Properties

Label 9702.2.a.dv.1.2
Level $9702$
Weight $2$
Character 9702.1
Self dual yes
Analytic conductor $77.471$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9702 = 2 \cdot 3^{2} \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9702.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(77.4708600410\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.2700.1
Defining polynomial: \( x^{3} - 15x - 20 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 462)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.61323\) of defining polynomial
Character \(\chi\) \(=\) 9702.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.61323 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +1.61323 q^{5} -1.00000 q^{8} -1.61323 q^{10} +1.00000 q^{11} +1.00000 q^{16} +7.34206 q^{17} +1.17103 q^{19} +1.61323 q^{20} -1.00000 q^{22} -3.55780 q^{23} -2.39749 q^{25} -10.3975 q^{29} +6.34206 q^{31} -1.00000 q^{32} -7.34206 q^{34} +2.82897 q^{37} -1.17103 q^{38} -1.61323 q^{40} -4.94457 q^{41} -11.5131 q^{43} +1.00000 q^{44} +3.55780 q^{46} -6.78426 q^{47} +2.39749 q^{50} -8.00000 q^{53} +1.61323 q^{55} +10.3975 q^{58} -4.39749 q^{59} -11.9553 q^{61} -6.34206 q^{62} +1.00000 q^{64} +2.94457 q^{67} +7.34206 q^{68} -15.5131 q^{71} -5.11560 q^{73} -2.82897 q^{74} +1.17103 q^{76} +5.61323 q^{79} +1.61323 q^{80} +4.94457 q^{82} -5.05543 q^{83} +11.8444 q^{85} +11.5131 q^{86} -1.00000 q^{88} +0.773540 q^{89} -3.55780 q^{92} +6.78426 q^{94} +1.88914 q^{95} +7.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{2} + 3 q^{4} - 3 q^{8} + 3 q^{11} + 3 q^{16} - 3 q^{17} - 9 q^{19} - 3 q^{22} - 3 q^{23} + 15 q^{25} - 9 q^{29} - 6 q^{31} - 3 q^{32} + 3 q^{34} + 21 q^{37} + 9 q^{38} - 12 q^{41} + 3 q^{43} + 3 q^{44} + 3 q^{46} - 3 q^{47} - 15 q^{50} - 24 q^{53} + 9 q^{58} + 9 q^{59} - 6 q^{61} + 6 q^{62} + 3 q^{64} + 6 q^{67} - 3 q^{68} - 9 q^{71} - 21 q^{74} - 9 q^{76} + 12 q^{79} + 12 q^{82} - 18 q^{83} - 3 q^{86} - 3 q^{88} + 12 q^{89} - 3 q^{92} + 3 q^{94} + 21 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 1.61323 0.721458 0.360729 0.932671i \(-0.382528\pi\)
0.360729 + 0.932671i \(0.382528\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.61323 −0.510148
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.34206 1.78071 0.890356 0.455266i \(-0.150456\pi\)
0.890356 + 0.455266i \(0.150456\pi\)
\(18\) 0 0
\(19\) 1.17103 0.268653 0.134326 0.990937i \(-0.457113\pi\)
0.134326 + 0.990937i \(0.457113\pi\)
\(20\) 1.61323 0.360729
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.55780 −0.741853 −0.370926 0.928662i \(-0.620960\pi\)
−0.370926 + 0.928662i \(0.620960\pi\)
\(24\) 0 0
\(25\) −2.39749 −0.479498
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −10.3975 −1.93077 −0.965383 0.260838i \(-0.916001\pi\)
−0.965383 + 0.260838i \(0.916001\pi\)
\(30\) 0 0
\(31\) 6.34206 1.13907 0.569534 0.821968i \(-0.307124\pi\)
0.569534 + 0.821968i \(0.307124\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −7.34206 −1.25915
\(35\) 0 0
\(36\) 0 0
\(37\) 2.82897 0.465080 0.232540 0.972587i \(-0.425296\pi\)
0.232540 + 0.972587i \(0.425296\pi\)
\(38\) −1.17103 −0.189966
\(39\) 0 0
\(40\) −1.61323 −0.255074
\(41\) −4.94457 −0.772212 −0.386106 0.922454i \(-0.626180\pi\)
−0.386106 + 0.922454i \(0.626180\pi\)
\(42\) 0 0
\(43\) −11.5131 −1.75573 −0.877865 0.478908i \(-0.841033\pi\)
−0.877865 + 0.478908i \(0.841033\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) 3.55780 0.524569
\(47\) −6.78426 −0.989586 −0.494793 0.869011i \(-0.664756\pi\)
−0.494793 + 0.869011i \(0.664756\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.39749 0.339056
\(51\) 0 0
\(52\) 0 0
\(53\) −8.00000 −1.09888 −0.549442 0.835532i \(-0.685160\pi\)
−0.549442 + 0.835532i \(0.685160\pi\)
\(54\) 0 0
\(55\) 1.61323 0.217528
\(56\) 0 0
\(57\) 0 0
\(58\) 10.3975 1.36526
\(59\) −4.39749 −0.572504 −0.286252 0.958154i \(-0.592410\pi\)
−0.286252 + 0.958154i \(0.592410\pi\)
\(60\) 0 0
\(61\) −11.9553 −1.53072 −0.765359 0.643604i \(-0.777439\pi\)
−0.765359 + 0.643604i \(0.777439\pi\)
\(62\) −6.34206 −0.805442
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.94457 0.359736 0.179868 0.983691i \(-0.442433\pi\)
0.179868 + 0.983691i \(0.442433\pi\)
\(68\) 7.34206 0.890356
\(69\) 0 0
\(70\) 0 0
\(71\) −15.5131 −1.84106 −0.920532 0.390666i \(-0.872245\pi\)
−0.920532 + 0.390666i \(0.872245\pi\)
\(72\) 0 0
\(73\) −5.11560 −0.598736 −0.299368 0.954138i \(-0.596776\pi\)
−0.299368 + 0.954138i \(0.596776\pi\)
\(74\) −2.82897 −0.328861
\(75\) 0 0
\(76\) 1.17103 0.134326
\(77\) 0 0
\(78\) 0 0
\(79\) 5.61323 0.631538 0.315769 0.948836i \(-0.397738\pi\)
0.315769 + 0.948836i \(0.397738\pi\)
\(80\) 1.61323 0.180365
\(81\) 0 0
\(82\) 4.94457 0.546036
\(83\) −5.05543 −0.554906 −0.277453 0.960739i \(-0.589490\pi\)
−0.277453 + 0.960739i \(0.589490\pi\)
\(84\) 0 0
\(85\) 11.8444 1.28471
\(86\) 11.5131 1.24149
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) 0.773540 0.0819951 0.0409976 0.999159i \(-0.486946\pi\)
0.0409976 + 0.999159i \(0.486946\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.55780 −0.370926
\(93\) 0 0
\(94\) 6.78426 0.699743
\(95\) 1.88914 0.193822
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.39749 −0.239749
\(101\) −13.6239 −1.35563 −0.677817 0.735231i \(-0.737074\pi\)
−0.677817 + 0.735231i \(0.737074\pi\)
\(102\) 0 0
\(103\) −12.3421 −1.21610 −0.608050 0.793899i \(-0.708048\pi\)
−0.608050 + 0.793899i \(0.708048\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) 15.7395 1.52160 0.760800 0.648987i \(-0.224807\pi\)
0.760800 + 0.648987i \(0.224807\pi\)
\(108\) 0 0
\(109\) 3.95529 0.378848 0.189424 0.981895i \(-0.439338\pi\)
0.189424 + 0.981895i \(0.439338\pi\)
\(110\) −1.61323 −0.153815
\(111\) 0 0
\(112\) 0 0
\(113\) 4.34206 0.408467 0.204233 0.978922i \(-0.434530\pi\)
0.204233 + 0.978922i \(0.434530\pi\)
\(114\) 0 0
\(115\) −5.73955 −0.535216
\(116\) −10.3975 −0.965383
\(117\) 0 0
\(118\) 4.39749 0.404822
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 11.9553 1.08238
\(123\) 0 0
\(124\) 6.34206 0.569534
\(125\) −11.9339 −1.06740
\(126\) 0 0
\(127\) −0.442200 −0.0392389 −0.0196195 0.999808i \(-0.506245\pi\)
−0.0196195 + 0.999808i \(0.506245\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 2.34206 0.204627 0.102313 0.994752i \(-0.467376\pi\)
0.102313 + 0.994752i \(0.467376\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −2.94457 −0.254372
\(135\) 0 0
\(136\) −7.34206 −0.629576
\(137\) −3.22646 −0.275655 −0.137828 0.990456i \(-0.544012\pi\)
−0.137828 + 0.990456i \(0.544012\pi\)
\(138\) 0 0
\(139\) 18.3975 1.56045 0.780227 0.625496i \(-0.215103\pi\)
0.780227 + 0.625496i \(0.215103\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 15.5131 1.30183
\(143\) 0 0
\(144\) 0 0
\(145\) −16.7735 −1.39297
\(146\) 5.11560 0.423370
\(147\) 0 0
\(148\) 2.82897 0.232540
\(149\) −19.6239 −1.60766 −0.803828 0.594861i \(-0.797207\pi\)
−0.803828 + 0.594861i \(0.797207\pi\)
\(150\) 0 0
\(151\) −0.331340 −0.0269641 −0.0134820 0.999909i \(-0.504292\pi\)
−0.0134820 + 0.999909i \(0.504292\pi\)
\(152\) −1.17103 −0.0949831
\(153\) 0 0
\(154\) 0 0
\(155\) 10.2312 0.821790
\(156\) 0 0
\(157\) 19.9660 1.59346 0.796730 0.604335i \(-0.206561\pi\)
0.796730 + 0.604335i \(0.206561\pi\)
\(158\) −5.61323 −0.446565
\(159\) 0 0
\(160\) −1.61323 −0.127537
\(161\) 0 0
\(162\) 0 0
\(163\) 21.2866 1.66730 0.833649 0.552295i \(-0.186248\pi\)
0.833649 + 0.552295i \(0.186248\pi\)
\(164\) −4.94457 −0.386106
\(165\) 0 0
\(166\) 5.05543 0.392377
\(167\) −22.0214 −1.70407 −0.852035 0.523485i \(-0.824632\pi\)
−0.852035 + 0.523485i \(0.824632\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) −11.8444 −0.908426
\(171\) 0 0
\(172\) −11.5131 −0.877865
\(173\) −1.65794 −0.126051 −0.0630254 0.998012i \(-0.520075\pi\)
−0.0630254 + 0.998012i \(0.520075\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −0.773540 −0.0579793
\(179\) −15.0602 −1.12565 −0.562825 0.826576i \(-0.690285\pi\)
−0.562825 + 0.826576i \(0.690285\pi\)
\(180\) 0 0
\(181\) 15.1156 1.12353 0.561767 0.827296i \(-0.310122\pi\)
0.561767 + 0.827296i \(0.310122\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.55780 0.262284
\(185\) 4.56378 0.335536
\(186\) 0 0
\(187\) 7.34206 0.536905
\(188\) −6.78426 −0.494793
\(189\) 0 0
\(190\) −1.88914 −0.137053
\(191\) 4.77354 0.345401 0.172701 0.984974i \(-0.444751\pi\)
0.172701 + 0.984974i \(0.444751\pi\)
\(192\) 0 0
\(193\) 3.11560 0.224266 0.112133 0.993693i \(-0.464232\pi\)
0.112133 + 0.993693i \(0.464232\pi\)
\(194\) −7.00000 −0.502571
\(195\) 0 0
\(196\) 0 0
\(197\) 4.82897 0.344050 0.172025 0.985093i \(-0.444969\pi\)
0.172025 + 0.985093i \(0.444969\pi\)
\(198\) 0 0
\(199\) 5.88914 0.417470 0.208735 0.977972i \(-0.433065\pi\)
0.208735 + 0.977972i \(0.433065\pi\)
\(200\) 2.39749 0.169528
\(201\) 0 0
\(202\) 13.6239 0.958578
\(203\) 0 0
\(204\) 0 0
\(205\) −7.97673 −0.557119
\(206\) 12.3421 0.859912
\(207\) 0 0
\(208\) 0 0
\(209\) 1.17103 0.0810018
\(210\) 0 0
\(211\) −13.6794 −0.941727 −0.470864 0.882206i \(-0.656058\pi\)
−0.470864 + 0.882206i \(0.656058\pi\)
\(212\) −8.00000 −0.549442
\(213\) 0 0
\(214\) −15.7395 −1.07593
\(215\) −18.5733 −1.26669
\(216\) 0 0
\(217\) 0 0
\(218\) −3.95529 −0.267886
\(219\) 0 0
\(220\) 1.61323 0.108764
\(221\) 0 0
\(222\) 0 0
\(223\) −5.11560 −0.342566 −0.171283 0.985222i \(-0.554791\pi\)
−0.171283 + 0.985222i \(0.554791\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.34206 −0.288830
\(227\) 5.28663 0.350886 0.175443 0.984490i \(-0.443864\pi\)
0.175443 + 0.984490i \(0.443864\pi\)
\(228\) 0 0
\(229\) −4.88440 −0.322770 −0.161385 0.986892i \(-0.551596\pi\)
−0.161385 + 0.986892i \(0.551596\pi\)
\(230\) 5.73955 0.378455
\(231\) 0 0
\(232\) 10.3975 0.682629
\(233\) −9.79498 −0.641690 −0.320845 0.947132i \(-0.603967\pi\)
−0.320845 + 0.947132i \(0.603967\pi\)
\(234\) 0 0
\(235\) −10.9446 −0.713945
\(236\) −4.39749 −0.286252
\(237\) 0 0
\(238\) 0 0
\(239\) 23.9106 1.54665 0.773323 0.634012i \(-0.218593\pi\)
0.773323 + 0.634012i \(0.218593\pi\)
\(240\) 0 0
\(241\) 1.88914 0.121690 0.0608451 0.998147i \(-0.480620\pi\)
0.0608451 + 0.998147i \(0.480620\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 0 0
\(244\) −11.9553 −0.765359
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −6.34206 −0.402721
\(249\) 0 0
\(250\) 11.9339 0.754763
\(251\) −0.939830 −0.0593215 −0.0296608 0.999560i \(-0.509443\pi\)
−0.0296608 + 0.999560i \(0.509443\pi\)
\(252\) 0 0
\(253\) −3.55780 −0.223677
\(254\) 0.442200 0.0277461
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 11.2265 0.700287 0.350144 0.936696i \(-0.386133\pi\)
0.350144 + 0.936696i \(0.386133\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −2.34206 −0.144693
\(263\) 1.22646 0.0756267 0.0378134 0.999285i \(-0.487961\pi\)
0.0378134 + 0.999285i \(0.487961\pi\)
\(264\) 0 0
\(265\) −12.9058 −0.792799
\(266\) 0 0
\(267\) 0 0
\(268\) 2.94457 0.179868
\(269\) −9.50237 −0.579370 −0.289685 0.957122i \(-0.593551\pi\)
−0.289685 + 0.957122i \(0.593551\pi\)
\(270\) 0 0
\(271\) 3.22646 0.195993 0.0979967 0.995187i \(-0.468757\pi\)
0.0979967 + 0.995187i \(0.468757\pi\)
\(272\) 7.34206 0.445178
\(273\) 0 0
\(274\) 3.22646 0.194918
\(275\) −2.39749 −0.144574
\(276\) 0 0
\(277\) −16.0000 −0.961347 −0.480673 0.876900i \(-0.659608\pi\)
−0.480673 + 0.876900i \(0.659608\pi\)
\(278\) −18.3975 −1.10341
\(279\) 0 0
\(280\) 0 0
\(281\) 11.2312 0.669997 0.334999 0.942219i \(-0.391264\pi\)
0.334999 + 0.942219i \(0.391264\pi\)
\(282\) 0 0
\(283\) −25.4577 −1.51330 −0.756650 0.653820i \(-0.773165\pi\)
−0.756650 + 0.653820i \(0.773165\pi\)
\(284\) −15.5131 −0.920532
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 36.9058 2.17093
\(290\) 16.7735 0.984976
\(291\) 0 0
\(292\) −5.11560 −0.299368
\(293\) −17.9446 −1.04833 −0.524166 0.851616i \(-0.675623\pi\)
−0.524166 + 0.851616i \(0.675623\pi\)
\(294\) 0 0
\(295\) −7.09416 −0.413038
\(296\) −2.82897 −0.164431
\(297\) 0 0
\(298\) 19.6239 1.13678
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0.331340 0.0190665
\(303\) 0 0
\(304\) 1.17103 0.0671632
\(305\) −19.2866 −1.10435
\(306\) 0 0
\(307\) −33.0262 −1.88490 −0.942452 0.334342i \(-0.891486\pi\)
−0.942452 + 0.334342i \(0.891486\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −10.2312 −0.581093
\(311\) 0.331340 0.0187886 0.00939429 0.999956i \(-0.497010\pi\)
0.00939429 + 0.999956i \(0.497010\pi\)
\(312\) 0 0
\(313\) −14.3975 −0.813794 −0.406897 0.913474i \(-0.633389\pi\)
−0.406897 + 0.913474i \(0.633389\pi\)
\(314\) −19.9660 −1.12675
\(315\) 0 0
\(316\) 5.61323 0.315769
\(317\) −17.5238 −0.984235 −0.492118 0.870529i \(-0.663777\pi\)
−0.492118 + 0.870529i \(0.663777\pi\)
\(318\) 0 0
\(319\) −10.3975 −0.582148
\(320\) 1.61323 0.0901823
\(321\) 0 0
\(322\) 0 0
\(323\) 8.59777 0.478393
\(324\) 0 0
\(325\) 0 0
\(326\) −21.2866 −1.17896
\(327\) 0 0
\(328\) 4.94457 0.273018
\(329\) 0 0
\(330\) 0 0
\(331\) −8.94457 −0.491638 −0.245819 0.969316i \(-0.579057\pi\)
−0.245819 + 0.969316i \(0.579057\pi\)
\(332\) −5.05543 −0.277453
\(333\) 0 0
\(334\) 22.0214 1.20496
\(335\) 4.75027 0.259535
\(336\) 0 0
\(337\) −3.33732 −0.181795 −0.0908977 0.995860i \(-0.528974\pi\)
−0.0908977 + 0.995860i \(0.528974\pi\)
\(338\) 13.0000 0.707107
\(339\) 0 0
\(340\) 11.8444 0.642354
\(341\) 6.34206 0.343442
\(342\) 0 0
\(343\) 0 0
\(344\) 11.5131 0.620744
\(345\) 0 0
\(346\) 1.65794 0.0891314
\(347\) 30.4237 1.63323 0.816614 0.577184i \(-0.195849\pi\)
0.816614 + 0.577184i \(0.195849\pi\)
\(348\) 0 0
\(349\) 17.5238 0.938028 0.469014 0.883191i \(-0.344609\pi\)
0.469014 + 0.883191i \(0.344609\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) −5.11560 −0.272276 −0.136138 0.990690i \(-0.543469\pi\)
−0.136138 + 0.990690i \(0.543469\pi\)
\(354\) 0 0
\(355\) −25.0262 −1.32825
\(356\) 0.773540 0.0409976
\(357\) 0 0
\(358\) 15.0602 0.795955
\(359\) 30.6841 1.61945 0.809723 0.586812i \(-0.199617\pi\)
0.809723 + 0.586812i \(0.199617\pi\)
\(360\) 0 0
\(361\) −17.6287 −0.927826
\(362\) −15.1156 −0.794458
\(363\) 0 0
\(364\) 0 0
\(365\) −8.25264 −0.431963
\(366\) 0 0
\(367\) 1.45766 0.0760892 0.0380446 0.999276i \(-0.487887\pi\)
0.0380446 + 0.999276i \(0.487887\pi\)
\(368\) −3.55780 −0.185463
\(369\) 0 0
\(370\) −4.56378 −0.237260
\(371\) 0 0
\(372\) 0 0
\(373\) −34.1865 −1.77011 −0.885055 0.465487i \(-0.845879\pi\)
−0.885055 + 0.465487i \(0.845879\pi\)
\(374\) −7.34206 −0.379649
\(375\) 0 0
\(376\) 6.78426 0.349871
\(377\) 0 0
\(378\) 0 0
\(379\) −9.28663 −0.477022 −0.238511 0.971140i \(-0.576659\pi\)
−0.238511 + 0.971140i \(0.576659\pi\)
\(380\) 1.88914 0.0969108
\(381\) 0 0
\(382\) −4.77354 −0.244236
\(383\) 3.62395 0.185175 0.0925876 0.995705i \(-0.470486\pi\)
0.0925876 + 0.995705i \(0.470486\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3.11560 −0.158580
\(387\) 0 0
\(388\) 7.00000 0.355371
\(389\) −7.16031 −0.363042 −0.181521 0.983387i \(-0.558102\pi\)
−0.181521 + 0.983387i \(0.558102\pi\)
\(390\) 0 0
\(391\) −26.1216 −1.32103
\(392\) 0 0
\(393\) 0 0
\(394\) −4.82897 −0.243280
\(395\) 9.05543 0.455628
\(396\) 0 0
\(397\) −30.3975 −1.52561 −0.762803 0.646631i \(-0.776177\pi\)
−0.762803 + 0.646631i \(0.776177\pi\)
\(398\) −5.88914 −0.295196
\(399\) 0 0
\(400\) −2.39749 −0.119874
\(401\) 12.0214 0.600322 0.300161 0.953889i \(-0.402960\pi\)
0.300161 + 0.953889i \(0.402960\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −13.6239 −0.677817
\(405\) 0 0
\(406\) 0 0
\(407\) 2.82897 0.140227
\(408\) 0 0
\(409\) 17.5685 0.868707 0.434354 0.900742i \(-0.356977\pi\)
0.434354 + 0.900742i \(0.356977\pi\)
\(410\) 7.97673 0.393943
\(411\) 0 0
\(412\) −12.3421 −0.608050
\(413\) 0 0
\(414\) 0 0
\(415\) −8.15557 −0.400341
\(416\) 0 0
\(417\) 0 0
\(418\) −1.17103 −0.0572769
\(419\) 27.1710 1.32739 0.663696 0.748003i \(-0.268987\pi\)
0.663696 + 0.748003i \(0.268987\pi\)
\(420\) 0 0
\(421\) 23.1710 1.12929 0.564643 0.825335i \(-0.309014\pi\)
0.564643 + 0.825335i \(0.309014\pi\)
\(422\) 13.6794 0.665902
\(423\) 0 0
\(424\) 8.00000 0.388514
\(425\) −17.6025 −0.853847
\(426\) 0 0
\(427\) 0 0
\(428\) 15.7395 0.760800
\(429\) 0 0
\(430\) 18.5733 0.895682
\(431\) 16.7735 0.807953 0.403977 0.914769i \(-0.367628\pi\)
0.403977 + 0.914769i \(0.367628\pi\)
\(432\) 0 0
\(433\) 17.3421 0.833406 0.416703 0.909043i \(-0.363185\pi\)
0.416703 + 0.909043i \(0.363185\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 3.95529 0.189424
\(437\) −4.16629 −0.199301
\(438\) 0 0
\(439\) 33.1478 1.58206 0.791028 0.611780i \(-0.209546\pi\)
0.791028 + 0.611780i \(0.209546\pi\)
\(440\) −1.61323 −0.0769077
\(441\) 0 0
\(442\) 0 0
\(443\) 12.0554 0.572771 0.286385 0.958115i \(-0.407546\pi\)
0.286385 + 0.958115i \(0.407546\pi\)
\(444\) 0 0
\(445\) 1.24790 0.0591561
\(446\) 5.11560 0.242231
\(447\) 0 0
\(448\) 0 0
\(449\) 36.5947 1.72701 0.863505 0.504340i \(-0.168264\pi\)
0.863505 + 0.504340i \(0.168264\pi\)
\(450\) 0 0
\(451\) −4.94457 −0.232831
\(452\) 4.34206 0.204233
\(453\) 0 0
\(454\) −5.28663 −0.248114
\(455\) 0 0
\(456\) 0 0
\(457\) 37.8212 1.76920 0.884600 0.466351i \(-0.154432\pi\)
0.884600 + 0.466351i \(0.154432\pi\)
\(458\) 4.88440 0.228233
\(459\) 0 0
\(460\) −5.73955 −0.267608
\(461\) −34.9707 −1.62875 −0.814375 0.580339i \(-0.802920\pi\)
−0.814375 + 0.580339i \(0.802920\pi\)
\(462\) 0 0
\(463\) 7.56852 0.351739 0.175869 0.984413i \(-0.443726\pi\)
0.175869 + 0.984413i \(0.443726\pi\)
\(464\) −10.3975 −0.482691
\(465\) 0 0
\(466\) 9.79498 0.453744
\(467\) 14.6287 0.676935 0.338468 0.940978i \(-0.390091\pi\)
0.338468 + 0.940978i \(0.390091\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 10.9446 0.504835
\(471\) 0 0
\(472\) 4.39749 0.202411
\(473\) −11.5131 −0.529372
\(474\) 0 0
\(475\) −2.80753 −0.128818
\(476\) 0 0
\(477\) 0 0
\(478\) −23.9106 −1.09364
\(479\) 1.22646 0.0560384 0.0280192 0.999607i \(-0.491080\pi\)
0.0280192 + 0.999607i \(0.491080\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −1.88914 −0.0860480
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 11.2926 0.512771
\(486\) 0 0
\(487\) 30.7056 1.39140 0.695701 0.718332i \(-0.255094\pi\)
0.695701 + 0.718332i \(0.255094\pi\)
\(488\) 11.9553 0.541191
\(489\) 0 0
\(490\) 0 0
\(491\) −30.9446 −1.39651 −0.698254 0.715850i \(-0.746040\pi\)
−0.698254 + 0.715850i \(0.746040\pi\)
\(492\) 0 0
\(493\) −76.3390 −3.43814
\(494\) 0 0
\(495\) 0 0
\(496\) 6.34206 0.284767
\(497\) 0 0
\(498\) 0 0
\(499\) −10.3421 −0.462974 −0.231487 0.972838i \(-0.574359\pi\)
−0.231487 + 0.972838i \(0.574359\pi\)
\(500\) −11.9339 −0.533698
\(501\) 0 0
\(502\) 0.939830 0.0419467
\(503\) −4.66268 −0.207899 −0.103949 0.994583i \(-0.533148\pi\)
−0.103949 + 0.994583i \(0.533148\pi\)
\(504\) 0 0
\(505\) −21.9786 −0.978033
\(506\) 3.55780 0.158163
\(507\) 0 0
\(508\) −0.442200 −0.0196195
\(509\) −25.5900 −1.13425 −0.567127 0.823630i \(-0.691945\pi\)
−0.567127 + 0.823630i \(0.691945\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −11.2265 −0.495178
\(515\) −19.9106 −0.877365
\(516\) 0 0
\(517\) −6.78426 −0.298371
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 30.3635 1.32770 0.663852 0.747864i \(-0.268921\pi\)
0.663852 + 0.747864i \(0.268921\pi\)
\(524\) 2.34206 0.102313
\(525\) 0 0
\(526\) −1.22646 −0.0534762
\(527\) 46.5638 2.02835
\(528\) 0 0
\(529\) −10.3421 −0.449655
\(530\) 12.9058 0.560594
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 25.3915 1.09777
\(536\) −2.94457 −0.127186
\(537\) 0 0
\(538\) 9.50237 0.409676
\(539\) 0 0
\(540\) 0 0
\(541\) 1.61323 0.0693582 0.0346791 0.999398i \(-0.488959\pi\)
0.0346791 + 0.999398i \(0.488959\pi\)
\(542\) −3.22646 −0.138588
\(543\) 0 0
\(544\) −7.34206 −0.314788
\(545\) 6.38079 0.273323
\(546\) 0 0
\(547\) 15.7348 0.672772 0.336386 0.941724i \(-0.390795\pi\)
0.336386 + 0.941724i \(0.390795\pi\)
\(548\) −3.22646 −0.137828
\(549\) 0 0
\(550\) 2.39749 0.102229
\(551\) −12.1758 −0.518705
\(552\) 0 0
\(553\) 0 0
\(554\) 16.0000 0.679775
\(555\) 0 0
\(556\) 18.3975 0.780227
\(557\) −11.2819 −0.478029 −0.239015 0.971016i \(-0.576824\pi\)
−0.239015 + 0.971016i \(0.576824\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −11.2312 −0.473760
\(563\) −20.9058 −0.881076 −0.440538 0.897734i \(-0.645212\pi\)
−0.440538 + 0.897734i \(0.645212\pi\)
\(564\) 0 0
\(565\) 7.00474 0.294692
\(566\) 25.4577 1.07007
\(567\) 0 0
\(568\) 15.5131 0.650915
\(569\) 7.83371 0.328406 0.164203 0.986427i \(-0.447495\pi\)
0.164203 + 0.986427i \(0.447495\pi\)
\(570\) 0 0
\(571\) 2.39749 0.100332 0.0501659 0.998741i \(-0.484025\pi\)
0.0501659 + 0.998741i \(0.484025\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.52979 0.355717
\(576\) 0 0
\(577\) 25.6287 1.06694 0.533468 0.845820i \(-0.320888\pi\)
0.533468 + 0.845820i \(0.320888\pi\)
\(578\) −36.9058 −1.53508
\(579\) 0 0
\(580\) −16.7735 −0.696483
\(581\) 0 0
\(582\) 0 0
\(583\) −8.00000 −0.331326
\(584\) 5.11560 0.211685
\(585\) 0 0
\(586\) 17.9446 0.741283
\(587\) −5.79972 −0.239380 −0.119690 0.992811i \(-0.538190\pi\)
−0.119690 + 0.992811i \(0.538190\pi\)
\(588\) 0 0
\(589\) 7.42674 0.306014
\(590\) 7.09416 0.292062
\(591\) 0 0
\(592\) 2.82897 0.116270
\(593\) −31.1925 −1.28092 −0.640461 0.767991i \(-0.721257\pi\)
−0.640461 + 0.767991i \(0.721257\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −19.6239 −0.803828
\(597\) 0 0
\(598\) 0 0
\(599\) 31.2926 1.27858 0.639291 0.768965i \(-0.279228\pi\)
0.639291 + 0.768965i \(0.279228\pi\)
\(600\) 0 0
\(601\) −22.1203 −0.902307 −0.451154 0.892446i \(-0.648987\pi\)
−0.451154 + 0.892446i \(0.648987\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.331340 −0.0134820
\(605\) 1.61323 0.0655871
\(606\) 0 0
\(607\) −20.6180 −0.836858 −0.418429 0.908250i \(-0.637419\pi\)
−0.418429 + 0.908250i \(0.637419\pi\)
\(608\) −1.17103 −0.0474915
\(609\) 0 0
\(610\) 19.2866 0.780893
\(611\) 0 0
\(612\) 0 0
\(613\) −15.7550 −0.636339 −0.318169 0.948034i \(-0.603068\pi\)
−0.318169 + 0.948034i \(0.603068\pi\)
\(614\) 33.0262 1.33283
\(615\) 0 0
\(616\) 0 0
\(617\) −34.2526 −1.37896 −0.689480 0.724305i \(-0.742161\pi\)
−0.689480 + 0.724305i \(0.742161\pi\)
\(618\) 0 0
\(619\) −21.9707 −0.883079 −0.441539 0.897242i \(-0.645567\pi\)
−0.441539 + 0.897242i \(0.645567\pi\)
\(620\) 10.2312 0.410895
\(621\) 0 0
\(622\) −0.331340 −0.0132855
\(623\) 0 0
\(624\) 0 0
\(625\) −7.26460 −0.290584
\(626\) 14.3975 0.575439
\(627\) 0 0
\(628\) 19.9660 0.796730
\(629\) 20.7705 0.828173
\(630\) 0 0
\(631\) −27.5685 −1.09749 −0.548743 0.835991i \(-0.684893\pi\)
−0.548743 + 0.835991i \(0.684893\pi\)
\(632\) −5.61323 −0.223282
\(633\) 0 0
\(634\) 17.5238 0.695959
\(635\) −0.713370 −0.0283092
\(636\) 0 0
\(637\) 0 0
\(638\) 10.3975 0.411641
\(639\) 0 0
\(640\) −1.61323 −0.0637685
\(641\) −5.65794 −0.223475 −0.111738 0.993738i \(-0.535642\pi\)
−0.111738 + 0.993738i \(0.535642\pi\)
\(642\) 0 0
\(643\) 17.4791 0.689308 0.344654 0.938730i \(-0.387996\pi\)
0.344654 + 0.938730i \(0.387996\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8.59777 −0.338275
\(647\) 8.83969 0.347524 0.173762 0.984788i \(-0.444408\pi\)
0.173762 + 0.984788i \(0.444408\pi\)
\(648\) 0 0
\(649\) −4.39749 −0.172617
\(650\) 0 0
\(651\) 0 0
\(652\) 21.2866 0.833649
\(653\) 24.7503 0.968553 0.484276 0.874915i \(-0.339083\pi\)
0.484276 + 0.874915i \(0.339083\pi\)
\(654\) 0 0
\(655\) 3.77828 0.147630
\(656\) −4.94457 −0.193053
\(657\) 0 0
\(658\) 0 0
\(659\) −5.62869 −0.219263 −0.109631 0.993972i \(-0.534967\pi\)
−0.109631 + 0.993972i \(0.534967\pi\)
\(660\) 0 0
\(661\) −13.4022 −0.521286 −0.260643 0.965435i \(-0.583935\pi\)
−0.260643 + 0.965435i \(0.583935\pi\)
\(662\) 8.94457 0.347641
\(663\) 0 0
\(664\) 5.05543 0.196189
\(665\) 0 0
\(666\) 0 0
\(667\) 36.9922 1.43234
\(668\) −22.0214 −0.852035
\(669\) 0 0
\(670\) −4.75027 −0.183519
\(671\) −11.9553 −0.461529
\(672\) 0 0
\(673\) −29.0262 −1.11888 −0.559438 0.828872i \(-0.688983\pi\)
−0.559438 + 0.828872i \(0.688983\pi\)
\(674\) 3.33732 0.128549
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) 20.3081 0.780502 0.390251 0.920708i \(-0.372388\pi\)
0.390251 + 0.920708i \(0.372388\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −11.8444 −0.454213
\(681\) 0 0
\(682\) −6.34206 −0.242850
\(683\) 10.7395 0.410937 0.205469 0.978664i \(-0.434128\pi\)
0.205469 + 0.978664i \(0.434128\pi\)
\(684\) 0 0
\(685\) −5.20502 −0.198874
\(686\) 0 0
\(687\) 0 0
\(688\) −11.5131 −0.438932
\(689\) 0 0
\(690\) 0 0
\(691\) 5.97075 0.227138 0.113569 0.993530i \(-0.463772\pi\)
0.113569 + 0.993530i \(0.463772\pi\)
\(692\) −1.65794 −0.0630254
\(693\) 0 0
\(694\) −30.4237 −1.15487
\(695\) 29.6794 1.12580
\(696\) 0 0
\(697\) −36.3033 −1.37509
\(698\) −17.5238 −0.663286
\(699\) 0 0
\(700\) 0 0
\(701\) 5.28189 0.199494 0.0997471 0.995013i \(-0.468197\pi\)
0.0997471 + 0.995013i \(0.468197\pi\)
\(702\) 0 0
\(703\) 3.31281 0.124945
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 5.11560 0.192528
\(707\) 0 0
\(708\) 0 0
\(709\) 39.3128 1.47642 0.738212 0.674569i \(-0.235671\pi\)
0.738212 + 0.674569i \(0.235671\pi\)
\(710\) 25.0262 0.939216
\(711\) 0 0
\(712\) −0.773540 −0.0289896
\(713\) −22.5638 −0.845020
\(714\) 0 0
\(715\) 0 0
\(716\) −15.0602 −0.562825
\(717\) 0 0
\(718\) −30.6841 −1.14512
\(719\) 35.3575 1.31861 0.659306 0.751874i \(-0.270850\pi\)
0.659306 + 0.751874i \(0.270850\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 17.6287 0.656072
\(723\) 0 0
\(724\) 15.1156 0.561767
\(725\) 24.9279 0.925798
\(726\) 0 0
\(727\) −40.2312 −1.49209 −0.746046 0.665894i \(-0.768050\pi\)
−0.746046 + 0.665894i \(0.768050\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 8.25264 0.305444
\(731\) −84.5298 −3.12645
\(732\) 0 0
\(733\) 28.7288 1.06112 0.530562 0.847646i \(-0.321981\pi\)
0.530562 + 0.847646i \(0.321981\pi\)
\(734\) −1.45766 −0.0538032
\(735\) 0 0
\(736\) 3.55780 0.131142
\(737\) 2.94457 0.108465
\(738\) 0 0
\(739\) −16.3421 −0.601152 −0.300576 0.953758i \(-0.597179\pi\)
−0.300576 + 0.953758i \(0.597179\pi\)
\(740\) 4.56378 0.167768
\(741\) 0 0
\(742\) 0 0
\(743\) −45.3897 −1.66519 −0.832593 0.553885i \(-0.813145\pi\)
−0.832593 + 0.553885i \(0.813145\pi\)
\(744\) 0 0
\(745\) −31.6579 −1.15986
\(746\) 34.1865 1.25166
\(747\) 0 0
\(748\) 7.34206 0.268452
\(749\) 0 0
\(750\) 0 0
\(751\) −27.7997 −1.01443 −0.507213 0.861821i \(-0.669324\pi\)
−0.507213 + 0.861821i \(0.669324\pi\)
\(752\) −6.78426 −0.247396
\(753\) 0 0
\(754\) 0 0
\(755\) −0.534528 −0.0194535
\(756\) 0 0
\(757\) 19.0816 0.693533 0.346766 0.937952i \(-0.387280\pi\)
0.346766 + 0.937952i \(0.387280\pi\)
\(758\) 9.28663 0.337306
\(759\) 0 0
\(760\) −1.88914 −0.0685263
\(761\) −47.2186 −1.71167 −0.855837 0.517245i \(-0.826958\pi\)
−0.855837 + 0.517245i \(0.826958\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 4.77354 0.172701
\(765\) 0 0
\(766\) −3.62395 −0.130939
\(767\) 0 0
\(768\) 0 0
\(769\) −9.56852 −0.345050 −0.172525 0.985005i \(-0.555192\pi\)
−0.172525 + 0.985005i \(0.555192\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.11560 0.112133
\(773\) −15.9553 −0.573872 −0.286936 0.957950i \(-0.592637\pi\)
−0.286936 + 0.957950i \(0.592637\pi\)
\(774\) 0 0
\(775\) −15.2050 −0.546180
\(776\) −7.00000 −0.251285
\(777\) 0 0
\(778\) 7.16031 0.256710
\(779\) −5.79024 −0.207457
\(780\) 0 0
\(781\) −15.5131 −0.555102
\(782\) 26.1216 0.934106
\(783\) 0 0
\(784\) 0 0
\(785\) 32.2098 1.14962
\(786\) 0 0
\(787\) 49.8551 1.77714 0.888572 0.458737i \(-0.151698\pi\)
0.888572 + 0.458737i \(0.151698\pi\)
\(788\) 4.82897 0.172025
\(789\) 0 0
\(790\) −9.05543 −0.322178
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 30.3975 1.07877
\(795\) 0 0
\(796\) 5.88914 0.208735
\(797\) −36.4177 −1.28998 −0.644990 0.764191i \(-0.723139\pi\)
−0.644990 + 0.764191i \(0.723139\pi\)
\(798\) 0 0
\(799\) −49.8104 −1.76217
\(800\) 2.39749 0.0847641
\(801\) 0 0
\(802\) −12.0214 −0.424492
\(803\) −5.11560 −0.180526
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 13.6239 0.479289
\(809\) −48.4237 −1.70249 −0.851243 0.524772i \(-0.824151\pi\)
−0.851243 + 0.524772i \(0.824151\pi\)
\(810\) 0 0
\(811\) −41.0262 −1.44062 −0.720312 0.693650i \(-0.756001\pi\)
−0.720312 + 0.693650i \(0.756001\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −2.82897 −0.0991554
\(815\) 34.3402 1.20289
\(816\) 0 0
\(817\) −13.4822 −0.471681
\(818\) −17.5685 −0.614269
\(819\) 0 0
\(820\) −7.97673 −0.278559
\(821\) −39.9320 −1.39364 −0.696819 0.717247i \(-0.745402\pi\)
−0.696819 + 0.717247i \(0.745402\pi\)
\(822\) 0 0
\(823\) −15.7997 −0.550744 −0.275372 0.961338i \(-0.588801\pi\)
−0.275372 + 0.961338i \(0.588801\pi\)
\(824\) 12.3421 0.429956
\(825\) 0 0
\(826\) 0 0
\(827\) 26.8766 0.934591 0.467295 0.884101i \(-0.345229\pi\)
0.467295 + 0.884101i \(0.345229\pi\)
\(828\) 0 0
\(829\) −8.30807 −0.288551 −0.144276 0.989538i \(-0.546085\pi\)
−0.144276 + 0.989538i \(0.546085\pi\)
\(830\) 8.15557 0.283084
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −35.5256 −1.22942
\(836\) 1.17103 0.0405009
\(837\) 0 0
\(838\) −27.1710 −0.938608
\(839\) 4.28787 0.148034 0.0740168 0.997257i \(-0.476418\pi\)
0.0740168 + 0.997257i \(0.476418\pi\)
\(840\) 0 0
\(841\) 79.1078 2.72785
\(842\) −23.1710 −0.798526
\(843\) 0 0
\(844\) −13.6794 −0.470864
\(845\) −20.9720 −0.721458
\(846\) 0 0
\(847\) 0 0
\(848\) −8.00000 −0.274721
\(849\) 0 0
\(850\) 17.6025 0.603761
\(851\) −10.0649 −0.345021
\(852\) 0 0
\(853\) −46.2973 −1.58519 −0.792596 0.609748i \(-0.791271\pi\)
−0.792596 + 0.609748i \(0.791271\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −15.7395 −0.537967
\(857\) 27.4624 0.938098 0.469049 0.883172i \(-0.344597\pi\)
0.469049 + 0.883172i \(0.344597\pi\)
\(858\) 0 0
\(859\) −12.1925 −0.416002 −0.208001 0.978129i \(-0.566696\pi\)
−0.208001 + 0.978129i \(0.566696\pi\)
\(860\) −18.5733 −0.633343
\(861\) 0 0
\(862\) −16.7735 −0.571309
\(863\) −0.839690 −0.0285834 −0.0142917 0.999898i \(-0.504549\pi\)
−0.0142917 + 0.999898i \(0.504549\pi\)
\(864\) 0 0
\(865\) −2.67464 −0.0909405
\(866\) −17.3421 −0.589307
\(867\) 0 0
\(868\) 0 0
\(869\) 5.61323 0.190416
\(870\) 0 0
\(871\) 0 0
\(872\) −3.95529 −0.133943
\(873\) 0 0
\(874\) 4.16629 0.140927
\(875\) 0 0
\(876\) 0 0
\(877\) −20.5285 −0.693200 −0.346600 0.938013i \(-0.612664\pi\)
−0.346600 + 0.938013i \(0.612664\pi\)
\(878\) −33.1478 −1.11868
\(879\) 0 0
\(880\) 1.61323 0.0543820
\(881\) −1.88914 −0.0636468 −0.0318234 0.999494i \(-0.510131\pi\)
−0.0318234 + 0.999494i \(0.510131\pi\)
\(882\) 0 0
\(883\) 26.5345 0.892958 0.446479 0.894794i \(-0.352678\pi\)
0.446479 + 0.894794i \(0.352678\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −12.0554 −0.405010
\(887\) −17.1156 −0.574686 −0.287343 0.957828i \(-0.592772\pi\)
−0.287343 + 0.957828i \(0.592772\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −1.24790 −0.0418296
\(891\) 0 0
\(892\) −5.11560 −0.171283
\(893\) −7.94457 −0.265855
\(894\) 0 0
\(895\) −24.2955 −0.812110
\(896\) 0 0
\(897\) 0 0
\(898\) −36.5947 −1.22118
\(899\) −65.9415 −2.19927
\(900\) 0 0
\(901\) −58.7365 −1.95680
\(902\) 4.94457 0.164636
\(903\) 0 0
\(904\) −4.34206 −0.144415
\(905\) 24.3849 0.810583
\(906\) 0 0
\(907\) 3.28663 0.109131 0.0545654 0.998510i \(-0.482623\pi\)
0.0545654 + 0.998510i \(0.482623\pi\)
\(908\) 5.28663 0.175443
\(909\) 0 0
\(910\) 0 0
\(911\) −14.0107 −0.464196 −0.232098 0.972692i \(-0.574559\pi\)
−0.232098 + 0.972692i \(0.574559\pi\)
\(912\) 0 0
\(913\) −5.05543 −0.167310
\(914\) −37.8212 −1.25101
\(915\) 0 0
\(916\) −4.88440 −0.161385
\(917\) 0 0
\(918\) 0 0
\(919\) −46.5160 −1.53442 −0.767211 0.641395i \(-0.778356\pi\)
−0.767211 + 0.641395i \(0.778356\pi\)
\(920\) 5.73955 0.189227
\(921\) 0 0
\(922\) 34.9707 1.15170
\(923\) 0 0
\(924\) 0 0
\(925\) −6.78243 −0.223005
\(926\) −7.56852 −0.248717
\(927\) 0 0
\(928\) 10.3975 0.341314
\(929\) 24.8844 0.816431 0.408215 0.912886i \(-0.366151\pi\)
0.408215 + 0.912886i \(0.366151\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −9.79498 −0.320845
\(933\) 0 0
\(934\) −14.6287 −0.478665
\(935\) 11.8444 0.387354
\(936\) 0 0
\(937\) −46.7950 −1.52873 −0.764363 0.644787i \(-0.776946\pi\)
−0.764363 + 0.644787i \(0.776946\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −10.9446 −0.356973
\(941\) −17.4917 −0.570212 −0.285106 0.958496i \(-0.592029\pi\)
−0.285106 + 0.958496i \(0.592029\pi\)
\(942\) 0 0
\(943\) 17.5918 0.572868
\(944\) −4.39749 −0.143126
\(945\) 0 0
\(946\) 11.5131 0.374323
\(947\) −14.6192 −0.475060 −0.237530 0.971380i \(-0.576338\pi\)
−0.237530 + 0.971380i \(0.576338\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 2.80753 0.0910884
\(951\) 0 0
\(952\) 0 0
\(953\) 20.0816 0.650507 0.325254 0.945627i \(-0.394550\pi\)
0.325254 + 0.945627i \(0.394550\pi\)
\(954\) 0 0
\(955\) 7.70082 0.249193
\(956\) 23.9106 0.773323
\(957\) 0 0
\(958\) −1.22646 −0.0396251
\(959\) 0 0
\(960\) 0 0
\(961\) 9.22172 0.297475
\(962\) 0 0
\(963\) 0 0
\(964\) 1.88914 0.0608451
\(965\) 5.02618 0.161798
\(966\) 0 0
\(967\) −60.2634 −1.93794 −0.968969 0.247180i \(-0.920496\pi\)
−0.968969 + 0.247180i \(0.920496\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 0 0
\(970\) −11.2926 −0.362584
\(971\) 52.8473 1.69595 0.847976 0.530035i \(-0.177821\pi\)
0.847976 + 0.530035i \(0.177821\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −30.7056 −0.983870
\(975\) 0 0
\(976\) −11.9553 −0.382679
\(977\) −24.9058 −0.796808 −0.398404 0.917210i \(-0.630436\pi\)
−0.398404 + 0.917210i \(0.630436\pi\)
\(978\) 0 0
\(979\) 0.773540 0.0247225
\(980\) 0 0
\(981\) 0 0
\(982\) 30.9446 0.987481
\(983\) 25.1263 0.801405 0.400703 0.916208i \(-0.368766\pi\)
0.400703 + 0.916208i \(0.368766\pi\)
\(984\) 0 0
\(985\) 7.79024 0.248218
\(986\) 76.3390 2.43113
\(987\) 0 0
\(988\) 0 0
\(989\) 40.9613 1.30249
\(990\) 0 0
\(991\) 57.9201 1.83989 0.919946 0.392046i \(-0.128233\pi\)
0.919946 + 0.392046i \(0.128233\pi\)
\(992\) −6.34206 −0.201361
\(993\) 0 0
\(994\) 0 0
\(995\) 9.50054 0.301187
\(996\) 0 0
\(997\) 17.3682 0.550058 0.275029 0.961436i \(-0.411313\pi\)
0.275029 + 0.961436i \(0.411313\pi\)
\(998\) 10.3421 0.327372
\(999\) 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 9702.2.a.dv.1.2 3
3.2 odd 2 3234.2.a.bf.1.2 3
7.2 even 3 1386.2.k.v.991.2 6
7.4 even 3 1386.2.k.v.793.2 6
7.6 odd 2 9702.2.a.dw.1.2 3
21.2 odd 6 462.2.i.g.67.2 6
21.11 odd 6 462.2.i.g.331.2 yes 6
21.20 even 2 3234.2.a.bh.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.i.g.67.2 6 21.2 odd 6
462.2.i.g.331.2 yes 6 21.11 odd 6
1386.2.k.v.793.2 6 7.4 even 3
1386.2.k.v.991.2 6 7.2 even 3
3234.2.a.bf.1.2 3 3.2 odd 2
3234.2.a.bh.1.2 3 21.20 even 2
9702.2.a.dv.1.2 3 1.1 even 1 trivial
9702.2.a.dw.1.2 3 7.6 odd 2