Properties

Label 2925.2.c.w.2224.6
Level $2925$
Weight $2$
Character 2925.2224
Analytic conductor $23.356$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2925.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.3562425912\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.399424.1
Defining polynomial: \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 195)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2224.6
Root \(0.264658 - 1.38923i\) of defining polynomial
Character \(\chi\) \(=\) 2925.2224
Dual form 2925.2.c.w.2224.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.77846i q^{2} -5.71982 q^{4} +2.71982i q^{7} -10.3354i q^{8} +O(q^{10})\) \(q+2.77846i q^{2} -5.71982 q^{4} +2.71982i q^{7} -10.3354i q^{8} +2.71982 q^{11} +1.00000i q^{13} -7.55691 q^{14} +17.2767 q^{16} -2.83709i q^{17} +3.55691 q^{19} +7.55691i q^{22} +4.83709i q^{23} -2.77846 q^{26} -15.5569i q^{28} +6.00000 q^{29} +7.55691 q^{31} +27.3319i q^{32} +7.88273 q^{34} +4.27674i q^{37} +9.88273i q^{38} -2.83709 q^{41} +11.1138i q^{43} -15.5569 q^{44} -13.4396 q^{46} -11.5569i q^{47} -0.397442 q^{49} -5.71982i q^{52} -1.16291i q^{53} +28.1104 q^{56} +16.6707i q^{58} -2.11727 q^{59} +6.60256 q^{61} +20.9966i q^{62} -41.3871 q^{64} -1.88273i q^{67} +16.2277i q^{68} +6.71982 q^{71} +9.11383i q^{73} -11.8827 q^{74} -20.3449 q^{76} +7.39744i q^{77} -10.2767 q^{79} -7.88273i q^{82} -2.11727i q^{83} -30.8793 q^{86} -28.1104i q^{88} +1.16291 q^{89} -2.71982 q^{91} -27.6673i q^{92} +32.1104 q^{94} +10.8371i q^{97} -1.10428i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 16 q^{4} - 2 q^{11} - 12 q^{14} + 52 q^{16} - 12 q^{19} + 36 q^{29} + 12 q^{31} + 44 q^{34} - 2 q^{41} - 60 q^{44} - 44 q^{46} - 24 q^{49} + 32 q^{56} - 16 q^{59} + 18 q^{61} - 60 q^{64} + 22 q^{71} - 68 q^{74} + 8 q^{76} - 10 q^{79} - 112 q^{86} + 22 q^{89} + 2 q^{91} + 56 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(2251\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.77846i 1.96467i 0.187142 + 0.982333i \(0.440078\pi\)
−0.187142 + 0.982333i \(0.559922\pi\)
\(3\) 0 0
\(4\) −5.71982 −2.85991
\(5\) 0 0
\(6\) 0 0
\(7\) 2.71982i 1.02800i 0.857791 + 0.513998i \(0.171836\pi\)
−0.857791 + 0.513998i \(0.828164\pi\)
\(8\) − 10.3354i − 3.65411i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.71982 0.820058 0.410029 0.912073i \(-0.365519\pi\)
0.410029 + 0.912073i \(0.365519\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) −7.55691 −2.01967
\(15\) 0 0
\(16\) 17.2767 4.31918
\(17\) − 2.83709i − 0.688095i −0.938952 0.344048i \(-0.888202\pi\)
0.938952 0.344048i \(-0.111798\pi\)
\(18\) 0 0
\(19\) 3.55691 0.816012 0.408006 0.912979i \(-0.366224\pi\)
0.408006 + 0.912979i \(0.366224\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 7.55691i 1.61114i
\(23\) 4.83709i 1.00860i 0.863528 + 0.504302i \(0.168250\pi\)
−0.863528 + 0.504302i \(0.831750\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.77846 −0.544900
\(27\) 0 0
\(28\) − 15.5569i − 2.93998i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 7.55691 1.35726 0.678631 0.734479i \(-0.262574\pi\)
0.678631 + 0.734479i \(0.262574\pi\)
\(32\) 27.3319i 4.83165i
\(33\) 0 0
\(34\) 7.88273 1.35188
\(35\) 0 0
\(36\) 0 0
\(37\) 4.27674i 0.703091i 0.936171 + 0.351546i \(0.114344\pi\)
−0.936171 + 0.351546i \(0.885656\pi\)
\(38\) 9.88273i 1.60319i
\(39\) 0 0
\(40\) 0 0
\(41\) −2.83709 −0.443079 −0.221540 0.975151i \(-0.571108\pi\)
−0.221540 + 0.975151i \(0.571108\pi\)
\(42\) 0 0
\(43\) 11.1138i 1.69484i 0.530921 + 0.847421i \(0.321846\pi\)
−0.530921 + 0.847421i \(0.678154\pi\)
\(44\) −15.5569 −2.34529
\(45\) 0 0
\(46\) −13.4396 −1.98157
\(47\) − 11.5569i − 1.68575i −0.538110 0.842875i \(-0.680862\pi\)
0.538110 0.842875i \(-0.319138\pi\)
\(48\) 0 0
\(49\) −0.397442 −0.0567775
\(50\) 0 0
\(51\) 0 0
\(52\) − 5.71982i − 0.793197i
\(53\) − 1.16291i − 0.159738i −0.996805 0.0798690i \(-0.974550\pi\)
0.996805 0.0798690i \(-0.0254502\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 28.1104 3.75641
\(57\) 0 0
\(58\) 16.6707i 2.18898i
\(59\) −2.11727 −0.275645 −0.137822 0.990457i \(-0.544010\pi\)
−0.137822 + 0.990457i \(0.544010\pi\)
\(60\) 0 0
\(61\) 6.60256 0.845371 0.422685 0.906276i \(-0.361088\pi\)
0.422685 + 0.906276i \(0.361088\pi\)
\(62\) 20.9966i 2.66657i
\(63\) 0 0
\(64\) −41.3871 −5.17339
\(65\) 0 0
\(66\) 0 0
\(67\) − 1.88273i − 0.230013i −0.993365 0.115006i \(-0.963311\pi\)
0.993365 0.115006i \(-0.0366888\pi\)
\(68\) 16.2277i 1.96789i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.71982 0.797496 0.398748 0.917060i \(-0.369445\pi\)
0.398748 + 0.917060i \(0.369445\pi\)
\(72\) 0 0
\(73\) 9.11383i 1.06669i 0.845897 + 0.533346i \(0.179066\pi\)
−0.845897 + 0.533346i \(0.820934\pi\)
\(74\) −11.8827 −1.38134
\(75\) 0 0
\(76\) −20.3449 −2.33372
\(77\) 7.39744i 0.843017i
\(78\) 0 0
\(79\) −10.2767 −1.15622 −0.578112 0.815958i \(-0.696210\pi\)
−0.578112 + 0.815958i \(0.696210\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) − 7.88273i − 0.870502i
\(83\) − 2.11727i − 0.232400i −0.993226 0.116200i \(-0.962929\pi\)
0.993226 0.116200i \(-0.0370714\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −30.8793 −3.32980
\(87\) 0 0
\(88\) − 28.1104i − 2.99658i
\(89\) 1.16291 0.123268 0.0616341 0.998099i \(-0.480369\pi\)
0.0616341 + 0.998099i \(0.480369\pi\)
\(90\) 0 0
\(91\) −2.71982 −0.285115
\(92\) − 27.6673i − 2.88452i
\(93\) 0 0
\(94\) 32.1104 3.31193
\(95\) 0 0
\(96\) 0 0
\(97\) 10.8371i 1.10034i 0.835053 + 0.550170i \(0.185437\pi\)
−0.835053 + 0.550170i \(0.814563\pi\)
\(98\) − 1.10428i − 0.111549i
\(99\) 0 0
\(100\) 0 0
\(101\) −7.67418 −0.763610 −0.381805 0.924243i \(-0.624697\pi\)
−0.381805 + 0.924243i \(0.624697\pi\)
\(102\) 0 0
\(103\) 3.76547i 0.371023i 0.982642 + 0.185511i \(0.0593941\pi\)
−0.982642 + 0.185511i \(0.940606\pi\)
\(104\) 10.3354 1.01347
\(105\) 0 0
\(106\) 3.23109 0.313832
\(107\) − 12.6026i − 1.21834i −0.793041 0.609168i \(-0.791504\pi\)
0.793041 0.609168i \(-0.208496\pi\)
\(108\) 0 0
\(109\) −11.4396 −1.09572 −0.547860 0.836570i \(-0.684557\pi\)
−0.547860 + 0.836570i \(0.684557\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 46.9897i 4.44011i
\(113\) 13.1138i 1.23365i 0.787102 + 0.616823i \(0.211580\pi\)
−0.787102 + 0.616823i \(0.788420\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −34.3189 −3.18643
\(117\) 0 0
\(118\) − 5.88273i − 0.541550i
\(119\) 7.71639 0.707360
\(120\) 0 0
\(121\) −3.60256 −0.327505
\(122\) 18.3449i 1.66087i
\(123\) 0 0
\(124\) −43.2242 −3.88165
\(125\) 0 0
\(126\) 0 0
\(127\) 13.4396i 1.19258i 0.802771 + 0.596288i \(0.203358\pi\)
−0.802771 + 0.596288i \(0.796642\pi\)
\(128\) − 60.3285i − 5.33234i
\(129\) 0 0
\(130\) 0 0
\(131\) 9.43965 0.824746 0.412373 0.911015i \(-0.364700\pi\)
0.412373 + 0.911015i \(0.364700\pi\)
\(132\) 0 0
\(133\) 9.67418i 0.838858i
\(134\) 5.23109 0.451898
\(135\) 0 0
\(136\) −29.3224 −2.51437
\(137\) 1.76547i 0.150834i 0.997152 + 0.0754170i \(0.0240288\pi\)
−0.997152 + 0.0754170i \(0.975971\pi\)
\(138\) 0 0
\(139\) 6.27674 0.532386 0.266193 0.963920i \(-0.414234\pi\)
0.266193 + 0.963920i \(0.414234\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 18.6707i 1.56681i
\(143\) 2.71982i 0.227443i
\(144\) 0 0
\(145\) 0 0
\(146\) −25.3224 −2.09570
\(147\) 0 0
\(148\) − 24.4622i − 2.01078i
\(149\) −20.8302 −1.70648 −0.853239 0.521520i \(-0.825365\pi\)
−0.853239 + 0.521520i \(0.825365\pi\)
\(150\) 0 0
\(151\) 4.99656 0.406614 0.203307 0.979115i \(-0.434831\pi\)
0.203307 + 0.979115i \(0.434831\pi\)
\(152\) − 36.7620i − 2.98179i
\(153\) 0 0
\(154\) −20.5535 −1.65625
\(155\) 0 0
\(156\) 0 0
\(157\) − 8.87930i − 0.708645i −0.935123 0.354322i \(-0.884712\pi\)
0.935123 0.354322i \(-0.115288\pi\)
\(158\) − 28.5535i − 2.27159i
\(159\) 0 0
\(160\) 0 0
\(161\) −13.1560 −1.03684
\(162\) 0 0
\(163\) − 13.8337i − 1.08354i −0.840528 0.541768i \(-0.817755\pi\)
0.840528 0.541768i \(-0.182245\pi\)
\(164\) 16.2277 1.26717
\(165\) 0 0
\(166\) 5.88273 0.456589
\(167\) − 9.88273i − 0.764749i −0.924007 0.382374i \(-0.875106\pi\)
0.924007 0.382374i \(-0.124894\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) − 63.5691i − 4.84710i
\(173\) − 13.1138i − 0.997026i −0.866882 0.498513i \(-0.833880\pi\)
0.866882 0.498513i \(-0.166120\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 46.9897 3.54198
\(177\) 0 0
\(178\) 3.23109i 0.242181i
\(179\) 8.55348 0.639317 0.319658 0.947533i \(-0.396432\pi\)
0.319658 + 0.947533i \(0.396432\pi\)
\(180\) 0 0
\(181\) 3.72326 0.276748 0.138374 0.990380i \(-0.455812\pi\)
0.138374 + 0.990380i \(0.455812\pi\)
\(182\) − 7.55691i − 0.560156i
\(183\) 0 0
\(184\) 49.9931 3.68554
\(185\) 0 0
\(186\) 0 0
\(187\) − 7.71639i − 0.564278i
\(188\) 66.1035i 4.82109i
\(189\) 0 0
\(190\) 0 0
\(191\) 4.23453 0.306400 0.153200 0.988195i \(-0.451042\pi\)
0.153200 + 0.988195i \(0.451042\pi\)
\(192\) 0 0
\(193\) − 23.3906i − 1.68369i −0.539719 0.841845i \(-0.681470\pi\)
0.539719 0.841845i \(-0.318530\pi\)
\(194\) −30.1104 −2.16180
\(195\) 0 0
\(196\) 2.27330 0.162379
\(197\) 14.5535i 1.03689i 0.855110 + 0.518446i \(0.173489\pi\)
−0.855110 + 0.518446i \(0.826511\pi\)
\(198\) 0 0
\(199\) 15.1138 1.07139 0.535695 0.844411i \(-0.320050\pi\)
0.535695 + 0.844411i \(0.320050\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) − 21.3224i − 1.50024i
\(203\) 16.3189i 1.14537i
\(204\) 0 0
\(205\) 0 0
\(206\) −10.4622 −0.728935
\(207\) 0 0
\(208\) 17.2767i 1.19793i
\(209\) 9.67418 0.669177
\(210\) 0 0
\(211\) −18.2277 −1.25484 −0.627422 0.778680i \(-0.715890\pi\)
−0.627422 + 0.778680i \(0.715890\pi\)
\(212\) 6.65164i 0.456836i
\(213\) 0 0
\(214\) 35.0157 2.39362
\(215\) 0 0
\(216\) 0 0
\(217\) 20.5535i 1.39526i
\(218\) − 31.7846i − 2.15272i
\(219\) 0 0
\(220\) 0 0
\(221\) 2.83709 0.190843
\(222\) 0 0
\(223\) 10.1173i 0.677502i 0.940876 + 0.338751i \(0.110004\pi\)
−0.940876 + 0.338751i \(0.889996\pi\)
\(224\) −74.3380 −4.96692
\(225\) 0 0
\(226\) −36.4362 −2.42370
\(227\) 11.3224i 0.751493i 0.926723 + 0.375746i \(0.122614\pi\)
−0.926723 + 0.375746i \(0.877386\pi\)
\(228\) 0 0
\(229\) 6.23453 0.411990 0.205995 0.978553i \(-0.433957\pi\)
0.205995 + 0.978553i \(0.433957\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) − 62.0122i − 4.07130i
\(233\) − 6.83709i − 0.447913i −0.974599 0.223956i \(-0.928103\pi\)
0.974599 0.223956i \(-0.0718973\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 12.1104 0.788319
\(237\) 0 0
\(238\) 21.4396i 1.38973i
\(239\) 1.28018 0.0828077 0.0414039 0.999142i \(-0.486817\pi\)
0.0414039 + 0.999142i \(0.486817\pi\)
\(240\) 0 0
\(241\) −6.00000 −0.386494 −0.193247 0.981150i \(-0.561902\pi\)
−0.193247 + 0.981150i \(0.561902\pi\)
\(242\) − 10.0096i − 0.643438i
\(243\) 0 0
\(244\) −37.7655 −2.41769
\(245\) 0 0
\(246\) 0 0
\(247\) 3.55691i 0.226321i
\(248\) − 78.1035i − 4.95958i
\(249\) 0 0
\(250\) 0 0
\(251\) −18.2277 −1.15052 −0.575260 0.817971i \(-0.695099\pi\)
−0.575260 + 0.817971i \(0.695099\pi\)
\(252\) 0 0
\(253\) 13.1560i 0.827113i
\(254\) −37.3415 −2.34301
\(255\) 0 0
\(256\) 84.8459 5.30287
\(257\) 1.11383i 0.0694787i 0.999396 + 0.0347394i \(0.0110601\pi\)
−0.999396 + 0.0347394i \(0.988940\pi\)
\(258\) 0 0
\(259\) −11.6320 −0.722776
\(260\) 0 0
\(261\) 0 0
\(262\) 26.2277i 1.62035i
\(263\) − 8.00000i − 0.493301i −0.969104 0.246651i \(-0.920670\pi\)
0.969104 0.246651i \(-0.0793300\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −26.8793 −1.64808
\(267\) 0 0
\(268\) 10.7689i 0.657816i
\(269\) 15.6742 0.955672 0.477836 0.878449i \(-0.341421\pi\)
0.477836 + 0.878449i \(0.341421\pi\)
\(270\) 0 0
\(271\) 0.443086 0.0269155 0.0134578 0.999909i \(-0.495716\pi\)
0.0134578 + 0.999909i \(0.495716\pi\)
\(272\) − 49.0157i − 2.97201i
\(273\) 0 0
\(274\) −4.90528 −0.296339
\(275\) 0 0
\(276\) 0 0
\(277\) 4.87930i 0.293168i 0.989198 + 0.146584i \(0.0468279\pi\)
−0.989198 + 0.146584i \(0.953172\pi\)
\(278\) 17.4396i 1.04596i
\(279\) 0 0
\(280\) 0 0
\(281\) 9.11383 0.543685 0.271843 0.962342i \(-0.412367\pi\)
0.271843 + 0.962342i \(0.412367\pi\)
\(282\) 0 0
\(283\) 33.3415i 1.98195i 0.134063 + 0.990973i \(0.457198\pi\)
−0.134063 + 0.990973i \(0.542802\pi\)
\(284\) −38.4362 −2.28077
\(285\) 0 0
\(286\) −7.55691 −0.446850
\(287\) − 7.71639i − 0.455484i
\(288\) 0 0
\(289\) 8.95092 0.526525
\(290\) 0 0
\(291\) 0 0
\(292\) − 52.1295i − 3.05065i
\(293\) 29.4328i 1.71948i 0.510731 + 0.859740i \(0.329375\pi\)
−0.510731 + 0.859740i \(0.670625\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 44.2017 2.56917
\(297\) 0 0
\(298\) − 57.8759i − 3.35266i
\(299\) −4.83709 −0.279736
\(300\) 0 0
\(301\) −30.2277 −1.74229
\(302\) 13.8827i 0.798862i
\(303\) 0 0
\(304\) 61.4519 3.52451
\(305\) 0 0
\(306\) 0 0
\(307\) 21.8337i 1.24611i 0.782177 + 0.623056i \(0.214109\pi\)
−0.782177 + 0.623056i \(0.785891\pi\)
\(308\) − 42.3121i − 2.41095i
\(309\) 0 0
\(310\) 0 0
\(311\) −25.1070 −1.42368 −0.711842 0.702339i \(-0.752139\pi\)
−0.711842 + 0.702339i \(0.752139\pi\)
\(312\) 0 0
\(313\) 8.22766i 0.465055i 0.972590 + 0.232527i \(0.0746995\pi\)
−0.972590 + 0.232527i \(0.925300\pi\)
\(314\) 24.6707 1.39225
\(315\) 0 0
\(316\) 58.7811 3.30670
\(317\) 27.6742i 1.55434i 0.629293 + 0.777168i \(0.283345\pi\)
−0.629293 + 0.777168i \(0.716655\pi\)
\(318\) 0 0
\(319\) 16.3189 0.913685
\(320\) 0 0
\(321\) 0 0
\(322\) − 36.5535i − 2.03705i
\(323\) − 10.0913i − 0.561494i
\(324\) 0 0
\(325\) 0 0
\(326\) 38.4362 2.12878
\(327\) 0 0
\(328\) 29.3224i 1.61906i
\(329\) 31.4328 1.73294
\(330\) 0 0
\(331\) −13.2311 −0.727247 −0.363623 0.931546i \(-0.618460\pi\)
−0.363623 + 0.931546i \(0.618460\pi\)
\(332\) 12.1104i 0.664644i
\(333\) 0 0
\(334\) 27.4588 1.50248
\(335\) 0 0
\(336\) 0 0
\(337\) 4.32582i 0.235642i 0.993035 + 0.117821i \(0.0375910\pi\)
−0.993035 + 0.117821i \(0.962409\pi\)
\(338\) − 2.77846i − 0.151128i
\(339\) 0 0
\(340\) 0 0
\(341\) 20.5535 1.11303
\(342\) 0 0
\(343\) 17.9578i 0.969630i
\(344\) 114.866 6.19314
\(345\) 0 0
\(346\) 36.4362 1.95882
\(347\) 6.27674i 0.336953i 0.985706 + 0.168476i \(0.0538847\pi\)
−0.985706 + 0.168476i \(0.946115\pi\)
\(348\) 0 0
\(349\) −17.6673 −0.945709 −0.472855 0.881140i \(-0.656776\pi\)
−0.472855 + 0.881140i \(0.656776\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 74.3380i 3.96223i
\(353\) 13.7655i 0.732662i 0.930485 + 0.366331i \(0.119386\pi\)
−0.930485 + 0.366331i \(0.880614\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.65164 −0.352536
\(357\) 0 0
\(358\) 23.7655i 1.25604i
\(359\) 0.996562 0.0525965 0.0262983 0.999654i \(-0.491628\pi\)
0.0262983 + 0.999654i \(0.491628\pi\)
\(360\) 0 0
\(361\) −6.34836 −0.334124
\(362\) 10.3449i 0.543717i
\(363\) 0 0
\(364\) 15.5569 0.815404
\(365\) 0 0
\(366\) 0 0
\(367\) − 14.2277i − 0.742678i −0.928497 0.371339i \(-0.878899\pi\)
0.928497 0.371339i \(-0.121101\pi\)
\(368\) 83.5691i 4.35634i
\(369\) 0 0
\(370\) 0 0
\(371\) 3.16291 0.164210
\(372\) 0 0
\(373\) 15.6742i 0.811578i 0.913967 + 0.405789i \(0.133003\pi\)
−0.913967 + 0.405789i \(0.866997\pi\)
\(374\) 21.4396 1.10862
\(375\) 0 0
\(376\) −119.445 −6.15991
\(377\) 6.00000i 0.309016i
\(378\) 0 0
\(379\) −26.2017 −1.34589 −0.672945 0.739693i \(-0.734971\pi\)
−0.672945 + 0.739693i \(0.734971\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 11.7655i 0.601974i
\(383\) − 22.4362i − 1.14644i −0.819403 0.573218i \(-0.805695\pi\)
0.819403 0.573218i \(-0.194305\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 64.9897 3.30789
\(387\) 0 0
\(388\) − 61.9862i − 3.14687i
\(389\) 31.6742 1.60594 0.802972 0.596016i \(-0.203251\pi\)
0.802972 + 0.596016i \(0.203251\pi\)
\(390\) 0 0
\(391\) 13.7233 0.694015
\(392\) 4.10771i 0.207471i
\(393\) 0 0
\(394\) −40.4362 −2.03715
\(395\) 0 0
\(396\) 0 0
\(397\) − 17.9509i − 0.900931i −0.892794 0.450465i \(-0.851258\pi\)
0.892794 0.450465i \(-0.148742\pi\)
\(398\) 41.9931i 2.10493i
\(399\) 0 0
\(400\) 0 0
\(401\) −13.5829 −0.678297 −0.339149 0.940733i \(-0.610139\pi\)
−0.339149 + 0.940733i \(0.610139\pi\)
\(402\) 0 0
\(403\) 7.55691i 0.376437i
\(404\) 43.8950 2.18386
\(405\) 0 0
\(406\) −45.3415 −2.25026
\(407\) 11.6320i 0.576576i
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) − 21.5378i − 1.06109i
\(413\) − 5.75859i − 0.283362i
\(414\) 0 0
\(415\) 0 0
\(416\) −27.3319 −1.34006
\(417\) 0 0
\(418\) 26.8793i 1.31471i
\(419\) 12.3189 0.601820 0.300910 0.953653i \(-0.402710\pi\)
0.300910 + 0.953653i \(0.402710\pi\)
\(420\) 0 0
\(421\) 22.7880 1.11062 0.555310 0.831644i \(-0.312600\pi\)
0.555310 + 0.831644i \(0.312600\pi\)
\(422\) − 50.6448i − 2.46535i
\(423\) 0 0
\(424\) −12.0191 −0.583699
\(425\) 0 0
\(426\) 0 0
\(427\) 17.9578i 0.869039i
\(428\) 72.0844i 3.48433i
\(429\) 0 0
\(430\) 0 0
\(431\) 8.99656 0.433349 0.216675 0.976244i \(-0.430479\pi\)
0.216675 + 0.976244i \(0.430479\pi\)
\(432\) 0 0
\(433\) − 20.3258i − 0.976797i −0.872621 0.488398i \(-0.837581\pi\)
0.872621 0.488398i \(-0.162419\pi\)
\(434\) −57.1070 −2.74122
\(435\) 0 0
\(436\) 65.4328 3.13366
\(437\) 17.2051i 0.823032i
\(438\) 0 0
\(439\) 25.3906 1.21183 0.605913 0.795531i \(-0.292808\pi\)
0.605913 + 0.795531i \(0.292808\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 7.88273i 0.374943i
\(443\) − 10.9284i − 0.519223i −0.965713 0.259611i \(-0.916406\pi\)
0.965713 0.259611i \(-0.0835945\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −28.1104 −1.33107
\(447\) 0 0
\(448\) − 112.566i − 5.31823i
\(449\) 2.83709 0.133891 0.0669453 0.997757i \(-0.478675\pi\)
0.0669453 + 0.997757i \(0.478675\pi\)
\(450\) 0 0
\(451\) −7.71639 −0.363350
\(452\) − 75.0088i − 3.52812i
\(453\) 0 0
\(454\) −31.4588 −1.47643
\(455\) 0 0
\(456\) 0 0
\(457\) 13.7164i 0.641625i 0.947143 + 0.320813i \(0.103956\pi\)
−0.947143 + 0.320813i \(0.896044\pi\)
\(458\) 17.3224i 0.809422i
\(459\) 0 0
\(460\) 0 0
\(461\) 19.6251 0.914032 0.457016 0.889458i \(-0.348918\pi\)
0.457016 + 0.889458i \(0.348918\pi\)
\(462\) 0 0
\(463\) 27.0388i 1.25660i 0.777972 + 0.628299i \(0.216249\pi\)
−0.777972 + 0.628299i \(0.783751\pi\)
\(464\) 103.660 4.81231
\(465\) 0 0
\(466\) 18.9966 0.879999
\(467\) 28.9215i 1.33833i 0.743115 + 0.669164i \(0.233348\pi\)
−0.743115 + 0.669164i \(0.766652\pi\)
\(468\) 0 0
\(469\) 5.12070 0.236452
\(470\) 0 0
\(471\) 0 0
\(472\) 21.8827i 1.00723i
\(473\) 30.2277i 1.38987i
\(474\) 0 0
\(475\) 0 0
\(476\) −44.1364 −2.02299
\(477\) 0 0
\(478\) 3.55691i 0.162689i
\(479\) −12.1595 −0.555580 −0.277790 0.960642i \(-0.589602\pi\)
−0.277790 + 0.960642i \(0.589602\pi\)
\(480\) 0 0
\(481\) −4.27674 −0.195002
\(482\) − 16.6707i − 0.759332i
\(483\) 0 0
\(484\) 20.6060 0.936636
\(485\) 0 0
\(486\) 0 0
\(487\) 0.159472i 0.00722636i 0.999993 + 0.00361318i \(0.00115011\pi\)
−0.999993 + 0.00361318i \(0.998850\pi\)
\(488\) − 68.2399i − 3.08907i
\(489\) 0 0
\(490\) 0 0
\(491\) 42.2277 1.90571 0.952854 0.303430i \(-0.0981318\pi\)
0.952854 + 0.303430i \(0.0981318\pi\)
\(492\) 0 0
\(493\) − 17.0225i − 0.766657i
\(494\) −9.88273 −0.444645
\(495\) 0 0
\(496\) 130.559 5.86226
\(497\) 18.2767i 0.819824i
\(498\) 0 0
\(499\) −7.79145 −0.348793 −0.174397 0.984676i \(-0.555797\pi\)
−0.174397 + 0.984676i \(0.555797\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) − 50.6448i − 2.26039i
\(503\) − 27.3484i − 1.21940i −0.792631 0.609702i \(-0.791289\pi\)
0.792631 0.609702i \(-0.208711\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −36.5535 −1.62500
\(507\) 0 0
\(508\) − 76.8724i − 3.41066i
\(509\) −33.4819 −1.48406 −0.742029 0.670368i \(-0.766136\pi\)
−0.742029 + 0.670368i \(0.766136\pi\)
\(510\) 0 0
\(511\) −24.7880 −1.09656
\(512\) 115.084i 5.08603i
\(513\) 0 0
\(514\) −3.09472 −0.136502
\(515\) 0 0
\(516\) 0 0
\(517\) − 31.4328i − 1.38241i
\(518\) − 32.3189i − 1.42001i
\(519\) 0 0
\(520\) 0 0
\(521\) 17.3484 0.760045 0.380023 0.924977i \(-0.375916\pi\)
0.380023 + 0.924977i \(0.375916\pi\)
\(522\) 0 0
\(523\) − 4.00000i − 0.174908i −0.996169 0.0874539i \(-0.972127\pi\)
0.996169 0.0874539i \(-0.0278730\pi\)
\(524\) −53.9931 −2.35870
\(525\) 0 0
\(526\) 22.2277 0.969172
\(527\) − 21.4396i − 0.933926i
\(528\) 0 0
\(529\) −0.397442 −0.0172801
\(530\) 0 0
\(531\) 0 0
\(532\) − 55.3346i − 2.39906i
\(533\) − 2.83709i − 0.122888i
\(534\) 0 0
\(535\) 0 0
\(536\) −19.4588 −0.840490
\(537\) 0 0
\(538\) 43.5500i 1.87758i
\(539\) −1.08097 −0.0465608
\(540\) 0 0
\(541\) −32.6448 −1.40351 −0.701754 0.712419i \(-0.747599\pi\)
−0.701754 + 0.712419i \(0.747599\pi\)
\(542\) 1.23109i 0.0528800i
\(543\) 0 0
\(544\) 77.5432 3.32464
\(545\) 0 0
\(546\) 0 0
\(547\) − 34.2277i − 1.46347i −0.681590 0.731734i \(-0.738711\pi\)
0.681590 0.731734i \(-0.261289\pi\)
\(548\) − 10.0982i − 0.431372i
\(549\) 0 0
\(550\) 0 0
\(551\) 21.3415 0.909178
\(552\) 0 0
\(553\) − 27.9509i − 1.18859i
\(554\) −13.5569 −0.575978
\(555\) 0 0
\(556\) −35.9018 −1.52258
\(557\) 6.65164i 0.281839i 0.990021 + 0.140919i \(0.0450059\pi\)
−0.990021 + 0.140919i \(0.954994\pi\)
\(558\) 0 0
\(559\) −11.1138 −0.470065
\(560\) 0 0
\(561\) 0 0
\(562\) 25.3224i 1.06816i
\(563\) − 40.2699i − 1.69717i −0.529057 0.848586i \(-0.677454\pi\)
0.529057 0.848586i \(-0.322546\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −92.6379 −3.89386
\(567\) 0 0
\(568\) − 69.4519i − 2.91414i
\(569\) −13.4328 −0.563131 −0.281566 0.959542i \(-0.590854\pi\)
−0.281566 + 0.959542i \(0.590854\pi\)
\(570\) 0 0
\(571\) −35.7164 −1.49468 −0.747342 0.664439i \(-0.768670\pi\)
−0.747342 + 0.664439i \(0.768670\pi\)
\(572\) − 15.5569i − 0.650467i
\(573\) 0 0
\(574\) 21.4396 0.894874
\(575\) 0 0
\(576\) 0 0
\(577\) 13.7164i 0.571021i 0.958376 + 0.285510i \(0.0921631\pi\)
−0.958376 + 0.285510i \(0.907837\pi\)
\(578\) 24.8697i 1.03444i
\(579\) 0 0
\(580\) 0 0
\(581\) 5.75859 0.238907
\(582\) 0 0
\(583\) − 3.16291i − 0.130994i
\(584\) 94.1948 3.89781
\(585\) 0 0
\(586\) −81.7777 −3.37821
\(587\) 30.6707i 1.26592i 0.774186 + 0.632959i \(0.218160\pi\)
−0.774186 + 0.632959i \(0.781840\pi\)
\(588\) 0 0
\(589\) 26.8793 1.10754
\(590\) 0 0
\(591\) 0 0
\(592\) 73.8881i 3.03678i
\(593\) 45.6673i 1.87533i 0.347538 + 0.937666i \(0.387018\pi\)
−0.347538 + 0.937666i \(0.612982\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 119.145 4.88038
\(597\) 0 0
\(598\) − 13.4396i − 0.549588i
\(599\) −40.2208 −1.64338 −0.821688 0.569937i \(-0.806968\pi\)
−0.821688 + 0.569937i \(0.806968\pi\)
\(600\) 0 0
\(601\) 17.3974 0.709656 0.354828 0.934932i \(-0.384539\pi\)
0.354828 + 0.934932i \(0.384539\pi\)
\(602\) − 83.9862i − 3.42302i
\(603\) 0 0
\(604\) −28.5795 −1.16288
\(605\) 0 0
\(606\) 0 0
\(607\) 14.2277i 0.577483i 0.957407 + 0.288741i \(0.0932368\pi\)
−0.957407 + 0.288741i \(0.906763\pi\)
\(608\) 97.2173i 3.94268i
\(609\) 0 0
\(610\) 0 0
\(611\) 11.5569 0.467543
\(612\) 0 0
\(613\) − 40.8302i − 1.64912i −0.565777 0.824558i \(-0.691424\pi\)
0.565777 0.824558i \(-0.308576\pi\)
\(614\) −60.6639 −2.44819
\(615\) 0 0
\(616\) 76.4553 3.08047
\(617\) 5.11383i 0.205875i 0.994688 + 0.102937i \(0.0328242\pi\)
−0.994688 + 0.102937i \(0.967176\pi\)
\(618\) 0 0
\(619\) −11.5569 −0.464512 −0.232256 0.972655i \(-0.574611\pi\)
−0.232256 + 0.972655i \(0.574611\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) − 69.7586i − 2.79706i
\(623\) 3.16291i 0.126719i
\(624\) 0 0
\(625\) 0 0
\(626\) −22.8602 −0.913677
\(627\) 0 0
\(628\) 50.7880i 2.02666i
\(629\) 12.1335 0.483794
\(630\) 0 0
\(631\) 35.2242 1.40225 0.701127 0.713036i \(-0.252681\pi\)
0.701127 + 0.713036i \(0.252681\pi\)
\(632\) 106.214i 4.22496i
\(633\) 0 0
\(634\) −76.8915 −3.05375
\(635\) 0 0
\(636\) 0 0
\(637\) − 0.397442i − 0.0157472i
\(638\) 45.3415i 1.79509i
\(639\) 0 0
\(640\) 0 0
\(641\) 21.9018 0.865071 0.432535 0.901617i \(-0.357619\pi\)
0.432535 + 0.901617i \(0.357619\pi\)
\(642\) 0 0
\(643\) 7.50783i 0.296080i 0.988981 + 0.148040i \(0.0472964\pi\)
−0.988981 + 0.148040i \(0.952704\pi\)
\(644\) 75.2502 2.96527
\(645\) 0 0
\(646\) 28.0382 1.10315
\(647\) − 14.0422i − 0.552056i −0.961150 0.276028i \(-0.910982\pi\)
0.961150 0.276028i \(-0.0890183\pi\)
\(648\) 0 0
\(649\) −5.75859 −0.226044
\(650\) 0 0
\(651\) 0 0
\(652\) 79.1261i 3.09882i
\(653\) − 7.99312i − 0.312795i −0.987694 0.156398i \(-0.950012\pi\)
0.987694 0.156398i \(-0.0499881\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −49.0157 −1.91374
\(657\) 0 0
\(658\) 87.3346i 3.40466i
\(659\) −25.3415 −0.987164 −0.493582 0.869699i \(-0.664313\pi\)
−0.493582 + 0.869699i \(0.664313\pi\)
\(660\) 0 0
\(661\) 27.4396 1.06728 0.533639 0.845712i \(-0.320824\pi\)
0.533639 + 0.845712i \(0.320824\pi\)
\(662\) − 36.7620i − 1.42880i
\(663\) 0 0
\(664\) −21.8827 −0.849215
\(665\) 0 0
\(666\) 0 0
\(667\) 29.0225i 1.12376i
\(668\) 56.5275i 2.18711i
\(669\) 0 0
\(670\) 0 0
\(671\) 17.9578 0.693253
\(672\) 0 0
\(673\) 27.1070i 1.04490i 0.852671 + 0.522448i \(0.174981\pi\)
−0.852671 + 0.522448i \(0.825019\pi\)
\(674\) −12.0191 −0.462959
\(675\) 0 0
\(676\) 5.71982 0.219993
\(677\) − 36.5957i − 1.40649i −0.710949 0.703243i \(-0.751735\pi\)
0.710949 0.703243i \(-0.248265\pi\)
\(678\) 0 0
\(679\) −29.4750 −1.13115
\(680\) 0 0
\(681\) 0 0
\(682\) 57.1070i 2.18674i
\(683\) 13.4656i 0.515248i 0.966245 + 0.257624i \(0.0829396\pi\)
−0.966245 + 0.257624i \(0.917060\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −49.8950 −1.90500
\(687\) 0 0
\(688\) 192.011i 7.32034i
\(689\) 1.16291 0.0443033
\(690\) 0 0
\(691\) 29.5500 1.12414 0.562068 0.827091i \(-0.310006\pi\)
0.562068 + 0.827091i \(0.310006\pi\)
\(692\) 75.0088i 2.85141i
\(693\) 0 0
\(694\) −17.4396 −0.662000
\(695\) 0 0
\(696\) 0 0
\(697\) 8.04908i 0.304881i
\(698\) − 49.0878i − 1.85800i
\(699\) 0 0
\(700\) 0 0
\(701\) −43.6604 −1.64903 −0.824516 0.565839i \(-0.808552\pi\)
−0.824516 + 0.565839i \(0.808552\pi\)
\(702\) 0 0
\(703\) 15.2120i 0.573731i
\(704\) −112.566 −4.24248
\(705\) 0 0
\(706\) −38.2468 −1.43944
\(707\) − 20.8724i − 0.784988i
\(708\) 0 0
\(709\) 26.7880 1.00604 0.503022 0.864273i \(-0.332221\pi\)
0.503022 + 0.864273i \(0.332221\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) − 12.0191i − 0.450435i
\(713\) 36.5535i 1.36894i
\(714\) 0 0
\(715\) 0 0
\(716\) −48.9244 −1.82839
\(717\) 0 0
\(718\) 2.76891i 0.103335i
\(719\) −34.8793 −1.30078 −0.650389 0.759601i \(-0.725394\pi\)
−0.650389 + 0.759601i \(0.725394\pi\)
\(720\) 0 0
\(721\) −10.2414 −0.381410
\(722\) − 17.6386i − 0.656443i
\(723\) 0 0
\(724\) −21.2964 −0.791475
\(725\) 0 0
\(726\) 0 0
\(727\) − 37.4396i − 1.38856i −0.719705 0.694280i \(-0.755723\pi\)
0.719705 0.694280i \(-0.244277\pi\)
\(728\) 28.1104i 1.04184i
\(729\) 0 0
\(730\) 0 0
\(731\) 31.5309 1.16621
\(732\) 0 0
\(733\) − 47.1560i − 1.74175i −0.491506 0.870874i \(-0.663554\pi\)
0.491506 0.870874i \(-0.336446\pi\)
\(734\) 39.5309 1.45911
\(735\) 0 0
\(736\) −132.207 −4.87322
\(737\) − 5.12070i − 0.188624i
\(738\) 0 0
\(739\) 31.7914 1.16947 0.584734 0.811225i \(-0.301199\pi\)
0.584734 + 0.811225i \(0.301199\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 8.78801i 0.322618i
\(743\) − 16.6776i − 0.611842i −0.952057 0.305921i \(-0.901036\pi\)
0.952057 0.305921i \(-0.0989644\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −43.5500 −1.59448
\(747\) 0 0
\(748\) 44.1364i 1.61379i
\(749\) 34.2767 1.25244
\(750\) 0 0
\(751\) 16.1855 0.590616 0.295308 0.955402i \(-0.404578\pi\)
0.295308 + 0.955402i \(0.404578\pi\)
\(752\) − 199.666i − 7.28106i
\(753\) 0 0
\(754\) −16.6707 −0.607113
\(755\) 0 0
\(756\) 0 0
\(757\) − 12.3258i − 0.447990i −0.974590 0.223995i \(-0.928090\pi\)
0.974590 0.223995i \(-0.0719099\pi\)
\(758\) − 72.8002i − 2.64422i
\(759\) 0 0
\(760\) 0 0
\(761\) 0.00687569 0.000249244 0 0.000124622 1.00000i \(-0.499960\pi\)
0.000124622 1.00000i \(0.499960\pi\)
\(762\) 0 0
\(763\) − 31.1138i − 1.12640i
\(764\) −24.2208 −0.876277
\(765\) 0 0
\(766\) 62.3380 2.25237
\(767\) − 2.11727i − 0.0764501i
\(768\) 0 0
\(769\) 20.3258 0.732968 0.366484 0.930424i \(-0.380561\pi\)
0.366484 + 0.930424i \(0.380561\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 133.790i 4.81520i
\(773\) − 9.90184i − 0.356144i −0.984017 0.178072i \(-0.943014\pi\)
0.984017 0.178072i \(-0.0569861\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 112.005 4.02076
\(777\) 0 0
\(778\) 88.0054i 3.15514i
\(779\) −10.0913 −0.361558
\(780\) 0 0
\(781\) 18.2767 0.653993
\(782\) 38.1295i 1.36351i
\(783\) 0 0
\(784\) −6.86651 −0.245232
\(785\) 0 0
\(786\) 0 0
\(787\) − 36.3449i − 1.29556i −0.761829 0.647778i \(-0.775698\pi\)
0.761829 0.647778i \(-0.224302\pi\)
\(788\) − 83.2433i − 2.96542i
\(789\) 0 0
\(790\) 0 0
\(791\) −35.6673 −1.26818
\(792\) 0 0
\(793\) 6.60256i 0.234464i
\(794\) 49.8759 1.77003
\(795\) 0 0
\(796\) −86.4484 −3.06408
\(797\) 18.8371i 0.667244i 0.942707 + 0.333622i \(0.108271\pi\)
−0.942707 + 0.333622i \(0.891729\pi\)
\(798\) 0 0
\(799\) −32.7880 −1.15996
\(800\) 0 0
\(801\) 0 0
\(802\) − 37.7395i − 1.33263i
\(803\) 24.7880i 0.874750i
\(804\) 0 0
\(805\) 0 0
\(806\) −20.9966 −0.739572
\(807\) 0 0
\(808\) 79.3155i 2.79031i
\(809\) 32.2277 1.13306 0.566532 0.824040i \(-0.308285\pi\)
0.566532 + 0.824040i \(0.308285\pi\)
\(810\) 0 0
\(811\) −23.0034 −0.807760 −0.403880 0.914812i \(-0.632339\pi\)
−0.403880 + 0.914812i \(0.632339\pi\)
\(812\) − 93.3415i − 3.27564i
\(813\) 0 0
\(814\) −32.3189 −1.13278
\(815\) 0 0
\(816\) 0 0
\(817\) 39.5309i 1.38301i
\(818\) 38.8984i 1.36005i
\(819\) 0 0
\(820\) 0 0
\(821\) −49.9372 −1.74282 −0.871410 0.490556i \(-0.836794\pi\)
−0.871410 + 0.490556i \(0.836794\pi\)
\(822\) 0 0
\(823\) 28.2345i 0.984194i 0.870540 + 0.492097i \(0.163769\pi\)
−0.870540 + 0.492097i \(0.836231\pi\)
\(824\) 38.9175 1.35576
\(825\) 0 0
\(826\) 16.0000 0.556711
\(827\) − 9.55004i − 0.332087i −0.986118 0.166044i \(-0.946901\pi\)
0.986118 0.166044i \(-0.0530993\pi\)
\(828\) 0 0
\(829\) 37.9862 1.31932 0.659658 0.751565i \(-0.270701\pi\)
0.659658 + 0.751565i \(0.270701\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) − 41.3871i − 1.43484i
\(833\) 1.12758i 0.0390683i
\(834\) 0 0
\(835\) 0 0
\(836\) −55.3346 −1.91379
\(837\) 0 0
\(838\) 34.2277i 1.18237i
\(839\) −4.72670 −0.163184 −0.0815919 0.996666i \(-0.526000\pi\)
−0.0815919 + 0.996666i \(0.526000\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 63.3155i 2.18200i
\(843\) 0 0
\(844\) 104.259 3.58874
\(845\) 0 0
\(846\) 0 0
\(847\) − 9.79832i − 0.336674i
\(848\) − 20.0913i − 0.689938i
\(849\) 0 0
\(850\) 0 0
\(851\) −20.6870 −0.709140
\(852\) 0 0
\(853\) − 48.3611i − 1.65585i −0.560836 0.827927i \(-0.689520\pi\)
0.560836 0.827927i \(-0.310480\pi\)
\(854\) −49.8950 −1.70737
\(855\) 0 0
\(856\) −130.252 −4.45193
\(857\) 6.83709i 0.233551i 0.993158 + 0.116775i \(0.0372557\pi\)
−0.993158 + 0.116775i \(0.962744\pi\)
\(858\) 0 0
\(859\) −12.6026 −0.429994 −0.214997 0.976615i \(-0.568974\pi\)
−0.214997 + 0.976615i \(0.568974\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 24.9966i 0.851386i
\(863\) − 8.20855i − 0.279422i −0.990192 0.139711i \(-0.955383\pi\)
0.990192 0.139711i \(-0.0446174\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 56.4744 1.91908
\(867\) 0 0
\(868\) − 117.562i − 3.99032i
\(869\) −27.9509 −0.948170
\(870\) 0 0
\(871\) 1.88273 0.0637940
\(872\) 118.233i 4.00387i
\(873\) 0 0
\(874\) −47.8037 −1.61698
\(875\) 0 0
\(876\) 0 0
\(877\) − 13.5309i − 0.456907i −0.973555 0.228454i \(-0.926633\pi\)
0.973555 0.228454i \(-0.0733669\pi\)
\(878\) 70.5466i 2.38083i
\(879\) 0 0
\(880\) 0 0
\(881\) 9.34836 0.314954 0.157477 0.987523i \(-0.449664\pi\)
0.157477 + 0.987523i \(0.449664\pi\)
\(882\) 0 0
\(883\) − 55.1001i − 1.85427i −0.374733 0.927133i \(-0.622266\pi\)
0.374733 0.927133i \(-0.377734\pi\)
\(884\) −16.2277 −0.545795
\(885\) 0 0
\(886\) 30.3640 1.02010
\(887\) 0.133492i 0.00448223i 0.999997 + 0.00224112i \(0.000713370\pi\)
−0.999997 + 0.00224112i \(0.999287\pi\)
\(888\) 0 0
\(889\) −36.5535 −1.22596
\(890\) 0 0
\(891\) 0 0
\(892\) − 57.8690i − 1.93760i
\(893\) − 41.1070i − 1.37559i
\(894\) 0 0
\(895\) 0 0
\(896\) 164.083 5.48162
\(897\) 0 0
\(898\) 7.88273i 0.263050i
\(899\) 45.3415 1.51222
\(900\) 0 0
\(901\) −3.29928 −0.109915
\(902\) − 21.4396i − 0.713862i
\(903\) 0 0
\(904\) 135.536 4.50787
\(905\) 0 0
\(906\) 0 0
\(907\) 58.5466i 1.94401i 0.234964 + 0.972004i \(0.424503\pi\)
−0.234964 + 0.972004i \(0.575497\pi\)
\(908\) − 64.7620i − 2.14920i
\(909\) 0 0
\(910\) 0 0
\(911\) −50.4622 −1.67189 −0.835943 0.548816i \(-0.815079\pi\)
−0.835943 + 0.548816i \(0.815079\pi\)
\(912\) 0 0
\(913\) − 5.75859i − 0.190582i
\(914\) −38.1104 −1.26058
\(915\) 0 0
\(916\) −35.6604 −1.17825
\(917\) 25.6742i 0.847836i
\(918\) 0 0
\(919\) −56.9735 −1.87938 −0.939691 0.342026i \(-0.888887\pi\)
−0.939691 + 0.342026i \(0.888887\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 54.5275i 1.79577i
\(923\) 6.71982i 0.221186i
\(924\) 0 0
\(925\) 0 0
\(926\) −75.1261 −2.46880
\(927\) 0 0
\(928\) 163.992i 5.38329i
\(929\) −36.5957 −1.20067 −0.600333 0.799750i \(-0.704965\pi\)
−0.600333 + 0.799750i \(0.704965\pi\)
\(930\) 0 0
\(931\) −1.41367 −0.0463311
\(932\) 39.1070i 1.28099i
\(933\) 0 0
\(934\) −80.3572 −2.62937
\(935\) 0 0
\(936\) 0 0
\(937\) 47.1070i 1.53892i 0.638697 + 0.769459i \(0.279474\pi\)
−0.638697 + 0.769459i \(0.720526\pi\)
\(938\) 14.2277i 0.464549i
\(939\) 0 0
\(940\) 0 0
\(941\) 36.3611 1.18534 0.592670 0.805446i \(-0.298074\pi\)
0.592670 + 0.805446i \(0.298074\pi\)
\(942\) 0 0
\(943\) − 13.7233i − 0.446891i
\(944\) −36.5795 −1.19056
\(945\) 0 0
\(946\) −83.9862 −2.73063
\(947\) 44.5795i 1.44864i 0.689465 + 0.724319i \(0.257846\pi\)
−0.689465 + 0.724319i \(0.742154\pi\)
\(948\) 0 0
\(949\) −9.11383 −0.295847
\(950\) 0 0
\(951\) 0 0
\(952\) − 79.7517i − 2.58477i
\(953\) − 19.8596i − 0.643317i −0.946856 0.321658i \(-0.895760\pi\)
0.946856 0.321658i \(-0.104240\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −7.32238 −0.236823
\(957\) 0 0
\(958\) − 33.7846i − 1.09153i
\(959\) −4.80176 −0.155057
\(960\) 0 0
\(961\) 26.1070 0.842160
\(962\) − 11.8827i − 0.383115i
\(963\) 0 0
\(964\) 34.3189 1.10534
\(965\) 0 0
\(966\) 0 0
\(967\) − 47.4068i − 1.52450i −0.647283 0.762250i \(-0.724095\pi\)
0.647283 0.762250i \(-0.275905\pi\)
\(968\) 37.2338i 1.19674i
\(969\) 0 0
\(970\) 0 0
\(971\) 10.6448 0.341607 0.170803 0.985305i \(-0.445364\pi\)
0.170803 + 0.985305i \(0.445364\pi\)
\(972\) 0 0
\(973\) 17.0716i 0.547291i
\(974\) −0.443086 −0.0141974
\(975\) 0 0
\(976\) 114.071 3.65131
\(977\) − 1.21199i − 0.0387750i −0.999812 0.0193875i \(-0.993828\pi\)
0.999812 0.0193875i \(-0.00617162\pi\)
\(978\) 0 0
\(979\) 3.16291 0.101087
\(980\) 0 0
\(981\) 0 0
\(982\) 117.328i 3.74408i
\(983\) − 51.8759i − 1.65458i −0.561773 0.827291i \(-0.689881\pi\)
0.561773 0.827291i \(-0.310119\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 47.2964 1.50622
\(987\) 0 0
\(988\) − 20.3449i − 0.647258i
\(989\) −53.7586 −1.70942
\(990\) 0 0
\(991\) −21.6251 −0.686944 −0.343472 0.939163i \(-0.611603\pi\)
−0.343472 + 0.939163i \(0.611603\pi\)
\(992\) 206.545i 6.55781i
\(993\) 0 0
\(994\) −50.7811 −1.61068
\(995\) 0 0
\(996\) 0 0
\(997\) − 23.2051i − 0.734913i −0.930041 0.367457i \(-0.880229\pi\)
0.930041 0.367457i \(-0.119771\pi\)
\(998\) − 21.6482i − 0.685262i
\(999\) 0 0
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 2925.2.c.w.2224.6 6
3.2 odd 2 975.2.c.i.274.1 6
5.2 odd 4 585.2.a.n.1.1 3
5.3 odd 4 2925.2.a.bh.1.3 3
5.4 even 2 inner 2925.2.c.w.2224.1 6
15.2 even 4 195.2.a.e.1.3 3
15.8 even 4 975.2.a.o.1.1 3
15.14 odd 2 975.2.c.i.274.6 6
20.7 even 4 9360.2.a.dd.1.3 3
60.47 odd 4 3120.2.a.bj.1.3 3
65.12 odd 4 7605.2.a.bx.1.3 3
105.62 odd 4 9555.2.a.bq.1.3 3
195.77 even 4 2535.2.a.bc.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
195.2.a.e.1.3 3 15.2 even 4
585.2.a.n.1.1 3 5.2 odd 4
975.2.a.o.1.1 3 15.8 even 4
975.2.c.i.274.1 6 3.2 odd 2
975.2.c.i.274.6 6 15.14 odd 2
2535.2.a.bc.1.1 3 195.77 even 4
2925.2.a.bh.1.3 3 5.3 odd 4
2925.2.c.w.2224.1 6 5.4 even 2 inner
2925.2.c.w.2224.6 6 1.1 even 1 trivial
3120.2.a.bj.1.3 3 60.47 odd 4
7605.2.a.bx.1.3 3 65.12 odd 4
9360.2.a.dd.1.3 3 20.7 even 4
9555.2.a.bq.1.3 3 105.62 odd 4