Properties

Label 7448.2.a.bq.1.6
Level $7448$
Weight $2$
Character 7448.1
Self dual yes
Analytic conductor $59.473$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - 15 x^{6} - x^{5} + 66 x^{4} + 4 x^{3} - 76 x^{2} + 8 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.912296\) of defining polynomial
Character \(\chi\) \(=\) 7448.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.912296 q^{3} -1.66528 q^{5} -2.16772 q^{9} +O(q^{10})\) \(q+0.912296 q^{3} -1.66528 q^{5} -2.16772 q^{9} -0.242241 q^{11} -5.76999 q^{13} -1.51923 q^{15} +5.76637 q^{17} +1.00000 q^{19} +6.61545 q^{23} -2.22684 q^{25} -4.71449 q^{27} +8.91381 q^{29} -5.93284 q^{31} -0.220995 q^{33} -9.80371 q^{37} -5.26394 q^{39} -2.00000 q^{41} -7.83237 q^{43} +3.60986 q^{45} +1.57918 q^{47} +5.26064 q^{51} +6.48146 q^{53} +0.403399 q^{55} +0.912296 q^{57} +1.07498 q^{59} +9.10907 q^{61} +9.60866 q^{65} +8.02541 q^{67} +6.03525 q^{69} +1.22955 q^{71} +0.801370 q^{73} -2.03153 q^{75} -7.58202 q^{79} +2.20214 q^{81} -8.91292 q^{83} -9.60264 q^{85} +8.13204 q^{87} -13.1146 q^{89} -5.41250 q^{93} -1.66528 q^{95} +1.11664 q^{97} +0.525109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{5} + 6q^{9} + O(q^{10}) \) \( 8q - q^{5} + 6q^{9} + 9q^{11} + 8q^{15} + 4q^{17} + 8q^{19} + 25q^{23} + 15q^{25} + 3q^{27} + 6q^{29} + 8q^{33} + 13q^{37} - 11q^{39} - 16q^{41} + 17q^{43} + 17q^{45} - 24q^{47} + 5q^{51} + 2q^{53} + 5q^{55} + 2q^{59} - 13q^{61} - 26q^{65} + 2q^{67} - 11q^{69} + 10q^{71} + 5q^{73} - 20q^{75} + 16q^{79} - 12q^{81} - 43q^{83} + 24q^{85} + 20q^{87} + 8q^{89} + 2q^{93} - q^{95} - 12q^{97} + 37q^{99} + O(q^{100}) \)

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
\(3\) 0.912296 0.526714 0.263357 0.964698i \(-0.415170\pi\)
0.263357 + 0.964698i \(0.415170\pi\)
\(4\) 0 0
\(5\) −1.66528 −0.744737 −0.372368 0.928085i \(-0.621454\pi\)
−0.372368 + 0.928085i \(0.621454\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −2.16772 −0.722572
\(10\) 0 0
\(11\) −0.242241 −0.0730384 −0.0365192 0.999333i \(-0.511627\pi\)
−0.0365192 + 0.999333i \(0.511627\pi\)
\(12\) 0 0
\(13\) −5.76999 −1.60031 −0.800154 0.599795i \(-0.795249\pi\)
−0.800154 + 0.599795i \(0.795249\pi\)
\(14\) 0 0
\(15\) −1.51923 −0.392264
\(16\) 0 0
\(17\) 5.76637 1.39855 0.699275 0.714852i \(-0.253506\pi\)
0.699275 + 0.714852i \(0.253506\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.61545 1.37942 0.689709 0.724087i \(-0.257739\pi\)
0.689709 + 0.724087i \(0.257739\pi\)
\(24\) 0 0
\(25\) −2.22684 −0.445367
\(26\) 0 0
\(27\) −4.71449 −0.907303
\(28\) 0 0
\(29\) 8.91381 1.65525 0.827627 0.561279i \(-0.189690\pi\)
0.827627 + 0.561279i \(0.189690\pi\)
\(30\) 0 0
\(31\) −5.93284 −1.06557 −0.532785 0.846251i \(-0.678854\pi\)
−0.532785 + 0.846251i \(0.678854\pi\)
\(32\) 0 0
\(33\) −0.220995 −0.0384704
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −9.80371 −1.61172 −0.805860 0.592106i \(-0.798297\pi\)
−0.805860 + 0.592106i \(0.798297\pi\)
\(38\) 0 0
\(39\) −5.26394 −0.842905
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −7.83237 −1.19443 −0.597213 0.802083i \(-0.703725\pi\)
−0.597213 + 0.802083i \(0.703725\pi\)
\(44\) 0 0
\(45\) 3.60986 0.538126
\(46\) 0 0
\(47\) 1.57918 0.230347 0.115173 0.993345i \(-0.463258\pi\)
0.115173 + 0.993345i \(0.463258\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 5.26064 0.736637
\(52\) 0 0
\(53\) 6.48146 0.890297 0.445148 0.895457i \(-0.353151\pi\)
0.445148 + 0.895457i \(0.353151\pi\)
\(54\) 0 0
\(55\) 0.403399 0.0543944
\(56\) 0 0
\(57\) 0.912296 0.120837
\(58\) 0 0
\(59\) 1.07498 0.139950 0.0699750 0.997549i \(-0.477708\pi\)
0.0699750 + 0.997549i \(0.477708\pi\)
\(60\) 0 0
\(61\) 9.10907 1.16630 0.583149 0.812366i \(-0.301821\pi\)
0.583149 + 0.812366i \(0.301821\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 9.60866 1.19181
\(66\) 0 0
\(67\) 8.02541 0.980460 0.490230 0.871593i \(-0.336913\pi\)
0.490230 + 0.871593i \(0.336913\pi\)
\(68\) 0 0
\(69\) 6.03525 0.726559
\(70\) 0 0
\(71\) 1.22955 0.145921 0.0729606 0.997335i \(-0.476755\pi\)
0.0729606 + 0.997335i \(0.476755\pi\)
\(72\) 0 0
\(73\) 0.801370 0.0937933 0.0468966 0.998900i \(-0.485067\pi\)
0.0468966 + 0.998900i \(0.485067\pi\)
\(74\) 0 0
\(75\) −2.03153 −0.234581
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −7.58202 −0.853044 −0.426522 0.904477i \(-0.640261\pi\)
−0.426522 + 0.904477i \(0.640261\pi\)
\(80\) 0 0
\(81\) 2.20214 0.244682
\(82\) 0 0
\(83\) −8.91292 −0.978320 −0.489160 0.872194i \(-0.662697\pi\)
−0.489160 + 0.872194i \(0.662697\pi\)
\(84\) 0 0
\(85\) −9.60264 −1.04155
\(86\) 0 0
\(87\) 8.13204 0.871846
\(88\) 0 0
\(89\) −13.1146 −1.39015 −0.695074 0.718938i \(-0.744628\pi\)
−0.695074 + 0.718938i \(0.744628\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −5.41250 −0.561250
\(94\) 0 0
\(95\) −1.66528 −0.170854
\(96\) 0 0
\(97\) 1.11664 0.113377 0.0566886 0.998392i \(-0.481946\pi\)
0.0566886 + 0.998392i \(0.481946\pi\)
\(98\) 0 0
\(99\) 0.525109 0.0527755
\(100\) 0 0
\(101\) 13.0276 1.29630 0.648149 0.761514i \(-0.275543\pi\)
0.648149 + 0.761514i \(0.275543\pi\)
\(102\) 0 0
\(103\) −13.7259 −1.35245 −0.676226 0.736694i \(-0.736386\pi\)
−0.676226 + 0.736694i \(0.736386\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.76847 0.364312 0.182156 0.983270i \(-0.441692\pi\)
0.182156 + 0.983270i \(0.441692\pi\)
\(108\) 0 0
\(109\) −0.674254 −0.0645819 −0.0322909 0.999479i \(-0.510280\pi\)
−0.0322909 + 0.999479i \(0.510280\pi\)
\(110\) 0 0
\(111\) −8.94388 −0.848916
\(112\) 0 0
\(113\) 10.1480 0.954646 0.477323 0.878728i \(-0.341607\pi\)
0.477323 + 0.878728i \(0.341607\pi\)
\(114\) 0 0
\(115\) −11.0166 −1.02730
\(116\) 0 0
\(117\) 12.5077 1.15634
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.9413 −0.994665
\(122\) 0 0
\(123\) −1.82459 −0.164518
\(124\) 0 0
\(125\) 12.0347 1.07642
\(126\) 0 0
\(127\) 18.5974 1.65025 0.825126 0.564949i \(-0.191104\pi\)
0.825126 + 0.564949i \(0.191104\pi\)
\(128\) 0 0
\(129\) −7.14544 −0.629121
\(130\) 0 0
\(131\) 7.97141 0.696465 0.348233 0.937408i \(-0.386782\pi\)
0.348233 + 0.937408i \(0.386782\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 7.85095 0.675702
\(136\) 0 0
\(137\) −0.318763 −0.0272338 −0.0136169 0.999907i \(-0.504335\pi\)
−0.0136169 + 0.999907i \(0.504335\pi\)
\(138\) 0 0
\(139\) −5.80115 −0.492047 −0.246024 0.969264i \(-0.579124\pi\)
−0.246024 + 0.969264i \(0.579124\pi\)
\(140\) 0 0
\(141\) 1.44068 0.121327
\(142\) 0 0
\(143\) 1.39773 0.116884
\(144\) 0 0
\(145\) −14.8440 −1.23273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 13.6701 1.11990 0.559948 0.828528i \(-0.310821\pi\)
0.559948 + 0.828528i \(0.310821\pi\)
\(150\) 0 0
\(151\) 11.0282 0.897464 0.448732 0.893666i \(-0.351876\pi\)
0.448732 + 0.893666i \(0.351876\pi\)
\(152\) 0 0
\(153\) −12.4999 −1.01055
\(154\) 0 0
\(155\) 9.87985 0.793568
\(156\) 0 0
\(157\) 17.8566 1.42511 0.712556 0.701616i \(-0.247538\pi\)
0.712556 + 0.701616i \(0.247538\pi\)
\(158\) 0 0
\(159\) 5.91301 0.468932
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 11.1970 0.877018 0.438509 0.898727i \(-0.355507\pi\)
0.438509 + 0.898727i \(0.355507\pi\)
\(164\) 0 0
\(165\) 0.368020 0.0286503
\(166\) 0 0
\(167\) 1.44712 0.111981 0.0559906 0.998431i \(-0.482168\pi\)
0.0559906 + 0.998431i \(0.482168\pi\)
\(168\) 0 0
\(169\) 20.2928 1.56098
\(170\) 0 0
\(171\) −2.16772 −0.165769
\(172\) 0 0
\(173\) 11.8941 0.904292 0.452146 0.891944i \(-0.350659\pi\)
0.452146 + 0.891944i \(0.350659\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.980697 0.0737137
\(178\) 0 0
\(179\) 25.1728 1.88150 0.940751 0.339098i \(-0.110122\pi\)
0.940751 + 0.339098i \(0.110122\pi\)
\(180\) 0 0
\(181\) 18.7410 1.39301 0.696503 0.717554i \(-0.254738\pi\)
0.696503 + 0.717554i \(0.254738\pi\)
\(182\) 0 0
\(183\) 8.31017 0.614305
\(184\) 0 0
\(185\) 16.3259 1.20031
\(186\) 0 0
\(187\) −1.39685 −0.102148
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.356002 0.0257594 0.0128797 0.999917i \(-0.495900\pi\)
0.0128797 + 0.999917i \(0.495900\pi\)
\(192\) 0 0
\(193\) 17.0988 1.23080 0.615398 0.788216i \(-0.288995\pi\)
0.615398 + 0.788216i \(0.288995\pi\)
\(194\) 0 0
\(195\) 8.76594 0.627742
\(196\) 0 0
\(197\) 13.1088 0.933964 0.466982 0.884267i \(-0.345341\pi\)
0.466982 + 0.884267i \(0.345341\pi\)
\(198\) 0 0
\(199\) 4.76977 0.338120 0.169060 0.985606i \(-0.445927\pi\)
0.169060 + 0.985606i \(0.445927\pi\)
\(200\) 0 0
\(201\) 7.32155 0.516422
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 3.33056 0.232617
\(206\) 0 0
\(207\) −14.3404 −0.996728
\(208\) 0 0
\(209\) −0.242241 −0.0167561
\(210\) 0 0
\(211\) 22.0442 1.51759 0.758794 0.651331i \(-0.225789\pi\)
0.758794 + 0.651331i \(0.225789\pi\)
\(212\) 0 0
\(213\) 1.12172 0.0768588
\(214\) 0 0
\(215\) 13.0431 0.889533
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0.731087 0.0494023
\(220\) 0 0
\(221\) −33.2719 −2.23811
\(222\) 0 0
\(223\) 19.5836 1.31142 0.655708 0.755014i \(-0.272370\pi\)
0.655708 + 0.755014i \(0.272370\pi\)
\(224\) 0 0
\(225\) 4.82715 0.321810
\(226\) 0 0
\(227\) −5.78829 −0.384182 −0.192091 0.981377i \(-0.561527\pi\)
−0.192091 + 0.981377i \(0.561527\pi\)
\(228\) 0 0
\(229\) −19.1074 −1.26266 −0.631328 0.775516i \(-0.717490\pi\)
−0.631328 + 0.775516i \(0.717490\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.17125 −0.404292 −0.202146 0.979355i \(-0.564792\pi\)
−0.202146 + 0.979355i \(0.564792\pi\)
\(234\) 0 0
\(235\) −2.62978 −0.171548
\(236\) 0 0
\(237\) −6.91705 −0.449311
\(238\) 0 0
\(239\) 26.1425 1.69101 0.845507 0.533964i \(-0.179298\pi\)
0.845507 + 0.533964i \(0.179298\pi\)
\(240\) 0 0
\(241\) −19.5916 −1.26201 −0.631003 0.775780i \(-0.717357\pi\)
−0.631003 + 0.775780i \(0.717357\pi\)
\(242\) 0 0
\(243\) 16.1525 1.03618
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −5.76999 −0.367136
\(248\) 0 0
\(249\) −8.13122 −0.515295
\(250\) 0 0
\(251\) −6.39080 −0.403384 −0.201692 0.979449i \(-0.564644\pi\)
−0.201692 + 0.979449i \(0.564644\pi\)
\(252\) 0 0
\(253\) −1.60253 −0.100750
\(254\) 0 0
\(255\) −8.76045 −0.548600
\(256\) 0 0
\(257\) 21.8742 1.36448 0.682238 0.731130i \(-0.261007\pi\)
0.682238 + 0.731130i \(0.261007\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −19.3226 −1.19604
\(262\) 0 0
\(263\) −29.7237 −1.83284 −0.916420 0.400218i \(-0.868934\pi\)
−0.916420 + 0.400218i \(0.868934\pi\)
\(264\) 0 0
\(265\) −10.7935 −0.663037
\(266\) 0 0
\(267\) −11.9644 −0.732211
\(268\) 0 0
\(269\) 13.3856 0.816133 0.408067 0.912952i \(-0.366203\pi\)
0.408067 + 0.912952i \(0.366203\pi\)
\(270\) 0 0
\(271\) −25.7732 −1.56561 −0.782805 0.622267i \(-0.786212\pi\)
−0.782805 + 0.622267i \(0.786212\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.539431 0.0325289
\(276\) 0 0
\(277\) −2.97402 −0.178692 −0.0893458 0.996001i \(-0.528478\pi\)
−0.0893458 + 0.996001i \(0.528478\pi\)
\(278\) 0 0
\(279\) 12.8607 0.769950
\(280\) 0 0
\(281\) −18.8947 −1.12716 −0.563582 0.826060i \(-0.690577\pi\)
−0.563582 + 0.826060i \(0.690577\pi\)
\(282\) 0 0
\(283\) 22.8300 1.35710 0.678551 0.734554i \(-0.262608\pi\)
0.678551 + 0.734554i \(0.262608\pi\)
\(284\) 0 0
\(285\) −1.51923 −0.0899914
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 16.2510 0.955944
\(290\) 0 0
\(291\) 1.01870 0.0597174
\(292\) 0 0
\(293\) 11.3710 0.664299 0.332150 0.943227i \(-0.392226\pi\)
0.332150 + 0.943227i \(0.392226\pi\)
\(294\) 0 0
\(295\) −1.79014 −0.104226
\(296\) 0 0
\(297\) 1.14204 0.0662680
\(298\) 0 0
\(299\) −38.1711 −2.20749
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 11.8851 0.682779
\(304\) 0 0
\(305\) −15.1692 −0.868584
\(306\) 0 0
\(307\) −3.87636 −0.221236 −0.110618 0.993863i \(-0.535283\pi\)
−0.110618 + 0.993863i \(0.535283\pi\)
\(308\) 0 0
\(309\) −12.5221 −0.712356
\(310\) 0 0
\(311\) 22.0561 1.25069 0.625344 0.780349i \(-0.284959\pi\)
0.625344 + 0.780349i \(0.284959\pi\)
\(312\) 0 0
\(313\) −31.0643 −1.75586 −0.877930 0.478790i \(-0.841076\pi\)
−0.877930 + 0.478790i \(0.841076\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 33.2863 1.86954 0.934772 0.355249i \(-0.115604\pi\)
0.934772 + 0.355249i \(0.115604\pi\)
\(318\) 0 0
\(319\) −2.15929 −0.120897
\(320\) 0 0
\(321\) 3.43796 0.191888
\(322\) 0 0
\(323\) 5.76637 0.320850
\(324\) 0 0
\(325\) 12.8488 0.712724
\(326\) 0 0
\(327\) −0.615120 −0.0340162
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 8.37379 0.460265 0.230133 0.973159i \(-0.426084\pi\)
0.230133 + 0.973159i \(0.426084\pi\)
\(332\) 0 0
\(333\) 21.2517 1.16458
\(334\) 0 0
\(335\) −13.3646 −0.730184
\(336\) 0 0
\(337\) −1.87908 −0.102360 −0.0511799 0.998689i \(-0.516298\pi\)
−0.0511799 + 0.998689i \(0.516298\pi\)
\(338\) 0 0
\(339\) 9.25801 0.502826
\(340\) 0 0
\(341\) 1.43718 0.0778274
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −10.0504 −0.541095
\(346\) 0 0
\(347\) −6.13726 −0.329465 −0.164733 0.986338i \(-0.552676\pi\)
−0.164733 + 0.986338i \(0.552676\pi\)
\(348\) 0 0
\(349\) −18.9103 −1.01225 −0.506123 0.862461i \(-0.668922\pi\)
−0.506123 + 0.862461i \(0.668922\pi\)
\(350\) 0 0
\(351\) 27.2025 1.45196
\(352\) 0 0
\(353\) −9.94453 −0.529294 −0.264647 0.964345i \(-0.585255\pi\)
−0.264647 + 0.964345i \(0.585255\pi\)
\(354\) 0 0
\(355\) −2.04755 −0.108673
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 18.3900 0.970590 0.485295 0.874351i \(-0.338712\pi\)
0.485295 + 0.874351i \(0.338712\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −9.98172 −0.523905
\(364\) 0 0
\(365\) −1.33451 −0.0698513
\(366\) 0 0
\(367\) −14.2152 −0.742029 −0.371014 0.928627i \(-0.620990\pi\)
−0.371014 + 0.928627i \(0.620990\pi\)
\(368\) 0 0
\(369\) 4.33543 0.225694
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 25.6016 1.32560 0.662800 0.748796i \(-0.269368\pi\)
0.662800 + 0.748796i \(0.269368\pi\)
\(374\) 0 0
\(375\) 10.9792 0.566965
\(376\) 0 0
\(377\) −51.4326 −2.64891
\(378\) 0 0
\(379\) −8.51685 −0.437481 −0.218741 0.975783i \(-0.570195\pi\)
−0.218741 + 0.975783i \(0.570195\pi\)
\(380\) 0 0
\(381\) 16.9663 0.869211
\(382\) 0 0
\(383\) −10.0169 −0.511841 −0.255921 0.966698i \(-0.582379\pi\)
−0.255921 + 0.966698i \(0.582379\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.9784 0.863059
\(388\) 0 0
\(389\) −20.2802 −1.02825 −0.514123 0.857717i \(-0.671882\pi\)
−0.514123 + 0.857717i \(0.671882\pi\)
\(390\) 0 0
\(391\) 38.1472 1.92918
\(392\) 0 0
\(393\) 7.27229 0.366838
\(394\) 0 0
\(395\) 12.6262 0.635293
\(396\) 0 0
\(397\) −26.8275 −1.34643 −0.673216 0.739446i \(-0.735088\pi\)
−0.673216 + 0.739446i \(0.735088\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.8582 −0.692047 −0.346023 0.938226i \(-0.612468\pi\)
−0.346023 + 0.938226i \(0.612468\pi\)
\(402\) 0 0
\(403\) 34.2324 1.70524
\(404\) 0 0
\(405\) −3.66719 −0.182224
\(406\) 0 0
\(407\) 2.37486 0.117717
\(408\) 0 0
\(409\) −6.19430 −0.306288 −0.153144 0.988204i \(-0.548940\pi\)
−0.153144 + 0.988204i \(0.548940\pi\)
\(410\) 0 0
\(411\) −0.290807 −0.0143444
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 14.8425 0.728591
\(416\) 0 0
\(417\) −5.29237 −0.259168
\(418\) 0 0
\(419\) 14.4938 0.708068 0.354034 0.935233i \(-0.384810\pi\)
0.354034 + 0.935233i \(0.384810\pi\)
\(420\) 0 0
\(421\) 29.8753 1.45603 0.728016 0.685560i \(-0.240443\pi\)
0.728016 + 0.685560i \(0.240443\pi\)
\(422\) 0 0
\(423\) −3.42321 −0.166442
\(424\) 0 0
\(425\) −12.8408 −0.622868
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 1.27514 0.0615644
\(430\) 0 0
\(431\) 21.8609 1.05300 0.526501 0.850175i \(-0.323504\pi\)
0.526501 + 0.850175i \(0.323504\pi\)
\(432\) 0 0
\(433\) −11.1847 −0.537500 −0.268750 0.963210i \(-0.586611\pi\)
−0.268750 + 0.963210i \(0.586611\pi\)
\(434\) 0 0
\(435\) −13.5421 −0.649296
\(436\) 0 0
\(437\) 6.61545 0.316460
\(438\) 0 0
\(439\) −15.4187 −0.735896 −0.367948 0.929846i \(-0.619940\pi\)
−0.367948 + 0.929846i \(0.619940\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.939483 −0.0446362 −0.0223181 0.999751i \(-0.507105\pi\)
−0.0223181 + 0.999751i \(0.507105\pi\)
\(444\) 0 0
\(445\) 21.8396 1.03529
\(446\) 0 0
\(447\) 12.4711 0.589865
\(448\) 0 0
\(449\) −28.2058 −1.33112 −0.665558 0.746346i \(-0.731806\pi\)
−0.665558 + 0.746346i \(0.731806\pi\)
\(450\) 0 0
\(451\) 0.484482 0.0228134
\(452\) 0 0
\(453\) 10.0610 0.472707
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.777826 0.0363852 0.0181926 0.999835i \(-0.494209\pi\)
0.0181926 + 0.999835i \(0.494209\pi\)
\(458\) 0 0
\(459\) −27.1855 −1.26891
\(460\) 0 0
\(461\) −19.3614 −0.901751 −0.450875 0.892587i \(-0.648888\pi\)
−0.450875 + 0.892587i \(0.648888\pi\)
\(462\) 0 0
\(463\) 34.5688 1.60655 0.803275 0.595608i \(-0.203089\pi\)
0.803275 + 0.595608i \(0.203089\pi\)
\(464\) 0 0
\(465\) 9.01335 0.417984
\(466\) 0 0
\(467\) −29.8545 −1.38150 −0.690750 0.723094i \(-0.742719\pi\)
−0.690750 + 0.723094i \(0.742719\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 16.2905 0.750626
\(472\) 0 0
\(473\) 1.89732 0.0872389
\(474\) 0 0
\(475\) −2.22684 −0.102174
\(476\) 0 0
\(477\) −14.0500 −0.643303
\(478\) 0 0
\(479\) −27.8865 −1.27416 −0.637082 0.770796i \(-0.719859\pi\)
−0.637082 + 0.770796i \(0.719859\pi\)
\(480\) 0 0
\(481\) 56.5673 2.57925
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.85951 −0.0844361
\(486\) 0 0
\(487\) 11.6224 0.526660 0.263330 0.964706i \(-0.415179\pi\)
0.263330 + 0.964706i \(0.415179\pi\)
\(488\) 0 0
\(489\) 10.2150 0.461938
\(490\) 0 0
\(491\) −25.4037 −1.14645 −0.573225 0.819398i \(-0.694308\pi\)
−0.573225 + 0.819398i \(0.694308\pi\)
\(492\) 0 0
\(493\) 51.4004 2.31496
\(494\) 0 0
\(495\) −0.874455 −0.0393038
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2.67840 0.119902 0.0599509 0.998201i \(-0.480906\pi\)
0.0599509 + 0.998201i \(0.480906\pi\)
\(500\) 0 0
\(501\) 1.32020 0.0589821
\(502\) 0 0
\(503\) −37.0893 −1.65373 −0.826866 0.562399i \(-0.809879\pi\)
−0.826866 + 0.562399i \(0.809879\pi\)
\(504\) 0 0
\(505\) −21.6947 −0.965401
\(506\) 0 0
\(507\) 18.5130 0.822192
\(508\) 0 0
\(509\) 14.8243 0.657075 0.328537 0.944491i \(-0.393444\pi\)
0.328537 + 0.944491i \(0.393444\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −4.71449 −0.208150
\(514\) 0 0
\(515\) 22.8575 1.00722
\(516\) 0 0
\(517\) −0.382542 −0.0168242
\(518\) 0 0
\(519\) 10.8509 0.476303
\(520\) 0 0
\(521\) −10.4922 −0.459670 −0.229835 0.973230i \(-0.573819\pi\)
−0.229835 + 0.973230i \(0.573819\pi\)
\(522\) 0 0
\(523\) −15.4757 −0.676707 −0.338353 0.941019i \(-0.609870\pi\)
−0.338353 + 0.941019i \(0.609870\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −34.2109 −1.49025
\(528\) 0 0
\(529\) 20.7642 0.902792
\(530\) 0 0
\(531\) −2.33024 −0.101124
\(532\) 0 0
\(533\) 11.5400 0.499852
\(534\) 0 0
\(535\) −6.27557 −0.271316
\(536\) 0 0
\(537\) 22.9650 0.991014
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −18.7927 −0.807961 −0.403980 0.914768i \(-0.632374\pi\)
−0.403980 + 0.914768i \(0.632374\pi\)
\(542\) 0 0
\(543\) 17.0973 0.733716
\(544\) 0 0
\(545\) 1.12282 0.0480965
\(546\) 0 0
\(547\) −0.809060 −0.0345929 −0.0172965 0.999850i \(-0.505506\pi\)
−0.0172965 + 0.999850i \(0.505506\pi\)
\(548\) 0 0
\(549\) −19.7459 −0.842734
\(550\) 0 0
\(551\) 8.91381 0.379741
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 14.8941 0.632219
\(556\) 0 0
\(557\) −17.4536 −0.739533 −0.369767 0.929125i \(-0.620562\pi\)
−0.369767 + 0.929125i \(0.620562\pi\)
\(558\) 0 0
\(559\) 45.1927 1.91145
\(560\) 0 0
\(561\) −1.27434 −0.0538027
\(562\) 0 0
\(563\) −3.68375 −0.155251 −0.0776257 0.996983i \(-0.524734\pi\)
−0.0776257 + 0.996983i \(0.524734\pi\)
\(564\) 0 0
\(565\) −16.8993 −0.710960
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.13224 −0.382843 −0.191422 0.981508i \(-0.561310\pi\)
−0.191422 + 0.981508i \(0.561310\pi\)
\(570\) 0 0
\(571\) 21.1247 0.884039 0.442020 0.897005i \(-0.354262\pi\)
0.442020 + 0.897005i \(0.354262\pi\)
\(572\) 0 0
\(573\) 0.324779 0.0135678
\(574\) 0 0
\(575\) −14.7315 −0.614347
\(576\) 0 0
\(577\) 5.24274 0.218258 0.109129 0.994028i \(-0.465194\pi\)
0.109129 + 0.994028i \(0.465194\pi\)
\(578\) 0 0
\(579\) 15.5991 0.648278
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −1.57007 −0.0650258
\(584\) 0 0
\(585\) −20.8288 −0.861167
\(586\) 0 0
\(587\) −3.26045 −0.134573 −0.0672865 0.997734i \(-0.521434\pi\)
−0.0672865 + 0.997734i \(0.521434\pi\)
\(588\) 0 0
\(589\) −5.93284 −0.244458
\(590\) 0 0
\(591\) 11.9591 0.491932
\(592\) 0 0
\(593\) 19.9230 0.818141 0.409070 0.912503i \(-0.365853\pi\)
0.409070 + 0.912503i \(0.365853\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.35144 0.178093
\(598\) 0 0
\(599\) 44.4649 1.81679 0.908394 0.418116i \(-0.137309\pi\)
0.908394 + 0.418116i \(0.137309\pi\)
\(600\) 0 0
\(601\) 22.3392 0.911233 0.455617 0.890176i \(-0.349419\pi\)
0.455617 + 0.890176i \(0.349419\pi\)
\(602\) 0 0
\(603\) −17.3968 −0.708453
\(604\) 0 0
\(605\) 18.2204 0.740764
\(606\) 0 0
\(607\) 34.4089 1.39661 0.698306 0.715799i \(-0.253937\pi\)
0.698306 + 0.715799i \(0.253937\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −9.11184 −0.368626
\(612\) 0 0
\(613\) −24.2940 −0.981226 −0.490613 0.871378i \(-0.663227\pi\)
−0.490613 + 0.871378i \(0.663227\pi\)
\(614\) 0 0
\(615\) 3.03846 0.122523
\(616\) 0 0
\(617\) −17.0255 −0.685422 −0.342711 0.939441i \(-0.611345\pi\)
−0.342711 + 0.939441i \(0.611345\pi\)
\(618\) 0 0
\(619\) 28.6795 1.15273 0.576363 0.817194i \(-0.304472\pi\)
0.576363 + 0.817194i \(0.304472\pi\)
\(620\) 0 0
\(621\) −31.1885 −1.25155
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −8.90703 −0.356281
\(626\) 0 0
\(627\) −0.220995 −0.00882570
\(628\) 0 0
\(629\) −56.5318 −2.25407
\(630\) 0 0
\(631\) −29.4675 −1.17308 −0.586542 0.809919i \(-0.699511\pi\)
−0.586542 + 0.809919i \(0.699511\pi\)
\(632\) 0 0
\(633\) 20.1109 0.799335
\(634\) 0 0
\(635\) −30.9699 −1.22900
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2.66532 −0.105439
\(640\) 0 0
\(641\) −16.1367 −0.637363 −0.318681 0.947862i \(-0.603240\pi\)
−0.318681 + 0.947862i \(0.603240\pi\)
\(642\) 0 0
\(643\) 22.8353 0.900535 0.450267 0.892894i \(-0.351329\pi\)
0.450267 + 0.892894i \(0.351329\pi\)
\(644\) 0 0
\(645\) 11.8992 0.468530
\(646\) 0 0
\(647\) 20.7399 0.815370 0.407685 0.913123i \(-0.366336\pi\)
0.407685 + 0.913123i \(0.366336\pi\)
\(648\) 0 0
\(649\) −0.260403 −0.0102217
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19.3767 −0.758268 −0.379134 0.925342i \(-0.623778\pi\)
−0.379134 + 0.925342i \(0.623778\pi\)
\(654\) 0 0
\(655\) −13.2746 −0.518683
\(656\) 0 0
\(657\) −1.73714 −0.0677724
\(658\) 0 0
\(659\) 7.33347 0.285672 0.142836 0.989746i \(-0.454378\pi\)
0.142836 + 0.989746i \(0.454378\pi\)
\(660\) 0 0
\(661\) −37.7069 −1.46663 −0.733315 0.679889i \(-0.762028\pi\)
−0.733315 + 0.679889i \(0.762028\pi\)
\(662\) 0 0
\(663\) −30.3538 −1.17884
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 58.9689 2.28329
\(668\) 0 0
\(669\) 17.8661 0.690742
\(670\) 0 0
\(671\) −2.20659 −0.0851844
\(672\) 0 0
\(673\) 48.4005 1.86570 0.932851 0.360263i \(-0.117313\pi\)
0.932851 + 0.360263i \(0.117313\pi\)
\(674\) 0 0
\(675\) 10.4984 0.404083
\(676\) 0 0
\(677\) 15.8658 0.609772 0.304886 0.952389i \(-0.401382\pi\)
0.304886 + 0.952389i \(0.401382\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −5.28063 −0.202354
\(682\) 0 0
\(683\) 17.2671 0.660707 0.330353 0.943857i \(-0.392832\pi\)
0.330353 + 0.943857i \(0.392832\pi\)
\(684\) 0 0
\(685\) 0.530831 0.0202820
\(686\) 0 0
\(687\) −17.4316 −0.665059
\(688\) 0 0
\(689\) −37.3979 −1.42475
\(690\) 0 0
\(691\) −49.2612 −1.87398 −0.936992 0.349351i \(-0.886402\pi\)
−0.936992 + 0.349351i \(0.886402\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.66056 0.366446
\(696\) 0 0
\(697\) −11.5327 −0.436834
\(698\) 0 0
\(699\) −5.63001 −0.212947
\(700\) 0 0
\(701\) 10.1609 0.383770 0.191885 0.981417i \(-0.438540\pi\)
0.191885 + 0.981417i \(0.438540\pi\)
\(702\) 0 0
\(703\) −9.80371 −0.369754
\(704\) 0 0
\(705\) −2.39914 −0.0903567
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 7.73019 0.290313 0.145157 0.989409i \(-0.453631\pi\)
0.145157 + 0.989409i \(0.453631\pi\)
\(710\) 0 0
\(711\) 16.4357 0.616386
\(712\) 0 0
\(713\) −39.2484 −1.46986
\(714\) 0 0
\(715\) −2.32761 −0.0870477
\(716\) 0 0
\(717\) 23.8497 0.890682
\(718\) 0 0
\(719\) 25.3207 0.944303 0.472152 0.881517i \(-0.343477\pi\)
0.472152 + 0.881517i \(0.343477\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −17.8733 −0.664717
\(724\) 0 0
\(725\) −19.8496 −0.737196
\(726\) 0 0
\(727\) 24.5601 0.910884 0.455442 0.890266i \(-0.349481\pi\)
0.455442 + 0.890266i \(0.349481\pi\)
\(728\) 0 0
\(729\) 8.12941 0.301089
\(730\) 0 0
\(731\) −45.1644 −1.67046
\(732\) 0 0
\(733\) −27.3033 −1.00847 −0.504235 0.863567i \(-0.668225\pi\)
−0.504235 + 0.863567i \(0.668225\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.94408 −0.0716112
\(738\) 0 0
\(739\) 48.0375 1.76709 0.883544 0.468348i \(-0.155151\pi\)
0.883544 + 0.468348i \(0.155151\pi\)
\(740\) 0 0
\(741\) −5.26394 −0.193376
\(742\) 0 0
\(743\) 10.8539 0.398190 0.199095 0.979980i \(-0.436200\pi\)
0.199095 + 0.979980i \(0.436200\pi\)
\(744\) 0 0
\(745\) −22.7645 −0.834027
\(746\) 0 0
\(747\) 19.3207 0.706906
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 17.9144 0.653705 0.326852 0.945075i \(-0.394012\pi\)
0.326852 + 0.945075i \(0.394012\pi\)
\(752\) 0 0
\(753\) −5.83030 −0.212468
\(754\) 0 0
\(755\) −18.3651 −0.668374
\(756\) 0 0
\(757\) 19.7888 0.719235 0.359617 0.933100i \(-0.382907\pi\)
0.359617 + 0.933100i \(0.382907\pi\)
\(758\) 0 0
\(759\) −1.46198 −0.0530667
\(760\) 0 0
\(761\) 51.4603 1.86543 0.932717 0.360609i \(-0.117431\pi\)
0.932717 + 0.360609i \(0.117431\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 20.8158 0.752596
\(766\) 0 0
\(767\) −6.20260 −0.223963
\(768\) 0 0
\(769\) −26.2468 −0.946485 −0.473243 0.880932i \(-0.656917\pi\)
−0.473243 + 0.880932i \(0.656917\pi\)
\(770\) 0 0
\(771\) 19.9558 0.718689
\(772\) 0 0
\(773\) 6.05223 0.217684 0.108842 0.994059i \(-0.465286\pi\)
0.108842 + 0.994059i \(0.465286\pi\)
\(774\) 0 0
\(775\) 13.2115 0.474569
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.00000 −0.0716574
\(780\) 0 0
\(781\) −0.297848 −0.0106578
\(782\) 0 0
\(783\) −42.0241 −1.50182
\(784\) 0 0
\(785\) −29.7363 −1.06133
\(786\) 0 0
\(787\) −12.4576 −0.444064 −0.222032 0.975039i \(-0.571269\pi\)
−0.222032 + 0.975039i \(0.571269\pi\)
\(788\) 0 0
\(789\) −27.1168 −0.965383
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −52.5592 −1.86643
\(794\) 0 0
\(795\) −9.84682 −0.349231
\(796\) 0 0
\(797\) 7.13423 0.252707 0.126354 0.991985i \(-0.459673\pi\)
0.126354 + 0.991985i \(0.459673\pi\)
\(798\) 0 0
\(799\) 9.10613 0.322152
\(800\) 0 0
\(801\) 28.4288 1.00448
\(802\) 0 0
\(803\) −0.194125 −0.00685051
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 12.2116 0.429869
\(808\) 0 0
\(809\) 9.75801 0.343074 0.171537 0.985178i \(-0.445127\pi\)
0.171537 + 0.985178i \(0.445127\pi\)
\(810\) 0 0
\(811\) −1.23879 −0.0434998 −0.0217499 0.999763i \(-0.506924\pi\)
−0.0217499 + 0.999763i \(0.506924\pi\)
\(812\) 0 0
\(813\) −23.5128 −0.824630
\(814\) 0 0
\(815\) −18.6462 −0.653148
\(816\) 0 0
\(817\) −7.83237 −0.274020
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 42.8811 1.49656 0.748281 0.663382i \(-0.230880\pi\)
0.748281 + 0.663382i \(0.230880\pi\)
\(822\) 0 0
\(823\) −12.7541 −0.444579 −0.222290 0.974981i \(-0.571353\pi\)
−0.222290 + 0.974981i \(0.571353\pi\)
\(824\) 0 0
\(825\) 0.492120 0.0171334
\(826\) 0 0
\(827\) 52.6536 1.83095 0.915473 0.402380i \(-0.131817\pi\)
0.915473 + 0.402380i \(0.131817\pi\)
\(828\) 0 0
\(829\) −0.121544 −0.00422139 −0.00211070 0.999998i \(-0.500672\pi\)
−0.00211070 + 0.999998i \(0.500672\pi\)
\(830\) 0 0
\(831\) −2.71319 −0.0941194
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −2.40986 −0.0833966
\(836\) 0 0
\(837\) 27.9703 0.966794
\(838\) 0 0
\(839\) 45.8707 1.58363 0.791816 0.610759i \(-0.209136\pi\)
0.791816 + 0.610759i \(0.209136\pi\)
\(840\) 0 0
\(841\) 50.4561 1.73987
\(842\) 0 0
\(843\) −17.2376 −0.593693
\(844\) 0 0
\(845\) −33.7932 −1.16252
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 20.8277 0.714805
\(850\) 0 0
\(851\) −64.8560 −2.22323
\(852\) 0 0
\(853\) −18.8106 −0.644064 −0.322032 0.946729i \(-0.604366\pi\)
−0.322032 + 0.946729i \(0.604366\pi\)
\(854\) 0 0
\(855\) 3.60986 0.123455
\(856\) 0 0
\(857\) −21.9936 −0.751288 −0.375644 0.926764i \(-0.622578\pi\)
−0.375644 + 0.926764i \(0.622578\pi\)
\(858\) 0 0
\(859\) 33.9757 1.15924 0.579619 0.814888i \(-0.303202\pi\)
0.579619 + 0.814888i \(0.303202\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −33.0442 −1.12484 −0.562419 0.826852i \(-0.690129\pi\)
−0.562419 + 0.826852i \(0.690129\pi\)
\(864\) 0 0
\(865\) −19.8070 −0.673459
\(866\) 0 0
\(867\) 14.8258 0.503509
\(868\) 0 0
\(869\) 1.83668 0.0623049
\(870\) 0 0
\(871\) −46.3065 −1.56904
\(872\) 0 0
\(873\) −2.42055 −0.0819232
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −26.7266 −0.902494 −0.451247 0.892399i \(-0.649021\pi\)
−0.451247 + 0.892399i \(0.649021\pi\)
\(878\) 0 0
\(879\) 10.3737 0.349896
\(880\) 0 0
\(881\) 33.6752 1.13454 0.567272 0.823530i \(-0.307999\pi\)
0.567272 + 0.823530i \(0.307999\pi\)
\(882\) 0 0
\(883\) −15.6753 −0.527516 −0.263758 0.964589i \(-0.584962\pi\)
−0.263758 + 0.964589i \(0.584962\pi\)
\(884\) 0 0
\(885\) −1.63314 −0.0548973
\(886\) 0 0
\(887\) 5.19711 0.174502 0.0872510 0.996186i \(-0.472192\pi\)
0.0872510 + 0.996186i \(0.472192\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.533448 −0.0178712
\(892\) 0 0
\(893\) 1.57918 0.0528452
\(894\) 0 0
\(895\) −41.9198 −1.40122
\(896\) 0 0
\(897\) −34.8233 −1.16272
\(898\) 0 0
\(899\) −52.8842 −1.76379
\(900\) 0 0
\(901\) 37.3745 1.24512
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −31.2090 −1.03742
\(906\) 0 0
\(907\) −37.5830 −1.24792 −0.623962 0.781455i \(-0.714478\pi\)
−0.623962 + 0.781455i \(0.714478\pi\)
\(908\) 0 0
\(909\) −28.2402 −0.936669
\(910\) 0 0
\(911\) 19.9982 0.662571 0.331286 0.943530i \(-0.392518\pi\)
0.331286 + 0.943530i \(0.392518\pi\)
\(912\) 0 0
\(913\) 2.15907 0.0714549
\(914\) 0 0
\(915\) −13.8388 −0.457496
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −41.6251 −1.37309 −0.686543 0.727089i \(-0.740873\pi\)
−0.686543 + 0.727089i \(0.740873\pi\)
\(920\) 0 0
\(921\) −3.53639 −0.116528
\(922\) 0 0
\(923\) −7.09451 −0.233519
\(924\) 0 0
\(925\) 21.8312 0.717807
\(926\) 0 0
\(927\) 29.7538 0.977244
\(928\) 0 0
\(929\) −32.3223 −1.06046 −0.530229 0.847854i \(-0.677894\pi\)
−0.530229 + 0.847854i \(0.677894\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 20.1217 0.658755
\(934\) 0 0
\(935\) 2.32615 0.0760733
\(936\) 0 0
\(937\) −23.8754 −0.779975 −0.389988 0.920820i \(-0.627521\pi\)
−0.389988 + 0.920820i \(0.627521\pi\)
\(938\) 0 0
\(939\) −28.3399 −0.924836
\(940\) 0 0
\(941\) −30.6962 −1.00067 −0.500334 0.865833i \(-0.666789\pi\)
−0.500334 + 0.865833i \(0.666789\pi\)
\(942\) 0 0
\(943\) −13.2309 −0.430858
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 27.7378 0.901357 0.450678 0.892686i \(-0.351182\pi\)
0.450678 + 0.892686i \(0.351182\pi\)
\(948\) 0 0
\(949\) −4.62390 −0.150098
\(950\) 0 0
\(951\) 30.3669 0.984715
\(952\) 0 0
\(953\) −29.9634 −0.970611 −0.485305 0.874345i \(-0.661292\pi\)
−0.485305 + 0.874345i \(0.661292\pi\)
\(954\) 0 0
\(955\) −0.592844 −0.0191840
\(956\) 0 0
\(957\) −1.96991 −0.0636782
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 4.19856 0.135437
\(962\) 0 0
\(963\) −8.16897 −0.263241
\(964\) 0 0
\(965\) −28.4743 −0.916619
\(966\) 0 0
\(967\) −19.2270 −0.618299 −0.309150 0.951013i \(-0.600044\pi\)
−0.309150 + 0.951013i \(0.600044\pi\)
\(968\) 0 0
\(969\) 5.26064 0.168996
\(970\) 0 0
\(971\) 16.2936 0.522887 0.261443 0.965219i \(-0.415802\pi\)
0.261443 + 0.965219i \(0.415802\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 11.7219 0.375402
\(976\) 0 0
\(977\) −21.3065 −0.681655 −0.340828 0.940126i \(-0.610707\pi\)
−0.340828 + 0.940126i \(0.610707\pi\)
\(978\) 0 0
\(979\) 3.17690 0.101534
\(980\) 0 0
\(981\) 1.46159 0.0466650
\(982\) 0 0
\(983\) −7.27409 −0.232007 −0.116004 0.993249i \(-0.537008\pi\)
−0.116004 + 0.993249i \(0.537008\pi\)
\(984\) 0 0
\(985\) −21.8299 −0.695558
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −51.8147 −1.64761
\(990\) 0 0
\(991\) −39.2758 −1.24764 −0.623818 0.781569i \(-0.714419\pi\)
−0.623818 + 0.781569i \(0.714419\pi\)
\(992\) 0 0
\(993\) 7.63938 0.242428
\(994\) 0 0
\(995\) −7.94301 −0.251811
\(996\) 0 0
\(997\) 8.97292 0.284175 0.142088 0.989854i \(-0.454619\pi\)
0.142088 + 0.989854i \(0.454619\pi\)
\(998\) 0 0
\(999\) 46.2195 1.46232
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 7448.2.a.bq.1.6 8
7.2 even 3 1064.2.q.n.305.3 16
7.4 even 3 1064.2.q.n.457.3 yes 16
7.6 odd 2 7448.2.a.br.1.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1064.2.q.n.305.3 16 7.2 even 3
1064.2.q.n.457.3 yes 16 7.4 even 3
7448.2.a.bq.1.6 8 1.1 even 1 trivial
7448.2.a.br.1.3 8 7.6 odd 2