Properties

Label 9702.2.a.dw.1.2
Level $9702$
Weight $2$
Character 9702.1
Self dual yes
Analytic conductor $77.471$
Analytic rank $0$
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: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.2700.1
Defining polynomial: \(x^{3} - 15 x - 20\)
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

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.61323 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.61323 q^{5} -1.00000 q^{8} +1.61323 q^{10} +1.00000 q^{11} +1.00000 q^{16} -7.34206 q^{17} -1.17103 q^{19} -1.61323 q^{20} -1.00000 q^{22} -3.55780 q^{23} -2.39749 q^{25} -10.3975 q^{29} -6.34206 q^{31} -1.00000 q^{32} +7.34206 q^{34} +2.82897 q^{37} +1.17103 q^{38} +1.61323 q^{40} +4.94457 q^{41} -11.5131 q^{43} +1.00000 q^{44} +3.55780 q^{46} +6.78426 q^{47} +2.39749 q^{50} -8.00000 q^{53} -1.61323 q^{55} +10.3975 q^{58} +4.39749 q^{59} +11.9553 q^{61} +6.34206 q^{62} +1.00000 q^{64} +2.94457 q^{67} -7.34206 q^{68} -15.5131 q^{71} +5.11560 q^{73} -2.82897 q^{74} -1.17103 q^{76} +5.61323 q^{79} -1.61323 q^{80} -4.94457 q^{82} +5.05543 q^{83} +11.8444 q^{85} +11.5131 q^{86} -1.00000 q^{88} -0.773540 q^{89} -3.55780 q^{92} -6.78426 q^{94} +1.88914 q^{95} -7.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{2} + 3q^{4} - 3q^{8} + O(q^{10}) \) \( 3q - 3q^{2} + 3q^{4} - 3q^{8} + 3q^{11} + 3q^{16} + 3q^{17} + 9q^{19} - 3q^{22} - 3q^{23} + 15q^{25} - 9q^{29} + 6q^{31} - 3q^{32} - 3q^{34} + 21q^{37} - 9q^{38} + 12q^{41} + 3q^{43} + 3q^{44} + 3q^{46} + 3q^{47} - 15q^{50} - 24q^{53} + 9q^{58} - 9q^{59} + 6q^{61} - 6q^{62} + 3q^{64} + 6q^{67} + 3q^{68} - 9q^{71} - 21q^{74} + 9q^{76} + 12q^{79} - 12q^{82} + 18q^{83} - 3q^{86} - 3q^{88} - 12q^{89} - 3q^{92} - 3q^{94} - 21q^{97} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.61323 −0.721458 −0.360729 0.932671i \(-0.617472\pi\)
−0.360729 + 0.932671i \(0.617472\pi\)
\(6\) 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 \(-0.849544\pi\)
−0.890356 + 0.455266i \(0.849544\pi\)
\(18\) 0 0
\(19\) −1.17103 −0.268653 −0.134326 0.990937i \(-0.542887\pi\)
−0.134326 + 0.990937i \(0.542887\pi\)
\(20\) −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 \(-0.692876\pi\)
−0.569534 + 0.821968i \(0.692876\pi\)
\(32\) −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 \(-0.373820\pi\)
0.386106 + 0.922454i \(0.373820\pi\)
\(42\) 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 \(-0.335244\pi\)
0.494793 + 0.869011i \(0.335244\pi\)
\(48\) 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 \(-0.407590\pi\)
0.286252 + 0.958154i \(0.407590\pi\)
\(60\) 0 0
\(61\) 11.9553 1.53072 0.765359 0.643604i \(-0.222561\pi\)
0.765359 + 0.643604i \(0.222561\pi\)
\(62\) 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 \(-0.403224\pi\)
0.299368 + 0.954138i \(0.403224\pi\)
\(74\) −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 \(-0.410510\pi\)
0.277453 + 0.960739i \(0.410510\pi\)
\(84\) 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 \(-0.513054\pi\)
−0.0409976 + 0.999159i \(0.513054\pi\)
\(90\) 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 \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.39749 −0.239749
\(101\) 13.6239 1.35563 0.677817 0.735231i \(-0.262926\pi\)
0.677817 + 0.735231i \(0.262926\pi\)
\(102\) 0 0
\(103\) 12.3421 1.21610 0.608050 0.793899i \(-0.291952\pi\)
0.608050 + 0.793899i \(0.291952\pi\)
\(104\) 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 \(-0.532624\pi\)
−0.102313 + 0.994752i \(0.532624\pi\)
\(132\) 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 \(-0.784897\pi\)
−0.780227 + 0.625496i \(0.784897\pi\)
\(140\) 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 \(-0.793439\pi\)
−0.796730 + 0.604335i \(0.793439\pi\)
\(158\) −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 \(-0.175368\pi\)
0.852035 + 0.523485i \(0.175368\pi\)
\(168\) 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 \(-0.479925\pi\)
0.0630254 + 0.998012i \(0.479925\pi\)
\(174\) 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 \(-0.689878\pi\)
−0.561767 + 0.827296i \(0.689878\pi\)
\(182\) 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 \(-0.566935\pi\)
−0.208735 + 0.977972i \(0.566935\pi\)
\(200\) 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 \(-0.445209\pi\)
0.171283 + 0.985222i \(0.445209\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.34206 −0.288830
\(227\) −5.28663 −0.350886 −0.175443 0.984490i \(-0.556136\pi\)
−0.175443 + 0.984490i \(0.556136\pi\)
\(228\) 0 0
\(229\) 4.88440 0.322770 0.161385 0.986892i \(-0.448404\pi\)
0.161385 + 0.986892i \(0.448404\pi\)
\(230\) −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 \(-0.519380\pi\)
−0.0608451 + 0.998147i \(0.519380\pi\)
\(242\) −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 \(-0.490557\pi\)
0.0296608 + 0.999560i \(0.490557\pi\)
\(252\) 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 \(-0.613867\pi\)
−0.350144 + 0.936696i \(0.613867\pi\)
\(258\) 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 \(-0.406449\pi\)
0.289685 + 0.957122i \(0.406449\pi\)
\(270\) 0 0
\(271\) −3.22646 −0.195993 −0.0979967 0.995187i \(-0.531243\pi\)
−0.0979967 + 0.995187i \(0.531243\pi\)
\(272\) −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 \(-0.226835\pi\)
0.756650 + 0.653820i \(0.226835\pi\)
\(284\) −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 \(-0.324377\pi\)
0.524166 + 0.851616i \(0.324377\pi\)
\(294\) 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 \(-0.108514\pi\)
0.942452 + 0.334342i \(0.108514\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −10.2312 −0.581093
\(311\) −0.331340 −0.0187886 −0.00939429 0.999956i \(-0.502990\pi\)
−0.00939429 + 0.999956i \(0.502990\pi\)
\(312\) 0 0
\(313\) 14.3975 0.813794 0.406897 0.913474i \(-0.366611\pi\)
0.406897 + 0.913474i \(0.366611\pi\)
\(314\) 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 \(-0.655391\pi\)
−0.469014 + 0.883191i \(0.655391\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) 5.11560 0.272276 0.136138 0.990690i \(-0.456531\pi\)
0.136138 + 0.990690i \(0.456531\pi\)
\(354\) 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 \(-0.512113\pi\)
−0.0380446 + 0.999276i \(0.512113\pi\)
\(368\) −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 \(-0.529514\pi\)
−0.0925876 + 0.995705i \(0.529514\pi\)
\(384\) 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 \(-0.223823\pi\)
0.762803 + 0.646631i \(0.223823\pi\)
\(398\) 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 \(-0.643023\pi\)
−0.434354 + 0.900742i \(0.643023\pi\)
\(410\) 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 \(-0.731013\pi\)
−0.663696 + 0.748003i \(0.731013\pi\)
\(420\) 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 \(-0.636815\pi\)
−0.416703 + 0.909043i \(0.636815\pi\)
\(434\) 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 \(-0.790454\pi\)
−0.791028 + 0.611780i \(0.790454\pi\)
\(440\) 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 \(-0.197080\pi\)
0.814375 + 0.580339i \(0.197080\pi\)
\(462\) 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 \(-0.609909\pi\)
−0.338468 + 0.940978i \(0.609909\pi\)
\(468\) 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 \(-0.508920\pi\)
−0.0280192 + 0.999607i \(0.508920\pi\)
\(480\) 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 \(-0.466852\pi\)
0.103949 + 0.994583i \(0.466852\pi\)
\(504\) 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 \(-0.308055\pi\)
0.567127 + 0.823630i \(0.308055\pi\)
\(510\) 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 \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) −30.3635 −1.32770 −0.663852 0.747864i \(-0.731079\pi\)
−0.663852 + 0.747864i \(0.731079\pi\)
\(524\) −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 \(-0.354788\pi\)
0.440538 + 0.897734i \(0.354788\pi\)
\(564\) 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 \(-0.679112\pi\)
−0.533468 + 0.845820i \(0.679112\pi\)
\(578\) −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 \(-0.461810\pi\)
0.119690 + 0.992811i \(0.461810\pi\)
\(588\) 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 \(-0.278743\pi\)
0.640461 + 0.767991i \(0.278743\pi\)
\(594\) 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 \(-0.351013\pi\)
0.451154 + 0.892446i \(0.351013\pi\)
\(602\) 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 \(-0.362581\pi\)
0.418429 + 0.908250i \(0.362581\pi\)
\(608\) 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 \(-0.354433\pi\)
0.441539 + 0.897242i \(0.354433\pi\)
\(620\) 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 \(-0.612004\pi\)
−0.344654 + 0.938730i \(0.612004\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8.59777 −0.338275
\(647\) −8.83969 −0.347524 −0.173762 0.984788i \(-0.555592\pi\)
−0.173762 + 0.984788i \(0.555592\pi\)
\(648\) 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 \(-0.416065\pi\)
0.260643 + 0.965435i \(0.416065\pi\)
\(662\) 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 \(-0.627612\pi\)
−0.390251 + 0.920708i \(0.627612\pi\)
\(678\) 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 \(-0.536228\pi\)
−0.113569 + 0.993530i \(0.536228\pi\)
\(692\) 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 \(-0.729150\pi\)
−0.659306 + 0.751874i \(0.729150\pi\)
\(720\) 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 \(-0.231950\pi\)
0.746046 + 0.665894i \(0.231950\pi\)
\(728\) 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 \(-0.678019\pi\)
−0.530562 + 0.847646i \(0.678019\pi\)
\(734\) 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 \(-0.173042\pi\)
0.855837 + 0.517245i \(0.173042\pi\)
\(762\) 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 \(-0.444808\pi\)
0.172525 + 0.985005i \(0.444808\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.11560 0.112133
\(773\) 15.9553 0.573872 0.286936 0.957950i \(-0.407363\pi\)
0.286936 + 0.957950i \(0.407363\pi\)
\(774\) 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 \(-0.848302\pi\)
−0.888572 + 0.458737i \(0.848302\pi\)
\(788\) 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 \(-0.276861\pi\)
0.644990 + 0.764191i \(0.276861\pi\)
\(798\) 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 \(-0.243999\pi\)
0.720312 + 0.693650i \(0.243999\pi\)
\(812\) 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 \(-0.453915\pi\)
0.144276 + 0.989538i \(0.453915\pi\)
\(830\) 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 \(-0.523582\pi\)
−0.0740168 + 0.997257i \(0.523582\pi\)
\(840\) 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 \(-0.208729\pi\)
0.792596 + 0.609748i \(0.208729\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −15.7395 −0.537967
\(857\) −27.4624 −0.938098 −0.469049 0.883172i \(-0.655403\pi\)
−0.469049 + 0.883172i \(0.655403\pi\)
\(858\) 0 0
\(859\) 12.1925 0.416002 0.208001 0.978129i \(-0.433304\pi\)
0.208001 + 0.978129i \(0.433304\pi\)
\(860\) 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 \(-0.489869\pi\)
0.0318234 + 0.999494i \(0.489869\pi\)
\(882\) 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 \(-0.407228\pi\)
0.287343 + 0.957828i \(0.407228\pi\)
\(888\) 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 \(-0.633849\pi\)
−0.408215 + 0.912886i \(0.633849\pi\)
\(930\) 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 \(-0.223054\pi\)
0.764363 + 0.644787i \(0.223054\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −10.9446 −0.356973
\(941\) 17.4917 0.570212 0.285106 0.958496i \(-0.407971\pi\)
0.285106 + 0.958496i \(0.407971\pi\)
\(942\) 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 \(-0.822179\pi\)
−0.847976 + 0.530035i \(0.822179\pi\)
\(972\) 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 \(-0.631234\pi\)
−0.400703 + 0.916208i \(0.631234\pi\)
\(984\) 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 \(-0.588687\pi\)
−0.275029 + 0.961436i \(0.588687\pi\)
\(998\) 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.dw.1.2 3
3.2 odd 2 3234.2.a.bh.1.2 3
7.3 odd 6 1386.2.k.v.793.2 6
7.5 odd 6 1386.2.k.v.991.2 6
7.6 odd 2 9702.2.a.dv.1.2 3
21.5 even 6 462.2.i.g.67.2 6
21.17 even 6 462.2.i.g.331.2 yes 6
21.20 even 2 3234.2.a.bf.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.i.g.67.2 6 21.5 even 6
462.2.i.g.331.2 yes 6 21.17 even 6
1386.2.k.v.793.2 6 7.3 odd 6
1386.2.k.v.991.2 6 7.5 odd 6
3234.2.a.bf.1.2 3 21.20 even 2
3234.2.a.bh.1.2 3 3.2 odd 2
9702.2.a.dv.1.2 3 7.6 odd 2
9702.2.a.dw.1.2 3 1.1 even 1 trivial