Properties

Label 690.2.j.a.643.10
Level $690$
Weight $2$
Character 690.643
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 643.10
Character \(\chi\) \(=\) 690.643
Dual form 690.2.j.a.367.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.397104 - 2.20052i) q^{5} -1.00000 q^{6} +(1.66838 + 1.66838i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(0.397104 - 2.20052i) q^{5} -1.00000 q^{6} +(1.66838 + 1.66838i) q^{7} +(-0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(-1.27521 - 1.83680i) q^{10} -3.67360i q^{11} +(-0.707107 + 0.707107i) q^{12} +(-4.53151 - 4.53151i) q^{13} +2.35944 q^{14} +(-1.83680 + 1.27521i) q^{15} -1.00000 q^{16} +(4.03339 + 4.03339i) q^{17} +(0.707107 + 0.707107i) q^{18} +0.786330 q^{19} +(-2.20052 - 0.397104i) q^{20} -2.35944i q^{21} +(-2.59763 - 2.59763i) q^{22} +(1.01740 - 4.68667i) q^{23} +1.00000i q^{24} +(-4.68462 - 1.74767i) q^{25} -6.40853 q^{26} +(0.707107 - 0.707107i) q^{27} +(1.66838 - 1.66838i) q^{28} +4.68811i q^{29} +(-0.397104 + 2.20052i) q^{30} -3.96306 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.59763 + 2.59763i) q^{33} +5.70407 q^{34} +(4.33382 - 3.00878i) q^{35} +1.00000 q^{36} +(-4.59728 - 4.59728i) q^{37} +(0.556019 - 0.556019i) q^{38} +6.40853i q^{39} +(-1.83680 + 1.27521i) q^{40} +6.32378 q^{41} +(-1.66838 - 1.66838i) q^{42} +(1.71558 - 1.71558i) q^{43} -3.67360 q^{44} +(2.20052 + 0.397104i) q^{45} +(-2.59457 - 4.03339i) q^{46} +(-5.71187 + 5.71187i) q^{47} +(0.707107 + 0.707107i) q^{48} -1.43304i q^{49} +(-4.54832 + 2.07673i) q^{50} -5.70407i q^{51} +(-4.53151 + 4.53151i) q^{52} +(-5.93438 + 5.93438i) q^{53} -1.00000i q^{54} +(-8.08385 - 1.45880i) q^{55} -2.35944i q^{56} +(-0.556019 - 0.556019i) q^{57} +(3.31499 + 3.31499i) q^{58} -13.2165i q^{59} +(1.27521 + 1.83680i) q^{60} +3.15365i q^{61} +(-2.80231 + 2.80231i) q^{62} +(-1.66838 + 1.66838i) q^{63} +1.00000i q^{64} +(-11.7712 + 8.17222i) q^{65} +3.67360i q^{66} +(3.28081 + 3.28081i) q^{67} +(4.03339 - 4.03339i) q^{68} +(-4.03339 + 2.59457i) q^{69} +(0.936943 - 5.19201i) q^{70} +6.19150 q^{71} +(0.707107 - 0.707107i) q^{72} +(5.62505 + 5.62505i) q^{73} -6.50154 q^{74} +(2.07673 + 4.54832i) q^{75} -0.786330i q^{76} +(6.12895 - 6.12895i) q^{77} +(4.53151 + 4.53151i) q^{78} +11.6580 q^{79} +(-0.397104 + 2.20052i) q^{80} -1.00000 q^{81} +(4.47158 - 4.47158i) q^{82} +(5.05048 - 5.05048i) q^{83} -2.35944 q^{84} +(10.4772 - 7.27389i) q^{85} -2.42620i q^{86} +(3.31499 - 3.31499i) q^{87} +(-2.59763 + 2.59763i) q^{88} +16.1572 q^{89} +(1.83680 - 1.27521i) q^{90} -15.1205i q^{91} +(-4.68667 - 1.01740i) q^{92} +(2.80231 + 2.80231i) q^{93} +8.07780i q^{94} +(0.312255 - 1.73034i) q^{95} +1.00000 q^{96} +(-2.18276 - 2.18276i) q^{97} +(-1.01331 - 1.01331i) q^{98} +3.67360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{6} + O(q^{10}) \) \( 24 q - 24 q^{6} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

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
\(5\) 0.397104 2.20052i 0.177590 0.984105i
\(6\) −1.00000 −0.408248
\(7\) 1.66838 + 1.66838i 0.630587 + 0.630587i 0.948215 0.317628i \(-0.102886\pi\)
−0.317628 + 0.948215i \(0.602886\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −1.27521 1.83680i −0.403257 0.580847i
\(11\) 3.67360i 1.10763i −0.832639 0.553816i \(-0.813171\pi\)
0.832639 0.553816i \(-0.186829\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −4.53151 4.53151i −1.25682 1.25682i −0.952605 0.304211i \(-0.901607\pi\)
−0.304211 0.952605i \(-0.598393\pi\)
\(14\) 2.35944 0.630587
\(15\) −1.83680 + 1.27521i −0.474260 + 0.329258i
\(16\) −1.00000 −0.250000
\(17\) 4.03339 + 4.03339i 0.978240 + 0.978240i 0.999768 0.0215283i \(-0.00685321\pi\)
−0.0215283 + 0.999768i \(0.506853\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) 0.786330 0.180396 0.0901982 0.995924i \(-0.471250\pi\)
0.0901982 + 0.995924i \(0.471250\pi\)
\(20\) −2.20052 0.397104i −0.492052 0.0887951i
\(21\) 2.35944i 0.514872i
\(22\) −2.59763 2.59763i −0.553816 0.553816i
\(23\) 1.01740 4.68667i 0.212142 0.977239i
\(24\) 1.00000i 0.204124i
\(25\) −4.68462 1.74767i −0.936923 0.349535i
\(26\) −6.40853 −1.25682
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) 1.66838 1.66838i 0.315293 0.315293i
\(29\) 4.68811i 0.870559i 0.900295 + 0.435280i \(0.143351\pi\)
−0.900295 + 0.435280i \(0.856649\pi\)
\(30\) −0.397104 + 2.20052i −0.0725009 + 0.401759i
\(31\) −3.96306 −0.711787 −0.355893 0.934527i \(-0.615823\pi\)
−0.355893 + 0.934527i \(0.615823\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −2.59763 + 2.59763i −0.452189 + 0.452189i
\(34\) 5.70407 0.978240
\(35\) 4.33382 3.00878i 0.732549 0.508577i
\(36\) 1.00000 0.166667
\(37\) −4.59728 4.59728i −0.755789 0.755789i 0.219764 0.975553i \(-0.429471\pi\)
−0.975553 + 0.219764i \(0.929471\pi\)
\(38\) 0.556019 0.556019i 0.0901982 0.0901982i
\(39\) 6.40853i 1.02619i
\(40\) −1.83680 + 1.27521i −0.290424 + 0.201629i
\(41\) 6.32378 0.987608 0.493804 0.869573i \(-0.335606\pi\)
0.493804 + 0.869573i \(0.335606\pi\)
\(42\) −1.66838 1.66838i −0.257436 0.257436i
\(43\) 1.71558 1.71558i 0.261624 0.261624i −0.564090 0.825714i \(-0.690773\pi\)
0.825714 + 0.564090i \(0.190773\pi\)
\(44\) −3.67360 −0.553816
\(45\) 2.20052 + 0.397104i 0.328035 + 0.0591968i
\(46\) −2.59457 4.03339i −0.382548 0.594690i
\(47\) −5.71187 + 5.71187i −0.833162 + 0.833162i −0.987948 0.154786i \(-0.950531\pi\)
0.154786 + 0.987948i \(0.450531\pi\)
\(48\) 0.707107 + 0.707107i 0.102062 + 0.102062i
\(49\) 1.43304i 0.204720i
\(50\) −4.54832 + 2.07673i −0.643229 + 0.293694i
\(51\) 5.70407i 0.798730i
\(52\) −4.53151 + 4.53151i −0.628408 + 0.628408i
\(53\) −5.93438 + 5.93438i −0.815150 + 0.815150i −0.985401 0.170251i \(-0.945542\pi\)
0.170251 + 0.985401i \(0.445542\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −8.08385 1.45880i −1.09003 0.196705i
\(56\) 2.35944i 0.315293i
\(57\) −0.556019 0.556019i −0.0736466 0.0736466i
\(58\) 3.31499 + 3.31499i 0.435280 + 0.435280i
\(59\) 13.2165i 1.72064i −0.509754 0.860320i \(-0.670264\pi\)
0.509754 0.860320i \(-0.329736\pi\)
\(60\) 1.27521 + 1.83680i 0.164629 + 0.237130i
\(61\) 3.15365i 0.403783i 0.979408 + 0.201892i \(0.0647089\pi\)
−0.979408 + 0.201892i \(0.935291\pi\)
\(62\) −2.80231 + 2.80231i −0.355893 + 0.355893i
\(63\) −1.66838 + 1.66838i −0.210196 + 0.210196i
\(64\) 1.00000i 0.125000i
\(65\) −11.7712 + 8.17222i −1.46004 + 1.01364i
\(66\) 3.67360i 0.452189i
\(67\) 3.28081 + 3.28081i 0.400815 + 0.400815i 0.878520 0.477705i \(-0.158531\pi\)
−0.477705 + 0.878520i \(0.658531\pi\)
\(68\) 4.03339 4.03339i 0.489120 0.489120i
\(69\) −4.03339 + 2.59457i −0.485563 + 0.312350i
\(70\) 0.936943 5.19201i 0.111986 0.620563i
\(71\) 6.19150 0.734795 0.367398 0.930064i \(-0.380249\pi\)
0.367398 + 0.930064i \(0.380249\pi\)
\(72\) 0.707107 0.707107i 0.0833333 0.0833333i
\(73\) 5.62505 + 5.62505i 0.658362 + 0.658362i 0.954992 0.296630i \(-0.0958629\pi\)
−0.296630 + 0.954992i \(0.595863\pi\)
\(74\) −6.50154 −0.755789
\(75\) 2.07673 + 4.54832i 0.239800 + 0.525194i
\(76\) 0.786330i 0.0901982i
\(77\) 6.12895 6.12895i 0.698459 0.698459i
\(78\) 4.53151 + 4.53151i 0.513093 + 0.513093i
\(79\) 11.6580 1.31163 0.655814 0.754923i \(-0.272326\pi\)
0.655814 + 0.754923i \(0.272326\pi\)
\(80\) −0.397104 + 2.20052i −0.0443976 + 0.246026i
\(81\) −1.00000 −0.111111
\(82\) 4.47158 4.47158i 0.493804 0.493804i
\(83\) 5.05048 5.05048i 0.554362 0.554362i −0.373335 0.927697i \(-0.621786\pi\)
0.927697 + 0.373335i \(0.121786\pi\)
\(84\) −2.35944 −0.257436
\(85\) 10.4772 7.27389i 1.13642 0.788964i
\(86\) 2.42620i 0.261624i
\(87\) 3.31499 3.31499i 0.355404 0.355404i
\(88\) −2.59763 + 2.59763i −0.276908 + 0.276908i
\(89\) 16.1572 1.71266 0.856329 0.516431i \(-0.172740\pi\)
0.856329 + 0.516431i \(0.172740\pi\)
\(90\) 1.83680 1.27521i 0.193616 0.134419i
\(91\) 15.1205i 1.58506i
\(92\) −4.68667 1.01740i −0.488619 0.106071i
\(93\) 2.80231 + 2.80231i 0.290586 + 0.290586i
\(94\) 8.07780i 0.833162i
\(95\) 0.312255 1.73034i 0.0320367 0.177529i
\(96\) 1.00000 0.102062
\(97\) −2.18276 2.18276i −0.221626 0.221626i 0.587557 0.809183i \(-0.300090\pi\)
−0.809183 + 0.587557i \(0.800090\pi\)
\(98\) −1.01331 1.01331i −0.102360 0.102360i
\(99\) 3.67360 0.369211
\(100\) −1.74767 + 4.68462i −0.174767 + 0.468462i
\(101\) 17.9481 1.78590 0.892950 0.450156i \(-0.148632\pi\)
0.892950 + 0.450156i \(0.148632\pi\)
\(102\) −4.03339 4.03339i −0.399365 0.399365i
\(103\) 3.77675 3.77675i 0.372134 0.372134i −0.496120 0.868254i \(-0.665242\pi\)
0.868254 + 0.496120i \(0.165242\pi\)
\(104\) 6.40853i 0.628408i
\(105\) −5.19201 0.936943i −0.506688 0.0914363i
\(106\) 8.39248i 0.815150i
\(107\) 2.84433 + 2.84433i 0.274972 + 0.274972i 0.831098 0.556126i \(-0.187713\pi\)
−0.556126 + 0.831098i \(0.687713\pi\)
\(108\) −0.707107 0.707107i −0.0680414 0.0680414i
\(109\) 6.76049 0.647537 0.323769 0.946136i \(-0.395050\pi\)
0.323769 + 0.946136i \(0.395050\pi\)
\(110\) −6.74767 + 4.68462i −0.643365 + 0.446661i
\(111\) 6.50154i 0.617099i
\(112\) −1.66838 1.66838i −0.157647 0.157647i
\(113\) −12.4926 + 12.4926i −1.17521 + 1.17521i −0.194257 + 0.980951i \(0.562230\pi\)
−0.980951 + 0.194257i \(0.937770\pi\)
\(114\) −0.786330 −0.0736466
\(115\) −9.90913 4.09990i −0.924031 0.382318i
\(116\) 4.68811 0.435280
\(117\) 4.53151 4.53151i 0.418939 0.418939i
\(118\) −9.34547 9.34547i −0.860320 0.860320i
\(119\) 13.4584i 1.23373i
\(120\) 2.20052 + 0.397104i 0.200879 + 0.0362505i
\(121\) −2.49535 −0.226850
\(122\) 2.22997 + 2.22997i 0.201892 + 0.201892i
\(123\) −4.47158 4.47158i −0.403189 0.403189i
\(124\) 3.96306i 0.355893i
\(125\) −5.70608 + 9.61461i −0.510367 + 0.859957i
\(126\) 2.35944i 0.210196i
\(127\) −1.27645 + 1.27645i −0.113267 + 0.113267i −0.761469 0.648202i \(-0.775521\pi\)
0.648202 + 0.761469i \(0.275521\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −2.42620 −0.213615
\(130\) −2.54485 + 14.1021i −0.223198 + 1.23684i
\(131\) 7.96128 0.695580 0.347790 0.937572i \(-0.386932\pi\)
0.347790 + 0.937572i \(0.386932\pi\)
\(132\) 2.59763 + 2.59763i 0.226095 + 0.226095i
\(133\) 1.31189 + 1.31189i 0.113756 + 0.113756i
\(134\) 4.63977 0.400815
\(135\) −1.27521 1.83680i −0.109753 0.158087i
\(136\) 5.70407i 0.489120i
\(137\) 9.80005 + 9.80005i 0.837275 + 0.837275i 0.988499 0.151225i \(-0.0483216\pi\)
−0.151225 + 0.988499i \(0.548322\pi\)
\(138\) −1.01740 + 4.68667i −0.0866066 + 0.398956i
\(139\) 17.2801i 1.46568i −0.680404 0.732838i \(-0.738195\pi\)
0.680404 0.732838i \(-0.261805\pi\)
\(140\) −3.00878 4.33382i −0.254289 0.366275i
\(141\) 8.07780 0.680274
\(142\) 4.37805 4.37805i 0.367398 0.367398i
\(143\) −16.6470 + 16.6470i −1.39209 + 1.39209i
\(144\) 1.00000i 0.0833333i
\(145\) 10.3163 + 1.86167i 0.856721 + 0.154603i
\(146\) 7.95502 0.658362
\(147\) −1.01331 + 1.01331i −0.0835768 + 0.0835768i
\(148\) −4.59728 + 4.59728i −0.377894 + 0.377894i
\(149\) 6.63038 0.543182 0.271591 0.962413i \(-0.412450\pi\)
0.271591 + 0.962413i \(0.412450\pi\)
\(150\) 4.68462 + 1.74767i 0.382497 + 0.142697i
\(151\) −5.31700 −0.432691 −0.216345 0.976317i \(-0.569414\pi\)
−0.216345 + 0.976317i \(0.569414\pi\)
\(152\) −0.556019 0.556019i −0.0450991 0.0450991i
\(153\) −4.03339 + 4.03339i −0.326080 + 0.326080i
\(154\) 8.66764i 0.698459i
\(155\) −1.57375 + 8.72082i −0.126406 + 0.700473i
\(156\) 6.40853 0.513093
\(157\) −4.64687 4.64687i −0.370860 0.370860i 0.496930 0.867791i \(-0.334461\pi\)
−0.867791 + 0.496930i \(0.834461\pi\)
\(158\) 8.24345 8.24345i 0.655814 0.655814i
\(159\) 8.39248 0.665567
\(160\) 1.27521 + 1.83680i 0.100814 + 0.145212i
\(161\) 9.51653 6.12173i 0.750008 0.482460i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) −11.0630 11.0630i −0.866523 0.866523i 0.125563 0.992086i \(-0.459926\pi\)
−0.992086 + 0.125563i \(0.959926\pi\)
\(164\) 6.32378i 0.493804i
\(165\) 4.68462 + 6.74767i 0.364697 + 0.525306i
\(166\) 7.14245i 0.554362i
\(167\) 6.27676 6.27676i 0.485710 0.485710i −0.421239 0.906949i \(-0.638405\pi\)
0.906949 + 0.421239i \(0.138405\pi\)
\(168\) −1.66838 + 1.66838i −0.128718 + 0.128718i
\(169\) 28.0692i 2.15917i
\(170\) 2.26511 12.5519i 0.173726 0.962690i
\(171\) 0.786330i 0.0601322i
\(172\) −1.71558 1.71558i −0.130812 0.130812i
\(173\) 3.53407 + 3.53407i 0.268690 + 0.268690i 0.828572 0.559882i \(-0.189154\pi\)
−0.559882 + 0.828572i \(0.689154\pi\)
\(174\) 4.68811i 0.355404i
\(175\) −4.89993 10.7315i −0.370400 0.811224i
\(176\) 3.67360i 0.276908i
\(177\) −9.34547 + 9.34547i −0.702449 + 0.702449i
\(178\) 11.4249 11.4249i 0.856329 0.856329i
\(179\) 9.16746i 0.685208i 0.939480 + 0.342604i \(0.111309\pi\)
−0.939480 + 0.342604i \(0.888691\pi\)
\(180\) 0.397104 2.20052i 0.0295984 0.164017i
\(181\) 20.5860i 1.53015i 0.643942 + 0.765074i \(0.277298\pi\)
−0.643942 + 0.765074i \(0.722702\pi\)
\(182\) −10.6918 10.6918i −0.792531 0.792531i
\(183\) 2.22997 2.22997i 0.164844 0.164844i
\(184\) −4.03339 + 2.59457i −0.297345 + 0.191274i
\(185\) −11.9420 + 8.29084i −0.877996 + 0.609554i
\(186\) 3.96306 0.290586
\(187\) 14.8171 14.8171i 1.08353 1.08353i
\(188\) 5.71187 + 5.71187i 0.416581 + 0.416581i
\(189\) 2.35944 0.171624
\(190\) −1.00274 1.44433i −0.0727462 0.104783i
\(191\) 15.4598i 1.11864i −0.828953 0.559318i \(-0.811063\pi\)
0.828953 0.559318i \(-0.188937\pi\)
\(192\) 0.707107 0.707107i 0.0510310 0.0510310i
\(193\) 1.12895 + 1.12895i 0.0812635 + 0.0812635i 0.746570 0.665307i \(-0.231699\pi\)
−0.665307 + 0.746570i \(0.731699\pi\)
\(194\) −3.08689 −0.221626
\(195\) 14.1021 + 2.54485i 1.00987 + 0.182241i
\(196\) −1.43304 −0.102360
\(197\) −14.7323 + 14.7323i −1.04963 + 1.04963i −0.0509309 + 0.998702i \(0.516219\pi\)
−0.998702 + 0.0509309i \(0.983781\pi\)
\(198\) 2.59763 2.59763i 0.184605 0.184605i
\(199\) −16.9393 −1.20080 −0.600399 0.799700i \(-0.704992\pi\)
−0.600399 + 0.799700i \(0.704992\pi\)
\(200\) 2.07673 + 4.54832i 0.146847 + 0.321615i
\(201\) 4.63977i 0.327264i
\(202\) 12.6912 12.6912i 0.892950 0.892950i
\(203\) −7.82152 + 7.82152i −0.548963 + 0.548963i
\(204\) −5.70407 −0.399365
\(205\) 2.51120 13.9156i 0.175390 0.971909i
\(206\) 5.34112i 0.372134i
\(207\) 4.68667 + 1.01740i 0.325746 + 0.0707140i
\(208\) 4.53151 + 4.53151i 0.314204 + 0.314204i
\(209\) 2.88866i 0.199813i
\(210\) −4.33382 + 3.00878i −0.299062 + 0.207626i
\(211\) 1.79018 0.123241 0.0616206 0.998100i \(-0.480373\pi\)
0.0616206 + 0.998100i \(0.480373\pi\)
\(212\) 5.93438 + 5.93438i 0.407575 + 0.407575i
\(213\) −4.37805 4.37805i −0.299979 0.299979i
\(214\) 4.02249 0.274972
\(215\) −3.09392 4.45645i −0.211003 0.303927i
\(216\) −1.00000 −0.0680414
\(217\) −6.61188 6.61188i −0.448843 0.448843i
\(218\) 4.78039 4.78039i 0.323769 0.323769i
\(219\) 7.95502i 0.537550i
\(220\) −1.45880 + 8.08385i −0.0983524 + 0.545013i
\(221\) 36.5547i 2.45893i
\(222\) 4.59728 + 4.59728i 0.308549 + 0.308549i
\(223\) −5.34860 5.34860i −0.358169 0.358169i 0.504969 0.863138i \(-0.331504\pi\)
−0.863138 + 0.504969i \(0.831504\pi\)
\(224\) −2.35944 −0.157647
\(225\) 1.74767 4.68462i 0.116512 0.312308i
\(226\) 17.6672i 1.17521i
\(227\) −3.63528 3.63528i −0.241282 0.241282i 0.576098 0.817380i \(-0.304574\pi\)
−0.817380 + 0.576098i \(0.804574\pi\)
\(228\) −0.556019 + 0.556019i −0.0368233 + 0.0368233i
\(229\) 19.7330 1.30399 0.651995 0.758223i \(-0.273932\pi\)
0.651995 + 0.758223i \(0.273932\pi\)
\(230\) −9.90588 + 4.10774i −0.653174 + 0.270856i
\(231\) −8.66764 −0.570289
\(232\) 3.31499 3.31499i 0.217640 0.217640i
\(233\) 11.0336 + 11.0336i 0.722834 + 0.722834i 0.969181 0.246348i \(-0.0792306\pi\)
−0.246348 + 0.969181i \(0.579231\pi\)
\(234\) 6.40853i 0.418939i
\(235\) 10.3009 + 14.8373i 0.671957 + 0.967880i
\(236\) −13.2165 −0.860320
\(237\) −8.24345 8.24345i −0.535470 0.535470i
\(238\) 9.51653 + 9.51653i 0.616865 + 0.616865i
\(239\) 29.2176i 1.88993i 0.327174 + 0.944964i \(0.393904\pi\)
−0.327174 + 0.944964i \(0.606096\pi\)
\(240\) 1.83680 1.27521i 0.118565 0.0823145i
\(241\) 0.443590i 0.0285742i 0.999898 + 0.0142871i \(0.00454788\pi\)
−0.999898 + 0.0142871i \(0.995452\pi\)
\(242\) −1.76448 + 1.76448i −0.113425 + 0.113425i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 3.15365 0.201892
\(245\) −3.15345 0.569067i −0.201466 0.0363564i
\(246\) −6.32378 −0.403189
\(247\) −3.56326 3.56326i −0.226725 0.226725i
\(248\) 2.80231 + 2.80231i 0.177947 + 0.177947i
\(249\) −7.14245 −0.452635
\(250\) 2.76375 + 10.8334i 0.174795 + 0.685162i
\(251\) 16.1442i 1.01901i −0.860467 0.509505i \(-0.829828\pi\)
0.860467 0.509505i \(-0.170172\pi\)
\(252\) 1.66838 + 1.66838i 0.105098 + 0.105098i
\(253\) −17.2170 3.73751i −1.08242 0.234975i
\(254\) 1.80517i 0.113267i
\(255\) −12.5519 2.26511i −0.786033 0.141847i
\(256\) 1.00000 0.0625000
\(257\) 11.2370 11.2370i 0.700942 0.700942i −0.263671 0.964613i \(-0.584933\pi\)
0.964613 + 0.263671i \(0.0849333\pi\)
\(258\) −1.71558 + 1.71558i −0.106808 + 0.106808i
\(259\) 15.3400i 0.953181i
\(260\) 8.17222 + 11.7712i 0.506820 + 0.730018i
\(261\) −4.68811 −0.290186
\(262\) 5.62947 5.62947i 0.347790 0.347790i
\(263\) 14.6564 14.6564i 0.903750 0.903750i −0.0920079 0.995758i \(-0.529329\pi\)
0.995758 + 0.0920079i \(0.0293285\pi\)
\(264\) 3.67360 0.226095
\(265\) 10.7022 + 15.4153i 0.657430 + 0.946955i
\(266\) 1.85530 0.113756
\(267\) −11.4249 11.4249i −0.699190 0.699190i
\(268\) 3.28081 3.28081i 0.200408 0.200408i
\(269\) 29.0834i 1.77325i −0.462491 0.886624i \(-0.653044\pi\)
0.462491 0.886624i \(-0.346956\pi\)
\(270\) −2.20052 0.397104i −0.133920 0.0241670i
\(271\) −13.4284 −0.815720 −0.407860 0.913044i \(-0.633725\pi\)
−0.407860 + 0.913044i \(0.633725\pi\)
\(272\) −4.03339 4.03339i −0.244560 0.244560i
\(273\) −10.6918 + 10.6918i −0.647099 + 0.647099i
\(274\) 13.8594 0.837275
\(275\) −6.42026 + 17.2094i −0.387156 + 1.03777i
\(276\) 2.59457 + 4.03339i 0.156175 + 0.242781i
\(277\) −5.20205 + 5.20205i −0.312561 + 0.312561i −0.845901 0.533340i \(-0.820937\pi\)
0.533340 + 0.845901i \(0.320937\pi\)
\(278\) −12.2188 12.2188i −0.732838 0.732838i
\(279\) 3.96306i 0.237262i
\(280\) −5.19201 0.936943i −0.310282 0.0559930i
\(281\) 12.8316i 0.765467i 0.923859 + 0.382734i \(0.125017\pi\)
−0.923859 + 0.382734i \(0.874983\pi\)
\(282\) 5.71187 5.71187i 0.340137 0.340137i
\(283\) −15.0828 + 15.0828i −0.896580 + 0.896580i −0.995132 0.0985516i \(-0.968579\pi\)
0.0985516 + 0.995132i \(0.468579\pi\)
\(284\) 6.19150i 0.367398i
\(285\) −1.44433 + 1.00274i −0.0855548 + 0.0593970i
\(286\) 23.5424i 1.39209i
\(287\) 10.5504 + 10.5504i 0.622772 + 0.622772i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 15.5364i 0.913907i
\(290\) 8.61112 5.97832i 0.505662 0.351059i
\(291\) 3.08689i 0.180957i
\(292\) 5.62505 5.62505i 0.329181 0.329181i
\(293\) 10.7905 10.7905i 0.630387 0.630387i −0.317778 0.948165i \(-0.602937\pi\)
0.948165 + 0.317778i \(0.102937\pi\)
\(294\) 1.43304i 0.0835768i
\(295\) −29.0832 5.24832i −1.69329 0.305569i
\(296\) 6.50154i 0.377894i
\(297\) −2.59763 2.59763i −0.150730 0.150730i
\(298\) 4.68838 4.68838i 0.271591 0.271591i
\(299\) −25.8481 + 16.6274i −1.49483 + 0.961586i
\(300\) 4.54832 2.07673i 0.262597 0.119900i
\(301\) 5.72447 0.329953
\(302\) −3.75968 + 3.75968i −0.216345 + 0.216345i
\(303\) −12.6912 12.6912i −0.729091 0.729091i
\(304\) −0.786330 −0.0450991
\(305\) 6.93968 + 1.25233i 0.397365 + 0.0717080i
\(306\) 5.70407i 0.326080i
\(307\) −13.6279 + 13.6279i −0.777786 + 0.777786i −0.979454 0.201668i \(-0.935364\pi\)
0.201668 + 0.979454i \(0.435364\pi\)
\(308\) −6.12895 6.12895i −0.349229 0.349229i
\(309\) −5.34112 −0.303846
\(310\) 5.05374 + 7.27936i 0.287033 + 0.413440i
\(311\) −17.5183 −0.993373 −0.496686 0.867930i \(-0.665450\pi\)
−0.496686 + 0.867930i \(0.665450\pi\)
\(312\) 4.53151 4.53151i 0.256546 0.256546i
\(313\) 14.1927 14.1927i 0.802219 0.802219i −0.181223 0.983442i \(-0.558006\pi\)
0.983442 + 0.181223i \(0.0580056\pi\)
\(314\) −6.57166 −0.370860
\(315\) 3.00878 + 4.33382i 0.169526 + 0.244183i
\(316\) 11.6580i 0.655814i
\(317\) −16.2313 + 16.2313i −0.911639 + 0.911639i −0.996401 0.0847624i \(-0.972987\pi\)
0.0847624 + 0.996401i \(0.472987\pi\)
\(318\) 5.93438 5.93438i 0.332784 0.332784i
\(319\) 17.2222 0.964260
\(320\) 2.20052 + 0.397104i 0.123013 + 0.0221988i
\(321\) 4.02249i 0.224514i
\(322\) 2.40049 11.0579i 0.133774 0.616234i
\(323\) 3.17157 + 3.17157i 0.176471 + 0.176471i
\(324\) 1.00000i 0.0555556i
\(325\) 13.3088 + 29.1480i 0.738239 + 1.61684i
\(326\) −15.6455 −0.866523
\(327\) −4.78039 4.78039i −0.264356 0.264356i
\(328\) −4.47158 4.47158i −0.246902 0.246902i
\(329\) −19.0591 −1.05076
\(330\) 8.08385 + 1.45880i 0.445001 + 0.0803044i
\(331\) −3.14011 −0.172596 −0.0862980 0.996269i \(-0.527504\pi\)
−0.0862980 + 0.996269i \(0.527504\pi\)
\(332\) −5.05048 5.05048i −0.277181 0.277181i
\(333\) 4.59728 4.59728i 0.251930 0.251930i
\(334\) 8.87668i 0.485710i
\(335\) 8.52234 5.91669i 0.465625 0.323263i
\(336\) 2.35944i 0.128718i
\(337\) −20.1525 20.1525i −1.09778 1.09778i −0.994670 0.103108i \(-0.967121\pi\)
−0.103108 0.994670i \(-0.532879\pi\)
\(338\) 19.8479 + 19.8479i 1.07959 + 1.07959i
\(339\) 17.6672 0.959553
\(340\) −7.27389 10.4772i −0.394482 0.568208i
\(341\) 14.5587i 0.788398i
\(342\) 0.556019 + 0.556019i 0.0300661 + 0.0300661i
\(343\) 14.0695 14.0695i 0.759681 0.759681i
\(344\) −2.42620 −0.130812
\(345\) 4.10774 + 9.90588i 0.221153 + 0.533315i
\(346\) 4.99793 0.268690
\(347\) −7.73799 + 7.73799i −0.415397 + 0.415397i −0.883614 0.468217i \(-0.844897\pi\)
0.468217 + 0.883614i \(0.344897\pi\)
\(348\) −3.31499 3.31499i −0.177702 0.177702i
\(349\) 16.2770i 0.871286i 0.900119 + 0.435643i \(0.143479\pi\)
−0.900119 + 0.435643i \(0.856521\pi\)
\(350\) −11.0531 4.12353i −0.590812 0.220412i
\(351\) −6.40853 −0.342062
\(352\) 2.59763 + 2.59763i 0.138454 + 0.138454i
\(353\) −15.7516 15.7516i −0.838375 0.838375i 0.150270 0.988645i \(-0.451986\pi\)
−0.988645 + 0.150270i \(0.951986\pi\)
\(354\) 13.2165i 0.702449i
\(355\) 2.45867 13.6245i 0.130493 0.723115i
\(356\) 16.1572i 0.856329i
\(357\) 9.51653 9.51653i 0.503668 0.503668i
\(358\) 6.48237 + 6.48237i 0.342604 + 0.342604i
\(359\) 21.4828 1.13382 0.566910 0.823780i \(-0.308139\pi\)
0.566910 + 0.823780i \(0.308139\pi\)
\(360\) −1.27521 1.83680i −0.0672095 0.0968079i
\(361\) −18.3817 −0.967457
\(362\) 14.5565 + 14.5565i 0.765074 + 0.765074i
\(363\) 1.76448 + 1.76448i 0.0926111 + 0.0926111i
\(364\) −15.1205 −0.792531
\(365\) 14.6118 10.1443i 0.764816 0.530978i
\(366\) 3.15365i 0.164844i
\(367\) 15.6149 + 15.6149i 0.815091 + 0.815091i 0.985392 0.170301i \(-0.0544741\pi\)
−0.170301 + 0.985392i \(0.554474\pi\)
\(368\) −1.01740 + 4.68667i −0.0530355 + 0.244310i
\(369\) 6.32378i 0.329203i
\(370\) −2.58179 + 14.3068i −0.134221 + 0.743775i
\(371\) −19.8016 −1.02805
\(372\) 2.80231 2.80231i 0.145293 0.145293i
\(373\) −24.9972 + 24.9972i −1.29430 + 1.29430i −0.362205 + 0.932098i \(0.617976\pi\)
−0.932098 + 0.362205i \(0.882024\pi\)
\(374\) 20.9545i 1.08353i
\(375\) 10.8334 2.76375i 0.559432 0.142719i
\(376\) 8.07780 0.416581
\(377\) 21.2442 21.2442i 1.09413 1.09413i
\(378\) 1.66838 1.66838i 0.0858120 0.0858120i
\(379\) 17.4047 0.894022 0.447011 0.894528i \(-0.352489\pi\)
0.447011 + 0.894528i \(0.352489\pi\)
\(380\) −1.73034 0.312255i −0.0887645 0.0160183i
\(381\) 1.80517 0.0924818
\(382\) −10.9318 10.9318i −0.559318 0.559318i
\(383\) −16.8119 + 16.8119i −0.859046 + 0.859046i −0.991226 0.132180i \(-0.957802\pi\)
0.132180 + 0.991226i \(0.457802\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −11.0531 15.9207i −0.563317 0.811396i
\(386\) 1.59657 0.0812635
\(387\) 1.71558 + 1.71558i 0.0872080 + 0.0872080i
\(388\) −2.18276 + 2.18276i −0.110813 + 0.110813i
\(389\) −18.5763 −0.941855 −0.470927 0.882172i \(-0.656081\pi\)
−0.470927 + 0.882172i \(0.656081\pi\)
\(390\) 11.7712 8.17222i 0.596057 0.413817i
\(391\) 23.0067 14.7996i 1.16350 0.748448i
\(392\) −1.01331 + 1.01331i −0.0511801 + 0.0511801i
\(393\) −5.62947 5.62947i −0.283969 0.283969i
\(394\) 20.8346i 1.04963i
\(395\) 4.62944 25.6537i 0.232932 1.29078i
\(396\) 3.67360i 0.184605i
\(397\) −10.1799 + 10.1799i −0.510914 + 0.510914i −0.914806 0.403892i \(-0.867657\pi\)
0.403892 + 0.914806i \(0.367657\pi\)
\(398\) −11.9779 + 11.9779i −0.600399 + 0.600399i
\(399\) 1.85530i 0.0928811i
\(400\) 4.68462 + 1.74767i 0.234231 + 0.0873837i
\(401\) 26.3514i 1.31593i 0.753049 + 0.657964i \(0.228582\pi\)
−0.753049 + 0.657964i \(0.771418\pi\)
\(402\) −3.28081 3.28081i −0.163632 0.163632i
\(403\) 17.9587 + 17.9587i 0.894585 + 0.894585i
\(404\) 17.9481i 0.892950i
\(405\) −0.397104 + 2.20052i −0.0197323 + 0.109345i
\(406\) 11.0613i 0.548963i
\(407\) −16.8886 + 16.8886i −0.837136 + 0.837136i
\(408\) −4.03339 + 4.03339i −0.199682 + 0.199682i
\(409\) 9.66258i 0.477784i −0.971046 0.238892i \(-0.923216\pi\)
0.971046 0.238892i \(-0.0767842\pi\)
\(410\) −8.06415 11.6155i −0.398260 0.573649i
\(411\) 13.8594i 0.683632i
\(412\) −3.77675 3.77675i −0.186067 0.186067i
\(413\) 22.0501 22.0501i 1.08501 1.08501i
\(414\) 4.03339 2.59457i 0.198230 0.127516i
\(415\) −9.10813 13.1193i −0.447101 0.643999i
\(416\) 6.40853 0.314204
\(417\) −12.2188 + 12.2188i −0.598359 + 0.598359i
\(418\) −2.04259 2.04259i −0.0999065 0.0999065i
\(419\) 6.10226 0.298115 0.149057 0.988829i \(-0.452376\pi\)
0.149057 + 0.988829i \(0.452376\pi\)
\(420\) −0.936943 + 5.19201i −0.0457181 + 0.253344i
\(421\) 36.0060i 1.75483i 0.479736 + 0.877413i \(0.340732\pi\)
−0.479736 + 0.877413i \(0.659268\pi\)
\(422\) 1.26585 1.26585i 0.0616206 0.0616206i
\(423\) −5.71187 5.71187i −0.277721 0.277721i
\(424\) 8.39248 0.407575
\(425\) −11.8458 25.9439i −0.574607 1.25846i
\(426\) −6.19150 −0.299979
\(427\) −5.26147 + 5.26147i −0.254620 + 0.254620i
\(428\) 2.84433 2.84433i 0.137486 0.137486i
\(429\) 23.5424 1.13664
\(430\) −5.33891 0.963454i −0.257465 0.0464619i
\(431\) 18.9507i 0.912823i −0.889769 0.456411i \(-0.849135\pi\)
0.889769 0.456411i \(-0.150865\pi\)
\(432\) −0.707107 + 0.707107i −0.0340207 + 0.0340207i
\(433\) −6.63048 + 6.63048i −0.318641 + 0.318641i −0.848245 0.529604i \(-0.822340\pi\)
0.529604 + 0.848245i \(0.322340\pi\)
\(434\) −9.35061 −0.448843
\(435\) −5.97832 8.61112i −0.286639 0.412871i
\(436\) 6.76049i 0.323769i
\(437\) 0.800010 3.68527i 0.0382697 0.176290i
\(438\) −5.62505 5.62505i −0.268775 0.268775i
\(439\) 13.5147i 0.645019i 0.946566 + 0.322510i \(0.104526\pi\)
−0.946566 + 0.322510i \(0.895474\pi\)
\(440\) 4.68462 + 6.74767i 0.223330 + 0.321683i
\(441\) 1.43304 0.0682402
\(442\) −25.8481 25.8481i −1.22947 1.22947i
\(443\) −0.351909 0.351909i −0.0167197 0.0167197i 0.698698 0.715417i \(-0.253763\pi\)
−0.715417 + 0.698698i \(0.753763\pi\)
\(444\) 6.50154 0.308549
\(445\) 6.41608 35.5543i 0.304151 1.68543i
\(446\) −7.56406 −0.358169
\(447\) −4.68838 4.68838i −0.221753 0.221753i
\(448\) −1.66838 + 1.66838i −0.0788234 + 0.0788234i
\(449\) 16.0808i 0.758899i −0.925212 0.379450i \(-0.876113\pi\)
0.925212 0.379450i \(-0.123887\pi\)
\(450\) −2.07673 4.54832i −0.0978981 0.214410i
\(451\) 23.2310i 1.09391i
\(452\) 12.4926 + 12.4926i 0.587604 + 0.587604i
\(453\) 3.75968 + 3.75968i 0.176645 + 0.176645i
\(454\) −5.14106 −0.241282
\(455\) −33.2731 6.00442i −1.55987 0.281492i
\(456\) 0.786330i 0.0368233i
\(457\) −16.4841 16.4841i −0.771092 0.771092i 0.207206 0.978297i \(-0.433563\pi\)
−0.978297 + 0.207206i \(0.933563\pi\)
\(458\) 13.9533 13.9533i 0.651995 0.651995i
\(459\) 5.70407 0.266243
\(460\) −4.09990 + 9.90913i −0.191159 + 0.462015i
\(461\) −19.0085 −0.885314 −0.442657 0.896691i \(-0.645964\pi\)
−0.442657 + 0.896691i \(0.645964\pi\)
\(462\) −6.12895 + 6.12895i −0.285144 + 0.285144i
\(463\) −5.51731 5.51731i −0.256411 0.256411i 0.567182 0.823593i \(-0.308034\pi\)
−0.823593 + 0.567182i \(0.808034\pi\)
\(464\) 4.68811i 0.217640i
\(465\) 7.27936 5.05374i 0.337572 0.234362i
\(466\) 15.6038 0.722834
\(467\) 7.96465 + 7.96465i 0.368560 + 0.368560i 0.866952 0.498392i \(-0.166076\pi\)
−0.498392 + 0.866952i \(0.666076\pi\)
\(468\) −4.53151 4.53151i −0.209469 0.209469i
\(469\) 10.9473i 0.505498i
\(470\) 17.7754 + 3.20773i 0.819918 + 0.147961i
\(471\) 6.57166i 0.302806i
\(472\) −9.34547 + 9.34547i −0.430160 + 0.430160i
\(473\) −6.30237 6.30237i −0.289783 0.289783i
\(474\) −11.6580 −0.535470
\(475\) −3.68365 1.37425i −0.169018 0.0630548i
\(476\) 13.4584 0.616865
\(477\) −5.93438 5.93438i −0.271717 0.271717i
\(478\) 20.6600 + 20.6600i 0.944964 + 0.944964i
\(479\) 20.8212 0.951345 0.475673 0.879622i \(-0.342205\pi\)
0.475673 + 0.879622i \(0.342205\pi\)
\(480\) 0.397104 2.20052i 0.0181252 0.100440i
\(481\) 41.6653i 1.89977i
\(482\) 0.313666 + 0.313666i 0.0142871 + 0.0142871i
\(483\) −11.0579 2.40049i −0.503153 0.109226i
\(484\) 2.49535i 0.113425i
\(485\) −5.67000 + 3.93643i −0.257461 + 0.178744i
\(486\) 1.00000 0.0453609
\(487\) −1.77520 + 1.77520i −0.0804421 + 0.0804421i −0.746183 0.665741i \(-0.768116\pi\)
0.665741 + 0.746183i \(0.268116\pi\)
\(488\) 2.22997 2.22997i 0.100946 0.100946i
\(489\) 15.6455i 0.707513i
\(490\) −2.63221 + 1.82743i −0.118911 + 0.0825550i
\(491\) 18.6403 0.841225 0.420612 0.907240i \(-0.361815\pi\)
0.420612 + 0.907240i \(0.361815\pi\)
\(492\) −4.47158 + 4.47158i −0.201595 + 0.201595i
\(493\) −18.9089 + 18.9089i −0.851616 + 0.851616i
\(494\) −5.03922 −0.226725
\(495\) 1.45880 8.08385i 0.0655683 0.363342i
\(496\) 3.96306 0.177947
\(497\) 10.3297 + 10.3297i 0.463352 + 0.463352i
\(498\) −5.05048 + 5.05048i −0.226317 + 0.226317i
\(499\) 17.8392i 0.798593i 0.916822 + 0.399296i \(0.130746\pi\)
−0.916822 + 0.399296i \(0.869254\pi\)
\(500\) 9.61461 + 5.70608i 0.429978 + 0.255184i
\(501\) −8.87668 −0.396581
\(502\) −11.4157 11.4157i −0.509505 0.509505i
\(503\) 28.8127 28.8127i 1.28470 1.28470i 0.346731 0.937965i \(-0.387292\pi\)
0.937965 0.346731i \(-0.112708\pi\)
\(504\) 2.35944 0.105098
\(505\) 7.12725 39.4952i 0.317158 1.75751i
\(506\) −14.8171 + 9.53142i −0.658698 + 0.423723i
\(507\) 19.8479 19.8479i 0.881478 0.881478i
\(508\) 1.27645 + 1.27645i 0.0566333 + 0.0566333i
\(509\) 5.84360i 0.259013i 0.991579 + 0.129506i \(0.0413393\pi\)
−0.991579 + 0.129506i \(0.958661\pi\)
\(510\) −10.4772 + 7.27389i −0.463940 + 0.322093i
\(511\) 18.7694i 0.830309i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0.556019 0.556019i 0.0245489 0.0245489i
\(514\) 15.8915i 0.700942i
\(515\) −6.81106 9.81058i −0.300131 0.432306i
\(516\) 2.42620i 0.106808i
\(517\) 20.9831 + 20.9831i 0.922837 + 0.922837i
\(518\) −10.8470 10.8470i −0.476590 0.476590i
\(519\) 4.99793i 0.219385i
\(520\) 14.1021 + 2.54485i 0.618419 + 0.111599i
\(521\) 3.19214i 0.139850i −0.997552 0.0699250i \(-0.977724\pi\)
0.997552 0.0699250i \(-0.0222760\pi\)
\(522\) −3.31499 + 3.31499i −0.145093 + 0.145093i
\(523\) −26.8233 + 26.8233i −1.17290 + 1.17290i −0.191388 + 0.981514i \(0.561299\pi\)
−0.981514 + 0.191388i \(0.938701\pi\)
\(524\) 7.96128i 0.347790i
\(525\) −4.12353 + 11.0531i −0.179966 + 0.482396i
\(526\) 20.7272i 0.903750i
\(527\) −15.9846 15.9846i −0.696298 0.696298i
\(528\) 2.59763 2.59763i 0.113047 0.113047i
\(529\) −20.9298 9.53641i −0.909992 0.414627i
\(530\) 18.4679 + 3.33269i 0.802193 + 0.144763i
\(531\) 13.2165 0.573547
\(532\) 1.31189 1.31189i 0.0568778 0.0568778i
\(533\) −28.6563 28.6563i −1.24124 1.24124i
\(534\) −16.1572 −0.699190
\(535\) 7.38852 5.12953i 0.319434 0.221769i
\(536\) 4.63977i 0.200408i
\(537\) 6.48237 6.48237i 0.279735 0.279735i
\(538\) −20.5651 20.5651i −0.886624 0.886624i
\(539\) −5.26443 −0.226755
\(540\) −1.83680 + 1.27521i −0.0790433 + 0.0548763i
\(541\) −22.2667 −0.957322 −0.478661 0.878000i \(-0.658878\pi\)
−0.478661 + 0.878000i \(0.658878\pi\)
\(542\) −9.49535 + 9.49535i −0.407860 + 0.407860i
\(543\) 14.5565 14.5565i 0.624681 0.624681i
\(544\) −5.70407 −0.244560
\(545\) 2.68462 14.8766i 0.114996 0.637244i
\(546\) 15.1205i 0.647099i
\(547\) 2.91934 2.91934i 0.124822 0.124822i −0.641936 0.766758i \(-0.721869\pi\)
0.766758 + 0.641936i \(0.221869\pi\)
\(548\) 9.80005 9.80005i 0.418637 0.418637i
\(549\) −3.15365 −0.134594
\(550\) 7.62909 + 16.7087i 0.325305 + 0.712461i
\(551\) 3.68640i 0.157046i
\(552\) 4.68667 + 1.01740i 0.199478 + 0.0433033i
\(553\) 19.4499 + 19.4499i 0.827095 + 0.827095i
\(554\) 7.35681i 0.312561i
\(555\) 14.3068 + 2.58179i 0.607290 + 0.109591i
\(556\) −17.2801 −0.732838
\(557\) 16.2953 + 16.2953i 0.690452 + 0.690452i 0.962331 0.271879i \(-0.0876451\pi\)
−0.271879 + 0.962331i \(0.587645\pi\)
\(558\) −2.80231 2.80231i −0.118631 0.118631i
\(559\) −15.5484 −0.657626
\(560\) −4.33382 + 3.00878i −0.183137 + 0.127144i
\(561\) −20.9545 −0.884699
\(562\) 9.07329 + 9.07329i 0.382734 + 0.382734i
\(563\) 13.7932 13.7932i 0.581316 0.581316i −0.353949 0.935265i \(-0.615161\pi\)
0.935265 + 0.353949i \(0.115161\pi\)
\(564\) 8.07780i 0.340137i
\(565\) 22.5295 + 32.4512i 0.947822 + 1.36523i
\(566\) 21.3303i 0.896580i
\(567\) −1.66838 1.66838i −0.0700652 0.0700652i
\(568\) −4.37805 4.37805i −0.183699 0.183699i
\(569\) −8.31567 −0.348611 −0.174305 0.984692i \(-0.555768\pi\)
−0.174305 + 0.984692i \(0.555768\pi\)
\(570\) −0.312255 + 1.73034i −0.0130789 + 0.0724759i
\(571\) 32.9103i 1.37725i 0.725116 + 0.688627i \(0.241786\pi\)
−0.725116 + 0.688627i \(0.758214\pi\)
\(572\) 16.6470 + 16.6470i 0.696045 + 0.696045i
\(573\) −10.9318 + 10.9318i −0.456681 + 0.456681i
\(574\) 14.9206 0.622772
\(575\) −12.9569 + 20.1772i −0.540340 + 0.841447i
\(576\) −1.00000 −0.0416667
\(577\) 28.4271 28.4271i 1.18344 1.18344i 0.204588 0.978848i \(-0.434415\pi\)
0.978848 0.204588i \(-0.0655855\pi\)
\(578\) 10.9859 + 10.9859i 0.456953 + 0.456953i
\(579\) 1.59657i 0.0663514i
\(580\) 1.86167 10.3163i 0.0773014 0.428361i
\(581\) 16.8522 0.699147
\(582\) 2.18276 + 2.18276i 0.0904783 + 0.0904783i
\(583\) 21.8005 + 21.8005i 0.902886 + 0.902886i
\(584\) 7.95502i 0.329181i
\(585\) −8.17222 11.7712i −0.337880 0.486679i
\(586\) 15.2601i 0.630387i
\(587\) 5.63929 5.63929i 0.232758 0.232758i −0.581085 0.813843i \(-0.697372\pi\)
0.813843 + 0.581085i \(0.197372\pi\)
\(588\) 1.01331 + 1.01331i 0.0417884 + 0.0417884i
\(589\) −3.11627 −0.128404
\(590\) −24.2761 + 16.8538i −0.999430 + 0.693861i
\(591\) 20.8346 0.857022
\(592\) 4.59728 + 4.59728i 0.188947 + 0.188947i
\(593\) 23.5246 + 23.5246i 0.966038 + 0.966038i 0.999442 0.0334034i \(-0.0106346\pi\)
−0.0334034 + 0.999442i \(0.510635\pi\)
\(594\) −3.67360 −0.150730
\(595\) 29.6156 + 5.34439i 1.21412 + 0.219099i
\(596\) 6.63038i 0.271591i
\(597\) 11.9779 + 11.9779i 0.490224 + 0.490224i
\(598\) −6.52001 + 30.0347i −0.266623 + 1.22821i
\(599\) 31.5446i 1.28888i −0.764655 0.644440i \(-0.777091\pi\)
0.764655 0.644440i \(-0.222909\pi\)
\(600\) 1.74767 4.68462i 0.0713485 0.191249i
\(601\) −31.2717 −1.27560 −0.637799 0.770203i \(-0.720155\pi\)
−0.637799 + 0.770203i \(0.720155\pi\)
\(602\) 4.04781 4.04781i 0.164977 0.164977i
\(603\) −3.28081 + 3.28081i −0.133605 + 0.133605i
\(604\) 5.31700i 0.216345i
\(605\) −0.990913 + 5.49107i −0.0402863 + 0.223244i
\(606\) −17.9481 −0.729091
\(607\) −1.12613 + 1.12613i −0.0457084 + 0.0457084i −0.729592 0.683883i \(-0.760290\pi\)
0.683883 + 0.729592i \(0.260290\pi\)
\(608\) −0.556019 + 0.556019i −0.0225496 + 0.0225496i
\(609\) 11.0613 0.448227
\(610\) 5.79262 4.02157i 0.234536 0.162828i
\(611\) 51.7668 2.09426
\(612\) 4.03339 + 4.03339i 0.163040 + 0.163040i
\(613\) 26.5829 26.5829i 1.07367 1.07367i 0.0766132 0.997061i \(-0.475589\pi\)
0.997061 0.0766132i \(-0.0244107\pi\)
\(614\) 19.2728i 0.777786i
\(615\) −11.6155 + 8.06415i −0.468383 + 0.325178i
\(616\) −8.66764 −0.349229
\(617\) 27.2723 + 27.2723i 1.09794 + 1.09794i 0.994651 + 0.103290i \(0.0329369\pi\)
0.103290 + 0.994651i \(0.467063\pi\)
\(618\) −3.77675 + 3.77675i −0.151923 + 0.151923i
\(619\) 13.9863 0.562157 0.281078 0.959685i \(-0.409308\pi\)
0.281078 + 0.959685i \(0.409308\pi\)
\(620\) 8.72082 + 1.57375i 0.350236 + 0.0632032i
\(621\) −2.59457 4.03339i −0.104117 0.161854i
\(622\) −12.3873 + 12.3873i −0.496686 + 0.496686i
\(623\) 26.9562 + 26.9562i 1.07998 + 1.07998i
\(624\) 6.40853i 0.256546i
\(625\) 18.8913 + 16.3744i 0.755651 + 0.654975i
\(626\) 20.0715i 0.802219i
\(627\) −2.04259 + 2.04259i −0.0815733 + 0.0815733i
\(628\) −4.64687 + 4.64687i −0.185430 + 0.185430i
\(629\) 37.0852i 1.47869i
\(630\) 5.19201 + 0.936943i 0.206854 + 0.0373287i
\(631\) 0.0291909i 0.00116207i 1.00000 0.000581037i \(0.000184950\pi\)
−1.00000 0.000581037i \(0.999815\pi\)
\(632\) −8.24345 8.24345i −0.327907 0.327907i
\(633\) −1.26585 1.26585i −0.0503130 0.0503130i
\(634\) 22.9545i 0.911639i
\(635\) 2.30198 + 3.31574i 0.0913512 + 0.131581i
\(636\) 8.39248i 0.332784i
\(637\) −6.49385 + 6.49385i −0.257296 + 0.257296i
\(638\) 12.1780 12.1780i 0.482130 0.482130i
\(639\) 6.19150i 0.244932i
\(640\) 1.83680 1.27521i 0.0726059 0.0504071i
\(641\) 35.5918i 1.40579i −0.711292 0.702897i \(-0.751890\pi\)
0.711292 0.702897i \(-0.248110\pi\)
\(642\) −2.84433 2.84433i −0.112257 0.112257i
\(643\) 21.0238 21.0238i 0.829097 0.829097i −0.158295 0.987392i \(-0.550600\pi\)
0.987392 + 0.158295i \(0.0505996\pi\)
\(644\) −6.12173 9.51653i −0.241230 0.375004i
\(645\) −0.963454 + 5.33891i −0.0379360 + 0.210219i
\(646\) 4.48528 0.176471
\(647\) 5.39555 5.39555i 0.212121 0.212121i −0.593047 0.805168i \(-0.702075\pi\)
0.805168 + 0.593047i \(0.202075\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) −48.5521 −1.90584
\(650\) 30.0215 + 11.2000i 1.17754 + 0.439301i
\(651\) 9.35061i 0.366479i
\(652\) −11.0630 + 11.0630i −0.433262 + 0.433262i
\(653\) −6.27260 6.27260i −0.245466 0.245466i 0.573641 0.819107i \(-0.305530\pi\)
−0.819107 + 0.573641i \(0.805530\pi\)
\(654\) −6.76049 −0.264356
\(655\) 3.16145 17.5190i 0.123528 0.684523i
\(656\) −6.32378 −0.246902
\(657\) −5.62505 + 5.62505i −0.219454 + 0.219454i
\(658\) −13.4768 + 13.4768i −0.525381 + 0.525381i
\(659\) −24.4164 −0.951126 −0.475563 0.879682i \(-0.657756\pi\)
−0.475563 + 0.879682i \(0.657756\pi\)
\(660\) 6.74767 4.68462i 0.262653 0.182348i
\(661\) 5.36247i 0.208576i 0.994547 + 0.104288i \(0.0332563\pi\)
−0.994547 + 0.104288i \(0.966744\pi\)
\(662\) −2.22039 + 2.22039i −0.0862980 + 0.0862980i
\(663\) −25.8481 + 25.8481i −1.00386 + 1.00386i
\(664\) −7.14245 −0.277181
\(665\) 3.40781 2.36590i 0.132149 0.0917455i
\(666\) 6.50154i 0.251930i
\(667\) 21.9716 + 4.76966i 0.850744 + 0.184682i
\(668\) −6.27676 6.27676i −0.242855 0.242855i
\(669\) 7.56406i 0.292443i
\(670\) 1.84247 10.2099i 0.0711809 0.394444i
\(671\) 11.5852 0.447243
\(672\) 1.66838 + 1.66838i 0.0643590 + 0.0643590i
\(673\) −7.83125 7.83125i −0.301872 0.301872i 0.539874 0.841746i \(-0.318472\pi\)
−0.841746 + 0.539874i \(0.818472\pi\)
\(674\) −28.5000 −1.09778
\(675\) −4.54832 + 2.07673i −0.175065 + 0.0799335i
\(676\) 28.0692 1.07959
\(677\) −17.8901 17.8901i −0.687573 0.687573i 0.274122 0.961695i \(-0.411613\pi\)
−0.961695 + 0.274122i \(0.911613\pi\)
\(678\) 12.4926 12.4926i 0.479776 0.479776i
\(679\) 7.28333i 0.279508i
\(680\) −12.5519 2.26511i −0.481345 0.0868630i
\(681\) 5.14106i 0.197006i
\(682\) 10.2946 + 10.2946i 0.394199 + 0.394199i
\(683\) −12.3778 12.3778i −0.473622 0.473622i 0.429463 0.903085i \(-0.358703\pi\)
−0.903085 + 0.429463i \(0.858703\pi\)
\(684\) 0.786330 0.0300661
\(685\) 25.4569 17.6736i 0.972658 0.675274i
\(686\) 19.8973i 0.759681i
\(687\) −13.9533 13.9533i −0.532352 0.532352i
\(688\) −1.71558 + 1.71558i −0.0654060 + 0.0654060i
\(689\) 53.7834 2.04899
\(690\) 9.90913 + 4.09990i 0.377234 + 0.156081i
\(691\) 40.8522 1.55409 0.777045 0.629445i \(-0.216718\pi\)
0.777045 + 0.629445i \(0.216718\pi\)
\(692\) 3.53407 3.53407i 0.134345 0.134345i
\(693\) 6.12895 + 6.12895i 0.232820 + 0.232820i
\(694\) 10.9432i 0.415397i
\(695\) −38.0252 6.86198i −1.44238 0.260290i
\(696\) −4.68811 −0.177702
\(697\) 25.5062 + 25.5062i 0.966117 + 0.966117i
\(698\) 11.5096 + 11.5096i 0.435643 + 0.435643i
\(699\) 15.6038i 0.590191i
\(700\) −10.7315 + 4.89993i −0.405612 + 0.185200i
\(701\) 17.8753i 0.675139i 0.941301 + 0.337570i \(0.109605\pi\)
−0.941301 + 0.337570i \(0.890395\pi\)
\(702\) −4.53151 + 4.53151i −0.171031 + 0.171031i
\(703\) −3.61498 3.61498i −0.136342 0.136342i
\(704\) 3.67360 0.138454
\(705\) 3.20773 17.7754i 0.120810 0.669460i
\(706\) −22.2762 −0.838375
\(707\) 29.9441 + 29.9441i 1.12616 + 1.12616i
\(708\) 9.34547 + 9.34547i 0.351224 + 0.351224i
\(709\) −41.7130 −1.56656 −0.783282 0.621667i \(-0.786456\pi\)
−0.783282 + 0.621667i \(0.786456\pi\)
\(710\) −7.89546 11.3725i −0.296311 0.426804i
\(711\) 11.6580i 0.437209i
\(712\) −11.4249 11.4249i −0.428164 0.428164i
\(713\) −4.03201 + 18.5736i −0.151000 + 0.695586i
\(714\) 13.4584i 0.503668i
\(715\) 30.0215 + 43.2427i 1.12274 + 1.61718i
\(716\) 9.16746 0.342604
\(717\) 20.6600 20.6600i 0.771560 0.771560i
\(718\) 15.1907 15.1907i 0.566910 0.566910i
\(719\) 0.928560i 0.0346295i 0.999850 + 0.0173147i \(0.00551172\pi\)
−0.999850 + 0.0173147i \(0.994488\pi\)
\(720\) −2.20052 0.397104i −0.0820087 0.0147992i
\(721\) 12.6021 0.469325
\(722\) −12.9978 + 12.9978i −0.483729 + 0.483729i
\(723\) 0.313666 0.313666i 0.0116654 0.0116654i
\(724\) 20.5860 0.765074
\(725\) 8.19328 21.9620i 0.304291 0.815647i
\(726\) 2.49535 0.0926111
\(727\) 17.7713 + 17.7713i 0.659101 + 0.659101i 0.955167 0.296066i \(-0.0956749\pi\)
−0.296066 + 0.955167i \(0.595675\pi\)
\(728\) −10.6918 + 10.6918i −0.396266 + 0.396266i
\(729\) 1.00000i 0.0370370i
\(730\) 3.15897 17.5052i 0.116919 0.647897i
\(731\) 13.8392 0.511862
\(732\) −2.22997 2.22997i −0.0824219 0.0824219i
\(733\) −14.2968 + 14.2968i −0.528065 + 0.528065i −0.919995 0.391930i \(-0.871807\pi\)
0.391930 + 0.919995i \(0.371807\pi\)
\(734\) 22.0828 0.815091
\(735\) 1.82743 + 2.63221i 0.0674059 + 0.0970907i
\(736\) 2.59457 + 4.03339i 0.0956371 + 0.148673i
\(737\) 12.0524 12.0524i 0.443956 0.443956i
\(738\) 4.47158 + 4.47158i 0.164601 + 0.164601i
\(739\) 43.2771i 1.59197i −0.605315 0.795986i \(-0.706953\pi\)
0.605315 0.795986i \(-0.293047\pi\)
\(740\) 8.29084 + 11.9420i 0.304777 + 0.438998i
\(741\) 5.03922i 0.185120i
\(742\) −14.0018 + 14.0018i −0.514023 + 0.514023i
\(743\) −34.4467 + 34.4467i −1.26373 + 1.26373i −0.314452 + 0.949273i \(0.601821\pi\)
−0.949273 + 0.314452i \(0.898179\pi\)
\(744\) 3.96306i 0.145293i
\(745\) 2.63295 14.5903i 0.0964638 0.534548i
\(746\) 35.3513i 1.29430i
\(747\) 5.05048 + 5.05048i 0.184787 + 0.184787i
\(748\) −14.8171 14.8171i −0.541765 0.541765i
\(749\) 9.49083i 0.346787i
\(750\) 5.70608 9.61461i 0.208357 0.351076i
\(751\) 6.81223i 0.248582i 0.992246 + 0.124291i \(0.0396656\pi\)
−0.992246 + 0.124291i \(0.960334\pi\)
\(752\) 5.71187 5.71187i 0.208290 0.208290i
\(753\) −11.4157 + 11.4157i −0.416009 + 0.416009i
\(754\) 30.0439i 1.09413i
\(755\) −2.11140 + 11.7002i −0.0768417 + 0.425813i
\(756\) 2.35944i 0.0858120i
\(757\) 9.32141 + 9.32141i 0.338793 + 0.338793i 0.855913 0.517120i \(-0.172996\pi\)
−0.517120 + 0.855913i \(0.672996\pi\)
\(758\) 12.3070 12.3070i 0.447011 0.447011i
\(759\) 9.53142 + 14.8171i 0.345969 + 0.537825i
\(760\) −1.44433 + 1.00274i −0.0523914 + 0.0363731i
\(761\) 12.3215 0.446654 0.223327 0.974744i \(-0.428308\pi\)
0.223327 + 0.974744i \(0.428308\pi\)
\(762\) 1.27645 1.27645i 0.0462409 0.0462409i
\(763\) 11.2790 + 11.2790i 0.408329 + 0.408329i
\(764\) −15.4598 −0.559318
\(765\) 7.27389 + 10.4772i 0.262988 + 0.378805i
\(766\) 23.7756i 0.859046i
\(767\) −59.8907 + 59.8907i −2.16253 + 2.16253i
\(768\) −0.707107 0.707107i −0.0255155 0.0255155i
\(769\) 10.6748 0.384944 0.192472 0.981302i \(-0.438350\pi\)
0.192472 + 0.981302i \(0.438350\pi\)
\(770\) −19.0734 3.44195i −0.687356 0.124039i
\(771\) −15.8915 −0.572317
\(772\) 1.12895 1.12895i 0.0406317 0.0406317i
\(773\) −7.08827 + 7.08827i −0.254947 + 0.254947i −0.822995 0.568048i \(-0.807699\pi\)
0.568048 + 0.822995i \(0.307699\pi\)
\(774\) 2.42620 0.0872080
\(775\) 18.5654 + 6.92614i 0.666890 + 0.248794i
\(776\) 3.08689i 0.110813i
\(777\) −10.8470 + 10.8470i −0.389134 + 0.389134i
\(778\) −13.1354 + 13.1354i −0.470927 + 0.470927i
\(779\) 4.97257 0.178161
\(780\) 2.54485 14.1021i 0.0911203