Properties

Label 448.3.s.d.129.2
Level $448$
Weight $3$
Character 448.129
Analytic conductor $12.207$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 448.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.2071158433\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 448.129
Dual form 448.3.s.d.257.2

$q$-expansion

\(f(q)\) \(=\) \(q+(3.62132 + 2.09077i) q^{3} +(-2.74264 + 1.58346i) q^{5} +(-2.24264 + 6.63103i) q^{7} +(4.24264 + 7.34847i) q^{9} +O(q^{10})\) \(q+(3.62132 + 2.09077i) q^{3} +(-2.74264 + 1.58346i) q^{5} +(-2.24264 + 6.63103i) q^{7} +(4.24264 + 7.34847i) q^{9} +(-6.62132 + 11.4685i) q^{11} -5.49333i q^{13} -13.2426 q^{15} +(-11.7426 - 6.77962i) q^{17} +(0.621320 - 0.358719i) q^{19} +(-21.9853 + 19.3242i) q^{21} +(1.13604 + 1.96768i) q^{23} +(-7.48528 + 12.9649i) q^{25} -2.15232i q^{27} -20.4853 q^{29} +(21.3198 + 12.3090i) q^{31} +(-47.9558 + 27.6873i) q^{33} +(-4.34924 - 21.7377i) q^{35} +(32.4706 + 56.2407i) q^{37} +(11.4853 - 19.8931i) q^{39} +21.0308i q^{41} -6.48528 q^{43} +(-23.2721 - 13.4361i) q^{45} +(41.3787 - 23.8900i) q^{47} +(-38.9411 - 29.7420i) q^{49} +(-28.3492 - 49.1023i) q^{51} +(11.0147 - 19.0781i) q^{53} -41.9385i q^{55} +3.00000 q^{57} +(72.5330 + 41.8770i) q^{59} +(-57.3823 + 33.1297i) q^{61} +(-58.2426 + 11.6531i) q^{63} +(8.69848 + 15.0662i) q^{65} +(46.3198 - 80.2283i) q^{67} +9.50079i q^{69} -48.4264 q^{71} +(113.441 + 65.4953i) q^{73} +(-54.2132 + 31.3000i) q^{75} +(-61.1985 - 69.6258i) q^{77} +(38.1066 + 66.0026i) q^{79} +(42.6838 - 73.9305i) q^{81} +107.981i q^{83} +42.9411 q^{85} +(-74.1838 - 42.8300i) q^{87} +(-145.412 + 83.9535i) q^{89} +(36.4264 + 12.3196i) q^{91} +(51.4706 + 89.1496i) q^{93} +(-1.13604 + 1.96768i) q^{95} -25.5816i q^{97} -112.368 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} + 6 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{3} + 6 q^{5} + 8 q^{7} - 18 q^{11} - 36 q^{15} - 30 q^{17} - 6 q^{19} - 54 q^{21} + 30 q^{23} + 4 q^{25} - 48 q^{29} - 42 q^{31} - 90 q^{33} + 42 q^{35} + 62 q^{37} + 12 q^{39} + 8 q^{43} - 144 q^{45} + 174 q^{47} - 20 q^{49} - 54 q^{51} + 78 q^{53} + 12 q^{57} + 78 q^{59} + 42 q^{61} - 216 q^{63} - 84 q^{65} + 58 q^{67} - 24 q^{71} + 318 q^{73} - 132 q^{75} - 126 q^{77} + 110 q^{79} + 18 q^{81} + 36 q^{85} - 144 q^{87} - 378 q^{89} - 24 q^{91} + 138 q^{93} - 30 q^{95} - 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) 3.62132 + 2.09077i 1.20711 + 0.696923i 0.962126 0.272605i \(-0.0878851\pi\)
0.244981 + 0.969528i \(0.421218\pi\)
\(4\) 0 0
\(5\) −2.74264 + 1.58346i −0.548528 + 0.316693i −0.748528 0.663103i \(-0.769239\pi\)
0.200000 + 0.979796i \(0.435906\pi\)
\(6\) 0 0
\(7\) −2.24264 + 6.63103i −0.320377 + 0.947290i
\(8\) 0 0
\(9\) 4.24264 + 7.34847i 0.471405 + 0.816497i
\(10\) 0 0
\(11\) −6.62132 + 11.4685i −0.601938 + 1.04259i 0.390589 + 0.920565i \(0.372271\pi\)
−0.992527 + 0.122022i \(0.961062\pi\)
\(12\) 0 0
\(13\) 5.49333i 0.422563i −0.977425 0.211282i \(-0.932236\pi\)
0.977425 0.211282i \(-0.0677638\pi\)
\(14\) 0 0
\(15\) −13.2426 −0.882843
\(16\) 0 0
\(17\) −11.7426 6.77962i −0.690744 0.398801i 0.113147 0.993578i \(-0.463907\pi\)
−0.803891 + 0.594777i \(0.797240\pi\)
\(18\) 0 0
\(19\) 0.621320 0.358719i 0.0327011 0.0188800i −0.483560 0.875311i \(-0.660657\pi\)
0.516261 + 0.856431i \(0.327323\pi\)
\(20\) 0 0
\(21\) −21.9853 + 19.3242i −1.04692 + 0.920202i
\(22\) 0 0
\(23\) 1.13604 + 1.96768i 0.0493930 + 0.0855512i 0.889665 0.456614i \(-0.150938\pi\)
−0.840272 + 0.542165i \(0.817605\pi\)
\(24\) 0 0
\(25\) −7.48528 + 12.9649i −0.299411 + 0.518596i
\(26\) 0 0
\(27\) 2.15232i 0.0797154i
\(28\) 0 0
\(29\) −20.4853 −0.706389 −0.353195 0.935550i \(-0.614905\pi\)
−0.353195 + 0.935550i \(0.614905\pi\)
\(30\) 0 0
\(31\) 21.3198 + 12.3090i 0.687736 + 0.397064i 0.802763 0.596298i \(-0.203362\pi\)
−0.115028 + 0.993362i \(0.536696\pi\)
\(32\) 0 0
\(33\) −47.9558 + 27.6873i −1.45321 + 0.839010i
\(34\) 0 0
\(35\) −4.34924 21.7377i −0.124264 0.621076i
\(36\) 0 0
\(37\) 32.4706 + 56.2407i 0.877583 + 1.52002i 0.853986 + 0.520296i \(0.174179\pi\)
0.0235970 + 0.999722i \(0.492488\pi\)
\(38\) 0 0
\(39\) 11.4853 19.8931i 0.294494 0.510079i
\(40\) 0 0
\(41\) 21.0308i 0.512946i 0.966551 + 0.256473i \(0.0825605\pi\)
−0.966551 + 0.256473i \(0.917439\pi\)
\(42\) 0 0
\(43\) −6.48528 −0.150820 −0.0754102 0.997153i \(-0.524027\pi\)
−0.0754102 + 0.997153i \(0.524027\pi\)
\(44\) 0 0
\(45\) −23.2721 13.4361i −0.517157 0.298581i
\(46\) 0 0
\(47\) 41.3787 23.8900i 0.880397 0.508298i 0.00960801 0.999954i \(-0.496942\pi\)
0.870789 + 0.491656i \(0.163608\pi\)
\(48\) 0 0
\(49\) −38.9411 29.7420i −0.794717 0.606980i
\(50\) 0 0
\(51\) −28.3492 49.1023i −0.555867 0.962791i
\(52\) 0 0
\(53\) 11.0147 19.0781i 0.207825 0.359963i −0.743204 0.669065i \(-0.766695\pi\)
0.951029 + 0.309101i \(0.100028\pi\)
\(54\) 0 0
\(55\) 41.9385i 0.762518i
\(56\) 0 0
\(57\) 3.00000 0.0526316
\(58\) 0 0
\(59\) 72.5330 + 41.8770i 1.22937 + 0.709779i 0.966899 0.255160i \(-0.0821282\pi\)
0.262474 + 0.964939i \(0.415462\pi\)
\(60\) 0 0
\(61\) −57.3823 + 33.1297i −0.940693 + 0.543109i −0.890177 0.455614i \(-0.849420\pi\)
−0.0505153 + 0.998723i \(0.516086\pi\)
\(62\) 0 0
\(63\) −58.2426 + 11.6531i −0.924486 + 0.184970i
\(64\) 0 0
\(65\) 8.69848 + 15.0662i 0.133823 + 0.231788i
\(66\) 0 0
\(67\) 46.3198 80.2283i 0.691340 1.19744i −0.280058 0.959983i \(-0.590354\pi\)
0.971399 0.237454i \(-0.0763128\pi\)
\(68\) 0 0
\(69\) 9.50079i 0.137693i
\(70\) 0 0
\(71\) −48.4264 −0.682062 −0.341031 0.940052i \(-0.610776\pi\)
−0.341031 + 0.940052i \(0.610776\pi\)
\(72\) 0 0
\(73\) 113.441 + 65.4953i 1.55399 + 0.897195i 0.997811 + 0.0661316i \(0.0210657\pi\)
0.556177 + 0.831064i \(0.312268\pi\)
\(74\) 0 0
\(75\) −54.2132 + 31.3000i −0.722843 + 0.417333i
\(76\) 0 0
\(77\) −61.1985 69.6258i −0.794786 0.904231i
\(78\) 0 0
\(79\) 38.1066 + 66.0026i 0.482362 + 0.835476i 0.999795 0.0202482i \(-0.00644564\pi\)
−0.517433 + 0.855724i \(0.673112\pi\)
\(80\) 0 0
\(81\) 42.6838 73.9305i 0.526960 0.912722i
\(82\) 0 0
\(83\) 107.981i 1.30098i 0.759514 + 0.650491i \(0.225437\pi\)
−0.759514 + 0.650491i \(0.774563\pi\)
\(84\) 0 0
\(85\) 42.9411 0.505190
\(86\) 0 0
\(87\) −74.1838 42.8300i −0.852687 0.492299i
\(88\) 0 0
\(89\) −145.412 + 83.9535i −1.63384 + 0.943297i −0.650945 + 0.759125i \(0.725627\pi\)
−0.982894 + 0.184173i \(0.941039\pi\)
\(90\) 0 0
\(91\) 36.4264 + 12.3196i 0.400290 + 0.135380i
\(92\) 0 0
\(93\) 51.4706 + 89.1496i 0.553447 + 0.958598i
\(94\) 0 0
\(95\) −1.13604 + 1.96768i −0.0119583 + 0.0207124i
\(96\) 0 0
\(97\) 25.5816i 0.263728i −0.991268 0.131864i \(-0.957904\pi\)
0.991268 0.131864i \(-0.0420962\pi\)
\(98\) 0 0
\(99\) −112.368 −1.13503
\(100\) 0 0
\(101\) −24.6838 14.2512i −0.244394 0.141101i 0.372801 0.927911i \(-0.378397\pi\)
−0.617194 + 0.786811i \(0.711731\pi\)
\(102\) 0 0
\(103\) 48.9228 28.2456i 0.474979 0.274229i −0.243343 0.969940i \(-0.578244\pi\)
0.718322 + 0.695711i \(0.244911\pi\)
\(104\) 0 0
\(105\) 29.6985 87.8124i 0.282843 0.836308i
\(106\) 0 0
\(107\) 23.8051 + 41.2316i 0.222477 + 0.385342i 0.955560 0.294798i \(-0.0952523\pi\)
−0.733082 + 0.680140i \(0.761919\pi\)
\(108\) 0 0
\(109\) 37.6543 65.2192i 0.345453 0.598341i −0.639983 0.768389i \(-0.721059\pi\)
0.985436 + 0.170047i \(0.0543921\pi\)
\(110\) 0 0
\(111\) 271.554i 2.44643i
\(112\) 0 0
\(113\) 85.4558 0.756246 0.378123 0.925755i \(-0.376570\pi\)
0.378123 + 0.925755i \(0.376570\pi\)
\(114\) 0 0
\(115\) −6.23149 3.59775i −0.0541869 0.0312848i
\(116\) 0 0
\(117\) 40.3675 23.3062i 0.345022 0.199198i
\(118\) 0 0
\(119\) 71.2904 62.6616i 0.599079 0.526568i
\(120\) 0 0
\(121\) −27.1838 47.0837i −0.224659 0.389121i
\(122\) 0 0
\(123\) −43.9706 + 76.1592i −0.357484 + 0.619181i
\(124\) 0 0
\(125\) 126.584i 1.01267i
\(126\) 0 0
\(127\) −60.6619 −0.477653 −0.238826 0.971062i \(-0.576763\pi\)
−0.238826 + 0.971062i \(0.576763\pi\)
\(128\) 0 0
\(129\) −23.4853 13.5592i −0.182056 0.105110i
\(130\) 0 0
\(131\) 115.136 66.4738i 0.878901 0.507434i 0.00860515 0.999963i \(-0.497261\pi\)
0.870296 + 0.492529i \(0.163928\pi\)
\(132\) 0 0
\(133\) 0.985281 + 4.92447i 0.00740813 + 0.0370261i
\(134\) 0 0
\(135\) 3.40812 + 5.90303i 0.0252453 + 0.0437262i
\(136\) 0 0
\(137\) 58.7132 101.694i 0.428564 0.742294i −0.568182 0.822903i \(-0.692353\pi\)
0.996746 + 0.0806089i \(0.0256865\pi\)
\(138\) 0 0
\(139\) 68.5857i 0.493422i 0.969089 + 0.246711i \(0.0793499\pi\)
−0.969089 + 0.246711i \(0.920650\pi\)
\(140\) 0 0
\(141\) 199.794 1.41698
\(142\) 0 0
\(143\) 63.0000 + 36.3731i 0.440559 + 0.254357i
\(144\) 0 0
\(145\) 56.1838 32.4377i 0.387474 0.223708i
\(146\) 0 0
\(147\) −78.8345 189.122i −0.536289 1.28655i
\(148\) 0 0
\(149\) −13.1985 22.8604i −0.0885804 0.153426i 0.818331 0.574747i \(-0.194900\pi\)
−0.906911 + 0.421322i \(0.861566\pi\)
\(150\) 0 0
\(151\) 67.1066 116.232i 0.444415 0.769749i −0.553597 0.832785i \(-0.686745\pi\)
0.998011 + 0.0630363i \(0.0200784\pi\)
\(152\) 0 0
\(153\) 115.054i 0.751986i
\(154\) 0 0
\(155\) −77.9634 −0.502990
\(156\) 0 0
\(157\) 196.323 + 113.347i 1.25047 + 0.721958i 0.971202 0.238256i \(-0.0765759\pi\)
0.279265 + 0.960214i \(0.409909\pi\)
\(158\) 0 0
\(159\) 79.7756 46.0585i 0.501734 0.289676i
\(160\) 0 0
\(161\) −15.5955 + 3.12032i −0.0968662 + 0.0193808i
\(162\) 0 0
\(163\) −45.9889 79.6550i −0.282140 0.488681i 0.689771 0.724027i \(-0.257711\pi\)
−0.971912 + 0.235346i \(0.924378\pi\)
\(164\) 0 0
\(165\) 87.6838 151.873i 0.531417 0.920441i
\(166\) 0 0
\(167\) 203.482i 1.21845i −0.792996 0.609227i \(-0.791480\pi\)
0.792996 0.609227i \(-0.208520\pi\)
\(168\) 0 0
\(169\) 138.823 0.821440
\(170\) 0 0
\(171\) 5.27208 + 3.04384i 0.0308309 + 0.0178002i
\(172\) 0 0
\(173\) −61.3234 + 35.4051i −0.354470 + 0.204654i −0.666652 0.745369i \(-0.732273\pi\)
0.312182 + 0.950022i \(0.398940\pi\)
\(174\) 0 0
\(175\) −69.1838 78.7107i −0.395336 0.449775i
\(176\) 0 0
\(177\) 175.110 + 303.300i 0.989323 + 1.71356i
\(178\) 0 0
\(179\) 54.4081 94.2376i 0.303956 0.526467i −0.673072 0.739577i \(-0.735026\pi\)
0.977028 + 0.213109i \(0.0683591\pi\)
\(180\) 0 0
\(181\) 99.6607i 0.550611i −0.961357 0.275306i \(-0.911221\pi\)
0.961357 0.275306i \(-0.0887791\pi\)
\(182\) 0 0
\(183\) −277.066 −1.51402
\(184\) 0 0
\(185\) −178.110 102.832i −0.962758 0.555848i
\(186\) 0 0
\(187\) 155.504 89.7800i 0.831570 0.480107i
\(188\) 0 0
\(189\) 14.2721 + 4.82687i 0.0755136 + 0.0255390i
\(190\) 0 0
\(191\) −34.9523 60.5391i −0.182996 0.316959i 0.759903 0.650036i \(-0.225246\pi\)
−0.942899 + 0.333077i \(0.891913\pi\)
\(192\) 0 0
\(193\) 16.1690 28.0056i 0.0837774 0.145107i −0.821092 0.570796i \(-0.806635\pi\)
0.904870 + 0.425689i \(0.139968\pi\)
\(194\) 0 0
\(195\) 72.7461i 0.373057i
\(196\) 0 0
\(197\) −277.103 −1.40661 −0.703306 0.710887i \(-0.748294\pi\)
−0.703306 + 0.710887i \(0.748294\pi\)
\(198\) 0 0
\(199\) 145.011 + 83.7222i 0.728699 + 0.420715i 0.817946 0.575295i \(-0.195113\pi\)
−0.0892469 + 0.996010i \(0.528446\pi\)
\(200\) 0 0
\(201\) 335.478 193.688i 1.66904 0.963623i
\(202\) 0 0
\(203\) 45.9411 135.839i 0.226311 0.669155i
\(204\) 0 0
\(205\) −33.3015 57.6799i −0.162446 0.281365i
\(206\) 0 0
\(207\) −9.63961 + 16.6963i −0.0465682 + 0.0806584i
\(208\) 0 0
\(209\) 9.50079i 0.0454583i
\(210\) 0 0
\(211\) 128.073 0.606982 0.303491 0.952834i \(-0.401848\pi\)
0.303491 + 0.952834i \(0.401848\pi\)
\(212\) 0 0
\(213\) −175.368 101.248i −0.823322 0.475345i
\(214\) 0 0
\(215\) 17.7868 10.2692i 0.0827293 0.0477638i
\(216\) 0 0
\(217\) −129.434 + 113.768i −0.596470 + 0.524275i
\(218\) 0 0
\(219\) 273.871 + 474.359i 1.25055 + 2.16602i
\(220\) 0 0
\(221\) −37.2426 + 64.5061i −0.168519 + 0.291883i
\(222\) 0 0
\(223\) 417.169i 1.87071i 0.353705 + 0.935357i \(0.384922\pi\)
−0.353705 + 0.935357i \(0.615078\pi\)
\(224\) 0 0
\(225\) −127.029 −0.564575
\(226\) 0 0
\(227\) −201.143 116.130i −0.886093 0.511586i −0.0134307 0.999910i \(-0.504275\pi\)
−0.872663 + 0.488324i \(0.837609\pi\)
\(228\) 0 0
\(229\) 72.4188 41.8110i 0.316239 0.182581i −0.333476 0.942759i \(-0.608222\pi\)
0.649715 + 0.760178i \(0.274888\pi\)
\(230\) 0 0
\(231\) −76.0477 380.089i −0.329211 1.64541i
\(232\) 0 0
\(233\) −109.537 189.723i −0.470114 0.814261i 0.529302 0.848434i \(-0.322454\pi\)
−0.999416 + 0.0341721i \(0.989121\pi\)
\(234\) 0 0
\(235\) −75.6579 + 131.043i −0.321949 + 0.557631i
\(236\) 0 0
\(237\) 318.689i 1.34468i
\(238\) 0 0
\(239\) 193.103 0.807961 0.403980 0.914768i \(-0.367626\pi\)
0.403980 + 0.914768i \(0.367626\pi\)
\(240\) 0 0
\(241\) 42.8970 + 24.7666i 0.177996 + 0.102766i 0.586351 0.810057i \(-0.300564\pi\)
−0.408355 + 0.912823i \(0.633897\pi\)
\(242\) 0 0
\(243\) 292.368 168.798i 1.20316 0.694644i
\(244\) 0 0
\(245\) 153.897 + 19.9098i 0.628151 + 0.0812646i
\(246\) 0 0
\(247\) −1.97056 3.41311i −0.00797799 0.0138183i
\(248\) 0 0
\(249\) −225.765 + 391.036i −0.906685 + 1.57042i
\(250\) 0 0
\(251\) 162.524i 0.647507i 0.946141 + 0.323754i \(0.104945\pi\)
−0.946141 + 0.323754i \(0.895055\pi\)
\(252\) 0 0
\(253\) −30.0883 −0.118926
\(254\) 0 0
\(255\) 155.504 + 89.7800i 0.609818 + 0.352079i
\(256\) 0 0
\(257\) −85.8747 + 49.5798i −0.334143 + 0.192917i −0.657679 0.753298i \(-0.728462\pi\)
0.323536 + 0.946216i \(0.395128\pi\)
\(258\) 0 0
\(259\) −445.753 + 89.1857i −1.72106 + 0.344346i
\(260\) 0 0
\(261\) −86.9117 150.535i −0.332995 0.576764i
\(262\) 0 0
\(263\) −217.173 + 376.154i −0.825751 + 1.43024i 0.0755923 + 0.997139i \(0.475915\pi\)
−0.901344 + 0.433105i \(0.857418\pi\)
\(264\) 0 0
\(265\) 69.7657i 0.263267i
\(266\) 0 0
\(267\) −702.110 −2.62962
\(268\) 0 0
\(269\) 79.1619 + 45.7041i 0.294282 + 0.169904i 0.639871 0.768482i \(-0.278988\pi\)
−0.345589 + 0.938386i \(0.612321\pi\)
\(270\) 0 0
\(271\) 14.8051 8.54772i 0.0546313 0.0315414i −0.472436 0.881365i \(-0.656625\pi\)
0.527067 + 0.849824i \(0.323292\pi\)
\(272\) 0 0
\(273\) 106.154 + 120.772i 0.388844 + 0.442389i
\(274\) 0 0
\(275\) −99.1249 171.689i −0.360454 0.624325i
\(276\) 0 0
\(277\) −200.206 + 346.766i −0.722764 + 1.25186i 0.237124 + 0.971479i \(0.423795\pi\)
−0.959888 + 0.280385i \(0.909538\pi\)
\(278\) 0 0
\(279\) 208.891i 0.748712i
\(280\) 0 0
\(281\) −538.690 −1.91705 −0.958524 0.285012i \(-0.908002\pi\)
−0.958524 + 0.285012i \(0.908002\pi\)
\(282\) 0 0
\(283\) 267.783 + 154.604i 0.946229 + 0.546306i 0.891907 0.452218i \(-0.149367\pi\)
0.0543215 + 0.998523i \(0.482700\pi\)
\(284\) 0 0
\(285\) −8.22792 + 4.75039i −0.0288699 + 0.0166680i
\(286\) 0 0
\(287\) −139.456 47.1645i −0.485909 0.164336i
\(288\) 0 0
\(289\) −52.5736 91.0601i −0.181916 0.315087i
\(290\) 0 0
\(291\) 53.4853 92.6392i 0.183798 0.318348i
\(292\) 0 0
\(293\) 327.391i 1.11738i 0.829378 + 0.558688i \(0.188695\pi\)
−0.829378 + 0.558688i \(0.811305\pi\)
\(294\) 0 0
\(295\) −265.243 −0.899128
\(296\) 0 0
\(297\) 24.6838 + 14.2512i 0.0831103 + 0.0479838i
\(298\) 0 0
\(299\) 10.8091 6.24063i 0.0361508 0.0208717i
\(300\) 0 0
\(301\) 14.5442 43.0041i 0.0483195 0.142871i
\(302\) 0 0
\(303\) −59.5919 103.216i −0.196673 0.340647i
\(304\) 0 0
\(305\) 104.919 181.725i 0.343998 0.595821i
\(306\) 0 0
\(307\) 256.140i 0.834331i 0.908831 + 0.417165i \(0.136976\pi\)
−0.908831 + 0.417165i \(0.863024\pi\)
\(308\) 0 0
\(309\) 236.220 0.764467
\(310\) 0 0
\(311\) 187.349 + 108.166i 0.602409 + 0.347801i 0.769989 0.638057i \(-0.220262\pi\)
−0.167580 + 0.985859i \(0.553595\pi\)
\(312\) 0 0
\(313\) 135.809 78.4092i 0.433893 0.250509i −0.267110 0.963666i \(-0.586069\pi\)
0.701004 + 0.713157i \(0.252736\pi\)
\(314\) 0 0
\(315\) 141.286 124.185i 0.448528 0.394239i
\(316\) 0 0
\(317\) −224.015 388.005i −0.706671 1.22399i −0.966085 0.258224i \(-0.916863\pi\)
0.259414 0.965766i \(-0.416471\pi\)
\(318\) 0 0
\(319\) 135.640 234.935i 0.425203 0.736472i
\(320\) 0 0
\(321\) 199.084i 0.620199i
\(322\) 0 0
\(323\) −9.72792 −0.0301174
\(324\) 0 0
\(325\) 71.2203 + 41.1191i 0.219140 + 0.126520i
\(326\) 0 0
\(327\) 272.717 157.453i 0.833996 0.481508i
\(328\) 0 0
\(329\) 65.6177 + 327.960i 0.199446 + 0.996839i
\(330\) 0 0
\(331\) −27.5036 47.6376i −0.0830924 0.143920i 0.821484 0.570231i \(-0.193146\pi\)
−0.904577 + 0.426311i \(0.859813\pi\)
\(332\) 0 0
\(333\) −275.522 + 477.218i −0.827393 + 1.43309i
\(334\) 0 0
\(335\) 293.383i 0.875770i
\(336\) 0 0
\(337\) −111.632 −0.331254 −0.165627 0.986189i \(-0.552965\pi\)
−0.165627 + 0.986189i \(0.552965\pi\)
\(338\) 0 0
\(339\) 309.463 + 178.669i 0.912870 + 0.527046i
\(340\) 0 0
\(341\) −282.331 + 163.004i −0.827949 + 0.478016i
\(342\) 0 0
\(343\) 284.551 191.519i 0.829596 0.558365i
\(344\) 0 0
\(345\) −15.0442 26.0572i −0.0436062 0.0755282i
\(346\) 0 0
\(347\) 188.628 326.714i 0.543598 0.941539i −0.455096 0.890442i \(-0.650395\pi\)
0.998694 0.0510967i \(-0.0162717\pi\)
\(348\) 0 0
\(349\) 204.034i 0.584624i −0.956323 0.292312i \(-0.905575\pi\)
0.956323 0.292312i \(-0.0944246\pi\)
\(350\) 0 0
\(351\) −11.8234 −0.0336848
\(352\) 0 0
\(353\) −361.198 208.538i −1.02323 0.590759i −0.108189 0.994130i \(-0.534505\pi\)
−0.915036 + 0.403371i \(0.867838\pi\)
\(354\) 0 0
\(355\) 132.816 76.6815i 0.374130 0.216004i
\(356\) 0 0
\(357\) 389.176 77.8658i 1.09013 0.218112i
\(358\) 0 0
\(359\) 89.4153 + 154.872i 0.249068 + 0.431398i 0.963267 0.268544i \(-0.0865425\pi\)
−0.714200 + 0.699942i \(0.753209\pi\)
\(360\) 0 0
\(361\) −180.243 + 312.189i −0.499287 + 0.864791i
\(362\) 0 0
\(363\) 227.340i 0.626281i
\(364\) 0 0
\(365\) −414.838 −1.13654
\(366\) 0 0
\(367\) −544.724 314.497i −1.48426 0.856939i −0.484422 0.874835i \(-0.660970\pi\)
−0.999840 + 0.0178960i \(0.994303\pi\)
\(368\) 0 0
\(369\) −154.544 + 89.2261i −0.418819 + 0.241805i
\(370\) 0 0
\(371\) 101.805 + 115.824i 0.274407 + 0.312194i
\(372\) 0 0
\(373\) −127.779 221.320i −0.342572 0.593351i 0.642338 0.766422i \(-0.277965\pi\)
−0.984910 + 0.173070i \(0.944631\pi\)
\(374\) 0 0
\(375\) 264.658 458.401i 0.705754 1.22240i
\(376\) 0 0
\(377\) 112.532i 0.298494i
\(378\) 0 0
\(379\) −219.750 −0.579816 −0.289908 0.957055i \(-0.593625\pi\)
−0.289908 + 0.957055i \(0.593625\pi\)
\(380\) 0 0
\(381\) −219.676 126.830i −0.576578 0.332887i
\(382\) 0 0
\(383\) −14.7534 + 8.51785i −0.0385205 + 0.0222398i −0.519137 0.854691i \(-0.673746\pi\)
0.480616 + 0.876931i \(0.340413\pi\)
\(384\) 0 0
\(385\) 278.095 + 94.0530i 0.722326 + 0.244293i
\(386\) 0 0
\(387\) −27.5147 47.6569i −0.0710975 0.123144i
\(388\) 0 0
\(389\) −76.1102 + 131.827i −0.195656 + 0.338886i −0.947115 0.320893i \(-0.896017\pi\)
0.751459 + 0.659779i \(0.229350\pi\)
\(390\) 0 0
\(391\) 30.8076i 0.0787919i
\(392\) 0 0
\(393\) 555.926 1.41457
\(394\) 0 0
\(395\) −209.025 120.681i −0.529178 0.305521i
\(396\) 0 0
\(397\) 322.786 186.361i 0.813064 0.469423i −0.0349549 0.999389i \(-0.511129\pi\)
0.848019 + 0.529966i \(0.177795\pi\)
\(398\) 0 0
\(399\) −6.72792 + 19.8931i −0.0168620 + 0.0498574i
\(400\) 0 0
\(401\) −325.786 564.279i −0.812435 1.40718i −0.911155 0.412063i \(-0.864808\pi\)
0.0987205 0.995115i \(-0.468525\pi\)
\(402\) 0 0
\(403\) 67.6173 117.117i 0.167785 0.290612i
\(404\) 0 0
\(405\) 270.353i 0.667538i
\(406\) 0 0
\(407\) −859.992 −2.11300
\(408\) 0 0
\(409\) 462.081 + 266.782i 1.12978 + 0.652280i 0.943880 0.330289i \(-0.107146\pi\)
0.185902 + 0.982568i \(0.440479\pi\)
\(410\) 0 0
\(411\) 425.239 245.512i 1.03464 0.597352i
\(412\) 0 0
\(413\) −440.353 + 387.054i −1.06623 + 0.937176i
\(414\) 0 0
\(415\) −170.985 296.154i −0.412012 0.713625i
\(416\) 0 0
\(417\) −143.397 + 248.371i −0.343878 + 0.595614i
\(418\) 0 0
\(419\) 534.252i 1.27507i 0.770423 + 0.637533i \(0.220045\pi\)
−0.770423 + 0.637533i \(0.779955\pi\)
\(420\) 0 0
\(421\) −157.220 −0.373445 −0.186723 0.982413i \(-0.559787\pi\)
−0.186723 + 0.982413i \(0.559787\pi\)
\(422\) 0 0
\(423\) 351.110 + 202.713i 0.830047 + 0.479228i
\(424\) 0 0
\(425\) 175.794 101.495i 0.413633 0.238811i
\(426\) 0 0
\(427\) −90.9960 454.801i −0.213105 1.06511i
\(428\) 0 0
\(429\) 152.095 + 263.437i 0.354535 + 0.614072i
\(430\) 0 0
\(431\) 114.268 197.918i 0.265123 0.459207i −0.702473 0.711711i \(-0.747921\pi\)
0.967596 + 0.252504i \(0.0812541\pi\)
\(432\) 0 0
\(433\) 47.5549i 0.109827i 0.998491 + 0.0549133i \(0.0174882\pi\)
−0.998491 + 0.0549133i \(0.982512\pi\)
\(434\) 0 0
\(435\) 271.279 0.623630
\(436\) 0 0
\(437\) 1.41169 + 0.815039i 0.00323041 + 0.00186508i
\(438\) 0 0
\(439\) −63.9594 + 36.9270i −0.145693 + 0.0841161i −0.571075 0.820898i \(-0.693473\pi\)
0.425381 + 0.905014i \(0.360140\pi\)
\(440\) 0 0
\(441\) 53.3452 412.342i 0.120964 0.935017i
\(442\) 0 0
\(443\) 117.320 + 203.204i 0.264830 + 0.458699i 0.967519 0.252798i \(-0.0813507\pi\)
−0.702689 + 0.711497i \(0.748017\pi\)
\(444\) 0 0
\(445\) 265.875 460.508i 0.597471 1.03485i
\(446\) 0 0
\(447\) 110.380i 0.246935i
\(448\) 0 0
\(449\) −255.161 −0.568288 −0.284144 0.958782i \(-0.591709\pi\)
−0.284144 + 0.958782i \(0.591709\pi\)
\(450\) 0 0
\(451\) −241.191 139.252i −0.534791 0.308762i
\(452\) 0 0
\(453\) 486.029 280.609i 1.07291 0.619446i
\(454\) 0 0
\(455\) −119.412 + 23.8918i −0.262444 + 0.0525095i
\(456\) 0 0
\(457\) 72.8675 + 126.210i 0.159448 + 0.276171i 0.934670 0.355518i \(-0.115695\pi\)
−0.775222 + 0.631689i \(0.782362\pi\)
\(458\) 0 0
\(459\) −14.5919 + 25.2739i −0.0317906 + 0.0550629i
\(460\) 0 0
\(461\) 888.329i 1.92696i −0.267777 0.963481i \(-0.586289\pi\)
0.267777 0.963481i \(-0.413711\pi\)
\(462\) 0 0
\(463\) 234.014 0.505430 0.252715 0.967541i \(-0.418676\pi\)
0.252715 + 0.967541i \(0.418676\pi\)
\(464\) 0 0
\(465\) −282.331 163.004i −0.607162 0.350545i
\(466\) 0 0
\(467\) −681.231 + 393.309i −1.45874 + 0.842204i −0.998950 0.0458237i \(-0.985409\pi\)
−0.459790 + 0.888028i \(0.652075\pi\)
\(468\) 0 0
\(469\) 428.117 + 487.071i 0.912830 + 1.03853i
\(470\) 0 0
\(471\) 473.967 + 820.934i 1.00630 + 1.74296i
\(472\) 0 0
\(473\) 42.9411 74.3762i 0.0907846 0.157244i
\(474\) 0 0
\(475\) 10.7405i 0.0226115i
\(476\) 0 0
\(477\) 186.926 0.391878
\(478\) 0 0
\(479\) 638.202 + 368.466i 1.33236 + 0.769240i 0.985661 0.168735i \(-0.0539682\pi\)
0.346702 + 0.937975i \(0.387302\pi\)
\(480\) 0 0
\(481\) 308.948 178.371i 0.642304 0.370834i
\(482\) 0 0
\(483\) −63.0000 21.3068i −0.130435 0.0441136i
\(484\) 0 0
\(485\) 40.5076 + 70.1612i 0.0835208 + 0.144662i
\(486\) 0 0
\(487\) −135.349 + 234.432i −0.277925 + 0.481379i −0.970869 0.239612i \(-0.922980\pi\)
0.692944 + 0.720991i \(0.256313\pi\)
\(488\) 0 0
\(489\) 384.609i 0.786520i
\(490\) 0 0
\(491\) −760.161 −1.54819 −0.774094 0.633070i \(-0.781794\pi\)
−0.774094 + 0.633070i \(0.781794\pi\)
\(492\) 0 0
\(493\) 240.551 + 138.882i 0.487934 + 0.281709i
\(494\) 0 0
\(495\) 308.184 177.930i 0.622593 0.359455i
\(496\) 0 0
\(497\) 108.603 321.117i 0.218517 0.646111i
\(498\) 0 0
\(499\) 62.7462 + 108.680i 0.125744 + 0.217795i 0.922023 0.387134i \(-0.126535\pi\)
−0.796280 + 0.604929i \(0.793202\pi\)
\(500\) 0 0
\(501\) 425.434 736.873i 0.849169 1.47080i
\(502\) 0 0
\(503\) 117.083i 0.232770i 0.993204 + 0.116385i \(0.0371306\pi\)
−0.993204 + 0.116385i \(0.962869\pi\)
\(504\) 0 0
\(505\) 90.2649 0.178742
\(506\) 0 0
\(507\) 502.724 + 290.248i 0.991566 + 0.572481i
\(508\) 0 0
\(509\) 574.110 331.463i 1.12792 0.651204i 0.184507 0.982831i \(-0.440931\pi\)
0.943410 + 0.331627i \(0.107598\pi\)
\(510\) 0 0
\(511\) −688.709 + 605.349i −1.34777 + 1.18464i
\(512\) 0 0
\(513\) −0.772078 1.33728i −0.00150503 0.00260678i
\(514\) 0 0
\(515\) −89.4518 + 154.935i −0.173693 + 0.300845i
\(516\) 0 0
\(517\) 632.733i 1.22386i
\(518\) 0 0
\(519\) −296.095 −0.570511
\(520\) 0 0
\(521\) −40.8229 23.5691i −0.0783550 0.0452383i 0.460311 0.887758i \(-0.347738\pi\)
−0.538666 + 0.842520i \(0.681071\pi\)
\(522\) 0 0
\(523\) −432.554 + 249.735i −0.827064 + 0.477506i −0.852846 0.522162i \(-0.825126\pi\)
0.0257824 + 0.999668i \(0.491792\pi\)
\(524\) 0 0
\(525\) −85.9706 429.684i −0.163753 0.818446i
\(526\) 0 0
\(527\) −166.901 289.080i −0.316699 0.548539i
\(528\) 0 0
\(529\) 261.919 453.657i 0.495121 0.857574i
\(530\) 0 0
\(531\) 710.675i 1.33837i
\(532\) 0 0
\(533\) 115.529 0.216752
\(534\) 0 0
\(535\) −130.578 75.3890i −0.244070 0.140914i
\(536\) 0 0
\(537\) 394.058 227.510i 0.733815 0.423668i
\(538\) 0 0
\(539\) 598.937 249.663i 1.11120 0.463197i
\(540\) 0 0
\(541\) 249.405 + 431.981i 0.461007 + 0.798487i 0.999011 0.0444550i \(-0.0141551\pi\)
−0.538005 + 0.842942i \(0.680822\pi\)
\(542\) 0 0
\(543\) 208.368 360.903i 0.383734 0.664647i
\(544\) 0 0
\(545\) 238.497i 0.437609i
\(546\) 0 0
\(547\) 279.897 0.511694 0.255847 0.966717i \(-0.417646\pi\)
0.255847 + 0.966717i \(0.417646\pi\)
\(548\) 0 0
\(549\) −486.905 281.114i −0.886894 0.512048i
\(550\) 0 0
\(551\) −12.7279 + 7.34847i −0.0230997 + 0.0133366i
\(552\) 0 0
\(553\) −523.124 + 104.666i −0.945976 + 0.189269i
\(554\) 0 0
\(555\) −429.996 744.775i −0.774768 1.34194i
\(556\) 0 0
\(557\) −130.890 + 226.708i −0.234991 + 0.407016i −0.959270 0.282491i \(-0.908839\pi\)
0.724279 + 0.689507i \(0.242173\pi\)
\(558\) 0 0
\(559\) 35.6258i 0.0637312i
\(560\) 0 0
\(561\) 750.838 1.33839
\(562\) 0 0
\(563\) 420.076 + 242.531i 0.746139 + 0.430784i 0.824297 0.566157i \(-0.191571\pi\)
−0.0781581 + 0.996941i \(0.524904\pi\)
\(564\) 0 0
\(565\) −234.375 + 135.316i −0.414822 + 0.239498i
\(566\) 0 0
\(567\) 394.511 + 448.837i 0.695786 + 0.791599i
\(568\) 0 0
\(569\) 227.000 + 393.175i 0.398945 + 0.690993i 0.993596 0.112991i \(-0.0360432\pi\)
−0.594651 + 0.803984i \(0.702710\pi\)
\(570\) 0 0
\(571\) −115.769 + 200.517i −0.202747 + 0.351168i −0.949413 0.314032i \(-0.898320\pi\)
0.746666 + 0.665200i \(0.231654\pi\)
\(572\) 0 0
\(573\) 292.309i 0.510137i
\(574\) 0 0
\(575\) −34.0143 −0.0591553
\(576\) 0 0
\(577\) 564.014 + 325.634i 0.977494 + 0.564356i 0.901513 0.432753i \(-0.142458\pi\)
0.0759812 + 0.997109i \(0.475791\pi\)
\(578\) 0 0
\(579\) 117.107 67.6115i 0.202257 0.116773i
\(580\) 0 0
\(581\) −716.029 242.164i −1.23241 0.416805i
\(582\) 0 0
\(583\) 145.864 + 252.644i 0.250195 + 0.433351i
\(584\) 0 0
\(585\) −73.8091 + 127.841i −0.126169 + 0.218532i
\(586\) 0 0
\(587\) 823.029i 1.40209i −0.713116 0.701046i \(-0.752717\pi\)
0.713116 0.701046i \(-0.247283\pi\)
\(588\) 0 0
\(589\) 17.6619 0.0299863
\(590\) 0 0
\(591\) −1003.48 579.358i −1.69793 0.980301i
\(592\) 0 0
\(593\) −700.110 + 404.209i −1.18062 + 0.681634i −0.956159 0.292848i \(-0.905397\pi\)
−0.224465 + 0.974482i \(0.572064\pi\)
\(594\) 0 0
\(595\) −96.3015 + 284.744i −0.161851 + 0.478561i
\(596\) 0 0
\(597\) 350.088 + 606.370i 0.586412 + 1.01570i
\(598\) 0 0
\(599\) −265.422 + 459.725i −0.443109 + 0.767488i −0.997918 0.0644900i \(-0.979458\pi\)
0.554809 + 0.831978i \(0.312791\pi\)
\(600\) 0 0
\(601\) 936.503i 1.55824i −0.626874 0.779121i \(-0.715666\pi\)
0.626874 0.779121i \(-0.284334\pi\)
\(602\) 0 0
\(603\) 786.073 1.30360
\(604\) 0 0
\(605\) 149.111 + 86.0890i 0.246464 + 0.142296i
\(606\) 0 0
\(607\) 521.452 301.060i 0.859064 0.495981i −0.00463474 0.999989i \(-0.501475\pi\)
0.863699 + 0.504008i \(0.168142\pi\)
\(608\) 0 0
\(609\) 450.375 395.862i 0.739531 0.650020i
\(610\) 0 0
\(611\) −131.235 227.307i −0.214788 0.372024i
\(612\) 0 0
\(613\) 548.448 949.940i 0.894695 1.54966i 0.0605142 0.998167i \(-0.480726\pi\)
0.834181 0.551491i \(-0.185941\pi\)
\(614\) 0 0
\(615\) 278.503i 0.452851i
\(616\) 0 0
\(617\) −432.956 −0.701712 −0.350856 0.936429i \(-0.614109\pi\)
−0.350856 + 0.936429i \(0.614109\pi\)
\(618\) 0 0
\(619\) −194.951 112.555i −0.314946 0.181834i 0.334192 0.942505i \(-0.391537\pi\)
−0.649137 + 0.760671i \(0.724870\pi\)
\(620\) 0 0
\(621\) 4.23506 2.44512i 0.00681975 0.00393738i
\(622\) 0 0
\(623\) −230.592 1152.51i −0.370131 1.84993i
\(624\) 0 0
\(625\) 13.3091 + 23.0520i 0.0212945 + 0.0368832i
\(626\) 0 0
\(627\) −19.8640 + 34.4054i −0.0316810 + 0.0548730i
\(628\) 0 0
\(629\) 880.552i 1.39992i
\(630\) 0 0
\(631\) 750.514 1.18940 0.594702 0.803946i \(-0.297270\pi\)
0.594702 + 0.803946i \(0.297270\pi\)
\(632\) 0 0
\(633\) 463.794 + 267.772i 0.732692 + 0.423020i
\(634\) 0 0
\(635\) 166.374 96.0560i 0.262006 0.151269i
\(636\) 0 0
\(637\) −163.383 + 213.916i −0.256488 + 0.335818i
\(638\) 0 0
\(639\) −205.456 355.860i −0.321527 0.556901i
\(640\) 0 0
\(641\) 580.926 1006.19i 0.906281 1.56973i 0.0870937 0.996200i \(-0.472242\pi\)
0.819188 0.573525i \(-0.194425\pi\)
\(642\) 0 0
\(643\) 121.957i 0.189669i −0.995493 0.0948347i \(-0.969768\pi\)
0.995493 0.0948347i \(-0.0302322\pi\)
\(644\) 0 0
\(645\) 85.8823 0.133151
\(646\) 0 0
\(647\) −137.504 79.3877i −0.212525 0.122701i 0.389959 0.920832i \(-0.372489\pi\)
−0.602484 + 0.798131i \(0.705822\pi\)
\(648\) 0 0
\(649\) −960.529 + 554.561i −1.48001 + 0.854486i
\(650\) 0 0
\(651\) −706.584 + 141.372i −1.08538 + 0.217162i
\(652\) 0 0
\(653\) −195.471 338.565i −0.299342 0.518476i 0.676643 0.736311i \(-0.263434\pi\)
−0.975986 + 0.217835i \(0.930101\pi\)
\(654\) 0 0
\(655\) −210.518 + 364.628i −0.321401 + 0.556683i
\(656\) 0 0
\(657\) 1111.49i 1.69177i
\(658\) 0 0
\(659\) 331.955 0.503726 0.251863 0.967763i \(-0.418957\pi\)
0.251863 + 0.967763i \(0.418957\pi\)
\(660\) 0 0
\(661\) −561.029 323.910i −0.848758 0.490031i 0.0114736 0.999934i \(-0.496348\pi\)
−0.860232 + 0.509904i \(0.829681\pi\)
\(662\) 0 0
\(663\) −269.735 + 155.732i −0.406840 + 0.234889i
\(664\) 0 0
\(665\) −10.5000 11.9459i −0.0157895 0.0179638i
\(666\) 0 0
\(667\) −23.2721 40.3084i −0.0348907 0.0604324i
\(668\) 0 0
\(669\) −872.205 + 1510.70i −1.30374 + 2.25815i
\(670\) 0 0
\(671\) 877.448i 1.30767i
\(672\) 0 0
\(673\) 100.956 0.150009 0.0750047 0.997183i \(-0.476103\pi\)
0.0750047 + 0.997183i \(0.476103\pi\)
\(674\) 0 0
\(675\) 27.9045 + 16.1107i 0.0413401 + 0.0238677i
\(676\) 0 0
\(677\) −643.610 + 371.588i −0.950679 + 0.548875i −0.893292 0.449477i \(-0.851610\pi\)
−0.0573873 + 0.998352i \(0.518277\pi\)
\(678\) 0 0
\(679\) 169.632 + 57.3704i 0.249827 + 0.0844924i
\(680\) 0 0
\(681\) −485.603 841.088i −0.713073 1.23508i
\(682\) 0 0
\(683\) 2.21721 3.84032i 0.00324628 0.00562272i −0.864398 0.502809i \(-0.832300\pi\)
0.867644 + 0.497186i \(0.165633\pi\)
\(684\) 0 0
\(685\) 371.881i 0.542892i
\(686\) 0 0
\(687\) 349.669 0.508980
\(688\) 0 0
\(689\) −104.802 60.5074i −0.152107 0.0878192i
\(690\) 0 0
\(691\) 846.253 488.584i 1.22468 0.707069i 0.258767 0.965940i \(-0.416684\pi\)
0.965912 + 0.258871i \(0.0833506\pi\)
\(692\) 0 0
\(693\) 252.000 745.113i 0.363636 1.07520i
\(694\) 0 0
\(695\) −108.603 188.106i −0.156263 0.270656i
\(696\) 0 0
\(697\) 142.581 246.957i 0.204563 0.354314i
\(698\) 0 0
\(699\) 916.063i 1.31053i
\(700\) 0 0
\(701\) 840.177 1.19854 0.599270 0.800547i \(-0.295458\pi\)
0.599270 + 0.800547i \(0.295458\pi\)
\(702\) 0 0
\(703\) 40.3492 + 23.2956i 0.0573958 + 0.0331375i
\(704\) 0 0
\(705\) −547.963 + 316.367i −0.777252 + 0.448747i
\(706\) 0 0
\(707\) 149.857 131.719i 0.211962 0.186306i
\(708\) 0 0
\(709\) 341.279 + 591.112i 0.481352 + 0.833727i 0.999771 0.0214003i \(-0.00681244\pi\)
−0.518419 + 0.855127i \(0.673479\pi\)
\(710\) 0 0
\(711\) −323.345 + 560.050i −0.454775 + 0.787694i
\(712\) 0 0
\(713\) 55.9340i 0.0784488i
\(714\) 0 0
\(715\) −230.382 −0.322212
\(716\) 0 0
\(717\) 699.286 + 403.733i 0.975295 + 0.563087i
\(718\) 0 0
\(719\) 119.187 68.8126i 0.165768 0.0957060i −0.414821 0.909903i \(-0.636156\pi\)
0.580589 + 0.814197i \(0.302822\pi\)
\(720\) 0 0
\(721\) 77.5812 + 387.754i 0.107602 + 0.537800i
\(722\) 0 0
\(723\) 103.562 + 179.375i 0.143240 + 0.248099i
\(724\) 0 0
\(725\) 153.338 265.589i 0.211501 0.366330i
\(726\) 0 0
\(727\) 264.137i 0.363325i 0.983361 + 0.181662i \(0.0581478\pi\)
−0.983361 + 0.181662i \(0.941852\pi\)
\(728\) 0 0
\(729\) 643.368 0.882534
\(730\) 0 0
\(731\) 76.1543 + 43.9677i 0.104178 + 0.0601474i
\(732\) 0 0
\(733\) −501.705 + 289.660i −0.684455 + 0.395170i −0.801531 0.597953i \(-0.795981\pi\)
0.117077 + 0.993123i \(0.462648\pi\)
\(734\) 0 0
\(735\) 515.683 + 393.863i 0.701610 + 0.535868i
\(736\) 0 0
\(737\) 613.397 + 1062.43i 0.832288 + 1.44157i
\(738\) 0 0
\(739\) −99.0477 + 171.556i −0.134029 + 0.232146i −0.925226 0.379416i \(-0.876125\pi\)
0.791197 + 0.611562i \(0.209458\pi\)
\(740\) 0 0
\(741\) 16.4800i 0.0222402i
\(742\) 0 0
\(743\) 976.690 1.31452 0.657261 0.753663i \(-0.271715\pi\)
0.657261 + 0.753663i \(0.271715\pi\)
\(744\) 0 0
\(745\) 72.3974 + 41.7987i 0.0971777 + 0.0561056i
\(746\) 0 0
\(747\) −793.499 + 458.127i −1.06225 + 0.613289i
\(748\) 0 0
\(749\) −326.794 + 65.3845i −0.436308 + 0.0872958i
\(750\) 0 0
\(751\) 417.665 + 723.417i 0.556145 + 0.963272i 0.997813 + 0.0660933i \(0.0210535\pi\)
−0.441668 + 0.897178i \(0.645613\pi\)
\(752\) 0 0
\(753\) −339.801 + 588.553i −0.451263 + 0.781611i
\(754\) 0 0
\(755\) 425.044i 0.562972i
\(756\) 0 0
\(757\) −104.221 −0.137677 −0.0688383 0.997628i \(-0.521929\pi\)
−0.0688383 + 0.997628i \(0.521929\pi\)
\(758\) 0 0
\(759\) −108.959 62.9077i −0.143557 0.0828824i
\(760\) 0 0
\(761\) −473.785 + 273.540i −0.622583 + 0.359448i −0.777874 0.628420i \(-0.783702\pi\)
0.155291 + 0.987869i \(0.450368\pi\)
\(762\) 0 0
\(763\) 348.025 + 395.950i 0.456128 + 0.518939i
\(764\) 0 0
\(765\) 182.184 + 315.552i 0.238149 + 0.412486i
\(766\) 0 0
\(767\) 230.044 398.447i 0.299927 0.519488i
\(768\) 0 0
\(769\) 341.205i 0.443700i −0.975081 0.221850i \(-0.928790\pi\)
0.975081 0.221850i \(-0.0712095\pi\)
\(770\) 0 0
\(771\) −414.640 −0.537795
\(772\) 0 0
\(773\) 425.213 + 245.497i 0.550081 + 0.317590i 0.749155 0.662395i \(-0.230460\pi\)
−0.199074 + 0.979985i \(0.563793\pi\)
\(774\) 0 0
\(775\) −319.169 + 184.273i −0.411832 + 0.237771i
\(776\) 0 0
\(777\) −1800.68 608.998i −2.31748 0.783781i
\(778\) 0 0
\(779\) 7.54416 + 13.0669i 0.00968441 + 0.0167739i
\(780\) 0 0
\(781\) 320.647 555.376i 0.410559 0.711109i
\(782\) 0 0
\(783\) 44.0908i 0.0563101i
\(784\) 0 0
\(785\) −717.926 −0.914555
\(786\) 0 0
\(787\) −260.202 150.228i −0.330625 0.190887i 0.325493 0.945544i \(-0.394470\pi\)
−0.656119 + 0.754658i \(0.727803\pi\)
\(788\) 0 0
\(789\) −1572.90 + 908.116i −1.99354 + 1.15097i
\(790\) 0 0
\(791\) −191.647 + 566.660i −0.242284 + 0.716385i
\(792\) 0 0