Properties

Label 76.5.j.a.33.7
Level $76$
Weight $5$
Character 76.33
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 33.7
Character \(\chi\) \(=\) 76.33
Dual form 76.5.j.a.53.7

$q$-expansion

\(f(q)\) \(=\) \(q+(14.9907 + 2.64326i) q^{3} +(1.74782 + 1.46659i) q^{5} +(22.6416 + 39.2164i) q^{7} +(141.618 + 51.5447i) q^{9} +O(q^{10})\) \(q+(14.9907 + 2.64326i) q^{3} +(1.74782 + 1.46659i) q^{5} +(22.6416 + 39.2164i) q^{7} +(141.618 + 51.5447i) q^{9} +(51.9608 - 89.9988i) q^{11} +(-220.896 + 38.9500i) q^{13} +(22.3243 + 26.6051i) q^{15} +(-69.3454 + 25.2397i) q^{17} +(340.990 + 118.520i) q^{19} +(235.753 + 647.727i) q^{21} +(547.158 - 459.120i) q^{23} +(-107.626 - 610.378i) q^{25} +(918.911 + 530.533i) q^{27} +(-295.925 + 813.048i) q^{29} +(-723.951 + 417.974i) q^{31} +(1016.82 - 1211.79i) q^{33} +(-17.9411 + 101.749i) q^{35} -603.379i q^{37} -3414.34 q^{39} +(-1040.36 - 183.444i) q^{41} +(-2617.31 - 2196.19i) q^{43} +(171.927 + 297.786i) q^{45} +(-1022.17 - 372.038i) q^{47} +(175.216 - 303.482i) q^{49} +(-1106.25 + 195.061i) q^{51} +(-1040.77 - 1240.34i) q^{53} +(222.810 - 81.0960i) q^{55} +(4798.38 + 2678.01i) q^{57} +(-653.388 - 1795.17i) q^{59} +(2687.88 - 2255.40i) q^{61} +(1185.06 + 6720.80i) q^{63} +(-443.210 - 255.888i) q^{65} +(-1445.83 + 3972.38i) q^{67} +(9415.82 - 5436.23i) q^{69} +(-3642.09 + 4340.47i) q^{71} +(-337.943 + 1916.57i) q^{73} -9434.45i q^{75} +4705.90 q^{77} +(-6050.83 - 1066.92i) q^{79} +(3021.46 + 2535.30i) q^{81} +(3629.32 + 6286.16i) q^{83} +(-158.219 - 57.5872i) q^{85} +(-6585.21 + 11405.9i) q^{87} +(10477.3 - 1847.43i) q^{89} +(-6528.93 - 7780.87i) q^{91} +(-11957.3 + 4352.11i) q^{93} +(422.168 + 707.244i) q^{95} +(-4970.62 - 13656.7i) q^{97} +(11997.5 - 10067.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 14.9907 + 2.64326i 1.66563 + 0.293695i 0.925494 0.378763i \(-0.123651\pi\)
0.740135 + 0.672459i \(0.234762\pi\)
\(4\) 0 0
\(5\) 1.74782 + 1.46659i 0.0699127 + 0.0586637i 0.677074 0.735915i \(-0.263248\pi\)
−0.607162 + 0.794578i \(0.707692\pi\)
\(6\) 0 0
\(7\) 22.6416 + 39.2164i 0.462074 + 0.800335i 0.999064 0.0432534i \(-0.0137723\pi\)
−0.536991 + 0.843588i \(0.680439\pi\)
\(8\) 0 0
\(9\) 141.618 + 51.5447i 1.74837 + 0.636354i
\(10\) 0 0
\(11\) 51.9608 89.9988i 0.429428 0.743791i −0.567394 0.823446i \(-0.692048\pi\)
0.996823 + 0.0796549i \(0.0253818\pi\)
\(12\) 0 0
\(13\) −220.896 + 38.9500i −1.30708 + 0.230473i −0.783440 0.621467i \(-0.786537\pi\)
−0.523639 + 0.851940i \(0.675426\pi\)
\(14\) 0 0
\(15\) 22.3243 + 26.6051i 0.0992193 + 0.118245i
\(16\) 0 0
\(17\) −69.3454 + 25.2397i −0.239950 + 0.0873345i −0.459196 0.888335i \(-0.651862\pi\)
0.219246 + 0.975670i \(0.429640\pi\)
\(18\) 0 0
\(19\) 340.990 + 118.520i 0.944570 + 0.328309i
\(20\) 0 0
\(21\) 235.753 + 647.727i 0.534588 + 1.46877i
\(22\) 0 0
\(23\) 547.158 459.120i 1.03432 0.867901i 0.0429653 0.999077i \(-0.486320\pi\)
0.991359 + 0.131175i \(0.0418751\pi\)
\(24\) 0 0
\(25\) −107.626 610.378i −0.172202 0.976605i
\(26\) 0 0
\(27\) 918.911 + 530.533i 1.26051 + 0.727755i
\(28\) 0 0
\(29\) −295.925 + 813.048i −0.351873 + 0.966763i 0.629895 + 0.776680i \(0.283098\pi\)
−0.981768 + 0.190083i \(0.939124\pi\)
\(30\) 0 0
\(31\) −723.951 + 417.974i −0.753331 + 0.434936i −0.826896 0.562354i \(-0.809896\pi\)
0.0735650 + 0.997290i \(0.476562\pi\)
\(32\) 0 0
\(33\) 1016.82 1211.79i 0.933716 1.11276i
\(34\) 0 0
\(35\) −17.9411 + 101.749i −0.0146458 + 0.0830605i
\(36\) 0 0
\(37\) 603.379i 0.440744i −0.975416 0.220372i \(-0.929273\pi\)
0.975416 0.220372i \(-0.0707272\pi\)
\(38\) 0 0
\(39\) −3414.34 −2.24480
\(40\) 0 0
\(41\) −1040.36 183.444i −0.618894 0.109128i −0.144594 0.989491i \(-0.546188\pi\)
−0.474300 + 0.880363i \(0.657299\pi\)
\(42\) 0 0
\(43\) −2617.31 2196.19i −1.41553 1.18777i −0.953685 0.300808i \(-0.902744\pi\)
−0.461844 0.886961i \(-0.652812\pi\)
\(44\) 0 0
\(45\) 171.927 + 297.786i 0.0849022 + 0.147055i
\(46\) 0 0
\(47\) −1022.17 372.038i −0.462728 0.168419i 0.100128 0.994975i \(-0.468075\pi\)
−0.562855 + 0.826555i \(0.690297\pi\)
\(48\) 0 0
\(49\) 175.216 303.482i 0.0729761 0.126398i
\(50\) 0 0
\(51\) −1106.25 + 195.061i −0.425317 + 0.0749948i
\(52\) 0 0
\(53\) −1040.77 1240.34i −0.370512 0.441559i 0.548284 0.836292i \(-0.315281\pi\)
−0.918796 + 0.394734i \(0.870837\pi\)
\(54\) 0 0
\(55\) 222.810 81.0960i 0.0736560 0.0268086i
\(56\) 0 0
\(57\) 4798.38 + 2678.01i 1.47688 + 0.824257i
\(58\) 0 0
\(59\) −653.388 1795.17i −0.187701 0.515705i 0.809772 0.586744i \(-0.199591\pi\)
−0.997474 + 0.0710395i \(0.977368\pi\)
\(60\) 0 0
\(61\) 2687.88 2255.40i 0.722355 0.606128i −0.205680 0.978619i \(-0.565941\pi\)
0.928036 + 0.372491i \(0.121496\pi\)
\(62\) 0 0
\(63\) 1185.06 + 6720.80i 0.298578 + 1.69332i
\(64\) 0 0
\(65\) −443.210 255.888i −0.104902 0.0605651i
\(66\) 0 0
\(67\) −1445.83 + 3972.38i −0.322082 + 0.884914i 0.667967 + 0.744191i \(0.267165\pi\)
−0.990049 + 0.140723i \(0.955057\pi\)
\(68\) 0 0
\(69\) 9415.82 5436.23i 1.97770 1.14182i
\(70\) 0 0
\(71\) −3642.09 + 4340.47i −0.722493 + 0.861033i −0.994870 0.101157i \(-0.967746\pi\)
0.272378 + 0.962190i \(0.412190\pi\)
\(72\) 0 0
\(73\) −337.943 + 1916.57i −0.0634159 + 0.359649i 0.936543 + 0.350553i \(0.114007\pi\)
−0.999959 + 0.00909602i \(0.997105\pi\)
\(74\) 0 0
\(75\) 9434.45i 1.67724i
\(76\) 0 0
\(77\) 4705.90 0.793710
\(78\) 0 0
\(79\) −6050.83 1066.92i −0.969529 0.170954i −0.333611 0.942711i \(-0.608267\pi\)
−0.635918 + 0.771757i \(0.719378\pi\)
\(80\) 0 0
\(81\) 3021.46 + 2535.30i 0.460518 + 0.386420i
\(82\) 0 0
\(83\) 3629.32 + 6286.16i 0.526828 + 0.912493i 0.999511 + 0.0312603i \(0.00995207\pi\)
−0.472683 + 0.881232i \(0.656715\pi\)
\(84\) 0 0
\(85\) −158.219 57.5872i −0.0218989 0.00797054i
\(86\) 0 0
\(87\) −6585.21 + 11405.9i −0.870023 + 1.50692i
\(88\) 0 0
\(89\) 10477.3 1847.43i 1.32272 0.233232i 0.532697 0.846306i \(-0.321178\pi\)
0.790025 + 0.613074i \(0.210067\pi\)
\(90\) 0 0
\(91\) −6528.93 7780.87i −0.788423 0.939605i
\(92\) 0 0
\(93\) −11957.3 + 4352.11i −1.38251 + 0.503192i
\(94\) 0 0
\(95\) 422.168 + 707.244i 0.0467776 + 0.0783650i
\(96\) 0 0
\(97\) −4970.62 13656.7i −0.528284 1.45145i −0.861090 0.508452i \(-0.830218\pi\)
0.332807 0.942995i \(-0.392004\pi\)
\(98\) 0 0
\(99\) 11997.5 10067.1i 1.22411 1.02715i
\(100\) 0 0
\(101\) 3332.38 + 18898.8i 0.326672 + 1.85265i 0.497659 + 0.867373i \(0.334193\pi\)
−0.170987 + 0.985273i \(0.554696\pi\)
\(102\) 0 0
\(103\) 16336.7 + 9432.00i 1.53989 + 0.889056i 0.998844 + 0.0480638i \(0.0153051\pi\)
0.541047 + 0.840993i \(0.318028\pi\)
\(104\) 0 0
\(105\) −537.898 + 1477.86i −0.0487890 + 0.134047i
\(106\) 0 0
\(107\) 19063.0 11006.0i 1.66503 0.961307i 0.694777 0.719225i \(-0.255503\pi\)
0.970256 0.242082i \(-0.0778301\pi\)
\(108\) 0 0
\(109\) 2125.72 2533.33i 0.178918 0.213226i −0.669131 0.743145i \(-0.733333\pi\)
0.848048 + 0.529919i \(0.177778\pi\)
\(110\) 0 0
\(111\) 1594.89 9045.04i 0.129444 0.734116i
\(112\) 0 0
\(113\) 22240.3i 1.74174i 0.491512 + 0.870871i \(0.336444\pi\)
−0.491512 + 0.870871i \(0.663556\pi\)
\(114\) 0 0
\(115\) 1629.67 0.123227
\(116\) 0 0
\(117\) −33290.5 5870.02i −2.43192 0.428813i
\(118\) 0 0
\(119\) −2559.90 2148.01i −0.180771 0.151685i
\(120\) 0 0
\(121\) 1920.65 + 3326.66i 0.131183 + 0.227216i
\(122\) 0 0
\(123\) −15110.8 5499.88i −0.998796 0.363532i
\(124\) 0 0
\(125\) 1420.07 2459.63i 0.0908845 0.157416i
\(126\) 0 0
\(127\) −18978.7 + 3346.45i −1.17668 + 0.207480i −0.727594 0.686008i \(-0.759361\pi\)
−0.449086 + 0.893489i \(0.648250\pi\)
\(128\) 0 0
\(129\) −33430.1 39840.5i −2.00890 2.39412i
\(130\) 0 0
\(131\) −8075.04 + 2939.07i −0.470546 + 0.171265i −0.566400 0.824131i \(-0.691664\pi\)
0.0958537 + 0.995395i \(0.469442\pi\)
\(132\) 0 0
\(133\) 3072.64 + 16055.9i 0.173703 + 0.907676i
\(134\) 0 0
\(135\) 828.012 + 2274.94i 0.0454327 + 0.124825i
\(136\) 0 0
\(137\) 27262.3 22875.8i 1.45252 1.21881i 0.521800 0.853068i \(-0.325261\pi\)
0.930718 0.365739i \(-0.119184\pi\)
\(138\) 0 0
\(139\) −1315.13 7458.49i −0.0680675 0.386030i −0.999742 0.0227348i \(-0.992763\pi\)
0.931674 0.363295i \(-0.118348\pi\)
\(140\) 0 0
\(141\) −14339.5 8278.94i −0.721269 0.416425i
\(142\) 0 0
\(143\) −7972.50 + 21904.3i −0.389872 + 1.07117i
\(144\) 0 0
\(145\) −1709.63 + 987.057i −0.0813143 + 0.0469468i
\(146\) 0 0
\(147\) 3428.78 4086.26i 0.158674 0.189100i
\(148\) 0 0
\(149\) −3595.41 + 20390.6i −0.161948 + 0.918452i 0.790208 + 0.612839i \(0.209973\pi\)
−0.952156 + 0.305613i \(0.901139\pi\)
\(150\) 0 0
\(151\) 15854.9i 0.695359i −0.937613 0.347679i \(-0.886970\pi\)
0.937613 0.347679i \(-0.113030\pi\)
\(152\) 0 0
\(153\) −11121.5 −0.475096
\(154\) 0 0
\(155\) −1878.33 331.201i −0.0781824 0.0137857i
\(156\) 0 0
\(157\) 153.155 + 128.512i 0.00621343 + 0.00521369i 0.645889 0.763431i \(-0.276487\pi\)
−0.639676 + 0.768645i \(0.720931\pi\)
\(158\) 0 0
\(159\) −12323.3 21344.5i −0.487451 0.844290i
\(160\) 0 0
\(161\) 30393.6 + 11062.3i 1.17255 + 0.426772i
\(162\) 0 0
\(163\) −4690.34 + 8123.92i −0.176534 + 0.305767i −0.940691 0.339264i \(-0.889822\pi\)
0.764157 + 0.645031i \(0.223155\pi\)
\(164\) 0 0
\(165\) 3554.42 626.740i 0.130557 0.0230207i
\(166\) 0 0
\(167\) 32828.4 + 39123.3i 1.17711 + 1.40282i 0.896525 + 0.442994i \(0.146084\pi\)
0.280584 + 0.959830i \(0.409472\pi\)
\(168\) 0 0
\(169\) 20439.5 7439.38i 0.715645 0.260474i
\(170\) 0 0
\(171\) 42181.2 + 34360.7i 1.44254 + 1.17509i
\(172\) 0 0
\(173\) 12496.4 + 34333.7i 0.417536 + 1.14717i 0.953095 + 0.302673i \(0.0978789\pi\)
−0.535558 + 0.844498i \(0.679899\pi\)
\(174\) 0 0
\(175\) 21500.0 18040.7i 0.702041 0.589083i
\(176\) 0 0
\(177\) −5049.62 28637.8i −0.161180 0.914099i
\(178\) 0 0
\(179\) 18153.5 + 10480.9i 0.566570 + 0.327110i 0.755778 0.654827i \(-0.227259\pi\)
−0.189208 + 0.981937i \(0.560592\pi\)
\(180\) 0 0
\(181\) 1559.86 4285.68i 0.0476133 0.130816i −0.913607 0.406599i \(-0.866715\pi\)
0.961220 + 0.275782i \(0.0889369\pi\)
\(182\) 0 0
\(183\) 46254.8 26705.2i 1.38119 0.797432i
\(184\) 0 0
\(185\) 884.911 1054.60i 0.0258557 0.0308136i
\(186\) 0 0
\(187\) −1331.71 + 7552.48i −0.0380825 + 0.215976i
\(188\) 0 0
\(189\) 48048.5i 1.34511i
\(190\) 0 0
\(191\) −30053.3 −0.823806 −0.411903 0.911228i \(-0.635136\pi\)
−0.411903 + 0.911228i \(0.635136\pi\)
\(192\) 0 0
\(193\) 2660.50 + 469.117i 0.0714246 + 0.0125941i 0.209246 0.977863i \(-0.432899\pi\)
−0.137822 + 0.990457i \(0.544010\pi\)
\(194\) 0 0
\(195\) −5967.64 5007.44i −0.156940 0.131688i
\(196\) 0 0
\(197\) −21955.7 38028.4i −0.565738 0.979886i −0.996981 0.0776504i \(-0.975258\pi\)
0.431243 0.902236i \(-0.358075\pi\)
\(198\) 0 0
\(199\) −66862.0 24335.8i −1.68839 0.614524i −0.693969 0.720005i \(-0.744140\pi\)
−0.994421 + 0.105481i \(0.966362\pi\)
\(200\) 0 0
\(201\) −32173.9 + 55726.9i −0.796365 + 1.37934i
\(202\) 0 0
\(203\) −38585.0 + 6803.58i −0.936325 + 0.165099i
\(204\) 0 0
\(205\) −1549.32 1846.41i −0.0368667 0.0439360i
\(206\) 0 0
\(207\) 101152. 36816.5i 2.36067 0.859214i
\(208\) 0 0
\(209\) 28384.7 24530.3i 0.649819 0.561578i
\(210\) 0 0
\(211\) 5157.13 + 14169.1i 0.115836 + 0.318256i 0.984039 0.177952i \(-0.0569473\pi\)
−0.868203 + 0.496209i \(0.834725\pi\)
\(212\) 0 0
\(213\) −66070.2 + 55439.5i −1.45629 + 1.22197i
\(214\) 0 0
\(215\) −1353.67 7677.06i −0.0292844 0.166080i
\(216\) 0 0
\(217\) −32782.8 18927.2i −0.696189 0.401945i
\(218\) 0 0
\(219\) −10132.0 + 27837.4i −0.211255 + 0.580417i
\(220\) 0 0
\(221\) 14335.1 8276.36i 0.293505 0.169455i
\(222\) 0 0
\(223\) 7463.74 8894.94i 0.150088 0.178868i −0.685762 0.727826i \(-0.740531\pi\)
0.835850 + 0.548958i \(0.184975\pi\)
\(224\) 0 0
\(225\) 16220.0 91988.0i 0.320394 1.81705i
\(226\) 0 0
\(227\) 47690.9i 0.925515i 0.886485 + 0.462757i \(0.153140\pi\)
−0.886485 + 0.462757i \(0.846860\pi\)
\(228\) 0 0
\(229\) 19081.8 0.363872 0.181936 0.983310i \(-0.441764\pi\)
0.181936 + 0.983310i \(0.441764\pi\)
\(230\) 0 0
\(231\) 70544.6 + 12438.9i 1.32203 + 0.233109i
\(232\) 0 0
\(233\) 43461.8 + 36468.8i 0.800564 + 0.671753i 0.948336 0.317269i \(-0.102766\pi\)
−0.147772 + 0.989021i \(0.547210\pi\)
\(234\) 0 0
\(235\) −1240.93 2149.35i −0.0224705 0.0389200i
\(236\) 0 0
\(237\) −87885.7 31987.8i −1.56467 0.569492i
\(238\) 0 0
\(239\) 39853.0 69027.3i 0.697694 1.20844i −0.271571 0.962419i \(-0.587543\pi\)
0.969264 0.246022i \(-0.0791236\pi\)
\(240\) 0 0
\(241\) −29149.5 + 5139.84i −0.501876 + 0.0884943i −0.418854 0.908053i \(-0.637568\pi\)
−0.0830218 + 0.996548i \(0.526457\pi\)
\(242\) 0 0
\(243\) −16653.1 19846.4i −0.282022 0.336101i
\(244\) 0 0
\(245\) 751.329 273.462i 0.0125169 0.00455579i
\(246\) 0 0
\(247\) −79939.8 12899.0i −1.31029 0.211428i
\(248\) 0 0
\(249\) 37789.9 + 103827.i 0.609505 + 1.67460i
\(250\) 0 0
\(251\) −84937.6 + 71271.1i −1.34819 + 1.13127i −0.368756 + 0.929526i \(0.620216\pi\)
−0.979438 + 0.201743i \(0.935339\pi\)
\(252\) 0 0
\(253\) −12889.5 73099.7i −0.201369 1.14202i
\(254\) 0 0
\(255\) −2219.60 1281.48i −0.0341345 0.0197076i
\(256\) 0 0
\(257\) 19104.6 52489.5i 0.289249 0.794705i −0.706923 0.707290i \(-0.749917\pi\)
0.996172 0.0874145i \(-0.0278604\pi\)
\(258\) 0 0
\(259\) 23662.4 13661.5i 0.352743 0.203656i
\(260\) 0 0
\(261\) −83816.6 + 99888.7i −1.23041 + 1.46634i
\(262\) 0 0
\(263\) 17609.9 99870.8i 0.254593 1.44387i −0.542524 0.840040i \(-0.682531\pi\)
0.797116 0.603826i \(-0.206358\pi\)
\(264\) 0 0
\(265\) 3694.27i 0.0526062i
\(266\) 0 0
\(267\) 161945. 2.27166
\(268\) 0 0
\(269\) −41529.3 7322.74i −0.573919 0.101197i −0.120847 0.992671i \(-0.538561\pi\)
−0.453072 + 0.891474i \(0.649672\pi\)
\(270\) 0 0
\(271\) 31060.4 + 26062.8i 0.422930 + 0.354880i 0.829276 0.558839i \(-0.188753\pi\)
−0.406346 + 0.913719i \(0.633197\pi\)
\(272\) 0 0
\(273\) −77306.0 133898.i −1.03726 1.79659i
\(274\) 0 0
\(275\) −60525.6 22029.5i −0.800339 0.291299i
\(276\) 0 0
\(277\) −48837.0 + 84588.2i −0.636487 + 1.10243i 0.349711 + 0.936858i \(0.386280\pi\)
−0.986198 + 0.165570i \(0.947054\pi\)
\(278\) 0 0
\(279\) −124069. + 21876.7i −1.59387 + 0.281043i
\(280\) 0 0
\(281\) 2277.32 + 2714.00i 0.0288411 + 0.0343714i 0.780272 0.625440i \(-0.215081\pi\)
−0.751431 + 0.659812i \(0.770636\pi\)
\(282\) 0 0
\(283\) −12326.9 + 4486.61i −0.153915 + 0.0560203i −0.417829 0.908526i \(-0.637209\pi\)
0.263914 + 0.964546i \(0.414987\pi\)
\(284\) 0 0
\(285\) 4459.14 + 11717.9i 0.0548987 + 0.144265i
\(286\) 0 0
\(287\) −16361.4 44952.6i −0.198636 0.545747i
\(288\) 0 0
\(289\) −59809.0 + 50185.8i −0.716096 + 0.600876i
\(290\) 0 0
\(291\) −38414.8 217861.i −0.453641 2.57273i
\(292\) 0 0
\(293\) 71409.0 + 41228.0i 0.831797 + 0.480238i 0.854468 0.519505i \(-0.173883\pi\)
−0.0226704 + 0.999743i \(0.507217\pi\)
\(294\) 0 0
\(295\) 1490.78 4095.88i 0.0171305 0.0470655i
\(296\) 0 0
\(297\) 95494.7 55133.9i 1.08260 0.625037i
\(298\) 0 0
\(299\) −102982. + 122730.i −1.15192 + 1.37280i
\(300\) 0 0
\(301\) 26866.4 152367.i 0.296535 1.68173i
\(302\) 0 0
\(303\) 292114.i 3.18176i
\(304\) 0 0
\(305\) 8005.69 0.0860595
\(306\) 0 0
\(307\) 67311.4 + 11868.8i 0.714187 + 0.125930i 0.518924 0.854821i \(-0.326333\pi\)
0.195263 + 0.980751i \(0.437444\pi\)
\(308\) 0 0
\(309\) 219967. + 184574.i 2.30377 + 1.93310i
\(310\) 0 0
\(311\) −39321.7 68107.2i −0.406548 0.704162i 0.587952 0.808896i \(-0.299934\pi\)
−0.994500 + 0.104734i \(0.966601\pi\)
\(312\) 0 0
\(313\) 54369.8 + 19789.0i 0.554970 + 0.201992i 0.604253 0.796792i \(-0.293472\pi\)
−0.0492835 + 0.998785i \(0.515694\pi\)
\(314\) 0 0
\(315\) −7785.41 + 13484.7i −0.0784622 + 0.135900i
\(316\) 0 0
\(317\) 20211.3 3563.80i 0.201130 0.0354646i −0.0721755 0.997392i \(-0.522994\pi\)
0.273305 + 0.961927i \(0.411883\pi\)
\(318\) 0 0
\(319\) 57796.8 + 68879.5i 0.567966 + 0.676875i
\(320\) 0 0
\(321\) 314858. 114599.i 3.05566 1.11217i
\(322\) 0 0
\(323\) −26637.5 + 387.671i −0.255322 + 0.00371585i
\(324\) 0 0
\(325\) 47548.4 + 130638.i 0.450163 + 1.23681i
\(326\) 0 0
\(327\) 38562.2 32357.5i 0.360634 0.302608i
\(328\) 0 0
\(329\) −8553.48 48509.2i −0.0790226 0.448159i
\(330\) 0 0
\(331\) −74022.2 42736.8i −0.675626 0.390073i 0.122579 0.992459i \(-0.460883\pi\)
−0.798205 + 0.602386i \(0.794217\pi\)
\(332\) 0 0
\(333\) 31101.0 85449.2i 0.280469 0.770583i
\(334\) 0 0
\(335\) −8352.91 + 4822.55i −0.0744300 + 0.0429722i
\(336\) 0 0
\(337\) 106192. 126555.i 0.935043 1.11434i −0.0582025 0.998305i \(-0.518537\pi\)
0.993245 0.116036i \(-0.0370187\pi\)
\(338\) 0 0
\(339\) −58786.8 + 333397.i −0.511541 + 2.90109i
\(340\) 0 0
\(341\) 86873.0i 0.747095i
\(342\) 0 0
\(343\) 124594. 1.05903
\(344\) 0 0
\(345\) 24429.9 + 4307.65i 0.205250 + 0.0361911i
\(346\) 0 0
\(347\) −78074.5 65512.3i −0.648411 0.544081i 0.258178 0.966097i \(-0.416878\pi\)
−0.906588 + 0.422016i \(0.861322\pi\)
\(348\) 0 0
\(349\) 15832.1 + 27422.1i 0.129984 + 0.225138i 0.923670 0.383189i \(-0.125174\pi\)
−0.793686 + 0.608327i \(0.791841\pi\)
\(350\) 0 0
\(351\) −223648. 81401.3i −1.81531 0.660720i
\(352\) 0 0
\(353\) 24201.5 41918.2i 0.194219 0.336397i −0.752425 0.658678i \(-0.771116\pi\)
0.946644 + 0.322280i \(0.104449\pi\)
\(354\) 0 0
\(355\) −12731.4 + 2244.89i −0.101023 + 0.0178131i
\(356\) 0 0
\(357\) −32696.8 38966.6i −0.256548 0.305743i
\(358\) 0 0
\(359\) −5651.88 + 2057.12i −0.0438535 + 0.0159614i −0.363854 0.931456i \(-0.618539\pi\)
0.320000 + 0.947417i \(0.396317\pi\)
\(360\) 0 0
\(361\) 102227. + 80828.0i 0.784426 + 0.620223i
\(362\) 0 0
\(363\) 19998.6 + 54945.6i 0.151770 + 0.416984i
\(364\) 0 0
\(365\) −3401.49 + 2854.19i −0.0255320 + 0.0214239i
\(366\) 0 0
\(367\) 1654.48 + 9383.00i 0.0122837 + 0.0696642i 0.990333 0.138707i \(-0.0442948\pi\)
−0.978050 + 0.208372i \(0.933184\pi\)
\(368\) 0 0
\(369\) −137878. 79603.9i −1.01261 0.584631i
\(370\) 0 0
\(371\) 25077.0 68898.4i 0.182191 0.500566i
\(372\) 0 0
\(373\) −102897. + 59407.9i −0.739583 + 0.426998i −0.821918 0.569606i \(-0.807096\pi\)
0.0823346 + 0.996605i \(0.473762\pi\)
\(374\) 0 0
\(375\) 27789.2 33117.9i 0.197612 0.235505i
\(376\) 0 0
\(377\) 33700.6 191126.i 0.237113 1.34473i
\(378\) 0 0
\(379\) 198715.i 1.38341i 0.722178 + 0.691707i \(0.243141\pi\)
−0.722178 + 0.691707i \(0.756859\pi\)
\(380\) 0 0
\(381\) −293348. −2.02085
\(382\) 0 0
\(383\) −105698. 18637.4i −0.720557 0.127054i −0.198668 0.980067i \(-0.563662\pi\)
−0.521889 + 0.853013i \(0.674773\pi\)
\(384\) 0 0
\(385\) 8225.06 + 6901.64i 0.0554904 + 0.0465619i
\(386\) 0 0
\(387\) −257456. 445927.i −1.71902 2.97744i
\(388\) 0 0
\(389\) −62934.1 22906.1i −0.415898 0.151375i 0.125591 0.992082i \(-0.459917\pi\)
−0.541489 + 0.840708i \(0.682139\pi\)
\(390\) 0 0
\(391\) −26354.9 + 45647.9i −0.172388 + 0.298585i
\(392\) 0 0
\(393\) −128819. + 22714.2i −0.834054 + 0.147066i
\(394\) 0 0
\(395\) −9011.00 10738.9i −0.0577536 0.0688280i
\(396\) 0 0
\(397\) 75943.7 27641.3i 0.481849 0.175379i −0.0896634 0.995972i \(-0.528579\pi\)
0.571512 + 0.820593i \(0.306357\pi\)
\(398\) 0 0
\(399\) 3621.07 + 248810.i 0.0227453 + 1.56287i
\(400\) 0 0
\(401\) 59805.6 + 164315.i 0.371923 + 1.02185i 0.974617 + 0.223878i \(0.0718719\pi\)
−0.602694 + 0.797973i \(0.705906\pi\)
\(402\) 0 0
\(403\) 143638. 120527.i 0.884423 0.742119i
\(404\) 0 0
\(405\) 1562.70 + 8862.49i 0.00952719 + 0.0540314i
\(406\) 0 0
\(407\) −54303.3 31352.1i −0.327822 0.189268i
\(408\) 0 0
\(409\) −73359.1 + 201552.i −0.438538 + 1.20487i 0.501905 + 0.864923i \(0.332633\pi\)
−0.940443 + 0.339951i \(0.889590\pi\)
\(410\) 0 0
\(411\) 469146. 270862.i 2.77731 1.60348i
\(412\) 0 0
\(413\) 55606.3 66269.0i 0.326005 0.388517i
\(414\) 0 0
\(415\) −2875.86 + 16309.8i −0.0166983 + 0.0947005i
\(416\) 0 0
\(417\) 115284.i 0.662974i
\(418\) 0 0
\(419\) 55056.9 0.313606 0.156803 0.987630i \(-0.449881\pi\)
0.156803 + 0.987630i \(0.449881\pi\)
\(420\) 0 0
\(421\) −118222. 20845.8i −0.667015 0.117613i −0.170120 0.985423i \(-0.554416\pi\)
−0.496895 + 0.867811i \(0.665527\pi\)
\(422\) 0 0
\(423\) −125580. 105374.i −0.701844 0.588917i
\(424\) 0 0
\(425\) 22869.1 + 39610.5i 0.126611 + 0.219297i
\(426\) 0 0
\(427\) 149307. + 54343.2i 0.818887 + 0.298050i
\(428\) 0 0
\(429\) −177412. + 307286.i −0.963979 + 1.66966i
\(430\) 0 0
\(431\) −50451.8 + 8896.02i −0.271595 + 0.0478896i −0.307787 0.951455i \(-0.599588\pi\)
0.0361916 + 0.999345i \(0.488477\pi\)
\(432\) 0 0
\(433\) −98086.0 116894.i −0.523156 0.623473i 0.438168 0.898893i \(-0.355628\pi\)
−0.961324 + 0.275420i \(0.911183\pi\)
\(434\) 0 0
\(435\) −28237.6 + 10277.6i −0.149227 + 0.0543144i
\(436\) 0 0
\(437\) 240990. 91706.2i 1.26193 0.480215i
\(438\) 0 0
\(439\) 1574.10 + 4324.80i 0.00816776 + 0.0224407i 0.943710 0.330775i \(-0.107310\pi\)
−0.935542 + 0.353216i \(0.885088\pi\)
\(440\) 0 0
\(441\) 40456.5 33947.1i 0.208023 0.174552i
\(442\) 0 0
\(443\) −19737.6 111938.i −0.100574 0.570386i −0.992896 0.118986i \(-0.962036\pi\)
0.892321 0.451401i \(-0.149075\pi\)
\(444\) 0 0
\(445\) 21021.8 + 12136.9i 0.106157 + 0.0612900i
\(446\) 0 0
\(447\) −107795. + 296164.i −0.539490 + 1.48224i
\(448\) 0 0
\(449\) −143782. + 83012.8i −0.713203 + 0.411768i −0.812246 0.583315i \(-0.801755\pi\)
0.0990431 + 0.995083i \(0.468422\pi\)
\(450\) 0 0
\(451\) −70567.6 + 84099.2i −0.346939 + 0.413465i
\(452\) 0 0
\(453\) 41908.5 237675.i 0.204224 1.15821i
\(454\) 0 0
\(455\) 23174.8i 0.111942i
\(456\) 0 0
\(457\) 24060.3 0.115205 0.0576023 0.998340i \(-0.481654\pi\)
0.0576023 + 0.998340i \(0.481654\pi\)
\(458\) 0 0
\(459\) −77112.8 13597.1i −0.366017 0.0645386i
\(460\) 0 0
\(461\) −57941.6 48618.7i −0.272639 0.228771i 0.496209 0.868203i \(-0.334725\pi\)
−0.768848 + 0.639432i \(0.779170\pi\)
\(462\) 0 0
\(463\) 90196.5 + 156225.i 0.420754 + 0.728767i 0.996013 0.0892042i \(-0.0284324\pi\)
−0.575260 + 0.817971i \(0.695099\pi\)
\(464\) 0 0
\(465\) −27282.0 9929.83i −0.126174 0.0459236i
\(466\) 0 0
\(467\) 42977.3 74438.9i 0.197063 0.341324i −0.750512 0.660857i \(-0.770193\pi\)
0.947575 + 0.319534i \(0.103526\pi\)
\(468\) 0 0
\(469\) −188518. + 33240.9i −0.857053 + 0.151122i
\(470\) 0 0
\(471\) 1956.20 + 2331.31i 0.00881803 + 0.0105089i
\(472\) 0 0
\(473\) −333652. + 121439.i −1.49132 + 0.542796i
\(474\) 0 0
\(475\) 35642.4 220889.i 0.157972 0.979008i
\(476\) 0 0
\(477\) −83458.4 229300.i −0.366803 1.00778i
\(478\) 0 0
\(479\) 252890. 212200.i 1.10220 0.924857i 0.104631 0.994511i \(-0.466634\pi\)
0.997571 + 0.0696541i \(0.0221895\pi\)
\(480\) 0 0
\(481\) 23501.6 + 133284.i 0.101580 + 0.576088i
\(482\) 0 0
\(483\) 426379. + 246170.i 1.82768 + 1.05521i
\(484\) 0 0
\(485\) 11341.0 31159.2i 0.0482136 0.132466i
\(486\) 0 0
\(487\) 383052. 221155.i 1.61510 0.932480i 0.626941 0.779067i \(-0.284307\pi\)
0.988162 0.153413i \(-0.0490265\pi\)
\(488\) 0 0
\(489\) −91784.9 + 109385.i −0.383843 + 0.457446i
\(490\) 0 0
\(491\) −25947.9 + 147158.i −0.107631 + 0.610408i 0.882505 + 0.470302i \(0.155855\pi\)
−0.990137 + 0.140105i \(0.955256\pi\)
\(492\) 0 0
\(493\) 63850.2i 0.262705i
\(494\) 0 0
\(495\) 35733.9 0.145838
\(496\) 0 0
\(497\) −252680. 44554.4i −1.02296 0.180375i
\(498\) 0 0
\(499\) 81269.1 + 68192.9i 0.326381 + 0.273866i 0.791223 0.611528i \(-0.209445\pi\)
−0.464843 + 0.885393i \(0.653889\pi\)
\(500\) 0 0
\(501\) 388706. + 673258.i 1.54862 + 2.68229i
\(502\) 0 0
\(503\) −377464. 137385.i −1.49190 0.543006i −0.537949 0.842977i \(-0.680801\pi\)
−0.953948 + 0.299971i \(0.903023\pi\)
\(504\) 0 0
\(505\) −21892.5 + 37919.0i −0.0858446 + 0.148687i
\(506\) 0 0
\(507\) 326066. 57494.3i 1.26850 0.223671i
\(508\) 0 0
\(509\) −303927. 362206.i −1.17310 1.39804i −0.899908 0.436080i \(-0.856366\pi\)
−0.273188 0.961961i \(-0.588078\pi\)
\(510\) 0 0
\(511\) −82812.7 + 30141.3i −0.317143 + 0.115431i
\(512\) 0 0
\(513\) 250461. + 289816.i 0.951710 + 1.10125i
\(514\) 0 0
\(515\) 14720.7 + 40444.7i 0.0555026 + 0.152492i
\(516\) 0 0
\(517\) −86595.5 + 72662.2i −0.323977 + 0.271849i
\(518\) 0 0
\(519\) 96577.0 + 547716.i 0.358541 + 2.03339i
\(520\) 0 0
\(521\) 190978. + 110261.i 0.703569 + 0.406206i 0.808675 0.588255i \(-0.200185\pi\)
−0.105106 + 0.994461i \(0.533518\pi\)
\(522\) 0 0
\(523\) −52251.1 + 143559.i −0.191026 + 0.524839i −0.997820 0.0659933i \(-0.978978\pi\)
0.806794 + 0.590833i \(0.201201\pi\)
\(524\) 0 0
\(525\) 369985. 213611.i 1.34235 0.775006i
\(526\) 0 0
\(527\) 39653.2 47256.9i 0.142777 0.170155i
\(528\) 0 0
\(529\) 39996.6 226832.i 0.142926 0.810575i
\(530\) 0 0
\(531\) 287906.i 1.02109i
\(532\) 0 0
\(533\) 236957. 0.834094
\(534\) 0 0
\(535\) 49459.9 + 8721.11i 0.172801 + 0.0304694i
\(536\) 0 0
\(537\) 244429. + 205100.i 0.847625 + 0.711242i
\(538\) 0 0
\(539\) −18208.7 31538.4i −0.0626759 0.108558i
\(540\) 0 0
\(541\) 46433.1 + 16900.3i 0.158647 + 0.0577430i 0.420123 0.907467i \(-0.361987\pi\)
−0.261476 + 0.965210i \(0.584209\pi\)
\(542\) 0 0
\(543\) 34711.4 60122.0i 0.117726 0.203908i
\(544\) 0 0
\(545\) 7430.74 1310.24i 0.0250172 0.00441121i
\(546\) 0 0
\(547\) −250370. 298379.i −0.836773 0.997227i −0.999944 0.0106295i \(-0.996616\pi\)
0.163170 0.986598i \(-0.447828\pi\)
\(548\) 0 0
\(549\) 496906. 180859.i 1.64866 0.600061i
\(550\) 0 0
\(551\) −197270. + 242168.i −0.649766 + 0.797652i
\(552\) 0 0
\(553\) −95159.5 261449.i −0.311173 0.854941i
\(554\) 0 0
\(555\) 16053.0 13470.0i 0.0521158 0.0437303i
\(556\) 0 0
\(557\) 39569.2 + 224408.i 0.127540 + 0.723316i 0.979767 + 0.200143i \(0.0641406\pi\)
−0.852227 + 0.523173i \(0.824748\pi\)
\(558\) 0 0
\(559\) 663696. + 383185.i 2.12396 + 1.22627i
\(560\) 0 0
\(561\) −39926.3 + 109697.i −0.126862 + 0.348552i
\(562\) 0 0
\(563\) 55165.1 31849.6i 0.174040 0.100482i −0.410450 0.911883i \(-0.634628\pi\)
0.584489 + 0.811401i \(0.301295\pi\)
\(564\) 0 0
\(565\) −32617.5 + 38872.0i −0.102177 + 0.121770i
\(566\) 0 0
\(567\) −31014.9 + 175894.i −0.0964726 + 0.547123i
\(568\) 0 0
\(569\) 158917.i 0.490848i −0.969416 0.245424i \(-0.921073\pi\)
0.969416 0.245424i \(-0.0789271\pi\)
\(570\) 0 0
\(571\) −529437. −1.62384 −0.811918 0.583772i \(-0.801576\pi\)
−0.811918 + 0.583772i \(0.801576\pi\)
\(572\) 0 0
\(573\) −450518. 79438.5i −1.37216 0.241948i
\(574\) 0 0
\(575\) −339125. 284560.i −1.02571 0.860672i
\(576\) 0 0
\(577\) −178205. 308660.i −0.535264 0.927104i −0.999151 0.0412098i \(-0.986879\pi\)
0.463887 0.885895i \(-0.346455\pi\)
\(578\) 0 0
\(579\) 38642.6 + 14064.7i 0.115268 + 0.0419541i
\(580\) 0 0
\(581\) −164347. + 284658.i −0.486866 + 0.843277i
\(582\) 0 0
\(583\) −165708. + 29218.8i −0.487536 + 0.0859657i
\(584\) 0 0
\(585\) −49576.8 59083.4i −0.144866 0.172645i
\(586\) 0 0
\(587\) −486773. + 177171.i −1.41270 + 0.514181i −0.931922 0.362660i \(-0.881869\pi\)
−0.480780 + 0.876841i \(0.659646\pi\)
\(588\) 0 0
\(589\) −296398. + 56722.2i −0.854368 + 0.163502i
\(590\) 0 0
\(591\) −228612. 628105.i −0.654521 1.79828i
\(592\) 0 0
\(593\) 246993. 207252.i 0.702385 0.589371i −0.220066 0.975485i \(-0.570627\pi\)
0.922451 + 0.386114i \(0.126183\pi\)
\(594\) 0 0
\(595\) −1323.98 7508.67i −0.00373979 0.0212094i
\(596\) 0 0
\(597\) −937979. 541542.i −2.63175 1.51944i
\(598\) 0 0
\(599\) 73922.5 203100.i 0.206026 0.566053i −0.793044 0.609165i \(-0.791505\pi\)
0.999070 + 0.0431116i \(0.0137271\pi\)
\(600\) 0 0
\(601\) −289330. + 167045.i −0.801022 + 0.462470i −0.843828 0.536613i \(-0.819703\pi\)
0.0428067 + 0.999083i \(0.486370\pi\)
\(602\) 0 0
\(603\) −409510. + 488035.i −1.12624 + 1.34220i
\(604\) 0 0
\(605\) −1521.92 + 8631.21i −0.00415795 + 0.0235809i
\(606\) 0 0
\(607\) 313650.i 0.851271i −0.904895 0.425636i \(-0.860051\pi\)
0.904895 0.425636i \(-0.139949\pi\)
\(608\) 0 0
\(609\) −596399. −1.60806
\(610\) 0 0
\(611\) 240284. + 42368.5i 0.643638 + 0.113491i
\(612\) 0 0
\(613\) 59956.8 + 50309.7i 0.159557 + 0.133885i 0.719071 0.694937i \(-0.244568\pi\)
−0.559514 + 0.828821i \(0.689012\pi\)
\(614\) 0 0
\(615\) −18344.8 31774.2i −0.0485024 0.0840086i
\(616\) 0 0
\(617\) 360615. + 131253.i 0.947269 + 0.344778i 0.769032 0.639210i \(-0.220738\pi\)
0.178237 + 0.983988i \(0.442961\pi\)
\(618\) 0 0
\(619\) 267081. 462598.i 0.697046 1.20732i −0.272440 0.962173i \(-0.587831\pi\)
0.969486 0.245146i \(-0.0788360\pi\)
\(620\) 0 0
\(621\) 746367. 131605.i 1.93539 0.341262i
\(622\) 0 0
\(623\) 309672. + 369053.i 0.797859 + 0.950851i
\(624\) 0 0
\(625\) −357921. + 130272.i −0.916277 + 0.333498i
\(626\) 0 0
\(627\) 490346. 292697.i 1.24729 0.744531i
\(628\) 0 0
\(629\) 15229.1 + 41841.6i 0.0384922 + 0.105756i
\(630\) 0 0
\(631\) 307667. 258163.i 0.772720 0.648389i −0.168684 0.985670i \(-0.553952\pi\)
0.941404 + 0.337281i \(0.109507\pi\)
\(632\) 0 0
\(633\) 39856.2 + 226036.i 0.0994691 + 0.564117i
\(634\) 0 0
\(635\) −38079.1 21985.0i −0.0944364 0.0545229i
\(636\) 0 0
\(637\) −26883.8 + 73862.7i −0.0662541 + 0.182032i
\(638\) 0 0
\(639\) −739512. + 426958.i −1.81111 + 1.04564i
\(640\) 0 0
\(641\) 322528. 384374.i 0.784967 0.935487i −0.214179 0.976794i \(-0.568708\pi\)
0.999146 + 0.0413071i \(0.0131522\pi\)
\(642\) 0 0
\(643\) −94880.3 + 538093.i −0.229485 + 1.30147i 0.624438 + 0.781074i \(0.285328\pi\)
−0.853923 + 0.520399i \(0.825783\pi\)
\(644\) 0 0
\(645\) 118662.i 0.285229i
\(646\) 0 0
\(647\) 761998. 1.82031 0.910155 0.414268i \(-0.135962\pi\)
0.910155 + 0.414268i \(0.135962\pi\)
\(648\) 0 0
\(649\) −195513. 34474.3i −0.464181 0.0818476i
\(650\) 0 0
\(651\) −441407. 370384.i −1.04154 0.873958i
\(652\) 0 0
\(653\) 168084. + 291130.i 0.394185 + 0.682748i 0.992997 0.118141i \(-0.0376936\pi\)
−0.598812 + 0.800890i \(0.704360\pi\)
\(654\) 0 0
\(655\) −18424.1 6705.83i −0.0429442 0.0156304i
\(656\) 0 0
\(657\) −146648. + 254002.i −0.339739 + 0.588445i
\(658\) 0 0
\(659\) −446874. + 78796.0i −1.02900 + 0.181440i −0.662565 0.749004i \(-0.730532\pi\)
−0.366433 + 0.930444i \(0.619421\pi\)
\(660\) 0 0
\(661\) −57916.7 69022.4i −0.132556 0.157975i 0.695683 0.718349i \(-0.255102\pi\)
−0.828240 + 0.560374i \(0.810657\pi\)
\(662\) 0 0
\(663\) 236769. 86176.7i 0.538638 0.196048i
\(664\) 0 0
\(665\) −18177.0 + 32569.0i −0.0411036 + 0.0736481i
\(666\) 0 0
\(667\) 211369. + 580730.i 0.475104 + 1.30534i
\(668\) 0 0
\(669\) 135398. 113612.i 0.302524 0.253848i
\(670\) 0 0
\(671\) −63318.8 359099.i −0.140633 0.797570i
\(672\) 0 0
\(673\) −182103. 105137.i −0.402056 0.232127i 0.285315 0.958434i \(-0.407902\pi\)
−0.687371 + 0.726307i \(0.741235\pi\)
\(674\) 0 0
\(675\) 224927. 617982.i 0.493667 1.35634i
\(676\) 0 0
\(677\) 197145. 113821.i 0.430138 0.248340i −0.269268 0.963065i \(-0.586782\pi\)
0.699405 + 0.714725i \(0.253448\pi\)
\(678\) 0 0
\(679\) 423023. 504139.i 0.917538 1.09348i
\(680\) 0 0
\(681\) −126059. + 714917.i −0.271819 + 1.54156i
\(682\) 0 0
\(683\) 517412.i 1.10916i 0.832130 + 0.554581i \(0.187121\pi\)
−0.832130 + 0.554581i \(0.812879\pi\)
\(684\) 0 0
\(685\) 81199.0 0.173049
\(686\) 0 0
\(687\) 286049. + 50438.2i 0.606076 + 0.106868i
\(688\) 0 0
\(689\) 278213. + 233448.i 0.586056 + 0.491759i
\(690\) 0 0
\(691\) 151640. + 262647.i 0.317582 + 0.550069i 0.979983 0.199081i \(-0.0637957\pi\)
−0.662401 + 0.749150i \(0.730462\pi\)
\(692\) 0 0
\(693\) 666440. + 242564.i 1.38770 + 0.505080i
\(694\) 0 0
\(695\) 8639.96 14964.8i 0.0178872 0.0309815i
\(696\) 0 0
\(697\) 76774.3 13537.4i 0.158034 0.0278656i
\(698\) 0 0
\(699\) 555125. + 661572.i 1.13615 + 1.35401i
\(700\) 0 0
\(701\) −161694. + 58851.8i −0.329047 + 0.119763i −0.501261 0.865296i \(-0.667130\pi\)
0.172214 + 0.985060i \(0.444908\pi\)
\(702\) 0 0
\(703\) 71512.3 205746.i 0.144701 0.416314i
\(704\) 0 0
\(705\) −12921.1 35500.3i −0.0259968 0.0714257i
\(706\) 0 0
\(707\) −665694. + 558584.i −1.33179 + 1.11751i
\(708\) 0 0
\(709\) −153332. 869587.i −0.305028 1.72990i −0.623374 0.781924i \(-0.714239\pi\)
0.318347 0.947974i \(-0.396872\pi\)
\(710\) 0 0
\(711\) −801911. 462983.i −1.58631 0.915854i
\(712\) 0 0
\(713\) −204216. + 561078.i −0.401708 + 1.10368i
\(714\) 0 0
\(715\) −46059.1 + 26592.2i −0.0900956 + 0.0520167i
\(716\) 0 0
\(717\) 779879. 929424.i 1.51701 1.80790i
\(718\) 0 0
\(719\) 82145.5 465870.i 0.158901 0.901171i −0.796232 0.604992i \(-0.793176\pi\)
0.955132 0.296179i \(-0.0957125\pi\)
\(720\) 0 0
\(721\) 854222.i 1.64324i
\(722\) 0 0
\(723\) −450556. −0.861929
\(724\) 0 0
\(725\) 528116. + 93121.1i 1.00474 + 0.177163i
\(726\) 0 0
\(727\) −333613. 279935.i −0.631210 0.529648i 0.270094 0.962834i \(-0.412945\pi\)
−0.901305 + 0.433185i \(0.857390\pi\)
\(728\) 0 0
\(729\) −356923. 618210.i −0.671614 1.16327i
\(730\) 0 0
\(731\) 236930. + 86235.3i 0.443389 + 0.161380i
\(732\) 0 0
\(733\) 298467. 516959.i 0.555505 0.962162i −0.442359 0.896838i \(-0.645858\pi\)
0.997864 0.0653246i \(-0.0208083\pi\)
\(734\) 0 0
\(735\) 11985.7 2113.41i 0.0221866 0.00391209i
\(736\) 0 0
\(737\) 282383. + 336531.i 0.519880 + 0.619569i
\(738\) 0 0
\(739\) −581638. + 211699.i −1.06504 + 0.387641i −0.814318 0.580419i \(-0.802889\pi\)
−0.250718 + 0.968060i \(0.580667\pi\)
\(740\) 0 0
\(741\) −1.16425e6 404666.i −2.12037 0.736988i
\(742\) 0 0
\(743\) 212892. + 584915.i 0.385639 + 1.05953i 0.968944 + 0.247281i \(0.0795370\pi\)
−0.583305 + 0.812253i \(0.698241\pi\)
\(744\) 0 0
\(745\) −36188.8 + 30366.0i −0.0652020 + 0.0547110i
\(746\) 0 0
\(747\) 189958. + 1.07730e6i 0.340421 + 1.93062i
\(748\) 0 0
\(749\) 863232. + 498387.i 1.53874 + 0.888389i
\(750\) 0 0
\(751\) 60368.6 165861.i 0.107036 0.294080i −0.874599 0.484847i \(-0.838875\pi\)
0.981635 + 0.190767i \(0.0610975\pi\)
\(752\) 0 0
\(753\) −1.46166e6 + 843889.i −2.57784 + 1.48832i
\(754\) 0 0
\(755\) 23252.6 27711.4i 0.0407923 0.0486144i
\(756\) 0 0
\(757\) 48880.6 277216.i 0.0852992 0.483756i −0.911992 0.410207i \(-0.865456\pi\)
0.997292 0.0735486i \(-0.0234324\pi\)
\(758\) 0 0
\(759\) 1.12988e6i 1.96133i
\(760\) 0 0
\(761\) 877643. 1.51547 0.757737 0.652560i \(-0.226305\pi\)
0.757737 + 0.652560i \(0.226305\pi\)
\(762\) 0 0
\(763\) 147478. + 26004.4i 0.253325 + 0.0446680i
\(764\) 0 0
\(765\) −19438.4 16310.7i −0.0332152 0.0278709i
\(766\) 0 0
\(767\) 214253. + 371097.i 0.364196 + 0.630807i
\(768\) 0 0
\(769\) 802513. + 292091.i 1.35706 + 0.493930i 0.915145 0.403126i \(-0.132076\pi\)
0.441917 + 0.897056i \(0.354298\pi\)
\(770\) 0 0
\(771\) 425134. 736353.i 0.715182 1.23873i
\(772\) 0 0
\(773\) 772475. 136208.i 1.29278 0.227953i 0.515384 0.856960i \(-0.327649\pi\)
0.777400 + 0.629007i \(0.216538\pi\)
\(774\) 0 0
\(775\) 333038. + 396899.i 0.554486 + 0.660810i
\(776\) 0 0
\(777\) 390825. 142249.i 0.647352 0.235617i
\(778\) 0 0
\(779\) −333011. 185856.i −0.548761 0.306267i
\(780\) 0 0
\(781\) 201391. + 553318.i 0.330170 + 0.907136i
\(782\) 0 0
\(783\) −703278. + 590120.i −1.14711 + 0.962536i
\(784\) 0 0
\(785\) 79.2117 + 449.232i 0.000128543 + 0.000729006i
\(786\) 0 0
\(787\) 70058.3 + 40448.2i 0.113112 + 0.0653054i 0.555489 0.831524i \(-0.312531\pi\)
−0.442377 + 0.896829i \(0.645865\pi\)
\(788\) 0 0
\(789\) 527968. 1.45058e6i 0.848113 2.33017i
\(790\) 0 0
\(791\) −872185. + 503556.i −1.39398 + 0.804813i
\(792\) 0 0