Properties

Label 7600.2.a.cb.1.2
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 950)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.91223\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.25561 q^{3} +4.22547 q^{7} +2.08777 q^{9} +O(q^{10})\) \(q+2.25561 q^{3} +4.22547 q^{7} +2.08777 q^{9} +5.13770 q^{11} -3.16784 q^{13} +6.48108 q^{17} +1.00000 q^{19} +9.53101 q^{21} +7.56885 q^{23} -2.05763 q^{27} +0.832162 q^{29} +4.51122 q^{31} +11.5886 q^{33} -0.137699 q^{37} -7.14540 q^{39} -11.6489 q^{41} -2.51122 q^{43} -5.96216 q^{47} +10.8546 q^{49} +14.6188 q^{51} -0.225470 q^{53} +2.25561 q^{57} -5.39331 q^{59} +14.4509 q^{61} +8.82181 q^{63} -4.11021 q^{67} +17.0724 q^{69} -3.82446 q^{71} -4.70655 q^{73} +21.7092 q^{77} -10.6265 q^{79} -10.9045 q^{81} -12.0999 q^{83} +1.87703 q^{87} -10.0000 q^{89} -13.3856 q^{91} +10.1755 q^{93} -3.93972 q^{97} +10.7263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 2q^{3} + 2q^{7} + 13q^{9} + O(q^{10}) \) \( 3q + 2q^{3} + 2q^{7} + 13q^{9} - 2q^{11} + 2q^{13} + 4q^{17} + 3q^{19} - 11q^{21} + 14q^{23} - 7q^{27} + 14q^{29} + 4q^{31} - 4q^{33} + 17q^{37} - 29q^{39} - 8q^{41} + 2q^{43} + 13q^{47} + 25q^{49} + 11q^{51} + 10q^{53} + 2q^{57} + 6q^{59} + 22q^{61} + 2q^{63} + 8q^{69} + 2q^{71} + 12q^{73} + 50q^{77} - 24q^{79} - q^{81} + 12q^{83} - 21q^{87} - 30q^{89} + 7q^{91} + 44q^{93} - 24q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.25561 1.30228 0.651138 0.758959i \(-0.274292\pi\)
0.651138 + 0.758959i \(0.274292\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.22547 1.59708 0.798539 0.601943i \(-0.205607\pi\)
0.798539 + 0.601943i \(0.205607\pi\)
\(8\) 0 0
\(9\) 2.08777 0.695924
\(10\) 0 0
\(11\) 5.13770 1.54907 0.774537 0.632528i \(-0.217983\pi\)
0.774537 + 0.632528i \(0.217983\pi\)
\(12\) 0 0
\(13\) −3.16784 −0.878600 −0.439300 0.898340i \(-0.644774\pi\)
−0.439300 + 0.898340i \(0.644774\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.48108 1.57189 0.785946 0.618295i \(-0.212176\pi\)
0.785946 + 0.618295i \(0.212176\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 9.53101 2.07984
\(22\) 0 0
\(23\) 7.56885 1.57821 0.789107 0.614256i \(-0.210544\pi\)
0.789107 + 0.614256i \(0.210544\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.05763 −0.395991
\(28\) 0 0
\(29\) 0.832162 0.154529 0.0772643 0.997011i \(-0.475381\pi\)
0.0772643 + 0.997011i \(0.475381\pi\)
\(30\) 0 0
\(31\) 4.51122 0.810239 0.405119 0.914264i \(-0.367230\pi\)
0.405119 + 0.914264i \(0.367230\pi\)
\(32\) 0 0
\(33\) 11.5886 2.01732
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −0.137699 −0.0226376 −0.0113188 0.999936i \(-0.503603\pi\)
−0.0113188 + 0.999936i \(0.503603\pi\)
\(38\) 0 0
\(39\) −7.14540 −1.14418
\(40\) 0 0
\(41\) −11.6489 −1.81926 −0.909628 0.415425i \(-0.863633\pi\)
−0.909628 + 0.415425i \(0.863633\pi\)
\(42\) 0 0
\(43\) −2.51122 −0.382957 −0.191479 0.981497i \(-0.561328\pi\)
−0.191479 + 0.981497i \(0.561328\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.96216 −0.869670 −0.434835 0.900510i \(-0.643193\pi\)
−0.434835 + 0.900510i \(0.643193\pi\)
\(48\) 0 0
\(49\) 10.8546 1.55066
\(50\) 0 0
\(51\) 14.6188 2.04704
\(52\) 0 0
\(53\) −0.225470 −0.0309707 −0.0154853 0.999880i \(-0.504929\pi\)
−0.0154853 + 0.999880i \(0.504929\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.25561 0.298763
\(58\) 0 0
\(59\) −5.39331 −0.702149 −0.351074 0.936348i \(-0.614184\pi\)
−0.351074 + 0.936348i \(0.614184\pi\)
\(60\) 0 0
\(61\) 14.4509 1.85025 0.925127 0.379659i \(-0.123959\pi\)
0.925127 + 0.379659i \(0.123959\pi\)
\(62\) 0 0
\(63\) 8.82181 1.11144
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.11021 −0.502142 −0.251071 0.967969i \(-0.580783\pi\)
−0.251071 + 0.967969i \(0.580783\pi\)
\(68\) 0 0
\(69\) 17.0724 2.05527
\(70\) 0 0
\(71\) −3.82446 −0.453880 −0.226940 0.973909i \(-0.572872\pi\)
−0.226940 + 0.973909i \(0.572872\pi\)
\(72\) 0 0
\(73\) −4.70655 −0.550860 −0.275430 0.961321i \(-0.588820\pi\)
−0.275430 + 0.961321i \(0.588820\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 21.7092 2.47399
\(78\) 0 0
\(79\) −10.6265 −1.19557 −0.597786 0.801655i \(-0.703953\pi\)
−0.597786 + 0.801655i \(0.703953\pi\)
\(80\) 0 0
\(81\) −10.9045 −1.21161
\(82\) 0 0
\(83\) −12.0999 −1.32813 −0.664066 0.747674i \(-0.731171\pi\)
−0.664066 + 0.747674i \(0.731171\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.87703 0.201239
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) −13.3856 −1.40319
\(92\) 0 0
\(93\) 10.1755 1.05515
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −3.93972 −0.400018 −0.200009 0.979794i \(-0.564097\pi\)
−0.200009 + 0.979794i \(0.564097\pi\)
\(98\) 0 0
\(99\) 10.7263 1.07804
\(100\) 0 0
\(101\) 3.19798 0.318211 0.159105 0.987262i \(-0.449139\pi\)
0.159105 + 0.987262i \(0.449139\pi\)
\(102\) 0 0
\(103\) −10.6868 −1.05300 −0.526499 0.850176i \(-0.676496\pi\)
−0.526499 + 0.850176i \(0.676496\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.8168 1.04570 0.522848 0.852426i \(-0.324870\pi\)
0.522848 + 0.852426i \(0.324870\pi\)
\(108\) 0 0
\(109\) 9.24791 0.885789 0.442894 0.896574i \(-0.353952\pi\)
0.442894 + 0.896574i \(0.353952\pi\)
\(110\) 0 0
\(111\) −0.310596 −0.0294804
\(112\) 0 0
\(113\) −17.6489 −1.66027 −0.830135 0.557562i \(-0.811737\pi\)
−0.830135 + 0.557562i \(0.811737\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −6.61372 −0.611439
\(118\) 0 0
\(119\) 27.3856 2.51043
\(120\) 0 0
\(121\) 15.3960 1.39963
\(122\) 0 0
\(123\) −26.2754 −2.36917
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −12.7866 −1.13463 −0.567314 0.823501i \(-0.692018\pi\)
−0.567314 + 0.823501i \(0.692018\pi\)
\(128\) 0 0
\(129\) −5.66432 −0.498716
\(130\) 0 0
\(131\) 2.11526 0.184811 0.0924057 0.995721i \(-0.470544\pi\)
0.0924057 + 0.995721i \(0.470544\pi\)
\(132\) 0 0
\(133\) 4.22547 0.366395
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.36317 0.458206 0.229103 0.973402i \(-0.426421\pi\)
0.229103 + 0.973402i \(0.426421\pi\)
\(138\) 0 0
\(139\) 10.1601 0.861771 0.430886 0.902407i \(-0.358201\pi\)
0.430886 + 0.902407i \(0.358201\pi\)
\(140\) 0 0
\(141\) −13.4483 −1.13255
\(142\) 0 0
\(143\) −16.2754 −1.36102
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 24.4837 2.01938
\(148\) 0 0
\(149\) −5.93972 −0.486601 −0.243301 0.969951i \(-0.578230\pi\)
−0.243301 + 0.969951i \(0.578230\pi\)
\(150\) 0 0
\(151\) 15.2978 1.24492 0.622460 0.782652i \(-0.286133\pi\)
0.622460 + 0.782652i \(0.286133\pi\)
\(152\) 0 0
\(153\) 13.5310 1.09392
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.7866 1.02048 0.510242 0.860031i \(-0.329556\pi\)
0.510242 + 0.860031i \(0.329556\pi\)
\(158\) 0 0
\(159\) −0.508572 −0.0403324
\(160\) 0 0
\(161\) 31.9819 2.52053
\(162\) 0 0
\(163\) −11.4734 −0.898664 −0.449332 0.893365i \(-0.648338\pi\)
−0.449332 + 0.893365i \(0.648338\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.4131 1.50223 0.751115 0.660171i \(-0.229516\pi\)
0.751115 + 0.660171i \(0.229516\pi\)
\(168\) 0 0
\(169\) −2.96480 −0.228062
\(170\) 0 0
\(171\) 2.08777 0.159656
\(172\) 0 0
\(173\) −9.78662 −0.744063 −0.372031 0.928220i \(-0.621339\pi\)
−0.372031 + 0.928220i \(0.621339\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −12.1652 −0.914392
\(178\) 0 0
\(179\) 6.82446 0.510084 0.255042 0.966930i \(-0.417911\pi\)
0.255042 + 0.966930i \(0.417911\pi\)
\(180\) 0 0
\(181\) −0.137699 −0.0102351 −0.00511755 0.999987i \(-0.501629\pi\)
−0.00511755 + 0.999987i \(0.501629\pi\)
\(182\) 0 0
\(183\) 32.5957 2.40954
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 33.2978 2.43498
\(188\) 0 0
\(189\) −8.69446 −0.632429
\(190\) 0 0
\(191\) −19.3779 −1.40214 −0.701068 0.713095i \(-0.747293\pi\)
−0.701068 + 0.713095i \(0.747293\pi\)
\(192\) 0 0
\(193\) 5.42851 0.390752 0.195376 0.980728i \(-0.437407\pi\)
0.195376 + 0.980728i \(0.437407\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.6489 1.11494 0.557470 0.830197i \(-0.311772\pi\)
0.557470 + 0.830197i \(0.311772\pi\)
\(198\) 0 0
\(199\) −18.0499 −1.27953 −0.639763 0.768572i \(-0.720967\pi\)
−0.639763 + 0.768572i \(0.720967\pi\)
\(200\) 0 0
\(201\) −9.27102 −0.653927
\(202\) 0 0
\(203\) 3.51628 0.246794
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 15.8020 1.09832
\(208\) 0 0
\(209\) 5.13770 0.355382
\(210\) 0 0
\(211\) 7.50857 0.516911 0.258456 0.966023i \(-0.416786\pi\)
0.258456 + 0.966023i \(0.416786\pi\)
\(212\) 0 0
\(213\) −8.62648 −0.591077
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 19.0620 1.29401
\(218\) 0 0
\(219\) −10.6161 −0.717372
\(220\) 0 0
\(221\) −20.5310 −1.38106
\(222\) 0 0
\(223\) 27.8091 1.86223 0.931116 0.364723i \(-0.118836\pi\)
0.931116 + 0.364723i \(0.118836\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 8.91223 0.591525 0.295763 0.955261i \(-0.404426\pi\)
0.295763 + 0.955261i \(0.404426\pi\)
\(228\) 0 0
\(229\) −13.6489 −0.901946 −0.450973 0.892538i \(-0.648923\pi\)
−0.450973 + 0.892538i \(0.648923\pi\)
\(230\) 0 0
\(231\) 48.9674 3.22182
\(232\) 0 0
\(233\) −23.2754 −1.52482 −0.762411 0.647093i \(-0.775985\pi\)
−0.762411 + 0.647093i \(0.775985\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −23.9692 −1.55697
\(238\) 0 0
\(239\) −3.72898 −0.241208 −0.120604 0.992701i \(-0.538483\pi\)
−0.120604 + 0.992701i \(0.538483\pi\)
\(240\) 0 0
\(241\) −1.48878 −0.0959009 −0.0479505 0.998850i \(-0.515269\pi\)
−0.0479505 + 0.998850i \(0.515269\pi\)
\(242\) 0 0
\(243\) −18.4234 −1.18186
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.16784 −0.201565
\(248\) 0 0
\(249\) −27.2925 −1.72959
\(250\) 0 0
\(251\) 8.78662 0.554606 0.277303 0.960782i \(-0.410559\pi\)
0.277303 + 0.960782i \(0.410559\pi\)
\(252\) 0 0
\(253\) 38.8865 2.44477
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.74175 −0.171025 −0.0855127 0.996337i \(-0.527253\pi\)
−0.0855127 + 0.996337i \(0.527253\pi\)
\(258\) 0 0
\(259\) −0.581844 −0.0361540
\(260\) 0 0
\(261\) 1.73736 0.107540
\(262\) 0 0
\(263\) 2.74704 0.169390 0.0846948 0.996407i \(-0.473008\pi\)
0.0846948 + 0.996407i \(0.473008\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −22.5561 −1.38041
\(268\) 0 0
\(269\) −9.74175 −0.593965 −0.296982 0.954883i \(-0.595980\pi\)
−0.296982 + 0.954883i \(0.595980\pi\)
\(270\) 0 0
\(271\) −26.3555 −1.60098 −0.800490 0.599346i \(-0.795427\pi\)
−0.800490 + 0.599346i \(0.795427\pi\)
\(272\) 0 0
\(273\) −30.1927 −1.82734
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.962158 0.0578104 0.0289052 0.999582i \(-0.490798\pi\)
0.0289052 + 0.999582i \(0.490798\pi\)
\(278\) 0 0
\(279\) 9.41839 0.563864
\(280\) 0 0
\(281\) −14.6714 −0.875219 −0.437610 0.899165i \(-0.644175\pi\)
−0.437610 + 0.899165i \(0.644175\pi\)
\(282\) 0 0
\(283\) −26.1601 −1.55506 −0.777529 0.628847i \(-0.783527\pi\)
−0.777529 + 0.628847i \(0.783527\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −49.2221 −2.90549
\(288\) 0 0
\(289\) 25.0044 1.47085
\(290\) 0 0
\(291\) −8.88647 −0.520934
\(292\) 0 0
\(293\) 22.4657 1.31246 0.656229 0.754562i \(-0.272150\pi\)
0.656229 + 0.754562i \(0.272150\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −10.5715 −0.613420
\(298\) 0 0
\(299\) −23.9769 −1.38662
\(300\) 0 0
\(301\) −10.6111 −0.611612
\(302\) 0 0
\(303\) 7.21338 0.414398
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 17.2204 0.982821 0.491410 0.870928i \(-0.336482\pi\)
0.491410 + 0.870928i \(0.336482\pi\)
\(308\) 0 0
\(309\) −24.1051 −1.37129
\(310\) 0 0
\(311\) 7.87439 0.446516 0.223258 0.974759i \(-0.428331\pi\)
0.223258 + 0.974759i \(0.428331\pi\)
\(312\) 0 0
\(313\) 25.1678 1.42257 0.711285 0.702904i \(-0.248113\pi\)
0.711285 + 0.702904i \(0.248113\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 23.9045 1.34261 0.671306 0.741180i \(-0.265734\pi\)
0.671306 + 0.741180i \(0.265734\pi\)
\(318\) 0 0
\(319\) 4.27540 0.239376
\(320\) 0 0
\(321\) 24.3984 1.36178
\(322\) 0 0
\(323\) 6.48108 0.360617
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 20.8597 1.15354
\(328\) 0 0
\(329\) −25.1929 −1.38893
\(330\) 0 0
\(331\) −30.7565 −1.69053 −0.845264 0.534348i \(-0.820557\pi\)
−0.845264 + 0.534348i \(0.820557\pi\)
\(332\) 0 0
\(333\) −0.287484 −0.0157540
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −13.4734 −0.733942 −0.366971 0.930232i \(-0.619605\pi\)
−0.366971 + 0.930232i \(0.619605\pi\)
\(338\) 0 0
\(339\) −39.8091 −2.16213
\(340\) 0 0
\(341\) 23.1773 1.25512
\(342\) 0 0
\(343\) 16.2875 0.879441
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.9468 1.55394 0.776971 0.629536i \(-0.216755\pi\)
0.776971 + 0.629536i \(0.216755\pi\)
\(348\) 0 0
\(349\) 27.9243 1.49475 0.747377 0.664400i \(-0.231313\pi\)
0.747377 + 0.664400i \(0.231313\pi\)
\(350\) 0 0
\(351\) 6.51825 0.347918
\(352\) 0 0
\(353\) −28.3099 −1.50678 −0.753392 0.657571i \(-0.771584\pi\)
−0.753392 + 0.657571i \(0.771584\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 61.7712 3.26928
\(358\) 0 0
\(359\) −2.60163 −0.137309 −0.0686545 0.997640i \(-0.521871\pi\)
−0.0686545 + 0.997640i \(0.521871\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 34.7272 1.82271
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 11.6489 0.608069 0.304034 0.952661i \(-0.401666\pi\)
0.304034 + 0.952661i \(0.401666\pi\)
\(368\) 0 0
\(369\) −24.3203 −1.26606
\(370\) 0 0
\(371\) −0.952717 −0.0494626
\(372\) 0 0
\(373\) 12.8064 0.663091 0.331545 0.943439i \(-0.392430\pi\)
0.331545 + 0.943439i \(0.392430\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.63615 −0.135769
\(378\) 0 0
\(379\) 20.9122 1.07419 0.537095 0.843522i \(-0.319522\pi\)
0.537095 + 0.843522i \(0.319522\pi\)
\(380\) 0 0
\(381\) −28.8416 −1.47760
\(382\) 0 0
\(383\) 10.3511 0.528916 0.264458 0.964397i \(-0.414807\pi\)
0.264458 + 0.964397i \(0.414807\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.24285 −0.266509
\(388\) 0 0
\(389\) 6.56620 0.332920 0.166460 0.986048i \(-0.446766\pi\)
0.166460 + 0.986048i \(0.446766\pi\)
\(390\) 0 0
\(391\) 49.0543 2.48078
\(392\) 0 0
\(393\) 4.77121 0.240676
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −23.5284 −1.18085 −0.590427 0.807091i \(-0.701041\pi\)
−0.590427 + 0.807091i \(0.701041\pi\)
\(398\) 0 0
\(399\) 9.53101 0.477147
\(400\) 0 0
\(401\) 6.22041 0.310633 0.155316 0.987865i \(-0.450360\pi\)
0.155316 + 0.987865i \(0.450360\pi\)
\(402\) 0 0
\(403\) −14.2908 −0.711876
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.707457 −0.0350674
\(408\) 0 0
\(409\) −34.4905 −1.70545 −0.852723 0.522363i \(-0.825051\pi\)
−0.852723 + 0.522363i \(0.825051\pi\)
\(410\) 0 0
\(411\) 12.0972 0.596711
\(412\) 0 0
\(413\) −22.7893 −1.12139
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 22.9173 1.12226
\(418\) 0 0
\(419\) 10.6265 0.519138 0.259569 0.965725i \(-0.416420\pi\)
0.259569 + 0.965725i \(0.416420\pi\)
\(420\) 0 0
\(421\) −1.98021 −0.0965095 −0.0482548 0.998835i \(-0.515366\pi\)
−0.0482548 + 0.998835i \(0.515366\pi\)
\(422\) 0 0
\(423\) −12.4476 −0.605224
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 61.0620 2.95500
\(428\) 0 0
\(429\) −36.7109 −1.77242
\(430\) 0 0
\(431\) −15.0774 −0.726254 −0.363127 0.931740i \(-0.618291\pi\)
−0.363127 + 0.931740i \(0.618291\pi\)
\(432\) 0 0
\(433\) −13.5337 −0.650386 −0.325193 0.945648i \(-0.605429\pi\)
−0.325193 + 0.945648i \(0.605429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.56885 0.362067
\(438\) 0 0
\(439\) −39.1773 −1.86983 −0.934915 0.354872i \(-0.884524\pi\)
−0.934915 + 0.354872i \(0.884524\pi\)
\(440\) 0 0
\(441\) 22.6619 1.07914
\(442\) 0 0
\(443\) 19.3132 0.917600 0.458800 0.888540i \(-0.348279\pi\)
0.458800 + 0.888540i \(0.348279\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −13.3977 −0.633689
\(448\) 0 0
\(449\) 41.4131 1.95440 0.977202 0.212310i \(-0.0680985\pi\)
0.977202 + 0.212310i \(0.0680985\pi\)
\(450\) 0 0
\(451\) −59.8486 −2.81816
\(452\) 0 0
\(453\) 34.5059 1.62123
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 37.8392 1.77004 0.885021 0.465551i \(-0.154144\pi\)
0.885021 + 0.465551i \(0.154144\pi\)
\(458\) 0 0
\(459\) −13.3357 −0.622456
\(460\) 0 0
\(461\) 1.58864 0.0739903 0.0369952 0.999315i \(-0.488221\pi\)
0.0369952 + 0.999315i \(0.488221\pi\)
\(462\) 0 0
\(463\) 40.3581 1.87560 0.937800 0.347175i \(-0.112859\pi\)
0.937800 + 0.347175i \(0.112859\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −39.5130 −1.82844 −0.914221 0.405217i \(-0.867196\pi\)
−0.914221 + 0.405217i \(0.867196\pi\)
\(468\) 0 0
\(469\) −17.3676 −0.801959
\(470\) 0 0
\(471\) 28.8416 1.32895
\(472\) 0 0
\(473\) −12.9019 −0.593229
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.470730 −0.0215532
\(478\) 0 0
\(479\) −7.61107 −0.347759 −0.173879 0.984767i \(-0.555630\pi\)
−0.173879 + 0.984767i \(0.555630\pi\)
\(480\) 0 0
\(481\) 0.436209 0.0198894
\(482\) 0 0
\(483\) 72.1388 3.28243
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −20.3907 −0.923989 −0.461995 0.886883i \(-0.652866\pi\)
−0.461995 + 0.886883i \(0.652866\pi\)
\(488\) 0 0
\(489\) −25.8794 −1.17031
\(490\) 0 0
\(491\) −25.0224 −1.12925 −0.564623 0.825349i \(-0.690979\pi\)
−0.564623 + 0.825349i \(0.690979\pi\)
\(492\) 0 0
\(493\) 5.39331 0.242902
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.1601 −0.724881
\(498\) 0 0
\(499\) −22.6111 −1.01221 −0.506105 0.862472i \(-0.668915\pi\)
−0.506105 + 0.862472i \(0.668915\pi\)
\(500\) 0 0
\(501\) 43.7884 1.95632
\(502\) 0 0
\(503\) 11.5035 0.512916 0.256458 0.966555i \(-0.417444\pi\)
0.256458 + 0.966555i \(0.417444\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −6.68744 −0.296999
\(508\) 0 0
\(509\) 9.11526 0.404027 0.202013 0.979383i \(-0.435252\pi\)
0.202013 + 0.979383i \(0.435252\pi\)
\(510\) 0 0
\(511\) −19.8874 −0.879766
\(512\) 0 0
\(513\) −2.05763 −0.0908467
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −30.6318 −1.34718
\(518\) 0 0
\(519\) −22.0748 −0.968975
\(520\) 0 0
\(521\) 15.4888 0.678576 0.339288 0.940683i \(-0.389814\pi\)
0.339288 + 0.940683i \(0.389814\pi\)
\(522\) 0 0
\(523\) 4.34073 0.189807 0.0949035 0.995486i \(-0.469746\pi\)
0.0949035 + 0.995486i \(0.469746\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 29.2376 1.27361
\(528\) 0 0
\(529\) 34.2875 1.49076
\(530\) 0 0
\(531\) −11.2600 −0.488642
\(532\) 0 0
\(533\) 36.9019 1.59840
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 15.3933 0.664270
\(538\) 0 0
\(539\) 55.7677 2.40208
\(540\) 0 0
\(541\) 19.5491 0.840480 0.420240 0.907413i \(-0.361946\pi\)
0.420240 + 0.907413i \(0.361946\pi\)
\(542\) 0 0
\(543\) −0.310596 −0.0133289
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −41.8038 −1.78740 −0.893700 0.448665i \(-0.851900\pi\)
−0.893700 + 0.448665i \(0.851900\pi\)
\(548\) 0 0
\(549\) 30.1703 1.28763
\(550\) 0 0
\(551\) 0.832162 0.0354513
\(552\) 0 0
\(553\) −44.9019 −1.90942
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.76418 0.413722 0.206861 0.978370i \(-0.433675\pi\)
0.206861 + 0.978370i \(0.433675\pi\)
\(558\) 0 0
\(559\) 7.95513 0.336466
\(560\) 0 0
\(561\) 75.1069 3.17102
\(562\) 0 0
\(563\) 11.4509 0.482600 0.241300 0.970451i \(-0.422426\pi\)
0.241300 + 0.970451i \(0.422426\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −46.0767 −1.93504
\(568\) 0 0
\(569\) −13.4338 −0.563174 −0.281587 0.959536i \(-0.590861\pi\)
−0.281587 + 0.959536i \(0.590861\pi\)
\(570\) 0 0
\(571\) −37.6335 −1.57491 −0.787457 0.616370i \(-0.788603\pi\)
−0.787457 + 0.616370i \(0.788603\pi\)
\(572\) 0 0
\(573\) −43.7090 −1.82597
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.56885 −0.0653121 −0.0326560 0.999467i \(-0.510397\pi\)
−0.0326560 + 0.999467i \(0.510397\pi\)
\(578\) 0 0
\(579\) 12.2446 0.508868
\(580\) 0 0
\(581\) −51.1276 −2.12113
\(582\) 0 0
\(583\) −1.15840 −0.0479759
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 25.8693 1.06774 0.533871 0.845566i \(-0.320737\pi\)
0.533871 + 0.845566i \(0.320737\pi\)
\(588\) 0 0
\(589\) 4.51122 0.185881
\(590\) 0 0
\(591\) 35.2978 1.45196
\(592\) 0 0
\(593\) 28.9243 1.18778 0.593890 0.804547i \(-0.297592\pi\)
0.593890 + 0.804547i \(0.297592\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −40.7136 −1.66630
\(598\) 0 0
\(599\) −41.3581 −1.68985 −0.844923 0.534887i \(-0.820354\pi\)
−0.844923 + 0.534887i \(0.820354\pi\)
\(600\) 0 0
\(601\) 2.68147 0.109379 0.0546897 0.998503i \(-0.482583\pi\)
0.0546897 + 0.998503i \(0.482583\pi\)
\(602\) 0 0
\(603\) −8.58117 −0.349452
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 3.31324 0.134480 0.0672401 0.997737i \(-0.478581\pi\)
0.0672401 + 0.997737i \(0.478581\pi\)
\(608\) 0 0
\(609\) 7.93134 0.321394
\(610\) 0 0
\(611\) 18.8871 0.764092
\(612\) 0 0
\(613\) 10.0603 0.406331 0.203165 0.979144i \(-0.434877\pi\)
0.203165 + 0.979144i \(0.434877\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 27.6265 1.11220 0.556100 0.831115i \(-0.312297\pi\)
0.556100 + 0.831115i \(0.312297\pi\)
\(618\) 0 0
\(619\) −16.6714 −0.670078 −0.335039 0.942204i \(-0.608750\pi\)
−0.335039 + 0.942204i \(0.608750\pi\)
\(620\) 0 0
\(621\) −15.5739 −0.624959
\(622\) 0 0
\(623\) −42.2547 −1.69290
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 11.5886 0.462806
\(628\) 0 0
\(629\) −0.892439 −0.0355839
\(630\) 0 0
\(631\) 0.709194 0.0282326 0.0141163 0.999900i \(-0.495506\pi\)
0.0141163 + 0.999900i \(0.495506\pi\)
\(632\) 0 0
\(633\) 16.9364 0.673162
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −34.3856 −1.36241
\(638\) 0 0
\(639\) −7.98459 −0.315866
\(640\) 0 0
\(641\) −2.43553 −0.0961978 −0.0480989 0.998843i \(-0.515316\pi\)
−0.0480989 + 0.998843i \(0.515316\pi\)
\(642\) 0 0
\(643\) 7.70390 0.303812 0.151906 0.988395i \(-0.451459\pi\)
0.151906 + 0.988395i \(0.451459\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.0499 −0.395103 −0.197552 0.980292i \(-0.563299\pi\)
−0.197552 + 0.980292i \(0.563299\pi\)
\(648\) 0 0
\(649\) −27.7092 −1.08768
\(650\) 0 0
\(651\) 42.9964 1.68516
\(652\) 0 0
\(653\) 7.09283 0.277564 0.138782 0.990323i \(-0.455681\pi\)
0.138782 + 0.990323i \(0.455681\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −9.82620 −0.383356
\(658\) 0 0
\(659\) 1.16346 0.0453218 0.0226609 0.999743i \(-0.492786\pi\)
0.0226609 + 0.999743i \(0.492786\pi\)
\(660\) 0 0
\(661\) 1.79432 0.0697909 0.0348955 0.999391i \(-0.488890\pi\)
0.0348955 + 0.999391i \(0.488890\pi\)
\(662\) 0 0
\(663\) −46.3099 −1.79853
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.29851 0.243879
\(668\) 0 0
\(669\) 62.7263 2.42514
\(670\) 0 0
\(671\) 74.2446 2.86618
\(672\) 0 0
\(673\) 25.2824 0.974566 0.487283 0.873244i \(-0.337988\pi\)
0.487283 + 0.873244i \(0.337988\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.89682 0.188200 0.0941001 0.995563i \(-0.470003\pi\)
0.0941001 + 0.995563i \(0.470003\pi\)
\(678\) 0 0
\(679\) −16.6472 −0.638860
\(680\) 0 0
\(681\) 20.1025 0.770330
\(682\) 0 0
\(683\) 10.1980 0.390215 0.195107 0.980782i \(-0.437494\pi\)
0.195107 + 0.980782i \(0.437494\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −30.7866 −1.17458
\(688\) 0 0
\(689\) 0.714253 0.0272109
\(690\) 0 0
\(691\) 39.9846 1.52109 0.760543 0.649288i \(-0.224933\pi\)
0.760543 + 0.649288i \(0.224933\pi\)
\(692\) 0 0
\(693\) 45.3238 1.72171
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −75.4975 −2.85967
\(698\) 0 0
\(699\) −52.5002 −1.98574
\(700\) 0 0
\(701\) 4.91729 0.185723 0.0928617 0.995679i \(-0.470399\pi\)
0.0928617 + 0.995679i \(0.470399\pi\)
\(702\) 0 0
\(703\) −0.137699 −0.00519342
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.5130 0.508207
\(708\) 0 0
\(709\) −36.8865 −1.38530 −0.692650 0.721274i \(-0.743557\pi\)
−0.692650 + 0.721274i \(0.743557\pi\)
\(710\) 0 0
\(711\) −22.1857 −0.832027
\(712\) 0 0
\(713\) 34.1447 1.27873
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8.41113 −0.314119
\(718\) 0 0
\(719\) 23.8891 0.890914 0.445457 0.895303i \(-0.353041\pi\)
0.445457 + 0.895303i \(0.353041\pi\)
\(720\) 0 0
\(721\) −45.1566 −1.68172
\(722\) 0 0
\(723\) −3.35811 −0.124889
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 19.6894 0.730240 0.365120 0.930961i \(-0.381028\pi\)
0.365120 + 0.930961i \(0.381028\pi\)
\(728\) 0 0
\(729\) −8.84251 −0.327500
\(730\) 0 0
\(731\) −16.2754 −0.601967
\(732\) 0 0
\(733\) −1.76418 −0.0651615 −0.0325808 0.999469i \(-0.510373\pi\)
−0.0325808 + 0.999469i \(0.510373\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −21.1170 −0.777855
\(738\) 0 0
\(739\) −28.1755 −1.03645 −0.518227 0.855243i \(-0.673408\pi\)
−0.518227 + 0.855243i \(0.673408\pi\)
\(740\) 0 0
\(741\) −7.14540 −0.262493
\(742\) 0 0
\(743\) −5.42851 −0.199153 −0.0995763 0.995030i \(-0.531749\pi\)
−0.0995763 + 0.995030i \(0.531749\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −25.2617 −0.924278
\(748\) 0 0
\(749\) 45.7059 1.67006
\(750\) 0 0
\(751\) −25.8640 −0.943792 −0.471896 0.881654i \(-0.656430\pi\)
−0.471896 + 0.881654i \(0.656430\pi\)
\(752\) 0 0
\(753\) 19.8192 0.722251
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 3.76947 0.137004 0.0685019 0.997651i \(-0.478178\pi\)
0.0685019 + 0.997651i \(0.478178\pi\)
\(758\) 0 0
\(759\) 87.7127 3.18377
\(760\) 0 0
\(761\) 18.3605 0.665568 0.332784 0.943003i \(-0.392012\pi\)
0.332784 + 0.943003i \(0.392012\pi\)
\(762\) 0 0
\(763\) 39.0767 1.41467
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 17.0851 0.616908
\(768\) 0 0
\(769\) −38.1300 −1.37500 −0.687501 0.726183i \(-0.741292\pi\)
−0.687501 + 0.726183i \(0.741292\pi\)
\(770\) 0 0
\(771\) −6.18431 −0.222722
\(772\) 0 0
\(773\) 29.1575 1.04872 0.524361 0.851496i \(-0.324304\pi\)
0.524361 + 0.851496i \(0.324304\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.31241 −0.0470825
\(778\) 0 0
\(779\) −11.6489 −0.417366
\(780\) 0 0
\(781\) −19.6489 −0.703094
\(782\) 0 0
\(783\) −1.71228 −0.0611920
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −47.0165 −1.67596 −0.837978 0.545704i \(-0.816262\pi\)
−0.837978 + 0.545704i \(0.816262\pi\)
\(788\) 0 0
\(789\) 6.19624 0.220592
\(790\) 0 0
\(791\) −74.5750 −2.65158
\(792\) 0 0
\(793\) −45.7782 −1.62563
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.6359 1.51024 0.755121 0.655586i \(-0.227578\pi\)
0.755121 + 0.655586i \(0.227578\pi\)
\(798\) 0 0
\(799\) −38.6412 −1.36703
\(800\) 0 0
\(801\) −20.8777 −0.737678
\(802\) 0 0
\(803\) −24.1808 −0.853323
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −21.9736 −0.773506
\(808\) 0 0
\(809\) 49.4630 1.73903 0.869514 0.493909i \(-0.164432\pi\)
0.869514 + 0.493909i \(0.164432\pi\)
\(810\) 0 0
\(811\) 16.7816 0.589280 0.294640 0.955608i \(-0.404800\pi\)
0.294640 + 0.955608i \(0.404800\pi\)
\(812\) 0 0
\(813\) −59.4476 −2.08492
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −2.51122 −0.0878564
\(818\) 0 0
\(819\) −27.9461 −0.976515
\(820\) 0 0
\(821\) 11.5337 0.402527 0.201264 0.979537i \(-0.435495\pi\)
0.201264 + 0.979537i \(0.435495\pi\)
\(822\) 0 0
\(823\) 32.6309 1.13744 0.568720 0.822531i \(-0.307439\pi\)
0.568720 + 0.822531i \(0.307439\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 6.64650 0.231122 0.115561 0.993300i \(-0.463133\pi\)
0.115561 + 0.993300i \(0.463133\pi\)
\(828\) 0 0
\(829\) −30.9217 −1.07395 −0.536977 0.843597i \(-0.680434\pi\)
−0.536977 + 0.843597i \(0.680434\pi\)
\(830\) 0 0
\(831\) 2.17025 0.0752852
\(832\) 0 0
\(833\) 70.3495 2.43747
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −9.28243 −0.320848
\(838\) 0 0
\(839\) 48.7109 1.68169 0.840844 0.541277i \(-0.182059\pi\)
0.840844 + 0.541277i \(0.182059\pi\)
\(840\) 0 0
\(841\) −28.3075 −0.976121
\(842\) 0 0
\(843\) −33.0928 −1.13978
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 65.0551 2.23532
\(848\) 0 0
\(849\) −59.0070 −2.02512
\(850\) 0 0
\(851\) −1.04222 −0.0357270
\(852\) 0 0
\(853\) −46.1447 −1.57997 −0.789983 0.613129i \(-0.789911\pi\)
−0.789983 + 0.613129i \(0.789911\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 8.40607 0.287146 0.143573 0.989640i \(-0.454141\pi\)
0.143573 + 0.989640i \(0.454141\pi\)
\(858\) 0 0
\(859\) 8.49581 0.289873 0.144937 0.989441i \(-0.453702\pi\)
0.144937 + 0.989441i \(0.453702\pi\)
\(860\) 0 0
\(861\) −111.026 −3.78375
\(862\) 0 0
\(863\) 3.37352 0.114836 0.0574179 0.998350i \(-0.481713\pi\)
0.0574179 + 0.998350i \(0.481713\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 56.4001 1.91545
\(868\) 0 0
\(869\) −54.5957 −1.85203
\(870\) 0 0
\(871\) 13.0205 0.441182
\(872\) 0 0
\(873\) −8.22524 −0.278382
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 13.2780 0.448368 0.224184 0.974547i \(-0.428028\pi\)
0.224184 + 0.974547i \(0.428028\pi\)
\(878\) 0 0
\(879\) 50.6738 1.70918
\(880\) 0 0
\(881\) −26.6489 −0.897825 −0.448912 0.893576i \(-0.648188\pi\)
−0.448912 + 0.893576i \(0.648188\pi\)
\(882\) 0 0
\(883\) −47.7884 −1.60821 −0.804103 0.594490i \(-0.797354\pi\)
−0.804103 + 0.594490i \(0.797354\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −36.3304 −1.21985 −0.609927 0.792457i \(-0.708801\pi\)
−0.609927 + 0.792457i \(0.708801\pi\)
\(888\) 0 0
\(889\) −54.0295 −1.81209
\(890\) 0 0
\(891\) −56.0242 −1.87688
\(892\) 0 0
\(893\) −5.96216 −0.199516
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −54.0825 −1.80576
\(898\) 0 0
\(899\) 3.75406 0.125205
\(900\) 0 0
\(901\) −1.46129 −0.0486826
\(902\) 0 0
\(903\) −23.9344 −0.796488
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −39.3873 −1.30784 −0.653918 0.756566i \(-0.726876\pi\)
−0.653918 + 0.756566i \(0.726876\pi\)
\(908\) 0 0
\(909\) 6.67664 0.221450
\(910\) 0 0
\(911\) 20.5561 0.681054 0.340527 0.940235i \(-0.389395\pi\)
0.340527 + 0.940235i \(0.389395\pi\)
\(912\) 0 0
\(913\) −62.1654 −2.05738
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.93799 0.295158
\(918\) 0 0
\(919\) −12.4054 −0.409216 −0.204608 0.978844i \(-0.565592\pi\)
−0.204608 + 0.978844i \(0.565592\pi\)
\(920\) 0 0
\(921\) 38.8425 1.27990
\(922\) 0 0
\(923\) 12.1153 0.398779
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −22.3115 −0.732806
\(928\) 0 0
\(929\) −31.3330 −1.02800 −0.514002 0.857789i \(-0.671838\pi\)
−0.514002 + 0.857789i \(0.671838\pi\)
\(930\) 0 0
\(931\) 10.8546 0.355745
\(932\) 0 0
\(933\) 17.7615 0.581487
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −7.27299 −0.237598 −0.118799 0.992918i \(-0.537904\pi\)
−0.118799 + 0.992918i \(0.537904\pi\)
\(938\) 0 0
\(939\) 56.7688 1.85258
\(940\) 0 0
\(941\) 6.72128 0.219107 0.109554 0.993981i \(-0.465058\pi\)
0.109554 + 0.993981i \(0.465058\pi\)
\(942\) 0 0
\(943\) −88.1689 −2.87117
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 10.0757 0.327416 0.163708 0.986509i \(-0.447655\pi\)
0.163708 + 0.986509i \(0.447655\pi\)
\(948\) 0 0
\(949\) 14.9096 0.483986
\(950\) 0 0
\(951\) 53.9193 1.74845
\(952\) 0 0
\(953\) 8.14473 0.263834 0.131917 0.991261i \(-0.457887\pi\)
0.131917 + 0.991261i \(0.457887\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 9.64363 0.311734
\(958\) 0 0
\(959\) 22.6619 0.731791
\(960\) 0 0
\(961\) −10.6489 −0.343513
\(962\) 0 0
\(963\) 22.5829 0.727724
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 47.1773 1.51712 0.758560 0.651604i \(-0.225903\pi\)
0.758560 + 0.651604i \(0.225903\pi\)
\(968\) 0 0
\(969\) 14.6188 0.469623
\(970\) 0 0
\(971\) −0.230528 −0.00739801 −0.00369901 0.999993i \(-0.501177\pi\)
−0.00369901 + 0.999993i \(0.501177\pi\)
\(972\) 0 0
\(973\) 42.9313 1.37632
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 5.80905 0.185848 0.0929240 0.995673i \(-0.470379\pi\)
0.0929240 + 0.995673i \(0.470379\pi\)
\(978\) 0 0
\(979\) −51.3770 −1.64202
\(980\) 0 0
\(981\) 19.3075 0.616441
\(982\) 0 0
\(983\) −22.3511 −0.712889 −0.356444 0.934317i \(-0.616011\pi\)
−0.356444 + 0.934317i \(0.616011\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −56.8254 −1.80877
\(988\) 0 0
\(989\) −19.0070 −0.604388
\(990\) 0 0
\(991\) 34.9415 1.10995 0.554976 0.831866i \(-0.312727\pi\)
0.554976 + 0.831866i \(0.312727\pi\)
\(992\) 0 0
\(993\) −69.3746 −2.20154
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 9.35282 0.296207 0.148103 0.988972i \(-0.452683\pi\)
0.148103 + 0.988972i \(0.452683\pi\)
\(998\) 0 0
\(999\) 0.283334 0.00896430
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 7600.2.a.cb.1.2 3
4.3 odd 2 950.2.a.k.1.2 3
5.4 even 2 7600.2.a.bm.1.2 3
12.11 even 2 8550.2.a.co.1.1 3
20.3 even 4 950.2.b.g.799.5 6
20.7 even 4 950.2.b.g.799.2 6
20.19 odd 2 950.2.a.m.1.2 yes 3
60.59 even 2 8550.2.a.cj.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.k.1.2 3 4.3 odd 2
950.2.a.m.1.2 yes 3 20.19 odd 2
950.2.b.g.799.2 6 20.7 even 4
950.2.b.g.799.5 6 20.3 even 4
7600.2.a.bm.1.2 3 5.4 even 2
7600.2.a.cb.1.2 3 1.1 even 1 trivial
8550.2.a.cj.1.3 3 60.59 even 2
8550.2.a.co.1.1 3 12.11 even 2