Properties

Label 1296.3.q.o.1025.1
Level $1296$
Weight $3$
Character 1296.1025
Analytic conductor $35.313$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1296.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(35.3134422611\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 3^{8} \)
Twist minimal: no (minimal twist has level 162)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1025.1
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1296.1025
Dual form 1296.3.q.o.593.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.01910 - 2.89778i) q^{5} +(-4.19615 - 7.26795i) q^{7} +O(q^{10})\) \(q+(-5.01910 - 2.89778i) q^{5} +(-4.19615 - 7.26795i) q^{7} +(-12.7279 + 7.34847i) q^{11} +(10.5981 - 18.3564i) q^{13} +7.76457i q^{17} -24.3923 q^{19} +(-12.7279 - 7.34847i) q^{23} +(4.29423 + 7.43782i) q^{25} +(30.7387 - 17.7470i) q^{29} +(4.00000 - 6.92820i) q^{31} +48.6381i q^{35} -60.5692 q^{37} +(29.1301 + 16.8183i) q^{41} +(4.58846 + 7.94744i) q^{43} +(14.6969 - 8.48528i) q^{47} +(-10.7154 + 18.5596i) q^{49} +25.7605i q^{53} +85.1769 q^{55} +(53.4083 + 30.8353i) q^{59} +(6.50000 + 11.2583i) q^{61} +(-106.386 + 61.4217i) q^{65} +(10.5885 - 18.3397i) q^{67} +101.214i q^{71} +40.4115 q^{73} +(106.817 + 61.6706i) q^{77} +(49.3731 + 85.5167i) q^{79} +(-89.6231 + 51.7439i) q^{83} +(22.5000 - 38.9711i) q^{85} +134.130i q^{89} -177.885 q^{91} +(122.427 + 70.6835i) q^{95} +(37.5692 + 65.0718i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{7} + 64 q^{13} - 112 q^{19} - 28 q^{25} + 32 q^{31} - 152 q^{37} - 88 q^{43} - 252 q^{49} + 432 q^{55} + 52 q^{61} - 40 q^{67} + 448 q^{73} + 104 q^{79} + 180 q^{85} - 176 q^{91} - 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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 0
\(4\) 0 0
\(5\) −5.01910 2.89778i −1.00382 0.579555i −0.0944434 0.995530i \(-0.530107\pi\)
−0.909376 + 0.415975i \(0.863440\pi\)
\(6\) 0 0
\(7\) −4.19615 7.26795i −0.599450 1.03828i −0.992902 0.118933i \(-0.962053\pi\)
0.393452 0.919345i \(-0.371281\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −12.7279 + 7.34847i −1.15708 + 0.668043i −0.950603 0.310408i \(-0.899534\pi\)
−0.206480 + 0.978451i \(0.566201\pi\)
\(12\) 0 0
\(13\) 10.5981 18.3564i 0.815237 1.41203i −0.0939212 0.995580i \(-0.529940\pi\)
0.909158 0.416452i \(-0.136726\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.76457i 0.456739i 0.973574 + 0.228370i \(0.0733395\pi\)
−0.973574 + 0.228370i \(0.926660\pi\)
\(18\) 0 0
\(19\) −24.3923 −1.28381 −0.641903 0.766786i \(-0.721855\pi\)
−0.641903 + 0.766786i \(0.721855\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −12.7279 7.34847i −0.553388 0.319499i 0.197099 0.980384i \(-0.436848\pi\)
−0.750487 + 0.660885i \(0.770181\pi\)
\(24\) 0 0
\(25\) 4.29423 + 7.43782i 0.171769 + 0.297513i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 30.7387 17.7470i 1.05996 0.611966i 0.134536 0.990909i \(-0.457046\pi\)
0.925420 + 0.378942i \(0.123712\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.129032 0.223490i −0.794270 0.607565i \(-0.792146\pi\)
0.923302 + 0.384075i \(0.125480\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 48.6381i 1.38966i
\(36\) 0 0
\(37\) −60.5692 −1.63701 −0.818503 0.574502i \(-0.805196\pi\)
−0.818503 + 0.574502i \(0.805196\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 29.1301 + 16.8183i 0.710490 + 0.410201i 0.811242 0.584710i \(-0.198792\pi\)
−0.100753 + 0.994912i \(0.532125\pi\)
\(42\) 0 0
\(43\) 4.58846 + 7.94744i 0.106708 + 0.184824i 0.914435 0.404733i \(-0.132636\pi\)
−0.807727 + 0.589557i \(0.799302\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 14.6969 8.48528i 0.312701 0.180538i −0.335434 0.942064i \(-0.608883\pi\)
0.648134 + 0.761526i \(0.275549\pi\)
\(48\) 0 0
\(49\) −10.7154 + 18.5596i −0.218681 + 0.378767i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 25.7605i 0.486046i 0.970020 + 0.243023i \(0.0781391\pi\)
−0.970020 + 0.243023i \(0.921861\pi\)
\(54\) 0 0
\(55\) 85.1769 1.54867
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 53.4083 + 30.8353i 0.905225 + 0.522632i 0.878892 0.477021i \(-0.158283\pi\)
0.0263336 + 0.999653i \(0.491617\pi\)
\(60\) 0 0
\(61\) 6.50000 + 11.2583i 0.106557 + 0.184563i 0.914373 0.404872i \(-0.132684\pi\)
−0.807816 + 0.589435i \(0.799351\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −106.386 + 61.4217i −1.63670 + 0.944950i
\(66\) 0 0
\(67\) 10.5885 18.3397i 0.158037 0.273728i −0.776124 0.630580i \(-0.782817\pi\)
0.934161 + 0.356853i \(0.116150\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 101.214i 1.42555i 0.701392 + 0.712776i \(0.252562\pi\)
−0.701392 + 0.712776i \(0.747438\pi\)
\(72\) 0 0
\(73\) 40.4115 0.553583 0.276791 0.960930i \(-0.410729\pi\)
0.276791 + 0.960930i \(0.410729\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 106.817 + 61.6706i 1.38723 + 0.800917i
\(78\) 0 0
\(79\) 49.3731 + 85.5167i 0.624976 + 1.08249i 0.988546 + 0.150923i \(0.0482244\pi\)
−0.363570 + 0.931567i \(0.618442\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −89.6231 + 51.7439i −1.07980 + 0.623420i −0.930841 0.365424i \(-0.880924\pi\)
−0.148954 + 0.988844i \(0.547591\pi\)
\(84\) 0 0
\(85\) 22.5000 38.9711i 0.264706 0.458484i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 134.130i 1.50708i 0.657403 + 0.753539i \(0.271655\pi\)
−0.657403 + 0.753539i \(0.728345\pi\)
\(90\) 0 0
\(91\) −177.885 −1.95478
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 122.427 + 70.6835i 1.28871 + 0.744037i
\(96\) 0 0
\(97\) 37.5692 + 65.0718i 0.387312 + 0.670843i 0.992087 0.125553i \(-0.0400705\pi\)
−0.604775 + 0.796396i \(0.706737\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −25.1920 + 14.5446i −0.249426 + 0.144006i −0.619501 0.784995i \(-0.712665\pi\)
0.370075 + 0.929002i \(0.379332\pi\)
\(102\) 0 0
\(103\) 48.3538 83.7513i 0.469455 0.813119i −0.529936 0.848038i \(-0.677784\pi\)
0.999390 + 0.0349186i \(0.0111172\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 177.582i 1.65964i −0.558030 0.829821i \(-0.688442\pi\)
0.558030 0.829821i \(-0.311558\pi\)
\(108\) 0 0
\(109\) 61.9423 0.568278 0.284139 0.958783i \(-0.408292\pi\)
0.284139 + 0.958783i \(0.408292\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −95.0991 54.9055i −0.841585 0.485889i 0.0162179 0.999868i \(-0.494837\pi\)
−0.857803 + 0.513979i \(0.828171\pi\)
\(114\) 0 0
\(115\) 42.5885 + 73.7654i 0.370334 + 0.641438i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 56.4325 32.5813i 0.474223 0.273793i
\(120\) 0 0
\(121\) 47.5000 82.2724i 0.392562 0.679937i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 95.1140i 0.760912i
\(126\) 0 0
\(127\) −141.177 −1.11163 −0.555815 0.831306i \(-0.687594\pi\)
−0.555815 + 0.831306i \(0.687594\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −46.0598 26.5927i −0.351602 0.202997i 0.313789 0.949493i \(-0.398402\pi\)
−0.665391 + 0.746495i \(0.731735\pi\)
\(132\) 0 0
\(133\) 102.354 + 177.282i 0.769578 + 1.33295i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.41555 0.817267i 0.0103325 0.00596545i −0.494825 0.868993i \(-0.664768\pi\)
0.505157 + 0.863027i \(0.331434\pi\)
\(138\) 0 0
\(139\) −9.60770 + 16.6410i −0.0691201 + 0.119720i −0.898514 0.438944i \(-0.855353\pi\)
0.829394 + 0.558664i \(0.188686\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 311.519i 2.17845i
\(144\) 0 0
\(145\) −205.708 −1.41867
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −81.6504 47.1409i −0.547989 0.316382i 0.200321 0.979730i \(-0.435801\pi\)
−0.748311 + 0.663348i \(0.769135\pi\)
\(150\) 0 0
\(151\) 16.0000 + 27.7128i 0.105960 + 0.183529i 0.914130 0.405421i \(-0.132875\pi\)
−0.808170 + 0.588949i \(0.799542\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −40.1528 + 23.1822i −0.259050 + 0.149563i
\(156\) 0 0
\(157\) −0.146171 + 0.253175i −0.000931025 + 0.00161258i −0.866491 0.499193i \(-0.833630\pi\)
0.865560 + 0.500806i \(0.166963\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 123.341i 0.766094i
\(162\) 0 0
\(163\) −28.7846 −0.176593 −0.0882963 0.996094i \(-0.528142\pi\)
−0.0882963 + 0.996094i \(0.528142\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 48.5564 + 28.0341i 0.290757 + 0.167869i 0.638283 0.769802i \(-0.279645\pi\)
−0.347526 + 0.937670i \(0.612978\pi\)
\(168\) 0 0
\(169\) −140.138 242.727i −0.829222 1.43625i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −191.350 + 110.476i −1.10607 + 0.638589i −0.937808 0.347154i \(-0.887148\pi\)
−0.168260 + 0.985743i \(0.553815\pi\)
\(174\) 0 0
\(175\) 36.0385 62.4205i 0.205934 0.356688i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 248.347i 1.38741i 0.720258 + 0.693706i \(0.244023\pi\)
−0.720258 + 0.693706i \(0.755977\pi\)
\(180\) 0 0
\(181\) −158.277 −0.874458 −0.437229 0.899350i \(-0.644040\pi\)
−0.437229 + 0.899350i \(0.644040\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 304.003 + 175.516i 1.64326 + 0.948736i
\(186\) 0 0
\(187\) −57.0577 98.8269i −0.305121 0.528486i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −29.9215 + 17.2752i −0.156657 + 0.0904459i −0.576279 0.817253i \(-0.695496\pi\)
0.419622 + 0.907699i \(0.362163\pi\)
\(192\) 0 0
\(193\) 27.5000 47.6314i 0.142487 0.246795i −0.785946 0.618296i \(-0.787823\pi\)
0.928433 + 0.371501i \(0.121157\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 35.7170i 0.181305i 0.995883 + 0.0906524i \(0.0288952\pi\)
−0.995883 + 0.0906524i \(0.971105\pi\)
\(198\) 0 0
\(199\) 375.138 1.88512 0.942559 0.334040i \(-0.108412\pi\)
0.942559 + 0.334040i \(0.108412\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −257.969 148.938i −1.27078 0.733687i
\(204\) 0 0
\(205\) −97.4711 168.825i −0.475469 0.823536i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 310.463 179.246i 1.48547 0.857637i
\(210\) 0 0
\(211\) 153.727 266.263i 0.728563 1.26191i −0.228927 0.973444i \(-0.573522\pi\)
0.957490 0.288465i \(-0.0931450\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 53.1853i 0.247374i
\(216\) 0 0
\(217\) −67.1384 −0.309394
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 142.530 + 82.2895i 0.644930 + 0.372351i
\(222\) 0 0
\(223\) −169.296 293.229i −0.759175 1.31493i −0.943272 0.332022i \(-0.892269\pi\)
0.184096 0.982908i \(-0.441064\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −107.344 + 61.9752i −0.472882 + 0.273019i −0.717445 0.696615i \(-0.754689\pi\)
0.244563 + 0.969633i \(0.421355\pi\)
\(228\) 0 0
\(229\) −37.0289 + 64.1359i −0.161698 + 0.280069i −0.935478 0.353386i \(-0.885030\pi\)
0.773780 + 0.633455i \(0.218364\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 273.223i 1.17263i −0.810082 0.586316i \(-0.800578\pi\)
0.810082 0.586316i \(-0.199422\pi\)
\(234\) 0 0
\(235\) −98.3538 −0.418527
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 392.210 + 226.443i 1.64105 + 0.947459i 0.980462 + 0.196708i \(0.0630252\pi\)
0.660585 + 0.750751i \(0.270308\pi\)
\(240\) 0 0
\(241\) 191.344 + 331.418i 0.793959 + 1.37518i 0.923498 + 0.383604i \(0.125317\pi\)
−0.129538 + 0.991574i \(0.541350\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 107.563 62.1016i 0.439033 0.253476i
\(246\) 0 0
\(247\) −258.512 + 447.755i −1.04661 + 1.81277i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 73.9307i 0.294544i −0.989096 0.147272i \(-0.952951\pi\)
0.989096 0.147272i \(-0.0470493\pi\)
\(252\) 0 0
\(253\) 216.000 0.853755
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −138.398 79.9044i −0.538515 0.310912i 0.205962 0.978560i \(-0.433968\pi\)
−0.744477 + 0.667648i \(0.767301\pi\)
\(258\) 0 0
\(259\) 254.158 + 440.214i 0.981304 + 1.69967i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 224.392 129.553i 0.853202 0.492596i −0.00852798 0.999964i \(-0.502715\pi\)
0.861730 + 0.507367i \(0.169381\pi\)
\(264\) 0 0
\(265\) 74.6481 129.294i 0.281691 0.487903i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 24.8168i 0.0922556i −0.998936 0.0461278i \(-0.985312\pi\)
0.998936 0.0461278i \(-0.0146881\pi\)
\(270\) 0 0
\(271\) −98.1154 −0.362050 −0.181025 0.983479i \(-0.557941\pi\)
−0.181025 + 0.983479i \(0.557941\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −109.313 63.1120i −0.397503 0.229498i
\(276\) 0 0
\(277\) 0.707658 + 1.22570i 0.00255472 + 0.00442491i 0.867300 0.497786i \(-0.165853\pi\)
−0.864745 + 0.502211i \(0.832520\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 87.2230 50.3582i 0.310402 0.179211i −0.336704 0.941610i \(-0.609312\pi\)
0.647106 + 0.762400i \(0.275979\pi\)
\(282\) 0 0
\(283\) −23.6462 + 40.9564i −0.0835554 + 0.144722i −0.904775 0.425890i \(-0.859961\pi\)
0.821219 + 0.570613i \(0.193294\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 282.288i 0.983582i
\(288\) 0 0
\(289\) 228.711 0.791389
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −288.920 166.808i −0.986074 0.569310i −0.0819755 0.996634i \(-0.526123\pi\)
−0.904098 + 0.427324i \(0.859456\pi\)
\(294\) 0 0
\(295\) −178.708 309.531i −0.605789 1.04926i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −269.783 + 155.759i −0.902284 + 0.520934i
\(300\) 0 0
\(301\) 38.5077 66.6973i 0.127933 0.221586i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 75.3422i 0.247024i
\(306\) 0 0
\(307\) −10.3538 −0.0337258 −0.0168629 0.999858i \(-0.505368\pi\)
−0.0168629 + 0.999858i \(0.505368\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 8.26229 + 4.77024i 0.0265669 + 0.0153384i 0.513225 0.858254i \(-0.328451\pi\)
−0.486658 + 0.873593i \(0.661784\pi\)
\(312\) 0 0
\(313\) 239.638 + 415.066i 0.765618 + 1.32609i 0.939919 + 0.341397i \(0.110900\pi\)
−0.174301 + 0.984692i \(0.555767\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −155.592 + 89.8311i −0.490827 + 0.283379i −0.724917 0.688836i \(-0.758122\pi\)
0.234091 + 0.972215i \(0.424789\pi\)
\(318\) 0 0
\(319\) −260.827 + 451.765i −0.817639 + 1.41619i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 189.396i 0.586365i
\(324\) 0 0
\(325\) 182.042 0.560130
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −123.341 71.2111i −0.374897 0.216447i
\(330\) 0 0
\(331\) 147.727 + 255.870i 0.446305 + 0.773023i 0.998142 0.0609292i \(-0.0194064\pi\)
−0.551837 + 0.833952i \(0.686073\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −106.289 + 61.3660i −0.317281 + 0.183182i
\(336\) 0 0
\(337\) −244.631 + 423.713i −0.725907 + 1.25731i 0.232692 + 0.972550i \(0.425246\pi\)
−0.958600 + 0.284758i \(0.908087\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 117.576i 0.344796i
\(342\) 0 0
\(343\) −231.369 −0.674546
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −577.363 333.341i −1.66387 0.960637i −0.970840 0.239730i \(-0.922941\pi\)
−0.693032 0.720907i \(-0.743726\pi\)
\(348\) 0 0
\(349\) −255.985 443.378i −0.733480 1.27042i −0.955387 0.295357i \(-0.904561\pi\)
0.221907 0.975068i \(-0.428772\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −508.081 + 293.340i −1.43932 + 0.830993i −0.997802 0.0662588i \(-0.978894\pi\)
−0.441519 + 0.897252i \(0.645560\pi\)
\(354\) 0 0
\(355\) 293.296 508.004i 0.826186 1.43100i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 534.573i 1.48906i −0.667589 0.744530i \(-0.732674\pi\)
0.667589 0.744530i \(-0.267326\pi\)
\(360\) 0 0
\(361\) 233.985 0.648157
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −202.829 117.104i −0.555697 0.320832i
\(366\) 0 0
\(367\) 7.64617 + 13.2436i 0.0208343 + 0.0360860i 0.876255 0.481848i \(-0.160034\pi\)
−0.855420 + 0.517934i \(0.826701\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 187.226 108.095i 0.504651 0.291361i
\(372\) 0 0
\(373\) −326.492 + 565.501i −0.875314 + 1.51609i −0.0188869 + 0.999822i \(0.506012\pi\)
−0.856427 + 0.516267i \(0.827321\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 752.337i 1.99559i
\(378\) 0 0
\(379\) 655.215 1.72880 0.864400 0.502804i \(-0.167698\pi\)
0.864400 + 0.502804i \(0.167698\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 259.410 + 149.771i 0.677311 + 0.391046i 0.798841 0.601542i \(-0.205447\pi\)
−0.121530 + 0.992588i \(0.538780\pi\)
\(384\) 0 0
\(385\) −357.415 619.061i −0.928351 1.60795i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 402.319 232.279i 1.03424 0.597119i 0.116043 0.993244i \(-0.462979\pi\)
0.918196 + 0.396126i \(0.129646\pi\)
\(390\) 0 0
\(391\) 57.0577 98.8269i 0.145928 0.252754i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 572.289i 1.44883i
\(396\) 0 0
\(397\) −185.708 −0.467777 −0.233889 0.972263i \(-0.575145\pi\)
−0.233889 + 0.972263i \(0.575145\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −54.4376 31.4296i −0.135755 0.0783780i 0.430585 0.902550i \(-0.358307\pi\)
−0.566339 + 0.824172i \(0.691641\pi\)
\(402\) 0 0
\(403\) −84.7846 146.851i −0.210384 0.364395i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 770.920 445.091i 1.89415 1.09359i
\(408\) 0 0
\(409\) 163.640 283.433i 0.400099 0.692991i −0.593639 0.804732i \(-0.702309\pi\)
0.993737 + 0.111741i \(0.0356425\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 517.558i 1.25317i
\(414\) 0 0
\(415\) 599.769 1.44523
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −562.808 324.937i −1.34322 0.775507i −0.355939 0.934509i \(-0.615839\pi\)
−0.987278 + 0.159003i \(0.949172\pi\)
\(420\) 0 0
\(421\) −1.65956 2.87445i −0.00394196 0.00682767i 0.864048 0.503410i \(-0.167921\pi\)
−0.867990 + 0.496582i \(0.834588\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −57.7515 + 33.3428i −0.135886 + 0.0784538i
\(426\) 0 0
\(427\) 54.5500 94.4833i 0.127752 0.221272i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 803.502i 1.86427i 0.362107 + 0.932136i \(0.382057\pi\)
−0.362107 + 0.932136i \(0.617943\pi\)
\(432\) 0 0
\(433\) −93.1230 −0.215065 −0.107532 0.994202i \(-0.534295\pi\)
−0.107532 + 0.994202i \(0.534295\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 310.463 + 179.246i 0.710442 + 0.410174i
\(438\) 0 0
\(439\) −236.000 408.764i −0.537585 0.931125i −0.999033 0.0439580i \(-0.986003\pi\)
0.461448 0.887167i \(-0.347330\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 493.365 284.844i 1.11369 0.642989i 0.173908 0.984762i \(-0.444361\pi\)
0.939783 + 0.341773i \(0.111027\pi\)
\(444\) 0 0
\(445\) 388.679 673.211i 0.873436 1.51283i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 559.115i 1.24524i 0.782523 + 0.622622i \(0.213933\pi\)
−0.782523 + 0.622622i \(0.786067\pi\)
\(450\) 0 0
\(451\) −494.354 −1.09613
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 892.820 + 515.470i 1.96224 + 1.13290i
\(456\) 0 0
\(457\) −302.148 523.336i −0.661155 1.14515i −0.980312 0.197453i \(-0.936733\pi\)
0.319157 0.947702i \(-0.396600\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.44669 2.56730i 0.00964575 0.00556897i −0.495169 0.868796i \(-0.664894\pi\)
0.504815 + 0.863227i \(0.331561\pi\)
\(462\) 0 0
\(463\) −80.7461 + 139.856i −0.174398 + 0.302066i −0.939953 0.341305i \(-0.889131\pi\)
0.765555 + 0.643370i \(0.222464\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 503.025i 1.07714i −0.842581 0.538570i \(-0.818965\pi\)
0.842581 0.538570i \(-0.181035\pi\)
\(468\) 0 0
\(469\) −177.723 −0.378941
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −116.803 67.4363i −0.246941 0.142571i
\(474\) 0 0
\(475\) −104.746 181.426i −0.220518 0.381949i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 185.153 106.898i 0.386541 0.223170i −0.294119 0.955769i \(-0.595026\pi\)
0.680660 + 0.732599i \(0.261693\pi\)
\(480\) 0 0
\(481\) −641.917 + 1111.83i −1.33455 + 2.31150i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 435.469i 0.897874i
\(486\) 0 0
\(487\) −8.63071 −0.0177222 −0.00886110 0.999961i \(-0.502821\pi\)
−0.00886110 + 0.999961i \(0.502821\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −798.873 461.229i −1.62703 0.939367i −0.984972 0.172713i \(-0.944747\pi\)
−0.642060 0.766654i \(-0.721920\pi\)
\(492\) 0 0
\(493\) 137.798 + 238.673i 0.279509 + 0.484124i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 735.619 424.710i 1.48012 0.854547i
\(498\) 0 0
\(499\) −217.296 + 376.368i −0.435463 + 0.754244i −0.997333 0.0729811i \(-0.976749\pi\)
0.561870 + 0.827225i \(0.310082\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 144.087i 0.286454i 0.989690 + 0.143227i \(0.0457480\pi\)
−0.989690 + 0.143227i \(0.954252\pi\)
\(504\) 0 0
\(505\) 168.588 0.333839
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −603.856 348.636i −1.18636 0.684943i −0.228880 0.973455i \(-0.573506\pi\)
−0.957477 + 0.288511i \(0.906840\pi\)
\(510\) 0 0
\(511\) −169.573 293.709i −0.331845 0.574773i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −485.385 + 280.237i −0.942496 + 0.544150i
\(516\) 0 0
\(517\) −124.708 + 216.000i −0.241214 + 0.417795i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 426.962i 0.819504i 0.912197 + 0.409752i \(0.134385\pi\)
−0.912197 + 0.409752i \(0.865615\pi\)
\(522\) 0 0
\(523\) −179.762 −0.343712 −0.171856 0.985122i \(-0.554976\pi\)
−0.171856 + 0.985122i \(0.554976\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 53.7945 + 31.0583i 0.102077 + 0.0589341i
\(528\) 0 0
\(529\) −156.500 271.066i −0.295841 0.512412i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 617.446 356.482i 1.15843 0.668822i
\(534\) 0 0
\(535\) −514.592 + 891.300i −0.961855 + 1.66598i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 314.967i 0.584354i
\(540\) 0 0
\(541\) 708.734 1.31005 0.655023 0.755609i \(-0.272659\pi\)
0.655023 + 0.755609i \(0.272659\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −310.894 179.495i −0.570448 0.329349i
\(546\) 0 0
\(547\) −98.1154 169.941i −0.179370 0.310678i 0.762295 0.647230i \(-0.224073\pi\)
−0.941665 + 0.336552i \(0.890739\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −749.789 + 432.891i −1.36078 + 0.785646i
\(552\) 0 0
\(553\) 414.354 717.682i 0.749284 1.29780i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 353.610i 0.634848i −0.948284 0.317424i \(-0.897182\pi\)
0.948284 0.317424i \(-0.102818\pi\)
\(558\) 0 0
\(559\) 194.515 0.347970
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −323.050 186.513i −0.573801 0.331284i 0.184865 0.982764i \(-0.440815\pi\)
−0.758666 + 0.651480i \(0.774149\pi\)
\(564\) 0 0
\(565\) 318.208 + 551.152i 0.563199 + 0.975490i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −52.0634 + 30.0588i −0.0914999 + 0.0528275i −0.545052 0.838402i \(-0.683490\pi\)
0.453552 + 0.891230i \(0.350157\pi\)
\(570\) 0 0
\(571\) 43.1000 74.6513i 0.0754815 0.130738i −0.825814 0.563943i \(-0.809284\pi\)
0.901296 + 0.433205i \(0.142617\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 126.224i 0.219520i
\(576\) 0 0
\(577\) 709.123 1.22898 0.614491 0.788924i \(-0.289361\pi\)
0.614491 + 0.788924i \(0.289361\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 752.144 + 434.251i 1.29457 + 0.747419i
\(582\) 0 0
\(583\) −189.300 327.877i −0.324700 0.562396i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −833.363 + 481.143i −1.41970 + 0.819664i −0.996272 0.0862666i \(-0.972506\pi\)
−0.423427 + 0.905930i \(0.639173\pi\)
\(588\) 0 0
\(589\) −97.5692 + 168.995i −0.165652 + 0.286918i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 104.350i 0.175969i 0.996122 + 0.0879847i \(0.0280427\pi\)
−0.996122 + 0.0879847i \(0.971957\pi\)
\(594\) 0 0
\(595\) −377.654 −0.634712
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −247.738 143.031i −0.413585 0.238784i 0.278744 0.960366i \(-0.410082\pi\)
−0.692329 + 0.721582i \(0.743415\pi\)
\(600\) 0 0
\(601\) 140.208 + 242.847i 0.233291 + 0.404071i 0.958775 0.284168i \(-0.0917173\pi\)
−0.725484 + 0.688239i \(0.758384\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −476.814 + 275.289i −0.788123 + 0.455023i
\(606\) 0 0
\(607\) 368.865 638.894i 0.607686 1.05254i −0.383935 0.923360i \(-0.625431\pi\)
0.991621 0.129183i \(-0.0412354\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 359.711i 0.588724i
\(612\) 0 0
\(613\) −679.415 −1.10834 −0.554172 0.832402i \(-0.686965\pi\)
−0.554172 + 0.832402i \(0.686965\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −409.326 236.325i −0.663414 0.383022i 0.130163 0.991493i \(-0.458450\pi\)
−0.793576 + 0.608471i \(0.791783\pi\)
\(618\) 0 0
\(619\) 443.177 + 767.605i 0.715956 + 1.24007i 0.962590 + 0.270964i \(0.0873423\pi\)
−0.246633 + 0.969109i \(0.579324\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 974.850 562.830i 1.56477 0.903419i
\(624\) 0 0
\(625\) 382.975 663.332i 0.612760 1.06133i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 470.294i 0.747685i
\(630\) 0 0
\(631\) 729.108 1.15548 0.577740 0.816221i \(-0.303935\pi\)
0.577740 + 0.816221i \(0.303935\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 708.581 + 409.099i 1.11588 + 0.644251i
\(636\) 0 0
\(637\) 227.125 + 393.392i 0.356554 + 0.617570i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −753.611 + 435.098i −1.17568 + 0.678780i −0.955011 0.296569i \(-0.904157\pi\)
−0.220669 + 0.975349i \(0.570824\pi\)
\(642\) 0 0
\(643\) −309.061 + 535.310i −0.480656 + 0.832520i −0.999754 0.0221949i \(-0.992935\pi\)
0.519098 + 0.854715i \(0.326268\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 425.439i 0.657556i 0.944407 + 0.328778i \(0.106637\pi\)
−0.944407 + 0.328778i \(0.893363\pi\)
\(648\) 0 0
\(649\) −906.369 −1.39656
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 163.513 + 94.4042i 0.250403 + 0.144570i 0.619949 0.784642i \(-0.287153\pi\)
−0.369546 + 0.929212i \(0.620487\pi\)
\(654\) 0 0
\(655\) 154.119 + 266.942i 0.235296 + 0.407545i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −571.984 + 330.235i −0.867958 + 0.501116i −0.866669 0.498884i \(-0.833744\pi\)
−0.00128859 + 0.999999i \(0.500410\pi\)
\(660\) 0 0
\(661\) 294.915 510.808i 0.446165 0.772781i −0.551967 0.833866i \(-0.686123\pi\)
0.998133 + 0.0610847i \(0.0194560\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1186.39i 1.78405i
\(666\) 0 0
\(667\) −521.654 −0.782090
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −165.463 95.5301i −0.246592 0.142370i
\(672\) 0 0
\(673\) 195.715 + 338.989i 0.290810 + 0.503698i 0.974002 0.226541i \(-0.0727418\pi\)
−0.683191 + 0.730240i \(0.739408\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 600.728 346.830i 0.887338 0.512305i 0.0142672 0.999898i \(-0.495458\pi\)
0.873071 + 0.487593i \(0.162125\pi\)
\(678\) 0 0
\(679\) 315.292 546.102i 0.464348 0.804274i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 678.170i 0.992928i 0.868057 + 0.496464i \(0.165368\pi\)
−0.868057 + 0.496464i \(0.834632\pi\)
\(684\) 0 0
\(685\) −9.47303 −0.0138292
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 472.869 + 273.011i 0.686313 + 0.396243i
\(690\) 0 0
\(691\) 337.888 + 585.240i 0.488985 + 0.846946i 0.999920 0.0126731i \(-0.00403409\pi\)
−0.510935 + 0.859619i \(0.670701\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 96.4439 55.6819i 0.138768 0.0801179i
\(696\) 0 0
\(697\) −130.587 + 226.183i −0.187355 + 0.324509i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 797.260i 1.13732i 0.822573 + 0.568659i \(0.192538\pi\)
−0.822573 + 0.568659i \(0.807462\pi\)
\(702\) 0 0
\(703\) 1477.42 2.10160
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 211.419 + 122.063i 0.299037 + 0.172649i
\(708\) 0 0
\(709\) −86.7520 150.259i −0.122358 0.211931i 0.798339 0.602208i \(-0.205712\pi\)
−0.920697 + 0.390278i \(0.872379\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −101.823 + 58.7878i −0.142810 + 0.0824513i
\(714\) 0 0
\(715\) 902.711 1563.54i 1.26253 2.18677i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 188.177i 0.261721i −0.991401 0.130860i \(-0.958226\pi\)
0.991401 0.130860i \(-0.0417740\pi\)
\(720\) 0 0
\(721\) −811.600 −1.12566
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 263.998 + 152.420i 0.364136 + 0.210234i
\(726\) 0 0
\(727\) 355.888 + 616.417i 0.489530 + 0.847891i 0.999927 0.0120478i \(-0.00383501\pi\)
−0.510397 + 0.859939i \(0.670502\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −61.7085 + 35.6274i −0.0844165 + 0.0487379i
\(732\) 0 0
\(733\) −613.415 + 1062.47i −0.836856 + 1.44948i 0.0556546 + 0.998450i \(0.482275\pi\)
−0.892510 + 0.451027i \(0.851058\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 311.236i 0.422301i
\(738\) 0 0
\(739\) −741.892 −1.00391 −0.501957 0.864893i \(-0.667386\pi\)
−0.501957 + 0.864893i \(0.667386\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 677.218 + 390.992i 0.911464 + 0.526234i 0.880902 0.473299i \(-0.156937\pi\)
0.0305622 + 0.999533i \(0.490270\pi\)
\(744\) 0 0
\(745\) 273.208 + 473.210i 0.366722 + 0.635181i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1290.65 + 745.160i −1.72317 + 0.994873i
\(750\) 0 0
\(751\) −516.665 + 894.891i −0.687970 + 1.19160i 0.284524 + 0.958669i \(0.408165\pi\)
−0.972494 + 0.232930i \(0.925169\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 185.458i 0.245639i
\(756\) 0 0
\(757\) 473.877 0.625993 0.312997 0.949754i \(-0.398667\pi\)
0.312997 + 0.949754i \(0.398667\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 814.458 + 470.227i 1.07025 + 0.617907i 0.928249 0.371960i \(-0.121314\pi\)
0.141998 + 0.989867i \(0.454647\pi\)
\(762\) 0 0
\(763\) −259.919 450.193i −0.340654 0.590031i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1132.05 653.590i 1.47595 0.852138i
\(768\) 0 0
\(769\) −490.408 + 849.411i −0.637721 + 1.10457i 0.348210 + 0.937416i \(0.386789\pi\)
−0.985932 + 0.167149i \(0.946544\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1042.20i 1.34825i 0.738618 + 0.674124i \(0.235479\pi\)
−0.738618 + 0.674124i \(0.764521\pi\)
\(774\) 0 0
\(775\) 68.7077 0.0886550
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −710.550 410.236i −0.912131 0.526619i
\(780\) 0 0
\(781\) −743.769 1288.25i −0.952329 1.64948i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.46729 0.847142i 0.00186916 0.00107916i
\(786\) 0 0
\(787\) −72.3501 + 125.314i −0.0919315 + 0.159230i −0.908324 0.418268i \(-0.862637\pi\)
0.816392 + 0.577498i \(0.195971\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 921.567i 1.16507i
\(792\) 0 0
\(793\) 275.550 0.347478
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −134.866 77.8647i −0.169217 0.0976972i 0.413000 0.910731i \(-0.364481\pi\)
−0.582216 + 0.813034i \(0.697814\pi\)
\(798\) 0 0
\(799\) 65.8846 + 114.115i 0.0824588 + 0.142823i
\(800\)