) 1.50056e7 0.776955 0.388478 0.921458i \(-0.373001\pi\)
0.388478 + 0.921458i \(0.373001\pi\)
\(822\) 7.70604e6 0.397788
\(823\) 2.08511e7 1.07307 0.536537 0.843877i \(-0.319732\pi\)
0.536537 + 0.843877i \(0.319732\pi\)
\(824\) 8.55355e6 0.438862
\(825\) 1.92848e6 0.0986460
\(826\) 0 0
\(827\) −1.11289e7 −0.565833 −0.282917 0.959145i \(-0.591302\pi\)
−0.282917 + 0.959145i \(0.591302\pi\)
\(828\) 8.64441e6 0.438187
\(829\) 1.49680e7 0.756446 0.378223 0.925714i \(-0.376535\pi\)
0.378223 + 0.925714i \(0.376535\pi\)
\(830\) −1.25601e7 −0.632848
\(831\) 1.87611e7 0.942444
\(832\) −7.01538e6 −0.351352
\(833\) 0 0
\(834\) 4.65117e7 2.31551
\(835\) 7.92344e6 0.393276
\(836\) 5.82797e6 0.288404
\(837\) 4.14485e7 2.04501
\(838\) −5.78835e7 −2.84738
\(839\) −3.53209e7 −1.73232 −0.866159 0.499769i \(-0.833418\pi\)
−0.866159 + 0.499769i \(0.833418\pi\)
\(840\) 0 0
\(841\) 3.01022e7 1.46760
\(842\) 2.99613e7 1.45640
\(843\) 2.51733e6 0.122003
\(844\) −4.15919e7 −2.00980
\(845\) 8.84212e6 0.426005
\(846\) 5.60382e6 0.269190
\(847\) 0 0
\(848\) 187401. 0.00894916
\(849\) 1.36526e7 0.650050
\(850\) −2.53184e6 −0.120196
\(851\) −2.44420e7 −1.15694
\(852\) −256516. −0.0121064
\(853\) −9.41887e6 −0.443227 −0.221613 0.975135i \(-0.571132\pi\)
−0.221613 + 0.975135i \(0.571132\pi\)
\(854\) 0 0
\(855\) 490098. 0.0229281
\(856\) −2.90251e7 −1.35391
\(857\) 1.05121e7 0.488918 0.244459 0.969660i \(-0.421390\pi\)
0.244459 + 0.969660i \(0.421390\pi\)
\(858\) −3.75563e6 −0.174167
\(859\) 3.10282e7 1.43474 0.717371 0.696692i \(-0.245345\pi\)
0.717371 + 0.696692i \(0.245345\pi\)
\(860\) 240223. 0.0110756
\(861\) 0 0
\(862\) 2.11900e7 0.971323
\(863\) −2.79996e7 −1.27975 −0.639876 0.768479i \(-0.721014\pi\)
−0.639876 + 0.768479i \(0.721014\pi\)
\(864\) −2.28219e7 −1.04008
\(865\) −9.00311e6 −0.409122
\(866\) 3.49999e7 1.58589
\(867\) −1.75464e7 −0.792757
\(868\) 0 0
\(869\) −1.60651e7 −0.721661
\(870\) 2.33711e7 1.04684
\(871\) −8.55136e6 −0.381935
\(872\) 2.61409e7 1.16421
\(873\) −729530. −0.0323972
\(874\) 2.08972e7 0.925359
\(875\) 0 0
\(876\) 3.38764e7 1.49155
\(877\) 2.14218e7 0.940497 0.470248 0.882534i \(-0.344164\pi\)
0.470248 + 0.882534i \(0.344164\pi\)
\(878\) 6.18126e6 0.270608
\(879\) 3.93994e6 0.171996
\(880\) −138693. −0.00603737
\(881\) 3.42843e7 1.48818 0.744090 0.668079i \(-0.232883\pi\)
0.744090 + 0.668079i \(0.232883\pi\)
\(882\) 0 0
\(883\) 1.15229e7 0.497346 0.248673 0.968587i \(-0.420006\pi\)
0.248673 + 0.968587i \(0.420006\pi\)
\(884\) 3.05533e6 0.131500
\(885\) 1.62245e7 0.696328
\(886\) 4.44500e7 1.90234
\(887\) −4.07371e6 −0.173853 −0.0869263 0.996215i \(-0.527704\pi\)
−0.0869263 + 0.996215i \(0.527704\pi\)
\(888\) −1.47323e7 −0.626956
\(889\) 0 0
\(890\) −2.44996e7 −1.03678
\(891\) −1.04340e7 −0.440310
\(892\) 6.10130e7 2.56750
\(893\) 8.39443e6 0.352259
\(894\) −9.68764e6 −0.405391
\(895\) 1.10237e7 0.460013
\(896\) 0 0
\(897\) −8.34465e6 −0.346280
\(898\) −2.84103e7 −1.17567
\(899\) −7.33110e7 −3.02531
\(900\) −1.23079e6 −0.0506499
\(901\) 3.21322e6 0.131865
\(902\) −1.43165e7 −0.585895
\(903\) 0 0
\(904\) 2.91269e7 1.18542
\(905\) −487226. −0.0197747
\(906\) 4.23904e7 1.71572
\(907\) 4.25486e7 1.71738 0.858690 0.512495i \(-0.171279\pi\)
0.858690 + 0.512495i \(0.171279\pi\)
\(908\) 2.18563e7 0.879755
\(909\) 926350. 0.0371848
\(910\) 0 0
\(911\) 2.33369e7 0.931638 0.465819 0.884880i \(-0.345760\pi\)
0.465819 + 0.884880i \(0.345760\pi\)
\(912\) 191507. 0.00762427
\(913\) −1.17973e7 −0.468388
\(914\) 6.04218e7 2.39237
\(915\) 2.63941e6 0.104221
\(916\) −2.38396e7 −0.938773
\(917\) 0 0
\(918\) 1.62940e7 0.638148
\(919\) −1.46257e7 −0.571251 −0.285626 0.958341i \(-0.592201\pi\)
−0.285626 + 0.958341i \(0.592201\pi\)
\(920\) −2.02683e7 −0.789491
\(921\) 6.79008e6 0.263770
\(922\) 4.82916e7 1.87087
\(923\) −45574.7 −0.00176084
\(924\) 0 0
\(925\) 3.48005e6 0.133731
\(926\) 2.56030e7 0.981213
\(927\) 1.74934e6 0.0668612
\(928\) 4.03656e7 1.53866
\(929\) −3.12828e7 −1.18923 −0.594616 0.804010i \(-0.702696\pi\)
−0.594616 + 0.804010i \(0.702696\pi\)
\(930\) −3.38519e7 −1.28344
\(931\) 0 0
\(932\) −3.49291e7 −1.31719
\(933\) 4.45330e7 1.67486
\(934\) 2.96552e7 1.11233
\(935\) −2.37806e6 −0.0889599
\(936\) 925718. 0.0345374
\(937\) 4.86044e7 1.80853 0.904266 0.426969i \(-0.140419\pi\)
0.904266 + 0.426969i \(0.140419\pi\)
\(938\) 0 0
\(939\) 2.17647e7 0.805543
\(940\) −2.10811e7 −0.778169
\(941\) 2.53759e7 0.934217 0.467109 0.884200i \(-0.345296\pi\)
0.467109 + 0.884200i \(0.345296\pi\)
\(942\) −2.95558e7 −1.08522
\(943\) −3.18098e7 −1.16488
\(944\) −1.16684e6 −0.0426169
\(945\) 0 0
\(946\) 364124. 0.0132288
\(947\) 2.04500e7 0.740999 0.370500 0.928833i \(-0.379186\pi\)
0.370500 + 0.928833i \(0.379186\pi\)
\(948\) −5.57078e7 −2.01324
\(949\) 6.01877e6 0.216941
\(950\) −2.97535e6 −0.106962
\(951\) 3.62779e7 1.30074
\(952\) 0 0
\(953\) −2.96732e7 −1.05836 −0.529178 0.848511i \(-0.677500\pi\)
−0.529178 + 0.848511i \(0.677500\pi\)
\(954\) 2.52079e6 0.0896738
\(955\) 1.04680e7 0.371411
\(956\) −2.86871e7 −1.01518
\(957\) 2.19517e7 0.774796
\(958\) −3.64844e7 −1.28438
\(959\) 0 0
\(960\) 1.89343e7 0.663089
\(961\) 7.75582e7 2.70906
\(962\) −6.77725e6 −0.236111
\(963\) −5.93608e6 −0.206269
\(964\) 8.49926e6 0.294570
\(965\) −100207. −0.00346402
\(966\) 0 0
\(967\) 4.86315e7 1.67245 0.836223 0.548390i \(-0.184759\pi\)
0.836223 + 0.548390i \(0.184759\pi\)
\(968\) 2.11767e7 0.726390
\(969\) 3.28363e6 0.112343
\(970\) 4.42893e6 0.151137
\(971\) 8.43394e6 0.287067 0.143533 0.989645i \(-0.454154\pi\)
0.143533 + 0.989645i \(0.454154\pi\)
\(972\) 1.47763e7 0.501649
\(973\) 0 0
\(974\) −4.74564e6 −0.160287
\(975\) 1.18811e6 0.0400263
\(976\) −189822. −0.00637857
\(977\) −2.01326e7 −0.674781 −0.337391 0.941365i \(-0.609544\pi\)
−0.337391 + 0.941365i \(0.609544\pi\)
\(978\) 2.07903e7 0.695045
\(979\) −2.30116e7 −0.767345
\(980\) 0 0
\(981\) 5.34623e6 0.177368
\(982\) 9.10270e6 0.301225
\(983\) 4.21959e7 1.39279 0.696396 0.717658i \(-0.254786\pi\)
0.696396 + 0.717658i \(0.254786\pi\)
\(984\) −1.91732e7 −0.631259
\(985\) −2.55150e7 −0.837926
\(986\) −2.88196e7 −0.944053
\(987\) 0 0
\(988\) 3.59054e6 0.117022
\(989\) 809048. 0.0263017
\(990\) −1.86560e6 −0.0604966
\(991\) 1.35590e6 0.0438574 0.0219287 0.999760i \(-0.493019\pi\)
0.0219287 + 0.999760i \(0.493019\pi\)
\(992\) −5.84676e7 −1.88641
\(993\) 7.98805e6 0.257080
\(994\) 0 0
\(995\) 3.92991e6 0.125842
\(996\) −4.09087e7 −1.30667
\(997\) −4.39971e7 −1.40180 −0.700900 0.713259i \(-0.747218\pi\)
−0.700900 + 0.713259i \(0.747218\pi\)
\(998\) −2.71504e7 −0.862880
\(999\) −2.23964e7 −0.710009
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.i.1.1 6
7.2 even 3 35.6.e.a.11.6 12
7.4 even 3 35.6.e.a.16.6 yes 12
7.6 odd 2 245.6.a.h.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.6.e.a.11.6 12 7.2 even 3
35.6.e.a.16.6 yes 12 7.4 even 3
245.6.a.h.1.1 6 7.6 odd 2
245.6.a.i.1.1 6 1.1 even 1 trivial