Properties

Label 378.3.s.d.53.1
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 53.1
Root \(4.76613 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 378.53
Dual form 378.3.s.d.107.1

$q$-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 −0.866503 0.499173i \(-0.833637\pi\)
−0.000955133 1.00000i \(0.500304\pi\)
\(6\) 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 0.559065 0.829124i \(-0.311160\pi\)
−0.438510 + 0.898726i \(0.644494\pi\)
\(12\) 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 0.858422 0.512944i \(-0.171445\pi\)
−0.0150117 + 0.999887i \(0.504779\pi\)
\(18\) 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 −0.708007 0.706205i \(-0.750406\pi\)
0.257588 + 0.966255i \(0.417072\pi\)
\(24\) 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 \(0.196184\pi\)
−0.816005 + 0.578045i \(0.803816\pi\)
\(30\) 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 \(0.0254123\pi\)
−0.996815 + 0.0797503i \(0.974588\pi\)
\(42\) 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 −0.904345 0.426803i \(-0.859640\pi\)
−0.0825503 + 0.996587i \(0.526307\pi\)
\(48\) 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 0.990438 0.137955i \(-0.0440530\pi\)
0.375746 + 0.926723i \(0.377386\pi\)
\(54\) 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 0.105873 0.994380i \(-0.466236\pi\)
−0.808222 + 0.588878i \(0.799570\pi\)
\(60\) 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 \(0.199601\pi\)
−0.809753 + 0.586772i \(0.800399\pi\)
\(72\) 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 \(-0.593697\pi\)
0.290126 0.956989i \(-0.406303\pi\)
\(84\) 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 −0.212200 0.977226i \(-0.568063\pi\)
0.740203 + 0.672384i \(0.234729\pi\)
\(90\) 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 \(-0.976795\pi\)
−0.561750 0.827307i \(-0.689872\pi\)
\(102\) 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 0.392177 0.919890i \(-0.371722\pi\)
0.992736 + 0.120310i \(0.0383887\pi\)
\(108\) 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 \(-0.989214\pi\)
0.999426 0.0338774i \(-0.0107856\pi\)
\(114\) 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 −0.714324 0.699815i \(-0.753266\pi\)
0.248895 + 0.968530i \(0.419933\pi\)
\(132\) 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 0.271362 0.962477i \(-0.412526\pi\)
−0.697849 + 0.716245i \(0.745859\pi\)
\(138\) 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 0.336517 0.941677i \(-0.390751\pi\)
0.983775 + 0.179406i \(0.0574176\pi\)
\(150\) 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 \(0.0206867\pi\)
−0.997889 + 0.0649433i \(0.979313\pi\)
\(168\) 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 −0.921108 0.389307i \(-0.872714\pi\)
−0.123404 + 0.992357i \(0.539381\pi\)
\(174\) 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 0.338596 0.940932i \(-0.390048\pi\)
−0.645573 + 0.763699i \(0.723381\pi\)
\(180\) 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 −0.627461 0.778648i \(-0.715906\pi\)
0.360599 + 0.932721i \(0.382572\pi\)
\(192\) 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 \(0.298585\pi\)
−0.591375 + 0.806396i \(0.701415\pi\)
\(198\) 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 0.990708 0.136003i \(-0.0434257\pi\)
0.377572 + 0.925980i \(0.376759\pi\)
\(228\) 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 −0.0499606 0.998751i \(-0.515910\pi\)
0.839964 + 0.542643i \(0.182576\pi\)
\(234\) 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 \(0.254519\pi\)
−0.696997 + 0.717074i \(0.745481\pi\)
\(240\) 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 \(-0.994721\pi\)
0.999863 0.0165822i \(-0.00527851\pi\)
\(252\) 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 −0.525997 0.850486i \(-0.676308\pi\)
0.473544 + 0.880770i \(0.342975\pi\)
\(258\) 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 0.489461 0.872025i \(-0.337193\pi\)
−0.510465 + 0.859899i \(0.670527\pi\)
\(264\) 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 −0.172971 0.984927i \(-0.555337\pi\)
−0.939457 + 0.342666i \(0.888670\pi\)
\(270\) 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 \(0.277777\pi\)
−0.642790 + 0.766042i \(0.722223\pi\)
\(282\) 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 \(0.237462\pi\)
−0.734404 + 0.678713i \(0.762538\pi\)
\(294\) 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 −0.364370 0.931254i \(-0.618716\pi\)
−0.988675 + 0.150073i \(0.952049\pi\)
\(312\) 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 −0.361838 0.932241i \(-0.617851\pi\)
0.626425 + 0.779482i \(0.284517\pi\)
\(318\) 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 0.738252 0.674525i \(-0.235652\pi\)
−0.215030 + 0.976607i \(0.568985\pi\)
\(348\) 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 0.690554 0.723280i \(-0.257367\pi\)
−0.281102 + 0.959678i \(0.590700\pi\)
\(354\) 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 −0.477052 0.878875i \(-0.658295\pi\)
0.522602 + 0.852577i \(0.324961\pi\)
\(360\) 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 −0.336996 0.941506i \(-0.609411\pi\)
0.646871 + 0.762600i \(0.276077\pi\)
\(384\) 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 0.834511 0.550991i \(-0.185750\pi\)
−0.0599172 + 0.998203i \(0.519084\pi\)
\(390\) 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 0.0610272 0.998136i \(-0.480562\pi\)
0.894925 + 0.446217i \(0.147229\pi\)
\(402\) 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 \(-0.870870\pi\)
0.918837 0.394638i \(-0.129130\pi\)
\(420\) 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 −0.359021 0.933330i \(-0.616889\pi\)
−0.987798 + 0.155744i \(0.950223\pi\)
\(432\) 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 −0.985676 0.168647i \(-0.946060\pi\)
−0.346785 + 0.937945i \(0.612727\pi\)
\(444\) 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 \(-0.646665\pi\)
0.444630 0.895714i \(-0.353335\pi\)
\(450\) 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 \(-0.615289\pi\)
0.354325 0.935122i \(-0.384711\pi\)
\(462\) 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 −0.228443 0.973557i \(-0.573363\pi\)
0.728904 + 0.684616i \(0.240030\pi\)
\(468\) 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 0.989810 0.142395i \(-0.0454804\pi\)
0.371587 + 0.928398i \(0.378814\pi\)
\(480\) 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 \(-0.946099\pi\)
0.985697 0.168526i \(-0.0539006\pi\)
\(492\) 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 \(-0.902800\pi\)
0.953738 0.300638i \(-0.0971996\pi\)
\(504\) 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 −0.374529 0.927215i \(-0.622196\pi\)
0.615728 + 0.787959i \(0.288862\pi\)
\(510\) 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 0.0765187 0.997068i \(-0.475620\pi\)
−0.825227 + 0.564801i \(0.808953\pi\)
\(522\) 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 0.919698 0.392628i \(-0.128434\pi\)
0.119823 + 0.992795i \(0.461767\pi\)
\(558\) 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 0.509709 0.860347i \(-0.329753\pi\)
−0.490228 + 0.871594i \(0.663086\pi\)
\(564\) 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 −0.875542 0.483142i \(-0.839496\pi\)
−0.0193580 + 0.999813i \(0.506162\pi\)
\(570\) 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 \(-0.935160\pi\)
0.979324 0.202296i \(-0.0648403\pi\)
\(588\) 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 −0.479739 0.877412i \(-0.659268\pi\)
0.519991 + 0.854172i \(0.325935\pi\)
\(594\) 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 0.989875 0.141944i \(-0.0453352\pi\)
0.372010 + 0.928229i \(0.378669\pi\)
\(600\) 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 \(0.00434500\pi\)
−0.999907 + 0.0136498i \(0.995655\pi\)
\(618\) 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 −0.0357315 0.999361i \(-0.511376\pi\)
−0.883338 + 0.468736i \(0.844709\pi\)
\(642\) 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 \(0.126377\pi\)
0.795979 + 0.605324i \(0.206956\pi\)
\(648\) 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 −0.272764 0.962081i \(-0.587938\pi\)
0.696804 + 0.717261i \(0.254605\pi\)
\(654\) 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 \(0.244486\pi\)
−0.719249 + 0.694753i \(0.755514\pi\)
\(660\) 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 −0.272939 0.962031i \(-0.587996\pi\)
0.696674 + 0.717387i \(0.254662\pi\)
\(678\) 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 0.972388 0.233369i \(-0.0749751\pi\)
0.284090 + 0.958797i \(0.408308\pi\)
\(684\) 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 \(0.0643835\pi\)
−0.979614 + 0.200890i \(0.935616\pi\)
\(702\) 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 −0.219240 0.975671i \(-0.570358\pi\)
0.735336 + 0.677703i \(0.237025\pi\)
\(720\) 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 \(-0.679908\pi\)
0.535584 0.844482i \(-0.320092\pi\)
\(744\) 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 −0.934217 0.356705i \(-0.883900\pi\)
−0.158192 + 0.987408i \(0.550567\pi\)
\(762\) 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 0.602620 0.798028i \(-0.294123\pi\)
−0.389802 + 0.920899i \(0.627457\pi\)
\(774\) 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
\(785\) 997.820i 1.27111i