Properties

Label 750.2.l.b.143.9
Level $750$
Weight $2$
Character 750.143
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 143.9
Character \(\chi\) \(=\) 750.143
Dual form 750.2.l.b.257.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.453990 - 0.891007i) q^{2} +(1.06061 + 1.36935i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(-3.13589 + 3.13589i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.750223 + 2.90468i) q^{9} +O(q^{10})\) \(q+(0.453990 - 0.891007i) q^{2} +(1.06061 + 1.36935i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(-3.13589 + 3.13589i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(-0.750223 + 2.90468i) q^{9} +(3.57685 - 1.16219i) q^{11} +(0.484416 - 1.66293i) q^{12} +(-3.49677 + 1.78169i) q^{13} +(1.37043 + 4.21776i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.0644499 + 0.406920i) q^{17} +(2.24749 + 1.98715i) q^{18} +(-2.93913 + 4.04536i) q^{19} +(-7.62006 - 0.968173i) q^{21} +(0.588338 - 3.71462i) q^{22} +(4.48117 + 2.28327i) q^{23} +(-1.26176 - 1.18657i) q^{24} +3.92451i q^{26} +(-4.77321 + 2.05341i) q^{27} +(4.38021 + 0.693758i) q^{28} +(-1.49299 + 1.08472i) q^{29} +(2.69808 + 1.96027i) q^{31} +(0.707107 + 0.707107i) q^{32} +(5.38508 + 3.66532i) q^{33} +(0.391828 + 0.127313i) q^{34} +(2.79091 - 1.10038i) q^{36} +(2.39714 + 4.70465i) q^{37} +(2.27011 + 4.45534i) q^{38} +(-6.14845 - 2.89861i) q^{39} +(-3.24600 - 1.05469i) q^{41} +(-4.32208 + 6.34998i) q^{42} +(-3.71639 - 3.71639i) q^{43} +(-3.04265 - 2.21062i) q^{44} +(4.06882 - 2.95617i) q^{46} +(5.10512 + 0.808572i) q^{47} +(-1.63007 + 0.585546i) q^{48} -12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(3.49677 + 1.78169i) q^{52} +(1.29952 - 8.20487i) q^{53} +(-0.337390 + 5.18519i) q^{54} +(2.60672 - 3.58784i) q^{56} +(-8.65677 + 0.265855i) q^{57} +(0.288689 + 1.82271i) q^{58} +(1.73564 - 5.34175i) q^{59} +(4.43829 + 13.6596i) q^{61} +(2.97152 - 1.51406i) q^{62} +(-6.75613 - 11.4614i) q^{63} +(0.951057 - 0.309017i) q^{64} +(5.71060 - 3.13412i) q^{66} +(6.11731 - 0.968887i) q^{67} +(0.291323 - 0.291323i) q^{68} +(1.62617 + 8.55793i) q^{69} +(0.992045 + 1.36543i) q^{71} +(0.286595 - 2.98628i) q^{72} +(1.62628 - 3.19175i) q^{73} +5.28015 q^{74} +5.00034 q^{76} +(-7.57211 + 14.8611i) q^{77} +(-5.37402 + 4.16237i) q^{78} +(-6.24842 - 8.60021i) q^{79} +(-7.87433 - 4.35832i) q^{81} +(-2.41339 + 2.41339i) q^{82} +(7.00394 - 1.10932i) q^{83} +(3.69569 + 6.73384i) q^{84} +(-4.99854 + 1.62412i) q^{86} +(-3.06883 - 0.893957i) q^{87} +(-3.35101 + 1.70742i) q^{88} +(-0.324819 - 0.999689i) q^{89} +(5.37828 - 16.5526i) q^{91} +(-0.786761 - 4.96742i) q^{92} +(0.177314 + 5.77369i) q^{93} +(3.03812 - 4.18162i) q^{94} +(-0.218312 + 1.71824i) q^{96} +(1.20630 - 7.61627i) q^{97} +(-11.2869 - 5.75096i) q^{98} +(0.692350 + 11.2615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{3} - 4q^{7} + O(q^{10}) \) \( 80q - 4q^{3} - 4q^{7} + 4q^{12} + 20q^{16} + 8q^{18} - 40q^{19} + 36q^{22} - 4q^{27} + 16q^{28} - 4q^{33} - 40q^{34} + 24q^{37} - 40q^{39} + 4q^{42} + 24q^{43} + 4q^{48} + 64q^{57} - 20q^{58} - 64q^{63} - 96q^{67} + 140q^{69} - 8q^{72} - 100q^{73} - 100q^{78} + 80q^{79} - 40q^{81} - 96q^{82} + 60q^{84} - 80q^{87} - 4q^{88} - 12q^{93} + 32q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{3}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.453990 0.891007i 0.321020 0.630037i
\(3\) 1.06061 + 1.36935i 0.612342 + 0.790593i
\(4\) −0.587785 0.809017i −0.293893 0.404508i
\(5\) 0 0
\(6\) 1.70160 0.323338i 0.694677 0.132002i
\(7\) −3.13589 + 3.13589i −1.18525 + 1.18525i −0.206890 + 0.978364i \(0.566334\pi\)
−0.978364 + 0.206890i \(0.933666\pi\)
\(8\) −0.987688 + 0.156434i −0.349201 + 0.0553079i
\(9\) −0.750223 + 2.90468i −0.250074 + 0.968227i
\(10\) 0 0
\(11\) 3.57685 1.16219i 1.07846 0.350413i 0.284684 0.958622i \(-0.408111\pi\)
0.793778 + 0.608208i \(0.208111\pi\)
\(12\) 0.484416 1.66293i 0.139839 0.480047i
\(13\) −3.49677 + 1.78169i −0.969828 + 0.494152i −0.865783 0.500420i \(-0.833179\pi\)
−0.104046 + 0.994573i \(0.533179\pi\)
\(14\) 1.37043 + 4.21776i 0.366264 + 1.12724i
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.0772542 + 0.237764i
\(17\) 0.0644499 + 0.406920i 0.0156314 + 0.0986927i 0.994271 0.106893i \(-0.0340902\pi\)
−0.978639 + 0.205585i \(0.934090\pi\)
\(18\) 2.24749 + 1.98715i 0.529739 + 0.468376i
\(19\) −2.93913 + 4.04536i −0.674282 + 0.928070i −0.999848 0.0174495i \(-0.994445\pi\)
0.325565 + 0.945520i \(0.394445\pi\)
\(20\) 0 0
\(21\) −7.62006 0.968173i −1.66283 0.211273i
\(22\) 0.588338 3.71462i 0.125434 0.791960i
\(23\) 4.48117 + 2.28327i 0.934389 + 0.476095i 0.853770 0.520650i \(-0.174310\pi\)
0.0806186 + 0.996745i \(0.474310\pi\)
\(24\) −1.26176 1.18657i −0.257556 0.242208i
\(25\) 0 0
\(26\) 3.92451i 0.769660i
\(27\) −4.77321 + 2.05341i −0.918604 + 0.395179i
\(28\) 4.38021 + 0.693758i 0.827783 + 0.131108i
\(29\) −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
\(33\) 5.38508 + 3.66532i 0.937421 + 0.638051i
\(34\) 0.391828 + 0.127313i 0.0671980 + 0.0218340i
\(35\) 0 0
\(36\) 2.79091 1.10038i 0.465151 0.183397i
\(37\) 2.39714 + 4.70465i 0.394087 + 0.773440i 0.999752 0.0222802i \(-0.00709259\pi\)
−0.605664 + 0.795720i \(0.707093\pi\)
\(38\) 2.27011 + 4.45534i 0.368260 + 0.722751i
\(39\) −6.14845 2.89861i −0.984540 0.464149i
\(40\) 0 0
\(41\) −3.24600 1.05469i −0.506941 0.164715i 0.0443698 0.999015i \(-0.485872\pi\)
−0.551310 + 0.834300i \(0.685872\pi\)
\(42\) −4.32208 + 6.34998i −0.666912 + 0.979824i
\(43\) −3.71639 3.71639i −0.566745 0.566745i 0.364470 0.931215i \(-0.381250\pi\)
−0.931215 + 0.364470i \(0.881250\pi\)
\(44\) −3.04265 2.21062i −0.458697 0.333263i
\(45\) 0 0
\(46\) 4.06882 2.95617i 0.599914 0.435863i
\(47\) 5.10512 + 0.808572i 0.744659 + 0.117942i 0.517223 0.855851i \(-0.326966\pi\)
0.227436 + 0.973793i \(0.426966\pi\)
\(48\) −1.63007 + 0.585546i −0.235281 + 0.0845163i
\(49\) 12.6676i 1.80965i
\(50\) 0 0
\(51\) −0.488859 + 0.519837i −0.0684540 + 0.0727917i
\(52\) 3.49677 + 1.78169i 0.484914 + 0.247076i
\(53\) 1.29952 8.20487i 0.178503 1.12703i −0.721909 0.691988i \(-0.756735\pi\)
0.900412 0.435037i \(-0.143265\pi\)
\(54\) −0.337390 + 5.18519i −0.0459130 + 0.705615i
\(55\) 0 0
\(56\) 2.60672 3.58784i 0.348337 0.479445i
\(57\) −8.65677 + 0.265855i −1.14662 + 0.0352134i
\(58\) 0.288689 + 1.82271i 0.0379068 + 0.239334i
\(59\) 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 \(0.528617\pi\)
\(62\) 2.97152 1.51406i 0.377383 0.192286i
\(63\) −6.75613 11.4614i −0.851193 1.44400i
\(64\) 0.951057 0.309017i 0.118882 0.0386271i
\(65\) 0 0
\(66\) 5.71060 3.13412i 0.702926 0.385783i
\(67\) 6.11731 0.968887i 0.747349 0.118368i 0.228868 0.973458i \(-0.426498\pi\)
0.518481 + 0.855089i \(0.326498\pi\)
\(68\) 0.291323 0.291323i 0.0353281 0.0353281i
\(69\) 1.62617 + 8.55793i 0.195768 + 1.03025i
\(70\) 0 0
\(71\) 0.992045 + 1.36543i 0.117734 + 0.162047i 0.863817 0.503806i \(-0.168068\pi\)
−0.746082 + 0.665854i \(0.768068\pi\)
\(72\) 0.286595 2.98628i 0.0337755 0.351936i
\(73\) 1.62628 3.19175i 0.190342 0.373567i −0.776038 0.630686i \(-0.782773\pi\)
0.966380 + 0.257120i \(0.0827735\pi\)
\(74\) 5.28015 0.613805
\(75\) 0 0
\(76\) 5.00034 0.573579
\(77\) −7.57211 + 14.8611i −0.862922 + 1.69358i
\(78\) −5.37402 + 4.16237i −0.608488 + 0.471295i
\(79\) −6.24842 8.60021i −0.703002 0.967599i −0.999919 0.0126959i \(-0.995959\pi\)
0.296918 0.954903i \(-0.404041\pi\)
\(80\) 0 0
\(81\) −7.87433 4.35832i −0.874926 0.484258i
\(82\) −2.41339 + 2.41339i −0.266514 + 0.266514i
\(83\) 7.00394 1.10932i 0.768782 0.121763i 0.240290 0.970701i \(-0.422757\pi\)
0.528493 + 0.848938i \(0.322757\pi\)
\(84\) 3.69569 + 6.73384i 0.403233 + 0.734722i
\(85\) 0 0
\(86\) −4.99854 + 1.62412i −0.539006 + 0.175134i
\(87\) −3.06883 0.893957i −0.329013 0.0958423i
\(88\) −3.35101 + 1.70742i −0.357219 + 0.182012i
\(89\) −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
\(92\) −0.786761 4.96742i −0.0820255 0.517889i
\(93\) 0.177314 + 5.77369i 0.0183866 + 0.598704i
\(94\) 3.03812 4.18162i 0.313358 0.431301i
\(95\) 0 0
\(96\) −0.218312 + 1.71824i −0.0222814 + 0.175367i
\(97\) 1.20630 7.61627i 0.122481 0.773315i −0.847618 0.530607i \(-0.821964\pi\)
0.970099 0.242709i \(-0.0780359\pi\)
\(98\) −11.2869 5.75096i −1.14015 0.580935i
\(99\) 0.692350 + 11.2615i 0.0695838 + 1.13182i
\(100\) 0 0
\(101\) 11.0847i 1.10297i 0.834184 + 0.551487i \(0.185939\pi\)
−0.834184 + 0.551487i \(0.814061\pi\)
\(102\) 0.241241 + 0.671578i 0.0238864 + 0.0664961i
\(103\) −2.42213 0.383628i −0.238660 0.0378000i 0.0359588 0.999353i \(-0.488552\pi\)
−0.274618 + 0.961553i \(0.588552\pi\)
\(104\) 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 \(-0.345122\pi\)
−0.883945 + 0.467590i \(0.845122\pi\)
\(108\) 4.46686 + 2.65464i 0.429824 + 0.255443i
\(109\) 4.46242 + 1.44993i 0.427422 + 0.138878i 0.514825 0.857295i \(-0.327857\pi\)
−0.0874029 + 0.996173i \(0.527857\pi\)
\(110\) 0 0
\(111\) −3.89988 + 8.27231i −0.370160 + 0.785173i
\(112\) −2.01336 3.95145i −0.190245 0.373377i
\(113\) 7.76223 + 15.2342i 0.730209 + 1.43312i 0.894668 + 0.446732i \(0.147412\pi\)
−0.164459 + 0.986384i \(0.552588\pi\)
\(114\) −3.69321 + 7.83393i −0.345901 + 0.733715i
\(115\) 0 0
\(116\) 1.75511 + 0.570270i 0.162958 + 0.0529483i
\(117\) −2.55189 11.4937i −0.235922 1.06259i
\(118\) −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
\(122\) 14.1858 + 2.24681i 1.28432 + 0.203416i
\(123\) −1.99850 5.56352i −0.180199 0.501646i
\(124\) 3.33501i 0.299493i
\(125\) 0 0
\(126\) −13.2794 + 0.816407i −1.18302 + 0.0727313i
\(127\) 17.4755 + 8.90421i 1.55070 + 0.790121i 0.999034 0.0439442i \(-0.0139924\pi\)
0.551666 + 0.834065i \(0.313992\pi\)
\(128\) 0.156434 0.987688i 0.0138270 0.0873001i
\(129\) 1.14740 9.03067i 0.101023 0.795106i
\(130\) 0 0
\(131\) 12.0644 16.6052i 1.05407 1.45080i 0.168841 0.985643i \(-0.445998\pi\)
0.885228 0.465158i \(-0.154002\pi\)
\(132\) −0.199959 6.51104i −0.0174042 0.566713i
\(133\) −3.46903 21.9026i −0.300803 1.89919i
\(134\) 1.91392 5.89043i 0.165337 0.508856i
\(135\) 0 0
\(136\) −0.127313 0.391828i −0.0109170 0.0335990i
\(137\) 6.44062 3.28166i 0.550259 0.280371i −0.156675 0.987650i \(-0.550078\pi\)
0.706935 + 0.707279i \(0.250078\pi\)
\(138\) 8.36344 + 2.43629i 0.711943 + 0.207391i
\(139\) 9.21867 2.99533i 0.781918 0.254060i 0.109259 0.994013i \(-0.465152\pi\)
0.672659 + 0.739953i \(0.265152\pi\)
\(140\) 0 0
\(141\) 4.30732 + 7.84827i 0.362742 + 0.660943i
\(142\) 1.66699 0.264025i 0.139891 0.0221565i
\(143\) −10.4367 + 10.4367i −0.872765 + 0.872765i
\(144\) −2.53068 1.61110i −0.210890 0.134258i
\(145\) 0 0
\(146\) −2.10556 2.89805i −0.174257 0.239845i
\(147\) 17.3463 13.4353i 1.43070 1.10813i
\(148\) 2.39714 4.70465i 0.197044 0.386720i
\(149\) −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 \(0.626343\pi\)
\(152\) 2.27011 4.45534i 0.184130 0.361376i
\(153\) −1.23033 0.118075i −0.0994659 0.00954580i
\(154\) 9.80367 + 13.4936i 0.790002 + 1.08734i
\(155\) 0 0
\(156\) 1.26894 + 6.67796i 0.101597 + 0.534665i
\(157\) −2.98265 + 2.98265i −0.238041 + 0.238041i −0.816039 0.577997i \(-0.803834\pi\)
0.577997 + 0.816039i \(0.303834\pi\)
\(158\) −10.4996 + 1.66297i −0.835300 + 0.132299i
\(159\) 12.6136 6.92265i 1.00032 0.549002i
\(160\) 0 0
\(161\) −21.2125 + 6.89237i −1.67178 + 0.543195i
\(162\) −7.45816 + 5.03744i −0.585968 + 0.395779i
\(163\) 9.28593 4.73142i 0.727330 0.370593i −0.0507896 0.998709i \(-0.516174\pi\)
0.778119 + 0.628116i \(0.216174\pi\)
\(164\) 1.05469 + 3.24600i 0.0823575 + 0.253470i
\(165\) 0 0
\(166\) 2.19132 6.74418i 0.170079 0.523450i
\(167\) −2.18995 13.8268i −0.169464 1.06995i −0.914990 0.403476i \(-0.867802\pi\)
0.745527 0.666476i \(-0.232198\pi\)
\(168\) 7.67770 0.235788i 0.592348 0.0181914i
\(169\) 1.41174 1.94309i 0.108595 0.149469i
\(170\) 0 0
\(171\) −9.54548 11.5722i −0.729961 0.884945i
\(172\) −0.822184 + 5.19107i −0.0626910 + 0.395815i
\(173\) −6.24576 3.18237i −0.474856 0.241951i 0.200147 0.979766i \(-0.435858\pi\)
−0.675003 + 0.737815i \(0.735858\pi\)
\(174\) −2.18974 + 2.32850i −0.166004 + 0.176523i
\(175\) 0 0
\(176\) 3.76092i 0.283490i
\(177\) 9.15555 3.28881i 0.688173 0.247202i
\(178\) −1.03819 0.164434i −0.0778159 0.0123248i
\(179\) −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
\(183\) −13.9975 + 20.5651i −1.03473 + 1.52021i
\(184\) −4.78318 1.55415i −0.352621 0.114573i
\(185\) 0 0
\(186\) 5.22490 + 2.46321i 0.383108 + 0.180612i
\(187\) 0.703446 + 1.38059i 0.0514411 + 0.100959i
\(188\) −2.34657 4.60540i −0.171141 0.335883i
\(189\) 8.52898 21.4075i 0.620392 1.55717i
\(190\) 0 0
\(191\) 1.07980 + 0.350849i 0.0781318 + 0.0253866i 0.347822 0.937561i \(-0.386921\pi\)
−0.269690 + 0.962947i \(0.586921\pi\)
\(192\) 1.43185 + 0.974581i 0.103335 + 0.0703343i
\(193\) −4.16176 4.16176i −0.299570 0.299570i 0.541275 0.840845i \(-0.317942\pi\)
−0.840845 + 0.541275i \(0.817942\pi\)
\(194\) −6.23850 4.53254i −0.447898 0.325417i
\(195\) 0 0
\(196\) −10.2483 + 7.44581i −0.732020 + 0.531844i
\(197\) −18.9787 3.00593i −1.35218 0.214164i −0.562048 0.827105i \(-0.689986\pi\)
−0.790129 + 0.612941i \(0.789986\pi\)
\(198\) 10.3484 + 4.49573i 0.735429 + 0.319498i
\(199\) 12.7124i 0.901157i 0.892737 + 0.450579i \(0.148782\pi\)
−0.892737 + 0.450579i \(0.851218\pi\)
\(200\) 0 0
\(201\) 7.81481 + 7.34912i 0.551214 + 0.518367i
\(202\) 9.87658 + 5.03237i 0.694914 + 0.354076i
\(203\) 1.28028 8.08340i 0.0898583 0.567343i
\(204\) 0.707901 + 0.0899429i 0.0495630 + 0.00629726i
\(205\) 0 0
\(206\) −1.44144 + 1.98397i −0.100430 + 0.138230i
\(207\) −9.99405 + 11.3034i −0.694634 + 0.785641i
\(208\) −0.613929 3.87619i −0.0425683 0.268766i
\(209\) −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 \(-0.304903\pi\)
\(212\) −7.40172 + 3.77136i −0.508352 + 0.259018i
\(213\) −0.817581 + 2.80664i −0.0560198 + 0.192308i
\(214\) −5.79265 + 1.88215i −0.395977 + 0.128661i
\(215\) 0 0
\(216\) 4.39322 2.77482i 0.298921 0.188803i
\(217\) −14.6081 + 2.31369i −0.991661 + 0.157064i
\(218\) 3.31779 3.31779i 0.224709 0.224709i
\(219\) 6.09547 1.15826i 0.411893 0.0782677i
\(220\) 0 0
\(221\) −0.950373 1.30808i −0.0639290 0.0879907i
\(222\) 5.60017 + 7.23036i 0.375859 + 0.485270i
\(223\) −10.2765 + 20.1688i −0.688167 + 1.35060i 0.237174 + 0.971467i \(0.423779\pi\)
−0.925341 + 0.379136i \(0.876221\pi\)
\(224\) −4.43481 −0.296313
\(225\) 0 0
\(226\) 17.0978 1.13733
\(227\) −8.76566 + 17.2036i −0.581797 + 1.14184i 0.393164 + 0.919468i \(0.371380\pi\)
−0.974962 + 0.222373i \(0.928620\pi\)
\(228\) 5.30340 + 6.84721i 0.351226 + 0.453467i
\(229\) 9.58051 + 13.1864i 0.633098 + 0.871384i 0.998224 0.0595738i \(-0.0189742\pi\)
−0.365126 + 0.930958i \(0.618974\pi\)
\(230\) 0 0
\(231\) −28.3810 + 5.39295i −1.86733 + 0.354830i
\(232\) 1.30492 1.30492i 0.0856721 0.0856721i
\(233\) 0.601093 0.0952038i 0.0393789 0.00623701i −0.136714 0.990611i \(-0.543654\pi\)
0.176093 + 0.984374i \(0.443654\pi\)
\(234\) −11.3995 2.94426i −0.745205 0.192472i
\(235\) 0 0
\(236\) −5.34175 + 1.73564i −0.347718 + 0.112981i
\(237\) 5.14955 17.6777i 0.334499 1.14829i
\(238\) −1.62797 + 0.829491i −0.105525 + 0.0537679i
\(239\) −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 \(0.174994\pi\)
\(242\) −0.491916 3.10583i −0.0316215 0.199650i
\(243\) −2.38352 15.4052i −0.152903 0.988241i
\(244\) 8.44212 11.6196i 0.540452 0.743868i
\(245\) 0 0
\(246\) −5.86443 0.745110i −0.373903 0.0475065i
\(247\) 3.06986 19.3823i 0.195330 1.23327i
\(248\) −2.97152 1.51406i −0.188692 0.0961432i
\(249\) 8.94747 + 8.41428i 0.567023 + 0.533233i
\(250\) 0 0
\(251\) 14.5520i 0.918511i 0.888304 + 0.459256i \(0.151884\pi\)
−0.888304 + 0.459256i \(0.848116\pi\)
\(252\) −5.30128 + 12.2026i −0.333949 + 0.768694i
\(253\) 18.6821 + 2.95895i 1.17453 + 0.186028i
\(254\) 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 \(-0.264583\pi\)
−0.738749 + 0.673981i \(0.764583\pi\)
\(258\) −7.52548 5.12218i −0.468516 0.318893i
\(259\) −22.2704 7.23610i −1.38382 0.449629i
\(260\) 0 0
\(261\) −2.03069 5.15043i −0.125696 0.318804i
\(262\) −9.31821 18.2880i −0.575681 1.12984i
\(263\) −10.1330 19.8871i −0.624825 1.22629i −0.958901 0.283743i \(-0.908424\pi\)
0.334075 0.942546i \(-0.391576\pi\)
\(264\) −5.89216 2.77779i −0.362637 0.170961i
\(265\) 0 0
\(266\) −21.0902 6.85264i −1.29313 0.420162i
\(267\) 1.02442 1.50507i 0.0626933 0.0921086i
\(268\) −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 \(0.464217\pi\)
\(272\) −0.406920 0.0644499i −0.0246732 0.00390785i
\(273\) 28.3706 10.1911i 1.71706 0.616795i
\(274\) 7.22848i 0.436688i
\(275\) 0 0
\(276\) 5.96767 6.34583i 0.359212 0.381974i
\(277\) 6.13564 + 3.12626i 0.368655 + 0.187839i 0.628497 0.777812i \(-0.283670\pi\)
−0.259842 + 0.965651i \(0.583670\pi\)
\(278\) 1.51633 9.57375i 0.0909436 0.574195i
\(279\) −7.71813 + 6.36643i −0.462072 + 0.381148i
\(280\) 0 0
\(281\) 14.3948 19.8128i 0.858723 1.18193i −0.123150 0.992388i \(-0.539300\pi\)
0.981873 0.189542i \(-0.0607004\pi\)
\(282\) 8.94834 0.274810i 0.532866 0.0163647i
\(283\) 1.14551 + 7.23244i 0.0680933 + 0.429924i 0.998059 + 0.0622774i \(0.0198363\pi\)
−0.929966 + 0.367646i \(0.880164\pi\)
\(284\) 0.521549 1.60516i 0.0309482 0.0952489i
\(285\) 0 0
\(286\) 4.56103 + 14.0374i 0.269699 + 0.830049i
\(287\) 13.4865 6.87171i 0.796083 0.405624i
\(288\) −2.58441 + 1.52343i −0.152288 + 0.0897690i
\(289\) 16.0065 5.20084i 0.941561 0.305932i
\(290\) 0 0
\(291\) 11.7087 6.42603i 0.686378 0.376701i
\(292\) −3.53809 + 0.560378i −0.207051 + 0.0327936i
\(293\) −1.14628 + 1.14628i −0.0669662 + 0.0669662i −0.739797 0.672830i \(-0.765078\pi\)
0.672830 + 0.739797i \(0.265078\pi\)
\(294\) −4.09590 21.5552i −0.238878 1.25712i
\(295\) 0 0
\(296\) −3.10360 4.27173i −0.180393 0.248290i
\(297\) −14.6866 + 12.8921i −0.852203 + 0.748076i
\(298\) −1.88370 + 3.69696i −0.109120 + 0.214159i
\(299\) −19.7377 −1.14146
\(300\) 0 0
\(301\) 23.3084 1.34347
\(302\) −4.31323 + 8.46519i −0.248198 + 0.487117i
\(303\) −15.1789 + 11.7566i −0.872003 + 0.675397i
\(304\) −2.93913 4.04536i −0.168571 0.232018i
\(305\) 0 0
\(306\) −0.663762 + 1.04262i −0.0379447 + 0.0596028i
\(307\) 8.29257 8.29257i 0.473282 0.473282i −0.429693 0.902975i \(-0.641378\pi\)
0.902975 + 0.429693i \(0.141378\pi\)
\(308\) 16.4737 2.60917i 0.938673 0.148671i
\(309\) −2.04361 3.72362i −0.116257 0.211829i
\(310\) 0 0
\(311\) 31.4637 10.2232i 1.78414 0.579703i 0.784937 0.619575i \(-0.212695\pi\)
0.999205 + 0.0398725i \(0.0126952\pi\)
\(312\) 6.52620 + 1.90110i 0.369473 + 0.107628i
\(313\) −3.90255 + 1.98845i −0.220585 + 0.112394i −0.560791 0.827957i \(-0.689503\pi\)
0.340206 + 0.940351i \(0.389503\pi\)
\(314\) 1.30346 + 4.01165i 0.0735587 + 0.226391i
\(315\) 0 0
\(316\) −3.28499 + 10.1102i −0.184795 + 0.568740i
\(317\) 4.38047 + 27.6572i 0.246032 + 1.55338i 0.733163 + 0.680053i \(0.238043\pi\)
−0.487131 + 0.873329i \(0.661957\pi\)
\(318\) −0.441669 14.3816i −0.0247676 0.806481i
\(319\) −4.07954 + 5.61501i −0.228411 + 0.314380i
\(320\) 0 0
\(321\) 1.32968 10.4654i 0.0742157 0.584119i
\(322\) −3.48914 + 22.0296i −0.194442 + 1.22766i
\(323\) −1.83557 0.935268i −0.102134 0.0520397i
\(324\) 1.10246 + 8.93222i 0.0612479 + 0.496235i
\(325\) 0 0
\(326\) 10.4218i 0.577212i
\(327\) 2.74742 + 7.64841i 0.151933 + 0.422958i
\(328\) 3.37103 + 0.533919i 0.186134 + 0.0294807i
\(329\) −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
\(333\) −15.4639 + 3.43338i −0.847416 + 0.188148i
\(334\) −13.3140 4.32598i −0.728510 0.236707i
\(335\) 0 0
\(336\) 3.27552 6.94793i 0.178694 0.379041i
\(337\) 7.11185 + 13.9578i 0.387407 + 0.760329i 0.999537 0.0304279i \(-0.00968701\pi\)
−0.612130 + 0.790757i \(0.709687\pi\)
\(338\) −1.09039 2.14002i −0.0593095 0.116401i
\(339\) −12.6283 + 26.7867i −0.685874 + 1.45485i
\(340\) 0 0
\(341\) 11.9289 + 3.87592i 0.645983 + 0.209893i
\(342\) −14.6444 + 3.25144i −0.791880 + 0.175818i
\(343\) 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
\(347\) 36.4678 + 5.77593i 1.95769 + 0.310068i 0.999731 + 0.0231773i \(0.00737823\pi\)
0.957963 + 0.286891i \(0.0926218\pi\)
\(348\) 1.08059 + 3.00819i 0.0579255 + 0.161256i
\(349\) 15.0145i 0.803705i 0.915704 + 0.401853i \(0.131634\pi\)
−0.915704 + 0.401853i \(0.868366\pi\)
\(350\) 0 0
\(351\) 13.0322 15.6847i 0.695610 0.837186i
\(352\) 3.35101 + 1.70742i 0.178609 + 0.0910060i
\(353\) −4.70953 + 29.7348i −0.250663 + 1.58263i 0.465729 + 0.884927i \(0.345792\pi\)
−0.716392 + 0.697698i \(0.754208\pi\)
\(354\) 1.22618 9.65074i 0.0651708 0.512931i
\(355\) 0 0
\(356\) −0.617842 + 0.850386i −0.0327456 + 0.0450704i
\(357\) −0.0971428 3.16316i −0.00514134 0.167412i
\(358\) 0.442795 + 2.79569i 0.0234024 + 0.147757i
\(359\) 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
\(362\) −0.311866 + 0.158904i −0.0163913 + 0.00835180i
\(363\) 5.22917 + 1.52327i 0.274460 + 0.0799508i
\(364\) −16.5526 + 5.37828i −0.867594 + 0.281898i
\(365\) 0 0
\(366\) 11.9689 + 21.8082i 0.625623 + 1.13993i
\(367\) −15.4679 + 2.44988i −0.807418 + 0.127882i −0.546479 0.837473i \(-0.684032\pi\)
−0.260939 + 0.965355i \(0.584032\pi\)
\(368\) −3.55628 + 3.55628i −0.185384 + 0.185384i
\(369\) 5.49877 8.63735i 0.286254 0.449642i
\(370\) 0 0
\(371\) 21.6544 + 29.8047i 1.12424 + 1.54738i
\(372\) 4.56679 3.53714i 0.236777 0.183392i
\(373\) −2.89590 + 5.68352i −0.149944 + 0.294282i −0.953745 0.300616i \(-0.902808\pi\)
0.803801 + 0.594898i \(0.202808\pi\)
\(374\) 1.54947 0.0801213
\(375\) 0 0
\(376\) −5.16876 −0.266558
\(377\) 3.28799 6.45305i 0.169340 0.332349i
\(378\) −15.2021 17.3182i −0.781914 0.890751i
\(379\) −15.8374 21.7983i −0.813510 1.11970i −0.990772 0.135537i \(-0.956724\pi\)
0.177262 0.984164i \(-0.443276\pi\)
\(380\) 0 0
\(381\) 6.34169 + 33.3739i 0.324895 + 1.70980i
\(382\) 0.802829 0.802829i 0.0410763 0.0410763i
\(383\) 29.5784 4.68475i 1.51138 0.239380i 0.654964 0.755660i \(-0.272684\pi\)
0.856420 + 0.516280i \(0.172684\pi\)
\(384\) 1.51840 0.833337i 0.0774857 0.0425260i
\(385\) 0 0
\(386\) −5.59756 + 1.81876i −0.284908 + 0.0925723i
\(387\) 13.5831 8.00681i 0.690466 0.407009i
\(388\) −6.87074 + 3.50082i −0.348809 + 0.177727i
\(389\) 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
\(392\) 1.98165 + 12.5116i 0.100088 + 0.631932i
\(393\) 35.5338 1.09127i 1.79244 0.0550472i
\(394\) −11.2945 + 15.5455i −0.569007 + 0.783170i
\(395\) 0 0
\(396\) 8.70380 7.17947i 0.437382 0.360782i
\(397\) 2.09608 13.2341i 0.105199 0.664203i −0.877581 0.479427i \(-0.840844\pi\)
0.982781 0.184775i \(-0.0591557\pi\)
\(398\) 11.3268 + 5.77130i 0.567762 + 0.289289i
\(399\) 26.3130 27.9803i 1.31730 1.40077i
\(400\) 0 0
\(401\) 22.2904i 1.11313i −0.830804 0.556565i \(-0.812119\pi\)
0.830804 0.556565i \(-0.187881\pi\)
\(402\) 10.0960 3.62662i 0.503541 0.180879i
\(403\) −12.9272 2.04746i −0.643948 0.101991i
\(404\) 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
\(408\) 0.401520 0.589911i 0.0198782 0.0292050i
\(409\) 13.3939 + 4.35194i 0.662285 + 0.215190i 0.620823 0.783951i \(-0.286798\pi\)
0.0414620 + 0.999140i \(0.486798\pi\)
\(410\) 0 0
\(411\) 11.3247 + 5.33889i 0.558606 + 0.263348i
\(412\) 1.11333 + 2.18504i 0.0548499 + 0.107649i
\(413\) 11.3084 + 22.1939i 0.556448 + 1.09209i
\(414\) 5.53420 + 14.0364i 0.271991 + 0.689851i
\(415\) 0 0
\(416\) −3.73243 1.21274i −0.182998 0.0594595i
\(417\) 13.8790 + 9.44670i 0.679660 + 0.462607i
\(418\) 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 \(0.250259\pi\)
\(422\) −17.2214 2.72761i −0.838327 0.132778i
\(423\) −6.17863 + 14.2221i −0.300415 + 0.691504i
\(424\) 8.30714i 0.403431i
\(425\) 0 0
\(426\) 2.12956 + 2.00266i 0.103178 + 0.0970292i
\(427\) −56.7531 28.9171i −2.74647 1.39940i
\(428\) −0.952804 + 6.01577i −0.0460555 + 0.290783i
\(429\) −25.3608 3.22224i −1.22443 0.155571i
\(430\) 0 0
\(431\) 11.7415 16.1608i 0.565568 0.778437i −0.426453 0.904510i \(-0.640237\pi\)
0.992021 + 0.126072i \(0.0402371\pi\)
\(432\) −0.477906 5.17413i −0.0229932 0.248940i
\(433\) 3.62919 + 22.9138i 0.174408 + 1.10117i 0.907195 + 0.420710i \(0.138219\pi\)
−0.732787 + 0.680458i \(0.761781\pi\)
\(434\) −4.57041 + 14.0663i −0.219387 + 0.675203i
\(435\) 0 0
\(436\) −1.44993 4.46242i −0.0694390 0.213711i
\(437\) −22.4074 + 11.4171i −1.07189 + 0.546156i
\(438\) 1.73527 5.95694i 0.0829144 0.284633i
\(439\) 10.7777 3.50189i 0.514393 0.167136i −0.0403065 0.999187i \(-0.512833\pi\)
0.554699 + 0.832051i \(0.312833\pi\)
\(440\) 0 0
\(441\) 36.7952 + 9.50351i 1.75215 + 0.452548i
\(442\) −1.59696 + 0.252934i −0.0759598 + 0.0120309i
\(443\) 5.43418 5.43418i 0.258186 0.258186i −0.566130 0.824316i \(-0.691560\pi\)
0.824316 + 0.566130i \(0.191560\pi\)
\(444\) 8.98473 1.70727i 0.426396 0.0810236i
\(445\) 0 0
\(446\) 13.3051 + 18.3129i 0.630015 + 0.867141i
\(447\) −4.40067 5.68169i −0.208144 0.268735i
\(448\) −2.01336 + 3.95145i −0.0951225 + 0.186688i
\(449\) 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
\(452\) 7.76223 15.2342i 0.365104 0.716558i
\(453\) −10.0765 13.0098i −0.473436 0.611252i
\(454\) 11.3490 + 15.6205i 0.532634 + 0.733108i
\(455\) 0 0
\(456\) 8.50860 1.61680i 0.398452 0.0757136i
\(457\) −24.1951 + 24.1951i −1.13180 + 1.13180i −0.141919 + 0.989878i \(0.545327\pi\)
−0.989878 + 0.141919i \(0.954673\pi\)
\(458\) 16.0987 2.54978i 0.752241 0.119143i
\(459\) −1.14321 1.80997i −0.0533603 0.0844823i
\(460\) 0 0
\(461\) −35.3066 + 11.4718i −1.64439 + 0.534295i −0.977513 0.210873i \(-0.932369\pi\)
−0.666877 + 0.745168i \(0.732369\pi\)
\(462\) −8.07957 + 27.7360i −0.375896 + 1.29040i
\(463\) −6.25735 + 3.18828i −0.290804 + 0.148172i −0.593307 0.804977i \(-0.702178\pi\)
0.302503 + 0.953149i \(0.402178\pi\)
\(464\) −0.570270 1.75511i −0.0264741 0.0814790i
\(465\) 0 0
\(466\) 0.188063 0.578799i 0.00871187 0.0268124i
\(467\) −4.48899 28.3424i −0.207726 1.31153i −0.842444 0.538785i \(-0.818884\pi\)
0.634718 0.772744i \(-0.281116\pi\)
\(468\) −7.79860 + 8.82032i −0.360490 + 0.407719i
\(469\) −16.1449 + 22.2215i −0.745502 + 1.02609i
\(470\) 0 0
\(471\) −7.24770 0.920861i −0.333956 0.0424310i
\(472\) −0.878638 + 5.54750i −0.0404426 + 0.255344i
\(473\) −17.6121 8.97383i −0.809807 0.412617i
\(474\) −13.4131 12.6138i −0.616084 0.579371i
\(475\) 0 0
\(476\) 1.82711i 0.0837455i
\(477\) 22.8576 + 9.93018i 1.04658 + 0.454672i
\(478\) −7.92207 1.25473i −0.362347 0.0573901i
\(479\) −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
\(483\) −31.9362 21.7372i −1.45315 0.989077i
\(484\) −2.99064 0.971718i −0.135938 0.0441690i
\(485\) 0 0
\(486\) −14.8082 4.87006i −0.671713 0.220910i
\(487\) −9.39682 18.4423i −0.425810 0.835700i −0.999858 0.0168777i \(-0.994627\pi\)
0.574047 0.818822i \(-0.305373\pi\)
\(488\) −6.52048 12.7972i −0.295168 0.579301i
\(489\) 16.3277 + 7.69748i 0.738363 + 0.348092i
\(490\) 0 0
\(491\) −26.5707 8.63333i −1.19912 0.389617i −0.359681 0.933075i \(-0.617114\pi\)
−0.839436 + 0.543459i \(0.817114\pi\)
\(492\) −3.32629 + 4.88697i −0.149961 + 0.220322i
\(493\) −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
\(497\) −7.39279 1.17090i −0.331612 0.0525221i
\(498\) 11.5592 4.15225i 0.517982 0.186067i
\(499\) 0.405848i 0.0181683i 0.999959 + 0.00908413i \(0.00289161\pi\)
−0.999959 + 0.00908413i \(0.997108\pi\)
\(500\) 0 0
\(501\) 16.6110 17.6636i 0.742126 0.789153i
\(502\) 12.9659 + 6.60645i 0.578696 + 0.294860i
\(503\) 0.948431 5.98816i 0.0422885 0.266999i −0.957480 0.288498i \(-0.906844\pi\)
0.999769 + 0.0214995i \(0.00684402\pi\)
\(504\) 8.46590 + 10.2634i 0.377101 + 0.457167i
\(505\) 0 0
\(506\) 11.1179 15.3025i 0.494252 0.680280i
\(507\) 4.15807 0.127697i 0.184666 0.00567123i
\(508\) −3.06818 19.3717i −0.136129 0.859482i
\(509\) 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
\(512\) −0.891007 + 0.453990i −0.0393773 + 0.0200637i
\(513\) 5.72229 25.3446i 0.252645 1.11899i
\(514\) −1.39651 + 0.453755i −0.0615976 + 0.0200143i
\(515\) 0 0
\(516\) −7.98039 + 4.37983i −0.351317 + 0.192811i
\(517\) 19.2000 3.04098i 0.844414 0.133742i
\(518\) −16.5580 + 16.5580i −0.727515 + 0.727515i
\(519\) −2.26652 11.9279i −0.0994894 0.523575i
\(520\) 0 0
\(521\) −1.70955 2.35299i −0.0748966 0.103086i 0.769925 0.638134i \(-0.220294\pi\)
−0.844822 + 0.535048i \(0.820294\pi\)
\(522\) −5.51098 0.528892i −0.241209 0.0231490i
\(523\) −4.02250 + 7.89460i −0.175892 + 0.345207i −0.962074 0.272787i \(-0.912054\pi\)
0.786183 + 0.617994i \(0.212054\pi\)
\(524\) −20.5251 −0.896645
\(525\) 0 0
\(526\) −22.3198 −0.973188
\(527\) −0.623784 + 1.22424i −0.0271724 + 0.0533289i
\(528\) −5.15001 + 3.98886i −0.224125 + 0.173593i
\(529\) 1.34851 + 1.85606i 0.0586307 + 0.0806982i
\(530\) 0 0
\(531\) 14.2140 + 9.04899i 0.616833 + 0.392693i
\(532\) −15.6805 + 15.6805i −0.679837 + 0.679837i
\(533\) 13.2296 2.09537i 0.573040 0.0907606i
\(534\) −0.875950 1.59605i −0.0379060 0.0690678i
\(535\) 0 0
\(536\) −5.89043 + 1.91392i −0.254428 + 0.0826686i
\(537\) −4.70700 1.37116i −0.203122 0.0591699i
\(538\) 22.2735 11.3489i 0.960280 0.489287i
\(539\) −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 \(0.808779\pi\)
\(542\) 2.54083 + 16.0422i 0.109138 + 0.689071i
\(543\) −0.0186094 0.605959i −0.000798607 0.0260042i
\(544\) −0.242163 + 0.333309i −0.0103827 + 0.0142905i
\(545\) 0 0
\(546\) 3.79961 29.9050i 0.162608 1.27982i
\(547\) −4.14971 + 26.2003i −0.177429 + 1.12024i 0.724792 + 0.688968i \(0.241936\pi\)
−0.902221 + 0.431274i \(0.858064\pi\)
\(548\) −6.44062 3.28166i −0.275130 0.140186i
\(549\) −43.0066 + 2.64402i −1.83548 + 0.112844i
\(550\) 0 0
\(551\) 9.22780i 0.393118i
\(552\) −2.94491 8.19818i −0.125344 0.348938i
\(553\) 46.5636 + 7.37495i 1.98009 + 0.313615i
\(554\) 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 \(-0.0340648\pi\)
−0.106814 + 0.994279i \(0.534065\pi\)
\(558\) 2.16857 + 9.76720i 0.0918029 + 0.413479i
\(559\) 19.6168 + 6.37389i 0.829703 + 0.269587i
\(560\) 0 0
\(561\) −1.14443 + 2.42753i −0.0483178 + 0.102490i
\(562\) −11.1182 21.8207i −0.468993 0.920450i
\(563\) 6.85128 + 13.4464i 0.288747 + 0.566698i 0.989126 0.147073i \(-0.0469854\pi\)
−0.700378 + 0.713772i \(0.746985\pi\)
\(564\) 3.81760 8.09779i 0.160750 0.340978i
\(565\) 0 0
\(566\) 6.96420 + 2.26281i 0.292727 + 0.0951128i
\(567\) 38.3602 11.0258i 1.61098 0.463041i
\(568\) −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 \(0.130487\pi\)
\(572\) 14.5781 + 2.30894i 0.609540 + 0.0965416i
\(573\) 0.664813 + 1.85074i 0.0277730 + 0.0773157i
\(574\) 15.1362i 0.631775i
\(575\) 0 0
\(576\) 0.184091 + 2.99435i 0.00767044 + 0.124764i
\(577\) −32.6160 16.6187i −1.35782 0.691845i −0.384896 0.922960i \(-0.625763\pi\)
−0.972927 + 0.231114i \(0.925763\pi\)
\(578\) 2.63283 16.6231i 0.109511 0.691428i
\(579\) 1.28490 10.1129i 0.0533987 0.420277i
\(580\) 0 0
\(581\) −18.4849 + 25.4423i −0.766882 + 1.05552i
\(582\) −0.409985 13.3499i −0.0169944 0.553372i
\(583\) −4.88741 30.8579i −0.202416 1.27800i
\(584\) −1.10696 + 3.40687i −0.0458062 + 0.140977i
\(585\) 0 0
\(586\) 0.500941 + 1.54174i 0.0206937 + 0.0636887i
\(587\) −10.1304 + 5.16169i −0.418126 + 0.213046i −0.650379 0.759609i \(-0.725390\pi\)
0.232254 + 0.972655i \(0.425390\pi\)
\(588\) −21.0653 6.13637i −0.868719 0.253060i
\(589\) −15.8600 + 5.15324i −0.653501 + 0.212335i
\(590\) 0 0
\(591\) −16.0128 29.1766i −0.658678 1.20016i
\(592\) −5.21515 + 0.825998i −0.214341 + 0.0339483i
\(593\) −16.4362 + 16.4362i −0.674952 + 0.674952i −0.958854 0.283901i \(-0.908371\pi\)
0.283901 + 0.958854i \(0.408371\pi\)
\(594\) 4.81937 + 18.9388i 0.197741 + 0.777066i
\(595\) 0 0
\(596\) 2.43884 + 3.35677i 0.0998986 + 0.137499i
\(597\) −17.4077 + 13.4829i −0.712449 + 0.551817i
\(598\) −8.96072 + 17.5864i −0.366431 + 0.719162i
\(599\) 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 \(0.678082\pi\)
\(602\) 10.5818 20.7679i 0.431281 0.846437i
\(603\) −1.77504 + 18.4957i −0.0722854 + 0.753204i
\(604\) 5.58437 + 7.68623i 0.227225 + 0.312748i
\(605\) 0 0
\(606\) 3.58411 + 18.8618i 0.145595 + 0.766210i
\(607\) 29.4219 29.4219i 1.19420 1.19420i 0.218322 0.975877i \(-0.429942\pi\)
0.975877 0.218322i \(-0.0700583\pi\)
\(608\) −4.93878 + 0.782226i −0.200294 + 0.0317235i
\(609\) 12.4269 6.82016i 0.503562 0.276367i
\(610\) 0 0
\(611\) −19.2921 + 6.26837i −0.780473 + 0.253591i
\(612\) 0.627642 + 1.06476i 0.0253709 + 0.0430402i
\(613\) −5.01575 + 2.55565i −0.202584 + 0.103222i −0.552339 0.833619i \(-0.686265\pi\)
0.349755 + 0.936841i \(0.386265\pi\)
\(614\) −3.62398 11.1535i −0.146252 0.450118i
\(615\) 0 0
\(616\) 5.15409 15.8627i 0.207664 0.639125i
\(617\) −5.57460 35.1967i −0.224425 1.41696i −0.800385 0.599486i \(-0.795372\pi\)
0.575960 0.817478i \(-0.304628\pi\)
\(618\) −4.24555 + 0.130384i −0.170781 + 0.00524480i
\(619\) −20.2991 + 27.9393i −0.815889 + 1.12297i 0.174499 + 0.984657i \(0.444169\pi\)
−0.990388 + 0.138317i \(0.955831\pi\)
\(620\) 0 0
\(621\) −26.0780 1.69685i −1.04648 0.0680922i
\(622\) 5.17530 32.6756i 0.207511 1.31017i
\(623\) 4.15351 + 2.11632i 0.166407 + 0.0847885i
\(624\) 4.65672 4.95180i 0.186418 0.198231i
\(625\) 0 0
\(626\) 4.37993i 0.175057i
\(627\) −30.6550 + 11.0117i −1.22424 + 0.439766i
\(628\) 4.16617 + 0.659856i 0.166248 + 0.0263311i
\(629\) −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
\(633\) 16.9929 24.9659i 0.675407 0.992305i
\(634\) 26.6314 + 8.65307i 1.05767 + 0.343657i
\(635\) 0 0
\(636\) −13.0146 6.13559i −0.516063 0.243292i
\(637\) 22.5697 + 44.2955i 0.894244 + 1.75505i
\(638\) 3.15094 + 6.18406i 0.124747 + 0.244829i
\(639\) −4.71040 + 1.85719i −0.186341 + 0.0734695i
\(640\) 0 0
\(641\) −12.9664 4.21305i −0.512144 0.166406i 0.0415332 0.999137i \(-0.486776\pi\)
−0.553677 + 0.832732i \(0.686776\pi\)
\(642\) −8.72104 5.93593i −0.344192 0.234273i
\(643\) 11.4059 + 11.4059i 0.449806 + 0.449806i 0.895290 0.445484i \(-0.146968\pi\)
−0.445484 + 0.895290i \(0.646968\pi\)
\(644\) 18.0445 + 13.1101i 0.711051 + 0.516609i
\(645\) 0 0
\(646\) −1.66666 + 1.21090i −0.0655739 + 0.0476422i
\(647\) −30.9551 4.90280i −1.21697 0.192749i −0.485263 0.874368i \(-0.661276\pi\)
−0.731707 + 0.681619i \(0.761276\pi\)
\(648\) 8.45917 + 3.07284i 0.332308 + 0.120713i
\(649\) 21.1238i 0.829181i
\(650\) 0 0
\(651\) −18.6617 17.5496i −0.731409 0.687823i
\(652\) −9.28593 4.73142i −0.363665 0.185297i
\(653\) 5.98789 37.8061i 0.234324 1.47947i −0.537302 0.843390i \(-0.680556\pi\)
0.771626 0.636076i \(-0.219444\pi\)
\(654\) 8.06209 + 1.02433i 0.315253 + 0.0400546i
\(655\) 0 0
\(656\) 2.00614 2.76122i 0.0783266 0.107807i
\(657\) 8.05095 + 7.11835i 0.314098 + 0.277713i
\(658\) 3.58587 + 22.6403i 0.139792 + 0.882610i
\(659\) 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 \(-0.422967\pi\)
\(662\) 8.53939 4.35103i 0.331893 0.169108i
\(663\) 0.783237 2.68874i 0.0304184 0.104422i
\(664\) −6.74418 + 2.19132i −0.261725 + 0.0850395i
\(665\) 0 0
\(666\) −3.96130 + 15.3372i −0.153497 + 0.594303i
\(667\) −9.16704 + 1.45192i −0.354949 + 0.0562184i
\(668\) −9.89891 + 9.89891i −0.383000 + 0.383000i
\(669\) −38.5175 + 7.31907i −1.48917 + 0.282971i
\(670\) 0 0
\(671\) 31.7502 + 43.7004i 1.22570 + 1.68703i
\(672\) −4.70360 6.07280i −0.181445 0.234263i
\(673\) 16.8283 33.0273i 0.648681 1.27311i −0.299110 0.954219i \(-0.596690\pi\)
0.947792 0.318890i \(-0.103310\pi\)
\(674\) 15.6652 0.603401
\(675\) 0 0
\(676\) −2.40180 −0.0923767
\(677\) 18.9516 37.1946i 0.728369 1.42951i −0.167813 0.985819i \(-0.553670\pi\)
0.896182 0.443686i \(-0.146330\pi\)
\(678\) 18.1340 + 23.4128i 0.696433 + 0.899163i
\(679\) 20.1010 + 27.6666i 0.771404 + 1.06175i
\(680\) 0 0
\(681\) −32.8546 + 6.24301i −1.25899 + 0.239233i
\(682\) 8.86905 8.86905i 0.339614 0.339614i
\(683\) −50.2616 + 7.96066i −1.92321 + 0.304606i −0.997318 0.0731865i \(-0.976683\pi\)
−0.925890 + 0.377793i \(0.876683\pi\)
\(684\) −3.75138 + 14.5244i −0.143437 + 0.555354i
\(685\) 0 0
\(686\) 23.9045 7.76703i 0.912677 0.296547i
\(687\) −7.89565 + 27.1047i −0.301238 + 1.03411i
\(688\) 4.68293 2.38607i 0.178535 0.0909681i
\(689\) 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 \(0.891128\pi\)
\(692\) 1.09657 + 6.92347i 0.0416854 + 0.263191i
\(693\) −37.4860 33.1437i −1.42397 1.25902i
\(694\) 21.7024 29.8708i 0.823813 1.13388i
\(695\) 0 0
\(696\) 3.17089 + 0.402880i 0.120192 + 0.0152711i
\(697\) 0.219971 1.38884i 0.00833198 0.0526061i
\(698\) 13.3780 + 6.81642i 0.506364 + 0.258005i
\(699\) 0.767891 + 0.722131i 0.0290443 + 0.0273135i
\(700\) 0 0
\(701\) 32.1785i 1.21536i 0.794180 + 0.607682i \(0.207900\pi\)
−0.794180 + 0.607682i \(0.792100\pi\)
\(702\) −8.05863 18.7325i −0.304153 0.707013i
\(703\) −26.0775 4.13027i −0.983533 0.155776i
\(704\) 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
\(708\) −8.04220 5.47388i −0.302244 0.205721i
\(709\) −2.62130 0.851713i −0.0984451 0.0319867i 0.259380 0.965775i \(-0.416482\pi\)
−0.357825 + 0.933789i \(0.616482\pi\)
\(710\) 0 0
\(711\) 29.6686 11.6976i 1.11266 0.438693i
\(712\) 0.477205 + 0.936569i 0.0178840 + 0.0350994i
\(713\) 7.61474 + 14.9448i 0.285174 + 0.559686i
\(714\) −2.86250 1.34949i −0.107126 0.0505033i
\(715\) 0 0
\(716\) 2.69201 + 0.874686i 0.100605 + 0.0326886i
\(717\) 7.81693 11.4846i 0.291929 0.428900i
\(718\) −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
\(722\) −5.92953 0.939145i −0.220674 0.0349514i
\(723\) −11.8140 + 4.24378i −0.439369 + 0.157828i
\(724\) 0.350016i 0.0130082i
\(725\) 0 0
\(726\) 3.73123 3.96767i 0.138479 0.147254i
\(727\) 30.4942 + 15.5376i 1.13097 + 0.576257i 0.916325 0.400435i \(-0.131141\pi\)
0.214644 + 0.976692i \(0.431141\pi\)
\(728\) −2.72266 + 17.1902i −0.100909 + 0.637111i
\(729\) 18.5670 19.6027i 0.687668 0.726026i
\(730\) 0 0
\(731\) 1.27276 1.75180i 0.0470746 0.0647926i
\(732\) 24.8650 0.763622i 0.919038 0.0282243i
\(733\) 6.22770 + 39.3201i 0.230025 + 1.45232i 0.784504 + 0.620124i \(0.212918\pi\)
−0.554478 + 0.832198i \(0.687082\pi\)
\(734\) −4.83943 + 14.8942i −0.178627 + 0.549756i
\(735\) 0 0
\(736\) 1.55415 + 4.78318i 0.0572867 + 0.176310i
\(737\) 20.7547 10.5750i 0.764509 0.389537i
\(738\) −5.19955 8.82071i −0.191398 0.324695i
\(739\) 19.6010 6.36874i 0.721033 0.234278i 0.0745620 0.997216i \(-0.476244\pi\)
0.646471 + 0.762939i \(0.276244\pi\)
\(740\) 0 0
\(741\) 29.7970 16.3533i 1.09462 0.600754i
\(742\) 36.3871 5.76314i 1.33581 0.211572i
\(743\) 25.7253 25.7253i 0.943771 0.943771i −0.0547306 0.998501i \(-0.517430\pi\)
0.998501 + 0.0547306i \(0.0174300\pi\)
\(744\) −1.07834 5.67487i −0.0395337 0.208051i
\(745\) 0 0
\(746\) 3.74935 + 5.16053i 0.137273 + 0.188940i
\(747\) −2.03232 + 21.1764i −0.0743585 + 0.774806i
\(748\) 0.703446 1.38059i 0.0257205 0.0504794i
\(749\) 27.0114 0.986973
\(750\) 0 0
\(751\) −13.8571 −0.505654 −0.252827 0.967511i \(-0.581360\pi\)
−0.252827 + 0.967511i \(0.581360\pi\)
\(752\) −2.34657 + 4.60540i −0.0855705 + 0.167942i
\(753\) −19.9267 + 15.4339i −0.726169 + 0.562443i
\(754\) −4.25699 5.85925i −0.155031 0.213381i
\(755\) 0 0
\(756\) −22.3322 + 5.68292i −0.812216 + 0.206686i
\(757\) 28.7075 28.7075i 1.04339 1.04339i 0.0443764 0.999015i \(-0.485870\pi\)
0.999015 0.0443764i \(-0.0141301\pi\)
\(758\) −26.6124 + 4.21499i −0.966606 + 0.153095i
\(759\) 15.7625 + 28.7205i 0.572143 + 1.04249i
\(760\) 0 0
\(761\) 36.3818 11.8212i 1.31884 0.428517i 0.436744 0.899586i \(-0.356132\pi\)
0.882096 + 0.471069i \(0.156132\pi\)
\(762\) 32.6154 + 9.50095i 1.18153 + 0.344183i
\(763\) −18.5405 + 9.44684i −0.671210 + 0.341998i
\(764\) −0.350849 1.07980i −0.0126933 0.0390659i
\(765\) 0 0
\(766\) 9.25415 28.4814i 0.334366 1.02907i
\(767\) 3.44822 + 21.7712i 0.124508 + 0.786114i
\(768\) −0.0531674 1.73123i −0.00191851 0.0624705i
\(769\) 23.2438 31.9924i 0.838194 1.15368i −0.148148 0.988965i \(-0.547331\pi\)
0.986342 0.164710i \(-0.0526688\pi\)
\(770\) 0 0
\(771\) 0.320565 2.52303i 0.0115449 0.0908646i
\(772\) −0.920714 + 5.81316i −0.0331372 + 0.209220i
\(773\) −32.0052 16.3075i −1.15115 0.586539i −0.229019 0.973422i \(-0.573552\pi\)
−0.922129 + 0.386883i \(0.873552\pi\)
\(774\) −0.967539 15.7376i −0.0347775 0.565677i
\(775\) 0 0
\(776\) 7.71121i 0.276816i
\(777\) −13.7114 38.1706i −0.491895 1.36936i
\(778\) 11.4191 + 1.80860i 0.409394 + 0.0648416i
\(779\) 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 + 0.0523940i
\(783\)