Properties

Label 7800.2.a.br.1.3
Level $7800$
Weight $2$
Character 7800.1
Self dual yes
Analytic conductor $62.283$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.2833135766\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.788.1
Defining polynomial: \( x^{3} - x^{2} - 7x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3.35386\) of defining polynomial
Character \(\chi\) \(=\) 7800.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{3} +3.35386 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +3.35386 q^{7} +1.00000 q^{9} -3.81322 q^{11} -1.00000 q^{13} -1.00000 q^{17} +4.24835 q^{19} +3.35386 q^{21} -6.24835 q^{23} +1.00000 q^{27} -6.78899 q^{29} -5.97577 q^{31} -3.81322 q^{33} -4.45936 q^{37} -1.00000 q^{39} -0.621911 q^{41} +1.54064 q^{43} -9.14284 q^{47} +4.24835 q^{49} -1.00000 q^{51} -7.08580 q^{53} +4.24835 q^{57} +0.272582 q^{59} +4.78899 q^{61} +3.35386 q^{63} +1.81322 q^{67} -6.24835 q^{69} -9.16707 q^{71} -3.32962 q^{73} -12.7890 q^{77} -5.54064 q^{79} +1.00000 q^{81} -6.27258 q^{83} -6.78899 q^{87} +3.78899 q^{89} -3.35386 q^{91} -5.97577 q^{93} -14.7077 q^{97} -3.81322 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 3 q^{3} + q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 3 q^{3} + q^{7} + 3 q^{9} - 3 q^{11} - 3 q^{13} - 3 q^{17} - 6 q^{19} + q^{21} + 3 q^{27} - q^{29} - 7 q^{31} - 3 q^{33} - 14 q^{37} - 3 q^{39} + 4 q^{43} + q^{47} - 6 q^{49} - 3 q^{51} - 5 q^{53} - 6 q^{57} - 7 q^{59} - 5 q^{61} + q^{63} - 3 q^{67} - 10 q^{71} + 10 q^{73} - 19 q^{77} - 16 q^{79} + 3 q^{81} - 11 q^{83} - q^{87} - 8 q^{89} - q^{91} - 7 q^{93} - 26 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.35386 1.26764 0.633819 0.773481i \(-0.281486\pi\)
0.633819 + 0.773481i \(0.281486\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.81322 −1.14973 −0.574864 0.818249i \(-0.694945\pi\)
−0.574864 + 0.818249i \(0.694945\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) 0 0
\(19\) 4.24835 0.974638 0.487319 0.873224i \(-0.337975\pi\)
0.487319 + 0.873224i \(0.337975\pi\)
\(20\) 0 0
\(21\) 3.35386 0.731871
\(22\) 0 0
\(23\) −6.24835 −1.30287 −0.651435 0.758704i \(-0.725833\pi\)
−0.651435 + 0.758704i \(0.725833\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.78899 −1.26068 −0.630341 0.776318i \(-0.717085\pi\)
−0.630341 + 0.776318i \(0.717085\pi\)
\(30\) 0 0
\(31\) −5.97577 −1.07328 −0.536640 0.843811i \(-0.680307\pi\)
−0.536640 + 0.843811i \(0.680307\pi\)
\(32\) 0 0
\(33\) −3.81322 −0.663796
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.45936 −0.733115 −0.366557 0.930395i \(-0.619464\pi\)
−0.366557 + 0.930395i \(0.619464\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −0.621911 −0.0971262 −0.0485631 0.998820i \(-0.515464\pi\)
−0.0485631 + 0.998820i \(0.515464\pi\)
\(42\) 0 0
\(43\) 1.54064 0.234945 0.117472 0.993076i \(-0.462521\pi\)
0.117472 + 0.993076i \(0.462521\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.14284 −1.33362 −0.666810 0.745228i \(-0.732341\pi\)
−0.666810 + 0.745228i \(0.732341\pi\)
\(48\) 0 0
\(49\) 4.24835 0.606907
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) 0 0
\(53\) −7.08580 −0.973310 −0.486655 0.873594i \(-0.661783\pi\)
−0.486655 + 0.873594i \(0.661783\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.24835 0.562708
\(58\) 0 0
\(59\) 0.272582 0.0354871 0.0177436 0.999843i \(-0.494352\pi\)
0.0177436 + 0.999843i \(0.494352\pi\)
\(60\) 0 0
\(61\) 4.78899 0.613167 0.306583 0.951844i \(-0.400814\pi\)
0.306583 + 0.951844i \(0.400814\pi\)
\(62\) 0 0
\(63\) 3.35386 0.422546
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 1.81322 0.221520 0.110760 0.993847i \(-0.464672\pi\)
0.110760 + 0.993847i \(0.464672\pi\)
\(68\) 0 0
\(69\) −6.24835 −0.752213
\(70\) 0 0
\(71\) −9.16707 −1.08793 −0.543966 0.839107i \(-0.683078\pi\)
−0.543966 + 0.839107i \(0.683078\pi\)
\(72\) 0 0
\(73\) −3.32962 −0.389703 −0.194851 0.980833i \(-0.562422\pi\)
−0.194851 + 0.980833i \(0.562422\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −12.7890 −1.45744
\(78\) 0 0
\(79\) −5.54064 −0.623370 −0.311685 0.950185i \(-0.600893\pi\)
−0.311685 + 0.950185i \(0.600893\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.27258 −0.688505 −0.344253 0.938877i \(-0.611868\pi\)
−0.344253 + 0.938877i \(0.611868\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −6.78899 −0.727856
\(88\) 0 0
\(89\) 3.78899 0.401632 0.200816 0.979629i \(-0.435641\pi\)
0.200816 + 0.979629i \(0.435641\pi\)
\(90\) 0 0
\(91\) −3.35386 −0.351580
\(92\) 0 0
\(93\) −5.97577 −0.619658
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.7077 −1.49334 −0.746671 0.665194i \(-0.768349\pi\)
−0.746671 + 0.665194i \(0.768349\pi\)
\(98\) 0 0
\(99\) −3.81322 −0.383243
\(100\) 0 0
\(101\) 7.03733 0.700241 0.350120 0.936705i \(-0.386141\pi\)
0.350120 + 0.936705i \(0.386141\pi\)
\(102\) 0 0
\(103\) 18.7935 1.85178 0.925890 0.377794i \(-0.123317\pi\)
0.925890 + 0.377794i \(0.123317\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.87026 0.470826 0.235413 0.971895i \(-0.424356\pi\)
0.235413 + 0.971895i \(0.424356\pi\)
\(108\) 0 0
\(109\) 1.32962 0.127355 0.0636774 0.997971i \(-0.479717\pi\)
0.0636774 + 0.997971i \(0.479717\pi\)
\(110\) 0 0
\(111\) −4.45936 −0.423264
\(112\) 0 0
\(113\) 5.78899 0.544582 0.272291 0.962215i \(-0.412219\pi\)
0.272291 + 0.962215i \(0.412219\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.00000 −0.0924500
\(118\) 0 0
\(119\) −3.35386 −0.307447
\(120\) 0 0
\(121\) 3.54064 0.321876
\(122\) 0 0
\(123\) −0.621911 −0.0560758
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.16707 −0.635975 −0.317988 0.948095i \(-0.603007\pi\)
−0.317988 + 0.948095i \(0.603007\pi\)
\(128\) 0 0
\(129\) 1.54064 0.135646
\(130\) 0 0
\(131\) −7.00453 −0.611988 −0.305994 0.952033i \(-0.598989\pi\)
−0.305994 + 0.952033i \(0.598989\pi\)
\(132\) 0 0
\(133\) 14.2483 1.23549
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.12974 −0.0965202 −0.0482601 0.998835i \(-0.515368\pi\)
−0.0482601 + 0.998835i \(0.515368\pi\)
\(138\) 0 0
\(139\) −4.16255 −0.353063 −0.176531 0.984295i \(-0.556488\pi\)
−0.176531 + 0.984295i \(0.556488\pi\)
\(140\) 0 0
\(141\) −9.14284 −0.769966
\(142\) 0 0
\(143\) 3.81322 0.318877
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 4.24835 0.350398
\(148\) 0 0
\(149\) 14.2857 1.17033 0.585164 0.810915i \(-0.301030\pi\)
0.585164 + 0.810915i \(0.301030\pi\)
\(150\) 0 0
\(151\) 9.85055 0.801627 0.400813 0.916160i \(-0.368728\pi\)
0.400813 + 0.916160i \(0.368728\pi\)
\(152\) 0 0
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −17.2483 −1.37657 −0.688284 0.725441i \(-0.741636\pi\)
−0.688284 + 0.725441i \(0.741636\pi\)
\(158\) 0 0
\(159\) −7.08580 −0.561941
\(160\) 0 0
\(161\) −20.9561 −1.65157
\(162\) 0 0
\(163\) 13.4922 1.05679 0.528394 0.848999i \(-0.322794\pi\)
0.528394 + 0.848999i \(0.322794\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.54064 −0.273983 −0.136991 0.990572i \(-0.543743\pi\)
−0.136991 + 0.990572i \(0.543743\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 4.24835 0.324879
\(172\) 0 0
\(173\) 2.37809 0.180803 0.0904014 0.995905i \(-0.471185\pi\)
0.0904014 + 0.995905i \(0.471185\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.272582 0.0204885
\(178\) 0 0
\(179\) −10.7935 −0.806745 −0.403372 0.915036i \(-0.632162\pi\)
−0.403372 + 0.915036i \(0.632162\pi\)
\(180\) 0 0
\(181\) −8.11861 −0.603451 −0.301726 0.953395i \(-0.597563\pi\)
−0.301726 + 0.953395i \(0.597563\pi\)
\(182\) 0 0
\(183\) 4.78899 0.354012
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.81322 0.278850
\(188\) 0 0
\(189\) 3.35386 0.243957
\(190\) 0 0
\(191\) −25.5780 −1.85076 −0.925379 0.379044i \(-0.876253\pi\)
−0.925379 + 0.379044i \(0.876253\pi\)
\(192\) 0 0
\(193\) 19.1671 1.37968 0.689838 0.723964i \(-0.257682\pi\)
0.689838 + 0.723964i \(0.257682\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.04394 −0.359366 −0.179683 0.983725i \(-0.557507\pi\)
−0.179683 + 0.983725i \(0.557507\pi\)
\(198\) 0 0
\(199\) −2.91873 −0.206903 −0.103451 0.994634i \(-0.532989\pi\)
−0.103451 + 0.994634i \(0.532989\pi\)
\(200\) 0 0
\(201\) 1.81322 0.127895
\(202\) 0 0
\(203\) −22.7693 −1.59809
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −6.24835 −0.434290
\(208\) 0 0
\(209\) −16.1999 −1.12057
\(210\) 0 0
\(211\) −15.1671 −1.04414 −0.522072 0.852901i \(-0.674841\pi\)
−0.522072 + 0.852901i \(0.674841\pi\)
\(212\) 0 0
\(213\) −9.16707 −0.628118
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −20.0419 −1.36053
\(218\) 0 0
\(219\) −3.32962 −0.224995
\(220\) 0 0
\(221\) 1.00000 0.0672673
\(222\) 0 0
\(223\) 28.4199 1.90314 0.951570 0.307431i \(-0.0994694\pi\)
0.951570 + 0.307431i \(0.0994694\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.4725 0.827827 0.413913 0.910316i \(-0.364162\pi\)
0.413913 + 0.910316i \(0.364162\pi\)
\(228\) 0 0
\(229\) −29.1559 −1.92668 −0.963339 0.268285i \(-0.913543\pi\)
−0.963339 + 0.268285i \(0.913543\pi\)
\(230\) 0 0
\(231\) −12.7890 −0.841453
\(232\) 0 0
\(233\) 2.21101 0.144848 0.0724242 0.997374i \(-0.476926\pi\)
0.0724242 + 0.997374i \(0.476926\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.54064 −0.359903
\(238\) 0 0
\(239\) −13.8506 −0.895918 −0.447959 0.894054i \(-0.647849\pi\)
−0.447959 + 0.894054i \(0.647849\pi\)
\(240\) 0 0
\(241\) 7.49217 0.482613 0.241307 0.970449i \(-0.422424\pi\)
0.241307 + 0.970449i \(0.422424\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.24835 −0.270316
\(248\) 0 0
\(249\) −6.27258 −0.397509
\(250\) 0 0
\(251\) −4.78446 −0.301992 −0.150996 0.988534i \(-0.548248\pi\)
−0.150996 + 0.988534i \(0.548248\pi\)
\(252\) 0 0
\(253\) 23.8263 1.49795
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 15.4199 0.961870 0.480935 0.876756i \(-0.340297\pi\)
0.480935 + 0.876756i \(0.340297\pi\)
\(258\) 0 0
\(259\) −14.9561 −0.929324
\(260\) 0 0
\(261\) −6.78899 −0.420228
\(262\) 0 0
\(263\) 29.8748 1.84216 0.921079 0.389375i \(-0.127309\pi\)
0.921079 + 0.389375i \(0.127309\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3.78899 0.231882
\(268\) 0 0
\(269\) 7.16255 0.436708 0.218354 0.975870i \(-0.429931\pi\)
0.218354 + 0.975870i \(0.429931\pi\)
\(270\) 0 0
\(271\) 16.1847 0.983151 0.491575 0.870835i \(-0.336421\pi\)
0.491575 + 0.870835i \(0.336421\pi\)
\(272\) 0 0
\(273\) −3.35386 −0.202985
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 25.5386 1.53446 0.767232 0.641370i \(-0.221634\pi\)
0.767232 + 0.641370i \(0.221634\pi\)
\(278\) 0 0
\(279\) −5.97577 −0.357760
\(280\) 0 0
\(281\) 8.65925 0.516567 0.258284 0.966069i \(-0.416843\pi\)
0.258284 + 0.966069i \(0.416843\pi\)
\(282\) 0 0
\(283\) −15.9121 −0.945877 −0.472939 0.881095i \(-0.656807\pi\)
−0.472939 + 0.881095i \(0.656807\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.08580 −0.123121
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) −14.7077 −0.862181
\(292\) 0 0
\(293\) 13.2529 0.774241 0.387121 0.922029i \(-0.373470\pi\)
0.387121 + 0.922029i \(0.373470\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.81322 −0.221265
\(298\) 0 0
\(299\) 6.24835 0.361351
\(300\) 0 0
\(301\) 5.16707 0.297825
\(302\) 0 0
\(303\) 7.03733 0.404284
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 2.12521 0.121292 0.0606462 0.998159i \(-0.480684\pi\)
0.0606462 + 0.998159i \(0.480684\pi\)
\(308\) 0 0
\(309\) 18.7935 1.06913
\(310\) 0 0
\(311\) 19.9121 1.12911 0.564556 0.825395i \(-0.309047\pi\)
0.564556 + 0.825395i \(0.309047\pi\)
\(312\) 0 0
\(313\) −6.50122 −0.367471 −0.183735 0.982976i \(-0.558819\pi\)
−0.183735 + 0.982976i \(0.558819\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −23.3296 −1.31032 −0.655161 0.755489i \(-0.727399\pi\)
−0.655161 + 0.755489i \(0.727399\pi\)
\(318\) 0 0
\(319\) 25.8879 1.44944
\(320\) 0 0
\(321\) 4.87026 0.271831
\(322\) 0 0
\(323\) −4.24835 −0.236384
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.32962 0.0735283
\(328\) 0 0
\(329\) −30.6638 −1.69055
\(330\) 0 0
\(331\) −7.32962 −0.402873 −0.201436 0.979502i \(-0.564561\pi\)
−0.201436 + 0.979502i \(0.564561\pi\)
\(332\) 0 0
\(333\) −4.45936 −0.244372
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −9.03733 −0.492295 −0.246147 0.969232i \(-0.579165\pi\)
−0.246147 + 0.969232i \(0.579165\pi\)
\(338\) 0 0
\(339\) 5.78899 0.314415
\(340\) 0 0
\(341\) 22.7869 1.23398
\(342\) 0 0
\(343\) −9.22864 −0.498300
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −21.1559 −1.13571 −0.567855 0.823128i \(-0.692227\pi\)
−0.567855 + 0.823128i \(0.692227\pi\)
\(348\) 0 0
\(349\) 0.956060 0.0511767 0.0255884 0.999673i \(-0.491854\pi\)
0.0255884 + 0.999673i \(0.491854\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 29.7869 1.58540 0.792699 0.609614i \(-0.208675\pi\)
0.792699 + 0.609614i \(0.208675\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −3.35386 −0.177505
\(358\) 0 0
\(359\) 35.2660 1.86127 0.930634 0.365953i \(-0.119257\pi\)
0.930634 + 0.365953i \(0.119257\pi\)
\(360\) 0 0
\(361\) −0.951534 −0.0500807
\(362\) 0 0
\(363\) 3.54064 0.185835
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 13.8375 0.722309 0.361155 0.932506i \(-0.382383\pi\)
0.361155 + 0.932506i \(0.382383\pi\)
\(368\) 0 0
\(369\) −0.621911 −0.0323754
\(370\) 0 0
\(371\) −23.7648 −1.23380
\(372\) 0 0
\(373\) −18.2812 −0.946562 −0.473281 0.880911i \(-0.656931\pi\)
−0.473281 + 0.880911i \(0.656931\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.78899 0.349651
\(378\) 0 0
\(379\) 15.0086 0.770939 0.385469 0.922721i \(-0.374040\pi\)
0.385469 + 0.922721i \(0.374040\pi\)
\(380\) 0 0
\(381\) −7.16707 −0.367180
\(382\) 0 0
\(383\) −15.5012 −0.792076 −0.396038 0.918234i \(-0.629615\pi\)
−0.396038 + 0.918234i \(0.629615\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 1.54064 0.0783150
\(388\) 0 0
\(389\) −17.0419 −0.864057 −0.432028 0.901860i \(-0.642202\pi\)
−0.432028 + 0.901860i \(0.642202\pi\)
\(390\) 0 0
\(391\) 6.24835 0.315993
\(392\) 0 0
\(393\) −7.00453 −0.353332
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −23.2044 −1.16460 −0.582298 0.812975i \(-0.697846\pi\)
−0.582298 + 0.812975i \(0.697846\pi\)
\(398\) 0 0
\(399\) 14.2483 0.713310
\(400\) 0 0
\(401\) −11.1186 −0.555237 −0.277618 0.960691i \(-0.589545\pi\)
−0.277618 + 0.960691i \(0.589545\pi\)
\(402\) 0 0
\(403\) 5.97577 0.297674
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 17.0045 0.842883
\(408\) 0 0
\(409\) 3.87479 0.191596 0.0957979 0.995401i \(-0.469460\pi\)
0.0957979 + 0.995401i \(0.469460\pi\)
\(410\) 0 0
\(411\) −1.12974 −0.0557260
\(412\) 0 0
\(413\) 0.914200 0.0449848
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4.16255 −0.203841
\(418\) 0 0
\(419\) 13.8748 0.677828 0.338914 0.940817i \(-0.389940\pi\)
0.338914 + 0.940817i \(0.389940\pi\)
\(420\) 0 0
\(421\) −37.5870 −1.83188 −0.915940 0.401316i \(-0.868553\pi\)
−0.915940 + 0.401316i \(0.868553\pi\)
\(422\) 0 0
\(423\) −9.14284 −0.444540
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 16.0616 0.777274
\(428\) 0 0
\(429\) 3.81322 0.184104
\(430\) 0 0
\(431\) 6.58250 0.317068 0.158534 0.987354i \(-0.449323\pi\)
0.158534 + 0.987354i \(0.449323\pi\)
\(432\) 0 0
\(433\) 20.5452 0.987338 0.493669 0.869650i \(-0.335656\pi\)
0.493669 + 0.869650i \(0.335656\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −26.5452 −1.26983
\(438\) 0 0
\(439\) −23.4922 −1.12122 −0.560610 0.828080i \(-0.689433\pi\)
−0.560610 + 0.828080i \(0.689433\pi\)
\(440\) 0 0
\(441\) 4.24835 0.202302
\(442\) 0 0
\(443\) −5.04394 −0.239645 −0.119822 0.992795i \(-0.538233\pi\)
−0.119822 + 0.992795i \(0.538233\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 14.2857 0.675690
\(448\) 0 0
\(449\) 18.3341 0.865242 0.432621 0.901576i \(-0.357589\pi\)
0.432621 + 0.901576i \(0.357589\pi\)
\(450\) 0 0
\(451\) 2.37148 0.111669
\(452\) 0 0
\(453\) 9.85055 0.462819
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 26.2089 1.22600 0.613001 0.790082i \(-0.289962\pi\)
0.613001 + 0.790082i \(0.289962\pi\)
\(458\) 0 0
\(459\) −1.00000 −0.0466760
\(460\) 0 0
\(461\) −34.4967 −1.60667 −0.803336 0.595526i \(-0.796943\pi\)
−0.803336 + 0.595526i \(0.796943\pi\)
\(462\) 0 0
\(463\) 5.43060 0.252382 0.126191 0.992006i \(-0.459725\pi\)
0.126191 + 0.992006i \(0.459725\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 35.0419 1.62154 0.810772 0.585362i \(-0.199048\pi\)
0.810772 + 0.585362i \(0.199048\pi\)
\(468\) 0 0
\(469\) 6.08127 0.280807
\(470\) 0 0
\(471\) −17.2483 −0.794762
\(472\) 0 0
\(473\) −5.87479 −0.270123
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −7.08580 −0.324437
\(478\) 0 0
\(479\) 24.0989 1.10111 0.550553 0.834800i \(-0.314417\pi\)
0.550553 + 0.834800i \(0.314417\pi\)
\(480\) 0 0
\(481\) 4.45936 0.203329
\(482\) 0 0
\(483\) −20.9561 −0.953534
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −31.2286 −1.41510 −0.707552 0.706661i \(-0.750201\pi\)
−0.707552 + 0.706661i \(0.750201\pi\)
\(488\) 0 0
\(489\) 13.4922 0.610137
\(490\) 0 0
\(491\) −13.2529 −0.598094 −0.299047 0.954238i \(-0.596669\pi\)
−0.299047 + 0.954238i \(0.596669\pi\)
\(492\) 0 0
\(493\) 6.78899 0.305761
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −30.7450 −1.37910
\(498\) 0 0
\(499\) −40.6329 −1.81898 −0.909490 0.415726i \(-0.863528\pi\)
−0.909490 + 0.415726i \(0.863528\pi\)
\(500\) 0 0
\(501\) −3.54064 −0.158184
\(502\) 0 0
\(503\) 31.0792 1.38575 0.692876 0.721056i \(-0.256343\pi\)
0.692876 + 0.721056i \(0.256343\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 0 0
\(509\) −20.4109 −0.904697 −0.452349 0.891841i \(-0.649414\pi\)
−0.452349 + 0.891841i \(0.649414\pi\)
\(510\) 0 0
\(511\) −11.1671 −0.494002
\(512\) 0 0
\(513\) 4.24835 0.187569
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 34.8637 1.53330
\(518\) 0 0
\(519\) 2.37809 0.104387
\(520\) 0 0
\(521\) −9.57797 −0.419619 −0.209809 0.977742i \(-0.567284\pi\)
−0.209809 + 0.977742i \(0.567284\pi\)
\(522\) 0 0
\(523\) 19.1297 0.836485 0.418243 0.908335i \(-0.362646\pi\)
0.418243 + 0.908335i \(0.362646\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 5.97577 0.260308
\(528\) 0 0
\(529\) 16.0419 0.697472
\(530\) 0 0
\(531\) 0.272582 0.0118290
\(532\) 0 0
\(533\) 0.621911 0.0269380
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −10.7935 −0.465774
\(538\) 0 0
\(539\) −16.1999 −0.697778
\(540\) 0 0
\(541\) −26.6572 −1.14608 −0.573041 0.819527i \(-0.694236\pi\)
−0.573041 + 0.819527i \(0.694236\pi\)
\(542\) 0 0
\(543\) −8.11861 −0.348403
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 16.9561 0.724989 0.362494 0.931986i \(-0.381925\pi\)
0.362494 + 0.931986i \(0.381925\pi\)
\(548\) 0 0
\(549\) 4.78899 0.204389
\(550\) 0 0
\(551\) −28.8420 −1.22871
\(552\) 0 0
\(553\) −18.5825 −0.790208
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −29.5012 −1.25001 −0.625003 0.780622i \(-0.714902\pi\)
−0.625003 + 0.780622i \(0.714902\pi\)
\(558\) 0 0
\(559\) −1.54064 −0.0651620
\(560\) 0 0
\(561\) 3.81322 0.160994
\(562\) 0 0
\(563\) −41.4043 −1.74498 −0.872491 0.488629i \(-0.837497\pi\)
−0.872491 + 0.488629i \(0.837497\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 3.35386 0.140849
\(568\) 0 0
\(569\) −46.4618 −1.94778 −0.973890 0.227020i \(-0.927102\pi\)
−0.973890 + 0.227020i \(0.927102\pi\)
\(570\) 0 0
\(571\) −1.82632 −0.0764291 −0.0382146 0.999270i \(-0.512167\pi\)
−0.0382146 + 0.999270i \(0.512167\pi\)
\(572\) 0 0
\(573\) −25.5780 −1.06854
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −35.7980 −1.49029 −0.745146 0.666901i \(-0.767620\pi\)
−0.745146 + 0.666901i \(0.767620\pi\)
\(578\) 0 0
\(579\) 19.1671 0.796556
\(580\) 0 0
\(581\) −21.0373 −0.872776
\(582\) 0 0
\(583\) 27.0197 1.11904
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −34.9297 −1.44170 −0.720852 0.693089i \(-0.756249\pi\)
−0.720852 + 0.693089i \(0.756249\pi\)
\(588\) 0 0
\(589\) −25.3871 −1.04606
\(590\) 0 0
\(591\) −5.04394 −0.207480
\(592\) 0 0
\(593\) 22.4967 0.923829 0.461914 0.886925i \(-0.347163\pi\)
0.461914 + 0.886925i \(0.347163\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.91873 −0.119455
\(598\) 0 0
\(599\) 24.7450 1.01106 0.505528 0.862810i \(-0.331298\pi\)
0.505528 + 0.862810i \(0.331298\pi\)
\(600\) 0 0
\(601\) −1.57345 −0.0641822 −0.0320911 0.999485i \(-0.510217\pi\)
−0.0320911 + 0.999485i \(0.510217\pi\)
\(602\) 0 0
\(603\) 1.81322 0.0738400
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 36.9449 1.49955 0.749774 0.661694i \(-0.230162\pi\)
0.749774 + 0.661694i \(0.230162\pi\)
\(608\) 0 0
\(609\) −22.7693 −0.922658
\(610\) 0 0
\(611\) 9.14284 0.369880
\(612\) 0 0
\(613\) −17.2529 −0.696837 −0.348419 0.937339i \(-0.613281\pi\)
−0.348419 + 0.937339i \(0.613281\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.9515 −0.642185 −0.321092 0.947048i \(-0.604050\pi\)
−0.321092 + 0.947048i \(0.604050\pi\)
\(618\) 0 0
\(619\) 11.7122 0.470755 0.235377 0.971904i \(-0.424367\pi\)
0.235377 + 0.971904i \(0.424367\pi\)
\(620\) 0 0
\(621\) −6.24835 −0.250738
\(622\) 0 0
\(623\) 12.7077 0.509124
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −16.1999 −0.646961
\(628\) 0 0
\(629\) 4.45936 0.177806
\(630\) 0 0
\(631\) −28.0373 −1.11615 −0.558074 0.829791i \(-0.688460\pi\)
−0.558074 + 0.829791i \(0.688460\pi\)
\(632\) 0 0
\(633\) −15.1671 −0.602837
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −4.24835 −0.168326
\(638\) 0 0
\(639\) −9.16707 −0.362644
\(640\) 0 0
\(641\) −35.6683 −1.40881 −0.704407 0.709797i \(-0.748787\pi\)
−0.704407 + 0.709797i \(0.748787\pi\)
\(642\) 0 0
\(643\) 34.0858 1.34421 0.672106 0.740455i \(-0.265390\pi\)
0.672106 + 0.740455i \(0.265390\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.7890 0.620729 0.310365 0.950618i \(-0.399549\pi\)
0.310365 + 0.950618i \(0.399549\pi\)
\(648\) 0 0
\(649\) −1.03941 −0.0408005
\(650\) 0 0
\(651\) −20.0419 −0.785502
\(652\) 0 0
\(653\) −16.9031 −0.661468 −0.330734 0.943724i \(-0.607296\pi\)
−0.330734 + 0.943724i \(0.607296\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −3.32962 −0.129901
\(658\) 0 0
\(659\) 16.1252 0.628149 0.314075 0.949398i \(-0.398306\pi\)
0.314075 + 0.949398i \(0.398306\pi\)
\(660\) 0 0
\(661\) 20.5250 0.798329 0.399165 0.916879i \(-0.369300\pi\)
0.399165 + 0.916879i \(0.369300\pi\)
\(662\) 0 0
\(663\) 1.00000 0.0388368
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 42.4199 1.64251
\(668\) 0 0
\(669\) 28.4199 1.09878
\(670\) 0 0
\(671\) −18.2614 −0.704975
\(672\) 0 0
\(673\) 39.9561 1.54019 0.770096 0.637927i \(-0.220208\pi\)
0.770096 + 0.637927i \(0.220208\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.49670 0.0959559 0.0479779 0.998848i \(-0.484722\pi\)
0.0479779 + 0.998848i \(0.484722\pi\)
\(678\) 0 0
\(679\) −49.3275 −1.89302
\(680\) 0 0
\(681\) 12.4725 0.477946
\(682\) 0 0
\(683\) −30.3099 −1.15978 −0.579888 0.814696i \(-0.696904\pi\)
−0.579888 + 0.814696i \(0.696904\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −29.1559 −1.11237
\(688\) 0 0
\(689\) 7.08580 0.269947
\(690\) 0 0
\(691\) −50.3563 −1.91564 −0.957822 0.287362i \(-0.907222\pi\)
−0.957822 + 0.287362i \(0.907222\pi\)
\(692\) 0 0
\(693\) −12.7890 −0.485813
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0.621911 0.0235566
\(698\) 0 0
\(699\) 2.21101 0.0836282
\(700\) 0 0
\(701\) 10.3670 0.391555 0.195777 0.980648i \(-0.437277\pi\)
0.195777 + 0.980648i \(0.437277\pi\)
\(702\) 0 0
\(703\) −18.9449 −0.714522
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 23.6022 0.887652
\(708\) 0 0
\(709\) −7.87479 −0.295744 −0.147872 0.989007i \(-0.547242\pi\)
−0.147872 + 0.989007i \(0.547242\pi\)
\(710\) 0 0
\(711\) −5.54064 −0.207790
\(712\) 0 0
\(713\) 37.3387 1.39834
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −13.8506 −0.517258
\(718\) 0 0
\(719\) 18.1252 0.675956 0.337978 0.941154i \(-0.390257\pi\)
0.337978 + 0.941154i \(0.390257\pi\)
\(720\) 0 0
\(721\) 63.0307 2.34739
\(722\) 0 0
\(723\) 7.49217 0.278637
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 28.5340 1.05827 0.529134 0.848538i \(-0.322517\pi\)
0.529134 + 0.848538i \(0.322517\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −1.54064 −0.0569825
\(732\) 0 0
\(733\) −27.4245 −1.01295 −0.506473 0.862256i \(-0.669051\pi\)
−0.506473 + 0.862256i \(0.669051\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.91420 −0.254688
\(738\) 0 0
\(739\) 2.52093 0.0927339 0.0463670 0.998924i \(-0.485236\pi\)
0.0463670 + 0.998924i \(0.485236\pi\)
\(740\) 0 0
\(741\) −4.24835 −0.156067
\(742\) 0 0
\(743\) 13.9364 0.511275 0.255638 0.966773i \(-0.417715\pi\)
0.255638 + 0.966773i \(0.417715\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −6.27258 −0.229502
\(748\) 0 0
\(749\) 16.3341 0.596837
\(750\) 0 0
\(751\) −24.2574 −0.885165 −0.442583 0.896728i \(-0.645938\pi\)
−0.442583 + 0.896728i \(0.645938\pi\)
\(752\) 0 0
\(753\) −4.78446 −0.174355
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.32510 −0.0481615 −0.0240807 0.999710i \(-0.507666\pi\)
−0.0240807 + 0.999710i \(0.507666\pi\)
\(758\) 0 0
\(759\) 23.8263 0.864841
\(760\) 0 0
\(761\) −7.32962 −0.265699 −0.132849 0.991136i \(-0.542413\pi\)
−0.132849 + 0.991136i \(0.542413\pi\)
\(762\) 0 0
\(763\) 4.45936 0.161440
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.272582 −0.00984235
\(768\) 0 0
\(769\) 4.70771 0.169764 0.0848822 0.996391i \(-0.472949\pi\)
0.0848822 + 0.996391i \(0.472949\pi\)
\(770\) 0 0
\(771\) 15.4199 0.555336
\(772\) 0 0
\(773\) −18.7077 −0.672870 −0.336435 0.941707i \(-0.609221\pi\)
−0.336435 + 0.941707i \(0.609221\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −14.9561 −0.536546
\(778\) 0 0
\(779\) −2.64210 −0.0946629
\(780\) 0 0
\(781\) 34.9561 1.25083
\(782\) 0 0
\(783\) −6.78899 −0.242619
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −15.0176 −0.535321 −0.267660 0.963513i \(-0.586250\pi\)
−0.267660 + 0.963513i \(0.586250\pi\)
\(788\) 0 0
\(789\) 29.8748 1.06357
\(790\) 0 0
\(791\) 19.4154 0.690333
\(792\) 0 0
\(793\) −4.78899 −0.170062
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −50.2135 −1.77865 −0.889326 0.457274i \(-0.848826\pi\)
−0.889326 + 0.457274i \(0.848826\pi\)
\(798\) 0 0
\(799\) 9.14284 0.323450
\(800\) 0 0
\(801\) 3.78899 0.133877
\(802\) 0 0
\(803\) 12.6966 0.448053
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 7.16255 0.252134
\(808\) 0 0
\(809\) −13.7143 −0.482170 −0.241085 0.970504i \(-0.577503\pi\)
−0.241085 + 0.970504i \(0.577503\pi\)
\(810\) 0 0
\(811\) 30.3473 1.06564 0.532818 0.846230i \(-0.321133\pi\)
0.532818 + 0.846230i \(0.321133\pi\)
\(812\) 0 0
\(813\) 16.1847 0.567622
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 6.54516 0.228986
\(818\) 0 0
\(819\) −3.35386 −0.117193
\(820\) 0 0
\(821\) −0.287762 −0.0100430 −0.00502148 0.999987i \(-0.501598\pi\)
−0.00502148 + 0.999987i \(0.501598\pi\)
\(822\) 0 0
\(823\) 41.1075 1.43292 0.716458 0.697630i \(-0.245762\pi\)
0.716458 + 0.697630i \(0.245762\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 37.0176 1.28723 0.643615 0.765350i \(-0.277434\pi\)
0.643615 + 0.765350i \(0.277434\pi\)
\(828\) 0 0
\(829\) −50.7011 −1.76092 −0.880461 0.474118i \(-0.842767\pi\)
−0.880461 + 0.474118i \(0.842767\pi\)
\(830\) 0 0
\(831\) 25.5386 0.885923
\(832\) 0 0
\(833\) −4.24835 −0.147197
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −5.97577 −0.206553
\(838\) 0 0
\(839\) 44.4199 1.53355 0.766773 0.641918i \(-0.221861\pi\)
0.766773 + 0.641918i \(0.221861\pi\)
\(840\) 0 0
\(841\) 17.0903 0.589322
\(842\) 0 0
\(843\) 8.65925 0.298240
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 11.8748 0.408022
\(848\) 0 0
\(849\) −15.9121 −0.546103
\(850\) 0 0
\(851\) 27.8637 0.955154
\(852\) 0 0
\(853\) 14.4088 0.493349 0.246674 0.969098i \(-0.420662\pi\)
0.246674 + 0.969098i \(0.420662\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 45.1559 1.54250 0.771249 0.636534i \(-0.219632\pi\)
0.771249 + 0.636534i \(0.219632\pi\)
\(858\) 0 0
\(859\) −7.54969 −0.257592 −0.128796 0.991671i \(-0.541111\pi\)
−0.128796 + 0.991671i \(0.541111\pi\)
\(860\) 0 0
\(861\) −2.08580 −0.0710839
\(862\) 0 0
\(863\) −28.8551 −0.982238 −0.491119 0.871092i \(-0.663412\pi\)
−0.491119 + 0.871092i \(0.663412\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −16.0000 −0.543388
\(868\) 0 0
\(869\) 21.1277 0.716707
\(870\) 0 0
\(871\) −1.81322 −0.0614386
\(872\) 0 0
\(873\) −14.7077 −0.497781
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −25.7011 −0.867865 −0.433932 0.900945i \(-0.642874\pi\)
−0.433932 + 0.900945i \(0.642874\pi\)
\(878\) 0 0
\(879\) 13.2529 0.447008
\(880\) 0 0
\(881\) 4.32962 0.145869 0.0729343 0.997337i \(-0.476764\pi\)
0.0729343 + 0.997337i \(0.476764\pi\)
\(882\) 0 0
\(883\) 53.3760 1.79625 0.898123 0.439745i \(-0.144931\pi\)
0.898123 + 0.439745i \(0.144931\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.19988 0.275325 0.137663 0.990479i \(-0.456041\pi\)
0.137663 + 0.990479i \(0.456041\pi\)
\(888\) 0 0
\(889\) −24.0373 −0.806186
\(890\) 0 0
\(891\) −3.81322 −0.127748
\(892\) 0 0
\(893\) −38.8420 −1.29980
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 6.24835 0.208626
\(898\) 0 0
\(899\) 40.5694 1.35307
\(900\) 0 0
\(901\) 7.08580 0.236062
\(902\) 0 0
\(903\) 5.16707 0.171949
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −22.4088 −0.744073 −0.372036 0.928218i \(-0.621340\pi\)
−0.372036 + 0.928218i \(0.621340\pi\)
\(908\) 0 0
\(909\) 7.03733 0.233414
\(910\) 0 0
\(911\) −2.57345 −0.0852620 −0.0426310 0.999091i \(-0.513574\pi\)
−0.0426310 + 0.999091i \(0.513574\pi\)
\(912\) 0 0
\(913\) 23.9187 0.791594
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −23.4922 −0.775780
\(918\) 0 0
\(919\) 22.7824 0.751521 0.375761 0.926717i \(-0.377381\pi\)
0.375761 + 0.926717i \(0.377381\pi\)
\(920\) 0 0
\(921\) 2.12521 0.0700282
\(922\) 0 0
\(923\) 9.16707 0.301738
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 18.7935 0.617260
\(928\) 0 0
\(929\) −14.5936 −0.478801 −0.239401 0.970921i \(-0.576951\pi\)
−0.239401 + 0.970921i \(0.576951\pi\)
\(930\) 0 0
\(931\) 18.0485 0.591515
\(932\) 0 0
\(933\) 19.9121 0.651894
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 5.11408 0.167070 0.0835349 0.996505i \(-0.473379\pi\)
0.0835349 + 0.996505i \(0.473379\pi\)
\(938\) 0 0
\(939\) −6.50122 −0.212159
\(940\) 0 0
\(941\) −44.5734 −1.45305 −0.726526 0.687139i \(-0.758867\pi\)
−0.726526 + 0.687139i \(0.758867\pi\)
\(942\) 0 0
\(943\) 3.88592 0.126543
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 28.3493 0.921229 0.460615 0.887600i \(-0.347629\pi\)
0.460615 + 0.887600i \(0.347629\pi\)
\(948\) 0 0
\(949\) 3.32962 0.108084
\(950\) 0 0
\(951\) −23.3296 −0.756515
\(952\) 0 0
\(953\) −49.7056 −1.61012 −0.805062 0.593191i \(-0.797868\pi\)
−0.805062 + 0.593191i \(0.797868\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 25.8879 0.836837
\(958\) 0 0
\(959\) −3.78899 −0.122353
\(960\) 0 0
\(961\) 4.70979 0.151929
\(962\) 0 0
\(963\) 4.87026 0.156942
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −5.21959 −0.167851 −0.0839253 0.996472i \(-0.526746\pi\)
−0.0839253 + 0.996472i \(0.526746\pi\)
\(968\) 0 0
\(969\) −4.24835 −0.136477
\(970\) 0 0
\(971\) 48.1978 1.54674 0.773371 0.633954i \(-0.218569\pi\)
0.773371 + 0.633954i \(0.218569\pi\)
\(972\) 0 0
\(973\) −13.9606 −0.447556
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −24.9187 −0.797221 −0.398610 0.917120i \(-0.630507\pi\)
−0.398610 + 0.917120i \(0.630507\pi\)
\(978\) 0 0
\(979\) −14.4482 −0.461767
\(980\) 0 0
\(981\) 1.32962 0.0424516
\(982\) 0 0
\(983\) −37.5537 −1.19778 −0.598889 0.800832i \(-0.704391\pi\)
−0.598889 + 0.800832i \(0.704391\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −30.6638 −0.976039
\(988\) 0 0
\(989\) −9.62644 −0.306103
\(990\) 0 0
\(991\) −47.8354 −1.51954 −0.759770 0.650192i \(-0.774689\pi\)
−0.759770 + 0.650192i \(0.774689\pi\)
\(992\) 0 0
\(993\) −7.32962 −0.232599
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 40.0509 1.26843 0.634213 0.773159i \(-0.281324\pi\)
0.634213 + 0.773159i \(0.281324\pi\)
\(998\) 0 0
\(999\) −4.45936 −0.141088
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 7800.2.a.br.1.3 yes 3
5.4 even 2 7800.2.a.bg.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7800.2.a.bg.1.1 3 5.4 even 2
7800.2.a.br.1.3 yes 3 1.1 even 1 trivial