Properties

Label 8016.2.a.ba.1.9
Level $8016$
Weight $2$
Character 8016.1
Self dual yes
Analytic conductor $64.008$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8016.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - 3 x^{8} - 16 x^{7} + 45 x^{6} + 67 x^{5} - 166 x^{4} - 83 x^{3} + 152 x^{2} + 51 x - 10\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 4008)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(3.54323\) of defining polynomial
Character \(\chi\) \(=\) 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} +2.54323 q^{5} +4.05015 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +2.54323 q^{5} +4.05015 q^{7} +1.00000 q^{9} -0.833896 q^{11} +2.46125 q^{13} -2.54323 q^{15} -1.83915 q^{17} +5.92708 q^{19} -4.05015 q^{21} +3.92292 q^{23} +1.46803 q^{25} -1.00000 q^{27} -7.78858 q^{29} +8.46269 q^{31} +0.833896 q^{33} +10.3005 q^{35} +3.96040 q^{37} -2.46125 q^{39} -11.0449 q^{41} +10.1144 q^{43} +2.54323 q^{45} -0.498289 q^{47} +9.40370 q^{49} +1.83915 q^{51} +2.45514 q^{53} -2.12079 q^{55} -5.92708 q^{57} -7.33541 q^{59} +2.76168 q^{61} +4.05015 q^{63} +6.25954 q^{65} -10.9183 q^{67} -3.92292 q^{69} +3.97515 q^{71} +6.83455 q^{73} -1.46803 q^{75} -3.37740 q^{77} -7.34900 q^{79} +1.00000 q^{81} +4.66163 q^{83} -4.67739 q^{85} +7.78858 q^{87} -4.56477 q^{89} +9.96844 q^{91} -8.46269 q^{93} +15.0739 q^{95} +10.8423 q^{97} -0.833896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q - 9q^{3} - 6q^{5} + 11q^{7} + 9q^{9} + O(q^{10}) \) \( 9q - 9q^{3} - 6q^{5} + 11q^{7} + 9q^{9} - q^{11} - 4q^{13} + 6q^{15} - 9q^{17} + 8q^{19} - 11q^{21} + 7q^{23} - q^{25} - 9q^{27} - 9q^{29} + 25q^{31} + q^{33} - 5q^{35} - 6q^{37} + 4q^{39} - 4q^{41} + 24q^{43} - 6q^{45} + 16q^{47} + 4q^{49} + 9q^{51} - 26q^{53} + 29q^{55} - 8q^{57} + 4q^{59} - 20q^{61} + 11q^{63} - 8q^{65} + 25q^{67} - 7q^{69} + 15q^{71} - 10q^{73} + q^{75} - 20q^{77} + 34q^{79} + 9q^{81} + 4q^{83} - 13q^{85} + 9q^{87} + 13q^{89} + 21q^{91} - 25q^{93} + 7q^{95} - 4q^{97} - q^{99} + O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 2.54323 1.13737 0.568684 0.822556i \(-0.307453\pi\)
0.568684 + 0.822556i \(0.307453\pi\)
\(6\) 0 0
\(7\) 4.05015 1.53081 0.765406 0.643548i \(-0.222538\pi\)
0.765406 + 0.643548i \(0.222538\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.833896 −0.251429 −0.125715 0.992066i \(-0.540122\pi\)
−0.125715 + 0.992066i \(0.540122\pi\)
\(12\) 0 0
\(13\) 2.46125 0.682629 0.341314 0.939949i \(-0.389128\pi\)
0.341314 + 0.939949i \(0.389128\pi\)
\(14\) 0 0
\(15\) −2.54323 −0.656660
\(16\) 0 0
\(17\) −1.83915 −0.446060 −0.223030 0.974812i \(-0.571595\pi\)
−0.223030 + 0.974812i \(0.571595\pi\)
\(18\) 0 0
\(19\) 5.92708 1.35976 0.679882 0.733321i \(-0.262031\pi\)
0.679882 + 0.733321i \(0.262031\pi\)
\(20\) 0 0
\(21\) −4.05015 −0.883815
\(22\) 0 0
\(23\) 3.92292 0.817986 0.408993 0.912538i \(-0.365880\pi\)
0.408993 + 0.912538i \(0.365880\pi\)
\(24\) 0 0
\(25\) 1.46803 0.293605
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −7.78858 −1.44630 −0.723152 0.690689i \(-0.757307\pi\)
−0.723152 + 0.690689i \(0.757307\pi\)
\(30\) 0 0
\(31\) 8.46269 1.51994 0.759972 0.649956i \(-0.225213\pi\)
0.759972 + 0.649956i \(0.225213\pi\)
\(32\) 0 0
\(33\) 0.833896 0.145163
\(34\) 0 0
\(35\) 10.3005 1.74110
\(36\) 0 0
\(37\) 3.96040 0.651086 0.325543 0.945527i \(-0.394453\pi\)
0.325543 + 0.945527i \(0.394453\pi\)
\(38\) 0 0
\(39\) −2.46125 −0.394116
\(40\) 0 0
\(41\) −11.0449 −1.72492 −0.862461 0.506124i \(-0.831078\pi\)
−0.862461 + 0.506124i \(0.831078\pi\)
\(42\) 0 0
\(43\) 10.1144 1.54243 0.771213 0.636577i \(-0.219650\pi\)
0.771213 + 0.636577i \(0.219650\pi\)
\(44\) 0 0
\(45\) 2.54323 0.379123
\(46\) 0 0
\(47\) −0.498289 −0.0726830 −0.0363415 0.999339i \(-0.511570\pi\)
−0.0363415 + 0.999339i \(0.511570\pi\)
\(48\) 0 0
\(49\) 9.40370 1.34339
\(50\) 0 0
\(51\) 1.83915 0.257533
\(52\) 0 0
\(53\) 2.45514 0.337240 0.168620 0.985681i \(-0.446069\pi\)
0.168620 + 0.985681i \(0.446069\pi\)
\(54\) 0 0
\(55\) −2.12079 −0.285967
\(56\) 0 0
\(57\) −5.92708 −0.785061
\(58\) 0 0
\(59\) −7.33541 −0.954990 −0.477495 0.878635i \(-0.658455\pi\)
−0.477495 + 0.878635i \(0.658455\pi\)
\(60\) 0 0
\(61\) 2.76168 0.353597 0.176798 0.984247i \(-0.443426\pi\)
0.176798 + 0.984247i \(0.443426\pi\)
\(62\) 0 0
\(63\) 4.05015 0.510271
\(64\) 0 0
\(65\) 6.25954 0.776400
\(66\) 0 0
\(67\) −10.9183 −1.33388 −0.666942 0.745110i \(-0.732397\pi\)
−0.666942 + 0.745110i \(0.732397\pi\)
\(68\) 0 0
\(69\) −3.92292 −0.472264
\(70\) 0 0
\(71\) 3.97515 0.471763 0.235882 0.971782i \(-0.424202\pi\)
0.235882 + 0.971782i \(0.424202\pi\)
\(72\) 0 0
\(73\) 6.83455 0.799924 0.399962 0.916532i \(-0.369023\pi\)
0.399962 + 0.916532i \(0.369023\pi\)
\(74\) 0 0
\(75\) −1.46803 −0.169513
\(76\) 0 0
\(77\) −3.37740 −0.384891
\(78\) 0 0
\(79\) −7.34900 −0.826827 −0.413413 0.910543i \(-0.635664\pi\)
−0.413413 + 0.910543i \(0.635664\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.66163 0.511680 0.255840 0.966719i \(-0.417648\pi\)
0.255840 + 0.966719i \(0.417648\pi\)
\(84\) 0 0
\(85\) −4.67739 −0.507334
\(86\) 0 0
\(87\) 7.78858 0.835024
\(88\) 0 0
\(89\) −4.56477 −0.483864 −0.241932 0.970293i \(-0.577781\pi\)
−0.241932 + 0.970293i \(0.577781\pi\)
\(90\) 0 0
\(91\) 9.96844 1.04498
\(92\) 0 0
\(93\) −8.46269 −0.877540
\(94\) 0 0
\(95\) 15.0739 1.54655
\(96\) 0 0
\(97\) 10.8423 1.10087 0.550434 0.834879i \(-0.314462\pi\)
0.550434 + 0.834879i \(0.314462\pi\)
\(98\) 0 0
\(99\) −0.833896 −0.0838097
\(100\) 0 0
\(101\) 1.34614 0.133946 0.0669731 0.997755i \(-0.478666\pi\)
0.0669731 + 0.997755i \(0.478666\pi\)
\(102\) 0 0
\(103\) 17.7990 1.75379 0.876893 0.480686i \(-0.159612\pi\)
0.876893 + 0.480686i \(0.159612\pi\)
\(104\) 0 0
\(105\) −10.3005 −1.00522
\(106\) 0 0
\(107\) 9.17441 0.886923 0.443462 0.896293i \(-0.353750\pi\)
0.443462 + 0.896293i \(0.353750\pi\)
\(108\) 0 0
\(109\) 10.0390 0.961558 0.480779 0.876842i \(-0.340354\pi\)
0.480779 + 0.876842i \(0.340354\pi\)
\(110\) 0 0
\(111\) −3.96040 −0.375905
\(112\) 0 0
\(113\) 18.2770 1.71936 0.859678 0.510837i \(-0.170664\pi\)
0.859678 + 0.510837i \(0.170664\pi\)
\(114\) 0 0
\(115\) 9.97690 0.930350
\(116\) 0 0
\(117\) 2.46125 0.227543
\(118\) 0 0
\(119\) −7.44884 −0.682834
\(120\) 0 0
\(121\) −10.3046 −0.936783
\(122\) 0 0
\(123\) 11.0449 0.995884
\(124\) 0 0
\(125\) −8.98263 −0.803431
\(126\) 0 0
\(127\) −8.49866 −0.754134 −0.377067 0.926186i \(-0.623067\pi\)
−0.377067 + 0.926186i \(0.623067\pi\)
\(128\) 0 0
\(129\) −10.1144 −0.890520
\(130\) 0 0
\(131\) 6.28622 0.549230 0.274615 0.961554i \(-0.411450\pi\)
0.274615 + 0.961554i \(0.411450\pi\)
\(132\) 0 0
\(133\) 24.0055 2.08154
\(134\) 0 0
\(135\) −2.54323 −0.218887
\(136\) 0 0
\(137\) 4.10350 0.350585 0.175293 0.984516i \(-0.443913\pi\)
0.175293 + 0.984516i \(0.443913\pi\)
\(138\) 0 0
\(139\) −4.54642 −0.385622 −0.192811 0.981236i \(-0.561760\pi\)
−0.192811 + 0.981236i \(0.561760\pi\)
\(140\) 0 0
\(141\) 0.498289 0.0419635
\(142\) 0 0
\(143\) −2.05243 −0.171633
\(144\) 0 0
\(145\) −19.8082 −1.64498
\(146\) 0 0
\(147\) −9.40370 −0.775604
\(148\) 0 0
\(149\) −13.9805 −1.14533 −0.572663 0.819791i \(-0.694090\pi\)
−0.572663 + 0.819791i \(0.694090\pi\)
\(150\) 0 0
\(151\) 2.44014 0.198575 0.0992877 0.995059i \(-0.468344\pi\)
0.0992877 + 0.995059i \(0.468344\pi\)
\(152\) 0 0
\(153\) −1.83915 −0.148687
\(154\) 0 0
\(155\) 21.5226 1.72874
\(156\) 0 0
\(157\) −17.2013 −1.37281 −0.686407 0.727218i \(-0.740813\pi\)
−0.686407 + 0.727218i \(0.740813\pi\)
\(158\) 0 0
\(159\) −2.45514 −0.194706
\(160\) 0 0
\(161\) 15.8884 1.25218
\(162\) 0 0
\(163\) 0.421952 0.0330498 0.0165249 0.999863i \(-0.494740\pi\)
0.0165249 + 0.999863i \(0.494740\pi\)
\(164\) 0 0
\(165\) 2.12079 0.165103
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −6.94223 −0.534018
\(170\) 0 0
\(171\) 5.92708 0.453255
\(172\) 0 0
\(173\) −16.6235 −1.26386 −0.631932 0.775024i \(-0.717738\pi\)
−0.631932 + 0.775024i \(0.717738\pi\)
\(174\) 0 0
\(175\) 5.94572 0.449454
\(176\) 0 0
\(177\) 7.33541 0.551364
\(178\) 0 0
\(179\) −1.25643 −0.0939098 −0.0469549 0.998897i \(-0.514952\pi\)
−0.0469549 + 0.998897i \(0.514952\pi\)
\(180\) 0 0
\(181\) −4.10641 −0.305227 −0.152614 0.988286i \(-0.548769\pi\)
−0.152614 + 0.988286i \(0.548769\pi\)
\(182\) 0 0
\(183\) −2.76168 −0.204149
\(184\) 0 0
\(185\) 10.0722 0.740524
\(186\) 0 0
\(187\) 1.53366 0.112152
\(188\) 0 0
\(189\) −4.05015 −0.294605
\(190\) 0 0
\(191\) −14.8331 −1.07328 −0.536642 0.843810i \(-0.680307\pi\)
−0.536642 + 0.843810i \(0.680307\pi\)
\(192\) 0 0
\(193\) −10.2047 −0.734549 −0.367275 0.930113i \(-0.619709\pi\)
−0.367275 + 0.930113i \(0.619709\pi\)
\(194\) 0 0
\(195\) −6.25954 −0.448255
\(196\) 0 0
\(197\) −12.2783 −0.874796 −0.437398 0.899268i \(-0.644100\pi\)
−0.437398 + 0.899268i \(0.644100\pi\)
\(198\) 0 0
\(199\) −3.70118 −0.262370 −0.131185 0.991358i \(-0.541878\pi\)
−0.131185 + 0.991358i \(0.541878\pi\)
\(200\) 0 0
\(201\) 10.9183 0.770118
\(202\) 0 0
\(203\) −31.5449 −2.21402
\(204\) 0 0
\(205\) −28.0897 −1.96187
\(206\) 0 0
\(207\) 3.92292 0.272662
\(208\) 0 0
\(209\) −4.94257 −0.341885
\(210\) 0 0
\(211\) 1.75230 0.120633 0.0603165 0.998179i \(-0.480789\pi\)
0.0603165 + 0.998179i \(0.480789\pi\)
\(212\) 0 0
\(213\) −3.97515 −0.272373
\(214\) 0 0
\(215\) 25.7232 1.75431
\(216\) 0 0
\(217\) 34.2752 2.32675
\(218\) 0 0
\(219\) −6.83455 −0.461836
\(220\) 0 0
\(221\) −4.52662 −0.304493
\(222\) 0 0
\(223\) 6.79814 0.455237 0.227619 0.973750i \(-0.426906\pi\)
0.227619 + 0.973750i \(0.426906\pi\)
\(224\) 0 0
\(225\) 1.46803 0.0978684
\(226\) 0 0
\(227\) −2.28779 −0.151846 −0.0759231 0.997114i \(-0.524190\pi\)
−0.0759231 + 0.997114i \(0.524190\pi\)
\(228\) 0 0
\(229\) −21.2604 −1.40493 −0.702463 0.711720i \(-0.747916\pi\)
−0.702463 + 0.711720i \(0.747916\pi\)
\(230\) 0 0
\(231\) 3.37740 0.222217
\(232\) 0 0
\(233\) 17.9559 1.17633 0.588164 0.808741i \(-0.299851\pi\)
0.588164 + 0.808741i \(0.299851\pi\)
\(234\) 0 0
\(235\) −1.26727 −0.0826673
\(236\) 0 0
\(237\) 7.34900 0.477369
\(238\) 0 0
\(239\) 9.32061 0.602900 0.301450 0.953482i \(-0.402529\pi\)
0.301450 + 0.953482i \(0.402529\pi\)
\(240\) 0 0
\(241\) 10.7267 0.690969 0.345485 0.938424i \(-0.387715\pi\)
0.345485 + 0.938424i \(0.387715\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 23.9158 1.52792
\(246\) 0 0
\(247\) 14.5880 0.928215
\(248\) 0 0
\(249\) −4.66163 −0.295419
\(250\) 0 0
\(251\) −14.6533 −0.924910 −0.462455 0.886643i \(-0.653031\pi\)
−0.462455 + 0.886643i \(0.653031\pi\)
\(252\) 0 0
\(253\) −3.27131 −0.205665
\(254\) 0 0
\(255\) 4.67739 0.292909
\(256\) 0 0
\(257\) 4.98675 0.311065 0.155532 0.987831i \(-0.450291\pi\)
0.155532 + 0.987831i \(0.450291\pi\)
\(258\) 0 0
\(259\) 16.0402 0.996690
\(260\) 0 0
\(261\) −7.78858 −0.482101
\(262\) 0 0
\(263\) −14.5146 −0.895008 −0.447504 0.894282i \(-0.647687\pi\)
−0.447504 + 0.894282i \(0.647687\pi\)
\(264\) 0 0
\(265\) 6.24400 0.383566
\(266\) 0 0
\(267\) 4.56477 0.279359
\(268\) 0 0
\(269\) 17.8787 1.09008 0.545042 0.838409i \(-0.316514\pi\)
0.545042 + 0.838409i \(0.316514\pi\)
\(270\) 0 0
\(271\) −26.2459 −1.59433 −0.797163 0.603764i \(-0.793667\pi\)
−0.797163 + 0.603764i \(0.793667\pi\)
\(272\) 0 0
\(273\) −9.96844 −0.603318
\(274\) 0 0
\(275\) −1.22418 −0.0738209
\(276\) 0 0
\(277\) −10.7923 −0.648445 −0.324222 0.945981i \(-0.605103\pi\)
−0.324222 + 0.945981i \(0.605103\pi\)
\(278\) 0 0
\(279\) 8.46269 0.506648
\(280\) 0 0
\(281\) 3.45938 0.206369 0.103185 0.994662i \(-0.467097\pi\)
0.103185 + 0.994662i \(0.467097\pi\)
\(282\) 0 0
\(283\) 7.01935 0.417257 0.208628 0.977995i \(-0.433100\pi\)
0.208628 + 0.977995i \(0.433100\pi\)
\(284\) 0 0
\(285\) −15.0739 −0.892902
\(286\) 0 0
\(287\) −44.7334 −2.64053
\(288\) 0 0
\(289\) −13.6175 −0.801031
\(290\) 0 0
\(291\) −10.8423 −0.635586
\(292\) 0 0
\(293\) −21.2689 −1.24254 −0.621270 0.783596i \(-0.713383\pi\)
−0.621270 + 0.783596i \(0.713383\pi\)
\(294\) 0 0
\(295\) −18.6557 −1.08617
\(296\) 0 0
\(297\) 0.833896 0.0483876
\(298\) 0 0
\(299\) 9.65531 0.558381
\(300\) 0 0
\(301\) 40.9647 2.36116
\(302\) 0 0
\(303\) −1.34614 −0.0773338
\(304\) 0 0
\(305\) 7.02359 0.402169
\(306\) 0 0
\(307\) −6.59119 −0.376179 −0.188090 0.982152i \(-0.560230\pi\)
−0.188090 + 0.982152i \(0.560230\pi\)
\(308\) 0 0
\(309\) −17.7990 −1.01255
\(310\) 0 0
\(311\) 9.88758 0.560673 0.280337 0.959902i \(-0.409554\pi\)
0.280337 + 0.959902i \(0.409554\pi\)
\(312\) 0 0
\(313\) 15.8236 0.894405 0.447202 0.894433i \(-0.352420\pi\)
0.447202 + 0.894433i \(0.352420\pi\)
\(314\) 0 0
\(315\) 10.3005 0.580365
\(316\) 0 0
\(317\) 19.7065 1.10683 0.553415 0.832906i \(-0.313324\pi\)
0.553415 + 0.832906i \(0.313324\pi\)
\(318\) 0 0
\(319\) 6.49487 0.363643
\(320\) 0 0
\(321\) −9.17441 −0.512065
\(322\) 0 0
\(323\) −10.9008 −0.606536
\(324\) 0 0
\(325\) 3.61318 0.200423
\(326\) 0 0
\(327\) −10.0390 −0.555156
\(328\) 0 0
\(329\) −2.01815 −0.111264
\(330\) 0 0
\(331\) 10.2190 0.561687 0.280844 0.959754i \(-0.409386\pi\)
0.280844 + 0.959754i \(0.409386\pi\)
\(332\) 0 0
\(333\) 3.96040 0.217029
\(334\) 0 0
\(335\) −27.7678 −1.51712
\(336\) 0 0
\(337\) 11.2996 0.615529 0.307764 0.951463i \(-0.400419\pi\)
0.307764 + 0.951463i \(0.400419\pi\)
\(338\) 0 0
\(339\) −18.2770 −0.992670
\(340\) 0 0
\(341\) −7.05700 −0.382158
\(342\) 0 0
\(343\) 9.73536 0.525660
\(344\) 0 0
\(345\) −9.97690 −0.537138
\(346\) 0 0
\(347\) 5.76457 0.309459 0.154729 0.987957i \(-0.450549\pi\)
0.154729 + 0.987957i \(0.450549\pi\)
\(348\) 0 0
\(349\) 29.3610 1.57166 0.785828 0.618445i \(-0.212237\pi\)
0.785828 + 0.618445i \(0.212237\pi\)
\(350\) 0 0
\(351\) −2.46125 −0.131372
\(352\) 0 0
\(353\) 3.57956 0.190521 0.0952603 0.995452i \(-0.469632\pi\)
0.0952603 + 0.995452i \(0.469632\pi\)
\(354\) 0 0
\(355\) 10.1097 0.536568
\(356\) 0 0
\(357\) 7.44884 0.394234
\(358\) 0 0
\(359\) 5.20874 0.274907 0.137453 0.990508i \(-0.456108\pi\)
0.137453 + 0.990508i \(0.456108\pi\)
\(360\) 0 0
\(361\) 16.1302 0.848960
\(362\) 0 0
\(363\) 10.3046 0.540852
\(364\) 0 0
\(365\) 17.3818 0.909808
\(366\) 0 0
\(367\) 7.05201 0.368112 0.184056 0.982916i \(-0.441077\pi\)
0.184056 + 0.982916i \(0.441077\pi\)
\(368\) 0 0
\(369\) −11.0449 −0.574974
\(370\) 0 0
\(371\) 9.94370 0.516251
\(372\) 0 0
\(373\) −28.5516 −1.47835 −0.739173 0.673515i \(-0.764784\pi\)
−0.739173 + 0.673515i \(0.764784\pi\)
\(374\) 0 0
\(375\) 8.98263 0.463861
\(376\) 0 0
\(377\) −19.1697 −0.987289
\(378\) 0 0
\(379\) 37.0375 1.90249 0.951244 0.308438i \(-0.0998062\pi\)
0.951244 + 0.308438i \(0.0998062\pi\)
\(380\) 0 0
\(381\) 8.49866 0.435400
\(382\) 0 0
\(383\) 14.3367 0.732571 0.366285 0.930503i \(-0.380629\pi\)
0.366285 + 0.930503i \(0.380629\pi\)
\(384\) 0 0
\(385\) −8.58952 −0.437762
\(386\) 0 0
\(387\) 10.1144 0.514142
\(388\) 0 0
\(389\) 27.7940 1.40921 0.704606 0.709599i \(-0.251124\pi\)
0.704606 + 0.709599i \(0.251124\pi\)
\(390\) 0 0
\(391\) −7.21485 −0.364871
\(392\) 0 0
\(393\) −6.28622 −0.317098
\(394\) 0 0
\(395\) −18.6902 −0.940406
\(396\) 0 0
\(397\) −18.2225 −0.914562 −0.457281 0.889322i \(-0.651177\pi\)
−0.457281 + 0.889322i \(0.651177\pi\)
\(398\) 0 0
\(399\) −24.0055 −1.20178
\(400\) 0 0
\(401\) 15.4736 0.772715 0.386357 0.922349i \(-0.373733\pi\)
0.386357 + 0.922349i \(0.373733\pi\)
\(402\) 0 0
\(403\) 20.8288 1.03756
\(404\) 0 0
\(405\) 2.54323 0.126374
\(406\) 0 0
\(407\) −3.30256 −0.163702
\(408\) 0 0
\(409\) −28.8220 −1.42515 −0.712577 0.701594i \(-0.752472\pi\)
−0.712577 + 0.701594i \(0.752472\pi\)
\(410\) 0 0
\(411\) −4.10350 −0.202411
\(412\) 0 0
\(413\) −29.7095 −1.46191
\(414\) 0 0
\(415\) 11.8556 0.581968
\(416\) 0 0
\(417\) 4.54642 0.222639
\(418\) 0 0
\(419\) 5.39623 0.263623 0.131812 0.991275i \(-0.457921\pi\)
0.131812 + 0.991275i \(0.457921\pi\)
\(420\) 0 0
\(421\) −39.5566 −1.92787 −0.963935 0.266137i \(-0.914253\pi\)
−0.963935 + 0.266137i \(0.914253\pi\)
\(422\) 0 0
\(423\) −0.498289 −0.0242277
\(424\) 0 0
\(425\) −2.69992 −0.130965
\(426\) 0 0
\(427\) 11.1852 0.541290
\(428\) 0 0
\(429\) 2.05243 0.0990923
\(430\) 0 0
\(431\) −13.6111 −0.655625 −0.327813 0.944743i \(-0.606311\pi\)
−0.327813 + 0.944743i \(0.606311\pi\)
\(432\) 0 0
\(433\) 8.00025 0.384468 0.192234 0.981349i \(-0.438427\pi\)
0.192234 + 0.981349i \(0.438427\pi\)
\(434\) 0 0
\(435\) 19.8082 0.949729
\(436\) 0 0
\(437\) 23.2515 1.11227
\(438\) 0 0
\(439\) 2.97754 0.142110 0.0710551 0.997472i \(-0.477363\pi\)
0.0710551 + 0.997472i \(0.477363\pi\)
\(440\) 0 0
\(441\) 9.40370 0.447795
\(442\) 0 0
\(443\) −21.5745 −1.02504 −0.512518 0.858677i \(-0.671287\pi\)
−0.512518 + 0.858677i \(0.671287\pi\)
\(444\) 0 0
\(445\) −11.6093 −0.550331
\(446\) 0 0
\(447\) 13.9805 0.661254
\(448\) 0 0
\(449\) 30.7847 1.45282 0.726409 0.687263i \(-0.241188\pi\)
0.726409 + 0.687263i \(0.241188\pi\)
\(450\) 0 0
\(451\) 9.21029 0.433696
\(452\) 0 0
\(453\) −2.44014 −0.114648
\(454\) 0 0
\(455\) 25.3521 1.18852
\(456\) 0 0
\(457\) 8.42006 0.393874 0.196937 0.980416i \(-0.436901\pi\)
0.196937 + 0.980416i \(0.436901\pi\)
\(458\) 0 0
\(459\) 1.83915 0.0858442
\(460\) 0 0
\(461\) 23.3100 1.08565 0.542827 0.839844i \(-0.317354\pi\)
0.542827 + 0.839844i \(0.317354\pi\)
\(462\) 0 0
\(463\) −1.50270 −0.0698364 −0.0349182 0.999390i \(-0.511117\pi\)
−0.0349182 + 0.999390i \(0.511117\pi\)
\(464\) 0 0
\(465\) −21.5226 −0.998086
\(466\) 0 0
\(467\) 8.68794 0.402030 0.201015 0.979588i \(-0.435576\pi\)
0.201015 + 0.979588i \(0.435576\pi\)
\(468\) 0 0
\(469\) −44.2208 −2.04193
\(470\) 0 0
\(471\) 17.2013 0.792594
\(472\) 0 0
\(473\) −8.43433 −0.387811
\(474\) 0 0
\(475\) 8.70110 0.399234
\(476\) 0 0
\(477\) 2.45514 0.112413
\(478\) 0 0
\(479\) 33.2228 1.51799 0.758994 0.651098i \(-0.225691\pi\)
0.758994 + 0.651098i \(0.225691\pi\)
\(480\) 0 0
\(481\) 9.74755 0.444450
\(482\) 0 0
\(483\) −15.8884 −0.722948
\(484\) 0 0
\(485\) 27.5744 1.25209
\(486\) 0 0
\(487\) 19.4634 0.881971 0.440985 0.897514i \(-0.354629\pi\)
0.440985 + 0.897514i \(0.354629\pi\)
\(488\) 0 0
\(489\) −0.421952 −0.0190813
\(490\) 0 0
\(491\) −42.1354 −1.90154 −0.950772 0.309892i \(-0.899707\pi\)
−0.950772 + 0.309892i \(0.899707\pi\)
\(492\) 0 0
\(493\) 14.3244 0.645138
\(494\) 0 0
\(495\) −2.12079 −0.0953225
\(496\) 0 0
\(497\) 16.0999 0.722181
\(498\) 0 0
\(499\) −21.5365 −0.964107 −0.482053 0.876142i \(-0.660109\pi\)
−0.482053 + 0.876142i \(0.660109\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 36.5611 1.63018 0.815090 0.579334i \(-0.196687\pi\)
0.815090 + 0.579334i \(0.196687\pi\)
\(504\) 0 0
\(505\) 3.42355 0.152346
\(506\) 0 0
\(507\) 6.94223 0.308315
\(508\) 0 0
\(509\) −20.4301 −0.905547 −0.452773 0.891626i \(-0.649565\pi\)
−0.452773 + 0.891626i \(0.649565\pi\)
\(510\) 0 0
\(511\) 27.6810 1.22453
\(512\) 0 0
\(513\) −5.92708 −0.261687
\(514\) 0 0
\(515\) 45.2669 1.99470
\(516\) 0 0
\(517\) 0.415522 0.0182746
\(518\) 0 0
\(519\) 16.6235 0.729692
\(520\) 0 0
\(521\) 16.7009 0.731678 0.365839 0.930678i \(-0.380782\pi\)
0.365839 + 0.930678i \(0.380782\pi\)
\(522\) 0 0
\(523\) −23.3167 −1.01957 −0.509784 0.860302i \(-0.670275\pi\)
−0.509784 + 0.860302i \(0.670275\pi\)
\(524\) 0 0
\(525\) −5.94572 −0.259493
\(526\) 0 0
\(527\) −15.5642 −0.677986
\(528\) 0 0
\(529\) −7.61069 −0.330899
\(530\) 0 0
\(531\) −7.33541 −0.318330
\(532\) 0 0
\(533\) −27.1843 −1.17748
\(534\) 0 0
\(535\) 23.3326 1.00876
\(536\) 0 0
\(537\) 1.25643 0.0542188
\(538\) 0 0
\(539\) −7.84171 −0.337766
\(540\) 0 0
\(541\) −25.6590 −1.10317 −0.551584 0.834119i \(-0.685976\pi\)
−0.551584 + 0.834119i \(0.685976\pi\)
\(542\) 0 0
\(543\) 4.10641 0.176223
\(544\) 0 0
\(545\) 25.5314 1.09364
\(546\) 0 0
\(547\) 36.7011 1.56923 0.784613 0.619985i \(-0.212862\pi\)
0.784613 + 0.619985i \(0.212862\pi\)
\(548\) 0 0
\(549\) 2.76168 0.117866
\(550\) 0 0
\(551\) −46.1635 −1.96663
\(552\) 0 0
\(553\) −29.7645 −1.26572
\(554\) 0 0
\(555\) −10.0722 −0.427542
\(556\) 0 0
\(557\) 9.41547 0.398946 0.199473 0.979903i \(-0.436077\pi\)
0.199473 + 0.979903i \(0.436077\pi\)
\(558\) 0 0
\(559\) 24.8940 1.05290
\(560\) 0 0
\(561\) −1.53366 −0.0647512
\(562\) 0 0
\(563\) 2.64266 0.111375 0.0556874 0.998448i \(-0.482265\pi\)
0.0556874 + 0.998448i \(0.482265\pi\)
\(564\) 0 0
\(565\) 46.4826 1.95554
\(566\) 0 0
\(567\) 4.05015 0.170090
\(568\) 0 0
\(569\) 33.1152 1.38826 0.694130 0.719850i \(-0.255789\pi\)
0.694130 + 0.719850i \(0.255789\pi\)
\(570\) 0 0
\(571\) −11.1000 −0.464521 −0.232261 0.972654i \(-0.574612\pi\)
−0.232261 + 0.972654i \(0.574612\pi\)
\(572\) 0 0
\(573\) 14.8331 0.619661
\(574\) 0 0
\(575\) 5.75895 0.240165
\(576\) 0 0
\(577\) −13.0188 −0.541981 −0.270991 0.962582i \(-0.587351\pi\)
−0.270991 + 0.962582i \(0.587351\pi\)
\(578\) 0 0
\(579\) 10.2047 0.424092
\(580\) 0 0
\(581\) 18.8803 0.783286
\(582\) 0 0
\(583\) −2.04734 −0.0847920
\(584\) 0 0
\(585\) 6.25954 0.258800
\(586\) 0 0
\(587\) −23.7173 −0.978917 −0.489458 0.872027i \(-0.662806\pi\)
−0.489458 + 0.872027i \(0.662806\pi\)
\(588\) 0 0
\(589\) 50.1590 2.06677
\(590\) 0 0
\(591\) 12.2783 0.505064
\(592\) 0 0
\(593\) −24.6798 −1.01348 −0.506739 0.862100i \(-0.669149\pi\)
−0.506739 + 0.862100i \(0.669149\pi\)
\(594\) 0 0
\(595\) −18.9441 −0.776633
\(596\) 0 0
\(597\) 3.70118 0.151479
\(598\) 0 0
\(599\) 41.1844 1.68275 0.841374 0.540454i \(-0.181748\pi\)
0.841374 + 0.540454i \(0.181748\pi\)
\(600\) 0 0
\(601\) −3.01949 −0.123168 −0.0615838 0.998102i \(-0.519615\pi\)
−0.0615838 + 0.998102i \(0.519615\pi\)
\(602\) 0 0
\(603\) −10.9183 −0.444628
\(604\) 0 0
\(605\) −26.2070 −1.06547
\(606\) 0 0
\(607\) 21.3274 0.865653 0.432826 0.901477i \(-0.357516\pi\)
0.432826 + 0.901477i \(0.357516\pi\)
\(608\) 0 0
\(609\) 31.5449 1.27826
\(610\) 0 0
\(611\) −1.22642 −0.0496155
\(612\) 0 0
\(613\) 38.6813 1.56232 0.781161 0.624330i \(-0.214628\pi\)
0.781161 + 0.624330i \(0.214628\pi\)
\(614\) 0 0
\(615\) 28.0897 1.13269
\(616\) 0 0
\(617\) 43.0717 1.73400 0.867001 0.498307i \(-0.166045\pi\)
0.867001 + 0.498307i \(0.166045\pi\)
\(618\) 0 0
\(619\) 9.34350 0.375547 0.187773 0.982212i \(-0.439873\pi\)
0.187773 + 0.982212i \(0.439873\pi\)
\(620\) 0 0
\(621\) −3.92292 −0.157421
\(622\) 0 0
\(623\) −18.4880 −0.740705
\(624\) 0 0
\(625\) −30.1850 −1.20740
\(626\) 0 0
\(627\) 4.94257 0.197387
\(628\) 0 0
\(629\) −7.28378 −0.290423
\(630\) 0 0
\(631\) −34.3258 −1.36649 −0.683245 0.730190i \(-0.739432\pi\)
−0.683245 + 0.730190i \(0.739432\pi\)
\(632\) 0 0
\(633\) −1.75230 −0.0696475
\(634\) 0 0
\(635\) −21.6141 −0.857728
\(636\) 0 0
\(637\) 23.1449 0.917034
\(638\) 0 0
\(639\) 3.97515 0.157254
\(640\) 0 0
\(641\) 29.5973 1.16902 0.584511 0.811386i \(-0.301286\pi\)
0.584511 + 0.811386i \(0.301286\pi\)
\(642\) 0 0
\(643\) 24.8427 0.979701 0.489850 0.871807i \(-0.337051\pi\)
0.489850 + 0.871807i \(0.337051\pi\)
\(644\) 0 0
\(645\) −25.7232 −1.01285
\(646\) 0 0
\(647\) −21.8126 −0.857542 −0.428771 0.903413i \(-0.641053\pi\)
−0.428771 + 0.903413i \(0.641053\pi\)
\(648\) 0 0
\(649\) 6.11697 0.240112
\(650\) 0 0
\(651\) −34.2752 −1.34335
\(652\) 0 0
\(653\) −31.0957 −1.21687 −0.608435 0.793604i \(-0.708202\pi\)
−0.608435 + 0.793604i \(0.708202\pi\)
\(654\) 0 0
\(655\) 15.9873 0.624676
\(656\) 0 0
\(657\) 6.83455 0.266641
\(658\) 0 0
\(659\) −8.55446 −0.333234 −0.166617 0.986022i \(-0.553284\pi\)
−0.166617 + 0.986022i \(0.553284\pi\)
\(660\) 0 0
\(661\) 24.3444 0.946887 0.473444 0.880824i \(-0.343011\pi\)
0.473444 + 0.880824i \(0.343011\pi\)
\(662\) 0 0
\(663\) 4.52662 0.175799
\(664\) 0 0
\(665\) 61.0517 2.36748
\(666\) 0 0
\(667\) −30.5540 −1.18306
\(668\) 0 0
\(669\) −6.79814 −0.262831
\(670\) 0 0
\(671\) −2.30295 −0.0889045
\(672\) 0 0
\(673\) −6.31282 −0.243341 −0.121671 0.992571i \(-0.538825\pi\)
−0.121671 + 0.992571i \(0.538825\pi\)
\(674\) 0 0
\(675\) −1.46803 −0.0565043
\(676\) 0 0
\(677\) −20.7946 −0.799200 −0.399600 0.916690i \(-0.630851\pi\)
−0.399600 + 0.916690i \(0.630851\pi\)
\(678\) 0 0
\(679\) 43.9129 1.68522
\(680\) 0 0
\(681\) 2.28779 0.0876685
\(682\) 0 0
\(683\) 36.3346 1.39030 0.695152 0.718862i \(-0.255337\pi\)
0.695152 + 0.718862i \(0.255337\pi\)
\(684\) 0 0
\(685\) 10.4361 0.398744
\(686\) 0 0
\(687\) 21.2604 0.811134
\(688\) 0 0
\(689\) 6.04273 0.230210
\(690\) 0 0
\(691\) −20.2826 −0.771587 −0.385794 0.922585i \(-0.626072\pi\)
−0.385794 + 0.922585i \(0.626072\pi\)
\(692\) 0 0
\(693\) −3.37740 −0.128297
\(694\) 0 0
\(695\) −11.5626 −0.438594
\(696\) 0 0
\(697\) 20.3132 0.769418
\(698\) 0 0
\(699\) −17.9559 −0.679154
\(700\) 0 0
\(701\) −1.45086 −0.0547982 −0.0273991 0.999625i \(-0.508723\pi\)
−0.0273991 + 0.999625i \(0.508723\pi\)
\(702\) 0 0
\(703\) 23.4736 0.885324
\(704\) 0 0
\(705\) 1.26727 0.0477280
\(706\) 0 0
\(707\) 5.45208 0.205046
\(708\) 0 0
\(709\) 21.8610 0.821006 0.410503 0.911859i \(-0.365353\pi\)
0.410503 + 0.911859i \(0.365353\pi\)
\(710\) 0 0
\(711\) −7.34900 −0.275609
\(712\) 0 0
\(713\) 33.1985 1.24329
\(714\) 0 0
\(715\) −5.21980 −0.195210
\(716\) 0 0
\(717\) −9.32061 −0.348085
\(718\) 0 0
\(719\) −48.2100 −1.79793 −0.898965 0.438020i \(-0.855680\pi\)
−0.898965 + 0.438020i \(0.855680\pi\)
\(720\) 0 0
\(721\) 72.0885 2.68472
\(722\) 0 0
\(723\) −10.7267 −0.398931
\(724\) 0 0
\(725\) −11.4338 −0.424642
\(726\) 0 0
\(727\) −5.64488 −0.209357 −0.104679 0.994506i \(-0.533381\pi\)
−0.104679 + 0.994506i \(0.533381\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −18.6018 −0.688014
\(732\) 0 0
\(733\) 9.56879 0.353431 0.176716 0.984262i \(-0.443453\pi\)
0.176716 + 0.984262i \(0.443453\pi\)
\(734\) 0 0
\(735\) −23.9158 −0.882147
\(736\) 0 0
\(737\) 9.10473 0.335377
\(738\) 0 0
\(739\) −29.7475 −1.09428 −0.547139 0.837041i \(-0.684283\pi\)
−0.547139 + 0.837041i \(0.684283\pi\)
\(740\) 0 0
\(741\) −14.5880 −0.535905
\(742\) 0 0
\(743\) 36.8506 1.35192 0.675959 0.736939i \(-0.263729\pi\)
0.675959 + 0.736939i \(0.263729\pi\)
\(744\) 0 0
\(745\) −35.5556 −1.30266
\(746\) 0 0
\(747\) 4.66163 0.170560
\(748\) 0 0
\(749\) 37.1577 1.35771
\(750\) 0 0
\(751\) −24.0585 −0.877908 −0.438954 0.898509i \(-0.644651\pi\)
−0.438954 + 0.898509i \(0.644651\pi\)
\(752\) 0 0
\(753\) 14.6533 0.533997
\(754\) 0 0
\(755\) 6.20583 0.225853
\(756\) 0 0
\(757\) −7.73664 −0.281193 −0.140596 0.990067i \(-0.544902\pi\)
−0.140596 + 0.990067i \(0.544902\pi\)
\(758\) 0 0
\(759\) 3.27131 0.118741
\(760\) 0 0
\(761\) −17.0837 −0.619285 −0.309643 0.950853i \(-0.600209\pi\)
−0.309643 + 0.950853i \(0.600209\pi\)
\(762\) 0 0
\(763\) 40.6593 1.47196
\(764\) 0 0
\(765\) −4.67739 −0.169111
\(766\) 0 0
\(767\) −18.0543 −0.651904
\(768\) 0 0
\(769\) −39.0339 −1.40760 −0.703800 0.710398i \(-0.748515\pi\)
−0.703800 + 0.710398i \(0.748515\pi\)
\(770\) 0 0
\(771\) −4.98675 −0.179593
\(772\) 0 0
\(773\) 18.5873 0.668540 0.334270 0.942477i \(-0.391510\pi\)
0.334270 + 0.942477i \(0.391510\pi\)
\(774\) 0 0
\(775\) 12.4234 0.446263
\(776\) 0 0
\(777\) −16.0402 −0.575439
\(778\) 0 0
\(779\) −65.4639 −2.34549
\(780\) 0 0
\(781\) −3.31486 −0.118615
\(782\) 0 0
\(783\) 7.78858 0.278341
\(784\) 0 0
\(785\) −43.7469 −1.56139
\(786\) 0 0
\(787\) 49.1552 1.75219 0.876097 0.482134i \(-0.160138\pi\)
0.876097 + 0.482134i \(0.160138\pi\)
\(788\) 0 0
\(789\) 14.5146 0.516733
\(790\) 0 0
\(791\) 74.0246 2.63201
\(792\) 0 0
\(793\) 6.79719 0.241375
\(794\) 0 0
\(795\) −6.24400 −0.221452
\(796\) 0 0
\(797\) −45.5162 −1.61227 −0.806133 0.591734i \(-0.798443\pi\)
−0.806133 + 0.591734i \(0.798443\pi\)
\(798\) 0 0
\(799\) 0.916430 0.0324210
\(800\) 0 0
\(801\) −4.56477 −0.161288
\(802\) 0 0
\(803\) −5.69931 −0.201124
\(804\) 0 0
\(805\) 40.4079 1.42419
\(806\) 0 0
\(807\) −17.8787 −0.629360
\(808\) 0 0
\(809\) −17.0876 −0.600768 −0.300384 0.953818i \(-0.597115\pi\)
−0.300384 + 0.953818i \(0.597115\pi\)
\(810\) 0 0
\(811\) −37.2942 −1.30958 −0.654789 0.755812i \(-0.727243\pi\)
−0.654789 + 0.755812i \(0.727243\pi\)
\(812\) 0 0
\(813\) 26.2459 0.920484
\(814\) 0 0
\(815\) 1.07312 0.0375898
\(816\) 0 0
\(817\) 59.9486 2.09734
\(818\) 0 0
\(819\) 9.96844 0.348326
\(820\) 0 0
\(821\) 35.4980 1.23889 0.619444 0.785041i \(-0.287358\pi\)
0.619444 + 0.785041i \(0.287358\pi\)
\(822\) 0 0
\(823\) 52.0090 1.81292 0.906460 0.422291i \(-0.138774\pi\)
0.906460 + 0.422291i \(0.138774\pi\)
\(824\) 0 0
\(825\) 1.22418 0.0426205
\(826\) 0 0
\(827\) 17.5986 0.611962 0.305981 0.952038i \(-0.401016\pi\)
0.305981 + 0.952038i \(0.401016\pi\)
\(828\) 0 0
\(829\) 31.8869 1.10748 0.553738 0.832691i \(-0.313201\pi\)
0.553738 + 0.832691i \(0.313201\pi\)
\(830\) 0 0
\(831\) 10.7923 0.374380
\(832\) 0 0
\(833\) −17.2948 −0.599231
\(834\) 0 0
\(835\) 2.54323 0.0880121
\(836\) 0 0
\(837\) −8.46269 −0.292513
\(838\) 0 0
\(839\) 22.6755 0.782846 0.391423 0.920211i \(-0.371983\pi\)
0.391423 + 0.920211i \(0.371983\pi\)
\(840\) 0 0
\(841\) 31.6620 1.09179
\(842\) 0 0
\(843\) −3.45938 −0.119147
\(844\) 0 0
\(845\) −17.6557 −0.607374
\(846\) 0 0
\(847\) −41.7352 −1.43404
\(848\) 0 0
\(849\) −7.01935 −0.240903
\(850\) 0 0
\(851\) 15.5363 0.532579
\(852\) 0 0
\(853\) −40.0438 −1.37107 −0.685537 0.728038i \(-0.740433\pi\)
−0.685537 + 0.728038i \(0.740433\pi\)
\(854\) 0 0
\(855\) 15.0739 0.515517
\(856\) 0 0
\(857\) −15.5167 −0.530039 −0.265019 0.964243i \(-0.585378\pi\)
−0.265019 + 0.964243i \(0.585378\pi\)
\(858\) 0 0
\(859\) −9.92115 −0.338505 −0.169253 0.985573i \(-0.554135\pi\)
−0.169253 + 0.985573i \(0.554135\pi\)
\(860\) 0 0
\(861\) 44.7334 1.52451
\(862\) 0 0
\(863\) 5.06567 0.172437 0.0862187 0.996276i \(-0.472522\pi\)
0.0862187 + 0.996276i \(0.472522\pi\)
\(864\) 0 0
\(865\) −42.2775 −1.43748
\(866\) 0 0
\(867\) 13.6175 0.462475
\(868\) 0 0
\(869\) 6.12830 0.207888
\(870\) 0 0
\(871\) −26.8727 −0.910547
\(872\) 0 0
\(873\) 10.8423 0.366956
\(874\) 0 0
\(875\) −36.3810 −1.22990
\(876\) 0 0
\(877\) 42.0614 1.42031 0.710157 0.704043i \(-0.248624\pi\)
0.710157 + 0.704043i \(0.248624\pi\)
\(878\) 0 0
\(879\) 21.2689 0.717381
\(880\) 0 0
\(881\) 2.70081 0.0909927 0.0454964 0.998965i \(-0.485513\pi\)
0.0454964 + 0.998965i \(0.485513\pi\)
\(882\) 0 0
\(883\) −30.7249 −1.03397 −0.516987 0.855993i \(-0.672946\pi\)
−0.516987 + 0.855993i \(0.672946\pi\)
\(884\) 0 0
\(885\) 18.6557 0.627103
\(886\) 0 0
\(887\) −52.0588 −1.74796 −0.873981 0.485960i \(-0.838470\pi\)
−0.873981 + 0.485960i \(0.838470\pi\)
\(888\) 0 0
\(889\) −34.4208 −1.15444
\(890\) 0 0
\(891\) −0.833896 −0.0279366
\(892\) 0 0
\(893\) −2.95340 −0.0988318
\(894\) 0 0
\(895\) −3.19538 −0.106810
\(896\) 0 0
\(897\) −9.65531 −0.322381
\(898\) 0 0
\(899\) −65.9124 −2.19830
\(900\) 0 0
\(901\) −4.51538 −0.150429
\(902\) 0 0
\(903\) −40.9647 −1.36322
\(904\) 0 0
\(905\) −10.4436 −0.347155
\(906\) 0 0
\(907\) 14.7456 0.489621 0.244811 0.969571i \(-0.421274\pi\)
0.244811 + 0.969571i \(0.421274\pi\)
\(908\) 0 0
\(909\) 1.34614 0.0446487
\(910\) 0 0
\(911\) −19.6554 −0.651212 −0.325606 0.945506i \(-0.605568\pi\)
−0.325606 + 0.945506i \(0.605568\pi\)
\(912\) 0 0
\(913\) −3.88731 −0.128651
\(914\) 0 0
\(915\) −7.02359 −0.232193
\(916\) 0 0
\(917\) 25.4601 0.840768
\(918\) 0 0
\(919\) −27.8835 −0.919792 −0.459896 0.887973i \(-0.652113\pi\)
−0.459896 + 0.887973i \(0.652113\pi\)
\(920\) 0 0
\(921\) 6.59119 0.217187
\(922\) 0 0
\(923\) 9.78384 0.322039
\(924\) 0 0
\(925\) 5.81397 0.191162
\(926\) 0 0
\(927\) 17.7990 0.584595
\(928\) 0 0
\(929\) 13.7960 0.452631 0.226316 0.974054i \(-0.427332\pi\)
0.226316 + 0.974054i \(0.427332\pi\)
\(930\) 0 0
\(931\) 55.7365 1.82669
\(932\) 0 0
\(933\) −9.88758 −0.323705
\(934\) 0 0
\(935\) 3.90046 0.127559
\(936\) 0 0
\(937\) −5.96881 −0.194993 −0.0974963 0.995236i \(-0.531083\pi\)
−0.0974963 + 0.995236i \(0.531083\pi\)
\(938\) 0 0
\(939\) −15.8236 −0.516385
\(940\) 0 0
\(941\) −57.6012 −1.87775 −0.938873 0.344264i \(-0.888128\pi\)
−0.938873 + 0.344264i \(0.888128\pi\)
\(942\) 0 0
\(943\) −43.3282 −1.41096
\(944\) 0 0
\(945\) −10.3005 −0.335074
\(946\) 0 0
\(947\) −50.1673 −1.63022 −0.815109 0.579308i \(-0.803323\pi\)
−0.815109 + 0.579308i \(0.803323\pi\)
\(948\) 0 0
\(949\) 16.8216 0.546051
\(950\) 0 0
\(951\) −19.7065 −0.639028
\(952\) 0 0
\(953\) −19.9024 −0.644703 −0.322352 0.946620i \(-0.604473\pi\)
−0.322352 + 0.946620i \(0.604473\pi\)
\(954\) 0 0
\(955\) −37.7240 −1.22072
\(956\) 0 0
\(957\) −6.49487 −0.209949
\(958\) 0 0
\(959\) 16.6198 0.536680
\(960\) 0 0
\(961\) 40.6171 1.31023
\(962\) 0 0
\(963\) 9.17441 0.295641
\(964\) 0 0
\(965\) −25.9529 −0.835453
\(966\) 0 0
\(967\) 44.9296 1.44484 0.722419 0.691456i \(-0.243030\pi\)
0.722419 + 0.691456i \(0.243030\pi\)
\(968\) 0 0
\(969\) 10.9008 0.350184
\(970\) 0 0
\(971\) −35.3274 −1.13371 −0.566855 0.823817i \(-0.691840\pi\)
−0.566855 + 0.823817i \(0.691840\pi\)
\(972\) 0 0
\(973\) −18.4137 −0.590315
\(974\) 0 0
\(975\) −3.61318 −0.115714
\(976\) 0 0
\(977\) −0.366186 −0.0117153 −0.00585766 0.999983i \(-0.501865\pi\)
−0.00585766 + 0.999983i \(0.501865\pi\)
\(978\) 0 0
\(979\) 3.80654 0.121658
\(980\) 0 0
\(981\) 10.0390 0.320519
\(982\) 0 0
\(983\) −26.9995 −0.861149 −0.430575 0.902555i \(-0.641689\pi\)
−0.430575 + 0.902555i \(0.641689\pi\)
\(984\) 0 0
\(985\) −31.2267 −0.994965
\(986\) 0 0
\(987\) 2.01815 0.0642383
\(988\) 0 0
\(989\) 39.6779 1.26168
\(990\) 0 0
\(991\) −53.3689 −1.69532 −0.847659 0.530542i \(-0.821989\pi\)
−0.847659 + 0.530542i \(0.821989\pi\)
\(992\) 0 0
\(993\) −10.2190 −0.324290
\(994\) 0 0
\(995\) −9.41296 −0.298411
\(996\) 0 0
\(997\) 55.2046 1.74835 0.874174 0.485613i \(-0.161404\pi\)
0.874174 + 0.485613i \(0.161404\pi\)
\(998\) 0 0
\(999\) −3.96040 −0.125302
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 8016.2.a.ba.1.9 9
4.3 odd 2 4008.2.a.i.1.9 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4008.2.a.i.1.9 9 4.3 odd 2
8016.2.a.ba.1.9 9 1.1 even 1 trivial