Properties

Label 750.2.l.c.107.9
Level $750$
Weight $2$
Character 750.107
Analytic conductor $5.989$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.98878015160\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(10\) over \(\Q(\zeta_{20})\)
Twist minimal: no (minimal twist has level 150)
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 107.9
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.c.743.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.891007 + 0.453990i) q^{2} +(0.974581 + 1.43185i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.218312 + 1.71824i) q^{6} +(3.13589 + 3.13589i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.10038 + 2.79091i) q^{9} +O(q^{10})\) \(q+(0.891007 + 0.453990i) q^{2} +(0.974581 + 1.43185i) q^{3} +(0.587785 + 0.809017i) q^{4} +(0.218312 + 1.71824i) q^{6} +(3.13589 + 3.13589i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-1.10038 + 2.79091i) q^{9} +(-3.57685 + 1.16219i) q^{11} +(-0.585546 + 1.63007i) q^{12} +(-1.78169 - 3.49677i) q^{13} +(1.37043 + 4.21776i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(-0.406920 + 0.0644499i) q^{17} +(-2.24749 + 1.98715i) q^{18} +(2.93913 - 4.04536i) q^{19} +(-1.43394 + 7.54629i) q^{21} +(-3.71462 - 0.588338i) q^{22} +(2.28327 - 4.48117i) q^{23} +(-1.26176 + 1.18657i) q^{24} -3.92451i q^{26} +(-5.06857 + 1.14438i) q^{27} +(-0.693758 + 4.38021i) q^{28} +(-1.49299 + 1.08472i) q^{29} +(2.69808 + 1.96027i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-5.15001 - 3.98886i) q^{33} +(-0.391828 - 0.127313i) q^{34} +(-2.90468 + 0.750223i) q^{36} +(4.70465 - 2.39714i) q^{37} +(4.45534 - 2.27011i) q^{38} +(3.27044 - 5.95899i) q^{39} +(3.24600 + 1.05469i) q^{41} +(-4.70360 + 6.07280i) q^{42} +(3.71639 - 3.71639i) q^{43} +(-3.04265 - 2.21062i) q^{44} +(4.06882 - 2.95617i) q^{46} +(-0.808572 + 5.10512i) q^{47} +(-1.66293 + 0.484416i) q^{48} +12.6676i q^{49} +(-0.488859 - 0.519837i) q^{51} +(1.78169 - 3.49677i) q^{52} +(-8.20487 - 1.29952i) q^{53} +(-5.03567 - 1.28143i) q^{54} +(-2.60672 + 3.58784i) q^{56} +(8.65677 + 0.265855i) q^{57} +(-1.82271 + 0.288689i) q^{58} +(1.73564 - 5.34175i) q^{59} +(4.43829 + 13.6596i) q^{61} +(1.51406 + 2.97152i) q^{62} +(-12.2026 + 5.30128i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-2.77779 - 5.89216i) q^{66} +(-0.968887 - 6.11731i) q^{67} +(-0.291323 - 0.291323i) q^{68} +(8.64159 - 1.09796i) q^{69} +(-0.992045 - 1.36543i) q^{71} +(-2.92868 - 0.650243i) q^{72} +(3.19175 + 1.62628i) q^{73} +5.28015 q^{74} +5.00034 q^{76} +(-14.8611 - 7.57211i) q^{77} +(5.61931 - 3.82475i) q^{78} +(6.24842 + 8.60021i) q^{79} +(-6.57831 - 6.14214i) q^{81} +(2.41339 + 2.41339i) q^{82} +(-1.10932 - 7.00394i) q^{83} +(-6.94793 + 3.27552i) q^{84} +(4.99854 - 1.62412i) q^{86} +(-3.00819 - 1.08059i) q^{87} +(-1.70742 - 3.35101i) q^{88} +(-0.324819 - 0.999689i) q^{89} +(5.37828 - 16.5526i) q^{91} +(4.96742 - 0.786761i) q^{92} +(-0.177314 + 5.77369i) q^{93} +(-3.03812 + 4.18162i) q^{94} +(-1.70160 - 0.323338i) q^{96} +(-7.61627 - 1.20630i) q^{97} +(-5.75096 + 11.2869i) q^{98} +(0.692350 - 11.2615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q + 4q^{3} + 4q^{7} + O(q^{10}) \) \( 80q + 4q^{3} + 4q^{7} + 16q^{12} + 20q^{16} - 8q^{18} + 40q^{19} + 4q^{22} - 56q^{27} + 4q^{28} - 96q^{33} + 40q^{34} - 64q^{37} + 40q^{39} - 4q^{42} - 24q^{43} + 16q^{48} - 64q^{57} + 20q^{58} + 4q^{63} - 104q^{67} - 140q^{69} + 8q^{72} - 60q^{73} - 60q^{78} - 80q^{79} - 40q^{81} + 96q^{82} - 60q^{84} + 80q^{87} + 24q^{88} + 12q^{93} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.891007 + 0.453990i 0.630037 + 0.321020i
\(3\) 0.974581 + 1.43185i 0.562674 + 0.826679i
\(4\) 0.587785 + 0.809017i 0.293893 + 0.404508i
\(5\) 0 0
\(6\) 0.218312 + 1.71824i 0.0891255 + 0.701467i
\(7\) 3.13589 + 3.13589i 1.18525 + 1.18525i 0.978364 + 0.206890i \(0.0663341\pi\)
0.206890 + 0.978364i \(0.433666\pi\)
\(8\) 0.156434 + 0.987688i 0.0553079 + 0.349201i
\(9\) −1.10038 + 2.79091i −0.366795 + 0.930302i
\(10\) 0 0
\(11\) −3.57685 + 1.16219i −1.07846 + 0.350413i −0.793778 0.608208i \(-0.791889\pi\)
−0.284684 + 0.958622i \(0.591889\pi\)
\(12\) −0.585546 + 1.63007i −0.169033 + 0.470561i
\(13\) −1.78169 3.49677i −0.494152 0.969828i −0.994573 0.104046i \(-0.966821\pi\)
0.500420 0.865783i \(-0.333179\pi\)
\(14\) 1.37043 + 4.21776i 0.366264 + 1.12724i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) −0.406920 + 0.0644499i −0.0986927 + 0.0156314i −0.205585 0.978639i \(-0.565910\pi\)
0.106893 + 0.994271i \(0.465910\pi\)
\(18\) −2.24749 + 1.98715i −0.529739 + 0.468376i
\(19\) 2.93913 4.04536i 0.674282 0.928070i −0.325565 0.945520i \(-0.605555\pi\)
0.999848 + 0.0174495i \(0.00555464\pi\)
\(20\) 0 0
\(21\) −1.43394 + 7.54629i −0.312912 + 1.64674i
\(22\) −3.71462 0.588338i −0.791960 0.125434i
\(23\) 2.28327 4.48117i 0.476095 0.934389i −0.520650 0.853770i \(-0.674310\pi\)
0.996745 0.0806186i \(-0.0256896\pi\)
\(24\) −1.26176 + 1.18657i −0.257556 + 0.242208i
\(25\) 0 0
\(26\) 3.92451i 0.769660i
\(27\) −5.06857 + 1.14438i −0.975447 + 0.220236i
\(28\) −0.693758 + 4.38021i −0.131108 + 0.827783i
\(29\) −1.49299 + 1.08472i −0.277241 + 0.201427i −0.717713 0.696339i \(-0.754811\pi\)
0.440472 + 0.897766i \(0.354811\pi\)
\(30\) 0 0
\(31\) 2.69808 + 1.96027i 0.484590 + 0.352075i 0.803100 0.595844i \(-0.203182\pi\)
−0.318510 + 0.947920i \(0.603182\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −5.15001 3.98886i −0.896502 0.694372i
\(34\) −0.391828 0.127313i −0.0671980 0.0218340i
\(35\) 0 0
\(36\) −2.90468 + 0.750223i −0.484113 + 0.125037i
\(37\) 4.70465 2.39714i 0.773440 0.394087i −0.0222802 0.999752i \(-0.507093\pi\)
0.795720 + 0.605664i \(0.207093\pi\)
\(38\) 4.45534 2.27011i 0.722751 0.368260i
\(39\) 3.27044 5.95899i 0.523689 0.954203i
\(40\) 0 0
\(41\) 3.24600 + 1.05469i 0.506941 + 0.164715i 0.551310 0.834300i \(-0.314128\pi\)
−0.0443698 + 0.999015i \(0.514128\pi\)
\(42\) −4.70360 + 6.07280i −0.725781 + 0.937053i
\(43\) 3.71639 3.71639i 0.566745 0.566745i −0.364470 0.931215i \(-0.618750\pi\)
0.931215 + 0.364470i \(0.118750\pi\)
\(44\) −3.04265 2.21062i −0.458697 0.333263i
\(45\) 0 0
\(46\) 4.06882 2.95617i 0.599914 0.435863i
\(47\) −0.808572 + 5.10512i −0.117942 + 0.744659i 0.855851 + 0.517223i \(0.173034\pi\)
−0.973793 + 0.227436i \(0.926966\pi\)
\(48\) −1.66293 + 0.484416i −0.240023 + 0.0699194i
\(49\) 12.6676i 1.80965i
\(50\) 0 0
\(51\) −0.488859 0.519837i −0.0684540 0.0727917i
\(52\) 1.78169 3.49677i 0.247076 0.484914i
\(53\) −8.20487 1.29952i −1.12703 0.178503i −0.435037 0.900412i \(-0.643265\pi\)
−0.691988 + 0.721909i \(0.743265\pi\)
\(54\) −5.03567 1.28143i −0.685267 0.174381i
\(55\) 0 0
\(56\) −2.60672 + 3.58784i −0.348337 + 0.479445i
\(57\) 8.65677 + 0.265855i 1.14662 + 0.0352134i
\(58\) −1.82271 + 0.288689i −0.239334 + 0.0379068i
\(59\) 1.73564 5.34175i 0.225961 0.695437i −0.772231 0.635341i \(-0.780859\pi\)
0.998193 0.0600956i \(-0.0191406\pi\)
\(60\) 0 0
\(61\) 4.43829 + 13.6596i 0.568264 + 1.74894i 0.658047 + 0.752977i \(0.271383\pi\)
−0.0897825 + 0.995961i \(0.528617\pi\)
\(62\) 1.51406 + 2.97152i 0.192286 + 0.377383i
\(63\) −12.2026 + 5.30128i −1.53739 + 0.667899i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) −2.77779 5.89216i −0.341922 0.725275i
\(67\) −0.968887 6.11731i −0.118368 0.747349i −0.973458 0.228868i \(-0.926498\pi\)
0.855089 0.518481i \(-0.173502\pi\)
\(68\) −0.291323 0.291323i −0.0353281 0.0353281i
\(69\) 8.64159 1.09796i 1.04033 0.132179i
\(70\) 0 0
\(71\) −0.992045 1.36543i −0.117734 0.162047i 0.746082 0.665854i \(-0.231932\pi\)
−0.863817 + 0.503806i \(0.831932\pi\)
\(72\) −2.92868 0.650243i −0.345149 0.0766319i
\(73\) 3.19175 + 1.62628i 0.373567 + 0.190342i 0.630686 0.776038i \(-0.282773\pi\)
−0.257120 + 0.966380i \(0.582773\pi\)
\(74\) 5.28015 0.613805
\(75\) 0 0
\(76\) 5.00034 0.573579
\(77\) −14.8611 7.57211i −1.69358 0.862922i
\(78\) 5.61931 3.82475i 0.636262 0.433068i
\(79\) 6.24842 + 8.60021i 0.703002 + 0.967599i 0.999919 + 0.0126959i \(0.00404134\pi\)
−0.296918 + 0.954903i \(0.595959\pi\)
\(80\) 0 0
\(81\) −6.57831 6.14214i −0.730923 0.682460i
\(82\) 2.41339 + 2.41339i 0.266514 + 0.266514i
\(83\) −1.10932 7.00394i −0.121763 0.768782i −0.970701 0.240290i \(-0.922757\pi\)
0.848938 0.528493i \(-0.177243\pi\)
\(84\) −6.94793 + 3.27552i −0.758081 + 0.357388i
\(85\) 0 0
\(86\) 4.99854 1.62412i 0.539006 0.175134i
\(87\) −3.00819 1.08059i −0.322512 0.115851i
\(88\) −1.70742 3.35101i −0.182012 0.357219i
\(89\) −0.324819 0.999689i −0.0344307 0.105967i 0.932364 0.361521i \(-0.117742\pi\)
−0.966795 + 0.255554i \(0.917742\pi\)
\(90\) 0 0
\(91\) 5.37828 16.5526i 0.563797 1.73519i
\(92\) 4.96742 0.786761i 0.517889 0.0820255i
\(93\) −0.177314 + 5.77369i −0.0183866 + 0.598704i
\(94\) −3.03812 + 4.18162i −0.313358 + 0.431301i
\(95\) 0 0
\(96\) −1.70160 0.323338i −0.173669 0.0330005i
\(97\) −7.61627 1.20630i −0.773315 0.122481i −0.242709 0.970099i \(-0.578036\pi\)
−0.530607 + 0.847618i \(0.678036\pi\)
\(98\) −5.75096 + 11.2869i −0.580935 + 1.14015i
\(99\) 0.692350 11.2615i 0.0695838 1.13182i
\(100\) 0 0
\(101\) 11.0847i 1.10297i −0.834184 0.551487i \(-0.814061\pi\)
0.834184 0.551487i \(-0.185939\pi\)
\(102\) −0.199576 0.685116i −0.0197609 0.0678366i
\(103\) 0.383628 2.42213i 0.0378000 0.238660i −0.961553 0.274618i \(-0.911448\pi\)
0.999353 + 0.0359588i \(0.0114485\pi\)
\(104\) 3.17500 2.30677i 0.311334 0.226197i
\(105\) 0 0
\(106\) −6.72062 4.88282i −0.652764 0.474261i
\(107\) 4.30681 4.30681i 0.416355 0.416355i −0.467590 0.883945i \(-0.654878\pi\)
0.883945 + 0.467590i \(0.154878\pi\)
\(108\) −3.90505 3.42791i −0.375764 0.329851i
\(109\) −4.46242 1.44993i −0.427422 0.138878i 0.0874029 0.996173i \(-0.472143\pi\)
−0.514825 + 0.857295i \(0.672143\pi\)
\(110\) 0 0
\(111\) 8.01741 + 4.40015i 0.760979 + 0.417643i
\(112\) −3.95145 + 2.01336i −0.373377 + 0.190245i
\(113\) 15.2342 7.76223i 1.43312 0.730209i 0.446732 0.894668i \(-0.352588\pi\)
0.986384 + 0.164459i \(0.0525879\pi\)
\(114\) 7.59254 + 4.16697i 0.711107 + 0.390272i
\(115\) 0 0
\(116\) −1.75511 0.570270i −0.162958 0.0529483i
\(117\) 11.7197 1.12475i 1.08349 0.103983i
\(118\) 3.97157 3.97157i 0.365613 0.365613i
\(119\) −1.47816 1.07395i −0.135503 0.0984487i
\(120\) 0 0
\(121\) 2.54399 1.84832i 0.231272 0.168029i
\(122\) −2.24681 + 14.1858i −0.203416 + 1.28432i
\(123\) 1.65334 + 5.67567i 0.149076 + 0.511758i
\(124\) 3.33501i 0.299493i
\(125\) 0 0
\(126\) −13.2794 0.816407i −1.18302 0.0727313i
\(127\) 8.90421 17.4755i 0.790121 1.55070i −0.0439442 0.999034i \(-0.513992\pi\)
0.834065 0.551666i \(-0.186008\pi\)
\(128\) −0.987688 0.156434i −0.0873001 0.0138270i
\(129\) 8.94324 + 1.69939i 0.787409 + 0.149623i
\(130\) 0 0
\(131\) −12.0644 + 16.6052i −1.05407 + 1.45080i −0.168841 + 0.985643i \(0.554002\pi\)
−0.885228 + 0.465158i \(0.845998\pi\)
\(132\) 0.199959 6.51104i 0.0174042 0.566713i
\(133\) 21.9026 3.46903i 1.89919 0.300803i
\(134\) 1.91392 5.89043i 0.165337 0.508856i
\(135\) 0 0
\(136\) −0.127313 0.391828i −0.0109170 0.0335990i
\(137\) 3.28166 + 6.44062i 0.280371 + 0.550259i 0.987650 0.156675i \(-0.0500775\pi\)
−0.707279 + 0.706935i \(0.750078\pi\)
\(138\) 8.19818 + 2.94491i 0.697875 + 0.250687i
\(139\) −9.21867 + 2.99533i −0.781918 + 0.254060i −0.672659 0.739953i \(-0.734848\pi\)
−0.109259 + 0.994013i \(0.534848\pi\)
\(140\) 0 0
\(141\) −8.09779 + 3.81760i −0.681957 + 0.321500i
\(142\) −0.264025 1.66699i −0.0221565 0.139891i
\(143\) 10.4367 + 10.4367i 0.872765 + 0.872765i
\(144\) −2.31427 1.90897i −0.192856 0.159080i
\(145\) 0 0
\(146\) 2.10556 + 2.89805i 0.174257 + 0.239845i
\(147\) −18.1381 + 12.3456i −1.49600 + 1.01825i
\(148\) 4.70465 + 2.39714i 0.386720 + 0.197044i
\(149\) −4.14920 −0.339915 −0.169958 0.985451i \(-0.554363\pi\)
−0.169958 + 0.985451i \(0.554363\pi\)
\(150\) 0 0
\(151\) −9.50070 −0.773156 −0.386578 0.922257i \(-0.626343\pi\)
−0.386578 + 0.922257i \(0.626343\pi\)
\(152\) 4.45534 + 2.27011i 0.361376 + 0.184130i
\(153\) 0.267895 1.20660i 0.0216581 0.0975475i
\(154\) −9.80367 13.4936i −0.790002 1.08734i
\(155\) 0 0
\(156\) 6.74324 0.856768i 0.539892 0.0685963i
\(157\) 2.98265 + 2.98265i 0.238041 + 0.238041i 0.816039 0.577997i \(-0.196166\pi\)
−0.577997 + 0.816039i \(0.696166\pi\)
\(158\) 1.66297 + 10.4996i 0.132299 + 0.835300i
\(159\) −6.13559 13.0146i −0.486584 1.03213i
\(160\) 0 0
\(161\) 21.2125 6.89237i 1.67178 0.543195i
\(162\) −3.07284 8.45917i −0.241425 0.664616i
\(163\) 4.73142 + 9.28593i 0.370593 + 0.727330i 0.998709 0.0507896i \(-0.0161738\pi\)
−0.628116 + 0.778119i \(0.716174\pi\)
\(164\) 1.05469 + 3.24600i 0.0823575 + 0.253470i
\(165\) 0 0
\(166\) 2.19132 6.74418i 0.170079 0.523450i
\(167\) 13.8268 2.18995i 1.06995 0.169464i 0.403476 0.914990i \(-0.367802\pi\)
0.666476 + 0.745527i \(0.267802\pi\)
\(168\) −7.67770 0.235788i −0.592348 0.0181914i
\(169\) −1.41174 + 1.94309i −0.108595 + 0.149469i
\(170\) 0 0
\(171\) 8.05606 + 12.6543i 0.616062 + 0.967697i
\(172\) 5.19107 + 0.822184i 0.395815 + 0.0626910i
\(173\) −3.18237 + 6.24576i −0.241951 + 0.474856i −0.979766 0.200147i \(-0.935858\pi\)
0.737815 + 0.675003i \(0.235858\pi\)
\(174\) −2.18974 2.32850i −0.166004 0.176523i
\(175\) 0 0
\(176\) 3.76092i 0.283490i
\(177\) 9.34011 2.72079i 0.702045 0.204507i
\(178\) 0.164434 1.03819i 0.0123248 0.0778159i
\(179\) −2.28996 + 1.66375i −0.171159 + 0.124355i −0.670067 0.742301i \(-0.733735\pi\)
0.498908 + 0.866655i \(0.333735\pi\)
\(180\) 0 0
\(181\) −0.283169 0.205734i −0.0210478 0.0152921i 0.577212 0.816595i \(-0.304141\pi\)
−0.598259 + 0.801302i \(0.704141\pi\)
\(182\) 12.3068 12.3068i 0.912243 0.912243i
\(183\) −15.2331 + 19.6674i −1.12606 + 1.45386i
\(184\) 4.78318 + 1.55415i 0.352621 + 0.114573i
\(185\) 0 0
\(186\) −2.77919 + 5.06390i −0.203780 + 0.371303i
\(187\) 1.38059 0.703446i 0.100959 0.0514411i
\(188\) −4.60540 + 2.34657i −0.335883 + 0.171141i
\(189\) −19.4831 12.3058i −1.41719 0.895117i
\(190\) 0 0
\(191\) −1.07980 0.350849i −0.0781318 0.0253866i 0.269690 0.962947i \(-0.413079\pi\)
−0.347822 + 0.937561i \(0.613079\pi\)
\(192\) −1.36935 1.06061i −0.0988241 0.0765428i
\(193\) 4.16176 4.16176i 0.299570 0.299570i −0.541275 0.840845i \(-0.682058\pi\)
0.840845 + 0.541275i \(0.182058\pi\)
\(194\) −6.23850 4.53254i −0.447898 0.325417i
\(195\) 0 0
\(196\) −10.2483 + 7.44581i −0.732020 + 0.531844i
\(197\) 3.00593 18.9787i 0.214164 1.35218i −0.612941 0.790129i \(-0.710014\pi\)
0.827105 0.562048i \(-0.189986\pi\)
\(198\) 5.72951 9.71976i 0.407178 0.690753i
\(199\) 12.7124i 0.901157i −0.892737 0.450579i \(-0.851218\pi\)
0.892737 0.450579i \(-0.148782\pi\)
\(200\) 0 0
\(201\) 7.81481 7.34912i 0.551214 0.518367i
\(202\) 5.03237 9.87658i 0.354076 0.694914i
\(203\) −8.08340 1.28028i −0.567343 0.0898583i
\(204\) 0.133213 0.701048i 0.00932676 0.0490832i
\(205\) 0 0
\(206\) 1.44144 1.98397i 0.100430 0.138230i
\(207\) 9.99405 + 11.3034i 0.694634 + 0.785641i
\(208\) 3.87619 0.613929i 0.268766 0.0425683i
\(209\) −5.81135 + 17.8855i −0.401979 + 1.23716i
\(210\) 0 0
\(211\) −5.38805 16.5827i −0.370929 1.14160i −0.946184 0.323628i \(-0.895097\pi\)
0.575255 0.817974i \(-0.304903\pi\)
\(212\) −3.77136 7.40172i −0.259018 0.508352i
\(213\) 0.988266 2.75118i 0.0677149 0.188508i
\(214\) 5.79265 1.88215i 0.395977 0.128661i
\(215\) 0 0
\(216\) −1.92319 4.82715i −0.130856 0.328446i
\(217\) 2.31369 + 14.6081i 0.157064 + 0.991661i
\(218\) −3.31779 3.31779i −0.224709 0.224709i
\(219\) 0.782035 + 6.15505i 0.0528450 + 0.415920i
\(220\) 0 0
\(221\) 0.950373 + 1.30808i 0.0639290 + 0.0879907i
\(222\) 5.14594 + 7.56039i 0.345373 + 0.507420i
\(223\) −20.1688 10.2765i −1.35060 0.688167i −0.379136 0.925341i \(-0.623779\pi\)
−0.971467 + 0.237174i \(0.923779\pi\)
\(224\) −4.43481 −0.296313
\(225\) 0 0
\(226\) 17.0978 1.13733
\(227\) −17.2036 8.76566i −1.14184 0.581797i −0.222373 0.974962i \(-0.571380\pi\)
−0.919468 + 0.393164i \(0.871380\pi\)
\(228\) 4.87324 + 7.15974i 0.322738 + 0.474165i
\(229\) −9.58051 13.1864i −0.633098 0.871384i 0.365126 0.930958i \(-0.381026\pi\)
−0.998224 + 0.0595738i \(0.981026\pi\)
\(230\) 0 0
\(231\) −3.64122 28.6585i −0.239575 1.88559i
\(232\) −1.30492 1.30492i −0.0856721 0.0856721i
\(233\) −0.0952038 0.601093i −0.00623701 0.0393789i 0.984374 0.176093i \(-0.0563459\pi\)
−0.990611 + 0.136714i \(0.956346\pi\)
\(234\) 10.9529 + 4.31847i 0.716016 + 0.282307i
\(235\) 0 0
\(236\) 5.34175 1.73564i 0.347718 0.112981i
\(237\) −6.22461 + 17.3284i −0.404332 + 1.12560i
\(238\) −0.829491 1.62797i −0.0537679 0.105525i
\(239\) −2.47857 7.62825i −0.160325 0.493430i 0.838336 0.545154i \(-0.183529\pi\)
−0.998661 + 0.0517231i \(0.983529\pi\)
\(240\) 0 0
\(241\) −2.23962 + 6.89284i −0.144267 + 0.444007i −0.996916 0.0784767i \(-0.974994\pi\)
0.852649 + 0.522484i \(0.174994\pi\)
\(242\) 3.10583 0.491916i 0.199650 0.0316215i
\(243\) 2.38352 15.4052i 0.152903 0.988241i
\(244\) −8.44212 + 11.6196i −0.540452 + 0.743868i
\(245\) 0 0
\(246\) −1.10357 + 5.80766i −0.0703609 + 0.370283i
\(247\) −19.3823 3.06986i −1.23327 0.195330i
\(248\) −1.51406 + 2.97152i −0.0961432 + 0.188692i
\(249\) 8.94747 8.41428i 0.567023 0.533233i
\(250\) 0 0
\(251\) 14.5520i 0.918511i −0.888304 0.459256i \(-0.848116\pi\)
0.888304 0.459256i \(-0.151884\pi\)
\(252\) −11.4614 6.75613i −0.721998 0.425596i
\(253\) −2.95895 + 18.6821i −0.186028 + 1.17453i
\(254\) 15.8674 11.5284i 0.995611 0.723353i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 1.03830 1.03830i 0.0647675 0.0647675i −0.673981 0.738749i \(-0.735417\pi\)
0.738749 + 0.673981i \(0.235417\pi\)
\(258\) 7.19698 + 5.57431i 0.448064 + 0.347042i
\(259\) 22.2704 + 7.23610i 1.38382 + 0.449629i
\(260\) 0 0
\(261\) −1.38449 5.36039i −0.0856976 0.331800i
\(262\) −18.2880 + 9.31821i −1.12984 + 0.575681i
\(263\) −19.8871 + 10.1330i −1.22629 + 0.624825i −0.942546 0.334075i \(-0.891576\pi\)
−0.283743 + 0.958901i \(0.591576\pi\)
\(264\) 3.13412 5.71060i 0.192891 0.351463i
\(265\) 0 0
\(266\) 21.0902 + 6.85264i 1.29313 + 0.420162i
\(267\) 1.11484 1.43937i 0.0682272 0.0880880i
\(268\) 4.37951 4.37951i 0.267521 0.267521i
\(269\) 20.2239 + 14.6936i 1.23308 + 0.895882i 0.997117 0.0758813i \(-0.0241770\pi\)
0.235959 + 0.971763i \(0.424177\pi\)
\(270\) 0 0
\(271\) −13.1402 + 9.54690i −0.798209 + 0.579933i −0.910388 0.413755i \(-0.864217\pi\)
0.112179 + 0.993688i \(0.464217\pi\)
\(272\) 0.0644499 0.406920i 0.00390785 0.0246732i
\(273\) 28.9425 8.43100i 1.75168 0.510268i
\(274\) 7.22848i 0.436688i
\(275\) 0 0
\(276\) 5.96767 + 6.34583i 0.359212 + 0.381974i
\(277\) 3.12626 6.13564i 0.187839 0.368655i −0.777812 0.628497i \(-0.783670\pi\)
0.965651 + 0.259842i \(0.0836705\pi\)
\(278\) −9.57375 1.51633i −0.574195 0.0909436i
\(279\) −8.43986 + 5.37304i −0.505281 + 0.321676i
\(280\) 0 0
\(281\) −14.3948 + 19.8128i −0.858723 + 1.18193i 0.123150 + 0.992388i \(0.460700\pi\)
−0.981873 + 0.189542i \(0.939300\pi\)
\(282\) −8.94834 0.274810i −0.532866 0.0163647i
\(283\) −7.23244 + 1.14551i −0.429924 + 0.0680933i −0.367646 0.929966i \(-0.619836\pi\)
−0.0622774 + 0.998059i \(0.519836\pi\)
\(284\) 0.521549 1.60516i 0.0309482 0.0952489i
\(285\) 0 0
\(286\) 4.56103 + 14.0374i 0.269699 + 0.830049i
\(287\) 6.87171 + 13.4865i 0.405624 + 0.796083i
\(288\) −1.19538 2.75156i −0.0704384 0.162137i
\(289\) −16.0065 + 5.20084i −0.941561 + 0.305932i
\(290\) 0 0
\(291\) −5.69543 12.0810i −0.333872 0.708200i
\(292\) 0.560378 + 3.53809i 0.0327936 + 0.207051i
\(293\) 1.14628 + 1.14628i 0.0669662 + 0.0669662i 0.739797 0.672830i \(-0.234922\pi\)
−0.672830 + 0.739797i \(0.734922\pi\)
\(294\) −21.7659 + 2.76548i −1.26941 + 0.161286i
\(295\) 0 0
\(296\) 3.10360 + 4.27173i 0.180393 + 0.248290i
\(297\) 16.7995 9.98391i 0.974808 0.579325i
\(298\) −3.69696 1.88370i −0.214159 0.109120i
\(299\) −19.7377 −1.14146
\(300\) 0 0
\(301\) 23.3084 1.34347
\(302\) −8.46519 4.31323i −0.487117 0.248198i
\(303\) 15.8717 10.8030i 0.911804 0.620615i
\(304\) 2.93913 + 4.04536i 0.168571 + 0.232018i
\(305\) 0 0
\(306\) 0.786480 0.953463i 0.0449600 0.0545058i
\(307\) −8.29257 8.29257i −0.473282 0.473282i 0.429693 0.902975i \(-0.358622\pi\)
−0.902975 + 0.429693i \(0.858622\pi\)
\(308\) −2.60917 16.4737i −0.148671 0.938673i
\(309\) 3.84200 1.81126i 0.218564 0.103039i
\(310\) 0 0
\(311\) −31.4637 + 10.2232i −1.78414 + 0.579703i −0.999205 0.0398725i \(-0.987305\pi\)
−0.784937 + 0.619575i \(0.787305\pi\)
\(312\) 6.39724 + 2.29798i 0.362172 + 0.130098i
\(313\) −1.98845 3.90255i −0.112394 0.220585i 0.827957 0.560791i \(-0.189503\pi\)
−0.940351 + 0.340206i \(0.889503\pi\)
\(314\) 1.30346 + 4.01165i 0.0735587 + 0.226391i
\(315\) 0 0
\(316\) −3.28499 + 10.1102i −0.184795 + 0.568740i
\(317\) −27.6572 + 4.38047i −1.55338 + 0.246032i −0.873329 0.487131i \(-0.838043\pi\)
−0.680053 + 0.733163i \(0.738043\pi\)
\(318\) 0.441669 14.3816i 0.0247676 0.806481i
\(319\) 4.07954 5.61501i 0.228411 0.314380i
\(320\) 0 0
\(321\) 10.3640 + 1.96937i 0.578464 + 0.109919i
\(322\) 22.0296 + 3.48914i 1.22766 + 0.194442i
\(323\) −0.935268 + 1.83557i −0.0520397 + 0.102134i
\(324\) 1.10246 8.93222i 0.0612479 0.496235i
\(325\) 0 0
\(326\) 10.4218i 0.577212i
\(327\) −2.27291 7.80259i −0.125692 0.431484i
\(328\) −0.533919 + 3.37103i −0.0294807 + 0.186134i
\(329\) −18.5447 + 13.4735i −1.02240 + 0.742818i
\(330\) 0 0
\(331\) 7.75360 + 5.63332i 0.426176 + 0.309635i 0.780118 0.625632i \(-0.215159\pi\)
−0.353942 + 0.935267i \(0.615159\pi\)
\(332\) 5.01427 5.01427i 0.275194 0.275194i
\(333\) 1.51327 + 15.7680i 0.0829264 + 0.864082i
\(334\) 13.3140 + 4.32598i 0.728510 + 0.236707i
\(335\) 0 0
\(336\) −6.73384 3.69569i −0.367361 0.201617i
\(337\) 13.9578 7.11185i 0.760329 0.387407i −0.0304279 0.999537i \(-0.509687\pi\)
0.790757 + 0.612130i \(0.209687\pi\)
\(338\) −2.14002 + 1.09039i −0.116401 + 0.0593095i
\(339\) 25.9613 + 14.2482i 1.41003 + 0.773856i
\(340\) 0 0
\(341\) −11.9289 3.87592i −0.645983 0.209893i
\(342\) 1.43307 + 14.9324i 0.0774917 + 0.807453i
\(343\) −17.7729 + 17.7729i −0.959645 + 0.959645i
\(344\) 4.25201 + 3.08927i 0.229253 + 0.166562i
\(345\) 0 0
\(346\) −5.67103 + 4.12024i −0.304876 + 0.221506i
\(347\) −5.77593 + 36.4678i −0.310068 + 1.95769i −0.0231773 + 0.999731i \(0.507378\pi\)
−0.286891 + 0.957963i \(0.592622\pi\)
\(348\) −0.893957 3.06883i −0.0479211 0.164507i
\(349\) 15.0145i 0.803705i −0.915704 0.401853i \(-0.868366\pi\)
0.915704 0.401853i \(-0.131634\pi\)
\(350\) 0 0
\(351\) 13.0322 + 15.6847i 0.695610 + 0.837186i
\(352\) 1.70742 3.35101i 0.0910060 0.178609i
\(353\) 29.7348 + 4.70953i 1.58263 + 0.250663i 0.884927 0.465729i \(-0.154208\pi\)
0.697698 + 0.716392i \(0.254208\pi\)
\(354\) 9.55731 + 1.81607i 0.507965 + 0.0965233i
\(355\) 0 0
\(356\) 0.617842 0.850386i 0.0327456 0.0450704i
\(357\) 0.0971428 3.16316i 0.00514134 0.167412i
\(358\) −2.79569 + 0.442795i −0.147757 + 0.0234024i
\(359\) 1.07807 3.31797i 0.0568986 0.175116i −0.918568 0.395263i \(-0.870654\pi\)
0.975467 + 0.220147i \(0.0706536\pi\)
\(360\) 0 0
\(361\) −1.85517 5.70961i −0.0976403 0.300506i
\(362\) −0.158904 0.311866i −0.00835180 0.0163913i
\(363\) 5.12584 + 1.84128i 0.269037 + 0.0966420i
\(364\) 16.5526 5.37828i 0.867594 0.281898i
\(365\) 0 0
\(366\) −22.5016 + 10.6081i −1.17618 + 0.554494i
\(367\) 2.44988 + 15.4679i 0.127882 + 0.807418i 0.965355 + 0.260939i \(0.0840322\pi\)
−0.837473 + 0.546479i \(0.815968\pi\)
\(368\) 3.55628 + 3.55628i 0.185384 + 0.185384i
\(369\) −6.51539 + 7.89873i −0.339178 + 0.411191i
\(370\) 0 0
\(371\) −21.6544 29.8047i −1.12424 1.54738i
\(372\) −4.77524 + 3.25024i −0.247585 + 0.168517i
\(373\) −5.68352 2.89590i −0.294282 0.149944i 0.300616 0.953745i \(-0.402808\pi\)
−0.594898 + 0.803801i \(0.702808\pi\)
\(374\) 1.54947 0.0801213
\(375\) 0 0
\(376\) −5.16876 −0.266558
\(377\) 6.45305 + 3.28799i 0.332349 + 0.169340i
\(378\) −11.7728 19.8097i −0.605530 1.01890i
\(379\) 15.8374 + 21.7983i 0.813510 + 1.11970i 0.990772 + 0.135537i \(0.0432760\pi\)
−0.177262 + 0.984164i \(0.556724\pi\)
\(380\) 0 0
\(381\) 33.7002 4.28180i 1.72651 0.219363i
\(382\) −0.802829 0.802829i −0.0410763 0.0410763i
\(383\) −4.68475 29.5784i −0.239380 1.51138i −0.755660 0.654964i \(-0.772684\pi\)
0.516280 0.856420i \(-0.327316\pi\)
\(384\) −0.738592 1.56668i −0.0376911 0.0799492i
\(385\) 0 0
\(386\) 5.59756 1.81876i 0.284908 0.0925723i
\(387\) 6.28264 + 14.4616i 0.319365 + 0.735123i
\(388\) −3.50082 6.87074i −0.177727 0.348809i
\(389\) 3.57268 + 10.9956i 0.181142 + 0.557497i 0.999861 0.0166975i \(-0.00531522\pi\)
−0.818719 + 0.574195i \(0.805315\pi\)
\(390\) 0 0
\(391\) −0.640299 + 1.97064i −0.0323813 + 0.0996594i
\(392\) −12.5116 + 1.98165i −0.631932 + 0.100088i
\(393\) −35.5338 1.09127i −1.79244 0.0550472i
\(394\) 11.2945 15.5455i 0.569007 0.783170i
\(395\) 0 0
\(396\) 9.51771 6.05923i 0.478283 0.304488i
\(397\) −13.2341 2.09608i −0.664203 0.105199i −0.184775 0.982781i \(-0.559156\pi\)
−0.479427 + 0.877581i \(0.659156\pi\)
\(398\) 5.77130 11.3268i 0.289289 0.567762i
\(399\) 26.3130 + 27.9803i 1.31730 + 1.40077i
\(400\) 0 0
\(401\) 22.2904i 1.11313i 0.830804 + 0.556565i \(0.187881\pi\)
−0.830804 + 0.556565i \(0.812119\pi\)
\(402\) 10.2995 3.00026i 0.513691 0.149639i
\(403\) 2.04746 12.9272i 0.101991 0.643948i
\(404\) 8.96775 6.51545i 0.446162 0.324156i
\(405\) 0 0
\(406\) −6.62112 4.81053i −0.328601 0.238742i
\(407\) −14.0419 + 14.0419i −0.696032 + 0.696032i
\(408\) 0.436963 0.564161i 0.0216329 0.0279301i
\(409\) −13.3939 4.35194i −0.662285 0.215190i −0.0414620 0.999140i \(-0.513202\pi\)
−0.620823 + 0.783951i \(0.713202\pi\)
\(410\) 0 0
\(411\) −6.02376 + 10.9757i −0.297130 + 0.541394i
\(412\) 2.18504 1.11333i 0.107649 0.0548499i
\(413\) 22.1939 11.3084i 1.09209 0.556448i
\(414\) 3.77313 + 14.6086i 0.185439 + 0.717974i
\(415\) 0 0
\(416\) 3.73243 + 1.21274i 0.182998 + 0.0594595i
\(417\) −13.2732 10.2806i −0.649992 0.503441i
\(418\) −13.2978 + 13.2978i −0.650416 + 0.650416i
\(419\) −4.58918 3.33423i −0.224196 0.162888i 0.470017 0.882657i \(-0.344248\pi\)
−0.694213 + 0.719769i \(0.744248\pi\)
\(420\) 0 0
\(421\) 5.16685 3.75393i 0.251817 0.182956i −0.454715 0.890637i \(-0.650259\pi\)
0.706532 + 0.707682i \(0.250259\pi\)
\(422\) 2.72761 17.2214i 0.132778 0.838327i
\(423\) −13.3582 7.87425i −0.649497 0.382859i
\(424\) 8.30714i 0.403431i
\(425\) 0 0
\(426\) 2.12956 2.00266i 0.103178 0.0970292i
\(427\) −28.9171 + 56.7531i −1.39940 + 2.74647i
\(428\) 6.01577 + 0.952804i 0.290783 + 0.0460555i
\(429\) −4.77240 + 25.1153i −0.230413 + 1.21258i
\(430\) 0 0
\(431\) −11.7415 + 16.1608i −0.565568 + 0.778437i −0.992021 0.126072i \(-0.959763\pi\)
0.426453 + 0.904510i \(0.359763\pi\)
\(432\) 0.477906 5.17413i 0.0229932 0.248940i
\(433\) −22.9138 + 3.62919i −1.10117 + 0.174408i −0.680458 0.732787i \(-0.738219\pi\)
−0.420710 + 0.907195i \(0.638219\pi\)
\(434\) −4.57041 + 14.0663i −0.219387 + 0.675203i
\(435\) 0 0
\(436\) −1.44993 4.46242i −0.0694390 0.213711i
\(437\) −11.4171 22.4074i −0.546156 1.07189i
\(438\) −2.09754 + 5.83923i −0.100224 + 0.279009i
\(439\) −10.7777 + 3.50189i −0.514393 + 0.167136i −0.554699 0.832051i \(-0.687167\pi\)
0.0403065 + 0.999187i \(0.487167\pi\)
\(440\) 0 0
\(441\) −35.3540 13.9392i −1.68352 0.663772i
\(442\) 0.252934 + 1.59696i 0.0120309 + 0.0759598i
\(443\) −5.43418 5.43418i −0.258186 0.258186i 0.566130 0.824316i \(-0.308440\pi\)
−0.824316 + 0.566130i \(0.808440\pi\)
\(444\) 1.15272 + 9.07256i 0.0547057 + 0.430565i
\(445\) 0 0
\(446\) −13.3051 18.3129i −0.630015 0.867141i
\(447\) −4.04373 5.94102i −0.191262 0.281001i
\(448\) −3.95145 2.01336i −0.186688 0.0951225i
\(449\) 26.9459 1.27165 0.635827 0.771831i \(-0.280659\pi\)
0.635827 + 0.771831i \(0.280659\pi\)
\(450\) 0 0
\(451\) −12.8362 −0.604434
\(452\) 15.2342 + 7.76223i 0.716558 + 0.365104i
\(453\) −9.25920 13.6036i −0.435035 0.639152i
\(454\) −11.3490 15.6205i −0.532634 0.733108i
\(455\) 0 0
\(456\) 1.09163 + 8.59178i 0.0511205 + 0.402347i
\(457\) 24.1951 + 24.1951i 1.13180 + 1.13180i 0.989878 + 0.141919i \(0.0453271\pi\)
0.141919 + 0.989878i \(0.454673\pi\)
\(458\) −2.54978 16.0987i −0.119143 0.752241i
\(459\) 1.98875 0.792339i 0.0928269 0.0369832i
\(460\) 0 0
\(461\) 35.3066 11.4718i 1.64439 0.534295i 0.666877 0.745168i \(-0.267631\pi\)
0.977513 + 0.210873i \(0.0676307\pi\)
\(462\) 9.76632 27.1880i 0.454370 1.26490i
\(463\) −3.18828 6.25735i −0.148172 0.290804i 0.804977 0.593307i \(-0.202178\pi\)
−0.953149 + 0.302503i \(0.902178\pi\)
\(464\) −0.570270 1.75511i −0.0264741 0.0814790i
\(465\) 0 0
\(466\) 0.188063 0.578799i 0.00871187 0.0268124i
\(467\) 28.3424 4.48899i 1.31153 0.207726i 0.538785 0.842444i \(-0.318884\pi\)
0.772744 + 0.634718i \(0.218884\pi\)
\(468\) 7.79860 + 8.82032i 0.360490 + 0.407719i
\(469\) 16.1449 22.2215i 0.745502 1.02609i
\(470\) 0 0
\(471\) −1.36387 + 7.17753i −0.0628438 + 0.330723i
\(472\) 5.54750 + 0.878638i 0.255344 + 0.0404426i
\(473\) −8.97383 + 17.6121i −0.412617 + 0.809807i
\(474\) −13.4131 + 12.6138i −0.616084 + 0.579371i
\(475\) 0 0
\(476\) 1.82711i 0.0837455i
\(477\) 12.6554 21.4690i 0.579449 0.983000i
\(478\) 1.25473 7.92207i 0.0573901 0.362347i
\(479\) −10.3928 + 7.55082i −0.474860 + 0.345006i −0.799332 0.600889i \(-0.794813\pi\)
0.324473 + 0.945895i \(0.394813\pi\)
\(480\) 0 0
\(481\) −16.7645 12.1801i −0.764394 0.555365i
\(482\) −5.12480 + 5.12480i −0.233428 + 0.233428i
\(483\) 30.5421 + 23.6560i 1.38972 + 1.07638i
\(484\) 2.99064 + 0.971718i 0.135938 + 0.0441690i
\(485\) 0 0
\(486\) 9.11753 12.6440i 0.413580 0.573543i
\(487\) −18.4423 + 9.39682i −0.835700 + 0.425810i −0.818822 0.574047i \(-0.805373\pi\)
−0.0168777 + 0.999858i \(0.505373\pi\)
\(488\) −12.7972 + 6.52048i −0.579301 + 0.295168i
\(489\) −8.68490 + 15.8246i −0.392745 + 0.715611i
\(490\) 0 0
\(491\) 26.5707 + 8.63333i 1.19912 + 0.389617i 0.839436 0.543459i \(-0.182886\pi\)
0.359681 + 0.933075i \(0.382886\pi\)
\(492\) −3.61991 + 4.67365i −0.163198 + 0.210704i
\(493\) 0.537617 0.537617i 0.0242131 0.0242131i
\(494\) −15.8761 11.5346i −0.714298 0.518968i
\(495\) 0 0
\(496\) −2.69808 + 1.96027i −0.121148 + 0.0880188i
\(497\) 1.17090 7.39279i 0.0525221 0.331612i
\(498\) 11.7923 3.43511i 0.528424 0.153931i
\(499\) 0.405848i 0.0181683i −0.999959 0.00908413i \(-0.997108\pi\)
0.999959 0.00908413i \(-0.00289161\pi\)
\(500\) 0 0
\(501\) 16.6110 + 17.6636i 0.742126 + 0.789153i
\(502\) 6.60645 12.9659i 0.294860 0.578696i
\(503\) −5.98816 0.948431i −0.266999 0.0422885i 0.0214995 0.999769i \(-0.493156\pi\)
−0.288498 + 0.957480i \(0.593156\pi\)
\(504\) −7.14493 11.2231i −0.318260 0.499917i
\(505\) 0 0
\(506\) −11.1179 + 15.3025i −0.494252 + 0.680280i
\(507\) −4.15807 0.127697i −0.184666 0.00567123i
\(508\) 19.3717 3.06818i 0.859482 0.136129i
\(509\) 1.17675 3.62167i 0.0521586 0.160528i −0.921584 0.388178i \(-0.873104\pi\)
0.973743 + 0.227651i \(0.0731044\pi\)
\(510\) 0 0
\(511\) 4.90915 + 15.1088i 0.217168 + 0.668375i
\(512\) −0.453990 0.891007i −0.0200637 0.0393773i
\(513\) −10.2678 + 23.8677i −0.453332 + 1.05378i
\(514\) 1.39651 0.453755i 0.0615976 0.0200143i
\(515\) 0 0
\(516\) 3.88187 + 8.23411i 0.170890 + 0.362487i
\(517\) −3.04098 19.2000i −0.133742 0.844414i
\(518\) 16.5580 + 16.5580i 0.727515 + 0.727515i
\(519\) −12.0445 + 1.53032i −0.528693 + 0.0671735i
\(520\) 0 0
\(521\) 1.70955 + 2.35299i 0.0748966 + 0.103086i 0.844822 0.535048i \(-0.179706\pi\)
−0.769925 + 0.638134i \(0.779706\pi\)
\(522\) 1.19998 5.40469i 0.0525217 0.236557i
\(523\) −7.89460 4.02250i −0.345207 0.175892i 0.272787 0.962074i \(-0.412054\pi\)
−0.617994 + 0.786183i \(0.712054\pi\)
\(524\) −20.5251 −0.896645
\(525\) 0 0
\(526\) −22.3198 −0.973188
\(527\) −1.22424 0.623784i −0.0533289 0.0271724i
\(528\) 5.38508 3.66532i 0.234355 0.159513i
\(529\) −1.34851 1.85606i −0.0586307 0.0806982i
\(530\) 0 0
\(531\) 12.9985 + 10.7220i 0.564085 + 0.465295i
\(532\) 15.6805 + 15.6805i 0.679837 + 0.679837i
\(533\) −2.09537 13.2296i −0.0907606 0.573040i
\(534\) 1.64679 0.776360i 0.0712636 0.0335964i
\(535\) 0 0
\(536\) 5.89043 1.91392i 0.254428 0.0826686i
\(537\) −4.61399 1.65741i −0.199108 0.0715227i
\(538\) 11.3489 + 22.2735i 0.489287 + 0.960280i
\(539\) −14.7221 45.3100i −0.634127 1.95164i
\(540\) 0 0
\(541\) −11.3923 + 35.0618i −0.489792 + 1.50742i 0.335128 + 0.942173i \(0.391221\pi\)
−0.824919 + 0.565251i \(0.808779\pi\)
\(542\) −16.0422 + 2.54083i −0.689071 + 0.109138i
\(543\) 0.0186094 0.605959i 0.000798607 0.0260042i
\(544\) 0.242163 0.333309i 0.0103827 0.0142905i
\(545\) 0 0
\(546\) 29.6155 + 5.62752i 1.26743 + 0.240836i
\(547\) 26.2003 + 4.14971i 1.12024 + 0.177429i 0.688968 0.724792i \(-0.258064\pi\)
0.431274 + 0.902221i \(0.358064\pi\)
\(548\) −3.28166 + 6.44062i −0.140186 + 0.275130i
\(549\) −43.0066 2.64402i −1.83548 0.112844i
\(550\) 0 0
\(551\) 9.22780i 0.393118i
\(552\) 2.43629 + 8.36344i 0.103695 + 0.355972i
\(553\) −7.37495 + 46.5636i −0.313615 + 1.98009i
\(554\) 5.57104 4.04760i 0.236691 0.171966i
\(555\) 0 0
\(556\) −7.84187 5.69745i −0.332569 0.241626i
\(557\) −20.9449 + 20.9449i −0.887465 + 0.887465i −0.994279 0.106814i \(-0.965935\pi\)
0.106814 + 0.994279i \(0.465935\pi\)
\(558\) −9.95928 + 0.955798i −0.421610 + 0.0404622i
\(559\) −19.6168 6.37389i −0.829703 0.269587i
\(560\) 0 0
\(561\) 2.35273 + 1.29123i 0.0993322 + 0.0545159i
\(562\) −21.8207 + 11.1182i −0.920450 + 0.468993i
\(563\) 13.4464 6.85128i 0.566698 0.288747i −0.147073 0.989126i \(-0.546985\pi\)
0.713772 + 0.700378i \(0.246985\pi\)
\(564\) −7.84827 4.30732i −0.330472 0.181371i
\(565\) 0 0
\(566\) −6.96420 2.26281i −0.292727 0.0951128i
\(567\) −1.36778 39.8899i −0.0574413 1.67522i
\(568\) 1.19343 1.19343i 0.0500753 0.0500753i
\(569\) 7.06373 + 5.13210i 0.296127 + 0.215149i 0.725921 0.687778i \(-0.241414\pi\)
−0.429794 + 0.902927i \(0.641414\pi\)
\(570\) 0 0
\(571\) 19.6305 14.2624i 0.821513 0.596864i −0.0956328 0.995417i \(-0.530487\pi\)
0.917145 + 0.398553i \(0.130487\pi\)
\(572\) −2.30894 + 14.5781i −0.0965416 + 0.609540i
\(573\) −0.549992 1.88805i −0.0229762 0.0788743i
\(574\) 15.1362i 0.631775i
\(575\) 0 0
\(576\) 0.184091 2.99435i 0.00767044 0.124764i
\(577\) −16.6187 + 32.6160i −0.691845 + 1.35782i 0.231114 + 0.972927i \(0.425763\pi\)
−0.922960 + 0.384896i \(0.874237\pi\)
\(578\) −16.6231 2.63283i −0.691428 0.109511i
\(579\) 10.0150 + 1.90304i 0.416209 + 0.0790877i
\(580\) 0 0
\(581\) 18.4849 25.4423i 0.766882 1.05552i
\(582\) 0.409985 13.3499i 0.0169944 0.553372i
\(583\) 30.8579 4.88741i 1.27800 0.202416i
\(584\) −1.10696 + 3.40687i −0.0458062 + 0.140977i
\(585\) 0 0
\(586\) 0.500941 + 1.54174i 0.0206937 + 0.0636887i
\(587\) −5.16169 10.1304i −0.213046 0.418126i 0.759609 0.650379i \(-0.225390\pi\)
−0.972655 + 0.232254i \(0.925390\pi\)
\(588\) −20.6491 7.41745i −0.851553 0.305890i
\(589\) 15.8600 5.15324i 0.653501 0.212335i
\(590\) 0 0
\(591\) 30.1042 14.1922i 1.23832 0.583791i
\(592\) 0.825998 + 5.21515i 0.0339483 + 0.214341i
\(593\) 16.4362 + 16.4362i 0.674952 + 0.674952i 0.958854 0.283901i \(-0.0916288\pi\)
−0.283901 + 0.958854i \(0.591629\pi\)
\(594\) 19.5011 1.26890i 0.800140 0.0520636i
\(595\) 0 0
\(596\) −2.43884 3.35677i −0.0998986 0.137499i
\(597\) 18.2022 12.3893i 0.744968 0.507058i
\(598\) −17.5864 8.96072i −0.719162 0.366431i
\(599\) 16.9386 0.692094 0.346047 0.938217i \(-0.387524\pi\)
0.346047 + 0.938217i \(0.387524\pi\)
\(600\) 0 0
\(601\) −26.0220 −1.06146 −0.530730 0.847541i \(-0.678082\pi\)
−0.530730 + 0.847541i \(0.678082\pi\)
\(602\) 20.7679 + 10.5818i 0.846437 + 0.431281i
\(603\) 18.1390 + 4.02732i 0.738677 + 0.164005i
\(604\) −5.58437 7.68623i −0.227225 0.312748i
\(605\) 0 0
\(606\) 19.0462 2.41993i 0.773700 0.0983030i
\(607\) −29.4219 29.4219i −1.19420 1.19420i −0.975877 0.218322i \(-0.929942\pi\)
−0.218322 0.975877i \(-0.570058\pi\)
\(608\) 0.782226 + 4.93878i 0.0317235 + 0.200294i
\(609\) −6.04475 12.8219i −0.244946 0.519571i
\(610\) 0 0
\(611\) 19.2921 6.26837i 0.780473 0.253591i
\(612\) 1.13362 0.492487i 0.0458239 0.0199076i
\(613\) −2.55565 5.01575i −0.103222 0.202584i 0.833619 0.552339i \(-0.186265\pi\)
−0.936841 + 0.349755i \(0.886265\pi\)
\(614\) −3.62398 11.1535i −0.146252 0.450118i
\(615\) 0 0
\(616\) 5.15409 15.8627i 0.207664 0.639125i
\(617\) 35.1967 5.57460i 1.41696 0.224425i 0.599486 0.800385i \(-0.295372\pi\)
0.817478 + 0.575960i \(0.195372\pi\)
\(618\) 4.24555 + 0.130384i 0.170781 + 0.00524480i
\(619\) 20.2991 27.9393i 0.815889 1.12297i −0.174499 0.984657i \(-0.555831\pi\)
0.990388 0.138317i \(-0.0441694\pi\)
\(620\) 0 0
\(621\) −6.44476 + 25.3261i −0.258619 + 1.01630i
\(622\) −32.6756 5.17530i −1.31017 0.207511i
\(623\) 2.11632 4.15351i 0.0847885 0.166407i
\(624\) 4.65672 + 4.95180i 0.186418 + 0.198231i
\(625\) 0 0
\(626\) 4.37993i 0.175057i
\(627\) −31.2729 + 9.10988i −1.24892 + 0.363814i
\(628\) −0.659856 + 4.16617i −0.0263311 + 0.166248i
\(629\) −1.75992 + 1.27866i −0.0701727 + 0.0509835i
\(630\) 0 0
\(631\) −6.95722 5.05472i −0.276963 0.201225i 0.440629 0.897689i \(-0.354755\pi\)
−0.717591 + 0.696464i \(0.754755\pi\)
\(632\) −7.51686 + 7.51686i −0.299005 + 0.299005i
\(633\) 18.4929 23.8761i 0.735026 0.948989i
\(634\) −26.6314 8.65307i −1.05767 0.343657i
\(635\) 0 0
\(636\) 6.92265 12.6136i 0.274501 0.500162i
\(637\) 44.2955 22.5697i 1.75505 0.894244i
\(638\) 6.18406 3.15094i 0.244829 0.124747i
\(639\) 4.90243 1.26620i 0.193937 0.0500902i
\(640\) 0 0
\(641\) 12.9664 + 4.21305i 0.512144 + 0.166406i 0.553677 0.832732i \(-0.313224\pi\)
−0.0415332 + 0.999137i \(0.513224\pi\)
\(642\) 8.34036 + 6.45990i 0.329168 + 0.254952i
\(643\) −11.4059 + 11.4059i −0.449806 + 0.449806i −0.895290 0.445484i \(-0.853032\pi\)
0.445484 + 0.895290i \(0.353032\pi\)
\(644\) 18.0445 + 13.1101i 0.711051 + 0.516609i
\(645\) 0 0
\(646\) −1.66666 + 1.21090i −0.0655739 + 0.0476422i
\(647\) 4.90280 30.9551i 0.192749 1.21697i −0.681619 0.731707i \(-0.738724\pi\)
0.874368 0.485263i \(-0.161276\pi\)
\(648\) 5.03744 7.45816i 0.197889 0.292984i
\(649\) 21.1238i 0.829181i
\(650\) 0 0
\(651\) −18.6617 + 17.5496i −0.731409 + 0.687823i
\(652\) −4.73142 + 9.28593i −0.185297 + 0.363665i
\(653\) −37.8061 5.98789i −1.47947 0.234324i −0.636076 0.771626i \(-0.719444\pi\)
−0.843390 + 0.537302i \(0.819444\pi\)
\(654\) 1.51712 7.98404i 0.0593242 0.312201i
\(655\) 0 0
\(656\) −2.00614 + 2.76122i −0.0783266 + 0.107807i
\(657\) −8.05095 + 7.11835i −0.314098 + 0.277713i
\(658\) −22.6403 + 3.58587i −0.882610 + 0.139792i
\(659\) 6.33270 19.4901i 0.246687 0.759225i −0.748667 0.662946i \(-0.769306\pi\)
0.995354 0.0962789i \(-0.0306941\pi\)
\(660\) 0 0
\(661\) −13.4948 41.5327i −0.524887 1.61544i −0.764539 0.644577i \(-0.777033\pi\)
0.239652 0.970859i \(-0.422967\pi\)
\(662\) 4.35103 + 8.53939i 0.169108 + 0.331893i
\(663\) −0.946752 + 2.63562i −0.0367688 + 0.102359i
\(664\) 6.74418 2.19132i 0.261725 0.0850395i
\(665\) 0 0
\(666\) −5.81020 + 14.7364i −0.225141 + 0.571024i
\(667\) 1.45192 + 9.16704i 0.0562184 + 0.354949i
\(668\) 9.89891 + 9.89891i 0.383000 + 0.383000i
\(669\) −4.94171 38.8940i −0.191057 1.50373i
\(670\) 0 0
\(671\) −31.7502 43.7004i −1.22570 1.68703i
\(672\) −4.32208 6.34998i −0.166728 0.244956i
\(673\) 33.0273 + 16.8283i 1.27311 + 0.648681i 0.954219 0.299110i \(-0.0966898\pi\)
0.318890 + 0.947792i \(0.396690\pi\)
\(674\) 15.6652 0.603401
\(675\) 0 0
\(676\) −2.40180 −0.0923767
\(677\) 37.1946 + 18.9516i 1.42951 + 0.728369i 0.985819 0.167813i \(-0.0536704\pi\)
0.443686 + 0.896182i \(0.353670\pi\)
\(678\) 16.6632 + 24.4814i 0.639945 + 0.940204i
\(679\) −20.1010 27.6666i −0.771404 1.06175i
\(680\) 0 0
\(681\) −4.21517 33.1758i −0.161526 1.27130i
\(682\) −8.86905 8.86905i −0.339614 0.339614i
\(683\) 7.96066 + 50.2616i 0.304606 + 1.92321i 0.377793 + 0.925890i \(0.376683\pi\)
−0.0731865 + 0.997318i \(0.523317\pi\)
\(684\) −5.50230 + 13.9555i −0.210386 + 0.533601i
\(685\) 0 0
\(686\) −23.9045 + 7.76703i −0.912677 + 0.296547i
\(687\) 9.54401 26.5691i 0.364127 1.01367i
\(688\) 2.38607 + 4.68293i 0.0909681 + 0.178535i
\(689\) 10.0744 + 31.0059i 0.383805 + 1.18123i
\(690\) 0 0
\(691\) −9.91187 + 30.5056i −0.377065 + 1.16049i 0.565010 + 0.825084i \(0.308872\pi\)
−0.942075 + 0.335403i \(0.891128\pi\)
\(692\) −6.92347 + 1.09657i −0.263191 + 0.0416854i
\(693\) 37.4860 33.1437i 1.42397 1.25902i
\(694\) −21.7024 + 29.8708i −0.823813 + 1.13388i
\(695\) 0 0
\(696\) 0.596698 3.14020i 0.0226178 0.119029i
\(697\) −1.38884 0.219971i −0.0526061 0.00833198i
\(698\) 6.81642 13.3780i 0.258005 0.506364i
\(699\) 0.767891 0.722131i 0.0290443 0.0273135i
\(700\) 0 0
\(701\) 32.1785i 1.21536i −0.794180 0.607682i \(-0.792100\pi\)
0.794180 0.607682i \(-0.207900\pi\)
\(702\) 4.49113 + 19.8917i 0.169507 + 0.750762i
\(703\) 4.13027 26.0775i 0.155776 0.983533i
\(704\) 3.04265 2.21062i 0.114674 0.0833157i
\(705\) 0 0
\(706\) 24.3558 + 17.6956i 0.916644 + 0.665981i
\(707\) 34.7605 34.7605i 1.30730 1.30730i
\(708\) 7.69114 + 5.95706i 0.289051 + 0.223880i
\(709\) 2.62130 + 0.851713i 0.0984451 + 0.0319867i 0.357825 0.933789i \(-0.383518\pi\)
−0.259380 + 0.965775i \(0.583518\pi\)
\(710\) 0 0
\(711\) −30.8780 + 7.97521i −1.15802 + 0.299094i
\(712\) 0.936569 0.477205i 0.0350994 0.0178840i
\(713\) 14.9448 7.61474i 0.559686 0.285174i
\(714\) 1.52260 2.77429i 0.0569818 0.103825i
\(715\) 0 0
\(716\) −2.69201 0.874686i −0.100605 0.0326886i
\(717\) 8.50694 10.9833i 0.317697 0.410178i
\(718\) 2.46690 2.46690i 0.0920639 0.0920639i
\(719\) −6.94235 5.04392i −0.258906 0.188106i 0.450759 0.892646i \(-0.351154\pi\)
−0.709665 + 0.704540i \(0.751154\pi\)
\(720\) 0 0
\(721\) 8.79854 6.39251i 0.327675 0.238070i
\(722\) 0.939145 5.92953i 0.0349514 0.220674i
\(723\) −12.0522 + 3.51083i −0.448226 + 0.130569i
\(724\) 0.350016i 0.0130082i
\(725\) 0 0
\(726\) 3.73123 + 3.96767i 0.138479 + 0.147254i
\(727\) 15.5376 30.4942i 0.576257 1.13097i −0.400435 0.916325i \(-0.631141\pi\)
0.976692 0.214644i \(-0.0688590\pi\)
\(728\) 17.1902 + 2.72266i 0.637111 + 0.100909i
\(729\) 24.3808 11.6007i 0.902992 0.429656i
\(730\) 0 0
\(731\) −1.27276 + 1.75180i −0.0470746 + 0.0647926i
\(732\) −24.8650 0.763622i −0.919038 0.0282243i
\(733\) −39.3201 + 6.22770i −1.45232 + 0.230025i −0.832198 0.554478i \(-0.812918\pi\)
−0.620124 + 0.784504i \(0.712918\pi\)
\(734\) −4.83943 + 14.8942i −0.178627 + 0.549756i
\(735\) 0 0
\(736\) 1.55415 + 4.78318i 0.0572867 + 0.176310i
\(737\) 10.5750 + 20.7547i 0.389537 + 0.764509i
\(738\) −9.39121 + 4.07989i −0.345695 + 0.150183i
\(739\) −19.6010 + 6.36874i −0.721033 + 0.234278i −0.646471 0.762939i \(-0.723756\pi\)
−0.0745620 + 0.997216i \(0.523756\pi\)
\(740\) 0 0
\(741\) −14.4941 30.7444i −0.532452 1.12942i
\(742\) −5.76314 36.3871i −0.211572 1.33581i
\(743\) −25.7253 25.7253i −0.943771 0.943771i 0.0547306 0.998501i \(-0.482570\pi\)
−0.998501 + 0.0547306i \(0.982570\pi\)
\(744\) −5.73035 + 0.728073i −0.210085 + 0.0266925i
\(745\) 0 0
\(746\) −3.74935 5.16053i −0.137273 0.188940i
\(747\) 20.7680 + 4.61103i 0.759862 + 0.168709i
\(748\) 1.38059 + 0.703446i 0.0504794 + 0.0257205i
\(749\) 27.0114 0.986973
\(750\) 0 0
\(751\) −13.8571 −0.505654 −0.252827 0.967511i \(-0.581360\pi\)
−0.252827 + 0.967511i \(0.581360\pi\)
\(752\) −4.60540 2.34657i −0.167942 0.0855705i
\(753\) 20.8362 14.1821i 0.759314 0.516823i
\(754\) 4.25699 + 5.85925i 0.155031 + 0.213381i
\(755\) 0 0
\(756\) −1.49626 22.9953i −0.0544186 0.836332i
\(757\) −28.7075 28.7075i −1.04339 1.04339i −0.999015 0.0443764i \(-0.985870\pi\)
−0.0443764 0.999015i \(-0.514130\pi\)
\(758\) 4.21499 + 26.6124i 0.153095 + 0.966606i
\(759\) −29.6336 + 13.9704i −1.07563 + 0.507094i
\(760\) 0 0
\(761\) −36.3818 + 11.8212i −1.31884 + 0.428517i −0.882096 0.471069i \(-0.843868\pi\)
−0.436744 + 0.899586i \(0.643868\pi\)
\(762\) 31.9710 + 11.4844i 1.15819 + 0.416037i
\(763\) −9.44684 18.5405i −0.341998 0.671210i
\(764\) −0.350849 1.07980i −0.0126933 0.0390659i
\(765\) 0 0
\(766\) 9.25415 28.4814i 0.334366 1.02907i
\(767\) −21.7712 + 3.44822i −0.786114 + 0.124508i
\(768\) 0.0531674 1.73123i 0.00191851 0.0624705i
\(769\) −23.2438 + 31.9924i −0.838194 + 1.15368i 0.148148 + 0.988965i \(0.452669\pi\)
−0.986342 + 0.164710i \(0.947331\pi\)
\(770\) 0 0
\(771\) 2.49860 + 0.474783i 0.0899850 + 0.0170989i
\(772\) 5.81316 + 0.920714i 0.209220 + 0.0331372i
\(773\) −16.3075 + 32.0052i −0.586539 + 1.15115i 0.386883 + 0.922129i \(0.373552\pi\)
−0.973422 + 0.229019i \(0.926448\pi\)
\(774\) −0.967539 + 15.7376i −0.0347775 + 0.565677i
\(775\) 0 0
\(776\) 7.71121i 0.276816i
\(777\) 11.3433 + 38.9400i 0.406939 + 1.39697i
\(778\) −1.80860 + 11.4191i −0.0648416 + 0.409394i
\(779\) 13.8070 10.0314i 0.494688 0.359412i
\(780\) 0 0
\(781\) 5.13529 + 3.73101i 0.183755 + 0.133506i
\(782\) −1.46516 + 1.46516i −0.0523940