Properties

Label 378.3.s.d.53.4
Level $378$
Weight $3$
Character 378.53
Analytic conductor $10.300$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 378.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.2997539928\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.621801639936.1
Defining polynomial: \( x^{8} - 4x^{7} - 34x^{6} + 116x^{5} + 413x^{4} - 1024x^{3} - 1664x^{2} + 2196x + 4467 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 53.4
Root \(2.31664 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 378.53
Dual form 378.3.s.d.107.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.33729 - 2.50413i) q^{5} +(0.0413813 - 6.99988i) q^{7} -2.82843i q^{8} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(4.33729 - 2.50413i) q^{5} +(0.0413813 - 6.99988i) q^{7} -2.82843i q^{8} +(3.54138 - 6.13385i) q^{10} +(-1.32611 - 0.765629i) q^{11} +0.917237 q^{13} +(-4.89898 - 8.60233i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-14.3380 - 8.27803i) q^{17} +(6.50000 + 11.2583i) q^{19} -10.0165i q^{20} -2.16553 q^{22} +(10.3596 - 5.98115i) q^{23} +(0.0413813 - 0.0716745i) q^{25} +(1.12338 - 0.648585i) q^{26} +(-12.0828 - 7.07155i) q^{28} -33.5266i q^{29} +(8.66553 - 15.0091i) q^{31} +(-4.89898 - 2.82843i) q^{32} -23.4138 q^{34} +(-17.3492 - 30.4641i) q^{35} +(27.8724 + 48.2765i) q^{37} +(15.9217 + 9.19239i) q^{38} +(-7.08276 - 12.2677i) q^{40} -6.53953i q^{41} +32.7449 q^{43} +(-2.65222 + 1.53126i) q^{44} +(8.45862 - 14.6508i) q^{46} +(46.3841 - 26.7799i) q^{47} +(-48.9966 - 0.579328i) q^{49} -0.117044i q^{50} +(0.917237 - 1.58870i) q^{52} +(-72.4078 - 41.8047i) q^{53} -7.66895 q^{55} +(-19.7986 - 0.117044i) q^{56} +(-23.7069 - 41.0616i) q^{58} +(41.4386 + 23.9246i) q^{59} +(40.2897 + 69.7838i) q^{61} -24.5098i q^{62} -8.00000 q^{64} +(3.97832 - 2.29689i) q^{65} +(1.21033 - 2.09636i) q^{67} +(-28.6759 + 16.5561i) q^{68} +(-42.7897 - 25.0431i) q^{70} -83.3216i q^{71} +(-36.0414 + 62.4255i) q^{73} +(68.2732 + 39.4176i) q^{74} +26.0000 q^{76} +(-5.41418 + 9.25091i) q^{77} +(61.1655 + 105.942i) q^{79} +(-17.3492 - 10.0165i) q^{80} +(-4.62414 - 8.00925i) q^{82} +158.860i q^{83} -82.9172 q^{85} +(40.1041 - 23.1541i) q^{86} +(-2.16553 + 3.75080i) q^{88} +(-46.9922 + 27.1310i) q^{89} +(0.0379564 - 6.42055i) q^{91} -23.9246i q^{92} +(37.8724 - 65.5970i) q^{94} +(56.3848 + 32.5538i) q^{95} +12.0828 q^{97} +(-60.4180 + 33.9363i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} - 24 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 24 q^{7} + 4 q^{10} + 56 q^{13} - 16 q^{16} + 52 q^{19} + 80 q^{22} - 24 q^{25} - 48 q^{28} - 28 q^{31} + 56 q^{34} + 4 q^{37} - 8 q^{40} - 176 q^{43} + 92 q^{46} - 100 q^{49} + 56 q^{52} - 256 q^{55} - 68 q^{58} + 152 q^{61} - 64 q^{64} + 180 q^{67} - 172 q^{70} - 264 q^{73} + 208 q^{76} + 392 q^{79} + 36 q^{82} - 712 q^{85} + 80 q^{88} - 316 q^{91} + 84 q^{94} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 0.707107i 0.612372 0.353553i
\(3\) 0 0
\(4\) 1.00000 1.73205i 0.250000 0.433013i
\(5\) 4.33729 2.50413i 0.867458 0.500827i 0.000955133 1.00000i \(-0.499696\pi\)
0.866503 + 0.499173i \(0.166363\pi\)
\(6\) 0 0
\(7\) 0.0413813 6.99988i 0.00591161 0.999983i
\(8\) 2.82843i 0.353553i
\(9\) 0 0
\(10\) 3.54138 6.13385i 0.354138 0.613385i
\(11\) −1.32611 0.765629i −0.120555 0.0696026i 0.438510 0.898726i \(-0.355506\pi\)
−0.559065 + 0.829124i \(0.688840\pi\)
\(12\) 0 0
\(13\) 0.917237 0.0705567 0.0352784 0.999378i \(-0.488768\pi\)
0.0352784 + 0.999378i \(0.488768\pi\)
\(14\) −4.89898 8.60233i −0.349927 0.614452i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −14.3380 8.27803i −0.843410 0.486943i 0.0150117 0.999887i \(-0.495221\pi\)
−0.858422 + 0.512944i \(0.828555\pi\)
\(18\) 0 0
\(19\) 6.50000 + 11.2583i 0.342105 + 0.592544i 0.984823 0.173559i \(-0.0555267\pi\)
−0.642718 + 0.766103i \(0.722193\pi\)
\(20\) 10.0165i 0.500827i
\(21\) 0 0
\(22\) −2.16553 −0.0984330
\(23\) 10.3596 5.98115i 0.450420 0.260050i −0.257588 0.966255i \(-0.582928\pi\)
0.708007 + 0.706205i \(0.249594\pi\)
\(24\) 0 0
\(25\) 0.0413813 0.0716745i 0.00165525 0.00286698i
\(26\) 1.12338 0.648585i 0.0432070 0.0249456i
\(27\) 0 0
\(28\) −12.0828 7.07155i −0.431527 0.252555i
\(29\) 33.5266i 1.15609i −0.816005 0.578045i \(-0.803816\pi\)
0.816005 0.578045i \(-0.196184\pi\)
\(30\) 0 0
\(31\) 8.66553 15.0091i 0.279533 0.484165i −0.691736 0.722151i \(-0.743154\pi\)
0.971269 + 0.237985i \(0.0764870\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) 0 0
\(34\) −23.4138 −0.688642
\(35\) −17.3492 30.4641i −0.495690 0.870403i
\(36\) 0 0
\(37\) 27.8724 + 48.2765i 0.753309 + 1.30477i 0.946211 + 0.323551i \(0.104877\pi\)
−0.192902 + 0.981218i \(0.561790\pi\)
\(38\) 15.9217 + 9.19239i 0.418992 + 0.241905i
\(39\) 0 0
\(40\) −7.08276 12.2677i −0.177069 0.306693i
\(41\) 6.53953i 0.159501i −0.996815 0.0797503i \(-0.974588\pi\)
0.996815 0.0797503i \(-0.0254123\pi\)
\(42\) 0 0
\(43\) 32.7449 0.761508 0.380754 0.924676i \(-0.375664\pi\)
0.380754 + 0.924676i \(0.375664\pi\)
\(44\) −2.65222 + 1.53126i −0.0602776 + 0.0348013i
\(45\) 0 0
\(46\) 8.45862 14.6508i 0.183883 0.318495i
\(47\) 46.3841 26.7799i 0.986895 0.569784i 0.0825503 0.996587i \(-0.473693\pi\)
0.904345 + 0.426803i \(0.140360\pi\)
\(48\) 0 0
\(49\) −48.9966 0.579328i −0.999930 0.0118230i
\(50\) 0.117044i 0.00234088i
\(51\) 0 0
\(52\) 0.917237 1.58870i 0.0176392 0.0305520i
\(53\) −72.4078 41.8047i −1.36618 0.788767i −0.375746 0.926723i \(-0.622614\pi\)
−0.990438 + 0.137955i \(0.955947\pi\)
\(54\) 0 0
\(55\) −7.66895 −0.139435
\(56\) −19.7986 0.117044i −0.353547 0.00209007i
\(57\) 0 0
\(58\) −23.7069 41.0616i −0.408740 0.707958i
\(59\) 41.4386 + 23.9246i 0.702349 + 0.405501i 0.808222 0.588878i \(-0.200430\pi\)
−0.105873 + 0.994380i \(0.533764\pi\)
\(60\) 0 0
\(61\) 40.2897 + 69.7838i 0.660486 + 1.14400i 0.980488 + 0.196579i \(0.0629832\pi\)
−0.320002 + 0.947417i \(0.603683\pi\)
\(62\) 24.5098i 0.395319i
\(63\) 0 0
\(64\) −8.00000 −0.125000
\(65\) 3.97832 2.29689i 0.0612050 0.0353367i
\(66\) 0 0
\(67\) 1.21033 2.09636i 0.0180646 0.0312889i −0.856852 0.515563i \(-0.827583\pi\)
0.874916 + 0.484274i \(0.160916\pi\)
\(68\) −28.6759 + 16.5561i −0.421705 + 0.243472i
\(69\) 0 0
\(70\) −42.7897 25.0431i −0.611281 0.357758i
\(71\) 83.3216i 1.17354i −0.809753 0.586772i \(-0.800399\pi\)
0.809753 0.586772i \(-0.199601\pi\)
\(72\) 0 0
\(73\) −36.0414 + 62.4255i −0.493718 + 0.855144i −0.999974 0.00723922i \(-0.997696\pi\)
0.506256 + 0.862383i \(0.331029\pi\)
\(74\) 68.2732 + 39.4176i 0.922611 + 0.532670i
\(75\) 0 0
\(76\) 26.0000 0.342105
\(77\) −5.41418 + 9.25091i −0.0703141 + 0.120142i
\(78\) 0 0
\(79\) 61.1655 + 105.942i 0.774247 + 1.34104i 0.935217 + 0.354076i \(0.115205\pi\)
−0.160969 + 0.986959i \(0.551462\pi\)
\(80\) −17.3492 10.0165i −0.216864 0.125207i
\(81\) 0 0
\(82\) −4.62414 8.00925i −0.0563920 0.0976738i
\(83\) 158.860i 1.91398i 0.290126 + 0.956989i \(0.406303\pi\)
−0.290126 + 0.956989i \(0.593697\pi\)
\(84\) 0 0
\(85\) −82.9172 −0.975497
\(86\) 40.1041 23.1541i 0.466327 0.269234i
\(87\) 0 0
\(88\) −2.16553 + 3.75080i −0.0246082 + 0.0426227i
\(89\) −46.9922 + 27.1310i −0.528003 + 0.304843i −0.740203 0.672384i \(-0.765271\pi\)
0.212200 + 0.977226i \(0.431937\pi\)
\(90\) 0 0
\(91\) 0.0379564 6.42055i 0.000417104 0.0705555i
\(92\) 23.9246i 0.260050i
\(93\) 0 0
\(94\) 37.8724 65.5970i 0.402898 0.697840i
\(95\) 56.3848 + 32.5538i 0.593524 + 0.342671i
\(96\) 0 0
\(97\) 12.0828 0.124565 0.0622823 0.998059i \(-0.480162\pi\)
0.0622823 + 0.998059i \(0.480162\pi\)
\(98\) −60.4180 + 33.9363i −0.616510 + 0.346289i
\(99\) 0 0
\(100\) −0.0827625 0.143349i −0.000827625 0.00143349i
\(101\) 157.468 + 90.9145i 1.55909 + 0.900143i 0.997344 + 0.0728364i \(0.0232051\pi\)
0.561750 + 0.827307i \(0.310128\pi\)
\(102\) 0 0
\(103\) 57.8724 + 100.238i 0.561868 + 0.973184i 0.997333 + 0.0729788i \(0.0232506\pi\)
−0.435465 + 0.900206i \(0.643416\pi\)
\(104\) 2.59434i 0.0249456i
\(105\) 0 0
\(106\) −118.241 −1.11549
\(107\) −148.186 + 85.5551i −1.38491 + 0.799580i −0.992736 0.120310i \(-0.961611\pi\)
−0.392177 + 0.919890i \(0.628278\pi\)
\(108\) 0 0
\(109\) 65.9586 114.244i 0.605125 1.04811i −0.386907 0.922119i \(-0.626456\pi\)
0.992032 0.125988i \(-0.0402102\pi\)
\(110\) −9.39251 + 5.42277i −0.0853864 + 0.0492979i
\(111\) 0 0
\(112\) −24.3311 + 13.8564i −0.217242 + 0.123718i
\(113\) 7.65629i 0.0677548i 0.999426 + 0.0338774i \(0.0107856\pi\)
−0.999426 + 0.0338774i \(0.989214\pi\)
\(114\) 0 0
\(115\) 29.9552 51.8839i 0.260480 0.451165i
\(116\) −58.0698 33.5266i −0.500602 0.289023i
\(117\) 0 0
\(118\) 67.6689 0.573466
\(119\) −58.5385 + 100.022i −0.491921 + 0.840517i
\(120\) 0 0
\(121\) −59.3276 102.758i −0.490311 0.849243i
\(122\) 98.6891 + 56.9782i 0.808927 + 0.467034i
\(123\) 0 0
\(124\) −17.3311 30.0183i −0.139767 0.242083i
\(125\) 124.792i 0.998338i
\(126\) 0 0
\(127\) −8.57934 −0.0675538 −0.0337769 0.999429i \(-0.510754\pi\)
−0.0337769 + 0.999429i \(0.510754\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 3.24829 5.62620i 0.0249868 0.0432785i
\(131\) 60.9713 35.2018i 0.465429 0.268716i −0.248895 0.968530i \(-0.580067\pi\)
0.714324 + 0.699815i \(0.246734\pi\)
\(132\) 0 0
\(133\) 79.0759 45.0333i 0.594556 0.338596i
\(134\) 3.42333i 0.0255473i
\(135\) 0 0
\(136\) −23.4138 + 40.5539i −0.172160 + 0.298191i
\(137\) 58.4288 + 33.7339i 0.426488 + 0.246233i 0.697849 0.716245i \(-0.254141\pi\)
−0.271362 + 0.962477i \(0.587474\pi\)
\(138\) 0 0
\(139\) 166.572 1.19836 0.599182 0.800613i \(-0.295493\pi\)
0.599182 + 0.800613i \(0.295493\pi\)
\(140\) −70.1145 0.414497i −0.500818 0.00296069i
\(141\) 0 0
\(142\) −58.9172 102.048i −0.414910 0.718645i
\(143\) −1.21636 0.702263i −0.00850598 0.00491093i
\(144\) 0 0
\(145\) −83.9552 145.415i −0.579001 1.00286i
\(146\) 101.940i 0.698222i
\(147\) 0 0
\(148\) 111.490 0.753309
\(149\) −196.724 + 113.578i −1.32029 + 0.762271i −0.983775 0.179406i \(-0.942582\pi\)
−0.336517 + 0.941677i \(0.609249\pi\)
\(150\) 0 0
\(151\) 137.824 238.719i 0.912743 1.58092i 0.102571 0.994726i \(-0.467293\pi\)
0.810172 0.586192i \(-0.199373\pi\)
\(152\) 31.8434 18.3848i 0.209496 0.120952i
\(153\) 0 0
\(154\) −0.0896122 + 15.1584i −0.000581897 + 0.0984312i
\(155\) 86.7986i 0.559991i
\(156\) 0 0
\(157\) −99.6173 + 172.542i −0.634505 + 1.09899i 0.352115 + 0.935957i \(0.385463\pi\)
−0.986620 + 0.163038i \(0.947871\pi\)
\(158\) 149.824 + 86.5011i 0.948255 + 0.547475i
\(159\) 0 0
\(160\) −28.3311 −0.177069
\(161\) −41.4386 72.7638i −0.257383 0.451949i
\(162\) 0 0
\(163\) 48.5000 + 84.0045i 0.297546 + 0.515365i 0.975574 0.219671i \(-0.0704985\pi\)
−0.678028 + 0.735036i \(0.737165\pi\)
\(164\) −11.3268 6.53953i −0.0690658 0.0398752i
\(165\) 0 0
\(166\) 112.331 + 194.563i 0.676693 + 1.17207i
\(167\) 21.6911i 0.129887i −0.997889 0.0649433i \(-0.979313\pi\)
0.997889 0.0649433i \(-0.0206867\pi\)
\(168\) 0 0
\(169\) −168.159 −0.995022
\(170\) −101.552 + 58.6313i −0.597367 + 0.344890i
\(171\) 0 0
\(172\) 32.7449 56.7158i 0.190377 0.329743i
\(173\) 180.701 104.328i 1.04451 0.603049i 0.123404 0.992357i \(-0.460619\pi\)
0.921108 + 0.389307i \(0.127286\pi\)
\(174\) 0 0
\(175\) −0.500000 0.292630i −0.00285714 0.00167217i
\(176\) 6.12503i 0.0348013i
\(177\) 0 0
\(178\) −38.3690 + 66.4571i −0.215556 + 0.373354i
\(179\) 54.9489 + 31.7248i 0.306977 + 0.177233i 0.645573 0.763699i \(-0.276619\pi\)
−0.338596 + 0.940932i \(0.609952\pi\)
\(180\) 0 0
\(181\) −212.311 −1.17299 −0.586493 0.809954i \(-0.699492\pi\)
−0.586493 + 0.809954i \(0.699492\pi\)
\(182\) −4.49353 7.89038i −0.0246897 0.0433537i
\(183\) 0 0
\(184\) −16.9172 29.3015i −0.0919415 0.159247i
\(185\) 241.782 + 139.593i 1.30693 + 0.754555i
\(186\) 0 0
\(187\) 12.6758 + 21.9551i 0.0677850 + 0.117407i
\(188\) 107.119i 0.569784i
\(189\) 0 0
\(190\) 92.0759 0.484610
\(191\) 50.9706 29.4279i 0.266862 0.154073i −0.360599 0.932721i \(-0.617428\pi\)
0.627461 + 0.778648i \(0.284094\pi\)
\(192\) 0 0
\(193\) −69.6173 + 120.581i −0.360711 + 0.624770i −0.988078 0.153954i \(-0.950799\pi\)
0.627367 + 0.778724i \(0.284133\pi\)
\(194\) 14.7983 8.54380i 0.0762799 0.0440402i
\(195\) 0 0
\(196\) −50.0000 + 84.2852i −0.255102 + 0.430027i
\(197\) 317.720i 1.61279i −0.591375 0.806396i \(-0.701415\pi\)
0.591375 0.806396i \(-0.298585\pi\)
\(198\) 0 0
\(199\) −124.869 + 216.279i −0.627482 + 1.08683i 0.360573 + 0.932731i \(0.382581\pi\)
−0.988055 + 0.154100i \(0.950752\pi\)
\(200\) −0.202726 0.117044i −0.00101363 0.000585219i
\(201\) 0 0
\(202\) 257.145 1.27299
\(203\) −234.682 1.38737i −1.15607 0.00683436i
\(204\) 0 0
\(205\) −16.3759 28.3638i −0.0798822 0.138360i
\(206\) 141.758 + 81.8440i 0.688145 + 0.397301i
\(207\) 0 0
\(208\) −1.83447 3.17740i −0.00881959 0.0152760i
\(209\) 19.9063i 0.0952457i
\(210\) 0 0
\(211\) −112.248 −0.531982 −0.265991 0.963975i \(-0.585699\pi\)
−0.265991 + 0.963975i \(0.585699\pi\)
\(212\) −144.816 + 83.6093i −0.683092 + 0.394384i
\(213\) 0 0
\(214\) −120.993 + 209.566i −0.565389 + 0.979282i
\(215\) 142.024 81.9975i 0.660576 0.381384i
\(216\) 0 0
\(217\) −104.703 61.2787i −0.482505 0.282390i
\(218\) 186.559i 0.855776i
\(219\) 0 0
\(220\) −7.66895 + 13.2830i −0.0348589 + 0.0603773i
\(221\) −13.1513 7.59292i −0.0595083 0.0343571i
\(222\) 0 0
\(223\) 79.2346 0.355312 0.177656 0.984093i \(-0.443149\pi\)
0.177656 + 0.984093i \(0.443149\pi\)
\(224\) −20.0014 + 34.1752i −0.0892918 + 0.152568i
\(225\) 0 0
\(226\) 5.41381 + 9.37700i 0.0239549 + 0.0414911i
\(227\) −310.600 179.325i −1.36828 0.789977i −0.377572 0.925980i \(-0.623241\pi\)
−0.990708 + 0.136003i \(0.956574\pi\)
\(228\) 0 0
\(229\) −61.1689 105.948i −0.267113 0.462654i 0.701002 0.713159i \(-0.252736\pi\)
−0.968115 + 0.250506i \(0.919403\pi\)
\(230\) 84.7261i 0.368374i
\(231\) 0 0
\(232\) −94.8276 −0.408740
\(233\) −184.071 + 106.273i −0.790003 + 0.456108i −0.839964 0.542643i \(-0.817424\pi\)
0.0499606 + 0.998751i \(0.484090\pi\)
\(234\) 0 0
\(235\) 134.121 232.304i 0.570726 0.988527i
\(236\) 82.8772 47.8492i 0.351175 0.202751i
\(237\) 0 0
\(238\) −0.968893 + 163.894i −0.00407098 + 0.688630i
\(239\) 342.762i 1.43415i −0.696997 0.717074i \(-0.745481\pi\)
0.696997 0.717074i \(-0.254519\pi\)
\(240\) 0 0
\(241\) −16.3724 + 28.3579i −0.0679354 + 0.117668i −0.897992 0.440011i \(-0.854975\pi\)
0.830057 + 0.557679i \(0.188308\pi\)
\(242\) −145.322 83.9019i −0.600506 0.346702i
\(243\) 0 0
\(244\) 161.159 0.660486
\(245\) −213.963 + 120.181i −0.873318 + 0.490536i
\(246\) 0 0
\(247\) 5.96204 + 10.3266i 0.0241378 + 0.0418079i
\(248\) −42.4522 24.5098i −0.171178 0.0988299i
\(249\) 0 0
\(250\) 88.2414 + 152.839i 0.352966 + 0.611355i
\(251\) 8.32425i 0.0331643i 0.999863 + 0.0165822i \(0.00527851\pi\)
−0.999863 + 0.0165822i \(0.994721\pi\)
\(252\) 0 0
\(253\) −18.3174 −0.0724006
\(254\) −10.5075 + 6.06651i −0.0413681 + 0.0238839i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 13.4806 7.78302i 0.0524536 0.0302841i −0.473544 0.880770i \(-0.657025\pi\)
0.525997 + 0.850486i \(0.323692\pi\)
\(258\) 0 0
\(259\) 339.083 193.106i 1.30920 0.745583i
\(260\) 9.18754i 0.0353367i
\(261\) 0 0
\(262\) 49.7828 86.2264i 0.190011 0.329108i
\(263\) 5.52394 + 3.18925i 0.0210036 + 0.0121264i 0.510465 0.859899i \(-0.329473\pi\)
−0.489461 + 0.872025i \(0.662807\pi\)
\(264\) 0 0
\(265\) −418.738 −1.58014
\(266\) 65.0045 111.069i 0.244378 0.417554i
\(267\) 0 0
\(268\) −2.42066 4.19271i −0.00903232 0.0156444i
\(269\) 299.243 + 172.768i 1.11243 + 0.642261i 0.939457 0.342666i \(-0.111330\pi\)
0.172971 + 0.984927i \(0.444663\pi\)
\(270\) 0 0
\(271\) −109.214 189.164i −0.403003 0.698021i 0.591084 0.806610i \(-0.298700\pi\)
−0.994087 + 0.108589i \(0.965367\pi\)
\(272\) 66.2243i 0.243472i
\(273\) 0 0
\(274\) 95.4138 0.348226
\(275\) −0.109752 + 0.0633654i −0.000399098 + 0.000230420i
\(276\) 0 0
\(277\) −65.3656 + 113.217i −0.235977 + 0.408724i −0.959556 0.281517i \(-0.909162\pi\)
0.723579 + 0.690241i \(0.242496\pi\)
\(278\) 204.009 117.785i 0.733845 0.423685i
\(279\) 0 0
\(280\) −86.1655 + 49.0708i −0.307734 + 0.175253i
\(281\) 430.516i 1.53208i −0.642790 0.766042i \(-0.722223\pi\)
0.642790 0.766042i \(-0.277777\pi\)
\(282\) 0 0
\(283\) 193.945 335.922i 0.685318 1.18701i −0.288019 0.957625i \(-0.592997\pi\)
0.973337 0.229380i \(-0.0736700\pi\)
\(284\) −144.317 83.3216i −0.508159 0.293386i
\(285\) 0 0
\(286\) −1.98630 −0.00694511
\(287\) −45.7759 0.270614i −0.159498 0.000942906i
\(288\) 0 0
\(289\) −7.44834 12.9009i −0.0257728 0.0446398i
\(290\) −205.647 118.731i −0.709129 0.409416i
\(291\) 0 0
\(292\) 72.0828 + 124.851i 0.246859 + 0.427572i
\(293\) 397.726i 1.35743i −0.734404 0.678713i \(-0.762538\pi\)
0.734404 0.678713i \(-0.237462\pi\)
\(294\) 0 0
\(295\) 239.642 0.812344
\(296\) 136.546 78.8351i 0.461306 0.266335i
\(297\) 0 0
\(298\) −160.624 + 278.209i −0.539007 + 0.933588i
\(299\) 9.50226 5.48613i 0.0317801 0.0183483i
\(300\) 0 0
\(301\) 1.35502 229.210i 0.00450174 0.761495i
\(302\) 389.826i 1.29081i
\(303\) 0 0
\(304\) 26.0000 45.0333i 0.0855263 0.148136i
\(305\) 349.496 + 201.782i 1.14589 + 0.661579i
\(306\) 0 0
\(307\) −116.669 −0.380029 −0.190015 0.981781i \(-0.560854\pi\)
−0.190015 + 0.981781i \(0.560854\pi\)
\(308\) 10.6089 + 18.6286i 0.0344444 + 0.0604823i
\(309\) 0 0
\(310\) −61.3759 106.306i −0.197987 0.342923i
\(311\) 420.797 + 242.947i 1.35305 + 0.781181i 0.988675 0.150073i \(-0.0479509\pi\)
0.364370 + 0.931254i \(0.381284\pi\)
\(312\) 0 0
\(313\) 76.8311 + 133.075i 0.245467 + 0.425161i 0.962263 0.272122i \(-0.0877255\pi\)
−0.716796 + 0.697283i \(0.754392\pi\)
\(314\) 281.760i 0.897326i
\(315\) 0 0
\(316\) 244.662 0.774247
\(317\) −83.8741 + 48.4247i −0.264587 + 0.152759i −0.626425 0.779482i \(-0.715483\pi\)
0.361838 + 0.932241i \(0.382149\pi\)
\(318\) 0 0
\(319\) −25.6689 + 44.4599i −0.0804669 + 0.139373i
\(320\) −34.6983 + 20.0331i −0.108432 + 0.0626034i
\(321\) 0 0
\(322\) −102.203 59.8156i −0.317402 0.185763i
\(323\) 215.229i 0.666343i
\(324\) 0 0
\(325\) 0.0379564 0.0657425i 0.000116789 0.000202285i
\(326\) 118.800 + 68.5894i 0.364418 + 0.210397i
\(327\) 0 0
\(328\) −18.4966 −0.0563920
\(329\) −185.536 325.791i −0.563940 0.990246i
\(330\) 0 0
\(331\) 36.6344 + 63.4527i 0.110678 + 0.191700i 0.916044 0.401078i \(-0.131364\pi\)
−0.805366 + 0.592778i \(0.798031\pi\)
\(332\) 275.154 + 158.860i 0.828776 + 0.478494i
\(333\) 0 0
\(334\) −15.3379 26.5660i −0.0459219 0.0795390i
\(335\) 12.1233i 0.0361890i
\(336\) 0 0
\(337\) −165.304 −0.490515 −0.245258 0.969458i \(-0.578873\pi\)
−0.245258 + 0.969458i \(0.578873\pi\)
\(338\) −205.951 + 118.906i −0.609324 + 0.351793i
\(339\) 0 0
\(340\) −82.9172 + 143.617i −0.243874 + 0.422403i
\(341\) −22.9828 + 13.2691i −0.0673984 + 0.0389125i
\(342\) 0 0
\(343\) −6.08276 + 342.946i −0.0177340 + 0.999843i
\(344\) 92.6165i 0.269234i
\(345\) 0 0
\(346\) 147.541 255.549i 0.426420 0.738581i
\(347\) −181.558 104.823i −0.523222 0.302082i 0.215030 0.976607i \(-0.431015\pi\)
−0.738252 + 0.674525i \(0.764348\pi\)
\(348\) 0 0
\(349\) −442.655 −1.26835 −0.634177 0.773188i \(-0.718661\pi\)
−0.634177 + 0.773188i \(0.718661\pi\)
\(350\) −0.819293 0.00484342i −0.00234084 1.38384e-5i
\(351\) 0 0
\(352\) 4.33105 + 7.50160i 0.0123041 + 0.0213114i
\(353\) −144.537 83.4483i −0.409452 0.236397i 0.281102 0.959678i \(-0.409300\pi\)
−0.690554 + 0.723280i \(0.742633\pi\)
\(354\) 0 0
\(355\) −208.648 361.390i −0.587742 1.01800i
\(356\) 108.524i 0.304843i
\(357\) 0 0
\(358\) 89.7312 0.250646
\(359\) −16.3523 + 9.44101i −0.0455496 + 0.0262981i −0.522602 0.852577i \(-0.675039\pi\)
0.477052 + 0.878875i \(0.341705\pi\)
\(360\) 0 0
\(361\) 96.0000 166.277i 0.265928 0.460601i
\(362\) −260.026 + 150.126i −0.718304 + 0.414713i
\(363\) 0 0
\(364\) −11.0828 6.48629i −0.0304471 0.0178195i
\(365\) 361.010i 0.989068i
\(366\) 0 0
\(367\) 196.110 339.673i 0.534361 0.925540i −0.464833 0.885398i \(-0.653886\pi\)
0.999194 0.0401419i \(-0.0127810\pi\)
\(368\) −41.4386 23.9246i −0.112605 0.0650125i
\(369\) 0 0
\(370\) 394.828 1.06710
\(371\) −295.624 + 505.116i −0.796830 + 1.36150i
\(372\) 0 0
\(373\) 277.811 + 481.182i 0.744800 + 1.29003i 0.950288 + 0.311372i \(0.100789\pi\)
−0.205488 + 0.978660i \(0.565878\pi\)
\(374\) 31.0492 + 17.9263i 0.0830194 + 0.0479313i
\(375\) 0 0
\(376\) −75.7449 131.194i −0.201449 0.348920i
\(377\) 30.7519i 0.0815700i
\(378\) 0 0
\(379\) 433.552 1.14394 0.571968 0.820276i \(-0.306180\pi\)
0.571968 + 0.820276i \(0.306180\pi\)
\(380\) 112.770 65.1075i 0.296762 0.171336i
\(381\) 0 0
\(382\) 41.6173 72.0833i 0.108946 0.188700i
\(383\) −118.682 + 68.5211i −0.309875 + 0.178906i −0.646871 0.762600i \(-0.723923\pi\)
0.336996 + 0.941506i \(0.390589\pi\)
\(384\) 0 0
\(385\) −0.317351 + 53.6817i −0.000824288 + 0.139433i
\(386\) 196.907i 0.510123i
\(387\) 0 0
\(388\) 12.0828 20.9280i 0.0311411 0.0539380i
\(389\) −301.317 173.965i −0.774594 0.447212i 0.0599172 0.998203i \(-0.480916\pi\)
−0.834511 + 0.550991i \(0.814250\pi\)
\(390\) 0 0
\(391\) −198.049 −0.506518
\(392\) −1.63859 + 138.583i −0.00418007 + 0.353529i
\(393\) 0 0
\(394\) −224.662 389.126i −0.570208 0.987630i
\(395\) 530.585 + 306.333i 1.34325 + 0.775528i
\(396\) 0 0
\(397\) −231.200 400.450i −0.582368 1.00869i −0.995198 0.0978827i \(-0.968793\pi\)
0.412830 0.910808i \(-0.364540\pi\)
\(398\) 353.183i 0.887394i
\(399\) 0 0
\(400\) −0.331050 −0.000827625
\(401\) −383.337 + 221.320i −0.955952 + 0.551919i −0.894925 0.446217i \(-0.852771\pi\)
−0.0610272 + 0.998136i \(0.519438\pi\)
\(402\) 0 0
\(403\) 7.94834 13.7669i 0.0197229 0.0341611i
\(404\) 314.937 181.829i 0.779547 0.450072i
\(405\) 0 0
\(406\) −288.407 + 164.246i −0.710362 + 0.404547i
\(407\) 85.3597i 0.209729i
\(408\) 0 0
\(409\) −28.1139 + 48.6947i −0.0687381 + 0.119058i −0.898346 0.439288i \(-0.855231\pi\)
0.829608 + 0.558346i \(0.188564\pi\)
\(410\) −40.1125 23.1590i −0.0978353 0.0564853i
\(411\) 0 0
\(412\) 231.490 0.561868
\(413\) 169.184 289.075i 0.409646 0.699940i
\(414\) 0 0
\(415\) 397.807 + 689.022i 0.958571 + 1.66029i
\(416\) −4.49353 2.59434i −0.0108017 0.00623639i
\(417\) 0 0
\(418\) −14.0759 24.3802i −0.0336744 0.0583258i
\(419\) 330.707i 0.789276i 0.918837 + 0.394638i \(0.129130\pi\)
−0.918837 + 0.394638i \(0.870870\pi\)
\(420\) 0 0
\(421\) −30.5930 −0.0726675 −0.0363338 0.999340i \(-0.511568\pi\)
−0.0363338 + 0.999340i \(0.511568\pi\)
\(422\) −137.476 + 79.3715i −0.325771 + 0.188084i
\(423\) 0 0
\(424\) −118.241 + 204.800i −0.278871 + 0.483019i
\(425\) −1.18665 + 0.685111i −0.00279211 + 0.00161203i
\(426\) 0 0
\(427\) 490.145 279.135i 1.14788 0.653712i
\(428\) 342.220i 0.799580i
\(429\) 0 0
\(430\) 115.962 200.852i 0.269679 0.467098i
\(431\) 580.479 + 335.140i 1.34682 + 0.777586i 0.987798 0.155744i \(-0.0497773\pi\)
0.359021 + 0.933330i \(0.383111\pi\)
\(432\) 0 0
\(433\) −192.276 −0.444055 −0.222027 0.975040i \(-0.571267\pi\)
−0.222027 + 0.975040i \(0.571267\pi\)
\(434\) −171.566 1.01425i −0.395313 0.00233697i
\(435\) 0 0
\(436\) −131.917 228.487i −0.302562 0.524054i
\(437\) 134.675 + 77.7549i 0.308182 + 0.177929i
\(438\) 0 0
\(439\) 80.5208 + 139.466i 0.183419 + 0.317691i 0.943043 0.332672i \(-0.107950\pi\)
−0.759624 + 0.650363i \(0.774617\pi\)
\(440\) 21.6911i 0.0492979i
\(441\) 0 0
\(442\) −21.4760 −0.0485883
\(443\) 590.281 340.799i 1.33246 0.769297i 0.346785 0.937945i \(-0.387273\pi\)
0.985676 + 0.168647i \(0.0539399\pi\)
\(444\) 0 0
\(445\) −135.879 + 235.350i −0.305347 + 0.528876i
\(446\) 97.0422 56.0273i 0.217583 0.125622i
\(447\) 0 0
\(448\) −0.331050 + 55.9990i −0.000738951 + 0.124998i
\(449\) 804.351i 1.79143i 0.444630 + 0.895714i \(0.353335\pi\)
−0.444630 + 0.895714i \(0.646665\pi\)
\(450\) 0 0
\(451\) −5.00685 + 8.67212i −0.0111017 + 0.0192286i
\(452\) 13.2611 + 7.65629i 0.0293387 + 0.0169387i
\(453\) 0 0
\(454\) −507.207 −1.11720
\(455\) −15.9133 27.9428i −0.0349743 0.0614128i
\(456\) 0 0
\(457\) 44.4415 + 76.9749i 0.0972462 + 0.168435i 0.910544 0.413413i \(-0.135663\pi\)
−0.813298 + 0.581848i \(0.802330\pi\)
\(458\) −149.833 86.5060i −0.327146 0.188878i
\(459\) 0 0
\(460\) −59.9104 103.768i −0.130240 0.225582i
\(461\) 862.183i 1.87024i 0.354325 + 0.935122i \(0.384711\pi\)
−0.354325 + 0.935122i \(0.615289\pi\)
\(462\) 0 0
\(463\) −140.938 −0.304401 −0.152201 0.988350i \(-0.548636\pi\)
−0.152201 + 0.988350i \(0.548636\pi\)
\(464\) −116.140 + 67.0533i −0.250301 + 0.144511i
\(465\) 0 0
\(466\) −150.293 + 260.315i −0.322517 + 0.558616i
\(467\) −233.715 + 134.936i −0.500461 + 0.288941i −0.728904 0.684616i \(-0.759970\pi\)
0.228443 + 0.973557i \(0.426637\pi\)
\(468\) 0 0
\(469\) −14.6241 8.55892i −0.0311815 0.0182493i
\(470\) 379.351i 0.807129i
\(471\) 0 0
\(472\) 67.6689 117.206i 0.143366 0.248318i
\(473\) −43.4232 25.0704i −0.0918038 0.0530030i
\(474\) 0 0
\(475\) 1.07591 0.00226508
\(476\) 114.704 + 201.413i 0.240974 + 0.423137i
\(477\) 0 0
\(478\) −242.369 419.795i −0.507048 0.878233i
\(479\) −652.109 376.495i −1.36140 0.786003i −0.371587 0.928398i \(-0.621186\pi\)
−0.989810 + 0.142395i \(0.954520\pi\)
\(480\) 0 0
\(481\) 25.5656 + 44.2810i 0.0531510 + 0.0920603i
\(482\) 46.3082i 0.0960752i
\(483\) 0 0
\(484\) −237.311 −0.490311
\(485\) 52.4064 30.2569i 0.108054 0.0623853i
\(486\) 0 0
\(487\) −375.969 + 651.198i −0.772011 + 1.33716i 0.164449 + 0.986386i \(0.447415\pi\)
−0.936459 + 0.350776i \(0.885918\pi\)
\(488\) 197.378 113.956i 0.404464 0.233517i
\(489\) 0 0
\(490\) −177.069 + 298.486i −0.361365 + 0.609155i
\(491\) 165.492i 0.337051i 0.985697 + 0.168526i \(0.0539006\pi\)
−0.985697 + 0.168526i \(0.946099\pi\)
\(492\) 0 0
\(493\) −277.535 + 480.704i −0.562950 + 0.975059i
\(494\) 14.6040 + 8.43160i 0.0295627 + 0.0170680i
\(495\) 0 0
\(496\) −69.3242 −0.139767
\(497\) −583.241 3.44795i −1.17352 0.00693753i
\(498\) 0 0
\(499\) 213.341 + 369.518i 0.427538 + 0.740517i 0.996654 0.0817402i \(-0.0260478\pi\)
−0.569116 + 0.822257i \(0.692714\pi\)
\(500\) 216.146 + 124.792i 0.432293 + 0.249584i
\(501\) 0 0
\(502\) 5.88613 + 10.1951i 0.0117254 + 0.0203089i
\(503\) 302.442i 0.601276i 0.953738 + 0.300638i \(0.0971996\pi\)
−0.953738 + 0.300638i \(0.902800\pi\)
\(504\) 0 0
\(505\) 910.648 1.80326
\(506\) −22.4341 + 12.9523i −0.0443361 + 0.0255975i
\(507\) 0 0
\(508\) −8.57934 + 14.8598i −0.0168885 + 0.0292517i
\(509\) −122.770 + 70.8814i −0.241199 + 0.139256i −0.615728 0.787959i \(-0.711138\pi\)
0.374529 + 0.927215i \(0.377804\pi\)
\(510\) 0 0
\(511\) 435.479 + 254.869i 0.852210 + 0.498764i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 11.0068 19.0644i 0.0214141 0.0370903i
\(515\) 502.019 + 289.841i 0.974794 + 0.562798i
\(516\) 0 0
\(517\) −82.0137 −0.158634
\(518\) 278.743 476.273i 0.538115 0.919446i
\(519\) 0 0
\(520\) −6.49658 11.2524i −0.0124934 0.0216392i
\(521\) 390.077 + 225.211i 0.748708 + 0.432267i 0.825227 0.564801i \(-0.191047\pi\)
−0.0765187 + 0.997068i \(0.524380\pi\)
\(522\) 0 0
\(523\) 156.221 + 270.583i 0.298702 + 0.517366i 0.975839 0.218490i \(-0.0701132\pi\)
−0.677138 + 0.735856i \(0.736780\pi\)
\(524\) 140.807i 0.268716i
\(525\) 0 0
\(526\) 9.02055 0.0171493
\(527\) −248.492 + 143.467i −0.471522 + 0.272233i
\(528\) 0 0
\(529\) −192.952 + 334.202i −0.364748 + 0.631762i
\(530\) −512.847 + 296.092i −0.967636 + 0.558665i
\(531\) 0 0
\(532\) 1.07591 181.997i 0.00202239 0.342099i
\(533\) 5.99830i 0.0112538i
\(534\) 0 0
\(535\) −428.483 + 742.154i −0.800903 + 1.38720i
\(536\) −5.92939 3.42333i −0.0110623 0.00638682i
\(537\) 0 0
\(538\) 488.662 0.908294
\(539\) 64.5312 + 38.2814i 0.119724 + 0.0710231i
\(540\) 0 0
\(541\) −307.173 532.039i −0.567787 0.983436i −0.996784 0.0801300i \(-0.974466\pi\)
0.428998 0.903306i \(-0.358867\pi\)
\(542\) −267.518 154.452i −0.493576 0.284966i
\(543\) 0 0
\(544\) 46.8276 + 81.1078i 0.0860802 + 0.149095i
\(545\) 660.677i 1.21225i
\(546\) 0 0
\(547\) −675.263 −1.23448 −0.617242 0.786773i \(-0.711750\pi\)
−0.617242 + 0.786773i \(0.711750\pi\)
\(548\) 116.858 67.4678i 0.213244 0.123116i
\(549\) 0 0
\(550\) −0.0896122 + 0.155213i −0.000162931 + 0.000282205i
\(551\) 377.454 217.923i 0.685034 0.395505i
\(552\) 0 0
\(553\) 744.111 423.767i 1.34559 0.766306i
\(554\) 184.882i 0.333722i
\(555\) 0 0
\(556\) 166.572 288.512i 0.299591 0.518906i
\(557\) −579.013 334.293i −1.03952 0.600168i −0.119823 0.992795i \(-0.538233\pi\)
−0.919698 + 0.392628i \(0.871566\pi\)
\(558\) 0 0
\(559\) 30.0348 0.0537295
\(560\) −70.8325 + 121.027i −0.126487 + 0.216120i
\(561\) 0 0
\(562\) −304.421 527.272i −0.541674 0.938207i
\(563\) −10.9678 6.33228i −0.0194810 0.0112474i 0.490228 0.871594i \(-0.336914\pi\)
−0.509709 + 0.860347i \(0.670247\pi\)
\(564\) 0 0
\(565\) 19.1724 + 33.2075i 0.0339334 + 0.0587744i
\(566\) 548.559i 0.969186i
\(567\) 0 0
\(568\) −235.669 −0.414910
\(569\) 509.198 293.986i 0.894900 0.516671i 0.0193580 0.999813i \(-0.493838\pi\)
0.875542 + 0.483142i \(0.160504\pi\)
\(570\) 0 0
\(571\) 386.759 669.886i 0.677336 1.17318i −0.298444 0.954427i \(-0.596468\pi\)
0.975780 0.218753i \(-0.0701990\pi\)
\(572\) −2.43271 + 1.40453i −0.00425299 + 0.00245547i
\(573\) 0 0
\(574\) −56.2551 + 32.0370i −0.0980055 + 0.0558136i
\(575\) 0.990030i 0.00172179i
\(576\) 0 0
\(577\) −45.7965 + 79.3219i −0.0793700 + 0.137473i −0.902978 0.429686i \(-0.858624\pi\)
0.823608 + 0.567159i \(0.191958\pi\)
\(578\) −18.2446 10.5335i −0.0315651 0.0182241i
\(579\) 0 0
\(580\) −335.821 −0.579001
\(581\) 1112.00 + 6.57383i 1.91394 + 0.0113147i
\(582\) 0 0
\(583\) 64.0137 + 110.875i 0.109801 + 0.190180i
\(584\) 176.566 + 101.940i 0.302339 + 0.174556i
\(585\) 0 0
\(586\) −281.235 487.113i −0.479923 0.831250i
\(587\) 237.495i 0.404592i 0.979324 + 0.202296i \(0.0648403\pi\)
−0.979324 + 0.202296i \(0.935160\pi\)
\(588\) 0 0
\(589\) 225.304 0.382519
\(590\) 293.500 169.452i 0.497457 0.287207i
\(591\) 0 0
\(592\) 111.490 193.106i 0.188327 0.326192i
\(593\) −23.8699 + 13.7813i −0.0402529 + 0.0232400i −0.519991 0.854172i \(-0.674065\pi\)
0.479739 + 0.877412i \(0.340732\pi\)
\(594\) 0 0
\(595\) −3.43122 + 580.411i −0.00576676 + 0.975480i
\(596\) 454.314i 0.762271i
\(597\) 0 0
\(598\) 7.75856 13.4382i 0.0129742 0.0224719i
\(599\) −815.769 470.985i −1.36189 0.786285i −0.372010 0.928229i \(-0.621331\pi\)
−0.989875 + 0.141944i \(0.954665\pi\)
\(600\) 0 0
\(601\) −374.262 −0.622732 −0.311366 0.950290i \(-0.600787\pi\)
−0.311366 + 0.950290i \(0.600787\pi\)
\(602\) −160.416 281.682i −0.266472 0.467910i
\(603\) 0 0
\(604\) −275.648 477.437i −0.456372 0.790459i
\(605\) −514.642 297.129i −0.850648 0.491122i
\(606\) 0 0
\(607\) −190.328 329.657i −0.313555 0.543092i 0.665575 0.746331i \(-0.268187\pi\)
−0.979129 + 0.203239i \(0.934853\pi\)
\(608\) 73.5391i 0.120952i
\(609\) 0 0
\(610\) 570.724 0.935614
\(611\) 42.5452 24.5635i 0.0696321 0.0402021i
\(612\) 0 0
\(613\) 455.283 788.573i 0.742713 1.28642i −0.208543 0.978013i \(-0.566872\pi\)
0.951256 0.308403i \(-0.0997945\pi\)
\(614\) −142.890 + 82.4974i −0.232719 + 0.134361i
\(615\) 0 0
\(616\) 26.1655 + 15.3136i 0.0424765 + 0.0248598i
\(617\) 16.8438i 0.0272996i −0.999907 0.0136498i \(-0.995655\pi\)
0.999907 0.0136498i \(-0.00434500\pi\)
\(618\) 0 0
\(619\) 391.707 678.456i 0.632806 1.09605i −0.354169 0.935181i \(-0.615236\pi\)
0.986975 0.160871i \(-0.0514303\pi\)
\(620\) −150.340 86.7986i −0.242483 0.139998i
\(621\) 0 0
\(622\) 687.159 1.10476
\(623\) 187.969 + 330.063i 0.301716 + 0.529796i
\(624\) 0 0
\(625\) 313.531 + 543.052i 0.501650 + 0.868883i
\(626\) 188.197 + 108.656i 0.300634 + 0.173571i
\(627\) 0 0
\(628\) 199.235 + 345.084i 0.317253 + 0.549497i
\(629\) 922.916i 1.46727i
\(630\) 0 0
\(631\) −679.228 −1.07643 −0.538215 0.842807i \(-0.680901\pi\)
−0.538215 + 0.842807i \(0.680901\pi\)
\(632\) 299.649 173.002i 0.474128 0.273738i
\(633\) 0 0
\(634\) −68.4829 + 118.616i −0.108017 + 0.187091i
\(635\) −37.2111 + 21.4838i −0.0586001 + 0.0338328i
\(636\) 0 0
\(637\) −44.9415 0.531381i −0.0705518 0.000834193i
\(638\) 72.6028i 0.113797i
\(639\) 0 0
\(640\) −28.3311 + 49.0708i −0.0442673 + 0.0766732i
\(641\) 589.124 + 340.131i 0.919070 + 0.530625i 0.883338 0.468736i \(-0.155291\pi\)
0.0357315 + 0.999361i \(0.488624\pi\)
\(642\) 0 0
\(643\) 843.966 1.31254 0.656272 0.754524i \(-0.272132\pi\)
0.656272 + 0.754524i \(0.272132\pi\)
\(644\) −167.469 0.990030i −0.260045 0.00153731i
\(645\) 0 0
\(646\) −152.190 263.600i −0.235588 0.408050i
\(647\) −1111.67 641.824i −1.71819 0.992000i −0.922216 0.386676i \(-0.873623\pi\)
−0.795979 0.605324i \(-0.793044\pi\)
\(648\) 0 0
\(649\) −36.6347 63.4532i −0.0564479 0.0977707i
\(650\) 0.107357i 0.000165165i
\(651\) 0 0
\(652\) 194.000 0.297546
\(653\) −276.898 + 159.867i −0.424040 + 0.244820i −0.696804 0.717261i \(-0.745395\pi\)
0.272764 + 0.962081i \(0.412062\pi\)
\(654\) 0 0
\(655\) 176.300 305.360i 0.269160 0.466199i
\(656\) −22.6536 + 13.0791i −0.0345329 + 0.0199376i
\(657\) 0 0
\(658\) −457.604 267.817i −0.695446 0.407017i
\(659\) 915.684i 1.38951i −0.719249 0.694753i \(-0.755514\pi\)
0.719249 0.694753i \(-0.244486\pi\)
\(660\) 0 0
\(661\) −251.183 + 435.061i −0.380004 + 0.658186i −0.991062 0.133399i \(-0.957411\pi\)
0.611058 + 0.791586i \(0.290744\pi\)
\(662\) 89.7356 + 51.8089i 0.135552 + 0.0782612i
\(663\) 0 0
\(664\) 449.324 0.676693
\(665\) 230.206 393.339i 0.346174 0.591488i
\(666\) 0 0
\(667\) −200.528 347.324i −0.300641 0.520726i
\(668\) −37.5700 21.6911i −0.0562426 0.0324717i
\(669\) 0 0
\(670\) −8.57249 14.8480i −0.0127948 0.0221612i
\(671\) 123.388i 0.183886i
\(672\) 0 0
\(673\) 299.724 0.445356 0.222678 0.974892i \(-0.428520\pi\)
0.222678 + 0.974892i \(0.428520\pi\)
\(674\) −202.455 + 116.887i −0.300378 + 0.173423i
\(675\) 0 0
\(676\) −168.159 + 291.259i −0.248755 + 0.430857i
\(677\) −286.869 + 165.624i −0.423736 + 0.244644i −0.696674 0.717387i \(-0.745338\pi\)
0.272939 + 0.962031i \(0.412004\pi\)
\(678\) 0 0
\(679\) 0.500000 84.5779i 0.000736377 0.124562i
\(680\) 234.525i 0.344890i
\(681\) 0 0
\(682\) −18.7654 + 32.5026i −0.0275153 + 0.0476578i
\(683\) −858.175 495.468i −1.25648 0.725428i −0.284090 0.958797i \(-0.591692\pi\)
−0.972388 + 0.233369i \(0.925025\pi\)
\(684\) 0 0
\(685\) 337.897 0.493280
\(686\) 235.050 + 424.323i 0.342638 + 0.618546i
\(687\) 0 0
\(688\) −65.4897 113.432i −0.0951886 0.164871i
\(689\) −66.4151 38.3448i −0.0963935 0.0556528i
\(690\) 0 0
\(691\) −326.842 566.106i −0.472998 0.819257i 0.526524 0.850160i \(-0.323495\pi\)
−0.999522 + 0.0309035i \(0.990162\pi\)
\(692\) 417.310i 0.603049i
\(693\) 0 0
\(694\) −296.483 −0.427209
\(695\) 722.473 417.120i 1.03953 0.600173i
\(696\) 0 0
\(697\) −54.1344 + 93.7636i −0.0776677 + 0.134524i
\(698\) −542.140 + 313.005i −0.776705 + 0.448431i
\(699\) 0 0
\(700\) −1.00685 + 0.573396i −0.00143836 + 0.000819137i
\(701\) 281.648i 0.401781i −0.979614 0.200890i \(-0.935616\pi\)
0.979614 0.200890i \(-0.0643835\pi\)
\(702\) 0 0
\(703\) −362.342 + 627.594i −0.515422 + 0.892737i
\(704\) 10.6089 + 6.12503i 0.0150694 + 0.00870033i
\(705\) 0 0
\(706\) −236.027 −0.334316
\(707\) 642.906 1098.50i 0.909344 1.55375i
\(708\) 0 0
\(709\) −250.372 433.658i −0.353135 0.611647i 0.633662 0.773610i \(-0.281551\pi\)
−0.986797 + 0.161963i \(0.948218\pi\)
\(710\) −511.082 295.073i −0.719834 0.415596i
\(711\) 0 0
\(712\) 76.7380 + 132.914i 0.107778 + 0.186677i
\(713\) 207.319i 0.290770i
\(714\) 0 0
\(715\) −7.03425 −0.00983811
\(716\) 109.898 63.4495i 0.153489 0.0886166i
\(717\) 0 0
\(718\) −13.3516 + 23.1256i −0.0185955 + 0.0322084i
\(719\) −371.073 + 214.239i −0.516095 + 0.297968i −0.735336 0.677703i \(-0.762975\pi\)
0.219240 + 0.975671i \(0.429642\pi\)
\(720\) 0 0
\(721\) 704.049 400.952i 0.976489 0.556105i
\(722\) 271.529i 0.376079i
\(723\) 0 0
\(724\) −212.311 + 367.733i −0.293247 + 0.507918i
\(725\) −2.40300 1.38737i −0.00331449 0.00191362i
\(726\) 0 0
\(727\) −1134.87 −1.56103 −0.780515 0.625137i \(-0.785043\pi\)
−0.780515 + 0.625137i \(0.785043\pi\)
\(728\) −18.1601 0.107357i −0.0249451 0.000147468i
\(729\) 0 0
\(730\) 255.273 + 442.145i 0.349688 + 0.605678i
\(731\) −469.495 271.063i −0.642264 0.370811i
\(732\) 0 0
\(733\) 322.786 + 559.082i 0.440363 + 0.762731i 0.997716 0.0675441i \(-0.0215163\pi\)
−0.557353 + 0.830276i \(0.688183\pi\)
\(734\) 554.684i 0.755700i
\(735\) 0 0
\(736\) −67.6689 −0.0919415
\(737\) −3.21006 + 1.85333i −0.00435558 + 0.00251469i
\(738\) 0 0
\(739\) 396.638 686.997i 0.536723 0.929631i −0.462355 0.886695i \(-0.652995\pi\)
0.999078 0.0429362i \(-0.0136712\pi\)
\(740\) 483.563 279.185i 0.653464 0.377277i
\(741\) 0 0
\(742\) −4.89298 + 827.676i −0.00659431 + 1.11547i
\(743\) 1254.90i 1.68896i 0.535584 + 0.844482i \(0.320092\pi\)
−0.535584 + 0.844482i \(0.679908\pi\)
\(744\) 0 0
\(745\) −568.831 + 985.245i −0.763532 + 1.32248i
\(746\) 680.494 + 392.883i 0.912190 + 0.526653i
\(747\) 0 0
\(748\) 50.7032 0.0677850
\(749\) 592.743 + 1040.82i 0.791379 + 1.38962i
\(750\) 0 0
\(751\) 427.766 + 740.912i 0.569595 + 0.986567i 0.996606 + 0.0823207i \(0.0262332\pi\)
−0.427011 + 0.904246i \(0.640433\pi\)
\(752\) −185.536 107.119i −0.246724 0.142446i
\(753\) 0 0
\(754\) −21.7449 37.6632i −0.0288393 0.0499512i
\(755\) 1380.52i 1.82851i
\(756\) 0 0
\(757\) 254.428 0.336100 0.168050 0.985778i \(-0.446253\pi\)
0.168050 + 0.985778i \(0.446253\pi\)
\(758\) 530.991 306.568i 0.700515 0.404443i
\(759\) 0 0
\(760\) 92.0759 159.480i 0.121153 0.209842i
\(761\) 831.324 479.965i 1.09241 0.630703i 0.158192 0.987408i \(-0.449433\pi\)
0.934217 + 0.356705i \(0.116100\pi\)
\(762\) 0 0
\(763\) −796.962 466.430i −1.04451 0.611310i
\(764\) 117.711i 0.154073i
\(765\) 0 0
\(766\) −96.9035 + 167.842i −0.126506 + 0.219115i
\(767\) 38.0090 + 21.9445i 0.0495555 + 0.0286109i
\(768\) 0 0
\(769\) 563.090 0.732236 0.366118 0.930568i \(-0.380687\pi\)
0.366118 + 0.930568i \(0.380687\pi\)
\(770\) 37.5700 + 65.9708i 0.0487922 + 0.0856764i
\(771\) 0 0
\(772\) 139.235 + 241.161i 0.180356 + 0.312385i
\(773\) −164.508 94.9789i −0.212818 0.122871i 0.389802 0.920899i \(-0.372543\pi\)
−0.602620 + 0.798028i \(0.705877\pi\)
\(774\) 0 0
\(775\) −0.717181 1.24219i −0.000925395 0.00160283i
\(776\) 34.1752i 0.0440402i
\(777\) 0 0
\(778\) −492.049 −0.632453
\(779\) 73.6242 42.5069i 0.0945111 0.0545660i
\(780\) 0 0
\(781\) −63.7934 + 110.493i −0.0816817 + 0.141477i
\(782\) −242.559 + 140.041i −0.310178 + 0.179081i
\(783\) 0 0
\(784\) 95.9863 + 170.888i 0.122432 + 0.217969i
\(785\)