Properties

Label 882.3.s.e.557.2
Level $882$
Weight $3$
Character 882.557
Analytic conductor $24.033$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 882.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.0327593166\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.12745506816.5
Defining polynomial: \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 557.2
Root \(2.23256 + 1.28897i\) of defining polynomial
Character \(\chi\) \(=\) 882.557
Dual form 882.3.s.e.863.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.70549 - 4.44876i) q^{5} +2.82843i q^{8} +O(q^{10})\) \(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(7.70549 - 4.44876i) q^{5} +2.82843i q^{8} +(-6.29150 + 10.8972i) q^{10} +(-15.4110 - 8.89753i) q^{11} +2.58301 q^{13} +(-2.00000 - 3.46410i) q^{16} +(22.4024 + 12.9340i) q^{17} +(-10.0000 - 17.3205i) q^{19} -17.7951i q^{20} +25.1660 q^{22} +(15.4110 - 8.89753i) q^{23} +(27.0830 - 46.9091i) q^{25} +(-3.16352 + 1.82646i) q^{26} +11.9034i q^{29} +(8.58301 - 14.8662i) q^{31} +(4.89898 + 2.82843i) q^{32} -36.5830 q^{34} +(-19.0000 - 32.9090i) q^{37} +(24.4949 + 14.1421i) q^{38} +(12.5830 + 21.7944i) q^{40} -15.7338i q^{41} -43.4980 q^{43} +(-30.8219 + 17.7951i) q^{44} +(-12.5830 + 21.7944i) q^{46} +(-14.6969 + 8.48528i) q^{47} +76.6023i q^{50} +(2.58301 - 4.47390i) q^{52} +(74.0947 + 42.7786i) q^{53} -158.332 q^{55} +(-8.41699 - 14.5787i) q^{58} +(-1.42807 - 0.824494i) q^{59} +(-50.1660 - 86.8901i) q^{61} +24.2764i q^{62} -8.00000 q^{64} +(19.9033 - 11.4912i) q^{65} +(-18.3320 + 31.7520i) q^{67} +(44.8048 - 25.8681i) q^{68} +17.7951i q^{71} +(-14.4575 + 25.0411i) q^{73} +(46.5403 + 26.8701i) q^{74} -40.0000 q^{76} +(-59.1660 - 102.479i) q^{79} +(-30.8219 - 17.7951i) q^{80} +(11.1255 + 19.2699i) q^{82} -120.443i q^{83} +230.162 q^{85} +(53.2740 - 30.7578i) q^{86} +(25.1660 - 43.5888i) q^{88} +(-120.789 + 69.7374i) q^{89} -35.5901i q^{92} +(12.0000 - 20.7846i) q^{94} +(-154.110 - 88.9753i) q^{95} +44.4131 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 8 q^{10} - 64 q^{13} - 16 q^{16} - 80 q^{19} + 32 q^{22} + 132 q^{25} - 16 q^{31} - 208 q^{34} - 152 q^{37} + 16 q^{40} + 160 q^{43} - 16 q^{46} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} + 96 q^{73} - 320 q^{76} - 304 q^{79} + 216 q^{82} + 656 q^{85} + 32 q^{88} + 96 q^{94} - 576 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 + 0.707107i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 7.70549 4.44876i 1.54110 0.889753i 0.542327 0.840167i \(-0.317543\pi\)
0.998770 0.0495855i \(-0.0157900\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) −6.29150 + 10.8972i −0.629150 + 1.08972i
\(11\) −15.4110 8.89753i −1.40100 0.808866i −0.406502 0.913650i \(-0.633252\pi\)
−0.994495 + 0.104784i \(0.966585\pi\)
\(12\) 0 0
\(13\) 2.58301 0.198693 0.0993464 0.995053i \(-0.468325\pi\)
0.0993464 + 0.995053i \(0.468325\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 22.4024 + 12.9340i 1.31779 + 0.760826i 0.983373 0.181599i \(-0.0581273\pi\)
0.334417 + 0.942425i \(0.391461\pi\)
\(18\) 0 0
\(19\) −10.0000 17.3205i −0.526316 0.911606i −0.999530 0.0306583i \(-0.990240\pi\)
0.473214 0.880947i \(-0.343094\pi\)
\(20\) 17.7951i 0.889753i
\(21\) 0 0
\(22\) 25.1660 1.14391
\(23\) 15.4110 8.89753i 0.670042 0.386849i −0.126050 0.992024i \(-0.540230\pi\)
0.796093 + 0.605175i \(0.206897\pi\)
\(24\) 0 0
\(25\) 27.0830 46.9091i 1.08332 1.87637i
\(26\) −3.16352 + 1.82646i −0.121674 + 0.0702485i
\(27\) 0 0
\(28\) 0 0
\(29\) 11.9034i 0.410463i 0.978713 + 0.205232i \(0.0657947\pi\)
−0.978713 + 0.205232i \(0.934205\pi\)
\(30\) 0 0
\(31\) 8.58301 14.8662i 0.276871 0.479555i −0.693734 0.720231i \(-0.744036\pi\)
0.970605 + 0.240676i \(0.0773692\pi\)
\(32\) 4.89898 + 2.82843i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −36.5830 −1.07597
\(35\) 0 0
\(36\) 0 0
\(37\) −19.0000 32.9090i −0.513514 0.889431i −0.999877 0.0156750i \(-0.995010\pi\)
0.486364 0.873757i \(-0.338323\pi\)
\(38\) 24.4949 + 14.1421i 0.644603 + 0.372161i
\(39\) 0 0
\(40\) 12.5830 + 21.7944i 0.314575 + 0.544860i
\(41\) 15.7338i 0.383752i −0.981419 0.191876i \(-0.938543\pi\)
0.981419 0.191876i \(-0.0614571\pi\)
\(42\) 0 0
\(43\) −43.4980 −1.01158 −0.505791 0.862656i \(-0.668799\pi\)
−0.505791 + 0.862656i \(0.668799\pi\)
\(44\) −30.8219 + 17.7951i −0.700499 + 0.404433i
\(45\) 0 0
\(46\) −12.5830 + 21.7944i −0.273544 + 0.473791i
\(47\) −14.6969 + 8.48528i −0.312701 + 0.180538i −0.648134 0.761526i \(-0.724451\pi\)
0.335434 + 0.942064i \(0.391117\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 76.6023i 1.53205i
\(51\) 0 0
\(52\) 2.58301 4.47390i 0.0496732 0.0860365i
\(53\) 74.0947 + 42.7786i 1.39801 + 0.807143i 0.994184 0.107692i \(-0.0343461\pi\)
0.403828 + 0.914835i \(0.367679\pi\)
\(54\) 0 0
\(55\) −158.332 −2.87876
\(56\) 0 0
\(57\) 0 0
\(58\) −8.41699 14.5787i −0.145121 0.251356i
\(59\) −1.42807 0.824494i −0.0242045 0.0139745i 0.487849 0.872928i \(-0.337782\pi\)
−0.512053 + 0.858954i \(0.671115\pi\)
\(60\) 0 0
\(61\) −50.1660 86.8901i −0.822394 1.42443i −0.903895 0.427754i \(-0.859305\pi\)
0.0815014 0.996673i \(-0.474028\pi\)
\(62\) 24.2764i 0.391555i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 19.9033 11.4912i 0.306205 0.176787i
\(66\) 0 0
\(67\) −18.3320 + 31.7520i −0.273612 + 0.473910i −0.969784 0.243965i \(-0.921552\pi\)
0.696172 + 0.717875i \(0.254885\pi\)
\(68\) 44.8048 25.8681i 0.658895 0.380413i
\(69\) 0 0
\(70\) 0 0
\(71\) 17.7951i 0.250635i 0.992117 + 0.125317i \(0.0399949\pi\)
−0.992117 + 0.125317i \(0.960005\pi\)
\(72\) 0 0
\(73\) −14.4575 + 25.0411i −0.198048 + 0.343029i −0.947895 0.318581i \(-0.896794\pi\)
0.749847 + 0.661611i \(0.230127\pi\)
\(74\) 46.5403 + 26.8701i 0.628923 + 0.363109i
\(75\) 0 0
\(76\) −40.0000 −0.526316
\(77\) 0 0
\(78\) 0 0
\(79\) −59.1660 102.479i −0.748937 1.29720i −0.948333 0.317278i \(-0.897231\pi\)
0.199396 0.979919i \(-0.436102\pi\)
\(80\) −30.8219 17.7951i −0.385274 0.222438i
\(81\) 0 0
\(82\) 11.1255 + 19.2699i 0.135677 + 0.234999i
\(83\) 120.443i 1.45112i −0.688159 0.725560i \(-0.741581\pi\)
0.688159 0.725560i \(-0.258419\pi\)
\(84\) 0 0
\(85\) 230.162 2.70779
\(86\) 53.2740 30.7578i 0.619465 0.357648i
\(87\) 0 0
\(88\) 25.1660 43.5888i 0.285977 0.495327i
\(89\) −120.789 + 69.7374i −1.35718 + 0.783566i −0.989242 0.146286i \(-0.953268\pi\)
−0.367934 + 0.929852i \(0.619935\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 35.5901i 0.386849i
\(93\) 0 0
\(94\) 12.0000 20.7846i 0.127660 0.221113i
\(95\) −154.110 88.9753i −1.62221 0.936582i
\(96\) 0 0
\(97\) 44.4131 0.457867 0.228933 0.973442i \(-0.426476\pi\)
0.228933 + 0.973442i \(0.426476\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −54.1660 93.8183i −0.541660 0.938183i
\(101\) −27.6088 15.9399i −0.273354 0.157821i 0.357057 0.934083i \(-0.383780\pi\)
−0.630411 + 0.776261i \(0.717114\pi\)
\(102\) 0 0
\(103\) −2.25098 3.89882i −0.0218542 0.0378526i 0.854891 0.518807i \(-0.173624\pi\)
−0.876746 + 0.480954i \(0.840290\pi\)
\(104\) 7.30584i 0.0702485i
\(105\) 0 0
\(106\) −120.996 −1.14147
\(107\) 149.111 86.0896i 1.39357 0.804575i 0.399857 0.916577i \(-0.369060\pi\)
0.993708 + 0.112002i \(0.0357263\pi\)
\(108\) 0 0
\(109\) 88.9150 154.005i 0.815734 1.41289i −0.0930653 0.995660i \(-0.529667\pi\)
0.908800 0.417233i \(-0.137000\pi\)
\(110\) 193.916 111.958i 1.76288 1.01780i
\(111\) 0 0
\(112\) 0 0
\(113\) 31.3475i 0.277411i 0.990334 + 0.138706i \(0.0442942\pi\)
−0.990334 + 0.138706i \(0.955706\pi\)
\(114\) 0 0
\(115\) 79.1660 137.120i 0.688400 1.19234i
\(116\) 20.6173 + 11.9034i 0.177736 + 0.102616i
\(117\) 0 0
\(118\) 2.33202 0.0197629
\(119\) 0 0
\(120\) 0 0
\(121\) 97.8320 + 169.450i 0.808529 + 1.40041i
\(122\) 122.881 + 70.9455i 1.00722 + 0.581520i
\(123\) 0 0
\(124\) −17.1660 29.7324i −0.138436 0.239777i
\(125\) 259.505i 2.07604i
\(126\) 0 0
\(127\) 214.332 1.68765 0.843827 0.536616i \(-0.180297\pi\)
0.843827 + 0.536616i \(0.180297\pi\)
\(128\) 9.79796 5.65685i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −16.2510 + 28.1475i −0.125008 + 0.216519i
\(131\) 79.1970 45.7244i 0.604557 0.349041i −0.166275 0.986079i \(-0.553174\pi\)
0.770832 + 0.637038i \(0.219841\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 51.8508i 0.386946i
\(135\) 0 0
\(136\) −36.5830 + 63.3636i −0.268993 + 0.465909i
\(137\) 92.5699 + 53.4453i 0.675693 + 0.390111i 0.798230 0.602353i \(-0.205770\pi\)
−0.122537 + 0.992464i \(0.539103\pi\)
\(138\) 0 0
\(139\) −121.328 −0.872864 −0.436432 0.899737i \(-0.643758\pi\)
−0.436432 + 0.899737i \(0.643758\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −12.5830 21.7944i −0.0886127 0.153482i
\(143\) −39.8066 22.9824i −0.278368 0.160716i
\(144\) 0 0
\(145\) 52.9555 + 91.7217i 0.365211 + 0.632563i
\(146\) 40.8920i 0.280082i
\(147\) 0 0
\(148\) −76.0000 −0.513514
\(149\) −15.3069 + 8.83744i −0.102731 + 0.0593117i −0.550485 0.834845i \(-0.685557\pi\)
0.447754 + 0.894157i \(0.352224\pi\)
\(150\) 0 0
\(151\) 25.4170 44.0235i 0.168324 0.291547i −0.769506 0.638639i \(-0.779498\pi\)
0.937831 + 0.347093i \(0.112831\pi\)
\(152\) 48.9898 28.2843i 0.322301 0.186081i
\(153\) 0 0
\(154\) 0 0
\(155\) 152.735i 0.985388i
\(156\) 0 0
\(157\) −34.4980 + 59.7523i −0.219733 + 0.380588i −0.954726 0.297486i \(-0.903852\pi\)
0.734994 + 0.678074i \(0.237185\pi\)
\(158\) 144.927 + 83.6734i 0.917257 + 0.529578i
\(159\) 0 0
\(160\) 50.3320 0.314575
\(161\) 0 0
\(162\) 0 0
\(163\) 83.4980 + 144.623i 0.512258 + 0.887257i 0.999899 + 0.0142125i \(0.00452412\pi\)
−0.487641 + 0.873044i \(0.662143\pi\)
\(164\) −27.2518 15.7338i −0.166169 0.0959379i
\(165\) 0 0
\(166\) 85.1660 + 147.512i 0.513048 + 0.888626i
\(167\) 120.443i 0.721215i 0.932718 + 0.360608i \(0.117431\pi\)
−0.932718 + 0.360608i \(0.882569\pi\)
\(168\) 0 0
\(169\) −162.328 −0.960521
\(170\) −281.890 + 162.749i −1.65818 + 0.957348i
\(171\) 0 0
\(172\) −43.4980 + 75.3408i −0.252896 + 0.438028i
\(173\) −79.5540 + 45.9305i −0.459850 + 0.265494i −0.711981 0.702199i \(-0.752202\pi\)
0.252131 + 0.967693i \(0.418868\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 71.1802i 0.404433i
\(177\) 0 0
\(178\) 98.6235 170.821i 0.554065 0.959668i
\(179\) −115.433 66.6455i −0.644879 0.372321i 0.141612 0.989922i \(-0.454771\pi\)
−0.786492 + 0.617601i \(0.788105\pi\)
\(180\) 0 0
\(181\) 83.0850 0.459033 0.229517 0.973305i \(-0.426286\pi\)
0.229517 + 0.973305i \(0.426286\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 25.1660 + 43.5888i 0.136772 + 0.236896i
\(185\) −292.808 169.053i −1.58275 0.913800i
\(186\) 0 0
\(187\) −230.162 398.652i −1.23081 2.13183i
\(188\) 33.9411i 0.180538i
\(189\) 0 0
\(190\) 251.660 1.32453
\(191\) 35.8202 20.6808i 0.187540 0.108276i −0.403290 0.915072i \(-0.632134\pi\)
0.590830 + 0.806796i \(0.298800\pi\)
\(192\) 0 0
\(193\) −67.0000 + 116.047i −0.347150 + 0.601282i −0.985742 0.168264i \(-0.946184\pi\)
0.638592 + 0.769546i \(0.279517\pi\)
\(194\) −54.3947 + 31.4048i −0.280385 + 0.161880i
\(195\) 0 0
\(196\) 0 0
\(197\) 68.8269i 0.349375i −0.984624 0.174688i \(-0.944108\pi\)
0.984624 0.174688i \(-0.0558916\pi\)
\(198\) 0 0
\(199\) 139.247 241.183i 0.699734 1.21197i −0.268825 0.963189i \(-0.586635\pi\)
0.968559 0.248786i \(-0.0800314\pi\)
\(200\) 132.679 + 76.6023i 0.663395 + 0.383012i
\(201\) 0 0
\(202\) 45.0850 0.223193
\(203\) 0 0
\(204\) 0 0
\(205\) −69.9961 121.237i −0.341444 0.591399i
\(206\) 5.51376 + 3.18337i 0.0267658 + 0.0154533i
\(207\) 0 0
\(208\) −5.16601 8.94779i −0.0248366 0.0430182i
\(209\) 355.901i 1.70288i
\(210\) 0 0
\(211\) −211.498 −1.00236 −0.501180 0.865343i \(-0.667101\pi\)
−0.501180 + 0.865343i \(0.667101\pi\)
\(212\) 148.189 85.5571i 0.699006 0.403571i
\(213\) 0 0
\(214\) −121.749 + 210.875i −0.568921 + 0.985399i
\(215\) −335.173 + 193.512i −1.55895 + 0.900058i
\(216\) 0 0
\(217\) 0 0
\(218\) 251.490i 1.15362i
\(219\) 0 0
\(220\) −158.332 + 274.239i −0.719691 + 1.24654i
\(221\) 57.8656 + 33.4087i 0.261835 + 0.151171i
\(222\) 0 0
\(223\) 222.494 0.997731 0.498866 0.866679i \(-0.333750\pi\)
0.498866 + 0.866679i \(0.333750\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −22.1660 38.3927i −0.0980797 0.169879i
\(227\) −88.1816 50.9117i −0.388465 0.224281i 0.293030 0.956103i \(-0.405337\pi\)
−0.681495 + 0.731823i \(0.738670\pi\)
\(228\) 0 0
\(229\) 81.5425 + 141.236i 0.356081 + 0.616750i 0.987302 0.158853i \(-0.0507795\pi\)
−0.631222 + 0.775603i \(0.717446\pi\)
\(230\) 223.915i 0.973545i
\(231\) 0 0
\(232\) −33.6680 −0.145121
\(233\) 314.244 181.429i 1.34869 0.778664i 0.360623 0.932712i \(-0.382564\pi\)
0.988063 + 0.154047i \(0.0492308\pi\)
\(234\) 0 0
\(235\) −75.4980 + 130.766i −0.321268 + 0.556453i
\(236\) −2.85613 + 1.64899i −0.0121022 + 0.00698724i
\(237\) 0 0
\(238\) 0 0
\(239\) 177.126i 0.741113i −0.928810 0.370557i \(-0.879167\pi\)
0.928810 0.370557i \(-0.120833\pi\)
\(240\) 0 0
\(241\) −76.3765 + 132.288i −0.316915 + 0.548913i −0.979843 0.199771i \(-0.935980\pi\)
0.662928 + 0.748683i \(0.269314\pi\)
\(242\) −239.639 138.355i −0.990242 0.571716i
\(243\) 0 0
\(244\) −200.664 −0.822394
\(245\) 0 0
\(246\) 0 0
\(247\) −25.8301 44.7390i −0.104575 0.181129i
\(248\) 42.0480 + 24.2764i 0.169548 + 0.0978887i
\(249\) 0 0
\(250\) 183.498 + 317.828i 0.733992 + 1.27131i
\(251\) 356.382i 1.41985i 0.704278 + 0.709924i \(0.251271\pi\)
−0.704278 + 0.709924i \(0.748729\pi\)
\(252\) 0 0
\(253\) −316.664 −1.25164
\(254\) −262.502 + 151.556i −1.03347 + 0.596676i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 51.5882 29.7844i 0.200732 0.115893i −0.396265 0.918136i \(-0.629694\pi\)
0.596997 + 0.802244i \(0.296360\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 45.9647i 0.176787i
\(261\) 0 0
\(262\) −64.6640 + 112.001i −0.246809 + 0.427486i
\(263\) 6.42629 + 3.71022i 0.0244346 + 0.0141073i 0.512168 0.858886i \(-0.328843\pi\)
−0.487733 + 0.872993i \(0.662176\pi\)
\(264\) 0 0
\(265\) 761.247 2.87263
\(266\) 0 0
\(267\) 0 0
\(268\) 36.6640 + 63.5040i 0.136806 + 0.236955i
\(269\) 372.571 + 215.104i 1.38502 + 0.799642i 0.992749 0.120207i \(-0.0383559\pi\)
0.392272 + 0.919849i \(0.371689\pi\)
\(270\) 0 0
\(271\) 20.5830 + 35.6508i 0.0759520 + 0.131553i 0.901500 0.432779i \(-0.142467\pi\)
−0.825548 + 0.564332i \(0.809134\pi\)
\(272\) 103.472i 0.380413i
\(273\) 0 0
\(274\) −151.166 −0.551701
\(275\) −834.751 + 481.944i −3.03546 + 1.75252i
\(276\) 0 0
\(277\) −16.0000 + 27.7128i −0.0577617 + 0.100046i −0.893460 0.449142i \(-0.851730\pi\)
0.835699 + 0.549188i \(0.185063\pi\)
\(278\) 148.596 85.7919i 0.534518 0.308604i
\(279\) 0 0
\(280\) 0 0
\(281\) 17.0907i 0.0608211i 0.999537 + 0.0304106i \(0.00968147\pi\)
−0.999537 + 0.0304106i \(0.990319\pi\)
\(282\) 0 0
\(283\) −219.830 + 380.757i −0.776785 + 1.34543i 0.157001 + 0.987598i \(0.449817\pi\)
−0.933786 + 0.357832i \(0.883516\pi\)
\(284\) 30.8219 + 17.7951i 0.108528 + 0.0626587i
\(285\) 0 0
\(286\) 65.0039 0.227286
\(287\) 0 0
\(288\) 0 0
\(289\) 190.079 + 329.227i 0.657713 + 1.13919i
\(290\) −129.714 74.8904i −0.447290 0.258243i
\(291\) 0 0
\(292\) 28.9150 + 50.0823i 0.0990241 + 0.171515i
\(293\) 394.377i 1.34600i −0.739644 0.672998i \(-0.765006\pi\)
0.739644 0.672998i \(-0.234994\pi\)
\(294\) 0 0
\(295\) −14.6719 −0.0497353
\(296\) 93.0806 53.7401i 0.314462 0.181554i
\(297\) 0 0
\(298\) 12.4980 21.6472i 0.0419397 0.0726417i
\(299\) 39.8066 22.9824i 0.133133 0.0768641i
\(300\) 0 0
\(301\) 0 0
\(302\) 71.8901i 0.238047i
\(303\) 0 0
\(304\) −40.0000 + 69.2820i −0.131579 + 0.227901i
\(305\) −773.107 446.353i −2.53478 1.46345i
\(306\) 0 0
\(307\) −23.3360 −0.0760129 −0.0380064 0.999277i \(-0.512101\pi\)
−0.0380064 + 0.999277i \(0.512101\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 108.000 + 187.061i 0.348387 + 0.603424i
\(311\) 456.617 + 263.628i 1.46822 + 0.847678i 0.999366 0.0355970i \(-0.0113333\pi\)
0.468855 + 0.883275i \(0.344667\pi\)
\(312\) 0 0
\(313\) 147.664 + 255.762i 0.471770 + 0.817130i 0.999478 0.0322959i \(-0.0102819\pi\)
−0.527708 + 0.849426i \(0.676949\pi\)
\(314\) 97.5752i 0.310749i
\(315\) 0 0
\(316\) −236.664 −0.748937
\(317\) 93.0758 53.7373i 0.293614 0.169518i −0.345956 0.938251i \(-0.612445\pi\)
0.639571 + 0.768732i \(0.279112\pi\)
\(318\) 0 0
\(319\) 105.911 183.443i 0.332010 0.575058i
\(320\) −61.6439 + 35.5901i −0.192637 + 0.111219i
\(321\) 0 0
\(322\) 0 0
\(323\) 517.362i 1.60174i
\(324\) 0 0
\(325\) 69.9555 121.167i 0.215248 0.372820i
\(326\) −204.528 118.084i −0.627385 0.362221i
\(327\) 0 0
\(328\) 44.5020 0.135677
\(329\) 0 0
\(330\) 0 0
\(331\) 136.745 + 236.849i 0.413127 + 0.715557i 0.995230 0.0975581i \(-0.0311032\pi\)
−0.582103 + 0.813115i \(0.697770\pi\)
\(332\) −208.613 120.443i −0.628353 0.362780i
\(333\) 0 0
\(334\) −85.1660 147.512i −0.254988 0.441652i
\(335\) 326.219i 0.973789i
\(336\) 0 0
\(337\) −341.166 −1.01236 −0.506181 0.862427i \(-0.668943\pi\)
−0.506181 + 0.862427i \(0.668943\pi\)
\(338\) 198.810 114.783i 0.588197 0.339596i
\(339\) 0 0
\(340\) 230.162 398.652i 0.676947 1.17251i
\(341\) −264.545 + 152.735i −0.775791 + 0.447903i
\(342\) 0 0
\(343\) 0 0
\(344\) 123.031i 0.357648i
\(345\) 0 0
\(346\) 64.9555 112.506i 0.187733 0.325163i
\(347\) −100.736 58.1602i −0.290307 0.167609i 0.347773 0.937579i \(-0.386938\pi\)
−0.638080 + 0.769970i \(0.720271\pi\)
\(348\) 0 0
\(349\) −158.324 −0.453651 −0.226825 0.973935i \(-0.572835\pi\)
−0.226825 + 0.973935i \(0.572835\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −50.3320 87.1776i −0.142989 0.247664i
\(353\) 199.480 + 115.170i 0.565098 + 0.326260i 0.755189 0.655507i \(-0.227545\pi\)
−0.190091 + 0.981766i \(0.560878\pi\)
\(354\) 0 0
\(355\) 79.1660 + 137.120i 0.223003 + 0.386252i
\(356\) 278.949i 0.783566i
\(357\) 0 0
\(358\) 188.502 0.526542
\(359\) 148.695 85.8492i 0.414193 0.239134i −0.278397 0.960466i \(-0.589803\pi\)
0.692590 + 0.721332i \(0.256470\pi\)
\(360\) 0 0
\(361\) −19.5000 + 33.7750i −0.0540166 + 0.0935595i
\(362\) −101.758 + 58.7499i −0.281099 + 0.162293i
\(363\) 0 0
\(364\) 0 0
\(365\) 257.272i 0.704856i
\(366\) 0 0
\(367\) −258.745 + 448.160i −0.705027 + 1.22114i 0.261654 + 0.965162i \(0.415732\pi\)
−0.966682 + 0.255982i \(0.917601\pi\)
\(368\) −61.6439 35.5901i −0.167511 0.0967123i
\(369\) 0 0
\(370\) 478.154 1.29231
\(371\) 0 0
\(372\) 0 0
\(373\) 116.668 + 202.075i 0.312783 + 0.541756i 0.978964 0.204035i \(-0.0654055\pi\)
−0.666181 + 0.745790i \(0.732072\pi\)
\(374\) 563.780 + 325.498i 1.50743 + 0.870316i
\(375\) 0 0
\(376\) −24.0000 41.5692i −0.0638298 0.110556i
\(377\) 30.7466i 0.0815560i
\(378\) 0 0
\(379\) 441.166 1.16403 0.582013 0.813179i \(-0.302265\pi\)
0.582013 + 0.813179i \(0.302265\pi\)
\(380\) −308.219 + 177.951i −0.811104 + 0.468291i
\(381\) 0 0
\(382\) −29.2470 + 50.6574i −0.0765630 + 0.132611i
\(383\) −184.515 + 106.530i −0.481763 + 0.278146i −0.721151 0.692778i \(-0.756387\pi\)
0.239388 + 0.970924i \(0.423053\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 189.505i 0.490945i
\(387\) 0 0
\(388\) 44.4131 76.9257i 0.114467 0.198262i
\(389\) 489.387 + 282.548i 1.25806 + 0.726344i 0.972698 0.232074i \(-0.0745512\pi\)
0.285367 + 0.958418i \(0.407885\pi\)
\(390\) 0 0
\(391\) 460.324 1.17730
\(392\) 0 0
\(393\) 0 0
\(394\) 48.6680 + 84.2954i 0.123523 + 0.213948i
\(395\) −911.806 526.431i −2.30837 1.33274i
\(396\) 0 0
\(397\) −249.162 431.561i −0.627612 1.08706i −0.988029 0.154265i \(-0.950699\pi\)
0.360417 0.932791i \(-0.382634\pi\)
\(398\) 393.850i 0.989573i
\(399\) 0 0
\(400\) −216.664 −0.541660
\(401\) −167.483 + 96.6962i −0.417662 + 0.241138i −0.694077 0.719901i \(-0.744187\pi\)
0.276414 + 0.961039i \(0.410854\pi\)
\(402\) 0 0
\(403\) 22.1699 38.3995i 0.0550123 0.0952841i
\(404\) −55.2176 + 31.8799i −0.136677 + 0.0789106i
\(405\) 0 0
\(406\) 0 0
\(407\) 676.212i 1.66145i
\(408\) 0 0
\(409\) 227.122 393.386i 0.555309 0.961824i −0.442570 0.896734i \(-0.645933\pi\)
0.997879 0.0650902i \(-0.0207335\pi\)
\(410\) 171.455 + 98.9894i 0.418182 + 0.241438i
\(411\) 0 0
\(412\) −9.00394 −0.0218542
\(413\) 0 0
\(414\) 0 0
\(415\) −535.822 928.071i −1.29114 2.23632i
\(416\) 12.6541 + 7.30584i 0.0304185 + 0.0175621i
\(417\) 0 0
\(418\) −251.660 435.888i −0.602058 1.04279i
\(419\) 339.411i 0.810051i 0.914305 + 0.405025i \(0.132737\pi\)
−0.914305 + 0.405025i \(0.867263\pi\)
\(420\) 0 0
\(421\) 247.320 0.587459 0.293729 0.955889i \(-0.405104\pi\)
0.293729 + 0.955889i \(0.405104\pi\)
\(422\) 259.031 149.552i 0.613818 0.354388i
\(423\) 0 0
\(424\) −120.996 + 209.571i −0.285368 + 0.494272i
\(425\) 1213.45 700.586i 2.85518 1.64844i
\(426\) 0 0
\(427\) 0 0
\(428\) 344.358i 0.804575i
\(429\) 0 0
\(430\) 273.668 474.007i 0.636437 1.10234i
\(431\) 395.271 + 228.210i 0.917101 + 0.529489i 0.882709 0.469920i \(-0.155717\pi\)
0.0343923 + 0.999408i \(0.489050\pi\)
\(432\) 0 0
\(433\) −637.984 −1.47340 −0.736702 0.676217i \(-0.763618\pi\)
−0.736702 + 0.676217i \(0.763618\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −177.830 308.011i −0.407867 0.706447i
\(437\) −308.219 177.951i −0.705308 0.407210i
\(438\) 0 0
\(439\) 392.073 + 679.091i 0.893105 + 1.54690i 0.836132 + 0.548528i \(0.184812\pi\)
0.0569728 + 0.998376i \(0.481855\pi\)
\(440\) 447.831i 1.01780i
\(441\) 0 0
\(442\) −94.4941 −0.213788
\(443\) −408.956 + 236.111i −0.923151 + 0.532981i −0.884639 0.466277i \(-0.845595\pi\)
−0.0385120 + 0.999258i \(0.512262\pi\)
\(444\) 0 0
\(445\) −620.490 + 1074.72i −1.39436 + 2.41510i
\(446\) −272.499 + 157.327i −0.610983 + 0.352751i
\(447\) 0 0
\(448\) 0 0
\(449\) 739.852i 1.64778i 0.566752 + 0.823888i \(0.308200\pi\)
−0.566752 + 0.823888i \(0.691800\pi\)
\(450\) 0 0
\(451\) −139.992 + 242.473i −0.310404 + 0.537635i
\(452\) 54.2954 + 31.3475i 0.120123 + 0.0693528i
\(453\) 0 0
\(454\) 144.000 0.317181
\(455\) 0 0
\(456\) 0 0
\(457\) 124.162 + 215.055i 0.271689 + 0.470580i 0.969295 0.245903i \(-0.0790843\pi\)
−0.697605 + 0.716482i \(0.745751\pi\)
\(458\) −199.737 115.318i −0.436108 0.251787i
\(459\) 0 0
\(460\) −158.332 274.239i −0.344200 0.596172i
\(461\) 355.970i 0.772168i −0.922464 0.386084i \(-0.873827\pi\)
0.922464 0.386084i \(-0.126173\pi\)
\(462\) 0 0
\(463\) −6.33202 −0.0136761 −0.00683804 0.999977i \(-0.502177\pi\)
−0.00683804 + 0.999977i \(0.502177\pi\)
\(464\) 41.2347 23.8069i 0.0888679 0.0513079i
\(465\) 0 0
\(466\) −256.579 + 444.408i −0.550599 + 0.953665i
\(467\) −760.968 + 439.345i −1.62948 + 0.940782i −0.645236 + 0.763984i \(0.723241\pi\)
−0.984247 + 0.176799i \(0.943426\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 213.541i 0.454342i
\(471\) 0 0
\(472\) 2.33202 4.03918i 0.00494072 0.00855758i
\(473\) 670.347 + 387.025i 1.41722 + 0.818235i
\(474\) 0 0
\(475\) −1083.32 −2.28067
\(476\) 0 0
\(477\) 0 0
\(478\) 125.247 + 216.934i 0.262023 + 0.453837i
\(479\) 194.333 + 112.198i 0.405705 + 0.234234i 0.688943 0.724816i \(-0.258075\pi\)
−0.283238 + 0.959050i \(0.591409\pi\)
\(480\) 0 0
\(481\) −49.0771 85.0040i −0.102031 0.176724i
\(482\) 216.025i 0.448185i
\(483\) 0 0
\(484\) 391.328 0.808529
\(485\) 342.224 197.583i 0.705617 0.407388i
\(486\) 0 0
\(487\) 358.745 621.365i 0.736643 1.27590i −0.217356 0.976092i \(-0.569743\pi\)
0.953999 0.299810i \(-0.0969234\pi\)
\(488\) 245.762 141.891i 0.503611 0.290760i
\(489\) 0 0
\(490\) 0 0
\(491\) 274.002i 0.558050i −0.960284 0.279025i \(-0.909989\pi\)
0.960284 0.279025i \(-0.0900112\pi\)
\(492\) 0 0
\(493\) −153.959 + 266.666i −0.312291 + 0.540904i
\(494\) 63.2704 + 36.5292i 0.128078 + 0.0739458i
\(495\) 0 0
\(496\) −68.6640 −0.138436
\(497\) 0 0
\(498\) 0 0
\(499\) 364.405 + 631.168i 0.730271 + 1.26487i 0.956767 + 0.290854i \(0.0939395\pi\)
−0.226496 + 0.974012i \(0.572727\pi\)
\(500\) −449.477 259.505i −0.898953 0.519011i
\(501\) 0 0
\(502\) −252.000 436.477i −0.501992 0.869476i
\(503\) 594.657i 1.18222i 0.806590 + 0.591111i \(0.201310\pi\)
−0.806590 + 0.591111i \(0.798690\pi\)
\(504\) 0 0
\(505\) −283.652 −0.561688
\(506\) 387.833 223.915i 0.766468 0.442520i
\(507\) 0 0
\(508\) 214.332 371.234i 0.421913 0.730775i
\(509\) 860.842 497.007i 1.69124 0.976439i 0.737723 0.675103i \(-0.235901\pi\)
0.953518 0.301336i \(-0.0974325\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −42.1216 + 72.9567i −0.0819486 + 0.141939i
\(515\) −34.6899 20.0282i −0.0673589 0.0388897i
\(516\) 0 0
\(517\) 301.992 0.584124
\(518\) 0 0
\(519\) 0 0
\(520\) 32.5020 + 56.2951i 0.0625038 + 0.108260i
\(521\) −35.3735 20.4229i −0.0678955 0.0391995i 0.465668 0.884960i \(-0.345814\pi\)
−0.533563 + 0.845760i \(0.679147\pi\)
\(522\) 0 0
\(523\) 116.000 + 200.918i 0.221797 + 0.384164i 0.955354 0.295464i \(-0.0954743\pi\)
−0.733556 + 0.679629i \(0.762141\pi\)
\(524\) 182.898i 0.349041i
\(525\) 0 0
\(526\) −10.4941 −0.0199507
\(527\) 384.560 222.026i 0.729716 0.421302i
\(528\) 0 0
\(529\) −106.168 + 183.888i −0.200696 + 0.347615i
\(530\) −932.333 + 538.283i −1.75912 + 1.01563i
\(531\) 0 0
\(532\) 0 0
\(533\) 40.6405i 0.0762487i
\(534\) 0 0
\(535\) 765.984 1326.72i 1.43175 2.47986i
\(536\) −89.8082 51.8508i −0.167553 0.0967365i
\(537\) 0 0
\(538\) −608.405 −1.13086
\(539\) 0 0
\(540\) 0 0
\(541\) −125.166 216.794i −0.231360 0.400728i 0.726848 0.686798i \(-0.240984\pi\)
−0.958209 + 0.286070i \(0.907651\pi\)
\(542\) −50.4179 29.1088i −0.0930219 0.0537062i
\(543\) 0 0
\(544\) 73.1660 + 126.727i 0.134496 + 0.232954i
\(545\) 1582.25i 2.90321i
\(546\) 0 0
\(547\) 888.324 1.62399 0.811996 0.583662i \(-0.198381\pi\)
0.811996 + 0.583662i \(0.198381\pi\)
\(548\) 185.140 106.891i 0.337846 0.195056i
\(549\) 0 0
\(550\) 681.571 1180.52i 1.23922 2.14639i
\(551\) 206.173 119.034i 0.374180 0.216033i
\(552\) 0 0
\(553\) 0 0
\(554\) 45.2548i 0.0816874i
\(555\) 0 0
\(556\) −121.328 + 210.146i −0.218216 + 0.377961i
\(557\) −273.931 158.154i −0.491798 0.283940i 0.233522 0.972351i \(-0.424975\pi\)
−0.725320 + 0.688412i \(0.758308\pi\)
\(558\) 0 0
\(559\) −112.356 −0.200994
\(560\) 0 0
\(561\) 0 0
\(562\) −12.0850 20.9318i −0.0215035 0.0372452i
\(563\) −50.6356 29.2345i −0.0899390 0.0519263i 0.454356 0.890820i \(-0.349869\pi\)
−0.544295 + 0.838894i \(0.683203\pi\)
\(564\) 0 0
\(565\) 139.458 + 241.547i 0.246827 + 0.427518i
\(566\) 621.773i 1.09854i
\(567\) 0 0
\(568\) −50.3320 −0.0886127
\(569\) 191.968 110.833i 0.337378 0.194785i −0.321734 0.946830i \(-0.604266\pi\)
0.659112 + 0.752045i \(0.270932\pi\)
\(570\) 0 0
\(571\) 243.822 422.312i 0.427009 0.739601i −0.569597 0.821924i \(-0.692901\pi\)
0.996606 + 0.0823230i \(0.0262339\pi\)
\(572\) −79.6132 + 45.9647i −0.139184 + 0.0803579i
\(573\) 0 0
\(574\) 0 0
\(575\) 963.887i 1.67633i
\(576\) 0 0
\(577\) 243.664 422.039i 0.422295 0.731436i −0.573869 0.818947i \(-0.694558\pi\)
0.996164 + 0.0875114i \(0.0278914\pi\)
\(578\) −465.597 268.812i −0.805531 0.465073i
\(579\) 0 0
\(580\) 211.822 0.365211
\(581\) 0 0
\(582\) 0 0
\(583\) −761.247 1318.52i −1.30574 2.26161i
\(584\) −70.8271 40.8920i −0.121279 0.0700206i
\(585\) 0 0
\(586\) 278.867 + 483.011i 0.475882 + 0.824251i
\(587\) 445.701i 0.759286i −0.925133 0.379643i \(-0.876047\pi\)
0.925133 0.379643i \(-0.123953\pi\)
\(588\) 0 0
\(589\) −343.320 −0.582887
\(590\) 17.9694 10.3746i 0.0304565 0.0175841i
\(591\) 0 0
\(592\) −76.0000 + 131.636i −0.128378 + 0.222358i
\(593\) −239.584 + 138.324i −0.404020 + 0.233261i −0.688217 0.725505i \(-0.741606\pi\)
0.284197 + 0.958766i \(0.408273\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 35.3498i 0.0593117i
\(597\) 0 0
\(598\) −32.5020 + 56.2951i −0.0543511 + 0.0941389i
\(599\) 71.3426 + 41.1897i 0.119103 + 0.0687641i 0.558368 0.829593i \(-0.311428\pi\)
−0.439265 + 0.898358i \(0.644761\pi\)
\(600\) 0 0
\(601\) −418.000 −0.695507 −0.347754 0.937586i \(-0.613055\pi\)
−0.347754 + 0.937586i \(0.613055\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −50.8340 88.0471i −0.0841622 0.145773i
\(605\) 1507.69 + 870.463i 2.49204 + 1.43878i
\(606\) 0 0
\(607\) −38.4209 66.5470i −0.0632964 0.109633i 0.832641 0.553814i \(-0.186828\pi\)
−0.895937 + 0.444181i \(0.853495\pi\)
\(608\) 113.137i 0.186081i
\(609\) 0 0
\(610\) 1262.48 2.06964
\(611\) −37.9623 + 21.9175i −0.0621314 + 0.0358716i
\(612\) 0 0
\(613\) −29.6640 + 51.3796i −0.0483916 + 0.0838167i −0.889207 0.457506i \(-0.848743\pi\)
0.840815 + 0.541323i \(0.182076\pi\)
\(614\) 28.5806 16.5010i 0.0465482 0.0268746i
\(615\) 0 0
\(616\) 0 0
\(617\) 29.1143i 0.0471869i 0.999722 + 0.0235935i \(0.00751073\pi\)
−0.999722 + 0.0235935i \(0.992489\pi\)
\(618\) 0 0
\(619\) −227.822 + 394.600i −0.368049 + 0.637479i −0.989260 0.146164i \(-0.953307\pi\)
0.621212 + 0.783643i \(0.286641\pi\)
\(620\) −264.545 152.735i −0.426685 0.246347i
\(621\) 0 0
\(622\) −745.652 −1.19880
\(623\) 0 0
\(624\) 0 0
\(625\) −477.403 826.887i −0.763845 1.32302i
\(626\) −361.702 208.828i −0.577798 0.333592i
\(627\) 0 0
\(628\) 68.9961 + 119.505i 0.109866 + 0.190294i
\(629\) 982.987i 1.56278i
\(630\) 0 0
\(631\) −45.0039 −0.0713216 −0.0356608 0.999364i \(-0.511354\pi\)
−0.0356608 + 0.999364i \(0.511354\pi\)
\(632\) 289.853 167.347i 0.458628 0.264789i
\(633\) 0 0
\(634\) −75.9961 + 131.629i −0.119868 + 0.207617i
\(635\) 1651.53 953.513i 2.60084 1.50159i
\(636\) 0 0
\(637\) 0 0
\(638\) 299.562i 0.469533i
\(639\) 0 0
\(640\) 50.3320 87.1776i 0.0786438 0.136215i
\(641\) 555.315 + 320.611i 0.866327 + 0.500174i 0.866126 0.499826i \(-0.166603\pi\)
0.000200774 1.00000i \(0.499936\pi\)
\(642\) 0 0
\(643\) −604.000 −0.939347 −0.469673 0.882840i \(-0.655628\pi\)
−0.469673 + 0.882840i \(0.655628\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 365.830 + 633.636i 0.566300 + 0.980861i
\(647\) 155.538 + 89.7998i 0.240398 + 0.138794i 0.615360 0.788246i \(-0.289011\pi\)
−0.374961 + 0.927040i \(0.622344\pi\)
\(648\) 0 0
\(649\) 14.6719 + 25.4125i 0.0226070 + 0.0391564i
\(650\) 197.864i 0.304406i
\(651\) 0 0
\(652\) 333.992 0.512258
\(653\) 339.562 196.046i 0.520003 0.300224i −0.216933 0.976186i \(-0.569605\pi\)
0.736936 + 0.675963i \(0.236272\pi\)
\(654\) 0 0
\(655\) 406.834 704.657i 0.621121 1.07581i
\(656\) −54.5036 + 31.4676i −0.0830847 + 0.0479690i
\(657\) 0 0
\(658\) 0 0
\(659\) 1266.54i 1.92191i 0.276701 + 0.960956i \(0.410759\pi\)
−0.276701 + 0.960956i \(0.589241\pi\)
\(660\) 0 0
\(661\) −458.822 + 794.703i −0.694133 + 1.20227i 0.276339 + 0.961060i \(0.410879\pi\)
−0.970472 + 0.241214i \(0.922454\pi\)
\(662\) −334.956 193.387i −0.505975 0.292125i
\(663\) 0 0
\(664\) 340.664 0.513048
\(665\) 0 0
\(666\) 0 0
\(667\) 105.911 + 183.443i 0.158787 + 0.275028i
\(668\) 208.613 + 120.443i 0.312295 + 0.180304i
\(669\) 0 0
\(670\) −230.672 399.535i −0.344286 0.596322i
\(671\) 1785.41i 2.66083i
\(672\) 0 0
\(673\) −152.008 −0.225866 −0.112933 0.993603i \(-0.536025\pi\)
−0.112933 + 0.993603i \(0.536025\pi\)
\(674\) 417.841 241.241i 0.619943 0.357924i
\(675\) 0 0
\(676\) −162.328 + 281.160i −0.240130 + 0.415918i
\(677\) 141.316 81.5891i 0.208739 0.120516i −0.391986 0.919971i \(-0.628212\pi\)
0.600725 + 0.799456i \(0.294879\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 650.997i 0.957348i
\(681\) 0 0
\(682\) 216.000 374.123i 0.316716 0.548567i
\(683\) 281.384 + 162.457i 0.411982 + 0.237858i 0.691641 0.722241i \(-0.256888\pi\)
−0.279659 + 0.960099i \(0.590221\pi\)
\(684\) 0 0
\(685\) 951.061 1.38841
\(686\) 0 0
\(687\) 0 0
\(688\) 86.9961 + 150.682i 0.126448 + 0.219014i
\(689\) 191.387 + 110.497i 0.277775 + 0.160373i
\(690\) 0 0
\(691\) −609.490 1055.67i −0.882041 1.52774i −0.849068 0.528283i \(-0.822836\pi\)
−0.0329725 0.999456i \(-0.510497\pi\)
\(692\) 183.722i 0.265494i
\(693\) 0 0
\(694\) 164.502 0.237035
\(695\) −934.892 + 539.760i −1.34517 + 0.776633i
\(696\) 0 0
\(697\) 203.502 352.476i 0.291968 0.505704i
\(698\) 193.907 111.952i 0.277803 0.160390i
\(699\) 0 0
\(700\) 0 0
\(701\) 427.202i 0.609417i −0.952446 0.304709i \(-0.901441\pi\)
0.952446 0.304709i \(-0.0985591\pi\)
\(702\) 0 0
\(703\) −380.000 + 658.179i −0.540541 + 0.936244i
\(704\) 123.288 + 71.1802i 0.175125 + 0.101108i
\(705\) 0 0
\(706\) −325.749 −0.461401
\(707\) 0 0
\(708\) 0 0
\(709\) −35.7490 61.9191i −0.0504217 0.0873330i 0.839713 0.543031i \(-0.182723\pi\)
−0.890135 + 0.455697i \(0.849390\pi\)
\(710\) −193.916 111.958i −0.273122 0.157687i
\(711\) 0 0
\(712\) −197.247 341.642i −0.277032 0.479834i
\(713\) 305.470i 0.428429i
\(714\) 0 0
\(715\) −408.972 −0.571989
\(716\) −230.867 + 133.291i −0.322440 + 0.186161i
\(717\) 0 0
\(718\) −121.409 + 210.287i −0.169093 + 0.292879i
\(719\) −96.1545 + 55.5148i −0.133734 + 0.0772112i −0.565374 0.824835i \(-0.691268\pi\)
0.431641 + 0.902046i \(0.357935\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 55.1543i 0.0763910i
\(723\) 0 0
\(724\) 83.0850 143.907i 0.114758 0.198767i
\(725\) 558.380 + 322.381i 0.770179 + 0.444663i
\(726\) 0 0
\(727\) −1338.82 −1.84157 −0.920783 0.390076i \(-0.872449\pi\)
−0.920783 + 0.390076i \(0.872449\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −181.919 315.093i −0.249204 0.431634i
\(731\) −974.461 562.606i −1.33305 0.769638i
\(732\) 0 0
\(733\) −24.5385 42.5020i −0.0334769 0.0579836i 0.848802 0.528712i \(-0.177325\pi\)
−0.882278 + 0.470728i \(0.843991\pi\)
\(734\) 731.842i 0.997059i
\(735\) 0 0
\(736\) 100.664 0.136772
\(737\) 565.028 326.219i 0.766660 0.442631i
\(738\) 0 0
\(739\) −715.158 + 1238.69i −0.967738 + 1.67617i −0.265665 + 0.964065i \(0.585592\pi\)
−0.702073 + 0.712105i \(0.747742\pi\)
\(740\) −585.617 + 338.106i −0.791374 + 0.456900i
\(741\) 0 0
\(742\) 0 0
\(743\) 875.736i 1.17865i 0.807896 + 0.589325i \(0.200606\pi\)
−0.807896 + 0.589325i \(0.799394\pi\)
\(744\) 0 0
\(745\) −78.6314 + 136.194i −0.105546 + 0.182810i
\(746\) −285.777 164.993i −0.383079 0.221171i
\(747\) 0 0
\(748\) −920.648 −1.23081
\(749\) 0 0
\(750\) 0 0
\(751\) −160.413 277.844i −0.213599 0.369965i 0.739239 0.673443i \(-0.235185\pi\)
−0.952838 + 0.303478i \(0.901852\pi\)
\(752\) 58.7878 + 33.9411i 0.0781752 + 0.0451345i
\(753\) 0 0
\(754\) −21.7411 37.6568i −0.0288344 0.0499427i
\(755\) 452.297i 0.599069i
\(756\) 0 0
\(757\) 289.830 0.382867 0.191433 0.981506i \(-0.438686\pi\)
0.191433 + 0.981506i \(0.438686\pi\)
\(758\) −540.316 + 311.951i −0.712818 + 0.411545i
\(759\) 0 0
\(760\) 251.660 435.888i 0.331132 0.573537i
\(761\) −610.251 + 352.329i −0.801907 + 0.462981i −0.844137 0.536127i \(-0.819887\pi\)
0.0422307 + 0.999108i \(0.486554\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 82.7231i 0.108276i
\(765\) 0 0
\(766\) 150.656 260.944i 0.196679 0.340658i
\(767\) −3.68870 2.12967i −0.00480926 0.00277663i
\(768\) 0 0
\(769\) −117.320 −0.152562 −0.0762810 0.997086i \(-0.524305\pi\)
−0.0762810 + 0.997086i \(0.524305\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 134.000 + 232.095i 0.173575 + 0.300641i
\(773\) −569.849 329.002i −0.737191 0.425618i 0.0838559 0.996478i \(-0.473276\pi\)
−0.821047 + 0.570860i \(0.806610\pi\)
\(774\) 0 0
\(775\) −464.907 805.243i −0.599880 1.03902i
\(776\) 125.619i 0.161880i
\(777\) 0 0
\(778\) −799.166 −1.02721
\(779\) −272.518 + 157.338i −0.349830 + 0.201975i
\(780\) 0 0
\(781\) 158.332 274.239i 0.202730 0.351138i
\(782\) −563.780 + 325.498i −0.720946 + 0.416238i
\(783\) 0 0
\(784\) 0 0
\(785\) 613.894i 0.782031i
\(786\) 0 0
\(787\) 600.324 1039.79i 0.762801 1.32121i −0.178601 0.983922i \(-0.557157\pi\)
0.941402 0.337288i \(-0.109510\pi\)
\(788\) −119.212 68.8269i −0.151284 0.0873438i
\(789\) 0 0
\(790\) 1488.97