Properties

Label 4008.2.a.l.1.9
Level 4008
Weight 2
Character 4008.1
Self dual Yes
Analytic conductor 32.004
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4008 = 2^{3} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0040411301\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(2.31305\)
Character \(\chi\) = 4008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+2.31305 q^{5}\) \(+4.58648 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+2.31305 q^{5}\) \(+4.58648 q^{7}\) \(+1.00000 q^{9}\) \(+3.21418 q^{11}\) \(-5.90839 q^{13}\) \(+2.31305 q^{15}\) \(+6.31037 q^{17}\) \(-7.08386 q^{19}\) \(+4.58648 q^{21}\) \(-1.12084 q^{23}\) \(+0.350210 q^{25}\) \(+1.00000 q^{27}\) \(-0.0956753 q^{29}\) \(+4.81707 q^{31}\) \(+3.21418 q^{33}\) \(+10.6088 q^{35}\) \(+3.60986 q^{37}\) \(-5.90839 q^{39}\) \(+8.59300 q^{41}\) \(-8.44278 q^{43}\) \(+2.31305 q^{45}\) \(+6.42753 q^{47}\) \(+14.0358 q^{49}\) \(+6.31037 q^{51}\) \(+2.56167 q^{53}\) \(+7.43455 q^{55}\) \(-7.08386 q^{57}\) \(+6.13741 q^{59}\) \(-5.66615 q^{61}\) \(+4.58648 q^{63}\) \(-13.6664 q^{65}\) \(-9.24652 q^{67}\) \(-1.12084 q^{69}\) \(-7.95267 q^{71}\) \(+14.9676 q^{73}\) \(+0.350210 q^{75}\) \(+14.7417 q^{77}\) \(+13.4092 q^{79}\) \(+1.00000 q^{81}\) \(-3.20203 q^{83}\) \(+14.5962 q^{85}\) \(-0.0956753 q^{87}\) \(-16.0148 q^{89}\) \(-27.0987 q^{91}\) \(+4.81707 q^{93}\) \(-16.3853 q^{95}\) \(+0.476438 q^{97}\) \(+3.21418 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 11q^{7} \) \(\mathstrut +\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut +\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 33q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 4q^{45} \) \(\mathstrut +\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut +\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 20q^{53} \) \(\mathstrut +\mathstrut 39q^{55} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 11q^{63} \) \(\mathstrut +\mathstrut 9q^{67} \) \(\mathstrut +\mathstrut 7q^{69} \) \(\mathstrut +\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut +\mathstrut 18q^{75} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 12q^{81} \) \(\mathstrut +\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 11q^{91} \) \(\mathstrut +\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.31305 1.03443 0.517214 0.855856i \(-0.326969\pi\)
0.517214 + 0.855856i \(0.326969\pi\)
\(6\) 0 0
\(7\) 4.58648 1.73353 0.866763 0.498720i \(-0.166196\pi\)
0.866763 + 0.498720i \(0.166196\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 3.21418 0.969110 0.484555 0.874761i \(-0.338981\pi\)
0.484555 + 0.874761i \(0.338981\pi\)
\(12\) 0 0
\(13\) −5.90839 −1.63869 −0.819346 0.573299i \(-0.805663\pi\)
−0.819346 + 0.573299i \(0.805663\pi\)
\(14\) 0 0
\(15\) 2.31305 0.597227
\(16\) 0 0
\(17\) 6.31037 1.53049 0.765244 0.643740i \(-0.222618\pi\)
0.765244 + 0.643740i \(0.222618\pi\)
\(18\) 0 0
\(19\) −7.08386 −1.62515 −0.812574 0.582858i \(-0.801934\pi\)
−0.812574 + 0.582858i \(0.801934\pi\)
\(20\) 0 0
\(21\) 4.58648 1.00085
\(22\) 0 0
\(23\) −1.12084 −0.233711 −0.116855 0.993149i \(-0.537281\pi\)
−0.116855 + 0.993149i \(0.537281\pi\)
\(24\) 0 0
\(25\) 0.350210 0.0700420
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −0.0956753 −0.0177665 −0.00888323 0.999961i \(-0.502828\pi\)
−0.00888323 + 0.999961i \(0.502828\pi\)
\(30\) 0 0
\(31\) 4.81707 0.865172 0.432586 0.901593i \(-0.357601\pi\)
0.432586 + 0.901593i \(0.357601\pi\)
\(32\) 0 0
\(33\) 3.21418 0.559516
\(34\) 0 0
\(35\) 10.6088 1.79321
\(36\) 0 0
\(37\) 3.60986 0.593458 0.296729 0.954962i \(-0.404104\pi\)
0.296729 + 0.954962i \(0.404104\pi\)
\(38\) 0 0
\(39\) −5.90839 −0.946100
\(40\) 0 0
\(41\) 8.59300 1.34200 0.671001 0.741457i \(-0.265865\pi\)
0.671001 + 0.741457i \(0.265865\pi\)
\(42\) 0 0
\(43\) −8.44278 −1.28751 −0.643756 0.765231i \(-0.722625\pi\)
−0.643756 + 0.765231i \(0.722625\pi\)
\(44\) 0 0
\(45\) 2.31305 0.344809
\(46\) 0 0
\(47\) 6.42753 0.937551 0.468776 0.883317i \(-0.344695\pi\)
0.468776 + 0.883317i \(0.344695\pi\)
\(48\) 0 0
\(49\) 14.0358 2.00511
\(50\) 0 0
\(51\) 6.31037 0.883628
\(52\) 0 0
\(53\) 2.56167 0.351873 0.175936 0.984402i \(-0.443705\pi\)
0.175936 + 0.984402i \(0.443705\pi\)
\(54\) 0 0
\(55\) 7.43455 1.00248
\(56\) 0 0
\(57\) −7.08386 −0.938280
\(58\) 0 0
\(59\) 6.13741 0.799022 0.399511 0.916728i \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(60\) 0 0
\(61\) −5.66615 −0.725476 −0.362738 0.931891i \(-0.618158\pi\)
−0.362738 + 0.931891i \(0.618158\pi\)
\(62\) 0 0
\(63\) 4.58648 0.577842
\(64\) 0 0
\(65\) −13.6664 −1.69511
\(66\) 0 0
\(67\) −9.24652 −1.12964 −0.564821 0.825213i \(-0.691055\pi\)
−0.564821 + 0.825213i \(0.691055\pi\)
\(68\) 0 0
\(69\) −1.12084 −0.134933
\(70\) 0 0
\(71\) −7.95267 −0.943808 −0.471904 0.881650i \(-0.656433\pi\)
−0.471904 + 0.881650i \(0.656433\pi\)
\(72\) 0 0
\(73\) 14.9676 1.75182 0.875911 0.482473i \(-0.160261\pi\)
0.875911 + 0.482473i \(0.160261\pi\)
\(74\) 0 0
\(75\) 0.350210 0.0404388
\(76\) 0 0
\(77\) 14.7417 1.67998
\(78\) 0 0
\(79\) 13.4092 1.50866 0.754328 0.656498i \(-0.227963\pi\)
0.754328 + 0.656498i \(0.227963\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −3.20203 −0.351468 −0.175734 0.984438i \(-0.556230\pi\)
−0.175734 + 0.984438i \(0.556230\pi\)
\(84\) 0 0
\(85\) 14.5962 1.58318
\(86\) 0 0
\(87\) −0.0956753 −0.0102575
\(88\) 0 0
\(89\) −16.0148 −1.69756 −0.848780 0.528746i \(-0.822662\pi\)
−0.848780 + 0.528746i \(0.822662\pi\)
\(90\) 0 0
\(91\) −27.0987 −2.84072
\(92\) 0 0
\(93\) 4.81707 0.499507
\(94\) 0 0
\(95\) −16.3853 −1.68110
\(96\) 0 0
\(97\) 0.476438 0.0483749 0.0241875 0.999707i \(-0.492300\pi\)
0.0241875 + 0.999707i \(0.492300\pi\)
\(98\) 0 0
\(99\) 3.21418 0.323037
\(100\) 0 0
\(101\) −15.3819 −1.53056 −0.765278 0.643699i \(-0.777399\pi\)
−0.765278 + 0.643699i \(0.777399\pi\)
\(102\) 0 0
\(103\) 8.09569 0.797692 0.398846 0.917018i \(-0.369411\pi\)
0.398846 + 0.917018i \(0.369411\pi\)
\(104\) 0 0
\(105\) 10.6088 1.03531
\(106\) 0 0
\(107\) −2.87538 −0.277974 −0.138987 0.990294i \(-0.544385\pi\)
−0.138987 + 0.990294i \(0.544385\pi\)
\(108\) 0 0
\(109\) 3.95551 0.378869 0.189435 0.981893i \(-0.439335\pi\)
0.189435 + 0.981893i \(0.439335\pi\)
\(110\) 0 0
\(111\) 3.60986 0.342633
\(112\) 0 0
\(113\) −12.7456 −1.19900 −0.599501 0.800374i \(-0.704634\pi\)
−0.599501 + 0.800374i \(0.704634\pi\)
\(114\) 0 0
\(115\) −2.59255 −0.241757
\(116\) 0 0
\(117\) −5.90839 −0.546231
\(118\) 0 0
\(119\) 28.9424 2.65314
\(120\) 0 0
\(121\) −0.669077 −0.0608252
\(122\) 0 0
\(123\) 8.59300 0.774805
\(124\) 0 0
\(125\) −10.7552 −0.961975
\(126\) 0 0
\(127\) 6.45367 0.572671 0.286335 0.958129i \(-0.407563\pi\)
0.286335 + 0.958129i \(0.407563\pi\)
\(128\) 0 0
\(129\) −8.44278 −0.743345
\(130\) 0 0
\(131\) 8.69274 0.759488 0.379744 0.925092i \(-0.376012\pi\)
0.379744 + 0.925092i \(0.376012\pi\)
\(132\) 0 0
\(133\) −32.4900 −2.81724
\(134\) 0 0
\(135\) 2.31305 0.199076
\(136\) 0 0
\(137\) 8.18280 0.699104 0.349552 0.936917i \(-0.386334\pi\)
0.349552 + 0.936917i \(0.386334\pi\)
\(138\) 0 0
\(139\) −8.00849 −0.679271 −0.339636 0.940557i \(-0.610304\pi\)
−0.339636 + 0.940557i \(0.610304\pi\)
\(140\) 0 0
\(141\) 6.42753 0.541295
\(142\) 0 0
\(143\) −18.9906 −1.58807
\(144\) 0 0
\(145\) −0.221302 −0.0183781
\(146\) 0 0
\(147\) 14.0358 1.15765
\(148\) 0 0
\(149\) −12.2148 −1.00067 −0.500336 0.865831i \(-0.666790\pi\)
−0.500336 + 0.865831i \(0.666790\pi\)
\(150\) 0 0
\(151\) 14.8534 1.20875 0.604377 0.796698i \(-0.293422\pi\)
0.604377 + 0.796698i \(0.293422\pi\)
\(152\) 0 0
\(153\) 6.31037 0.510163
\(154\) 0 0
\(155\) 11.1421 0.894958
\(156\) 0 0
\(157\) −14.3909 −1.14852 −0.574259 0.818674i \(-0.694710\pi\)
−0.574259 + 0.818674i \(0.694710\pi\)
\(158\) 0 0
\(159\) 2.56167 0.203154
\(160\) 0 0
\(161\) −5.14070 −0.405144
\(162\) 0 0
\(163\) 9.84431 0.771066 0.385533 0.922694i \(-0.374018\pi\)
0.385533 + 0.922694i \(0.374018\pi\)
\(164\) 0 0
\(165\) 7.43455 0.578779
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) 21.9091 1.68531
\(170\) 0 0
\(171\) −7.08386 −0.541716
\(172\) 0 0
\(173\) −21.4914 −1.63396 −0.816981 0.576665i \(-0.804354\pi\)
−0.816981 + 0.576665i \(0.804354\pi\)
\(174\) 0 0
\(175\) 1.60623 0.121420
\(176\) 0 0
\(177\) 6.13741 0.461316
\(178\) 0 0
\(179\) −12.7394 −0.952190 −0.476095 0.879394i \(-0.657948\pi\)
−0.476095 + 0.879394i \(0.657948\pi\)
\(180\) 0 0
\(181\) 16.1252 1.19858 0.599288 0.800534i \(-0.295451\pi\)
0.599288 + 0.800534i \(0.295451\pi\)
\(182\) 0 0
\(183\) −5.66615 −0.418854
\(184\) 0 0
\(185\) 8.34980 0.613890
\(186\) 0 0
\(187\) 20.2826 1.48321
\(188\) 0 0
\(189\) 4.58648 0.333617
\(190\) 0 0
\(191\) −3.06940 −0.222094 −0.111047 0.993815i \(-0.535420\pi\)
−0.111047 + 0.993815i \(0.535420\pi\)
\(192\) 0 0
\(193\) −20.3544 −1.46514 −0.732572 0.680689i \(-0.761680\pi\)
−0.732572 + 0.680689i \(0.761680\pi\)
\(194\) 0 0
\(195\) −13.6664 −0.978672
\(196\) 0 0
\(197\) −6.35545 −0.452807 −0.226404 0.974034i \(-0.572697\pi\)
−0.226404 + 0.974034i \(0.572697\pi\)
\(198\) 0 0
\(199\) −12.8698 −0.912315 −0.456158 0.889899i \(-0.650775\pi\)
−0.456158 + 0.889899i \(0.650775\pi\)
\(200\) 0 0
\(201\) −9.24652 −0.652200
\(202\) 0 0
\(203\) −0.438813 −0.0307986
\(204\) 0 0
\(205\) 19.8761 1.38820
\(206\) 0 0
\(207\) −1.12084 −0.0779035
\(208\) 0 0
\(209\) −22.7688 −1.57495
\(210\) 0 0
\(211\) 12.5752 0.865714 0.432857 0.901463i \(-0.357506\pi\)
0.432857 + 0.901463i \(0.357506\pi\)
\(212\) 0 0
\(213\) −7.95267 −0.544908
\(214\) 0 0
\(215\) −19.5286 −1.33184
\(216\) 0 0
\(217\) 22.0934 1.49980
\(218\) 0 0
\(219\) 14.9676 1.01141
\(220\) 0 0
\(221\) −37.2841 −2.50800
\(222\) 0 0
\(223\) −13.4007 −0.897375 −0.448688 0.893689i \(-0.648108\pi\)
−0.448688 + 0.893689i \(0.648108\pi\)
\(224\) 0 0
\(225\) 0.350210 0.0233473
\(226\) 0 0
\(227\) 24.2416 1.60897 0.804486 0.593972i \(-0.202441\pi\)
0.804486 + 0.593972i \(0.202441\pi\)
\(228\) 0 0
\(229\) 1.58387 0.104665 0.0523325 0.998630i \(-0.483334\pi\)
0.0523325 + 0.998630i \(0.483334\pi\)
\(230\) 0 0
\(231\) 14.7417 0.969936
\(232\) 0 0
\(233\) 18.0966 1.18554 0.592772 0.805370i \(-0.298033\pi\)
0.592772 + 0.805370i \(0.298033\pi\)
\(234\) 0 0
\(235\) 14.8672 0.969829
\(236\) 0 0
\(237\) 13.4092 0.871023
\(238\) 0 0
\(239\) 14.8153 0.958321 0.479161 0.877727i \(-0.340941\pi\)
0.479161 + 0.877727i \(0.340941\pi\)
\(240\) 0 0
\(241\) −28.7654 −1.85294 −0.926472 0.376363i \(-0.877175\pi\)
−0.926472 + 0.376363i \(0.877175\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) 32.4655 2.07415
\(246\) 0 0
\(247\) 41.8542 2.66312
\(248\) 0 0
\(249\) −3.20203 −0.202920
\(250\) 0 0
\(251\) 24.2143 1.52839 0.764196 0.644985i \(-0.223136\pi\)
0.764196 + 0.644985i \(0.223136\pi\)
\(252\) 0 0
\(253\) −3.60257 −0.226491
\(254\) 0 0
\(255\) 14.5962 0.914050
\(256\) 0 0
\(257\) −0.609749 −0.0380351 −0.0190175 0.999819i \(-0.506054\pi\)
−0.0190175 + 0.999819i \(0.506054\pi\)
\(258\) 0 0
\(259\) 16.5566 1.02878
\(260\) 0 0
\(261\) −0.0956753 −0.00592216
\(262\) 0 0
\(263\) −15.6789 −0.966801 −0.483401 0.875399i \(-0.660599\pi\)
−0.483401 + 0.875399i \(0.660599\pi\)
\(264\) 0 0
\(265\) 5.92528 0.363987
\(266\) 0 0
\(267\) −16.0148 −0.980087
\(268\) 0 0
\(269\) −21.4228 −1.30617 −0.653087 0.757283i \(-0.726526\pi\)
−0.653087 + 0.757283i \(0.726526\pi\)
\(270\) 0 0
\(271\) −12.2126 −0.741864 −0.370932 0.928660i \(-0.620962\pi\)
−0.370932 + 0.928660i \(0.620962\pi\)
\(272\) 0 0
\(273\) −27.0987 −1.64009
\(274\) 0 0
\(275\) 1.12564 0.0678784
\(276\) 0 0
\(277\) 14.4046 0.865489 0.432744 0.901517i \(-0.357545\pi\)
0.432744 + 0.901517i \(0.357545\pi\)
\(278\) 0 0
\(279\) 4.81707 0.288391
\(280\) 0 0
\(281\) 4.73061 0.282204 0.141102 0.989995i \(-0.454935\pi\)
0.141102 + 0.989995i \(0.454935\pi\)
\(282\) 0 0
\(283\) −18.9197 −1.12466 −0.562329 0.826914i \(-0.690094\pi\)
−0.562329 + 0.826914i \(0.690094\pi\)
\(284\) 0 0
\(285\) −16.3853 −0.970583
\(286\) 0 0
\(287\) 39.4116 2.32639
\(288\) 0 0
\(289\) 22.8207 1.34239
\(290\) 0 0
\(291\) 0.476438 0.0279293
\(292\) 0 0
\(293\) 4.27544 0.249774 0.124887 0.992171i \(-0.460143\pi\)
0.124887 + 0.992171i \(0.460143\pi\)
\(294\) 0 0
\(295\) 14.1961 0.826531
\(296\) 0 0
\(297\) 3.21418 0.186505
\(298\) 0 0
\(299\) 6.62234 0.382980
\(300\) 0 0
\(301\) −38.7226 −2.23193
\(302\) 0 0
\(303\) −15.3819 −0.883667
\(304\) 0 0
\(305\) −13.1061 −0.750453
\(306\) 0 0
\(307\) 20.2247 1.15429 0.577143 0.816643i \(-0.304167\pi\)
0.577143 + 0.816643i \(0.304167\pi\)
\(308\) 0 0
\(309\) 8.09569 0.460548
\(310\) 0 0
\(311\) −19.1435 −1.08553 −0.542763 0.839886i \(-0.682622\pi\)
−0.542763 + 0.839886i \(0.682622\pi\)
\(312\) 0 0
\(313\) −27.2504 −1.54028 −0.770141 0.637874i \(-0.779814\pi\)
−0.770141 + 0.637874i \(0.779814\pi\)
\(314\) 0 0
\(315\) 10.6088 0.597736
\(316\) 0 0
\(317\) 5.80299 0.325928 0.162964 0.986632i \(-0.447895\pi\)
0.162964 + 0.986632i \(0.447895\pi\)
\(318\) 0 0
\(319\) −0.307517 −0.0172177
\(320\) 0 0
\(321\) −2.87538 −0.160488
\(322\) 0 0
\(323\) −44.7017 −2.48727
\(324\) 0 0
\(325\) −2.06918 −0.114777
\(326\) 0 0
\(327\) 3.95551 0.218740
\(328\) 0 0
\(329\) 29.4797 1.62527
\(330\) 0 0
\(331\) −10.6624 −0.586056 −0.293028 0.956104i \(-0.594663\pi\)
−0.293028 + 0.956104i \(0.594663\pi\)
\(332\) 0 0
\(333\) 3.60986 0.197819
\(334\) 0 0
\(335\) −21.3877 −1.16853
\(336\) 0 0
\(337\) −23.0252 −1.25426 −0.627132 0.778913i \(-0.715771\pi\)
−0.627132 + 0.778913i \(0.715771\pi\)
\(338\) 0 0
\(339\) −12.7456 −0.692244
\(340\) 0 0
\(341\) 15.4829 0.838447
\(342\) 0 0
\(343\) 32.2695 1.74239
\(344\) 0 0
\(345\) −2.59255 −0.139578
\(346\) 0 0
\(347\) −10.3802 −0.557238 −0.278619 0.960402i \(-0.589877\pi\)
−0.278619 + 0.960402i \(0.589877\pi\)
\(348\) 0 0
\(349\) 31.7466 1.69935 0.849677 0.527303i \(-0.176797\pi\)
0.849677 + 0.527303i \(0.176797\pi\)
\(350\) 0 0
\(351\) −5.90839 −0.315367
\(352\) 0 0
\(353\) 29.5012 1.57019 0.785094 0.619376i \(-0.212615\pi\)
0.785094 + 0.619376i \(0.212615\pi\)
\(354\) 0 0
\(355\) −18.3949 −0.976302
\(356\) 0 0
\(357\) 28.9424 1.53179
\(358\) 0 0
\(359\) 36.5925 1.93128 0.965639 0.259888i \(-0.0836855\pi\)
0.965639 + 0.259888i \(0.0836855\pi\)
\(360\) 0 0
\(361\) 31.1810 1.64111
\(362\) 0 0
\(363\) −0.669077 −0.0351174
\(364\) 0 0
\(365\) 34.6208 1.81213
\(366\) 0 0
\(367\) 13.2131 0.689718 0.344859 0.938655i \(-0.387927\pi\)
0.344859 + 0.938655i \(0.387927\pi\)
\(368\) 0 0
\(369\) 8.59300 0.447334
\(370\) 0 0
\(371\) 11.7491 0.609980
\(372\) 0 0
\(373\) 10.4903 0.543169 0.271585 0.962415i \(-0.412452\pi\)
0.271585 + 0.962415i \(0.412452\pi\)
\(374\) 0 0
\(375\) −10.7552 −0.555396
\(376\) 0 0
\(377\) 0.565287 0.0291138
\(378\) 0 0
\(379\) 18.9819 0.975035 0.487517 0.873113i \(-0.337903\pi\)
0.487517 + 0.873113i \(0.337903\pi\)
\(380\) 0 0
\(381\) 6.45367 0.330632
\(382\) 0 0
\(383\) −7.61342 −0.389028 −0.194514 0.980900i \(-0.562313\pi\)
−0.194514 + 0.980900i \(0.562313\pi\)
\(384\) 0 0
\(385\) 34.0984 1.73782
\(386\) 0 0
\(387\) −8.44278 −0.429170
\(388\) 0 0
\(389\) 11.1854 0.567124 0.283562 0.958954i \(-0.408484\pi\)
0.283562 + 0.958954i \(0.408484\pi\)
\(390\) 0 0
\(391\) −7.07289 −0.357691
\(392\) 0 0
\(393\) 8.69274 0.438491
\(394\) 0 0
\(395\) 31.0162 1.56060
\(396\) 0 0
\(397\) 14.4789 0.726675 0.363338 0.931658i \(-0.381637\pi\)
0.363338 + 0.931658i \(0.381637\pi\)
\(398\) 0 0
\(399\) −32.4900 −1.62653
\(400\) 0 0
\(401\) −18.3950 −0.918602 −0.459301 0.888281i \(-0.651900\pi\)
−0.459301 + 0.888281i \(0.651900\pi\)
\(402\) 0 0
\(403\) −28.4611 −1.41775
\(404\) 0 0
\(405\) 2.31305 0.114936
\(406\) 0 0
\(407\) 11.6027 0.575126
\(408\) 0 0
\(409\) −31.8381 −1.57429 −0.787146 0.616767i \(-0.788442\pi\)
−0.787146 + 0.616767i \(0.788442\pi\)
\(410\) 0 0
\(411\) 8.18280 0.403628
\(412\) 0 0
\(413\) 28.1491 1.38513
\(414\) 0 0
\(415\) −7.40646 −0.363569
\(416\) 0 0
\(417\) −8.00849 −0.392177
\(418\) 0 0
\(419\) −35.5931 −1.73883 −0.869417 0.494078i \(-0.835506\pi\)
−0.869417 + 0.494078i \(0.835506\pi\)
\(420\) 0 0
\(421\) −27.2164 −1.32644 −0.663222 0.748423i \(-0.730812\pi\)
−0.663222 + 0.748423i \(0.730812\pi\)
\(422\) 0 0
\(423\) 6.42753 0.312517
\(424\) 0 0
\(425\) 2.20995 0.107198
\(426\) 0 0
\(427\) −25.9877 −1.25763
\(428\) 0 0
\(429\) −18.9906 −0.916875
\(430\) 0 0
\(431\) 11.7305 0.565036 0.282518 0.959262i \(-0.408830\pi\)
0.282518 + 0.959262i \(0.408830\pi\)
\(432\) 0 0
\(433\) −6.60527 −0.317429 −0.158715 0.987325i \(-0.550735\pi\)
−0.158715 + 0.987325i \(0.550735\pi\)
\(434\) 0 0
\(435\) −0.221302 −0.0106106
\(436\) 0 0
\(437\) 7.93985 0.379814
\(438\) 0 0
\(439\) −8.99747 −0.429426 −0.214713 0.976677i \(-0.568882\pi\)
−0.214713 + 0.976677i \(0.568882\pi\)
\(440\) 0 0
\(441\) 14.0358 0.668371
\(442\) 0 0
\(443\) −11.4240 −0.542771 −0.271385 0.962471i \(-0.587482\pi\)
−0.271385 + 0.962471i \(0.587482\pi\)
\(444\) 0 0
\(445\) −37.0430 −1.75600
\(446\) 0 0
\(447\) −12.2148 −0.577738
\(448\) 0 0
\(449\) −8.51165 −0.401690 −0.200845 0.979623i \(-0.564369\pi\)
−0.200845 + 0.979623i \(0.564369\pi\)
\(450\) 0 0
\(451\) 27.6194 1.30055
\(452\) 0 0
\(453\) 14.8534 0.697875
\(454\) 0 0
\(455\) −62.6807 −2.93852
\(456\) 0 0
\(457\) 8.37503 0.391767 0.195884 0.980627i \(-0.437243\pi\)
0.195884 + 0.980627i \(0.437243\pi\)
\(458\) 0 0
\(459\) 6.31037 0.294543
\(460\) 0 0
\(461\) −14.6981 −0.684557 −0.342279 0.939599i \(-0.611199\pi\)
−0.342279 + 0.939599i \(0.611199\pi\)
\(462\) 0 0
\(463\) −8.96089 −0.416448 −0.208224 0.978081i \(-0.566768\pi\)
−0.208224 + 0.978081i \(0.566768\pi\)
\(464\) 0 0
\(465\) 11.1421 0.516704
\(466\) 0 0
\(467\) 13.5404 0.626576 0.313288 0.949658i \(-0.398570\pi\)
0.313288 + 0.949658i \(0.398570\pi\)
\(468\) 0 0
\(469\) −42.4090 −1.95827
\(470\) 0 0
\(471\) −14.3909 −0.663097
\(472\) 0 0
\(473\) −27.1366 −1.24774
\(474\) 0 0
\(475\) −2.48084 −0.113829
\(476\) 0 0
\(477\) 2.56167 0.117291
\(478\) 0 0
\(479\) −8.28706 −0.378646 −0.189323 0.981915i \(-0.560629\pi\)
−0.189323 + 0.981915i \(0.560629\pi\)
\(480\) 0 0
\(481\) −21.3285 −0.972495
\(482\) 0 0
\(483\) −5.14070 −0.233910
\(484\) 0 0
\(485\) 1.10203 0.0500404
\(486\) 0 0
\(487\) −36.4042 −1.64963 −0.824815 0.565402i \(-0.808721\pi\)
−0.824815 + 0.565402i \(0.808721\pi\)
\(488\) 0 0
\(489\) 9.84431 0.445175
\(490\) 0 0
\(491\) 25.7273 1.16105 0.580527 0.814241i \(-0.302846\pi\)
0.580527 + 0.814241i \(0.302846\pi\)
\(492\) 0 0
\(493\) −0.603746 −0.0271914
\(494\) 0 0
\(495\) 7.43455 0.334158
\(496\) 0 0
\(497\) −36.4747 −1.63612
\(498\) 0 0
\(499\) −34.6775 −1.55238 −0.776190 0.630499i \(-0.782850\pi\)
−0.776190 + 0.630499i \(0.782850\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 0 0
\(503\) −12.6211 −0.562748 −0.281374 0.959598i \(-0.590790\pi\)
−0.281374 + 0.959598i \(0.590790\pi\)
\(504\) 0 0
\(505\) −35.5792 −1.58325
\(506\) 0 0
\(507\) 21.9091 0.973017
\(508\) 0 0
\(509\) 29.2360 1.29586 0.647931 0.761699i \(-0.275635\pi\)
0.647931 + 0.761699i \(0.275635\pi\)
\(510\) 0 0
\(511\) 68.6484 3.03683
\(512\) 0 0
\(513\) −7.08386 −0.312760
\(514\) 0 0
\(515\) 18.7258 0.825155
\(516\) 0 0
\(517\) 20.6592 0.908591
\(518\) 0 0
\(519\) −21.4914 −0.943368
\(520\) 0 0
\(521\) −29.0135 −1.27110 −0.635551 0.772059i \(-0.719227\pi\)
−0.635551 + 0.772059i \(0.719227\pi\)
\(522\) 0 0
\(523\) 13.5844 0.594003 0.297001 0.954877i \(-0.404013\pi\)
0.297001 + 0.954877i \(0.404013\pi\)
\(524\) 0 0
\(525\) 1.60623 0.0701016
\(526\) 0 0
\(527\) 30.3975 1.32414
\(528\) 0 0
\(529\) −21.7437 −0.945379
\(530\) 0 0
\(531\) 6.13741 0.266341
\(532\) 0 0
\(533\) −50.7708 −2.19913
\(534\) 0 0
\(535\) −6.65091 −0.287544
\(536\) 0 0
\(537\) −12.7394 −0.549747
\(538\) 0 0
\(539\) 45.1135 1.94318
\(540\) 0 0
\(541\) 29.2472 1.25743 0.628717 0.777634i \(-0.283581\pi\)
0.628717 + 0.777634i \(0.283581\pi\)
\(542\) 0 0
\(543\) 16.1252 0.691998
\(544\) 0 0
\(545\) 9.14930 0.391913
\(546\) 0 0
\(547\) −15.7016 −0.671353 −0.335676 0.941977i \(-0.608965\pi\)
−0.335676 + 0.941977i \(0.608965\pi\)
\(548\) 0 0
\(549\) −5.66615 −0.241825
\(550\) 0 0
\(551\) 0.677751 0.0288731
\(552\) 0 0
\(553\) 61.5011 2.61529
\(554\) 0 0
\(555\) 8.34980 0.354429
\(556\) 0 0
\(557\) −22.6588 −0.960083 −0.480041 0.877246i \(-0.659378\pi\)
−0.480041 + 0.877246i \(0.659378\pi\)
\(558\) 0 0
\(559\) 49.8832 2.10984
\(560\) 0 0
\(561\) 20.2826 0.856333
\(562\) 0 0
\(563\) −34.2384 −1.44298 −0.721488 0.692427i \(-0.756542\pi\)
−0.721488 + 0.692427i \(0.756542\pi\)
\(564\) 0 0
\(565\) −29.4812 −1.24028
\(566\) 0 0
\(567\) 4.58648 0.192614
\(568\) 0 0
\(569\) −35.2105 −1.47610 −0.738050 0.674746i \(-0.764253\pi\)
−0.738050 + 0.674746i \(0.764253\pi\)
\(570\) 0 0
\(571\) 38.6184 1.61613 0.808065 0.589093i \(-0.200515\pi\)
0.808065 + 0.589093i \(0.200515\pi\)
\(572\) 0 0
\(573\) −3.06940 −0.128226
\(574\) 0 0
\(575\) −0.392528 −0.0163696
\(576\) 0 0
\(577\) −42.9247 −1.78698 −0.893490 0.449084i \(-0.851750\pi\)
−0.893490 + 0.449084i \(0.851750\pi\)
\(578\) 0 0
\(579\) −20.3544 −0.845901
\(580\) 0 0
\(581\) −14.6860 −0.609280
\(582\) 0 0
\(583\) 8.23366 0.341003
\(584\) 0 0
\(585\) −13.6664 −0.565037
\(586\) 0 0
\(587\) 16.7904 0.693013 0.346507 0.938048i \(-0.387368\pi\)
0.346507 + 0.938048i \(0.387368\pi\)
\(588\) 0 0
\(589\) −34.1235 −1.40603
\(590\) 0 0
\(591\) −6.35545 −0.261428
\(592\) 0 0
\(593\) −1.96900 −0.0808573 −0.0404287 0.999182i \(-0.512872\pi\)
−0.0404287 + 0.999182i \(0.512872\pi\)
\(594\) 0 0
\(595\) 66.9452 2.74449
\(596\) 0 0
\(597\) −12.8698 −0.526725
\(598\) 0 0
\(599\) 1.97393 0.0806528 0.0403264 0.999187i \(-0.487160\pi\)
0.0403264 + 0.999187i \(0.487160\pi\)
\(600\) 0 0
\(601\) 21.9942 0.897160 0.448580 0.893743i \(-0.351930\pi\)
0.448580 + 0.893743i \(0.351930\pi\)
\(602\) 0 0
\(603\) −9.24652 −0.376548
\(604\) 0 0
\(605\) −1.54761 −0.0629193
\(606\) 0 0
\(607\) 13.8801 0.563378 0.281689 0.959506i \(-0.409105\pi\)
0.281689 + 0.959506i \(0.409105\pi\)
\(608\) 0 0
\(609\) −0.438813 −0.0177816
\(610\) 0 0
\(611\) −37.9763 −1.53636
\(612\) 0 0
\(613\) 35.7685 1.44468 0.722338 0.691540i \(-0.243067\pi\)
0.722338 + 0.691540i \(0.243067\pi\)
\(614\) 0 0
\(615\) 19.8761 0.801480
\(616\) 0 0
\(617\) −21.5812 −0.868825 −0.434413 0.900714i \(-0.643044\pi\)
−0.434413 + 0.900714i \(0.643044\pi\)
\(618\) 0 0
\(619\) 35.1766 1.41387 0.706933 0.707280i \(-0.250078\pi\)
0.706933 + 0.707280i \(0.250078\pi\)
\(620\) 0 0
\(621\) −1.12084 −0.0449776
\(622\) 0 0
\(623\) −73.4513 −2.94277
\(624\) 0 0
\(625\) −26.6284 −1.06514
\(626\) 0 0
\(627\) −22.7688 −0.909297
\(628\) 0 0
\(629\) 22.7796 0.908281
\(630\) 0 0
\(631\) 28.6537 1.14068 0.570342 0.821407i \(-0.306811\pi\)
0.570342 + 0.821407i \(0.306811\pi\)
\(632\) 0 0
\(633\) 12.5752 0.499820
\(634\) 0 0
\(635\) 14.9277 0.592387
\(636\) 0 0
\(637\) −82.9290 −3.28577
\(638\) 0 0
\(639\) −7.95267 −0.314603
\(640\) 0 0
\(641\) 6.25764 0.247162 0.123581 0.992334i \(-0.460562\pi\)
0.123581 + 0.992334i \(0.460562\pi\)
\(642\) 0 0
\(643\) −3.84712 −0.151716 −0.0758578 0.997119i \(-0.524170\pi\)
−0.0758578 + 0.997119i \(0.524170\pi\)
\(644\) 0 0
\(645\) −19.5286 −0.768937
\(646\) 0 0
\(647\) −24.4438 −0.960986 −0.480493 0.876998i \(-0.659542\pi\)
−0.480493 + 0.876998i \(0.659542\pi\)
\(648\) 0 0
\(649\) 19.7267 0.774341
\(650\) 0 0
\(651\) 22.0934 0.865909
\(652\) 0 0
\(653\) 47.9659 1.87705 0.938525 0.345212i \(-0.112193\pi\)
0.938525 + 0.345212i \(0.112193\pi\)
\(654\) 0 0
\(655\) 20.1068 0.785636
\(656\) 0 0
\(657\) 14.9676 0.583940
\(658\) 0 0
\(659\) 14.0165 0.546006 0.273003 0.962013i \(-0.411983\pi\)
0.273003 + 0.962013i \(0.411983\pi\)
\(660\) 0 0
\(661\) −16.7905 −0.653075 −0.326538 0.945184i \(-0.605882\pi\)
−0.326538 + 0.945184i \(0.605882\pi\)
\(662\) 0 0
\(663\) −37.2841 −1.44799
\(664\) 0 0
\(665\) −75.1510 −2.91423
\(666\) 0 0
\(667\) 0.107236 0.00415221
\(668\) 0 0
\(669\) −13.4007 −0.518100
\(670\) 0 0
\(671\) −18.2120 −0.703066
\(672\) 0 0
\(673\) −51.0281 −1.96699 −0.983494 0.180939i \(-0.942086\pi\)
−0.983494 + 0.180939i \(0.942086\pi\)
\(674\) 0 0
\(675\) 0.350210 0.0134796
\(676\) 0 0
\(677\) 24.3164 0.934556 0.467278 0.884111i \(-0.345235\pi\)
0.467278 + 0.884111i \(0.345235\pi\)
\(678\) 0 0
\(679\) 2.18517 0.0838592
\(680\) 0 0
\(681\) 24.2416 0.928940
\(682\) 0 0
\(683\) 4.89320 0.187233 0.0936165 0.995608i \(-0.470157\pi\)
0.0936165 + 0.995608i \(0.470157\pi\)
\(684\) 0 0
\(685\) 18.9272 0.723173
\(686\) 0 0
\(687\) 1.58387 0.0604284
\(688\) 0 0
\(689\) −15.1354 −0.576611
\(690\) 0 0
\(691\) 24.0140 0.913536 0.456768 0.889586i \(-0.349007\pi\)
0.456768 + 0.889586i \(0.349007\pi\)
\(692\) 0 0
\(693\) 14.7417 0.559993
\(694\) 0 0
\(695\) −18.5240 −0.702657
\(696\) 0 0
\(697\) 54.2250 2.05392
\(698\) 0 0
\(699\) 18.0966 0.684475
\(700\) 0 0
\(701\) 19.0044 0.717785 0.358893 0.933379i \(-0.383154\pi\)
0.358893 + 0.933379i \(0.383154\pi\)
\(702\) 0 0
\(703\) −25.5718 −0.964457
\(704\) 0 0
\(705\) 14.8672 0.559931
\(706\) 0 0
\(707\) −70.5488 −2.65326
\(708\) 0 0
\(709\) 33.6743 1.26467 0.632333 0.774697i \(-0.282098\pi\)
0.632333 + 0.774697i \(0.282098\pi\)
\(710\) 0 0
\(711\) 13.4092 0.502885
\(712\) 0 0
\(713\) −5.39915 −0.202200
\(714\) 0 0
\(715\) −43.9263 −1.64275
\(716\) 0 0
\(717\) 14.8153 0.553287
\(718\) 0 0
\(719\) 31.8777 1.18884 0.594419 0.804155i \(-0.297382\pi\)
0.594419 + 0.804155i \(0.297382\pi\)
\(720\) 0 0
\(721\) 37.1307 1.38282
\(722\) 0 0
\(723\) −28.7654 −1.06980
\(724\) 0 0
\(725\) −0.0335065 −0.00124440
\(726\) 0 0
\(727\) 14.5765 0.540614 0.270307 0.962774i \(-0.412875\pi\)
0.270307 + 0.962774i \(0.412875\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −53.2770 −1.97052
\(732\) 0 0
\(733\) 2.08605 0.0770501 0.0385251 0.999258i \(-0.487734\pi\)
0.0385251 + 0.999258i \(0.487734\pi\)
\(734\) 0 0
\(735\) 32.4655 1.19751
\(736\) 0 0
\(737\) −29.7200 −1.09475
\(738\) 0 0
\(739\) 17.9185 0.659142 0.329571 0.944131i \(-0.393096\pi\)
0.329571 + 0.944131i \(0.393096\pi\)
\(740\) 0 0
\(741\) 41.8542 1.53755
\(742\) 0 0
\(743\) 41.3924 1.51854 0.759270 0.650776i \(-0.225556\pi\)
0.759270 + 0.650776i \(0.225556\pi\)
\(744\) 0 0
\(745\) −28.2534 −1.03512
\(746\) 0 0
\(747\) −3.20203 −0.117156
\(748\) 0 0
\(749\) −13.1879 −0.481875
\(750\) 0 0
\(751\) 1.50906 0.0550663 0.0275332 0.999621i \(-0.491235\pi\)
0.0275332 + 0.999621i \(0.491235\pi\)
\(752\) 0 0
\(753\) 24.2143 0.882417
\(754\) 0 0
\(755\) 34.3567 1.25037
\(756\) 0 0
\(757\) −28.8730 −1.04941 −0.524704 0.851285i \(-0.675824\pi\)
−0.524704 + 0.851285i \(0.675824\pi\)
\(758\) 0 0
\(759\) −3.60257 −0.130765
\(760\) 0 0
\(761\) −15.2833 −0.554019 −0.277009 0.960867i \(-0.589343\pi\)
−0.277009 + 0.960867i \(0.589343\pi\)
\(762\) 0 0
\(763\) 18.1419 0.656780
\(764\) 0 0
\(765\) 14.5962 0.527727
\(766\) 0 0
\(767\) −36.2622 −1.30935
\(768\) 0 0
\(769\) −30.0530 −1.08374 −0.541869 0.840463i \(-0.682283\pi\)
−0.541869 + 0.840463i \(0.682283\pi\)
\(770\) 0 0
\(771\) −0.609749 −0.0219596
\(772\) 0 0
\(773\) −36.7691 −1.32249 −0.661247 0.750168i \(-0.729972\pi\)
−0.661247 + 0.750168i \(0.729972\pi\)
\(774\) 0 0
\(775\) 1.68699 0.0605983
\(776\) 0 0
\(777\) 16.5566 0.593964
\(778\) 0 0
\(779\) −60.8716 −2.18095
\(780\) 0 0
\(781\) −25.5613 −0.914654
\(782\) 0 0
\(783\) −0.0956753 −0.00341916
\(784\) 0 0
\(785\) −33.2869 −1.18806
\(786\) 0 0
\(787\) 5.24409 0.186932 0.0934658 0.995622i \(-0.470205\pi\)
0.0934658 + 0.995622i \(0.470205\pi\)
\(788\) 0 0
\(789\) −15.6789 −0.558183
\(790\) 0 0
\(791\) −58.4573 −2.07850
\(792\) 0 0
\(793\) 33.4778 1.18883
\(794\) 0 0
\(795\) 5.92528 0.210148
\(796\) 0 0
\(797\) −20.4374 −0.723928 −0.361964 0.932192i \(-0.617894\pi\)
−0.361964 + 0.932192i \(0.617894\pi\)
\(798\) 0 0
\(799\) 40.5600 1.43491
\(800\) 0 0
\(801\) −16.0148 −0.565853
\(802\) 0 0
\(803\) 48.1084 1.69771
\(804\) 0 0
\(805\) −11.8907 −0.419092
\(806\) 0 0
\(807\) −21.4228 −0.754120
\(808\) 0 0
\(809\) −39.2523 −1.38004 −0.690019 0.723791i \(-0.742398\pi\)
−0.690019 + 0.723791i \(0.742398\pi\)
\(810\) 0 0
\(811\) −3.47145 −0.121899 −0.0609495 0.998141i \(-0.519413\pi\)
−0.0609495 + 0.998141i \(0.519413\pi\)
\(812\) 0 0
\(813\) −12.2126 −0.428315
\(814\) 0 0
\(815\) 22.7704 0.797612
\(816\) 0 0
\(817\) 59.8074 2.09240
\(818\) 0 0
\(819\) −27.0987 −0.946906
\(820\) 0 0
\(821\) −41.2347 −1.43910 −0.719551 0.694440i \(-0.755652\pi\)
−0.719551 + 0.694440i \(0.755652\pi\)
\(822\) 0 0
\(823\) 27.6439 0.963607 0.481803 0.876279i \(-0.339982\pi\)
0.481803 + 0.876279i \(0.339982\pi\)
\(824\) 0 0
\(825\) 1.12564 0.0391896
\(826\) 0 0
\(827\) −46.1297 −1.60409 −0.802043 0.597266i \(-0.796254\pi\)
−0.802043 + 0.597266i \(0.796254\pi\)
\(828\) 0 0
\(829\) −45.2938 −1.57312 −0.786559 0.617515i \(-0.788139\pi\)
−0.786559 + 0.617515i \(0.788139\pi\)
\(830\) 0 0
\(831\) 14.4046 0.499690
\(832\) 0 0
\(833\) 88.5710 3.06880
\(834\) 0 0
\(835\) 2.31305 0.0800465
\(836\) 0 0
\(837\) 4.81707 0.166502
\(838\) 0 0
\(839\) 52.7011 1.81945 0.909723 0.415216i \(-0.136294\pi\)
0.909723 + 0.415216i \(0.136294\pi\)
\(840\) 0 0
\(841\) −28.9908 −0.999684
\(842\) 0 0
\(843\) 4.73061 0.162931
\(844\) 0 0
\(845\) 50.6769 1.74334
\(846\) 0 0
\(847\) −3.06871 −0.105442
\(848\) 0 0
\(849\) −18.9197 −0.649321
\(850\) 0 0
\(851\) −4.04607 −0.138697
\(852\) 0 0
\(853\) 34.3615 1.17651 0.588257 0.808674i \(-0.299814\pi\)
0.588257 + 0.808674i \(0.299814\pi\)
\(854\) 0 0
\(855\) −16.3853 −0.560367
\(856\) 0 0
\(857\) 9.28567 0.317192 0.158596 0.987344i \(-0.449303\pi\)
0.158596 + 0.987344i \(0.449303\pi\)
\(858\) 0 0
\(859\) 17.8965 0.610622 0.305311 0.952253i \(-0.401240\pi\)
0.305311 + 0.952253i \(0.401240\pi\)
\(860\) 0 0
\(861\) 39.4116 1.34314
\(862\) 0 0
\(863\) −29.3429 −0.998845 −0.499422 0.866359i \(-0.666454\pi\)
−0.499422 + 0.866359i \(0.666454\pi\)
\(864\) 0 0
\(865\) −49.7108 −1.69022
\(866\) 0 0
\(867\) 22.8207 0.775032
\(868\) 0 0
\(869\) 43.0996 1.46205
\(870\) 0 0
\(871\) 54.6321 1.85114
\(872\) 0 0
\(873\) 0.476438 0.0161250
\(874\) 0 0
\(875\) −49.3285 −1.66761
\(876\) 0 0
\(877\) −43.6823 −1.47505 −0.737523 0.675322i \(-0.764005\pi\)
−0.737523 + 0.675322i \(0.764005\pi\)
\(878\) 0 0
\(879\) 4.27544 0.144207
\(880\) 0 0
\(881\) −22.1789 −0.747227 −0.373614 0.927584i \(-0.621881\pi\)
−0.373614 + 0.927584i \(0.621881\pi\)
\(882\) 0 0
\(883\) 7.72940 0.260115 0.130057 0.991506i \(-0.458484\pi\)
0.130057 + 0.991506i \(0.458484\pi\)
\(884\) 0 0
\(885\) 14.1961 0.477198
\(886\) 0 0
\(887\) −24.0092 −0.806150 −0.403075 0.915167i \(-0.632059\pi\)
−0.403075 + 0.915167i \(0.632059\pi\)
\(888\) 0 0
\(889\) 29.5996 0.992740
\(890\) 0 0
\(891\) 3.21418 0.107679
\(892\) 0 0
\(893\) −45.5317 −1.52366
\(894\) 0 0
\(895\) −29.4670 −0.984972
\(896\) 0 0
\(897\) 6.62234 0.221114
\(898\) 0 0
\(899\) −0.460875 −0.0153710
\(900\) 0 0
\(901\) 16.1651 0.538537
\(902\) 0 0
\(903\) −38.7226 −1.28861
\(904\) 0 0
\(905\) 37.2984 1.23984
\(906\) 0 0
\(907\) 17.6999 0.587715 0.293857 0.955849i \(-0.405061\pi\)
0.293857 + 0.955849i \(0.405061\pi\)
\(908\) 0 0
\(909\) −15.3819 −0.510186
\(910\) 0 0
\(911\) −9.84469 −0.326169 −0.163085 0.986612i \(-0.552144\pi\)
−0.163085 + 0.986612i \(0.552144\pi\)
\(912\) 0 0
\(913\) −10.2919 −0.340612
\(914\) 0 0
\(915\) −13.1061 −0.433274
\(916\) 0 0
\(917\) 39.8691 1.31659
\(918\) 0 0
\(919\) −16.2682 −0.536638 −0.268319 0.963330i \(-0.586468\pi\)
−0.268319 + 0.963330i \(0.586468\pi\)
\(920\) 0 0
\(921\) 20.2247 0.666428
\(922\) 0 0
\(923\) 46.9875 1.54661
\(924\) 0 0
\(925\) 1.26421 0.0415670
\(926\) 0 0
\(927\) 8.09569 0.265897
\(928\) 0 0
\(929\) −1.38263 −0.0453625 −0.0226812 0.999743i \(-0.507220\pi\)
−0.0226812 + 0.999743i \(0.507220\pi\)
\(930\) 0 0
\(931\) −99.4276 −3.25861
\(932\) 0 0
\(933\) −19.1435 −0.626729
\(934\) 0 0
\(935\) 46.9148 1.53428
\(936\) 0 0
\(937\) 47.9877 1.56769 0.783845 0.620956i \(-0.213256\pi\)
0.783845 + 0.620956i \(0.213256\pi\)
\(938\) 0 0
\(939\) −27.2504 −0.889282
\(940\) 0 0
\(941\) 38.3869 1.25138 0.625688 0.780073i \(-0.284818\pi\)
0.625688 + 0.780073i \(0.284818\pi\)
\(942\) 0 0
\(943\) −9.63135 −0.313640
\(944\) 0 0
\(945\) 10.6088 0.345103
\(946\) 0 0
\(947\) −46.9162 −1.52457 −0.762285 0.647241i \(-0.775923\pi\)
−0.762285 + 0.647241i \(0.775923\pi\)
\(948\) 0 0
\(949\) −88.4342 −2.87070
\(950\) 0 0
\(951\) 5.80299 0.188175
\(952\) 0 0
\(953\) 21.6138 0.700139 0.350070 0.936724i \(-0.386158\pi\)
0.350070 + 0.936724i \(0.386158\pi\)
\(954\) 0 0
\(955\) −7.09968 −0.229740
\(956\) 0 0
\(957\) −0.307517 −0.00994062
\(958\) 0 0
\(959\) 37.5302 1.21191
\(960\) 0 0
\(961\) −7.79581 −0.251478
\(962\) 0 0
\(963\) −2.87538 −0.0926579
\(964\) 0 0
\(965\) −47.0809 −1.51559
\(966\) 0 0
\(967\) 38.9732 1.25330 0.626648 0.779303i \(-0.284427\pi\)
0.626648 + 0.779303i \(0.284427\pi\)
\(968\) 0 0
\(969\) −44.7017 −1.43603
\(970\) 0 0
\(971\) −31.0949 −0.997882 −0.498941 0.866636i \(-0.666278\pi\)
−0.498941 + 0.866636i \(0.666278\pi\)
\(972\) 0 0
\(973\) −36.7308 −1.17753
\(974\) 0 0
\(975\) −2.06918 −0.0662667
\(976\) 0 0
\(977\) −25.3796 −0.811966 −0.405983 0.913881i \(-0.633071\pi\)
−0.405983 + 0.913881i \(0.633071\pi\)
\(978\) 0 0
\(979\) −51.4742 −1.64512
\(980\) 0 0
\(981\) 3.95551 0.126290
\(982\) 0 0
\(983\) −9.01822 −0.287636 −0.143818 0.989604i \(-0.545938\pi\)
−0.143818 + 0.989604i \(0.545938\pi\)
\(984\) 0 0
\(985\) −14.7005 −0.468397
\(986\) 0 0
\(987\) 29.4797 0.938350
\(988\) 0 0
\(989\) 9.46297 0.300905
\(990\) 0 0
\(991\) −3.25211 −0.103307 −0.0516534 0.998665i \(-0.516449\pi\)
−0.0516534 + 0.998665i \(0.516449\pi\)
\(992\) 0 0
\(993\) −10.6624 −0.338360
\(994\) 0 0
\(995\) −29.7685 −0.943725
\(996\) 0 0
\(997\) 44.1469 1.39815 0.699073 0.715051i \(-0.253596\pi\)
0.699073 + 0.715051i \(0.253596\pi\)
\(998\) 0 0
\(999\) 3.60986 0.114211
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 \(a_p\))