Properties

Label 750.2.l.c.107.2
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 107.2
Character \(\chi\) \(=\) 750.107
Dual form 750.2.l.c.743.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.891007 - 0.453990i) q^{2} +(-1.36935 + 1.06061i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.750223 - 2.90468i) q^{9} +O(q^{10})\) \(q+(-0.891007 - 0.453990i) q^{2} +(-1.36935 + 1.06061i) q^{3} +(0.587785 + 0.809017i) q^{4} +(1.70160 - 0.323338i) q^{6} +(3.13589 + 3.13589i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(0.750223 - 2.90468i) q^{9} +(3.57685 - 1.16219i) q^{11} +(-1.66293 - 0.484416i) 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} +(-1.98715 + 2.24749i) q^{18} +(2.93913 - 4.04536i) q^{19} +(-7.62006 - 0.968173i) q^{21} +(-3.71462 - 0.588338i) q^{22} +(-2.28327 + 4.48117i) q^{23} +(1.26176 + 1.18657i) q^{24} +3.92451i q^{26} +(2.05341 + 4.77321i) 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} +(-3.66532 + 5.38508i) q^{33} +(-0.391828 - 0.127313i) q^{34} +(2.79091 - 1.10038i) q^{36} +(4.70465 - 2.39714i) q^{37} +(-4.45534 + 2.27011i) q^{38} +(6.14845 + 2.89861i) q^{39} +(-3.24600 - 1.05469i) q^{41} +(6.34998 + 4.32208i) 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} +(-0.585546 - 1.63007i) q^{48} +12.6676i q^{49} +(-0.488859 + 0.519837i) q^{51} +(1.78169 - 3.49677i) q^{52} +(8.20487 + 1.29952i) q^{53} +(0.337390 - 5.18519i) q^{54} +(2.60672 - 3.58784i) q^{56} +(0.265855 + 8.65677i) 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} +(11.4614 - 6.75613i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(5.71060 - 3.13412i) q^{66} +(-0.968887 - 6.11731i) q^{67} +(0.291323 + 0.291323i) q^{68} +(-1.62617 - 8.55793i) q^{69} +(0.992045 + 1.36543i) q^{71} +(-2.98628 - 0.286595i) q^{72} +(3.19175 + 1.62628i) q^{73} -5.28015 q^{74} +5.00034 q^{76} +(14.8611 + 7.57211i) q^{77} +(-4.16237 - 5.37402i) q^{78} +(6.24842 + 8.60021i) q^{79} +(-7.87433 - 4.35832i) q^{81} +(2.41339 + 2.41339i) q^{82} +(1.10932 + 7.00394i) q^{83} +(-3.69569 - 6.73384i) q^{84} +(-4.99854 + 1.62412i) q^{86} +(-0.893957 + 3.06883i) 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} +(-5.77369 + 0.177314i) q^{93} +(-3.03812 + 4.18162i) q^{94} +(-0.218312 + 1.71824i) 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
\(3\) −1.36935 + 1.06061i −0.790593 + 0.612342i
\(4\) 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 0.978364 + 0.206890i \(0.0663341\pi\)
0.206890 + 0.978364i \(0.433666\pi\)
\(8\) −0.156434 0.987688i −0.0553079 0.349201i
\(9\) 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 \(0.208111\pi\)
\(12\) −1.66293 0.484416i −0.480047 0.139839i
\(13\) −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 −0.106893 0.994271i \(-0.534090\pi\)
0.205585 + 0.978639i \(0.434090\pi\)
\(18\) −1.98715 + 2.24749i −0.468376 + 0.529739i
\(19\) 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
\(21\) −7.62006 0.968173i −1.66283 0.211273i
\(22\) −3.71462 0.588338i −0.791960 0.125434i
\(23\) −2.28327 + 4.48117i −0.476095 + 0.934389i 0.520650 + 0.853770i \(0.325690\pi\)
−0.996745 + 0.0806186i \(0.974310\pi\)
\(24\) 1.26176 + 1.18657i 0.257556 + 0.242208i
\(25\) 0 0
\(26\) 3.92451i 0.769660i
\(27\) 2.05341 + 4.77321i 0.395179 + 0.918604i
\(28\) −0.693758 + 4.38021i −0.131108 + 0.827783i
\(29\) 1.49299 1.08472i 0.277241 0.201427i −0.440472 0.897766i \(-0.645189\pi\)
0.717713 + 0.696339i \(0.245189\pi\)
\(30\) 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
\(33\) −3.66532 + 5.38508i −0.638051 + 0.937421i
\(34\) −0.391828 0.127313i −0.0671980 0.0218340i
\(35\) 0 0
\(36\) 2.79091 1.10038i 0.465151 0.183397i
\(37\) 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
\(39\) 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 \(0.685872\pi\)
\(42\) 6.34998 + 4.32208i 0.979824 + 0.666912i
\(43\) 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 \(-0.826966\pi\)
0.973793 0.227436i \(-0.0730342\pi\)
\(48\) −0.585546 1.63007i −0.0845163 0.235281i
\(49\) 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 0.691988 0.721909i \(-0.256735\pi\)
0.435037 + 0.900412i \(0.356735\pi\)
\(54\) 0.337390 5.18519i 0.0459130 0.705615i
\(55\) 0 0
\(56\) 2.60672 3.58784i 0.348337 0.479445i
\(57\) 0.265855 + 8.65677i 0.0352134 + 1.14662i
\(58\) −1.82271 + 0.288689i −0.239334 + 0.0379068i
\(59\) −1.73564 + 5.34175i −0.225961 + 0.695437i 0.772231 + 0.635341i \(0.219141\pi\)
−0.998193 + 0.0600956i \(0.980859\pi\)
\(60\) 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
\(63\) 11.4614 6.75613i 1.44400 0.851193i
\(64\) −0.951057 + 0.309017i −0.118882 + 0.0386271i
\(65\) 0 0
\(66\) 5.71060 3.13412i 0.702926 0.385783i
\(67\) −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
\(69\) −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 \(0.768068\pi\)
\(72\) −2.98628 0.286595i −0.351936 0.0337755i
\(73\) 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
\(78\) −4.16237 5.37402i −0.471295 0.608488i
\(79\) 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
\(81\) −7.87433 4.35832i −0.874926 0.484258i
\(82\) 2.41339 + 2.41339i 0.266514 + 0.266514i
\(83\) 1.10932 + 7.00394i 0.121763 + 0.768782i 0.970701 + 0.240290i \(0.0772425\pi\)
−0.848938 + 0.528493i \(0.822757\pi\)
\(84\) −3.69569 6.73384i −0.403233 0.734722i
\(85\) 0 0
\(86\) −4.99854 + 1.62412i −0.539006 + 0.175134i
\(87\) −0.893957 + 3.06883i −0.0958423 + 0.329013i
\(88\) −1.70742 3.35101i −0.182012 0.357219i
\(89\) 0.324819 + 0.999689i 0.0344307 + 0.105967i 0.966795 0.255554i \(-0.0822577\pi\)
−0.932364 + 0.361521i \(0.882258\pi\)
\(90\) 0 0
\(91\) 5.37828 16.5526i 0.563797 1.73519i
\(92\) −4.96742 + 0.786761i −0.517889 + 0.0820255i
\(93\) −5.77369 + 0.177314i −0.598704 + 0.0183866i
\(94\) −3.03812 + 4.18162i −0.313358 + 0.431301i
\(95\) 0 0
\(96\) −0.218312 + 1.71824i −0.0222814 + 0.175367i
\(97\) −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 \(0.185939\pi\)
−0.834184 + 0.551487i \(0.814061\pi\)
\(102\) 0.671578 0.241241i 0.0664961 0.0238864i
\(103\) 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 −0.883945 0.467590i \(-0.845122\pi\)
0.467590 + 0.883945i \(0.345122\pi\)
\(108\) −2.65464 + 4.46686i −0.255443 + 0.429824i
\(109\) −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
\(111\) −3.89988 + 8.27231i −0.370160 + 0.785173i
\(112\) −3.95145 + 2.01336i −0.373377 + 0.190245i
\(113\) −15.2342 + 7.76223i −1.43312 + 0.730209i −0.986384 0.164459i \(-0.947412\pi\)
−0.446732 + 0.894668i \(0.647412\pi\)
\(114\) 3.69321 7.83393i 0.345901 0.733715i
\(115\) 0 0
\(116\) 1.75511 + 0.570270i 0.162958 + 0.0529483i
\(117\) −11.4937 + 2.55189i −1.06259 + 0.235922i
\(118\) 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
\(123\) 5.56352 1.99850i 0.501646 0.180199i
\(124\) 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
\(129\) −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 \(-0.154002\pi\)
\(132\) −6.51104 + 0.199959i −0.566713 + 0.0174042i
\(133\) 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 0.707279 0.706935i \(-0.249922\pi\)
−0.987650 + 0.156675i \(0.949922\pi\)
\(138\) −2.43629 + 8.36344i −0.207391 + 0.711943i
\(139\) −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
\(141\) 4.30732 + 7.84827i 0.362742 + 0.660943i
\(142\) −0.264025 1.66699i −0.0221565 0.139891i
\(143\) −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
\(147\) −13.4353 17.3463i −1.10813 1.43070i
\(148\) 4.70465 + 2.39714i 0.386720 + 0.197044i
\(149\) 4.14920 0.339915 0.169958 0.985451i \(-0.445637\pi\)
0.169958 + 0.985451i \(0.445637\pi\)
\(150\) 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
\(153\) 0.118075 1.23033i 0.00954580 0.0994659i
\(154\) −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 \(-0.196166\pi\)
−0.577997 + 0.816039i \(0.696166\pi\)
\(158\) −1.66297 10.4996i −0.132299 0.835300i
\(159\) −12.6136 + 6.92265i −1.00032 + 0.549002i
\(160\) 0 0
\(161\) −21.2125 + 6.89237i −1.67178 + 0.543195i
\(162\) 5.03744 + 7.45816i 0.395779 + 0.585968i
\(163\) 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 −0.666476 0.745527i \(-0.732198\pi\)
−0.403476 + 0.914990i \(0.632198\pi\)
\(168\) 0.235788 + 7.67770i 0.0181914 + 0.592348i
\(169\) −1.41174 + 1.94309i −0.108595 + 0.149469i
\(170\) 0 0
\(171\) −9.54548 11.5722i −0.729961 0.884945i
\(172\) 5.19107 + 0.822184i 0.395815 + 0.0626910i
\(173\) 3.18237 6.24576i 0.241951 0.474856i −0.737815 0.675003i \(-0.764142\pi\)
0.979766 + 0.200147i \(0.0641421\pi\)
\(174\) 2.18974 2.32850i 0.166004 0.176523i
\(175\) 0 0
\(176\) 3.76092i 0.283490i
\(177\) −3.28881 9.15555i −0.247202 0.688173i
\(178\) 0.164434 1.03819i 0.0123248 0.0778159i
\(179\) 2.28996 1.66375i 0.171159 0.124355i −0.498908 0.866655i \(-0.666265\pi\)
0.670067 + 0.742301i \(0.266265\pi\)
\(180\) 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
\(183\) −20.5651 13.9975i −1.52021 1.03473i
\(184\) 4.78318 + 1.55415i 0.352621 + 0.114573i
\(185\) 0 0
\(186\) 5.22490 + 2.46321i 0.383108 + 0.180612i
\(187\) 1.38059 0.703446i 0.100959 0.0514411i
\(188\) 4.60540 2.34657i 0.335883 0.171141i
\(189\) −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 \(0.586921\pi\)
\(192\) 0.974581 1.43185i 0.0703343 0.103335i
\(193\) 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 \(0.289986\pi\)
−0.827105 + 0.562048i \(0.810014\pi\)
\(198\) −4.49573 + 10.3484i −0.319498 + 0.735429i
\(199\) 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
\(204\) −0.707901 0.0899429i −0.0495630 0.00629726i
\(205\) 0 0
\(206\) −1.44144 + 1.98397i −0.100430 + 0.138230i
\(207\) 11.3034 + 9.99405i 0.785641 + 0.694634i
\(208\) 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
\(213\) −2.80664 0.817581i −0.192308 0.0560198i
\(214\) 5.79265 1.88215i 0.395977 0.128661i
\(215\) 0 0
\(216\) 4.39322 2.77482i 0.298921 0.188803i
\(217\) 2.31369 + 14.6081i 0.157064 + 0.991661i
\(218\) 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
\(222\) 7.23036 5.60017i 0.485270 0.375859i
\(223\) −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 0.919468 0.393164i \(-0.128620\pi\)
0.222373 + 0.974962i \(0.428620\pi\)
\(228\) −6.84721 + 5.30340i −0.453467 + 0.351226i
\(229\) −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
\(231\) −28.3810 + 5.39295i −1.86733 + 0.354830i
\(232\) −1.30492 1.30492i −0.0856721 0.0856721i
\(233\) 0.0952038 + 0.601093i 0.00623701 + 0.0393789i 0.990611 0.136714i \(-0.0436541\pi\)
−0.984374 + 0.176093i \(0.943654\pi\)
\(234\) 11.3995 + 2.94426i 0.745205 + 0.192472i
\(235\) 0 0
\(236\) −5.34175 + 1.73564i −0.347718 + 0.112981i
\(237\) −17.6777 5.14955i −1.14829 0.334499i
\(238\) −0.829491 1.62797i −0.0537679 0.105525i
\(239\) 2.47857 + 7.62825i 0.160325 + 0.493430i 0.998661 0.0517231i \(-0.0164713\pi\)
−0.838336 + 0.545154i \(0.816471\pi\)
\(240\) 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
\(243\) 15.4052 2.38352i 0.988241 0.152903i
\(244\) −8.44212 + 11.6196i −0.540452 + 0.743868i
\(245\) 0 0
\(246\) −5.86443 0.745110i −0.373903 0.0475065i
\(247\) −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 \(0.151884\pi\)
−0.888304 + 0.459256i \(0.848116\pi\)
\(252\) 12.2026 + 5.30128i 0.768694 + 0.333949i
\(253\) −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 −0.738749 0.673981i \(-0.764583\pi\)
0.673981 + 0.738749i \(0.264583\pi\)
\(258\) 5.12218 7.52548i 0.318893 0.468516i
\(259\) 22.2704 + 7.23610i 1.38382 + 0.449629i
\(260\) 0 0
\(261\) −2.03069 5.15043i −0.125696 0.318804i
\(262\) −18.2880 + 9.31821i −1.12984 + 0.575681i
\(263\) 19.8871 10.1330i 1.22629 0.624825i 0.283743 0.958901i \(-0.408424\pi\)
0.942546 + 0.334075i \(0.108424\pi\)
\(264\) 5.89216 + 2.77779i 0.362637 + 0.170961i
\(265\) 0 0
\(266\) −21.0902 6.85264i −1.29313 0.420162i
\(267\) −1.50507 1.02442i −0.0921086 0.0626933i
\(268\) 4.37951 4.37951i 0.267521 0.267521i
\(269\) −20.2239 14.6936i −1.23308 0.895882i −0.235959 0.971763i \(-0.575823\pi\)
−0.997117 + 0.0758813i \(0.975823\pi\)
\(270\) 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
\(273\) 10.1911 + 28.3706i 0.616795 + 1.71706i
\(274\) 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
\(279\) 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 \(-0.0607004\pi\)
\(282\) −0.274810 8.94834i −0.0163647 0.532866i
\(283\) −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
\(288\) −1.52343 2.58441i −0.0897690 0.152288i
\(289\) −16.0065 + 5.20084i −0.941561 + 0.305932i
\(290\) 0 0
\(291\) 11.7087 6.42603i 0.686378 0.376701i
\(292\) 0.560378 + 3.53809i 0.0327936 + 0.207051i
\(293\) −1.14628 1.14628i −0.0669662 0.0669662i 0.672830 0.739797i \(-0.265078\pi\)
−0.739797 + 0.672830i \(0.765078\pi\)
\(294\) 4.09590 + 21.5552i 0.238878 + 1.25712i
\(295\) 0 0
\(296\) −3.10360 4.27173i −0.180393 0.248290i
\(297\) 12.8921 + 14.6866i 0.748076 + 0.852203i
\(298\) −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
\(303\) −11.7566 15.1789i −0.675397 0.872003i
\(304\) 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 \(-0.358622\pi\)
−0.902975 + 0.429693i \(0.858622\pi\)
\(308\) 2.60917 + 16.4737i 0.148671 + 0.938673i
\(309\) 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 \(0.0126952\pi\)
\(312\) 1.90110 6.52620i 0.107628 0.369473i
\(313\) −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 0.680053 0.733163i \(-0.261957\pi\)
0.873329 + 0.487131i \(0.161957\pi\)
\(318\) 14.3816 0.441669i 0.806481 0.0247676i
\(319\) 4.07954 5.61501i 0.228411 0.314380i
\(320\) 0 0
\(321\) 1.32968 10.4654i 0.0742157 0.584119i
\(322\) 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
\(327\) 7.64841 2.74742i 0.422958 0.151933i
\(328\) −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
\(333\) −3.43338 15.4639i −0.188148 0.847416i
\(334\) 13.3140 + 4.32598i 0.728510 + 0.236707i
\(335\) 0 0
\(336\) 3.27552 6.94793i 0.178694 0.379041i
\(337\) 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
\(339\) 12.6283 26.7867i 0.685874 1.45485i
\(340\) 0 0
\(341\) 11.9289 + 3.87592i 0.645983 + 0.209893i
\(342\) 3.25144 + 14.6444i 0.175818 + 0.791880i
\(343\) −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 \(-0.492622\pi\)
0.286891 0.957963i \(-0.407378\pi\)
\(348\) −3.00819 + 1.08059i −0.161256 + 0.0579255i
\(349\) 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 −0.697698 0.716392i \(-0.745792\pi\)
−0.884927 + 0.465729i \(0.845792\pi\)
\(354\) −1.22618 + 9.65074i −0.0651708 + 0.512931i
\(355\) 0 0
\(356\) −0.617842 + 0.850386i −0.0327456 + 0.0450704i
\(357\) −3.16316 + 0.0971428i −0.167412 + 0.00514134i
\(358\) −2.79569 + 0.442795i −0.147757 + 0.0234024i
\(359\) −1.07807 + 3.31797i −0.0568986 + 0.175116i −0.975467 0.220147i \(-0.929346\pi\)
0.918568 + 0.395263i \(0.129346\pi\)
\(360\) 0 0
\(361\) −1.85517 5.70961i −0.0976403 0.300506i
\(362\) 0.158904 + 0.311866i 0.00835180 + 0.0163913i
\(363\) −1.52327 + 5.22917i −0.0799508 + 0.274460i
\(364\) 16.5526 5.37828i 0.867594 0.281898i
\(365\) 0 0
\(366\) 11.9689 + 21.8082i 0.625623 + 1.13993i
\(367\) 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
\(369\) −5.49877 + 8.63735i −0.286254 + 0.449642i
\(370\) 0 0
\(371\) 21.6544 + 29.8047i 1.12424 + 1.54738i
\(372\) −3.53714 4.56679i −0.183392 0.236777i
\(373\) −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
\(378\) 17.3182 15.2021i 0.890751 0.781914i
\(379\) 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
\(381\) 6.34169 + 33.3739i 0.324895 + 1.70980i
\(382\) −0.802829 0.802829i −0.0410763 0.0410763i
\(383\) 4.68475 + 29.5784i 0.239380 + 1.51138i 0.755660 + 0.654964i \(0.227316\pi\)
−0.516280 + 0.856420i \(0.672684\pi\)
\(384\) −1.51840 + 0.833337i −0.0774857 + 0.0425260i
\(385\) 0 0
\(386\) −5.59756 + 1.81876i −0.284908 + 0.0925723i
\(387\) −8.00681 13.5831i −0.407009 0.690466i
\(388\) −3.50082 6.87074i −0.177727 0.348809i
\(389\) −3.57268 10.9956i −0.181142 0.557497i 0.818719 0.574195i \(-0.194685\pi\)
−0.999861 + 0.0166975i \(0.994685\pi\)
\(390\) 0 0
\(391\) −0.640299 + 1.97064i −0.0323813 + 0.0996594i
\(392\) 12.5116 1.98165i 0.631932 0.100088i
\(393\) 1.09127 + 35.5338i 0.0550472 + 1.79244i
\(394\) 11.2945 15.5455i 0.569007 0.783170i
\(395\) 0 0
\(396\) 8.70380 7.17947i 0.437382 0.360782i
\(397\) −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 \(-0.812119\pi\)
0.830804 0.556565i \(-0.187881\pi\)
\(402\) −3.62662 10.0960i −0.180879 0.503541i
\(403\) 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
\(408\) 0.589911 + 0.401520i 0.0292050 + 0.0198782i
\(409\) −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
\(411\) 11.3247 + 5.33889i 0.558606 + 0.263348i
\(412\) 2.18504 1.11333i 0.107649 0.0548499i
\(413\) −22.1939 + 11.3084i −1.09209 + 0.556448i
\(414\) −5.53420 14.0364i −0.271991 0.689851i
\(415\) 0 0
\(416\) −3.73243 1.21274i −0.182998 0.0594595i
\(417\) 9.44670 13.8790i 0.462607 0.679660i
\(418\) −13.2978 + 13.2978i −0.650416 + 0.650416i
\(419\) 4.58918 + 3.33423i 0.224196 + 0.162888i 0.694213 0.719769i \(-0.255752\pi\)
−0.470017 + 0.882657i \(0.655752\pi\)
\(420\) 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
\(423\) −14.2221 6.17863i −0.691504 0.300415i
\(424\) 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
\(429\) 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 \(0.0402371\pi\)
\(432\) −5.17413 + 0.477906i −0.248940 + 0.0229932i
\(433\) −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
\(438\) 5.95694 + 1.73527i 0.284633 + 0.0829144i
\(439\) −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
\(441\) 36.7952 + 9.50351i 1.75215 + 0.452548i
\(442\) 0.252934 + 1.59696i 0.0120309 + 0.0759598i
\(443\) 5.43418 + 5.43418i 0.258186 + 0.258186i 0.824316 0.566130i \(-0.191560\pi\)
−0.566130 + 0.824316i \(0.691560\pi\)
\(444\) −8.98473 + 1.70727i −0.426396 + 0.0810236i
\(445\) 0 0
\(446\) 13.3051 + 18.3129i 0.630015 + 0.867141i
\(447\) −5.68169 + 4.40067i −0.268735 + 0.208144i
\(448\) −3.95145 2.01336i −0.186688 0.0951225i
\(449\) −26.9459 −1.27165 −0.635827 0.771831i \(-0.719341\pi\)
−0.635827 + 0.771831i \(0.719341\pi\)
\(450\) 0 0
\(451\) −12.8362 −0.604434
\(452\) −15.2342 7.76223i −0.716558 0.365104i
\(453\) 13.0098 10.0765i 0.611252 0.473436i
\(454\) −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 0.989878 + 0.141919i \(0.0453271\pi\)
0.141919 + 0.989878i \(0.454673\pi\)
\(458\) 2.54978 + 16.0987i 0.119143 + 0.752241i
\(459\) 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 \(0.732369\pi\)
\(462\) 27.7360 + 8.07957i 1.29040 + 0.375896i
\(463\) −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 −0.772744 0.634718i \(-0.781116\pi\)
−0.538785 + 0.842444i \(0.681116\pi\)
\(468\) −8.82032 7.79860i −0.407719 0.360490i
\(469\) 16.1449 22.2215i 0.745502 1.02609i
\(470\) 0 0
\(471\) −7.24770 0.920861i −0.333956 0.0424310i
\(472\) 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
\(477\) 9.93018 22.8576i 0.454672 1.04658i
\(478\) 1.25473 7.92207i 0.0573901 0.362347i
\(479\) 10.3928 7.55082i 0.474860 0.345006i −0.324473 0.945895i \(-0.605187\pi\)
0.799332 + 0.600889i \(0.205187\pi\)
\(480\) 0 0
\(481\) −16.7645 12.1801i −0.764394 0.555365i
\(482\) 5.12480 5.12480i 0.233428 0.233428i
\(483\) 21.7372 31.9362i 0.989077 1.45315i
\(484\) 2.99064 + 0.971718i 0.135938 + 0.0441690i
\(485\) 0 0
\(486\) −14.8082 4.87006i −0.671713 0.220910i
\(487\) −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
\(489\) −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 \(0.817114\pi\)
\(492\) 4.88697 + 3.32629i 0.220322 + 0.149961i
\(493\) 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
\(498\) 4.15225 + 11.5592i 0.186067 + 0.517982i
\(499\) 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 0.288498 0.957480i \(-0.406844\pi\)
−0.0214995 + 0.999769i \(0.506844\pi\)
\(504\) −8.46590 10.2634i −0.377101 0.457167i
\(505\) 0 0
\(506\) 11.1179 15.3025i 0.494252 0.680280i
\(507\) −0.127697 4.15807i −0.00567123 0.184666i
\(508\) 19.3717 3.06818i 0.859482 0.136129i
\(509\) −1.17675 + 3.62167i −0.0521586 + 0.160528i −0.973743 0.227651i \(-0.926896\pi\)
0.921584 + 0.388178i \(0.126896\pi\)
\(510\) 0 0
\(511\) 4.90915 + 15.1088i 0.217168 + 0.668375i
\(512\) 0.453990 + 0.891007i 0.0200637 + 0.0393773i
\(513\) 25.3446 + 5.72229i 1.11899 + 0.252645i
\(514\) 1.39651 0.453755i 0.0615976 0.0200143i
\(515\) 0 0
\(516\) −7.98039 + 4.37983i −0.351317 + 0.192811i
\(517\) −3.04098 19.2000i −0.133742 0.844414i
\(518\) −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 \(0.820294\pi\)
\(522\) −0.528892 + 5.51098i −0.0231490 + 0.241209i
\(523\) −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
\(528\) −3.98886 5.15001i −0.173593 0.224125i
\(529\) −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
\(533\) 2.09537 + 13.2296i 0.0907606 + 0.573040i
\(534\) 0.875950 + 1.59605i 0.0379060 + 0.0690678i
\(535\) 0 0
\(536\) −5.89043 + 1.91392i −0.254428 + 0.0826686i
\(537\) −1.37116 + 4.70700i −0.0591699 + 0.203122i
\(538\) 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
\(543\) 0.605959 0.0186094i 0.0260042 0.000798607i
\(544\) 0.242163 0.333309i 0.0103827 0.0142905i
\(545\) 0 0
\(546\) 3.79961 29.9050i 0.162608 1.27982i
\(547\) 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
\(552\) −8.19818 + 2.94491i −0.348938 + 0.125344i
\(553\) −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 −0.106814 0.994279i \(-0.534065\pi\)
0.994279 + 0.106814i \(0.0340648\pi\)
\(558\) −9.76720 + 2.16857i −0.413479 + 0.0918029i
\(559\) −19.6168 6.37389i −0.829703 0.269587i
\(560\) 0 0
\(561\) −1.14443 + 2.42753i −0.0483178 + 0.102490i
\(562\) −21.8207 + 11.1182i −0.920450 + 0.468993i
\(563\) −13.4464 + 6.85128i −0.566698 + 0.288747i −0.713772 0.700378i \(-0.753015\pi\)
0.147073 + 0.989126i \(0.453015\pi\)
\(564\) −3.81760 + 8.09779i −0.160750 + 0.340978i
\(565\) 0 0
\(566\) 6.96420 + 2.26281i 0.292727 + 0.0951128i
\(567\) −11.0258 38.3602i −0.463041 1.61098i
\(568\) 1.19343 1.19343i 0.0500753 0.0500753i
\(569\) −7.06373 5.13210i −0.296127 0.215149i 0.429794 0.902927i \(-0.358586\pi\)
−0.725921 + 0.687778i \(0.758586\pi\)
\(570\) 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
\(573\) −1.85074 + 0.664813i −0.0773157 + 0.0277730i
\(574\) 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
\(579\) −1.28490 + 10.1129i −0.0533987 + 0.420277i
\(580\) 0 0
\(581\) −18.4849 + 25.4423i −0.766882 + 1.05552i
\(582\) −13.3499 + 0.409985i −0.553372 + 0.0169944i
\(583\) 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 0.972655 0.232254i \(-0.0746099\pi\)
−0.759609 + 0.650379i \(0.774610\pi\)
\(588\) 6.13637 21.0653i 0.253060 0.868719i
\(589\) 15.8600 5.15324i 0.653501 0.212335i
\(590\) 0 0
\(591\) −16.0128 29.1766i −0.658678 1.20016i
\(592\) 0.825998 + 5.21515i 0.0339483 + 0.214341i
\(593\) −16.4362 16.4362i −0.674952 0.674952i 0.283901 0.958854i \(-0.408371\pi\)
−0.958854 + 0.283901i \(0.908371\pi\)
\(594\) −4.81937 18.9388i −0.197741 0.777066i
\(595\) 0 0
\(596\) 2.43884 + 3.35677i 0.0998986 + 0.137499i
\(597\) 13.4829 + 17.4077i 0.551817 + 0.712449i
\(598\) −17.5864 8.96072i −0.719162 0.366431i
\(599\) −16.9386 −0.692094 −0.346047 0.938217i \(-0.612476\pi\)
−0.346047 + 0.938217i \(0.612476\pi\)
\(600\) 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
\(603\) −18.4957 1.77504i −0.753204 0.0722854i
\(604\) −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 −0.975877 0.218322i \(-0.929942\pi\)
−0.218322 0.975877i \(-0.570058\pi\)
\(608\) −0.782226 4.93878i −0.0317235 0.200294i
\(609\) −12.4269 + 6.82016i −0.503562 + 0.276367i
\(610\) 0 0
\(611\) −19.2921 + 6.26837i −0.780473 + 0.253591i
\(612\) 1.06476 0.627642i 0.0430402 0.0253709i
\(613\) −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 −0.817478 0.575960i \(-0.804628\pi\)
−0.599486 + 0.800385i \(0.704628\pi\)
\(618\) −0.130384 4.24555i −0.00524480 0.170781i
\(619\) 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
\(621\) −26.0780 1.69685i −1.04648 0.0680922i
\(622\) −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
\(627\) 11.0117 + 30.6550i 0.439766 + 1.22424i
\(628\) −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
\(633\) 24.9659 + 16.9929i 0.992305 + 0.675407i
\(634\) −26.6314 8.65307i −1.05767 0.343657i
\(635\) 0 0
\(636\) −13.0146 6.13559i −0.516063 0.243292i
\(637\) 44.2955 22.5697i 1.75505 0.894244i
\(638\) −6.18406 + 3.15094i −0.244829 + 0.124747i
\(639\) 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 \(0.686776\pi\)
\(642\) −5.93593 + 8.72104i −0.234273 + 0.344192i
\(643\) −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 \(0.261276\pi\)
−0.874368 + 0.485263i \(0.838724\pi\)
\(648\) −3.07284 + 8.45917i −0.120713 + 0.332308i
\(649\) 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 0.843390 0.537302i \(-0.180556\pi\)
0.636076 + 0.771626i \(0.280556\pi\)
\(654\) −8.06209 1.02433i −0.315253 0.0400546i
\(655\) 0 0
\(656\) 2.00614 2.76122i 0.0783266 0.107807i
\(657\) 7.11835 8.05095i 0.277713 0.314098i
\(658\) −22.6403 + 3.58587i −0.882610 + 0.139792i
\(659\) −6.33270 + 19.4901i −0.246687 + 0.759225i 0.748667 + 0.662946i \(0.230694\pi\)
−0.995354 + 0.0962789i \(0.969306\pi\)
\(660\) 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
\(663\) 2.68874 + 0.783237i 0.104422 + 0.0304184i
\(664\) 6.74418 2.19132i 0.261725 0.0850395i
\(665\) 0 0
\(666\) −3.96130 + 15.3372i −0.153497 + 0.594303i
\(667\) 1.45192 + 9.16704i 0.0562184 + 0.354949i
\(668\) −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
\(672\) −6.07280 + 4.70360i −0.234263 + 0.181445i
\(673\) 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 −0.443686 0.896182i \(-0.646330\pi\)
−0.985819 + 0.167813i \(0.946330\pi\)
\(678\) −23.4128 + 18.1340i −0.899163 + 0.696433i
\(679\) −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
\(683\) −7.96066 50.2616i −0.304606 1.92321i −0.377793 0.925890i \(-0.623317\pi\)
0.0731865 0.997318i \(-0.476683\pi\)
\(684\) 3.75138 14.5244i 0.143437 0.555354i
\(685\) 0 0
\(686\) 23.9045 7.76703i 0.912677 0.296547i
\(687\) 27.1047 + 7.89565i 1.03411 + 0.301238i
\(688\) 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
\(693\) 33.1437 37.4860i 1.25902 1.42397i
\(694\) −21.7024 + 29.8708i −0.823813 + 1.13388i
\(695\) 0 0
\(696\) 3.17089 + 0.402880i 0.120192 + 0.0152711i
\(697\) −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 \(0.207900\pi\)
−0.794180 + 0.607682i \(0.792100\pi\)
\(702\) −18.7325 + 8.05863i −0.707013 + 0.304153i
\(703\) 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
\(708\) 5.47388 8.04220i 0.205721 0.302244i
\(709\) 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
\(711\) 29.6686 11.6976i 1.11266 0.438693i
\(712\) 0.936569 0.477205i 0.0350994 0.0178840i
\(713\) −14.9448 + 7.61474i −0.559686 + 0.285174i
\(714\) 2.86250 + 1.34949i 0.107126 + 0.0505033i
\(715\) 0 0
\(716\) 2.69201 + 0.874686i 0.100605 + 0.0326886i
\(717\) −11.4846 7.81693i −0.428900 0.291929i
\(718\) 2.46690 2.46690i 0.0920639 0.0920639i
\(719\) 6.94235 + 5.04392i 0.258906 + 0.188106i 0.709665 0.704540i \(-0.248846\pi\)
−0.450759 + 0.892646i \(0.648846\pi\)
\(720\) 0 0
\(721\) 8.79854 6.39251i 0.327675 0.238070i
\(722\) −0.939145 + 5.92953i −0.0349514 + 0.220674i
\(723\) −4.24378 11.8140i −0.157828 0.439369i
\(724\) 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
\(729\) −18.5670 + 19.6027i −0.687668 + 0.726026i
\(730\) 0 0
\(731\) 1.27276 1.75180i 0.0470746 0.0647926i
\(732\) −0.763622 24.8650i −0.0282243 0.919038i
\(733\) −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
\(738\) 8.82071 5.19955i 0.324695 0.191398i
\(739\) −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
\(741\) 29.7970 16.3533i 1.09462 0.600754i
\(742\) −5.76314 36.3871i −0.211572 1.33581i
\(743\) 25.7253 + 25.7253i 0.943771 + 0.943771i 0.998501 0.0547306i \(-0.0174300\pi\)
−0.0547306 + 0.998501i \(0.517430\pi\)
\(744\) 1.07834 + 5.67487i 0.0395337 + 0.208051i
\(745\) 0 0
\(746\) 3.74935 + 5.16053i 0.137273 + 0.188940i
\(747\) 21.1764 + 2.03232i 0.774806 + 0.0743585i
\(748\) 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
\(753\) −15.4339 19.9267i −0.562443 0.726169i
\(754\) 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 −0.999015 0.0443764i \(-0.985870\pi\)
−0.0443764 0.999015i \(-0.514130\pi\)
\(758\) −4.21499 26.6124i −0.153095 0.966606i
\(759\) −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 \(0.156132\pi\)
\(762\) 9.50095 32.6154i 0.344183 1.18153i
\(763\) −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
\(768\) 1.73123 0.0531674i 0.0624705 0.00191851i
\(769\) −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
\(771\) 0.320565 2.52303i 0.0115449 0.0908646i
\(772\) 5.81316 + 0.920714i 0.209220 + 0.0331372i
\(773\) 16.3075 32.0052i 0.586539 1.15115i −0.386883 0.922129i \(-0.626448\pi\)
0.973422 0.229019i \(-0.0735518\pi\)
\(774\) 0.967539 + 15.7376i 0.0347775 + 0.565677i
\(775\) 0 0
\(776\) 7.71121i 0.276816i
\(777\) −38.1706 + 13.7114i −1.36936 + 0.491895i
\(778\) −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 0.0523940i </