Properties

Label 690.2.j.b.367.10
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 367.10
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.b.643.10

$q$-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} +(4.79147 - 0.204508i) 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} +(0.204508 + 4.79147i) 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 −0.214391 0.976748i \(-0.568777\pi\)
0.976748 + 0.214391i \(0.0687768\pi\)
\(8\) −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 \(0.280313\pi\)
−0.636666 + 0.771139i \(0.719687\pi\)
\(12\) 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 −0.752930 0.658100i \(-0.771360\pi\)
0.658100 + 0.752930i \(0.271360\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −6.15278 −1.41154 −0.705772 0.708439i \(-0.749400\pi\)
−0.705772 + 0.708439i \(0.749400\pi\)
\(20\) −2.14152 + 0.643329i −0.478859 + 0.143853i
\(21\) 2.85248i 0.622461i
\(22\) −3.61696 + 3.61696i −0.771139 + 0.771139i
\(23\) 4.79147 0.204508i 0.999090 0.0426429i
\(24\) 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 −0.557350 0.830277i \(-0.688182\pi\)
0.830277 + 0.557350i \(0.188182\pi\)
\(38\) −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 0.922370 0.386307i \(-0.126249\pi\)
−0.386307 + 0.922370i \(0.626249\pi\)
\(44\) −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 0.445699 0.895183i \(-0.352955\pi\)
−0.895183 + 0.445699i \(0.852955\pi\)
\(54\) 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 \(-0.854156\pi\)
0.896857 0.442320i \(-0.145844\pi\)
\(62\) 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 −0.219712 0.975565i \(-0.570512\pi\)
0.975565 + 0.219712i \(0.0705118\pi\)
\(68\) −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 \(-0.514991\pi\)
−0.0470772 + 0.998891i \(0.514991\pi\)
\(80\) −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 0.145322 0.989384i \(-0.453578\pi\)
−0.989384 + 0.145322i \(0.953578\pi\)
\(84\) 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 \(-0.650954\pi\)
−0.456659 + 0.889642i \(0.650954\pi\)
\(90\) 1.96919 + 1.05938i 0.207571 + 0.111669i
\(91\) 17.6196i 1.84704i
\(92\) 0.204508 + 4.79147i 0.0213214 + 0.499545i
\(93\) 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 −0.969479 0.245175i \(-0.921155\pi\)
0.245175 + 0.969479i \(0.421155\pi\)
\(98\) 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 \(-0.932677\pi\)
−0.209929 0.977717i \(-0.567323\pi\)
\(104\) 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 −0.393808 0.919193i \(-0.628843\pi\)
0.919193 + 0.393808i \(0.128843\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) 1.98889 0.190501 0.0952507 0.995453i \(-0.469635\pi\)
0.0952507 + 0.995453i \(0.469635\pi\)
\(110\) −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 0.731426 0.681921i \(-0.238855\pi\)
−0.681921 + 0.731426i \(0.738855\pi\)
\(114\) −6.15278 −0.576261
\(115\) 3.52045 + 10.1295i 0.328284 + 0.944579i
\(116\) −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 −0.610133 0.792299i \(-0.708884\pi\)
0.792299 + 0.610133i \(0.208884\pi\)
\(138\) 4.79147 0.204508i 0.407877 0.0174089i
\(139\) 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 \(-0.764163\pi\)
−0.737859 + 0.674955i \(0.764163\pi\)
\(150\) −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 −0.642326 0.766431i \(-0.722031\pi\)
0.766431 + 0.642326i \(0.222031\pi\)
\(158\) −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 \(-0.720032\pi\)
0.637502 0.770449i \(-0.279968\pi\)
\(182\) 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 \(0.113675\pi\)
−0.936908 + 0.349577i \(0.886325\pi\)
\(192\) −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 \(-0.521766\pi\)
−0.0683262 + 0.997663i \(0.521766\pi\)
\(200\) 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
\(207\) −0.204508 4.79147i −0.0142143 0.333030i
\(208\) −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 \(-0.414116\pi\)
0.963821 0.266550i \(-0.0858837\pi\)
\(228\) −4.35067 4.35067i −0.288130 0.288130i
\(229\) −9.30733 −0.615046 −0.307523 0.951541i \(-0.599500\pi\)
−0.307523 + 0.951541i \(0.599500\pi\)
\(230\) −4.67329 + 9.65196i −0.308148 + 0.636431i
\(231\) 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 \(0.0574966\pi\)
−0.983731 + 0.179650i \(0.942503\pi\)
\(242\) −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 \(0.348554\pi\)
−0.458033 + 0.888935i \(0.651446\pi\)
\(252\) 2.01701 2.01701i 0.127059 0.127059i
\(253\) 1.04609 + 24.5091i 0.0657672 + 1.54088i
\(254\) 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 0.938534 0.345186i \(-0.112184\pi\)
−0.345186 + 0.938534i \(0.612184\pi\)
\(264\) −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 \(-0.792537\pi\)
0.795015 0.606590i \(-0.207463\pi\)
\(282\) −3.69444 3.69444i −0.220000 0.220000i
\(283\) 17.8450 + 17.8450i 1.06078 + 1.06078i 0.998029 + 0.0627483i \(0.0199865\pi\)
0.0627483 + 0.998029i \(0.480013\pi\)
\(284\) 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 0.971695 0.236241i \(-0.0759153\pi\)
−0.236241 + 0.971695i \(0.575915\pi\)
\(294\) 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 0.408204 0.912891i \(-0.366155\pi\)
−0.912891 + 0.408204i \(0.866155\pi\)
\(314\) 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
\(322\) 13.6676 0.583354i 0.761663 0.0325091i
\(323\) 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 −0.696485 0.717571i \(-0.745254\pi\)
0.717571 + 0.696485i \(0.245254\pi\)
\(338\) 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
\(345\) 9.65196 + 4.67329i 0.519644 + 0.251602i
\(346\) −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 \(-0.584573\pi\)
−0.262579 + 0.964911i \(0.584573\pi\)
\(360\) −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 \(0.566345\pi\)
−0.978358 + 0.206922i \(0.933655\pi\)
\(368\) −4.79147 + 0.204508i −0.249773 + 0.0106607i
\(369\) 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 0.996809 0.0798177i \(-0.0254338\pi\)
−0.0798177 + 0.996809i \(0.525434\pi\)
\(374\) 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 \(-0.595843\pi\)
−0.296571 + 0.955011i \(0.595843\pi\)
\(380\) 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 \(-0.958333\pi\)
−0.130527 0.991445i \(-0.541667\pi\)
\(384\) 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 \(-0.675168\pi\)
−0.522947 + 0.852365i \(0.675168\pi\)
\(390\) 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 \(0.277836\pi\)
−0.642646 + 0.766163i \(0.722164\pi\)
\(402\) 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 \(-0.432757\pi\)
0.209681 + 0.977770i \(0.432757\pi\)
\(420\) 1.83508 + 6.10865i 0.0895428 + 0.298072i
\(421\) 7.06186i 0.344174i 0.985082 + 0.172087i \(0.0550510\pi\)
−0.985082 + 0.172087i \(0.944949\pi\)
\(422\) 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 \(-0.840401\pi\)
0.876914 0.480648i \(-0.159599\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 15.9071 + 15.9071i 0.764447 + 0.764447i 0.977123 0.212676i \(-0.0682179\pi\)
−0.212676 + 0.977123i \(0.568218\pi\)
\(434\) 15.8442 0.760548
\(435\) −5.45983 + 10.1488i −0.261779 + 0.486596i
\(436\) 1.98889i 0.0952507i
\(437\) −29.4809 + 1.25829i −1.41026 + 0.0601923i
\(438\) −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 \(-0.370026\pi\)
0.917787 0.397074i \(-0.129974\pi\)
\(458\) −6.58128 6.58128i −0.307523 0.307523i
\(459\) 0.552950 0.0258095
\(460\) −10.1295 + 3.52045i −0.472290 + 0.164142i
\(461\) −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 −0.904685 0.426081i \(-0.859894\pi\)
0.426081 + 0.904685i \(0.359894\pi\)
\(468\) 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 \(-0.283126\pi\)
0.629826 + 0.776736i \(0.283126\pi\)
\(480\) −0.643329 2.14152i −0.0293638 0.0977468i
\(481\) 14.5023i 0.661249i
\(482\) −3.94413 + 3.94413i −0.179650 + 0.179650i
\(483\) −0.583354 13.6676i −0.0265435 0.621895i
\(484\) 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 \(0.0484027\pi\)
0.151476 + 0.988461i \(0.451597\pi\)
\(504\) 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 \(0.161517\pi\)
−0.874001 + 0.485925i \(0.838483\pi\)
\(522\) 3.64427 + 3.64427i 0.159505 + 0.159505i
\(523\) −14.7292 14.7292i −0.644064 0.644064i 0.307488 0.951552i \(-0.400512\pi\)
−0.951552 + 0.307488i \(0.900512\pi\)
\(524\) 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
\(552\) 0.204508 + 4.79147i 0.00870444 + 0.203938i
\(553\) −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 −0.754048 0.656819i \(-0.771901\pi\)
0.656819 + 0.754048i \(0.271901\pi\)
\(558\) 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 0.482941 0.875653i \(-0.339569\pi\)
−0.875653 + 0.482941i \(0.839569\pi\)
\(564\) 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 \(-0.699727\pi\)
−0.587090 + 0.809522i \(0.699727\pi\)
\(570\) −3.95826 13.1763i −0.165793 0.551896i
\(571\) 36.3711i 1.52208i 0.648703 + 0.761042i \(0.275312\pi\)
−0.648703 + 0.761042i \(0.724688\pi\)
\(572\) −22.3418 + 22.3418i −0.934159 + 0.934159i
\(573\) 6.83241 + 6.83241i 0.285428 + 0.285428i
\(574\) −23.4128 −0.977232
\(575\) −19.4277 + 14.0557i −0.810192 + 0.586164i
\(576\) −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
\(598\) 29.5967 1.26324i 1.21030 0.0516576i
\(599\) 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 0.942852 0.333213i \(-0.108133\pi\)
−0.333213 + 0.942852i \(0.608133\pi\)
\(614\) 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 −0.385883 0.922548i \(-0.626103\pi\)
0.922548 + 0.385883i \(0.126103\pi\)
\(618\) −12.0533 12.0533i −0.484854 0.484854i
\(619\) 31.9076 1.28247 0.641236 0.767343i \(-0.278422\pi\)
0.641236 + 0.767343i \(0.278422\pi\)
\(620\) −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 \(-0.918050\pi\)
0.967041 0.254619i \(-0.0819500\pi\)
\(632\) 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 \(-0.888216\pi\)
0.938967 0.344007i \(-0.111784\pi\)
\(642\) 5.43462 5.43462i 0.214487 0.214487i
\(643\) −27.1429 27.1429i −1.07041 1.07041i −0.997326 0.0730859i \(-0.976715\pi\)
−0.0730859 0.997326i \(-0.523285\pi\)
\(644\) 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 \(-0.324871\pi\)
0.522843 + 0.852429i \(0.324871\pi\)
\(660\) −10.0727 5.41892i −0.392080 0.210931i
\(661\) 29.5722i 1.15023i −0.818074 0.575113i \(-0.804958\pi\)
0.818074 0.575113i \(-0.195042\pi\)
\(662\) −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
\(667\) 1.05399 + 24.6942i 0.0408106 + 0.956162i
\(668\) −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 −0.598323 0.801255i \(-0.704166\pi\)
0.801255 + 0.598323i \(0.204166\pi\)
\(678\) 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
\(690\) 3.52045 + 10.1295i 0.134021 + 0.385623i
\(691\) −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 \(-0.933652\pi\)
0.978356 0.206931i \(-0.0663476\pi\)
\(702\) −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 \(-0.570263\pi\)
−0.218950 + 0.975736i \(0.570263\pi\)
\(710\) −10.6366 + 19.7713i −0.399184 + 0.742004i
\(711\) 0.836863i 0.0313848i
\(712\) 6.09259 6.09259i 0.228329 0.228329i
\(713\) 26.6145 1.13595i 0.996721 0.0425417i
\(714\) 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 −0.466101 0.884731i \(-0.654342\pi\)
0.884731 + 0.466101i \(0.154342\pi\)
\(728\) 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 0.0371743 0.999309i \(-0.488164\pi\)
−0.999309 + 0.0371743i \(0.988164\pi\)
\(734\) −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 0.954460 0.298338i \(-0.0964323\pi\)
−0.298338 + 0.954460i \(0.596432\pi\)
\(744\) 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 \(-0.944099\pi\)
0.984619 0.174716i \(-0.0559007\pi\)
\(752\) 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 \(0.595358\pi\)
−0.955461 + 0.295116i \(0.904642\pi\)
\(758\) −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 \(-0.356248\pi\)
0.436415 + 0.899745i \(0.356248\pi\)
\(770\) −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 0.361286 0.932455i \(-0.382338\pi\)
−0.932455 + 0.361286i \(0.882338\pi\)
\(774\) 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 +