Properties

Label 690.2.j.b.367.9
Level $690$
Weight $2$
Character 690.367
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 367.9
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.b.643.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.643329 - 2.14152i) q^{5} +1.00000 q^{6} +(-2.01701 + 2.01701i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(-0.643329 - 2.14152i) q^{5} +1.00000 q^{6} +(-2.01701 + 2.01701i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.05938 - 1.96919i) q^{10} -5.11516i q^{11} +(0.707107 + 0.707107i) q^{12} +(4.36777 - 4.36777i) q^{13} -2.85248 q^{14} +(-1.96919 - 1.05938i) q^{15} -1.00000 q^{16} +(0.390995 - 0.390995i) q^{17} +(0.707107 - 0.707107i) q^{18} +6.15278 q^{19} +(2.14152 - 0.643329i) q^{20} +2.85248i q^{21} +(3.61696 - 3.61696i) q^{22} +(0.204508 - 4.79147i) q^{23} +1.00000i q^{24} +(-4.17226 + 2.75541i) q^{25} +6.17696 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-2.01701 - 2.01701i) q^{28} +5.15378i q^{29} +(-0.643329 - 2.14152i) q^{30} +5.55456 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.61696 - 3.61696i) q^{33} +0.552950 q^{34} +(5.61707 + 3.02187i) q^{35} +1.00000 q^{36} +(-1.66015 + 1.66015i) q^{37} +(4.35067 + 4.35067i) q^{38} -6.17696i q^{39} +(1.96919 + 1.05938i) q^{40} -8.20789 q^{41} +(-2.01701 + 2.01701i) q^{42} +(-3.51520 - 3.51520i) q^{43} +5.11516 q^{44} +(-2.14152 + 0.643329i) q^{45} +(3.53269 - 3.24347i) q^{46} +(-3.69444 - 3.69444i) q^{47} +(-0.707107 + 0.707107i) q^{48} -1.13662i q^{49} +(-4.89860 - 1.00186i) q^{50} -0.552950i q^{51} +(4.36777 + 4.36777i) q^{52} +(3.27229 + 3.27229i) q^{53} -1.00000i q^{54} +(-10.9542 + 3.29073i) q^{55} -2.85248i q^{56} +(4.35067 - 4.35067i) q^{57} +(-3.64427 + 3.64427i) q^{58} -9.42889i q^{59} +(1.05938 - 1.96919i) q^{60} +6.90926i q^{61} +(3.92767 + 3.92767i) q^{62} +(2.01701 + 2.01701i) q^{63} -1.00000i q^{64} +(-12.1636 - 6.54377i) q^{65} -5.11516i q^{66} +(-6.18692 + 6.18692i) q^{67} +(0.390995 + 0.390995i) q^{68} +(-3.24347 - 3.53269i) q^{69} +(1.83508 + 6.10865i) q^{70} +10.0403 q^{71} +(0.707107 + 0.707107i) q^{72} +(-9.69041 + 9.69041i) q^{73} -2.34781 q^{74} +(-1.00186 + 4.89860i) q^{75} +6.15278i q^{76} +(10.3173 + 10.3173i) q^{77} +(4.36777 - 4.36777i) q^{78} +0.836863 q^{79} +(0.643329 + 2.14152i) q^{80} -1.00000 q^{81} +(-5.80385 - 5.80385i) q^{82} +(7.68978 + 7.68978i) q^{83} -2.85248 q^{84} +(-1.08886 - 0.585786i) q^{85} -4.97125i q^{86} +(3.64427 + 3.64427i) q^{87} +(3.61696 + 3.61696i) q^{88} +8.61622 q^{89} +(-1.96919 - 1.05938i) q^{90} +17.6196i q^{91} +(4.79147 + 0.204508i) q^{92} +(3.92767 - 3.92767i) q^{93} -5.22472i q^{94} +(-3.95826 - 13.1763i) q^{95} -1.00000 q^{96} +(7.13357 - 7.13357i) q^{97} +(0.803714 - 0.803714i) q^{98} -5.11516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{6} + O(q^{10}) \) \( 24q + 24q^{6} + 16q^{13} - 24q^{16} + 16q^{23} - 16q^{25} + 16q^{31} + 24q^{36} + 8q^{46} + 40q^{47} - 8q^{50} + 16q^{52} - 56q^{55} - 16q^{58} - 8q^{62} + 32q^{70} + 64q^{71} - 16q^{73} + 32q^{75} + 16q^{77} + 16q^{78} - 24q^{81} + 24q^{82} - 48q^{85} + 16q^{87} + 16q^{92} - 8q^{93} + 24q^{95} - 24q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) −0.643329 2.14152i −0.287706 0.957719i
\(6\) 1.00000 0.408248
\(7\) −2.01701 + 2.01701i −0.762356 + 0.762356i −0.976748 0.214391i \(-0.931223\pi\)
0.214391 + 0.976748i \(0.431223\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.05938 1.96919i 0.335007 0.622712i
\(11\) 5.11516i 1.54228i −0.636666 0.771139i \(-0.719687\pi\)
0.636666 0.771139i \(-0.280313\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 4.36777 4.36777i 1.21140 1.21140i 0.240836 0.970566i \(-0.422578\pi\)
0.970566 0.240836i \(-0.0774215\pi\)
\(14\) −2.85248 −0.762356
\(15\) −1.96919 1.05938i −0.508442 0.273532i
\(16\) −1.00000 −0.250000
\(17\) 0.390995 0.390995i 0.0948301 0.0948301i −0.658100 0.752930i \(-0.728640\pi\)
0.752930 + 0.658100i \(0.228640\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) 6.15278 1.41154 0.705772 0.708439i \(-0.250600\pi\)
0.705772 + 0.708439i \(0.250600\pi\)
\(20\) 2.14152 0.643329i 0.478859 0.143853i
\(21\) 2.85248i 0.622461i
\(22\) 3.61696 3.61696i 0.771139 0.771139i
\(23\) 0.204508 4.79147i 0.0426429 0.999090i
\(24\) 1.00000i 0.204124i
\(25\) −4.17226 + 2.75541i −0.834451 + 0.551082i
\(26\) 6.17696 1.21140
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) −2.01701 2.01701i −0.381178 0.381178i
\(29\) 5.15378i 0.957032i 0.878079 + 0.478516i \(0.158825\pi\)
−0.878079 + 0.478516i \(0.841175\pi\)
\(30\) −0.643329 2.14152i −0.117455 0.390987i
\(31\) 5.55456 0.997628 0.498814 0.866709i \(-0.333769\pi\)
0.498814 + 0.866709i \(0.333769\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −3.61696 3.61696i −0.629633 0.629633i
\(34\) 0.552950 0.0948301
\(35\) 5.61707 + 3.02187i 0.949457 + 0.510789i
\(36\) 1.00000 0.166667
\(37\) −1.66015 + 1.66015i −0.272927 + 0.272927i −0.830277 0.557350i \(-0.811818\pi\)
0.557350 + 0.830277i \(0.311818\pi\)
\(38\) 4.35067 + 4.35067i 0.705772 + 0.705772i
\(39\) 6.17696i 0.989105i
\(40\) 1.96919 + 1.05938i 0.311356 + 0.167503i
\(41\) −8.20789 −1.28186 −0.640928 0.767601i \(-0.721450\pi\)
−0.640928 + 0.767601i \(0.721450\pi\)
\(42\) −2.01701 + 2.01701i −0.311231 + 0.311231i
\(43\) −3.51520 3.51520i −0.536063 0.536063i 0.386307 0.922370i \(-0.373751\pi\)
−0.922370 + 0.386307i \(0.873751\pi\)
\(44\) 5.11516 0.771139
\(45\) −2.14152 + 0.643329i −0.319240 + 0.0959018i
\(46\) 3.53269 3.24347i 0.520867 0.478224i
\(47\) −3.69444 3.69444i −0.538889 0.538889i 0.384314 0.923203i \(-0.374438\pi\)
−0.923203 + 0.384314i \(0.874438\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 1.13662i 0.162375i
\(50\) −4.89860 1.00186i −0.692767 0.141684i
\(51\) 0.552950i 0.0774285i
\(52\) 4.36777 + 4.36777i 0.605701 + 0.605701i
\(53\) 3.27229 + 3.27229i 0.449484 + 0.449484i 0.895183 0.445699i \(-0.147045\pi\)
−0.445699 + 0.895183i \(0.647045\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −10.9542 + 3.29073i −1.47707 + 0.443722i
\(56\) 2.85248i 0.381178i
\(57\) 4.35067 4.35067i 0.576261 0.576261i
\(58\) −3.64427 + 3.64427i −0.478516 + 0.478516i
\(59\) 9.42889i 1.22754i −0.789486 0.613768i \(-0.789653\pi\)
0.789486 0.613768i \(-0.210347\pi\)
\(60\) 1.05938 1.96919i 0.136766 0.254221i
\(61\) 6.90926i 0.884639i 0.896857 + 0.442320i \(0.145844\pi\)
−0.896857 + 0.442320i \(0.854156\pi\)
\(62\) 3.92767 + 3.92767i 0.498814 + 0.498814i
\(63\) 2.01701 + 2.01701i 0.254119 + 0.254119i
\(64\) 1.00000i 0.125000i
\(65\) −12.1636 6.54377i −1.50871 0.811655i
\(66\) 5.11516i 0.629633i
\(67\) −6.18692 + 6.18692i −0.755853 + 0.755853i −0.975565 0.219712i \(-0.929488\pi\)
0.219712 + 0.975565i \(0.429488\pi\)
\(68\) 0.390995 + 0.390995i 0.0474151 + 0.0474151i
\(69\) −3.24347 3.53269i −0.390468 0.425286i
\(70\) 1.83508 + 6.10865i 0.219334 + 0.730123i
\(71\) 10.0403 1.19157 0.595784 0.803144i \(-0.296841\pi\)
0.595784 + 0.803144i \(0.296841\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) −9.69041 + 9.69041i −1.13418 + 1.13418i −0.144702 + 0.989475i \(0.546222\pi\)
−0.989475 + 0.144702i \(0.953778\pi\)
\(74\) −2.34781 −0.272927
\(75\) −1.00186 + 4.89860i −0.115685 + 0.565642i
\(76\) 6.15278i 0.705772i
\(77\) 10.3173 + 10.3173i 1.17577 + 1.17577i
\(78\) 4.36777 4.36777i 0.494553 0.494553i
\(79\) 0.836863 0.0941545 0.0470772 0.998891i \(-0.485009\pi\)
0.0470772 + 0.998891i \(0.485009\pi\)
\(80\) 0.643329 + 2.14152i 0.0719264 + 0.239430i
\(81\) −1.00000 −0.111111
\(82\) −5.80385 5.80385i −0.640928 0.640928i
\(83\) 7.68978 + 7.68978i 0.844063 + 0.844063i 0.989384 0.145322i \(-0.0464217\pi\)
−0.145322 + 0.989384i \(0.546422\pi\)
\(84\) −2.85248 −0.311231
\(85\) −1.08886 0.585786i −0.118104 0.0635375i
\(86\) 4.97125i 0.536063i
\(87\) 3.64427 + 3.64427i 0.390707 + 0.390707i
\(88\) 3.61696 + 3.61696i 0.385570 + 0.385570i
\(89\) 8.61622 0.913317 0.456659 0.889642i \(-0.349046\pi\)
0.456659 + 0.889642i \(0.349046\pi\)
\(90\) −1.96919 1.05938i −0.207571 0.111669i
\(91\) 17.6196i 1.84704i
\(92\) 4.79147 + 0.204508i 0.499545 + 0.0213214i
\(93\) 3.92767 3.92767i 0.407280 0.407280i
\(94\) 5.22472i 0.538889i
\(95\) −3.95826 13.1763i −0.406109 1.35186i
\(96\) −1.00000 −0.102062
\(97\) 7.13357 7.13357i 0.724304 0.724304i −0.245175 0.969479i \(-0.578845\pi\)
0.969479 + 0.245175i \(0.0788453\pi\)
\(98\) 0.803714 0.803714i 0.0811874 0.0811874i
\(99\) −5.11516 −0.514093
\(100\) −2.75541 4.17226i −0.275541 0.417226i
\(101\) 4.31730 0.429588 0.214794 0.976659i \(-0.431092\pi\)
0.214794 + 0.976659i \(0.431092\pi\)
\(102\) 0.390995 0.390995i 0.0387142 0.0387142i
\(103\) 12.0533 + 12.0533i 1.18765 + 1.18765i 0.977717 + 0.209929i \(0.0673234\pi\)
0.209929 + 0.977717i \(0.432677\pi\)
\(104\) 6.17696i 0.605701i
\(105\) 6.10865 1.83508i 0.596143 0.179086i
\(106\) 4.62772i 0.449484i
\(107\) −5.43462 + 5.43462i −0.525384 + 0.525384i −0.919193 0.393808i \(-0.871157\pi\)
0.393808 + 0.919193i \(0.371157\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −1.98889 −0.190501 −0.0952507 0.995453i \(-0.530365\pi\)
−0.0952507 + 0.995453i \(0.530365\pi\)
\(110\) −10.0727 5.41892i −0.960396 0.516674i
\(111\) 2.34781i 0.222844i
\(112\) 2.01701 2.01701i 0.190589 0.190589i
\(113\) −0.526241 0.526241i −0.0495045 0.0495045i 0.681921 0.731426i \(-0.261145\pi\)
−0.731426 + 0.681921i \(0.761145\pi\)
\(114\) 6.15278 0.576261
\(115\) −10.3926 + 2.64453i −0.969116 + 0.246604i
\(116\) −5.15378 −0.478516
\(117\) −4.36777 4.36777i −0.403801 0.403801i
\(118\) 6.66723 6.66723i 0.613768 0.613768i
\(119\) 1.57728i 0.144589i
\(120\) 2.14152 0.643329i 0.195494 0.0587276i
\(121\) −15.1649 −1.37862
\(122\) −4.88558 + 4.88558i −0.442320 + 0.442320i
\(123\) −5.80385 + 5.80385i −0.523316 + 0.523316i
\(124\) 5.55456i 0.498814i
\(125\) 8.58491 + 7.16235i 0.767858 + 0.640620i
\(126\) 2.85248i 0.254119i
\(127\) −15.6798 15.6798i −1.39136 1.39136i −0.822291 0.569068i \(-0.807304\pi\)
−0.569068 0.822291i \(-0.692696\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −4.97125 −0.437694
\(130\) −3.97382 13.2281i −0.348527 1.16018i
\(131\) −3.31192 −0.289364 −0.144682 0.989478i \(-0.546216\pi\)
−0.144682 + 0.989478i \(0.546216\pi\)
\(132\) 3.61696 3.61696i 0.314816 0.314816i
\(133\) −12.4102 + 12.4102i −1.07610 + 1.07610i
\(134\) −8.74963 −0.755853
\(135\) −1.05938 + 1.96919i −0.0911773 + 0.169481i
\(136\) 0.552950i 0.0474151i
\(137\) −2.13220 + 2.13220i −0.182166 + 0.182166i −0.792299 0.610133i \(-0.791116\pi\)
0.610133 + 0.792299i \(0.291116\pi\)
\(138\) 0.204508 4.79147i 0.0174089 0.407877i
\(139\) 8.40570i 0.712963i 0.934302 + 0.356481i \(0.116024\pi\)
−0.934302 + 0.356481i \(0.883976\pi\)
\(140\) −3.02187 + 5.61707i −0.255395 + 0.474729i
\(141\) −5.22472 −0.440001
\(142\) 7.09959 + 7.09959i 0.595784 + 0.595784i
\(143\) −22.3418 22.3418i −1.86832 1.86832i
\(144\) 1.00000i 0.0833333i
\(145\) 11.0369 3.31558i 0.916568 0.275344i
\(146\) −13.7043 −1.13418
\(147\) −0.803714 0.803714i −0.0662892 0.0662892i
\(148\) −1.66015 1.66015i −0.136464 0.136464i
\(149\) 18.0134 1.47572 0.737859 0.674955i \(-0.235837\pi\)
0.737859 + 0.674955i \(0.235837\pi\)
\(150\) −4.17226 + 2.75541i −0.340663 + 0.224978i
\(151\) 12.3312 1.00350 0.501749 0.865013i \(-0.332690\pi\)
0.501749 + 0.865013i \(0.332690\pi\)
\(152\) −4.35067 + 4.35067i −0.352886 + 0.352886i
\(153\) −0.390995 0.390995i −0.0316100 0.0316100i
\(154\) 14.5909i 1.17577i
\(155\) −3.57341 11.8952i −0.287023 0.955447i
\(156\) 6.17696 0.494553
\(157\) −1.55503 + 1.55503i −0.124105 + 0.124105i −0.766431 0.642326i \(-0.777969\pi\)
0.642326 + 0.766431i \(0.277969\pi\)
\(158\) 0.591752 + 0.591752i 0.0470772 + 0.0470772i
\(159\) 4.62772 0.367002
\(160\) −1.05938 + 1.96919i −0.0837517 + 0.155678i
\(161\) 9.25193 + 10.0769i 0.729154 + 0.794172i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 5.61838 5.61838i 0.440065 0.440065i −0.451968 0.892034i \(-0.649278\pi\)
0.892034 + 0.451968i \(0.149278\pi\)
\(164\) 8.20789i 0.640928i
\(165\) −5.41892 + 10.0727i −0.421862 + 0.784160i
\(166\) 10.8750i 0.844063i
\(167\) 5.78732 + 5.78732i 0.447836 + 0.447836i 0.894635 0.446798i \(-0.147436\pi\)
−0.446798 + 0.894635i \(0.647436\pi\)
\(168\) −2.01701 2.01701i −0.155615 0.155615i
\(169\) 25.1548i 1.93499i
\(170\) −0.355729 1.18416i −0.0272832 0.0908206i
\(171\) 6.15278i 0.470515i
\(172\) 3.51520 3.51520i 0.268032 0.268032i
\(173\) −3.65117 + 3.65117i −0.277593 + 0.277593i −0.832147 0.554554i \(-0.812889\pi\)
0.554554 + 0.832147i \(0.312889\pi\)
\(174\) 5.15378i 0.390707i
\(175\) 2.85778 13.9731i 0.216028 1.05627i
\(176\) 5.11516i 0.385570i
\(177\) −6.66723 6.66723i −0.501140 0.501140i
\(178\) 6.09259 + 6.09259i 0.456659 + 0.456659i
\(179\) 18.7393i 1.40064i −0.713830 0.700319i \(-0.753041\pi\)
0.713830 0.700319i \(-0.246959\pi\)
\(180\) −0.643329 2.14152i −0.0479509 0.159620i
\(181\) 20.7307i 1.54090i 0.637502 + 0.770449i \(0.279968\pi\)
−0.637502 + 0.770449i \(0.720032\pi\)
\(182\) −12.4590 + 12.4590i −0.923520 + 0.923520i
\(183\) 4.88558 + 4.88558i 0.361153 + 0.361153i
\(184\) 3.24347 + 3.53269i 0.239112 + 0.260433i
\(185\) 4.62328 + 2.48723i 0.339910 + 0.182865i
\(186\) 5.55456 0.407280
\(187\) −2.00000 2.00000i −0.146254 0.146254i
\(188\) 3.69444 3.69444i 0.269444 0.269444i
\(189\) 2.85248 0.207487
\(190\) 6.51816 12.1160i 0.472877 0.878986i
\(191\) 9.66249i 0.699153i −0.936908 0.349577i \(-0.886325\pi\)
0.936908 0.349577i \(-0.113675\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) −5.41019 + 5.41019i −0.389434 + 0.389434i −0.874486 0.485052i \(-0.838801\pi\)
0.485052 + 0.874486i \(0.338801\pi\)
\(194\) 10.0884 0.724304
\(195\) −13.2281 + 3.97382i −0.947285 + 0.284571i
\(196\) 1.13662 0.0811874
\(197\) 9.68778 + 9.68778i 0.690226 + 0.690226i 0.962282 0.272056i \(-0.0877035\pi\)
−0.272056 + 0.962282i \(0.587703\pi\)
\(198\) −3.61696 3.61696i −0.257046 0.257046i
\(199\) 1.92772 0.136652 0.0683262 0.997663i \(-0.478234\pi\)
0.0683262 + 0.997663i \(0.478234\pi\)
\(200\) 1.00186 4.89860i 0.0708422 0.346383i
\(201\) 8.74963i 0.617151i
\(202\) 3.05280 + 3.05280i 0.214794 + 0.214794i
\(203\) −10.3952 10.3952i −0.729600 0.729600i
\(204\) 0.552950 0.0387142
\(205\) 5.28037 + 17.5774i 0.368797 + 1.22766i
\(206\) 17.0459i 1.18765i
\(207\) −4.79147 0.204508i −0.333030 0.0142143i
\(208\) −4.36777 + 4.36777i −0.302850 + 0.302850i
\(209\) 31.4724i 2.17699i
\(210\) 5.61707 + 3.02187i 0.387614 + 0.208529i
\(211\) 13.4119 0.923310 0.461655 0.887059i \(-0.347256\pi\)
0.461655 + 0.887059i \(0.347256\pi\)
\(212\) −3.27229 + 3.27229i −0.224742 + 0.224742i
\(213\) 7.09959 7.09959i 0.486456 0.486456i
\(214\) −7.68571 −0.525384
\(215\) −5.26646 + 9.78932i −0.359169 + 0.667626i
\(216\) 1.00000 0.0680414
\(217\) −11.2036 + 11.2036i −0.760548 + 0.760548i
\(218\) −1.40636 1.40636i −0.0952507 0.0952507i
\(219\) 13.7043i 0.926052i
\(220\) −3.29073 10.9542i −0.221861 0.738535i
\(221\) 3.41555i 0.229755i
\(222\) −1.66015 + 1.66015i −0.111422 + 0.111422i
\(223\) −7.77131 + 7.77131i −0.520405 + 0.520405i −0.917694 0.397289i \(-0.869951\pi\)
0.397289 + 0.917694i \(0.369951\pi\)
\(224\) 2.85248 0.190589
\(225\) 2.75541 + 4.17226i 0.183694 + 0.278150i
\(226\) 0.744216i 0.0495045i
\(227\) −18.5374 + 18.5374i −1.23037 + 1.23037i −0.266550 + 0.963821i \(0.585884\pi\)
−0.963821 + 0.266550i \(0.914116\pi\)
\(228\) 4.35067 + 4.35067i 0.288130 + 0.288130i
\(229\) 9.30733 0.615046 0.307523 0.951541i \(-0.400500\pi\)
0.307523 + 0.951541i \(0.400500\pi\)
\(230\) −9.21866 5.47872i −0.607860 0.361256i
\(231\) 14.5909 0.960009
\(232\) −3.64427 3.64427i −0.239258 0.239258i
\(233\) −12.4073 + 12.4073i −0.812826 + 0.812826i −0.985057 0.172230i \(-0.944903\pi\)
0.172230 + 0.985057i \(0.444903\pi\)
\(234\) 6.17696i 0.403801i
\(235\) −5.53499 + 10.2885i −0.361063 + 0.671145i
\(236\) 9.42889 0.613768
\(237\) 0.591752 0.591752i 0.0384384 0.0384384i
\(238\) −1.11530 + 1.11530i −0.0722944 + 0.0722944i
\(239\) 12.7394i 0.824041i 0.911174 + 0.412021i \(0.135177\pi\)
−0.911174 + 0.412021i \(0.864823\pi\)
\(240\) 1.96919 + 1.05938i 0.127111 + 0.0683830i
\(241\) 5.57785i 0.359301i −0.983731 0.179650i \(-0.942503\pi\)
0.983731 0.179650i \(-0.0574966\pi\)
\(242\) −10.7232 10.7232i −0.689312 0.689312i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) −6.90926 −0.442320
\(245\) −2.43411 + 0.731223i −0.155509 + 0.0467161i
\(246\) −8.20789 −0.523316
\(247\) 26.8739 26.8739i 1.70995 1.70995i
\(248\) −3.92767 + 3.92767i −0.249407 + 0.249407i
\(249\) 10.8750 0.689174
\(250\) 1.00590 + 11.1350i 0.0636189 + 0.704239i
\(251\) 28.1668i 1.77787i −0.458033 0.888935i \(-0.651446\pi\)
0.458033 0.888935i \(-0.348554\pi\)
\(252\) −2.01701 + 2.01701i −0.127059 + 0.127059i
\(253\) −24.5091 1.04609i −1.54088 0.0657672i
\(254\) 22.1746i 1.39136i
\(255\) −1.18416 + 0.355729i −0.0741547 + 0.0222766i
\(256\) 1.00000 0.0625000
\(257\) −7.11158 7.11158i −0.443608 0.443608i 0.449614 0.893223i \(-0.351561\pi\)
−0.893223 + 0.449614i \(0.851561\pi\)
\(258\) −3.51520 3.51520i −0.218847 0.218847i
\(259\) 6.69707i 0.416135i
\(260\) 6.54377 12.1636i 0.405828 0.754355i
\(261\) 5.15378 0.319011
\(262\) −2.34188 2.34188i −0.144682 0.144682i
\(263\) −9.62249 9.62249i −0.593348 0.593348i 0.345186 0.938534i \(-0.387816\pi\)
−0.938534 + 0.345186i \(0.887816\pi\)
\(264\) 5.11516 0.314816
\(265\) 4.90253 9.11286i 0.301160 0.559798i
\(266\) −17.5507 −1.07610
\(267\) 6.09259 6.09259i 0.372860 0.372860i
\(268\) −6.18692 6.18692i −0.377926 0.377926i
\(269\) 6.89166i 0.420192i 0.977681 + 0.210096i \(0.0673776\pi\)
−0.977681 + 0.210096i \(0.932622\pi\)
\(270\) −2.14152 + 0.643329i −0.130329 + 0.0391518i
\(271\) 24.2167 1.47106 0.735530 0.677492i \(-0.236933\pi\)
0.735530 + 0.677492i \(0.236933\pi\)
\(272\) −0.390995 + 0.390995i −0.0237075 + 0.0237075i
\(273\) 12.4590 + 12.4590i 0.754051 + 0.754051i
\(274\) −3.01539 −0.182166
\(275\) 14.0944 + 21.3418i 0.849922 + 1.28696i
\(276\) 3.53269 3.24347i 0.212643 0.195234i
\(277\) 19.0881 + 19.0881i 1.14690 + 1.14690i 0.987160 + 0.159736i \(0.0510642\pi\)
0.159736 + 0.987160i \(0.448936\pi\)
\(278\) −5.94373 + 5.94373i −0.356481 + 0.356481i
\(279\) 5.55456i 0.332543i
\(280\) −6.10865 + 1.83508i −0.365062 + 0.109667i
\(281\) 20.3366i 1.21318i 0.795015 + 0.606590i \(0.207463\pi\)
−0.795015 + 0.606590i \(0.792537\pi\)
\(282\) −3.69444 3.69444i −0.220000 0.220000i
\(283\) −17.8450 17.8450i −1.06078 1.06078i −0.998029 0.0627483i \(-0.980013\pi\)
−0.0627483 0.998029i \(-0.519987\pi\)
\(284\) 10.0403i 0.595784i
\(285\) −12.1160 6.51816i −0.717689 0.386102i
\(286\) 31.5961i 1.86832i
\(287\) 16.5554 16.5554i 0.977232 0.977232i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 16.6942i 0.982014i
\(290\) 10.1488 + 5.45983i 0.595956 + 0.320612i
\(291\) 10.0884i 0.591392i
\(292\) −9.69041 9.69041i −0.567088 0.567088i
\(293\) −12.5889 12.5889i −0.735454 0.735454i 0.236241 0.971695i \(-0.424085\pi\)
−0.971695 + 0.236241i \(0.924085\pi\)
\(294\) 1.13662i 0.0662892i
\(295\) −20.1922 + 6.06588i −1.17563 + 0.353169i
\(296\) 2.34781i 0.136464i
\(297\) −3.61696 + 3.61696i −0.209878 + 0.209878i
\(298\) 12.7374 + 12.7374i 0.737859 + 0.737859i
\(299\) −20.0348 21.8213i −1.15864 1.26196i
\(300\) −4.89860 1.00186i −0.282821 0.0578425i
\(301\) 14.1804 0.817342
\(302\) 8.71948 + 8.71948i 0.501749 + 0.501749i
\(303\) 3.05280 3.05280i 0.175379 0.175379i
\(304\) −6.15278 −0.352886
\(305\) 14.7963 4.44493i 0.847236 0.254516i
\(306\) 0.552950i 0.0316100i
\(307\) 4.59148 + 4.59148i 0.262049 + 0.262049i 0.825886 0.563837i \(-0.190675\pi\)
−0.563837 + 0.825886i \(0.690675\pi\)
\(308\) −10.3173 + 10.3173i −0.587883 + 0.587883i
\(309\) 17.0459 0.969709
\(310\) 5.88441 10.9380i 0.334212 0.621235i
\(311\) −16.9139 −0.959097 −0.479549 0.877515i \(-0.659200\pi\)
−0.479549 + 0.877515i \(0.659200\pi\)
\(312\) 4.36777 + 4.36777i 0.247276 + 0.247276i
\(313\) 8.92881 + 8.92881i 0.504686 + 0.504686i 0.912891 0.408204i \(-0.133845\pi\)
−0.408204 + 0.912891i \(0.633845\pi\)
\(314\) −2.19914 −0.124105
\(315\) 3.02187 5.61707i 0.170263 0.316486i
\(316\) 0.836863i 0.0470772i
\(317\) 2.16941 + 2.16941i 0.121846 + 0.121846i 0.765400 0.643554i \(-0.222541\pi\)
−0.643554 + 0.765400i \(0.722541\pi\)
\(318\) 3.27229 + 3.27229i 0.183501 + 0.183501i
\(319\) 26.3624 1.47601
\(320\) −2.14152 + 0.643329i −0.119715 + 0.0359632i
\(321\) 7.68571i 0.428974i
\(322\) −0.583354 + 13.6676i −0.0325091 + 0.761663i
\(323\) 2.40570 2.40570i 0.133857 0.133857i
\(324\) 1.00000i 0.0555556i
\(325\) −6.18845 + 30.2585i −0.343274 + 1.67844i
\(326\) 7.94559 0.440065
\(327\) −1.40636 + 1.40636i −0.0777719 + 0.0777719i
\(328\) 5.80385 5.80385i 0.320464 0.320464i
\(329\) 14.9034 0.821651
\(330\) −10.9542 + 3.29073i −0.603011 + 0.181149i
\(331\) −4.44874 −0.244525 −0.122262 0.992498i \(-0.539015\pi\)
−0.122262 + 0.992498i \(0.539015\pi\)
\(332\) −7.68978 + 7.68978i −0.422031 + 0.422031i
\(333\) 1.66015 + 1.66015i 0.0909757 + 0.0909757i
\(334\) 8.18451i 0.447836i
\(335\) 17.2297 + 9.26921i 0.941357 + 0.506431i
\(336\) 2.85248i 0.155615i
\(337\) −0.387079 + 0.387079i −0.0210856 + 0.0210856i −0.717571 0.696485i \(-0.754746\pi\)
0.696485 + 0.717571i \(0.254746\pi\)
\(338\) 17.7872 17.7872i 0.967494 0.967494i
\(339\) −0.744216 −0.0404203
\(340\) 0.585786 1.08886i 0.0317687 0.0590519i
\(341\) 28.4124i 1.53862i
\(342\) 4.35067 4.35067i 0.235257 0.235257i
\(343\) −11.8265 11.8265i −0.638569 0.638569i
\(344\) 4.97125 0.268032
\(345\) −5.47872 + 9.21866i −0.294964 + 0.496316i
\(346\) −5.16353 −0.277593
\(347\) 21.9216 + 21.9216i 1.17681 + 1.17681i 0.980551 + 0.196262i \(0.0628804\pi\)
0.196262 + 0.980551i \(0.437120\pi\)
\(348\) −3.64427 + 3.64427i −0.195353 + 0.195353i
\(349\) 29.6703i 1.58821i −0.607779 0.794106i \(-0.707939\pi\)
0.607779 0.794106i \(-0.292061\pi\)
\(350\) 11.9013 7.85974i 0.636149 0.420121i
\(351\) −6.17696 −0.329702
\(352\) −3.61696 + 3.61696i −0.192785 + 0.192785i
\(353\) −1.26153 + 1.26153i −0.0671442 + 0.0671442i −0.739881 0.672737i \(-0.765118\pi\)
0.672737 + 0.739881i \(0.265118\pi\)
\(354\) 9.42889i 0.501140i
\(355\) −6.45924 21.5016i −0.342821 1.14119i
\(356\) 8.61622i 0.456659i
\(357\) 1.11530 + 1.11530i 0.0590281 + 0.0590281i
\(358\) 13.2507 13.2507i 0.700319 0.700319i
\(359\) 9.95032 0.525158 0.262579 0.964911i \(-0.415427\pi\)
0.262579 + 0.964911i \(0.415427\pi\)
\(360\) 1.05938 1.96919i 0.0558344 0.103785i
\(361\) 18.8567 0.992458
\(362\) −14.6588 + 14.6588i −0.770449 + 0.770449i
\(363\) −10.7232 + 10.7232i −0.562821 + 0.562821i
\(364\) −17.6196 −0.923520
\(365\) 26.9864 + 14.5181i 1.41253 + 0.759914i
\(366\) 6.90926i 0.361153i
\(367\) 22.7067 22.7067i 1.18528 1.18528i 0.206922 0.978358i \(-0.433655\pi\)
0.978358 0.206922i \(-0.0663445\pi\)
\(368\) −0.204508 + 4.79147i −0.0106607 + 0.249773i
\(369\) 8.20789i 0.427286i
\(370\) 1.51041 + 5.02789i 0.0785226 + 0.261387i
\(371\) −13.2005 −0.685334
\(372\) 3.92767 + 3.92767i 0.203640 + 0.203640i
\(373\) −17.7101 17.7101i −0.916992 0.916992i 0.0798177 0.996809i \(-0.474566\pi\)
−0.996809 + 0.0798177i \(0.974566\pi\)
\(374\) 2.82843i 0.146254i
\(375\) 11.1350 1.00590i 0.575009 0.0519446i
\(376\) 5.22472 0.269444
\(377\) 22.5105 + 22.5105i 1.15935 + 1.15935i
\(378\) 2.01701 + 2.01701i 0.103744 + 0.103744i
\(379\) 11.5472 0.593142 0.296571 0.955011i \(-0.404157\pi\)
0.296571 + 0.955011i \(0.404157\pi\)
\(380\) 13.1763 3.95826i 0.675931 0.203055i
\(381\) −22.1746 −1.13604
\(382\) 6.83241 6.83241i 0.349577 0.349577i
\(383\) 21.9574 + 21.9574i 1.12197 + 1.12197i 0.991445 + 0.130527i \(0.0416668\pi\)
0.130527 + 0.991445i \(0.458333\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 15.4573 28.7322i 0.787779 1.46433i
\(386\) −7.65117 −0.389434
\(387\) −3.51520 + 3.51520i −0.178688 + 0.178688i
\(388\) 7.13357 + 7.13357i 0.362152 + 0.362152i
\(389\) 20.6283 1.04589 0.522947 0.852365i \(-0.324832\pi\)
0.522947 + 0.852365i \(0.324832\pi\)
\(390\) −12.1636 6.54377i −0.615928 0.331357i
\(391\) −1.79348 1.95340i −0.0907000 0.0987877i
\(392\) 0.803714 + 0.803714i 0.0405937 + 0.0405937i
\(393\) −2.34188 + 2.34188i −0.118132 + 0.118132i
\(394\) 13.7006i 0.690226i
\(395\) −0.538379 1.79216i −0.0270888 0.0901735i
\(396\) 5.11516i 0.257046i
\(397\) −1.70732 1.70732i −0.0856879 0.0856879i 0.662964 0.748652i \(-0.269298\pi\)
−0.748652 + 0.662964i \(0.769298\pi\)
\(398\) 1.36310 + 1.36310i 0.0683262 + 0.0683262i
\(399\) 17.5507i 0.878632i
\(400\) 4.17226 2.75541i 0.208613 0.137771i
\(401\) 30.6848i 1.53233i −0.642646 0.766163i \(-0.722164\pi\)
0.642646 0.766163i \(-0.277836\pi\)
\(402\) −6.18692 + 6.18692i −0.308575 + 0.308575i
\(403\) 24.2610 24.2610i 1.20853 1.20853i
\(404\) 4.31730i 0.214794i
\(405\) 0.643329 + 2.14152i 0.0319673 + 0.106413i
\(406\) 14.7010i 0.729600i
\(407\) 8.49194 + 8.49194i 0.420930 + 0.420930i
\(408\) 0.390995 + 0.390995i 0.0193571 + 0.0193571i
\(409\) 9.11463i 0.450689i 0.974279 + 0.225345i \(0.0723508\pi\)
−0.974279 + 0.225345i \(0.927649\pi\)
\(410\) −8.69531 + 16.1629i −0.429431 + 0.798228i
\(411\) 3.01539i 0.148738i
\(412\) −12.0533 + 12.0533i −0.593823 + 0.593823i
\(413\) 19.0181 + 19.0181i 0.935820 + 0.935820i
\(414\) −3.24347 3.53269i −0.159408 0.173622i
\(415\) 11.5208 21.4149i 0.565533 1.05122i
\(416\) −6.17696 −0.302850
\(417\) 5.94373 + 5.94373i 0.291066 + 0.291066i
\(418\) 22.2544 22.2544i 1.08850 1.08850i
\(419\) −8.58413 −0.419362 −0.209681 0.977770i \(-0.567243\pi\)
−0.209681 + 0.977770i \(0.567243\pi\)
\(420\) 1.83508 + 6.10865i 0.0895428 + 0.298072i
\(421\) 7.06186i 0.344174i −0.985082 0.172087i \(-0.944949\pi\)
0.985082 0.172087i \(-0.0550510\pi\)
\(422\) 9.48362 + 9.48362i 0.461655 + 0.461655i
\(423\) −3.69444 + 3.69444i −0.179630 + 0.179630i
\(424\) −4.62772 −0.224742
\(425\) −0.553979 + 2.70868i −0.0268719 + 0.131390i
\(426\) 10.0403 0.486456
\(427\) −13.9360 13.9360i −0.674411 0.674411i
\(428\) −5.43462 5.43462i −0.262692 0.262692i
\(429\) −31.5961 −1.52548
\(430\) −10.6460 + 3.19815i −0.513398 + 0.154228i
\(431\) 19.9570i 0.961296i 0.876914 + 0.480648i \(0.159599\pi\)
−0.876914 + 0.480648i \(0.840401\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −15.9071 15.9071i −0.764447 0.764447i 0.212676 0.977123i \(-0.431782\pi\)
−0.977123 + 0.212676i \(0.931782\pi\)
\(434\) −15.8442 −0.760548
\(435\) 5.45983 10.1488i 0.261779 0.486596i
\(436\) 1.98889i 0.0952507i
\(437\) 1.25829 29.4809i 0.0601923 1.41026i
\(438\) −9.69041 + 9.69041i −0.463026 + 0.463026i
\(439\) 15.0024i 0.716028i 0.933716 + 0.358014i \(0.116546\pi\)
−0.933716 + 0.358014i \(0.883454\pi\)
\(440\) 5.41892 10.0727i 0.258337 0.480198i
\(441\) −1.13662 −0.0541249
\(442\) 2.41516 2.41516i 0.114877 0.114877i
\(443\) 13.3100 13.3100i 0.632377 0.632377i −0.316287 0.948664i \(-0.602436\pi\)
0.948664 + 0.316287i \(0.102436\pi\)
\(444\) −2.34781 −0.111422
\(445\) −5.54306 18.4518i −0.262766 0.874701i
\(446\) −10.9903 −0.520405
\(447\) 12.7374 12.7374i 0.602459 0.602459i
\(448\) 2.01701 + 2.01701i 0.0952946 + 0.0952946i
\(449\) 29.8217i 1.40737i 0.710510 + 0.703687i \(0.248464\pi\)
−0.710510 + 0.703687i \(0.751536\pi\)
\(450\) −1.00186 + 4.89860i −0.0472282 + 0.230922i
\(451\) 41.9847i 1.97698i
\(452\) 0.526241 0.526241i 0.0247523 0.0247523i
\(453\) 8.71948 8.71948i 0.409677 0.409677i
\(454\) −26.2159 −1.23037
\(455\) 37.7329 11.3352i 1.76894 0.531404i
\(456\) 6.15278i 0.288130i
\(457\) −28.1085 + 28.1085i −1.31486 + 1.31486i −0.397074 + 0.917787i \(0.629974\pi\)
−0.917787 + 0.397074i \(0.870026\pi\)
\(458\) 6.58128 + 6.58128i 0.307523 + 0.307523i
\(459\) −0.552950 −0.0258095
\(460\) −2.64453 10.3926i −0.123302 0.484558i
\(461\) −30.4481 −1.41811 −0.709054 0.705154i \(-0.750878\pi\)
−0.709054 + 0.705154i \(0.750878\pi\)
\(462\) 10.3173 + 10.3173i 0.480004 + 0.480004i
\(463\) 2.16221 2.16221i 0.100486 0.100486i −0.655076 0.755563i \(-0.727364\pi\)
0.755563 + 0.655076i \(0.227364\pi\)
\(464\) 5.15378i 0.239258i
\(465\) −10.9380 5.88441i −0.507236 0.272883i
\(466\) −17.5465 −0.812826
\(467\) 10.3427 10.3427i 0.478604 0.478604i −0.426081 0.904685i \(-0.640106\pi\)
0.904685 + 0.426081i \(0.140106\pi\)
\(468\) 4.36777 4.36777i 0.201900 0.201900i
\(469\) 24.9581i 1.15246i
\(470\) −11.1889 + 3.36121i −0.516104 + 0.155041i
\(471\) 2.19914i 0.101331i
\(472\) 6.66723 + 6.66723i 0.306884 + 0.306884i
\(473\) −17.9808 + 17.9808i −0.826759 + 0.826759i
\(474\) 0.836863 0.0384384
\(475\) −25.6710 + 16.9534i −1.17786 + 0.777877i
\(476\) −1.57728 −0.0722944
\(477\) 3.27229 3.27229i 0.149828 0.149828i
\(478\) −9.00810 + 9.00810i −0.412021 + 0.412021i
\(479\) −27.5688 −1.25965 −0.629826 0.776736i \(-0.716874\pi\)
−0.629826 + 0.776736i \(0.716874\pi\)
\(480\) 0.643329 + 2.14152i 0.0293638 + 0.0977468i
\(481\) 14.5023i 0.661249i
\(482\) 3.94413 3.94413i 0.179650 0.179650i
\(483\) 13.6676 + 0.583354i 0.621895 + 0.0265435i
\(484\) 15.1649i 0.689312i
\(485\) −19.8659 10.6875i −0.902066 0.485293i
\(486\) −1.00000 −0.0453609
\(487\) −11.1321 11.1321i −0.504442 0.504442i 0.408373 0.912815i \(-0.366096\pi\)
−0.912815 + 0.408373i \(0.866096\pi\)
\(488\) −4.88558 4.88558i −0.221160 0.221160i
\(489\) 7.94559i 0.359312i
\(490\) −2.23823 1.20412i −0.101113 0.0543966i
\(491\) 12.2648 0.553501 0.276750 0.960942i \(-0.410742\pi\)
0.276750 + 0.960942i \(0.410742\pi\)
\(492\) −5.80385 5.80385i −0.261658 0.261658i
\(493\) 2.01510 + 2.01510i 0.0907555 + 0.0907555i
\(494\) 38.0055 1.70995
\(495\) 3.29073 + 10.9542i 0.147907 + 0.492356i
\(496\) −5.55456 −0.249407
\(497\) −20.2514 + 20.2514i −0.908400 + 0.908400i
\(498\) 7.68978 + 7.68978i 0.344587 + 0.344587i
\(499\) 10.1093i 0.452555i 0.974063 + 0.226277i \(0.0726556\pi\)
−0.974063 + 0.226277i \(0.927344\pi\)
\(500\) −7.16235 + 8.58491i −0.320310 + 0.383929i
\(501\) 8.18451 0.365657
\(502\) 19.9169 19.9169i 0.888935 0.888935i
\(503\) −25.5661 25.5661i −1.13994 1.13994i −0.988461 0.151476i \(-0.951597\pi\)
−0.151476 0.988461i \(-0.548403\pi\)
\(504\) −2.85248 −0.127059
\(505\) −2.77745 9.24561i −0.123595 0.411424i
\(506\) −16.5909 18.0703i −0.737554 0.803321i
\(507\) −17.7872 17.7872i −0.789955 0.789955i
\(508\) 15.6798 15.6798i 0.695679 0.695679i
\(509\) 23.2951i 1.03254i 0.856427 + 0.516268i \(0.172679\pi\)
−0.856427 + 0.516268i \(0.827321\pi\)
\(510\) −1.08886 0.585786i −0.0482157 0.0259391i
\(511\) 39.0912i 1.72929i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −4.35067 4.35067i −0.192087 0.192087i
\(514\) 10.0573i 0.443608i
\(515\) 18.0582 33.5666i 0.795739 1.47912i
\(516\) 4.97125i 0.218847i
\(517\) −18.8976 + 18.8976i −0.831117 + 0.831117i
\(518\) 4.73554 4.73554i 0.208068 0.208068i
\(519\) 5.16353i 0.226654i
\(520\) 13.2281 3.97382i 0.580091 0.174263i
\(521\) 22.1829i 0.971850i −0.874001 0.485925i \(-0.838483\pi\)
0.874001 0.485925i \(-0.161517\pi\)
\(522\) 3.64427 + 3.64427i 0.159505 + 0.159505i
\(523\) 14.7292 + 14.7292i 0.644064 + 0.644064i 0.951552 0.307488i \(-0.0994883\pi\)
−0.307488 + 0.951552i \(0.599488\pi\)
\(524\) 3.31192i 0.144682i
\(525\) −7.85974 11.9013i −0.343027 0.519414i
\(526\) 13.6083i 0.593348i
\(527\) 2.17180 2.17180i 0.0946052 0.0946052i
\(528\) 3.61696 + 3.61696i 0.157408 + 0.157408i
\(529\) −22.9164 1.95979i −0.996363 0.0852082i
\(530\) 9.91038 2.97715i 0.430479 0.129319i
\(531\) −9.42889 −0.409179
\(532\) −12.4102 12.4102i −0.538050 0.538050i
\(533\) −35.8502 + 35.8502i −1.55284 + 1.55284i
\(534\) 8.61622 0.372860
\(535\) 15.1346 + 8.14212i 0.654326 + 0.352014i
\(536\) 8.74963i 0.377926i
\(537\) −13.2507 13.2507i −0.571808 0.571808i
\(538\) −4.87314 + 4.87314i −0.210096 + 0.210096i
\(539\) −5.81401 −0.250427
\(540\) −1.96919 1.05938i −0.0847404 0.0455886i
\(541\) 25.8534 1.11152 0.555762 0.831341i \(-0.312426\pi\)
0.555762 + 0.831341i \(0.312426\pi\)
\(542\) 17.1238 + 17.1238i 0.735530 + 0.735530i
\(543\) 14.6588 + 14.6588i 0.629069 + 0.629069i
\(544\) −0.552950 −0.0237075
\(545\) 1.27951 + 4.25926i 0.0548083 + 0.182447i
\(546\) 17.6196i 0.754051i
\(547\) −9.64881 9.64881i −0.412553 0.412553i 0.470074 0.882627i \(-0.344227\pi\)
−0.882627 + 0.470074i \(0.844227\pi\)
\(548\) −2.13220 2.13220i −0.0910831 0.0910831i
\(549\) 6.90926 0.294880
\(550\) −5.12468 + 25.0571i −0.218517 + 1.06844i
\(551\) 31.7101i 1.35089i
\(552\) 4.79147 + 0.204508i 0.203938 + 0.00870444i
\(553\) −1.68796 + 1.68796i −0.0717793 + 0.0717793i
\(554\) 26.9947i 1.14690i
\(555\) 5.02789 1.51041i 0.213422 0.0641135i
\(556\) −8.40570 −0.356481
\(557\) 2.29468 2.29468i 0.0972289 0.0972289i −0.656819 0.754048i \(-0.728099\pi\)
0.754048 + 0.656819i \(0.228099\pi\)
\(558\) 3.92767 3.92767i 0.166271 0.166271i
\(559\) −30.7072 −1.29878
\(560\) −5.61707 3.02187i −0.237364 0.127697i
\(561\) −2.82843 −0.119416
\(562\) −14.3801 + 14.3801i −0.606590 + 0.606590i
\(563\) 9.31814 + 9.31814i 0.392713 + 0.392713i 0.875653 0.482941i \(-0.160431\pi\)
−0.482941 + 0.875653i \(0.660431\pi\)
\(564\) 5.22472i 0.220000i
\(565\) −0.788411 + 1.46550i −0.0331687 + 0.0616542i
\(566\) 25.2367i 1.06078i
\(567\) 2.01701 2.01701i 0.0847063 0.0847063i
\(568\) −7.09959 + 7.09959i −0.297892 + 0.297892i
\(569\) 28.0086 1.17418 0.587090 0.809522i \(-0.300273\pi\)
0.587090 + 0.809522i \(0.300273\pi\)
\(570\) −3.95826 13.1763i −0.165793 0.551896i
\(571\) 36.3711i 1.52208i −0.648703 0.761042i \(-0.724688\pi\)
0.648703 0.761042i \(-0.275312\pi\)
\(572\) 22.3418 22.3418i 0.934159 0.934159i
\(573\) −6.83241 6.83241i −0.285428 0.285428i
\(574\) 23.4128 0.977232
\(575\) 12.3492 + 20.5547i 0.514997 + 0.857192i
\(576\) −1.00000 −0.0416667
\(577\) −19.8564 19.8564i −0.826634 0.826634i 0.160416 0.987050i \(-0.448716\pi\)
−0.987050 + 0.160416i \(0.948716\pi\)
\(578\) −11.8046 + 11.8046i −0.491007 + 0.491007i
\(579\) 7.65117i 0.317972i
\(580\) 3.31558 + 11.0369i 0.137672 + 0.458284i
\(581\) −31.0206 −1.28695
\(582\) 7.13357 7.13357i 0.295696 0.295696i
\(583\) 16.7383 16.7383i 0.693229 0.693229i
\(584\) 13.7043i 0.567088i
\(585\) −6.54377 + 12.1636i −0.270552 + 0.502903i
\(586\) 17.8035i 0.735454i
\(587\) −26.7004 26.7004i −1.10204 1.10204i −0.994164 0.107879i \(-0.965594\pi\)
−0.107879 0.994164i \(-0.534406\pi\)
\(588\) 0.803714 0.803714i 0.0331446 0.0331446i
\(589\) 34.1760 1.40820
\(590\) −18.5673 9.98881i −0.764402 0.411233i
\(591\) 13.7006 0.563567
\(592\) 1.66015 1.66015i 0.0682318 0.0682318i
\(593\) −3.37233 + 3.37233i −0.138485 + 0.138485i −0.772951 0.634466i \(-0.781220\pi\)
0.634466 + 0.772951i \(0.281220\pi\)
\(594\) −5.11516 −0.209878
\(595\) 3.37778 1.01471i 0.138475 0.0415990i
\(596\) 18.0134i 0.737859i
\(597\) 1.36310 1.36310i 0.0557881 0.0557881i
\(598\) 1.26324 29.5967i 0.0516576 1.21030i
\(599\) 16.1347i 0.659248i −0.944112 0.329624i \(-0.893078\pi\)
0.944112 0.329624i \(-0.106922\pi\)
\(600\) −2.75541 4.17226i −0.112489 0.170332i
\(601\) 22.7683 0.928740 0.464370 0.885641i \(-0.346281\pi\)
0.464370 + 0.885641i \(0.346281\pi\)
\(602\) 10.0270 + 10.0270i 0.408671 + 0.408671i
\(603\) 6.18692 + 6.18692i 0.251951 + 0.251951i
\(604\) 12.3312i 0.501749i
\(605\) 9.75599 + 32.4759i 0.396638 + 1.32033i
\(606\) 4.31730 0.175379
\(607\) 22.8209 + 22.8209i 0.926273 + 0.926273i 0.997463 0.0711898i \(-0.0226796\pi\)
−0.0711898 + 0.997463i \(0.522680\pi\)
\(608\) −4.35067 4.35067i −0.176443 0.176443i
\(609\) −14.7010 −0.595716
\(610\) 13.6056 + 7.31956i 0.550876 + 0.296360i
\(611\) −32.2729 −1.30562
\(612\) 0.390995 0.390995i 0.0158050 0.0158050i
\(613\) −15.0940 15.0940i −0.609639 0.609639i 0.333213 0.942852i \(-0.391867\pi\)
−0.942852 + 0.333213i \(0.891867\pi\)
\(614\) 6.49333i 0.262049i
\(615\) 16.1629 + 8.69531i 0.651750 + 0.350629i
\(616\) −14.5909 −0.587883
\(617\) −13.3305 + 13.3305i −0.536665 + 0.536665i −0.922548 0.385883i \(-0.873897\pi\)
0.385883 + 0.922548i \(0.373897\pi\)
\(618\) 12.0533 + 12.0533i 0.484854 + 0.484854i
\(619\) −31.9076 −1.28247 −0.641236 0.767343i \(-0.721578\pi\)
−0.641236 + 0.767343i \(0.721578\pi\)
\(620\) 11.8952 3.57341i 0.477724 0.143512i
\(621\) −3.53269 + 3.24347i −0.141762 + 0.130156i
\(622\) −11.9599 11.9599i −0.479549 0.479549i
\(623\) −17.3790 + 17.3790i −0.696273 + 0.696273i
\(624\) 6.17696i 0.247276i
\(625\) 9.81543 22.9926i 0.392617 0.919702i
\(626\) 12.6272i 0.504686i
\(627\) −22.2544 22.2544i −0.888754 0.888754i
\(628\) −1.55503 1.55503i −0.0620523 0.0620523i
\(629\) 1.29822i 0.0517634i
\(630\) 6.10865 1.83508i 0.243374 0.0731114i
\(631\) 12.7919i 0.509238i 0.967041 + 0.254619i \(0.0819500\pi\)
−0.967041 + 0.254619i \(0.918050\pi\)
\(632\) −0.591752 + 0.591752i −0.0235386 + 0.0235386i
\(633\) 9.48362 9.48362i 0.376940 0.376940i
\(634\) 3.06801i 0.121846i
\(635\) −23.4914 + 43.6660i −0.932229 + 1.73283i
\(636\) 4.62772i 0.183501i
\(637\) −4.96451 4.96451i −0.196701 0.196701i
\(638\) 18.6410 + 18.6410i 0.738005 + 0.738005i
\(639\) 10.0403i 0.397190i
\(640\) −1.96919 1.05938i −0.0778390 0.0418758i
\(641\) 17.4191i 0.688014i 0.938967 + 0.344007i \(0.111784\pi\)
−0.938967 + 0.344007i \(0.888216\pi\)
\(642\) −5.43462 + 5.43462i −0.214487 + 0.214487i
\(643\) 27.1429 + 27.1429i 1.07041 + 1.07041i 0.997326 + 0.0730859i \(0.0232847\pi\)
0.0730859 + 0.997326i \(0.476715\pi\)
\(644\) −10.0769 + 9.25193i −0.397086 + 0.364577i
\(645\) 3.19815 + 10.6460i 0.125927 + 0.419188i
\(646\) 3.40218 0.133857
\(647\) −26.3595 26.3595i −1.03630 1.03630i −0.999316 0.0369830i \(-0.988225\pi\)
−0.0369830 0.999316i \(-0.511775\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) −48.2303 −1.89320
\(650\) −25.7719 + 17.0201i −1.01086 + 0.667582i
\(651\) 15.8442i 0.620985i
\(652\) 5.61838 + 5.61838i 0.220033 + 0.220033i
\(653\) 13.2363 13.2363i 0.517978 0.517978i −0.398981 0.916959i \(-0.630636\pi\)
0.916959 + 0.398981i \(0.130636\pi\)
\(654\) −1.98889 −0.0777719
\(655\) 2.13065 + 7.09255i 0.0832515 + 0.277129i
\(656\) 8.20789 0.320464
\(657\) 9.69041 + 9.69041i 0.378059 + 0.378059i
\(658\) 10.5383 + 10.5383i 0.410825 + 0.410825i
\(659\) −26.8438 −1.04569 −0.522843 0.852429i \(-0.675129\pi\)
−0.522843 + 0.852429i \(0.675129\pi\)
\(660\) −10.0727 5.41892i −0.392080 0.210931i
\(661\) 29.5722i 1.15023i 0.818074 + 0.575113i \(0.195042\pi\)
−0.818074 + 0.575113i \(0.804958\pi\)
\(662\) −3.14573 3.14573i −0.122262 0.122262i
\(663\) −2.41516 2.41516i −0.0937970 0.0937970i
\(664\) −10.8750 −0.422031
\(665\) 34.5606 + 18.5929i 1.34020 + 0.721001i
\(666\) 2.34781i 0.0909757i
\(667\) 24.6942 + 1.05399i 0.956162 + 0.0408106i
\(668\) −5.78732 + 5.78732i −0.223918 + 0.223918i
\(669\) 10.9903i 0.424909i
\(670\) 5.62889 + 18.7375i 0.217463 + 0.723894i
\(671\) 35.3419 1.36436
\(672\) 2.01701 2.01701i 0.0778077 0.0778077i
\(673\) −11.0151 + 11.0151i −0.424602 + 0.424602i −0.886785 0.462182i \(-0.847067\pi\)
0.462182 + 0.886785i \(0.347067\pi\)
\(674\) −0.547413 −0.0210856
\(675\) 4.89860 + 1.00186i 0.188547 + 0.0385616i
\(676\) 25.1548 0.967494
\(677\) −5.28014 + 5.28014i −0.202932 + 0.202932i −0.801255 0.598323i \(-0.795834\pi\)
0.598323 + 0.801255i \(0.295834\pi\)
\(678\) −0.526241 0.526241i −0.0202101 0.0202101i
\(679\) 28.7769i 1.10436i
\(680\) 1.18416 0.355729i 0.0454103 0.0136416i
\(681\) 26.2159i 1.00459i
\(682\) 20.0906 20.0906i 0.769310 0.769310i
\(683\) −9.53627 + 9.53627i −0.364895 + 0.364895i −0.865611 0.500716i \(-0.833070\pi\)
0.500716 + 0.865611i \(0.333070\pi\)
\(684\) 6.15278 0.235257
\(685\) 5.93787 + 3.19445i 0.226874 + 0.122054i
\(686\) 16.7251i 0.638569i
\(687\) 6.58128 6.58128i 0.251091 0.251091i
\(688\) 3.51520 + 3.51520i 0.134016 + 0.134016i
\(689\) 28.5852 1.08901
\(690\) −10.3926 + 2.64453i −0.395640 + 0.100676i
\(691\) −40.3146 −1.53364 −0.766820 0.641862i \(-0.778162\pi\)
−0.766820 + 0.641862i \(0.778162\pi\)
\(692\) −3.65117 3.65117i −0.138796 0.138796i
\(693\) 10.3173 10.3173i 0.391922 0.391922i
\(694\) 31.0018i 1.17681i
\(695\) 18.0010 5.40763i 0.682818 0.205123i
\(696\) −5.15378 −0.195353
\(697\) −3.20924 + 3.20924i −0.121559 + 0.121559i
\(698\) 20.9800 20.9800i 0.794106 0.794106i
\(699\) 17.5465i 0.663670i
\(700\) 13.9731 + 2.85778i 0.528135 + 0.108014i
\(701\) 10.9576i 0.413862i 0.978356 + 0.206931i \(0.0663476\pi\)
−0.978356 + 0.206931i \(0.933652\pi\)
\(702\) −4.36777 4.36777i −0.164851 0.164851i
\(703\) −10.2145 + 10.2145i −0.385249 + 0.385249i
\(704\) −5.11516 −0.192785
\(705\) 3.36121 + 11.1889i 0.126591 + 0.421397i
\(706\) −1.78407 −0.0671442
\(707\) −8.70803 + 8.70803i −0.327499 + 0.327499i
\(708\) 6.66723 6.66723i 0.250570 0.250570i
\(709\) 11.6600 0.437899 0.218950 0.975736i \(-0.429737\pi\)
0.218950 + 0.975736i \(0.429737\pi\)
\(710\) 10.6366 19.7713i 0.399184 0.742004i
\(711\) 0.836863i 0.0313848i
\(712\) −6.09259 + 6.09259i −0.228329 + 0.228329i
\(713\) 1.13595 26.6145i 0.0425417 0.996721i
\(714\) 1.57728i 0.0590281i
\(715\) −33.4724 + 62.2188i −1.25180 + 2.32685i
\(716\) 18.7393 0.700319
\(717\) 9.00810 + 9.00810i 0.336414 + 0.336414i
\(718\) 7.03594 + 7.03594i 0.262579 + 0.262579i
\(719\) 17.1352i 0.639036i 0.947580 + 0.319518i \(0.103521\pi\)
−0.947580 + 0.319518i \(0.896479\pi\)
\(720\) 2.14152 0.643329i 0.0798099 0.0239755i
\(721\) −48.6231 −1.81082
\(722\) 13.3337 + 13.3337i 0.496229 + 0.496229i
\(723\) −3.94413 3.94413i −0.146684 0.146684i
\(724\) −20.7307 −0.770449
\(725\) −14.2008 21.5029i −0.527403 0.798597i
\(726\) −15.1649 −0.562821
\(727\) −11.2875 + 11.2875i −0.418630 + 0.418630i −0.884731 0.466101i \(-0.845658\pi\)
0.466101 + 0.884731i \(0.345658\pi\)
\(728\) −12.4590 12.4590i −0.461760 0.461760i
\(729\) 1.00000i 0.0370370i
\(730\) 8.81638 + 29.3481i 0.326309 + 1.08622i
\(731\) −2.74885 −0.101670
\(732\) −4.88558 + 4.88558i −0.180576 + 0.180576i
\(733\) 26.0488 + 26.0488i 0.962134 + 0.962134i 0.999309 0.0371743i \(-0.0118357\pi\)
−0.0371743 + 0.999309i \(0.511836\pi\)
\(734\) 32.1121 1.18528
\(735\) −1.20412 + 2.23823i −0.0444147 + 0.0825582i
\(736\) −3.53269 + 3.24347i −0.130217 + 0.119556i
\(737\) 31.6471 + 31.6471i 1.16574 + 1.16574i
\(738\) −5.80385 + 5.80385i −0.213643 + 0.213643i
\(739\) 27.4713i 1.01055i −0.862959 0.505275i \(-0.831391\pi\)
0.862959 0.505275i \(-0.168609\pi\)
\(740\) −2.48723 + 4.62328i −0.0914324 + 0.169955i
\(741\) 38.0055i 1.39617i
\(742\) −9.33414 9.33414i −0.342667 0.342667i
\(743\) −17.8846 17.8846i −0.656122 0.656122i 0.298338 0.954460i \(-0.403568\pi\)
−0.954460 + 0.298338i \(0.903568\pi\)
\(744\) 5.55456i 0.203640i
\(745\) −11.5886 38.5762i −0.424572 1.41332i
\(746\) 25.0458i 0.916992i
\(747\) 7.68978 7.68978i 0.281354 0.281354i
\(748\) 2.00000 2.00000i 0.0731272 0.0731272i
\(749\) 21.9233i 0.801060i
\(750\) 8.58491 + 7.16235i 0.313477 + 0.261532i
\(751\) 9.57596i 0.349432i 0.984619 + 0.174716i \(0.0559007\pi\)
−0.984619 + 0.174716i \(0.944099\pi\)
\(752\) 3.69444 + 3.69444i 0.134722 + 0.134722i
\(753\) −19.9169 19.9169i −0.725812 0.725812i
\(754\) 31.8347i 1.15935i
\(755\) −7.93302 26.4076i −0.288712 0.961070i
\(756\) 2.85248i 0.103744i
\(757\) 34.4079 34.4079i 1.25058 1.25058i 0.295116 0.955461i \(-0.404642\pi\)
0.955461 0.295116i \(-0.0953584\pi\)
\(758\) 8.16513 + 8.16513i 0.296571 + 0.296571i
\(759\) −18.0703 + 16.5909i −0.655909 + 0.602211i
\(760\) 12.1160 + 6.51816i 0.439493 + 0.236438i
\(761\) −26.3481 −0.955116 −0.477558 0.878600i \(-0.658478\pi\)
−0.477558 + 0.878600i \(0.658478\pi\)
\(762\) −15.6798 15.6798i −0.568020 0.568020i
\(763\) 4.01161 4.01161i 0.145230 0.145230i
\(764\) 9.66249 0.349577
\(765\) −0.585786 + 1.08886i −0.0211792 + 0.0393679i
\(766\) 31.0525i 1.12197i
\(767\) −41.1832 41.1832i −1.48704 1.48704i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) −24.2043 −0.872830 −0.436415 0.899745i \(-0.643752\pi\)
−0.436415 + 0.899745i \(0.643752\pi\)
\(770\) 31.2467 9.38673i 1.12605 0.338274i
\(771\) −10.0573 −0.362205
\(772\) −5.41019 5.41019i −0.194717 0.194717i
\(773\) 15.8801 + 15.8801i 0.571168 + 0.571168i 0.932455 0.361286i \(-0.117662\pi\)
−0.361286 + 0.932455i \(0.617662\pi\)
\(774\) −4.97125 −0.178688
\(775\) −23.1750 + 15.3051i −0.832472 + 0.549775i
\(776\) 10.0884i 0.362152i
\(777\) −4.73554 4.73554i −0.169887 0.169887i
\(778\) 14.5864 + 14.5864i 0.522947 + 0.522947i
\(779\) −50.5013 −1.80940
\(780\) −3.97382 13.2281i −0.142286 0.473642i